id	sid	tid	token	lemma	pos
ejpam-4453	1	1	european	european	PROPN
ejpam-4453	1	2	journal	journal	PROPN
ejpam-4453	1	3	of	of	ADP
ejpam-4453	1	4	pure	pure	ADJ
ejpam-4453	1	5	and	and	CCONJ
ejpam-4453	1	6	applied	apply	VERB
ejpam-4453	1	7	mathematics	mathematic	NOUN
ejpam-4453	1	8	vol	vol	NOUN
ejpam-4453	1	9	.	.	PROPN
ejpam-4453	2	1	15	15	NUM
ejpam-4453	2	2	,	,	PUNCT
ejpam-4453	2	3	no	no	INTJ
ejpam-4453	2	4	.	.	NOUN
ejpam-4453	2	5	4	4	NUM
ejpam-4453	2	6	,	,	PUNCT
ejpam-4453	2	7	2022	2022	NUM
ejpam-4453	2	8	,	,	PUNCT
ejpam-4453	2	9	1536	1536	NUM
ejpam-4453	2	10	-	-	SYM
ejpam-4453	2	11	1548	1548	NUM
ejpam-4453	2	12	issn	issn	PROPN
ejpam-4453	2	13	1307	1307	NUM
ejpam-4453	2	14	-	-	SYM
ejpam-4453	2	15	5543	5543	NUM
ejpam-4453	2	16	–	–	PUNCT
ejpam-4453	2	17	ejpam.com	ejpam.com	X
ejpam-4453	2	18	published	publish	VERB
ejpam-4453	2	19	by	by	ADP
ejpam-4453	2	20	new	new	PROPN
ejpam-4453	2	21	york	york	PROPN
ejpam-4453	2	22	business	business	PROPN
ejpam-4453	2	23	global	global	ADJ
ejpam-4453	2	24	on	on	ADP
ejpam-4453	2	25	some	some	DET
ejpam-4453	2	26	properties	property	NOUN
ejpam-4453	2	27	of	of	ADP
ejpam-4453	2	28	non	non	ADJ
ejpam-4453	2	29	-	-	ADJ
ejpam-4453	2	30	traceable	traceable	ADJ
ejpam-4453	2	31	cubic	cubic	ADJ
ejpam-4453	2	32	bridge	bridge	NOUN
ejpam-4453	2	33	graph	graph	NOUN
ejpam-4453	2	34	alex	alex	PROPN
ejpam-4453	2	35	ralph	ralph	PROPN
ejpam-4453	2	36	baisa	baisa	PROPN
ejpam-4453	2	37	nieva1,∗	nieva1,∗	PROPN
ejpam-4453	2	38	,	,	PUNCT
ejpam-4453	2	39	karen	karen	PROPN
ejpam-4453	2	40	p.	p.	PROPN
ejpam-4453	2	41	nocum2	nocum2	PROPN
ejpam-4453	3	1	1	1	NUM
ejpam-4453	3	2	college	college	NOUN
ejpam-4453	3	3	of	of	ADP
ejpam-4453	3	4	arts	art	NOUN
ejpam-4453	3	5	and	and	CCONJ
ejpam-4453	3	6	sciences	science	NOUN
ejpam-4453	3	7	,	,	PUNCT
ejpam-4453	3	8	faculty	faculty	NOUN
ejpam-4453	3	9	/	/	SYM
ejpam-4453	3	10	camarines	camarines	PROPN
ejpam-4453	3	11	sur	sur	PROPN
ejpam-4453	3	12	polytechnic	polytechnic	ADJ
ejpam-4453	3	13	colleges	college	NOUN
ejpam-4453	3	14	,	,	PUNCT
ejpam-4453	3	15	nabua	nabua	PROPN
ejpam-4453	3	16	,	,	PUNCT
ejpam-4453	3	17	philippines	philippine	NOUN
ejpam-4453	3	18	2	2	NUM
ejpam-4453	3	19	college	college	NOUN
ejpam-4453	3	20	of	of	ADP
ejpam-4453	3	21	arts	art	NOUN
ejpam-4453	3	22	and	and	CCONJ
ejpam-4453	3	23	sciences	science	NOUN
ejpam-4453	3	24	,	,	PUNCT
ejpam-4453	3	25	faculty	faculty	NOUN
ejpam-4453	3	26	/	/	SYM
ejpam-4453	3	27	batangas	batangas	PROPN
ejpam-4453	3	28	state	state	PROPN
ejpam-4453	3	29	university	university	PROPN
ejpam-4453	3	30	,	,	PUNCT
ejpam-4453	3	31	batangas	batangas	PROPN
ejpam-4453	3	32	city	city	PROPN
ejpam-4453	3	33	,	,	PUNCT
ejpam-4453	3	34	philippines	philippine	NOUN
ejpam-4453	3	35	abstract	abstract	ADJ
ejpam-4453	3	36	.	.	PUNCT
ejpam-4453	4	1	graphs	graph	NOUN
ejpam-4453	4	2	considered	consider	VERB
ejpam-4453	4	3	in	in	ADP
ejpam-4453	4	4	this	this	DET
ejpam-4453	4	5	paper	paper	NOUN
ejpam-4453	4	6	are	be	AUX
ejpam-4453	4	7	simple	simple	ADJ
ejpam-4453	4	8	finite	finite	ADJ
ejpam-4453	4	9	undirected	undirected	ADJ
ejpam-4453	4	10	graph	graph	NOUN
ejpam-4453	4	11	without	without	ADP
ejpam-4453	4	12	loops	loop	NOUN
ejpam-4453	4	13	or	or	CCONJ
ejpam-4453	4	14	multiple	multiple	ADJ
ejpam-4453	4	15	edges	edge	NOUN
ejpam-4453	4	16	.	.	PUNCT
ejpam-4453	5	1	a	a	DET
ejpam-4453	5	2	simple	simple	ADJ
ejpam-4453	5	3	graph	graph	NOUN
ejpam-4453	5	4	where	where	SCONJ
ejpam-4453	5	5	each	each	DET
ejpam-4453	5	6	vertex	vertex	NOUN
ejpam-4453	5	7	has	have	VERB
ejpam-4453	5	8	degree	degree	NOUN
ejpam-4453	5	9	3	3	NUM
ejpam-4453	5	10	is	be	AUX
ejpam-4453	5	11	called	call	VERB
ejpam-4453	5	12	a	a	DET
ejpam-4453	5	13	cubic	cubic	ADJ
ejpam-4453	5	14	graph	graph	NOUN
ejpam-4453	5	15	.	.	PUNCT
ejpam-4453	6	1	a	a	DET
ejpam-4453	6	2	cubic	cubic	ADJ
ejpam-4453	6	3	graph	graph	NOUN
ejpam-4453	6	4	,	,	PUNCT
ejpam-4453	6	5	that	that	ADV
ejpam-4453	6	6	is	is	ADV
ejpam-4453	6	7	,	,	PUNCT
ejpam-4453	6	8	1	1	NUM
ejpam-4453	6	9	-	-	PUNCT
ejpam-4453	6	10	connected	connected	ADJ
ejpam-4453	6	11	or	or	CCONJ
ejpam-4453	6	12	cubic	cubic	ADJ
ejpam-4453	6	13	bridge	bridge	NOUN
ejpam-4453	6	14	graph	graph	NOUN
ejpam-4453	6	15	is	be	AUX
ejpam-4453	6	16	traceable	traceable	ADJ
ejpam-4453	6	17	if	if	SCONJ
ejpam-4453	6	18	it	it	PRON
ejpam-4453	6	19	contains	contain	VERB
ejpam-4453	6	20	a	a	DET
ejpam-4453	6	21	hamiltonian	hamiltonian	ADJ
ejpam-4453	6	22	path	path	NOUN
ejpam-4453	6	23	.	.	PUNCT
ejpam-4453	7	1	otherwise	otherwise	ADV
ejpam-4453	7	2	,	,	PUNCT
ejpam-4453	7	3	we	we	PRON
ejpam-4453	7	4	called	call	VERB
ejpam-4453	7	5	it	it	PRON
ejpam-4453	7	6	non	non	ADJ
ejpam-4453	7	7	-	-	ADJ
ejpam-4453	7	8	traceable	traceable	ADJ
ejpam-4453	7	9	.	.	PUNCT
ejpam-4453	8	1	in	in	ADP
ejpam-4453	8	2	this	this	DET
ejpam-4453	8	3	paper	paper	NOUN
ejpam-4453	8	4	,	,	PUNCT
ejpam-4453	8	5	we	we	PRON
ejpam-4453	8	6	introduce	introduce	VERB
ejpam-4453	8	7	a	a	DET
ejpam-4453	8	8	new	new	ADJ
ejpam-4453	8	9	family	family	NOUN
ejpam-4453	8	10	of	of	ADP
ejpam-4453	8	11	cubic	cubic	ADJ
ejpam-4453	8	12	graphs	graph	NOUN
ejpam-4453	8	13	called	call	VERB
ejpam-4453	8	14	non	non	ADJ
ejpam-4453	8	15	-	-	ADJ
ejpam-4453	8	16	traceable	traceable	ADJ
ejpam-4453	8	17	cubic	cubic	ADJ
ejpam-4453	8	18	bridge	bridge	NOUN
ejpam-4453	8	19	graph	graph	NOUN
ejpam-4453	8	20	(	(	PUNCT
ejpam-4453	8	21	ntcbg	ntcbg	NUM
ejpam-4453	8	22	)	)	PUNCT
ejpam-4453	8	23	that	that	PRON
ejpam-4453	8	24	satisfies	satisfy	VERB
ejpam-4453	8	25	the	the	DET
ejpam-4453	8	26	conjecture	conjecture	NOUN
ejpam-4453	8	27	of	of	ADP
ejpam-4453	8	28	zoeram	zoeram	NOUN
ejpam-4453	8	29	and	and	CCONJ
ejpam-4453	8	30	yaqubi	yaqubi	NOUN
ejpam-4453	8	31	(	(	PUNCT
ejpam-4453	8	32	2017	2017	NUM
ejpam-4453	8	33	)	)	PUNCT
ejpam-4453	8	34	.	.	PUNCT
ejpam-4453	9	1	in	in	ADP
ejpam-4453	9	2	addition	addition	NOUN
ejpam-4453	9	3	,	,	PUNCT
ejpam-4453	9	4	we	we	PRON
ejpam-4453	9	5	define	define	VERB
ejpam-4453	9	6	two	two	NUM
ejpam-4453	9	7	important	important	ADJ
ejpam-4453	9	8	connected	connected	ADJ
ejpam-4453	9	9	components	component	NOUN
ejpam-4453	9	10	of	of	ADP
ejpam-4453	9	11	ntcbg	ntcbg	DET
ejpam-4453	9	12	those	those	PRON
ejpam-4453	9	13	are	be	AUX
ejpam-4453	9	14	the	the	DET
ejpam-4453	9	15	central	central	ADJ
ejpam-4453	9	16	fragment	fragment	NOUN
ejpam-4453	9	17	that	that	PRON
ejpam-4453	9	18	gives	give	VERB
ejpam-4453	9	19	assurance	assurance	NOUN
ejpam-4453	9	20	for	for	ADP
ejpam-4453	9	21	a	a	DET
ejpam-4453	9	22	graph	graph	NOUN
ejpam-4453	9	23	to	to	PART
ejpam-4453	9	24	be	be	AUX
ejpam-4453	9	25	non	non	ADJ
ejpam-4453	9	26	-	-	ADJ
ejpam-4453	9	27	traceable	traceable	ADJ
ejpam-4453	9	28	and	and	CCONJ
ejpam-4453	9	29	its	its	PRON
ejpam-4453	9	30	branch	branch	NOUN
ejpam-4453	9	31	.	.	PUNCT
ejpam-4453	10	1	some	some	DET
ejpam-4453	10	2	properties	property	NOUN
ejpam-4453	10	3	of	of	ADP
ejpam-4453	10	4	a	a	DET
ejpam-4453	10	5	ntcbg	ntcbg	NOUN
ejpam-4453	10	6	such	such	ADJ
ejpam-4453	10	7	as	as	ADP
ejpam-4453	10	8	chromatic	chromatic	ADJ
ejpam-4453	10	9	number	number	NOUN
ejpam-4453	10	10	and	and	CCONJ
ejpam-4453	10	11	clique	clique	ADJ
ejpam-4453	10	12	number	number	NOUN
ejpam-4453	10	13	are	be	AUX
ejpam-4453	10	14	also	also	ADV
ejpam-4453	10	15	provided	provide	VERB
ejpam-4453	10	16	.	.	PUNCT
ejpam-4453	11	1	2020	2020	NUM
ejpam-4453	11	2	mathematics	mathematic	NOUN
ejpam-4453	11	3	subject	subject	NOUN
ejpam-4453	11	4	classifications	classification	NOUN
ejpam-4453	11	5	:	:	PUNCT
ejpam-4453	11	6	05c07,05c15,05c62	05c07,05c15,05c62	NUM
ejpam-4453	11	7	key	key	ADJ
ejpam-4453	11	8	words	word	NOUN
ejpam-4453	11	9	and	and	CCONJ
ejpam-4453	11	10	phrases	phrase	NOUN
ejpam-4453	11	11	:	:	PUNCT
ejpam-4453	11	12	cubic	cubic	ADJ
ejpam-4453	11	13	graph	graph	NOUN
ejpam-4453	11	14	,	,	PUNCT
ejpam-4453	11	15	bridge	bridge	NOUN
ejpam-4453	11	16	graph	graph	NOUN
ejpam-4453	11	17	,	,	PUNCT
ejpam-4453	11	18	non	non	ADJ
ejpam-4453	11	19	-	-	ADJ
ejpam-4453	11	20	traceable	traceable	ADJ
ejpam-4453	11	21	,	,	PUNCT
ejpam-4453	11	22	central	central	ADJ
ejpam-4453	11	23	fragment	fragment	NOUN
ejpam-4453	11	24	,	,	PUNCT
ejpam-4453	11	25	ntcbg	ntcbg	NOUN
ejpam-4453	11	26	1	1	NUM
ejpam-4453	11	27	.	.	PUNCT
ejpam-4453	12	1	introduction	introduction	NOUN
ejpam-4453	12	2	cubic	cubic	ADJ
ejpam-4453	12	3	graph	graph	NOUN
ejpam-4453	12	4	is	be	AUX
ejpam-4453	12	5	one	one	NUM
ejpam-4453	12	6	of	of	ADP
ejpam-4453	12	7	the	the	DET
ejpam-4453	12	8	classes	class	NOUN
ejpam-4453	12	9	of	of	ADP
ejpam-4453	12	10	graphs	graph	NOUN
ejpam-4453	12	11	that	that	PRON
ejpam-4453	12	12	fascinates	fascinate	VERB
ejpam-4453	12	13	graph	graph	NOUN
ejpam-4453	12	14	theorist	theorist	NOUN
ejpam-4453	12	15	over	over	ADP
ejpam-4453	12	16	the	the	DET
ejpam-4453	12	17	years	year	NOUN
ejpam-4453	12	18	because	because	SCONJ
ejpam-4453	12	19	of	of	ADP
ejpam-4453	12	20	its	its	PRON
ejpam-4453	12	21	interesting	interesting	ADJ
ejpam-4453	12	22	application	application	NOUN
ejpam-4453	12	23	and	and	CCONJ
ejpam-4453	12	24	appearances	appearance	NOUN
ejpam-4453	12	25	as	as	ADP
ejpam-4453	12	26	a	a	DET
ejpam-4453	12	27	counterexample	counterexample	NOUN
ejpam-4453	12	28	in	in	ADP
ejpam-4453	12	29	so	so	ADV
ejpam-4453	12	30	many	many	ADJ
ejpam-4453	12	31	areas	area	NOUN
ejpam-4453	12	32	of	of	ADP
ejpam-4453	12	33	the	the	DET
ejpam-4453	12	34	subject	subject	NOUN
ejpam-4453	12	35	.	.	PUNCT
ejpam-4453	13	1	a	a	DET
ejpam-4453	13	2	cubic	cubic	ADJ
ejpam-4453	13	3	graph	graph	NOUN
ejpam-4453	13	4	can	can	AUX
ejpam-4453	13	5	be	be	AUX
ejpam-4453	13	6	classified	classify	VERB
ejpam-4453	13	7	into	into	ADP
ejpam-4453	13	8	3	3	NUM
ejpam-4453	13	9	different	different	ADJ
ejpam-4453	13	10	types	type	NOUN
ejpam-4453	13	11	namely	namely	ADV
ejpam-4453	13	12	,	,	PUNCT
ejpam-4453	13	13	1connected	1connected	NUM
ejpam-4453	13	14	,	,	PUNCT
ejpam-4453	13	15	2	2	NUM
ejpam-4453	13	16	-	-	PUNCT
ejpam-4453	13	17	connected	connect	VERB
ejpam-4453	13	18	and	and	CCONJ
ejpam-4453	13	19	3	3	NUM
ejpam-4453	13	20	-	-	PUNCT
ejpam-4453	13	21	connected	connect	VERB
ejpam-4453	13	22	.	.	PUNCT
ejpam-4453	14	1	several	several	ADJ
ejpam-4453	14	2	papers	paper	NOUN
ejpam-4453	14	3	in	in	ADP
ejpam-4453	14	4	graph	graph	NOUN
ejpam-4453	14	5	theory	theory	NOUN
ejpam-4453	14	6	discussed	discuss	VERB
ejpam-4453	14	7	certain	certain	ADJ
ejpam-4453	14	8	types	type	NOUN
ejpam-4453	14	9	of	of	ADP
ejpam-4453	14	10	cubic	cubic	ADJ
ejpam-4453	14	11	graphs	graph	NOUN
ejpam-4453	14	12	,	,	PUNCT
ejpam-4453	14	13	that	that	ADV
ejpam-4453	14	14	is	is	ADV
ejpam-4453	14	15	,	,	PUNCT
ejpam-4453	14	16	1	1	NUM
ejpam-4453	14	17	-	-	PUNCT
ejpam-4453	14	18	connected	connected	ADJ
ejpam-4453	14	19	or	or	CCONJ
ejpam-4453	14	20	cubic	cubic	ADJ
ejpam-4453	14	21	bridge	bridge	NOUN
ejpam-4453	14	22	graph	graph	NOUN
ejpam-4453	14	23	.	.	PUNCT
ejpam-4453	15	1	fillar	fillar	ADJ
ejpam-4453	15	2	et	et	PROPN
ejpam-4453	15	3	al	al	PROPN
ejpam-4453	15	4	.	.	PROPN
ejpam-4453	16	1	in	in	ADP
ejpam-4453	16	2	2010	2010	NUM
ejpam-4453	16	3	presented	present	VERB
ejpam-4453	16	4	in	in	ADP
ejpam-4453	16	5	their	their	PRON
ejpam-4453	16	6	paper	paper	NOUN
ejpam-4453	16	7	the	the	DET
ejpam-4453	16	8	ratio	ratio	NOUN
ejpam-4453	16	9	of	of	ADP
ejpam-4453	16	10	cubic	cubic	ADJ
ejpam-4453	16	11	bridge	bridge	NOUN
ejpam-4453	16	12	graphs	graph	NOUN
ejpam-4453	16	13	over	over	ADP
ejpam-4453	16	14	cubic	cubic	ADJ
ejpam-4453	16	15	non	non	ADJ
ejpam-4453	16	16	-	-	ADJ
ejpam-4453	16	17	hamiltonian	hamiltonian	ADJ
ejpam-4453	16	18	graph	graph	NOUN
ejpam-4453	16	19	and	and	CCONJ
ejpam-4453	16	20	observed	observe	VERB
ejpam-4453	16	21	that	that	SCONJ
ejpam-4453	16	22	the	the	DET
ejpam-4453	16	23	ratio	ratio	NOUN
ejpam-4453	16	24	is	be	AUX
ejpam-4453	16	25	closer	close	ADJ
ejpam-4453	16	26	to	to	ADP
ejpam-4453	16	27	1	1	NUM
ejpam-4453	16	28	[	[	X
ejpam-4453	16	29	4	4	NUM
ejpam-4453	16	30	]	]	PUNCT
ejpam-4453	16	31	.	.	PUNCT
ejpam-4453	17	1	this	this	DET
ejpam-4453	17	2	observation	observation	NOUN
ejpam-4453	17	3	gave	give	VERB
ejpam-4453	17	4	rise	rise	NOUN
ejpam-4453	17	5	to	to	ADP
ejpam-4453	17	6	a	a	DET
ejpam-4453	17	7	conjecture	conjecture	NOUN
ejpam-4453	17	8	that	that	SCONJ
ejpam-4453	17	9	almost	almost	ADV
ejpam-4453	17	10	all	all	PRON
ejpam-4453	17	11	cubic	cubic	ADJ
ejpam-4453	17	12	non	non	ADJ
ejpam-4453	17	13	-	-	ADJ
ejpam-4453	17	14	hamiltonian	hamiltonian	ADJ
ejpam-4453	17	15	graphs	graph	NOUN
ejpam-4453	17	16	are	be	AUX
ejpam-4453	17	17	bridge	bridge	NOUN
ejpam-4453	17	18	graphs	graph	NOUN
ejpam-4453	17	19	.	.	PUNCT
ejpam-4453	18	1	a	a	DET
ejpam-4453	18	2	cubic	cubic	ADJ
ejpam-4453	18	3	bridge	bridge	NOUN
ejpam-4453	18	4	graph	graph	NOUN
ejpam-4453	18	5	can	can	AUX
ejpam-4453	18	6	be	be	AUX
ejpam-4453	18	7	divided	divide	VERB
ejpam-4453	18	8	into	into	ADP
ejpam-4453	18	9	two	two	NUM
ejpam-4453	18	10	classes	class	NOUN
ejpam-4453	18	11	namely	namely	ADV
ejpam-4453	18	12	,	,	PUNCT
ejpam-4453	18	13	traceable	traceable	ADJ
ejpam-4453	18	14	which	which	PRON
ejpam-4453	18	15	contains	contain	VERB
ejpam-4453	18	16	a	a	DET
ejpam-4453	18	17	hamiltonian	hamiltonian	ADJ
ejpam-4453	18	18	path	path	NOUN
ejpam-4453	18	19	and	and	CCONJ
ejpam-4453	18	20	non	non	ADJ
ejpam-4453	18	21	-	-	ADJ
ejpam-4453	18	22	traceable	traceable	ADJ
ejpam-4453	18	23	which	which	PRON
ejpam-4453	18	24	does	do	AUX
ejpam-4453	18	25	not	not	PART
ejpam-4453	18	26	contain	contain	VERB
ejpam-4453	18	27	hamiltonian	hamiltonian	ADJ
ejpam-4453	18	28	path	path	NOUN
ejpam-4453	18	29	.	.	PUNCT
ejpam-4453	19	1	zoeram	zoeram	NOUN
ejpam-4453	19	2	and	and	CCONJ
ejpam-4453	19	3	yaqubi	yaqubi	NOUN
ejpam-4453	19	4	in	in	ADP
ejpam-4453	19	5	2017	2017	NUM
ejpam-4453	19	6	gave	give	VERB
ejpam-4453	19	7	a	a	DET
ejpam-4453	19	8	construction	construction	NOUN
ejpam-4453	19	9	sequence	sequence	NOUN
ejpam-4453	19	10	of	of	ADP
ejpam-4453	19	11	a	a	DET
ejpam-4453	19	12	cubic	cubic	ADJ
ejpam-4453	19	13	graph	graph	NOUN
ejpam-4453	19	14	and	and	CCONJ
ejpam-4453	19	15	presented	present	VERB
ejpam-4453	19	16	a	a	DET
ejpam-4453	19	17	conjecture	conjecture	NOUN
ejpam-4453	19	18	that	that	SCONJ
ejpam-4453	19	19	there	there	PRON
ejpam-4453	19	20	exist	exist	VERB
ejpam-4453	19	21	an	an	DET
ejpam-4453	19	22	n	n	NUM
ejpam-4453	19	23	∈	∈	NOUN
ejpam-4453	19	24	n	n	NOUN
ejpam-4453	19	25	such	such	ADJ
ejpam-4453	19	26	that	that	SCONJ
ejpam-4453	19	27	each	each	DET
ejpam-4453	19	28	cubic	cubic	ADJ
ejpam-4453	19	29	graph	graph	NOUN
ejpam-4453	19	30	with	with	ADP
ejpam-4453	19	31	at	at	ADV
ejpam-4453	19	32	least	least	ADJ
ejpam-4453	19	33	n	n	PRON
ejpam-4453	19	34	vertices	vertex	NOUN
ejpam-4453	19	35	has	have	VERB
ejpam-4453	19	36	a	a	DET
ejpam-4453	19	37	spanning	span	VERB
ejpam-4453	19	38	⌊	⌊	PROPN
ejpam-4453	19	39	n+2	n+2	NUM
ejpam-4453	19	40	6	6	NUM
ejpam-4453	19	41	⌋	⌋	ADJ
ejpam-4453	19	42	-ended	-ended	ADJ
ejpam-4453	19	43	tree	tree	NOUN
ejpam-4453	20	1	[	[	X
ejpam-4453	20	2	7	7	NUM
ejpam-4453	20	3	]	]	PUNCT
ejpam-4453	20	4	.	.	PUNCT
ejpam-4453	21	1	∗corresponding	∗corresponde	VERB
ejpam-4453	21	2	author	author	NOUN
ejpam-4453	21	3	.	.	PUNCT
ejpam-4453	22	1	doi	doi	NOUN
ejpam-4453	22	2	:	:	PUNCT
ejpam-4453	22	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4453	https://doi.org/10.29020/nybg.ejpam.v15i4.4453	DET
ejpam-4453	22	4	email	email	NOUN
ejpam-4453	22	5	addresses	address	NOUN
ejpam-4453	22	6	:	:	PUNCT
ejpam-4453	22	7	alexralph.nieva08@gmail.com	alexralph.nieva08@gmail.com	X
ejpam-4453	22	8	(	(	PUNCT
ejpam-4453	22	9	a.r	a.r	PROPN
ejpam-4453	22	10	nieva	nieva	PROPN
ejpam-4453	22	11	)	)	PUNCT
ejpam-4453	22	12	,	,	PUNCT
ejpam-4453	22	13	karen.nocum@g.batstate-u.edu.ph	karen.nocum@g.batstate-u.edu.ph	PROPN
ejpam-4453	22	14	(	(	PUNCT
ejpam-4453	22	15	k.nocum	k.nocum	PROPN
ejpam-4453	22	16	)	)	PUNCT
ejpam-4453	22	17	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4453	22	18	1536	1536	NUM
ejpam-4453	23	1	©	©	ADP
ejpam-4453	23	2	2022	2022	NUM
ejpam-4453	23	3	ejpam	ejpam	VERB
ejpam-4453	23	4	all	all	DET
ejpam-4453	23	5	rights	right	NOUN
ejpam-4453	23	6	reserved	reserve	VERB
ejpam-4453	23	7	.	.	PUNCT
ejpam-4453	24	1	a.r	a.r	PROPN
ejpam-4453	24	2	nieva	nieva	PROPN
ejpam-4453	24	3	and	and	CCONJ
ejpam-4453	24	4	k.nocum	k.nocum	PROPN
ejpam-4453	24	5	/	/	SYM
ejpam-4453	24	6	eur	eur	PROPN
ejpam-4453	24	7	.	.	PUNCT
ejpam-4453	25	1	j.	j.	PROPN
ejpam-4453	25	2	pure	pure	PROPN
ejpam-4453	25	3	appl	appl	PROPN
ejpam-4453	25	4	.	.	PROPN
ejpam-4453	25	5	math	math	PROPN
ejpam-4453	25	6	,	,	PUNCT
ejpam-4453	25	7	15	15	NUM
ejpam-4453	25	8	(	(	PUNCT
ejpam-4453	25	9	4	4	NUM
ejpam-4453	25	10	)	)	PUNCT
ejpam-4453	25	11	(	(	PUNCT
ejpam-4453	25	12	2022	2022	NUM
ejpam-4453	25	13	)	)	PUNCT
ejpam-4453	25	14	,	,	PUNCT
ejpam-4453	25	15	1536	1536	NUM
ejpam-4453	25	16	-	-	SYM
ejpam-4453	25	17	1548	1548	NUM
ejpam-4453	25	18	1537	1537	NUM
ejpam-4453	25	19	2	2	NUM
ejpam-4453	25	20	.	.	PUNCT
ejpam-4453	25	21	preliminaries	preliminary	NOUN
ejpam-4453	25	22	throughout	throughout	ADP
ejpam-4453	25	23	this	this	DET
ejpam-4453	25	24	article	article	NOUN
ejpam-4453	25	25	,	,	PUNCT
ejpam-4453	25	26	we	we	PRON
ejpam-4453	25	27	only	only	ADV
ejpam-4453	25	28	consider	consider	VERB
ejpam-4453	25	29	a	a	DET
ejpam-4453	25	30	finite	finite	ADJ
ejpam-4453	25	31	simple	simple	ADJ
ejpam-4453	25	32	undirected	undirected	ADJ
ejpam-4453	25	33	graph	graph	NOUN
ejpam-4453	25	34	.	.	PUNCT
ejpam-4453	26	1	for	for	ADP
ejpam-4453	26	2	graphtheoretic	graphtheoretic	ADJ
ejpam-4453	26	3	terms	term	NOUN
ejpam-4453	26	4	that	that	PRON
ejpam-4453	26	5	have	have	AUX
ejpam-4453	26	6	not	not	PART
ejpam-4453	26	7	been	be	AUX
ejpam-4453	26	8	defined	define	VERB
ejpam-4453	26	9	but	but	CCONJ
ejpam-4453	26	10	are	be	AUX
ejpam-4453	26	11	used	use	VERB
ejpam-4453	26	12	in	in	ADP
ejpam-4453	26	13	the	the	DET
ejpam-4453	26	14	paper	paper	NOUN
ejpam-4453	26	15	,	,	PUNCT
ejpam-4453	26	16	see	see	VERB
ejpam-4453	26	17	bollobas	bollobas	NOUN
ejpam-4453	26	18	and	and	CCONJ
ejpam-4453	26	19	chartrand	chartrand	NOUN
ejpam-4453	27	1	[	[	X
ejpam-4453	27	2	2	2	NUM
ejpam-4453	27	3	,	,	PUNCT
ejpam-4453	27	4	5	5	NUM
ejpam-4453	27	5	]	]	PUNCT
ejpam-4453	27	6	.	.	PUNCT
ejpam-4453	28	1	a	a	DET
ejpam-4453	28	2	graph	graph	NOUN
ejpam-4453	28	3	g	g	NOUN
ejpam-4453	28	4	is	be	AUX
ejpam-4453	28	5	an	an	DET
ejpam-4453	28	6	ordered	order	VERB
ejpam-4453	28	7	pair	pair	NOUN
ejpam-4453	28	8	g	g	NOUN
ejpam-4453	28	9	=	=	PUNCT
ejpam-4453	28	10	(	(	PUNCT
ejpam-4453	28	11	v	v	NOUN
ejpam-4453	28	12	(	(	PUNCT
ejpam-4453	28	13	g	g	NOUN
ejpam-4453	28	14	)	)	PUNCT
ejpam-4453	28	15	,	,	PUNCT
ejpam-4453	28	16	e(g	e(g	PROPN
ejpam-4453	28	17	)	)	PUNCT
ejpam-4453	28	18	)	)	PUNCT
ejpam-4453	28	19	where	where	SCONJ
ejpam-4453	28	20	v	v	X
ejpam-4453	28	21	(	(	PUNCT
ejpam-4453	28	22	g	g	NOUN
ejpam-4453	28	23	)	)	PUNCT
ejpam-4453	28	24	is	be	AUX
ejpam-4453	28	25	a	a	DET
ejpam-4453	28	26	nonempty	nonempty	ADJ
ejpam-4453	28	27	set	set	NOUN
ejpam-4453	28	28	of	of	ADP
ejpam-4453	28	29	elements	element	NOUN
ejpam-4453	28	30	called	call	VERB
ejpam-4453	28	31	vertices	vertex	NOUN
ejpam-4453	28	32	,	,	PUNCT
ejpam-4453	28	33	and	and	CCONJ
ejpam-4453	28	34	e(g	e(g	NOUN
ejpam-4453	28	35	)	)	PUNCT
ejpam-4453	28	36	is	be	AUX
ejpam-4453	28	37	a	a	DET
ejpam-4453	28	38	set	set	NOUN
ejpam-4453	28	39	of	of	ADP
ejpam-4453	28	40	unordered	unordered	ADJ
ejpam-4453	28	41	pairs	pair	NOUN
ejpam-4453	28	42	of	of	ADP
ejpam-4453	28	43	vertices	vertex	NOUN
ejpam-4453	28	44	called	call	VERB
ejpam-4453	28	45	edges	edge	NOUN
ejpam-4453	28	46	.	.	PUNCT
ejpam-4453	29	1	the	the	DET
ejpam-4453	29	2	number	number	NOUN
ejpam-4453	29	3	|v	|v	NOUN
ejpam-4453	29	4	(	(	PUNCT
ejpam-4453	29	5	g)|	g)|	PROPN
ejpam-4453	29	6	is	be	AUX
ejpam-4453	29	7	called	call	VERB
ejpam-4453	29	8	the	the	DET
ejpam-4453	29	9	order	order	NOUN
ejpam-4453	29	10	of	of	ADP
ejpam-4453	29	11	g	g	NOUN
ejpam-4453	29	12	and	and	CCONJ
ejpam-4453	29	13	the	the	DET
ejpam-4453	29	14	number	number	NOUN
ejpam-4453	29	15	|e(g)|	|e(g)|	PROPN
ejpam-4453	29	16	is	be	AUX
ejpam-4453	29	17	called	call	VERB
ejpam-4453	29	18	the	the	DET
ejpam-4453	29	19	size	size	NOUN
ejpam-4453	29	20	of	of	ADP
ejpam-4453	29	21	g.	g.	PROPN
ejpam-4453	29	22	the	the	DET
ejpam-4453	29	23	degree	degree	NOUN
ejpam-4453	29	24	of	of	ADP
ejpam-4453	29	25	a	a	DET
ejpam-4453	29	26	vertex	vertex	NOUN
ejpam-4453	29	27	u	u	NOUN
ejpam-4453	29	28	in	in	ADP
ejpam-4453	29	29	a	a	DET
ejpam-4453	29	30	graph	graph	NOUN
ejpam-4453	29	31	g	g	NOUN
ejpam-4453	29	32	is	be	AUX
ejpam-4453	29	33	the	the	DET
ejpam-4453	29	34	number	number	NOUN
ejpam-4453	29	35	of	of	ADP
ejpam-4453	29	36	edges	edge	NOUN
ejpam-4453	29	37	incident	incident	NOUN
ejpam-4453	29	38	with	with	ADP
ejpam-4453	29	39	u	u	NOUN
ejpam-4453	29	40	and	and	CCONJ
ejpam-4453	29	41	denoted	denote	VERB
ejpam-4453	29	42	by	by	ADP
ejpam-4453	29	43	degg(u	degg(u	PROPN
ejpam-4453	29	44	)	)	PUNCT
ejpam-4453	29	45	.	.	PUNCT
ejpam-4453	30	1	a	a	DET
ejpam-4453	30	2	vertex	vertex	NOUN
ejpam-4453	30	3	in	in	ADP
ejpam-4453	30	4	a	a	DET
ejpam-4453	30	5	graph	graph	NOUN
ejpam-4453	30	6	with	with	ADP
ejpam-4453	30	7	degree	degree	NOUN
ejpam-4453	30	8	1	1	NUM
ejpam-4453	30	9	is	be	AUX
ejpam-4453	30	10	called	call	VERB
ejpam-4453	30	11	a	a	DET
ejpam-4453	30	12	pendant	pendant	ADJ
ejpam-4453	30	13	vertex	vertex	NOUN
ejpam-4453	30	14	or	or	CCONJ
ejpam-4453	30	15	end	end	NOUN
ejpam-4453	30	16	-	-	PUNCT
ejpam-4453	30	17	vertex	vertex	NOUN
ejpam-4453	30	18	denoted	denote	VERB
ejpam-4453	30	19	by	by	ADP
ejpam-4453	30	20	end(g	end(g	PROPN
ejpam-4453	30	21	)	)	PUNCT
ejpam-4453	30	22	while	while	SCONJ
ejpam-4453	30	23	an	an	DET
ejpam-4453	30	24	edge	edge	NOUN
ejpam-4453	30	25	of	of	ADP
ejpam-4453	30	26	the	the	DET
ejpam-4453	30	27	graph	graph	NOUN
ejpam-4453	30	28	incident	incident	NOUN
ejpam-4453	30	29	to	to	ADP
ejpam-4453	30	30	a	a	DET
ejpam-4453	30	31	pendant	pendant	ADJ
ejpam-4453	30	32	vertex	vertex	NOUN
ejpam-4453	30	33	is	be	AUX
ejpam-4453	30	34	called	call	VERB
ejpam-4453	30	35	pendant	pendant	ADJ
ejpam-4453	30	36	edge	edge	NOUN
ejpam-4453	30	37	.	.	PUNCT
ejpam-4453	31	1	if	if	SCONJ
ejpam-4453	31	2	the	the	DET
ejpam-4453	31	3	vertices	vertex	NOUN
ejpam-4453	31	4	of	of	ADP
ejpam-4453	31	5	a	a	DET
ejpam-4453	31	6	graph	graph	NOUN
ejpam-4453	31	7	g	g	NOUN
ejpam-4453	31	8	of	of	ADP
ejpam-4453	31	9	order	order	NOUN
ejpam-4453	31	10	n	n	PRON
ejpam-4453	31	11	can	can	AUX
ejpam-4453	31	12	be	be	AUX
ejpam-4453	31	13	labeled	label	VERB
ejpam-4453	31	14	x1	x1	PROPN
ejpam-4453	31	15	,	,	PUNCT
ejpam-4453	31	16	x2	x2	PROPN
ejpam-4453	31	17	,	,	PUNCT
ejpam-4453	31	18	...	...	PUNCT
ejpam-4453	31	19	,	,	PUNCT
ejpam-4453	31	20	xn	xn	PROPN
ejpam-4453	31	21	so	so	SCONJ
ejpam-4453	31	22	that	that	SCONJ
ejpam-4453	31	23	the	the	DET
ejpam-4453	31	24	edges	edge	NOUN
ejpam-4453	31	25	are	be	AUX
ejpam-4453	31	26	[	[	X
ejpam-4453	31	27	x1	x1	PROPN
ejpam-4453	31	28	,	,	PUNCT
ejpam-4453	31	29	x2	x2	PROPN
ejpam-4453	31	30	]	]	PUNCT
ejpam-4453	31	31	,	,	PUNCT
ejpam-4453	32	1	[	[	X
ejpam-4453	32	2	x2	x2	X
ejpam-4453	32	3	,	,	PUNCT
ejpam-4453	32	4	x3	x3	ADJ
ejpam-4453	32	5	]	]	PUNCT
ejpam-4453	32	6	,	,	PUNCT
ejpam-4453	32	7	...	...	PUNCT
ejpam-4453	32	8	,	,	PUNCT
ejpam-4453	32	9	[	[	X
ejpam-4453	32	10	xn−1	xn−1	PROPN
ejpam-4453	32	11	,	,	PUNCT
ejpam-4453	32	12	xn	xn	PROPN
ejpam-4453	32	13	]	]	X
ejpam-4453	32	14	,	,	PUNCT
ejpam-4453	32	15	then	then	ADV
ejpam-4453	32	16	g	g	PROPN
ejpam-4453	32	17	is	be	AUX
ejpam-4453	32	18	called	call	VERB
ejpam-4453	32	19	a	a	DET
ejpam-4453	32	20	path	path	NOUN
ejpam-4453	32	21	of	of	ADP
ejpam-4453	32	22	order	order	NOUN
ejpam-4453	32	23	n	n	CCONJ
ejpam-4453	32	24	,	,	PUNCT
ejpam-4453	32	25	denoted	denote	VERB
ejpam-4453	32	26	by	by	ADP
ejpam-4453	32	27	pn	pn	PROPN
ejpam-4453	32	28	.	.	PUNCT
ejpam-4453	32	29	a	a	DET
ejpam-4453	32	30	path	path	NOUN
ejpam-4453	32	31	in	in	ADP
ejpam-4453	32	32	g	g	PROPN
ejpam-4453	32	33	that	that	PRON
ejpam-4453	32	34	contains	contain	VERB
ejpam-4453	32	35	every	every	DET
ejpam-4453	32	36	vertex	vertex	NOUN
ejpam-4453	32	37	of	of	ADP
ejpam-4453	32	38	g	g	PROPN
ejpam-4453	32	39	is	be	AUX
ejpam-4453	32	40	called	call	VERB
ejpam-4453	32	41	a	a	DET
ejpam-4453	32	42	hamiltonian	hamiltonian	ADJ
ejpam-4453	32	43	path	path	NOUN
ejpam-4453	32	44	of	of	ADP
ejpam-4453	32	45	g	g	NOUN
ejpam-4453	32	46	,	,	PUNCT
ejpam-4453	32	47	while	while	SCONJ
ejpam-4453	32	48	a	a	DET
ejpam-4453	32	49	cycle	cycle	NOUN
ejpam-4453	32	50	in	in	ADP
ejpam-4453	32	51	g	g	PROPN
ejpam-4453	32	52	that	that	PRON
ejpam-4453	32	53	contains	contain	VERB
ejpam-4453	32	54	every	every	DET
ejpam-4453	32	55	vertex	vertex	NOUN
ejpam-4453	32	56	of	of	ADP
ejpam-4453	32	57	g	g	PROPN
ejpam-4453	32	58	is	be	AUX
ejpam-4453	32	59	called	call	VERB
ejpam-4453	32	60	a	a	DET
ejpam-4453	32	61	hamiltonian	hamiltonian	ADJ
ejpam-4453	32	62	cycle	cycle	NOUN
ejpam-4453	32	63	of	of	ADP
ejpam-4453	32	64	g.	g.	PROPN
ejpam-4453	32	65	a	a	DET
ejpam-4453	32	66	graph	graph	NOUN
ejpam-4453	32	67	that	that	PRON
ejpam-4453	32	68	contains	contain	VERB
ejpam-4453	32	69	a	a	DET
ejpam-4453	32	70	hamiltonian	hamiltonian	ADJ
ejpam-4453	32	71	cycle	cycle	NOUN
ejpam-4453	32	72	is	be	AUX
ejpam-4453	32	73	itself	itself	PRON
ejpam-4453	32	74	called	call	VERB
ejpam-4453	32	75	hamiltonian	hamiltonian	ADJ
ejpam-4453	32	76	.	.	PUNCT
ejpam-4453	33	1	a	a	DET
ejpam-4453	33	2	graph	graph	NOUN
ejpam-4453	33	3	h	h	NOUN
ejpam-4453	33	4	is	be	AUX
ejpam-4453	33	5	a	a	DET
ejpam-4453	33	6	subgraph	subgraph	NOUN
ejpam-4453	33	7	of	of	ADP
ejpam-4453	33	8	a	a	DET
ejpam-4453	33	9	graph	graph	NOUN
ejpam-4453	33	10	g	g	NOUN
ejpam-4453	33	11	if	if	SCONJ
ejpam-4453	33	12	v	v	X
ejpam-4453	33	13	(	(	PUNCT
ejpam-4453	33	14	h	h	NOUN
ejpam-4453	33	15	)	)	PUNCT
ejpam-4453	33	16	⊆	⊆	NUM
ejpam-4453	33	17	v	v	NOUN
ejpam-4453	33	18	(	(	PUNCT
ejpam-4453	33	19	g	g	NOUN
ejpam-4453	33	20	)	)	PUNCT
ejpam-4453	33	21	and	and	CCONJ
ejpam-4453	33	22	e(h	e(h	NOUN
ejpam-4453	33	23	)	)	PUNCT
ejpam-4453	33	24	⊆	⊆	NUM
ejpam-4453	33	25	e(g	e(g	PROPN
ejpam-4453	33	26	)	)	PUNCT
ejpam-4453	33	27	,	,	PUNCT
ejpam-4453	33	28	in	in	ADP
ejpam-4453	33	29	which	which	DET
ejpam-4453	33	30	case	case	NOUN
ejpam-4453	33	31	we	we	PRON
ejpam-4453	33	32	write	write	VERB
ejpam-4453	33	33	h	h	NOUN
ejpam-4453	33	34	⊆	⊆	NUM
ejpam-4453	33	35	g.	g.	NOUN
ejpam-4453	33	36	if	if	SCONJ
ejpam-4453	33	37	h	h	NOUN
ejpam-4453	33	38	is	be	AUX
ejpam-4453	33	39	a	a	DET
ejpam-4453	33	40	subgraph	subgraph	NOUN
ejpam-4453	33	41	of	of	ADP
ejpam-4453	33	42	g	g	NOUN
ejpam-4453	33	43	,	,	PUNCT
ejpam-4453	33	44	then	then	ADV
ejpam-4453	33	45	g	g	PROPN
ejpam-4453	33	46	is	be	AUX
ejpam-4453	33	47	a	a	DET
ejpam-4453	33	48	supergraph	supergraph	NOUN
ejpam-4453	33	49	of	of	ADP
ejpam-4453	33	50	h.	h.	PROPN
ejpam-4453	33	51	if	if	SCONJ
ejpam-4453	33	52	v	v	X
ejpam-4453	33	53	(	(	PUNCT
ejpam-4453	33	54	h	h	NOUN
ejpam-4453	33	55	)	)	PUNCT
ejpam-4453	33	56	=	=	NOUN
ejpam-4453	33	57	v	v	X
ejpam-4453	33	58	(	(	PUNCT
ejpam-4453	33	59	g	g	NOUN
ejpam-4453	33	60	)	)	PUNCT
ejpam-4453	33	61	,	,	PUNCT
ejpam-4453	33	62	then	then	ADV
ejpam-4453	33	63	h	h	PROPN
ejpam-4453	33	64	is	be	AUX
ejpam-4453	33	65	a	a	DET
ejpam-4453	33	66	spanning	span	VERB
ejpam-4453	33	67	subgraph	subgraph	NOUN
ejpam-4453	33	68	of	of	ADP
ejpam-4453	33	69	g.	g.	PROPN
ejpam-4453	33	70	the	the	DET
ejpam-4453	33	71	union	union	PROPN
ejpam-4453	33	72	g	g	PROPN
ejpam-4453	33	73	=	=	PROPN
ejpam-4453	33	74	g1	g1	PROPN
ejpam-4453	33	75	⊕g2	⊕g2	PROPN
ejpam-4453	33	76	of	of	ADP
ejpam-4453	33	77	graphs	graph	NOUN
ejpam-4453	33	78	g1	g1	PROPN
ejpam-4453	33	79	and	and	CCONJ
ejpam-4453	33	80	g2	g2	PROPN
ejpam-4453	33	81	has	have	VERB
ejpam-4453	33	82	vertex	vertex	NOUN
ejpam-4453	33	83	set	set	VERB
ejpam-4453	33	84	v	v	NOUN
ejpam-4453	33	85	(	(	PUNCT
ejpam-4453	33	86	g	g	NOUN
ejpam-4453	33	87	)	)	PUNCT
ejpam-4453	33	88	=	=	NOUN
ejpam-4453	33	89	v	v	X
ejpam-4453	33	90	(	(	PUNCT
ejpam-4453	33	91	g1	g1	PROPN
ejpam-4453	33	92	)	)	PUNCT
ejpam-4453	33	93	∪	∪	NOUN
ejpam-4453	33	94	v	v	PROPN
ejpam-4453	33	95	(	(	PUNCT
ejpam-4453	33	96	g2	g2	PROPN
ejpam-4453	33	97	)	)	PUNCT
ejpam-4453	33	98	and	and	CCONJ
ejpam-4453	33	99	edge	edge	NOUN
ejpam-4453	33	100	set	set	VERB
ejpam-4453	33	101	e(g	e(g	NOUN
ejpam-4453	33	102	)	)	PUNCT
ejpam-4453	34	1	=	=	SYM
ejpam-4453	34	2	e(g1	e(g1	X
ejpam-4453	34	3	)	)	PUNCT
ejpam-4453	34	4	∪	∪	ADP
ejpam-4453	34	5	e(g2	e(g2	ADV
ejpam-4453	34	6	)	)	PUNCT
ejpam-4453	34	7	.	.	PUNCT
ejpam-4453	35	1	a	a	DET
ejpam-4453	35	2	graph	graph	NOUN
ejpam-4453	35	3	containing	contain	VERB
ejpam-4453	35	4	exactly	exactly	ADV
ejpam-4453	35	5	one	one	NUM
ejpam-4453	35	6	cycle	cycle	NOUN
ejpam-4453	35	7	as	as	SCONJ
ejpam-4453	35	8	a	a	DET
ejpam-4453	35	9	subgraph	subgraph	NOUN
ejpam-4453	35	10	is	be	AUX
ejpam-4453	35	11	called	call	VERB
ejpam-4453	35	12	unicyclic	unicyclic	ADJ
ejpam-4453	35	13	graph	graph	NOUN
ejpam-4453	35	14	.	.	PUNCT
ejpam-4453	36	1	a	a	DET
ejpam-4453	36	2	unicyclic	unicyclic	ADJ
ejpam-4453	36	3	graph	graph	NOUN
ejpam-4453	36	4	g	g	NOUN
ejpam-4453	36	5	,	,	PUNCT
ejpam-4453	36	6	other	other	ADJ
ejpam-4453	36	7	than	than	ADP
ejpam-4453	36	8	a	a	DET
ejpam-4453	36	9	cycle	cycle	NOUN
ejpam-4453	36	10	,	,	PUNCT
ejpam-4453	36	11	is	be	AUX
ejpam-4453	36	12	called	call	VERB
ejpam-4453	36	13	a	a	DET
ejpam-4453	36	14	hairy	hairy	ADJ
ejpam-4453	36	15	cycle	cycle	NOUN
ejpam-4453	36	16	if	if	SCONJ
ejpam-4453	36	17	the	the	DET
ejpam-4453	36	18	deletion	deletion	NOUN
ejpam-4453	36	19	of	of	ADP
ejpam-4453	36	20	any	any	DET
ejpam-4453	36	21	edge	edge	NOUN
ejpam-4453	36	22	e	e	NOUN
ejpam-4453	36	23	in	in	ADP
ejpam-4453	36	24	the	the	DET
ejpam-4453	36	25	cycle	cycle	NOUN
ejpam-4453	36	26	of	of	ADP
ejpam-4453	36	27	g	g	PROPN
ejpam-4453	36	28	results	result	NOUN
ejpam-4453	36	29	in	in	ADP
ejpam-4453	36	30	a	a	DET
ejpam-4453	36	31	caterpillar	caterpillar	NOUN
ejpam-4453	36	32	[	[	X
ejpam-4453	36	33	1	1	NUM
ejpam-4453	36	34	]	]	PUNCT
ejpam-4453	36	35	.	.	PUNCT
ejpam-4453	37	1	in	in	ADP
ejpam-4453	37	2	other	other	ADJ
ejpam-4453	37	3	words	word	NOUN
ejpam-4453	37	4	,	,	PUNCT
ejpam-4453	37	5	all	all	DET
ejpam-4453	37	6	the	the	DET
ejpam-4453	37	7	graphs	graph	NOUN
ejpam-4453	37	8	that	that	PRON
ejpam-4453	37	9	are	be	AUX
ejpam-4453	37	10	constructed	construct	VERB
ejpam-4453	37	11	by	by	ADP
ejpam-4453	37	12	attaching	attach	VERB
ejpam-4453	37	13	pendants	pendant	NOUN
ejpam-4453	37	14	to	to	ADP
ejpam-4453	37	15	the	the	DET
ejpam-4453	37	16	vertices	vertex	NOUN
ejpam-4453	37	17	of	of	ADP
ejpam-4453	37	18	a	a	DET
ejpam-4453	37	19	cycle	cycle	NOUN
ejpam-4453	37	20	is	be	AUX
ejpam-4453	37	21	called	call	VERB
ejpam-4453	37	22	hairy	hairy	ADJ
ejpam-4453	37	23	cycles	cycle	NOUN
ejpam-4453	37	24	.	.	PUNCT
ejpam-4453	38	1	the	the	DET
ejpam-4453	38	2	cycle	cycle	NOUN
ejpam-4453	38	3	cn	cn	PROPN
ejpam-4453	38	4	with	with	ADP
ejpam-4453	38	5	m	m	PROPN
ejpam-4453	38	6	pendants	pendant	NOUN
ejpam-4453	38	7	attached	attach	VERB
ejpam-4453	38	8	to	to	ADP
ejpam-4453	38	9	each	each	DET
ejpam-4453	38	10	cycle	cycle	NOUN
ejpam-4453	38	11	vertex	vertex	NOUN
ejpam-4453	38	12	is	be	AUX
ejpam-4453	38	13	called	call	VERB
ejpam-4453	38	14	m	m	ADJ
ejpam-4453	38	15	-	-	ADJ
ejpam-4453	38	16	hairy	hairy	ADJ
ejpam-4453	38	17	n	n	CCONJ
ejpam-4453	38	18	-	-	PUNCT
ejpam-4453	38	19	cycle	cycle	NOUN
ejpam-4453	38	20	for	for	ADP
ejpam-4453	38	21	all	all	DET
ejpam-4453	38	22	m	m	PROPN
ejpam-4453	38	23	,	,	PUNCT
ejpam-4453	38	24	n	n	PROPN
ejpam-4453	38	25	∈	∈	PROPN
ejpam-4453	38	26	n	n	NOUN
ejpam-4453	38	27	with	with	ADP
ejpam-4453	38	28	n	n	PRON
ejpam-4453	38	29	≥	≥	NUM
ejpam-4453	38	30	3	3	NUM
ejpam-4453	38	31	,	,	PUNCT
ejpam-4453	38	32	and	and	CCONJ
ejpam-4453	38	33	denoted	denote	VERB
ejpam-4453	38	34	by	by	ADP
ejpam-4453	38	35	cn	cn	PROPN
ejpam-4453	38	36	⊙	⊙	PROPN
ejpam-4453	38	37	sm	sm	PROPN
ejpam-4453	38	38	.	.	PUNCT
ejpam-4453	39	1	in	in	ADP
ejpam-4453	39	2	the	the	DET
ejpam-4453	39	3	definition	definition	NOUN
ejpam-4453	39	4	,	,	PUNCT
ejpam-4453	39	5	the	the	DET
ejpam-4453	39	6	symbol	symbol	NOUN
ejpam-4453	39	7	⊙	⊙	PROPN
ejpam-4453	39	8	indicates	indicate	VERB
ejpam-4453	39	9	that	that	SCONJ
ejpam-4453	39	10	we	we	PRON
ejpam-4453	39	11	attach	attach	VERB
ejpam-4453	39	12	a	a	DET
ejpam-4453	39	13	copy	copy	NOUN
ejpam-4453	39	14	of	of	ADP
ejpam-4453	39	15	the	the	DET
ejpam-4453	39	16	sm	sm	NOUN
ejpam-4453	39	17	at	at	ADP
ejpam-4453	39	18	its	its	PRON
ejpam-4453	39	19	vertex	vertex	NOUN
ejpam-4453	39	20	of	of	ADP
ejpam-4453	39	21	degree	degree	NOUN
ejpam-4453	39	22	m	m	VERB
ejpam-4453	39	23	to	to	ADP
ejpam-4453	39	24	each	each	DET
ejpam-4453	39	25	cycle	cycle	NOUN
ejpam-4453	39	26	vertex	vertex	NOUN
ejpam-4453	39	27	of	of	ADP
ejpam-4453	39	28	cn	cn	PROPN
ejpam-4453	39	29	.	.	PUNCT
ejpam-4453	40	1	the	the	DET
ejpam-4453	40	2	new	new	ADJ
ejpam-4453	40	3	graph	graph	NOUN
ejpam-4453	40	4	will	will	AUX
ejpam-4453	40	5	have	have	VERB
ejpam-4453	40	6	m	m	NOUN
ejpam-4453	40	7	pendant	pendant	ADJ
ejpam-4453	40	8	at	at	ADP
ejpam-4453	40	9	each	each	DET
ejpam-4453	40	10	cycle	cycle	NOUN
ejpam-4453	40	11	vertex	vertex	NOUN
ejpam-4453	40	12	.	.	PUNCT
ejpam-4453	41	1	theorem	theorem	NOUN
ejpam-4453	41	2	1	1	NUM
ejpam-4453	41	3	.	.	PUNCT
ejpam-4453	42	1	[	[	X
ejpam-4453	42	2	5	5	NUM
ejpam-4453	42	3	]	]	PUNCT
ejpam-4453	42	4	a	a	DET
ejpam-4453	42	5	3	3	NUM
ejpam-4453	42	6	-	-	PUNCT
ejpam-4453	42	7	regular	regular	ADJ
ejpam-4453	42	8	graph	graph	NOUN
ejpam-4453	42	9	must	must	AUX
ejpam-4453	42	10	have	have	VERB
ejpam-4453	42	11	an	an	DET
ejpam-4453	42	12	even	even	ADJ
ejpam-4453	42	13	number	number	NOUN
ejpam-4453	42	14	of	of	ADP
ejpam-4453	42	15	vertices	vertex	NOUN
ejpam-4453	42	16	.	.	PUNCT
ejpam-4453	43	1	the	the	DET
ejpam-4453	43	2	next	next	ADJ
ejpam-4453	43	3	theorem	theorem	NOUN
ejpam-4453	43	4	gives	give	VERB
ejpam-4453	43	5	an	an	DET
ejpam-4453	43	6	upper	upper	ADJ
ejpam-4453	43	7	bound	bind	VERB
ejpam-4453	43	8	for	for	ADP
ejpam-4453	43	9	the	the	DET
ejpam-4453	43	10	chromatic	chromatic	ADJ
ejpam-4453	43	11	number	number	NOUN
ejpam-4453	43	12	of	of	ADP
ejpam-4453	43	13	any	any	DET
ejpam-4453	43	14	connected	connected	ADJ
ejpam-4453	43	15	graph	graph	NOUN
ejpam-4453	43	16	.	.	PUNCT
ejpam-4453	44	1	theorem	theorem	NOUN
ejpam-4453	44	2	2	2	NUM
ejpam-4453	44	3	.	.	PUNCT
ejpam-4453	45	1	[	[	X
ejpam-4453	45	2	5	5	NUM
ejpam-4453	45	3	]	]	PUNCT
ejpam-4453	45	4	for	for	ADP
ejpam-4453	45	5	every	every	DET
ejpam-4453	45	6	graph	graph	NOUN
ejpam-4453	45	7	g	g	NOUN
ejpam-4453	45	8	,	,	PUNCT
ejpam-4453	45	9	χ(g	χ(g	PROPN
ejpam-4453	45	10	)	)	PUNCT
ejpam-4453	45	11	≤	≤	NUM
ejpam-4453	45	12	1	1	NUM
ejpam-4453	45	13	+	+	CCONJ
ejpam-4453	45	14	∆(g	∆(g	NOUN
ejpam-4453	45	15	)	)	PUNCT
ejpam-4453	45	16	.	.	PUNCT
ejpam-4453	46	1	corollary	corollary	ADJ
ejpam-4453	46	2	1	1	NUM
ejpam-4453	46	3	.	.	PUNCT
ejpam-4453	47	1	[	[	X
ejpam-4453	47	2	5	5	NUM
ejpam-4453	47	3	]	]	PUNCT
ejpam-4453	47	4	for	for	ADP
ejpam-4453	47	5	every	every	DET
ejpam-4453	47	6	graph	graph	NOUN
ejpam-4453	47	7	g	g	NOUN
ejpam-4453	47	8	,	,	PUNCT
ejpam-4453	47	9	χ(g	χ(g	PROPN
ejpam-4453	47	10	)	)	PUNCT
ejpam-4453	47	11	≥	≥	NOUN
ejpam-4453	47	12	ω(g	ω(g	NOUN
ejpam-4453	47	13	)	)	PUNCT
ejpam-4453	47	14	.	.	PUNCT
ejpam-4453	48	1	brooks	brooks	PROPN
ejpam-4453	48	2	’	'	PUNCT
ejpam-4453	48	3	suggests	suggest	VERB
ejpam-4453	48	4	that	that	SCONJ
ejpam-4453	48	5	theorem	theorem	VERB
ejpam-4453	48	6	2	2	NUM
ejpam-4453	48	7	occurs	occur	VERB
ejpam-4453	48	8	only	only	ADV
ejpam-4453	48	9	in	in	ADP
ejpam-4453	48	10	very	very	ADV
ejpam-4453	48	11	special	special	ADJ
ejpam-4453	48	12	cases	case	NOUN
ejpam-4453	48	13	such	such	ADJ
ejpam-4453	48	14	as	as	ADP
ejpam-4453	48	15	an	an	DET
ejpam-4453	48	16	odd	odd	ADJ
ejpam-4453	48	17	cycle	cycle	NOUN
ejpam-4453	48	18	graph	graph	NOUN
ejpam-4453	48	19	,	,	PUNCT
ejpam-4453	48	20	that	that	ADV
ejpam-4453	48	21	is	is	ADV
ejpam-4453	48	22	,	,	PUNCT
ejpam-4453	48	23	a	a	DET
ejpam-4453	48	24	cycle	cycle	NOUN
ejpam-4453	48	25	of	of	ADP
ejpam-4453	48	26	odd	odd	ADJ
ejpam-4453	48	27	order	order	NOUN
ejpam-4453	48	28	and	and	CCONJ
ejpam-4453	48	29	a	a	DET
ejpam-4453	48	30	complete	complete	ADJ
ejpam-4453	48	31	graph	graph	NOUN
ejpam-4453	48	32	.	.	PUNCT
ejpam-4453	49	1	the	the	DET
ejpam-4453	49	2	next	next	ADJ
ejpam-4453	49	3	theorem	theorem	NOUN
ejpam-4453	49	4	will	will	AUX
ejpam-4453	49	5	discuss	discuss	VERB
ejpam-4453	49	6	about	about	ADP
ejpam-4453	49	7	restriction	restriction	NOUN
ejpam-4453	49	8	of	of	ADP
ejpam-4453	49	9	particular	particular	ADJ
ejpam-4453	49	10	types	type	NOUN
ejpam-4453	49	11	of	of	ADP
ejpam-4453	49	12	graphs	graph	NOUN
ejpam-4453	49	13	.	.	PUNCT
ejpam-4453	50	1	theorem	theorem	VERB
ejpam-4453	50	2	3	3	NUM
ejpam-4453	50	3	.	.	PUNCT
ejpam-4453	51	1	[	[	X
ejpam-4453	51	2	3	3	NUM
ejpam-4453	51	3	]	]	X
ejpam-4453	51	4	(	(	PUNCT
ejpam-4453	51	5	brooks	brooks	PROPN
ejpam-4453	51	6	’	'	PUNCT
ejpam-4453	51	7	theorem	theorem	NOUN
ejpam-4453	51	8	)	)	PUNCT
ejpam-4453	51	9	for	for	ADP
ejpam-4453	51	10	every	every	DET
ejpam-4453	51	11	connected	connected	ADJ
ejpam-4453	51	12	graph	graph	NOUN
ejpam-4453	51	13	g	g	NOUN
ejpam-4453	51	14	that	that	PRON
ejpam-4453	51	15	is	be	AUX
ejpam-4453	51	16	not	not	PART
ejpam-4453	51	17	an	an	DET
ejpam-4453	51	18	odd	odd	ADJ
ejpam-4453	51	19	cycle	cycle	NOUN
ejpam-4453	51	20	or	or	CCONJ
ejpam-4453	51	21	a	a	DET
ejpam-4453	51	22	complete	complete	ADJ
ejpam-4453	51	23	graph	graph	NOUN
ejpam-4453	51	24	,	,	PUNCT
ejpam-4453	51	25	χ(g	χ(g	PROPN
ejpam-4453	51	26	)	)	PUNCT
ejpam-4453	51	27	≤	≤	NUM
ejpam-4453	51	28	∆(g	∆(g	NOUN
ejpam-4453	51	29	)	)	PUNCT
ejpam-4453	51	30	a	a	DET
ejpam-4453	51	31	rather	rather	ADV
ejpam-4453	51	32	obvious	obvious	ADJ
ejpam-4453	51	33	,	,	PUNCT
ejpam-4453	51	34	but	but	CCONJ
ejpam-4453	51	35	often	often	ADV
ejpam-4453	51	36	useful	useful	ADJ
ejpam-4453	51	37	,	,	PUNCT
ejpam-4453	51	38	lower	lower	ADV
ejpam-4453	51	39	bound	bind	VERB
ejpam-4453	51	40	for	for	ADP
ejpam-4453	51	41	the	the	DET
ejpam-4453	51	42	chromatic	chromatic	ADJ
ejpam-4453	51	43	number	number	NOUN
ejpam-4453	51	44	of	of	ADP
ejpam-4453	51	45	a	a	DET
ejpam-4453	51	46	graph	graph	NOUN
ejpam-4453	51	47	involves	involve	VERB
ejpam-4453	51	48	the	the	DET
ejpam-4453	51	49	chromatic	chromatic	ADJ
ejpam-4453	51	50	numbers	number	NOUN
ejpam-4453	51	51	of	of	ADP
ejpam-4453	51	52	its	its	PRON
ejpam-4453	51	53	subgraphs	subgraph	NOUN
ejpam-4453	51	54	.	.	PUNCT
ejpam-4453	52	1	a.r	a.r	PROPN
ejpam-4453	52	2	nieva	nieva	PROPN
ejpam-4453	52	3	and	and	CCONJ
ejpam-4453	52	4	k.nocum	k.nocum	PROPN
ejpam-4453	52	5	/	/	SYM
ejpam-4453	52	6	eur	eur	PROPN
ejpam-4453	52	7	.	.	PUNCT
ejpam-4453	53	1	j.	j.	PROPN
ejpam-4453	53	2	pure	pure	PROPN
ejpam-4453	53	3	appl	appl	PROPN
ejpam-4453	53	4	.	.	PROPN
ejpam-4453	53	5	math	math	PROPN
ejpam-4453	53	6	,	,	PUNCT
ejpam-4453	53	7	15	15	NUM
ejpam-4453	53	8	(	(	PUNCT
ejpam-4453	53	9	4	4	NUM
ejpam-4453	53	10	)	)	PUNCT
ejpam-4453	53	11	(	(	PUNCT
ejpam-4453	53	12	2022	2022	NUM
ejpam-4453	53	13	)	)	PUNCT
ejpam-4453	53	14	,	,	PUNCT
ejpam-4453	53	15	1536	1536	NUM
ejpam-4453	53	16	-	-	SYM
ejpam-4453	53	17	1548	1548	NUM
ejpam-4453	53	18	1538	1538	NUM
ejpam-4453	53	19	theorem	theorem	NOUN
ejpam-4453	53	20	4	4	NUM
ejpam-4453	53	21	.	.	PUNCT
ejpam-4453	54	1	[	[	X
ejpam-4453	54	2	5	5	X
ejpam-4453	54	3	]	]	PUNCT
ejpam-4453	54	4	if	if	SCONJ
ejpam-4453	54	5	h	h	NOUN
ejpam-4453	54	6	is	be	AUX
ejpam-4453	54	7	a	a	DET
ejpam-4453	54	8	subgraph	subgraph	NOUN
ejpam-4453	54	9	of	of	ADP
ejpam-4453	54	10	g	g	PROPN
ejpam-4453	54	11	,	,	PUNCT
ejpam-4453	54	12	then	then	ADV
ejpam-4453	54	13	χ(h	χ(h	PROPN
ejpam-4453	54	14	)	)	PUNCT
ejpam-4453	54	15	≤	≤	NUM
ejpam-4453	54	16	χ(g	χ(g	PROPN
ejpam-4453	54	17	)	)	PUNCT
ejpam-4453	54	18	.	.	PUNCT
ejpam-4453	55	1	the	the	DET
ejpam-4453	55	2	following	follow	VERB
ejpam-4453	55	3	theorem	theorem	NOUN
ejpam-4453	55	4	of	of	ADP
ejpam-4453	55	5	zeoram	zeoram	PROPN
ejpam-4453	55	6	and	and	CCONJ
ejpam-4453	55	7	yaqubi	yaqubi	NOUN
ejpam-4453	55	8	[	[	X
ejpam-4453	55	9	7	7	NUM
ejpam-4453	55	10	]	]	PUNCT
ejpam-4453	55	11	gives	give	VERB
ejpam-4453	55	12	an	an	DET
ejpam-4453	55	13	important	important	ADJ
ejpam-4453	55	14	characteristic	characteristic	NOUN
ejpam-4453	55	15	of	of	ADP
ejpam-4453	55	16	a	a	DET
ejpam-4453	55	17	tree	tree	NOUN
ejpam-4453	55	18	with	with	ADP
ejpam-4453	55	19	maximum	maximum	ADJ
ejpam-4453	55	20	degree	degree	NOUN
ejpam-4453	55	21	equal	equal	ADJ
ejpam-4453	55	22	to	to	ADP
ejpam-4453	55	23	3	3	NUM
ejpam-4453	55	24	.	.	PUNCT
ejpam-4453	56	1	theorem	theorem	NOUN
ejpam-4453	56	2	5	5	NUM
ejpam-4453	56	3	.	.	PUNCT
ejpam-4453	57	1	[	[	X
ejpam-4453	57	2	7	7	X
ejpam-4453	57	3	]	]	PUNCT
ejpam-4453	57	4	let	let	VERB
ejpam-4453	57	5	t	t	NOUN
ejpam-4453	57	6	be	be	AUX
ejpam-4453	57	7	a	a	DET
ejpam-4453	57	8	tree	tree	NOUN
ejpam-4453	57	9	with	with	ADP
ejpam-4453	57	10	n	n	ADP
ejpam-4453	57	11	vertices	vertice	VERB
ejpam-4453	57	12	such	such	ADJ
ejpam-4453	57	13	that	that	DET
ejpam-4453	57	14	∆(t	∆(t	NOUN
ejpam-4453	57	15	)	)	PUNCT
ejpam-4453	57	16	≤	≤	NOUN
ejpam-4453	57	17	3	3	NUM
ejpam-4453	57	18	.	.	PUNCT
ejpam-4453	58	1	if	if	SCONJ
ejpam-4453	58	2	|leaf(t	|leaf(t	PROPN
ejpam-4453	58	3	)	)	PUNCT
ejpam-4453	58	4	|	|	ADV
ejpam-4453	58	5	=	=	SYM
ejpam-4453	58	6	k	k	PROPN
ejpam-4453	58	7	and	and	CCONJ
ejpam-4453	58	8	p	p	NOUN
ejpam-4453	58	9	be	be	AUX
ejpam-4453	58	10	the	the	DET
ejpam-4453	58	11	number	number	NOUN
ejpam-4453	58	12	of	of	ADP
ejpam-4453	58	13	vertices	vertex	NOUN
ejpam-4453	58	14	of	of	ADP
ejpam-4453	58	15	degree	degree	NOUN
ejpam-4453	58	16	3	3	NUM
ejpam-4453	58	17	in	in	ADP
ejpam-4453	58	18	t	t	PROPN
ejpam-4453	58	19	,	,	PUNCT
ejpam-4453	58	20	then	then	ADV
ejpam-4453	58	21	k	k	PROPN
ejpam-4453	58	22	=	=	X
ejpam-4453	58	23	p+	p+	ADJ
ejpam-4453	58	24	2	2	NUM
ejpam-4453	58	25	.	.	PUNCT
ejpam-4453	58	26	theorem	theorem	VERB
ejpam-4453	58	27	6	6	NUM
ejpam-4453	58	28	.	.	PUNCT
ejpam-4453	59	1	[	[	X
ejpam-4453	59	2	7	7	X
ejpam-4453	59	3	]	]	PUNCT
ejpam-4453	59	4	let	let	VERB
ejpam-4453	59	5	g	g	PRON
ejpam-4453	59	6	be	be	AUX
ejpam-4453	59	7	a	a	DET
ejpam-4453	59	8	graph	graph	NOUN
ejpam-4453	59	9	and	and	CCONJ
ejpam-4453	59	10	k	k	PROPN
ejpam-4453	59	11	≤	≤	ADJ
ejpam-4453	59	12	3	3	NUM
ejpam-4453	59	13	be	be	AUX
ejpam-4453	59	14	the	the	DET
ejpam-4453	59	15	smallest	small	ADJ
ejpam-4453	59	16	integer	integer	NOUN
ejpam-4453	59	17	such	such	ADJ
ejpam-4453	59	18	that	that	SCONJ
ejpam-4453	59	19	g	g	PROPN
ejpam-4453	59	20	has	have	VERB
ejpam-4453	59	21	a	a	DET
ejpam-4453	59	22	spanning	span	VERB
ejpam-4453	59	23	tree	tree	NOUN
ejpam-4453	59	24	t	t	NOUN
ejpam-4453	59	25	with	with	ADP
ejpam-4453	59	26	k	k	PROPN
ejpam-4453	59	27	leaves	leave	NOUN
ejpam-4453	59	28	.	.	PUNCT
ejpam-4453	60	1	then	then	ADV
ejpam-4453	60	2	,	,	PUNCT
ejpam-4453	60	3	no	no	DET
ejpam-4453	60	4	two	two	NUM
ejpam-4453	60	5	leaves	leave	NOUN
ejpam-4453	60	6	of	of	ADP
ejpam-4453	60	7	t	t	PROPN
ejpam-4453	60	8	are	be	AUX
ejpam-4453	60	9	adjacent	adjacent	ADJ
ejpam-4453	60	10	in	in	ADP
ejpam-4453	60	11	g.	g.	PROPN
ejpam-4453	60	12	the	the	DET
ejpam-4453	60	13	next	next	ADJ
ejpam-4453	60	14	theorem	theorem	NOUN
ejpam-4453	60	15	is	be	AUX
ejpam-4453	60	16	a	a	DET
ejpam-4453	60	17	necessary	necessary	ADJ
ejpam-4453	60	18	condition	condition	NOUN
ejpam-4453	60	19	for	for	ADP
ejpam-4453	60	20	hamiltonian	hamiltonian	ADJ
ejpam-4453	60	21	graphs	graph	NOUN
ejpam-4453	60	22	.	.	PUNCT
ejpam-4453	61	1	recall	recall	VERB
ejpam-4453	61	2	k(g	k(g	PROPN
ejpam-4453	61	3	−	−	PROPN
ejpam-4453	61	4	s	s	NOUN
ejpam-4453	61	5	)	)	PUNCT
ejpam-4453	61	6	which	which	PRON
ejpam-4453	61	7	is	be	AUX
ejpam-4453	61	8	the	the	DET
ejpam-4453	61	9	number	number	NOUN
ejpam-4453	61	10	of	of	ADP
ejpam-4453	61	11	components	component	NOUN
ejpam-4453	61	12	in	in	ADP
ejpam-4453	61	13	g−	g−	PROPN
ejpam-4453	61	14	s.	s.	PROPN
ejpam-4453	61	15	theorem	theorem	VERB
ejpam-4453	61	16	7	7	NUM
ejpam-4453	61	17	.	.	PUNCT
ejpam-4453	62	1	[	[	X
ejpam-4453	62	2	5	5	X
ejpam-4453	62	3	]	]	PUNCT
ejpam-4453	62	4	if	if	SCONJ
ejpam-4453	62	5	g	g	PROPN
ejpam-4453	62	6	is	be	AUX
ejpam-4453	62	7	a	a	DET
ejpam-4453	62	8	hamiltonian	hamiltonian	ADJ
ejpam-4453	62	9	graph	graph	NOUN
ejpam-4453	62	10	,	,	PUNCT
ejpam-4453	62	11	then	then	ADV
ejpam-4453	62	12	k(g	k(g	PROPN
ejpam-4453	62	13	−	−	PROPN
ejpam-4453	62	14	s	s	NOUN
ejpam-4453	62	15	)	)	PUNCT
ejpam-4453	62	16	≤	≤	NUM
ejpam-4453	62	17	|s|	|s|	PROPN
ejpam-4453	62	18	for	for	ADP
ejpam-4453	62	19	every	every	DET
ejpam-4453	62	20	nonempty	nonempty	ADJ
ejpam-4453	62	21	proper	proper	ADJ
ejpam-4453	62	22	subset	subset	NOUN
ejpam-4453	62	23	s	s	PROPN
ejpam-4453	62	24	of	of	ADP
ejpam-4453	62	25	v	v	NOUN
ejpam-4453	62	26	(	(	PUNCT
ejpam-4453	62	27	g	g	NOUN
ejpam-4453	62	28	)	)	PUNCT
ejpam-4453	62	29	.	.	PUNCT
ejpam-4453	63	1	since	since	SCONJ
ejpam-4453	63	2	theorem	theorem	VERB
ejpam-4453	63	3	7	7	NUM
ejpam-4453	63	4	gives	give	VERB
ejpam-4453	63	5	a	a	DET
ejpam-4453	63	6	necessary	necessary	ADJ
ejpam-4453	63	7	condition	condition	NOUN
ejpam-4453	63	8	for	for	ADP
ejpam-4453	63	9	a	a	DET
ejpam-4453	63	10	graph	graph	NOUN
ejpam-4453	63	11	to	to	PART
ejpam-4453	63	12	be	be	AUX
ejpam-4453	63	13	hamiltonian	hamiltonian	ADJ
ejpam-4453	63	14	,	,	PUNCT
ejpam-4453	63	15	that	that	ADV
ejpam-4453	63	16	is	is	ADV
ejpam-4453	63	17	,	,	PUNCT
ejpam-4453	63	18	this	this	DET
ejpam-4453	63	19	theorem	theorem	NOUN
ejpam-4453	63	20	describes	describe	VERB
ejpam-4453	63	21	a	a	DET
ejpam-4453	63	22	property	property	NOUN
ejpam-4453	63	23	possessed	possess	VERB
ejpam-4453	63	24	by	by	ADP
ejpam-4453	63	25	every	every	DET
ejpam-4453	63	26	hamiltonian	hamiltonian	ADJ
ejpam-4453	63	27	graph	graph	NOUN
ejpam-4453	63	28	.	.	PUNCT
ejpam-4453	64	1	this	this	DET
ejpam-4453	64	2	theorem	theorem	NOUN
ejpam-4453	64	3	is	be	AUX
ejpam-4453	64	4	most	most	ADV
ejpam-4453	64	5	useful	useful	ADJ
ejpam-4453	64	6	in	in	ADP
ejpam-4453	64	7	its	its	PRON
ejpam-4453	64	8	contrapositive	contrapositive	ADJ
ejpam-4453	64	9	statement	statement	NOUN
ejpam-4453	64	10	:	:	PUNCT
ejpam-4453	64	11	if	if	SCONJ
ejpam-4453	64	12	there	there	PRON
ejpam-4453	64	13	exist	exist	VERB
ejpam-4453	64	14	a	a	DET
ejpam-4453	64	15	nonempty	nonempty	ADJ
ejpam-4453	64	16	proper	proper	ADJ
ejpam-4453	64	17	subset	subset	NOUN
ejpam-4453	64	18	s	s	NOUN
ejpam-4453	64	19	of	of	ADP
ejpam-4453	64	20	the	the	DET
ejpam-4453	64	21	vertex	vertex	NOUN
ejpam-4453	64	22	set	set	NOUN
ejpam-4453	64	23	of	of	ADP
ejpam-4453	64	24	a	a	DET
ejpam-4453	64	25	graph	graph	NOUN
ejpam-4453	64	26	g	g	ADP
ejpam-4453	64	27	such	such	ADJ
ejpam-4453	64	28	that	that	SCONJ
ejpam-4453	64	29	k(g−	k(g−	PROPN
ejpam-4453	64	30	s	s	PROPN
ejpam-4453	64	31	)	)	PUNCT
ejpam-4453	64	32	>	>	X
ejpam-4453	64	33	|s|	|s|	PROPN
ejpam-4453	64	34	,	,	PUNCT
ejpam-4453	64	35	then	then	ADV
ejpam-4453	64	36	g	g	PROPN
ejpam-4453	64	37	is	be	AUX
ejpam-4453	64	38	not	not	PART
ejpam-4453	64	39	hamiltonian	hamiltonian	ADJ
ejpam-4453	64	40	the	the	DET
ejpam-4453	64	41	next	next	ADJ
ejpam-4453	64	42	theorem	theorem	NOUN
ejpam-4453	64	43	is	be	AUX
ejpam-4453	64	44	analogous	analogous	ADJ
ejpam-4453	64	45	to	to	PART
ejpam-4453	64	46	theorem	theorem	VERB
ejpam-4453	64	47	7	7	NUM
ejpam-4453	64	48	which	which	PRON
ejpam-4453	64	49	is	be	AUX
ejpam-4453	64	50	a	a	DET
ejpam-4453	64	51	necessary	necessary	ADJ
ejpam-4453	64	52	condition	condition	NOUN
ejpam-4453	64	53	for	for	ADP
ejpam-4453	64	54	a	a	DET
ejpam-4453	64	55	graph	graph	NOUN
ejpam-4453	64	56	to	to	PART
ejpam-4453	64	57	contain	contain	VERB
ejpam-4453	64	58	a	a	DET
ejpam-4453	64	59	hamiltonian	hamiltonian	ADJ
ejpam-4453	64	60	path	path	NOUN
ejpam-4453	64	61	.	.	PUNCT
ejpam-4453	65	1	this	this	DET
ejpam-4453	65	2	theorem	theorem	NOUN
ejpam-4453	65	3	describes	describe	VERB
ejpam-4453	65	4	a	a	DET
ejpam-4453	65	5	property	property	NOUN
ejpam-4453	65	6	possessed	possess	VERB
ejpam-4453	65	7	by	by	ADP
ejpam-4453	65	8	every	every	DET
ejpam-4453	65	9	graph	graph	NOUN
ejpam-4453	65	10	that	that	PRON
