id	sid	tid	token	lemma	pos
jd472v26441	1	1	given	give	VERB
jd472v26441	1	2	two	two	NUM
jd472v26441	1	3	graphs	graph	NOUN
jd472v26441	1	4	g	g	PROPN
jd472v26441	1	5	and	and	CCONJ
jd472v26441	1	6	h	h	NOUN
jd472v26441	1	7	,	,	PUNCT
jd472v26441	1	8	a	a	DET
jd472v26441	1	9	homomorphism	homomorphism	NOUN
jd472v26441	1	10	from	from	ADP
jd472v26441	1	11	g	g	PROPN
jd472v26441	1	12	to	to	ADP
jd472v26441	1	13	h	h	PROPN
jd472v26441	1	14	is	be	AUX
jd472v26441	1	15	a	a	DET
jd472v26441	1	16	map	map	NOUN
jd472v26441	1	17	from	from	ADP
jd472v26441	1	18	the	the	DET
jd472v26441	1	19	vertices	vertex	NOUN
jd472v26441	1	20	of	of	ADP
jd472v26441	1	21	g	g	NOUN
jd472v26441	1	22	to	to	ADP
jd472v26441	1	23	the	the	DET
jd472v26441	1	24	vertices	vertex	NOUN
jd472v26441	1	25	of	of	ADP
jd472v26441	1	26	h	h	NOUN
jd472v26441	1	27	that	that	PRON
jd472v26441	1	28	preserves	preserve	VERB
jd472v26441	1	29	adjacency	adjacency	NOUN
jd472v26441	1	30	.	.	PUNCT
jd472v26441	2	1	many	many	ADJ
jd472v26441	2	2	graph	graph	NOUN
jd472v26441	2	3	notions	notion	NOUN
jd472v26441	2	4	can	can	AUX
jd472v26441	2	5	be	be	AUX
jd472v26441	2	6	described	describe	VERB
jd472v26441	2	7	using	use	VERB
jd472v26441	2	8	graph	graph	NOUN
jd472v26441	2	9	homomorphisms	homomorphism	NOUN
jd472v26441	2	10	,	,	PUNCT
jd472v26441	2	11	including	include	VERB
jd472v26441	2	12	independent	independent	ADJ
jd472v26441	2	13	sets	set	NOUN
jd472v26441	2	14	,	,	PUNCT
jd472v26441	2	15	matchings	matching	NOUN
jd472v26441	2	16	,	,	PUNCT
jd472v26441	2	17	and	and	CCONJ
jd472v26441	2	18	graph	graph	NOUN
jd472v26441	2	19	colorings	coloring	NOUN
jd472v26441	2	20	.	.	PUNCT
jd472v26441	3	1	in	in	ADP
jd472v26441	3	2	this	this	DET
jd472v26441	3	3	dissertation	dissertation	NOUN
jd472v26441	3	4	,	,	PUNCT
jd472v26441	3	5	we	we	PRON
jd472v26441	3	6	consider	consider	VERB
jd472v26441	3	7	questions	question	NOUN
jd472v26441	3	8	in	in	ADP
jd472v26441	3	9	each	each	PRON
jd472v26441	3	10	of	of	ADP
jd472v26441	3	11	these	these	DET
jd472v26441	3	12	areas	area	NOUN
jd472v26441	3	13	.	.	PUNCT
jd472v26441	4	1	wang	wang	PROPN
jd472v26441	4	2	and	and	CCONJ
jd472v26441	4	3	zhu	zhu	PROPN
jd472v26441	4	4	[	[	PUNCT
jd472v26441	4	5	49	49	NUM
jd472v26441	4	6	]	]	PUNCT
jd472v26441	4	7	demonstrated	demonstrate	VERB
jd472v26441	4	8	the	the	DET
jd472v26441	4	9	log	log	NOUN
jd472v26441	4	10	-	-	PUNCT
jd472v26441	4	11	concavity	concavity	NOUN
jd472v26441	4	12	of	of	ADP
jd472v26441	4	13	the	the	DET
jd472v26441	4	14	independence	independence	NOUN
jd472v26441	4	15	polynomial	polynomial	ADJ
jd472v26441	4	16	for	for	ADP
jd472v26441	4	17	a	a	DET
jd472v26441	4	18	number	number	NOUN
jd472v26441	4	19	of	of	ADP
jd472v26441	4	20	infinite	infinite	ADJ
