id	sid	tid	token	lemma	pos
cana-2601	1	1	communications	communication	NOUN
cana-2601	1	2	on	on	ADP
cana-2601	1	3	applied	apply	VERB
cana-2601	1	4	nonlinear	nonlinear	ADJ
cana-2601	1	5	analysis	analysis	NOUN
cana-2601	1	6	issn	issn	NOUN
cana-2601	1	7	:	:	PUNCT
cana-2601	1	8	1074	1074	NUM
cana-2601	1	9	-	-	PUNCT
cana-2601	1	10	133x	133x	NUM
cana-2601	1	11	vol	vol	NOUN
cana-2601	1	12	32	32	NUM
cana-2601	1	13	no	no	NOUN
cana-2601	1	14	.	.	PUNCT
cana-2601	2	1	3s	3s	NUM
cana-2601	2	2	(	(	PUNCT
cana-2601	2	3	2025	2025	NUM
cana-2601	2	4	)	)	PUNCT
cana-2601	2	5	212	212	NUM
cana-2601	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2601	2	7	locally	locally	ADV
cana-2601	2	8	harmonious	harmonious	ADJ
cana-2601	2	9	chromatic	chromatic	ADJ
cana-2601	2	10	number	number	NOUN
cana-2601	2	11	of	of	ADP
cana-2601	2	12	certain	certain	ADJ
cana-2601	2	13	tree	tree	NOUN
cana-2601	2	14	-	-	PUNCT
cana-2601	2	15	structured	structure	VERB
cana-2601	2	16	networks	network	NOUN
cana-2601	2	17	m.	m.	NOUN
cana-2601	2	18	siva1	siva1	PROPN
cana-2601	2	19	,	,	PUNCT
cana-2601	2	20	k.	k.	PROPN
cana-2601	2	21	lenin	lenin	PROPN
cana-2601	2	22	muthu	muthu	PROPN
cana-2601	2	23	kumaran1	kumaran1	PROPN
cana-2601	2	24	,	,	PUNCT
cana-2601	2	25	a	a	DET
cana-2601	2	26	nelson2	nelson2	NOUN
cana-2601	2	27	,	,	PUNCT
cana-2601	2	28	k.	k.	PROPN
cana-2601	2	29	suresh3	suresh3	PROPN
cana-2601	2	30	,	,	PUNCT
cana-2601	2	31	*	*	PROPN
cana-2601	2	32	,	,	PUNCT
cana-2601	2	33	s.	s.	PROPN
cana-2601	2	34	arul	arul	PROPN
cana-2601	2	35	amirtha	amirtha	PROPN
cana-2601	2	36	raja3	raja3	PROPN
cana-2601	3	1	1department	1department	NUM
cana-2601	3	2	of	of	ADP
cana-2601	3	3	mathematics	mathematic	NOUN
cana-2601	3	4	,	,	PUNCT
cana-2601	3	5	shanmuga	shanmuga	PROPN
cana-2601	3	6	industries	industry	NOUN
cana-2601	3	7	arts	art	NOUN
cana-2601	3	8	and	and	CCONJ
cana-2601	3	9	science	science	PROPN
cana-2601	3	10	college	college	PROPN
cana-2601	3	11	,	,	PUNCT
cana-2601	3	12	tiruvannamalai	tiruvannamalai	PROPN
cana-2601	3	13	606603	606603	NUM
cana-2601	4	1	2department	2department	NUM
cana-2601	4	2	of	of	ADP
cana-2601	4	3	mathematics	mathematic	NOUN
cana-2601	4	4	,	,	PUNCT
cana-2601	4	5	panimalar	panimalar	ADJ
cana-2601	4	6	engineering	engineering	NOUN
cana-2601	4	7	college	college	NOUN
cana-2601	4	8	,	,	PUNCT
cana-2601	4	9	chennai	chennai	PROPN
cana-2601	4	10	600123	600123	NUM
cana-2601	4	11	.	.	PUNCT
cana-2601	5	1	3department	3department	NUM
cana-2601	5	2	of	of	ADP
cana-2601	5	3	mathematics	mathematics	PROPN
cana-2601	5	4	,	,	PUNCT
cana-2601	5	5	st	st	PROPN
cana-2601	5	6	.	.	PROPN
cana-2601	5	7	joseph	joseph	PROPN
cana-2601	5	8	's	's	PART
cana-2601	5	9	college	college	PROPN
cana-2601	5	10	of	of	ADP
cana-2601	5	11	engineering	engineering	PROPN
cana-2601	5	12	,	,	PUNCT
cana-2601	5	13	omr	omr	PROPN
cana-2601	5	14	,	,	PUNCT
cana-2601	5	15	chennai	chennai	NOUN
cana-2601	5	16	600119	600119	NUM
cana-2601	5	17	∗corresponding	∗corresponde	VERB
cana-2601	5	18	author	author	NOUN
cana-2601	5	19	:	:	PUNCT
cana-2601	5	20	dhivasuresh@gmail.com	dhivasuresh@gmail.com	X
cana-2601	6	1	article	article	NOUN
cana-2601	6	2	history	history	NOUN
cana-2601	6	3	:	:	PUNCT
cana-2601	6	4	received	receive	VERB
cana-2601	6	5	:	:	PUNCT
cana-2601	6	6	24	24	NUM
cana-2601	6	7	-	-	PUNCT
cana-2601	6	8	09	09	NUM
cana-2601	6	9	-	-	PUNCT
cana-2601	6	10	2024	2024	NUM
cana-2601	6	11	revised	revise	VERB
cana-2601	6	12	:	:	PUNCT
cana-2601	6	13	04	04	NUM
cana-2601	6	14	-	-	SYM
cana-2601	6	15	11	11	NUM
cana-2601	6	16	-	-	PUNCT
cana-2601	6	17	2024	2024	NUM
cana-2601	6	18	accepted	accept	VERB
cana-2601	6	19	:	:	PUNCT
cana-2601	6	20	19	19	NUM
cana-2601	6	21	-	-	SYM
cana-2601	6	22	11	11	NUM
cana-2601	6	23	-	-	PUNCT
cana-2601	6	24	2024	2024	NUM
cana-2601	6	25	abstract	abstract	NOUN
cana-2601	6	26	:	:	PUNCT
cana-2601	6	27	graph	graph	NOUN
cana-2601	6	28	coloring	coloring	NOUN
cana-2601	6	29	is	be	AUX
cana-2601	6	30	one	one	NUM
cana-2601	6	31	of	of	ADP
cana-2601	6	32	the	the	DET
cana-2601	6	33	oldest	old	ADJ
cana-2601	6	34	and	and	CCONJ
cana-2601	6	35	best	well	ADV
cana-2601	6	36	-	-	PUNCT
cana-2601	6	37	known	know	VERB
cana-2601	6	38	problems	problem	NOUN
cana-2601	6	39	of	of	ADP
cana-2601	6	40	graph	graph	NOUN
cana-2601	6	41	theory	theory	NOUN
cana-2601	6	42	.	.	PUNCT
cana-2601	7	1	the	the	DET
cana-2601	7	2	locally	locally	ADV
cana-2601	7	3	harmonious	harmonious	ADJ
cana-2601	7	4	coloring	coloring	NOUN
cana-2601	7	5	of	of	ADP
cana-2601	7	6	g	g	PROPN
cana-2601	7	7	is	be	AUX
cana-2601	7	8	a	a	DET
cana-2601	7	9	proper	proper	ADJ
cana-2601	7	10	vertex	vertex	NOUN
cana-2601	7	11	coloring	coloring	NOUN
cana-2601	7	12	in	in	ADP
cana-2601	7	13	which	which	PRON
cana-2601	7	14	adjacent	adjacent	ADJ
cana-2601	7	15	edges	edge	NOUN
cana-2601	7	16	receive	receive	VERB
cana-2601	7	17	different	different	ADJ
cana-2601	7	18	color	color	NOUN
cana-2601	7	19	pairs	pair	NOUN
cana-2601	7	20	[	[	X
cana-2601	7	21	3	3	NUM
cana-2601	7	22	]	]	PUNCT
cana-2601	7	23	.	.	PUNCT
cana-2601	8	1	in	in	ADP
cana-2601	8	2	another	another	DET
cana-2601	8	3	way	way	NOUN
cana-2601	8	4	,	,	PUNCT
cana-2601	8	5	all	all	DET
cana-2601	8	6	the	the	DET
cana-2601	8	7	vertices	vertex	NOUN
cana-2601	8	8	in	in	ADP
cana-2601	8	9	n	n	PROPN
cana-2601	8	10	[	[	X
cana-2601	8	11	v	v	NOUN
cana-2601	8	12	]	]	PUNCT
cana-2601	8	13	receive	receive	VERB
cana-2601	8	14	different	different	ADJ
cana-2601	8	15	colors	color	NOUN
cana-2601	8	16	for	for	ADP
cana-2601	8	17	all	all	DET
cana-2601	8	18	v	v	NOUN
cana-2601	8	19	in	in	ADP
cana-2601	8	20	g.	g.	PROPN
cana-2601	8	21	the	the	DET
cana-2601	8	22	minimum	minimum	ADJ
cana-2601	8	23	number	number	NOUN
cana-2601	8	24	of	of	ADP
cana-2601	8	25	colors	color	NOUN
cana-2601	8	26	required	require	VERB
cana-2601	8	27	to	to	PART
cana-2601	8	28	obtain	obtain	VERB
cana-2601	8	29	a	a	DET
cana-2601	8	30	locally	locally	ADV
cana-2601	8	31	harmonious	harmonious	ADJ
cana-2601	8	32	coloring	coloring	NOUN
cana-2601	8	33	of	of	ADP
cana-2601	8	34	a	a	DET
cana-2601	8	35	graph	graph	NOUN
cana-2601	8	36	g	g	NOUN
cana-2601	8	37	is	be	AUX
cana-2601	8	38	called	call	VERB
cana-2601	8	39	the	the	DET
cana-2601	8	40	locally	locally	ADV
cana-2601	8	41	harmonious	harmonious	ADJ
cana-2601	8	42	chromatic	chromatic	ADJ
cana-2601	8	43	number	number	NOUN
cana-2601	8	44	of	of	ADP
cana-2601	8	45	g	g	NOUN
cana-2601	8	46	and	and	CCONJ
cana-2601	8	47	is	be	AUX
cana-2601	8	48	denoted	denote	VERB
cana-2601	8	49	by	by	ADP
cana-2601	8	50	h1(g	h1(g	PROPN
cana-2601	8	51	)	)	PUNCT
cana-2601	8	52	.	.	PUNCT
cana-2601	9	1	in	in	ADP
cana-2601	9	2	this	this	DET
cana-2601	9	3	paper	paper	NOUN
cana-2601	9	4	,	,	PUNCT
cana-2601	9	5	we	we	PRON
cana-2601	9	6	investigate	investigate	VERB
cana-2601	9	7	the	the	DET
cana-2601	9	8	locally	locally	ADV
cana-2601	9	9	harmonious	harmonious	ADJ
cana-2601	9	10	chromatic	chromatic	ADJ
cana-2601	9	11	number	number	NOUN
cana-2601	9	12	of	of	ADP
cana-2601	9	13	slim	slim	ADJ
cana-2601	9	14	tree	tree	NOUN
cana-2601	9	15	,	,	PUNCT
cana-2601	9	16	hypertree	hypertree	NOUN
cana-2601	9	17	,	,	PUNCT
cana-2601	9	18	shuffle	shuffle	NOUN
cana-2601	9	19	hypertree	hypertree	NOUN
cana-2601	9	20	and	and	CCONJ
cana-2601	9	21	l	l	NOUN
cana-2601	9	22	-	-	ADJ
cana-2601	9	23	complete	complete	ADJ
cana-2601	9	24	binary	binary	ADJ
cana-2601	9	25	tree	tree	NOUN
cana-2601	9	26	.	.	PUNCT
cana-2601	10	1	keywords	keyword	NOUN
cana-2601	10	2	:	:	PUNCT
cana-2601	10	3	coloring	color	VERB
cana-2601	10	4	;	;	PUNCT
cana-2601	10	5	locally	locally	ADV
cana-2601	10	6	harmonious	harmonious	ADJ
cana-2601	10	7	coloring	coloring	NOUN
cana-2601	10	8	;	;	PUNCT
cana-2601	10	9	slim	slim	ADJ
cana-2601	10	10	tree	tree	NOUN
cana-2601	10	11	;	;	PUNCT
cana-2601	10	12	hypertree	hypertree	NOUN
cana-2601	10	13	;	;	PUNCT
cana-2601	10	14	shuffle	shuffle	NOUN
cana-2601	10	15	hypertree	hypertree	NOUN
cana-2601	10	16	;	;	PUNCT
cana-2601	10	17	lcomplete	lcomplete	VERB
cana-2601	10	18	binary	binary	NOUN
cana-2601	10	19	tree	tree	NOUN
cana-2601	10	20	.	.	PUNCT
cana-2601	11	1	1	1	X
cana-2601	11	2	.	.	X
cana-2601	11	3	introduction	introduction	NOUN
cana-2601	11	4	the	the	DET
cana-2601	11	5	introduction	introduction	NOUN
cana-2601	11	6	of	of	ADP
cana-2601	11	7	a	a	DET
cana-2601	11	8	method	method	NOUN
cana-2601	11	9	for	for	ADP
cana-2601	11	10	very	very	ADV
cana-2601	11	11	high	high	ADJ
cana-2601	11	12	scale	scale	NOUN
cana-2601	11	13	integration	integration	NOUN
cana-2601	11	14	,	,	PUNCT
cana-2601	11	15	which	which	PRON
cana-2601	11	16	will	will	AUX
cana-2601	11	17	allow	allow	VERB
cana-2601	11	18	the	the	DET
cana-2601	11	19	manufacture	manufacture	NOUN
cana-2601	11	20	of	of	ADP
cana-2601	11	21	a	a	DET
cana-2601	11	22	single	single	ADJ
cana-2601	11	23	silicon	silicon	NOUN
cana-2601	11	24	chip	chip	NOUN
cana-2601	11	25	with	with	ADP
cana-2601	11	26	one	one	NUM
cana-2601	11	27	million	million	NUM
cana-2601	11	28	active	active	ADJ
cana-2601	11	29	devices	device	NOUN
cana-2601	11	30	in	in	ADP
cana-2601	11	31	five	five	NUM
cana-2601	11	32	years	year	NOUN
cana-2601	11	33	,	,	PUNCT
cana-2601	11	34	has	have	AUX
cana-2601	11	35	also	also	ADV
cana-2601	11	36	changed	change	VERB
cana-2601	11	37	the	the	DET
cana-2601	11	38	limits	limit	NOUN
cana-2601	11	39	on	on	ADP
cana-2601	11	40	a	a	DET
cana-2601	11	41	multiprocessor	multiprocessor	NOUN
cana-2601	11	42	interconnection	interconnection	NOUN
cana-2601	11	43	network	network	NOUN
cana-2601	11	44	.	.	PUNCT
cana-2601	12	1	with	with	ADP
cana-2601	12	2	advancements	advancement	NOUN
cana-2601	12	3	in	in	ADP
cana-2601	12	4	technology	technology	NOUN
cana-2601	12	5	,	,	PUNCT
cana-2601	12	6	active	active	ADJ
cana-2601	12	7	devices	device	NOUN
cana-2601	12	8	are	be	AUX
cana-2601	12	9	becoming	become	VERB
cana-2601	12	10	smaller	small	ADJ
cana-2601	12	11	,	,	PUNCT
cana-2601	12	12	faster	fast	ADV
cana-2601	12	13	,	,	PUNCT
cana-2601	12	14	and	and	CCONJ
cana-2601	12	15	consuming	consume	VERB
cana-2601	12	16	less	less	ADJ
cana-2601	12	17	power	power	NOUN
cana-2601	12	18	.	.	PUNCT
cana-2601	13	1	the	the	DET
cana-2601	13	2	speed	speed	NOUN
cana-2601	13	3	gap	gap	NOUN
cana-2601	13	4	between	between	ADP
cana-2601	13	5	signals	signal	NOUN
cana-2601	13	6	that	that	PRON
cana-2601	13	7	are	be	AUX
cana-2601	13	8	wholly	wholly	ADV
cana-2601	13	9	internal	internal	ADJ
cana-2601	13	10	to	to	ADP
cana-2601	13	11	the	the	DET
cana-2601	13	12	device	device	NOUN
cana-2601	13	13	and	and	CCONJ
cana-2601	13	14	those	those	PRON
cana-2601	13	15	that	that	PRON
cana-2601	13	16	must	must	AUX
cana-2601	13	17	transit	transit	VERB
cana-2601	13	18	through	through	ADP
cana-2601	13	19	package	package	NOUN
cana-2601	13	20	pins	pin	NOUN
cana-2601	13	21	,	,	PUNCT
cana-2601	13	22	on	on	ADP
cana-2601	13	23	the	the	DET
cana-2601	13	24	other	other	ADJ
cana-2601	13	25	hand	hand	NOUN
cana-2601	13	26	,	,	PUNCT
cana-2601	13	27	is	be	AUX
cana-2601	13	28	expanding	expand	VERB
cana-2601	13	29	.	.	PUNCT
cana-2601	14	1	consequently	consequently	ADV
cana-2601	14	2	,	,	PUNCT
cana-2601	14	3	a	a	DET
cana-2601	14	4	good	good	ADJ
cana-2601	14	5	vlsi	vlsi	PROPN
cana-2601	14	6	building	building	NOUN
cana-2601	14	7	block	block	NOUN
cana-2601	14	8	could	could	AUX
cana-2601	14	9	be	be	AUX
cana-2601	14	10	a	a	DET
cana-2601	14	11	single	single	ADJ
cana-2601	14	12	integrated	integrate	VERB
cana-2601	14	13	circuit	circuit	NOUN
cana-2601	14	14	standalone	standalone	ADJ
cana-2601	14	15	device	device	NOUN
cana-2601	14	16	[	[	X
cana-2601	14	17	10	10	NUM
cana-2601	14	18	]	]	PUNCT
cana-2601	14	19	.	.	PUNCT
cana-2601	15	1	later	later	ADV
cana-2601	15	2	,	,	PUNCT
cana-2601	15	3	a	a	DET
cana-2601	15	4	wide	wide	ADJ
cana-2601	15	5	range	range	NOUN
cana-2601	15	6	of	of	ADP
cana-2601	15	7	networks	network	NOUN
cana-2601	15	8	,	,	PUNCT
cana-2601	15	9	including	include	VERB
cana-2601	15	10	lattices	lattice	NOUN
cana-2601	15	11	or	or	CCONJ
cana-2601	15	12	trees	tree	NOUN
cana-2601	15	13	,	,	PUNCT
cana-2601	15	14	are	be	AUX
cana-2601	15	15	considered	consider	VERB
cana-2601	15	16	because	because	SCONJ
cana-2601	15	17	these	these	DET
cana-2601	15	18	structures	structure	NOUN
cana-2601	15	19	seem	seem	VERB
cana-2601	15	20	to	to	PART
cana-2601	15	21	be	be	AUX
cana-2601	15	22	appealing	appeal	VERB
cana-2601	15	23	because	because	SCONJ
cana-2601	15	24	the	the	DET
cana-2601	15	25	future	future	ADJ
cana-2601	15	26	computer	computer	NOUN
cana-2601	15	27	systems	system	NOUN
cana-2601	15	28	are	be	AUX
cana-2601	15	29	easily	easily	ADV
cana-2601	15	30	expandable	expandable	ADJ
cana-2601	15	31	.	.	PUNCT
cana-2601	16	1	it	it	PRON
cana-2601	16	2	’s	’	VERB
cana-2601	16	3	not	not	PART
cana-2601	16	4	shocking	shocking	ADJ
cana-2601	16	5	,	,	PUNCT
cana-2601	16	6	then	then	ADV
cana-2601	16	7	,	,	PUNCT
cana-2601	16	8	that	that	SCONJ
cana-2601	16	9	tree	tree	NOUN
cana-2601	16	10	-	-	PUNCT
cana-2601	16	11	structured	structure	VERB
cana-2601	16	12	networks	network	NOUN
cana-2601	16	13	have	have	AUX
cana-2601	16	14	recently	recently	ADV
cana-2601	16	15	sparked	spark	VERB
cana-2601	16	16	a	a	DET
cana-2601	16	17	lot	lot	NOUN
cana-2601	16	18	of	of	ADP
cana-2601	16	19	interest	interest	NOUN
cana-2601	16	20	.	.	PUNCT
cana-2601	17	1	trees	tree	NOUN
cana-2601	17	2	are	be	AUX
cana-2601	17	3	a	a	DET
cana-2601	17	4	specific	specific	ADJ
cana-2601	17	5	type	type	NOUN
cana-2601	17	6	of	of	ADP
cana-2601	17	7	graph	graph	NOUN
cana-2601	17	8	that	that	PRON
cana-2601	17	9	are	be	AUX
cana-2601	17	10	worth	worth	ADJ
cana-2601	17	11	studying	study	VERB
cana-2601	17	12	if	if	SCONJ
cana-2601	17	13	only	only	ADV
cana-2601	17	14	because	because	SCONJ
cana-2601	17	15	they	they	PRON
cana-2601	17	16	are	be	AUX
cana-2601	17	17	used	use	VERB
cana-2601	17	18	in	in	ADP
cana-2601	17	19	so	so	ADV
cana-2601	17	20	many	many	ADJ
cana-2601	17	21	different	different	ADJ
cana-2601	17	22	domains	domain	NOUN
cana-2601	17	23	of	of	ADP
cana-2601	17	24	practise	practise	NOUN
cana-2601	17	25	and	and	CCONJ
cana-2601	17	26	science	science	NOUN
cana-2601	17	27	.	.	PUNCT
cana-2601	18	1	these	these	DET
cana-2601	18	2	graphs	graph	NOUN
cana-2601	18	3	that	that	PRON
cana-2601	18	4	do	do	AUX
cana-2601	18	5	not	not	PART
cana-2601	18	6	have	have	VERB
cana-2601	18	7	any	any	DET
cana-2601	18	8	cycles	cycle	NOUN
cana-2601	18	9	.	.	PUNCT
cana-2601	19	1	they	they	PRON
cana-2601	19	2	are	be	AUX
cana-2601	19	3	naturally	naturally	ADV
cana-2601	19	4	expandable	expandable	ADJ
cana-2601	19	5	,	,	PUNCT
cana-2601	19	6	and	and	CCONJ
cana-2601	19	7	even	even	ADV
cana-2601	19	8	unbalanced	unbalanced	ADJ
cana-2601	19	9	trees	tree	NOUN
cana-2601	19	10	retain	retain	VERB
cana-2601	19	11	the	the	DET
cana-2601	19	12	majority	majority	NOUN
cana-2601	19	13	of	of	ADP
cana-2601	19	14	the	the	DET
cana-2601	19	15	features	feature	NOUN
cana-2601	19	16	that	that	PRON
cana-2601	19	17	make	make	VERB
cana-2601	19	18	them	they	PRON
cana-2601	19	19	interesting	interesting	ADJ
cana-2601	19	20	.	.	PUNCT
cana-2601	20	1	as	as	ADP
cana-2601	20	2	a	a	DET
cana-2601	20	3	result	result	NOUN
cana-2601	20	4	,	,	PUNCT
