id	sid	tid	token	lemma	pos
cana-1543	1	1	communications	communication	NOUN
cana-1543	1	2	on	on	ADP
cana-1543	1	3	applied	apply	VERB
cana-1543	1	4	nonlinear	nonlinear	ADJ
cana-1543	1	5	analysis	analysis	NOUN
cana-1543	1	6	issn	issn	NOUN
cana-1543	1	7	:	:	PUNCT
cana-1543	1	8	1074	1074	NUM
cana-1543	1	9	-	-	PUNCT
cana-1543	1	10	133x	133x	NUM
cana-1543	1	11	vol	vol	NOUN
cana-1543	1	12	31	31	NUM
cana-1543	1	13	no	no	NOUN
cana-1543	1	14	.	.	PUNCT
cana-1543	2	1	8s	8s	PROPN
cana-1543	2	2	(	(	PUNCT
cana-1543	2	3	2024	2024	NUM
cana-1543	2	4	)	)	PUNCT
cana-1543	2	5	494	494	NUM
cana-1543	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1543	2	7	on	on	ADP
cana-1543	2	8	total	total	ADJ
cana-1543	2	9	coloring	coloring	NOUN
cana-1543	2	10	of	of	ADP
cana-1543	2	11	triple	triple	ADJ
cana-1543	2	12	star	star	NOUN
cana-1543	2	13	and	and	CCONJ
cana-1543	2	14	lobster	lobster	NOUN
cana-1543	2	15	graphs	graph	NOUN
cana-1543	2	16	a.	a.	NOUN
cana-1543	2	17	punitha1	punitha1	PROPN
cana-1543	2	18	,	,	PUNCT
cana-1543	2	19	g.	g.	PROPN
cana-1543	2	20	jayaraman2	jayaraman2	PROPN
cana-1543	3	1	*	*	PUNCT
cana-1543	4	1	1,2department	1,2department	NUM
cana-1543	4	2	of	of	ADP
cana-1543	4	3	mathematics	mathematic	NOUN
cana-1543	4	4	,	,	PUNCT
cana-1543	4	5	1,2	1,2	NUM
cana-1543	4	6	vels	vel	NOUN
cana-1543	4	7	institute	institute	NOUN
cana-1543	4	8	of	of	ADP
cana-1543	4	9	science	science	NOUN
cana-1543	4	10	,	,	PUNCT
cana-1543	4	11	technology	technology	NOUN
cana-1543	4	12	and	and	CCONJ
cana-1543	4	13	advanced	advanced	ADJ
cana-1543	4	14	studies	study	NOUN
cana-1543	4	15	(	(	PUNCT
cana-1543	4	16	vistas	vista	NOUN
cana-1543	4	17	)	)	PUNCT
cana-1543	4	18	,	,	PUNCT
cana-1543	4	19	pallavaram	pallavaram	PROPN
cana-1543	4	20	,	,	PUNCT
cana-1543	4	21	chennai-117	chennai-117	NOUN
cana-1543	4	22	,	,	PUNCT
cana-1543	4	23	india.*corresponding	india.*corresponding	PROPN
cana-1543	4	24	author	author	NOUN
cana-1543	4	25	email	email	NOUN
cana-1543	4	26	:	:	PUNCT
cana-1543	4	27	jayaram07maths@gmail.com	jayaram07maths@gmail.com	X
cana-1543	4	28	article	article	NOUN
cana-1543	4	29	history	history	NOUN
cana-1543	4	30	:	:	PUNCT
cana-1543	4	31	received	receive	VERB
cana-1543	4	32	:	:	PUNCT
cana-1543	4	33	11	11	NUM
cana-1543	4	34	-	-	SYM
cana-1543	4	35	05	05	NUM
cana-1543	4	36	-	-	PUNCT
cana-1543	4	37	2024	2024	NUM
cana-1543	4	38	revised	revise	VERB
cana-1543	4	39	:	:	PUNCT
cana-1543	4	40	25	25	NUM
cana-1543	4	41	-	-	PUNCT
cana-1543	4	42	06	06	NUM
cana-1543	4	43	-	-	PUNCT
cana-1543	4	44	2024	2024	NUM
cana-1543	4	45	accepted	accept	VERB
cana-1543	4	46	:	:	PUNCT
cana-1543	4	47	12	12	NUM
cana-1543	4	48	-	-	PUNCT
cana-1543	4	49	07	07	NUM
cana-1543	4	50	-	-	PUNCT
cana-1543	4	51	2024	2024	NUM
cana-1543	4	52	abstract	abstract	NOUN
cana-1543	4	53	a	a	DET
cana-1543	4	54	k	k	ADJ
cana-1543	4	55	-	-	ADJ
cana-1543	4	56	total	total	ADJ
cana-1543	4	57	coloring	coloring	NOUN
cana-1543	4	58	of	of	ADP
cana-1543	4	59	a	a	DET
cana-1543	4	60	graph	graph	NOUN
cana-1543	4	61	g	g	NOUN
cana-1543	4	62	is	be	AUX
cana-1543	4	63	an	an	DET
cana-1543	4	64	assignment	assignment	NOUN
cana-1543	4	65	of	of	ADP
cana-1543	4	66	k	k	PROPN
cana-1543	4	67	colors	color	NOUN
cana-1543	4	68	to	to	ADP
cana-1543	4	69	the	the	DET
cana-1543	4	70	elements	element	NOUN
cana-1543	4	71	(	(	PUNCT
cana-1543	4	72	vertices	vertex	NOUN
cana-1543	4	73	and	and	CCONJ
cana-1543	4	74	edges	edge	NOUN
cana-1543	4	75	)	)	PUNCT
cana-1543	4	76	of	of	ADP
cana-1543	4	77	g	g	PROPN
cana-1543	4	78	such	such	ADJ
cana-1543	4	79	that	that	PRON
cana-1543	4	80	adjacent	adjacent	ADJ
cana-1543	4	81	or	or	CCONJ
cana-1543	4	82	incident	incident	NOUN
cana-1543	4	83	elements	element	NOUN
cana-1543	4	84	have	have	AUX
cana-1543	4	85	different	different	ADJ
cana-1543	4	86	colors	color	NOUN
cana-1543	4	87	.	.	PUNCT
cana-1543	5	1	the	the	DET
cana-1543	5	2	total	total	ADJ
cana-1543	5	3	chromatic	chromatic	ADJ
cana-1543	5	4	number	number	NOUN
cana-1543	5	5	is	be	AUX
cana-1543	5	6	the	the	DET
cana-1543	5	7	smallest	small	ADJ
cana-1543	5	8	integer	integer	NOUN
cana-1543	5	9	k	k	PROPN
cana-1543	5	10	for	for	ADP
cana-1543	5	11	which	which	PRON
cana-1543	5	12	g	g	NOUN
cana-1543	5	13	has	have	VERB
cana-1543	5	14	a	a	DET
cana-1543	5	15	k	k	ADJ
cana-1543	5	16	-	-	ADJ
cana-1543	5	17	total	total	ADJ
cana-1543	5	18	coloring	coloring	NOUN
cana-1543	5	19	.	.	PUNCT
cana-1543	6	1	the	the	DET
cana-1543	6	2	wellknown	wellknown	ADJ
cana-1543	6	3	total	total	ADJ
cana-1543	6	4	coloring	coloring	NOUN
cana-1543	6	5	conjecture	conjecture	NOUN
cana-1543	6	6	asserts	assert	VERB
cana-1543	6	7	that	that	SCONJ
cana-1543	6	8	the	the	DET
cana-1543	6	9	total	total	ADJ
cana-1543	6	10	chromatic	chromatic	ADJ
cana-1543	6	11	number	number	NOUN
cana-1543	6	12	of	of	ADP
cana-1543	6	13	a	a	DET
cana-1543	6	14	graph	graph	NOUN
cana-1543	6	15	is	be	AUX
cana-1543	6	16	either	either	CCONJ
cana-1543	6	17	∆(g	∆(g	NOUN
cana-1543	6	18	)	)	PUNCT
cana-1543	6	19	+	+	CCONJ
cana-1543	6	20	1	1	NUM
cana-1543	6	21	or	or	CCONJ
cana-1543	6	22	∆(g	∆(g	NOUN
cana-1543	6	23	)	)	PUNCT
cana-1543	6	24	+	+	NUM
cana-1543	6	25	2	2	NUM
cana-1543	6	26	,	,	PUNCT
cana-1543	6	27	where	where	SCONJ
cana-1543	6	28	∆(g	∆(g	NOUN
cana-1543	6	29	)	)	PUNCT
cana-1543	6	30	is	be	AUX
cana-1543	6	31	the	the	DET
cana-1543	6	32	maximum	maximum	ADJ
cana-1543	6	33	degree	degree	NOUN
cana-1543	6	34	of	of	ADP
cana-1543	6	35	g.	g.	PROPN
cana-1543	6	36	in	in	ADP
cana-1543	6	37	this	this	DET
cana-1543	6	38	paper	paper	NOUN
cana-1543	6	39	,	,	PUNCT
cana-1543	6	40	we	we	PRON
cana-1543	6	41	consider	consider	VERB
cana-1543	6	42	the	the	DET
cana-1543	6	43	triple	triple	ADJ
cana-1543	6	44	star	star	NOUN
cana-1543	6	45	graph	graph	NOUN
cana-1543	6	46	,	,	PUNCT
cana-1543	6	47	lobster	lobster	NOUN
cana-1543	6	48	graph	graph	NOUN
cana-1543	6	49	and	and	CCONJ
cana-1543	6	50	its	its	PRON
cana-1543	6	51	line	line	NOUN
cana-1543	6	52	,	,	PUNCT
cana-1543	6	53	middle	middle	ADJ
cana-1543	6	54	,	,	PUNCT
cana-1543	6	55	total	total	ADJ
cana-1543	6	56	graphs	graph	NOUN
cana-1543	6	57	and	and	CCONJ
cana-1543	6	58	also	also	ADV
cana-1543	6	59	splitting	split	VERB
cana-1543	6	60	graph	graph	NOUN
cana-1543	6	61	of	of	ADP
cana-1543	6	62	triple	triple	ADJ
cana-1543	6	63	star	star	NOUN
cana-1543	6	64	.	.	PUNCT
cana-1543	7	1	we	we	PRON
cana-1543	7	2	obtained	obtain	VERB
cana-1543	7	3	the	the	DET
cana-1543	7	4	preceding	precede	VERB
cana-1543	7	5	graphs	graph	NOUN
cana-1543	7	6	has	have	VERB
cana-1543	7	7	total	total	ADJ
cana-1543	7	8	chromatic	chromatic	ADJ
cana-1543	7	9	number	number	NOUN
cana-1543	7	10	equal	equal	ADJ
cana-1543	7	11	to	to	ADP
cana-1543	7	12	∆(g	∆(g	PROPN
cana-1543	7	13	)	)	PUNCT
cana-1543	8	1	+	+	NOUN
cana-1543	8	2	1	1	X
cana-1543	8	3	.	.	PUNCT
cana-1543	9	1	keywords	keyword	NOUN
cana-1543	9	2	:	:	PUNCT
cana-1543	9	3	total	total	ADJ
cana-1543	9	4	coloring	coloring	NOUN
cana-1543	9	5	,	,	PUNCT
cana-1543	9	6	total	total	ADJ
cana-1543	9	7	chromatic	chromatic	ADJ
cana-1543	9	8	number	number	NOUN
cana-1543	9	9	,	,	PUNCT
cana-1543	9	10	triple	triple	ADJ
cana-1543	9	11	star	star	NOUN
cana-1543	9	12	graph	graph	NOUN
cana-1543	9	13	,	,	PUNCT
cana-1543	9	14	lobster	lobster	NOUN
cana-1543	9	15	graph	graph	NOUN
cana-1543	9	16	,	,	PUNCT
cana-1543	9	17	line	line	NOUN
cana-1543	9	18	,	,	PUNCT
cana-1543	9	19	middle	middle	ADJ
cana-1543	9	20	,	,	PUNCT
cana-1543	9	21	total	total	ADJ
cana-1543	9	22	,	,	PUNCT
cana-1543	9	23	splitting	splitting	NOUN
cana-1543	9	24	graph	graph	NOUN
cana-1543	9	25	.	.	PUNCT
cana-1543	10	1	ams	am	NOUN
cana-1543	10	2	subject	subject	ADJ
cana-1543	10	3	classification	classification	NOUN
cana-1543	10	4	:	:	PUNCT
cana-1543	10	5	05c15	05c15	NUM
cana-1543	10	6	.	.	PUNCT
cana-1543	11	1	1	1	X
cana-1543	11	2	.	.	X
cana-1543	11	3	introduction	introduction	NOUN
cana-1543	11	4	the	the	DET
cana-1543	11	5	graph	graph	NOUN
cana-1543	11	6	described	describe	VERB
cana-1543	11	7	is	be	AUX
cana-1543	11	8	finite	finite	ADJ
cana-1543	11	9	,	,	PUNCT
cana-1543	11	10	undirected	undirected	ADJ
cana-1543	11	11	,	,	PUNCT
cana-1543	11	12	and	and	CCONJ
cana-1543	11	13	has	have	VERB
cana-1543	11	14	no	no	DET
cana-1543	11	15	loops	loop	NOUN
cana-1543	11	16	or	or	CCONJ
cana-1543	11	17	multiple	multiple	ADJ
cana-1543	11	18	edges	edge	NOUN
cana-1543	11	19	.	.	PUNCT
cana-1543	12	1	a	a	DET
cana-1543	12	2	k	k	PROPN
cana-1543	12	3	-total	-total	PROPN
cana-1543	12	4	coloring	coloring	NOUN
cana-1543	12	5	is	be	AUX
cana-1543	12	6	an	an	DET
cana-1543	12	7	assignment	assignment	NOUN
cana-1543	12	8	of	of	ADP
cana-1543	12	9	k	k	PROPN
cana-1543	12	10	colors	color	NOUN
cana-1543	12	11	to	to	ADP
cana-1543	12	12	the	the	DET
cana-1543	12	13	elements	element	NOUN
cana-1543	12	14	(	(	PUNCT
cana-1543	12	15	ie	ie	X
cana-1543	12	16	,	,	PUNCT
cana-1543	12	17	vertices	vertex	NOUN
cana-1543	12	18	and	and	CCONJ
cana-1543	12	19	edges	edge	NOUN
cana-1543	12	20	)	)	PUNCT
cana-1543	12	21	of	of	ADP
cana-1543	12	22	g	g	PROPN
cana-1543	12	23	,	,	PUNCT
cana-1543	12	24	for	for	ADP
cana-1543	12	25	which	which	PRON
cana-1543	12	26	two	two	NUM
cana-1543	12	27	adjacent	adjacent	ADJ
cana-1543	12	28	or	or	CCONJ
cana-1543	12	29	incident	incident	NOUN
cana-1543	12	30	elements	element	NOUN
cana-1543	12	31	have	have	VERB
cana-1543	12	32	distinct	distinct	ADJ
cana-1543	12	33	colors	color	NOUN
cana-1543	12	34	.	.	PUNCT
cana-1543	13	1	the	the	DET
cana-1543	13	2	total	total	ADJ
cana-1543	13	3	chromatic	chromatic	ADJ
cana-1543	13	4	number	number	NOUN
cana-1543	13	5	''	''	PUNCT
cana-1543	13	6	(	(	PUNCT
cana-1543	13	7	)	)	PUNCT
cana-1543	13	8	g	g	NOUN
cana-1543	13	9	,	,	PUNCT
cana-1543	13	10	is	be	AUX
cana-1543	13	11	the	the	DET
cana-1543	13	12	least	least	ADJ
cana-1543	13	13	k	k	NOUN
cana-1543	13	14	,	,	PUNCT
cana-1543	13	15	for	for	ADP
cana-1543	13	16	which	which	PRON
cana-1543	13	17	g	g	NOUN
cana-1543	13	18	has	have	VERB
cana-1543	13	19	a	a	DET
cana-1543	13	20	k	k	PROPN
cana-1543	13	21	-total	-total	PROPN
cana-1543	13	22	coloring	coloring	NOUN
cana-1543	13	23	.	.	PUNCT
cana-1543	14	1	behzad	behzad	PROPN
cana-1543	15	1	[	[	X
cana-1543	15	2	2	2	NUM
cana-1543	15	3	]	]	PUNCT
cana-1543	15	4	and	and	CCONJ
cana-1543	15	5	vizing	vize	VERB
cana-1543	16	1	[	[	X
cana-1543	16	2	17	17	NUM
cana-1543	16	3	]	]	PUNCT
cana-1543	16	4	independently	independently	ADV
cana-1543	16	5	,	,	PUNCT
cana-1543	16	6	suggested	suggest	VERB
cana-1543	16	7	the	the	DET
cana-1543	16	8	famous	famous	ADJ
cana-1543	16	9	conjecture	conjecture	NOUN
cana-1543	16	10	,	,	PUNCT
cana-1543	16	11	known	know	VERB
cana-1543	16	12	as	as	ADP
cana-1543	16	13	tcc	tcc	PROPN
cana-1543	16	14	:	:	PUNCT
cana-1543	16	15	for	for	ADP
cana-1543	16	16	any	any	DET
cana-1543	16	17	graph	graph	NOUN
cana-1543	16	18	,	,	PUNCT
cana-1543	16	19	g	g	NOUN
cana-1543	16	20	''	''	PUNCT
cana-1543	16	21	(	(	PUNCT
cana-1543	16	22	)	)	PUNCT
cana-1543	16	23	1	1	NUM
cana-1543	16	24	(	(	PUNCT
cana-1543	16	25	)	)	PUNCT
cana-1543	16	26	(	(	PUNCT
cana-1543	16	27	)	)	PUNCT
cana-1543	16	28	2.g	2.g	NUM
cana-1543	16	29	g	g	ADP
cana-1543	16	30	g	g	PROPN
cana-1543	16	31	+	+	CCONJ
cana-1543	16	32			NOUN
cana-1543	16	33			NOUN
cana-1543	16	34			PUNCT
cana-1543	17	1	+	+	CCONJ
cana-1543	17	2	this	this	DET
cana-1543	17	3	conjecture	conjecture	NOUN
cana-1543	17	4	was	be	AUX
cana-1543	17	5	authenticated	authenticate	VERB
cana-1543	17	6	by	by	ADP
cana-1543	17	7	rosenfeld	rosenfeld	PROPN
cana-1543	17	8	[	[	X
cana-1543	17	9	15	15	NUM
cana-1543	17	10	]	]	PUNCT
cana-1543	17	11	and	and	CCONJ
cana-1543	17	12	vijayadithya	vijayadithya	PROPN
cana-1543	18	1	[	[	X
cana-1543	18	2	16	16	NUM
cana-1543	18	3	]	]	PUNCT
cana-1543	18	4	for	for	ADP
cana-1543	18	5	3,	3,	NUM
cana-1543	18	6	=	=	SYM
cana-1543	18	7	and	and	CCONJ
cana-1543	18	8	by	by	ADP
cana-1543	18	9	kostochka	kostochka	NOUN
cana-1543	19	1	[	[	X
cana-1543	19	2	8	8	NUM
cana-1543	19	3	,	,	PUNCT
cana-1543	19	4	9	9	NUM
cana-1543	19	5	]	]	PUNCT
cana-1543	19	6	for	for	ADP
cana-1543	19	7	5.	5.	NUM
cana-1543	19	8	this	this	DET
cana-1543	19	9	result	result	NOUN
cana-1543	19	10	was	be	AUX
cana-1543	19	11	firstly	firstly	ADV
cana-1543	19	12	given	give	VERB
cana-1543	19	13	in	in	ADP
cana-1543	19	14	[	[	X
cana-1543	19	15	3	3	NUM
cana-1543	19	16	]	]	PUNCT
cana-1543	19	17	for	for	ADP
cana-1543	19	18	14.	14.	NUM
cana-1543	19	19	in	in	ADP
cana-1543	19	20	[	[	X
cana-1543	19	21	10	10	NUM
cana-1543	19	22	]	]	PUNCT
cana-1543	19	23	,	,	PUNCT
cana-1543	19	24	this	this	DET
cana-1543	19	25	result	result	NOUN
cana-1543	19	26	was	be	AUX
cana-1543	19	27	protracted	protract	VERB
cana-1543	19	28	to	to	ADP
cana-1543	19	29	9.	9.	NUM
cana-1543	19	30	a	a	DET
cana-1543	19	31	survey	survey	NOUN
cana-1543	19	32	paper	paper	NOUN
cana-1543	19	33	on	on	ADP
cana-1543	19	34	total	total	ADJ
cana-1543	19	35	coloring	coloring	NOUN
cana-1543	19	36	would	would	AUX
cana-1543	19	37	likely	likely	ADV
cana-1543	19	38	include	include	VERB
cana-1543	19	39	a	a	DET
cana-1543	19	40	comprehensive	comprehensive	ADJ
cana-1543	19	41	collection	collection	NOUN
cana-1543	19	42	of	of	ADP
cana-1543	19	43	articles	article	NOUN
cana-1543	19	44	covering	cover	VERB
cana-1543	19	45	various	various	ADJ
cana-1543	19	46	aspects	aspect	NOUN
cana-1543	19	47	of	of	ADP
cana-1543	19	48	total	total	ADJ
cana-1543	19	49	coloring	coloring	NOUN
cana-1543	19	50	[	[	X
cana-1543	19	51	4	4	NUM
cana-1543	19	52	]	]	PUNCT
cana-1543	19	53	.	.	PUNCT
cana-1543	20	1	jayaraman	jayaraman	PROPN
cana-1543	20	2	et	et	PROPN
cana-1543	20	3	al	al	PROPN
cana-1543	20	4	.	.	PUNCT
cana-1543	21	1	[	[	X
cana-1543	21	2	7	7	NUM
cana-1543	21	3	,	,	PUNCT
cana-1543	21	4	11	11	NUM
cana-1543	21	5	,	,	PUNCT
cana-1543	21	6	12	12	NUM
cana-1543	21	7	,	,	PUNCT
cana-1543	21	8	13	13	NUM
cana-1543	21	9	,	,	PUNCT
cana-1543	21	10	14	14	NUM
cana-1543	21	11	]	]	PUNCT
cana-1543	21	12	discussed	discuss	VERB
cana-1543	21	13	the	the	DET
cana-1543	21	14	total	total	ADJ
cana-1543	21	15	coloring	coloring	NOUN
cana-1543	21	16	of	of	ADP
cana-1543	21	17	line	line	NOUN
cana-1543	21	18	,	,	PUNCT
cana-1543	21	19	middle	middle	ADJ
cana-1543	21	20	,	,	PUNCT
cana-1543	21	21	total	total	ADJ
cana-1543	21	22	and	and	CCONJ
cana-1543	21	23	splitting	splitting	NOUN
cana-1543	21	24	graph	graph	NOUN
cana-1543	21	25	of	of	ADP
cana-1543	21	26	double	double	ADJ
cana-1543	21	27	star	star	NOUN
cana-1543	21	28	graph	graph	NOUN
cana-1543	21	29	,	,	PUNCT
cana-1543	21	30	snake	snake	NOUN
cana-1543	21	31	graph	graph	NOUN
cana-1543	21	32	families	family	NOUN
cana-1543	21	33	,	,	PUNCT
cana-1543	21	34	splitting	splitting	NOUN
cana-1543	21	35	graph	graph	NOUN
cana-1543	21	36	of	of	ADP
cana-1543	21	37	path	path	NOUN
cana-1543	21	38	,	,	PUNCT
cana-1543	21	39	cycle	cycle	NOUN
cana-1543	21	40	and	and	CCONJ
cana-1543	21	41	star	star	NOUN
cana-1543	21	42	graph	graph	NOUN
cana-1543	21	43	and	and	CCONJ
cana-1543	22	1	certain	certain	ADJ
cana-1543	22	2	convex	convex	NOUN
cana-1543	22	3	polytope	polytope	NOUN
cana-1543	22	4	graphs	graph	VERB
cana-1543	22	5	total	total	ADJ
cana-1543	22	6	coloring	coloring	NOUN
cana-1543	22	7	provides	provide	VERB
cana-1543	22	8	a	a	DET
cana-1543	22	9	powerful	powerful	ADJ
cana-1543	22	10	tool	tool	NOUN
cana-1543	22	11	for	for	ADP
cana-1543	22	12	modeling	modeling	NOUN
cana-1543	22	13	and	and	CCONJ
cana-1543	22	14	solving	solve	VERB
cana-1543	22	15	various	various	ADJ
cana-1543	22	16	practical	practical	ADJ
cana-1543	22	17	problems	problem	NOUN
cana-1543	22	18	arising	arise	VERB
cana-1543	22	19	in	in	ADP
cana-1543	22	20	scheduling	scheduling	NOUN
cana-1543	22	21	,	,	PUNCT
cana-1543	22	22	wireless	wireless	ADJ
cana-1543	22	23	networks	network	NOUN
cana-1543	22	24	,	,	PUNCT
cana-1543	22	25	telecommunications	telecommunication	NOUN
cana-1543	22	26	.	.	PUNCT
cana-1543	23	1	in	in	ADP
cana-1543	23	2	[	[	X
cana-1543	23	3	1	1	NUM
cana-1543	23	4	]	]	PUNCT
cana-1543	23	5	,	,	PUNCT
cana-1543	23	6	the	the	DET
cana-1543	23	7	author	author	NOUN
cana-1543	23	8	has	have	AUX
cana-1543	23	9	extended	extend	VERB
cana-1543	23	10	the	the	DET
cana-1543	23	11	concept	concept	NOUN
cana-1543	23	12	of	of	ADP
cana-1543	23	13	the	the	DET
cana-1543	23	14	double	double	ADJ
cana-1543	23	15	star	star	NOUN
cana-1543	23	16	graph	graph	NOUN
cana-1543	23	17	to	to	PART
cana-1543	23	18	introduce	introduce	VERB
cana-1543	23	19	the	the	DET
cana-1543	23	20	triple	triple	ADJ
cana-1543	23	21	star	star	NOUN
cana-1543	23	22	graph	graph	NOUN
cana-1543	23	23	.	.	PUNCT
cana-1543	24	1	in	in	ADP
cana-1543	24	2	this	this	DET
cana-1543	24	3	paper	paper	NOUN
cana-1543	24	4	,	,	PUNCT
cana-1543	24	5	we	we	PRON
cana-1543	24	6	obtained	obtain	VERB
cana-1543	24	7	the	the	DET
cana-1543	24	8	total	total	ADJ
cana-1543	24	9	chromatic	chromatic	ADJ
cana-1543	24	10	number	number	NOUN
cana-1543	24	11	of	of	ADP
cana-1543	24	12	triple	triple	ADJ
cana-1543	24	13	star	star	NOUN
cana-1543	24	14	,	,	PUNCT
cana-1543	24	15	lobster	lobster	NOUN
cana-1543	24	16	graph	graph	NOUN
cana-1543	24	17	and	and	CCONJ
cana-1543	24	18	its	its	PRON
cana-1543	24	19	line	line	NOUN
cana-1543	24	20	,	,	PUNCT
cana-1543	24	21	middle	middle	ADJ
cana-1543	24	22	,	,	PUNCT
cana-1543	24	23	total	total	ADJ
cana-1543	24	24	graph	graph	NOUN
cana-1543	24	25	and	and	CCONJ
cana-1543	24	26	also	also	ADV
cana-1543	24	27	splitting	split	VERB
cana-1543	24	28	graph	graph	NOUN
cana-1543	24	29	of	of	ADP
cana-1543	24	30	triple	triple	ADJ
cana-1543	24	31	star	star	NOUN
cana-1543	24	32	graph	graph	NOUN
cana-1543	24	33	.	.	PUNCT
cana-1543	25	1	communications	communication	NOUN
cana-1543	25	2	on	on	ADP
cana-1543	25	3	applied	apply	VERB
cana-1543	25	4	nonlinear	nonlinear	ADJ
cana-1543	25	5	analysis	analysis	NOUN
cana-1543	25	6	issn	issn	NOUN
cana-1543	25	7	:	:	PUNCT
cana-1543	25	8	1074	1074	NUM
cana-1543	25	9	-	-	PUNCT
cana-1543	25	10	133x	133x	NUM
cana-1543	25	11	vol	vol	NOUN
cana-1543	25	12	31	31	NUM
cana-1543	25	13	no	no	NOUN
cana-1543	25	14	.	.	PUNCT
cana-1543	26	1	8s	8s	PROPN
cana-1543	26	2	(	(	PUNCT
cana-1543	26	3	2024	2024	NUM
cana-1543	26	4	)	)	PUNCT
cana-1543	26	5	495	495	NUM
cana-1543	26	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1543	26	7	2	2	NUM
cana-1543	26	8	.	.	PUNCT
cana-1543	26	9	preliminaries	preliminary	NOUN
cana-1543	26	10	definition	definition	NOUN
cana-1543	26	11	2.1	2.1	NUM
cana-1543	26	12	triple	triple	ADJ
cana-1543	26	13	star	star	NOUN
cana-1543	26	14	graph	graph	NOUN
cana-1543	26	15	1	1	NUM
cana-1543	26	16	,	,	PUNCT
cana-1543	26	17	,	,	PUNCT
cana-1543	26	18	,	,	PUNCT
cana-1543	26	19	k	k	X
cana-1543	26	20			NUM
cana-1543	26	21			NUM
cana-1543	26	22			NOUN
cana-1543	26	23	=	=	PUNCT
cana-1543	27	1	[	[	X
cana-1543	27	2	1	1	NUM
cana-1543	27	3	]	]	PUNCT
cana-1543	27	4	is	be	AUX
cana-1543	27	5	constructed	construct	VERB
cana-1543	27	6	from	from	ADP
cana-1543	27	7	the	the	DET
cana-1543	27	8	double	double	ADJ
cana-1543	27	9	star	star	NOUN
cana-1543	27	10	graph	graph	NOUN
cana-1543	27	11	1	1	NUM
cana-1543	27	12	,	,	PUNCT
cana-1543	27	13	,	,	PUNCT
cana-1543	27	14	k	k	X
cana-1543	27	15			NUM
cana-1543	27	16			NUM
cana-1543	27	17	by	by	ADP
cana-1543	27	18	adding	add	VERB
cana-1543	27	19	a	a	DET
cana-1543	27	20	new	new	ADJ
cana-1543	27	21	pendent	pendent	ADJ
cana-1543	27	22	edge	edge	NOUN
cana-1543	27	23	to	to	ADP
cana-1543	27	24	each	each	DET
cana-1543	27	25	existing	exist	VERB
cana-1543	27	26	pendant	pendant	ADJ
cana-1543	27	27	node	node	NOUN
cana-1543	27	28	,	,	PUNCT
cana-1543	27	29	then	then	ADV
cana-1543	27	30	it	it	PRON
cana-1543	27	31	forms	form	VERB
cana-1543	27	32	a	a	DET
cana-1543	27	33	tree	tree	NOUN
cana-1543	27	34	structure	structure	NOUN
cana-1543	27	35	.	.	PUNCT
cana-1543	28	1	it	it	PRON
cana-1543	28	2	has	have	VERB
cana-1543	28	3	3	3	NUM
cana-1543	28	4	1	1	NUM
cana-1543	28	5	+	+	NUM
cana-1543	28	6	nodes	node	NOUN
cana-1543	28	7	and	and	CCONJ
cana-1543	28	8	3	3	NUM
cana-1543	28	9	edges	edge	NOUN
cana-1543	28	10	.	.	PUNCT
cana-1543	29	1	definition	definition	NOUN
cana-1543	29	2	2.2	2.2	NUM
cana-1543	29	3	.	.	PUNCT
cana-1543	30	1	the	the	DET
cana-1543	30	2	lobster	lobster	NOUN
cana-1543	30	3	graph	graph	NOUN
cana-1543	30	4	(	(	PUNCT
cana-1543	30	5	2	2	NUM
cana-1543	30	6	,	,	PUNCT
cana-1543	30	7	)	)	PUNCT
cana-1543	30	8	l	l	NOUN
cana-1543	30	9	r	r	NOUN
cana-1543	30	10			VERB
cana-1543	30	11	=	=	PUNCT
cana-1543	31	1	[	[	X
cana-1543	31	2	6	6	NUM
cana-1543	31	3	]	]	PUNCT
cana-1543	31	4	is	be	AUX
cana-1543	31	5	constructed	construct	VERB
cana-1543	31	6	by	by	ADP
cana-1543	31	7	the	the	DET
cana-1543	31	8	path	path	NOUN
cana-1543	31	9	on	on	ADP
cana-1543	31	10			ADJ
cana-1543	31	11	nodes	node	NOUN
cana-1543	31	12	as	as	ADP
cana-1543	31	13	a	a	DET
cana-1543	31	14	backbone	backbone	NOUN
cana-1543	31	15	.	.	PUNCT
cana-1543	32	1	each	each	DET
cana-1543	32	2	node	node	NOUN
cana-1543	32	3	in	in	ADP
cana-1543	32	4	the	the	DET
cana-1543	32	5	backbone	backbone	NOUN
cana-1543	32	6	is	be	AUX
cana-1543	32	7	attached	attach	VERB
cana-1543	32	8	to	to	ADP
cana-1543	32	9	two	two	NUM
cana-1543	32	10	distinct	distinct	ADJ
cana-1543	32	11	node	node	ADJ
cana-1543	32	12	hands	hand	NOUN
cana-1543	32	13	,	,	PUNCT
cana-1543	32	14	and	and	CCONJ
cana-1543	32	15	each	each	DET
cana-1543	32	16	node	node	ADJ
cana-1543	32	17	hand	hand	NOUN
cana-1543	32	18	is	be	AUX
cana-1543	32	19	connected	connect	VERB
cana-1543	32	20	to	to	ADP
cana-1543	32	21	r	r	VERB
cana-1543	32	22	distinct	distinct	ADJ
cana-1543	32	23	node	node	ADJ
cana-1543	32	24	fingers	finger	NOUN
cana-1543	32	25	,	,	PUNCT
cana-1543	32	26	each	each	PRON
cana-1543	32	27	of	of	ADP
cana-1543	32	28	which	which	PRON
cana-1543	32	29	has	have	AUX
cana-1543	32	30	degree	degree	NOUN
cana-1543	32	31	one	one	NUM
cana-1543	32	32	,	,	PUNCT
cana-1543	32	33	throughout	throughout	ADP
cana-1543	32	34	this	this	DET
cana-1543	32	35	article	article	NOUN
cana-1543	32	36	,	,	PUNCT
cana-1543	32	37	we	we	PRON
cana-1543	32	38	take	take	VERB
cana-1543	32	39	1.r	1.r	NUM
cana-1543	32	40	=	=	SYM
cana-1543	32	41	definition	definition	NOUN
cana-1543	32	42	2.3	2.3	NUM
cana-1543	32	43	.	.	PUNCT
cana-1543	33	1	the	the	DET
cana-1543	33	2	line	line	NOUN
cana-1543	33	3	graph	graph	NOUN
cana-1543	33	4	(	(	PUNCT
cana-1543	33	5	)	)	PUNCT
cana-1543	33	6	l	l	NOUN