jd472v26441	4	21	recursively	recursively	ADV
jd472v26441	4	22	-	-	PUNCT
jd472v26441	4	23	defined	define	VERB
jd472v26441	4	24	graph	graph	NOUN
jd472v26441	4	25	classes	class	NOUN
jd472v26441	4	26	.	.	PUNCT
jd472v26441	5	1	for	for	ADP
jd472v26441	5	2	the	the	DET
jd472v26441	5	3	first	first	ADJ
jd472v26441	5	4	question	question	NOUN
jd472v26441	5	5	that	that	PRON
jd472v26441	5	6	we	we	PRON
jd472v26441	5	7	consider	consider	VERB
jd472v26441	5	8	,	,	PUNCT
jd472v26441	5	9	we	we	PRON
jd472v26441	5	10	extend	extend	VERB
jd472v26441	5	11	their	their	PRON
jd472v26441	5	12	method	method	NOUN
jd472v26441	5	13	to	to	PART
jd472v26441	5	14	demonstrate	demonstrate	VERB
jd472v26441	5	15	the	the	DET
jd472v26441	5	16	log	log	NOUN
jd472v26441	5	17	-	-	PUNCT
jd472v26441	5	18	concavity	concavity	NOUN
jd472v26441	5	19	of	of	ADP
jd472v26441	5	20	the	the	DET
jd472v26441	5	21	independence	independence	NOUN
jd472v26441	5	22	polynomial	polynomial	ADJ
jd472v26441	5	23	for	for	ADP
jd472v26441	5	24	a	a	DET
jd472v26441	5	25	wider	wide	ADJ
jd472v26441	5	26	range	range	NOUN
jd472v26441	5	27	of	of	ADP
jd472v26441	5	28	such	such	ADJ
jd472v26441	5	29	classes	class	NOUN
jd472v26441	5	30	,	,	PUNCT
jd472v26441	5	31	showing	show	VERB
jd472v26441	5	32	,	,	PUNCT
jd472v26441	5	33	for	for	ADP
jd472v26441	5	34	example	example	NOUN
jd472v26441	5	35	,	,	PUNCT
jd472v26441	5	36	that	that	SCONJ
jd472v26441	5	37	the	the	DET
jd472v26441	5	38	(	(	PUNCT
jd472v26441	5	39	n,2)-centipede	n,2)-centipede	NOUN
jd472v26441	5	40	and	and	CCONJ
jd472v26441	5	41	(	(	PUNCT
jd472v26441	5	42	n,2,k)-star	n,2,k)-star	PROPN
jd472v26441	5	43	-	-	PUNCT
jd472v26441	5	44	centipede	centipede	NOUN
jd472v26441	5	45	have	have	VERB
jd472v26441	5	46	log	log	NOUN
jd472v26441	5	47	-	-	PUNCT
jd472v26441	5	48	concave	concave	NOUN
jd472v26441	5	49	independence	independence	NOUN
jd472v26441	5	50	polynomials	polynomial	NOUN
jd472v26441	5	51	for	for	ADP
jd472v26441	5	52	even	even	ADV
jd472v26441	5	53	n	n	NOUN
jd472v26441	5	54	and	and	CCONJ
jd472v26441	5	55	all	all	DET
jd472v26441	5	56	k	k	NOUN
jd472v26441	5	57	,	,	PUNCT
jd472v26441	5	58	and	and	CCONJ
jd472v26441	5	59	we	we	PRON
jd472v26441	5	60	describe	describe	VERB
jd472v26441	5	61	a	a	DET
jd472v26441	5	62	technique	technique	NOUN
jd472v26441	5	63	that	that	PRON
jd472v26441	5	64	can	can	AUX
jd472v26441	5	65	be	be	AUX
jd472v26441	5	66	applied	apply	VERB
jd472v26441	5	67	in	in	ADP
jd472v26441	5	68	the	the	DET
jd472v26441	5	69	pursuit	pursuit	NOUN
jd472v26441	5	70	of	of	ADP
jd472v26441	5	71	results	result	NOUN
jd472v26441	5	72	for	for	ADP
jd472v26441	5	73	other	other	ADJ
jd472v26441	5	74	similarly	similarly	ADV
jd472v26441	5	75	-	-	PUNCT