cana-2601	20	5	the	the	DET
cana-2601	20	6	package	package	NOUN
cana-2601	20	7	periphery	periphery	NOUN
cana-2601	20	8	is	be	AUX
cana-2601	20	9	still	still	ADV
cana-2601	20	10	another	another	DET
cana-2601	20	11	physical	physical	ADJ
cana-2601	20	12	hindrance	hindrance	NOUN
cana-2601	20	13	,	,	PUNCT
cana-2601	20	14	and	and	CCONJ
cana-2601	20	15	connectivity	connectivity	NOUN
cana-2601	20	16	topologies	topology	NOUN
cana-2601	20	17	with	with	ADP
cana-2601	20	18	few	few	ADJ
cana-2601	20	19	ports	port	NOUN
cana-2601	20	20	per	per	ADP
cana-2601	20	21	node	node	NOUN
cana-2601	20	22	should	should	AUX
cana-2601	20	23	be	be	AUX
cana-2601	20	24	considered	consider	VERB
cana-2601	20	25	.	.	PUNCT
cana-2601	21	1	a	a	DET
cana-2601	21	2	binary	binary	ADJ
cana-2601	21	3	tree	tree	NOUN
cana-2601	21	4	structure	structure	NOUN
cana-2601	21	5	with	with	ADP
cana-2601	21	6	only	only	ADV
cana-2601	21	7	three	three	NUM
cana-2601	21	8	ports	port	NOUN
cana-2601	21	9	per	per	ADP
cana-2601	21	10	node	node	NOUN
cana-2601	21	11	appears	appear	VERB
cana-2601	21	12	to	to	PART
cana-2601	21	13	be	be	AUX
cana-2601	21	14	particularly	particularly	ADV
cana-2601	21	15	suitable	suitable	ADJ
cana-2601	21	16	if	if	SCONJ
cana-2601	21	17	the	the	DET
cana-2601	21	18	number	number	NOUN
cana-2601	21	19	of	of	ADP
cana-2601	21	20	ports	port	NOUN
cana-2601	21	21	per	per	ADP
cana-2601	21	22	node	node	NOUN
cana-2601	21	23	must	must	AUX
cana-2601	21	24	be	be	AUX
cana-2601	21	25	limited	limit	VERB
cana-2601	21	26	to	to	ADP
cana-2601	21	27	a	a	DET
cana-2601	21	28	minimum	minimum	NOUN
cana-2601	21	29	.	.	PUNCT
cana-2601	22	1	additional	additional	ADJ
cana-2601	22	2	links	link	NOUN
cana-2601	22	3	,	,	PUNCT
cana-2601	22	4	on	on	ADP
cana-2601	22	5	the	the	DET
cana-2601	22	6	other	other	ADJ
cana-2601	22	7	hand	hand	NOUN
cana-2601	22	8	,	,	PUNCT
cana-2601	22	9	are	be	AUX
cana-2601	22	10	required	require	VERB
cana-2601	22	11	to	to	PART
cana-2601	22	12	provide	provide	VERB
cana-2601	22	13	redundant	redundant	ADJ
cana-2601	22	14	paths	path	NOUN
cana-2601	22	15	,	,	PUNCT
cana-2601	22	16	which	which	PRON
cana-2601	22	17	are	be	AUX
cana-2601	22	18	communications	communication	NOUN
cana-2601	22	19	on	on	ADP
cana-2601	22	20	applied	apply	VERB
cana-2601	22	21	nonlinear	nonlinear	ADJ
cana-2601	22	22	analysis	analysis	NOUN
cana-2601	22	23	issn	issn	NOUN
cana-2601	22	24	:	:	PUNCT
cana-2601	22	25	1074	1074	NUM
cana-2601	22	26	-	-	PUNCT
cana-2601	22	27	133x	133x	NUM
cana-2601	22	28	vol	vol	NOUN
cana-2601	22	29	32	32	NUM
cana-2601	23	1	no	no	NOUN
cana-2601	23	2	.	.	PUNCT
cana-2601	24	1	3s	3s	NUM
cana-2601	24	2	(	(	PUNCT
cana-2601	24	3	2025	2025	NUM
cana-2601	24	4	)	)	PUNCT
cana-2601	24	5	213	213	NUM
cana-2601	24	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2601	24	7	the	the	DET
cana-2601	24	8	foundation	foundation	NOUN
cana-2601	24	9	for	for	ADP
cana-2601	24	10	a	a	DET
cana-2601	24	11	fault	fault	NOUN
cana-2601	24	12	-	-	PUNCT
cana-2601	24	13	tolerant	tolerant	ADJ
cana-2601	24	14	message	message	NOUN
cana-2601	24	15	routing	routing	NOUN
cana-2601	24	16	system	system	NOUN
cana-2601	24	17	.	.	PUNCT
cana-2601	25	1	these	these	DET
cana-2601	25	2	linkages	linkage	NOUN
cana-2601	25	3	can	can	AUX
cana-2601	25	4	also	also	ADV
cana-2601	25	5	be	be	AUX
cana-2601	25	6	used	use	VERB
cana-2601	25	7	to	to	PART
cana-2601	25	8	reduce	reduce	VERB
cana-2601	25	9	the	the	DET
cana-2601	25	10	average	average	ADJ
cana-2601	25	11	distance	distance	NOUN
cana-2601	25	12	between	between	ADP
cana-2601	25	13	nodes	node	NOUN
cana-2601	25	14	and	and	CCONJ
cana-2601	25	15	ensure	ensure	VERB
cana-2601	25	16	that	that	SCONJ
cana-2601	25	17	message	message	NOUN
cana-2601	25	18	density	density	NOUN
cana-2601	25	19	is	be	AUX
cana-2601	25	20	consistent	consistent	ADJ
cana-2601	25	21	across	across	ADP
cana-2601	25	22	all	all	DET
cana-2601	25	23	routes	route	NOUN
cana-2601	25	24	.	.	PUNCT
cana-2601	26	1	because	because	SCONJ
cana-2601	26	2	of	of	ADP
cana-2601	26	3	their	their	PRON
cana-2601	26	4	simple	simple	ADJ
cana-2601	26	5	routing	routing	NOUN
cana-2601	26	6	algorithms	algorithm	NOUN
cana-2601	26	7	,	,	PUNCT
cana-2601	26	8	the	the	DET
cana-2601	26	9	binary	binary	NOUN
cana-2601	26	10	trees	tree	NOUN
cana-2601	26	11	which	which	PRON
cana-2601	26	12	contain	contain	VERB
cana-2601	26	13	half	half	ADJ
cana-2601	26	14	-	-	PUNCT
cana-2601	26	15	ring	ring	NOUN
cana-2601	26	16	and	and	CCONJ
cana-2601	26	17	full	full	ADJ
cana-2601	26	18	ring	ring	NOUN
cana-2601	26	19	emerged	emerge	VERB
cana-2601	26	20	as	as	ADP
cana-2601	26	21	potential	potential	ADJ
cana-2601	26	22	competitors	competitor	NOUN
cana-2601	26	23	after	after	ADP
cana-2601	26	24	an	an	DET
cana-2601	26	25	intense	intense	ADJ
cana-2601	26	26	search	search	NOUN
cana-2601	26	27	for	for	ADP
cana-2601	26	28	the	the	DET
cana-2601	26	29	ideal	ideal	ADJ
cana-2601	26	30	placement	placement	NOUN
cana-2601	26	31	of	of	ADP
cana-2601	26	32	these	these	DET
cana-2601	26	33	additional	additional	ADJ
cana-2601	26	34	linkages	linkage	NOUN
cana-2601	26	35	.	.	PUNCT
cana-2601	27	1	trees	tree	NOUN
cana-2601	27	2	are	be	AUX
cana-2601	27	3	essential	essential	ADJ
cana-2601	27	4	for	for	ADP
cana-2601	27	5	understanding	understand	VERB
cana-2601	27	6	the	the	DET
cana-2601	27	7	structure	structure	NOUN
cana-2601	27	8	of	of	ADP
cana-2601	27	9	graphs	graph	NOUN
cana-2601	27	10	and	and	CCONJ
cana-2601	27	11	have	have	VERB
cana-2601	27	12	a	a	DET
cana-2601	27	13	far	far	ADV
cana-2601	27	14	-	-	PUNCT
cana-2601	27	15	reaching	reach	VERB
cana-2601	27	16	range	range	NOUN
cana-2601	27	17	of	of	ADP
cana-2601	27	18	ap	ap	PROPN
cana-2601	27	19	plications	plication	NOUN
cana-2601	27	20	,	,	PUNCT
cana-2601	27	21	which	which	PRON
cana-2601	27	22	includes	include	VERB
cana-2601	27	23	data	datum	NOUN
cana-2601	27	24	processing	processing	NOUN
cana-2601	27	25	.	.	PUNCT
cana-2601	28	1	additional	additional	ADJ
cana-2601	28	2	properties	property	NOUN
cana-2601	28	3	such	such	ADJ
cana-2601	28	4	as	as	ADP
cana-2601	28	5	roots	root	NOUN
cana-2601	28	6	and	and	CCONJ
cana-2601	28	7	vertexorderings	vertexordering	NOUN
cana-2601	28	8	are	be	AUX
cana-2601	28	9	common	common	ADJ
cana-2601	28	10	in	in	ADP
cana-2601	28	11	tree	tree	NOUN
cana-2601	28	12	architectures	architecture	NOUN
cana-2601	28	13	.	.	PUNCT
cana-2601	29	1	trees	tree	NOUN
cana-2601	29	2	play	play	VERB
cana-2601	29	3	a	a	DET
cana-2601	29	4	crucial	crucial	ADJ
cana-2601	29	5	role	role	NOUN
cana-2601	29	6	in	in	ADP
cana-2601	29	7	the	the	DET
cana-2601	29	8	structuring	structuring	NOUN
cana-2601	29	9	and	and	CCONJ
cana-2601	29	10	scrutinizing	scrutinizing	NOUN
cana-2601	29	11	of	of	ADP
cana-2601	29	12	connected	connected	ADJ
cana-2601	29	13	networks	network	NOUN
cana-2601	29	14	,	,	PUNCT
cana-2601	29	15	as	as	ADV
cana-2601	29	16	well	well	ADV
cana-2601	29	17	as	as	ADP
cana-2601	29	18	in	in	ADP
cana-2601	29	19	the	the	DET
cana-2601	29	20	structural	structural	ADJ
cana-2601	29	21	comprehension	comprehension	NOUN
cana-2601	29	22	of	of	ADP
cana-2601	29	23	graphs	graph	NOUN
cana-2601	29	24	and	and	CCONJ
cana-2601	29	25	the	the	DET
cana-2601	29	26	algorithms	algorithm	NOUN
cana-2601	29	27	of	of	ADP
cana-2601	29	28	information	information	NOUN
cana-2601	29	29	processing	processing	NOUN
cana-2601	29	30	.	.	PUNCT
cana-2601	30	1	trees	tree	NOUN
cana-2601	30	2	,	,	PUNCT
cana-2601	30	3	in	in	ADP
cana-2601	30	4	fact	fact	NOUN
cana-2601	30	5	,	,	PUNCT
cana-2601	30	6	form	form	VERB
cana-2601	30	7	the	the	DET
cana-2601	30	8	foundation	foundation	NOUN
cana-2601	30	9	of	of	ADP
cana-2601	30	10	optimally	optimally	ADV
cana-2601	30	11	connected	connect	VERB
cana-2601	30	12	networks	network	NOUN
cana-2601	30	13	.	.	PUNCT
cana-2601	31	1	one	one	NUM
cana-2601	31	2	of	of	ADP
cana-2601	31	3	the	the	DET
cana-2601	31	4	most	most	ADV
cana-2601	31	5	important	important	ADJ
cana-2601	31	6	tasks	task	NOUN
cana-2601	31	7	in	in	ADP
cana-2601	31	8	information	information	NOUN
cana-2601	31	9	management	management	NOUN
cana-2601	31	10	is	be	AUX
cana-2601	31	11	determining	determine	VERB
cana-2601	31	12	how	how	SCONJ
cana-2601	31	13	to	to	PART
cana-2601	31	14	store	store	VERB
cana-2601	31	15	data	datum	NOUN
cana-2601	31	16	in	in	ADP
cana-2601	31	17	a	a	DET
cana-2601	31	18	spaceefficient	spaceefficient	NOUN
cana-2601	31	19	manner	manner	NOUN
cana-2601	31	20	that	that	PRON
cana-2601	31	21	simultaneously	simultaneously	ADV
cana-2601	31	22	allows	allow	VERB
cana-2601	31	23	for	for	ADP
cana-2601	31	24	quick	quick	ADJ
cana-2601	31	25	retrieval	retrieval	NOUN
cana-2601	31	26	and	and	CCONJ
cana-2601	31	27	change	change	NOUN
cana-2601	31	28	.	.	PUNCT
cana-2601	32	1	tree	tree	NOUN
cana-2601	32	2	-	-	PUNCT
cana-2601	32	3	based	base	VERB
cana-2601	32	4	systems	system	NOUN
cana-2601	32	5	are	be	AUX
cana-2601	32	6	frequently	frequently	ADV
cana-2601	32	7	the	the	DET
cana-2601	32	8	most	most	ADV
cana-2601	32	9	effective	effective	ADJ
cana-2601	32	10	means	mean	NOUN
cana-2601	32	11	of	of	ADP
cana-2601	32	12	reconciling	reconcile	VERB
cana-2601	32	13	these	these	DET
cana-2601	32	14	competing	compete	VERB
cana-2601	32	15	objectives	objective	NOUN
cana-2601	32	16	.	.	PUNCT
cana-2601	33	1	the	the	DET
cana-2601	33	2	locally	locally	ADV
cana-2601	33	3	harmonious	harmonious	ADJ
cana-2601	33	4	coloring	coloring	NOUN
cana-2601	33	5	[	[	X
cana-2601	33	6	3	3	NUM
cana-2601	33	7	]	]	PUNCT
cana-2601	33	8	of	of	ADP
cana-2601	33	9	a	a	DET
cana-2601	33	10	graph	graph	NOUN
cana-2601	33	11	g	g	NOUN
cana-2601	33	12	is	be	AUX
cana-2601	33	13	a	a	DET
cana-2601	33	14	proper	proper	ADJ
cana-2601	33	15	vertex	vertex	NOUN
cana-2601	33	16	coloring	coloring	NOUN
cana-2601	33	17	in	in	ADP
cana-2601	33	18	which	which	PRON
cana-2601	33	19	every	every	DET
cana-2601	33	20	colorpair	colorpair	NOUN
cana-2601	33	21	is	be	AUX
cana-2601	33	22	present	present	ADJ
cana-2601	33	23	only	only	ADV
cana-2601	33	24	once	once	ADV
cana-2601	33	25	for	for	ADP
cana-2601	33	26	every	every	DET
cana-2601	33	27	edge	edge	NOUN
cana-2601	33	28	within	within	ADP
cana-2601	33	29	distance	distance	NOUN
cana-2601	33	30	one	one	NUM
cana-2601	33	31	from	from	ADP
cana-2601	33	32	any	any	DET
cana-2601	33	33	vertex	vertex	NOUN
cana-2601	33	34	v	v	NOUN
cana-2601	33	35	in	in	ADP
cana-2601	33	36	v	v	NOUN
cana-2601	33	37	(	(	PUNCT
cana-2601	33	38	g	g	NOUN
cana-2601	33	39	)	)	PUNCT
cana-2601	33	40	.	.	PUNCT
cana-2601	34	1	it	it	PRON
cana-2601	34	2	leads	lead	VERB
cana-2601	34	3	to	to	ADP
cana-2601	34	4	the	the	DET
cana-2601	34	5	constraint	constraint	NOUN
cana-2601	34	6	that	that	PRON
cana-2601	34	7	all	all	DET
cana-2601	34	8	vertices	vertex	NOUN
cana-2601	34	9	in	in	ADP
cana-2601	34	10	the	the	DET
cana-2601	34	11	closed	closed	ADJ
cana-2601	34	12	neighborhood	neighborhood	NOUN
cana-2601	34	13	n	n	CCONJ
cana-2601	34	14	[	[	X
cana-2601	34	15	v	v	X
cana-2601	34	16	]	]	PUNCT
cana-2601	34	17	receive	receive	VERB
cana-2601	34	18	different	different	ADJ
cana-2601	34	19	colors	color	NOUN
cana-2601	34	20	for	for	ADP
cana-2601	34	21	every	every	DET
cana-2601	34	22	vertex	vertex	NOUN
cana-2601	34	23	v	v	NOUN
cana-2601	34	24	in	in	ADP
cana-2601	34	25	g.	g.	PROPN
cana-2601	34	26	the	the	DET
cana-2601	34	27	minimum	minimum	ADJ
cana-2601	34	28	number	number	NOUN
cana-2601	34	29	of	of	ADP
cana-2601	34	30	colors	color	NOUN
cana-2601	34	31	required	require	VERB
cana-2601	34	32	to	to	PART
cana-2601	34	33	obtain	obtain	VERB
cana-2601	34	34	a	a	DET
cana-2601	34	35	locally	locally	ADV
cana-2601	34	36	harmonious	harmonious	ADJ
cana-2601	34	37	coloring	coloring	NOUN
cana-2601	34	38	of	of	ADP
cana-2601	34	39	a	a	DET
cana-2601	34	40	graph	graph	NOUN
cana-2601	34	41	g	g	NOUN
cana-2601	34	42	is	be	AUX
cana-2601	34	43	called	call	VERB
cana-2601	34	44	the	the	DET
cana-2601	34	45	locally	locally	ADV
cana-2601	34	46	harmonious	harmonious	ADJ
cana-2601	34	47	chromatic	chromatic	ADJ
cana-2601	34	48	number	number	NOUN
cana-2601	34	49	of	of	ADP
cana-2601	34	50	g	g	NOUN
cana-2601	34	51	and	and	CCONJ
cana-2601	34	52	is	be	AUX
cana-2601	34	53	denoted	denote	VERB
cana-2601	34	54	by	by	ADP
cana-2601	34	55	h1(g	h1(g	PROPN
cana-2601	34	56	)	)	PUNCT
cana-2601	34	57	.	.	PUNCT
cana-2601	35	1	given	give	VERB
cana-2601	35	2	a	a	DET
cana-2601	35	3	graph	graph	NOUN
cana-2601	35	4	g	g	NOUN
cana-2601	35	5	,	,	PUNCT
cana-2601	35	6	the	the	DET
cana-2601	35	7	locally	locally	ADV
cana-2601	35	8	harmonious	harmonious	ADJ
cana-2601	35	9	coloring	coloring	NOUN
cana-2601	35	10	problem	problem	NOUN
cana-2601	35	11	is	be	AUX
cana-2601	35	12	to	to	PART
cana-2601	35	13	determine	determine	VERB
cana-2601	35	14	h1(g	h1(g	PROPN
cana-2601	35	15	)	)	PUNCT
cana-2601	35	16	.	.	PUNCT
cana-2601	36	1	in	in	ADP
cana-2601	36	2	2015	2015	NUM
cana-2601	36	3	,	,	PUNCT
cana-2601	36	4	w.	w.	PROPN
cana-2601	36	5	gao	gao	PROPN
cana-2601	36	6	[	[	X
cana-2601	36	7	3	3	NUM
cana-2601	36	8	]	]	PUNCT
cana-2601	36	9	proposed	propose	VERB
cana-2601	36	10	three	three	NUM
cana-2601	36	11	algorithms	algorithm	NOUN
cana-2601	36	12	to	to	PART
cana-2601	36	13	estimate	estimate	VERB
cana-2601	36	14	h1(g	h1(g	PROPN
cana-2601	36	15	)	)	PUNCT
cana-2601	36	16	.	.	PUNCT
cana-2601	37	1	these	these	DET
cana-2601	37	2	algorithms	algorithm	NOUN
cana-2601	37	3	have	have	VERB
cana-2601	37	4	high	high	ADJ
cana-2601	37	5	impact	impact	NOUN
cana-2601	37	6	on	on	ADP
cana-2601	37	7	time	time	NOUN
cana-2601	37	8	complexity	complexity	NOUN
cana-2601	37	9	due	due	ADP
cana-2601	37	10	to	to	ADP
cana-2601	37	11	an	an	DET
cana-2601	37	12	exhaustive	exhaustive	ADJ
cana-2601	37	13	search	search	NOUN
cana-2601	37	14	on	on	ADP
cana-2601	37	15	vertices	vertex	NOUN
cana-2601	37	16	and	and	CCONJ
cana-2601	37	17	branching	branch	VERB
cana-2601	37	18	rules	rule	NOUN
cana-2601	37	19	.	.	PUNCT
cana-2601	38	1	the	the	DET
cana-2601	38	2	concept	concept	NOUN
cana-2601	38	3	of	of	ADP
cana-2601	38	4	locally	locally	ADV
cana-2601	38	5	harmonious	harmonious	ADJ
cana-2601	38	6	coloring	coloring	NOUN
cana-2601	38	7	is	be	AUX
cana-2601	38	8	derived	derive	VERB
cana-2601	38	9	from	from	ADP
cana-2601	38	10	d	d	PROPN
cana-2601	38	11	harmonious	harmonious	ADJ
cana-2601	38	12	coloring	coloring	NOUN
cana-2601	38	13	[	[	X
cana-2601	38	14	11	11	NUM
cana-2601	38	15	]	]	PUNCT
cana-2601	38	16	,	,	PUNCT
cana-2601	38	17	as	as	ADP
cana-2601	38	18	a	a	DET
cana-2601	38	19	proper	proper	ADJ
cana-2601	38	20	vertex	vertex	NOUN
cana-2601	38	21	coloring	color	VERB
cana-2601	38	22	such	such	ADJ
cana-2601	38	23	that	that	SCONJ
cana-2601	38	24	every	every	DET
cana-2601	38	25	color	color	NOUN
cana-2601	38	26	pair	pair	NOUN
cana-2601	38	27	is	be	AUX
cana-2601	38	28	present	present	ADJ
cana-2601	38	29	at	at	ADP
cana-2601	38	30	most	most	ADV
cana-2601	38	31	once	once	ADV
cana-2601	38	32	for	for	ADP
cana-2601	38	33	every	every	DET
cana-2601	38	34	edge	edge	NOUN
cana-2601	38	35	within	within	ADP
cana-2601	38	36	distance	distance	NOUN
cana-2601	38	37	d	d	NOUN
cana-2601	38	38	;	;	PUNCT
cana-2601	38	39	during	during	ADP
cana-2601	38	40	the	the	DET
cana-2601	38	41	conference	conference	NOUN