cana-1543	33	7	g	g	NOUN
cana-1543	34	1	[	[	X
cana-1543	34	2	7	7	NUM
cana-1543	34	3	]	]	PUNCT
cana-1543	34	4	has	have	VERB
cana-1543	34	5	nodes	node	NOUN
cana-1543	34	6	that	that	PRON
cana-1543	34	7	are	be	AUX
cana-1543	34	8	edges	edge	NOUN
cana-1543	34	9	of	of	ADP
cana-1543	34	10	,	,	PUNCT
cana-1543	34	11	g	g	PROPN
cana-1543	34	12	and	and	CCONJ
cana-1543	34	13	two	two	NUM
cana-1543	34	14	nodes	node	NOUN
cana-1543	34	15	in	in	ADP
cana-1543	34	16	(	(	PUNCT
cana-1543	34	17	)	)	PUNCT
cana-1543	34	18	l	l	NOUN
cana-1543	34	19	g	g	NOUN
cana-1543	34	20	are	be	AUX
cana-1543	34	21	adjacent	adjacent	ADJ
cana-1543	34	22	,	,	PUNCT
cana-1543	34	23	whenever	whenever	SCONJ
cana-1543	34	24	their	their	PRON
cana-1543	34	25	edges	edge	NOUN
cana-1543	34	26	are	be	AUX
cana-1543	34	27	adjacent	adjacent	ADJ
cana-1543	34	28	in	in	ADP
cana-1543	34	29	.g	.g	PROPN
cana-1543	34	30	definition	definition	NOUN
cana-1543	34	31	2.4	2.4	NUM
cana-1543	34	32	.	.	PUNCT
cana-1543	35	1	the	the	DET
cana-1543	35	2	middle	middle	ADJ
cana-1543	35	3	graph	graph	NOUN
cana-1543	35	4	(	(	PUNCT
cana-1543	35	5	)	)	PUNCT
cana-1543	35	6	m	m	VERB
cana-1543	35	7	g	g	NOUN
cana-1543	35	8	[	[	X
cana-1543	35	9	5	5	NUM
cana-1543	35	10	,	,	PUNCT
cana-1543	35	11	13	13	NUM
cana-1543	35	12	]	]	PUNCT
cana-1543	35	13	is	be	AUX
cana-1543	35	14	formed	form	VERB
cana-1543	35	15	by	by	ADP
cana-1543	35	16	subdividing	subdivide	VERB
cana-1543	35	17	each	each	DET
cana-1543	35	18	edge	edge	NOUN
cana-1543	35	19	exactly	exactly	ADV
cana-1543	35	20	once	once	ADV
cana-1543	35	21	and	and	CCONJ
cana-1543	35	22	connecting	connect	VERB
cana-1543	35	23	these	these	DET
cana-1543	35	24	newly	newly	ADV
cana-1543	35	25	obtained	obtain	VERB
cana-1543	35	26	nodes	node	NOUN
cana-1543	35	27	of	of	ADP
cana-1543	35	28	adjacent	adjacent	ADJ
cana-1543	35	29	edges	edge	NOUN
cana-1543	35	30	of	of	ADP
cana-1543	35	31	.g	.g	PROPN
cana-1543	35	32	definition	definition	NOUN
cana-1543	35	33	2.5	2.5	NUM
cana-1543	35	34	.	.	PUNCT
cana-1543	36	1	the	the	DET
cana-1543	36	2	total	total	ADJ
cana-1543	36	3	graph	graph	NOUN
cana-1543	36	4	(	(	PUNCT
cana-1543	36	5	)	)	PUNCT
cana-1543	36	6	t	t	NOUN
cana-1543	36	7	g	g	NOUN
cana-1543	36	8	[	[	X
cana-1543	36	9	13	13	NUM
cana-1543	36	10	]	]	PUNCT
cana-1543	36	11	is	be	AUX
cana-1543	36	12	a	a	DET
cana-1543	36	13	middle	middle	ADJ
cana-1543	36	14	graph	graph	NOUN
cana-1543	36	15	,	,	PUNCT
cana-1543	36	16	adding	add	VERB
cana-1543	36	17	an	an	DET
cana-1543	36	18	edge	edge	NOUN
cana-1543	36	19	between	between	ADP
cana-1543	36	20	the	the	DET
cana-1543	36	21	vertices	vertex	NOUN
cana-1543	36	22	whenever	whenever	SCONJ
cana-1543	36	23	they	they	PRON
cana-1543	36	24	are	be	AUX
cana-1543	36	25	adjacent	adjacent	ADJ
cana-1543	36	26	in	in	ADP
cana-1543	36	27	g	g	PROPN
cana-1543	36	28	.	.	PUNCT
cana-1543	37	1	definition	definition	NOUN
cana-1543	37	2	2.6	2.6	NUM
cana-1543	37	3	.	.	PUNCT
cana-1543	38	1	the	the	DET
cana-1543	38	2	splitting	splitting	NOUN
cana-1543	38	3	graph	graph	NOUN
cana-1543	38	4	(	(	PUNCT
cana-1543	38	5	)	)	PUNCT
cana-1543	38	6	s	s	PART
cana-1543	38	7	g	g	NOUN
cana-1543	38	8	[	[	X
cana-1543	38	9	12	12	NUM
cana-1543	38	10	]	]	PUNCT
cana-1543	38	11	is	be	AUX
cana-1543	38	12	obtained	obtain	VERB
cana-1543	38	13	by	by	ADP
cana-1543	38	14	adding	add	VERB
cana-1543	38	15	a	a	DET
cana-1543	38	16	new	new	ADJ
cana-1543	38	17	vertex	vertex	NOUN
cana-1543	38	18	'	'	PUNCT
cana-1543	38	19	v	v	NOUN
cana-1543	38	20	corresponding	correspond	VERB
cana-1543	38	21	to	to	ADP
cana-1543	38	22	each	each	DET
cana-1543	38	23	vertex	vertex	NOUN
cana-1543	38	24	v	v	NOUN
cana-1543	38	25	of	of	ADP
cana-1543	38	26	g	g	NOUN
cana-1543	38	27	such	such	ADJ
cana-1543	38	28	that	that	SCONJ
cana-1543	38	29	'	'	PUNCT
cana-1543	38	30	(	(	PUNCT
cana-1543	38	31	)	)	PUNCT
cana-1543	38	32	(	(	PUNCT
cana-1543	38	33	)	)	PUNCT
cana-1543	38	34	.n	.n	PROPN
cana-1543	38	35	v	v	NUM
cana-1543	38	36	n	n	NOUN
cana-1543	38	37	v=	v=	NOUN
cana-1543	38	38	lemma	lemma	PROPN
cana-1543	38	39	2.7	2.7	NUM
cana-1543	38	40	.	.	PUNCT
cana-1543	39	1	[	[	X
cana-1543	39	2	18	18	NUM
cana-1543	39	3	]	]	PUNCT
cana-1543	39	4	for	for	ADP
cana-1543	39	5	any	any	DET
cana-1543	39	6	simple	simple	ADJ
cana-1543	39	7	graph	graph	NOUN
cana-1543	39	8	,	,	PUNCT
cana-1543	39	9	g	g	NOUN
cana-1543	39	10	''	''	PUNCT
cana-1543	39	11	(	(	PUNCT
cana-1543	39	12	)	)	PUNCT
cana-1543	39	13	(	(	PUNCT
cana-1543	39	14	)	)	PUNCT
cana-1543	39	15	1.g	1.g	NUM
cana-1543	39	16	g	g	NOUN
cana-1543	39	17			NUM
cana-1543	39	18			PUNCT
cana-1543	40	1	+	+	CCONJ
cana-1543	40	2	theorem	theorem	ADJ
cana-1543	40	3	2.8	2.8	NUM
cana-1543	40	4	.	.	PUNCT
cana-1543	41	1	[	[	X
cana-1543	41	2	18	18	NUM
cana-1543	41	3	]	]	PUNCT
cana-1543	41	4	let	let	VERB
cana-1543	41	5	nk	nk	PROPN
cana-1543	41	6	be	be	AUX
cana-1543	41	7	the	the	DET
cana-1543	41	8	complete	complete	ADJ
cana-1543	41	9	graph	graph	NOUN
cana-1543	41	10	,	,	PUNCT
cana-1543	41	11	then	then	ADV
cana-1543	41	12	''	''	PUNCT
cana-1543	41	13	,	,	PUNCT
cana-1543	41	14	(	(	PUNCT
cana-1543	41	15	)	)	PUNCT
cana-1543	41	16	1	1	NUM
cana-1543	41	17	,	,	PUNCT
cana-1543	41	18	n	n	CCONJ
cana-1543	41	19	n	n	NOUN
cana-1543	41	20	if	if	SCONJ
cana-1543	41	21	n	n	PRON
cana-1543	41	22	is	be	AUX
cana-1543	41	23	odd	odd	ADJ
cana-1543	42	1	k	k	PROPN
cana-1543	42	2	n	n	NOUN
cana-1543	42	3	if	if	SCONJ
cana-1543	42	4	n	n	PRON
cana-1543	42	5	is	be	AUX
cana-1543	42	6	even	even	ADV
cana-1543	42	7			VERB
cana-1543	42	8			ADV
cana-1543	42	9	=	=	PUNCT
cana-1543	43	1			NUM
cana-1543	43	2	+	+	NOUN
cana-1543	43	3			PROPN
cana-1543	43	4	3	3	NUM
cana-1543	43	5	.	.	NOUN
cana-1543	43	6	results	result	NOUN
cana-1543	43	7	and	and	CCONJ
cana-1543	43	8	discussion	discussion	NOUN
cana-1543	43	9	theorem	theorem	VERB
cana-1543	43	10	3.1	3.1	NUM
cana-1543	43	11	.	.	PUNCT
cana-1543	44	1	for	for	ADP
cana-1543	44	2	any	any	DET
cana-1543	44	3	4	4	NUM
cana-1543	44	4			NUM
cana-1543	44	5	,	,	PUNCT
cana-1543	44	6	''	''	PUNCT
cana-1543	44	7	(	(	PUNCT
cana-1543	44	8	)	)	PUNCT
cana-1543	44	9	1	1	NUM
cana-1543	44	10			NOUN
cana-1543	45	1	=	=	X
cana-1543	45	2	+	+	CCONJ
cana-1543	45	3	.	.	PUNCT
cana-1543	46	1	proof	proof	NOUN
cana-1543	46	2	:	:	PUNCT
cana-1543	46	3	let	let	VERB
cana-1543	46	4	(	(	PUNCT
cana-1543	46	5	)	)	PUNCT
cana-1543	46	6	{	{	PUNCT
cana-1543	46	7	}	}	PUNCT
cana-1543	46	8	{	{	PUNCT
cana-1543	46	9	:1	:1	PUNCT
cana-1543	46	10	}	}	PUNCT
cana-1543	46	11	{	{	PUNCT
cana-1543	46	12	;	;	PUNCT
cana-1543	46	13	1	1	X
cana-1543	46	14	}	}	PUNCT
cana-1543	46	15	{	{	PUNCT
cana-1543	46	16	;	;	PUNCT
cana-1543	46	17	1	1	NUM
cana-1543	46	18	}	}	PUNCT
cana-1543	46	19	v	v	NOUN
cana-1543	46	20	u	u	NOUN
cana-1543	46	21	u	u	NOUN
cana-1543	46	22	v	v	NOUN
cana-1543	46	23	w	w	NOUN
cana-1543	46	24			NOUN
cana-1543	46	25			NOUN
cana-1543	46	26			SYM
cana-1543	46	27			NOUN
cana-1543	46	28			NUM
cana-1543	46	29			NOUN
cana-1543	46	30			NUM
cana-1543	46	31			NOUN
cana-1543	46	32	=	=	PUNCT
cana-1543	46	33			NOUN
cana-1543	46	34			NOUN
cana-1543	46	35			NOUN
cana-1543	46	36			NOUN
cana-1543	46	37			NOUN
cana-1543	46	38			NOUN
cana-1543	46	39	,	,	PUNCT
cana-1543	46	40	where	where	SCONJ
cana-1543	46	41	u	u	NOUN
cana-1543	46	42	is	be	AUX
cana-1543	46	43	the	the	DET
cana-1543	46	44	root	root	NOUN
cana-1543	46	45	vertex	vertex	NOUN
cana-1543	46	46	of	of	ADP
cana-1543	46	47	the	the	DET
cana-1543	46	48	triple	triple	ADJ
cana-1543	46	49	star	star	NOUN
cana-1543	46	50	graph	graph	NOUN
cana-1543	46	51	.	.	PUNCT
cana-1543	47	1	(	(	PUNCT
cana-1543	47	2	)	)	PUNCT
cana-1543	47	3	{	{	PUNCT
cana-1543	47	4	,	,	PUNCT
cana-1543	47	5	,	,	PUNCT
cana-1543	47	6	:1	:1	PUNCT
cana-1543	47	7	}	}	PUNCT
cana-1543	47	8	e	e	X
cana-1543	47	9	e	e	X
cana-1543	47	10	uu	uu	X
cana-1543	47	11	f	f	PROPN
cana-1543	47	12	u	u	NOUN
cana-1543	47	13	v	v	ADP
cana-1543	47	14	e	e	X
cana-1543	47	15	v	v	NOUN
cana-1543	47	16	w	w	X
cana-1543	47	17			NOUN
cana-1543	47	18			PUNCT
cana-1543	47	19			NOUN
cana-1543	47	20			NOUN
cana-1543	47	21			NOUN
cana-1543	47	22			NOUN
cana-1543	47	23			NOUN
cana-1543	47	24			SYM
cana-1543	47	25			NOUN
cana-1543	47	26	=	=	PUNCT
cana-1543	47	27	=	=	SYM
cana-1543	47	28	=	=	SYM
cana-1543	47	29	=	=	SYM
cana-1543	47	30			NOUN
cana-1543	47	31			NOUN
cana-1543	47	32	define	define	VERB
cana-1543	47	33	total	total	ADJ
cana-1543	47	34	coloring	coloring	NOUN
cana-1543	47	35			PROPN
cana-1543	47	36	,	,	PUNCT
cana-1543	47	37	such	such	ADJ
cana-1543	47	38	that	that	PRON
cana-1543	47	39	:	:	PUNCT
cana-1543	47	40	(	(	PUNCT
cana-1543	47	41	)	)	PUNCT
cana-1543	47	42	(	(	PUNCT
cana-1543	47	43	)	)	PUNCT
cana-1543	47	44	{	{	PUNCT
cana-1543	47	45	1,2,3	1,2,3	NUM
cana-1543	47	46	,	,	PUNCT
cana-1543	47	47	...	...	PUNCT
cana-1543	47	48	,	,	PUNCT
cana-1543	47	49	1}v	1}v	NUM
cana-1543	47	50	e	e	X
cana-1543	48	1			PRON
cana-1543	48	2			X
cana-1543	48	3			X
cana-1543	49	1	→	→	VERB
cana-1543	50	1	+	+	CCONJ
cana-1543	50	2	for	for	ADP
cana-1543	50	3	1	1	NUM
cana-1543	50	4			NOUN
cana-1543	50	5			PROPN
cana-1543	50	6			PROPN
cana-1543	50	7	(	(	PUNCT
cana-1543	50	8	)	)	PUNCT
cana-1543	50	9	1u	1u	NOUN
cana-1543	50	10	=	=	PUNCT
cana-1543	50	11	+	+	CCONJ
cana-1543	50	12	;	;	PUNCT
cana-1543	50	13	(	(	PUNCT
cana-1543	50	14	)	)	PUNCT
cana-1543	50	15	(	(	PUNCT
cana-1543	50	16	)	)	PUNCT
cana-1543	50	17	1(mod	1(mod	X
cana-1543	50	18	)	)	PUNCT
cana-1543	50	19	u	u	NOUN
cana-1543	50	20	w	w	NOUN
cana-1543	50	21			NOUN
cana-1543	50	22			ADJ
cana-1543	50	23			NOUN
cana-1543	50	24	=	=	PUNCT
cana-1543	50	25	=	=	SYM
cana-1543	50	26	+	+	CCONJ
cana-1543	50	27	;	;	PUNCT
cana-1543	50	28	(	(	PUNCT
cana-1543	50	29	)	)	PUNCT
cana-1543	50	30	4(mod	4(mod	NUM
cana-1543	50	31	)	)	PUNCT
cana-1543	50	32	v	v	NOUN
cana-1543	50	33			NOUN
cana-1543	50	34	=	=	PUNCT
cana-1543	50	35	+	+	CCONJ
cana-1543	50	36	;	;	PUNCT
cana-1543	50	37	(	(	PUNCT
cana-1543	50	38	)	)	PUNCT
cana-1543	50	39	(	(	PUNCT
cana-1543	50	40	)	)	PUNCT
cana-1543	50	41	(	(	PUNCT
cana-1543	50	42	mod	mod	PROPN
cana-1543	50	43	)	)	PUNCT
cana-1543	50	44	e	e	NOUN
cana-1543	50	45	g	g	PROPN
cana-1543	50	46			VERB
cana-1543	50	47			ADJ
cana-1543	50	48			NOUN
cana-1543	50	49	=	=	X
cana-1543	50	50	=	=	PUNCT
cana-1543	50	51	;	;	PUNCT
cana-1543	50	52	(	(	PUNCT
cana-1543	50	53	)	)	PUNCT
cana-1543	50	54	3(mod	3(mod	NUM
cana-1543	50	55	)	)	PUNCT
cana-1543	50	56	f	f	NOUN
cana-1543	50	57			NOUN
cana-1543	50	58	=	=	X
cana-1543	50	59	+	+	CCONJ
cana-1543	50	60	by	by	ADP
cana-1543	50	61	this	this	DET
cana-1543	50	62	procedure	procedure	NOUN
cana-1543	50	63	,	,	PUNCT
cana-1543	50	64	the	the	DET
cana-1543	50	65	graph	graph	NOUN
cana-1543	50	66			NOUN
cana-1543	50	67	is	be	AUX
cana-1543	50	68	attained	attain	VERB
cana-1543	50	69	with	with	ADP
cana-1543	50	70	1	1	NUM
cana-1543	50	71	+	+	CCONJ
cana-1543	50	72	total	total	ADJ
cana-1543	50	73	colorable	colorable	ADJ
cana-1543	50	74	.	.	PUNCT
cana-1543	51	1	so	so	ADV
cana-1543	51	2	,	,	PUNCT
cana-1543	51	3	it	it	PRON
cana-1543	51	4	is	be	AUX
cana-1543	51	5	clear	clear	ADJ
cana-1543	51	6	that	that	SCONJ
cana-1543	51	7	''	''	PUNCT
cana-1543	51	8	(	(	PUNCT
cana-1543	51	9	)	)	PUNCT
cana-1543	51	10	1.	1.	NUM
cana-1543	51	11			NOUN
cana-1543	51	12			PROPN
cana-1543	51	13	+	+	CCONJ
cana-1543	51	14	since	since	SCONJ
cana-1543	51	15	(	(	PUNCT
cana-1543	51	16	)	)	PUNCT
cana-1543	51	17			NOUN
cana-1543	51	18			NOUN
cana-1543	51	19	=	=	PROPN
cana-1543	51	20	and	and	CCONJ
cana-1543	51	21	by	by	ADP
cana-1543	51	22	lemma	lemma	PROPN
cana-1543	51	23	2.7	2.7	NUM
cana-1543	51	24	,	,	PUNCT
cana-1543	51	25	it	it	PRON
cana-1543	51	26	follows	follow	VERB
cana-1543	51	27	that	that	SCONJ
cana-1543	52	1	''	''	PUNCT
cana-1543	52	2	(	(	PUNCT
cana-1543	52	3	)	)	PUNCT
cana-1543	52	4	(	(	PUNCT
cana-1543	52	5	)	)	PUNCT
cana-1543	52	6	1	1	NUM
cana-1543	52	7			PROPN
cana-1543	52	8			X
cana-1543	52	9			PROPN
cana-1543	52	10			PROPN
cana-1543	53	1	+	+	CCONJ
cana-1543	53	2	1.	1.	NUM
cana-1543	53	3	+	+	CCONJ
cana-1543	53	4	therefore	therefore	ADV
cana-1543	53	5	''	''	PUNCT
cana-1543	53	6	(	(	PUNCT
cana-1543	53	7	)	)	PUNCT
cana-1543	53	8	1.	1.	NUM
cana-1543	53	9			NOUN
cana-1543	54	1	=	=	X
cana-1543	54	2	+	+	CCONJ
cana-1543	54	3	equivalently	equivalently	ADV
cana-1543	54	4	,	,	PUNCT
cana-1543	54	5	this	this	PRON
cana-1543	54	6	is	be	AUX
cana-1543	54	7	true	true	ADJ
cana-1543	54	8	for	for	ADP
cana-1543	54	9	all	all	DET
cana-1543	54	10	other	other	ADJ
cana-1543	54	11	values	value	NOUN
cana-1543	54	12	of	of	ADP
cana-1543	54	13	4.	4.	NOUN
cana-1543	54	14			NUM
cana-1543	54	15	hence	hence	ADV
cana-1543	54	16	''	''	PUNCT
cana-1543	54	17	(	(	PUNCT
cana-1543	54	18	)	)	PUNCT
cana-1543	54	19	1.	1.	NUM
cana-1543	54	20			NOUN
cana-1543	54	21	=	=	SYM
cana-1543	55	1	+	+	NUM
cana-1543	55	2	communications	communication	NOUN
cana-1543	55	3	on	on	ADP
cana-1543	55	4	applied	apply	VERB
cana-1543	55	5	nonlinear	nonlinear	ADJ
cana-1543	55	6	analysis	analysis	NOUN
cana-1543	55	7	issn	issn	NOUN
cana-1543	55	8	:	:	PUNCT
cana-1543	55	9	1074	1074	NUM
cana-1543	55	10	-	-	PUNCT
cana-1543	55	11	133x	133x	NUM
cana-1543	55	12	vol	vol	NOUN
cana-1543	55	13	31	31	NUM
cana-1543	55	14	no	no	NOUN
cana-1543	55	15	.	.	PUNCT
cana-1543	56	1	8s	8s	PROPN
cana-1543	56	2	(	(	PUNCT
cana-1543	56	3	2024	2024	NUM
cana-1543	56	4	)	)	PUNCT
cana-1543	56	5	496	496	NUM
cana-1543	56	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1543	56	7	fig	fig	NOUN
cana-1543	56	8	1	1	NUM
cana-1543	56	9	:	:	PUNCT
cana-1543	56	10	total	total	ADJ
cana-1543	56	11	coloring	coloring	NOUN
cana-1543	56	12	of	of	ADP
cana-1543	56	13	triple	triple	ADJ
cana-1543	56	14	star	star	NOUN
cana-1543	56	15	graph	graph	NOUN
cana-1543	56	16	7	7	NUM
cana-1543	56	17	theorem	theorem	ADJ
cana-1543	56	18	3.2	3.2	NUM
cana-1543	56	19	:	:	PUNCT
cana-1543	56	20	for	for	ADP
cana-1543	56	21	any	any	DET
cana-1543	56	22	4	4	NUM
cana-1543	56	23			NUM
cana-1543	56	24	,	,	PUNCT
cana-1543	56	25	''	''	PUNCT
cana-1543	56	26	(	(	PUNCT
cana-1543	56	27	(	(	PUNCT
cana-1543	56	28	)	)	PUNCT
cana-1543	56	29	)	)	PUNCT
cana-1543	57	1	1l	1l	NUM
cana-1543	57	2			X
cana-1543	58	1			NOUN
cana-1543	59	1	=	=	X
cana-1543	59	2	+	+	CCONJ
cana-1543	59	3	.	.	PUNCT
cana-1543	60	1	proof	proof	NOUN
cana-1543	60	2	:	:	PUNCT
cana-1543	60	3	let	let	VERB
cana-1543	60	4	(	(	PUNCT
cana-1543	60	5	(	(	PUNCT
cana-1543	60	6	)	)	PUNCT
cana-1543	60	7	)	)	PUNCT
cana-1543	60	8	{	{	PUNCT
cana-1543	60	9	,	,	PUNCT
cana-1543	60	10	,	,	PUNCT
cana-1543	60	11	:1	:1	PUNCT
cana-1543	60	12	}	}	PUNCT
cana-1543	60	13	v	v	NUM
cana-1543	60	14	l	l	NOUN
cana-1543	60	15	u	u	NOUN
cana-1543	60	16	v	v	NOUN
cana-1543	60	17	w	w	NOUN
cana-1543	60	18			NOUN
cana-1543	60	19			NOUN
cana-1543	60	20			SYM
cana-1543	60	21			NOUN
cana-1543	60	22	=	=	NUM
cana-1543	60	23			NUM
cana-1543	60	24			NOUN
cana-1543	60	25	and	and	CCONJ
cana-1543	60	26	(	(	PUNCT
cana-1543	60	27	(	(	PUNCT
cana-1543	60	28	)	)	PUNCT
cana-1543	60	29	)	)	PUNCT
cana-1543	60	30	{	{	PUNCT
cana-1543	60	31	,	,	PUNCT
cana-1543	60	32	:1	:1	PUNCT
cana-1543	60	33	}	}	PUNCT
cana-1543	60	34	{	{	PUNCT
cana-1543	60	35	:1	:1	PUNCT
cana-1543	60	36	,	,	PUNCT
cana-1543	60	37	,	,	PUNCT
cana-1543	60	38	1	1	X
cana-1543	60	39	}	}	PUNCT
cana-1543	60	40	e	e	NOUN
cana-1543	60	41	l	l	NOUN
cana-1543	60	42	u	u	NOUN
cana-1543	60	43	v	v	NOUN
cana-1543	60	44	v	v	NOUN
cana-1543	60	45	w	w	NOUN
cana-1543	60	46	u	u	NOUN
cana-1543	60	47	v	v	ADP
cana-1543	60	48			NOUN
cana-1543	60	49			ADP
cana-1543	60	50			NOUN
cana-1543	60	51			NOUN
cana-1543	60	52			NOUN
cana-1543	60	53			PROPN
cana-1543	60	54			NOUN
cana-1543	60	55			NUM
cana-1543	60	56			NOUN
cana-1543	60	57			NUM
cana-1543	60	58			NOUN
cana-1543	60	59			NOUN
cana-1543	60	60			NOUN
cana-1543	60	61			NUM
cana-1543	60	62	=	=	NUM
cana-1543	60	63			NOUN
cana-1543	60	64			NOUN
cana-1543	60	65			NOUN
cana-1543	60	66			NOUN
cana-1543	60	67			VERB
cana-1543	60	68	+	+	CCONJ
cana-1543	60	69			NOUN
cana-1543	60	70			NOUN
cana-1543	60	71	define	define	VERB
cana-1543	60	72			PROPN
cana-1543	60	73	,	,	PUNCT
cana-1543	60	74	such	such	ADJ
cana-1543	60	75	that	that	PRON
cana-1543	60	76	:	:	PUNCT
cana-1543	60	77	(	(	PUNCT
cana-1543	60	78	(	(	PUNCT
cana-1543	60	79	)	)	PUNCT
cana-1543	60	80	)	)	PUNCT
cana-1543	60	81	(	(	PUNCT
cana-1543	60	82	(	(	PUNCT
cana-1543	60	83	)	)	PUNCT
cana-1543	60	84	)	)	PUNCT
cana-1543	60	85	{	{	PUNCT
cana-1543	60	86	1,2,3	1,2,3	NUM
cana-1543	60	87	,	,	PUNCT
cana-1543	60	88	...	...	PUNCT
cana-1543	60	89	,	,	PUNCT
cana-1543	60	90	1}.v	1}.v	NUM
cana-1543	60	91	l	l	NOUN
cana-1543	60	92	e	e	X
cana-1543	60	93	l	l	X
cana-1543	60	94			PUNCT
cana-1543	60	95			X
cana-1543	60	96			X
cana-1543	60	97	→	→	VERB
cana-1543	60	98	+	+	PUNCT
cana-1543	60	99	(	(	PUNCT
cana-1543	60	100	)	)	PUNCT
cana-1543	60	101	,	,	PUNCT
cana-1543	60	102	for	for	ADP
cana-1543	60	103	all	all	DET
cana-1543	60	104	1u	1u	NUM
cana-1543	60	105			NOUN
cana-1543	60	106			NOUN
cana-1543	60	107	=	=	PUNCT
cana-1543	60	108			NUM
cana-1543	60	109			NOUN
cana-1543	60	110	;	;	PUNCT
cana-1543	60	111	1	1	NUM
cana-1543	60	112	,	,	PUNCT
cana-1543	60	113	1	1	NUM
cana-1543	60	114	,	,	PUNCT
cana-1543	60	115	(	(	PUNCT
cana-1543	60	116	)	)	PUNCT
cana-1543	60	117	1	1	NUM
cana-1543	60	118	,	,	PUNCT
cana-1543	60	119	2	2	NUM
cana-1543	60	120	1	1	NUM
cana-1543	60	121	if	if	SCONJ
cana-1543	60	122	v	v	X
cana-1543	61	1	if	if	SCONJ
cana-1543	61	2			NOUN
cana-1543	61	3			CCONJ
cana-1543	61	4			NOUN
cana-1543	61	5			NUM
cana-1543	61	6			ADJ
cana-1543	61	7			NOUN
cana-1543	61	8			NOUN
cana-1543	61	9			X
cana-1543	61	10	+	+	CCONJ
cana-1543	61	11	=	=	NOUN
cana-1543	61	12			NOUN
cana-1543	61	13	=	=	PUNCT
cana-1543	62	1			NUM
cana-1543	62	2	−	−	NOUN
cana-1543	62	3			NOUN
cana-1543	62	4			NOUN
cana-1543	62	5	−	−	VERB
cana-1543	62	6	;	;	PUNCT
cana-1543	62	7	2	2	X
cana-1543	62	8	,	,	PUNCT
cana-1543	62	9	1	1	NUM
cana-1543	62	10	1	1	NUM
cana-1543	62	11	(	(	PUNCT
cana-1543	62	12	)	)	PUNCT
cana-1543	62	13	1	1	NUM
cana-1543	62	14	,	,	PUNCT
cana-1543	62	15	if	if	SCONJ
cana-1543	62	16	w	w	NOUN
cana-1543	62	17	if	if	SCONJ
cana-1543	62	18			NOUN
cana-1543	62	19			NOUN
cana-1543	62	20			X
cana-1543	62	21			NUM
cana-1543	62	22			ADJ
cana-1543	62	23			NOUN
cana-1543	62	24			CCONJ
cana-1543	62	25	+	+	NUM
cana-1543	62	26			NOUN
cana-1543	62	27			NOUN
cana-1543	62	28	−	−	NOUN
cana-1543	62	29	=	=	PUNCT
cana-1543	63	1			NUM
cana-1543	63	2	=	=	SYM
cana-1543	63	3			PROPN
cana-1543	63	4	2	2	NUM
cana-1543	63	5	,	,	PUNCT
cana-1543	63	6	2	2	NUM
cana-1543	63	7	0	0	NUM
cana-1543	63	8	(	(	PUNCT
cana-1543	63	9	mod	mod	NOUN
cana-1543	63	10	1	1	NUM
cana-1543	63	11	)	)	PUNCT
cana-1543	63	12	(	(	PUNCT
cana-1543	63	13	)	)	PUNCT
cana-1543	63	14	1	1	NUM
cana-1543	63	15	,	,	PUNCT
cana-1543	63	16	otherwise	otherwise	ADV
cana-1543	63	17	if	if	SCONJ
cana-1543	63	18	u	u	NOUN
cana-1543	63	19	v	v	X
cana-1543	63	20			NOUN
cana-1543	63	21			PUNCT
cana-1543	63	22			NOUN
cana-1543	63	23			CCONJ
cana-1543	63	24			PROPN
cana-1543	63	25			NUM
cana-1543	63	26			PROPN
cana-1543	63	27	+	+	NOUN
cana-1543	63	28			ADV
cana-1543	63	29			NOUN
cana-1543	63	30	=	=	PUNCT
cana-1543	64	1			NUM
cana-1543	64	2	+	+	NOUN
cana-1543	64	3			INTJ
cana-1543	64	4	;	;	PUNCT
cana-1543	64	5	(	(	PUNCT
cana-1543	64	6	)	)	PUNCT
cana-1543	64	7	,	,	PUNCT
cana-1543	64	8	for	for	ADP
cana-1543	64	9	all	all	DET
cana-1543	64	10	1v	1v	NUM
cana-1543	64	11	w	w	NOUN
cana-1543	64	12			NOUN
cana-1543	64	13			NOUN
cana-1543	64	14			NOUN
cana-1543	64	15	=	=	PUNCT
cana-1543	64	16			NUM
cana-1543	64	17			NOUN
cana-1543	64	18	;	;	PUNCT
cana-1543	64	19	,	,	PUNCT
cana-1543	64	20	(	(	PUNCT
cana-1543	64	21	)	)	PUNCT
cana-1543	64	22	0	0	NUM
cana-1543	65	1	(	(	PUNCT
cana-1543	65	2	mod	mod	NOUN
cana-1543	65	3	1	1	NUM
cana-1543	65	4	)	)	PUNCT
cana-1543	65	5	(	(	PUNCT
cana-1543	65	6	)	)	PUNCT
cana-1543	65	7	1	1	NUM
cana-1543	65	8	,	,	PUNCT
cana-1543	65	9	otherwise	otherwise	ADV
cana-1543	65	10	,	,	PUNCT
cana-1543	65	11	1	1	NUM
cana-1543	65	12	if	if	SCONJ
cana-1543	65	13	u	u	NOUN
cana-1543	65	14	u	u	NOUN
cana-1543	65	15			NUM
cana-1543	65	16			NOUN
cana-1543	65	17			NUM
cana-1543	65	18			NOUN
cana-1543	65	19			PRON
cana-1543	65	20			ADV
cana-1543	65	21			PROPN
cana-1543	65	22			NUM
cana-1543	65	23			NOUN
cana-1543	65	24			NOUN
cana-1543	65	25			X
cana-1543	65	26			NUM
cana-1543	65	27			NUM
cana-1543	65	28	+	+	PUNCT
cana-1543	65	29	+	+	CCONJ
cana-1543	65	30			NOUN
cana-1543	65	31	+	+	NOUN
cana-1543	65	32			NOUN
cana-1543	65	33			NOUN
cana-1543	65	34	=	=	PUNCT
cana-1543	66	1			NUM
cana-1543	66	2	+	+	CCONJ
cana-1543	66	3			NOUN
cana-1543	66	4	+	+	CCONJ
cana-1543	66	5			NUM
cana-1543	66	6			ADJ
cana-1543	66	7	fig	fig	NOUN
cana-1543	66	8	2	2	NUM
cana-1543	66	9	:	:	PUNCT
cana-1543	66	10	total	total	ADJ
cana-1543	66	11	coloring	coloring	NOUN
cana-1543	66	12	of	of	ADP
cana-1543	66	13	7	7	NUM
cana-1543	66	14	(	(	PUNCT
cana-1543	66	15	)	)	PUNCT
cana-1543	66	16	l	l	NOUN
cana-1543	66	17			NOUN
cana-1543	66	18	by	by	ADP
cana-1543	66	19	this	this	DET
cana-1543	66	20	procedure	procedure	NOUN
cana-1543	66	21	,	,	PUNCT
cana-1543	66	22	the	the	DET
cana-1543	66	23	graph	graph	NOUN
cana-1543	66	24	(	(	PUNCT
cana-1543	66	25	)	)	PUNCT
cana-1543	66	26	l	l	NOUN
cana-1543	66	27			NOUN
cana-1543	66	28	is	be	AUX
cana-1543	66	29	attained	attain	VERB
cana-1543	66	30	with	with	ADP
cana-1543	66	31	1	1	NUM
cana-1543	66	32	+	+	CCONJ
cana-1543	66	33	total	total	ADJ
cana-1543	66	34	colorable	colorable	ADJ
cana-1543	66	35	.	.	PUNCT
cana-1543	67	1	so	so	ADV
cana-1543	67	2	,	,	PUNCT
cana-1543	67	3	it	it	PRON
cana-1543	67	4	is	be	AUX
cana-1543	67	5	clear	clear	ADJ
cana-1543	67	6	that	that	SCONJ
cana-1543	67	7	''	''	PUNCT
cana-1543	67	8	(	(	PUNCT
cana-1543	67	9	(	(	PUNCT
cana-1543	67	10	)	)	PUNCT
cana-1543	67	11	)	)	PUNCT
cana-1543	67	12	1.l	1.l	NUM
cana-1543	67	13			NOUN
cana-1543	67	14			X
cana-1543	68	1			PROPN
cana-1543	68	2	+	+	CCONJ
cana-1543	68	3	since	since	SCONJ
cana-1543	68	4	(	(	PUNCT
cana-1543	68	5	(	(	PUNCT
cana-1543	68	6	)	)	PUNCT
cana-1543	68	7	)	)	PUNCT
cana-1543	68	8	l	l	NOUN
cana-1543	68	9			NOUN
cana-1543	68	10			PROPN
cana-1543	68	11	=	=	PROPN
cana-1543	68	12	and	and	CCONJ
cana-1543	68	13	by	by	ADP
cana-1543	68	14	lemma2.7	lemma2.7	PROPN
cana-1543	68	15	,	,	PUNCT