ejpam-4453	65	11	contains	contain	VERB
ejpam-4453	65	12	a	a	DET
ejpam-4453	65	13	hamiltonian	hamiltonian	ADJ
ejpam-4453	65	14	path	path	NOUN
ejpam-4453	65	15	.	.	PUNCT
ejpam-4453	66	1	it	it	PRON
ejpam-4453	66	2	is	be	AUX
ejpam-4453	66	3	stated	state	VERB
ejpam-4453	66	4	as	as	SCONJ
ejpam-4453	66	5	follows	follow	VERB
ejpam-4453	66	6	.	.	PUNCT
ejpam-4453	67	1	theorem	theorem	ADJ
ejpam-4453	67	2	8	8	NUM
ejpam-4453	67	3	.	.	PUNCT
ejpam-4453	68	1	[	[	X
ejpam-4453	68	2	6	6	NUM
ejpam-4453	68	3	]	]	X
ejpam-4453	68	4	if	if	SCONJ
ejpam-4453	68	5	g	g	PROPN
ejpam-4453	68	6	contains	contain	VERB
ejpam-4453	68	7	a	a	DET
ejpam-4453	68	8	hamiltonian	hamiltonian	ADJ
ejpam-4453	68	9	path	path	NOUN
ejpam-4453	68	10	,	,	PUNCT
ejpam-4453	68	11	then	then	ADV
ejpam-4453	68	12	k(g	k(g	PROPN
ejpam-4453	68	13	−	−	PROPN
ejpam-4453	68	14	s	s	NOUN
ejpam-4453	68	15	)	)	PUNCT
ejpam-4453	68	16	≤	≤	NUM
ejpam-4453	68	17	|s|	|s|	PROPN
ejpam-4453	68	18	+	+	CCONJ
ejpam-4453	68	19	1	1	NUM
ejpam-4453	68	20	for	for	ADP
ejpam-4453	68	21	every	every	DET
ejpam-4453	68	22	nonempty	nonempty	ADJ
ejpam-4453	68	23	proper	proper	ADJ
ejpam-4453	68	24	subset	subset	NOUN
ejpam-4453	68	25	s	s	PROPN
ejpam-4453	68	26	of	of	ADP
ejpam-4453	68	27	v	v	NOUN
ejpam-4453	68	28	(	(	PUNCT
ejpam-4453	68	29	g	g	NOUN
ejpam-4453	68	30	)	)	PUNCT
ejpam-4453	68	31	.	.	PUNCT
ejpam-4453	69	1	since	since	SCONJ
ejpam-4453	69	2	theorem	theorem	ADJ
ejpam-4453	69	3	8	8	NUM
ejpam-4453	69	4	is	be	AUX
ejpam-4453	69	5	a	a	DET
ejpam-4453	69	6	necessary	necessary	ADJ
ejpam-4453	69	7	condition	condition	NOUN
ejpam-4453	69	8	for	for	ADP
ejpam-4453	69	9	the	the	DET
ejpam-4453	69	10	existence	existence	NOUN
ejpam-4453	69	11	of	of	ADP
ejpam-4453	69	12	a	a	DET
ejpam-4453	69	13	hamiltonian	hamiltonian	ADJ
ejpam-4453	69	14	path	path	NOUN
ejpam-4453	69	15	in	in	ADP
ejpam-4453	69	16	a	a	DET
ejpam-4453	69	17	graph	graph	NOUN
ejpam-4453	69	18	,	,	PUNCT
ejpam-4453	69	19	the	the	DET
ejpam-4453	69	20	contrapositive	contrapositive	NOUN
ejpam-4453	69	21	to	to	ADP
ejpam-4453	69	22	this	this	DET
ejpam-4453	69	23	statement	statement	NOUN
ejpam-4453	69	24	is	be	AUX
ejpam-4453	69	25	given	give	VERB
ejpam-4453	69	26	by	by	ADP
ejpam-4453	69	27	:	:	PUNCT
ejpam-4453	69	28	if	if	SCONJ
ejpam-4453	69	29	there	there	PRON
ejpam-4453	69	30	exist	exist	VERB
ejpam-4453	69	31	a	a	DET
ejpam-4453	69	32	nonempty	nonempty	ADJ
ejpam-4453	69	33	proper	proper	ADJ
ejpam-4453	69	34	subset	subset	NOUN
ejpam-4453	69	35	s	s	NOUN
ejpam-4453	69	36	of	of	ADP
ejpam-4453	69	37	the	the	DET
ejpam-4453	69	38	vertex	vertex	NOUN
ejpam-4453	69	39	set	set	NOUN
ejpam-4453	69	40	of	of	ADP
ejpam-4453	69	41	a	a	DET
ejpam-4453	69	42	graph	graph	NOUN
ejpam-4453	69	43	g	g	ADP
ejpam-4453	69	44	such	such	ADJ
ejpam-4453	69	45	that	that	SCONJ
ejpam-4453	69	46	k(g	k(g	PROPN
ejpam-4453	69	47	−	−	PROPN
ejpam-4453	69	48	s	s	NOUN
ejpam-4453	69	49	)	)	PUNCT
ejpam-4453	69	50	>	>	X
ejpam-4453	69	51	|s|	|s|	PROPN
ejpam-4453	70	1	+	+	ADP
ejpam-4453	70	2	1	1	NUM
ejpam-4453	70	3	,	,	PUNCT
ejpam-4453	70	4	then	then	ADV
ejpam-4453	70	5	g	g	PROPN
ejpam-4453	70	6	does	do	AUX
ejpam-4453	70	7	not	not	PART
ejpam-4453	70	8	contains	contain	VERB
ejpam-4453	70	9	hamiltonian	hamiltonian	ADJ
ejpam-4453	70	10	path	path	NOUN
ejpam-4453	70	11	.	.	PUNCT
ejpam-4453	71	1	in	in	ADP
ejpam-4453	71	2	particular	particular	ADJ
ejpam-4453	71	3	,	,	PUNCT
ejpam-4453	71	4	if	if	SCONJ
ejpam-4453	71	5	removing	remove	VERB
ejpam-4453	71	6	a	a	DET
ejpam-4453	71	7	set	set	NOUN
ejpam-4453	71	8	of	of	ADP
ejpam-4453	71	9	vertices	vertex	NOUN
ejpam-4453	71	10	s	s	PART
ejpam-4453	71	11	to	to	ADP
ejpam-4453	71	12	a	a	DET
ejpam-4453	71	13	graph	graph	NOUN
ejpam-4453	71	14	results	result	NOUN
ejpam-4453	71	15	to	to	ADP
ejpam-4453	71	16	k(g	k(g	PROPN
ejpam-4453	71	17	−	−	PROPN
ejpam-4453	71	18	s	s	NOUN
ejpam-4453	71	19	)	)	PUNCT
ejpam-4453	71	20	>	>	X
ejpam-4453	71	21	|s|	|s|	PROPN
ejpam-4453	72	1	+	+	CCONJ
ejpam-4453	72	2	1	1	NUM
ejpam-4453	72	3	then	then	ADV
ejpam-4453	72	4	we	we	PRON
ejpam-4453	72	5	can	can	AUX
ejpam-4453	72	6	say	say	VERB
ejpam-4453	72	7	that	that	SCONJ
ejpam-4453	72	8	the	the	DET
ejpam-4453	72	9	graph	graph	NOUN
ejpam-4453	72	10	does	do	AUX
ejpam-4453	72	11	not	not	PART
ejpam-4453	72	12	contain	contain	VERB
ejpam-4453	72	13	a	a	DET
ejpam-4453	72	14	hamiltonian	hamiltonian	ADJ
ejpam-4453	72	15	path	path	NOUN
ejpam-4453	72	16	.	.	PUNCT
ejpam-4453	73	1	3	3	X
ejpam-4453	73	2	.	.	X
ejpam-4453	73	3	construction	construction	NOUN
ejpam-4453	73	4	of	of	ADP
ejpam-4453	73	5	ntcbg	ntcbg	NOUN
ejpam-4453	73	6	in	in	ADP
ejpam-4453	73	7	this	this	DET
ejpam-4453	73	8	section	section	NOUN
ejpam-4453	73	9	we	we	PRON
ejpam-4453	73	10	will	will	AUX
ejpam-4453	73	11	define	define	VERB
ejpam-4453	73	12	a	a	DET
ejpam-4453	73	13	non	non	ADJ
ejpam-4453	73	14	-	-	ADJ
ejpam-4453	73	15	traceable	traceable	ADJ
ejpam-4453	73	16	cubic	cubic	ADJ
ejpam-4453	73	17	bridge	bridge	NOUN
ejpam-4453	73	18	graph	graph	NOUN
ejpam-4453	73	19	g	g	PROPN
ejpam-4453	73	20	together	together	ADV
ejpam-4453	73	21	with	with	ADP
ejpam-4453	73	22	its	its	PRON
ejpam-4453	73	23	two	two	NUM
ejpam-4453	73	24	important	important	ADJ
ejpam-4453	73	25	connected	connected	ADJ
ejpam-4453	73	26	components	component	NOUN
ejpam-4453	73	27	,	,	PUNCT
ejpam-4453	73	28	that	that	ADV
ejpam-4453	73	29	is	is	ADV
ejpam-4453	73	30	,	,	PUNCT
ejpam-4453	73	31	its	its	PRON
ejpam-4453	73	32	central	central	ADJ
ejpam-4453	73	33	fragment	fragment	NOUN
ejpam-4453	73	34	that	that	PRON
ejpam-4453	73	35	provides	provide	VERB
ejpam-4453	73	36	an	an	DET
ejpam-4453	73	37	assurance	assurance	NOUN
ejpam-4453	73	38	that	that	PRON
ejpam-4453	73	39	g	g	PROPN
ejpam-4453	73	40	will	will	AUX
ejpam-4453	73	41	be	be	AUX
ejpam-4453	73	42	non	non	ADJ
ejpam-4453	73	43	-	-	ADJ
ejpam-4453	73	44	traceable	traceable	ADJ
ejpam-4453	73	45	and	and	CCONJ
ejpam-4453	73	46	the	the	DET
ejpam-4453	73	47	set	set	NOUN
ejpam-4453	73	48	of	of	ADP
ejpam-4453	73	49	branches	branch	NOUN
ejpam-4453	73	50	that	that	PRON
ejpam-4453	73	51	are	be	AUX
ejpam-4453	73	52	also	also	ADV
ejpam-4453	73	53	a	a	DET
ejpam-4453	73	54	cubic	cubic	ADJ
ejpam-4453	73	55	graph	graph	NOUN
ejpam-4453	73	56	.	.	PUNCT
ejpam-4453	74	1	throughout	throughout	ADP
ejpam-4453	74	2	this	this	DET
ejpam-4453	74	3	paper	paper	NOUN
ejpam-4453	74	4	,	,	PUNCT
ejpam-4453	74	5	we	we	PRON
ejpam-4453	74	6	denote	denote	VERB
ejpam-4453	74	7	g	g	NOUN
ejpam-4453	74	8	as	as	ADP
ejpam-4453	74	9	non	non	ADJ
ejpam-4453	74	10	-	-	ADJ
ejpam-4453	74	11	traceable	traceable	ADJ
ejpam-4453	74	12	cubic	cubic	ADJ
ejpam-4453	74	13	bridge	bridge	NOUN
ejpam-4453	74	14	graph	graph	NOUN
ejpam-4453	74	15	.	.	PUNCT
ejpam-4453	75	1	definition	definition	NOUN
ejpam-4453	75	2	1	1	NUM
ejpam-4453	75	3	.	.	PUNCT
ejpam-4453	76	1	a	a	DET
ejpam-4453	76	2	3	3	NUM
ejpam-4453	76	3	-	-	PUNCT
ejpam-4453	76	4	regular	regular	ADJ
ejpam-4453	76	5	graph	graph	NOUN
ejpam-4453	76	6	g	g	PROPN
ejpam-4453	76	7	is	be	AUX
ejpam-4453	76	8	said	say	VERB
ejpam-4453	76	9	to	to	PART
ejpam-4453	76	10	be	be	AUX
ejpam-4453	76	11	non	non	ADJ
ejpam-4453	76	12	-	-	ADJ
ejpam-4453	76	13	traceable	traceable	ADJ
ejpam-4453	76	14	cubic	cubic	ADJ
ejpam-4453	76	15	bridge	bridge	NOUN
ejpam-4453	76	16	graph	graph	NOUN
ejpam-4453	76	17	if	if	SCONJ
ejpam-4453	76	18	g	g	PROPN
ejpam-4453	76	19	is	be	AUX
ejpam-4453	76	20	a	a	DET
ejpam-4453	76	21	cubic	cubic	ADJ
ejpam-4453	76	22	bridge	bridge	NOUN
ejpam-4453	76	23	graph	graph	NOUN
ejpam-4453	76	24	such	such	ADJ
ejpam-4453	76	25	that	that	SCONJ
ejpam-4453	76	26	g	g	PROPN
ejpam-4453	76	27	does	do	AUX
ejpam-4453	76	28	not	not	PART
ejpam-4453	76	29	contain	contain	VERB
ejpam-4453	76	30	a	a	DET
ejpam-4453	76	31	hamiltonian	hamiltonian	ADJ
ejpam-4453	76	32	path	path	NOUN
ejpam-4453	76	33	,	,	PUNCT
ejpam-4453	76	34	otherwise	otherwise	ADV
ejpam-4453	76	35	g	g	PROPN
ejpam-4453	76	36	is	be	AUX
ejpam-4453	76	37	traceable	traceable	ADJ
ejpam-4453	76	38	cubic	cubic	ADJ
ejpam-4453	76	39	bridge	bridge	NOUN
ejpam-4453	76	40	graph	graph	NOUN
ejpam-4453	76	41	.	.	PUNCT
ejpam-4453	77	1	a	a	DET
ejpam-4453	77	2	central	central	ADJ
ejpam-4453	77	3	fragment	fragment	NOUN
ejpam-4453	77	4	of	of	ADP
ejpam-4453	77	5	a	a	DET
ejpam-4453	77	6	non	non	ADJ
ejpam-4453	77	7	-	-	ADJ
ejpam-4453	77	8	traceable	traceable	ADJ
ejpam-4453	77	9	cubic	cubic	ADJ
ejpam-4453	77	10	bridge	bridge	NOUN
ejpam-4453	77	11	graph	graph	NOUN
ejpam-4453	77	12	g	g	PROPN
ejpam-4453	77	13	denoted	denote	VERB
ejpam-4453	77	14	by	by	ADP
ejpam-4453	77	15	c	c	PROPN
ejpam-4453	77	16	,	,	PUNCT
ejpam-4453	77	17	where	where	SCONJ
ejpam-4453	77	18	c	c	PROPN
ejpam-4453	77	19	is	be	AUX
ejpam-4453	77	20	a	a	DET
ejpam-4453	77	21	subgraph	subgraph	NOUN
ejpam-4453	77	22	of	of	ADP
ejpam-4453	77	23	g	g	NOUN
ejpam-4453	77	24	satisfying	satisfy	VERB
ejpam-4453	77	25	the	the	DET
ejpam-4453	77	26	following	follow	VERB
ejpam-4453	77	27	properties	property	NOUN
ejpam-4453	77	28	,	,	PUNCT
ejpam-4453	77	29	(	(	PUNCT
ejpam-4453	77	30	i	i	NOUN
ejpam-4453	77	31	)	)	PUNCT
ejpam-4453	77	32	c	c	PROPN
ejpam-4453	77	33	is	be	AUX
ejpam-4453	77	34	connected	connect	VERB
ejpam-4453	77	35	,	,	PUNCT
ejpam-4453	77	36	(	(	PUNCT
ejpam-4453	77	37	ii	ii	NOUN
ejpam-4453	77	38	)	)	PUNCT
ejpam-4453	77	39	c	c	PROPN
ejpam-4453	77	40	is	be	AUX
ejpam-4453	77	41	a	a	DET
ejpam-4453	77	42	bridge	bridge	NOUN
ejpam-4453	77	43	graph	graph	NOUN
ejpam-4453	77	44	,	,	PUNCT
ejpam-4453	77	45	(	(	PUNCT
ejpam-4453	77	46	iii	iii	X
ejpam-4453	77	47	)	)	PUNCT
ejpam-4453	77	48	c	c	NOUN
ejpam-4453	77	49	is	be	AUX
ejpam-4453	77	50	non	non	ADJ
ejpam-4453	77	51	-	-	ADJ
ejpam-4453	77	52	traceable	traceable	ADJ
ejpam-4453	77	53	and	and	CCONJ
ejpam-4453	77	54	(	(	PUNCT
ejpam-4453	77	55	iv	iv	X
ejpam-4453	77	56	)	)	PUNCT
ejpam-4453	77	57	c	c	NOUN
ejpam-4453	77	58	must	must	AUX
ejpam-4453	77	59	contain	contain	VERB
ejpam-4453	77	60	vertices	vertex	NOUN
ejpam-4453	77	61	of	of	ADP
ejpam-4453	77	62	degree	degree	NOUN
ejpam-4453	77	63	1	1	NUM
ejpam-4453	77	64	and	and	CCONJ
ejpam-4453	77	65	of	of	ADP
ejpam-4453	77	66	degree	degree	NOUN
ejpam-4453	77	67	3	3	NUM
ejpam-4453	77	68	only	only	ADV
ejpam-4453	77	69	.	.	PUNCT
ejpam-4453	78	1	a.r	a.r	PROPN
ejpam-4453	78	2	nieva	nieva	PROPN
ejpam-4453	78	3	and	and	CCONJ
ejpam-4453	78	4	k.nocum	k.nocum	PROPN
ejpam-4453	78	5	/	/	SYM
ejpam-4453	78	6	eur	eur	PROPN
ejpam-4453	78	7	.	.	PUNCT
ejpam-4453	79	1	j.	j.	PROPN
ejpam-4453	79	2	pure	pure	PROPN
ejpam-4453	79	3	appl	appl	PROPN
ejpam-4453	79	4	.	.	PROPN
ejpam-4453	79	5	math	math	PROPN
ejpam-4453	79	6	,	,	PUNCT
ejpam-4453	79	7	15	15	NUM
ejpam-4453	79	8	(	(	PUNCT
ejpam-4453	79	9	4	4	NUM
ejpam-4453	79	10	)	)	PUNCT
ejpam-4453	79	11	(	(	PUNCT
ejpam-4453	79	12	2022	2022	NUM
ejpam-4453	79	13	)	)	PUNCT
ejpam-4453	79	14	,	,	PUNCT
ejpam-4453	79	15	1536	1536	NUM
ejpam-4453	79	16	-	-	SYM
ejpam-4453	79	17	1548	1548	NUM
ejpam-4453	79	18	1539	1539	NUM
ejpam-4453	79	19	consider	consider	VERB
ejpam-4453	79	20	the	the	DET
ejpam-4453	79	21	graph	graph	NOUN
ejpam-4453	79	22	g	g	NOUN
ejpam-4453	79	23	in	in	ADP
ejpam-4453	79	24	figure	figure	NOUN
ejpam-4453	79	25	1	1	NUM
ejpam-4453	79	26	which	which	PRON
ejpam-4453	79	27	is	be	AUX
ejpam-4453	79	28	a	a	DET
ejpam-4453	79	29	cubic	cubic	ADJ
ejpam-4453	79	30	bridge	bridge	NOUN
ejpam-4453	79	31	graph	graph	NOUN
ejpam-4453	79	32	since	since	SCONJ
ejpam-4453	79	33	it	it	PRON
ejpam-4453	79	34	is	be	AUX
ejpam-4453	79	35	a	a	DET
ejpam-4453	79	36	cubic	cubic	ADJ
ejpam-4453	79	37	graph	graph	NOUN
ejpam-4453	79	38	contains	contain	VERB
ejpam-4453	79	39	a	a	DET
ejpam-4453	79	40	cut	cut	ADJ
ejpam-4453	79	41	edge	edge	NOUN
ejpam-4453	79	42	.	.	PUNCT
ejpam-4453	80	1	notice	notice	VERB
ejpam-4453	80	2	that	that	SCONJ
ejpam-4453	80	3	if	if	SCONJ
ejpam-4453	80	4	we	we	PRON
ejpam-4453	80	5	let	let	VERB
ejpam-4453	80	6	s	s	PRON
ejpam-4453	80	7	=	=	PUNCT
ejpam-4453	80	8	{	{	PUNCT
ejpam-4453	80	9	u	u	NOUN
ejpam-4453	80	10	}	}	PUNCT
ejpam-4453	80	11	then	then	ADV
ejpam-4453	80	12	g	g	NOUN
ejpam-4453	80	13	satisfies	satisfy	VERB
ejpam-4453	80	14	the	the	DET
ejpam-4453	80	15	contrapositive	contrapositive	NOUN
ejpam-4453	80	16	of	of	ADP
ejpam-4453	80	17	theorem	theorem	NOUN
ejpam-4453	80	18	8	8	NUM
ejpam-4453	80	19	.	.	PUNCT
ejpam-4453	81	1	this	this	PRON
ejpam-4453	81	2	implies	imply	VERB
ejpam-4453	81	3	that	that	SCONJ
ejpam-4453	81	4	g	g	PROPN
ejpam-4453	81	5	is	be	AUX
ejpam-4453	81	6	a	a	DET
ejpam-4453	81	7	non	non	ADJ
ejpam-4453	81	8	-	-	ADJ
ejpam-4453	81	9	traceable	traceable	ADJ
ejpam-4453	81	10	cubic	cubic	ADJ
ejpam-4453	81	11	bridge	bridge	NOUN
ejpam-4453	81	12	graph	graph	NOUN
ejpam-4453	81	13	.	.	PUNCT
ejpam-4453	82	1	g	g	NOUN
ejpam-4453	82	2	u	u	PROPN
ejpam-4453	82	3	.........................	.........................	PUNCT
ejpam-4453	82	4	..........	..........	PUNCT
ejpam-4453	82	5	.............................................	.............................................	PUNCT
ejpam-4453	82	6	.	.	PUNCT
ejpam-4453	82	7	..........................................	..........................................	PUNCT
ejpam-4453	83	1	..........	..........	PUNCT
ejpam-4453	83	2	.............................................	.............................................	PUNCT
ejpam-4453	83	3	.	.	PUNCT
ejpam-4453	84	1	.........	.........	PUNCT
ejpam-4453	84	2	........	........	PUNCT
ejpam-4453	84	3	........	........	PUNCT
ejpam-4453	84	4	........	........	PUNCT
ejpam-4453	85	1	........	........	PUNCT
ejpam-4453	85	2	.	.	PUNCT
ejpam-4453	86	1	..........	..........	PUNCT
ejpam-4453	86	2	.............................................	.............................................	PUNCT
ejpam-4453	86	3	.	.	PUNCT
ejpam-4453	87	1	....................................................	....................................................	PUNCT
ejpam-4453	87	2	.............................................	.............................................	PUNCT
ejpam-4453	87	3	.	.	PUNCT
ejpam-4453	87	4	............	............	PUNCT
ejpam-4453	88	1	...........	...........	PUNCT
ejpam-4453	88	2	..	..	PUNCT
ejpam-4453	88	3	..........	..........	PUNCT
ejpam-4453	88	4	.............................................	.............................................	PUNCT
ejpam-4453	88	5	.	.	PUNCT
ejpam-4453	89	1	.......................	.......................	PUNCT
ejpam-4453	89	2	.............................................	.............................................	PUNCT
ejpam-4453	89	3	.	.	PUNCT
ejpam-4453	90	1	.......................	.......................	PUNCT
ejpam-4453	90	2	.............................................	.............................................	PUNCT
ejpam-4453	90	3	.	.	PUNCT
ejpam-4453	91	1	..........	..........	PUNCT
ejpam-4453	91	2	.............................................	.............................................	PUNCT
ejpam-4453	91	3	.	.	PUNCT
ejpam-4453	92	1	.................................................................	.................................................................	PUNCT
ejpam-4453	93	1	..........	..........	PUNCT
ejpam-4453	93	2	.............................................	.............................................	PUNCT
ejpam-4453	93	3	.	.	PUNCT
ejpam-4453	94	1	..........	..........	PUNCT
ejpam-4453	94	2	.............................................	.............................................	PUNCT
ejpam-4453	95	1	.............	.............	PUNCT
ejpam-4453	95	2	...........	...........	PUNCT
ejpam-4453	95	3	...........	...........	PUNCT
ejpam-4453	95	4	...........	...........	PUNCT
ejpam-4453	95	5	...........	...........	PUNCT
ejpam-4453	95	6	.........	.........	PUNCT
ejpam-4453	96	1	..........	..........	PUNCT
ejpam-4453	96	2	.............................................	.............................................	PUNCT
ejpam-4453	96	3	.	.	PUNCT
ejpam-4453	97	1	..........	..........	PUNCT
ejpam-4453	97	2	.............................................	.............................................	PUNCT
ejpam-4453	97	3	.	.	PUNCT
ejpam-4453	97	4	............	............	PUNCT
ejpam-4453	98	1	...........	...........	PUNCT
ejpam-4453	98	2	..	..	PUNCT
ejpam-4453	98	3	..........	..........	PUNCT
ejpam-4453	98	4	.............................................	.............................................	PUNCT
ejpam-4453	98	5	.	.	PUNCT
ejpam-4453	99	1	....................................................	....................................................	PUNCT
ejpam-4453	99	2	.............................................	.............................................	PUNCT
ejpam-4453	99	3	.	.	PUNCT
ejpam-4453	100	1	.........	.........	PUNCT
ejpam-4453	100	2	........	........	PUNCT
ejpam-4453	100	3	........	........	PUNCT
ejpam-4453	100	4	........	........	PUNCT
ejpam-4453	101	1	........	........	PUNCT
ejpam-4453	101	2	.	.	PUNCT
ejpam-4453	102	1	..........	..........	PUNCT
ejpam-4453	102	2	.............................................	.............................................	PUNCT
ejpam-4453	102	3	.	.	PUNCT
ejpam-4453	103	1	..........................................	..........................................	PUNCT
ejpam-4453	103	2	..........	..........	PUNCT
ejpam-4453	104	1	.............................................	.............................................	PUNCT
ejpam-4453	104	2	.	.	PUNCT
ejpam-4453	105	1	.........................	.........................	PUNCT
ejpam-4453	105	2	..........	..........	PUNCT
ejpam-4453	106	1	.............................................	.............................................	PUNCT
ejpam-4453	106	2	.	.	PUNCT
ejpam-4453	107	1	..........	..........	PUNCT
ejpam-4453	107	2	.............................................	.............................................	PUNCT
ejpam-4453	107	3	.	.	PUNCT
ejpam-4453	107	4	............	............	PUNCT
ejpam-4453	108	1	...........	...........	PUNCT
ejpam-4453	108	2	...........	...........	PUNCT
ejpam-4453	108	3	...........	...........	PUNCT
ejpam-4453	108	4	...........	...........	PUNCT
ejpam-4453	108	5	.........	.........	PUNCT
ejpam-4453	109	1	..........	..........	PUNCT
ejpam-4453	109	2	.............................................	.............................................	PUNCT
ejpam-4453	109	3	.	.	PUNCT
ejpam-4453	110	1	..........	..........	PUNCT
ejpam-4453	110	2	.............................................	.............................................	PUNCT
ejpam-4453	110	3	.	.	PUNCT
ejpam-4453	111	1	.................................................................	.................................................................	PUNCT
ejpam-4453	112	1	..........	..........	PUNCT
ejpam-4453	112	2	.............................................	.............................................	PUNCT
ejpam-4453	112	3	.	.	PUNCT
ejpam-4453	113	1	..........	..........	PUNCT
ejpam-4453	113	2	.............................................	.............................................	PUNCT
ejpam-4453	113	3	.	.	PUNCT
ejpam-4453	114	1	.........	.........	PUNCT
ejpam-4453	115	1	....	....	PUNCT
ejpam-4453	115	2	..........	..........	PUNCT
ejpam-4453	115	3	.............................................	.............................................	PUNCT
ejpam-4453	115	4	.	.	PUNCT
ejpam-4453	116	1	.........................	.........................	PUNCT
ejpam-4453	116	2	..........	..........	PUNCT
ejpam-4453	117	1	.............................................	.............................................	PUNCT
ejpam-4453	117	2	.	.	PUNCT
ejpam-4453	118	1	.........	.........	PUNCT
ejpam-4453	118	2	........	........	PUNCT
ejpam-4453	118	3	........	........	PUNCT
ejpam-4453	118	4	........	........	PUNCT
ejpam-4453	119	1	........	........	PUNCT
ejpam-4453	119	2	.	.	PUNCT
ejpam-4453	120	1	..........	..........	PUNCT
ejpam-4453	120	2	.............................................	.............................................	PUNCT
ejpam-4453	120	3	.	.	PUNCT
ejpam-4453	121	1	....................................................	....................................................	PUNCT
ejpam-4453	121	2	.............................................	.............................................	PUNCT
ejpam-4453	121	3	.	.	PUNCT
ejpam-4453	122	1	.........	.........	PUNCT
ejpam-4453	122	2	........	........	PUNCT
ejpam-4453	122	3	........	........	PUNCT
ejpam-4453	122	4	........	........	PUNCT
ejpam-4453	123	1	........	........	PUNCT
ejpam-4453	123	2	.	.	PUNCT
ejpam-4453	124	1	..........	..........	PUNCT
ejpam-4453	124	2	.............................................	.............................................	PUNCT
ejpam-4453	124	3	.	.	PUNCT
ejpam-4453	124	4	............	............	PUNCT
ejpam-4453	125	1	...........	...........	PUNCT
ejpam-4453	125	2	..	..	PUNCT
ejpam-4453	125	3	..........	..........	PUNCT
ejpam-4453	125	4	.............................................	.............................................	PUNCT
ejpam-4453	125	5	.	.	PUNCT
ejpam-4453	126	1	..........	..........	PUNCT
ejpam-4453	126	2	.............................................	.............................................	PUNCT
ejpam-4453	126	3	.	.	PUNCT
ejpam-4453	127	1	.................................................................	.................................................................	PUNCT
ejpam-4453	128	1	..........	..........	PUNCT
ejpam-4453	128	2	.............................................	.............................................	PUNCT
ejpam-4453	128	3	.	.	PUNCT
ejpam-4453	129	1	..........	..........	PUNCT
ejpam-4453	129	2	.............................................	.............................................	PUNCT
ejpam-4453	130	1	.............	.............	PUNCT
ejpam-4453	130	2	...........	...........	PUNCT
ejpam-4453	130	3	...........	...........	PUNCT
ejpam-4453	130	4	...........	...........	PUNCT
ejpam-4453	130	5	...........	...........	PUNCT
ejpam-4453	130	6	.........	.........	PUNCT
ejpam-4453	131	1	..........	..........	PUNCT
ejpam-4453	131	2	.............................................	.............................................	PUNCT
ejpam-4453	131	3	.	.	PUNCT
ejpam-4453	132	1	..........	..........	PUNCT
ejpam-4453	132	2	.............................................	.............................................	PUNCT
ejpam-4453	132	3	.	.	PUNCT
ejpam-4453	133	1	g−	g−	PROPN
ejpam-4453	133	2	s	s	PART
ejpam-4453	133	3	....................	....................	PUNCT
ejpam-4453	133	4	............................................	............................................	PUNCT
ejpam-4453	133	5	.................................	.................................	PUNCT
ejpam-4453	133	6	............................................	............................................	PUNCT
ejpam-4453	133	7	..................	..................	PUNCT
ejpam-4453	133	8	...............	...............	PUNCT
ejpam-4453	133	9	............................................	............................................	PUNCT
ejpam-4453	133	10	.............................................................................	.............................................................................	PUNCT
ejpam-4453	133	11	................................................................	................................................................	PUNCT
ejpam-4453	134	1	............................................	............................................	PUNCT
ejpam-4453	134	2	...................................................	...................................................	PUNCT
ejpam-4453	134	3	............................................	............................................	PUNCT
ejpam-4453	134	4	....................................................................	....................................................................	PUNCT
ejpam-4453	135	1	.......................	.......................	PUNCT
ejpam-4453	135	2	....	....	PUNCT
ejpam-4453	136	1	............................................	............................................	PUNCT
ejpam-4453	136	2	............................................	............................................	PUNCT
ejpam-4453	136	3	................................................................	................................................................	PUNCT
ejpam-4453	136	4	.............................................................................	.............................................................................	PUNCT
ejpam-4453	136	5	..................	..................	PUNCT
ejpam-4453	136	6	...............	...............	PUNCT
ejpam-4453	136	7	............................................	............................................	PUNCT
ejpam-4453	136	8	.................................	.................................	PUNCT
ejpam-4453	137	1	............................................	............................................	PUNCT
ejpam-4453	137	2	....................	....................	PUNCT
ejpam-4453	137	3	............................................	............................................	PUNCT
ejpam-4453	137	4	............................................	............................................	PUNCT
ejpam-4453	137	5	........................	........................	PUNCT
ejpam-4453	137	6	.......................	.......................	PUNCT
ejpam-4453	138	1	....	....	PUNCT
ejpam-4453	138	2	............................................	............................................	PUNCT
ejpam-4453	139	1	............................................	............................................	PUNCT
ejpam-4453	139	2	...................................................	...................................................	PUNCT
ejpam-4453	139	3	............................................	............................................	PUNCT
ejpam-4453	139	4	............................................	............................................	PUNCT
ejpam-4453	139	5	....................	....................	PUNCT
ejpam-4453	140	1	............................................	............................................	PUNCT
ejpam-4453	140	2	..................	..................	PUNCT
ejpam-4453	140	3	...............	...............	PUNCT
ejpam-4453	140	4	............................................	............................................	PUNCT
ejpam-4453	140	5	.............................................................................	.............................................................................	PUNCT
ejpam-4453	140	6	..................	..................	PUNCT
ejpam-4453	140	7	...............	...............	PUNCT
ejpam-4453	140	8	............................................	............................................	PUNCT
ejpam-4453	140	9	....................	....................	PUNCT
ejpam-4453	141	1	........................................................................................	........................................................................................	PUNCT
ejpam-4453	141	2	...................................................	...................................................	PUNCT
ejpam-4453	141	3	............................................	............................................	PUNCT
ejpam-4453	141	4	....................................................................	....................................................................	PUNCT
ejpam-4453	142	1	.......................	.......................	PUNCT
ejpam-4453	142	2	....	....	PUNCT
ejpam-4453	143	1	............................................	............................................	PUNCT
ejpam-4453	143	2	............................................	............................................	PUNCT
ejpam-4453	143	3	figure	figure	VERB
ejpam-4453	143	4	1	1	NUM
ejpam-4453	143	5	:	:	PUNCT
ejpam-4453	143	6	example	example	NOUN
ejpam-4453	143	7	of	of	ADP
ejpam-4453	143	8	ntcbg	ntcbg	NOUN
ejpam-4453	143	9	since	since	SCONJ
ejpam-4453	143	10	a	a	DET
ejpam-4453	143	11	central	central	ADJ
ejpam-4453	143	12	fragment	fragment	NOUN
ejpam-4453	143	13	must	must	AUX
ejpam-4453	143	14	be	be	AUX
ejpam-4453	143	15	connected	connect	VERB
ejpam-4453	143	16	and	and	CCONJ
ejpam-4453	143	17	contains	contain	VERB
ejpam-4453	143	18	vertices	vertex	NOUN
ejpam-4453	143	19	of	of	ADP
ejpam-4453	143	20	degree	degree	NOUN
ejpam-4453	143	21	1	1	NUM
ejpam-4453	143	22	and	and	CCONJ
ejpam-4453	143	23	3	3	NUM
ejpam-4453	143	24	only	only	ADV
ejpam-4453	143	25	,	,	PUNCT
ejpam-4453	143	26	the	the	DET
ejpam-4453	143	27	smallest	small	ADJ
ejpam-4453	143	28	possible	possible	ADJ
ejpam-4453	143	29	graphs	graph	NOUN
ejpam-4453	143	30	are	be	AUX
ejpam-4453	143	31	those	those	PRON
ejpam-4453	143	32	with	with	ADP
ejpam-4453	143	33	4	4	NUM
ejpam-4453	143	34	vertices	vertex	NOUN
ejpam-4453	143	35	which	which	PRON
ejpam-4453	143	36	are	be	AUX
ejpam-4453	143	37	shown	show	VERB
ejpam-4453	143	38	in	in	ADP
ejpam-4453	143	39	figure	figure	NOUN
ejpam-4453	143	40	2	2	NUM
ejpam-4453	143	41	.	.	PUNCT
ejpam-4453	144	1	we	we	PRON
ejpam-4453	144	2	may	may	AUX
ejpam-4453	144	3	notice	notice	VERB
ejpam-4453	144	4	from	from	ADP
ejpam-4453	144	5	figure	figure	NOUN
ejpam-4453	144	6	2	2	NUM
ejpam-4453	144	7	that	that	PRON
ejpam-4453	144	8	h1	h1	VERB
ejpam-4453	144	9	and	and	CCONJ
ejpam-4453	144	10	h2	h2	NOUN
ejpam-4453	144	11	are	be	AUX
ejpam-4453	144	12	the	the	DET
ejpam-4453	144	13	only	only	ADJ
ejpam-4453	144	14	bridge	bridge	NOUN
ejpam-4453	144	15	graphs	graph	NOUN
ejpam-4453	144	16	.	.	PUNCT
ejpam-4453	145	1	furthermore	furthermore	ADV
ejpam-4453	145	2	,	,	PUNCT
ejpam-4453	145	3	h2	h2	PROPN
ejpam-4453	145	4	is	be	AUX
ejpam-4453	145	5	the	the	DET
ejpam-4453	145	6	only	only	ADJ
ejpam-4453	145	7	non	non	ADJ
ejpam-4453	145	8	-	-	ADJ
ejpam-4453	145	9	traceable	traceable	ADJ
ejpam-4453	145	10	graph	graph	NOUN
ejpam-4453	145	11	by	by	ADP
ejpam-4453	145	12	the	the	DET
ejpam-4453	145	13	contrapositive	contrapositive	NOUN
ejpam-4453	145	14	of	of	ADP
ejpam-4453	145	15	theorem	theorem	NOUN
ejpam-4453	145	16	8	8	NUM
ejpam-4453	145	17	.	.	PUNCT
ejpam-4453	146	1	we	we	PRON
ejpam-4453	146	2	can	can	AUX
ejpam-4453	146	3	also	also	ADV
ejpam-4453	146	4	say	say	VERB
ejpam-4453	146	5	that	that	SCONJ
ejpam-4453	146	6	since	since	SCONJ
ejpam-4453	146	7	a	a	DET
ejpam-4453	146	8	hamiltonian	hamiltonian	ADJ
ejpam-4453	146	9	path	path	NOUN
ejpam-4453	146	10	must	must	AUX
ejpam-4453	146	11	contain	contain	VERB
ejpam-4453	146	12	2	2	NUM
ejpam-4453	146	13	end	end	NOUN
ejpam-4453	146	14	-	-	PUNCT
ejpam-4453	146	15	vertices	vertex	NOUN
ejpam-4453	146	16	and	and	CCONJ
ejpam-4453	146	17	h2	h2	NOUN
ejpam-4453	146	18	contains	contain	VERB
ejpam-4453	146	19	3	3	NUM
ejpam-4453	146	20	end	end	NOUN
ejpam-4453	146	21	-	-	PUNCT
ejpam-4453	146	22	vertices	vertex	NOUN
ejpam-4453	146	23	,	,	PUNCT
ejpam-4453	146	24	thus	thus	ADV
ejpam-4453	146	25	h2	h2	NOUN
ejpam-4453	146	26	does	do	AUX
ejpam-4453	146	27	not	not	PART
ejpam-4453	146	28	contains	contain	VERB
ejpam-4453	146	29	a	a	DET
ejpam-4453	146	30	hamiltonian	hamiltonian	ADJ
ejpam-4453	146	31	path	path	NOUN
ejpam-4453	146	32	which	which	PRON
ejpam-4453	146	33	implies	imply	VERB
ejpam-4453	146	34	that	that	SCONJ
ejpam-4453	146	35	it	it	PRON
ejpam-4453	146	36	is	be	AUX
ejpam-4453	146	37	non	non	ADJ
ejpam-4453	146	38	-	-	ADJ
ejpam-4453	146	39	traceable	traceable	ADJ
ejpam-4453	146	40	.	.	PUNCT
ejpam-4453	147	1	since	since	SCONJ
ejpam-4453	147	2	h2	h2	NOUN
ejpam-4453	147	3	satisfies	satisfie	NOUN
ejpam-4453	147	4	definition	definition	NOUN
ejpam-4453	147	5	1	1	NUM
ejpam-4453	147	6	,	,	PUNCT
ejpam-4453	147	7	then	then	ADV
ejpam-4453	147	8	h2	h2	NOUN
ejpam-4453	147	9	is	be	AUX
ejpam-4453	147	10	the	the	DET
ejpam-4453	147	11	smallest	small	ADJ
ejpam-4453	147	12	possible	possible	ADJ
ejpam-4453	147	13	central	central	ADJ
ejpam-4453	147	14	fragment	fragment	NOUN
ejpam-4453	147	15	.	.	PUNCT
ejpam-4453	148	1	hence	hence	ADV
ejpam-4453	148	2	,	,	PUNCT
ejpam-4453	148	3	we	we	PRON
ejpam-4453	148	4	can	can	AUX
ejpam-4453	148	5	use	use	VERB
ejpam-4453	148	6	this	this	PRON
ejpam-4453	148	7	as	as	ADP
ejpam-4453	148	8	our	our	PRON
ejpam-4453	148	9	basis	basis	NOUN
ejpam-4453	148	10	of	of	ADP
ejpam-4453	148	11	central	central	ADJ
ejpam-4453	148	12	fragment	fragment	NOUN
ejpam-4453	148	13	construction	construction	NOUN
ejpam-4453	148	14	.	.	PUNCT
ejpam-4453	148	15	.........	.........	PUNCT
ejpam-4453	148	16	........	........	PUNCT
ejpam-4453	148	17	........	........	PUNCT
ejpam-4453	148	18	........	........	PUNCT
ejpam-4453	148	19	........	........	PUNCT
ejpam-4453	148	20	.	.	PUNCT
ejpam-4453	149	1	..........	..........	PUNCT
ejpam-4453	149	2	.............................................	.............................................	PUNCT
ejpam-4453	149	3	.	.	PUNCT
ejpam-4453	150	1	....................................................	....................................................	PUNCT
ejpam-4453	150	2	.............................................	.............................................	PUNCT
ejpam-4453	150	3	.	.	PUNCT
ejpam-4453	151	1	.........	.........	PUNCT
ejpam-4453	151	2	........	........	PUNCT
ejpam-4453	151	3	........	........	PUNCT
ejpam-4453	151	4	........	........	PUNCT
ejpam-4453	152	1	........	........	PUNCT
ejpam-4453	152	2	.	.	PUNCT
ejpam-4453	153	1	..........	..........	PUNCT
ejpam-4453	153	2	.............................................	.............................................	PUNCT
ejpam-4453	153	3	.	.	PUNCT
ejpam-4453	154	1	..........	..........	PUNCT
ejpam-4453	154	2	.............................................	.............................................	PUNCT
ejpam-4453	154	3	.	.	PUNCT
ejpam-4453	155	1	h1	h1	PROPN
ejpam-4453	155	2	....................................................	....................................................	PUNCT
ejpam-4453	155	3	.............................................	.............................................	PUNCT
ejpam-4453	155	4	.	.	PUNCT
ejpam-4453	155	5	....................................................	....................................................	PUNCT
ejpam-4453	155	6	.............................................	.............................................	PUNCT
ejpam-4453	155	7	.	.	PUNCT
ejpam-4453	156	1	..........	..........	PUNCT
ejpam-4453	156	2	.............................................	.............................................	PUNCT
ejpam-4453	156	3	.	.	PUNCT
ejpam-4453	157	1	.........	.........	PUNCT
ejpam-4453	157	2	........	........	PUNCT
ejpam-4453	157	3	........	........	PUNCT
ejpam-4453	157	4	........	........	PUNCT
ejpam-4453	158	1	........	........	PUNCT
ejpam-4453	158	2	.	.	PUNCT
ejpam-4453	159	1	..........	..........	PUNCT
ejpam-4453	159	2	.............................................	.............................................	PUNCT
ejpam-4453	159	3	.	.	PUNCT
ejpam-4453	160	1	..........	..........	PUNCT
ejpam-4453	160	2	.............................................	.............................................	PUNCT
ejpam-4453	160	3	.	.	PUNCT
ejpam-4453	161	1	h2	h2	NOUN
ejpam-4453	161	2	.........	.........	PUNCT
ejpam-4453	161	3	........	........	PUNCT
ejpam-4453	161	4	........	........	PUNCT
ejpam-4453	161	5	........	........	PUNCT
ejpam-4453	161	6	........	........	PUNCT
ejpam-4453	161	7	.	.	PUNCT
ejpam-4453	162	1	..........	..........	PUNCT
ejpam-4453	162	2	.............................................	.............................................	PUNCT
ejpam-4453	162	3	.	.	PUNCT
ejpam-4453	163	1	....................................................	....................................................	PUNCT
ejpam-4453	163	2	.............................................	.............................................	PUNCT
ejpam-4453	163	3	.	.	PUNCT
ejpam-4453	164	1	.........	.........	PUNCT
ejpam-4453	164	2	........	........	PUNCT
ejpam-4453	164	3	........	........	PUNCT
ejpam-4453	164	4	........	........	PUNCT
ejpam-4453	165	1	........	........	PUNCT
ejpam-4453	165	2	.	.	PUNCT
ejpam-4453	166	1	..........	..........	PUNCT
ejpam-4453	166	2	.............................................	.............................................	PUNCT
ejpam-4453	166	3	.	.	PUNCT
ejpam-4453	167	1	..........	..........	PUNCT
ejpam-4453	167	2	.............................................	.............................................	PUNCT
ejpam-4453	168	1	.............	.............	PUNCT
ejpam-4453	168	2	...........	...........	PUNCT
ejpam-4453	168	3	...........	...........	PUNCT
ejpam-4453	168	4	...........	...........	PUNCT
ejpam-4453	168	5	...........	...........	PUNCT
ejpam-4453	168	6	.........	.........	PUNCT
ejpam-4453	168	7	h3	h3	NOUN
ejpam-4453	168	8	.........	.........	PUNCT
ejpam-4453	168	9	........	........	PUNCT
ejpam-4453	168	10	........	........	PUNCT
ejpam-4453	168	11	........	........	PUNCT
ejpam-4453	168	12	........	........	PUNCT
ejpam-4453	168	13	.	.	PUNCT
ejpam-4453	169	1	..........	..........	PUNCT
ejpam-4453	169	2	.............................................	.............................................	PUNCT
ejpam-4453	169	3	.	.	PUNCT
ejpam-4453	170	1	....................................................	....................................................	PUNCT
ejpam-4453	170	2	.............................................	.............................................	PUNCT
ejpam-4453	170	3	.	.	PUNCT
ejpam-4453	171	1	.........	.........	PUNCT
ejpam-4453	171	2	........	........	PUNCT
ejpam-4453	171	3	........	........	PUNCT
ejpam-4453	171	4	........	........	PUNCT
ejpam-4453	172	1	........	........	PUNCT
ejpam-4453	172	2	.	.	PUNCT
ejpam-4453	173	1	..........	..........	PUNCT
ejpam-4453	173	2	.............................................	.............................................	PUNCT
ejpam-4453	173	3	.	.	PUNCT
ejpam-4453	174	1	..........	..........	PUNCT
ejpam-4453	174	2	.............................................	.............................................	PUNCT
ejpam-4453	175	1	...........................................	...........................................	PUNCT
ejpam-4453	176	1	h4	h4	NOUN
ejpam-4453	176	2	.........	.........	PUNCT
ejpam-4453	176	3	........	........	PUNCT
ejpam-4453	176	4	........	........	PUNCT
ejpam-4453	176	5	........	........	PUNCT
ejpam-4453	176	6	........	........	PUNCT
ejpam-4453	176	7	.	.	PUNCT
ejpam-4453	176	8	..........	..........	PUNCT
ejpam-4453	176	9	.............................................	.............................................	PUNCT
ejpam-4453	176	10	.	.	PUNCT
ejpam-4453	176	11	....................................................	....................................................	PUNCT
ejpam-4453	176	12	.............................................	.............................................	PUNCT
ejpam-4453	176	13	.	.	PUNCT
ejpam-4453	176	14	.........	.........	PUNCT
ejpam-4453	176	15	........	........	PUNCT
ejpam-4453	176	16	........	........	PUNCT
ejpam-4453	176	17	........	........	PUNCT
ejpam-4453	176	18	........	........	PUNCT
ejpam-4453	176	19	.	.	PUNCT
ejpam-4453	176	20	..........	..........	PUNCT
ejpam-4453	176	21	.............................................	.............................................	PUNCT
ejpam-4453	176	22	.	.	PUNCT
ejpam-4453	176	23	..........	..........	PUNCT
ejpam-4453	176	24	.............................................	.............................................	PUNCT
ejpam-4453	176	25	.......................................................	.......................................................	PUNCT
ejpam-4453	176	26	...........	...........	PUNCT
ejpam-4453	176	27	...........	...........	PUNCT
ejpam-4453	176	28	...........	...........	PUNCT
ejpam-4453	176	29	...........	...........	PUNCT
ejpam-4453	176	30	.........	.........	PUNCT
ejpam-4453	176	31	h5	h5	PROPN
ejpam-4453	176	32	.........	.........	PUNCT
ejpam-4453	176	33	........	........	PUNCT
ejpam-4453	176	34	........	........	PUNCT
ejpam-4453	176	35	........	........	PUNCT
ejpam-4453	176	36	........	........	PUNCT
ejpam-4453	176	37	.	.	PUNCT
ejpam-4453	176	38	..........	..........	PUNCT
ejpam-4453	176	39	.............................................	.............................................	PUNCT
ejpam-4453	176	40	.	.	PUNCT
ejpam-4453	176	41	....................................................	....................................................	PUNCT
ejpam-4453	176	42	.............................................	.............................................	PUNCT
ejpam-4453	176	43	.	.	PUNCT
ejpam-4453	176	44	.........	.........	PUNCT
ejpam-4453	176	45	........	........	PUNCT
ejpam-4453	176	46	........	........	PUNCT
ejpam-4453	176	47	........	........	PUNCT
ejpam-4453	176	48	........	........	PUNCT
ejpam-4453	176	49	.	.	PUNCT
ejpam-4453	176	50	..........	..........	PUNCT
ejpam-4453	176	51	.............................................	.............................................	PUNCT
ejpam-4453	176	52	.	.	PUNCT
ejpam-4453	176	53	..........	..........	PUNCT
ejpam-4453	176	54	.............................................	.............................................	PUNCT
ejpam-4453	176	55	.......................................................	.......................................................	PUNCT
ejpam-4453	176	56	...........	...........	PUNCT
ejpam-4453	176	57	...........	...........	PUNCT
ejpam-4453	176	58	...........	...........	PUNCT
ejpam-4453	176	59	...........	...........	PUNCT
ejpam-4453	176	60	..........................................................................	..........................................................................	PUNCT
ejpam-4453	177	1	h6	h6	PROPN
ejpam-4453	177	2	figure	figure	NOUN
ejpam-4453	177	3	2	2	NUM
ejpam-4453	177	4	:	:	PUNCT
ejpam-4453	177	5	all	all	DET
ejpam-4453	177	6	possible	possible	ADJ
ejpam-4453	177	7	connected	connected	ADJ
ejpam-4453	177	8	graphs	graph	NOUN
ejpam-4453	177	9	with	with	ADP
ejpam-4453	177	10	4	4	NUM
ejpam-4453	177	11	vertices	vertex	NOUN
ejpam-4453	177	12	there	there	PRON
ejpam-4453	177	13	are	be	VERB
ejpam-4453	177	14	two	two	NUM
ejpam-4453	177	15	possible	possible	ADJ
ejpam-4453	177	16	classes	class	NOUN
ejpam-4453	177	17	of	of	ADP
ejpam-4453	177	18	graphs	graph	NOUN
ejpam-4453	177	19	that	that	PRON
ejpam-4453	177	20	can	can	AUX
ejpam-4453	177	21	be	be	AUX
ejpam-4453	177	22	formed	form	VERB
ejpam-4453	177	23	satisfying	satisfy	VERB
ejpam-4453	177	24	the	the	DET
ejpam-4453	177	25	definition	definition	NOUN
ejpam-4453	177	26	of	of	ADP
ejpam-4453	177	27	central	central	ADJ
ejpam-4453	177	28	fragment	fragment	NOUN
ejpam-4453	177	29	.	.	PUNCT
ejpam-4453	178	1	these	these	PRON
ejpam-4453	178	2	are	be	AUX
ejpam-4453	178	3	a	a	DET
ejpam-4453	178	4	central	central	ADJ
ejpam-4453	178	5	fragment	fragment	NOUN
ejpam-4453	178	6	which	which	PRON
ejpam-4453	178	7	is	be	AUX
ejpam-4453	178	8	a	a	DET
ejpam-4453	178	9	tree	tree	NOUN
ejpam-4453	178	10	or	or	CCONJ
ejpam-4453	178	11	a	a	DET
ejpam-4453	178	12	central	central	ADJ
ejpam-4453	178	13	fragment	fragment	NOUN
ejpam-4453	178	14	which	which	PRON
ejpam-4453	178	15	is	be	AUX
ejpam-4453	178	16	not	not	PART
ejpam-4453	178	17	a	a	DET
ejpam-4453	178	18	tree	tree	NOUN
ejpam-4453	178	19	.	.	PUNCT
ejpam-4453	179	1	for	for	ADP
ejpam-4453	179	2	simplicity	simplicity	NOUN
ejpam-4453	179	3	,	,	PUNCT
ejpam-4453	179	4	we	we	PRON
ejpam-4453	179	5	write	write	VERB
ejpam-4453	179	6	a	a	DET
ejpam-4453	179	7	general	general	ADJ
ejpam-4453	179	8	central	central	ADJ
ejpam-4453	179	9	fragment	fragment	NOUN
ejpam-4453	179	10	,	,	PUNCT
ejpam-4453	179	11	a	a	DET
ejpam-4453	179	12	central	central	ADJ
ejpam-4453	179	13	fragment	fragment	NOUN
ejpam-4453	179	14	which	which	PRON
ejpam-4453	179	15	is	be	AUX
ejpam-4453	179	16	a	a	DET
ejpam-4453	179	17	tree	tree	NOUN
ejpam-4453	179	18	,	,	PUNCT
ejpam-4453	179	19	and	and	CCONJ
ejpam-4453	179	20	not	not	PART
ejpam-4453	179	21	a	a	DET
ejpam-4453	179	22	tree	tree	NOUN
ejpam-4453	179	23	as	as	ADP
ejpam-4453	179	24	c	c	PROPN
ejpam-4453	179	25	,	,	PUNCT
ejpam-4453	179	26	c	c	NOUN
ejpam-4453	179	27	∗	∗	NOUN
ejpam-4453	179	28	,	,	PUNCT
ejpam-4453	179	29	and	and	CCONJ
ejpam-4453	179	30	c	c	PROPN
ejpam-4453	179	31	∗∗	∗∗	PROPN
ejpam-4453	179	32	,	,	PUNCT
ejpam-4453	179	33	respectively	respectively	ADV
ejpam-4453	179	34	.	.	PUNCT
ejpam-4453	180	1	since	since	SCONJ
ejpam-4453	180	2	we	we	PRON
ejpam-4453	180	3	know	know	VERB
ejpam-4453	180	4	that	that	SCONJ
ejpam-4453	180	5	c	c	PROPN
ejpam-4453	180	6	∗	∗	NOUN
ejpam-4453	180	7	1	1	NUM
ejpam-4453	180	8	is	be	AUX
ejpam-4453	180	9	the	the	DET
ejpam-4453	180	10	smallest	small	ADJ
ejpam-4453	180	11	order	order	NOUN
ejpam-4453	180	12	of	of	ADP
ejpam-4453	180	13	a	a	DET
ejpam-4453	180	14	central	central	ADJ
ejpam-4453	180	15	fragment	fragment	NOUN
ejpam-4453	180	16	shown	show	VERB
ejpam-4453	180	17	in	in	ADP
ejpam-4453	180	18	figure	figure	NOUN
ejpam-4453	180	19	3	3	NUM
ejpam-4453	180	20	,	,	PUNCT
ejpam-4453	180	21	we	we	PRON
ejpam-4453	180	22	can	can	AUX
ejpam-4453	180	23	extend	extend	VERB
ejpam-4453	180	24	c	c	PROPN
ejpam-4453	180	25	∗	∗	NOUN
ejpam-4453	180	26	1	1	NUM
ejpam-4453	180	27	our	our	PRON
ejpam-4453	180	28	basis	basis	NOUN
ejpam-4453	180	29	which	which	PRON
ejpam-4453	180	30	preserves	preserve	VERB
ejpam-4453	180	31	its	its	PRON
ejpam-4453	180	32	tree	tree	NOUN
ejpam-4453	180	33	structure	structure	NOUN
ejpam-4453	180	34	(	(	PUNCT
ejpam-4453	180	35	see	see	VERB
ejpam-4453	180	36	figure	figure	NOUN
ejpam-4453	180	37	3	3	NUM
ejpam-4453	180	38	)	)	PUNCT
ejpam-4453	180	39	.	.	PUNCT
ejpam-4453	181	1	from	from	ADP
ejpam-4453	181	2	this	this	PRON
ejpam-4453	181	3	,	,	PUNCT
ejpam-4453	181	4	we	we	PRON
ejpam-4453	181	5	have	have	VERB
ejpam-4453	181	6	the	the	DET
ejpam-4453	181	7	following	follow	VERB
ejpam-4453	181	8	proposition	proposition	NOUN
ejpam-4453	181	9	.	.	PUNCT
ejpam-4453	182	1	....................................................	....................................................	PUNCT
ejpam-4453	182	2	.............................................	.............................................	PUNCT
ejpam-4453	182	3	.	.	PUNCT
ejpam-4453	183	1	....................................................	....................................................	PUNCT
ejpam-4453	183	2	.............................................	.............................................	PUNCT
ejpam-4453	183	3	.	.	PUNCT
ejpam-4453	184	1	..........	..........	PUNCT
ejpam-4453	184	2	.............................................	.............................................	PUNCT
ejpam-4453	184	3	.	.	PUNCT
ejpam-4453	185	1	.........	.........	PUNCT
ejpam-4453	185	2	........	........	PUNCT
ejpam-4453	185	3	........	........	PUNCT
ejpam-4453	185	4	........	........	PUNCT
ejpam-4453	186	1	........	........	PUNCT
ejpam-4453	186	2	.	.	PUNCT
ejpam-4453	187	1	..........	..........	PUNCT
ejpam-4453	187	2	.............................................	.............................................	PUNCT
ejpam-4453	187	3	.	.	PUNCT
ejpam-4453	188	1	..........	..........	PUNCT
ejpam-4453	188	2	.............................................	.............................................	PUNCT
ejpam-4453	188	3	.	.	PUNCT
ejpam-4453	189	1	c	c	NOUN
ejpam-4453	189	2	∗	∗	NOUN
ejpam-4453	189	3	1	1	NUM
ejpam-4453	189	4	.	.	PUNCT
ejpam-4453	189	5	....................................................	....................................................	PUNCT
ejpam-4453	189	6	.............................................	.............................................	PUNCT
ejpam-4453	189	7	.	.	PUNCT
ejpam-4453	190	1	....................................................	....................................................	PUNCT