cana-2601	38	42	held	hold	VERB
cana-2601	38	43	in	in	ADP
cana-2601	38	44	taiwan	taiwan	PROPN
cana-2601	38	45	.	.	PUNCT
cana-2601	39	1	the	the	DET
cana-2601	39	2	locally	locally	ADV
cana-2601	39	3	harmonious	harmonious	ADJ
cana-2601	39	4	coloring	coloring	NOUN
cana-2601	39	5	is	be	AUX
cana-2601	39	6	exactly	exactly	ADV
cana-2601	39	7	same	same	ADJ
cana-2601	39	8	as	as	ADP
cana-2601	39	9	d	d	X
cana-2601	39	10	harmonious	harmonious	ADJ
cana-2601	39	11	coloring	coloring	NOUN
cana-2601	39	12	when	when	SCONJ
cana-2601	39	13	d=1	d=1	NOUN
cana-2601	39	14	.	.	NOUN
cana-2601	40	1	2	2	NUM
cana-2601	40	2	.	.	X
cana-2601	40	3	lh	lh	NOUN
cana-2601	40	4	-	-	PUNCT
cana-2601	40	5	coloring	coloring	NOUN
cana-2601	40	6	of	of	ADP
cana-2601	40	7	certain	certain	ADJ
cana-2601	40	8	tree	tree	NOUN
cana-2601	40	9	-	-	PUNCT
cana-2601	40	10	derived	derive	VERB
cana-2601	40	11	networks	network	NOUN
cana-2601	40	12	in	in	ADP
cana-2601	40	13	this	this	DET
cana-2601	40	14	section	section	NOUN
cana-2601	40	15	,	,	PUNCT
cana-2601	40	16	we	we	PRON
cana-2601	40	17	present	present	VERB
cana-2601	40	18	the	the	DET
cana-2601	40	19	lh	lh	NOUN
cana-2601	40	20	-	-	PUNCT
cana-2601	40	21	coloring	color	VERB
cana-2601	40	22	lemma	lemma	PROPN
cana-2601	40	23	in	in	ADP
cana-2601	40	24	which	which	PRON
cana-2601	40	25	we	we	PRON
cana-2601	40	26	obtain	obtain	VERB
cana-2601	40	27	the	the	DET
cana-2601	40	28	lower	low	ADJ
cana-2601	40	29	bound	bind	VERB
cana-2601	40	30	of	of	ADP
cana-2601	40	31	locally	locally	ADV
cana-2601	40	32	harmonious	harmonious	ADJ
cana-2601	40	33	coloring	coloring	NOUN
cana-2601	40	34	for	for	ADP
cana-2601	40	35	hypertree	hypertree	NOUN
cana-2601	40	36	,	,	PUNCT
cana-2601	40	37	shuffle	shuffle	NOUN
cana-2601	40	38	hypertree	hypertree	NOUN
cana-2601	40	39	,	,	PUNCT
cana-2601	40	40	l	l	NOUN
cana-2601	40	41	-	-	ADJ
cana-2601	40	42	complete	complete	ADJ
cana-2601	40	43	binary	binary	ADJ
cana-2601	40	44	tree	tree	NOUN
cana-2601	40	45	.	.	PUNCT
cana-2601	41	1	lh	lh	PROPN
cana-2601	41	2	-	-	PUNCT
cana-2601	41	3	coloring	color	VERB
cana-2601	41	4	lemma	lemma	NOUN
cana-2601	41	5	.	.	PUNCT
cana-2601	42	1	[	[	X
cana-2601	42	2	6	6	NUM
cana-2601	42	3	]	]	PUNCT
cana-2601	42	4	let	let	VERB
cana-2601	42	5	g	g	PRON
cana-2601	42	6	be	be	AUX
cana-2601	42	7	a	a	DET
cana-2601	42	8	connected	connected	ADJ
cana-2601	42	9	graph	graph	NOUN
cana-2601	42	10	on	on	ADP
cana-2601	42	11	n	n	DET
cana-2601	42	12	vertices	vertex	NOUN
cana-2601	42	13	and	and	CCONJ
cana-2601	42	14	k	k	PROPN
cana-2601	42	15	be	be	AUX
cana-2601	42	16	the	the	DET
cana-2601	42	17	number	number	NOUN
cana-2601	42	18	of	of	ADP
cana-2601	42	19	vertices	vertex	NOUN
cana-2601	42	20	has	have	VERB
cana-2601	42	21	∆(g	∆(g	NOUN
cana-2601	42	22	)	)	PUNCT
cana-2601	42	23	number	number	NOUN
cana-2601	42	24	of	of	ADP
cana-2601	42	25	common	common	ADJ
cana-2601	42	26	neighbors	neighbor	NOUN
cana-2601	42	27	.	.	PUNCT
cana-2601	43	1	then	then	ADV
cana-2601	43	2	h1(g	h1(g	PROPN
cana-2601	43	3	)	)	PUNCT
cana-2601	43	4	≥	≥	NOUN
cana-2601	43	5	∆(g	∆(g	NOUN
cana-2601	43	6	)	)	PUNCT
cana-2601	43	7	+	+	CCONJ
cana-2601	43	8	k.	k.	PROPN
cana-2601	43	9	theorem	theorem	VERB
cana-2601	43	10	2.1	2.1	NUM
cana-2601	43	11	.	.	PUNCT
cana-2601	44	1	[	[	X
cana-2601	44	2	7	7	X
cana-2601	44	3	]	]	PUNCT
cana-2601	44	4	let	let	VERB
cana-2601	44	5	g	g	PRON
cana-2601	44	6	be	be	AUX
cana-2601	44	7	a	a	DET
cana-2601	44	8	simple	simple	ADJ
cana-2601	44	9	connected	connect	VERB
cana-2601	44	10	graph	graph	NOUN
cana-2601	44	11	and	and	CCONJ
cana-2601	44	12	h	h	NOUN
cana-2601	44	13	be	be	AUX
cana-2601	44	14	any	any	DET
cana-2601	44	15	induced	induced	ADJ
cana-2601	44	16	subgraph	subgraph	NOUN
cana-2601	44	17	of	of	ADP
cana-2601	44	18	g	g	PROPN
cana-2601	44	19	,	,	PUNCT
cana-2601	44	20	then	then	ADV
cana-2601	44	21	h1(g	h1(g	PROPN
cana-2601	44	22	)	)	PUNCT
cana-2601	44	23	≥	≥	NOUN
cana-2601	44	24	h1(h	h1(h	PROPN
cana-2601	44	25	)	)	PUNCT
cana-2601	44	26	.	.	PUNCT
cana-2601	45	1	figure	figure	VERB
cana-2601	45	2	1	1	NUM
cana-2601	45	3	:	:	PUNCT
cana-2601	45	4	vertex	vertex	NOUN
cana-2601	45	5	representation	representation	NOUN
cana-2601	45	6	of	of	ADP
cana-2601	45	7	st	st	PROPN
cana-2601	45	8	(	(	PUNCT
cana-2601	45	9	4	4	NUM
cana-2601	45	10	)	)	PUNCT
cana-2601	45	11	communications	communication	NOUN
cana-2601	45	12	on	on	ADP
cana-2601	45	13	applied	apply	VERB
cana-2601	45	14	nonlinear	nonlinear	ADJ
cana-2601	45	15	analysis	analysis	NOUN
cana-2601	45	16	issn	issn	NOUN
cana-2601	45	17	:	:	PUNCT
cana-2601	45	18	1074	1074	NUM
cana-2601	45	19	-	-	PUNCT
cana-2601	45	20	133x	133x	NUM
cana-2601	45	21	vol	vol	NOUN
cana-2601	45	22	32	32	NUM
cana-2601	46	1	no	no	NOUN
cana-2601	46	2	.	.	PUNCT
cana-2601	47	1	3s	3s	NUM
cana-2601	47	2	(	(	PUNCT
cana-2601	47	3	2025	2025	NUM
cana-2601	47	4	)	)	PUNCT
cana-2601	47	5	214	214	NUM
cana-2601	47	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2601	47	7	3	3	X
cana-2601	47	8	.	.	PUNCT
cana-2601	47	9	slim	slim	ADJ
cana-2601	47	10	tree	tree	NOUN
cana-2601	47	11	the	the	DET
cana-2601	47	12	nth	nth	PROPN
cana-2601	47	13	slim	slim	ADJ
cana-2601	47	14	tree	tree	PROPN
cana-2601	47	15	st	st	PROPN
cana-2601	47	16	(	(	PUNCT
cana-2601	47	17	n	n	CCONJ
cana-2601	47	18	)	)	PUNCT
cana-2601	47	19	,	,	PUNCT
cana-2601	47	20	n	n	PRON
cana-2601	47	21	≥	≥	NOUN
cana-2601	47	22	2	2	NUM
cana-2601	47	23	is	be	AUX
cana-2601	47	24	recursively	recursively	ADV
cana-2601	47	25	defined	define	VERB
cana-2601	47	26	as	as	SCONJ
cana-2601	47	27	follows	follow	VERB
cana-2601	47	28	and	and	CCONJ
cana-2601	47	29	is	be	AUX
cana-2601	47	30	denoted	denote	VERB
cana-2601	47	31	by	by	ADP
cana-2601	47	32	st	st	PROPN
cana-2601	47	33	(	(	PUNCT
cana-2601	47	34	n	n	CCONJ
cana-2601	47	35	)	)	PUNCT
cana-2601	47	36	=	=	SYM
cana-2601	47	37	(	(	PUNCT
cana-2601	47	38	v	v	NOUN
cana-2601	47	39	,	,	PUNCT
cana-2601	47	40	e	e	NOUN
cana-2601	47	41	,	,	PUNCT
cana-2601	47	42	u	u	NOUN
cana-2601	47	43	,	,	PUNCT
cana-2601	47	44	l	l	NOUN
cana-2601	47	45	,	,	PUNCT
cana-2601	47	46	r	r	NOUN
cana-2601	47	47	)	)	PUNCT
cana-2601	47	48	,	,	PUNCT
cana-2601	47	49	where	where	SCONJ
cana-2601	47	50	v	v	NOUN
cana-2601	47	51	is	be	AUX
cana-2601	47	52	the	the	DET
cana-2601	47	53	node	node	NOUN
cana-2601	47	54	set	set	NOUN
cana-2601	47	55	,	,	PUNCT
cana-2601	47	56	e	e	X
cana-2601	47	57	is	be	AUX
cana-2601	47	58	the	the	DET
cana-2601	47	59	edge	edge	NOUN
cana-2601	47	60	set	set	VERB
cana-2601	47	61	and	and	CCONJ
cana-2601	47	62	u	u	NOUN
cana-2601	47	63	,	,	PUNCT
cana-2601	47	64	l	l	PROPN
cana-2601	47	65	,	,	PUNCT
cana-2601	47	66	r	r	NOUN
cana-2601	47	67	are	be	AUX
cana-2601	47	68	vertices	vertex	NOUN
cana-2601	47	69	addressed	address	VERB
cana-2601	47	70	as	as	ADP
cana-2601	47	71	root	root	NOUN
cana-2601	47	72	node	node	NOUN
cana-2601	47	73	,	,	PUNCT
cana-2601	47	74	left	leave	VERB
cana-2601	47	75	node	node	NOUN
cana-2601	47	76	and	and	CCONJ
cana-2601	47	77	right	right	ADJ
cana-2601	47	78	node	node	NOUN
cana-2601	47	79	respectively	respectively	ADV
cana-2601	47	80	.	.	PUNCT
cana-2601	48	1	1	1	X
cana-2601	48	2	.	.	X
cana-2601	48	3	st	st	PROPN
cana-2601	48	4	(	(	PUNCT
cana-2601	48	5	2	2	NUM
cana-2601	48	6	)	)	PUNCT
cana-2601	48	7	is	be	AUX
cana-2601	48	8	the	the	DET
cana-2601	48	9	complete	complete	ADJ
cana-2601	48	10	graph	graph	NOUN
cana-2601	48	11	k3	k3	VERB
cana-2601	48	12	with	with	ADP
cana-2601	48	13	its	its	PRON
cana-2601	48	14	nodes	node	NOUN
cana-2601	48	15	labeled	label	VERB
cana-2601	48	16	as	as	ADP
cana-2601	48	17	u	u	NOUN
cana-2601	48	18	,	,	PUNCT
cana-2601	48	19	l	l	PROPN
cana-2601	48	20	and	and	CCONJ
cana-2601	48	21	r.	r.	PROPN
cana-2601	48	22	2	2	NUM
cana-2601	48	23	.	.	PUNCT
cana-2601	49	1	the	the	DET
cana-2601	49	2	sth	sth	PROPN
cana-2601	49	3	slim	slim	PROPN
cana-2601	49	4	tree	tree	PROPN
cana-2601	49	5	st	st	PROPN
cana-2601	49	6	(	(	PUNCT
cana-2601	49	7	s	s	PROPN
cana-2601	49	8	)	)	PUNCT
cana-2601	49	9	,	,	PUNCT
cana-2601	49	10	with	with	ADP
cana-2601	49	11	s	s	PRON
cana-2601	49	12	≥	≥	NUM
cana-2601	49	13	3	3	NUM
cana-2601	49	14	,	,	PUNCT
cana-2601	49	15	is	be	AUX
cana-2601	49	16	composed	compose	VERB
cana-2601	49	17	of	of	ADP
cana-2601	49	18	a	a	DET
cana-2601	49	19	root	root	NOUN
cana-2601	49	20	node	node	NOUN
cana-2601	49	21	u	u	NOUN
cana-2601	49	22	and	and	CCONJ
cana-2601	49	23	two	two	NUM
cana-2601	49	24	disjoint	disjoint	ADJ
cana-2601	49	25	copies	copy	NOUN
cana-2601	49	26	of	of	ADP
cana-2601	49	27	(	(	PUNCT
cana-2601	49	28	s−	s−	PROPN
cana-2601	49	29	1)th	1)th	NUM
cana-2601	49	30	slim	slim	ADJ
cana-2601	49	31	trees	tree	NOUN
cana-2601	49	32	as	as	ADP
cana-2601	49	33	the	the	DET
cana-2601	49	34	left	left	ADJ
cana-2601	49	35	subtree	subtree	NOUN
cana-2601	49	36	and	and	CCONJ
cana-2601	49	37	right	right	ADJ
cana-2601	49	38	sub	sub	ADJ
cana-2601	49	39	-	-	ADJ
cana-2601	49	40	tree	tree	ADJ
cana-2601	49	41	,	,	PUNCT
cana-2601	49	42	denoted	denote	VERB
cana-2601	49	43	by	by	ADP
cana-2601	49	44	st	st	PROPN
cana-2601	49	45	l(n−1	l(n−1	PROPN
cana-2601	49	46	)	)	PUNCT
cana-2601	49	47	=	=	SYM
cana-2601	49	48	(	(	PUNCT
cana-2601	49	49	v1	v1	PROPN
cana-2601	49	50	,	,	PUNCT
cana-2601	49	51	e1	e1	NOUN
cana-2601	49	52	,	,	PUNCT
cana-2601	49	53	u1	u1	NOUN
cana-2601	49	54	,	,	PUNCT
cana-2601	49	55	l1	l1	PROPN
cana-2601	49	56	,	,	PUNCT
cana-2601	49	57	r1	r1	PROPN
cana-2601	49	58	)	)	PUNCT
cana-2601	49	59	and	and	CCONJ
cana-2601	49	60	st	st	PROPN
cana-2601	49	61	r(n−1	r(n−1	PROPN
cana-2601	49	62	)	)	PUNCT
cana-2601	49	63	=	=	SYM
cana-2601	49	64	(	(	PUNCT
cana-2601	49	65	v2	v2	PROPN
cana-2601	49	66	,	,	PUNCT
cana-2601	49	67	e2	e2	PROPN
cana-2601	49	68	,	,	PUNCT
cana-2601	49	69	u2	u2	NOUN
cana-2601	49	70	,	,	PUNCT
cana-2601	49	71	l2	l2	NOUN
cana-2601	49	72	,	,	PUNCT
cana-2601	49	73	r2	r2	PROPN
cana-2601	49	74	)	)	PUNCT
cana-2601	49	75	,	,	PUNCT
cana-2601	49	76	respectively	respectively	ADV
cana-2601	49	77	.	.	PUNCT
cana-2601	50	1	to	to	PART
cana-2601	50	2	be	be	AUX
cana-2601	50	3	specific	specific	ADJ
cana-2601	50	4	,	,	PUNCT
cana-2601	50	5	st	st	PROPN
cana-2601	50	6	(	(	PUNCT
cana-2601	50	7	n	n	CCONJ
cana-2601	50	8	)	)	PUNCT
cana-2601	50	9	=	=	SYM
cana-2601	50	10	(	(	PUNCT
cana-2601	50	11	v	v	NOUN
cana-2601	50	12	,	,	PUNCT
cana-2601	50	13	e	e	NOUN
cana-2601	50	14	,	,	PUNCT
cana-2601	50	15	u	u	NOUN
cana-2601	50	16	,	,	PUNCT
cana-2601	50	17	l	l	NOUN
cana-2601	50	18	,	,	PUNCT
cana-2601	50	19	r	r	NOUN
cana-2601	50	20	)	)	PUNCT
cana-2601	50	21	is	be	AUX
cana-2601	50	22	given	give	VERB
cana-2601	50	23	by	by	ADP
cana-2601	50	24	v	v	NOUN
cana-2601	50	25	=	=	SYM
cana-2601	50	26	v1	v1	NOUN
cana-2601	50	27	∪	∪	ADJ
cana-2601	50	28	v2	v2	PROPN
cana-2601	50	29	∪	∪	X
cana-2601	50	30	{	{	PUNCT
cana-2601	50	31	u	u	NOUN
cana-2601	50	32	}	}	PUNCT
cana-2601	50	33	,	,	PUNCT
cana-2601	50	34	e	e	X
cana-2601	50	35	=	=	AUX
cana-2601	50	36	e1	e1	PROPN
cana-2601	50	37	∪	∪	PROPN
cana-2601	50	38	e2	e2	PROPN
cana-2601	50	39	∪	∪	X
cana-2601	50	40	{	{	PUNCT
cana-2601	50	41	(	(	PUNCT
cana-2601	50	42	u	u	NOUN
cana-2601	50	43	,	,	PUNCT
cana-2601	50	44	u1	u1	NOUN
cana-2601	50	45	)	)	PUNCT
cana-2601	50	46	,	,	PUNCT
cana-2601	50	47	(	(	PUNCT
cana-2601	50	48	u	u	NOUN
cana-2601	50	49	,	,	PUNCT
cana-2601	50	50	u2	u2	PROPN
cana-2601	50	51	)	)	PUNCT
cana-2601	50	52	,	,	PUNCT
cana-2601	50	53	(	(	PUNCT
cana-2601	50	54	r1	r1	NOUN
cana-2601	50	55	,	,	PUNCT
cana-2601	50	56	l2	l2	NOUN
cana-2601	50	57	)	)	PUNCT
cana-2601	50	58	}	}	PUNCT
cana-2601	50	59	,	,	PUNCT
cana-2601	50	60	l	l	NOUN
cana-2601	50	61	=	=	SYM
cana-2601	50	62	l1	l1	PROPN
cana-2601	50	63	,	,	PUNCT
cana-2601	50	64	r	r	NOUN
cana-2601	50	65	=	=	SYM
cana-2601	50	66	r2	r2	PROPN
cana-2601	50	67	.	.	PUNCT
cana-2601	51	1	to	to	PART
cana-2601	51	2	simplify	simplify	VERB
cana-2601	51	3	our	our	PRON
cana-2601	51	4	coloring	coloring	NOUN
cana-2601	51	5	scheme	scheme	NOUN
cana-2601	51	6	,	,	PUNCT
cana-2601	51	7	here	here	ADV
cana-2601	51	8	the	the	DET
cana-2601	51	9	vertices	vertex	NOUN
cana-2601	51	10	of	of	ADP
cana-2601	51	11	the	the	DET
cana-2601	51	12	slim	slim	ADJ
cana-2601	51	13	tree	tree	PROPN
cana-2601	51	14	st	st	PROPN
cana-2601	51	15	(	(	PUNCT
cana-2601	51	16	n	n	CCONJ
cana-2601	51	17	)	)	PUNCT
cana-2601	51	18	are	be	AUX
cana-2601	51	19	labeled	label	VERB
cana-2601	51	20	as	as	ADP
cana-2601	51	21	vij	vij	PROPN
cana-2601	51	22	,	,	PUNCT
cana-2601	51	23	1	1	NUM
cana-2601	51	24	≤	≤	NUM
cana-2601	51	25	i	i	PRON
cana-2601	51	26	≤	≤	PROPN
cana-2601	51	27	n	n	CCONJ
cana-2601	51	28	,	,	PUNCT
cana-2601	51	29	1	1	NUM
cana-2601	51	30	≤	≤	NUM
cana-2601	51	31	j	j	PROPN
cana-2601	51	32	≤	≤	PROPN
cana-2601	51	33	2i−1	2i−1	NUM
cana-2601	51	34	,	,	PUNCT
cana-2601	51	35	where	where	SCONJ
cana-2601	51	36	i	i	PRON
cana-2601	51	37	represents	represent	VERB
cana-2601	51	38	the	the	DET
cana-2601	51	39	level	level	NOUN
cana-2601	51	40	and	and	CCONJ
cana-2601	51	41	j	j	PROPN
cana-2601	51	42	represents	represent	VERB
cana-2601	51	43	the	the	DET
cana-2601	51	44	position	position	NOUN
cana-2601	51	45	of	of	ADP
cana-2601	51	46	the	the	DET
cana-2601	51	47	vertices	vertex	NOUN
cana-2601	51	48	at	at	ADP
cana-2601	51	49	a	a	DET
cana-2601	51	50	particular	particular	ADJ
cana-2601	51	51	level	level	NOUN
cana-2601	51	52	as	as	SCONJ
cana-2601	51	53	shown	show	VERB
cana-2601	51	54	in	in	ADP
cana-2601	51	55	figure	figure	NOUN
cana-2601	51	56	1	1	NUM
cana-2601	51	57	.	.	PUNCT
cana-2601	52	1	in	in	ADP
cana-2601	52	2	this	this	DET
cana-2601	52	3	section	section	NOUN
cana-2601	52	4	we	we	PRON
cana-2601	52	5	shall	shall	AUX
cana-2601	52	6	prove	prove	VERB
cana-2601	52	7	that	that	DET
cana-2601	52	8	st	st	PROPN
cana-2601	52	9	(	(	PUNCT
cana-2601	52	10	n	n	CCONJ
cana-2601	52	11	)	)	PUNCT
cana-2601	52	12	,	,	PUNCT
cana-2601	52	13	n	n	PRON
cana-2601	52	14	≥	≥	NOUN
cana-2601	52	15	2	2	NUM
cana-2601	52	16	admits	admit	VERB
cana-2601	52	17	locally	locally	ADV
cana-2601	52	18	harmonious	harmonious	ADJ
cana-2601	52	19	coloring	coloring	NOUN
cana-2601	52	20	.	.	PUNCT
cana-2601	53	1	theorem	theorem	VERB
cana-2601	53	2	3.1	3.1	NUM
cana-2601	53	3	.	.	PUNCT
cana-2601	54	1	the	the	DET
cana-2601	54	2	locally	locally	ADV
cana-2601	54	3	harmonious	harmonious	ADJ
cana-2601	54	4	chromatic	chromatic	ADJ
cana-2601	54	5	number	number	NOUN
cana-2601	54	6	of	of	ADP
cana-2601	54	7	slim	slim	ADJ
cana-2601	54	8	tree	tree	NOUN
cana-2601	54	9	network	network	NOUN
cana-2601	54	10	st	st	PROPN
cana-2601	54	11	(	(	PUNCT
cana-2601	54	12	n	n	CCONJ
cana-2601	54	13	)	)	PUNCT
cana-2601	54	14	,	,	PUNCT
cana-2601	54	15	n	n	PRON
cana-2601	54	16	≥	≥	NOUN
cana-2601	54	17	2	2	NUM
cana-2601	54	18	,	,	PUNCT
cana-2601	54	19	is	be	AUX
cana-2601	54	20	given	give	VERB
cana-2601	54	21	by	by	ADP
cana-2601	54	22	h1(st	h1(st	PROPN
cana-2601	54	23	(	(	PUNCT
cana-2601	54	24	n	n	CCONJ
cana-2601	54	25	)	)	PUNCT
cana-2601	54	26	)	)	PUNCT
cana-2601	55	1	=	=	SYM
cana-2601	55	2	5	5	X
cana-2601	55	3	.	.	PUNCT
cana-2601	55	4	proof	proof	NOUN
cana-2601	55	5	.	.	PUNCT
cana-2601	56	1	since	since	SCONJ
cana-2601	56	2	st	st	PROPN
cana-2601	56	3	(	(	PUNCT
cana-2601	56	4	2	2	NUM
cana-2601	56	5	)	)	PUNCT
