id	sid	tid	token	lemma	pos
ejpam-4821	1	1	european	european	PROPN
ejpam-4821	1	2	journal	journal	PROPN
ejpam-4821	1	3	of	of	ADP
ejpam-4821	1	4	pure	pure	ADJ
ejpam-4821	1	5	and	and	CCONJ
ejpam-4821	1	6	applied	apply	VERB
ejpam-4821	1	7	mathematics	mathematic	NOUN
ejpam-4821	1	8	vol	vol	NOUN
ejpam-4821	1	9	.	.	PUNCT
ejpam-4821	2	1	16	16	NUM
ejpam-4821	2	2	,	,	PUNCT
ejpam-4821	2	3	no	no	INTJ
ejpam-4821	2	4	.	.	NOUN
ejpam-4821	2	5	3	3	NUM
ejpam-4821	2	6	,	,	PUNCT
ejpam-4821	2	7	2023	2023	NUM
ejpam-4821	2	8	,	,	PUNCT
ejpam-4821	2	9	1647	1647	NUM
ejpam-4821	2	10	-	-	SYM
ejpam-4821	2	11	1662	1662	NUM
ejpam-4821	3	1	issn	issn	PROPN
ejpam-4821	3	2	1307	1307	NUM
ejpam-4821	3	3	-	-	SYM
ejpam-4821	3	4	5543	5543	NUM
ejpam-4821	3	5	–	–	PUNCT
ejpam-4821	3	6	ejpam.com	ejpam.com	X
ejpam-4821	3	7	published	publish	VERB
ejpam-4821	3	8	by	by	ADP
ejpam-4821	3	9	new	new	PROPN
ejpam-4821	3	10	york	york	PROPN
ejpam-4821	3	11	business	business	PROPN
ejpam-4821	3	12	global	global	ADJ
ejpam-4821	3	13	2	2	NUM
ejpam-4821	3	14	-	-	PUNCT
ejpam-4821	3	15	locating	locate	VERB
ejpam-4821	3	16	sets	set	NOUN
ejpam-4821	3	17	in	in	ADP
ejpam-4821	3	18	a	a	DET
ejpam-4821	3	19	graph	graph	NOUN
ejpam-4821	3	20	gymaima	gymaima	PROPN
ejpam-4821	3	21	cañete1	cañete1	PROPN
ejpam-4821	3	22	,	,	PUNCT
ejpam-4821	3	23	helen	helen	PROPN
ejpam-4821	3	24	rara2	rara2	PROPN
ejpam-4821	3	25	,	,	PUNCT
ejpam-4821	3	26	angelica	angelica	PROPN
ejpam-4821	3	27	mae	mae	PROPN
ejpam-4821	3	28	mahistrado1,∗	mahistrado1,∗	PROPN
ejpam-4821	3	29	1	1	NUM
ejpam-4821	3	30	department	department	NOUN
ejpam-4821	3	31	of	of	ADP
ejpam-4821	3	32	mathematics	mathematic	NOUN
ejpam-4821	3	33	and	and	CCONJ
ejpam-4821	3	34	statistics	statistic	NOUN
ejpam-4821	3	35	,	,	PUNCT
ejpam-4821	3	36	college	college	NOUN
ejpam-4821	3	37	of	of	ADP
ejpam-4821	3	38	science	science	NOUN
ejpam-4821	3	39	and	and	CCONJ
ejpam-4821	3	40	mathematics	mathematic	NOUN
ejpam-4821	3	41	,	,	PUNCT
ejpam-4821	3	42	mindanao	mindanao	PROPN
ejpam-4821	3	43	state	state	PROPN
ejpam-4821	3	44	university	university	PROPN
ejpam-4821	3	45	-	-	PUNCT
ejpam-4821	3	46	iligan	iligan	PROPN
ejpam-4821	3	47	institute	institute	PROPN
ejpam-4821	3	48	of	of	ADP
ejpam-4821	3	49	technology	technology	PROPN
ejpam-4821	3	50	,	,	PUNCT
ejpam-4821	3	51	9200	9200	NUM
ejpam-4821	3	52	iligan	iligan	ADJ
ejpam-4821	3	53	city	city	NOUN
ejpam-4821	3	54	,	,	PUNCT
ejpam-4821	3	55	philippines	philippines	PROPN
ejpam-4821	3	56	2	2	NUM
ejpam-4821	3	57	department	department	NOUN
ejpam-4821	3	58	of	of	ADP
ejpam-4821	3	59	mathematics	mathematic	NOUN
ejpam-4821	3	60	and	and	CCONJ
ejpam-4821	3	61	statistics	statistic	NOUN
ejpam-4821	3	62	,	,	PUNCT
ejpam-4821	3	63	college	college	NOUN
ejpam-4821	3	64	of	of	ADP
ejpam-4821	3	65	science	science	NOUN
ejpam-4821	3	66	and	and	CCONJ
ejpam-4821	3	67	mathematics	mathematic	NOUN
ejpam-4821	3	68	,	,	PUNCT
ejpam-4821	3	69	center	center	NOUN
ejpam-4821	3	70	of	of	ADP
ejpam-4821	3	71	graph	graph	NOUN
ejpam-4821	3	72	theory	theory	NOUN
ejpam-4821	3	73	,	,	PUNCT
ejpam-4821	3	74	algebra	algebra	NOUN
ejpam-4821	3	75	,	,	PUNCT
ejpam-4821	3	76	and	and	CCONJ
ejpam-4821	3	77	analysis	analysis	NOUN
ejpam-4821	3	78	-	-	PUNCT
ejpam-4821	3	79	premier	premier	NOUN
ejpam-4821	3	80	research	research	NOUN
ejpam-4821	3	81	institute	institute	PROPN
ejpam-4821	3	82	of	of	ADP
ejpam-4821	3	83	science	science	NOUN
ejpam-4821	3	84	and	and	CCONJ
ejpam-4821	3	85	mathematics	mathematic	NOUN
ejpam-4821	3	86	,	,	PUNCT
ejpam-4821	3	87	mindanao	mindanao	PROPN
ejpam-4821	3	88	state	state	PROPN
ejpam-4821	3	89	university	university	PROPN
ejpam-4821	3	90	-	-	PUNCT
ejpam-4821	3	91	iligan	iligan	PROPN
ejpam-4821	3	92	institute	institute	PROPN
ejpam-4821	3	93	of	of	ADP
ejpam-4821	3	94	technology	technology	PROPN
ejpam-4821	3	95	,	,	PUNCT
ejpam-4821	3	96	9200	9200	NUM
ejpam-4821	3	97	iligan	iligan	ADJ
ejpam-4821	3	98	city	city	NOUN
ejpam-4821	3	99	,	,	PUNCT
ejpam-4821	3	100	philippines	philippine	NOUN
ejpam-4821	3	101	abstract	abstract	ADJ
ejpam-4821	3	102	.	.	PUNCT
ejpam-4821	4	1	let	let	VERB
ejpam-4821	4	2	g	g	PRON
ejpam-4821	4	3	be	be	AUX
ejpam-4821	4	4	an	an	DET
ejpam-4821	4	5	undirected	undirected	ADJ
ejpam-4821	4	6	graph	graph	NOUN
ejpam-4821	4	7	with	with	ADP
ejpam-4821	4	8	vertex	vertex	NOUN
ejpam-4821	4	9	-	-	PUNCT
ejpam-4821	4	10	set	set	VERB
ejpam-4821	4	11	v	v	NOUN
ejpam-4821	4	12	(	(	PUNCT
ejpam-4821	4	13	g	g	NOUN
ejpam-4821	4	14	)	)	PUNCT
ejpam-4821	4	15	and	and	CCONJ
ejpam-4821	4	16	edge	edge	NOUN
ejpam-4821	4	17	-	-	PUNCT
ejpam-4821	4	18	set	set	VERB
ejpam-4821	4	19	e(g	e(g	NOUN
ejpam-4821	4	20	)	)	PUNCT
ejpam-4821	4	21	,	,	PUNCT
ejpam-4821	4	22	respectively	respectively	ADV
ejpam-4821	4	23	.	.	PUNCT
ejpam-4821	5	1	a	a	DET
ejpam-4821	5	2	set	set	NOUN
ejpam-4821	5	3	s	s	NOUN
ejpam-4821	5	4	⊆	⊆	NUM
ejpam-4821	5	5	v	v	NOUN
ejpam-4821	5	6	(	(	PUNCT
ejpam-4821	5	7	g	g	NOUN
ejpam-4821	5	8	)	)	PUNCT
ejpam-4821	5	9	is	be	AUX
ejpam-4821	5	10	a	a	DET
ejpam-4821	5	11	2	2	NUM
ejpam-4821	5	12	-	-	PUNCT
ejpam-4821	5	13	locating	locate	VERB
ejpam-4821	5	14	set	set	NOUN
ejpam-4821	5	15	of	of	ADP
ejpam-4821	5	16	g	g	PROPN
ejpam-4821	5	17	if	if	SCONJ
ejpam-4821	5	18	∣∣[(ng(x)\ng(y	∣∣[(ng(x)\ng(y	NOUN
ejpam-4821	5	19	)	)	PUNCT
ejpam-4821	5	20	)	)	PUNCT
ejpam-4821	6	1	∩	∩	PROPN
ejpam-4821	6	2	s]∪	s]∪	PROPN
ejpam-4821	6	3	[	[	PUNCT
ejpam-4821	6	4	(	(	PUNCT
ejpam-4821	6	5	ng(y)\ng(x	ng(y)\ng(x	ADV
ejpam-4821	6	6	)	)	PUNCT
ejpam-4821	6	7	)	)	PUNCT
ejpam-4821	7	1	∩	∩	NOUN
ejpam-4821	7	2	s	s	X
ejpam-4821	7	3	]	]	PUNCT
ejpam-4821	7	4	∣∣	∣∣	X
ejpam-4821	7	5	≥	≥	X
ejpam-4821	7	6	2	2	NUM
ejpam-4821	7	7	,	,	PUNCT
ejpam-4821	7	8	for	for	ADP
ejpam-4821	7	9	all	all	DET
ejpam-4821	7	10	x	x	NOUN
ejpam-4821	7	11	,	,	PUNCT
ejpam-4821	7	12	y	y	PROPN
ejpam-4821	7	13	∈	∈	PROPN
ejpam-4821	7	14	v	v	X
ejpam-4821	7	15	(	(	PUNCT
ejpam-4821	7	16	g)\s	g)\s	VERB
ejpam-4821	7	17	with	with	ADP
ejpam-4821	7	18	x	x	PROPN
ejpam-4821	7	19	̸=	̸=	PROPN
ejpam-4821	7	20	y	y	PROPN
ejpam-4821	7	21	,	,	PUNCT
ejpam-4821	7	22	and	and	CCONJ
ejpam-4821	7	23	for	for	ADP
ejpam-4821	7	24	all	all	PRON
ejpam-4821	7	25	v	v	ADP
ejpam-4821	7	26	∈	∈	NOUN
ejpam-4821	7	27	s	s	NOUN
ejpam-4821	7	28	and	and	CCONJ
ejpam-4821	7	29	w	w	PROPN
ejpam-4821	7	30	∈	∈	PROPN
ejpam-4821	7	31	v	v	NOUN
ejpam-4821	7	32	(	(	PUNCT
ejpam-4821	7	33	g)\s	g)\s	NOUN
ejpam-4821	7	34	,	,	PUNCT
ejpam-4821	7	35	(	(	PUNCT
ejpam-4821	7	36	ng(v)\ng(w	ng(v)\ng(w	ADJ
ejpam-4821	7	37	)	)	PUNCT
ejpam-4821	7	38	)	)	PUNCT
ejpam-4821	7	39	∩	∩	PROPN
ejpam-4821	7	40	s	s	PART
ejpam-4821	7	41	̸=	̸=	PROPN
ejpam-4821	7	42	∅	∅	NOUN
ejpam-4821	7	43	or	or	CCONJ
ejpam-4821	7	44	(	(	PUNCT
ejpam-4821	7	45	ng(w)\ng[v	ng(w)\ng[v	PROPN
ejpam-4821	7	46	]	]	PUNCT
ejpam-4821	7	47	)	)	PUNCT
ejpam-4821	7	48	∩	∩	PROPN
ejpam-4821	7	49	s	s	PART
ejpam-4821	7	50	̸=	̸=	PROPN
ejpam-4821	7	51	∅.	∅.	NOUN
ejpam-4821	7	52	in	in	ADP
ejpam-4821	7	53	this	this	DET
ejpam-4821	7	54	paper	paper	NOUN
ejpam-4821	7	55	,	,	PUNCT
ejpam-4821	7	56	we	we	PRON
ejpam-4821	7	57	investigate	investigate	VERB
ejpam-4821	7	58	the	the	DET
ejpam-4821	7	59	concept	concept	NOUN
ejpam-4821	7	60	and	and	CCONJ
ejpam-4821	7	61	study	study	VERB
ejpam-4821	7	62	2	2	NUM
ejpam-4821	7	63	-	-	PUNCT
ejpam-4821	7	64	locating	locate	VERB
ejpam-4821	7	65	sets	set	NOUN
ejpam-4821	7	66	in	in	ADP
ejpam-4821	7	67	graphs	graph	NOUN
ejpam-4821	7	68	resulting	result	VERB
ejpam-4821	7	69	from	from	ADP
ejpam-4821	7	70	some	some	DET
ejpam-4821	7	71	binary	binary	ADJ
ejpam-4821	7	72	operations	operation	NOUN
ejpam-4821	7	73	.	.	PUNCT
ejpam-4821	8	1	specifically	specifically	ADV
ejpam-4821	8	2	,	,	PUNCT
ejpam-4821	8	3	we	we	PRON
ejpam-4821	8	4	characterize	characterize	VERB
ejpam-4821	8	5	the	the	DET
ejpam-4821	8	6	2	2	NUM
ejpam-4821	8	7	-	-	PUNCT
ejpam-4821	8	8	locating	locate	VERB
ejpam-4821	8	9	sets	set	NOUN
ejpam-4821	8	10	in	in	ADP
ejpam-4821	8	11	the	the	DET
ejpam-4821	8	12	join	join	NOUN
ejpam-4821	8	13	,	,	PUNCT
ejpam-4821	8	14	corona	corona	PROPN
ejpam-4821	8	15	,	,	PUNCT
ejpam-4821	8	16	edge	edge	NOUN
ejpam-4821	8	17	corona	corona	NOUN
ejpam-4821	8	18	and	and	CCONJ
ejpam-4821	8	19	lexicographic	lexicographic	ADJ
ejpam-4821	8	20	product	product	NOUN
ejpam-4821	8	21	of	of	ADP
ejpam-4821	8	22	graphs	graph	NOUN
ejpam-4821	8	23	,	,	PUNCT
ejpam-4821	8	24	and	and	CCONJ
ejpam-4821	8	25	determine	determine	VERB
ejpam-4821	8	26	bounds	bound	NOUN
ejpam-4821	8	27	or	or	CCONJ
ejpam-4821	8	28	exact	exact	ADJ
ejpam-4821	8	29	values	value	NOUN
ejpam-4821	8	30	of	of	ADP
ejpam-4821	8	31	the	the	DET
ejpam-4821	8	32	2	2	NUM
ejpam-4821	8	33	-	-	PUNCT
ejpam-4821	8	34	locating	locate	VERB
ejpam-4821	8	35	number	number	NOUN
ejpam-4821	8	36	of	of	ADP
ejpam-4821	8	37	each	each	PRON
ejpam-4821	8	38	of	of	ADP
ejpam-4821	8	39	these	these	DET
ejpam-4821	8	40	graphs	graph	NOUN
ejpam-4821	8	41	.	.	PUNCT
ejpam-4821	9	1	2020	2020	NUM
ejpam-4821	9	2	mathematics	mathematic	NOUN
ejpam-4821	9	3	subject	subject	NOUN
ejpam-4821	9	4	classifications	classification	NOUN
ejpam-4821	9	5	:	:	PUNCT
ejpam-4821	9	6	05c69	05c69	X
ejpam-4821	9	7	key	key	ADJ
ejpam-4821	9	8	words	word	NOUN
ejpam-4821	9	9	and	and	CCONJ
ejpam-4821	9	10	phrases	phrase	NOUN
ejpam-4821	9	11	:	:	PUNCT
ejpam-4821	9	12	2	2	NUM
ejpam-4821	9	13	-	-	PUNCT
ejpam-4821	9	14	locating	locate	VERB
ejpam-4821	9	15	set	set	NOUN
ejpam-4821	9	16	,	,	PUNCT
ejpam-4821	9	17	2	2	NUM
ejpam-4821	9	18	-	-	PUNCT
ejpam-4821	9	19	locating	locate	VERB
ejpam-4821	9	20	number	number	NOUN
ejpam-4821	9	21	,	,	PUNCT
ejpam-4821	9	22	join	join	NOUN
ejpam-4821	9	23	,	,	PUNCT
ejpam-4821	9	24	corona	corona	PROPN
ejpam-4821	9	25	,	,	PUNCT
ejpam-4821	9	26	edge	edge	NOUN
ejpam-4821	9	27	corona	corona	NOUN
ejpam-4821	9	28	,	,	PUNCT
ejpam-4821	9	29	lexicographic	lexicographic	ADJ
ejpam-4821	9	30	product	product	NOUN
ejpam-4821	9	31	1	1	NUM
ejpam-4821	9	32	.	.	PUNCT
ejpam-4821	10	1	introduction	introduction	NOUN
ejpam-4821	10	2	resolving	resolve	VERB
ejpam-4821	10	3	sets	set	NOUN
ejpam-4821	10	4	and	and	CCONJ
ejpam-4821	10	5	metric	metric	ADJ
ejpam-4821	10	6	basis	basis	NOUN
ejpam-4821	10	7	are	be	AUX
ejpam-4821	10	8	emphasized	emphasize	VERB
ejpam-4821	10	9	for	for	ADP
ejpam-4821	10	10	their	their	PRON
ejpam-4821	10	11	application	application	NOUN
ejpam-4821	10	12	in	in	ADP
ejpam-4821	10	13	computer	computer	NOUN
ejpam-4821	10	14	science	science	NOUN
ejpam-4821	10	15	,	,	PUNCT
ejpam-4821	10	16	medical	medical	ADJ
ejpam-4821	10	17	sciences	science	NOUN
ejpam-4821	10	18	and	and	CCONJ
ejpam-4821	10	19	chemistry	chemistry	NOUN
ejpam-4821	10	20	.	.	PUNCT
ejpam-4821	11	1	the	the	DET
ejpam-4821	11	2	locating	locating	NOUN
ejpam-4821	11	3	set	set	VERB
ejpam-4821	11	4	in	in	ADP
ejpam-4821	11	5	graphs	graph	NOUN
ejpam-4821	11	6	can	can	AUX
ejpam-4821	11	7	be	be	AUX
ejpam-4821	11	8	viewed	view	VERB
ejpam-4821	11	9	as	as	ADP
ejpam-4821	11	10	the	the	DET
ejpam-4821	11	11	set	set	NOUN
ejpam-4821	11	12	of	of	ADP
ejpam-4821	11	13	monitors	monitor	NOUN
ejpam-4821	11	14	that	that	PRON
ejpam-4821	11	15	can	can	AUX
ejpam-4821	11	16	determine	determine	VERB
ejpam-4821	11	17	the	the	DET
ejpam-4821	11	18	exact	exact	ADJ
ejpam-4821	11	19	location	location	NOUN
ejpam-4821	11	20	of	of	ADP
ejpam-4821	11	21	an	an	DET
ejpam-4821	11	22	intruder	intruder	NOUN
ejpam-4821	11	23	.	.	PUNCT
ejpam-4821	12	1	the	the	DET
ejpam-4821	12	2	concept	concept	NOUN
ejpam-4821	12	3	of	of	ADP
ejpam-4821	12	4	2	2	NUM
ejpam-4821	12	5	-	-	PUNCT
ejpam-4821	12	6	locating	locate	VERB
ejpam-4821	12	7	set	set	NOUN
ejpam-4821	12	8	is	be	AUX
ejpam-4821	12	9	obtained	obtain	VERB
ejpam-4821	12	10	from	from	ADP
ejpam-4821	12	11	the	the	DET
ejpam-4821	12	12	concept	concept	NOUN
ejpam-4821	12	13	of	of	ADP
ejpam-4821	12	14	locating	locate	VERB
ejpam-4821	12	15	set	set	NOUN
ejpam-4821	12	16	.	.	PUNCT
ejpam-4821	13	1	requiring	require	VERB
ejpam-4821	13	2	such	such	DET
ejpam-4821	13	3	a	a	DET
ejpam-4821	13	4	set	set	NOUN
ejpam-4821	13	5	to	to	PART
ejpam-4821	13	6	be	be	AUX
ejpam-4821	13	7	2	2	NUM
ejpam-4821	13	8	-	-	PUNCT
ejpam-4821	13	9	locating	locating	NOUN
ejpam-4821	13	10	implies	imply	VERB
ejpam-4821	13	11	that	that	SCONJ
ejpam-4821	13	12	every	every	DET
ejpam-4821	13	13	pair	pair	NOUN
ejpam-4821	13	14	of	of	ADP
ejpam-4821	13	15	vertices	vertex	NOUN
ejpam-4821	13	16	where	where	SCONJ
ejpam-4821	13	17	there	there	PRON
ejpam-4821	13	18	is	be	VERB
ejpam-4821	13	19	no	no	DET
ejpam-4821	13	20	monitor	monitor	NOUN
ejpam-4821	13	21	must	must	AUX
ejpam-4821	13	22	be	be	AUX
ejpam-4821	13	23	connected	connect	VERB
ejpam-4821	13	24	to	to	ADP
ejpam-4821	13	25	at	at	ADV
ejpam-4821	13	26	least	least	ADV
ejpam-4821	13	27	two	two	NUM
ejpam-4821	13	28	monitoring	monitoring	NOUN
ejpam-4821	13	29	devices	device	NOUN
ejpam-4821	13	30	that	that	PRON
ejpam-4821	13	31	are	be	AUX
ejpam-4821	13	32	connected	connect	VERB
ejpam-4821	13	33	to	to	ADP
ejpam-4821	13	34	other	other	ADJ
ejpam-4821	13	35	monitors	monitor	NOUN
ejpam-4821	13	36	.	.	PUNCT
ejpam-4821	14	1	also	also	ADV
ejpam-4821	14	2	,	,	PUNCT
ejpam-4821	14	3	for	for	ADP
ejpam-4821	14	4	every	every	DET
ejpam-4821	14	5	vertex	vertex	NOUN
ejpam-4821	14	6	and	and	CCONJ
ejpam-4821	14	7	monitoring	monitor	VERB
ejpam-4821	14	8	device	device	NOUN
ejpam-4821	14	9	there	there	PRON
ejpam-4821	14	10	exists	exist	VERB
ejpam-4821	14	11	at	at	ADV
ejpam-4821	14	12	least	least	ADV
ejpam-4821	14	13	one	one	NUM
ejpam-4821	14	14	monitor	monitor	NOUN
ejpam-4821	14	15	that	that	PRON
ejpam-4821	14	16	is	be	AUX
ejpam-4821	14	17	connected	connect	VERB
ejpam-4821	14	18	to	to	ADP
ejpam-4821	14	19	it	it	PRON
ejpam-4821	14	20	.	.	PUNCT
ejpam-4821	15	1	hence	hence	ADV
ejpam-4821	15	2	,	,	PUNCT
ejpam-4821	15	3	2	2	X
ejpam-4821	15	4	-	-	PUNCT
ejpam-4821	15	5	locating	locate	VERB
ejpam-4821	15	6	set	set	NOUN
ejpam-4821	15	7	can	can	AUX
ejpam-4821	15	8	be	be	AUX
ejpam-4821	15	9	viewed	view	VERB
ejpam-4821	15	10	as	as	ADP
ejpam-4821	15	11	the	the	DET
ejpam-4821	15	12	set	set	NOUN
ejpam-4821	15	13	of	of	ADP
ejpam-4821	15	14	monitors	monitor	NOUN
ejpam-4821	15	15	that	that	PRON
ejpam-4821	15	16	can	can	AUX
ejpam-4821	15	17	determine	determine	VERB
ejpam-4821	15	18	the	the	DET
ejpam-4821	15	19	presence	presence	NOUN
ejpam-4821	15	20	of	of	ADP
ejpam-4821	15	21	an	an	DET
ejpam-4821	15	22	intruder	intruder	NOUN
ejpam-4821	15	23	.	.	PUNCT
ejpam-4821	16	1	∗corresponding	∗corresponde	VERB
ejpam-4821	16	2	author	author	NOUN
ejpam-4821	16	3	.	.	PUNCT
ejpam-4821	17	1	doi	doi	NOUN
ejpam-4821	17	2	:	:	PUNCT
ejpam-4821	17	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4821	https://doi.org/10.29020/nybg.ejpam.v16i3.4821	ADJ
ejpam-4821	17	4	email	email	NOUN
ejpam-4821	17	5	addresses	address	NOUN
ejpam-4821	17	6	:	:	PUNCT
ejpam-4821	17	7	gymaima.canete@g.msuiit.edu.ph	gymaima.canete@g.msuiit.edu.ph	PROPN
ejpam-4821	17	8	(	(	PUNCT
ejpam-4821	17	9	g.	g.	PROPN
ejpam-4821	17	10	canete	canete	PROPN
ejpam-4821	17	11	)	)	PUNCT
ejpam-4821	17	12	,	,	PUNCT
ejpam-4821	17	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4821	17	14	(	(	PUNCT
ejpam-4821	17	15	h.	h.	PROPN
ejpam-4821	17	16	rara	rara	PROPN
ejpam-4821	17	17	)	)	PUNCT
ejpam-4821	17	18	,	,	PUNCT
ejpam-4821	17	19	angelicamae.mahistrado@g.msuiit.edu.ph	angelicamae.mahistrado@g.msuiit.edu.ph	PROPN
ejpam-4821	17	20	(	(	PUNCT
ejpam-4821	17	21	a.m.	a.m.	NOUN
ejpam-4821	17	22	mahistrado	mahistrado	NOUN
ejpam-4821	17	23	)	)	PUNCT
ejpam-4821	17	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4821	17	25	1647	1647	NUM
ejpam-4821	17	26	©	©	PROPN
ejpam-4821	17	27	2023	2023	NUM
ejpam-4821	17	28	ejpam	ejpam	NOUN
ejpam-4821	17	29	all	all	DET
ejpam-4821	17	30	rights	right	NOUN
ejpam-4821	17	31	reserved	reserve	VERB
ejpam-4821	17	32	.	.	PUNCT
ejpam-4821	18	1	g.cañete	g.cañete	PROPN
ejpam-4821	18	2	,	,	PUNCT
ejpam-4821	18	3	h.	h.	PROPN
ejpam-4821	18	4	rara	rara	PROPN
ejpam-4821	18	5	,	,	PUNCT
ejpam-4821	18	6	a.m.	a.m.	PROPN
ejpam-4821	18	7	mahistrado	mahistrado	PROPN
ejpam-4821	18	8	/	/	SYM
ejpam-4821	18	9	eur	eur	PROPN
ejpam-4821	18	10	.	.	PUNCT
ejpam-4821	19	1	j.	j.	PROPN
ejpam-4821	19	2	pure	pure	PROPN
ejpam-4821	19	3	appl	appl	PROPN
ejpam-4821	19	4	.	.	PROPN
ejpam-4821	19	5	math	math	PROPN
ejpam-4821	19	6	,	,	PUNCT
ejpam-4821	19	7	16	16	NUM
ejpam-4821	19	8	(	(	PUNCT
ejpam-4821	19	9	3	3	NUM
ejpam-4821	19	10	)	)	PUNCT
ejpam-4821	19	11	(	(	PUNCT
ejpam-4821	19	12	2023	2023	NUM
ejpam-4821	19	13	)	)	PUNCT
ejpam-4821	19	14	,	,	PUNCT
ejpam-4821	19	15	1647	1647	NUM
ejpam-4821	19	16	-	-	SYM
ejpam-4821	19	17	1662	1662	NUM
ejpam-4821	19	18	1648	1648	NUM
ejpam-4821	19	19	in	in	ADP
ejpam-4821	19	20	1975	1975	NUM
ejpam-4821	19	21	,	,	PUNCT
ejpam-4821	19	22	slater	slater	NOUN
ejpam-4821	20	1	[	[	X
ejpam-4821	20	2	19	19	NUM
ejpam-4821	20	3	]	]	PUNCT
ejpam-4821	20	4	introduced	introduce	VERB
ejpam-4821	20	5	the	the	DET
ejpam-4821	20	6	concept	concept	NOUN
ejpam-4821	20	7	of	of	ADP
ejpam-4821	20	8	locating	locate	VERB
ejpam-4821	20	9	sets	set	NOUN
ejpam-4821	20	10	and	and	CCONJ
ejpam-4821	20	11	its	its	PRON
ejpam-4821	20	12	minimum	minimum	ADJ
ejpam-4821	20	13	cardinality	cardinality	NOUN
ejpam-4821	20	14	as	as	ADP
ejpam-4821	20	15	locating	locate	VERB
ejpam-4821	20	16	number	number	NOUN
ejpam-4821	20	17	.	.	PUNCT
ejpam-4821	21	1	harary	harary	NOUN
ejpam-4821	21	2	and	and	CCONJ
ejpam-4821	21	3	melter	melter	NOUN
ejpam-4821	21	4	also	also	ADV
ejpam-4821	21	5	utilized	utilize	VERB
ejpam-4821	21	6	a	a	DET
ejpam-4821	21	7	similar	similar	ADJ
ejpam-4821	21	8	idea	idea	NOUN
ejpam-4821	21	9	,	,	PUNCT
ejpam-4821	21	10	although	although	SCONJ
ejpam-4821	21	11	they	they	PRON
ejpam-4821	21	12	referred	refer	VERB
ejpam-4821	21	13	to	to	ADP
ejpam-4821	21	14	the	the	DET
ejpam-4821	21	15	locating	locating	NOUN
ejpam-4821	21	16	set	set	NOUN
ejpam-4821	21	17	and	and	CCONJ
ejpam-4821	21	18	the	the	DET
ejpam-4821	21	19	locating	locate	VERB
ejpam-4821	21	20	number	number	NOUN
ejpam-4821	21	21	,	,	PUNCT
ejpam-4821	21	22	respectively	respectively	ADV
ejpam-4821	21	23	,	,	PUNCT
ejpam-4821	21	24	using	use	VERB
ejpam-4821	21	25	the	the	DET
ejpam-4821	21	26	terms	term	NOUN
ejpam-4821	21	27	resolving	resolve	VERB
ejpam-4821	21	28	set	set	VERB
ejpam-4821	21	29	and	and	CCONJ
ejpam-4821	21	30	metric	metric	ADJ
ejpam-4821	21	31	dimension	dimension	NOUN
ejpam-4821	21	32	.	.	PUNCT
ejpam-4821	22	1	resolving	resolve	VERB
ejpam-4821	22	2	sets	set	NOUN
ejpam-4821	22	3	and	and	CCONJ
ejpam-4821	22	4	locating	locating	NOUN
ejpam-4821	22	5	sets	set	NOUN
ejpam-4821	22	6	,	,	PUNCT
ejpam-4821	22	7	however	however	ADV
ejpam-4821	22	8	,	,	PUNCT
ejpam-4821	22	9	are	be	AUX
ejpam-4821	22	10	defined	define	VERB
ejpam-4821	22	11	differently	differently	ADV
ejpam-4821	22	12	in	in	ADP
ejpam-4821	22	13	more	more	ADJ
ejpam-4821	22	14	recent	recent	ADJ
ejpam-4821	22	15	studies	study	NOUN
ejpam-4821	22	16	.	.	PUNCT
ejpam-4821	23	1	in	in	ADP
ejpam-4821	23	2	2013	2013	NUM
ejpam-4821	23	3	,	,	PUNCT
ejpam-4821	23	4	bailey	bailey	PROPN
ejpam-4821	23	5	et	et	PROPN
ejpam-4821	23	6	al	al	PROPN
ejpam-4821	23	7	.	.	PUNCT
ejpam-4821	24	1	[	[	X
ejpam-4821	24	2	1	1	X
ejpam-4821	24	3	]	]	PUNCT
ejpam-4821	24	4	defined	define	VERB
ejpam-4821	24	5	a	a	DET
ejpam-4821	24	6	resolving	resolving	NOUN
ejpam-4821	24	7	set	set	VERB
ejpam-4821	24	8	as	as	ADP
ejpam-4821	24	9	a	a	DET
ejpam-4821	24	10	set	set	NOUN
ejpam-4821	24	11	of	of	ADP
ejpam-4821	24	12	vertices	vertex	NOUN
ejpam-4821	24	13	s	s	PART
ejpam-4821	24	14	in	in	ADP
ejpam-4821	24	15	a	a	DET
ejpam-4821	24	16	graph	graph	NOUN
ejpam-4821	24	17	g	g	ADP
ejpam-4821	24	18	such	such	ADJ
ejpam-4821	24	19	that	that	PRON
ejpam-4821	24	20	for	for	ADP
ejpam-4821	24	21	any	any	DET
ejpam-4821	24	22	two	two	NUM
ejpam-4821	24	23	vertices	vertex	NOUN
ejpam-4821	24	24	u	u	NOUN
ejpam-4821	24	25	,	,	PUNCT
ejpam-4821	24	26	v	v	NOUN
ejpam-4821	24	27	,	,	PUNCT
ejpam-4821	24	28	there	there	PRON
ejpam-4821	24	29	exists	exist	VERB
ejpam-4821	24	30	x	x	X
ejpam-4821	24	31	∈	∈	PROPN
ejpam-4821	24	32	s	s	VERB
ejpam-4821	24	33	such	such	ADJ
ejpam-4821	24	34	that	that	SCONJ
ejpam-4821	24	35	the	the	DET
ejpam-4821	24	36	distance	distance	NOUN
ejpam-4821	24	37	d(u	d(u	PROPN
ejpam-4821	24	38	,	,	PUNCT
ejpam-4821	24	39	x	x	NOUN
ejpam-4821	24	40	)	)	PUNCT
ejpam-4821	24	41	̸=	̸=	PROPN
ejpam-4821	24	42	d(v	d(v	PROPN
ejpam-4821	24	43	,	,	PUNCT
ejpam-4821	24	44	x	x	NOUN
ejpam-4821	24	45	)	)	PUNCT
ejpam-4821	24	46	.	.	PUNCT
ejpam-4821	25	1	on	on	ADP
ejpam-4821	25	2	the	the	DET
ejpam-4821	25	3	other	other	ADJ
ejpam-4821	25	4	hand	hand	NOUN
ejpam-4821	25	5	,	,	PUNCT
ejpam-4821	25	6	canoy	canoy	NOUN
ejpam-4821	25	7	and	and	CCONJ
ejpam-4821	25	8	malacas	malacas	NOUN
ejpam-4821	26	1	[	[	X
ejpam-4821	26	2	8	8	NUM
ejpam-4821	26	3	]	]	PUNCT
ejpam-4821	26	4	defined	define	VERB
ejpam-4821	26	5	a	a	DET
ejpam-4821	26	6	locating	locating	NOUN
ejpam-4821	26	7	set	set	VERB
ejpam-4821	26	8	as	as	ADP
ejpam-4821	26	9	a	a	DET
ejpam-4821	26	10	set	set	NOUN
ejpam-4821	26	11	s	s	NOUN
ejpam-4821	26	12	⊆	⊆	NUM
ejpam-4821	26	13	v	v	NOUN
ejpam-4821	26	14	(	(	PUNCT
ejpam-4821	26	15	g	g	NOUN
ejpam-4821	26	16	)	)	PUNCT
ejpam-4821	26	17	of	of	ADP
ejpam-4821	26	18	g	g	NOUN
ejpam-4821	26	19	such	such	ADJ
ejpam-4821	26	20	that	that	PRON
ejpam-4821	26	21	for	for	ADP
ejpam-4821	26	22	every	every	DET
ejpam-4821	26	23	two	two	NUM
ejpam-4821	26	24	distinct	distinct	ADJ
ejpam-4821	26	25	vertices	vertex	NOUN
ejpam-4821	26	26	u	u	NOUN
ejpam-4821	26	27	and	and	CCONJ
ejpam-4821	26	28	v	v	NOUN
ejpam-4821	26	29	of	of	ADP
ejpam-4821	26	30	v	v	NOUN
ejpam-4821	26	31	(	(	PUNCT
ejpam-4821	26	32	g	g	NOUN
ejpam-4821	26	33	)	)	PUNCT
ejpam-4821	26	34	\	\	PROPN
ejpam-4821	27	1	s	s	X
ejpam-4821	27	2	,	,	PUNCT
ejpam-4821	27	3	ng(u)∩s	ng(u)∩s	PROPN
ejpam-4821	27	4	̸=	̸=	PROPN
ejpam-4821	27	5	ng(v)∩s	ng(v)∩s	PROPN
ejpam-4821	27	6	.	.	PUNCT
ejpam-4821	28	1	other	other	ADJ
ejpam-4821	28	2	variations	variation	NOUN
ejpam-4821	28	3	of	of	ADP
ejpam-4821	28	4	locating	locate	VERB
ejpam-4821	28	5	sets	set	NOUN
ejpam-4821	28	6	are	be	AUX
ejpam-4821	28	7	studied	study	VERB
ejpam-4821	28	8	in	in	ADP
ejpam-4821	28	9	[	[	X
ejpam-4821	28	10	16	16	NUM
ejpam-4821	28	11	]	]	PUNCT
ejpam-4821	28	12	,	,	PUNCT
ejpam-4821	28	13	[	[	X
ejpam-4821	28	14	6	6	NUM
ejpam-4821	28	15	]	]	PUNCT
ejpam-4821	28	16	,	,	PUNCT
ejpam-4821	28	17	[	[	X
ejpam-4821	28	18	11	11	NUM
ejpam-4821	28	19	]	]	PUNCT
ejpam-4821	28	20	,	,	PUNCT
ejpam-4821	28	21	[	[	X
ejpam-4821	28	22	13	13	NUM
ejpam-4821	28	23	]	]	PUNCT
ejpam-4821	28	24	,	,	PUNCT
ejpam-4821	28	25	[	[	X
ejpam-4821	28	26	14	14	NUM
ejpam-4821	28	27	]	]	PUNCT
ejpam-4821	28	28	,	,	PUNCT
ejpam-4821	28	29	[	[	X
ejpam-4821	28	30	15	15	NUM
ejpam-4821	28	31	]	]	PUNCT
ejpam-4821	28	32	and	and	CCONJ
ejpam-4821	28	33	[	[	X
ejpam-4821	28	34	7	7	NUM
ejpam-4821	28	35	]	]	PUNCT
ejpam-4821	28	36	.	.	PUNCT
ejpam-4821	29	1	in	in	ADP
ejpam-4821	29	2	2021	2021	NUM
ejpam-4821	29	3	,	,	PUNCT
ejpam-4821	29	4	j.	j.	PROPN
ejpam-4821	29	5	cabaro	cabaro	PROPN
ejpam-4821	29	6	and	and	CCONJ
ejpam-4821	29	7	h.	h.	PROPN
ejpam-4821	29	8	rara	rara	NOUN
ejpam-4821	30	1	[	[	X
ejpam-4821	30	2	5	5	NUM
ejpam-4821	30	3	]	]	PUNCT
ejpam-4821	30	4	studied	study	VERB
ejpam-4821	30	5	the	the	DET
ejpam-4821	30	6	idea	idea	NOUN
ejpam-4821	30	7	of	of	ADP
ejpam-4821	30	8	the	the	DET
ejpam-4821	30	9	2	2	NUM
ejpam-4821	30	10	-	-	PUNCT
ejpam-4821	30	11	resolving	resolve	VERB
ejpam-4821	30	12	sets	set	NOUN
ejpam-4821	30	13	in	in	ADP
ejpam-4821	30	14	the	the	DET
ejpam-4821	30	15	join	join	NOUN
ejpam-4821	30	16	and	and	CCONJ
ejpam-4821	30	17	corona	corona	NOUN
ejpam-4821	30	18	of	of	ADP
ejpam-4821	30	19	graphs	graph	NOUN
ejpam-4821	30	20	wherein	wherein	SCONJ
ejpam-4821	30	21	they	they	PRON
ejpam-4821	30	22	introduced	introduce	VERB
ejpam-4821	30	23	the	the	DET
ejpam-4821	30	24	idea	idea	NOUN
ejpam-4821	30	25	of	of	ADP
ejpam-4821	30	26	2	2	NUM
ejpam-4821	30	27	-	-	PUNCT
ejpam-4821	30	28	locating	locate	VERB
ejpam-4821	30	29	sets	set	NOUN
ejpam-4821	30	30	.	.	PUNCT
ejpam-4821	31	1	this	this	DET
ejpam-4821	31	2	work	work	NOUN
ejpam-4821	31	3	is	be	AUX
ejpam-4821	31	4	therefore	therefore	ADV
ejpam-4821	31	5	motivated	motivate	VERB
ejpam-4821	31	6	by	by	ADP
ejpam-4821	31	7	the	the	DET
ejpam-4821	31	8	recent	recent	ADJ
ejpam-4821	31	9	studies	study	NOUN
ejpam-4821	31	10	on	on	ADP
ejpam-4821	31	11	these	these	DET
ejpam-4821	31	12	variations	variation	NOUN
ejpam-4821	31	13	of	of	ADP
ejpam-4821	31	14	2	2	NUM
ejpam-4821	31	15	-	-	PUNCT
ejpam-4821	31	16	resolving	resolve	VERB
ejpam-4821	31	17	set	set	VERB
ejpam-4821	31	18	and	and	CCONJ
ejpam-4821	31	19	2	2	NUM
ejpam-4821	31	20	-	-	PUNCT
ejpam-4821	31	21	metric	metric	ADJ
ejpam-4821	31	22	dimension	dimension	NOUN
ejpam-4821	31	23	that	that	PRON
ejpam-4821	31	24	utilize	utilize	VERB
ejpam-4821	31	25	the	the	DET
ejpam-4821	31	26	concepts	concept	NOUN
ejpam-4821	31	27	of	of	ADP
ejpam-4821	31	28	2	2	NUM
ejpam-4821	31	29	-	-	PUNCT
ejpam-4821	31	30	locating	locate	VERB
ejpam-4821	31	31	set	set	NOUN
ejpam-4821	31	32	and	and	CCONJ
ejpam-4821	31	33	2	2	NUM
ejpam-4821	31	34	-	-	PUNCT
ejpam-4821	31	35	locating	locate	VERB
ejpam-4821	31	36	number	number	NOUN
ejpam-4821	31	37	.	.	PUNCT
ejpam-4821	32	1	other	other	ADJ
ejpam-4821	32	2	studies	study	NOUN
ejpam-4821	32	3	that	that	PRON
ejpam-4821	32	4	deal	deal	VERB
ejpam-4821	32	5	with	with	ADP
ejpam-4821	32	6	the	the	DET
ejpam-4821	32	7	concept	concept	NOUN
ejpam-4821	32	8	of	of	ADP
ejpam-4821	32	9	2	2	NUM
ejpam-4821	32	10	-	-	PUNCT
ejpam-4821	32	11	locating	locate	VERB
ejpam-4821	32	12	sets	set	NOUN
ejpam-4821	32	13	are	be	AUX
ejpam-4821	32	14	located	locate	VERB
ejpam-4821	32	15	in	in	ADP
ejpam-4821	32	16	[	[	X
ejpam-4821	32	17	6	6	NUM
ejpam-4821	32	18	]	]	PUNCT
ejpam-4821	32	19	,	,	PUNCT
ejpam-4821	32	20	[	[	X
ejpam-4821	32	21	9	9	NUM
ejpam-4821	32	22	]	]	PUNCT
ejpam-4821	32	23	,	,	PUNCT
ejpam-4821	32	24	[	[	X
ejpam-4821	32	25	10	10	NUM
ejpam-4821	32	26	]	]	PUNCT
ejpam-4821	32	27	,	,	PUNCT
ejpam-4821	32	28	[	[	X
ejpam-4821	32	29	12	12	NUM
ejpam-4821	32	30	]	]	PUNCT
ejpam-4821	32	31	and	and	CCONJ
ejpam-4821	32	32	[	[	X
ejpam-4821	32	33	18	18	NUM
ejpam-4821	32	34	]	]	SYM
ejpam-4821	32	35	.	.	PUNCT
ejpam-4821	33	1	2	2	X
ejpam-4821	33	2	.	.	X
ejpam-4821	33	3	terminology	terminology	NOUN