ejpam-4453	190	2	.............................................	.............................................	PUNCT
ejpam-4453	190	3	.	.	PUNCT
ejpam-4453	191	1	....................................................	....................................................	PUNCT
ejpam-4453	191	2	.............................................	.............................................	PUNCT
ejpam-4453	191	3	.	.	PUNCT
ejpam-4453	192	1	..........	..........	PUNCT
ejpam-4453	192	2	.............................................	.............................................	PUNCT
ejpam-4453	192	3	.	.	PUNCT
ejpam-4453	193	1	.........	.........	PUNCT
ejpam-4453	193	2	........	........	PUNCT
ejpam-4453	193	3	........	........	PUNCT
ejpam-4453	193	4	........	........	PUNCT
ejpam-4453	194	1	........	........	PUNCT
ejpam-4453	194	2	.	.	PUNCT
ejpam-4453	195	1	..........	..........	PUNCT
ejpam-4453	195	2	.............................................	.............................................	PUNCT
ejpam-4453	195	3	.	.	PUNCT
ejpam-4453	196	1	..........	..........	PUNCT
ejpam-4453	196	2	.............................................	.............................................	PUNCT
ejpam-4453	196	3	.	.	PUNCT
ejpam-4453	197	1	.........	.........	PUNCT
ejpam-4453	197	2	........	........	PUNCT
ejpam-4453	197	3	........	........	PUNCT
ejpam-4453	197	4	........	........	PUNCT
ejpam-4453	198	1	........	........	PUNCT
ejpam-4453	198	2	.	.	PUNCT
ejpam-4453	199	1	..........	..........	PUNCT
ejpam-4453	199	2	.............................................	.............................................	PUNCT
ejpam-4453	199	3	.	.	PUNCT
ejpam-4453	200	1	..........	..........	PUNCT
ejpam-4453	200	2	.............................................	.............................................	PUNCT
ejpam-4453	200	3	.	.	PUNCT
ejpam-4453	201	1	c	c	NOUN
ejpam-4453	201	2	∗	∗	PROPN
ejpam-4453	201	3	2	2	NUM
ejpam-4453	201	4	..	..	PUNCT
ejpam-4453	201	5	....................................................	....................................................	PUNCT
ejpam-4453	201	6	.............................................	.............................................	PUNCT
ejpam-4453	201	7	.	.	PUNCT
ejpam-4453	202	1	....................................................	....................................................	PUNCT
ejpam-4453	202	2	.............................................	.............................................	PUNCT
ejpam-4453	202	3	.	.	PUNCT
ejpam-4453	203	1	....................................................	....................................................	PUNCT
ejpam-4453	203	2	.............................................	.............................................	PUNCT
ejpam-4453	203	3	.	.	PUNCT
ejpam-4453	204	1	....................................................	....................................................	PUNCT
ejpam-4453	204	2	.............................................	.............................................	PUNCT
ejpam-4453	204	3	.	.	PUNCT
ejpam-4453	205	1	..........	..........	PUNCT
ejpam-4453	205	2	.............................................	.............................................	PUNCT
ejpam-4453	205	3	.	.	PUNCT
ejpam-4453	206	1	.........	.........	PUNCT
ejpam-4453	206	2	........	........	PUNCT
ejpam-4453	206	3	........	........	PUNCT
ejpam-4453	206	4	........	........	PUNCT
ejpam-4453	207	1	........	........	PUNCT
ejpam-4453	207	2	.	.	PUNCT
ejpam-4453	208	1	..........	..........	PUNCT
ejpam-4453	208	2	.............................................	.............................................	PUNCT
ejpam-4453	208	3	.	.	PUNCT
ejpam-4453	209	1	..........	..........	PUNCT
ejpam-4453	209	2	.............................................	.............................................	PUNCT
ejpam-4453	209	3	.	.	PUNCT
ejpam-4453	210	1	.........	.........	PUNCT
ejpam-4453	210	2	........	........	PUNCT
ejpam-4453	210	3	........	........	PUNCT
ejpam-4453	210	4	........	........	PUNCT
ejpam-4453	211	1	........	........	PUNCT
ejpam-4453	211	2	.	.	PUNCT
ejpam-4453	212	1	..........	..........	PUNCT
ejpam-4453	212	2	.............................................	.............................................	PUNCT
ejpam-4453	212	3	.	.	PUNCT
ejpam-4453	213	1	..........	..........	PUNCT
ejpam-4453	213	2	.............................................	.............................................	PUNCT
ejpam-4453	213	3	.	.	PUNCT
ejpam-4453	214	1	.........	.........	PUNCT
ejpam-4453	214	2	........	........	PUNCT
ejpam-4453	214	3	........	........	PUNCT
ejpam-4453	214	4	........	........	PUNCT
ejpam-4453	215	1	........	........	PUNCT
ejpam-4453	215	2	.	.	PUNCT
ejpam-4453	216	1	..........	..........	PUNCT
ejpam-4453	216	2	.............................................	.............................................	PUNCT
ejpam-4453	216	3	.	.	PUNCT
ejpam-4453	217	1	..........	..........	PUNCT
ejpam-4453	217	2	.............................................	.............................................	PUNCT
ejpam-4453	217	3	.	.	PUNCT
ejpam-4453	218	1	c	c	NOUN
ejpam-4453	218	2	∗	∗	PROPN
ejpam-4453	218	3	3	3	NUM
ejpam-4453	218	4	...	...	PUNCT
ejpam-4453	218	5	....................................................	....................................................	PUNCT
ejpam-4453	218	6	.............................................	.............................................	PUNCT
ejpam-4453	218	7	.	.	PUNCT
ejpam-4453	218	8	....................................................	....................................................	PUNCT
ejpam-4453	218	9	.............................................	.............................................	PUNCT
ejpam-4453	218	10	.	.	PUNCT
ejpam-4453	219	1	..........	..........	PUNCT
ejpam-4453	219	2	.............................................	.............................................	PUNCT
ejpam-4453	219	3	.	.	PUNCT
ejpam-4453	220	1	....................................................	....................................................	PUNCT
ejpam-4453	220	2	.............................................	.............................................	PUNCT
ejpam-4453	220	3	.	.	PUNCT
ejpam-4453	221	1	....................................................	....................................................	PUNCT
ejpam-4453	221	2	.............................................	.............................................	PUNCT
ejpam-4453	221	3	.	.	PUNCT
ejpam-4453	222	1	..........	..........	PUNCT
ejpam-4453	222	2	.............................................	.............................................	PUNCT
ejpam-4453	222	3	.	.	PUNCT
ejpam-4453	223	1	.........	.........	PUNCT
ejpam-4453	223	2	........	........	PUNCT
ejpam-4453	223	3	........	........	PUNCT
ejpam-4453	223	4	........	........	PUNCT
ejpam-4453	224	1	........	........	PUNCT
ejpam-4453	224	2	.	.	PUNCT
ejpam-4453	225	1	..........	..........	PUNCT
ejpam-4453	225	2	.............................................	.............................................	PUNCT
ejpam-4453	225	3	.	.	PUNCT
ejpam-4453	226	1	..........	..........	PUNCT
ejpam-4453	226	2	.............................................	.............................................	PUNCT
ejpam-4453	226	3	.	.	PUNCT
ejpam-4453	227	1	.........	.........	PUNCT
ejpam-4453	227	2	........	........	PUNCT
ejpam-4453	227	3	........	........	PUNCT
ejpam-4453	227	4	........	........	PUNCT
ejpam-4453	228	1	........	........	PUNCT
ejpam-4453	228	2	.	.	PUNCT
ejpam-4453	229	1	..........	..........	PUNCT
ejpam-4453	229	2	.............................................	.............................................	PUNCT
ejpam-4453	229	3	.	.	PUNCT
ejpam-4453	230	1	..........	..........	PUNCT
ejpam-4453	230	2	.............................................	.............................................	PUNCT
ejpam-4453	230	3	.	.	PUNCT
ejpam-4453	231	1	...........................................	...........................................	PUNCT
ejpam-4453	231	2	.............................................	.............................................	PUNCT
ejpam-4453	231	3	.	.	PUNCT
ejpam-4453	232	1	..........	..........	PUNCT
ejpam-4453	232	2	.............................................	.............................................	PUNCT
ejpam-4453	233	1	...........................................	...........................................	PUNCT
ejpam-4453	233	2	.........	.........	PUNCT
ejpam-4453	233	3	........	........	PUNCT
ejpam-4453	233	4	........	........	PUNCT
ejpam-4453	233	5	........	........	PUNCT
ejpam-4453	233	6	........	........	PUNCT
ejpam-4453	233	7	.	.	PUNCT
ejpam-4453	234	1	..........	..........	PUNCT
ejpam-4453	234	2	.............................................	.............................................	PUNCT
ejpam-4453	234	3	.	.	PUNCT
ejpam-4453	235	1	..........	..........	PUNCT
ejpam-4453	235	2	.............................................	.............................................	PUNCT
ejpam-4453	235	3	.	.	PUNCT
ejpam-4453	236	1	.........	.........	PUNCT
ejpam-4453	236	2	........	........	PUNCT
ejpam-4453	236	3	........	........	PUNCT
ejpam-4453	236	4	........	........	PUNCT
ejpam-4453	237	1	........	........	PUNCT
ejpam-4453	237	2	.	.	PUNCT
ejpam-4453	238	1	..........	..........	PUNCT
ejpam-4453	238	2	.............................................	.............................................	PUNCT
ejpam-4453	238	3	.	.	PUNCT
ejpam-4453	239	1	..........	..........	PUNCT
ejpam-4453	239	2	.............................................	.............................................	PUNCT
ejpam-4453	239	3	.	.	PUNCT
ejpam-4453	240	1	c	c	NOUN
ejpam-4453	240	2	∗	∗	PROPN
ejpam-4453	240	3	n	n	X
ejpam-4453	240	4	.....................................	.....................................	PUNCT
ejpam-4453	240	5	figure	figure	NOUN
ejpam-4453	240	6	3	3	NUM
ejpam-4453	240	7	:	:	PUNCT
ejpam-4453	240	8	possible	possible	ADJ
ejpam-4453	240	9	central	central	ADJ
ejpam-4453	240	10	fragment	fragment	NOUN
ejpam-4453	240	11	which	which	PRON
ejpam-4453	240	12	is	be	AUX
ejpam-4453	240	13	a	a	DET
ejpam-4453	240	14	tree	tree	NOUN
ejpam-4453	240	15	proposition	proposition	NOUN
ejpam-4453	240	16	1	1	NUM
ejpam-4453	240	17	.	.	PUNCT
ejpam-4453	241	1	any	any	DET
ejpam-4453	241	2	central	central	ADJ
ejpam-4453	241	3	fragment	fragment	NOUN
ejpam-4453	241	4	c	c	NOUN
ejpam-4453	241	5	∗	∗	NOUN
ejpam-4453	241	6	with	with	ADP
ejpam-4453	241	7	kc	kc	PROPN
ejpam-4453	241	8	-	-	PUNCT
ejpam-4453	241	9	leaves	leave	NOUN
ejpam-4453	241	10	has	have	VERB
ejpam-4453	241	11	|v	|v	VERB
ejpam-4453	241	12	(	(	PUNCT
ejpam-4453	241	13	c	c	NOUN
ejpam-4453	241	14	∗)|	∗)|	PROPN
ejpam-4453	241	15	=	=	SYM
ejpam-4453	241	16	2(kc	2(kc	PROPN
ejpam-4453	242	1	−	−	NOUN
ejpam-4453	242	2	1	1	NUM
ejpam-4453	242	3	)	)	PUNCT
ejpam-4453	242	4	where	where	SCONJ
ejpam-4453	242	5	kc	kc	PROPN
ejpam-4453	242	6	≥	≥	PROPN
ejpam-4453	242	7	3	3	NUM
ejpam-4453	242	8	.	.	PUNCT
ejpam-4453	242	9	proof	proof	NOUN
ejpam-4453	242	10	.	.	PUNCT
ejpam-4453	243	1	suppose	suppose	VERB
ejpam-4453	243	2	we	we	PRON
ejpam-4453	243	3	have	have	VERB
ejpam-4453	243	4	c	c	NOUN
ejpam-4453	243	5	∗.	∗.	ADP
ejpam-4453	243	6	then	then	ADV
ejpam-4453	243	7	it	it	PRON
ejpam-4453	243	8	contains	contain	VERB
ejpam-4453	243	9	vertices	vertex	NOUN
ejpam-4453	243	10	of	of	ADP
ejpam-4453	243	11	degree	degree	NOUN
ejpam-4453	243	12	1	1	NUM
ejpam-4453	243	13	and	and	CCONJ
ejpam-4453	243	14	of	of	ADP
ejpam-4453	243	15	degree	degree	NOUN
ejpam-4453	243	16	3	3	NUM
ejpam-4453	243	17	only	only	ADV
ejpam-4453	243	18	.	.	PUNCT
ejpam-4453	244	1	now	now	ADV
ejpam-4453	244	2	,	,	PUNCT
ejpam-4453	244	3	let	let	VERB
ejpam-4453	244	4	p	p	PRON
ejpam-4453	244	5	be	be	AUX
ejpam-4453	244	6	the	the	DET
ejpam-4453	244	7	number	number	NOUN
ejpam-4453	244	8	of	of	ADP
ejpam-4453	244	9	vertices	vertex	NOUN
ejpam-4453	244	10	of	of	ADP
ejpam-4453	244	11	degree	degree	NOUN
ejpam-4453	244	12	3	3	NUM
ejpam-4453	244	13	.	.	PUNCT
ejpam-4453	245	1	since	since	SCONJ
ejpam-4453	245	2	c	c	PROPN
ejpam-4453	245	3	∗	∗	NOUN
ejpam-4453	245	4	has	have	VERB
ejpam-4453	245	5	kc	kc	NOUN
ejpam-4453	245	6	-	-	PUNCT
ejpam-4453	245	7	leaves	leave	NOUN
ejpam-4453	245	8	and	and	CCONJ
ejpam-4453	245	9	by	by	ADP
ejpam-4453	245	10	theorems	theorem	NOUN
ejpam-4453	245	11	a.r	a.r	PROPN
ejpam-4453	245	12	nieva	nieva	PROPN
ejpam-4453	245	13	and	and	CCONJ
ejpam-4453	245	14	k.nocum	k.nocum	PROPN
ejpam-4453	245	15	/	/	SYM
ejpam-4453	245	16	eur	eur	PROPN
ejpam-4453	245	17	.	.	PUNCT
ejpam-4453	246	1	j.	j.	PROPN
ejpam-4453	246	2	pure	pure	PROPN
ejpam-4453	246	3	appl	appl	PROPN
ejpam-4453	246	4	.	.	PROPN
ejpam-4453	246	5	math	math	PROPN
ejpam-4453	246	6	,	,	PUNCT
ejpam-4453	246	7	15	15	NUM
ejpam-4453	246	8	(	(	PUNCT
ejpam-4453	246	9	4	4	NUM
ejpam-4453	246	10	)	)	PUNCT
ejpam-4453	246	11	(	(	PUNCT
ejpam-4453	246	12	2022	2022	NUM
ejpam-4453	246	13	)	)	PUNCT
ejpam-4453	246	14	,	,	PUNCT
ejpam-4453	246	15	1536	1536	NUM
ejpam-4453	246	16	-	-	SYM
ejpam-4453	246	17	1548	1548	NUM
ejpam-4453	246	18	1540	1540	NUM
ejpam-4453	246	19	5	5	NUM
ejpam-4453	246	20	and	and	CCONJ
ejpam-4453	246	21	6	6	NUM
ejpam-4453	246	22	,	,	PUNCT
ejpam-4453	246	23	p	p	NOUN
ejpam-4453	246	24	=	=	PUNCT
ejpam-4453	246	25	kc	kc	PROPN
ejpam-4453	246	26	−	−	PROPN
ejpam-4453	246	27	2	2	NUM
ejpam-4453	246	28	where	where	SCONJ
ejpam-4453	246	29	kc	kc	PROPN
ejpam-4453	246	30	≥	≥	PROPN
ejpam-4453	246	31	3	3	NUM
ejpam-4453	246	32	.	.	PUNCT
ejpam-4453	247	1	hence	hence	ADV
ejpam-4453	247	2	|v	|v	PROPN
ejpam-4453	247	3	(	(	PUNCT
ejpam-4453	247	4	c	c	NOUN
ejpam-4453	247	5	)	)	PUNCT
ejpam-4453	247	6	|	|	ADV
ejpam-4453	248	1	=	=	SYM
ejpam-4453	248	2	|leaf(c	|leaf(c	PROPN
ejpam-4453	248	3	∗)|	∗)|	PROPN
ejpam-4453	248	4	+	+	CCONJ
ejpam-4453	248	5	p	p	NOUN
ejpam-4453	248	6	and	and	CCONJ
ejpam-4453	248	7	it	it	PRON
ejpam-4453	248	8	implies	imply	VERB
ejpam-4453	248	9	that	that	SCONJ
ejpam-4453	248	10	|v	|v	PROPN
ejpam-4453	248	11	(	(	PUNCT
ejpam-4453	248	12	c	c	NOUN
ejpam-4453	248	13	∗)|	∗)|	PROPN
ejpam-4453	248	14	=	=	SYM
ejpam-4453	248	15	kc	kc	PROPN
ejpam-4453	249	1	+	+	CCONJ
ejpam-4453	249	2	kc	kc	PROPN
ejpam-4453	249	3	−	−	PROPN
ejpam-4453	249	4	2	2	NUM
ejpam-4453	249	5	=	=	SYM
ejpam-4453	249	6	2kc	2kc	ADJ
ejpam-4453	249	7	−	−	NOUN
ejpam-4453	249	8	2	2	NUM
ejpam-4453	249	9	=	=	SYM
ejpam-4453	249	10	2(kc	2(kc	NUM
ejpam-4453	250	1	−	−	NOUN
ejpam-4453	250	2	1	1	NUM
ejpam-4453	250	3	)	)	PUNCT
ejpam-4453	250	4	.	.	PUNCT
ejpam-4453	251	1	therefore	therefore	ADV
ejpam-4453	251	2	|v	|v	PROPN
ejpam-4453	251	3	(	(	PUNCT
ejpam-4453	251	4	c	c	NOUN
ejpam-4453	251	5	∗)|	∗)|	PROPN
ejpam-4453	251	6	=	=	SYM
ejpam-4453	251	7	2(kc	2(kc	PROPN
ejpam-4453	252	1	−	−	NOUN
ejpam-4453	252	2	1	1	NUM
ejpam-4453	252	3	)	)	PUNCT
ejpam-4453	252	4	where	where	SCONJ
ejpam-4453	252	5	kc	kc	PROPN
ejpam-4453	252	6	≥	≥	PROPN
ejpam-4453	252	7	3	3	NUM
ejpam-4453	252	8	.	.	PUNCT
ejpam-4453	252	9	remark	remark	NOUN
ejpam-4453	252	10	1	1	NUM
ejpam-4453	252	11	.	.	PUNCT
ejpam-4453	253	1	the	the	DET
ejpam-4453	253	2	order	order	NOUN
ejpam-4453	253	3	of	of	ADP
ejpam-4453	253	4	the	the	DET
ejpam-4453	253	5	central	central	ADJ
ejpam-4453	253	6	fragment	fragment	NOUN
ejpam-4453	253	7	which	which	PRON
ejpam-4453	253	8	is	be	AUX
ejpam-4453	253	9	a	a	DET
ejpam-4453	253	10	tree	tree	NOUN
ejpam-4453	253	11	can	can	AUX
ejpam-4453	253	12	be	be	AUX
ejpam-4453	253	13	simply	simply	ADV
ejpam-4453	253	14	determined	determine	VERB
ejpam-4453	253	15	by	by	ADP
ejpam-4453	253	16	the	the	DET
ejpam-4453	253	17	number	number	NOUN
ejpam-4453	253	18	of	of	ADP
ejpam-4453	253	19	its	its	PRON
ejpam-4453	253	20	end	end	NOUN
ejpam-4453	253	21	-	-	PUNCT
ejpam-4453	253	22	vertices	vertex	NOUN
ejpam-4453	253	23	,	,	PUNCT
ejpam-4453	253	24	that	that	ADV
ejpam-4453	253	25	is	is	ADV
ejpam-4453	253	26	,	,	PUNCT
ejpam-4453	253	27	|v	|v	PROPN
ejpam-4453	253	28	(	(	PUNCT
ejpam-4453	253	29	c	c	NOUN
ejpam-4453	253	30	∗)|	∗)|	PROPN
ejpam-4453	253	31	=	=	SYM
ejpam-4453	253	32	2(kc	2(kc	PROPN
ejpam-4453	254	1	−	−	NOUN
ejpam-4453	254	2	1	1	NUM
ejpam-4453	254	3	)	)	PUNCT
ejpam-4453	254	4	where	where	SCONJ
ejpam-4453	254	5	kc	kc	PROPN
ejpam-4453	254	6	is	be	AUX
ejpam-4453	254	7	the	the	DET
ejpam-4453	254	8	number	number	NOUN
ejpam-4453	254	9	of	of	ADP
ejpam-4453	254	10	its	its	PRON
ejpam-4453	254	11	end	end	NOUN
ejpam-4453	254	12	-	-	PUNCT
ejpam-4453	254	13	vertices	vertex	NOUN
ejpam-4453	254	14	.	.	PUNCT
ejpam-4453	255	1	we	we	PRON
ejpam-4453	255	2	can	can	AUX
ejpam-4453	255	3	also	also	ADV
ejpam-4453	255	4	determine	determine	VERB
ejpam-4453	255	5	it	it	PRON
ejpam-4453	255	6	by	by	ADP
ejpam-4453	255	7	the	the	DET
ejpam-4453	255	8	number	number	NOUN
ejpam-4453	255	9	of	of	ADP
ejpam-4453	255	10	its	its	PRON
ejpam-4453	255	11	vertices	vertex	NOUN
ejpam-4453	255	12	of	of	ADP
ejpam-4453	255	13	degree	degree	NOUN
ejpam-4453	255	14	3	3	NUM
ejpam-4453	255	15	,	,	PUNCT
ejpam-4453	255	16	that	that	ADV
ejpam-4453	255	17	is	is	ADV
ejpam-4453	255	18	,	,	PUNCT
ejpam-4453	255	19	|v	|v	PROPN
ejpam-4453	255	20	(	(	PUNCT
ejpam-4453	255	21	c	c	NOUN
ejpam-4453	255	22	∗)|	∗)|	PROPN
ejpam-4453	255	23	=	=	SYM
ejpam-4453	255	24	2(p+	2(p+	NUM
ejpam-4453	255	25	1	1	NUM
ejpam-4453	255	26	)	)	PUNCT
ejpam-4453	255	27	where	where	SCONJ
ejpam-4453	255	28	p	p	NOUN
ejpam-4453	255	29	is	be	AUX
ejpam-4453	255	30	the	the	DET
ejpam-4453	255	31	number	number	NOUN
ejpam-4453	255	32	of	of	ADP
ejpam-4453	255	33	its	its	PRON
ejpam-4453	255	34	vertices	vertex	NOUN
ejpam-4453	255	35	of	of	ADP
ejpam-4453	255	36	degree	degree	NOUN
ejpam-4453	255	37	3	3	NUM
ejpam-4453	255	38	.	.	X
ejpam-4453	256	1	for	for	ADP
ejpam-4453	256	2	instance	instance	NOUN
ejpam-4453	256	3	,	,	PUNCT
ejpam-4453	256	4	c	c	PROPN
ejpam-4453	256	5	is	be	AUX
ejpam-4453	256	6	no	no	ADV
ejpam-4453	256	7	longer	long	ADV
ejpam-4453	256	8	a	a	DET
ejpam-4453	256	9	tree	tree	NOUN
ejpam-4453	256	10	as	as	SCONJ
ejpam-4453	256	11	illustrated	illustrate	VERB
ejpam-4453	256	12	in	in	ADP
ejpam-4453	256	13	figure	figure	NOUN
ejpam-4453	256	14	4	4	NUM
ejpam-4453	256	15	(	(	PUNCT
ejpam-4453	256	16	b	b	NOUN
ejpam-4453	256	17	)	)	PUNCT
ejpam-4453	256	18	and	and	CCONJ
ejpam-4453	256	19	(	(	PUNCT
ejpam-4453	256	20	c	c	NOUN
ejpam-4453	256	21	)	)	PUNCT
ejpam-4453	256	22	.	.	PUNCT
ejpam-4453	257	1	this	this	PRON
ejpam-4453	257	2	can	can	AUX
ejpam-4453	257	3	be	be	AUX
ejpam-4453	257	4	done	do	VERB
ejpam-4453	257	5	by	by	ADP
ejpam-4453	257	6	extending	extend	VERB
ejpam-4453	257	7	a	a	DET
ejpam-4453	257	8	tree	tree	NOUN
ejpam-4453	257	9	c	c	NOUN
ejpam-4453	257	10	while	while	SCONJ
ejpam-4453	257	11	preserving	preserve	VERB
ejpam-4453	257	12	the	the	DET
ejpam-4453	257	13	number	number	NOUN
ejpam-4453	257	14	of	of	ADP
ejpam-4453	257	15	its	its	PRON
ejpam-4453	257	16	end	end	NOUN
ejpam-4453	257	17	-	-	PUNCT
ejpam-4453	257	18	vertices	vertex	NOUN
ejpam-4453	257	19	.	.	PUNCT
ejpam-4453	258	1	now	now	ADV
ejpam-4453	258	2	,	,	PUNCT
ejpam-4453	258	3	consider	consider	VERB
ejpam-4453	258	4	a	a	DET
ejpam-4453	258	5	central	central	ADJ
ejpam-4453	258	6	fragment	fragment	NOUN
ejpam-4453	258	7	having	have	VERB
ejpam-4453	258	8	fixed	fix	VERB
ejpam-4453	258	9	number	number	NOUN
ejpam-4453	258	10	of	of	ADP
ejpam-4453	258	11	end	end	NOUN
ejpam-4453	258	12	-	-	PUNCT
ejpam-4453	258	13	vertices	vertex	NOUN
ejpam-4453	258	14	that	that	PRON
ejpam-4453	258	15	is	be	AUX
ejpam-4453	258	16	3	3	NUM
ejpam-4453	258	17	shown	show	VERB
ejpam-4453	258	18	in	in	ADP
ejpam-4453	258	19	figure	figure	NOUN
ejpam-4453	258	20	4	4	NUM
ejpam-4453	258	21	(	(	PUNCT
ejpam-4453	258	22	a	a	NOUN
ejpam-4453	258	23	)	)	PUNCT
ejpam-4453	258	24	.	.	PUNCT
ejpam-4453	259	1	here	here	ADV
ejpam-4453	259	2	,	,	PUNCT
ejpam-4453	259	3	the	the	DET
ejpam-4453	259	4	new	new	ADJ
ejpam-4453	259	5	formed	form	VERB
ejpam-4453	259	6	graph	graph	NOUN
ejpam-4453	259	7	should	should	AUX
ejpam-4453	259	8	have	have	VERB
ejpam-4453	259	9	equal	equal	ADJ
ejpam-4453	259	10	number	number	NOUN
ejpam-4453	259	11	of	of	ADP
ejpam-4453	259	12	end	end	NOUN
ejpam-4453	259	13	-	-	PUNCT
ejpam-4453	259	14	vertices	vertex	NOUN
ejpam-4453	259	15	as	as	ADP
ejpam-4453	259	16	the	the	DET
ejpam-4453	259	17	base	base	NOUN
ejpam-4453	259	18	graph	graph	NOUN
ejpam-4453	259	19	which	which	PRON
ejpam-4453	259	20	forms	form	VERB
ejpam-4453	259	21	a	a	DET
ejpam-4453	259	22	new	new	ADJ
ejpam-4453	259	23	central	central	ADJ
ejpam-4453	259	24	fragment	fragment	NOUN
ejpam-4453	259	25	.	.	PUNCT
ejpam-4453	260	1	....................................................	....................................................	PUNCT
ejpam-4453	260	2	.............................................	.............................................	PUNCT
ejpam-4453	260	3	.	.	PUNCT
ejpam-4453	261	1	....................................................	....................................................	PUNCT
ejpam-4453	261	2	.............................................	.............................................	PUNCT
ejpam-4453	261	3	.	.	PUNCT
ejpam-4453	262	1	..........	..........	PUNCT
ejpam-4453	262	2	.............................................	.............................................	PUNCT
ejpam-4453	262	3	.	.	PUNCT
ejpam-4453	263	1	p	p	X
ejpam-4453	263	2	=	=	SYM
ejpam-4453	263	3	1	1	NUM
ejpam-4453	263	4	(	(	PUNCT
ejpam-4453	263	5	a	a	NOUN
ejpam-4453	263	6	)	)	PUNCT
ejpam-4453	263	7	.........	.........	PUNCT
ejpam-4453	263	8	........	........	PUNCT
ejpam-4453	263	9	........	........	PUNCT
ejpam-4453	263	10	........	........	PUNCT
ejpam-4453	263	11	........	........	PUNCT
ejpam-4453	263	12	.	.	PUNCT
ejpam-4453	263	13	..........	..........	PUNCT
ejpam-4453	263	14	.............................................	.............................................	PUNCT
ejpam-4453	263	15	.	.	PUNCT
ejpam-4453	263	16	..........	..........	PUNCT
ejpam-4453	264	1	.............................................	.............................................	PUNCT
ejpam-4453	264	2	..	..	PUNCT
ejpam-4453	265	1	(	(	PUNCT
ejpam-4453	265	2	b	b	X
ejpam-4453	265	3	)	)	PUNCT
ejpam-4453	265	4	p	p	NOUN
ejpam-4453	265	5	=	=	SYM
ejpam-4453	265	6	3	3	NUM
ejpam-4453	265	7	....................................................	....................................................	PUNCT
ejpam-4453	265	8	.............................................	.............................................	PUNCT
ejpam-4453	265	9	.	.	PUNCT
ejpam-4453	265	10	....................................................	....................................................	PUNCT
ejpam-4453	265	11	.............................................	.............................................	PUNCT
ejpam-4453	265	12	.	.	PUNCT
ejpam-4453	265	13	....................................................	....................................................	PUNCT
ejpam-4453	265	14	.............................................	.............................................	PUNCT
ejpam-4453	265	15	.	.	PUNCT
ejpam-4453	266	1	..........	..........	PUNCT
ejpam-4453	266	2	.............................................	.............................................	PUNCT
ejpam-4453	266	3	.	.	PUNCT
ejpam-4453	267	1	.........	.........	PUNCT
ejpam-4453	267	2	........	........	PUNCT
ejpam-4453	267	3	........	........	PUNCT
ejpam-4453	267	4	........	........	PUNCT
ejpam-4453	268	1	........	........	PUNCT
ejpam-4453	268	2	.	.	PUNCT
ejpam-4453	269	1	..........	..........	PUNCT
ejpam-4453	269	2	.............................................	.............................................	PUNCT
ejpam-4453	269	3	.	.	PUNCT
ejpam-4453	270	1	.........	.........	PUNCT
ejpam-4453	270	2	........	........	PUNCT
ejpam-4453	270	3	........	........	PUNCT
ejpam-4453	270	4	........	........	PUNCT
ejpam-4453	271	1	........	........	PUNCT
ejpam-4453	271	2	.	.	PUNCT
ejpam-4453	272	1	..........	..........	PUNCT
ejpam-4453	272	2	.............................................	.............................................	PUNCT
ejpam-4453	272	3	.	.	PUNCT
ejpam-4453	273	1	..........	..........	PUNCT
ejpam-4453	273	2	.............................................	.............................................	PUNCT
ejpam-4453	273	3	.	.	PUNCT
ejpam-4453	274	1	.................................................................	.................................................................	PUNCT
ejpam-4453	275	1	..........	..........	PUNCT
ejpam-4453	275	2	.............................................	.............................................	PUNCT
ejpam-4453	275	3	.	.	PUNCT
ejpam-4453	276	1	..........	..........	PUNCT
ejpam-4453	276	2	.............................................	.............................................	PUNCT
ejpam-4453	276	3	.	.	PUNCT
ejpam-4453	277	1	v1	v1	VERB
ejpam-4453	277	2	v2	v2	NOUN
ejpam-4453	277	3	...	...	PUNCT
ejpam-4453	278	1	p	p	X
ejpam-4453	278	2	=	=	SYM
ejpam-4453	278	3	5	5	NUM
ejpam-4453	278	4	(	(	PUNCT
ejpam-4453	278	5	c	c	NOUN
ejpam-4453	278	6	)	)	PUNCT
ejpam-4453	278	7	....................................................	....................................................	PUNCT
ejpam-4453	278	8	.............................................	.............................................	PUNCT
ejpam-4453	278	9	.	.	PUNCT
ejpam-4453	278	10	....................................................	....................................................	PUNCT
ejpam-4453	278	11	.............................................	.............................................	PUNCT
ejpam-4453	278	12	.	.	PUNCT
ejpam-4453	278	13	....................................................	....................................................	PUNCT
ejpam-4453	278	14	.............................................	.............................................	PUNCT
ejpam-4453	278	15	.	.	PUNCT
ejpam-4453	278	16	....................................................	....................................................	PUNCT
ejpam-4453	278	17	.............................................	.............................................	PUNCT
ejpam-4453	278	18	.	.	PUNCT
ejpam-4453	278	19	....................................................	....................................................	PUNCT
ejpam-4453	278	20	.............................................	.............................................	PUNCT
ejpam-4453	278	21	.	.	PUNCT
ejpam-4453	279	1	..........	..........	PUNCT
ejpam-4453	279	2	.............................................	.............................................	PUNCT
ejpam-4453	279	3	.	.	PUNCT
ejpam-4453	280	1	.........	.........	PUNCT
ejpam-4453	280	2	........	........	PUNCT
ejpam-4453	280	3	........	........	PUNCT
ejpam-4453	280	4	........	........	PUNCT
ejpam-4453	281	1	........	........	PUNCT
ejpam-4453	281	2	.	.	PUNCT
ejpam-4453	282	1	..........	..........	PUNCT
ejpam-4453	282	2	.............................................	.............................................	PUNCT
ejpam-4453	282	3	.	.	PUNCT
ejpam-4453	283	1	.........	.........	PUNCT
ejpam-4453	283	2	........	........	PUNCT
ejpam-4453	283	3	........	........	PUNCT
ejpam-4453	283	4	........	........	PUNCT
ejpam-4453	284	1	........	........	PUNCT
ejpam-4453	284	2	.	.	PUNCT
ejpam-4453	285	1	..........	..........	PUNCT
ejpam-4453	285	2	.............................................	.............................................	PUNCT
ejpam-4453	285	3	.	.	PUNCT
ejpam-4453	286	1	..........	..........	PUNCT
ejpam-4453	286	2	.............................................	.............................................	PUNCT
ejpam-4453	286	3	.	.	PUNCT
ejpam-4453	287	1	.................................................................	.................................................................	PUNCT
ejpam-4453	288	1	..........	..........	PUNCT
ejpam-4453	288	2	.............................................	.............................................	PUNCT
ejpam-4453	288	3	.	.	PUNCT
ejpam-4453	289	1	..........	..........	PUNCT
ejpam-4453	289	2	.............................................	.............................................	PUNCT
ejpam-4453	290	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4453	290	2	................	................	PUNCT
ejpam-4453	290	3	.............	.............	PUNCT
ejpam-4453	290	4	............	............	PUNCT
ejpam-4453	290	5	...........	...........	PUNCT
ejpam-4453	290	6	...........	...........	PUNCT
ejpam-4453	290	7	..	..	PUNCT
ejpam-4453	291	1	v4	v4	NOUN
ejpam-4453	291	2	v1	v1	PROPN
ejpam-4453	291	3	v2	v2	PROPN
ejpam-4453	291	4	v3	v3	PROPN
ejpam-4453	291	5	....	....	PUNCT
ejpam-4453	291	6	.	.	PUNCT
ejpam-4453	292	1	figure	figure	VERB
ejpam-4453	292	2	4	4	NUM
ejpam-4453	292	3	:	:	PUNCT
ejpam-4453	292	4	construction	construction	NOUN
ejpam-4453	292	5	sequence	sequence	NOUN
ejpam-4453	292	6	from	from	ADP
ejpam-4453	292	7	c	c	NOUN
ejpam-4453	292	8	∗	∗	NOUN
ejpam-4453	292	9	to	to	ADP
ejpam-4453	292	10	c	c	PROPN
ejpam-4453	292	11	∗∗	∗∗	PROPN
ejpam-4453	292	12	where	where	SCONJ
ejpam-4453	292	13	kc	kc	PROPN
ejpam-4453	292	14	=	=	NOUN
ejpam-4453	292	15	3	3	NUM
ejpam-4453	292	16	we	we	PRON
ejpam-4453	292	17	can	can	AUX
ejpam-4453	292	18	further	far	ADV
ejpam-4453	292	19	extend	extend	VERB
ejpam-4453	292	20	a	a	DET
ejpam-4453	292	21	central	central	ADJ
ejpam-4453	292	22	fragment	fragment	NOUN
ejpam-4453	292	23	which	which	PRON
ejpam-4453	292	24	is	be	AUX
ejpam-4453	292	25	a	a	DET
ejpam-4453	292	26	tree	tree	NOUN
ejpam-4453	292	27	with	with	ADP
ejpam-4453	292	28	n	n	NOUN
ejpam-4453	292	29	end	end	NOUN
ejpam-4453	292	30	-	-	PUNCT
ejpam-4453	292	31	vertices	vertex	NOUN
ejpam-4453	292	32	as	as	SCONJ
ejpam-4453	292	33	shown	show	VERB
ejpam-4453	292	34	in	in	ADP
ejpam-4453	292	35	figures	figure	NOUN
ejpam-4453	292	36	5	5	NUM
ejpam-4453	292	37	and	and	CCONJ
ejpam-4453	292	38	6	6	NUM
ejpam-4453	292	39	.	.	PUNCT
ejpam-4453	293	1	noticed	notice	VERB
ejpam-4453	293	2	that	that	SCONJ
ejpam-4453	293	3	each	each	DET
ejpam-4453	293	4	time	time	NOUN
ejpam-4453	293	5	we	we	PRON
ejpam-4453	293	6	extend	extend	VERB
ejpam-4453	293	7	a	a	DET
ejpam-4453	293	8	central	central	ADJ
ejpam-4453	293	9	fragment	fragment	NOUN
ejpam-4453	293	10	we	we	PRON
ejpam-4453	293	11	add	add	VERB
ejpam-4453	293	12	2(m−	2(m−	NUM
ejpam-4453	293	13	1	1	NUM
ejpam-4453	293	14	)	)	PUNCT
ejpam-4453	293	15	vertices	vertice	VERB
ejpam-4453	293	16	to	to	PART
ejpam-4453	293	17	preserve	preserve	VERB
ejpam-4453	293	18	the	the	DET
ejpam-4453	293	19	number	number	NOUN
ejpam-4453	293	20	of	of	ADP
ejpam-4453	293	21	its	its	PRON
ejpam-4453	293	22	end	end	NOUN
ejpam-4453	293	23	-	-	PUNCT
ejpam-4453	293	24	vertices	vertex	NOUN
ejpam-4453	293	25	and	and	CCONJ
ejpam-4453	293	26	to	to	PART
ejpam-4453	293	27	satisfy	satisfy	VERB
ejpam-4453	293	28	definition	definition	NOUN
ejpam-4453	293	29	1	1	NUM
ejpam-4453	293	30	.	.	PUNCT
ejpam-4453	294	1	p	p	X
ejpam-4453	294	2	=	=	SYM
ejpam-4453	294	3	2	2	NUM
ejpam-4453	294	4	....................................................	....................................................	PUNCT
ejpam-4453	294	5	.............................................	.............................................	PUNCT
ejpam-4453	294	6	.	.	PUNCT
ejpam-4453	294	7	....................................................	....................................................	PUNCT
ejpam-4453	294	8	.............................................	.............................................	PUNCT
ejpam-4453	294	9	.	.	PUNCT
ejpam-4453	294	10	....................................................	....................................................	PUNCT
ejpam-4453	294	11	.............................................	.............................................	PUNCT
ejpam-4453	294	12	.	.	PUNCT
ejpam-4453	295	1	..........	..........	PUNCT
ejpam-4453	295	2	.............................................	.............................................	PUNCT
ejpam-4453	295	3	.	.	PUNCT
ejpam-4453	296	1	.........	.........	PUNCT
ejpam-4453	296	2	........	........	PUNCT
ejpam-4453	296	3	........	........	PUNCT
ejpam-4453	296	4	........	........	PUNCT
ejpam-4453	297	1	........	........	PUNCT
ejpam-4453	297	2	.	.	PUNCT
ejpam-4453	298	1	..........	..........	PUNCT
ejpam-4453	298	2	.............................................	.............................................	PUNCT
ejpam-4453	298	3	.	.	PUNCT
ejpam-4453	299	1	..........	..........	PUNCT
ejpam-4453	299	2	.............................................	.............................................	PUNCT
ejpam-4453	299	3	.	.	PUNCT
ejpam-4453	300	1	.........	.........	PUNCT
ejpam-4453	300	2	........	........	PUNCT
ejpam-4453	300	3	........	........	PUNCT
ejpam-4453	300	4	........	........	PUNCT
ejpam-4453	301	1	........	........	PUNCT
ejpam-4453	301	2	.	.	PUNCT
ejpam-4453	302	1	..........	..........	PUNCT
ejpam-4453	302	2	.............................................	.............................................	PUNCT
ejpam-4453	302	3	.	.	PUNCT
ejpam-4453	303	1	..........	..........	PUNCT
ejpam-4453	303	2	.............................................	.............................................	PUNCT
ejpam-4453	304	1	...	...	PUNCT
ejpam-4453	305	1	p	p	X
ejpam-4453	305	2	=	=	PUNCT
ejpam-4453	305	3	4	4	NUM
ejpam-4453	305	4	....................................................	....................................................	PUNCT
ejpam-4453	305	5	.............................................	.............................................	PUNCT
ejpam-4453	305	6	.	.	PUNCT
ejpam-4453	305	7	....................................................	....................................................	PUNCT
ejpam-4453	305	8	.............................................	.............................................	PUNCT
ejpam-4453	305	9	.	.	PUNCT
ejpam-4453	305	10	....................................................	....................................................	PUNCT
ejpam-4453	305	11	.............................................	.............................................	PUNCT
ejpam-4453	305	12	.	.	PUNCT
ejpam-4453	305	13	..........	..........	PUNCT
ejpam-4453	305	14	.............................................	.............................................	PUNCT
ejpam-4453	305	15	.	.	PUNCT
ejpam-4453	305	16	.........	.........	PUNCT
ejpam-4453	305	17	........	........	PUNCT
ejpam-4453	305	18	........	........	PUNCT
ejpam-4453	305	19	........	........	PUNCT
ejpam-4453	305	20	........	........	PUNCT
ejpam-4453	305	21	.	.	PUNCT
ejpam-4453	305	22	..........	..........	PUNCT
ejpam-4453	305	23	.............................................	.............................................	PUNCT
ejpam-4453	305	24	.	.	PUNCT
ejpam-4453	305	25	.........	.........	PUNCT
ejpam-4453	305	26	........	........	PUNCT
ejpam-4453	305	27	........	........	PUNCT
ejpam-4453	305	28	........	........	PUNCT
ejpam-4453	305	29	........	........	PUNCT
ejpam-4453	305	30	.	.	PUNCT
ejpam-4453	305	31	..........	..........	PUNCT
ejpam-4453	305	32	.............................................	.............................................	PUNCT
ejpam-4453	305	33	.	.	PUNCT
ejpam-4453	305	34	..........	..........	PUNCT
ejpam-4453	305	35	.............................................	.............................................	PUNCT
ejpam-4453	305	36	.	.	PUNCT
ejpam-4453	305	37	.........	.........	PUNCT
ejpam-4453	305	38	........	........	PUNCT
ejpam-4453	305	39	........	........	PUNCT
ejpam-4453	305	40	........	........	PUNCT
ejpam-4453	305	41	........	........	PUNCT
ejpam-4453	305	42	.	.	PUNCT
ejpam-4453	305	43	..........	..........	PUNCT
ejpam-4453	305	44	.............................................	.............................................	PUNCT
ejpam-4453	305	45	.	.	PUNCT
ejpam-4453	305	46	.........	.........	PUNCT
ejpam-4453	305	47	........	........	PUNCT
ejpam-4453	305	48	........	........	PUNCT
ejpam-4453	305	49	........	........	PUNCT
ejpam-4453	305	50	........	........	PUNCT
ejpam-4453	305	51	.	.	PUNCT
ejpam-4453	305	52	..........	..........	PUNCT
ejpam-4453	305	53	.............................................	.............................................	PUNCT
ejpam-4453	305	54	.	.	PUNCT
ejpam-4453	305	55	..........	..........	PUNCT
ejpam-4453	305	56	.............................................	.............................................	PUNCT
ejpam-4453	305	57	.	.	PUNCT
ejpam-4453	305	58	..........................................	..........................................	PUNCT
ejpam-4453	305	59	....................................................	....................................................	PUNCT
ejpam-4453	305	60	.............................................	.............................................	PUNCT
ejpam-4453	305	61	.	.	PUNCT
ejpam-4453	306	1	..........	..........	PUNCT
ejpam-4453	306	2	.............................................	.............................................	PUNCT
ejpam-4453	307	1	.v1v2	.v1v2	PUNCT
ejpam-4453	307	2	....	....	PUNCT
ejpam-4453	308	1	p	p	X
ejpam-4453	308	2	=	=	PUNCT
ejpam-4453	308	3	6	6	NUM
ejpam-4453	308	4	....................................................	....................................................	PUNCT
ejpam-4453	308	5	.............................................	.............................................	PUNCT
ejpam-4453	308	6	.	.	PUNCT
ejpam-4453	308	7	....................................................	....................................................	PUNCT
ejpam-4453	308	8	.............................................	.............................................	PUNCT
ejpam-4453	308	9	.	.	PUNCT
ejpam-4453	308	10	....................................................	....................................................	PUNCT
ejpam-4453	308	11	.............................................	.............................................	PUNCT
ejpam-4453	308	12	.	.	PUNCT
ejpam-4453	308	13	....................................................	....................................................	PUNCT
ejpam-4453	308	14	.............................................	.............................................	PUNCT
ejpam-4453	308	15	.	.	PUNCT
ejpam-4453	308	16	....................................................	....................................................	PUNCT
ejpam-4453	308	17	.............................................	.............................................	PUNCT
ejpam-4453	308	18	.	.	PUNCT
ejpam-4453	309	1	..........	..........	PUNCT
ejpam-4453	309	2	.............................................	.............................................	PUNCT
ejpam-4453	309	3	.	.	PUNCT
ejpam-4453	310	1	.........	.........	PUNCT
ejpam-4453	310	2	........	........	PUNCT
ejpam-4453	310	3	........	........	PUNCT
ejpam-4453	310	4	........	........	PUNCT
ejpam-4453	311	1	........	........	PUNCT
ejpam-4453	311	2	.	.	PUNCT
ejpam-4453	312	1	..........	..........	PUNCT
ejpam-4453	312	2	.............................................	.............................................	PUNCT
ejpam-4453	312	3	.	.	PUNCT
ejpam-4453	313	1	.........	.........	PUNCT
ejpam-4453	313	2	........	........	PUNCT
ejpam-4453	313	3	........	........	PUNCT
ejpam-4453	313	4	........	........	PUNCT
ejpam-4453	314	1	........	........	PUNCT
ejpam-4453	314	2	.	.	PUNCT
ejpam-4453	315	1	..........	..........	PUNCT
ejpam-4453	315	2	.............................................	.............................................	PUNCT
ejpam-4453	315	3	.	.	PUNCT
ejpam-4453	316	1	..........	..........	PUNCT
ejpam-4453	316	2	.............................................	.............................................	PUNCT
ejpam-4453	316	3	.	.	PUNCT
ejpam-4453	317	1	.........	.........	PUNCT
ejpam-4453	317	2	........	........	PUNCT
ejpam-4453	317	3	........	........	PUNCT
ejpam-4453	317	4	........	........	PUNCT
ejpam-4453	318	1	........	........	PUNCT
ejpam-4453	318	2	.	.	PUNCT
ejpam-4453	319	1	..........	..........	PUNCT
ejpam-4453	319	2	.............................................	.............................................	PUNCT
ejpam-4453	319	3	.	.	PUNCT
ejpam-4453	320	1	.........	.........	PUNCT
ejpam-4453	320	2	........	........	PUNCT
ejpam-4453	320	3	........	........	PUNCT
ejpam-4453	320	4	........	........	PUNCT
ejpam-4453	321	1	........	........	PUNCT
ejpam-4453	321	2	.	.	PUNCT
ejpam-4453	322	1	..........	..........	PUNCT
ejpam-4453	322	2	.............................................	.............................................	PUNCT
ejpam-4453	322	3	.	.	PUNCT
ejpam-4453	323	1	..........	..........	PUNCT
ejpam-4453	323	2	.............................................	.............................................	PUNCT
ejpam-4453	323	3	.	.	PUNCT
ejpam-4453	324	1	..........................................	..........................................	PUNCT
ejpam-4453	324	2	....................................................	....................................................	PUNCT
ejpam-4453	325	1	.............................................	.............................................	PUNCT
ejpam-4453	325	2	.	.	PUNCT
ejpam-4453	326	1	..........	..........	PUNCT
ejpam-4453	326	2	.............................................	.............................................	PUNCT
ejpam-4453	326	3	.	.	PUNCT
ejpam-4453	327	1	.................................................................................................................................	.................................................................................................................................	PUNCT
ejpam-4453	327	2	.....................	.....................	PUNCT
ejpam-4453	328	1	.................	.................	PUNCT
ejpam-4453	329	1	v1v2	v1v2	X
ejpam-4453	329	2	v3	v3	PROPN
ejpam-4453	329	3	v2	v2	PROPN
ejpam-4453	329	4	.....	.....	PUNCT
ejpam-4453	329	5	.	.	PUNCT
ejpam-4453	330	1	figure	figure	VERB
ejpam-4453	330	2	5	5	NUM
ejpam-4453	330	3	:	:	PUNCT
ejpam-4453	330	4	construction	construction	NOUN
ejpam-4453	330	5	sequence	sequence	NOUN
ejpam-4453	330	6	from	from	ADP
ejpam-4453	330	7	c	c	NOUN
ejpam-4453	330	8	∗	∗	NOUN
ejpam-4453	330	9	to	to	ADP
ejpam-4453	330	10	c	c	PROPN
ejpam-4453	330	11	∗∗	∗∗	PROPN
ejpam-4453	330	12	where	where	SCONJ
ejpam-4453	330	13	kc	kc	PROPN
ejpam-4453	330	14	=	=	PROPN
ejpam-4453	330	15	4	4	NUM
ejpam-4453	330	16	..........	..........	PUNCT
ejpam-4453	330	17	.............................................	.............................................	PUNCT
ejpam-4453	330	18	.	.	PUNCT
ejpam-4453	331	1	..........	..........	PUNCT
ejpam-4453	331	2	.............................................	.............................................	PUNCT
ejpam-4453	331	3	.	.	PUNCT
ejpam-4453	332	1	..........	..........	PUNCT
ejpam-4453	332	2	.............................................	.............................................	PUNCT
ejpam-4453	332	3	.	.	PUNCT
ejpam-4453	333	1	..........	..........	PUNCT
ejpam-4453	333	2	.............................................	.............................................	PUNCT
ejpam-4453	333	3	.	.	PUNCT
ejpam-4453	334	1	..........	..........	PUNCT
ejpam-4453	334	2	.............................................	.............................................	PUNCT
ejpam-4453	334	3	.	.	PUNCT
ejpam-4453	335	1	..........	..........	PUNCT
ejpam-4453	335	2	.............................................	.............................................	PUNCT
ejpam-4453	335	3	.	.	PUNCT
ejpam-4453	336	1	..........	..........	PUNCT
ejpam-4453	336	2	.............................................	.............................................	PUNCT
ejpam-4453	336	3	.	.	PUNCT
ejpam-4453	337	1	..........	..........	PUNCT
ejpam-4453	337	2	.............................................	.............................................	PUNCT
ejpam-4453	337	3	.	.	PUNCT
ejpam-4453	338	1	..........	..........	PUNCT
ejpam-4453	338	2	.............................................	.............................................	PUNCT
ejpam-4453	338	3	.	.	PUNCT
ejpam-4453	339	1	..........	..........	PUNCT
ejpam-4453	339	2	.............................................	.............................................	PUNCT
ejpam-4453	339	3	.	.	PUNCT
ejpam-4453	340	1	..........................................	..........................................	PUNCT
ejpam-4453	340	2	..........................................	..........................................	PUNCT
ejpam-4453	341	1	.........	.........	PUNCT
ejpam-4453	341	2	........	........	PUNCT
ejpam-4453	341	3	........	........	PUNCT
ejpam-4453	341	4	........	........	PUNCT
ejpam-4453	342	1	........	........	PUNCT
ejpam-4453	342	2	.	.	PUNCT
ejpam-4453	343	1	.........	.........	PUNCT
ejpam-4453	343	2	........	........	PUNCT
ejpam-4453	343	3	........	........	PUNCT
ejpam-4453	343	4	........	........	PUNCT
ejpam-4453	344	1	........	........	PUNCT
ejpam-4453	344	2	.	.	PUNCT
ejpam-4453	345	1	..........................................	..........................................	PUNCT
ejpam-4453	345	2	.........	.........	PUNCT
ejpam-4453	346	1	........	........	PUNCT
ejpam-4453	346	2	........	........	PUNCT
ejpam-4453	346	3	........	........	PUNCT
ejpam-4453	346	4	........	........	PUNCT
ejpam-4453	346	5	.	.	PUNCT
ejpam-4453	347	1	..........................................	..........................................	PUNCT
ejpam-4453	347	2	.........	.........	PUNCT
ejpam-4453	348	1	........	........	PUNCT
ejpam-4453	348	2	........	........	PUNCT
ejpam-4453	348	3	........	........	PUNCT
ejpam-4453	348	4	........	........	PUNCT
ejpam-4453	348	5	.	.	PUNCT
ejpam-4453	349	1	p	p	X
ejpam-4453	350	1	=	=	PUNCT
ejpam-4453	350	2	k	k	PROPN
ejpam-4453	350	3	−	−	PROPN
ejpam-4453	350	4	2	2	NUM
ejpam-4453	350	5	.....................................	.....................................	PUNCT
ejpam-4453	350	6	p	p	X
ejpam-4453	350	7	=	=	PUNCT
ejpam-4453	350	8	k	k	PROPN
ejpam-4453	350	9	..........	..........	PUNCT
ejpam-4453	350	10	.............................................	.............................................	PUNCT
ejpam-4453	350	11	.	.	PUNCT
ejpam-4453	350	12	..........	..........	PUNCT
ejpam-4453	350	13	.............................................	.............................................	PUNCT
ejpam-4453	350	14	.	.	PUNCT
ejpam-4453	350	15	..........	..........	PUNCT
ejpam-4453	350	16	.............................................	.............................................	PUNCT
ejpam-4453	350	17	.	.	PUNCT
ejpam-4453	350	18	..........	..........	PUNCT
ejpam-4453	350	19	.............................................	.............................................	PUNCT
ejpam-4453	350	20	.	.	PUNCT
ejpam-4453	350	21	..........	..........	PUNCT
ejpam-4453	350	22	.............................................	.............................................	PUNCT
ejpam-4453	350	23	.	.	PUNCT
ejpam-4453	350	24	..........	..........	PUNCT
ejpam-4453	350	25	.............................................	.............................................	PUNCT
ejpam-4453	350	26	.	.	PUNCT
ejpam-4453	350	27	..........	..........	PUNCT
ejpam-4453	350	28	.............................................	.............................................	PUNCT
ejpam-4453	350	29	.	.	PUNCT
ejpam-4453	350	30	..........	..........	PUNCT
ejpam-4453	350	31	.............................................	.............................................	PUNCT
ejpam-4453	350	32	.	.	PUNCT
ejpam-4453	350	33	..........	..........	PUNCT
ejpam-4453	350	34	.............................................	.............................................	PUNCT
ejpam-4453	350	35	.	.	PUNCT
ejpam-4453	350	36	..........	..........	PUNCT
ejpam-4453	350	37	.............................................	.............................................	PUNCT