cana-1543	68	16	it	it	PRON
cana-1543	68	17	follows	follow	VERB
cana-1543	68	18	that	that	SCONJ
cana-1543	68	19	''	''	PUNCT
cana-1543	68	20	(	(	PUNCT
cana-1543	68	21	(	(	PUNCT
cana-1543	68	22	)	)	PUNCT
cana-1543	68	23	)	)	PUNCT
cana-1543	69	1	(	(	PUNCT
cana-1543	69	2	(	(	PUNCT
cana-1543	69	3	)	)	PUNCT
cana-1543	69	4	)	)	PUNCT
cana-1543	69	5	1l	1l	X
cana-1543	69	6	l	l	NUM
cana-1543	70	1			PROPN
cana-1543	70	2			PROPN
cana-1543	70	3			PROPN
cana-1543	70	4			PROPN
cana-1543	71	1	+	+	CCONJ
cana-1543	71	2	1.	1.	NUM
cana-1543	71	3	+	+	CCONJ
cana-1543	71	4	therefore	therefore	ADV
cana-1543	71	5	''	''	PUNCT
cana-1543	71	6	(	(	PUNCT
cana-1543	71	7	(	(	PUNCT
cana-1543	71	8	)	)	PUNCT
cana-1543	71	9	)	)	PUNCT
cana-1543	72	1	1.l	1.l	NUM
cana-1543	72	2			NOUN
cana-1543	72	3			NOUN
cana-1543	73	1	=	=	X
cana-1543	73	2	+	+	CCONJ
cana-1543	73	3	equivalently	equivalently	ADV
cana-1543	73	4	,	,	PUNCT
cana-1543	73	5	this	this	PRON
cana-1543	73	6	is	be	AUX
cana-1543	73	7	true	true	ADJ
cana-1543	73	8	for	for	ADP
cana-1543	73	9	all	all	DET
cana-1543	73	10	other	other	ADJ
cana-1543	73	11	values	value	NOUN
cana-1543	73	12	of	of	ADP
cana-1543	73	13	4.	4.	NOUN
cana-1543	73	14			NUM
cana-1543	73	15	hence	hence	ADV
cana-1543	73	16	''	''	PUNCT
cana-1543	73	17	(	(	PUNCT
cana-1543	73	18	(	(	PUNCT
cana-1543	73	19	)	)	PUNCT
cana-1543	73	20	)	)	PUNCT
cana-1543	74	1	1.l	1.l	NUM
cana-1543	74	2			NOUN
cana-1543	74	3			NOUN
cana-1543	75	1	=	=	NOUN
cana-1543	75	2	+	+	NUM
cana-1543	75	3	communications	communication	NOUN
cana-1543	75	4	on	on	ADP
cana-1543	75	5	applied	apply	VERB
cana-1543	75	6	nonlinear	nonlinear	ADJ
cana-1543	75	7	analysis	analysis	NOUN
cana-1543	75	8	issn	issn	NOUN
cana-1543	75	9	:	:	PUNCT
cana-1543	75	10	1074	1074	NUM
cana-1543	75	11	-	-	PUNCT
cana-1543	75	12	133x	133x	NUM
cana-1543	75	13	vol	vol	NOUN
cana-1543	75	14	31	31	NUM
cana-1543	75	15	no	no	NOUN
cana-1543	75	16	.	.	PUNCT
cana-1543	76	1	8s	8s	PROPN
cana-1543	76	2	(	(	PUNCT
cana-1543	76	3	2024	2024	NUM
cana-1543	76	4	)	)	PUNCT
cana-1543	76	5	497	497	NUM
cana-1543	76	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1543	76	7	theorem	theorem	VERB
cana-1543	76	8	3.3	3.3	NUM
cana-1543	76	9	:	:	PUNCT
cana-1543	76	10	for	for	ADP
cana-1543	76	11	any	any	DET
cana-1543	76	12	4	4	NUM
cana-1543	76	13			NUM
cana-1543	76	14	,	,	PUNCT
cana-1543	76	15	''	''	PUNCT
cana-1543	76	16	(	(	PUNCT
cana-1543	76	17	(	(	PUNCT
cana-1543	76	18	)	)	PUNCT
cana-1543	76	19	)	)	PUNCT
cana-1543	77	1	3.m	3.m	NUM
cana-1543	77	2			NOUN
cana-1543	77	3			NOUN
cana-1543	77	4	=	=	NOUN
cana-1543	78	1	+	+	NUM
cana-1543	78	2	proof	proof	NOUN
cana-1543	78	3	:	:	PUNCT
cana-1543	78	4			PROPN
cana-1543	78	5			PROPN
cana-1543	78	6	'	'	PUNCT
cana-1543	78	7	'	'	PUNCT
cana-1543	78	8	'	'	PUNCT
cana-1543	78	9	(	(	PUNCT
cana-1543	78	10	(	(	PUNCT
cana-1543	78	11	)	)	PUNCT
cana-1543	78	12	)	)	PUNCT
cana-1543	78	13	{	{	PUNCT
cana-1543	78	14	}	}	PUNCT
cana-1543	78	15	{	{	PUNCT
cana-1543	78	16	}	}	PUNCT
cana-1543	78	17	{	{	PUNCT
cana-1543	78	18	}	}	PUNCT
cana-1543	78	19	{	{	PUNCT
cana-1543	78	20	}	}	PUNCT
cana-1543	78	21	{	{	PUNCT
cana-1543	78	22	}	}	PUNCT
cana-1543	78	23	{	{	PUNCT
cana-1543	78	24	}	}	PUNCT
cana-1543	78	25	{	{	PUNCT
cana-1543	78	26	}	}	PUNCT
cana-1543	78	27	:	:	PUNCT
cana-1543	78	28	1v	1v	NUM
cana-1543	78	29	m	m	NOUN
cana-1543	78	30	v	v	NOUN
cana-1543	78	31	v	v	NUM
cana-1543	78	32	v	v	ADP
cana-1543	78	33	u	u	PROPN
cana-1543	78	34	u	u	NOUN
cana-1543	78	35	w	w	NOUN
cana-1543	78	36	w	w	X
cana-1543	78	37			NOUN
cana-1543	78	38			PUNCT
cana-1543	78	39			NOUN
cana-1543	78	40			NOUN
cana-1543	78	41			NOUN
cana-1543	78	42			SYM
cana-1543	78	43			NOUN
cana-1543	78	44	=	=	NUM
cana-1543	78	45			NUM
cana-1543	78	46			NOUN
cana-1543	78	47	and	and	CCONJ
cana-1543	78	48			PROPN
cana-1543	78	49			PROPN
cana-1543	78	50			PROPN
cana-1543	78	51			PROPN
cana-1543	78	52	'	'	PUNCT
cana-1543	78	53	'	'	PUNCT
cana-1543	78	54	'	'	PUNCT
cana-1543	78	55	'	'	PUNCT
cana-1543	78	56	'	'	PUNCT
cana-1543	78	57	'	'	PUNCT
cana-1543	78	58	'	'	PUNCT
cana-1543	78	59	'	'	PUNCT
cana-1543	78	60	'	'	PUNCT
cana-1543	78	61	'	'	PUNCT
cana-1543	78	62	'	'	PUNCT
cana-1543	78	63	'	'	PUNCT
cana-1543	78	64	(	(	PUNCT
cana-1543	78	65	(	(	PUNCT
cana-1543	78	66	)	)	PUNCT
cana-1543	78	67	)	)	PUNCT
cana-1543	78	68	;	;	PUNCT
cana-1543	78	69	;	;	PUNCT
cana-1543	78	70	;	;	PUNCT
cana-1543	78	71	;	;	PUNCT
cana-1543	78	72	;	;	PUNCT
cana-1543	78	73	;	;	PUNCT
cana-1543	78	74	;	;	PUNCT
cana-1543	78	75	:1	:1	PUNCT
cana-1543	78	76	:1	:1	PUNCT
cana-1543	78	77	1	1	NUM
cana-1543	78	78	,	,	PUNCT
cana-1543	78	79	1	1	NUM
cana-1543	78	80	e	e	VERB
cana-1543	78	81	m	m	VERB
cana-1543	78	82	vv	vv	ADP
cana-1543	78	83	v	v	ADP
cana-1543	78	84	v	v	NUM
cana-1543	78	85	v	v	NOUN
cana-1543	78	86	u	u	NOUN
cana-1543	78	87	u	u	NOUN
cana-1543	78	88	u	u	NOUN
cana-1543	78	89	u	u	PROPN
cana-1543	78	90	w	w	PROPN
cana-1543	78	91	w	w	PROPN
cana-1543	78	92	w	w	PROPN
cana-1543	78	93	w	w	PROPN
cana-1543	78	94	u	u	PROPN
cana-1543	78	95	u	u	NOUN
cana-1543	78	96	v	v	ADP
cana-1543	78	97	v	v	ADP
cana-1543	78	98	v	v	ADP
cana-1543	78	99	t	t	NOUN
cana-1543	78	100			PUNCT
cana-1543	78	101			ADP
cana-1543	78	102			VERB
cana-1543	78	103			NOUN
cana-1543	78	104			NOUN
cana-1543	78	105			NOUN
cana-1543	78	106			NOUN
cana-1543	78	107			NOUN
cana-1543	78	108			NOUN
cana-1543	78	109			NOUN
cana-1543	78	110			NOUN
cana-1543	78	111			NOUN
cana-1543	78	112			NOUN
cana-1543	78	113			NOUN
cana-1543	78	114			NOUN
cana-1543	78	115			NOUN
cana-1543	78	116			X
cana-1543	78	117			NUM
cana-1543	78	118			NOUN
cana-1543	79	1			NOUN
cana-1543	79	2			NUM
cana-1543	79	3			CCONJ
cana-1543	79	4			X
cana-1543	79	5			NUM
cana-1543	79	6			NUM
cana-1543	79	7	=	=	NOUN
cana-1543	79	8			NOUN
cana-1543	79	9			NOUN
cana-1543	79	10			NOUN
cana-1543	79	11			NOUN
cana-1543	79	12	−	−	NOUN
cana-1543	80	1	+	+	CCONJ
cana-1543	80	2			NOUN
cana-1543	80	3			NOUN
cana-1543	80	4	the	the	DET
cana-1543	80	5	vertices	vertex	NOUN
cana-1543	80	6	,	,	PUNCT
cana-1543	80	7	(	(	PUNCT
cana-1543	80	8	1	1	X
cana-1543	80	9	)	)	PUNCT
cana-1543	80	10	u	u	NOUN
cana-1543	80	11	u	u	NOUN
cana-1543	80	12			NOUN
cana-1543	80	13			PROPN
cana-1543	80	14			NOUN
cana-1543	80	15	induced	induce	VERB
cana-1543	80	16	a	a	DET
cana-1543	80	17	clique	clique	NOUN
cana-1543	80	18	of	of	ADP
cana-1543	80	19	order	order	NOUN
cana-1543	80	20	3	3	NUM
cana-1543	80	21	+	+	CCONJ
cana-1543	80	22	in	in	ADP
cana-1543	80	23	(	(	PUNCT
cana-1543	80	24	)	)	PUNCT
cana-1543	80	25	m	m	NOUN
cana-1543	80	26			NOUN
cana-1543	80	27	.	.	PUNCT
cana-1543	81	1	define	define	VERB
cana-1543	81	2			PROPN
cana-1543	81	3	,	,	PUNCT
cana-1543	81	4	such	such	ADJ
cana-1543	81	5	that	that	PRON
cana-1543	81	6	:	:	PUNCT
cana-1543	81	7	(	(	PUNCT
cana-1543	81	8	(	(	PUNCT
cana-1543	81	9	)	)	PUNCT
cana-1543	81	10	)	)	PUNCT
cana-1543	81	11	(	(	PUNCT
cana-1543	81	12	(	(	PUNCT
cana-1543	81	13	)	)	PUNCT
cana-1543	81	14	)	)	PUNCT
cana-1543	81	15	{	{	PUNCT
cana-1543	81	16	1,2,3	1,2,3	NUM
cana-1543	81	17	...	...	PUNCT
cana-1543	81	18	,	,	PUNCT
cana-1543	82	1	3}v	3}v	NUM
cana-1543	82	2	m	m	VERB
cana-1543	82	3	e	e	NOUN
cana-1543	82	4	m	m	PUNCT
cana-1543	83	1			X
cana-1543	83	2			X
cana-1543	83	3			X
cana-1543	83	4	→	→	X
cana-1543	84	1	+	+	CCONJ
cana-1543	84	2	.	.	PUNCT
cana-1543	85	1	consider	consider	VERB
cana-1543	85	2	the	the	DET
cana-1543	85	3	following	follow	VERB
cana-1543	85	4	two	two	NUM
cana-1543	85	5	cases	case	NOUN
cana-1543	85	6	case	case	NOUN
cana-1543	85	7	(	(	PUNCT
cana-1543	85	8	i	i	NOUN
cana-1543	85	9	):	):	PUNCT
cana-1543	85	10	when	when	SCONJ
cana-1543	85	11			NUM
cana-1543	85	12	is	be	AUX
cana-1543	85	13	even	even	ADV
cana-1543	85	14	,	,	PUNCT
cana-1543	85	15	for	for	ADP
cana-1543	85	16	1	1	NUM
cana-1543	85	17			NOUN
cana-1543	85	18			PROPN
cana-1543	85	19			PROPN
cana-1543	85	20	(	(	PUNCT
cana-1543	85	21	)	)	PUNCT
cana-1543	85	22	3v	3v	NUM
cana-1543	85	23	=	=	PUNCT
cana-1543	86	1	+	+	CCONJ
cana-1543	86	2	;	;	PUNCT
cana-1543	86	3	(	(	PUNCT
cana-1543	86	4	)	)	PUNCT
cana-1543	86	5	2	2	NUM
cana-1543	86	6	,	,	PUNCT
cana-1543	86	7	(	(	PUNCT
cana-1543	86	8	)	)	PUNCT
cana-1543	86	9	v	v	NOUN
cana-1543	86	10	u	u	NOUN
cana-1543	86	11			NOUN
cana-1543	86	12			PUNCT
cana-1543	86	13			ADJ
cana-1543	86	14	=	=	PUNCT
cana-1543	87	1	+	+	NUM
cana-1543	87	2	=	=	SYM
cana-1543	87	3	;	;	PUNCT
cana-1543	87	4	'	'	PUNCT
cana-1543	87	5	(	(	PUNCT
cana-1543	87	6	)	)	PUNCT
cana-1543	87	7	v	v	PROPN
cana-1543	87	8	=	=	NOUN
cana-1543	87	9	;	;	PUNCT
cana-1543	87	10	'	'	PUNCT
cana-1543	87	11	(	(	PUNCT
cana-1543	87	12	)	)	PUNCT
cana-1543	87	13	1u	1u	NOUN
cana-1543	87	14	=	=	PUNCT
cana-1543	88	1	+	+	CCONJ
cana-1543	88	2	;	;	PUNCT
cana-1543	88	3	'	'	PUNCT
cana-1543	88	4	(	(	PUNCT
cana-1543	88	5	)	)	PUNCT
cana-1543	88	6	3w	3w	NUM
cana-1543	88	7	=	=	NOUN
cana-1543	89	1	+	+	CCONJ
cana-1543	89	2	;	;	PUNCT
cana-1543	89	3	(	(	PUNCT
cana-1543	89	4	)	)	PUNCT
cana-1543	89	5	2w	2w	NUM
cana-1543	89	6	=	=	NOUN
cana-1543	89	7	+	+	CCONJ
cana-1543	89	8	;	;	PUNCT
cana-1543	89	9	'	'	PUNCT
cana-1543	89	10	,	,	PUNCT
cana-1543	89	11	1	1	NUM
cana-1543	89	12	(	(	PUNCT
cana-1543	89	13	)	)	PUNCT
cana-1543	89	14	1	1	NUM
cana-1543	89	15	,	,	PUNCT
cana-1543	89	16	2	2	NUM
cana-1543	89	17	v	v	NOUN
cana-1543	89	18	v	v	CCONJ
cana-1543	89	19			NOUN
cana-1543	89	20			NUM
cana-1543	89	21			NOUN
cana-1543	89	22			ADJ
cana-1543	89	23			NOUN
cana-1543	89	24			NOUN
cana-1543	89	25			CCONJ
cana-1543	89	26	=	=	NOUN
cana-1543	89	27			NOUN
cana-1543	89	28	=	=	PUNCT
cana-1543	90	1			NUM
cana-1543	90	2	−	−	NOUN
cana-1543	90	3			NOUN
cana-1543	90	4			NOUN
cana-1543	90	5	;	;	PUNCT
cana-1543	90	6	'	'	PUNCT
cana-1543	90	7	(	(	PUNCT
cana-1543	90	8	)	)	PUNCT
cana-1543	90	9	v	v	NOUN
cana-1543	90	10	u	u	NOUN
cana-1543	90	11			NOUN
cana-1543	90	12	=	=	NOUN
cana-1543	90	13	;	;	PUNCT
cana-1543	90	14	'	'	PUNCT
cana-1543	90	15	(	(	PUNCT
cana-1543	90	16	)	)	PUNCT
cana-1543	90	17	3u	3u	PROPN
cana-1543	90	18	u	u	NOUN
cana-1543	90	19			NOUN
cana-1543	90	20	=	=	X
cana-1543	91	1	+	+	CCONJ
cana-1543	91	2	;	;	PUNCT
cana-1543	91	3	'	'	PUNCT
cana-1543	91	4	(	(	PUNCT
cana-1543	91	5	)	)	PUNCT
cana-1543	91	6	2u	2u	NOUN
cana-1543	91	7	w	w	NUM
cana-1543	91	8			NOUN
cana-1543	91	9	=	=	NOUN
cana-1543	91	10	−	−	NOUN
cana-1543	91	11	;	;	PUNCT
cana-1543	91	12	'	'	PUNCT
cana-1543	91	13	(	(	PUNCT
cana-1543	91	14	)	)	PUNCT
cana-1543	91	15	3w	3w	NUM
cana-1543	91	16	w	w	NUM
cana-1543	91	17			NOUN
cana-1543	91	18	=	=	NOUN
cana-1543	91	19	−	−	NOUN
cana-1543	91	20	;	;	PUNCT
cana-1543	91	21	'	'	PUNCT
cana-1543	91	22	'	'	PUNCT
cana-1543	91	23	(	(	PUNCT
cana-1543	91	24	)	)	PUNCT
cana-1543	91	25	1w	1w	NUM
cana-1543	91	26	u	u	NOUN
cana-1543	91	27			NOUN
cana-1543	91	28	=	=	PUNCT
cana-1543	91	29	−	−	NOUN
cana-1543	91	30	;	;	PUNCT
cana-1543	91	31	'	'	PUNCT
cana-1543	91	32	'	'	PUNCT
cana-1543	91	33	(	(	PUNCT
cana-1543	91	34	)	)	PUNCT
cana-1543	91	35	2u	2u	NOUN
cana-1543	91	36	v	v	NOUN
cana-1543	91	37			NOUN
cana-1543	91	38	=	=	X
cana-1543	92	1	+	+	NUM
cana-1543	92	2	'	'	PUNCT
cana-1543	92	3	(	(	PUNCT
cana-1543	92	4	)	)	PUNCT
cana-1543	92	5	2	2	NUM
cana-1543	92	6	,	,	PUNCT
cana-1543	92	7	2	2	NUM
cana-1543	92	8	0	0	NUM
cana-1543	92	9	(	(	PUNCT
cana-1543	92	10	mod	mod	NOUN
cana-1543	92	11	3	3	X
cana-1543	92	12	)	)	PUNCT
cana-1543	92	13	vv	vv	ADP
cana-1543	92	14	if	if	ADJ
cana-1543	92	15			NOUN
cana-1543	92	16			NOUN
cana-1543	92	17	=	=	PUNCT
cana-1543	92	18			PROPN
cana-1543	92	19	+	+	PROPN
cana-1543	92	20			PROPN
cana-1543	92	21	;	;	PUNCT
cana-1543	92	22	'	'	PUNCT
cana-1543	92	23	'	'	PUNCT
cana-1543	92	24	,	,	PUNCT
cana-1543	92	25	(	(	PUNCT
cana-1543	92	26	)	)	PUNCT
cana-1543	92	27	0	0	NUM
cana-1543	93	1	(	(	PUNCT
cana-1543	93	2	mod	mod	NOUN
cana-1543	93	3	3	3	NUM
cana-1543	93	4	)	)	PUNCT
cana-1543	93	5	1,2	1,2	NUM
cana-1543	93	6	,	,	PUNCT
cana-1543	93	7	...	...	PUNCT
cana-1543	93	8	,	,	PUNCT
cana-1543	93	9	1	1	NUM
cana-1543	93	10	(	(	PUNCT
cana-1543	93	11	)	)	PUNCT
cana-1543	93	12	3	3	NUM
cana-1543	93	13	,	,	PUNCT
cana-1543	93	14	,	,	PUNCT
cana-1543	93	15	1	1	NUM
cana-1543	93	16	if	if	SCONJ
cana-1543	93	17	for	for	ADP
cana-1543	93	18	v	v	NUM
cana-1543	93	19	v	v	NOUN
cana-1543	93	20	otherwise	otherwise	ADV
cana-1543	93	21			VERB
cana-1543	93	22			NUM
cana-1543	93	23			NOUN
cana-1543	93	24			NUM
cana-1543	93	25			NOUN
cana-1543	93	26			NUM
cana-1543	93	27			NUM
cana-1543	93	28			CCONJ
cana-1543	93	29			PROPN
cana-1543	93	30			NUM
cana-1543	93	31			NOUN
cana-1543	93	32			NOUN
cana-1543	93	33			X
cana-1543	93	34			NUM
cana-1543	93	35			NUM
cana-1543	93	36	+	+	PUNCT
cana-1543	93	37	+	+	CCONJ
cana-1543	93	38			PROPN
cana-1543	93	39	+	+	CCONJ
cana-1543	93	40	−	−	NOUN
cana-1543	93	41			NOUN
cana-1543	93	42	=	=	PUNCT
cana-1543	94	1			NUM
cana-1543	94	2	+	+	CCONJ
cana-1543	94	3			NOUN
cana-1543	94	4	+	+	CCONJ
cana-1543	94	5			NUM
cana-1543	94	6			ADJ
cana-1543	94	7	case	case	NOUN
cana-1543	94	8	(	(	PUNCT
cana-1543	94	9	ii	ii	NOUN
cana-1543	94	10	):	):	PUNCT
cana-1543	94	11	when	when	SCONJ
cana-1543	94	12			NUM
cana-1543	94	13	is	be	AUX
cana-1543	94	14	odd	odd	ADJ
cana-1543	94	15	,	,	PUNCT
cana-1543	94	16	for	for	ADP
cana-1543	94	17	1	1	NUM
cana-1543	94	18			NOUN
cana-1543	94	19			PROPN
cana-1543	94	20			PROPN
cana-1543	94	21	(	(	PUNCT
cana-1543	94	22	)	)	PUNCT
cana-1543	94	23	3v	3v	NUM
cana-1543	94	24	=	=	PUNCT
cana-1543	94	25	+	+	CCONJ
cana-1543	94	26	;	;	PUNCT
cana-1543	94	27	(	(	PUNCT
cana-1543	94	28	)	)	PUNCT
cana-1543	94	29	2	2	NUM
cana-1543	94	30	,	,	PUNCT
cana-1543	94	31	(	(	PUNCT
cana-1543	94	32	)	)	PUNCT
cana-1543	94	33	v	v	NOUN
cana-1543	94	34	u	u	NOUN
cana-1543	94	35			NOUN
cana-1543	94	36			PUNCT
cana-1543	94	37			ADJ
cana-1543	94	38	=	=	PUNCT
cana-1543	94	39	+	+	NUM
cana-1543	94	40	=	=	SYM
cana-1543	94	41	;	;	PUNCT
cana-1543	94	42	'	'	PUNCT
cana-1543	94	43	(	(	PUNCT
cana-1543	94	44	)	)	PUNCT
cana-1543	94	45	v	v	PROPN
cana-1543	94	46	=	=	NOUN
cana-1543	94	47	;	;	PUNCT
cana-1543	94	48	'	'	PUNCT
cana-1543	94	49	(	(	PUNCT
cana-1543	94	50	)	)	PUNCT
cana-1543	94	51	1u	1u	NOUN
cana-1543	94	52	=	=	PUNCT
cana-1543	95	1	+	+	CCONJ
cana-1543	95	2	;	;	PUNCT
cana-1543	95	3	'	'	PUNCT
cana-1543	95	4	(	(	PUNCT
cana-1543	95	5	)	)	PUNCT
cana-1543	95	6	3w	3w	NUM
cana-1543	95	7	=	=	NOUN
cana-1543	96	1	+	+	CCONJ
cana-1543	96	2	;	;	PUNCT
cana-1543	96	3	(	(	PUNCT
cana-1543	96	4	)	)	PUNCT
cana-1543	96	5	2w	2w	NUM
cana-1543	96	6	=	=	NOUN
cana-1543	96	7	+	+	CCONJ
cana-1543	96	8	;	;	PUNCT
cana-1543	96	9	'	'	PUNCT
cana-1543	96	10	3	3	NUM
cana-1543	96	11	,	,	PUNCT
cana-1543	96	12	1	1	NUM
cana-1543	96	13	(	(	PUNCT
cana-1543	96	14	)	)	PUNCT
cana-1543	96	15	1	1	NUM
cana-1543	96	16	,	,	PUNCT
cana-1543	96	17	2	2	NUM
cana-1543	96	18	v	v	NOUN
cana-1543	96	19	v	v	CCONJ
cana-1543	96	20			NOUN
cana-1543	96	21			NUM
cana-1543	96	22			NOUN
cana-1543	96	23			ADJ
cana-1543	96	24			NOUN
cana-1543	96	25			NOUN
cana-1543	96	26			X
cana-1543	96	27	+	+	CCONJ
cana-1543	96	28	=	=	NOUN
cana-1543	96	29			NOUN
cana-1543	96	30	=	=	PUNCT
cana-1543	97	1			NUM
cana-1543	97	2	−	−	NOUN
cana-1543	97	3			NOUN
cana-1543	97	4			NOUN
cana-1543	97	5	;	;	PUNCT
cana-1543	97	6	'	'	PUNCT
cana-1543	97	7	(	(	PUNCT
cana-1543	97	8	)	)	PUNCT
cana-1543	97	9	v	v	NOUN
cana-1543	97	10	u	u	NOUN
cana-1543	97	11			NOUN
cana-1543	97	12	=	=	NOUN
cana-1543	97	13	;	;	PUNCT
cana-1543	97	14	'	'	PUNCT
cana-1543	97	15	(	(	PUNCT
cana-1543	97	16	)	)	PUNCT
cana-1543	97	17	2u	2u	PROPN
cana-1543	97	18	u	u	NOUN
cana-1543	97	19			NOUN
cana-1543	97	20	=	=	X
cana-1543	98	1	+	+	CCONJ
cana-1543	98	2	;	;	PUNCT
cana-1543	98	3	'	'	PUNCT
cana-1543	98	4	(	(	PUNCT
cana-1543	98	5	)	)	PUNCT
cana-1543	98	6	2u	2u	NOUN
cana-1543	98	7	w	w	NUM
cana-1543	98	8			NOUN
cana-1543	98	9	=	=	NOUN
cana-1543	98	10	−	−	NOUN
cana-1543	98	11	;	;	PUNCT
cana-1543	98	12	'	'	PUNCT
cana-1543	98	13	(	(	PUNCT
cana-1543	98	14	)	)	PUNCT
cana-1543	98	15	3w	3w	NUM
cana-1543	98	16	w	w	NUM
cana-1543	98	17			NOUN
cana-1543	98	18	=	=	NOUN
cana-1543	98	19	−	−	NOUN
cana-1543	98	20	;	;	PUNCT
cana-1543	98	21	'	'	PUNCT
cana-1543	98	22	'	'	PUNCT
cana-1543	98	23	(	(	PUNCT
cana-1543	98	24	)	)	PUNCT
cana-1543	98	25	1w	1w	NUM
cana-1543	98	26	u	u	NOUN
cana-1543	98	27			NOUN
cana-1543	98	28	=	=	PUNCT
cana-1543	98	29	−	−	NOUN
cana-1543	98	30	;	;	PUNCT
cana-1543	98	31	'	'	PUNCT
cana-1543	98	32	'	'	PUNCT
cana-1543	98	33	(	(	PUNCT
cana-1543	98	34	)	)	PUNCT
cana-1543	98	35	2u	2u	NOUN
cana-1543	98	36	v	v	NOUN
cana-1543	98	37			NOUN
cana-1543	98	38	=	=	X
cana-1543	99	1	+	+	CCONJ
cana-1543	99	2	;	;	PUNCT
cana-1543	99	3	'	'	PUNCT
cana-1543	99	4	(	(	PUNCT
cana-1543	99	5	)	)	PUNCT
cana-1543	99	6	2	2	NUM
cana-1543	99	7	,	,	PUNCT
cana-1543	99	8	2	2	NUM
cana-1543	99	9	0	0	NUM
cana-1543	99	10	(	(	PUNCT
cana-1543	99	11	mod	mod	NOUN
cana-1543	99	12	2	2	X
cana-1543	99	13	)	)	PUNCT
cana-1543	99	14	vv	vv	CCONJ
cana-1543	99	15	if	if	ADJ
cana-1543	99	16			NOUN
cana-1543	99	17			NOUN
cana-1543	99	18	=	=	PUNCT
cana-1543	99	19			PROPN
cana-1543	99	20	+	+	PROPN
cana-1543	99	21			PROPN
cana-1543	99	22	;	;	PUNCT
cana-1543	99	23	'	'	PUNCT
cana-1543	99	24	'	'	PUNCT
cana-1543	99	25	,	,	PUNCT
cana-1543	99	26	(	(	PUNCT
cana-1543	99	27	)	)	PUNCT
cana-1543	99	28	0	0	NUM
cana-1543	100	1	(	(	PUNCT
cana-1543	100	2	mod	mod	NOUN
cana-1543	100	3	2	2	NUM
cana-1543	100	4	)	)	PUNCT
cana-1543	100	5	1,2	1,2	NUM
cana-1543	100	6	,	,	PUNCT
cana-1543	100	7	...	...	PUNCT
cana-1543	100	8	,	,	PUNCT
cana-1543	100	9	1	1	NUM
cana-1543	100	10	(	(	PUNCT
cana-1543	100	11	)	)	PUNCT
cana-1543	100	12	2	2	NUM
cana-1543	100	13	,	,	PUNCT
cana-1543	100	14	otherwise	otherwise	ADV
cana-1543	100	15	,	,	PUNCT
cana-1543	100	16	1	1	NUM
cana-1543	100	17	if	if	SCONJ
cana-1543	100	18	for	for	ADP
cana-1543	100	19	v	v	NOUN
cana-1543	100	20	v	v	NOUN
cana-1543	100	21			NUM
cana-1543	100	22			NOUN
cana-1543	100	23			NUM
cana-1543	100	24			NOUN
cana-1543	100	25			NUM
cana-1543	100	26			NUM
cana-1543	100	27			CCONJ
cana-1543	100	28			PROPN
cana-1543	100	29			NUM
cana-1543	100	30			NOUN
cana-1543	100	31			NOUN
cana-1543	100	32			X
cana-1543	100	33			NUM
cana-1543	100	34			NUM
cana-1543	101	1	+	+	PUNCT
cana-1543	101	2	+	+	CCONJ
cana-1543	101	3			PROPN
cana-1543	101	4	+	+	CCONJ
cana-1543	101	5	−	−	NOUN
cana-1543	101	6			NOUN
cana-1543	101	7	=	=	PUNCT
cana-1543	102	1			NUM
cana-1543	102	2	+	+	CCONJ
cana-1543	102	3			NOUN
cana-1543	102	4	+	+	CCONJ
cana-1543	102	5			NUM
cana-1543	102	6			ADJ
cana-1543	102	7	fig	fig	NOUN
cana-1543	102	8	3	3	NUM
cana-1543	102	9	:	:	PUNCT
cana-1543	102	10	total	total	ADJ
cana-1543	102	11	coloring	coloring	NOUN
cana-1543	102	12	of	of	ADP
cana-1543	102	13	7	7	NUM
cana-1543	102	14	(	(	PUNCT
cana-1543	102	15	)	)	PUNCT
cana-1543	102	16	m	m	NOUN
cana-1543	102	17			NOUN
cana-1543	102	18	communications	communication	NOUN
cana-1543	102	19	on	on	ADP
cana-1543	102	20	applied	apply	VERB
cana-1543	102	21	nonlinear	nonlinear	ADJ
cana-1543	102	22	analysis	analysis	NOUN
cana-1543	102	23	issn	issn	NOUN
cana-1543	102	24	:	:	PUNCT
cana-1543	102	25	1074	1074	NUM
cana-1543	102	26	-	-	PUNCT
cana-1543	102	27	133x	133x	NUM
cana-1543	102	28	vol	vol	NOUN
cana-1543	102	29	31	31	NUM
cana-1543	102	30	no	no	NOUN
cana-1543	102	31	.	.	PUNCT
cana-1543	103	1	8s	8s	PROPN
cana-1543	103	2	(	(	PUNCT
cana-1543	103	3	2024	2024	NUM
cana-1543	103	4	)	)	PUNCT
cana-1543	103	5	498	498	NUM
cana-1543	103	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1543	103	7	by	by	ADP
cana-1543	103	8	this	this	DET
cana-1543	103	9	procedure	procedure	NOUN
cana-1543	103	10	,	,	PUNCT
cana-1543	103	11	the	the	DET
cana-1543	103	12	graph	graph	NOUN
cana-1543	103	13	(	(	PUNCT
cana-1543	103	14	)	)	PUNCT
cana-1543	103	15	m	m	NOUN
cana-1543	103	16			NOUN
cana-1543	103	17	is	be	AUX
cana-1543	103	18	attained	attain	VERB
cana-1543	103	19	with	with	ADP
cana-1543	103	20	3	3	NUM
cana-1543	103	21	+	+	CCONJ
cana-1543	103	22	total	total	ADJ
cana-1543	103	23	colorable	colorable	ADJ
cana-1543	103	24	.	.	PUNCT
cana-1543	104	1	so	so	ADV
cana-1543	104	2	,	,	PUNCT
cana-1543	104	3	it	it	PRON
cana-1543	104	4	is	be	AUX
cana-1543	104	5	clear	clear	ADJ
cana-1543	104	6	that	that	SCONJ
cana-1543	104	7	''	''	PUNCT
cana-1543	104	8	(	(	PUNCT
cana-1543	104	9	(	(	PUNCT
cana-1543	104	10	)	)	PUNCT
cana-1543	104	11	)	)	PUNCT
cana-1543	104	12	3.m	3.m	NUM
cana-1543	104	13			NOUN
cana-1543	104	14			X
cana-1543	105	1			PROPN
cana-1543	105	2	+	+	CCONJ
cana-1543	105	3	since	since	SCONJ
cana-1543	105	4	(	(	PUNCT
cana-1543	105	5	(	(	PUNCT
cana-1543	105	6	)	)	PUNCT
cana-1543	105	7	)	)	PUNCT
cana-1543	105	8	m	m	PROPN
cana-1543	105	9			PROPN
cana-1543	105	10			PROPN
cana-1543	105	11	=	=	PROPN
cana-1543	105	12	and	and	CCONJ
cana-1543	105	13	by	by	ADP
cana-1543	105	14	lemma	lemma	PROPN
cana-1543	105	15	2.7	2.7	NUM
cana-1543	105	16	,	,	PUNCT
cana-1543	105	17	it	it	PRON
cana-1543	105	18	follows	follow	VERB
cana-1543	105	19	that	that	SCONJ
cana-1543	105	20	''	''	PUNCT
cana-1543	105	21	(	(	PUNCT
cana-1543	105	22	(	(	PUNCT
cana-1543	105	23	)	)	PUNCT
cana-1543	105	24	)	)	PUNCT
cana-1543	106	1	(	(	PUNCT
cana-1543	106	2	(	(	PUNCT
cana-1543	106	3	)	)	PUNCT
cana-1543	106	4	)	)	PUNCT
cana-1543	106	5	1	1	NUM
cana-1543	106	6	m	m	NOUN
cana-1543	106	7	m	m	NOUN
cana-1543	107	1			PROPN
cana-1543	107	2			X
cana-1543	107	3			PROPN
cana-1543	107	4			PUNCT
cana-1543	108	1	+	+	CCONJ
cana-1543	108	2	3.	3.	NUM
cana-1543	108	3	+	+	CCONJ
cana-1543	108	4	therefore	therefore	ADV
cana-1543	108	5	''	''	PUNCT
cana-1543	108	6	(	(	PUNCT
cana-1543	108	7	(	(	PUNCT
cana-1543	108	8	)	)	PUNCT
cana-1543	108	9	)	)	PUNCT
cana-1543	109	1	3.m	3.m	NUM
cana-1543	109	2			X
cana-1543	109	3			NOUN
cana-1543	110	1	=	=	X
cana-1543	110	2	+	+	CCONJ
cana-1543	110	3	equivalently	equivalently	ADV
cana-1543	110	4	,	,	PUNCT
cana-1543	110	5	this	this	PRON
cana-1543	110	6	is	be	AUX
cana-1543	110	7	true	true	ADJ
cana-1543	110	8	for	for	ADP
cana-1543	110	9	all	all	DET
cana-1543	110	10	other	other	ADJ
cana-1543	110	11	values	value	NOUN
cana-1543	110	12	of	of	ADP
cana-1543	110	13	4.	4.	NOUN
cana-1543	110	14			NUM
cana-1543	110	15	hence	hence	ADV
cana-1543	110	16	''	''	PUNCT
cana-1543	110	17	(	(	PUNCT
cana-1543	110	18	(	(	PUNCT
cana-1543	110	19	)	)	PUNCT
cana-1543	110	20	)	)	PUNCT