ejpam-4821	33	4	and	and	CCONJ
ejpam-4821	33	5	notation	notation	NOUN
ejpam-4821	33	6	in	in	ADP
ejpam-4821	33	7	this	this	DET
ejpam-4821	33	8	study	study	NOUN
ejpam-4821	33	9	,	,	PUNCT
ejpam-4821	33	10	we	we	PRON
ejpam-4821	33	11	consider	consider	VERB
ejpam-4821	33	12	finite	finite	ADJ
ejpam-4821	33	13	,	,	PUNCT
ejpam-4821	33	14	simple	simple	ADJ
ejpam-4821	33	15	,	,	PUNCT
ejpam-4821	33	16	connected	connect	VERB
ejpam-4821	33	17	,	,	PUNCT
ejpam-4821	33	18	undirected	undirected	ADJ
ejpam-4821	33	19	graphs	graph	NOUN
ejpam-4821	33	20	.	.	PUNCT
ejpam-4821	34	1	for	for	ADP
ejpam-4821	34	2	basic	basic	ADJ
ejpam-4821	34	3	graphtheoretic	graphtheoretic	ADJ
ejpam-4821	34	4	concepts	concept	NOUN
ejpam-4821	34	5	,	,	PUNCT
ejpam-4821	34	6	we	we	PRON
ejpam-4821	34	7	then	then	ADV
ejpam-4821	34	8	refer	refer	VERB
ejpam-4821	34	9	readers	reader	NOUN
ejpam-4821	34	10	to	to	ADP
ejpam-4821	34	11	[	[	X
ejpam-4821	34	12	3	3	NUM
ejpam-4821	34	13	]	]	PUNCT
ejpam-4821	34	14	and	and	CCONJ
ejpam-4821	34	15	[	[	X
ejpam-4821	34	16	4	4	NUM
ejpam-4821	34	17	]	]	PUNCT
ejpam-4821	34	18	.	.	PUNCT
ejpam-4821	35	1	the	the	DET
ejpam-4821	35	2	following	follow	VERB
ejpam-4821	35	3	concepts	concept	NOUN
ejpam-4821	35	4	are	be	AUX
ejpam-4821	35	5	found	find	VERB
ejpam-4821	35	6	in	in	ADP
ejpam-4821	35	7	[	[	X
ejpam-4821	35	8	2	2	NUM
ejpam-4821	35	9	]	]	PUNCT
ejpam-4821	35	10	,	,	PUNCT
ejpam-4821	35	11	[	[	X
ejpam-4821	35	12	3	3	NUM
ejpam-4821	35	13	]	]	PUNCT
ejpam-4821	35	14	,	,	PUNCT
ejpam-4821	35	15	[	[	X
ejpam-4821	35	16	5	5	NUM
ejpam-4821	35	17	]	]	PUNCT
ejpam-4821	35	18	and	and	CCONJ
ejpam-4821	35	19	[	[	X
ejpam-4821	35	20	17	17	NUM
ejpam-4821	35	21	]	]	PUNCT
ejpam-4821	35	22	respectively	respectively	ADV
ejpam-4821	35	23	.	.	PUNCT
ejpam-4821	36	1	the	the	DET
ejpam-4821	36	2	open	open	ADJ
ejpam-4821	36	3	neighborhood	neighborhood	NOUN
ejpam-4821	36	4	of	of	ADP
ejpam-4821	36	5	a	a	DET
ejpam-4821	36	6	vertex	vertex	NOUN
ejpam-4821	36	7	v	v	NOUN
ejpam-4821	36	8	in	in	ADP
ejpam-4821	36	9	a	a	DET
ejpam-4821	36	10	graph	graph	NOUN
ejpam-4821	36	11	g	g	NOUN
ejpam-4821	36	12	is	be	AUX
ejpam-4821	36	13	defined	define	VERB
ejpam-4821	36	14	as	as	ADP
ejpam-4821	36	15	the	the	DET
ejpam-4821	36	16	set	set	NOUN
ejpam-4821	36	17	ng(v	ng(v	PUNCT
ejpam-4821	36	18	)	)	PUNCT
ejpam-4821	36	19	=	=	SYM
ejpam-4821	37	1	{	{	PUNCT
ejpam-4821	37	2	u	u	NOUN
ejpam-4821	37	3	∈	∈	PROPN
ejpam-4821	37	4	v	v	NOUN
ejpam-4821	37	5	(	(	PUNCT
ejpam-4821	37	6	g	g	NOUN
ejpam-4821	37	7	)	)	PUNCT
ejpam-4821	37	8	:	:	PUNCT
ejpam-4821	37	9	uv	uv	PROPN
ejpam-4821	37	10	∈	∈	PROPN
ejpam-4821	37	11	e(g	e(g	PROPN
ejpam-4821	37	12	)	)	PUNCT
ejpam-4821	37	13	}	}	PUNCT
ejpam-4821	37	14	,	,	PUNCT
ejpam-4821	37	15	while	while	SCONJ
ejpam-4821	37	16	the	the	DET
ejpam-4821	37	17	closed	closed	ADJ
ejpam-4821	37	18	neighborhood	neighborhood	NOUN
ejpam-4821	37	19	of	of	ADP
ejpam-4821	37	20	a	a	DET
ejpam-4821	37	21	vertex	vertex	NOUN
ejpam-4821	37	22	v	v	NOUN
ejpam-4821	37	23	in	in	ADP
ejpam-4821	37	24	g	g	PROPN
ejpam-4821	37	25	is	be	AUX
ejpam-4821	37	26	defined	define	VERB
ejpam-4821	37	27	as	as	ADP
ejpam-4821	37	28	ng[v	ng[v	NOUN
ejpam-4821	37	29	]	]	X
ejpam-4821	37	30	=	=	SYM
ejpam-4821	37	31	ng(v	ng(v	X
ejpam-4821	37	32	)	)	PUNCT
ejpam-4821	37	33	∪	∪	ADP
ejpam-4821	37	34	{	{	PUNCT
ejpam-4821	37	35	v	v	NOUN
ejpam-4821	37	36	}	}	PUNCT
ejpam-4821	37	37	.	.	PUNCT
ejpam-4821	38	1	the	the	DET
ejpam-4821	38	2	open	open	ADJ
ejpam-4821	38	3	neighborhood	neighborhood	NOUN
ejpam-4821	38	4	of	of	ADP
ejpam-4821	38	5	a	a	DET
ejpam-4821	38	6	set	set	NOUN
ejpam-4821	38	7	s	s	NOUN
ejpam-4821	38	8	⊆	⊆	NUM
ejpam-4821	38	9	v	v	NOUN
ejpam-4821	38	10	(	(	PUNCT
ejpam-4821	38	11	g	g	NOUN
ejpam-4821	38	12	)	)	PUNCT
ejpam-4821	38	13	is	be	AUX
ejpam-4821	38	14	defined	define	VERB
ejpam-4821	38	15	as	as	ADP
ejpam-4821	38	16	ng(s	ng(s	NUM
ejpam-4821	38	17	)	)	PUNCT
ejpam-4821	39	1	=	=	SYM
ejpam-4821	39	2	⋃	⋃	NOUN
ejpam-4821	39	3	v∈x	v∈x	NOUN
ejpam-4821	39	4	ng(v	ng(v	NOUN
ejpam-4821	39	5	)	)	PUNCT
ejpam-4821	39	6	,	,	PUNCT
ejpam-4821	39	7	while	while	SCONJ
ejpam-4821	39	8	its	its	PRON
ejpam-4821	39	9	closed	closed	ADJ
ejpam-4821	39	10	neighborhood	neighborhood	NOUN
ejpam-4821	39	11	is	be	AUX
ejpam-4821	39	12	ng[s	ng[	NOUN
ejpam-4821	39	13	]	]	PUNCT
ejpam-4821	39	14	=	=	SYM
ejpam-4821	39	15	ng(s)∪s	ng(s)∪s	PROPN
ejpam-4821	39	16	.	.	PUNCT
ejpam-4821	40	1	a	a	DET
ejpam-4821	40	2	connected	connected	ADJ
ejpam-4821	40	3	graph	graph	NOUN
ejpam-4821	40	4	g	g	NOUN
ejpam-4821	40	5	of	of	ADP
ejpam-4821	40	6	order	order	NOUN
ejpam-4821	40	7	n	n	PRON
ejpam-4821	40	8	≥	≥	NOUN
ejpam-4821	40	9	3	3	NUM
ejpam-4821	40	10	is	be	AUX
ejpam-4821	40	11	point	point	NOUN
ejpam-4821	40	12	distinguishing	distinguish	VERB
ejpam-4821	40	13	if	if	SCONJ
ejpam-4821	40	14	for	for	ADP
ejpam-4821	40	15	any	any	DET
ejpam-4821	40	16	two	two	NUM
ejpam-4821	40	17	distinct	distinct	ADJ
ejpam-4821	40	18	vertices	vertex	NOUN
ejpam-4821	40	19	u	u	NOUN
ejpam-4821	40	20	and	and	CCONJ
ejpam-4821	40	21	v	v	NOUN
ejpam-4821	40	22	of	of	ADP
ejpam-4821	40	23	g	g	NOUN
ejpam-4821	40	24	,	,	PUNCT
ejpam-4821	40	25	ng[u	ng[u	PROPN
ejpam-4821	40	26	]	]	X
ejpam-4821	40	27	̸=	̸=	PROPN
ejpam-4821	40	28	ng[v	ng[v	PROPN
ejpam-4821	40	29	]	]	PUNCT
ejpam-4821	40	30	.	.	PUNCT
ejpam-4821	41	1	it	it	PRON
ejpam-4821	41	2	is	be	AUX
ejpam-4821	41	3	totally	totally	ADV
ejpam-4821	41	4	point	point	NOUN
ejpam-4821	41	5	determining	determine	VERB
ejpam-4821	41	6	if	if	SCONJ
ejpam-4821	41	7	for	for	ADP
ejpam-4821	41	8	any	any	DET
ejpam-4821	41	9	two	two	NUM
ejpam-4821	41	10	distinct	distinct	ADJ
ejpam-4821	41	11	vertices	vertex	NOUN
ejpam-4821	41	12	u	u	NOUN
ejpam-4821	41	13	and	and	CCONJ
ejpam-4821	41	14	v	v	NOUN
ejpam-4821	41	15	of	of	ADP
ejpam-4821	41	16	g	g	NOUN
ejpam-4821	41	17	,	,	PUNCT
ejpam-4821	41	18	ng(u	ng(u	NOUN
ejpam-4821	41	19	)	)	PUNCT
ejpam-4821	41	20	̸=	̸=	PROPN
ejpam-4821	41	21	ng(v	ng(v	PUNCT
ejpam-4821	41	22	)	)	PUNCT
ejpam-4821	41	23	and	and	CCONJ
ejpam-4821	41	24	ng[u	ng[u	PROPN
ejpam-4821	41	25	]	]	X
ejpam-4821	41	26	̸=	̸=	PROPN
ejpam-4821	41	27	ng[v	ng[v	PROPN
ejpam-4821	41	28	]	]	PUNCT
ejpam-4821	41	29	.	.	PUNCT
ejpam-4821	42	1	for	for	ADP
ejpam-4821	42	2	an	an	DET
ejpam-4821	42	3	ordered	order	VERB
ejpam-4821	42	4	set	set	NOUN
ejpam-4821	42	5	of	of	ADP
ejpam-4821	42	6	vertices	vertex	NOUN
ejpam-4821	42	7	w	w	NOUN
ejpam-4821	42	8	=	=	SYM
ejpam-4821	42	9	{	{	PUNCT
ejpam-4821	42	10	w1	w1	NOUN
ejpam-4821	42	11	,	,	PUNCT
ejpam-4821	42	12	w2	w2	NOUN
ejpam-4821	42	13	,	,	PUNCT
ejpam-4821	42	14	...	...	PUNCT
ejpam-4821	42	15	,	,	PUNCT
ejpam-4821	42	16	wk	wk	ADP
ejpam-4821	42	17	}	}	PUNCT
ejpam-4821	42	18	⊆	⊆	NUM
ejpam-4821	42	19	v	v	NOUN
ejpam-4821	42	20	(	(	PUNCT
ejpam-4821	42	21	g	g	NOUN
ejpam-4821	42	22	)	)	PUNCT
ejpam-4821	42	23	and	and	CCONJ
ejpam-4821	42	24	a	a	DET
ejpam-4821	42	25	vertex	vertex	NOUN
ejpam-4821	42	26	v	v	NOUN
ejpam-4821	42	27	in	in	ADP
ejpam-4821	42	28	g	g	NOUN
ejpam-4821	42	29	,	,	PUNCT
ejpam-4821	42	30	we	we	PRON
ejpam-4821	42	31	refer	refer	VERB
ejpam-4821	42	32	to	to	ADP
ejpam-4821	42	33	the	the	DET
ejpam-4821	42	34	k	k	NOUN
ejpam-4821	42	35	-	-	NOUN
ejpam-4821	42	36	vector	vector	NOUN
ejpam-4821	42	37	(	(	PUNCT
ejpam-4821	42	38	ordered	order	VERB
ejpam-4821	42	39	k	k	NOUN
ejpam-4821	42	40	-	-	PUNCT
ejpam-4821	42	41	tuple	tuple	NOUN
ejpam-4821	42	42	)	)	PUNCT
ejpam-4821	42	43	rg(v	rg(v	PROPN
ejpam-4821	42	44	/	/	SYM
ejpam-4821	42	45	w	w	NOUN
ejpam-4821	42	46	)	)	PUNCT
ejpam-4821	43	1	=	=	SYM
ejpam-4821	43	2	(	(	PUNCT
ejpam-4821	43	3	dg(v	dg(v	X
ejpam-4821	43	4	,	,	PUNCT
ejpam-4821	43	5	w1	w1	NOUN
ejpam-4821	43	6	)	)	PUNCT
ejpam-4821	43	7	,	,	PUNCT
ejpam-4821	43	8	dg(v	dg(v	X
ejpam-4821	43	9	,	,	PUNCT
ejpam-4821	43	10	w2	w2	NOUN
ejpam-4821	43	11	)	)	PUNCT
ejpam-4821	43	12	,	,	PUNCT
ejpam-4821	43	13	...	...	PUNCT
ejpam-4821	43	14	,	,	PUNCT
ejpam-4821	43	15	dg(v	dg(v	X
ejpam-4821	43	16	,	,	PUNCT
ejpam-4821	43	17	wk	wk	NOUN
ejpam-4821	43	18	)	)	PUNCT
ejpam-4821	43	19	)	)	PUNCT
ejpam-4821	44	1	as	as	ADP
ejpam-4821	44	2	the	the	DET
ejpam-4821	44	3	(	(	PUNCT
ejpam-4821	44	4	metric	metric	ADJ
ejpam-4821	44	5	)	)	PUNCT
ejpam-4821	44	6	representation	representation	NOUN
ejpam-4821	44	7	of	of	ADP
ejpam-4821	44	8	v	v	NOUN
ejpam-4821	44	9	with	with	ADP
ejpam-4821	44	10	respect	respect	NOUN
ejpam-4821	44	11	to	to	ADP
ejpam-4821	44	12	w	w	PROPN
ejpam-4821	44	13	.	.	PUNCT
ejpam-4821	45	1	the	the	DET
ejpam-4821	45	2	set	set	NOUN
ejpam-4821	45	3	w	w	NOUN
ejpam-4821	45	4	is	be	AUX
ejpam-4821	45	5	called	call	VERB
ejpam-4821	45	6	a	a	DET
ejpam-4821	45	7	resolving	resolving	NOUN
ejpam-4821	45	8	set	set	VERB
ejpam-4821	45	9	for	for	ADP
ejpam-4821	45	10	g	g	PROPN
ejpam-4821	45	11	if	if	SCONJ
ejpam-4821	45	12	distinct	distinct	ADJ
ejpam-4821	45	13	vertices	vertex	NOUN
ejpam-4821	45	14	have	have	VERB
ejpam-4821	45	15	distinct	distinct	ADJ
ejpam-4821	45	16	representations	representation	NOUN
ejpam-4821	45	17	with	with	ADP
ejpam-4821	45	18	respect	respect	NOUN
ejpam-4821	45	19	to	to	ADP
ejpam-4821	45	20	w	w	PROPN
ejpam-4821	45	21	.	.	PUNCT
ejpam-4821	46	1	hence	hence	ADV
ejpam-4821	46	2	,	,	PUNCT
ejpam-4821	46	3	if	if	SCONJ
ejpam-4821	46	4	w	w	NOUN
ejpam-4821	46	5	is	be	AUX
ejpam-4821	46	6	a	a	DET
ejpam-4821	46	7	resolving	resolving	NOUN
ejpam-4821	46	8	set	set	NOUN
ejpam-4821	46	9	of	of	ADP
ejpam-4821	46	10	cardinality	cardinality	PROPN
ejpam-4821	46	11	k	k	PROPN
ejpam-4821	46	12	for	for	ADP
ejpam-4821	46	13	a	a	DET
ejpam-4821	46	14	graph	graph	NOUN
ejpam-4821	46	15	g	g	NOUN
ejpam-4821	46	16	of	of	ADP
ejpam-4821	46	17	order	order	NOUN
ejpam-4821	46	18	n	n	CCONJ
ejpam-4821	46	19	,	,	PUNCT
ejpam-4821	46	20	then	then	ADV
ejpam-4821	46	21	the	the	DET
ejpam-4821	46	22	set	set	NOUN
ejpam-4821	46	23	{	{	PUNCT
ejpam-4821	46	24	rg(v	rg(v	NOUN
ejpam-4821	46	25	/	/	SYM
ejpam-4821	46	26	w	w	NOUN
ejpam-4821	46	27	)	)	PUNCT
ejpam-4821	46	28	:	:	PUNCT
ejpam-4821	46	29	v	v	X
ejpam-4821	46	30	∈	∈	PROPN
ejpam-4821	46	31	v	v	NOUN
ejpam-4821	46	32	(	(	PUNCT
ejpam-4821	46	33	g	g	NOUN
ejpam-4821	46	34	)	)	PUNCT
ejpam-4821	46	35	}	}	PUNCT
ejpam-4821	46	36	consists	consist	VERB
ejpam-4821	46	37	of	of	ADP
ejpam-4821	46	38	n	n	PRON
ejpam-4821	46	39	distinct	distinct	ADJ
ejpam-4821	46	40	k	k	NOUN
ejpam-4821	46	41	-	-	NOUN
ejpam-4821	46	42	vectors	vector	NOUN
ejpam-4821	46	43	.	.	PUNCT
ejpam-4821	47	1	a	a	DET
ejpam-4821	47	2	resolving	resolving	NOUN
ejpam-4821	47	3	set	set	NOUN
ejpam-4821	47	4	of	of	ADP
ejpam-4821	47	5	minimum	minimum	ADJ
ejpam-4821	47	6	cardinality	cardinality	NOUN
ejpam-4821	47	7	is	be	AUX
ejpam-4821	47	8	called	call	VERB
ejpam-4821	47	9	aminimum	aminimum	ADJ
ejpam-4821	47	10	resolving	resolving	NOUN
ejpam-4821	47	11	set	set	VERB
ejpam-4821	47	12	or	or	CCONJ
ejpam-4821	47	13	a	a	DET
ejpam-4821	47	14	basis	basis	NOUN
ejpam-4821	47	15	,	,	PUNCT
ejpam-4821	47	16	and	and	CCONJ
ejpam-4821	47	17	the	the	DET
ejpam-4821	47	18	cardinality	cardinality	NOUN
ejpam-4821	47	19	of	of	ADP
ejpam-4821	47	20	a	a	DET
ejpam-4821	47	21	basis	basis	NOUN
ejpam-4821	47	22	for	for	ADP
ejpam-4821	47	23	g	g	PROPN
ejpam-4821	47	24	is	be	AUX
ejpam-4821	47	25	the	the	DET
ejpam-4821	47	26	dimension	dimension	NOUN
ejpam-4821	47	27	dim(g	dim(g	PROPN
ejpam-4821	47	28	)	)	PUNCT
ejpam-4821	47	29	of	of	ADP
ejpam-4821	47	30	g.	g.	PROPN
ejpam-4821	47	31	an	an	DET
ejpam-4821	47	32	ordered	order	VERB
ejpam-4821	47	33	set	set	NOUN
ejpam-4821	47	34	of	of	ADP
ejpam-4821	47	35	vertices	vertex	NOUN
ejpam-4821	47	36	w	w	NOUN
ejpam-4821	47	37	=	=	SYM
ejpam-4821	47	38	{	{	PUNCT
ejpam-4821	47	39	w1	w1	NOUN
ejpam-4821	47	40	,	,	PUNCT
ejpam-4821	47	41	...	...	PUNCT
ejpam-4821	47	42	,	,	PUNCT
ejpam-4821	47	43	wk	wk	X
ejpam-4821	47	44	}	}	PUNCT
ejpam-4821	47	45	is	be	AUX
ejpam-4821	47	46	a	a	DET
ejpam-4821	47	47	k	k	NOUN
ejpam-4821	47	48	-	-	PUNCT
ejpam-4821	47	49	resolving	resolving	NOUN
ejpam-4821	47	50	set	set	NOUN
ejpam-4821	47	51	for	for	ADP
ejpam-4821	47	52	g	g	PROPN
ejpam-4821	47	53	if	if	SCONJ
ejpam-4821	47	54	,	,	PUNCT
ejpam-4821	47	55	for	for	ADP
ejpam-4821	47	56	any	any	DET
ejpam-4821	47	57	distinct	distinct	ADJ
ejpam-4821	47	58	vertices	vertex	NOUN
ejpam-4821	47	59	u	u	NOUN
ejpam-4821	47	60	,	,	PUNCT
ejpam-4821	47	61	v	v	NOUN
ejpam-4821	47	62	∈	∈	PROPN
ejpam-4821	47	63	v	v	NOUN
ejpam-4821	47	64	(	(	PUNCT
ejpam-4821	47	65	g	g	NOUN
ejpam-4821	47	66	)	)	PUNCT
ejpam-4821	47	67	,	,	PUNCT
ejpam-4821	47	68	the	the	DET
ejpam-4821	47	69	(	(	PUNCT
ejpam-4821	47	70	metric	metric	ADJ
ejpam-4821	47	71	)	)	PUNCT
ejpam-4821	47	72	representations	representation	NOUN
ejpam-4821	47	73	rg(u	rg(u	NOUN
ejpam-4821	47	74	/	/	SYM
ejpam-4821	47	75	w	w	NOUN
ejpam-4821	47	76	)	)	PUNCT
ejpam-4821	47	77	and	and	CCONJ
ejpam-4821	47	78	rg(v	rg(v	PROPN
ejpam-4821	47	79	/	/	SYM
ejpam-4821	47	80	w	w	NOUN
ejpam-4821	47	81	)	)	PUNCT
ejpam-4821	47	82	of	of	ADP
ejpam-4821	47	83	u	u	NOUN
ejpam-4821	47	84	and	and	CCONJ
ejpam-4821	47	85	v	v	NOUN
ejpam-4821	47	86	,	,	PUNCT
ejpam-4821	47	87	respectively	respectively	ADV
ejpam-4821	47	88	,	,	PUNCT
ejpam-4821	47	89	differ	differ	VERB
ejpam-4821	47	90	in	in	ADP
ejpam-4821	47	91	at	at	ADP
ejpam-4821	47	92	least	least	ADJ
ejpam-4821	47	93	k	k	NOUN
ejpam-4821	47	94	positions	position	NOUN
ejpam-4821	47	95	.	.	PUNCT
ejpam-4821	48	1	if	if	SCONJ
ejpam-4821	48	2	k	k	PROPN
ejpam-4821	48	3	=	=	SYM
ejpam-4821	48	4	1	1	NUM
ejpam-4821	48	5	,	,	PUNCT
ejpam-4821	48	6	then	then	ADV
ejpam-4821	48	7	the	the	DET
ejpam-4821	48	8	k	k	NOUN
ejpam-4821	48	9	-	-	PUNCT
ejpam-4821	48	10	resolving	resolving	ADJ
ejpam-4821	48	11	set	set	NOUN
ejpam-4821	48	12	is	be	AUX
ejpam-4821	48	13	called	call	VERB
ejpam-4821	48	14	a	a	DET
ejpam-4821	48	15	resolving	resolving	NOUN
ejpam-4821	48	16	set	set	VERB
ejpam-4821	48	17	for	for	ADP
ejpam-4821	48	18	g.	g.	PROPN
ejpam-4821	48	19	if	if	SCONJ
ejpam-4821	48	20	k	k	PROPN
ejpam-4821	48	21	=	=	SYM
ejpam-4821	48	22	2	2	NUM
ejpam-4821	48	23	,	,	PUNCT
ejpam-4821	48	24	then	then	ADV
ejpam-4821	48	25	the	the	DET
ejpam-4821	48	26	k	k	NOUN
ejpam-4821	48	27	-	-	PUNCT
ejpam-4821	48	28	resolving	resolving	ADJ
ejpam-4821	48	29	set	set	NOUN
ejpam-4821	48	30	is	be	AUX
ejpam-4821	48	31	called	call	VERB
ejpam-4821	48	32	a	a	DET
ejpam-4821	48	33	2	2	NUM
ejpam-4821	48	34	-	-	PUNCT
ejpam-4821	48	35	resolving	resolving	NOUN
ejpam-4821	48	36	set	set	NOUN
ejpam-4821	48	37	for	for	ADP
ejpam-4821	48	38	g.	g.	PROPN
ejpam-4821	48	39	if	if	SCONJ
ejpam-4821	48	40	g	g	PROPN
ejpam-4821	48	41	has	have	VERB
ejpam-4821	48	42	a	a	DET
ejpam-4821	48	43	k	k	ADJ
ejpam-4821	48	44	-	-	ADJ
ejpam-4821	48	45	resolving	resolving	ADJ
ejpam-4821	48	46	set	set	NOUN
ejpam-4821	48	47	,	,	PUNCT
ejpam-4821	48	48	the	the	DET
ejpam-4821	48	49	minimum	minimum	ADJ
ejpam-4821	48	50	cardinality	cardinality	PROPN
ejpam-4821	48	51	dimk(g	dimk(g	PROPN
ejpam-4821	48	52	)	)	PUNCT
ejpam-4821	48	53	of	of	ADP
ejpam-4821	48	54	a	a	DET
ejpam-4821	48	55	k	k	NOUN
ejpam-4821	48	56	-	-	PUNCT
ejpam-4821	48	57	resolving	resolving	ADJ
ejpam-4821	48	58	set	set	NOUN
ejpam-4821	48	59	is	be	AUX
ejpam-4821	48	60	called	call	VERB
ejpam-4821	48	61	g.cañete	g.cañete	PROPN
ejpam-4821	48	62	,	,	PUNCT
ejpam-4821	48	63	h.	h.	PROPN
ejpam-4821	48	64	rara	rara	PROPN
ejpam-4821	48	65	,	,	PUNCT
ejpam-4821	48	66	a.m.	a.m.	PROPN
ejpam-4821	48	67	mahistrado	mahistrado	PROPN
ejpam-4821	48	68	/	/	SYM
ejpam-4821	48	69	eur	eur	PROPN
ejpam-4821	48	70	.	.	PUNCT
ejpam-4821	49	1	j.	j.	PROPN
ejpam-4821	49	2	pure	pure	PROPN
ejpam-4821	49	3	appl	appl	PROPN
ejpam-4821	49	4	.	.	PROPN
ejpam-4821	49	5	math	math	PROPN
ejpam-4821	49	6	,	,	PUNCT
ejpam-4821	49	7	16	16	NUM
ejpam-4821	49	8	(	(	PUNCT
ejpam-4821	49	9	3	3	NUM
ejpam-4821	49	10	)	)	PUNCT
ejpam-4821	49	11	(	(	PUNCT
ejpam-4821	49	12	2023	2023	NUM
ejpam-4821	49	13	)	)	PUNCT
ejpam-4821	49	14	,	,	PUNCT
ejpam-4821	49	15	1647	1647	NUM
ejpam-4821	49	16	-	-	SYM
ejpam-4821	49	17	1662	1662	NUM
ejpam-4821	49	18	1649	1649	NUM
ejpam-4821	49	19	the	the	DET
ejpam-4821	49	20	k	k	ADJ
ejpam-4821	49	21	-	-	ADJ
ejpam-4821	49	22	metric	metric	ADJ
ejpam-4821	49	23	dimension	dimension	NOUN
ejpam-4821	49	24	of	of	ADP
ejpam-4821	49	25	g.	g.	PROPN
ejpam-4821	49	26	if	if	SCONJ
ejpam-4821	49	27	g	g	PROPN
ejpam-4821	49	28	has	have	VERB
ejpam-4821	49	29	a	a	DET
ejpam-4821	49	30	2	2	NUM
ejpam-4821	49	31	-	-	PUNCT
ejpam-4821	49	32	resolving	resolve	VERB
ejpam-4821	49	33	set	set	NOUN
ejpam-4821	49	34	,	,	PUNCT
ejpam-4821	49	35	we	we	PRON
ejpam-4821	49	36	denote	denote	VERB
ejpam-4821	49	37	the	the	DET
ejpam-4821	49	38	least	least	ADJ
ejpam-4821	49	39	size	size	NOUN
ejpam-4821	49	40	of	of	ADP
ejpam-4821	49	41	a	a	PRON
ejpam-4821	49	42	2	2	NUM
ejpam-4821	49	43	-	-	PUNCT
ejpam-4821	49	44	resolving	resolving	NOUN
ejpam-4821	49	45	set	set	VERB
ejpam-4821	49	46	by	by	ADP
ejpam-4821	49	47	dim2(g	dim2(g	NOUN
ejpam-4821	49	48	)	)	PUNCT
ejpam-4821	49	49	is	be	AUX
ejpam-4821	49	50	called	call	VERB
ejpam-4821	49	51	a	a	DET
ejpam-4821	49	52	2	2	NUM
ejpam-4821	49	53	-	-	PUNCT
ejpam-4821	49	54	metric	metric	ADJ
ejpam-4821	49	55	dimension	dimension	NOUN
ejpam-4821	49	56	of	of	ADP
ejpam-4821	49	57	g.	g.	PROPN
ejpam-4821	49	58	a	a	DET
ejpam-4821	49	59	resolving	resolving	NOUN
ejpam-4821	49	60	set	set	VERB
ejpam-4821	49	61	of	of	ADP
ejpam-4821	49	62	size	size	NOUN
ejpam-4821	49	63	dim2(g	dim2(g	NOUN
ejpam-4821	49	64	)	)	PUNCT
ejpam-4821	49	65	is	be	AUX
ejpam-4821	49	66	called	call	VERB
ejpam-4821	49	67	a	a	DET
ejpam-4821	49	68	2	2	NUM
ejpam-4821	49	69	-	-	PUNCT
ejpam-4821	49	70	metric	metric	ADJ
ejpam-4821	49	71	basis	basis	NOUN
ejpam-4821	49	72	for	for	ADP
ejpam-4821	49	73	g.	g.	PROPN
ejpam-4821	49	74	let	let	VERB
ejpam-4821	49	75	g	g	NOUN
ejpam-4821	49	76	be	be	AUX
ejpam-4821	49	77	any	any	DET
ejpam-4821	49	78	nontrivial	nontrivial	ADJ
ejpam-4821	49	79	connected	connect	VERB
ejpam-4821	49	80	graph	graph	NOUN
ejpam-4821	49	81	and	and	CCONJ
ejpam-4821	49	82	s	s	VERB
ejpam-4821	49	83	⊆	⊆	NUM
ejpam-4821	49	84	v	v	NOUN
ejpam-4821	49	85	(	(	PUNCT
ejpam-4821	49	86	g	g	NOUN
ejpam-4821	49	87	)	)	PUNCT
ejpam-4821	49	88	.	.	PUNCT
ejpam-4821	50	1	a	a	DET
ejpam-4821	50	2	set	set	NOUN
ejpam-4821	50	3	s	s	NOUN
ejpam-4821	50	4	⊆	⊆	NUM
ejpam-4821	50	5	v	v	NOUN
ejpam-4821	50	6	(	(	PUNCT
ejpam-4821	50	7	g	g	NOUN
ejpam-4821	50	8	)	)	PUNCT
ejpam-4821	50	9	is	be	AUX
ejpam-4821	50	10	a	a	DET
ejpam-4821	50	11	2	2	NUM
ejpam-4821	50	12	-	-	PUNCT
ejpam-4821	50	13	locating	locate	VERB
ejpam-4821	50	14	set	set	NOUN
ejpam-4821	50	15	of	of	ADP
ejpam-4821	50	16	g	g	NOUN
ejpam-4821	50	17	if	if	SCONJ
ejpam-4821	50	18	it	it	PRON
ejpam-4821	50	19	satisfies	satisfy	VERB
ejpam-4821	50	20	the	the	DET
ejpam-4821	50	21	following	follow	VERB
ejpam-4821	50	22	conditions	condition	NOUN
ejpam-4821	50	23	:	:	PUNCT
ejpam-4821	50	24	(	(	PUNCT
ejpam-4821	50	25	i	i	NOUN
ejpam-4821	50	26	)	)	PUNCT
ejpam-4821	50	27	∣∣[(ng(x)\ng(y	∣∣[(ng(x)\ng(y	PROPN
ejpam-4821	50	28	)	)	PUNCT
ejpam-4821	50	29	)	)	PUNCT
ejpam-4821	51	1	∩s]∪	∩s]∪	VERB
ejpam-4821	51	2	[	[	PUNCT
ejpam-4821	51	3	(	(	PUNCT
ejpam-4821	51	4	ng(y)\ng(x	ng(y)\ng(x	NOUN
ejpam-4821	51	5	)	)	PUNCT
ejpam-4821	51	6	)	)	PUNCT
ejpam-4821	52	1	∩s	∩s	PROPN
ejpam-4821	52	2	]	]	PUNCT
ejpam-4821	52	3	∣∣	∣∣	NUM
ejpam-4821	52	4	≥	≥	NOUN
ejpam-4821	52	5	2	2	NUM
ejpam-4821	52	6	,	,	PUNCT
ejpam-4821	52	7	for	for	ADP
ejpam-4821	52	8	all	all	DET
ejpam-4821	52	9	x	x	NOUN
ejpam-4821	52	10	,	,	PUNCT
ejpam-4821	52	11	y	y	PROPN
ejpam-4821	52	12	∈	∈	PROPN
ejpam-4821	52	13	v	v	X
ejpam-4821	52	14	(	(	PUNCT
ejpam-4821	52	15	g)\s	g)\s	VERB
ejpam-4821	52	16	with	with	ADP
ejpam-4821	52	17	x	x	PROPN
ejpam-4821	52	18	̸=	̸=	PROPN
ejpam-4821	52	19	y.	y.	PROPN
ejpam-4821	52	20	(	(	PUNCT
ejpam-4821	52	21	ii	ii	PROPN
ejpam-4821	52	22	)	)	PUNCT
ejpam-4821	52	23	(	(	PUNCT
ejpam-4821	52	24	ng(v)\ng(w	ng(v)\ng(w	ADJ
ejpam-4821	52	25	)	)	PUNCT
ejpam-4821	52	26	)	)	PUNCT
ejpam-4821	52	27	∩	∩	PROPN
ejpam-4821	52	28	s	s	PART
ejpam-4821	52	29	̸=	̸=	PROPN
ejpam-4821	52	30	∅	∅	NOUN
ejpam-4821	52	31	or	or	CCONJ
ejpam-4821	52	32	(	(	PUNCT
ejpam-4821	52	33	ng(w)\ng[v	ng(w)\ng[v	PROPN
ejpam-4821	52	34	]	]	PUNCT
ejpam-4821	52	35	)	)	PUNCT
ejpam-4821	52	36	∩	∩	PROPN
ejpam-4821	52	37	s	s	PART
ejpam-4821	52	38	̸=	̸=	PROPN
ejpam-4821	52	39	∅	∅	NOUN
ejpam-4821	52	40	,	,	PUNCT
ejpam-4821	52	41	for	for	ADP
ejpam-4821	52	42	all	all	PRON
ejpam-4821	52	43	v	v	ADP
ejpam-4821	52	44	∈	∈	NOUN
ejpam-4821	52	45	s	s	NOUN
ejpam-4821	52	46	and	and	CCONJ
ejpam-4821	52	47	for	for	ADP
ejpam-4821	52	48	all	all	PRON
ejpam-4821	52	49	w	w	PROPN
ejpam-4821	52	50	∈	∈	PROPN
ejpam-4821	52	51	v	v	NOUN
ejpam-4821	52	52	(	(	PUNCT
ejpam-4821	52	53	g)\s	g)\s	NOUN
ejpam-4821	52	54	.	.	PUNCT
ejpam-4821	53	1	the	the	DET
ejpam-4821	53	2	2	2	NUM
ejpam-4821	53	3	-	-	PUNCT
ejpam-4821	53	4	locating	locate	VERB
ejpam-4821	53	5	number	number	NOUN
ejpam-4821	53	6	of	of	ADP
ejpam-4821	53	7	g	g	NOUN
ejpam-4821	53	8	,	,	PUNCT
ejpam-4821	53	9	denoted	denote	VERB
ejpam-4821	53	10	by	by	ADP
ejpam-4821	53	11	ln2(g	ln2(g	NOUN
ejpam-4821	53	12	)	)	PUNCT
ejpam-4821	53	13	,	,	PUNCT
ejpam-4821	53	14	is	be	AUX
ejpam-4821	53	15	the	the	DET
ejpam-4821	53	16	smallest	small	ADJ
ejpam-4821	53	17	cardinality	cardinality	NOUN
ejpam-4821	53	18	of	of	ADP
ejpam-4821	53	19	a	a	DET
ejpam-4821	53	20	2	2	NUM
ejpam-4821	53	21	-	-	PUNCT
ejpam-4821	53	22	locating	locate	VERB
ejpam-4821	53	23	set	set	NOUN
ejpam-4821	53	24	of	of	ADP
ejpam-4821	53	25	g.	g.	PROPN
ejpam-4821	53	26	a	a	DET
ejpam-4821	53	27	2	2	NUM
ejpam-4821	53	28	-	-	PUNCT
ejpam-4821	53	29	locating	locate	VERB
ejpam-4821	53	30	set	set	NOUN
ejpam-4821	53	31	of	of	ADP
ejpam-4821	53	32	g	g	NOUN
ejpam-4821	53	33	of	of	ADP
ejpam-4821	53	34	cardinality	cardinality	PROPN
ejpam-4821	53	35	ln2(g	ln2(g	PROPN
ejpam-4821	53	36	)	)	PUNCT
ejpam-4821	53	37	is	be	AUX
ejpam-4821	53	38	referred	refer	VERB
ejpam-4821	53	39	to	to	ADP
ejpam-4821	53	40	as	as	ADP
ejpam-4821	53	41	an	an	DET
ejpam-4821	53	42	ln2	ln2	NOUN
ejpam-4821	53	43	-	-	PUNCT
ejpam-4821	53	44	set	set	NOUN
ejpam-4821	53	45	of	of	ADP
ejpam-4821	53	46	g.	g.	PROPN
ejpam-4821	53	47	a	a	DET
ejpam-4821	53	48	set	set	NOUN
ejpam-4821	53	49	s	s	PROPN
ejpam-4821	53	50	⊆	⊆	NUM
ejpam-4821	53	51	v	v	NOUN
ejpam-4821	53	52	(	(	PUNCT
ejpam-4821	53	53	g	g	NOUN
ejpam-4821	53	54	)	)	PUNCT
ejpam-4821	53	55	is	be	AUX
ejpam-4821	53	56	a	a	DET
ejpam-4821	53	57	(	(	PUNCT
ejpam-4821	53	58	2	2	NUM
ejpam-4821	53	59	,	,	PUNCT
ejpam-4821	53	60	2)-locating	2)-locating	NUM
ejpam-4821	53	61	(	(	PUNCT
ejpam-4821	53	62	(	(	PUNCT
ejpam-4821	53	63	2	2	NUM
ejpam-4821	53	64	,	,	PUNCT
ejpam-4821	53	65	1)-locating	1)-locating	NUM
ejpam-4821	53	66	,	,	PUNCT
ejpam-4821	53	67	respectively	respectively	ADV
ejpam-4821	53	68	)	)	PUNCT
ejpam-4821	53	69	set	set	VERB
ejpam-4821	53	70	in	in	ADP
ejpam-4821	53	71	g	g	PROPN
ejpam-4821	53	72	if	if	SCONJ
ejpam-4821	53	73	s	s	NOUN
ejpam-4821	53	74	is	be	AUX
ejpam-4821	53	75	2locating	2locating	NUM
ejpam-4821	53	76	and	and	CCONJ
ejpam-4821	53	77	|ng(y)∩s|	|ng(y)∩s|	PROPN
ejpam-4821	53	78	≤	≤	PROPN
ejpam-4821	53	79	|s|−2	|s|−2	PROPN
ejpam-4821	53	80	(	(	PUNCT
ejpam-4821	53	81	|ng(y)∩s|	|ng(y)∩s|	PROPN
ejpam-4821	53	82	≤	≤	PROPN
ejpam-4821	53	83	|s|−1	|s|−1	NUM
ejpam-4821	53	84	,	,	PUNCT
ejpam-4821	53	85	respectively	respectively	ADV
ejpam-4821	53	86	)	)	PUNCT
ejpam-4821	53	87	,	,	PUNCT
ejpam-4821	53	88	for	for	ADP
ejpam-4821	53	89	all	all	DET
ejpam-4821	53	90	y	y	PROPN
ejpam-4821	53	91	∈	∈	PROPN
ejpam-4821	53	92	v	v	NOUN
ejpam-4821	53	93	(	(	PUNCT
ejpam-4821	53	94	g	g	NOUN
ejpam-4821	53	95	)	)	PUNCT
ejpam-4821	53	96	.	.	PUNCT
ejpam-4821	54	1	the	the	DET
ejpam-4821	54	2	(	(	PUNCT
ejpam-4821	54	3	2	2	NUM
ejpam-4821	54	4	,	,	PUNCT
ejpam-4821	54	5	2)-locating	2)-locating	NUM
ejpam-4821	54	6	(	(	PUNCT
ejpam-4821	54	7	(	(	PUNCT
ejpam-4821	54	8	2	2	NUM
ejpam-4821	54	9	,	,	PUNCT
ejpam-4821	54	10	1)-locating	1)-locating	NUM
ejpam-4821	54	11	,	,	PUNCT
ejpam-4821	54	12	respectively	respectively	ADV
ejpam-4821	54	13	)	)	PUNCT
ejpam-4821	54	14	number	number	NOUN
ejpam-4821	54	15	ofg	ofg	PROPN
ejpam-4821	54	16	,	,	PUNCT
ejpam-4821	54	17	denoted	denote	VERB
ejpam-4821	54	18	by	by	ADP
ejpam-4821	54	19	ln(2,2)(g	ln(2,2)(g	NOUN
ejpam-4821	54	20	)	)	PUNCT
ejpam-4821	54	21	(	(	PUNCT
ejpam-4821	54	22	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4821	54	23	)	)	PUNCT
ejpam-4821	54	24	,	,	PUNCT
ejpam-4821	54	25	respectively	respectively	ADV
ejpam-4821	54	26	)	)	PUNCT
ejpam-4821	54	27	,	,	PUNCT
ejpam-4821	54	28	is	be	AUX
ejpam-4821	54	29	the	the	DET
ejpam-4821	54	30	smallest	small	ADJ
ejpam-4821	54	31	cardinality	cardinality	NOUN
ejpam-4821	54	32	of	of	ADP
ejpam-4821	54	33	a	a	DET
ejpam-4821	54	34	(	(	PUNCT
ejpam-4821	54	35	2	2	NUM
ejpam-4821	54	36	,	,	PUNCT
ejpam-4821	54	37	2)-locating	2)-locating	NUM
ejpam-4821	54	38	(	(	PUNCT
ejpam-4821	54	39	(	(	PUNCT
ejpam-4821	54	40	2	2	NUM
ejpam-4821	54	41	,	,	PUNCT
ejpam-4821	54	42	1)-locating	1)-locating	NUM
ejpam-4821	54	43	,	,	PUNCT
ejpam-4821	54	44	respectively	respectively	ADV
ejpam-4821	54	45	)	)	PUNCT
ejpam-4821	54	46	set	set	VERB
ejpam-4821	54	47	in	in	ADP
ejpam-4821	54	48	g.	g.	PROPN
ejpam-4821	54	49	a	a	PRON
ejpam-4821	54	50	(	(	PUNCT
ejpam-4821	54	51	2	2	NUM
ejpam-4821	54	52	,	,	PUNCT
ejpam-4821	54	53	2)-locating	2)-locating	NUM
ejpam-4821	54	54	(	(	PUNCT
ejpam-4821	54	55	(	(	PUNCT
ejpam-4821	54	56	2	2	NUM
ejpam-4821	54	57	,	,	PUNCT
ejpam-4821	54	58	1)-locating	1)-locating	NUM
ejpam-4821	54	59	,	,	PUNCT
ejpam-4821	54	60	respectively	respectively	ADV
ejpam-4821	54	61	)	)	PUNCT
ejpam-4821	54	62	set	set	VERB
ejpam-4821	54	63	in	in	ADP
ejpam-4821	54	64	g	g	NOUN
ejpam-4821	54	65	of	of	ADP
ejpam-4821	54	66	cardinality	cardinality	NOUN
ejpam-4821	54	67	ln(2,2)(g	ln(2,2)(g	PROPN
ejpam-4821	54	68	)	)	PUNCT
ejpam-4821	54	69	(	(	PUNCT
ejpam-4821	54	70	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4821	54	71	)	)	PUNCT
ejpam-4821	54	72	,	,	PUNCT
ejpam-4821	54	73	respectively	respectively	ADV
ejpam-4821	54	74	)	)	PUNCT
ejpam-4821	54	75	is	be	AUX
ejpam-4821	54	76	referred	refer	VERB
ejpam-4821	54	77	to	to	ADP
ejpam-4821	54	78	as	as	ADP
ejpam-4821	54	79	an	an	DET
ejpam-4821	54	80	ln(2,2)-set	ln(2,2)-set	NOUN
ejpam-4821	54	81	(	(	PUNCT
ejpam-4821	54	82	ln(2,1)-set	ln(2,1)-set	PROPN
ejpam-4821	54	83	,	,	PUNCT