ejpam-4453	350	38	.	.	PUNCT
ejpam-4453	350	39	..........	..........	PUNCT
ejpam-4453	350	40	.............................................	.............................................	PUNCT
ejpam-4453	350	41	.	.	PUNCT
ejpam-4453	350	42	..........	..........	PUNCT
ejpam-4453	350	43	.............................................	.............................................	PUNCT
ejpam-4453	350	44	.	.	PUNCT
ejpam-4453	350	45	..........................................	..........................................	PUNCT
ejpam-4453	350	46	..........................................	..........................................	PUNCT
ejpam-4453	350	47	.........	.........	PUNCT
ejpam-4453	350	48	........	........	PUNCT
ejpam-4453	350	49	........	........	PUNCT
ejpam-4453	350	50	........	........	PUNCT
ejpam-4453	350	51	........	........	PUNCT
ejpam-4453	350	52	.	.	PUNCT
ejpam-4453	350	53	.........	.........	PUNCT
ejpam-4453	350	54	........	........	PUNCT
ejpam-4453	350	55	........	........	PUNCT
ejpam-4453	350	56	........	........	PUNCT
ejpam-4453	350	57	........	........	PUNCT
ejpam-4453	350	58	.	.	PUNCT
ejpam-4453	350	59	.........	.........	PUNCT
ejpam-4453	350	60	........	........	PUNCT
ejpam-4453	350	61	........	........	PUNCT
ejpam-4453	350	62	........	........	PUNCT
ejpam-4453	350	63	........	........	PUNCT
ejpam-4453	350	64	.	.	PUNCT
ejpam-4453	350	65	............................................................................................................................................................	............................................................................................................................................................	PUNCT
ejpam-4453	350	66	..........................................	..........................................	PUNCT
ejpam-4453	350	67	.........	.........	PUNCT
ejpam-4453	350	68	........	........	PUNCT
ejpam-4453	350	69	........	........	PUNCT
ejpam-4453	350	70	........	........	PUNCT
ejpam-4453	350	71	........	........	PUNCT
ejpam-4453	350	72	.	.	PUNCT
ejpam-4453	350	73	..........................................	..........................................	PUNCT
ejpam-4453	350	74	.........	.........	PUNCT
ejpam-4453	350	75	........	........	PUNCT
ejpam-4453	350	76	........	........	PUNCT
ejpam-4453	350	77	........	........	PUNCT
ejpam-4453	350	78	........	........	PUNCT
ejpam-4453	350	79	.	.	PUNCT
ejpam-4453	350	80	.........	.........	PUNCT
ejpam-4453	350	81	........	........	PUNCT
ejpam-4453	350	82	........	........	PUNCT
ejpam-4453	350	83	........	........	PUNCT
ejpam-4453	350	84	........	........	PUNCT
ejpam-4453	350	85	.	.	PUNCT
ejpam-4453	350	86	......................................	......................................	PUNCT
ejpam-4453	350	87	.	.	PUNCT
ejpam-4453	351	1	p	p	X
ejpam-4453	352	1	=	=	PUNCT
ejpam-4453	352	2	k	k	PROPN
ejpam-4453	353	1	+	+	PROPN
ejpam-4453	353	2	2	2	NUM
ejpam-4453	353	3	..........	..........	PUNCT
ejpam-4453	353	4	.............................................	.............................................	PUNCT
ejpam-4453	353	5	.	.	PUNCT
ejpam-4453	354	1	..........	..........	PUNCT
ejpam-4453	354	2	.............................................	.............................................	PUNCT
ejpam-4453	354	3	.	.	PUNCT
ejpam-4453	355	1	..........	..........	PUNCT
ejpam-4453	355	2	.............................................	.............................................	PUNCT
ejpam-4453	355	3	.	.	PUNCT
ejpam-4453	356	1	..........	..........	PUNCT
ejpam-4453	356	2	.............................................	.............................................	PUNCT
ejpam-4453	356	3	.	.	PUNCT
ejpam-4453	357	1	..........	..........	PUNCT
ejpam-4453	357	2	.............................................	.............................................	PUNCT
ejpam-4453	357	3	.	.	PUNCT
ejpam-4453	358	1	..........	..........	PUNCT
ejpam-4453	358	2	.............................................	.............................................	PUNCT
ejpam-4453	358	3	.	.	PUNCT
ejpam-4453	359	1	..........	..........	PUNCT
ejpam-4453	359	2	.............................................	.............................................	PUNCT
ejpam-4453	359	3	.	.	PUNCT
ejpam-4453	360	1	..........	..........	PUNCT
ejpam-4453	360	2	.............................................	.............................................	PUNCT
ejpam-4453	360	3	.	.	PUNCT
ejpam-4453	361	1	..........	..........	PUNCT
ejpam-4453	361	2	.............................................	.............................................	PUNCT
ejpam-4453	361	3	.	.	PUNCT
ejpam-4453	362	1	..........	..........	PUNCT
ejpam-4453	362	2	.............................................	.............................................	PUNCT
ejpam-4453	362	3	.	.	PUNCT
ejpam-4453	363	1	..........	..........	PUNCT
ejpam-4453	363	2	.............................................	.............................................	PUNCT
ejpam-4453	363	3	.	.	PUNCT
ejpam-4453	364	1	..........	..........	PUNCT
ejpam-4453	364	2	.............................................	.............................................	PUNCT
ejpam-4453	364	3	.	.	PUNCT
ejpam-4453	365	1	..........................................	..........................................	PUNCT
ejpam-4453	365	2	..........................................	..........................................	PUNCT
ejpam-4453	366	1	.........	.........	PUNCT
ejpam-4453	366	2	........	........	PUNCT
ejpam-4453	366	3	........	........	PUNCT
ejpam-4453	366	4	........	........	PUNCT
ejpam-4453	367	1	........	........	PUNCT
ejpam-4453	367	2	.	.	PUNCT
ejpam-4453	368	1	.........	.........	PUNCT
ejpam-4453	368	2	........	........	PUNCT
ejpam-4453	368	3	........	........	PUNCT
ejpam-4453	368	4	........	........	PUNCT
ejpam-4453	369	1	........	........	PUNCT
ejpam-4453	369	2	.	.	PUNCT
ejpam-4453	370	1	.........	.........	PUNCT
ejpam-4453	370	2	........	........	PUNCT
ejpam-4453	370	3	........	........	PUNCT
ejpam-4453	370	4	........	........	PUNCT
ejpam-4453	371	1	........	........	PUNCT
ejpam-4453	371	2	.	.	PUNCT
ejpam-4453	372	1	............................................................................................................................................................	............................................................................................................................................................	PUNCT
ejpam-4453	372	2	..........................................	..........................................	PUNCT
ejpam-4453	373	1	.........	.........	PUNCT
ejpam-4453	373	2	........	........	PUNCT
ejpam-4453	373	3	........	........	PUNCT
ejpam-4453	373	4	........	........	PUNCT
ejpam-4453	373	5	........	........	PUNCT
ejpam-4453	373	6	.	.	PUNCT
ejpam-4453	374	1	..........................................	..........................................	PUNCT
ejpam-4453	374	2	.........	.........	PUNCT
ejpam-4453	375	1	........	........	PUNCT
ejpam-4453	375	2	........	........	PUNCT
ejpam-4453	375	3	........	........	PUNCT
ejpam-4453	375	4	........	........	PUNCT
ejpam-4453	375	5	.	.	PUNCT
ejpam-4453	376	1	.........	.........	PUNCT
ejpam-4453	376	2	........	........	PUNCT
ejpam-4453	376	3	........	........	PUNCT
ejpam-4453	376	4	........	........	PUNCT
ejpam-4453	377	1	........	........	PUNCT
ejpam-4453	377	2	.	.	PUNCT
ejpam-4453	378	1	............................................................................................................................................................	............................................................................................................................................................	PUNCT
ejpam-4453	378	2	......................................	......................................	PUNCT
ejpam-4453	378	3	..	..	PUNCT
ejpam-4453	378	4	.	.	PUNCT
ejpam-4453	379	1	figure	figure	VERB
ejpam-4453	379	2	6	6	NUM
ejpam-4453	379	3	:	:	PUNCT
ejpam-4453	379	4	construction	construction	NOUN
ejpam-4453	379	5	sequence	sequence	NOUN
ejpam-4453	379	6	from	from	ADP
ejpam-4453	379	7	c	c	NOUN
ejpam-4453	379	8	∗	∗	NOUN
ejpam-4453	379	9	to	to	ADP
ejpam-4453	379	10	c	c	PROPN
ejpam-4453	379	11	∗∗	∗∗	PROPN
ejpam-4453	379	12	where	where	SCONJ
ejpam-4453	379	13	kc	kc	PROPN
ejpam-4453	379	14	=	=	PUNCT
ejpam-4453	379	15	n	n	X
ejpam-4453	379	16	by	by	ADP
ejpam-4453	379	17	this	this	DET
ejpam-4453	379	18	observation	observation	NOUN
ejpam-4453	379	19	,	,	PUNCT
ejpam-4453	379	20	we	we	PRON
ejpam-4453	379	21	have	have	VERB
ejpam-4453	379	22	the	the	DET
ejpam-4453	379	23	following	follow	VERB
ejpam-4453	379	24	proposition	proposition	NOUN
ejpam-4453	379	25	.	.	PUNCT
ejpam-4453	380	1	a.r	a.r	PROPN
ejpam-4453	380	2	nieva	nieva	PROPN
ejpam-4453	380	3	and	and	CCONJ
ejpam-4453	380	4	k.nocum	k.nocum	PROPN
ejpam-4453	380	5	/	/	SYM
ejpam-4453	380	6	eur	eur	PROPN
ejpam-4453	380	7	.	.	PUNCT
ejpam-4453	381	1	j.	j.	PROPN
ejpam-4453	381	2	pure	pure	PROPN
ejpam-4453	381	3	appl	appl	PROPN
ejpam-4453	381	4	.	.	PROPN
ejpam-4453	381	5	math	math	PROPN
ejpam-4453	381	6	,	,	PUNCT
ejpam-4453	381	7	15	15	NUM
ejpam-4453	381	8	(	(	PUNCT
ejpam-4453	381	9	4	4	NUM
ejpam-4453	381	10	)	)	PUNCT
ejpam-4453	381	11	(	(	PUNCT
ejpam-4453	381	12	2022	2022	NUM
ejpam-4453	381	13	)	)	PUNCT
ejpam-4453	381	14	,	,	PUNCT
ejpam-4453	381	15	1536	1536	NUM
ejpam-4453	381	16	-	-	SYM
ejpam-4453	381	17	1548	1548	NUM
ejpam-4453	381	18	1541	1541	NUM
ejpam-4453	381	19	proposition	proposition	NOUN
ejpam-4453	381	20	2	2	NUM
ejpam-4453	381	21	.	.	PUNCT
ejpam-4453	382	1	let	let	VERB
ejpam-4453	382	2	c	c	NOUN
ejpam-4453	382	3	∗∗	∗∗	PROPN
ejpam-4453	382	4	be	be	AUX
ejpam-4453	382	5	a	a	DET
ejpam-4453	382	6	central	central	ADJ
ejpam-4453	382	7	fragment	fragment	NOUN
ejpam-4453	382	8	with	with	ADP
ejpam-4453	382	9	kc	kc	PROPN
ejpam-4453	382	10	-	-	PUNCT
ejpam-4453	382	11	leaves	leave	VERB
ejpam-4453	382	12	such	such	ADJ
ejpam-4453	382	13	that	that	SCONJ
ejpam-4453	382	14	kc	kc	PROPN
ejpam-4453	382	15	≥	≥	NUM
ejpam-4453	382	16	3	3	NUM
ejpam-4453	382	17	and	and	CCONJ
ejpam-4453	382	18	p′	p′	NOUN
ejpam-4453	382	19	be	be	AUX
ejpam-4453	382	20	the	the	DET
ejpam-4453	382	21	number	number	NOUN
ejpam-4453	382	22	of	of	ADP
ejpam-4453	382	23	vertices	vertex	NOUN
ejpam-4453	382	24	of	of	ADP
ejpam-4453	382	25	degree	degree	NOUN
ejpam-4453	382	26	3	3	NUM
ejpam-4453	382	27	in	in	ADP
ejpam-4453	382	28	c	c	PROPN
ejpam-4453	382	29	∗∗.	∗∗.	PROPN
ejpam-4453	382	30	then	then	ADV
ejpam-4453	382	31	p′	p′	NOUN
ejpam-4453	382	32	=	=	SYM
ejpam-4453	382	33	kc	kc	PROPN
ejpam-4453	383	1	−	−	PROPN
ejpam-4453	383	2	2(2−m	2(2−m	NUM
ejpam-4453	383	3	)	)	PUNCT
ejpam-4453	383	4	where	where	SCONJ
ejpam-4453	383	5	m	m	PROPN
ejpam-4453	383	6	∈	∈	PROPN
ejpam-4453	383	7	n.	n.	NOUN
ejpam-4453	383	8	proof	proof	NOUN
ejpam-4453	383	9	.	.	PUNCT
ejpam-4453	384	1	let	let	VERB
ejpam-4453	384	2	c	c	X
ejpam-4453	384	3	∗∗	∗∗	PROPN
ejpam-4453	384	4	be	be	AUX
ejpam-4453	384	5	a	a	DET
ejpam-4453	384	6	central	central	ADJ
ejpam-4453	384	7	fragment	fragment	NOUN
ejpam-4453	384	8	.	.	PUNCT
ejpam-4453	385	1	suppose	suppose	VERB
ejpam-4453	385	2	kc	kc	PROPN
ejpam-4453	385	3	≥	≥	PROPN
ejpam-4453	385	4	3	3	NUM
ejpam-4453	385	5	be	be	AUX
ejpam-4453	385	6	the	the	DET
ejpam-4453	385	7	number	number	NOUN
ejpam-4453	385	8	of	of	ADP
ejpam-4453	385	9	end	end	NOUN
ejpam-4453	385	10	-	-	PUNCT
ejpam-4453	385	11	vertices	vertex	NOUN
ejpam-4453	385	12	and	and	CCONJ
ejpam-4453	385	13	p′	p′	PRON
ejpam-4453	385	14	the	the	DET
ejpam-4453	385	15	number	number	NOUN
ejpam-4453	385	16	of	of	ADP
ejpam-4453	385	17	vertices	vertex	NOUN
ejpam-4453	385	18	of	of	ADP
ejpam-4453	385	19	degree	degree	NOUN
ejpam-4453	385	20	3	3	NUM
ejpam-4453	385	21	in	in	ADP
ejpam-4453	385	22	c	c	NOUN
ejpam-4453	385	23	∗∗.	∗∗.	NOUN
ejpam-4453	385	24	by	by	ADP
ejpam-4453	385	25	the	the	DET
ejpam-4453	385	26	remark	remark	NOUN
ejpam-4453	385	27	of	of	ADP
ejpam-4453	385	28	proposition	proposition	NOUN
ejpam-4453	385	29	1	1	NUM
ejpam-4453	385	30	,	,	PUNCT
ejpam-4453	385	31	we	we	PRON
ejpam-4453	385	32	have	have	VERB
ejpam-4453	385	33	|v	|v	VERB
ejpam-4453	385	34	(	(	PUNCT
ejpam-4453	385	35	c	c	NOUN
ejpam-4453	385	36	∗)|	∗)|	PROPN
ejpam-4453	386	1	=	=	SYM
ejpam-4453	386	2	kc	kc	PROPN
ejpam-4453	386	3	+	+	CCONJ
ejpam-4453	386	4	p′.	p′.	NOUN
ejpam-4453	386	5	also	also	ADV
ejpam-4453	386	6	,	,	PUNCT
ejpam-4453	386	7	note	note	VERB
ejpam-4453	386	8	that	that	SCONJ
ejpam-4453	386	9	for	for	ADP
ejpam-4453	386	10	m	m	PROPN
ejpam-4453	386	11	∈	∈	NOUN
ejpam-4453	386	12	n	n	PRON
ejpam-4453	386	13	we	we	PRON
ejpam-4453	386	14	add	add	VERB
ejpam-4453	386	15	2(m−	2(m−	NUM
ejpam-4453	386	16	1	1	NUM
ejpam-4453	386	17	)	)	PUNCT
ejpam-4453	386	18	vertices	vertex	NOUN
ejpam-4453	386	19	to	to	ADP
ejpam-4453	386	20	c	c	NOUN
ejpam-4453	386	21	∗	∗	NOUN
ejpam-4453	386	22	to	to	PART
ejpam-4453	386	23	form	form	VERB
ejpam-4453	386	24	c	c	PROPN
ejpam-4453	386	25	∗∗	∗∗	X
ejpam-4453	386	26	that	that	PRON
ejpam-4453	386	27	preserves	preserve	VERB
ejpam-4453	386	28	the	the	DET
ejpam-4453	386	29	order	order	NOUN
ejpam-4453	386	30	of	of	ADP
ejpam-4453	386	31	the	the	DET
ejpam-4453	386	32	leaf	leaf	NOUN
ejpam-4453	386	33	of	of	ADP
ejpam-4453	386	34	c	c	NOUN
ejpam-4453	386	35	∗.	∗.	PROPN
ejpam-4453	386	36	thus	thus	ADV
ejpam-4453	386	37	,	,	PUNCT
ejpam-4453	386	38	we	we	PRON
ejpam-4453	386	39	have	have	VERB
ejpam-4453	386	40	kc	kc	PROPN
ejpam-4453	386	41	+	+	NUM
ejpam-4453	386	42	p′	p′	X
ejpam-4453	386	43	=	=	SYM
ejpam-4453	386	44	|v	|v	PROPN
ejpam-4453	386	45	(	(	PUNCT
ejpam-4453	386	46	c	c	PROPN
ejpam-4453	386	47	∗)|	∗)|	PROPN
ejpam-4453	386	48	kc	kc	PROPN
ejpam-4453	386	49	+	+	CCONJ
ejpam-4453	386	50	p′	p′	X
ejpam-4453	386	51	=	=	SYM
ejpam-4453	386	52	|v	|v	PROPN
ejpam-4453	386	53	(	(	PUNCT
ejpam-4453	386	54	c	c	NOUN
ejpam-4453	386	55	∗)|+	∗)|+	PROPN
ejpam-4453	386	56	2(m−	2(m−	PROPN
ejpam-4453	386	57	1	1	NUM
ejpam-4453	386	58	)	)	PUNCT
ejpam-4453	386	59	(	(	PUNCT
ejpam-4453	386	60	we	we	PRON
ejpam-4453	386	61	add	add	VERB
ejpam-4453	386	62	2(m−	2(m−	NUM
ejpam-4453	386	63	1	1	NUM
ejpam-4453	386	64	)	)	PUNCT
ejpam-4453	386	65	vertices	vertex	NOUN
ejpam-4453	386	66	)	)	PUNCT
ejpam-4453	387	1	kc	kc	PROPN
ejpam-4453	387	2	+	+	CCONJ
ejpam-4453	387	3	p′	p′	X
ejpam-4453	387	4	=	=	SYM
ejpam-4453	387	5	kc	kc	PROPN
ejpam-4453	387	6	+	+	PROPN
ejpam-4453	387	7	p+	p+	PROPN
ejpam-4453	387	8	2(m−	2(m−	PROPN
ejpam-4453	387	9	1	1	NUM
ejpam-4453	387	10	)	)	PUNCT
ejpam-4453	387	11	(	(	PUNCT
ejpam-4453	387	12	since	since	SCONJ
ejpam-4453	387	13	c	c	PROPN
ejpam-4453	387	14	∗	∗	NOUN
ejpam-4453	387	15	is	be	AUX
ejpam-4453	387	16	the	the	DET
ejpam-4453	387	17	base	base	NOUN
ejpam-4453	387	18	graph	graph	NOUN
ejpam-4453	387	19	)	)	PUNCT
ejpam-4453	387	20	p′	p′	NOUN
ejpam-4453	388	1	=	=	SYM
ejpam-4453	388	2	kc	kc	PROPN
ejpam-4453	389	1	+	+	CCONJ
ejpam-4453	389	2	kc	kc	PROPN
ejpam-4453	389	3	−	−	PROPN
ejpam-4453	389	4	2	2	NUM
ejpam-4453	390	1	+	+	CCONJ
ejpam-4453	390	2	2(m−	2(m−	PROPN
ejpam-4453	390	3	1)−	1)−	NUM
ejpam-4453	390	4	kc	kc	PROPN
ejpam-4453	390	5	p′	p′	NOUN
ejpam-4453	390	6	=	=	PUNCT
ejpam-4453	390	7	kc	kc	PROPN
ejpam-4453	390	8	−	−	PROPN
ejpam-4453	390	9	2	2	NUM
ejpam-4453	391	1	+	+	PROPN
ejpam-4453	391	2	2m−	2m−	PROPN
ejpam-4453	391	3	2	2	NUM
ejpam-4453	391	4	p′	p′	NOUN
ejpam-4453	391	5	=	=	SYM
ejpam-4453	391	6	kc	kc	PROPN
ejpam-4453	392	1	+	+	PROPN
ejpam-4453	392	2	2m−	2m−	PROPN
ejpam-4453	392	3	4	4	NUM
ejpam-4453	392	4	p′	p′	NOUN
ejpam-4453	392	5	=	=	SYM
ejpam-4453	392	6	kc	kc	PROPN
ejpam-4453	392	7	−	−	PROPN
ejpam-4453	392	8	2(2−m	2(2−m	NUM
ejpam-4453	392	9	)	)	PUNCT
ejpam-4453	392	10	therefore	therefore	ADV
ejpam-4453	392	11	p′	p′	X
ejpam-4453	393	1	=	=	SYM
ejpam-4453	393	2	kc	kc	PROPN
ejpam-4453	393	3	−	−	PROPN
ejpam-4453	393	4	2(2−m	2(2−m	NUM
ejpam-4453	393	5	)	)	PUNCT
ejpam-4453	393	6	where	where	SCONJ
ejpam-4453	393	7	m	m	PROPN
ejpam-4453	393	8	∈	∈	PROPN
ejpam-4453	393	9	n.	n.	NOUN
ejpam-4453	393	10	proposition	proposition	NOUN
ejpam-4453	393	11	3	3	X
ejpam-4453	393	12	.	.	PUNCT
ejpam-4453	394	1	any	any	DET
ejpam-4453	394	2	central	central	ADJ
ejpam-4453	394	3	fragment	fragment	NOUN
ejpam-4453	394	4	c	c	NOUN
ejpam-4453	394	5	with	with	ADP
ejpam-4453	394	6	kc	kc	PROPN
ejpam-4453	394	7	-	-	PUNCT
ejpam-4453	394	8	leaves	leave	NOUN
ejpam-4453	394	9	has	have	VERB
ejpam-4453	394	10	|v	|v	VERB
ejpam-4453	394	11	(	(	PUNCT
ejpam-4453	394	12	c	c	NOUN
ejpam-4453	394	13	)	)	PUNCT
ejpam-4453	395	1	|	|	ADV
ejpam-4453	395	2	≥	≥	NOUN
ejpam-4453	395	3	2(kc	2(kc	NUM
ejpam-4453	396	1	−	−	NOUN
ejpam-4453	396	2	1	1	NUM
ejpam-4453	396	3	)	)	PUNCT
ejpam-4453	396	4	where	where	SCONJ
ejpam-4453	396	5	kc	kc	PROPN
ejpam-4453	396	6	≥	≥	PROPN
ejpam-4453	396	7	3	3	NUM
ejpam-4453	396	8	.	.	PUNCT
ejpam-4453	396	9	proof	proof	NOUN
ejpam-4453	396	10	.	.	PUNCT
ejpam-4453	397	1	suppose	suppose	VERB
ejpam-4453	397	2	c	c	NOUN
ejpam-4453	397	3	is	be	AUX
ejpam-4453	397	4	a	a	DET
ejpam-4453	397	5	central	central	ADJ
ejpam-4453	397	6	fragment	fragment	NOUN
ejpam-4453	397	7	.	.	PUNCT
ejpam-4453	398	1	then	then	ADV
ejpam-4453	398	2	|v	|v	PROPN
ejpam-4453	398	3	(	(	PUNCT
ejpam-4453	398	4	c	c	NOUN
ejpam-4453	398	5	)	)	PUNCT
ejpam-4453	398	6	|	|	ADV
ejpam-4453	398	7	=	=	SYM
ejpam-4453	398	8	kc	kc	PROPN
ejpam-4453	399	1	+	+	CCONJ
ejpam-4453	399	2	p′.	p′.	NOUN
ejpam-4453	399	3	note	note	NOUN
ejpam-4453	399	4	that	that	SCONJ
ejpam-4453	399	5	by	by	ADP
ejpam-4453	399	6	proposition	proposition	NOUN
ejpam-4453	399	7	2	2	NUM
ejpam-4453	399	8	,	,	PUNCT
ejpam-4453	399	9	the	the	DET
ejpam-4453	399	10	value	value	NOUN
ejpam-4453	399	11	of	of	ADP
ejpam-4453	399	12	p′	p′	NOUN
ejpam-4453	399	13	increases	increase	NOUN
ejpam-4453	399	14	whenever	whenever	SCONJ
ejpam-4453	399	15	m	m	VERB
ejpam-4453	399	16	increases	increase	VERB
ejpam-4453	399	17	in	in	ADP
ejpam-4453	399	18	the	the	DET
ejpam-4453	399	19	equation	equation	NOUN
ejpam-4453	399	20	p′	p′	NOUN
ejpam-4453	399	21	=	=	SYM
ejpam-4453	399	22	kc	kc	PROPN
ejpam-4453	399	23	−	−	PROPN
ejpam-4453	399	24	2(2−m	2(2−m	NUM
ejpam-4453	399	25	)	)	PUNCT
ejpam-4453	399	26	.	.	PUNCT
ejpam-4453	400	1	it	it	PRON
ejpam-4453	400	2	is	be	AUX
ejpam-4453	400	3	clear	clear	ADJ
ejpam-4453	400	4	that	that	SCONJ
ejpam-4453	400	5	p′	p′	NOUN
ejpam-4453	400	6	≥	≥	NOUN
ejpam-4453	400	7	kc	kc	PROPN
ejpam-4453	400	8	−	−	PROPN
ejpam-4453	400	9	2	2	NUM
ejpam-4453	400	10	.	.	PUNCT
ejpam-4453	401	1	thus	thus	ADV
ejpam-4453	401	2	,	,	PUNCT
ejpam-4453	401	3	we	we	PRON
ejpam-4453	401	4	have	have	VERB
ejpam-4453	401	5	|v	|v	VERB
ejpam-4453	401	6	(	(	PUNCT
ejpam-4453	401	7	c	c	NOUN
ejpam-4453	401	8	)	)	PUNCT
ejpam-4453	402	1	|	|	ADV
ejpam-4453	402	2	=	=	SYM
ejpam-4453	402	3	kc	kc	PROPN
ejpam-4453	402	4	+	+	NUM
ejpam-4453	402	5	p′	p′	NOUN
ejpam-4453	402	6	which	which	PRON
ejpam-4453	402	7	implies	imply	VERB
ejpam-4453	402	8	that	that	SCONJ
ejpam-4453	402	9	|v	|v	PROPN
ejpam-4453	402	10	(	(	PUNCT
ejpam-4453	402	11	c	c	NOUN
ejpam-4453	402	12	)	)	PUNCT
ejpam-4453	402	13	|	|	ADV
ejpam-4453	402	14	≥	≥	NOUN
ejpam-4453	403	1	kc	kc	PROPN
ejpam-4453	404	1	+	+	CCONJ
ejpam-4453	404	2	kc	kc	PROPN
ejpam-4453	404	3	−	−	PROPN
ejpam-4453	404	4	2	2	NUM
ejpam-4453	404	5	=	=	SYM
ejpam-4453	404	6	2kc	2kc	ADJ
ejpam-4453	404	7	−	−	NOUN
ejpam-4453	404	8	2	2	NUM
ejpam-4453	404	9	=	=	SYM
ejpam-4453	404	10	2(kc	2(kc	NUM
ejpam-4453	405	1	−	−	NOUN
ejpam-4453	405	2	1	1	NUM
ejpam-4453	405	3	)	)	PUNCT
ejpam-4453	405	4	now	now	ADV
ejpam-4453	405	5	,	,	PUNCT
ejpam-4453	405	6	recall	recall	VERB
ejpam-4453	405	7	the	the	DET
ejpam-4453	405	8	notion	notion	NOUN
ejpam-4453	405	9	of	of	ADP
ejpam-4453	405	10	hairy	hairy	ADJ
ejpam-4453	405	11	cycle	cycle	NOUN
ejpam-4453	405	12	.	.	PUNCT
ejpam-4453	406	1	observe	observe	VERB
ejpam-4453	406	2	that	that	SCONJ
ejpam-4453	406	3	the	the	DET
ejpam-4453	406	4	family	family	NOUN
ejpam-4453	406	5	of	of	ADP
ejpam-4453	406	6	hairy	hairy	ADJ
ejpam-4453	406	7	cycles	cycle	NOUN
ejpam-4453	406	8	in	in	ADP
ejpam-4453	406	9	the	the	DET
ejpam-4453	406	10	form	form	NOUN
ejpam-4453	406	11	of	of	ADP
ejpam-4453	406	12	ck⊙1k1	ck⊙1k1	PROPN
ejpam-4453	406	13	can	can	AUX
ejpam-4453	406	14	be	be	AUX
ejpam-4453	406	15	classified	classify	VERB
ejpam-4453	406	16	as	as	ADP
ejpam-4453	406	17	a	a	DET
ejpam-4453	406	18	central	central	ADJ
ejpam-4453	406	19	fragment	fragment	NOUN
ejpam-4453	406	20	.	.	PUNCT
ejpam-4453	407	1	for	for	ADP
ejpam-4453	407	2	simplicity	simplicity	NOUN
ejpam-4453	407	3	,	,	PUNCT
ejpam-4453	407	4	we	we	PRON
ejpam-4453	407	5	use	use	VERB
ejpam-4453	407	6	hk	hk	PROPN
ejpam-4453	407	7	instead	instead	ADV
ejpam-4453	407	8	of	of	ADP
ejpam-4453	407	9	ck	ck	PROPN
ejpam-4453	407	10	⊙	⊙	PROPN
ejpam-4453	407	11	1k1	1k1	NUM
ejpam-4453	407	12	to	to	PART
ejpam-4453	407	13	represent	represent	VERB
ejpam-4453	407	14	a	a	DET
ejpam-4453	407	15	hairy	hairy	ADJ
ejpam-4453	407	16	cycle	cycle	NOUN
ejpam-4453	407	17	see	see	NOUN
ejpam-4453	407	18	figure	figure	NOUN
ejpam-4453	407	19	7	7	NUM
ejpam-4453	407	20	.	.	PUNCT
ejpam-4453	408	1	in	in	ADP
ejpam-4453	408	2	the	the	DET
ejpam-4453	408	3	next	next	ADJ
ejpam-4453	408	4	theorem	theorem	NOUN
ejpam-4453	408	5	,	,	PUNCT
ejpam-4453	408	6	we	we	PRON
ejpam-4453	408	7	will	will	AUX
ejpam-4453	408	8	show	show	VERB
ejpam-4453	408	9	that	that	SCONJ
ejpam-4453	408	10	every	every	DET
ejpam-4453	408	11	hk	hk	NOUN
ejpam-4453	408	12	is	be	AUX
ejpam-4453	408	13	indeed	indeed	ADV
ejpam-4453	408	14	a	a	DET
ejpam-4453	408	15	central	central	ADJ
ejpam-4453	408	16	fragment	fragment	NOUN
ejpam-4453	408	17	of	of	ADP
ejpam-4453	408	18	some	some	DET
ejpam-4453	408	19	ntcbg	ntcbg	NOUN
ejpam-4453	408	20	,	,	PUNCT
ejpam-4453	408	21	stated	state	VERB
ejpam-4453	408	22	as	as	SCONJ
ejpam-4453	408	23	follows	follow	VERB
ejpam-4453	408	24	.	.	PUNCT
ejpam-4453	408	25	...........................................................	...........................................................	PUNCT
ejpam-4453	409	1	..........	..........	PUNCT
ejpam-4453	409	2	.............................................	.............................................	PUNCT
ejpam-4453	409	3	.	.	PUNCT
ejpam-4453	409	4	............	............	PUNCT
ejpam-4453	410	1	...........	...........	PUNCT
ejpam-4453	410	2	...........	...........	PUNCT
ejpam-4453	410	3	...........	...........	PUNCT
ejpam-4453	410	4	........	........	PUNCT
ejpam-4453	411	1	..........	..........	PUNCT
ejpam-4453	411	2	.............................................	.............................................	PUNCT
ejpam-4453	411	3	.	.	PUNCT
ejpam-4453	412	1	.........	.........	PUNCT
ejpam-4453	412	2	........	........	PUNCT
ejpam-4453	412	3	........	........	PUNCT
ejpam-4453	412	4	........	........	PUNCT
ejpam-4453	412	5	........	........	PUNCT
ejpam-4453	412	6	........	........	PUNCT
ejpam-4453	413	1	........	........	PUNCT
ejpam-4453	413	2	..	..	PUNCT
ejpam-4453	413	3	..........	..........	PUNCT
ejpam-4453	413	4	.............................................	.............................................	PUNCT
ejpam-4453	413	5	.	.	PUNCT
ejpam-4453	413	6	.....................................................	.....................................................	PUNCT
ejpam-4453	414	1	..........	..........	PUNCT
ejpam-4453	414	2	.............................................	.............................................	PUNCT
ejpam-4453	414	3	.	.	PUNCT
ejpam-4453	414	4	.....................................................................	.....................................................................	PUNCT
ejpam-4453	414	5	.............................................	.............................................	PUNCT
ejpam-4453	414	6	.	.	PUNCT
ejpam-4453	415	1	..........	..........	PUNCT
ejpam-4453	415	2	.............................................	.............................................	PUNCT
ejpam-4453	415	3	.	.	PUNCT
ejpam-4453	416	1	.........	.........	PUNCT
ejpam-4453	416	2	........	........	PUNCT
ejpam-4453	416	3	........	........	PUNCT
ejpam-4453	416	4	........	........	PUNCT
ejpam-4453	416	5	........	........	PUNCT
ejpam-4453	416	6	........	........	PUNCT
ejpam-4453	417	1	........	........	PUNCT
ejpam-4453	417	2	..	..	PUNCT
ejpam-4453	417	3	..........	..........	PUNCT
ejpam-4453	417	4	.............................................	.............................................	PUNCT
ejpam-4453	417	5	.	.	PUNCT
ejpam-4453	417	6	.....................................................	.....................................................	PUNCT
ejpam-4453	418	1	..........	..........	PUNCT
ejpam-4453	418	2	.............................................	.............................................	PUNCT
ejpam-4453	418	3	.	.	PUNCT
ejpam-4453	419	1	..........	..........	PUNCT
ejpam-4453	419	2	.............................................	.............................................	PUNCT
ejpam-4453	419	3	.	.	PUNCT
ejpam-4453	420	1	..........	..........	PUNCT
ejpam-4453	420	2	.........	.........	PUNCT
ejpam-4453	421	1	.........	.........	PUNCT
ejpam-4453	421	2	.........	.........	PUNCT
ejpam-4453	422	1	....	....	PUNCT
ejpam-4453	423	1	c1c2	c1c2	X
ejpam-4453	423	2	c3	c3	PROPN
ejpam-4453	423	3	c4	c4	NOUN
ejpam-4453	423	4	c5	c5	PROPN
ejpam-4453	423	5	c6	c6	PROPN
ejpam-4453	424	1	ck−1	ck−1	PROPN
ejpam-4453	424	2	ck	ck	INTJ
ejpam-4453	424	3	ck	ck	INTJ
ejpam-4453	424	4	..........	..........	PUNCT
ejpam-4453	424	5	.............................................	.............................................	PUNCT
ejpam-4453	424	6	.	.	PUNCT
ejpam-4453	425	1	k1	k1	PROPN
ejpam-4453	425	2	...........................................................	...........................................................	PUNCT
ejpam-4453	425	3	..........	..........	PUNCT
ejpam-4453	425	4	.............................................	.............................................	PUNCT
ejpam-4453	425	5	.	.	PUNCT
ejpam-4453	425	6	............	............	PUNCT
ejpam-4453	425	7	...........	...........	PUNCT
ejpam-4453	425	8	...........	...........	PUNCT
ejpam-4453	425	9	...........	...........	PUNCT
ejpam-4453	425	10	........	........	PUNCT
ejpam-4453	425	11	..........	..........	PUNCT
ejpam-4453	425	12	.............................................	.............................................	PUNCT
ejpam-4453	425	13	.	.	PUNCT
ejpam-4453	425	14	.........	.........	PUNCT
ejpam-4453	426	1	........	........	PUNCT
ejpam-4453	426	2	........	........	PUNCT
ejpam-4453	426	3	........	........	PUNCT
ejpam-4453	426	4	........	........	PUNCT
ejpam-4453	426	5	........	........	PUNCT
ejpam-4453	427	1	........	........	PUNCT
ejpam-4453	427	2	..	..	PUNCT
ejpam-4453	427	3	..........	..........	PUNCT
ejpam-4453	427	4	.............................................	.............................................	PUNCT
ejpam-4453	427	5	.	.	PUNCT
ejpam-4453	427	6	.....................................................	.....................................................	PUNCT
ejpam-4453	428	1	..........	..........	PUNCT
ejpam-4453	428	2	.............................................	.............................................	PUNCT
ejpam-4453	428	3	.	.	PUNCT
ejpam-4453	428	4	.....................................................................	.....................................................................	PUNCT
ejpam-4453	428	5	.............................................	.............................................	PUNCT
ejpam-4453	428	6	.	.	PUNCT
ejpam-4453	429	1	..........	..........	PUNCT
ejpam-4453	429	2	.............................................	.............................................	PUNCT
ejpam-4453	429	3	.	.	PUNCT
ejpam-4453	430	1	.........	.........	PUNCT
ejpam-4453	430	2	........	........	PUNCT
ejpam-4453	430	3	........	........	PUNCT
ejpam-4453	430	4	........	........	PUNCT
ejpam-4453	430	5	........	........	PUNCT
ejpam-4453	430	6	........	........	PUNCT
ejpam-4453	431	1	........	........	PUNCT
ejpam-4453	431	2	..	..	PUNCT
ejpam-4453	431	3	..........	..........	PUNCT
ejpam-4453	431	4	.............................................	.............................................	PUNCT
ejpam-4453	431	5	.	.	PUNCT
ejpam-4453	431	6	.....................................................	.....................................................	PUNCT
ejpam-4453	432	1	..........	..........	PUNCT
ejpam-4453	432	2	.............................................	.............................................	PUNCT
ejpam-4453	432	3	.	.	PUNCT
ejpam-4453	433	1	..........	..........	PUNCT
ejpam-4453	433	2	.............................................	.............................................	PUNCT
ejpam-4453	433	3	.	.	PUNCT
ejpam-4453	434	1	..........	..........	PUNCT
ejpam-4453	434	2	.........	.........	PUNCT
ejpam-4453	435	1	.........	.........	PUNCT
ejpam-4453	435	2	.........	.........	PUNCT
ejpam-4453	436	1	....	....	PUNCT
ejpam-4453	437	1	c1c2	c1c2	X
ejpam-4453	437	2	c3	c3	PROPN
ejpam-4453	437	3	c4	c4	NOUN
ejpam-4453	437	4	c5	c5	PROPN
ejpam-4453	437	5	c6	c6	PROPN
ejpam-4453	437	6	ck−1	ck−1	PROPN
ejpam-4453	437	7	ck	ck	INTJ
ejpam-4453	437	8	.........	.........	PUNCT
ejpam-4453	437	9	........	........	PUNCT
ejpam-4453	437	10	........	........	PUNCT
ejpam-4453	437	11	........	........	PUNCT
ejpam-4453	437	12	........	........	PUNCT
ejpam-4453	437	13	.	.	PUNCT
ejpam-4453	438	1	..........	..........	PUNCT
ejpam-4453	438	2	.............................................	.............................................	PUNCT
ejpam-4453	438	3	.	.	PUNCT
ejpam-4453	439	1	..........	..........	PUNCT
ejpam-4453	439	2	.............................................	.............................................	PUNCT
ejpam-4453	439	3	.	.	PUNCT
ejpam-4453	440	1	.........	.........	PUNCT
ejpam-4453	440	2	........	........	PUNCT
ejpam-4453	440	3	........	........	PUNCT
ejpam-4453	440	4	........	........	PUNCT
ejpam-4453	441	1	........	........	PUNCT
ejpam-4453	441	2	.	.	PUNCT
ejpam-4453	442	1	..........	..........	PUNCT
ejpam-4453	442	2	.............................................	.............................................	PUNCT
ejpam-4453	442	3	.	.	PUNCT
ejpam-4453	443	1	..........	..........	PUNCT
ejpam-4453	443	2	.............................................	.............................................	PUNCT
ejpam-4453	443	3	.	.	PUNCT
ejpam-4453	444	1	......................................................................	......................................................................	PUNCT
ejpam-4453	445	1	..........	..........	PUNCT
ejpam-4453	445	2	.............................................	.............................................	PUNCT
ejpam-4453	445	3	...........	...........	PUNCT
ejpam-4453	445	4	.............................................	.............................................	PUNCT
ejpam-4453	445	5	.	.	PUNCT
ejpam-4453	446	1	......................................................................	......................................................................	PUNCT
ejpam-4453	447	1	..........	..........	PUNCT
ejpam-4453	447	2	.............................................	.............................................	PUNCT
ejpam-4453	447	3	...........	...........	PUNCT
ejpam-4453	447	4	.............................................	.............................................	PUNCT
ejpam-4453	447	5	.	.	PUNCT
ejpam-4453	448	1	.........	.........	PUNCT
ejpam-4453	448	2	........	........	PUNCT
ejpam-4453	448	3	........	........	PUNCT
ejpam-4453	448	4	........	........	PUNCT
ejpam-4453	449	1	........	........	PUNCT
ejpam-4453	449	2	.	.	PUNCT
ejpam-4453	450	1	..........	..........	PUNCT
ejpam-4453	450	2	.............................................	.............................................	PUNCT
ejpam-4453	450	3	.	.	PUNCT
ejpam-4453	451	1	..........	..........	PUNCT
ejpam-4453	451	2	.............................................	.............................................	PUNCT
ejpam-4453	451	3	.	.	PUNCT
ejpam-4453	452	1	.........	.........	PUNCT
ejpam-4453	452	2	........	........	PUNCT
ejpam-4453	452	3	........	........	PUNCT
ejpam-4453	452	4	........	........	PUNCT
ejpam-4453	453	1	........	........	PUNCT
ejpam-4453	453	2	.	.	PUNCT
ejpam-4453	454	1	..........	..........	PUNCT
ejpam-4453	454	2	.............................................	.............................................	PUNCT
ejpam-4453	454	3	.	.	PUNCT
ejpam-4453	455	1	..........	..........	PUNCT
ejpam-4453	455	2	.............................................	.............................................	PUNCT
ejpam-4453	455	3	.	.	PUNCT
ejpam-4453	456	1	................................................................................	................................................................................	PUNCT
ejpam-4453	456	2	.............................................	.............................................	PUNCT
ejpam-4453	456	3	.	.	PUNCT
ejpam-4453	457	1	..........	..........	PUNCT
ejpam-4453	457	2	.............................................	.............................................	PUNCT
ejpam-4453	457	3	.	.	PUNCT
ejpam-4453	458	1	................................................................................	................................................................................	PUNCT
ejpam-4453	458	2	.............................................	.............................................	PUNCT
ejpam-4453	458	3	.	.	PUNCT
ejpam-4453	459	1	..........	..........	PUNCT
ejpam-4453	459	2	.............................................	.............................................	PUNCT
ejpam-4453	459	3	.	.	PUNCT
ejpam-4453	460	1	a1a2	a1a2	PRON
ejpam-4453	460	2	a3	a3	PROPN
ejpam-4453	460	3	a4	a4	NOUN
ejpam-4453	460	4	a5	a5	PROPN
ejpam-4453	460	5	a6	a6	PROPN
ejpam-4453	460	6	ak−1	ak−1	PROPN
ejpam-4453	460	7	ak	ak	PROPN
ejpam-4453	460	8	ck	ck	PROPN
ejpam-4453	460	9	⊙	⊙	PROPN
ejpam-4453	460	10	1k1	1k1	NUM
ejpam-4453	460	11	=	=	SYM
ejpam-4453	460	12	hk	hk	PROPN
ejpam-4453	460	13	figure	figure	NOUN
ejpam-4453	460	14	7	7	NUM
ejpam-4453	460	15	:	:	PUNCT
ejpam-4453	460	16	general	general	ADJ
ejpam-4453	460	17	form	form	NOUN
ejpam-4453	460	18	of	of	ADP
ejpam-4453	460	19	a	a	DET
ejpam-4453	460	20	hairy	hairy	ADJ
ejpam-4453	460	21	cycle	cycle	NOUN
ejpam-4453	460	22	theorem	theorem	VERB
ejpam-4453	460	23	9	9	NUM
ejpam-4453	460	24	.	.	PUNCT
ejpam-4453	461	1	any	any	DET
ejpam-4453	461	2	hairy	hairy	ADJ
ejpam-4453	461	3	cycle	cycle	NOUN
ejpam-4453	461	4	hk	hk	PROPN
ejpam-4453	461	5	is	be	AUX
ejpam-4453	461	6	a	a	DET
ejpam-4453	461	7	central	central	ADJ
ejpam-4453	461	8	fragment	fragment	NOUN
ejpam-4453	461	9	of	of	ADP
ejpam-4453	461	10	ntcbg	ntcbg	PROPN
ejpam-4453	461	11	.	.	PUNCT
ejpam-4453	462	1	a.r	a.r	PROPN
ejpam-4453	462	2	nieva	nieva	PROPN
ejpam-4453	462	3	and	and	CCONJ
ejpam-4453	462	4	k.nocum	k.nocum	PROPN
ejpam-4453	462	5	/	/	SYM
ejpam-4453	462	6	eur	eur	PROPN
ejpam-4453	462	7	.	.	PUNCT
ejpam-4453	463	1	j.	j.	PROPN
ejpam-4453	463	2	pure	pure	PROPN
ejpam-4453	463	3	appl	appl	PROPN
ejpam-4453	463	4	.	.	PROPN
ejpam-4453	463	5	math	math	PROPN
ejpam-4453	463	6	,	,	PUNCT
ejpam-4453	463	7	15	15	NUM
ejpam-4453	463	8	(	(	PUNCT
ejpam-4453	463	9	4	4	NUM
ejpam-4453	463	10	)	)	PUNCT
ejpam-4453	463	11	(	(	PUNCT
ejpam-4453	463	12	2022	2022	NUM
ejpam-4453	463	13	)	)	PUNCT
ejpam-4453	463	14	,	,	PUNCT
ejpam-4453	463	15	1536	1536	NUM
ejpam-4453	463	16	-	-	SYM
ejpam-4453	463	17	1548	1548	NUM
ejpam-4453	463	18	1542	1542	NUM
ejpam-4453	463	19	proof	proof	NOUN
ejpam-4453	463	20	.	.	PUNCT
ejpam-4453	464	1	let	let	VERB
ejpam-4453	464	2	hk	hk	PROPN
ejpam-4453	464	3	be	be	AUX
ejpam-4453	464	4	a	a	DET
ejpam-4453	464	5	graph	graph	NOUN
ejpam-4453	464	6	.	.	PUNCT
ejpam-4453	465	1	we	we	PRON
ejpam-4453	465	2	will	will	AUX
ejpam-4453	465	3	show	show	VERB
ejpam-4453	465	4	that	that	SCONJ
ejpam-4453	465	5	hk	hk	PROPN
ejpam-4453	465	6	satisfies	satisfy	VERB
ejpam-4453	465	7	all	all	DET
ejpam-4453	465	8	properties	property	NOUN
ejpam-4453	465	9	of	of	ADP
ejpam-4453	465	10	a	a	DET
ejpam-4453	465	11	central	central	ADJ
ejpam-4453	465	12	fragment	fragment	NOUN
ejpam-4453	465	13	.	.	PUNCT
ejpam-4453	466	1	by	by	ADP
ejpam-4453	466	2	definition	definition	NOUN
ejpam-4453	466	3	of	of	ADP
ejpam-4453	466	4	a	a	DET
ejpam-4453	466	5	hairy	hairy	ADJ
ejpam-4453	466	6	cycle	cycle	NOUN
ejpam-4453	466	7	,	,	PUNCT
ejpam-4453	466	8	hk	hk	PROPN
ejpam-4453	466	9	is	be	AUX
ejpam-4453	466	10	connected	connect	VERB
ejpam-4453	466	11	and	and	CCONJ
ejpam-4453	466	12	is	be	AUX
ejpam-4453	466	13	also	also	ADV
ejpam-4453	466	14	a	a	DET
ejpam-4453	466	15	bridge	bridge	NOUN
ejpam-4453	466	16	graph	graph	NOUN
ejpam-4453	466	17	.	.	PUNCT
ejpam-4453	467	1	by	by	ADP
ejpam-4453	467	2	definition	definition	NOUN
ejpam-4453	467	3	of	of	ADP
ejpam-4453	467	4	a	a	DET
ejpam-4453	467	5	hairy	hairy	ADJ
ejpam-4453	467	6	cycle	cycle	NOUN
ejpam-4453	467	7	,	,	PUNCT
ejpam-4453	467	8	every	every	DET
ejpam-4453	467	9	vertex	vertex	NOUN
ejpam-4453	467	10	of	of	ADP
ejpam-4453	467	11	a	a	DET
ejpam-4453	467	12	cycle	cycle	NOUN
ejpam-4453	467	13	ck	ck	INTJ
ejpam-4453	467	14	is	be	AUX
ejpam-4453	467	15	attached	attach	VERB
ejpam-4453	467	16	to	to	ADP
ejpam-4453	467	17	one	one	NUM
ejpam-4453	467	18	copy	copy	NOUN
ejpam-4453	467	19	of	of	ADP
ejpam-4453	467	20	k1	k1	NOUN
ejpam-4453	467	21	such	such	ADJ
ejpam-4453	467	22	that	that	SCONJ
ejpam-4453	467	23	it	it	PRON
ejpam-4453	467	24	forms	form	VERB
ejpam-4453	467	25	a	a	DET
ejpam-4453	467	26	pendant	pendant	ADJ
ejpam-4453	467	27	edge	edge	NOUN
ejpam-4453	467	28	.	.	PUNCT
ejpam-4453	468	1	it	it	PRON
ejpam-4453	468	2	follows	follow	VERB
ejpam-4453	468	3	that	that	SCONJ
ejpam-4453	468	4	each	each	DET
ejpam-4453	468	5	vertex	vertex	NOUN
ejpam-4453	468	6	in	in	ADP
ejpam-4453	468	7	the	the	DET
ejpam-4453	468	8	cycle	cycle	NOUN
ejpam-4453	468	9	has	have	VERB
ejpam-4453	468	10	degree	degree	NOUN
ejpam-4453	468	11	3	3	NUM
ejpam-4453	468	12	and	and	CCONJ
ejpam-4453	468	13	each	each	DET
ejpam-4453	468	14	end	end	NOUN
ejpam-4453	468	15	-	-	PUNCT
ejpam-4453	468	16	vertex	vertex	NOUN
ejpam-4453	468	17	of	of	ADP
ejpam-4453	468	18	a	a	DET
ejpam-4453	468	19	pendant	pendant	ADJ
ejpam-4453	468	20	edge	edge	NOUN
ejpam-4453	468	21	has	have	VERB
ejpam-4453	468	22	degree	degree	NOUN
ejpam-4453	468	23	1	1	NUM
ejpam-4453	468	24	.	.	PUNCT
ejpam-4453	469	1	thus	thus	ADV
ejpam-4453	469	2	,	,	PUNCT
ejpam-4453	469	3	every	every	DET
ejpam-4453	469	4	vertex	vertex	NOUN
ejpam-4453	469	5	of	of	ADP
ejpam-4453	469	6	hk	hk	PROPN
ejpam-4453	469	7	must	must	AUX
ejpam-4453	469	8	contain	contain	VERB
ejpam-4453	469	9	vertices	vertex	NOUN
ejpam-4453	469	10	is	be	AUX
ejpam-4453	469	11	of	of	ADP
ejpam-4453	469	12	degree	degree	NOUN
ejpam-4453	469	13	1	1	NUM
ejpam-4453	469	14	and	and	CCONJ
ejpam-4453	469	15	of	of	ADP
ejpam-4453	469	16	degree	degree	NOUN
ejpam-4453	469	17	3	3	NUM
ejpam-4453	469	18	only	only	ADV
ejpam-4453	469	19	.	.	PUNCT
ejpam-4453	470	1	we	we	PRON
ejpam-4453	470	2	need	need	VERB
ejpam-4453	470	3	to	to	PART
ejpam-4453	470	4	show	show	VERB
ejpam-4453	470	5	that	that	SCONJ
ejpam-4453	470	6	hk	hk	PROPN
ejpam-4453	470	7	is	be	AUX
ejpam-4453	470	8	non	non	ADJ
ejpam-4453	470	9	-	-	ADJ
ejpam-4453	470	10	traceable	traceable	ADJ
ejpam-4453	470	11	.	.	PUNCT
ejpam-4453	471	1	suppose	suppose	VERB
ejpam-4453	471	2	hk	hk	PROPN
ejpam-4453	471	3	is	be	AUX
ejpam-4453	471	4	traceable	traceable	ADJ
ejpam-4453	471	5	.	.	PUNCT
ejpam-4453	472	1	then	then	ADV
ejpam-4453	472	2	it	it	PRON
ejpam-4453	472	3	implies	imply	VERB
ejpam-4453	472	4	that	that	SCONJ
ejpam-4453	472	5	it	it	PRON
ejpam-4453	472	6	contains	contain	VERB
ejpam-4453	472	7	a	a	DET
ejpam-4453	472	8	hamiltonian	hamiltonian	ADJ
ejpam-4453	472	9	path	path	NOUN
ejpam-4453	472	10	.	.	PUNCT
ejpam-4453	473	1	since	since	SCONJ
ejpam-4453	473	2	hk	hk	PROPN
ejpam-4453	473	3	contains	contain	VERB
ejpam-4453	473	4	atleast	atleast	ADJ
ejpam-4453	473	5	3	3	NUM
ejpam-4453	473	6	end	end	NOUN
ejpam-4453	473	7	-	-	PUNCT
ejpam-4453	473	8	vertices	vertex	NOUN
ejpam-4453	473	9	and	and	CCONJ
ejpam-4453	473	10	a	a	DET
ejpam-4453	473	11	hamiltonian	hamiltonian	ADJ
ejpam-4453	473	12	path	path	NOUN
ejpam-4453	473	13	contains	contain	VERB
ejpam-4453	473	14	2	2	NUM
ejpam-4453	473	15	end	end	NOUN
ejpam-4453	473	16	-	-	PUNCT
ejpam-4453	473	17	vertices	vertex	NOUN
ejpam-4453	473	18	it	it	PRON
ejpam-4453	473	19	follows	follow	VERB
ejpam-4453	473	20	that	that	SCONJ
ejpam-4453	473	21	hk	hk	PROPN
ejpam-4453	473	22	is	be	AUX
ejpam-4453	473	23	non	non	ADJ
ejpam-4453	473	24	-	-	ADJ
ejpam-4453	473	25	traceable	traceable	ADJ
ejpam-4453	473	26	.	.	PUNCT
ejpam-4453	474	1	since	since	SCONJ
ejpam-4453	474	2	all	all	DET
ejpam-4453	474	3	the	the	DET
ejpam-4453	474	4	properties	property	NOUN
ejpam-4453	474	5	of	of	ADP
ejpam-4453	474	6	a	a	DET
ejpam-4453	474	7	central	central	ADJ
ejpam-4453	474	8	fragment	fragment	NOUN
ejpam-4453	474	9	are	be	AUX
ejpam-4453	474	10	satisfied	satisfied	ADJ
ejpam-4453	474	11	,	,	PUNCT
ejpam-4453	474	12	therefore	therefore	ADV
ejpam-4453	474	13	hk	hk	PROPN
ejpam-4453	474	14	is	be	AUX
ejpam-4453	474	15	a	a	DET
ejpam-4453	474	16	central	central	ADJ
ejpam-4453	474	17	fragment	fragment	NOUN
ejpam-4453	474	18	.	.	PUNCT
ejpam-4453	475	1	here	here	ADV
ejpam-4453	475	2	are	be	AUX
ejpam-4453	475	3	some	some	DET
ejpam-4453	475	4	important	important	ADJ
ejpam-4453	475	5	properties	property	NOUN
ejpam-4453	475	6	of	of	ADP
ejpam-4453	475	7	a	a	DET
ejpam-4453	475	8	central	central	ADJ
ejpam-4453	475	9	fragment	fragment	NOUN
ejpam-4453	475	10	being	be	AUX
ejpam-4453	475	11	a	a	DET
ejpam-4453	475	12	hairy	hairy	ADJ
ejpam-4453	475	13	cycle	cycle	NOUN
ejpam-4453	475	14	.	.	PUNCT
ejpam-4453	476	1	we	we	PRON
ejpam-4453	476	2	present	present	VERB
ejpam-4453	476	3	it	it	PRON
ejpam-4453	476	4	as	as	ADP
ejpam-4453	476	5	a	a	DET
ejpam-4453	476	6	remark	remark	NOUN
ejpam-4453	476	7	as	as	SCONJ
ejpam-4453	476	8	follows	follow	VERB
ejpam-4453	476	9	.	.	PUNCT
ejpam-4453	477	1	remark	remark	NOUN
ejpam-4453	477	2	2	2	NUM
ejpam-4453	477	3	.	.	PUNCT
ejpam-4453	478	1	every	every	DET
ejpam-4453	478	2	hairy	hairy	ADJ
ejpam-4453	478	3	cycle	cycle	NOUN
ejpam-4453	478	4	hk	hk	PROPN
ejpam-4453	478	5	is	be	AUX
ejpam-4453	478	6	unique	unique	ADJ
ejpam-4453	478	7	up	up	ADP
ejpam-4453	478	8	to	to	ADP
ejpam-4453	478	9	isomorphism	isomorphism	NOUN
ejpam-4453	478	10	.	.	PUNCT
ejpam-4453	479	1	proposition	proposition	NOUN
ejpam-4453	479	2	4	4	NUM
ejpam-4453	479	3	.	.	PUNCT
ejpam-4453	480	1	let	let	VERB
ejpam-4453	480	2	hk	hk	PROPN
ejpam-4453	480	3	be	be	AUX
ejpam-4453	480	4	a	a	DET
ejpam-4453	480	5	central	central	ADJ
ejpam-4453	480	6	fragment	fragment	NOUN
ejpam-4453	480	7	.	.	PUNCT
ejpam-4453	481	1	then	then	ADV
ejpam-4453	481	2	|v	|v	PROPN
ejpam-4453	481	3	(	(	PUNCT
ejpam-4453	481	4	hk)|	hk)|	X
ejpam-4453	481	5	=	=	SYM
ejpam-4453	481	6	|e(hk)|	|e(hk)|	NOUN
ejpam-4453	481	7	=	=	SYM
ejpam-4453	481	8	2k	2k	NUM
ejpam-4453	481	9	,	,	PUNCT
ejpam-4453	481	10	where	where	SCONJ
ejpam-4453	481	11	k	k	PROPN
ejpam-4453	481	12	is	be	AUX
ejpam-4453	481	13	the	the	DET
ejpam-4453	481	14	order	order	NOUN
ejpam-4453	481	15	and	and	CCONJ
ejpam-4453	481	16	size	size	NOUN
ejpam-4453	481	17	of	of	ADP
ejpam-4453	481	18	ck	ck	PROPN
ejpam-4453	481	19	,	,	PUNCT
ejpam-4453	481	20	respectively	respectively	ADV
ejpam-4453	481	21	.	.	PUNCT
ejpam-4453	482	1	proof	proof	NOUN
ejpam-4453	482	2	.	.	PUNCT
ejpam-4453	483	1	let	let	VERB
ejpam-4453	483	2	hk	hk	PROPN
ejpam-4453	483	3	be	be	AUX
ejpam-4453	483	4	a	a	DET
ejpam-4453	483	5	central	central	ADJ
ejpam-4453	483	6	fragment	fragment	NOUN
ejpam-4453	483	7	.	.	PUNCT
ejpam-4453	484	1	it	it	PRON
ejpam-4453	484	2	follows	follow	VERB
ejpam-4453	484	3	that	that	SCONJ
ejpam-4453	484	4	we	we	PRON
ejpam-4453	484	5	have	have	VERB
ejpam-4453	484	6	a	a	DET
ejpam-4453	484	7	cycle	cycle	NOUN
ejpam-4453	484	8	ck	ck	NOUN
ejpam-4453	484	9	of	of	ADP
ejpam-4453	484	10	order	order	NOUN
ejpam-4453	484	11	k.	k.	INTJ
ejpam-4453	484	12	by	by	ADP
ejpam-4453	484	13	definition	definition	NOUN
ejpam-4453	484	14	of	of	ADP
ejpam-4453	484	15	a	a	DET
ejpam-4453	484	16	hairy	hairy	ADJ
ejpam-4453	484	17	cycle	cycle	NOUN
ejpam-4453	484	18	,	,	PUNCT
ejpam-4453	484	19	hk	hk	PROPN
ejpam-4453	484	20	can	can	AUX
ejpam-4453	484	21	be	be	AUX
ejpam-4453	484	22	constructed	construct	VERB
ejpam-4453	484	23	by	by	ADP
ejpam-4453	484	24	attaching	attach	VERB
ejpam-4453	484	25	one	one	NUM
ejpam-4453	484	26	copy	copy	NOUN
ejpam-4453	484	27	of	of	ADP
ejpam-4453	484	28	k1	k1	NOUN
ejpam-4453	484	29	to	to	ADP
ejpam-4453	484	30	the	the	DET
ejpam-4453	484	31	vertices	vertex	NOUN
ejpam-4453	484	32	of	of	ADP
ejpam-4453	484	33	the	the	DET
ejpam-4453	484	34	cycle	cycle	NOUN
ejpam-4453	484	35	such	such	ADJ
ejpam-4453	484	36	that	that	SCONJ
ejpam-4453	484	37	it	it	PRON
ejpam-4453	484	38	forms	form	VERB
ejpam-4453	484	39	a	a	DET
ejpam-4453	484	40	pendant	pendant	ADJ
ejpam-4453	484	41	edge	edge	NOUN
ejpam-4453	484	42	.	.	PUNCT
ejpam-4453	485	1	it	it	PRON
ejpam-4453	485	2	follows	follow	VERB
ejpam-4453	485	3	that	that	SCONJ
ejpam-4453	485	4	we	we	PRON
ejpam-4453	485	5	have	have	VERB
ejpam-4453	485	6	k	k	PROPN
ejpam-4453	485	7	pendant	pendant	ADJ
ejpam-4453	485	8	edges	edge	NOUN
ejpam-4453	485	9	,	,	PUNCT
ejpam-4453	485	10	thus	thus	ADV
ejpam-4453	485	11	it	it	PRON
ejpam-4453	485	12	must	must	AUX
ejpam-4453	485	13	have	have	VERB
ejpam-4453	485	14	k	k	PROPN
ejpam-4453	485	15	end	end	NOUN
ejpam-4453	485	16	-	-	PUNCT
ejpam-4453	485	17	vertices	vertex	NOUN
ejpam-4453	485	18	as	as	ADV
ejpam-4453	485	19	well	well	ADV
ejpam-4453	485	20	.	.	PUNCT
ejpam-4453	486	1	thus	thus	ADV
ejpam-4453	486	2	,	,	PUNCT
ejpam-4453	486	3	|v	|v	PROPN
ejpam-4453	486	4	(	(	PUNCT
ejpam-4453	486	5	hk)|	hk)|	X
ejpam-4453	486	6	=	=	SYM
ejpam-4453	486	7	k	k	PROPN
ejpam-4453	487	1	+	+	CCONJ
ejpam-4453	487	2	k	k	X
ejpam-4453	487	3	=	=	PUNCT
ejpam-4453	487	4	2k	2k	NUM
ejpam-4453	487	5	,	,	PUNCT
ejpam-4453	487	6	where	where	SCONJ
ejpam-4453	487	7	k	k	PROPN
ejpam-4453	487	8	is	be	AUX
ejpam-4453	487	9	the	the	DET
ejpam-4453	487	10	order	order	NOUN
ejpam-4453	487	11	of	of	ADP
ejpam-4453	487	12	ck	ck	PROPN
ejpam-4453	487	13	.	.	PUNCT
ejpam-4453	487	14	analogous	analogous	ADJ
ejpam-4453	487	15	to	to	ADP
ejpam-4453	487	16	the	the	DET
ejpam-4453	487	17	argument	argument	NOUN
ejpam-4453	487	18	above	above	ADV
ejpam-4453	487	19	,	,	PUNCT
ejpam-4453	487	20	we	we	PRON
ejpam-4453	487	21	can	can	AUX
ejpam-4453	487	22	show	show	VERB
ejpam-4453	487	23	that	that	SCONJ
ejpam-4453	487	24	|e(hk)|	|e(hk)|	PRON
ejpam-4453	487	25	=	=	SYM
ejpam-4453	487	26	2k	2k	NUM
ejpam-4453	487	27	.	.	PUNCT
ejpam-4453	488	1	thus	thus	ADV
ejpam-4453	488	2	,	,	PUNCT
ejpam-4453	488	3	|v	|v	PROPN
ejpam-4453	488	4	(	(	PUNCT
ejpam-4453	488	5	hk)|	hk)|	X
ejpam-4453	488	6	=	=	SYM
ejpam-4453	488	7	|e(hk)|	|e(hk)|	NOUN
ejpam-4453	488	8	=	=	SYM
ejpam-4453	488	9	2k	2k	NUM
ejpam-4453	488	10	,	,	PUNCT
ejpam-4453	488	11	where	where	SCONJ
ejpam-4453	488	12	k	k	PROPN
ejpam-4453	488	13	is	be	AUX
ejpam-4453	488	14	the	the	DET
ejpam-4453	488	15	order	order	NOUN
ejpam-4453	488	16	and	and	CCONJ
ejpam-4453	488	17	size	size	NOUN
ejpam-4453	488	18	of	of	ADP
ejpam-4453	488	19	ck	ck	PROPN
ejpam-4453	488	20	,	,	PUNCT
ejpam-4453	488	21	respectively	respectively	ADV
ejpam-4453	488	22	.	.	PUNCT
ejpam-4453	489	1	now	now	ADV
ejpam-4453	489	2	we	we	PRON
ejpam-4453	489	3	are	be	AUX
ejpam-4453	489	4	ready	ready	ADJ
ejpam-4453	489	5	to	to	PART
ejpam-4453	489	6	discuss	discuss	VERB
ejpam-4453	489	7	the	the	DET
ejpam-4453	489	8	branch	branch	NOUN
ejpam-4453	489	9	of	of	ADP
ejpam-4453	489	10	a	a	DET
ejpam-4453	489	11	ntcbg	ntcbg	PROPN
ejpam-4453	489	12	.	.	PUNCT
ejpam-4453	490	1	definition	definition	NOUN
ejpam-4453	490	2	2	2	NUM
ejpam-4453	490	3	.	.	PUNCT
ejpam-4453	491	1	let	let	VERB
