id	sid	tid	token	lemma	pos
ejpam-6951	1	1	european	european	PROPN
ejpam-6951	1	2	journal	journal	PROPN
ejpam-6951	1	3	of	of	ADP
ejpam-6951	1	4	pure	pure	ADJ
ejpam-6951	1	5	and	and	CCONJ
ejpam-6951	1	6	applied	applied	ADJ
ejpam-6951	1	7	mathematics	mathematic	NOUN
ejpam-6951	1	8	2025	2025	NUM
ejpam-6951	1	9	,	,	PUNCT
ejpam-6951	1	10	vol	vol	NOUN
ejpam-6951	1	11	.	.	PROPN
ejpam-6951	1	12	18	18	NUM
ejpam-6951	1	13	,	,	PUNCT
ejpam-6951	1	14	issue	issue	NOUN
ejpam-6951	1	15	4	4	NUM
ejpam-6951	1	16	,	,	PUNCT
ejpam-6951	1	17	article	article	NOUN
ejpam-6951	1	18	number	number	NOUN
ejpam-6951	1	19	6951	6951	NUM
ejpam-6951	1	20	issn	issn	PROPN
ejpam-6951	1	21	1307	1307	NUM
ejpam-6951	1	22	-	-	SYM
ejpam-6951	1	23	5543	5543	NUM
ejpam-6951	1	24	–	–	PUNCT
ejpam-6951	1	25	ejpam.com	ejpam.com	X
ejpam-6951	1	26	published	publish	VERB
ejpam-6951	1	27	by	by	ADP
ejpam-6951	1	28	new	new	PROPN
ejpam-6951	1	29	york	york	PROPN
ejpam-6951	1	30	business	business	PROPN
ejpam-6951	1	31	global	global	ADJ
ejpam-6951	1	32	vertex	vertex	NOUN
ejpam-6951	1	33	-	-	PUNCT
ejpam-6951	1	34	generator	generator	NOUN
ejpam-6951	1	35	subgraphs	subgraph	NOUN
ejpam-6951	1	36	of	of	ADP
ejpam-6951	1	37	complete	complete	ADJ
ejpam-6951	1	38	bipartite	bipartite	PROPN
ejpam-6951	1	39	and	and	CCONJ
ejpam-6951	1	40	tadpole	tadpole	NOUN
ejpam-6951	1	41	graphs	graph	VERB
ejpam-6951	1	42	gino	gino	PROPN
ejpam-6951	1	43	derek	derek	PROPN
ejpam-6951	1	44	m.	m.	PROPN
ejpam-6951	1	45	sepillo1,∗	sepillo1,∗	PROPN
ejpam-6951	1	46	,	,	PUNCT
ejpam-6951	1	47	ma	ma	PROPN
ejpam-6951	1	48	.	.	PROPN
ejpam-6951	1	49	joyce	joyce	PROPN
ejpam-6951	1	50	g.	g.	PROPN
ejpam-6951	1	51	valdez1	valdez1	PROPN
ejpam-6951	1	52	,	,	PUNCT
ejpam-6951	1	53	meguilito	meguilito	PROPN
ejpam-6951	1	54	y.	y.	PROPN
ejpam-6951	1	55	eyao1	eyao1	PROPN
ejpam-6951	1	56	,	,	PUNCT
ejpam-6951	1	57	neil	neil	PROPN
ejpam-6951	1	58	m.	m.	PROPN
ejpam-6951	1	59	mame1	mame1	PROPN
ejpam-6951	1	60	1	1	NUM
ejpam-6951	1	61	college	college	NOUN
ejpam-6951	1	62	of	of	ADP
ejpam-6951	1	63	arts	art	NOUN
ejpam-6951	1	64	and	and	CCONJ
ejpam-6951	1	65	sciences	sciences	PROPN
ejpam-6951	1	66	,	,	PUNCT
ejpam-6951	1	67	batangas	batangas	PROPN
ejpam-6951	1	68	state	state	PROPN
ejpam-6951	1	69	university	university	PROPN
ejpam-6951	1	70	,	,	PUNCT
ejpam-6951	1	71	the	the	DET
ejpam-6951	1	72	national	national	PROPN
ejpam-6951	1	73	engineering	engineering	PROPN
ejpam-6951	1	74	university	university	PROPN
ejpam-6951	1	75	,	,	PUNCT
ejpam-6951	1	76	pablo	pablo	PROPN
ejpam-6951	1	77	borbon	borbon	PROPN
ejpam-6951	1	78	campus	campus	PROPN
ejpam-6951	1	79	,	,	PUNCT
ejpam-6951	1	80	batangas	batangas	PROPN
ejpam-6951	1	81	city	city	PROPN
ejpam-6951	1	82	,	,	PUNCT
ejpam-6951	1	83	batangas	batangas	PROPN
ejpam-6951	1	84	,	,	PUNCT
ejpam-6951	1	85	philippines	philippine	NOUN
ejpam-6951	1	86	abstract	abstract	ADJ
ejpam-6951	1	87	.	.	PUNCT
ejpam-6951	2	1	graphs	graph	NOUN
ejpam-6951	2	2	considered	consider	VERB
ejpam-6951	2	3	in	in	ADP
ejpam-6951	2	4	this	this	DET
ejpam-6951	2	5	paper	paper	NOUN
ejpam-6951	2	6	are	be	AUX
ejpam-6951	2	7	finite	finite	ADJ
ejpam-6951	2	8	simple	simple	ADJ
ejpam-6951	2	9	undirected	undirected	ADJ
ejpam-6951	2	10	graphs	graph	NOUN
ejpam-6951	2	11	.	.	PUNCT
ejpam-6951	3	1	let	let	VERB
ejpam-6951	3	2	g	g	PROPN
ejpam-6951	3	3	=	=	SYM
ejpam-6951	3	4	(	(	PUNCT
ejpam-6951	3	5	v	v	NOUN
ejpam-6951	3	6	(	(	PUNCT
ejpam-6951	3	7	g	g	NOUN
ejpam-6951	3	8	)	)	PUNCT
ejpam-6951	3	9	,	,	PUNCT
ejpam-6951	3	10	e(g	e(g	PROPN
ejpam-6951	3	11	)	)	PUNCT
ejpam-6951	3	12	)	)	PUNCT
ejpam-6951	4	1	be	be	AUX
ejpam-6951	4	2	a	a	DET
ejpam-6951	4	3	graph	graph	NOUN
ejpam-6951	4	4	with	with	ADP
ejpam-6951	4	5	the	the	DET
ejpam-6951	4	6	vertex	vertex	NOUN
ejpam-6951	4	7	set	set	VERB
ejpam-6951	4	8	v	v	NOUN
ejpam-6951	4	9	(	(	PUNCT
ejpam-6951	4	10	g	g	NOUN
ejpam-6951	4	11	)	)	PUNCT
ejpam-6951	4	12	=	=	SYM
ejpam-6951	4	13	{	{	PUNCT
ejpam-6951	4	14	x1	x1	PROPN
ejpam-6951	4	15	,	,	PUNCT
ejpam-6951	4	16	x2	x2	PROPN
ejpam-6951	4	17	,	,	PUNCT
ejpam-6951	4	18	.	.	PUNCT
ejpam-6951	4	19	.	.	PUNCT
ejpam-6951	5	1	.	.	PUNCT
ejpam-6951	6	1	,	,	PUNCT
ejpam-6951	6	2	xn	xn	PROPN
ejpam-6951	6	3	}	}	PUNCT
ejpam-6951	6	4	,	,	PUNCT
ejpam-6951	6	5	for	for	ADP
ejpam-6951	6	6	some	some	DET
ejpam-6951	6	7	positive	positive	ADJ
ejpam-6951	6	8	integer	integer	NOUN
ejpam-6951	6	9	n.	n.	NOUN
ejpam-6951	6	10	the	the	DET
ejpam-6951	6	11	vertex	vertex	NOUN
ejpam-6951	6	12	space	space	NOUN
ejpam-6951	6	13	v	v	NOUN
ejpam-6951	6	14	(	(	PUNCT
ejpam-6951	6	15	g	g	NOUN
ejpam-6951	6	16	)	)	PUNCT
ejpam-6951	6	17	of	of	ADP
ejpam-6951	6	18	g	g	NOUN
ejpam-6951	6	19	,	,	PUNCT
ejpam-6951	6	20	is	be	AUX
ejpam-6951	6	21	a	a	DET
ejpam-6951	6	22	vector	vector	NOUN
ejpam-6951	6	23	space	space	NOUN
ejpam-6951	6	24	over	over	ADP
ejpam-6951	6	25	the	the	DET
ejpam-6951	6	26	field	field	NOUN
ejpam-6951	6	27	z2	z2	NOUN
ejpam-6951	6	28	=	=	SYM
ejpam-6951	6	29	{	{	PUNCT
ejpam-6951	6	30	0	0	NUM
ejpam-6951	6	31	,	,	PUNCT
ejpam-6951	6	32	1	1	NUM
ejpam-6951	6	33	}	}	PUNCT
ejpam-6951	6	34	.	.	PUNCT
ejpam-6951	7	1	the	the	DET
ejpam-6951	7	2	elements	element	NOUN
ejpam-6951	7	3	of	of	ADP
ejpam-6951	7	4	v	v	NOUN
ejpam-6951	7	5	(	(	PUNCT
ejpam-6951	7	6	g	g	NOUN
ejpam-6951	7	7	)	)	PUNCT
ejpam-6951	7	8	are	be	AUX
ejpam-6951	7	9	all	all	DET
ejpam-6951	7	10	the	the	DET
ejpam-6951	7	11	subsets	subset	NOUN
ejpam-6951	7	12	of	of	ADP
ejpam-6951	7	13	v	v	NOUN
ejpam-6951	7	14	(	(	PUNCT
ejpam-6951	7	15	g	g	NOUN
ejpam-6951	7	16	)	)	PUNCT
ejpam-6951	7	17	.	.	PUNCT
ejpam-6951	8	1	vector	vector	NOUN
ejpam-6951	8	2	addition	addition	NOUN
ejpam-6951	8	3	is	be	AUX
ejpam-6951	8	4	defined	define	VERB
ejpam-6951	8	5	as	as	ADP
ejpam-6951	8	6	a+b	a+b	NUM
ejpam-6951	8	7	=	=	PUNCT
ejpam-6951	8	8	a	a	DET
ejpam-6951	8	9	△	△	PROPN
ejpam-6951	8	10	b	b	NOUN
ejpam-6951	8	11	,	,	PUNCT
ejpam-6951	8	12	the	the	DET
ejpam-6951	8	13	symmetric	symmetric	ADJ
ejpam-6951	8	14	difference	difference	NOUN
ejpam-6951	8	15	of	of	ADP
ejpam-6951	8	16	sets	set	NOUN
ejpam-6951	8	17	a	a	PRON
ejpam-6951	8	18	and	and	CCONJ
ejpam-6951	8	19	b	b	NOUN
ejpam-6951	8	20	,	,	PUNCT
ejpam-6951	8	21	for	for	ADP
ejpam-6951	8	22	all	all	DET
ejpam-6951	8	23	a	a	PRON
ejpam-6951	8	24	,	,	PUNCT
ejpam-6951	8	25	b	b	PROPN
ejpam-6951	8	26	∈	∈	PROPN
ejpam-6951	8	27	v	v	NOUN
ejpam-6951	8	28	(	(	PUNCT
ejpam-6951	8	29	g	g	NOUN
ejpam-6951	8	30	)	)	PUNCT
ejpam-6951	8	31	.	.	PUNCT
ejpam-6951	9	1	scalar	scalar	ADJ
ejpam-6951	9	2	multiplication	multiplication	NOUN
ejpam-6951	9	3	is	be	AUX
ejpam-6951	9	4	defined	define	VERB
ejpam-6951	9	5	as	as	ADP
ejpam-6951	9	6	1	1	NUM
ejpam-6951	9	7	·	·	PUNCT
ejpam-6951	9	8	a	a	PRON
ejpam-6951	9	9	=	=	X
ejpam-6951	9	10	a	a	PRON
ejpam-6951	9	11	and	and	CCONJ
ejpam-6951	9	12	0	0	NUM
ejpam-6951	9	13	·	·	PUNCT
ejpam-6951	9	14	a	a	DET
ejpam-6951	9	15	=	=	NOUN
ejpam-6951	9	16	∅	∅	NOUN
ejpam-6951	9	17	,	,	PUNCT
ejpam-6951	9	18	for	for	ADP
ejpam-6951	9	19	all	all	DET
ejpam-6951	9	20	a	a	DET
ejpam-6951	9	21	∈	∈	PROPN
ejpam-6951	9	22	v	v	NOUN
ejpam-6951	9	23	(	(	PUNCT
ejpam-6951	9	24	g	g	NOUN
ejpam-6951	9	25	)	)	PUNCT
ejpam-6951	9	26	.	.	PUNCT
ejpam-6951	10	1	the	the	DET
ejpam-6951	10	2	subgraph	subgraph	NOUN
ejpam-6951	10	3	g⟨s⟩	g⟨s⟩	PROPN
ejpam-6951	10	4	of	of	ADP
ejpam-6951	10	5	g	g	PROPN
ejpam-6951	10	6	induced	induce	VERB
ejpam-6951	10	7	by	by	ADP
ejpam-6951	10	8	a	a	DET
ejpam-6951	10	9	subset	subset	NOUN
ejpam-6951	10	10	s	s	NOUN
ejpam-6951	10	11	of	of	ADP
ejpam-6951	10	12	v	v	NOUN
ejpam-6951	10	13	(	(	PUNCT
ejpam-6951	10	14	g	g	NOUN
ejpam-6951	10	15	)	)	PUNCT
ejpam-6951	10	16	,	,	PUNCT
ejpam-6951	10	17	is	be	AUX
ejpam-6951	10	18	the	the	DET
ejpam-6951	10	19	largest	large	ADJ
ejpam-6951	10	20	subgraph	subgraph	NOUN
ejpam-6951	10	21	whose	whose	DET
ejpam-6951	10	22	vertex	vertex	NOUN
ejpam-6951	10	23	set	set	NOUN
ejpam-6951	10	24	is	be	AUX
ejpam-6951	10	25	s.	s.	PROPN
ejpam-6951	10	26	the	the	DET
ejpam-6951	10	27	vertex	vertex	NOUN
ejpam-6951	10	28	-	-	PUNCT
ejpam-6951	10	29	uniform	uniform	NOUN
ejpam-6951	10	30	set	set	VERB
ejpam-6951	10	31	vh(g	vh(g	NOUN
ejpam-6951	10	32	)	)	PUNCT
ejpam-6951	10	33	of	of	ADP
ejpam-6951	10	34	a	a	DET
ejpam-6951	10	35	subgraph	subgraph	NOUN
ejpam-6951	10	36	h	h	NOUN
ejpam-6951	10	37	with	with	ADP
ejpam-6951	10	38	respect	respect	NOUN
ejpam-6951	10	39	to	to	ADP
ejpam-6951	10	40	g	g	NOUN
ejpam-6951	10	41	,	,	PUNCT
ejpam-6951	10	42	is	be	AUX
ejpam-6951	10	43	the	the	DET
ejpam-6951	10	44	set	set	NOUN
ejpam-6951	10	45	of	of	ADP
ejpam-6951	10	46	all	all	DET
ejpam-6951	10	47	elements	element	NOUN
ejpam-6951	10	48	of	of	ADP
ejpam-6951	10	49	v	v	NOUN
ejpam-6951	10	50	(	(	PUNCT
ejpam-6951	10	51	g	g	NOUN
ejpam-6951	10	52	)	)	PUNCT
ejpam-6951	10	53	that	that	PRON
ejpam-6951	10	54	induces	induce	VERB
ejpam-6951	10	55	a	a	DET
ejpam-6951	10	56	subgraph	subgraph	NOUN
ejpam-6951	10	57	isomorphic	isomorphic	ADJ
ejpam-6951	10	58	to	to	ADP
ejpam-6951	10	59	h.	h.	PROPN
ejpam-6951	10	60	the	the	DET
ejpam-6951	10	61	span	span	NOUN
ejpam-6951	10	62	of	of	ADP
ejpam-6951	10	63	vh(g	vh(g	NOUN
ejpam-6951	10	64	)	)	PUNCT
ejpam-6951	10	65	shall	shall	AUX
ejpam-6951	10	66	be	be	AUX
ejpam-6951	10	67	denoted	denote	VERB
ejpam-6951	10	68	by	by	ADP
ejpam-6951	10	69	vh(g	vh(g	NOUN
ejpam-6951	10	70	)	)	PUNCT
ejpam-6951	10	71	.	.	PUNCT
ejpam-6951	11	1	if	if	SCONJ
ejpam-6951	11	2	vh(g	vh(g	NOUN
ejpam-6951	11	3	)	)	PUNCT
ejpam-6951	11	4	is	be	AUX
ejpam-6951	11	5	a	a	DET
ejpam-6951	11	6	generating	generate	VERB
ejpam-6951	11	7	set	set	NOUN
ejpam-6951	11	8	,	,	PUNCT
ejpam-6951	11	9	that	that	ADV
ejpam-6951	11	10	is	be	AUX
ejpam-6951	11	11	vh(g	vh(g	NOUN
ejpam-6951	11	12	)	)	PUNCT
ejpam-6951	12	1	=	=	SYM
ejpam-6951	12	2	v	v	X
ejpam-6951	12	3	(	(	PUNCT
ejpam-6951	12	4	g	g	NOUN
ejpam-6951	12	5	)	)	PUNCT
ejpam-6951	12	6	,	,	PUNCT
ejpam-6951	12	7	then	then	ADV
ejpam-6951	12	8	h	h	PROPN
ejpam-6951	12	9	is	be	AUX
ejpam-6951	12	10	called	call	VERB
ejpam-6951	12	11	a	a	DET
ejpam-6951	12	12	vertex	vertex	NOUN
ejpam-6951	12	13	-	-	PUNCT
ejpam-6951	12	14	generator	generator	NOUN
ejpam-6951	12	15	subgraph	subgraph	NOUN
ejpam-6951	12	16	of	of	ADP
ejpam-6951	12	17	g.	g.	PROPN
ejpam-6951	12	18	this	this	DET
ejpam-6951	12	19	study	study	NOUN
ejpam-6951	12	20	determines	determine	VERB
ejpam-6951	12	21	some	some	DET
ejpam-6951	12	22	vertex	vertex	NOUN
ejpam-6951	12	23	-	-	PUNCT
ejpam-6951	12	24	generator	generator	NOUN
ejpam-6951	12	25	subgraphs	subgraph	NOUN
ejpam-6951	12	26	of	of	ADP
ejpam-6951	12	27	complete	complete	ADJ
ejpam-6951	12	28	bipartite	bipartite	PROPN
ejpam-6951	12	29	graph	graph	NOUN
ejpam-6951	12	30	km	km	PROPN
ejpam-6951	12	31	,	,	PUNCT
ejpam-6951	12	32	n	n	NOUN
ejpam-6951	12	33	and	and	CCONJ
ejpam-6951	12	34	tadpole	tadpole	PROPN
ejpam-6951	12	35	graph	graph	PROPN
ejpam-6951	12	36	tn	tn	PROPN
ejpam-6951	12	37	,	,	PUNCT
ejpam-6951	12	38	m.	m.	NOUN
ejpam-6951	12	39	2020	2020	NUM
ejpam-6951	12	40	mathematics	mathematics	PROPN
ejpam-6951	12	41	subject	subject	NOUN
ejpam-6951	12	42	classifications	classification	NOUN
ejpam-6951	12	43	:	:	PUNCT
ejpam-6951	12	44	05c50	05c50	NUM
ejpam-6951	12	45	key	key	ADJ
ejpam-6951	12	46	words	word	NOUN
ejpam-6951	12	47	and	and	CCONJ
ejpam-6951	12	48	phrases	phrase	NOUN
ejpam-6951	12	49	:	:	PUNCT
ejpam-6951	12	50	vertex	vertex	NOUN
ejpam-6951	12	51	space	space	NOUN
ejpam-6951	12	52	,	,	PUNCT
ejpam-6951	12	53	induced	induced	ADJ
ejpam-6951	12	54	subgraph	subgraph	NOUN
ejpam-6951	12	55	,	,	PUNCT
ejpam-6951	12	56	vertex	vertex	NOUN
ejpam-6951	12	57	-	-	PUNCT
ejpam-6951	12	58	uniform	uniform	NOUN
ejpam-6951	12	59	set	set	NOUN
ejpam-6951	12	60	,	,	PUNCT
ejpam-6951	12	61	generating	generate	VERB
ejpam-6951	12	62	set	set	NOUN
ejpam-6951	12	63	,	,	PUNCT
ejpam-6951	12	64	vertex	vertex	NOUN
ejpam-6951	12	65	-	-	PUNCT
ejpam-6951	12	66	generator	generator	NOUN
ejpam-6951	12	67	subgraph	subgraph	NOUN
ejpam-6951	12	68	1	1	NUM
ejpam-6951	12	69	.	.	PUNCT
ejpam-6951	12	70	introduction	introduction	NOUN
ejpam-6951	12	71	graph	graph	NOUN
ejpam-6951	12	72	theory	theory	NOUN
ejpam-6951	12	73	,	,	PUNCT
ejpam-6951	12	74	a	a	DET
ejpam-6951	12	75	fundamental	fundamental	ADJ
ejpam-6951	12	76	area	area	NOUN
ejpam-6951	12	77	of	of	ADP
ejpam-6951	12	78	mathematics	mathematic	NOUN
ejpam-6951	12	79	concerned	concern	VERB
ejpam-6951	12	80	with	with	ADP
ejpam-6951	12	81	the	the	DET
ejpam-6951	12	82	study	study	NOUN
ejpam-6951	12	83	of	of	ADP
ejpam-6951	12	84	relationships	relationship	NOUN
ejpam-6951	12	85	through	through	ADP
ejpam-6951	12	86	networks	network	NOUN
ejpam-6951	12	87	,	,	PUNCT
ejpam-6951	12	88	has	have	AUX
ejpam-6951	12	89	evolved	evolve	VERB
ejpam-6951	12	90	into	into	ADP
ejpam-6951	12	91	a	a	DET
ejpam-6951	12	92	vital	vital	ADJ
ejpam-6951	12	93	tool	tool	NOUN
ejpam-6951	12	94	across	across	ADP
ejpam-6951	12	95	numerous	numerous	ADJ
ejpam-6951	12	96	scientific	scientific	ADJ
ejpam-6951	12	97	and	and	CCONJ
ejpam-6951	12	98	technological	technological	ADJ
ejpam-6951	12	99	disciplines	discipline	NOUN
ejpam-6951	12	100	.	.	PUNCT
ejpam-6951	13	1	its	its	PRON
ejpam-6951	13	2	capacity	capacity	NOUN
ejpam-6951	13	3	to	to	PART
ejpam-6951	13	4	model	model	VERB
ejpam-6951	13	5	complex	complex	ADJ
ejpam-6951	13	6	systems	system	NOUN
ejpam-6951	13	7	has	have	AUX
ejpam-6951	13	8	led	lead	VERB
ejpam-6951	13	9	to	to	ADP
ejpam-6951	13	10	significant	significant	ADJ
ejpam-6951	13	11	advancements	advancement	NOUN
ejpam-6951	13	12	in	in	ADP
ejpam-6951	13	13	fields	field	NOUN
ejpam-6951	13	14	ranging	range	VERB
ejpam-6951	13	15	from	from	ADP
ejpam-6951	13	16	computer	computer	NOUN
ejpam-6951	13	17	science	science	NOUN
ejpam-6951	13	18	to	to	ADP
ejpam-6951	13	19	social	social	ADJ
ejpam-6951	13	20	network	network	NOUN
ejpam-6951	13	21	analysis	analysis	NOUN
ejpam-6951	13	22	.	.	PUNCT
ejpam-6951	14	1	the	the	DET
ejpam-6951	14	2	integration	integration	NOUN
ejpam-6951	14	3	of	of	ADP
ejpam-6951	14	4	algebraic	algebraic	ADJ
ejpam-6951	14	5	structures	structure	NOUN
ejpam-6951	14	6	has	have	AUX
ejpam-6951	14	7	significantly	significantly	ADV
ejpam-6951	14	8	broadened	broaden	VERB
ejpam-6951	14	9	the	the	DET
ejpam-6951	14	10	scope	scope	NOUN
ejpam-6951	14	11	of	of	ADP
ejpam-6951	14	12	graph	graph	NOUN
ejpam-6951	14	13	theory	theory	NOUN
ejpam-6951	14	14	.	.	PUNCT
ejpam-6951	15	1	a	a	DET
ejpam-6951	15	2	key	key	ADJ
ejpam-6951	15	3	development	development	NOUN
ejpam-6951	15	4	in	in	ADP
ejpam-6951	15	5	this	this	DET
ejpam-6951	15	6	direction	direction	NOUN
ejpam-6951	15	7	is	be	AUX
ejpam-6951	15	8	the	the	DET
ejpam-6951	15	9	concept	concept	NOUN
ejpam-6951	15	10	of	of	ADP
ejpam-6951	15	11	vector	vector	NOUN
ejpam-6951	15	12	spaces	space	NOUN
ejpam-6951	15	13	,	,	PUNCT
ejpam-6951	15	14	notably	notably	ADV
ejpam-6951	15	15	edge	edge	VERB
ejpam-6951	15	16	spaces	space	NOUN
ejpam-6951	15	17	and	and	CCONJ
ejpam-6951	15	18	vertex	vertex	NOUN
ejpam-6951	15	19	spaces	space	NOUN
ejpam-6951	15	20	[	[	X
ejpam-6951	15	21	1	1	NUM
ejpam-6951	15	22	]	]	PUNCT
ejpam-6951	15	23	.	.	PUNCT
ejpam-6951	16	1	within	within	ADP
ejpam-6951	16	2	this	this	DET
ejpam-6951	16	3	framework	framework	NOUN
ejpam-6951	16	4	,	,	PUNCT
ejpam-6951	16	5	these	these	DET
ejpam-6951	16	6	spaces	space	NOUN
ejpam-6951	16	7	are	be	AUX
ejpam-6951	16	8	treated	treat	VERB
ejpam-6951	16	9	as	as	ADP
ejpam-6951	16	10	vector	vector	NOUN
ejpam-6951	16	11	∗corresponding	∗corresponde	VERB
ejpam-6951	16	12	author	author	NOUN
ejpam-6951	16	13	.	.	PUNCT
ejpam-6951	17	1	doi	doi	NOUN
ejpam-6951	17	2	:	:	PUNCT
ejpam-6951	17	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6951	https://doi.org/10.29020/nybg.ejpam.v18i4.6951	NOUN
ejpam-6951	17	4	email	email	NOUN
ejpam-6951	17	5	addresses	address	VERB
ejpam-6951	17	6	:	:	PUNCT
ejpam-6951	17	7	21-58341@g.batstate-u.edu.ph	21-58341@g.batstate-u.edu.ph	NUM
ejpam-6951	17	8	(	(	PUNCT
ejpam-6951	17	9	g.	g.	PROPN
ejpam-6951	17	10	d.	d.	PROPN
ejpam-6951	17	11	sepillo	sepillo	PROPN
ejpam-6951	17	12	)	)	PUNCT
ejpam-6951	17	13	,	,	PUNCT
ejpam-6951	17	14	20-59247@g.batstate-u.edu.ph	20-59247@g.batstate-u.edu.ph	NUM
ejpam-6951	17	15	(	(	PUNCT
ejpam-6951	17	16	m.	m.	PROPN
ejpam-6951	17	17	j.	j.	PROPN
ejpam-6951	17	18	valdez	valdez	PROPN
ejpam-6951	17	19	)	)	PUNCT
ejpam-6951	17	20	,	,	PUNCT
ejpam-6951	17	21	15-52878@g.batstate-u.edu.ph	15-52878@g.batstate-u.edu.ph	NUM
ejpam-6951	17	22	(	(	PUNCT
ejpam-6951	17	23	m.	m.	NOUN
ejpam-6951	17	24	y.	y.	PROPN
ejpam-6951	17	25	eyao	eyao	PROPN
ejpam-6951	17	26	)	)	PUNCT
ejpam-6951	17	27	,	,	PUNCT
ejpam-6951	17	28	neil.mame@g.batstate-u.edu.ph	neil.mame@g.batstate-u.edu.ph	PROPN
ejpam-6951	17	29	(	(	PUNCT
ejpam-6951	17	30	n.	n.	PROPN
ejpam-6951	17	31	m.	m.	NOUN
ejpam-6951	17	32	mame	mame	PROPN
ejpam-6951	17	33	)	)	PUNCT
ejpam-6951	17	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6951	18	1	1	1	NUM
ejpam-6951	18	2	copyright	copyright	NOUN
ejpam-6951	18	3	:	:	PUNCT
ejpam-6951	18	4	©	©	PROPN
ejpam-6951	18	5	2025	2025	NUM
ejpam-6951	18	6	the	the	DET
ejpam-6951	18	7	author(s	author(s	NOUN
ejpam-6951	18	8	)	)	PUNCT
ejpam-6951	18	9	.	.	PUNCT
ejpam-6951	19	1	(	(	PUNCT
ejpam-6951	19	2	cc	cc	NOUN
ejpam-6951	19	3	by	by	ADP
ejpam-6951	19	4	-	-	PUNCT
ejpam-6951	19	5	nc	nc	PROPN
ejpam-6951	19	6	4.0	4.0	NUM
ejpam-6951	19	7	)	)	PUNCT
ejpam-6951	19	8	g.	g.	PROPN
ejpam-6951	19	9	d.	d.	PROPN
ejpam-6951	19	10	sepillo	sepillo	PROPN
ejpam-6951	19	11	et	et	PROPN
ejpam-6951	19	12	al	al	PROPN
ejpam-6951	19	13	.	.	PUNCT
ejpam-6951	19	14	/	/	SYM
ejpam-6951	19	15	eur	eur	PROPN
ejpam-6951	19	16	.	.	PUNCT
ejpam-6951	20	1	j.	j.	PROPN
ejpam-6951	20	2	pure	pure	PROPN
ejpam-6951	20	3	appl	appl	PROPN
ejpam-6951	20	4	.	.	PROPN
ejpam-6951	20	5	math	math	PROPN
ejpam-6951	20	6	,	,	PUNCT
ejpam-6951	20	7	18	18	NUM
ejpam-6951	20	8	(	(	PUNCT
ejpam-6951	20	9	4	4	NUM
ejpam-6951	20	10	)	)	PUNCT
ejpam-6951	20	11	(	(	PUNCT
ejpam-6951	20	12	2025	2025	NUM
ejpam-6951	20	13	)	)	PUNCT
ejpam-6951	20	14	,	,	PUNCT
ejpam-6951	20	15	6951	6951	NUM
ejpam-6951	20	16	2	2	NUM
ejpam-6951	20	17	of	of	ADP
ejpam-6951	20	18	23	23	NUM
ejpam-6951	20	19	spaces	space	NOUN
ejpam-6951	20	20	over	over	ADP
ejpam-6951	20	21	the	the	DET
ejpam-6951	20	22	finite	finite	ADJ
ejpam-6951	20	23	field	field	NOUN
ejpam-6951	20	24	z2	z2	NOUN
ejpam-6951	20	25	=	=	SYM
ejpam-6951	20	26	{	{	PUNCT
ejpam-6951	20	27	0	0	NUM
ejpam-6951	20	28	,	,	PUNCT
ejpam-6951	20	29	1	1	NUM
ejpam-6951	20	30	}	}	PUNCT
ejpam-6951	20	31	,	,	PUNCT
ejpam-6951	20	32	with	with	ADP
ejpam-6951	20	33	vector	vector	NOUN
ejpam-6951	20	34	addition	addition	NOUN
ejpam-6951	20	35	defined	define	VERB
ejpam-6951	20	36	as	as	ADP
ejpam-6951	20	37	the	the	DET
ejpam-6951	20	38	symmetric	symmetric	ADJ
ejpam-6951	20	39	difference	difference	NOUN
ejpam-6951	20	40	of	of	ADP
ejpam-6951	20	41	sets	set	NOUN
ejpam-6951	20	42	and	and	CCONJ
ejpam-6951	20	43	scalar	scalar	ADJ
ejpam-6951	20	44	multiplication	multiplication	NOUN
ejpam-6951	20	45	resulting	result	VERB
ejpam-6951	20	46	in	in	ADP
ejpam-6951	20	47	either	either	CCONJ
ejpam-6951	20	48	the	the	DET
ejpam-6951	20	49	empty	empty	ADJ
ejpam-6951	20	50	set	set	NOUN
ejpam-6951	20	51	(	(	PUNCT
ejpam-6951	20	52	multiplication	multiplication	NOUN
ejpam-6951	20	53	by	by	ADP
ejpam-6951	20	54	0	0	NUM
ejpam-6951	20	55	)	)	PUNCT
ejpam-6951	20	56	or	or	CCONJ
ejpam-6951	20	57	the	the	DET
ejpam-6951	20	58	original	original	ADJ
ejpam-6951	20	59	set	set	NOUN
ejpam-6951	20	60	(	(	PUNCT
ejpam-6951	20	61	multiplication	multiplication	NOUN
ejpam-6951	20	62	by	by	ADP
ejpam-6951	20	63	1	1	NUM
ejpam-6951	20	64	)	)	PUNCT
ejpam-6951	20	65	.	.	PUNCT
ejpam-6951	21	1	the	the	DET
ejpam-6951	21	2	only	only	ADJ
ejpam-6951	21	3	difference	difference	NOUN
ejpam-6951	21	4	is	be	AUX
ejpam-6951	21	5	that	that	SCONJ
ejpam-6951	21	6	,	,	PUNCT
ejpam-6951	21	7	the	the	DET
ejpam-6951	21	8	edge	edge	NOUN
ejpam-6951	21	9	spaces	space	NOUN
ejpam-6951	21	10	contains	contain	VERB
ejpam-6951	21	11	all	all	DET
ejpam-6951	21	12	the	the	DET
ejpam-6951	21	13	subsets	subset	NOUN
ejpam-6951	21	14	of	of	ADP
ejpam-6951	21	15	the	the	DET
ejpam-6951	21	16	edge	edge	NOUN
ejpam-6951	21	17	set	set	NOUN
ejpam-6951	21	18	of	of	ADP
ejpam-6951	21	19	that	that	DET
ejpam-6951	21	20	graph	graph	NOUN
ejpam-6951	21	21	,	,	PUNCT
ejpam-6951	21	22	while	while	SCONJ
ejpam-6951	21	23	the	the	DET
ejpam-6951	21	24	vertex	vertex	NOUN
ejpam-6951	21	25	spaces	space	NOUN
ejpam-6951	21	26	contains	contain	VERB
ejpam-6951	21	27	all	all	DET
ejpam-6951	21	28	the	the	DET
ejpam-6951	21	29	subsets	subset	NOUN
ejpam-6951	21	30	of	of	ADP
ejpam-6951	21	31	the	the	DET
ejpam-6951	21	32	vertex	vertex	NOUN
ejpam-6951	21	33	set	set	NOUN
ejpam-6951	21	34	of	of	ADP
ejpam-6951	21	35	that	that	DET
ejpam-6951	21	36	graph	graph	NOUN
ejpam-6951	21	37	.	.	PUNCT
ejpam-6951	22	1	the	the	DET
ejpam-6951	22	2	notion	notion	NOUN
ejpam-6951	22	3	of	of	ADP
ejpam-6951	22	4	vertex	vertex	NOUN
ejpam-6951	22	5	space	space	NOUN
ejpam-6951	22	6	has	have	AUX
ejpam-6951	22	7	been	be	AUX
ejpam-6951	22	8	applied	apply	VERB
ejpam-6951	22	9	in	in	ADP
ejpam-6951	22	10	studies	study	NOUN
ejpam-6951	22	11	such	such	ADJ
ejpam-6951	22	12	as	as	ADP
ejpam-6951	22	13	that	that	PRON
ejpam-6951	22	14	by	by	ADP
ejpam-6951	22	15	butenko	butenko	PROPN
ejpam-6951	22	16	,	,	PUNCT
ejpam-6951	22	17	festa	festa	NOUN
ejpam-6951	22	18	,	,	PUNCT
ejpam-6951	22	19	and	and	CCONJ
ejpam-6951	22	20	pardalos	pardalo	NOUN
ejpam-6951	23	1	[	[	X
ejpam-6951	23	2	2	2	NUM
ejpam-6951	23	3	]	]	PUNCT
ejpam-6951	23	4	,	,	PUNCT
ejpam-6951	23	5	who	who	PRON
ejpam-6951	23	6	utilized	utilize	VERB
ejpam-6951	23	7	it	it	PRON
ejpam-6951	23	8	to	to	PART
ejpam-6951	23	9	analyze	analyze	VERB
ejpam-6951	23	10	colored	colored	ADJ
ejpam-6951	23	11	vertex	vertex	NOUN
ejpam-6951	23	12	sets	set	NOUN
ejpam-6951	23	13	with	with	ADP
ejpam-6951	23	14	adjacency	adjacency	NOUN
ejpam-6951	23	15	and	and	CCONJ
ejpam-6951	23	16	coloring	coloring	NOUN
ejpam-6951	23	17	constraints	constraint	NOUN
ejpam-6951	23	18	.	.	PUNCT
ejpam-6951	24	1	building	build	VERB
ejpam-6951	24	2	on	on	ADP
ejpam-6951	24	3	the	the	DET
ejpam-6951	24	4	concept	concept	NOUN
ejpam-6951	24	5	of	of	ADP
ejpam-6951	24	6	vertex	vertex	NOUN
ejpam-6951	24	7	spaces	space	NOUN
ejpam-6951	24	8	and	and	CCONJ
ejpam-6951	24	9	induced	induced	ADJ
ejpam-6951	24	10	subgraphs	subgraph	NOUN
ejpam-6951	24	11	,	,	PUNCT
ejpam-6951	24	12	torino	torino	NOUN
ejpam-6951	24	13	and	and	CCONJ
ejpam-6951	24	14	mame	mame	PROPN
ejpam-6951	24	15	[	[	X
ejpam-6951	24	16	3	3	X
ejpam-6951	24	17	]	]	PUNCT
ejpam-6951	24	18	introduced	introduce	VERB
ejpam-6951	24	19	the	the	DET
ejpam-6951	24	20	vertex	vertex	NOUN
ejpam-6951	24	21	-	-	PUNCT
ejpam-6951	24	22	generator	generator	NOUN
ejpam-6951	24	23	subgraph	subgraph	NOUN
ejpam-6951	24	24	,	,	PUNCT
ejpam-6951	24	25	a	a	DET
ejpam-6951	24	26	concept	concept	NOUN
ejpam-6951	24	27	parallel	parallel	NOUN
ejpam-6951	24	28	to	to	ADP
ejpam-6951	24	29	the	the	DET
ejpam-6951	24	30	edgegenerator	edgegenerator	NOUN
ejpam-6951	24	31	subgraph	subgraph	NOUN
ejpam-6951	24	32	(	(	PUNCT
ejpam-6951	24	33	or	or	CCONJ
ejpam-6951	24	34	generator	generator	NOUN
ejpam-6951	24	35	subgraph	subgraph	NOUN
ejpam-6951	24	36	)	)	PUNCT
ejpam-6951	24	37	first	first	ADV
ejpam-6951	24	38	explored	explore	VERB
ejpam-6951	24	39	by	by	ADP
ejpam-6951	24	40	gervacio	gervacio	NOUN
ejpam-6951	24	41	[	[	X
ejpam-6951	24	42	4	4	NUM
ejpam-6951	24	43	]	]	PUNCT
ejpam-6951	24	44	;	;	PUNCT
ejpam-6951	24	45	see	see	VERB
ejpam-6951	24	46	also	also	ADV
ejpam-6951	24	47	[	[	X
ejpam-6951	24	48	5	5	NUM
ejpam-6951	24	49	]	]	PUNCT
ejpam-6951	24	50	.	.	PUNCT
ejpam-6951	25	1	a	a	DET
ejpam-6951	25	2	key	key	ADJ
ejpam-6951	25	3	difference	difference	NOUN
ejpam-6951	25	4	is	be	AUX
ejpam-6951	25	5	that	that	SCONJ
ejpam-6951	25	6	vertex	vertex	NOUN
ejpam-6951	25	7	-	-	PUNCT
ejpam-6951	25	8	generator	generator	NOUN
ejpam-6951	25	9	subgraphs	subgraph	NOUN
ejpam-6951	25	10	can	can	AUX
ejpam-6951	25	11	contain	contain	VERB
ejpam-6951	25	12	isolated	isolated	ADJ
ejpam-6951	25	13	vertices	vertex	NOUN
ejpam-6951	25	14	,	,	PUNCT
ejpam-6951	25	15	while	while	SCONJ
ejpam-6951	25	16	generator	generator	NOUN
ejpam-6951	25	17	subgraphs	subgraph	NOUN
ejpam-6951	25	18	do	do	AUX
ejpam-6951	25	19	not	not	PART
ejpam-6951	25	20	allow	allow	VERB
ejpam-6951	25	21	isolated	isolated	ADJ
ejpam-6951	25	22	vertices	vertex	NOUN
ejpam-6951	25	23	.	.	PUNCT
ejpam-6951	26	1	while	while	SCONJ
ejpam-6951	26	2	generator	generator	NOUN
ejpam-6951	26	3	subgraphs	subgraph	NOUN
ejpam-6951	26	4	have	have	AUX
ejpam-6951	26	5	been	be	AUX
ejpam-6951	26	6	studied	study	VERB
ejpam-6951	26	7	for	for	ADP
ejpam-6951	26	8	various	various	ADJ
ejpam-6951	26	9	graph	graph	NOUN
ejpam-6951	26	10	classes	class	NOUN
ejpam-6951	26	11	,	,	PUNCT
ejpam-6951	26	12	research	research	NOUN
ejpam-6951	26	13	on	on	ADP
ejpam-6951	26	14	vertex	vertex	NOUN
ejpam-6951	26	15	-	-	PUNCT
ejpam-6951	26	16	generator	generator	NOUN
ejpam-6951	26	17	subgraphs	subgraphs	NOUN
ejpam-6951	26	18	remains	remain	VERB
ejpam-6951	26	19	less	less	ADV
ejpam-6951	26	20	extensive	extensive	ADJ
ejpam-6951	26	21	,	,	PUNCT
ejpam-6951	26	22	with	with	ADP
ejpam-6951	26	23	torino	torino	NOUN
ejpam-6951	26	24	and	and	CCONJ
ejpam-6951	26	25	mame	mame	PROPN
ejpam-6951	26	26	’s	’s	PART
ejpam-6951	26	27	work	work	NOUN
ejpam-6951	26	28	being	be	AUX
ejpam-6951	26	29	a	a	DET
ejpam-6951	26	30	significant	significant	ADJ
ejpam-6951	26	31	contribution	contribution	NOUN
ejpam-6951	26	32	.	.	PUNCT
ejpam-6951	27	1	a	a	DET
ejpam-6951	27	2	related	relate	VERB
ejpam-6951	27	3	concept	concept	NOUN
ejpam-6951	27	4	,	,	PUNCT
ejpam-6951	27	5	the	the	DET
ejpam-6951	27	6	even	even	ADJ
ejpam-6951	27	7	vertex	vertex	NOUN
ejpam-6951	27	8	space	space	NOUN
ejpam-6951	27	9	(	(	PUNCT
ejpam-6951	27	10	elements	element	NOUN
ejpam-6951	27	11	of	of	ADP
ejpam-6951	27	12	the	the	DET
ejpam-6951	27	13	vertex	vertex	NOUN
ejpam-6951	27	14	space	space	NOUN
ejpam-6951	27	15	with	with	ADP
ejpam-6951	27	16	even	even	ADV
ejpam-6951	27	17	cardinality	cardinality	NOUN
ejpam-6951	27	18	)	)	PUNCT
ejpam-6951	27	19	offers	offer	VERB
ejpam-6951	27	20	another	another	DET
ejpam-6951	27	21	perspective	perspective	NOUN
ejpam-6951	27	22	for	for	ADP
ejpam-6951	27	23	studying	study	VERB
ejpam-6951	27	24	graph	graph	NOUN
ejpam-6951	27	25	structure	structure	NOUN
ejpam-6951	27	26	and	and	CCONJ
ejpam-6951	27	27	identifying	identify	VERB
ejpam-6951	27	28	vertex	vertex	NOUN
ejpam-6951	27	29	-	-	PUNCT
ejpam-6951	27	30	generator	generator	NOUN
ejpam-6951	27	31	subgraphs	subgraph	NOUN
ejpam-6951	27	32	.	.	PUNCT
ejpam-6951	28	1	a	a	DET
ejpam-6951	28	2	graph	graph	NOUN
ejpam-6951	28	3	g	g	NOUN
ejpam-6951	28	4	is	be	AUX
ejpam-6951	28	5	an	an	DET
ejpam-6951	28	6	ordered	order	VERB
ejpam-6951	28	7	pair	pair	NOUN
ejpam-6951	28	8	(	(	PUNCT
ejpam-6951	28	9	v	v	NOUN
ejpam-6951	28	10	(	(	PUNCT
ejpam-6951	28	11	g	g	NOUN
ejpam-6951	28	12	)	)	PUNCT
ejpam-6951	28	13	,	,	PUNCT
ejpam-6951	28	14	e(g	e(g	PROPN
ejpam-6951	28	15	)	)	PUNCT
ejpam-6951	28	16	)	)	PUNCT
ejpam-6951	28	17	,	,	PUNCT
ejpam-6951	28	18	where	where	SCONJ
ejpam-6951	28	19	the	the	DET
ejpam-6951	28	20	vertex	vertex	NOUN
ejpam-6951	28	21	set	set	VERB
ejpam-6951	28	22	v	v	NOUN
ejpam-6951	28	23	(	(	PUNCT
ejpam-6951	28	24	g	g	NOUN
ejpam-6951	28	25	)	)	PUNCT
ejpam-6951	28	26	is	be	AUX
ejpam-6951	28	27	a	a	DET
ejpam-6951	28	28	finite	finite	NOUN
ejpam-6951	28	29	nonempty	nonempty	NOUN
ejpam-6951	28	30	set	set	NOUN
ejpam-6951	28	31	of	of	ADP
ejpam-6951	28	32	objects	object	NOUN
ejpam-6951	28	33	called	call	VERB
ejpam-6951	28	34	vertices	vertex	NOUN
ejpam-6951	28	35	,	,	PUNCT
ejpam-6951	28	36	and	and	CCONJ
ejpam-6951	28	37	the	the	DET
ejpam-6951	28	38	edge	edge	NOUN
ejpam-6951	28	39	set	set	VERB
ejpam-6951	28	40	e(g	e(g	PROPN
ejpam-6951	28	41	)	)	PUNCT
ejpam-6951	28	42	is	be	AUX
ejpam-6951	28	43	a	a	DET
ejpam-6951	28	44	set	set	NOUN
ejpam-6951	28	45	of	of	ADP
ejpam-6951	28	46	unordered	unordered	ADJ
ejpam-6951	28	47	pairs	pair	NOUN
ejpam-6951	28	48	of	of	ADP
ejpam-6951	28	49	vertices	vertex	NOUN
ejpam-6951	28	50	called	call	VERB
ejpam-6951	28	51	edges	edge	NOUN
ejpam-6951	28	52	.	.	PUNCT
ejpam-6951	29	1	the	the	DET
ejpam-6951	29	2	order	order	NOUN
ejpam-6951	29	3	n	n	NOUN
ejpam-6951	29	4	of	of	ADP
ejpam-6951	29	5	g	g	PROPN
ejpam-6951	29	6	is	be	AUX
ejpam-6951	29	7	the	the	DET
ejpam-6951	29	8	number	number	NOUN
ejpam-6951	29	9	of	of	ADP
ejpam-6951	29	10	elements	element	NOUN
ejpam-6951	29	11	of	of	ADP
ejpam-6951	29	12	v	v	NOUN
ejpam-6951	29	13	(	(	PUNCT
ejpam-6951	29	14	g	g	NOUN
ejpam-6951	29	15	)	)	PUNCT
ejpam-6951	29	16	,	,	PUNCT
ejpam-6951	29	17	and	and	CCONJ
ejpam-6951	29	18	the	the	DET
ejpam-6951	29	19	size	size	NOUN
ejpam-6951	29	20	m	m	PROPN
ejpam-6951	29	21	of	of	ADP
ejpam-6951	29	22	g	g	PROPN
ejpam-6951	29	23	is	be	AUX
ejpam-6951	29	24	the	the	DET
ejpam-6951	29	25	number	number	NOUN
ejpam-6951	29	26	of	of	ADP
ejpam-6951	29	27	elements	element	NOUN
ejpam-6951	29	28	of	of	ADP
ejpam-6951	29	29	e(g	e(g	NOUN
ejpam-6951	29	30	)	)	PUNCT
ejpam-6951	29	31	.	.	PUNCT
ejpam-6951	30	1	let	let	VERB
ejpam-6951	30	2	h	h	NOUN
ejpam-6951	30	3	=	=	PUNCT
ejpam-6951	30	4	(	(	PUNCT
ejpam-6951	30	5	v	v	NOUN
ejpam-6951	30	6	(	(	PUNCT
ejpam-6951	30	7	h	h	NOUN
ejpam-6951	30	8	)	)	PUNCT
ejpam-6951	30	9	,	,	PUNCT
ejpam-6951	30	10	e(h	e(h	PROPN
ejpam-6951	30	11	)	)	PUNCT
ejpam-6951	30	12	)	)	PUNCT
ejpam-6951	30	13	be	be	AUX
ejpam-6951	30	14	another	another	DET
ejpam-6951	30	15	graph	graph	NOUN
ejpam-6951	30	16	.	.	PUNCT
ejpam-6951	31	1	a	a	DET
ejpam-6951	31	2	mapping	mapping	NOUN
ejpam-6951	31	3	ϕ	ϕ	NOUN
ejpam-6951	31	4	:	:	PUNCT
ejpam-6951	31	5	v	v	X
ejpam-6951	31	6	(	(	PUNCT
ejpam-6951	31	7	g	g	NOUN
ejpam-6951	31	8	)	)	PUNCT
ejpam-6951	31	9	7→	7→	NUM
ejpam-6951	31	10	v	v	NOUN
ejpam-6951	31	11	(	(	PUNCT
ejpam-6951	31	12	h	h	NOUN
ejpam-6951	31	13	)	)	PUNCT
ejpam-6951	31	14	is	be	AUX
ejpam-6951	31	15	called	call	VERB
ejpam-6951	31	16	a	a	DET
ejpam-6951	31	17	graph	graph	NOUN
ejpam-6951	31	18	isomorphism	isomorphism	NOUN
ejpam-6951	31	19	if	if	SCONJ
ejpam-6951	31	20	the	the	DET
ejpam-6951	31	21	following	follow	VERB
ejpam-6951	31	22	conditions	condition	NOUN
ejpam-6951	31	23	are	be	AUX
ejpam-6951	31	24	satisfied	satisfied	ADJ
ejpam-6951	31	25	:	:	PUNCT
ejpam-6951	31	26	(	(	PUNCT
ejpam-6951	31	27	i	i	NOUN
ejpam-6951	31	28	)	)	PUNCT
ejpam-6951	31	29	ϕ	ϕ	PROPN
ejpam-6951	31	30	is	be	AUX
ejpam-6951	31	31	bijective	bijective	ADJ
ejpam-6951	31	32	;	;	PUNCT
ejpam-6951	31	33	(	(	PUNCT
ejpam-6951	31	34	ii	ii	NOUN
ejpam-6951	31	35	)	)	PUNCT
ejpam-6951	32	1	[	[	X
ejpam-6951	32	2	a	a	PRON
ejpam-6951	32	3	,	,	PUNCT
ejpam-6951	32	4	b	b	X
ejpam-6951	32	5	]	]	X
ejpam-6951	32	6	∈	∈	PROPN
ejpam-6951	32	7	e(g	e(g	PROPN
ejpam-6951	32	8	)	)	PUNCT
ejpam-6951	32	9	implies	imply	VERB
ejpam-6951	32	10	that	that	SCONJ
ejpam-6951	32	11	[	[	X
ejpam-6951	32	12	ϕ(a	ϕ(a	NOUN
ejpam-6951	32	13	)	)	PUNCT
ejpam-6951	32	14	,	,	PUNCT
ejpam-6951	32	15	ϕ(b	ϕ(b	PROPN
ejpam-6951	32	16	)	)	PUNCT
ejpam-6951	32	17	]	]	PUNCT
ejpam-6951	33	1	∈	∈	PROPN
ejpam-6951	33	2	e(h	e(h	PROPN
ejpam-6951	33	3	)	)	PUNCT
ejpam-6951	33	4	;	;	PUNCT
ejpam-6951	33	5	and	and	CCONJ
ejpam-6951	33	6	(	(	PUNCT
ejpam-6951	33	7	iii	iii	X
ejpam-6951	33	8	)	)	PUNCT
ejpam-6951	34	1	[	[	X
ejpam-6951	34	2	c	c	X
ejpam-6951	34	3	,	,	PUNCT
ejpam-6951	34	4	d	d	X
ejpam-6951	34	5	]	]	X
ejpam-6951	34	6	∈	∈	PROPN
ejpam-6951	34	7	e(h	e(h	PROPN
ejpam-6951	34	8	)	)	PUNCT
ejpam-6951	34	9	implies	imply	VERB
ejpam-6951	34	10	that	that	SCONJ
ejpam-6951	35	1	[	[	X
ejpam-6951	35	2	ϕ−1(c	ϕ−1(c	NOUN
ejpam-6951	35	3	)	)	PUNCT
ejpam-6951	35	4	,	,	PUNCT
ejpam-6951	35	5	ϕ−1(d	ϕ−1(d	PROPN
ejpam-6951	35	6	)	)	PUNCT
ejpam-6951	35	7	]	]	PUNCT
ejpam-6951	36	1	∈	∈	PROPN
ejpam-6951	36	2	e(g	e(g	PROPN
ejpam-6951	36	3	)	)	PUNCT
ejpam-6951	36	4	.	.	PUNCT
ejpam-6951	37	1	a	a	DET
ejpam-6951	37	2	graph	graph	NOUN
ejpam-6951	37	3	g	g	NOUN
ejpam-6951	37	4	is	be	AUX
ejpam-6951	37	5	isomorphic	isomorphic	ADJ
ejpam-6951	37	6	to	to	ADP
ejpam-6951	37	7	a	a	DET
ejpam-6951	37	8	graph	graph	NOUN
ejpam-6951	37	9	h	h	NOUN
ejpam-6951	37	10	,	,	PUNCT
ejpam-6951	37	11	denoted	denote	VERB
ejpam-6951	37	12	as	as	ADP
ejpam-6951	37	13	g	g	PROPN
ejpam-6951	37	14	≃	≃	ADJ
ejpam-6951	37	15	h	h	NOUN
ejpam-6951	37	16	,	,	PUNCT
ejpam-6951	37	17	if	if	SCONJ
ejpam-6951	37	18	there	there	PRON
ejpam-6951	37	19	is	be	VERB
ejpam-6951	37	20	an	an	DET
ejpam-6951	37	21	isomorphism	isomorphism	NOUN
ejpam-6951	37	22	ϕ	ϕ	NOUN
ejpam-6951	37	23	:	:	PUNCT
ejpam-6951	37	24	v	v	NOUN
ejpam-6951	37	25	(	(	PUNCT
ejpam-6951	37	26	g	g	NOUN
ejpam-6951	37	27	)	)	PUNCT
ejpam-6951	37	28	7→	7→	NUM
ejpam-6951	37	29	v	v	NOUN
ejpam-6951	37	30	(	(	PUNCT
ejpam-6951	37	31	h	h	NOUN
ejpam-6951	37	32	)	)	PUNCT
ejpam-6951	37	33	between	between	ADP
ejpam-6951	37	34	their	their	PRON
ejpam-6951	37	35	vertex	vertex	NOUN
ejpam-6951	37	36	sets	set	NOUN
ejpam-6951	37	37	.	.	PUNCT
ejpam-6951	38	1	a	a	DET
ejpam-6951	38	2	graph	graph	NOUN
ejpam-6951	38	3	h	h	NOUN
ejpam-6951	38	4	is	be	AUX
ejpam-6951	38	5	a	a	DET
ejpam-6951	38	6	subgraph	subgraph	NOUN
ejpam-6951	38	7	of	of	ADP
ejpam-6951	38	8	g	g	NOUN
ejpam-6951	38	9	,	,	PUNCT
ejpam-6951	38	10	denoted	denote	VERB
ejpam-6951	38	11	by	by	ADP
ejpam-6951	38	12	h	h	PROPN
ejpam-6951	38	13	⊆	⊆	NUM
ejpam-6951	38	14	g	g	NOUN
ejpam-6951	38	15	,	,	PUNCT
ejpam-6951	38	16	if	if	SCONJ
ejpam-6951	38	17	v	v	X
ejpam-6951	38	18	(	(	PUNCT
ejpam-6951	38	19	h	h	NOUN
ejpam-6951	38	20	)	)	PUNCT
ejpam-6951	38	21	⊆	⊆	NUM
ejpam-6951	38	22	v	v	NOUN
ejpam-6951	38	23	(	(	PUNCT
ejpam-6951	38	24	g	g	NOUN
ejpam-6951	38	25	)	)	PUNCT
ejpam-6951	38	26	and	and	CCONJ
ejpam-6951	38	27	e(h	e(h	NOUN
ejpam-6951	38	28	)	)	PUNCT
ejpam-6951	38	29	⊆	⊆	NUM
ejpam-6951	38	30	e(g	e(g	PROPN
ejpam-6951	38	31	)	)	PUNCT
ejpam-6951	38	32	.	.	PUNCT
ejpam-6951	39	1	for	for	ADP
ejpam-6951	39	2	a	a	DET
ejpam-6951	39	3	non	non	ADJ
ejpam-6951	39	4	-	-	ADJ
ejpam-6951	39	5	empty	empty	ADJ
ejpam-6951	39	6	subset	subset	NOUN
ejpam-6951	39	7	s	s	NOUN
ejpam-6951	39	8	of	of	ADP
ejpam-6951	39	9	v	v	NOUN
ejpam-6951	39	10	(	(	PUNCT
ejpam-6951	39	11	g	g	NOUN
ejpam-6951	39	12	)	)	PUNCT
ejpam-6951	39	13	,	,	PUNCT
ejpam-6951	39	14	the	the	DET
ejpam-6951	39	15	subgraph	subgraph	NOUN
ejpam-6951	39	16	of	of	ADP
ejpam-6951	39	17	g	g	PROPN
ejpam-6951	39	18	vertex	vertex	NOUN
ejpam-6951	39	19	-	-	PUNCT
ejpam-6951	39	20	induced	induce	VERB
ejpam-6951	39	21	by	by	ADP
ejpam-6951	39	22	s	s	PROPN
ejpam-6951	39	23	,	,	PUNCT
ejpam-6951	39	24	denoted	denote	VERB
ejpam-6951	39	25	by	by	ADP
ejpam-6951	39	26	g⟨s⟩	g⟨s⟩	PROPN
ejpam-6951	39	27	,	,	PUNCT
ejpam-6951	39	28	is	be	AUX
ejpam-6951	39	29	the	the	DET
ejpam-6951	39	30	subgraph	subgraph	NOUN
ejpam-6951	39	31	of	of	ADP
ejpam-6951	39	32	g	g	ADP
ejpam-6951	39	33	whose	whose	DET
ejpam-6951	39	34	vertex	vertex	NOUN
ejpam-6951	39	35	set	set	NOUN
ejpam-6951	39	36	is	be	AUX
ejpam-6951	39	37	v	v	NOUN
ejpam-6951	39	38	(	(	PUNCT
ejpam-6951	39	39	g⟨s⟩	g⟨s⟩	PROPN
ejpam-6951	39	40	)	)	PUNCT
ejpam-6951	39	41	=	=	SYM
ejpam-6951	39	42	s	s	X
ejpam-6951	39	43	and	and	CCONJ
ejpam-6951	39	44	whose	whose	DET
ejpam-6951	39	45	edge	edge	NOUN
ejpam-6951	39	46	set	set	NOUN
ejpam-6951	39	47	is	be	AUX
ejpam-6951	39	48	e(g⟨s⟩	e(g⟨s⟩	NOUN
ejpam-6951	39	49	)	)	PUNCT
ejpam-6951	39	50	=	=	PRON
ejpam-6951	40	1	{	{	PUNCT
ejpam-6951	40	2	[	[	X
ejpam-6951	40	3	x	x	X
ejpam-6951	40	4	,	,	PUNCT
ejpam-6951	40	5	y	y	PROPN
ejpam-6951	40	6	]	]	X
ejpam-6951	40	7	∈	∈	PROPN
ejpam-6951	40	8	e(g	e(g	PROPN
ejpam-6951	40	9	)	)	PUNCT
ejpam-6951	41	1	|	|	ADV
ejpam-6951	41	2	x	x	X
ejpam-6951	41	3	,	,	PUNCT
ejpam-6951	41	4	y	y	PROPN
ejpam-6951	41	5	∈	∈	PROPN
ejpam-6951	41	6	s	s	PART
ejpam-6951	41	7	}	}	PUNCT
ejpam-6951	41	8	.	.	PUNCT
ejpam-6951	42	1	a	a	DET
ejpam-6951	42	2	subgraph	subgraph	NOUN
ejpam-6951	42	3	h	h	NOUN
ejpam-6951	42	4	of	of	ADP
ejpam-6951	42	5	g	g	PROPN
ejpam-6951	42	6	is	be	AUX
ejpam-6951	42	7	called	call	VERB
ejpam-6951	42	8	a	a	DET
ejpam-6951	42	9	vertex	vertex	NOUN
ejpam-6951	42	10	-	-	PUNCT
ejpam-6951	42	11	induced	induce	VERB
ejpam-6951	42	12	subgraph	subgraph	NOUN
ejpam-6951	42	13	or	or	CCONJ
ejpam-6951	42	14	simply	simply	ADV
ejpam-6951	42	15	induced	induce	VERB
ejpam-6951	42	16	subgraph	subgraph	NOUN
ejpam-6951	42	17	,	,	PUNCT
ejpam-6951	42	18	if	if	SCONJ
ejpam-6951	42	19	there	there	PRON
ejpam-6951	42	20	exists	exist	VERB
ejpam-6951	42	21	a	a	DET
ejpam-6951	42	22	non	non	ADJ
ejpam-6951	42	23	-	-	ADJ
ejpam-6951	42	24	empty	empty	ADJ
ejpam-6951	42	25	subset	subset	NOUN
ejpam-6951	42	26	s	s	VERB
ejpam-6951	42	27	⊆	⊆	NUM
ejpam-6951	42	28	v	v	NOUN
ejpam-6951	42	29	(	(	PUNCT
ejpam-6951	42	30	g	g	NOUN
ejpam-6951	42	31	)	)	PUNCT
ejpam-6951	42	32	such	such	ADJ
ejpam-6951	42	33	that	that	DET
ejpam-6951	42	34	h	h	NOUN
ejpam-6951	42	35	=	=	SYM
ejpam-6951	42	36	g⟨s⟩.	g⟨s⟩.	ADJ
ejpam-6951	42	37	torino	torino	NOUN
ejpam-6951	42	38	and	and	CCONJ
ejpam-6951	42	39	mame	mame	PROPN
ejpam-6951	42	40	’s	’s	PART
ejpam-6951	42	41	work	work	NOUN
ejpam-6951	43	1	[	[	X
ejpam-6951	43	2	3	3	X
ejpam-6951	43	3	]	]	PUNCT
ejpam-6951	43	4	primarily	primarily	ADV
ejpam-6951	43	5	focused	focus	VERB
ejpam-6951	43	6	on	on	ADP
ejpam-6951	43	7	characterizing	characterize	VERB
ejpam-6951	43	8	vertex	vertex	NOUN
ejpam-6951	43	9	-	-	PUNCT
ejpam-6951	43	10	generator	generator	NOUN
ejpam-6951	43	11	subgraphs	subgraph	NOUN
ejpam-6951	43	12	for	for	ADP
ejpam-6951	43	13	several	several	ADJ
ejpam-6951	43	14	well	well	ADV
ejpam-6951	43	15	-	-	PUNCT
ejpam-6951	43	16	known	know	VERB
ejpam-6951	43	17	graph	graph	NOUN
ejpam-6951	43	18	classes	class	NOUN
ejpam-6951	43	19	,	,	PUNCT
ejpam-6951	43	20	including	include	VERB
ejpam-6951	43	21	path	path	NOUN
ejpam-6951	43	22	graphs	graph	NOUN
ejpam-6951	43	23	,	,	PUNCT
ejpam-6951	43	24	cycle	cycle	NOUN
ejpam-6951	43	25	graphs	graph	NOUN
ejpam-6951	43	26	,	,	PUNCT
ejpam-6951	43	27	empty	empty	ADJ
ejpam-6951	43	28	graphs	graph	NOUN
ejpam-6951	43	29	,	,	PUNCT
ejpam-6951	43	30	complete	complete	ADJ
ejpam-6951	43	31	graphs	graph	NOUN
ejpam-6951	43	32	,	,	PUNCT
ejpam-6951	43	33	star	star	NOUN
ejpam-6951	43	34	graphs	graph	NOUN
ejpam-6951	43	35	,	,	PUNCT
ejpam-6951	43	36	and	and	CCONJ
ejpam-6951	43	37	wheel	wheel	NOUN
ejpam-6951	43	38	graphs	graph	NOUN
ejpam-6951	43	39	.	.	PUNCT
ejpam-6951	44	1	however	however	ADV
ejpam-6951	44	2	,	,	PUNCT
ejpam-6951	44	3	the	the	DET
ejpam-6951	44	4	study	study	NOUN
ejpam-6951	44	5	of	of	ADP
ejpam-6951	44	6	vertexgenerator	vertexgenerator	NOUN
ejpam-6951	44	7	subgraphs	subgraph	NOUN
ejpam-6951	44	8	in	in	ADP
ejpam-6951	44	9	other	other	ADJ
ejpam-6951	44	10	graph	graph	NOUN
ejpam-6951	44	11	classes	class	NOUN
ejpam-6951	44	12	,	,	PUNCT
ejpam-6951	44	13	such	such	ADJ
ejpam-6951	44	14	as	as	ADP
ejpam-6951	44	15	complete	complete	ADJ
ejpam-6951	44	16	bipartite	bipartite	NOUN
ejpam-6951	44	17	graphs	graph	NOUN
ejpam-6951	44	18	and	and	CCONJ
ejpam-6951	44	19	tadpole	tadpole	NOUN
ejpam-6951	44	20	graphs	graph	NOUN
ejpam-6951	44	21	,	,	PUNCT
ejpam-6951	44	22	remains	remain	VERB
ejpam-6951	44	23	an	an	DET
ejpam-6951	44	24	open	open	ADJ
ejpam-6951	44	25	area	area	NOUN
ejpam-6951	44	26	of	of	ADP
ejpam-6951	44	27	research	research	NOUN
ejpam-6951	44	28	.	.	PUNCT
ejpam-6951	45	1	a	a	DET
ejpam-6951	45	2	complete	complete	ADJ
ejpam-6951	45	3	bipartite	bipartite	NOUN
ejpam-6951	45	4	graph	graph	NOUN
ejpam-6951	45	5	km	km	PROPN
ejpam-6951	45	6	,	,	PUNCT
ejpam-6951	45	7	n	n	PRON
ejpam-6951	45	8	is	be	AUX
ejpam-6951	45	9	a	a	DET
ejpam-6951	45	10	graph	graph	NOUN
ejpam-6951	45	11	in	in	ADP
ejpam-6951	45	12	which	which	PRON
ejpam-6951	45	13	v	v	NOUN
ejpam-6951	45	14	(	(	PUNCT
ejpam-6951	45	15	g	g	NOUN
ejpam-6951	45	16	)	)	PUNCT
ejpam-6951	45	17	is	be	AUX
ejpam-6951	45	18	partitioned	partition	VERB
ejpam-6951	45	19	into	into	ADP
ejpam-6951	45	20	subsets	subset	NOUN
ejpam-6951	45	21	u	u	PROPN
ejpam-6951	45	22	and	and	CCONJ
ejpam-6951	45	23	v	v	ADP
ejpam-6951	45	24	called	call	VERB
ejpam-6951	45	25	partite	partite	ADJ
ejpam-6951	45	26	sets	set	NOUN
ejpam-6951	45	27	,	,	PUNCT
ejpam-6951	45	28	where	where	SCONJ
ejpam-6951	45	29	the	the	DET
ejpam-6951	45	30	cardinality	cardinality	NOUN
ejpam-6951	45	31	of	of	ADP
ejpam-6951	45	32	u	u	PROPN
ejpam-6951	45	33	and	and	CCONJ
ejpam-6951	45	34	v	v	NOUN
ejpam-6951	45	35	are	be	AUX
ejpam-6951	45	36	m	m	PRON
ejpam-6951	45	37	and	and	CCONJ
ejpam-6951	45	38	n	n	CCONJ
ejpam-6951	45	39	,	,	PUNCT
ejpam-6951	45	40	respectively	respectively	ADV
ejpam-6951	45	41	,	,	PUNCT
ejpam-6951	45	42	and	and	CCONJ
ejpam-6951	45	43	every	every	DET
ejpam-6951	45	44	vertex	vertex	NOUN
ejpam-6951	45	45	of	of	ADP
ejpam-6951	45	46	u	u	NOUN
ejpam-6951	45	47	is	be	AUX
ejpam-6951	45	48	adjacent	adjacent	ADJ
ejpam-6951	45	49	to	to	ADP
ejpam-6951	45	50	every	every	DET
ejpam-6951	45	51	vertex	vertex	NOUN
ejpam-6951	45	52	of	of	ADP
ejpam-6951	45	53	v	v	NOUN
ejpam-6951	45	54	[	[	X
ejpam-6951	45	55	6	6	NUM
ejpam-6951	45	56	]	]	PUNCT
ejpam-6951	45	57	.	.	PUNCT
ejpam-6951	46	1	a	a	DET
ejpam-6951	46	2	tadpole	tadpole	PROPN
ejpam-6951	46	3	graph	graph	NOUN
ejpam-6951	46	4	tn	tn	PROPN
ejpam-6951	46	5	,	,	PUNCT
ejpam-6951	46	6	m	m	VERB
ejpam-6951	46	7	is	be	AUX
ejpam-6951	46	8	the	the	DET
ejpam-6951	46	9	graph	graph	NOUN
ejpam-6951	46	10	obtained	obtain	VERB
ejpam-6951	46	11	by	by	ADP
ejpam-6951	46	12	joining	join	VERB
ejpam-6951	46	13	a	a	DET
ejpam-6951	46	14	cycle	cycle	NOUN
ejpam-6951	46	15	cn	cn	NOUN
ejpam-6951	46	16	to	to	ADP
ejpam-6951	46	17	a	a	DET
ejpam-6951	46	18	path	path	NOUN
ejpam-6951	46	19	pm	pm	NOUN
ejpam-6951	46	20	,	,	PUNCT
ejpam-6951	46	21	with	with	ADP
ejpam-6951	46	22	a	a	DET
ejpam-6951	46	23	bridge	bridge	NOUN
ejpam-6951	46	24	[	[	X
ejpam-6951	46	25	x	x	X
ejpam-6951	46	26	,	,	PUNCT
ejpam-6951	46	27	y	y	PROPN
ejpam-6951	46	28	]	]	X
ejpam-6951	46	29	,	,	PUNCT
ejpam-6951	46	30	where	where	SCONJ
ejpam-6951	46	31	x	x	PUNCT
ejpam-6951	46	32	∈	∈	PROPN
ejpam-6951	46	33	v	v	X
ejpam-6951	46	34	(	(	PUNCT
ejpam-6951	46	35	cn	cn	PROPN
ejpam-6951	46	36	)	)	PUNCT
ejpam-6951	46	37	and	and	CCONJ
ejpam-6951	46	38	y	y	PROPN
ejpam-6951	46	39	∈	∈	PROPN
ejpam-6951	46	40	v	v	X
ejpam-6951	46	41	(	(	PUNCT
ejpam-6951	46	42	pm	pm	NOUN
ejpam-6951	46	43	)	)	PUNCT
ejpam-6951	46	44	and	and	CCONJ
ejpam-6951	46	45	degpm	degpm	NOUN
ejpam-6951	46	46	(	(	PUNCT
ejpam-6951	46	47	y	y	NOUN
ejpam-6951	46	48	)	)	PUNCT
ejpam-6951	46	49	is	be	AUX
ejpam-6951	46	50	either	either	CCONJ
ejpam-6951	46	51	0	0	NUM
ejpam-6951	46	52	or	or	CCONJ
ejpam-6951	46	53	1	1	NUM
ejpam-6951	46	54	[	[	X
ejpam-6951	46	55	7	7	NUM
ejpam-6951	46	56	]	]	PUNCT
ejpam-6951	46	57	.	.	PUNCT
ejpam-6951	47	1	other	other	ADJ
ejpam-6951	47	2	graph	graph	NOUN
ejpam-6951	47	3	classes	class	NOUN
ejpam-6951	47	4	that	that	PRON
ejpam-6951	47	5	have	have	AUX
ejpam-6951	47	6	been	be	AUX
ejpam-6951	47	7	identified	identify	VERB
ejpam-6951	47	8	as	as	ADP
ejpam-6951	47	9	vertex	vertex	NOUN
ejpam-6951	47	10	-	-	PUNCT
ejpam-6951	47	11	generator	generator	NOUN
ejpam-6951	47	12	subgraphs	subgraph	NOUN
ejpam-6951	47	13	of	of	ADP
ejpam-6951	47	14	tadpole	tadpole	NOUN
ejpam-6951	47	15	and	and	CCONJ
ejpam-6951	47	16	complete	complete	ADJ