ejpam-4821	54	84	respectively	respectively	ADV
ejpam-4821	54	85	)	)	PUNCT
ejpam-4821	54	86	in	in	ADP
ejpam-4821	54	87	g.	g.	PROPN
ejpam-4821	54	88	3	3	NUM
ejpam-4821	54	89	.	.	PUNCT
ejpam-4821	54	90	known	know	VERB
ejpam-4821	54	91	results	result	VERB
ejpam-4821	54	92	the	the	DET
ejpam-4821	54	93	following	follow	VERB
ejpam-4821	54	94	known	know	VERB
ejpam-4821	54	95	results	result	NOUN
ejpam-4821	54	96	are	be	AUX
ejpam-4821	54	97	taken	take	VERB
ejpam-4821	54	98	from	from	ADP
ejpam-4821	54	99	[	[	X
ejpam-4821	54	100	5	5	NUM
ejpam-4821	54	101	]	]	PUNCT
ejpam-4821	54	102	.	.	PUNCT
ejpam-4821	55	1	remark	remark	PROPN
ejpam-4821	55	2	1	1	NUM
ejpam-4821	55	3	.	.	PUNCT
ejpam-4821	56	1	for	for	ADP
ejpam-4821	56	2	any	any	DET
ejpam-4821	56	3	connected	connected	ADJ
ejpam-4821	56	4	nontrivial	nontrivial	NOUN
ejpam-4821	56	5	graph	graph	NOUN
ejpam-4821	56	6	g	g	NOUN
ejpam-4821	56	7	of	of	ADP
ejpam-4821	56	8	order	order	NOUN
ejpam-4821	56	9	n	n	PRON
ejpam-4821	56	10	≥	≥	NOUN
ejpam-4821	56	11	2	2	NUM
ejpam-4821	56	12	,	,	PUNCT
ejpam-4821	56	13	2	2	NUM
ejpam-4821	56	14	≤	≤	NUM
ejpam-4821	56	15	ln2(g	ln2(g	PROPN
ejpam-4821	56	16	)	)	PUNCT
ejpam-4821	56	17	≤	≤	PUNCT
ejpam-4821	56	18	n.	n.	NOUN
ejpam-4821	56	19	moreover	moreover	ADV
ejpam-4821	56	20	,	,	PUNCT
ejpam-4821	56	21	ln2(kn	ln2(kn	NUM
ejpam-4821	56	22	)	)	PUNCT
ejpam-4821	56	23	=	=	SYM
ejpam-4821	56	24	n	n	CCONJ
ejpam-4821	56	25	,	,	PUNCT
ejpam-4821	56	26	for	for	ADP
ejpam-4821	56	27	n	n	PRON
ejpam-4821	56	28	≥	≥	NUM
ejpam-4821	56	29	2	2	NUM
ejpam-4821	56	30	.	.	PUNCT
ejpam-4821	56	31	theorem	theorem	NOUN
ejpam-4821	56	32	1	1	NUM
ejpam-4821	56	33	.	.	PUNCT
ejpam-4821	56	34	let	let	VERB
ejpam-4821	56	35	g	g	PRON
ejpam-4821	56	36	be	be	AUX
ejpam-4821	56	37	a	a	DET
ejpam-4821	56	38	connected	connected	ADJ
ejpam-4821	56	39	nontrivial	nontrivial	ADJ
ejpam-4821	56	40	graph	graph	NOUN
ejpam-4821	56	41	.	.	PUNCT
ejpam-4821	57	1	then	then	ADV
ejpam-4821	57	2	ln2(g	ln2(g	PROPN
ejpam-4821	57	3	)	)	PUNCT
ejpam-4821	57	4	=	=	SYM
ejpam-4821	57	5	2	2	NUM
ejpam-4821	57	6	if	if	SCONJ
ejpam-4821	57	7	and	and	CCONJ
ejpam-4821	57	8	only	only	ADV
ejpam-4821	57	9	if	if	SCONJ
ejpam-4821	57	10	g	g	PROPN
ejpam-4821	57	11	∼=	∼=	NOUN
ejpam-4821	57	12	p2	p2	NOUN
ejpam-4821	57	13	or	or	CCONJ
ejpam-4821	57	14	g	g	NOUN
ejpam-4821	57	15	∼=	∼=	PROPN
ejpam-4821	57	16	p3	p3	NOUN
ejpam-4821	57	17	.	.	PUNCT
ejpam-4821	58	1	remark	remark	PROPN
ejpam-4821	58	2	2	2	NUM
ejpam-4821	58	3	.	.	PUNCT
ejpam-4821	59	1	let	let	VERB
ejpam-4821	59	2	s	s	PRON
ejpam-4821	59	3	⊆	⊆	NUM
ejpam-4821	59	4	v	v	NOUN
ejpam-4821	59	5	(	(	PUNCT
ejpam-4821	59	6	g	g	NOUN
ejpam-4821	59	7	)	)	PUNCT
ejpam-4821	59	8	for	for	ADP
ejpam-4821	59	9	any	any	DET
ejpam-4821	59	10	pair	pair	NOUN
ejpam-4821	59	11	of	of	ADP
ejpam-4821	59	12	vertices	vertex	NOUN
ejpam-4821	59	13	x	x	X
ejpam-4821	59	14	,	,	PUNCT
ejpam-4821	59	15	y	y	PROPN
ejpam-4821	59	16	∈	∈	PROPN
ejpam-4821	59	17	s	s	PROPN
ejpam-4821	59	18	,	,	PUNCT
ejpam-4821	59	19	r(x	r(x	PROPN
ejpam-4821	59	20	/	/	SYM
ejpam-4821	59	21	s	s	NOUN
ejpam-4821	59	22	)	)	PUNCT
ejpam-4821	59	23	and	and	CCONJ
ejpam-4821	59	24	r(y	r(y	VERB
ejpam-4821	59	25	/	/	SYM
ejpam-4821	59	26	s	s	PART
ejpam-4821	59	27	)	)	PUNCT
ejpam-4821	59	28	differ	differ	VERB
ejpam-4821	59	29	in	in	ADP
ejpam-4821	59	30	at	at	ADV
ejpam-4821	59	31	least	least	ADJ
ejpam-4821	59	32	2	2	NUM
ejpam-4821	59	33	positions	position	NOUN
ejpam-4821	59	34	.	.	PUNCT
ejpam-4821	60	1	hence	hence	ADV
ejpam-4821	60	2	,	,	PUNCT
ejpam-4821	60	3	to	to	PART
ejpam-4821	60	4	prove	prove	VERB
ejpam-4821	60	5	that	that	SCONJ
ejpam-4821	60	6	s	s	VERB
ejpam-4821	60	7	is	be	AUX
ejpam-4821	60	8	a	a	DET
ejpam-4821	60	9	2	2	NUM
ejpam-4821	60	10	-	-	PUNCT
ejpam-4821	60	11	resolving	resolving	NOUN
ejpam-4821	60	12	set	set	NOUN
ejpam-4821	60	13	in	in	ADP
ejpam-4821	60	14	g	g	NOUN
ejpam-4821	60	15	,	,	PUNCT
ejpam-4821	60	16	we	we	PRON
ejpam-4821	60	17	only	only	ADV
ejpam-4821	60	18	need	need	VERB
ejpam-4821	60	19	to	to	PART
ejpam-4821	60	20	show	show	VERB
ejpam-4821	60	21	that	that	SCONJ
ejpam-4821	60	22	for	for	ADP
ejpam-4821	60	23	every	every	DET
ejpam-4821	60	24	pair	pair	NOUN
ejpam-4821	60	25	of	of	ADP
ejpam-4821	60	26	vertices	vertex	NOUN
ejpam-4821	60	27	x	x	X
ejpam-4821	60	28	,	,	PUNCT
ejpam-4821	60	29	y	y	PROPN
ejpam-4821	60	30	∈	∈	PROPN
ejpam-4821	60	31	v	v	ADP
ejpam-4821	60	32	(	(	PUNCT
ejpam-4821	60	33	g	g	NOUN
ejpam-4821	60	34	)	)	PUNCT
ejpam-4821	60	35	where	where	SCONJ
ejpam-4821	60	36	x	x	PUNCT
ejpam-4821	60	37	∈	∈	PROPN
ejpam-4821	60	38	s	s	X
ejpam-4821	60	39	and	and	CCONJ
ejpam-4821	60	40	y	y	PROPN
ejpam-4821	60	41	∈	∈	PROPN
ejpam-4821	60	42	v	v	ADP
ejpam-4821	60	43	(	(	PUNCT
ejpam-4821	60	44	g	g	NOUN
ejpam-4821	60	45	)	)	PUNCT
ejpam-4821	60	46	\	\	PROPN
ejpam-4821	60	47	s	s	PART
ejpam-4821	60	48	or	or	CCONJ
ejpam-4821	60	49	both	both	PRON
ejpam-4821	60	50	x	x	NOUN
ejpam-4821	60	51	,	,	PUNCT
ejpam-4821	60	52	y	y	PROPN
ejpam-4821	60	53	∈	∈	PROPN
ejpam-4821	60	54	v	v	ADP
ejpam-4821	60	55	(	(	PUNCT
ejpam-4821	60	56	g	g	NOUN
ejpam-4821	60	57	)	)	PUNCT
ejpam-4821	60	58	\	\	PROPN
ejpam-4821	60	59	s	s	PROPN
ejpam-4821	60	60	,	,	PUNCT
ejpam-4821	60	61	r(x	r(x	PROPN
ejpam-4821	60	62	/	/	SYM
ejpam-4821	60	63	s	s	NOUN
ejpam-4821	60	64	)	)	PUNCT
ejpam-4821	60	65	and	and	CCONJ
ejpam-4821	60	66	r(y	r(y	VERB
ejpam-4821	60	67	/	/	SYM
ejpam-4821	60	68	s	s	PART
ejpam-4821	60	69	)	)	PUNCT
ejpam-4821	60	70	differ	differ	VERB
ejpam-4821	60	71	in	in	ADP
ejpam-4821	60	72	at	at	ADV
ejpam-4821	60	73	least	least	ADJ
ejpam-4821	60	74	2	2	NUM
ejpam-4821	60	75	positions	position	NOUN
ejpam-4821	60	76	.	.	PUNCT
ejpam-4821	61	1	remark	remark	NOUN
ejpam-4821	61	2	3	3	NUM
ejpam-4821	61	3	.	.	PUNCT
ejpam-4821	62	1	every	every	DET
ejpam-4821	62	2	2	2	NUM
ejpam-4821	62	3	-	-	PUNCT
ejpam-4821	62	4	locating	locate	VERB
ejpam-4821	62	5	set	set	NOUN
ejpam-4821	62	6	in	in	ADP
ejpam-4821	62	7	g	g	PROPN
ejpam-4821	62	8	is	be	AUX
ejpam-4821	62	9	a	a	DET
ejpam-4821	62	10	2	2	NUM
ejpam-4821	62	11	-	-	PUNCT
ejpam-4821	62	12	resolving	resolving	NOUN
ejpam-4821	62	13	set	set	VERB
ejpam-4821	62	14	in	in	ADP
ejpam-4821	62	15	g.	g.	PROPN
ejpam-4821	62	16	however	however	ADV
ejpam-4821	62	17	,	,	PUNCT
ejpam-4821	62	18	a	a	DET
ejpam-4821	62	19	2	2	NUM
ejpam-4821	62	20	-	-	PUNCT
ejpam-4821	62	21	resolving	resolving	NOUN
ejpam-4821	62	22	set	set	NOUN
ejpam-4821	62	23	in	in	ADP
ejpam-4821	62	24	g	g	NOUN
ejpam-4821	62	25	need	need	AUX
ejpam-4821	62	26	not	not	PART
ejpam-4821	62	27	be	be	AUX
ejpam-4821	62	28	a	a	DET
ejpam-4821	62	29	2	2	NUM
ejpam-4821	62	30	-	-	PUNCT
ejpam-4821	62	31	locating	locate	VERB
ejpam-4821	62	32	set	set	NOUN
ejpam-4821	62	33	in	in	ADP
ejpam-4821	62	34	g.	g.	PROPN
ejpam-4821	62	35	thus	thus	ADV
ejpam-4821	62	36	,	,	PUNCT
ejpam-4821	62	37	dim2(g	dim2(g	NOUN
ejpam-4821	62	38	)	)	PUNCT
ejpam-4821	62	39	≤	≤	NOUN
ejpam-4821	62	40	ln2(g	ln2(g	PROPN
ejpam-4821	62	41	)	)	PUNCT
ejpam-4821	62	42	.	.	PUNCT
ejpam-4821	63	1	4	4	X
ejpam-4821	63	2	.	.	X
ejpam-4821	63	3	preliminary	preliminary	ADJ
ejpam-4821	63	4	results	result	NOUN
ejpam-4821	63	5	every	every	DET
ejpam-4821	63	6	nontrivial	nontrivial	ADJ
ejpam-4821	63	7	connected	connect	VERB
ejpam-4821	63	8	graph	graph	NOUN
ejpam-4821	63	9	g	g	PROPN
ejpam-4821	63	10	admits	admit	VERB
ejpam-4821	63	11	a	a	DET
ejpam-4821	63	12	2	2	NUM
ejpam-4821	63	13	-	-	PUNCT
ejpam-4821	63	14	locating	locate	VERB
ejpam-4821	63	15	set	set	NOUN
ejpam-4821	63	16	.	.	PUNCT
ejpam-4821	64	1	indeed	indeed	ADV
ejpam-4821	64	2	,	,	PUNCT
ejpam-4821	64	3	the	the	DET
ejpam-4821	64	4	vertex	vertex	NOUN
ejpam-4821	64	5	-	-	PUNCT
ejpam-4821	64	6	set	set	NOUN
ejpam-4821	64	7	of	of	ADP
ejpam-4821	64	8	g	g	PROPN
ejpam-4821	64	9	is	be	AUX
ejpam-4821	64	10	a	a	DET
ejpam-4821	64	11	2	2	NUM
ejpam-4821	64	12	-	-	PUNCT
ejpam-4821	64	13	locating	locate	VERB
ejpam-4821	64	14	set	set	NOUN
ejpam-4821	64	15	.	.	PUNCT
ejpam-4821	65	1	proposition	proposition	NOUN
ejpam-4821	65	2	1	1	NUM
ejpam-4821	65	3	.	.	PUNCT
ejpam-4821	66	1	for	for	ADP
ejpam-4821	66	2	any	any	DET
ejpam-4821	66	3	connected	connected	ADJ
ejpam-4821	66	4	graph	graph	NOUN
ejpam-4821	66	5	g	g	NOUN
ejpam-4821	66	6	of	of	ADP
ejpam-4821	66	7	order	order	NOUN
ejpam-4821	66	8	n	n	PRON
ejpam-4821	66	9	≥	≥	NOUN
ejpam-4821	66	10	2	2	NUM
ejpam-4821	66	11	,	,	PUNCT
ejpam-4821	66	12	2	2	NUM
ejpam-4821	66	13	≤	≤	NUM
ejpam-4821	66	14	ln2(g	ln2(g	PROPN
ejpam-4821	66	15	)	)	PUNCT
ejpam-4821	66	16	≤	≤	PUNCT
ejpam-4821	66	17	n.	n.	NOUN
ejpam-4821	67	1	moreover	moreover	ADV
ejpam-4821	67	2	,	,	PUNCT
ejpam-4821	67	3	g.cañete	g.cañete	PROPN
ejpam-4821	67	4	,	,	PUNCT
ejpam-4821	67	5	h.	h.	PROPN
ejpam-4821	67	6	rara	rara	PROPN
ejpam-4821	67	7	,	,	PUNCT
ejpam-4821	67	8	a.m.	a.m.	PROPN
ejpam-4821	67	9	mahistrado	mahistrado	PROPN
ejpam-4821	67	10	/	/	SYM
ejpam-4821	67	11	eur	eur	PROPN
ejpam-4821	67	12	.	.	PUNCT
ejpam-4821	68	1	j.	j.	PROPN
ejpam-4821	68	2	pure	pure	PROPN
ejpam-4821	68	3	appl	appl	PROPN
ejpam-4821	68	4	.	.	PROPN
ejpam-4821	68	5	math	math	PROPN
ejpam-4821	68	6	,	,	PUNCT
ejpam-4821	68	7	16	16	NUM
ejpam-4821	68	8	(	(	PUNCT
ejpam-4821	68	9	3	3	NUM
ejpam-4821	68	10	)	)	PUNCT
ejpam-4821	68	11	(	(	PUNCT
ejpam-4821	68	12	2023	2023	NUM
ejpam-4821	68	13	)	)	PUNCT
ejpam-4821	68	14	,	,	PUNCT
ejpam-4821	68	15	1647	1647	NUM
ejpam-4821	68	16	-	-	SYM
ejpam-4821	68	17	1662	1662	NUM
ejpam-4821	68	18	1650	1650	NUM
ejpam-4821	68	19	(	(	PUNCT
ejpam-4821	68	20	i	i	NOUN
ejpam-4821	68	21	)	)	PUNCT
ejpam-4821	68	22	ln2(g	ln2(g	PROPN
ejpam-4821	68	23	)	)	PUNCT
ejpam-4821	68	24	=	=	SYM
ejpam-4821	68	25	2	2	NUM
ejpam-4821	68	26	if	if	SCONJ
ejpam-4821	68	27	and	and	CCONJ
ejpam-4821	68	28	only	only	ADV
ejpam-4821	68	29	if	if	SCONJ
ejpam-4821	68	30	g	g	PROPN
ejpam-4821	68	31	=	=	SYM
ejpam-4821	68	32	k2	k2	PROPN
ejpam-4821	68	33	or	or	CCONJ
ejpam-4821	68	34	g	g	PROPN
ejpam-4821	68	35	=	=	PROPN
ejpam-4821	68	36	p3	p3	PROPN
ejpam-4821	68	37	;	;	PUNCT
ejpam-4821	68	38	(	(	PUNCT
ejpam-4821	68	39	ii	ii	NOUN
ejpam-4821	68	40	)	)	PUNCT
ejpam-4821	68	41	if	if	SCONJ
ejpam-4821	68	42	g	g	PROPN
ejpam-4821	68	43	=	=	PROPN
ejpam-4821	68	44	kn	kn	PROPN
ejpam-4821	68	45	,	,	PUNCT
ejpam-4821	68	46	then	then	ADV
ejpam-4821	68	47	ln2(g	ln2(g	PROPN
ejpam-4821	68	48	)	)	PUNCT
ejpam-4821	68	49	=	=	SYM
ejpam-4821	68	50	n	n	CCONJ
ejpam-4821	68	51	;	;	PUNCT
ejpam-4821	68	52	(	(	PUNCT
ejpam-4821	68	53	iii	iii	X
ejpam-4821	68	54	)	)	PUNCT
ejpam-4821	68	55	if	if	SCONJ
ejpam-4821	68	56	n	n	NOUN
ejpam-4821	68	57	=	=	SYM
ejpam-4821	68	58	3	3	NUM
ejpam-4821	68	59	,	,	PUNCT
ejpam-4821	68	60	then	then	ADV
ejpam-4821	68	61	ln2(g	ln2(g	PROPN
ejpam-4821	68	62	)	)	PUNCT
ejpam-4821	68	63	=	=	SYM
ejpam-4821	68	64	3	3	NUM
ejpam-4821	69	1	if	if	SCONJ
ejpam-4821	69	2	and	and	CCONJ
ejpam-4821	69	3	only	only	ADV
ejpam-4821	69	4	if	if	SCONJ
ejpam-4821	69	5	g	g	NOUN
ejpam-4821	69	6	=	=	SYM
ejpam-4821	69	7	k3	k3	X
ejpam-4821	69	8	;	;	PUNCT
ejpam-4821	69	9	and	and	CCONJ
ejpam-4821	69	10	(	(	PUNCT
ejpam-4821	69	11	iv	iv	X
ejpam-4821	69	12	)	)	PUNCT
ejpam-4821	69	13	if	if	SCONJ
ejpam-4821	69	14	n	n	NOUN
ejpam-4821	69	15	=	=	SYM
ejpam-4821	69	16	4	4	NUM
ejpam-4821	69	17	,	,	PUNCT
ejpam-4821	69	18	then	then	ADV
ejpam-4821	69	19	ln2(g	ln2(g	PROPN
ejpam-4821	69	20	)	)	PUNCT
ejpam-4821	69	21	=	=	NOUN
ejpam-4821	69	22	4	4	NUM
ejpam-4821	69	23	if	if	SCONJ
ejpam-4821	69	24	and	and	CCONJ
ejpam-4821	69	25	only	only	ADV
ejpam-4821	69	26	if	if	SCONJ
ejpam-4821	69	27	g	g	PROPN
ejpam-4821	69	28	∈	∈	PROPN
ejpam-4821	69	29	{	{	PUNCT
ejpam-4821	69	30	c4,k4	c4,k4	PROPN
ejpam-4821	69	31	,	,	PUNCT
ejpam-4821	69	32	t	t	PROPN
ejpam-4821	69	33	}	}	PUNCT
ejpam-4821	69	34	.	.	PUNCT
ejpam-4821	70	1	otherwise	otherwise	ADV
ejpam-4821	70	2	,	,	PUNCT
ejpam-4821	70	3	ln2(g	ln2(g	PROPN
ejpam-4821	70	4	)	)	PUNCT
ejpam-4821	70	5	=	=	SYM
ejpam-4821	70	6	3	3	NUM
ejpam-4821	70	7	if	if	SCONJ
ejpam-4821	70	8	and	and	CCONJ
ejpam-4821	70	9	only	only	ADV
ejpam-4821	70	10	if	if	SCONJ
ejpam-4821	70	11	g	g	PROPN
ejpam-4821	70	12	∈	∈	PROPN
ejpam-4821	70	13	{	{	PUNCT
ejpam-4821	70	14	p4,k1,3	p4,k1,3	PROPN
ejpam-4821	70	15	,	,	PUNCT
ejpam-4821	70	16	t	t	PROPN
ejpam-4821	70	17	′	′	NOUN
ejpam-4821	70	18	}	}	PUNCT
ejpam-4821	70	19	where	where	SCONJ
ejpam-4821	70	20	t	t	PROPN
ejpam-4821	70	21	and	and	CCONJ
ejpam-4821	70	22	t	t	PROPN
ejpam-4821	70	23	′	′	NOUN
ejpam-4821	70	24	are	be	AUX
ejpam-4821	70	25	graphs	graph	NOUN
ejpam-4821	70	26	shown	show	VERB
ejpam-4821	70	27	in	in	ADP
ejpam-4821	70	28	figure	figure	NOUN
ejpam-4821	70	29	1	1	NUM
ejpam-4821	70	30	.	.	PUNCT
ejpam-4821	70	31	..................................................................................................................................................................	..................................................................................................................................................................	PROPN
ejpam-4821	70	32	.........	.........	PUNCT
ejpam-4821	70	33	........	........	PUNCT
ejpam-4821	70	34	........	........	PUNCT
ejpam-4821	70	35	........	........	PUNCT
ejpam-4821	70	36	........	........	PUNCT
ejpam-4821	70	37	........	........	PUNCT
ejpam-4821	70	38	........	........	PUNCT
ejpam-4821	70	39	........	........	PUNCT
ejpam-4821	70	40	........	........	PUNCT
ejpam-4821	70	41	........	........	PUNCT
ejpam-4821	70	42	........	........	PUNCT
ejpam-4821	70	43	........	........	PUNCT
ejpam-4821	70	44	........	........	PUNCT
ejpam-4821	70	45	........	........	PUNCT
ejpam-4821	70	46	........	........	PUNCT
ejpam-4821	70	47	........	........	PUNCT
ejpam-4821	70	48	........	........	PUNCT
ejpam-4821	70	49	........	........	PUNCT
ejpam-4821	70	50	........	........	PUNCT
ejpam-4821	70	51	........	........	PUNCT
ejpam-4821	70	52	.	.	PUNCT
ejpam-4821	70	53	...........................................................................................................................................................................	...........................................................................................................................................................................	PUNCT
ejpam-4821	70	54	........	........	PUNCT
ejpam-4821	70	55	........	........	PUNCT
ejpam-4821	70	56	........	........	PUNCT
ejpam-4821	70	57	........	........	PUNCT
ejpam-4821	70	58	........	........	PUNCT
ejpam-4821	70	59	........	........	PUNCT
ejpam-4821	70	60	........	........	PUNCT
ejpam-4821	70	61	........	........	PUNCT
ejpam-4821	70	62	........	........	PUNCT
ejpam-4821	70	63	........	........	PUNCT
ejpam-4821	70	64	........	........	PUNCT
ejpam-4821	70	65	........	........	PUNCT
ejpam-4821	70	66	........	........	PUNCT
ejpam-4821	70	67	........	........	PUNCT
ejpam-4821	70	68	........	........	PUNCT
ejpam-4821	70	69	........	........	PUNCT
ejpam-4821	70	70	........	........	PUNCT
ejpam-4821	70	71	........	........	PUNCT
ejpam-4821	70	72	........	........	PUNCT
ejpam-4821	71	1	...........................................................................................................................................................................................................................................	...........................................................................................................................................................................................................................................	PUNCT
ejpam-4821	71	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4821	72	1	...........	...........	PUNCT
ejpam-4821	72	2	..........	..........	PUNCT
ejpam-4821	73	1	..........	..........	PUNCT
ejpam-4821	73	2	..........	..........	PUNCT
ejpam-4821	74	1	..........	..........	PUNCT
ejpam-4821	74	2	..........	..........	PUNCT
ejpam-4821	75	1	..........	..........	PUNCT
ejpam-4821	75	2	..........	..........	PUNCT
ejpam-4821	76	1	..........	..........	PUNCT
ejpam-4821	76	2	...............................................................................................	...............................................................................................	PUNCT
ejpam-4821	76	3	.........	.........	PUNCT
ejpam-4821	76	4	........	........	PUNCT
ejpam-4821	76	5	........	........	PUNCT
ejpam-4821	76	6	........	........	PUNCT
ejpam-4821	76	7	........	........	PUNCT
ejpam-4821	76	8	........	........	PUNCT
ejpam-4821	76	9	........	........	PUNCT
ejpam-4821	76	10	........	........	PUNCT
ejpam-4821	76	11	........	........	PUNCT
ejpam-4821	76	12	...	...	PUNCT
ejpam-4821	77	1	....................................	....................................	PUNCT
ejpam-4821	77	2	....................................	....................................	PUNCT
ejpam-4821	78	1	....................................	....................................	PUNCT
ejpam-4821	78	2	....................................	....................................	PUNCT
ejpam-4821	79	1	....................................	....................................	PUNCT
ejpam-4821	79	2	........................................................................	........................................................................	PUNCT
ejpam-4821	80	1	....................................	....................................	PUNCT
ejpam-4821	81	1	t	t	NOUN
ejpam-4821	81	2	:	:	PUNCT
ejpam-4821	81	3	t	t	PROPN
ejpam-4821	82	1	′	′	NUM
ejpam-4821	82	2	:	:	PUNCT
ejpam-4821	82	3	figure	figure	VERB
ejpam-4821	82	4	1	1	NUM
ejpam-4821	82	5	:	:	PUNCT
ejpam-4821	82	6	graphs	graphs	VERB
ejpam-4821	82	7	t	t	PROPN
ejpam-4821	82	8	and	and	CCONJ
ejpam-4821	82	9	t	t	NOUN
ejpam-4821	82	10	′	′	NUM
ejpam-4821	82	11	proof	proof	NOUN
ejpam-4821	82	12	.	.	PUNCT
ejpam-4821	83	1	from	from	ADP
ejpam-4821	83	2	theorem	theorem	ADJ
ejpam-4821	83	3	1	1	NUM
ejpam-4821	83	4	and	and	CCONJ
ejpam-4821	83	5	remark	remark	NOUN
ejpam-4821	83	6	1	1	NUM
ejpam-4821	83	7	,	,	PUNCT
ejpam-4821	83	8	(	(	PUNCT
ejpam-4821	83	9	i	i	NOUN
ejpam-4821	83	10	)	)	PUNCT
ejpam-4821	83	11	and	and	CCONJ
ejpam-4821	83	12	(	(	PUNCT
ejpam-4821	83	13	ii	ii	NOUN
ejpam-4821	83	14	)	)	PUNCT
ejpam-4821	83	15	hold	hold	VERB
ejpam-4821	83	16	.	.	PUNCT
ejpam-4821	84	1	from	from	ADP
ejpam-4821	84	2	(	(	PUNCT
ejpam-4821	84	3	ii	ii	NOUN
ejpam-4821	84	4	)	)	PUNCT
ejpam-4821	84	5	,	,	PUNCT
ejpam-4821	84	6	(	(	PUNCT
ejpam-4821	84	7	iii	iii	X
ejpam-4821	84	8	)	)	PUNCT
ejpam-4821	84	9	holds	hold	VERB
ejpam-4821	84	10	.	.	PUNCT
ejpam-4821	85	1	(	(	PUNCT
ejpam-4821	85	2	iv	iv	X
ejpam-4821	85	3	)	)	PUNCT
ejpam-4821	85	4	suppose	suppose	VERB
ejpam-4821	85	5	n	n	PROPN
ejpam-4821	85	6	=	=	SYM
ejpam-4821	85	7	4	4	NUM
ejpam-4821	85	8	,	,	PUNCT
ejpam-4821	85	9	then	then	ADV
ejpam-4821	85	10	the	the	DET
ejpam-4821	85	11	possible	possible	ADJ
ejpam-4821	85	12	connected	connected	ADJ
ejpam-4821	85	13	isomorphic	isomorphic	ADJ
ejpam-4821	85	14	graphs	graph	NOUN
ejpam-4821	85	15	are	be	AUX
ejpam-4821	85	16	k4	k4	ADJ
ejpam-4821	85	17	,	,	PUNCT
ejpam-4821	85	18	p4	p4	ADJ
ejpam-4821	85	19	,	,	PUNCT
ejpam-4821	85	20	c4	c4	NOUN
ejpam-4821	85	21	,	,	PUNCT
ejpam-4821	85	22	k1,3	k1,3	PROPN
ejpam-4821	85	23	,	,	PUNCT
ejpam-4821	85	24	t	t	PROPN
ejpam-4821	85	25	and	and	CCONJ
ejpam-4821	85	26	t	t	PROPN
ejpam-4821	85	27	′.	′.	NOUN
ejpam-4821	85	28	thus	thus	ADV
ejpam-4821	85	29	,	,	PUNCT
ejpam-4821	85	30	it	it	PRON
ejpam-4821	85	31	can	can	AUX
ejpam-4821	85	32	be	be	AUX
ejpam-4821	85	33	verified	verify	VERB
ejpam-4821	85	34	that	that	SCONJ
ejpam-4821	85	35	ln2(g	ln2(g	NOUN
ejpam-4821	85	36	)	)	PUNCT
ejpam-4821	85	37	=	=	SYM
ejpam-4821	85	38	4	4	NUM
ejpam-4821	86	1	if	if	SCONJ
ejpam-4821	86	2	and	and	CCONJ
ejpam-4821	86	3	only	only	ADV
ejpam-4821	86	4	if	if	SCONJ
ejpam-4821	86	5	g	g	PROPN
ejpam-4821	86	6	∈	∈	PROPN
ejpam-4821	86	7	{	{	PUNCT
ejpam-4821	86	8	k4	k4	PROPN
ejpam-4821	86	9	,	,	PUNCT
ejpam-4821	86	10	c4	c4	NOUN
ejpam-4821	86	11	,	,	PUNCT
ejpam-4821	86	12	t	t	PROPN
ejpam-4821	86	13	}	}	PUNCT
ejpam-4821	86	14	and	and	CCONJ
ejpam-4821	86	15	ln2(g	ln2(g	PROPN
ejpam-4821	86	16	)	)	PUNCT
ejpam-4821	86	17	=	=	SYM
ejpam-4821	86	18	3	3	NUM
ejpam-4821	86	19	if	if	SCONJ
ejpam-4821	86	20	and	and	CCONJ
ejpam-4821	86	21	only	only	ADV
ejpam-4821	86	22	if	if	SCONJ
ejpam-4821	86	23	g	g	PROPN
ejpam-4821	86	24	∈	∈	PROPN
ejpam-4821	86	25	{	{	PUNCT
ejpam-4821	86	26	p4,k3	p4,k3	PROPN
ejpam-4821	86	27	,	,	PUNCT
ejpam-4821	86	28	t	t	NOUN
ejpam-4821	86	29	′	′	NUM
ejpam-4821	86	30	}	}	PUNCT
ejpam-4821	86	31	.	.	PUNCT
ejpam-4821	86	32	remark	remark	NOUN
ejpam-4821	86	33	4	4	NUM
ejpam-4821	86	34	.	.	PUNCT
ejpam-4821	87	1	[	[	X
ejpam-4821	87	2	5	5	NUM
ejpam-4821	87	3	]	]	PUNCT
ejpam-4821	87	4	every	every	DET
ejpam-4821	87	5	2	2	NUM
ejpam-4821	87	6	-	-	PUNCT
ejpam-4821	87	7	locating	locate	VERB
ejpam-4821	87	8	set	set	NOUN
ejpam-4821	87	9	of	of	ADP
ejpam-4821	87	10	a	a	DET
ejpam-4821	87	11	connected	connected	ADJ
ejpam-4821	87	12	graph	graph	NOUN
ejpam-4821	87	13	g	g	PROPN
ejpam-4821	87	14	is	be	AUX
ejpam-4821	87	15	2resolving	2resolving	NUM
ejpam-4821	87	16	.	.	PUNCT
ejpam-4821	88	1	thus	thus	ADV
ejpam-4821	88	2	,	,	PUNCT
ejpam-4821	88	3	dim2(g	dim2(g	NOUN
ejpam-4821	88	4	)	)	PUNCT
ejpam-4821	88	5	≤	≤	NOUN
ejpam-4821	88	6	ln2(g	ln2(g	PROPN
ejpam-4821	88	7	)	)	PUNCT
ejpam-4821	88	8	.	.	PUNCT
ejpam-4821	89	1	theorem	theorem	NOUN
ejpam-4821	89	2	2	2	NUM
ejpam-4821	89	3	.	.	PUNCT
ejpam-4821	89	4	let	let	VERB
ejpam-4821	89	5	a	a	PRON
ejpam-4821	89	6	and	and	CCONJ
ejpam-4821	89	7	b	b	NOUN
ejpam-4821	89	8	be	be	AUX
ejpam-4821	89	9	any	any	DET
ejpam-4821	89	10	positive	positive	ADJ
ejpam-4821	89	11	integers	integer	NOUN
ejpam-4821	89	12	such	such	ADJ
ejpam-4821	89	13	that	that	SCONJ
ejpam-4821	89	14	2	2	NUM
ejpam-4821	89	15	≤	≤	NUM
ejpam-4821	89	16	a	a	DET
ejpam-4821	89	17	≤	≤	PROPN
ejpam-4821	89	18	b.	b.	NOUN
ejpam-4821	90	1	then	then	ADV
ejpam-4821	90	2	there	there	PRON
ejpam-4821	90	3	exists	exist	VERB
ejpam-4821	90	4	a	a	DET
ejpam-4821	90	5	connected	connected	ADJ
ejpam-4821	90	6	graph	graph	NOUN
ejpam-4821	90	7	g	g	ADP
ejpam-4821	90	8	such	such	ADJ
ejpam-4821	90	9	that	that	SCONJ
ejpam-4821	90	10	dim2(g	dim2(g	NOUN
ejpam-4821	90	11	)	)	PUNCT
ejpam-4821	90	12	=	=	SYM
ejpam-4821	90	13	a	a	PRON
ejpam-4821	90	14	and	and	CCONJ
ejpam-4821	90	15	ln2(g	ln2(g	PROPN
ejpam-4821	90	16	)	)	PUNCT
ejpam-4821	90	17	=	=	SYM
ejpam-4821	90	18	b.	b.	PROPN
ejpam-4821	90	19	proof	proof	NOUN
ejpam-4821	90	20	.	.	PUNCT
ejpam-4821	91	1	suppose	suppose	VERB
ejpam-4821	91	2	that	that	SCONJ
ejpam-4821	91	3	a	a	DET
ejpam-4821	91	4	=	=	X
ejpam-4821	91	5	b.	b.	NOUN
ejpam-4821	91	6	consider	consider	VERB
ejpam-4821	91	7	the	the	DET
ejpam-4821	91	8	graph	graph	NOUN
ejpam-4821	91	9	g	g	PROPN
ejpam-4821	91	10	=	=	SYM
ejpam-4821	91	11	ka	ka	PROPN
ejpam-4821	91	12	.	.	PROPN
ejpam-4821	91	13	then	then	ADV
ejpam-4821	91	14	dim2(g	dim2(g	NOUN
ejpam-4821	91	15	)	)	PUNCT
ejpam-4821	91	16	=	=	PUNCT
ejpam-4821	91	17	ln2(g	ln2(g	PROPN
ejpam-4821	91	18	)	)	PUNCT
ejpam-4821	91	19	=	=	PUNCT
ejpam-4821	91	20	a.	a.	NOUN
ejpam-4821	91	21	next	next	ADV
ejpam-4821	91	22	,	,	PUNCT
ejpam-4821	91	23	suppose	suppose	VERB
ejpam-4821	91	24	that	that	SCONJ
ejpam-4821	91	25	a	a	DET
ejpam-4821	91	26	<	<	X
ejpam-4821	91	27	b.	b.	NOUN
ejpam-4821	91	28	consider	consider	VERB
ejpam-4821	91	29	the	the	DET
ejpam-4821	91	30	following	follow	VERB
ejpam-4821	91	31	cases	case	NOUN
ejpam-4821	91	32	:	:	PUNCT
ejpam-4821	91	33	case	case	NOUN
ejpam-4821	91	34	1	1	NUM
ejpam-4821	91	35	:	:	PUNCT
ejpam-4821	91	36	a	a	DET
ejpam-4821	91	37	=	=	SYM
ejpam-4821	91	38	2	2	NUM
ejpam-4821	91	39	let	let	VERB
ejpam-4821	91	40	m	m	VERB
ejpam-4821	91	41	=	=	VERB
ejpam-4821	92	1	b	b	X
ejpam-4821	92	2	−	−	PROPN
ejpam-4821	92	3	a	a	PRON
ejpam-4821	93	1	and	and	CCONJ
ejpam-4821	93	2	consider	consider	VERB
ejpam-4821	93	3	the	the	DET
ejpam-4821	93	4	graph	graph	NOUN
ejpam-4821	93	5	g	g	NOUN
ejpam-4821	93	6	in	in	ADP
ejpam-4821	93	7	figure	figure	NOUN
ejpam-4821	93	8	2	2	NUM
ejpam-4821	93	9	.	.	PUNCT
ejpam-4821	94	1	let	let	VERB
ejpam-4821	94	2	s1	s1	PROPN
ejpam-4821	94	3	=	=	PUNCT
ejpam-4821	94	4	{	{	PUNCT
ejpam-4821	94	5	x1	x1	PROPN
ejpam-4821	94	6	,	,	PUNCT
ejpam-4821	94	7	x2	x2	PROPN
ejpam-4821	94	8	}	}	PUNCT
ejpam-4821	94	9	and	and	CCONJ
ejpam-4821	94	10	s2	s2	NOUN
ejpam-4821	94	11	=	=	SYM
ejpam-4821	94	12	s1	s1	PROPN
ejpam-4821	94	13	∪	∪	X
ejpam-4821	94	14	{	{	PUNCT
ejpam-4821	94	15	v1	v1	NOUN
ejpam-4821	94	16	,	,	PUNCT
ejpam-4821	94	17	v2	v2	NOUN
ejpam-4821	94	18	,	,	PUNCT
ejpam-4821	94	19	.	.	PUNCT
ejpam-4821	94	20	.	.	PUNCT
ejpam-4821	95	1	.	.	PUNCT
ejpam-4821	96	1	,	,	PUNCT
ejpam-4821	97	1	vm	vm	NOUN
ejpam-4821	97	2	}	}	PUNCT
ejpam-4821	97	3	.	.	PUNCT
ejpam-4821	98	1	then	then	ADV
ejpam-4821	98	2	s1	s1	PROPN
ejpam-4821	98	3	and	and	CCONJ
ejpam-4821	98	4	s2	s2	PROPN
ejpam-4821	98	5	are	be	AUX
ejpam-4821	98	6	dim2	dim2	ADJ
ejpam-4821	98	7	−	−	NOUN
ejpam-4821	98	8	set	set	NOUN
ejpam-4821	98	9	and	and	CCONJ
ejpam-4821	98	10	ln2	ln2	ADJ
ejpam-4821	98	11	−	−	NOUN
ejpam-4821	98	12	set	set	NOUN
ejpam-4821	98	13	of	of	ADP
ejpam-4821	98	14	g	g	NOUN
ejpam-4821	98	15	,	,	PUNCT
ejpam-4821	98	16	respectively	respectively	ADV
ejpam-4821	98	17	.	.	PUNCT
ejpam-4821	99	1	hence	hence	ADV
ejpam-4821	99	2	,	,	PUNCT
ejpam-4821	99	3	dim2(g	dim2(g	NOUN
ejpam-4821	99	4	)	)	PUNCT
ejpam-4821	99	5	=	=	PUNCT
ejpam-4821	99	6	a	a	PRON
ejpam-4821	99	7	and	and	CCONJ
ejpam-4821	99	8	ln2(g	ln2(g	PROPN
ejpam-4821	99	9	)	)	PUNCT
ejpam-4821	99	10	=	=	PUNCT
ejpam-4821	99	11	a+m	a+m	NUM
ejpam-4821	99	12	=	=	SYM
ejpam-4821	99	13	b.	b.	PROPN
ejpam-4821	99	14	...............................................	...............................................	PUNCT
ejpam-4821	99	15	...............................................	...............................................	PUNCT
ejpam-4821	99	16	...............................................	...............................................	PUNCT
ejpam-4821	99	17	...............................................	...............................................	PUNCT
ejpam-4821	99	18	...............................................	...............................................	PUNCT
ejpam-4821	99	19	...............................................	...............................................	PUNCT