cana-1543	111	1	3.m	3.m	NUM
cana-1543	111	2			NOUN
cana-1543	111	3			NOUN
cana-1543	112	1	=	=	X
cana-1543	112	2	+	+	CCONJ
cana-1543	112	3	theorem	theorem	VERB
cana-1543	112	4	3.4	3.4	NUM
cana-1543	112	5	:	:	PUNCT
cana-1543	112	6	for	for	ADP
cana-1543	112	7	any	any	DET
cana-1543	112	8	4	4	NUM
cana-1543	112	9			NUM
cana-1543	112	10	,	,	PUNCT
cana-1543	112	11	''	''	PUNCT
cana-1543	112	12	(	(	PUNCT
cana-1543	112	13	(	(	PUNCT
cana-1543	112	14	)	)	PUNCT
cana-1543	112	15	)	)	PUNCT
cana-1543	112	16	2	2	NUM
cana-1543	112	17	1.t	1.t	NUM
cana-1543	112	18			NOUN
cana-1543	112	19			NOUN
cana-1543	113	1	=	=	NOUN
cana-1543	113	2	+	+	NUM
cana-1543	113	3	proof	proof	NOUN
cana-1543	113	4	:	:	PUNCT
cana-1543	113	5	let	let	VERB
cana-1543	113	6			PRON
cana-1543	113	7			VERB
cana-1543	113	8	'	'	PUNCT
cana-1543	113	9	'	'	PUNCT
cana-1543	113	10	'	'	PUNCT
cana-1543	113	11	(	(	PUNCT
cana-1543	113	12	(	(	PUNCT
cana-1543	113	13	)	)	PUNCT
cana-1543	113	14	)	)	PUNCT
cana-1543	113	15	{	{	PUNCT
cana-1543	113	16	}	}	PUNCT
cana-1543	113	17	{	{	PUNCT
cana-1543	113	18	,	,	PUNCT
cana-1543	113	19	,	,	PUNCT
cana-1543	113	20	}	}	PUNCT
cana-1543	113	21	{	{	PUNCT
cana-1543	113	22	,	,	PUNCT
cana-1543	113	23	,	,	PUNCT
cana-1543	113	24	}	}	PUNCT
cana-1543	113	25	:	:	PUNCT
cana-1543	113	26	1v	1v	NUM
cana-1543	113	27	t	t	NOUN
cana-1543	113	28	v	v	NUM
cana-1543	113	29	u	u	PROPN
cana-1543	113	30	v	v	PROPN
cana-1543	113	31	w	w	NOUN
cana-1543	113	32	u	u	NOUN
cana-1543	113	33	v	v	NOUN
cana-1543	113	34	w	w	NOUN
cana-1543	113	35			NOUN
cana-1543	113	36			PUNCT
cana-1543	113	37			NOUN
cana-1543	113	38			NOUN
cana-1543	113	39			NOUN
cana-1543	113	40			SYM
cana-1543	113	41			NOUN
cana-1543	113	42	=	=	NUM
cana-1543	113	43			NUM
cana-1543	113	44			NOUN
cana-1543	113	45	and	and	CCONJ
cana-1543	113	46			PROPN
cana-1543	113	47			PROPN
cana-1543	113	48			PROPN
cana-1543	113	49			PROPN
cana-1543	113	50	'	'	PUNCT
cana-1543	113	51	'	'	PUNCT
cana-1543	113	52	'	'	PUNCT
cana-1543	113	53	'	'	PUNCT
cana-1543	113	54	'	'	PUNCT
cana-1543	113	55	'	'	PUNCT
cana-1543	113	56	'	'	PUNCT
cana-1543	113	57	'	'	PUNCT
cana-1543	113	58	'	'	PUNCT
cana-1543	113	59	'	'	PUNCT
cana-1543	113	60	'	'	PUNCT
cana-1543	113	61	'	'	PUNCT
cana-1543	113	62	(	(	PUNCT
cana-1543	113	63	(	(	PUNCT
cana-1543	113	64	)	)	PUNCT
cana-1543	113	65	)	)	PUNCT
cana-1543	113	66	;	;	PUNCT
cana-1543	113	67	;	;	PUNCT
cana-1543	113	68	;	;	PUNCT
cana-1543	113	69	;	;	PUNCT
cana-1543	113	70	;	;	PUNCT
cana-1543	113	71	;	;	PUNCT
cana-1543	113	72	;	;	PUNCT
cana-1543	113	73	;	;	PUNCT
cana-1543	113	74	;	;	PUNCT
cana-1543	113	75	;	;	PUNCT
cana-1543	113	76	:1	:1	PUNCT
cana-1543	113	77	:1	:1	PUNCT
cana-1543	113	78	1	1	NUM
cana-1543	113	79	,	,	PUNCT
cana-1543	113	80	1	1	NUM
cana-1543	113	81	e	e	NOUN
cana-1543	113	82	t	t	NOUN
cana-1543	113	83	vv	vv	ADP
cana-1543	113	84	v	v	ADP
cana-1543	113	85	v	v	NUM
cana-1543	113	86	v	v	NOUN
cana-1543	113	87	u	u	NOUN
cana-1543	113	88	u	u	NOUN
cana-1543	113	89	u	u	NOUN
cana-1543	113	90	u	u	PROPN
cana-1543	113	91	w	w	PROPN
cana-1543	113	92	w	w	PROPN
cana-1543	113	93	w	w	PROPN
cana-1543	113	94	w	w	PROPN
cana-1543	113	95	u	u	PROPN
cana-1543	113	96	u	u	NOUN
cana-1543	113	97	v	v	ADP
cana-1543	113	98	u	u	NOUN
cana-1543	113	99	v	v	INTJ
cana-1543	113	100	vv	vv	INTJ
cana-1543	113	101	w	w	PROPN
cana-1543	113	102	u	u	PROPN
cana-1543	113	103	v	v	ADP
cana-1543	113	104	v	v	NOUN
cana-1543	113	105			NUM
cana-1543	113	106			NOUN
cana-1543	113	107			VERB
cana-1543	113	108			NOUN
cana-1543	113	109			NOUN
cana-1543	113	110			NOUN
cana-1543	113	111			NOUN
cana-1543	113	112			NOUN
cana-1543	113	113			NOUN
cana-1543	113	114			NOUN
cana-1543	113	115			NOUN
cana-1543	113	116			NOUN
cana-1543	113	117			NOUN
cana-1543	113	118			NOUN
cana-1543	113	119			NOUN
cana-1543	113	120			NOUN
cana-1543	113	121			NOUN
cana-1543	113	122			NOUN
cana-1543	113	123			NOUN
cana-1543	113	124			NOUN
cana-1543	113	125			NOUN
cana-1543	113	126			NOUN
cana-1543	113	127			NOUN
cana-1543	113	128			X
cana-1543	113	129			NOUN
cana-1543	113	130			NUM
cana-1543	113	131			NOUN
cana-1543	113	132			NUM
cana-1543	113	133			NOUN
cana-1543	113	134			NUM
cana-1543	113	135			NUM
cana-1543	113	136	=	=	NOUN
cana-1543	113	137			NOUN
cana-1543	113	138			NOUN
cana-1543	113	139			NOUN
cana-1543	113	140			NOUN
cana-1543	113	141	−	−	NOUN
cana-1543	114	1	+	+	CCONJ
cana-1543	114	2			NOUN
cana-1543	114	3			NOUN
cana-1543	114	4	the	the	DET
cana-1543	114	5	vertices	vertex	NOUN
cana-1543	114	6	,	,	PUNCT
cana-1543	114	7	(	(	PUNCT
cana-1543	114	8	1	1	X
cana-1543	114	9	)	)	PUNCT
cana-1543	114	10	u	u	NOUN
cana-1543	114	11	u	u	NOUN
cana-1543	114	12			NOUN
cana-1543	114	13			PROPN
cana-1543	114	14			NOUN
cana-1543	114	15	induced	induce	VERB
cana-1543	114	16	a	a	DET
cana-1543	114	17	clique	clique	NOUN
cana-1543	114	18	of	of	ADP
cana-1543	114	19	order	order	NOUN
cana-1543	114	20	3	3	NUM
cana-1543	114	21	+	+	CCONJ
cana-1543	114	22	in	in	ADP
cana-1543	114	23	(	(	PUNCT
cana-1543	114	24	)	)	PUNCT
cana-1543	114	25	t	t	NOUN
cana-1543	114	26			NOUN
cana-1543	114	27	.	.	PUNCT
cana-1543	115	1	define	define	VERB
cana-1543	115	2			PROPN
cana-1543	115	3	,	,	PUNCT
cana-1543	115	4	such	such	ADJ
cana-1543	115	5	that	that	PRON
cana-1543	115	6	:	:	PUNCT
cana-1543	115	7	(	(	PUNCT
cana-1543	115	8	(	(	PUNCT
cana-1543	115	9	)	)	PUNCT
cana-1543	115	10	)	)	PUNCT
cana-1543	115	11	(	(	PUNCT
cana-1543	115	12	(	(	PUNCT
cana-1543	115	13	)	)	PUNCT
cana-1543	115	14	)	)	PUNCT
cana-1543	115	15	{	{	PUNCT
cana-1543	115	16	1,2,3	1,2,3	NUM
cana-1543	115	17	...	...	PUNCT
cana-1543	115	18	,	,	PUNCT
cana-1543	115	19	2	2	NUM
cana-1543	115	20	1}v	1}v	NUM
cana-1543	115	21	t	t	PROPN
cana-1543	115	22	e	e	X
cana-1543	115	23	t	t	PUNCT
cana-1543	115	24			NUM
cana-1543	115	25			X
cana-1543	115	26			X
cana-1543	115	27	→	→	X
cana-1543	116	1	+	+	X
cana-1543	116	2	.	.	PUNCT
cana-1543	116	3	fig	fig	NOUN
cana-1543	116	4	4	4	NUM
cana-1543	116	5	:	:	PUNCT
cana-1543	116	6	total	total	ADJ
cana-1543	116	7	coloring	coloring	NOUN
cana-1543	116	8	of	of	ADP
cana-1543	116	9	7	7	NUM
cana-1543	116	10	(	(	PUNCT
cana-1543	116	11	)	)	PUNCT
cana-1543	116	12	t	t	NOUN
cana-1543	116	13			NOUN
cana-1543	116	14	for	for	ADP
cana-1543	116	15	1	1	NUM
cana-1543	116	16			NOUN
cana-1543	116	17			PROPN
cana-1543	116	18			PROPN
cana-1543	116	19	(	(	PUNCT
cana-1543	116	20	)	)	PUNCT
cana-1543	116	21	2	2	NUM
cana-1543	116	22	1v	1v	PROPN
cana-1543	116	23	=	=	PUNCT
cana-1543	117	1	+	+	CCONJ
cana-1543	117	2	;	;	PUNCT
cana-1543	117	3	'	'	PUNCT
cana-1543	117	4	(	(	PUNCT
cana-1543	117	5	)	)	PUNCT
cana-1543	117	6	v	v	PROPN
cana-1543	117	7	=	=	NOUN
cana-1543	117	8	;	;	PUNCT
cana-1543	117	9	(	(	PUNCT
cana-1543	117	10	)	)	PUNCT
cana-1543	117	11	2	2	NUM
cana-1543	117	12	;	;	PUNCT
cana-1543	117	13	(	(	PUNCT
cana-1543	117	14	)	)	PUNCT
cana-1543	117	15	v	v	NOUN
cana-1543	117	16	u	u	NOUN
cana-1543	117	17			NOUN
cana-1543	117	18			NOUN
cana-1543	117	19			PROPN
cana-1543	117	20	=	=	NOUN
cana-1543	117	21	=	=	SYM
cana-1543	117	22	;	;	PUNCT
cana-1543	117	23	(	(	PUNCT
cana-1543	117	24	)	)	PUNCT
cana-1543	117	25	2	2	NUM
cana-1543	117	26	1w	1w	NUM
cana-1543	117	27	=	=	PUNCT
cana-1543	117	28	+	+	CCONJ
cana-1543	117	29	;	;	PUNCT
cana-1543	117	30	'	'	PUNCT
cana-1543	117	31	2	2	NUM
cana-1543	117	32	,	,	PUNCT
cana-1543	117	33	2	2	NUM
cana-1543	117	34	0	0	NUM
cana-1543	117	35	(	(	PUNCT
cana-1543	117	36	mod	mod	NOUN
cana-1543	117	37	2	2	NUM
cana-1543	117	38	)	)	PUNCT
cana-1543	117	39	(	(	PUNCT
cana-1543	117	40	)	)	PUNCT
cana-1543	117	41	2	2	NUM
cana-1543	117	42	,	,	PUNCT
cana-1543	117	43	if	if	SCONJ
cana-1543	117	44	u	u	PRON
cana-1543	117	45	otherwise	otherwise	ADV
cana-1543	117	46			VERB
cana-1543	117	47			ADP
cana-1543	117	48			X
cana-1543	117	49			X
cana-1543	117	50			PROPN
cana-1543	117	51			NUM
cana-1543	117	52	+	+	PUNCT
cana-1543	117	53	+	+	CCONJ
cana-1543	117	54			NOUN
cana-1543	117	55	+	+	NOUN
cana-1543	117	56			NOUN
cana-1543	117	57			NOUN
cana-1543	117	58	=	=	PUNCT
cana-1543	118	1			NUM
cana-1543	118	2	+	+	ADV
cana-1543	118	3			PROPN
cana-1543	118	4	;	;	PUNCT
cana-1543	118	5	'	'	PUNCT
cana-1543	118	6	1	1	NUM
cana-1543	118	7	,	,	PUNCT
cana-1543	118	8	1	1	NUM
cana-1543	118	9	0	0	NUM
cana-1543	118	10	(	(	PUNCT
cana-1543	118	11	mod	mod	NOUN
cana-1543	118	12	1	1	NUM
cana-1543	118	13	)	)	PUNCT
cana-1543	118	14	(	(	PUNCT
cana-1543	118	15	)	)	PUNCT
cana-1543	118	16	1	1	NUM
cana-1543	118	17	,	,	PUNCT
cana-1543	118	18	if	if	SCONJ
cana-1543	118	19	w	w	NOUN
cana-1543	118	20	otherwise	otherwise	ADV
cana-1543	118	21			CCONJ
cana-1543	118	22			ADP
cana-1543	118	23			X
cana-1543	118	24			X
cana-1543	118	25			PROPN
cana-1543	118	26			NUM
cana-1543	118	27	+	+	PUNCT
cana-1543	118	28	+	+	CCONJ
cana-1543	118	29			NOUN
cana-1543	118	30	+	+	NOUN
cana-1543	118	31			NOUN
cana-1543	118	32			NOUN
cana-1543	118	33	=	=	PUNCT
cana-1543	119	1			NUM
cana-1543	119	2	+	+	ADV
cana-1543	119	3			PROPN
cana-1543	119	4	;	;	PUNCT
cana-1543	119	5	'	'	PUNCT
cana-1543	119	6	2	2	NUM
cana-1543	119	7	,	,	PUNCT
cana-1543	119	8	2	2	NUM
cana-1543	119	9	0	0	NUM
cana-1543	119	10	(	(	PUNCT
cana-1543	119	11	mod	mod	NOUN
cana-1543	119	12	2	2	NUM
cana-1543	119	13	)	)	PUNCT
cana-1543	119	14	(	(	PUNCT
cana-1543	119	15	)	)	PUNCT
cana-1543	119	16	2	2	NUM
cana-1543	119	17	,	,	PUNCT
cana-1543	119	18	if	if	SCONJ
cana-1543	119	19	vv	vv	PRON
cana-1543	119	20	otherwise	otherwise	ADV
cana-1543	119	21			VERB
cana-1543	119	22			ADP
cana-1543	119	23			X
cana-1543	119	24			PUNCT
cana-1543	119	25			PROPN
cana-1543	119	26			NUM
cana-1543	119	27			PROPN
cana-1543	119	28			NOUN
cana-1543	119	29	=	=	PUNCT
cana-1543	119	30			NUM
cana-1543	119	31			INTJ
cana-1543	119	32	;	;	PUNCT
cana-1543	119	33	'	'	PUNCT
cana-1543	119	34	1	1	NUM
cana-1543	119	35	,	,	PUNCT
cana-1543	119	36	+1	+1	PROPN
cana-1543	120	1	+	+	CCONJ
cana-1543	120	2	0	0	NUM
cana-1543	120	3	(	(	PUNCT
cana-1543	120	4	mod	mod	PROPN
cana-1543	120	5	2	2	NUM
cana-1543	120	6	1	1	NUM
cana-1543	120	7	)	)	PUNCT
cana-1543	120	8	(	(	PUNCT
cana-1543	120	9	)	)	PUNCT
cana-1543	120	10	2	2	NUM
cana-1543	120	11	1	1	NUM
cana-1543	120	12	,	,	PUNCT
cana-1543	120	13	if	if	SCONJ
cana-1543	120	14	v	v	NOUN
cana-1543	120	15	v	v	NOUN
cana-1543	120	16	otherwise	otherwise	ADV
cana-1543	120	17			VERB
cana-1543	120	18			NOUN
cana-1543	120	19			NUM
cana-1543	120	20			NOUN
cana-1543	120	21			NUM
cana-1543	120	22			NOUN
cana-1543	120	23			NUM
cana-1543	120	24			PROPN
cana-1543	120	25			NUM
cana-1543	120	26	+	+	PUNCT
cana-1543	120	27	+	+	CCONJ
cana-1543	120	28			NOUN
cana-1543	120	29	+	+	NOUN
cana-1543	120	30			NOUN
cana-1543	120	31			NOUN
cana-1543	120	32	=	=	PUNCT
cana-1543	121	1			NUM
cana-1543	121	2	+	+	NOUN
cana-1543	121	3			NUM
cana-1543	121	4	'	'	PUNCT
cana-1543	121	5	'	'	PUNCT
cana-1543	121	6	,	,	PUNCT
cana-1543	121	7	(	(	PUNCT
cana-1543	121	8	)	)	PUNCT
cana-1543	121	9	0	0	NUM
cana-1543	121	10	(	(	PUNCT
cana-1543	121	11	mod	mod	NOUN
cana-1543	121	12	2	2	NUM
cana-1543	121	13	1	1	NUM
cana-1543	121	14	)	)	PUNCT
cana-1543	121	15	1	1	NUM
cana-1543	121	16	1	1	NUM
cana-1543	121	17	(	(	PUNCT
cana-1543	121	18	)	)	PUNCT
cana-1543	121	19	2	2	NUM
cana-1543	121	20	1	1	NUM
cana-1543	121	21	,	,	PUNCT
cana-1543	121	22	,	,	PUNCT
cana-1543	121	23	1	1	NUM
cana-1543	121	24	if	if	SCONJ
cana-1543	121	25	for	for	ADP
cana-1543	121	26	v	v	NUM
cana-1543	121	27	v	v	NOUN
cana-1543	121	28	otherwise	otherwise	ADV
cana-1543	121	29			NOUN
cana-1543	121	30			ADP
cana-1543	121	31			NOUN
cana-1543	121	32			NUM
cana-1543	121	33			NOUN
cana-1543	121	34			NUM
cana-1543	121	35			NUM
cana-1543	121	36			X
cana-1543	121	37			NUM
cana-1543	121	38			PROPN
cana-1543	121	39			NUM
cana-1543	121	40			NOUN
cana-1543	121	41			NOUN
cana-1543	121	42			X
cana-1543	121	43			NUM
cana-1543	121	44			NUM
cana-1543	122	1	+	+	PUNCT
cana-1543	122	2	+	+	CCONJ
cana-1543	122	3			PROPN
cana-1543	122	4	−	−	PROPN
cana-1543	122	5			NOUN
cana-1543	122	6			NOUN
cana-1543	122	7	−	−	NOUN
cana-1543	122	8			NOUN
cana-1543	122	9	=	=	PUNCT
cana-1543	123	1			NUM
cana-1543	123	2	−	−	ADP
cana-1543	123	3			VERB
cana-1543	123	4	+	+	CCONJ
cana-1543	123	5			NOUN
cana-1543	123	6			NOUN
cana-1543	123	7	;	;	PUNCT
cana-1543	123	8	communications	communication	NOUN
cana-1543	123	9	on	on	ADP
cana-1543	123	10	applied	apply	VERB
cana-1543	123	11	nonlinear	nonlinear	ADJ
cana-1543	123	12	analysis	analysis	NOUN
cana-1543	123	13	issn	issn	NOUN
cana-1543	123	14	:	:	PUNCT
cana-1543	123	15	1074	1074	NUM
cana-1543	123	16	-	-	PUNCT
cana-1543	123	17	133x	133x	NUM
cana-1543	123	18	vol	vol	NOUN
cana-1543	123	19	31	31	NUM
cana-1543	123	20	no	no	NOUN
cana-1543	123	21	.	.	PUNCT
cana-1543	124	1	8s	8s	PROPN
cana-1543	124	2	(	(	PUNCT
cana-1543	124	3	2024	2024	NUM
cana-1543	124	4	)	)	PUNCT
cana-1543	124	5	499	499	NUM
cana-1543	124	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1543	124	7	'	'	PART
cana-1543	124	8	3	3	NUM
cana-1543	124	9	,	,	PUNCT
cana-1543	124	10	+3	+3	PROPN
cana-1543	124	11	+	+	NUM
cana-1543	124	12	0	0	NUM
cana-1543	124	13	(	(	PUNCT
cana-1543	124	14	mod	mod	PROPN
cana-1543	124	15	2	2	NUM
cana-1543	124	16	1	1	NUM
cana-1543	124	17	)	)	PUNCT
cana-1543	124	18	(	(	PUNCT
cana-1543	124	19	)	)	PUNCT
cana-1543	124	20	2	2	NUM
cana-1543	124	21	1	1	NUM
cana-1543	124	22	,	,	PUNCT
cana-1543	124	23	if	if	SCONJ
cana-1543	124	24	v	v	NUM
cana-1543	124	25	u	u	NOUN
cana-1543	124	26	otherwise	otherwise	ADV
cana-1543	124	27			VERB
cana-1543	124	28			NOUN
cana-1543	124	29			NUM
cana-1543	124	30			NOUN
cana-1543	124	31			NUM
cana-1543	124	32			NOUN
cana-1543	124	33			NUM
cana-1543	124	34			PROPN
cana-1543	124	35			NUM
cana-1543	124	36	+	+	PUNCT
cana-1543	124	37	+	+	CCONJ
cana-1543	124	38			NOUN
cana-1543	124	39	+	+	NOUN
cana-1543	124	40			NOUN
cana-1543	124	41			NOUN
cana-1543	124	42	=	=	PUNCT
cana-1543	125	1			NUM
cana-1543	125	2	+	+	ADV
cana-1543	125	3			PROPN
cana-1543	125	4	;	;	PUNCT
cana-1543	125	5	'	'	PUNCT
cana-1543	125	6	1	1	NUM
cana-1543	125	7	,	,	PUNCT
cana-1543	125	8	1	1	NUM
cana-1543	125	9	0	0	NUM
cana-1543	125	10	(	(	PUNCT
cana-1543	125	11	mod	mod	NOUN
cana-1543	125	12	1	1	NUM
cana-1543	125	13	)	)	PUNCT
cana-1543	125	14	(	(	PUNCT
cana-1543	125	15	)	)	PUNCT
cana-1543	125	16	1	1	NUM
cana-1543	125	17	,	,	PUNCT
cana-1543	125	18	if	if	SCONJ
cana-1543	125	19	u	u	NOUN
cana-1543	125	20	u	u	NOUN
cana-1543	125	21	otherwise	otherwise	ADV
cana-1543	125	22			VERB
cana-1543	125	23			ADP
cana-1543	125	24			ADP
cana-1543	125	25			X
cana-1543	125	26			X
cana-1543	125	27			PROPN
cana-1543	125	28			NUM
cana-1543	125	29	+	+	PUNCT
cana-1543	125	30	+	+	CCONJ
cana-1543	125	31			NOUN
cana-1543	125	32	+	+	NOUN
cana-1543	125	33			NOUN
cana-1543	125	34			NOUN
cana-1543	125	35	=	=	PUNCT
cana-1543	126	1			NUM
cana-1543	126	2	+	+	NOUN
cana-1543	126	3			PROPN
cana-1543	126	4	'	'	PUNCT
cana-1543	126	5	(	(	PUNCT
cana-1543	126	6	)	)	PUNCT
cana-1543	126	7	2	2	NUM
cana-1543	126	8	1u	1u	NUM
cana-1543	126	9	w	w	NOUN
cana-1543	126	10			NOUN
cana-1543	126	11	=	=	PUNCT
cana-1543	126	12	+	+	CCONJ
cana-1543	126	13	;	;	PUNCT
cana-1543	126	14	'	'	PUNCT
cana-1543	126	15	(	(	PUNCT
cana-1543	126	16	)	)	PUNCT
cana-1543	126	17	1w	1w	NUM
cana-1543	126	18	w	w	NUM
cana-1543	126	19			NOUN
cana-1543	126	20	=	=	SYM
cana-1543	126	21	;	;	PUNCT
cana-1543	126	22	2	2	NUM
cana-1543	126	23	1	1	NUM
cana-1543	126	24	,	,	PUNCT
cana-1543	126	25	2	2	NUM
cana-1543	126	26	1	1	NUM
cana-1543	126	27	0mod(2	0mod(2	NUM
cana-1543	126	28	1	1	NUM
cana-1543	126	29	)	)	PUNCT
cana-1543	126	30	(	(	PUNCT
cana-1543	126	31	)	)	PUNCT
cana-1543	126	32	2	2	NUM
cana-1543	126	33	1	1	NUM
cana-1543	126	34	,	,	PUNCT
cana-1543	126	35	if	if	SCONJ
cana-1543	126	36	vv	vv	PRON
cana-1543	126	37	otherwise	otherwise	ADV
cana-1543	126	38			VERB
cana-1543	126	39			ADP
cana-1543	126	40			X
cana-1543	126	41			PUNCT
cana-1543	126	42			ADJ
cana-1543	126	43			NUM
cana-1543	126	44	−	−	PROPN
cana-1543	126	45	−	−	PROPN
cana-1543	126	46			NOUN
cana-1543	126	47	−	−	NOUN
cana-1543	126	48			NOUN
cana-1543	126	49	=	=	PUNCT
cana-1543	127	1			NUM
cana-1543	127	2	−	−	VERB
cana-1543	127	3	;	;	PUNCT
cana-1543	127	4	'	'	PUNCT
cana-1543	127	5	'	'	NUM
cana-1543	127	6	2	2	NUM
cana-1543	127	7	,	,	PUNCT
cana-1543	127	8	2	2	NUM
cana-1543	127	9	0	0	NUM
cana-1543	127	10	mod(2	mod(2	NOUN
cana-1543	127	11	1	1	NUM
cana-1543	127	12	)	)	PUNCT
cana-1543	127	13	(	(	PUNCT
cana-1543	127	14	)	)	PUNCT
cana-1543	127	15	(	(	PUNCT
cana-1543	127	16	)	)	PUNCT
cana-1543	127	17	2	2	NUM
cana-1543	127	18	1	1	NUM
cana-1543	127	19	,	,	PUNCT
cana-1543	127	20	if	if	SCONJ
cana-1543	127	21	u	u	PRON
cana-1543	127	22	v	v	VERB
cana-1543	127	23	u	u	PRON
cana-1543	127	24	v	v	ADP
cana-1543	127	25	otherwise	otherwise	ADV
cana-1543	127	26			VERB
cana-1543	127	27			ADP
cana-1543	127	28			ADP
cana-1543	127	29			NOUN
cana-1543	127	30			NUM
cana-1543	127	31			NOUN
cana-1543	127	32			NUM
cana-1543	127	33			NOUN
cana-1543	127	34			NUM
cana-1543	127	35			ADJ
cana-1543	127	36			ADJ
cana-1543	127	37			NUM
cana-1543	127	38	+	+	CCONJ
cana-1543	127	39	+	+	PUNCT
cana-1543	127	40	+	+	PUNCT
cana-1543	127	41	+	+	CCONJ
cana-1543	127	42			NOUN
cana-1543	127	43	+	+	NOUN
cana-1543	127	44			NOUN
cana-1543	127	45			NOUN
cana-1543	128	1	=	=	PUNCT
cana-1543	129	1	=	=	PUNCT
cana-1543	130	1			NUM
cana-1543	130	2	+	+	NOUN
cana-1543	130	3			PROPN
cana-1543	130	4	;	;	PUNCT
cana-1543	130	5	'	'	PUNCT
cana-1543	130	6	'	'	PUNCT
cana-1543	130	7	(	(	PUNCT
cana-1543	130	8	)	)	PUNCT
cana-1543	130	9	2w	2w	NUM
cana-1543	130	10	u	u	NOUN
cana-1543	130	11			NOUN
cana-1543	130	12	=	=	X
cana-1543	130	13	+	+	CCONJ
cana-1543	130	14	;	;	PUNCT
cana-1543	130	15	(	(	PUNCT
cana-1543	130	16	)	)	PUNCT
cana-1543	130	17	2w	2w	NUM
cana-1543	130	18	u	u	NOUN
cana-1543	130	19			NOUN
cana-1543	130	20	=	=	NOUN
cana-1543	130	21	+	+	SYM
cana-1543	130	22	by	by	ADP
cana-1543	130	23	this	this	DET
cana-1543	130	24	procedure	procedure	NOUN
cana-1543	130	25	,	,	PUNCT
cana-1543	130	26	the	the	DET
cana-1543	130	27	graph	graph	NOUN
cana-1543	130	28	(	(	PUNCT
cana-1543	130	29	)	)	PUNCT
cana-1543	130	30	t	t	NOUN
cana-1543	130	31			NOUN
cana-1543	130	32	is	be	AUX
cana-1543	130	33	attained	attain	VERB
cana-1543	130	34	with	with	ADP
cana-1543	130	35	2	2	NUM
cana-1543	130	36	1	1	NUM
cana-1543	130	37	+	+	CCONJ
cana-1543	130	38	total	total	ADJ
cana-1543	130	39	colorable	colorable	ADJ
cana-1543	130	40	.	.	PUNCT
cana-1543	131	1	so	so	ADV
cana-1543	131	2	,	,	PUNCT
cana-1543	131	3	it	it	PRON
cana-1543	131	4	is	be	AUX
cana-1543	131	5	clear	clear	ADJ
cana-1543	131	6	that	that	SCONJ
cana-1543	131	7	''	''	PUNCT
cana-1543	131	8	(	(	PUNCT
cana-1543	131	9	(	(	PUNCT
cana-1543	131	10	)	)	PUNCT
cana-1543	131	11	)	)	PUNCT
cana-1543	131	12	2	2	NUM
cana-1543	131	13	1.t	1.t	NUM
cana-1543	131	14			NOUN
cana-1543	131	15			NOUN
cana-1543	131	16			PROPN
cana-1543	131	17	+	+	CCONJ
cana-1543	131	18	since	since	SCONJ
cana-1543	131	19	(	(	PUNCT
cana-1543	131	20	(	(	PUNCT
cana-1543	131	21	)	)	PUNCT
cana-1543	131	22	)	)	PUNCT
cana-1543	131	23	t	t	NOUN
cana-1543	131	24			NOUN
cana-1543	131	25			PROPN
cana-1543	131	26	=	=	PROPN
cana-1543	131	27	and	and	CCONJ
cana-1543	131	28	by	by	ADP
cana-1543	131	29	lemma	lemma	PROPN
cana-1543	131	30	2.7	2.7	NUM
cana-1543	131	31	,	,	PUNCT
cana-1543	131	32	it	it	PRON
cana-1543	131	33	follows	follow	VERB
cana-1543	131	34	that	that	SCONJ
cana-1543	131	35	''	''	PUNCT
cana-1543	131	36	(	(	PUNCT
cana-1543	131	37	(	(	PUNCT
cana-1543	131	38	)	)	PUNCT
cana-1543	131	39	)	)	PUNCT
cana-1543	132	1	(	(	PUNCT
cana-1543	132	2	(	(	PUNCT
cana-1543	132	3	)	)	PUNCT
cana-1543	132	4	)	)	PUNCT
cana-1543	132	5	1	1	NUM
cana-1543	132	6	t	t	NOUN
cana-1543	132	7	t	t	ADJ
cana-1543	132	8			PROPN
cana-1543	132	9			X
cana-1543	132	10			PROPN
cana-1543	132	11			PUNCT
cana-1543	133	1	+	+	CCONJ
cana-1543	133	2	3.	3.	NUM
cana-1543	133	3	+	+	CCONJ
cana-1543	133	4	therefore	therefore	ADV
cana-1543	133	5	''	''	PUNCT
cana-1543	133	6	(	(	PUNCT
cana-1543	133	7	(	(	PUNCT
cana-1543	133	8	)	)	PUNCT
cana-1543	133	9	)	)	PUNCT
cana-1543	134	1	2	2	NUM
cana-1543	134	2	1.t	1.t	NUM
cana-1543	134	3			NOUN
cana-1543	134	4			NOUN
cana-1543	135	1	=	=	X
cana-1543	135	2	+	+	CCONJ
cana-1543	135	3	equivalently	equivalently	ADV
cana-1543	135	4	,	,	PUNCT
cana-1543	135	5	this	this	PRON
cana-1543	135	6	is	be	AUX
cana-1543	135	7	true	true	ADJ
cana-1543	135	8	for	for	ADP
cana-1543	135	9	all	all	DET
cana-1543	135	10	other	other	ADJ
cana-1543	135	11	values	value	NOUN
cana-1543	135	12	of	of	ADP
cana-1543	135	13	4.	4.	NOUN
cana-1543	135	14			NUM
cana-1543	135	15	hence	hence	ADV
cana-1543	135	16	''	''	PUNCT
cana-1543	135	17	(	(	PUNCT
cana-1543	135	18	(	(	PUNCT
cana-1543	135	19	)	)	PUNCT
cana-1543	135	20	)	)	PUNCT
cana-1543	135	21	2	2	NUM
cana-1543	135	22	1.t	1.t	NUM
cana-1543	135	23			NOUN
cana-1543	135	24			NOUN
cana-1543	136	1	=	=	X
cana-1543	136	2	+	+	CCONJ
cana-1543	136	3	theorem	theorem	VERB
cana-1543	136	4	3.5	3.5	NUM
cana-1543	136	5	:	:	PUNCT
cana-1543	136	6	for	for	ADP
cana-1543	136	7	any	any	DET
cana-1543	136	8	4	4	NUM
cana-1543	136	9			NUM
cana-1543	136	10	,	,	PUNCT
cana-1543	136	11	''	''	PUNCT
cana-1543	136	12	(	(	PUNCT
cana-1543	136	13	(	(	PUNCT
cana-1543	136	14	)	)	PUNCT
cana-1543	136	15	)	)	PUNCT
cana-1543	136	16	2	2	NUM
cana-1543	136	17	1.s	1.s	NUM
cana-1543	136	18			NOUN
cana-1543	136	19			NOUN
cana-1543	137	1	=	=	NOUN
cana-1543	137	2	+	+	NUM
cana-1543	137	3	proof	proof	NOUN
cana-1543	137	4	:	:	PUNCT
cana-1543	137	5	let	let	VERB
cana-1543	137	6			PRON
cana-1543	137	7			VERB
cana-1543	137	8	'	'	PUNCT
cana-1543	137	9	'	'	PUNCT
cana-1543	137	10	'	'	PUNCT
cana-1543	137	11	(	(	PUNCT
cana-1543	137	12	(	(	PUNCT
cana-1543	137	13	)	)	PUNCT
cana-1543	137	14	)	)	PUNCT
cana-1543	137	15	{	{	PUNCT
cana-1543	137	16	}	}	PUNCT
cana-1543	137	17	{	{	PUNCT
cana-1543	137	18	,	,	PUNCT
cana-1543	137	19	,	,	PUNCT
cana-1543	137	20	}	}	PUNCT
cana-1543	137	21	{	{	PUNCT
cana-1543	137	22	,	,	PUNCT
cana-1543	137	23	,	,	PUNCT
cana-1543	137	24	}	}	PUNCT
cana-1543	137	25	:	:	PUNCT
cana-1543	137	26	1v	1v	NUM
cana-1543	137	27	s	s	NOUN
cana-1543	137	28	v	v	NUM
cana-1543	137	29	u	u	NOUN
cana-1543	137	30	v	v	NOUN
cana-1543	137	31	w	w	NOUN
cana-1543	137	32	u	u	NOUN
cana-1543	137	33	v	v	NOUN