cana-2601	56	6	is	be	AUX
cana-2601	56	7	the	the	DET
cana-2601	56	8	complete	complete	ADJ
cana-2601	56	9	graph	graph	NOUN
cana-2601	56	10	k3	k3	PROPN
cana-2601	56	11	,	,	PUNCT
cana-2601	56	12	by	by	ADP
cana-2601	56	13	lh	lh	PROPN
cana-2601	56	14	-	-	PUNCT
cana-2601	56	15	coloring	color	VERB
cana-2601	56	16	lemma	lemma	PROPN
cana-2601	56	17	,	,	PUNCT
cana-2601	56	18	h1(st	h1(st	PROPN
cana-2601	56	19	(	(	PUNCT
cana-2601	56	20	2	2	NUM
cana-2601	56	21	)	)	PUNCT
cana-2601	56	22	)	)	PUNCT
cana-2601	57	1	=	=	SYM
cana-2601	57	2	∆	∆	PROPN
cana-2601	57	3	(	(	PUNCT
cana-2601	57	4	st	st	PROPN
cana-2601	57	5	(	(	PUNCT
cana-2601	57	6	2	2	NUM
cana-2601	57	7	)	)	PUNCT
cana-2601	57	8	)	)	PUNCT
cana-2601	58	1	+	+	CCONJ
cana-2601	58	2	1	1	X
cana-2601	58	3	.	.	X
cana-2601	58	4	for	for	ADP
cana-2601	58	5	n	n	PROPN
cana-2601	58	6	>	>	X
cana-2601	58	7	2	2	NUM
cana-2601	58	8	,	,	PUNCT
cana-2601	58	9	we	we	PRON
cana-2601	58	10	now	now	ADV
cana-2601	58	11	show	show	VERB
cana-2601	58	12	that	that	SCONJ
cana-2601	58	13	st	st	PROPN
cana-2601	58	14	(	(	PUNCT
cana-2601	58	15	n	n	CCONJ
cana-2601	58	16	)	)	PUNCT
cana-2601	58	17	can	can	AUX
cana-2601	58	18	not	not	PART
cana-2601	58	19	be	be	AUX
cana-2601	58	20	colored	color	VERB
cana-2601	58	21	with	with	ADP
cana-2601	58	22	∆	∆	PROPN
cana-2601	58	23	(	(	PUNCT
cana-2601	58	24	st	st	PROPN
cana-2601	58	25	(	(	PUNCT
cana-2601	58	26	n	n	CCONJ
cana-2601	58	27	)	)	PUNCT
cana-2601	58	28	)	)	PUNCT
cana-2601	59	1	+	+	CCONJ
cana-2601	59	2	1	1	NUM
cana-2601	59	3	colors	color	NOUN
cana-2601	59	4	with	with	ADP
cana-2601	59	5	the	the	DET
cana-2601	59	6	illustration	illustration	NOUN
cana-2601	59	7	by	by	ADP
cana-2601	59	8	considering	consider	VERB
cana-2601	59	9	an	an	DET
cana-2601	59	10	induced	induced	ADJ
cana-2601	59	11	subgraph	subgraph	NOUN
cana-2601	59	12	st	st	PROPN
cana-2601	59	13	(	(	PUNCT
cana-2601	59	14	3	3	NUM
cana-2601	59	15	)	)	PUNCT
cana-2601	59	16	.	.	PUNCT
cana-2601	60	1	without	without	ADP
cana-2601	60	2	loss	loss	NOUN
cana-2601	60	3	of	of	ADP
cana-2601	60	4	generality	generality	NOUN
cana-2601	60	5	,	,	PUNCT
cana-2601	60	6	let	let	VERB
cana-2601	60	7	us	we	PRON
cana-2601	60	8	color	color	VERB
cana-2601	60	9	the	the	DET
cana-2601	60	10	vertex	vertex	NOUN
cana-2601	60	11	v21	v21	NOUN
cana-2601	60	12	in	in	ADP
cana-2601	60	13	st	st	PROPN
cana-2601	60	14	(	(	PUNCT
cana-2601	60	15	3	3	NUM
cana-2601	60	16	)	)	PUNCT
cana-2601	60	17	with	with	ADP
cana-2601	60	18	the	the	DET
cana-2601	60	19	color	color	NOUN
cana-2601	60	20	1	1	NUM
cana-2601	60	21	and	and	CCONJ
cana-2601	60	22	denoted	denote	VERB
cana-2601	60	23	by	by	ADP
cana-2601	60	24	c(v21	c(v21	NOUN
cana-2601	60	25	)	)	PUNCT
cana-2601	60	26	=	=	SYM
cana-2601	61	1	1	1	X
cana-2601	61	2	.	.	PUNCT
cana-2601	61	3	then	then	ADV
cana-2601	61	4	its	its	PRON
cana-2601	61	5	neighboring	neighboring	NOUN
cana-2601	61	6	vertices	vertex	NOUN
cana-2601	61	7	v11	v11	NOUN
cana-2601	61	8	,	,	PUNCT
cana-2601	61	9	v31	v31	NOUN
cana-2601	61	10	and	and	CCONJ
cana-2601	61	11	v32	v32	PROPN
cana-2601	61	12	can	can	AUX
cana-2601	61	13	be	be	AUX
cana-2601	61	14	colored	color	VERB
cana-2601	61	15	from	from	ADP
cana-2601	61	16	the	the	DET
cana-2601	61	17	set	set	NOUN
cana-2601	61	18	{	{	PUNCT
cana-2601	61	19	2	2	NUM
cana-2601	61	20	,	,	PUNCT
cana-2601	61	21	3	3	NUM
cana-2601	61	22	,	,	PUNCT
cana-2601	61	23	4	4	NUM
cana-2601	61	24	}	}	PUNCT
cana-2601	61	25	in	in	ADP
cana-2601	61	26	some	some	DET
cana-2601	61	27	order	order	NOUN
cana-2601	61	28	.	.	PUNCT
cana-2601	62	1	again	again	ADV
cana-2601	62	2	,	,	PUNCT
cana-2601	62	3	without	without	ADP
cana-2601	62	4	loss	loss	NOUN
cana-2601	62	5	of	of	ADP
cana-2601	62	6	generality	generality	NOUN
cana-2601	62	7	,	,	PUNCT
cana-2601	62	8	assume	assume	VERB
cana-2601	62	9	c(v11	c(v11	NOUN
cana-2601	62	10	)	)	PUNCT
cana-2601	62	11	=	=	SYM
cana-2601	62	12	2	2	NUM
cana-2601	62	13	,	,	PUNCT
cana-2601	62	14	c(v31	c(v31	NOUN
cana-2601	62	15	)	)	PUNCT
cana-2601	62	16	=	=	SYM
cana-2601	62	17	3	3	NUM
cana-2601	62	18	and	and	CCONJ
cana-2601	62	19	c(v32	c(v32	NUM
cana-2601	62	20	)	)	PUNCT
cana-2601	63	1	=	=	SYM
cana-2601	63	2	4	4	X
cana-2601	63	3	.	.	PUNCT
cana-2601	64	1	it	it	PRON
cana-2601	64	2	follows	follow	VERB
cana-2601	64	3	,	,	PUNCT
cana-2601	64	4	the	the	DET
cana-2601	64	5	vertices	vertex	NOUN
cana-2601	64	6	v33	v33	ADV
cana-2601	64	7	and	and	CCONJ
cana-2601	64	8	v34	v34	NOUN
cana-2601	64	9	can	can	AUX
cana-2601	64	10	be	be	AUX
cana-2601	64	11	colored	color	VERB
cana-2601	64	12	in	in	ADP
cana-2601	64	13	the	the	DET
cana-2601	64	14	following	following	ADJ
cana-2601	64	15	ways	way	NOUN
cana-2601	64	16	:	:	PUNCT
cana-2601	64	17	1	1	NUM
cana-2601	64	18	.	.	NUM
cana-2601	64	19	c(v33	c(v33	ADJ
cana-2601	64	20	)	)	PUNCT
cana-2601	65	1	=	=	SYM
cana-2601	65	2	2	2	NUM
cana-2601	65	3	2	2	NUM
cana-2601	65	4	.	.	NOUN
cana-2601	65	5	c(v34	c(v34	NOUN
cana-2601	65	6	)	)	PUNCT
cana-2601	65	7	=	=	SYM
cana-2601	65	8	1	1	NUM
cana-2601	65	9	or	or	CCONJ
cana-2601	65	10	3	3	NUM
cana-2601	65	11	.	.	PUNCT
cana-2601	66	1	now	now	ADV
cana-2601	66	2	,	,	PUNCT
cana-2601	66	3	whatever	whatever	PRON
cana-2601	66	4	may	may	AUX
cana-2601	66	5	be	be	AUX
cana-2601	66	6	the	the	DET
cana-2601	66	7	case	case	NOUN
cana-2601	66	8	,	,	PUNCT
cana-2601	66	9	since	since	SCONJ
cana-2601	66	10	c(v33	c(v33	ADV
cana-2601	66	11	)	)	PUNCT
cana-2601	67	1	=	=	SYM
cana-2601	67	2	2	2	X
cana-2601	67	3	,	,	PUNCT
cana-2601	67	4	it	it	PRON
cana-2601	67	5	is	be	AUX
cana-2601	67	6	easy	easy	ADJ
cana-2601	67	7	to	to	PART
cana-2601	67	8	see	see	VERB
cana-2601	67	9	that	that	SCONJ
cana-2601	67	10	the	the	DET
cana-2601	67	11	vertex	vertex	NOUN
cana-2601	67	12	v22	v22	NOUN
cana-2601	67	13	is	be	AUX
cana-2601	67	14	now	now	ADV
cana-2601	67	15	adjacent	adjacent	ADJ
cana-2601	67	16	with	with	ADP
cana-2601	67	17	two	two	NUM
cana-2601	67	18	vertices	vertex	NOUN
cana-2601	67	19	colored	color	VERB
cana-2601	67	20	with	with	ADP
cana-2601	67	21	2	2	NUM
cana-2601	67	22	.	.	PUNCT
cana-2601	68	1	therefore	therefore	ADV
cana-2601	68	2	,	,	PUNCT
cana-2601	68	3	h1(st	h1(st	PROPN
cana-2601	68	4	(	(	PUNCT
cana-2601	68	5	3	3	NUM
cana-2601	68	6	)	)	PUNCT
cana-2601	68	7	)	)	PUNCT
cana-2601	68	8	>	>	X
cana-2601	68	9	4	4	NUM
cana-2601	68	10	as	as	SCONJ
cana-2601	68	11	shown	show	VERB
cana-2601	68	12	in	in	ADP
cana-2601	68	13	figure	figure	NOUN
cana-2601	68	14	2	2	NUM
cana-2601	68	15	.	.	PUNCT
cana-2601	68	16	by	by	ADP
cana-2601	68	17	theorem	theorem	NOUN
cana-2601	68	18	2.1	2.1	NUM
cana-2601	68	19	,	,	PUNCT
cana-2601	68	20	we	we	PRON
cana-2601	68	21	have	have	VERB
cana-2601	68	22	h1(st	h1(st	PROPN
cana-2601	68	23	(	(	PUNCT
cana-2601	68	24	n	n	CCONJ
cana-2601	68	25	)	)	PUNCT
cana-2601	68	26	)	)	PUNCT
cana-2601	69	1	≥	≥	NOUN
cana-2601	69	2	h1(st	h1(st	PROPN
cana-2601	69	3	(	(	PUNCT
cana-2601	69	4	3	3	NUM
cana-2601	69	5	)	)	PUNCT
cana-2601	69	6	)	)	PUNCT
cana-2601	69	7	≥	≥	NOUN
cana-2601	70	1	5	5	NUM
cana-2601	70	2	.	.	PUNCT
cana-2601	71	1	we	we	PRON
cana-2601	71	2	now	now	ADV
cana-2601	71	3	color	color	VERB
cana-2601	71	4	the	the	DET
cana-2601	71	5	vertices	vertex	NOUN
cana-2601	71	6	of	of	ADP
cana-2601	71	7	st	st	PROPN
cana-2601	71	8	(	(	PUNCT
cana-2601	71	9	n	n	CCONJ
cana-2601	71	10	)	)	PUNCT
cana-2601	71	11	level	level	NOUN
cana-2601	71	12	-	-	PUNCT
cana-2601	71	13	wise	wise	ADJ
cana-2601	71	14	with	with	ADP
cana-2601	71	15	the	the	DET
cana-2601	71	16	color	color	NOUN
cana-2601	71	17	order	order	NOUN
cana-2601	71	18	from	from	ADP
cana-2601	71	19	left	leave	VERB
cana-2601	71	20	to	to	ADP
cana-2601	71	21	right	right	ADV
cana-2601	71	22	repeatedly	repeatedly	ADV
cana-2601	71	23	using	use	VERB
cana-2601	71	24	the	the	DET
cana-2601	71	25	colors	color	NOUN
cana-2601	71	26	from	from	ADP
cana-2601	71	27	the	the	DET
cana-2601	71	28	set	set	NOUN
cana-2601	71	29	{	{	PUNCT
cana-2601	71	30	1	1	NUM
cana-2601	71	31	,	,	PUNCT
cana-2601	71	32	2	2	NUM
cana-2601	71	33	,	,	PUNCT
cana-2601	71	34	3	3	NUM
cana-2601	71	35	,	,	PUNCT
cana-2601	71	36	4	4	NUM
cana-2601	71	37	,	,	PUNCT
cana-2601	71	38	5	5	NUM
cana-2601	71	39	}	}	PUNCT
cana-2601	71	40	as	as	SCONJ
cana-2601	71	41	described	describe	VERB
cana-2601	71	42	in	in	ADP
cana-2601	71	43	table	table	NOUN
cana-2601	71	44	1	1	NUM
cana-2601	71	45	.	.	PUNCT
cana-2601	71	46	table	table	NOUN
cana-2601	71	47	1	1	NUM
cana-2601	71	48	:	:	PUNCT
cana-2601	71	49	locally	locally	ADV
cana-2601	71	50	harmonious	harmonious	ADJ
cana-2601	71	51	coloring	coloring	NOUN
cana-2601	71	52	order	order	NOUN
cana-2601	71	53	of	of	ADP
cana-2601	71	54	st	st	PROPN
cana-2601	71	55	(	(	PUNCT
cana-2601	71	56	n	n	CCONJ
cana-2601	71	57	)	)	PUNCT
cana-2601	71	58	s.	s.	PROPN
cana-2601	71	59	no	no	INTJ
cana-2601	71	60	.	.	PUNCT
cana-2601	72	1	(	(	PUNCT
cana-2601	72	2	𝒏	𝒏	PROPN
cana-2601	72	3	−	−	PROPN
cana-2601	72	4	𝒊	𝒊	X
cana-2601	72	5	+	+	NOUN
cana-2601	72	6	𝟏	𝟏	X
cana-2601	72	7	)	)	PUNCT
cana-2601	72	8	(	(	PUNCT
cana-2601	72	9	𝒎𝒐𝒅	𝒎𝒐𝒅	NOUN
cana-2601	72	10	𝟒	𝟒	NUM
cana-2601	72	11	)	)	PUNCT
cana-2601	72	12	color	color	NOUN
cana-2601	72	13	order	order	NOUN
cana-2601	72	14	of	of	ADP
cana-2601	72	15	level	level	NOUN
cana-2601	72	16	i	i	NOUN
cana-2601	72	17	1	1	NUM
cana-2601	72	18	1	1	NUM
cana-2601	72	19	<	<	X
cana-2601	72	20	1	1	NUM
cana-2601	72	21	,	,	PUNCT
cana-2601	72	22	2	2	NUM
cana-2601	72	23	,	,	PUNCT
cana-2601	72	24	3	3	NUM
cana-2601	72	25	,	,	PUNCT
cana-2601	72	26	4	4	NUM
cana-2601	72	27	,	,	PUNCT
cana-2601	72	28	5	5	NUM
cana-2601	72	29	>	>	SYM
cana-2601	72	30	2	2	NUM
cana-2601	72	31	2	2	NUM
cana-2601	72	32	<	<	X
cana-2601	72	33	4	4	NUM
cana-2601	72	34	,	,	PUNCT
cana-2601	72	35	1	1	NUM
cana-2601	72	36	,	,	PUNCT
cana-2601	72	37	3	3	NUM
cana-2601	72	38	,	,	PUNCT
cana-2601	72	39	5	5	NUM
cana-2601	72	40	,	,	PUNCT
cana-2601	72	41	2	2	NUM
cana-2601	72	42	>	>	SYM
cana-2601	72	43	3	3	NUM
cana-2601	72	44	3	3	NUM
cana-2601	72	45	<	<	X
cana-2601	72	46	5	5	NUM
cana-2601	72	47	,	,	PUNCT
cana-2601	72	48	4	4	NUM
cana-2601	72	49	,	,	PUNCT
cana-2601	72	50	3	3	NUM
cana-2601	72	51	,	,	PUNCT
cana-2601	72	52	2	2	NUM
cana-2601	72	53	,	,	PUNCT
cana-2601	72	54	1	1	NUM
cana-2601	72	55	>	>	SYM
cana-2601	72	56	4	4	NUM
cana-2601	72	57	0	0	NUM
cana-2601	72	58	<	<	X
cana-2601	72	59	2	2	NUM
cana-2601	72	60	,	,	PUNCT
cana-2601	72	61	5	5	NUM
cana-2601	72	62	,	,	PUNCT
cana-2601	72	63	3	3	NUM
cana-2601	72	64	,	,	PUNCT
cana-2601	72	65	1	1	NUM
cana-2601	72	66	,	,	PUNCT
cana-2601	72	67	4	4	NUM
cana-2601	72	68	>	>	NOUN
cana-2601	72	69	communications	communication	NOUN
cana-2601	72	70	on	on	ADP
cana-2601	72	71	applied	apply	VERB
cana-2601	72	72	nonlinear	nonlinear	ADJ
cana-2601	72	73	analysis	analysis	NOUN
cana-2601	72	74	issn	issn	NOUN
cana-2601	72	75	:	:	PUNCT
cana-2601	72	76	1074	1074	NUM
cana-2601	72	77	-	-	PUNCT
cana-2601	72	78	133x	133x	NUM
cana-2601	72	79	vol	vol	NOUN
cana-2601	72	80	32	32	NUM
cana-2601	72	81	no	no	NOUN
cana-2601	72	82	.	.	PUNCT
cana-2601	73	1	3s	3s	NUM
cana-2601	73	2	(	(	PUNCT
cana-2601	73	3	2025	2025	NUM
cana-2601	73	4	)	)	PUNCT
cana-2601	73	5	215	215	NUM
cana-2601	73	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-2601	73	7	2	2	NUM
cana-2601	73	8	3	3	NUM
cana-2601	73	9	4	4	NUM
cana-2601	73	10	2	2	NUM
cana-2601	73	11	1	1	NUM
cana-2601	73	12	2	2	NUM
cana-2601	73	13	3	3	NUM
cana-2601	73	14	4	4	NUM
cana-2601	73	15	2	2	NUM
cana-2601	73	16	3	3	NUM
cana-2601	73	17	figure	figure	NOUN
cana-2601	73	18	2	2	NUM
cana-2601	73	19	:	:	PUNCT
cana-2601	73	20	illustration	illustration	NOUN
cana-2601	73	21	for	for	ADP
cana-2601	73	22	h1(st	h1(st	PROPN
cana-2601	73	23	(	(	PUNCT
cana-2601	73	24	3	3	NUM
cana-2601	73	25	)	)	PUNCT
cana-2601	73	26	)	)	PUNCT
cana-2601	73	27	>	>	X
cana-2601	73	28	4	4	NUM
cana-2601	73	29	from	from	ADP
cana-2601	73	30	the	the	DET
cana-2601	73	31	construction	construction	NOUN
cana-2601	73	32	of	of	ADP
cana-2601	73	33	st	st	PROPN
cana-2601	73	34	(	(	PUNCT
cana-2601	73	35	n	n	CCONJ
cana-2601	73	36	)	)	PUNCT
cana-2601	73	37	,	,	PUNCT
cana-2601	73	38	it	it	PRON
cana-2601	73	39	is	be	AUX
cana-2601	73	40	clear	clear	ADJ
cana-2601	73	41	that	that	SCONJ
cana-2601	73	42	all	all	DET
cana-2601	73	43	levels	level	NOUN
cana-2601	73	44	are	be	AUX
cana-2601	73	45	independent	independent	ADJ
cana-2601	73	46	except	except	SCONJ
cana-2601	73	47	the	the	DET
cana-2601	73	48	level	level	NOUN
cana-2601	73	49	n.	n.	NOUN
cana-2601	73	50	three	three	NUM
cana-2601	73	51	adjacent	adjacent	ADJ
cana-2601	73	52	vertices	vertex	NOUN
cana-2601	73	53	at	at	ADP
cana-2601	73	54	level	level	NOUN
cana-2601	74	1	i	i	PRON
cana-2601	74	2	=	=	SYM
cana-2601	74	3	n	n	PRON
cana-2601	74	4	have	have	VERB
cana-2601	74	5	consecutive	consecutive	ADJ
cana-2601	74	6	coloring	coloring	NOUN
cana-2601	74	7	say	say	VERB
cana-2601	74	8	k	k	NOUN
cana-2601	75	1	−	−	PROPN
cana-2601	76	1	1	1	NUM
cana-2601	76	2	,	,	PUNCT
cana-2601	76	3	k	k	NOUN
cana-2601	76	4	,	,	PUNCT
cana-2601	76	5	k	k	PROPN
cana-2601	77	1	+	+	NOUN
cana-2601	77	2	1	1	X
cana-2601	77	3	.	.	PUNCT
cana-2601	77	4	table	table	NOUN
cana-2601	77	5	1	1	NUM
cana-2601	77	6	shows	show	VERB
cana-2601	77	7	that	that	SCONJ
cana-2601	77	8	for	for	ADP
cana-2601	77	9	the	the	DET
cana-2601	77	10	vertexc	vertexc	NOUN
cana-2601	77	11	o	o	NOUN
cana-2601	77	12	l	l	NOUN
cana-2601	77	13	o	o	NOUN
cana-2601	77	14	r	r	NOUN
cana-2601	77	15	e	e	NOUN
cana-2601	77	16	d	d	X
cana-2601	77	17	k	k	PROPN
cana-2601	77	18	at	at	ADP
cana-2601	77	19	any	any	DET
cana-2601	77	20	level	level	NOUN
cana-2601	77	21	i	i	PRON
cana-2601	77	22	,	,	PUNCT
cana-2601	77	23	1	1	NUM
cana-2601	77	24	≤	≤	NUM
cana-2601	77	25	i	i	PRON
cana-2601	77	26	≤	≤	PROPN
cana-2601	77	27	n	n	CCONJ
cana-2601	77	28	,	,	PUNCT
cana-2601	77	29	its	its	PRON
cana-2601	77	30	neighboring	neighboring	NOUN
cana-2601	77	31	vertices	vertex	NOUN
cana-2601	77	32	receives	receive	VERB
cana-2601	77	33	the	the	DET
cana-2601	77	34	distinct	distinct	ADJ
cana-2601	77	35	colors	color	NOUN
cana-2601	77	36	from	from	ADP
cana-2601	77	37	the	the	DET
cana-2601	77	38	color	color	NOUN
cana-2601	77	39	-	-	PUNCT
cana-2601	77	40	set	set	NOUN
cana-2601	77	41	(	(	PUNCT
cana-2601	77	42	k	k	NOUN
cana-2601	77	43	+	+	PROPN
cana-2601	77	44	2	2	NUM
cana-2601	77	45	)	)	PUNCT
cana-2601	77	46	,	,	PUNCT
cana-2601	77	47	(	(	PUNCT
cana-2601	77	48	k	k	X
cana-2601	77	49	+	+	PROPN
cana-2601	77	50	3	3	NUM
cana-2601	77	51	)	)	PUNCT
cana-2601	77	52	,	,	PUNCT
cana-2601	77	53	(	(	PUNCT
cana-2601	77	54	k	k	X
cana-2601	77	55	+	+	PROPN
cana-2601	77	56	4	4	NUM
cana-2601	77	57	)	)	PUNCT
cana-2601	77	58	,	,	PUNCT
cana-2601	77	59	(	(	PUNCT
cana-2601	77	60	k	k	X
cana-2601	77	61	+	+	PROPN
cana-2601	77	62	6	6	NUM
cana-2601	77	63	)	)	PUNCT
cana-2601	77	64	,	,	PUNCT
cana-2601	77	65	(	(	PUNCT
cana-2601	77	66	k	k	X
cana-2601	77	67	+	+	NOUN
cana-2601	77	68	9	9	NUM
cana-2601	77	69	)	)	PUNCT
cana-2601	77	70	with	with	ADP
cana-2601	77	71	the	the	DET
cana-2601	77	72	numbers	number	NOUN
cana-2601	77	73	taken	take	VERB
cana-2601	77	74	modulo	modulo	NOUN
cana-2601	77	75	5	5	NUM
cana-2601	77	76	.	.	PUNCT
cana-2601	78	1	therefore	therefore	ADV
cana-2601	78	2	,	,	PUNCT
cana-2601	78	3	no	no	DET