ejpam-4821	99	20	.....................................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................................	PUNCT
ejpam-4821	99	21	....................................	....................................	PUNCT
ejpam-4821	99	22	....................................	....................................	PUNCT
ejpam-4821	99	23	....................................	....................................	PUNCT
ejpam-4821	99	24	....................................	....................................	PUNCT
ejpam-4821	99	25	....................................	....................................	PUNCT
ejpam-4821	99	26	....................................	....................................	PUNCT
ejpam-4821	99	27	....................................	....................................	PUNCT
ejpam-4821	99	28	....................................	....................................	PUNCT
ejpam-4821	100	1	v1	v1	VERB
ejpam-4821	100	2	v2	v2	NOUN
ejpam-4821	100	3	vmx1	vmx1	NOUN
ejpam-4821	101	1	x2	x2	PROPN
ejpam-4821	101	2	g	g	NOUN
ejpam-4821	101	3	:	:	PUNCT
ejpam-4821	101	4	•	•	NUM
ejpam-4821	101	5	•	•	NUM
ejpam-4821	101	6	•	•	NUM
ejpam-4821	101	7	•	•	NOUN
ejpam-4821	101	8	•	•	NOUN
ejpam-4821	101	9	.	.	PUNCT
ejpam-4821	101	10	.	.	PUNCT
ejpam-4821	101	11	.	.	PUNCT
ejpam-4821	102	1	figure	figure	VERB
ejpam-4821	102	2	2	2	NUM
ejpam-4821	102	3	:	:	PUNCT
ejpam-4821	102	4	a	a	DET
ejpam-4821	102	5	graph	graph	NOUN
ejpam-4821	102	6	g	g	NOUN
ejpam-4821	102	7	case	case	NOUN
ejpam-4821	102	8	2	2	NUM
ejpam-4821	102	9	:	:	PUNCT
ejpam-4821	102	10	a	a	DET
ejpam-4821	102	11	≥	≥	NOUN
ejpam-4821	102	12	3	3	X
ejpam-4821	102	13	.	.	PUNCT
ejpam-4821	103	1	let	let	VERB
ejpam-4821	103	2	m	m	VERB
ejpam-4821	103	3	=	=	VERB
ejpam-4821	104	1	b	b	X
ejpam-4821	104	2	−	−	PROPN
ejpam-4821	104	3	a	a	PRON
ejpam-4821	105	1	and	and	CCONJ
ejpam-4821	105	2	consider	consider	VERB
ejpam-4821	105	3	the	the	DET
ejpam-4821	105	4	graph	graph	NOUN
ejpam-4821	105	5	g′	g′	NOUN
ejpam-4821	105	6	in	in	ADP
ejpam-4821	105	7	figure	figure	NOUN
ejpam-4821	105	8	3	3	NUM
ejpam-4821	105	9	.	.	PUNCT
ejpam-4821	106	1	let	let	VERB
ejpam-4821	106	2	s1	s1	PROPN
ejpam-4821	106	3	=	=	PUNCT
ejpam-4821	106	4	{	{	PUNCT
ejpam-4821	106	5	y1	y1	PROPN
ejpam-4821	106	6	,	,	PUNCT
ejpam-4821	106	7	y2	y2	PROPN
ejpam-4821	106	8	,	,	PUNCT
ejpam-4821	106	9	.	.	PUNCT
ejpam-4821	106	10	.	.	PUNCT
ejpam-4821	107	1	.	.	PUNCT
ejpam-4821	108	1	,	,	PUNCT
ejpam-4821	108	2	ya	ya	PROPN
ejpam-4821	108	3	}	}	PUNCT
ejpam-4821	108	4	and	and	CCONJ
ejpam-4821	108	5	s2	s2	NOUN
ejpam-4821	108	6	=	=	SYM
ejpam-4821	108	7	s1	s1	PROPN
ejpam-4821	108	8	∪	∪	ADJ
ejpam-4821	108	9	{	{	PUNCT
ejpam-4821	108	10	u1	u1	NOUN
ejpam-4821	108	11	,	,	PUNCT
ejpam-4821	108	12	u2	u2	NOUN
ejpam-4821	108	13	,	,	PUNCT
ejpam-4821	108	14	.	.	PUNCT
ejpam-4821	108	15	.	.	PUNCT
ejpam-4821	109	1	.	.	PUNCT
ejpam-4821	110	1	,	,	PUNCT
ejpam-4821	110	2	um	um	INTJ
ejpam-4821	110	3	}	}	PUNCT
ejpam-4821	110	4	.	.	PUNCT
ejpam-4821	111	1	then	then	ADV
ejpam-4821	111	2	s1	s1	PROPN
ejpam-4821	111	3	and	and	CCONJ
ejpam-4821	111	4	s2	s2	PROPN
ejpam-4821	111	5	are	be	AUX
ejpam-4821	111	6	dim2	dim2	NOUN
ejpam-4821	111	7	-	-	PUNCT
ejpam-4821	111	8	set	set	VERB
ejpam-4821	111	9	and	and	CCONJ
ejpam-4821	111	10	ln2	ln2	NOUN
ejpam-4821	111	11	-	-	PUNCT
ejpam-4821	111	12	set	set	NOUN
ejpam-4821	111	13	of	of	ADP
ejpam-4821	111	14	g	g	PROPN
ejpam-4821	111	15	′	′	NUM
ejpam-4821	111	16	,	,	PUNCT
ejpam-4821	111	17	respectively	respectively	ADV
ejpam-4821	111	18	.	.	PUNCT
ejpam-4821	112	1	hence	hence	ADV
ejpam-4821	112	2	,	,	PUNCT
ejpam-4821	112	3	dim2(g	dim2(g	NOUN
ejpam-4821	112	4	′	′	NOUN
ejpam-4821	112	5	)	)	PUNCT
ejpam-4821	112	6	=	=	PUNCT
ejpam-4821	112	7	a	a	PRON
ejpam-4821	112	8	and	and	CCONJ
ejpam-4821	112	9	ln2(g	ln2(g	PROPN
ejpam-4821	112	10	′	′	NUM
ejpam-4821	112	11	)	)	PUNCT
ejpam-4821	112	12	=	=	PUNCT
ejpam-4821	112	13	a+m	a+m	NUM
ejpam-4821	112	14	=	=	SYM
ejpam-4821	112	15	b.	b.	PROPN
ejpam-4821	113	1	g.cañete	g.cañete	PROPN
ejpam-4821	113	2	,	,	PUNCT
ejpam-4821	113	3	h.	h.	PROPN
ejpam-4821	113	4	rara	rara	PROPN
ejpam-4821	113	5	,	,	PUNCT
ejpam-4821	113	6	a.m.	a.m.	PROPN
ejpam-4821	113	7	mahistrado	mahistrado	PROPN
ejpam-4821	113	8	/	/	SYM
ejpam-4821	113	9	eur	eur	PROPN
ejpam-4821	113	10	.	.	PUNCT
ejpam-4821	114	1	j.	j.	PROPN
ejpam-4821	114	2	pure	pure	PROPN
ejpam-4821	114	3	appl	appl	PROPN
ejpam-4821	114	4	.	.	PROPN
ejpam-4821	114	5	math	math	PROPN
ejpam-4821	114	6	,	,	PUNCT
ejpam-4821	114	7	16	16	NUM
ejpam-4821	114	8	(	(	PUNCT
ejpam-4821	114	9	3	3	NUM
ejpam-4821	114	10	)	)	PUNCT
ejpam-4821	114	11	(	(	PUNCT
ejpam-4821	114	12	2023	2023	NUM
ejpam-4821	114	13	)	)	PUNCT
ejpam-4821	114	14	,	,	PUNCT
ejpam-4821	114	15	1647	1647	NUM
ejpam-4821	114	16	-	-	SYM
ejpam-4821	114	17	1662	1662	NUM
ejpam-4821	114	18	1651	1651	NUM
ejpam-4821	114	19	.........	.........	PUNCT
ejpam-4821	114	20	........	........	PUNCT
ejpam-4821	114	21	........	........	PUNCT
ejpam-4821	114	22	........	........	PUNCT
ejpam-4821	114	23	........	........	PUNCT
ejpam-4821	114	24	......	......	PUNCT
ejpam-4821	114	25	...............................................	...............................................	PUNCT
ejpam-4821	115	1	....	....	PUNCT
ejpam-4821	115	2	........	........	PUNCT
ejpam-4821	115	3	........	........	PUNCT
ejpam-4821	115	4	........	........	PUNCT
ejpam-4821	115	5	........	........	PUNCT
ejpam-4821	115	6	........	........	PUNCT
ejpam-4821	115	7	...	...	PUNCT
ejpam-4821	115	8	...............................................	...............................................	PUNCT
ejpam-4821	116	1	....	....	PUNCT
ejpam-4821	116	2	........	........	PUNCT
ejpam-4821	116	3	........	........	PUNCT
ejpam-4821	116	4	........	........	PUNCT
ejpam-4821	116	5	........	........	PUNCT
ejpam-4821	116	6	........	........	PUNCT
ejpam-4821	116	7	...	...	PUNCT
ejpam-4821	116	8	.........	.........	PUNCT
ejpam-4821	116	9	........	........	PUNCT
ejpam-4821	116	10	........	........	PUNCT
ejpam-4821	116	11	........	........	PUNCT
ejpam-4821	116	12	........	........	PUNCT
ejpam-4821	117	1	......	......	PUNCT
ejpam-4821	117	2	...................	...................	PUNCT
ejpam-4821	118	1	..................	..................	PUNCT
ejpam-4821	118	2	.................	.................	PUNCT
ejpam-4821	119	1	......................................................	......................................................	PUNCT
ejpam-4821	119	2	..........................................	..........................................	PUNCT
ejpam-4821	119	3	.........	.........	PUNCT
ejpam-4821	119	4	........	........	PUNCT
ejpam-4821	119	5	........	........	PUNCT
ejpam-4821	119	6	........	........	PUNCT
ejpam-4821	119	7	........	........	PUNCT
ejpam-4821	120	1	......	......	PUNCT
ejpam-4821	120	2	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-4821	121	1	....................................	....................................	PUNCT
ejpam-4821	121	2	....................................	....................................	PUNCT
ejpam-4821	122	1	....................................	....................................	PUNCT
ejpam-4821	122	2	....................................	....................................	PUNCT
ejpam-4821	123	1	....................................	....................................	PUNCT
ejpam-4821	123	2	....................................	....................................	PUNCT
ejpam-4821	124	1	....................................	....................................	PUNCT
ejpam-4821	124	2	....................................	....................................	PUNCT
ejpam-4821	125	1	....................................	....................................	PUNCT
ejpam-4821	125	2	....................................	....................................	PUNCT
ejpam-4821	126	1	....................................	....................................	PUNCT
ejpam-4821	126	2	u1	u1	VERB
ejpam-4821	126	3	um−1	um−1	PROPN
ejpam-4821	127	1	um−2	um−2	INTJ
ejpam-4821	127	2	um−3	um−3	INTJ
ejpam-4821	127	3	um	um	INTJ
ejpam-4821	127	4	y1	y1	INTJ
ejpam-4821	127	5	y2	y2	NOUN
ejpam-4821	127	6	y3	y3	NOUN
ejpam-4821	127	7	ya	ya	PROPN
ejpam-4821	127	8	g′	g′	NOUN
ejpam-4821	127	9	:	:	PUNCT
ejpam-4821	128	1	•	•	NUM
ejpam-4821	128	2	•	•	NUM
ejpam-4821	128	3	•	•	NUM
ejpam-4821	128	4	•	•	NUM
ejpam-4821	128	5	•	•	NOUN
ejpam-4821	128	6	•	•	NOUN
ejpam-4821	128	7	•••	•••	ADV
ejpam-4821	128	8	.	.	PUNCT
ejpam-4821	128	9	.	.	PUNCT
ejpam-4821	128	10	.	.	PUNCT
ejpam-4821	128	11	.	.	PUNCT
ejpam-4821	128	12	.	.	PUNCT
ejpam-4821	128	13	.	.	PUNCT
ejpam-4821	129	1	figure	figure	VERB
ejpam-4821	129	2	3	3	NUM
ejpam-4821	129	3	:	:	PUNCT
ejpam-4821	129	4	a	a	DET
ejpam-4821	129	5	graph	graph	NOUN
ejpam-4821	129	6	g′	g′	NOUN
ejpam-4821	129	7	.	.	PUNCT
ejpam-4821	130	1	corollary	corollary	ADJ
ejpam-4821	130	2	1	1	NUM
ejpam-4821	130	3	.	.	PUNCT
ejpam-4821	131	1	for	for	ADP
ejpam-4821	131	2	each	each	DET
ejpam-4821	131	3	positive	positive	ADJ
ejpam-4821	131	4	integer	integer	NOUN
ejpam-4821	131	5	n	n	CCONJ
ejpam-4821	131	6	,	,	PUNCT
ejpam-4821	131	7	there	there	PRON
ejpam-4821	131	8	exists	exist	VERB
ejpam-4821	131	9	a	a	DET
ejpam-4821	131	10	connected	connected	ADJ
ejpam-4821	131	11	graph	graph	NOUN
ejpam-4821	131	12	g	g	ADP
ejpam-4821	131	13	such	such	ADJ
ejpam-4821	131	14	that	that	SCONJ
ejpam-4821	131	15	ln2(g)−	ln2(g)−	NOUN
ejpam-4821	131	16	dim2(g	dim2(g	NOUN
ejpam-4821	131	17	)	)	PUNCT
ejpam-4821	131	18	=	=	SYM
ejpam-4821	131	19	n	n	CCONJ
ejpam-4821	131	20	,	,	PUNCT
ejpam-4821	131	21	that	that	ADV
ejpam-4821	131	22	is	is	ADV
ejpam-4821	131	23	,	,	PUNCT
ejpam-4821	131	24	ln2	ln2	ADJ
ejpam-4821	131	25	−	−	PROPN
ejpam-4821	131	26	dim2	dim2	NOUN
ejpam-4821	131	27	can	can	AUX
ejpam-4821	131	28	be	be	AUX
ejpam-4821	131	29	made	make	VERB
ejpam-4821	131	30	arbitrarily	arbitrarily	ADV
ejpam-4821	131	31	large	large	ADJ
ejpam-4821	131	32	.	.	PUNCT
ejpam-4821	132	1	we	we	PRON
ejpam-4821	132	2	now	now	ADV
ejpam-4821	132	3	characterize	characterize	VERB
ejpam-4821	132	4	the	the	DET
ejpam-4821	132	5	2	2	NUM
ejpam-4821	132	6	-	-	PUNCT
ejpam-4821	132	7	locating	locate	VERB
ejpam-4821	132	8	sets	set	NOUN
ejpam-4821	132	9	in	in	ADP
ejpam-4821	132	10	some	some	DET
ejpam-4821	132	11	graphs	graph	NOUN
ejpam-4821	132	12	under	under	ADP
ejpam-4821	132	13	some	some	DET
ejpam-4821	132	14	binary	binary	ADJ
ejpam-4821	132	15	operations	operation	NOUN
ejpam-4821	132	16	.	.	PUNCT
ejpam-4821	133	1	5	5	X
ejpam-4821	133	2	.	.	X
ejpam-4821	133	3	join	join	VERB
ejpam-4821	133	4	of	of	ADP
ejpam-4821	133	5	graphs	graph	NOUN
ejpam-4821	133	6	this	this	DET
ejpam-4821	133	7	section	section	NOUN
ejpam-4821	133	8	presents	present	VERB
ejpam-4821	133	9	the	the	DET
ejpam-4821	133	10	characterizations	characterization	NOUN
ejpam-4821	133	11	on	on	ADP
ejpam-4821	133	12	the	the	DET
ejpam-4821	133	13	2	2	NUM
ejpam-4821	133	14	-	-	PUNCT
ejpam-4821	133	15	locating	locate	VERB
ejpam-4821	133	16	sets	set	NOUN
ejpam-4821	133	17	in	in	ADP
ejpam-4821	133	18	the	the	DET
ejpam-4821	133	19	join	join	NOUN
ejpam-4821	133	20	of	of	ADP
ejpam-4821	133	21	graphs	graph	NOUN
ejpam-4821	133	22	.	.	PUNCT
ejpam-4821	134	1	theorem	theorem	VERB
ejpam-4821	134	2	3	3	NUM
ejpam-4821	134	3	.	.	PUNCT
ejpam-4821	135	1	[	[	X
ejpam-4821	135	2	6	6	NUM
ejpam-4821	135	3	]	]	PUNCT
ejpam-4821	135	4	let	let	VERB
ejpam-4821	135	5	g	g	NOUN
ejpam-4821	135	6	and	and	CCONJ
ejpam-4821	135	7	h	h	NOUN
ejpam-4821	135	8	be	be	AUX
ejpam-4821	135	9	nontrivial	nontrivial	ADJ
ejpam-4821	135	10	connected	connected	ADJ
ejpam-4821	135	11	graphs	graph	NOUN
ejpam-4821	135	12	.	.	PUNCT
ejpam-4821	136	1	a	a	DET
ejpam-4821	136	2	proper	proper	ADJ
ejpam-4821	136	3	subset	subset	NOUN
ejpam-4821	136	4	s	s	NOUN
ejpam-4821	136	5	of	of	ADP
ejpam-4821	136	6	v	v	NOUN
ejpam-4821	136	7	(	(	PUNCT
ejpam-4821	136	8	g+h	g+h	PROPN
ejpam-4821	136	9	)	)	PUNCT
ejpam-4821	136	10	is	be	AUX
ejpam-4821	136	11	a	a	DET
ejpam-4821	136	12	2	2	NUM
ejpam-4821	136	13	-	-	PUNCT
ejpam-4821	136	14	resolving	resolving	NOUN
ejpam-4821	136	15	set	set	NOUN
ejpam-4821	136	16	in	in	ADP
ejpam-4821	136	17	g+h	g+h	PROPN
ejpam-4821	136	18	if	if	SCONJ
ejpam-4821	136	19	and	and	CCONJ
ejpam-4821	136	20	only	only	ADV
ejpam-4821	136	21	if	if	SCONJ
ejpam-4821	136	22	sg	sg	PROPN
ejpam-4821	136	23	=	=	SYM
ejpam-4821	136	24	v	v	NOUN
ejpam-4821	136	25	(	(	PUNCT
ejpam-4821	136	26	g)∩s	g)∩s	PROPN
ejpam-4821	136	27	and	and	CCONJ
ejpam-4821	136	28	sh	sh	PROPN
ejpam-4821	136	29	=	=	SYM
ejpam-4821	136	30	v	v	PROPN
ejpam-4821	136	31	(	(	PUNCT
ejpam-4821	136	32	h)∩s	h)∩s	PROPN
ejpam-4821	136	33	are	be	AUX
ejpam-4821	136	34	2	2	NUM
ejpam-4821	136	35	-	-	PUNCT
ejpam-4821	136	36	locating	locate	VERB
ejpam-4821	136	37	sets	set	NOUN
ejpam-4821	136	38	in	in	ADP
ejpam-4821	136	39	g	g	PROPN
ejpam-4821	136	40	and	and	CCONJ
ejpam-4821	136	41	h	h	NOUN
ejpam-4821	136	42	,	,	PUNCT
ejpam-4821	136	43	respectively	respectively	ADV
ejpam-4821	136	44	,	,	PUNCT
ejpam-4821	136	45	where	where	SCONJ
ejpam-4821	136	46	sg	sg	NOUN
ejpam-4821	136	47	or	or	CCONJ
ejpam-4821	136	48	sh	sh	PROPN
ejpam-4821	136	49	is	be	AUX
ejpam-4821	136	50	(	(	PUNCT
ejpam-4821	136	51	2,2)-locating	2,2)-locating	NUM
ejpam-4821	136	52	set	set	NOUN
ejpam-4821	136	53	or	or	CCONJ
ejpam-4821	136	54	sg	sg	PROPN
ejpam-4821	136	55	and	and	CCONJ
ejpam-4821	136	56	sh	sh	PROPN
ejpam-4821	136	57	are	be	AUX
ejpam-4821	136	58	(	(	PUNCT
ejpam-4821	136	59	2,1)-locating	2,1)-locating	NUM
ejpam-4821	136	60	sets	set	NOUN
ejpam-4821	136	61	.	.	PUNCT
ejpam-4821	137	1	theorem	theorem	ADJ
ejpam-4821	137	2	4	4	NUM
ejpam-4821	137	3	.	.	PUNCT
ejpam-4821	138	1	[	[	X
ejpam-4821	138	2	6	6	NUM
ejpam-4821	138	3	]	]	PUNCT
ejpam-4821	138	4	let	let	VERB
ejpam-4821	138	5	g	g	PRON
ejpam-4821	138	6	be	be	AUX
ejpam-4821	138	7	a	a	DET
ejpam-4821	138	8	connected	connected	ADJ
ejpam-4821	138	9	graph	graph	NOUN
ejpam-4821	138	10	of	of	ADP
ejpam-4821	138	11	order	order	NOUN
ejpam-4821	138	12	greater	great	ADJ
ejpam-4821	138	13	than	than	ADP
ejpam-4821	138	14	3	3	NUM
ejpam-4821	138	15	and	and	CCONJ
ejpam-4821	138	16	let	let	VERB
ejpam-4821	138	17	k1	k1	NOUN
ejpam-4821	138	18	=	=	SYM
ejpam-4821	138	19	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4821	138	20	then	then	ADV
ejpam-4821	138	21	s	s	VERB
ejpam-4821	138	22	⊆	⊆	NUM
ejpam-4821	138	23	v	v	NOUN
ejpam-4821	138	24	(	(	PUNCT
ejpam-4821	138	25	k1	k1	NOUN
ejpam-4821	138	26	+	+	NOUN
ejpam-4821	138	27	g	g	NOUN
ejpam-4821	138	28	)	)	PUNCT
ejpam-4821	138	29	is	be	AUX
ejpam-4821	138	30	a	a	DET
ejpam-4821	138	31	2	2	NUM
ejpam-4821	138	32	-	-	PUNCT
ejpam-4821	138	33	resolving	resolve	VERB
ejpam-4821	138	34	set	set	NOUN
ejpam-4821	138	35	of	of	ADP
ejpam-4821	138	36	k1	k1	NOUN
ejpam-4821	139	1	+	+	ADP
ejpam-4821	139	2	g	g	PROPN
ejpam-4821	139	3	if	if	SCONJ
ejpam-4821	139	4	and	and	CCONJ
ejpam-4821	139	5	only	only	ADV
ejpam-4821	139	6	if	if	SCONJ
ejpam-4821	139	7	either	either	PRON
ejpam-4821	139	8	v	v	NOUN
ejpam-4821	139	9	/∈	/∈	PUNCT
ejpam-4821	139	10	s	s	PART
ejpam-4821	140	1	and	and	CCONJ
ejpam-4821	140	2	s	s	VERB
ejpam-4821	140	3	is	be	AUX
ejpam-4821	140	4	a	a	DET
ejpam-4821	140	5	(	(	PUNCT
ejpam-4821	140	6	2,2)-locating	2,2)-locating	NUM
ejpam-4821	140	7	set	set	VERB
ejpam-4821	140	8	in	in	ADP
ejpam-4821	140	9	g	g	PROPN
ejpam-4821	140	10	or	or	CCONJ
ejpam-4821	140	11	s	s	NOUN
ejpam-4821	140	12	=	=	PUNCT
ejpam-4821	140	13	{	{	PUNCT
ejpam-4821	140	14	v	v	NOUN
ejpam-4821	140	15	}	}	PUNCT
ejpam-4821	140	16	∪	∪	NOUN
ejpam-4821	140	17	t	t	PROPN
ejpam-4821	140	18	is	be	AUX
ejpam-4821	140	19	(	(	PUNCT
ejpam-4821	140	20	2,1)-locating	2,1)-locating	NUM
ejpam-4821	140	21	set	set	NOUN
ejpam-4821	140	22	in	in	ADP
ejpam-4821	140	23	g.	g.	PROPN
ejpam-4821	140	24	theorem	theorem	NOUN
ejpam-4821	140	25	5	5	X
ejpam-4821	140	26	.	.	PUNCT
ejpam-4821	141	1	let	let	VERB
ejpam-4821	141	2	g	g	NOUN
ejpam-4821	141	3	and	and	CCONJ
ejpam-4821	141	4	h	h	NOUN
ejpam-4821	141	5	be	be	AUX
ejpam-4821	141	6	connected	connect	VERB
ejpam-4821	141	7	graphs	graph	NOUN
ejpam-4821	141	8	.	.	PUNCT
ejpam-4821	142	1	then	then	ADV
ejpam-4821	142	2	s	s	VERB
ejpam-4821	142	3	⊆	⊆	NUM
ejpam-4821	142	4	v	v	NOUN
ejpam-4821	142	5	(	(	PUNCT
ejpam-4821	142	6	g+h	g+h	PROPN
ejpam-4821	142	7	)	)	PUNCT
ejpam-4821	142	8	is	be	AUX
ejpam-4821	142	9	a	a	DET
ejpam-4821	142	10	2	2	NUM
ejpam-4821	142	11	-	-	PUNCT
ejpam-4821	142	12	locating	locate	VERB
ejpam-4821	142	13	set	set	NOUN
ejpam-4821	142	14	in	in	ADP
ejpam-4821	142	15	g	g	PROPN
ejpam-4821	143	1	+	+	NOUN
ejpam-4821	143	2	h	h	NOUN
ejpam-4821	143	3	if	if	SCONJ
ejpam-4821	143	4	and	and	CCONJ
ejpam-4821	143	5	only	only	ADV
ejpam-4821	143	6	if	if	SCONJ
ejpam-4821	143	7	s	s	NOUN
ejpam-4821	143	8	is	be	AUX
ejpam-4821	143	9	a	a	DET
ejpam-4821	143	10	2	2	NUM
ejpam-4821	143	11	-	-	PUNCT
ejpam-4821	143	12	resolving	resolving	NOUN
ejpam-4821	143	13	set	set	NOUN
ejpam-4821	143	14	in	in	ADP
ejpam-4821	143	15	g	g	PROPN
ejpam-4821	143	16	+	+	NOUN
ejpam-4821	143	17	h	h	NOUN
ejpam-4821	143	18	where	where	SCONJ
ejpam-4821	143	19	s	s	VERB
ejpam-4821	143	20	=	=	PUNCT
ejpam-4821	143	21	sg	sg	X
ejpam-4821	143	22	∪	∪	PROPN
ejpam-4821	143	23	sh	sh	PROPN
ejpam-4821	143	24	,	,	PUNCT
ejpam-4821	143	25	sg	sg	ADP
ejpam-4821	143	26	⊆	⊆	NUM
ejpam-4821	143	27	v	v	NOUN
ejpam-4821	143	28	(	(	PUNCT
ejpam-4821	143	29	g	g	NOUN
ejpam-4821	143	30	)	)	PUNCT
ejpam-4821	143	31	and	and	CCONJ
ejpam-4821	143	32	sh	sh	PROPN
ejpam-4821	143	33	⊆	⊆	NUM
ejpam-4821	143	34	v	v	NOUN
ejpam-4821	143	35	(	(	PUNCT
ejpam-4821	143	36	h	h	NOUN
ejpam-4821	143	37	)	)	PUNCT
ejpam-4821	143	38	.	.	PUNCT
ejpam-4821	144	1	proof	proof	NOUN
ejpam-4821	144	2	.	.	PUNCT
ejpam-4821	145	1	suppose	suppose	VERB
ejpam-4821	145	2	s	s	NOUN
ejpam-4821	145	3	is	be	AUX
ejpam-4821	145	4	a	a	DET
ejpam-4821	145	5	2	2	NUM
ejpam-4821	145	6	-	-	PUNCT
ejpam-4821	145	7	locating	locate	VERB
ejpam-4821	145	8	set	set	NOUN
ejpam-4821	145	9	in	in	ADP
ejpam-4821	145	10	g	g	PROPN
ejpam-4821	145	11	+	+	CCONJ
ejpam-4821	145	12	h.	h.	PROPN
ejpam-4821	145	13	let	let	VERB
ejpam-4821	145	14	p	p	PRON
ejpam-4821	145	15	,	,	PUNCT
ejpam-4821	145	16	q	q	PROPN
ejpam-4821	145	17	∈	∈	PROPN
ejpam-4821	145	18	v	v	NOUN
ejpam-4821	145	19	(	(	PUNCT
ejpam-4821	145	20	g	g	PROPN
ejpam-4821	145	21	+	+	NOUN
ejpam-4821	145	22	h	h	NOUN
ejpam-4821	145	23	)	)	PUNCT
ejpam-4821	145	24	.	.	PUNCT
ejpam-4821	146	1	consider	consider	VERB
ejpam-4821	146	2	p	p	PRON
ejpam-4821	146	3	,	,	PUNCT
ejpam-4821	146	4	q	q	PROPN
ejpam-4821	146	5	∈	∈	PROPN
ejpam-4821	146	6	v	v	NOUN
ejpam-4821	146	7	(	(	PUNCT
ejpam-4821	146	8	g	g	PROPN
ejpam-4821	146	9	+	+	NOUN
ejpam-4821	146	10	h	h	NOUN
ejpam-4821	146	11	)	)	PUNCT
ejpam-4821	146	12	\	\	PROPN
ejpam-4821	146	13	s	s	PART
ejpam-4821	146	14	or	or	CCONJ
ejpam-4821	146	15	[	[	X
ejpam-4821	146	16	p	p	X
ejpam-4821	146	17	∈	∈	PROPN
ejpam-4821	146	18	v	v	NOUN
ejpam-4821	146	19	(	(	PUNCT
ejpam-4821	146	20	g	g	PROPN
ejpam-4821	146	21	+	+	NOUN
ejpam-4821	146	22	h	h	NOUN
ejpam-4821	146	23	)	)	PUNCT
ejpam-4821	146	24	\	\	PROPN
ejpam-4821	147	1	s	s	PART
ejpam-4821	147	2	or	or	CCONJ
ejpam-4821	147	3	q	q	ADJ
ejpam-4821	147	4	∈	∈	PROPN
ejpam-4821	147	5	s	s	PART
ejpam-4821	147	6	]	]	X
ejpam-4821	147	7	.	.	PUNCT
ejpam-4821	148	1	since	since	SCONJ
ejpam-4821	148	2	s	s	PROPN
ejpam-4821	148	3	is	be	AUX
ejpam-4821	148	4	a	a	DET
ejpam-4821	148	5	2	2	NUM
ejpam-4821	148	6	-	-	PUNCT
ejpam-4821	148	7	locating	locate	VERB
ejpam-4821	148	8	set	set	NOUN
ejpam-4821	148	9	,	,	PUNCT
ejpam-4821	148	10	then	then	ADV
ejpam-4821	148	11	rg+h(p	rg+h(p	PROPN
ejpam-4821	148	12	/	/	SYM
ejpam-4821	148	13	s	s	NOUN
ejpam-4821	148	14	)	)	PUNCT
ejpam-4821	148	15	and	and	CCONJ
ejpam-4821	148	16	rg+h(q	rg+h(q	PROPN
ejpam-4821	148	17	/	/	SYM
ejpam-4821	148	18	s	s	X
ejpam-4821	148	19	)	)	PUNCT
ejpam-4821	148	20	differ	differ	VERB
ejpam-4821	148	21	in	in	ADP
ejpam-4821	148	22	at	at	ADV
ejpam-4821	148	23	least	least	ADJ
ejpam-4821	148	24	2	2	NUM
ejpam-4821	148	25	positions	position	NOUN
ejpam-4821	148	26	.	.	PUNCT
ejpam-4821	149	1	by	by	ADP
ejpam-4821	149	2	definition	definition	NOUN
ejpam-4821	149	3	of	of	ADP
ejpam-4821	149	4	2	2	NUM
ejpam-4821	149	5	-	-	PUNCT
ejpam-4821	149	6	resolving	resolve	VERB
ejpam-4821	149	7	set	set	NOUN
ejpam-4821	149	8	and	and	CCONJ
ejpam-4821	149	9	remark	remark	NOUN
ejpam-4821	149	10	2	2	NUM
ejpam-4821	149	11	,	,	PUNCT
ejpam-4821	149	12	s	s	VERB
ejpam-4821	149	13	is	be	AUX
ejpam-4821	149	14	a	a	DET
ejpam-4821	149	15	2	2	NUM
ejpam-4821	149	16	-	-	PUNCT
ejpam-4821	149	17	resolving	resolve	VERB
ejpam-4821	149	18	set	set	NOUN
ejpam-4821	149	19	.	.	PUNCT
ejpam-4821	150	1	for	for	ADP
ejpam-4821	150	2	the	the	DET
ejpam-4821	150	3	converse	converse	NOUN
ejpam-4821	150	4	,	,	PUNCT
ejpam-4821	150	5	suppose	suppose	VERB
ejpam-4821	150	6	s	s	NOUN
ejpam-4821	150	7	is	be	AUX
ejpam-4821	150	8	a	a	DET
ejpam-4821	150	9	2	2	NUM
ejpam-4821	150	10	-	-	PUNCT
ejpam-4821	150	11	resolving	resolving	NOUN
ejpam-4821	150	12	set	set	NOUN
ejpam-4821	150	13	in	in	ADP
ejpam-4821	150	14	g	g	PROPN
ejpam-4821	150	15	+	+	CCONJ
ejpam-4821	150	16	h.	h.	PROPN
ejpam-4821	150	17	let	let	VERB
ejpam-4821	150	18	s	s	PRON
ejpam-4821	150	19	=	=	VERB
ejpam-4821	150	20	sg	sg	X
ejpam-4821	150	21	∪	∪	NOUN
ejpam-4821	150	22	sh	sh	PROPN
ejpam-4821	150	23	where	where	SCONJ
ejpam-4821	150	24	sg	sg	PROPN
ejpam-4821	150	25	⊆	⊆	NUM
ejpam-4821	150	26	v	v	NOUN
ejpam-4821	150	27	(	(	PUNCT
ejpam-4821	150	28	g	g	NOUN
ejpam-4821	150	29	)	)	PUNCT
ejpam-4821	150	30	and	and	CCONJ
ejpam-4821	150	31	sh	sh	PROPN
ejpam-4821	150	32	⊆	⊆	NUM
ejpam-4821	150	33	v	v	NOUN
ejpam-4821	150	34	(	(	PUNCT
ejpam-4821	150	35	h	h	NOUN
ejpam-4821	150	36	)	)	PUNCT
ejpam-4821	150	37	.	.	PUNCT
ejpam-4821	151	1	let	let	VERB
ejpam-4821	151	2	p	p	PRON
ejpam-4821	151	3	,	,	PUNCT
ejpam-4821	151	4	q	q	PROPN
ejpam-4821	151	5	∈	∈	PROPN
ejpam-4821	151	6	v	v	NOUN
ejpam-4821	151	7	(	(	PUNCT
ejpam-4821	151	8	g+h	g+h	NOUN
ejpam-4821	151	9	)	)	PUNCT
ejpam-4821	151	10	\	\	PUNCT
ejpam-4821	152	1	s.	s.	PROPN
ejpam-4821	152	2	consider	consider	VERB
ejpam-4821	152	3	the	the	DET
ejpam-4821	152	4	following	follow	VERB
ejpam-4821	152	5	cases	case	NOUN
ejpam-4821	152	6	.	.	PUNCT
ejpam-4821	153	1	case	case	NOUN
ejpam-4821	153	2	1	1	NUM
ejpam-4821	153	3	p	p	NOUN
ejpam-4821	153	4	,	,	PUNCT
ejpam-4821	153	5	q	q	PROPN
ejpam-4821	153	6	∈	∈	PROPN
ejpam-4821	153	7	v	v	ADP
ejpam-4821	153	8	(	(	PUNCT
ejpam-4821	153	9	g	g	NOUN
ejpam-4821	153	10	)	)	PUNCT
ejpam-4821	153	11	\	\	PROPN
ejpam-4821	153	12	sg	sg	PROPN
ejpam-4821	153	13	.	.	PUNCT
ejpam-4821	154	1	since	since	SCONJ
ejpam-4821	154	2	s	s	PROPN
ejpam-4821	154	3	is	be	AUX
ejpam-4821	154	4	a	a	DET
ejpam-4821	154	5	2	2	NUM
ejpam-4821	154	6	-	-	PUNCT
ejpam-4821	154	7	resolving	resolve	VERB
ejpam-4821	154	8	set	set	NOUN
ejpam-4821	154	9	,	,	PUNCT
ejpam-4821	154	10	rg+h(p	rg+h(p	PROPN
ejpam-4821	154	11	/	/	SYM
ejpam-4821	154	12	s	s	NOUN
ejpam-4821	154	13	)	)	PUNCT
ejpam-4821	154	14	and	and	CCONJ
ejpam-4821	154	15	rg+h(q	rg+h(q	PROPN
ejpam-4821	154	16	/	/	SYM
ejpam-4821	154	17	s	s	X
ejpam-4821	154	18	)	)	PUNCT
ejpam-4821	154	19	differ	differ	VERB
ejpam-4821	154	20	in	in	ADP
ejpam-4821	154	21	at	at	ADV
ejpam-4821	154	22	least	least	ADJ
ejpam-4821	154	23	2	2	NUM
ejpam-4821	154	24	positions	position	NOUN
ejpam-4821	154	25	.	.	PUNCT
ejpam-4821	155	1	by	by	ADP
ejpam-4821	155	2	definition	definition	NOUN
ejpam-4821	155	3	of	of	ADP
ejpam-4821	155	4	g+h	g+h	PROPN
ejpam-4821	155	5	,	,	PUNCT
ejpam-4821	155	6	rg(p	rg(p	X
ejpam-4821	155	7	/	/	SYM
ejpam-4821	155	8	sg	sg	PROPN
ejpam-4821	155	9	)	)	PUNCT
ejpam-4821	155	10	and	and	CCONJ
ejpam-4821	155	11	rg(q	rg(q	NOUN
ejpam-4821	155	12	/	/	SYM
ejpam-4821	155	13	sg	sg	PROPN
ejpam-4821	155	14	)	)	PUNCT
ejpam-4821	155	15	differ	differ	VERB
ejpam-4821	155	16	in	in	ADP
ejpam-4821	155	17	at	at	ADV
ejpam-4821	155	18	least	least	ADJ
ejpam-4821	155	19	2	2	NUM
ejpam-4821	155	20	positions	position	NOUN
ejpam-4821	155	21	.	.	PUNCT
ejpam-4821	156	1	since	since	SCONJ
ejpam-4821	156	2	dg+h(p	dg+h(p	PROPN
ejpam-4821	156	3	,	,	PUNCT
ejpam-4821	156	4	u	u	NOUN
ejpam-4821	156	5	)	)	PUNCT
ejpam-4821	156	6	and	and	CCONJ
ejpam-4821	156	7	dg+h(q	dg+h(q	PROPN
ejpam-4821	156	8	,	,	PUNCT
ejpam-4821	156	9	u	u	NOUN
ejpam-4821	156	10	)	)	PUNCT
ejpam-4821	156	11	is	be	AUX
ejpam-4821	156	12	either	either	PRON
ejpam-4821	156	13	0,1	0,1	NUM
ejpam-4821	156	14	or	or	CCONJ
ejpam-4821	156	15	2	2	NUM
ejpam-4821	156	16	for	for	ADP
ejpam-4821	156	17	each	each	DET
ejpam-4821	156	18	u	u	PROPN
ejpam-4821	156	19	∈	∈	PROPN
ejpam-4821	156	20	v	v	NOUN
ejpam-4821	156	21	(	(	PUNCT
ejpam-4821	156	22	g+h	g+h	PROPN
ejpam-4821	156	23	)	)	PUNCT
ejpam-4821	156	24	,	,	PUNCT
ejpam-4821	156	25	there	there	PRON
ejpam-4821	156	26	exist	exist	VERB
ejpam-4821	156	27	at	at	ADV
ejpam-4821	156	28	least	least	ADV
ejpam-4821	156	29	two	two	NUM
ejpam-4821	156	30	vertices	vertex	NOUN
ejpam-4821	156	31	x	x	X
ejpam-4821	156	32	,	,	PUNCT
ejpam-4821	156	33	y	y	PROPN
ejpam-4821	156	34	∈	∈	PROPN
ejpam-4821	156	35	sg	sg	ADP
ejpam-4821	156	36	such	such	ADJ
ejpam-4821	156	37	that	that	SCONJ
ejpam-4821	156	38	x	x	NOUN
ejpam-4821	156	39	,	,	PUNCT
ejpam-4821	156	40	y	y	PROPN
ejpam-4821	156	41	∈	∈	PROPN
ejpam-4821	156	42	ng(p	ng(p	NOUN
ejpam-4821	156	43	)	)	PUNCT
ejpam-4821	156	44	\ng(q	\ng(q	NOUN
ejpam-4821	156	45	)	)	PUNCT
ejpam-4821	156	46	or	or	CCONJ
ejpam-4821	156	47	x	x	SYM
ejpam-4821	156	48	,	,	PUNCT
ejpam-4821	156	49	y	y	PROPN
ejpam-4821	156	50	∈	∈	PROPN
ejpam-4821	156	51	ng(q	ng(q	NOUN
ejpam-4821	156	52	)	)	PUNCT
ejpam-4821	156	53	\ng(p	\ng(p	NOUN
ejpam-4821	156	54	)	)	PUNCT
ejpam-4821	156	55	or	or	CCONJ
ejpam-4821	156	56	x	x	PUNCT
ejpam-4821	156	57	∈	∈	NOUN
ejpam-4821	156	58	ng(p	ng(p	NOUN
ejpam-4821	156	59	)	)	PUNCT
ejpam-4821	156	60	\ng(q	\ng(q	NOUN
ejpam-4821	156	61	)	)	PUNCT
ejpam-4821	156	62	and	and	CCONJ
ejpam-4821	156	63	y	y	PROPN
ejpam-4821	156	64	∈	∈	PROPN
ejpam-4821	156	65	ng(q	ng(q	NOUN
ejpam-4821	156	66	)	)	PUNCT
ejpam-4821	156	67	\ng(p	\ng(p	NOUN
ejpam-4821	156	68	)	)	PUNCT
ejpam-4821	156	69	.	.	PUNCT
ejpam-4821	156	70	hence,∣∣[(ng+h(p)\ng+h(q	hence,∣∣[(ng+h(p)\ng+h(q	NOUN