ejpam-6951	47	17	bipartite	bipartite	NOUN
ejpam-6951	47	18	graphs	graph	NOUN
ejpam-6951	47	19	are	be	AUX
ejpam-6951	47	20	defined	define	VERB
ejpam-6951	47	21	in	in	ADP
ejpam-6951	47	22	the	the	DET
ejpam-6951	47	23	pertinent	pertinent	ADJ
ejpam-6951	47	24	part	part	NOUN
ejpam-6951	47	25	of	of	ADP
ejpam-6951	47	26	this	this	DET
ejpam-6951	47	27	work	work	NOUN
ejpam-6951	47	28	.	.	PUNCT
ejpam-6951	48	1	readers	reader	NOUN
ejpam-6951	48	2	may	may	AUX
ejpam-6951	48	3	refer	refer	VERB
ejpam-6951	48	4	to	to	ADP
ejpam-6951	48	5	the	the	DET
ejpam-6951	48	6	books	book	NOUN
ejpam-6951	48	7	written	write	VERB
ejpam-6951	48	8	by	by	ADP
ejpam-6951	48	9	bollobás	bollobás	NOUN
ejpam-6951	48	10	[	[	NOUN
ejpam-6951	48	11	8	8	NUM
ejpam-6951	48	12	]	]	PUNCT
ejpam-6951	48	13	,	,	PUNCT
ejpam-6951	48	14	bondy	bondy	NOUN
ejpam-6951	48	15	and	and	CCONJ
ejpam-6951	48	16	murty	murty	NOUN
ejpam-6951	49	1	[	[	X
ejpam-6951	49	2	9	9	NUM
ejpam-6951	49	3	]	]	PUNCT
ejpam-6951	49	4	,	,	PUNCT
ejpam-6951	49	5	chartrand	chartrand	PROPN
ejpam-6951	49	6	,	,	PUNCT
ejpam-6951	49	7	lesniak	lesniak	PROPN
ejpam-6951	49	8	and	and	CCONJ
ejpam-6951	49	9	zhang	zhang	PROPN
ejpam-6951	50	1	[	[	X
ejpam-6951	50	2	10	10	NUM
ejpam-6951	50	3	]	]	PUNCT
ejpam-6951	50	4	,	,	PUNCT
ejpam-6951	50	5	and	and	CCONJ
ejpam-6951	50	6	harary	harary	NOUN
ejpam-6951	51	1	[	[	X
ejpam-6951	51	2	6	6	NUM
ejpam-6951	51	3	]	]	PUNCT
ejpam-6951	51	4	,	,	PUNCT
ejpam-6951	51	5	for	for	ADP
ejpam-6951	51	6	other	other	ADJ
ejpam-6951	51	7	basic	basic	ADJ
ejpam-6951	51	8	g.	g.	PROPN
ejpam-6951	51	9	d.	d.	PROPN
ejpam-6951	51	10	sepillo	sepillo	PROPN
ejpam-6951	51	11	et	et	PROPN
ejpam-6951	51	12	al	al	PROPN
ejpam-6951	51	13	.	.	PUNCT
ejpam-6951	51	14	/	/	SYM
ejpam-6951	51	15	eur	eur	PROPN
ejpam-6951	51	16	.	.	PUNCT
ejpam-6951	52	1	j.	j.	PROPN
ejpam-6951	52	2	pure	pure	PROPN
ejpam-6951	52	3	appl	appl	PROPN
ejpam-6951	52	4	.	.	PROPN
ejpam-6951	52	5	math	math	PROPN
ejpam-6951	52	6	,	,	PUNCT
ejpam-6951	52	7	18	18	NUM
ejpam-6951	52	8	(	(	PUNCT
ejpam-6951	52	9	4	4	NUM
ejpam-6951	52	10	)	)	PUNCT
ejpam-6951	52	11	(	(	PUNCT
ejpam-6951	52	12	2025	2025	NUM
ejpam-6951	52	13	)	)	PUNCT
ejpam-6951	52	14	,	,	PUNCT
ejpam-6951	52	15	6951	6951	NUM
ejpam-6951	52	16	3	3	NUM
ejpam-6951	52	17	of	of	ADP
ejpam-6951	52	18	23	23	NUM
ejpam-6951	52	19	concepts	concept	NOUN
ejpam-6951	52	20	in	in	ADP
ejpam-6951	52	21	graph	graph	NOUN
ejpam-6951	52	22	theory	theory	NOUN
ejpam-6951	52	23	.	.	PUNCT
ejpam-6951	53	1	also	also	ADV
ejpam-6951	53	2	,	,	PUNCT
ejpam-6951	53	3	readers	reader	NOUN
ejpam-6951	53	4	may	may	AUX
ejpam-6951	53	5	refer	refer	VERB
ejpam-6951	53	6	to	to	ADP
ejpam-6951	53	7	the	the	DET
ejpam-6951	53	8	books	book	NOUN
ejpam-6951	53	9	written	write	VERB
ejpam-6951	53	10	by	by	ADP
ejpam-6951	53	11	nering	nere	VERB
ejpam-6951	53	12	[	[	X
ejpam-6951	53	13	11	11	NUM
ejpam-6951	53	14	]	]	PUNCT
ejpam-6951	53	15	,	,	PUNCT
ejpam-6951	53	16	and	and	CCONJ
ejpam-6951	53	17	larson	larson	PROPN
ejpam-6951	53	18	and	and	CCONJ
ejpam-6951	53	19	falvo	falvo	NOUN
ejpam-6951	54	1	[	[	X
ejpam-6951	54	2	12	12	NUM
ejpam-6951	54	3	]	]	PUNCT
ejpam-6951	54	4	,	,	PUNCT
ejpam-6951	54	5	for	for	ADP
ejpam-6951	54	6	the	the	DET
ejpam-6951	54	7	linear	linear	ADJ
ejpam-6951	54	8	algebra	algebra	PROPN
ejpam-6951	54	9	concepts	concept	NOUN
ejpam-6951	54	10	,	,	PUNCT
ejpam-6951	54	11	particularly	particularly	ADV
ejpam-6951	54	12	the	the	DET
ejpam-6951	54	13	vector	vector	NOUN
ejpam-6951	54	14	spaces	space	VERB
ejpam-6951	54	15	.	.	PUNCT
ejpam-6951	55	1	the	the	DET
ejpam-6951	55	2	objective	objective	NOUN
ejpam-6951	55	3	of	of	ADP
ejpam-6951	55	4	this	this	DET
ejpam-6951	55	5	research	research	NOUN
ejpam-6951	55	6	is	be	AUX
ejpam-6951	55	7	to	to	PART
ejpam-6951	55	8	determine	determine	VERB
ejpam-6951	55	9	some	some	DET
ejpam-6951	55	10	vertex	vertex	NOUN
ejpam-6951	55	11	-	-	PUNCT
ejpam-6951	55	12	generator	generator	NOUN
ejpam-6951	55	13	subgraphs	subgraph	NOUN
ejpam-6951	55	14	of	of	ADP
ejpam-6951	55	15	complete	complete	ADJ
ejpam-6951	55	16	bipartite	bipartite	PROPN
ejpam-6951	55	17	and	and	CCONJ
ejpam-6951	55	18	tadpole	tadpole	NOUN
ejpam-6951	55	19	graphs	graph	NOUN
ejpam-6951	55	20	.	.	PUNCT
ejpam-6951	56	1	the	the	DET
ejpam-6951	56	2	researchers	researcher	NOUN
ejpam-6951	56	3	first	first	ADV
ejpam-6951	56	4	established	establish	VERB
ejpam-6951	56	5	a	a	DET
ejpam-6951	56	6	fixed	fix	VERB
ejpam-6951	56	7	labeling	labeling	NOUN
ejpam-6951	56	8	for	for	ADP
ejpam-6951	56	9	each	each	PRON
ejpam-6951	56	10	of	of	ADP
ejpam-6951	56	11	the	the	DET
ejpam-6951	56	12	two	two	NUM
ejpam-6951	56	13	graphs	graph	NOUN
ejpam-6951	56	14	,	,	PUNCT
ejpam-6951	56	15	and	and	CCONJ
ejpam-6951	56	16	this	this	DET
ejpam-6951	56	17	labeling	labeling	NOUN
ejpam-6951	56	18	was	be	AUX
ejpam-6951	56	19	then	then	ADV
ejpam-6951	56	20	used	use	VERB
ejpam-6951	56	21	to	to	PART
ejpam-6951	56	22	determine	determine	VERB
ejpam-6951	56	23	some	some	DET
ejpam-6951	56	24	vertexuniform	vertexuniform	NOUN
ejpam-6951	56	25	sets	set	NOUN
ejpam-6951	56	26	of	of	ADP
ejpam-6951	56	27	subgraphs	subgraph	NOUN
ejpam-6951	56	28	with	with	ADP
ejpam-6951	56	29	respect	respect	NOUN
ejpam-6951	56	30	to	to	ADP
ejpam-6951	56	31	these	these	DET
ejpam-6951	56	32	two	two	NUM
ejpam-6951	56	33	graphs	graph	NOUN
ejpam-6951	56	34	.	.	PUNCT
ejpam-6951	57	1	by	by	ADP
ejpam-6951	57	2	applying	apply	VERB
ejpam-6951	57	3	the	the	DET
ejpam-6951	57	4	symmetric	symmetric	ADJ
ejpam-6951	57	5	difference	difference	NOUN
ejpam-6951	57	6	to	to	ADP
ejpam-6951	57	7	the	the	DET
ejpam-6951	57	8	elements	element	NOUN
ejpam-6951	57	9	of	of	ADP
ejpam-6951	57	10	a	a	DET
ejpam-6951	57	11	vertex	vertex	NOUN
ejpam-6951	57	12	-	-	PUNCT
ejpam-6951	57	13	uniform	uniform	NOUN
ejpam-6951	57	14	set	set	NOUN
ejpam-6951	57	15	,	,	PUNCT
ejpam-6951	57	16	it	it	PRON
ejpam-6951	57	17	can	can	AUX
ejpam-6951	57	18	be	be	AUX
ejpam-6951	57	19	shown	show	VERB
ejpam-6951	57	20	that	that	SCONJ
ejpam-6951	57	21	a	a	DET
ejpam-6951	57	22	subgraph	subgraph	NOUN
ejpam-6951	57	23	is	be	AUX
ejpam-6951	57	24	a	a	DET
ejpam-6951	57	25	vertex	vertex	NOUN
ejpam-6951	57	26	-	-	PUNCT
ejpam-6951	57	27	generator	generator	NOUN
ejpam-6951	57	28	subgraph	subgraph	NOUN
ejpam-6951	57	29	by	by	ADP
ejpam-6951	57	30	applying	apply	VERB
ejpam-6951	57	31	the	the	DET
ejpam-6951	57	32	existing	exist	VERB
ejpam-6951	57	33	results	result	NOUN
ejpam-6951	57	34	of	of	ADP
ejpam-6951	57	35	torino	torino	NOUN
ejpam-6951	57	36	and	and	CCONJ
ejpam-6951	57	37	mame	mame	NOUN
ejpam-6951	57	38	[	[	X
ejpam-6951	57	39	3	3	NUM
ejpam-6951	57	40	]	]	PUNCT
ejpam-6951	57	41	.	.	PUNCT
ejpam-6951	58	1	the	the	DET
ejpam-6951	58	2	researchers	researcher	NOUN
ejpam-6951	58	3	tested	test	VERB
ejpam-6951	58	4	several	several	ADJ
ejpam-6951	58	5	smaller	small	ADJ
ejpam-6951	58	6	subgraphs	subgraph	NOUN
ejpam-6951	58	7	to	to	PART
ejpam-6951	58	8	identify	identify	VERB
ejpam-6951	58	9	patterns	pattern	NOUN
ejpam-6951	58	10	and	and	CCONJ
ejpam-6951	58	11	eventually	eventually	ADV
ejpam-6951	58	12	formulated	formulate	VERB
ejpam-6951	58	13	a	a	DET
ejpam-6951	58	14	general	general	ADJ
ejpam-6951	58	15	result	result	NOUN
ejpam-6951	58	16	.	.	PUNCT
ejpam-6951	59	1	2	2	X
ejpam-6951	59	2	.	.	NUM
ejpam-6951	59	3	preliminaries	preliminary	NOUN
ejpam-6951	59	4	2.1	2.1	NUM
ejpam-6951	59	5	.	.	PUNCT
ejpam-6951	60	1	vertex	vertex	NOUN
ejpam-6951	60	2	-	-	PUNCT
ejpam-6951	60	3	generator	generator	NOUN
ejpam-6951	60	4	subgraph	subgraph	NOUN
ejpam-6951	60	5	of	of	ADP
ejpam-6951	60	6	a	a	DET
ejpam-6951	60	7	graph	graph	NOUN
ejpam-6951	60	8	this	this	DET
ejpam-6951	60	9	section	section	NOUN
ejpam-6951	60	10	gives	give	VERB
ejpam-6951	60	11	the	the	DET
ejpam-6951	60	12	definition	definition	NOUN
ejpam-6951	60	13	of	of	ADP
ejpam-6951	60	14	the	the	DET
ejpam-6951	60	15	vertex	vertex	NOUN
ejpam-6951	60	16	space	space	NOUN
ejpam-6951	60	17	,	,	PUNCT
ejpam-6951	60	18	the	the	DET
ejpam-6951	60	19	vertex	vertex	NOUN
ejpam-6951	60	20	-	-	PUNCT
ejpam-6951	60	21	uniform	uniform	NOUN
ejpam-6951	60	22	set	set	NOUN
ejpam-6951	60	23	,	,	PUNCT
ejpam-6951	60	24	the	the	DET
ejpam-6951	60	25	span	span	NOUN
ejpam-6951	60	26	of	of	ADP
ejpam-6951	60	27	a	a	DET
ejpam-6951	60	28	vertex	vertex	NOUN
ejpam-6951	60	29	-	-	PUNCT
ejpam-6951	60	30	uniform	uniform	NOUN
ejpam-6951	60	31	set	set	NOUN
ejpam-6951	60	32	,	,	PUNCT
ejpam-6951	60	33	and	and	CCONJ
ejpam-6951	60	34	the	the	DET
ejpam-6951	60	35	vertex	vertex	NOUN
ejpam-6951	60	36	-	-	PUNCT
ejpam-6951	60	37	generator	generator	NOUN
ejpam-6951	60	38	subgraph	subgraph	NOUN
ejpam-6951	60	39	.	.	PUNCT
ejpam-6951	61	1	this	this	DET
ejpam-6951	61	2	section	section	NOUN
ejpam-6951	61	3	also	also	ADV
ejpam-6951	61	4	provides	provide	VERB
ejpam-6951	61	5	results	result	NOUN
ejpam-6951	61	6	relevant	relevant	ADJ
ejpam-6951	61	7	to	to	ADP
ejpam-6951	61	8	the	the	DET
ejpam-6951	61	9	said	say	VERB
ejpam-6951	61	10	concepts	concept	NOUN
ejpam-6951	61	11	.	.	PUNCT
ejpam-6951	62	1	the	the	DET
ejpam-6951	62	2	main	main	ADJ
ejpam-6951	62	3	reference	reference	NOUN
ejpam-6951	62	4	for	for	ADP
ejpam-6951	62	5	this	this	DET
ejpam-6951	62	6	section	section	NOUN
ejpam-6951	62	7	is	be	AUX
ejpam-6951	62	8	[	[	X
ejpam-6951	62	9	3	3	NUM
ejpam-6951	62	10	]	]	PUNCT
ejpam-6951	62	11	.	.	PUNCT
ejpam-6951	63	1	definition	definition	NOUN
ejpam-6951	63	2	1	1	NUM
ejpam-6951	63	3	.	.	PUNCT
ejpam-6951	64	1	[	[	X
ejpam-6951	64	2	1	1	X
ejpam-6951	64	3	]	]	PUNCT
ejpam-6951	64	4	let	let	VERB
ejpam-6951	64	5	g	g	NOUN
ejpam-6951	64	6	=	=	SYM
ejpam-6951	64	7	(	(	PUNCT
ejpam-6951	64	8	v	v	NOUN
ejpam-6951	64	9	(	(	PUNCT
ejpam-6951	64	10	g	g	NOUN
ejpam-6951	64	11	)	)	PUNCT
ejpam-6951	64	12	,	,	PUNCT
ejpam-6951	64	13	e(g	e(g	PROPN
ejpam-6951	64	14	)	)	PUNCT
ejpam-6951	64	15	)	)	PUNCT
ejpam-6951	64	16	be	be	AUX
ejpam-6951	64	17	a	a	DET
ejpam-6951	64	18	graph	graph	NOUN
ejpam-6951	64	19	.	.	PUNCT
ejpam-6951	65	1	the	the	DET
ejpam-6951	65	2	vertex	vertex	NOUN
ejpam-6951	65	3	space	space	NOUN
ejpam-6951	65	4	of	of	ADP
ejpam-6951	65	5	g	g	NOUN
ejpam-6951	65	6	,	,	PUNCT
ejpam-6951	65	7	denoted	denote	VERB
ejpam-6951	65	8	by	by	ADP
ejpam-6951	65	9	v	v	NOUN
ejpam-6951	65	10	(	(	PUNCT
ejpam-6951	65	11	g	g	NOUN
ejpam-6951	65	12	)	)	PUNCT
ejpam-6951	65	13	,	,	PUNCT
ejpam-6951	65	14	is	be	AUX
ejpam-6951	65	15	a	a	DET
ejpam-6951	65	16	vector	vector	NOUN
ejpam-6951	65	17	space	space	NOUN
ejpam-6951	65	18	over	over	ADP
ejpam-6951	65	19	a	a	DET
ejpam-6951	65	20	field	field	NOUN
ejpam-6951	65	21	z2	z2	NOUN
ejpam-6951	65	22	=	=	SYM
ejpam-6951	65	23	{	{	PUNCT
ejpam-6951	65	24	0	0	NUM
ejpam-6951	65	25	,	,	PUNCT
ejpam-6951	65	26	1	1	NUM
ejpam-6951	65	27	}	}	PUNCT
ejpam-6951	65	28	,	,	PUNCT
ejpam-6951	65	29	which	which	PRON
ejpam-6951	65	30	composes	compose	VERB
ejpam-6951	65	31	of	of	ADP
ejpam-6951	65	32	all	all	DET
ejpam-6951	65	33	subsets	subset	NOUN
ejpam-6951	65	34	of	of	ADP
ejpam-6951	65	35	v	v	NOUN
ejpam-6951	65	36	(	(	PUNCT
ejpam-6951	65	37	g	g	NOUN
ejpam-6951	65	38	)	)	PUNCT
ejpam-6951	65	39	,	,	PUNCT
ejpam-6951	65	40	where	where	SCONJ
ejpam-6951	65	41	for	for	ADP
ejpam-6951	65	42	a	a	DET
ejpam-6951	65	43	,	,	PUNCT
ejpam-6951	65	44	b	b	PROPN
ejpam-6951	65	45	∈	∈	PROPN
ejpam-6951	65	46	v	v	NOUN
ejpam-6951	65	47	(	(	PUNCT
ejpam-6951	65	48	g	g	NOUN
ejpam-6951	65	49	)	)	PUNCT
ejpam-6951	65	50	,	,	PUNCT
ejpam-6951	65	51	vector	vector	NOUN
ejpam-6951	65	52	addition	addition	NOUN
ejpam-6951	65	53	and	and	CCONJ
ejpam-6951	65	54	scalar	scalar	ADJ
ejpam-6951	65	55	multiplication	multiplication	NOUN
ejpam-6951	65	56	are	be	AUX
ejpam-6951	65	57	given	give	VERB
ejpam-6951	65	58	by	by	ADP
ejpam-6951	65	59	(	(	PUNCT
ejpam-6951	65	60	i	i	NOUN
ejpam-6951	65	61	)	)	PUNCT
ejpam-6951	65	62	a+b	a+b	PROPN
ejpam-6951	65	63	=	=	PUNCT
ejpam-6951	65	64	a	a	DET
ejpam-6951	65	65	△	△	PROPN
ejpam-6951	65	66	b	b	NOUN
ejpam-6951	65	67	,	,	PUNCT
ejpam-6951	65	68	the	the	DET
ejpam-6951	65	69	symmetric	symmetric	ADJ
ejpam-6951	65	70	difference	difference	NOUN
ejpam-6951	65	71	of	of	ADP
ejpam-6951	65	72	a	a	PRON
ejpam-6951	65	73	and	and	CCONJ
ejpam-6951	65	74	b.	b.	PROPN
ejpam-6951	65	75	(	(	PUNCT
ejpam-6951	65	76	ii	ii	NOUN
ejpam-6951	65	77	)	)	PUNCT
ejpam-6951	65	78	ca	ca	NOUN
ejpam-6951	65	79	=	=	PUNCT
ejpam-6951	65	80	a	a	PRON
ejpam-6951	65	81	if	if	SCONJ
ejpam-6951	65	82	c	c	NOUN
ejpam-6951	65	83	=	=	SYM
ejpam-6951	65	84	1	1	NUM
ejpam-6951	65	85	and	and	CCONJ
ejpam-6951	65	86	ca	ca	NOUN
ejpam-6951	65	87	=	=	NOUN
ejpam-6951	65	88	∅	∅	NOUN
ejpam-6951	65	89	if	if	SCONJ
ejpam-6951	65	90	c	c	PROPN
ejpam-6951	65	91	=	=	NOUN
ejpam-6951	65	92	0	0	X
ejpam-6951	65	93	.	.	PUNCT
ejpam-6951	66	1	notably	notably	ADV
ejpam-6951	66	2	,	,	PUNCT
ejpam-6951	66	3	the	the	DET
ejpam-6951	66	4	basis	basis	NOUN
ejpam-6951	66	5	of	of	ADP
ejpam-6951	66	6	the	the	DET
ejpam-6951	66	7	vertex	vertex	NOUN
ejpam-6951	66	8	space	space	NOUN
ejpam-6951	66	9	can	can	AUX
ejpam-6951	66	10	be	be	AUX
ejpam-6951	66	11	found	find	VERB
ejpam-6951	66	12	in	in	ADP
ejpam-6951	66	13	the	the	DET
ejpam-6951	66	14	book	book	NOUN
ejpam-6951	66	15	of	of	ADP
ejpam-6951	66	16	diestel	diestel	NOUN
ejpam-6951	66	17	[	[	X
ejpam-6951	66	18	1	1	NUM
ejpam-6951	66	19	]	]	PUNCT
ejpam-6951	66	20	,	,	PUNCT
ejpam-6951	66	21	which	which	PRON
ejpam-6951	66	22	is	be	AUX
ejpam-6951	66	23	presented	present	VERB
ejpam-6951	66	24	in	in	ADP
ejpam-6951	66	25	the	the	DET
ejpam-6951	66	26	following	follow	VERB
ejpam-6951	66	27	theorem	theorem	PROPN
ejpam-6951	66	28	.	.	PUNCT
ejpam-6951	66	29	theorem	theorem	NOUN
ejpam-6951	66	30	1	1	NUM
ejpam-6951	66	31	.	.	PUNCT
ejpam-6951	67	1	[	[	X
ejpam-6951	67	2	1	1	X
ejpam-6951	67	3	]	]	PUNCT
ejpam-6951	67	4	let	let	VERB
ejpam-6951	67	5	g	g	PRON
ejpam-6951	67	6	be	be	AUX
ejpam-6951	67	7	a	a	DET
ejpam-6951	67	8	graph	graph	NOUN
ejpam-6951	67	9	with	with	ADP
ejpam-6951	67	10	v	v	NOUN
ejpam-6951	67	11	(	(	PUNCT
ejpam-6951	67	12	g	g	NOUN
ejpam-6951	67	13	)	)	PUNCT
ejpam-6951	67	14	=	=	SYM
ejpam-6951	67	15	{	{	PUNCT
ejpam-6951	67	16	x1	x1	PROPN
ejpam-6951	67	17	,	,	PUNCT
ejpam-6951	67	18	x2	x2	PROPN
ejpam-6951	67	19	,	,	PUNCT
ejpam-6951	67	20	x3	x3	ADJ
ejpam-6951	67	21	,	,	PUNCT
ejpam-6951	67	22	...	...	PUNCT
ejpam-6951	67	23	,	,	PUNCT
ejpam-6951	67	24	xn	xn	PROPN
ejpam-6951	67	25	}	}	PUNCT
ejpam-6951	67	26	.	.	PUNCT
ejpam-6951	68	1	then	then	ADV
ejpam-6951	68	2	the	the	DET
ejpam-6951	68	3	set	set	NOUN
ejpam-6951	68	4	a	a	X
ejpam-6951	68	5	=	=	X
ejpam-6951	68	6	{	{	PUNCT
ejpam-6951	68	7	{	{	PUNCT
ejpam-6951	68	8	x1	x1	PROPN
ejpam-6951	68	9	}	}	PUNCT
ejpam-6951	68	10	,	,	PUNCT
ejpam-6951	68	11	{	{	PUNCT
ejpam-6951	68	12	x2	x2	ADJ
ejpam-6951	68	13	}	}	PUNCT
ejpam-6951	68	14	,	,	PUNCT
ejpam-6951	68	15	{	{	PUNCT
ejpam-6951	68	16	x3	x3	ADJ
ejpam-6951	68	17	}	}	PUNCT
ejpam-6951	68	18	,	,	PUNCT
ejpam-6951	68	19	...	...	PUNCT
ejpam-6951	68	20	,	,	PUNCT
ejpam-6951	68	21	{	{	PUNCT
ejpam-6951	68	22	xn	xn	X
ejpam-6951	68	23	}	}	PUNCT
ejpam-6951	68	24	}	}	PUNCT
ejpam-6951	68	25	forms	form	VERB
ejpam-6951	68	26	a	a	DET
ejpam-6951	68	27	basis	basis	NOUN
ejpam-6951	68	28	for	for	ADP
ejpam-6951	68	29	v	v	NOUN
ejpam-6951	68	30	(	(	PUNCT
ejpam-6951	68	31	g	g	NOUN
ejpam-6951	68	32	)	)	PUNCT
ejpam-6951	68	33	.	.	PUNCT
ejpam-6951	69	1	hence	hence	ADV
ejpam-6951	69	2	,	,	PUNCT
ejpam-6951	69	3	dimv	dimv	NOUN
ejpam-6951	69	4	(	(	PUNCT
ejpam-6951	69	5	g	g	NOUN
ejpam-6951	69	6	)	)	PUNCT
ejpam-6951	69	7	=	=	SYM
ejpam-6951	69	8	n	n	CCONJ
ejpam-6951	69	9	,	,	PUNCT
ejpam-6951	69	10	the	the	DET
ejpam-6951	69	11	order	order	NOUN
ejpam-6951	69	12	of	of	ADP
ejpam-6951	69	13	g.	g.	PROPN
ejpam-6951	69	14	knowing	know	VERB
ejpam-6951	69	15	the	the	DET
ejpam-6951	69	16	structure	structure	NOUN
ejpam-6951	69	17	of	of	ADP
ejpam-6951	69	18	the	the	DET
ejpam-6951	69	19	vertex	vertex	NOUN
ejpam-6951	69	20	space	space	NOUN
ejpam-6951	69	21	through	through	ADP
ejpam-6951	69	22	its	its	PRON
ejpam-6951	69	23	basis	basis	NOUN
ejpam-6951	69	24	,	,	PUNCT
ejpam-6951	69	25	we	we	PRON
ejpam-6951	69	26	now	now	ADV
ejpam-6951	69	27	explore	explore	VERB
ejpam-6951	69	28	specific	specific	ADJ
ejpam-6951	69	29	subsets	subset	NOUN
ejpam-6951	69	30	of	of	ADP
ejpam-6951	69	31	this	this	DET
ejpam-6951	69	32	space	space	NOUN
ejpam-6951	69	33	—	—	PUNCT
ejpam-6951	69	34	particularly	particularly	ADV
ejpam-6951	69	35	those	those	PRON
ejpam-6951	69	36	associated	associate	VERB
ejpam-6951	69	37	with	with	ADP
ejpam-6951	69	38	induced	induced	ADJ
ejpam-6951	69	39	subgraphs	subgraph	NOUN
ejpam-6951	69	40	—	—	PUNCT
ejpam-6951	69	41	and	and	CCONJ
ejpam-6951	69	42	how	how	SCONJ
ejpam-6951	69	43	they	they	PRON
ejpam-6951	69	44	contribute	contribute	VERB
ejpam-6951	69	45	to	to	ADP
ejpam-6951	69	46	generating	generate	VERB
ejpam-6951	69	47	the	the	DET
ejpam-6951	69	48	entire	entire	ADJ
ejpam-6951	69	49	vertex	vertex	NOUN
ejpam-6951	69	50	space	space	NOUN
ejpam-6951	69	51	.	.	PUNCT
ejpam-6951	70	1	this	this	PRON
ejpam-6951	70	2	leads	lead	VERB
ejpam-6951	70	3	to	to	ADP
ejpam-6951	70	4	the	the	DET
ejpam-6951	70	5	notions	notion	NOUN
ejpam-6951	70	6	of	of	ADP
ejpam-6951	70	7	vertexuniform	vertexuniform	NOUN
ejpam-6951	70	8	sets	set	NOUN
ejpam-6951	70	9	,	,	PUNCT
ejpam-6951	70	10	their	their	PRON
ejpam-6951	70	11	span	span	NOUN
ejpam-6951	70	12	,	,	PUNCT
ejpam-6951	70	13	and	and	CCONJ
ejpam-6951	70	14	the	the	DET
ejpam-6951	70	15	concept	concept	NOUN
ejpam-6951	70	16	of	of	ADP
ejpam-6951	70	17	vertex	vertex	NOUN
ejpam-6951	70	18	-	-	PUNCT
ejpam-6951	70	19	generator	generator	NOUN
ejpam-6951	70	20	subgraphs	subgraph	NOUN
ejpam-6951	70	21	.	.	PUNCT
ejpam-6951	71	1	definition	definition	NOUN
ejpam-6951	71	2	2	2	NUM
ejpam-6951	71	3	.	.	PUNCT
ejpam-6951	72	1	[	[	X
ejpam-6951	72	2	3	3	X
ejpam-6951	72	3	]	]	PUNCT
ejpam-6951	72	4	let	let	VERB
ejpam-6951	72	5	h	h	NOUN
ejpam-6951	72	6	be	be	AUX
ejpam-6951	72	7	a	a	DET
ejpam-6951	72	8	subgraph	subgraph	NOUN
ejpam-6951	72	9	of	of	ADP
ejpam-6951	72	10	a	a	DET
ejpam-6951	72	11	graph	graph	NOUN
ejpam-6951	72	12	g.	g.	NOUN
ejpam-6951	72	13	the	the	DET
ejpam-6951	72	14	vertex	vertex	NOUN
ejpam-6951	72	15	-	-	PUNCT
ejpam-6951	72	16	uniform	uniform	NOUN
ejpam-6951	72	17	set	set	NOUN
ejpam-6951	72	18	of	of	ADP
ejpam-6951	72	19	h	h	NOUN
ejpam-6951	72	20	with	with	ADP
ejpam-6951	72	21	respect	respect	NOUN
ejpam-6951	72	22	to	to	ADP
ejpam-6951	72	23	g	g	NOUN
ejpam-6951	72	24	,	,	PUNCT
ejpam-6951	72	25	denoted	denote	VERB
ejpam-6951	72	26	by	by	ADP
ejpam-6951	72	27	vh(g	vh(g	NOUN
ejpam-6951	72	28	)	)	PUNCT
ejpam-6951	72	29	,	,	PUNCT
ejpam-6951	72	30	is	be	AUX
ejpam-6951	72	31	the	the	DET
ejpam-6951	72	32	set	set	NOUN
ejpam-6951	72	33	of	of	ADP
ejpam-6951	72	34	all	all	DET
ejpam-6951	72	35	elements	element	NOUN
ejpam-6951	72	36	of	of	ADP
ejpam-6951	72	37	v	v	NOUN
ejpam-6951	72	38	(	(	PUNCT
ejpam-6951	72	39	g	g	NOUN
ejpam-6951	72	40	)	)	PUNCT
ejpam-6951	72	41	that	that	PRON
ejpam-6951	72	42	induces	induce	VERB
ejpam-6951	72	43	a	a	DET
ejpam-6951	72	44	subgraph	subgraph	NOUN
ejpam-6951	72	45	isomorphic	isomorphic	ADJ
ejpam-6951	72	46	to	to	ADP
ejpam-6951	72	47	h.	h.	PROPN
ejpam-6951	72	48	definition	definition	NOUN
ejpam-6951	72	49	3	3	NUM
ejpam-6951	72	50	.	.	PUNCT
ejpam-6951	73	1	[	[	X
ejpam-6951	73	2	3	3	X
ejpam-6951	73	3	]	]	PUNCT
ejpam-6951	73	4	let	let	AUX
ejpam-6951	73	5	vh(g	vh(g	NOUN
ejpam-6951	73	6	)	)	PUNCT
ejpam-6951	73	7	be	be	AUX
ejpam-6951	73	8	a	a	DET
ejpam-6951	73	9	vertex	vertex	NOUN
ejpam-6951	73	10	-	-	PUNCT
ejpam-6951	73	11	uniform	uniform	NOUN
ejpam-6951	73	12	set	set	NOUN
ejpam-6951	73	13	of	of	ADP
ejpam-6951	73	14	h	h	NOUN
ejpam-6951	73	15	with	with	ADP
ejpam-6951	73	16	respect	respect	NOUN
ejpam-6951	73	17	to	to	ADP
ejpam-6951	73	18	g.	g.	VERB
ejpam-6951	73	19	the	the	DET
ejpam-6951	73	20	span	span	NOUN
ejpam-6951	73	21	of	of	ADP
ejpam-6951	73	22	vh(g	vh(g	NOUN
ejpam-6951	73	23	)	)	PUNCT
ejpam-6951	73	24	,	,	PUNCT
ejpam-6951	73	25	denoted	denote	VERB
ejpam-6951	73	26	by	by	ADP
ejpam-6951	73	27	vh(g	vh(g	NOUN
ejpam-6951	73	28	)	)	PUNCT
ejpam-6951	73	29	,	,	PUNCT
ejpam-6951	73	30	is	be	AUX
ejpam-6951	73	31	the	the	DET
ejpam-6951	73	32	set	set	NOUN
ejpam-6951	73	33	of	of	ADP
ejpam-6951	73	34	all	all	DET
ejpam-6951	73	35	linear	linear	ADJ
ejpam-6951	73	36	combinations	combination	NOUN
ejpam-6951	73	37	of	of	ADP
ejpam-6951	73	38	the	the	DET
ejpam-6951	73	39	elements	element	NOUN
ejpam-6951	73	40	of	of	ADP
ejpam-6951	73	41	vh(g	vh(g	NOUN
ejpam-6951	73	42	)	)	PUNCT
ejpam-6951	73	43	.	.	PUNCT
ejpam-6951	74	1	that	that	PRON
ejpam-6951	74	2	is	be	AUX
ejpam-6951	74	3	,	,	PUNCT
ejpam-6951	74	4	if	if	SCONJ
ejpam-6951	74	5	vh(g	vh(g	NOUN
ejpam-6951	74	6	)	)	PUNCT
ejpam-6951	75	1	=	=	PRON
ejpam-6951	75	2	{	{	PUNCT
ejpam-6951	75	3	a1	a1	PROPN
ejpam-6951	75	4	,	,	PUNCT
ejpam-6951	75	5	a2	a2	PROPN
ejpam-6951	75	6	,	,	PUNCT
ejpam-6951	75	7	a3	a3	NOUN
ejpam-6951	75	8	,	,	PUNCT
ejpam-6951	75	9	...	...	PUNCT
ejpam-6951	75	10	,	,	PUNCT
ejpam-6951	75	11	ak	ak	PROPN
ejpam-6951	75	12	}	}	PUNCT
ejpam-6951	75	13	where	where	SCONJ
ejpam-6951	75	14	ai	ai	VERB
ejpam-6951	75	15	∈	∈	PROPN
ejpam-6951	75	16	v	v	NOUN
ejpam-6951	75	17	(	(	PUNCT
ejpam-6951	75	18	g	g	NOUN
ejpam-6951	75	19	)	)	PUNCT
ejpam-6951	75	20	,	,	PUNCT
ejpam-6951	75	21	then	then	ADV
ejpam-6951	75	22	vh(g	vh(g	NOUN
ejpam-6951	75	23	)	)	PUNCT
ejpam-6951	76	1	=	=	PRON
ejpam-6951	76	2	{	{	PUNCT
ejpam-6951	76	3	k∑	k∑	PROPN
ejpam-6951	76	4	i=1	i=1	PROPN
ejpam-6951	77	1	ciai	ciai	NOUN
ejpam-6951	78	1	|	|	ADV
ejpam-6951	78	2	ci	ci	PROPN
ejpam-6951	78	3	∈	∈	PROPN
ejpam-6951	78	4	{	{	PUNCT
ejpam-6951	78	5	0	0	NUM
ejpam-6951	78	6	,	,	PUNCT
ejpam-6951	78	7	1	1	NUM
ejpam-6951	78	8	}	}	PUNCT
ejpam-6951	78	9	}	}	PUNCT
ejpam-6951	78	10	.	.	PUNCT
ejpam-6951	79	1	g.	g.	PROPN
ejpam-6951	79	2	d.	d.	PROPN
ejpam-6951	79	3	sepillo	sepillo	PROPN
ejpam-6951	79	4	et	et	PROPN
ejpam-6951	79	5	al	al	PROPN
ejpam-6951	79	6	.	.	PUNCT
ejpam-6951	79	7	/	/	SYM
ejpam-6951	79	8	eur	eur	PROPN
ejpam-6951	79	9	.	.	PUNCT
ejpam-6951	80	1	j.	j.	PROPN
ejpam-6951	80	2	pure	pure	PROPN
ejpam-6951	80	3	appl	appl	PROPN
ejpam-6951	80	4	.	.	PROPN
ejpam-6951	80	5	math	math	PROPN
ejpam-6951	80	6	,	,	PUNCT
ejpam-6951	80	7	18	18	NUM
ejpam-6951	80	8	(	(	PUNCT
ejpam-6951	80	9	4	4	NUM
ejpam-6951	80	10	)	)	PUNCT
ejpam-6951	80	11	(	(	PUNCT
ejpam-6951	80	12	2025	2025	NUM
ejpam-6951	80	13	)	)	PUNCT
ejpam-6951	80	14	,	,	PUNCT
ejpam-6951	80	15	6951	6951	NUM
ejpam-6951	80	16	4	4	NUM
ejpam-6951	80	17	of	of	ADP
ejpam-6951	80	18	23	23	NUM
ejpam-6951	80	19	definition	definition	NOUN
ejpam-6951	80	20	4	4	NUM
ejpam-6951	80	21	.	.	PUNCT
ejpam-6951	81	1	[	[	X
ejpam-6951	81	2	3	3	X
ejpam-6951	81	3	]	]	PUNCT
ejpam-6951	81	4	let	let	AUX
ejpam-6951	81	5	vh(g	vh(g	NOUN
ejpam-6951	81	6	)	)	PUNCT
ejpam-6951	81	7	be	be	AUX
ejpam-6951	81	8	the	the	DET
ejpam-6951	81	9	span	span	NOUN
ejpam-6951	81	10	of	of	ADP
ejpam-6951	81	11	vh(g	vh(g	NOUN
ejpam-6951	81	12	)	)	PUNCT
ejpam-6951	81	13	.	.	PUNCT
ejpam-6951	82	1	if	if	SCONJ
ejpam-6951	82	2	vh(g	vh(g	NOUN
ejpam-6951	82	3	)	)	PUNCT
ejpam-6951	82	4	=	=	SYM
ejpam-6951	82	5	v	v	X
ejpam-6951	82	6	(	(	PUNCT
ejpam-6951	82	7	g	g	NOUN
ejpam-6951	82	8	)	)	PUNCT
ejpam-6951	82	9	,	,	PUNCT
ejpam-6951	82	10	then	then	ADV
ejpam-6951	82	11	h	h	PROPN
ejpam-6951	82	12	is	be	AUX
ejpam-6951	82	13	a	a	DET
ejpam-6951	82	14	vertex	vertex	NOUN
ejpam-6951	82	15	-	-	PUNCT
ejpam-6951	82	16	generator	generator	NOUN
ejpam-6951	82	17	subgraph	subgraph	NOUN
ejpam-6951	82	18	of	of	ADP
ejpam-6951	82	19	g.	g.	PROPN
ejpam-6951	82	20	note	note	VERB
ejpam-6951	82	21	that	that	SCONJ
ejpam-6951	82	22	a	a	PRON
ejpam-6951	82	23	=	=	X
ejpam-6951	82	24	{	{	PUNCT
ejpam-6951	82	25	{	{	PUNCT
ejpam-6951	82	26	x1	x1	PROPN
ejpam-6951	82	27	}	}	PUNCT
ejpam-6951	82	28	,	,	PUNCT
ejpam-6951	82	29	{	{	PUNCT
ejpam-6951	82	30	x2	x2	ADJ
ejpam-6951	82	31	}	}	PUNCT
ejpam-6951	82	32	,	,	PUNCT
ejpam-6951	82	33	{	{	PUNCT
ejpam-6951	82	34	x3	x3	ADJ
ejpam-6951	82	35	}	}	PUNCT
ejpam-6951	82	36	,	,	PUNCT
ejpam-6951	82	37	...	...	PUNCT
ejpam-6951	82	38	,	,	PUNCT
ejpam-6951	82	39	{	{	PUNCT
ejpam-6951	82	40	xn	xn	X
ejpam-6951	82	41	}	}	PUNCT
ejpam-6951	82	42	}	}	PUNCT
ejpam-6951	82	43	forms	form	VERB
ejpam-6951	82	44	a	a	DET
ejpam-6951	82	45	basis	basis	NOUN
ejpam-6951	82	46	for	for	ADP
ejpam-6951	82	47	v	v	NOUN
ejpam-6951	82	48	(	(	PUNCT
ejpam-6951	82	49	g	g	NOUN
ejpam-6951	82	50	)	)	PUNCT
ejpam-6951	82	51	by	by	ADP
ejpam-6951	82	52	theorem	theorem	NOUN
ejpam-6951	82	53	1	1	NUM
ejpam-6951	82	54	.	.	PUNCT
ejpam-6951	82	55	additionally	additionally	ADV
ejpam-6951	82	56	,	,	PUNCT
ejpam-6951	82	57	vh(g	vh(g	NOUN
ejpam-6951	82	58	)	)	PUNCT
ejpam-6951	82	59	⊆	⊆	NUM
ejpam-6951	82	60	v	v	X
ejpam-6951	82	61	(	(	PUNCT
ejpam-6951	82	62	g	g	NOUN
ejpam-6951	82	63	)	)	PUNCT
ejpam-6951	82	64	.	.	PUNCT
ejpam-6951	83	1	to	to	PART
ejpam-6951	83	2	show	show	VERB
ejpam-6951	83	3	that	that	SCONJ
ejpam-6951	83	4	h	h	NOUN
ejpam-6951	83	5	is	be	AUX
ejpam-6951	83	6	a	a	DET
ejpam-6951	83	7	vertex	vertex	NOUN
ejpam-6951	83	8	-	-	PUNCT
ejpam-6951	83	9	generator	generator	NOUN
ejpam-6951	83	10	subgraph	subgraph	NOUN
ejpam-6951	83	11	of	of	ADP
ejpam-6951	83	12	g	g	PROPN
ejpam-6951	83	13	,	,	PUNCT
ejpam-6951	83	14	it	it	PRON
ejpam-6951	83	15	is	be	AUX
ejpam-6951	83	16	sufficient	sufficient	ADJ
ejpam-6951	83	17	to	to	PART
ejpam-6951	83	18	show	show	VERB
ejpam-6951	83	19	that	that	SCONJ
ejpam-6951	83	20	v	v	NOUN
ejpam-6951	83	21	(	(	PUNCT
ejpam-6951	83	22	g	g	NOUN
ejpam-6951	83	23	)	)	PUNCT
ejpam-6951	83	24	⊆	⊆	NUM
ejpam-6951	83	25	vh(g	vh(g	NOUN
ejpam-6951	83	26	)	)	PUNCT
ejpam-6951	83	27	.	.	PUNCT
ejpam-6951	84	1	that	that	PRON
ejpam-6951	84	2	is	is	ADV
ejpam-6951	84	3	,	,	PUNCT
ejpam-6951	84	4	{	{	PUNCT
ejpam-6951	84	5	{	{	PUNCT
ejpam-6951	84	6	x1	x1	PROPN
ejpam-6951	84	7	}	}	PUNCT
ejpam-6951	84	8	,	,	PUNCT
ejpam-6951	84	9	{	{	PUNCT
ejpam-6951	84	10	x2	x2	ADJ
ejpam-6951	84	11	}	}	PUNCT
ejpam-6951	84	12	,	,	PUNCT
ejpam-6951	84	13	{	{	PUNCT
ejpam-6951	84	14	x3	x3	ADJ
ejpam-6951	84	15	}	}	PUNCT
ejpam-6951	84	16	,	,	PUNCT
ejpam-6951	84	17	...	...	PUNCT
ejpam-6951	84	18	,	,	PUNCT
ejpam-6951	84	19	{	{	PUNCT
ejpam-6951	84	20	xn	xn	X
ejpam-6951	84	21	}	}	PUNCT
ejpam-6951	84	22	}	}	PUNCT
ejpam-6951	84	23	⊆	⊆	NUM
ejpam-6951	84	24	vh(g	vh(g	NOUN
ejpam-6951	84	25	)	)	PUNCT
ejpam-6951	84	26	.	.	PUNCT
ejpam-6951	85	1	thus	thus	ADV
ejpam-6951	85	2	,	,	PUNCT
ejpam-6951	85	3	the	the	DET
ejpam-6951	85	4	following	follow	VERB
ejpam-6951	85	5	remark	remark	NOUN
ejpam-6951	85	6	gives	give	VERB
ejpam-6951	85	7	a	a	DET
ejpam-6951	85	8	necessary	necessary	ADJ
ejpam-6951	85	9	and	and	CCONJ
ejpam-6951	85	10	sufficient	sufficient	ADJ
ejpam-6951	85	11	condition	condition	NOUN
ejpam-6951	85	12	for	for	ADP
ejpam-6951	85	13	a	a	DET
ejpam-6951	85	14	subgraph	subgraph	NOUN
ejpam-6951	85	15	to	to	PART
ejpam-6951	85	16	be	be	AUX
ejpam-6951	85	17	a	a	DET
ejpam-6951	85	18	vertex	vertex	NOUN
ejpam-6951	85	19	-	-	PUNCT
ejpam-6951	85	20	generator	generator	NOUN
ejpam-6951	85	21	subgraph	subgraph	NOUN
ejpam-6951	85	22	of	of	ADP
ejpam-6951	85	23	a	a	DET
ejpam-6951	85	24	graph	graph	NOUN
ejpam-6951	85	25	.	.	PUNCT
ejpam-6951	86	1	remark	remark	NOUN
ejpam-6951	86	2	1	1	NUM
ejpam-6951	86	3	.	.	PUNCT
ejpam-6951	87	1	[	[	X
ejpam-6951	87	2	3	3	X
ejpam-6951	87	3	]	]	PUNCT
ejpam-6951	87	4	let	let	VERB
ejpam-6951	87	5	g	g	PRON
ejpam-6951	87	6	be	be	AUX
ejpam-6951	87	7	a	a	DET
ejpam-6951	87	8	graph	graph	NOUN
ejpam-6951	87	9	with	with	ADP
ejpam-6951	87	10	vertex	vertex	NOUN
ejpam-6951	87	11	set	set	VERB
ejpam-6951	87	12	v	v	NOUN
ejpam-6951	87	13	(	(	PUNCT
ejpam-6951	87	14	g	g	NOUN
ejpam-6951	87	15	)	)	PUNCT
ejpam-6951	87	16	=	=	SYM
ejpam-6951	87	17	{	{	PUNCT
ejpam-6951	87	18	x1	x1	PROPN
ejpam-6951	87	19	,	,	PUNCT
ejpam-6951	87	20	x2	x2	PROPN
ejpam-6951	87	21	,	,	PUNCT
ejpam-6951	87	22	x3	x3	ADJ
ejpam-6951	87	23	,	,	PUNCT
ejpam-6951	87	24	...	...	PUNCT
ejpam-6951	87	25	,	,	PUNCT
ejpam-6951	87	26	xn	xn	PROPN
ejpam-6951	87	27	}	}	PUNCT
ejpam-6951	87	28	.	.	PUNCT
ejpam-6951	88	1	let	let	VERB
ejpam-6951	88	2	h	h	PRON
ejpam-6951	88	3	be	be	AUX
ejpam-6951	88	4	a	a	DET
ejpam-6951	88	5	subgraph	subgraph	NOUN
ejpam-6951	88	6	of	of	ADP
ejpam-6951	88	7	g.	g.	PROPN
ejpam-6951	89	1	then	then	ADV
ejpam-6951	89	2	h	h	PROPN
ejpam-6951	89	3	is	be	AUX
ejpam-6951	89	4	a	a	DET
ejpam-6951	89	5	vertex	vertex	NOUN
ejpam-6951	89	6	-	-	PUNCT
ejpam-6951	89	7	generator	generator	NOUN
ejpam-6951	89	8	subgraph	subgraph	NOUN
ejpam-6951	89	9	of	of	ADP
ejpam-6951	89	10	g	g	PROPN
ejpam-6951	89	11	if	if	SCONJ
ejpam-6951	90	1	and	and	CCONJ
ejpam-6951	90	2	only	only	ADV
ejpam-6951	90	3	if	if	SCONJ
ejpam-6951	90	4	{	{	PUNCT
ejpam-6951	90	5	xi	xi	NOUN
ejpam-6951	90	6	}	}	PUNCT
ejpam-6951	90	7	∈	∈	PROPN
ejpam-6951	90	8	vh(g	vh(g	NOUN
ejpam-6951	90	9	)	)	PUNCT
ejpam-6951	90	10	for	for	ADP
ejpam-6951	90	11	all	all	DET
ejpam-6951	90	12	1	1	NUM
ejpam-6951	90	13	≤	≤	NUM
ejpam-6951	90	14	i	i	PRON
ejpam-6951	90	15	≤	≤	ADJ
ejpam-6951	90	16	n.	n.	NOUN
ejpam-6951	90	17	for	for	ADP
ejpam-6951	90	18	example	example	NOUN
ejpam-6951	90	19	,	,	PUNCT
ejpam-6951	90	20	consider	consider	VERB
ejpam-6951	90	21	the	the	DET
ejpam-6951	90	22	cycle	cycle	NOUN
ejpam-6951	90	23	graph	graph	NOUN
ejpam-6951	90	24	c5	c5	PROPN
ejpam-6951	90	25	in	in	ADP
ejpam-6951	90	26	figure	figure	NOUN
ejpam-6951	90	27	1	1	NUM
ejpam-6951	90	28	,	,	PUNCT
ejpam-6951	90	29	with	with	ADP
ejpam-6951	90	30	v	v	PROPN
ejpam-6951	90	31	(	(	PUNCT
ejpam-6951	90	32	c5	c5	PROPN
ejpam-6951	90	33	)	)	PUNCT
ejpam-6951	90	34	=	=	PRON
ejpam-6951	90	35	{	{	PUNCT
ejpam-6951	90	36	a1	a1	PROPN
ejpam-6951	90	37	,	,	PUNCT
ejpam-6951	90	38	a2	a2	PROPN
ejpam-6951	90	39	,	,	PUNCT
ejpam-6951	90	40	a3	a3	NOUN
ejpam-6951	90	41	,	,	PUNCT
ejpam-6951	90	42	a4	a4	NOUN
ejpam-6951	90	43	,	,	PUNCT
ejpam-6951	90	44	a5	a5	NOUN
ejpam-6951	90	45	}	}	PUNCT
ejpam-6951	90	46	and	and	CCONJ
ejpam-6951	90	47	e(c5	e(c5	ADJ
ejpam-6951	90	48	)	)	PUNCT
ejpam-6951	90	49	=	=	PRON
ejpam-6951	90	50	{	{	PUNCT
ejpam-6951	90	51	[	[	X
ejpam-6951	90	52	a1	a1	NOUN
ejpam-6951	90	53	,	,	PUNCT
ejpam-6951	90	54	a2	a2	PROPN
ejpam-6951	90	55	]	]	PUNCT
ejpam-6951	90	56	,	,	PUNCT
ejpam-6951	91	1	[	[	X
ejpam-6951	91	2	a2	a2	NOUN
ejpam-6951	91	3	,	,	PUNCT
ejpam-6951	91	4	a3	a3	NOUN
ejpam-6951	91	5	]	]	PUNCT
ejpam-6951	91	6	,	,	PUNCT
ejpam-6951	91	7	[	[	X
ejpam-6951	91	8	a3	a3	NOUN
ejpam-6951	91	9	,	,	PUNCT
ejpam-6951	91	10	a4	a4	PROPN
ejpam-6951	91	11	]	]	PUNCT
ejpam-6951	91	12	,	,	PUNCT
ejpam-6951	91	13	[	[	X
ejpam-6951	91	14	a4	a4	NOUN
ejpam-6951	91	15	,	,	PUNCT
ejpam-6951	91	16	a5	a5	PROPN
ejpam-6951	91	17	]	]	PUNCT
ejpam-6951	91	18	,	,	PUNCT
ejpam-6951	91	19	[	[	X
ejpam-6951	91	20	a1	a1	NOUN
ejpam-6951	91	21	,	,	PUNCT
ejpam-6951	91	22	a5	a5	PROPN
ejpam-6951	91	23	]	]	PUNCT
ejpam-6951	91	24	}	}	PUNCT
ejpam-6951	91	25	.	.	PUNCT
ejpam-6951	92	1	a1	a1	NOUN
ejpam-6951	92	2	a2	a2	PROPN
ejpam-6951	92	3	a3	a3	PROPN
ejpam-6951	92	4	a4	a4	PROPN
ejpam-6951	92	5	a5	a5	PROPN
ejpam-6951	92	6	c5	c5	PROPN
ejpam-6951	92	7	:	:	PUNCT
ejpam-6951	92	8	figure	figure	VERB
ejpam-6951	92	9	1	1	NUM
ejpam-6951	92	10	:	:	PUNCT
ejpam-6951	92	11	a	a	DET
ejpam-6951	92	12	cycle	cycle	NOUN
ejpam-6951	92	13	graph	graph	NOUN
ejpam-6951	92	14	c5	c5	PROPN
ejpam-6951	92	15	we	we	PRON
ejpam-6951	92	16	show	show	VERB
ejpam-6951	92	17	that	that	SCONJ
ejpam-6951	92	18	the	the	DET
ejpam-6951	92	19	path	path	NOUN
ejpam-6951	92	20	graph	graph	NOUN
ejpam-6951	92	21	p3	p3	PROPN
ejpam-6951	92	22	is	be	AUX
ejpam-6951	92	23	a	a	DET
ejpam-6951	92	24	vertex	vertex	NOUN
ejpam-6951	92	25	-	-	PUNCT
ejpam-6951	92	26	generator	generator	NOUN
ejpam-6951	92	27	subgraph	subgraph	NOUN
ejpam-6951	92	28	of	of	ADP
ejpam-6951	92	29	c5	c5	PROPN
ejpam-6951	92	30	.	.	PUNCT
ejpam-6951	93	1	first	first	ADV
ejpam-6951	93	2	,	,	PUNCT
ejpam-6951	93	3	we	we	PRON
ejpam-6951	93	4	determine	determine	VERB
ejpam-6951	93	5	the	the	DET
ejpam-6951	93	6	vertex	vertex	NOUN
ejpam-6951	93	7	-	-	PUNCT
ejpam-6951	93	8	uniform	uniform	NOUN
ejpam-6951	93	9	set	set	NOUN
ejpam-6951	93	10	of	of	ADP
ejpam-6951	93	11	p3	p3	PROPN
ejpam-6951	93	12	with	with	ADP
ejpam-6951	93	13	respect	respect	NOUN
ejpam-6951	93	14	to	to	ADP
ejpam-6951	93	15	c5	c5	PROPN
ejpam-6951	93	16	,	,	PUNCT
ejpam-6951	93	17	as	as	SCONJ
ejpam-6951	93	18	follows	follow	VERB
ejpam-6951	93	19	.	.	PUNCT
ejpam-6951	94	1	a	a	DET
ejpam-6951	94	2	=	=	X
ejpam-6951	94	3	{	{	PUNCT
ejpam-6951	94	4	{	{	PUNCT
ejpam-6951	94	5	a1	a1	PROPN
ejpam-6951	94	6	,	,	PUNCT
ejpam-6951	94	7	a2	a2	PROPN
ejpam-6951	94	8	,	,	PUNCT
ejpam-6951	94	9	a3	a3	NOUN
ejpam-6951	94	10	}	}	PUNCT
ejpam-6951	94	11	,	,	PUNCT
ejpam-6951	94	12	{	{	PUNCT
ejpam-6951	94	13	a1	a1	NOUN
ejpam-6951	94	14	,	,	PUNCT
ejpam-6951	94	15	a2	a2	PROPN
ejpam-6951	94	16	,	,	PUNCT
ejpam-6951	94	17	a5	a5	PROPN
ejpam-6951	94	18	}	}	PUNCT
ejpam-6951	94	19	,	,	PUNCT
ejpam-6951	94	20	{	{	PUNCT
ejpam-6951	94	21	a1	a1	NOUN
ejpam-6951	94	22	,	,	PUNCT
ejpam-6951	94	23	a4	a4	NOUN
ejpam-6951	94	24	,	,	PUNCT
ejpam-6951	94	25	a5	a5	PROPN
ejpam-6951	94	26	}	}	PUNCT
ejpam-6951	94	27	,	,	PUNCT
ejpam-6951	94	28	{	{	PUNCT
ejpam-6951	94	29	a2	a2	PROPN
ejpam-6951	94	30	,	,	PUNCT
ejpam-6951	94	31	a3	a3	NOUN
ejpam-6951	94	32	,	,	PUNCT
ejpam-6951	94	33	a4	a4	PROPN
ejpam-6951	94	34	}	}	PUNCT
ejpam-6951	94	35	,	,	PUNCT
ejpam-6951	94	36	{	{	PUNCT
ejpam-6951	94	37	a3	a3	NOUN
ejpam-6951	94	38	,	,	PUNCT
ejpam-6951	94	39	a4	a4	PROPN
ejpam-6951	94	40	,	,	PUNCT
ejpam-6951	94	41	a5	a5	NOUN
ejpam-6951	94	42	}	}	PUNCT
ejpam-6951	94	43	}	}	PUNCT
ejpam-6951	94	44	.	.	PUNCT
ejpam-6951	95	1	it	it	PRON
ejpam-6951	95	2	can	can	AUX
ejpam-6951	95	3	be	be	AUX
ejpam-6951	95	4	observed	observe	VERB
ejpam-6951	95	5	that	that	SCONJ
ejpam-6951	95	6	each	each	DET
ejpam-6951	95	7	element	element	NOUN
ejpam-6951	95	8	of	of	ADP
ejpam-6951	95	9	a	a	DET
ejpam-6951	95	10	induces	induce	NOUN
ejpam-6951	95	11	a	a	DET
ejpam-6951	95	12	subgraph	subgraph	NOUN
ejpam-6951	95	13	that	that	PRON
ejpam-6951	95	14	is	be	AUX
ejpam-6951	95	15	isomorphic	isomorphic	ADJ
ejpam-6951	95	16	to	to	ADP
ejpam-6951	95	17	p3	p3	PROPN
ejpam-6951	95	18	,	,	PUNCT
ejpam-6951	95	19	hence	hence	ADV
ejpam-6951	95	20	a	a	DET
ejpam-6951	95	21	⊆	⊆	NUM
ejpam-6951	95	22	vp3(c5	vp3(c5	NOUN
ejpam-6951	95	23	)	)	PUNCT
ejpam-6951	95	24	.	.	PUNCT
ejpam-6951	96	1	next	next	ADV
ejpam-6951	96	2	,	,	PUNCT
ejpam-6951	96	3	we	we	PRON
ejpam-6951	96	4	show	show	VERB
ejpam-6951	96	5	that	that	SCONJ
ejpam-6951	96	6	each	each	DET
ejpam-6951	96	7	singleton	singleton	NOUN
ejpam-6951	96	8	is	be	AUX
ejpam-6951	96	9	a	a	DET
ejpam-6951	96	10	linear	linear	ADJ
ejpam-6951	96	11	combination	combination	NOUN
ejpam-6951	96	12	of	of	ADP
ejpam-6951	96	13	the	the	DET
ejpam-6951	96	14	elements	element	NOUN
ejpam-6951	96	15	of	of	ADP
ejpam-6951	96	16	a.	a.	NOUN
ejpam-6951	96	17	{	{	PUNCT
ejpam-6951	96	18	a2	a2	PROPN
ejpam-6951	96	19	,	,	PUNCT
ejpam-6951	96	20	a3	a3	NOUN
ejpam-6951	96	21	,	,	PUNCT
ejpam-6951	96	22	a4	a4	PROPN
ejpam-6951	96	23	}	}	PUNCT
ejpam-6951	96	24	△	△	X
ejpam-6951	96	25	{	{	PUNCT
ejpam-6951	96	26	a3	a3	NOUN
ejpam-6951	96	27	,	,	PUNCT
ejpam-6951	96	28	a4	a4	PROPN
ejpam-6951	96	29	,	,	PUNCT
ejpam-6951	96	30	a5	a5	PROPN
ejpam-6951	96	31	}	}	PUNCT
ejpam-6951	96	32	△	△	X
ejpam-6951	96	33	{	{	PUNCT
ejpam-6951	96	34	a1	a1	PROPN
ejpam-6951	96	35	,	,	PUNCT
ejpam-6951	96	36	a2	a2	PROPN
ejpam-6951	96	37	,	,	PUNCT
ejpam-6951	96	38	a5	a5	PROPN
ejpam-6951	96	39	}	}	PUNCT
ejpam-6951	96	40	=	=	SYM
ejpam-6951	96	41	{	{	PUNCT
ejpam-6951	96	42	a1	a1	NOUN
ejpam-6951	96	43	}	}	PUNCT
ejpam-6951	96	44	,	,	PUNCT
ejpam-6951	96	45	{	{	PUNCT
ejpam-6951	96	46	a3	a3	NOUN
ejpam-6951	96	47	,	,	PUNCT
ejpam-6951	96	48	a4	a4	PROPN
ejpam-6951	96	49	,	,	PUNCT
ejpam-6951	96	50	a5	a5	PROPN
ejpam-6951	96	51	}	}	PUNCT
ejpam-6951	96	52	△	△	X
ejpam-6951	96	53	{	{	PUNCT
ejpam-6951	96	54	a1	a1	NOUN
ejpam-6951	96	55	,	,	PUNCT
ejpam-6951	96	56	a4	a4	NOUN
ejpam-6951	96	57	,	,	PUNCT
ejpam-6951	96	58	a5	a5	PROPN
ejpam-6951	96	59	}	}	PUNCT
ejpam-6951	96	60	△	△	X
ejpam-6951	96	61	{	{	PUNCT
ejpam-6951	96	62	a1	a1	PROPN
ejpam-6951	96	63	,	,	PUNCT
ejpam-6951	96	64	a2	a2	PROPN
ejpam-6951	96	65	,	,	PUNCT
ejpam-6951	96	66	a3	a3	NOUN
ejpam-6951	96	67	}	}	PUNCT
ejpam-6951	96	68	=	=	SYM
ejpam-6951	96	69	{	{	PUNCT
ejpam-6951	96	70	a2	a2	PROPN
ejpam-6951	96	71	}	}	PUNCT
ejpam-6951	96	72	,	,	PUNCT
ejpam-6951	96	73	{	{	PUNCT
ejpam-6951	96	74	a1	a1	NOUN
ejpam-6951	96	75	,	,	PUNCT
ejpam-6951	96	76	a4	a4	NOUN
ejpam-6951	96	77	,	,	PUNCT
ejpam-6951	96	78	a5	a5	PROPN
ejpam-6951	96	79	}	}	PUNCT
ejpam-6951	96	80	△	△	X
ejpam-6951	96	81	{	{	PUNCT
ejpam-6951	96	82	a1	a1	PROPN
ejpam-6951	96	83	,	,	PUNCT
ejpam-6951	96	84	a2	a2	PROPN
ejpam-6951	96	85	,	,	PUNCT
ejpam-6951	96	86	a5	a5	PROPN
ejpam-6951	96	87	}	}	PUNCT
ejpam-6951	96	88	△	△	X
ejpam-6951	96	89	{	{	PUNCT
ejpam-6951	96	90	a2	a2	PROPN
ejpam-6951	96	91	,	,	PUNCT
ejpam-6951	96	92	a3	a3	NOUN
ejpam-6951	96	93	,	,	PUNCT
ejpam-6951	96	94	a4	a4	NOUN
ejpam-6951	96	95	}	}	PUNCT
ejpam-6951	96	96	=	=	SYM
ejpam-6951	96	97	{	{	PUNCT
ejpam-6951	96	98	a3	a3	NOUN
ejpam-6951	96	99	}	}	PUNCT
ejpam-6951	96	100	,	,	PUNCT
ejpam-6951	96	101	{	{	PUNCT
ejpam-6951	96	102	a1	a1	NOUN
ejpam-6951	96	103	,	,	PUNCT
ejpam-6951	96	104	a2	a2	PROPN
ejpam-6951	96	105	,	,	PUNCT
ejpam-6951	96	106	a5	a5	PROPN
ejpam-6951	96	107	}	}	PUNCT
ejpam-6951	96	108	△	△	X
ejpam-6951	96	109	{	{	PUNCT
ejpam-6951	96	110	a1	a1	PROPN
ejpam-6951	96	111	,	,	PUNCT
ejpam-6951	96	112	a2	a2	PROPN
ejpam-6951	96	113	,	,	PUNCT
ejpam-6951	96	114	a3	a3	NOUN
ejpam-6951	96	115	}	}	PUNCT
ejpam-6951	96	116	△	△	X
ejpam-6951	96	117	{	{	PUNCT
ejpam-6951	96	118	a3	a3	NOUN
ejpam-6951	96	119	,	,	PUNCT
ejpam-6951	96	120	a4	a4	PROPN
ejpam-6951	96	121	,	,	PUNCT
ejpam-6951	96	122	a5	a5	NOUN
ejpam-6951	96	123	}	}	PUNCT
ejpam-6951	96	124	=	=	SYM
ejpam-6951	96	125	{	{	PUNCT
ejpam-6951	96	126	a4	a4	NOUN
ejpam-6951	96	127	}	}	PUNCT
ejpam-6951	96	128	,	,	PUNCT
ejpam-6951	96	129	and	and	CCONJ
ejpam-6951	96	130	{	{	PUNCT
ejpam-6951	96	131	a1	a1	PROPN
ejpam-6951	96	132	,	,	PUNCT
ejpam-6951	96	133	a2	a2	PROPN
ejpam-6951	96	134	,	,	PUNCT
ejpam-6951	96	135	a3	a3	NOUN
ejpam-6951	96	136	}	}	PUNCT
ejpam-6951	96	137	△	△	X
ejpam-6951	96	138	{	{	PUNCT
ejpam-6951	96	139	a2	a2	PROPN
ejpam-6951	96	140	,	,	PUNCT
ejpam-6951	96	141	a3	a3	NOUN
ejpam-6951	96	142	,	,	PUNCT
ejpam-6951	96	143	a4	a4	PROPN
ejpam-6951	96	144	}	}	PUNCT
ejpam-6951	96	145	△	△	X
ejpam-6951	96	146	{	{	PUNCT
ejpam-6951	96	147	a1	a1	NOUN
ejpam-6951	96	148	,	,	PUNCT
ejpam-6951	96	149	a4	a4	NOUN
ejpam-6951	96	150	,	,	PUNCT
ejpam-6951	96	151	a5	a5	NOUN
ejpam-6951	96	152	}	}	PUNCT
ejpam-6951	96	153	=	=	SYM
ejpam-6951	96	154	{	{	PUNCT
ejpam-6951	96	155	a5	a5	PROPN
ejpam-6951	96	156	}	}	PUNCT
ejpam-6951	96	157	.	.	PUNCT
ejpam-6951	97	1	hence	hence	ADV
ejpam-6951	97	2	,	,	PUNCT
ejpam-6951	97	3	{	{	PUNCT
ejpam-6951	97	4	ai	ai	VERB
ejpam-6951	97	5	}	}	PUNCT
ejpam-6951	97	6	∈	∈	PROPN
ejpam-6951	97	7	vp3(c5	vp3(c5	NOUN
ejpam-6951	97	8	)	)	PUNCT
ejpam-6951	97	9	for	for	ADP
ejpam-6951	97	10	all	all	DET
ejpam-6951	97	11	1	1	NUM
ejpam-6951	97	12	≤	≤	NUM
ejpam-6951	97	13	i	i	PRON
ejpam-6951	97	14	≤	≤	ADV
ejpam-6951	97	15	5	5	NUM
ejpam-6951	97	16	.	.	PUNCT
ejpam-6951	98	1	therefore	therefore	ADV
ejpam-6951	98	2	,	,	PUNCT
ejpam-6951	98	3	by	by	ADP
ejpam-6951	98	4	remark	remark	NOUN
ejpam-6951	98	5	1	1	NUM
ejpam-6951	98	6	,	,	PUNCT
ejpam-6951	98	7	p3	p3	PROPN
ejpam-6951	98	8	is	be	AUX
ejpam-6951	98	9	a	a	DET
ejpam-6951	98	10	vertex	vertex	NOUN
ejpam-6951	98	11	-	-	PUNCT
ejpam-6951	98	12	generator	generator	NOUN
ejpam-6951	98	13	subgraph	subgraph	NOUN
ejpam-6951	98	14	of	of	ADP
ejpam-6951	98	15	c5	c5	PROPN
ejpam-6951	98	16	.	.	PUNCT
ejpam-6951	99	1	g.	g.	PROPN
ejpam-6951	99	2	d.	d.	PROPN
ejpam-6951	99	3	sepillo	sepillo	PROPN
ejpam-6951	99	4	et	et	PROPN
ejpam-6951	99	5	al	al	PROPN
ejpam-6951	99	6	.	.	PUNCT
ejpam-6951	99	7	/	/	SYM
ejpam-6951	99	8	eur	eur	PROPN
ejpam-6951	99	9	.	.	PUNCT
ejpam-6951	100	1	j.	j.	PROPN
ejpam-6951	100	2	pure	pure	PROPN
ejpam-6951	100	3	appl	appl	PROPN
ejpam-6951	100	4	.	.	PROPN
ejpam-6951	100	5	math	math	PROPN
ejpam-6951	100	6	,	,	PUNCT
ejpam-6951	100	7	18	18	NUM
ejpam-6951	100	8	(	(	PUNCT
ejpam-6951	100	9	4	4	NUM
ejpam-6951	100	10	)	)	PUNCT
ejpam-6951	100	11	(	(	PUNCT
ejpam-6951	100	12	2025	2025	NUM
ejpam-6951	100	13	)	)	PUNCT
ejpam-6951	100	14	,	,	PUNCT
ejpam-6951	100	15	6951	6951	NUM
ejpam-6951	100	16	5	5	NUM
ejpam-6951	100	17	of	of	ADP
ejpam-6951	100	18	23	23	NUM
ejpam-6951	100	19	2.1.1	2.1.1	NUM
ejpam-6951	100	20	.	.	PUNCT
ejpam-6951	101	1	some	some	DET
ejpam-6951	101	2	known	know	VERB
ejpam-6951	101	3	results	result	VERB
ejpam-6951	101	4	the	the	DET
ejpam-6951	101	5	first	first	ADJ
ejpam-6951	101	6	theorem	theorem	NOUN
ejpam-6951	101	7	shows	show	VERB
ejpam-6951	101	8	that	that	SCONJ
ejpam-6951	101	9	the	the	DET
ejpam-6951	101	10	trivial	trivial	ADJ
ejpam-6951	101	11	graph	graph	NOUN
ejpam-6951	101	12	is	be	AUX
ejpam-6951	101	13	a	a	DET
ejpam-6951	101	14	vertex	vertex	NOUN
ejpam-6951	101	15	-	-	PUNCT
ejpam-6951	101	16	generator	generator	NOUN
ejpam-6951	101	17	subgraph	subgraph	NOUN
ejpam-6951	101	18	of	of	ADP
ejpam-6951	101	19	any	any	DET
ejpam-6951	101	20	graph	graph	NOUN
ejpam-6951	101	21	.	.	PUNCT
ejpam-6951	102	1	theorem	theorem	NOUN
ejpam-6951	102	2	2	2	NUM
ejpam-6951	102	3	.	.	PUNCT
ejpam-6951	103	1	[	[	X
ejpam-6951	103	2	3	3	X
ejpam-6951	103	3	]	]	PUNCT
ejpam-6951	103	4	the	the	DET
ejpam-6951	103	5	trivial	trivial	ADJ
ejpam-6951	103	6	graph	graph	NOUN
ejpam-6951	103	7	k1	k1	NOUN
ejpam-6951	103	8	is	be	AUX
ejpam-6951	103	9	a	a	DET
ejpam-6951	103	10	vertex	vertex	NOUN
ejpam-6951	103	11	-	-	PUNCT
ejpam-6951	103	12	generator	generator	NOUN
ejpam-6951	103	13	subgraph	subgraph	NOUN
ejpam-6951	103	14	of	of	ADP
ejpam-6951	103	15	any	any	DET
ejpam-6951	103	16	graph	graph	NOUN
ejpam-6951	103	17	g.	g.	NOUN
ejpam-6951	103	18	the	the	DET
ejpam-6951	103	19	trivial	trivial	ADJ
ejpam-6951	103	20	graph	graph	NOUN
ejpam-6951	103	21	is	be	AUX
ejpam-6951	103	22	clearly	clearly	ADV
ejpam-6951	103	23	a	a	DET
ejpam-6951	103	24	vertex	vertex	NOUN
ejpam-6951	103	25	-	-	PUNCT
ejpam-6951	103	26	generator	generator	NOUN
ejpam-6951	103	27	subgraph	subgraph	NOUN
ejpam-6951	103	28	,	,	PUNCT
ejpam-6951	103	29	because	because	SCONJ
ejpam-6951	103	30	it	it	PRON
ejpam-6951	103	31	is	be	AUX
ejpam-6951	103	32	always	always	ADV
ejpam-6951	103	33	isomorphic	isomorphic	ADJ
ejpam-6951	103	34	to	to	ADP
ejpam-6951	103	35	each	each	DET
ejpam-6951	103	36	vertex	vertex	NOUN
ejpam-6951	103	37	of	of	ADP
ejpam-6951	103	38	any	any	DET
ejpam-6951	103	39	graph	graph	NOUN
ejpam-6951	103	40	,	,	PUNCT
ejpam-6951	103	41	so	so	ADV
ejpam-6951	103	42	its	its	PRON
ejpam-6951	103	43	uniform	uniform	NOUN
ejpam-6951	103	44	set	set	NOUN
ejpam-6951	103	45	always	always	ADV
ejpam-6951	103	46	consists	consist	VERB
ejpam-6951	103	47	of	of	ADP
ejpam-6951	103	48	singletons	singleton	NOUN
ejpam-6951	103	49	.	.	PUNCT
ejpam-6951	104	1	the	the	DET
ejpam-6951	104	2	next	next	ADJ
ejpam-6951	104	3	theorem	theorem	NOUN
ejpam-6951	104	4	is	be	AUX
ejpam-6951	104	5	very	very	ADV
ejpam-6951	104	6	useful	useful	ADJ
ejpam-6951	104	7	in	in	ADP
ejpam-6951	104	8	finding	find	VERB