cana-1543	137	34	w	w	NOUN
cana-1543	137	35			NOUN
cana-1543	137	36			PUNCT
cana-1543	137	37			NOUN
cana-1543	137	38			NOUN
cana-1543	137	39			NOUN
cana-1543	137	40			SYM
cana-1543	137	41			NOUN
cana-1543	137	42	=	=	NUM
cana-1543	137	43			NUM
cana-1543	137	44			NOUN
cana-1543	137	45	and	and	CCONJ
cana-1543	137	46			PROPN
cana-1543	137	47			PROPN
cana-1543	137	48	'	'	PUNCT
cana-1543	137	49	'	'	PUNCT
cana-1543	137	50	'	'	PUNCT
cana-1543	137	51	'	'	PUNCT
cana-1543	137	52	'	'	PUNCT
cana-1543	137	53	'	'	PUNCT
cana-1543	137	54	(	(	PUNCT
cana-1543	137	55	(	(	PUNCT
cana-1543	137	56	)	)	PUNCT
cana-1543	137	57	)	)	PUNCT
cana-1543	137	58	;	;	PUNCT
cana-1543	137	59	;	;	PUNCT
cana-1543	137	60	;	;	PUNCT
cana-1543	137	61	;	;	PUNCT
cana-1543	137	62	;	;	PUNCT
cana-1543	137	63	;	;	PUNCT
cana-1543	137	64	;	;	PUNCT
cana-1543	137	65	;	;	PUNCT
cana-1543	137	66	:	:	PUNCT
cana-1543	137	67	1e	1e	PROPN
cana-1543	137	68	s	s	VERB
cana-1543	137	69	uu	uu	VERB
cana-1543	137	70	u	u	NOUN
cana-1543	137	71	u	u	NOUN
cana-1543	137	72	uu	uu	ADP
cana-1543	137	73	u	u	NOUN
cana-1543	137	74	v	v	ADP
cana-1543	137	75	u	u	NOUN
cana-1543	137	76	v	v	ADP
cana-1543	137	77	u	u	NOUN
cana-1543	137	78	v	v	ADP
cana-1543	137	79	v	v	NOUN
cana-1543	137	80	w	w	NOUN
cana-1543	137	81	v	v	PROPN
cana-1543	137	82	w	w	PROPN
cana-1543	137	83	v	v	NOUN
cana-1543	137	84	w	w	NOUN
cana-1543	137	85			NOUN
cana-1543	137	86			PUNCT
cana-1543	137	87			NOUN
cana-1543	137	88			NOUN
cana-1543	137	89			NOUN
cana-1543	137	90			NOUN
cana-1543	137	91			NOUN
cana-1543	137	92			NOUN
cana-1543	137	93			NOUN
cana-1543	137	94			NOUN
cana-1543	137	95			NOUN
cana-1543	137	96			NOUN
cana-1543	137	97			NOUN
cana-1543	137	98			NOUN
cana-1543	137	99			SYM
cana-1543	137	100			NOUN
cana-1543	137	101	=	=	PUNCT
cana-1543	137	102			NOUN
cana-1543	137	103			NOUN
cana-1543	137	104	define	define	VERB
cana-1543	137	105			PROPN
cana-1543	137	106	,	,	PUNCT
cana-1543	137	107	such	such	ADJ
cana-1543	137	108	that	that	PRON
cana-1543	137	109	:	:	PUNCT
cana-1543	137	110	(	(	PUNCT
cana-1543	137	111	(	(	PUNCT
cana-1543	137	112	)	)	PUNCT
cana-1543	137	113	)	)	PUNCT
cana-1543	137	114	(	(	PUNCT
cana-1543	137	115	(	(	PUNCT
cana-1543	137	116	)	)	PUNCT
cana-1543	137	117	)	)	PUNCT
cana-1543	137	118	{	{	PUNCT
cana-1543	137	119	1,2,3	1,2,3	NUM
cana-1543	137	120	...	...	SYM
cana-1543	137	121	2	2	NUM
cana-1543	137	122	1}v	1}v	NUM
cana-1543	137	123	s	s	PART
cana-1543	137	124	e	e	X
cana-1543	137	125	s	s	X
cana-1543	137	126			PUNCT
cana-1543	137	127			X
cana-1543	137	128			X
cana-1543	137	129	→	→	X
cana-1543	137	130	+	+	X
cana-1543	137	131	.	.	PUNCT
cana-1543	138	1	'	'	PUNCT
cana-1543	138	2	(	(	PUNCT
cana-1543	138	3	)	)	PUNCT
cana-1543	138	4	(	(	PUNCT
cana-1543	138	5	)	)	PUNCT
cana-1543	138	6	2	2	NUM
cana-1543	138	7	1u	1u	NUM
cana-1543	138	8	u	u	SYM
cana-1543	138	9			PROPN
cana-1543	138	10	=	=	PUNCT
cana-1543	138	11	=	=	SYM
cana-1543	139	1	+	+	CCONJ
cana-1543	139	2	;	;	PUNCT
cana-1543	139	3	'	'	PUNCT
cana-1543	139	4	1	1	NUM
cana-1543	139	5	,	,	PUNCT
cana-1543	139	6	(	(	PUNCT
cana-1543	139	7	1	1	NUM
cana-1543	139	8	)	)	PUNCT
cana-1543	139	9	0	0	NUM
cana-1543	140	1	(	(	PUNCT
cana-1543	140	2	mod	mod	NOUN
cana-1543	140	3	1	1	NUM
cana-1543	140	4	)	)	PUNCT
cana-1543	140	5	(	(	PUNCT
cana-1543	140	6	)	)	PUNCT
cana-1543	140	7	(	(	PUNCT
cana-1543	140	8	)	)	PUNCT
cana-1543	140	9	1	1	NUM
cana-1543	140	10	,	,	PUNCT
cana-1543	140	11	if	if	SCONJ
cana-1543	140	12	u	u	NOUN
cana-1543	140	13	u	u	NOUN
cana-1543	140	14	otherwise	otherwise	ADV
cana-1543	140	15			VERB
cana-1543	140	16			ADP
cana-1543	140	17			ADP
cana-1543	140	18			NOUN
cana-1543	140	19			NUM
cana-1543	140	20			ADJ
cana-1543	140	21			ADJ
cana-1543	140	22			NUM
cana-1543	140	23	+	+	PUNCT
cana-1543	140	24	+	+	CCONJ
cana-1543	140	25			NOUN
cana-1543	140	26	+	+	NOUN
cana-1543	140	27			NOUN
cana-1543	140	28			NOUN
cana-1543	140	29	=	=	PUNCT
cana-1543	141	1	=	=	PUNCT
cana-1543	142	1			NUM
cana-1543	142	2	+	+	NOUN
cana-1543	142	3			INTJ
cana-1543	142	4	;	;	PUNCT
cana-1543	142	5	'	'	PUNCT
cana-1543	142	6	(	(	PUNCT
cana-1543	142	7	)	)	PUNCT
cana-1543	142	8	(	(	PUNCT
cana-1543	142	9	)	)	PUNCT
cana-1543	142	10	2v	2v	PROPN
cana-1543	142	11	v	v	PUNCT
cana-1543	142	12			NOUN
cana-1543	142	13			ADJ
cana-1543	142	14	=	=	PUNCT
cana-1543	142	15	=	=	SYM
cana-1543	142	16	+	+	CCONJ
cana-1543	142	17	;	;	PUNCT
cana-1543	142	18	'	'	PUNCT
cana-1543	142	19	(	(	PUNCT
cana-1543	142	20	)	)	PUNCT
cana-1543	142	21	(	(	PUNCT
cana-1543	142	22	)	)	PUNCT
cana-1543	142	23	3w	3w	NUM
cana-1543	142	24	w	w	NOUN
cana-1543	142	25			NOUN
cana-1543	142	26			ADJ
cana-1543	142	27	=	=	PUNCT
cana-1543	142	28	=	=	SYM
cana-1543	142	29	+	+	CCONJ
cana-1543	142	30	,	,	PUNCT
cana-1543	142	31	0	0	NUM
cana-1543	142	32	(	(	PUNCT
cana-1543	142	33	mod	mod	NOUN
cana-1543	142	34	2	2	NUM
cana-1543	142	35	)	)	PUNCT
cana-1543	142	36	(	(	PUNCT
cana-1543	142	37	)	)	PUNCT
cana-1543	142	38	2	2	NUM
cana-1543	142	39	,	,	PUNCT
cana-1543	142	40	if	if	SCONJ
cana-1543	142	41	uu	uu	VERB
cana-1543	142	42	otherwise	otherwise	ADV
cana-1543	142	43			NOUN
cana-1543	142	44			NUM
cana-1543	142	45			NOUN
cana-1543	142	46			NUM
cana-1543	142	47			NOUN
cana-1543	142	48			NUM
cana-1543	142	49			PROPN
cana-1543	142	50			NUM
cana-1543	142	51	+	+	CCONJ
cana-1543	142	52	+	+	CCONJ
cana-1543	142	53			PRON
cana-1543	142	54			NOUN
cana-1543	142	55	=	=	PUNCT
cana-1543	142	56			NUM
cana-1543	142	57			INTJ
cana-1543	142	58	;	;	PUNCT
cana-1543	142	59	'	'	PUNCT
cana-1543	142	60	'	'	PUNCT
cana-1543	142	61	,	,	PUNCT
cana-1543	142	62	0	0	NUM
cana-1543	142	63	(	(	PUNCT
cana-1543	142	64	mod	mod	PROPN
cana-1543	142	65	)	)	PUNCT
cana-1543	142	66	(	(	PUNCT
cana-1543	142	67	)	)	PUNCT
cana-1543	142	68	(	(	PUNCT
cana-1543	142	69	)	)	PUNCT
cana-1543	142	70	,	,	PUNCT
cana-1543	142	71	if	if	SCONJ
cana-1543	142	72	uu	uu	PUNCT
cana-1543	142	73	u	u	NOUN
cana-1543	142	74	u	u	NOUN
cana-1543	142	75	otherwise	otherwise	ADV
cana-1543	142	76			VERB
cana-1543	142	77			ADP
cana-1543	142	78			ADP
cana-1543	142	79			NOUN
cana-1543	142	80			NUM
cana-1543	142	81			ADJ
cana-1543	142	82			PROPN
cana-1543	142	83			NUM
cana-1543	142	84			PROPN
cana-1543	142	85			X
cana-1543	142	86	=	=	PUNCT
cana-1543	143	1	=	=	SYM
cana-1543	143	2			NUM
cana-1543	143	3			INTJ
cana-1543	143	4	;	;	PUNCT
cana-1543	143	5	2	2	NUM
cana-1543	143	6	,	,	PUNCT
cana-1543	143	7	1	1	NUM
cana-1543	143	8	1	1	NUM
cana-1543	143	9	(	(	PUNCT
cana-1543	143	10	)	)	PUNCT
cana-1543	143	11	2	2	NUM
cana-1543	143	12	,	,	PUNCT
cana-1543	143	13	if	if	SCONJ
cana-1543	143	14	u	u	NOUN
cana-1543	143	15	v	v	X
cana-1543	143	16			PUNCT
cana-1543	143	17			NUM
cana-1543	143	18			NOUN
cana-1543	143	19			NUM
cana-1543	143	20			ADJ
cana-1543	143	21			NUM
cana-1543	143	22			NOUN
cana-1543	143	23			NUM
cana-1543	143	24			NOUN
cana-1543	143	25			NOUN
cana-1543	143	26	−	−	NOUN
cana-1543	143	27	=	=	PUNCT
cana-1543	143	28			NUM
cana-1543	143	29	−	−	NOUN
cana-1543	144	1	=	=	NOUN
cana-1543	144	2			X
cana-1543	144	3	;	;	PUNCT
cana-1543	144	4	(	(	PUNCT
cana-1543	144	5	)	)	PUNCT
cana-1543	144	6	v	v	NOUN
cana-1543	144	7	w	w	NOUN
cana-1543	144	8			NOUN
cana-1543	144	9	=	=	NOUN
cana-1543	144	10	;	;	PUNCT
cana-1543	144	11	'	'	PUNCT
cana-1543	144	12	'	'	PUNCT
cana-1543	144	13	(	(	PUNCT
cana-1543	144	14	)	)	PUNCT
cana-1543	144	15	(	(	PUNCT
cana-1543	144	16	)	)	PUNCT
cana-1543	144	17	2	2	NUM
cana-1543	144	18	1u	1u	NUM
cana-1543	144	19	v	v	ADP
cana-1543	144	20	u	u	NOUN
cana-1543	144	21	v	v	DET
cana-1543	144	22			NOUN
cana-1543	144	23			VERB
cana-1543	144	24			NOUN
cana-1543	144	25			ADJ
cana-1543	144	26	=	=	PUNCT
cana-1543	144	27	=	=	SYM
cana-1543	145	1	+	+	CCONJ
cana-1543	145	2	;	;	PUNCT
cana-1543	145	3	'	'	PUNCT
cana-1543	145	4	(	(	PUNCT
cana-1543	145	5	)	)	PUNCT
cana-1543	145	6	1v	1v	NUM
cana-1543	145	7	w	w	NOUN
cana-1543	145	8			NOUN
cana-1543	145	9	=	=	SYM
cana-1543	145	10	;	;	PUNCT
cana-1543	145	11	'	'	PUNCT
cana-1543	145	12	(	(	PUNCT
cana-1543	145	13	)	)	PUNCT
cana-1543	145	14	2v	2v	PROPN
cana-1543	145	15	w	w	NUM
cana-1543	145	16			NOUN
cana-1543	145	17	=	=	SYM
cana-1543	145	18	communications	communication	NOUN
cana-1543	145	19	on	on	ADP
cana-1543	145	20	applied	apply	VERB
cana-1543	145	21	nonlinear	nonlinear	ADJ
cana-1543	145	22	analysis	analysis	NOUN
cana-1543	145	23	issn	issn	NOUN
cana-1543	145	24	:	:	PUNCT
cana-1543	145	25	1074	1074	NUM
cana-1543	145	26	-	-	PUNCT
cana-1543	145	27	133x	133x	NUM
cana-1543	145	28	vol	vol	NOUN
cana-1543	145	29	31	31	NUM
cana-1543	145	30	no	no	NOUN
cana-1543	145	31	.	.	PUNCT
cana-1543	146	1	8s	8s	PROPN
cana-1543	146	2	(	(	PUNCT
cana-1543	146	3	2024	2024	NUM
cana-1543	146	4	)	)	PUNCT
cana-1543	146	5	500	500	NUM
cana-1543	146	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1543	146	7	fig	fig	NOUN
cana-1543	146	8	5	5	NUM
cana-1543	146	9	:	:	PUNCT
cana-1543	146	10	total	total	ADJ
cana-1543	146	11	coloring	coloring	NOUN
cana-1543	146	12	of	of	ADP
cana-1543	146	13	7	7	NUM
cana-1543	146	14	(	(	PUNCT
cana-1543	146	15	)	)	PUNCT
cana-1543	146	16	s	s	PART
cana-1543	146	17			X
cana-1543	146	18	based	base	VERB
cana-1543	146	19	on	on	ADP
cana-1543	146	20	the	the	DET
cana-1543	146	21	above	above	ADJ
cana-1543	146	22	procedure	procedure	NOUN
cana-1543	146	23	,	,	PUNCT
cana-1543	146	24	the	the	DET
cana-1543	146	25	graph	graph	NOUN
cana-1543	146	26	(	(	PUNCT
cana-1543	146	27	)	)	PUNCT
cana-1543	146	28	s	s	PART
cana-1543	146	29			NOUN
cana-1543	146	30	is	be	AUX
cana-1543	146	31	attained	attain	VERB
cana-1543	146	32	with	with	ADP
cana-1543	146	33	2	2	NUM
cana-1543	146	34	1	1	NUM
cana-1543	146	35	+	+	CCONJ
cana-1543	146	36	total	total	ADJ
cana-1543	146	37	colorable	colorable	ADJ
cana-1543	146	38	.	.	PUNCT
cana-1543	147	1	so	so	ADV
cana-1543	147	2	,	,	PUNCT
cana-1543	147	3	it	it	PRON
cana-1543	147	4	is	be	AUX
cana-1543	147	5	clear	clear	ADJ
cana-1543	147	6	that	that	SCONJ
cana-1543	147	7	''	''	PUNCT
cana-1543	147	8	(	(	PUNCT
cana-1543	147	9	(	(	PUNCT
cana-1543	147	10	)	)	PUNCT
cana-1543	147	11	)	)	PUNCT
cana-1543	147	12	2	2	NUM
cana-1543	147	13	1.s	1.s	NUM
cana-1543	147	14			NOUN
cana-1543	147	15			X
cana-1543	148	1			PROPN
cana-1543	148	2	+	+	CCONJ
cana-1543	148	3	since	since	SCONJ
cana-1543	148	4	(	(	PUNCT
cana-1543	148	5	(	(	PUNCT
cana-1543	148	6	)	)	PUNCT
cana-1543	148	7	)	)	PUNCT
cana-1543	148	8	s	s	PART
cana-1543	148	9			NOUN
cana-1543	148	10			NOUN
cana-1543	148	11	=	=	PROPN
cana-1543	148	12	and	and	CCONJ
cana-1543	148	13	by	by	ADP
cana-1543	148	14	lemma	lemma	PROPN
cana-1543	148	15	2.7	2.7	NUM
cana-1543	148	16	,	,	PUNCT
cana-1543	148	17	it	it	PRON
cana-1543	148	18	follows	follow	VERB
cana-1543	148	19	that	that	SCONJ
cana-1543	148	20	''	''	PUNCT
cana-1543	148	21	(	(	PUNCT
cana-1543	148	22	(	(	PUNCT
cana-1543	148	23	)	)	PUNCT
cana-1543	148	24	)	)	PUNCT
cana-1543	149	1	(	(	PUNCT
cana-1543	149	2	(	(	PUNCT
cana-1543	149	3	)	)	PUNCT
cana-1543	149	4	)	)	PUNCT
cana-1543	149	5	1s	1	NOUN
cana-1543	149	6	s	s	X
cana-1543	150	1			PROPN
cana-1543	150	2			PROPN
cana-1543	150	3			PROPN
cana-1543	150	4			PUNCT
cana-1543	151	1	+	+	CCONJ
cana-1543	151	2	3.	3.	NUM
cana-1543	151	3	+	+	CCONJ
cana-1543	151	4	therefore	therefore	ADV
cana-1543	151	5	''	''	PUNCT
cana-1543	151	6	(	(	PUNCT
cana-1543	151	7	(	(	PUNCT
cana-1543	151	8	)	)	PUNCT
cana-1543	151	9	)	)	PUNCT
cana-1543	152	1	2	2	NUM
cana-1543	152	2	1.s	1.s	NUM
cana-1543	152	3			NOUN
cana-1543	152	4			NOUN
cana-1543	153	1	=	=	X
cana-1543	153	2	+	+	CCONJ
cana-1543	153	3	similarly	similarly	ADV
cana-1543	153	4	,	,	PUNCT
cana-1543	153	5	this	this	DET
cana-1543	153	6	result	result	NOUN
cana-1543	153	7	is	be	AUX
cana-1543	153	8	true	true	ADJ
cana-1543	153	9	for	for	ADP
cana-1543	153	10	all	all	DET
cana-1543	153	11	values	value	NOUN
cana-1543	153	12	of	of	ADP
cana-1543	153	13	4.	4.	NOUN
cana-1543	153	14			NUM
cana-1543	153	15	hence	hence	ADV
cana-1543	153	16	''	''	PUNCT
cana-1543	153	17	(	(	PUNCT
cana-1543	153	18	(	(	PUNCT
cana-1543	153	19	)	)	PUNCT
cana-1543	153	20	)	)	PUNCT
cana-1543	153	21	2	2	NUM
cana-1543	153	22	1.s	1.s	NUM
cana-1543	153	23			NOUN
cana-1543	153	24			NOUN
cana-1543	154	1	=	=	X
cana-1543	154	2	+	+	CCONJ
cana-1543	154	3	theorem	theorem	VERB
cana-1543	154	4	3.6	3.6	NUM
cana-1543	154	5	:	:	PUNCT
cana-1543	154	6	let	let	VERB
cana-1543	154	7	(	(	PUNCT
cana-1543	154	8	2,1)l	2,1)l	NUM
cana-1543	154	9			X
cana-1543	154	10	=	=	PUNCT
cana-1543	154	11	be	be	AUX
cana-1543	154	12	the	the	DET
cana-1543	154	13	lobster	lobster	NOUN
cana-1543	154	14	,	,	PUNCT
cana-1543	154	15	then	then	ADV
cana-1543	154	16	''	''	PUNCT
cana-1543	154	17	(	(	PUNCT
cana-1543	154	18	)	)	PUNCT
cana-1543	154	19	5.t	5.t	NUM
cana-1543	154	20			NUM
cana-1543	154	21	=	=	PUNCT
cana-1543	154	22	proof	proof	NOUN
cana-1543	154	23	:	:	PUNCT
cana-1543	154	24	let	let	VERB
cana-1543	154	25	'	'	PUNCT
cana-1543	154	26	'	'	PUNCT
cana-1543	154	27	(	(	PUNCT
cana-1543	154	28	)	)	PUNCT
cana-1543	154	29	{	{	PUNCT
cana-1543	154	30	,	,	PUNCT
cana-1543	154	31	,	,	PUNCT
cana-1543	154	32	,	,	PUNCT
cana-1543	154	33	,	,	PUNCT
cana-1543	154	34	:1	:1	PUNCT
cana-1543	154	35	}	}	PUNCT
cana-1543	154	36	v	v	NOUN
cana-1543	154	37	v	v	NUM
cana-1543	154	38	u	u	PROPN
cana-1543	154	39	w	w	PROPN
cana-1543	154	40	w	w	PROPN
cana-1543	154	41	u	u	ADJ
cana-1543	154	42			NOUN
cana-1543	154	43			NOUN
cana-1543	154	44			NOUN
cana-1543	154	45			NOUN
cana-1543	154	46			X
cana-1543	154	47			VERB
cana-1543	154	48	=	=	NUM
cana-1543	154	49			NUM
cana-1543	154	50			NOUN
cana-1543	154	51	and	and	CCONJ
cana-1543	154	52	'	'	PUNCT
cana-1543	154	53	'	'	PUNCT
cana-1543	154	54	(	(	PUNCT
cana-1543	154	55	)	)	PUNCT
cana-1543	154	56	{	{	PUNCT
cana-1543	154	57	,	,	PUNCT
cana-1543	154	58	,	,	PUNCT
cana-1543	154	59	,	,	PUNCT
cana-1543	154	60	:1	:1	PUNCT
cana-1543	154	61	}	}	PUNCT
cana-1543	154	62	e	e	X
cana-1543	154	63	v	v	NUM
cana-1543	154	64	u	u	X
cana-1543	154	65	u	u	NOUN
cana-1543	154	66	u	u	NOUN
cana-1543	154	67	v	v	PROPN
cana-1543	154	68	w	w	PROPN
cana-1543	154	69	w	w	PROPN
cana-1543	154	70	w	w	X
cana-1543	154	71			NOUN
cana-1543	154	72			PUNCT
cana-1543	154	73			NOUN
cana-1543	154	74			NOUN
cana-1543	154	75			NOUN
cana-1543	154	76			NOUN
cana-1543	154	77			NOUN
cana-1543	154	78			X
cana-1543	154	79			VERB
cana-1543	154	80	=	=	NUM
cana-1543	154	81			NUM
cana-1543	154	82			NOUN
cana-1543	154	83	1	1	NUM
cana-1543	154	84	{	{	PUNCT
cana-1543	154	85	:1	:1	PUNCT
cana-1543	154	86	1}v	1}v	NUM
cana-1543	154	87	v	v	CCONJ
cana-1543	154	88			NOUN
cana-1543	154	89			PUNCT
cana-1543	154	90	+	+	ADJ
cana-1543	154	91			NOUN
cana-1543	154	92			NOUN
cana-1543	154	93	−	−	ADP
cana-1543	154	94	define	define	VERB
cana-1543	154	95	:	:	PUNCT
cana-1543	154	96	(	(	PUNCT
cana-1543	154	97	)	)	PUNCT
cana-1543	154	98	(	(	PUNCT
cana-1543	154	99	)	)	PUNCT
cana-1543	154	100	{	{	PUNCT
cana-1543	154	101	1,2,3,4,5}v	1,2,3,4,5}v	NOUN
cana-1543	154	102	e	e	NOUN
cana-1543	155	1			NUM
cana-1543	155	2			NUM
cana-1543	155	3			NUM
cana-1543	155	4	→	→	PUNCT
cana-1543	155	5	as	as	SCONJ
cana-1543	155	6	follows	follow	VERB
cana-1543	155	7	.	.	PUNCT
cana-1543	156	1	the	the	DET
cana-1543	156	2	assigning	assigning	NOUN
cana-1543	156	3	of	of	ADP
cana-1543	156	4	colors	color	NOUN
cana-1543	156	5	is	be	AUX
cana-1543	156	6	given	give	VERB
cana-1543	156	7	below	below	ADV
cana-1543	156	8	:	:	PUNCT
cana-1543	156	9	for	for	ADP
cana-1543	156	10	1	1	NUM
cana-1543	156	11			NOUN
cana-1543	156	12			PROPN
cana-1543	156	13			PROPN
cana-1543	156	14	(	(	PUNCT
cana-1543	156	15	)	)	PUNCT
cana-1543	156	16	(	(	PUNCT
cana-1543	156	17	)	)	PUNCT
cana-1543	156	18	2,1	2,1	NUM
cana-1543	156	19	;	;	PUNCT
cana-1543	156	20	1,0	1,0	NUM
cana-1543	156	21	(	(	PUNCT
cana-1543	156	22	mod	mod	PROPN
cana-1543	156	23	2)u	2)u	NUM
cana-1543	156	24	v	v	NOUN
cana-1543	156	25	w	w	NOUN
cana-1543	156	26	if	if	DET
cana-1543	156	27			NOUN
cana-1543	156	28			NOUN
cana-1543	156	29			PROPN
cana-1543	156	30	=	=	NOUN
cana-1543	156	31	=	=	SYM
cana-1543	156	32			PROPN
cana-1543	156	33	;	;	PUNCT
cana-1543	156	34	(	(	PUNCT
cana-1543	156	35	)	)	PUNCT
cana-1543	156	36	1	1	NUM
cana-1543	156	37	,	,	PUNCT
cana-1543	156	38	2	2	NUM
cana-1543	156	39	;	;	PUNCT
cana-1543	156	40	1,0	1,0	NUM
cana-1543	156	41	(	(	PUNCT
cana-1543	156	42	mod	mod	PROPN
cana-1543	156	43	2)v	2)v	NUM
cana-1543	156	44	if	if	PROPN
cana-1543	156	45	=	=	NOUN
cana-1543	157	1			PROPN
cana-1543	157	2	;	;	PUNCT
cana-1543	157	3	(	(	PUNCT
cana-1543	157	4	)	)	PUNCT
cana-1543	157	5	3,4	3,4	NUM
cana-1543	157	6	;	;	PUNCT
cana-1543	157	7	1,0	1,0	NUM
cana-1543	157	8	(	(	PUNCT
cana-1543	157	9	mod	mod	PROPN
cana-1543	157	10	2)w	2)w	NUM
cana-1543	157	11	if	if	PROPN
cana-1543	157	12	=	=	NOUN
cana-1543	157	13			PROPN
cana-1543	157	14	;	;	PUNCT
cana-1543	157	15	(	(	PUNCT
cana-1543	157	16	)	)	PUNCT
cana-1543	157	17	5v	5v	NOUN
cana-1543	157	18	u	u	NOUN
cana-1543	157	19			NOUN
cana-1543	157	20	=	=	X
cana-1543	157	21	;	;	PUNCT
cana-1543	157	22	'	'	PUNCT
cana-1543	157	23	(	(	PUNCT
cana-1543	157	24	)	)	PUNCT
cana-1543	157	25	5w	5w	PROPN
cana-1543	157	26	w	w	NOUN
cana-1543	157	27			NOUN
cana-1543	157	28	=	=	SYM
cana-1543	157	29	;	;	PUNCT
cana-1543	157	30	'	'	PUNCT
cana-1543	157	31	(	(	PUNCT
cana-1543	157	32	)	)	PUNCT
cana-1543	157	33	3u	3u	NOUN
cana-1543	157	34	=	=	NOUN
cana-1543	157	35	;	;	PUNCT
cana-1543	157	36	'	'	PUNCT
cana-1543	157	37	(	(	PUNCT
cana-1543	157	38	)	)	PUNCT
cana-1543	157	39	2w	2w	NUM
cana-1543	157	40	=	=	SYM
cana-1543	157	41	;	;	PUNCT
cana-1543	157	42	'	'	PUNCT
cana-1543	157	43	(	(	PUNCT
cana-1543	157	44	)	)	PUNCT
cana-1543	157	45	4u	4u	NOUN
cana-1543	157	46	u	u	NOUN
cana-1543	157	47			NOUN
cana-1543	157	48	=	=	PUNCT
cana-1543	157	49	for	for	ADP
cana-1543	157	50	1	1	NUM
cana-1543	157	51	1	1	PROPN
cana-1543	157	52			PROPN
cana-1543	157	53			NOUN
cana-1543	157	54	−	−	NOUN
cana-1543	157	55	1	1	NUM
cana-1543	157	56	(	(	PUNCT
cana-1543	157	57	)	)	PUNCT
cana-1543	157	58	3,4	3,4	NUM
cana-1543	157	59	;	;	PUNCT
cana-1543	157	60	1,0	1,0	NUM
cana-1543	157	61	(	(	PUNCT
cana-1543	157	62	mod	mod	PROPN
cana-1543	157	63	2)v	2)v	NUM
cana-1543	157	64	v	v	NOUN
cana-1543	157	65	if	if	NOUN
cana-1543	157	66			NOUN
cana-1543	157	67	+	+	PUNCT
cana-1543	157	68	=	=	SYM
cana-1543	157	69			VERB
cana-1543	157	70	communications	communication	NOUN
cana-1543	157	71	on	on	ADP
cana-1543	157	72	applied	apply	VERB
cana-1543	157	73	nonlinear	nonlinear	ADJ
cana-1543	157	74	analysis	analysis	NOUN
cana-1543	157	75	issn	issn	NOUN
cana-1543	157	76	:	:	PUNCT
cana-1543	157	77	1074	1074	NUM
cana-1543	157	78	-	-	PUNCT
cana-1543	157	79	133x	133x	NUM
cana-1543	157	80	vol	vol	NOUN
cana-1543	157	81	31	31	NUM
cana-1543	157	82	no	no	NOUN
cana-1543	157	83	.	.	PUNCT
cana-1543	158	1	8s	8s	PROPN
cana-1543	158	2	(	(	PUNCT
cana-1543	158	3	2024	2024	NUM
cana-1543	158	4	)	)	PUNCT
cana-1543	158	5	501	501	NUM
cana-1543	158	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1543	158	7	fig	fig	NOUN
cana-1543	158	8	6	6	NUM
cana-1543	158	9	:	:	PUNCT
cana-1543	158	10	total	total	ADJ
cana-1543	158	11	coloring	coloring	NOUN
cana-1543	158	12	of	of	ADP
cana-1543	158	13	lobster	lobster	NOUN
cana-1543	158	14	graph	graph	NOUN
cana-1543	158	15	5	5	NUM
cana-1543	158	16	based	base	VERB
cana-1543	158	17	on	on	ADP
cana-1543	158	18	the	the	DET
cana-1543	158	19	above	above	ADJ
cana-1543	158	20	coloring	coloring	NOUN
cana-1543	158	21	approach	approach	NOUN
cana-1543	158	22	,	,	PUNCT
cana-1543	158	23	the	the	DET
cana-1543	158	24	graph	graph	NOUN
cana-1543	158	25			NOUN
cana-1543	158	26	is	be	AUX
cana-1543	158	27	total	total	NOUN
cana-1543	158	28	colored	color	VERB
cana-1543	158	29	with	with	ADP
cana-1543	158	30	5	5	NUM
cana-1543	158	31	colors	color	NOUN
cana-1543	158	32	.	.	PUNCT
cana-1543	159	1	thus	thus	ADV
cana-1543	159	2	''	''	PUNCT
cana-1543	159	3	(	(	PUNCT
cana-1543	159	4	)	)	PUNCT
cana-1543	159	5	5.	5.	NUM
cana-1543	159	6			NUM
cana-1543	159	7			NOUN
cana-1543	159	8	since	since	SCONJ
cana-1543	159	9	(	(	PUNCT
cana-1543	159	10	)	)	PUNCT
cana-1543	159	11	4	4	NUM
cana-1543	159	12	=	=	PUNCT
cana-1543	159	13	and	and	CCONJ
cana-1543	159	14	by	by	ADP
cana-1543	159	15	lemma	lemma	PROPN
cana-1543	159	16	2.7	2.7	NUM
cana-1543	159	17	,	,	PUNCT
cana-1543	159	18	''	''	PUNCT
cana-1543	159	19	(	(	PUNCT
cana-1543	159	20	)	)	PUNCT
cana-1543	159	21	(	(	PUNCT
cana-1543	159	22	)	)	PUNCT
cana-1543	159	23	1	1	NUM
cana-1543	159	24	4	4	NUM
cana-1543	159	25	1	1	NUM
cana-1543	159	26	5	5	NUM
cana-1543	159	27			NOUN
cana-1543	159	28			NUM
cana-1543	159	29			PROPN
cana-1543	159	30			PUNCT
cana-1543	160	1	+	+	PUNCT
cana-1543	160	2	=	=	SYM
cana-1543	161	1	+	+	NUM
cana-1543	161	2			NUM
cana-1543	161	3	and	and	CCONJ
cana-1543	161	4	hence	hence	ADV
cana-1543	161	5	''	''	PUNCT
cana-1543	161	6	(	(	PUNCT
cana-1543	161	7	)	)	PUNCT
cana-1543	161	8	5.	5.	NUM
cana-1543	161	9			NUM
cana-1543	161	10	=	=	PUNCT
cana-1543	161	11	theorem	theorem	VERB
cana-1543	161	12	3.7	3.7	NUM
cana-1543	161	13	:	:	PUNCT
cana-1543	161	14	let	let	VERB
cana-1543	161	15	(	(	PUNCT
cana-1543	161	16	)	)	PUNCT
cana-1543	161	17	l	l	NOUN
cana-1543	161	18			NOUN
cana-1543	161	19	be	be	AUX
cana-1543	161	20	the	the	DET
cana-1543	161	21	line	line	NOUN
cana-1543	161	22	graph	graph	NOUN
cana-1543	161	23	of	of	ADP
cana-1543	161	24	lobster	lobster	NOUN
cana-1543	161	25	graph	graph	NOUN
cana-1543	161	26	,	,	PUNCT
cana-1543	161	27	then	then	ADV
cana-1543	161	28	''	''	PUNCT
cana-1543	161	29	(	(	PUNCT
cana-1543	161	30	(	(	PUNCT
cana-1543	161	31	)	)	PUNCT
cana-1543	161	32	)	)	PUNCT
cana-1543	162	1	5.l	5.l	NUM
cana-1543	162	2			X
cana-1543	162	3			NUM
cana-1543	162	4	=	=	PUNCT
cana-1543	162	5	proof	proof	NOUN
cana-1543	162	6	:	:	PUNCT
cana-1543	162	7	let	let	VERB
cana-1543	162	8	'	'	PUNCT
cana-1543	162	9	'	'	PUNCT
cana-1543	162	10	(	(	PUNCT
cana-1543	162	11	(	(	PUNCT
cana-1543	162	12	)	)	PUNCT
cana-1543	162	13	)	)	PUNCT
cana-1543	162	14	{	{	PUNCT
cana-1543	162	15	,	,	PUNCT
cana-1543	162	16	,	,	PUNCT
cana-1543	162	17	,	,	PUNCT
cana-1543	162	18	:1	:1	PUNCT
cana-1543	162	19	}	}	PUNCT
cana-1543	162	20	{	{	PUNCT
cana-1543	162	21	:1	:1	PUNCT
cana-1543	162	22	1}v	1}v	NUM
cana-1543	162	23	l	l	X
cana-1543	162	24	u	u	PROPN
cana-1543	162	25	w	w	PROPN
cana-1543	162	26	w	w	PROPN