cana-2601	78	4	two	two	NUM
cana-2601	78	5	incident	incident	NOUN
cana-2601	78	6	edges	edge	NOUN
cana-2601	78	7	share	share	VERB
cana-2601	78	8	the	the	DET
cana-2601	78	9	same	same	ADJ
cana-2601	78	10	color	color	NOUN
cana-2601	78	11	-	-	PUNCT
cana-2601	78	12	pair	pair	NOUN
cana-2601	78	13	.	.	PUNCT
cana-2601	79	1	by	by	ADP
cana-2601	79	2	lh	lh	PROPN
cana-2601	79	3	-	-	PUNCT
cana-2601	79	4	coloring	color	VERB
cana-2601	79	5	lemma	lemma	PROPN
cana-2601	79	6	,	,	PUNCT
cana-2601	79	7	h1(st	h1(st	PROPN
cana-2601	79	8	(	(	PUNCT
cana-2601	79	9	n	n	CCONJ
cana-2601	79	10	)	)	PUNCT
cana-2601	79	11	)	)	PUNCT
cana-2601	80	1	=	=	SYM
cana-2601	80	2	5	5	X
cana-2601	80	3	.	.	PUNCT
cana-2601	81	1	see	see	VERB
cana-2601	81	2	figure	figure	NOUN
cana-2601	81	3	3	3	NUM
cana-2601	81	4	.	.	NOUN
cana-2601	81	5	2	2	NUM
cana-2601	81	6	1	1	NUM
cana-2601	81	7	2	2	NUM
cana-2601	81	8	3	3	NUM
cana-2601	81	9	4	4	NUM
cana-2601	81	10	5	5	NUM
cana-2601	81	11	1	1	NUM
cana-2601	81	12	2	2	NUM
cana-2601	81	13	3	3	NUM
cana-2601	81	14	figure	figure	NOUN
cana-2601	81	15	3	3	NUM
cana-2601	81	16	:	:	PUNCT
cana-2601	81	17	h1(st	h1(st	PROPN
cana-2601	81	18	(	(	PUNCT
cana-2601	81	19	4	4	NUM
cana-2601	81	20	)	)	PUNCT
cana-2601	81	21	)	)	PUNCT
cana-2601	82	1	=	=	PUNCT
cana-2601	82	2	5	5	NUM
cana-2601	82	3	4	4	NUM
cana-2601	82	4	.	.	PUNCT
cana-2601	82	5	hypertree	hypertree	NOUN
cana-2601	82	6	definition	definition	NOUN
cana-2601	82	7	4.1	4.1	NUM
cana-2601	82	8	.	.	PUNCT
cana-2601	83	1	a	a	DET
cana-2601	83	2	complete	complete	ADJ
cana-2601	83	3	binary	binary	ADJ
cana-2601	83	4	tree	tree	NOUN
cana-2601	83	5	tn	tn	PROPN
cana-2601	83	6	is	be	AUX
cana-2601	83	7	the	the	DET
cana-2601	83	8	basic	basic	ADJ
cana-2601	83	9	scaffolding	scaffolding	NOUN
cana-2601	83	10	of	of	ADP
cana-2601	83	11	a	a	DET
cana-2601	83	12	hypertree	hypertree	NOUN
cana-2601	83	13	.	.	PUNCT
cana-2601	84	1	here	here	ADV
cana-2601	84	2	the	the	DET
cana-2601	84	3	vertices	vertex	NOUN
cana-2601	84	4	of	of	ADP
cana-2601	84	5	the	the	DET
cana-2601	84	6	tree	tree	NOUN
cana-2601	84	7	are	be	AUX
cana-2601	84	8	labeled	label	VERB
cana-2601	84	9	as	as	ADP
cana-2601	84	10	𝑣𝑖𝑗	𝑣𝑖𝑗	PROPN
cana-2601	84	11	,	,	PUNCT
cana-2601	84	12	0	0	NUM
cana-2601	84	13	≤	≤	NUM
cana-2601	84	14	i	i	PRON
cana-2601	84	15	≤	≤	PROPN
cana-2601	84	16	n	n	CCONJ
cana-2601	84	17	,	,	PUNCT
cana-2601	84	18	1	1	NUM
cana-2601	84	19	≤	≤	NUM
cana-2601	84	20	j	j	PROPN
cana-2601	84	21	≤	≤	NUM
cana-2601	84	22	2n	2n	NUM
cana-2601	84	23	,	,	PUNCT
cana-2601	84	24	where	where	SCONJ
cana-2601	84	25	i	i	PRON
cana-2601	84	26	represents	represent	VERB
cana-2601	84	27	the	the	DET
cana-2601	84	28	level	level	NOUN
cana-2601	84	29	and	and	CCONJ
cana-2601	84	30	j	j	PROPN
cana-2601	84	31	represents	represent	VERB
cana-2601	84	32	the	the	DET
cana-2601	84	33	position	position	NOUN
cana-2601	84	34	of	of	ADP
cana-2601	84	35	vertices	vertex	NOUN
cana-2601	84	36	of	of	ADP
cana-2601	84	37	the	the	DET
cana-2601	84	38	tree	tree	NOUN
cana-2601	84	39	at	at	ADP
cana-2601	84	40	any	any	DET
cana-2601	84	41	level	level	NOUN
cana-2601	84	42	i.	i.	NOUN
cana-2601	84	43	the	the	DET
cana-2601	84	44	root	root	NOUN
cana-2601	84	45	node	node	NOUN
cana-2601	84	46	receives	receive	VERB
cana-2601	84	47	the	the	DET
cana-2601	84	48	label	label	NOUN
cana-2601	84	49	𝑣01	𝑣01	NOUN
cana-2601	84	50	and	and	CCONJ
cana-2601	84	51	the	the	DET
cana-2601	84	52	root	root	NOUN
cana-2601	84	53	is	be	AUX
cana-2601	84	54	said	say	VERB
cana-2601	84	55	to	to	PART
cana-2601	84	56	be	be	AUX
cana-2601	84	57	at	at	ADP
cana-2601	84	58	level	level	NOUN
cana-2601	84	59	0	0	NUM
cana-2601	84	60	.	.	PUNCT
cana-2601	85	1	horizontal	horizontal	ADJ
cana-2601	85	2	links	link	NOUN
cana-2601	85	3	are	be	AUX
cana-2601	85	4	added	add	VERB
cana-2601	85	5	additionally	additionally	ADV
cana-2601	85	6	in	in	ADP
cana-2601	85	7	a	a	DET
cana-2601	85	8	hypertree	hypertree	NOUN
cana-2601	85	9	,	,	PUNCT
cana-2601	85	10	and	and	CCONJ
cana-2601	85	11	two	two	NUM
cana-2601	85	12	vertices	vertex	NOUN
cana-2601	85	13	of	of	ADP
cana-2601	85	14	the	the	DET
cana-2601	85	15	tree	tree	NOUN
cana-2601	85	16	are	be	AUX
cana-2601	85	17	united	unite	VERB
cana-2601	85	18	in	in	ADP
cana-2601	85	19	their	their	PRON
cana-2601	85	20	own	own	ADJ
cana-2601	85	21	level	level	NOUN
cana-2601	86	1	i	i	PRON
cana-2601	86	2	if	if	SCONJ
cana-2601	86	3	their	their	PRON
cana-2601	86	4	j	j	NOUN
cana-2601	86	5	’s	’s	PART
cana-2601	86	6	difference	difference	NOUN
cana-2601	86	7	is	be	AUX
cana-2601	86	8	2i−1	2i−1	NUM
cana-2601	86	9	.	.	PUNCT
cana-2601	87	1	we	we	PRON
cana-2601	87	2	denote	denote	VERB
cana-2601	87	3	an	an	DET
cana-2601	87	4	n	n	NUM
cana-2601	87	5	-	-	PUNCT
cana-2601	87	6	level	level	NOUN
cana-2601	87	7	hypertree	hypertree	NOUN
cana-2601	87	8	as	as	ADP
cana-2601	87	9	ht	ht	PROPN
cana-2601	87	10	(	(	PUNCT
cana-2601	87	11	n	n	CCONJ
cana-2601	87	12	)	)	PUNCT
cana-2601	87	13	.	.	PUNCT
cana-2601	88	1	it	it	PRON
cana-2601	88	2	has	have	VERB
cana-2601	88	3	2n+1−	2n+1−	PROPN
cana-2601	88	4	vertices	vertex	NOUN
cana-2601	88	5	and	and	CCONJ
cana-2601	88	6	3(2n	3(2n	NUM
cana-2601	88	7	−	−	NOUN
cana-2601	88	8	1	1	NUM
cana-2601	88	9	)	)	PUNCT
cana-2601	88	10	edges	edge	NOUN
cana-2601	88	11	.	.	PUNCT
cana-2601	89	1	see	see	VERB
cana-2601	89	2	figure	figure	NOUN
cana-2601	89	3	4	4	NUM
cana-2601	89	4	.	.	PUNCT
cana-2601	89	5	communications	communication	NOUN
cana-2601	89	6	on	on	ADP
cana-2601	89	7	applied	apply	VERB
cana-2601	89	8	nonlinear	nonlinear	ADJ
cana-2601	89	9	analysis	analysis	NOUN
cana-2601	89	10	issn	issn	NOUN
cana-2601	89	11	:	:	PUNCT
cana-2601	89	12	1074	1074	NUM
cana-2601	89	13	-	-	PUNCT
cana-2601	89	14	133x	133x	NUM
cana-2601	89	15	vol	vol	NOUN
cana-2601	89	16	32	32	NUM
cana-2601	90	1	no	no	NOUN
cana-2601	90	2	.	.	PUNCT
cana-2601	91	1	3s	3s	NUM
cana-2601	91	2	(	(	PUNCT
cana-2601	91	3	2025	2025	NUM
cana-2601	91	4	)	)	PUNCT
cana-2601	91	5	216	216	NUM
cana-2601	91	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2601	91	7	for	for	ADP
cana-2601	91	8	n	n	PRON
cana-2601	91	9	≥	≥	NUM
cana-2601	91	10	2	2	NUM
cana-2601	91	11	,	,	PUNCT
cana-2601	91	12	we	we	PRON
cana-2601	91	13	now	now	ADV
cana-2601	91	14	propose	propose	VERB
cana-2601	91	15	a	a	DET
cana-2601	91	16	locally	locally	ADV
cana-2601	91	17	harmonious	harmonious	ADJ
cana-2601	91	18	coloring	coloring	NOUN
cana-2601	91	19	algorithm	algorithm	NOUN
cana-2601	91	20	of	of	ADP
cana-2601	91	21	ht	ht	PROPN
cana-2601	91	22	(	(	PUNCT
cana-2601	91	23	n	n	CCONJ
cana-2601	91	24	)	)	PUNCT
cana-2601	91	25	.	.	PUNCT
cana-2601	92	1	for	for	ADP
cana-2601	92	2	2	2	NUM
cana-2601	92	3	≤	≤	NOUN
cana-2601	92	4	i	i	PRON
cana-2601	92	5	≤	≤	PROPN
cana-2601	92	6	n	n	CCONJ
cana-2601	92	7	,	,	PUNCT
cana-2601	92	8	the	the	DET
cana-2601	92	9	color	color	NOUN
cana-2601	92	10	order	order	NOUN
cana-2601	92	11	given	give	VERB
cana-2601	92	12	in	in	ADP
cana-2601	92	13	the	the	DET
cana-2601	92	14	algorithm	algorithm	NOUN
cana-2601	92	15	implies	imply	VERB
cana-2601	92	16	to	to	PART
cana-2601	92	17	color	color	VERB
cana-2601	92	18	the	the	DET
cana-2601	92	19	vertices	vertex	NOUN
cana-2601	92	20	vij	vij	PROPN
cana-2601	92	21	from	from	ADP
cana-2601	92	22	the	the	DET
cana-2601	92	23	left	left	NOUN
cana-2601	92	24	to	to	ADP
cana-2601	92	25	the	the	DET
cana-2601	92	26	right	right	NOUN
cana-2601	92	27	repeatedly	repeatedly	ADV
cana-2601	92	28	as	as	SCONJ
cana-2601	92	29	construed	construe	VERB
cana-2601	92	30	in	in	ADP
cana-2601	92	31	table	table	NOUN
cana-2601	92	32	2	2	NUM
cana-2601	92	33	.	.	PUNCT
cana-2601	92	34	algorithm	algorithm	NOUN
cana-2601	92	35	1	1	NUM
cana-2601	92	36	is	be	AUX
cana-2601	92	37	illustrated	illustrate	VERB
cana-2601	92	38	in	in	ADP
cana-2601	92	39	figure	figure	NOUN
cana-2601	92	40	5	5	NUM
cana-2601	92	41	.	.	PUNCT
cana-2601	92	42	figure	figure	VERB
cana-2601	92	43	4	4	NUM
cana-2601	92	44	:	:	PUNCT
cana-2601	92	45	vertex	vertex	NOUN
cana-2601	92	46	labeling	labeling	NOUN
cana-2601	92	47	of	of	ADP
cana-2601	92	48	ht	ht	PROPN
cana-2601	92	49	(	(	PUNCT
cana-2601	92	50	3	3	NUM
cana-2601	92	51	)	)	PUNCT
cana-2601	92	52	table	table	NOUN
cana-2601	92	53	2	2	NUM
cana-2601	92	54	:	:	PUNCT
cana-2601	92	55	locally	locally	ADV
cana-2601	92	56	harmonious	harmonious	ADJ
cana-2601	92	57	coloring	coloring	NOUN
cana-2601	92	58	order	order	NOUN
cana-2601	92	59	of	of	ADP
cana-2601	92	60	ht	ht	PROPN
cana-2601	92	61	(	(	PUNCT
cana-2601	92	62	n	n	CCONJ
cana-2601	92	63	)	)	PUNCT
cana-2601	92	64	,	,	PUNCT
cana-2601	93	1	n	n	X
cana-2601	93	2	≥	≥	NOUN
cana-2601	93	3	2	2	NUM
cana-2601	93	4	proof	proof	NOUN
cana-2601	93	5	of	of	ADP
cana-2601	93	6	correctness	correctness	NOUN
cana-2601	93	7	(	(	PUNCT
cana-2601	93	8	algorithm	algorithm	NOUN
cana-2601	93	9	1	1	NUM
cana-2601	93	10	):	):	PUNCT
cana-2601	93	11	it	it	PRON
cana-2601	93	12	is	be	AUX
cana-2601	93	13	to	to	PART
cana-2601	93	14	be	be	AUX
cana-2601	93	15	noted	note	VERB
cana-2601	93	16	that	that	SCONJ
cana-2601	93	17	any	any	DET
cana-2601	93	18	vertex	vertex	NOUN
cana-2601	93	19	v	v	ADP
cana-2601	93	20	∈	∈	NOUN
cana-2601	93	21	v	v	NOUN
cana-2601	93	22	(	(	PUNCT
cana-2601	93	23	ht	ht	PROPN
cana-2601	93	24	(	(	PUNCT
cana-2601	93	25	n	n	CCONJ
cana-2601	93	26	)	)	PUNCT
cana-2601	93	27	)	)	PUNCT
cana-2601	93	28	at	at	ADP
cana-2601	93	29	a	a	DET
cana-2601	93	30	particular	particular	ADJ
cana-2601	93	31	communications	communication	NOUN
cana-2601	93	32	on	on	ADP
cana-2601	93	33	applied	apply	VERB
cana-2601	93	34	nonlinear	nonlinear	ADJ
cana-2601	93	35	analysis	analysis	NOUN
cana-2601	93	36	issn	issn	NOUN
cana-2601	93	37	:	:	PUNCT
cana-2601	93	38	1074	1074	NUM
cana-2601	93	39	-	-	PUNCT
cana-2601	93	40	133x	133x	NUM
cana-2601	93	41	vol	vol	NOUN
cana-2601	93	42	32	32	NUM
cana-2601	94	1	no	no	NOUN
cana-2601	94	2	.	.	PUNCT
cana-2601	95	1	3s	3s	NUM
cana-2601	95	2	(	(	PUNCT
cana-2601	95	3	2025	2025	NUM
cana-2601	95	4	)	)	PUNCT
cana-2601	95	5	217	217	NUM
cana-2601	95	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2601	95	7	level	level	NOUN
cana-2601	95	8	i	i	PRON
cana-2601	95	9	have	have	VERB
cana-2601	95	10	its	its	PRON
cana-2601	95	11	neighborhood	neighborhood	NOUN
cana-2601	95	12	vertices	vertex	NOUN
cana-2601	95	13	n	n	X
cana-2601	95	14	(	(	PUNCT
cana-2601	95	15	v	v	NOUN
cana-2601	95	16	)	)	PUNCT
cana-2601	95	17	in	in	ADP
cana-2601	95	18	the	the	DET
cana-2601	95	19	level	level	NOUN
cana-2601	96	1	i	i	PRON
cana-2601	96	2	−	−	PROPN
cana-2601	96	3	1	1	NUM
cana-2601	96	4	,	,	PUNCT
cana-2601	96	5	i	i	PRON
cana-2601	96	6	,	,	PUNCT
cana-2601	96	7	i	i	PRON
cana-2601	96	8	+	+	NOUN
cana-2601	96	9	1	1	X
cana-2601	96	10	.	.	X
cana-2601	96	11	two	two	NUM
cana-2601	96	12	vertices	vertex	NOUN
cana-2601	96	13	adjacent	adjacent	ADJ
cana-2601	96	14	at	at	ADP
cana-2601	96	15	a	a	DET
cana-2601	96	16	particular	particular	ADJ
cana-2601	96	17	level	level	NOUN
cana-2601	96	18	‘	'	PUNCT
cana-2601	96	19	i	i	PRON
cana-2601	96	20	’	'	PUNCT
cana-2601	96	21	have	have	VERB
cana-2601	96	22	consecutive	consecutive	ADJ
cana-2601	96	23	coloring	coloring	NOUN
cana-2601	96	24	say	say	VERB
cana-2601	96	25	k	k	PROPN
cana-2601	96	26	and	and	CCONJ
cana-2601	96	27	k	k	PROPN
cana-2601	97	1	+	+	CCONJ
cana-2601	97	2	1	1	NUM
cana-2601	97	3	or	or	CCONJ
cana-2601	97	4	vice	vice	NOUN
cana-2601	97	5	versa	versa	ADV
cana-2601	97	6	.	.	PUNCT
cana-2601	98	1	from	from	ADP
cana-2601	98	2	the	the	DET
cana-2601	98	3	proposed	propose	VERB
cana-2601	98	4	algorithm	algorithm	NOUN
cana-2601	98	5	,	,	PUNCT
cana-2601	98	6	vertices	vertex	NOUN
cana-2601	98	7	of	of	ADP
cana-2601	98	8	any	any	DET
cana-2601	98	9	three	three	NUM
cana-2601	98	10	consecutive	consecutive	ADJ
cana-2601	98	11	levels	level	NOUN
cana-2601	98	12	in	in	ADP
cana-2601	98	13	ht	ht	PROPN
cana-2601	98	14	(	(	PUNCT
cana-2601	98	15	n	n	CCONJ
cana-2601	98	16	)	)	PUNCT
cana-2601	98	17	have	have	AUX
cana-2601	98	18	colored	color	VERB
cana-2601	98	19	using	use	VERB
cana-2601	98	20	three	three	NUM
cana-2601	98	21	distinct	distinct	ADJ
cana-2601	98	22	colorpairs	colorpair	NOUN
cana-2601	98	23	from	from	ADP
cana-2601	98	24	the	the	DET
cana-2601	98	25	color	color	NOUN
cana-2601	98	26	set	set	NOUN
cana-2601	98	27	{	{	PUNCT
cana-2601	98	28	1	1	NUM
cana-2601	98	29	,	,	PUNCT
cana-2601	98	30	2	2	NUM
cana-2601	98	31	,	,	PUNCT
cana-2601	98	32	3	3	NUM
cana-2601	98	33	,	,	PUNCT
cana-2601	98	34	4	4	NUM
cana-2601	98	35	,	,	PUNCT
cana-2601	98	36	5	5	NUM
cana-2601	98	37	,	,	PUNCT
cana-2601	98	38	6	6	NUM
cana-2601	98	39	}	}	PUNCT
cana-2601	98	40	.	.	PUNCT
cana-2601	99	1	therefore	therefore	ADV
cana-2601	99	2	,	,	PUNCT
cana-2601	99	3	for	for	ADP
cana-2601	99	4	any	any	DET
cana-2601	99	5	vertex	vertex	NOUN
cana-2601	99	6	v	v	ADP
cana-2601	99	7	∈	∈	NOUN
cana-2601	99	8	v	v	NOUN
cana-2601	99	9	(	(	PUNCT
cana-2601	99	10	ht	ht	PROPN
cana-2601	99	11	(	(	PUNCT
cana-2601	99	12	n	n	CCONJ
cana-2601	99	13	)	)	PUNCT
cana-2601	99	14	)	)	PUNCT
cana-2601	99	15	,	,	PUNCT
cana-2601	99	16	the	the	DET
cana-2601	99	17	vertices	vertex	NOUN
cana-2601	99	18	of	of	ADP
cana-2601	99	19	n	n	NOUN
cana-2601	99	20	[	[	X
cana-2601	99	21	v	v	NOUN
cana-2601	99	22	]	]	PUNCT
cana-2601	99	23	receives	receive	VERB
cana-2601	99	24	distinct	distinct	ADJ
cana-2601	99	25	colors	color	NOUN
cana-2601	99	26	.	.	PUNCT
cana-2601	100	1	thus	thus	ADV
cana-2601	100	2	,	,	PUNCT
cana-2601	100	3	the	the	DET
cana-2601	100	4	coloring	coloring	NOUN
cana-2601	100	5	is	be	AUX
cana-2601	100	6	locally	locally	ADV
cana-2601	100	7	harmonious	harmonious	ADJ
cana-2601	100	8	coloring	coloring	NOUN
cana-2601	100	9	.	.	PUNCT
cana-2601	101	1	1	1	NUM
cana-2601	101	2	1	1	NUM
cana-2601	101	3	1	1	NUM
cana-2601	101	4	figure	figure	NOUN
cana-2601	101	5	5	5	NUM
cana-2601	101	6	:	:	PUNCT
cana-2601	101	7	locally	locally	ADV
cana-2601	101	8	harmonious	harmonious	ADJ
cana-2601	101	9	coloring	coloring	NOUN
cana-2601	101	10	of	of	ADP
cana-2601	101	11	ht	ht	PROPN
cana-2601	101	12	(	(	PUNCT
cana-2601	101	13	3	3	NUM
cana-2601	101	14	)	)	PUNCT
cana-2601	101	15	theorem	theorem	VERB
cana-2601	101	16	4.2	4.2	NUM
cana-2601	101	17	.	.	PUNCT
cana-2601	102	1	let	let	VERB
cana-2601	102	2	g	g	NOUN
cana-2601	102	3	be	be	AUX
cana-2601	102	4	the	the	DET
cana-2601	102	5	hypertree	hypertree	NOUN
cana-2601	102	6	ht	ht	PROPN
cana-2601	102	7	(	(	PUNCT
cana-2601	102	8	n	n	CCONJ
cana-2601	102	9	)	)	PUNCT
cana-2601	102	10	,	,	PUNCT
cana-2601	103	1	n	n	PRON
cana-2601	103	2	≥	≥	NOUN
cana-2601	103	3	2	2	NUM
cana-2601	103	4	.	.	PUNCT
cana-2601	104	1	then	then	ADV
cana-2601	104	2	g	g	PROPN
cana-2601	104	3	admits	admit	VERB
cana-2601	104	4	locally	locally	ADV
cana-2601	104	5	harmonious	harmonious	ADJ
cana-2601	104	6	coloring	coloring	NOUN
cana-2601	104	7	with	with	ADP
cana-2601	104	8	the	the	DET
cana-2601	104	9	chromatic	chromatic	ADJ
cana-2601	104	10	number	number	NOUN
cana-2601	104	11	h1(g	h1(g	NOUN
cana-2601	104	12	)	)	PUNCT
cana-2601	104	13	=	=	SYM
cana-2601	105	1	6	6	X
cana-2601	105	2	.	.	PUNCT
cana-2601	105	3	proof	proof	NOUN
cana-2601	105	4	.	.	PUNCT
cana-2601	106	1	from	from	ADP
cana-2601	106	2	the	the	DET