ejpam-6951	104	9	a	a	DET
ejpam-6951	104	10	vertex	vertex	NOUN
ejpam-6951	104	11	-	-	PUNCT
ejpam-6951	104	12	generator	generator	NOUN
ejpam-6951	104	13	subgraph	subgraph	NOUN
ejpam-6951	104	14	of	of	ADP
ejpam-6951	104	15	a	a	DET
ejpam-6951	104	16	certain	certain	ADJ
ejpam-6951	104	17	graph	graph	NOUN
ejpam-6951	104	18	,	,	PUNCT
ejpam-6951	104	19	which	which	PRON
ejpam-6951	104	20	is	be	AUX
ejpam-6951	104	21	based	base	VERB
ejpam-6951	104	22	on	on	ADP
ejpam-6951	104	23	the	the	DET
ejpam-6951	104	24	order	order	NOUN
ejpam-6951	104	25	of	of	ADP
ejpam-6951	104	26	that	that	DET
ejpam-6951	104	27	graph	graph	NOUN
ejpam-6951	104	28	.	.	PUNCT
ejpam-6951	105	1	theorem	theorem	NOUN
ejpam-6951	105	2	3	3	NUM
ejpam-6951	105	3	.	.	PUNCT
ejpam-6951	106	1	[	[	X
ejpam-6951	106	2	3	3	X
ejpam-6951	106	3	]	]	PUNCT
ejpam-6951	106	4	let	let	VERB
ejpam-6951	106	5	h	h	NOUN
ejpam-6951	106	6	be	be	AUX
ejpam-6951	106	7	a	a	DET
ejpam-6951	106	8	subgraph	subgraph	NOUN
ejpam-6951	106	9	of	of	ADP
ejpam-6951	106	10	g.	g.	PROPN
ejpam-6951	106	11	if	if	SCONJ
ejpam-6951	106	12	h	h	NOUN
ejpam-6951	106	13	is	be	AUX
ejpam-6951	106	14	a	a	DET
ejpam-6951	106	15	vertex	vertex	NOUN
ejpam-6951	106	16	-	-	PUNCT
ejpam-6951	106	17	generator	generator	NOUN
ejpam-6951	106	18	subgraph	subgraph	NOUN
ejpam-6951	106	19	of	of	ADP
ejpam-6951	106	20	g	g	PROPN
ejpam-6951	106	21	,	,	PUNCT
ejpam-6951	106	22	then	then	ADV
ejpam-6951	106	23	|v	|v	PROPN
ejpam-6951	106	24	(	(	PUNCT
ejpam-6951	106	25	h)|	h)|	PROPN
ejpam-6951	106	26	is	be	AUX
ejpam-6951	106	27	odd	odd	ADJ
ejpam-6951	106	28	.	.	PUNCT
ejpam-6951	107	1	the	the	DET
ejpam-6951	107	2	next	next	ADJ
ejpam-6951	107	3	theorem	theorem	NOUN
ejpam-6951	107	4	tells	tell	VERB
ejpam-6951	107	5	us	we	PRON
ejpam-6951	107	6	the	the	DET
ejpam-6951	107	7	relationship	relationship	NOUN
ejpam-6951	107	8	of	of	ADP
ejpam-6951	107	9	the	the	DET
ejpam-6951	107	10	cardinality	cardinality	NOUN
ejpam-6951	107	11	of	of	ADP
ejpam-6951	107	12	the	the	DET
ejpam-6951	107	13	sets	set	NOUN
ejpam-6951	107	14	v	v	ADP
ejpam-6951	107	15	(	(	PUNCT
ejpam-6951	107	16	g	g	NOUN
ejpam-6951	107	17	)	)	PUNCT
ejpam-6951	107	18	and	and	CCONJ
ejpam-6951	107	19	vh(g	vh(g	NOUN
ejpam-6951	107	20	)	)	PUNCT
ejpam-6951	107	21	,	,	PUNCT
ejpam-6951	107	22	where	where	SCONJ
ejpam-6951	107	23	h	h	NOUN
ejpam-6951	107	24	is	be	AUX
ejpam-6951	107	25	a	a	DET
ejpam-6951	107	26	subgraph	subgraph	NOUN
ejpam-6951	107	27	of	of	ADP
ejpam-6951	107	28	any	any	DET
ejpam-6951	107	29	graph	graph	NOUN
ejpam-6951	107	30	g.	g.	NOUN
ejpam-6951	107	31	theorem	theorem	NOUN
ejpam-6951	107	32	4	4	NUM
ejpam-6951	107	33	.	.	PUNCT
ejpam-6951	108	1	[	[	X
ejpam-6951	108	2	3	3	X
ejpam-6951	108	3	]	]	PUNCT
ejpam-6951	108	4	let	let	VERB
ejpam-6951	108	5	h	h	NOUN
ejpam-6951	108	6	be	be	AUX
ejpam-6951	108	7	a	a	DET
ejpam-6951	108	8	subgraph	subgraph	NOUN
ejpam-6951	108	9	of	of	ADP
ejpam-6951	108	10	the	the	DET
ejpam-6951	108	11	graph	graph	NOUN
ejpam-6951	108	12	g.	g.	NOUN
ejpam-6951	108	13	if	if	SCONJ
ejpam-6951	108	14	h	h	NOUN
ejpam-6951	108	15	is	be	AUX
ejpam-6951	108	16	a	a	DET
ejpam-6951	108	17	vertex	vertex	NOUN
ejpam-6951	108	18	-	-	PUNCT
ejpam-6951	108	19	generator	generator	NOUN
ejpam-6951	108	20	subgraph	subgraph	NOUN
ejpam-6951	108	21	of	of	ADP
ejpam-6951	108	22	g	g	PROPN
ejpam-6951	108	23	,	,	PUNCT
ejpam-6951	108	24	then	then	ADV
ejpam-6951	108	25	|vh(g)|	|vh(g)|	PROPN
ejpam-6951	108	26	≥	≥	PRON
ejpam-6951	108	27	|v	|v	PROPN
ejpam-6951	108	28	(	(	PUNCT
ejpam-6951	108	29	g)|	g)|	PROPN
ejpam-6951	108	30	.	.	PUNCT
ejpam-6951	109	1	the	the	DET
ejpam-6951	109	2	next	next	ADJ
ejpam-6951	109	3	theorem	theorem	NOUN
ejpam-6951	109	4	gives	give	VERB
ejpam-6951	109	5	a	a	DET
ejpam-6951	109	6	necessary	necessary	ADJ
ejpam-6951	109	7	and	and	CCONJ
ejpam-6951	109	8	sufficient	sufficient	ADJ
ejpam-6951	109	9	condition	condition	NOUN
ejpam-6951	109	10	for	for	ADP
ejpam-6951	109	11	a	a	DET
ejpam-6951	109	12	vertex	vertex	NOUN
ejpam-6951	109	13	-	-	PUNCT
ejpam-6951	109	14	generator	generator	NOUN
ejpam-6951	109	15	subgraph	subgraph	NOUN
ejpam-6951	109	16	of	of	ADP
ejpam-6951	109	17	any	any	DET
ejpam-6951	109	18	graph	graph	NOUN
ejpam-6951	109	19	g	g	NOUN
ejpam-6951	109	20	,	,	PUNCT
ejpam-6951	109	21	where	where	SCONJ
ejpam-6951	109	22	|v	|v	PROPN
ejpam-6951	109	23	(	(	PUNCT
ejpam-6951	109	24	g)|	g)|	VERB
ejpam-6951	109	25	≤	≤	ADJ
ejpam-6951	109	26	3	3	NUM
ejpam-6951	109	27	.	.	PUNCT
ejpam-6951	110	1	theorem	theorem	NOUN
ejpam-6951	110	2	5	5	NUM
ejpam-6951	110	3	.	.	PUNCT
ejpam-6951	111	1	[	[	X
ejpam-6951	111	2	3	3	X
ejpam-6951	111	3	]	]	PUNCT
ejpam-6951	111	4	let	let	VERB
ejpam-6951	111	5	h	h	NOUN
ejpam-6951	111	6	be	be	AUX
ejpam-6951	111	7	a	a	DET
ejpam-6951	111	8	subgraph	subgraph	NOUN
ejpam-6951	111	9	of	of	ADP
ejpam-6951	111	10	g	g	NOUN
ejpam-6951	111	11	,	,	PUNCT
ejpam-6951	111	12	where	where	SCONJ
ejpam-6951	111	13	|v	|v	PROPN
ejpam-6951	111	14	(	(	PUNCT
ejpam-6951	111	15	g)|	g)|	VERB
ejpam-6951	111	16	≤	≤	ADJ
ejpam-6951	111	17	3	3	NUM
ejpam-6951	111	18	.	.	PUNCT
ejpam-6951	112	1	then	then	ADV
ejpam-6951	112	2	h	h	PROPN
ejpam-6951	112	3	is	be	AUX
ejpam-6951	112	4	a	a	DET
ejpam-6951	112	5	vertexgenerator	vertexgenerator	NOUN
ejpam-6951	112	6	subgraph	subgraph	NOUN
ejpam-6951	112	7	of	of	ADP
ejpam-6951	112	8	g	g	PROPN
ejpam-6951	112	9	if	if	SCONJ
ejpam-6951	113	1	and	and	CCONJ
ejpam-6951	113	2	only	only	ADV
ejpam-6951	113	3	if	if	SCONJ
ejpam-6951	113	4	h	h	NOUN
ejpam-6951	113	5	≃	≃	PROPN
ejpam-6951	113	6	k1	k1	PROPN
ejpam-6951	113	7	.	.	PUNCT
ejpam-6951	114	1	let	let	VERB
ejpam-6951	114	2	v	v	NOUN
ejpam-6951	114	3	∗(g	∗(g	PROPN
ejpam-6951	114	4	)	)	PUNCT
ejpam-6951	114	5	be	be	VERB
ejpam-6951	114	6	the	the	DET
ejpam-6951	114	7	set	set	NOUN
ejpam-6951	114	8	of	of	ADP
ejpam-6951	114	9	all	all	DET
ejpam-6951	114	10	elements	element	NOUN
ejpam-6951	114	11	of	of	ADP
ejpam-6951	114	12	v	v	NOUN
ejpam-6951	114	13	(	(	PUNCT
ejpam-6951	114	14	g	g	NOUN
ejpam-6951	114	15	)	)	PUNCT
ejpam-6951	114	16	with	with	ADP
ejpam-6951	114	17	even	even	ADV
ejpam-6951	114	18	cardinality	cardinality	NOUN
ejpam-6951	114	19	.	.	PUNCT
ejpam-6951	115	1	torino	torino	PROPN
ejpam-6951	115	2	and	and	CCONJ
ejpam-6951	115	3	mame	mame	PROPN
ejpam-6951	115	4	called	call	VERB
ejpam-6951	115	5	v	v	ADP
ejpam-6951	115	6	∗(g	∗(g	PROPN
ejpam-6951	115	7	)	)	PUNCT
ejpam-6951	115	8	as	as	ADP
ejpam-6951	115	9	the	the	DET
ejpam-6951	115	10	even	even	ADJ
ejpam-6951	115	11	vertex	vertex	NOUN
ejpam-6951	115	12	space	space	NOUN
ejpam-6951	115	13	of	of	ADP
ejpam-6951	115	14	g	g	PROPN
ejpam-6951	115	15	[	[	X
ejpam-6951	115	16	3	3	NUM
ejpam-6951	115	17	]	]	PUNCT
ejpam-6951	115	18	.	.	PUNCT
ejpam-6951	116	1	the	the	DET
ejpam-6951	116	2	following	follow	VERB
ejpam-6951	116	3	theorem	theorem	NOUN
ejpam-6951	116	4	presents	present	VERB
ejpam-6951	116	5	the	the	DET
ejpam-6951	116	6	relevance	relevance	NOUN
ejpam-6951	116	7	of	of	ADP
ejpam-6951	116	8	the	the	DET
ejpam-6951	116	9	even	even	ADJ
ejpam-6951	116	10	vertex	vertex	NOUN
ejpam-6951	116	11	space	space	NOUN
ejpam-6951	116	12	of	of	ADP
ejpam-6951	116	13	a	a	DET
ejpam-6951	116	14	graph	graph	NOUN
ejpam-6951	116	15	,	,	PUNCT
ejpam-6951	116	16	to	to	ADP
ejpam-6951	116	17	the	the	DET
ejpam-6951	116	18	vertex	vertex	NOUN
ejpam-6951	116	19	space	space	NOUN
ejpam-6951	116	20	of	of	ADP
ejpam-6951	116	21	the	the	DET
ejpam-6951	116	22	graph	graph	NOUN
ejpam-6951	116	23	.	.	PUNCT
ejpam-6951	117	1	theorem	theorem	NOUN
ejpam-6951	117	2	6	6	NUM
ejpam-6951	117	3	.	.	PUNCT
ejpam-6951	118	1	[	[	X
ejpam-6951	118	2	3	3	X
ejpam-6951	118	3	]	]	PUNCT
ejpam-6951	118	4	let	let	VERB
ejpam-6951	118	5	g	g	PRON
ejpam-6951	118	6	be	be	AUX
ejpam-6951	118	7	a	a	DET
ejpam-6951	118	8	graph	graph	NOUN
ejpam-6951	118	9	of	of	ADP
ejpam-6951	118	10	order	order	NOUN
ejpam-6951	118	11	n.	n.	NOUN
ejpam-6951	118	12	then	then	ADV
ejpam-6951	118	13	,	,	PUNCT
ejpam-6951	118	14	v	v	X
ejpam-6951	118	15	∗(g	∗(g	PROPN
ejpam-6951	118	16	)	)	PUNCT
ejpam-6951	118	17	is	be	AUX
ejpam-6951	118	18	a	a	DET
ejpam-6951	118	19	subspace	subspace	NOUN
ejpam-6951	118	20	of	of	ADP
ejpam-6951	118	21	v	v	NOUN
ejpam-6951	118	22	(	(	PUNCT
ejpam-6951	118	23	g	g	NOUN
ejpam-6951	118	24	)	)	PUNCT
ejpam-6951	118	25	.	.	PUNCT
ejpam-6951	119	1	moreover	moreover	ADV
ejpam-6951	119	2	,	,	PUNCT
ejpam-6951	119	3	dimv	dimv	NOUN
ejpam-6951	119	4	∗(g	∗(g	PROPN
ejpam-6951	119	5	)	)	PUNCT
ejpam-6951	120	1	=	=	PUNCT
ejpam-6951	120	2	n−	n−	NOUN
ejpam-6951	120	3	1	1	NUM
ejpam-6951	120	4	.	.	PUNCT
ejpam-6951	121	1	a	a	DET
ejpam-6951	121	2	basis	basis	NOUN
ejpam-6951	121	3	formed	form	VERB
ejpam-6951	121	4	from	from	ADP
ejpam-6951	121	5	the	the	DET
ejpam-6951	121	6	even	even	ADJ
ejpam-6951	121	7	vertex	vertex	NOUN
ejpam-6951	121	8	space	space	NOUN
ejpam-6951	121	9	of	of	ADP
ejpam-6951	121	10	any	any	DET
ejpam-6951	121	11	graph	graph	NOUN
ejpam-6951	121	12	is	be	AUX
ejpam-6951	121	13	presented	present	VERB
ejpam-6951	121	14	in	in	ADP
ejpam-6951	121	15	the	the	DET
ejpam-6951	121	16	theorem	theorem	NOUN
ejpam-6951	121	17	below	below	ADV
ejpam-6951	121	18	,	,	PUNCT
ejpam-6951	121	19	which	which	PRON
ejpam-6951	121	20	is	be	AUX
ejpam-6951	121	21	parallel	parallel	ADJ
ejpam-6951	121	22	to	to	ADP
ejpam-6951	121	23	theorem	theorem	ADJ
ejpam-6951	121	24	1	1	NUM
ejpam-6951	121	25	.	.	PUNCT
ejpam-6951	121	26	theorem	theorem	VERB
ejpam-6951	121	27	7	7	NUM
ejpam-6951	121	28	.	.	PUNCT
ejpam-6951	122	1	[	[	X
ejpam-6951	122	2	3	3	X
ejpam-6951	122	3	]	]	PUNCT
ejpam-6951	122	4	let	let	VERB
ejpam-6951	122	5	g	g	PRON
ejpam-6951	122	6	be	be	AUX
ejpam-6951	122	7	a	a	DET
ejpam-6951	122	8	graph	graph	NOUN
ejpam-6951	122	9	with	with	ADP
ejpam-6951	122	10	v	v	NOUN
ejpam-6951	122	11	(	(	PUNCT
ejpam-6951	122	12	g	g	NOUN
ejpam-6951	122	13	)	)	PUNCT
ejpam-6951	122	14	=	=	SYM
ejpam-6951	122	15	{	{	PUNCT
ejpam-6951	122	16	x1	x1	PROPN
ejpam-6951	122	17	,	,	PUNCT
ejpam-6951	122	18	x2	x2	PROPN
ejpam-6951	122	19	,	,	PUNCT
ejpam-6951	122	20	x3	x3	ADJ
ejpam-6951	122	21	,	,	PUNCT
ejpam-6951	122	22	...	...	PUNCT
ejpam-6951	122	23	xn	xn	NUM
ejpam-6951	122	24	}	}	PUNCT
ejpam-6951	122	25	.	.	PUNCT
ejpam-6951	123	1	then	then	ADV
ejpam-6951	123	2	the	the	DET
ejpam-6951	123	3	set	set	NOUN
ejpam-6951	123	4	b	b	NOUN
ejpam-6951	123	5	=	=	PRON
ejpam-6951	123	6	{	{	PUNCT
ejpam-6951	123	7	{	{	PUNCT
ejpam-6951	123	8	x1	x1	PROPN
ejpam-6951	123	9	,	,	PUNCT
ejpam-6951	123	10	x2	x2	PROPN
ejpam-6951	123	11	}	}	PUNCT
ejpam-6951	123	12	,	,	PUNCT
ejpam-6951	123	13	{	{	PUNCT
ejpam-6951	123	14	x1	x1	ADJ
ejpam-6951	123	15	,	,	PUNCT
ejpam-6951	123	16	x3	x3	ADJ
ejpam-6951	123	17	}	}	PUNCT
ejpam-6951	123	18	,	,	PUNCT
ejpam-6951	123	19	{	{	PUNCT
ejpam-6951	123	20	x1	x1	PROPN
ejpam-6951	123	21	,	,	PUNCT
ejpam-6951	123	22	x4	x4	PROPN
ejpam-6951	123	23	}	}	PUNCT
ejpam-6951	123	24	,	,	PUNCT
ejpam-6951	123	25	...	...	PUNCT
ejpam-6951	123	26	,	,	PUNCT
ejpam-6951	123	27	{	{	PUNCT
ejpam-6951	123	28	x1	x1	PROPN
ejpam-6951	123	29	,	,	PUNCT
ejpam-6951	123	30	xn	xn	PROPN
ejpam-6951	123	31	}	}	PUNCT
ejpam-6951	123	32	}	}	PUNCT
ejpam-6951	123	33	forms	form	VERB
ejpam-6951	123	34	a	a	DET
ejpam-6951	123	35	basis	basis	NOUN
ejpam-6951	123	36	for	for	ADP
ejpam-6951	123	37	v	v	NOUN
ejpam-6951	123	38	∗(g	∗(g	PROPN
ejpam-6951	123	39	)	)	PUNCT
ejpam-6951	123	40	.	.	PUNCT
ejpam-6951	124	1	the	the	DET
ejpam-6951	124	2	next	next	ADJ
ejpam-6951	124	3	theorem	theorem	NOUN
ejpam-6951	124	4	is	be	AUX
ejpam-6951	124	5	also	also	ADV
ejpam-6951	124	6	important	important	ADJ
ejpam-6951	124	7	in	in	ADP
ejpam-6951	124	8	the	the	DET
ejpam-6951	124	9	concept	concept	NOUN
ejpam-6951	124	10	of	of	ADP
ejpam-6951	124	11	the	the	DET
ejpam-6951	124	12	even	even	ADJ
ejpam-6951	124	13	vertex	vertex	NOUN
ejpam-6951	124	14	space	space	NOUN
ejpam-6951	124	15	,	,	PUNCT
ejpam-6951	124	16	which	which	PRON
ejpam-6951	124	17	is	be	AUX
ejpam-6951	124	18	presented	present	VERB
ejpam-6951	124	19	below	below	ADV
ejpam-6951	124	20	.	.	PUNCT
ejpam-6951	125	1	theorem	theorem	VERB
ejpam-6951	125	2	8	8	NUM
ejpam-6951	125	3	.	.	PUNCT
ejpam-6951	126	1	[	[	X
ejpam-6951	126	2	3	3	X
ejpam-6951	126	3	]	]	PUNCT
ejpam-6951	126	4	let	let	VERB
ejpam-6951	126	5	g	g	NOUN
ejpam-6951	126	6	and	and	CCONJ
ejpam-6951	126	7	h	h	NOUN
ejpam-6951	126	8	be	be	AUX
ejpam-6951	126	9	graphs	graph	NOUN
ejpam-6951	126	10	such	such	ADJ
ejpam-6951	126	11	that	that	DET
ejpam-6951	126	12	h	h	NOUN
ejpam-6951	126	13	⊆	⊆	NUM
ejpam-6951	126	14	g	g	NOUN
ejpam-6951	126	15	,	,	PUNCT
ejpam-6951	126	16	and	and	CCONJ
ejpam-6951	126	17	|v	|v	PROPN
ejpam-6951	126	18	(	(	PUNCT
ejpam-6951	126	19	h)|	h)|	PROPN
ejpam-6951	126	20	is	be	AUX
ejpam-6951	126	21	odd	odd	ADJ
ejpam-6951	126	22	.	.	PUNCT
ejpam-6951	127	1	if	if	SCONJ
ejpam-6951	127	2	v	v	PROPN
ejpam-6951	127	3	∗(g	∗(g	PROPN
ejpam-6951	127	4	)	)	PUNCT
ejpam-6951	127	5	⊆	⊆	NUM
ejpam-6951	127	6	vh(g	vh(g	NOUN
ejpam-6951	127	7	)	)	PUNCT
ejpam-6951	127	8	,	,	PUNCT
ejpam-6951	127	9	then	then	ADV
ejpam-6951	127	10	h	h	PROPN
ejpam-6951	127	11	is	be	AUX
ejpam-6951	127	12	vertex	vertex	NOUN
ejpam-6951	127	13	-	-	PUNCT
ejpam-6951	127	14	generator	generator	NOUN
ejpam-6951	127	15	subgraph	subgraph	NOUN
ejpam-6951	127	16	of	of	ADP
ejpam-6951	127	17	g.	g.	PROPN
ejpam-6951	127	18	theorem	theorem	VERB
ejpam-6951	127	19	8	8	NUM
ejpam-6951	127	20	tells	tell	VERB
ejpam-6951	127	21	us	we	PRON
ejpam-6951	127	22	that	that	SCONJ
ejpam-6951	127	23	we	we	PRON
ejpam-6951	127	24	only	only	ADV
ejpam-6951	127	25	need	need	VERB
ejpam-6951	127	26	to	to	PART
ejpam-6951	127	27	show	show	VERB
ejpam-6951	127	28	the	the	DET
ejpam-6951	127	29	basis	basis	NOUN
ejpam-6951	127	30	for	for	ADP
ejpam-6951	127	31	the	the	DET
ejpam-6951	127	32	even	even	ADJ
ejpam-6951	127	33	vertex	vertex	NOUN
ejpam-6951	127	34	space	space	NOUN
ejpam-6951	127	35	of	of	ADP
ejpam-6951	127	36	the	the	DET
ejpam-6951	127	37	graph	graph	NOUN
ejpam-6951	127	38	is	be	AUX
ejpam-6951	127	39	a	a	DET
ejpam-6951	127	40	subset	subset	NOUN
ejpam-6951	127	41	of	of	ADP
ejpam-6951	127	42	the	the	DET
ejpam-6951	127	43	span	span	NOUN
ejpam-6951	127	44	of	of	ADP
ejpam-6951	127	45	the	the	DET
ejpam-6951	127	46	the	the	DET
ejpam-6951	127	47	vertex	vertex	NOUN
ejpam-6951	127	48	-	-	PUNCT
ejpam-6951	127	49	uniform	uniform	NOUN
ejpam-6951	127	50	set	set	NOUN
ejpam-6951	127	51	,	,	PUNCT
ejpam-6951	127	52	in	in	ADP
ejpam-6951	127	53	order	order	NOUN
ejpam-6951	127	54	to	to	PART
ejpam-6951	127	55	show	show	VERB
ejpam-6951	127	56	that	that	SCONJ
ejpam-6951	127	57	a	a	DET
ejpam-6951	127	58	subgraph	subgraph	NOUN
ejpam-6951	127	59	is	be	AUX
ejpam-6951	127	60	a	a	DET
ejpam-6951	127	61	vertex	vertex	NOUN
ejpam-6951	127	62	-	-	PUNCT
ejpam-6951	127	63	generator	generator	NOUN
ejpam-6951	127	64	subgraph	subgraph	NOUN
ejpam-6951	127	65	of	of	ADP
ejpam-6951	127	66	a	a	DET
ejpam-6951	127	67	graph	graph	NOUN
ejpam-6951	127	68	.	.	PUNCT
ejpam-6951	128	1	this	this	PRON
ejpam-6951	128	2	follows	follow	VERB
ejpam-6951	128	3	a	a	DET
ejpam-6951	128	4	useful	useful	ADJ
ejpam-6951	128	5	remark	remark	NOUN
ejpam-6951	128	6	,	,	PUNCT
ejpam-6951	128	7	which	which	PRON
ejpam-6951	128	8	is	be	AUX
ejpam-6951	128	9	parallel	parallel	ADJ
ejpam-6951	128	10	to	to	PART
ejpam-6951	128	11	remark	remark	VERB
ejpam-6951	128	12	1	1	NUM
ejpam-6951	128	13	.	.	PUNCT
ejpam-6951	128	14	g.	g.	PROPN
ejpam-6951	128	15	d.	d.	PROPN
ejpam-6951	128	16	sepillo	sepillo	PROPN
ejpam-6951	128	17	et	et	PROPN
ejpam-6951	128	18	al	al	PROPN
ejpam-6951	128	19	.	.	PUNCT
ejpam-6951	128	20	/	/	SYM
ejpam-6951	128	21	eur	eur	PROPN
ejpam-6951	128	22	.	.	PUNCT
ejpam-6951	129	1	j.	j.	PROPN
ejpam-6951	129	2	pure	pure	PROPN
ejpam-6951	129	3	appl	appl	PROPN
ejpam-6951	129	4	.	.	PROPN
ejpam-6951	129	5	math	math	PROPN
ejpam-6951	129	6	,	,	PUNCT
ejpam-6951	129	7	18	18	NUM
ejpam-6951	129	8	(	(	PUNCT
ejpam-6951	129	9	4	4	NUM
ejpam-6951	129	10	)	)	PUNCT
ejpam-6951	129	11	(	(	PUNCT
ejpam-6951	129	12	2025	2025	NUM
ejpam-6951	129	13	)	)	PUNCT
ejpam-6951	129	14	,	,	PUNCT
ejpam-6951	129	15	6951	6951	NUM
ejpam-6951	129	16	6	6	NUM
ejpam-6951	129	17	of	of	ADP
ejpam-6951	129	18	23	23	NUM
ejpam-6951	129	19	remark	remark	NOUN
ejpam-6951	129	20	2	2	NUM
ejpam-6951	129	21	.	.	PUNCT
ejpam-6951	130	1	[	[	X
ejpam-6951	130	2	3	3	X
ejpam-6951	130	3	]	]	PUNCT
ejpam-6951	130	4	let	let	VERB
ejpam-6951	130	5	g	g	PRON
ejpam-6951	130	6	be	be	AUX
ejpam-6951	130	7	a	a	DET
ejpam-6951	130	8	graph	graph	NOUN
ejpam-6951	130	9	with	with	ADP
ejpam-6951	130	10	vertex	vertex	NOUN
ejpam-6951	130	11	set	set	VERB
ejpam-6951	130	12	v	v	NOUN
ejpam-6951	130	13	(	(	PUNCT
ejpam-6951	130	14	g	g	NOUN
ejpam-6951	130	15	)	)	PUNCT
ejpam-6951	130	16	=	=	SYM
ejpam-6951	130	17	{	{	PUNCT
ejpam-6951	130	18	x1	x1	PROPN
ejpam-6951	130	19	,	,	PUNCT
ejpam-6951	130	20	x2	x2	PROPN
ejpam-6951	130	21	,	,	PUNCT
ejpam-6951	130	22	x3	x3	ADJ
ejpam-6951	130	23	,	,	PUNCT
ejpam-6951	130	24	...	...	PUNCT
ejpam-6951	130	25	,	,	PUNCT
ejpam-6951	130	26	xn	xn	PROPN
ejpam-6951	130	27	}	}	PUNCT
ejpam-6951	130	28	.	.	PUNCT
ejpam-6951	131	1	let	let	VERB
ejpam-6951	131	2	h	h	PRON
ejpam-6951	131	3	be	be	AUX
ejpam-6951	131	4	a	a	DET
ejpam-6951	131	5	subgraph	subgraph	NOUN
ejpam-6951	131	6	of	of	ADP
ejpam-6951	131	7	g.	g.	PROPN
ejpam-6951	132	1	then	then	ADV
ejpam-6951	132	2	h	h	PROPN
ejpam-6951	132	3	is	be	AUX
ejpam-6951	132	4	a	a	DET
ejpam-6951	132	5	vertex	vertex	NOUN
ejpam-6951	132	6	-	-	PUNCT
ejpam-6951	132	7	generator	generator	NOUN
ejpam-6951	132	8	subgraph	subgraph	NOUN
ejpam-6951	132	9	of	of	ADP
ejpam-6951	132	10	g	g	PROPN
ejpam-6951	132	11	if	if	SCONJ
ejpam-6951	133	1	and	and	CCONJ
ejpam-6951	133	2	only	only	ADV
ejpam-6951	133	3	if	if	SCONJ
ejpam-6951	133	4	{	{	PUNCT
ejpam-6951	133	5	x1	x1	NUM
ejpam-6951	133	6	,	,	PUNCT
ejpam-6951	133	7	xi	xi	ADJ
ejpam-6951	133	8	}	}	PUNCT
ejpam-6951	133	9	∈	∈	PROPN
ejpam-6951	133	10	vh(g	vh(g	NOUN
ejpam-6951	133	11	)	)	PUNCT
ejpam-6951	133	12	for	for	ADP
ejpam-6951	133	13	all	all	DET
ejpam-6951	133	14	2	2	NUM
ejpam-6951	133	15	≤	≤	NUM
ejpam-6951	133	16	i	i	PRON
ejpam-6951	133	17	≤	≤	PROPN
ejpam-6951	133	18	n.	n.	VERB
ejpam-6951	133	19	the	the	DET
ejpam-6951	133	20	following	follow	VERB
ejpam-6951	133	21	theorem	theorem	NOUN
ejpam-6951	133	22	provides	provide	VERB
ejpam-6951	133	23	the	the	DET
ejpam-6951	133	24	necessary	necessary	ADJ
ejpam-6951	133	25	and	and	CCONJ
ejpam-6951	133	26	sufficient	sufficient	ADJ
ejpam-6951	133	27	conditions	condition	NOUN
ejpam-6951	133	28	for	for	SCONJ
ejpam-6951	133	29	a	a	DET
ejpam-6951	133	30	subgraph	subgraph	NOUN
ejpam-6951	133	31	h	h	NOUN
ejpam-6951	133	32	to	to	PART
ejpam-6951	133	33	be	be	AUX
ejpam-6951	133	34	a	a	DET
ejpam-6951	133	35	vertex	vertex	NOUN
ejpam-6951	133	36	generator	generator	NOUN
ejpam-6951	133	37	of	of	ADP
ejpam-6951	133	38	an	an	DET
ejpam-6951	133	39	empty	empty	ADJ
ejpam-6951	133	40	graph	graph	NOUN
ejpam-6951	133	41	kn	kn	PROPN
ejpam-6951	133	42	.	.	PUNCT
ejpam-6951	134	1	this	this	DET
ejpam-6951	134	2	particular	particular	ADJ
ejpam-6951	134	3	result	result	NOUN
ejpam-6951	134	4	will	will	AUX
ejpam-6951	134	5	be	be	AUX
ejpam-6951	134	6	used	use	VERB
ejpam-6951	134	7	in	in	ADP
ejpam-6951	134	8	following	follow	VERB
ejpam-6951	134	9	discussion	discussion	NOUN
ejpam-6951	134	10	.	.	PUNCT
ejpam-6951	135	1	theorem	theorem	VERB
ejpam-6951	135	2	9	9	NUM
ejpam-6951	135	3	.	.	PUNCT
ejpam-6951	136	1	[	[	X
ejpam-6951	136	2	3	3	X
ejpam-6951	136	3	]	]	X
ejpam-6951	136	4	let	let	VERB
ejpam-6951	136	5	n	n	PRON
ejpam-6951	136	6	and	and	CCONJ
ejpam-6951	136	7	t	t	PROPN
ejpam-6951	136	8	be	be	AUX
ejpam-6951	136	9	postive	postive	ADJ
ejpam-6951	136	10	integers	integer	NOUN
ejpam-6951	136	11	.	.	PUNCT
ejpam-6951	137	1	let	let	VERB
ejpam-6951	137	2	h	h	PRON
ejpam-6951	137	3	be	be	AUX
ejpam-6951	137	4	a	a	DET
ejpam-6951	137	5	subgraph	subgraph	NOUN
ejpam-6951	137	6	of	of	ADP
ejpam-6951	137	7	kn	kn	PROPN
ejpam-6951	137	8	,	,	PUNCT
ejpam-6951	137	9	where	where	SCONJ
ejpam-6951	137	10	|v	|v	PROPN
ejpam-6951	137	11	(	(	PUNCT
ejpam-6951	137	12	h)|	h)|	NOUN
ejpam-6951	137	13	=	=	PROPN
ejpam-6951	137	14	t.	t.	NOUN
ejpam-6951	137	15	then	then	ADV
ejpam-6951	137	16	h	h	PROPN
ejpam-6951	137	17	is	be	AUX
ejpam-6951	137	18	a	a	DET
ejpam-6951	137	19	vertex	vertex	NOUN
ejpam-6951	137	20	-	-	PUNCT
ejpam-6951	137	21	generator	generator	NOUN
ejpam-6951	137	22	subgraph	subgraph	NOUN
ejpam-6951	137	23	of	of	ADP
ejpam-6951	137	24	kn	kn	PROPN
ejpam-6951	137	25	if	if	SCONJ
ejpam-6951	137	26	and	and	CCONJ
ejpam-6951	137	27	only	only	ADV
ejpam-6951	137	28	if	if	SCONJ
ejpam-6951	137	29	the	the	DET
ejpam-6951	137	30	following	follow	VERB
ejpam-6951	137	31	conditions	condition	NOUN
ejpam-6951	137	32	are	be	AUX
ejpam-6951	137	33	satisfied	satisfied	ADJ
ejpam-6951	137	34	:	:	PUNCT
ejpam-6951	137	35	(	(	PUNCT
ejpam-6951	137	36	i	i	NOUN
ejpam-6951	137	37	)	)	PUNCT
ejpam-6951	137	38	t	t	PROPN
ejpam-6951	137	39	is	be	AUX
ejpam-6951	137	40	odd	odd	ADJ
ejpam-6951	137	41	;	;	PUNCT
ejpam-6951	138	1	(	(	PUNCT
ejpam-6951	138	2	ii	ii	NOUN
ejpam-6951	138	3	)	)	PUNCT
ejpam-6951	138	4	1	1	NUM
ejpam-6951	138	5	≤	≤	NOUN
ejpam-6951	138	6	t	t	PROPN
ejpam-6951	138	7	≤	≤	NUM
ejpam-6951	138	8	n−	n−	PROPN
ejpam-6951	138	9	1	1	NUM
ejpam-6951	138	10	;	;	PUNCT
ejpam-6951	138	11	and	and	CCONJ
ejpam-6951	138	12	(	(	PUNCT
ejpam-6951	138	13	iii	iii	X
ejpam-6951	138	14	)	)	PUNCT
ejpam-6951	138	15	h	h	NOUN
ejpam-6951	138	16	≃	≃	PROPN
ejpam-6951	138	17	kt	kt	PROPN
ejpam-6951	138	18	.	.	PROPN
ejpam-6951	138	19	3	3	NUM
ejpam-6951	138	20	.	.	X
ejpam-6951	138	21	main	main	ADJ
ejpam-6951	138	22	results	result	NOUN
ejpam-6951	138	23	3.1	3.1	NUM
ejpam-6951	138	24	.	.	PUNCT
ejpam-6951	138	25	vertex	vertex	NOUN
ejpam-6951	138	26	-	-	PUNCT
ejpam-6951	138	27	generator	generator	NOUN
ejpam-6951	138	28	subgraph	subgraph	NOUN
ejpam-6951	138	29	of	of	ADP
ejpam-6951	138	30	complete	complete	ADJ
ejpam-6951	138	31	bipartite	bipartite	PROPN
ejpam-6951	138	32	graph	graph	NOUN
ejpam-6951	138	33	km	km	PROPN
ejpam-6951	138	34	,	,	PUNCT
ejpam-6951	138	35	n	n	CCONJ
ejpam-6951	138	36	this	this	DET
ejpam-6951	138	37	section	section	NOUN
ejpam-6951	138	38	provides	provide	VERB
ejpam-6951	138	39	some	some	DET
ejpam-6951	138	40	vertex	vertex	NOUN
ejpam-6951	138	41	-	-	PUNCT
ejpam-6951	138	42	generator	generator	NOUN
ejpam-6951	138	43	subgraphs	subgraph	NOUN
ejpam-6951	138	44	of	of	ADP
ejpam-6951	138	45	complete	complete	ADJ
ejpam-6951	138	46	bipartite	bipartite	PROPN
ejpam-6951	138	47	graph	graph	NOUN
ejpam-6951	138	48	km	km	PROPN
ejpam-6951	138	49	,	,	PUNCT
ejpam-6951	138	50	n.	n.	PROPN
ejpam-6951	138	51	let	let	VERB
ejpam-6951	138	52	km	km	PROPN
ejpam-6951	138	53	,	,	PUNCT
ejpam-6951	138	54	n	n	CCONJ
ejpam-6951	138	55	be	be	VERB
ejpam-6951	138	56	the	the	DET
ejpam-6951	138	57	complete	complete	ADJ
ejpam-6951	138	58	bipartite	bipartite	NOUN
ejpam-6951	138	59	graph	graph	NOUN
ejpam-6951	138	60	with	with	ADP
ejpam-6951	138	61	vertex	vertex	NOUN
ejpam-6951	138	62	set	set	VERB
ejpam-6951	138	63	v	v	NOUN
ejpam-6951	138	64	(	(	PUNCT
ejpam-6951	138	65	km	km	PROPN
ejpam-6951	138	66	,	,	PUNCT
ejpam-6951	138	67	n	n	CCONJ
ejpam-6951	138	68	)	)	PUNCT
ejpam-6951	138	69	=	=	SYM
ejpam-6951	139	1	m	m	VERB
ejpam-6951	139	2	∪n	∪n	X
ejpam-6951	139	3	,	,	PUNCT
ejpam-6951	139	4	where	where	SCONJ
ejpam-6951	139	5	m	m	VERB
ejpam-6951	139	6	=	=	PUNCT
ejpam-6951	139	7	{	{	PUNCT
ejpam-6951	139	8	x1	x1	PROPN
ejpam-6951	139	9	,	,	PUNCT
ejpam-6951	139	10	x2	x2	PROPN
ejpam-6951	139	11	,	,	PUNCT
ejpam-6951	139	12	x3	x3	ADJ
ejpam-6951	139	13	,	,	PUNCT
ejpam-6951	139	14	...	...	PUNCT
ejpam-6951	139	15	,	,	PUNCT
ejpam-6951	139	16	xm−1	xm−1	PROPN
ejpam-6951	139	17	,	,	PUNCT
ejpam-6951	139	18	xm	xm	PROPN
ejpam-6951	139	19	}	}	PUNCT
ejpam-6951	139	20	and	and	CCONJ
ejpam-6951	139	21	n	n	CCONJ
ejpam-6951	139	22	=	=	SYM
ejpam-6951	139	23	{	{	PUNCT
ejpam-6951	139	24	y1	y1	PROPN
ejpam-6951	139	25	,	,	PUNCT
ejpam-6951	139	26	y2	y2	PROPN
ejpam-6951	139	27	,	,	PUNCT
ejpam-6951	139	28	y3	y3	PROPN
ejpam-6951	139	29	,	,	PUNCT
ejpam-6951	139	30	...	...	PUNCT
ejpam-6951	139	31	,	,	PUNCT
ejpam-6951	139	32	yn−1	yn−1	PROPN
ejpam-6951	139	33	,	,	PUNCT
ejpam-6951	139	34	yn	yn	PROPN
ejpam-6951	139	35	}	}	PUNCT
ejpam-6951	139	36	are	be	AUX
ejpam-6951	139	37	the	the	DET
ejpam-6951	139	38	partite	partite	ADJ
ejpam-6951	139	39	sets	set	NOUN
ejpam-6951	139	40	,	,	PUNCT
ejpam-6951	139	41	and	and	CCONJ
ejpam-6951	139	42	edge	edge	VERB
ejpam-6951	139	43	set	set	VERB
ejpam-6951	139	44	e(km	e(km	PROPN
ejpam-6951	139	45	,	,	PUNCT
ejpam-6951	139	46	n	n	CCONJ
ejpam-6951	139	47	)	)	PUNCT
ejpam-6951	139	48	=	=	PRON
ejpam-6951	139	49	{	{	PUNCT
ejpam-6951	140	1	[	[	X
ejpam-6951	140	2	xi	xi	X
ejpam-6951	140	3	,	,	PUNCT
ejpam-6951	140	4	yj	yj	PROPN
ejpam-6951	140	5	]	]	X
ejpam-6951	140	6	}	}	PUNCT
ejpam-6951	140	7	for	for	ADP
ejpam-6951	140	8	all	all	DET
ejpam-6951	140	9	1	1	NUM
ejpam-6951	140	10	≤	≤	NUM
ejpam-6951	140	11	i	i	PRON
ejpam-6951	140	12	≤	≤	NOUN
ejpam-6951	140	13	m	m	VERB
ejpam-6951	140	14	and	and	CCONJ
ejpam-6951	140	15	1	1	NUM
ejpam-6951	140	16	≤	≤	NUM
ejpam-6951	140	17	j	j	PROPN
ejpam-6951	140	18	≤	≤	PROPN
ejpam-6951	140	19	n.	n.	PROPN
ejpam-6951	140	20	presented	present	VERB
ejpam-6951	140	21	in	in	ADP
ejpam-6951	140	22	figure	figure	NOUN
ejpam-6951	140	23	2	2	NUM
ejpam-6951	140	24	is	be	AUX
ejpam-6951	140	25	the	the	DET
ejpam-6951	140	26	labeling	labeling	NOUN
ejpam-6951	140	27	of	of	ADP
ejpam-6951	140	28	a	a	DET
ejpam-6951	140	29	complete	complete	ADJ
ejpam-6951	140	30	bipartite	bipartite	NOUN
ejpam-6951	140	31	graph	graph	NOUN
ejpam-6951	140	32	,	,	PUNCT
ejpam-6951	140	33	which	which	PRON
ejpam-6951	140	34	will	will	AUX
ejpam-6951	140	35	be	be	AUX
ejpam-6951	140	36	considered	consider	VERB
ejpam-6951	140	37	in	in	ADP
ejpam-6951	140	38	the	the	DET
ejpam-6951	140	39	discussion	discussion	NOUN
ejpam-6951	140	40	of	of	ADP
ejpam-6951	140	41	this	this	DET
ejpam-6951	140	42	section	section	NOUN
ejpam-6951	140	43	.	.	PUNCT
ejpam-6951	141	1	x1	x1	PROPN
ejpam-6951	142	1	x2	x2	PROPN
ejpam-6951	142	2	x3	x3	PROPN
ejpam-6951	142	3	xm−1	xm−1	PROPN
ejpam-6951	142	4	xm	xm	PROPN
ejpam-6951	143	1	y1	y1	INTJ
ejpam-6951	143	2	y2	y2	INTJ
ejpam-6951	143	3	yn−1	yn−1	NOUN
ejpam-6951	143	4	yn	yn	PROPN
ejpam-6951	143	5	km	km	PROPN
ejpam-6951	143	6	,	,	PUNCT
ejpam-6951	143	7	n	n	PRON
ejpam-6951	143	8	:	:	PUNCT
ejpam-6951	143	9	figure	figure	NOUN
ejpam-6951	143	10	2	2	NUM
ejpam-6951	143	11	:	:	PUNCT
ejpam-6951	143	12	the	the	DET
ejpam-6951	143	13	labeling	labeling	NOUN
ejpam-6951	143	14	of	of	ADP
ejpam-6951	143	15	km	km	PROPN
ejpam-6951	143	16	,	,	PUNCT
ejpam-6951	143	17	n	n	PRON
ejpam-6951	143	18	a	a	DET
ejpam-6951	143	19	complete	complete	ADJ
ejpam-6951	143	20	bipartite	bipartite	NOUN
ejpam-6951	143	21	graph	graph	NOUN
ejpam-6951	143	22	km	km	PROPN
ejpam-6951	143	23	,	,	PUNCT
ejpam-6951	143	24	n	n	PRON
ejpam-6951	143	25	has	have	VERB
ejpam-6951	143	26	order	order	NOUN
ejpam-6951	143	27	m	m	NOUN
ejpam-6951	143	28	+	+	ADJ
ejpam-6951	143	29	n	n	CCONJ
ejpam-6951	143	30	and	and	CCONJ
ejpam-6951	143	31	size	size	NOUN
ejpam-6951	143	32	mn	mn	PROPN
ejpam-6951	143	33	for	for	ADP
ejpam-6951	143	34	all	all	DET
ejpam-6951	143	35	positive	positive	ADJ
ejpam-6951	143	36	integers	integer	NOUN
ejpam-6951	143	37	m	m	VERB
ejpam-6951	143	38	and	and	CCONJ
ejpam-6951	143	39	n.	n.	VERB
ejpam-6951	143	40	by	by	ADP
ejpam-6951	143	41	definition	definition	NOUN
ejpam-6951	143	42	1	1	NUM
ejpam-6951	143	43	,	,	PUNCT
ejpam-6951	143	44	the	the	DET
ejpam-6951	143	45	vertex	vertex	NOUN
ejpam-6951	143	46	space	space	NOUN
ejpam-6951	143	47	of	of	ADP
ejpam-6951	143	48	km	km	PROPN
ejpam-6951	143	49	,	,	PUNCT
ejpam-6951	143	50	n	n	PUNCT
ejpam-6951	143	51	is	be	AUX
ejpam-6951	143	52	given	give	VERB
ejpam-6951	143	53	by	by	ADP
ejpam-6951	143	54	v	v	PROPN
ejpam-6951	143	55	(	(	PUNCT
ejpam-6951	143	56	km	km	PROPN
ejpam-6951	143	57	,	,	PUNCT
ejpam-6951	143	58	n	n	CCONJ
ejpam-6951	143	59	)	)	PUNCT
ejpam-6951	144	1	=	=	PRON
ejpam-6951	144	2	{	{	PUNCT
ejpam-6951	144	3	s	s	AUX
ejpam-6951	144	4	|	|	NOUN
ejpam-6951	144	5	s	s	VERB
ejpam-6951	144	6	⊆	⊆	NUM
ejpam-6951	144	7	v	v	NOUN
ejpam-6951	144	8	(	(	PUNCT
ejpam-6951	144	9	km	km	PROPN
ejpam-6951	144	10	,	,	PUNCT
ejpam-6951	144	11	n	n	CCONJ
ejpam-6951	144	12	)	)	PUNCT
ejpam-6951	144	13	}	}	PUNCT
ejpam-6951	144	14	.	.	PUNCT
ejpam-6951	145	1	given	give	VERB
ejpam-6951	145	2	the	the	DET
ejpam-6951	145	3	vertex	vertex	NOUN
ejpam-6951	145	4	set	set	VERB
ejpam-6951	145	5	v	v	NOUN
ejpam-6951	145	6	(	(	PUNCT
ejpam-6951	145	7	km	km	PROPN
ejpam-6951	145	8	,	,	PUNCT
ejpam-6951	145	9	n	n	CCONJ
ejpam-6951	145	10	)	)	PUNCT
ejpam-6951	145	11	,	,	PUNCT
ejpam-6951	145	12	the	the	DET
ejpam-6951	145	13	set	set	NOUN
ejpam-6951	145	14	a	a	X
ejpam-6951	145	15	=	=	X
ejpam-6951	145	16	{	{	PUNCT
ejpam-6951	145	17	{	{	PUNCT
ejpam-6951	145	18	x1	x1	PROPN
ejpam-6951	145	19	}	}	PUNCT
ejpam-6951	145	20	,	,	PUNCT
ejpam-6951	145	21	{	{	PUNCT
ejpam-6951	145	22	x2	x2	ADJ
ejpam-6951	145	23	}	}	PUNCT
ejpam-6951	145	24	,	,	PUNCT
ejpam-6951	145	25	{	{	PUNCT
ejpam-6951	145	26	x3	x3	ADJ
ejpam-6951	145	27	}	}	PUNCT
ejpam-6951	145	28	,	,	PUNCT
ejpam-6951	145	29	...	...	PUNCT
ejpam-6951	145	30	,	,	PUNCT
ejpam-6951	145	31	{	{	PUNCT
ejpam-6951	145	32	xm−1	xm−1	PROPN
ejpam-6951	145	33	}	}	PUNCT
ejpam-6951	145	34	,	,	PUNCT
ejpam-6951	145	35	{	{	PUNCT
ejpam-6951	145	36	xm	xm	X
ejpam-6951	145	37	}	}	PUNCT
ejpam-6951	145	38	,	,	PUNCT
ejpam-6951	145	39	{	{	PUNCT
ejpam-6951	145	40	y1	y1	NOUN
ejpam-6951	145	41	}	}	PUNCT
ejpam-6951	145	42	,	,	PUNCT
ejpam-6951	145	43	{	{	PUNCT
ejpam-6951	145	44	y2	y2	NOUN
ejpam-6951	145	45	}	}	PUNCT
ejpam-6951	145	46	,	,	PUNCT
ejpam-6951	145	47	{	{	PUNCT
ejpam-6951	145	48	y3	y3	NOUN
ejpam-6951	145	49	}	}	PUNCT
ejpam-6951	145	50	,	,	PUNCT
ejpam-6951	145	51	.	.	PUNCT
ejpam-6951	145	52	.	.	PUNCT
ejpam-6951	145	53	.	.	PUNCT
ejpam-6951	146	1	,	,	PUNCT
ejpam-6951	146	2	{	{	PUNCT
ejpam-6951	146	3	yn−1	yn−1	NOUN
ejpam-6951	146	4	}	}	PUNCT
ejpam-6951	146	5	,	,	PUNCT
ejpam-6951	146	6	{	{	PUNCT
ejpam-6951	146	7	yn	yn	NOUN
ejpam-6951	146	8	}	}	PUNCT
ejpam-6951	146	9	}	}	PUNCT
ejpam-6951	146	10	g.	g.	PROPN
ejpam-6951	146	11	d.	d.	PROPN
ejpam-6951	146	12	sepillo	sepillo	PROPN
ejpam-6951	146	13	et	et	PROPN
ejpam-6951	146	14	al	al	PROPN
ejpam-6951	146	15	.	.	PUNCT
ejpam-6951	146	16	/	/	SYM
ejpam-6951	146	17	eur	eur	PROPN
ejpam-6951	146	18	.	.	PUNCT
ejpam-6951	147	1	j.	j.	PROPN
ejpam-6951	147	2	pure	pure	PROPN
ejpam-6951	147	3	appl	appl	PROPN
ejpam-6951	147	4	.	.	PROPN
ejpam-6951	147	5	math	math	PROPN
ejpam-6951	147	6	,	,	PUNCT
ejpam-6951	147	7	18	18	NUM
ejpam-6951	147	8	(	(	PUNCT
ejpam-6951	147	9	4	4	NUM
ejpam-6951	147	10	)	)	PUNCT
ejpam-6951	147	11	(	(	PUNCT
ejpam-6951	147	12	2025	2025	NUM
ejpam-6951	147	13	)	)	PUNCT
ejpam-6951	147	14	,	,	PUNCT
ejpam-6951	147	15	6951	6951	NUM
ejpam-6951	147	16	7	7	NUM
ejpam-6951	147	17	of	of	ADP
ejpam-6951	147	18	23	23	NUM
ejpam-6951	147	19	forms	form	NOUN
ejpam-6951	147	20	a	a	DET
ejpam-6951	147	21	basis	basis	NOUN
ejpam-6951	147	22	for	for	ADP
ejpam-6951	147	23	v	v	NOUN
ejpam-6951	147	24	(	(	PUNCT
ejpam-6951	147	25	km	km	PROPN
ejpam-6951	147	26	,	,	PUNCT
ejpam-6951	147	27	n	n	CCONJ
ejpam-6951	147	28	)	)	PUNCT
ejpam-6951	147	29	,	,	PUNCT
ejpam-6951	147	30	thus	thus	ADV
ejpam-6951	147	31	dimv	dimv	NOUN
ejpam-6951	147	32	(	(	PUNCT
ejpam-6951	147	33	km	km	NOUN
ejpam-6951	147	34	,	,	PUNCT
ejpam-6951	147	35	n	n	CCONJ
ejpam-6951	147	36	)	)	PUNCT
ejpam-6951	147	37	=	=	SYM
ejpam-6951	148	1	m+	m+	NUM
ejpam-6951	148	2	n	n	CCONJ
ejpam-6951	148	3	by	by	ADP
ejpam-6951	148	4	theorem	theorem	NOUN
ejpam-6951	148	5	1	1	NUM
ejpam-6951	148	6	.	.	PUNCT
ejpam-6951	149	1	furthermore	furthermore	ADV
ejpam-6951	149	2	,	,	PUNCT
ejpam-6951	149	3	the	the	DET
ejpam-6951	149	4	even	even	ADJ
ejpam-6951	149	5	vertex	vertex	NOUN
ejpam-6951	149	6	space	space	NOUN
ejpam-6951	149	7	of	of	ADP
ejpam-6951	149	8	km	km	PROPN
ejpam-6951	149	9	,	,	PUNCT
ejpam-6951	149	10	n	n	PUNCT
ejpam-6951	149	11	is	be	AUX
ejpam-6951	149	12	given	give	VERB
ejpam-6951	149	13	by	by	ADP
ejpam-6951	149	14	v	v	NOUN
ejpam-6951	149	15	∗(km	∗(km	PROPN
ejpam-6951	149	16	,	,	PUNCT
ejpam-6951	149	17	n	n	CCONJ
ejpam-6951	149	18	)	)	PUNCT
ejpam-6951	149	19	=	=	PRON
ejpam-6951	149	20	{	{	PUNCT
ejpam-6951	149	21	s	s	NOUN
ejpam-6951	149	22	∈	∈	X
ejpam-6951	149	23	v	v	NOUN
ejpam-6951	149	24	(	(	PUNCT
ejpam-6951	149	25	km	km	PROPN
ejpam-6951	149	26	,	,	PUNCT
ejpam-6951	149	27	n	n	CCONJ
ejpam-6951	149	28	)	)	PUNCT
ejpam-6951	149	29	|	|	ADV
ejpam-6951	149	30	|s|	|s|	PROPN
ejpam-6951	149	31	is	be	AUX
ejpam-6951	149	32	even	even	ADV
ejpam-6951	149	33	}	}	PUNCT
ejpam-6951	149	34	.	.	PUNCT
ejpam-6951	150	1	in	in	ADP
ejpam-6951	150	2	view	view	NOUN
ejpam-6951	150	3	of	of	ADP
ejpam-6951	150	4	theorem	theorem	NOUN
ejpam-6951	150	5	7	7	NUM
ejpam-6951	150	6	,	,	PUNCT
ejpam-6951	150	7	the	the	DET
ejpam-6951	150	8	set	set	NOUN
ejpam-6951	150	9	b	b	NOUN
ejpam-6951	150	10	=	=	PRON
ejpam-6951	150	11	{	{	PUNCT
ejpam-6951	150	12	{	{	PUNCT
ejpam-6951	150	13	x1	x1	PROPN
ejpam-6951	150	14	,	,	PUNCT
ejpam-6951	150	15	x2	x2	PROPN
ejpam-6951	150	16	}	}	PUNCT
ejpam-6951	150	17	,	,	PUNCT
ejpam-6951	150	18	{	{	PUNCT
ejpam-6951	150	19	x1	x1	ADJ
ejpam-6951	150	20	,	,	PUNCT
ejpam-6951	150	21	x3	x3	ADJ
ejpam-6951	150	22	}	}	PUNCT
ejpam-6951	150	23	,	,	PUNCT
ejpam-6951	150	24	...	...	PUNCT
ejpam-6951	150	25	,	,	PUNCT
ejpam-6951	150	26	{	{	PUNCT
ejpam-6951	150	27	x1	x1	PROPN
ejpam-6951	150	28	,	,	PUNCT
ejpam-6951	150	29	xm	xm	PROPN
ejpam-6951	150	30	}	}	PUNCT
ejpam-6951	150	31	,	,	PUNCT
ejpam-6951	150	32	{	{	PUNCT
ejpam-6951	150	33	x1	x1	PROPN
ejpam-6951	150	34	,	,	PUNCT
ejpam-6951	150	35	y1	y1	PROPN
ejpam-6951	150	36	}	}	PUNCT
ejpam-6951	150	37	,	,	PUNCT
ejpam-6951	150	38	{	{	PUNCT
ejpam-6951	150	39	x1	x1	PROPN
ejpam-6951	150	40	,	,	PUNCT
ejpam-6951	150	41	y2	y2	PROPN
ejpam-6951	150	42	}	}	PUNCT
ejpam-6951	150	43	,	,	PUNCT
ejpam-6951	150	44	...	...	PUNCT
ejpam-6951	150	45	,	,	PUNCT
ejpam-6951	150	46	{	{	PUNCT
ejpam-6951	150	47	x1	x1	PROPN
ejpam-6951	150	48	,	,	PUNCT
ejpam-6951	150	49	yn	yn	PROPN
ejpam-6951	150	50	}	}	PUNCT
ejpam-6951	150	51	}	}	PUNCT
ejpam-6951	150	52	forms	form	VERB
ejpam-6951	150	53	a	a	DET
ejpam-6951	150	54	basis	basis	NOUN
ejpam-6951	150	55	for	for	ADP
ejpam-6951	150	56	v	v	NOUN
ejpam-6951	150	57	∗(km	∗(km	PROPN
ejpam-6951	150	58	,	,	PUNCT
ejpam-6951	150	59	n	n	CCONJ
ejpam-6951	150	60	)	)	PUNCT
ejpam-6951	150	61	.	.	PUNCT
ejpam-6951	151	1	hence	hence	ADV
ejpam-6951	151	2	,	,	PUNCT
ejpam-6951	151	3	dimv	dimv	PROPN
ejpam-6951	151	4	∗(km	∗(km	PROPN
ejpam-6951	151	5	,	,	PUNCT
ejpam-6951	151	6	n	n	CCONJ
ejpam-6951	151	7	)	)	PUNCT
ejpam-6951	151	8	=	=	SYM
ejpam-6951	152	1	m+	m+	NUM
ejpam-6951	152	2	n−	n−	NOUN
ejpam-6951	152	3	1	1	NUM
ejpam-6951	152	4	by	by	ADP
ejpam-6951	152	5	theorem	theorem	NOUN
ejpam-6951	152	6	6	6	NUM
ejpam-6951	152	7	.	.	PUNCT
ejpam-6951	152	8	by	by	ADP
ejpam-6951	152	9	theorem	theorem	NOUN
ejpam-6951	152	10	2	2	NUM
ejpam-6951	152	11	,	,	PUNCT
ejpam-6951	152	12	we	we	PRON
ejpam-6951	152	13	know	know	VERB
ejpam-6951	152	14	that	that	SCONJ
ejpam-6951	152	15	trivial	trivial	ADJ
ejpam-6951	152	16	subgraph	subgraph	NOUN
ejpam-6951	152	17	k1	k1	NOUN
ejpam-6951	152	18	is	be	AUX
ejpam-6951	152	19	a	a	DET
ejpam-6951	152	20	vertex	vertex	NOUN
ejpam-6951	152	21	-	-	PUNCT
ejpam-6951	152	22	generator	generator	NOUN
ejpam-6951	152	23	subgraph	subgraph	NOUN
ejpam-6951	152	24	of	of	ADP
ejpam-6951	152	25	km	km	PROPN
ejpam-6951	152	26	,	,	PUNCT
ejpam-6951	152	27	n.	n.	PROPN
ejpam-6951	152	28	additionally	additionally	ADV
ejpam-6951	152	29	,	,	PUNCT
ejpam-6951	152	30	we	we	PRON
ejpam-6951	152	31	can	can	AUX
ejpam-6951	152	32	observe	observe	VERB
ejpam-6951	152	33	that	that	DET
ejpam-6951	152	34	km	km	NOUN
ejpam-6951	152	35	,	,	PUNCT
ejpam-6951	152	36	n	n	PRON
ejpam-6951	152	37	exhibits	exhibit	VERB
ejpam-6951	152	38	some	some	DET
ejpam-6951	152	39	well	well	ADV
ejpam-6951	152	40	-	-	PUNCT
ejpam-6951	152	41	known	know	VERB
ejpam-6951	152	42	isomorphisms	isomorphism	NOUN
ejpam-6951	152	43	for	for	ADP
ejpam-6951	152	44	small	small	ADJ
ejpam-6951	152	45	values	value	NOUN
ejpam-6951	152	46	of	of	ADP
ejpam-6951	152	47	m	m	PROPN
ejpam-6951	152	48	and	and	CCONJ
ejpam-6951	152	49	n	n	CCONJ
ejpam-6951	152	50	,	,	PUNCT
ejpam-6951	152	51	such	such	ADJ
ejpam-6951	152	52	as	as	ADP
ejpam-6951	152	53	k1,1	k1,1	PROPN
ejpam-6951	152	54	≃	≃	NOUN
ejpam-6951	152	55	p2	p2	NOUN
ejpam-6951	152	56	,	,	PUNCT
ejpam-6951	152	57	k2,1	k2,1	PROPN
ejpam-6951	152	58	≃	≃	PROPN
ejpam-6951	152	59	s2	s2	PROPN
ejpam-6951	152	60	≃	≃	PROPN
ejpam-6951	152	61	p3	p3	PROPN
ejpam-6951	152	62	,	,	PUNCT
ejpam-6951	152	63	and	and	CCONJ
ejpam-6951	152	64	k2,2	k2,2	PROPN
ejpam-6951	152	65	≃	≃	ADJ
ejpam-6951	152	66	c4	c4	NOUN
ejpam-6951	152	67	.	.	PUNCT
ejpam-6951	153	1	by	by	ADP
ejpam-6951	153	2	theorem	theorem	NOUN
ejpam-6951	153	3	5	5	NUM
ejpam-6951	153	4	,	,	PUNCT
ejpam-6951	153	5	the	the	DET
ejpam-6951	153	6	vertex	vertex	NOUN
ejpam-6951	153	7	-	-	PUNCT
ejpam-6951	153	8	generator	generator	NOUN
ejpam-6951	153	9	subgraph	subgraph	NOUN
ejpam-6951	153	10	of	of	ADP
ejpam-6951	153	11	p2	p2	PROPN
ejpam-6951	153	12	and	and	CCONJ
ejpam-6951	153	13	p3	p3	PROPN
ejpam-6951	153	14	is	be	AUX
ejpam-6951	153	15	the	the	DET
ejpam-6951	153	16	trivial	trivial	ADJ
ejpam-6951	153	17	graph	graph	NOUN
ejpam-6951	153	18	.	.	PUNCT
ejpam-6951	154	1	the	the	DET
ejpam-6951	154	2	vertex	vertex	NOUN
ejpam-6951	154	3	-	-	PUNCT
ejpam-6951	154	4	generator	generator	NOUN
ejpam-6951	154	5	subgraph	subgraph	NOUN
ejpam-6951	154	6	of	of	ADP
ejpam-6951	154	7	the	the	DET
ejpam-6951	154	8	cycle	cycle	NOUN
ejpam-6951	154	9	graph	graph	NOUN
ejpam-6951	154	10	c4	c4	NOUN
ejpam-6951	154	11	was	be	AUX
ejpam-6951	154	12	also	also	ADV
ejpam-6951	154	13	studied	study	VERB
ejpam-6951	154	14	.	.	PUNCT
ejpam-6951	155	1	hence	hence	ADV
ejpam-6951	155	2	,	,	PUNCT
ejpam-6951	155	3	will	will	AUX
ejpam-6951	155	4	now	now	ADV
ejpam-6951	155	5	focus	focus	VERB
ejpam-6951	155	6	our	our	PRON
ejpam-6951	155	7	investigation	investigation	NOUN
ejpam-6951	155	8	on	on	ADP
ejpam-6951	155	9	determining	determine	VERB
ejpam-6951	155	10	the	the	DET
ejpam-6951	155	11	vertex	vertex	NOUN
ejpam-6951	155	12	-	-	PUNCT
ejpam-6951	155	13	generator	generator	NOUN
ejpam-6951	155	14	subgraphs	subgraph	NOUN
ejpam-6951	155	15	of	of	ADP
ejpam-6951	155	16	km	km	PROPN
ejpam-6951	155	17	,	,	PUNCT
ejpam-6951	155	18	n	n	CCONJ
ejpam-6951	155	19	where	where	SCONJ
ejpam-6951	155	20	min{m	min{m	NOUN
ejpam-6951	155	21	,	,	PUNCT
ejpam-6951	155	22	n	n	CCONJ
ejpam-6951	155	23	}	}	PUNCT
ejpam-6951	155	24	≥	≥	NOUN
ejpam-6951	155	25	2	2	NUM
ejpam-6951	155	26	and	and	CCONJ
ejpam-6951	155	27	m+n	m+n	NOUN
ejpam-6951	155	28	≥	≥	NUM
ejpam-6951	155	29	5	5	NUM
ejpam-6951	155	30	.	.	PUNCT
ejpam-6951	156	1	the	the	DET
ejpam-6951	156	2	following	follow	VERB
ejpam-6951	156	3	theorem	theorem	ADJ
ejpam-6951	156	4	presents	present	VERB
ejpam-6951	156	5	a	a	DET
ejpam-6951	156	6	necessary	necessary	ADJ
ejpam-6951	156	7	condition	condition	NOUN
ejpam-6951	156	8	for	for	ADP
ejpam-6951	156	9	an	an	DET
ejpam-6951	156	10	empty	empty	ADJ
ejpam-6951	156	11	graph	graph	NOUN
ejpam-6951	156	12	kt	kt	NOUN
ejpam-6951	156	13	to	to	PART
ejpam-6951	156	14	be	be	AUX
ejpam-6951	156	15	a	a	DET
ejpam-6951	156	16	vertex	vertex	NOUN
ejpam-6951	156	17	-	-	PUNCT
ejpam-6951	156	18	generator	generator	NOUN
ejpam-6951	156	19	subgraph	subgraph	NOUN
ejpam-6951	156	20	of	of	ADP
ejpam-6951	156	21	km	km	PROPN
ejpam-6951	156	22	,	,	PUNCT
ejpam-6951	156	23	n.	n.	PROPN
ejpam-6951	156	24	theorem	theorem	VERB
ejpam-6951	156	25	10	10	NUM
ejpam-6951	156	26	.	.	PUNCT
ejpam-6951	157	1	let	let	VERB
ejpam-6951	157	2	m	m	PRON
ejpam-6951	157	3	,	,	PUNCT
ejpam-6951	157	4	n	n	PROPN
ejpam-6951	157	5	and	and	CCONJ
ejpam-6951	157	6	t	t	PROPN
ejpam-6951	157	7	be	be	AUX
ejpam-6951	157	8	positive	positive	ADJ
ejpam-6951	157	9	integers	integer	NOUN
ejpam-6951	157	10	such	such	ADJ
ejpam-6951	157	11	that	that	DET
ejpam-6951	157	12	min{m	min{m	NOUN
ejpam-6951	157	13	,	,	PUNCT
ejpam-6951	157	14	n	n	CCONJ
ejpam-6951	157	15	}	}	PUNCT
ejpam-6951	157	16	≥	≥	NUM
ejpam-6951	157	17	2	2	NUM
ejpam-6951	157	18	,	,	PUNCT
ejpam-6951	158	1	m	m	VERB
ejpam-6951	158	2	+	+	ADJ
ejpam-6951	158	3	n	n	PRON
ejpam-6951	158	4	≥	≥	NUM
ejpam-6951	158	5	5	5	NUM
ejpam-6951	158	6	,	,	PUNCT
ejpam-6951	158	7	and	and	CCONJ
ejpam-6951	158	8	t	t	PROPN
ejpam-6951	158	9	is	be	AUX
ejpam-6951	158	10	odd	odd	ADJ
ejpam-6951	158	11	.	.	PUNCT
ejpam-6951	159	1	if	if	SCONJ
ejpam-6951	159	2	t	t	PROPN
ejpam-6951	159	3	<	<	X
ejpam-6951	159	4	min{m	min{m	PROPN
ejpam-6951	159	5	,	,	PUNCT
ejpam-6951	159	6	n	n	CCONJ
ejpam-6951	159	7	}	}	PUNCT
ejpam-6951	159	8	,	,	PUNCT
ejpam-6951	159	9	then	then	ADV
ejpam-6951	159	10	kt	kt	PROPN
ejpam-6951	159	11	is	be	AUX
ejpam-6951	159	12	a	a	DET
ejpam-6951	159	13	vertex	vertex	NOUN
ejpam-6951	159	14	-	-	PUNCT
ejpam-6951	159	15	generator	generator	NOUN
ejpam-6951	159	16	subgraph	subgraph	NOUN
ejpam-6951	159	17	of	of	ADP
ejpam-6951	159	18	km	km	PROPN
ejpam-6951	159	19	,	,	PUNCT
ejpam-6951	159	20	n.	n.	NOUN
ejpam-6951	159	21	proof	proof	NOUN
ejpam-6951	159	22	.	.	PUNCT
ejpam-6951	160	1	from	from	ADP
ejpam-6951	160	2	the	the	DET
ejpam-6951	160	3	labeling	labeling	NOUN
ejpam-6951	160	4	of	of	ADP
ejpam-6951	160	5	complete	complete	ADJ
ejpam-6951	160	6	bipartite	bipartite	NOUN
ejpam-6951	160	7	graph	graph	NOUN
ejpam-6951	160	8	,	,	PUNCT
ejpam-6951	160	9	it	it	PRON
ejpam-6951	160	10	can	can	AUX
ejpam-6951	160	11	be	be	AUX
ejpam-6951	160	12	observed	observe	VERB
ejpam-6951	160	13	that	that	SCONJ
ejpam-6951	160	14	the	the	DET
ejpam-6951	160	15	subgraphs	subgraph	NOUN
ejpam-6951	160	16	of	of	ADP
ejpam-6951	160	17	km	km	PROPN
ejpam-6951	160	18	,	,	PUNCT
ejpam-6951	160	19	n	n	CCONJ
ejpam-6951	160	20	induced	induce	VERB
ejpam-6951	160	21	by	by	ADP
ejpam-6951	160	22	the	the	DET
ejpam-6951	160	23	partite	partite	ADJ
ejpam-6951	160	24	sets	set	NOUN
ejpam-6951	160	25	m	m	VERB
ejpam-6951	160	26	and	and	CCONJ
ejpam-6951	160	27	n	n	PROPN
ejpam-6951	160	28	,	,	PUNCT
ejpam-6951	160	29	denoted	denote	VERB
ejpam-6951	160	30	by	by	ADP
ejpam-6951	160	31	km	km	PROPN
ejpam-6951	160	32	,	,	PUNCT
ejpam-6951	160	33	n⟨m⟩	n⟨m⟩	NUM
ejpam-6951	160	34	and	and	CCONJ
ejpam-6951	160	35	km	km	PROPN
ejpam-6951	160	36	,	,	PUNCT
ejpam-6951	160	37	n⟨n⟩	n⟨n⟩	VERB
ejpam-6951	160	38	,	,	PUNCT
ejpam-6951	160	39	are	be	AUX
ejpam-6951	160	40	isomorphic	isomorphic	ADJ
ejpam-6951	160	41	to	to	ADP
ejpam-6951	160	42	the	the	DET
ejpam-6951	160	43	empty	empty	ADJ
ejpam-6951	160	44	graphs	graph	NOUN
ejpam-6951	160	45	km	km	NOUN
ejpam-6951	160	46	and	and	CCONJ
ejpam-6951	160	47	km	km	NOUN
ejpam-6951	160	48	,	,	PUNCT
ejpam-6951	160	49	respectively	respectively	ADV
ejpam-6951	160	50	.	.	PUNCT
ejpam-6951	161	1	this	this	PRON
ejpam-6951	161	2	is	be	AUX
ejpam-6951	161	3	shown	show	VERB
ejpam-6951	161	4	in	in	ADP
ejpam-6951	161	5	figure	figure	NOUN
ejpam-6951	161	6	3	3	NUM
ejpam-6951	161	7	.	.	PUNCT
ejpam-6951	162	1	x1	x1	NUM
ejpam-6951	163	1	x2	x2	PROPN
ejpam-6951	163	2	x3	x3	PROPN
ejpam-6951	163	3	xm−1	xm−1	PROPN
ejpam-6951	163	4	xm	xm	PROPN