ejpam-4453	491	2	g	g	PRON
ejpam-4453	491	3	be	be	AUX
ejpam-4453	491	4	a	a	DET
ejpam-4453	491	5	ntcbg	ntcbg	NOUN
ejpam-4453	491	6	.	.	PUNCT
ejpam-4453	492	1	a	a	DET
ejpam-4453	492	2	branch	branch	NOUN
ejpam-4453	492	3	of	of	ADP
ejpam-4453	492	4	a	a	DET
ejpam-4453	492	5	graph	graph	NOUN
ejpam-4453	492	6	g	g	NOUN
ejpam-4453	492	7	denoted	denote	VERB
ejpam-4453	492	8	by	by	ADP
ejpam-4453	492	9	bi	bi	NOUN
ejpam-4453	492	10	,	,	PUNCT
ejpam-4453	492	11	such	such	ADJ
ejpam-4453	492	12	that	that	SCONJ
ejpam-4453	492	13	every	every	DET
ejpam-4453	492	14	bi	bi	NOUN
ejpam-4453	492	15	is	be	AUX
ejpam-4453	492	16	a	a	DET
ejpam-4453	492	17	subgraph	subgraph	NOUN
ejpam-4453	492	18	of	of	ADP
ejpam-4453	492	19	g	g	PROPN
ejpam-4453	492	20	is	be	AUX
ejpam-4453	492	21	a	a	DET
ejpam-4453	492	22	cubic	cubic	ADJ
ejpam-4453	492	23	graph	graph	NOUN
ejpam-4453	492	24	.	.	PUNCT
ejpam-4453	493	1	a	a	DET
ejpam-4453	493	2	cubic	cubic	ADJ
ejpam-4453	493	3	graph	graph	NOUN
ejpam-4453	493	4	whose	whose	DET
ejpam-4453	493	5	one	one	NUM
ejpam-4453	493	6	edge	edge	NOUN
ejpam-4453	493	7	is	be	AUX
ejpam-4453	493	8	subdivided	subdivide	VERB
ejpam-4453	493	9	which	which	PRON
ejpam-4453	493	10	produces	produce	VERB
ejpam-4453	493	11	a	a	DET
ejpam-4453	493	12	path	path	NOUN
ejpam-4453	493	13	of	of	ADP
ejpam-4453	493	14	length	length	NOUN
ejpam-4453	493	15	2	2	NUM
ejpam-4453	493	16	such	such	ADJ
ejpam-4453	493	17	that	that	SCONJ
ejpam-4453	493	18	the	the	DET
ejpam-4453	493	19	new	new	ADJ
ejpam-4453	493	20	vertex	vertex	NOUN
ejpam-4453	493	21	should	should	AUX
ejpam-4453	493	22	equal	equal	VERB
ejpam-4453	493	23	to	to	ADP
ejpam-4453	493	24	exactly	exactly	ADV
ejpam-4453	493	25	one	one	NUM
ejpam-4453	493	26	end	end	NOUN
ejpam-4453	493	27	-	-	PUNCT
ejpam-4453	493	28	vertex	vertex	NOUN
ejpam-4453	493	29	in	in	ADP
ejpam-4453	493	30	the	the	DET
ejpam-4453	493	31	central	central	ADJ
ejpam-4453	493	32	fragment	fragment	NOUN
ejpam-4453	493	33	is	be	AUX
ejpam-4453	493	34	called	call	VERB
ejpam-4453	493	35	constructed	construct	VERB
ejpam-4453	493	36	b̂i	b̂i	PROPN
ejpam-4453	493	37	of	of	ADP
ejpam-4453	493	38	bi	bi	PROPN
ejpam-4453	493	39	.	.	PUNCT
ejpam-4453	494	1	now	now	ADV
ejpam-4453	494	2	,	,	PUNCT
ejpam-4453	494	3	we	we	PRON
ejpam-4453	494	4	will	will	AUX
ejpam-4453	494	5	discuss	discuss	VERB
ejpam-4453	494	6	the	the	DET
ejpam-4453	494	7	construction	construction	NOUN
ejpam-4453	494	8	of	of	ADP
ejpam-4453	494	9	a	a	DET
ejpam-4453	494	10	ntcbg	ntcbg	NOUN
ejpam-4453	494	11	.	.	PUNCT
ejpam-4453	495	1	first	first	ADV
ejpam-4453	495	2	,	,	PUNCT
ejpam-4453	495	3	consider	consider	VERB
ejpam-4453	495	4	a	a	DET
ejpam-4453	495	5	central	central	ADJ
ejpam-4453	495	6	fragment	fragment	NOUN
ejpam-4453	495	7	with	with	ADP
ejpam-4453	495	8	s	s	NOUN
ejpam-4453	495	9	=	=	PUNCT
ejpam-4453	495	10	{	{	PUNCT
ejpam-4453	495	11	v1	v1	PROPN
ejpam-4453	495	12	,	,	PUNCT
ejpam-4453	495	13	v2	v2	PROPN
ejpam-4453	495	14	,	,	PUNCT
ejpam-4453	495	15	v3	v3	PROPN
ejpam-4453	495	16	}	}	PUNCT
ejpam-4453	495	17	,	,	PUNCT
ejpam-4453	495	18	where	where	SCONJ
ejpam-4453	495	19	s	s	NOUN
ejpam-4453	495	20	is	be	AUX
ejpam-4453	495	21	the	the	DET
ejpam-4453	495	22	set	set	NOUN
ejpam-4453	495	23	of	of	ADP
ejpam-4453	495	24	end	end	NOUN
ejpam-4453	495	25	-	-	PUNCT
ejpam-4453	495	26	vertices	vertex	NOUN
ejpam-4453	495	27	of	of	ADP
ejpam-4453	495	28	the	the	DET
ejpam-4453	495	29	central	central	ADJ
ejpam-4453	495	30	fragment	fragment	NOUN
ejpam-4453	495	31	as	as	SCONJ
ejpam-4453	495	32	shown	show	VERB
ejpam-4453	495	33	in	in	ADP
ejpam-4453	495	34	figure	figure	NOUN
ejpam-4453	495	35	8	8	NUM
ejpam-4453	495	36	(	(	PUNCT
ejpam-4453	495	37	a	a	NOUN
ejpam-4453	495	38	)	)	PUNCT
ejpam-4453	495	39	.	.	PUNCT
ejpam-4453	496	1	secondly	secondly	ADV
ejpam-4453	496	2	,	,	PUNCT
ejpam-4453	496	3	consider	consider	VERB
ejpam-4453	496	4	an	an	DET
ejpam-4453	496	5	arbitrary	arbitrary	ADJ
ejpam-4453	496	6	branch	branch	NOUN
ejpam-4453	496	7	of	of	ADP
ejpam-4453	496	8	ntcbg	ntcbg	PROPN
ejpam-4453	496	9	,	,	PUNCT
ejpam-4453	496	10	say	say	VERB
ejpam-4453	496	11	bi	bi	NOUN
ejpam-4453	496	12	,	,	PUNCT
ejpam-4453	496	13	shown	show	VERB
ejpam-4453	496	14	in	in	ADP
ejpam-4453	496	15	figure	figure	NOUN
ejpam-4453	496	16	8(b	8(b	NUM
ejpam-4453	496	17	)	)	PUNCT
ejpam-4453	496	18	.	.	PUNCT
ejpam-4453	497	1	choose	choose	VERB
ejpam-4453	497	2	any	any	DET
ejpam-4453	497	3	edge	edge	NOUN
ejpam-4453	497	4	for	for	ADP
ejpam-4453	497	5	each	each	DET
ejpam-4453	497	6	graph	graph	NOUN
ejpam-4453	497	7	.	.	PUNCT
ejpam-4453	498	1	then	then	ADV
ejpam-4453	498	2	divide	divide	VERB
ejpam-4453	498	3	this	this	DET
ejpam-4453	498	4	edge	edge	NOUN
ejpam-4453	498	5	into	into	ADP
ejpam-4453	498	6	two	two	NUM
ejpam-4453	498	7	such	such	ADJ
ejpam-4453	498	8	that	that	SCONJ
ejpam-4453	498	9	it	it	PRON
ejpam-4453	498	10	produces	produce	VERB
ejpam-4453	498	11	a	a	DET
ejpam-4453	498	12	path	path	NOUN
ejpam-4453	498	13	of	of	ADP
ejpam-4453	498	14	length	length	NOUN
ejpam-4453	498	15	2	2	NUM
ejpam-4453	498	16	.	.	PUNCT
ejpam-4453	499	1	now	now	ADV
ejpam-4453	499	2	,	,	PUNCT
ejpam-4453	499	3	the	the	DET
ejpam-4453	499	4	new	new	ADJ
ejpam-4453	499	5	vertex	vertex	NOUN
ejpam-4453	499	6	should	should	AUX
ejpam-4453	499	7	be	be	AUX
ejpam-4453	499	8	equal	equal	ADJ
ejpam-4453	499	9	to	to	ADP
ejpam-4453	499	10	exactly	exactly	ADV
ejpam-4453	499	11	one	one	NUM
ejpam-4453	499	12	of	of	ADP
ejpam-4453	499	13	the	the	DET
ejpam-4453	499	14	vertices	vertex	NOUN
ejpam-4453	499	15	in	in	ADP
ejpam-4453	499	16	s.	s.	PROPN
ejpam-4453	499	17	this	this	PRON
ejpam-4453	499	18	will	will	AUX
ejpam-4453	499	19	produce	produce	VERB
ejpam-4453	499	20	the	the	DET
ejpam-4453	499	21	graph	graph	NOUN
ejpam-4453	499	22	in	in	ADP
ejpam-4453	499	23	figure	figure	NOUN
ejpam-4453	499	24	8	8	NUM
ejpam-4453	499	25	(	(	PUNCT
ejpam-4453	499	26	b	b	NOUN
ejpam-4453	499	27	)	)	PUNCT
ejpam-4453	499	28	.	.	PUNCT
ejpam-4453	500	1	take	take	VERB
ejpam-4453	500	2	the	the	DET
ejpam-4453	500	3	union	union	NOUN
ejpam-4453	500	4	to	to	ADP
ejpam-4453	500	5	the	the	DET
ejpam-4453	500	6	central	central	ADJ
ejpam-4453	500	7	fragment	fragment	NOUN
ejpam-4453	500	8	c	c	PROPN
ejpam-4453	500	9	and	and	CCONJ
ejpam-4453	500	10	3	3	NUM
ejpam-4453	500	11	copies	copy	NOUN
ejpam-4453	500	12	of	of	ADP
ejpam-4453	500	13	branch	branch	NOUN
ejpam-4453	500	14	bi	bi	NOUN
ejpam-4453	500	15	.	.	PUNCT
ejpam-4453	501	1	the	the	DET
ejpam-4453	501	2	resulting	result	VERB
ejpam-4453	501	3	graph	graph	NOUN
ejpam-4453	501	4	is	be	AUX
ejpam-4453	501	5	shown	show	VERB
ejpam-4453	501	6	in	in	ADP
ejpam-4453	501	7	figure	figure	NOUN
ejpam-4453	501	8	8	8	NUM
ejpam-4453	501	9	(	(	PUNCT
ejpam-4453	501	10	c	c	NOUN
ejpam-4453	501	11	)	)	PUNCT
ejpam-4453	501	12	.	.	PUNCT
ejpam-4453	502	1	observe	observe	VERB
ejpam-4453	502	2	that	that	SCONJ
ejpam-4453	502	3	the	the	DET
ejpam-4453	502	4	result	result	NOUN
ejpam-4453	502	5	is	be	AUX
ejpam-4453	502	6	a	a	DET
ejpam-4453	502	7	non	non	ADJ
ejpam-4453	502	8	-	-	ADJ
ejpam-4453	502	9	traceable	traceable	ADJ
ejpam-4453	502	10	cubic	cubic	ADJ
ejpam-4453	502	11	graph	graph	NOUN
ejpam-4453	502	12	of	of	ADP
ejpam-4453	502	13	order	order	NOUN
ejpam-4453	502	14	|v	|v	X
ejpam-4453	502	15	(	(	PUNCT
ejpam-4453	502	16	g)|	g)|	NOUN
ejpam-4453	502	17	=	=	PUNCT
ejpam-4453	502	18	|v	|v	X
ejpam-4453	502	19	(	(	PUNCT
ejpam-4453	502	20	c	c	NOUN
ejpam-4453	502	21	)	)	PUNCT
ejpam-4453	502	22	|+	|+	PROPN
ejpam-4453	502	23	∑	∑	PUNCT
ejpam-4453	502	24	|v	|v	PROPN
ejpam-4453	502	25	(	(	PUNCT
ejpam-4453	502	26	bi)|	bi)|	PROPN
ejpam-4453	502	27	.	.	PUNCT
ejpam-4453	503	1	proposition	proposition	NOUN
ejpam-4453	503	2	5	5	NUM
ejpam-4453	503	3	.	.	PUNCT
ejpam-4453	504	1	let	let	VERB
ejpam-4453	504	2	bi	bi	NOUN
ejpam-4453	504	3	,	,	PUNCT
ejpam-4453	504	4	i	i	PROPN
ejpam-4453	504	5	∈	∈	PROPN
ejpam-4453	504	6	n	n	AUX
ejpam-4453	504	7	,	,	PUNCT
ejpam-4453	504	8	be	be	AUX
ejpam-4453	504	9	the	the	DET
ejpam-4453	504	10	branch	branch	NOUN
ejpam-4453	504	11	of	of	ADP
ejpam-4453	504	12	ntcbg	ntcbg	PROPN
ejpam-4453	504	13	g	g	PROPN
ejpam-4453	504	14	then	then	ADV
ejpam-4453	504	15	|v	|v	PROPN
ejpam-4453	504	16	(	(	PUNCT
ejpam-4453	504	17	bi)|	bi)|	PROPN
ejpam-4453	504	18	=	=	SYM
ejpam-4453	504	19	2(b−1	2(b−1	NOUN
ejpam-4453	504	20	)	)	PUNCT
ejpam-4453	505	1	where	where	SCONJ
ejpam-4453	505	2	b	b	X
ejpam-4453	505	3	≥	≥	NOUN
ejpam-4453	505	4	3	3	NUM
ejpam-4453	505	5	.	.	PUNCT
ejpam-4453	505	6	a.r	a.r	PROPN
ejpam-4453	505	7	nieva	nieva	PROPN
ejpam-4453	505	8	and	and	CCONJ
ejpam-4453	505	9	k.nocum	k.nocum	PROPN
ejpam-4453	505	10	/	/	SYM
ejpam-4453	505	11	eur	eur	PROPN
ejpam-4453	505	12	.	.	PUNCT
ejpam-4453	506	1	j.	j.	PROPN
ejpam-4453	506	2	pure	pure	PROPN
ejpam-4453	506	3	appl	appl	PROPN
ejpam-4453	506	4	.	.	PROPN
ejpam-4453	506	5	math	math	PROPN
ejpam-4453	506	6	,	,	PUNCT
ejpam-4453	506	7	15	15	NUM
ejpam-4453	506	8	(	(	PUNCT
ejpam-4453	506	9	4	4	NUM
ejpam-4453	506	10	)	)	PUNCT
ejpam-4453	506	11	(	(	PUNCT
ejpam-4453	506	12	2022	2022	NUM
ejpam-4453	506	13	)	)	PUNCT
ejpam-4453	506	14	,	,	PUNCT
ejpam-4453	506	15	1536	1536	NUM
ejpam-4453	506	16	-	-	SYM
ejpam-4453	506	17	1548	1548	NUM
ejpam-4453	506	18	1543	1543	NUM
ejpam-4453	506	19	(	(	PUNCT
ejpam-4453	506	20	a	a	DET
ejpam-4453	506	21	)	)	PUNCT
ejpam-4453	506	22	v1	v1	PROPN
ejpam-4453	506	23	v2	v2	PROPN
ejpam-4453	506	24	v3	v3	PROPN
ejpam-4453	506	25	.......................................................	.......................................................	PUNCT
ejpam-4453	506	26	.............................................	.............................................	PUNCT
ejpam-4453	506	27	.	.	PUNCT
ejpam-4453	507	1	....................................................	....................................................	PUNCT
ejpam-4453	507	2	.............................................	.............................................	PUNCT
ejpam-4453	507	3	.	.	PUNCT
ejpam-4453	508	1	..........	..........	PUNCT
ejpam-4453	508	2	.............................................	.............................................	PUNCT
ejpam-4453	508	3	.	.	PUNCT
ejpam-4453	509	1	.........	.........	PUNCT
ejpam-4453	509	2	........	........	PUNCT
ejpam-4453	509	3	........	........	PUNCT
ejpam-4453	509	4	........	........	PUNCT
ejpam-4453	510	1	........	........	PUNCT
ejpam-4453	510	2	.	.	PUNCT
ejpam-4453	511	1	..........	..........	PUNCT
ejpam-4453	511	2	.............................................	.............................................	PUNCT
ejpam-4453	511	3	.	.	PUNCT
ejpam-4453	512	1	..........	..........	PUNCT
ejpam-4453	512	2	.............................................	.............................................	PUNCT
ejpam-4453	512	3	.	.	PUNCT
ejpam-4453	513	1	v1	v1	PROPN
ejpam-4453	513	2	...........................................	...........................................	PUNCT
ejpam-4453	513	3	............................................................................................................	............................................................................................................	PUNCT
ejpam-4453	513	4	.............................................	.............................................	PUNCT
ejpam-4453	513	5	.	.	PUNCT
ejpam-4453	513	6	.........	.........	PUNCT
ejpam-4453	513	7	........	........	PUNCT
ejpam-4453	513	8	........	........	PUNCT
ejpam-4453	513	9	........	........	PUNCT
ejpam-4453	513	10	........	........	PUNCT
ejpam-4453	513	11	.	.	PUNCT
ejpam-4453	514	1	..........	..........	PUNCT
ejpam-4453	514	2	.............................................	.............................................	PUNCT
ejpam-4453	514	3	.	.	PUNCT
ejpam-4453	515	1	..........	..........	PUNCT
ejpam-4453	515	2	.............................................	.............................................	PUNCT
ejpam-4453	515	3	....................	....................	PUNCT
ejpam-4453	516	1	..........	..........	PUNCT
ejpam-4453	516	2	.........	.........	PUNCT
ejpam-4453	517	1	.................................................................	.................................................................	PUNCT
ejpam-4453	517	2	..........	..........	PUNCT
ejpam-4453	517	3	.............................................	.............................................	PUNCT
ejpam-4453	517	4	.	.	PUNCT
ejpam-4453	518	1	..........	..........	PUNCT
ejpam-4453	518	2	.............................................	.............................................	PUNCT
ejpam-4453	519	1	.............	.............	PUNCT
ejpam-4453	519	2	...........	...........	PUNCT
ejpam-4453	519	3	...........	...........	PUNCT
ejpam-4453	519	4	...........	...........	PUNCT
ejpam-4453	519	5	...........	...........	PUNCT
ejpam-4453	519	6	.........	.........	PUNCT
ejpam-4453	520	1	..........	..........	PUNCT
ejpam-4453	520	2	.............................................	.............................................	PUNCT
ejpam-4453	520	3	.	.	PUNCT
ejpam-4453	521	1	..........	..........	PUNCT
ejpam-4453	521	2	.............................................	.............................................	PUNCT
ejpam-4453	521	3	.	.	PUNCT
ejpam-4453	522	1	.........	.........	PUNCT
ejpam-4453	522	2	........	........	PUNCT
ejpam-4453	522	3	........	........	PUNCT
ejpam-4453	522	4	........	........	PUNCT
ejpam-4453	523	1	........	........	PUNCT
ejpam-4453	523	2	.	.	PUNCT
ejpam-4453	524	1	..........	..........	PUNCT
ejpam-4453	524	2	.............................................	.............................................	PUNCT
ejpam-4453	524	3	.	.	PUNCT
ejpam-4453	525	1	....................................................	....................................................	PUNCT
ejpam-4453	525	2	.............................................	.............................................	PUNCT
ejpam-4453	525	3	.	.	PUNCT
ejpam-4453	526	1	.........	.........	PUNCT
ejpam-4453	526	2	........	........	PUNCT
ejpam-4453	526	3	........	........	PUNCT
ejpam-4453	526	4	........	........	PUNCT
ejpam-4453	527	1	........	........	PUNCT
ejpam-4453	527	2	.	.	PUNCT
ejpam-4453	528	1	..........	..........	PUNCT
ejpam-4453	528	2	.............................................	.............................................	PUNCT
ejpam-4453	528	3	.	.	PUNCT
ejpam-4453	529	1	..........................................	..........................................	PUNCT
ejpam-4453	530	1	..........	..........	PUNCT
ejpam-4453	531	1	.............................................	.............................................	PUNCT
ejpam-4453	532	1	...........	...........	PUNCT
ejpam-4453	533	1	.............................................	.............................................	PUNCT
ejpam-4453	533	2	.	.	PUNCT
ejpam-4453	534	1	.................................................................	.................................................................	PUNCT
ejpam-4453	535	1	..........	..........	PUNCT
ejpam-4453	535	2	.............................................	.............................................	PUNCT
ejpam-4453	535	3	.	.	PUNCT
ejpam-4453	536	1	..........	..........	PUNCT
ejpam-4453	536	2	.............................................	.............................................	PUNCT
ejpam-4453	537	1	.............	.............	PUNCT
ejpam-4453	537	2	...........	...........	PUNCT
ejpam-4453	537	3	...........	...........	PUNCT
ejpam-4453	537	4	...........	...........	PUNCT
ejpam-4453	537	5	...........	...........	PUNCT
ejpam-4453	537	6	.........	.........	PUNCT
ejpam-4453	538	1	..........	..........	PUNCT
ejpam-4453	538	2	.............................................	.............................................	PUNCT
ejpam-4453	538	3	.	.	PUNCT
ejpam-4453	539	1	..........	..........	PUNCT
ejpam-4453	539	2	.............................................	.............................................	PUNCT
ejpam-4453	539	3	.	.	PUNCT
ejpam-4453	540	1	v2	v2	INTJ
ejpam-4453	540	2	.	.	PUNCT
ejpam-4453	541	1	(	(	PUNCT
ejpam-4453	541	2	b	b	X
ejpam-4453	541	3	)	)	PUNCT
ejpam-4453	541	4	.........	.........	PUNCT
ejpam-4453	541	5	........	........	PUNCT
ejpam-4453	541	6	........	........	PUNCT
ejpam-4453	541	7	........	........	PUNCT
ejpam-4453	541	8	........	........	PUNCT
ejpam-4453	541	9	.	.	PUNCT
ejpam-4453	542	1	..........	..........	PUNCT
ejpam-4453	542	2	.............................................	.............................................	PUNCT
ejpam-4453	542	3	.	.	PUNCT
ejpam-4453	543	1	....................................................	....................................................	PUNCT
ejpam-4453	543	2	.............................................	.............................................	PUNCT
ejpam-4453	543	3	.	.	PUNCT
ejpam-4453	544	1	.........	.........	PUNCT
ejpam-4453	544	2	........	........	PUNCT
ejpam-4453	544	3	........	........	PUNCT
ejpam-4453	544	4	........	........	PUNCT
ejpam-4453	545	1	........	........	PUNCT
ejpam-4453	545	2	.	.	PUNCT
ejpam-4453	546	1	..........	..........	PUNCT
ejpam-4453	546	2	.............................................	.............................................	PUNCT
ejpam-4453	546	3	.	.	PUNCT
ejpam-4453	547	1	..........	..........	PUNCT
ejpam-4453	547	2	.............................................	.............................................	PUNCT
ejpam-4453	547	3	....................	....................	PUNCT
ejpam-4453	548	1	..........	..........	PUNCT
ejpam-4453	548	2	.........	.........	PUNCT
ejpam-4453	549	1	.................................................................	.................................................................	PUNCT
ejpam-4453	549	2	..........	..........	PUNCT
ejpam-4453	549	3	.............................................	.............................................	PUNCT
ejpam-4453	549	4	.	.	PUNCT
ejpam-4453	550	1	..........	..........	PUNCT
ejpam-4453	550	2	.............................................	.............................................	PUNCT
ejpam-4453	551	1	.............	.............	PUNCT
ejpam-4453	551	2	...........	...........	PUNCT
ejpam-4453	551	3	...........	...........	PUNCT
ejpam-4453	551	4	...........	...........	PUNCT
ejpam-4453	551	5	...........	...........	PUNCT
ejpam-4453	551	6	.........	.........	PUNCT
ejpam-4453	552	1	..........	..........	PUNCT
ejpam-4453	552	2	.............................................	.............................................	PUNCT
ejpam-4453	552	3	.	.	PUNCT
ejpam-4453	553	1	..........	..........	PUNCT
ejpam-4453	553	2	.............................................	.............................................	PUNCT
ejpam-4453	553	3	.	.	PUNCT
ejpam-4453	554	1	.........	.........	PUNCT
ejpam-4453	554	2	........	........	PUNCT
ejpam-4453	554	3	........	........	PUNCT
ejpam-4453	554	4	........	........	PUNCT
ejpam-4453	555	1	........	........	PUNCT
ejpam-4453	555	2	.	.	PUNCT
ejpam-4453	556	1	..........	..........	PUNCT
ejpam-4453	556	2	.............................................	.............................................	PUNCT
ejpam-4453	556	3	.	.	PUNCT
ejpam-4453	557	1	....................................................	....................................................	PUNCT
ejpam-4453	557	2	.............................................	.............................................	PUNCT
ejpam-4453	557	3	.	.	PUNCT
ejpam-4453	558	1	.........	.........	PUNCT
ejpam-4453	558	2	........	........	PUNCT
ejpam-4453	558	3	........	........	PUNCT
ejpam-4453	558	4	........	........	PUNCT
ejpam-4453	559	1	........	........	PUNCT
ejpam-4453	559	2	.	.	PUNCT
ejpam-4453	560	1	..........	..........	PUNCT
ejpam-4453	560	2	.............................................	.............................................	PUNCT
ejpam-4453	560	3	.	.	PUNCT
ejpam-4453	561	1	..........................................	..........................................	PUNCT
ejpam-4453	562	1	..........	..........	PUNCT
ejpam-4453	563	1	.............................................	.............................................	PUNCT
ejpam-4453	564	1	...........	...........	PUNCT
ejpam-4453	565	1	.............................................	.............................................	PUNCT
ejpam-4453	565	2	.	.	PUNCT
ejpam-4453	566	1	.................................................................	.................................................................	PUNCT
ejpam-4453	567	1	..........	..........	PUNCT
ejpam-4453	567	2	.............................................	.............................................	PUNCT
ejpam-4453	567	3	.	.	PUNCT
ejpam-4453	568	1	..........	..........	PUNCT
ejpam-4453	568	2	.............................................	.............................................	PUNCT
ejpam-4453	569	1	.............	.............	PUNCT
ejpam-4453	569	2	...........	...........	PUNCT
ejpam-4453	569	3	...........	...........	PUNCT
ejpam-4453	569	4	...........	...........	PUNCT
ejpam-4453	569	5	...........	...........	PUNCT
ejpam-4453	569	6	.........	.........	PUNCT
ejpam-4453	570	1	..........	..........	PUNCT
ejpam-4453	570	2	.............................................	.............................................	PUNCT
ejpam-4453	570	3	.	.	PUNCT
ejpam-4453	571	1	..........	..........	PUNCT
ejpam-4453	571	2	.............................................	.............................................	PUNCT
ejpam-4453	571	3	.	.	PUNCT
ejpam-4453	572	1	v3	v3	PROPN
ejpam-4453	572	2	...........................................	...........................................	PUNCT
ejpam-4453	572	3	............................................................................................................	............................................................................................................	PROPN
ejpam-4453	572	4	.............................................	.............................................	PUNCT
ejpam-4453	572	5	.	.	PUNCT
ejpam-4453	572	6	.........	.........	PUNCT
ejpam-4453	573	1	........	........	PUNCT
ejpam-4453	573	2	........	........	PUNCT
ejpam-4453	573	3	........	........	PUNCT
ejpam-4453	573	4	........	........	PUNCT
ejpam-4453	573	5	.	.	PUNCT
ejpam-4453	574	1	..........	..........	PUNCT
ejpam-4453	574	2	.............................................	.............................................	PUNCT
ejpam-4453	574	3	.	.	PUNCT
ejpam-4453	575	1	..........	..........	PUNCT
ejpam-4453	575	2	.............................................	.............................................	PUNCT
ejpam-4453	575	3	....................	....................	PUNCT
ejpam-4453	576	1	..........	..........	PUNCT
ejpam-4453	576	2	.........	.........	PUNCT
ejpam-4453	577	1	.................................................................	.................................................................	PUNCT
ejpam-4453	577	2	..........	..........	PUNCT
ejpam-4453	577	3	.............................................	.............................................	PUNCT
ejpam-4453	577	4	.	.	PUNCT
ejpam-4453	578	1	..........	..........	PUNCT
ejpam-4453	578	2	.............................................	.............................................	PUNCT
ejpam-4453	579	1	.............	.............	PUNCT
ejpam-4453	579	2	...........	...........	PUNCT
ejpam-4453	579	3	...........	...........	PUNCT
ejpam-4453	579	4	...........	...........	PUNCT
ejpam-4453	579	5	...........	...........	PUNCT
ejpam-4453	579	6	.........	.........	PUNCT
ejpam-4453	580	1	..........	..........	PUNCT
ejpam-4453	580	2	.............................................	.............................................	PUNCT
ejpam-4453	580	3	.	.	PUNCT
ejpam-4453	581	1	..........	..........	PUNCT
ejpam-4453	581	2	.............................................	.............................................	PUNCT
ejpam-4453	581	3	.	.	PUNCT
ejpam-4453	582	1	.........	.........	PUNCT
ejpam-4453	582	2	........	........	PUNCT
ejpam-4453	582	3	........	........	PUNCT
ejpam-4453	582	4	........	........	PUNCT
ejpam-4453	583	1	........	........	PUNCT
ejpam-4453	583	2	.	.	PUNCT
ejpam-4453	584	1	..........	..........	PUNCT
ejpam-4453	584	2	.............................................	.............................................	PUNCT
ejpam-4453	584	3	.	.	PUNCT
ejpam-4453	585	1	....................................................	....................................................	PUNCT
ejpam-4453	585	2	.............................................	.............................................	PUNCT
ejpam-4453	585	3	.	.	PUNCT
ejpam-4453	586	1	.........	.........	PUNCT
ejpam-4453	586	2	........	........	PUNCT
ejpam-4453	586	3	........	........	PUNCT
ejpam-4453	586	4	........	........	PUNCT
ejpam-4453	587	1	........	........	PUNCT
ejpam-4453	587	2	.	.	PUNCT
ejpam-4453	588	1	..........	..........	PUNCT
ejpam-4453	588	2	.............................................	.............................................	PUNCT
ejpam-4453	588	3	.	.	PUNCT
ejpam-4453	589	1	..........................................	..........................................	PUNCT
ejpam-4453	590	1	..........	..........	PUNCT
ejpam-4453	591	1	.............................................	.............................................	PUNCT
ejpam-4453	592	1	...........	...........	PUNCT
ejpam-4453	593	1	.............................................	.............................................	PUNCT
ejpam-4453	593	2	.	.	PUNCT
ejpam-4453	594	1	.................................................................	.................................................................	PUNCT
ejpam-4453	595	1	..........	..........	PUNCT
ejpam-4453	595	2	.............................................	.............................................	PUNCT
ejpam-4453	595	3	.	.	PUNCT
ejpam-4453	596	1	..........	..........	PUNCT
ejpam-4453	596	2	.............................................	.............................................	PUNCT
ejpam-4453	597	1	.............	.............	PUNCT
ejpam-4453	597	2	...........	...........	PUNCT
ejpam-4453	597	3	...........	...........	PUNCT
ejpam-4453	597	4	...........	...........	PUNCT
ejpam-4453	597	5	...........	...........	PUNCT
ejpam-4453	597	6	.........	.........	PUNCT
ejpam-4453	598	1	..........	..........	PUNCT
ejpam-4453	598	2	.............................................	.............................................	PUNCT
ejpam-4453	598	3	.	.	PUNCT
ejpam-4453	599	1	..........	..........	PUNCT
ejpam-4453	599	2	.............................................	.............................................	PUNCT
ejpam-4453	599	3	.	.	PUNCT
ejpam-4453	600	1	(	(	PUNCT
ejpam-4453	600	2	c	c	NOUN
ejpam-4453	600	3	)	)	PUNCT
ejpam-4453	600	4	.	.	PUNCT
ejpam-4453	601	1	..	..	PUNCT
ejpam-4453	601	2	v1	v1	VERB
ejpam-4453	601	3	v2	v2	PROPN
ejpam-4453	601	4	v3	v3	PROPN
ejpam-4453	601	5	.........................	.........................	PUNCT
ejpam-4453	601	6	..........	..........	PUNCT
ejpam-4453	601	7	.............................................	.............................................	PUNCT
ejpam-4453	601	8	.	.	PUNCT
ejpam-4453	601	9	..........................................	..........................................	PUNCT
ejpam-4453	602	1	..........	..........	PUNCT
ejpam-4453	602	2	.............................................	.............................................	PUNCT
ejpam-4453	602	3	.	.	PUNCT
ejpam-4453	603	1	.........	.........	PUNCT
ejpam-4453	603	2	........	........	PUNCT
ejpam-4453	603	3	........	........	PUNCT
ejpam-4453	603	4	........	........	PUNCT
ejpam-4453	604	1	........	........	PUNCT
ejpam-4453	604	2	.	.	PUNCT
ejpam-4453	605	1	..........	..........	PUNCT
ejpam-4453	605	2	.............................................	.............................................	PUNCT
ejpam-4453	605	3	.	.	PUNCT
ejpam-4453	606	1	....................................................	....................................................	PUNCT
ejpam-4453	606	2	.............................................	.............................................	PUNCT
ejpam-4453	606	3	.	.	PUNCT
ejpam-4453	606	4	............	............	PUNCT
ejpam-4453	607	1	...........	...........	PUNCT
ejpam-4453	607	2	..	..	PUNCT
ejpam-4453	607	3	..........	..........	PUNCT
ejpam-4453	607	4	.............................................	.............................................	PUNCT
ejpam-4453	607	5	.	.	PUNCT
ejpam-4453	608	1	....................................................	....................................................	PUNCT
ejpam-4453	608	2	.............................................	.............................................	PUNCT
ejpam-4453	608	3	.	.	PUNCT
ejpam-4453	609	1	....................................................	....................................................	PUNCT
ejpam-4453	609	2	.............................................	.............................................	PUNCT
ejpam-4453	609	3	.	.	PUNCT
ejpam-4453	610	1	..........	..........	PUNCT
ejpam-4453	610	2	.............................................	.............................................	PUNCT
ejpam-4453	610	3	.	.	PUNCT
ejpam-4453	611	1	.................................................................	.................................................................	PUNCT
ejpam-4453	612	1	..........	..........	PUNCT
ejpam-4453	612	2	.............................................	.............................................	PUNCT
ejpam-4453	612	3	.	.	PUNCT
ejpam-4453	613	1	..........	..........	PUNCT
ejpam-4453	613	2	.............................................	.............................................	PUNCT
ejpam-4453	614	1	.............	.............	PUNCT
ejpam-4453	614	2	...........	...........	PUNCT
ejpam-4453	614	3	...........	...........	PUNCT
ejpam-4453	614	4	...........	...........	PUNCT
ejpam-4453	614	5	...........	...........	PUNCT
ejpam-4453	614	6	.........	.........	PUNCT
ejpam-4453	615	1	..........	..........	PUNCT
ejpam-4453	615	2	.............................................	.............................................	PUNCT
ejpam-4453	615	3	.	.	PUNCT
ejpam-4453	616	1	..........	..........	PUNCT
ejpam-4453	616	2	.............................................	.............................................	PUNCT
ejpam-4453	616	3	.	.	PUNCT
ejpam-4453	616	4	............	............	PUNCT
ejpam-4453	617	1	...........	...........	PUNCT
ejpam-4453	617	2	..	..	PUNCT
ejpam-4453	617	3	..........	..........	PUNCT
ejpam-4453	617	4	.............................................	.............................................	PUNCT
ejpam-4453	617	5	.	.	PUNCT
ejpam-4453	618	1	....................................................	....................................................	PUNCT
ejpam-4453	618	2	.............................................	.............................................	PUNCT
ejpam-4453	618	3	.	.	PUNCT
ejpam-4453	619	1	.........	.........	PUNCT
ejpam-4453	619	2	........	........	PUNCT
ejpam-4453	619	3	........	........	PUNCT
ejpam-4453	619	4	........	........	PUNCT
ejpam-4453	620	1	........	........	PUNCT
ejpam-4453	620	2	.	.	PUNCT
ejpam-4453	621	1	..........	..........	PUNCT
ejpam-4453	621	2	.............................................	.............................................	PUNCT
ejpam-4453	621	3	.	.	PUNCT
ejpam-4453	622	1	..........................................	..........................................	PUNCT
ejpam-4453	622	2	..........	..........	PUNCT
ejpam-4453	623	1	.............................................	.............................................	PUNCT
ejpam-4453	623	2	.	.	PUNCT
ejpam-4453	624	1	.........................	.........................	PUNCT
ejpam-4453	624	2	..........	..........	PUNCT
ejpam-4453	625	1	.............................................	.............................................	PUNCT
ejpam-4453	625	2	.	.	PUNCT
ejpam-4453	626	1	..........	..........	PUNCT
ejpam-4453	626	2	.............................................	.............................................	PUNCT
ejpam-4453	626	3	.	.	PUNCT
ejpam-4453	626	4	............	............	PUNCT
ejpam-4453	627	1	...........	...........	PUNCT
ejpam-4453	627	2	...........	...........	PUNCT
ejpam-4453	627	3	...........	...........	PUNCT
ejpam-4453	627	4	...........	...........	PUNCT
ejpam-4453	627	5	.........	.........	PUNCT
ejpam-4453	628	1	..........	..........	PUNCT
ejpam-4453	628	2	.............................................	.............................................	PUNCT
ejpam-4453	628	3	.	.	PUNCT
ejpam-4453	629	1	..........	..........	PUNCT
ejpam-4453	629	2	.............................................	.............................................	PUNCT
ejpam-4453	629	3	.	.	PUNCT
ejpam-4453	630	1	.................................................................	.................................................................	PUNCT
ejpam-4453	631	1	..........	..........	PUNCT
ejpam-4453	631	2	.............................................	.............................................	PUNCT
ejpam-4453	631	3	.	.	PUNCT
ejpam-4453	632	1	..........	..........	PUNCT
ejpam-4453	632	2	.............................................	.............................................	PUNCT
ejpam-4453	632	3	.	.	PUNCT
ejpam-4453	633	1	.........	.........	PUNCT
ejpam-4453	633	2	........	........	PUNCT
ejpam-4453	633	3	........	........	PUNCT
ejpam-4453	633	4	........	........	PUNCT
ejpam-4453	634	1	........	........	PUNCT
ejpam-4453	634	2	.	.	PUNCT
ejpam-4453	635	1	..........	..........	PUNCT
ejpam-4453	635	2	.............................................	.............................................	PUNCT
ejpam-4453	635	3	.	.	PUNCT
ejpam-4453	636	1	.........................	.........................	PUNCT
ejpam-4453	636	2	..........	..........	PUNCT
ejpam-4453	637	1	.............................................	.............................................	PUNCT
ejpam-4453	637	2	.	.	PUNCT
ejpam-4453	638	1	.........	.........	PUNCT
ejpam-4453	638	2	........	........	PUNCT
ejpam-4453	638	3	........	........	PUNCT
ejpam-4453	638	4	........	........	PUNCT
ejpam-4453	639	1	........	........	PUNCT
ejpam-4453	639	2	.	.	PUNCT
ejpam-4453	640	1	..........	..........	PUNCT
ejpam-4453	640	2	.............................................	.............................................	PUNCT
ejpam-4453	640	3	.	.	PUNCT
ejpam-4453	641	1	....................................................	....................................................	PUNCT
ejpam-4453	641	2	.............................................	.............................................	PUNCT
ejpam-4453	641	3	.	.	PUNCT
ejpam-4453	642	1	.........	.........	PUNCT
ejpam-4453	642	2	........	........	PUNCT
ejpam-4453	642	3	........	........	PUNCT
ejpam-4453	642	4	........	........	PUNCT
ejpam-4453	643	1	........	........	PUNCT
ejpam-4453	643	2	.	.	PUNCT
ejpam-4453	644	1	..........	..........	PUNCT
ejpam-4453	644	2	.............................................	.............................................	PUNCT
ejpam-4453	644	3	.	.	PUNCT
ejpam-4453	644	4	............	............	PUNCT
ejpam-4453	645	1	...........	...........	PUNCT
ejpam-4453	645	2	..	..	PUNCT
ejpam-4453	645	3	..........	..........	PUNCT
ejpam-4453	645	4	.............................................	.............................................	PUNCT
ejpam-4453	645	5	.	.	PUNCT
ejpam-4453	646	1	..........	..........	PUNCT
ejpam-4453	646	2	.............................................	.............................................	PUNCT
ejpam-4453	646	3	.	.	PUNCT
ejpam-4453	647	1	.................................................................	.................................................................	PUNCT
ejpam-4453	648	1	..........	..........	PUNCT
ejpam-4453	648	2	.............................................	.............................................	PUNCT
ejpam-4453	648	3	.	.	PUNCT
ejpam-4453	649	1	..........	..........	PUNCT
ejpam-4453	649	2	.............................................	.............................................	PUNCT
ejpam-4453	650	1	.............	.............	PUNCT
ejpam-4453	650	2	...........	...........	PUNCT
ejpam-4453	650	3	...........	...........	PUNCT
ejpam-4453	650	4	...........	...........	PUNCT
ejpam-4453	650	5	...........	...........	PUNCT
ejpam-4453	650	6	.........	.........	PUNCT
ejpam-4453	651	1	..........	..........	PUNCT
ejpam-4453	651	2	.............................................	.............................................	PUNCT
ejpam-4453	651	3	.	.	PUNCT
ejpam-4453	652	1	..........	..........	PUNCT
ejpam-4453	652	2	.............................................	.............................................	PUNCT
ejpam-4453	652	3	.	.	PUNCT
ejpam-4453	653	1	figure	figure	VERB
ejpam-4453	653	2	8	8	NUM
ejpam-4453	653	3	:	:	PUNCT
ejpam-4453	653	4	construction	construction	NOUN
ejpam-4453	653	5	of	of	ADP
ejpam-4453	653	6	ntcbg	ntcbg	DET
ejpam-4453	653	7	proof	proof	NOUN
ejpam-4453	653	8	.	.	PUNCT
ejpam-4453	654	1	note	note	VERB
ejpam-4453	654	2	that	that	SCONJ
ejpam-4453	654	3	every	every	DET
ejpam-4453	654	4	bi	bi	NOUN
ejpam-4453	654	5	is	be	AUX
ejpam-4453	654	6	a	a	DET
ejpam-4453	654	7	cubic	cubic	ADJ
ejpam-4453	654	8	graph	graph	NOUN
ejpam-4453	654	9	.	.	PUNCT
ejpam-4453	655	1	then	then	ADV
ejpam-4453	655	2	by	by	ADP
ejpam-4453	655	3	theorem	theorem	NOUN
ejpam-4453	655	4	1	1	NUM
ejpam-4453	655	5	,	,	PUNCT
ejpam-4453	655	6	bi	bi	NOUN
ejpam-4453	655	7	has	have	VERB
ejpam-4453	655	8	even	even	ADV
ejpam-4453	655	9	order	order	NOUN
ejpam-4453	655	10	.	.	PUNCT
ejpam-4453	656	1	hence	hence	ADV
ejpam-4453	656	2	,	,	PUNCT
ejpam-4453	656	3	|v	|v	PROPN
ejpam-4453	656	4	(	(	PUNCT
ejpam-4453	656	5	bi)|	bi)|	PROPN
ejpam-4453	656	6	can	can	AUX
ejpam-4453	656	7	be	be	AUX
ejpam-4453	656	8	represented	represent	VERB
ejpam-4453	656	9	as	as	ADP
ejpam-4453	656	10	2b	2b	NUM
ejpam-4453	656	11	where	where	SCONJ
ejpam-4453	656	12	b	b	X
ejpam-4453	656	13	∈	∈	PROPN
ejpam-4453	656	14	n.	n.	NOUN
ejpam-4453	656	15	since	since	SCONJ
ejpam-4453	656	16	k4	k4	PROPN
ejpam-4453	656	17	is	be	AUX
ejpam-4453	656	18	the	the	DET
ejpam-4453	656	19	smallest	small	ADJ
ejpam-4453	656	20	cubic	cubic	ADJ
ejpam-4453	656	21	graph	graph	NOUN
ejpam-4453	656	22	,	,	PUNCT
ejpam-4453	656	23	|v	|v	X
ejpam-4453	656	24	(	(	PUNCT
ejpam-4453	656	25	bi)|	bi)|	X
ejpam-4453	656	26	≥	≥	NUM
ejpam-4453	656	27	4	4	X
ejpam-4453	656	28	.	.	PUNCT
ejpam-4453	657	1	it	it	PRON
ejpam-4453	657	2	follows	follow	VERB
ejpam-4453	657	3	that	that	SCONJ
ejpam-4453	657	4	we	we	PRON
ejpam-4453	657	5	have	have	VERB
ejpam-4453	657	6	|v	|v	NOUN
ejpam-4453	657	7	(	(	PUNCT
ejpam-4453	657	8	bi)|	bi)|	PROPN
ejpam-4453	657	9	=	=	PUNCT
ejpam-4453	657	10	2(b−	2(b−	NUM
ejpam-4453	657	11	1	1	NUM
ejpam-4453	657	12	)	)	PUNCT
ejpam-4453	657	13	where	where	SCONJ
ejpam-4453	657	14	b	b	X
ejpam-4453	657	15	≥	≥	NOUN
ejpam-4453	657	16	3	3	NUM
ejpam-4453	657	17	.	.	PUNCT
ejpam-4453	657	18	proposition	proposition	NOUN
ejpam-4453	657	19	6	6	NUM
ejpam-4453	657	20	.	.	PUNCT
ejpam-4453	658	1	let	let	VERB
ejpam-4453	658	2	g	g	PRON
ejpam-4453	658	3	be	be	AUX
ejpam-4453	658	4	a	a	DET
ejpam-4453	658	5	ntcbg	ntcbg	NOUN
ejpam-4453	658	6	with	with	ADP
ejpam-4453	658	7	kc	kc	PROPN
ejpam-4453	658	8	-	-	PUNCT
ejpam-4453	658	9	leaves	leave	NOUN
ejpam-4453	658	10	.	.	PUNCT
ejpam-4453	659	1	then	then	ADV
ejpam-4453	659	2	∑	∑	ADV
ejpam-4453	659	3	|v	|v	PROPN
ejpam-4453	659	4	(	(	PUNCT
ejpam-4453	659	5	bi)|	bi)|	PROPN
ejpam-4453	659	6	≥	≥	NOUN
ejpam-4453	659	7	4kc	4kc	NOUN
ejpam-4453	659	8	.	.	PUNCT
ejpam-4453	660	1	proof	proof	NOUN
ejpam-4453	660	2	.	.	PUNCT
ejpam-4453	661	1	suppose	suppose	VERB
ejpam-4453	661	2	bi	bi	NOUN
ejpam-4453	661	3	is	be	AUX
ejpam-4453	661	4	a	a	DET
ejpam-4453	661	5	branch	branch	NOUN
ejpam-4453	661	6	of	of	ADP
ejpam-4453	661	7	a	a	DET
ejpam-4453	661	8	ntcbg	ntcbg	NOUN
ejpam-4453	661	9	.	.	PUNCT
ejpam-4453	662	1	then	then	ADV
ejpam-4453	662	2	by	by	ADP
ejpam-4453	662	3	proposition	proposition	NOUN
ejpam-4453	662	4	5	5	NUM
ejpam-4453	662	5	,	,	PUNCT
ejpam-4453	662	6	each	each	DET
ejpam-4453	662	7	bi	bi	NOUN
ejpam-4453	662	8	has	have	VERB
ejpam-4453	662	9	order	order	NOUN
ejpam-4453	662	10	equal	equal	ADJ
ejpam-4453	662	11	to	to	ADP
ejpam-4453	662	12	2(b−	2(b−	PROPN
ejpam-4453	662	13	1	1	NUM
ejpam-4453	662	14	)	)	PUNCT
ejpam-4453	662	15	.	.	PUNCT
ejpam-4453	663	1	now	now	ADV
ejpam-4453	663	2	,	,	PUNCT
ejpam-4453	663	3	let	let	VERB
ejpam-4453	663	4	kc	kc	PROPN
ejpam-4453	663	5	be	be	AUX
ejpam-4453	663	6	the	the	DET
ejpam-4453	663	7	order	order	NOUN
ejpam-4453	663	8	of	of	ADP
ejpam-4453	663	9	end	end	NOUN
ejpam-4453	663	10	-	-	PUNCT
ejpam-4453	663	11	vertices	vertex	NOUN
ejpam-4453	663	12	of	of	ADP
ejpam-4453	663	13	ci	ci	NOUN
ejpam-4453	663	14	.	.	PUNCT
ejpam-4453	664	1	then	then	ADV
ejpam-4453	664	2	,	,	PUNCT
ejpam-4453	664	3	we	we	PRON
ejpam-4453	664	4	have∑	have∑	VERB
ejpam-4453	664	5	|v	|v	PROPN
ejpam-4453	664	6	(	(	PUNCT
ejpam-4453	664	7	bi)|	bi)|	PROPN
ejpam-4453	664	8	=	=	PUNCT
ejpam-4453	664	9	2(b1	2(b1	NUM
ejpam-4453	665	1	−	−	NOUN
ejpam-4453	665	2	1	1	NUM
ejpam-4453	665	3	)	)	PUNCT
ejpam-4453	665	4	+	+	CCONJ
ejpam-4453	666	1	2(b2	2(b2	NUM
ejpam-4453	666	2	−	−	NOUN
ejpam-4453	666	3	1	1	NUM
ejpam-4453	666	4	)	)	PUNCT
ejpam-4453	666	5	+	+	CCONJ
ejpam-4453	666	6	...	...	PUNCT
ejpam-4453	667	1	+	+	NUM
ejpam-4453	667	2	2(bkc	2(bkc	NUM
ejpam-4453	667	3	−	−	NOUN
ejpam-4453	667	4	1)∑	1)∑	NUM
ejpam-4453	667	5	|v	|v	X
ejpam-4453	667	6	(	(	PUNCT
ejpam-4453	667	7	bi	bi	NOUN
ejpam-4453	667	8	)	)	PUNCT
ejpam-4453	667	9	=	=	SYM
ejpam-4453	667	10	2(b1	2(b1	NUM
ejpam-4453	667	11	+	+	CCONJ
ejpam-4453	667	12	b2	b2	NOUN
ejpam-4453	667	13	+	+	CCONJ
ejpam-4453	667	14	...	...	PUNCT
ejpam-4453	667	15	+	+	CCONJ
ejpam-4453	667	16	bkc)−	bkc)−	PROPN
ejpam-4453	667	17	2kc	2kc	NOUN
ejpam-4453	667	18	(	(	PUNCT
ejpam-4453	667	19	since	since	SCONJ
ejpam-4453	667	20	b	b	PROPN
ejpam-4453	667	21	≥	≥	X
ejpam-4453	667	22	3)∑	3)∑	NUM
ejpam-4453	667	23	|v	|v	NOUN
ejpam-4453	667	24	(	(	PUNCT
ejpam-4453	667	25	bi)|	bi)|	X
ejpam-4453	667	26	≥	≥	VERB
ejpam-4453	667	27	2(3kc)−	2(3kc)−	NUM
ejpam-4453	667	28	2kc∑	2kc∑	NUM
ejpam-4453	667	29	|v	|v	NOUN
ejpam-4453	667	30	(	(	PUNCT
ejpam-4453	667	31	bi)|	bi)|	X
ejpam-4453	667	32	≥	≥	AUX
ejpam-4453	667	33	4kc	4kc	ADV
ejpam-4453	667	34	therefore	therefore	ADV
ejpam-4453	667	35	,	,	PUNCT
ejpam-4453	667	36	if	if	SCONJ
ejpam-4453	667	37	g	g	PROPN
ejpam-4453	667	38	is	be	AUX
ejpam-4453	667	39	a	a	DET
ejpam-4453	667	40	ntcbg	ntcbg	NOUN
ejpam-4453	667	41	,	,	PUNCT
ejpam-4453	667	42	then	then	ADV
ejpam-4453	667	43	∑	∑	ADP
ejpam-4453	667	44	|v	|v	PROPN
ejpam-4453	667	45	(	(	PUNCT
ejpam-4453	667	46	bi)|	bi)|	PROPN
ejpam-4453	667	47	≥	≥	NOUN
ejpam-4453	667	48	4kc	4kc	NOUN
ejpam-4453	667	49	.	.	PUNCT
ejpam-4453	668	1	4	4	X
ejpam-4453	668	2	.	.	X
ejpam-4453	668	3	minimum	minimum	ADJ
ejpam-4453	668	4	leaf	leaf	NOUN
ejpam-4453	668	5	number	number	NOUN
ejpam-4453	668	6	of	of	ADP
ejpam-4453	668	7	ntcbg	ntcbg	NOUN
ejpam-4453	668	8	now	now	ADV
ejpam-4453	668	9	,	,	PUNCT
ejpam-4453	668	10	we	we	PRON
ejpam-4453	668	11	present	present	VERB
ejpam-4453	668	12	the	the	DET
ejpam-4453	668	13	following	follow	VERB
ejpam-4453	668	14	lemma	lemma	PROPN
ejpam-4453	668	15	that	that	PRON
ejpam-4453	668	16	is	be	AUX
ejpam-4453	668	17	necessary	necessary	ADJ
ejpam-4453	668	18	to	to	PART
ejpam-4453	668	19	prove	prove	VERB
ejpam-4453	668	20	one	one	NUM
ejpam-4453	668	21	of	of	ADP
ejpam-4453	668	22	the	the	DET
ejpam-4453	668	23	main	main	ADJ
ejpam-4453	668	24	result	result	NOUN
ejpam-4453	668	25	of	of	ADP
ejpam-4453	668	26	the	the	DET
ejpam-4453	668	27	paper	paper	NOUN
ejpam-4453	668	28	.	.	PUNCT
ejpam-4453	669	1	lemma	lemma	PROPN
ejpam-4453	669	2	1	1	X
ejpam-4453	669	3	.	.	PUNCT
ejpam-4453	670	1	let	let	VERB
ejpam-4453	670	2	g	g	PRON
ejpam-4453	670	3	be	be	AUX
ejpam-4453	670	4	a	a	DET
ejpam-4453	670	5	simple	simple	ADJ
ejpam-4453	670	6	undirected	undirected	ADJ
ejpam-4453	670	7	graph	graph	NOUN
ejpam-4453	670	8	with	with	ADP
ejpam-4453	670	9	a	a	DET
ejpam-4453	670	10	spanning	span	VERB
ejpam-4453	670	11	tree	tree	NOUN
ejpam-4453	670	12	t	t	NOUN
ejpam-4453	670	13	with	with	ADP
ejpam-4453	670	14	minimum	minimum	ADJ
ejpam-4453	670	15	k	k	NOUN
ejpam-4453	670	16	-	-	NOUN
ejpam-4453	670	17	leaves	leave	VERB
ejpam-4453	670	18	such	such	ADJ
ejpam-4453	670	19	that	that	DET
ejpam-4453	670	20	∆(t	∆(t	NOUN
ejpam-4453	670	21	)	)	PUNCT
ejpam-4453	670	22	≤	≤	NOUN
ejpam-4453	670	23	3	3	NUM
ejpam-4453	670	24	.	.	PUNCT
ejpam-4453	671	1	then	then	ADV
ejpam-4453	671	2	k	k	PROPN
ejpam-4453	671	3	≥	≥	NUM
ejpam-4453	671	4	3	3	NUM
ejpam-4453	671	5	if	if	SCONJ
ejpam-4453	671	6	and	and	CCONJ
ejpam-4453	671	7	only	only	ADV
ejpam-4453	671	8	if	if	SCONJ
ejpam-4453	671	9	g	g	PROPN
ejpam-4453	671	10	is	be	AUX
ejpam-4453	671	11	non	non	ADJ
ejpam-4453	671	12	-	-	ADJ
ejpam-4453	671	13	traceable	traceable	ADJ
ejpam-4453	671	14	.	.	PUNCT
ejpam-4453	672	1	proof	proof	NOUN
ejpam-4453	672	2	.	.	PUNCT
ejpam-4453	673	1	assume	assume	VERB
ejpam-4453	673	2	that	that	SCONJ
ejpam-4453	673	3	a	a	DET
ejpam-4453	673	4	spanning	span	VERB
ejpam-4453	673	5	tree	tree	NOUN
ejpam-4453	673	6	t	t	PROPN
ejpam-4453	673	7	of	of	ADP
ejpam-4453	673	8	g	g	PROPN
ejpam-4453	673	9	has	have	VERB
ejpam-4453	673	10	minimum	minimum	ADJ
ejpam-4453	673	11	k	k	X
ejpam-4453	673	12	≥	≥	NUM
ejpam-4453	673	13	3	3	NUM
ejpam-4453	673	14	leaves	leave	NOUN
ejpam-4453	673	15	.	.	PUNCT
ejpam-4453	674	1	it	it	PRON
ejpam-4453	674	2	follows	follow	VERB
ejpam-4453	674	3	that	that	SCONJ
ejpam-4453	674	4	t	t	PROPN
ejpam-4453	674	5	is	be	AUX
ejpam-4453	674	6	not	not	PART
ejpam-4453	674	7	a	a	DET
ejpam-4453	674	8	path	path	NOUN
ejpam-4453	674	9	,	,	PUNCT
ejpam-4453	674	10	since	since	SCONJ
ejpam-4453	674	11	the	the	DET
ejpam-4453	674	12	only	only	ADJ
ejpam-4453	674	13	tree	tree	NOUN
ejpam-4453	674	14	that	that	PRON
ejpam-4453	674	15	admits	admit	VERB
ejpam-4453	674	16	a	a	DET
ejpam-4453	674	17	hamiltonian	hamiltonian	ADJ
ejpam-4453	674	18	path	path	NOUN
ejpam-4453	674	19	are	be	AUX
ejpam-4453	674	20	paths	path	NOUN
ejpam-4453	674	21	.	.	PUNCT
ejpam-4453	675	1	in	in	ADP
ejpam-4453	675	2	other	other	ADJ
ejpam-4453	675	3	words	word	NOUN
ejpam-4453	675	4	,	,	PUNCT
ejpam-4453	675	5	the	the	DET
ejpam-4453	675	6	only	only	ADJ
ejpam-4453	675	7	tree	tree	NOUN
ejpam-4453	675	8	that	that	PRON
ejpam-4453	675	9	admits	admit	VERB
ejpam-4453	675	10	traceability	traceability	NOUN
ejpam-4453	675	11	is	be	AUX
ejpam-4453	675	12	a	a	DET
ejpam-4453	675	13	path	path	NOUN
ejpam-4453	675	14	,	,	PUNCT
ejpam-4453	675	15	then	then	ADV
ejpam-4453	675	16	t	t	PROPN
ejpam-4453	675	17	is	be	AUX
ejpam-4453	675	18	non	non	ADJ
ejpam-4453	675	19	-	-	ADJ
ejpam-4453	675	20	traceable	traceable	ADJ
ejpam-4453	675	21	.	.	PUNCT
ejpam-4453	676	1	for	for	ADP
ejpam-4453	676	2	the	the	DET
ejpam-4453	676	3	converse	converse	NOUN
ejpam-4453	676	4	,	,	PUNCT
ejpam-4453	676	5	suppose	suppose	VERB
ejpam-4453	676	6	g	g	PROPN
ejpam-4453	676	7	is	be	AUX
ejpam-4453	676	8	non	non	ADJ
ejpam-4453	676	9	-	-	ADJ
ejpam-4453	676	10	traceable	traceable	ADJ
ejpam-4453	676	11	graph	graph	NOUN
ejpam-4453	676	12	.	.	PUNCT
ejpam-4453	677	1	it	it	PRON
ejpam-4453	677	2	implies	imply	VERB
ejpam-4453	677	3	that	that	SCONJ
ejpam-4453	677	4	g	g	PROPN
ejpam-4453	677	5	does	do	AUX
ejpam-4453	677	6	not	not	PART
ejpam-4453	677	7	contain	contain	VERB
ejpam-4453	677	8	any	any	DET
ejpam-4453	677	9	hamiltonian	hamiltonian	ADJ
ejpam-4453	677	10	path	path	NOUN
ejpam-4453	677	11	.	.	PUNCT
ejpam-4453	678	1	now	now	ADV
ejpam-4453	678	2	,	,	PUNCT
ejpam-4453	678	3	let	let	VERB
ejpam-4453	678	4	pn	pn	VERB
ejpam-4453	678	5	=	=	PUNCT
ejpam-4453	679	1	[	[	X
ejpam-4453	679	2	v1	v1	NOUN