ejpam-4821	156	71	)	)	PUNCT
ejpam-4821	156	72	)	)	PUNCT
ejpam-4821	157	1	∩	∩	PROPN
ejpam-4821	157	2	s	s	X
ejpam-4821	157	3	]	]	X
ejpam-4821	157	4	∪	∪	X
ejpam-4821	157	5	[	[	PUNCT
ejpam-4821	157	6	(	(	PUNCT
ejpam-4821	157	7	ng+h(q)\ng+h(p	ng+h(q)\ng+h(p	NOUN
ejpam-4821	157	8	)	)	PUNCT
ejpam-4821	157	9	)	)	PUNCT
ejpam-4821	158	1	∩	∩	NOUN
ejpam-4821	158	2	s	s	X
ejpam-4821	158	3	]	]	PUNCT
ejpam-4821	158	4	∣∣	∣∣	X
ejpam-4821	158	5	≥	≥	NOUN
ejpam-4821	158	6	2	2	NUM
ejpam-4821	158	7	.	.	PUNCT
ejpam-4821	158	8	(	(	PUNCT
ejpam-4821	158	9	1	1	X
ejpam-4821	158	10	)	)	PUNCT
ejpam-4821	158	11	case	case	NOUN
ejpam-4821	158	12	2	2	NUM
ejpam-4821	158	13	.	.	X
ejpam-4821	159	1	p	p	X
ejpam-4821	159	2	,	,	PUNCT
ejpam-4821	159	3	q	q	PROPN
ejpam-4821	159	4	∈	∈	PROPN
ejpam-4821	159	5	v	v	ADP
ejpam-4821	159	6	(	(	PUNCT
ejpam-4821	159	7	h	h	NOUN
ejpam-4821	159	8	)	)	PUNCT
ejpam-4821	159	9	\	\	PUNCT
ejpam-4821	160	1	sh	sh	PROPN
ejpam-4821	160	2	proof	proof	NOUN
ejpam-4821	160	3	is	be	AUX
ejpam-4821	160	4	similar	similar	ADJ
ejpam-4821	160	5	to	to	ADP
ejpam-4821	160	6	case	case	NOUN
ejpam-4821	160	7	1	1	NUM
ejpam-4821	160	8	.	.	PUNCT
ejpam-4821	161	1	g.cañete	g.cañete	PROPN
ejpam-4821	161	2	,	,	PUNCT
ejpam-4821	161	3	h.	h.	PROPN
ejpam-4821	161	4	rara	rara	PROPN
ejpam-4821	161	5	,	,	PUNCT
ejpam-4821	161	6	a.m.	a.m.	PROPN
ejpam-4821	161	7	mahistrado	mahistrado	PROPN
ejpam-4821	161	8	/	/	SYM
ejpam-4821	161	9	eur	eur	PROPN
ejpam-4821	161	10	.	.	PUNCT
ejpam-4821	162	1	j.	j.	PROPN
ejpam-4821	162	2	pure	pure	PROPN
ejpam-4821	162	3	appl	appl	PROPN
ejpam-4821	162	4	.	.	PROPN
ejpam-4821	162	5	math	math	PROPN
ejpam-4821	162	6	,	,	PUNCT
ejpam-4821	162	7	16	16	NUM
ejpam-4821	162	8	(	(	PUNCT
ejpam-4821	162	9	3	3	NUM
ejpam-4821	162	10	)	)	PUNCT
ejpam-4821	162	11	(	(	PUNCT
ejpam-4821	162	12	2023	2023	NUM
ejpam-4821	162	13	)	)	PUNCT
ejpam-4821	162	14	,	,	PUNCT
ejpam-4821	162	15	1647	1647	NUM
ejpam-4821	162	16	-	-	SYM
ejpam-4821	162	17	1662	1662	NUM
ejpam-4821	162	18	1652	1652	NUM
ejpam-4821	162	19	case	case	NOUN
ejpam-4821	162	20	3	3	NUM
ejpam-4821	162	21	.	.	PUNCT
ejpam-4821	163	1	p	p	PROPN
ejpam-4821	163	2	∈	∈	PROPN
ejpam-4821	163	3	v	v	ADP
ejpam-4821	163	4	(	(	PUNCT
ejpam-4821	163	5	g	g	NOUN
ejpam-4821	163	6	)	)	PUNCT
ejpam-4821	163	7	\	\	PROPN
ejpam-4821	163	8	sg	sg	NOUN
ejpam-4821	163	9	and	and	CCONJ
ejpam-4821	163	10	q	q	PROPN
ejpam-4821	163	11	∈	∈	PROPN
ejpam-4821	163	12	v	v	ADP
ejpam-4821	163	13	(	(	PUNCT
ejpam-4821	163	14	h	h	NOUN
ejpam-4821	163	15	)	)	PUNCT
ejpam-4821	163	16	\	\	PUNCT
ejpam-4821	164	1	sh	sh	PROPN
ejpam-4821	164	2	note	note	VERB
ejpam-4821	164	3	that	that	SCONJ
ejpam-4821	164	4	rg+h(p	rg+h(p	PROPN
ejpam-4821	164	5	/	/	SYM
ejpam-4821	164	6	s	s	NOUN
ejpam-4821	164	7	)	)	PUNCT
ejpam-4821	164	8	=	=	SYM
ejpam-4821	164	9	(	(	PUNCT
ejpam-4821	164	10	2	2	NUM
ejpam-4821	164	11	,	,	PUNCT
ejpam-4821	164	12	2	2	NUM
ejpam-4821	164	13	,	,	PUNCT
ejpam-4821	164	14	2	2	NUM
ejpam-4821	164	15	,	,	PUNCT
ejpam-4821	164	16	.	.	PUNCT
ejpam-4821	164	17	.	.	PUNCT
ejpam-4821	164	18	.	.	PUNCT
ejpam-4821	165	1	,	,	PUNCT
ejpam-4821	165	2	1	1	NUM
ejpam-4821	165	3	,	,	PUNCT
ejpam-4821	165	4	1	1	NUM
ejpam-4821	165	5	,	,	PUNCT
ejpam-4821	165	6	.	.	PUNCT
ejpam-4821	165	7	.	.	PUNCT
ejpam-4821	165	8	.	.	PUNCT
ejpam-4821	166	1	,	,	PUNCT
ejpam-4821	166	2	1	1	X
ejpam-4821	166	3	)	)	PUNCT
ejpam-4821	166	4	and	and	CCONJ
ejpam-4821	166	5	rg+h(q	rg+h(q	PROPN
ejpam-4821	166	6	/	/	SYM
ejpam-4821	166	7	s	s	NOUN
ejpam-4821	166	8	)	)	PUNCT
ejpam-4821	166	9	=	=	SYM
ejpam-4821	166	10	(	(	PUNCT
ejpam-4821	166	11	1	1	NUM
ejpam-4821	166	12	,	,	PUNCT
ejpam-4821	166	13	1	1	NUM
ejpam-4821	166	14	,	,	PUNCT
ejpam-4821	166	15	1	1	NUM
ejpam-4821	166	16	,	,	PUNCT
ejpam-4821	166	17	.	.	PUNCT
ejpam-4821	166	18	.	.	PUNCT
ejpam-4821	166	19	.	.	PUNCT
ejpam-4821	167	1	,	,	PUNCT
ejpam-4821	167	2	2	2	NUM
ejpam-4821	167	3	,	,	PUNCT
ejpam-4821	167	4	2	2	NUM
ejpam-4821	167	5	,	,	PUNCT
ejpam-4821	167	6	.	.	PUNCT
ejpam-4821	167	7	.	.	PUNCT
ejpam-4821	167	8	.	.	PUNCT
ejpam-4821	168	1	,	,	PUNCT
ejpam-4821	168	2	2	2	NUM
ejpam-4821	168	3	)	)	PUNCT
ejpam-4821	168	4	.	.	PUNCT
ejpam-4821	169	1	then	then	ADV
ejpam-4821	169	2	there	there	PRON
ejpam-4821	169	3	exist	exist	VERB
ejpam-4821	169	4	x	x	SYM
ejpam-4821	169	5	∈	∈	NOUN
ejpam-4821	169	6	sg	sg	ADP
ejpam-4821	169	7	\	\	PROPN
ejpam-4821	169	8	ng(p	ng(p	NOUN
ejpam-4821	169	9	)	)	PUNCT
ejpam-4821	169	10	and	and	CCONJ
ejpam-4821	169	11	y	y	PROPN
ejpam-4821	169	12	∈	∈	PROPN
ejpam-4821	169	13	sh	sh	INTJ
ejpam-4821	169	14	\	\	PROPN
ejpam-4821	169	15	nh(q	nh(q	PROPN
ejpam-4821	169	16	)	)	PUNCT
ejpam-4821	169	17	or	or	CCONJ
ejpam-4821	169	18	∃w	∃w	PROPN
ejpam-4821	169	19	,	,	PUNCT
ejpam-4821	169	20	r	r	NOUN
ejpam-4821	169	21	∈	∈	PROPN
ejpam-4821	169	22	sg	sg	ADP
ejpam-4821	169	23	\	\	PROPN
ejpam-4821	169	24	ng(p	ng(p	NOUN
ejpam-4821	169	25	)	)	PUNCT
ejpam-4821	169	26	or	or	CCONJ
ejpam-4821	169	27	w	w	NOUN
ejpam-4821	169	28	,	,	PUNCT
ejpam-4821	169	29	r	r	NOUN
ejpam-4821	169	30	∈	∈	PROPN
ejpam-4821	169	31	sh	sh	NOUN
ejpam-4821	169	32	\nh(q	\nh(q	PROPN
ejpam-4821	169	33	)	)	PUNCT
ejpam-4821	169	34	.	.	PUNCT
ejpam-4821	170	1	hence	hence	ADV
ejpam-4821	170	2	,	,	PUNCT
ejpam-4821	170	3	inequality	inequality	NOUN
ejpam-4821	170	4	(	(	PUNCT
ejpam-4821	170	5	1	1	NUM
ejpam-4821	170	6	)	)	PUNCT
ejpam-4821	170	7	holds	hold	VERB
ejpam-4821	170	8	.	.	PUNCT
ejpam-4821	171	1	suppose	suppose	VERB
ejpam-4821	171	2	p	p	PROPN
ejpam-4821	171	3	∈	∈	PROPN
ejpam-4821	171	4	s	s	PART
ejpam-4821	171	5	and	and	CCONJ
ejpam-4821	171	6	q	q	PROPN
ejpam-4821	171	7	∈	∈	PROPN
ejpam-4821	171	8	v	v	NOUN
ejpam-4821	171	9	(	(	PUNCT
ejpam-4821	171	10	g+h	g+h	NOUN
ejpam-4821	171	11	)	)	PUNCT
ejpam-4821	171	12	\	\	PUNCT
ejpam-4821	172	1	s.	s.	PROPN
ejpam-4821	172	2	consider	consider	VERB
ejpam-4821	172	3	the	the	DET
ejpam-4821	172	4	following	follow	VERB
ejpam-4821	172	5	cases	case	NOUN
ejpam-4821	172	6	.	.	PUNCT
ejpam-4821	173	1	case	case	NOUN
ejpam-4821	173	2	1	1	NUM
ejpam-4821	173	3	p	p	NOUN
ejpam-4821	173	4	∈	∈	PROPN
ejpam-4821	173	5	sg	sg	NOUN
ejpam-4821	173	6	and	and	CCONJ
ejpam-4821	173	7	q	q	PROPN
ejpam-4821	173	8	∈	∈	PROPN
ejpam-4821	173	9	v	v	ADP
ejpam-4821	173	10	(	(	PUNCT
ejpam-4821	173	11	g	g	NOUN
ejpam-4821	173	12	)	)	PUNCT
ejpam-4821	173	13	\	\	PROPN
ejpam-4821	173	14	sg	sg	PROPN
ejpam-4821	173	15	.	.	PUNCT
ejpam-4821	174	1	since	since	SCONJ
ejpam-4821	174	2	rg+h(p	rg+h(p	PROPN
ejpam-4821	174	3	/	/	SYM
ejpam-4821	174	4	s	s	NOUN
ejpam-4821	174	5	)	)	PUNCT
ejpam-4821	174	6	and	and	CCONJ
ejpam-4821	174	7	rg+h(q	rg+h(q	PROPN
ejpam-4821	174	8	/	/	SYM
ejpam-4821	174	9	s	s	X
ejpam-4821	174	10	)	)	PUNCT
ejpam-4821	174	11	differ	differ	VERB
ejpam-4821	174	12	in	in	ADP
ejpam-4821	174	13	at	at	ADV
ejpam-4821	174	14	least	least	ADJ
ejpam-4821	174	15	2	2	NUM
ejpam-4821	174	16	positions	position	NOUN
ejpam-4821	174	17	,	,	PUNCT
ejpam-4821	174	18	by	by	ADP
ejpam-4821	174	19	definition	definition	NOUN
ejpam-4821	174	20	of	of	ADP
ejpam-4821	174	21	g	g	PROPN
ejpam-4821	174	22	+	+	CCONJ
ejpam-4821	174	23	h	h	NOUN
ejpam-4821	174	24	,	,	PUNCT
ejpam-4821	174	25	rg(p	rg(p	VERB
ejpam-4821	174	26	/	/	SYM
ejpam-4821	174	27	sg	sg	PROPN
ejpam-4821	174	28	)	)	PUNCT
ejpam-4821	174	29	and	and	CCONJ
ejpam-4821	174	30	rg(q	rg(q	NOUN
ejpam-4821	174	31	/	/	SYM
ejpam-4821	174	32	sg	sg	PROPN
ejpam-4821	174	33	)	)	PUNCT
ejpam-4821	174	34	differ	differ	VERB
ejpam-4821	174	35	in	in	ADP
ejpam-4821	174	36	at	at	ADV
ejpam-4821	174	37	least	least	ADJ
ejpam-4821	174	38	2	2	NUM
ejpam-4821	174	39	positions	position	NOUN
ejpam-4821	174	40	,	,	PUNCT
ejpam-4821	174	41	this	this	PRON
ejpam-4821	174	42	implies	imply	VERB
ejpam-4821	174	43	that	that	SCONJ
ejpam-4821	174	44	(	(	PUNCT
ejpam-4821	174	45	ng(p)\ng(q	ng(p)\ng(q	ADJ
ejpam-4821	174	46	)	)	PUNCT
ejpam-4821	174	47	)	)	PUNCT
ejpam-4821	174	48	∩	∩	NOUN
ejpam-4821	174	49	sg	sg	ADP
ejpam-4821	174	50	̸=	̸=	PROPN
ejpam-4821	174	51	∅	∅	NOUN
ejpam-4821	174	52	or	or	CCONJ
ejpam-4821	174	53	(	(	PUNCT
ejpam-4821	174	54	ng(q)\ng(p	ng(q)\ng(p	ADJ
ejpam-4821	174	55	)	)	PUNCT
ejpam-4821	174	56	)	)	PUNCT
ejpam-4821	175	1	∩	∩	NOUN
ejpam-4821	175	2	sg	sg	ADP
ejpam-4821	175	3	̸=	̸=	PROPN
ejpam-4821	175	4	∅.	∅.	PRON
ejpam-4821	175	5	hence	hence	ADV
ejpam-4821	175	6	,	,	PUNCT
ejpam-4821	175	7	(	(	PUNCT
ejpam-4821	175	8	ng+h(p)\ng+h(q	ng+h(p)\ng+h(q	ADV
ejpam-4821	175	9	)	)	PUNCT
ejpam-4821	175	10	)	)	PUNCT
ejpam-4821	175	11	∩	∩	PROPN
ejpam-4821	175	12	s	s	PART
ejpam-4821	175	13	̸=	̸=	PROPN
ejpam-4821	175	14	∅	∅	NOUN
ejpam-4821	175	15	or	or	CCONJ
ejpam-4821	175	16	(	(	PUNCT
ejpam-4821	175	17	ng+h(q)\ng+h(p	ng+h(q)\ng+h(p	NOUN
ejpam-4821	175	18	)	)	PUNCT
ejpam-4821	175	19	)	)	PUNCT
ejpam-4821	175	20	∩	∩	PROPN
ejpam-4821	175	21	s	s	PART
ejpam-4821	175	22	̸=	̸=	PROPN
ejpam-4821	175	23	∅.	∅.	PRON
ejpam-4821	175	24	case	case	NOUN
ejpam-4821	175	25	2	2	NUM
ejpam-4821	175	26	.	.	PUNCT
ejpam-4821	176	1	p	p	PROPN
ejpam-4821	176	2	∈	∈	PROPN
ejpam-4821	176	3	sg	sg	NOUN
ejpam-4821	176	4	and	and	CCONJ
ejpam-4821	176	5	q	q	PROPN
ejpam-4821	176	6	∈	∈	PROPN
ejpam-4821	176	7	v	v	ADP
ejpam-4821	176	8	(	(	PUNCT
ejpam-4821	176	9	h	h	NOUN
ejpam-4821	176	10	)	)	PUNCT
ejpam-4821	176	11	\	\	PUNCT
ejpam-4821	177	1	sh	sh	PROPN
ejpam-4821	177	2	note	note	VERB
ejpam-4821	177	3	that	that	SCONJ
ejpam-4821	177	4	rg+h(p	rg+h(p	PROPN
ejpam-4821	177	5	/	/	SYM
ejpam-4821	177	6	s	s	NOUN
ejpam-4821	177	7	)	)	PUNCT
ejpam-4821	177	8	=	=	SYM
ejpam-4821	177	9	(	(	PUNCT
ejpam-4821	177	10	.	.	PUNCT
ejpam-4821	177	11	.	.	PUNCT
ejpam-4821	177	12	.	.	PUNCT
ejpam-4821	178	1	,	,	PUNCT
ejpam-4821	178	2	0	0	NUM
ejpam-4821	178	3	,	,	PUNCT
ejpam-4821	178	4	.	.	PUNCT
ejpam-4821	178	5	.	.	PUNCT
ejpam-4821	179	1	.	.	PUNCT
ejpam-4821	180	1	,	,	PUNCT
ejpam-4821	180	2	1	1	NUM
ejpam-4821	180	3	,	,	PUNCT
ejpam-4821	180	4	1	1	NUM
ejpam-4821	180	5	,	,	PUNCT
ejpam-4821	180	6	.	.	PUNCT
ejpam-4821	180	7	.	.	PUNCT
ejpam-4821	180	8	.	.	PUNCT
ejpam-4821	181	1	,	,	PUNCT
ejpam-4821	181	2	1	1	X
ejpam-4821	181	3	)	)	PUNCT
ejpam-4821	181	4	and	and	CCONJ
ejpam-4821	181	5	rg+h(q	rg+h(q	PROPN
ejpam-4821	181	6	/	/	SYM
ejpam-4821	181	7	s	s	NOUN
ejpam-4821	181	8	)	)	PUNCT
ejpam-4821	181	9	=	=	SYM
ejpam-4821	181	10	(	(	PUNCT
ejpam-4821	181	11	1	1	NUM
ejpam-4821	181	12	,	,	PUNCT
ejpam-4821	181	13	1	1	NUM
ejpam-4821	181	14	,	,	PUNCT
ejpam-4821	181	15	.	.	PUNCT
ejpam-4821	181	16	.	.	PUNCT
ejpam-4821	181	17	.	.	PUNCT
ejpam-4821	182	1	,	,	PUNCT
ejpam-4821	182	2	0	0	NUM
ejpam-4821	182	3	,	,	PUNCT
ejpam-4821	182	4	.	.	PUNCT
ejpam-4821	182	5	.	.	PUNCT
ejpam-4821	182	6	.	.	PUNCT
ejpam-4821	182	7	)	)	PUNCT
ejpam-4821	182	8	.	.	PUNCT
ejpam-4821	183	1	hence	hence	ADV
ejpam-4821	183	2	,	,	PUNCT
ejpam-4821	183	3	there	there	PRON
ejpam-4821	183	4	exist	exist	VERB
ejpam-4821	183	5	at	at	ADV
ejpam-4821	183	6	least	least	ADV
ejpam-4821	183	7	one	one	NUM
ejpam-4821	183	8	vertex	vertex	NOUN
ejpam-4821	183	9	x	x	SYM
ejpam-4821	183	10	∈	∈	NOUN
ejpam-4821	183	11	sg	sg	ADP
ejpam-4821	183	12	\	\	PROPN
ejpam-4821	183	13	ng(p	ng(p	NOUN
ejpam-4821	183	14	)	)	PUNCT
ejpam-4821	183	15	or	or	CCONJ
ejpam-4821	183	16	there	there	PRON
ejpam-4821	183	17	exist	exist	VERB
ejpam-4821	183	18	at	at	ADV
ejpam-4821	183	19	least	least	ADV
ejpam-4821	183	20	one	one	NUM
ejpam-4821	183	21	vertex	vertex	NOUN
ejpam-4821	183	22	y	y	PROPN
ejpam-4821	183	23	∈	∈	PROPN
ejpam-4821	183	24	sh	sh	ADP
ejpam-4821	183	25	\ng(q	\ng(q	NOUN
ejpam-4821	183	26	)	)	PUNCT
ejpam-4821	183	27	.	.	PUNCT
ejpam-4821	184	1	thus	thus	ADV
ejpam-4821	184	2	,	,	PUNCT
ejpam-4821	184	3	(	(	PUNCT
ejpam-4821	184	4	ng+h(p)\ng+h(q	ng+h(p)\ng+h(q	ADV
ejpam-4821	184	5	)	)	PUNCT
ejpam-4821	184	6	)	)	PUNCT
ejpam-4821	184	7	∩	∩	PROPN
ejpam-4821	184	8	s	s	PART
ejpam-4821	184	9	̸=	̸=	PROPN
ejpam-4821	184	10	∅	∅	NOUN
ejpam-4821	184	11	or	or	CCONJ
ejpam-4821	184	12	(	(	PUNCT
ejpam-4821	184	13	ng+h(q)\ng+h(p	ng+h(q)\ng+h(p	NOUN
ejpam-4821	184	14	)	)	PUNCT
ejpam-4821	184	15	)	)	PUNCT
ejpam-4821	185	1	∩	∩	PROPN
ejpam-4821	185	2	s	s	PART
ejpam-4821	185	3	̸=	̸=	PROPN
ejpam-4821	185	4	∅.	∅.	ADP
ejpam-4821	185	5	the	the	DET
ejpam-4821	185	6	proof	proof	NOUN
ejpam-4821	185	7	that	that	SCONJ
ejpam-4821	185	8	p	p	PROPN
ejpam-4821	185	9	∈	∈	PROPN
ejpam-4821	185	10	v	v	NOUN
ejpam-4821	185	11	(	(	PUNCT
ejpam-4821	185	12	g+h	g+h	NOUN
ejpam-4821	185	13	)	)	PUNCT
ejpam-4821	185	14	\	\	PROPN
ejpam-4821	185	15	s	s	PROPN
ejpam-4821	185	16	and	and	CCONJ
ejpam-4821	185	17	q	q	PROPN
ejpam-4821	185	18	∈	∈	PROPN
ejpam-4821	185	19	s	s	VERB
ejpam-4821	185	20	is	be	AUX
ejpam-4821	185	21	similar	similar	ADJ
ejpam-4821	185	22	.	.	PUNCT
ejpam-4821	186	1	therefore	therefore	ADV
ejpam-4821	186	2	,	,	PUNCT
ejpam-4821	186	3	s	s	VERB
ejpam-4821	186	4	is	be	AUX
ejpam-4821	186	5	a	a	DET
ejpam-4821	186	6	2	2	NUM
ejpam-4821	186	7	-	-	PUNCT
ejpam-4821	186	8	locating	locate	VERB
ejpam-4821	186	9	set	set	NOUN
ejpam-4821	186	10	of	of	ADP
ejpam-4821	186	11	g+h	g+h	PROPN
ejpam-4821	186	12	.	.	PUNCT
ejpam-4821	187	1	the	the	DET
ejpam-4821	187	2	following	follow	VERB
ejpam-4821	187	3	corollaries	corollary	NOUN
ejpam-4821	187	4	follow	follow	VERB
ejpam-4821	187	5	immediately	immediately	ADV
ejpam-4821	187	6	from	from	ADP
ejpam-4821	187	7	theorem	theorem	ADJ
ejpam-4821	187	8	5	5	NUM
ejpam-4821	187	9	,	,	PUNCT
ejpam-4821	187	10	theorem	theorem	VERB
ejpam-4821	187	11	4	4	NUM
ejpam-4821	187	12	,	,	PUNCT
ejpam-4821	187	13	and	and	CCONJ
ejpam-4821	187	14	theorem	theorem	VERB
ejpam-4821	187	15	3	3	NUM
ejpam-4821	187	16	.	.	PUNCT
ejpam-4821	187	17	corollary	corollary	ADJ
ejpam-4821	187	18	2	2	NUM
ejpam-4821	187	19	.	.	PUNCT
ejpam-4821	188	1	let	let	VERB
ejpam-4821	188	2	g	g	PRON
ejpam-4821	188	3	be	be	AUX
ejpam-4821	188	4	a	a	DET
ejpam-4821	188	5	nontrivial	nontrivial	ADJ
ejpam-4821	188	6	connected	connect	VERB
ejpam-4821	188	7	graph	graph	NOUN
ejpam-4821	188	8	and	and	CCONJ
ejpam-4821	188	9	k1	k1	NOUN
ejpam-4821	188	10	=	=	SYM
ejpam-4821	188	11	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4821	188	12	then	then	ADV
ejpam-4821	188	13	s	s	VERB
ejpam-4821	188	14	⊆	⊆	NUM
ejpam-4821	188	15	v	v	NOUN
ejpam-4821	188	16	(	(	PUNCT
ejpam-4821	188	17	k1+g	k1+g	NOUN
ejpam-4821	188	18	)	)	PUNCT
ejpam-4821	188	19	is	be	AUX
ejpam-4821	188	20	a	a	DET
ejpam-4821	188	21	2	2	NUM
ejpam-4821	188	22	-	-	PUNCT
ejpam-4821	188	23	locating	locate	VERB
ejpam-4821	188	24	set	set	NOUN
ejpam-4821	188	25	in	in	ADP
ejpam-4821	188	26	k1	k1	NOUN
ejpam-4821	189	1	+	+	ADP
ejpam-4821	189	2	g	g	PROPN
ejpam-4821	189	3	if	if	SCONJ
ejpam-4821	189	4	and	and	CCONJ
ejpam-4821	189	5	only	only	ADV
ejpam-4821	189	6	if	if	SCONJ
ejpam-4821	189	7	it	it	PRON
ejpam-4821	189	8	satisfies	satisfy	VERB
ejpam-4821	189	9	the	the	DET
ejpam-4821	189	10	following	follow	VERB
ejpam-4821	189	11	conditions	condition	NOUN
ejpam-4821	189	12	:	:	PUNCT
ejpam-4821	189	13	(	(	PUNCT
ejpam-4821	189	14	i	i	NOUN
ejpam-4821	189	15	)	)	PUNCT
ejpam-4821	189	16	v	v	ADP
ejpam-4821	189	17	/∈	/∈	PUNCT
ejpam-4821	190	1	s	s	PART
ejpam-4821	190	2	and	and	CCONJ
ejpam-4821	190	3	s	s	VERB
ejpam-4821	190	4	is	be	AUX
ejpam-4821	190	5	(	(	PUNCT
ejpam-4821	190	6	2,2)-locating	2,2)-locating	NUM
ejpam-4821	190	7	set	set	NOUN
ejpam-4821	190	8	of	of	ADP
ejpam-4821	190	9	g.	g.	PROPN
ejpam-4821	190	10	(	(	PUNCT
ejpam-4821	190	11	ii	ii	PROPN
ejpam-4821	190	12	)	)	PUNCT
ejpam-4821	190	13	s	s	PART
ejpam-4821	191	1	=	=	VERB
ejpam-4821	191	2	{	{	PUNCT
ejpam-4821	191	3	v	v	NOUN
ejpam-4821	191	4	}	}	PUNCT
ejpam-4821	191	5	∪	∪	NOUN
ejpam-4821	191	6	t	t	PROPN
ejpam-4821	191	7	and	and	CCONJ
ejpam-4821	191	8	t	t	PROPN
ejpam-4821	191	9	is	be	AUX
ejpam-4821	191	10	(	(	PUNCT
ejpam-4821	191	11	2,1)-locating	2,1)-locating	NUM
ejpam-4821	191	12	set	set	NOUN
ejpam-4821	191	13	in	in	ADP
ejpam-4821	191	14	g.	g.	PROPN
ejpam-4821	191	15	corollary	corollary	PROPN
ejpam-4821	191	16	3	3	X
ejpam-4821	191	17	.	.	PUNCT
ejpam-4821	192	1	let	let	VERB
ejpam-4821	192	2	g	g	NOUN
ejpam-4821	192	3	be	be	AUX
ejpam-4821	192	4	any	any	DET
ejpam-4821	192	5	nontrivial	nontrivial	ADJ
ejpam-4821	192	6	connected	connect	VERB
ejpam-4821	192	7	graph	graph	NOUN
ejpam-4821	192	8	.	.	PUNCT
ejpam-4821	193	1	then	then	ADV
ejpam-4821	193	2	ln2(k1	ln2(k1	PUNCT
ejpam-4821	193	3	+	+	NOUN
ejpam-4821	193	4	g	g	NOUN
ejpam-4821	193	5	)	)	PUNCT
ejpam-4821	193	6	=	=	SYM
ejpam-4821	193	7	min{ln(2,2)(g	min{ln(2,2)(g	NOUN
ejpam-4821	193	8	)	)	PUNCT
ejpam-4821	193	9	,	,	PUNCT
ejpam-4821	193	10	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4821	193	11	)	)	PUNCT
ejpam-4821	193	12	+	+	NOUN
ejpam-4821	193	13	1	1	NUM
ejpam-4821	193	14	}	}	PUNCT
ejpam-4821	193	15	.	.	PUNCT
ejpam-4821	194	1	corollary	corollary	ADJ
ejpam-4821	194	2	4	4	NUM
ejpam-4821	194	3	.	.	PUNCT
ejpam-4821	195	1	let	let	VERB
ejpam-4821	195	2	g	g	NOUN
ejpam-4821	195	3	and	and	CCONJ
ejpam-4821	195	4	h	h	NOUN
ejpam-4821	195	5	be	be	AUX
ejpam-4821	195	6	nontrivial	nontrivial	ADJ
ejpam-4821	195	7	connected	connected	ADJ
ejpam-4821	195	8	graphs	graph	NOUN
ejpam-4821	195	9	.	.	PUNCT
ejpam-4821	196	1	a	a	DET
ejpam-4821	196	2	set	set	NOUN
ejpam-4821	196	3	s	s	NOUN
ejpam-4821	196	4	⊆	⊆	NUM
ejpam-4821	196	5	v	v	NOUN
ejpam-4821	196	6	(	(	PUNCT
ejpam-4821	196	7	g+h	g+h	PROPN
ejpam-4821	196	8	)	)	PUNCT
ejpam-4821	196	9	is	be	AUX
ejpam-4821	196	10	a	a	DET
ejpam-4821	196	11	2locating	2locating	NUM
ejpam-4821	196	12	set	set	NOUN
ejpam-4821	196	13	in	in	ADP
ejpam-4821	196	14	g+h	g+h	PROPN
ejpam-4821	196	15	if	if	SCONJ
ejpam-4821	196	16	and	and	CCONJ
ejpam-4821	196	17	only	only	ADV
ejpam-4821	196	18	if	if	SCONJ
ejpam-4821	196	19	s	s	X
ejpam-4821	196	20	=	=	PUNCT
ejpam-4821	196	21	sg∪sh	sg∪sh	PROPN
ejpam-4821	196	22	where	where	SCONJ
ejpam-4821	196	23	sg	sg	PROPN
ejpam-4821	196	24	=	=	SYM
ejpam-4821	196	25	v	v	PROPN
ejpam-4821	196	26	(	(	PUNCT
ejpam-4821	196	27	g)∩s	g)∩s	PROPN
ejpam-4821	196	28	and	and	CCONJ
ejpam-4821	196	29	sh	sh	PROPN
ejpam-4821	196	30	=	=	SYM
ejpam-4821	196	31	v	v	PROPN
ejpam-4821	196	32	(	(	PUNCT
ejpam-4821	196	33	h)∩s	h)∩s	PROPN
ejpam-4821	196	34	are	be	AUX
ejpam-4821	196	35	2	2	NUM
ejpam-4821	196	36	-	-	PUNCT
ejpam-4821	196	37	locating	locate	VERB
ejpam-4821	196	38	sets	set	NOUN
ejpam-4821	196	39	of	of	ADP
ejpam-4821	196	40	g	g	PROPN
ejpam-4821	196	41	and	and	CCONJ
ejpam-4821	196	42	h	h	NOUN
ejpam-4821	196	43	,	,	PUNCT
ejpam-4821	196	44	respectively	respectively	ADV
ejpam-4821	196	45	,	,	PUNCT
ejpam-4821	196	46	where	where	SCONJ
ejpam-4821	196	47	sg	sg	NOUN
ejpam-4821	196	48	or	or	CCONJ
ejpam-4821	196	49	sh	sh	PROPN
ejpam-4821	196	50	is	be	AUX
ejpam-4821	196	51	a	a	DET
ejpam-4821	196	52	(	(	PUNCT
ejpam-4821	196	53	2	2	NUM
ejpam-4821	196	54	,	,	PUNCT
ejpam-4821	196	55	2)-locating	2)-locating	NUM
ejpam-4821	196	56	set	set	NOUN
ejpam-4821	196	57	or	or	CCONJ
ejpam-4821	196	58	sg	sg	PROPN
ejpam-4821	196	59	and	and	CCONJ
ejpam-4821	196	60	sh	sh	PROPN
ejpam-4821	196	61	are	be	AUX
ejpam-4821	196	62	(	(	PUNCT
ejpam-4821	196	63	2	2	NUM
ejpam-4821	196	64	,	,	PUNCT
ejpam-4821	196	65	1)-locating	1)-locating	NUM
ejpam-4821	196	66	sets	set	NOUN
ejpam-4821	196	67	.	.	PUNCT
ejpam-4821	197	1	corollary	corollary	ADJ
ejpam-4821	197	2	5	5	NUM
ejpam-4821	197	3	.	.	PUNCT
ejpam-4821	198	1	let	let	VERB
ejpam-4821	198	2	g	g	NOUN
ejpam-4821	198	3	and	and	CCONJ
ejpam-4821	198	4	h	h	NOUN
ejpam-4821	198	5	be	be	AUX
ejpam-4821	198	6	nontrivial	nontrivial	ADJ
ejpam-4821	198	7	connected	connected	ADJ
ejpam-4821	198	8	graphs	graph	NOUN
ejpam-4821	198	9	.	.	PUNCT
ejpam-4821	199	1	then	then	ADV
ejpam-4821	199	2	ln2(g+h	ln2(g+h	VERB
ejpam-4821	199	3	)	)	PUNCT
ejpam-4821	200	1	=	=	SYM
ejpam-4821	200	2	min{ln(2,2)(g	min{ln(2,2)(g	NOUN
ejpam-4821	200	3	)	)	PUNCT
ejpam-4821	201	1	+	+	CCONJ
ejpam-4821	201	2	ln2(h	ln2(h	PROPN
ejpam-4821	201	3	)	)	PUNCT
ejpam-4821	201	4	,	,	PUNCT
ejpam-4821	201	5	ln2(g	ln2(g	PROPN
ejpam-4821	201	6	)	)	PUNCT
ejpam-4821	201	7	+	+	CCONJ
ejpam-4821	201	8	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4821	201	9	)	)	PUNCT
ejpam-4821	201	10	,	,	PUNCT
ejpam-4821	201	11	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4821	201	12	)	)	PUNCT
ejpam-4821	201	13	+	+	PUNCT
ejpam-4821	201	14	ln(2,1)(h	ln(2,1)(h	NOUN
ejpam-4821	201	15	)	)	PUNCT
ejpam-4821	201	16	}	}	PUNCT
ejpam-4821	201	17	.	.	PUNCT
ejpam-4821	202	1	g.cañete	g.cañete	PROPN
ejpam-4821	202	2	,	,	PUNCT
ejpam-4821	202	3	h.	h.	PROPN
ejpam-4821	202	4	rara	rara	PROPN
ejpam-4821	202	5	,	,	PUNCT
ejpam-4821	202	6	a.m.	a.m.	PROPN
ejpam-4821	202	7	mahistrado	mahistrado	PROPN
ejpam-4821	202	8	/	/	SYM
ejpam-4821	202	9	eur	eur	PROPN
ejpam-4821	202	10	.	.	PUNCT
ejpam-4821	203	1	j.	j.	PROPN
ejpam-4821	203	2	pure	pure	PROPN
ejpam-4821	203	3	appl	appl	PROPN
ejpam-4821	203	4	.	.	PROPN
ejpam-4821	203	5	math	math	PROPN
ejpam-4821	203	6	,	,	PUNCT
ejpam-4821	203	7	16	16	NUM
ejpam-4821	203	8	(	(	PUNCT
ejpam-4821	203	9	3	3	NUM
ejpam-4821	203	10	)	)	PUNCT
ejpam-4821	203	11	(	(	PUNCT
ejpam-4821	203	12	2023	2023	NUM
ejpam-4821	203	13	)	)	PUNCT
ejpam-4821	203	14	,	,	PUNCT
ejpam-4821	203	15	1647	1647	NUM
ejpam-4821	203	16	-	-	SYM
ejpam-4821	203	17	1662	1662	NUM
ejpam-4821	203	18	1653	1653	NUM
ejpam-4821	203	19	6	6	NUM
ejpam-4821	203	20	.	.	PUNCT
ejpam-4821	204	1	corona	corona	NOUN
ejpam-4821	204	2	of	of	ADP
ejpam-4821	204	3	graphs	graph	NOUN
ejpam-4821	204	4	this	this	DET
ejpam-4821	204	5	section	section	NOUN
ejpam-4821	204	6	presents	present	VERB
ejpam-4821	204	7	the	the	DET
ejpam-4821	204	8	characterizations	characterization	NOUN
ejpam-4821	204	9	on	on	ADP
ejpam-4821	204	10	the	the	DET
ejpam-4821	204	11	2	2	NUM
ejpam-4821	204	12	-	-	PUNCT
ejpam-4821	204	13	locating	locate	VERB
ejpam-4821	204	14	sets	set	NOUN
ejpam-4821	204	15	in	in	ADP
ejpam-4821	204	16	the	the	DET
ejpam-4821	204	17	corona	corona	NOUN
ejpam-4821	204	18	of	of	ADP
ejpam-4821	204	19	graphs	graph	NOUN
ejpam-4821	204	20	.	.	PUNCT
ejpam-4821	205	1	theorem	theorem	ADJ
ejpam-4821	205	2	6	6	NUM
ejpam-4821	205	3	.	.	PUNCT
ejpam-4821	206	1	let	let	VERB
ejpam-4821	206	2	g	g	NOUN
ejpam-4821	206	3	and	and	CCONJ
ejpam-4821	206	4	h	h	NOUN
ejpam-4821	206	5	be	be	AUX
ejpam-4821	206	6	nontrivial	nontrivial	ADJ
ejpam-4821	206	7	connected	connect	VERB
ejpam-4821	206	8	graphs	graph	NOUN
ejpam-4821	206	9	with	with	ADP
ejpam-4821	206	10	∆(h	∆(h	NOUN
ejpam-4821	206	11	)	)	PUNCT
ejpam-4821	206	12	≤	≤	NOUN
ejpam-4821	206	13	|v	|v	X
ejpam-4821	206	14	(	(	PUNCT
ejpam-4821	206	15	h)|	h)|	NOUN
ejpam-4821	206	16	−	−	PROPN
ejpam-4821	206	17	3	3	NUM
ejpam-4821	206	18	.	.	PUNCT
ejpam-4821	207	1	a	a	DET
ejpam-4821	207	2	set	set	NOUN
ejpam-4821	207	3	s	s	NOUN
ejpam-4821	207	4	⊆	⊆	NUM
ejpam-4821	207	5	v	v	NOUN
ejpam-4821	207	6	(	(	PUNCT
ejpam-4821	207	7	g	g	PROPN
ejpam-4821	207	8	◦	◦	NOUN
ejpam-4821	207	9	h	h	NOUN
ejpam-4821	207	10	)	)	PUNCT
ejpam-4821	207	11	is	be	AUX
ejpam-4821	207	12	a	a	DET
ejpam-4821	207	13	2	2	NUM
ejpam-4821	207	14	-	-	PUNCT
ejpam-4821	207	15	locating	locate	VERB
ejpam-4821	207	16	set	set	NOUN
ejpam-4821	207	17	of	of	ADP
ejpam-4821	207	18	g	g	PROPN
ejpam-4821	207	19	◦	◦	NOUN
ejpam-4821	207	20	h	h	NOUN
ejpam-4821	207	21	if	if	SCONJ
ejpam-4821	208	1	and	and	CCONJ
ejpam-4821	208	2	only	only	ADV
ejpam-4821	208	3	if	if	SCONJ
ejpam-4821	208	4	s	s	VERB
ejpam-4821	208	5	=	=	NOUN
ejpam-4821	208	6	a	a	PRON
ejpam-4821	208	7	∪	∪	X
ejpam-4821	208	8	(	(	PUNCT
ejpam-4821	208	9	⋃	⋃	NOUN
ejpam-4821	208	10	v∈v	v∈v	NOUN
ejpam-4821	208	11	(	(	PUNCT
ejpam-4821	208	12	g	g	NOUN
ejpam-4821	208	13	)	)	PUNCT
ejpam-4821	208	14	sv	sv	NOUN
ejpam-4821	208	15	)	)	PUNCT
ejpam-4821	208	16	where	where	SCONJ
ejpam-4821	208	17	a	a	DET
ejpam-4821	208	18	⊆	⊆	NUM
ejpam-4821	208	19	v	v	NOUN
ejpam-4821	208	20	(	(	PUNCT
ejpam-4821	208	21	g	g	NOUN
ejpam-4821	208	22	)	)	PUNCT
ejpam-4821	208	23	and	and	CCONJ
ejpam-4821	208	24	v	v	NOUN
ejpam-4821	208	25	(	(	PUNCT
ejpam-4821	208	26	hv	hv	NOUN
ejpam-4821	208	27	)	)	PUNCT
ejpam-4821	208	28	∩	∩	PROPN
ejpam-4821	208	29	s	s	PART
ejpam-4821	208	30	̸=	̸=	PROPN
ejpam-4821	208	31	∅	∅	NOUN
ejpam-4821	208	32	for	for	ADP
ejpam-4821	208	33	each	each	DET
ejpam-4821	208	34	v	v	NUM
ejpam-4821	208	35	∈	∈	PROPN
ejpam-4821	208	36	v	v	NOUN
ejpam-4821	208	37	(	(	PUNCT
ejpam-4821	208	38	g	g	NOUN
ejpam-4821	208	39	)	)	PUNCT
ejpam-4821	208	40	and	and	CCONJ
ejpam-4821	208	41	the	the	DET
ejpam-4821	208	42	following	following	NOUN
ejpam-4821	208	43	are	be	AUX
ejpam-4821	208	44	satisfied	satisfied	ADJ
ejpam-4821	208	45	(	(	PUNCT
ejpam-4821	208	46	i	i	NOUN
ejpam-4821	208	47	)	)	PUNCT
ejpam-4821	208	48	sv	sv	PROPN
ejpam-4821	208	49	is	be	AUX
ejpam-4821	208	50	a	a	DET
ejpam-4821	208	51	2	2	NUM
ejpam-4821	208	52	-	-	PUNCT
ejpam-4821	208	53	locating	locate	VERB
ejpam-4821	208	54	set	set	NOUN
ejpam-4821	208	55	of	of	ADP
ejpam-4821	208	56	hv	hv	PROPN
ejpam-4821	208	57	for	for	ADP
ejpam-4821	208	58	each	each	DET
ejpam-4821	208	59	v	v	NUM
ejpam-4821	208	60	∈	∈	PROPN
ejpam-4821	208	61	v	v	NOUN
ejpam-4821	208	62	(	(	PUNCT
ejpam-4821	208	63	g	g	NOUN
ejpam-4821	208	64	)	)	PUNCT
ejpam-4821	208	65	and	and	CCONJ
ejpam-4821	208	66	su	su	PROPN
ejpam-4821	208	67	or	or	CCONJ
ejpam-4821	208	68	sv	sv	PROPN
ejpam-4821	208	69	is	be	AUX
ejpam-4821	208	70	total	total	ADJ
ejpam-4821	208	71	2	2	NUM
ejpam-4821	208	72	-	-	PUNCT
ejpam-4821	208	73	dominating	dominating	NOUN
ejpam-4821	208	74	for	for	ADP
ejpam-4821	208	75	u	u	NOUN
ejpam-4821	208	76	,	,	PUNCT
ejpam-4821	208	77	v	v	PROPN
ejpam-4821	208	78	∈	∈	PROPN
ejpam-4821	208	79	v	v	NOUN
ejpam-4821	208	80	(	(	PUNCT
ejpam-4821	208	81	g	g	NOUN
ejpam-4821	208	82	)	)	PUNCT
ejpam-4821	208	83	\a	\a	ADJ
ejpam-4821	208	84	or	or	CCONJ
ejpam-4821	208	85	otherwise	otherwise	ADV
ejpam-4821	208	86	,	,	PUNCT
ejpam-4821	208	87	su	su	PROPN
ejpam-4821	208	88	and	and	CCONJ
ejpam-4821	208	89	sv	sv	PROPN
ejpam-4821	208	90	are	be	AUX
ejpam-4821	208	91	total	total	ADJ
ejpam-4821	208	92	dominating	dominating	NOUN
ejpam-4821	208	93	;	;	PUNCT
ejpam-4821	208	94	(	(	PUNCT
ejpam-4821	208	95	ii	ii	NOUN
ejpam-4821	208	96	)	)	PUNCT
ejpam-4821	208	97	for	for	ADP
ejpam-4821	208	98	each	each	DET
ejpam-4821	208	99	v	v	NUM
ejpam-4821	208	100	∈	∈	PROPN
ejpam-4821	208	101	v	v	NOUN
ejpam-4821	208	102	(	(	PUNCT
ejpam-4821	208	103	g	g	NOUN
ejpam-4821	208	104	)	)	PUNCT
ejpam-4821	208	105	\	\	PROPN
ejpam-4821	209	1	a	a	PRON
ejpam-4821	209	2	,	,	PUNCT
ejpam-4821	209	3	sv	sv	PROPN