cana-2601	106	3	proposed	propose	VERB
cana-2601	106	4	algorithm	algorithm	NOUN
cana-2601	106	5	,	,	PUNCT
cana-2601	106	6	it	it	PRON
cana-2601	106	7	is	be	AUX
cana-2601	106	8	clear	clear	ADJ
cana-2601	106	9	that	that	SCONJ
cana-2601	106	10	no	no	DET
cana-2601	106	11	two	two	NUM
cana-2601	106	12	adjacent	adjacent	ADJ
cana-2601	106	13	edges	edge	NOUN
cana-2601	106	14	share	share	VERB
cana-2601	106	15	the	the	DET
cana-2601	106	16	same	same	ADJ
cana-2601	106	17	colorpair	colorpair	NOUN
cana-2601	106	18	and	and	CCONJ
cana-2601	106	19	the	the	DET
cana-2601	106	20	number	number	NOUN
cana-2601	106	21	of	of	ADP
cana-2601	106	22	colors	color	NOUN
cana-2601	106	23	used	use	VERB
cana-2601	106	24	to	to	PART
cana-2601	106	25	color	color	VERB
cana-2601	106	26	g	g	PROPN
cana-2601	106	27	is	be	AUX
cana-2601	106	28	6	6	NUM
cana-2601	106	29	.	.	PUNCT
cana-2601	107	1	hence	hence	ADV
cana-2601	107	2	,	,	PUNCT
cana-2601	107	3	by	by	ADP
cana-2601	107	4	lh	lh	PROPN
cana-2601	107	5	-	-	PUNCT
cana-2601	107	6	coloring	color	VERB
cana-2601	107	7	lemma	lemma	PROPN
cana-2601	107	8	,	,	PUNCT
cana-2601	107	9	h1(g	h1(g	PROPN
cana-2601	107	10	)	)	PUNCT
cana-2601	107	11	=	=	PUNCT
cana-2601	107	12	6	6	NUM
cana-2601	107	13	.	.	NOUN
cana-2601	107	14	5	5	NUM
cana-2601	107	15	.	.	X
cana-2601	107	16	shuffle	shuffle	PROPN
cana-2601	107	17	hypertree	hypertree	PROPN
cana-2601	107	18	definition	definition	NOUN
cana-2601	107	19	5.1	5.1	NUM
cana-2601	107	20	.	.	PUNCT
cana-2601	108	1	shuffle	shuffle	PROPN
cana-2601	108	2	hypertree	hypertree	PROPN
cana-2601	108	3	sht	sht	PROPN
cana-2601	108	4	(	(	PUNCT
cana-2601	108	5	n	n	CCONJ
cana-2601	108	6	)	)	PUNCT
cana-2601	109	1	[	[	X
cana-2601	109	2	8	8	NUM
cana-2601	109	3	]	]	PUNCT
cana-2601	109	4	have	have	AUX
cana-2601	109	5	been	be	AUX
cana-2601	109	6	constructed	construct	VERB
cana-2601	109	7	by	by	ADP
cana-2601	109	8	doing	do	VERB
cana-2601	109	9	certain	certain	ADJ
cana-2601	109	10	modifications	modification	NOUN
cana-2601	109	11	in	in	ADP
cana-2601	109	12	ht	ht	PROPN
cana-2601	109	13	(	(	PUNCT
cana-2601	109	14	n	n	CCONJ
cana-2601	109	15	)	)	PUNCT
cana-2601	109	16	,	,	PUNCT
cana-2601	109	17	which	which	PRON
cana-2601	109	18	is	be	AUX
cana-2601	109	19	stated	state	VERB
cana-2601	109	20	as	as	SCONJ
cana-2601	109	21	follows	follow	VERB
cana-2601	109	22	:	:	PUNCT
cana-2601	109	23	the	the	DET
cana-2601	109	24	deletion	deletion	NOUN
cana-2601	109	25	of	of	ADP
cana-2601	109	26	hyper	hyper	ADJ
cana-2601	109	27	edges	edge	NOUN
cana-2601	109	28	in	in	ADP
cana-2601	109	29	ht	ht	PROPN
cana-2601	109	30	(	(	PUNCT
cana-2601	109	31	n	n	CCONJ
cana-2601	109	32	)	)	PUNCT
cana-2601	109	33	and	and	CCONJ
cana-2601	109	34	replacing	replace	VERB
cana-2601	109	35	with	with	ADP
cana-2601	109	36	the	the	DET
cana-2601	109	37	new	new	ADJ
cana-2601	109	38	hyper	hyper	ADJ
cana-2601	109	39	edges	edge	NOUN
cana-2601	109	40	(	(	PUNCT
cana-2601	109	41	2i	2i	NOUN
cana-2601	109	42	+	+	NOUN
cana-2601	109	43	2k	2k	NOUN
cana-2601	109	44	−	−	NOUN
cana-2601	109	45	1	1	NUM
cana-2601	109	46	,	,	PUNCT
cana-2601	109	47	2i	2i	NOUN
cana-2601	109	48	+	+	CCONJ
cana-2601	109	49	2k	2k	NUM
cana-2601	109	50	)	)	PUNCT
cana-2601	109	51	and	and	CCONJ
cana-2601	109	52	(	(	PUNCT
cana-2601	109	53	2i	2i	NUM
cana-2601	109	54	,	,	PUNCT
cana-2601	109	55	2i+1	2i+1	PROPN
cana-2601	109	56	−	−	NOUN
cana-2601	109	57	1	1	NUM
cana-2601	109	58	)	)	PUNCT
cana-2601	109	59	where	where	SCONJ
cana-2601	109	60	1	1	NUM
cana-2601	109	61	≤	≤	NUM
cana-2601	109	62	i	i	PRON
cana-2601	109	63	≤	≤	PROPN
cana-2601	109	64	n	n	CCONJ
cana-2601	109	65	,	,	PUNCT
cana-2601	109	66	1	1	NUM
cana-2601	109	67	≤	≤	NUM
cana-2601	109	68	k	k	X
cana-2601	109	69	≤	≤	PROPN
cana-2601	109	70	2i−1	2i−1	NUM
cana-2601	109	71	−	−	PROPN
cana-2601	109	72	1	1	NUM
cana-2601	109	73	,	,	PUNCT
cana-2601	109	74	resulting	result	VERB
cana-2601	109	75	into	into	ADP
cana-2601	109	76	a	a	DET
cana-2601	109	77	new	new	ADJ
cana-2601	109	78	graph	graph	NOUN
cana-2601	109	79	called	call	VERB
cana-2601	109	80	shuffle	shuffle	PROPN
cana-2601	109	81	hyper	hyper	ADJ
cana-2601	109	82	tree	tree	NOUN
cana-2601	109	83	.	.	PUNCT
cana-2601	110	1	it	it	PRON
cana-2601	110	2	is	be	AUX
cana-2601	110	3	denoted	denote	VERB
cana-2601	110	4	by	by	ADP
cana-2601	110	5	sht	sht	PROPN
cana-2601	110	6	(	(	PUNCT
cana-2601	110	7	n	n	CCONJ
cana-2601	110	8	)	)	PUNCT
cana-2601	110	9	.	.	PUNCT
cana-2601	111	1	it	it	PRON
cana-2601	111	2	is	be	AUX
cana-2601	111	3	made	make	VERB
cana-2601	111	4	up	up	ADP
cana-2601	111	5	of	of	ADP
cana-2601	111	6	2n+1	2n+1	PROPN
cana-2601	111	7	−	−	PROPN
cana-2601	111	8	1	1	NUM
cana-2601	111	9	,	,	PUNCT
cana-2601	111	10	3(2n	3(2n	NUM
cana-2601	111	11	−	−	NOUN
cana-2601	111	12	1	1	NUM
cana-2601	111	13	)	)	PUNCT
cana-2601	111	14	vertices	vertex	NOUN
cana-2601	111	15	and	and	CCONJ
cana-2601	111	16	edges	edge	NOUN
cana-2601	111	17	respectively	respectively	ADV
cana-2601	111	18	.	.	PUNCT
cana-2601	112	1	see	see	VERB
cana-2601	112	2	figure	figure	NOUN
cana-2601	112	3	6	6	NUM
cana-2601	112	4	.	.	PUNCT
cana-2601	112	5	figure	figure	VERB
cana-2601	112	6	6	6	NUM
cana-2601	112	7	:	:	PUNCT
cana-2601	112	8	vertex	vertex	NOUN
cana-2601	112	9	representation	representation	NOUN
cana-2601	112	10	of	of	ADP
cana-2601	112	11	sht	sht	NOUN
cana-2601	112	12	(	(	PUNCT
cana-2601	112	13	3	3	NUM
cana-2601	112	14	)	)	PUNCT
cana-2601	112	15	11	11	NUM
cana-2601	112	16	12	12	NUM
cana-2601	112	17	21	21	NUM
cana-2601	112	18	22	22	NUM
cana-2601	112	19	v	v	NUM
cana-2601	112	20	3	3	NUM
cana-2601	112	21	24	24	NUM
cana-2601	112	22	31	31	NUM
cana-2601	112	23	32	32	NUM
cana-2601	112	24	33	33	NUM
cana-2601	112	25	34	34	NUM
cana-2601	112	26	35	35	NUM
cana-2601	112	27	36	36	NUM
cana-2601	112	28	37	37	NUM
cana-2601	112	29	38	38	NUM
cana-2601	112	30	v	v	NUM
cana-2601	112	31	01	01	NUM
cana-2601	112	32	communications	communication	NOUN
cana-2601	112	33	on	on	ADP
cana-2601	112	34	applied	apply	VERB
cana-2601	112	35	nonlinear	nonlinear	ADJ
cana-2601	112	36	analysis	analysis	NOUN
cana-2601	112	37	issn	issn	NOUN
cana-2601	112	38	:	:	PUNCT
cana-2601	112	39	1074	1074	NUM
cana-2601	112	40	-	-	PUNCT
cana-2601	112	41	133x	133x	NUM
cana-2601	112	42	vol	vol	NOUN
cana-2601	112	43	32	32	NUM
cana-2601	112	44	no	no	NOUN
cana-2601	112	45	.	.	PUNCT
cana-2601	113	1	3s	3s	NUM
cana-2601	113	2	(	(	PUNCT
cana-2601	113	3	2025	2025	NUM
cana-2601	113	4	)	)	PUNCT
cana-2601	113	5	218	218	NUM
cana-2601	113	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2601	113	7	for	for	ADP
cana-2601	113	8	n	n	PRON
cana-2601	113	9	≥	≥	NUM
cana-2601	113	10	2	2	NUM
cana-2601	113	11	,	,	PUNCT
cana-2601	113	12	we	we	PRON
cana-2601	113	13	now	now	ADV
cana-2601	113	14	propose	propose	VERB
cana-2601	113	15	a	a	DET
cana-2601	113	16	locally	locally	ADV
cana-2601	113	17	harmonious	harmonious	ADJ
cana-2601	113	18	coloring	coloring	NOUN
cana-2601	113	19	algorithm	algorithm	NOUN
cana-2601	113	20	of	of	ADP
cana-2601	113	21	sht	sht	PROPN
cana-2601	113	22	(	(	PUNCT
cana-2601	113	23	n	n	CCONJ
cana-2601	113	24	)	)	PUNCT
cana-2601	113	25	.	.	PUNCT
cana-2601	114	1	color	color	NOUN
cana-2601	114	2	order	order	NOUN
cana-2601	114	3	given	give	VERB
cana-2601	114	4	in	in	ADP
cana-2601	114	5	an	an	DET
cana-2601	114	6	algorithm	algorithm	NOUN
cana-2601	114	7	have	have	VERB
cana-2601	114	8	to	to	PART
cana-2601	114	9	be	be	AUX
cana-2601	114	10	color	color	VERB
cana-2601	114	11	the	the	DET
cana-2601	114	12	vertices	vertex	NOUN
cana-2601	114	13	vij	vij	PROPN
cana-2601	114	14	from	from	ADP
cana-2601	114	15	the	the	DET
cana-2601	114	16	left	left	NOUN
cana-2601	114	17	to	to	ADP
cana-2601	114	18	the	the	DET
cana-2601	114	19	right	right	NOUN
cana-2601	114	20	repeatedly	repeatedly	ADV
cana-2601	114	21	in	in	ADP
cana-2601	114	22	the	the	DET
cana-2601	114	23	particular	particular	ADJ
cana-2601	114	24	level	level	NOUN
cana-2601	114	25	i	i	PRON
cana-2601	114	26	using	use	VERB
cana-2601	114	27	the	the	DET
cana-2601	114	28	color	color	NOUN
cana-2601	114	29	in	in	ADP
cana-2601	114	30	the	the	DET
cana-2601	114	31	order	order	NOUN
cana-2601	114	32	as	as	SCONJ
cana-2601	114	33	construed	construe	VERB
cana-2601	114	34	in	in	ADP
cana-2601	114	35	table	table	NOUN
cana-2601	114	36	3	3	NUM
cana-2601	114	37	.	.	PUNCT
cana-2601	114	38	table	table	NOUN
cana-2601	114	39	3	3	NUM
cana-2601	114	40	:	:	PUNCT
cana-2601	114	41	locally	locally	ADV
cana-2601	114	42	harmonious	harmonious	ADJ
cana-2601	114	43	coloring	coloring	NOUN
cana-2601	114	44	order	order	NOUN
cana-2601	114	45	of	of	ADP
cana-2601	114	46	sht	sht	NOUN
cana-2601	114	47	(	(	PUNCT
cana-2601	114	48	n	n	CCONJ
cana-2601	114	49	)	)	PUNCT
cana-2601	114	50	,	,	PUNCT
cana-2601	114	51	n	n	PRON
cana-2601	114	52	≥	≥	NOUN
cana-2601	114	53	2	2	NUM
cana-2601	114	54	theorem	theorem	VERB
cana-2601	114	55	5.2	5.2	NUM
cana-2601	114	56	.	.	PUNCT
cana-2601	115	1	the	the	DET
cana-2601	115	2	shuffle	shuffle	PROPN
cana-2601	115	3	hypertree	hypertree	NOUN
cana-2601	115	4	network	network	NOUN
cana-2601	115	5	sht	sht	PROPN
cana-2601	115	6	(	(	PUNCT
cana-2601	115	7	n	n	CCONJ
cana-2601	115	8	)	)	PUNCT
cana-2601	115	9	,	,	PUNCT
cana-2601	115	10	n	n	PRON
cana-2601	115	11	≥	≥	NOUN
cana-2601	115	12	2	2	NUM
cana-2601	115	13	admits	admit	VERB
cana-2601	115	14	locally	locally	ADV
cana-2601	115	15	harmonious	harmonious	ADJ
cana-2601	115	16	coloring	coloring	NOUN
cana-2601	115	17	with	with	ADP
cana-2601	115	18	the	the	DET
cana-2601	115	19	chromatic	chromatic	ADJ
cana-2601	115	20	number	number	NOUN
cana-2601	115	21	proof	proof	NOUN
cana-2601	115	22	.	.	PUNCT
cana-2601	116	1	from	from	ADP
cana-2601	116	2	the	the	DET
cana-2601	116	3	proposed	propose	VERB
cana-2601	116	4	algorithm	algorithm	NOUN
cana-2601	116	5	,	,	PUNCT
cana-2601	116	6	it	it	PRON
cana-2601	116	7	is	be	AUX
cana-2601	116	8	clear	clear	ADJ
cana-2601	116	9	that	that	SCONJ
cana-2601	116	10	the	the	DET
cana-2601	116	11	number	number	NOUN
cana-2601	116	12	of	of	ADP
cana-2601	116	13	colors	color	NOUN
cana-2601	116	14	mandatory	mandatory	ADJ
cana-2601	116	15	for	for	ADP
cana-2601	116	16	solv	solv	ADJ
cana-2601	116	17	ing	e	VERB
cana-2601	116	18	the	the	DET
cana-2601	116	19	locally	locally	ADV
cana-2601	116	20	harmonious	harmonious	ADJ
cana-2601	116	21	coloring	coloring	NOUN
cana-2601	116	22	problem	problem	NOUN
cana-2601	116	23	of	of	ADP
cana-2601	116	24	sht	sht	NOUN
cana-2601	116	25	(	(	PUNCT
cana-2601	116	26	2	2	NUM
cana-2601	116	27	)	)	PUNCT
cana-2601	116	28	is	be	AUX
cana-2601	116	29	5	5	NUM
cana-2601	116	30	.	.	PUNCT
cana-2601	116	31	hence	hence	ADV
cana-2601	116	32	,	,	PUNCT
cana-2601	116	33	by	by	ADP
cana-2601	116	34	lh	lh	PROPN
cana-2601	116	35	-	-	PUNCT
cana-2601	116	36	coloring	color	VERB
cana-2601	116	37	lemma	lemma	PROPN
cana-2601	116	38	,	,	PUNCT
cana-2601	116	39	h1(sht	h1(sht	PROPN
cana-2601	116	40	(	(	PUNCT
cana-2601	116	41	2	2	NUM
cana-2601	116	42	)	)	PUNCT
cana-2601	116	43	)	)	PUNCT
cana-2601	117	1	=	=	SYM
cana-2601	117	2	5	5	X
cana-2601	117	3	.	.	X
cana-2601	117	4	similarly	similarly	ADV
cana-2601	117	5	,	,	PUNCT
cana-2601	117	6	for	for	ADP
cana-2601	117	7	the	the	DET
cana-2601	117	8	case	case	NOUN
cana-2601	117	9	n	n	ADP
cana-2601	117	10	>	>	X
cana-2601	117	11	2	2	NUM
cana-2601	117	12	,	,	PUNCT
cana-2601	117	13	we	we	PRON
cana-2601	117	14	arrive	arrive	VERB
cana-2601	117	15	that	that	SCONJ
cana-2601	117	16	h1(sht	h1(sht	PROPN
cana-2601	117	17	(	(	PUNCT
cana-2601	117	18	n	n	CCONJ
cana-2601	117	19	)	)	PUNCT
cana-2601	117	20	)	)	PUNCT
cana-2601	118	1	=	=	SYM
cana-2601	118	2	6	6	X
cana-2601	118	3	.	.	X
cana-2601	119	1	see	see	VERB
cana-2601	119	2	figure	figure	NOUN
cana-2601	119	3	7	7	NUM
cana-2601	119	4	.	.	PUNCT
cana-2601	119	5	communications	communication	NOUN
cana-2601	119	6	on	on	ADP
cana-2601	119	7	applied	apply	VERB
cana-2601	119	8	nonlinear	nonlinear	ADJ
cana-2601	119	9	analysis	analysis	NOUN
cana-2601	119	10	issn	issn	NOUN
cana-2601	119	11	:	:	PUNCT
cana-2601	119	12	1074	1074	NUM
cana-2601	119	13	-	-	PUNCT
cana-2601	119	14	133x	133x	NUM
cana-2601	119	15	vol	vol	NOUN
cana-2601	119	16	32	32	NUM
cana-2601	119	17	no	no	NOUN
cana-2601	119	18	.	.	PUNCT
cana-2601	120	1	3s	3s	NUM
cana-2601	120	2	(	(	PUNCT
cana-2601	120	3	2025	2025	NUM
cana-2601	120	4	)	)	PUNCT
cana-2601	120	5	219	219	NUM
cana-2601	120	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2601	120	7	algorithm	algorithm	NOUN
cana-2601	120	8	10	10	NUM
cana-2601	120	9	is	be	AUX
cana-2601	120	10	illustrated	illustrate	VERB
cana-2601	120	11	in	in	ADP
cana-2601	120	12	figure	figure	NOUN
cana-2601	120	13	7	7	NUM
cana-2601	120	14	.	.	PUNCT
cana-2601	121	1	proof	proof	NOUN
cana-2601	121	2	of	of	ADP
cana-2601	121	3	correctness	correctness	NOUN
cana-2601	121	4	(	(	PUNCT
cana-2601	121	5	algorithm	algorithm	NOUN
cana-2601	121	6	10	10	NUM
cana-2601	121	7	):	):	PUNCT
cana-2601	121	8	two	two	NUM
cana-2601	121	9	vertices	vertex	NOUN
cana-2601	121	10	adjacent	adjacent	ADJ
cana-2601	121	11	at	at	ADP
cana-2601	121	12	a	a	DET
cana-2601	121	13	particular	particular	ADJ
cana-2601	121	14	level	level	NOUN
cana-2601	121	15	‘	'	PUNCT
cana-2601	121	16	i	i	PRON
cana-2601	121	17	’	'	PUNCT
cana-2601	121	18	have	have	VERB
cana-2601	121	19	consecutive	consecutive	ADJ
cana-2601	121	20	coloring	coloring	NOUN
cana-2601	121	21	say	say	VERB
cana-2601	121	22	k	k	PROPN
cana-2601	121	23	and	and	CCONJ
cana-2601	121	24	k	k	PROPN
cana-2601	122	1	+	+	PROPN
cana-2601	122	2	1	1	NUM
cana-2601	122	3	,	,	PUNCT
cana-2601	122	4	vise	vise	ADV
cana-2601	122	5	versa	versa	ADV
cana-2601	122	6	.	.	PUNCT
cana-2601	123	1	from	from	ADP
cana-2601	123	2	the	the	DET
cana-2601	123	3	proposed	propose	VERB
cana-2601	123	4	algorithm	algorithm	NOUN
cana-2601	123	5	,	,	PUNCT
cana-2601	123	6	it	it	PRON
cana-2601	123	7	is	be	AUX
cana-2601	123	8	clear	clear	ADJ
cana-2601	123	9	that	that	SCONJ
cana-2601	123	10	the	the	DET
cana-2601	123	11	vertices	vertex	NOUN
cana-2601	123	12	of	of	ADP
cana-2601	123	13	any	any	DET
cana-2601	123	14	three	three	NUM
cana-2601	123	15	consecutive	consecutive	ADJ
cana-2601	123	16	levels	level	NOUN
cana-2601	123	17	in	in	ADP
cana-2601	123	18	sht	sht	PROPN
cana-2601	123	19	(	(	PUNCT
cana-2601	123	20	n	n	CCONJ
cana-2601	123	21	)	)	PUNCT
cana-2601	123	22	have	have	AUX
cana-2601	123	23	colored	color	VERB
cana-2601	123	24	using	use	VERB
cana-2601	123	25	three	three	NUM
cana-2601	123	26	distinct	distinct	ADJ
cana-2601	123	27	colorpairs	colorpair	NOUN
cana-2601	123	28	from	from	ADP
cana-2601	123	29	the	the	DET
cana-2601	123	30	color	color	NOUN
cana-2601	123	31	set	set	NOUN
cana-2601	123	32	{	{	PUNCT
cana-2601	123	33	1	1	NUM
cana-2601	123	34	,	,	PUNCT
cana-2601	123	35	2	2	NUM
cana-2601	123	36	,	,	PUNCT
cana-2601	123	37	3	3	NUM
cana-2601	123	38	,	,	PUNCT
cana-2601	123	39	4	4	NUM
cana-2601	123	40	,	,	PUNCT
cana-2601	123	41	5	5	NUM
cana-2601	123	42	,	,	PUNCT
cana-2601	123	43	6	6	NUM
cana-2601	123	44	}	}	PUNCT
cana-2601	123	45	.	.	PUNCT
cana-2601	124	1	therefore	therefore	ADV
cana-2601	124	2	,	,	PUNCT
cana-2601	124	3	every	every	DET
cana-2601	124	4	color	color	NOUN
cana-2601	124	5	pair	pair	NOUN
cana-2601	124	6	of	of	ADP