ejpam-4453	679	3	,	,	PUNCT
ejpam-4453	679	4	v2	v2	PROPN
ejpam-4453	679	5	,	,	PUNCT
ejpam-4453	679	6	...	...	PUNCT
ejpam-4453	679	7	,	,	PUNCT
ejpam-4453	679	8	vn	vn	PROPN
ejpam-4453	679	9	]	]	X
ejpam-4453	679	10	be	be	AUX
ejpam-4453	679	11	the	the	DET
ejpam-4453	679	12	longest	long	ADJ
ejpam-4453	679	13	path	path	NOUN
ejpam-4453	679	14	that	that	PRON
ejpam-4453	679	15	almost	almost	ADV
ejpam-4453	679	16	visits	visit	VERB
ejpam-4453	679	17	all	all	DET
ejpam-4453	679	18	the	the	DET
ejpam-4453	679	19	vertices	vertex	NOUN
ejpam-4453	679	20	of	of	ADP
ejpam-4453	679	21	g	g	NOUN
ejpam-4453	679	22	such	such	ADJ
ejpam-4453	679	23	that	that	DET
ejpam-4453	679	24	v1	v1	NOUN
ejpam-4453	679	25	and	and	CCONJ
ejpam-4453	679	26	vn	vn	PROPN
ejpam-4453	679	27	are	be	AUX
ejpam-4453	679	28	not	not	PART
ejpam-4453	679	29	adjacent	adjacent	ADJ
ejpam-4453	679	30	.	.	PUNCT
ejpam-4453	680	1	it	it	PRON
ejpam-4453	680	2	follows	follow	VERB
ejpam-4453	680	3	that	that	SCONJ
ejpam-4453	680	4	there	there	PRON
ejpam-4453	680	5	exist	exist	VERB
ejpam-4453	680	6	at	at	ADP
ejpam-4453	680	7	least	least	ADJ
ejpam-4453	680	8	vi	vi	NOUN
ejpam-4453	680	9	∈	∈	NOUN
ejpam-4453	680	10	g	g	NOUN
ejpam-4453	680	11	such	such	ADJ
ejpam-4453	680	12	that	that	PRON
ejpam-4453	680	13	vi	vi	PROPN
ejpam-4453	680	14	/∈	/∈	PUNCT
ejpam-4453	681	1	pn	pn	INTJ
ejpam-4453	681	2	.	.	PROPN
ejpam-4453	682	1	since	since	SCONJ
ejpam-4453	682	2	t	t	PROPN
ejpam-4453	682	3	is	be	AUX
ejpam-4453	682	4	connected	connect	VERB
ejpam-4453	682	5	,	,	PUNCT
ejpam-4453	682	6	vi	vi	PROPN
ejpam-4453	682	7	must	must	AUX
ejpam-4453	682	8	be	be	AUX
ejpam-4453	682	9	connected	connect	VERB
ejpam-4453	682	10	to	to	ADP
ejpam-4453	682	11	any	any	DET
ejpam-4453	682	12	vertex	vertex	NOUN
ejpam-4453	682	13	in	in	ADP
ejpam-4453	682	14	pn	pn	PROPN
ejpam-4453	682	15	except	except	SCONJ
ejpam-4453	682	16	for	for	ADP
ejpam-4453	682	17	v1	v1	NOUN
ejpam-4453	682	18	and	and	CCONJ
ejpam-4453	682	19	vn	vn	NOUN
ejpam-4453	682	20	since	since	SCONJ
ejpam-4453	682	21	it	it	PRON
ejpam-4453	682	22	will	will	AUX
ejpam-4453	682	23	contradict	contradict	VERB
ejpam-4453	682	24	that	that	PRON
ejpam-4453	682	25	pn	pn	PROPN
ejpam-4453	682	26	is	be	AUX
ejpam-4453	682	27	the	the	DET
ejpam-4453	682	28	longest	long	ADJ
ejpam-4453	682	29	path	path	NOUN
ejpam-4453	682	30	that	that	PRON
ejpam-4453	682	31	almost	almost	ADV
ejpam-4453	682	32	visits	visit	VERB
ejpam-4453	682	33	all	all	DET
ejpam-4453	682	34	the	the	DET
ejpam-4453	682	35	vertices	vertex	NOUN
ejpam-4453	682	36	of	of	ADP
ejpam-4453	682	37	g.	g.	PROPN
ejpam-4453	682	38	thus	thus	ADV
ejpam-4453	682	39	vi	vi	PROPN
ejpam-4453	682	40	must	must	AUX
ejpam-4453	682	41	be	be	AUX
ejpam-4453	682	42	connected	connect	VERB
ejpam-4453	682	43	to	to	ADP
ejpam-4453	682	44	one	one	NUM
ejpam-4453	682	45	of	of	ADP
ejpam-4453	682	46	v2	v2	PROPN
ejpam-4453	682	47	,	,	PUNCT
ejpam-4453	682	48	v3	v3	PROPN
ejpam-4453	682	49	,	,	PUNCT
ejpam-4453	682	50	...	...	PUNCT
ejpam-4453	682	51	,	,	PUNCT
ejpam-4453	682	52	vn−1	vn−1	PROPN
ejpam-4453	682	53	.	.	PUNCT
ejpam-4453	683	1	thus	thus	ADV
ejpam-4453	683	2	,	,	PUNCT
ejpam-4453	683	3	a.r	a.r	PROPN
ejpam-4453	683	4	nieva	nieva	PROPN
ejpam-4453	683	5	and	and	CCONJ
ejpam-4453	683	6	k.nocum	k.nocum	PROPN
ejpam-4453	683	7	/	/	SYM
ejpam-4453	683	8	eur	eur	PROPN
ejpam-4453	683	9	.	.	PUNCT
ejpam-4453	684	1	j.	j.	PROPN
ejpam-4453	684	2	pure	pure	PROPN
ejpam-4453	684	3	appl	appl	PROPN
ejpam-4453	684	4	.	.	PROPN
ejpam-4453	684	5	math	math	PROPN
ejpam-4453	684	6	,	,	PUNCT
ejpam-4453	684	7	15	15	NUM
ejpam-4453	684	8	(	(	PUNCT
ejpam-4453	684	9	4	4	NUM
ejpam-4453	684	10	)	)	PUNCT
ejpam-4453	684	11	(	(	PUNCT
ejpam-4453	684	12	2022	2022	NUM
ejpam-4453	684	13	)	)	PUNCT
ejpam-4453	684	14	,	,	PUNCT
ejpam-4453	684	15	1536	1536	NUM
ejpam-4453	684	16	-	-	SYM
ejpam-4453	684	17	1548	1548	NUM
ejpam-4453	684	18	1544	1544	NUM
ejpam-4453	684	19	by	by	ADP
ejpam-4453	684	20	theorem	theorem	NOUN
ejpam-4453	684	21	5	5	NUM
ejpam-4453	684	22	we	we	PRON
ejpam-4453	684	23	have	have	VERB
ejpam-4453	684	24	k	k	NOUN
ejpam-4453	684	25	=	=	PUNCT
ejpam-4453	685	1	p	p	X
ejpam-4453	686	1	+	+	CCONJ
ejpam-4453	686	2	2	2	NUM
ejpam-4453	686	3	≥	≥	NOUN
ejpam-4453	686	4	1	1	NUM
ejpam-4453	686	5	+	+	CCONJ
ejpam-4453	686	6	2	2	NUM
ejpam-4453	686	7	=	=	SYM
ejpam-4453	686	8	3	3	NUM
ejpam-4453	686	9	.	.	PUNCT
ejpam-4453	686	10	therefore	therefore	ADV
ejpam-4453	686	11	,	,	PUNCT
ejpam-4453	686	12	the	the	DET
ejpam-4453	686	13	spanning	span	VERB
ejpam-4453	686	14	tree	tree	NOUN
ejpam-4453	686	15	t	t	PROPN
ejpam-4453	686	16	of	of	ADP
ejpam-4453	686	17	g	g	PROPN
ejpam-4453	686	18	has	have	VERB
ejpam-4453	686	19	minimum	minimum	ADJ
ejpam-4453	686	20	k	k	X
ejpam-4453	686	21	≥	≥	NUM
ejpam-4453	686	22	3	3	NUM
ejpam-4453	686	23	leaves	leave	NOUN
ejpam-4453	686	24	.	.	PUNCT
ejpam-4453	687	1	lemma	lemma	PROPN
ejpam-4453	687	2	2	2	NUM
ejpam-4453	687	3	.	.	PUNCT
ejpam-4453	688	1	if	if	SCONJ
ejpam-4453	688	2	g	g	PROPN
ejpam-4453	688	3	is	be	AUX
ejpam-4453	688	4	a	a	DET
ejpam-4453	688	5	ntcbg	ntcbg	NOUN
ejpam-4453	688	6	with	with	ADP
ejpam-4453	688	7	kc	kc	PROPN
ejpam-4453	688	8	-	-	PUNCT
ejpam-4453	688	9	leaves	leave	NOUN
ejpam-4453	688	10	,	,	PUNCT
ejpam-4453	688	11	then	then	ADV
ejpam-4453	688	12	|v	|v	PROPN
ejpam-4453	688	13	(	(	PUNCT
ejpam-4453	688	14	g)|	g)|	PROPN
ejpam-4453	688	15	≥	≥	PROPN
ejpam-4453	688	16	6kc	6kc	NOUN
ejpam-4453	688	17	−	−	NOUN
ejpam-4453	688	18	2	2	NUM
ejpam-4453	688	19	.	.	PUNCT
ejpam-4453	689	1	proof	proof	NOUN
ejpam-4453	689	2	.	.	PUNCT
ejpam-4453	690	1	suppose	suppose	VERB
ejpam-4453	690	2	g	g	PROPN
ejpam-4453	690	3	is	be	AUX
ejpam-4453	690	4	a	a	DET
ejpam-4453	690	5	ntcbg	ntcbg	NOUN
ejpam-4453	690	6	.	.	PUNCT
ejpam-4453	691	1	then	then	ADV
ejpam-4453	691	2	it	it	PRON
ejpam-4453	691	3	has	have	VERB
ejpam-4453	691	4	a	a	DET
ejpam-4453	691	5	central	central	ADJ
ejpam-4453	691	6	fragment	fragment	NOUN
ejpam-4453	691	7	c	c	NOUN
ejpam-4453	691	8	and	and	CCONJ
ejpam-4453	691	9	a	a	DET
ejpam-4453	691	10	branch	branch	NOUN
ejpam-4453	691	11	bi	bi	NOUN
ejpam-4453	691	12	.	.	PUNCT
ejpam-4453	692	1	it	it	PRON
ejpam-4453	692	2	follows	follow	VERB
ejpam-4453	692	3	that	that	SCONJ
ejpam-4453	692	4	|v	|v	PROPN
ejpam-4453	692	5	(	(	PUNCT
ejpam-4453	692	6	g)|	g)|	PROPN
ejpam-4453	692	7	=	=	PUNCT
ejpam-4453	692	8	|v	|v	X
ejpam-4453	692	9	(	(	PUNCT
ejpam-4453	692	10	c	c	NOUN
ejpam-4453	692	11	)	)	PUNCT
ejpam-4453	692	12	|+	|+	PROPN
ejpam-4453	692	13	∑	∑	PUNCT
ejpam-4453	692	14	|v	|v	PROPN
ejpam-4453	692	15	(	(	PUNCT
ejpam-4453	692	16	bi)|	bi)|	PROPN
ejpam-4453	692	17	.	.	PUNCT
ejpam-4453	693	1	by	by	ADP
ejpam-4453	693	2	proposition	proposition	NOUN
ejpam-4453	693	3	3	3	NUM
ejpam-4453	693	4	and	and	CCONJ
ejpam-4453	693	5	proposition	proposition	NOUN
ejpam-4453	693	6	6	6	NUM
ejpam-4453	693	7	,	,	PUNCT
ejpam-4453	693	8	we	we	PRON
ejpam-4453	693	9	have	have	VERB
ejpam-4453	693	10	|v	|v	NOUN
ejpam-4453	693	11	(	(	PUNCT
ejpam-4453	693	12	g)|	g)|	NOUN
ejpam-4453	693	13	=	=	PUNCT
ejpam-4453	693	14	|v	|v	X
ejpam-4453	693	15	(	(	PUNCT
ejpam-4453	693	16	c	c	NOUN
ejpam-4453	693	17	)	)	PUNCT
ejpam-4453	693	18	|+	|+	PROPN
ejpam-4453	693	19	∑	∑	PUNCT
ejpam-4453	693	20	|v	|v	PROPN
ejpam-4453	693	21	(	(	PUNCT
ejpam-4453	693	22	bi)|	bi)|	PROPN
ejpam-4453	693	23	|v	|v	PROPN
ejpam-4453	693	24	(	(	PUNCT
ejpam-4453	693	25	g)|	g)|	X
ejpam-4453	693	26	≥	≥	NOUN
ejpam-4453	693	27	2(kc	2(kc	NUM
ejpam-4453	694	1	−	−	NOUN
ejpam-4453	694	2	1	1	NUM
ejpam-4453	694	3	)	)	PUNCT
ejpam-4453	694	4	+	+	CCONJ
ejpam-4453	694	5	4kc	4kc	ADJ
ejpam-4453	694	6	|v	|v	NOUN
ejpam-4453	694	7	(	(	PUNCT
ejpam-4453	694	8	g)|	g)|	PROPN
ejpam-4453	694	9	≥	≥	NUM
ejpam-4453	694	10	2kc	2kc	ADJ
ejpam-4453	694	11	−	−	NUM
ejpam-4453	694	12	2	2	NUM
ejpam-4453	694	13	+	+	CCONJ
ejpam-4453	694	14	4kc	4kc	ADJ
ejpam-4453	694	15	|v	|v	NOUN
ejpam-4453	694	16	(	(	PUNCT
ejpam-4453	694	17	g)|	g)|	PROPN
ejpam-4453	694	18	≥	≥	PROPN
ejpam-4453	694	19	6kc	6kc	NOUN
ejpam-4453	694	20	−	−	PROPN
ejpam-4453	694	21	2	2	NUM
ejpam-4453	694	22	therefore	therefore	ADV
ejpam-4453	694	23	,	,	PUNCT
ejpam-4453	694	24	if	if	SCONJ
ejpam-4453	694	25	g	g	PROPN
ejpam-4453	694	26	is	be	AUX
ejpam-4453	694	27	a	a	DET
ejpam-4453	694	28	ntcbg	ntcbg	NOUN
ejpam-4453	694	29	with	with	ADP
ejpam-4453	694	30	kc	kc	PROPN
ejpam-4453	694	31	-	-	PUNCT
ejpam-4453	694	32	leaves	leave	NOUN
ejpam-4453	694	33	,	,	PUNCT
ejpam-4453	694	34	then	then	ADV
ejpam-4453	694	35	|v	|v	PROPN
ejpam-4453	694	36	(	(	PUNCT
ejpam-4453	694	37	g)|	g)|	PROPN
ejpam-4453	694	38	≥	≥	PROPN
ejpam-4453	694	39	6kc	6kc	NOUN
ejpam-4453	694	40	−	−	NOUN
ejpam-4453	694	41	2	2	NUM
ejpam-4453	694	42	.	.	NOUN
ejpam-4453	694	43	remark	remark	NOUN
ejpam-4453	694	44	3	3	NUM
ejpam-4453	694	45	.	.	PUNCT
ejpam-4453	695	1	the	the	DET
ejpam-4453	695	2	smallest	small	ADJ
ejpam-4453	695	3	non	non	ADJ
ejpam-4453	695	4	-	-	ADJ
ejpam-4453	695	5	traceable	traceable	ADJ
ejpam-4453	695	6	cubic	cubic	ADJ
ejpam-4453	695	7	bridge	bridge	NOUN
ejpam-4453	695	8	graph	graph	NOUN
ejpam-4453	695	9	is	be	AUX
ejpam-4453	695	10	of	of	ADP
ejpam-4453	695	11	order	order	NOUN
ejpam-4453	695	12	16	16	NUM
ejpam-4453	695	13	.	.	PUNCT
ejpam-4453	696	1	lemma	lemma	PROPN
ejpam-4453	696	2	3	3	X
ejpam-4453	696	3	.	.	PUNCT
ejpam-4453	697	1	let	let	VERB
ejpam-4453	697	2	g	g	PRON
ejpam-4453	697	3	be	be	AUX
ejpam-4453	697	4	a	a	DET
ejpam-4453	697	5	ntcbg	ntcbg	NOUN
ejpam-4453	697	6	with	with	ADP
ejpam-4453	697	7	spanning	span	VERB
ejpam-4453	697	8	tree	tree	NOUN
ejpam-4453	697	9	t	t	NOUN
ejpam-4453	697	10	and	and	CCONJ
ejpam-4453	697	11	let	let	VERB
ejpam-4453	697	12	a1	a1	NOUN
ejpam-4453	697	13	,	,	PUNCT
ejpam-4453	697	14	a2	a2	PROPN
ejpam-4453	697	15	,	,	PUNCT
ejpam-4453	697	16	and	and	CCONJ
ejpam-4453	697	17	a3	a3	NOUN
ejpam-4453	697	18	be	be	VERB
ejpam-4453	697	19	the	the	DET
ejpam-4453	697	20	set	set	NOUN
ejpam-4453	697	21	of	of	ADP
ejpam-4453	697	22	vertices	vertex	NOUN
ejpam-4453	697	23	of	of	ADP
ejpam-4453	697	24	t	t	PROPN
ejpam-4453	697	25	of	of	ADP
ejpam-4453	697	26	degree	degree	NOUN
ejpam-4453	697	27	1	1	NUM
ejpam-4453	697	28	,	,	PUNCT
ejpam-4453	697	29	degree	degree	NOUN
ejpam-4453	697	30	2	2	NUM
ejpam-4453	697	31	and	and	CCONJ
ejpam-4453	697	32	degree	degree	NOUN
ejpam-4453	697	33	3	3	NUM
ejpam-4453	697	34	respectively	respectively	ADV
ejpam-4453	697	35	.	.	PUNCT
ejpam-4453	698	1	then	then	ADV
ejpam-4453	698	2	a2	a2	PROPN
ejpam-4453	698	3	≥	≥	PROPN
ejpam-4453	698	4	4a1	4a1	NUM
ejpam-4453	698	5	.	.	PUNCT
ejpam-4453	698	6	proof	proof	NOUN
ejpam-4453	698	7	.	.	PUNCT
ejpam-4453	699	1	suppose	suppose	VERB
ejpam-4453	699	2	g	g	PROPN
ejpam-4453	699	3	is	be	AUX
ejpam-4453	699	4	a	a	DET
ejpam-4453	699	5	ntcbg	ntcbg	NOUN
ejpam-4453	699	6	with	with	ADP
ejpam-4453	699	7	spanning	span	VERB
ejpam-4453	699	8	tree	tree	NOUN
ejpam-4453	699	9	t	t	NOUN
ejpam-4453	699	10	.	.	PUNCT
ejpam-4453	700	1	note	note	VERB
ejpam-4453	700	2	that	that	SCONJ
ejpam-4453	700	3	by	by	ADP
ejpam-4453	700	4	lemma	lemma	PROPN
ejpam-4453	700	5	2	2	NUM
ejpam-4453	700	6	the	the	DET
ejpam-4453	700	7	order	order	NOUN
ejpam-4453	700	8	of	of	ADP
ejpam-4453	700	9	non	non	ADJ
ejpam-4453	700	10	-	-	ADJ
ejpam-4453	700	11	traceble	traceble	ADJ
ejpam-4453	700	12	cubic	cubic	ADJ
ejpam-4453	700	13	bridge	bridge	NOUN
ejpam-4453	700	14	graph	graph	NOUN
ejpam-4453	700	15	g	g	PROPN
ejpam-4453	700	16	is	be	AUX
ejpam-4453	700	17	|v	|v	PROPN
ejpam-4453	700	18	(	(	PUNCT
ejpam-4453	700	19	g)|	g)|	X
ejpam-4453	700	20	≥	≥	PROPN
ejpam-4453	700	21	6kc	6kc	NOUN
ejpam-4453	700	22	−	−	NOUN
ejpam-4453	700	23	2	2	X
ejpam-4453	700	24	.	.	PUNCT
ejpam-4453	701	1	it	it	PRON
ejpam-4453	701	2	follows	follow	VERB
ejpam-4453	701	3	that	that	SCONJ
ejpam-4453	701	4	the	the	DET
ejpam-4453	701	5	spanning	span	VERB
ejpam-4453	701	6	tree	tree	NOUN
ejpam-4453	701	7	t	t	PROPN
ejpam-4453	701	8	of	of	ADP
ejpam-4453	701	9	g	g	PROPN
ejpam-4453	701	10	has	have	VERB
ejpam-4453	701	11	|v	|v	X
ejpam-4453	701	12	(	(	PUNCT
ejpam-4453	701	13	t	t	NOUN
ejpam-4453	701	14	)	)	PUNCT
ejpam-4453	701	15	|	|	ADV
ejpam-4453	701	16	≥	≥	NOUN
ejpam-4453	701	17	6kc	6kc	NOUN
ejpam-4453	701	18	−	−	NOUN
ejpam-4453	701	19	2	2	NUM
ejpam-4453	701	20	.	.	PUNCT
ejpam-4453	701	21	by	by	ADP
ejpam-4453	701	22	theorem	theorem	NOUN
ejpam-4453	701	23	5	5	NUM
ejpam-4453	701	24	we	we	PRON
ejpam-4453	701	25	know	know	VERB
ejpam-4453	701	26	that	that	SCONJ
ejpam-4453	701	27	a1	a1	NOUN
ejpam-4453	701	28	=	=	PUNCT
ejpam-4453	701	29	kc	kc	PROPN
ejpam-4453	701	30	and	and	CCONJ
ejpam-4453	701	31	a3	a3	PROPN
ejpam-4453	701	32	=	=	PROPN
ejpam-4453	701	33	kc	kc	PROPN
ejpam-4453	702	1	−	−	PROPN
ejpam-4453	702	2	2	2	NUM
ejpam-4453	702	3	.	.	PUNCT
ejpam-4453	703	1	since	since	SCONJ
ejpam-4453	703	2	n	n	NOUN
ejpam-4453	703	3	=	=	SYM
ejpam-4453	703	4	a1	a1	PROPN
ejpam-4453	703	5	+	+	PROPN
ejpam-4453	703	6	a2	a2	PROPN
ejpam-4453	703	7	+	+	NOUN
ejpam-4453	703	8	a3	a3	NOUN
ejpam-4453	703	9	,	,	PUNCT
ejpam-4453	703	10	it	it	PRON
ejpam-4453	703	11	follows	follow	VERB
ejpam-4453	703	12	that	that	SCONJ
ejpam-4453	703	13	,	,	PUNCT
ejpam-4453	703	14	|v	|v	PROPN
ejpam-4453	703	15	(	(	PUNCT
ejpam-4453	703	16	t	t	NOUN
ejpam-4453	703	17	)	)	PUNCT
ejpam-4453	703	18	|	|	NOUN
ejpam-4453	704	1	=	=	SYM
ejpam-4453	704	2	a1	a1	PROPN
ejpam-4453	704	3	+	+	PROPN
ejpam-4453	704	4	a2	a2	PROPN
ejpam-4453	704	5	+	+	NOUN
ejpam-4453	704	6	a3	a3	NOUN
ejpam-4453	704	7	≥	≥	NOUN
ejpam-4453	704	8	6kc	6kc	NOUN
ejpam-4453	704	9	−	−	PROPN
ejpam-4453	704	10	2	2	NUM
ejpam-4453	704	11	kc	kc	PROPN
ejpam-4453	704	12	+	+	PROPN
ejpam-4453	704	13	a2	a2	PROPN
ejpam-4453	704	14	+	+	CCONJ
ejpam-4453	704	15	kc	kc	PROPN
ejpam-4453	704	16	−	−	PROPN
ejpam-4453	704	17	2	2	NUM
ejpam-4453	704	18	≥	≥	NOUN
ejpam-4453	704	19	6kc	6kc	NOUN
ejpam-4453	704	20	−	−	PROPN
ejpam-4453	704	21	2	2	NUM
ejpam-4453	704	22	a2	a2	PROPN
ejpam-4453	704	23	≥	≥	NOUN
ejpam-4453	704	24	6kc	6kc	NOUN
ejpam-4453	704	25	−	−	PROPN
ejpam-4453	704	26	2−	2−	NUM
ejpam-4453	704	27	2kc	2kc	ADJ
ejpam-4453	704	28	+	+	CCONJ
ejpam-4453	704	29	2	2	NUM
ejpam-4453	704	30	=	=	SYM
ejpam-4453	704	31	4kc	4kc	NOUN
ejpam-4453	704	32	since	since	SCONJ
ejpam-4453	704	33	a1	a1	NOUN
ejpam-4453	704	34	=	=	SYM
ejpam-4453	704	35	kc	kc	PROPN
ejpam-4453	704	36	,	,	PUNCT
ejpam-4453	704	37	therefore	therefore	ADV
ejpam-4453	704	38	a2	a2	PROPN
ejpam-4453	704	39	≥	≥	PROPN
ejpam-4453	704	40	4a1	4a1	NUM
ejpam-4453	704	41	.	.	PUNCT
ejpam-4453	704	42	theorem	theorem	VERB
ejpam-4453	704	43	10	10	NUM
ejpam-4453	704	44	.	.	PUNCT
ejpam-4453	705	1	let	let	VERB
ejpam-4453	705	2	g	g	PRON
ejpam-4453	705	3	be	be	AUX
ejpam-4453	705	4	a	a	DET
ejpam-4453	705	5	ntcbg	ntcbg	NOUN
ejpam-4453	705	6	such	such	ADJ
ejpam-4453	705	7	that	that	SCONJ
ejpam-4453	705	8	|v	|v	PROPN
ejpam-4453	705	9	(	(	PUNCT
ejpam-4453	705	10	g)|	g)|	NOUN
ejpam-4453	705	11	=	=	PUNCT
ejpam-4453	705	12	n	n	NOUN
ejpam-4453	705	13	with	with	ADP
ejpam-4453	705	14	spanning	span	VERB
ejpam-4453	705	15	tree	tree	NOUN
ejpam-4453	705	16	t	t	NOUN
ejpam-4453	705	17	.	.	PUNCT
ejpam-4453	706	1	then	then	ADV
ejpam-4453	706	2	3	3	NUM
ejpam-4453	706	3	≤	≤	NOUN
ejpam-4453	706	4	|leaf(t	|leaf(t	PROPN
ejpam-4453	706	5	)	)	PUNCT
ejpam-4453	706	6	|	|	ADV
ejpam-4453	706	7	≤	≤	NUM
ejpam-4453	706	8	⌊	⌊	VERB
ejpam-4453	706	9	n+2	n+2	PRON
ejpam-4453	706	10	6	6	NUM
ejpam-4453	706	11	⌋	⌋	NOUN
ejpam-4453	706	12	.	.	PUNCT
ejpam-4453	707	1	proof	proof	NOUN
ejpam-4453	707	2	.	.	PUNCT
ejpam-4453	708	1	since	since	SCONJ
ejpam-4453	708	2	t	t	PROPN
ejpam-4453	708	3	is	be	AUX
ejpam-4453	708	4	spanning	span	VERB
ejpam-4453	708	5	tree	tree	NOUN
ejpam-4453	708	6	of	of	ADP
ejpam-4453	708	7	g	g	PROPN
ejpam-4453	708	8	,	,	PUNCT
ejpam-4453	708	9	|v	|v	PROPN
ejpam-4453	708	10	(	(	PUNCT
ejpam-4453	708	11	t	t	NOUN
ejpam-4453	708	12	)	)	PUNCT
ejpam-4453	708	13	|	|	ADV
ejpam-4453	708	14	=	=	SYM
ejpam-4453	708	15	|v	|v	PROPN
ejpam-4453	708	16	(	(	PUNCT
ejpam-4453	708	17	g)|	g)|	NOUN
ejpam-4453	708	18	.	.	PUNCT
ejpam-4453	709	1	since	since	SCONJ
ejpam-4453	709	2	g	g	PROPN
ejpam-4453	709	3	is	be	AUX
ejpam-4453	709	4	non	non	ADJ
ejpam-4453	709	5	-	-	ADJ
ejpam-4453	709	6	traceable	traceable	ADJ
ejpam-4453	709	7	,	,	PUNCT
ejpam-4453	709	8	by	by	ADP
ejpam-4453	709	9	lemma	lemma	PROPN
ejpam-4453	709	10	1	1	NUM
ejpam-4453	709	11	,	,	PUNCT
ejpam-4453	709	12	the	the	DET
ejpam-4453	709	13	spanning	span	VERB
ejpam-4453	709	14	tree	tree	NOUN
ejpam-4453	709	15	of	of	ADP
ejpam-4453	709	16	g	g	NOUN
ejpam-4453	709	17	can	can	AUX
ejpam-4453	709	18	be	be	AUX
ejpam-4453	709	19	represented	represent	VERB
ejpam-4453	709	20	as	as	ADP
ejpam-4453	709	21	a	a	DET
ejpam-4453	709	22	3	3	NUM
ejpam-4453	709	23	-	-	PUNCT
ejpam-4453	709	24	ended	end	VERB
ejpam-4453	709	25	tree	tree	NOUN
ejpam-4453	709	26	.	.	PUNCT
ejpam-4453	710	1	it	it	PRON
ejpam-4453	710	2	follows	follow	VERB
ejpam-4453	710	3	that	that	SCONJ
ejpam-4453	710	4	3	3	NUM
ejpam-4453	710	5	≤	≤	NOUN
ejpam-4453	710	6	|leaf(t	|leaf(t	PROPN
ejpam-4453	710	7	)	)	PUNCT
ejpam-4453	710	8	|	|	ADV
ejpam-4453	710	9	.	.	PUNCT
ejpam-4453	711	1	we	we	PRON
ejpam-4453	711	2	only	only	ADV
ejpam-4453	711	3	need	need	VERB
ejpam-4453	711	4	to	to	PART
ejpam-4453	711	5	show	show	VERB
ejpam-4453	711	6	that	that	SCONJ
ejpam-4453	711	7	|leaf(t	|leaf(t	PROPN
ejpam-4453	711	8	)	)	PUNCT
ejpam-4453	711	9	|	|	ADV
ejpam-4453	711	10	≤	≤	NUM
ejpam-4453	711	11	⌊	⌊	VERB
ejpam-4453	711	12	n+2	n+2	PRON
ejpam-4453	711	13	6	6	NUM
ejpam-4453	711	14	⌋	⌋	NOUN
ejpam-4453	711	15	.	.	PUNCT
ejpam-4453	712	1	by	by	ADP
ejpam-4453	712	2	lemma	lemma	PROPN
ejpam-4453	712	3	2	2	NUM
ejpam-4453	712	4	,	,	PUNCT
ejpam-4453	712	5	the	the	DET
ejpam-4453	712	6	order	order	NOUN
ejpam-4453	712	7	of	of	ADP
ejpam-4453	712	8	t	t	PROPN
ejpam-4453	712	9	is	be	AUX
ejpam-4453	712	10	n	n	PRON
ejpam-4453	712	11	≥	≥	NOUN
ejpam-4453	712	12	6kc	6kc	NOUN
ejpam-4453	712	13	−	−	PROPN
ejpam-4453	712	14	2	2	NUM
ejpam-4453	712	15	and	and	CCONJ
ejpam-4453	712	16	by	by	ADP
ejpam-4453	712	17	lemma	lemma	PROPN
ejpam-4453	712	18	3	3	NUM
ejpam-4453	712	19	,	,	PUNCT
ejpam-4453	712	20	a2	a2	PROPN
ejpam-4453	712	21	≥	≥	PROPN
ejpam-4453	712	22	4a1	4a1	NUM
ejpam-4453	712	23	.	.	PUNCT
ejpam-4453	713	1	thus	thus	ADV
ejpam-4453	713	2	,	,	PUNCT
ejpam-4453	713	3	|v	|v	PROPN
ejpam-4453	713	4	(	(	PUNCT
ejpam-4453	713	5	t	t	NOUN
ejpam-4453	713	6	)	)	PUNCT
ejpam-4453	713	7	|	|	NOUN
ejpam-4453	713	8	=	=	SYM
ejpam-4453	713	9	n	n	NOUN
ejpam-4453	713	10	=	=	NOUN
ejpam-4453	713	11	a1	a1	PROPN
ejpam-4453	713	12	+	+	PROPN
ejpam-4453	713	13	a2	a2	PROPN
ejpam-4453	713	14	+	+	NOUN
ejpam-4453	713	15	a3	a3	NOUN
ejpam-4453	713	16	n	n	NOUN
ejpam-4453	713	17	=	=	SYM
ejpam-4453	713	18	a1	a1	PROPN
ejpam-4453	713	19	+	+	CCONJ
ejpam-4453	713	20	4a1	4a1	NUM
ejpam-4453	713	21	+	+	NOUN
ejpam-4453	713	22	a3	a3	NOUN
ejpam-4453	713	23	n	n	PRON
ejpam-4453	713	24	≥	≥	NOUN
ejpam-4453	713	25	kc	kc	PROPN
ejpam-4453	713	26	+	+	CCONJ
ejpam-4453	713	27	4k	4k	PRON
ejpam-4453	713	28	+	+	CCONJ
ejpam-4453	713	29	kc	kc	PROPN
ejpam-4453	713	30	−	−	NUM
ejpam-4453	713	31	2	2	NUM
ejpam-4453	713	32	6kc	6kc	NOUN
ejpam-4453	713	33	≤	≤	NOUN
ejpam-4453	713	34	n+	n+	PUNCT
ejpam-4453	713	35	2	2	NUM
ejpam-4453	713	36	a.r	a.r	PROPN
ejpam-4453	713	37	nieva	nieva	PROPN
ejpam-4453	713	38	and	and	CCONJ
ejpam-4453	713	39	k.nocum	k.nocum	PROPN
ejpam-4453	713	40	/	/	SYM
ejpam-4453	713	41	eur	eur	PROPN
ejpam-4453	713	42	.	.	PUNCT
ejpam-4453	714	1	j.	j.	PROPN
ejpam-4453	714	2	pure	pure	PROPN
ejpam-4453	714	3	appl	appl	PROPN
ejpam-4453	714	4	.	.	PROPN
ejpam-4453	714	5	math	math	PROPN
ejpam-4453	714	6	,	,	PUNCT
ejpam-4453	714	7	15	15	NUM
ejpam-4453	714	8	(	(	PUNCT
ejpam-4453	714	9	4	4	NUM
ejpam-4453	714	10	)	)	PUNCT
ejpam-4453	714	11	(	(	PUNCT
ejpam-4453	714	12	2022	2022	NUM
ejpam-4453	714	13	)	)	PUNCT
ejpam-4453	714	14	,	,	PUNCT
ejpam-4453	714	15	1536	1536	NUM
ejpam-4453	714	16	-	-	SYM
ejpam-4453	714	17	1548	1548	NUM
ejpam-4453	714	18	1545	1545	NUM
ejpam-4453	714	19	kc	kc	PROPN
ejpam-4453	714	20	≤	≤	PROPN
ejpam-4453	714	21	n+	n+	PUNCT
ejpam-4453	714	22	2	2	NUM
ejpam-4453	714	23	6	6	NUM
ejpam-4453	714	24	since	since	SCONJ
ejpam-4453	714	25	kc	kc	PROPN
ejpam-4453	714	26	is	be	AUX
ejpam-4453	714	27	the	the	DET
ejpam-4453	714	28	number	number	NOUN
ejpam-4453	714	29	of	of	ADP
ejpam-4453	714	30	end	end	NOUN
ejpam-4453	714	31	-	-	PUNCT
ejpam-4453	714	32	vertices	vertex	NOUN
ejpam-4453	714	33	or	or	CCONJ
ejpam-4453	714	34	leaves	leave	NOUN
ejpam-4453	714	35	of	of	ADP
ejpam-4453	714	36	a	a	DET
ejpam-4453	714	37	spanning	span	VERB
ejpam-4453	714	38	tree	tree	NOUN
ejpam-4453	714	39	,	,	PUNCT
ejpam-4453	714	40	kc	kc	PROPN
ejpam-4453	714	41	should	should	AUX
ejpam-4453	714	42	be	be	AUX
ejpam-4453	714	43	an	an	DET
ejpam-4453	714	44	element	element	NOUN
ejpam-4453	714	45	of	of	ADP
ejpam-4453	714	46	n.	n.	NOUN
ejpam-4453	714	47	therefore	therefore	ADV
ejpam-4453	714	48	3	3	NUM
ejpam-4453	714	49	≤	≤	NOUN
ejpam-4453	714	50	|leaf(t	|leaf(t	PROPN
ejpam-4453	714	51	)	)	PUNCT
ejpam-4453	714	52	|	|	ADV
ejpam-4453	714	53	≤	≤	NUM
ejpam-4453	714	54	⌊	⌊	VERB
ejpam-4453	714	55	n+2	n+2	PRON
ejpam-4453	714	56	6	6	NUM
ejpam-4453	714	57	⌋	⌋	NOUN
ejpam-4453	714	58	.	.	PUNCT
ejpam-4453	715	1	corollary	corollary	ADJ
ejpam-4453	715	2	2	2	NUM
ejpam-4453	715	3	.	.	PUNCT
ejpam-4453	716	1	let	let	VERB
ejpam-4453	716	2	g	g	PRON
ejpam-4453	716	3	be	be	AUX
ejpam-4453	716	4	a	a	DET
ejpam-4453	716	5	ntcbg	ntcbg	NOUN
ejpam-4453	716	6	with	with	ADP
ejpam-4453	716	7	spanning	span	VERB
ejpam-4453	716	8	tree	tree	NOUN
ejpam-4453	716	9	t	t	NOUN
ejpam-4453	716	10	.	.	PUNCT
ejpam-4453	717	1	then	then	ADV
ejpam-4453	717	2	we	we	PRON
ejpam-4453	717	3	can	can	AUX
ejpam-4453	717	4	find	find	VERB
ejpam-4453	717	5	a	a	DET
ejpam-4453	717	6	ntcbg	ntcbg	ADJ
ejpam-4453	717	7	g′	g′	NOUN
ejpam-4453	717	8	with	with	ADP
ejpam-4453	717	9	spanning	span	VERB
ejpam-4453	717	10	tree	tree	NOUN
ejpam-4453	717	11	t	t	NOUN
ejpam-4453	717	12	′	′	NUM
ejpam-4453	717	13	where	where	SCONJ
ejpam-4453	717	14	|v	|v	PROPN
ejpam-4453	717	15	(	(	PUNCT
ejpam-4453	717	16	g′)|	g′)|	PROPN
ejpam-4453	717	17	≤	≤	PROPN
ejpam-4453	717	18	|v	|v	X
ejpam-4453	717	19	(	(	PUNCT
ejpam-4453	717	20	g)|	g)|	VERB
ejpam-4453	717	21	such	such	ADJ
ejpam-4453	717	22	that	that	SCONJ
ejpam-4453	717	23	3	3	NUM
ejpam-4453	717	24	≤	≤	NOUN
ejpam-4453	717	25	|leaf(t	|leaf(t	PROPN
ejpam-4453	717	26	′)|	′)|	PRON
ejpam-4453	717	27	≤	≤	NUM
ejpam-4453	717	28	|leaf(t	|leaf(t	PROPN
ejpam-4453	717	29	)	)	PUNCT
ejpam-4453	717	30	|	|	ADV
ejpam-4453	717	31	≤⌊	≤⌊	PROPN
ejpam-4453	717	32	n+2	n+2	NUM
ejpam-4453	717	33	6	6	NUM
ejpam-4453	717	34	⌋	⌋	NOUN
ejpam-4453	717	35	.	.	PUNCT
ejpam-4453	718	1	the	the	DET
ejpam-4453	718	2	proof	proof	NOUN
ejpam-4453	718	3	of	of	ADP
ejpam-4453	718	4	this	this	DET
ejpam-4453	718	5	corollary	corollary	NOUN
ejpam-4453	718	6	follows	follow	VERB
ejpam-4453	718	7	from	from	ADP
ejpam-4453	718	8	theorem	theorem	ADJ
ejpam-4453	718	9	10	10	NUM
ejpam-4453	718	10	.	.	PUNCT
ejpam-4453	719	1	5	5	NUM
ejpam-4453	719	2	.	.	PUNCT
ejpam-4453	719	3	chromatic	chromatic	ADJ
ejpam-4453	719	4	number	number	NOUN
ejpam-4453	719	5	and	and	CCONJ
ejpam-4453	719	6	coloring	coloring	NOUN
ejpam-4453	719	7	of	of	ADP
ejpam-4453	719	8	ntcbg	ntcbg	DET
ejpam-4453	719	9	note	note	NOUN
ejpam-4453	719	10	that	that	SCONJ
ejpam-4453	719	11	a	a	DET
ejpam-4453	719	12	ntcbg	ntcbg	NOUN
ejpam-4453	719	13	can	can	AUX
ejpam-4453	719	14	be	be	AUX
ejpam-4453	719	15	partitioned	partition	VERB
ejpam-4453	719	16	into	into	ADP
ejpam-4453	719	17	two	two	NUM
ejpam-4453	719	18	subgraphs	subgraph	NOUN
ejpam-4453	719	19	,	,	PUNCT
ejpam-4453	719	20	those	those	PRON
ejpam-4453	719	21	are	be	AUX
ejpam-4453	719	22	,	,	PUNCT
ejpam-4453	719	23	the	the	DET
ejpam-4453	719	24	central	central	ADJ
ejpam-4453	719	25	fragment	fragment	NOUN
ejpam-4453	719	26	and	and	CCONJ
ejpam-4453	719	27	its	its	PRON
ejpam-4453	719	28	branch	branch	NOUN
ejpam-4453	719	29	.	.	PUNCT
ejpam-4453	720	1	the	the	DET
ejpam-4453	720	2	next	next	ADJ
ejpam-4453	720	3	lemma	lemma	PROPN
ejpam-4453	720	4	will	will	AUX
ejpam-4453	720	5	discuss	discuss	VERB
ejpam-4453	720	6	the	the	DET
ejpam-4453	720	7	possible	possible	ADJ
ejpam-4453	720	8	coloring	coloring	NOUN
ejpam-4453	720	9	of	of	ADP
ejpam-4453	720	10	an	an	DET
ejpam-4453	720	11	arbitrary	arbitrary	ADJ
ejpam-4453	720	12	branch	branch	NOUN
ejpam-4453	720	13	of	of	ADP
ejpam-4453	720	14	ntcbg	ntcbg	PROPN
ejpam-4453	720	15	.	.	PUNCT
ejpam-4453	720	16	theorem	theorem	VERB
ejpam-4453	720	17	11	11	NUM
ejpam-4453	720	18	.	.	PUNCT
ejpam-4453	721	1	for	for	ADP
ejpam-4453	721	2	any	any	DET
ejpam-4453	721	3	branch	branch	NOUN
ejpam-4453	721	4	bi	bi	NOUN
ejpam-4453	721	5	of	of	ADP
ejpam-4453	721	6	a	a	DET
ejpam-4453	721	7	ntcbg	ntcbg	PROPN
ejpam-4453	721	8	,	,	PUNCT
ejpam-4453	721	9	the	the	DET
ejpam-4453	721	10	constructed	construct	VERB
ejpam-4453	721	11	b̂i	b̂i	PROPN
ejpam-4453	721	12	has	have	VERB
ejpam-4453	721	13	chromatic	chromatic	ADJ
ejpam-4453	721	14	number	number	NOUN
ejpam-4453	721	15	3	3	NUM
ejpam-4453	721	16	.	.	PUNCT
ejpam-4453	722	1	proof	proof	NOUN
ejpam-4453	722	2	.	.	PUNCT
ejpam-4453	723	1	let	let	VERB
ejpam-4453	723	2	bi	bi	NOUN
ejpam-4453	723	3	be	be	AUX
ejpam-4453	723	4	any	any	DET
ejpam-4453	723	5	branch	branch	NOUN
ejpam-4453	723	6	of	of	ADP
ejpam-4453	723	7	a	a	DET
ejpam-4453	723	8	ntcbg	ntcbg	NOUN
ejpam-4453	723	9	.	.	PUNCT
ejpam-4453	723	10	by	by	ADP
ejpam-4453	723	11	theorem	theorem	NOUN
ejpam-4453	723	12	2	2	NUM
ejpam-4453	723	13	,	,	PUNCT
ejpam-4453	723	14	χ(bi	χ(bi	PROPN
ejpam-4453	723	15	)	)	PUNCT
ejpam-4453	723	16	≤	≤	NOUN
ejpam-4453	723	17	∆(bi	∆(bi	NOUN
ejpam-4453	723	18	)	)	PUNCT
ejpam-4453	723	19	+	+	NOUN
ejpam-4453	724	1	1	1	X
ejpam-4453	724	2	.	.	PUNCT
ejpam-4453	724	3	it	it	PRON
ejpam-4453	724	4	follows	follow	VERB
ejpam-4453	724	5	that	that	SCONJ
ejpam-4453	724	6	χ(bi	χ(bi	PROPN
ejpam-4453	724	7	)	)	PUNCT
ejpam-4453	724	8	≤	≤	NOUN
ejpam-4453	724	9	4	4	NUM
ejpam-4453	724	10	.	.	PUNCT
ejpam-4453	724	11	note	note	VERB
ejpam-4453	724	12	that	that	SCONJ
ejpam-4453	724	13	the	the	DET
ejpam-4453	724	14	only	only	ADJ
ejpam-4453	724	15	possible	possible	ADJ
ejpam-4453	724	16	chromatic	chromatic	ADJ
ejpam-4453	724	17	number	number	NOUN
ejpam-4453	724	18	for	for	ADP
ejpam-4453	724	19	bi	bi	NOUN
ejpam-4453	724	20	is	be	AUX
ejpam-4453	724	21	2,3	2,3	NUM
ejpam-4453	724	22	and	and	CCONJ
ejpam-4453	724	23	4	4	NUM
ejpam-4453	724	24	only	only	ADV
ejpam-4453	724	25	.	.	PUNCT
ejpam-4453	725	1	now	now	ADV
ejpam-4453	725	2	,	,	PUNCT
ejpam-4453	725	3	we	we	PRON
ejpam-4453	725	4	will	will	AUX
ejpam-4453	725	5	show	show	VERB
ejpam-4453	725	6	that	that	SCONJ
ejpam-4453	725	7	for	for	ADP
ejpam-4453	725	8	every	every	DET
ejpam-4453	725	9	possible	possible	ADJ
ejpam-4453	725	10	chromatic	chromatic	ADJ
ejpam-4453	725	11	number	number	NOUN
ejpam-4453	725	12	of	of	ADP
ejpam-4453	725	13	bi	bi	NOUN
ejpam-4453	725	14	,	,	PUNCT
ejpam-4453	725	15	b̂i	b̂i	PROPN
ejpam-4453	725	16	has	have	VERB
ejpam-4453	725	17	chromatic	chromatic	ADJ
ejpam-4453	725	18	number	number	NOUN
ejpam-4453	725	19	3	3	NUM
ejpam-4453	725	20	.	.	PUNCT
ejpam-4453	726	1	then	then	ADV
ejpam-4453	726	2	we	we	PRON
ejpam-4453	726	3	have	have	VERB
ejpam-4453	726	4	the	the	DET
ejpam-4453	726	5	following	follow	VERB
ejpam-4453	726	6	cases	case	NOUN
ejpam-4453	726	7	to	to	PART
ejpam-4453	726	8	consider	consider	VERB
ejpam-4453	726	9	.	.	PUNCT
ejpam-4453	727	1	case	case	NOUN
ejpam-4453	727	2	1	1	NUM
ejpam-4453	727	3	:	:	PUNCT
ejpam-4453	727	4	if	if	SCONJ
ejpam-4453	727	5	for	for	ADP
ejpam-4453	727	6	every	every	DET
ejpam-4453	727	7	vertex	vertex	NOUN
ejpam-4453	727	8	v	v	NOUN
ejpam-4453	727	9	of	of	ADP
ejpam-4453	727	10	bi	bi	NOUN
ejpam-4453	727	11	,	,	PUNCT
ejpam-4453	727	12	each	each	DET
ejpam-4453	727	13	neighborhood	neighborhood	NOUN
ejpam-4453	727	14	of	of	ADP
ejpam-4453	727	15	v	v	NOUN
ejpam-4453	727	16	have	have	VERB
ejpam-4453	727	17	the	the	DET
ejpam-4453	727	18	same	same	ADJ
ejpam-4453	727	19	color	color	NOUN
ejpam-4453	727	20	different	different	ADJ
ejpam-4453	727	21	from	from	ADP
ejpam-4453	727	22	v.	v.	ADP
ejpam-4453	727	23	it	it	PRON
ejpam-4453	727	24	follows	follow	VERB
ejpam-4453	727	25	that	that	SCONJ
ejpam-4453	727	26	bi	bi	NOUN
ejpam-4453	727	27	is	be	AUX
ejpam-4453	727	28	2	2	NUM
ejpam-4453	727	29	-	-	PUNCT
ejpam-4453	727	30	colorable	colorable	ADJ
ejpam-4453	727	31	which	which	PRON
ejpam-4453	727	32	implies	imply	VERB
ejpam-4453	727	33	that	that	SCONJ
ejpam-4453	727	34	χ(bi	χ(bi	PROPN
ejpam-4453	727	35	)	)	PUNCT
ejpam-4453	727	36	=	=	SYM
ejpam-4453	728	1	2	2	X
ejpam-4453	728	2	.	.	PUNCT
ejpam-4453	728	3	now	now	ADV
ejpam-4453	728	4	,	,	PUNCT
ejpam-4453	728	5	we	we	PRON
ejpam-4453	728	6	need	need	VERB
ejpam-4453	728	7	to	to	PART
ejpam-4453	728	8	show	show	VERB
ejpam-4453	728	9	that	that	SCONJ
ejpam-4453	728	10	b̂i	b̂i	PROPN
ejpam-4453	728	11	has	have	VERB
ejpam-4453	728	12	chromatic	chromatic	ADJ
ejpam-4453	728	13	number	number	NOUN
ejpam-4453	728	14	3	3	NUM
ejpam-4453	728	15	.	.	PUNCT
ejpam-4453	729	1	since	since	SCONJ
ejpam-4453	729	2	χ(bi	χ(bi	PROPN
ejpam-4453	729	3	)	)	PUNCT
ejpam-4453	729	4	=	=	SYM
ejpam-4453	729	5	2	2	NUM
ejpam-4453	729	6	,	,	PUNCT
ejpam-4453	729	7	we	we	PRON
ejpam-4453	729	8	can	can	AUX
ejpam-4453	729	9	color	color	VERB
ejpam-4453	729	10	the	the	DET
ejpam-4453	729	11	vertices	vertex	NOUN
ejpam-4453	729	12	of	of	ADP
ejpam-4453	729	13	bi	bi	NOUN
ejpam-4453	729	14	with	with	ADP
ejpam-4453	729	15	color	color	NOUN
ejpam-4453	729	16	1	1	NUM
ejpam-4453	729	17	and	and	CCONJ
ejpam-4453	729	18	2	2	NUM
ejpam-4453	729	19	.	.	PUNCT
ejpam-4453	730	1	also	also	ADV
ejpam-4453	730	2	,	,	PUNCT
ejpam-4453	730	3	for	for	ADP
ejpam-4453	730	4	every	every	DET
ejpam-4453	730	5	vertex	vertex	NOUN
ejpam-4453	730	6	vi	vi	PROPN
ejpam-4453	730	7	∈	∈	PROPN
ejpam-4453	730	8	bi	bi	NOUN
ejpam-4453	730	9	,	,	PUNCT
ejpam-4453	730	10	the	the	DET
ejpam-4453	730	11	three	three	NUM
ejpam-4453	730	12	neighborhoods	neighborhood	NOUN
ejpam-4453	730	13	of	of	ADP
ejpam-4453	730	14	vi	vi	PROPN
ejpam-4453	730	15	must	must	AUX
ejpam-4453	730	16	share	share	VERB
ejpam-4453	730	17	the	the	DET
ejpam-4453	730	18	same	same	ADJ
ejpam-4453	730	19	color	color	NOUN
ejpam-4453	730	20	different	different	ADJ
ejpam-4453	730	21	from	from	ADP
ejpam-4453	730	22	vi	vi	PROPN
ejpam-4453	730	23	.	.	PUNCT
ejpam-4453	731	1	now	now	ADV
ejpam-4453	731	2	,	,	PUNCT
ejpam-4453	731	3	recall	recall	VERB
ejpam-4453	731	4	the	the	DET
ejpam-4453	731	5	constructed	construct	VERB
ejpam-4453	731	6	b̂i	b̂i	PROPN
ejpam-4453	731	7	of	of	ADP
ejpam-4453	731	8	bi	bi	PROPN
ejpam-4453	731	9	.	.	PROPN
ejpam-4453	731	10	note	note	VERB
ejpam-4453	731	11	that	that	SCONJ
ejpam-4453	731	12	we	we	PRON
ejpam-4453	731	13	pick	pick	VERB
ejpam-4453	731	14	any	any	DET
ejpam-4453	731	15	edge	edge	NOUN
ejpam-4453	731	16	in	in	ADP
ejpam-4453	731	17	bi	bi	NOUN
ejpam-4453	731	18	then	then	ADV
ejpam-4453	731	19	subdivide	subdivide	VERB
ejpam-4453	731	20	it	it	PRON
ejpam-4453	731	21	such	such	ADJ
ejpam-4453	731	22	that	that	SCONJ
ejpam-4453	731	23	it	it	PRON
ejpam-4453	731	24	produces	produce	VERB
ejpam-4453	731	25	a	a	DET
ejpam-4453	731	26	path	path	NOUN
ejpam-4453	731	27	of	of	ADP
ejpam-4453	731	28	length	length	NOUN
ejpam-4453	731	29	2	2	NUM
ejpam-4453	731	30	.	.	PUNCT
ejpam-4453	732	1	let	let	VERB
ejpam-4453	732	2	vj	vj	INTJ
ejpam-4453	732	3	be	be	AUX
ejpam-4453	732	4	the	the	DET
ejpam-4453	732	5	new	new	ADJ
ejpam-4453	732	6	vertex	vertex	NOUN
ejpam-4453	732	7	in	in	ADP
ejpam-4453	732	8	the	the	DET
ejpam-4453	732	9	subdivision	subdivision	NOUN
ejpam-4453	732	10	of	of	ADP
ejpam-4453	732	11	constructed	construct	VERB
ejpam-4453	732	12	b̂i	b̂i	PROPN
ejpam-4453	732	13	.	.	PUNCT
ejpam-4453	733	1	then	then	ADV
ejpam-4453	733	2	vj	vj	PROPN
ejpam-4453	733	3	must	must	AUX
ejpam-4453	733	4	be	be	AUX
ejpam-4453	733	5	colored	color	VERB
ejpam-4453	733	6	differently	differently	ADV
ejpam-4453	733	7	from	from	ADP
ejpam-4453	733	8	1	1	NUM
ejpam-4453	733	9	and	and	CCONJ
ejpam-4453	733	10	2	2	NUM
ejpam-4453	733	11	,	,	PUNCT
ejpam-4453	733	12	since	since	SCONJ
ejpam-4453	733	13	vj	vj	INTJ
ejpam-4453	733	14	is	be	AUX
ejpam-4453	733	15	adjacent	adjacent	ADJ
ejpam-4453	733	16	to	to	ADP
ejpam-4453	733	17	both	both	PRON
ejpam-4453	733	18	of	of	ADP
ejpam-4453	733	19	this	this	DET
ejpam-4453	733	20	color	color	NOUN
ejpam-4453	733	21	.	.	PUNCT
ejpam-4453	734	1	without	without	ADP
ejpam-4453	734	2	loss	loss	NOUN
ejpam-4453	734	3	of	of	ADP
ejpam-4453	734	4	generality	generality	NOUN
ejpam-4453	734	5	,	,	PUNCT
ejpam-4453	734	6	we	we	PRON
ejpam-4453	734	7	must	must	AUX
ejpam-4453	734	8	color	color	VERB
ejpam-4453	734	9	vj	vj	NOUN
ejpam-4453	734	10	using	use	VERB
ejpam-4453	734	11	color	color	NOUN
ejpam-4453	734	12	3	3	NUM
ejpam-4453	734	13	.	.	PUNCT
ejpam-4453	735	1	thus	thus	ADV
ejpam-4453	735	2	,	,	PUNCT
ejpam-4453	735	3	the	the	DET
ejpam-4453	735	4	constructed	construct	VERB
ejpam-4453	735	5	b̂i	b̂i	PROPN
ejpam-4453	735	6	of	of	ADP
ejpam-4453	735	7	bi	bi	NOUN
ejpam-4453	735	8	has	have	VERB
ejpam-4453	735	9	chromatic	chromatic	ADJ
ejpam-4453	735	10	number	number	NOUN
ejpam-4453	735	11	3	3	NUM
ejpam-4453	735	12	.	.	PUNCT
ejpam-4453	735	13	case	case	NOUN
ejpam-4453	735	14	2	2	NUM
ejpam-4453	735	15	:	:	PUNCT
ejpam-4453	735	16	if	if	SCONJ
ejpam-4453	735	17	for	for	ADP
ejpam-4453	735	18	every	every	DET
ejpam-4453	735	19	vertex	vertex	NOUN
ejpam-4453	735	20	v	v	NOUN
ejpam-4453	735	21	of	of	ADP
ejpam-4453	735	22	bi	bi	NOUN
ejpam-4453	735	23	,	,	PUNCT
ejpam-4453	735	24	each	each	DET
ejpam-4453	735	25	neighborhood	neighborhood	NOUN
ejpam-4453	735	26	of	of	ADP
ejpam-4453	735	27	v	v	NOUN
ejpam-4453	735	28	has	have	VERB
ejpam-4453	735	29	two	two	NUM
ejpam-4453	735	30	vertices	vertex	NOUN
ejpam-4453	735	31	of	of	ADP
ejpam-4453	735	32	the	the	DET
ejpam-4453	735	33	same	same	ADJ
ejpam-4453	735	34	color	color	NOUN
ejpam-4453	735	35	different	different	ADJ
ejpam-4453	735	36	from	from	ADP
ejpam-4453	735	37	v	v	ADP
ejpam-4453	735	38	which	which	PRON
ejpam-4453	735	39	is	be	AUX
ejpam-4453	735	40	also	also	ADV
ejpam-4453	735	41	a	a	DET
ejpam-4453	735	42	different	different	ADJ
ejpam-4453	735	43	color	color	NOUN
ejpam-4453	735	44	from	from	ADP
ejpam-4453	735	45	the	the	DET
ejpam-4453	735	46	last	last	ADJ
ejpam-4453	735	47	vertex	vertex	NOUN
ejpam-4453	735	48	which	which	PRON
ejpam-4453	735	49	is	be	AUX
ejpam-4453	735	50	also	also	ADV
ejpam-4453	735	51	a	a	DET
ejpam-4453	735	52	neighbor	neighbor	NOUN
ejpam-4453	735	53	of	of	ADP
ejpam-4453	735	54	v.	v.	ADP
ejpam-4453	735	55	it	it	PRON
ejpam-4453	735	56	follows	follow	VERB
ejpam-4453	735	57	that	that	SCONJ
ejpam-4453	735	58	bi	bi	PROPN
ejpam-4453	735	59	is	be	AUX
ejpam-4453	735	60	3	3	NUM
ejpam-4453	735	61	-	-	PUNCT
ejpam-4453	735	62	colorable	colorable	ADJ
ejpam-4453	735	63	which	which	PRON
ejpam-4453	735	64	implies	imply	VERB
ejpam-4453	735	65	that	that	SCONJ
ejpam-4453	735	66	χ(bi	χ(bi	PROPN
ejpam-4453	735	67	)	)	PUNCT
ejpam-4453	735	68	=	=	SYM
ejpam-4453	736	1	3	3	X
ejpam-4453	736	2	.	.	PUNCT
ejpam-4453	737	1	now	now	ADV
ejpam-4453	737	2	,	,	PUNCT
ejpam-4453	737	3	we	we	PRON
ejpam-4453	737	4	need	need	VERB
ejpam-4453	737	5	to	to	PART
ejpam-4453	737	6	show	show	VERB
ejpam-4453	737	7	that	that	SCONJ
ejpam-4453	737	8	b̂i	b̂i	PROPN
ejpam-4453	737	9	has	have	VERB
ejpam-4453	737	10	chromatic	chromatic	ADJ
ejpam-4453	737	11	number	number	NOUN
ejpam-4453	737	12	3	3	NUM
ejpam-4453	737	13	.	.	PUNCT
ejpam-4453	738	1	since	since	SCONJ
ejpam-4453	738	2	χ(bi	χ(bi	PROPN
ejpam-4453	738	3	)	)	PUNCT
ejpam-4453	738	4	=	=	SYM
ejpam-4453	738	5	3	3	X
ejpam-4453	738	6	,	,	PUNCT
ejpam-4453	738	7	we	we	PRON
ejpam-4453	738	8	can	can	AUX
ejpam-4453	738	9	color	color	VERB
ejpam-4453	738	10	the	the	DET
ejpam-4453	738	11	vertices	vertex	NOUN
ejpam-4453	738	12	of	of	ADP
ejpam-4453	738	13	bi	bi	NOUN
ejpam-4453	738	14	with	with	ADP
ejpam-4453	738	15	color	color	NOUN
ejpam-4453	738	16	1,2	1,2	NUM
ejpam-4453	738	17	and	and	CCONJ
ejpam-4453	738	18	3	3	NUM
ejpam-4453	738	19	.	.	PUNCT
ejpam-4453	739	1	also	also	ADV
ejpam-4453	739	2	,	,	PUNCT
ejpam-4453	739	3	for	for	ADP
ejpam-4453	739	4	every	every	DET
ejpam-4453	739	5	vertex	vertex	NOUN
ejpam-4453	739	6	vi	vi	PROPN
ejpam-4453	739	7	∈	∈	PROPN
ejpam-4453	739	8	bi	bi	NOUN
ejpam-4453	739	9	,	,	PUNCT
ejpam-4453	739	10	two	two	NUM
ejpam-4453	739	11	vertices	vertex	NOUN
ejpam-4453	739	12	in	in	ADP
ejpam-4453	739	13	neighborhood	neighborhood	NOUN
ejpam-4453	739	14	of	of	ADP
ejpam-4453	739	15	vi	vi	PROPN
ejpam-4453	739	16	must	must	AUX
ejpam-4453	739	17	share	share	VERB
ejpam-4453	739	18	the	the	DET
ejpam-4453	739	19	same	same	ADJ
ejpam-4453	739	20	color	color	NOUN
ejpam-4453	739	21	different	different	ADJ
ejpam-4453	739	22	from	from	ADP
ejpam-4453	739	23	vi	vi	ADP
ejpam-4453	739	24	which	which	PRON
ejpam-4453	739	25	is	be	AUX
ejpam-4453	739	26	also	also	ADV
ejpam-4453	739	27	a	a	DET
ejpam-4453	739	28	different	different	ADJ
ejpam-4453	739	29	color	color	NOUN
ejpam-4453	739	30	from	from	ADP
ejpam-4453	739	31	the	the	DET
ejpam-4453	739	32	last	last	ADJ
ejpam-4453	739	33	vertex	vertex	NOUN
ejpam-4453	739	34	which	which	PRON
ejpam-4453	739	35	is	be	AUX
ejpam-4453	739	36	also	also	ADV
ejpam-4453	739	37	a	a	DET
ejpam-4453	739	38	neighbor	neighbor	NOUN
ejpam-4453	739	39	of	of	ADP
ejpam-4453	739	40	v.	v.	ADP
ejpam-4453	739	41	now	now	ADV
ejpam-4453	739	42	,	,	PUNCT
ejpam-4453	739	43	recall	recall	VERB
ejpam-4453	739	44	the	the	DET
ejpam-4453	739	45	constructed	construct	VERB
ejpam-4453	739	46	b̂i	b̂i	PROPN
ejpam-4453	739	47	of	of	ADP
ejpam-4453	739	48	bi	bi	PROPN
ejpam-4453	739	49	.	.	PROPN
ejpam-4453	739	50	note	note	VERB
ejpam-4453	739	51	that	that	SCONJ
ejpam-4453	739	52	we	we	PRON
ejpam-4453	739	53	pick	pick	VERB
ejpam-4453	739	54	any	any	DET
ejpam-4453	739	55	edge	edge	NOUN
ejpam-4453	739	56	in	in	ADP
ejpam-4453	739	57	bi	bi	NOUN
ejpam-4453	739	58	,	,	PUNCT
ejpam-4453	739	59	then	then	ADV
ejpam-4453	739	60	subdivide	subdivide	VERB
ejpam-4453	739	61	it	it	PRON
ejpam-4453	739	62	such	such	ADJ
ejpam-4453	739	63	that	that	SCONJ
ejpam-4453	739	64	it	it	PRON
ejpam-4453	739	65	produces	produce	VERB
ejpam-4453	739	66	a	a	DET
ejpam-4453	739	67	path	path	NOUN
ejpam-4453	739	68	of	of	ADP
ejpam-4453	739	69	length	length	NOUN
ejpam-4453	739	70	2	2	NUM
ejpam-4453	739	71	.	.	PUNCT
ejpam-4453	740	1	let	let	VERB
ejpam-4453	740	2	vj	vj	INTJ
ejpam-4453	740	3	be	be	AUX
ejpam-4453	740	4	the	the	DET
ejpam-4453	740	5	new	new	ADJ
ejpam-4453	740	6	vertex	vertex	NOUN
ejpam-4453	740	7	in	in	ADP
ejpam-4453	740	8	the	the	DET
ejpam-4453	740	9	subdivision	subdivision	NOUN
ejpam-4453	740	10	of	of	ADP
ejpam-4453	740	11	constructed	construct	VERB
ejpam-4453	740	12	b̂i	b̂i	PROPN
ejpam-4453	740	13	.	.	PUNCT
ejpam-4453	741	1	since	since	SCONJ
ejpam-4453	741	2	vj	vj	PROPN
ejpam-4453	741	3	is	be	AUX
ejpam-4453	741	4	adjacent	adjacent	ADJ
ejpam-4453	741	5	to	to	ADP
ejpam-4453	741	6	two	two	NUM
ejpam-4453	741	7	colors	color	NOUN
ejpam-4453	741	8	,	,	PUNCT
ejpam-4453	741	9	a.r	a.r	PROPN
ejpam-4453	741	10	nieva	nieva	PROPN
ejpam-4453	741	11	and	and	CCONJ
ejpam-4453	741	12	k.nocum	k.nocum	PROPN
ejpam-4453	741	13	/	/	SYM
ejpam-4453	741	14	eur	eur	PROPN
ejpam-4453	741	15	.	.	PUNCT
ejpam-4453	742	1	j.	j.	PROPN
ejpam-4453	742	2	pure	pure	PROPN
ejpam-4453	742	3	appl	appl	PROPN
ejpam-4453	742	4	.	.	PROPN
ejpam-4453	742	5	math	math	PROPN
ejpam-4453	742	6	,	,	PUNCT
ejpam-4453	742	7	15	15	NUM
ejpam-4453	742	8	(	(	PUNCT
ejpam-4453	742	9	4	4	NUM
ejpam-4453	742	10	)	)	PUNCT
ejpam-4453	742	11	(	(	PUNCT
ejpam-4453	742	12	2022	2022	NUM
ejpam-4453	742	13	)	)	PUNCT
ejpam-4453	742	14	,	,	PUNCT
ejpam-4453	742	15	1536	1536	NUM
ejpam-4453	742	16	-	-	SYM
ejpam-4453	742	17	1548	1548	NUM
ejpam-4453	742	18	1546	1546	NUM
ejpam-4453	742	19	we	we	PRON
ejpam-4453	742	20	can	can	AUX
ejpam-4453	742	21	color	color	VERB
ejpam-4453	742	22	vj	vj	NOUN
ejpam-4453	742	23	using	use	VERB
ejpam-4453	742	24	colors	color	NOUN
ejpam-4453	742	25	either	either	CCONJ
ejpam-4453	742	26	1,2	1,2	NUM
ejpam-4453	742	27	,	,	PUNCT
ejpam-4453	742	28	or	or	CCONJ
ejpam-4453	742	29	3	3	NUM
ejpam-4453	742	30	depending	depend	VERB
ejpam-4453	742	31	on	on	ADP
ejpam-4453	742	32	which	which	PRON
ejpam-4453	742	33	two	two	NUM
ejpam-4453	742	34	adjacent	adjacent	ADJ
ejpam-4453	742	35	vertices	vertex	NOUN
ejpam-4453	742	36	it	it	PRON
ejpam-4453	742	37	lies	lie	VERB
ejpam-4453	742	38	.	.	PUNCT
ejpam-4453	743	1	thus	thus	ADV
ejpam-4453	743	2	,	,	PUNCT
ejpam-4453	743	3	the	the	DET
ejpam-4453	743	4	constructed	construct	VERB
ejpam-4453	743	5	b̂i	b̂i	PROPN
ejpam-4453	743	6	of	of	ADP
ejpam-4453	743	7	bi	bi	NOUN
ejpam-4453	743	8	has	have	VERB
ejpam-4453	743	9	chromatic	chromatic	ADJ
ejpam-4453	743	10	number	number	NOUN
ejpam-4453	743	11	3	3	NUM
ejpam-4453	743	12	.	.	PUNCT
ejpam-4453	743	13	case	case	NOUN
ejpam-4453	743	14	3	3	NUM
ejpam-4453	743	15	:	:	PUNCT
ejpam-4453	743	16	if	if	SCONJ
ejpam-4453	743	17	for	for	ADP
ejpam-4453	743	18	every	every	DET
ejpam-4453	743	19	vertex	vertex	NOUN
ejpam-4453	743	20	v	v	NOUN
ejpam-4453	743	21	of	of	ADP
ejpam-4453	743	22	bi	bi	NOUN
ejpam-4453	743	23	,	,	PUNCT
ejpam-4453	743	24	each	each	DET
ejpam-4453	743	25	neighborhood	neighborhood	NOUN
ejpam-4453	743	26	of	of	ADP
ejpam-4453	743	27	v	v	NOUN
ejpam-4453	743	28	has	have	VERB
ejpam-4453	743	29	different	different	ADJ
ejpam-4453	743	30	color	color	NOUN
ejpam-4453	743	31	which	which	PRON
ejpam-4453	743	32	is	be	AUX
ejpam-4453	743	33	also	also	ADV
ejpam-4453	743	34	different	different	ADJ
ejpam-4453	743	35	from	from	ADP
ejpam-4453	743	36	the	the	DET
ejpam-4453	743	37	color	color	NOUN
ejpam-4453	743	38	of	of	ADP
ejpam-4453	743	39	v.	v.	ADP
ejpam-4453	743	40	it	it	PRON
ejpam-4453	743	41	follows	follow	VERB
ejpam-4453	743	42	that	that	SCONJ
ejpam-4453	743	43	bi	bi	NOUN
ejpam-4453	743	44	is	be	AUX
ejpam-4453	743	45	4	4	NUM
ejpam-4453	743	46	-	-	PUNCT
ejpam-4453	743	47	colorable	colorable	ADJ
ejpam-4453	743	48	which	which	PRON
ejpam-4453	743	49	implies	imply	VERB
ejpam-4453	743	50	that	that	SCONJ
ejpam-4453	743	51	χ(bi	χ(bi	PROPN
ejpam-4453	743	52	)	)	PUNCT
ejpam-4453	743	53	=	=	PUNCT
ejpam-4453	743	54	4	4	X
ejpam-4453	743	55	.	.	PUNCT
ejpam-4453	743	56	by	by	ADP
ejpam-4453	743	57	brooks	brooks	PROPN
ejpam-4453	743	58	theorem	theorem	PROPN
ejpam-4453	743	59	and	and	CCONJ
ejpam-4453	743	60	theorem	theorem	VERB
ejpam-4453	743	61	2	2	NUM
ejpam-4453	743	62	,	,	PUNCT
ejpam-4453	743	63	bi	bi	NOUN
ejpam-4453	743	64	∼=	∼=	PROPN
ejpam-4453	743	65	k4	k4	NOUN
ejpam-4453	743	66	.	.	PUNCT
ejpam-4453	744	1	now	now	ADV
ejpam-4453	744	2	,	,	PUNCT
ejpam-4453	744	3	we	we	PRON
ejpam-4453	744	4	need	need	VERB
ejpam-4453	744	5	to	to	PART
ejpam-4453	744	6	show	show	VERB
ejpam-4453	744	7	that	that	SCONJ
ejpam-4453	744	8	b̂i	b̂i	PROPN
ejpam-4453	744	9	has	have	VERB
ejpam-4453	744	10	chromatic	chromatic	ADJ
ejpam-4453	744	11	number	number	NOUN
ejpam-4453	744	12	3	3	NUM
ejpam-4453	744	13	.	.	PUNCT
ejpam-4453	745	1	since	since	SCONJ
ejpam-4453	745	2	χ(bi	χ(bi	PROPN
ejpam-4453	745	3	)	)	PUNCT
ejpam-4453	745	4	=	=	SYM
ejpam-4453	745	5	4	4	NUM
ejpam-4453	745	6	,	,	PUNCT
ejpam-4453	745	7	it	it	PRON
ejpam-4453	745	8	implies	imply	VERB
ejpam-4453	745	9	that	that	SCONJ
ejpam-4453	745	10	each	each	DET
ejpam-4453	745	11	neighborhood	neighborhood	NOUN
ejpam-4453	745	12	of	of	ADP
ejpam-4453	745	13	v	v	NOUN
ejpam-4453	745	14	has	have	VERB
ejpam-4453	745	15	a	a	DET
ejpam-4453	745	16	different	different	ADJ
ejpam-4453	745	17	color	color	NOUN
ejpam-4453	745	18	which	which	PRON
ejpam-4453	745	19	is	be	AUX
ejpam-4453	745	20	also	also	ADV
ejpam-4453	745	21	a	a	DET
ejpam-4453	745	22	different	different	ADJ
ejpam-4453	745	23	from	from	ADP
ejpam-4453	745	24	the	the	DET
ejpam-4453	745	25	color	color	NOUN
ejpam-4453	745	26	of	of	ADP
ejpam-4453	745	27	v.	v.	ADP
ejpam-4453	745	28	now	now	ADV
ejpam-4453	745	29	,	,	PUNCT
ejpam-4453	745	30	recall	recall	VERB
ejpam-4453	745	31	the	the	DET
ejpam-4453	745	32	constructed	construct	VERB
ejpam-4453	745	33	b̂i	b̂i	PROPN
ejpam-4453	745	34	of	of	ADP
ejpam-4453	745	35	bi	bi	PROPN
ejpam-4453	745	36	,	,	PUNCT
ejpam-4453	745	37	note	note	VERB
ejpam-4453	745	38	that	that	SCONJ
ejpam-4453	745	39	we	we	PRON
ejpam-4453	745	40	choose	choose	VERB
ejpam-4453	745	41	any	any	DET
ejpam-4453	745	42	edge	edge	NOUN
ejpam-4453	745	43	in	in	ADP
ejpam-4453	745	44	bi	bi	NOUN
ejpam-4453	745	45	such	such	ADJ
ejpam-4453	745	46	that	that	SCONJ
ejpam-4453	745	47	it	it	PRON
ejpam-4453	745	48	produces	produce	VERB
ejpam-4453	745	49	a	a	DET
ejpam-4453	745	50	path	path	NOUN
ejpam-4453	745	51	of	of	ADP
ejpam-4453	745	52	length	length	NOUN
ejpam-4453	745	53	2	2	NUM
ejpam-4453	745	54	.	.	PUNCT
ejpam-4453	745	55	suppose	suppose	VERB
ejpam-4453	745	56	we	we	PRON
ejpam-4453	745	57	choose	choose	VERB
ejpam-4453	745	58	an	an	DET
ejpam-4453	745	59	edge	edge	NOUN
ejpam-4453	746	1	e	e	NOUN
ejpam-4453	746	2	=	=	PUNCT
ejpam-4453	747	1	[	[	X
ejpam-4453	747	2	x	x	X
ejpam-4453	747	3	,	,	PUNCT
ejpam-4453	747	4	y	y	PROPN
ejpam-4453	747	5	]	]	X
ejpam-4453	747	6	∈	∈	PROPN
ejpam-4453	747	7	e(bi	e(bi	PROPN
ejpam-4453	747	8	)	)	PUNCT
ejpam-4453	747	9	and	and	CCONJ
ejpam-4453	747	10	let	let	VERB
ejpam-4453	747	11	vi	vi	PROPN
ejpam-4453	747	12	be	be	AUX
ejpam-4453	747	13	the	the	DET
ejpam-4453	747	14	new	new	ADJ
ejpam-4453	747	15	vertex	vertex	NOUN
ejpam-4453	747	16	in	in	ADP
ejpam-4453	747	17	the	the	DET
ejpam-4453	747	18	subdivision	subdivision	NOUN
ejpam-4453	747	19	of	of	ADP
ejpam-4453	747	20	the	the	DET
ejpam-4453	747	21	edge	edge	NOUN
ejpam-4453	747	22	e	e	NOUN
ejpam-4453	747	23	in	in	ADP
ejpam-4453	747	24	b̂i	b̂i	PROPN
ejpam-4453	747	25	.	.	PUNCT
ejpam-4453	748	1	then	then	ADV
ejpam-4453	748	2	vi	vi	PROPN
ejpam-4453	748	3	must	must	AUX
ejpam-4453	748	4	be	be	AUX
ejpam-4453	748	5	adjacent	adjacent	ADJ
ejpam-4453	748	6	to	to	ADP
ejpam-4453	748	7	only	only	ADV
ejpam-4453	748	8	two	two	NUM
ejpam-4453	748	9	colors	color	NOUN
ejpam-4453	748	10	in	in	ADP
ejpam-4453	748	11	bi	bi	PROPN
ejpam-4453	748	12	.	.	PROPN
ejpam-4453	748	13	suppose	suppose	VERB
ejpam-4453	748	14	we	we	PRON
ejpam-4453	748	15	color	color	VERB
ejpam-4453	748	16	bi	bi	NOUN
ejpam-4453	748	17	with	with	ADP
ejpam-4453	748	18	1,2,3	1,2,3	NUM
ejpam-4453	748	19	and	and	CCONJ
ejpam-4453	748	20	4	4	NUM
ejpam-4453	748	21	.	.	NOUN
ejpam-4453	748	22	without	without	ADP
ejpam-4453	748	23	loss	loss	NOUN
ejpam-4453	748	24	of	of	ADP
ejpam-4453	748	25	generality	generality	NOUN
ejpam-4453	748	26	,	,	PUNCT
ejpam-4453	748	27	let	let	VERB
ejpam-4453	748	28	1	1	NUM
ejpam-4453	748	29	and	and	CCONJ
ejpam-4453	748	30	2	2	NUM
ejpam-4453	748	31	be	be	AUX
ejpam-4453	748	32	the	the	DET
ejpam-4453	748	33	colors	color	NOUN
ejpam-4453	748	34	of	of	ADP
ejpam-4453	748	35	vertices	vertex	NOUN
ejpam-4453	748	36	x	x	PUNCT
ejpam-4453	748	37	and	and	CCONJ
ejpam-4453	748	38	y	y	PROPN
ejpam-4453	748	39	which	which	PRON
ejpam-4453	748	40	are	be	AUX
ejpam-4453	748	41	adjacent	adjacent	ADJ
ejpam-4453	748	42	in	in	ADP
ejpam-4453	748	43	vi	vi	PROPN
ejpam-4453	748	44	.	.	PUNCT
ejpam-4453	749	1	then	then	ADV
ejpam-4453	749	2	we	we	PRON
ejpam-4453	749	3	can	can	AUX
ejpam-4453	749	4	color	color	VERB
ejpam-4453	749	5	vi	vi	PROPN
ejpam-4453	749	6	with	with	ADP
ejpam-4453	749	7	the	the	DET
ejpam-4453	749	8	remaining	remain	VERB
ejpam-4453	749	9	colors	color	NOUN
ejpam-4453	749	10	in	in	ADP
ejpam-4453	749	11	bi	bi	NOUN
ejpam-4453	749	12	,	,	PUNCT
ejpam-4453	749	13	3	3	NUM
ejpam-4453	749	14	and	and	CCONJ
ejpam-4453	749	15	4	4	NUM
ejpam-4453	749	16	.	.	X
ejpam-4453	749	17	note	note	VERB
ejpam-4453	749	18	that	that	SCONJ
ejpam-4453	749	19	the	the	DET
ejpam-4453	749	20	vertices	vertex	NOUN
ejpam-4453	749	21	x	x	X
ejpam-4453	749	22	and	and	CCONJ
ejpam-4453	749	23	y	y	PROPN
ejpam-4453	749	24	are	be	AUX
ejpam-4453	749	25	no	no	ADV
ejpam-4453	749	26	longer	long	ADV
ejpam-4453	749	27	adjacent	adjacent	ADJ
ejpam-4453	749	28	in	in	ADP
ejpam-4453	749	29	b̂i	b̂i	PROPN