ejpam-4821	209	4	is	be	AUX
ejpam-4821	209	5	a	a	DET
ejpam-4821	209	6	(	(	PUNCT
ejpam-4821	209	7	2	2	NUM
ejpam-4821	209	8	,	,	PUNCT
ejpam-4821	209	9	2)-locating	2)-locating	NUM
ejpam-4821	209	10	set	set	NOUN
ejpam-4821	209	11	of	of	ADP
ejpam-4821	209	12	hv	hv	PROPN
ejpam-4821	209	13	with	with	ADP
ejpam-4821	209	14	ng(v	ng(v	NOUN
ejpam-4821	209	15	)	)	PUNCT
ejpam-4821	209	16	∩a	∩a	NOUN
ejpam-4821	209	17	=	=	PUNCT
ejpam-4821	209	18	∅	∅	NOUN
ejpam-4821	209	19	and	and	CCONJ
ejpam-4821	209	20	sv	sv	PROPN
ejpam-4821	209	21	is	be	AUX
ejpam-4821	209	22	(	(	PUNCT
ejpam-4821	209	23	2,1)-locating	2,1)-locating	NUM
ejpam-4821	209	24	set	set	NOUN
ejpam-4821	209	25	,	,	PUNCT
ejpam-4821	209	26	otherwise	otherwise	ADV
ejpam-4821	209	27	;	;	PUNCT
ejpam-4821	209	28	and	and	CCONJ
ejpam-4821	209	29	(	(	PUNCT
ejpam-4821	209	30	iii	iii	NOUN
ejpam-4821	209	31	)	)	PUNCT
ejpam-4821	209	32	for	for	ADP
ejpam-4821	209	33	each	each	DET
ejpam-4821	209	34	v	v	ADP
ejpam-4821	209	35	∈	∈	PRON
ejpam-4821	209	36	a	a	PRON
ejpam-4821	209	37	,	,	PUNCT
ejpam-4821	209	38	sv	sv	PROPN
ejpam-4821	209	39	is	be	AUX
ejpam-4821	209	40	a	a	DET
ejpam-4821	209	41	(	(	PUNCT
ejpam-4821	209	42	2	2	NUM
ejpam-4821	209	43	,	,	PUNCT
ejpam-4821	209	44	1)-locating	1)-locating	NUM
ejpam-4821	209	45	set	set	NOUN
ejpam-4821	209	46	of	of	ADP
ejpam-4821	209	47	hv	hv	PROPN
ejpam-4821	209	48	if	if	SCONJ
ejpam-4821	209	49	ng(v	ng(v	PUNCT
ejpam-4821	209	50	)	)	PUNCT
ejpam-4821	210	1	∩a	∩a	NOUN
ejpam-4821	210	2	=	=	PUNCT
ejpam-4821	210	3	∅.	∅.	NOUN
ejpam-4821	210	4	proof	proof	NOUN
ejpam-4821	210	5	.	.	PUNCT
ejpam-4821	211	1	suppose	suppose	VERB
ejpam-4821	211	2	s	s	VERB
ejpam-4821	211	3	⊆	⊆	NUM
ejpam-4821	211	4	v	v	NOUN
ejpam-4821	211	5	(	(	PUNCT
ejpam-4821	211	6	g	g	PROPN
ejpam-4821	211	7	◦	◦	NOUN
ejpam-4821	211	8	h	h	NOUN
ejpam-4821	211	9	)	)	PUNCT
ejpam-4821	211	10	is	be	AUX
ejpam-4821	211	11	a	a	DET
ejpam-4821	211	12	2	2	NUM
ejpam-4821	211	13	-	-	PUNCT
ejpam-4821	211	14	locating	locate	VERB
ejpam-4821	211	15	set	set	NOUN
ejpam-4821	211	16	in	in	ADP
ejpam-4821	211	17	g	g	PROPN
ejpam-4821	211	18	◦	◦	PROPN
ejpam-4821	211	19	h.	h.	PROPN
ejpam-4821	211	20	let	let	VERB
ejpam-4821	211	21	a	a	DET
ejpam-4821	211	22	=	=	X
ejpam-4821	211	23	v	v	X
ejpam-4821	211	24	(	(	PUNCT
ejpam-4821	211	25	g	g	NOUN
ejpam-4821	211	26	)	)	PUNCT
ejpam-4821	211	27	∩	∩	PROPN
ejpam-4821	211	28	s	s	NOUN
ejpam-4821	211	29	,	,	PUNCT
ejpam-4821	211	30	sv	sv	INTJ
ejpam-4821	211	31	=	=	SYM
ejpam-4821	211	32	s	s	PROPN
ejpam-4821	211	33	∩	∩	ADJ
ejpam-4821	211	34	v	v	X
ejpam-4821	211	35	(	(	PUNCT
ejpam-4821	211	36	hv	hv	PROPN
ejpam-4821	211	37	)	)	PUNCT
ejpam-4821	211	38	for	for	ADP
ejpam-4821	211	39	all	all	DET
ejpam-4821	211	40	v	v	ADP
ejpam-4821	211	41	∈	∈	NOUN
ejpam-4821	211	42	v	v	NOUN
ejpam-4821	211	43	(	(	PUNCT
ejpam-4821	211	44	g	g	NOUN
ejpam-4821	211	45	)	)	PUNCT
ejpam-4821	211	46	.	.	PUNCT
ejpam-4821	212	1	then	then	ADV
ejpam-4821	212	2	s	s	VERB
ejpam-4821	212	3	=	=	PUNCT
ejpam-4821	212	4	a	a	PRON
ejpam-4821	212	5	∪	∪	X
ejpam-4821	212	6	(	(	PUNCT
ejpam-4821	212	7	⋃	⋃	NOUN
ejpam-4821	212	8	v∈v	v∈v	NOUN
ejpam-4821	212	9	(	(	PUNCT
ejpam-4821	212	10	g	g	NOUN
ejpam-4821	212	11	)	)	PUNCT
ejpam-4821	212	12	sv	sv	NOUN
ejpam-4821	212	13	)	)	PUNCT
ejpam-4821	212	14	where	where	SCONJ
ejpam-4821	212	15	a	a	DET
ejpam-4821	212	16	⊆	⊆	NUM
ejpam-4821	212	17	v	v	NOUN
ejpam-4821	212	18	(	(	PUNCT
ejpam-4821	212	19	g	g	NOUN
ejpam-4821	212	20	)	)	PUNCT
ejpam-4821	212	21	and	and	CCONJ
ejpam-4821	212	22	sv	sv	X
ejpam-4821	212	23	⊆	⊆	NUM
ejpam-4821	212	24	v	v	X
ejpam-4821	212	25	(	(	PUNCT
ejpam-4821	212	26	hv	hv	PROPN
ejpam-4821	212	27	)	)	PUNCT
ejpam-4821	212	28	.	.	PUNCT
ejpam-4821	213	1	now	now	ADV
ejpam-4821	213	2	,	,	PUNCT
ejpam-4821	213	3	suppose	suppose	VERB
ejpam-4821	213	4	sv	sv	X
ejpam-4821	213	5	=	=	NOUN
ejpam-4821	213	6	∅	∅	NOUN
ejpam-4821	213	7	for	for	ADP
ejpam-4821	213	8	some	some	DET
ejpam-4821	213	9	v	v	ADP
ejpam-4821	213	10	∈	∈	NOUN
ejpam-4821	213	11	v	v	NOUN
ejpam-4821	213	12	(	(	PUNCT
ejpam-4821	213	13	g	g	NOUN
ejpam-4821	213	14	)	)	PUNCT
ejpam-4821	213	15	.	.	PUNCT
ejpam-4821	214	1	let	let	VERB
ejpam-4821	214	2	x	x	PRON
ejpam-4821	214	3	,	,	PUNCT
ejpam-4821	214	4	y	y	PROPN
ejpam-4821	214	5	∈	∈	PROPN
ejpam-4821	214	6	v	v	NOUN
ejpam-4821	214	7	(	(	PUNCT
ejpam-4821	214	8	hv)\sv	hv)\sv	PROPN
ejpam-4821	214	9	.	.	PUNCT
ejpam-4821	214	10	then∣∣[(nhv(x)\nhv(y	then∣∣[(nhv(x)\nhv(y	NUM
ejpam-4821	214	11	)	)	PUNCT
ejpam-4821	214	12	)	)	PUNCT
ejpam-4821	215	1	∩	∩	PROPN
ejpam-4821	215	2	sv	sv	ADP
ejpam-4821	215	3	]	]	X
ejpam-4821	215	4	∪	∪	X
ejpam-4821	215	5	[	[	PUNCT
ejpam-4821	215	6	(	(	PUNCT
ejpam-4821	215	7	nhv(y)\nhv(x	nhv(y)\nhv(x	X
ejpam-4821	215	8	)	)	PUNCT
ejpam-4821	215	9	)	)	PUNCT
ejpam-4821	215	10	∩	∩	NOUN
ejpam-4821	215	11	sv	sv	ADP
ejpam-4821	215	12	]	]	X
ejpam-4821	215	13	∣∣	∣∣	X
ejpam-4821	215	14	=	=	SYM
ejpam-4821	215	15	0	0	NUM
ejpam-4821	215	16	,	,	PUNCT
ejpam-4821	215	17	for	for	ADP
ejpam-4821	215	18	all	all	DET
ejpam-4821	215	19	x	x	NOUN
ejpam-4821	215	20	,	,	PUNCT
ejpam-4821	215	21	y	y	PROPN
ejpam-4821	215	22	∈	∈	PROPN
ejpam-4821	215	23	v	v	NOUN
ejpam-4821	215	24	(	(	PUNCT
ejpam-4821	215	25	hv)\sv	hv)\sv	ADJ
ejpam-4821	215	26	with	with	ADP
ejpam-4821	215	27	x	x	PROPN
ejpam-4821	215	28	̸=	̸=	PROPN
ejpam-4821	215	29	y	y	PROPN
ejpam-4821	215	30	,	,	PUNCT
ejpam-4821	215	31	a	a	DET
ejpam-4821	215	32	contradiction	contradiction	NOUN
ejpam-4821	215	33	to	to	ADP
ejpam-4821	215	34	the	the	DET
ejpam-4821	215	35	assumption	assumption	NOUN
ejpam-4821	215	36	of	of	ADP
ejpam-4821	215	37	s.	s.	PROPN
ejpam-4821	215	38	thus	thus	ADV
ejpam-4821	215	39	,	,	PUNCT
ejpam-4821	215	40	sv	sv	PROPN
ejpam-4821	215	41	̸=	̸=	PROPN
ejpam-4821	215	42	∅	∅	NOUN
ejpam-4821	215	43	for	for	ADP
ejpam-4821	215	44	all	all	PRON
ejpam-4821	215	45	v	v	ADP
ejpam-4821	215	46	∈	∈	NOUN
ejpam-4821	215	47	v	v	NOUN
ejpam-4821	215	48	(	(	PUNCT
ejpam-4821	215	49	g	g	PROPN
ejpam-4821	215	50	◦	◦	NOUN
ejpam-4821	215	51	h	h	NOUN
ejpam-4821	215	52	)	)	PUNCT
ejpam-4821	215	53	.	.	PUNCT
ejpam-4821	216	1	to	to	PART
ejpam-4821	216	2	prove	prove	VERB
ejpam-4821	216	3	(	(	PUNCT
ejpam-4821	216	4	i	i	NOUN
ejpam-4821	216	5	)	)	PUNCT
ejpam-4821	216	6	,	,	PUNCT
ejpam-4821	216	7	let	let	VERB
ejpam-4821	216	8	x	x	PRON
ejpam-4821	216	9	,	,	PUNCT
ejpam-4821	216	10	y	y	PROPN
ejpam-4821	216	11	∈	∈	PROPN
ejpam-4821	216	12	v	v	PROPN
ejpam-4821	216	13	(	(	PUNCT
ejpam-4821	216	14	hv	hv	PROPN
ejpam-4821	216	15	)	)	PUNCT
ejpam-4821	216	16	where	where	SCONJ
ejpam-4821	216	17	v	v	X
ejpam-4821	216	18	∈	∈	PROPN
ejpam-4821	216	19	v	v	NOUN
ejpam-4821	216	20	(	(	PUNCT
ejpam-4821	216	21	g	g	NOUN
ejpam-4821	216	22	)	)	PUNCT
ejpam-4821	216	23	.	.	PUNCT
ejpam-4821	217	1	then	then	ADV
ejpam-4821	217	2	x	x	X
ejpam-4821	217	3	,	,	PUNCT
ejpam-4821	217	4	y	y	PROPN
ejpam-4821	217	5	∈	∈	PROPN
ejpam-4821	217	6	v	v	NOUN
ejpam-4821	217	7	(	(	PUNCT
ejpam-4821	217	8	g	g	PROPN
ejpam-4821	217	9	◦	◦	NOUN
ejpam-4821	217	10	h	h	NOUN
ejpam-4821	217	11	)	)	PUNCT
ejpam-4821	217	12	.	.	PUNCT
ejpam-4821	218	1	since	since	SCONJ
ejpam-4821	218	2	nhv(x	nhv(x	PRON
ejpam-4821	218	3	)	)	PUNCT
ejpam-4821	218	4	=	=	SYM
ejpam-4821	218	5	ng	ng	PROPN
ejpam-4821	218	6	◦	◦	NOUN
ejpam-4821	218	7	h(x)\{v	h(x)\{v	PROPN
ejpam-4821	218	8	}	}	PUNCT
ejpam-4821	218	9	and	and	CCONJ
ejpam-4821	218	10	nhv(y	nhv(y	PROPN
ejpam-4821	218	11	)	)	PUNCT
ejpam-4821	218	12	=	=	SYM
ejpam-4821	218	13	ng	ng	PROPN
ejpam-4821	218	14	◦	◦	NOUN
ejpam-4821	218	15	h(y)\{v	h(y)\{v	PROPN
ejpam-4821	218	16	}	}	PUNCT
ejpam-4821	218	17	,	,	PUNCT
ejpam-4821	218	18	and	and	CCONJ
ejpam-4821	218	19	s	s	VERB
ejpam-4821	218	20	is	be	AUX
ejpam-4821	218	21	a	a	DET
ejpam-4821	218	22	2	2	NUM
ejpam-4821	218	23	-	-	PUNCT
ejpam-4821	218	24	locating	locate	VERB
ejpam-4821	218	25	set	set	NOUN
ejpam-4821	218	26	,	,	PUNCT
ejpam-4821	218	27	this	this	PRON
ejpam-4821	218	28	implies	imply	VERB
ejpam-4821	218	29	that	that	SCONJ
ejpam-4821	218	30	sv	sv	PROPN
ejpam-4821	218	31	is	be	AUX
ejpam-4821	218	32	also	also	ADV
ejpam-4821	218	33	2	2	NUM
ejpam-4821	218	34	-	-	PUNCT
ejpam-4821	218	35	locating	locate	VERB
ejpam-4821	218	36	set	set	NOUN
ejpam-4821	218	37	in	in	ADP
ejpam-4821	218	38	hv	hv	PROPN
ejpam-4821	218	39	.	.	PUNCT
ejpam-4821	219	1	next	next	ADV
ejpam-4821	219	2	,	,	PUNCT
ejpam-4821	219	3	suppose	suppose	VERB
ejpam-4821	219	4	su	su	PROPN
ejpam-4821	219	5	or	or	CCONJ
ejpam-4821	219	6	sv	sv	PROPN
ejpam-4821	219	7	is	be	AUX
ejpam-4821	219	8	not	not	PART
ejpam-4821	219	9	a	a	DET
ejpam-4821	219	10	total	total	ADJ
ejpam-4821	219	11	dominating	dominating	NOUN
ejpam-4821	219	12	,	,	PUNCT
ejpam-4821	219	13	say	say	VERB
ejpam-4821	219	14	sv	sv	PROPN
ejpam-4821	219	15	is	be	AUX
ejpam-4821	219	16	not	not	PART
ejpam-4821	219	17	a	a	DET
ejpam-4821	219	18	total	total	ADJ
ejpam-4821	219	19	dominating	dominating	NOUN
ejpam-4821	219	20	set	set	NOUN
ejpam-4821	219	21	for	for	ADP
ejpam-4821	219	22	some	some	DET
ejpam-4821	219	23	v	v	NUM
ejpam-4821	219	24	∈	∈	PROPN
ejpam-4821	219	25	v	v	NOUN
ejpam-4821	219	26	(	(	PUNCT
ejpam-4821	219	27	g	g	NOUN
ejpam-4821	219	28	)	)	PUNCT
ejpam-4821	219	29	\a	\a	ADJ
ejpam-4821	219	30	.	.	PUNCT
ejpam-4821	220	1	let	let	VERB
ejpam-4821	220	2	x	x	SYM
ejpam-4821	220	3	∈	∈	PROPN
ejpam-4821	220	4	v	v	NOUN
ejpam-4821	220	5	(	(	PUNCT
ejpam-4821	220	6	hu)\su	hu)\su	NOUN
ejpam-4821	220	7	and	and	CCONJ
ejpam-4821	220	8	y	y	PROPN
ejpam-4821	220	9	∈	∈	PROPN
ejpam-4821	220	10	v	v	NOUN
ejpam-4821	220	11	(	(	PUNCT
ejpam-4821	220	12	hv)\sv	hv)\sv	PROPN
ejpam-4821	220	13	.	.	PUNCT
ejpam-4821	221	1	since	since	SCONJ
ejpam-4821	221	2	s	s	PROPN
ejpam-4821	221	3	is	be	AUX
ejpam-4821	221	4	a	a	DET
ejpam-4821	221	5	2	2	NUM
ejpam-4821	221	6	-	-	PUNCT
ejpam-4821	221	7	locating	locate	VERB
ejpam-4821	221	8	set	set	NOUN
ejpam-4821	221	9	,	,	PUNCT
ejpam-4821	221	10	there	there	PRON
ejpam-4821	221	11	exist	exist	VERB
ejpam-4821	221	12	w	w	NOUN
ejpam-4821	221	13	,	,	PUNCT
ejpam-4821	221	14	z	z	NOUN
ejpam-4821	221	15	∈	∈	PROPN
ejpam-4821	221	16	(	(	PUNCT
ejpam-4821	221	17	nhv(x)\nhv(y	nhv(x)\nhv(y	NUM
ejpam-4821	221	18	)	)	PUNCT
ejpam-4821	221	19	)	)	PUNCT
ejpam-4821	222	1	∩	∩	PROPN
ejpam-4821	222	2	su	su	PROPN
ejpam-4821	222	3	implying	imply	VERB
ejpam-4821	222	4	that	that	SCONJ
ejpam-4821	222	5	su	su	PROPN
ejpam-4821	222	6	is	be	AUX
ejpam-4821	222	7	a	a	DET
ejpam-4821	222	8	total	total	ADJ
ejpam-4821	222	9	2	2	NUM
ejpam-4821	222	10	-	-	PUNCT
ejpam-4821	222	11	dominating	dominating	NOUN
ejpam-4821	222	12	set	set	NOUN
ejpam-4821	222	13	.	.	PUNCT
ejpam-4821	223	1	to	to	PART
ejpam-4821	223	2	prove	prove	VERB
ejpam-4821	223	3	(	(	PUNCT
ejpam-4821	223	4	ii	ii	NOUN
ejpam-4821	223	5	)	)	PUNCT
ejpam-4821	223	6	,	,	PUNCT
ejpam-4821	223	7	let	let	VERB
ejpam-4821	223	8	v	v	NUM
ejpam-4821	223	9	∈	∈	PROPN
ejpam-4821	223	10	v	v	NOUN
ejpam-4821	223	11	(	(	PUNCT
ejpam-4821	223	12	g)\a	g)\a	NOUN
ejpam-4821	223	13	.	.	PUNCT
ejpam-4821	223	14	suppose	suppose	VERB
ejpam-4821	223	15	ng(v)∩a	ng(v)∩a	NOUN
ejpam-4821	223	16	=	=	X
ejpam-4821	223	17	∅.	∅.	NOUN
ejpam-4821	223	18	since	since	SCONJ
ejpam-4821	223	19	sv	sv	PROPN
ejpam-4821	224	1	⊆	⊆	NUM
ejpam-4821	224	2	ng	ng	PROPN
ejpam-4821	224	3	◦	◦	NOUN
ejpam-4821	224	4	h(v	h(v	NOUN
ejpam-4821	224	5	)	)	PUNCT
ejpam-4821	224	6	and	and	CCONJ
ejpam-4821	224	7	s	s	NOUN
ejpam-4821	224	8	is	be	AUX
ejpam-4821	224	9	2	2	NUM
ejpam-4821	224	10	-	-	PUNCT
ejpam-4821	224	11	locating	locating	NOUN
ejpam-4821	225	1	,	,	PUNCT
ejpam-4821	225	2	there	there	PRON
ejpam-4821	225	3	exist	exist	VERB
ejpam-4821	225	4	at	at	ADV
ejpam-4821	225	5	least	least	ADV
ejpam-4821	225	6	two	two	NUM
ejpam-4821	225	7	vertices	vertex	NOUN
ejpam-4821	225	8	x	x	X
ejpam-4821	225	9	,	,	PUNCT
ejpam-4821	225	10	y	y	PROPN
ejpam-4821	225	11	∈	∈	PROPN
ejpam-4821	225	12	sv	sv	PROPN
ejpam-4821	225	13	\nhv(p	\nhv(p	PROPN
ejpam-4821	225	14	)	)	PUNCT
ejpam-4821	225	15	for	for	ADP
ejpam-4821	225	16	each	each	DET
ejpam-4821	225	17	p	p	PROPN
ejpam-4821	225	18	∈	∈	PROPN
ejpam-4821	225	19	v	v	ADP
ejpam-4821	225	20	(	(	PUNCT
ejpam-4821	225	21	hv	hv	PROPN
ejpam-4821	225	22	)	)	PUNCT
ejpam-4821	225	23	.	.	PUNCT
ejpam-4821	226	1	thus	thus	ADV
ejpam-4821	226	2	,	,	PUNCT
ejpam-4821	226	3	sv	sv	PROPN
ejpam-4821	226	4	is	be	AUX
ejpam-4821	226	5	(	(	PUNCT
ejpam-4821	226	6	2	2	NUM
ejpam-4821	226	7	,	,	PUNCT
ejpam-4821	226	8	2)locating	2)locating	NUM
ejpam-4821	226	9	set	set	NOUN
ejpam-4821	226	10	.	.	PUNCT
ejpam-4821	227	1	on	on	ADP
ejpam-4821	227	2	the	the	DET
ejpam-4821	227	3	other	other	ADJ
ejpam-4821	227	4	hand	hand	NOUN
ejpam-4821	227	5	,	,	PUNCT
ejpam-4821	227	6	if	if	SCONJ
ejpam-4821	227	7	ng(v	ng(v	NOUN
ejpam-4821	227	8	)	)	PUNCT
ejpam-4821	227	9	∩	∩	NOUN
ejpam-4821	227	10	a	a	DET
ejpam-4821	227	11	̸=	̸=	PROPN
ejpam-4821	227	12	∅	∅	NOUN
ejpam-4821	227	13	,	,	PUNCT
ejpam-4821	227	14	there	there	PRON
ejpam-4821	227	15	exists	exist	VERB
ejpam-4821	227	16	at	at	ADV
ejpam-4821	227	17	least	least	ADV
ejpam-4821	227	18	one	one	NUM
ejpam-4821	227	19	vertex	vertex	NOUN
ejpam-4821	227	20	z	z	PROPN
ejpam-4821	227	21	∈	∈	PROPN
ejpam-4821	227	22	sv	sv	X
ejpam-4821	227	23	\nhv(p	\nhv(p	NOUN
ejpam-4821	227	24	)	)	PUNCT
ejpam-4821	227	25	.	.	PUNCT
ejpam-4821	228	1	this	this	PRON
ejpam-4821	228	2	implies	imply	VERB
ejpam-4821	228	3	that	that	SCONJ
ejpam-4821	228	4	sv	sv	PROPN
ejpam-4821	228	5	is	be	AUX
ejpam-4821	228	6	(	(	PUNCT
ejpam-4821	228	7	2	2	NUM
ejpam-4821	228	8	,	,	PUNCT
ejpam-4821	228	9	1	1	NUM
ejpam-4821	228	10	)	)	PUNCT
ejpam-4821	228	11	-locating	-locate	VERB
ejpam-4821	228	12	.	.	PUNCT
ejpam-4821	229	1	to	to	PART
ejpam-4821	229	2	prove	prove	VERB
ejpam-4821	229	3	(	(	PUNCT
ejpam-4821	229	4	iii	iii	NOUN
ejpam-4821	229	5	)	)	PUNCT
ejpam-4821	229	6	,	,	PUNCT
ejpam-4821	229	7	let	let	VERB
ejpam-4821	229	8	v	v	PRON
ejpam-4821	229	9	∈	∈	VERB
ejpam-4821	229	10	a	a	PRON
ejpam-4821	229	11	and	and	CCONJ
ejpam-4821	229	12	ng(v	ng(v	NUM
ejpam-4821	229	13	)	)	PUNCT
ejpam-4821	230	1	∩a	∩a	NOUN
ejpam-4821	231	1	=	=	PUNCT
ejpam-4821	231	2	∅.	∅.	NOUN
ejpam-4821	231	3	since	since	SCONJ
ejpam-4821	231	4	sv	sv	PROPN
ejpam-4821	231	5	is	be	AUX
ejpam-4821	231	6	a	a	DET
ejpam-4821	231	7	2	2	NUM
ejpam-4821	231	8	-	-	PUNCT
ejpam-4821	231	9	locating	locate	VERB
ejpam-4821	231	10	set	set	NOUN
ejpam-4821	231	11	,	,	PUNCT
ejpam-4821	231	12	there	there	PRON
ejpam-4821	231	13	exists	exist	VERB
ejpam-4821	231	14	r	r	NOUN
ejpam-4821	231	15	∈	∈	PROPN
ejpam-4821	231	16	sv	sv	X
ejpam-4821	231	17	\nhv(p	\nhv(p	PROPN
ejpam-4821	231	18	)	)	PUNCT
ejpam-4821	231	19	for	for	ADP
ejpam-4821	231	20	every	every	DET
ejpam-4821	231	21	p	p	PROPN
ejpam-4821	231	22	∈	∈	PROPN
ejpam-4821	231	23	v	v	ADP
ejpam-4821	231	24	(	(	PUNCT
ejpam-4821	231	25	hv	hv	PROPN
ejpam-4821	231	26	)	)	PUNCT
ejpam-4821	231	27	.	.	PUNCT
ejpam-4821	232	1	thus	thus	ADV
ejpam-4821	232	2	,	,	PUNCT
ejpam-4821	232	3	sv	sv	PROPN
ejpam-4821	232	4	is	be	AUX
ejpam-4821	232	5	a	a	DET
ejpam-4821	232	6	(	(	PUNCT
ejpam-4821	232	7	2,1)-locating	2,1)-locating	NUM
ejpam-4821	232	8	set	set	NOUN
ejpam-4821	232	9	in	in	ADP
ejpam-4821	232	10	hv	hv	PROPN
ejpam-4821	232	11	.	.	PROPN
ejpam-4821	233	1	for	for	ADP
ejpam-4821	233	2	the	the	DET
ejpam-4821	233	3	converse	converse	NOUN
ejpam-4821	233	4	,	,	PUNCT
ejpam-4821	233	5	suppose	suppose	VERB
ejpam-4821	233	6	s	s	NOUN
ejpam-4821	233	7	is	be	AUX
ejpam-4821	233	8	a	a	DET
ejpam-4821	233	9	set	set	NOUN
ejpam-4821	233	10	as	as	SCONJ
ejpam-4821	233	11	described	describe	VERB
ejpam-4821	233	12	and	and	CCONJ
ejpam-4821	233	13	satisfies	satisfy	VERB
ejpam-4821	233	14	the	the	DET
ejpam-4821	233	15	given	give	VERB
ejpam-4821	233	16	conditions	condition	NOUN
ejpam-4821	233	17	.	.	PUNCT
ejpam-4821	234	1	let	let	VERB
ejpam-4821	234	2	p	p	PRON
ejpam-4821	234	3	,	,	PUNCT
ejpam-4821	234	4	q	q	PROPN
ejpam-4821	234	5	∈	∈	PROPN
ejpam-4821	234	6	v	v	NOUN
ejpam-4821	234	7	(	(	PUNCT
ejpam-4821	234	8	g	g	PROPN
ejpam-4821	234	9	◦	◦	NOUN
ejpam-4821	234	10	h	h	NOUN
ejpam-4821	234	11	)	)	PUNCT
ejpam-4821	234	12	with	with	ADP
ejpam-4821	234	13	p	p	PROPN
ejpam-4821	234	14	̸=	̸=	PROPN
ejpam-4821	234	15	q	q	PROPN
ejpam-4821	234	16	and	and	CCONJ
ejpam-4821	234	17	let	let	VERB
ejpam-4821	234	18	u	u	NOUN
ejpam-4821	234	19	,	,	PUNCT
ejpam-4821	234	20	v	v	PROPN
ejpam-4821	234	21	∈	∈	PROPN
ejpam-4821	234	22	v	v	NOUN
ejpam-4821	234	23	(	(	PUNCT
ejpam-4821	234	24	g	g	NOUN
ejpam-4821	234	25	)	)	PUNCT
ejpam-4821	234	26	such	such	ADJ
ejpam-4821	234	27	that	that	SCONJ
ejpam-4821	234	28	p	p	PROPN
ejpam-4821	234	29	∈	∈	PROPN
ejpam-4821	234	30	v	v	ADP
ejpam-4821	234	31	(	(	PUNCT
ejpam-4821	234	32	u	u	NOUN
ejpam-4821	234	33	+	+	X
ejpam-4821	234	34	hu	hu	PROPN
ejpam-4821	234	35	)	)	PUNCT
ejpam-4821	234	36	and	and	CCONJ
ejpam-4821	234	37	q	q	PROPN
ejpam-4821	234	38	∈	∈	PROPN
ejpam-4821	234	39	v	v	NOUN
ejpam-4821	234	40	(	(	PUNCT
ejpam-4821	234	41	v	v	PROPN
ejpam-4821	234	42	+	+	PROPN
ejpam-4821	234	43	hv	hv	NOUN
ejpam-4821	234	44	)	)	PUNCT
ejpam-4821	234	45	.	.	PUNCT
ejpam-4821	235	1	suppose	suppose	VERB
ejpam-4821	235	2	p	p	X
ejpam-4821	235	3	,	,	PUNCT
ejpam-4821	235	4	q	q	PROPN
ejpam-4821	235	5	∈	∈	PROPN
ejpam-4821	235	6	v	v	NOUN
ejpam-4821	235	7	(	(	PUNCT
ejpam-4821	235	8	g	g	PROPN
ejpam-4821	235	9	◦	◦	NOUN
ejpam-4821	235	10	h)\s	h)\s	NOUN
ejpam-4821	235	11	.	.	PUNCT
ejpam-4821	236	1	consider	consider	VERB
ejpam-4821	236	2	the	the	DET
ejpam-4821	236	3	following	follow	VERB
ejpam-4821	236	4	cases	case	NOUN
ejpam-4821	236	5	:	:	PUNCT
ejpam-4821	236	6	case	case	NOUN
ejpam-4821	236	7	1	1	NUM
ejpam-4821	236	8	.	.	X
ejpam-4821	237	1	u	u	NOUN
ejpam-4821	237	2	=	=	PROPN
ejpam-4821	237	3	v	v	NUM
ejpam-4821	237	4	subcase	subcase	NOUN
ejpam-4821	237	5	1.1	1.1	NUM
ejpam-4821	237	6	p	p	NOUN
ejpam-4821	237	7	,	,	PUNCT
ejpam-4821	237	8	q	q	PROPN
ejpam-4821	237	9	∈	∈	PROPN
ejpam-4821	237	10	v	v	ADP
ejpam-4821	237	11	(	(	PUNCT
ejpam-4821	237	12	hu	hu	PROPN
ejpam-4821	237	13	)	)	PUNCT
ejpam-4821	237	14	\	\	PROPN
ejpam-4821	237	15	su	su	PROPN
ejpam-4821	237	16	since	since	SCONJ
ejpam-4821	237	17	su	su	PROPN
ejpam-4821	237	18	is	be	AUX
ejpam-4821	237	19	a	a	DET
ejpam-4821	237	20	2	2	NUM
ejpam-4821	237	21	-	-	PUNCT
ejpam-4821	237	22	locating	locate	VERB
ejpam-4821	237	23	set	set	NOUN
ejpam-4821	237	24	of	of	ADP
ejpam-4821	237	25	hu	hu	PROPN
ejpam-4821	237	26	,	,	PUNCT
ejpam-4821	237	27	nhu(p	nhu(p	PROPN
ejpam-4821	237	28	)	)	PUNCT
ejpam-4821	237	29	=	=	SYM
ejpam-4821	237	30	ng	ng	PROPN
ejpam-4821	237	31	◦	◦	NOUN
ejpam-4821	237	32	h(p	h(p	NOUN
ejpam-4821	237	33	)	)	PUNCT
ejpam-4821	237	34	and	and	CCONJ
ejpam-4821	237	35	nhu(q	nhu(q	NOUN
ejpam-4821	237	36	)	)	PUNCT
ejpam-4821	237	37	=	=	SYM
ejpam-4821	237	38	ng	ng	PROPN
ejpam-4821	237	39	◦	◦	NOUN
ejpam-4821	237	40	h(q	h(q	ADV
ejpam-4821	237	41	)	)	PUNCT
ejpam-4821	237	42	.	.	PUNCT
ejpam-4821	238	1	then	then	ADV
ejpam-4821	238	2	|[(ng	|[(ng	ADP
ejpam-4821	238	3	◦	◦	NOUN
ejpam-4821	238	4	h(q)\ng	h(q)\ng	NOUN
ejpam-4821	238	5	◦	◦	NOUN
ejpam-4821	238	6	h(p	h(p	NOUN
ejpam-4821	238	7	)	)	PUNCT
ejpam-4821	238	8	)	)	PUNCT
ejpam-4821	238	9	∩	∩	NOUN
ejpam-4821	238	10	s	s	X
ejpam-4821	238	11	]	]	X
ejpam-4821	238	12	∪	∪	X
ejpam-4821	238	13	[	[	X
ejpam-4821	238	14	(	(	PUNCT
ejpam-4821	238	15	ng	ng	PROPN
ejpam-4821	238	16	◦	◦	NOUN
ejpam-4821	238	17	h(p)\ng	h(p)\ng	NOUN
ejpam-4821	238	18	◦	◦	NOUN
ejpam-4821	238	19	h(q	h(q	ADV
ejpam-4821	238	20	)	)	PUNCT
ejpam-4821	238	21	)	)	PUNCT
ejpam-4821	239	1	∩	∩	PROPN
ejpam-4821	239	2	s]|	s]|	NOUN
ejpam-4821	239	3	≥	≥	NUM
ejpam-4821	239	4	2	2	NUM
ejpam-4821	239	5	g.cañete	g.cañete	PROPN
ejpam-4821	239	6	,	,	PUNCT
ejpam-4821	239	7	h.	h.	PROPN
ejpam-4821	239	8	rara	rara	PROPN
ejpam-4821	239	9	,	,	PUNCT
ejpam-4821	239	10	a.m.	a.m.	PROPN
ejpam-4821	239	11	mahistrado	mahistrado	PROPN
ejpam-4821	239	12	/	/	SYM
ejpam-4821	239	13	eur	eur	PROPN
ejpam-4821	239	14	.	.	PUNCT
ejpam-4821	240	1	j.	j.	PROPN
ejpam-4821	240	2	pure	pure	PROPN
ejpam-4821	240	3	appl	appl	PROPN
ejpam-4821	240	4	.	.	PROPN
ejpam-4821	240	5	math	math	PROPN
ejpam-4821	240	6	,	,	PUNCT
ejpam-4821	240	7	16	16	NUM
ejpam-4821	240	8	(	(	PUNCT
ejpam-4821	240	9	3	3	NUM
ejpam-4821	240	10	)	)	PUNCT
ejpam-4821	240	11	(	(	PUNCT
ejpam-4821	240	12	2023	2023	NUM
ejpam-4821	240	13	)	)	PUNCT
ejpam-4821	240	14	,	,	PUNCT
ejpam-4821	240	15	1647	1647	NUM
ejpam-4821	240	16	-	-	SYM
ejpam-4821	240	17	1662	1662	NUM
ejpam-4821	240	18	1654	1654	NUM
ejpam-4821	240	19	and	and	CCONJ
ejpam-4821	240	20	for	for	ADP
ejpam-4821	240	21	all	all	DET
ejpam-4821	240	22	r	r	NOUN
ejpam-4821	240	23	∈	∈	PROPN
ejpam-4821	240	24	su	su	PROPN
ejpam-4821	240	25	,	,	PUNCT
ejpam-4821	240	26	(	(	PUNCT
ejpam-4821	240	27	ng	ng	NOUN
ejpam-4821	240	28	◦	◦	NOUN
ejpam-4821	240	29	h(r)\ng	h(r)\ng	NUM
ejpam-4821	240	30	◦	◦	NOUN
ejpam-4821	240	31	h(q	h(q	ADV
ejpam-4821	240	32	)	)	PUNCT
ejpam-4821	240	33	)	)	PUNCT
ejpam-4821	241	1	∩	∩	PROPN
ejpam-4821	241	2	s	s	PART
ejpam-4821	241	3	̸=	̸=	PROPN
ejpam-4821	241	4	∅.	∅.	ADV
ejpam-4821	241	5	thus	thus	ADV
ejpam-4821	241	6	,	,	PUNCT
ejpam-4821	241	7	s	s	VERB
ejpam-4821	241	8	is	be	AUX
ejpam-4821	241	9	a	a	DET
ejpam-4821	241	10	2	2	NUM
ejpam-4821	241	11	-	-	PUNCT
ejpam-4821	241	12	locating	locate	VERB
ejpam-4821	241	13	set	set	NOUN
ejpam-4821	241	14	.	.	PUNCT
ejpam-4821	242	1	subcase	subcase	VERB
ejpam-4821	242	2	1.2	1.2	NUM
ejpam-4821	242	3	p	p	NOUN
ejpam-4821	242	4	=	=	X
ejpam-4821	242	5	v	v	NOUN
ejpam-4821	242	6	and	and	CCONJ
ejpam-4821	242	7	q	q	NOUN
ejpam-4821	242	8	∈	∈	PROPN
ejpam-4821	242	9	v	v	ADP
ejpam-4821	242	10	(	(	PUNCT
ejpam-4821	242	11	hv	hv	PROPN
ejpam-4821	242	12	)	)	PUNCT
ejpam-4821	242	13	\	\	PUNCT
ejpam-4821	243	1	sv	sv	INTJ
ejpam-4821	243	2	if	if	SCONJ
ejpam-4821	243	3	ng(v)∩a	ng(v)∩a	NOUN
ejpam-4821	243	4	=	=	SYM
ejpam-4821	243	5	∅	∅	NOUN
ejpam-4821	243	6	,	,	PUNCT
ejpam-4821	243	7	by	by	ADP
ejpam-4821	243	8	(	(	PUNCT
ejpam-4821	243	9	ii	ii	NOUN
ejpam-4821	243	10	)	)	PUNCT
ejpam-4821	243	11	sv	sv	PROPN
ejpam-4821	243	12	is	be	AUX
ejpam-4821	243	13	a	a	DET
ejpam-4821	243	14	(	(	PUNCT
ejpam-4821	243	15	2,2)-locating	2,2)-locating	NUM
ejpam-4821	243	16	set	set	NOUN
ejpam-4821	243	17	.	.	PUNCT
ejpam-4821	244	1	hence	hence	ADV
ejpam-4821	244	2	,	,	PUNCT
ejpam-4821	244	3	there	there	PRON
ejpam-4821	244	4	exist	exist	VERB
ejpam-4821	244	5	at	at	ADV
ejpam-4821	244	6	least	least	ADV
ejpam-4821	244	7	two	two	NUM
ejpam-4821	244	8	distinct	distinct	ADJ
ejpam-4821	244	9	vertices	vertex	NOUN
ejpam-4821	244	10	x	x	X
ejpam-4821	244	11	,	,	PUNCT
ejpam-4821	244	12	y	y	PROPN
ejpam-4821	244	13	∈	∈	PROPN
ejpam-4821	244	14	v	v	PROPN
ejpam-4821	244	15	(	(	PUNCT
ejpam-4821	244	16	hv	hv	NOUN
ejpam-4821	244	17	)	)	PUNCT
ejpam-4821	244	18	\nhv(q	\nhv(q	NOUN
ejpam-4821	244	19	)	)	PUNCT
ejpam-4821	244	20	.	.	PUNCT
ejpam-4821	245	1	thus	thus	ADV
ejpam-4821	245	2	,	,	PUNCT
ejpam-4821	245	3	x	x	PRON
ejpam-4821	245	4	,	,	PUNCT
ejpam-4821	245	5	y	y	PROPN
ejpam-4821	245	6	∈	∈	PROPN
ejpam-4821	245	7	ng	ng	PROPN
ejpam-4821	245	8	◦	◦	NOUN
ejpam-4821	245	9	h(p	h(p	NOUN
ejpam-4821	245	10	)	)	PUNCT
ejpam-4821	245	11	\ng	\ng	PROPN
ejpam-4821	245	12	◦	◦	NOUN
ejpam-4821	245	13	h(q	h(q	ADV
ejpam-4821	245	14	)	)	PUNCT
ejpam-4821	245	15	.	.	PUNCT
ejpam-4821	246	1	if	if	SCONJ
ejpam-4821	246	2	ng(v	ng(v	NOUN
ejpam-4821	246	3	)	)	PUNCT
ejpam-4821	246	4	∩a	∩a	PROPN
ejpam-4821	246	5	̸=	̸=	PROPN
ejpam-4821	246	6	∅	∅	NOUN
ejpam-4821	246	7	,	,	PUNCT
ejpam-4821	246	8	then	then	ADV
ejpam-4821	246	9	there	there	PRON
ejpam-4821	246	10	exists	exist	VERB
ejpam-4821	246	11	z	z	PROPN
ejpam-4821	246	12	∈	∈	PROPN
ejpam-4821	246	13	(	(	PUNCT
ejpam-4821	246	14	ng	ng	NOUN
ejpam-4821	246	15	◦	◦	NOUN
ejpam-4821	246	16	h(v	h(v	NOUN
ejpam-4821	246	17	)	)	PUNCT
ejpam-4821	246	18	∩a	∩a	PROPN
ejpam-4821	246	19	)	)	PUNCT
ejpam-4821	246	20	\ng	\ng	PROPN
ejpam-4821	246	21	◦	◦	NOUN
ejpam-4821	246	22	h(q	h(q	ADV
ejpam-4821	246	23	)	)	PUNCT
ejpam-4821	246	24	.	.	PUNCT
ejpam-4821	247	1	since	since	SCONJ
ejpam-4821	247	2	γ(h	γ(h	NOUN
ejpam-4821	247	3	)	)	PUNCT
ejpam-4821	247	4	̸=	̸=	PROPN
ejpam-4821	247	5	1	1	NUM
ejpam-4821	247	6	,	,	PUNCT
ejpam-4821	247	7	there	there	PRON
ejpam-4821	247	8	exists	exist	VERB
ejpam-4821	247	9	w	w	PROPN
ejpam-4821	247	10	∈	∈	PROPN
ejpam-4821	247	11	sv	sv	X
ejpam-4821	247	12	\nhv(q	\nhv(q	NOUN
ejpam-4821	247	13	)	)	PUNCT
ejpam-4821	247	14	.	.	PUNCT
ejpam-4821	248	1	hence	hence	ADV
ejpam-4821	248	2	,	,	PUNCT
ejpam-4821	248	3	w	w	PROPN
ejpam-4821	248	4	,	,	PUNCT
ejpam-4821	248	5	z	z	PROPN
ejpam-4821	248	6	∈	∈	PROPN
ejpam-4821	248	7	ng	ng	PROPN
ejpam-4821	248	8	◦	◦	NOUN
ejpam-4821	248	9	h(p	h(p	NOUN
ejpam-4821	248	10	)	)	PUNCT
ejpam-4821	248	11	\ng	\ng	PROPN
ejpam-4821	248	12	◦	◦	NOUN
ejpam-4821	248	13	h(q	h(q	ADV
ejpam-4821	248	14	)	)	PUNCT
ejpam-4821	249	1	∩	∩	PROPN
ejpam-4821	249	2	s.	s.	PROPN
ejpam-4821	249	3	thus	thus	ADV
ejpam-4821	249	4	,	,	PUNCT
ejpam-4821	249	5	|(ng	|(ng	PROPN
ejpam-4821	249	6	◦	◦	NOUN
ejpam-4821	249	7	h(p	h(p	NOUN
ejpam-4821	249	8	)	)	PUNCT
ejpam-4821	249	9	\ng	\ng	PROPN
ejpam-4821	249	10	◦	◦	NOUN
ejpam-4821	249	11	h(q	h(q	ADV
ejpam-4821	249	12	)	)	PUNCT
ejpam-4821	249	13	∩	∩	PROPN
ejpam-4821	249	14	s)|	s)|	PROPN
ejpam-4821	249	15	≥	≥	NUM
ejpam-4821	249	16	2	2	NUM
ejpam-4821	249	17	.	.	PUNCT
ejpam-4821	249	18	subcase	subcase	VERB
ejpam-4821	249	19	1.3	1.3	NUM
ejpam-4821	249	20	q	q	NOUN
ejpam-4821	249	21	=	=	X
ejpam-4821	249	22	v	v	NOUN
ejpam-4821	249	23	and	and	CCONJ
ejpam-4821	249	24	p	p	NOUN
ejpam-4821	249	25	∈	∈	PROPN
ejpam-4821	249	26	v	v	ADP
ejpam-4821	249	27	(	(	PUNCT
ejpam-4821	249	28	hu	hu	PROPN
ejpam-4821	249	29	)	)	PUNCT
ejpam-4821	249	30	\	\	PROPN
ejpam-4821	249	31	su	su	PROPN
ejpam-4821	250	1	the	the	DET
ejpam-4821	250	2	proof	proof	NOUN
ejpam-4821	250	3	is	be	AUX
ejpam-4821	250	4	similar	similar	ADJ
ejpam-4821	250	5	to	to	ADP
ejpam-4821	250	6	the	the	DET
ejpam-4821	250	7	proof	proof	NOUN
ejpam-4821	250	8	of	of	ADP
ejpam-4821	250	9	subcase	subcase	NOUN
ejpam-4821	250	10	1.2	1.2	NUM
ejpam-4821	250	11	.	.	PUNCT
ejpam-4821	250	12	case	case	NOUN
ejpam-4821	250	13	2	2	NUM
ejpam-4821	250	14	.	.	X
ejpam-4821	250	15	u	u	NOUN
ejpam-4821	250	16	̸=	̸=	PROPN
ejpam-4821	250	17	v	v	NUM
ejpam-4821	250	18	subcase	subcase	NOUN
ejpam-4821	250	19	2.1	2.1	NUM
ejpam-4821	250	20	p	p	NOUN
ejpam-4821	250	21	∈	∈	PROPN
ejpam-4821	250	22	v	v	NOUN