ejpam-6951	164	1	y1	y1	INTJ
ejpam-6951	164	2	y2	y2	INTJ
ejpam-6951	164	3	yn−1	yn−1	PROPN
ejpam-6951	164	4	yn	yn	PROPN
ejpam-6951	164	5	km	km	PROPN
ejpam-6951	164	6	,	,	PUNCT
ejpam-6951	164	7	n⟨m⟩	n⟨m⟩	NUM
ejpam-6951	164	8	:	:	PUNCT
ejpam-6951	165	1	x1	x1	PROPN
ejpam-6951	166	1	x2	x2	PROPN
ejpam-6951	167	1	x3	x3	PROPN
ejpam-6951	167	2	xm−1	xm−1	PROPN
ejpam-6951	167	3	xm	xm	PROPN
ejpam-6951	168	1	y1	y1	INTJ
ejpam-6951	168	2	y2	y2	INTJ
ejpam-6951	168	3	yn−1	yn−1	NOUN
ejpam-6951	168	4	yn	yn	PROPN
ejpam-6951	168	5	km	km	PROPN
ejpam-6951	168	6	,	,	PUNCT
ejpam-6951	168	7	n⟨n⟩	n⟨n⟩	ADJ
ejpam-6951	168	8	:	:	PUNCT
ejpam-6951	168	9	figure	figure	NOUN
ejpam-6951	168	10	3	3	NUM
ejpam-6951	168	11	:	:	PUNCT
ejpam-6951	168	12	illustrating	illustrate	VERB
ejpam-6951	168	13	the	the	DET
ejpam-6951	168	14	subgraphs	subgraph	NOUN
ejpam-6951	168	15	of	of	ADP
ejpam-6951	168	16	km	km	PROPN
ejpam-6951	168	17	,	,	PUNCT
ejpam-6951	168	18	n	n	CCONJ
ejpam-6951	168	19	induced	induce	VERB
ejpam-6951	168	20	by	by	ADP
ejpam-6951	168	21	m	m	NOUN
ejpam-6951	168	22	and	and	CCONJ
ejpam-6951	168	23	n	n	ADV
ejpam-6951	168	24	let	let	VERB
ejpam-6951	168	25	kt	kt	PART
ejpam-6951	168	26	be	be	AUX
ejpam-6951	168	27	a	a	DET
ejpam-6951	168	28	subgraph	subgraph	NOUN
ejpam-6951	168	29	of	of	ADP
ejpam-6951	168	30	both	both	DET
ejpam-6951	168	31	km	km	PROPN
ejpam-6951	168	32	and	and	CCONJ
ejpam-6951	168	33	kn	kn	PROPN
ejpam-6951	168	34	.	.	PUNCT
ejpam-6951	169	1	it	it	PRON
ejpam-6951	169	2	was	be	AUX
ejpam-6951	169	3	given	give	VERB
ejpam-6951	169	4	that	that	SCONJ
ejpam-6951	169	5	t	t	PROPN
ejpam-6951	169	6	is	be	AUX
ejpam-6951	169	7	odd	odd	ADJ
ejpam-6951	169	8	,	,	PUNCT
ejpam-6951	169	9	so	so	ADV
ejpam-6951	169	10	condition	condition	NOUN
ejpam-6951	169	11	(	(	PUNCT
ejpam-6951	169	12	i	i	NOUN
ejpam-6951	169	13	)	)	PUNCT
ejpam-6951	169	14	of	of	ADP
ejpam-6951	169	15	theorem	theorem	NOUN
ejpam-6951	169	16	9	9	NUM
ejpam-6951	169	17	is	be	AUX
ejpam-6951	169	18	sastified	sastifie	VERB
ejpam-6951	169	19	.	.	PUNCT
ejpam-6951	170	1	next	next	ADV
ejpam-6951	170	2	,	,	PUNCT
ejpam-6951	170	3	since	since	SCONJ
ejpam-6951	170	4	t	t	PROPN
ejpam-6951	170	5	<	<	X
ejpam-6951	170	6	min{m	min{m	PROPN
ejpam-6951	170	7	,	,	PUNCT
ejpam-6951	170	8	n	n	CCONJ
ejpam-6951	170	9	}	}	PUNCT
ejpam-6951	170	10	,	,	PUNCT
ejpam-6951	170	11	it	it	PRON
ejpam-6951	170	12	follows	follow	VERB
ejpam-6951	170	13	that	that	SCONJ
ejpam-6951	170	14	t	t	NOUN
ejpam-6951	170	15	<	<	X
ejpam-6951	170	16	m	m	PROPN
ejpam-6951	170	17	and	and	CCONJ
ejpam-6951	170	18	t	t	X
ejpam-6951	170	19	<	<	X
ejpam-6951	170	20	n	n	CCONJ
ejpam-6951	170	21	,	,	PUNCT
ejpam-6951	170	22	or	or	CCONJ
ejpam-6951	170	23	t	t	X
ejpam-6951	170	24	≤	≤	NUM
ejpam-6951	170	25	m	m	VERB
ejpam-6951	170	26	−	−	PROPN
ejpam-6951	170	27	1	1	NUM
ejpam-6951	170	28	and	and	CCONJ
ejpam-6951	170	29	t	t	X
ejpam-6951	170	30	≤	≤	NUM
ejpam-6951	170	31	n	n	CCONJ
ejpam-6951	170	32	−	−	PROPN
ejpam-6951	170	33	1	1	NUM
ejpam-6951	170	34	,	,	PUNCT
ejpam-6951	170	35	which	which	PRON
ejpam-6951	170	36	satisfies	satisfy	VERB
ejpam-6951	170	37	condition	condition	NOUN
ejpam-6951	170	38	(	(	PUNCT
ejpam-6951	170	39	ii	ii	NOUN
ejpam-6951	170	40	)	)	PUNCT
ejpam-6951	170	41	of	of	ADP
ejpam-6951	170	42	theorem	theorem	NOUN
ejpam-6951	170	43	9	9	NUM
ejpam-6951	170	44	.	.	PUNCT
ejpam-6951	171	1	lastly	lastly	ADV
ejpam-6951	171	2	,	,	PUNCT
ejpam-6951	171	3	since	since	SCONJ
ejpam-6951	171	4	kt	kt	PROPN
ejpam-6951	171	5	is	be	AUX
ejpam-6951	171	6	isomorphic	isomorphic	ADJ
ejpam-6951	171	7	to	to	ADP
ejpam-6951	171	8	itself	itself	PRON
ejpam-6951	171	9	,	,	PUNCT
ejpam-6951	171	10	condition	condition	NOUN
ejpam-6951	171	11	(	(	PUNCT
ejpam-6951	171	12	iii	iii	NOUN
ejpam-6951	171	13	)	)	PUNCT
ejpam-6951	171	14	of	of	ADP
ejpam-6951	171	15	theorem	theorem	NOUN
ejpam-6951	171	16	9	9	NUM
ejpam-6951	171	17	is	be	AUX
ejpam-6951	171	18	also	also	ADV
ejpam-6951	171	19	satisfied	satisfied	ADJ
ejpam-6951	171	20	.	.	PUNCT
ejpam-6951	172	1	all	all	DET
ejpam-6951	172	2	the	the	DET
ejpam-6951	172	3	conditions	condition	NOUN
ejpam-6951	172	4	have	have	AUX
ejpam-6951	172	5	met	meet	VERB
ejpam-6951	172	6	,	,	PUNCT
ejpam-6951	172	7	hence	hence	ADV
ejpam-6951	172	8	kt	kt	PROPN
ejpam-6951	172	9	is	be	AUX
ejpam-6951	172	10	a	a	DET
ejpam-6951	172	11	vertex	vertex	NOUN
ejpam-6951	172	12	-	-	PUNCT
ejpam-6951	172	13	generator	generator	NOUN
ejpam-6951	172	14	subgraph	subgraph	NOUN
ejpam-6951	172	15	of	of	ADP
ejpam-6951	172	16	both	both	DET
ejpam-6951	172	17	km	km	PROPN
ejpam-6951	172	18	and	and	CCONJ
ejpam-6951	172	19	kn	kn	PROPN
ejpam-6951	172	20	.	.	PUNCT
ejpam-6951	173	1	it	it	PRON
ejpam-6951	173	2	follows	follow	VERB
ejpam-6951	173	3	that	that	SCONJ
ejpam-6951	173	4	{	{	PUNCT
ejpam-6951	173	5	xi	xi	NOUN
ejpam-6951	173	6	}	}	PUNCT
ejpam-6951	173	7	∈	∈	NOUN
ejpam-6951	173	8	vkt	vkt	ADJ
ejpam-6951	173	9	(	(	PUNCT
ejpam-6951	173	10	km	km	NOUN
ejpam-6951	173	11	)	)	PUNCT
ejpam-6951	173	12	for	for	ADP
ejpam-6951	173	13	1	1	NUM
ejpam-6951	173	14	≤	≤	NUM
ejpam-6951	173	15	i	i	PRON
ejpam-6951	173	16	≤	≤	NOUN
ejpam-6951	173	17	m	m	ADP
ejpam-6951	173	18	,	,	PUNCT
ejpam-6951	173	19	and	and	CCONJ
ejpam-6951	173	20	{	{	PUNCT
ejpam-6951	173	21	yj	yj	PROPN
ejpam-6951	173	22	}	}	PUNCT
ejpam-6951	173	23	∈	∈	PROPN
ejpam-6951	173	24	vkt	vkt	ADJ
ejpam-6951	173	25	(	(	PUNCT
ejpam-6951	173	26	kn	kn	PROPN
ejpam-6951	173	27	)	)	PUNCT
ejpam-6951	173	28	for	for	ADP
ejpam-6951	173	29	1	1	NUM
ejpam-6951	173	30	≤	≤	NUM
ejpam-6951	173	31	j	j	PROPN
ejpam-6951	173	32	≤	≤	NUM
ejpam-6951	173	33	n	n	CCONJ
ejpam-6951	173	34	,	,	PUNCT
ejpam-6951	173	35	by	by	ADP
ejpam-6951	173	36	remark	remark	NOUN
ejpam-6951	173	37	1	1	NUM
ejpam-6951	173	38	.	.	PUNCT
ejpam-6951	174	1	now	now	ADV
ejpam-6951	174	2	,	,	PUNCT
ejpam-6951	174	3	we	we	PRON
ejpam-6951	174	4	know	know	VERB
ejpam-6951	174	5	that	that	SCONJ
ejpam-6951	174	6	vkt	vkt	ADJ
ejpam-6951	174	7	(	(	PUNCT
ejpam-6951	174	8	km	km	NOUN
ejpam-6951	174	9	)	)	PUNCT
ejpam-6951	174	10	∪	∪	NOUN
ejpam-6951	175	1	vkt	vkt	X
ejpam-6951	176	1	(	(	PUNCT
ejpam-6951	176	2	kn	kn	PROPN
ejpam-6951	176	3	)	)	PUNCT
ejpam-6951	176	4	=	=	PUNCT
ejpam-6951	177	1	vkt	vkt	ADJ
ejpam-6951	177	2	(	(	PUNCT
ejpam-6951	177	3	km	km	NOUN
ejpam-6951	177	4	,	,	PUNCT
ejpam-6951	177	5	n⟨m⟩	n⟨m⟩	NUM
ejpam-6951	177	6	)	)	PUNCT
ejpam-6951	177	7	∪	∪	ADP
ejpam-6951	177	8	vkt	vkt	ADJ
ejpam-6951	177	9	(	(	PUNCT
ejpam-6951	177	10	km	km	NOUN
ejpam-6951	177	11	,	,	PUNCT
ejpam-6951	177	12	n⟨n⟩	n⟨n⟩	ADJ
ejpam-6951	177	13	)	)	PUNCT
ejpam-6951	177	14	=	=	VERB
ejpam-6951	178	1	vkt	vkt	ADJ
ejpam-6951	178	2	(	(	PUNCT
ejpam-6951	178	3	km	km	PROPN
ejpam-6951	178	4	,	,	PUNCT
ejpam-6951	178	5	n	n	CCONJ
ejpam-6951	178	6	)	)	PUNCT
ejpam-6951	178	7	,	,	PUNCT
ejpam-6951	178	8	this	this	PRON
ejpam-6951	178	9	means	mean	VERB
ejpam-6951	178	10	that	that	SCONJ
ejpam-6951	178	11	{	{	PUNCT
ejpam-6951	178	12	xi	xi	NOUN
ejpam-6951	178	13	}	}	PUNCT
ejpam-6951	178	14	,	,	PUNCT
ejpam-6951	178	15	{	{	PUNCT
ejpam-6951	178	16	yj	yj	PROPN
ejpam-6951	178	17	}	}	PUNCT
ejpam-6951	178	18	∈	∈	PROPN
ejpam-6951	178	19	vkt	vkt	ADJ
ejpam-6951	178	20	(	(	PUNCT
ejpam-6951	178	21	km	km	PROPN
ejpam-6951	178	22	,	,	PUNCT
ejpam-6951	178	23	n	n	CCONJ
ejpam-6951	178	24	)	)	PUNCT
ejpam-6951	178	25	.	.	PUNCT
ejpam-6951	179	1	therefore	therefore	ADV
ejpam-6951	179	2	,	,	PUNCT
ejpam-6951	179	3	by	by	ADP
ejpam-6951	179	4	remark	remark	NOUN
ejpam-6951	179	5	1	1	NUM
ejpam-6951	179	6	,	,	PUNCT
ejpam-6951	179	7	kt	kt	PROPN
ejpam-6951	179	8	is	be	AUX
ejpam-6951	179	9	a	a	DET
ejpam-6951	179	10	vertex	vertex	NOUN
ejpam-6951	179	11	-	-	PUNCT
ejpam-6951	179	12	generator	generator	NOUN
ejpam-6951	179	13	subgraph	subgraph	NOUN
ejpam-6951	179	14	of	of	ADP
ejpam-6951	179	15	km	km	PROPN
ejpam-6951	179	16	,	,	PUNCT
ejpam-6951	179	17	n.	n.	NOUN
ejpam-6951	179	18	the	the	DET
ejpam-6951	179	19	following	follow	VERB
ejpam-6951	179	20	theorem	theorem	NOUN
ejpam-6951	179	21	will	will	AUX
ejpam-6951	179	22	give	give	VERB
ejpam-6951	179	23	a	a	DET
ejpam-6951	179	24	necessary	necessary	ADJ
ejpam-6951	179	25	condition	condition	NOUN
ejpam-6951	179	26	for	for	SCONJ
ejpam-6951	179	27	the	the	DET
ejpam-6951	179	28	path	path	NOUN
ejpam-6951	179	29	graph	graph	NOUN
ejpam-6951	179	30	pt	pt	PROPN
ejpam-6951	179	31	to	to	PART
ejpam-6951	179	32	be	be	AUX
ejpam-6951	179	33	a	a	DET
ejpam-6951	179	34	vertex	vertex	NOUN
ejpam-6951	179	35	-	-	PUNCT
ejpam-6951	179	36	generator	generator	NOUN
ejpam-6951	179	37	subgraph	subgraph	NOUN
ejpam-6951	179	38	of	of	ADP
ejpam-6951	179	39	km	km	PROPN
ejpam-6951	179	40	,	,	PUNCT
ejpam-6951	179	41	n.	n.	PROPN
ejpam-6951	179	42	g.	g.	PROPN
ejpam-6951	179	43	d.	d.	PROPN
ejpam-6951	179	44	sepillo	sepillo	PROPN
ejpam-6951	179	45	et	et	PROPN
ejpam-6951	179	46	al	al	PROPN
ejpam-6951	179	47	.	.	PUNCT
ejpam-6951	179	48	/	/	SYM
ejpam-6951	179	49	eur	eur	PROPN
ejpam-6951	179	50	.	.	PUNCT
ejpam-6951	180	1	j.	j.	PROPN
ejpam-6951	180	2	pure	pure	PROPN
ejpam-6951	180	3	appl	appl	PROPN
ejpam-6951	180	4	.	.	PROPN
ejpam-6951	180	5	math	math	PROPN
ejpam-6951	180	6	,	,	PUNCT
ejpam-6951	180	7	18	18	NUM
ejpam-6951	180	8	(	(	PUNCT
ejpam-6951	180	9	4	4	NUM
ejpam-6951	180	10	)	)	PUNCT
ejpam-6951	180	11	(	(	PUNCT
ejpam-6951	180	12	2025	2025	NUM
ejpam-6951	180	13	)	)	PUNCT
ejpam-6951	180	14	,	,	PUNCT
ejpam-6951	180	15	6951	6951	NUM
ejpam-6951	180	16	8	8	NUM
ejpam-6951	180	17	of	of	ADP
ejpam-6951	180	18	23	23	NUM
ejpam-6951	180	19	theorem	theorem	NOUN
ejpam-6951	180	20	11	11	NUM
ejpam-6951	180	21	.	.	PUNCT
ejpam-6951	181	1	let	let	VERB
ejpam-6951	181	2	m	m	PRON
ejpam-6951	181	3	and	and	CCONJ
ejpam-6951	181	4	n	n	ADV
ejpam-6951	181	5	be	be	VERB
ejpam-6951	181	6	positive	positive	ADJ
ejpam-6951	181	7	integers	integer	NOUN
ejpam-6951	181	8	such	such	ADJ
ejpam-6951	181	9	that	that	DET
ejpam-6951	181	10	min{m	min{m	NOUN
ejpam-6951	181	11	,	,	PUNCT
ejpam-6951	181	12	n	n	CCONJ
ejpam-6951	181	13	}	}	PUNCT
ejpam-6951	181	14	≥	≥	NOUN
ejpam-6951	181	15	2	2	NUM
ejpam-6951	181	16	and	and	CCONJ
ejpam-6951	181	17	m+	m+	NUM
ejpam-6951	181	18	n	n	CCONJ
ejpam-6951	181	19	≥	≥	NOUN
ejpam-6951	181	20	5	5	NUM
ejpam-6951	181	21	.	.	PUNCT
ejpam-6951	182	1	if	if	SCONJ
ejpam-6951	182	2	t	t	NOUN
ejpam-6951	182	3	=	=	SYM
ejpam-6951	182	4	1	1	NUM
ejpam-6951	182	5	or	or	CCONJ
ejpam-6951	182	6	t	t	NOUN
ejpam-6951	182	7	=	=	SYM
ejpam-6951	182	8	3	3	NUM
ejpam-6951	182	9	,	,	PUNCT
ejpam-6951	182	10	then	then	ADV
ejpam-6951	182	11	pt	pt	PROPN
ejpam-6951	182	12	is	be	AUX
ejpam-6951	182	13	a	a	DET
ejpam-6951	182	14	vertex	vertex	NOUN
ejpam-6951	182	15	-	-	PUNCT
ejpam-6951	182	16	generator	generator	NOUN
ejpam-6951	182	17	subgraph	subgraph	NOUN
ejpam-6951	182	18	of	of	ADP
ejpam-6951	182	19	km	km	PROPN
ejpam-6951	182	20	,	,	PUNCT
ejpam-6951	182	21	n.	n.	NOUN
ejpam-6951	182	22	proof	proof	NOUN
ejpam-6951	182	23	.	.	PUNCT
ejpam-6951	183	1	suppose	suppose	VERB
ejpam-6951	183	2	t	t	NOUN
ejpam-6951	183	3	=	=	SYM
ejpam-6951	183	4	1	1	NUM
ejpam-6951	183	5	or	or	CCONJ
ejpam-6951	183	6	t	t	NOUN
ejpam-6951	183	7	=	=	SYM
ejpam-6951	183	8	3	3	X
ejpam-6951	183	9	.	.	PUNCT
ejpam-6951	183	10	by	by	ADP
ejpam-6951	183	11	theorem	theorem	NOUN
ejpam-6951	183	12	2	2	NUM
ejpam-6951	183	13	,	,	PUNCT
ejpam-6951	183	14	p1	p1	NOUN
ejpam-6951	183	15	is	be	AUX
ejpam-6951	183	16	a	a	DET
ejpam-6951	183	17	trivial	trivial	ADJ
ejpam-6951	183	18	vertex	vertex	NOUN
ejpam-6951	183	19	-	-	PUNCT
ejpam-6951	183	20	generator	generator	NOUN
ejpam-6951	183	21	subgraph	subgraph	NOUN
ejpam-6951	183	22	of	of	ADP
ejpam-6951	183	23	km	km	PROPN
ejpam-6951	183	24	,	,	PUNCT
ejpam-6951	183	25	n.	n.	PROPN
ejpam-6951	183	26	now	now	ADV
ejpam-6951	183	27	,	,	PUNCT
ejpam-6951	183	28	consider	consider	VERB
ejpam-6951	183	29	the	the	DET
ejpam-6951	183	30	labeling	labeling	NOUN
ejpam-6951	183	31	of	of	ADP
ejpam-6951	183	32	km	km	PROPN
ejpam-6951	183	33	,	,	PUNCT
ejpam-6951	183	34	n.	n.	NOUN
ejpam-6951	183	35	for	for	ADP
ejpam-6951	183	36	any	any	DET
ejpam-6951	183	37	1	1	NUM
ejpam-6951	183	38	≤	≤	NUM
ejpam-6951	183	39	i	i	PRON
ejpam-6951	183	40	≤	≤	NOUN
ejpam-6951	183	41	m	m	VERB
ejpam-6951	183	42	,	,	PUNCT
ejpam-6951	183	43	let	let	VERB
ejpam-6951	183	44	xi	xi	PRON
ejpam-6951	183	45	be	be	AUX
ejpam-6951	183	46	an	an	DET
ejpam-6951	183	47	arbitrary	arbitrary	ADJ
ejpam-6951	183	48	vertex	vertex	NOUN
ejpam-6951	183	49	of	of	ADP
ejpam-6951	183	50	partite	partite	ADJ
ejpam-6951	183	51	set	set	NOUN
ejpam-6951	183	52	m	m	VERB
ejpam-6951	183	53	in	in	ADP
ejpam-6951	183	54	the	the	DET
ejpam-6951	183	55	complete	complete	ADJ
ejpam-6951	183	56	bipartite	bipartite	PROPN
ejpam-6951	183	57	graph	graph	NOUN
ejpam-6951	183	58	km	km	PROPN
ejpam-6951	183	59	,	,	PUNCT
ejpam-6951	183	60	n	n	CCONJ
ejpam-6951	183	61	,	,	PUNCT
ejpam-6951	183	62	and	and	CCONJ
ejpam-6951	183	63	let	let	VERB
ejpam-6951	183	64	a	a	DET
ejpam-6951	183	65	,	,	PUNCT
ejpam-6951	183	66	b	b	NOUN
ejpam-6951	183	67	,	,	PUNCT
ejpam-6951	183	68	and	and	CCONJ
ejpam-6951	183	69	c	c	PROPN
ejpam-6951	183	70	be	be	AUX
ejpam-6951	183	71	defined	define	VERB
ejpam-6951	183	72	as	as	SCONJ
ejpam-6951	183	73	follows	follow	VERB
ejpam-6951	183	74	:	:	PUNCT
ejpam-6951	183	75	a	a	PRON
ejpam-6951	183	76	=	=	PUNCT
ejpam-6951	183	77	{	{	PUNCT
ejpam-6951	183	78	x1	x1	PROPN
ejpam-6951	183	79	,	,	PUNCT
ejpam-6951	183	80	x2	x2	PROPN
ejpam-6951	183	81	,	,	PUNCT
ejpam-6951	183	82	y1	y1	PROPN
ejpam-6951	183	83	}	}	PUNCT
ejpam-6951	183	84	,	,	PUNCT
ejpam-6951	184	1	b	b	X
ejpam-6951	184	2	=	=	PRON
ejpam-6951	184	3	{	{	PUNCT
ejpam-6951	184	4	x1	x1	PROPN
ejpam-6951	184	5	,	,	PUNCT
ejpam-6951	184	6	x2	x2	PROPN
ejpam-6951	184	7	,	,	PUNCT
ejpam-6951	184	8	y2	y2	PROPN
ejpam-6951	184	9	}	}	PUNCT
ejpam-6951	184	10	,	,	PUNCT
ejpam-6951	184	11	and	and	CCONJ
ejpam-6951	184	12	c	c	X
ejpam-6951	184	13	=	=	SYM
ejpam-6951	184	14	{	{	PUNCT
ejpam-6951	184	15	xi	xi	PROPN
ejpam-6951	184	16	,	,	PUNCT
ejpam-6951	184	17	y1	y1	NOUN
ejpam-6951	184	18	,	,	PUNCT
ejpam-6951	184	19	y2	y2	NOUN
ejpam-6951	184	20	}	}	PUNCT
ejpam-6951	184	21	where	where	SCONJ
ejpam-6951	184	22	1	1	NUM
ejpam-6951	184	23	≤	≤	NUM
ejpam-6951	184	24	i	i	PRON
ejpam-6951	184	25	≤	≤	NUM
ejpam-6951	184	26	m.	m.	NOUN
ejpam-6951	184	27	it	it	PRON
ejpam-6951	184	28	can	can	AUX
ejpam-6951	184	29	be	be	AUX
ejpam-6951	184	30	verified	verify	VERB
ejpam-6951	184	31	that	that	SCONJ
ejpam-6951	184	32	a	a	DET
ejpam-6951	184	33	,	,	PUNCT
ejpam-6951	184	34	b	b	NOUN
ejpam-6951	184	35	,	,	PUNCT
ejpam-6951	184	36	c	c	PROPN
ejpam-6951	184	37	∈	∈	PROPN
ejpam-6951	184	38	vp3(km	vp3(km	PROPN
ejpam-6951	184	39	,	,	PUNCT
ejpam-6951	184	40	n	n	CCONJ
ejpam-6951	184	41	)	)	PUNCT
ejpam-6951	184	42	,	,	PUNCT
ejpam-6951	184	43	as	as	SCONJ
ejpam-6951	184	44	shown	show	VERB
ejpam-6951	184	45	in	in	ADP
ejpam-6951	184	46	figure	figure	NOUN
ejpam-6951	184	47	4	4	NUM
ejpam-6951	184	48	.	.	PUNCT
ejpam-6951	185	1	x1	x1	NUM
ejpam-6951	186	1	x2	x2	PROPN
ejpam-6951	186	2	x3	x3	PROPN
ejpam-6951	186	3	xm−1	xm−1	PROPN
ejpam-6951	186	4	xm	xm	PROPN
ejpam-6951	187	1	y1	y1	INTJ
ejpam-6951	187	2	y2	y2	INTJ
ejpam-6951	187	3	yn−1	yn−1	NOUN
ejpam-6951	187	4	yn	yn	PROPN
ejpam-6951	187	5	km	km	PROPN
ejpam-6951	187	6	,	,	PUNCT
ejpam-6951	187	7	n⟨a⟩	n⟨a⟩	NOUN
ejpam-6951	187	8	:	:	PUNCT
ejpam-6951	187	9	x1	x1	NUM
ejpam-6951	188	1	x2	x2	NOUN
ejpam-6951	188	2	x3	x3	PROPN
ejpam-6951	188	3	xm−1	xm−1	PROPN
ejpam-6951	188	4	xm	xm	PROPN
ejpam-6951	189	1	y1	y1	INTJ
ejpam-6951	189	2	y2	y2	INTJ
ejpam-6951	189	3	yn−1	yn−1	NOUN
ejpam-6951	189	4	yn	yn	PROPN
ejpam-6951	189	5	km	km	PROPN
ejpam-6951	189	6	,	,	PUNCT
ejpam-6951	189	7	n⟨b⟩	n⟨b⟩	ADV
ejpam-6951	189	8	:	:	PUNCT
ejpam-6951	190	1	x1	x1	NUM
ejpam-6951	190	2	x2	x2	INTJ
ejpam-6951	190	3	xi	xi	PROPN
ejpam-6951	190	4	xm−1	xm−1	PROPN
ejpam-6951	190	5	xm	xm	PROPN
ejpam-6951	191	1	y1	y1	INTJ
ejpam-6951	191	2	y2	y2	INTJ
ejpam-6951	191	3	yn−1	yn−1	PROPN
ejpam-6951	191	4	yn	yn	PROPN
ejpam-6951	191	5	km	km	PROPN
ejpam-6951	191	6	,	,	PUNCT
ejpam-6951	191	7	n⟨c⟩	n⟨c⟩	PROPN
ejpam-6951	191	8	:	:	PUNCT
ejpam-6951	191	9	figure	figure	VERB
ejpam-6951	191	10	4	4	NUM
ejpam-6951	191	11	:	:	PUNCT
ejpam-6951	191	12	illustrating	illustrate	VERB
ejpam-6951	191	13	the	the	DET
ejpam-6951	191	14	subgraphs	subgraph	NOUN
ejpam-6951	191	15	of	of	ADP
ejpam-6951	191	16	km	km	PROPN
ejpam-6951	191	17	,	,	PUNCT
ejpam-6951	191	18	n	n	CCONJ
ejpam-6951	191	19	induced	induce	VERB
ejpam-6951	191	20	by	by	ADP
ejpam-6951	191	21	a	a	DET
ejpam-6951	191	22	,	,	PUNCT
ejpam-6951	191	23	b	b	NOUN
ejpam-6951	191	24	,	,	PUNCT
ejpam-6951	191	25	and	and	CCONJ
ejpam-6951	191	26	c	c	AUX
ejpam-6951	191	27	hence	hence	ADV
ejpam-6951	191	28	,	,	PUNCT
ejpam-6951	191	29	for	for	ADP
ejpam-6951	191	30	any	any	DET
ejpam-6951	191	31	i	i	NOUN
ejpam-6951	191	32	=	=	NOUN
ejpam-6951	191	33	1	1	NUM
ejpam-6951	191	34	,	,	PUNCT
ejpam-6951	191	35	2	2	NUM
ejpam-6951	191	36	,	,	PUNCT
ejpam-6951	191	37	3	3	NUM
ejpam-6951	191	38	,	,	PUNCT
ejpam-6951	191	39	...	...	PUNCT
ejpam-6951	191	40	,	,	PUNCT
ejpam-6951	191	41	m	m	PRON
ejpam-6951	191	42	,	,	PUNCT
ejpam-6951	191	43	we	we	PRON
ejpam-6951	191	44	get	get	VERB
ejpam-6951	191	45	a	a	DET
ejpam-6951	191	46	△	△	X
ejpam-6951	191	47	b	b	NOUN
ejpam-6951	191	48	△	△	X
ejpam-6951	191	49	c	c	NOUN
ejpam-6951	191	50	=	=	SYM
ejpam-6951	191	51	{	{	PUNCT
ejpam-6951	191	52	x1	x1	PROPN
ejpam-6951	191	53	,	,	PUNCT
ejpam-6951	191	54	x2	x2	PROPN
ejpam-6951	191	55	,	,	PUNCT
ejpam-6951	191	56	y1	y1	PROPN
ejpam-6951	191	57	}	}	PUNCT
ejpam-6951	191	58	△	△	X
ejpam-6951	191	59	{	{	PUNCT
ejpam-6951	191	60	x1	x1	PROPN
ejpam-6951	191	61	,	,	PUNCT
ejpam-6951	191	62	x2	x2	PROPN
ejpam-6951	191	63	,	,	PUNCT
ejpam-6951	191	64	y2	y2	PROPN
ejpam-6951	191	65	}	}	PUNCT
ejpam-6951	191	66	△	△	X
ejpam-6951	191	67	{	{	PUNCT
ejpam-6951	191	68	xi	xi	PROPN
ejpam-6951	191	69	,	,	PUNCT
ejpam-6951	191	70	y1	y1	NOUN
ejpam-6951	191	71	,	,	PUNCT
ejpam-6951	191	72	y2	y2	NOUN
ejpam-6951	191	73	}	}	PUNCT
ejpam-6951	191	74	=	=	SYM
ejpam-6951	191	75	{	{	PUNCT
ejpam-6951	191	76	y1	y1	NOUN
ejpam-6951	191	77	,	,	PUNCT
ejpam-6951	191	78	y2	y2	PROPN
ejpam-6951	191	79	}	}	PUNCT
ejpam-6951	191	80	△	△	X
ejpam-6951	191	81	{	{	PUNCT
ejpam-6951	191	82	xi	xi	PROPN
ejpam-6951	191	83	,	,	PUNCT
ejpam-6951	191	84	y1	y1	NOUN
ejpam-6951	191	85	,	,	PUNCT
ejpam-6951	191	86	y2	y2	NOUN
ejpam-6951	191	87	}	}	PUNCT
ejpam-6951	191	88	=	=	SYM
ejpam-6951	191	89	{	{	PUNCT
ejpam-6951	191	90	xi	xi	X
ejpam-6951	191	91	}	}	PUNCT
ejpam-6951	191	92	.	.	PUNCT
ejpam-6951	192	1	hence	hence	ADV
ejpam-6951	192	2	,	,	PUNCT
ejpam-6951	192	3	{	{	PUNCT
ejpam-6951	192	4	xi	xi	PROPN
ejpam-6951	192	5	}	}	PUNCT
ejpam-6951	192	6	∈	∈	PROPN
ejpam-6951	192	7	vp3(km	vp3(km	NOUN
ejpam-6951	192	8	,	,	PUNCT
ejpam-6951	192	9	n	n	CCONJ
ejpam-6951	192	10	)	)	PUNCT
ejpam-6951	192	11	for	for	ADP
ejpam-6951	192	12	all	all	DET
ejpam-6951	192	13	1	1	NUM
ejpam-6951	192	14	≤	≤	NUM
ejpam-6951	192	15	i	i	PRON
ejpam-6951	192	16	≤	≤	ADJ
ejpam-6951	192	17	m.	m.	NOUN
ejpam-6951	192	18	similarly	similarly	ADV
ejpam-6951	192	19	,	,	PUNCT
ejpam-6951	192	20	for	for	ADP
ejpam-6951	192	21	any	any	DET
ejpam-6951	192	22	1	1	NUM
ejpam-6951	192	23	≤	≤	NUM
ejpam-6951	192	24	j	j	PROPN
ejpam-6951	192	25	≤	≤	NUM
ejpam-6951	192	26	n	n	CCONJ
ejpam-6951	192	27	,	,	PUNCT
ejpam-6951	192	28	let	let	VERB
ejpam-6951	192	29	yj	yj	PRON
ejpam-6951	192	30	be	be	AUX
ejpam-6951	192	31	an	an	DET
ejpam-6951	192	32	arbitrary	arbitrary	ADJ
ejpam-6951	192	33	vertex	vertex	NOUN
ejpam-6951	192	34	of	of	ADP
ejpam-6951	192	35	partite	partite	ADJ
ejpam-6951	192	36	set	set	NOUN
ejpam-6951	192	37	n	n	NOUN
ejpam-6951	192	38	in	in	ADP
ejpam-6951	192	39	the	the	DET
ejpam-6951	192	40	complete	complete	ADJ
ejpam-6951	192	41	bipartite	bipartite	PROPN
ejpam-6951	192	42	graph	graph	NOUN
ejpam-6951	192	43	km	km	PROPN
ejpam-6951	192	44	,	,	PUNCT
ejpam-6951	192	45	n	n	CCONJ
ejpam-6951	192	46	,	,	PUNCT
ejpam-6951	192	47	and	and	CCONJ
ejpam-6951	192	48	let	let	VERB
ejpam-6951	192	49	d	d	NOUN
ejpam-6951	192	50	,	,	PUNCT
ejpam-6951	192	51	e	e	NOUN
ejpam-6951	192	52	,	,	PUNCT
ejpam-6951	192	53	and	and	CCONJ
ejpam-6951	192	54	f	f	PROPN
ejpam-6951	192	55	be	be	AUX
ejpam-6951	192	56	defined	define	VERB
ejpam-6951	192	57	as	as	SCONJ
ejpam-6951	192	58	follows	follow	VERB
ejpam-6951	192	59	:	:	PUNCT
ejpam-6951	193	1	d	d	X
ejpam-6951	193	2	=	=	SYM
ejpam-6951	193	3	{	{	PUNCT
ejpam-6951	193	4	x1	x1	PROPN
ejpam-6951	193	5	,	,	PUNCT
ejpam-6951	193	6	y1	y1	NOUN
ejpam-6951	193	7	,	,	PUNCT
ejpam-6951	193	8	y2	y2	PROPN
ejpam-6951	193	9	}	}	PUNCT
ejpam-6951	193	10	,	,	PUNCT
ejpam-6951	193	11	e	e	X
ejpam-6951	193	12	=	=	PRON
ejpam-6951	193	13	{	{	PUNCT
ejpam-6951	193	14	x2	x2	PROPN
ejpam-6951	193	15	,	,	PUNCT
ejpam-6951	193	16	y1	y1	NOUN
ejpam-6951	193	17	,	,	PUNCT
ejpam-6951	193	18	y2	y2	PROPN
ejpam-6951	193	19	}	}	PUNCT
ejpam-6951	193	20	,	,	PUNCT
ejpam-6951	193	21	and	and	CCONJ
ejpam-6951	193	22	f	f	X
ejpam-6951	193	23	=	=	PRON
ejpam-6951	193	24	{	{	PUNCT
ejpam-6951	193	25	x1	x1	PROPN
ejpam-6951	193	26	,	,	PUNCT
ejpam-6951	193	27	x2	x2	PROPN
ejpam-6951	193	28	,	,	PUNCT
ejpam-6951	193	29	yj	yj	PROPN
ejpam-6951	193	30	}	}	PUNCT
ejpam-6951	193	31	where	where	SCONJ
ejpam-6951	193	32	1	1	NUM
ejpam-6951	193	33	≤	≤	NUM
ejpam-6951	193	34	j	j	PROPN
ejpam-6951	193	35	≤	≤	PROPN
ejpam-6951	193	36	n.	n.	NOUN
ejpam-6951	193	37	it	it	PRON
ejpam-6951	193	38	can	can	AUX
ejpam-6951	193	39	be	be	AUX
ejpam-6951	193	40	verified	verify	VERB
ejpam-6951	193	41	that	that	SCONJ
ejpam-6951	193	42	d	d	NOUN
ejpam-6951	193	43	,	,	PUNCT
ejpam-6951	193	44	e	e	NOUN
ejpam-6951	193	45	,	,	PUNCT
ejpam-6951	193	46	f	f	PROPN
ejpam-6951	193	47	∈	∈	PROPN
ejpam-6951	193	48	vp3(km	vp3(km	PROPN
ejpam-6951	193	49	,	,	PUNCT
ejpam-6951	193	50	n	n	CCONJ
ejpam-6951	193	51	)	)	PUNCT
ejpam-6951	193	52	,	,	PUNCT
ejpam-6951	193	53	as	as	SCONJ
ejpam-6951	193	54	shown	show	VERB
ejpam-6951	193	55	in	in	ADP
ejpam-6951	193	56	figure	figure	NOUN
ejpam-6951	193	57	5	5	NUM
ejpam-6951	193	58	.	.	PUNCT
ejpam-6951	193	59	g.	g.	PROPN
ejpam-6951	193	60	d.	d.	PROPN
ejpam-6951	193	61	sepillo	sepillo	PROPN
ejpam-6951	193	62	et	et	PROPN
ejpam-6951	193	63	al	al	PROPN
ejpam-6951	193	64	.	.	PUNCT
ejpam-6951	193	65	/	/	SYM
ejpam-6951	193	66	eur	eur	PROPN
ejpam-6951	193	67	.	.	PUNCT
ejpam-6951	194	1	j.	j.	PROPN
ejpam-6951	194	2	pure	pure	PROPN
ejpam-6951	194	3	appl	appl	PROPN
ejpam-6951	194	4	.	.	PROPN
ejpam-6951	194	5	math	math	PROPN
ejpam-6951	194	6	,	,	PUNCT
ejpam-6951	194	7	18	18	NUM
ejpam-6951	194	8	(	(	PUNCT
ejpam-6951	194	9	4	4	NUM
ejpam-6951	194	10	)	)	PUNCT
ejpam-6951	194	11	(	(	PUNCT
ejpam-6951	194	12	2025	2025	NUM
ejpam-6951	194	13	)	)	PUNCT
ejpam-6951	194	14	,	,	PUNCT
ejpam-6951	194	15	6951	6951	NUM
ejpam-6951	194	16	9	9	NUM
ejpam-6951	194	17	of	of	ADP
ejpam-6951	194	18	23	23	NUM
ejpam-6951	195	1	x1	x1	NUM
ejpam-6951	195	2	x2	x2	NOUN
ejpam-6951	196	1	x3	x3	PROPN
ejpam-6951	196	2	xm−1	xm−1	PROPN
ejpam-6951	196	3	xm	xm	PROPN
ejpam-6951	197	1	y1	y1	INTJ
ejpam-6951	197	2	y2	y2	INTJ
ejpam-6951	197	3	yn−1	yn−1	NOUN
ejpam-6951	197	4	yn	yn	PROPN
ejpam-6951	197	5	km	km	PROPN
ejpam-6951	197	6	,	,	PUNCT
ejpam-6951	197	7	n⟨d⟩	n⟨d⟩	NOUN
ejpam-6951	197	8	:	:	PUNCT
ejpam-6951	198	1	x1	x1	NUM
ejpam-6951	198	2	x2	x2	NOUN
ejpam-6951	198	3	x3	x3	PROPN
ejpam-6951	198	4	xm−1	xm−1	PROPN
ejpam-6951	198	5	xm	xm	PROPN
ejpam-6951	199	1	y1	y1	INTJ
ejpam-6951	199	2	y2	y2	INTJ
ejpam-6951	199	3	yn−1	yn−1	NOUN
ejpam-6951	199	4	yn	yn	PROPN
ejpam-6951	199	5	km	km	PROPN
ejpam-6951	199	6	,	,	PUNCT
ejpam-6951	199	7	n⟨e⟩	n⟨e⟩	PROPN
ejpam-6951	199	8	:	:	PUNCT
ejpam-6951	199	9	x1	x1	PROPN
ejpam-6951	200	1	x2	x2	PROPN
ejpam-6951	200	2	x3	x3	PROPN
ejpam-6951	200	3	xm−1	xm−1	PROPN
ejpam-6951	200	4	xm	xm	PROPN
ejpam-6951	201	1	y1	y1	INTJ
ejpam-6951	201	2	y2	y2	PROPN
ejpam-6951	201	3	yj	yj	PROPN
ejpam-6951	201	4	yn	yn	PROPN
ejpam-6951	201	5	km	km	PROPN
ejpam-6951	201	6	,	,	PUNCT
ejpam-6951	201	7	n⟨f	n⟨f	NUM
ejpam-6951	201	8	⟩	⟩	NOUN
ejpam-6951	201	9	:	:	PUNCT
ejpam-6951	201	10	figure	figure	NOUN
ejpam-6951	201	11	5	5	NUM
ejpam-6951	201	12	:	:	PUNCT
ejpam-6951	201	13	illustrating	illustrate	VERB
ejpam-6951	201	14	the	the	DET
ejpam-6951	201	15	subgraphs	subgraph	NOUN
ejpam-6951	201	16	of	of	ADP
ejpam-6951	201	17	km	km	PROPN
ejpam-6951	201	18	,	,	PUNCT
ejpam-6951	201	19	n	n	CCONJ
ejpam-6951	201	20	induced	induce	VERB
ejpam-6951	201	21	by	by	ADP
ejpam-6951	201	22	d	d	PROPN
ejpam-6951	201	23	,	,	PUNCT
ejpam-6951	201	24	e	e	NOUN
ejpam-6951	201	25	,	,	PUNCT
ejpam-6951	201	26	and	and	CCONJ
ejpam-6951	201	27	f	f	X
ejpam-6951	201	28	consequently	consequently	ADV
ejpam-6951	201	29	,	,	PUNCT
ejpam-6951	201	30	for	for	ADP
ejpam-6951	201	31	any	any	DET
ejpam-6951	201	32	j	j	NOUN
ejpam-6951	201	33	=	=	SYM
ejpam-6951	201	34	1	1	NUM
ejpam-6951	201	35	,	,	PUNCT
ejpam-6951	201	36	2	2	NUM
ejpam-6951	201	37	,	,	PUNCT
ejpam-6951	201	38	3	3	NUM
ejpam-6951	201	39	,	,	PUNCT
ejpam-6951	201	40	...	...	PUNCT
ejpam-6951	201	41	,	,	PUNCT
ejpam-6951	201	42	n	n	CCONJ
ejpam-6951	201	43	,	,	PUNCT
ejpam-6951	201	44	we	we	PRON
ejpam-6951	201	45	obtain	obtain	VERB
ejpam-6951	201	46	d	d	ADP
ejpam-6951	201	47	△	△	X
ejpam-6951	201	48	e	e	X
ejpam-6951	201	49	△	△	X
ejpam-6951	201	50	f	f	X
ejpam-6951	201	51	=	=	PRON
ejpam-6951	201	52	{	{	PUNCT
ejpam-6951	201	53	x1	x1	PROPN
ejpam-6951	201	54	,	,	PUNCT
ejpam-6951	201	55	y1	y1	NOUN
ejpam-6951	201	56	,	,	PUNCT
ejpam-6951	201	57	y2	y2	NOUN
ejpam-6951	201	58	}	}	PUNCT
ejpam-6951	201	59	△	△	X
ejpam-6951	201	60	{	{	PUNCT
ejpam-6951	201	61	x2	x2	PROPN
ejpam-6951	201	62	,	,	PUNCT
ejpam-6951	201	63	y1	y1	NOUN
ejpam-6951	201	64	,	,	PUNCT
ejpam-6951	201	65	y2	y2	NOUN
ejpam-6951	201	66	}	}	PUNCT
ejpam-6951	201	67	△	△	X
ejpam-6951	201	68	{	{	PUNCT
ejpam-6951	201	69	x1	x1	PROPN
ejpam-6951	201	70	,	,	PUNCT
ejpam-6951	201	71	x2	x2	PROPN
ejpam-6951	201	72	,	,	PUNCT
ejpam-6951	201	73	yj	yj	PROPN
ejpam-6951	201	74	}	}	PUNCT
ejpam-6951	201	75	=	=	PUNCT
ejpam-6951	201	76	{	{	PUNCT
ejpam-6951	201	77	x1	x1	PROPN
ejpam-6951	201	78	,	,	PUNCT
ejpam-6951	201	79	x2	x2	PROPN
ejpam-6951	201	80	}	}	PUNCT
ejpam-6951	201	81	△	△	X
ejpam-6951	201	82	{	{	PUNCT
ejpam-6951	201	83	x1	x1	PROPN
ejpam-6951	201	84	,	,	PUNCT
ejpam-6951	201	85	x2	x2	PROPN
ejpam-6951	201	86	,	,	PUNCT
ejpam-6951	201	87	yj	yj	PROPN
ejpam-6951	201	88	}	}	PUNCT
ejpam-6951	201	89	=	=	SYM
ejpam-6951	201	90	{	{	PUNCT
ejpam-6951	201	91	yj	yj	PROPN
ejpam-6951	201	92	}	}	PUNCT
ejpam-6951	201	93	.	.	PUNCT
ejpam-6951	202	1	hence	hence	ADV
ejpam-6951	202	2	,	,	PUNCT
ejpam-6951	202	3	{	{	PUNCT
ejpam-6951	202	4	yj	yj	PROPN
ejpam-6951	202	5	}	}	PUNCT
ejpam-6951	202	6	∈	∈	PROPN
ejpam-6951	202	7	vp3(km	vp3(km	NOUN
ejpam-6951	202	8	,	,	PUNCT
ejpam-6951	202	9	n	n	CCONJ
ejpam-6951	202	10	)	)	PUNCT
ejpam-6951	202	11	for	for	ADP
ejpam-6951	202	12	all	all	PRON
ejpam-6951	202	13	1	1	NUM
ejpam-6951	202	14	≤	≤	NUM
ejpam-6951	202	15	j	j	PROPN
ejpam-6951	202	16	≤	≤	PROPN
ejpam-6951	202	17	n.	n.	PROPN
ejpam-6951	202	18	therefore	therefore	ADV
ejpam-6951	202	19	,	,	PUNCT
ejpam-6951	202	20	p3	p3	PROPN
ejpam-6951	202	21	is	be	AUX
ejpam-6951	202	22	a	a	DET
ejpam-6951	202	23	vertex	vertex	NOUN
ejpam-6951	202	24	-	-	PUNCT
ejpam-6951	202	25	generator	generator	NOUN
ejpam-6951	202	26	subgraph	subgraph	NOUN
ejpam-6951	202	27	of	of	ADP
ejpam-6951	202	28	km	km	PROPN
ejpam-6951	202	29	,	,	PUNCT
ejpam-6951	202	30	n	n	CCONJ
ejpam-6951	202	31	by	by	ADP
ejpam-6951	202	32	remark	remark	NOUN
ejpam-6951	202	33	1	1	NUM
ejpam-6951	202	34	.	.	PUNCT
ejpam-6951	203	1	it	it	PRON
ejpam-6951	203	2	is	be	AUX
ejpam-6951	203	3	notable	notable	ADJ
ejpam-6951	203	4	that	that	SCONJ
ejpam-6951	203	5	the	the	DET
ejpam-6951	203	6	path	path	NOUN
ejpam-6951	203	7	graph	graph	NOUN
ejpam-6951	203	8	p3	p3	PROPN
ejpam-6951	203	9	,	,	PUNCT
ejpam-6951	203	10	as	as	ADP
ejpam-6951	203	11	a	a	DET
ejpam-6951	203	12	vertex	vertex	NOUN
ejpam-6951	203	13	-	-	PUNCT
ejpam-6951	203	14	generator	generator	NOUN
ejpam-6951	203	15	subgraph	subgraph	NOUN
ejpam-6951	203	16	of	of	ADP
ejpam-6951	203	17	km	km	PROPN
ejpam-6951	203	18	,	,	PUNCT
ejpam-6951	203	19	n	n	CCONJ
ejpam-6951	203	20	,	,	PUNCT
ejpam-6951	203	21	is	be	AUX
ejpam-6951	203	22	isomorphic	isomorphic	ADJ
ejpam-6951	203	23	to	to	ADP
ejpam-6951	203	24	a	a	DET
ejpam-6951	203	25	star	star	NOUN
ejpam-6951	203	26	graph	graph	NOUN
ejpam-6951	203	27	s2	s2	PROPN
ejpam-6951	203	28	.	.	PUNCT
ejpam-6951	204	1	we	we	PRON
ejpam-6951	204	2	can	can	AUX
ejpam-6951	204	3	extend	extend	VERB
ejpam-6951	204	4	this	this	PRON
ejpam-6951	204	5	up	up	ADP
ejpam-6951	204	6	to	to	ADP
ejpam-6951	204	7	st	st	PROPN
ejpam-6951	204	8	of	of	ADP
ejpam-6951	204	9	order	order	NOUN
ejpam-6951	204	10	t	t	NOUN
ejpam-6951	205	1	+	+	NOUN
ejpam-6951	205	2	1	1	NUM
ejpam-6951	205	3	,	,	PUNCT
ejpam-6951	205	4	hence	hence	ADV
ejpam-6951	205	5	t	t	PROPN
ejpam-6951	205	6	must	must	AUX
ejpam-6951	205	7	be	be	AUX
ejpam-6951	205	8	even	even	ADV
ejpam-6951	205	9	.	.	PUNCT
ejpam-6951	206	1	with	with	ADP
ejpam-6951	206	2	this	this	PRON
ejpam-6951	206	3	,	,	PUNCT
ejpam-6951	206	4	the	the	DET
ejpam-6951	206	5	following	follow	VERB
ejpam-6951	206	6	theorem	theorem	NOUN
ejpam-6951	206	7	gives	give	VERB
ejpam-6951	206	8	us	we	PRON
ejpam-6951	206	9	a	a	DET
ejpam-6951	206	10	necessary	necessary	ADJ
ejpam-6951	206	11	condition	condition	NOUN
ejpam-6951	206	12	for	for	SCONJ
ejpam-6951	206	13	st	st	PROPN
ejpam-6951	206	14	to	to	PART
ejpam-6951	206	15	be	be	AUX
ejpam-6951	206	16	a	a	DET
ejpam-6951	206	17	vertex	vertex	NOUN
ejpam-6951	206	18	-	-	PUNCT
ejpam-6951	206	19	generator	generator	NOUN
ejpam-6951	206	20	subgraph	subgraph	NOUN
ejpam-6951	206	21	of	of	ADP
ejpam-6951	206	22	km	km	PROPN
ejpam-6951	206	23	,	,	PUNCT
ejpam-6951	206	24	n.	n.	PROPN
ejpam-6951	206	25	theorem	theorem	VERB
ejpam-6951	206	26	12	12	NUM
ejpam-6951	206	27	.	.	PUNCT
ejpam-6951	207	1	let	let	VERB
ejpam-6951	207	2	m	m	PRON
ejpam-6951	207	3	,	,	PUNCT
ejpam-6951	207	4	n	n	CCONJ
ejpam-6951	207	5	,	,	PUNCT
ejpam-6951	207	6	and	and	CCONJ
ejpam-6951	207	7	t	t	PROPN
ejpam-6951	207	8	be	be	AUX
ejpam-6951	207	9	positive	positive	ADJ
ejpam-6951	207	10	integers	integer	NOUN
ejpam-6951	207	11	such	such	ADJ
ejpam-6951	207	12	that	that	DET
ejpam-6951	207	13	min{m	min{m	NOUN
ejpam-6951	207	14	,	,	PUNCT
ejpam-6951	207	15	n	n	CCONJ
ejpam-6951	207	16	}	}	PUNCT
ejpam-6951	207	17	≥	≥	NUM
ejpam-6951	207	18	2	2	NUM
ejpam-6951	207	19	,	,	PUNCT
ejpam-6951	207	20	m+	m+	NUM
ejpam-6951	207	21	n	n	CCONJ
ejpam-6951	207	22	≥	≥	NOUN
ejpam-6951	207	23	5	5	NUM
ejpam-6951	207	24	,	,	PUNCT
ejpam-6951	207	25	and	and	CCONJ
ejpam-6951	207	26	t	t	PROPN
ejpam-6951	207	27	is	be	AUX
ejpam-6951	207	28	even	even	ADV
ejpam-6951	207	29	.	.	PUNCT
ejpam-6951	208	1	if	if	SCONJ
ejpam-6951	208	2	t	t	NOUN
ejpam-6951	208	3	≤	≤	NUM
ejpam-6951	208	4	min{m	min{m	NOUN
ejpam-6951	208	5	,	,	PUNCT
ejpam-6951	208	6	n	n	CCONJ
ejpam-6951	208	7	}	}	PUNCT
ejpam-6951	208	8	,	,	PUNCT
ejpam-6951	208	9	then	then	ADV
ejpam-6951	208	10	st	st	PROPN
ejpam-6951	208	11	is	be	AUX
ejpam-6951	208	12	a	a	DET
ejpam-6951	208	13	vertex	vertex	NOUN
ejpam-6951	208	14	-	-	PUNCT
ejpam-6951	208	15	generator	generator	NOUN
ejpam-6951	208	16	subgraph	subgraph	NOUN
ejpam-6951	208	17	of	of	ADP
ejpam-6951	208	18	km	km	PROPN
ejpam-6951	208	19	,	,	PUNCT
ejpam-6951	208	20	n.	n.	NOUN
ejpam-6951	208	21	proof	proof	NOUN
ejpam-6951	208	22	.	.	PUNCT
ejpam-6951	209	1	let	let	VERB
ejpam-6951	209	2	t	t	NOUN
ejpam-6951	209	3	≤	≤	NUM
ejpam-6951	209	4	min{m	min{m	PROPN
ejpam-6951	209	5	,	,	PUNCT
ejpam-6951	209	6	n	n	CCONJ
ejpam-6951	209	7	}	}	PUNCT
ejpam-6951	209	8	.	.	PUNCT
ejpam-6951	210	1	for	for	ADP
ejpam-6951	210	2	any	any	DET
ejpam-6951	210	3	1	1	NUM
ejpam-6951	210	4	≤	≤	NUM
ejpam-6951	210	5	i	i	PRON
ejpam-6951	210	6	≤	≤	NOUN
ejpam-6951	210	7	m	m	VERB
ejpam-6951	210	8	,	,	PUNCT
ejpam-6951	210	9	let	let	VERB
ejpam-6951	210	10	xi	xi	PRON
ejpam-6951	210	11	be	be	AUX
ejpam-6951	210	12	an	an	DET
ejpam-6951	210	13	arbitrary	arbitrary	ADJ
ejpam-6951	210	14	vertex	vertex	NOUN
ejpam-6951	210	15	of	of	ADP
ejpam-6951	210	16	partite	partite	ADJ
ejpam-6951	210	17	set	set	NOUN
ejpam-6951	210	18	m	m	VERB
ejpam-6951	210	19	in	in	ADP
ejpam-6951	210	20	the	the	DET
ejpam-6951	210	21	complete	complete	ADJ
ejpam-6951	210	22	bipartite	bipartite	PROPN
ejpam-6951	210	23	km	km	PROPN
ejpam-6951	210	24	,	,	PUNCT
ejpam-6951	210	25	n	n	CCONJ
ejpam-6951	210	26	,	,	PUNCT
ejpam-6951	210	27	and	and	CCONJ
ejpam-6951	210	28	for	for	ADP
ejpam-6951	210	29	any	any	DET
ejpam-6951	210	30	1	1	NUM
ejpam-6951	210	31	≤	≤	NOUN
ejpam-6951	210	32	p	p	PROPN
ejpam-6951	210	33	≤	≤	PROPN
ejpam-6951	210	34	t	t	PROPN
ejpam-6951	210	35	,	,	PUNCT
ejpam-6951	210	36	let	let	VERB
ejpam-6951	210	37	ap	ap	PRON
ejpam-6951	210	38	and	and	CCONJ
ejpam-6951	210	39	a	a	PRON
ejpam-6951	210	40	be	be	AUX
ejpam-6951	210	41	defined	define	VERB
ejpam-6951	210	42	as	as	SCONJ
ejpam-6951	210	43	follows	follow	VERB
ejpam-6951	210	44	:	:	PUNCT
ejpam-6951	210	45	ap	ap	PROPN
ejpam-6951	210	46	=	=	PUNCT
ejpam-6951	210	47	{	{	PUNCT
ejpam-6951	210	48	x1	x1	PROPN
ejpam-6951	210	49	,	,	PUNCT
ejpam-6951	210	50	x2	x2	PROPN
ejpam-6951	210	51	,	,	PUNCT
ejpam-6951	210	52	x3	x3	ADJ
ejpam-6951	210	53	,	,	PUNCT
ejpam-6951	210	54	...	...	PUNCT
ejpam-6951	210	55	,	,	PUNCT
ejpam-6951	210	56	xt	xt	X
ejpam-6951	210	57	,	,	PUNCT
ejpam-6951	210	58	yp	yp	X
ejpam-6951	210	59	}	}	PUNCT
ejpam-6951	210	60	where	where	SCONJ
ejpam-6951	210	61	1	1	NUM
ejpam-6951	210	62	≤	≤	NOUN
ejpam-6951	210	63	p	p	PROPN
ejpam-6951	210	64	≤	≤	PROPN
ejpam-6951	210	65	t	t	PROPN
ejpam-6951	210	66	,	,	PUNCT
ejpam-6951	210	67	and	and	CCONJ
ejpam-6951	210	68	a	a	DET
ejpam-6951	210	69	=	=	X
ejpam-6951	210	70	{	{	PUNCT
ejpam-6951	210	71	xi	xi	PROPN
ejpam-6951	210	72	,	,	PUNCT
ejpam-6951	210	73	y1	y1	PROPN
ejpam-6951	210	74	,	,	PUNCT
ejpam-6951	210	75	y2	y2	PROPN
ejpam-6951	210	76	,	,	PUNCT
ejpam-6951	210	77	y3	y3	PROPN
ejpam-6951	210	78	,	,	PUNCT
ejpam-6951	210	79	...	...	PUNCT
ejpam-6951	210	80	,	,	PUNCT
ejpam-6951	210	81	yt	yt	INTJ
ejpam-6951	210	82	}	}	PUNCT
ejpam-6951	210	83	where	where	SCONJ
ejpam-6951	210	84	1	1	NUM
ejpam-6951	210	85	≤	≤	NUM
ejpam-6951	210	86	i	i	PRON
ejpam-6951	210	87	≤	≤	NUM
ejpam-6951	210	88	m.	m.	NOUN
ejpam-6951	210	89	it	it	PRON
ejpam-6951	210	90	can	can	AUX
ejpam-6951	210	91	be	be	AUX
ejpam-6951	210	92	verified	verify	VERB
ejpam-6951	210	93	that	that	SCONJ
ejpam-6951	210	94	ap	ap	PROPN
ejpam-6951	210	95	,	,	PUNCT
ejpam-6951	210	96	a	a	DET
ejpam-6951	210	97	∈	∈	PROPN
ejpam-6951	210	98	vst(km	vst(km	NOUN
ejpam-6951	210	99	,	,	PUNCT
ejpam-6951	210	100	n	n	CCONJ
ejpam-6951	210	101	)	)	PUNCT
ejpam-6951	210	102	,	,	PUNCT
ejpam-6951	210	103	as	as	SCONJ
ejpam-6951	210	104	shown	show	VERB
ejpam-6951	210	105	in	in	ADP
ejpam-6951	210	106	figure	figure	NOUN
ejpam-6951	210	107	6	6	NUM
ejpam-6951	210	108	.	.	PUNCT
ejpam-6951	211	1	hence	hence	ADV
ejpam-6951	211	2	,	,	PUNCT
ejpam-6951	211	3	for	for	ADP
ejpam-6951	211	4	any	any	DET
ejpam-6951	211	5	i	i	NOUN
ejpam-6951	211	6	=	=	NOUN
ejpam-6951	211	7	1	1	NUM
ejpam-6951	211	8	,	,	PUNCT
ejpam-6951	211	9	2	2	NUM
ejpam-6951	211	10	,	,	PUNCT
ejpam-6951	211	11	3	3	NUM
ejpam-6951	211	12	,	,	PUNCT
ejpam-6951	211	13	...	...	PUNCT
ejpam-6951	211	14	,	,	PUNCT
ejpam-6951	211	15	m	m	PRON
ejpam-6951	211	16	,	,	PUNCT
ejpam-6951	211	17	we	we	PRON
ejpam-6951	211	18	have	have	VERB
ejpam-6951	211	19	t∑	t∑	ADJ
ejpam-6951	211	20	p=1	p=1	X
ejpam-6951	211	21	ap	ap	PROPN
ejpam-6951	212	1	+	+	NOUN
ejpam-6951	212	2	a	a	NOUN
ejpam-6951	212	3	=	=	X
ejpam-6951	212	4	(	(	PUNCT
ejpam-6951	212	5	a1	a1	NOUN
ejpam-6951	212	6	+	+	PROPN
ejpam-6951	212	7	a2	a2	PROPN
ejpam-6951	212	8	+	+	NOUN
ejpam-6951	212	9	a3	a3	NOUN
ejpam-6951	212	10	+	+	X
ejpam-6951	212	11	·	·	PUNCT
ejpam-6951	212	12	·	·	PUNCT
ejpam-6951	212	13	·	·	PUNCT
ejpam-6951	212	14	+	+	ADJ
ejpam-6951	212	15	at	at	ADP
ejpam-6951	212	16	)	)	PUNCT
ejpam-6951	212	17	+	+	ADP
ejpam-6951	212	18	a	a	DET
ejpam-6951	212	19	g.	g.	PROPN
ejpam-6951	212	20	d.	d.	PROPN
ejpam-6951	212	21	sepillo	sepillo	PROPN
ejpam-6951	212	22	et	et	PROPN
ejpam-6951	212	23	al	al	PROPN
ejpam-6951	212	24	.	.	PUNCT
ejpam-6951	212	25	/	/	SYM
ejpam-6951	212	26	eur	eur	PROPN
ejpam-6951	212	27	.	.	PUNCT
ejpam-6951	213	1	j.	j.	PROPN
ejpam-6951	213	2	pure	pure	PROPN
ejpam-6951	213	3	appl	appl	PROPN
ejpam-6951	213	4	.	.	PROPN
ejpam-6951	213	5	math	math	PROPN
ejpam-6951	213	6	,	,	PUNCT
ejpam-6951	213	7	18	18	NUM
ejpam-6951	213	8	(	(	PUNCT
ejpam-6951	213	9	4	4	NUM
ejpam-6951	213	10	)	)	PUNCT
ejpam-6951	213	11	(	(	PUNCT
ejpam-6951	213	12	2025	2025	NUM
ejpam-6951	213	13	)	)	PUNCT
ejpam-6951	213	14	,	,	PUNCT
ejpam-6951	213	15	6951	6951	NUM
ejpam-6951	213	16	10	10	NUM
ejpam-6951	213	17	of	of	ADP
ejpam-6951	213	18	23	23	NUM
ejpam-6951	214	1	x1	x1	NUM
ejpam-6951	215	1	x2	x2	PROPN
ejpam-6951	215	2	xt−1	xt−1	PROPN
ejpam-6951	215	3	xt	xt	PROPN
ejpam-6951	216	1	xt+1	xt+1	PROPN
ejpam-6951	217	1	xm−1	xm−1	PROPN
ejpam-6951	217	2	xm	xm	PROPN
ejpam-6951	218	1	y1	y1	INTJ
ejpam-6951	219	1	y2	y2	INTJ
ejpam-6951	220	1	yt−1	yt−1	NOUN
ejpam-6951	220	2	yt	yt	VERB
ejpam-6951	220	3	yn−1	yn−1	PROPN
ejpam-6951	220	4	yn	yn	PROPN
ejpam-6951	220	5	km	km	PROPN
ejpam-6951	220	6	,	,	PUNCT
ejpam-6951	220	7	n⟨ap⟩	n⟨ap⟩	ADV
ejpam-6951	220	8	:	:	PUNCT
ejpam-6951	221	1	x1	x1	NUM
ejpam-6951	221	2	x2	x2	NOUN
ejpam-6951	221	3	x3	x3	INTJ
ejpam-6951	221	4	xi	xi	PROPN
ejpam-6951	222	1	xm−2	xm−2	PROPN
ejpam-6951	222	2	xm−1	xm−1	PROPN
ejpam-6951	222	3	xm	xm	PROPN
ejpam-6951	223	1	y1	y1	INTJ
ejpam-6951	224	1	y2	y2	INTJ
ejpam-6951	225	1	yt−1	yt−1	NOUN
ejpam-6951	225	2	yt	yt	VERB
ejpam-6951	225	3	yn−1	yn−1	PROPN
ejpam-6951	225	4	yn	yn	PROPN
ejpam-6951	225	5	km	km	PROPN
ejpam-6951	225	6	,	,	PUNCT
ejpam-6951	225	7	n⟨a⟩	n⟨a⟩	NOUN
ejpam-6951	225	8	:	:	PUNCT
ejpam-6951	225	9	figure	figure	VERB
ejpam-6951	225	10	6	6	NUM
ejpam-6951	225	11	:	:	PUNCT
ejpam-6951	225	12	illustrating	illustrate	VERB
ejpam-6951	225	13	the	the	DET
ejpam-6951	225	14	subgraphs	subgraph	NOUN
ejpam-6951	225	15	of	of	ADP
ejpam-6951	225	16	km	km	PROPN
ejpam-6951	225	17	,	,	PUNCT
ejpam-6951	225	18	n	n	CCONJ
ejpam-6951	225	19	induced	induce	VERB
ejpam-6951	225	20	by	by	ADP
ejpam-6951	225	21	ap	ap	PROPN
ejpam-6951	225	22	and	and	CCONJ
ejpam-6951	225	23	a	a	DET
ejpam-6951	225	24	=	=	X
ejpam-6951	225	25	(	(	PUNCT
ejpam-6951	225	26	a1	a1	PROPN
ejpam-6951	225	27	△	△	PROPN
ejpam-6951	225	28	a2	a2	PROPN
ejpam-6951	225	29	△	△	PROPN
ejpam-6951	225	30	a3	a3	NOUN
ejpam-6951	225	31	△	△	X
ejpam-6951	225	32	·	·	PUNCT
ejpam-6951	225	33	·	·	PUNCT
ejpam-6951	225	34	·	·	PUNCT
ejpam-6951	225	35	△	△	X
ejpam-6951	225	36	at)	at)	X
ejpam-6951	225	37	△	△	X
ejpam-6951	225	38	a	a	DET
ejpam-6951	225	39	=	=	SYM
ejpam-6951	225	40	{	{	PUNCT
ejpam-6951	225	41	y1	y1	PROPN
ejpam-6951	225	42	,	,	PUNCT
ejpam-6951	225	43	y2	y2	PROPN
ejpam-6951	225	44	,	,	PUNCT
ejpam-6951	225	45	y3	y3	PROPN
ejpam-6951	225	46	,	,	PUNCT
ejpam-6951	225	47	...	...	PUNCT
ejpam-6951	225	48	,	,	PUNCT
ejpam-6951	225	49	yt	yt	PROPN
ejpam-6951	225	50	}	}	PUNCT
ejpam-6951	225	51	△	△	X
ejpam-6951	225	52	{	{	PUNCT
ejpam-6951	225	53	xi	xi	PROPN
ejpam-6951	225	54	,	,	PUNCT
ejpam-6951	225	55	y1	y1	PROPN
ejpam-6951	225	56	,	,	PUNCT
ejpam-6951	225	57	y2	y2	PROPN
ejpam-6951	225	58	,	,	PUNCT
ejpam-6951	225	59	y3	y3	PROPN
ejpam-6951	225	60	,	,	PUNCT
ejpam-6951	225	61	...	...	PUNCT
ejpam-6951	225	62	,	,	PUNCT
ejpam-6951	225	63	yt	yt	NOUN
ejpam-6951	225	64	}	}	PUNCT
ejpam-6951	225	65	=	=	PUNCT
ejpam-6951	225	66	{	{	PUNCT
ejpam-6951	225	67	xi	xi	X
ejpam-6951	225	68	}	}	PUNCT
ejpam-6951	225	69	.	.	PUNCT
ejpam-6951	226	1	thus	thus	ADV
ejpam-6951	226	2	,	,	PUNCT
ejpam-6951	226	3	{	{	PUNCT
ejpam-6951	226	4	xi	xi	NOUN
ejpam-6951	226	5	}	}	PUNCT
ejpam-6951	226	6	∈	∈	PROPN
ejpam-6951	226	7	vst(km	vst(km	NOUN
ejpam-6951	226	8	,	,	PUNCT
ejpam-6951	226	9	n	n	CCONJ
ejpam-6951	226	10	)	)	PUNCT
ejpam-6951	226	11	for	for	ADP
ejpam-6951	226	12	all	all	DET
ejpam-6951	226	13	1	1	NUM
ejpam-6951	226	14	≤	≤	NUM
ejpam-6951	226	15	i	i	PRON
ejpam-6951	226	16	≤	≤	ADJ
ejpam-6951	226	17	m.	m.	NOUN
ejpam-6951	226	18	in	in	ADP
ejpam-6951	226	19	a	a	DET
ejpam-6951	226	20	similar	similar	ADJ
ejpam-6951	226	21	manner	manner	NOUN
ejpam-6951	226	22	,	,	PUNCT
ejpam-6951	226	23	for	for	ADP
ejpam-6951	226	24	any	any	DET
ejpam-6951	226	25	1	1	NUM
ejpam-6951	226	26	≤	≤	NUM
ejpam-6951	226	27	j	j	PROPN
ejpam-6951	226	28	≤	≤	NUM
ejpam-6951	226	29	n	n	CCONJ
ejpam-6951	226	30	,	,	PUNCT
ejpam-6951	226	31	let	let	VERB
ejpam-6951	226	32	yj	yj	PRON
ejpam-6951	226	33	be	be	AUX
ejpam-6951	226	34	an	an	DET
ejpam-6951	226	35	arbitrary	arbitrary	ADJ
ejpam-6951	226	36	vertex	vertex	NOUN
ejpam-6951	226	37	of	of	ADP
ejpam-6951	226	38	partite	partite	ADJ
ejpam-6951	226	39	set	set	NOUN
ejpam-6951	226	40	n	n	NOUN
ejpam-6951	226	41	in	in	ADP
ejpam-6951	226	42	the	the	DET
ejpam-6951	226	43	complete	complete	ADJ
ejpam-6951	226	44	bipartite	bipartite	PROPN
ejpam-6951	226	45	graph	graph	NOUN
ejpam-6951	226	46	km	km	PROPN
ejpam-6951	226	47	,	,	PUNCT
ejpam-6951	226	48	n	n	CCONJ
ejpam-6951	226	49	,	,	PUNCT
ejpam-6951	226	50	and	and	CCONJ
ejpam-6951	226	51	for	for	ADP
ejpam-6951	226	52	any	any	DET
ejpam-6951	226	53	1	1	NUM
ejpam-6951	226	54	≤	≤	NOUN
ejpam-6951	226	55	q	q	PROPN
ejpam-6951	226	56	≤	≤	PROPN
ejpam-6951	226	57	t	t	PROPN
ejpam-6951	226	58	,	,	PUNCT
ejpam-6951	226	59	let	let	VERB
ejpam-6951	226	60	bq	bq	INTJ
ejpam-6951	226	61	and	and	CCONJ
ejpam-6951	226	62	b	b	NOUN
ejpam-6951	226	63	be	be	AUX
ejpam-6951	226	64	defined	define	VERB
ejpam-6951	226	65	as	as	SCONJ
ejpam-6951	226	66	follows	follow	VERB
ejpam-6951	226	67	:	:	PUNCT
ejpam-6951	226	68	bq	bq	INTJ
ejpam-6951	226	69	=	=	SYM
ejpam-6951	226	70	{	{	PUNCT
ejpam-6951	226	71	xq	xq	PROPN
ejpam-6951	226	72	,	,	PUNCT
ejpam-6951	226	73	y1	y1	PROPN
ejpam-6951	226	74	,	,	PUNCT
ejpam-6951	226	75	y2	y2	PROPN
ejpam-6951	226	76	,	,	PUNCT
ejpam-6951	226	77	y3	y3	PROPN
ejpam-6951	226	78	,	,	PUNCT
ejpam-6951	226	79	...	...	PUNCT
ejpam-6951	226	80	,	,	PUNCT
ejpam-6951	226	81	yt	yt	INTJ
ejpam-6951	226	82	}	}	PUNCT
ejpam-6951	226	83	where	where	SCONJ
ejpam-6951	226	84	1	1	NUM
ejpam-6951	226	85	≤	≤	NOUN
ejpam-6951	226	86	q	q	PROPN
ejpam-6951	226	87	≤	≤	NUM
ejpam-6951	226	88	t	t	PROPN
ejpam-6951	226	89	,	,	PUNCT
ejpam-6951	226	90	and	and	CCONJ
ejpam-6951	226	91	b	b	X
ejpam-6951	226	92	=	=	SYM
ejpam-6951	226	93	{	{	PUNCT
ejpam-6951	226	94	x1	x1	PROPN
ejpam-6951	226	95	,	,	PUNCT
ejpam-6951	226	96	x2	x2	PROPN
ejpam-6951	226	97	,	,	PUNCT
ejpam-6951	226	98	x3	x3	ADJ
ejpam-6951	226	99	,	,	PUNCT
ejpam-6951	226	100	...	...	PUNCT
ejpam-6951	226	101	,	,	PUNCT
ejpam-6951	226	102	xt	xt	PROPN
ejpam-6951	226	103	,	,	PUNCT
ejpam-6951	226	104	yj	yj	PROPN
ejpam-6951	226	105	}	}	PUNCT
ejpam-6951	226	106	where	where	SCONJ
ejpam-6951	226	107	1	1	NUM
ejpam-6951	226	108	≤	≤	NUM
ejpam-6951	226	109	j	j	PROPN
ejpam-6951	226	110	≤	≤	PROPN
ejpam-6951	226	111	n.	n.	NOUN
ejpam-6951	226	112	it	it	PRON
ejpam-6951	226	113	can	can	AUX
ejpam-6951	226	114	be	be	AUX
ejpam-6951	226	115	verified	verify	VERB
ejpam-6951	226	116	that	that	SCONJ
ejpam-6951	226	117	bq	bq	PROPN
ejpam-6951	226	118	,	,	PUNCT
ejpam-6951	226	119	b	b	PROPN
ejpam-6951	226	120	∈	∈	PROPN