ejpam-4453	749	30	.	.	PUNCT
ejpam-4453	750	1	hence	hence	ADV
ejpam-4453	750	2	,	,	PUNCT
ejpam-4453	750	3	we	we	PRON
ejpam-4453	750	4	can	can	AUX
ejpam-4453	750	5	color	color	VERB
ejpam-4453	750	6	x	x	PRON
ejpam-4453	750	7	,	,	PUNCT
ejpam-4453	750	8	y	y	PROPN
ejpam-4453	750	9	by	by	ADP
ejpam-4453	750	10	the	the	DET
ejpam-4453	750	11	same	same	ADJ
ejpam-4453	750	12	color	color	NOUN
ejpam-4453	750	13	as	as	ADP
ejpam-4453	750	14	1	1	NUM
ejpam-4453	750	15	or	or	CCONJ
ejpam-4453	750	16	2	2	NUM
ejpam-4453	750	17	.	.	PUNCT
ejpam-4453	750	18	by	by	ADP
ejpam-4453	750	19	this	this	DET
ejpam-4453	750	20	argument	argument	NOUN
ejpam-4453	750	21	,	,	PUNCT
ejpam-4453	750	22	the	the	DET
ejpam-4453	750	23	possible	possible	ADJ
ejpam-4453	750	24	coloring	coloring	NOUN
ejpam-4453	750	25	of	of	ADP
ejpam-4453	750	26	constructed	construct	VERB
ejpam-4453	750	27	b̂i	b̂i	PROPN
ejpam-4453	750	28	is	be	AUX
ejpam-4453	750	29	3,4	3,4	NUM
ejpam-4453	750	30	and	and	CCONJ
ejpam-4453	750	31	either	either	DET
ejpam-4453	750	32	1	1	NUM
ejpam-4453	750	33	or	or	CCONJ
ejpam-4453	750	34	2	2	NUM
ejpam-4453	750	35	.	.	PUNCT
ejpam-4453	751	1	this	this	PRON
ejpam-4453	751	2	implies	imply	VERB
ejpam-4453	751	3	that	that	SCONJ
ejpam-4453	751	4	the	the	DET
ejpam-4453	751	5	constructed	construct	VERB
ejpam-4453	751	6	b̂i	b̂i	PROPN
ejpam-4453	751	7	has	have	VERB
ejpam-4453	751	8	chromatic	chromatic	ADJ
ejpam-4453	751	9	number	number	NOUN
ejpam-4453	751	10	3	3	NUM
ejpam-4453	751	11	.	.	PUNCT
ejpam-4453	751	12	therefore	therefore	ADV
ejpam-4453	751	13	for	for	ADP
ejpam-4453	751	14	any	any	DET
ejpam-4453	751	15	constructed	construct	VERB
ejpam-4453	751	16	b̂i	b̂i	PROPN
ejpam-4453	751	17	of	of	ADP
ejpam-4453	751	18	bi	bi	NOUN
ejpam-4453	751	19	has	have	VERB
ejpam-4453	751	20	chromatic	chromatic	ADJ
ejpam-4453	751	21	number	number	NOUN
ejpam-4453	751	22	3	3	NUM
ejpam-4453	751	23	.	.	PUNCT
ejpam-4453	751	24	consider	consider	VERB
ejpam-4453	751	25	the	the	DET
ejpam-4453	751	26	graph	graph	NOUN
ejpam-4453	751	27	representation	representation	NOUN
ejpam-4453	751	28	in	in	ADP
ejpam-4453	751	29	figure	figure	NOUN
ejpam-4453	751	30	9	9	NUM
ejpam-4453	751	31	(	(	PUNCT
ejpam-4453	751	32	a	a	NOUN
ejpam-4453	751	33	)	)	PUNCT
ejpam-4453	751	34	.	.	PUNCT
ejpam-4453	752	1	a	a	DET
ejpam-4453	752	2	cubic	cubic	ADJ
ejpam-4453	752	3	graph	graph	NOUN
ejpam-4453	752	4	that	that	PRON
ejpam-4453	752	5	has	have	VERB
ejpam-4453	752	6	2	2	NUM
ejpam-4453	752	7	coloring	coloring	NOUN
ejpam-4453	752	8	can	can	AUX
ejpam-4453	752	9	be	be	AUX
ejpam-4453	752	10	presented	present	VERB
ejpam-4453	752	11	as	as	ADP
ejpam-4453	752	12	(	(	PUNCT
ejpam-4453	752	13	a	a	NOUN
ejpam-4453	752	14	)	)	PUNCT
ejpam-4453	752	15	where	where	SCONJ
ejpam-4453	752	16	a	a	DET
ejpam-4453	752	17	vertex	vertex	NOUN
ejpam-4453	752	18	color	color	NOUN
ejpam-4453	752	19	1	1	NUM
ejpam-4453	752	20	has	have	VERB
ejpam-4453	752	21	neighbors	neighbor	NOUN
ejpam-4453	752	22	having	have	VERB
ejpam-4453	752	23	the	the	DET
ejpam-4453	752	24	same	same	ADJ
ejpam-4453	752	25	color	color	NOUN
ejpam-4453	752	26	2	2	NUM
ejpam-4453	752	27	.	.	X
ejpam-4453	752	28	recall	recall	VERB
ejpam-4453	752	29	that	that	PRON
ejpam-4453	752	30	for	for	ADP
ejpam-4453	752	31	any	any	DET
ejpam-4453	752	32	branch	branch	NOUN
ejpam-4453	752	33	of	of	ADP
ejpam-4453	752	34	ntcbg	ntcbg	PROPN
ejpam-4453	752	35	,	,	PUNCT
ejpam-4453	752	36	we	we	PRON
ejpam-4453	752	37	pick	pick	VERB
ejpam-4453	752	38	any	any	DET
ejpam-4453	752	39	edge	edge	NOUN
ejpam-4453	752	40	in	in	ADP
ejpam-4453	752	41	particular	particular	ADJ
ejpam-4453	752	42	branch	branch	NOUN
ejpam-4453	752	43	since	since	SCONJ
ejpam-4453	752	44	any	any	DET
ejpam-4453	752	45	edge	edge	NOUN
ejpam-4453	752	46	has	have	VERB
ejpam-4453	752	47	color	color	NOUN
ejpam-4453	752	48	1	1	NUM
ejpam-4453	752	49	and	and	CCONJ
ejpam-4453	752	50	2	2	NUM
ejpam-4453	752	51	.	.	PUNCT
ejpam-4453	753	1	then	then	ADV
ejpam-4453	753	2	the	the	DET
ejpam-4453	753	3	new	new	ADJ
ejpam-4453	753	4	vertex	vertex	NOUN
ejpam-4453	753	5	must	must	AUX
ejpam-4453	753	6	be	be	AUX
ejpam-4453	753	7	different	different	ADJ
ejpam-4453	753	8	from	from	ADP
ejpam-4453	753	9	1	1	NUM
ejpam-4453	753	10	and	and	CCONJ
ejpam-4453	753	11	2	2	NUM
ejpam-4453	753	12	,	,	PUNCT
ejpam-4453	753	13	see	see	VERB
ejpam-4453	753	14	figure	figure	NOUN
ejpam-4453	753	15	9	9	NUM
ejpam-4453	753	16	(	(	PUNCT
ejpam-4453	753	17	b	b	NOUN
ejpam-4453	753	18	)	)	PUNCT
ejpam-4453	753	19	.	.	PUNCT
ejpam-4453	754	1	hence	hence	ADV
ejpam-4453	754	2	,	,	PUNCT
ejpam-4453	754	3	for	for	ADP
ejpam-4453	754	4	any	any	DET
ejpam-4453	754	5	cubic	cubic	ADJ
ejpam-4453	754	6	graph	graph	NOUN
ejpam-4453	754	7	that	that	PRON
ejpam-4453	754	8	admits	admit	VERB
ejpam-4453	754	9	2	2	NUM
ejpam-4453	754	10	-	-	PUNCT
ejpam-4453	754	11	coloring	color	VERB
ejpam-4453	754	12	the	the	DET
ejpam-4453	754	13	constructed	construct	VERB
ejpam-4453	754	14	b̂i	b̂i	PROPN
ejpam-4453	754	15	has	have	VERB
ejpam-4453	754	16	chromatic	chromatic	ADJ
ejpam-4453	754	17	number	number	NOUN
ejpam-4453	754	18	3	3	NUM
ejpam-4453	754	19	.	.	PUNCT
ejpam-4453	755	1	for	for	ADP
ejpam-4453	755	2	a	a	DET
ejpam-4453	755	3	cubic	cubic	ADJ
ejpam-4453	755	4	graph	graph	NOUN
ejpam-4453	755	5	that	that	PRON
ejpam-4453	755	6	admits	admit	VERB
ejpam-4453	755	7	3	3	NUM
ejpam-4453	755	8	-	-	PUNCT
ejpam-4453	755	9	coloring	coloring	NOUN
ejpam-4453	755	10	,	,	PUNCT
ejpam-4453	755	11	we	we	PRON
ejpam-4453	755	12	have	have	VERB
ejpam-4453	755	13	an	an	DET
ejpam-4453	755	14	example	example	NOUN
ejpam-4453	755	15	as	as	SCONJ
ejpam-4453	755	16	shown	show	VERB
ejpam-4453	755	17	in	in	ADP
ejpam-4453	755	18	figure	figure	NOUN
ejpam-4453	755	19	10	10	NUM
ejpam-4453	755	20	.	.	PUNCT
ejpam-4453	756	1	note	note	VERB
ejpam-4453	756	2	that	that	SCONJ
ejpam-4453	756	3	for	for	ADP
ejpam-4453	756	4	any	any	DET
ejpam-4453	756	5	vertex	vertex	NOUN
ejpam-4453	756	6	vi	vi	NOUN
ejpam-4453	756	7	in	in	ADP
ejpam-4453	756	8	(	(	PUNCT
ejpam-4453	756	9	a	a	X
ejpam-4453	756	10	)	)	PUNCT
ejpam-4453	756	11	,	,	PUNCT
ejpam-4453	756	12	the	the	DET
ejpam-4453	756	13	neighbor	neighbor	NOUN
ejpam-4453	756	14	vi	vi	PROPN
ejpam-4453	756	15	has	have	VERB
ejpam-4453	756	16	two	two	NUM
ejpam-4453	756	17	vertices	vertex	NOUN
ejpam-4453	756	18	that	that	PRON
ejpam-4453	756	19	have	have	VERB
ejpam-4453	756	20	the	the	DET
ejpam-4453	756	21	same	same	ADJ
ejpam-4453	756	22	color	color	NOUN
ejpam-4453	756	23	.	.	PUNCT
ejpam-4453	757	1	it	it	PRON
ejpam-4453	757	2	is	be	AUX
ejpam-4453	757	3	clear	clear	ADJ
ejpam-4453	757	4	that	that	SCONJ
ejpam-4453	757	5	for	for	ADP
ejpam-4453	757	6	any	any	DET
ejpam-4453	757	7	edge	edge	NOUN
ejpam-4453	757	8	we	we	PRON
ejpam-4453	757	9	pick	pick	VERB
ejpam-4453	757	10	in	in	ADP
ejpam-4453	757	11	(	(	PUNCT
ejpam-4453	757	12	a	a	X
ejpam-4453	757	13	)	)	PUNCT
ejpam-4453	757	14	,	,	PUNCT
ejpam-4453	757	15	we	we	PRON
ejpam-4453	757	16	can	can	AUX
ejpam-4453	757	17	color	color	VERB
ejpam-4453	757	18	it	it	PRON
ejpam-4453	757	19	by	by	ADP
ejpam-4453	757	20	different	different	ADJ
ejpam-4453	757	21	colors	color	NOUN
ejpam-4453	757	22	than	than	ADP
ejpam-4453	757	23	its	its	PRON
ejpam-4453	757	24	two	two	NUM
ejpam-4453	757	25	adjacent	adjacent	ADJ
ejpam-4453	757	26	vertices	vertex	NOUN
ejpam-4453	757	27	.	.	PUNCT
ejpam-4453	758	1	thus	thus	ADV
ejpam-4453	758	2	,	,	PUNCT
ejpam-4453	758	3	for	for	ADP
ejpam-4453	758	4	any	any	DET
ejpam-4453	758	5	cubic	cubic	ADJ
ejpam-4453	758	6	graph	graph	NOUN
ejpam-4453	758	7	that	that	PRON
ejpam-4453	758	8	admits	admit	VERB
ejpam-4453	758	9	3	3	NUM
ejpam-4453	758	10	-	-	PUNCT
ejpam-4453	758	11	coloring	coloring	NOUN
ejpam-4453	758	12	,	,	PUNCT
ejpam-4453	758	13	the	the	DET
ejpam-4453	758	14	constructed	construct	VERB
ejpam-4453	758	15	b̂i	b̂i	PROPN
ejpam-4453	758	16	has	have	VERB
ejpam-4453	758	17	also	also	ADV
ejpam-4453	758	18	chromatic	chromatic	ADJ
ejpam-4453	758	19	number	number	NOUN
ejpam-4453	758	20	3	3	NUM
ejpam-4453	758	21	.	.	PUNCT
ejpam-4453	759	1	lastly	lastly	ADV
ejpam-4453	759	2	,	,	PUNCT
ejpam-4453	759	3	figure	figure	VERB
ejpam-4453	759	4	11	11	NUM
ejpam-4453	759	5	illustrates	illustrate	VERB
ejpam-4453	759	6	case	case	NOUN
ejpam-4453	759	7	3	3	NUM
ejpam-4453	759	8	of	of	ADP
ejpam-4453	759	9	theorem	theorem	NOUN
ejpam-4453	759	10	11	11	NUM
ejpam-4453	759	11	since	since	SCONJ
ejpam-4453	759	12	k4	k4	NOUN
ejpam-4453	759	13	is	be	AUX
ejpam-4453	759	14	the	the	DET
ejpam-4453	759	15	only	only	ADJ
ejpam-4453	759	16	3	3	NUM
ejpam-4453	759	17	-	-	PUNCT
ejpam-4453	759	18	regular	regular	ADJ
ejpam-4453	759	19	graph	graph	NOUN
ejpam-4453	759	20	that	that	PRON
ejpam-4453	759	21	admits	admit	VERB
ejpam-4453	759	22	4	4	NUM
ejpam-4453	759	23	-	-	PUNCT
ejpam-4453	759	24	coloring	coloring	NOUN
ejpam-4453	759	25	.	.	PUNCT
ejpam-4453	760	1	(	(	PUNCT
ejpam-4453	760	2	a	a	X
ejpam-4453	760	3	)	)	PUNCT
ejpam-4453	760	4	.........	.........	PUNCT
ejpam-4453	760	5	.............	.............	PUNCT
ejpam-4453	760	6	.............................................................................	.............................................................................	PUNCT
ejpam-4453	760	7	.........	.........	PUNCT
ejpam-4453	760	8	.........	.........	PUNCT
ejpam-4453	760	9	.............	.............	PUNCT
ejpam-4453	760	10	.............................................................................	.............................................................................	PUNCT
ejpam-4453	760	11	.........	.........	PUNCT
ejpam-4453	760	12	.........	.........	PUNCT
ejpam-4453	760	13	.............	.............	PUNCT
ejpam-4453	760	14	.............................................................................	.............................................................................	PUNCT
ejpam-4453	760	15	.........	.........	PUNCT
ejpam-4453	760	16	.........	.........	PUNCT
ejpam-4453	760	17	.............	.............	PUNCT
ejpam-4453	760	18	.............................................................................	.............................................................................	PUNCT
ejpam-4453	761	1	.........	.........	PUNCT
ejpam-4453	762	1	1	1	NUM
ejpam-4453	762	2	2	2	NUM
ejpam-4453	762	3	2	2	NUM
ejpam-4453	762	4	2	2	NUM
ejpam-4453	762	5	.........	.........	PUNCT
ejpam-4453	762	6	........	........	PUNCT
ejpam-4453	762	7	........	........	PUNCT
ejpam-4453	762	8	........	........	PUNCT
ejpam-4453	762	9	........	........	PUNCT
ejpam-4453	762	10	........	........	PUNCT
ejpam-4453	762	11	........	........	PUNCT
ejpam-4453	762	12	........	........	PUNCT
ejpam-4453	762	13	........	........	PUNCT
ejpam-4453	762	14	........	........	PUNCT
ejpam-4453	762	15	.	.	PUNCT
ejpam-4453	762	16	...............	...............	PUNCT
ejpam-4453	762	17	..............	..............	PUNCT
ejpam-4453	762	18	..............	..............	PUNCT
ejpam-4453	762	19	..............	..............	PUNCT
ejpam-4453	762	20	..............	..............	PUNCT
ejpam-4453	762	21	..............	..............	PUNCT
ejpam-4453	762	22	..............	..............	PUNCT
ejpam-4453	762	23	..............	..............	PUNCT
ejpam-4453	762	24	..............	..............	PUNCT
ejpam-4453	762	25	..............	..............	PUNCT
ejpam-4453	762	26	..............	..............	PUNCT
ejpam-4453	762	27	..............	..............	PUNCT
ejpam-4453	763	1	.....	.....	PUNCT
ejpam-4453	763	2	..............................................................................................................................................................................	..............................................................................................................................................................................	PUNCT
ejpam-4453	763	3	.........	.........	PUNCT
ejpam-4453	763	4	.............	.............	PUNCT
ejpam-4453	763	5	.............................................................................	.............................................................................	PUNCT
ejpam-4453	763	6	.........	.........	PUNCT
ejpam-4453	764	1	.........	.........	PUNCT
ejpam-4453	764	2	.............	.............	PUNCT
ejpam-4453	764	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	764	4	.........	.........	PUNCT
ejpam-4453	764	5	..............................................................................................................................	..............................................................................................................................	PUNCT
ejpam-4453	765	1	.........	.........	PUNCT
ejpam-4453	766	1	.........	.........	PUNCT
ejpam-4453	766	2	.........	.........	PUNCT
ejpam-4453	767	1	.........	.........	PUNCT
ejpam-4453	767	2	.........	.........	PUNCT
ejpam-4453	768	1	.........	.........	PUNCT
ejpam-4453	768	2	.........	.........	PUNCT
ejpam-4453	769	1	.........	.........	PUNCT
ejpam-4453	769	2	.........	.........	PUNCT
ejpam-4453	770	1	.........	.........	PUNCT
ejpam-4453	770	2	.........	.........	PUNCT
ejpam-4453	770	3	.......	.......	PUNCT
ejpam-4453	770	4	.........	.........	PUNCT
ejpam-4453	770	5	.............	.............	PUNCT
ejpam-4453	770	6	.............................................................................	.............................................................................	PUNCT
ejpam-4453	770	7	.........	.........	PUNCT
ejpam-4453	771	1	.........	.........	PUNCT
ejpam-4453	771	2	.............	.............	PUNCT
ejpam-4453	771	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	771	4	.........	.........	PUNCT
ejpam-4453	772	1	..........	..........	PUNCT
ejpam-4453	772	2	.........	.........	PUNCT
ejpam-4453	773	1	.........	.........	PUNCT
ejpam-4453	773	2	.........	.........	PUNCT
ejpam-4453	774	1	.........	.........	PUNCT
ejpam-4453	774	2	.........	.........	PUNCT
ejpam-4453	775	1	.........	.........	PUNCT
ejpam-4453	775	2	.........	.........	PUNCT
ejpam-4453	776	1	.........	.........	PUNCT
ejpam-4453	776	2	.........	.........	PUNCT
ejpam-4453	777	1	.........	.........	PUNCT
ejpam-4453	777	2	.........	.........	PUNCT
ejpam-4453	777	3	.......	.......	PUNCT
ejpam-4453	777	4	....................................................................................................................	....................................................................................................................	PUNCT
ejpam-4453	778	1	.........	.........	PUNCT
ejpam-4453	778	2	.............	.............	PUNCT
ejpam-4453	779	1	.............................................................................	.............................................................................	PUNCT
ejpam-4453	779	2	.........	.........	PUNCT
ejpam-4453	780	1	.........	.........	PUNCT
ejpam-4453	780	2	.............	.............	PUNCT
ejpam-4453	780	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	780	4	.........	.........	PUNCT
ejpam-4453	781	1	..........	..........	PUNCT
ejpam-4453	781	2	.........	.........	PUNCT
ejpam-4453	782	1	.........	.........	PUNCT
ejpam-4453	782	2	.........	.........	PUNCT
ejpam-4453	783	1	.........	.........	PUNCT
ejpam-4453	783	2	.........	.........	PUNCT
ejpam-4453	784	1	.........	.........	PUNCT
ejpam-4453	784	2	.........	.........	PUNCT
ejpam-4453	785	1	.........	.........	PUNCT
ejpam-4453	785	2	.........	.........	PUNCT
ejpam-4453	786	1	.........	.........	PUNCT
ejpam-4453	786	2	.........	.........	PUNCT
ejpam-4453	786	3	.......	.......	PUNCT
ejpam-4453	787	1	....................................................................................................................	....................................................................................................................	PUNCT
ejpam-4453	788	1	1	1	NUM
ejpam-4453	788	2	1	1	NUM
ejpam-4453	788	3	1	1	NUM
ejpam-4453	788	4	1	1	NUM
ejpam-4453	788	5	11	11	NUM
ejpam-4453	788	6	(	(	PUNCT
ejpam-4453	788	7	b	b	NOUN
ejpam-4453	788	8	)	)	PUNCT
ejpam-4453	788	9	.........	.........	PUNCT
ejpam-4453	788	10	.............	.............	PUNCT
ejpam-4453	788	11	.............................................................................	.............................................................................	PUNCT
ejpam-4453	788	12	.........	.........	PUNCT
ejpam-4453	788	13	.........	.........	PUNCT
ejpam-4453	788	14	.............	.............	PUNCT
ejpam-4453	788	15	.............................................................................	.............................................................................	PUNCT
ejpam-4453	788	16	.........	.........	PUNCT
ejpam-4453	788	17	.........	.........	PUNCT
ejpam-4453	788	18	.............	.............	PUNCT
ejpam-4453	788	19	.............................................................................	.............................................................................	PUNCT
ejpam-4453	788	20	.........	.........	PUNCT
ejpam-4453	788	21	.........	.........	PUNCT
ejpam-4453	788	22	.............	.............	PUNCT
ejpam-4453	788	23	.............................................................................	.............................................................................	PUNCT
ejpam-4453	788	24	.........	.........	PUNCT
ejpam-4453	788	25	1	1	NUM
ejpam-4453	788	26	2	2	NUM
ejpam-4453	788	27	2	2	NUM
ejpam-4453	788	28	2	2	NUM
ejpam-4453	788	29	.........	.........	PUNCT
ejpam-4453	788	30	........	........	PUNCT
ejpam-4453	788	31	........	........	PUNCT
ejpam-4453	788	32	........	........	PUNCT
ejpam-4453	788	33	........	........	PUNCT
ejpam-4453	788	34	........	........	PUNCT
ejpam-4453	788	35	........	........	PUNCT
ejpam-4453	788	36	........	........	PUNCT
ejpam-4453	788	37	........	........	PUNCT
ejpam-4453	788	38	........	........	PUNCT
ejpam-4453	788	39	.	.	PUNCT
ejpam-4453	788	40	...............	...............	PUNCT
ejpam-4453	788	41	..............	..............	PUNCT
ejpam-4453	788	42	..............	..............	PUNCT
ejpam-4453	788	43	..............	..............	PUNCT
ejpam-4453	788	44	.............	.............	PUNCT
ejpam-4453	788	45	...............	...............	PUNCT
ejpam-4453	788	46	..............	..............	PUNCT
ejpam-4453	788	47	..............	..............	PUNCT
ejpam-4453	788	48	..............	..............	PUNCT
ejpam-4453	788	49	.............	.............	PUNCT
ejpam-4453	788	50	......................................................................	......................................................................	PUNCT
ejpam-4453	788	51	......................................................................	......................................................................	PUNCT
ejpam-4453	788	52	.........	.........	PUNCT
ejpam-4453	788	53	.............	.............	PUNCT
ejpam-4453	788	54	.............................................................................	.............................................................................	PUNCT
ejpam-4453	788	55	.........	.........	PUNCT
ejpam-4453	788	56	.........	.........	PUNCT
ejpam-4453	788	57	.............	.............	PUNCT
ejpam-4453	788	58	.............................................................................	.............................................................................	PUNCT
ejpam-4453	788	59	.........	.........	PUNCT
ejpam-4453	788	60	..........................................	..........................................	PUNCT
ejpam-4453	788	61	.........................................	.........................................	PUNCT
ejpam-4453	788	62	.........	.........	PUNCT
ejpam-4453	788	63	........	........	PUNCT
ejpam-4453	788	64	........	........	PUNCT
ejpam-4453	788	65	........	........	PUNCT
ejpam-4453	788	66	........	........	PUNCT
ejpam-4453	788	67	..........	..........	PUNCT
ejpam-4453	788	68	.........	.........	PUNCT
ejpam-4453	788	69	.........	.........	PUNCT
ejpam-4453	788	70	.........	.........	PUNCT
ejpam-4453	788	71	......	......	PUNCT
ejpam-4453	788	72	.........	.........	PUNCT
ejpam-4453	788	73	.............	.............	PUNCT
ejpam-4453	788	74	.............................................................................	.............................................................................	PUNCT
ejpam-4453	788	75	.........	.........	PUNCT
ejpam-4453	788	76	.........	.........	PUNCT
ejpam-4453	788	77	.............	.............	PUNCT
ejpam-4453	788	78	.............................................................................	.............................................................................	PUNCT
ejpam-4453	788	79	.........	.........	PUNCT
ejpam-4453	788	80	..........	..........	PUNCT
ejpam-4453	788	81	.........	.........	PUNCT
ejpam-4453	788	82	.........	.........	PUNCT
ejpam-4453	788	83	.........	.........	PUNCT
ejpam-4453	788	84	.........	.........	PUNCT
ejpam-4453	788	85	.........	.........	PUNCT
ejpam-4453	788	86	.........	.........	PUNCT
ejpam-4453	788	87	.........	.........	PUNCT
ejpam-4453	788	88	.........	.........	PUNCT
ejpam-4453	788	89	.........	.........	PUNCT
ejpam-4453	788	90	.........	.........	PUNCT
ejpam-4453	788	91	.........	.........	PUNCT
ejpam-4453	788	92	.......	.......	PUNCT
ejpam-4453	788	93	....................................................................................................................	....................................................................................................................	PUNCT
ejpam-4453	788	94	.........	.........	PUNCT
ejpam-4453	788	95	.............	.............	PUNCT
ejpam-4453	788	96	.............................................................................	.............................................................................	PUNCT
ejpam-4453	788	97	.........	.........	PUNCT
ejpam-4453	788	98	.........	.........	PUNCT
ejpam-4453	788	99	.............	.............	PUNCT
ejpam-4453	788	100	.............................................................................	.............................................................................	PUNCT
ejpam-4453	788	101	.........	.........	PUNCT
ejpam-4453	788	102	..........	..........	PUNCT
ejpam-4453	788	103	.........	.........	PUNCT
ejpam-4453	788	104	.........	.........	PUNCT
ejpam-4453	788	105	.........	.........	PUNCT
ejpam-4453	788	106	.........	.........	PUNCT
ejpam-4453	788	107	.........	.........	PUNCT
ejpam-4453	788	108	.........	.........	PUNCT
ejpam-4453	788	109	.........	.........	PUNCT
ejpam-4453	788	110	.........	.........	PUNCT
ejpam-4453	788	111	.........	.........	PUNCT
ejpam-4453	788	112	.........	.........	PUNCT
ejpam-4453	788	113	.........	.........	PUNCT
ejpam-4453	788	114	.......	.......	PUNCT
ejpam-4453	788	115	....................................................................................................................	....................................................................................................................	PUNCT
ejpam-4453	789	1	1	1	NUM
ejpam-4453	789	2	1	1	NUM
ejpam-4453	789	3	1	1	NUM
ejpam-4453	789	4	1	1	NUM
ejpam-4453	789	5	11	11	NUM
ejpam-4453	789	6	.........	.........	PUNCT
ejpam-4453	789	7	..............................................................	..............................................................	PUNCT
ejpam-4453	789	8	.....	.....	PUNCT
ejpam-4453	789	9	.........	.........	PUNCT
ejpam-4453	789	10	..............................................................	..............................................................	PUNCT
ejpam-4453	790	1	.....	.....	PUNCT
ejpam-4453	790	2	.........	.........	PUNCT
ejpam-4453	791	1	..............................................................	..............................................................	PUNCT
ejpam-4453	791	2	.....	.....	PUNCT
ejpam-4453	791	3	.........	.........	PUNCT
ejpam-4453	792	1	..............................................................	..............................................................	PUNCT
ejpam-4453	793	1	.....	.....	PUNCT
ejpam-4453	794	1	3	3	NUM
ejpam-4453	794	2	3	3	NUM
ejpam-4453	794	3	3	3	NUM
ejpam-4453	794	4	3	3	NUM
ejpam-4453	794	5	figure	figure	NOUN
ejpam-4453	794	6	9	9	NUM
ejpam-4453	794	7	:	:	PUNCT
ejpam-4453	794	8	coloring	coloring	NOUN
ejpam-4453	794	9	of	of	ADP
ejpam-4453	794	10	branch	branch	NOUN
ejpam-4453	794	11	bi	bi	NOUN
ejpam-4453	794	12	with	with	ADP
ejpam-4453	794	13	2	2	NUM
ejpam-4453	794	14	colors	color	NOUN
ejpam-4453	794	15	theorem	theorem	VERB
ejpam-4453	794	16	12	12	NUM
ejpam-4453	794	17	.	.	PUNCT
ejpam-4453	795	1	let	let	VERB
ejpam-4453	795	2	g	g	PRON
ejpam-4453	795	3	be	be	AUX
ejpam-4453	795	4	a	a	DET
ejpam-4453	795	5	ntcbg	ntcbg	NOUN
ejpam-4453	795	6	graph	graph	NOUN
ejpam-4453	795	7	of	of	ADP
ejpam-4453	795	8	order	order	NOUN
ejpam-4453	795	9	n.	n.	NOUN
ejpam-4453	795	10	then	then	ADV
ejpam-4453	795	11	the	the	DET
ejpam-4453	795	12	chromatic	chromatic	ADJ
ejpam-4453	795	13	number	number	NOUN
ejpam-4453	795	14	of	of	ADP
ejpam-4453	795	15	g	g	PROPN
ejpam-4453	795	16	is	be	AUX
ejpam-4453	795	17	χ(g	χ(g	PROPN
ejpam-4453	795	18	)	)	PUNCT
ejpam-4453	795	19	=	=	SYM
ejpam-4453	796	1	3	3	X
ejpam-4453	796	2	.	.	X
ejpam-4453	796	3	a.r	a.r	PROPN
ejpam-4453	796	4	nieva	nieva	PROPN
ejpam-4453	796	5	and	and	CCONJ
ejpam-4453	796	6	k.nocum	k.nocum	PROPN
ejpam-4453	796	7	/	/	SYM
ejpam-4453	796	8	eur	eur	PROPN
ejpam-4453	796	9	.	.	PUNCT
ejpam-4453	797	1	j.	j.	PROPN
ejpam-4453	797	2	pure	pure	PROPN
ejpam-4453	797	3	appl	appl	PROPN
ejpam-4453	797	4	.	.	PROPN
ejpam-4453	797	5	math	math	PROPN
ejpam-4453	797	6	,	,	PUNCT
ejpam-4453	797	7	15	15	NUM
ejpam-4453	797	8	(	(	PUNCT
ejpam-4453	797	9	4	4	NUM
ejpam-4453	797	10	)	)	PUNCT
ejpam-4453	797	11	(	(	PUNCT
ejpam-4453	797	12	2022	2022	NUM
ejpam-4453	797	13	)	)	PUNCT
ejpam-4453	797	14	,	,	PUNCT
ejpam-4453	797	15	1536	1536	NUM
ejpam-4453	797	16	-	-	SYM
ejpam-4453	797	17	1548	1548	NUM
ejpam-4453	797	18	1547	1547	NUM
ejpam-4453	797	19	..............................................................	..............................................................	PUNCT
ejpam-4453	797	20	.............	.............	PUNCT
ejpam-4453	797	21	.............................................................................	.............................................................................	PUNCT
ejpam-4453	797	22	.........	.........	PUNCT
ejpam-4453	797	23	...............................	...............................	PUNCT
ejpam-4453	797	24	.........	.........	PUNCT
ejpam-4453	797	25	.............	.............	PUNCT
ejpam-4453	797	26	.............................................................................	.............................................................................	PUNCT
ejpam-4453	797	27	.........	.........	PUNCT
ejpam-4453	798	1	..........	..........	PUNCT
ejpam-4453	798	2	.........	.........	PUNCT
ejpam-4453	799	1	.........	.........	PUNCT
ejpam-4453	799	2	...	...	PUNCT
ejpam-4453	799	3	.........	.........	PUNCT
ejpam-4453	799	4	.............	.............	PUNCT
ejpam-4453	799	5	.............................................................................	.............................................................................	PUNCT
ejpam-4453	799	6	.........	.........	PUNCT
ejpam-4453	799	7	.....................................................	.....................................................	PUNCT
ejpam-4453	799	8	.........	.........	PUNCT
ejpam-4453	799	9	.............	.............	PUNCT
ejpam-4453	799	10	.............................................................................	.............................................................................	PUNCT
ejpam-4453	799	11	.........	.........	PUNCT
ejpam-4453	799	12	...............................	...............................	PUNCT
ejpam-4453	799	13	.........	.........	PUNCT
ejpam-4453	799	14	.............	.............	PUNCT
ejpam-4453	799	15	.............................................................................	.............................................................................	PUNCT
ejpam-4453	799	16	.........	.........	PUNCT
ejpam-4453	800	1	..........	..........	PUNCT
ejpam-4453	800	2	.........	.........	PUNCT
ejpam-4453	801	1	.........	.........	PUNCT
ejpam-4453	801	2	...	...	PUNCT
ejpam-4453	801	3	.........	.........	PUNCT
ejpam-4453	801	4	.............	.............	PUNCT
ejpam-4453	801	5	.............................................................................	.............................................................................	PUNCT
ejpam-4453	801	6	.........	.........	PUNCT
ejpam-4453	802	1	.........	.........	PUNCT
ejpam-4453	802	2	.............	.............	PUNCT
ejpam-4453	802	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	802	4	.........	.........	PUNCT
ejpam-4453	802	5	.........	.........	PUNCT
ejpam-4453	802	6	........	........	PUNCT
ejpam-4453	802	7	........	........	PUNCT
ejpam-4453	802	8	........	........	PUNCT
ejpam-4453	802	9	........	........	PUNCT
ejpam-4453	802	10	........	........	PUNCT
ejpam-4453	802	11	........	........	PUNCT
ejpam-4453	802	12	........	........	PUNCT
ejpam-4453	802	13	........	........	PUNCT
ejpam-4453	802	14	........	........	PUNCT
ejpam-4453	802	15	.	.	PUNCT
ejpam-4453	803	1	.........	.........	PUNCT
ejpam-4453	803	2	.............	.............	PUNCT
ejpam-4453	804	1	.............................................................................	.............................................................................	PUNCT
ejpam-4453	804	2	.........	.........	PUNCT
ejpam-4453	805	1	.........	.........	PUNCT
ejpam-4453	805	2	.............	.............	PUNCT
ejpam-4453	805	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	805	4	.........	.........	PUNCT
ejpam-4453	805	5	.........	.........	PUNCT
ejpam-4453	805	6	........	........	PUNCT
ejpam-4453	805	7	........	........	PUNCT
ejpam-4453	805	8	........	........	PUNCT
ejpam-4453	805	9	........	........	PUNCT
ejpam-4453	805	10	........	........	PUNCT
ejpam-4453	805	11	........	........	PUNCT
ejpam-4453	805	12	........	........	PUNCT
ejpam-4453	805	13	........	........	PUNCT
ejpam-4453	805	14	........	........	PUNCT
ejpam-4453	805	15	.	.	PUNCT
ejpam-4453	806	1	.........	.........	PUNCT
ejpam-4453	806	2	.............	.............	PUNCT
ejpam-4453	807	1	.............................................................................	.............................................................................	PUNCT
ejpam-4453	807	2	.........	.........	PUNCT
ejpam-4453	808	1	.........	.........	PUNCT
ejpam-4453	808	2	.............	.............	PUNCT
ejpam-4453	808	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	808	4	.........	.........	PUNCT
ejpam-4453	808	5	.......................................................................................................................	.......................................................................................................................	PUNCT
ejpam-4453	808	6	.............	.............	PUNCT
ejpam-4453	808	7	.............................................................................	.............................................................................	PUNCT
ejpam-4453	808	8	.........	.........	PUNCT
ejpam-4453	809	1	.........	.........	PUNCT
ejpam-4453	809	2	.............	.............	PUNCT
ejpam-4453	810	1	.............................................................................	.............................................................................	PUNCT
ejpam-4453	810	2	.........	.........	PUNCT
ejpam-4453	811	1	1	1	NUM
ejpam-4453	811	2	2	2	NUM
ejpam-4453	811	3	3	3	NUM
ejpam-4453	811	4	2	2	NUM
ejpam-4453	811	5	3	3	NUM
ejpam-4453	811	6	1	1	NUM
ejpam-4453	811	7	(	(	PUNCT
ejpam-4453	811	8	a	a	NOUN
ejpam-4453	811	9	)	)	PUNCT
ejpam-4453	811	10	b	b	NOUN
ejpam-4453	811	11	)	)	PUNCT
ejpam-4453	811	12	.........	.........	PUNCT
ejpam-4453	811	13	..............................................................	..............................................................	PUNCT
ejpam-4453	811	14	.....	.....	PUNCT
ejpam-4453	811	15	.........	.........	PUNCT
ejpam-4453	811	16	..............................................................	..............................................................	PUNCT
ejpam-4453	811	17	.....	.....	PUNCT
ejpam-4453	811	18	..........	..........	PUNCT
ejpam-4453	812	1	..........	..........	PUNCT
ejpam-4453	812	2	...............................	...............................	PUNCT
ejpam-4453	812	3	.........	.........	PUNCT
ejpam-4453	812	4	.............	.............	PUNCT
ejpam-4453	812	5	.............................................................................	.............................................................................	PUNCT
ejpam-4453	812	6	.........	.........	PUNCT
ejpam-4453	813	1	..........	..........	PUNCT
ejpam-4453	813	2	.........	.........	PUNCT
ejpam-4453	814	1	.........	.........	PUNCT
ejpam-4453	814	2	...	...	PUNCT
ejpam-4453	814	3	.........	.........	PUNCT
ejpam-4453	814	4	.............	.............	PUNCT
ejpam-4453	814	5	.............................................................................	.............................................................................	PUNCT
ejpam-4453	814	6	.........	.........	PUNCT
ejpam-4453	814	7	.....................................................	.....................................................	PUNCT
ejpam-4453	814	8	.........	.........	PUNCT
ejpam-4453	814	9	.............	.............	PUNCT
ejpam-4453	814	10	.............................................................................	.............................................................................	PUNCT
ejpam-4453	814	11	.........	.........	PUNCT
ejpam-4453	814	12	...............................	...............................	PUNCT
ejpam-4453	814	13	.........	.........	PUNCT
ejpam-4453	814	14	.............	.............	PUNCT
ejpam-4453	814	15	.............................................................................	.............................................................................	PUNCT
ejpam-4453	814	16	.........	.........	PUNCT
ejpam-4453	815	1	..........	..........	PUNCT
ejpam-4453	815	2	.........	.........	PUNCT
ejpam-4453	816	1	.........	.........	PUNCT
ejpam-4453	816	2	...	...	PUNCT
ejpam-4453	816	3	.........	.........	PUNCT
ejpam-4453	816	4	.............	.............	PUNCT
ejpam-4453	816	5	.............................................................................	.............................................................................	PUNCT
ejpam-4453	816	6	.........	.........	PUNCT
ejpam-4453	817	1	.........	.........	PUNCT
ejpam-4453	817	2	.............	.............	PUNCT
ejpam-4453	817	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	817	4	.........	.........	PUNCT
ejpam-4453	817	5	.........	.........	PUNCT
ejpam-4453	817	6	........	........	PUNCT
ejpam-4453	817	7	........	........	PUNCT
ejpam-4453	817	8	........	........	PUNCT
ejpam-4453	817	9	........	........	PUNCT
ejpam-4453	817	10	........	........	PUNCT
ejpam-4453	817	11	........	........	PUNCT
ejpam-4453	817	12	........	........	PUNCT
ejpam-4453	817	13	........	........	PUNCT
ejpam-4453	817	14	........	........	PUNCT
ejpam-4453	817	15	.	.	PUNCT
ejpam-4453	818	1	.........	.........	PUNCT
ejpam-4453	818	2	.............	.............	PUNCT
ejpam-4453	819	1	.............................................................................	.............................................................................	PUNCT
ejpam-4453	819	2	.........	.........	PUNCT
ejpam-4453	820	1	.........	.........	PUNCT
ejpam-4453	820	2	.............	.............	PUNCT
ejpam-4453	820	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	820	4	.........	.........	PUNCT
ejpam-4453	820	5	.........	.........	PUNCT
ejpam-4453	820	6	........	........	PUNCT
ejpam-4453	820	7	........	........	PUNCT
ejpam-4453	820	8	........	........	PUNCT
ejpam-4453	820	9	........	........	PUNCT
ejpam-4453	820	10	........	........	PUNCT
ejpam-4453	820	11	........	........	PUNCT
ejpam-4453	820	12	........	........	PUNCT
ejpam-4453	820	13	........	........	PUNCT
ejpam-4453	820	14	........	........	PUNCT
ejpam-4453	820	15	.	.	PUNCT
ejpam-4453	821	1	.........	.........	PUNCT
ejpam-4453	821	2	.............	.............	PUNCT
ejpam-4453	822	1	.............................................................................	.............................................................................	PUNCT
ejpam-4453	822	2	.........	.........	PUNCT
ejpam-4453	823	1	.........	.........	PUNCT
ejpam-4453	823	2	.............	.............	PUNCT
ejpam-4453	823	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	823	4	.........	.........	PUNCT
ejpam-4453	823	5	.......................................................................................................................	.......................................................................................................................	PUNCT
ejpam-4453	823	6	.............	.............	PUNCT
ejpam-4453	823	7	.............................................................................	.............................................................................	PUNCT
ejpam-4453	823	8	.........	.........	PUNCT
ejpam-4453	824	1	.........	.........	PUNCT
ejpam-4453	824	2	.............	.............	PUNCT
ejpam-4453	825	1	.............................................................................	.............................................................................	PUNCT
ejpam-4453	825	2	.........	.........	PUNCT
ejpam-4453	826	1	31	31	NUM
ejpam-4453	826	2	2	2	NUM
ejpam-4453	826	3	3	3	NUM
ejpam-4453	826	4	2	2	NUM
ejpam-4453	826	5	3	3	NUM
ejpam-4453	826	6	1	1	NUM
ejpam-4453	826	7	figure	figure	NOUN
ejpam-4453	826	8	10	10	NUM
ejpam-4453	826	9	:	:	PUNCT
ejpam-4453	826	10	coloring	coloring	NOUN
ejpam-4453	826	11	of	of	ADP
ejpam-4453	826	12	branch	branch	NOUN
ejpam-4453	826	13	bi	bi	NOUN
ejpam-4453	826	14	with	with	ADP
ejpam-4453	826	15	3	3	NUM
ejpam-4453	826	16	colors	color	NOUN
ejpam-4453	826	17	.........	.........	PUNCT
ejpam-4453	826	18	.............	.............	PUNCT
ejpam-4453	826	19	.............................................................................	.............................................................................	PUNCT
ejpam-4453	826	20	.........	.........	PUNCT
ejpam-4453	826	21	.........	.........	PUNCT
ejpam-4453	826	22	.............	.............	PUNCT
ejpam-4453	826	23	.............................................................................	.............................................................................	PUNCT
ejpam-4453	826	24	.........	.........	PUNCT
ejpam-4453	826	25	.........	.........	PUNCT
ejpam-4453	826	26	.............	.............	PUNCT
ejpam-4453	826	27	.............................................................................	.............................................................................	PUNCT
ejpam-4453	826	28	.........	.........	PUNCT
ejpam-4453	826	29	.........	.........	PUNCT
ejpam-4453	826	30	.............	.............	PUNCT
ejpam-4453	826	31	.............................................................................	.............................................................................	PUNCT
ejpam-4453	826	32	.........	.........	PUNCT
ejpam-4453	827	1	(	(	PUNCT
ejpam-4453	827	2	a	a	X
ejpam-4453	827	3	)	)	PUNCT
ejpam-4453	827	4	1	1	NUM
ejpam-4453	827	5	4	4	NUM
ejpam-4453	827	6	3	3	NUM
ejpam-4453	827	7	1	1	NUM
ejpam-4453	827	8	.........	.........	PUNCT
ejpam-4453	827	9	........	........	PUNCT
ejpam-4453	827	10	........	........	PUNCT
ejpam-4453	827	11	........	........	PUNCT
ejpam-4453	827	12	......	......	PUNCT
ejpam-4453	827	13	.................	.................	PUNCT
ejpam-4453	828	1	................	................	PUNCT
ejpam-4453	828	2	................	................	PUNCT
ejpam-4453	828	3	..	..	PUNCT
ejpam-4453	828	4	..............................................................	..............................................................	PUNCT
ejpam-4453	829	1	..........	..........	PUNCT
ejpam-4453	829	2	..........	..........	PUNCT
ejpam-4453	830	1	..........	..........	PUNCT
ejpam-4453	830	2	..........	..........	PUNCT
ejpam-4453	831	1	..........	..........	PUNCT
ejpam-4453	831	2	..........	..........	PUNCT
ejpam-4453	832	1	..........	..........	PUNCT
ejpam-4453	832	2	..........	..........	PUNCT
ejpam-4453	833	1	..........	..........	PUNCT
ejpam-4453	833	2	.	.	PUNCT
ejpam-4453	834	1	......................................................................................................	......................................................................................................	PUNCT
ejpam-4453	834	2	..............................................................................................................	..............................................................................................................	PUNCT
ejpam-4453	835	1	.........	.........	PUNCT
ejpam-4453	835	2	.............	.............	PUNCT
ejpam-4453	836	1	.............................................................................	.............................................................................	PUNCT
ejpam-4453	836	2	.........	.........	PUNCT
ejpam-4453	837	1	.........	.........	PUNCT
ejpam-4453	837	2	.............	.............	PUNCT
ejpam-4453	837	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	837	4	.........	.........	PUNCT
ejpam-4453	838	1	.........	.........	PUNCT
ejpam-4453	838	2	.............	.............	PUNCT
ejpam-4453	838	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	838	4	.........	.........	PUNCT
ejpam-4453	839	1	.........	.........	PUNCT
ejpam-4453	839	2	.............	.............	PUNCT
ejpam-4453	839	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	839	4	.........	.........	PUNCT
ejpam-4453	840	1	(	(	PUNCT
ejpam-4453	840	2	b	b	X
ejpam-4453	840	3	)	)	PUNCT
ejpam-4453	840	4	1	1	NUM
ejpam-4453	840	5	4	4	NUM
ejpam-4453	840	6	3	3	NUM
ejpam-4453	840	7	2	2	NUM
ejpam-4453	840	8	3	3	NUM
ejpam-4453	840	9	,	,	PUNCT
ejpam-4453	840	10	4	4	NUM
ejpam-4453	840	11	.........	.........	PUNCT
ejpam-4453	840	12	........	........	PUNCT
ejpam-4453	840	13	........	........	PUNCT
ejpam-4453	840	14	........	........	PUNCT
ejpam-4453	841	1	......	......	PUNCT
ejpam-4453	841	2	.................	.................	PUNCT
ejpam-4453	842	1	................	................	PUNCT
ejpam-4453	842	2	................	................	PUNCT
ejpam-4453	842	3	..	..	PUNCT
ejpam-4453	842	4	..............................................................	..............................................................	PUNCT
ejpam-4453	843	1	..........	..........	PUNCT
ejpam-4453	843	2	..........	..........	PUNCT
ejpam-4453	844	1	..........	..........	PUNCT
ejpam-4453	844	2	..........	..........	PUNCT
ejpam-4453	845	1	..........	..........	PUNCT
ejpam-4453	845	2	..........	..........	PUNCT
ejpam-4453	846	1	..........	..........	PUNCT
ejpam-4453	846	2	..........	..........	PUNCT
ejpam-4453	847	1	..........	..........	PUNCT
ejpam-4453	847	2	.	.	PUNCT
ejpam-4453	848	1	...................................	...................................	PUNCT
ejpam-4453	848	2	...................................	...................................	PUNCT
ejpam-4453	849	1	..............................................................................................................	..............................................................................................................	PUNCT
ejpam-4453	849	2	.........	.........	PUNCT
ejpam-4453	850	1	..............................................................	..............................................................	PUNCT
ejpam-4453	850	2	.....	.....	PUNCT
ejpam-4453	850	3	.........	.........	PUNCT
ejpam-4453	850	4	.............	.............	PUNCT
ejpam-4453	850	5	.............................................................................	.............................................................................	PUNCT
ejpam-4453	850	6	.........	.........	PUNCT
ejpam-4453	851	1	.........	.........	PUNCT
ejpam-4453	851	2	.............	.............	PUNCT
ejpam-4453	851	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	851	4	.........	.........	PUNCT
ejpam-4453	852	1	.........	.........	PUNCT
ejpam-4453	852	2	.............	.............	PUNCT
ejpam-4453	852	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	852	4	.........	.........	PUNCT
ejpam-4453	853	1	.........	.........	PUNCT
ejpam-4453	853	2	.............	.............	PUNCT
ejpam-4453	853	3	.............................................................................	.............................................................................	PUNCT
ejpam-4453	853	4	.........	.........	PUNCT
ejpam-4453	854	1	(	(	PUNCT
ejpam-4453	854	2	c	c	X
ejpam-4453	854	3	)	)	PUNCT
ejpam-4453	854	4	1	1	NUM
ejpam-4453	854	5	,	,	PUNCT
ejpam-4453	854	6	2	2	NUM
ejpam-4453	854	7	4	4	NUM
ejpam-4453	854	8	3	3	NUM
ejpam-4453	854	9	1	1	NUM
ejpam-4453	854	10	,	,	PUNCT
ejpam-4453	854	11	2	2	NUM
ejpam-4453	854	12	3	3	NUM
ejpam-4453	854	13	,	,	PUNCT
ejpam-4453	854	14	4	4	NUM
ejpam-4453	854	15	.........	.........	PUNCT
ejpam-4453	854	16	........	........	PUNCT
ejpam-4453	854	17	........	........	PUNCT
ejpam-4453	854	18	........	........	PUNCT
ejpam-4453	855	1	......	......	PUNCT
ejpam-4453	855	2	.................	.................	PUNCT
ejpam-4453	856	1	................	................	PUNCT
ejpam-4453	856	2	................	................	PUNCT
ejpam-4453	856	3	..	..	PUNCT
ejpam-4453	856	4	..............................................................	..............................................................	PUNCT
ejpam-4453	857	1	..........	..........	PUNCT
ejpam-4453	857	2	..........	..........	PUNCT
ejpam-4453	858	1	..........	..........	PUNCT
ejpam-4453	858	2	..........	..........	PUNCT
ejpam-4453	859	1	..........	..........	PUNCT
ejpam-4453	859	2	..........	..........	PUNCT
ejpam-4453	860	1	..........	..........	PUNCT
ejpam-4453	860	2	..........	..........	PUNCT
ejpam-4453	861	1	..........	..........	PUNCT
ejpam-4453	861	2	.	.	PUNCT
ejpam-4453	862	1	...................................	...................................	PUNCT
ejpam-4453	862	2	...................................	...................................	PUNCT
ejpam-4453	863	1	..............................................................................................................	..............................................................................................................	PUNCT
ejpam-4453	863	2	.........	.........	PUNCT
ejpam-4453	864	1	..............................................................	..............................................................	PUNCT
ejpam-4453	864	2	.....	.....	PUNCT
ejpam-4453	864	3	figure	figure	VERB
ejpam-4453	864	4	11	11	NUM
ejpam-4453	864	5	:	:	PUNCT
ejpam-4453	864	6	coloring	coloring	NOUN
ejpam-4453	864	7	of	of	ADP
ejpam-4453	864	8	the	the	DET
ejpam-4453	864	9	only	only	ADJ
ejpam-4453	864	10	branch	branch	NOUN
ejpam-4453	864	11	with	with	ADP
ejpam-4453	864	12	4	4	NUM
ejpam-4453	864	13	colors	color	NOUN
ejpam-4453	864	14	proof	proof	NOUN
ejpam-4453	864	15	.	.	PUNCT
ejpam-4453	865	1	let	let	VERB
ejpam-4453	865	2	g	g	PRON
ejpam-4453	865	3	be	be	AUX
ejpam-4453	865	4	a	a	DET
ejpam-4453	865	5	ntcbg	ntcbg	NOUN
ejpam-4453	865	6	and	and	CCONJ
ejpam-4453	865	7	suppose	suppose	VERB
ejpam-4453	865	8	b̂i	b̂i	PROPN
ejpam-4453	865	9	be	be	AUX
ejpam-4453	865	10	an	an	DET