cana-2601	124	7	colors	color	NOUN
cana-2601	124	8	is	be	AUX
cana-2601	124	9	present	present	ADJ
cana-2601	124	10	only	only	ADV
cana-2601	124	11	once	once	ADV
cana-2601	124	12	for	for	ADP
cana-2601	124	13	each	each	DET
cana-2601	124	14	edge	edge	NOUN
cana-2601	124	15	within	within	ADP
cana-2601	124	16	distance	distance	NOUN
cana-2601	124	17	one	one	NUM
cana-2601	124	18	of	of	ADP
cana-2601	124	19	any	any	DET
cana-2601	124	20	vertex	vertex	NOUN
cana-2601	124	21	v	v	ADP
cana-2601	124	22	∈	∈	PROPN
cana-2601	124	23	sht	sht	NOUN
cana-2601	124	24	(	(	PUNCT
cana-2601	124	25	n	n	CCONJ
cana-2601	124	26	)	)	PUNCT
cana-2601	124	27	.	.	PUNCT
cana-2601	125	1	thus	thus	ADV
cana-2601	125	2	,	,	PUNCT
cana-2601	125	3	the	the	DET
cana-2601	125	4	coloring	coloring	NOUN
cana-2601	125	5	is	be	AUX
cana-2601	125	6	locally	locally	ADV
cana-2601	125	7	harmonious	harmonious	ADJ
cana-2601	125	8	coloring	coloring	NOUN
cana-2601	125	9	.	.	PUNCT
cana-2601	126	1	1	1	NUM
cana-2601	126	2	1	1	NUM
cana-2601	126	3	2	2	NUM
cana-2601	126	4	figure	figure	NOUN
cana-2601	126	5	7	7	NUM
cana-2601	126	6	:	:	SYM
cana-2601	126	7	h1(sht	h1(sht	NUM
cana-2601	126	8	(	(	PUNCT
cana-2601	126	9	3	3	NUM
cana-2601	126	10	)	)	PUNCT
cana-2601	126	11	)	)	PUNCT
cana-2601	127	1	=	=	PUNCT
cana-2601	127	2	6	6	NUM
cana-2601	127	3	6	6	NUM
cana-2601	127	4	.	.	PUNCT
cana-2601	128	1	l	l	NOUN
cana-2601	128	2	-	-	ADJ
cana-2601	128	3	complete	complete	ADJ
cana-2601	128	4	binary	binary	ADJ
cana-2601	128	5	tree	tree	NOUN
cana-2601	128	6	definition	definition	NOUN
cana-2601	128	7	6.1	6.1	NUM
cana-2601	128	8	.	.	PUNCT
cana-2601	129	1	a	a	DET
cana-2601	129	2	graph	graph	NOUN
cana-2601	129	3	made	make	VERB
cana-2601	129	4	up	up	ADP
cana-2601	129	5	of	of	ADP
cana-2601	129	6	2	2	NUM
cana-2601	129	7	-	-	PUNCT
cana-2601	129	8	copies	copy	NOUN
cana-2601	129	9	of	of	ADP
cana-2601	129	10	the	the	DET
cana-2601	129	11	complete	complete	ADJ
cana-2601	129	12	binary	binary	PROPN
cana-2601	129	13	tree	tree	PROPN
cana-2601	129	14	tn	tn	PROPN
cana-2601	129	15	,	,	PUNCT
cana-2601	129	16	n	n	X
cana-2601	129	17	≥	≥	NOUN
cana-2601	129	18	1	1	NUM
cana-2601	129	19	,	,	PUNCT
cana-2601	129	20	say	say	VERB
cana-2601	129	21	t1	t1	NOUN
cana-2601	129	22	,	,	PUNCT
cana-2601	129	23	t2	t2	NOUN
cana-2601	129	24	by	by	ADP
cana-2601	129	25	merging	merge	VERB
cana-2601	129	26	all	all	PRON
cana-2601	129	27	of	of	ADP
cana-2601	129	28	the	the	DET
cana-2601	129	29	vertices	vertex	NOUN
cana-2601	129	30	in	in	ADP
cana-2601	129	31	the	the	DET
cana-2601	129	32	last	last	ADJ
cana-2601	129	33	level	level	NOUN
cana-2601	129	34	of	of	ADP
cana-2601	129	35	t1	t1	NOUN
cana-2601	129	36	with	with	ADP
cana-2601	129	37	the	the	DET
cana-2601	129	38	associated	associated	ADJ
cana-2601	129	39	vertex	vertex	NOUN
cana-2601	129	40	of	of	ADP
cana-2601	129	41	t2	t2	NOUN
cana-2601	129	42	is	be	AUX
cana-2601	129	43	called	call	VERB
cana-2601	129	44	the	the	DET
cana-2601	129	45	l	l	NOUN
cana-2601	129	46	-	-	ADJ
cana-2601	129	47	complete	complete	ADJ
cana-2601	129	48	binary	binary	ADJ
cana-2601	129	49	tree	tree	NOUN
cana-2601	129	50	,	,	PUNCT
cana-2601	129	51	denoted	denote	VERB
cana-2601	129	52	by	by	ADP
cana-2601	129	53	l	l	PROPN
cana-2601	129	54	-	-	NOUN
cana-2601	129	55	tn	tn	NOUN
cana-2601	129	56	.	.	PUNCT
cana-2601	130	1	the	the	DET
cana-2601	130	2	vertices	vertex	NOUN
cana-2601	130	3	of	of	ADP
cana-2601	130	4	l	l	PROPN
cana-2601	130	5	-	-	PUNCT
cana-2601	130	6	tn	tn	NOUN
cana-2601	130	7	denoted	denote	VERB
cana-2601	130	8	as	as	ADP
cana-2601	130	9	𝑣𝑖𝑗	𝑣𝑖𝑗	NUM
cana-2601	130	10	,	,	PUNCT
cana-2601	130	11	0	0	NUM
cana-2601	130	12	≤	≤	NUM
cana-2601	130	13	𝑖	𝑖	SYM
cana-2601	130	14	≤	≤	NUM
cana-2601	130	15	𝑛	𝑛	NOUN
cana-2601	130	16	,	,	PUNCT
cana-2601	130	17	1	1	NUM
cana-2601	130	18	≤	≤	NUM
cana-2601	130	19	𝑗	𝑗	PRON
cana-2601	130	20	≤	≤	ADJ
cana-2601	130	21	2𝑖	2𝑖	NOUN
cana-2601	130	22	and	and	CCONJ
cana-2601	130	23	𝑣𝑖𝑗	𝑣𝑖𝑗	NUM
cana-2601	130	24	′	′	NOUN
cana-2601	130	25	,	,	PUNCT
cana-2601	130	26	𝑛	𝑛	PRON
cana-2601	130	27	+	+	NOUN
cana-2601	130	28	1	1	NUM
cana-2601	130	29	≤	≤	NUM
cana-2601	130	30	𝑖	𝑖	PRON
cana-2601	130	31	≤	≤	NOUN
cana-2601	130	32	2𝑛	2𝑛	NUM
cana-2601	130	33	,	,	PUNCT
cana-2601	130	34	1	1	NUM
cana-2601	130	35	≤	≤	NUM
cana-2601	130	36	𝑗	𝑗	PRON
cana-2601	130	37	≤	≤	NUM
cana-2601	130	38	2(𝑛−𝑖(𝑚𝑜𝑑	2(𝑛−𝑖(𝑚𝑜𝑑	NUM
cana-2601	130	39	𝑛))𝑚𝑜𝑑	𝑛))𝑚𝑜𝑑	NOUN
cana-2601	130	40	𝑛	𝑛	ADP
cana-2601	130	41	where	where	SCONJ
cana-2601	130	42	i	i	PRON
cana-2601	130	43	representing	represent	VERB
cana-2601	130	44	a	a	DET
cana-2601	130	45	level	level	NOUN
cana-2601	130	46	and	and	CCONJ
cana-2601	130	47	j	j	PROPN
cana-2601	130	48	represents	represent	VERB
cana-2601	130	49	the	the	DET
cana-2601	130	50	position	position	NOUN
cana-2601	130	51	of	of	ADP
cana-2601	130	52	a	a	DET
cana-2601	130	53	vertex	vertex	NOUN
cana-2601	130	54	at	at	ADP
cana-2601	130	55	any	any	DET
cana-2601	130	56	particular	particular	ADJ
cana-2601	130	57	level	level	NOUN
cana-2601	130	58	i.	i.	NOUN
cana-2601	130	59	formally	formally	ADV
cana-2601	130	60	,	,	PUNCT
cana-2601	130	61	we	we	PRON
cana-2601	130	62	define	define	VERB
cana-2601	130	63	the	the	DET
cana-2601	130	64	vertex	vertex	NOUN
cana-2601	130	65	set	set	NOUN
cana-2601	130	66	as	as	SCONJ
cana-2601	130	67	shown	show	VERB
cana-2601	130	68	in	in	ADP
cana-2601	130	69	figure	figure	NOUN
cana-2601	130	70	8	8	NUM
cana-2601	130	71	.	.	PUNCT
cana-2601	131	1	the	the	DET
cana-2601	131	2	l	l	NOUN
cana-2601	131	3	-	-	ADJ
cana-2601	131	4	complete	complete	ADJ
cana-2601	131	5	binary	binary	ADJ
cana-2601	131	6	tree	tree	NOUN
cana-2601	131	7	l	l	PROPN
cana-2601	131	8	-	-	NOUN
cana-2601	131	9	tn	tn	PROPN
cana-2601	131	10	,	,	PUNCT
cana-2601	131	11	n	n	X
cana-2601	131	12	≥	≥	NOUN
cana-2601	131	13	1	1	NUM
cana-2601	131	14	,	,	PUNCT
cana-2601	131	15	contains	contain	VERB
cana-2601	131	16	2n−1	2n−1	NUM
cana-2601	131	17	number	number	NOUN
cana-2601	131	18	of	of	ADP
cana-2601	131	19	vertex	vertex	NOUN
cana-2601	131	20	disjoint	disjoint	NOUN
cana-2601	131	21	copies	copy	NOUN
cana-2601	131	22	of	of	ADP
cana-2601	131	23	c4	c4	NOUN
cana-2601	131	24	,	,	PUNCT
cana-2601	131	25	where	where	SCONJ
cana-2601	131	26	c4	c4	NOUN
cana-2601	131	27	is	be	AUX
cana-2601	131	28	the	the	DET
cana-2601	131	29	cycle	cycle	NOUN
cana-2601	131	30	on	on	ADP
cana-2601	131	31	four	four	NUM
cana-2601	131	32	vertices	vertex	NOUN
cana-2601	131	33	and	and	CCONJ
cana-2601	131	34	the	the	DET
cana-2601	131	35	number	number	NOUN
cana-2601	131	36	of	of	ADP
cana-2601	131	37	vertices	vertex	NOUN
cana-2601	131	38	in	in	ADP
cana-2601	131	39	l	l	NOUN
cana-2601	131	40	-	-	NOUN
cana-2601	131	41	tn	tn	PROPN
cana-2601	131	42	is	be	AUX
cana-2601	131	43	3.2n−1	3.2n−1	NUM
cana-2601	131	44	−	−	NOUN
cana-2601	131	45	2	2	NUM
cana-2601	131	46	,	,	PUNCT
cana-2601	131	47	n	n	PRON
cana-2601	131	48	≥	≥	NOUN
cana-2601	131	49	1	1	NUM
cana-2601	131	50	.	.	PUNCT
cana-2601	132	1	communications	communication	NOUN
cana-2601	132	2	on	on	ADP
cana-2601	132	3	applied	apply	VERB
cana-2601	132	4	nonlinear	nonlinear	ADJ
cana-2601	132	5	analysis	analysis	NOUN
cana-2601	132	6	issn	issn	NOUN
cana-2601	132	7	:	:	PUNCT
cana-2601	132	8	1074	1074	NUM
cana-2601	132	9	-	-	PUNCT
cana-2601	132	10	133x	133x	NUM
cana-2601	132	11	vol	vol	NOUN
cana-2601	132	12	32	32	NUM
cana-2601	132	13	no	no	NOUN
cana-2601	132	14	.	.	PUNCT
cana-2601	133	1	3s	3s	NUM
cana-2601	133	2	(	(	PUNCT
cana-2601	133	3	2025	2025	NUM
cana-2601	133	4	)	)	PUNCT
cana-2601	133	5	220	220	NUM
cana-2601	133	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2601	133	7	figure	figure	NOUN
cana-2601	133	8	8	8	NUM
cana-2601	133	9	:	:	PUNCT
cana-2601	133	10	vertex	vertex	NOUN
cana-2601	133	11	labeling	labeling	NOUN
cana-2601	133	12	of	of	ADP
cana-2601	133	13	l	l	NOUN
cana-2601	133	14	-	-	NOUN
cana-2601	133	15	t2	t2	NOUN
cana-2601	133	16	theorem	theorem	VERB
cana-2601	133	17	6.2	6.2	NUM
cana-2601	133	18	.	.	PUNCT
cana-2601	134	1	let	let	VERB
cana-2601	134	2	g	g	PRON
cana-2601	134	3	be	be	AUX
cana-2601	134	4	the	the	DET
cana-2601	134	5	l	l	NOUN
cana-2601	134	6	-	-	ADJ
cana-2601	134	7	complete	complete	ADJ
cana-2601	134	8	binary	binary	ADJ
cana-2601	134	9	tree	tree	NOUN
cana-2601	134	10	l	l	PROPN
cana-2601	134	11	-	-	NOUN
cana-2601	134	12	tn	tn	PROPN
cana-2601	134	13	,	,	PUNCT
cana-2601	134	14	n	n	X
cana-2601	134	15	≥	≥	NOUN
cana-2601	134	16	2	2	NUM
cana-2601	134	17	.	.	PUNCT
cana-2601	135	1	then	then	ADV
cana-2601	135	2	g	g	PROPN
cana-2601	135	3	admits	admit	VERB
cana-2601	135	4	locally	locally	ADV
cana-2601	135	5	harmonious	harmonious	ADJ
cana-2601	135	6	coloring	coloring	NOUN
cana-2601	135	7	with	with	ADP
cana-2601	135	8	the	the	DET
cana-2601	135	9	chromatic	chromatic	ADJ
cana-2601	135	10	number	number	NOUN
cana-2601	135	11	h1(g	h1(g	NOUN
cana-2601	135	12	)	)	PUNCT
cana-2601	135	13	=	=	SYM
cana-2601	136	1	6	6	X
cana-2601	136	2	.	.	PUNCT
cana-2601	136	3	proof	proof	NOUN
cana-2601	136	4	.	.	PUNCT
cana-2601	137	1	w.l.g	w.l.g	ADJ
cana-2601	137	2	,	,	PUNCT
cana-2601	137	3	let	let	VERB
cana-2601	137	4	us	we	PRON
cana-2601	137	5	color	color	VERB
cana-2601	137	6	the	the	DET
cana-2601	137	7	vertex	vertex	NOUN
cana-2601	137	8	v01	v01	NOUN
cana-2601	137	9	at	at	ADP
cana-2601	137	10	the	the	DET
cana-2601	137	11	level	level	NOUN
cana-2601	137	12	0	0	NUM
cana-2601	137	13	of	of	ADP
cana-2601	137	14	g	g	NOUN
cana-2601	137	15	with	with	ADP
cana-2601	137	16	1	1	NUM
cana-2601	137	17	.	.	PUNCT
cana-2601	138	1	we	we	PRON
cana-2601	138	2	shall	shall	AUX
cana-2601	138	3	show	show	VERB
cana-2601	138	4	that	that	SCONJ
cana-2601	138	5	h1(g	h1(g	PROPN
cana-2601	138	6	)	)	PUNCT
cana-2601	138	7	=	=	SYM
cana-2601	138	8	6	6	NUM
cana-2601	138	9	by	by	ADP
cana-2601	138	10	labeling	label	VERB
cana-2601	138	11	the	the	DET
cana-2601	138	12	vertices	vertex	NOUN
cana-2601	138	13	vi1	vi1	NOUN
cana-2601	138	14	and	and	CCONJ
cana-2601	138	15	v	v	NOUN
cana-2601	138	16	′	′	NOUN
cana-2601	138	17	define	define	VERB
cana-2601	138	18	a	a	DET
cana-2601	138	19	labeling	labeling	NOUN
cana-2601	138	20	function	function	NOUN
cana-2601	138	21	𝑙	𝑙	X
cana-2601	138	22	∶	∶	NOUN
cana-2601	138	23	𝑣1	𝑣1	NOUN
cana-2601	138	24	𝑖	𝑖	SYM
cana-2601	138	25	→	→	PUNCT
cana-2601	138	26	{	{	PUNCT
cana-2601	138	27	0	0	NUM
cana-2601	138	28	,	,	PUNCT
cana-2601	138	29	1	1	NUM
cana-2601	138	30	,	,	PUNCT
cana-2601	138	31	2	2	NUM
cana-2601	138	32	}	}	PUNCT
cana-2601	138	33	,	,	PUNCT
cana-2601	138	34	1	1	NUM
cana-2601	138	35	≤	≤	NUM
cana-2601	138	36	𝑖	𝑖	SYM
cana-2601	138	37	≤	≤	NOUN
cana-2601	138	38	2𝑛	2𝑛	NUM
cana-2601	138	39	such	such	ADJ
cana-2601	138	40	that	that	SCONJ
cana-2601	138	41	𝑙	𝑙	X
cana-2601	138	42	(	(	PUNCT
cana-2601	138	43	𝑣1	𝑣1	PROPN
cana-2601	138	44	𝑖	𝑖	PROPN
cana-2601	138	45	)	)	PUNCT
cana-2601	138	46	=	=	SYM
cana-2601	138	47	(	(	PUNCT
cana-2601	138	48	𝑖	𝑖	SYM
cana-2601	138	49	+	+	NOUN
cana-2601	138	50	1)𝑚𝑜𝑑	1)𝑚𝑜𝑑	NUM
cana-2601	138	51	3	3	NUM
cana-2601	138	52	depending	depend	VERB
cana-2601	138	53	on	on	ADP
cana-2601	138	54	the	the	DET
cana-2601	138	55	values	value	NOUN
cana-2601	138	56	the	the	DET
cana-2601	138	57	vertices	vertex	NOUN
cana-2601	138	58	of	of	ADP
cana-2601	138	59	g	g	NOUN
cana-2601	138	60	can	can	AUX
cana-2601	138	61	be	be	AUX
cana-2601	138	62	colored	color	VERB
cana-2601	138	63	level	level	NOUN
cana-2601	138	64	-	-	PUNCT
cana-2601	138	65	wise	wise	ADV
cana-2601	138	66	using	use	VERB
cana-2601	138	67	the	the	DET
cana-2601	138	68	color	color	NOUN
cana-2601	138	69	set	set	NOUN
cana-2601	138	70	{	{	PUNCT
cana-2601	138	71	1	1	NUM
cana-2601	138	72	,	,	PUNCT
cana-2601	138	73	2	2	NUM
cana-2601	138	74	,	,	PUNCT
cana-2601	138	75	3	3	NUM
cana-2601	138	76	,	,	PUNCT
cana-2601	138	77	4	4	NUM
cana-2601	138	78	,	,	PUNCT
cana-2601	138	79	5	5	NUM
cana-2601	138	80	,	,	PUNCT
cana-2601	138	81	6	6	NUM
cana-2601	138	82	}	}	PUNCT
cana-2601	138	83	from	from	ADP
cana-2601	138	84	the	the	DET
cana-2601	138	85	left	left	NOUN
cana-2601	138	86	to	to	ADP
cana-2601	138	87	the	the	DET
cana-2601	138	88	right	right	NOUN
cana-2601	138	89	repeatedly	repeatedly	ADV
cana-2601	138	90	as	as	ADP
cana-2601	138	91	in	in	ADP
cana-2601	138	92	the	the	DET
cana-2601	138	93	given	give	VERB
cana-2601	138	94	order	order	NOUN
cana-2601	138	95	construed	construe	VERB
cana-2601	138	96	in	in	ADP
cana-2601	138	97	table	table	NOUN
cana-2601	138	98	4	4	NUM
cana-2601	138	99	.	.	PUNCT
cana-2601	139	1	the	the	DET
cana-2601	139	2	vertices	vertex	NOUN
cana-2601	139	3	in	in	ADP
cana-2601	139	4	each	each	DET
cana-2601	139	5	level	level	NOUN
cana-2601	139	6	are	be	AUX
cana-2601	139	7	independent	independent	ADJ
cana-2601	139	8	and	and	CCONJ
cana-2601	139	9	any	any	DET
cana-2601	139	10	vertex	vertex	NOUN
cana-2601	139	11	vij	vij	PROPN
cana-2601	139	12	neighborhoods	neighborhood	NOUN
cana-2601	139	13	can	can	AUX
cana-2601	139	14	be	be	AUX
cana-2601	139	15	found	find	VERB
cana-2601	139	16	only	only	ADV
cana-2601	139	17	in	in	ADP
cana-2601	139	18	the	the	DET
cana-2601	139	19	levels	level	NOUN
cana-2601	139	20	i	i	PRON
cana-2601	140	1	+	+	CCONJ
cana-2601	140	2	1	1	NUM
cana-2601	140	3	and	and	CCONJ
cana-2601	140	4	i	i	PRON
cana-2601	140	5	−	−	PROPN
cana-2601	141	1	1	1	X
cana-2601	141	2	.	.	PUNCT
cana-2601	142	1	since	since	SCONJ
cana-2601	142	2	the	the	DET
cana-2601	142	3	vertices	vertex	NOUN
cana-2601	142	4	of	of	ADP
cana-2601	142	5	any	any	DET
cana-2601	142	6	three	three	NUM
cana-2601	142	7	consecutive	consecutive	ADJ
cana-2601	142	8	levels	level	NOUN
cana-2601	142	9	are	be	AUX
cana-2601	142	10	colored	color	VERB
cana-2601	142	11	with	with	ADP
cana-2601	142	12	3	3	NUM
cana-2601	142	13	different	different	ADJ
cana-2601	142	14	pair	pair	NOUN
cana-2601	142	15	of	of	ADP
cana-2601	142	16	colors	color	NOUN
cana-2601	142	17	{	{	PUNCT
cana-2601	142	18	1	1	NUM
cana-2601	142	19	,	,	PUNCT
cana-2601	142	20	2	2	NUM
cana-2601	142	21	}	}	PUNCT
cana-2601	142	22	,	,	PUNCT
cana-2601	142	23	{	{	PUNCT
cana-2601	142	24	3	3	NUM
cana-2601	142	25	,	,	PUNCT
cana-2601	142	26	4	4	NUM
cana-2601	142	27	}	}	PUNCT
cana-2601	142	28	and	and	CCONJ
cana-2601	142	29	{	{	PUNCT
cana-2601	142	30	5	5	NUM
cana-2601	142	31	,	,	PUNCT
cana-2601	142	32	6	6	NUM
cana-2601	142	33	}	}	PUNCT
cana-2601	142	34	respectively	respectively	ADV
cana-2601	142	35	.	.	PUNCT
cana-2601	143	1	by	by	ADP
cana-2601	143	2	lh	lh	PROPN
cana-2601	143	3	-	-	PUNCT
cana-2601	143	4	coloring	color	VERB
cana-2601	143	5	lemma	lemma	PROPN
cana-2601	143	6	,	,	PUNCT
cana-2601	143	7	h1(g	h1(g	PROPN
cana-2601	143	8	)	)	PUNCT
cana-2601	143	9	=	=	SYM
cana-2601	143	10	6	6	X
cana-2601	143	11	.	.	X
cana-2601	143	12	see	see	VERB
cana-2601	143	13	figure	figure	NOUN
cana-2601	143	14	9	9	NUM
cana-2601	143	15	.	.	PUNCT
cana-2601	144	1	communications	communication	NOUN
cana-2601	144	2	on	on	ADP
cana-2601	144	3	applied	apply	VERB
cana-2601	144	4	nonlinear	nonlinear	ADJ
cana-2601	144	5	analysis	analysis	NOUN
cana-2601	144	6	issn	issn	NOUN
cana-2601	144	7	:	:	PUNCT
cana-2601	144	8	1074	1074	NUM
cana-2601	144	9	-	-	PUNCT
cana-2601	144	10	133x	133x	NUM
cana-2601	144	11	vol	vol	NOUN
cana-2601	144	12	32	32	NUM