jd472v26441	5	76	structured	structure	VERB
jd472v26441	5	77	graphs	graph	NOUN
jd472v26441	5	78	.	.	PUNCT
jd472v26441	6	1	the	the	DET
jd472v26441	6	2	graphs	graph	NOUN
jd472v26441	6	3	in	in	ADP
jd472v26441	6	4	question	question	NOUN
jd472v26441	6	5	give	give	VERB
jd472v26441	6	6	rise	rise	NOUN
jd472v26441	6	7	to	to	ADP
jd472v26441	6	8	k	k	X
jd472v26441	6	9	-	-	ADJ
jd472v26441	6	10	periodic	periodic	ADJ
jd472v26441	6	11	recurrence	recurrence	NOUN
jd472v26441	6	12	relations	relation	NOUN
jd472v26441	6	13	.	.	PUNCT
jd472v26441	7	1	we	we	PRON
jd472v26441	7	2	present	present	VERB
jd472v26441	7	3	a	a	DET
jd472v26441	7	4	system	system	NOUN
jd472v26441	7	5	for	for	ADP
jd472v26441	7	6	reducing	reduce	VERB
jd472v26441	7	7	these	these	DET
jd472v26441	7	8	periodic	periodic	ADJ
jd472v26441	7	9	recurrence	recurrence	NOUN
jd472v26441	7	10	relations	relation	NOUN
jd472v26441	7	11	to	to	ADP
jd472v26441	7	12	ordinary	ordinary	ADJ
jd472v26441	7	13	second	second	ADJ
jd472v26441	7	14	-	-	PUNCT
jd472v26441	7	15	order	order	NOUN
jd472v26441	7	16	recurrence	recurrence	NOUN
jd472v26441	7	17	relations	relation	NOUN
jd472v26441	7	18	that	that	PRON
jd472v26441	7	19	is	be	AUX
jd472v26441	7	20	more	more	ADV
jd472v26441	7	21	applicable	applicable	ADJ
jd472v26441	7	22	than	than	ADP
jd472v26441	7	23	existing	exist	VERB
jd472v26441	7	24	work	work	NOUN
jd472v26441	7	25	in	in	ADP
jd472v26441	7	26	the	the	DET
jd472v26441	7	27	field	field	NOUN
jd472v26441	7	28	.	.	PUNCT
jd472v26441	8	1	there	there	PRON
jd472v26441	8	2	has	have	AUX
jd472v26441	8	3	been	be	AUX
jd472v26441	8	4	much	much	ADJ
jd472v26441	8	5	discussion	discussion	NOUN
jd472v26441	8	6	(	(	PUNCT
jd472v26441	8	7	for	for	ADP
jd472v26441	8	8	example	example	NOUN
jd472v26441	8	9	,	,	PUNCT
jd472v26441	8	10	[	[	PUNCT
jd472v26441	8	11	52	52	NUM
jd472v26441	8	12	]	]	PUNCT
jd472v26441	8	13	,	,	PUNCT
jd472v26441	8	14	[	[	X
jd472v26441	8	15	26	26	NUM
jd472v26441	8	16	]	]	PUNCT
jd472v26441	8	17	,	,	PUNCT
jd472v26441	8	18	and	and	CCONJ
jd472v26441	8	19	[	[	X
jd472v26441	8	20	22	22	NUM
jd472v26441	8	21	]	]	PUNCT
jd472v26441	8	22	)	)	PUNCT
jd472v26441	8	23	,	,	PUNCT
jd472v26441	8	24	on	on	ADP
jd472v26441	8	25	the	the	DET
jd472v26441	8	26	following	following	ADJ
jd472v26441	8	27	question	question	NOUN
jd472v26441	8	28	:	:	PUNCT
jd472v26441	8	29	for	for	ADP
jd472v26441	8	30	each	each	DET
jd472v26441	8	31	fixed	fix	VERB
jd472v26441	8	32	h	h	NOUN
jd472v26441	8	33	,	,	PUNCT
jd472v26441	8	34	n	n	NOUN
jd472v26441	8	35	and	and	CCONJ
jd472v26441	8	36	d	d	PROPN
jd472v26441	8	37	,	,	PUNCT
jd472v26441	8	38	what	what	PRON
jd472v26441	8	39	is	be	AUX
jd472v26441	8	40	the	the	DET
jd472v26441	8	41	maximum	maximum	ADJ
jd472v26441	8	42	,	,	PUNCT