ejpam-4453	865	11	arbitrary	arbitrary	ADJ
ejpam-4453	865	12	branch	branch	NOUN
ejpam-4453	865	13	of	of	ADP
ejpam-4453	865	14	g.	g.	PROPN
ejpam-4453	865	15	since	since	SCONJ
ejpam-4453	865	16	b̂i	b̂i	PROPN
ejpam-4453	865	17	is	be	AUX
ejpam-4453	865	18	a	a	DET
ejpam-4453	865	19	subgraph	subgraph	NOUN
ejpam-4453	865	20	of	of	ADP
ejpam-4453	865	21	g	g	NOUN
ejpam-4453	865	22	,	,	PUNCT
ejpam-4453	865	23	by	by	ADP
ejpam-4453	865	24	theorem	theorem	NOUN
ejpam-4453	865	25	4	4	NUM
ejpam-4453	865	26	χ(b̂i	χ(b̂i	PART
ejpam-4453	865	27	)	)	PUNCT
ejpam-4453	865	28	≤	≤	NUM
ejpam-4453	865	29	χ(g	χ(g	PROPN
ejpam-4453	865	30	)	)	PUNCT
ejpam-4453	865	31	.	.	PUNCT
ejpam-4453	866	1	now	now	ADV
ejpam-4453	866	2	,	,	PUNCT
ejpam-4453	866	3	recall	recall	PROPN
ejpam-4453	866	4	theorem	theorem	VERB
ejpam-4453	866	5	11	11	NUM
ejpam-4453	866	6	.	.	PUNCT
ejpam-4453	867	1	since	since	SCONJ
ejpam-4453	867	2	χ(b̂i	χ(b̂i	PART
ejpam-4453	867	3	)	)	PUNCT
ejpam-4453	867	4	=	=	SYM
ejpam-4453	867	5	3	3	NUM
ejpam-4453	867	6	,	,	PUNCT
ejpam-4453	867	7	χ(b̂i	χ(b̂i	NUM
ejpam-4453	867	8	)	)	PUNCT
ejpam-4453	867	9	≤	≤	NUM
ejpam-4453	867	10	χ(g	χ(g	PROPN
ejpam-4453	867	11	)	)	PUNCT
ejpam-4453	867	12	implying	imply	VERB
ejpam-4453	867	13	3	3	NUM
ejpam-4453	867	14	≤	≤	NUM
ejpam-4453	867	15	χ(g	χ(g	PROPN
ejpam-4453	867	16	)	)	PUNCT
ejpam-4453	867	17	.	.	PUNCT
ejpam-4453	868	1	since	since	SCONJ
ejpam-4453	868	2	g	g	PROPN
ejpam-4453	868	3	is	be	AUX
ejpam-4453	868	4	a	a	DET
ejpam-4453	868	5	cubic	cubic	ADJ
ejpam-4453	868	6	gaph	gaph	NOUN
ejpam-4453	868	7	it	it	PRON
ejpam-4453	868	8	implies	imply	VERB
ejpam-4453	868	9	that	that	SCONJ
ejpam-4453	868	10	∆(g	∆(g	NOUN
ejpam-4453	868	11	)	)	PUNCT
ejpam-4453	868	12	=	=	SYM
ejpam-4453	868	13	3	3	NUM
ejpam-4453	868	14	by	by	ADP
ejpam-4453	868	15	brooks	brooks	PROPN
ejpam-4453	868	16	’	'	PUNCT
ejpam-4453	868	17	theorem	theorem	PROPN
ejpam-4453	868	18	,	,	PUNCT
ejpam-4453	868	19	χ(g	χ(g	PROPN
ejpam-4453	868	20	)	)	PUNCT
ejpam-4453	868	21	≤	≤	NUM
ejpam-4453	868	22	∆(g	∆(g	NOUN
ejpam-4453	868	23	)	)	PUNCT
ejpam-4453	868	24	hence	hence	ADV
ejpam-4453	868	25	χ(g	χ(g	PROPN
ejpam-4453	868	26	)	)	PUNCT
ejpam-4453	868	27	≤	≤	NOUN
ejpam-4453	868	28	3	3	NUM
ejpam-4453	868	29	.	.	PUNCT
ejpam-4453	869	1	taking	take	VERB
ejpam-4453	869	2	the	the	DET
ejpam-4453	869	3	lower	low	ADJ
ejpam-4453	869	4	and	and	CCONJ
ejpam-4453	869	5	upper	upper	ADJ
ejpam-4453	869	6	bounds	bound	NOUN
ejpam-4453	869	7	we	we	PRON
ejpam-4453	869	8	have	have	VERB
ejpam-4453	869	9	3	3	NUM
ejpam-4453	869	10	≤	≤	NUM
ejpam-4453	869	11	χ(g	χ(g	PROPN
ejpam-4453	869	12	)	)	PUNCT
ejpam-4453	869	13	≤	≤	NOUN
ejpam-4453	869	14	3	3	NUM
ejpam-4453	869	15	.	.	PUNCT
ejpam-4453	870	1	therefore	therefore	ADV
ejpam-4453	870	2	,	,	PUNCT
ejpam-4453	870	3	the	the	DET
ejpam-4453	870	4	least	least	ADJ
ejpam-4453	870	5	number	number	NOUN
ejpam-4453	870	6	of	of	ADP
ejpam-4453	870	7	coloring	coloring	NOUN
ejpam-4453	870	8	of	of	ADP
ejpam-4453	870	9	a	a	DET
ejpam-4453	870	10	cubic	cubic	ADJ
ejpam-4453	870	11	bridge	bridge	NOUN
ejpam-4453	870	12	graph	graph	NOUN
ejpam-4453	870	13	is	be	AUX
ejpam-4453	870	14	3	3	NUM
ejpam-4453	870	15	.	.	NOUN
ejpam-4453	870	16	1	1	NUM
ejpam-4453	870	17	1	1	NUM
ejpam-4453	870	18	1	1	NUM
ejpam-4453	870	19	1	1	NUM
ejpam-4453	870	20	1	1	NUM
ejpam-4453	870	21	1	1	NUM
ejpam-4453	870	22	1	1	NUM
ejpam-4453	870	23	2	2	NUM
ejpam-4453	870	24	2	2	NUM
ejpam-4453	870	25	2	2	NUM
ejpam-4453	870	26	2	2	NUM
ejpam-4453	870	27	2	2	NUM
ejpam-4453	870	28	2	2	NUM
ejpam-4453	870	29	3	3	NUM
ejpam-4453	870	30	3	3	NUM
ejpam-4453	870	31	3	3	NUM
ejpam-4453	870	32	3	3	NUM
ejpam-4453	870	33	3	3	NUM
ejpam-4453	870	34	g1	g1	NOUN
ejpam-4453	870	35	.........	.........	PUNCT
ejpam-4453	871	1	............................................................	............................................................	PUNCT
ejpam-4453	871	2	...	...	PUNCT
ejpam-4453	871	3	.........	.........	PUNCT
ejpam-4453	872	1	............................................................	............................................................	PUNCT
ejpam-4453	872	2	...	...	PUNCT
ejpam-4453	872	3	.........	.........	PUNCT
ejpam-4453	873	1	............................................................	............................................................	PUNCT
ejpam-4453	873	2	...	...	PUNCT
ejpam-4453	873	3	.........	.........	PUNCT
ejpam-4453	874	1	............................................................	............................................................	PUNCT
ejpam-4453	874	2	...	...	PUNCT
ejpam-4453	874	3	.........	.........	PUNCT
ejpam-4453	875	1	............................................................	............................................................	PUNCT
ejpam-4453	875	2	...	...	PUNCT
ejpam-4453	875	3	.........	.........	PUNCT
ejpam-4453	876	1	............................................................	............................................................	PUNCT
ejpam-4453	876	2	...	...	PUNCT
ejpam-4453	876	3	.........	.........	PUNCT
ejpam-4453	877	1	............................................................	............................................................	PUNCT
ejpam-4453	877	2	...	...	PUNCT
ejpam-4453	877	3	.........	.........	PUNCT
ejpam-4453	878	1	............................................................	............................................................	PUNCT
ejpam-4453	878	2	...	...	PUNCT
ejpam-4453	878	3	.........	.........	PUNCT
ejpam-4453	879	1	............................................................	............................................................	PUNCT
ejpam-4453	879	2	...	...	PUNCT
ejpam-4453	879	3	.........	.........	PUNCT
ejpam-4453	880	1	............................................................	............................................................	PUNCT
ejpam-4453	880	2	...	...	PUNCT
ejpam-4453	880	3	.........	.........	PUNCT
ejpam-4453	881	1	............................................................	............................................................	PUNCT
ejpam-4453	881	2	...	...	PUNCT
ejpam-4453	881	3	.........	.........	PUNCT
ejpam-4453	882	1	............................................................	............................................................	PUNCT
ejpam-4453	882	2	...	...	PUNCT
ejpam-4453	882	3	.........	.........	PUNCT
ejpam-4453	883	1	............................................................	............................................................	PUNCT
ejpam-4453	883	2	...	...	PUNCT
ejpam-4453	883	3	.........	.........	PUNCT
ejpam-4453	884	1	............................................................	............................................................	PUNCT
ejpam-4453	884	2	...	...	PUNCT
ejpam-4453	884	3	.........	.........	PUNCT
ejpam-4453	885	1	............................................................	............................................................	PUNCT
ejpam-4453	885	2	...	...	PUNCT
ejpam-4453	885	3	.........	.........	PUNCT
ejpam-4453	886	1	............................................................	............................................................	PUNCT
ejpam-4453	886	2	...	...	PUNCT
ejpam-4453	886	3	.........	.........	PUNCT
ejpam-4453	887	1	............................................................	............................................................	PUNCT
ejpam-4453	887	2	...	...	PUNCT
ejpam-4453	887	3	.........	.........	PUNCT
ejpam-4453	888	1	............................................................	............................................................	PUNCT
ejpam-4453	888	2	...	...	PUNCT
ejpam-4453	889	1	....................................	....................................	PUNCT
ejpam-4453	889	2	.......................................	.......................................	PUNCT
ejpam-4453	889	3	......................	......................	PUNCT
ejpam-4453	889	4	.......................................	.......................................	PUNCT
ejpam-4453	889	5	............	............	PUNCT
ejpam-4453	889	6	...........	...........	PUNCT
ejpam-4453	889	7	...........	...........	PUNCT
ejpam-4453	889	8	.....	.....	PUNCT
ejpam-4453	889	9	.......................................	.......................................	PUNCT
ejpam-4453	889	10	.........	.........	PUNCT
ejpam-4453	890	1	........	........	PUNCT
ejpam-4453	890	2	.....	.....	PUNCT
ejpam-4453	890	3	.........	.........	PUNCT
ejpam-4453	890	4	........	........	PUNCT
ejpam-4453	890	5	........	........	PUNCT
ejpam-4453	890	6	........	........	PUNCT
ejpam-4453	890	7	........	........	PUNCT
ejpam-4453	890	8	........	........	PUNCT
ejpam-4453	890	9	........	........	PUNCT
ejpam-4453	890	10	.......	.......	PUNCT
ejpam-4453	890	11	................................................................	................................................................	PUNCT
ejpam-4453	890	12	............	............	PUNCT
ejpam-4453	890	13	...........	...........	PUNCT
ejpam-4453	890	14	...........	...........	PUNCT
ejpam-4453	890	15	.....	.....	PUNCT
ejpam-4453	890	16	...........	...........	PUNCT
ejpam-4453	891	1	..........	..........	PUNCT
ejpam-4453	891	2	.........	.........	PUNCT
ejpam-4453	891	3	......................	......................	PUNCT
ejpam-4453	891	4	............	............	PUNCT
ejpam-4453	891	5	...........	...........	PUNCT
ejpam-4453	891	6	...........	...........	PUNCT
ejpam-4453	892	1	.....	.....	PUNCT
ejpam-4453	892	2	...................................................	...................................................	PUNCT
ejpam-4453	892	3	...........	...........	PUNCT
ejpam-4453	892	4	...........	...........	PUNCT
ejpam-4453	892	5	.....	.....	PUNCT
ejpam-4453	892	6	.........	.........	PUNCT
ejpam-4453	892	7	........	........	PUNCT
ejpam-4453	893	1	.....	.....	PUNCT
ejpam-4453	893	2	.........	.........	PUNCT
ejpam-4453	893	3	........	........	PUNCT
ejpam-4453	893	4	........	........	PUNCT
ejpam-4453	893	5	........	........	PUNCT
ejpam-4453	893	6	........	........	PUNCT
ejpam-4453	893	7	........	........	PUNCT
ejpam-4453	893	8	........	........	PUNCT
ejpam-4453	893	9	.......	.......	PUNCT
ejpam-4453	893	10	................................................................	................................................................	PUNCT
ejpam-4453	893	11	.........	.........	PUNCT
ejpam-4453	894	1	........	........	PUNCT
ejpam-4453	894	2	.....	.....	PUNCT
ejpam-4453	894	3	..............................	..............................	PUNCT
ejpam-4453	894	4	............	............	PUNCT
ejpam-4453	894	5	...........	...........	PUNCT
ejpam-4453	894	6	...........	...........	PUNCT
ejpam-4453	894	7	.....	.....	PUNCT
ejpam-4453	894	8	.........	.........	PUNCT
ejpam-4453	895	1	........	........	PUNCT
ejpam-4453	895	2	.....	.....	PUNCT
ejpam-4453	896	1	...................	...................	PUNCT
ejpam-4453	896	2	..................	..................	PUNCT
ejpam-4453	897	1	..................	..................	PUNCT
ejpam-4453	897	2	..................	..................	PUNCT
ejpam-4453	897	3	.	.	PUNCT
ejpam-4453	898	1	.........	.........	PUNCT
ejpam-4453	898	2	........	........	PUNCT
ejpam-4453	899	1	.....	.....	PUNCT
ejpam-4453	899	2	..........................................................................	..........................................................................	PUNCT
ejpam-4453	899	3	.......................................	.......................................	PUNCT
ejpam-4453	900	1	................................................................	................................................................	PUNCT
ejpam-4453	900	2	1	1	NUM
ejpam-4453	900	3	1	1	NUM
ejpam-4453	900	4	1	1	NUM
ejpam-4453	900	5	1	1	NUM
ejpam-4453	900	6	1	1	NUM
ejpam-4453	900	7	1	1	NUM
ejpam-4453	900	8	2	2	NUM
ejpam-4453	900	9	2	2	NUM
ejpam-4453	900	10	2	2	NUM
ejpam-4453	900	11	2	2	NUM
ejpam-4453	900	12	3	3	NUM
ejpam-4453	900	13	3	3	NUM
ejpam-4453	900	14	3	3	NUM
ejpam-4453	900	15	3	3	NUM
ejpam-4453	900	16	g2	g2	PROPN
ejpam-4453	900	17	.........	.........	PUNCT
ejpam-4453	901	1	............................................................	............................................................	PUNCT
ejpam-4453	901	2	...	...	PUNCT
ejpam-4453	901	3	.........	.........	PUNCT
ejpam-4453	902	1	............................................................	............................................................	PUNCT
ejpam-4453	902	2	...	...	PUNCT
ejpam-4453	902	3	.........	.........	PUNCT
ejpam-4453	903	1	............................................................	............................................................	PUNCT
ejpam-4453	903	2	...	...	PUNCT
ejpam-4453	903	3	.........	.........	PUNCT
ejpam-4453	904	1	............................................................	............................................................	PUNCT
ejpam-4453	904	2	...	...	PUNCT
ejpam-4453	904	3	.........	.........	PUNCT
ejpam-4453	905	1	............................................................	............................................................	PUNCT
ejpam-4453	905	2	...	...	PUNCT
ejpam-4453	905	3	.........	.........	PUNCT
ejpam-4453	906	1	............................................................	............................................................	PUNCT
ejpam-4453	906	2	...	...	PUNCT
ejpam-4453	906	3	.........	.........	PUNCT
ejpam-4453	907	1	............................................................	............................................................	PUNCT
ejpam-4453	907	2	...	...	PUNCT
ejpam-4453	907	3	.........	.........	PUNCT
ejpam-4453	908	1	............................................................	............................................................	PUNCT
ejpam-4453	908	2	...	...	PUNCT
ejpam-4453	908	3	.........	.........	PUNCT
ejpam-4453	909	1	............................................................	............................................................	PUNCT
ejpam-4453	909	2	...	...	PUNCT
ejpam-4453	909	3	.........	.........	PUNCT
ejpam-4453	910	1	............................................................	............................................................	PUNCT
ejpam-4453	910	2	...	...	PUNCT
ejpam-4453	910	3	.........	.........	PUNCT
ejpam-4453	911	1	............................................................	............................................................	PUNCT
ejpam-4453	911	2	...	...	PUNCT
ejpam-4453	911	3	.........	.........	PUNCT
ejpam-4453	912	1	............................................................	............................................................	PUNCT
ejpam-4453	912	2	...	...	PUNCT
ejpam-4453	912	3	.........	.........	PUNCT
ejpam-4453	913	1	............................................................	............................................................	PUNCT
ejpam-4453	913	2	...	...	PUNCT
ejpam-4453	913	3	.........	.........	PUNCT
ejpam-4453	914	1	............................................................	............................................................	PUNCT
ejpam-4453	914	2	...	...	PUNCT
ejpam-4453	915	1	....................................	....................................	PUNCT
ejpam-4453	915	2	.......................................	.......................................	PUNCT
ejpam-4453	915	3	......................	......................	PUNCT
ejpam-4453	915	4	.......................................	.......................................	PUNCT
ejpam-4453	915	5	............	............	PUNCT
ejpam-4453	915	6	...........	...........	PUNCT
ejpam-4453	915	7	...........	...........	PUNCT
ejpam-4453	915	8	.....	.....	PUNCT
ejpam-4453	915	9	.......................................	.......................................	PUNCT
ejpam-4453	915	10	.........	.........	PUNCT
ejpam-4453	916	1	........	........	PUNCT
ejpam-4453	916	2	.....	.....	PUNCT
ejpam-4453	916	3	.........	.........	PUNCT
ejpam-4453	916	4	........	........	PUNCT
ejpam-4453	916	5	........	........	PUNCT
ejpam-4453	916	6	........	........	PUNCT
ejpam-4453	916	7	........	........	PUNCT
ejpam-4453	916	8	........	........	PUNCT
ejpam-4453	916	9	........	........	PUNCT
ejpam-4453	916	10	.......	.......	PUNCT
ejpam-4453	916	11	................................................................	................................................................	PUNCT
ejpam-4453	916	12	............	............	PUNCT
ejpam-4453	916	13	...........	...........	PUNCT
ejpam-4453	916	14	...........	...........	PUNCT
ejpam-4453	916	15	.....	.....	PUNCT
ejpam-4453	916	16	...........	...........	PUNCT
ejpam-4453	917	1	..........	..........	PUNCT
ejpam-4453	917	2	.........	.........	PUNCT
ejpam-4453	917	3	......................	......................	PUNCT
ejpam-4453	917	4	............	............	PUNCT
ejpam-4453	917	5	...........	...........	PUNCT
ejpam-4453	917	6	...........	...........	PUNCT
ejpam-4453	918	1	.....	.....	PUNCT
ejpam-4453	918	2	...................................................	...................................................	PUNCT
ejpam-4453	918	3	...........	...........	PUNCT
ejpam-4453	918	4	...........	...........	PUNCT
ejpam-4453	918	5	.....	.....	PUNCT
ejpam-4453	918	6	.........	.........	PUNCT
ejpam-4453	918	7	........	........	PUNCT
ejpam-4453	919	1	.....	.....	PUNCT
ejpam-4453	919	2	.........	.........	PUNCT
ejpam-4453	919	3	........	........	PUNCT
ejpam-4453	919	4	........	........	PUNCT
ejpam-4453	919	5	........	........	PUNCT
ejpam-4453	919	6	........	........	PUNCT
ejpam-4453	919	7	........	........	PUNCT
ejpam-4453	919	8	........	........	PUNCT
ejpam-4453	919	9	.......	.......	PUNCT
ejpam-4453	919	10	................................................................	................................................................	PUNCT
ejpam-4453	919	11	..............................	..............................	PUNCT
ejpam-4453	919	12	.........	.........	PUNCT
ejpam-4453	920	1	........	........	PUNCT
ejpam-4453	921	1	.....	.....	PUNCT
ejpam-4453	922	1	1	1	NUM
ejpam-4453	922	2	1	1	NUM
ejpam-4453	922	3	1	1	NUM
ejpam-4453	922	4	2	2	NUM
ejpam-4453	922	5	2	2	NUM
ejpam-4453	922	6	3	3	NUM
ejpam-4453	922	7	3	3	NUM
ejpam-4453	922	8	3	3	NUM
ejpam-4453	922	9	.........	.........	PUNCT
ejpam-4453	922	10	............................................................	............................................................	PUNCT
ejpam-4453	922	11	...	...	PUNCT
ejpam-4453	922	12	.........	.........	PUNCT
ejpam-4453	923	1	............................................................	............................................................	PUNCT
ejpam-4453	923	2	...	...	PUNCT
ejpam-4453	923	3	.........	.........	PUNCT
ejpam-4453	924	1	............................................................	............................................................	PUNCT
ejpam-4453	924	2	...	...	PUNCT
ejpam-4453	924	3	.........	.........	PUNCT
ejpam-4453	925	1	............................................................	............................................................	PUNCT
ejpam-4453	925	2	...	...	PUNCT
ejpam-4453	925	3	.........	.........	PUNCT
ejpam-4453	926	1	............................................................	............................................................	PUNCT
ejpam-4453	926	2	...	...	PUNCT
ejpam-4453	926	3	.........	.........	PUNCT
ejpam-4453	927	1	............................................................	............................................................	PUNCT
ejpam-4453	927	2	...	...	PUNCT
ejpam-4453	927	3	.........	.........	PUNCT
ejpam-4453	928	1	............................................................	............................................................	PUNCT
ejpam-4453	928	2	...	...	PUNCT
ejpam-4453	928	3	.........	.........	PUNCT
ejpam-4453	929	1	............................................................	............................................................	PUNCT
ejpam-4453	929	2	................................................................................................	................................................................................................	PUNCT
ejpam-4453	929	3	.............................................................................................	.............................................................................................	PUNCT
ejpam-4453	929	4	.......	.......	PUNCT
ejpam-4453	929	5	.......	.......	PUNCT
ejpam-4453	929	6	....................................	....................................	PUNCT
ejpam-4453	929	7	...........	...........	PUNCT
ejpam-4453	930	1	..........	..........	PUNCT
ejpam-4453	930	2	.........	.........	PUNCT
ejpam-4453	930	3	..............................	..............................	PUNCT
ejpam-4453	930	4	..............................	..............................	PUNCT
ejpam-4453	930	5	...........	...........	PUNCT
ejpam-4453	931	1	..........	..........	PUNCT
ejpam-4453	931	2	.........	.........	PUNCT
ejpam-4453	932	1	..............	..............	PUNCT
ejpam-4453	932	2	.........	.........	PUNCT
ejpam-4453	932	3	........	........	PUNCT
ejpam-4453	932	4	........	........	PUNCT
ejpam-4453	932	5	........	........	PUNCT
ejpam-4453	932	6	........	........	PUNCT
ejpam-4453	932	7	........	........	PUNCT
ejpam-4453	932	8	........	........	PUNCT
ejpam-4453	932	9	........	........	PUNCT
ejpam-4453	932	10	........	........	PUNCT
ejpam-4453	932	11	........	........	PUNCT
ejpam-4453	932	12	........	........	PUNCT
ejpam-4453	933	1	....	....	PUNCT
ejpam-4453	933	2	.........	.........	PUNCT
ejpam-4453	933	3	........	........	PUNCT
ejpam-4453	933	4	........	........	PUNCT
ejpam-4453	933	5	........	........	PUNCT
ejpam-4453	933	6	........	........	PUNCT
ejpam-4453	933	7	........	........	PUNCT
ejpam-4453	933	8	........	........	PUNCT
ejpam-4453	933	9	........	........	PUNCT
ejpam-4453	933	10	........	........	PUNCT
ejpam-4453	933	11	........	........	PUNCT
ejpam-4453	933	12	........	........	PUNCT
ejpam-4453	934	1	....	....	PUNCT
ejpam-4453	934	2	g3	g3	NOUN
ejpam-4453	934	3	1	1	NUM
ejpam-4453	934	4	1	1	NUM
ejpam-4453	934	5	1	1	NUM
ejpam-4453	934	6	1	1	NUM
ejpam-4453	934	7	1	1	NUM
ejpam-4453	934	8	1	1	NUM
ejpam-4453	934	9	2	2	NUM
ejpam-4453	934	10	2	2	NUM
ejpam-4453	934	11	2	2	NUM
ejpam-4453	934	12	2	2	NUM
ejpam-4453	934	13	2	2	NUM
ejpam-4453	934	14	22	22	NUM
ejpam-4453	934	15	3	3	NUM
ejpam-4453	934	16	3	3	NUM
ejpam-4453	934	17	3	3	NUM
ejpam-4453	934	18	3	3	NUM
ejpam-4453	934	19	3	3	NUM
ejpam-4453	934	20	33	33	NUM
ejpam-4453	934	21	.........	.........	PUNCT
ejpam-4453	934	22	............................................................	............................................................	PUNCT
ejpam-4453	934	23	...	...	PUNCT
ejpam-4453	934	24	.........	.........	PUNCT
ejpam-4453	935	1	............................................................	............................................................	PUNCT
ejpam-4453	935	2	...	...	PUNCT
ejpam-4453	935	3	.........	.........	PUNCT
ejpam-4453	936	1	............................................................	............................................................	PUNCT
ejpam-4453	936	2	...	...	PUNCT
ejpam-4453	936	3	.........	.........	PUNCT
ejpam-4453	937	1	............................................................	............................................................	PUNCT
ejpam-4453	937	2	...	...	PUNCT
ejpam-4453	937	3	......................	......................	PUNCT
ejpam-4453	937	4	.......................................	.......................................	PUNCT
ejpam-4453	937	5	............	............	PUNCT
ejpam-4453	937	6	...........	...........	PUNCT
ejpam-4453	937	7	...........	...........	PUNCT
ejpam-4453	937	8	.....	.....	PUNCT
ejpam-4453	937	9	.......................................	.......................................	PUNCT
ejpam-4453	937	10	.........	.........	PUNCT
ejpam-4453	938	1	........	........	PUNCT
ejpam-4453	938	2	.....	.....	PUNCT
ejpam-4453	938	3	.........	.........	PUNCT
ejpam-4453	938	4	........	........	PUNCT
ejpam-4453	938	5	........	........	PUNCT
ejpam-4453	938	6	........	........	PUNCT
ejpam-4453	938	7	........	........	PUNCT
ejpam-4453	938	8	........	........	PUNCT
ejpam-4453	938	9	........	........	PUNCT
ejpam-4453	938	10	.......	.......	PUNCT
ejpam-4453	939	1	................................................................	................................................................	PUNCT
ejpam-4453	939	2	.........	.........	PUNCT
ejpam-4453	940	1	............................................................	............................................................	PUNCT
ejpam-4453	940	2	...	...	PUNCT
ejpam-4453	940	3	.........	.........	PUNCT
ejpam-4453	941	1	............................................................	............................................................	PUNCT
ejpam-4453	941	2	...	...	PUNCT
ejpam-4453	941	3	.........	.........	PUNCT
ejpam-4453	942	1	............................................................	............................................................	PUNCT
ejpam-4453	942	2	...	...	PUNCT
ejpam-4453	942	3	.........	.........	PUNCT
ejpam-4453	943	1	............................................................	............................................................	PUNCT
ejpam-4453	943	2	...	...	PUNCT
ejpam-4453	943	3	......................	......................	PUNCT
ejpam-4453	943	4	............	............	PUNCT
ejpam-4453	943	5	...........	...........	PUNCT
ejpam-4453	943	6	...........	...........	PUNCT
ejpam-4453	944	1	.....	.....	PUNCT
ejpam-4453	944	2	...................................................	...................................................	PUNCT
ejpam-4453	944	3	...........	...........	PUNCT
ejpam-4453	944	4	...........	...........	PUNCT
ejpam-4453	944	5	.....	.....	PUNCT
ejpam-4453	944	6	.........	.........	PUNCT
ejpam-4453	944	7	........	........	PUNCT
ejpam-4453	945	1	.....	.....	PUNCT
ejpam-4453	945	2	.........	.........	PUNCT
ejpam-4453	945	3	........	........	PUNCT
ejpam-4453	945	4	........	........	PUNCT
ejpam-4453	945	5	........	........	PUNCT
ejpam-4453	945	6	........	........	PUNCT
ejpam-4453	945	7	........	........	PUNCT
ejpam-4453	945	8	........	........	PUNCT
ejpam-4453	945	9	.......	.......	PUNCT
ejpam-4453	945	10	................................................................	................................................................	PUNCT
ejpam-4453	946	1	.........	.........	PUNCT
ejpam-4453	947	1	............................................................	............................................................	PUNCT
ejpam-4453	947	2	...	...	PUNCT
ejpam-4453	947	3	.........	.........	PUNCT
ejpam-4453	948	1	............................................................	............................................................	PUNCT
ejpam-4453	948	2	...	...	PUNCT
ejpam-4453	948	3	.........	.........	PUNCT
ejpam-4453	949	1	............................................................	............................................................	PUNCT
ejpam-4453	949	2	...	...	PUNCT
ejpam-4453	949	3	.........	.........	PUNCT
ejpam-4453	950	1	............................................................	............................................................	PUNCT
ejpam-4453	950	2	...	...	PUNCT
ejpam-4453	950	3	............	............	PUNCT
ejpam-4453	950	4	...........	...........	PUNCT
ejpam-4453	950	5	...........	...........	PUNCT
ejpam-4453	950	6	.....	.....	PUNCT
ejpam-4453	950	7	.........	.........	PUNCT
ejpam-4453	950	8	........	........	PUNCT
ejpam-4453	951	1	.....	.....	PUNCT
ejpam-4453	951	2	...................	...................	PUNCT
ejpam-4453	952	1	..................	..................	PUNCT
ejpam-4453	952	2	..................	..................	PUNCT
ejpam-4453	952	3	..................	..................	PUNCT
ejpam-4453	952	4	.	.	PUNCT
ejpam-4453	953	1	.........	.........	PUNCT
ejpam-4453	953	2	........	........	PUNCT
ejpam-4453	954	1	.....	.....	PUNCT
ejpam-4453	954	2	..........................................................................	..........................................................................	PUNCT
ejpam-4453	954	3	.......................................	.......................................	PUNCT
ejpam-4453	954	4	................................................................	................................................................	PUNCT
ejpam-4453	954	5	.........	.........	PUNCT
ejpam-4453	955	1	............................................................	............................................................	PUNCT
ejpam-4453	955	2	...	...	PUNCT
ejpam-4453	955	3	.........	.........	PUNCT
ejpam-4453	956	1	............................................................	............................................................	PUNCT
ejpam-4453	956	2	...	...	PUNCT
ejpam-4453	956	3	.........	.........	PUNCT
ejpam-4453	957	1	............................................................	............................................................	PUNCT
ejpam-4453	957	2	...	...	PUNCT
ejpam-4453	957	3	.........	.........	PUNCT
ejpam-4453	958	1	............................................................	............................................................	PUNCT
ejpam-4453	958	2	...	...	PUNCT
ejpam-4453	958	3	.........	.........	PUNCT
ejpam-4453	959	1	............................................................	............................................................	PUNCT
ejpam-4453	959	2	...	...	PUNCT
ejpam-4453	959	3	.........	.........	PUNCT
ejpam-4453	960	1	............................................................	............................................................	PUNCT
ejpam-4453	960	2	...	...	PUNCT
ejpam-4453	960	3	.........	.........	PUNCT
ejpam-4453	961	1	............................................................	............................................................	PUNCT
ejpam-4453	961	2	...	...	PUNCT
ejpam-4453	961	3	.........	.........	PUNCT
ejpam-4453	962	1	............................................................	............................................................	PUNCT
ejpam-4453	962	2	...	...	PUNCT
ejpam-4453	962	3	.........	.........	PUNCT
ejpam-4453	963	1	............................................................	............................................................	PUNCT
ejpam-4453	963	2	...	...	PUNCT
ejpam-4453	963	3	................................................................	................................................................	PUNCT
ejpam-4453	964	1	......	......	PUNCT
ejpam-4453	964	2	......	......	PUNCT
ejpam-4453	965	1	..........................	..........................	PUNCT
ejpam-4453	965	2	....................	....................	PUNCT
ejpam-4453	966	1	......	......	PUNCT
ejpam-4453	966	2	....................................	....................................	PUNCT
ejpam-4453	966	3	.......................................	.......................................	PUNCT
ejpam-4453	966	4	............	............	PUNCT
ejpam-4453	966	5	...........	...........	PUNCT
ejpam-4453	966	6	...........	...........	PUNCT
ejpam-4453	966	7	.....	.....	PUNCT
ejpam-4453	966	8	.........	.........	PUNCT
ejpam-4453	966	9	........	........	PUNCT
ejpam-4453	967	1	.....	.....	PUNCT
ejpam-4453	967	2	figure	figure	VERB
ejpam-4453	967	3	12	12	NUM
ejpam-4453	967	4	:	:	PUNCT
ejpam-4453	967	5	example	example	NOUN
ejpam-4453	967	6	of	of	ADP
ejpam-4453	967	7	ntcbg	ntcbg	PRON
ejpam-4453	967	8	minimum	minimum	ADJ
ejpam-4453	967	9	coloring	coloring	NOUN
ejpam-4453	967	10	remark	remark	NOUN
ejpam-4453	967	11	4	4	NUM
ejpam-4453	967	12	.	.	PUNCT
ejpam-4453	968	1	every	every	DET
ejpam-4453	968	2	ntcbg	ntcbg	NOUN
ejpam-4453	968	3	of	of	ADP
ejpam-4453	968	4	order	order	NOUN
ejpam-4453	968	5	n	n	PRON
ejpam-4453	968	6	has	have	VERB
ejpam-4453	968	7	proper	proper	ADJ
ejpam-4453	968	8	k	k	NOUN
ejpam-4453	968	9	-	-	NOUN
ejpam-4453	968	10	coloring	coloring	NOUN
ejpam-4453	968	11	where	where	SCONJ
ejpam-4453	968	12	3	3	NUM
ejpam-4453	968	13	≤	≤	NUM
ejpam-4453	968	14	k	k	PROPN
ejpam-4453	968	15	≤	≤	PROPN
ejpam-4453	968	16	n.	n.	NOUN
ejpam-4453	968	17	corollary	corollary	NOUN
ejpam-4453	968	18	3	3	X
ejpam-4453	968	19	.	.	PUNCT
ejpam-4453	969	1	let	let	VERB
ejpam-4453	969	2	g	g	PRON
ejpam-4453	969	3	be	be	AUX
ejpam-4453	969	4	a	a	DET
ejpam-4453	969	5	ntcbg	ntcbg	ADJ
ejpam-4453	969	6	,	,	PUNCT
ejpam-4453	969	7	then	then	ADV
ejpam-4453	969	8	ω(g	ω(g	NOUN
ejpam-4453	969	9	)	)	PUNCT
ejpam-4453	969	10	≤	≤	NOUN
ejpam-4453	969	11	3	3	NUM
ejpam-4453	969	12	.	.	PUNCT
ejpam-4453	970	1	proof	proof	NOUN
ejpam-4453	970	2	.	.	PUNCT
ejpam-4453	971	1	by	by	ADP
ejpam-4453	971	2	corollary	corollary	ADJ
ejpam-4453	971	3	1	1	NUM
ejpam-4453	971	4	,	,	PUNCT
ejpam-4453	971	5	χ(g	χ(g	PROPN
ejpam-4453	971	6	)	)	PUNCT
ejpam-4453	971	7	≥	≥	NOUN
ejpam-4453	971	8	ω(g	ω(g	NOUN
ejpam-4453	971	9	)	)	PUNCT
ejpam-4453	971	10	.	.	PUNCT
ejpam-4453	972	1	by	by	ADP
ejpam-4453	972	2	theorem	theorem	NOUN
ejpam-4453	972	3	12	12	NUM
ejpam-4453	972	4	,	,	PUNCT
ejpam-4453	972	5	χ(g	χ(g	PROPN
ejpam-4453	972	6	)	)	PUNCT
ejpam-4453	972	7	=	=	SYM
ejpam-4453	973	1	3	3	X
ejpam-4453	973	2	.	.	X
ejpam-4453	973	3	therefore	therefore	ADV
ejpam-4453	973	4	3	3	NUM
ejpam-4453	973	5	≥	≥	NOUN
ejpam-4453	973	6	ω(g	ω(g	NOUN
ejpam-4453	973	7	)	)	PUNCT
ejpam-4453	973	8	from	from	ADP
ejpam-4453	973	9	this	this	DET
ejpam-4453	973	10	corollary	corollary	NOUN
ejpam-4453	973	11	,	,	PUNCT
ejpam-4453	973	12	we	we	PRON
ejpam-4453	973	13	can	can	AUX
ejpam-4453	973	14	say	say	VERB
ejpam-4453	973	15	that	that	SCONJ
ejpam-4453	973	16	there	there	PRON
ejpam-4453	973	17	are	be	VERB
ejpam-4453	973	18	only	only	ADV
ejpam-4453	973	19	two	two	NUM
ejpam-4453	973	20	possibilities	possibility	NOUN
ejpam-4453	973	21	of	of	ADP
ejpam-4453	973	22	ω(g	ω(g	NOUN
ejpam-4453	973	23	)	)	PUNCT
ejpam-4453	973	24	,	,	PUNCT
ejpam-4453	973	25	one	one	NUM
ejpam-4453	973	26	is	be	AUX
ejpam-4453	973	27	,	,	PUNCT
ejpam-4453	973	28	if	if	SCONJ
ejpam-4453	973	29	g	g	PROPN
ejpam-4453	973	30	is	be	AUX
ejpam-4453	973	31	a	a	DET
ejpam-4453	973	32	triangle	triangle	NOUN
ejpam-4453	973	33	free	free	ADJ
ejpam-4453	973	34	graph	graph	NOUN
ejpam-4453	973	35	then	then	ADV
ejpam-4453	973	36	we	we	PRON
ejpam-4453	973	37	have	have	VERB
ejpam-4453	973	38	ω(g	ω(g	NOUN
ejpam-4453	973	39	)	)	PUNCT
ejpam-4453	973	40	=	=	SYM
ejpam-4453	974	1	2	2	X
ejpam-4453	974	2	.	.	PUNCT
ejpam-4453	974	3	otherwise	otherwise	ADV
ejpam-4453	974	4	,	,	PUNCT
ejpam-4453	974	5	g	g	PROPN
ejpam-4453	974	6	has	have	VERB
ejpam-4453	974	7	ω(g	ω(g	NOUN
ejpam-4453	974	8	)	)	PUNCT
ejpam-4453	974	9	=	=	SYM
ejpam-4453	975	1	3	3	X
ejpam-4453	975	2	.	.	NOUN
ejpam-4453	975	3	references	reference	NOUN
ejpam-4453	975	4	1548	1548	NUM
ejpam-4453	975	5	6	6	NUM
ejpam-4453	975	6	.	.	PUNCT
ejpam-4453	976	1	summary	summary	NOUN
ejpam-4453	976	2	and	and	CCONJ
ejpam-4453	976	3	conclusion	conclusion	NOUN
ejpam-4453	976	4	in	in	ADP
ejpam-4453	976	5	this	this	DET
ejpam-4453	976	6	paper	paper	NOUN
ejpam-4453	976	7	,	,	PUNCT
ejpam-4453	976	8	a	a	DET
ejpam-4453	976	9	new	new	ADJ
ejpam-4453	976	10	classification	classification	NOUN
ejpam-4453	976	11	of	of	ADP
ejpam-4453	976	12	cubic	cubic	ADJ
ejpam-4453	976	13	graphs	graph	NOUN
ejpam-4453	976	14	called	call	VERB
ejpam-4453	976	15	non	non	ADJ
ejpam-4453	976	16	-	-	ADJ
ejpam-4453	976	17	traceable	traceable	ADJ
ejpam-4453	976	18	cubic	cubic	ADJ
ejpam-4453	976	19	bridge	bridge	NOUN
ejpam-4453	976	20	graph	graph	NOUN
ejpam-4453	976	21	(	(	PUNCT
ejpam-4453	976	22	ntcbg	ntcbg	NUM
ejpam-4453	976	23	)	)	PUNCT
ejpam-4453	976	24	is	be	AUX
ejpam-4453	976	25	provided	provide	VERB
ejpam-4453	976	26	.	.	PUNCT
ejpam-4453	977	1	here	here	ADV
ejpam-4453	977	2	,	,	PUNCT
ejpam-4453	977	3	basic	basic	ADJ
ejpam-4453	977	4	construction	construction	NOUN
ejpam-4453	977	5	of	of	ADP
ejpam-4453	977	6	a	a	DET
ejpam-4453	977	7	ntcbg	ntcbg	NOUN
ejpam-4453	977	8	were	be	AUX
ejpam-4453	977	9	discussed	discuss	VERB
ejpam-4453	977	10	.	.	PUNCT
ejpam-4453	978	1	the	the	DET
ejpam-4453	978	2	concept	concept	NOUN
ejpam-4453	978	3	of	of	ADP
ejpam-4453	978	4	a	a	DET
ejpam-4453	978	5	central	central	ADJ
ejpam-4453	978	6	fragment	fragment	NOUN
ejpam-4453	978	7	was	be	AUX
ejpam-4453	978	8	introduced	introduce	VERB
ejpam-4453	978	9	as	as	ADP
ejpam-4453	978	10	the	the	DET
ejpam-4453	978	11	main	main	ADJ
ejpam-4453	978	12	component	component	NOUN
ejpam-4453	978	13	of	of	ADP
ejpam-4453	978	14	a	a	DET
ejpam-4453	978	15	ntcbg	ntcbg	NOUN
ejpam-4453	978	16	.	.	PUNCT
ejpam-4453	979	1	the	the	DET
ejpam-4453	979	2	order	order	NOUN
ejpam-4453	979	3	,	,	PUNCT
ejpam-4453	979	4	size	size	NOUN
ejpam-4453	979	5	,	,	PUNCT
ejpam-4453	979	6	and	and	CCONJ
ejpam-4453	979	7	classes	class	NOUN
ejpam-4453	979	8	of	of	ADP
ejpam-4453	979	9	the	the	DET
ejpam-4453	979	10	central	central	ADJ
ejpam-4453	979	11	fragments	fragment	NOUN
ejpam-4453	979	12	were	be	AUX
ejpam-4453	979	13	also	also	ADV
ejpam-4453	979	14	determined	determine	VERB
ejpam-4453	979	15	.	.	PUNCT
ejpam-4453	980	1	we	we	PRON
ejpam-4453	980	2	also	also	ADV
ejpam-4453	980	3	show	show	VERB
ejpam-4453	980	4	that	that	SCONJ
ejpam-4453	980	5	the	the	DET
ejpam-4453	980	6	family	family	NOUN
ejpam-4453	980	7	of	of	ADP
ejpam-4453	980	8	hairy	hairy	ADJ
ejpam-4453	980	9	cycles	cycle	NOUN
ejpam-4453	980	10	hk	hk	PROPN
ejpam-4453	980	11	is	be	AUX
ejpam-4453	980	12	a	a	DET
ejpam-4453	980	13	central	central	ADJ
ejpam-4453	980	14	fragment	fragment	NOUN
ejpam-4453	980	15	.	.	PUNCT
ejpam-4453	981	1	in	in	ADP
ejpam-4453	981	2	addition	addition	NOUN
ejpam-4453	981	3	,	,	PUNCT
ejpam-4453	981	4	the	the	DET
ejpam-4453	981	5	lower	low	ADJ
ejpam-4453	981	6	and	and	CCONJ
ejpam-4453	981	7	upper	upper	ADJ
ejpam-4453	981	8	bounds	bound	NOUN
ejpam-4453	981	9	for	for	ADP
ejpam-4453	981	10	a	a	DET
ejpam-4453	981	11	ntcbg	ntcbg	NOUN
ejpam-4453	981	12	to	to	PART
ejpam-4453	981	13	have	have	VERB
ejpam-4453	981	14	a	a	DET
ejpam-4453	981	15	spanning	span	VERB
ejpam-4453	981	16	k	k	NOUN
ejpam-4453	981	17	-	-	PUNCT
ejpam-4453	981	18	trees	tree	NOUN
ejpam-4453	981	19	were	be	AUX
ejpam-4453	981	20	determined	determine	VERB
ejpam-4453	981	21	.	.	PUNCT
ejpam-4453	982	1	it	it	PRON
ejpam-4453	982	2	was	be	AUX
ejpam-4453	982	3	found	find	VERB
ejpam-4453	982	4	out	out	ADP
ejpam-4453	982	5	that	that	SCONJ
ejpam-4453	982	6	a	a	DET
ejpam-4453	982	7	ntcbg	ntcbg	NOUN
ejpam-4453	982	8	has	have	AUX
ejpam-4453	982	9	spanning	span	VERB
ejpam-4453	982	10	k	k	NOUN
ejpam-4453	982	11	-	-	NOUN
ejpam-4453	982	12	trees	tree	NOUN
ejpam-4453	982	13	where	where	SCONJ
ejpam-4453	982	14	3	3	NUM
ejpam-4453	982	15	≤	≤	NUM
ejpam-4453	982	16	k	k	X
ejpam-4453	982	17	≤	≤	NUM
ejpam-4453	982	18	⌊	⌊	VERB
ejpam-4453	982	19	n+2	n+2	ADV
ejpam-4453	982	20	6	6	NUM
ejpam-4453	982	21	⌋	⌋	NOUN
ejpam-4453	982	22	.	.	PUNCT
ejpam-4453	983	1	lastly	lastly	ADV
ejpam-4453	983	2	,	,	PUNCT
ejpam-4453	983	3	the	the	DET
ejpam-4453	983	4	chromatic	chromatic	ADJ
ejpam-4453	983	5	number	number	NOUN
ejpam-4453	983	6	,	,	PUNCT
ejpam-4453	983	7	coloring	coloring	NOUN
ejpam-4453	983	8	and	and	CCONJ
ejpam-4453	983	9	clique	clique	ADJ
ejpam-4453	983	10	number	number	NOUN
ejpam-4453	983	11	of	of	ADP
ejpam-4453	983	12	a	a	DET
ejpam-4453	983	13	ntcbg	ntcbg	NOUN
ejpam-4453	983	14	were	be	AUX
ejpam-4453	983	15	discussed	discuss	VERB
ejpam-4453	983	16	.	.	PUNCT
ejpam-4453	984	1	acknowledgements	acknowledgement	NOUN
ejpam-4453	984	2	we	we	PRON
ejpam-4453	984	3	sincerely	sincerely	ADV
ejpam-4453	984	4	thank	thank	VERB
ejpam-4453	984	5	the	the	DET
ejpam-4453	984	6	anonymous	anonymous	ADJ
ejpam-4453	984	7	referees	referee	NOUN
ejpam-4453	984	8	of	of	ADP
ejpam-4453	984	9	european	european	PROPN
ejpam-4453	984	10	journal	journal	PROPN
ejpam-4453	984	11	of	of	ADP
ejpam-4453	984	12	pure	pure	ADJ
ejpam-4453	984	13	and	and	CCONJ
ejpam-4453	984	14	applied	applied	ADJ
ejpam-4453	984	15	mathematics	mathematic	NOUN
ejpam-4453	984	16	,	,	PUNCT
ejpam-4453	984	17	for	for	ADP
ejpam-4453	984	18	their	their	PRON
ejpam-4453	984	19	useful	useful	ADJ
ejpam-4453	984	20	comments	comment	NOUN
ejpam-4453	984	21	to	to	PART
ejpam-4453	984	22	improve	improve	VERB
ejpam-4453	984	23	the	the	DET
ejpam-4453	984	24	paper	paper	NOUN
ejpam-4453	984	25	.	.	PUNCT
ejpam-4453	985	1	furthermore	furthermore	ADV
ejpam-4453	985	2	,	,	PUNCT
ejpam-4453	985	3	we	we	PRON
ejpam-4453	985	4	thank	thank	VERB
ejpam-4453	985	5	the	the	DET
ejpam-4453	985	6	department	department	PROPN
ejpam-4453	985	7	of	of	ADP
ejpam-4453	985	8	science	science	NOUN
ejpam-4453	985	9	and	and	CCONJ
ejpam-4453	985	10	technology	technology	NOUN
ejpam-4453	985	11	(	(	PUNCT
ejpam-4453	985	12	dost	dost	NOUN
ejpam-4453	985	13	-	-	PUNCT
ejpam-4453	985	14	sei	sei	NOUN
ejpam-4453	985	15	)	)	PUNCT
ejpam-4453	985	16	for	for	ADP
ejpam-4453	985	17	the	the	DET
ejpam-4453	985	18	financial	financial	ADJ
ejpam-4453	985	19	support	support	NOUN
ejpam-4453	985	20	while	while	SCONJ
ejpam-4453	985	21	this	this	DET
ejpam-4453	985	22	research	research	NOUN
ejpam-4453	985	23	was	be	AUX
ejpam-4453	985	24	ongoing	ongoing	ADJ
ejpam-4453	985	25	.	.	PUNCT
ejpam-4453	986	1	references	reference	NOUN
ejpam-4453	986	2	[	[	X
ejpam-4453	986	3	1	1	NUM
ejpam-4453	986	4	]	]	X
ejpam-4453	986	5	c	c	PROPN
ejpam-4453	986	6	barrientos	barrientos	PROPN
ejpam-4453	986	7	.	.	PUNCT
ejpam-4453	987	1	graceful	graceful	ADJ
ejpam-4453	987	2	graphs	graph	NOUN
ejpam-4453	987	3	with	with	ADP
ejpam-4453	987	4	pendant	pendant	ADJ
ejpam-4453	987	5	edges	edge	NOUN
ejpam-4453	987	6	.	.	PUNCT
ejpam-4453	988	1	australasian	australasian	ADJ
ejpam-4453	988	2	journal	journal	NOUN
ejpam-4453	988	3	of	of	ADP
ejpam-4453	988	4	combinatorics	combinatoric	NOUN
ejpam-4453	988	5	,	,	PUNCT
ejpam-4453	988	6	33:99–107	33:99–107	NUM
ejpam-4453	988	7	,	,	PUNCT
ejpam-4453	988	8	2005	2005	NUM
ejpam-4453	988	9	.	.	PUNCT
ejpam-4453	989	1	[	[	X
ejpam-4453	989	2	2	2	NUM
ejpam-4453	989	3	]	]	SYM
ejpam-4453	989	4	b	b	X
ejpam-4453	989	5	bollobas	bollobas	NOUN
ejpam-4453	989	6	.	.	PUNCT
ejpam-4453	990	1	graduate	graduate	NOUN
ejpam-4453	990	2	texts	text	NOUN
ejpam-4453	990	3	in	in	ADP
ejpam-4453	990	4	mathematics	mathematic	NOUN
ejpam-4453	990	5	,	,	PUNCT
ejpam-4453	990	6	modern	modern	ADJ
ejpam-4453	990	7	graph	graph	NOUN
ejpam-4453	990	8	theory	theory	NOUN
ejpam-4453	990	9	.	.	PUNCT
ejpam-4453	991	1	springer	springer	NOUN
ejpam-4453	991	2	science+business	science+business	PROPN
ejpam-4453	991	3	media	medium	NOUN
ejpam-4453	991	4	,	,	PUNCT
ejpam-4453	991	5	inc	inc	PROPN
ejpam-4453	991	6	.	.	PROPN
ejpam-4453	991	7	,	,	PUNCT
ejpam-4453	991	8	new	new	PROPN
ejpam-4453	991	9	york	york	PROPN
ejpam-4453	991	10	,	,	PUNCT
ejpam-4453	991	11	1998	1998	NUM
ejpam-4453	991	12	.	.	PUNCT
ejpam-4453	992	1	[	[	X
ejpam-4453	992	2	3	3	NUM
ejpam-4453	992	3	]	]	X
ejpam-4453	992	4	r	r	NOUN
ejpam-4453	992	5	brooks	brooks	NOUN
ejpam-4453	992	6	.	.	PUNCT
ejpam-4453	993	1	on	on	ADP
ejpam-4453	993	2	coloring	color	VERB
ejpam-4453	993	3	the	the	DET
ejpam-4453	993	4	nodes	node	NOUN
ejpam-4453	993	5	of	of	ADP
ejpam-4453	993	6	a	a	DET
ejpam-4453	993	7	network	network	NOUN
ejpam-4453	993	8	.	.	PUNCT
ejpam-4453	993	9	proc	proc	PROPN
ejpam-4453	993	10	.	.	PUNCT
ejpam-4453	994	1	cambridge	cambridge	PROPN
ejpam-4453	994	2	philos	philos	PROPN
ejpam-4453	994	3	.	.	PUNCT
ejpam-4453	994	4	soc	soc	PROPN
ejpam-4453	994	5	.	.	PUNCT
ejpam-4453	994	6	,	,	PUNCT
ejpam-4453	994	7	37:194	37:194	NUM
ejpam-4453	994	8	–	–	PUNCT
ejpam-4453	994	9	197	197	NUM
ejpam-4453	994	10	,	,	PUNCT
ejpam-4453	994	11	1941	1941	NUM
ejpam-4453	994	12	.	.	PUNCT
ejpam-4453	995	1	[	[	X
ejpam-4453	995	2	4	4	X
ejpam-4453	995	3	]	]	X
ejpam-4453	995	4	j	j	PROPN
ejpam-4453	995	5	filar	filar	PROPN
ejpam-4453	995	6	m	m	VERB
ejpam-4453	995	7	haythorpe	haythorpe	NOUN
ejpam-4453	995	8	and	and	CCONJ
ejpam-4453	995	9	g	g	PROPN
ejpam-4453	995	10	nguyen	nguyen	NOUN
ejpam-4453	995	11	.	.	PUNCT
ejpam-4453	996	1	a	a	DET
ejpam-4453	996	2	conjecture	conjecture	NOUN
ejpam-4453	996	3	on	on	ADP
ejpam-4453	996	4	the	the	DET
ejpam-4453	996	5	prevalence	prevalence	NOUN
ejpam-4453	996	6	of	of	ADP
ejpam-4453	996	7	cubic	cubic	ADJ
ejpam-4453	996	8	bridge	bridge	NOUN
ejpam-4453	996	9	graphs	graph	NOUN
ejpam-4453	996	10	.	.	PUNCT
ejpam-4453	997	1	discussiones	discussione	NOUN
ejpam-4453	997	2	mathematicae	mathematicae	VERB
ejpam-4453	997	3	.	.	PUNCT
ejpam-4453	998	1	graph	graph	NOUN
ejpam-4453	998	2	theory	theory	NOUN
ejpam-4453	998	3	,	,	PUNCT
ejpam-4453	998	4	30(1):175–179	30(1):175–179	PROPN
ejpam-4453	998	5	,	,	PUNCT
ejpam-4453	998	6	2010	2010	NUM
ejpam-4453	998	7	.	.	PUNCT
ejpam-4453	999	1	[	[	X
ejpam-4453	999	2	5	5	X
ejpam-4453	999	3	]	]	PUNCT
ejpam-4453	999	4	g	g	PROPN
ejpam-4453	999	5	chartrand	chartrand	PROPN
ejpam-4453	999	6	l	l	PROPN
ejpam-4453	999	7	lesniak	lesniak	PROPN
ejpam-4453	999	8	and	and	CCONJ
ejpam-4453	999	9	p	p	PROPN
ejpam-4453	999	10	zhang	zhang	PROPN
ejpam-4453	999	11	.	.	PUNCT
ejpam-4453	999	12	textbook	textbook	NOUN
ejpam-4453	999	13	in	in	ADP
ejpam-4453	999	14	mathematics	mathematic	NOUN
ejpam-4453	999	15	,	,	PUNCT
ejpam-4453	999	16	graph	graph	NOUN
ejpam-4453	999	17	and	and	CCONJ
ejpam-4453	999	18	digraphs	digraph	NOUN
ejpam-4453	999	19	,	,	PUNCT
ejpam-4453	999	20	sixth	sixth	ADJ
ejpam-4453	999	21	edition	edition	NOUN
ejpam-4453	999	22	.	.	PUNCT
ejpam-4453	1000	1	crc	crc	PROPN
ejpam-4453	1000	2	press	press	PROPN
ejpam-4453	1000	3	,	,	PUNCT
ejpam-4453	1000	4	sound	sound	PROPN
ejpam-4453	1000	5	parkway	parkway	PROPN
ejpam-4453	1000	6	nw	nw	PROPN
ejpam-4453	1000	7	,	,	PUNCT
ejpam-4453	1000	8	suite	suite	NOUN
ejpam-4453	1000	9	300	300	NUM
ejpam-4453	1000	10	,	,	PUNCT
ejpam-4453	1000	11	2016	2016	NUM
ejpam-4453	1000	12	.	.	PUNCT
ejpam-4453	1001	1	[	[	X
ejpam-4453	1001	2	6	6	NUM
ejpam-4453	1001	3	]	]	X
ejpam-4453	1001	4	d	d	X
ejpam-4453	1001	5	west	west	PROPN
ejpam-4453	1001	6	.	.	PUNCT
ejpam-4453	1002	1	introduction	introduction	NOUN
ejpam-4453	1002	2	to	to	AUX
ejpam-4453	1002	3	graph	graph	NOUN
ejpam-4453	1002	4	theory	theory	NOUN
ejpam-4453	1002	5	,	,	PUNCT
ejpam-4453	1002	6	second	second	ADJ
ejpam-4453	1002	7	edition	edition	NOUN
ejpam-4453	1002	8	.	.	PUNCT
ejpam-4453	1003	1	pearson	pearson	PROPN
ejpam-4453	1003	2	education	education	PROPN
ejpam-4453	1003	3	,	,	PUNCT
ejpam-4453	1003	4	inc	inc	PROPN
ejpam-4453	1003	5	,	,	PUNCT
ejpam-4453	1003	6	singapore	singapore	PROPN
ejpam-4453	1003	7	,	,	PUNCT
ejpam-4453	1003	8	2001	2001	NUM
ejpam-4453	1003	9	.	.	PUNCT
ejpam-4453	1004	1	[	[	X
ejpam-4453	1004	2	7	7	X
ejpam-4453	1004	3	]	]	X
ejpam-4453	1004	4	h	h	NOUN
ejpam-4453	1004	5	zoeram	zoeram	NOUN
ejpam-4453	1004	6	and	and	CCONJ
ejpam-4453	1004	7	d	d	ADP
ejpam-4453	1004	8	yaqubi	yaqubi	NOUN
ejpam-4453	1004	9	.	.	PUNCT
ejpam-4453	1005	1	spanning	span	VERB
ejpam-4453	1005	2	k	k	ADV
ejpam-4453	1005	3	-	-	PUNCT
ejpam-4453	1005	4	ended	end	VERB
ejpam-4453	1005	5	trees	tree	NOUN
ejpam-4453	1005	6	of	of	ADP
ejpam-4453	1005	7	3	3	NUM
ejpam-4453	1005	8	-	-	PUNCT
ejpam-4453	1005	9	regular	regular	ADJ
ejpam-4453	1005	10	connected	connected	ADJ
ejpam-4453	1005	11	graph	graph	NOUN
ejpam-4453	1005	12	.	.	PUNCT
ejpam-4453	1006	1	electronic	electronic	ADJ
ejpam-4453	1006	2	journal	journal	NOUN
ejpam-4453	1006	3	of	of	ADP
ejpam-4453	1006	4	graph	graph	NOUN
ejpam-4453	1006	5	theory	theory	NOUN
ejpam-4453	1006	6	and	and	CCONJ
ejpam-4453	1006	7	application	application	NOUN
ejpam-4453	1006	8	,	,	PUNCT
ejpam-4453	1006	9	5(2):207–211	5(2):207–211	NUM
ejpam-4453	1006	10	,	,	PUNCT
ejpam-4453	1006	11	2017	2017	NUM
ejpam-4453	1006	12	.	.	PUNCT