ejpam-6951	226	121	vst(km	vst(km	NOUN
ejpam-6951	226	122	,	,	PUNCT
ejpam-6951	226	123	n	n	CCONJ
ejpam-6951	226	124	)	)	PUNCT
ejpam-6951	226	125	,	,	PUNCT
ejpam-6951	226	126	as	as	SCONJ
ejpam-6951	226	127	shown	show	VERB
ejpam-6951	226	128	in	in	ADP
ejpam-6951	226	129	figure	figure	NOUN
ejpam-6951	226	130	7	7	NUM
ejpam-6951	226	131	.	.	PUNCT
ejpam-6951	227	1	x1	x1	NUM
ejpam-6951	228	1	x2	x2	PROPN
ejpam-6951	228	2	xt−1	xt−1	PROPN
ejpam-6951	228	3	xt	xt	PROPN
ejpam-6951	229	1	xt+1	xt+1	PROPN
ejpam-6951	230	1	xm−1	xm−1	PROPN
ejpam-6951	230	2	xm	xm	PROPN
ejpam-6951	231	1	y1	y1	INTJ
ejpam-6951	232	1	y2	y2	INTJ
ejpam-6951	233	1	yt−1	yt−1	NOUN
ejpam-6951	233	2	yt	yt	VERB
ejpam-6951	233	3	yn−1	yn−1	PROPN
ejpam-6951	233	4	yn	yn	PROPN
ejpam-6951	233	5	km	km	PROPN
ejpam-6951	233	6	,	,	PUNCT
ejpam-6951	233	7	n⟨bq⟩	n⟨bq⟩	NOUN
ejpam-6951	233	8	:	:	PUNCT
ejpam-6951	234	1	x1	x1	PROPN
ejpam-6951	234	2	x2	x2	PROPN
ejpam-6951	234	3	xt−1	xt−1	PROPN
ejpam-6951	234	4	xt	xt	PROPN
ejpam-6951	234	5	xt+1	xt+1	PROPN
ejpam-6951	235	1	xm−1	xm−1	PROPN
ejpam-6951	235	2	xm	xm	PROPN
ejpam-6951	236	1	y1	y1	INTJ
ejpam-6951	236	2	y2	y2	PROPN
ejpam-6951	236	3	y3	y3	NOUN
ejpam-6951	236	4	yj	yj	PROPN
ejpam-6951	236	5	yn−1	yn−1	PROPN
ejpam-6951	236	6	yn	yn	PROPN
ejpam-6951	236	7	km	km	PROPN
ejpam-6951	236	8	,	,	PUNCT
ejpam-6951	236	9	n⟨b⟩	n⟨b⟩	ADV
ejpam-6951	236	10	:	:	PUNCT
ejpam-6951	236	11	figure	figure	VERB
ejpam-6951	236	12	7	7	NUM
ejpam-6951	236	13	:	:	PUNCT
ejpam-6951	236	14	illustrating	illustrate	VERB
ejpam-6951	236	15	the	the	DET
ejpam-6951	236	16	subgraphs	subgraph	NOUN
ejpam-6951	236	17	of	of	ADP
ejpam-6951	236	18	km	km	PROPN
ejpam-6951	236	19	,	,	PUNCT
ejpam-6951	236	20	n	n	CCONJ
ejpam-6951	236	21	induced	induce	VERB
ejpam-6951	236	22	by	by	ADP
ejpam-6951	236	23	bq	bq	INTJ
ejpam-6951	236	24	and	and	CCONJ
ejpam-6951	236	25	b	b	PROPN
ejpam-6951	236	26	g.	g.	PROPN
ejpam-6951	236	27	d.	d.	PROPN
ejpam-6951	236	28	sepillo	sepillo	PROPN
ejpam-6951	236	29	et	et	PROPN
ejpam-6951	236	30	al	al	PROPN
ejpam-6951	236	31	.	.	PUNCT
ejpam-6951	236	32	/	/	SYM
ejpam-6951	236	33	eur	eur	PROPN
ejpam-6951	236	34	.	.	PUNCT
ejpam-6951	237	1	j.	j.	PROPN
ejpam-6951	237	2	pure	pure	PROPN
ejpam-6951	237	3	appl	appl	PROPN
ejpam-6951	237	4	.	.	PROPN
ejpam-6951	237	5	math	math	PROPN
ejpam-6951	237	6	,	,	PUNCT
ejpam-6951	237	7	18	18	NUM
ejpam-6951	237	8	(	(	PUNCT
ejpam-6951	237	9	4	4	NUM
ejpam-6951	237	10	)	)	PUNCT
ejpam-6951	237	11	(	(	PUNCT
ejpam-6951	237	12	2025	2025	NUM
ejpam-6951	237	13	)	)	PUNCT
ejpam-6951	237	14	,	,	PUNCT
ejpam-6951	237	15	6951	6951	NUM
ejpam-6951	237	16	11	11	NUM
ejpam-6951	237	17	of	of	ADP
ejpam-6951	237	18	23	23	NUM
ejpam-6951	237	19	hence	hence	ADV
ejpam-6951	237	20	,	,	PUNCT
ejpam-6951	237	21	for	for	ADP
ejpam-6951	237	22	any	any	DET
ejpam-6951	237	23	j	j	NOUN
ejpam-6951	237	24	=	=	SYM
ejpam-6951	237	25	1	1	NUM
ejpam-6951	237	26	,	,	PUNCT
ejpam-6951	237	27	2	2	NUM
ejpam-6951	237	28	,	,	PUNCT
ejpam-6951	237	29	3	3	NUM
ejpam-6951	237	30	,	,	PUNCT
ejpam-6951	237	31	...	...	PUNCT
ejpam-6951	237	32	,	,	PUNCT
ejpam-6951	237	33	n	n	CCONJ
ejpam-6951	237	34	,	,	PUNCT
ejpam-6951	238	1	we	we	PRON
ejpam-6951	238	2	get	get	VERB
ejpam-6951	238	3	t∑	t∑	ADV
ejpam-6951	238	4	q=1	q=1	X
ejpam-6951	238	5	bq	bq	X
ejpam-6951	239	1	+	+	NOUN
ejpam-6951	239	2	b	b	X
ejpam-6951	239	3	=	=	SYM
ejpam-6951	239	4	(	(	PUNCT
ejpam-6951	239	5	b1	b1	NOUN
ejpam-6951	239	6	+	+	NOUN
ejpam-6951	239	7	b2	b2	NOUN
ejpam-6951	239	8	+	+	NOUN
ejpam-6951	239	9	b3	b3	NOUN
ejpam-6951	239	10	+	+	CCONJ
ejpam-6951	239	11	·	·	PUNCT
ejpam-6951	239	12	·	·	PUNCT
ejpam-6951	239	13	·	·	PUNCT
ejpam-6951	239	14	+	+	NOUN
ejpam-6951	239	15	bt	bt	ADJ
ejpam-6951	239	16	)	)	PUNCT
ejpam-6951	239	17	+	+	NOUN
ejpam-6951	239	18	b	b	NOUN
ejpam-6951	239	19	=	=	SYM
ejpam-6951	239	20	(	(	PUNCT
ejpam-6951	239	21	b1	b1	PROPN
ejpam-6951	239	22	△	△	PROPN
ejpam-6951	239	23	b2	b2	PROPN
ejpam-6951	239	24	△	△	NOUN
ejpam-6951	239	25	b3	b3	PROPN
ejpam-6951	239	26	△	△	X
ejpam-6951	239	27	·	·	PUNCT
ejpam-6951	239	28	·	·	PUNCT
ejpam-6951	239	29	·	·	PUNCT
ejpam-6951	239	30	△	△	X
ejpam-6951	239	31	bt)	bt)	X
ejpam-6951	239	32	△	△	X
ejpam-6951	239	33	b	b	NOUN
ejpam-6951	239	34	=	=	SYM
ejpam-6951	239	35	{	{	PUNCT
ejpam-6951	239	36	x1	x1	PROPN
ejpam-6951	239	37	,	,	PUNCT
ejpam-6951	239	38	x2	x2	PROPN
ejpam-6951	239	39	,	,	PUNCT
ejpam-6951	239	40	x3	x3	ADJ
ejpam-6951	239	41	,	,	PUNCT
ejpam-6951	239	42	...	...	PUNCT
ejpam-6951	239	43	,	,	PUNCT
ejpam-6951	239	44	xt	xt	X
ejpam-6951	239	45	}	}	PUNCT
ejpam-6951	239	46	△	△	X
ejpam-6951	239	47	{	{	PUNCT
ejpam-6951	239	48	x1	x1	PROPN
ejpam-6951	239	49	,	,	PUNCT
ejpam-6951	239	50	x2	x2	PROPN
ejpam-6951	239	51	,	,	PUNCT
ejpam-6951	239	52	x3	x3	ADJ
ejpam-6951	239	53	,	,	PUNCT
ejpam-6951	239	54	...	...	PUNCT
ejpam-6951	239	55	,	,	PUNCT
ejpam-6951	239	56	xt	xt	PROPN
ejpam-6951	239	57	,	,	PUNCT
ejpam-6951	239	58	yj	yj	PROPN
ejpam-6951	239	59	}	}	PUNCT
ejpam-6951	239	60	=	=	SYM
ejpam-6951	239	61	{	{	PUNCT
ejpam-6951	239	62	yj	yj	PROPN
ejpam-6951	239	63	}	}	PUNCT
ejpam-6951	239	64	.	.	PUNCT
ejpam-6951	240	1	thus	thus	ADV
ejpam-6951	240	2	,	,	PUNCT
ejpam-6951	240	3	{	{	PUNCT
ejpam-6951	240	4	yj	yj	PROPN
ejpam-6951	240	5	}	}	PUNCT
ejpam-6951	240	6	∈	∈	PROPN
ejpam-6951	240	7	vst(km	vst(km	NOUN
ejpam-6951	240	8	,	,	PUNCT
ejpam-6951	240	9	n	n	CCONJ
ejpam-6951	240	10	)	)	PUNCT
ejpam-6951	240	11	for	for	ADP
ejpam-6951	240	12	all	all	PRON
ejpam-6951	240	13	1	1	NUM
ejpam-6951	240	14	≤	≤	NUM
ejpam-6951	240	15	j	j	PROPN
ejpam-6951	240	16	≤	≤	PROPN
ejpam-6951	240	17	n.	n.	NOUN
ejpam-6951	240	18	therefore	therefore	ADV
ejpam-6951	240	19	,	,	PUNCT
ejpam-6951	240	20	by	by	ADP
ejpam-6951	240	21	remark	remark	NOUN
ejpam-6951	240	22	1	1	NUM
ejpam-6951	240	23	,	,	PUNCT
ejpam-6951	240	24	st	st	PROPN
ejpam-6951	240	25	is	be	AUX
ejpam-6951	240	26	a	a	DET
ejpam-6951	240	27	vertex	vertex	NOUN
ejpam-6951	240	28	-	-	PUNCT
ejpam-6951	240	29	generator	generator	NOUN
ejpam-6951	240	30	subgraph	subgraph	NOUN
ejpam-6951	240	31	of	of	ADP
ejpam-6951	240	32	km	km	PROPN
ejpam-6951	240	33	,	,	PUNCT
ejpam-6951	240	34	n.	n.	NOUN
ejpam-6951	240	35	the	the	DET
ejpam-6951	240	36	following	follow	VERB
ejpam-6951	240	37	theorem	theorem	NOUN
ejpam-6951	240	38	provides	provide	VERB
ejpam-6951	240	39	a	a	DET
ejpam-6951	240	40	necessary	necessary	ADJ
ejpam-6951	240	41	condition	condition	NOUN
ejpam-6951	240	42	for	for	ADP
ejpam-6951	240	43	the	the	DET
ejpam-6951	240	44	complete	complete	ADJ
ejpam-6951	240	45	bipartite	bipartite	PROPN
ejpam-6951	240	46	graph	graph	NOUN
ejpam-6951	240	47	kr	kr	PROPN
ejpam-6951	240	48	,	,	PUNCT
ejpam-6951	240	49	r+1	r+1	PROPN
ejpam-6951	240	50	to	to	PART
ejpam-6951	240	51	be	be	AUX
ejpam-6951	240	52	a	a	DET
ejpam-6951	240	53	vertex	vertex	NOUN
ejpam-6951	240	54	-	-	PUNCT
ejpam-6951	240	55	generator	generator	NOUN
ejpam-6951	240	56	subgraph	subgraph	NOUN
ejpam-6951	240	57	of	of	ADP
ejpam-6951	240	58	km	km	PROPN
ejpam-6951	240	59	,	,	PUNCT
ejpam-6951	240	60	n.	n.	PROPN
ejpam-6951	240	61	theorem	theorem	VERB
ejpam-6951	240	62	13	13	NUM
ejpam-6951	240	63	.	.	PUNCT
ejpam-6951	241	1	let	let	VERB
ejpam-6951	241	2	m	m	PRON
ejpam-6951	241	3	,	,	PUNCT
ejpam-6951	241	4	n	n	CCONJ
ejpam-6951	241	5	,	,	PUNCT
ejpam-6951	241	6	and	and	CCONJ
ejpam-6951	241	7	r	r	NOUN
ejpam-6951	241	8	be	be	VERB
ejpam-6951	241	9	positive	positive	ADJ
ejpam-6951	241	10	integers	integer	NOUN
ejpam-6951	241	11	such	such	ADJ
ejpam-6951	241	12	that	that	DET
ejpam-6951	241	13	min{m	min{m	NOUN
ejpam-6951	241	14	,	,	PUNCT
ejpam-6951	241	15	n	n	CCONJ
ejpam-6951	241	16	}	}	PUNCT
ejpam-6951	241	17	≥	≥	NOUN
ejpam-6951	241	18	2	2	NUM
ejpam-6951	241	19	and	and	CCONJ
ejpam-6951	241	20	m+n	m+n	NOUN
ejpam-6951	241	21	≥	≥	NUM
ejpam-6951	241	22	5	5	NUM
ejpam-6951	241	23	.	.	PUNCT
ejpam-6951	242	1	if	if	SCONJ
ejpam-6951	242	2	r	r	PRON
ejpam-6951	242	3	+	+	CCONJ
ejpam-6951	242	4	1	1	NUM
ejpam-6951	242	5	≤	≤	ADJ
ejpam-6951	242	6	min{m	min{m	NOUN
ejpam-6951	242	7	,	,	PUNCT
ejpam-6951	242	8	n	n	CCONJ
ejpam-6951	242	9	}	}	PUNCT
ejpam-6951	242	10	,	,	PUNCT
ejpam-6951	242	11	then	then	ADV
ejpam-6951	242	12	kr	kr	PROPN
ejpam-6951	242	13	,	,	PUNCT
ejpam-6951	242	14	r+1	r+1	PROPN
ejpam-6951	242	15	is	be	AUX
ejpam-6951	242	16	a	a	DET
ejpam-6951	242	17	vertex	vertex	NOUN
ejpam-6951	242	18	-	-	PUNCT
ejpam-6951	242	19	generator	generator	NOUN
ejpam-6951	242	20	subgraph	subgraph	NOUN
ejpam-6951	242	21	of	of	ADP
ejpam-6951	242	22	km	km	PROPN
ejpam-6951	242	23	,	,	PUNCT
ejpam-6951	242	24	n.	n.	NOUN
ejpam-6951	242	25	proof	proof	NOUN
ejpam-6951	242	26	.	.	PUNCT
ejpam-6951	243	1	let	let	VERB
ejpam-6951	243	2	r	r	NOUN
ejpam-6951	243	3	+	+	CCONJ
ejpam-6951	243	4	1	1	NUM
ejpam-6951	243	5	≤	≤	ADJ
ejpam-6951	243	6	min{m	min{m	NOUN
ejpam-6951	243	7	,	,	PUNCT
ejpam-6951	243	8	n	n	CCONJ
ejpam-6951	243	9	}	}	PUNCT
ejpam-6951	243	10	.	.	PUNCT
ejpam-6951	244	1	then	then	ADV
ejpam-6951	244	2	,	,	PUNCT
ejpam-6951	244	3	we	we	PRON
ejpam-6951	244	4	have	have	VERB
ejpam-6951	244	5	the	the	DET
ejpam-6951	244	6	following	follow	VERB
ejpam-6951	244	7	cases	case	NOUN
ejpam-6951	244	8	:	:	PUNCT
ejpam-6951	244	9	case	case	NOUN
ejpam-6951	244	10	1	1	NUM
ejpam-6951	244	11	.	.	PUNCT
ejpam-6951	245	1	if	if	SCONJ
ejpam-6951	245	2	r	r	NOUN
ejpam-6951	245	3	=	=	SYM
ejpam-6951	245	4	1	1	NUM
ejpam-6951	245	5	,	,	PUNCT
ejpam-6951	245	6	then	then	ADV
ejpam-6951	245	7	we	we	PRON
ejpam-6951	245	8	have	have	VERB
ejpam-6951	245	9	a	a	DET
ejpam-6951	245	10	subgraph	subgraph	NOUN
ejpam-6951	245	11	k1,2	k1,2	PROPN
ejpam-6951	245	12	of	of	ADP
ejpam-6951	245	13	km	km	PROPN
ejpam-6951	245	14	,	,	PUNCT
ejpam-6951	245	15	n.	n.	NOUN
ejpam-6951	245	16	it	it	PRON
ejpam-6951	245	17	can	can	AUX
ejpam-6951	245	18	be	be	AUX
ejpam-6951	245	19	observed	observe	VERB
ejpam-6951	245	20	that	that	SCONJ
ejpam-6951	245	21	k1,2	k1,2	PROPN
ejpam-6951	245	22	is	be	AUX
ejpam-6951	245	23	isomorphic	isomorphic	ADJ
ejpam-6951	245	24	to	to	ADP
ejpam-6951	245	25	the	the	DET
ejpam-6951	245	26	path	path	NOUN
ejpam-6951	245	27	graph	graph	NOUN
ejpam-6951	245	28	p3	p3	PROPN
ejpam-6951	245	29	.	.	PUNCT
ejpam-6951	246	1	since	since	SCONJ
ejpam-6951	246	2	we	we	PRON
ejpam-6951	246	3	have	have	AUX
ejpam-6951	246	4	shown	show	VERB
ejpam-6951	246	5	in	in	ADP
ejpam-6951	246	6	theorem	theorem	ADJ
ejpam-6951	246	7	11	11	NUM
ejpam-6951	246	8	that	that	SCONJ
ejpam-6951	246	9	p3	p3	PROPN
ejpam-6951	246	10	is	be	AUX
ejpam-6951	246	11	a	a	DET
ejpam-6951	246	12	vertex	vertex	NOUN
ejpam-6951	246	13	-	-	PUNCT
ejpam-6951	246	14	generator	generator	NOUN
ejpam-6951	246	15	subgraph	subgraph	NOUN
ejpam-6951	246	16	of	of	ADP
ejpam-6951	246	17	km	km	PROPN
ejpam-6951	246	18	,	,	PUNCT
ejpam-6951	246	19	n	n	CCONJ
ejpam-6951	246	20	,	,	PUNCT
ejpam-6951	246	21	it	it	PRON
ejpam-6951	246	22	follows	follow	VERB
ejpam-6951	246	23	that	that	SCONJ
ejpam-6951	246	24	k1,2	k1,2	PROPN
ejpam-6951	246	25	is	be	AUX
ejpam-6951	246	26	a	a	DET
ejpam-6951	246	27	vertex	vertex	NOUN
ejpam-6951	246	28	-	-	PUNCT
ejpam-6951	246	29	generator	generator	NOUN
ejpam-6951	246	30	subgraph	subgraph	NOUN
ejpam-6951	246	31	of	of	ADP
ejpam-6951	246	32	km	km	PROPN
ejpam-6951	246	33	,	,	PUNCT
ejpam-6951	246	34	n.	n.	NOUN
ejpam-6951	246	35	case	case	NOUN
ejpam-6951	247	1	2	2	X
ejpam-6951	247	2	.	.	X
ejpam-6951	247	3	we	we	PRON
ejpam-6951	247	4	let	let	VERB
ejpam-6951	247	5	r	r	NOUN
ejpam-6951	247	6	≥	≥	NOUN
ejpam-6951	247	7	2	2	NUM
ejpam-6951	247	8	.	.	PUNCT
ejpam-6951	248	1	then	then	ADV
ejpam-6951	248	2	,	,	PUNCT
ejpam-6951	248	3	for	for	ADP
ejpam-6951	248	4	any	any	DET
ejpam-6951	248	5	2	2	NUM
ejpam-6951	248	6	≤	≤	NOUN
ejpam-6951	248	7	p	p	NOUN
ejpam-6951	248	8	≤	≤	NUM
ejpam-6951	248	9	m	m	VERB
ejpam-6951	248	10	−	−	NOUN
ejpam-6951	248	11	r	r	NOUN
ejpam-6951	248	12	and	and	CCONJ
ejpam-6951	248	13	for	for	ADP
ejpam-6951	248	14	any	any	DET
ejpam-6951	248	15	m	m	NOUN
ejpam-6951	248	16	−	−	NOUN
ejpam-6951	249	1	r	r	NOUN
ejpam-6951	249	2	+	+	CCONJ
ejpam-6951	249	3	2	2	NUM
ejpam-6951	249	4	≤	≤	NOUN
ejpam-6951	249	5	q	q	PROPN
ejpam-6951	249	6	≤	≤	NUM
ejpam-6951	249	7	m	m	ADP
ejpam-6951	249	8	,	,	PUNCT
ejpam-6951	249	9	let	let	VERB
ejpam-6951	249	10	xp	xp	INTJ
ejpam-6951	249	11	and	and	CCONJ
ejpam-6951	249	12	xq	xq	PROPN
ejpam-6951	249	13	be	be	VERB
ejpam-6951	249	14	arbitrary	arbitrary	ADJ
ejpam-6951	249	15	vertices	vertex	NOUN
ejpam-6951	249	16	of	of	ADP
ejpam-6951	249	17	partite	partite	ADJ
ejpam-6951	249	18	set	set	NOUN
ejpam-6951	249	19	m	m	VERB
ejpam-6951	249	20	in	in	ADP
ejpam-6951	249	21	the	the	DET
ejpam-6951	249	22	complete	complete	ADJ
ejpam-6951	249	23	bipartite	bipartite	PROPN
ejpam-6951	249	24	graph	graph	NOUN
ejpam-6951	249	25	km	km	PROPN
ejpam-6951	249	26	,	,	PUNCT
ejpam-6951	249	27	n	n	CCONJ
ejpam-6951	249	28	,	,	PUNCT
ejpam-6951	249	29	and	and	CCONJ
ejpam-6951	249	30	let	let	VERB
ejpam-6951	249	31	sets	set	NOUN
ejpam-6951	249	32	a	a	DET
ejpam-6951	249	33	,	,	PUNCT
ejpam-6951	249	34	b	b	NOUN
ejpam-6951	249	35	,	,	PUNCT
ejpam-6951	249	36	c	c	NOUN
ejpam-6951	249	37	,	,	PUNCT
ejpam-6951	249	38	and	and	CCONJ
ejpam-6951	249	39	d	d	NOUN
ejpam-6951	249	40	be	be	AUX
ejpam-6951	249	41	defined	define	VERB
ejpam-6951	249	42	as	as	SCONJ
ejpam-6951	249	43	follows	follow	VERB
ejpam-6951	249	44	:	:	PUNCT
ejpam-6951	249	45	a	a	PRON
ejpam-6951	249	46	=	=	X
ejpam-6951	249	47	{	{	PUNCT
ejpam-6951	249	48	x1	x1	PROPN
ejpam-6951	249	49	,	,	PUNCT
ejpam-6951	249	50	r−1	r−1	PROPN
ejpam-6951	249	51	vertices︷	vertices︷	PROPN
ejpam-6951	249	52	︸︸	︸︸	VERB
ejpam-6951	249	53	︷	︷	PROPN
ejpam-6951	250	1	xm−r+2	xm−r+2	PROPN
ejpam-6951	250	2	,	,	PUNCT
ejpam-6951	250	3	xm−r+3	xm−r+3	PROPN
ejpam-6951	250	4	,	,	PUNCT
ejpam-6951	250	5	...	...	PUNCT
ejpam-6951	250	6	,	,	PUNCT
ejpam-6951	250	7	xm	xm	PROPN
ejpam-6951	250	8	,	,	PUNCT
ejpam-6951	250	9	r+1	r+1	PROPN
ejpam-6951	250	10	vertices︷	vertices︷	VERB
ejpam-6951	250	11	︸︸	︸︸	NUM
ejpam-6951	250	12	︷	︷	PROPN
ejpam-6951	250	13	y1	y1	INTJ
ejpam-6951	250	14	,	,	PUNCT
ejpam-6951	250	15	y2	y2	PROPN
ejpam-6951	250	16	,	,	PUNCT
ejpam-6951	250	17	...	...	PUNCT
ejpam-6951	250	18	,	,	PUNCT
ejpam-6951	250	19	yr	yr	INTJ
ejpam-6951	250	20	,	,	PUNCT
ejpam-6951	250	21	yr+1	yr+1	NOUN
ejpam-6951	250	22	}	}	PUNCT
ejpam-6951	250	23	,	,	PUNCT
ejpam-6951	250	24	b	b	X
ejpam-6951	250	25	=	=	PUNCT
ejpam-6951	250	26	a	a	PRON
ejpam-6951	250	27	\	\	PROPN
ejpam-6951	250	28	{	{	PUNCT
ejpam-6951	250	29	x1	x1	PROPN
ejpam-6951	250	30	}	}	PUNCT
ejpam-6951	250	31	∪	∪	X
ejpam-6951	250	32	{	{	PUNCT
ejpam-6951	250	33	xp	xp	INTJ
ejpam-6951	250	34	}	}	PUNCT
ejpam-6951	250	35	where	where	SCONJ
ejpam-6951	250	36	2	2	NUM
ejpam-6951	250	37	≤	≤	NOUN
ejpam-6951	250	38	p	p	X
ejpam-6951	250	39	≤	≤	NUM
ejpam-6951	250	40	m−	m−	PROPN
ejpam-6951	250	41	r	r	NOUN
ejpam-6951	250	42	,	,	PUNCT
ejpam-6951	250	43	c	c	NOUN
ejpam-6951	250	44	=	=	PRON
ejpam-6951	250	45	{	{	PUNCT
ejpam-6951	250	46	r	r	NOUN
ejpam-6951	250	47	vertices︷	vertices︷	NOUN
ejpam-6951	250	48	︸︸	︸︸	NUM
ejpam-6951	250	49	︷	︷	PROPN
ejpam-6951	251	1	xm−r+1	xm−r+1	PROPN
ejpam-6951	251	2	,	,	PUNCT
ejpam-6951	251	3	xm−r+2	xm−r+2	PROPN
ejpam-6951	251	4	,	,	PUNCT
ejpam-6951	251	5	xm−r+3	xm−r+3	PROPN
ejpam-6951	251	6	,	,	PUNCT
ejpam-6951	251	7	...	...	PUNCT
ejpam-6951	251	8	,	,	PUNCT
ejpam-6951	251	9	xm	xm	PROPN
ejpam-6951	251	10	,	,	PUNCT
ejpam-6951	251	11	r+1	r+1	PROPN
ejpam-6951	251	12	vertices︷	vertices︷	VERB
ejpam-6951	251	13	︸︸	︸︸	NUM
ejpam-6951	251	14	︷	︷	PROPN
ejpam-6951	251	15	y1	y1	INTJ
ejpam-6951	251	16	,	,	PUNCT
ejpam-6951	251	17	y2	y2	PROPN
ejpam-6951	251	18	,	,	PUNCT
ejpam-6951	251	19	...	...	PUNCT
ejpam-6951	251	20	,	,	PUNCT
ejpam-6951	251	21	yr	yr	INTJ
ejpam-6951	251	22	,	,	PUNCT
ejpam-6951	251	23	yr+1	yr+1	NOUN
ejpam-6951	251	24	}	}	PUNCT
ejpam-6951	251	25	,	,	PUNCT
ejpam-6951	251	26	and	and	CCONJ
ejpam-6951	251	27	d	d	X
ejpam-6951	251	28	=	=	SYM
ejpam-6951	251	29	c	c	X
ejpam-6951	251	30	\	\	PROPN
ejpam-6951	251	31	{	{	PUNCT
ejpam-6951	251	32	xq	xq	PROPN
ejpam-6951	251	33	}	}	PUNCT
ejpam-6951	251	34	∪	∪	VERB
ejpam-6951	251	35	{	{	PUNCT
ejpam-6951	251	36	x1	x1	PROPN
ejpam-6951	251	37	}	}	PUNCT
ejpam-6951	251	38	where	where	SCONJ
ejpam-6951	251	39	m−	m−	PROPN
ejpam-6951	251	40	r	r	NOUN
ejpam-6951	251	41	+	+	CCONJ
ejpam-6951	251	42	2	2	NUM
ejpam-6951	251	43	≤	≤	NOUN
ejpam-6951	251	44	q	q	PROPN
ejpam-6951	251	45	≤	≤	NUM
ejpam-6951	251	46	m.	m.	NOUN
ejpam-6951	251	47	it	it	PRON
ejpam-6951	251	48	can	can	AUX
ejpam-6951	251	49	be	be	AUX
ejpam-6951	251	50	verified	verify	VERB
ejpam-6951	251	51	that	that	SCONJ
ejpam-6951	251	52	a	a	DET
ejpam-6951	251	53	,	,	PUNCT
ejpam-6951	251	54	b	b	NOUN
ejpam-6951	251	55	,	,	PUNCT
ejpam-6951	251	56	c	c	NOUN
ejpam-6951	251	57	,	,	PUNCT
ejpam-6951	251	58	d	d	PROPN
ejpam-6951	251	59	∈	∈	PROPN
ejpam-6951	251	60	vkr	vkr	NOUN
ejpam-6951	251	61	,	,	PUNCT
ejpam-6951	251	62	r+1(km	r+1(km	NOUN
ejpam-6951	251	63	,	,	PUNCT
ejpam-6951	251	64	n	n	CCONJ
ejpam-6951	251	65	)	)	PUNCT
ejpam-6951	251	66	,	,	PUNCT
ejpam-6951	251	67	as	as	SCONJ
ejpam-6951	251	68	shown	show	VERB
ejpam-6951	251	69	in	in	ADP
ejpam-6951	251	70	figure	figure	NOUN
ejpam-6951	251	71	8	8	NUM
ejpam-6951	251	72	.	.	PUNCT
ejpam-6951	252	1	consequently	consequently	ADV
ejpam-6951	252	2	,	,	PUNCT
ejpam-6951	252	3	for	for	ADP
ejpam-6951	252	4	p	p	NOUN
ejpam-6951	252	5	=	=	SYM
ejpam-6951	252	6	2	2	NUM
ejpam-6951	252	7	,	,	PUNCT
ejpam-6951	252	8	3	3	NUM
ejpam-6951	252	9	,	,	PUNCT
ejpam-6951	252	10	4	4	NUM
ejpam-6951	252	11	,	,	PUNCT
ejpam-6951	252	12	...	...	PUNCT
ejpam-6951	252	13	,	,	PUNCT
ejpam-6951	252	14	m−	m−	PROPN
ejpam-6951	252	15	r	r	NOUN
ejpam-6951	252	16	and	and	CCONJ
ejpam-6951	252	17	for	for	ADP
ejpam-6951	252	18	q	q	NOUN
ejpam-6951	253	1	=	=	PUNCT
ejpam-6951	253	2	m−	m−	PROPN
ejpam-6951	253	3	r	r	NOUN
ejpam-6951	253	4	+	+	CCONJ
ejpam-6951	253	5	2,m−	2,m−	NUM
ejpam-6951	253	6	r	r	NOUN
ejpam-6951	253	7	+	+	NOUN
ejpam-6951	253	8	3	3	NUM
ejpam-6951	253	9	,	,	PUNCT
ejpam-6951	253	10	...	...	PUNCT
ejpam-6951	253	11	,	,	PUNCT
ejpam-6951	253	12	m	m	PRON
ejpam-6951	253	13	,	,	PUNCT
ejpam-6951	253	14	we	we	PRON
ejpam-6951	253	15	obtain	obtain	VERB
ejpam-6951	253	16	a	a	DET
ejpam-6951	253	17	△	△	X
ejpam-6951	253	18	b	b	NOUN
ejpam-6951	253	19	=	=	SYM
ejpam-6951	253	20	{	{	PUNCT
ejpam-6951	253	21	x1	x1	PROPN
ejpam-6951	253	22	,	,	PUNCT
ejpam-6951	253	23	xp	xp	ADJ
ejpam-6951	253	24	}	}	PUNCT
ejpam-6951	253	25	,	,	PUNCT
ejpam-6951	253	26	a	a	DET
ejpam-6951	253	27	△	△	X
ejpam-6951	253	28	c	c	NOUN
ejpam-6951	253	29	=	=	SYM
ejpam-6951	253	30	{	{	PUNCT
ejpam-6951	253	31	x1	x1	PROPN
ejpam-6951	253	32	,	,	PUNCT
ejpam-6951	253	33	xm−r+1	xm−r+1	PROPN
ejpam-6951	253	34	}	}	PUNCT
ejpam-6951	253	35	,	,	PUNCT
ejpam-6951	253	36	and	and	CCONJ
ejpam-6951	253	37	c	c	X
ejpam-6951	253	38	△	△	X
ejpam-6951	253	39	d	d	X
ejpam-6951	253	40	=	=	SYM
ejpam-6951	253	41	{	{	PUNCT
ejpam-6951	253	42	x1	x1	PROPN
ejpam-6951	253	43	,	,	PUNCT
ejpam-6951	253	44	xq	xq	PROPN
ejpam-6951	253	45	}	}	PUNCT
ejpam-6951	253	46	.	.	PUNCT
ejpam-6951	254	1	hence	hence	ADV
ejpam-6951	254	2	,	,	PUNCT
ejpam-6951	254	3	{	{	PUNCT
ejpam-6951	254	4	x1	x1	PROPN
ejpam-6951	254	5	,	,	PUNCT
ejpam-6951	254	6	xp	xp	ADJ
ejpam-6951	254	7	}	}	PUNCT
ejpam-6951	254	8	,	,	PUNCT
ejpam-6951	254	9	{	{	PUNCT
ejpam-6951	254	10	x1	x1	PROPN
ejpam-6951	254	11	,	,	PUNCT
ejpam-6951	254	12	xm−r+1	xm−r+1	PROPN
ejpam-6951	254	13	}	}	PUNCT
ejpam-6951	254	14	,	,	PUNCT
ejpam-6951	254	15	{	{	PUNCT
ejpam-6951	254	16	x1	x1	PROPN
ejpam-6951	254	17	,	,	PUNCT
ejpam-6951	254	18	xq	xq	PROPN
ejpam-6951	254	19	}	}	PUNCT
ejpam-6951	254	20	∈	∈	PROPN
ejpam-6951	254	21	vkr	vkr	NOUN
ejpam-6951	254	22	,	,	PUNCT
ejpam-6951	254	23	r+1(km	r+1(km	NOUN
ejpam-6951	254	24	,	,	PUNCT
ejpam-6951	254	25	n	n	CCONJ
ejpam-6951	254	26	)	)	PUNCT
ejpam-6951	254	27	for	for	ADP
ejpam-6951	254	28	all	all	DET
ejpam-6951	254	29	2	2	NUM
ejpam-6951	254	30	≤	≤	NOUN
ejpam-6951	254	31	p	p	NOUN
ejpam-6951	254	32	≤	≤	NUM
ejpam-6951	254	33	m	m	VERB
ejpam-6951	254	34	−	−	NOUN
ejpam-6951	254	35	r	r	NOUN
ejpam-6951	254	36	and	and	CCONJ
ejpam-6951	254	37	for	for	ADP
ejpam-6951	254	38	all	all	DET
ejpam-6951	254	39	m−	m−	PROPN
ejpam-6951	255	1	r	r	NOUN
ejpam-6951	255	2	+	+	CCONJ
ejpam-6951	255	3	2	2	NUM
ejpam-6951	255	4	≤	≤	NOUN
ejpam-6951	255	5	q	q	PROPN
ejpam-6951	255	6	≤	≤	NUM
ejpam-6951	255	7	m	m	PROPN
ejpam-6951	255	8	,	,	PUNCT
ejpam-6951	255	9	or	or	CCONJ
ejpam-6951	255	10	equivalently	equivalently	ADV
ejpam-6951	255	11	,	,	PUNCT
ejpam-6951	255	12	{	{	PUNCT
ejpam-6951	255	13	x1	x1	PROPN
ejpam-6951	255	14	,	,	PUNCT
ejpam-6951	255	15	xi	xi	ADJ
ejpam-6951	255	16	}	}	PUNCT
ejpam-6951	255	17	∈	∈	PROPN
ejpam-6951	255	18	vkr	vkr	NOUN
ejpam-6951	255	19	,	,	PUNCT
ejpam-6951	255	20	r+1(km	r+1(km	NOUN
ejpam-6951	255	21	,	,	PUNCT
ejpam-6951	255	22	n	n	CCONJ
ejpam-6951	255	23	)	)	PUNCT
ejpam-6951	255	24	for	for	ADP
ejpam-6951	255	25	all	all	DET
ejpam-6951	255	26	2	2	NUM
ejpam-6951	255	27	≤	≤	NUM
ejpam-6951	255	28	i	i	PRON
ejpam-6951	255	29	≤	≤	ADJ
ejpam-6951	255	30	m.	m.	NOUN
ejpam-6951	255	31	by	by	ADP
ejpam-6951	255	32	similar	similar	ADJ
ejpam-6951	255	33	argument	argument	NOUN
ejpam-6951	255	34	,	,	PUNCT
ejpam-6951	255	35	for	for	SCONJ
ejpam-6951	255	36	any	any	DET
ejpam-6951	255	37	1	1	NUM
ejpam-6951	255	38	≤	≤	NOUN
ejpam-6951	255	39	s	s	PART
ejpam-6951	255	40	≤	≤	NUM
ejpam-6951	255	41	n	n	CCONJ
ejpam-6951	255	42	−	−	NOUN
ejpam-6951	255	43	r	r	NOUN
ejpam-6951	255	44	−	−	NOUN
ejpam-6951	255	45	1	1	NUM
ejpam-6951	255	46	and	and	CCONJ
ejpam-6951	255	47	for	for	ADP
ejpam-6951	255	48	any	any	DET
ejpam-6951	255	49	n	n	NOUN
ejpam-6951	255	50	−	−	NOUN
ejpam-6951	255	51	r	r	NOUN
ejpam-6951	255	52	+	+	NOUN
ejpam-6951	255	53	1	1	NUM
ejpam-6951	255	54	≤	≤	NUM
ejpam-6951	255	55	t	t	PROPN
ejpam-6951	255	56	≤	≤	NOUN
ejpam-6951	255	57	n	n	CCONJ
ejpam-6951	255	58	,	,	PUNCT
ejpam-6951	255	59	let	let	VERB
ejpam-6951	255	60	ys	ys	PRON
ejpam-6951	255	61	and	and	CCONJ
ejpam-6951	255	62	yt	yt	PROPN
ejpam-6951	255	63	be	be	VERB
ejpam-6951	255	64	g.	g.	PROPN
ejpam-6951	255	65	d.	d.	PROPN
ejpam-6951	255	66	sepillo	sepillo	PROPN
ejpam-6951	255	67	et	et	PROPN
ejpam-6951	256	1	al	al	PROPN
ejpam-6951	256	2	.	.	PUNCT
ejpam-6951	256	3	/	/	SYM
ejpam-6951	256	4	eur	eur	PROPN
ejpam-6951	256	5	.	.	PUNCT
ejpam-6951	257	1	j.	j.	PROPN
ejpam-6951	257	2	pure	pure	PROPN
ejpam-6951	257	3	appl	appl	PROPN
ejpam-6951	257	4	.	.	PROPN
ejpam-6951	257	5	math	math	PROPN
ejpam-6951	257	6	,	,	PUNCT
ejpam-6951	257	7	18	18	NUM
ejpam-6951	257	8	(	(	PUNCT
ejpam-6951	257	9	4	4	NUM
ejpam-6951	257	10	)	)	PUNCT
ejpam-6951	257	11	(	(	PUNCT
ejpam-6951	257	12	2025	2025	NUM
ejpam-6951	257	13	)	)	PUNCT
ejpam-6951	257	14	,	,	PUNCT
ejpam-6951	257	15	6951	6951	NUM
ejpam-6951	257	16	12	12	NUM
ejpam-6951	257	17	of	of	ADP
ejpam-6951	257	18	23	23	NUM
ejpam-6951	258	1	x1	x1	NUM
ejpam-6951	258	2	x2	x2	PROPN
ejpam-6951	258	3	xm−r	xm−r	PROPN
ejpam-6951	258	4	xm−r+1xm−r+2xm−r+3	xm−r+1xm−r+2xm−r+3	PROPN
ejpam-6951	258	5	xm	xm	PROPN
ejpam-6951	259	1	y1	y1	INTJ
ejpam-6951	260	1	y2	y2	INTJ
ejpam-6951	261	1	yr	yr	NOUN
ejpam-6951	262	1	yr+1	yr+1	INTJ
ejpam-6951	262	2	yn−1	yn−1	INTJ
ejpam-6951	262	3	yn	yn	PROPN
ejpam-6951	262	4	km	km	PROPN
ejpam-6951	262	5	,	,	PUNCT
ejpam-6951	262	6	n⟨a⟩	n⟨a⟩	NOUN
ejpam-6951	262	7	:	:	PUNCT
ejpam-6951	262	8	x1	x1	PROPN
ejpam-6951	262	9	x2	x2	PROPN
ejpam-6951	262	10	xm−r	xm−r	PROPN
ejpam-6951	262	11	xm−r+1xm−r+2xm−r+3	xm−r+1xm−r+2xm−r+3	PROPN
ejpam-6951	262	12	xm	xm	PROPN
ejpam-6951	263	1	y1	y1	INTJ
ejpam-6951	264	1	y2	y2	INTJ
ejpam-6951	265	1	yr	yr	NOUN
ejpam-6951	266	1	yr+1	yr+1	INTJ
ejpam-6951	266	2	yn−1	yn−1	INTJ
ejpam-6951	266	3	yn	yn	PROPN
ejpam-6951	266	4	km	km	PROPN
ejpam-6951	266	5	,	,	PUNCT
ejpam-6951	266	6	n⟨b⟩	n⟨b⟩	ADV
ejpam-6951	266	7	:	:	PUNCT
ejpam-6951	266	8	x1	x1	NUM
ejpam-6951	266	9	x2	x2	PROPN
ejpam-6951	266	10	xm−r	xm−r	PROPN
ejpam-6951	266	11	xm−r+1xm−r+2xm−r+3	xm−r+1xm−r+2xm−r+3	PROPN
ejpam-6951	266	12	xm	xm	PROPN
ejpam-6951	267	1	y1	y1	INTJ
ejpam-6951	268	1	y2	y2	INTJ
ejpam-6951	269	1	yr	yr	NOUN
ejpam-6951	270	1	yr+1	yr+1	INTJ
ejpam-6951	270	2	yn−1	yn−1	INTJ
ejpam-6951	270	3	yn	yn	PROPN
ejpam-6951	270	4	km	km	PROPN
ejpam-6951	270	5	,	,	PUNCT
ejpam-6951	270	6	n⟨c⟩	n⟨c⟩	PROPN
ejpam-6951	270	7	:	:	PUNCT
ejpam-6951	271	1	x1	x1	NUM
ejpam-6951	271	2	x2	x2	PROPN
ejpam-6951	271	3	xm−r	xm−r	PROPN
ejpam-6951	271	4	xm−r+1xm−r+2xm−r+3	xm−r+1xm−r+2xm−r+3	PROPN
ejpam-6951	271	5	xm	xm	PROPN
ejpam-6951	272	1	y1	y1	INTJ
ejpam-6951	273	1	y2	y2	INTJ
ejpam-6951	274	1	yr	yr	NOUN
ejpam-6951	275	1	yr+1	yr+1	INTJ
ejpam-6951	275	2	yn−1	yn−1	INTJ
ejpam-6951	275	3	yn	yn	PROPN
ejpam-6951	275	4	km	km	PROPN
ejpam-6951	275	5	,	,	PUNCT
ejpam-6951	275	6	n⟨d⟩	n⟨d⟩	NOUN
ejpam-6951	275	7	:	:	PUNCT
ejpam-6951	275	8	figure	figure	NOUN
ejpam-6951	275	9	8	8	NUM
ejpam-6951	275	10	:	:	PUNCT
ejpam-6951	275	11	illustrating	illustrate	VERB
ejpam-6951	275	12	the	the	DET
ejpam-6951	275	13	subgraphs	subgraph	NOUN
ejpam-6951	275	14	of	of	ADP
ejpam-6951	275	15	km	km	PROPN
ejpam-6951	275	16	,	,	PUNCT
ejpam-6951	275	17	n	n	CCONJ
ejpam-6951	275	18	induced	induce	VERB
ejpam-6951	275	19	by	by	ADP
ejpam-6951	275	20	a	a	DET
ejpam-6951	275	21	,	,	PUNCT
ejpam-6951	275	22	b	b	PROPN
ejpam-6951	275	23	,	,	PUNCT
ejpam-6951	275	24	c	c	NOUN
ejpam-6951	275	25	,	,	PUNCT
ejpam-6951	275	26	and	and	CCONJ
ejpam-6951	275	27	d	d	ADP
ejpam-6951	275	28	arbitrary	arbitrary	ADJ
ejpam-6951	275	29	vertices	vertex	NOUN
ejpam-6951	275	30	of	of	ADP
ejpam-6951	275	31	partite	partite	ADJ
ejpam-6951	275	32	set	set	NOUN
ejpam-6951	275	33	n	n	NOUN
ejpam-6951	275	34	in	in	ADP
ejpam-6951	275	35	the	the	DET
ejpam-6951	275	36	complete	complete	ADJ
ejpam-6951	275	37	bipartite	bipartite	PROPN
ejpam-6951	275	38	graph	graph	NOUN
ejpam-6951	275	39	km	km	PROPN
ejpam-6951	275	40	,	,	PUNCT
ejpam-6951	275	41	n	n	CCONJ
ejpam-6951	275	42	,	,	PUNCT
ejpam-6951	275	43	and	and	CCONJ
ejpam-6951	275	44	let	let	VERB
ejpam-6951	275	45	sets	set	NOUN
ejpam-6951	275	46	w	w	ADP
ejpam-6951	275	47	,	,	PUNCT
ejpam-6951	275	48	x	x	PROPN
ejpam-6951	275	49	,	,	PUNCT
ejpam-6951	275	50	y	y	PROPN
ejpam-6951	275	51	,	,	PUNCT
ejpam-6951	275	52	and	and	CCONJ
ejpam-6951	275	53	z	z	NOUN
ejpam-6951	275	54	be	be	AUX
ejpam-6951	275	55	defined	define	VERB
ejpam-6951	275	56	as	as	SCONJ
ejpam-6951	275	57	follows	follow	VERB
ejpam-6951	275	58	:	:	PUNCT
ejpam-6951	275	59	w	w	X
ejpam-6951	275	60	=	=	PUNCT
ejpam-6951	275	61	{	{	PUNCT
ejpam-6951	275	62	r+1	r+1	X
ejpam-6951	275	63	vertices︷	vertices︷	NOUN
ejpam-6951	275	64	︸︸	︸︸	NUM
ejpam-6951	275	65	︷	︷	PROPN
ejpam-6951	276	1	x1	x1	ADJ
ejpam-6951	276	2	,	,	PUNCT
ejpam-6951	276	3	x2	x2	PROPN
ejpam-6951	276	4	,	,	PUNCT
ejpam-6951	276	5	x3	x3	ADJ
ejpam-6951	276	6	,	,	PUNCT
ejpam-6951	276	7	...	...	PUNCT
ejpam-6951	276	8	,	,	PUNCT
ejpam-6951	276	9	xr	xr	PROPN
ejpam-6951	276	10	,	,	PUNCT
ejpam-6951	276	11	xr+1	xr+1	PROPN
ejpam-6951	276	12	,	,	PUNCT
ejpam-6951	276	13	r	r	NOUN
ejpam-6951	276	14	vertices︷	vertices︷	NOUN
ejpam-6951	276	15	︸︸	︸︸	NUM
ejpam-6951	276	16	︷	︷	PROPN
ejpam-6951	277	1	yn−r+1	yn−r+1	PROPN
ejpam-6951	277	2	,	,	PUNCT
ejpam-6951	277	3	yn−r+2	yn−r+2	PROPN
ejpam-6951	277	4	,	,	PUNCT
ejpam-6951	277	5	...	...	PUNCT
ejpam-6951	277	6	,	,	PUNCT
ejpam-6951	277	7	yn	yn	PROPN
ejpam-6951	277	8	}	}	PUNCT
ejpam-6951	277	9	,	,	PUNCT
ejpam-6951	277	10	x	x	PUNCT
ejpam-6951	277	11	=	=	PUNCT
ejpam-6951	277	12	w	w	PROPN
ejpam-6951	277	13	\	\	NOUN
ejpam-6951	277	14	{	{	PUNCT
ejpam-6951	277	15	x1	x1	PROPN
ejpam-6951	277	16	}	}	PUNCT
ejpam-6951	277	17	∪	∪	ADJ
ejpam-6951	277	18	{	{	PUNCT
ejpam-6951	277	19	ys	ys	NOUN
ejpam-6951	277	20	}	}	PUNCT
ejpam-6951	277	21	where	where	SCONJ
ejpam-6951	277	22	1	1	NUM
ejpam-6951	277	23	≤	≤	NOUN
ejpam-6951	277	24	s	s	PART
ejpam-6951	277	25	≤	≤	NOUN
ejpam-6951	277	26	n−	n−	NOUN
ejpam-6951	277	27	r	r	NOUN
ejpam-6951	277	28	−	−	NOUN
ejpam-6951	277	29	1	1	NUM
ejpam-6951	277	30	,	,	PUNCT
ejpam-6951	277	31	y	y	NOUN
ejpam-6951	277	32	=	=	PUNCT
ejpam-6951	277	33	{	{	PUNCT
ejpam-6951	277	34	r	r	NOUN
ejpam-6951	277	35	vertices︷	vertices︷	NOUN
ejpam-6951	277	36	︸︸	︸︸	PUNCT
ejpam-6951	277	37	︷	︷	PROPN
ejpam-6951	277	38	x2	x2	ADJ
ejpam-6951	277	39	,	,	PUNCT
ejpam-6951	277	40	x3	x3	ADJ
ejpam-6951	277	41	,	,	PUNCT
ejpam-6951	277	42	...	...	PUNCT
ejpam-6951	277	43	,	,	PUNCT
ejpam-6951	277	44	xr	xr	PROPN
ejpam-6951	277	45	,	,	PUNCT
ejpam-6951	277	46	xr+1	xr+1	PROPN
ejpam-6951	277	47	,	,	PUNCT
ejpam-6951	277	48	r+1	r+1	PROPN
ejpam-6951	277	49	vertices︷	vertices︷	VERB
ejpam-6951	277	50	︸︸	︸︸	NUM
ejpam-6951	277	51	︷	︷	X
ejpam-6951	277	52	yn−r	yn−r	NOUN
ejpam-6951	277	53	,	,	PUNCT
ejpam-6951	277	54	yn−r+1	yn−r+1	PROPN
ejpam-6951	277	55	,	,	PUNCT
ejpam-6951	277	56	yn−r+2	yn−r+2	PROPN
ejpam-6951	277	57	,	,	PUNCT
ejpam-6951	277	58	...	...	PUNCT
ejpam-6951	277	59	,	,	PUNCT
ejpam-6951	277	60	yn	yn	PROPN
ejpam-6951	277	61	}	}	PUNCT
ejpam-6951	277	62	,	,	PUNCT
ejpam-6951	277	63	and	and	CCONJ
ejpam-6951	277	64	z	z	X
ejpam-6951	277	65	=	=	SYM
ejpam-6951	277	66	y	y	PROPN
ejpam-6951	277	67	\	\	PROPN
ejpam-6951	277	68	{	{	PUNCT
ejpam-6951	277	69	yt	yt	NOUN
ejpam-6951	277	70	}	}	PUNCT
ejpam-6951	277	71	∪	∪	X
ejpam-6951	277	72	{	{	PUNCT
ejpam-6951	277	73	x1	x1	PROPN
ejpam-6951	277	74	}	}	PUNCT
ejpam-6951	277	75	where	where	SCONJ
ejpam-6951	277	76	n−	n−	PROPN
ejpam-6951	277	77	r	r	NOUN
ejpam-6951	277	78	+	+	CCONJ
ejpam-6951	277	79	1	1	NUM
ejpam-6951	277	80	≤	≤	NUM
ejpam-6951	277	81	t	t	PROPN
ejpam-6951	277	82	≤	≤	NUM
ejpam-6951	277	83	n.	n.	NOUN
ejpam-6951	277	84	it	it	PRON
ejpam-6951	277	85	can	can	AUX
ejpam-6951	277	86	be	be	AUX
ejpam-6951	277	87	verified	verify	VERB
ejpam-6951	277	88	that	that	SCONJ
ejpam-6951	277	89	w	w	NOUN
ejpam-6951	277	90	,	,	PUNCT
ejpam-6951	277	91	x	x	NOUN
ejpam-6951	277	92	,	,	PUNCT
ejpam-6951	277	93	y	y	PROPN
ejpam-6951	277	94	,	,	PUNCT
ejpam-6951	277	95	z	z	PROPN
ejpam-6951	277	96	∈	∈	PROPN
ejpam-6951	277	97	vkr	vkr	NOUN
ejpam-6951	277	98	,	,	PUNCT
ejpam-6951	277	99	r+1(km	r+1(km	NOUN
ejpam-6951	277	100	,	,	PUNCT
ejpam-6951	277	101	n	n	CCONJ
ejpam-6951	277	102	)	)	PUNCT
ejpam-6951	277	103	,	,	PUNCT
ejpam-6951	277	104	as	as	SCONJ
ejpam-6951	277	105	shown	show	VERB
ejpam-6951	277	106	in	in	ADP
ejpam-6951	277	107	figure	figure	NOUN
ejpam-6951	277	108	9	9	NUM
ejpam-6951	277	109	.	.	PUNCT
ejpam-6951	278	1	as	as	ADP
ejpam-6951	278	2	a	a	DET
ejpam-6951	278	3	consequence	consequence	NOUN
ejpam-6951	278	4	,	,	PUNCT
ejpam-6951	278	5	for	for	ADP
ejpam-6951	278	6	s	s	NOUN
ejpam-6951	278	7	=	=	SYM
ejpam-6951	278	8	1	1	NUM
ejpam-6951	278	9	,	,	PUNCT
ejpam-6951	278	10	2	2	NUM
ejpam-6951	278	11	,	,	PUNCT
ejpam-6951	278	12	3	3	NUM
ejpam-6951	278	13	,	,	PUNCT
ejpam-6951	278	14	...	...	PUNCT
ejpam-6951	278	15	,	,	PUNCT
ejpam-6951	278	16	n−	n−	NOUN
ejpam-6951	278	17	r	r	NOUN
ejpam-6951	278	18	−	−	NOUN
ejpam-6951	278	19	1	1	NUM
ejpam-6951	278	20	and	and	CCONJ
ejpam-6951	278	21	for	for	ADP
ejpam-6951	278	22	t	t	NOUN
ejpam-6951	278	23	=	=	SYM
ejpam-6951	278	24	n−	n−	PROPN
ejpam-6951	278	25	r+1	r+1	PROPN
ejpam-6951	278	26	,	,	PUNCT
ejpam-6951	278	27	n−	n−	NOUN
ejpam-6951	278	28	r+2	r+2	NUM
ejpam-6951	278	29	,	,	PUNCT
ejpam-6951	278	30	...	...	PUNCT
ejpam-6951	278	31	,	,	PUNCT
ejpam-6951	278	32	n	n	CCONJ
ejpam-6951	278	33	,	,	PUNCT
ejpam-6951	278	34	we	we	PRON
ejpam-6951	278	35	get	get	VERB
ejpam-6951	278	36	w	w	ADP
ejpam-6951	278	37	△	△	NOUN
ejpam-6951	278	38	x	x	X
ejpam-6951	278	39	=	=	X
ejpam-6951	278	40	{	{	PUNCT
ejpam-6951	278	41	x1	x1	PROPN
ejpam-6951	278	42	,	,	PUNCT
ejpam-6951	278	43	ys	ys	ADJ
ejpam-6951	278	44	}	}	PUNCT
ejpam-6951	278	45	,	,	PUNCT
ejpam-6951	278	46	w	w	PROPN
ejpam-6951	278	47	△	△	X
ejpam-6951	278	48	y	y	NOUN
ejpam-6951	278	49	=	=	SYM
ejpam-6951	278	50	{	{	PUNCT
ejpam-6951	278	51	x1	x1	PROPN
ejpam-6951	278	52	,	,	PUNCT
ejpam-6951	278	53	yn−r	yn−r	NOUN
ejpam-6951	278	54	}	}	PUNCT
ejpam-6951	278	55	,	,	PUNCT
ejpam-6951	278	56	and	and	CCONJ
ejpam-6951	278	57	y	y	PROPN
ejpam-6951	278	58	△	△	PROPN
ejpam-6951	278	59	z	z	PROPN
ejpam-6951	279	1	=	=	PRON
ejpam-6951	279	2	{	{	PUNCT
ejpam-6951	279	3	x1	x1	PROPN
ejpam-6951	279	4	,	,	PUNCT
ejpam-6951	279	5	yt	yt	NOUN
ejpam-6951	279	6	}	}	PUNCT
ejpam-6951	279	7	.	.	PUNCT
ejpam-6951	280	1	g.	g.	PROPN
ejpam-6951	280	2	d.	d.	PROPN
ejpam-6951	280	3	sepillo	sepillo	PROPN
ejpam-6951	280	4	et	et	PROPN
ejpam-6951	280	5	al	al	PROPN
ejpam-6951	280	6	.	.	PUNCT
ejpam-6951	280	7	/	/	SYM
ejpam-6951	280	8	eur	eur	PROPN
ejpam-6951	280	9	.	.	PUNCT
ejpam-6951	281	1	j.	j.	PROPN
ejpam-6951	281	2	pure	pure	PROPN
ejpam-6951	281	3	appl	appl	PROPN
ejpam-6951	281	4	.	.	PROPN
ejpam-6951	281	5	math	math	PROPN
ejpam-6951	281	6	,	,	PUNCT
ejpam-6951	281	7	18	18	NUM
ejpam-6951	281	8	(	(	PUNCT
ejpam-6951	281	9	4	4	NUM
ejpam-6951	281	10	)	)	PUNCT
ejpam-6951	281	11	(	(	PUNCT
ejpam-6951	281	12	2025	2025	NUM
ejpam-6951	281	13	)	)	PUNCT
ejpam-6951	281	14	,	,	PUNCT
ejpam-6951	281	15	6951	6951	NUM
ejpam-6951	281	16	13	13	NUM
ejpam-6951	281	17	of	of	ADP
ejpam-6951	281	18	23	23	NUM
ejpam-6951	282	1	x1	x1	NUM
ejpam-6951	283	1	x2	x2	NOUN
ejpam-6951	284	1	x3	x3	PROPN
ejpam-6951	284	2	xr	xr	PROPN
ejpam-6951	284	3	xr+1	xr+1	PROPN
ejpam-6951	285	1	xm−1	xm−1	PROPN
ejpam-6951	285	2	xm	xm	PROPN
ejpam-6951	286	1	y1	y1	INTJ
ejpam-6951	286	2	yn−r−1	yn−r−1	DET
ejpam-6951	286	3	yn−r	yn−r	NOUN
ejpam-6951	286	4	yn−r+1	yn−r+1	PROPN
ejpam-6951	286	5	yn−r+2	yn−r+2	PROPN
ejpam-6951	286	6	yn	yn	PROPN
ejpam-6951	286	7	km	km	PROPN
ejpam-6951	286	8	,	,	PUNCT
ejpam-6951	286	9	n⟨w	n⟨w	X
ejpam-6951	286	10	⟩	⟩	NOUN
ejpam-6951	286	11	:	:	PUNCT
ejpam-6951	287	1	x1	x1	PROPN
ejpam-6951	287	2	x2	x2	NOUN
ejpam-6951	288	1	x3	x3	PROPN
ejpam-6951	288	2	xr	xr	PROPN
ejpam-6951	288	3	xr+1	xr+1	PROPN
ejpam-6951	289	1	xm−1	xm−1	PROPN
ejpam-6951	289	2	xm	xm	PROPN
ejpam-6951	290	1	y1	y1	INTJ
ejpam-6951	290	2	yn−r−1	yn−r−1	DET
ejpam-6951	290	3	yn−r	yn−r	NOUN
ejpam-6951	290	4	yn−r+1	yn−r+1	PROPN
ejpam-6951	290	5	yn−r+2	yn−r+2	PROPN
ejpam-6951	290	6	yn	yn	PROPN
ejpam-6951	290	7	km	km	PROPN
ejpam-6951	290	8	,	,	PUNCT
ejpam-6951	290	9	n⟨x⟩	n⟨x⟩	PROPN
ejpam-6951	290	10	:	:	PUNCT
ejpam-6951	291	1	x1	x1	PROPN
ejpam-6951	292	1	x2	x2	NOUN
ejpam-6951	293	1	x3	x3	PROPN
ejpam-6951	293	2	xr	xr	PROPN
ejpam-6951	293	3	xr+1	xr+1	PROPN
ejpam-6951	294	1	xm−1	xm−1	PROPN
ejpam-6951	294	2	xm	xm	PROPN
ejpam-6951	295	1	y1	y1	INTJ
ejpam-6951	295	2	yn−r−1	yn−r−1	DET
ejpam-6951	295	3	yn−r	yn−r	NOUN
ejpam-6951	295	4	yn−r+1	yn−r+1	PROPN
ejpam-6951	295	5	yn−r+2	yn−r+2	PROPN
ejpam-6951	295	6	yn	yn	PROPN
ejpam-6951	295	7	km	km	PROPN
ejpam-6951	295	8	,	,	PUNCT
ejpam-6951	295	9	n⟨y	n⟨y	PROPN
ejpam-6951	295	10	⟩	⟩	NOUN
ejpam-6951	295	11	:	:	PUNCT
ejpam-6951	296	1	x1	x1	PROPN
ejpam-6951	296	2	x2	x2	NOUN
ejpam-6951	297	1	x3	x3	PROPN
ejpam-6951	297	2	xr	xr	PROPN
ejpam-6951	297	3	xr+1	xr+1	PROPN
ejpam-6951	298	1	xm−1	xm−1	PROPN
ejpam-6951	298	2	xm	xm	PROPN
ejpam-6951	299	1	y1	y1	INTJ
ejpam-6951	299	2	yn−r−1	yn−r−1	DET
ejpam-6951	299	3	yn−r	yn−r	NOUN
ejpam-6951	299	4	yn−r+1	yn−r+1	PROPN
ejpam-6951	299	5	yn−r+2	yn−r+2	PROPN
ejpam-6951	299	6	yn	yn	PROPN
ejpam-6951	299	7	km	km	PROPN
ejpam-6951	299	8	,	,	PUNCT
ejpam-6951	299	9	n⟨z⟩	n⟨z⟩	ADJ
ejpam-6951	299	10	:	:	PUNCT
ejpam-6951	299	11	figure	figure	NOUN
ejpam-6951	299	12	9	9	NUM
ejpam-6951	299	13	:	:	PUNCT
ejpam-6951	299	14	illustrating	illustrate	VERB
ejpam-6951	299	15	the	the	DET
ejpam-6951	299	16	subgraphs	subgraph	NOUN
ejpam-6951	299	17	of	of	ADP
ejpam-6951	299	18	km	km	PROPN
ejpam-6951	299	19	,	,	PUNCT
ejpam-6951	299	20	n	n	CCONJ
ejpam-6951	299	21	induced	induce	VERB
ejpam-6951	299	22	by	by	ADP
ejpam-6951	299	23	w	w	PROPN
ejpam-6951	299	24	,	,	PUNCT
ejpam-6951	299	25	x	x	PROPN
ejpam-6951	299	26	,	,	PUNCT
ejpam-6951	299	27	y	y	PROPN
ejpam-6951	299	28	,	,	PUNCT
ejpam-6951	299	29	and	and	CCONJ
ejpam-6951	299	30	z	z	NOUN
ejpam-6951	299	31	hence	hence	ADV
ejpam-6951	299	32	,	,	PUNCT
ejpam-6951	299	33	{	{	PUNCT
ejpam-6951	299	34	x1	x1	ADJ
ejpam-6951	299	35	,	,	PUNCT
ejpam-6951	299	36	ys	ys	NOUN
ejpam-6951	299	37	}	}	PUNCT
ejpam-6951	299	38	,	,	PUNCT
ejpam-6951	299	39	{	{	PUNCT
ejpam-6951	299	40	x1	x1	ADJ
ejpam-6951	299	41	,	,	PUNCT
ejpam-6951	299	42	yn−r	yn−r	NOUN
ejpam-6951	299	43	}	}	PUNCT
ejpam-6951	299	44	,	,	PUNCT
ejpam-6951	299	45	{	{	PUNCT
ejpam-6951	299	46	x1	x1	PROPN
ejpam-6951	299	47	,	,	PUNCT
ejpam-6951	299	48	yt	yt	PROPN
ejpam-6951	299	49	}	}	PUNCT
ejpam-6951	299	50	∈	∈	PROPN
ejpam-6951	299	51	vkr	vkr	NOUN
ejpam-6951	299	52	,	,	PUNCT
ejpam-6951	299	53	r+1(km	r+1(km	NOUN
ejpam-6951	299	54	,	,	PUNCT
ejpam-6951	299	55	n	n	CCONJ
ejpam-6951	299	56	)	)	PUNCT
ejpam-6951	299	57	for	for	ADP
ejpam-6951	299	58	all	all	DET
ejpam-6951	299	59	1	1	NUM
ejpam-6951	299	60	≤	≤	NUM
ejpam-6951	299	61	s	s	PART
ejpam-6951	299	62	≤	≤	NUM
ejpam-6951	299	63	n	n	CCONJ
ejpam-6951	299	64	−	−	NOUN
ejpam-6951	299	65	r	r	NOUN
ejpam-6951	299	66	−	−	NOUN
ejpam-6951	299	67	1	1	NUM
ejpam-6951	299	68	and	and	CCONJ
ejpam-6951	299	69	for	for	ADP
ejpam-6951	299	70	all	all	DET
ejpam-6951	299	71	n	n	PRON
ejpam-6951	299	72	−	−	NOUN
ejpam-6951	300	1	r	r	NOUN
ejpam-6951	300	2	+	+	CCONJ
ejpam-6951	300	3	1	1	NUM
ejpam-6951	300	4	≤	≤	NUM
ejpam-6951	300	5	t	t	PROPN
ejpam-6951	300	6	≤	≤	NOUN
ejpam-6951	300	7	n	n	CCONJ
ejpam-6951	300	8	,	,	PUNCT
ejpam-6951	300	9	or	or	CCONJ
ejpam-6951	300	10	equivalently	equivalently	ADV
ejpam-6951	300	11	,	,	PUNCT
ejpam-6951	300	12	{	{	PUNCT
ejpam-6951	300	13	x1	x1	PROPN
ejpam-6951	300	14	,	,	PUNCT
ejpam-6951	300	15	yj	yj	PROPN
ejpam-6951	300	16	}	}	PUNCT
ejpam-6951	300	17	∈	∈	PROPN
ejpam-6951	300	18	vkr	vkr	NOUN
ejpam-6951	300	19	,	,	PUNCT
ejpam-6951	300	20	r+1(km	r+1(km	NOUN
ejpam-6951	300	21	,	,	PUNCT
ejpam-6951	300	22	n	n	CCONJ
ejpam-6951	300	23	)	)	PUNCT
ejpam-6951	300	24	for	for	ADP
ejpam-6951	300	25	all	all	PRON
ejpam-6951	300	26	1	1	NUM
ejpam-6951	300	27	≤	≤	NUM
ejpam-6951	300	28	j	j	PROPN
ejpam-6951	300	29	≤	≤	PROPN
ejpam-6951	300	30	n.	n.	PROPN
ejpam-6951	300	31	thus	thus	ADV
ejpam-6951	300	32	,	,	PUNCT
ejpam-6951	300	33	by	by	ADP
ejpam-6951	300	34	remark	remark	NOUN
ejpam-6951	300	35	2	2	NUM
ejpam-6951	300	36	,	,	PUNCT
ejpam-6951	300	37	kr	kr	PROPN
ejpam-6951	300	38	,	,	PUNCT
ejpam-6951	300	39	r+1	r+1	PROPN
ejpam-6951	300	40	is	be	AUX
ejpam-6951	300	41	a	a	DET
ejpam-6951	300	42	vertex	vertex	NOUN
ejpam-6951	300	43	-	-	PUNCT
ejpam-6951	300	44	generator	generator	NOUN
ejpam-6951	300	45	subgraph	subgraph	NOUN
ejpam-6951	300	46	of	of	ADP
ejpam-6951	300	47	km	km	PROPN
ejpam-6951	300	48	,	,	PUNCT
ejpam-6951	300	49	n	n	CCONJ
ejpam-6951	300	50	if	if	SCONJ
ejpam-6951	300	51	r	r	NOUN
ejpam-6951	300	52	≥	≥	NOUN
ejpam-6951	300	53	2	2	NUM
ejpam-6951	300	54	.	.	PUNCT
ejpam-6951	301	1	therefore	therefore	ADV
ejpam-6951	301	2	,	,	PUNCT
ejpam-6951	301	3	in	in	ADP
ejpam-6951	301	4	all	all	DET
ejpam-6951	301	5	cases	case	NOUN
ejpam-6951	301	6	,	,	PUNCT
ejpam-6951	301	7	kr	kr	PROPN
ejpam-6951	301	8	,	,	PUNCT
ejpam-6951	301	9	r+1	r+1	PROPN
ejpam-6951	301	10	is	be	AUX
ejpam-6951	301	11	a	a	DET
ejpam-6951	301	12	vertex	vertex	NOUN
ejpam-6951	301	13	-	-	PUNCT
ejpam-6951	301	14	generator	generator	NOUN
ejpam-6951	301	15	subgraph	subgraph	NOUN
ejpam-6951	301	16	of	of	ADP
ejpam-6951	301	17	km	km	PROPN
ejpam-6951	301	18	,	,	PUNCT
ejpam-6951	301	19	n.	n.	NOUN
ejpam-6951	301	20	3.2	3.2	NUM
ejpam-6951	301	21	.	.	PUNCT
ejpam-6951	302	1	vertex	vertex	NOUN
ejpam-6951	302	2	-	-	PUNCT
ejpam-6951	302	3	generator	generator	NOUN
ejpam-6951	302	4	subgraph	subgraph	NOUN
ejpam-6951	302	5	of	of	ADP
ejpam-6951	302	6	tadpole	tadpole	PROPN
ejpam-6951	302	7	graph	graph	PROPN
ejpam-6951	302	8	tn	tn	PROPN
ejpam-6951	302	9	,	,	PUNCT
ejpam-6951	302	10	m	m	VERB
ejpam-6951	302	11	this	this	DET
ejpam-6951	302	12	section	section	NOUN
ejpam-6951	302	13	provides	provide	VERB
ejpam-6951	302	14	some	some	DET
ejpam-6951	302	15	vertex	vertex	NOUN
ejpam-6951	302	16	-	-	PUNCT
ejpam-6951	302	17	generator	generator	NOUN
ejpam-6951	302	18	subgraphs	subgraph	NOUN
ejpam-6951	302	19	of	of	ADP
ejpam-6951	302	20	tadpole	tadpole	PROPN
ejpam-6951	302	21	graph	graph	PROPN
ejpam-6951	302	22	tn	tn	PROPN
ejpam-6951	302	23	,	,	PUNCT
ejpam-6951	302	24	m.	m.	NOUN
ejpam-6951	302	25	let	let	VERB
ejpam-6951	302	26	tn	tn	NOUN
ejpam-6951	302	27	,	,	PUNCT
ejpam-6951	302	28	m	m	AUX
ejpam-6951	302	29	be	be	VERB
ejpam-6951	302	30	a	a	DET
ejpam-6951	302	31	tadpole	tadpole	NOUN
ejpam-6951	302	32	graph	graph	NOUN
ejpam-6951	302	33	whose	whose	DET
ejpam-6951	302	34	vertex	vertex	NOUN
ejpam-6951	302	35	set	set	NOUN
ejpam-6951	302	36	is	be	AUX
ejpam-6951	302	37	given	give	VERB
ejpam-6951	302	38	by	by	ADP
ejpam-6951	302	39	v	v	PROPN
ejpam-6951	302	40	(	(	PUNCT
ejpam-6951	302	41	tn	tn	PROPN
ejpam-6951	302	42	,	,	PUNCT
ejpam-6951	302	43	m	m	NOUN
ejpam-6951	302	44	)	)	PUNCT
ejpam-6951	303	1	=	=	SYM
ejpam-6951	303	2	v	v	X
ejpam-6951	303	3	(	(	PUNCT
ejpam-6951	303	4	cn	cn	NOUN
ejpam-6951	303	5	)	)	PUNCT
ejpam-6951	303	6	∪	∪	NOUN
ejpam-6951	303	7	v	v	NOUN
ejpam-6951	303	8	(	(	PUNCT
ejpam-6951	303	9	pm	pm	NOUN
ejpam-6951	303	10	)	)	PUNCT
ejpam-6951	303	11	,	,	PUNCT
ejpam-6951	303	12	where	where	SCONJ
ejpam-6951	303	13	v	v	X
ejpam-6951	303	14	(	(	PUNCT
ejpam-6951	303	15	cn	cn	PROPN
ejpam-6951	303	16	)	)	PUNCT
ejpam-6951	303	17	=	=	PRON
ejpam-6951	303	18	{	{	PUNCT
ejpam-6951	303	19	x1	x1	PROPN
ejpam-6951	303	20	,	,	PUNCT
ejpam-6951	303	21	x2	x2	PROPN
ejpam-6951	303	22	,	,	PUNCT
ejpam-6951	303	23	x3	x3	ADJ
ejpam-6951	303	24	,	,	PUNCT
ejpam-6951	303	25	...	...	PUNCT
ejpam-6951	303	26	,	,	PUNCT
ejpam-6951	303	27	xn−1	xn−1	PROPN
ejpam-6951	303	28	,	,	PUNCT
ejpam-6951	303	29	xn	xn	PUNCT
ejpam-6951	303	30	}	}	PUNCT
ejpam-6951	303	31	and	and	CCONJ
ejpam-6951	303	32	v	v	NOUN
ejpam-6951	303	33	(	(	PUNCT
ejpam-6951	303	34	pm	pm	NOUN
ejpam-6951	303	35	)	)	PUNCT
ejpam-6951	303	36	=	=	SYM
ejpam-6951	303	37	{	{	PUNCT
ejpam-6951	303	38	y1	y1	PROPN
ejpam-6951	303	39	,	,	PUNCT
ejpam-6951	303	40	y2	y2	PROPN
ejpam-6951	303	41	,	,	PUNCT
ejpam-6951	303	42	y3	y3	PROPN
ejpam-6951	303	43	,	,	PUNCT
ejpam-6951	303	44	...	...	PUNCT
ejpam-6951	303	45	,	,	PUNCT
ejpam-6951	303	46	ym−1	ym−1	PROPN
ejpam-6951	303	47	,	,	PUNCT
ejpam-6951	303	48	ym	ym	PROPN
ejpam-6951	303	49	}	}	PUNCT
ejpam-6951	303	50	,	,	PUNCT
ejpam-6951	303	51	and	and	CCONJ
ejpam-6951	303	52	the	the	DET
ejpam-6951	303	53	edge	edge	NOUN
ejpam-6951	303	54	set	set	NOUN
ejpam-6951	303	55	is	be	AUX
ejpam-6951	303	56	given	give	VERB
ejpam-6951	303	57	by	by	ADP
ejpam-6951	303	58	e(tn	e(tn	NOUN
ejpam-6951	303	59	,	,	PUNCT
ejpam-6951	303	60	m	m	NOUN
ejpam-6951	303	61	)	)	PUNCT
ejpam-6951	303	62	=	=	SYM
ejpam-6951	303	63	e(cn	e(cn	NOUN
ejpam-6951	303	64	)	)	PUNCT
ejpam-6951	303	65	∪	∪	ADP
ejpam-6951	303	66	e(pm	e(pm	PROPN
ejpam-6951	303	67	)	)	PUNCT
ejpam-6951	303	68	∪	∪	NOUN
ejpam-6951	303	69	{	{	PUNCT
ejpam-6951	303	70	[	[	X
ejpam-6951	303	71	x1	x1	PROPN
ejpam-6951	303	72	,	,	PUNCT
ejpam-6951	303	73	y1	y1	NOUN
ejpam-6951	303	74	]	]	X
ejpam-6951	303	75	}	}	PUNCT
ejpam-6951	303	76	where	where	SCONJ
ejpam-6951	303	77	[	[	X
ejpam-6951	303	78	x1	x1	ADJ
ejpam-6951	303	79	,	,	PUNCT
ejpam-6951	303	80	y1	y1	PROPN
ejpam-6951	303	81	]	]	PUNCT
ejpam-6951	303	82	is	be	AUX
ejpam-6951	303	83	a	a	DET
ejpam-6951	303	84	bridge	bridge	NOUN
ejpam-6951	303	85	.	.	PUNCT