jd472v26441	8	43	over	over	ADP
jd472v26441	8	44	all	all	DET
jd472v26441	8	45	n	n	NOUN
jd472v26441	8	46	-	-	PUNCT
jd472v26441	8	47	vertex	vertex	NOUN
jd472v26441	8	48	,	,	PUNCT
jd472v26441	8	49	d	d	VERB
jd472v26441	8	50	-	-	NOUN
jd472v26441	8	51	regular	regular	ADJ
jd472v26441	8	52	g	g	NOUN
jd472v26441	8	53	,	,	PUNCT
jd472v26441	8	54	of	of	ADP
jd472v26441	8	55	hom(g	hom(g	PROPN
jd472v26441	8	56	,	,	PUNCT
jd472v26441	8	57	h	h	PROPN
jd472v26441	8	58	)	)	PUNCT
jd472v26441	8	59	,	,	PUNCT
jd472v26441	8	60	the	the	DET
jd472v26441	8	61	number	number	NOUN
jd472v26441	8	62	of	of	ADP
jd472v26441	8	63	homomorphisms	homomorphism	NOUN
jd472v26441	8	64	from	from	ADP
jd472v26441	8	65	g	g	PROPN
jd472v26441	8	66	to	to	ADP
jd472v26441	8	67	h	h	PROPN
jd472v26441	8	68	?	?	PUNCT
jd472v26441	9	1	while	while	SCONJ
jd472v26441	9	2	the	the	DET
jd472v26441	9	3	question	question	NOUN
jd472v26441	9	4	has	have	AUX
jd472v26441	9	5	been	be	AUX
jd472v26441	9	6	largely	largely	ADV
jd472v26441	9	7	settled	settle	VERB
jd472v26441	9	8	for	for	ADP
jd472v26441	9	9	bipartite	bipartite	PROPN
jd472v26441	9	10	g	g	PROPN
jd472v26441	9	11	,	,	PUNCT
jd472v26441	9	12	it	it	PRON
jd472v26441	9	13	is	be	AUX
jd472v26441	9	14	still	still	ADV
jd472v26441	9	15	quite	quite	ADV
jd472v26441	9	16	open	open	ADJ
jd472v26441	9	17	for	for	ADP
jd472v26441	9	18	non	non	ADJ
jd472v26441	9	19	-	-	ADJ
jd472v26441	9	20	bipartite	bipartite	ADJ
jd472v26441	9	21	g.	g.	PROPN
jd472v26441	9	22	offering	offer	VERB
jd472v26441	9	23	further	further	ADJ
jd472v26441	9	24	progress	progress	NOUN
jd472v26441	9	25	on	on	ADP
jd472v26441	9	26	this	this	DET
jd472v26441	9	27	question	question	NOUN
jd472v26441	9	28	,	,	PUNCT
jd472v26441	9	29	we	we	PRON
jd472v26441	9	30	next	next	ADV
jd472v26441	9	31	establish	establish	VERB
jd472v26441	9	32	conditions	condition	NOUN
jd472v26441	9	33	on	on	ADP
jd472v26441	9	34	h	h	PROPN
jd472v26441	9	35	,	,	PUNCT
jd472v26441	9	36	in	in	ADP
jd472v26441	9	37	terms	term	NOUN
jd472v26441	9	38	of	of	ADP
jd472v26441	9	39	certain	certain	ADJ
jd472v26441	9	40	linear	linear	NOUN
jd472v26441	9	41	programming	programming	NOUN
jd472v26441	9	42	problems	problem	NOUN
jd472v26441	9	43	,	,	PUNCT
jd472v26441	9	44	under	under	ADP
jd472v26441	9	45	which	which	PRON
jd472v26441	9	46	we	we	PRON
jd472v26441	9	47	can	can	AUX
jd472v26441	9	48	obtain	obtain	VERB
jd472v26441	9	49	an	an	DET
jd472v26441	9	50	upper	upper	ADJ
jd472v26441	9	51	bound	bind	VERB
jd472v26441	9	52	on	on	ADP
jd472v26441	9	53	hom(g;h	hom(g;h	NUM
jd472v26441	9	54	)	)	PUNCT
jd472v26441	9	55	,	,	PUNCT
jd472v26441	9	56	valid	valid	ADJ
jd472v26441	9	57	for	for	ADP
jd472v26441	9	58	all	all	PRON
jd472v26441	9	59	regular	regular	ADJ