cana-2601	144	13	no	no	NOUN
cana-2601	144	14	.	.	PUNCT
cana-2601	145	1	3s	3s	NUM
cana-2601	145	2	(	(	PUNCT
cana-2601	145	3	2025	2025	NUM
cana-2601	145	4	)	)	PUNCT
cana-2601	145	5	221	221	NUM
cana-2601	145	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2601	145	7	7	7	X
cana-2601	145	8	.	.	X
cana-2601	145	9	concluding	conclude	VERB
cana-2601	145	10	remarks	remark	NOUN
cana-2601	145	11	in	in	ADP
cana-2601	145	12	this	this	DET
cana-2601	145	13	paper	paper	NOUN
cana-2601	145	14	,	,	PUNCT
cana-2601	145	15	we	we	PRON
cana-2601	145	16	obtained	obtain	VERB
cana-2601	145	17	the	the	DET
cana-2601	145	18	locally	locally	ADV
cana-2601	145	19	harmonious	harmonious	ADJ
cana-2601	145	20	chromatic	chromatic	ADJ
cana-2601	145	21	number	number	NOUN
cana-2601	145	22	for	for	ADP
cana-2601	145	23	certain	certain	ADJ
cana-2601	145	24	tree	tree	NOUN
cana-2601	145	25	-	-	PUNCT
cana-2601	145	26	derived	derive	VERB
cana-2601	145	27	net	net	ADJ
cana-2601	145	28	works	work	NOUN
cana-2601	145	29	which	which	PRON
cana-2601	145	30	includes	include	VERB
cana-2601	145	31	slim	slim	ADJ
cana-2601	145	32	tree	tree	NOUN
cana-2601	145	33	,	,	PUNCT
cana-2601	145	34	hypertree	hypertree	NOUN
cana-2601	145	35	,	,	PUNCT
cana-2601	145	36	shuffle	shuffle	NOUN
cana-2601	145	37	hypertree	hypertree	NOUN
cana-2601	145	38	and	and	CCONJ
cana-2601	145	39	l	l	NOUN
cana-2601	145	40	-	-	ADJ
cana-2601	145	41	complete	complete	ADJ
cana-2601	145	42	binary	binary	ADJ
cana-2601	145	43	tree	tree	NOUN
cana-2601	145	44	.	.	PUNCT
cana-2601	146	1	an	an	DET
cana-2601	146	2	elegant	elegant	ADJ
cana-2601	146	3	way	way	NOUN
cana-2601	146	4	of	of	ADP
cana-2601	146	5	coloring	coloring	NOUN
cana-2601	146	6	algorithms	algorithm	NOUN
cana-2601	146	7	has	have	AUX
cana-2601	146	8	been	be	AUX
cana-2601	146	9	proposed	propose	VERB
cana-2601	146	10	in	in	ADP
cana-2601	146	11	finding	find	VERB
cana-2601	146	12	the	the	DET
cana-2601	146	13	bounds	bound	NOUN
cana-2601	146	14	of	of	ADP
cana-2601	146	15	these	these	DET
cana-2601	146	16	graphs	graph	NOUN
cana-2601	146	17	.	.	PUNCT
cana-2601	147	1	locally	locally	ADV
cana-2601	147	2	harmonious	harmonious	ADJ
cana-2601	147	3	chromatic	chromatic	ADJ
cana-2601	147	4	number	number	NOUN
cana-2601	147	5	of	of	ADP
cana-2601	147	6	other	other	ADJ
cana-2601	147	7	interesting	interesting	ADJ
cana-2601	147	8	tree	tree	NOUN
cana-2601	147	9	derived	derive	VERB
cana-2601	147	10	networks	network	NOUN
cana-2601	147	11	like	like	ADP
cana-2601	147	12	sierpinski	sierpinski	ADJ
cana-2601	147	13	graph	graph	NOUN
cana-2601	147	14	,	,	PUNCT
cana-2601	147	15	sierpinski	sierpinski	ADJ
cana-2601	147	16	gasket	gasket	NOUN
cana-2601	147	17	,	,	PUNCT
cana-2601	147	18	christmas	christmas	NOUN
cana-2601	147	19	tree	tree	NOUN
cana-2601	147	20	,	,	PUNCT
cana-2601	147	21	x	x	X
cana-2601	147	22	-	-	NOUN
cana-2601	147	23	tree	tree	NOUN
cana-2601	147	24	are	be	AUX
cana-2601	147	25	open	open	ADJ
cana-2601	147	26	and	and	CCONJ
cana-2601	147	27	under	under	ADP
cana-2601	147	28	study	study	NOUN
cana-2601	147	29	.	.	PUNCT
cana-2601	148	1	references	reference	NOUN
cana-2601	148	2	[	[	X
cana-2601	148	3	1	1	NUM
cana-2601	148	4	]	]	PUNCT
cana-2601	148	5	a.	a.	NOUN
cana-2601	148	6	brandstadt	brandstadt	NOUN
cana-2601	148	7	,	,	PUNCT
cana-2601	148	8	v.	v.	CCONJ
cana-2601	148	9	d.	d.	PROPN
cana-2601	148	10	chepoi	chepoi	PROPN
cana-2601	148	11	and	and	CCONJ
cana-2601	148	12	f.	f.	PROPN
cana-2601	148	13	f.	f.	PROPN
cana-2601	148	14	dragan	dragan	PROPN
cana-2601	148	15	,	,	PUNCT
cana-2601	148	16	the	the	DET
cana-2601	148	17	algorithmic	algorithmic	ADJ
cana-2601	148	18	use	use	NOUN
cana-2601	148	19	of	of	ADP
cana-2601	148	20	hypertree	hypertree	NOUN
cana-2601	148	21	structure	structure	NOUN
cana-2601	148	22	and	and	CCONJ
cana-2601	148	23	maximum	maximum	ADJ
cana-2601	148	24	neighborhood	neighborhood	NOUN
cana-2601	148	25	orderings	ordering	NOUN
cana-2601	148	26	,	,	PUNCT
cana-2601	148	27	discrete	discrete	ADJ
cana-2601	148	28	applied	apply	VERB
cana-2601	148	29	mathematics	mathematic	NOUN
cana-2601	148	30	,	,	PUNCT
cana-2601	148	31	82	82	NUM
cana-2601	148	32	(	(	PUNCT
cana-2601	148	33	1998	1998	NUM
cana-2601	148	34	)	)	PUNCT
cana-2601	148	35	43–77	43–77	NUM
cana-2601	148	36	.	.	PUNCT
cana-2601	149	1	[	[	X
cana-2601	149	2	2	2	X
cana-2601	149	3	]	]	PUNCT
cana-2601	149	4	t.	t.	PROPN
cana-2601	149	5	h.	h.	PROPN
cana-2601	149	6	cormen	cormen	PROPN
cana-2601	149	7	,	,	PUNCT
cana-2601	149	8	c.	c.	PROPN
cana-2601	149	9	e.	e.	PROPN
cana-2601	149	10	leiserson	leiserson	PROPN
cana-2601	149	11	,	,	PUNCT
cana-2601	149	12	r.	r.	PROPN
cana-2601	149	13	l.	l.	PROPN
cana-2601	149	14	rivest	rivest	PROPN
cana-2601	149	15	,	,	PUNCT
cana-2601	149	16	introduction	introduction	NOUN
cana-2601	149	17	to	to	ADP
cana-2601	149	18	algorithms	algorithm	NOUN
cana-2601	149	19	,	,	PUNCT
cana-2601	149	20	mit	mit	NOUN
cana-2601	149	21	press	press	NOUN
cana-2601	149	22	,	,	PUNCT
cana-2601	149	23	(	(	PUNCT
cana-2601	149	24	1989	1989	NUM
cana-2601	149	25	)	)	PUNCT
cana-2601	149	26	.	.	PUNCT
cana-2601	150	1	[	[	X
cana-2601	150	2	3	3	X
cana-2601	150	3	]	]	X
cana-2601	150	4	w.	w.	PROPN
cana-2601	150	5	gao	gao	PROPN
cana-2601	150	6	,	,	PUNCT
cana-2601	150	7	three	three	NUM
cana-2601	150	8	algorithms	algorithm	NOUN
cana-2601	150	9	for	for	ADP
cana-2601	150	10	graph	graph	NOUN
cana-2601	150	11	locally	locally	ADV
cana-2601	150	12	harmonious	harmonious	ADJ
cana-2601	150	13	coloring	coloring	NOUN
cana-2601	150	14	,	,	PUNCT
cana-2601	150	15	j.	j.	PROPN
cana-2601	150	16	differ	differ	VERB
cana-2601	150	17	.	.	PUNCT
cana-2601	151	1	equ	equ	PROPN
cana-2601	151	2	.	.	PUNCT
cana-2601	151	3	appl	appl	PROPN
cana-2601	151	4	.	.	PUNCT
cana-2601	152	1	23(1–2	23(1–2	X
cana-2601	152	2	)	)	PUNCT
cana-2601	152	3	(	(	PUNCT
cana-2601	152	4	2015	2015	NUM
cana-2601	152	5	)	)	PUNCT
cana-2601	152	6	8–20	8–20	NOUN
cana-2601	152	7	.	.	PUNCT
cana-2601	153	1	[	[	X
cana-2601	153	2	4	4	X
cana-2601	153	3	]	]	PUNCT
cana-2601	153	4	j.	j.	PROPN
cana-2601	153	5	l.	l.	PROPN
cana-2601	153	6	gross	gross	PROPN
cana-2601	153	7	and	and	CCONJ
cana-2601	153	8	j.	j.	PROPN
cana-2601	153	9	yellen	yellen	PROPN
cana-2601	153	10	,	,	PUNCT
cana-2601	153	11	graph	graph	NOUN
cana-2601	153	12	theory	theory	NOUN
cana-2601	153	13	and	and	CCONJ
cana-2601	153	14	its	its	PRON
cana-2601	153	15	applications	application	NOUN
cana-2601	153	16	,	,	PUNCT
cana-2601	153	17	crc	crc	NOUN
cana-2601	153	18	press	press	NOUN
cana-2601	153	19	,	,	PUNCT
cana-2601	153	20	(	(	PUNCT
cana-2601	153	21	2006	2006	NUM
cana-2601	153	22	)	)	PUNCT
cana-2601	153	23	.	.	PUNCT
cana-2601	154	1	[	[	X
cana-2601	154	2	5	5	X
cana-2601	154	3	]	]	PUNCT
cana-2601	154	4	j.	j.	PROPN
cana-2601	154	5	v.	v.	PROPN
cana-2601	154	6	d.	d.	PROPN
cana-2601	154	7	heuvel	heuvel	PROPN
cana-2601	154	8	and	and	CCONJ
cana-2601	154	9	m.	m.	PROPN
cana-2601	154	10	johnson	johnson	PROPN
cana-2601	154	11	,	,	PUNCT
cana-2601	154	12	transversals	transversal	NOUN
cana-2601	154	13	of	of	ADP
cana-2601	154	14	subtree	subtree	ADJ
cana-2601	154	15	hypergraphs	hypergraph	NOUN
cana-2601	154	16	and	and	CCONJ
cana-2601	154	17	the	the	DET
cana-2601	154	18	source	source	NOUN
cana-2601	154	19	location	location	NOUN
cana-2601	154	20	problem	problem	NOUN
cana-2601	154	21	in	in	ADP
cana-2601	154	22	digraphs	digraph	NOUN
cana-2601	154	23	,	,	PUNCT
cana-2601	154	24	networks	network	NOUN
cana-2601	154	25	,	,	PUNCT
cana-2601	154	26	51(2	51(2	NUM
cana-2601	154	27	)	)	PUNCT
cana-2601	154	28	(	(	PUNCT
cana-2601	154	29	2008	2008	NUM
cana-2601	154	30	)	)	PUNCT
cana-2601	154	31	113–119	113–119	NUM
cana-2601	154	32	.	.	PUNCT
cana-2601	155	1	[	[	X
cana-2601	155	2	6	6	NUM
cana-2601	155	3	]	]	PUNCT
cana-2601	155	4	j.	j.	PROPN
cana-2601	155	5	b.	b.	PROPN
cana-2601	155	6	liu	liu	PROPN
cana-2601	155	7	,	,	PUNCT
cana-2601	155	8	m.	m.	NOUN
cana-2601	155	9	arockiaraj	arockiaraj	PROPN
cana-2601	155	10	,	,	PUNCT
cana-2601	155	11	a.	a.	PROPN
cana-2601	155	12	nelson	nelson	PROPN
cana-2601	155	13	,	,	PUNCT
cana-2601	155	14	tight	tight	ADJ
cana-2601	155	15	bounds	bound	NOUN
cana-2601	155	16	on	on	ADP
cana-2601	155	17	1	1	NUM
cana-2601	155	18	-	-	PUNCT
cana-2601	155	19	harmonious	harmonious	ADJ
cana-2601	155	20	coloring	coloring	NOUN
cana-2601	155	21	of	of	ADP
cana-2601	155	22	certain	certain	ADJ
cana-2601	155	23	graphs	graph	NOUN
cana-2601	155	24	,	,	PUNCT
cana-2601	155	25	symmetry	symmetry	NOUN
cana-2601	155	26	,	,	PUNCT
cana-2601	155	27	11(7	11(7	NUM
cana-2601	155	28	)	)	PUNCT
cana-2601	155	29	(	(	PUNCT
cana-2601	155	30	2019	2019	NUM
cana-2601	155	31	)	)	PUNCT
cana-2601	155	32	1–11	1–11	PROPN
cana-2601	155	33	.	.	PUNCT
cana-2601	156	1	[	[	X
cana-2601	156	2	7	7	X
cana-2601	156	3	]	]	PUNCT
cana-2601	156	4	a.	a.	NOUN
cana-2601	156	5	nelson	nelson	PROPN
cana-2601	156	6	,	,	PUNCT
cana-2601	156	7	on	on	ADP
cana-2601	156	8	1	1	NUM
cana-2601	156	9	-	-	PUNCT
cana-2601	156	10	harmonious	harmonious	ADJ
cana-2601	156	11	chromatic	chromatic	ADJ
cana-2601	156	12	number	number	NOUN
cana-2601	156	13	of	of	ADP
cana-2601	156	14	certain	certain	ADJ
cana-2601	156	15	interconnection	interconnection	NOUN
cana-2601	156	16	networks	network	NOUN
cana-2601	156	17	,	,	PUNCT
cana-2601	156	18	journal	journal	NOUN
cana-2601	156	19	of	of	ADP
cana-2601	156	20	information	information	NOUN
cana-2601	156	21	and	and	CCONJ
cana-2601	156	22	computational	computational	ADJ
cana-2601	156	23	science	science	NOUN
cana-2601	156	24	,	,	PUNCT
cana-2601	156	25	9(12	9(12	NUM
cana-2601	156	26	)	)	PUNCT
cana-2601	156	27	(	(	PUNCT
cana-2601	156	28	2019	2019	NUM
cana-2601	156	29	)	)	PUNCT
cana-2601	156	30	338	338	NUM
cana-2601	156	31	-	-	SYM
cana-2601	156	32	353	353	NUM
cana-2601	156	33	.	.	PUNCT
cana-2601	157	1	[	[	X
cana-2601	157	2	8	8	NUM
cana-2601	157	3	]	]	X
cana-2601	157	4	d.	d.	PROPN
cana-2601	157	5	paul	paul	PROPN
cana-2601	157	6	,	,	PUNCT
cana-2601	157	7	i.	i.	PROPN
cana-2601	157	8	rajasingh	rajasingh	PROPN
cana-2601	157	9	and	and	CCONJ
cana-2601	157	10	r.	r.	PROPN
cana-2601	157	11	sundara	sundara	PROPN
cana-2601	157	12	rajan	rajan	PROPN
cana-2601	157	13	,	,	PUNCT
cana-2601	157	14	acyclic	acyclic	ADJ
cana-2601	157	15	edge	edge	NOUN
cana-2601	157	16	-	-	PUNCT
cana-2601	157	17	coloring	coloring	NOUN
cana-2601	157	18	of	of	ADP
cana-2601	157	19	hypertree	hypertree	NOUN
cana-2601	157	20	and	and	CCONJ
cana-2601	157	21	shuffle	shuffle	NOUN
cana-2601	157	22	hypertree	hypertree	NOUN
cana-2601	157	23	,	,	PUNCT
cana-2601	157	24	international	international	ADJ
cana-2601	157	25	journal	journal	NOUN
cana-2601	157	26	of	of	ADP
cana-2601	157	27	pure	pure	ADJ
cana-2601	157	28	and	and	CCONJ
cana-2601	157	29	applied	applied	ADJ
cana-2601	157	30	mathematics	mathematic	NOUN
cana-2601	157	31	,	,	PUNCT
cana-2601	157	32	101(5	101(5	NUM
cana-2601	157	33	)	)	PUNCT
cana-2601	157	34	(	(	PUNCT
cana-2601	157	35	2015	2015	NUM
cana-2601	157	36	)	)	PUNCT
cana-2601	157	37	623	623	NUM
cana-2601	157	38	-	-	SYM
cana-2601	157	39	629	629	NUM
cana-2601	157	40	.	.	PUNCT
cana-2601	158	1	[	[	X
cana-2601	158	2	9	9	NUM
cana-2601	158	3	]	]	X
cana-2601	158	4	d.	d.	PROPN
cana-2601	158	5	paul	paul	PROPN
cana-2601	158	6	,	,	PUNCT
cana-2601	158	7	i.	i.	PROPN
cana-2601	158	8	rajasingh	rajasingh	PROPN
cana-2601	158	9	and	and	CCONJ
cana-2601	158	10	r.	r.	PROPN
cana-2601	158	11	sundara	sundara	PROPN
cana-2601	158	12	rajan	rajan	PROPN
cana-2601	158	13	,	,	PUNCT
cana-2601	158	14	tree	tree	NOUN
cana-2601	158	15	derived	derive	VERB
cana-2601	158	16	architectures	architecture	NOUN
cana-2601	158	17	with	with	ADP
cana-2601	158	18	decycling	decycle	VERB
cana-2601	158	19	number	number	NOUN
cana-2601	158	20	equal	equal	ADJ
cana-2601	158	21	to	to	ADP
cana-2601	158	22	cycle	cycle	NOUN
cana-2601	158	23	packing	packing	NOUN
cana-2601	158	24	number	number	NOUN
cana-2601	158	25	,	,	PUNCT
cana-2601	158	26	procedia	procedia	NOUN
cana-2601	158	27	computer	computer	NOUN
cana-2601	158	28	science	science	NOUN
cana-2601	158	29	,	,	PUNCT
cana-2601	158	30	57	57	NUM
cana-2601	158	31	(	(	PUNCT
cana-2601	158	32	2015	2015	NUM
cana-2601	158	33	)	)	PUNCT
cana-2601	158	34	716	716	NUM
cana-2601	158	35	-	-	SYM
cana-2601	158	36	726	726	NUM
cana-2601	158	37	.	.	PUNCT
cana-2601	159	1	[	[	X
cana-2601	159	2	10	10	NUM
cana-2601	159	3	]	]	X
cana-2601	159	4	c.	c.	PROPN
cana-2601	159	5	h.	h.	PROPN
cana-2601	159	6	tsai	tsai	PROPN
cana-2601	159	7	,	,	PUNCT
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cana-2601	159	9	array	array	NOUN
cana-2601	159	10	and	and	CCONJ
cana-2601	159	11	ring	ring	NOUN
cana-2601	159	12	embeddings	embedding	NOUN
cana-2601	159	13	in	in	ADP
cana-2601	159	14	conditional	conditional	ADJ
cana-2601	159	15	faulty	faulty	ADJ
cana-2601	159	16	hypercubes	hypercube	NOUN
cana-2601	159	17	,	,	PUNCT
cana-2601	159	18	theoretical	theoretical	ADJ
cana-2601	159	19	computer	computer	NOUN
cana-2601	159	20	science	science	NOUN
cana-2601	159	21	,	,	PUNCT
cana-2601	159	22	314	314	NUM
cana-2601	159	23	(	(	PUNCT
cana-2601	159	24	2004	2004	NUM
cana-2601	159	25	)	)	PUNCT
cana-2601	159	26	431	431	NUM
cana-2601	159	27	-	-	SYM
cana-2601	159	28	443	443	NUM
cana-2601	159	29	.	.	PUNCT
cana-2601	160	1	[	[	X
cana-2601	160	2	11	11	NUM
cana-2601	160	3	]	]	X
cana-2601	160	4	y.l	y.l	PROPN
cana-2601	160	5	.	.	PROPN
cana-2601	160	6	wang	wang	PROPN
cana-2601	160	7	,	,	PUNCT
cana-2601	160	8	t.w	t.w	PROPN
cana-2601	160	9	.	.	PROPN
cana-2601	160	10	lin	lin	PROPN
cana-2601	160	11	,	,	PUNCT
cana-2601	160	12	l.y	l.y	PROPN
cana-2601	160	13	.	.	PROPN
cana-2601	160	14	wang	wang	PROPN
cana-2601	160	15	,	,	PUNCT
cana-2601	160	16	the	the	DET
cana-2601	160	17	local	local	ADJ
cana-2601	160	18	harmonious	harmonious	ADJ
cana-2601	160	19	chromatic	chromatic	ADJ
cana-2601	160	20	problem	problem	NOUN
cana-2601	160	21	,	,	PUNCT
cana-2601	160	22	proceedings	proceeding	NOUN
cana-2601	160	23	of	of	ADP
cana-2601	160	24	the	the	DET
cana-2601	160	25	27th	27th	ADJ
cana-2601	160	26	workshop	workshop	NOUN
cana-2601	160	27	on	on	ADP
cana-2601	160	28	combinatorial	combinatorial	ADJ
cana-2601	160	29	mathematics	mathematic	NOUN
cana-2601	160	30	and	and	CCONJ
cana-2601	160	31	computation	computation	NOUN
cana-2601	160	32	theory	theory	NOUN
cana-2601	160	33	,	,	PUNCT
cana-2601	160	34	taiwan	taiwan	PROPN
cana-2601	160	35	,	,	PUNCT
cana-2601	160	36	(	(	PUNCT
cana-2601	160	37	2010	2010	NUM
cana-2601	160	38	)	)	PUNCT
cana-2601	160	39	.	.	PUNCT
cana-2601	161	1	[	[	X
cana-2601	161	2	12	12	NUM
cana-2601	161	3	]	]	PUNCT
cana-2601	161	4	p.	p.	PROPN
cana-2601	161	5	zhang	zhang	PROPN
cana-2601	161	6	,	,	PUNCT
cana-2601	161	7	a	a	DET
cana-2601	161	8	kaleidoscopic	kaleidoscopic	ADJ
cana-2601	161	9	view	view	NOUN
cana-2601	161	10	of	of	ADP
cana-2601	161	11	graph	graph	NOUN
cana-2601	161	12	colorings	coloring	NOUN
cana-2601	161	13	,	,	PUNCT
cana-2601	161	14	springer	springer	NOUN
cana-2601	161	15	international	international	ADJ
cana-2601	161	16	publishing	publishing	NOUN
cana-2601	161	17	,	,	PUNCT
cana-2601	161	18	ag	ag	PROPN
cana-2601	161	19	,	,	PUNCT
cana-2601	161	20	2016	2016	NUM
cana-2601	161	21	.	.	PUNCT