cana-1543	162	27	u	u	NOUN
cana-1543	162	28	v	v	ADP
cana-1543	162	29			NOUN
cana-1543	162	30			PUNCT
cana-1543	162	31			NOUN
cana-1543	162	32			X
cana-1543	162	33			X
cana-1543	162	34			VERB
cana-1543	162	35			NUM
cana-1543	162	36			NOUN
cana-1543	162	37	=	=	PUNCT
cana-1543	162	38			NOUN
cana-1543	162	39			NOUN
cana-1543	162	40			NOUN
cana-1543	162	41			NOUN
cana-1543	162	42	−	−	PROPN
cana-1543	162	43	and	and	CCONJ
cana-1543	162	44	'	'	PUNCT
cana-1543	162	45	'	'	PUNCT
cana-1543	162	46	(	(	PUNCT
cana-1543	162	47	(	(	PUNCT
cana-1543	162	48	)	)	PUNCT
cana-1543	162	49	)	)	PUNCT
cana-1543	162	50	{	{	PUNCT
cana-1543	162	51	,	,	PUNCT
cana-1543	162	52	,	,	PUNCT
cana-1543	162	53	:1	:1	PUNCT
cana-1543	162	54	}	}	PUNCT
cana-1543	162	55	e	e	X
cana-1543	162	56	l	l	NOUN
cana-1543	162	57	u	u	PROPN
cana-1543	162	58	w	w	PROPN
cana-1543	162	59	u	u	X
cana-1543	162	60	u	u	PROPN
cana-1543	162	61	w	w	NOUN
cana-1543	162	62	w	w	X
cana-1543	162	63			NOUN
cana-1543	162	64			PUNCT
cana-1543	162	65			NOUN
cana-1543	162	66			NOUN
cana-1543	162	67			NOUN
cana-1543	162	68			X
cana-1543	162	69			VERB
cana-1543	162	70	=	=	NUM
cana-1543	162	71			NOUN
cana-1543	162	72			NOUN
cana-1543	162	73	1	1	NUM
cana-1543	162	74	1	1	NUM
cana-1543	162	75	{	{	PUNCT
cana-1543	162	76	,	,	PUNCT
cana-1543	162	77	,	,	PUNCT
cana-1543	162	78	,	,	PUNCT
cana-1543	162	79	:1	:1	PUNCT
cana-1543	162	80	1}.v	1}.v	NUM
cana-1543	162	81	u	u	NOUN
cana-1543	162	82	u	u	NOUN
cana-1543	162	83	v	v	ADP
cana-1543	162	84	w	w	PROPN
cana-1543	162	85	v	v	ADP
cana-1543	162	86	v	v	NOUN
cana-1543	162	87	w	w	NOUN
cana-1543	162	88			NOUN
cana-1543	162	89			NOUN
cana-1543	162	90			NOUN
cana-1543	162	91			NOUN
cana-1543	162	92			NOUN
cana-1543	162	93			NOUN
cana-1543	162	94			NOUN
cana-1543	162	95			PUNCT
cana-1543	162	96	+	+	ADJ
cana-1543	162	97	+	+	NUM
cana-1543	162	98			NOUN
cana-1543	162	99			NOUN
cana-1543	162	100	−	−	NOUN
cana-1543	162	101	define	define	VERB
cana-1543	162	102	:	:	PUNCT
cana-1543	162	103	(	(	PUNCT
cana-1543	162	104	(	(	PUNCT
cana-1543	162	105	)	)	PUNCT
cana-1543	162	106	)	)	PUNCT
cana-1543	162	107	(	(	PUNCT
cana-1543	162	108	(	(	PUNCT
cana-1543	162	109	)	)	PUNCT
cana-1543	162	110	)	)	PUNCT
cana-1543	163	1	{	{	PUNCT
cana-1543	163	2	1,2,3,4,5}v	1,2,3,4,5}v	PROPN
cana-1543	163	3	l	l	NOUN
cana-1543	163	4	e	e	X
cana-1543	163	5	l	l	X
cana-1543	163	6			NUM
cana-1543	163	7			NUM
cana-1543	163	8			NUM
cana-1543	163	9	→	→	PUNCT
cana-1543	163	10	as	as	SCONJ
cana-1543	163	11	follows	follow	VERB
cana-1543	163	12	.	.	PUNCT
cana-1543	164	1	the	the	DET
cana-1543	164	2	assigning	assigning	NOUN
cana-1543	164	3	of	of	ADP
cana-1543	164	4	colors	color	NOUN
cana-1543	164	5	is	be	AUX
cana-1543	164	6	given	give	VERB
cana-1543	164	7	below	below	ADV
cana-1543	164	8	:	:	PUNCT
cana-1543	164	9	fig	fig	NOUN
cana-1543	164	10	7	7	NUM
cana-1543	164	11	:	:	PUNCT
cana-1543	164	12	total	total	ADJ
cana-1543	164	13	coloring	coloring	NOUN
cana-1543	164	14	of	of	ADP
cana-1543	164	15	5	5	NUM
cana-1543	164	16	(	(	PUNCT
cana-1543	164	17	)	)	PUNCT
cana-1543	164	18	l	l	NOUN
cana-1543	164	19			NUM
cana-1543	164	20	for	for	ADP
cana-1543	164	21	1	1	NUM
cana-1543	164	22			NOUN
cana-1543	164	23			PROPN
cana-1543	164	24			PROPN
cana-1543	164	25	(	(	PUNCT
cana-1543	164	26	)	)	PUNCT
cana-1543	164	27	1	1	NUM
cana-1543	164	28	,	,	PUNCT
cana-1543	164	29	2	2	NUM
cana-1543	164	30	;	;	PUNCT
cana-1543	164	31	1,0	1,0	NUM
cana-1543	164	32	(	(	PUNCT
cana-1543	164	33	mod	mod	PROPN
cana-1543	164	34	2)u	2)u	PROPN
cana-1543	164	35	if	if	NOUN
cana-1543	164	36	=	=	NOUN
cana-1543	165	1			PROPN
cana-1543	165	2	;	;	PUNCT
cana-1543	165	3	'	'	PUNCT
cana-1543	165	4	(	(	PUNCT
cana-1543	165	5	)	)	PUNCT
cana-1543	165	6	2,1	2,1	NUM
cana-1543	165	7	;	;	PUNCT
cana-1543	165	8	1,0	1,0	NUM
cana-1543	165	9	(	(	PUNCT
cana-1543	165	10	mod	mod	PROPN
cana-1543	165	11	2)u	2)u	NUM
cana-1543	165	12	u	u	NOUN
cana-1543	165	13	if	if	NOUN
cana-1543	165	14			NOUN
cana-1543	165	15	=	=	ADJ
cana-1543	165	16			PROPN
cana-1543	165	17	;	;	PUNCT
cana-1543	165	18	(	(	PUNCT
cana-1543	165	19	)	)	PUNCT
cana-1543	165	20	3w	3w	NUM
cana-1543	165	21	=	=	NOUN
cana-1543	165	22	;	;	PUNCT
cana-1543	165	23	'	'	PUNCT
cana-1543	165	24	(	(	PUNCT
cana-1543	165	25	)	)	PUNCT
cana-1543	165	26	3u	3u	NOUN
cana-1543	165	27	=	=	NOUN
cana-1543	165	28	;	;	PUNCT
cana-1543	165	29	'	'	PUNCT
cana-1543	165	30	(	(	PUNCT
cana-1543	165	31	)	)	PUNCT
cana-1543	166	1	5w	5w	NUM
cana-1543	166	2	=	=	SYM
cana-1543	166	3	;	;	PUNCT
cana-1543	166	4	'	'	PUNCT
cana-1543	166	5	(	(	PUNCT
cana-1543	166	6	)	)	PUNCT
cana-1543	166	7	4w	4w	X
cana-1543	166	8	w	w	NOUN
cana-1543	166	9			NOUN
cana-1543	166	10	=	=	PUNCT
cana-1543	166	11	for	for	ADP
cana-1543	166	12	1	1	NUM
cana-1543	166	13	1	1	PROPN
cana-1543	166	14			PROPN
cana-1543	166	15			NOUN
cana-1543	166	16	−	−	PROPN
cana-1543	166	17	(	(	PUNCT
cana-1543	166	18	)	)	PUNCT
cana-1543	166	19	5v	5v	NUM
cana-1543	166	20	=	=	SYM
cana-1543	166	21	;	;	PUNCT
cana-1543	166	22	(	(	PUNCT
cana-1543	166	23	)	)	PUNCT
cana-1543	166	24	3u	3u	NUM
cana-1543	166	25	v	v	PUNCT
cana-1543	166	26			NOUN
cana-1543	166	27	=	=	X
cana-1543	166	28	;	;	PUNCT
cana-1543	166	29	1	1	NUM
cana-1543	166	30	(	(	PUNCT
cana-1543	166	31	)	)	PUNCT
cana-1543	166	32	4v	4v	NUM
cana-1543	166	33	u	u	NOUN
cana-1543	166	34			NOUN
cana-1543	166	35	+	+	X
cana-1543	166	36	=	=	SYM
cana-1543	166	37	;	;	PUNCT
cana-1543	166	38	(	(	PUNCT
cana-1543	166	39	)	)	PUNCT
cana-1543	166	40	1w	1w	NUM
cana-1543	166	41	v	v	PUNCT
cana-1543	166	42			NOUN
cana-1543	166	43	=	=	X
cana-1543	166	44	;	;	PUNCT
cana-1543	166	45	1	1	NUM
cana-1543	166	46	(	(	PUNCT
cana-1543	166	47	)	)	PUNCT
cana-1543	166	48	2v	2v	PROPN
cana-1543	166	49	w	w	NUM
cana-1543	166	50			NOUN
cana-1543	166	51	+	+	X
cana-1543	166	52	=	=	SYM
cana-1543	166	53	hence	hence	ADV
cana-1543	166	54			ADJ
cana-1543	166	55	is	be	AUX
cana-1543	166	56	a	a	DET
cana-1543	166	57	total	total	ADJ
cana-1543	166	58	coloring	coloring	NOUN
cana-1543	166	59	of	of	ADP
cana-1543	166	60	(	(	PUNCT
cana-1543	166	61	)	)	PUNCT
cana-1543	166	62	l	l	NOUN
cana-1543	166	63			NOUN
cana-1543	166	64	and	and	CCONJ
cana-1543	166	65	therefore	therefore	ADV
cana-1543	166	66	''	''	PUNCT
cana-1543	166	67	(	(	PUNCT
cana-1543	166	68	(	(	PUNCT
cana-1543	166	69	)	)	PUNCT
cana-1543	166	70	)	)	PUNCT
cana-1543	167	1	5l	5l	NUM
cana-1543	167	2			PROPN
cana-1543	167	3			NUM
cana-1543	167	4			NOUN
cana-1543	167	5	.	.	PUNCT
cana-1543	168	1	since	since	SCONJ
cana-1543	168	2	(	(	PUNCT
cana-1543	168	3	(	(	PUNCT
cana-1543	168	4	)	)	PUNCT
cana-1543	168	5	)	)	PUNCT
cana-1543	168	6	l	l	NOUN
cana-1543	168	7			X
cana-1543	168	8			NOUN
cana-1543	168	9	=	=	NOUN
cana-1543	168	10	and	and	CCONJ
cana-1543	168	11	by	by	ADP
cana-1543	168	12	lemma	lemma	PROPN
cana-1543	168	13	2.7	2.7	NUM
cana-1543	168	14	,	,	PUNCT
cana-1543	168	15	''	''	PUNCT
cana-1543	168	16	(	(	PUNCT
cana-1543	168	17	(	(	PUNCT
cana-1543	168	18	)	)	PUNCT
cana-1543	168	19	)	)	PUNCT
cana-1543	168	20	(	(	PUNCT
cana-1543	168	21	(	(	PUNCT
cana-1543	168	22	)	)	PUNCT
cana-1543	168	23	)	)	PUNCT
cana-1543	168	24	1	1	NUM
cana-1543	168	25	4	4	NUM
cana-1543	168	26	1	1	NUM
cana-1543	168	27	5l	5l	NUM
cana-1543	168	28	l	l	NUM
cana-1543	168	29			PROPN
cana-1543	168	30			NUM
cana-1543	168	31			PROPN
cana-1543	168	32			PUNCT
cana-1543	169	1	+	+	PUNCT
cana-1543	169	2	=	=	SYM
cana-1543	170	1	+	+	NUM
cana-1543	170	2			NUM
cana-1543	170	3	and	and	CCONJ
cana-1543	170	4	''	''	PUNCT
cana-1543	170	5	(	(	PUNCT
cana-1543	170	6	(	(	PUNCT
cana-1543	170	7	)	)	PUNCT
cana-1543	170	8	)	)	PUNCT
cana-1543	171	1	5.l	5.l	NUM
cana-1543	171	2			NOUN
cana-1543	171	3			NUM
cana-1543	171	4	=	=	PUNCT
cana-1543	171	5	theorem	theorem	VERB
cana-1543	171	6	3.8	3.8	NUM
cana-1543	171	7	:	:	PUNCT
cana-1543	171	8	let	let	VERB
cana-1543	171	9	(	(	PUNCT
cana-1543	171	10	)	)	PUNCT
cana-1543	171	11	m	m	VERB
cana-1543	171	12			VERB
cana-1543	171	13	be	be	AUX
cana-1543	171	14	the	the	DET
cana-1543	171	15	middle	middle	ADJ
cana-1543	171	16	graph	graph	NOUN
cana-1543	171	17	of	of	ADP
cana-1543	171	18	lobster	lobster	NOUN
cana-1543	171	19	graph	graph	NOUN
cana-1543	171	20	,	,	PUNCT
cana-1543	171	21	then	then	ADV
cana-1543	171	22	''	''	PUNCT
cana-1543	171	23	(	(	PUNCT
cana-1543	171	24	(	(	PUNCT
cana-1543	171	25	)	)	PUNCT
cana-1543	171	26	)	)	PUNCT
cana-1543	171	27	9.m	9.m	NUM
cana-1543	171	28			X
cana-1543	171	29			NUM
cana-1543	172	1	=	=	PUNCT
cana-1543	172	2	proof	proof	NOUN
cana-1543	172	3	:	:	PUNCT
cana-1543	172	4	let	let	VERB
cana-1543	172	5	'	'	PUNCT
cana-1543	172	6	''	''	PUNCT
cana-1543	172	7	'	'	PUNCT
cana-1543	172	8	''	''	PUNCT
cana-1543	172	9	'	'	PUNCT
cana-1543	172	10	''	''	PUNCT
cana-1543	172	11	'	'	PUNCT
cana-1543	172	12	''	''	PUNCT
cana-1543	172	13	(	(	PUNCT
cana-1543	172	14	(	(	PUNCT
cana-1543	172	15	)	)	PUNCT
cana-1543	172	16	)	)	PUNCT
cana-1543	172	17	{	{	PUNCT
cana-1543	172	18	,	,	PUNCT
cana-1543	172	19	,	,	PUNCT
cana-1543	172	20	,	,	PUNCT
cana-1543	172	21	,	,	PUNCT
cana-1543	172	22	,	,	PUNCT
cana-1543	172	23	,	,	PUNCT
cana-1543	172	24	,	,	PUNCT
cana-1543	172	25	,	,	PUNCT
cana-1543	172	26	:1	:1	PUNCT
cana-1543	172	27	}	}	PUNCT
cana-1543	172	28	{	{	PUNCT
cana-1543	172	29	:1	:1	PUNCT
cana-1543	172	30	1}v	1}v	NUM
cana-1543	172	31	m	m	PROPN
cana-1543	172	32	v	v	ADP
cana-1543	172	33	u	u	X
cana-1543	172	34	u	u	NOUN
cana-1543	172	35	u	u	NOUN
cana-1543	172	36	u	u	PROPN
cana-1543	172	37	w	w	PROPN
cana-1543	172	38	w	w	PROPN
cana-1543	172	39	w	w	PROPN
cana-1543	172	40	w	w	PROPN
cana-1543	172	41	x	x	PUNCT
cana-1543	173	1			NOUN
cana-1543	173	2			SYM
cana-1543	173	3			NOUN
cana-1543	173	4			NOUN
cana-1543	173	5			NOUN
cana-1543	173	6			NOUN
cana-1543	173	7			NOUN
cana-1543	173	8			NOUN
cana-1543	173	9			NOUN
cana-1543	173	10			X
cana-1543	173	11			VERB
cana-1543	173	12			NUM
cana-1543	173	13			NOUN
cana-1543	173	14	=	=	PUNCT
cana-1543	173	15			NOUN
cana-1543	173	16			NOUN
cana-1543	173	17			NOUN
cana-1543	173	18			NOUN
cana-1543	173	19	−	−	PROPN
cana-1543	173	20	and	and	CCONJ
cana-1543	173	21	'	'	PUNCT
cana-1543	173	22	'	'	PUNCT
cana-1543	173	23	''	''	PUNCT
cana-1543	173	24	''	''	PUNCT
cana-1543	174	1	'	'	PUNCT
cana-1543	174	2	''	''	PUNCT
cana-1543	174	3	'	'	PUNCT
cana-1543	174	4	'	'	PUNCT
cana-1543	174	5	''	''	PUNCT
cana-1543	174	6	''	''	PUNCT
cana-1543	174	7	'	'	PUNCT
cana-1543	174	8	''	''	PUNCT
cana-1543	174	9	''	''	PUNCT
cana-1543	175	1	''	''	PUNCT
cana-1543	175	2	(	(	PUNCT
cana-1543	175	3	(	(	PUNCT
cana-1543	175	4	)	)	PUNCT
cana-1543	175	5	)	)	PUNCT
cana-1543	175	6	{	{	PUNCT
cana-1543	175	7	,	,	PUNCT
cana-1543	175	8	,	,	PUNCT
cana-1543	175	9	,	,	PUNCT
cana-1543	175	10	,	,	PUNCT
cana-1543	175	11	,	,	PUNCT
cana-1543	175	12	,	,	PUNCT
cana-1543	175	13	,	,	PUNCT
cana-1543	175	14	,	,	PUNCT
cana-1543	175	15	,	,	PUNCT
cana-1543	175	16	,	,	PUNCT
cana-1543	175	17	:1	:1	PUNCT
cana-1543	175	18	}	}	PUNCT
cana-1543	175	19	e	e	X
cana-1543	175	20	m	m	NOUN
cana-1543	175	21	v	v	ADP
cana-1543	175	22	u	u	X
cana-1543	175	23	u	u	NOUN
cana-1543	175	24	u	u	NOUN
cana-1543	175	25	u	u	NOUN
cana-1543	175	26	u	u	NOUN
cana-1543	175	27	u	u	NOUN
cana-1543	175	28	u	u	NOUN
cana-1543	175	29	v	v	PROPN
cana-1543	175	30	w	w	PROPN
cana-1543	175	31	w	w	PROPN
cana-1543	175	32	w	w	PROPN
cana-1543	175	33	w	w	PROPN
cana-1543	175	34	w	w	PROPN
cana-1543	175	35	w	w	PROPN
cana-1543	175	36	w	w	PROPN
cana-1543	175	37	u	u	PROPN
cana-1543	175	38	u	u	NOUN
cana-1543	175	39	u	u	PROPN
cana-1543	175	40	w	w	PROPN
cana-1543	175	41	w	w	PROPN
cana-1543	175	42	w	w	X
cana-1543	175	43			NOUN
cana-1543	175	44			PUNCT
cana-1543	175	45			NOUN
cana-1543	175	46			NOUN
cana-1543	175	47			NOUN
cana-1543	175	48			NOUN
cana-1543	175	49			NOUN
cana-1543	175	50			NOUN
cana-1543	175	51			NOUN
cana-1543	175	52			NOUN
cana-1543	175	53			NOUN
cana-1543	175	54			NOUN
cana-1543	175	55			NOUN
cana-1543	175	56			NOUN
cana-1543	175	57			NOUN
cana-1543	175	58			NOUN
cana-1543	175	59			NOUN
cana-1543	175	60			NOUN
cana-1543	175	61			NOUN
cana-1543	175	62			NOUN
cana-1543	175	63			NOUN
cana-1543	175	64			X
cana-1543	175	65			VERB
cana-1543	175	66	=	=	NUM
cana-1543	175	67			NOUN
cana-1543	175	68			NOUN
cana-1543	175	69	1	1	NUM
cana-1543	175	70	1	1	NUM
cana-1543	175	71	1	1	NUM
cana-1543	175	72	{	{	PUNCT
cana-1543	175	73	,	,	PUNCT
cana-1543	175	74	,	,	PUNCT
cana-1543	175	75	,	,	PUNCT
cana-1543	175	76	,	,	PUNCT
cana-1543	175	77	,	,	PUNCT
cana-1543	175	78	:1	:1	PUNCT
cana-1543	175	79	1}w	1}w	NUM
cana-1543	175	80	x	x	SYM
cana-1543	175	81	x	x	PUNCT
cana-1543	176	1	w	w	NOUN
cana-1543	176	2	v	v	NUM
cana-1543	176	3	x	x	SYM
cana-1543	176	4	x	x	X
cana-1543	176	5	v	v	X
cana-1543	176	6	u	u	NOUN
cana-1543	176	7	x	x	X
cana-1543	176	8	x	x	SYM
cana-1543	176	9	y	y	PRON
cana-1543	176	10			NOUN
cana-1543	176	11			NOUN
cana-1543	176	12			NOUN
cana-1543	176	13			NOUN
cana-1543	176	14			NOUN
cana-1543	176	15			NOUN
cana-1543	176	16			NOUN
cana-1543	176	17			NOUN
cana-1543	176	18			NOUN
cana-1543	176	19			NOUN
cana-1543	176	20			NOUN
cana-1543	176	21			PUNCT
cana-1543	176	22	+	+	ADJ
cana-1543	176	23	+	+	CCONJ
cana-1543	176	24	+	+	NUM
cana-1543	176	25			NOUN
cana-1543	176	26			NOUN
cana-1543	176	27	−	−	NOUN
cana-1543	176	28	1	1	NUM
cana-1543	176	29	{	{	PUNCT
cana-1543	176	30	:1	:1	PUNCT
cana-1543	176	31	2}x	2}x	NUM
cana-1543	176	32	x	x	PUNCT
cana-1543	177	1			NOUN
cana-1543	177	2			PUNCT
cana-1543	177	3	+	+	ADJ
cana-1543	177	4			NOUN
cana-1543	177	5			NOUN
cana-1543	177	6	−	−	NOUN
cana-1543	177	7	.	.	PUNCT
cana-1543	178	1	define	define	VERB
cana-1543	178	2	:	:	PUNCT
cana-1543	178	3	(	(	PUNCT
cana-1543	178	4	(	(	PUNCT
cana-1543	178	5	)	)	PUNCT
cana-1543	178	6	)	)	PUNCT
cana-1543	178	7	(	(	PUNCT
cana-1543	178	8	(	(	PUNCT
cana-1543	178	9	)	)	PUNCT
cana-1543	178	10	)	)	PUNCT
cana-1543	178	11	{	{	PUNCT
cana-1543	178	12	1,2,	1,2,	NUM
cana-1543	178	13	...	...	SYM
cana-1543	178	14	9}v	9}v	NUM
cana-1543	178	15	m	m	VERB
cana-1543	178	16	e	e	NOUN
cana-1543	178	17	m	m	X
cana-1543	179	1			NUM
cana-1543	179	2			NUM
cana-1543	179	3			NUM
cana-1543	179	4	→	→	PUNCT
cana-1543	179	5	as	as	SCONJ
cana-1543	179	6	follows	follow	VERB
cana-1543	179	7	.	.	PUNCT
cana-1543	180	1	the	the	DET
cana-1543	180	2	assigning	assigning	NOUN
cana-1543	180	3	of	of	ADP
cana-1543	180	4	colors	color	NOUN
cana-1543	180	5	as	as	SCONJ
cana-1543	180	6	noted	note	VERB
cana-1543	180	7	below	below	ADV
cana-1543	180	8	:	:	PUNCT
cana-1543	180	9	communications	communication	NOUN
cana-1543	180	10	on	on	ADP
cana-1543	180	11	applied	apply	VERB
cana-1543	180	12	nonlinear	nonlinear	ADJ
cana-1543	180	13	analysis	analysis	NOUN
cana-1543	180	14	issn	issn	NOUN
cana-1543	180	15	:	:	PUNCT
cana-1543	180	16	1074	1074	NUM
cana-1543	180	17	-	-	PUNCT
cana-1543	180	18	133x	133x	NUM
cana-1543	180	19	vol	vol	NOUN
cana-1543	180	20	31	31	NUM
cana-1543	180	21	no	no	NOUN
cana-1543	180	22	.	.	PUNCT
cana-1543	181	1	8s	8s	PROPN
cana-1543	181	2	(	(	PUNCT
cana-1543	181	3	2024	2024	NUM
cana-1543	181	4	)	)	PUNCT
cana-1543	181	5	502	502	NUM
cana-1543	181	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1543	181	7	fig	fig	NOUN
cana-1543	181	8	8	8	NUM
cana-1543	181	9	:	:	PUNCT
cana-1543	181	10	total	total	ADJ
cana-1543	181	11	coloring	coloring	NOUN
cana-1543	181	12	of	of	ADP
cana-1543	181	13	5	5	NUM
cana-1543	181	14	(	(	PUNCT
cana-1543	181	15	)	)	PUNCT
cana-1543	181	16	m	m	NOUN
cana-1543	181	17			NUM
cana-1543	181	18	for	for	ADP
cana-1543	181	19	1	1	NUM
cana-1543	181	20			NOUN
cana-1543	181	21			PROPN
cana-1543	181	22			PROPN
cana-1543	181	23	(	(	PUNCT
cana-1543	181	24	)	)	PUNCT
cana-1543	181	25	1,2,3	1,2,3	NUM
cana-1543	181	26	;	;	PUNCT
cana-1543	181	27	1	1	NUM
cana-1543	181	28	,	,	PUNCT
cana-1543	181	29	2,0	2,0	NUM
cana-1543	181	30	(	(	PUNCT
cana-1543	181	31	mod3)v	mod3)v	PROPN
cana-1543	181	32	if	if	PROPN
cana-1543	181	33	=	=	NOUN
cana-1543	181	34			PROPN
cana-1543	181	35	;	;	PUNCT
cana-1543	181	36	'	'	PUNCT
cana-1543	181	37	(	(	PUNCT
cana-1543	181	38	)	)	PUNCT
cana-1543	181	39	1,2	1,2	NUM
cana-1543	181	40	;	;	PUNCT
cana-1543	181	41	1,0	1,0	NUM
cana-1543	181	42	(	(	PUNCT
cana-1543	181	43	mod	mod	PROPN
cana-1543	181	44	2)w	2)w	NUM
cana-1543	181	45	if	if	PROPN
cana-1543	181	46	=	=	NOUN
cana-1543	181	47			PROPN
cana-1543	181	48	;	;	PUNCT
cana-1543	181	49	'	'	PUNCT
cana-1543	181	50	''	''	PUNCT
cana-1543	181	51	(	(	PUNCT
cana-1543	181	52	)	)	PUNCT
cana-1543	181	53	2w	2w	NUM
cana-1543	181	54	=	=	SYM
cana-1543	181	55	''	''	PUNCT
cana-1543	181	56	(	(	PUNCT
cana-1543	181	57	)	)	PUNCT
cana-1543	181	58	5,6	5,6	NUM
cana-1543	181	59	;	;	PUNCT
cana-1543	181	60	1,0	1,0	NUM
cana-1543	181	61	(	(	PUNCT
cana-1543	181	62	mod	mod	PROPN
cana-1543	181	63	2)w	2)w	NUM
cana-1543	181	64	if	if	PROPN
cana-1543	181	65	=	=	NOUN
cana-1543	182	1			PROPN
cana-1543	182	2	;	;	PUNCT
cana-1543	182	3	'	'	PUNCT
cana-1543	182	4	''	''	PUNCT
cana-1543	182	5	(	(	PUNCT
cana-1543	182	6	)	)	PUNCT
cana-1543	183	1	1u	1u	NUM
cana-1543	183	2	=	=	SYM
cana-1543	183	3	;	;	PUNCT
cana-1543	183	4	''	''	PUNCT
cana-1543	183	5	(	(	PUNCT
cana-1543	183	6	)	)	PUNCT
cana-1543	183	7	9u	9u	PROPN
cana-1543	183	8	=	=	SYM
cana-1543	183	9	;	;	PUNCT
cana-1543	183	10	(	(	PUNCT
cana-1543	183	11	)	)	PUNCT
cana-1543	183	12	6u	6u	NOUN
cana-1543	183	13	=	=	PUNCT
cana-1543	183	14	;	;	PUNCT
cana-1543	183	15	'	'	PUNCT
cana-1543	183	16	(	(	PUNCT
cana-1543	183	17	)	)	PUNCT
cana-1543	183	18	8u	8u	PROPN
cana-1543	183	19	=	=	SYM
cana-1543	183	20	;	;	PUNCT
cana-1543	183	21	(	(	PUNCT
cana-1543	183	22	)	)	PUNCT
cana-1543	183	23	9w	9w	NUM
cana-1543	183	24	=	=	SYM
cana-1543	183	25	;	;	PUNCT
cana-1543	183	26	(	(	PUNCT
cana-1543	183	27	)	)	PUNCT
cana-1543	183	28	7v	7v	NUM
cana-1543	183	29	u	u	NOUN
cana-1543	183	30			NOUN
cana-1543	183	31	=	=	X
cana-1543	183	32	;	;	PUNCT
cana-1543	183	33	'	'	PUNCT
cana-1543	183	34	(	(	PUNCT
cana-1543	183	35	)	)	PUNCT
cana-1543	183	36	4u	4u	NOUN
cana-1543	183	37	u	u	NOUN
cana-1543	183	38			NOUN
cana-1543	183	39	=	=	X
cana-1543	183	40	;	;	PUNCT
cana-1543	183	41	'	'	PUNCT
cana-1543	183	42	''	''	PUNCT
cana-1543	183	43	(	(	PUNCT
cana-1543	183	44	)	)	PUNCT
cana-1543	183	45	7u	7u	NUM
cana-1543	183	46	u	u	NOUN
cana-1543	183	47			NOUN
cana-1543	183	48	=	=	SYM
cana-1543	183	49	;	;	PUNCT
cana-1543	183	50	''	''	PUNCT
cana-1543	183	51	'	'	PUNCT
cana-1543	183	52	''	''	PUNCT
cana-1543	183	53	(	(	PUNCT
cana-1543	183	54	)	)	PUNCT
cana-1543	183	55	5u	5u	NUM
cana-1543	183	56	u	u	NOUN
cana-1543	183	57			NOUN
cana-1543	183	58	=	=	X
cana-1543	183	59	;	;	PUNCT
cana-1543	183	60	(	(	PUNCT
cana-1543	183	61	)	)	PUNCT
cana-1543	183	62	6v	6v	NOUN
cana-1543	183	63	w	w	NUM
cana-1543	183	64			NOUN
cana-1543	183	65	=	=	SYM
cana-1543	183	66	;	;	PUNCT
cana-1543	183	67	'	'	PUNCT
cana-1543	183	68	(	(	PUNCT
cana-1543	183	69	)	)	PUNCT
cana-1543	183	70	5w	5w	PROPN
cana-1543	183	71	w	w	NOUN
cana-1543	183	72			NOUN
cana-1543	183	73	=	=	SYM
cana-1543	183	74	;	;	PUNCT
cana-1543	183	75	'	'	PUNCT
cana-1543	183	76	''	''	PUNCT
cana-1543	183	77	(	(	PUNCT
cana-1543	183	78	)	)	PUNCT
cana-1543	183	79	8w	8w	NOUN
cana-1543	183	80	w	w	NOUN
cana-1543	183	81			NOUN
cana-1543	183	82	=	=	SYM
cana-1543	183	83	''	''	PUNCT
cana-1543	183	84	'	'	PUNCT
cana-1543	183	85	''	''	PUNCT
cana-1543	183	86	(	(	PUNCT
cana-1543	183	87	)	)	PUNCT
cana-1543	183	88	4w	4w	X
cana-1543	183	89	w	w	NOUN
cana-1543	183	90			NOUN
cana-1543	183	91	=	=	SYM
cana-1543	183	92	;	;	PUNCT
cana-1543	183	93	''	''	PUNCT
cana-1543	183	94	(	(	PUNCT
cana-1543	183	95	)	)	PUNCT
cana-1543	183	96	3u	3u	NUM
cana-1543	183	97	u	u	NOUN
cana-1543	183	98			NOUN
cana-1543	183	99	=	=	X
cana-1543	183	100	;	;	PUNCT
cana-1543	183	101	(	(	PUNCT
cana-1543	183	102	)	)	PUNCT
cana-1543	183	103	2u	2u	NOUN
cana-1543	183	104	w	w	NOUN
cana-1543	183	105			NOUN
cana-1543	183	106	=	=	SYM
cana-1543	183	107	;	;	PUNCT
cana-1543	183	108	''	''	PUNCT
cana-1543	183	109	(	(	PUNCT
cana-1543	183	110	)	)	PUNCT
cana-1543	183	111	3w	3w	NUM
cana-1543	183	112	w	w	NUM
cana-1543	183	113			NOUN
cana-1543	183	114	=	=	PUNCT
cana-1543	183	115	for	for	ADP
cana-1543	183	116	1	1	NUM
cana-1543	183	117	1	1	PROPN
cana-1543	183	118			PROPN
cana-1543	183	119			NOUN
cana-1543	183	120	−	−	PROPN
cana-1543	183	121	(	(	PUNCT
cana-1543	183	122	)	)	PUNCT
cana-1543	183	123	2,1,3	2,1,3	NUM
cana-1543	183	124	;	;	PUNCT
cana-1543	183	125	1	1	NUM
cana-1543	183	126	,	,	PUNCT
cana-1543	183	127	2,0	2,0	NUM
cana-1543	183	128	(	(	PUNCT
cana-1543	183	129	mod3)x	mod3)x	PROPN
cana-1543	183	130	if	if	PROPN
cana-1543	183	131	=	=	NOUN
cana-1543	184	1			PROPN
cana-1543	184	2	;	;	PUNCT
cana-1543	184	3	(	(	PUNCT
cana-1543	184	4	)	)	PUNCT
cana-1543	184	5	3,2,4	3,2,4	NUM
cana-1543	184	6	;	;	PUNCT
cana-1543	184	7	1	1	NUM
cana-1543	184	8	,	,	PUNCT
cana-1543	184	9	2,0	2,0	NUM
cana-1543	184	10	(	(	PUNCT
cana-1543	184	11	mod	mod	PROPN
cana-1543	184	12	3)v	3)v	NUM
cana-1543	184	13	x	x	SYM
cana-1543	184	14	if	if	PRON
cana-1543	184	15			NOUN
cana-1543	184	16	=	=	ADJ
cana-1543	184	17			NOUN
cana-1543	184	18	;	;	PUNCT
cana-1543	184	19	1	1	NUM
cana-1543	184	20	(	(	PUNCT
cana-1543	184	21	)	)	PUNCT
cana-1543	184	22	1,3,2	1,3,2	NUM
cana-1543	184	23	;	;	PUNCT
cana-1543	184	24	1,2,0	1,2,0	NUM
cana-1543	184	25	(	(	PUNCT
cana-1543	184	26	mod3)x	mod3)x	PROPN
cana-1543	184	27	v	v	ADP
cana-1543	184	28	if	if	NOUN
cana-1543	184	29			NOUN
cana-1543	184	30	+	+	PUNCT
cana-1543	184	31	=	=	SYM
cana-1543	184	32			PROPN
cana-1543	184	33	;	;	PUNCT
cana-1543	184	34	(	(	PUNCT
cana-1543	184	35	)	)	PUNCT
cana-1543	184	36	4w	4w	NOUN
cana-1543	184	37	x	x	PUNCT
cana-1543	185	1			NOUN
cana-1543	185	2	=	=	X
cana-1543	185	3	;	;	PUNCT
cana-1543	185	4	1	1	NUM
cana-1543	185	5	(	(	PUNCT
cana-1543	185	6	)	)	PUNCT
cana-1543	185	7	7x	7x	NUM
cana-1543	185	8	w	w	NOUN
cana-1543	185	9			NOUN
cana-1543	185	10	+	+	X
cana-1543	185	11	=	=	SYM
cana-1543	185	12	;	;	PUNCT
cana-1543	185	13	(	(	PUNCT
cana-1543	185	14	)	)	PUNCT
cana-1543	185	15	5u	5u	NUM
cana-1543	185	16	x	x	PUNCT
cana-1543	185	17			NOUN
cana-1543	185	18	=	=	X
cana-1543	185	19	;	;	PUNCT
cana-1543	185	20	1	1	NUM
cana-1543	185	21	(	(	PUNCT
cana-1543	185	22	)	)	PUNCT
cana-1543	185	23	6x	6x	NUM
cana-1543	185	24	u	u	NOUN
cana-1543	185	25			NOUN
cana-1543	185	26	+	+	CCONJ
cana-1543	185	27	=	=	SYM
cana-1543	185	28	for	for	ADP