ejpam-6951	304	1	presented	present	VERB
ejpam-6951	304	2	in	in	ADP
ejpam-6951	304	3	figure	figure	NOUN
ejpam-6951	304	4	10	10	NUM
ejpam-6951	304	5	is	be	AUX
ejpam-6951	304	6	the	the	DET
ejpam-6951	304	7	labeling	labeling	NOUN
ejpam-6951	304	8	of	of	ADP
ejpam-6951	304	9	a	a	DET
ejpam-6951	304	10	tadpole	tadpole	NOUN
ejpam-6951	304	11	graph	graph	NOUN
ejpam-6951	304	12	,	,	PUNCT
ejpam-6951	304	13	which	which	PRON
ejpam-6951	304	14	will	will	AUX
ejpam-6951	304	15	be	be	AUX
ejpam-6951	304	16	considered	consider	VERB
ejpam-6951	304	17	in	in	ADP
ejpam-6951	304	18	the	the	DET
ejpam-6951	304	19	discussion	discussion	NOUN
ejpam-6951	304	20	of	of	ADP
ejpam-6951	304	21	this	this	DET
ejpam-6951	304	22	section	section	NOUN
ejpam-6951	304	23	.	.	PUNCT
ejpam-6951	305	1	a	a	DET
ejpam-6951	305	2	tadpole	tadpole	PROPN
ejpam-6951	305	3	graph	graph	NOUN
ejpam-6951	305	4	tn	tn	PROPN
ejpam-6951	305	5	,	,	PUNCT
ejpam-6951	305	6	m	m	VERB
ejpam-6951	305	7	has	have	VERB
ejpam-6951	305	8	order	order	NOUN
ejpam-6951	305	9	n+m	n+m	NUM
ejpam-6951	305	10	and	and	CCONJ
ejpam-6951	305	11	size	size	NOUN
ejpam-6951	305	12	n+m	n+m	NUM
ejpam-6951	305	13	for	for	ADP
ejpam-6951	305	14	all	all	DET
ejpam-6951	305	15	positive	positive	ADJ
ejpam-6951	305	16	integers	integer	NOUN
ejpam-6951	305	17	n	n	PRON
ejpam-6951	305	18	≥	≥	NOUN
ejpam-6951	305	19	3	3	NUM
ejpam-6951	305	20	and	and	CCONJ
ejpam-6951	305	21	m.	m.	NOUN
ejpam-6951	305	22	by	by	ADP
ejpam-6951	305	23	definition	definition	NOUN
ejpam-6951	305	24	1	1	NUM
ejpam-6951	305	25	,	,	PUNCT
ejpam-6951	305	26	the	the	DET
ejpam-6951	305	27	vertex	vertex	NOUN
ejpam-6951	305	28	space	space	NOUN
ejpam-6951	305	29	of	of	ADP
ejpam-6951	305	30	tn	tn	PROPN
ejpam-6951	305	31	,	,	PUNCT
ejpam-6951	305	32	m	m	VERB
ejpam-6951	305	33	is	be	AUX
ejpam-6951	305	34	given	give	VERB
ejpam-6951	305	35	by	by	ADP
ejpam-6951	305	36	v	v	PROPN
ejpam-6951	305	37	(	(	PUNCT
ejpam-6951	305	38	tn	tn	PROPN
ejpam-6951	305	39	,	,	PUNCT
ejpam-6951	305	40	m	m	NOUN
ejpam-6951	305	41	)	)	PUNCT
ejpam-6951	306	1	=	=	PRON
ejpam-6951	306	2	{	{	PUNCT
ejpam-6951	306	3	s	s	AUX
ejpam-6951	306	4	|	|	NOUN
ejpam-6951	306	5	s	s	VERB
ejpam-6951	306	6	⊆	⊆	NUM
ejpam-6951	306	7	v	v	NOUN
ejpam-6951	306	8	(	(	PUNCT
ejpam-6951	306	9	tn	tn	PROPN
ejpam-6951	306	10	,	,	PUNCT
ejpam-6951	306	11	m	m	NOUN
ejpam-6951	306	12	)	)	PUNCT
ejpam-6951	306	13	}	}	PUNCT
ejpam-6951	306	14	.	.	PUNCT
ejpam-6951	307	1	g.	g.	PROPN
ejpam-6951	307	2	d.	d.	PROPN
ejpam-6951	307	3	sepillo	sepillo	PROPN
ejpam-6951	307	4	et	et	PROPN
ejpam-6951	307	5	al	al	PROPN
ejpam-6951	307	6	.	.	PUNCT
ejpam-6951	307	7	/	/	SYM
ejpam-6951	307	8	eur	eur	PROPN
ejpam-6951	307	9	.	.	PUNCT
ejpam-6951	308	1	j.	j.	PROPN
ejpam-6951	308	2	pure	pure	PROPN
ejpam-6951	308	3	appl	appl	PROPN
ejpam-6951	308	4	.	.	PROPN
ejpam-6951	308	5	math	math	PROPN
ejpam-6951	308	6	,	,	PUNCT
ejpam-6951	308	7	18	18	NUM
ejpam-6951	308	8	(	(	PUNCT
ejpam-6951	308	9	4	4	NUM
ejpam-6951	308	10	)	)	PUNCT
ejpam-6951	308	11	(	(	PUNCT
ejpam-6951	308	12	2025	2025	NUM
ejpam-6951	308	13	)	)	PUNCT
ejpam-6951	308	14	,	,	PUNCT
ejpam-6951	308	15	6951	6951	NUM
ejpam-6951	308	16	14	14	NUM
ejpam-6951	308	17	of	of	ADP
ejpam-6951	308	18	23	23	NUM
ejpam-6951	309	1	x2	x2	NOUN
ejpam-6951	309	2	x3	x3	PROPN
ejpam-6951	309	3	x4	x4	PROPN
ejpam-6951	309	4	x5	x5	PROPN
ejpam-6951	309	5	x6	x6	PROPN
ejpam-6951	309	6	xn−2	xn−2	PROPN
ejpam-6951	309	7	xn−1	xn−1	PROPN
ejpam-6951	309	8	xn	xn	PROPN
ejpam-6951	310	1	x1	x1	PROPN
ejpam-6951	310	2	y1	y1	NOUN
ejpam-6951	310	3	y2	y2	INTJ
ejpam-6951	310	4	ym−1	ym−1	PROPN
ejpam-6951	310	5	ym	ym	PROPN
ejpam-6951	310	6	tn	tn	PROPN
ejpam-6951	310	7	,	,	PUNCT
ejpam-6951	310	8	m	m	VERB
ejpam-6951	310	9	:	:	PUNCT
ejpam-6951	310	10	figure	figure	VERB
ejpam-6951	310	11	10	10	NUM
ejpam-6951	310	12	:	:	PUNCT
ejpam-6951	310	13	the	the	DET
ejpam-6951	310	14	labeling	labeling	NOUN
ejpam-6951	310	15	of	of	ADP
ejpam-6951	310	16	tn	tn	PROPN
ejpam-6951	310	17	,	,	PUNCT
ejpam-6951	310	18	m	m	AUX
ejpam-6951	310	19	given	give	VERB
ejpam-6951	310	20	the	the	DET
ejpam-6951	310	21	vertex	vertex	NOUN
ejpam-6951	310	22	set	set	VERB
ejpam-6951	310	23	v	v	PROPN
ejpam-6951	310	24	(	(	PUNCT
ejpam-6951	310	25	tn	tn	PROPN
ejpam-6951	310	26	,	,	PUNCT
ejpam-6951	310	27	m	m	PROPN
ejpam-6951	310	28	)	)	PUNCT
ejpam-6951	310	29	,	,	PUNCT
ejpam-6951	310	30	the	the	DET
ejpam-6951	310	31	set	set	NOUN
ejpam-6951	310	32	a	a	X
ejpam-6951	310	33	=	=	X
ejpam-6951	310	34	{	{	PUNCT
ejpam-6951	310	35	{	{	PUNCT
ejpam-6951	310	36	x1	x1	PROPN
ejpam-6951	310	37	}	}	PUNCT
ejpam-6951	310	38	,	,	PUNCT
ejpam-6951	310	39	{	{	PUNCT
ejpam-6951	310	40	x2	x2	ADJ
ejpam-6951	310	41	}	}	PUNCT
ejpam-6951	310	42	,	,	PUNCT
ejpam-6951	310	43	{	{	PUNCT
ejpam-6951	310	44	x3	x3	ADJ
ejpam-6951	310	45	}	}	PUNCT
ejpam-6951	310	46	,	,	PUNCT
ejpam-6951	310	47	.	.	PUNCT
ejpam-6951	310	48	.	.	PUNCT
ejpam-6951	310	49	.	.	PUNCT
ejpam-6951	311	1	,	,	PUNCT
ejpam-6951	311	2	{	{	PUNCT
ejpam-6951	311	3	xn−1	xn−1	PROPN
ejpam-6951	311	4	}	}	PUNCT
ejpam-6951	311	5	,	,	PUNCT
ejpam-6951	311	6	{	{	PUNCT
ejpam-6951	311	7	xn	xn	PUNCT
ejpam-6951	311	8	}	}	PUNCT
ejpam-6951	311	9	,	,	PUNCT
ejpam-6951	311	10	{	{	PUNCT
ejpam-6951	311	11	y1	y1	NOUN
ejpam-6951	311	12	}	}	PUNCT
ejpam-6951	311	13	,	,	PUNCT
ejpam-6951	311	14	{	{	PUNCT
ejpam-6951	311	15	y2	y2	NOUN
ejpam-6951	311	16	}	}	PUNCT
ejpam-6951	311	17	,	,	PUNCT
ejpam-6951	311	18	{	{	PUNCT
ejpam-6951	311	19	y3	y3	NOUN
ejpam-6951	311	20	}	}	PUNCT
ejpam-6951	311	21	,	,	PUNCT
ejpam-6951	311	22	.	.	PUNCT
ejpam-6951	311	23	.	.	PUNCT
ejpam-6951	312	1	.	.	PUNCT
ejpam-6951	313	1	,	,	PUNCT
ejpam-6951	313	2	{	{	PUNCT
ejpam-6951	313	3	ym−1	ym−1	PROPN
ejpam-6951	313	4	}	}	PUNCT
ejpam-6951	313	5	,	,	PUNCT
ejpam-6951	313	6	{	{	PUNCT
ejpam-6951	313	7	ym	ym	NOUN
ejpam-6951	313	8	}	}	PUNCT
ejpam-6951	313	9	}	}	PUNCT
ejpam-6951	313	10	forms	form	VERB
ejpam-6951	313	11	a	a	DET
ejpam-6951	313	12	basis	basis	NOUN
ejpam-6951	313	13	for	for	ADP
ejpam-6951	313	14	v	v	PROPN
ejpam-6951	313	15	(	(	PUNCT
ejpam-6951	313	16	tn	tn	PROPN
ejpam-6951	313	17	,	,	PUNCT
ejpam-6951	313	18	m	m	NOUN
ejpam-6951	313	19	)	)	PUNCT
ejpam-6951	313	20	.	.	PUNCT
ejpam-6951	314	1	it	it	PRON
ejpam-6951	314	2	follows	follow	VERB
ejpam-6951	314	3	that	that	DET
ejpam-6951	314	4	dimv	dimv	NOUN
ejpam-6951	314	5	(	(	PUNCT
ejpam-6951	314	6	tn	tn	PROPN
ejpam-6951	314	7	,	,	PUNCT
ejpam-6951	314	8	m	m	NOUN
ejpam-6951	314	9	)	)	PUNCT
ejpam-6951	314	10	=	=	SYM
ejpam-6951	314	11	n+m	n+m	NUM
ejpam-6951	314	12	by	by	ADP
ejpam-6951	314	13	theorem	theorem	NOUN
ejpam-6951	314	14	1	1	NUM
ejpam-6951	314	15	.	.	PUNCT
ejpam-6951	314	16	by	by	ADP
ejpam-6951	314	17	theorem	theorem	NOUN
ejpam-6951	314	18	2	2	NUM
ejpam-6951	314	19	,	,	PUNCT
ejpam-6951	314	20	the	the	DET
ejpam-6951	314	21	trivial	trivial	ADJ
ejpam-6951	314	22	graph	graph	NOUN
ejpam-6951	314	23	is	be	AUX
ejpam-6951	314	24	a	a	DET
ejpam-6951	314	25	vertex	vertex	NOUN
ejpam-6951	314	26	-	-	PUNCT
ejpam-6951	314	27	generator	generator	NOUN
ejpam-6951	314	28	subgraph	subgraph	NOUN
ejpam-6951	314	29	of	of	ADP
ejpam-6951	314	30	tn	tn	PROPN
ejpam-6951	314	31	,	,	PUNCT
ejpam-6951	314	32	m	m	PRON
ejpam-6951	314	33	,	,	PUNCT
ejpam-6951	314	34	so	so	SCONJ
ejpam-6951	314	35	we	we	PRON
ejpam-6951	314	36	are	be	AUX
ejpam-6951	314	37	interested	interested	ADJ
ejpam-6951	314	38	in	in	ADP
ejpam-6951	314	39	the	the	DET
ejpam-6951	314	40	finding	finding	NOUN
ejpam-6951	314	41	the	the	DET
ejpam-6951	314	42	nontrivial	nontrivial	ADJ
ejpam-6951	314	43	vertex	vertex	NOUN
ejpam-6951	314	44	-	-	PUNCT
ejpam-6951	314	45	generator	generator	NOUN
ejpam-6951	314	46	subgraph	subgraph	NOUN
ejpam-6951	314	47	of	of	ADP
ejpam-6951	314	48	tn	tn	PROPN
ejpam-6951	314	49	,	,	PUNCT
ejpam-6951	314	50	m.	m.	NOUN
ejpam-6951	314	51	the	the	DET
ejpam-6951	314	52	following	follow	VERB
ejpam-6951	314	53	theorem	theorem	NOUN
ejpam-6951	314	54	gives	give	VERB
ejpam-6951	314	55	us	we	PRON
ejpam-6951	314	56	a	a	DET
ejpam-6951	314	57	necessary	necessary	ADJ
ejpam-6951	314	58	condition	condition	NOUN
ejpam-6951	314	59	for	for	ADP
ejpam-6951	314	60	the	the	DET
ejpam-6951	314	61	disjoint	disjoint	PROPN
ejpam-6951	314	62	union	union	NOUN
ejpam-6951	314	63	of	of	ADP
ejpam-6951	314	64	a	a	DET
ejpam-6951	314	65	path	path	NOUN
ejpam-6951	314	66	graph	graph	NOUN
ejpam-6951	314	67	pt	pt	NOUN
ejpam-6951	314	68	of	of	ADP
ejpam-6951	314	69	order	order	NOUN
ejpam-6951	314	70	t	t	PROPN
ejpam-6951	314	71	,	,	PUNCT
ejpam-6951	314	72	so	so	SCONJ
ejpam-6951	314	73	t	t	PROPN
ejpam-6951	314	74	should	should	AUX
ejpam-6951	314	75	be	be	AUX
ejpam-6951	314	76	even	even	ADV
ejpam-6951	314	77	,	,	PUNCT
ejpam-6951	314	78	and	and	CCONJ
ejpam-6951	314	79	a	a	DET
ejpam-6951	314	80	trivial	trivial	ADJ
ejpam-6951	314	81	graph	graph	NOUN
ejpam-6951	314	82	k1	k1	NOUN
ejpam-6951	314	83	,	,	PUNCT
ejpam-6951	314	84	denoted	denote	VERB
ejpam-6951	314	85	by	by	ADP
ejpam-6951	314	86	pt	pt	X
ejpam-6951	314	87	⊔k1	⊔k1	NOUN
ejpam-6951	314	88	,	,	PUNCT
ejpam-6951	314	89	to	to	PART
ejpam-6951	314	90	be	be	AUX
ejpam-6951	314	91	a	a	DET
ejpam-6951	314	92	vertex	vertex	NOUN
ejpam-6951	314	93	-	-	PUNCT
ejpam-6951	314	94	generator	generator	NOUN
ejpam-6951	314	95	subgraph	subgraph	NOUN
ejpam-6951	314	96	of	of	ADP
ejpam-6951	314	97	tn	tn	PROPN
ejpam-6951	314	98	,	,	PUNCT
ejpam-6951	314	99	m.	m.	NOUN
ejpam-6951	314	100	theorem	theorem	VERB
ejpam-6951	314	101	14	14	NUM
ejpam-6951	314	102	.	.	PUNCT
ejpam-6951	315	1	let	let	VERB
ejpam-6951	315	2	n	n	PRON
ejpam-6951	315	3	,	,	PUNCT
ejpam-6951	315	4	m	m	VERB
ejpam-6951	315	5	≥	≥	NOUN
ejpam-6951	315	6	3	3	NUM
ejpam-6951	315	7	and	and	CCONJ
ejpam-6951	315	8	t	t	PROPN
ejpam-6951	315	9	≥	≥	NUM
ejpam-6951	315	10	2	2	NUM
ejpam-6951	315	11	be	be	AUX
ejpam-6951	315	12	positive	positive	ADJ
ejpam-6951	315	13	integers	integer	NOUN
ejpam-6951	315	14	such	such	ADJ
ejpam-6951	315	15	that	that	SCONJ
ejpam-6951	315	16	t	t	PROPN
ejpam-6951	315	17	is	be	AUX
ejpam-6951	315	18	even	even	ADV
ejpam-6951	315	19	.	.	PUNCT
ejpam-6951	316	1	if	if	SCONJ
ejpam-6951	316	2	t+	t+	VERB
ejpam-6951	316	3	1	1	NUM
ejpam-6951	316	4	≤	≤	NUM
ejpam-6951	316	5	min{n	min{n	NOUN
ejpam-6951	316	6	,	,	PUNCT
ejpam-6951	316	7	m	m	NOUN
ejpam-6951	316	8	}	}	PUNCT
ejpam-6951	316	9	,	,	PUNCT
ejpam-6951	316	10	then	then	ADV
ejpam-6951	316	11	pt	pt	X
ejpam-6951	316	12	⊔k1	⊔k1	X
ejpam-6951	316	13	is	be	AUX
ejpam-6951	316	14	a	a	DET
ejpam-6951	316	15	vertex	vertex	NOUN
ejpam-6951	316	16	-	-	PUNCT
ejpam-6951	316	17	generator	generator	NOUN
ejpam-6951	316	18	subgraph	subgraph	NOUN
ejpam-6951	316	19	of	of	ADP
ejpam-6951	316	20	tn	tn	PROPN
ejpam-6951	316	21	,	,	PUNCT
ejpam-6951	316	22	m.	m.	NOUN
ejpam-6951	316	23	proof	proof	NOUN
ejpam-6951	316	24	.	.	PUNCT
ejpam-6951	317	1	let	let	VERB
ejpam-6951	317	2	t	t	PROPN
ejpam-6951	317	3	<	<	X
ejpam-6951	317	4	min{n	min{n	PROPN
ejpam-6951	317	5	,	,	PUNCT
ejpam-6951	317	6	m	m	NOUN
ejpam-6951	317	7	}	}	PUNCT
ejpam-6951	317	8	.	.	PUNCT
ejpam-6951	318	1	for	for	ADP
ejpam-6951	318	2	any	any	DET
ejpam-6951	318	3	1	1	NUM
ejpam-6951	318	4	≤	≤	NUM
ejpam-6951	318	5	i	i	PRON
ejpam-6951	318	6	≤	≤	NOUN
ejpam-6951	318	7	m	m	VERB
ejpam-6951	318	8	,	,	PUNCT
ejpam-6951	318	9	let	let	VERB
ejpam-6951	318	10	xi	xi	PRON
ejpam-6951	318	11	be	be	AUX
ejpam-6951	318	12	an	an	DET
ejpam-6951	318	13	arbitrary	arbitrary	ADJ
ejpam-6951	318	14	vertex	vertex	NOUN
ejpam-6951	318	15	of	of	ADP
ejpam-6951	318	16	cn	cn	PROPN
ejpam-6951	318	17	in	in	ADP
ejpam-6951	318	18	the	the	DET
ejpam-6951	318	19	tadpole	tadpole	NOUN
ejpam-6951	318	20	graph	graph	PROPN
ejpam-6951	318	21	tn	tn	PROPN
ejpam-6951	318	22	,	,	PUNCT
ejpam-6951	318	23	m	m	PROPN
ejpam-6951	318	24	,	,	PUNCT
ejpam-6951	318	25	and	and	CCONJ
ejpam-6951	318	26	for	for	ADP
ejpam-6951	318	27	any	any	DET
ejpam-6951	318	28	1	1	NUM
ejpam-6951	318	29	≤	≤	NOUN
ejpam-6951	318	30	p	p	PROPN
ejpam-6951	318	31	≤	≤	PROPN
ejpam-6951	318	32	t	t	PROPN
ejpam-6951	318	33	,	,	PUNCT
ejpam-6951	318	34	let	let	VERB
ejpam-6951	318	35	ap	ap	PRON
ejpam-6951	318	36	and	and	CCONJ
ejpam-6951	318	37	a	a	PRON
ejpam-6951	318	38	be	be	AUX
ejpam-6951	318	39	defined	define	VERB
ejpam-6951	318	40	as	as	SCONJ
ejpam-6951	318	41	follows	follow	VERB
ejpam-6951	318	42	:	:	PUNCT
ejpam-6951	318	43	ap	ap	PROPN
ejpam-6951	318	44	=	=	PUNCT
ejpam-6951	318	45	{	{	PUNCT
ejpam-6951	318	46	t	t	PROPN
ejpam-6951	318	47	vertices︷	vertices︷	NOUN
ejpam-6951	318	48	︸︸	︸︸	PUNCT
ejpam-6951	318	49	︷	︷	PROPN
ejpam-6951	318	50	x2	x2	ADJ
ejpam-6951	318	51	,	,	PUNCT
ejpam-6951	318	52	x3	x3	PROPN
ejpam-6951	318	53	,	,	PUNCT
ejpam-6951	318	54	x4	x4	PROPN
ejpam-6951	318	55	,	,	PUNCT
ejpam-6951	318	56	...	...	PUNCT
ejpam-6951	318	57	,	,	PUNCT
ejpam-6951	318	58	xt+1	xt+1	PROPN
ejpam-6951	318	59	,	,	PUNCT
ejpam-6951	318	60	yp+1	yp+1	NOUN
ejpam-6951	318	61	}	}	PUNCT
ejpam-6951	318	62	where	where	SCONJ
ejpam-6951	318	63	1	1	NUM
ejpam-6951	318	64	≤	≤	NOUN
ejpam-6951	318	65	p	p	PROPN
ejpam-6951	318	66	≤	≤	PROPN
ejpam-6951	318	67	t	t	PROPN
ejpam-6951	318	68	,	,	PUNCT
ejpam-6951	318	69	and	and	CCONJ
ejpam-6951	318	70	a	a	PRON
ejpam-6951	318	71	=	=	X
ejpam-6951	318	72	{	{	PUNCT
ejpam-6951	318	73	xi	xi	PROPN
ejpam-6951	318	74	,	,	PUNCT
ejpam-6951	318	75	t	t	PROPN
ejpam-6951	318	76	vertices︷	vertices︷	NOUN
ejpam-6951	318	77	︸︸	︸︸	PUNCT
ejpam-6951	318	78	︷	︷	PUNCT
ejpam-6951	319	1	y2	y2	VERB
ejpam-6951	319	2	,	,	PUNCT
ejpam-6951	319	3	y3	y3	PROPN
ejpam-6951	319	4	,	,	PUNCT
ejpam-6951	319	5	y4	y4	PROPN
ejpam-6951	319	6	,	,	PUNCT
ejpam-6951	319	7	...	...	PUNCT
ejpam-6951	319	8	,	,	PUNCT
ejpam-6951	319	9	yt+1	yt+1	CCONJ
ejpam-6951	319	10	}	}	PUNCT
ejpam-6951	319	11	where	where	SCONJ
ejpam-6951	319	12	1	1	NUM
ejpam-6951	319	13	≤	≤	NUM
ejpam-6951	319	14	i	i	PRON
ejpam-6951	319	15	≤	≤	NUM
ejpam-6951	319	16	n.	n.	NOUN
ejpam-6951	319	17	it	it	PRON
ejpam-6951	319	18	can	can	AUX
ejpam-6951	319	19	be	be	AUX
ejpam-6951	319	20	verified	verify	VERB
ejpam-6951	319	21	that	that	SCONJ
ejpam-6951	319	22	ap	ap	PROPN
ejpam-6951	319	23	,	,	PUNCT
ejpam-6951	319	24	a	a	DET
ejpam-6951	319	25	∈	∈	PROPN
ejpam-6951	319	26	vpt⊔k1(tn	vpt⊔k1(tn	NOUN
ejpam-6951	319	27	,	,	PUNCT
ejpam-6951	319	28	m	m	PROPN
ejpam-6951	319	29	)	)	PUNCT
ejpam-6951	319	30	,	,	PUNCT
ejpam-6951	319	31	as	as	SCONJ
ejpam-6951	319	32	shown	show	VERB
ejpam-6951	319	33	in	in	ADP
ejpam-6951	319	34	figure	figure	NOUN
ejpam-6951	319	35	11	11	NUM
ejpam-6951	319	36	.	.	PUNCT
ejpam-6951	320	1	thus	thus	ADV
ejpam-6951	320	2	,	,	PUNCT
ejpam-6951	320	3	for	for	ADP
ejpam-6951	320	4	i	i	PROPN
ejpam-6951	320	5	=	=	SYM
ejpam-6951	320	6	1	1	NUM
ejpam-6951	320	7	,	,	PUNCT
ejpam-6951	320	8	2	2	NUM
ejpam-6951	320	9	,	,	PUNCT
ejpam-6951	320	10	3	3	NUM
ejpam-6951	320	11	,	,	PUNCT
ejpam-6951	320	12	...	...	PUNCT
ejpam-6951	320	13	,	,	PUNCT
ejpam-6951	320	14	n	n	CCONJ
ejpam-6951	320	15	,	,	PUNCT
ejpam-6951	320	16	we	we	PRON
ejpam-6951	320	17	obtain	obtain	VERB
ejpam-6951	320	18	t∑	t∑	PRON
ejpam-6951	320	19	p=1	p=1	X
ejpam-6951	320	20	ap	ap	PROPN
ejpam-6951	321	1	+	+	NOUN
ejpam-6951	321	2	a	a	NOUN
ejpam-6951	321	3	=	=	X
ejpam-6951	321	4	(	(	PUNCT
ejpam-6951	321	5	a1	a1	NOUN
ejpam-6951	321	6	+	+	PROPN
ejpam-6951	321	7	a2	a2	PROPN
ejpam-6951	321	8	+	+	NOUN
ejpam-6951	321	9	a3	a3	NOUN
ejpam-6951	321	10	+	+	X
ejpam-6951	321	11	·	·	PUNCT
ejpam-6951	321	12	·	·	PUNCT
ejpam-6951	321	13	·	·	PUNCT
ejpam-6951	321	14	+	+	ADJ
ejpam-6951	321	15	at	at	ADP
ejpam-6951	321	16	)	)	PUNCT
ejpam-6951	321	17	+	+	NOUN
ejpam-6951	321	18	a	a	PRON
ejpam-6951	321	19	=	=	PUNCT
ejpam-6951	321	20	(	(	PUNCT
ejpam-6951	321	21	a1	a1	PROPN
ejpam-6951	321	22	△	△	PROPN
ejpam-6951	321	23	a2	a2	PROPN
ejpam-6951	321	24	△	△	PROPN
ejpam-6951	321	25	a3	a3	NOUN
ejpam-6951	321	26	△	△	X
ejpam-6951	321	27	·	·	PUNCT
ejpam-6951	321	28	·	·	PUNCT
ejpam-6951	321	29	·	·	PUNCT
ejpam-6951	321	30	△	△	X
ejpam-6951	321	31	at)	at)	X
ejpam-6951	321	32	△	△	X
ejpam-6951	321	33	a	a	DET
ejpam-6951	321	34	=	=	X
ejpam-6951	321	35	{	{	PUNCT
ejpam-6951	321	36	y2	y2	PROPN
ejpam-6951	321	37	,	,	PUNCT
ejpam-6951	321	38	y3	y3	PROPN
ejpam-6951	321	39	,	,	PUNCT
ejpam-6951	321	40	y4	y4	PROPN
ejpam-6951	321	41	,	,	PUNCT
ejpam-6951	321	42	...	...	PUNCT
ejpam-6951	321	43	,	,	PUNCT
ejpam-6951	321	44	yt+1	yt+1	CCONJ
ejpam-6951	321	45	}	}	PUNCT
ejpam-6951	321	46	△	△	X
ejpam-6951	321	47	{	{	PUNCT
ejpam-6951	321	48	xi	xi	PROPN
ejpam-6951	321	49	,	,	PUNCT
ejpam-6951	321	50	y2	y2	PROPN
ejpam-6951	321	51	,	,	PUNCT
ejpam-6951	321	52	y3	y3	PROPN
ejpam-6951	321	53	,	,	PUNCT
ejpam-6951	321	54	y4	y4	PROPN
ejpam-6951	321	55	,	,	PUNCT
ejpam-6951	321	56	...	...	PUNCT
ejpam-6951	321	57	,	,	PUNCT
ejpam-6951	321	58	yt+1	yt+1	CCONJ
ejpam-6951	321	59	}	}	PUNCT
ejpam-6951	321	60	=	=	SYM
ejpam-6951	321	61	{	{	PUNCT
ejpam-6951	321	62	xi	xi	X
ejpam-6951	321	63	}	}	PUNCT
ejpam-6951	321	64	.	.	PUNCT
ejpam-6951	322	1	g.	g.	PROPN
ejpam-6951	322	2	d.	d.	PROPN
ejpam-6951	322	3	sepillo	sepillo	PROPN
ejpam-6951	322	4	et	et	PROPN
ejpam-6951	322	5	al	al	PROPN
ejpam-6951	322	6	.	.	PUNCT
ejpam-6951	322	7	/	/	SYM
ejpam-6951	322	8	eur	eur	PROPN
ejpam-6951	322	9	.	.	PUNCT
ejpam-6951	323	1	j.	j.	PROPN
ejpam-6951	323	2	pure	pure	PROPN
ejpam-6951	323	3	appl	appl	PROPN
ejpam-6951	323	4	.	.	PROPN
ejpam-6951	323	5	math	math	PROPN
ejpam-6951	323	6	,	,	PUNCT
ejpam-6951	323	7	18	18	NUM
ejpam-6951	323	8	(	(	PUNCT
ejpam-6951	323	9	4	4	NUM
ejpam-6951	323	10	)	)	PUNCT
ejpam-6951	323	11	(	(	PUNCT
ejpam-6951	323	12	2025	2025	NUM
ejpam-6951	323	13	)	)	PUNCT
ejpam-6951	323	14	,	,	PUNCT
ejpam-6951	323	15	6951	6951	NUM
ejpam-6951	323	16	15	15	NUM
ejpam-6951	323	17	of	of	ADP
ejpam-6951	323	18	23	23	NUM
ejpam-6951	324	1	x2	x2	NOUN
ejpam-6951	324	2	x3	x3	PROPN
ejpam-6951	324	3	x4	x4	PROPN
ejpam-6951	324	4	xt+1	xt+1	PROPN
ejpam-6951	325	1	xn−2	xn−2	PROPN
ejpam-6951	325	2	xn−1	xn−1	PROPN
ejpam-6951	325	3	xn	xn	PROPN
ejpam-6951	326	1	x1	x1	NUM
ejpam-6951	326	2	y1	y1	NOUN
ejpam-6951	326	3	y2	y2	NOUN
ejpam-6951	326	4	y3	y3	NOUN
ejpam-6951	326	5	y4	y4	NOUN
ejpam-6951	326	6	yt+1	yt+1	PROPN
ejpam-6951	326	7	ym−1	ym−1	PROPN
ejpam-6951	326	8	ym	ym	PROPN
ejpam-6951	326	9	tn	tn	PROPN
ejpam-6951	326	10	,	,	PUNCT
ejpam-6951	326	11	m⟨ap⟩	m⟨ap⟩	VERB
ejpam-6951	326	12	:	:	PUNCT
ejpam-6951	327	1	x2	x2	PROPN
ejpam-6951	327	2	x3	x3	PROPN
ejpam-6951	327	3	x4	x4	PROPN
ejpam-6951	327	4	xn−3	xn−3	PROPN
ejpam-6951	327	5	xn−2	xn−2	PROPN
ejpam-6951	327	6	xn−1	xn−1	PROPN
ejpam-6951	327	7	xn	xn	PROPN
ejpam-6951	328	1	x1	x1	NUM
ejpam-6951	328	2	y1	y1	NOUN
ejpam-6951	328	3	y2	y2	NOUN
ejpam-6951	328	4	y3	y3	NOUN
ejpam-6951	328	5	y4	y4	NOUN
ejpam-6951	328	6	yt+1	yt+1	PROPN
ejpam-6951	328	7	ym−1	ym−1	PROPN
ejpam-6951	328	8	ym	ym	PROPN
ejpam-6951	328	9	tn	tn	PROPN
ejpam-6951	328	10	,	,	PUNCT
ejpam-6951	328	11	m⟨a⟩	m⟨a⟩	NOUN
ejpam-6951	328	12	:	:	PUNCT
ejpam-6951	328	13	figure	figure	NOUN
ejpam-6951	328	14	11	11	NUM
ejpam-6951	328	15	:	:	PUNCT
ejpam-6951	328	16	illustrating	illustrate	VERB
ejpam-6951	328	17	the	the	DET
ejpam-6951	328	18	subgraphs	subgraph	NOUN
ejpam-6951	328	19	of	of	ADP
ejpam-6951	328	20	tn	tn	NOUN
ejpam-6951	328	21	,	,	PUNCT
ejpam-6951	328	22	m	m	AUX
ejpam-6951	328	23	induced	induce	VERB
ejpam-6951	328	24	by	by	ADP
ejpam-6951	328	25	ap	ap	PROPN
ejpam-6951	328	26	and	and	CCONJ
ejpam-6951	328	27	a	a	DET
ejpam-6951	328	28	hence	hence	ADV
ejpam-6951	328	29	,	,	PUNCT
ejpam-6951	328	30	{	{	PUNCT
ejpam-6951	328	31	xi	xi	NOUN
ejpam-6951	328	32	}	}	PUNCT
ejpam-6951	328	33	∈	∈	PROPN
ejpam-6951	328	34	vpt⊔k1(tn	vpt⊔k1(tn	NOUN
ejpam-6951	328	35	,	,	PUNCT
ejpam-6951	328	36	m	m	PROPN
ejpam-6951	328	37	)	)	PUNCT
ejpam-6951	328	38	for	for	ADP
ejpam-6951	328	39	all	all	DET
ejpam-6951	328	40	1	1	NUM
ejpam-6951	328	41	≤	≤	NUM
ejpam-6951	328	42	i	i	PRON
ejpam-6951	328	43	≤	≤	ADJ
ejpam-6951	328	44	n.	n.	NOUN
ejpam-6951	328	45	similarly	similarly	ADV
ejpam-6951	328	46	,	,	PUNCT
ejpam-6951	328	47	for	for	ADP
ejpam-6951	328	48	any	any	DET
ejpam-6951	328	49	1	1	NUM
ejpam-6951	328	50	≤	≤	NUM
ejpam-6951	328	51	j	j	PROPN
ejpam-6951	328	52	≤	≤	PROPN
ejpam-6951	328	53	m	m	ADP
ejpam-6951	328	54	,	,	PUNCT
ejpam-6951	328	55	let	let	VERB
ejpam-6951	328	56	yj	yj	PRON
ejpam-6951	328	57	be	be	AUX
ejpam-6951	328	58	an	an	DET
ejpam-6951	328	59	arbitrary	arbitrary	ADJ
ejpam-6951	328	60	vertex	vertex	NOUN
ejpam-6951	328	61	of	of	ADP
ejpam-6951	328	62	pm	pm	NOUN
ejpam-6951	328	63	in	in	ADP
ejpam-6951	328	64	the	the	DET
ejpam-6951	328	65	tadpole	tadpole	NOUN
ejpam-6951	328	66	graph	graph	PROPN
ejpam-6951	328	67	tn	tn	PROPN
ejpam-6951	328	68	,	,	PUNCT
ejpam-6951	328	69	m	m	PROPN
ejpam-6951	328	70	,	,	PUNCT
ejpam-6951	328	71	and	and	CCONJ
ejpam-6951	328	72	for	for	ADP
ejpam-6951	328	73	any	any	DET
ejpam-6951	328	74	1	1	NUM
ejpam-6951	328	75	≤	≤	NOUN
ejpam-6951	328	76	q	q	PROPN
ejpam-6951	328	77	≤	≤	PROPN
ejpam-6951	328	78	t	t	PROPN
ejpam-6951	328	79	,	,	PUNCT
ejpam-6951	328	80	let	let	VERB
ejpam-6951	328	81	bq	bq	INTJ
ejpam-6951	328	82	and	and	CCONJ
ejpam-6951	328	83	b	b	NOUN
ejpam-6951	328	84	be	be	AUX
ejpam-6951	328	85	defined	define	VERB
ejpam-6951	328	86	as	as	SCONJ
ejpam-6951	328	87	follows	follow	VERB
ejpam-6951	328	88	:	:	PUNCT
ejpam-6951	328	89	bq	bq	INTJ
ejpam-6951	328	90	=	=	PRON
ejpam-6951	328	91	{	{	PUNCT
ejpam-6951	328	92	xq+1	xq+1	PROPN
ejpam-6951	328	93	,	,	PUNCT
ejpam-6951	328	94	t	t	PROPN
ejpam-6951	328	95	vertices︷	vertices︷	NOUN
ejpam-6951	328	96	︸︸	︸︸	PUNCT
ejpam-6951	328	97	︷	︷	PUNCT
ejpam-6951	329	1	y2	y2	VERB
ejpam-6951	329	2	,	,	PUNCT
ejpam-6951	329	3	y3	y3	PROPN
ejpam-6951	329	4	,	,	PUNCT
ejpam-6951	329	5	y4	y4	PROPN
ejpam-6951	329	6	,	,	PUNCT
ejpam-6951	329	7	...	...	PUNCT
ejpam-6951	329	8	,	,	PUNCT
ejpam-6951	329	9	yt+1	yt+1	CCONJ
ejpam-6951	329	10	}	}	PUNCT
ejpam-6951	329	11	where	where	SCONJ
ejpam-6951	329	12	1	1	NUM
ejpam-6951	329	13	≤	≤	NOUN
ejpam-6951	329	14	q	q	PROPN
ejpam-6951	329	15	≤	≤	NUM
ejpam-6951	329	16	t	t	PROPN
ejpam-6951	329	17	,	,	PUNCT
ejpam-6951	329	18	and	and	CCONJ
ejpam-6951	329	19	b	b	X
ejpam-6951	329	20	=	=	SYM
ejpam-6951	329	21	{	{	PUNCT
ejpam-6951	329	22	t	t	PROPN
ejpam-6951	329	23	vertices︷	vertices︷	NOUN
ejpam-6951	329	24	︸︸	︸︸	PUNCT
ejpam-6951	329	25	︷	︷	PROPN
ejpam-6951	330	1	x2	x2	ADJ
ejpam-6951	330	2	,	,	PUNCT
ejpam-6951	330	3	x3	x3	PROPN
ejpam-6951	330	4	,	,	PUNCT
ejpam-6951	330	5	x4	x4	PROPN
ejpam-6951	330	6	,	,	PUNCT
ejpam-6951	330	7	...	...	PUNCT
ejpam-6951	330	8	,	,	PUNCT
ejpam-6951	330	9	xt+1	xt+1	PROPN
ejpam-6951	330	10	,	,	PUNCT
ejpam-6951	330	11	yj	yj	PROPN
ejpam-6951	330	12	}	}	PUNCT
ejpam-6951	330	13	where	where	SCONJ
ejpam-6951	330	14	1	1	NUM
ejpam-6951	330	15	≤	≤	NUM
ejpam-6951	330	16	j	j	PROPN
ejpam-6951	330	17	≤	≤	PROPN
ejpam-6951	330	18	m.	m.	NOUN
ejpam-6951	330	19	it	it	PRON
ejpam-6951	330	20	can	can	AUX
ejpam-6951	330	21	be	be	AUX
ejpam-6951	330	22	verified	verify	VERB
ejpam-6951	330	23	that	that	SCONJ
ejpam-6951	330	24	bq	bq	PROPN
ejpam-6951	330	25	,	,	PUNCT
ejpam-6951	330	26	b	b	PROPN
ejpam-6951	330	27	∈	∈	PROPN
ejpam-6951	330	28	vpt⊔k1(tn	vpt⊔k1(tn	NOUN
ejpam-6951	330	29	,	,	PUNCT
ejpam-6951	330	30	m	m	PROPN
ejpam-6951	330	31	)	)	PUNCT
ejpam-6951	330	32	,	,	PUNCT
ejpam-6951	330	33	as	as	SCONJ
ejpam-6951	330	34	shown	show	VERB
ejpam-6951	330	35	in	in	ADP
ejpam-6951	330	36	figure	figure	NOUN
ejpam-6951	330	37	12	12	NUM
ejpam-6951	330	38	.	.	PUNCT
ejpam-6951	331	1	x2	x2	PROPN
ejpam-6951	331	2	x3	x3	PROPN
ejpam-6951	332	1	x4	x4	PROPN
ejpam-6951	332	2	xt+1	xt+1	PROPN
ejpam-6951	333	1	xn−2	xn−2	PROPN
ejpam-6951	333	2	xn−1	xn−1	PROPN
ejpam-6951	333	3	xn	xn	PROPN
ejpam-6951	334	1	x1	x1	NUM
ejpam-6951	334	2	y1	y1	NOUN
ejpam-6951	334	3	y2	y2	NOUN
ejpam-6951	334	4	y3	y3	NOUN
ejpam-6951	334	5	y4	y4	NOUN
ejpam-6951	334	6	yt+1	yt+1	PROPN
ejpam-6951	334	7	ym−1	ym−1	PROPN
ejpam-6951	334	8	ym	ym	PROPN
ejpam-6951	334	9	tm	tm	PROPN
ejpam-6951	334	10	,	,	PUNCT
ejpam-6951	334	11	n⟨bq⟩	n⟨bq⟩	NOUN
ejpam-6951	334	12	:	:	PUNCT
ejpam-6951	335	1	x2	x2	NOUN
ejpam-6951	335	2	x3	x3	PROPN
ejpam-6951	335	3	x4	x4	PROPN
ejpam-6951	335	4	xt+1	xt+1	PROPN
ejpam-6951	336	1	xn−2	xn−2	PROPN
ejpam-6951	336	2	xn−1	xn−1	PROPN
ejpam-6951	336	3	xn	xn	PROPN
ejpam-6951	337	1	x1	x1	NUM
ejpam-6951	337	2	y1	y1	NOUN
ejpam-6951	337	3	y2	y2	NOUN
ejpam-6951	337	4	y3	y3	NOUN
ejpam-6951	337	5	y4	y4	PROPN
ejpam-6951	337	6	ym−2	ym−2	PROPN
ejpam-6951	337	7	ym−1	ym−1	PROPN
ejpam-6951	337	8	ym	ym	PROPN
ejpam-6951	337	9	tm	tm	NOUN
ejpam-6951	337	10	,	,	PUNCT
ejpam-6951	337	11	n⟨b⟩	n⟨b⟩	ADV
ejpam-6951	337	12	:	:	PUNCT
ejpam-6951	337	13	figure	figure	NOUN
ejpam-6951	337	14	12	12	NUM
ejpam-6951	337	15	:	:	PUNCT
ejpam-6951	337	16	illustrating	illustrate	VERB
ejpam-6951	337	17	the	the	DET
ejpam-6951	337	18	subgraphs	subgraph	NOUN
ejpam-6951	337	19	of	of	ADP
ejpam-6951	337	20	tn	tn	NOUN
ejpam-6951	337	21	,	,	PUNCT
ejpam-6951	337	22	m	m	AUX
ejpam-6951	337	23	induced	induce	VERB
ejpam-6951	337	24	by	by	ADP
ejpam-6951	337	25	bq	bq	INTJ
ejpam-6951	337	26	and	and	CCONJ
ejpam-6951	337	27	b	b	NOUN
ejpam-6951	337	28	hence	hence	ADV
ejpam-6951	337	29	,	,	PUNCT
ejpam-6951	337	30	for	for	ADP
ejpam-6951	337	31	j	j	PROPN
ejpam-6951	337	32	=	=	SYM
ejpam-6951	337	33	1	1	NUM
ejpam-6951	337	34	,	,	PUNCT
ejpam-6951	337	35	2	2	NUM
ejpam-6951	337	36	,	,	PUNCT
ejpam-6951	337	37	3	3	NUM
ejpam-6951	337	38	,	,	PUNCT
ejpam-6951	337	39	...	...	PUNCT
ejpam-6951	337	40	,	,	PUNCT
ejpam-6951	337	41	m	m	PRON
ejpam-6951	337	42	,	,	PUNCT
ejpam-6951	337	43	we	we	PRON
ejpam-6951	337	44	get	get	VERB
ejpam-6951	337	45	t∑	t∑	ADV
ejpam-6951	337	46	q=1	q=1	X
ejpam-6951	337	47	bq	bq	X
ejpam-6951	338	1	+	+	NOUN
ejpam-6951	338	2	b	b	X
ejpam-6951	338	3	=	=	SYM
ejpam-6951	338	4	(	(	PUNCT
ejpam-6951	338	5	b1	b1	NOUN
ejpam-6951	338	6	+	+	NOUN
ejpam-6951	338	7	b2	b2	NOUN
ejpam-6951	338	8	+	+	NOUN
ejpam-6951	338	9	b3	b3	NOUN
ejpam-6951	338	10	+	+	CCONJ
ejpam-6951	338	11	·	·	PUNCT
ejpam-6951	338	12	·	·	PUNCT
ejpam-6951	338	13	·	·	PUNCT
ejpam-6951	338	14	+	+	NOUN
ejpam-6951	338	15	bt	bt	X
ejpam-6951	338	16	)	)	PUNCT
ejpam-6951	338	17	+	+	PROPN
ejpam-6951	338	18	b	b	PROPN
ejpam-6951	338	19	g.	g.	PROPN
ejpam-6951	338	20	d.	d.	PROPN
ejpam-6951	338	21	sepillo	sepillo	PROPN
ejpam-6951	338	22	et	et	PROPN
ejpam-6951	338	23	al	al	PROPN
ejpam-6951	338	24	.	.	PUNCT
ejpam-6951	338	25	/	/	SYM
ejpam-6951	338	26	eur	eur	PROPN
ejpam-6951	338	27	.	.	PUNCT
ejpam-6951	339	1	j.	j.	PROPN
ejpam-6951	339	2	pure	pure	PROPN
ejpam-6951	339	3	appl	appl	PROPN
ejpam-6951	339	4	.	.	PROPN
ejpam-6951	339	5	math	math	PROPN
ejpam-6951	339	6	,	,	PUNCT
ejpam-6951	339	7	18	18	NUM
ejpam-6951	339	8	(	(	PUNCT
ejpam-6951	339	9	4	4	NUM
ejpam-6951	339	10	)	)	PUNCT
ejpam-6951	339	11	(	(	PUNCT
ejpam-6951	339	12	2025	2025	NUM
ejpam-6951	339	13	)	)	PUNCT
ejpam-6951	339	14	,	,	PUNCT
ejpam-6951	339	15	6951	6951	NUM
ejpam-6951	339	16	16	16	NUM
ejpam-6951	339	17	of	of	ADP
ejpam-6951	339	18	23	23	NUM
ejpam-6951	339	19	=	=	SYM
ejpam-6951	339	20	(	(	PUNCT
ejpam-6951	339	21	b1	b1	PROPN
ejpam-6951	339	22	△	△	PROPN
ejpam-6951	339	23	b2	b2	PROPN
ejpam-6951	339	24	△	△	NOUN
ejpam-6951	339	25	b3	b3	PROPN
ejpam-6951	339	26	△	△	X
ejpam-6951	339	27	·	·	PUNCT
ejpam-6951	339	28	·	·	PUNCT
ejpam-6951	339	29	·	·	PUNCT
ejpam-6951	339	30	△	△	X
ejpam-6951	339	31	bt)	bt)	X
ejpam-6951	339	32	△	△	X
ejpam-6951	339	33	b	b	NOUN
ejpam-6951	339	34	=	=	SYM
ejpam-6951	339	35	{	{	PUNCT
ejpam-6951	339	36	x2	x2	PROPN
ejpam-6951	339	37	,	,	PUNCT
ejpam-6951	339	38	x3	x3	PROPN
ejpam-6951	339	39	,	,	PUNCT
ejpam-6951	339	40	x4	x4	PROPN
ejpam-6951	339	41	,	,	PUNCT
ejpam-6951	339	42	...	...	PUNCT
ejpam-6951	339	43	,	,	PUNCT
ejpam-6951	339	44	xt+1	xt+1	PROPN
ejpam-6951	339	45	}	}	PUNCT
ejpam-6951	339	46	△	△	X
ejpam-6951	339	47	{	{	PUNCT
ejpam-6951	339	48	x2	x2	PROPN
ejpam-6951	339	49	,	,	PUNCT
ejpam-6951	339	50	x3	x3	PROPN
ejpam-6951	339	51	,	,	PUNCT
ejpam-6951	339	52	x4	x4	PROPN
ejpam-6951	339	53	,	,	PUNCT
ejpam-6951	339	54	...	...	PUNCT
ejpam-6951	339	55	,	,	PUNCT
ejpam-6951	339	56	xt+1	xt+1	PROPN
ejpam-6951	339	57	,	,	PUNCT
ejpam-6951	339	58	yj	yj	PROPN
ejpam-6951	339	59	}	}	PUNCT
ejpam-6951	339	60	=	=	SYM
ejpam-6951	339	61	{	{	PUNCT
ejpam-6951	339	62	yj	yj	PROPN
ejpam-6951	339	63	}	}	PUNCT
ejpam-6951	339	64	.	.	PUNCT
ejpam-6951	340	1	thus	thus	ADV
ejpam-6951	340	2	,	,	PUNCT
ejpam-6951	340	3	{	{	PUNCT
ejpam-6951	340	4	yj	yj	PROPN
ejpam-6951	340	5	}	}	PUNCT
ejpam-6951	340	6	∈	∈	PROPN
ejpam-6951	340	7	vpt⊔k1(tn	vpt⊔k1(tn	NOUN
ejpam-6951	340	8	,	,	PUNCT
ejpam-6951	340	9	m	m	PROPN
ejpam-6951	340	10	)	)	PUNCT
ejpam-6951	340	11	for	for	ADP
ejpam-6951	340	12	all	all	PRON
ejpam-6951	340	13	1	1	NUM
ejpam-6951	340	14	≤	≤	NUM
ejpam-6951	340	15	j	j	PROPN
ejpam-6951	340	16	≤	≤	PROPN
ejpam-6951	340	17	m.	m.	NOUN
ejpam-6951	340	18	therefore	therefore	ADV
ejpam-6951	340	19	,	,	PUNCT
ejpam-6951	340	20	by	by	ADP
ejpam-6951	340	21	remark	remark	NOUN
ejpam-6951	340	22	1	1	NUM
ejpam-6951	340	23	,	,	PUNCT
ejpam-6951	340	24	pt	pt	X
ejpam-6951	340	25	⊔	⊔	PROPN
ejpam-6951	340	26	k1	k1	PROPN
ejpam-6951	340	27	is	be	AUX
ejpam-6951	340	28	a	a	DET
ejpam-6951	340	29	vertex	vertex	NOUN
ejpam-6951	340	30	-	-	PUNCT
ejpam-6951	340	31	generator	generator	NOUN
ejpam-6951	340	32	subgraph	subgraph	NOUN
ejpam-6951	340	33	of	of	ADP
ejpam-6951	340	34	tn	tn	PROPN
ejpam-6951	340	35	,	,	PUNCT
ejpam-6951	340	36	m.	m.	NOUN
ejpam-6951	340	37	the	the	DET
ejpam-6951	340	38	next	next	ADJ
ejpam-6951	340	39	theorem	theorem	NOUN
ejpam-6951	340	40	gives	give	VERB
ejpam-6951	340	41	us	we	PRON
ejpam-6951	340	42	a	a	DET
ejpam-6951	340	43	necessary	necessary	ADJ
ejpam-6951	340	44	condition	condition	NOUN
ejpam-6951	340	45	for	for	ADP
ejpam-6951	340	46	the	the	DET
ejpam-6951	340	47	empty	empty	ADJ
ejpam-6951	340	48	graph	graph	NOUN
ejpam-6951	340	49	kt	kt	X
ejpam-6951	340	50	of	of	ADP
ejpam-6951	340	51	order	order	NOUN
ejpam-6951	340	52	t	t	PROPN
ejpam-6951	340	53	,	,	PUNCT
ejpam-6951	340	54	so	so	SCONJ
ejpam-6951	340	55	t	t	PROPN
ejpam-6951	340	56	should	should	AUX
ejpam-6951	340	57	be	be	AUX
ejpam-6951	340	58	odd	odd	ADJ
ejpam-6951	340	59	,	,	PUNCT
ejpam-6951	340	60	to	to	PART
ejpam-6951	340	61	be	be	AUX
ejpam-6951	340	62	a	a	DET
ejpam-6951	340	63	vertex	vertex	NOUN
ejpam-6951	340	64	-	-	PUNCT
ejpam-6951	340	65	generator	generator	NOUN
ejpam-6951	340	66	subgraph	subgraph	NOUN
ejpam-6951	340	67	of	of	ADP
ejpam-6951	340	68	tn	tn	PROPN
ejpam-6951	340	69	,	,	PUNCT
ejpam-6951	340	70	m.	m.	NOUN
ejpam-6951	340	71	theorem	theorem	VERB
ejpam-6951	340	72	15	15	NUM
ejpam-6951	340	73	.	.	PUNCT
ejpam-6951	341	1	let	let	VERB
ejpam-6951	341	2	n	n	PRON
ejpam-6951	341	3	,	,	PUNCT
ejpam-6951	341	4	m	m	VERB
ejpam-6951	341	5	≥	≥	NOUN
ejpam-6951	341	6	4	4	NUM
ejpam-6951	341	7	and	and	CCONJ
ejpam-6951	341	8	t	t	PROPN
ejpam-6951	341	9	≥	≥	NUM
ejpam-6951	341	10	3	3	NUM
ejpam-6951	341	11	be	be	AUX
ejpam-6951	341	12	positive	positive	ADJ
ejpam-6951	341	13	integers	integer	NOUN
ejpam-6951	341	14	where	where	SCONJ
ejpam-6951	341	15	t	t	PROPN
ejpam-6951	341	16	is	be	AUX
ejpam-6951	341	17	odd	odd	ADJ
ejpam-6951	341	18	.	.	PUNCT
ejpam-6951	342	1	if	if	SCONJ
ejpam-6951	342	2	2t−	2t−	PROPN
ejpam-6951	342	3	2	2	NUM
ejpam-6951	342	4	≤	≤	NUM
ejpam-6951	342	5	min{n	min{n	NOUN
ejpam-6951	342	6	,	,	PUNCT
ejpam-6951	342	7	m	m	NOUN
ejpam-6951	342	8	}	}	PUNCT
ejpam-6951	342	9	,	,	PUNCT
ejpam-6951	342	10	then	then	ADV
ejpam-6951	342	11	kt	kt	PROPN
ejpam-6951	342	12	is	be	AUX
ejpam-6951	342	13	a	a	DET
ejpam-6951	342	14	vertex	vertex	NOUN
ejpam-6951	342	15	-	-	PUNCT
ejpam-6951	342	16	generator	generator	NOUN
ejpam-6951	342	17	subgraph	subgraph	NOUN
ejpam-6951	342	18	of	of	ADP
ejpam-6951	342	19	tn	tn	PROPN
ejpam-6951	342	20	,	,	PUNCT
ejpam-6951	342	21	m.	m.	NOUN
ejpam-6951	342	22	proof	proof	NOUN
ejpam-6951	342	23	.	.	PUNCT
ejpam-6951	343	1	let	let	VERB
ejpam-6951	343	2	2t−	2t−	NUM
ejpam-6951	343	3	2	2	NUM
ejpam-6951	343	4	≤	≤	NUM
ejpam-6951	343	5	min{n	min{n	NOUN
ejpam-6951	343	6	,	,	PUNCT
ejpam-6951	343	7	m	m	NOUN
ejpam-6951	343	8	}	}	PUNCT
ejpam-6951	343	9	.	.	PUNCT
ejpam-6951	344	1	for	for	ADP
ejpam-6951	344	2	any	any	DET
ejpam-6951	344	3	1	1	NUM
ejpam-6951	344	4	≤	≤	NUM
ejpam-6951	344	5	i	i	PRON
ejpam-6951	344	6	≤	≤	PROPN
ejpam-6951	344	7	n	n	CCONJ
ejpam-6951	344	8	,	,	PUNCT
ejpam-6951	344	9	let	let	VERB
ejpam-6951	344	10	xi	xi	PRON
ejpam-6951	344	11	be	be	AUX
ejpam-6951	344	12	an	an	DET
ejpam-6951	344	13	arbitrary	arbitrary	ADJ
ejpam-6951	344	14	vertex	vertex	NOUN
ejpam-6951	344	15	of	of	ADP
ejpam-6951	344	16	cn	cn	PROPN
ejpam-6951	344	17	in	in	ADP
ejpam-6951	344	18	the	the	DET
ejpam-6951	344	19	tadpole	tadpole	NOUN
ejpam-6951	344	20	graph	graph	PROPN
ejpam-6951	344	21	tn	tn	PROPN
ejpam-6951	344	22	,	,	PUNCT
ejpam-6951	344	23	m	m	PROPN
ejpam-6951	344	24	,	,	PUNCT
ejpam-6951	344	25	and	and	CCONJ
ejpam-6951	344	26	for	for	ADP
ejpam-6951	344	27	any	any	DET
ejpam-6951	344	28	1	1	NUM
ejpam-6951	344	29	≤	≤	NOUN
ejpam-6951	344	30	p	p	NOUN
ejpam-6951	344	31	≤	≤	NOUN
ejpam-6951	344	32	t−	t−	PROPN
ejpam-6951	344	33	1	1	NUM
ejpam-6951	344	34	,	,	PUNCT
ejpam-6951	344	35	we	we	PRON
ejpam-6951	344	36	define	define	VERB
ejpam-6951	344	37	ap	ap	PROPN
ejpam-6951	344	38	and	and	CCONJ
ejpam-6951	344	39	a	a	PRON
ejpam-6951	344	40	as	as	SCONJ
ejpam-6951	344	41	follows	follow	VERB
ejpam-6951	344	42	:	:	PUNCT
ejpam-6951	345	1	ap	ap	PROPN
ejpam-6951	345	2	=	=	PUNCT
ejpam-6951	345	3	{	{	PUNCT
ejpam-6951	345	4	t−1	t−1	PROPN
ejpam-6951	345	5	vertices︷	vertices︷	NOUN
ejpam-6951	345	6	︸︸	︸︸	PUNCT
ejpam-6951	345	7	︷	︷	PROPN
ejpam-6951	346	1	x2	x2	SYM
ejpam-6951	346	2	,	,	PUNCT
ejpam-6951	346	3	x4	x4	PROPN
ejpam-6951	346	4	,	,	PUNCT
ejpam-6951	346	5	x6	x6	PROPN
ejpam-6951	346	6	,	,	PUNCT
ejpam-6951	346	7	...	...	PUNCT
ejpam-6951	346	8	,	,	PUNCT
ejpam-6951	346	9	x2t−2	x2t−2	PROPN
ejpam-6951	346	10	,	,	PUNCT
ejpam-6951	346	11	y2p	y2p	PROPN
ejpam-6951	346	12	}	}	PUNCT
ejpam-6951	346	13	where	where	SCONJ
ejpam-6951	346	14	1	1	NUM
ejpam-6951	346	15	≤	≤	NOUN
ejpam-6951	346	16	p	p	NOUN
ejpam-6951	346	17	≤	≤	NOUN
ejpam-6951	346	18	t−	t−	PROPN
ejpam-6951	346	19	1	1	NUM
ejpam-6951	346	20	,	,	PUNCT
ejpam-6951	346	21	and	and	CCONJ
ejpam-6951	346	22	a	a	DET
ejpam-6951	346	23	=	=	X
ejpam-6951	346	24	{	{	PUNCT
ejpam-6951	346	25	xi	xi	PROPN
ejpam-6951	346	26	,	,	PUNCT
ejpam-6951	346	27	t−1	t−1	PROPN
ejpam-6951	346	28	vertices︷	vertices︷	NOUN
ejpam-6951	346	29	︸︸	︸︸	PUNCT
ejpam-6951	346	30	︷	︷	PUNCT
ejpam-6951	347	1	y2	y2	VERB
ejpam-6951	347	2	,	,	PUNCT
ejpam-6951	347	3	y4	y4	PROPN
ejpam-6951	347	4	,	,	PUNCT
ejpam-6951	347	5	y6	y6	ADJ
ejpam-6951	347	6	,	,	PUNCT
ejpam-6951	347	7	...	...	PUNCT
ejpam-6951	347	8	,	,	PUNCT
ejpam-6951	347	9	y2t−2	y2t−2	NOUN
ejpam-6951	347	10	}	}	PUNCT
ejpam-6951	347	11	where	where	SCONJ
ejpam-6951	347	12	1	1	NUM
ejpam-6951	347	13	≤	≤	NUM
ejpam-6951	347	14	i	i	PRON
ejpam-6951	347	15	≤	≤	NUM
ejpam-6951	347	16	n.	n.	NOUN
ejpam-6951	347	17	it	it	PRON
ejpam-6951	347	18	can	can	AUX
ejpam-6951	347	19	be	be	AUX
ejpam-6951	347	20	verified	verify	VERB
ejpam-6951	347	21	that	that	SCONJ
ejpam-6951	347	22	ap	ap	PROPN
ejpam-6951	347	23	,	,	PUNCT
ejpam-6951	347	24	a	a	DET
ejpam-6951	347	25	∈	∈	PROPN
ejpam-6951	347	26	vkt	vkt	X
ejpam-6951	347	27	(	(	PUNCT
ejpam-6951	347	28	tn	tn	PROPN
ejpam-6951	347	29	,	,	PUNCT
ejpam-6951	347	30	m	m	PROPN
ejpam-6951	347	31	)	)	PUNCT
ejpam-6951	347	32	,	,	PUNCT
ejpam-6951	347	33	as	as	SCONJ
ejpam-6951	347	34	shown	show	VERB
ejpam-6951	347	35	in	in	ADP
ejpam-6951	347	36	figure	figure	NOUN
ejpam-6951	347	37	13	13	NUM
ejpam-6951	347	38	.	.	PUNCT
ejpam-6951	348	1	x2	x2	PRON
ejpam-6951	348	2	x3	x3	PROPN
ejpam-6951	348	3	x4x5	x4x5	NUM
ejpam-6951	349	1	x6	x6	PROPN
ejpam-6951	349	2	x2t−3	x2t−3	PROPN
ejpam-6951	350	1	x2t−2	x2t−2	PROPN
ejpam-6951	350	2	x2t−1	x2t−1	PROPN
ejpam-6951	351	1	x2	x2	INTJ
ejpam-6951	351	2	t	t	PROPN
ejpam-6951	352	1	xn−1	xn−1	PROPN
ejpam-6951	352	2	xn	xn	PROPN
ejpam-6951	353	1	x1	x1	NUM
ejpam-6951	353	2	y1	y1	NOUN
ejpam-6951	353	3	y2	y2	PROPN
ejpam-6951	353	4	y3	y3	PROPN
ejpam-6951	353	5	y4	y4	NOUN
ejpam-6951	353	6	y5	y5	NOUN
ejpam-6951	353	7	y6	y6	ADJ
ejpam-6951	353	8	y2t−3	y2t−3	NOUN
ejpam-6951	353	9	y2t−2	y2t−2	NOUN
ejpam-6951	353	10	y2t−1	y2t−1	PROPN
ejpam-6951	353	11	ym−1	ym−1	PROPN
ejpam-6951	353	12	ym	ym	PROPN
ejpam-6951	353	13	tn	tn	PROPN
ejpam-6951	353	14	,	,	PUNCT
ejpam-6951	353	15	m⟨ap⟩	m⟨ap⟩	VERB
ejpam-6951	353	16	:	:	PUNCT
ejpam-6951	354	1	x2	x2	PROPN
ejpam-6951	354	2	x3	x3	PROPN
ejpam-6951	354	3	x4x5	x4x5	NUM
ejpam-6951	354	4	x6	x6	PROPN
ejpam-6951	354	5	xn−5	xn−5	PROPN
ejpam-6951	354	6	xn−4	xn−4	PROPN
ejpam-6951	354	7	xn−3xn−2	xn−3xn−2	PROPN
ejpam-6951	355	1	xn−1	xn−1	PROPN
ejpam-6951	355	2	xn	xn	PROPN
ejpam-6951	356	1	x1	x1	NUM
ejpam-6951	356	2	y1	y1	NOUN
ejpam-6951	356	3	y2	y2	PROPN
ejpam-6951	356	4	y3	y3	PROPN
ejpam-6951	356	5	y4	y4	NOUN
ejpam-6951	356	6	y5	y5	NOUN
ejpam-6951	356	7	y6	y6	ADJ
ejpam-6951	356	8	y2t−3	y2t−3	NOUN
ejpam-6951	356	9	y2t−2	y2t−2	NOUN
ejpam-6951	356	10	y2t−1	y2t−1	PROPN
ejpam-6951	356	11	ym−1	ym−1	PROPN
ejpam-6951	356	12	ym	ym	PROPN
ejpam-6951	356	13	tn	tn	PROPN
ejpam-6951	356	14	,	,	PUNCT
ejpam-6951	356	15	m⟨a⟩	m⟨a⟩	NOUN
ejpam-6951	356	16	:	:	PUNCT
ejpam-6951	356	17	figure	figure	NOUN
ejpam-6951	356	18	13	13	NUM
ejpam-6951	356	19	:	:	PUNCT
ejpam-6951	356	20	illustrating	illustrate	VERB
ejpam-6951	356	21	the	the	DET
ejpam-6951	356	22	subgraphs	subgraph	NOUN
ejpam-6951	356	23	of	of	ADP
ejpam-6951	356	24	tn	tn	NOUN
ejpam-6951	356	25	,	,	PUNCT
ejpam-6951	356	26	m	m	AUX
ejpam-6951	356	27	induced	induce	VERB
ejpam-6951	356	28	by	by	ADP
ejpam-6951	356	29	ap	ap	PROPN
ejpam-6951	356	30	and	and	CCONJ
ejpam-6951	356	31	a	a	DET
ejpam-6951	356	32	hence	hence	ADV
ejpam-6951	356	33	,	,	PUNCT
ejpam-6951	356	34	for	for	ADP
ejpam-6951	356	35	i	i	PROPN
ejpam-6951	356	36	=	=	SYM
ejpam-6951	356	37	1	1	NUM
ejpam-6951	356	38	,	,	PUNCT
ejpam-6951	356	39	2	2	NUM
ejpam-6951	356	40	,	,	PUNCT
ejpam-6951	356	41	3	3	NUM
ejpam-6951	356	42	,	,	PUNCT
ejpam-6951	356	43	...	...	PUNCT
ejpam-6951	356	44	,	,	PUNCT
ejpam-6951	356	45	n	n	CCONJ
ejpam-6951	356	46	,	,	PUNCT
ejpam-6951	356	47	we	we	PRON
ejpam-6951	356	48	have	have	VERB
ejpam-6951	356	49	t−1∑	t−1∑	NUM
ejpam-6951	356	50	p=1	p=1	PROPN
ejpam-6951	356	51	ap	ap	NOUN
ejpam-6951	357	1	+	+	NOUN
ejpam-6951	357	2	a	a	NOUN
ejpam-6951	357	3	=	=	X
ejpam-6951	357	4	(	(	PUNCT
ejpam-6951	357	5	a1	a1	NOUN
ejpam-6951	357	6	+	+	PROPN
ejpam-6951	357	7	a2	a2	PROPN
ejpam-6951	357	8	+	+	NOUN
ejpam-6951	357	9	a3	a3	NOUN
ejpam-6951	357	10	+	+	X
ejpam-6951	357	11	·	·	PUNCT
ejpam-6951	357	12	·	·	PUNCT
ejpam-6951	357	13	·	·	PUNCT
ejpam-6951	357	14	+	+	NOUN
ejpam-6951	357	15	at−1	at−1	PROPN
ejpam-6951	357	16	)	)	PUNCT
ejpam-6951	357	17	+	+	ADP
ejpam-6951	357	18	a	a	DET
ejpam-6951	357	19	g.	g.	PROPN
ejpam-6951	357	20	d.	d.	PROPN
ejpam-6951	357	21	sepillo	sepillo	PROPN
ejpam-6951	357	22	et	et	PROPN
ejpam-6951	357	23	al	al	PROPN
ejpam-6951	357	24	.	.	PUNCT
ejpam-6951	357	25	/	/	SYM
ejpam-6951	357	26	eur	eur	PROPN
ejpam-6951	357	27	.	.	PUNCT
ejpam-6951	358	1	j.	j.	PROPN
ejpam-6951	358	2	pure	pure	PROPN
ejpam-6951	358	3	appl	appl	PROPN
ejpam-6951	358	4	.	.	PROPN
ejpam-6951	358	5	math	math	PROPN
ejpam-6951	358	6	,	,	PUNCT
ejpam-6951	358	7	18	18	NUM
ejpam-6951	358	8	(	(	PUNCT
ejpam-6951	358	9	4	4	NUM
ejpam-6951	358	10	)	)	PUNCT
ejpam-6951	358	11	(	(	PUNCT
ejpam-6951	358	12	2025	2025	NUM
ejpam-6951	358	13	)	)	PUNCT
ejpam-6951	358	14	,	,	PUNCT
ejpam-6951	358	15	6951	6951	NUM
ejpam-6951	358	16	17	17	NUM
ejpam-6951	358	17	of	of	ADP
ejpam-6951	358	18	23	23	NUM
ejpam-6951	358	19	=	=	SYM
ejpam-6951	358	20	(	(	PUNCT
ejpam-6951	358	21	a1	a1	PROPN
ejpam-6951	358	22	△	△	PROPN
ejpam-6951	358	23	a2	a2	PROPN
ejpam-6951	358	24	△	△	PROPN
ejpam-6951	358	25	a3	a3	NOUN
ejpam-6951	358	26	△	△	X
ejpam-6951	358	27	·	·	PUNCT
ejpam-6951	358	28	·	·	PUNCT
ejpam-6951	358	29	·	·	PUNCT
ejpam-6951	359	1	△	△	X
ejpam-6951	359	2	at−1)	at−1)	X
ejpam-6951	359	3	△	△	X
ejpam-6951	359	4	a	a	PRON
ejpam-6951	359	5	=	=	X
ejpam-6951	359	6	{	{	PUNCT
ejpam-6951	359	7	y2	y2	PROPN
ejpam-6951	359	8	,	,	PUNCT
ejpam-6951	359	9	y4	y4	PROPN
ejpam-6951	359	10	,	,	PUNCT
ejpam-6951	359	11	y6	y6	ADJ
ejpam-6951	359	12	,	,	PUNCT
ejpam-6951	359	13	...	...	PUNCT
ejpam-6951	359	14	,	,	PUNCT
ejpam-6951	359	15	y2t−2	y2t−2	NOUN
ejpam-6951	359	16	}	}	PUNCT
ejpam-6951	359	17	△	△	X
ejpam-6951	359	18	{	{	PUNCT
ejpam-6951	359	19	xi	xi	PROPN
ejpam-6951	359	20	,	,	PUNCT
ejpam-6951	359	21	y2	y2	PROPN
ejpam-6951	359	22	,	,	PUNCT
ejpam-6951	359	23	y4	y4	PROPN
ejpam-6951	359	24	,	,	PUNCT
ejpam-6951	359	25	y6	y6	ADJ
ejpam-6951	359	26	,	,	PUNCT
ejpam-6951	359	27	...	...	PUNCT
ejpam-6951	359	28	,	,	PUNCT
ejpam-6951	359	29	y2t−2	y2t−2	NOUN
ejpam-6951	359	30	}	}	PUNCT
ejpam-6951	359	31	=	=	SYM
ejpam-6951	359	32	{	{	PUNCT
ejpam-6951	359	33	xi	xi	X
ejpam-6951	359	34	}	}	PUNCT
ejpam-6951	359	35	.	.	PUNCT
ejpam-6951	360	1	thus	thus	ADV
ejpam-6951	360	2	,	,	PUNCT
ejpam-6951	360	3	{	{	PUNCT
ejpam-6951	360	4	xi	xi	PROPN
ejpam-6951	360	5	}	}	PUNCT
ejpam-6951	360	6	∈	∈	NOUN
ejpam-6951	360	7	vkt	vkt	ADJ
ejpam-6951	360	8	(	(	PUNCT
ejpam-6951	360	9	tn	tn	PROPN
ejpam-6951	360	10	,	,	PUNCT
ejpam-6951	360	11	m	m	NOUN
ejpam-6951	360	12	)	)	PUNCT
ejpam-6951	360	13	for	for	ADP
ejpam-6951	360	14	all	all	DET
ejpam-6951	360	15	1	1	NUM
ejpam-6951	360	16	≤	≤	NUM
ejpam-6951	360	17	i	i	PRON
ejpam-6951	360	18	≤	≤	ADJ
ejpam-6951	360	19	n.	n.	NOUN
ejpam-6951	360	20	in	in	ADP
ejpam-6951	360	21	similar	similar	ADJ
ejpam-6951	360	22	manner	manner	NOUN
ejpam-6951	360	23	,	,	PUNCT
ejpam-6951	360	24	for	for	ADP
ejpam-6951	360	25	any	any	DET
ejpam-6951	360	26	1	1	NUM
ejpam-6951	360	27	≤	≤	NUM
ejpam-6951	360	28	j	j	PROPN
ejpam-6951	360	29	≤	≤	PROPN
ejpam-6951	360	30	m	m	ADP
ejpam-6951	360	31	,	,	PUNCT
ejpam-6951	360	32	let	let	VERB
ejpam-6951	360	33	yj	yj	PRON
ejpam-6951	360	34	be	be	AUX
ejpam-6951	360	35	an	an	DET
ejpam-6951	360	36	arbitrary	arbitrary	ADJ
ejpam-6951	360	37	vertex	vertex	NOUN
ejpam-6951	360	38	of	of	ADP
ejpam-6951	360	39	pm	pm	NOUN
ejpam-6951	360	40	in	in	ADP
ejpam-6951	360	41	the	the	DET
ejpam-6951	360	42	tadpole	tadpole	NOUN
ejpam-6951	360	43	graph	graph	PROPN
ejpam-6951	360	44	tn	tn	PROPN
ejpam-6951	360	45	,	,	PUNCT
ejpam-6951	360	46	m	m	PROPN
ejpam-6951	360	47	,	,	PUNCT
ejpam-6951	360	48	and	and	CCONJ
ejpam-6951	360	49	for	for	ADP
ejpam-6951	360	50	any	any	DET
ejpam-6951	360	51	1	1	NUM
ejpam-6951	360	52	≤	≤	NOUN
ejpam-6951	360	53	q	q	NOUN
ejpam-6951	360	54	≤	≤	NUM
ejpam-6951	360	55	t−	t−	PROPN
ejpam-6951	360	56	1	1	NUM
ejpam-6951	360	57	,	,	PUNCT
ejpam-6951	360	58	we	we	PRON
ejpam-6951	360	59	define	define	VERB
ejpam-6951	360	60	bq	bq	INTJ
ejpam-6951	360	61	and	and	CCONJ
ejpam-6951	360	62	b	b	NOUN
ejpam-6951	360	63	as	as	SCONJ
ejpam-6951	360	64	follows	follow	VERB
ejpam-6951	360	65	:	:	PUNCT
ejpam-6951	360	66	bq	bq	INTJ
ejpam-6951	360	67	=	=	SYM
ejpam-6951	360	68	{	{	PUNCT
ejpam-6951	360	69	x2q	x2q	PROPN
ejpam-6951	360	70	,	,	PUNCT
ejpam-6951	360	71	t−1	t−1	PROPN
ejpam-6951	360	72	vertices︷	vertices︷	NOUN
ejpam-6951	360	73	︸︸	︸︸	PUNCT
ejpam-6951	360	74	︷	︷	PUNCT
ejpam-6951	361	1	y2	y2	VERB
ejpam-6951	361	2	,	,	PUNCT
ejpam-6951	361	3	y4	y4	PROPN
ejpam-6951	361	4	,	,	PUNCT
ejpam-6951	361	5	y6	y6	ADJ
ejpam-6951	361	6	,	,	PUNCT
ejpam-6951	361	7	...	...	PUNCT
ejpam-6951	361	8	,	,	PUNCT