jd472v26441	9	60	g	g	NOUN
jd472v26441	9	61	,	,	PUNCT
jd472v26441	9	62	that	that	PRON
jd472v26441	9	63	is	be	AUX
jd472v26441	9	64	very	very	ADV
jd472v26441	9	65	close	close	ADJ
jd472v26441	9	66	to	to	ADP
jd472v26441	9	67	best	well	ADV
jd472v26441	9	68	possible	possible	ADJ
jd472v26441	9	69	.	.	PUNCT
jd472v26441	10	1	we	we	PRON
jd472v26441	10	2	then	then	ADV
jd472v26441	10	3	establish	establish	VERB
jd472v26441	10	4	a	a	DET
jd472v26441	10	5	number	number	NOUN
jd472v26441	10	6	of	of	ADP
jd472v26441	10	7	infinite	infinite	ADJ
jd472v26441	10	8	families	family	NOUN
jd472v26441	10	9	of	of	ADP
jd472v26441	10	10	graphs	graph	NOUN
jd472v26441	10	11	that	that	PRON
jd472v26441	10	12	satisfy	satisfy	VERB
jd472v26441	10	13	these	these	DET
jd472v26441	10	14	conditions	condition	NOUN
jd472v26441	10	15	.	.	PUNCT
jd472v26441	11	1	finally	finally	ADV
jd472v26441	11	2	,	,	PUNCT
jd472v26441	11	3	we	we	PRON
jd472v26441	11	4	present	present	VERB
jd472v26441	11	5	a	a	DET
jd472v26441	11	6	q	q	ADJ
jd472v26441	11	7	-	-	ADJ
jd472v26441	11	8	weighted	weighted	ADJ
jd472v26441	11	9	enumeration	enumeration	NOUN
jd472v26441	11	10	of	of	ADP
jd472v26441	11	11	matchings	matching	NOUN
jd472v26441	11	12	of	of	ADP
jd472v26441	11	13	complete	complete	ADJ
jd472v26441	11	14	bipartite	bipartite	ADJ
jd472v26441	11	15	graphs	graph	NOUN
jd472v26441	11	16	,	,	PUNCT
jd472v26441	11	17	an	an	DET
jd472v26441	11	18	enumeration	enumeration	NOUN
jd472v26441	11	19	which	which	PRON
jd472v26441	11	20	was	be	AUX
jd472v26441	11	21	key	key	ADJ
jd472v26441	11	22	to	to	ADP
jd472v26441	11	23	proving	prove	VERB
jd472v26441	11	24	the	the	DET
jd472v26441	11	25	validity	validity	NOUN
jd472v26441	11	26	of	of	ADP
jd472v26441	11	27	a	a	DET
jd472v26441	11	28	new	new	ADJ
jd472v26441	11	29	combinatorial	combinatorial	ADJ
jd472v26441	11	30	interpretation	interpretation	NOUN
jd472v26441	11	31	of	of	ADP
jd472v26441	11	32	the	the	DET
jd472v26441	11	33	q	q	NOUN
jd472v26441	11	34	-	-	NOUN
jd472v26441	11	35	analog	analog	NOUN
jd472v26441	11	36	of	of	ADP
jd472v26441	11	37	a	a	DET
jd472v26441	11	38	generalization	generalization	NOUN
jd472v26441	11	39	of	of	ADP
jd472v26441	11	40	the	the	DET
jd472v26441	11	41	stirling	stirling	NOUN
jd472v26441	11	42	numbers	number	NOUN
jd472v26441	11	43	of	of	ADP
jd472v26441	11	44	the	the	DET
jd472v26441	11	45	second	second	ADJ
jd472v26441	11	46	kind	kind	NOUN
jd472v26441	11	47	in	in	ADP
jd472v26441	11	48	work	work	NOUN
jd472v26441	11	49	with	with	ADP
jd472v26441	11	50	engbers	engber	NOUN
jd472v26441	11	51	and	and	CCONJ
jd472v26441	11	52	galvin	galvin	NOUN
jd472v26441	11	53	[	[	X
jd472v26441	11	54	20	20	NUM
jd472v26441	11	55	]	]	PUNCT
jd472v26441	11	56	.	.	PUNCT