cana-1543	185	29	1	1	NUM
cana-1543	185	30	2	2	PROPN
cana-1543	185	31			PROPN
cana-1543	185	32			NOUN
cana-1543	185	33	−	−	NOUN
cana-1543	185	34	,	,	PUNCT
cana-1543	185	35	1	1	NUM
cana-1543	185	36	(	(	PUNCT
cana-1543	185	37	)	)	PUNCT
cana-1543	185	38	8,9	8,9	NUM
cana-1543	185	39	;	;	PUNCT
cana-1543	185	40	1,0	1,0	NUM
cana-1543	185	41	(	(	PUNCT
cana-1543	185	42	mod	mod	PROPN
cana-1543	185	43	2)x	2)x	NUM
cana-1543	185	44	x	x	NOUN
cana-1543	185	45	if	if	PRON
cana-1543	185	46			NOUN
cana-1543	185	47	+	+	VERB
cana-1543	185	48	=	=	SYM
cana-1543	185	49			PROPN
cana-1543	185	50	hence	hence	ADV
cana-1543	185	51			ADJ
cana-1543	185	52	is	be	AUX
cana-1543	185	53	a	a	DET
cana-1543	185	54	total	total	ADJ
cana-1543	185	55	coloring	coloring	NOUN
cana-1543	185	56	of	of	ADP
cana-1543	185	57	(	(	PUNCT
cana-1543	185	58	)	)	PUNCT
cana-1543	185	59	m	m	VERB
cana-1543	185	60			NOUN
cana-1543	185	61	and	and	CCONJ
cana-1543	185	62	therefore	therefore	ADV
cana-1543	185	63	''	''	PUNCT
cana-1543	185	64	(	(	PUNCT
cana-1543	185	65	(	(	PUNCT
cana-1543	185	66	)	)	PUNCT
cana-1543	185	67	)	)	PUNCT
cana-1543	185	68	9	9	NUM
cana-1543	185	69	m	m	NOUN
cana-1543	185	70			X
cana-1543	185	71			NUM
cana-1543	185	72			NOUN
cana-1543	185	73	.	.	PUNCT
cana-1543	186	1	since	since	SCONJ
cana-1543	186	2	(	(	PUNCT
cana-1543	186	3	(	(	PUNCT
cana-1543	186	4	)	)	PUNCT
cana-1543	186	5	)	)	PUNCT
cana-1543	186	6	m	m	VERB
cana-1543	186	7			VERB
cana-1543	186	8			NOUN
cana-1543	186	9	=	=	PROPN
cana-1543	186	10	and	and	CCONJ
cana-1543	186	11	by	by	ADP
cana-1543	186	12	lemma	lemma	PROPN
cana-1543	186	13	2.7	2.7	NUM
cana-1543	186	14	,	,	PUNCT
cana-1543	186	15	''	''	PUNCT
cana-1543	186	16	(	(	PUNCT
cana-1543	186	17	(	(	PUNCT
cana-1543	186	18	)	)	PUNCT
cana-1543	186	19	)	)	PUNCT
cana-1543	186	20	(	(	PUNCT
cana-1543	186	21	(	(	PUNCT
cana-1543	186	22	)	)	PUNCT
cana-1543	186	23	)	)	PUNCT
cana-1543	186	24	1	1	NUM
cana-1543	186	25	8	8	NUM
cana-1543	186	26	1	1	NUM
cana-1543	186	27	9	9	NUM
cana-1543	186	28	m	m	NOUN
cana-1543	186	29	m	m	NOUN
cana-1543	187	1			X
cana-1543	187	2			NUM
cana-1543	187	3			PROPN
cana-1543	187	4			PUNCT
cana-1543	188	1	+	+	PUNCT
cana-1543	188	2	=	=	SYM
cana-1543	189	1	+	+	NUM
cana-1543	189	2			NUM
cana-1543	189	3	and	and	CCONJ
cana-1543	189	4	''	''	PUNCT
cana-1543	189	5	(	(	PUNCT
cana-1543	189	6	(	(	PUNCT
cana-1543	189	7	)	)	PUNCT
cana-1543	189	8	)	)	PUNCT
cana-1543	190	1	9.tm	9.tm	NUM
cana-1543	190	2			NUM
cana-1543	190	3	=	=	PUNCT
cana-1543	190	4	theorem	theorem	VERB
cana-1543	190	5	3.9	3.9	NUM
cana-1543	190	6	:	:	PUNCT
cana-1543	190	7	let	let	VERB
cana-1543	190	8	(	(	PUNCT
cana-1543	190	9	)	)	PUNCT
cana-1543	190	10	t	t	PROPN
cana-1543	190	11			NOUN
cana-1543	190	12	be	be	AUX
cana-1543	190	13	the	the	DET
cana-1543	190	14	middle	middle	ADJ
cana-1543	190	15	graph	graph	NOUN
cana-1543	190	16	of	of	ADP
cana-1543	190	17	lobster	lobster	NOUN
cana-1543	190	18	graph	graph	NOUN
cana-1543	190	19	,	,	PUNCT
cana-1543	190	20	then	then	ADV
cana-1543	190	21	''	''	PUNCT
cana-1543	190	22	(	(	PUNCT
cana-1543	190	23	(	(	PUNCT
cana-1543	190	24	)	)	PUNCT
cana-1543	190	25	)	)	PUNCT
cana-1543	191	1	9.t	9.t	NUM
cana-1543	191	2			NOUN
cana-1543	191	3			NUM
cana-1543	191	4	=	=	PUNCT
cana-1543	191	5	proof	proof	NOUN
cana-1543	191	6	:	:	PUNCT
cana-1543	191	7	let	let	VERB
cana-1543	191	8	'	'	PUNCT
cana-1543	191	9	''	''	PUNCT
cana-1543	191	10	'	'	PUNCT
cana-1543	191	11	''	''	PUNCT
cana-1543	191	12	'	'	PUNCT
cana-1543	191	13	''	''	PUNCT
cana-1543	191	14	'	'	PUNCT
cana-1543	191	15	''	''	PUNCT
cana-1543	191	16	(	(	PUNCT
cana-1543	191	17	(	(	PUNCT
cana-1543	191	18	)	)	PUNCT
cana-1543	191	19	)	)	PUNCT
cana-1543	191	20	{	{	PUNCT
cana-1543	191	21	,	,	PUNCT
cana-1543	191	22	,	,	PUNCT
cana-1543	191	23	,	,	PUNCT
cana-1543	191	24	,	,	PUNCT
cana-1543	191	25	,	,	PUNCT
cana-1543	191	26	,	,	PUNCT
cana-1543	191	27	,	,	PUNCT
cana-1543	191	28	,	,	PUNCT
cana-1543	191	29	:1	:1	PUNCT
cana-1543	191	30	}	}	PUNCT
cana-1543	191	31	{	{	PUNCT
cana-1543	191	32	:1	:1	PUNCT
cana-1543	192	1	1}v	1}v	NUM
cana-1543	192	2	t	t	NOUN
cana-1543	192	3	v	v	NUM
cana-1543	192	4	u	u	PROPN
cana-1543	192	5	u	u	NOUN
cana-1543	192	6	u	u	NOUN
cana-1543	192	7	u	u	PROPN
cana-1543	192	8	w	w	PROPN
cana-1543	192	9	w	w	PROPN
cana-1543	192	10	w	w	PROPN
cana-1543	192	11	w	w	PROPN
cana-1543	192	12	x	x	PUNCT
cana-1543	192	13			NOUN
cana-1543	192	14			SYM
cana-1543	192	15			NOUN
cana-1543	192	16			NOUN
cana-1543	192	17			NOUN
cana-1543	192	18			NOUN
cana-1543	192	19			NOUN
cana-1543	192	20			NOUN
cana-1543	192	21			NOUN
cana-1543	192	22			X
cana-1543	192	23			VERB
cana-1543	192	24			NUM
cana-1543	192	25			NOUN
cana-1543	192	26	=	=	PUNCT
cana-1543	192	27			NOUN
cana-1543	192	28			NOUN
cana-1543	192	29			NOUN
cana-1543	192	30			NOUN
cana-1543	192	31	−	−	PROPN
cana-1543	192	32	and	and	CCONJ
cana-1543	192	33	'	'	PUNCT
cana-1543	192	34	'	'	PUNCT
cana-1543	192	35	''	''	PUNCT
cana-1543	192	36	''	''	PUNCT
cana-1543	193	1	'	'	PUNCT
cana-1543	193	2	''	''	PUNCT
cana-1543	193	3	'	'	PUNCT
cana-1543	193	4	'	'	PUNCT
cana-1543	193	5	''	''	PUNCT
cana-1543	193	6	''	''	PUNCT
cana-1543	193	7	'	'	PUNCT
cana-1543	193	8	''	''	PUNCT
cana-1543	193	9	''	''	PUNCT
cana-1543	193	10	'	'	PUNCT
cana-1543	193	11	''	''	PUNCT
cana-1543	193	12	'	'	PUNCT
cana-1543	193	13	'	'	PUNCT
cana-1543	193	14	'	'	PUNCT
cana-1543	193	15	'	'	PUNCT
cana-1543	193	16	'	'	PUNCT
cana-1543	193	17	''	''	PUNCT
cana-1543	193	18	''	''	PUNCT
cana-1543	193	19	1	1	NUM
cana-1543	193	20	1	1	NUM
cana-1543	193	21	1	1	NUM
cana-1543	193	22	1	1	NUM
cana-1543	193	23	(	(	PUNCT
cana-1543	193	24	(	(	PUNCT
cana-1543	193	25	)	)	PUNCT
cana-1543	193	26	)	)	PUNCT
cana-1543	193	27	{	{	PUNCT
cana-1543	193	28	,	,	PUNCT
cana-1543	193	29	,	,	PUNCT
cana-1543	193	30	,	,	PUNCT
cana-1543	193	31	,	,	PUNCT
cana-1543	193	32	,	,	PUNCT
cana-1543	193	33	,	,	PUNCT
cana-1543	193	34	,	,	PUNCT
cana-1543	193	35	,	,	PUNCT
cana-1543	193	36	,	,	PUNCT
cana-1543	193	37	,	,	PUNCT
cana-1543	193	38	,	,	PUNCT
cana-1543	193	39	,	,	PUNCT
cana-1543	193	40	,	,	PUNCT
cana-1543	193	41	,	,	PUNCT
cana-1543	193	42	:1	:1	PUNCT
cana-1543	193	43	}	}	PUNCT
cana-1543	193	44	{	{	PUNCT
cana-1543	193	45	,	,	PUNCT
cana-1543	193	46	,	,	PUNCT
cana-1543	193	47	,	,	PUNCT
cana-1543	193	48	,	,	PUNCT
cana-1543	193	49	,	,	PUNCT
cana-1543	193	50	,	,	PUNCT
cana-1543	193	51	:1	:1	PUNCT
cana-1543	193	52	1	1	X
cana-1543	193	53	}	}	PUNCT
cana-1543	193	54	e	e	PROPN
cana-1543	193	55	t	t	NOUN
cana-1543	193	56	v	v	NUM
cana-1543	193	57	u	u	X
cana-1543	193	58	u	u	X
cana-1543	193	59	u	u	NOUN
cana-1543	193	60	u	u	NOUN
cana-1543	193	61	u	u	NOUN
cana-1543	193	62	u	u	NOUN
cana-1543	193	63	u	u	NOUN
cana-1543	193	64	v	v	PROPN
cana-1543	193	65	w	w	PROPN
cana-1543	193	66	w	w	PROPN
cana-1543	193	67	w	w	PROPN
cana-1543	193	68	w	w	PROPN
cana-1543	193	69	w	w	PROPN
cana-1543	193	70	w	w	PROPN
cana-1543	193	71	w	w	PROPN
cana-1543	193	72	u	u	PROPN
cana-1543	193	73	u	u	NOUN
cana-1543	193	74	u	u	NOUN
cana-1543	193	75	u	u	NOUN
cana-1543	193	76	u	u	NOUN
cana-1543	193	77	v	v	ADP
cana-1543	193	78	v	v	PROPN
cana-1543	193	79	w	w	PROPN
cana-1543	193	80	w	w	PROPN
cana-1543	193	81	w	w	PROPN
cana-1543	193	82	u	u	PROPN
cana-1543	193	83	w	w	PROPN
cana-1543	193	84	w	w	PROPN
cana-1543	193	85	w	w	PROPN
cana-1543	193	86	u	u	PROPN
cana-1543	193	87	x	x	PROPN
cana-1543	193	88	v	v	ADP
cana-1543	193	89	v	v	NOUN
cana-1543	193	90	x	x	SYM
cana-1543	193	91	u	u	NOUN
cana-1543	193	92	w	w	NOUN
cana-1543	193	93	x	x	X
cana-1543	193	94	x	x	X
cana-1543	194	1	w	w	NOUN
cana-1543	194	2	v	v	NUM
cana-1543	194	3	x	x	SYM
cana-1543	194	4	x	x	SYM
cana-1543	194	5	v	v	ADP
cana-1543	194	6			PUNCT
cana-1543	194	7			NOUN
cana-1543	194	8			ADP
cana-1543	194	9			NOUN
cana-1543	194	10			NOUN
cana-1543	194	11			NOUN
cana-1543	194	12			NOUN
cana-1543	194	13			NOUN
cana-1543	194	14			NOUN
cana-1543	194	15			NOUN
cana-1543	194	16			NOUN
cana-1543	194	17			NOUN
cana-1543	194	18			NOUN
cana-1543	194	19			NOUN
cana-1543	194	20			NOUN
cana-1543	194	21			NOUN
cana-1543	194	22			NOUN
cana-1543	194	23			NOUN
cana-1543	194	24			NOUN
cana-1543	194	25			NOUN
cana-1543	194	26			NOUN
cana-1543	194	27			NOUN
cana-1543	194	28			NOUN
cana-1543	194	29			NOUN
cana-1543	194	30			NOUN
cana-1543	194	31			NOUN
cana-1543	194	32			NOUN
cana-1543	194	33			NOUN
cana-1543	194	34			NOUN
cana-1543	194	35			NOUN
cana-1543	194	36			NOUN
cana-1543	194	37			NOUN
cana-1543	194	38			NOUN
cana-1543	194	39			NOUN
cana-1543	194	40			NOUN
cana-1543	194	41			NOUN
cana-1543	194	42			NOUN
cana-1543	194	43			NOUN
cana-1543	194	44			NOUN
cana-1543	194	45			NOUN
cana-1543	194	46			NOUN
cana-1543	194	47			NOUN
cana-1543	194	48			NOUN
cana-1543	194	49			NOUN
cana-1543	194	50			NOUN
cana-1543	194	51			NUM
cana-1543	194	52			NOUN
cana-1543	194	53			NUM
cana-1543	194	54			NOUN
cana-1543	194	55	+	+	X
cana-1543	194	56	+	+	X
cana-1543	194	57	+	+	PUNCT
cana-1543	194	58	+	+	CCONJ
cana-1543	194	59	=	=	NOUN
cana-1543	194	60			NOUN
cana-1543	194	61			NOUN
cana-1543	194	62			NOUN
cana-1543	194	63			NOUN
cana-1543	194	64	−	−	NOUN
cana-1543	194	65	1	1	NUM
cana-1543	194	66	{	{	PUNCT
cana-1543	194	67	:1	:1	PUNCT
cana-1543	194	68	2}x	2}x	NUM
cana-1543	194	69	x	x	PUNCT
cana-1543	195	1			NOUN
cana-1543	195	2			PUNCT
cana-1543	195	3	+	+	ADJ
cana-1543	195	4			NOUN
cana-1543	195	5			NOUN
cana-1543	195	6	−	−	NOUN
cana-1543	195	7	.	.	PUNCT
cana-1543	196	1	define	define	VERB
cana-1543	196	2	:	:	PUNCT
cana-1543	196	3	(	(	PUNCT
cana-1543	196	4	(	(	PUNCT
cana-1543	196	5	)	)	PUNCT
cana-1543	196	6	)	)	PUNCT
cana-1543	196	7	(	(	PUNCT
cana-1543	196	8	(	(	PUNCT
cana-1543	196	9	)	)	PUNCT
cana-1543	196	10	)	)	PUNCT
cana-1543	196	11	{	{	PUNCT
cana-1543	196	12	1,2,	1,2,	NUM
cana-1543	196	13	...	...	SYM
cana-1543	196	14	9}v	9}v	NUM
cana-1543	196	15	t	t	NOUN
cana-1543	196	16	e	e	X
cana-1543	196	17	t	t	PUNCT
cana-1543	196	18			PUNCT
cana-1543	196	19			NUM
cana-1543	196	20			NUM
cana-1543	196	21	→	→	PUNCT
cana-1543	196	22	as	as	SCONJ
cana-1543	196	23	follows	follow	VERB
cana-1543	196	24	.	.	PUNCT
cana-1543	197	1	the	the	DET
cana-1543	197	2	assigning	assigning	NOUN
cana-1543	197	3	of	of	ADP
cana-1543	197	4	colors	color	NOUN
cana-1543	197	5	as	as	SCONJ
cana-1543	197	6	noted	note	VERB
cana-1543	197	7	below	below	ADV
cana-1543	197	8	:	:	PUNCT
cana-1543	197	9	communications	communication	NOUN
cana-1543	197	10	on	on	ADP
cana-1543	197	11	applied	apply	VERB
cana-1543	197	12	nonlinear	nonlinear	ADJ
cana-1543	197	13	analysis	analysis	NOUN
cana-1543	197	14	issn	issn	NOUN
cana-1543	197	15	:	:	PUNCT
cana-1543	197	16	1074	1074	NUM
cana-1543	197	17	-	-	PUNCT
cana-1543	197	18	133x	133x	NUM
cana-1543	197	19	vol	vol	NOUN
cana-1543	197	20	31	31	NUM
cana-1543	197	21	no	no	NOUN
cana-1543	197	22	.	.	PUNCT
cana-1543	198	1	8s	8s	PROPN
cana-1543	198	2	(	(	PUNCT
cana-1543	198	3	2024	2024	NUM
cana-1543	198	4	)	)	PUNCT
cana-1543	198	5	503	503	NUM
cana-1543	198	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1543	198	7	fig	fig	NOUN
cana-1543	198	8	9	9	NUM
cana-1543	198	9	:	:	PUNCT
cana-1543	198	10	total	total	ADJ
cana-1543	198	11	coloring	coloring	NOUN
cana-1543	198	12	of	of	ADP
cana-1543	198	13	5	5	NUM
cana-1543	198	14	(	(	PUNCT
cana-1543	198	15	)	)	PUNCT
cana-1543	198	16	t	t	NOUN
cana-1543	198	17			NUM
cana-1543	198	18	for	for	ADP
cana-1543	198	19	1	1	NUM
cana-1543	198	20			NOUN
cana-1543	198	21			PROPN
cana-1543	198	22			PROPN
cana-1543	198	23	(	(	PUNCT
cana-1543	198	24	)	)	PUNCT
cana-1543	198	25	1,2,3	1,2,3	NUM
cana-1543	198	26	;	;	PUNCT
cana-1543	198	27	1	1	NUM
cana-1543	198	28	,	,	PUNCT
cana-1543	198	29	2,0	2,0	NUM
cana-1543	198	30	(	(	PUNCT
cana-1543	198	31	mod3)v	mod3)v	PROPN
cana-1543	198	32	if	if	PROPN
cana-1543	198	33	=	=	NOUN
cana-1543	199	1			PROPN
cana-1543	199	2	;	;	PUNCT
cana-1543	199	3	(	(	PUNCT
cana-1543	199	4	)	)	PUNCT
cana-1543	200	1	6u	6u	NOUN
cana-1543	200	2	=	=	PUNCT
cana-1543	200	3	;	;	PUNCT
cana-1543	200	4	'	'	PUNCT
cana-1543	200	5	(	(	PUNCT
cana-1543	200	6	)	)	PUNCT
cana-1543	200	7	5u	5u	PROPN
cana-1543	200	8	=	=	SYM
cana-1543	200	9	;	;	PUNCT
cana-1543	200	10	''	''	PUNCT
cana-1543	200	11	(	(	PUNCT
cana-1543	200	12	)	)	PUNCT
cana-1543	200	13	7u	7u	PROPN
cana-1543	200	14	=	=	SYM
cana-1543	200	15	;	;	PUNCT
cana-1543	200	16	'	'	PUNCT
cana-1543	200	17	''	''	PUNCT
cana-1543	200	18	(	(	PUNCT
cana-1543	200	19	)	)	PUNCT
cana-1543	200	20	1u	1u	PROPN
cana-1543	200	21	=	=	SYM
cana-1543	200	22	;	;	PUNCT
cana-1543	200	23	(	(	PUNCT
cana-1543	200	24	)	)	PUNCT
cana-1543	200	25	9w	9w	NUM
cana-1543	200	26	=	=	SYM
cana-1543	200	27	;	;	PUNCT
cana-1543	200	28	'	'	PUNCT
cana-1543	200	29	(	(	PUNCT
cana-1543	200	30	)	)	PUNCT
cana-1543	200	31	4w	4w	PROPN
cana-1543	200	32	=	=	PUNCT
cana-1543	200	33	;	;	PUNCT
cana-1543	200	34	''	''	PUNCT
cana-1543	200	35	(	(	PUNCT
cana-1543	200	36	)	)	PUNCT
cana-1543	200	37	2w	2w	NUM
cana-1543	200	38	=	=	SYM
cana-1543	200	39	;	;	PUNCT
cana-1543	200	40	'	'	PUNCT
cana-1543	200	41	''	''	PUNCT
cana-1543	200	42	(	(	PUNCT
cana-1543	200	43	)	)	PUNCT
cana-1543	200	44	1w	1w	NUM
cana-1543	200	45	=	=	SYM
cana-1543	200	46	;	;	PUNCT
cana-1543	200	47	(	(	PUNCT
cana-1543	200	48	)	)	PUNCT
cana-1543	200	49	7v	7v	NUM
cana-1543	200	50	u	u	NOUN
cana-1543	201	1			NOUN
cana-1543	201	2	=	=	X
cana-1543	201	3	;	;	PUNCT
cana-1543	201	4	'	'	PUNCT
cana-1543	201	5	(	(	PUNCT
cana-1543	201	6	)	)	PUNCT
cana-1543	201	7	8u	8u	PROPN
cana-1543	201	8	u	u	NOUN
cana-1543	201	9			NOUN
cana-1543	201	10	=	=	X
cana-1543	201	11	;	;	PUNCT
cana-1543	201	12	'	'	PUNCT
cana-1543	201	13	''	''	PUNCT
cana-1543	201	14	(	(	PUNCT
cana-1543	201	15	)	)	PUNCT
cana-1543	201	16	9u	9u	X
cana-1543	201	17	u	u	NOUN
cana-1543	201	18			NOUN
cana-1543	201	19	=	=	X
cana-1543	201	20	;	;	PUNCT
cana-1543	201	21	''	''	PUNCT
cana-1543	201	22	'	'	PUNCT
cana-1543	201	23	''	''	PUNCT
cana-1543	201	24	(	(	PUNCT
cana-1543	201	25	)	)	PUNCT
cana-1543	201	26	8u	8u	PROPN
cana-1543	201	27	u	u	NOUN
cana-1543	201	28			NOUN
cana-1543	201	29	=	=	X
cana-1543	201	30	;	;	PUNCT
cana-1543	201	31	(	(	PUNCT
cana-1543	201	32	)	)	PUNCT
cana-1543	201	33	5v	5v	NOUN
cana-1543	201	34	w	w	NUM
cana-1543	201	35			NOUN
cana-1543	201	36	=	=	SYM
cana-1543	201	37	;	;	PUNCT
cana-1543	201	38	'	'	PUNCT
cana-1543	201	39	(	(	PUNCT
cana-1543	201	40	)	)	PUNCT
cana-1543	201	41	1w	1w	NUM
cana-1543	201	42	w	w	NUM
cana-1543	201	43			NOUN
cana-1543	201	44	=	=	SYM
cana-1543	201	45	;	;	PUNCT
cana-1543	201	46	'	'	PUNCT
cana-1543	201	47	''	''	PUNCT
cana-1543	201	48	(	(	PUNCT
cana-1543	201	49	)	)	PUNCT
cana-1543	201	50	5w	5w	PROPN
cana-1543	201	51	w	w	NOUN
cana-1543	201	52			NOUN
cana-1543	201	53	=	=	PUNCT
cana-1543	201	54	;	;	PUNCT
cana-1543	201	55	''	''	PUNCT
cana-1543	201	56	'	'	PUNCT
cana-1543	201	57	''	''	PUNCT
cana-1543	201	58	(	(	PUNCT
cana-1543	201	59	)	)	PUNCT
cana-1543	201	60	7w	7w	NOUN
cana-1543	201	61	w	w	NOUN
cana-1543	201	62			NOUN
cana-1543	201	63	=	=	SYM
cana-1543	201	64	;	;	PUNCT
cana-1543	201	65	''	''	PUNCT
cana-1543	201	66	(	(	PUNCT
cana-1543	201	67	)	)	PUNCT
cana-1543	201	68	3u	3u	NUM
cana-1543	201	69	u	u	NOUN
cana-1543	201	70			NOUN
cana-1543	201	71	=	=	X
cana-1543	201	72	;	;	PUNCT
cana-1543	201	73	'	'	PUNCT
cana-1543	201	74	''	''	PUNCT
cana-1543	201	75	'	'	PUNCT
cana-1543	201	76	(	(	PUNCT
cana-1543	201	77	)	)	PUNCT
cana-1543	201	78	2u	2u	PROPN
cana-1543	201	79	u	u	NOUN
cana-1543	201	80			NOUN
cana-1543	201	81	=	=	X
cana-1543	201	82	;	;	PUNCT
cana-1543	201	83	'	'	PUNCT
cana-1543	201	84	(	(	PUNCT
cana-1543	201	85	)	)	PUNCT
cana-1543	201	86	4u	4u	NOUN
cana-1543	201	87	v	v	PRON
cana-1543	201	88			NOUN
cana-1543	201	89	=	=	X
cana-1543	201	90	;	;	PUNCT
cana-1543	201	91	'	'	PUNCT
cana-1543	201	92	(	(	PUNCT
cana-1543	201	93	)	)	PUNCT
cana-1543	201	94	6v	6v	NOUN
cana-1543	201	95	w	w	NUM
cana-1543	201	96			NOUN
cana-1543	201	97	=	=	SYM
cana-1543	201	98	;	;	PUNCT
cana-1543	201	99	'	'	PUNCT
cana-1543	201	100	'	'	PUNCT
cana-1543	201	101	''	''	PUNCT
cana-1543	201	102	(	(	PUNCT
cana-1543	201	103	)	)	PUNCT
cana-1543	201	104	3w	3w	NUM
cana-1543	201	105	w	w	NUM
cana-1543	201	106			NOUN
cana-1543	201	107	=	=	SYM
cana-1543	201	108	;	;	PUNCT
cana-1543	201	109	(	(	PUNCT
cana-1543	201	110	)	)	PUNCT
cana-1543	201	111	2u	2u	NOUN
cana-1543	201	112	w	w	NOUN
cana-1543	201	113			NOUN
cana-1543	201	114	=	=	SYM
cana-1543	201	115	;	;	PUNCT
cana-1543	201	116	''	''	PUNCT
cana-1543	201	117	(	(	PUNCT
cana-1543	201	118	)	)	PUNCT
cana-1543	201	119	3w	3w	NUM
cana-1543	201	120	w	w	NUM
cana-1543	201	121			NOUN
cana-1543	201	122	=	=	PUNCT
cana-1543	201	123	for	for	ADP
cana-1543	201	124	1	1	NUM
cana-1543	201	125	1	1	PROPN
cana-1543	201	126			PROPN
cana-1543	201	127			NOUN
cana-1543	201	128	−	−	PROPN
cana-1543	201	129	(	(	PUNCT
cana-1543	201	130	)	)	PUNCT
cana-1543	201	131	3,1,2	3,1,2	NUM
cana-1543	201	132	;	;	PUNCT
cana-1543	201	133	1	1	NUM
cana-1543	201	134	,	,	PUNCT
cana-1543	201	135	2,0	2,0	NUM
cana-1543	201	136	(	(	PUNCT
cana-1543	201	137	mod3)x	mod3)x	PROPN
cana-1543	201	138	if	if	PROPN
cana-1543	201	139	=	=	NOUN
cana-1543	202	1			PROPN
cana-1543	202	2	;	;	PUNCT
cana-1543	202	3	(	(	PUNCT
cana-1543	202	4	)	)	PUNCT
cana-1543	202	5	2,1,3	2,1,3	NUM
cana-1543	202	6	;	;	PUNCT
cana-1543	202	7	1	1	NUM
cana-1543	202	8	,	,	PUNCT
cana-1543	202	9	2,0	2,0	NUM
cana-1543	202	10	(	(	PUNCT
cana-1543	202	11	mod	mod	PROPN
cana-1543	202	12	3)v	3)v	NUM
cana-1543	202	13	x	x	SYM
cana-1543	202	14	if	if	PRON
cana-1543	202	15			NOUN
cana-1543	202	16	=	=	ADJ
cana-1543	202	17			NOUN
cana-1543	202	18	;	;	PUNCT
cana-1543	202	19	1	1	NUM
cana-1543	202	20	(	(	PUNCT
cana-1543	202	21	)	)	PUNCT
cana-1543	202	22	1,2,3	1,2,3	NUM
cana-1543	202	23	;	;	PUNCT
cana-1543	202	24	1,2,0	1,2,0	NUM
cana-1543	202	25	(	(	PUNCT
cana-1543	202	26	mod3)x	mod3)x	PROPN
cana-1543	202	27	v	v	ADP
cana-1543	202	28	if	if	NOUN
cana-1543	202	29			NOUN
cana-1543	202	30	+	+	PUNCT
cana-1543	202	31	=	=	SYM
cana-1543	202	32			PROPN
cana-1543	202	33	;	;	PUNCT
cana-1543	202	34	(	(	PUNCT
cana-1543	202	35	)	)	PUNCT
cana-1543	202	36	6w	6w	X
cana-1543	202	37	x	x	PUNCT
cana-1543	202	38			NOUN
cana-1543	202	39	=	=	SYM
cana-1543	202	40	;	;	PUNCT
cana-1543	202	41	1	1	NUM
cana-1543	202	42	(	(	PUNCT
cana-1543	202	43	)	)	PUNCT
cana-1543	202	44	7x	7x	NUM
cana-1543	202	45	w	w	NOUN
cana-1543	202	46			NOUN
cana-1543	202	47	+	+	X
cana-1543	202	48	=	=	SYM
cana-1543	202	49	;	;	PUNCT
cana-1543	202	50	(	(	PUNCT
cana-1543	202	51	)	)	PUNCT
cana-1543	202	52	5u	5u	NUM
cana-1543	202	53	x	x	PUNCT
cana-1543	203	1			NOUN
cana-1543	203	2	=	=	X
cana-1543	203	3	;	;	PUNCT
cana-1543	203	4	1	1	NUM
cana-1543	203	5	(	(	PUNCT
cana-1543	203	6	)	)	PUNCT
cana-1543	203	7	4x	4x	NUM
cana-1543	203	8	u	u	NOUN
cana-1543	203	9			NOUN
cana-1543	203	10	+	+	X
cana-1543	203	11	=	=	SYM
cana-1543	203	12	;	;	PUNCT
cana-1543	203	13	1	1	NUM
cana-1543	203	14	(	(	PUNCT
cana-1543	203	15	)	)	PUNCT
cana-1543	203	16	8,9	8,9	NUM
cana-1543	203	17	;	;	PUNCT
cana-1543	203	18	1,0	1,0	NUM
cana-1543	203	19	(	(	PUNCT
cana-1543	203	20	mod	mod	PROPN
cana-1543	203	21	2)v	2)v	NUM
cana-1543	203	22	v	v	NOUN
cana-1543	203	23	if	if	NOUN
cana-1543	203	24			NOUN
cana-1543	203	25	+	+	PUNCT
cana-1543	203	26	=	=	SYM
cana-1543	203	27			PROPN
cana-1543	203	28	for	for	ADP
cana-1543	203	29	1	1	NUM
cana-1543	203	30	2	2	PROPN
cana-1543	203	31			PROPN
cana-1543	203	32			NOUN
cana-1543	203	33	−	−	NOUN
cana-1543	203	34	1	1	NUM
cana-1543	203	35	(	(	PUNCT
cana-1543	203	36	)	)	PUNCT
cana-1543	203	37	8,9	8,9	NUM
cana-1543	203	38	;	;	PUNCT
cana-1543	203	39	1,0	1,0	NUM
cana-1543	203	40	(	(	PUNCT
cana-1543	203	41	mod	mod	PROPN
cana-1543	203	42	2)x	2)x	NUM
cana-1543	203	43	x	x	NOUN
cana-1543	203	44	if	if	PRON
cana-1543	203	45			NOUN
cana-1543	203	46	+	+	VERB
cana-1543	203	47	=	=	SYM
cana-1543	203	48			PROPN
cana-1543	203	49	based	base	VERB
cana-1543	203	50	on	on	ADP
cana-1543	203	51	the	the	DET
cana-1543	203	52	above	above	ADJ
cana-1543	203	53	procedure	procedure	NOUN
cana-1543	203	54	,	,	PUNCT
cana-1543	203	55	the	the	DET
cana-1543	203	56	graph	graph	NOUN
cana-1543	203	57	(	(	PUNCT
cana-1543	203	58	)	)	PUNCT
cana-1543	203	59	t	t	NOUN
cana-1543	203	60			NOUN
cana-1543	203	61	is	be	AUX
cana-1543	203	62	attained	attain	VERB
cana-1543	203	63	with	with	ADP
cana-1543	203	64	9	9	NUM
cana-1543	203	65	total	total	NOUN
cana-1543	203	66	colourable	colourable	ADJ
cana-1543	203	67	.	.	PUNCT
cana-1543	204	1	thus	thus	ADV
cana-1543	204	2	''	''	PUNCT
cana-1543	204	3	(	(	PUNCT
cana-1543	204	4	(	(	PUNCT
cana-1543	204	5	)	)	PUNCT
cana-1543	204	6	)	)	PUNCT
cana-1543	204	7	9	9	NUM
cana-1543	204	8	t	t	NOUN
cana-1543	204	9			X
cana-1543	204	10			NUM
cana-1543	204	11			NOUN
cana-1543	204	12	.	.	PUNCT
cana-1543	205	1	since	since	SCONJ
cana-1543	205	2	(	(	PUNCT
cana-1543	205	3	(	(	PUNCT
cana-1543	205	4	)	)	PUNCT
cana-1543	205	5	)	)	PUNCT
cana-1543	205	6	8	8	NUM
cana-1543	205	7	t	t	NOUN
cana-1543	205	8			NOUN
cana-1543	205	9	=	=	PUNCT
cana-1543	205	10	and	and	CCONJ
cana-1543	205	11	by	by	ADP
cana-1543	205	12	lemma	lemma	PROPN
cana-1543	205	13	2.7	2.7	NUM
cana-1543	205	14	,	,	PUNCT
cana-1543	205	15	''	''	PUNCT
cana-1543	205	16	(	(	PUNCT
cana-1543	205	17	(	(	PUNCT
cana-1543	205	18	)	)	PUNCT
cana-1543	205	19	)	)	PUNCT
cana-1543	205	20	(	(	PUNCT
cana-1543	205	21	(	(	PUNCT
cana-1543	205	22	)	)	PUNCT
cana-1543	205	23	)	)	PUNCT
cana-1543	205	24	1	1	NUM
cana-1543	205	25	8	8	NUM
cana-1543	205	26	1	1	NUM
cana-1543	205	27	9	9	NUM
cana-1543	205	28	t	t	NOUN
cana-1543	205	29	t	t	ADJ
cana-1543	205	30			PROPN
cana-1543	205	31			NUM
cana-1543	205	32			PROPN
cana-1543	205	33			PUNCT
cana-1543	206	1	+	+	PUNCT
cana-1543	206	2	=	=	SYM
cana-1543	207	1	+	+	NUM
cana-1543	207	2			NUM
cana-1543	207	3	and	and	CCONJ
cana-1543	207	4	hence	hence	ADV
cana-1543	207	5	''	''	PUNCT
cana-1543	207	6	(	(	PUNCT
cana-1543	207	7	(	(	PUNCT
cana-1543	207	8	)	)	PUNCT
cana-1543	207	9	)	)	PUNCT
cana-1543	208	1	9.t	9.t	NUM
cana-1543	208	2			NOUN
cana-1543	208	3			NUM
cana-1543	208	4	=	=	NOUN
cana-1543	208	5	conclusion	conclusion	NOUN
cana-1543	208	6	in	in	ADP
cana-1543	208	7	this	this	DET
cana-1543	208	8	paper	paper	NOUN
cana-1543	208	9	,	,	PUNCT
cana-1543	208	10	the	the	DET
cana-1543	208	11	total	total	ADJ
cana-1543	208	12	chromatic	chromatic	ADJ