ejpam-6951	361	9	y2t−2	y2t−2	NOUN
ejpam-6951	361	10	}	}	PUNCT
ejpam-6951	361	11	where	where	SCONJ
ejpam-6951	361	12	1	1	NUM
ejpam-6951	361	13	≤	≤	NOUN
ejpam-6951	361	14	q	q	ADJ
ejpam-6951	361	15	≤	≤	NUM
ejpam-6951	361	16	t−	t−	PROPN
ejpam-6951	361	17	1	1	NUM
ejpam-6951	361	18	,	,	PUNCT
ejpam-6951	361	19	and	and	CCONJ
ejpam-6951	361	20	b	b	X
ejpam-6951	361	21	=	=	PRON
ejpam-6951	361	22	{	{	PUNCT
ejpam-6951	361	23	t−1	t−1	PROPN
ejpam-6951	361	24	vertices︷	vertices︷	NOUN
ejpam-6951	361	25	︸︸	︸︸	PUNCT
ejpam-6951	361	26	︷	︷	PROPN
ejpam-6951	362	1	x2	x2	SYM
ejpam-6951	362	2	,	,	PUNCT
ejpam-6951	362	3	x4	x4	PROPN
ejpam-6951	362	4	,	,	PUNCT
ejpam-6951	362	5	x6	x6	PROPN
ejpam-6951	362	6	,	,	PUNCT
ejpam-6951	362	7	...	...	PUNCT
ejpam-6951	362	8	,	,	PUNCT
ejpam-6951	362	9	x2t−2	x2t−2	PROPN
ejpam-6951	362	10	,	,	PUNCT
ejpam-6951	362	11	yj	yj	PROPN
ejpam-6951	362	12	}	}	PUNCT
ejpam-6951	362	13	where	where	SCONJ
ejpam-6951	362	14	1	1	NUM
ejpam-6951	362	15	≤	≤	NUM
ejpam-6951	362	16	j	j	PROPN
ejpam-6951	362	17	≤	≤	PROPN
ejpam-6951	362	18	m.	m.	NOUN
ejpam-6951	362	19	it	it	PRON
ejpam-6951	362	20	can	can	AUX
ejpam-6951	362	21	be	be	AUX
ejpam-6951	362	22	verified	verify	VERB
ejpam-6951	362	23	that	that	SCONJ
ejpam-6951	362	24	bq	bq	PROPN
ejpam-6951	362	25	,	,	PUNCT
ejpam-6951	362	26	b	b	PROPN
ejpam-6951	362	27	∈	∈	PROPN
ejpam-6951	362	28	vkt	vkt	X
ejpam-6951	362	29	(	(	PUNCT
ejpam-6951	362	30	tn	tn	PROPN
ejpam-6951	362	31	,	,	PUNCT
ejpam-6951	362	32	m	m	PROPN
ejpam-6951	362	33	)	)	PUNCT
ejpam-6951	362	34	,	,	PUNCT
ejpam-6951	362	35	as	as	SCONJ
ejpam-6951	362	36	shown	show	VERB
ejpam-6951	362	37	in	in	ADP
ejpam-6951	362	38	figure	figure	NOUN
ejpam-6951	362	39	14	14	NUM
ejpam-6951	362	40	.	.	PUNCT
ejpam-6951	363	1	x2	x2	PROPN
ejpam-6951	363	2	x3	x3	PROPN
ejpam-6951	363	3	x4x5	x4x5	NUM
ejpam-6951	364	1	x6	x6	PROPN
ejpam-6951	364	2	x2t−3	x2t−3	PROPN
ejpam-6951	365	1	x2t−2	x2t−2	PROPN
ejpam-6951	365	2	x2t−1	x2t−1	PROPN
ejpam-6951	366	1	x2	x2	INTJ
ejpam-6951	366	2	t	t	PROPN
ejpam-6951	367	1	xn−1	xn−1	PROPN
ejpam-6951	367	2	xn	xn	PROPN
ejpam-6951	368	1	x1	x1	NUM
ejpam-6951	368	2	y1	y1	NOUN
ejpam-6951	368	3	y2	y2	PROPN
ejpam-6951	368	4	y3	y3	PROPN
ejpam-6951	368	5	y4	y4	NOUN
ejpam-6951	368	6	y5	y5	NOUN
ejpam-6951	368	7	y6	y6	ADJ
ejpam-6951	368	8	y2t−3	y2t−3	NOUN
ejpam-6951	368	9	y2t−2	y2t−2	NOUN
ejpam-6951	368	10	y2t−1	y2t−1	PROPN
ejpam-6951	368	11	ym−1	ym−1	PROPN
ejpam-6951	368	12	ym	ym	PROPN
ejpam-6951	368	13	tn	tn	PROPN
ejpam-6951	368	14	,	,	PUNCT
ejpam-6951	368	15	m⟨bq⟩	m⟨bq⟩	NOUN
ejpam-6951	368	16	:	:	PUNCT
ejpam-6951	369	1	x2	x2	INTJ
ejpam-6951	369	2	x3	x3	PROPN
ejpam-6951	369	3	x4x5	x4x5	NUM
ejpam-6951	370	1	x6	x6	PROPN
ejpam-6951	370	2	x2t−3	x2t−3	PROPN
ejpam-6951	371	1	x2t−2	x2t−2	PROPN
ejpam-6951	371	2	x2t−1	x2t−1	PROPN
ejpam-6951	372	1	x2	x2	INTJ
ejpam-6951	372	2	t	t	PROPN
ejpam-6951	373	1	xn−1	xn−1	PROPN
ejpam-6951	373	2	xn	xn	PROPN
ejpam-6951	374	1	x1	x1	NUM
ejpam-6951	374	2	y1	y1	NOUN
ejpam-6951	374	3	y2	y2	PROPN
ejpam-6951	374	4	y3	y3	NOUN
ejpam-6951	374	5	y4	y4	NOUN
ejpam-6951	374	6	y5	y5	PROPN
ejpam-6951	374	7	y6	y6	ADJ
ejpam-6951	374	8	ym−4	ym−4	PROPN
ejpam-6951	374	9	ym−3	ym−3	PROPN
ejpam-6951	374	10	ym−2	ym−2	PROPN
ejpam-6951	374	11	ym−1	ym−1	PROPN
ejpam-6951	374	12	ym	ym	PROPN
ejpam-6951	374	13	tn	tn	PROPN
ejpam-6951	374	14	,	,	PUNCT
ejpam-6951	374	15	m⟨b⟩	m⟨b⟩	PROPN
ejpam-6951	374	16	:	:	PUNCT
ejpam-6951	374	17	figure	figure	NOUN
ejpam-6951	374	18	14	14	NUM
ejpam-6951	374	19	:	:	PUNCT
ejpam-6951	374	20	illustrating	illustrate	VERB
ejpam-6951	374	21	the	the	DET
ejpam-6951	374	22	subgraphs	subgraph	NOUN
ejpam-6951	374	23	of	of	ADP
ejpam-6951	374	24	tn	tn	NOUN
ejpam-6951	374	25	,	,	PUNCT
ejpam-6951	374	26	m	m	AUX
ejpam-6951	374	27	induced	induce	VERB
ejpam-6951	374	28	by	by	ADP
ejpam-6951	374	29	bq	bq	INTJ
ejpam-6951	374	30	and	and	CCONJ
ejpam-6951	374	31	b	b	NOUN
ejpam-6951	374	32	thus	thus	ADV
ejpam-6951	374	33	,	,	PUNCT
ejpam-6951	374	34	for	for	ADP
ejpam-6951	374	35	j	j	PROPN
ejpam-6951	374	36	=	=	SYM
ejpam-6951	374	37	1	1	NUM
ejpam-6951	374	38	,	,	PUNCT
ejpam-6951	374	39	2	2	NUM
ejpam-6951	374	40	,	,	PUNCT
ejpam-6951	374	41	3	3	NUM
ejpam-6951	374	42	,	,	PUNCT
ejpam-6951	374	43	...	...	PUNCT
ejpam-6951	374	44	,	,	PUNCT
ejpam-6951	374	45	m	m	PRON
ejpam-6951	374	46	,	,	PUNCT
ejpam-6951	374	47	we	we	PRON
ejpam-6951	374	48	get	get	VERB
ejpam-6951	374	49	t−1∑	t−1∑	NUM
ejpam-6951	374	50	q=1	q=1	NOUN
ejpam-6951	374	51	bq	bq	X
ejpam-6951	375	1	+	+	NOUN
ejpam-6951	375	2	b	b	X
ejpam-6951	375	3	=	=	SYM
ejpam-6951	375	4	(	(	PUNCT
ejpam-6951	375	5	b1	b1	NOUN
ejpam-6951	375	6	+	+	NOUN
ejpam-6951	375	7	b2	b2	NOUN
ejpam-6951	375	8	+	+	NOUN
ejpam-6951	375	9	b3	b3	NOUN
ejpam-6951	375	10	+	+	CCONJ
ejpam-6951	375	11	·	·	PUNCT
ejpam-6951	375	12	·	·	PUNCT
ejpam-6951	375	13	·	·	PUNCT
ejpam-6951	375	14	+	+	NOUN
ejpam-6951	375	15	bt−1	bt−1	NOUN
ejpam-6951	375	16	)	)	PUNCT
ejpam-6951	375	17	+	+	NOUN
ejpam-6951	375	18	b	b	NOUN
ejpam-6951	375	19	=	=	SYM
ejpam-6951	375	20	(	(	PUNCT
ejpam-6951	375	21	b1	b1	PROPN
ejpam-6951	375	22	△	△	PROPN
ejpam-6951	375	23	b2	b2	PROPN
ejpam-6951	375	24	△	△	NOUN
ejpam-6951	375	25	b3	b3	PROPN
ejpam-6951	375	26	△	△	X
ejpam-6951	375	27	·	·	PUNCT
ejpam-6951	375	28	·	·	PUNCT
ejpam-6951	375	29	·	·	PUNCT
ejpam-6951	375	30	△	△	X
ejpam-6951	375	31	bt−1)	bt−1)	X
ejpam-6951	375	32	△	△	X
ejpam-6951	375	33	b	b	NOUN
ejpam-6951	375	34	=	=	SYM
ejpam-6951	375	35	{	{	PUNCT
ejpam-6951	375	36	x2	x2	PROPN
ejpam-6951	375	37	,	,	PUNCT
ejpam-6951	375	38	x4	x4	PROPN
ejpam-6951	375	39	,	,	PUNCT
ejpam-6951	375	40	x6	x6	PROPN
ejpam-6951	375	41	,	,	PUNCT
ejpam-6951	375	42	...	...	PUNCT
ejpam-6951	375	43	,	,	PUNCT
ejpam-6951	375	44	x2t−2	x2t−2	PROPN
ejpam-6951	375	45	}	}	PUNCT
ejpam-6951	375	46	△	△	X
ejpam-6951	375	47	{	{	PUNCT
ejpam-6951	375	48	x2	x2	PROPN
ejpam-6951	375	49	,	,	PUNCT
ejpam-6951	375	50	x4	x4	PROPN
ejpam-6951	375	51	,	,	PUNCT
ejpam-6951	375	52	x6	x6	PROPN
ejpam-6951	375	53	,	,	PUNCT
ejpam-6951	375	54	...	...	PUNCT
ejpam-6951	375	55	,	,	PUNCT
ejpam-6951	375	56	x2t−2	x2t−2	PROPN
ejpam-6951	375	57	,	,	PUNCT
ejpam-6951	375	58	yj	yj	PROPN
ejpam-6951	375	59	}	}	PUNCT
ejpam-6951	375	60	=	=	SYM
ejpam-6951	375	61	{	{	PUNCT
ejpam-6951	375	62	yj	yj	PROPN
ejpam-6951	375	63	}	}	PUNCT
ejpam-6951	375	64	.	.	PUNCT
ejpam-6951	376	1	hence	hence	ADV
ejpam-6951	376	2	,	,	PUNCT
ejpam-6951	376	3	{	{	PUNCT
ejpam-6951	376	4	yj	yj	PROPN
ejpam-6951	376	5	}	}	PUNCT
ejpam-6951	376	6	∈	∈	PROPN
ejpam-6951	376	7	vkt	vkt	ADJ
ejpam-6951	376	8	(	(	PUNCT
ejpam-6951	376	9	tn	tn	PROPN
ejpam-6951	376	10	,	,	PUNCT
ejpam-6951	376	11	m	m	NOUN
ejpam-6951	376	12	)	)	PUNCT
ejpam-6951	376	13	for	for	ADP
ejpam-6951	376	14	all	all	PRON
ejpam-6951	376	15	1	1	NUM
ejpam-6951	376	16	≤	≤	NUM
ejpam-6951	376	17	j	j	PROPN
ejpam-6951	376	18	≤	≤	PROPN
ejpam-6951	376	19	m.	m.	NOUN
ejpam-6951	376	20	therefore	therefore	ADV
ejpam-6951	376	21	,	,	PUNCT
ejpam-6951	376	22	by	by	ADP
ejpam-6951	376	23	remark	remark	NOUN
ejpam-6951	376	24	1	1	NUM
ejpam-6951	376	25	,	,	PUNCT
ejpam-6951	376	26	kt	kt	PROPN
ejpam-6951	376	27	is	be	AUX
ejpam-6951	376	28	a	a	DET
ejpam-6951	376	29	vertexgenerator	vertexgenerator	NOUN
ejpam-6951	376	30	subgraph	subgraph	NOUN
ejpam-6951	376	31	of	of	ADP
ejpam-6951	376	32	tn	tn	PROPN
ejpam-6951	376	33	,	,	PUNCT
ejpam-6951	376	34	m.	m.	NOUN
ejpam-6951	376	35	g.	g.	PROPN
ejpam-6951	376	36	d.	d.	PROPN
ejpam-6951	376	37	sepillo	sepillo	PROPN
ejpam-6951	376	38	et	et	PROPN
ejpam-6951	376	39	al	al	PROPN
ejpam-6951	376	40	.	.	PUNCT
ejpam-6951	376	41	/	/	SYM
ejpam-6951	376	42	eur	eur	PROPN
ejpam-6951	376	43	.	.	PUNCT
ejpam-6951	377	1	j.	j.	PROPN
ejpam-6951	377	2	pure	pure	PROPN
ejpam-6951	377	3	appl	appl	PROPN
ejpam-6951	377	4	.	.	PROPN
ejpam-6951	377	5	math	math	PROPN
ejpam-6951	377	6	,	,	PUNCT
ejpam-6951	377	7	18	18	NUM
ejpam-6951	377	8	(	(	PUNCT
ejpam-6951	377	9	4	4	NUM
ejpam-6951	377	10	)	)	PUNCT
ejpam-6951	377	11	(	(	PUNCT
ejpam-6951	377	12	2025	2025	NUM
ejpam-6951	377	13	)	)	PUNCT
ejpam-6951	377	14	,	,	PUNCT
ejpam-6951	377	15	6951	6951	NUM
ejpam-6951	377	16	18	18	NUM
ejpam-6951	377	17	of	of	ADP
ejpam-6951	377	18	23	23	NUM
ejpam-6951	377	19	the	the	DET
ejpam-6951	377	20	next	next	ADJ
ejpam-6951	377	21	theorem	theorem	NOUN
ejpam-6951	377	22	gives	give	VERB
ejpam-6951	377	23	us	we	PRON
ejpam-6951	377	24	a	a	DET
ejpam-6951	377	25	necessary	necessary	ADJ
ejpam-6951	377	26	condition	condition	NOUN
ejpam-6951	377	27	for	for	ADP
ejpam-6951	377	28	the	the	DET
ejpam-6951	377	29	graph	graph	NOUN
ejpam-6951	377	30	kp2	kp2	VERB
ejpam-6951	377	31	⊔k1	⊔k1	X
ejpam-6951	377	32	,	,	PUNCT
ejpam-6951	377	33	which	which	PRON
ejpam-6951	377	34	is	be	AUX
ejpam-6951	377	35	the	the	DET
ejpam-6951	377	36	disjoint	disjoint	PROPN
ejpam-6951	377	37	union	union	NOUN
ejpam-6951	377	38	of	of	ADP
ejpam-6951	377	39	the	the	DET
ejpam-6951	377	40	graph	graph	NOUN
ejpam-6951	377	41	kp2	kp2	VERB
ejpam-6951	377	42	and	and	CCONJ
ejpam-6951	377	43	a	a	DET
ejpam-6951	377	44	trivial	trivial	ADJ
ejpam-6951	377	45	graph	graph	NOUN
ejpam-6951	377	46	k1	k1	NOUN
ejpam-6951	377	47	,	,	PUNCT
ejpam-6951	377	48	to	to	PART
ejpam-6951	377	49	be	be	AUX
ejpam-6951	377	50	a	a	DET
ejpam-6951	377	51	vertex	vertex	NOUN
ejpam-6951	377	52	-	-	PUNCT
ejpam-6951	377	53	generator	generator	NOUN
ejpam-6951	377	54	subgraph	subgraph	NOUN
ejpam-6951	377	55	of	of	ADP
ejpam-6951	377	56	tn	tn	PROPN
ejpam-6951	377	57	,	,	PUNCT
ejpam-6951	377	58	m.	m.	NOUN
ejpam-6951	377	59	theorem	theorem	VERB
ejpam-6951	377	60	16	16	NUM
ejpam-6951	377	61	.	.	PUNCT
ejpam-6951	378	1	let	let	VERB
ejpam-6951	378	2	n	n	PRON
ejpam-6951	378	3	,	,	PUNCT
ejpam-6951	378	4	m	m	VERB
ejpam-6951	378	5	≥	≥	NOUN
ejpam-6951	378	6	3	3	NUM
ejpam-6951	378	7	and	and	CCONJ
ejpam-6951	378	8	k	k	PROPN
ejpam-6951	378	9	be	be	AUX
ejpam-6951	378	10	positive	positive	ADJ
ejpam-6951	378	11	integers	integer	NOUN
ejpam-6951	378	12	.	.	PUNCT
ejpam-6951	379	1	if	if	SCONJ
ejpam-6951	379	2	3k	3k	PRON
ejpam-6951	379	3	≤	≤	NUM
ejpam-6951	379	4	min{n	min{n	NOUN
ejpam-6951	379	5	,	,	PUNCT
ejpam-6951	379	6	m	m	NOUN
ejpam-6951	379	7	}	}	PUNCT
ejpam-6951	379	8	,	,	PUNCT
ejpam-6951	379	9	then	then	ADV
ejpam-6951	379	10	kp2	kp2	VERB
ejpam-6951	379	11	⊔k1	⊔k1	X
ejpam-6951	379	12	is	be	AUX
ejpam-6951	379	13	a	a	DET
ejpam-6951	379	14	vertex	vertex	NOUN
ejpam-6951	379	15	-	-	PUNCT
ejpam-6951	379	16	generator	generator	NOUN
ejpam-6951	379	17	subgraph	subgraph	NOUN
ejpam-6951	379	18	of	of	ADP
ejpam-6951	379	19	tn	tn	PROPN
ejpam-6951	379	20	,	,	PUNCT
ejpam-6951	379	21	m.	m.	NOUN
ejpam-6951	379	22	proof	proof	NOUN
ejpam-6951	379	23	.	.	PUNCT
ejpam-6951	380	1	let	let	VERB
ejpam-6951	380	2	3k	3k	PRON
ejpam-6951	380	3	≤	≤	NUM
ejpam-6951	380	4	min{n	min{n	NOUN
ejpam-6951	380	5	,	,	PUNCT
ejpam-6951	380	6	m	m	NOUN
ejpam-6951	380	7	}	}	PUNCT
ejpam-6951	380	8	.	.	PUNCT
ejpam-6951	381	1	then	then	ADV
ejpam-6951	381	2	,	,	PUNCT
ejpam-6951	381	3	for	for	ADP
ejpam-6951	381	4	any	any	DET
ejpam-6951	381	5	1	1	NUM
ejpam-6951	381	6	≤	≤	NUM
ejpam-6951	381	7	i	i	PRON
ejpam-6951	381	8	≤	≤	PROPN
ejpam-6951	381	9	n	n	CCONJ
ejpam-6951	381	10	,	,	PUNCT
ejpam-6951	381	11	let	let	VERB
ejpam-6951	381	12	xi	xi	PRON
ejpam-6951	381	13	be	be	AUX
ejpam-6951	381	14	an	an	DET
ejpam-6951	381	15	arbitrary	arbitrary	ADJ
ejpam-6951	381	16	vertex	vertex	NOUN
ejpam-6951	381	17	of	of	ADP
ejpam-6951	381	18	cn	cn	PROPN
ejpam-6951	381	19	in	in	ADP
ejpam-6951	381	20	the	the	DET
ejpam-6951	381	21	tadpole	tadpole	NOUN
ejpam-6951	381	22	graph	graph	PROPN
ejpam-6951	381	23	tn	tn	PROPN
ejpam-6951	381	24	,	,	PUNCT
ejpam-6951	381	25	m	m	PROPN
ejpam-6951	381	26	,	,	PUNCT
ejpam-6951	381	27	and	and	CCONJ
ejpam-6951	381	28	for	for	ADP
ejpam-6951	381	29	any	any	DET
ejpam-6951	381	30	1	1	NUM
ejpam-6951	381	31	≤	≤	NOUN
ejpam-6951	381	32	p	p	NOUN
ejpam-6951	381	33	≤	≤	PUNCT
ejpam-6951	381	34	k	k	NOUN
ejpam-6951	381	35	,	,	PUNCT
ejpam-6951	381	36	let	let	AUX
ejpam-6951	381	37	a2p−1	a2p−1	VERB
ejpam-6951	381	38	,	,	PUNCT
ejpam-6951	381	39	a2p	a2p	NOUN
ejpam-6951	381	40	and	and	CCONJ
ejpam-6951	381	41	a	a	PRON
ejpam-6951	381	42	be	be	AUX
ejpam-6951	381	43	defined	define	VERB
ejpam-6951	381	44	as	as	SCONJ
ejpam-6951	381	45	follows	follow	VERB
ejpam-6951	381	46	:	:	PUNCT
ejpam-6951	382	1	a2p−1	a2p−1	PROPN
ejpam-6951	382	2	=	=	PUNCT
ejpam-6951	382	3	{	{	PUNCT
ejpam-6951	382	4	k	k	X
ejpam-6951	382	5	copies	copy	NOUN
ejpam-6951	382	6	of	of	ADP
ejpam-6951	382	7	p2︷	p2︷	PROPN
ejpam-6951	382	8	︸︸	︸︸	PUNCT
ejpam-6951	382	9	︷	︷	PROPN
ejpam-6951	382	10	p2︷	p2︷	X
ejpam-6951	382	11	︸︸	︸︸	PUNCT
ejpam-6951	382	12	︷	︷	PROPN
ejpam-6951	382	13	x2	x2	ADJ
ejpam-6951	382	14	,	,	PUNCT
ejpam-6951	382	15	x3	x3	ADJ
ejpam-6951	382	16	,	,	PUNCT
ejpam-6951	382	17	p2︷	p2︷	X
ejpam-6951	382	18	︸︸	︸︸	PUNCT
ejpam-6951	382	19	︷	︷	PROPN
ejpam-6951	382	20	x5	x5	PROPN
ejpam-6951	382	21	,	,	PUNCT
ejpam-6951	382	22	x6	x6	PROPN
ejpam-6951	382	23	,	,	PUNCT
ejpam-6951	382	24	...	...	PUNCT
ejpam-6951	382	25	,	,	PUNCT
ejpam-6951	382	26	p2︷	p2︷	PROPN
ejpam-6951	382	27	︸︸	︸︸	PUNCT
ejpam-6951	382	28	︷	︷	PROPN
ejpam-6951	382	29	x3k−1	x3k−1	PROPN
ejpam-6951	382	30	,	,	PUNCT
ejpam-6951	382	31	x3k	x3k	NOUN
ejpam-6951	382	32	,	,	PUNCT
ejpam-6951	382	33	y3p−1	y3p−1	PROPN
ejpam-6951	382	34	}	}	PUNCT
ejpam-6951	382	35	where	where	SCONJ
ejpam-6951	382	36	1	1	NUM
ejpam-6951	382	37	≤	≤	NOUN
ejpam-6951	382	38	p	p	NOUN
ejpam-6951	382	39	≤	≤	ADJ
ejpam-6951	382	40	k	k	NOUN
ejpam-6951	382	41	,	,	PUNCT
ejpam-6951	382	42	a2p	a2p	NOUN
ejpam-6951	382	43	=	=	SYM
ejpam-6951	382	44	a2p−1	a2p−1	PROPN
ejpam-6951	382	45	\	\	PROPN
ejpam-6951	382	46	{	{	PUNCT
ejpam-6951	382	47	y3p−1	y3p−1	NOUN
ejpam-6951	382	48	}	}	PUNCT
ejpam-6951	382	49	∪	∪	NOUN
ejpam-6951	382	50	{	{	PUNCT
ejpam-6951	382	51	y3p	y3p	NOUN
ejpam-6951	382	52	}	}	PUNCT
ejpam-6951	382	53	where	where	SCONJ
ejpam-6951	382	54	1	1	NUM
ejpam-6951	382	55	≤	≤	NOUN
ejpam-6951	382	56	p	p	NOUN
ejpam-6951	382	57	≤	≤	ADJ
ejpam-6951	382	58	k	k	NOUN
ejpam-6951	382	59	,	,	PUNCT
ejpam-6951	382	60	and	and	CCONJ
ejpam-6951	382	61	a	a	DET
ejpam-6951	382	62	=	=	X
ejpam-6951	382	63	{	{	PUNCT
ejpam-6951	382	64	xi	xi	PROPN
ejpam-6951	382	65	,	,	PUNCT
ejpam-6951	382	66	k	k	PROPN
ejpam-6951	382	67	copies	copy	NOUN
ejpam-6951	382	68	of	of	ADP
ejpam-6951	382	69	p2︷	p2︷	PROPN
ejpam-6951	382	70	︸︸	︸︸	PUNCT
ejpam-6951	382	71	︷	︷	PROPN
ejpam-6951	382	72	p2︷	p2︷	X
ejpam-6951	382	73	︸︸	︸︸	PUNCT
ejpam-6951	382	74	︷	︷	PROPN
ejpam-6951	383	1	y2	y2	NOUN
ejpam-6951	383	2	,	,	PUNCT
ejpam-6951	383	3	y3	y3	PROPN
ejpam-6951	383	4	,	,	PUNCT
ejpam-6951	383	5	p2︷	p2︷	X
ejpam-6951	383	6	︸︸	︸︸	PUNCT
ejpam-6951	383	7	︷	︷	X
ejpam-6951	383	8	y5	y5	VERB
ejpam-6951	383	9	,	,	PUNCT
ejpam-6951	383	10	y6	y6	ADJ
ejpam-6951	383	11	,	,	PUNCT
ejpam-6951	383	12	...	...	PUNCT
ejpam-6951	383	13	,	,	PUNCT
ejpam-6951	383	14	p2︷	p2︷	PROPN
ejpam-6951	383	15	︸︸	︸︸	PUNCT
ejpam-6951	383	16	︷	︷	PROPN
ejpam-6951	383	17	y3k−1	y3k−1	NOUN
ejpam-6951	383	18	,	,	PUNCT
ejpam-6951	383	19	y3k	y3k	NOUN
ejpam-6951	383	20	}	}	PUNCT
ejpam-6951	383	21	where	where	SCONJ
ejpam-6951	383	22	1	1	NUM
ejpam-6951	383	23	≤	≤	NUM
ejpam-6951	383	24	i	i	PRON
ejpam-6951	383	25	≤	≤	NUM
ejpam-6951	383	26	n.	n.	NOUN
ejpam-6951	383	27	it	it	PRON
ejpam-6951	383	28	can	can	AUX
ejpam-6951	383	29	be	be	AUX
ejpam-6951	383	30	verified	verify	VERB
ejpam-6951	383	31	that	that	SCONJ
ejpam-6951	383	32	that	that	DET
ejpam-6951	383	33	a2p−1	a2p−1	PROPN
ejpam-6951	383	34	,	,	PUNCT
ejpam-6951	383	35	a2p	a2p	NOUN
ejpam-6951	383	36	,	,	PUNCT
ejpam-6951	383	37	a	a	DET
ejpam-6951	383	38	∈	∈	PROPN
ejpam-6951	383	39	vkp2⊔k1(tn	vkp2⊔k1(tn	NOUN
ejpam-6951	383	40	,	,	PUNCT
ejpam-6951	383	41	m	m	NOUN
ejpam-6951	383	42	)	)	PUNCT
ejpam-6951	383	43	,	,	PUNCT
ejpam-6951	383	44	as	as	SCONJ
ejpam-6951	383	45	shown	show	VERB
ejpam-6951	383	46	in	in	ADP
ejpam-6951	383	47	figure	figure	NOUN
ejpam-6951	383	48	15	15	NUM
ejpam-6951	383	49	.	.	PUNCT
ejpam-6951	384	1	thus	thus	ADV
ejpam-6951	384	2	,	,	PUNCT
ejpam-6951	384	3	for	for	ADP
ejpam-6951	384	4	i	i	PROPN
ejpam-6951	384	5	=	=	SYM
ejpam-6951	384	6	1	1	NUM
ejpam-6951	384	7	,	,	PUNCT
ejpam-6951	384	8	2	2	NUM
ejpam-6951	384	9	,	,	PUNCT
ejpam-6951	384	10	3	3	NUM
ejpam-6951	384	11	,	,	PUNCT
ejpam-6951	384	12	...	...	PUNCT
ejpam-6951	384	13	,	,	PUNCT
ejpam-6951	384	14	n	n	CCONJ
ejpam-6951	384	15	,	,	PUNCT
ejpam-6951	384	16	we	we	PRON
ejpam-6951	384	17	obtain	obtain	VERB
ejpam-6951	384	18	k∑	k∑	ADJ
ejpam-6951	385	1	p=1	p=1	X
ejpam-6951	386	1	a2p−1	a2p−1	PROPN
ejpam-6951	386	2	+	+	CCONJ
ejpam-6951	386	3	k∑	k∑	ADJ
ejpam-6951	386	4	p=1	p=1	PROPN
ejpam-6951	386	5	a2p	a2p	NOUN
ejpam-6951	386	6	+	+	NOUN
ejpam-6951	386	7	a	a	NOUN
ejpam-6951	386	8	=	=	PUNCT
ejpam-6951	386	9	(	(	PUNCT
ejpam-6951	386	10	a1	a1	NOUN
ejpam-6951	386	11	+	+	NOUN
ejpam-6951	386	12	a3	a3	NOUN
ejpam-6951	386	13	+	+	X
ejpam-6951	386	14	·	·	PUNCT
ejpam-6951	386	15	·	·	PUNCT
ejpam-6951	386	16	·	·	PUNCT
ejpam-6951	386	17	+	+	NOUN
ejpam-6951	386	18	a2k−1	a2k−1	PROPN
ejpam-6951	386	19	)	)	PUNCT
ejpam-6951	387	1	+	+	CCONJ
ejpam-6951	387	2	(	(	PUNCT
ejpam-6951	387	3	a2	a2	NOUN
ejpam-6951	387	4	+	+	NOUN
ejpam-6951	387	5	a4	a4	NOUN
ejpam-6951	387	6	+	+	NUM
ejpam-6951	387	7	·	·	PUNCT
ejpam-6951	387	8	·	·	PUNCT
ejpam-6951	387	9	·	·	PUNCT
ejpam-6951	387	10	+	+	ADJ
ejpam-6951	387	11	a2k	a2k	X
ejpam-6951	387	12	)	)	PUNCT
ejpam-6951	387	13	+	+	ADP
ejpam-6951	387	14	a	a	PRON
ejpam-6951	387	15	=	=	X
ejpam-6951	387	16	(	(	PUNCT
ejpam-6951	387	17	a1	a1	NOUN
ejpam-6951	387	18	+	+	PROPN
ejpam-6951	387	19	a2	a2	PROPN
ejpam-6951	387	20	+	+	NOUN
ejpam-6951	387	21	a3	a3	NOUN
ejpam-6951	387	22	+	+	NOUN
ejpam-6951	387	23	a4	a4	NOUN
ejpam-6951	387	24	+	+	NUM
ejpam-6951	387	25	·	·	PUNCT
ejpam-6951	387	26	·	·	PUNCT
ejpam-6951	387	27	·	·	PUNCT
ejpam-6951	388	1	+	+	PROPN
ejpam-6951	388	2	a2k−1	a2k−1	PROPN
ejpam-6951	388	3	+	+	PROPN
ejpam-6951	388	4	a2k	a2k	ADJ
ejpam-6951	388	5	)	)	PUNCT
ejpam-6951	388	6	+	+	ADP
ejpam-6951	388	7	a	a	PRON
ejpam-6951	388	8	=	=	PUNCT
ejpam-6951	388	9	(	(	PUNCT
ejpam-6951	388	10	a1	a1	PROPN
ejpam-6951	388	11	△	△	PROPN
ejpam-6951	388	12	a2	a2	PROPN
ejpam-6951	388	13	△	△	PROPN
ejpam-6951	388	14	a3	a3	NOUN
ejpam-6951	388	15	△	△	X
ejpam-6951	388	16	a4	a4	X
ejpam-6951	388	17	△	△	X
ejpam-6951	388	18	·	·	PUNCT
ejpam-6951	388	19	·	·	PUNCT
ejpam-6951	388	20	·	·	PUNCT
ejpam-6951	388	21	△	△	X
ejpam-6951	388	22	a2k−1	a2k−1	PROPN
ejpam-6951	388	23	△	△	PROPN
ejpam-6951	388	24	a2k)	a2k)	NOUN
ejpam-6951	388	25	△	△	X
ejpam-6951	388	26	a	a	PRON
ejpam-6951	388	27	=	=	X
ejpam-6951	388	28	{	{	PUNCT
ejpam-6951	388	29	y2	y2	PROPN
ejpam-6951	388	30	,	,	PUNCT
ejpam-6951	388	31	y3	y3	PROPN
ejpam-6951	388	32	,	,	PUNCT
ejpam-6951	388	33	y5	y5	PROPN
ejpam-6951	388	34	,	,	PUNCT
ejpam-6951	388	35	y6	y6	ADJ
ejpam-6951	388	36	,	,	PUNCT
ejpam-6951	388	37	...	...	PUNCT
ejpam-6951	388	38	,	,	PUNCT
ejpam-6951	388	39	y3k−1	y3k−1	PROPN
ejpam-6951	388	40	,	,	PUNCT
ejpam-6951	388	41	y3k	y3k	NOUN
ejpam-6951	388	42	}	}	PUNCT
ejpam-6951	388	43	△	△	X
ejpam-6951	388	44	{	{	PUNCT
ejpam-6951	388	45	xi	xi	PROPN
ejpam-6951	388	46	,	,	PUNCT
ejpam-6951	388	47	y2	y2	PROPN
ejpam-6951	388	48	,	,	PUNCT
ejpam-6951	388	49	y3	y3	PROPN
ejpam-6951	388	50	,	,	PUNCT
ejpam-6951	388	51	y5	y5	PROPN
ejpam-6951	388	52	,	,	PUNCT
ejpam-6951	388	53	y6	y6	ADJ
ejpam-6951	388	54	,	,	PUNCT
ejpam-6951	388	55	...	...	PUNCT
ejpam-6951	388	56	,	,	PUNCT
ejpam-6951	388	57	y3k−1	y3k−1	PROPN
ejpam-6951	388	58	,	,	PUNCT
ejpam-6951	388	59	y3k	y3k	NOUN
ejpam-6951	388	60	}	}	PUNCT
ejpam-6951	388	61	=	=	PUNCT
ejpam-6951	388	62	{	{	PUNCT
ejpam-6951	388	63	xi	xi	X
ejpam-6951	388	64	}	}	PUNCT
ejpam-6951	388	65	.	.	PUNCT
ejpam-6951	389	1	hence	hence	ADV
ejpam-6951	389	2	,	,	PUNCT
ejpam-6951	389	3	{	{	PUNCT
ejpam-6951	389	4	xi	xi	PROPN
ejpam-6951	389	5	}	}	PUNCT
ejpam-6951	389	6	∈	∈	PROPN
ejpam-6951	389	7	vkp2⊔k1(tn	vkp2⊔k1(tn	NOUN
ejpam-6951	389	8	,	,	PUNCT
ejpam-6951	389	9	m	m	NOUN
ejpam-6951	389	10	)	)	PUNCT
ejpam-6951	389	11	for	for	ADP
ejpam-6951	389	12	all	all	DET
ejpam-6951	389	13	1	1	NUM
ejpam-6951	389	14	≤	≤	NUM
ejpam-6951	389	15	i	i	PRON
ejpam-6951	389	16	≤	≤	ADJ
ejpam-6951	389	17	n.	n.	NOUN
ejpam-6951	389	18	similarly	similarly	ADV
ejpam-6951	389	19	,	,	PUNCT
ejpam-6951	389	20	for	for	ADP
ejpam-6951	389	21	any	any	DET
ejpam-6951	389	22	1	1	NUM
ejpam-6951	389	23	≤	≤	NUM
ejpam-6951	389	24	j	j	PROPN
ejpam-6951	389	25	≤	≤	PROPN
ejpam-6951	389	26	m	m	ADP
ejpam-6951	389	27	,	,	PUNCT
ejpam-6951	389	28	let	let	VERB
ejpam-6951	389	29	yj	yj	PRON
ejpam-6951	389	30	be	be	AUX
ejpam-6951	389	31	an	an	DET
ejpam-6951	389	32	arbitrary	arbitrary	ADJ
ejpam-6951	389	33	vertex	vertex	NOUN
ejpam-6951	389	34	of	of	ADP
ejpam-6951	389	35	pm	pm	NOUN
ejpam-6951	389	36	in	in	ADP
ejpam-6951	389	37	the	the	DET
ejpam-6951	389	38	tadpole	tadpole	NOUN
ejpam-6951	389	39	graph	graph	PROPN
ejpam-6951	389	40	tn	tn	PROPN
ejpam-6951	389	41	,	,	PUNCT
ejpam-6951	389	42	m	m	PROPN
ejpam-6951	389	43	,	,	PUNCT
ejpam-6951	389	44	and	and	CCONJ
ejpam-6951	389	45	for	for	ADP
ejpam-6951	389	46	any	any	DET
ejpam-6951	389	47	j	j	NOUN
ejpam-6951	389	48	where	where	SCONJ
ejpam-6951	389	49	1	1	NUM
ejpam-6951	389	50	≤	≤	NOUN
ejpam-6951	389	51	q	q	PROPN
ejpam-6951	389	52	≤	≤	NUM
ejpam-6951	389	53	k	k	NOUN
ejpam-6951	389	54	,	,	PUNCT
ejpam-6951	389	55	let	let	VERB
ejpam-6951	389	56	b2q−1	b2q−1	PROPN
ejpam-6951	389	57	,	,	PUNCT
ejpam-6951	389	58	b2q	b2q	PROPN
ejpam-6951	389	59	and	and	CCONJ
ejpam-6951	389	60	b	b	AUX
ejpam-6951	389	61	be	be	AUX
ejpam-6951	389	62	defined	define	VERB
ejpam-6951	389	63	as	as	SCONJ
ejpam-6951	389	64	follows	follow	VERB
ejpam-6951	389	65	:	:	PUNCT
ejpam-6951	390	1	b2q−1	b2q−1	PROPN
ejpam-6951	390	2	=	=	PUNCT
ejpam-6951	390	3	{	{	PUNCT
ejpam-6951	390	4	x3q−1	x3q−1	PROPN
ejpam-6951	390	5	,	,	PUNCT
ejpam-6951	390	6	k	k	PROPN
ejpam-6951	390	7	copies	copy	NOUN
ejpam-6951	390	8	of	of	ADP
ejpam-6951	390	9	p2︷	p2︷	PROPN
ejpam-6951	390	10	︸︸	︸︸	PUNCT
ejpam-6951	390	11	︷	︷	PROPN
ejpam-6951	390	12	p2︷	p2︷	X
ejpam-6951	390	13	︸︸	︸︸	PUNCT
ejpam-6951	390	14	︷	︷	PROPN
ejpam-6951	391	1	y2	y2	NOUN
ejpam-6951	391	2	,	,	PUNCT
ejpam-6951	391	3	y3	y3	PROPN
ejpam-6951	391	4	,	,	PUNCT
ejpam-6951	391	5	p2︷	p2︷	X
ejpam-6951	391	6	︸︸	︸︸	PUNCT
ejpam-6951	391	7	︷	︷	X
ejpam-6951	391	8	y5	y5	VERB
ejpam-6951	391	9	,	,	PUNCT
ejpam-6951	391	10	y6	y6	ADJ
ejpam-6951	391	11	,	,	PUNCT
ejpam-6951	391	12	...	...	PUNCT
ejpam-6951	391	13	,	,	PUNCT
ejpam-6951	391	14	p2︷	p2︷	PROPN
ejpam-6951	391	15	︸︸	︸︸	PUNCT
ejpam-6951	391	16	︷	︷	PROPN
ejpam-6951	391	17	y3k−1	y3k−1	NOUN
ejpam-6951	391	18	,	,	PUNCT
ejpam-6951	391	19	y3k	y3k	NOUN
ejpam-6951	391	20	}	}	PUNCT
ejpam-6951	391	21	where	where	SCONJ
ejpam-6951	391	22	1	1	NUM
ejpam-6951	391	23	≤	≤	NOUN
ejpam-6951	391	24	q	q	PROPN
ejpam-6951	391	25	≤	≤	NUM
ejpam-6951	391	26	k	k	NOUN
ejpam-6951	391	27	,	,	PUNCT
ejpam-6951	391	28	b2q	b2q	X
ejpam-6951	391	29	=	=	PROPN
ejpam-6951	391	30	b2q−1	b2q−1	PROPN
ejpam-6951	391	31	\	\	PROPN
ejpam-6951	391	32	{	{	PUNCT
ejpam-6951	391	33	x3q−1	x3q−1	PROPN
ejpam-6951	391	34	}	}	PUNCT
ejpam-6951	391	35	∪	∪	X
ejpam-6951	391	36	{	{	PUNCT
ejpam-6951	391	37	x3q	x3q	NOUN
ejpam-6951	391	38	}	}	PUNCT
ejpam-6951	391	39	where	where	SCONJ
ejpam-6951	391	40	1	1	NUM
ejpam-6951	391	41	≤	≤	NOUN
ejpam-6951	391	42	q	q	PROPN
ejpam-6951	391	43	≤	≤	NUM
ejpam-6951	391	44	k	k	NOUN
ejpam-6951	391	45	,	,	PUNCT
ejpam-6951	391	46	and	and	CCONJ
ejpam-6951	391	47	b	b	X
ejpam-6951	391	48	=	=	PRON
ejpam-6951	391	49	{	{	PUNCT
ejpam-6951	391	50	k	k	X
ejpam-6951	391	51	copies	copy	NOUN
ejpam-6951	391	52	of	of	ADP
ejpam-6951	391	53	p2︷	p2︷	PROPN
ejpam-6951	391	54	︸︸	︸︸	PUNCT
ejpam-6951	391	55	︷	︷	PROPN
ejpam-6951	391	56	p2︷	p2︷	X
ejpam-6951	391	57	︸︸	︸︸	PUNCT
ejpam-6951	391	58	︷	︷	PROPN
ejpam-6951	392	1	x2	x2	ADJ
ejpam-6951	392	2	,	,	PUNCT
ejpam-6951	392	3	x3	x3	ADJ
ejpam-6951	392	4	,	,	PUNCT
ejpam-6951	392	5	p2︷	p2︷	X
ejpam-6951	392	6	︸︸	︸︸	PUNCT
ejpam-6951	392	7	︷	︷	PROPN
ejpam-6951	392	8	x5	x5	PROPN
ejpam-6951	392	9	,	,	PUNCT
ejpam-6951	392	10	x6	x6	PROPN
ejpam-6951	392	11	,	,	PUNCT
ejpam-6951	392	12	...	...	PUNCT
ejpam-6951	392	13	,	,	PUNCT
ejpam-6951	392	14	p2︷	p2︷	PROPN
ejpam-6951	392	15	︸︸	︸︸	PUNCT
ejpam-6951	392	16	︷	︷	PROPN
ejpam-6951	393	1	x3k−1	x3k−1	PROPN
ejpam-6951	393	2	,	,	PUNCT
ejpam-6951	393	3	x3k	x3k	PROPN
ejpam-6951	393	4	,	,	PUNCT
ejpam-6951	393	5	yj	yj	PROPN
ejpam-6951	393	6	}	}	PUNCT
ejpam-6951	393	7	where	where	SCONJ
ejpam-6951	393	8	1	1	NUM
ejpam-6951	393	9	≤	≤	NUM
ejpam-6951	393	10	j	j	PROPN
ejpam-6951	393	11	≤	≤	PROPN
ejpam-6951	393	12	m.	m.	NOUN
ejpam-6951	393	13	it	it	PRON
ejpam-6951	393	14	can	can	AUX
ejpam-6951	393	15	be	be	AUX
ejpam-6951	393	16	verified	verify	VERB
ejpam-6951	393	17	that	that	SCONJ
ejpam-6951	393	18	b2q−1	b2q−1	PROPN
ejpam-6951	393	19	,	,	PUNCT
ejpam-6951	393	20	b2q	b2q	PROPN
ejpam-6951	393	21	,	,	PUNCT
ejpam-6951	393	22	b	b	PROPN
ejpam-6951	393	23	∈	∈	PROPN
ejpam-6951	393	24	vkp2⊔k1(tn	vkp2⊔k1(tn	PROPN
ejpam-6951	393	25	,	,	PUNCT
ejpam-6951	393	26	m	m	NOUN
ejpam-6951	393	27	)	)	PUNCT
ejpam-6951	393	28	,	,	PUNCT
ejpam-6951	393	29	as	as	SCONJ
ejpam-6951	393	30	shown	show	VERB
ejpam-6951	393	31	in	in	ADP
ejpam-6951	393	32	figure	figure	NOUN
ejpam-6951	393	33	16	16	NUM
ejpam-6951	393	34	.	.	PUNCT
ejpam-6951	394	1	g.	g.	PROPN
ejpam-6951	394	2	d.	d.	PROPN
ejpam-6951	394	3	sepillo	sepillo	PROPN
ejpam-6951	394	4	et	et	PROPN
ejpam-6951	394	5	al	al	PROPN
ejpam-6951	394	6	.	.	PUNCT
ejpam-6951	394	7	/	/	SYM
ejpam-6951	394	8	eur	eur	PROPN
ejpam-6951	394	9	.	.	PUNCT
ejpam-6951	395	1	j.	j.	PROPN
ejpam-6951	395	2	pure	pure	PROPN
ejpam-6951	395	3	appl	appl	PROPN
ejpam-6951	395	4	.	.	PROPN
ejpam-6951	395	5	math	math	PROPN
ejpam-6951	395	6	,	,	PUNCT
ejpam-6951	395	7	18	18	NUM
ejpam-6951	395	8	(	(	PUNCT
ejpam-6951	395	9	4	4	NUM
ejpam-6951	395	10	)	)	PUNCT
ejpam-6951	395	11	(	(	PUNCT
ejpam-6951	395	12	2025	2025	NUM
ejpam-6951	395	13	)	)	PUNCT
ejpam-6951	395	14	,	,	PUNCT
ejpam-6951	395	15	6951	6951	NUM
ejpam-6951	395	16	19	19	NUM
ejpam-6951	395	17	of	of	ADP
ejpam-6951	395	18	23	23	NUM
ejpam-6951	396	1	x2	x2	NUM
ejpam-6951	396	2	x3	x3	PROPN
ejpam-6951	396	3	x4x5	x4x5	NUM
ejpam-6951	397	1	x6	x6	PROPN
ejpam-6951	397	2	x3k−2	x3k−2	PROPN
ejpam-6951	397	3	x3k−1	x3k−1	PROPN
ejpam-6951	397	4	x3k	x3k	PROPN
ejpam-6951	398	1	x3k+1	x3k+1	SCONJ
ejpam-6951	399	1	xn−1	xn−1	PROPN
ejpam-6951	399	2	xn	xn	PROPN
ejpam-6951	400	1	x1	x1	NUM
ejpam-6951	400	2	y1	y1	NOUN
ejpam-6951	400	3	y2	y2	PROPN
ejpam-6951	400	4	y3	y3	NOUN
ejpam-6951	400	5	y4	y4	NOUN
ejpam-6951	400	6	y5	y5	PROPN
ejpam-6951	400	7	y6	y6	PROPN
ejpam-6951	400	8	y3k−2	y3k−2	PROPN
ejpam-6951	400	9	y3k−1	y3k−1	PROPN
ejpam-6951	400	10	y3k	y3k	VERB
ejpam-6951	400	11	ym−1	ym−1	PROPN
ejpam-6951	400	12	ym	ym	PROPN
ejpam-6951	400	13	tn	tn	PROPN
ejpam-6951	400	14	,	,	PUNCT
ejpam-6951	400	15	m⟨a2p−1⟩	m⟨a2p−1⟩	PROPN
ejpam-6951	400	16	:	:	PUNCT
ejpam-6951	400	17	x2	x2	PROPN
ejpam-6951	400	18	x3	x3	PROPN
ejpam-6951	400	19	x4x5	x4x5	NUM
ejpam-6951	401	1	x6	x6	PROPN
ejpam-6951	401	2	x3k−2	x3k−2	PROPN
ejpam-6951	401	3	x3k−1	x3k−1	PROPN
ejpam-6951	401	4	x3k	x3k	PROPN
ejpam-6951	402	1	x3k+1	x3k+1	SCONJ
ejpam-6951	403	1	xn−1	xn−1	PROPN
ejpam-6951	403	2	xn	xn	PROPN
ejpam-6951	404	1	x1	x1	NUM
ejpam-6951	404	2	y1	y1	NOUN
ejpam-6951	404	3	y2	y2	PROPN
ejpam-6951	404	4	y3	y3	NOUN
ejpam-6951	404	5	y4	y4	NOUN
ejpam-6951	404	6	y5	y5	PROPN
ejpam-6951	404	7	y6	y6	PROPN
ejpam-6951	404	8	y3k−2	y3k−2	PROPN
ejpam-6951	404	9	y3k−1	y3k−1	PROPN
ejpam-6951	404	10	y3k	y3k	VERB
ejpam-6951	404	11	ym−1	ym−1	PROPN
ejpam-6951	404	12	ym	ym	PROPN
ejpam-6951	404	13	tn	tn	PROPN
ejpam-6951	404	14	,	,	PUNCT
ejpam-6951	404	15	m⟨a2p⟩	m⟨a2p⟩	PROPN
ejpam-6951	404	16	:	:	PUNCT
ejpam-6951	405	1	x2	x2	PROPN
ejpam-6951	405	2	x3	x3	PROPN
ejpam-6951	405	3	x4x5	x4x5	NUM
ejpam-6951	405	4	x6	x6	PROPN
ejpam-6951	405	5	xn−5	xn−5	PROPN
ejpam-6951	405	6	xn−4	xn−4	PROPN
ejpam-6951	405	7	xn−3xn−2	xn−3xn−2	PROPN
ejpam-6951	406	1	xn−1	xn−1	PROPN
ejpam-6951	406	2	xn	xn	PROPN
ejpam-6951	407	1	x1	x1	NUM
ejpam-6951	407	2	y1	y1	NOUN
ejpam-6951	407	3	y2	y2	PROPN
ejpam-6951	407	4	y3	y3	NOUN
ejpam-6951	407	5	y4	y4	NOUN
ejpam-6951	407	6	y5	y5	PROPN
ejpam-6951	407	7	y6	y6	PROPN
ejpam-6951	407	8	y3k−2	y3k−2	PROPN
ejpam-6951	407	9	y3k−1	y3k−1	PROPN
ejpam-6951	407	10	y3k	y3k	VERB
ejpam-6951	407	11	ym−1	ym−1	PROPN
ejpam-6951	407	12	ym	ym	PROPN
ejpam-6951	407	13	tn	tn	PROPN
ejpam-6951	407	14	,	,	PUNCT
ejpam-6951	407	15	m⟨a⟩	m⟨a⟩	NOUN
ejpam-6951	407	16	:	:	PUNCT
ejpam-6951	407	17	figure	figure	NOUN
ejpam-6951	407	18	15	15	NUM
ejpam-6951	407	19	:	:	PUNCT
ejpam-6951	407	20	illustrating	illustrate	VERB
ejpam-6951	407	21	the	the	DET
ejpam-6951	407	22	subgraphs	subgraph	NOUN
ejpam-6951	407	23	of	of	ADP
ejpam-6951	407	24	tn	tn	NOUN
ejpam-6951	407	25	,	,	PUNCT
ejpam-6951	407	26	m	m	AUX
ejpam-6951	407	27	induced	induce	VERB
ejpam-6951	407	28	by	by	ADP
ejpam-6951	407	29	a2p−1	a2p−1	PROPN
ejpam-6951	407	30	,	,	PUNCT
ejpam-6951	407	31	a2p	a2p	NOUN
ejpam-6951	407	32	,	,	PUNCT
ejpam-6951	407	33	and	and	CCONJ
ejpam-6951	407	34	a	a	DET
ejpam-6951	407	35	thus	thus	ADV
ejpam-6951	407	36	,	,	PUNCT
ejpam-6951	407	37	for	for	ADP
ejpam-6951	407	38	j	j	PROPN
ejpam-6951	407	39	=	=	SYM
ejpam-6951	407	40	1	1	NUM
ejpam-6951	407	41	,	,	PUNCT
ejpam-6951	407	42	2	2	NUM
ejpam-6951	407	43	,	,	PUNCT
ejpam-6951	407	44	3	3	NUM
ejpam-6951	407	45	,	,	PUNCT
ejpam-6951	407	46	...	...	PUNCT
ejpam-6951	407	47	,	,	PUNCT
ejpam-6951	407	48	m	m	PRON
ejpam-6951	407	49	,	,	PUNCT
ejpam-6951	407	50	we	we	PRON
ejpam-6951	407	51	have	have	AUX
ejpam-6951	407	52	k∑	k∑	VERB
ejpam-6951	407	53	q=1	q=1	PROPN
ejpam-6951	408	1	b2q−1	b2q−1	PROPN
ejpam-6951	408	2	+	+	CCONJ
ejpam-6951	408	3	k∑	k∑	VERB
ejpam-6951	408	4	q=1	q=1	PUNCT
ejpam-6951	409	1	b2q	b2q	X
ejpam-6951	410	1	+	+	NOUN
ejpam-6951	410	2	b	b	X
ejpam-6951	410	3	=	=	SYM
ejpam-6951	410	4	(	(	PUNCT
ejpam-6951	410	5	b1	b1	NOUN
ejpam-6951	410	6	+	+	NOUN
ejpam-6951	410	7	b3	b3	PROPN
ejpam-6951	410	8	+	+	CCONJ
ejpam-6951	410	9	·	·	PUNCT
ejpam-6951	410	10	·	·	PUNCT
ejpam-6951	410	11	·	·	PUNCT
ejpam-6951	410	12	+	+	NOUN
ejpam-6951	410	13	b2k−1	b2k−1	NOUN
ejpam-6951	410	14	)	)	PUNCT
ejpam-6951	410	15	+	+	CCONJ
ejpam-6951	410	16	(	(	PUNCT
ejpam-6951	410	17	b2	b2	NOUN
ejpam-6951	410	18	+	+	NOUN
ejpam-6951	410	19	b4	b4	NOUN
ejpam-6951	410	20	+	+	X
ejpam-6951	410	21	·	·	PUNCT
ejpam-6951	410	22	·	·	PUNCT
ejpam-6951	410	23	·	·	PUNCT
ejpam-6951	410	24	+	+	NOUN
ejpam-6951	410	25	b2k	b2k	X
ejpam-6951	410	26	)	)	PUNCT
ejpam-6951	411	1	+	+	NOUN
ejpam-6951	411	2	b	b	NOUN
ejpam-6951	411	3	=	=	SYM
ejpam-6951	411	4	(	(	PUNCT
ejpam-6951	411	5	b1	b1	NOUN
ejpam-6951	411	6	+	+	NOUN
ejpam-6951	411	7	b2	b2	NOUN
ejpam-6951	411	8	+	+	NOUN
ejpam-6951	411	9	b3	b3	NOUN
ejpam-6951	411	10	+	+	NOUN
ejpam-6951	411	11	b4	b4	NOUN
ejpam-6951	411	12	+	+	X
ejpam-6951	411	13	·	·	PUNCT
ejpam-6951	411	14	·	·	PUNCT
ejpam-6951	411	15	·	·	PUNCT
ejpam-6951	411	16	+	+	X
ejpam-6951	411	17	b2k−1	b2k−1	PROPN
ejpam-6951	411	18	+	+	ADJ
ejpam-6951	411	19	b2k	b2k	PROPN
ejpam-6951	411	20	)	)	PUNCT
ejpam-6951	412	1	+	+	NOUN
ejpam-6951	412	2	b	b	NOUN
ejpam-6951	412	3	=	=	SYM
ejpam-6951	412	4	(	(	PUNCT
ejpam-6951	412	5	b1	b1	PROPN
ejpam-6951	412	6	△	△	PROPN
ejpam-6951	412	7	b2	b2	PROPN
ejpam-6951	412	8	△	△	PROPN
ejpam-6951	412	9	b3	b3	PROPN
ejpam-6951	412	10	△	△	PROPN
ejpam-6951	412	11	b4	b4	NOUN
ejpam-6951	412	12	△	△	X
ejpam-6951	412	13	·	·	PUNCT
ejpam-6951	412	14	·	·	PUNCT
ejpam-6951	412	15	·	·	PUNCT
ejpam-6951	412	16	△	△	X
ejpam-6951	412	17	b2k−1	b2k−1	PROPN
ejpam-6951	412	18	△	△	PROPN
ejpam-6951	412	19	b2k)	b2k)	NOUN
ejpam-6951	412	20	△	△	NOUN
ejpam-6951	412	21	b	b	NOUN
ejpam-6951	412	22	=	=	SYM
ejpam-6951	412	23	{	{	PUNCT
ejpam-6951	412	24	x2	x2	PROPN
ejpam-6951	412	25	,	,	PUNCT
ejpam-6951	412	26	x3	x3	ADJ
ejpam-6951	412	27	,	,	PUNCT
ejpam-6951	412	28	x5	x5	NOUN
ejpam-6951	412	29	,	,	PUNCT
ejpam-6951	412	30	x6	x6	PROPN
ejpam-6951	412	31	,	,	PUNCT
ejpam-6951	412	32	...	...	PUNCT
ejpam-6951	412	33	,	,	PUNCT
ejpam-6951	412	34	x3k−1	x3k−1	PROPN
ejpam-6951	412	35	,	,	PUNCT
ejpam-6951	412	36	x3k	x3k	NOUN
ejpam-6951	412	37	}	}	PUNCT
ejpam-6951	412	38	△	△	X
ejpam-6951	412	39	{	{	PUNCT
ejpam-6951	412	40	x2	x2	PROPN
ejpam-6951	412	41	,	,	PUNCT
ejpam-6951	412	42	x3	x3	ADJ
ejpam-6951	412	43	,	,	PUNCT
ejpam-6951	412	44	x5	x5	NOUN
ejpam-6951	412	45	,	,	PUNCT
ejpam-6951	412	46	x6	x6	PROPN
ejpam-6951	412	47	,	,	PUNCT
ejpam-6951	412	48	...	...	PUNCT
ejpam-6951	412	49	,	,	PUNCT
ejpam-6951	412	50	x3k−1	x3k−1	PROPN
ejpam-6951	412	51	,	,	PUNCT
ejpam-6951	412	52	x3k	x3k	PROPN
ejpam-6951	412	53	,	,	PUNCT
ejpam-6951	412	54	yj	yj	PROPN
ejpam-6951	412	55	}	}	PUNCT
ejpam-6951	412	56	=	=	SYM
ejpam-6951	412	57	{	{	PUNCT
ejpam-6951	412	58	yj	yj	PROPN
ejpam-6951	412	59	}	}	PUNCT
ejpam-6951	412	60	.	.	PUNCT
ejpam-6951	413	1	hence	hence	ADV
ejpam-6951	413	2	,	,	PUNCT
ejpam-6951	413	3	{	{	PUNCT
ejpam-6951	413	4	yj	yj	PROPN
ejpam-6951	413	5	}	}	PUNCT
ejpam-6951	413	6	∈	∈	PROPN
ejpam-6951	413	7	vkp2⊔k1(tn	vkp2⊔k1(tn	PROPN
ejpam-6951	413	8	,	,	PUNCT
ejpam-6951	413	9	m	m	NOUN
ejpam-6951	413	10	)	)	PUNCT
ejpam-6951	413	11	for	for	ADP
ejpam-6951	413	12	all	all	PRON
ejpam-6951	413	13	1	1	NUM
ejpam-6951	413	14	≤	≤	NUM
ejpam-6951	413	15	j	j	PROPN
ejpam-6951	413	16	≤	≤	PROPN
ejpam-6951	413	17	m.	m.	NOUN
ejpam-6951	413	18	therefore	therefore	ADV
ejpam-6951	413	19	,	,	PUNCT
ejpam-6951	413	20	by	by	ADP
ejpam-6951	413	21	remark	remark	NOUN
ejpam-6951	413	22	1	1	NUM
ejpam-6951	413	23	,	,	PUNCT
ejpam-6951	413	24	kp2	kp2	VERB
ejpam-6951	413	25	⊔k1	⊔k1	X
ejpam-6951	413	26	is	be	AUX
ejpam-6951	413	27	a	a	DET
ejpam-6951	413	28	vertex	vertex	NOUN
ejpam-6951	413	29	-	-	PUNCT
ejpam-6951	413	30	generator	generator	NOUN
ejpam-6951	413	31	subgraph	subgraph	NOUN
ejpam-6951	413	32	of	of	ADP
ejpam-6951	413	33	tn	tn	PROPN
ejpam-6951	413	34	,	,	PUNCT
ejpam-6951	413	35	m.	m.	NOUN
ejpam-6951	413	36	the	the	DET
ejpam-6951	413	37	following	follow	VERB
ejpam-6951	413	38	theorem	theorem	NOUN
ejpam-6951	413	39	gives	give	VERB
ejpam-6951	413	40	us	we	PRON
ejpam-6951	413	41	a	a	DET
ejpam-6951	413	42	necessary	necessary	ADJ
ejpam-6951	413	43	condition	condition	NOUN
ejpam-6951	413	44	for	for	ADP
ejpam-6951	413	45	the	the	DET
ejpam-6951	413	46	graph	graph	NOUN
ejpam-6951	413	47	p2	p2	NOUN
ejpam-6951	413	48	⊔kt	⊔kt	PROPN
ejpam-6951	413	49	,	,	PUNCT
ejpam-6951	413	50	which	which	PRON
ejpam-6951	413	51	is	be	AUX
ejpam-6951	413	52	the	the	DET
ejpam-6951	413	53	disjoint	disjoint	PROPN
ejpam-6951	413	54	union	union	NOUN
ejpam-6951	413	55	of	of	ADP
ejpam-6951	413	56	a	a	DET
ejpam-6951	413	57	path	path	NOUN
ejpam-6951	413	58	graph	graph	NOUN
ejpam-6951	413	59	p2	p2	NOUN
ejpam-6951	413	60	,	,	PUNCT
ejpam-6951	413	61	and	and	CCONJ
ejpam-6951	413	62	an	an	DET
ejpam-6951	413	63	empty	empty	ADJ
ejpam-6951	413	64	graph	graph	NOUN
ejpam-6951	413	65	kt	kt	NOUN
ejpam-6951	413	66	of	of	ADP
ejpam-6951	413	67	order	order	NOUN
ejpam-6951	413	68	t	t	PROPN
ejpam-6951	413	69	,	,	PUNCT
ejpam-6951	413	70	so	so	SCONJ
ejpam-6951	413	71	t	t	PROPN
ejpam-6951	413	72	should	should	AUX
ejpam-6951	413	73	be	be	AUX
ejpam-6951	413	74	odd	odd	ADJ
ejpam-6951	413	75	,	,	PUNCT
ejpam-6951	413	76	to	to	PART
ejpam-6951	413	77	be	be	AUX
ejpam-6951	413	78	a	a	DET
ejpam-6951	413	79	vertex	vertex	NOUN
ejpam-6951	413	80	-	-	PUNCT
ejpam-6951	413	81	generator	generator	NOUN
ejpam-6951	413	82	subgraph	subgraph	NOUN
ejpam-6951	413	83	of	of	ADP
ejpam-6951	413	84	tn	tn	PROPN
ejpam-6951	413	85	,	,	PUNCT
ejpam-6951	413	86	m.	m.	NOUN
ejpam-6951	413	87	theorem	theorem	VERB
ejpam-6951	413	88	17	17	NUM
ejpam-6951	413	89	.	.	PUNCT
ejpam-6951	414	1	let	let	VERB
ejpam-6951	414	2	n	n	PRON
ejpam-6951	414	3	,	,	PUNCT
ejpam-6951	414	4	m	m	VERB
ejpam-6951	414	5	≥	≥	NOUN
ejpam-6951	414	6	3	3	NUM
ejpam-6951	414	7	and	and	CCONJ
ejpam-6951	414	8	t	t	PROPN
ejpam-6951	414	9	be	be	AUX
ejpam-6951	414	10	positive	positive	ADJ
ejpam-6951	414	11	integers	integer	NOUN
ejpam-6951	414	12	where	where	SCONJ
ejpam-6951	414	13	t	t	PROPN
ejpam-6951	414	14	is	be	AUX
ejpam-6951	414	15	odd	odd	ADJ
ejpam-6951	414	16	.	.	PUNCT
ejpam-6951	415	1	if	if	SCONJ
ejpam-6951	415	2	2t+1	2t+1	PROPN
ejpam-6951	415	3	≤	≤	PROPN
ejpam-6951	415	4	min{n	min{n	NOUN
ejpam-6951	415	5	,	,	PUNCT
ejpam-6951	415	6	m	m	NOUN
ejpam-6951	415	7	}	}	PUNCT
ejpam-6951	415	8	,	,	PUNCT
ejpam-6951	415	9	then	then	ADV
ejpam-6951	415	10	p2	p2	PROPN
ejpam-6951	415	11	⊔kt	⊔kt	PROPN
ejpam-6951	415	12	is	be	AUX
ejpam-6951	415	13	a	a	DET
ejpam-6951	415	14	vertex	vertex	NOUN
ejpam-6951	415	15	-	-	PUNCT
ejpam-6951	415	16	generator	generator	NOUN
ejpam-6951	415	17	subgraph	subgraph	NOUN
ejpam-6951	415	18	of	of	ADP
ejpam-6951	415	19	tn	tn	PROPN
ejpam-6951	415	20	,	,	PUNCT
ejpam-6951	415	21	m.	m.	NOUN
ejpam-6951	415	22	g.	g.	PROPN
ejpam-6951	415	23	d.	d.	PROPN
ejpam-6951	415	24	sepillo	sepillo	PROPN
ejpam-6951	416	1	et	et	PROPN
ejpam-6951	416	2	al	al	PROPN
ejpam-6951	416	3	.	.	PUNCT
ejpam-6951	416	4	/	/	SYM
ejpam-6951	416	5	eur	eur	PROPN
ejpam-6951	416	6	.	.	PUNCT
ejpam-6951	417	1	j.	j.	PROPN
ejpam-6951	417	2	pure	pure	PROPN
ejpam-6951	417	3	appl	appl	PROPN
ejpam-6951	417	4	.	.	PROPN
ejpam-6951	417	5	math	math	PROPN
ejpam-6951	417	6	,	,	PUNCT
ejpam-6951	417	7	18	18	NUM
ejpam-6951	417	8	(	(	PUNCT
ejpam-6951	417	9	4	4	NUM
ejpam-6951	417	10	)	)	PUNCT
ejpam-6951	417	11	(	(	PUNCT
ejpam-6951	417	12	2025	2025	NUM
ejpam-6951	417	13	)	)	PUNCT
ejpam-6951	417	14	,	,	PUNCT
ejpam-6951	417	15	6951	6951	NUM
ejpam-6951	417	16	20	20	NUM
ejpam-6951	417	17	of	of	ADP
ejpam-6951	417	18	23	23	NUM
ejpam-6951	418	1	x2	x2	NUM
ejpam-6951	418	2	x3	x3	PROPN
ejpam-6951	418	3	x4x5	x4x5	NUM
ejpam-6951	419	1	x6	x6	PROPN
ejpam-6951	419	2	x3k−2	x3k−2	PROPN
ejpam-6951	419	3	x3k−1	x3k−1	PROPN
ejpam-6951	419	4	x3k	x3k	PROPN
ejpam-6951	420	1	x3k+1	x3k+1	SCONJ
ejpam-6951	421	1	xn−1	xn−1	PROPN
ejpam-6951	421	2	xn	xn	PROPN
ejpam-6951	422	1	x1	x1	NUM
ejpam-6951	422	2	y1	y1	NOUN
ejpam-6951	422	3	y2	y2	PROPN
ejpam-6951	422	4	y3	y3	NOUN
ejpam-6951	422	5	y4	y4	NOUN
ejpam-6951	422	6	y5	y5	PROPN
ejpam-6951	422	7	y6	y6	PROPN
ejpam-6951	422	8	y3k−2	y3k−2	PROPN
ejpam-6951	422	9	y3k−1	y3k−1	PROPN
ejpam-6951	422	10	y3k	y3k	VERB
ejpam-6951	422	11	ym−1	ym−1	PROPN
ejpam-6951	422	12	ym	ym	PROPN
ejpam-6951	422	13	tn	tn	PROPN
ejpam-6951	422	14	,	,	PUNCT
ejpam-6951	422	15	m⟨b2q−1⟩	m⟨b2q−1⟩	NOUN
ejpam-6951	422	16	:	:	PUNCT
ejpam-6951	422	17	x2	x2	PROPN
ejpam-6951	422	18	x3	x3	PROPN
ejpam-6951	422	19	x4x5	x4x5	NUM
ejpam-6951	423	1	x6	x6	PROPN
ejpam-6951	423	2	x3k−2	x3k−2	PROPN
ejpam-6951	423	3	x3k−1	x3k−1	PROPN
ejpam-6951	423	4	x3k	x3k	PROPN
ejpam-6951	424	1	x3k+1	x3k+1	SCONJ
ejpam-6951	425	1	xn−1	xn−1	PROPN
ejpam-6951	425	2	xn	xn	PROPN
ejpam-6951	426	1	x1	x1	NUM
ejpam-6951	426	2	y1	y1	NOUN
ejpam-6951	426	3	y2	y2	PROPN
ejpam-6951	426	4	y3	y3	NOUN
ejpam-6951	426	5	y4	y4	NOUN
ejpam-6951	426	6	y5	y5	PROPN
ejpam-6951	426	7	y6	y6	PROPN
ejpam-6951	426	8	y3k−2	y3k−2	PROPN
ejpam-6951	426	9	y3k−1	y3k−1	PROPN
ejpam-6951	426	10	y3k	y3k	VERB
ejpam-6951	426	11	ym−1	ym−1	PROPN
ejpam-6951	426	12	ym	ym	PROPN
ejpam-6951	426	13	tn	tn	PROPN
ejpam-6951	426	14	,	,	PUNCT
ejpam-6951	426	15	m⟨b2q⟩	m⟨b2q⟩	PROPN
ejpam-6951	426	16	:	:	PUNCT
ejpam-6951	427	1	x2	x2	PROPN
ejpam-6951	427	2	x3	x3	PROPN
ejpam-6951	427	3	x4x5	x4x5	NUM
ejpam-6951	427	4	x6	x6	PROPN
ejpam-6951	427	5	x3k−2	x3k−2	PROPN
ejpam-6951	427	6	x3k−1	x3k−1	PROPN
ejpam-6951	427	7	x3k	x3k	PROPN
ejpam-6951	427	8	x3k+1	x3k+1	SCONJ
ejpam-6951	428	1	xn−1	xn−1	PROPN
ejpam-6951	428	2	xn	xn	PROPN
ejpam-6951	429	1	x1	x1	NUM
ejpam-6951	429	2	y1	y1	NOUN
ejpam-6951	429	3	y2	y2	PROPN
ejpam-6951	429	4	y3	y3	NOUN
ejpam-6951	429	5	y4	y4	NOUN
ejpam-6951	429	6	y5	y5	PROPN
ejpam-6951	429	7	y6	y6	ADJ
ejpam-6951	429	8	ym−4	ym−4	PROPN
ejpam-6951	429	9	ym−3	ym−3	PROPN
ejpam-6951	429	10	ym−2	ym−2	PROPN
ejpam-6951	429	11	ym−1	ym−1	PROPN
ejpam-6951	429	12	ym	ym	PROPN
ejpam-6951	429	13	tn	tn	PROPN
ejpam-6951	429	14	,	,	PUNCT
ejpam-6951	429	15	m⟨b⟩	m⟨b⟩	PROPN
ejpam-6951	429	16	:	:	PUNCT
ejpam-6951	429	17	figure	figure	NOUN
ejpam-6951	429	18	16	16	NUM
ejpam-6951	429	19	:	:	PUNCT
ejpam-6951	429	20	illustrating	illustrate	VERB
ejpam-6951	429	21	the	the	DET
ejpam-6951	429	22	subgraphs	subgraph	NOUN
ejpam-6951	429	23	of	of	ADP
ejpam-6951	429	24	tn	tn	NOUN
ejpam-6951	429	25	,	,	PUNCT
ejpam-6951	429	26	m	m	AUX
ejpam-6951	429	27	induced	induce	VERB
ejpam-6951	429	28	by	by	ADP
ejpam-6951	429	29	b2q−1	b2q−1	PROPN
ejpam-6951	429	30	,	,	PUNCT
ejpam-6951	429	31	b2q	b2q	PROPN
ejpam-6951	429	32	,	,	PUNCT
ejpam-6951	429	33	and	and	CCONJ
ejpam-6951	429	34	b	b	NOUN
ejpam-6951	429	35	proof	proof	NOUN
ejpam-6951	429	36	.	.	PUNCT
ejpam-6951	430	1	let	let	VERB
ejpam-6951	430	2	2t+	2t+	NUM
ejpam-6951	430	3	1	1	NUM
ejpam-6951	430	4	≤	≤	NUM
ejpam-6951	430	5	min{n	min{n	NOUN
ejpam-6951	430	6	,	,	PUNCT
ejpam-6951	430	7	m	m	NOUN
ejpam-6951	430	8	}	}	PUNCT
ejpam-6951	430	9	.	.	PUNCT
ejpam-6951	431	1	then	then	ADV
ejpam-6951	431	2	,	,	PUNCT
ejpam-6951	431	3	for	for	ADP
ejpam-6951	431	4	any	any	DET
ejpam-6951	431	5	1	1	NUM
ejpam-6951	431	6	≤	≤	NUM
ejpam-6951	431	7	i	i	PRON
ejpam-6951	431	8	≤	≤	PROPN
ejpam-6951	431	9	n	n	CCONJ
ejpam-6951	431	10	,	,	PUNCT
ejpam-6951	431	11	let	let	VERB
ejpam-6951	431	12	xi	xi	PRON
ejpam-6951	431	13	be	be	AUX
ejpam-6951	431	14	an	an	DET
ejpam-6951	431	15	arbitrary	arbitrary	ADJ
ejpam-6951	431	16	vertex	vertex	NOUN
ejpam-6951	431	17	of	of	ADP
ejpam-6951	431	18	cn	cn	PROPN
ejpam-6951	431	19	in	in	ADP
ejpam-6951	431	20	the	the	DET
ejpam-6951	431	21	tadpole	tadpole	NOUN
ejpam-6951	431	22	graph	graph	PROPN
ejpam-6951	431	23	tn	tn	PROPN
ejpam-6951	431	24	,	,	PUNCT
ejpam-6951	431	25	m	m	PROPN
ejpam-6951	431	26	,	,	PUNCT
ejpam-6951	431	27	and	and	CCONJ
ejpam-6951	431	28	for	for	ADP
ejpam-6951	431	29	any	any	DET
ejpam-6951	431	30	1	1	NUM
ejpam-6951	431	31	≤	≤	NOUN
ejpam-6951	431	32	p	p	PROPN
ejpam-6951	431	33	≤	≤	PROPN
ejpam-6951	431	34	t	t	PROPN
ejpam-6951	431	35	,	,	PUNCT
ejpam-6951	431	36	let	let	VERB
ejpam-6951	431	37	a1	a1	NOUN
ejpam-6951	431	38	,	,	PUNCT
ejpam-6951	431	39	ap+1	ap+1	NOUN
ejpam-6951	431	40	,	,	PUNCT
ejpam-6951	431	41	and	and	CCONJ
ejpam-6951	431	42	a	a	PRON
ejpam-6951	431	43	be	be	AUX
ejpam-6951	431	44	defined	define	VERB
ejpam-6951	431	45	as	as	SCONJ
ejpam-6951	431	46	follows	follow	VERB
ejpam-6951	431	47	:	:	PUNCT
ejpam-6951	431	48	a1	a1	NOUN
ejpam-6951	431	49	=	=	SYM
ejpam-6951	431	50	{	{	PUNCT
ejpam-6951	431	51	p2︷	p2︷	NOUN
ejpam-6951	431	52	︸︸	︸︸	PUNCT
ejpam-6951	431	53	︷	︷	PROPN
ejpam-6951	431	54	x2	x2	ADJ
ejpam-6951	431	55	,	,	PUNCT
ejpam-6951	431	56	x3	x3	ADJ
ejpam-6951	431	57	,	,	PUNCT
ejpam-6951	432	1	t−1	t−1	PROPN
ejpam-6951	432	2	vertices︷	vertices︷	ADJ
ejpam-6951	432	3	︸︸	︸︸	NUM
ejpam-6951	432	4	︷	︷	X
ejpam-6951	432	5	x5	x5	NOUN
ejpam-6951	432	6	,	,	PUNCT
ejpam-6951	432	7	x7	x7	NOUN
ejpam-6951	432	8	,	,	PUNCT
ejpam-6951	432	9	...	...	PUNCT
ejpam-6951	432	10	,	,	PUNCT
ejpam-6951	432	11	x2t+1	x2t+1	PROPN
ejpam-6951	432	12	,	,	PUNCT
ejpam-6951	432	13	y2	y2	PROPN
ejpam-6951	432	14	}	}	PUNCT
ejpam-6951	432	15	,	,	PUNCT
ejpam-6951	432	16	ap+1	ap+1	NOUN
ejpam-6951	432	17	=	=	SYM
ejpam-6951	432	18	a1	a1	NOUN
ejpam-6951	432	19	\	\	NOUN