ejpam-4821	250	23	(	(	PUNCT
ejpam-4821	250	24	hu	hu	PROPN
ejpam-4821	250	25	)	)	PUNCT
ejpam-4821	250	26	\	\	PROPN
ejpam-4821	250	27	su	su	PROPN
ejpam-4821	250	28	and	and	CCONJ
ejpam-4821	250	29	q	q	PROPN
ejpam-4821	250	30	∈	∈	PROPN
ejpam-4821	250	31	v	v	ADP
ejpam-4821	250	32	(	(	PUNCT
ejpam-4821	250	33	hv	hv	PROPN
ejpam-4821	250	34	)	)	PUNCT
ejpam-4821	250	35	\	\	PROPN
ejpam-4821	251	1	sv	sv	INTJ
ejpam-4821	251	2	if	if	SCONJ
ejpam-4821	251	3	u	u	PROPN
ejpam-4821	251	4	,	,	PUNCT
ejpam-4821	251	5	v	v	ADP
ejpam-4821	251	6	∈	∈	PROPN
ejpam-4821	251	7	a	a	PRON
ejpam-4821	251	8	,	,	PUNCT
ejpam-4821	251	9	then	then	ADV
ejpam-4821	251	10	we	we	PRON
ejpam-4821	251	11	are	be	AUX
ejpam-4821	251	12	done	do	VERB
ejpam-4821	251	13	.	.	PUNCT
ejpam-4821	252	1	suppose	suppose	VERB
ejpam-4821	252	2	u	u	NOUN
ejpam-4821	252	3	,	,	PUNCT
ejpam-4821	252	4	v	v	NOUN
ejpam-4821	252	5	/∈	/∈	NOUN
ejpam-4821	252	6	a.	a.	NOUN
ejpam-4821	252	7	since	since	SCONJ
ejpam-4821	252	8	su	su	PROPN
ejpam-4821	252	9	and	and	CCONJ
ejpam-4821	252	10	sv	sv	PROPN
ejpam-4821	252	11	are	be	AUX
ejpam-4821	252	12	total	total	ADJ
ejpam-4821	252	13	dominating	dominating	NOUN
ejpam-4821	252	14	,	,	PUNCT
ejpam-4821	252	15	there	there	PRON
ejpam-4821	252	16	exist	exist	VERB
ejpam-4821	252	17	x	x	SYM
ejpam-4821	252	18	∈	∈	PROPN
ejpam-4821	252	19	(	(	PUNCT
ejpam-4821	252	20	nhu(p	nhu(p	PROPN
ejpam-4821	252	21	)	)	PUNCT
ejpam-4821	252	22	∩	∩	PROPN
ejpam-4821	252	23	su	su	PROPN
ejpam-4821	252	24	)	)	PUNCT
ejpam-4821	252	25	\	\	PROPN
ejpam-4821	252	26	nhv(q	nhv(q	PROPN
ejpam-4821	252	27	)	)	PUNCT
ejpam-4821	252	28	and	and	CCONJ
ejpam-4821	252	29	y	y	PROPN
ejpam-4821	252	30	∈	∈	PROPN
ejpam-4821	252	31	(	(	PUNCT
ejpam-4821	252	32	nhv(q	nhv(q	PROPN
ejpam-4821	252	33	)	)	PUNCT
ejpam-4821	252	34	∩	∩	PROPN
ejpam-4821	252	35	sv	sv	PROPN
ejpam-4821	252	36	)	)	PUNCT
ejpam-4821	252	37	\nhu(p	\nhu(p	NOUN
ejpam-4821	252	38	)	)	PUNCT
ejpam-4821	252	39	.	.	PUNCT
ejpam-4821	253	1	subcase	subcase	PROPN
ejpam-4821	253	2	2.2	2.2	NUM
ejpam-4821	253	3	p	p	NOUN
ejpam-4821	253	4	=	=	PUNCT
ejpam-4821	253	5	u	u	NOUN
ejpam-4821	253	6	and	and	CCONJ
ejpam-4821	253	7	q	q	NOUN
ejpam-4821	253	8	∈	∈	PROPN
ejpam-4821	253	9	v	v	ADP
ejpam-4821	253	10	(	(	PUNCT
ejpam-4821	253	11	hv	hv	PROPN
ejpam-4821	253	12	)	)	PUNCT
ejpam-4821	253	13	\	\	PROPN
ejpam-4821	254	1	sv	sv	INTJ
ejpam-4821	254	2	since	since	SCONJ
ejpam-4821	254	3	p	p	PROPN
ejpam-4821	254	4	/∈	/∈	PROPN
ejpam-4821	255	1	a	a	PRON
ejpam-4821	255	2	,	,	PUNCT
ejpam-4821	255	3	su	su	PROPN
ejpam-4821	255	4	is	be	AUX
ejpam-4821	255	5	a	a	DET
ejpam-4821	255	6	total	total	ADJ
ejpam-4821	255	7	dominating	dominating	NOUN
ejpam-4821	255	8	set	set	NOUN
ejpam-4821	255	9	of	of	ADP
ejpam-4821	255	10	hu	hu	PROPN
ejpam-4821	255	11	.	.	PUNCT
ejpam-4821	256	1	hence	hence	ADV
ejpam-4821	256	2	,	,	PUNCT
ejpam-4821	256	3	|su|	|su|	PROPN
ejpam-4821	256	4	≥	≥	NOUN
ejpam-4821	256	5	2	2	NUM
ejpam-4821	256	6	.	.	PUNCT
ejpam-4821	257	1	thus	thus	ADV
ejpam-4821	257	2	,	,	PUNCT
ejpam-4821	257	3	|(ng	|(ng	PROPN
ejpam-4821	257	4	◦	◦	NOUN
ejpam-4821	257	5	h(p	h(p	NOUN
ejpam-4821	257	6	)	)	PUNCT
ejpam-4821	257	7	\	\	PROPN
ejpam-4821	257	8	ng	ng	PROPN
ejpam-4821	257	9	◦	◦	NOUN
ejpam-4821	257	10	h(q	h(q	ADV
ejpam-4821	257	11	)	)	PUNCT
ejpam-4821	257	12	)	)	PUNCT
ejpam-4821	257	13	∩	∩	NOUN
ejpam-4821	257	14	s|	s|	VERB
ejpam-4821	257	15	≥	≥	NOUN
ejpam-4821	257	16	2	2	X
ejpam-4821	257	17	.	.	PUNCT
ejpam-4821	257	18	suppose	suppose	VERB
ejpam-4821	257	19	p	p	PROPN
ejpam-4821	257	20	∈	∈	PROPN
ejpam-4821	257	21	s	s	PART
ejpam-4821	257	22	and	and	CCONJ
ejpam-4821	257	23	q	q	PROPN
ejpam-4821	257	24	∈	∈	PROPN
ejpam-4821	257	25	v	v	NOUN
ejpam-4821	257	26	(	(	PUNCT
ejpam-4821	257	27	g	g	PROPN
ejpam-4821	257	28	◦	◦	NOUN
ejpam-4821	257	29	h	h	NOUN
ejpam-4821	257	30	)	)	PUNCT
ejpam-4821	257	31	\	\	PUNCT
ejpam-4821	258	1	s.	s.	PROPN
ejpam-4821	258	2	consider	consider	VERB
ejpam-4821	258	3	the	the	DET
ejpam-4821	258	4	following	follow	VERB
ejpam-4821	258	5	cases	case	NOUN
ejpam-4821	258	6	case	case	NOUN
ejpam-4821	258	7	1	1	NUM
ejpam-4821	258	8	u	u	NOUN
ejpam-4821	258	9	=	=	PROPN
ejpam-4821	258	10	v	v	NUM
ejpam-4821	258	11	subcase	subcase	NOUN
ejpam-4821	258	12	1.1	1.1	NUM
ejpam-4821	258	13	p	p	NOUN
ejpam-4821	258	14	∈	∈	PROPN
ejpam-4821	258	15	sv	sv	NOUN
ejpam-4821	258	16	and	and	CCONJ
ejpam-4821	258	17	q	q	PROPN
ejpam-4821	258	18	∈	∈	PROPN
ejpam-4821	258	19	v	v	ADP
ejpam-4821	258	20	(	(	PUNCT
ejpam-4821	258	21	hv	hv	PROPN
ejpam-4821	258	22	)	)	PUNCT
ejpam-4821	258	23	\	\	PROPN
ejpam-4821	259	1	sv	sv	INTJ
ejpam-4821	259	2	since	since	SCONJ
ejpam-4821	259	3	sv	sv	PROPN
ejpam-4821	259	4	is	be	AUX
ejpam-4821	259	5	a	a	DET
ejpam-4821	259	6	2	2	NUM
ejpam-4821	259	7	-	-	PUNCT
ejpam-4821	259	8	locating	locating	NOUN
ejpam-4821	259	9	,	,	PUNCT
ejpam-4821	259	10	then	then	ADV
ejpam-4821	259	11	(	(	PUNCT
ejpam-4821	259	12	ng	ng	PROPN
ejpam-4821	259	13	◦	◦	NOUN
ejpam-4821	259	14	h(p)\ng	h(p)\ng	NOUN
ejpam-4821	259	15	◦	◦	NOUN
ejpam-4821	259	16	h(q	h(q	ADV
ejpam-4821	259	17	)	)	PUNCT
ejpam-4821	259	18	)	)	PUNCT
ejpam-4821	259	19	∩	∩	PROPN
ejpam-4821	259	20	s	s	PART
ejpam-4821	259	21	̸=	̸=	PROPN
ejpam-4821	259	22	∅.	∅.	PRON
ejpam-4821	259	23	subcase	subcase	PROPN
ejpam-4821	259	24	1.2	1.2	NUM
ejpam-4821	259	25	u	u	NOUN
ejpam-4821	259	26	=	=	PROPN
ejpam-4821	259	27	p	p	NOUN
ejpam-4821	259	28	and	and	CCONJ
ejpam-4821	259	29	q	q	NOUN
ejpam-4821	259	30	∈	∈	PROPN
ejpam-4821	259	31	v	v	ADP
ejpam-4821	259	32	(	(	PUNCT
ejpam-4821	259	33	hv	hv	PROPN
ejpam-4821	259	34	)	)	PUNCT
ejpam-4821	259	35	\	\	PROPN
ejpam-4821	260	1	sv	sv	PROPN
ejpam-4821	260	2	.	.	PUNCT
ejpam-4821	261	1	then	then	ADV
ejpam-4821	261	2	u	u	PROPN
ejpam-4821	261	3	∈	∈	PROPN
ejpam-4821	261	4	a.	a.	NOUN
ejpam-4821	261	5	if	if	SCONJ
ejpam-4821	261	6	ng(p	ng(p	NOUN
ejpam-4821	261	7	)	)	PUNCT
ejpam-4821	261	8	∩	∩	NOUN
ejpam-4821	261	9	a	a	DET
ejpam-4821	261	10	̸=	̸=	PROPN
ejpam-4821	261	11	∅	∅	NOUN
ejpam-4821	261	12	,	,	PUNCT
ejpam-4821	261	13	then	then	ADV
ejpam-4821	261	14	we	we	PRON
ejpam-4821	261	15	are	be	AUX
ejpam-4821	261	16	done	do	VERB
ejpam-4821	261	17	.	.	PUNCT
ejpam-4821	262	1	suppose	suppose	VERB
ejpam-4821	262	2	ng(p	ng(p	X
ejpam-4821	262	3	)	)	PUNCT
ejpam-4821	262	4	∩	∩	NOUN
ejpam-4821	262	5	a	a	DET
ejpam-4821	262	6	=	=	SYM
ejpam-4821	262	7	∅.	∅.	NOUN
ejpam-4821	262	8	then	then	ADV
ejpam-4821	262	9	by	by	ADP
ejpam-4821	262	10	(	(	PUNCT
ejpam-4821	262	11	iii	iii	NOUN
ejpam-4821	262	12	)	)	PUNCT
ejpam-4821	262	13	,	,	PUNCT
ejpam-4821	262	14	sv	sv	PROPN
ejpam-4821	262	15	is	be	AUX
ejpam-4821	262	16	a	a	DET
ejpam-4821	262	17	(	(	PUNCT
ejpam-4821	262	18	2,1)-locating	2,1)-locating	NUM
ejpam-4821	262	19	.	.	PUNCT
ejpam-4821	263	1	thus	thus	ADV
ejpam-4821	263	2	,	,	PUNCT
ejpam-4821	263	3	(	(	PUNCT
ejpam-4821	263	4	ng	ng	NOUN
ejpam-4821	263	5	◦	◦	NOUN
ejpam-4821	263	6	h(p	h(p	NOUN
ejpam-4821	263	7	)	)	PUNCT
ejpam-4821	263	8	\ng	\ng	PROPN
ejpam-4821	263	9	◦	◦	NOUN
ejpam-4821	263	10	h(q	h(q	ADV
ejpam-4821	263	11	)	)	PUNCT
ejpam-4821	263	12	)	)	PUNCT
ejpam-4821	264	1	∩	∩	PROPN
ejpam-4821	264	2	s	s	PART
ejpam-4821	264	3	̸=	̸=	PROPN
ejpam-4821	264	4	∅.	∅.	PRON
ejpam-4821	264	5	case	case	NOUN
ejpam-4821	264	6	2	2	NUM
ejpam-4821	264	7	u	u	NOUN
ejpam-4821	264	8	̸=	̸=	PROPN
ejpam-4821	264	9	v	v	NUM
ejpam-4821	264	10	subcase	subcase	NOUN
ejpam-4821	264	11	2.1	2.1	NUM
ejpam-4821	264	12	p	p	NOUN
ejpam-4821	264	13	∈	∈	PROPN
ejpam-4821	264	14	su	su	NOUN
ejpam-4821	264	15	and	and	CCONJ
ejpam-4821	264	16	q	q	PROPN
ejpam-4821	264	17	∈	∈	PROPN
ejpam-4821	264	18	v	v	ADP
ejpam-4821	264	19	(	(	PUNCT
ejpam-4821	264	20	hv	hv	PROPN
ejpam-4821	264	21	)	)	PUNCT
ejpam-4821	264	22	\	\	PUNCT
ejpam-4821	265	1	sv	sv	INTJ
ejpam-4821	265	2	if	if	SCONJ
ejpam-4821	265	3	u	u	PROPN
ejpam-4821	265	4	∈	∈	VERB
ejpam-4821	265	5	a	a	DET
ejpam-4821	265	6	or	or	CCONJ
ejpam-4821	265	7	v	v	ADP
ejpam-4821	265	8	∈	∈	PROPN
ejpam-4821	265	9	a	a	PRON
ejpam-4821	265	10	,	,	PUNCT
ejpam-4821	265	11	then	then	ADV
ejpam-4821	265	12	we	we	PRON
ejpam-4821	265	13	are	be	AUX
ejpam-4821	265	14	done	do	VERB
ejpam-4821	265	15	.	.	PUNCT
ejpam-4821	266	1	if	if	SCONJ
ejpam-4821	266	2	u	u	PROPN
ejpam-4821	266	3	,	,	PUNCT
ejpam-4821	266	4	v	v	INTJ
ejpam-4821	266	5	/∈	/∈	PROPN
ejpam-4821	266	6	a	a	PRON
ejpam-4821	266	7	,	,	PUNCT
ejpam-4821	266	8	then	then	ADV
ejpam-4821	266	9	by	by	ADP
ejpam-4821	266	10	(	(	PUNCT
ejpam-4821	266	11	i	i	NOUN
ejpam-4821	266	12	)	)	PUNCT
ejpam-4821	266	13	su	su	PROPN
ejpam-4821	266	14	and	and	CCONJ
ejpam-4821	266	15	sv	sv	PROPN
ejpam-4821	266	16	are	be	AUX
ejpam-4821	266	17	total	total	ADJ
ejpam-4821	266	18	dominating	dominating	NOUN
ejpam-4821	266	19	.	.	PUNCT
ejpam-4821	267	1	hence	hence	ADV
ejpam-4821	267	2	,	,	PUNCT
ejpam-4821	267	3	there	there	PRON
ejpam-4821	267	4	exist	exist	VERB
ejpam-4821	267	5	x	x	SYM
ejpam-4821	267	6	∈	∈	PROPN
ejpam-4821	267	7	(	(	PUNCT
ejpam-4821	267	8	ng	ng	NOUN
ejpam-4821	267	9	◦	◦	NOUN
ejpam-4821	267	10	h(p	h(p	NOUN
ejpam-4821	267	11	)	)	PUNCT
ejpam-4821	267	12	∩	∩	NOUN
ejpam-4821	267	13	s	s	X
ejpam-4821	267	14	)	)	PUNCT
ejpam-4821	267	15	\ng	\ng	PROPN
ejpam-4821	267	16	◦	◦	NOUN
ejpam-4821	267	17	h(q	h(q	ADV
ejpam-4821	267	18	)	)	PUNCT
ejpam-4821	267	19	and	and	CCONJ
ejpam-4821	267	20	y	y	PROPN
ejpam-4821	267	21	∈	∈	PROPN
ejpam-4821	267	22	(	(	PUNCT
ejpam-4821	267	23	ng	ng	INTJ
ejpam-4821	267	24	◦	◦	NOUN
ejpam-4821	267	25	h(q	h(q	ADJ
ejpam-4821	267	26	)	)	PUNCT
ejpam-4821	267	27	∩	∩	PROPN
ejpam-4821	267	28	s	s	X
ejpam-4821	267	29	)	)	PUNCT
ejpam-4821	267	30	\ng	\ng	PROPN
ejpam-4821	267	31	◦	◦	NOUN
ejpam-4821	267	32	h(p	h(p	NOUN
ejpam-4821	267	33	)	)	PUNCT
ejpam-4821	267	34	.	.	PUNCT
ejpam-4821	268	1	subcase	subcase	VERB
ejpam-4821	268	2	2.2	2.2	NUM
ejpam-4821	268	3	p	p	NOUN
ejpam-4821	268	4	=	=	PUNCT
ejpam-4821	268	5	u	u	NOUN
ejpam-4821	268	6	and	and	CCONJ
ejpam-4821	268	7	q	q	NOUN
ejpam-4821	268	8	∈	∈	PROPN
ejpam-4821	268	9	v	v	ADP
ejpam-4821	268	10	(	(	PUNCT
ejpam-4821	268	11	hv	hv	PROPN
ejpam-4821	268	12	)	)	PUNCT
ejpam-4821	268	13	\	\	PROPN
ejpam-4821	269	1	sv	sv	PROPN
ejpam-4821	269	2	since	since	SCONJ
ejpam-4821	269	3	su	su	PROPN
ejpam-4821	269	4	̸=	̸=	PROPN
ejpam-4821	269	5	∅	∅	NOUN
ejpam-4821	269	6	,	,	PUNCT
ejpam-4821	269	7	(	(	PUNCT
ejpam-4821	269	8	ng	ng	NOUN
ejpam-4821	269	9	◦	◦	NOUN
ejpam-4821	269	10	h(p	h(p	NOUN
ejpam-4821	269	11	)	)	PUNCT
ejpam-4821	269	12	∩	∩	NOUN
ejpam-4821	269	13	s	s	X
ejpam-4821	269	14	)	)	PUNCT
ejpam-4821	269	15	\ng	\ng	PROPN
ejpam-4821	269	16	◦	◦	NOUN
ejpam-4821	269	17	h(q	h(q	ADV
ejpam-4821	269	18	)	)	PUNCT
ejpam-4821	270	1	̸=	̸=	PROPN
ejpam-4821	270	2	∅.	∅.	PRON
ejpam-4821	270	3	subcase	subcase	VERB
ejpam-4821	270	4	2.3	2.3	NUM
ejpam-4821	270	5	p	p	NOUN
ejpam-4821	270	6	∈	∈	PROPN
ejpam-4821	270	7	su	su	PROPN
ejpam-4821	270	8	and	and	CCONJ
ejpam-4821	270	9	q	q	NOUN
ejpam-4821	271	1	=	=	X
ejpam-4821	271	2	v	v	NOUN
ejpam-4821	271	3	similar	similar	ADJ
ejpam-4821	271	4	to	to	ADP
ejpam-4821	271	5	the	the	DET
ejpam-4821	271	6	proof	proof	NOUN
ejpam-4821	271	7	of	of	ADP
ejpam-4821	271	8	subcase	subcase	NOUN
ejpam-4821	271	9	2.2	2.2	NUM
ejpam-4821	271	10	.	.	PUNCT
ejpam-4821	272	1	accordingly	accordingly	ADV
ejpam-4821	272	2	,	,	PUNCT
ejpam-4821	272	3	s	s	VERB
ejpam-4821	272	4	is	be	AUX
ejpam-4821	272	5	a	a	DET
ejpam-4821	272	6	2	2	NUM
ejpam-4821	272	7	-	-	PUNCT
ejpam-4821	272	8	locating	locate	VERB
ejpam-4821	272	9	set	set	NOUN
ejpam-4821	272	10	of	of	ADP
ejpam-4821	272	11	g	g	PROPN
ejpam-4821	272	12	◦	◦	NOUN
ejpam-4821	272	13	h.	h.	PROPN
ejpam-4821	272	14	corollary	corollary	ADJ
ejpam-4821	272	15	6	6	NUM
ejpam-4821	272	16	.	.	PUNCT
ejpam-4821	273	1	let	let	VERB
ejpam-4821	273	2	g	g	NOUN
ejpam-4821	273	3	of	of	ADP
ejpam-4821	273	4	order	order	NOUN
ejpam-4821	273	5	n	n	NOUN
ejpam-4821	274	1	and	and	CCONJ
ejpam-4821	274	2	h	h	NOUN
ejpam-4821	274	3	be	be	AUX
ejpam-4821	274	4	nontrivial	nontrivial	ADJ
ejpam-4821	274	5	connected	connect	VERB
ejpam-4821	274	6	graphs	graph	NOUN
ejpam-4821	274	7	with	with	ADP
ejpam-4821	274	8	γ(h	γ(h	NOUN
ejpam-4821	274	9	)	)	PUNCT
ejpam-4821	274	10	̸=	̸=	PROPN
ejpam-4821	274	11	1	1	NUM
ejpam-4821	274	12	.	.	PUNCT
ejpam-4821	275	1	then	then	ADV
ejpam-4821	275	2	(	(	PUNCT
ejpam-4821	275	3	i	i	NOUN
ejpam-4821	275	4	)	)	PUNCT
ejpam-4821	275	5	ln2(g	ln2(g	PROPN
ejpam-4821	275	6	◦	◦	NOUN
ejpam-4821	275	7	h	h	NOUN
ejpam-4821	275	8	)	)	PUNCT
ejpam-4821	275	9	≤	≤	NOUN
ejpam-4821	275	10	γt(g	γt(g	PUNCT
ejpam-4821	275	11	)	)	PUNCT
ejpam-4821	276	1	+	+	CCONJ
ejpam-4821	276	2	n	n	CCONJ
ejpam-4821	276	3	·	·	PUNCT
ejpam-4821	276	4	ln2(h	ln2(h	PROPN
ejpam-4821	276	5	)	)	PUNCT
ejpam-4821	276	6	;	;	PUNCT
ejpam-4821	276	7	and	and	CCONJ
ejpam-4821	276	8	(	(	PUNCT
ejpam-4821	276	9	ii	ii	NOUN
ejpam-4821	276	10	)	)	PUNCT
ejpam-4821	276	11	if	if	SCONJ
ejpam-4821	276	12	ln2(h	ln2(h	PROPN
ejpam-4821	276	13	)	)	PUNCT
ejpam-4821	276	14	=	=	PUNCT
ejpam-4821	276	15	ln(2,1)(h	ln(2,1)(h	PRON
ejpam-4821	276	16	)	)	PUNCT
ejpam-4821	276	17	=	=	PUNCT
ejpam-4821	277	1	ln(2,2)(h	ln(2,2)(h	PROPN
ejpam-4821	277	2	)	)	PUNCT
ejpam-4821	277	3	.	.	PUNCT
ejpam-4821	278	1	then	then	ADV
ejpam-4821	278	2	ln2(g	ln2(g	PROPN
ejpam-4821	278	3	◦	◦	NOUN
ejpam-4821	278	4	h	h	NOUN
ejpam-4821	278	5	)	)	PUNCT
ejpam-4821	278	6	=	=	SYM
ejpam-4821	278	7	n	n	PROPN
ejpam-4821	278	8	·	·	PUNCT
ejpam-4821	278	9	ln2(h	ln2(h	PROPN
ejpam-4821	278	10	)	)	PUNCT
ejpam-4821	278	11	.	.	PUNCT
ejpam-4821	279	1	proof	proof	NOUN
ejpam-4821	279	2	.	.	PUNCT
ejpam-4821	280	1	(	(	PUNCT
ejpam-4821	280	2	i.	i.	NOUN
ejpam-4821	280	3	)	)	PUNCT
ejpam-4821	280	4	let	let	VERB
ejpam-4821	280	5	s	s	NOUN
ejpam-4821	280	6	=	=	X
ejpam-4821	280	7	v	v	X
ejpam-4821	280	8	(	(	PUNCT
ejpam-4821	280	9	g	g	PROPN
ejpam-4821	280	10	◦	◦	NOUN
ejpam-4821	280	11	h	h	NOUN
ejpam-4821	280	12	)	)	PUNCT
ejpam-4821	280	13	be	be	VERB
ejpam-4821	280	14	a	a	DET
ejpam-4821	280	15	2	2	NUM
ejpam-4821	280	16	-	-	PUNCT
ejpam-4821	280	17	locating	locate	VERB
ejpam-4821	280	18	set	set	NOUN
ejpam-4821	280	19	in	in	ADP
ejpam-4821	280	20	g	g	PROPN
ejpam-4821	280	21	◦	◦	NOUN
ejpam-4821	280	22	h.	h.	NOUN
ejpam-4821	280	23	let	let	VERB
ejpam-4821	280	24	a	a	PRON
ejpam-4821	280	25	be	be	AUX
ejpam-4821	280	26	a	a	DET
ejpam-4821	280	27	γt	γt	NOUN
ejpam-4821	280	28	-	-	NOUN
ejpam-4821	280	29	set	set	NOUN
ejpam-4821	280	30	of	of	ADP
ejpam-4821	280	31	g	g	PROPN
ejpam-4821	280	32	and	and	CCONJ
ejpam-4821	280	33	sv	sv	PROPN
ejpam-4821	280	34	be	be	AUX
ejpam-4821	280	35	an	an	DET
ejpam-4821	280	36	ln2	ln2	NOUN
ejpam-4821	280	37	-	-	PUNCT
ejpam-4821	280	38	set	set	NOUN
ejpam-4821	280	39	of	of	ADP
ejpam-4821	280	40	h	h	NOUN
ejpam-4821	281	1	v.	v.	CCONJ
ejpam-4821	281	2	then	then	ADV
ejpam-4821	281	3	s	s	VERB
ejpam-4821	281	4	=	=	PUNCT
ejpam-4821	281	5	a	a	PRON
ejpam-4821	281	6	∪	∪	X
ejpam-4821	281	7	(	(	PUNCT
ejpam-4821	281	8	⋃	⋃	NOUN
ejpam-4821	281	9	v∈v	v∈v	NOUN
ejpam-4821	281	10	(	(	PUNCT
ejpam-4821	281	11	g	g	NOUN
ejpam-4821	281	12	)	)	PUNCT
ejpam-4821	281	13	sv	sv	NOUN
ejpam-4821	281	14	)	)	PUNCT
ejpam-4821	281	15	is	be	AUX
ejpam-4821	281	16	a	a	DET
ejpam-4821	281	17	2	2	NUM
ejpam-4821	281	18	-	-	PUNCT
ejpam-4821	281	19	locating	locate	VERB
ejpam-4821	281	20	set	set	NOUN
ejpam-4821	281	21	of	of	ADP
ejpam-4821	281	22	g	g	PROPN
ejpam-4821	281	23	◦	◦	NOUN
ejpam-4821	281	24	h.	h.	PROPN
ejpam-4821	281	25	thus	thus	ADV
ejpam-4821	281	26	,	,	PUNCT
ejpam-4821	281	27	g.cañete	g.cañete	PROPN
ejpam-4821	281	28	,	,	PUNCT
ejpam-4821	281	29	h.	h.	PROPN
ejpam-4821	281	30	rara	rara	PROPN
ejpam-4821	281	31	,	,	PUNCT
ejpam-4821	281	32	a.m.	a.m.	PROPN
ejpam-4821	281	33	mahistrado	mahistrado	PROPN
ejpam-4821	281	34	/	/	SYM
ejpam-4821	281	35	eur	eur	PROPN
ejpam-4821	281	36	.	.	PUNCT
ejpam-4821	282	1	j.	j.	PROPN
ejpam-4821	282	2	pure	pure	PROPN
ejpam-4821	282	3	appl	appl	PROPN
ejpam-4821	282	4	.	.	PROPN
ejpam-4821	282	5	math	math	PROPN
ejpam-4821	282	6	,	,	PUNCT
ejpam-4821	282	7	16	16	NUM
ejpam-4821	282	8	(	(	PUNCT
ejpam-4821	282	9	3	3	NUM
ejpam-4821	282	10	)	)	PUNCT
ejpam-4821	282	11	(	(	PUNCT
ejpam-4821	282	12	2023	2023	NUM
ejpam-4821	282	13	)	)	PUNCT
ejpam-4821	282	14	,	,	PUNCT
ejpam-4821	282	15	1647	1647	NUM
ejpam-4821	282	16	-	-	SYM
ejpam-4821	282	17	1662	1662	NUM
ejpam-4821	282	18	1655	1655	NUM
ejpam-4821	282	19	ln2(g	ln2(g	PROPN
ejpam-4821	282	20	◦	◦	NOUN
ejpam-4821	282	21	h	h	NOUN
ejpam-4821	282	22	)	)	PUNCT
ejpam-4821	282	23	≤	≤	NUM
ejpam-4821	282	24	|s|	|s|	NOUN
ejpam-4821	283	1	=	=	SYM
ejpam-4821	283	2	|a|+	|a|+	NOUN
ejpam-4821	283	3	∑	∑	PUNCT
ejpam-4821	283	4	v∈v	v∈v	NOUN
ejpam-4821	283	5	(	(	PUNCT
ejpam-4821	283	6	g	g	NOUN
ejpam-4821	283	7	)	)	PUNCT
ejpam-4821	283	8	|sv|	|sv|	PROPN
ejpam-4821	283	9	=	=	PUNCT
ejpam-4821	283	10	γt(g	γt(g	PUNCT
ejpam-4821	283	11	)	)	PUNCT
ejpam-4821	284	1	+	+	CCONJ
ejpam-4821	284	2	|v	|v	PROPN
ejpam-4821	284	3	(	(	PUNCT
ejpam-4821	284	4	g)|(ln2(h	g)|(ln2(h	NOUN
ejpam-4821	284	5	)	)	PUNCT
ejpam-4821	284	6	)	)	PUNCT
ejpam-4821	285	1	=	=	PUNCT
ejpam-4821	285	2	γt(g	γt(g	X
ejpam-4821	285	3	)	)	PUNCT
ejpam-4821	286	1	+	+	CCONJ
ejpam-4821	286	2	n	n	CCONJ
ejpam-4821	286	3	·	·	PUNCT
ejpam-4821	286	4	ln2(h	ln2(h	PROPN
ejpam-4821	286	5	)	)	PUNCT
ejpam-4821	286	6	.	.	PUNCT
ejpam-4821	287	1	(	(	PUNCT
ejpam-4821	287	2	ii	ii	NOUN
ejpam-4821	287	3	.	.	PUNCT
ejpam-4821	287	4	)	)	PUNCT
ejpam-4821	288	1	let	let	VERB
ejpam-4821	288	2	a	a	DET
ejpam-4821	288	3	=	=	NOUN
ejpam-4821	288	4	∅	∅	NOUN
ejpam-4821	288	5	and	and	CCONJ
ejpam-4821	288	6	sv	sv	AUX
ejpam-4821	288	7	be	be	AUX
ejpam-4821	288	8	an	an	DET
ejpam-4821	288	9	ln2	ln2	NOUN
ejpam-4821	288	10	-	-	PUNCT
ejpam-4821	288	11	set	set	NOUN
ejpam-4821	288	12	of	of	ADP
ejpam-4821	288	13	hv	hv	PROPN
ejpam-4821	288	14	.	.	PUNCT
ejpam-4821	289	1	then	then	ADV
ejpam-4821	289	2	s	s	VERB
ejpam-4821	289	3	=	=	PUNCT
ejpam-4821	289	4	a	a	DET
ejpam-4821	289	5	∪	∪	X
ejpam-4821	289	6	(	(	PUNCT
ejpam-4821	289	7	⋃	⋃	NOUN
ejpam-4821	289	8	v∈v	v∈v	NOUN
ejpam-4821	289	9	(	(	PUNCT
ejpam-4821	289	10	g	g	NOUN
ejpam-4821	289	11	)	)	PUNCT
ejpam-4821	289	12	sv	sv	NOUN
ejpam-4821	289	13	)	)	PUNCT
ejpam-4821	289	14	is	be	AUX
ejpam-4821	289	15	a	a	DET
ejpam-4821	289	16	2	2	NUM
ejpam-4821	289	17	-	-	PUNCT
ejpam-4821	289	18	locating	locate	VERB
ejpam-4821	289	19	set	set	NOUN
ejpam-4821	289	20	of	of	ADP
ejpam-4821	289	21	g	g	PROPN
ejpam-4821	289	22	◦	◦	NOUN
ejpam-4821	289	23	h.	h.	PROPN
ejpam-4821	290	1	thus	thus	ADV
ejpam-4821	290	2	,	,	PUNCT
ejpam-4821	290	3	ln2(g	ln2(g	PROPN
ejpam-4821	290	4	◦	◦	NOUN
ejpam-4821	290	5	h	h	NOUN
ejpam-4821	290	6	)	)	PUNCT
ejpam-4821	290	7	≤	≤	NUM
ejpam-4821	290	8	|s|	|s|	PROPN
ejpam-4821	290	9	=	=	SYM
ejpam-4821	290	10	∑	∑	PUNCT
ejpam-4821	290	11	v∈v	v∈v	NOUN
ejpam-4821	290	12	(	(	PUNCT
ejpam-4821	290	13	g	g	NOUN
ejpam-4821	290	14	)	)	PUNCT
ejpam-4821	290	15	|sv|	|sv|	PROPN
ejpam-4821	291	1	=	=	SYM
ejpam-4821	291	2	|v	|v	PROPN
ejpam-4821	291	3	(	(	PUNCT
ejpam-4821	291	4	g)|ln2(h	g)|ln2(h	X
ejpam-4821	291	5	)	)	PUNCT
ejpam-4821	291	6	=	=	SYM
ejpam-4821	291	7	n	n	PROPN
ejpam-4821	291	8	·	·	PUNCT
ejpam-4821	291	9	ln2(h	ln2(h	PROPN
ejpam-4821	291	10	)	)	PUNCT
ejpam-4821	291	11	.	.	PUNCT
ejpam-4821	292	1	next	next	ADV
ejpam-4821	292	2	,	,	PUNCT
ejpam-4821	292	3	let	let	VERB
ejpam-4821	292	4	s0	s0	PROPN
ejpam-4821	292	5	be	be	AUX
ejpam-4821	292	6	an	an	DET
ejpam-4821	292	7	ln2	ln2	NOUN
ejpam-4821	292	8	-	-	PUNCT
ejpam-4821	292	9	set	set	NOUN
ejpam-4821	292	10	in	in	ADP
ejpam-4821	292	11	g	g	PROPN
ejpam-4821	292	12	◦	◦	NOUN
ejpam-4821	292	13	h.	h.	NOUN
ejpam-4821	292	14	then	then	ADV
ejpam-4821	292	15	by	by	ADP
ejpam-4821	292	16	theorem	theorem	NOUN
ejpam-4821	292	17	6	6	NUM
ejpam-4821	292	18	,	,	PUNCT
ejpam-4821	293	1	s0	s0	NOUN
ejpam-4821	293	2	=	=	PUNCT
ejpam-4821	293	3	a0∪	a0∪	PROPN
ejpam-4821	293	4	(	(	PUNCT
ejpam-4821	293	5	⋃	⋃	ADJ
ejpam-4821	293	6	v∈v	v∈v	NOUN
ejpam-4821	293	7	(	(	PUNCT
ejpam-4821	293	8	g	g	NOUN
ejpam-4821	293	9	)	)	PUNCT
ejpam-4821	293	10	sv	sv	NOUN
ejpam-4821	293	11	)	)	PUNCT
ejpam-4821	293	12	where	where	SCONJ
ejpam-4821	293	13	a0	a0	PROPN
ejpam-4821	293	14	⊆	⊆	NUM
ejpam-4821	293	15	v	v	NOUN
ejpam-4821	293	16	(	(	PUNCT
ejpam-4821	293	17	g	g	NOUN
ejpam-4821	293	18	)	)	PUNCT
ejpam-4821	293	19	and	and	CCONJ
ejpam-4821	293	20	sv	sv	PROPN
ejpam-4821	293	21	is	be	AUX
ejpam-4821	293	22	a	a	DET
ejpam-4821	293	23	2	2	NUM
ejpam-4821	293	24	-	-	PUNCT
ejpam-4821	293	25	locating	locate	VERB
ejpam-4821	293	26	set	set	NOUN
ejpam-4821	293	27	of	of	ADP
ejpam-4821	293	28	hv	hv	PROPN
ejpam-4821	293	29	,	,	PUNCT
ejpam-4821	293	30	for	for	ADP
ejpam-4821	293	31	all	all	PRON
ejpam-4821	293	32	v	v	ADP
ejpam-4821	293	33	∈	∈	NUM
ejpam-4821	293	34	v	v	NOUN
ejpam-4821	293	35	(	(	PUNCT
ejpam-4821	293	36	g	g	NOUN
ejpam-4821	293	37	)	)	PUNCT
ejpam-4821	293	38	.	.	PUNCT
ejpam-4821	294	1	thus	thus	ADV
ejpam-4821	294	2	,	,	PUNCT
ejpam-4821	294	3	ln2(g	ln2(g	PROPN
ejpam-4821	294	4	◦	◦	NOUN
ejpam-4821	294	5	h	h	NOUN
ejpam-4821	294	6	)	)	PUNCT
ejpam-4821	294	7	=	=	SYM
ejpam-4821	294	8	|s0|	|s0|	NOUN
ejpam-4821	294	9	=	=	SYM
ejpam-4821	294	10	|a0|+	|a0|+	X
ejpam-4821	294	11	|	|	ADV
ejpam-4821	294	12	⋃	⋃	ADJ
ejpam-4821	294	13	v∈v	v∈v	NOUN
ejpam-4821	294	14	(	(	PUNCT
ejpam-4821	294	15	g	g	NOUN
ejpam-4821	294	16	)	)	PUNCT
ejpam-4821	294	17	sv|	sv|	NOUN
ejpam-4821	294	18	≥	≥	NUM
ejpam-4821	294	19	∑	∑	PUNCT
ejpam-4821	294	20	v∈v	v∈v	PROPN
ejpam-4821	294	21	(	(	PUNCT
ejpam-4821	294	22	g	g	NOUN
ejpam-4821	294	23	)	)	PUNCT
ejpam-4821	294	24	|sv|	|sv|	PROPN
ejpam-4821	294	25	≥	≥	NOUN
ejpam-4821	294	26	n	n	CCONJ
ejpam-4821	294	27	·	·	PUNCT
ejpam-4821	294	28	ln2(h	ln2(h	PROPN
ejpam-4821	294	29	)	)	PUNCT
ejpam-4821	294	30	thus	thus	ADV
ejpam-4821	294	31	,	,	PUNCT
ejpam-4821	294	32	equality	equality	NOUN
ejpam-4821	294	33	holds	hold	VERB
ejpam-4821	294	34	.	.	PUNCT
ejpam-4821	295	1	7	7	X
ejpam-4821	295	2	.	.	X
ejpam-4821	295	3	edge	edge	NOUN
ejpam-4821	295	4	corona	corona	NOUN
ejpam-4821	295	5	of	of	ADP
ejpam-4821	295	6	graphs	graph	NOUN
ejpam-4821	295	7	this	this	DET
ejpam-4821	295	8	section	section	NOUN
ejpam-4821	295	9	presents	present	VERB
ejpam-4821	295	10	characterizations	characterization	NOUN
ejpam-4821	295	11	on	on	ADP
ejpam-4821	295	12	the	the	DET
ejpam-4821	295	13	2	2	NUM
ejpam-4821	295	14	-	-	PUNCT
ejpam-4821	295	15	locating	locate	VERB
ejpam-4821	295	16	sets	set	NOUN
ejpam-4821	295	17	in	in	ADP
ejpam-4821	295	18	the	the	DET
ejpam-4821	295	19	edge	edge	NOUN
ejpam-4821	295	20	corona	corona	NOUN
ejpam-4821	295	21	of	of	ADP
ejpam-4821	295	22	graphs	graph	NOUN
ejpam-4821	295	23	.	.	PUNCT
ejpam-4821	296	1	theorem	theorem	ADJ
ejpam-4821	296	2	7	7	NUM
ejpam-4821	296	3	.	.	PUNCT
ejpam-4821	297	1	let	let	VERB
ejpam-4821	297	2	g	g	NOUN
ejpam-4821	297	3	and	and	CCONJ
ejpam-4821	297	4	h	h	NOUN
ejpam-4821	297	5	be	be	AUX
ejpam-4821	297	6	nontrivial	nontrivial	ADJ
ejpam-4821	297	7	connected	connect	VERB
ejpam-4821	297	8	graphs	graph	NOUN
ejpam-4821	297	9	where	where	SCONJ
ejpam-4821	297	10	g	g	PROPN
ejpam-4821	297	11	̸=	̸=	PROPN
ejpam-4821	297	12	p2	p2	PROPN
ejpam-4821	297	13	and	and	CCONJ
ejpam-4821	297	14	∆(h	∆(h	NOUN
ejpam-4821	297	15	)	)	PUNCT
ejpam-4821	297	16	≤	≤	NOUN
ejpam-4821	297	17	|v	|v	X
ejpam-4821	297	18	(	(	PUNCT
ejpam-4821	297	19	h)|	h)|	NOUN
ejpam-4821	297	20	−	−	PROPN
ejpam-4821	297	21	3	3	NUM
ejpam-4821	297	22	.	.	PUNCT
ejpam-4821	298	1	a	a	DET
ejpam-4821	298	2	set	set	NOUN
ejpam-4821	298	3	c	c	NOUN
ejpam-4821	298	4	⊆	⊆	NUM
ejpam-4821	298	5	v	v	NOUN
ejpam-4821	298	6	(	(	PUNCT
ejpam-4821	298	7	g	g	PROPN
ejpam-4821	298	8	⋄	⋄	PROPN
ejpam-4821	298	9	h	h	NOUN
ejpam-4821	298	10	)	)	PUNCT
ejpam-4821	298	11	is	be	AUX
ejpam-4821	298	12	a	a	DET
ejpam-4821	298	13	2	2	NUM
ejpam-4821	298	14	-	-	PUNCT
ejpam-4821	298	15	locating	locate	VERB
ejpam-4821	298	16	set	set	NOUN
ejpam-4821	298	17	of	of	ADP
ejpam-4821	298	18	g	g	PROPN
ejpam-4821	298	19	⋄	⋄	PROPN
ejpam-4821	298	20	h	h	NOUN
ejpam-4821	299	1	if	if	SCONJ
ejpam-4821	299	2	and	and	CCONJ
ejpam-4821	299	3	only	only	ADV
ejpam-4821	299	4	if	if	SCONJ
ejpam-4821	299	5	c	c	PROPN
ejpam-4821	299	6	is	be	AUX
ejpam-4821	299	7	a	a	DET
ejpam-4821	299	8	2	2	NUM
ejpam-4821	299	9	-	-	PUNCT
ejpam-4821	299	10	resolving	resolve	VERB
ejpam-4821	299	11	set	set	NOUN
ejpam-4821	299	12	of	of	ADP
ejpam-4821	299	13	g	g	PROPN
ejpam-4821	299	14	⋄h	⋄h	PROPN
ejpam-4821	299	15	.	.	PUNCT
ejpam-4821	300	1	proof	proof	NOUN
ejpam-4821	300	2	.	.	PUNCT
ejpam-4821	301	1	let	let	VERB
ejpam-4821	301	2	c	c	PRON
ejpam-4821	301	3	be	be	AUX
ejpam-4821	301	4	a	a	DET
ejpam-4821	301	5	2	2	NUM
ejpam-4821	301	6	-	-	PUNCT
ejpam-4821	301	7	locating	locate	VERB
ejpam-4821	301	8	set	set	NOUN
ejpam-4821	301	9	of	of	ADP
ejpam-4821	301	10	g	g	PROPN
ejpam-4821	301	11	⋄	⋄	PROPN
ejpam-4821	301	12	h.	h.	NOUN
ejpam-4821	301	13	by	by	ADP
ejpam-4821	301	14	remark	remark	NOUN
ejpam-4821	301	15	3	3	NUM
ejpam-4821	301	16	,	,	PUNCT
ejpam-4821	301	17	c	c	PROPN
ejpam-4821	301	18	is	be	AUX
ejpam-4821	301	19	a	a	DET
ejpam-4821	301	20	2	2	NUM
ejpam-4821	301	21	-	-	PUNCT
ejpam-4821	301	22	resolving	resolve	VERB
ejpam-4821	301	23	set	set	NOUN
ejpam-4821	301	24	of	of	ADP
ejpam-4821	301	25	g	g	PROPN
ejpam-4821	301	26	⋄h	⋄h	PROPN
ejpam-4821	301	27	.	.	PUNCT
ejpam-4821	302	1	g.cañete	g.cañete	PROPN
ejpam-4821	302	2	,	,	PUNCT
ejpam-4821	302	3	h.	h.	PROPN
ejpam-4821	302	4	rara	rara	PROPN
ejpam-4821	302	5	,	,	PUNCT
ejpam-4821	302	6	a.m.	a.m.	PROPN
ejpam-4821	302	7	mahistrado	mahistrado	PROPN
ejpam-4821	302	8	/	/	SYM
ejpam-4821	302	9	eur	eur	PROPN
ejpam-4821	302	10	.	.	PUNCT
ejpam-4821	303	1	j.	j.	PROPN
ejpam-4821	303	2	pure	pure	PROPN
ejpam-4821	303	3	appl	appl	PROPN
ejpam-4821	303	4	.	.	PROPN
ejpam-4821	303	5	math	math	PROPN
ejpam-4821	303	6	,	,	PUNCT
ejpam-4821	303	7	16	16	NUM
ejpam-4821	303	8	(	(	PUNCT
ejpam-4821	303	9	3	3	NUM
ejpam-4821	303	10	)	)	PUNCT
ejpam-4821	303	11	(	(	PUNCT
ejpam-4821	303	12	2023	2023	NUM
ejpam-4821	303	13	)	)	PUNCT
ejpam-4821	303	14	,	,	PUNCT
ejpam-4821	303	15	1647	1647	NUM
ejpam-4821	303	16	-	-	SYM
ejpam-4821	303	17	1662	1662	NUM
ejpam-4821	303	18	1656	1656	NUM
ejpam-4821	303	19	conversely	conversely	ADV
ejpam-4821	303	20	,	,	PUNCT
ejpam-4821	303	21	suppose	suppose	VERB
ejpam-4821	303	22	c	c	NOUN
ejpam-4821	303	23	is	be	AUX
ejpam-4821	303	24	a	a	DET
ejpam-4821	303	25	2	2	NUM
ejpam-4821	303	26	-	-	PUNCT