cana-1543	208	13	number	number	NOUN
cana-1543	208	14	of	of	ADP
cana-1543	208	15	triple	triple	ADJ
cana-1543	208	16	star	star	NOUN
cana-1543	208	17	graph	graph	NOUN
cana-1543	208	18	and	and	CCONJ
cana-1543	208	19	its	its	PRON
cana-1543	208	20	line	line	NOUN
cana-1543	208	21	,	,	PUNCT
cana-1543	208	22	middle	middle	ADJ
cana-1543	208	23	,	,	PUNCT
cana-1543	208	24	total	total	ADJ
cana-1543	208	25	,	,	PUNCT
cana-1543	208	26	splitting	splitting	NOUN
cana-1543	208	27	graph	graph	NOUN
cana-1543	208	28	and	and	CCONJ
cana-1543	208	29	lobster	lobster	NOUN
cana-1543	208	30	graph	graph	NOUN
cana-1543	208	31	are	be	AUX
cana-1543	208	32	obtained	obtain	VERB
cana-1543	208	33	,	,	PUNCT
cana-1543	208	34	the	the	DET
cana-1543	208	35	proofs	proof	NOUN
cana-1543	208	36	provides	provide	VERB
cana-1543	208	37	an	an	DET
cana-1543	208	38	optimal	optimal	ADJ
cana-1543	208	39	solution	solution	NOUN
cana-1543	208	40	to	to	ADP
cana-1543	208	41	the	the	DET
cana-1543	208	42	total	total	ADJ
cana-1543	208	43	chromatic	chromatic	ADJ
cana-1543	208	44	number	number	NOUN
cana-1543	208	45	for	for	ADP
cana-1543	208	46	these	these	DET
cana-1543	208	47	graphs	graph	NOUN
cana-1543	208	48	.	.	PUNCT
cana-1543	209	1	overall	overall	ADJ
cana-1543	209	2	,	,	PUNCT
cana-1543	209	3	delving	delve	VERB
cana-1543	209	4	into	into	ADP
cana-1543	209	5	the	the	DET
cana-1543	209	6	total	total	ADJ
cana-1543	209	7	chromatic	chromatic	ADJ
cana-1543	209	8	number	number	NOUN
cana-1543	209	9	of	of	ADP
cana-1543	209	10	different	different	ADJ
cana-1543	209	11	graph	graph	NOUN
cana-1543	209	12	classes	class	NOUN
cana-1543	209	13	and	and	CCONJ
cana-1543	209	14	exploring	explore	VERB
cana-1543	209	15	the	the	DET
cana-1543	209	16	determination	determination	NOUN
cana-1543	209	17	of	of	ADP
cana-1543	209	18	total	total	ADJ
cana-1543	209	19	coloring	coloring	NOUN
cana-1543	209	20	in	in	ADP
cana-1543	209	21	allocation	allocation	NOUN
cana-1543	209	22	across	across	ADP
cana-1543	209	23	various	various	ADJ
cana-1543	209	24	families	family	NOUN
cana-1543	209	25	of	of	ADP
cana-1543	209	26	graphs	graph	NOUN
cana-1543	209	27	can	can	AUX
cana-1543	209	28	contribute	contribute	VERB
cana-1543	209	29	significantly	significantly	ADV
cana-1543	209	30	to	to	PART
cana-1543	209	31	graph	graph	VERB
cana-1543	209	32	theory	theory	NOUN
cana-1543	209	33	and	and	CCONJ
cana-1543	209	34	related	related	ADJ
cana-1543	209	35	fields	field	NOUN
cana-1543	209	36	.	.	PUNCT
cana-1543	210	1	communications	communication	NOUN
cana-1543	210	2	on	on	ADP
cana-1543	210	3	applied	apply	VERB
cana-1543	210	4	nonlinear	nonlinear	ADJ
cana-1543	210	5	analysis	analysis	NOUN
cana-1543	210	6	issn	issn	NOUN
cana-1543	210	7	:	:	PUNCT
cana-1543	210	8	1074	1074	NUM
cana-1543	210	9	-	-	PUNCT
cana-1543	210	10	133x	133x	NUM
cana-1543	210	11	vol	vol	NOUN
cana-1543	210	12	31	31	NUM
cana-1543	210	13	no	no	NOUN
cana-1543	210	14	.	.	PUNCT
cana-1543	211	1	8s	8s	PROPN
cana-1543	211	2	(	(	PUNCT
cana-1543	211	3	2024	2024	NUM
cana-1543	211	4	)	)	PUNCT
cana-1543	211	5	504	504	NUM
cana-1543	211	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1543	211	7	reference	reference	NOUN
cana-1543	211	8	[	[	X
cana-1543	211	9	1	1	NUM
cana-1543	211	10	]	]	X
cana-1543	211	11	akhlak	akhlak	ADJ
cana-1543	211	12	mansuri	mansuri	PROPN
cana-1543	211	13	,	,	PUNCT
cana-1543	211	14	on	on	ADP
cana-1543	211	15	harmonious	harmonious	ADJ
cana-1543	211	16	chromatic	chromatic	ADJ
cana-1543	211	17	number	number	NOUN
cana-1543	211	18	of	of	ADP
cana-1543	211	19	triple	triple	ADJ
cana-1543	211	20	star	star	NOUN
cana-1543	211	21	graph	graph	NOUN
cana-1543	211	22	,	,	PUNCT
cana-1543	211	23	journal	journal	NOUN
cana-1543	211	24	of	of	ADP
cana-1543	211	25	hyperstructures	hyperstructure	NOUN
cana-1543	211	26	5	5	NUM
cana-1543	211	27	(	(	PUNCT
cana-1543	211	28	1	1	NUM
cana-1543	211	29	)	)	PUNCT
cana-1543	211	30	(	(	PUNCT
cana-1543	211	31	2016	2016	NUM
cana-1543	211	32	)	)	PUNCT
cana-1543	211	33	,	,	PUNCT
cana-1543	211	34	2632	2632	NUM
cana-1543	211	35	.	.	PUNCT
cana-1543	212	1	10.22098	10.22098	NUM
cana-1543	212	2	/	/	SYM
cana-1543	212	3	jhs.2016.2651	jhs.2016.2651	NOUN
cana-1543	213	1	[	[	X
cana-1543	213	2	2	2	NUM
cana-1543	213	3	]	]	SYM
cana-1543	213	4	behzad.m	behzad.m	PROPN
cana-1543	213	5	,	,	PUNCT
cana-1543	213	6	graphs	graph	NOUN
cana-1543	213	7	and	and	CCONJ
cana-1543	213	8	their	their	PRON
cana-1543	213	9	chromatic	chromatic	ADJ
cana-1543	213	10	numbers	number	NOUN
cana-1543	213	11	,	,	PUNCT
cana-1543	213	12	doctoral	doctoral	ADJ
cana-1543	213	13	thesis	thesis	NOUN
cana-1543	213	14	,	,	PUNCT
cana-1543	213	15	michigan	michigan	PROPN
cana-1543	213	16	state	state	PROPN
cana-1543	213	17	university	university	PROPN
cana-1543	213	18	,	,	PUNCT
cana-1543	213	19	(	(	PUNCT
cana-1543	213	20	1965	1965	NUM
cana-1543	213	21	)	)	PUNCT
cana-1543	213	22	,	,	PUNCT
cana-1543	213	23	https://doi.org/doi:10.25335/j5he-k143	https://doi.org/doi:10.25335/j5he-k143	NOUN
cana-1543	214	1	[	[	X
cana-1543	214	2	3	3	X
cana-1543	214	3	]	]	X
cana-1543	214	4	borodin	borodin	ADJ
cana-1543	214	5	o.v	o.v	PROPN
cana-1543	214	6	,	,	PUNCT
cana-1543	214	7	on	on	ADP
cana-1543	214	8	the	the	DET
cana-1543	214	9	total	total	ADJ
cana-1543	214	10	coloring	coloring	NOUN
cana-1543	214	11	of	of	ADP
cana-1543	214	12	planar	planar	ADJ
cana-1543	214	13	graphs	graph	NOUN
cana-1543	214	14	,	,	PUNCT
cana-1543	214	15	j	j	PROPN
cana-1543	214	16	reine	reine	PROPN
cana-1543	214	17	angene	angene	PROPN
cana-1543	214	18	math	math	PROPN
cana-1543	214	19	.	.	PUNCT
cana-1543	215	1	1989	1989	NUM
cana-1543	215	2	,	,	PUNCT
cana-1543	215	3	394:180	394:180	NOUN
cana-1543	215	4	-	-	PUNCT
cana-1543	215	5	185	185	NUM
cana-1543	215	6	.	.	PUNCT
cana-1543	216	1	ur	ur	INTJ
cana-1543	216	2	http://eudml.org/doc/153105	http://eudml.org/doc/153105	NOUN
cana-1543	217	1	[	[	X
cana-1543	217	2	4	4	X
cana-1543	217	3	]	]	X
cana-1543	217	4	geetha	geetha	PROPN
cana-1543	217	5	j	j	PROPN
cana-1543	217	6	,	,	PUNCT
cana-1543	217	7	narayanan	narayanan	PROPN
cana-1543	217	8	.	.	PUNCT
cana-1543	217	9	n	n	CCONJ
cana-1543	217	10	,	,	PUNCT
cana-1543	217	11	and	and	CCONJ
cana-1543	217	12	somasundaram	somasundaram	PROPN
cana-1543	217	13	k	k	PROPN
cana-1543	217	14	,	,	PUNCT
cana-1543	217	15	total	total	ADJ
cana-1543	217	16	colorings	coloring	NOUN
cana-1543	217	17	-	-	PUNCT
cana-1543	217	18	a	a	DET
cana-1543	217	19	survey	survey	NOUN
cana-1543	217	20	,	,	PUNCT
cana-1543	217	21	akce	akce	PROPN
cana-1543	217	22	international	international	ADJ
cana-1543	217	23	journal	journal	NOUN
cana-1543	217	24	of	of	ADP
cana-1543	217	25	graphs	graph	NOUN
cana-1543	217	26	and	and	CCONJ
cana-1543	217	27	combinatorics	combinatoric	NOUN
cana-1543	217	28	,	,	PUNCT
cana-1543	217	29	20	20	NUM
cana-1543	217	30	(	(	PUNCT
cana-1543	217	31	2023	2023	NUM
cana-1543	217	32	)	)	PUNCT
cana-1543	217	33	3	3	NUM
cana-1543	217	34	,	,	PUNCT
cana-1543	217	35	339	339	NUM
cana-1543	217	36	-	-	SYM
cana-1543	217	37	351	351	NUM
cana-1543	217	38	.	.	PUNCT
cana-1543	217	39	https://doi.org/10.1080/09728600.2023.2187960	https://doi.org/10.1080/09728600.2023.2187960	PUNCT
cana-1543	218	1	[	[	X
cana-1543	218	2	5	5	X
cana-1543	218	3	]	]	X
cana-1543	218	4	hamada	hamada	PROPN
cana-1543	218	5	t	t	PROPN
cana-1543	218	6	,	,	PUNCT
cana-1543	218	7	yoshimura	yoshimura	VERB
cana-1543	218	8	i	i	PROPN
cana-1543	218	9	,	,	PUNCT
cana-1543	218	10	traversability	traversability	NOUN
cana-1543	218	11	and	and	CCONJ
cana-1543	218	12	connectivity	connectivity	NOUN
cana-1543	218	13	of	of	ADP
cana-1543	218	14	the	the	DET
cana-1543	218	15	middle	middle	ADJ
cana-1543	218	16	graph	graph	NOUN
cana-1543	218	17	of	of	ADP
cana-1543	218	18	a	a	DET
cana-1543	218	19	graph	graph	NOUN
cana-1543	218	20	,	,	PUNCT
cana-1543	218	21	[	[	X
cana-1543	218	22	6	6	NUM
cana-1543	218	23	]	]	SYM
cana-1543	218	24	discrete	discrete	ADJ
cana-1543	218	25	mathematics	mathematic	NOUN
cana-1543	218	26	,	,	PUNCT
cana-1543	218	27	14(1976):247–256	14(1976):247–256	NUM
cana-1543	218	28	.	.	PUNCT
cana-1543	219	1	https://doi.org/10.1016/0012-365x(76)90037-6	https://doi.org/10.1016/0012-365x(76)90037-6	PROPN
cana-1543	220	1	[	[	X
cana-1543	220	2	7	7	X
cana-1543	220	3	]	]	X
cana-1543	220	4	l.o	l.o	PROPN
cana-1543	220	5	.	.	PROPN
cana-1543	220	6	harjito	harjito	PROPN
cana-1543	220	7	dafik	dafik	PROPN
cana-1543	220	8	a	a	DET
cana-1543	220	9	i.	i.	PROPN
cana-1543	220	10	kristiana	kristiana	PROPN
cana-1543	220	11	r.	r.	PROPN
cana-1543	220	12	m.prihandini	m.prihandini	PROPN
cana-1543	220	13	,	,	PUNCT
cana-1543	220	14	r.	r.	PROPN
cana-1543	220	15	alfarisi	alfarisi	PROPN
cana-1543	220	16	,	,	PUNCT
cana-1543	220	17	on	on	ADP
cana-1543	220	18	r	r	NOUN
cana-1543	220	19	-	-	PUNCT
cana-1543	220	20	dynamic	dynamic	ADJ
cana-1543	220	21	vertex	vertex	NOUN
cana-1543	220	22	coloring	coloring	NOUN
cana-1543	220	23	of	of	ADP
cana-1543	220	24	line	line	NOUN
cana-1543	220	25	,	,	PUNCT
cana-1543	220	26	middle	middle	ADJ
cana-1543	220	27	,	,	PUNCT
cana-1543	220	28	total	total	NOUN
cana-1543	220	29	of	of	ADP
cana-1543	220	30	lobster	lobster	NOUN
cana-1543	220	31	graph	graph	NOUN
cana-1543	220	32	,	,	PUNCT
cana-1543	220	33	journal	journal	NOUN
cana-1543	220	34	of	of	ADP
cana-1543	220	35	physics	physics	PROPN
cana-1543	220	36	:	:	PUNCT
cana-1543	220	37	conference	conference	NOUN
cana-1543	220	38	series	series	NOUN
cana-1543	220	39	,	,	PUNCT
cana-1543	220	40	1465	1465	NUM
cana-1543	220	41	(	(	PUNCT
cana-1543	220	42	2020	2020	NUM
cana-1543	220	43	)	)	PUNCT
cana-1543	220	44	,	,	PUNCT
cana-1543	220	45	012014	012014	NUM
cana-1543	220	46	.	.	PUNCT
cana-1543	221	1	doi	doi	PROPN
cana-1543	221	2	10.1088/1742	10.1088/1742	NUM
cana-1543	221	3	-	-	SYM
cana-1543	221	4	6596/1465/1/012014	6596/1465/1/012014	PROPN
cana-1543	222	1	[	[	X
cana-1543	222	2	8	8	NUM
cana-1543	222	3	]	]	X
cana-1543	222	4	jayaraman	jayaraman	NOUN
cana-1543	222	5	g	g	PROPN
cana-1543	222	6	and	and	CCONJ
cana-1543	222	7	d.	d.	PROPN
cana-1543	222	8	muthuramakrishnan	muthuramakrishnan	PROPN
cana-1543	222	9	,	,	PUNCT
cana-1543	222	10	total	total	ADJ
cana-1543	222	11	chromatic	chromatic	ADJ
cana-1543	222	12	number	number	NOUN
cana-1543	222	13	of	of	ADP
cana-1543	222	14	double	double	ADJ
cana-1543	222	15	star	star	NOUN
cana-1543	222	16	graph	graph	NOUN
cana-1543	222	17	families	family	NOUN
cana-1543	222	18	,	,	PUNCT
cana-1543	222	19	journal	journal	NOUN
cana-1543	222	20	of	of	ADP
cana-1543	222	21	adv	adv	PROPN
cana-1543	222	22	.	.	PUNCT
cana-1543	222	23	research	research	NOUN
cana-1543	222	24	in	in	ADP
cana-1543	222	25	dynamics	dynamic	NOUN
cana-1543	222	26	and	and	CCONJ
cana-1543	222	27	control	control	NOUN
cana-1543	222	28	systems	system	NOUN
cana-1543	222	29	,	,	PUNCT
cana-1543	222	30	10(5	10(5	NUM
cana-1543	222	31	)	)	PUNCT
cana-1543	222	32	,	,	PUNCT
cana-1543	222	33	2018	2018	NUM
cana-1543	222	34	,	,	PUNCT
cana-1543	222	35	pp	pp	ADV
cana-1543	222	36	631	631	NUM
cana-1543	222	37	-	-	SYM
cana-1543	222	38	635	635	NUM
cana-1543	222	39	.	.	PUNCT
cana-1543	223	1	[	[	X
cana-1543	223	2	9	9	NUM
cana-1543	223	3	]	]	PUNCT
cana-1543	223	4	kostochka	kostochka	PROPN
cana-1543	223	5	a.v	a.v	PROPN
cana-1543	223	6	,	,	PUNCT
cana-1543	223	7	the	the	DET
cana-1543	223	8	total	total	ADJ
cana-1543	223	9	chromatic	chromatic	ADJ
cana-1543	223	10	number	number	NOUN
cana-1543	223	11	of	of	ADP
cana-1543	223	12	any	any	DET
cana-1543	223	13	multigraph	multigraph	NOUN
cana-1543	223	14	with	with	ADP
cana-1543	223	15	maximum	maximum	ADJ
cana-1543	223	16	degree	degree	NOUN
cana-1543	223	17	five	five	NUM
cana-1543	223	18	is	be	AUX
cana-1543	223	19	atmost	atmost	ADJ
cana-1543	223	20	seven	seven	NUM
cana-1543	223	21	,	,	PUNCT
cana-1543	223	22	discrete	discrete	ADJ
cana-1543	223	23	math	math	NOUN
cana-1543	223	24	,	,	PUNCT
cana-1543	223	25	1996	1996	NUM
cana-1543	223	26	,	,	PUNCT
cana-1543	223	27	162	162	NUM
cana-1543	223	28	:	:	SYM
cana-1543	223	29	199	199	NUM
cana-1543	223	30	-	-	SYM
cana-1543	223	31	214	214	NUM
cana-1543	223	32	.	.	PUNCT
cana-1543	224	1	https://doi.org/10.1016/0012-365x(95)00286-6	https://doi.org/10.1016/0012-365x(95)00286-6	PROPN
cana-1543	225	1	[	[	X
cana-1543	225	2	10	10	NUM
cana-1543	225	3	]	]	X
cana-1543	225	4	kostochka	kostochka	PROPN
cana-1543	225	5	a.v	a.v	PROPN
cana-1543	225	6	,	,	PUNCT
cana-1543	225	7	the	the	DET
cana-1543	225	8	total	total	ADJ
cana-1543	225	9	coloring	coloring	NOUN
cana-1543	225	10	of	of	ADP
cana-1543	225	11	a	a	DET
cana-1543	225	12	multigraph	multigraph	NOUN
cana-1543	225	13	with	with	ADP
cana-1543	225	14	maximum	maximum	ADJ
cana-1543	225	15	degree	degree	NOUN
cana-1543	225	16	4	4	NUM
cana-1543	225	17	,	,	PUNCT
cana-1543	225	18	discrete	discrete	ADJ
cana-1543	225	19	math	math	NOUN
cana-1543	225	20	,	,	PUNCT
cana-1543	225	21	1977	1977	NUM
cana-1543	225	22	,	,	PUNCT
cana-1543	225	23	17	17	NUM
cana-1543	225	24	:	:	SYM
cana-1543	225	25	161	161	NUM
cana-1543	225	26	-	-	SYM
cana-1543	225	27	163	163	NUM
cana-1543	225	28	.	.	PUNCT
cana-1543	226	1	https://doi.org/10.1016/0012-365x(77)90146-7	https://doi.org/10.1016/0012-365x(77)90146-7	PROPN
cana-1543	226	2	[	[	X
cana-1543	226	3	11	11	NUM
cana-1543	226	4	]	]	X
cana-1543	226	5	kowalik	kowalik	PROPN
cana-1543	226	6	l	l	PROPN
cana-1543	226	7	,	,	PUNCT
cana-1543	226	8	sereni	sereni	ADJ
cana-1543	226	9	js	js	PROPN
cana-1543	226	10	,	,	PUNCT
cana-1543	226	11	skrekovski	skrekovski	PROPN
cana-1543	226	12	r	r	NOUN
cana-1543	226	13	,	,	PUNCT
cana-1543	226	14	total	total	ADJ
cana-1543	226	15	coloring	coloring	NOUN
cana-1543	226	16	of	of	ADP
cana-1543	226	17	plane	plane	NOUN
cana-1543	226	18	graph	graph	NOUN
cana-1543	226	19	with	with	ADP
cana-1543	226	20	maximum	maximum	ADJ
cana-1543	226	21	degree	degree	NOUN
cana-1543	226	22	nine	nine	NUM
cana-1543	226	23	,	,	PUNCT
cana-1543	226	24	siam	siam	PROPN
cana-1543	226	25	j	j	PROPN
cana-1543	226	26	discrete	discrete	ADJ
cana-1543	226	27	math	math	NOUN
cana-1543	226	28	,	,	PUNCT
cana-1543	226	29	2008	2008	NUM
cana-1543	226	30	,	,	PUNCT
cana-1543	226	31	22	22	NUM
cana-1543	226	32	:	:	SYM
cana-1543	226	33	1462	1462	NUM
cana-1543	226	34	-	-	SYM
cana-1543	226	35	1479	1479	NUM
cana-1543	226	36	.	.	PUNCT
cana-1543	226	37	⟨10.1137/070688389⟩⟨hal-00487320⟩	⟨10.1137/070688389⟩⟨hal-00487320⟩	PUNCT
cana-1543	227	1	[	[	X
cana-1543	227	2	12	12	NUM
cana-1543	227	3	]	]	X
cana-1543	227	4	muthuramakrishnan	muthuramakrishnan	NOUN
cana-1543	227	5	.	.	PUNCT
cana-1543	228	1	d	d	NOUN
cana-1543	228	2	and	and	CCONJ
cana-1543	228	3	jayaraman	jayaraman	NOUN
cana-1543	228	4	.	.	PUNCT
cana-1543	229	1	g	g	NOUN
cana-1543	229	2	,	,	PUNCT
cana-1543	229	3	total	total	ADJ
cana-1543	229	4	chromatic	chromatic	ADJ
cana-1543	229	5	number	number	NOUN
cana-1543	229	6	of	of	ADP
cana-1543	229	7	star	star	NOUN
cana-1543	229	8	and	and	CCONJ
cana-1543	229	9	bistar	bistar	PROPN
cana-1543	229	10	graphs	graph	NOUN
cana-1543	229	11	,	,	PUNCT
cana-1543	229	12	international	international	ADJ
cana-1543	229	13	journal	journal	NOUN
cana-1543	229	14	of	of	ADP
cana-1543	229	15	pure	pure	ADJ
cana-1543	229	16	and	and	CCONJ
cana-1543	229	17	applied	applied	ADJ
cana-1543	229	18	mathematics	mathematic	NOUN
cana-1543	229	19	,	,	PUNCT
cana-1543	229	20	117	117	NUM
cana-1543	229	21	(	(	PUNCT
cana-1543	229	22	21	21	NUM
cana-1543	229	23	)	)	PUNCT
cana-1543	229	24	2017	2017	NUM
cana-1543	229	25	,	,	PUNCT
cana-1543	229	26	699	699	NUM
cana-1543	229	27	-	-	SYM
cana-1543	229	28	708	708	NUM
cana-1543	229	29	.	.	PUNCT
cana-1543	229	30	url	url	PROPN
cana-1543	229	31	:	:	PUNCT
cana-1543	229	32	http://www.ijpam.eu	http://www.ijpam.eu	NOUN
cana-1543	230	1	[	[	X
cana-1543	230	2	13	13	NUM
cana-1543	230	3	]	]	X
cana-1543	230	4	muthuramakrishnan	muthuramakrishnan	NOUN
cana-1543	230	5	.	.	PUNCT
cana-1543	231	1	d	d	NOUN
cana-1543	231	2	and	and	CCONJ
cana-1543	231	3	jayaraman	jayaraman	NOUN
cana-1543	231	4	.	.	PUNCT
cana-1543	232	1	g	g	NOUN
cana-1543	232	2	,	,	PUNCT
cana-1543	232	3	total	total	ADJ
cana-1543	232	4	coloring	coloring	NOUN
cana-1543	232	5	of	of	ADP
cana-1543	232	6	splitting	splitting	NOUN
cana-1543	232	7	graph	graph	NOUN
cana-1543	232	8	of	of	ADP
cana-1543	232	9	path	path	NOUN
cana-1543	232	10	,	,	PUNCT
cana-1543	232	11	cycle	cycle	NOUN
cana-1543	232	12	and	and	CCONJ
cana-1543	232	13	star	star	NOUN
cana-1543	232	14	graphs	graphs	PROPN
cana-1543	232	15	international	international	ADJ
cana-1543	232	16	journal	journal	NOUN
cana-1543	232	17	of	of	ADP
cana-1543	232	18	mathematics	mathematic	NOUN
cana-1543	232	19	and	and	CCONJ
cana-1543	232	20	its	its	PRON
cana-1543	232	21	applications	application	NOUN
cana-1543	232	22	,	,	PUNCT
cana-1543	232	23	6(1	6(1	NUM
cana-1543	232	24	-	-	SYM
cana-1543	232	25	d	d	NOUN
cana-1543	232	26	)	)	PUNCT
cana-1543	232	27	2018	2018	NUM
cana-1543	232	28	,	,	PUNCT
cana-1543	232	29	659	659	NUM
cana-1543	232	30	-	-	SYM
cana-1543	232	31	664	664	NUM
cana-1543	232	32	.	.	PUNCT
cana-1543	232	33	https://ijmaa.in/index.php/ijmaa/article/view/1124	https://ijmaa.in/index.php/ijmaa/article/view/1124	PUNCT
cana-1543	233	1	[	[	X
cana-1543	233	2	14	14	NUM
cana-1543	233	3	]	]	PUNCT
cana-1543	233	4	punitha	punitha	NOUN
cana-1543	233	5	.	.	PUNCT
cana-1543	234	1	a	a	PRON
cana-1543	234	2	and	and	CCONJ
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cana-1543	234	4	.	.	PUNCT
cana-1543	235	1	g	g	NOUN
cana-1543	235	2	,	,	PUNCT
cana-1543	235	3	total	total	ADJ
cana-1543	235	4	coloring	coloring	NOUN
cana-1543	235	5	middle	middle	ADJ
cana-1543	235	6	graph	graph	NOUN
cana-1543	235	7	of	of	ADP
cana-1543	235	8	certain	certain	ADJ
cana-1543	235	9	snake	snake	NOUN
cana-1543	235	10	graph	graph	NOUN
cana-1543	235	11	families	family	NOUN
cana-1543	235	12	,	,	PUNCT
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cana-1543	235	20	42(2	42(2	PROPN
cana-1543	235	21	)	)	PUNCT
cana-1543	235	22	,	,	PUNCT
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cana-1543	235	24	,	,	PUNCT
cana-1543	235	25	353	353	NUM
cana-1543	235	26	-	-	SYM
cana-1543	235	27	366	366	NUM
cana-1543	235	28	.	.	PUNCT
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cana-1543	236	2	[	[	X
cana-1543	236	3	15	15	NUM
cana-1543	236	4	]	]	X
cana-1543	236	5	punitha	punitha	NOUN
cana-1543	236	6	.	.	PUNCT
cana-1543	237	1	a	a	PRON
cana-1543	237	2	and	and	CCONJ
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cana-1543	237	4	.	.	PUNCT
cana-1543	238	1	g	g	NOUN
cana-1543	238	2	,	,	PUNCT
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cana-1543	238	6	chromatic	chromatic	ADJ
cana-1543	238	7	number	number	NOUN
cana-1543	238	8	for	for	ADP
cana-1543	238	9	certain	certain	ADJ
cana-1543	238	10	convex	convex	NOUN
cana-1543	238	11	polytope	polytope	NOUN
cana-1543	238	12	graphs	graph	NOUN
cana-1543	238	13	,	,	PUNCT
cana-1543	238	14	journal	journal	NOUN
cana-1543	238	15	of	of	ADP
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cana-1543	238	17	mathematics	mathematics	PROPN
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cana-1543	238	25	-	-	SYM
cana-1543	238	26	582	582	NUM
cana-1543	238	27	.	.	PUNCT
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cana-1543	239	3	16	16	NUM
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cana-1543	239	6	m	m	PROPN
cana-1543	239	7	,	,	PUNCT
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cana-1543	239	10	total	total	ADJ
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cana-1543	239	12	of	of	ADP
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cana-1543	239	14	graphs	graph	NOUN
cana-1543	239	15	,	,	PUNCT
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cana-1543	239	21	,	,	PUNCT
cana-1543	239	22	9:396	9:396	NUM
cana-1543	239	23	-	-	SYM
cana-1543	239	24	402	402	NUM
cana-1543	239	25	.	.	PUNCT
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cana-1543	240	11	of	of	ADP
cana-1543	240	12	a	a	DET
cana-1543	240	13	graph	graph	NOUN
cana-1543	240	14	,	,	PUNCT
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cana-1543	240	17	math	math	PROPN
cana-1543	240	18	soc	soc	PROPN
cana-1543	240	19	,	,	PUNCT
cana-1543	240	20	1971	1971	NUM
cana-1543	240	21	,	,	PUNCT
cana-1543	240	22	3:405	3:405	NUM
cana-1543	240	23	-	-	SYM
cana-1543	240	24	408	408	NUM
cana-1543	240	25	.	.	PUNCT
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cana-1543	242	2	18	18	NUM
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cana-1543	242	5	v.g	v.g	PROPN
cana-1543	242	6	,	,	PUNCT
cana-1543	242	7	some	some	DET
cana-1543	242	8	unsolved	unsolved	ADJ
cana-1543	242	9	problems	problem	NOUN
cana-1543	242	10	in	in	ADP
cana-1543	242	11	graph	graph	NOUN
cana-1543	242	12	theory	theory	NOUN
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cana-1543	242	21	)	)	PUNCT
cana-1543	242	22	,	,	PUNCT
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cana-1543	242	24	-	-	PUNCT
cana-1543	242	25	134(in	134(in	NUM
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cana-1543	242	28	and	and	CCONJ
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cana-1543	242	30	russian	russian	ADJ
cana-1543	242	31	mathematical	mathematical	ADJ
cana-1543	242	32	survey	survey	NOUN
cana-1543	242	33	,	,	PUNCT
cana-1543	242	34	23(6	23(6	NUM
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cana-1543	242	36	(	(	PUNCT
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cana-1543	242	38	)	)	PUNCT
cana-1543	242	39	,	,	PUNCT
cana-1543	242	40	125	125	NUM
cana-1543	242	41	-	-	SYM
cana-1543	242	42	141	141	NUM
cana-1543	242	43	.	.	PUNCT
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cana-1543	243	2	/	/	SYM
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cana-1543	244	11	graphs	graph	NOUN
cana-1543	244	12	.	.	PUNCT
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cana-1543	245	2	lecture	lecture	NOUN
cana-1543	245	3	notes	note	NOUN
cana-1543	245	4	in	in	ADP
cana-1543	245	5	mathematics	mathematic	NOUN
cana-1543	245	6	;	;	PUNCT
cana-1543	245	7	springer	springer	NOUN
cana-1543	245	8	:	:	PUNCT
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cana-1543	245	14	;	;	PUNCT
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cana-1543	245	16	1623	1623	NUM
cana-1543	245	17	.	.	PUNCT
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