ejpam-6951	432	20	{	{	PUNCT
ejpam-6951	432	21	y2	y2	NOUN
ejpam-6951	432	22	}	}	PUNCT
ejpam-6951	432	23	∪	∪	X
ejpam-6951	432	24	{	{	PUNCT
ejpam-6951	432	25	y2p+1	y2p+1	NOUN
ejpam-6951	432	26	}	}	PUNCT
ejpam-6951	432	27	where	where	SCONJ
ejpam-6951	432	28	1	1	NUM
ejpam-6951	432	29	≤	≤	NOUN
ejpam-6951	432	30	p	p	PROPN
ejpam-6951	432	31	≤	≤	PROPN
ejpam-6951	432	32	t	t	PROPN
ejpam-6951	432	33	,	,	PUNCT
ejpam-6951	432	34	and	and	CCONJ
ejpam-6951	432	35	a	a	DET
ejpam-6951	432	36	=	=	X
ejpam-6951	432	37	{	{	PUNCT
ejpam-6951	432	38	xi	xi	PROPN
ejpam-6951	432	39	,	,	PUNCT
ejpam-6951	432	40	p2︷	p2︷	X
ejpam-6951	432	41	︸︸	︸︸	PUNCT
ejpam-6951	432	42	︷	︷	PROPN
ejpam-6951	433	1	y2	y2	NOUN
ejpam-6951	433	2	,	,	PUNCT
ejpam-6951	433	3	y3	y3	PROPN
ejpam-6951	433	4	,	,	PUNCT
ejpam-6951	433	5	t−1	t−1	PROPN
ejpam-6951	433	6	vertices︷	vertices︷	NOUN
ejpam-6951	433	7	︸︸	︸︸	NUM
ejpam-6951	433	8	︷	︷	X
ejpam-6951	433	9	y5	y5	VERB
ejpam-6951	433	10	,	,	PUNCT
ejpam-6951	433	11	y7	y7	PROPN
ejpam-6951	433	12	,	,	PUNCT
ejpam-6951	433	13	...	...	PUNCT
ejpam-6951	433	14	,	,	PUNCT
ejpam-6951	433	15	y2t+1	y2t+1	PROPN
ejpam-6951	433	16	}	}	PUNCT
ejpam-6951	433	17	where	where	SCONJ
ejpam-6951	433	18	1	1	NUM
ejpam-6951	433	19	≤	≤	NUM
ejpam-6951	433	20	i	i	PRON
ejpam-6951	433	21	≤	≤	NUM
ejpam-6951	433	22	n.	n.	NOUN
ejpam-6951	433	23	it	it	PRON
ejpam-6951	433	24	can	can	AUX
ejpam-6951	433	25	be	be	AUX
ejpam-6951	433	26	verified	verify	VERB
ejpam-6951	433	27	that	that	SCONJ
ejpam-6951	433	28	that	that	DET
ejpam-6951	433	29	a1	a1	NOUN
ejpam-6951	433	30	,	,	PUNCT
ejpam-6951	433	31	ap+1	ap+1	NOUN
ejpam-6951	433	32	,	,	PUNCT
ejpam-6951	433	33	a	a	DET
ejpam-6951	433	34	∈	∈	PROPN
ejpam-6951	433	35	vp2⊔kt	vp2⊔kt	X
ejpam-6951	433	36	(	(	PUNCT
ejpam-6951	433	37	tn	tn	PROPN
ejpam-6951	433	38	,	,	PUNCT
ejpam-6951	433	39	m	m	PROPN
ejpam-6951	433	40	)	)	PUNCT
ejpam-6951	433	41	,	,	PUNCT
ejpam-6951	433	42	as	as	SCONJ
ejpam-6951	433	43	shown	show	VERB
ejpam-6951	433	44	in	in	ADP
ejpam-6951	433	45	figure	figure	NOUN
ejpam-6951	433	46	17	17	NUM
ejpam-6951	433	47	.	.	PUNCT
ejpam-6951	434	1	hence	hence	ADV
ejpam-6951	434	2	,	,	PUNCT
ejpam-6951	434	3	for	for	ADP
ejpam-6951	434	4	i	i	PROPN
ejpam-6951	434	5	=	=	SYM
ejpam-6951	434	6	1	1	NUM
ejpam-6951	434	7	,	,	PUNCT
ejpam-6951	434	8	2	2	NUM
ejpam-6951	434	9	,	,	PUNCT
ejpam-6951	434	10	3	3	NUM
ejpam-6951	434	11	,	,	PUNCT
ejpam-6951	434	12	...	...	PUNCT
ejpam-6951	434	13	,	,	PUNCT
ejpam-6951	434	14	n	n	CCONJ
ejpam-6951	434	15	,	,	PUNCT
ejpam-6951	434	16	we	we	PRON
ejpam-6951	434	17	get	get	VERB
ejpam-6951	434	18	a1	a1	NOUN
ejpam-6951	434	19	+	+	CCONJ
ejpam-6951	434	20	t∑	t∑	ADJ
ejpam-6951	434	21	p=1	p=1	NOUN
ejpam-6951	434	22	ap+1	ap+1	NOUN
ejpam-6951	435	1	+	+	NOUN
ejpam-6951	435	2	a	a	DET
ejpam-6951	435	3	=	=	NOUN
ejpam-6951	435	4	a1	a1	NOUN
ejpam-6951	435	5	+	+	CCONJ
ejpam-6951	435	6	(	(	PUNCT
ejpam-6951	435	7	a2	a2	PROPN
ejpam-6951	435	8	+	+	NOUN
ejpam-6951	435	9	a3	a3	NOUN
ejpam-6951	435	10	+	+	NOUN
ejpam-6951	435	11	a4	a4	NOUN
ejpam-6951	435	12	+	+	NUM
ejpam-6951	435	13	·	·	PUNCT
ejpam-6951	435	14	·	·	PUNCT
ejpam-6951	435	15	·	·	PUNCT
ejpam-6951	435	16	+	+	NOUN
ejpam-6951	435	17	at+1	at+1	X
ejpam-6951	435	18	)	)	PUNCT
ejpam-6951	436	1	+	+	NOUN
ejpam-6951	436	2	a	a	PRON
ejpam-6951	436	3	=	=	X
ejpam-6951	436	4	(	(	PUNCT
ejpam-6951	436	5	a1	a1	NOUN
ejpam-6951	436	6	+	+	PROPN
ejpam-6951	436	7	a2	a2	PROPN
ejpam-6951	436	8	+	+	NOUN
ejpam-6951	436	9	a3	a3	NOUN
ejpam-6951	436	10	+	+	NOUN
ejpam-6951	436	11	a4	a4	NOUN
ejpam-6951	436	12	+	+	NUM
ejpam-6951	436	13	·	·	PUNCT
ejpam-6951	436	14	·	·	PUNCT
ejpam-6951	436	15	·	·	PUNCT
ejpam-6951	436	16	+	+	NOUN
ejpam-6951	436	17	at+1	at+1	X
ejpam-6951	436	18	)	)	PUNCT
ejpam-6951	437	1	+	+	NOUN
ejpam-6951	437	2	a	a	PRON
ejpam-6951	437	3	=	=	PUNCT
ejpam-6951	437	4	(	(	PUNCT
ejpam-6951	437	5	a1	a1	PROPN
ejpam-6951	437	6	△	△	PROPN
ejpam-6951	437	7	a2	a2	PROPN
ejpam-6951	437	8	△	△	PROPN
ejpam-6951	437	9	a3	a3	NOUN
ejpam-6951	437	10	△	△	X
ejpam-6951	437	11	a4	a4	X
ejpam-6951	437	12	△	△	X
ejpam-6951	437	13	·	·	PUNCT
ejpam-6951	437	14	·	·	PUNCT
ejpam-6951	437	15	·	·	PUNCT
ejpam-6951	437	16	△	△	X
ejpam-6951	437	17	at+1)	at+1)	X
ejpam-6951	437	18	△	△	PROPN
ejpam-6951	437	19	a	a	DET
ejpam-6951	437	20	g.	g.	PROPN
ejpam-6951	437	21	d.	d.	PROPN
ejpam-6951	437	22	sepillo	sepillo	PROPN
ejpam-6951	437	23	et	et	PROPN
ejpam-6951	437	24	al	al	PROPN
ejpam-6951	437	25	.	.	PUNCT
ejpam-6951	437	26	/	/	SYM
ejpam-6951	437	27	eur	eur	PROPN
ejpam-6951	437	28	.	.	PUNCT
ejpam-6951	438	1	j.	j.	PROPN
ejpam-6951	438	2	pure	pure	PROPN
ejpam-6951	438	3	appl	appl	PROPN
ejpam-6951	438	4	.	.	PROPN
ejpam-6951	438	5	math	math	PROPN
ejpam-6951	438	6	,	,	PUNCT
ejpam-6951	438	7	18	18	NUM
ejpam-6951	438	8	(	(	PUNCT
ejpam-6951	438	9	4	4	NUM
ejpam-6951	438	10	)	)	PUNCT
ejpam-6951	438	11	(	(	PUNCT
ejpam-6951	438	12	2025	2025	NUM
ejpam-6951	438	13	)	)	PUNCT
ejpam-6951	438	14	,	,	PUNCT
ejpam-6951	438	15	6951	6951	NUM
ejpam-6951	438	16	21	21	NUM
ejpam-6951	438	17	of	of	ADP
ejpam-6951	438	18	23	23	NUM
ejpam-6951	439	1	x2	x2	NUM
ejpam-6951	439	2	x3	x3	PROPN
ejpam-6951	439	3	x4x5	x4x5	SYM
ejpam-6951	440	1	x6	x6	NOUN
ejpam-6951	440	2	x7	x7	NOUN
ejpam-6951	440	3	x2	x2	PROPN
ejpam-6951	440	4	t	t	PROPN
ejpam-6951	440	5	x2t+1xn−2	x2t+1xn−2	PROPN
ejpam-6951	441	1	xn−1	xn−1	PROPN
ejpam-6951	441	2	xn	xn	PROPN
ejpam-6951	442	1	x1	x1	NUM
ejpam-6951	442	2	y1	y1	NOUN
ejpam-6951	442	3	y2	y2	PROPN
ejpam-6951	442	4	y3	y3	NOUN
ejpam-6951	442	5	y4	y4	NOUN
ejpam-6951	442	6	y5	y5	NOUN
ejpam-6951	442	7	y6	y6	ADJ
ejpam-6951	442	8	y7	y7	ADJ
ejpam-6951	443	1	y2	y2	PROPN
ejpam-6951	443	2	t	t	PROPN
ejpam-6951	443	3	y2t+1	y2t+1	PROPN
ejpam-6951	444	1	ym−1	ym−1	PROPN
ejpam-6951	444	2	ym	ym	PROPN
ejpam-6951	444	3	tn	tn	PROPN
ejpam-6951	444	4	,	,	PUNCT
ejpam-6951	444	5	m⟨a1⟩	m⟨a1⟩	NOUN
ejpam-6951	444	6	:	:	PUNCT
ejpam-6951	445	1	x2	x2	INTJ
ejpam-6951	445	2	x3	x3	PROPN
ejpam-6951	445	3	x4x5	x4x5	SYM
ejpam-6951	446	1	x6	x6	NOUN
ejpam-6951	447	1	x7	x7	NOUN
ejpam-6951	448	1	x2	x2	PROPN
ejpam-6951	448	2	t	t	PROPN
ejpam-6951	448	3	x2t+1xn−2	x2t+1xn−2	PROPN
ejpam-6951	449	1	xn−1	xn−1	PROPN
ejpam-6951	449	2	xn	xn	PROPN
ejpam-6951	450	1	x1	x1	NUM
ejpam-6951	450	2	y1	y1	NOUN
ejpam-6951	450	3	y2	y2	PROPN
ejpam-6951	450	4	y3	y3	NOUN
ejpam-6951	450	5	y4	y4	NOUN
ejpam-6951	450	6	y5	y5	NOUN
ejpam-6951	450	7	y6	y6	ADJ
ejpam-6951	450	8	y7	y7	ADJ
ejpam-6951	451	1	y2	y2	PROPN
ejpam-6951	451	2	t	t	PROPN
ejpam-6951	451	3	y2t+1	y2t+1	PROPN
ejpam-6951	452	1	ym−1	ym−1	PROPN
ejpam-6951	452	2	ym	ym	PROPN
ejpam-6951	452	3	tn	tn	PROPN
ejpam-6951	452	4	,	,	PUNCT
ejpam-6951	452	5	m⟨ap+1⟩	m⟨ap+1⟩	X
ejpam-6951	452	6	:	:	PUNCT
ejpam-6951	452	7	x2	x2	PROPN
ejpam-6951	452	8	x3	x3	PROPN
ejpam-6951	452	9	x4x5	x4x5	NUM
ejpam-6951	452	10	x6	x6	PROPN
ejpam-6951	452	11	xn−5	xn−5	PROPN
ejpam-6951	452	12	xn−4	xn−4	PROPN
ejpam-6951	452	13	xn−3xn−2	xn−3xn−2	PROPN
ejpam-6951	453	1	xn−1	xn−1	PROPN
ejpam-6951	453	2	xn	xn	PROPN
ejpam-6951	454	1	x1	x1	NUM
ejpam-6951	454	2	y1	y1	NOUN
ejpam-6951	454	3	y2	y2	PROPN
ejpam-6951	454	4	y3	y3	NOUN
ejpam-6951	454	5	y4	y4	NOUN
ejpam-6951	454	6	y5	y5	NOUN
ejpam-6951	454	7	y6	y6	ADJ
ejpam-6951	454	8	y7	y7	ADJ
ejpam-6951	455	1	y2	y2	PROPN
ejpam-6951	455	2	t	t	PROPN
ejpam-6951	455	3	y2t+1	y2t+1	PROPN
ejpam-6951	456	1	ym−1	ym−1	PROPN
ejpam-6951	456	2	ym	ym	PROPN
ejpam-6951	456	3	tn	tn	PROPN
ejpam-6951	456	4	,	,	PUNCT
ejpam-6951	456	5	m⟨a⟩	m⟨a⟩	NOUN
ejpam-6951	456	6	:	:	PUNCT
ejpam-6951	456	7	figure	figure	NOUN
ejpam-6951	456	8	17	17	NUM
ejpam-6951	456	9	:	:	PUNCT
ejpam-6951	456	10	illustrating	illustrate	VERB
ejpam-6951	456	11	the	the	DET
ejpam-6951	456	12	subgraphs	subgraph	NOUN
ejpam-6951	456	13	of	of	ADP
ejpam-6951	456	14	tn	tn	NOUN
ejpam-6951	456	15	,	,	PUNCT
ejpam-6951	456	16	m	m	AUX
ejpam-6951	456	17	induced	induce	VERB
ejpam-6951	456	18	by	by	ADP
ejpam-6951	456	19	a1	a1	PROPN
ejpam-6951	456	20	,	,	PUNCT
ejpam-6951	456	21	ap+1	ap+1	NOUN
ejpam-6951	456	22	,	,	PUNCT
ejpam-6951	456	23	and	and	CCONJ
ejpam-6951	456	24	a	a	DET
ejpam-6951	456	25	=	=	X
ejpam-6951	456	26	{	{	PUNCT
ejpam-6951	456	27	y2	y2	PROPN
ejpam-6951	456	28	,	,	PUNCT
ejpam-6951	456	29	y3	y3	PROPN
ejpam-6951	456	30	,	,	PUNCT
ejpam-6951	456	31	y5	y5	NOUN
ejpam-6951	456	32	,	,	PUNCT
ejpam-6951	456	33	y7	y7	PROPN
ejpam-6951	456	34	,	,	PUNCT
ejpam-6951	456	35	...	...	PUNCT
ejpam-6951	456	36	,	,	PUNCT
ejpam-6951	456	37	y2t+1	y2t+1	PROPN
ejpam-6951	456	38	}	}	PUNCT
ejpam-6951	456	39	△	△	X
ejpam-6951	456	40	{	{	PUNCT
ejpam-6951	456	41	xi	xi	PROPN
ejpam-6951	456	42	,	,	PUNCT
ejpam-6951	456	43	y2	y2	PROPN
ejpam-6951	456	44	,	,	PUNCT
ejpam-6951	456	45	y3	y3	NOUN
ejpam-6951	456	46	,	,	PUNCT
ejpam-6951	456	47	y5	y5	NOUN
ejpam-6951	456	48	,	,	PUNCT
ejpam-6951	456	49	y7	y7	PROPN
ejpam-6951	456	50	,	,	PUNCT
ejpam-6951	456	51	...	...	PUNCT
ejpam-6951	456	52	,	,	PUNCT
ejpam-6951	456	53	y2t+1	y2t+1	PROPN
ejpam-6951	456	54	}	}	PUNCT
ejpam-6951	456	55	=	=	SYM
ejpam-6951	456	56	{	{	PUNCT
ejpam-6951	456	57	xi	xi	X
ejpam-6951	456	58	}	}	PUNCT
ejpam-6951	456	59	.	.	PUNCT
ejpam-6951	457	1	consequently	consequently	ADV
ejpam-6951	457	2	,	,	PUNCT
ejpam-6951	457	3	{	{	PUNCT
ejpam-6951	457	4	xi	xi	PROPN
ejpam-6951	457	5	}	}	PUNCT
ejpam-6951	457	6	∈	∈	PROPN
ejpam-6951	457	7	vp2⊔kt	vp2⊔kt	X
ejpam-6951	457	8	(	(	PUNCT
ejpam-6951	457	9	tn	tn	PROPN
ejpam-6951	457	10	,	,	PUNCT
ejpam-6951	457	11	m	m	NOUN
ejpam-6951	457	12	)	)	PUNCT
ejpam-6951	457	13	for	for	ADP
ejpam-6951	457	14	all	all	DET
ejpam-6951	457	15	1	1	NUM
ejpam-6951	457	16	≤	≤	NUM
ejpam-6951	457	17	i	i	PRON
ejpam-6951	457	18	≤	≤	ADJ
ejpam-6951	457	19	n.	n.	NOUN
ejpam-6951	457	20	similarly	similarly	ADV
ejpam-6951	457	21	,	,	PUNCT
ejpam-6951	457	22	for	for	ADP
ejpam-6951	457	23	any	any	DET
ejpam-6951	457	24	1	1	NUM
ejpam-6951	457	25	≤	≤	NUM
ejpam-6951	457	26	j	j	PROPN
ejpam-6951	457	27	≤	≤	PROPN
ejpam-6951	457	28	m	m	ADP
ejpam-6951	457	29	,	,	PUNCT
ejpam-6951	457	30	let	let	VERB
ejpam-6951	457	31	yj	yj	PRON
ejpam-6951	457	32	be	be	AUX
ejpam-6951	457	33	an	an	DET
ejpam-6951	457	34	arbitrary	arbitrary	ADJ
ejpam-6951	457	35	vertex	vertex	NOUN
ejpam-6951	457	36	of	of	ADP
ejpam-6951	457	37	pm	pm	NOUN
ejpam-6951	457	38	in	in	ADP
ejpam-6951	457	39	the	the	DET
ejpam-6951	457	40	tadpole	tadpole	NOUN
ejpam-6951	457	41	graph	graph	PROPN
ejpam-6951	457	42	tn	tn	PROPN
ejpam-6951	457	43	,	,	PUNCT
ejpam-6951	457	44	m	m	PROPN
ejpam-6951	457	45	,	,	PUNCT
ejpam-6951	457	46	and	and	CCONJ
ejpam-6951	457	47	for	for	ADP
ejpam-6951	457	48	any	any	DET
ejpam-6951	457	49	1	1	NUM
ejpam-6951	457	50	≤	≤	NOUN
ejpam-6951	457	51	q	q	PROPN
ejpam-6951	457	52	≤	≤	PROPN
ejpam-6951	457	53	t	t	PROPN
ejpam-6951	457	54	,	,	PUNCT
ejpam-6951	457	55	let	let	VERB
ejpam-6951	457	56	b1	b1	NOUN
ejpam-6951	457	57	,	,	PUNCT
ejpam-6951	457	58	bq+1	bq+1	PROPN
ejpam-6951	457	59	and	and	CCONJ
ejpam-6951	457	60	b	b	NOUN
ejpam-6951	457	61	be	be	AUX
ejpam-6951	457	62	defined	define	VERB
ejpam-6951	457	63	as	as	SCONJ
ejpam-6951	457	64	follows	follow	VERB
ejpam-6951	457	65	:	:	PUNCT
ejpam-6951	457	66	b1	b1	NOUN
ejpam-6951	457	67	=	=	SYM
ejpam-6951	457	68	{	{	PUNCT
ejpam-6951	457	69	x2	x2	PROPN
ejpam-6951	457	70	,	,	PUNCT
ejpam-6951	457	71	p2︷	p2︷	X
ejpam-6951	457	72	︸︸	︸︸	PUNCT
ejpam-6951	457	73	︷	︷	PROPN
ejpam-6951	458	1	y2	y2	NOUN
ejpam-6951	458	2	,	,	PUNCT
ejpam-6951	458	3	y3	y3	PROPN
ejpam-6951	458	4	,	,	PUNCT
ejpam-6951	458	5	t−1	t−1	PROPN
ejpam-6951	458	6	vertices︷	vertices︷	NOUN
ejpam-6951	458	7	︸︸	︸︸	NUM
ejpam-6951	458	8	︷	︷	X
ejpam-6951	458	9	y5	y5	VERB
ejpam-6951	458	10	,	,	PUNCT
ejpam-6951	458	11	y7	y7	PROPN
ejpam-6951	458	12	,	,	PUNCT
ejpam-6951	458	13	...	...	PUNCT
ejpam-6951	458	14	,	,	PUNCT
ejpam-6951	458	15	y2t+1	y2t+1	PROPN
ejpam-6951	458	16	}	}	PUNCT
ejpam-6951	458	17	,	,	PUNCT
ejpam-6951	458	18	bq+1	bq+1	X
ejpam-6951	458	19	=	=	SYM
ejpam-6951	458	20	b1	b1	PROPN
ejpam-6951	458	21	\	\	PROPN
ejpam-6951	458	22	{	{	PUNCT
ejpam-6951	458	23	x2	x2	PROPN
ejpam-6951	458	24	}	}	PUNCT
ejpam-6951	458	25	∪	∪	X
ejpam-6951	458	26	{	{	PUNCT
ejpam-6951	458	27	x2q+1	x2q+1	ADJ
ejpam-6951	458	28	}	}	PUNCT
ejpam-6951	458	29	where	where	SCONJ
ejpam-6951	458	30	1	1	NUM
ejpam-6951	458	31	≤	≤	NOUN
ejpam-6951	458	32	q	q	PROPN
ejpam-6951	458	33	≤	≤	NUM
ejpam-6951	458	34	t	t	PROPN
ejpam-6951	458	35	,	,	PUNCT
ejpam-6951	458	36	and	and	CCONJ
ejpam-6951	458	37	b	b	X
ejpam-6951	458	38	=	=	SYM
ejpam-6951	458	39	{	{	PUNCT
ejpam-6951	458	40	p2︷	p2︷	PROPN
ejpam-6951	458	41	︸︸	︸︸	PUNCT
ejpam-6951	458	42	︷	︷	PROPN
ejpam-6951	458	43	x2	x2	ADJ
ejpam-6951	458	44	,	,	PUNCT
ejpam-6951	458	45	x3	x3	ADJ
ejpam-6951	458	46	,	,	PUNCT
ejpam-6951	458	47	t−1	t−1	PROPN
ejpam-6951	458	48	vertices︷	vertices︷	ADJ
ejpam-6951	458	49	︸︸	︸︸	NUM
ejpam-6951	458	50	︷	︷	X
ejpam-6951	458	51	x5	x5	NOUN
ejpam-6951	458	52	,	,	PUNCT
ejpam-6951	458	53	x7	x7	NOUN
ejpam-6951	458	54	,	,	PUNCT
ejpam-6951	458	55	...	...	PUNCT
ejpam-6951	458	56	,	,	PUNCT
ejpam-6951	458	57	x2t+1	x2t+1	PROPN
ejpam-6951	458	58	,	,	PUNCT
ejpam-6951	458	59	yj	yj	PROPN
ejpam-6951	458	60	}	}	PUNCT
ejpam-6951	458	61	where	where	SCONJ
ejpam-6951	458	62	1	1	NUM
ejpam-6951	458	63	≤	≤	NUM
ejpam-6951	458	64	j	j	PROPN
ejpam-6951	458	65	≤	≤	PROPN
ejpam-6951	458	66	m.	m.	NOUN
ejpam-6951	458	67	it	it	PRON
ejpam-6951	458	68	can	can	AUX
ejpam-6951	458	69	be	be	AUX
ejpam-6951	458	70	verified	verify	VERB
ejpam-6951	458	71	that	that	SCONJ
ejpam-6951	458	72	b1	b1	NOUN
ejpam-6951	458	73	,	,	PUNCT
ejpam-6951	458	74	bq+1	bq+1	PROPN
ejpam-6951	458	75	,	,	PUNCT
ejpam-6951	458	76	b	b	PROPN
ejpam-6951	458	77	∈	∈	PROPN
ejpam-6951	458	78	vp2⊔kt	vp2⊔kt	X
ejpam-6951	458	79	(	(	PUNCT
ejpam-6951	458	80	tn	tn	PROPN
ejpam-6951	458	81	,	,	PUNCT
ejpam-6951	458	82	m	m	PROPN
ejpam-6951	458	83	)	)	PUNCT
ejpam-6951	458	84	,	,	PUNCT
ejpam-6951	458	85	as	as	SCONJ
ejpam-6951	458	86	shown	show	VERB
ejpam-6951	458	87	in	in	ADP
ejpam-6951	458	88	figure	figure	NOUN
ejpam-6951	458	89	18	18	NUM
ejpam-6951	458	90	.	.	PUNCT
ejpam-6951	459	1	thus	thus	ADV
ejpam-6951	459	2	,	,	PUNCT
ejpam-6951	459	3	for	for	ADP
ejpam-6951	459	4	j	j	PROPN
ejpam-6951	459	5	=	=	SYM
ejpam-6951	459	6	1	1	NUM
ejpam-6951	459	7	,	,	PUNCT
ejpam-6951	459	8	2	2	NUM
ejpam-6951	459	9	,	,	PUNCT
ejpam-6951	459	10	3	3	NUM
ejpam-6951	459	11	,	,	PUNCT
ejpam-6951	459	12	...	...	PUNCT
ejpam-6951	459	13	,	,	PUNCT
ejpam-6951	459	14	m	m	PRON
ejpam-6951	459	15	,	,	PUNCT
ejpam-6951	459	16	we	we	PRON
ejpam-6951	459	17	get	get	VERB
ejpam-6951	459	18	b1	b1	NOUN
ejpam-6951	459	19	+	+	CCONJ
ejpam-6951	459	20	t∑	t∑	PROPN
ejpam-6951	459	21	q=1	q=1	X
ejpam-6951	459	22	bq+1	bq+1	PUNCT
ejpam-6951	460	1	+	+	NOUN
ejpam-6951	460	2	b	b	NOUN
ejpam-6951	460	3	=	=	SYM
ejpam-6951	460	4	b1	b1	PROPN
ejpam-6951	460	5	+	+	CCONJ
ejpam-6951	460	6	(	(	PUNCT
ejpam-6951	460	7	b2	b2	NOUN
ejpam-6951	460	8	+	+	NOUN
ejpam-6951	460	9	b3	b3	PROPN
ejpam-6951	460	10	+	+	NOUN
ejpam-6951	460	11	b4	b4	NOUN
ejpam-6951	460	12	+	+	X
ejpam-6951	460	13	·	·	PUNCT
ejpam-6951	460	14	·	·	PUNCT
ejpam-6951	460	15	·	·	PUNCT
ejpam-6951	460	16	+	+	NOUN
ejpam-6951	460	17	bt+1	bt+1	X
ejpam-6951	460	18	)	)	PUNCT
ejpam-6951	461	1	+	+	NOUN
ejpam-6951	461	2	b	b	PROPN
ejpam-6951	461	3	g.	g.	PROPN
ejpam-6951	461	4	d.	d.	PROPN
ejpam-6951	461	5	sepillo	sepillo	PROPN
ejpam-6951	461	6	et	et	PROPN
ejpam-6951	461	7	al	al	PROPN
ejpam-6951	461	8	.	.	PUNCT
ejpam-6951	461	9	/	/	SYM
ejpam-6951	461	10	eur	eur	PROPN
ejpam-6951	461	11	.	.	PUNCT
ejpam-6951	462	1	j.	j.	PROPN
ejpam-6951	462	2	pure	pure	PROPN
ejpam-6951	462	3	appl	appl	PROPN
ejpam-6951	462	4	.	.	PROPN
ejpam-6951	462	5	math	math	PROPN
ejpam-6951	462	6	,	,	PUNCT
ejpam-6951	462	7	18	18	NUM
ejpam-6951	462	8	(	(	PUNCT
ejpam-6951	462	9	4	4	NUM
ejpam-6951	462	10	)	)	PUNCT
ejpam-6951	462	11	(	(	PUNCT
ejpam-6951	462	12	2025	2025	NUM
ejpam-6951	462	13	)	)	PUNCT
ejpam-6951	462	14	,	,	PUNCT
ejpam-6951	462	15	6951	6951	NUM
ejpam-6951	462	16	22	22	NUM
ejpam-6951	462	17	of	of	ADP
ejpam-6951	462	18	23	23	NUM
ejpam-6951	463	1	x2	x2	NUM
ejpam-6951	463	2	x3	x3	PROPN
ejpam-6951	463	3	x4x5	x4x5	SYM
ejpam-6951	464	1	x6	x6	NOUN
ejpam-6951	464	2	x7	x7	NOUN
ejpam-6951	464	3	x2	x2	PROPN
ejpam-6951	464	4	t	t	PROPN
ejpam-6951	464	5	x2t+1xn−2	x2t+1xn−2	PROPN
ejpam-6951	465	1	xn−1	xn−1	PROPN
ejpam-6951	465	2	xn	xn	PROPN
ejpam-6951	466	1	x1	x1	NUM
ejpam-6951	466	2	y1	y1	NOUN
ejpam-6951	466	3	y2	y2	PROPN
ejpam-6951	466	4	y3	y3	NOUN
ejpam-6951	466	5	y4	y4	NOUN
ejpam-6951	466	6	y5	y5	NOUN
ejpam-6951	466	7	y6	y6	ADJ
ejpam-6951	466	8	y7	y7	ADJ
ejpam-6951	467	1	y2	y2	PROPN
ejpam-6951	467	2	t	t	PROPN
ejpam-6951	467	3	y2t+1	y2t+1	PROPN
ejpam-6951	468	1	ym−1	ym−1	PROPN
ejpam-6951	468	2	ym	ym	PROPN
ejpam-6951	468	3	tn	tn	PROPN
ejpam-6951	468	4	,	,	PUNCT
ejpam-6951	468	5	m⟨b1⟩	m⟨b1⟩	PROPN
ejpam-6951	468	6	:	:	PUNCT
ejpam-6951	469	1	x2	x2	PROPN
ejpam-6951	469	2	x3	x3	PROPN
ejpam-6951	469	3	x4x5	x4x5	SYM
ejpam-6951	470	1	x6	x6	NOUN
ejpam-6951	471	1	x7	x7	NOUN
ejpam-6951	472	1	x2	x2	PROPN
ejpam-6951	472	2	t	t	PROPN
ejpam-6951	472	3	x2t+1xn−2	x2t+1xn−2	PROPN
ejpam-6951	473	1	xn−1	xn−1	PROPN
ejpam-6951	473	2	xn	xn	PROPN
ejpam-6951	474	1	x1	x1	NUM
ejpam-6951	474	2	y1	y1	NOUN
ejpam-6951	474	3	y2	y2	PROPN
ejpam-6951	474	4	y3	y3	NOUN
ejpam-6951	474	5	y4	y4	NOUN
ejpam-6951	474	6	y5	y5	NOUN
ejpam-6951	474	7	y6	y6	ADJ
ejpam-6951	474	8	y7	y7	ADJ
ejpam-6951	475	1	y2	y2	PROPN
ejpam-6951	475	2	t	t	PROPN
ejpam-6951	475	3	y2t+1	y2t+1	PROPN
ejpam-6951	476	1	ym−1	ym−1	PROPN
ejpam-6951	476	2	ym	ym	PROPN
ejpam-6951	476	3	tn	tn	PROPN
ejpam-6951	476	4	,	,	PUNCT
ejpam-6951	476	5	m⟨bq+1⟩	m⟨bq+1⟩	X
ejpam-6951	476	6	:	:	PUNCT
ejpam-6951	477	1	x2	x2	PROPN
ejpam-6951	477	2	x3	x3	PROPN
ejpam-6951	477	3	x4x5	x4x5	SYM
ejpam-6951	478	1	x6	x6	NOUN
ejpam-6951	479	1	x7	x7	NOUN
ejpam-6951	480	1	x2	x2	PROPN
ejpam-6951	480	2	t	t	PROPN
ejpam-6951	480	3	x2t+1xn−2	x2t+1xn−2	PROPN
ejpam-6951	481	1	xn−1	xn−1	PROPN
ejpam-6951	481	2	xn	xn	PROPN
ejpam-6951	482	1	x1	x1	NUM
ejpam-6951	482	2	y1	y1	NOUN
ejpam-6951	482	3	y2	y2	PROPN
ejpam-6951	482	4	y3	y3	NOUN
ejpam-6951	482	5	y4	y4	NOUN
ejpam-6951	482	6	y5	y5	PROPN
ejpam-6951	482	7	y6	y6	ADJ
ejpam-6951	482	8	ym−4	ym−4	PROPN
ejpam-6951	482	9	ym−3	ym−3	PROPN
ejpam-6951	482	10	ym−2	ym−2	PROPN
ejpam-6951	482	11	ym−1	ym−1	PROPN
ejpam-6951	482	12	ym	ym	PROPN
ejpam-6951	482	13	tn	tn	PROPN
ejpam-6951	482	14	,	,	PUNCT
ejpam-6951	482	15	m⟨b⟩	m⟨b⟩	PROPN
ejpam-6951	482	16	:	:	PUNCT
ejpam-6951	482	17	figure	figure	NOUN
ejpam-6951	482	18	18	18	NUM
ejpam-6951	482	19	:	:	PUNCT
ejpam-6951	482	20	illustrating	illustrate	VERB
ejpam-6951	482	21	the	the	DET
ejpam-6951	482	22	subgraphs	subgraph	NOUN
ejpam-6951	482	23	of	of	ADP
ejpam-6951	482	24	tn	tn	NOUN
ejpam-6951	482	25	,	,	PUNCT
ejpam-6951	482	26	m	m	AUX
ejpam-6951	482	27	induced	induce	VERB
ejpam-6951	482	28	by	by	ADP
ejpam-6951	482	29	b1	b1	PROPN
ejpam-6951	482	30	,	,	PUNCT
ejpam-6951	482	31	bq+1	bq+1	PROPN
ejpam-6951	482	32	,	,	PUNCT
ejpam-6951	482	33	and	and	CCONJ
ejpam-6951	482	34	b	b	X
ejpam-6951	482	35	=	=	SYM
ejpam-6951	482	36	(	(	PUNCT
ejpam-6951	482	37	b1	b1	NOUN
ejpam-6951	482	38	+	+	NOUN
ejpam-6951	482	39	b2	b2	NOUN
ejpam-6951	482	40	+	+	NOUN
ejpam-6951	482	41	b3	b3	NOUN
ejpam-6951	482	42	+	+	NOUN
ejpam-6951	482	43	b4	b4	NOUN
ejpam-6951	482	44	+	+	X
ejpam-6951	482	45	·	·	PUNCT
ejpam-6951	482	46	·	·	PUNCT
ejpam-6951	482	47	·	·	PUNCT
ejpam-6951	482	48	+	+	NOUN
ejpam-6951	482	49	bt+1	bt+1	X
ejpam-6951	482	50	)	)	PUNCT
ejpam-6951	483	1	+	+	NOUN
ejpam-6951	483	2	b	b	X
ejpam-6951	483	3	=	=	SYM
ejpam-6951	483	4	(	(	PUNCT
ejpam-6951	483	5	b1	b1	PROPN
ejpam-6951	483	6	△	△	PROPN
ejpam-6951	483	7	b2	b2	PROPN
ejpam-6951	483	8	△	△	PROPN
ejpam-6951	483	9	b3	b3	PROPN
ejpam-6951	483	10	△	△	PROPN
ejpam-6951	483	11	b4	b4	NOUN
ejpam-6951	483	12	△	△	X
ejpam-6951	483	13	·	·	PUNCT
ejpam-6951	483	14	·	·	PUNCT
ejpam-6951	483	15	·	·	PUNCT
ejpam-6951	483	16	△	△	X
ejpam-6951	483	17	bt+1)	bt+1)	X
ejpam-6951	483	18	△	△	NOUN
ejpam-6951	483	19	b	b	NOUN
ejpam-6951	483	20	=	=	SYM
ejpam-6951	483	21	{	{	PUNCT
ejpam-6951	483	22	x2	x2	PROPN
ejpam-6951	483	23	,	,	PUNCT
ejpam-6951	483	24	x3	x3	ADJ
ejpam-6951	483	25	,	,	PUNCT
ejpam-6951	483	26	x5	x5	NOUN
ejpam-6951	483	27	,	,	PUNCT
ejpam-6951	483	28	x7	x7	NOUN
ejpam-6951	483	29	,	,	PUNCT
ejpam-6951	483	30	...	...	PUNCT
ejpam-6951	483	31	,	,	PUNCT
ejpam-6951	483	32	x2t+1	x2t+1	PROPN
ejpam-6951	483	33	}	}	PUNCT
ejpam-6951	483	34	△	△	X
ejpam-6951	483	35	{	{	PUNCT
ejpam-6951	483	36	x2	x2	PROPN
ejpam-6951	483	37	,	,	PUNCT
ejpam-6951	483	38	x3	x3	ADJ
ejpam-6951	483	39	,	,	PUNCT
ejpam-6951	483	40	x5	x5	NOUN
ejpam-6951	483	41	,	,	PUNCT
ejpam-6951	483	42	x7	x7	NOUN
ejpam-6951	483	43	,	,	PUNCT
ejpam-6951	483	44	...	...	PUNCT
ejpam-6951	483	45	,	,	PUNCT
ejpam-6951	483	46	x2t+1	x2t+1	PROPN
ejpam-6951	483	47	,	,	PUNCT
ejpam-6951	483	48	yj	yj	PROPN
ejpam-6951	483	49	}	}	PUNCT
ejpam-6951	483	50	=	=	SYM
ejpam-6951	483	51	{	{	PUNCT
ejpam-6951	483	52	yj	yj	PROPN
ejpam-6951	483	53	}	}	PUNCT
ejpam-6951	483	54	.	.	PUNCT
ejpam-6951	484	1	hence	hence	ADV
ejpam-6951	484	2	,	,	PUNCT
ejpam-6951	484	3	{	{	PUNCT
ejpam-6951	484	4	yj	yj	PROPN
ejpam-6951	484	5	}	}	PUNCT
ejpam-6951	484	6	∈	∈	PROPN
ejpam-6951	484	7	vp2⊔kt	vp2⊔kt	X
ejpam-6951	484	8	(	(	PUNCT
ejpam-6951	484	9	tn	tn	PROPN
ejpam-6951	484	10	,	,	PUNCT
ejpam-6951	484	11	m	m	NOUN
ejpam-6951	484	12	)	)	PUNCT
ejpam-6951	484	13	for	for	ADP
ejpam-6951	484	14	all	all	PRON
ejpam-6951	484	15	1	1	NUM
ejpam-6951	484	16	≤	≤	NUM
ejpam-6951	484	17	j	j	PROPN
ejpam-6951	484	18	≤	≤	PROPN
ejpam-6951	484	19	m.	m.	NOUN
ejpam-6951	484	20	therefore	therefore	ADV
ejpam-6951	484	21	,	,	PUNCT
ejpam-6951	484	22	by	by	ADP
ejpam-6951	484	23	remark	remark	NOUN
ejpam-6951	484	24	1	1	NUM
ejpam-6951	484	25	,	,	PUNCT
ejpam-6951	484	26	p2	p2	X
ejpam-6951	484	27	⊔	⊔	PROPN
ejpam-6951	484	28	kt	kt	PROPN
ejpam-6951	484	29	is	be	AUX
ejpam-6951	484	30	a	a	DET
ejpam-6951	484	31	vertex	vertex	NOUN
ejpam-6951	484	32	-	-	PUNCT
ejpam-6951	484	33	generator	generator	NOUN
ejpam-6951	484	34	subgraph	subgraph	NOUN
ejpam-6951	484	35	of	of	ADP
ejpam-6951	484	36	tn	tn	PROPN
ejpam-6951	484	37	,	,	PUNCT
ejpam-6951	484	38	m.	m.	NOUN
ejpam-6951	484	39	4	4	NUM
ejpam-6951	484	40	.	.	PUNCT
ejpam-6951	485	1	conclusions	conclusion	NOUN
ejpam-6951	485	2	this	this	DET
ejpam-6951	485	3	paper	paper	NOUN
ejpam-6951	485	4	provides	provide	VERB
ejpam-6951	485	5	some	some	DET
ejpam-6951	485	6	vertex	vertex	NOUN
ejpam-6951	485	7	-	-	PUNCT
ejpam-6951	485	8	generator	generator	NOUN
ejpam-6951	485	9	subgraphs	subgraph	NOUN
ejpam-6951	485	10	of	of	ADP
ejpam-6951	485	11	km	km	PROPN
ejpam-6951	485	12	,	,	PUNCT
ejpam-6951	485	13	n	n	CCONJ
ejpam-6951	485	14	,	,	PUNCT
ejpam-6951	485	15	such	such	ADJ
ejpam-6951	485	16	as	as	ADP
ejpam-6951	485	17	the	the	DET
ejpam-6951	485	18	empty	empty	ADJ
ejpam-6951	485	19	graph	graph	NOUN
ejpam-6951	485	20	,	,	PUNCT
ejpam-6951	485	21	path	path	NOUN
ejpam-6951	485	22	graph	graph	NOUN
ejpam-6951	485	23	,	,	PUNCT
ejpam-6951	485	24	star	star	NOUN
ejpam-6951	485	25	graph	graph	NOUN
ejpam-6951	485	26	,	,	PUNCT
ejpam-6951	485	27	and	and	CCONJ
ejpam-6951	485	28	complete	complete	ADJ
ejpam-6951	485	29	bipartite	bipartite	PROPN
ejpam-6951	485	30	graph	graph	NOUN
ejpam-6951	485	31	kr	kr	PROPN
ejpam-6951	485	32	,	,	PUNCT
ejpam-6951	485	33	r+1	r+1	PROPN
ejpam-6951	485	34	.	.	PUNCT
ejpam-6951	486	1	this	this	DET
ejpam-6951	486	2	study	study	NOUN
ejpam-6951	486	3	also	also	ADV
ejpam-6951	486	4	provides	provide	VERB
ejpam-6951	486	5	some	some	DET
ejpam-6951	486	6	vertex	vertex	NOUN
ejpam-6951	486	7	-	-	PUNCT
ejpam-6951	486	8	generator	generator	NOUN
ejpam-6951	486	9	subgraphs	subgraph	NOUN
ejpam-6951	486	10	of	of	ADP
ejpam-6951	486	11	tn	tn	PROPN
ejpam-6951	486	12	,	,	PUNCT
ejpam-6951	486	13	m	m	PROPN
ejpam-6951	486	14	,	,	PUNCT
ejpam-6951	486	15	such	such	ADJ
ejpam-6951	486	16	as	as	ADP
ejpam-6951	486	17	the	the	DET
ejpam-6951	486	18	empty	empty	ADJ
ejpam-6951	486	19	graph	graph	NOUN
ejpam-6951	486	20	and	and	CCONJ
ejpam-6951	486	21	the	the	DET
ejpam-6951	486	22	disjoint	disjoint	PROPN
ejpam-6951	486	23	union	union	NOUN
ejpam-6951	486	24	of	of	ADP
ejpam-6951	486	25	graphs	graph	NOUN
ejpam-6951	486	26	pt	pt	X
ejpam-6951	486	27	⊔	⊔	PROPN
ejpam-6951	486	28	k1	k1	PROPN
ejpam-6951	486	29	,	,	PUNCT
ejpam-6951	486	30	kp2	kp2	VERB
ejpam-6951	486	31	⊔	⊔	NUM
ejpam-6951	486	32	k1	k1	PROPN
ejpam-6951	486	33	,	,	PUNCT
ejpam-6951	486	34	and	and	CCONJ
ejpam-6951	486	35	p2	p2	PROPN
ejpam-6951	486	36	⊔	⊔	PROPN
ejpam-6951	486	37	kt	kt	PROPN
ejpam-6951	486	38	.	.	PUNCT
ejpam-6951	487	1	it	it	PRON
ejpam-6951	487	2	is	be	AUX
ejpam-6951	487	3	recommended	recommend	VERB
ejpam-6951	487	4	to	to	PART
ejpam-6951	487	5	find	find	VERB
ejpam-6951	487	6	the	the	DET
ejpam-6951	487	7	other	other	ADJ
ejpam-6951	487	8	vertex	vertex	NOUN
ejpam-6951	487	9	-	-	PUNCT
ejpam-6951	487	10	generator	generator	NOUN
ejpam-6951	487	11	subgraphs	subgraph	NOUN
ejpam-6951	487	12	of	of	ADP
ejpam-6951	487	13	km	km	PROPN
ejpam-6951	487	14	,	,	PUNCT
ejpam-6951	487	15	n	n	PROPN
ejpam-6951	487	16	and	and	CCONJ
ejpam-6951	487	17	tn	tn	PROPN
ejpam-6951	487	18	,	,	PUNCT
ejpam-6951	487	19	m.	m.	NOUN
ejpam-6951	487	20	furthermore	furthermore	ADV
ejpam-6951	487	21	,	,	PUNCT
ejpam-6951	487	22	characterization	characterization	NOUN
ejpam-6951	487	23	for	for	ADP
ejpam-6951	487	24	the	the	DET
ejpam-6951	487	25	vertex	vertex	NOUN
ejpam-6951	487	26	-	-	PUNCT
ejpam-6951	487	27	generator	generator	NOUN
ejpam-6951	487	28	subgraphs	subgraphs	NOUN
ejpam-6951	487	29	of	of	ADP
ejpam-6951	487	30	the	the	DET
ejpam-6951	487	31	two	two	NUM
ejpam-6951	487	32	graphs	graph	NOUN
ejpam-6951	487	33	remains	remain	VERB
ejpam-6951	487	34	open	open	ADJ
ejpam-6951	487	35	for	for	ADP
ejpam-6951	487	36	research	research	NOUN
ejpam-6951	487	37	.	.	PUNCT
ejpam-6951	488	1	g.	g.	PROPN
ejpam-6951	488	2	d.	d.	PROPN
ejpam-6951	488	3	sepillo	sepillo	PROPN
ejpam-6951	488	4	et	et	PROPN
ejpam-6951	488	5	al	al	PROPN
ejpam-6951	488	6	.	.	PUNCT
ejpam-6951	488	7	/	/	SYM
ejpam-6951	488	8	eur	eur	PROPN
ejpam-6951	488	9	.	.	PUNCT
ejpam-6951	489	1	j.	j.	PROPN
ejpam-6951	489	2	pure	pure	PROPN
ejpam-6951	489	3	appl	appl	PROPN
ejpam-6951	489	4	.	.	PROPN
ejpam-6951	489	5	math	math	PROPN
ejpam-6951	489	6	,	,	PUNCT
ejpam-6951	489	7	18	18	NUM
ejpam-6951	489	8	(	(	PUNCT
ejpam-6951	489	9	4	4	NUM
ejpam-6951	489	10	)	)	PUNCT
ejpam-6951	489	11	(	(	PUNCT
ejpam-6951	489	12	2025	2025	NUM
ejpam-6951	489	13	)	)	PUNCT
ejpam-6951	489	14	,	,	PUNCT
ejpam-6951	489	15	6951	6951	NUM
ejpam-6951	489	16	23	23	NUM
ejpam-6951	489	17	of	of	ADP
ejpam-6951	489	18	23	23	NUM
ejpam-6951	489	19	acknowledgements	acknowledgement	NOUN
ejpam-6951	489	20	part	part	NOUN
ejpam-6951	489	21	of	of	ADP
ejpam-6951	489	22	this	this	DET
ejpam-6951	489	23	research	research	NOUN
ejpam-6951	489	24	was	be	AUX
ejpam-6951	489	25	done	do	VERB
ejpam-6951	489	26	while	while	SCONJ
ejpam-6951	489	27	the	the	DET
ejpam-6951	489	28	authors	author	NOUN
ejpam-6951	489	29	were	be	AUX
ejpam-6951	489	30	taking	take	VERB
ejpam-6951	489	31	bachelor	bachelor	NOUN
ejpam-6951	489	32	’s	’s	PART
ejpam-6951	489	33	degrees	degree	NOUN
ejpam-6951	489	34	at	at	ADP
ejpam-6951	489	35	the	the	DET
ejpam-6951	489	36	batangas	batangas	PROPN
ejpam-6951	489	37	state	state	PROPN
ejpam-6951	489	38	university	university	PROPN
ejpam-6951	489	39	,	,	PUNCT
ejpam-6951	489	40	the	the	DET
ejpam-6951	489	41	national	national	PROPN
ejpam-6951	489	42	engineering	engineering	PROPN
ejpam-6951	489	43	university	university	PROPN
ejpam-6951	489	44	(	(	PUNCT
ejpam-6951	489	45	batstateu	batstateu	VERB
ejpam-6951	489	46	the	the	DET
ejpam-6951	489	47	neu	neu	PROPN
ejpam-6951	489	48	)	)	PUNCT
ejpam-6951	489	49	.	.	PUNCT
ejpam-6951	490	1	additionally	additionally	ADV
ejpam-6951	490	2	,	,	PUNCT
ejpam-6951	490	3	the	the	DET
ejpam-6951	490	4	first	first	ADJ
ejpam-6951	490	5	author	author	NOUN
ejpam-6951	490	6	wishes	wish	VERB
ejpam-6951	490	7	to	to	PART
ejpam-6951	490	8	thank	thank	VERB
ejpam-6951	490	9	the	the	DET
ejpam-6951	490	10	department	department	NOUN
ejpam-6951	490	11	of	of	ADP
ejpam-6951	490	12	science	science	NOUN
ejpam-6951	490	13	and	and	CCONJ
ejpam-6951	490	14	technology	technology	NOUN
ejpam-6951	490	15	science	science	PROPN
ejpam-6951	490	16	education	education	PROPN
ejpam-6951	490	17	institute	institute	PROPN
ejpam-6951	490	18	(	(	PUNCT
ejpam-6951	490	19	dost	dost	NOUN
ejpam-6951	490	20	-	-	PUNCT
ejpam-6951	490	21	sei	sei	NOUN
ejpam-6951	490	22	)	)	PUNCT
ejpam-6951	490	23	for	for	ADP
ejpam-6951	490	24	extending	extend	VERB
ejpam-6951	490	25	financial	financial	ADJ
ejpam-6951	490	26	support	support	NOUN
ejpam-6951	490	27	,	,	PUNCT
ejpam-6951	490	28	which	which	PRON
ejpam-6951	490	29	helped	help	VERB
ejpam-6951	490	30	him	he	PRON
ejpam-6951	490	31	pursue	pursue	VERB
ejpam-6951	490	32	his	his	PRON
ejpam-6951	490	33	career	career	NOUN
ejpam-6951	490	34	in	in	ADP
ejpam-6951	490	35	the	the	DET
ejpam-6951	490	36	field	field	NOUN
ejpam-6951	490	37	of	of	ADP
ejpam-6951	490	38	mathematics	mathematic	NOUN
ejpam-6951	490	39	.	.	PUNCT
ejpam-6951	491	1	furthermore	furthermore	ADV
ejpam-6951	491	2	,	,	PUNCT
ejpam-6951	491	3	the	the	DET
ejpam-6951	491	4	authors	author	NOUN
ejpam-6951	491	5	would	would	AUX
ejpam-6951	491	6	like	like	VERB
ejpam-6951	491	7	to	to	PART
ejpam-6951	491	8	express	express	VERB
ejpam-6951	491	9	their	their	PRON
ejpam-6951	491	10	sincere	sincere	ADJ
ejpam-6951	491	11	appreciation	appreciation	NOUN
ejpam-6951	491	12	to	to	ADP
ejpam-6951	491	13	the	the	DET
ejpam-6951	491	14	anonymous	anonymous	ADJ
ejpam-6951	491	15	reviewers	reviewer	NOUN
ejpam-6951	491	16	and	and	CCONJ
ejpam-6951	491	17	the	the	DET
ejpam-6951	491	18	editors	editor	NOUN
ejpam-6951	491	19	of	of	ADP
ejpam-6951	491	20	this	this	DET
ejpam-6951	491	21	journal	journal	NOUN
ejpam-6951	491	22	for	for	ADP
ejpam-6951	491	23	their	their	PRON
ejpam-6951	491	24	assistance	assistance	NOUN
ejpam-6951	491	25	in	in	ADP
ejpam-6951	491	26	improving	improve	VERB
ejpam-6951	491	27	the	the	DET
ejpam-6951	491	28	paper	paper	NOUN
ejpam-6951	491	29	for	for	ADP
ejpam-6951	491	30	publication	publication	NOUN
ejpam-6951	491	31	.	.	PUNCT
ejpam-6951	492	1	references	reference	NOUN
ejpam-6951	492	2	[	[	X
ejpam-6951	492	3	1	1	NUM
ejpam-6951	492	4	]	]	PUNCT
ejpam-6951	492	5	r.	r.	PROPN
ejpam-6951	492	6	diestel	diestel	PROPN
ejpam-6951	492	7	.	.	PUNCT
ejpam-6951	493	1	graph	graph	NOUN
ejpam-6951	493	2	theory	theory	NOUN
ejpam-6951	493	3	,	,	PUNCT
ejpam-6951	493	4	volume	volume	NOUN
ejpam-6951	493	5	173	173	NUM
ejpam-6951	493	6	of	of	ADP
ejpam-6951	493	7	graduate	graduate	NOUN
ejpam-6951	493	8	text	text	NOUN
ejpam-6951	493	9	in	in	ADP
ejpam-6951	493	10	mathematics	mathematics	PROPN
ejpam-6951	493	11	.	.	PUNCT
ejpam-6951	494	1	springerverlag	springerverlag	PROPN
ejpam-6951	494	2	,	,	PUNCT
ejpam-6951	494	3	new	new	PROPN
ejpam-6951	494	4	york	york	PROPN
ejpam-6951	494	5	,	,	PUNCT
ejpam-6951	494	6	second	second	ADJ
ejpam-6951	494	7	edition	edition	NOUN
ejpam-6951	494	8	,	,	PUNCT
ejpam-6951	494	9	2000	2000	NUM
ejpam-6951	494	10	.	.	PUNCT
ejpam-6951	495	1	[	[	X
ejpam-6951	495	2	2	2	X
ejpam-6951	495	3	]	]	X
ejpam-6951	495	4	s.	s.	PROPN
ejpam-6951	495	5	butenko	butenko	PROPN
ejpam-6951	495	6	,	,	PUNCT
ejpam-6951	495	7	p.	p.	NOUN
ejpam-6951	495	8	festa	festa	NOUN
ejpam-6951	495	9	,	,	PUNCT
ejpam-6951	495	10	and	and	CCONJ
ejpam-6951	495	11	p.m.	p.m.	NOUN
ejpam-6951	495	12	pardalos	pardalo	NOUN
ejpam-6951	495	13	.	.	PUNCT
ejpam-6951	496	1	on	on	ADP
ejpam-6951	496	2	the	the	DET
ejpam-6951	496	3	chromatic	chromatic	ADJ
ejpam-6951	496	4	number	number	NOUN
ejpam-6951	496	5	of	of	ADP
ejpam-6951	496	6	graphs	graph	NOUN
ejpam-6951	496	7	.	.	PUNCT
ejpam-6951	497	1	journal	journal	NOUN
ejpam-6951	497	2	of	of	ADP
ejpam-6951	497	3	optimization	optimization	NOUN
ejpam-6951	497	4	theory	theory	NOUN
ejpam-6951	497	5	and	and	CCONJ
ejpam-6951	497	6	application	application	NOUN
ejpam-6951	497	7	,	,	PUNCT
ejpam-6951	497	8	109:69–82	109:69–82	NUM
ejpam-6951	497	9	,	,	PUNCT
ejpam-6951	497	10	2001	2001	NUM
ejpam-6951	497	11	.	.	PUNCT
ejpam-6951	498	1	[	[	X
ejpam-6951	498	2	3	3	X
ejpam-6951	498	3	]	]	X
ejpam-6951	498	4	j.	j.	PROPN
ejpam-6951	498	5	torino	torino	PROPN
ejpam-6951	498	6	and	and	CCONJ
ejpam-6951	498	7	n.	n.	PROPN
ejpam-6951	498	8	mame	mame	PROPN
ejpam-6951	498	9	.	.	PUNCT
ejpam-6951	499	1	on	on	ADP
ejpam-6951	499	2	the	the	DET
ejpam-6951	499	3	vertex	vertex	NOUN
ejpam-6951	499	4	-	-	PUNCT
ejpam-6951	499	5	generator	generator	NOUN
ejpam-6951	499	6	subgraph	subgraph	NOUN
ejpam-6951	499	7	of	of	ADP
ejpam-6951	499	8	a	a	DET
ejpam-6951	499	9	graph	graph	NOUN
ejpam-6951	499	10	.	.	PUNCT
ejpam-6951	499	11	contributed	contribute	VERB
ejpam-6951	499	12	paper	paper	NOUN
ejpam-6951	499	13	,	,	PUNCT
ejpam-6951	499	14	the	the	DET
ejpam-6951	499	15	asian	asian	PROPN
ejpam-6951	499	16	mathematical	mathematical	ADJ
ejpam-6951	499	17	conference	conference	NOUN
ejpam-6951	499	18	,	,	PUNCT
ejpam-6951	499	19	chiang	chiang	PROPN
ejpam-6951	499	20	mai	mai	PROPN
ejpam-6951	499	21	,	,	PUNCT
ejpam-6951	499	22	thailand	thailand	PROPN
ejpam-6951	499	23	,	,	PUNCT
ejpam-6951	499	24	august	august	PROPN
ejpam-6951	499	25	3	3	NUM
ejpam-6951	499	26	-	-	SYM
ejpam-6951	499	27	7	7	NUM
ejpam-6951	499	28	,	,	PUNCT
ejpam-6951	499	29	2025	2025	NUM
ejpam-6951	499	30	.	.	PUNCT
ejpam-6951	500	1	[	[	X
ejpam-6951	500	2	4	4	NUM
ejpam-6951	500	3	]	]	X
ejpam-6951	500	4	n.	n.	NOUN
ejpam-6951	500	5	mame	mame	PROPN
ejpam-6951	500	6	and	and	CCONJ
ejpam-6951	500	7	s.	s.	PROPN
ejpam-6951	500	8	gervacio	gervacio	PROPN
ejpam-6951	500	9	.	.	PUNCT
ejpam-6951	501	1	a	a	DET
ejpam-6951	501	2	note	note	NOUN
ejpam-6951	501	3	on	on	ADP
ejpam-6951	501	4	the	the	DET
ejpam-6951	501	5	generator	generator	NOUN
ejpam-6951	501	6	subgraph	subgraph	NOUN
ejpam-6951	501	7	of	of	ADP
ejpam-6951	501	8	a	a	DET
ejpam-6951	501	9	graph	graph	NOUN
ejpam-6951	501	10	.	.	PUNCT
ejpam-6951	502	1	electronic	electronic	ADJ
ejpam-6951	502	2	journal	journal	NOUN
ejpam-6951	502	3	of	of	ADP
ejpam-6951	502	4	graph	graph	NOUN
ejpam-6951	502	5	theory	theory	NOUN
ejpam-6951	502	6	and	and	CCONJ
ejpam-6951	502	7	applications	application	NOUN
ejpam-6951	502	8	,	,	PUNCT
ejpam-6951	502	9	8(1):17–27	8(1):17–27	NUM
ejpam-6951	502	10	,	,	PUNCT
ejpam-6951	502	11	2020	2020	NUM
ejpam-6951	502	12	.	.	PUNCT
ejpam-6951	503	1	[	[	X
ejpam-6951	503	2	5	5	NUM
ejpam-6951	503	3	]	]	PUNCT
ejpam-6951	503	4	r.	r.	PROPN
ejpam-6951	503	5	mame	mame	PROPN
ejpam-6951	503	6	.	.	PUNCT
ejpam-6951	504	1	some	some	DET
ejpam-6951	504	2	generator	generator	NOUN
ejpam-6951	504	3	subgraphs	subgraphs	NOUN
ejpam-6951	504	4	of	of	ADP
ejpam-6951	504	5	the	the	DET
ejpam-6951	504	6	square	square	NOUN
ejpam-6951	504	7	of	of	ADP
ejpam-6951	504	8	a	a	DET
ejpam-6951	504	9	cycle	cycle	NOUN
ejpam-6951	504	10	.	.	PUNCT
ejpam-6951	505	1	euporean	euporean	ADJ
ejpam-6951	505	2	journal	journal	NOUN
ejpam-6951	505	3	of	of	ADP
ejpam-6951	505	4	pure	pure	ADJ
ejpam-6951	505	5	and	and	CCONJ
ejpam-6951	505	6	applied	applied	ADJ
ejpam-6951	505	7	mathematics	mathematic	NOUN
ejpam-6951	505	8	,	,	PUNCT
ejpam-6951	505	9	17(4):3815–3825	17(4):3815–3825	NUM
ejpam-6951	505	10	,	,	PUNCT
ejpam-6951	505	11	2024	2024	NUM
ejpam-6951	505	12	.	.	PUNCT
ejpam-6951	506	1	[	[	X
ejpam-6951	506	2	6	6	NUM
ejpam-6951	506	3	]	]	PUNCT
ejpam-6951	506	4	f.	f.	PROPN
ejpam-6951	506	5	harary	harary	PROPN
ejpam-6951	506	6	.	.	PUNCT
ejpam-6951	507	1	graph	graph	NOUN
ejpam-6951	507	2	theory	theory	NOUN
ejpam-6951	507	3	.	.	PUNCT
ejpam-6951	508	1	addison	addison	PROPN
ejpam-6951	508	2	-	-	PUNCT
ejpam-6951	508	3	wesley	wesley	PROPN
ejpam-6951	508	4	series	series	PROPN
ejpam-6951	508	5	in	in	ADP
ejpam-6951	508	6	mathematics	mathematics	PROPN
ejpam-6951	508	7	.	.	PUNCT
ejpam-6951	509	1	addison	addison	PROPN
ejpam-6951	509	2	-	-	PUNCT
ejpam-6951	509	3	wesley	wesley	PROPN
ejpam-6951	509	4	publishing	publishing	PROPN
ejpam-6951	509	5	company	company	PROPN
ejpam-6951	509	6	,	,	PUNCT
ejpam-6951	509	7	inc	inc	PROPN
ejpam-6951	509	8	.	.	PROPN
ejpam-6951	509	9	,	,	PUNCT
ejpam-6951	509	10	new	new	PROPN
ejpam-6951	509	11	york	york	PROPN
ejpam-6951	509	12	,	,	PUNCT
ejpam-6951	509	13	1969	1969	NUM
ejpam-6951	509	14	.	.	PUNCT
ejpam-6951	510	1	[	[	X
ejpam-6951	510	2	7	7	X
ejpam-6951	510	3	]	]	X
ejpam-6951	510	4	h.	h.	PROPN
ejpam-6951	510	5	komarullah	komarullah	PROPN
ejpam-6951	510	6	,	,	PUNCT
ejpam-6951	510	7	j.	j.	PROPN
ejpam-6951	510	8	halilim	halilim	PROPN
ejpam-6951	510	9	,	,	PUNCT
ejpam-6951	510	10	and	and	CCONJ
ejpam-6951	510	11	k.	k.	PROPN
ejpam-6951	510	12	santoso	santoso	PROPN
ejpam-6951	510	13	.	.	PUNCT
ejpam-6951	511	1	on	on	ADP
ejpam-6951	511	2	the	the	DET
ejpam-6951	511	3	minimum	minimum	ADJ
ejpam-6951	511	4	span	span	NOUN
ejpam-6951	511	5	of	of	ADP
ejpam-6951	511	6	cone	cone	NOUN
ejpam-6951	511	7	,	,	PUNCT
ejpam-6951	511	8	tadpole	tadpole	NOUN
ejpam-6951	511	9	,	,	PUNCT
ejpam-6951	511	10	and	and	CCONJ
ejpam-6951	511	11	barbell	barbell	NOUN
ejpam-6951	511	12	graphs	graph	NOUN
ejpam-6951	511	13	.	.	PUNCT
ejpam-6951	512	1	in	in	ADP
ejpam-6951	512	2	proceedings	proceeding	NOUN
ejpam-6951	512	3	of	of	ADP
ejpam-6951	512	4	international	international	ADJ
ejpam-6951	512	5	conference	conference	NOUN
ejpam-6951	512	6	on	on	ADP
ejpam-6951	512	7	mathematics	mathematic	NOUN
ejpam-6951	512	8	,	,	PUNCT
ejpam-6951	512	9	geometry	geometry	NOUN
ejpam-6951	512	10	,	,	PUNCT
ejpam-6951	512	11	statistics	statistic	NOUN
ejpam-6951	512	12	and	and	CCONJ
ejpam-6951	512	13	computation	computation	NOUN
ejpam-6951	512	14	,	,	PUNCT
ejpam-6951	512	15	page	page	NOUN
ejpam-6951	512	16	41	41	NUM
ejpam-6951	512	17	,	,	PUNCT
ejpam-6951	512	18	2021	2021	NUM
ejpam-6951	512	19	.	.	PUNCT
ejpam-6951	513	1	[	[	X
ejpam-6951	513	2	8	8	NUM
ejpam-6951	513	3	]	]	X
ejpam-6951	513	4	b.	b.	PROPN
ejpam-6951	513	5	bollobás	bollobás	PROPN
ejpam-6951	513	6	.	.	PUNCT
ejpam-6951	514	1	random	random	ADJ
ejpam-6951	514	2	graphs	graph	NOUN
ejpam-6951	514	3	.	.	PUNCT
ejpam-6951	515	1	number	number	NOUN
ejpam-6951	515	2	73	73	NUM
ejpam-6951	515	3	in	in	ADP
ejpam-6951	515	4	cambridge	cambridge	PROPN
ejpam-6951	515	5	studies	study	NOUN
ejpam-6951	515	6	in	in	ADP
ejpam-6951	515	7	advanced	advanced	ADJ
ejpam-6951	515	8	mathematics	mathematic	NOUN
ejpam-6951	515	9	.	.	PUNCT
ejpam-6951	516	1	cambridge	cambridge	PROPN
ejpam-6951	516	2	university	university	PROPN
ejpam-6951	516	3	press	press	PROPN
ejpam-6951	516	4	,	,	PUNCT
ejpam-6951	516	5	new	new	PROPN
ejpam-6951	516	6	york	york	PROPN
ejpam-6951	516	7	,	,	PUNCT
ejpam-6951	516	8	second	second	ADJ
ejpam-6951	516	9	edition	edition	NOUN
ejpam-6951	516	10	,	,	PUNCT
ejpam-6951	516	11	2001	2001	NUM
ejpam-6951	516	12	.	.	PUNCT
ejpam-6951	517	1	[	[	X
ejpam-6951	517	2	9	9	NUM
ejpam-6951	517	3	]	]	PUNCT
ejpam-6951	517	4	j.	j.	PROPN
ejpam-6951	517	5	a.	a.	PROPN
ejpam-6951	517	6	bondy	bondy	PROPN
ejpam-6951	517	7	and	and	CCONJ
ejpam-6951	517	8	u.	u.	PROPN
ejpam-6951	517	9	s.	s.	PROPN
ejpam-6951	517	10	r.	r.	PROPN
ejpam-6951	517	11	murty	murty	PROPN
ejpam-6951	517	12	.	.	PUNCT
ejpam-6951	518	1	graph	graph	NOUN
ejpam-6951	518	2	theory	theory	NOUN
ejpam-6951	518	3	,	,	PUNCT
ejpam-6951	518	4	volume	volume	NOUN
ejpam-6951	518	5	244	244	NUM
ejpam-6951	518	6	of	of	ADP
ejpam-6951	518	7	graduate	graduate	NOUN
ejpam-6951	518	8	text	text	NOUN
ejpam-6951	518	9	in	in	ADP
ejpam-6951	518	10	mathematics	mathematics	PROPN
ejpam-6951	518	11	.	.	PUNCT
ejpam-6951	519	1	springer	springer	NOUN
ejpam-6951	519	2	-	-	PUNCT
ejpam-6951	519	3	verlag	verlag	PROPN
ejpam-6951	519	4	,	,	PUNCT
ejpam-6951	519	5	london	london	PROPN
ejpam-6951	519	6	,	,	PUNCT
ejpam-6951	519	7	first	first	ADJ
ejpam-6951	519	8	edition	edition	NOUN
ejpam-6951	519	9	,	,	PUNCT
ejpam-6951	519	10	2008	2008	NUM
ejpam-6951	519	11	.	.	PUNCT
ejpam-6951	520	1	[	[	X
ejpam-6951	520	2	10	10	NUM
ejpam-6951	520	3	]	]	X
ejpam-6951	520	4	g.	g.	PROPN
ejpam-6951	520	5	chartrand	chartrand	PROPN
ejpam-6951	520	6	,	,	PUNCT
ejpam-6951	520	7	l.	l.	PROPN
ejpam-6951	520	8	d.	d.	PROPN
ejpam-6951	520	9	lesniak	lesniak	PROPN
ejpam-6951	520	10	,	,	PUNCT
ejpam-6951	520	11	and	and	CCONJ
ejpam-6951	520	12	p.	p.	PROPN
ejpam-6951	520	13	zhang	zhang	PROPN
ejpam-6951	520	14	.	.	PUNCT
ejpam-6951	521	1	graphs	graph	NOUN
ejpam-6951	521	2	and	and	CCONJ
ejpam-6951	521	3	digraphs	digraph	NOUN
ejpam-6951	521	4	,	,	PUNCT
ejpam-6951	521	5	volume	volume	NOUN
ejpam-6951	521	6	39	39	NUM
ejpam-6951	521	7	of	of	ADP
ejpam-6951	521	8	textbooks	textbook	NOUN
ejpam-6951	521	9	in	in	ADP
ejpam-6951	521	10	mathematics	mathematic	NOUN
ejpam-6951	521	11	.	.	PUNCT
ejpam-6951	522	1	crc	crc	PROPN
ejpam-6951	522	2	press	press	PROPN
ejpam-6951	522	3	,	,	PUNCT
ejpam-6951	522	4	taylor	taylor	PROPN
ejpam-6951	522	5	&	&	CCONJ
ejpam-6951	522	6	francis	francis	PROPN
ejpam-6951	522	7	group	group	PROPN
ejpam-6951	522	8	,	,	PUNCT
ejpam-6951	522	9	boca	boca	PROPN
ejpam-6951	522	10	raton	raton	PROPN
ejpam-6951	522	11	,	,	PUNCT
ejpam-6951	522	12	sixth	sixth	ADJ
ejpam-6951	522	13	edition	edition	NOUN
ejpam-6951	522	14	,	,	PUNCT
ejpam-6951	522	15	2016	2016	NUM
ejpam-6951	522	16	.	.	PUNCT
ejpam-6951	523	1	[	[	X
ejpam-6951	523	2	11	11	NUM
ejpam-6951	523	3	]	]	PUNCT
ejpam-6951	523	4	e.	e.	PROPN
ejpam-6951	523	5	d.	d.	PROPN
ejpam-6951	523	6	nering	nering	PROPN
ejpam-6951	523	7	.	.	PUNCT
ejpam-6951	524	1	linear	linear	PROPN
ejpam-6951	524	2	algebra	algebra	NOUN
ejpam-6951	524	3	and	and	CCONJ
ejpam-6951	524	4	matrix	matrix	NOUN
ejpam-6951	524	5	theory	theory	NOUN
ejpam-6951	524	6	.	.	PUNCT
ejpam-6951	525	1	john	john	PROPN
ejpam-6951	525	2	wiley	wiley	PROPN
ejpam-6951	525	3	&	&	CCONJ
ejpam-6951	525	4	sons	sons	PROPN
ejpam-6951	525	5	,	,	PUNCT
ejpam-6951	525	6	inc	inc	PROPN
ejpam-6951	525	7	.	.	PROPN
ejpam-6951	525	8	,	,	PUNCT
ejpam-6951	525	9	new	new	PROPN
ejpam-6951	525	10	york	york	PROPN
ejpam-6951	525	11	,	,	PUNCT
ejpam-6951	525	12	second	second	ADJ
ejpam-6951	525	13	edition	edition	NOUN
ejpam-6951	525	14	,	,	PUNCT
ejpam-6951	525	15	1970	1970	NUM
ejpam-6951	525	16	.	.	PUNCT
ejpam-6951	526	1	[	[	X
ejpam-6951	526	2	12	12	NUM
ejpam-6951	526	3	]	]	X
ejpam-6951	526	4	r.	r.	PROPN
ejpam-6951	526	5	larson	larson	PROPN
ejpam-6951	526	6	and	and	CCONJ
ejpam-6951	526	7	d.	d.	PROPN
ejpam-6951	526	8	c.	c.	PROPN
ejpam-6951	526	9	falvo	falvo	PROPN
ejpam-6951	526	10	.	.	PUNCT
ejpam-6951	527	1	elementary	elementary	ADJ
ejpam-6951	527	2	linear	linear	PROPN
ejpam-6951	527	3	algebra	algebra	PROPN
ejpam-6951	527	4	,	,	PUNCT
ejpam-6951	527	5	chapter	chapter	NOUN
ejpam-6951	527	6	vector	vector	NOUN
ejpam-6951	527	7	spaces	space	NOUN
ejpam-6951	527	8	,	,	PUNCT
ejpam-6951	527	9	pages	page	NOUN
ejpam-6951	527	10	179–230	179–230	NUM
ejpam-6951	527	11	.	.	PUNCT
ejpam-6951	528	1	houghton	houghton	PROPN
ejpam-6951	528	2	mifflin	mifflin	PROPN
ejpam-6951	528	3	harcourt	harcourt	PROPN
ejpam-6951	528	4	publishing	publishing	PROPN
ejpam-6951	528	5	company	company	PROPN
ejpam-6951	528	6	,	,	PUNCT
ejpam-6951	528	7	boston	boston	PROPN
ejpam-6951	528	8	,	,	PUNCT
ejpam-6951	528	9	sixth	sixth	ADJ
ejpam-6951	528	10	edition	edition	NOUN
ejpam-6951	528	11	,	,	PUNCT
ejpam-6951	528	12	2009	2009	NUM
ejpam-6951	528	13	.	.	PUNCT