ejpam-4821	303	27	resolving	resolve	VERB
ejpam-4821	303	28	set	set	NOUN
ejpam-4821	303	29	of	of	ADP
ejpam-4821	303	30	g	g	PROPN
ejpam-4821	303	31	⋄	⋄	PROPN
ejpam-4821	303	32	h.	h.	PROPN
ejpam-4821	303	33	let	let	VERB
ejpam-4821	303	34	a	a	DET
ejpam-4821	303	35	,	,	PUNCT
ejpam-4821	303	36	b	b	PROPN
ejpam-4821	303	37	∈	∈	PROPN
ejpam-4821	303	38	v	v	NOUN
ejpam-4821	303	39	(	(	PUNCT
ejpam-4821	303	40	huv)\suv	huv)\suv	X
ejpam-4821	303	41	where	where	SCONJ
ejpam-4821	303	42	a	a	DET
ejpam-4821	303	43	̸=	̸=	PROPN
ejpam-4821	303	44	b	b	PROPN
ejpam-4821	303	45	or	or	CCONJ
ejpam-4821	303	46	[	[	X
ejpam-4821	303	47	a	a	DET
ejpam-4821	303	48	∈	∈	PROPN
ejpam-4821	303	49	suv	suv	NOUN
ejpam-4821	303	50	and	and	CCONJ
ejpam-4821	303	51	b	b	PROPN
ejpam-4821	303	52	/∈	/∈	PUNCT
ejpam-4821	303	53	suv	suv	PROPN
ejpam-4821	303	54	]	]	PUNCT
ejpam-4821	303	55	.	.	PUNCT
ejpam-4821	304	1	since	since	SCONJ
ejpam-4821	304	2	c	c	PROPN
ejpam-4821	304	3	is	be	AUX
ejpam-4821	304	4	a	a	DET
ejpam-4821	304	5	2	2	NUM
ejpam-4821	304	6	-	-	PUNCT
ejpam-4821	304	7	resolving	resolving	NOUN
ejpam-4821	304	8	set	set	NOUN
ejpam-4821	304	9	in	in	ADP
ejpam-4821	304	10	g	g	PROPN
ejpam-4821	304	11	⋄	⋄	PROPN
ejpam-4821	304	12	h	h	NOUN
ejpam-4821	304	13	,	,	PUNCT
ejpam-4821	304	14	rg⋄h(a	rg⋄h(a	NOUN
ejpam-4821	304	15	/	/	SYM
ejpam-4821	304	16	c	c	NOUN
ejpam-4821	304	17	)	)	PUNCT
ejpam-4821	304	18	and	and	CCONJ
ejpam-4821	304	19	rg⋄h(b	rg⋄h(b	PROPN
ejpam-4821	304	20	/	/	SYM
ejpam-4821	304	21	c	c	NOUN
ejpam-4821	304	22	)	)	PUNCT
ejpam-4821	304	23	differ	differ	VERB
ejpam-4821	304	24	in	in	ADP
ejpam-4821	304	25	at	at	ADV
ejpam-4821	304	26	least	least	ADJ
ejpam-4821	304	27	2	2	NUM
ejpam-4821	304	28	positions	position	NOUN
ejpam-4821	304	29	.	.	PUNCT
ejpam-4821	305	1	since	since	SCONJ
ejpam-4821	305	2	ng⋄h(a	ng⋄h(a	NOUN
ejpam-4821	305	3	)	)	PUNCT
ejpam-4821	305	4	=	=	SYM
ejpam-4821	305	5	nhuv(a)∪{u	nhuv(a)∪{u	PROPN
ejpam-4821	305	6	,	,	PUNCT
ejpam-4821	305	7	v	v	NOUN
ejpam-4821	305	8	}	}	PUNCT
ejpam-4821	305	9	and	and	CCONJ
ejpam-4821	305	10	ng⋄h(b	ng⋄h(b	NOUN
ejpam-4821	305	11	)	)	PUNCT
ejpam-4821	305	12	=	=	SYM
ejpam-4821	305	13	nhuv(b	nhuv(b	PROPN
ejpam-4821	305	14	)	)	PUNCT
ejpam-4821	305	15	∪	∪	NOUN
ejpam-4821	305	16	{	{	PUNCT
ejpam-4821	305	17	u	u	NOUN
ejpam-4821	305	18	,	,	PUNCT
ejpam-4821	305	19	v	v	NOUN
ejpam-4821	305	20	}	}	PUNCT
ejpam-4821	305	21	,	,	PUNCT
ejpam-4821	305	22	rhuv(a	rhuv(a	NOUN
ejpam-4821	305	23	/	/	SYM
ejpam-4821	305	24	suv	suv	NOUN
ejpam-4821	305	25	)	)	PUNCT
ejpam-4821	305	26	and	and	CCONJ
ejpam-4821	305	27	rhuv(b	rhuv(b	PROPN
ejpam-4821	305	28	/	/	SYM
ejpam-4821	305	29	suv	suv	PROPN
ejpam-4821	305	30	)	)	PUNCT
ejpam-4821	305	31	must	must	AUX
ejpam-4821	305	32	differ	differ	VERB
ejpam-4821	305	33	in	in	ADP
ejpam-4821	305	34	at	at	ADV
ejpam-4821	305	35	least	least	ADJ
ejpam-4821	305	36	2	2	NUM
ejpam-4821	305	37	positions	position	NOUN
ejpam-4821	305	38	.	.	PUNCT
ejpam-4821	306	1	by	by	ADP
ejpam-4821	306	2	definition	definition	NOUN
ejpam-4821	306	3	of	of	ADP
ejpam-4821	306	4	g	g	PROPN
ejpam-4821	306	5	⋄	⋄	PROPN
ejpam-4821	306	6	h	h	NOUN
ejpam-4821	306	7	,	,	PUNCT
ejpam-4821	306	8	there	there	PRON
ejpam-4821	306	9	exist	exist	VERB
ejpam-4821	306	10	at	at	ADV
ejpam-4821	306	11	least	least	ADV
ejpam-4821	306	12	two	two	NUM
ejpam-4821	306	13	vertices	vertex	NOUN
ejpam-4821	306	14	say	say	VERB
ejpam-4821	306	15	p	p	NOUN
ejpam-4821	306	16	,	,	PUNCT
ejpam-4821	306	17	q	q	PROPN
ejpam-4821	306	18	∈	∈	PROPN
ejpam-4821	306	19	v	v	NOUN
ejpam-4821	306	20	(	(	PUNCT
ejpam-4821	306	21	huv	huv	PROPN
ejpam-4821	306	22	)	)	PUNCT
ejpam-4821	306	23	∩	∩	PROPN
ejpam-4821	306	24	suv	suv	NOUN
ejpam-4821	306	25	such	such	ADJ
ejpam-4821	306	26	that	that	SCONJ
ejpam-4821	306	27	either	either	CCONJ
ejpam-4821	306	28	p	p	X
ejpam-4821	306	29	,	,	PUNCT
ejpam-4821	306	30	q	q	PROPN
ejpam-4821	306	31	∈	∈	PROPN
ejpam-4821	306	32	nhuv(a)\nhuv(b	nhuv(a)\nhuv(b	PROPN
ejpam-4821	306	33	)	)	PUNCT
ejpam-4821	306	34	or	or	CCONJ
ejpam-4821	306	35	p	p	X
ejpam-4821	306	36	,	,	PUNCT
ejpam-4821	306	37	q	q	PROPN
ejpam-4821	306	38	∈	∈	PROPN
ejpam-4821	306	39	nhuv(b)\nhuv(a	nhuv(b)\nhuv(a	NUM
ejpam-4821	306	40	)	)	PUNCT
ejpam-4821	306	41	or	or	CCONJ
ejpam-4821	306	42	p	p	NOUN
ejpam-4821	306	43	∈	∈	PROPN
ejpam-4821	306	44	nhuv(a)\nhuv(b	nhuv(a)\nhuv(b	PROPN
ejpam-4821	306	45	)	)	PUNCT
ejpam-4821	306	46	and	and	CCONJ
ejpam-4821	306	47	q	q	PROPN
ejpam-4821	306	48	∈	∈	PROPN
ejpam-4821	306	49	nhuv(b)\nhuv(a	nhuv(b)\nhuv(a	NUM
ejpam-4821	306	50	)	)	PUNCT
ejpam-4821	306	51	.	.	PUNCT
ejpam-4821	307	1	similarly	similarly	ADV
ejpam-4821	307	2	,	,	PUNCT
ejpam-4821	307	3	if	if	SCONJ
ejpam-4821	307	4	a	a	DET
ejpam-4821	307	5	∈	∈	PROPN
ejpam-4821	307	6	suv	suv	NOUN
ejpam-4821	307	7	and	and	CCONJ
ejpam-4821	307	8	b	b	PROPN
ejpam-4821	307	9	∈	∈	PROPN
ejpam-4821	307	10	v	v	NOUN
ejpam-4821	307	11	(	(	PUNCT
ejpam-4821	307	12	huv)\suv	huv)\suv	PROPN
ejpam-4821	307	13	,	,	PUNCT
ejpam-4821	307	14	then	then	ADV
ejpam-4821	307	15	there	there	PRON
ejpam-4821	307	16	exists	exist	VERB
ejpam-4821	307	17	a	a	DET
ejpam-4821	307	18	vertex	vertex	NOUN
ejpam-4821	307	19	s	s	NOUN
ejpam-4821	307	20	∈	∈	NOUN
ejpam-4821	307	21	v	v	NOUN
ejpam-4821	307	22	(	(	PUNCT
ejpam-4821	307	23	huv	huv	PROPN
ejpam-4821	307	24	)	)	PUNCT
ejpam-4821	307	25	∩	∩	PROPN
ejpam-4821	307	26	suv	suv	NOUN
ejpam-4821	307	27	such	such	ADJ
ejpam-4821	307	28	that	that	DET
ejpam-4821	307	29	s	s	PROPN
ejpam-4821	307	30	∈	∈	PROPN
ejpam-4821	307	31	nhuv(a)\nhuv(b	nhuv(a)\nhuv(b	PROPN
ejpam-4821	307	32	)	)	PUNCT
ejpam-4821	307	33	or	or	CCONJ
ejpam-4821	307	34	s	s	NOUN
ejpam-4821	307	35	∈	∈	NOUN
ejpam-4821	307	36	nhuv(b)\nhuv(a	nhuv(b)\nhuv(a	NUM
ejpam-4821	307	37	)	)	PUNCT
ejpam-4821	307	38	.	.	PUNCT
ejpam-4821	308	1	thus	thus	ADV
ejpam-4821	308	2	,	,	PUNCT
ejpam-4821	308	3	it	it	PRON
ejpam-4821	308	4	follows	follow	VERB
ejpam-4821	308	5	that	that	SCONJ
ejpam-4821	308	6	suv	suv	PROPN
ejpam-4821	308	7	is	be	AUX
ejpam-4821	308	8	a	a	DET
ejpam-4821	308	9	2	2	NUM
ejpam-4821	308	10	-	-	PUNCT
ejpam-4821	308	11	locating	locate	VERB
ejpam-4821	308	12	set	set	NOUN
ejpam-4821	308	13	of	of	ADP
ejpam-4821	308	14	huv	huv	PROPN
ejpam-4821	308	15	.	.	PUNCT
ejpam-4821	309	1	accordingly	accordingly	ADV
ejpam-4821	309	2	,	,	PUNCT
ejpam-4821	309	3	c	c	PROPN
ejpam-4821	309	4	is	be	AUX
ejpam-4821	309	5	a	a	DET
ejpam-4821	309	6	2	2	NUM
ejpam-4821	309	7	-	-	PUNCT
ejpam-4821	309	8	locating	locate	VERB
ejpam-4821	309	9	set	set	NOUN
ejpam-4821	309	10	in	in	ADP
ejpam-4821	309	11	g	g	PROPN
ejpam-4821	309	12	⋄h	⋄h	PROPN
ejpam-4821	309	13	.	.	PUNCT
ejpam-4821	310	1	theorem	theorem	VERB
ejpam-4821	310	2	8	8	NUM
ejpam-4821	310	3	.	.	PUNCT
ejpam-4821	311	1	let	let	VERB
ejpam-4821	311	2	g	g	NOUN
ejpam-4821	312	1	and	and	CCONJ
ejpam-4821	312	2	h	h	NOUN
ejpam-4821	312	3	be	be	VERB
ejpam-4821	312	4	any	any	DET
ejpam-4821	312	5	nontrivial	nontrivial	ADJ
ejpam-4821	312	6	connected	connect	VERB
ejpam-4821	312	7	graphs	graph	NOUN
ejpam-4821	312	8	where	where	SCONJ
ejpam-4821	312	9	g	g	PROPN
ejpam-4821	312	10	̸=	̸=	PROPN
ejpam-4821	312	11	p2	p2	PROPN
ejpam-4821	312	12	and	and	CCONJ
ejpam-4821	312	13	∆(h	∆(h	NOUN
ejpam-4821	312	14	)	)	PUNCT
ejpam-4821	312	15	≤	≤	NOUN
ejpam-4821	312	16	|v	|v	X
ejpam-4821	312	17	(	(	PUNCT
ejpam-4821	312	18	h)|	h)|	NOUN
ejpam-4821	312	19	−	−	PROPN
ejpam-4821	312	20	3	3	NUM
ejpam-4821	312	21	.	.	PUNCT
ejpam-4821	313	1	a	a	DET
ejpam-4821	313	2	set	set	NOUN
ejpam-4821	313	3	c	c	NOUN
ejpam-4821	313	4	⊆	⊆	NUM
ejpam-4821	313	5	v	v	NOUN
ejpam-4821	313	6	(	(	PUNCT
ejpam-4821	313	7	g	g	PROPN
ejpam-4821	313	8	⋄h	⋄h	PROPN
ejpam-4821	313	9	)	)	PUNCT
ejpam-4821	313	10	is	be	AUX
ejpam-4821	313	11	a	a	DET
ejpam-4821	313	12	2	2	NUM
ejpam-4821	313	13	-	-	PUNCT
ejpam-4821	313	14	locating	locate	VERB
ejpam-4821	313	15	set	set	NOUN
ejpam-4821	313	16	of	of	ADP
ejpam-4821	313	17	g	g	NOUN
ejpam-4821	313	18	⋄h	⋄h	X
ejpam-4821	313	19	if	if	SCONJ
ejpam-4821	314	1	and	and	CCONJ
ejpam-4821	314	2	only	only	ADV
ejpam-4821	314	3	if	if	SCONJ
ejpam-4821	314	4	c	c	X
ejpam-4821	314	5	=	=	PUNCT
ejpam-4821	314	6	a	a	DET
ejpam-4821	314	7	∪	∪	ADJ
ejpam-4821	314	8			PROPN
ejpam-4821	314	9	⋃	⋃	ADJ
ejpam-4821	314	10	uv∈e(g	uv∈e(g	NOUN
ejpam-4821	314	11	)	)	PUNCT
ejpam-4821	314	12	suv	suv	NOUN
ejpam-4821	314	13			PROPN
ejpam-4821	315	1	where	where	SCONJ
ejpam-4821	315	2	(	(	PUNCT
ejpam-4821	315	3	i	i	NOUN
ejpam-4821	315	4	)	)	PUNCT
ejpam-4821	315	5	a	a	DET
ejpam-4821	315	6	⊆	⊆	NUM
ejpam-4821	315	7	v	v	NOUN
ejpam-4821	315	8	(	(	PUNCT
ejpam-4821	315	9	g	g	NOUN
ejpam-4821	315	10	)	)	PUNCT
ejpam-4821	315	11	,	,	PUNCT
ejpam-4821	315	12	suv	suv	PROPN
ejpam-4821	315	13	⊆	⊆	NUM
ejpam-4821	315	14	v	v	PROPN
ejpam-4821	315	15	(	(	PUNCT
ejpam-4821	315	16	huv	huv	PROPN
ejpam-4821	315	17	)	)	PUNCT
ejpam-4821	315	18	and	and	CCONJ
ejpam-4821	315	19	v	v	X
ejpam-4821	315	20	(	(	PUNCT
ejpam-4821	315	21	huv	huv	PROPN
ejpam-4821	315	22	)	)	PUNCT
ejpam-4821	315	23	∩	∩	PROPN
ejpam-4821	315	24	c	c	PROPN
ejpam-4821	315	25	̸=	̸=	PROPN
ejpam-4821	315	26	∅	∅	NOUN
ejpam-4821	315	27	;	;	PUNCT
ejpam-4821	315	28	(	(	PUNCT
ejpam-4821	315	29	ii	ii	X
ejpam-4821	315	30	)	)	PUNCT
ejpam-4821	315	31	suv	suv	PROPN
ejpam-4821	315	32	⊆	⊆	NUM
ejpam-4821	315	33	v	v	NOUN
ejpam-4821	315	34	(	(	PUNCT
ejpam-4821	315	35	huv	huv	PROPN
ejpam-4821	315	36	)	)	PUNCT
ejpam-4821	315	37	is	be	AUX
ejpam-4821	315	38	a	a	DET
ejpam-4821	315	39	2	2	NUM
ejpam-4821	315	40	-	-	PUNCT
ejpam-4821	315	41	locating	locate	VERB
ejpam-4821	315	42	set	set	NOUN
ejpam-4821	315	43	of	of	ADP
ejpam-4821	315	44	huv	huv	PROPN
ejpam-4821	315	45	for	for	ADP
ejpam-4821	315	46	all	all	DET
ejpam-4821	315	47	uv	uv	PROPN
ejpam-4821	315	48	∈	∈	PROPN
ejpam-4821	315	49	e(g	e(g	PROPN
ejpam-4821	315	50	)	)	PUNCT
ejpam-4821	315	51	or	or	CCONJ
ejpam-4821	315	52	if	if	SCONJ
ejpam-4821	315	53	uv	uv	NOUN
ejpam-4821	315	54	is	be	AUX
ejpam-4821	315	55	a	a	DET
ejpam-4821	315	56	pendant	pendant	ADJ
ejpam-4821	315	57	edge	edge	NOUN
ejpam-4821	315	58	,	,	PUNCT
ejpam-4821	315	59	then	then	ADV
ejpam-4821	315	60	suv	suv	PROPN
ejpam-4821	315	61	is	be	AUX
ejpam-4821	315	62	a	a	DET
ejpam-4821	315	63	(	(	PUNCT
ejpam-4821	315	64	2	2	NUM
ejpam-4821	315	65	,	,	PUNCT
ejpam-4821	315	66	1)-locating	1)-locating	NUM
ejpam-4821	315	67	set	set	NOUN
ejpam-4821	315	68	of	of	ADP
ejpam-4821	315	69	huv	huv	PROPN
ejpam-4821	315	70	whenever	whenever	SCONJ
ejpam-4821	315	71	l(⟨{u	l(⟨{u	PROPN
ejpam-4821	315	72	,	,	PUNCT
ejpam-4821	315	73	v}⟩	v}⟩	PROPN
ejpam-4821	315	74	)	)	PUNCT
ejpam-4821	315	75	⊆	⊆	NUM
ejpam-4821	315	76	a	a	PRON
ejpam-4821	315	77	and	and	CCONJ
ejpam-4821	315	78	suv	suv	PROPN
ejpam-4821	315	79	is	be	AUX
ejpam-4821	315	80	a	a	DET
ejpam-4821	315	81	(	(	PUNCT
ejpam-4821	315	82	2	2	NUM
ejpam-4821	315	83	,	,	PUNCT
ejpam-4821	315	84	2)-locating	2)-locating	NUM
ejpam-4821	315	85	set	set	NOUN
ejpam-4821	315	86	of	of	ADP
ejpam-4821	315	87	huv	huv	PROPN
ejpam-4821	315	88	otherwise	otherwise	ADV
ejpam-4821	315	89	.	.	PUNCT
ejpam-4821	316	1	proof	proof	NOUN
ejpam-4821	316	2	.	.	PUNCT
ejpam-4821	317	1	suppose	suppose	VERB
ejpam-4821	317	2	that	that	SCONJ
ejpam-4821	317	3	c	c	PROPN
ejpam-4821	317	4	⊆	⊆	NUM
ejpam-4821	317	5	v	v	PROPN
ejpam-4821	317	6	(	(	PUNCT
ejpam-4821	317	7	g⋄h	g⋄h	X
ejpam-4821	317	8	)	)	PUNCT
ejpam-4821	317	9	is	be	AUX
ejpam-4821	317	10	a	a	DET
ejpam-4821	317	11	2	2	NUM
ejpam-4821	317	12	-	-	PUNCT
ejpam-4821	317	13	locating	locate	VERB
ejpam-4821	317	14	set	set	NOUN
ejpam-4821	317	15	in	in	ADP
ejpam-4821	317	16	g⋄h	g⋄h	PROPN
ejpam-4821	317	17	.	.	PUNCT
ejpam-4821	318	1	let	let	VERB
ejpam-4821	318	2	a	a	DET
ejpam-4821	318	3	=	=	X
ejpam-4821	318	4	v	v	NOUN
ejpam-4821	318	5	(	(	PUNCT
ejpam-4821	318	6	g)∩c	g)∩c	NOUN
ejpam-4821	318	7	and	and	CCONJ
ejpam-4821	318	8	suv	suv	PROPN
ejpam-4821	318	9	=	=	PROPN
ejpam-4821	318	10	c	c	PROPN
ejpam-4821	318	11	∩	∩	X
ejpam-4821	318	12	v	v	X
ejpam-4821	318	13	(	(	PUNCT
ejpam-4821	318	14	huv	huv	PROPN
ejpam-4821	318	15	)	)	PUNCT
ejpam-4821	318	16	for	for	ADP
ejpam-4821	318	17	all	all	DET
ejpam-4821	318	18	uv	uv	PROPN
ejpam-4821	318	19	∈	∈	PROPN
ejpam-4821	318	20	e(g	e(g	PROPN
ejpam-4821	318	21	)	)	PUNCT
ejpam-4821	318	22	.	.	PUNCT
ejpam-4821	319	1	then	then	ADV
ejpam-4821	319	2	c	c	X
ejpam-4821	319	3	=	=	SYM
ejpam-4821	319	4	a∪	a∪	PROPN
ejpam-4821	319	5	(	(	PUNCT
ejpam-4821	319	6	⋃	⋃	NOUN
ejpam-4821	319	7	uv∈e(g	uv∈e(g	NOUN
ejpam-4821	319	8	)	)	PUNCT
ejpam-4821	319	9	suv	suv	PROPN
ejpam-4821	319	10	)	)	PUNCT
ejpam-4821	319	11	where	where	SCONJ
ejpam-4821	319	12	a	a	DET
ejpam-4821	319	13	⊆	⊆	NUM
ejpam-4821	319	14	v	v	NOUN
ejpam-4821	319	15	(	(	PUNCT
ejpam-4821	319	16	g	g	NOUN
ejpam-4821	319	17	)	)	PUNCT
ejpam-4821	319	18	and	and	CCONJ
ejpam-4821	319	19	suv	suv	PROPN
ejpam-4821	319	20	⊆	⊆	NUM
ejpam-4821	319	21	v	v	NOUN
ejpam-4821	319	22	(	(	PUNCT
ejpam-4821	319	23	huv	huv	PROPN
ejpam-4821	319	24	)	)	PUNCT
ejpam-4821	319	25	.	.	PUNCT
ejpam-4821	320	1	now	now	ADV
ejpam-4821	320	2	,	,	PUNCT
ejpam-4821	320	3	suppose	suppose	VERB
ejpam-4821	320	4	that	that	SCONJ
ejpam-4821	320	5	suv	suv	PROPN
ejpam-4821	320	6	=	=	NOUN
ejpam-4821	320	7	∅	∅	NOUN
ejpam-4821	320	8	for	for	ADP
ejpam-4821	320	9	some	some	DET
ejpam-4821	320	10	uv	uv	PROPN
ejpam-4821	320	11	∈	∈	PROPN
ejpam-4821	320	12	e(g	e(g	PROPN
ejpam-4821	320	13	)	)	PUNCT
ejpam-4821	320	14	.	.	PUNCT
ejpam-4821	321	1	let	let	VERB
ejpam-4821	321	2	x	x	PRON
ejpam-4821	321	3	,	,	PUNCT
ejpam-4821	321	4	y	y	PROPN
ejpam-4821	321	5	∈	∈	PROPN
ejpam-4821	321	6	v	v	NOUN
ejpam-4821	321	7	(	(	PUNCT
ejpam-4821	321	8	huv)\suv	huv)\suv	PROPN
ejpam-4821	321	9	.	.	PUNCT
ejpam-4821	322	1	then	then	ADV
ejpam-4821	322	2	∣∣[(nhuv(x)\nhuv(y	∣∣[(nhuv(x)\nhuv(y	NUM
ejpam-4821	322	3	)	)	PUNCT
ejpam-4821	322	4	)	)	PUNCT
ejpam-4821	322	5	∩	∩	PROPN
ejpam-4821	322	6	suv	suv	PROPN
ejpam-4821	322	7	]	]	PUNCT
ejpam-4821	322	8	∪	∪	X
ejpam-4821	322	9	[	[	PUNCT
ejpam-4821	322	10	(	(	PUNCT
ejpam-4821	322	11	nhuv(y)\nhuv(x	nhuv(y)\nhuv(x	NUM
ejpam-4821	322	12	)	)	PUNCT
ejpam-4821	322	13	)	)	PUNCT
ejpam-4821	322	14	∩	∩	PROPN
ejpam-4821	322	15	suv	suv	PROPN
ejpam-4821	322	16	]	]	PUNCT
ejpam-4821	322	17	∣∣	∣∣	X
ejpam-4821	322	18	=	=	SYM
ejpam-4821	322	19	0	0	NUM
ejpam-4821	322	20	,	,	PUNCT
ejpam-4821	322	21	a	a	DET
ejpam-4821	322	22	contradiction	contradiction	NOUN
ejpam-4821	322	23	to	to	ADP
ejpam-4821	322	24	the	the	DET
ejpam-4821	322	25	assumption	assumption	NOUN
ejpam-4821	322	26	of	of	ADP
ejpam-4821	322	27	c.	c.	PROPN
ejpam-4821	322	28	thus	thus	ADV
ejpam-4821	322	29	,	,	PUNCT
ejpam-4821	322	30	suv	suv	PROPN
ejpam-4821	322	31	̸=	̸=	PROPN
ejpam-4821	322	32	∅	∅	NOUN
ejpam-4821	322	33	for	for	ADP
ejpam-4821	322	34	all	all	DET
ejpam-4821	322	35	uv	uv	PROPN
ejpam-4821	322	36	∈	∈	PROPN
ejpam-4821	322	37	e(g	e(g	PROPN
ejpam-4821	322	38	)	)	PUNCT
ejpam-4821	322	39	.	.	PUNCT
ejpam-4821	323	1	next	next	ADV
ejpam-4821	323	2	,	,	PUNCT
ejpam-4821	323	3	we	we	PRON
ejpam-4821	323	4	claim	claim	VERB
ejpam-4821	323	5	that	that	SCONJ
ejpam-4821	323	6	suv	suv	PROPN
ejpam-4821	323	7	is	be	AUX
ejpam-4821	323	8	a	a	DET
ejpam-4821	323	9	2	2	NUM
ejpam-4821	323	10	-	-	PUNCT
ejpam-4821	323	11	locating	locate	VERB
ejpam-4821	323	12	set	set	NOUN
ejpam-4821	323	13	in	in	ADP
ejpam-4821	323	14	huv	huv	PROPN
ejpam-4821	323	15	for	for	ADP
ejpam-4821	323	16	each	each	DET
ejpam-4821	323	17	uv	uv	PROPN
ejpam-4821	323	18	∈	∈	PROPN
ejpam-4821	323	19	e(g	e(g	PROPN
ejpam-4821	323	20	)	)	PUNCT
ejpam-4821	323	21	.	.	PUNCT
ejpam-4821	324	1	let	let	VERB
ejpam-4821	324	2	a	a	DET
ejpam-4821	324	3	,	,	PUNCT
ejpam-4821	324	4	b	b	PROPN
ejpam-4821	324	5	∈	∈	PROPN
ejpam-4821	324	6	v	v	NOUN
ejpam-4821	324	7	(	(	PUNCT
ejpam-4821	324	8	huv	huv	PROPN
ejpam-4821	324	9	)	)	PUNCT
ejpam-4821	324	10	where	where	SCONJ
ejpam-4821	324	11	uv	uv	NOUN
ejpam-4821	324	12	∈	∈	PROPN
ejpam-4821	324	13	e(g	e(g	PROPN
ejpam-4821	324	14	)	)	PUNCT
ejpam-4821	324	15	.	.	PUNCT
ejpam-4821	325	1	then	then	ADV
ejpam-4821	325	2	a	a	DET
ejpam-4821	325	3	,	,	PUNCT
ejpam-4821	325	4	b	b	PROPN
ejpam-4821	325	5	∈	∈	PROPN
ejpam-4821	325	6	v	v	NOUN
ejpam-4821	325	7	(	(	PUNCT
ejpam-4821	325	8	g	g	PROPN
ejpam-4821	325	9	⋄h	⋄h	PROPN
ejpam-4821	325	10	)	)	PUNCT
ejpam-4821	325	11	.	.	PUNCT
ejpam-4821	326	1	since	since	SCONJ
ejpam-4821	326	2	nhuv(a	nhuv(a	NUM
ejpam-4821	326	3	)	)	PUNCT
ejpam-4821	326	4	=	=	SYM
ejpam-4821	326	5	ng⋄h(a	ng⋄h(a	NOUN
ejpam-4821	326	6	)	)	PUNCT
ejpam-4821	326	7	\	\	NOUN
ejpam-4821	326	8	{	{	PUNCT
ejpam-4821	326	9	u	u	NOUN
ejpam-4821	326	10	,	,	PUNCT
ejpam-4821	326	11	v	v	NOUN
ejpam-4821	326	12	}	}	PUNCT
ejpam-4821	326	13	and	and	CCONJ
ejpam-4821	326	14	nhuv(b	nhuv(b	PROPN
ejpam-4821	326	15	)	)	PUNCT
ejpam-4821	326	16	=	=	SYM
ejpam-4821	326	17	ng⋄h(b	ng⋄h(b	PROPN
ejpam-4821	326	18	)	)	PUNCT
ejpam-4821	326	19	\	\	NOUN
ejpam-4821	326	20	{	{	PUNCT
ejpam-4821	326	21	u	u	NOUN
ejpam-4821	326	22	,	,	PUNCT
ejpam-4821	326	23	v	v	NOUN
ejpam-4821	326	24	}	}	PUNCT
ejpam-4821	326	25	and	and	CCONJ
ejpam-4821	326	26	c	c	PROPN
ejpam-4821	326	27	is	be	AUX
ejpam-4821	326	28	a	a	DET
ejpam-4821	326	29	2	2	NUM
ejpam-4821	326	30	-	-	PUNCT
ejpam-4821	326	31	locating	locate	VERB
ejpam-4821	326	32	set	set	NOUN
ejpam-4821	326	33	,	,	PUNCT
ejpam-4821	326	34	this	this	PRON
ejpam-4821	326	35	implies	imply	VERB
ejpam-4821	326	36	that	that	SCONJ
ejpam-4821	326	37	suv	suv	PROPN
ejpam-4821	326	38	is	be	AUX
ejpam-4821	326	39	also	also	ADV
ejpam-4821	326	40	a	a	DET
ejpam-4821	326	41	2	2	NUM
ejpam-4821	326	42	-	-	PUNCT
ejpam-4821	326	43	locating	locate	VERB
ejpam-4821	326	44	set	set	NOUN
ejpam-4821	326	45	in	in	ADP
ejpam-4821	326	46	huv	huv	PROPN
ejpam-4821	326	47	.	.	PUNCT
ejpam-4821	327	1	next	next	ADV
ejpam-4821	327	2	,	,	PUNCT
ejpam-4821	327	3	suppose	suppose	VERB
ejpam-4821	327	4	that	that	SCONJ
ejpam-4821	327	5	uv	uv	NOUN
ejpam-4821	327	6	is	be	AUX
ejpam-4821	327	7	a	a	DET
ejpam-4821	327	8	pendant	pendant	ADJ
ejpam-4821	327	9	edge	edge	NOUN
ejpam-4821	327	10	and	and	CCONJ
ejpam-4821	327	11	suppose	suppose	VERB
ejpam-4821	327	12	u	u	PRON
ejpam-4821	327	13	is	be	AUX
ejpam-4821	327	14	an	an	DET
ejpam-4821	327	15	end	end	NOUN
ejpam-4821	327	16	-	-	PUNCT
ejpam-4821	327	17	vertex	vertex	NOUN
ejpam-4821	327	18	.	.	PUNCT
ejpam-4821	328	1	then	then	ADV
ejpam-4821	328	2	⟨u⟩+huv	⟨u⟩+huv	PROPN
ejpam-4821	328	3	is	be	AUX
ejpam-4821	328	4	a	a	DET
ejpam-4821	328	5	subgraph	subgraph	NOUN
ejpam-4821	328	6	of	of	ADP
ejpam-4821	328	7	g⋄h	g⋄h	PROPN
ejpam-4821	328	8	.	.	PUNCT
ejpam-4821	329	1	since	since	SCONJ
ejpam-4821	329	2	suv	suv	NOUN
ejpam-4821	329	3	=	=	PROPN
ejpam-4821	329	4	c	c	PROPN
ejpam-4821	329	5	∩v	∩v	NOUN
ejpam-4821	329	6	(	(	PUNCT
ejpam-4821	329	7	huv	huv	PROPN
ejpam-4821	329	8	)	)	PUNCT
ejpam-4821	329	9	⊆	⊆	NUM
ejpam-4821	329	10	c	c	NOUN
ejpam-4821	329	11	and	and	CCONJ
ejpam-4821	329	12	c	c	PROPN
ejpam-4821	329	13	is	be	AUX
ejpam-4821	329	14	a	a	DET
ejpam-4821	329	15	2	2	NUM
ejpam-4821	329	16	-	-	PUNCT
ejpam-4821	329	17	locating	locate	VERB
ejpam-4821	329	18	set	set	NOUN
ejpam-4821	329	19	,	,	PUNCT
ejpam-4821	329	20	it	it	PRON
ejpam-4821	329	21	follows	follow	VERB
ejpam-4821	329	22	by	by	ADP
ejpam-4821	329	23	corollary	corollary	ADJ
ejpam-4821	329	24	2	2	NUM
ejpam-4821	329	25	,	,	PUNCT
ejpam-4821	329	26	suv	suv	PROPN
ejpam-4821	329	27	is	be	AUX
ejpam-4821	329	28	a	a	DET
ejpam-4821	329	29	(	(	PUNCT
ejpam-4821	329	30	2,1)-locating	2,1)-locating	NUM
ejpam-4821	329	31	set	set	NOUN
ejpam-4821	329	32	of	of	ADP
ejpam-4821	329	33	huv	huv	PROPN
ejpam-4821	329	34	whenever	whenever	SCONJ
ejpam-4821	329	35	u	u	PROPN
ejpam-4821	329	36	∈	∈	PROPN
ejpam-4821	329	37	c	c	PROPN
ejpam-4821	329	38	and	and	CCONJ
ejpam-4821	329	39	suv	suv	PROPN
ejpam-4821	329	40	is	be	AUX
ejpam-4821	329	41	a	a	DET
ejpam-4821	329	42	(	(	PUNCT
ejpam-4821	329	43	2,2)-locating	2,2)-locating	NUM
ejpam-4821	329	44	set	set	NOUN
ejpam-4821	329	45	of	of	ADP
ejpam-4821	329	46	huv	huv	PROPN
ejpam-4821	329	47	,	,	PUNCT
ejpam-4821	329	48	otherwise	otherwise	ADV
ejpam-4821	329	49	.	.	PUNCT
ejpam-4821	330	1	conversely	conversely	ADV
ejpam-4821	330	2	,	,	PUNCT
ejpam-4821	330	3	let	let	VERB
ejpam-4821	330	4	c	c	PRON
ejpam-4821	330	5	be	be	AUX
ejpam-4821	330	6	the	the	DET
ejpam-4821	330	7	set	set	NOUN
ejpam-4821	330	8	as	as	SCONJ
ejpam-4821	330	9	described	describe	VERB
ejpam-4821	330	10	and	and	CCONJ
ejpam-4821	330	11	satisfies	satisfy	VERB
ejpam-4821	330	12	the	the	DET
ejpam-4821	330	13	given	give	VERB
ejpam-4821	330	14	conditions	condition	NOUN
ejpam-4821	330	15	.	.	PUNCT
ejpam-4821	331	1	let	let	VERB
ejpam-4821	331	2	x	x	PRON
ejpam-4821	331	3	,	,	PUNCT
ejpam-4821	331	4	y	y	PROPN
ejpam-4821	331	5	∈	∈	PROPN
ejpam-4821	331	6	v	v	PROPN
ejpam-4821	331	7	(	(	PUNCT
ejpam-4821	331	8	g⋄h	g⋄h	X
ejpam-4821	331	9	)	)	PUNCT
ejpam-4821	331	10	with	with	ADP
ejpam-4821	331	11	x	x	SYM
ejpam-4821	331	12	̸=	̸=	PROPN
ejpam-4821	331	13	y.	y.	NOUN
ejpam-4821	331	14	then	then	ADV
ejpam-4821	331	15	it	it	PRON
ejpam-4821	331	16	can	can	AUX
ejpam-4821	331	17	be	be	AUX
ejpam-4821	331	18	easily	easily	ADV
ejpam-4821	331	19	verified	verify	VERB
ejpam-4821	331	20	that	that	SCONJ
ejpam-4821	331	21	rg⋄h(x	rg⋄h(x	PROPN
ejpam-4821	331	22	/	/	SYM
ejpam-4821	331	23	c	c	NOUN
ejpam-4821	331	24	)	)	PUNCT
ejpam-4821	331	25	and	and	CCONJ
ejpam-4821	331	26	rg⋄h(y	rg⋄h(y	ADJ
ejpam-4821	331	27	/	/	SYM
ejpam-4821	331	28	c	c	NOUN
ejpam-4821	331	29	)	)	PUNCT
ejpam-4821	331	30	differ	differ	VERB
ejpam-4821	331	31	in	in	ADP
ejpam-4821	331	32	at	at	ADV
ejpam-4821	331	33	least	least	ADV
ejpam-4821	331	34	two	two	NUM
ejpam-4821	331	35	positions	position	NOUN
ejpam-4821	331	36	for	for	ADP
ejpam-4821	331	37	all	all	DET
ejpam-4821	331	38	x	x	NOUN
ejpam-4821	331	39	,	,	PUNCT
ejpam-4821	331	40	y	y	PROPN
ejpam-4821	331	41	∈	∈	PROPN
ejpam-4821	331	42	v	v	ADP
ejpam-4821	331	43	(	(	PUNCT
ejpam-4821	331	44	g	g	NOUN
ejpam-4821	331	45	)	)	PUNCT
ejpam-4821	331	46	or	or	CCONJ
ejpam-4821	331	47	x	x	PUNCT
ejpam-4821	331	48	∈	∈	NOUN
ejpam-4821	331	49	v	v	X
ejpam-4821	331	50	(	(	PUNCT
ejpam-4821	331	51	huv	huv	PROPN
ejpam-4821	331	52	)	)	PUNCT
ejpam-4821	331	53	and	and	CCONJ
ejpam-4821	331	54	y	y	PROPN
ejpam-4821	331	55	∈	∈	PROPN
ejpam-4821	331	56	v	v	ADP
ejpam-4821	331	57	(	(	PUNCT
ejpam-4821	331	58	g	g	NOUN
ejpam-4821	331	59	)	)	PUNCT
ejpam-4821	331	60	for	for	ADP
ejpam-4821	331	61	all	all	DET
ejpam-4821	331	62	edges	edge	NOUN
ejpam-4821	331	63	uv	uv	PROPN
ejpam-4821	331	64	∈	∈	PROPN
ejpam-4821	331	65	e(g	e(g	PROPN
ejpam-4821	331	66	)	)	PUNCT
ejpam-4821	331	67	or	or	CCONJ
ejpam-4821	331	68	x	x	PUNCT
ejpam-4821	331	69	∈	∈	NOUN
ejpam-4821	331	70	v	v	PROPN
ejpam-4821	331	71	(	(	PUNCT
ejpam-4821	331	72	hpq	hpq	PROPN
ejpam-4821	331	73	)	)	PUNCT
ejpam-4821	331	74	and	and	CCONJ
ejpam-4821	331	75	y	y	PROPN
ejpam-4821	331	76	∈	∈	PROPN
ejpam-4821	331	77	v	v	PROPN
ejpam-4821	331	78	(	(	PUNCT
ejpam-4821	331	79	hab	hab	NOUN
ejpam-4821	331	80	)	)	PUNCT
ejpam-4821	331	81	,	,	PUNCT
ejpam-4821	331	82	for	for	ADP
ejpam-4821	331	83	some	some	DET
ejpam-4821	331	84	pq	pq	NOUN
ejpam-4821	331	85	,	,	PUNCT
ejpam-4821	331	86	ab	ab	PROPN
ejpam-4821	331	87	∈	∈	PROPN
ejpam-4821	331	88	e(g	e(g	PROPN
ejpam-4821	331	89	)	)	PUNCT
ejpam-4821	331	90	.	.	PUNCT
ejpam-4821	332	1	hence	hence	ADV
ejpam-4821	332	2	,	,	PUNCT
ejpam-4821	332	3	consider	consider	VERB
ejpam-4821	332	4	only	only	ADV
ejpam-4821	332	5	the	the	DET
ejpam-4821	332	6	following	following	ADJ
ejpam-4821	332	7	cases	case	NOUN
ejpam-4821	332	8	:	:	PUNCT
ejpam-4821	332	9	g.cañete	g.cañete	PROPN
ejpam-4821	332	10	,	,	PUNCT
ejpam-4821	332	11	h.	h.	PROPN
ejpam-4821	332	12	rara	rara	PROPN
ejpam-4821	332	13	,	,	PUNCT
ejpam-4821	332	14	a.m.	a.m.	PROPN
ejpam-4821	332	15	mahistrado	mahistrado	PROPN
ejpam-4821	332	16	/	/	SYM
ejpam-4821	332	17	eur	eur	PROPN
ejpam-4821	332	18	.	.	PUNCT
ejpam-4821	333	1	j.	j.	PROPN
ejpam-4821	333	2	pure	pure	PROPN
ejpam-4821	333	3	appl	appl	PROPN
ejpam-4821	333	4	.	.	PROPN
ejpam-4821	333	5	math	math	PROPN
ejpam-4821	333	6	,	,	PUNCT
ejpam-4821	333	7	16	16	NUM
ejpam-4821	333	8	(	(	PUNCT
ejpam-4821	333	9	3	3	NUM
ejpam-4821	333	10	)	)	PUNCT
ejpam-4821	333	11	(	(	PUNCT
ejpam-4821	333	12	2023	2023	NUM
ejpam-4821	333	13	)	)	PUNCT
ejpam-4821	333	14	,	,	PUNCT
ejpam-4821	333	15	1647	1647	NUM
ejpam-4821	333	16	-	-	SYM
ejpam-4821	333	17	1662	1662	NUM
ejpam-4821	333	18	1657	1657	NUM
ejpam-4821	333	19	case	case	NOUN
ejpam-4821	333	20	1	1	NUM
ejpam-4821	333	21	:	:	PUNCT
ejpam-4821	333	22	x	x	X
ejpam-4821	333	23	,	,	PUNCT
ejpam-4821	333	24	y	y	PROPN
ejpam-4821	333	25	∈	∈	PROPN
ejpam-4821	333	26	v	v	PROPN
ejpam-4821	333	27	(	(	PUNCT
ejpam-4821	333	28	huv	huv	PROPN
ejpam-4821	333	29	)	)	PUNCT
ejpam-4821	333	30	\	\	PROPN
ejpam-4821	333	31	suv	suv	PROPN
ejpam-4821	333	32	or	or	CCONJ
ejpam-4821	333	33	x	x	PROPN
ejpam-4821	333	34	∈	∈	PROPN
ejpam-4821	333	35	v	v	NOUN
ejpam-4821	333	36	(	(	PUNCT
ejpam-4821	333	37	huv	huv	PROPN
ejpam-4821	333	38	)	)	PUNCT
ejpam-4821	333	39	\	\	PROPN
ejpam-4821	333	40	suv	suv	PROPN
ejpam-4821	333	41	and	and	CCONJ
ejpam-4821	333	42	y	y	PROPN
ejpam-4821	333	43	∈	∈	PROPN
ejpam-4821	333	44	suv	suv	PROPN
ejpam-4821	333	45	for	for	ADP
ejpam-4821	333	46	some	some	DET
ejpam-4821	333	47	edge	edge	NOUN
ejpam-4821	333	48	uv	uv	PROPN
ejpam-4821	333	49	∈	∈	PROPN
ejpam-4821	333	50	e(g	e(g	PROPN
ejpam-4821	333	51	)	)	PUNCT
ejpam-4821	333	52	.	.	PUNCT
ejpam-4821	334	1	now	now	ADV
ejpam-4821	334	2	,	,	PUNCT
ejpam-4821	334	3	since	since	SCONJ
ejpam-4821	334	4	suv	suv	PROPN
ejpam-4821	334	5	is	be	AUX
ejpam-4821	334	6	2	2	NUM
ejpam-4821	334	7	-	-	PUNCT
ejpam-4821	334	8	locating	locate	VERB
ejpam-4821	334	9	set	set	NOUN
ejpam-4821	334	10	,	,	PUNCT
ejpam-4821	334	11	rhuv(x	rhuv(x	PROPN
ejpam-4821	334	12	/	/	SYM
ejpam-4821	334	13	suv	suv	PROPN
ejpam-4821	334	14	)	)	PUNCT
ejpam-4821	334	15	and	and	CCONJ
ejpam-4821	334	16	rhuv(x	rhuv(x	PROPN
ejpam-4821	334	17	/	/	SYM
ejpam-4821	334	18	suv	suv	PROPN
ejpam-4821	334	19	)	)	PUNCT
ejpam-4821	334	20	differ	differ	VERB
ejpam-4821	334	21	in	in	ADP
ejpam-4821	334	22	at	at	ADV
ejpam-4821	334	23	least	least	ADV
ejpam-4821	334	24	two	two	NUM
ejpam-4821	334	25	positions	position	NOUN
ejpam-4821	334	26	.	.	PUNCT
ejpam-4821	335	1	then	then	ADV
ejpam-4821	335	2	by	by	ADP
ejpam-4821	335	3	definition	definition	NOUN
ejpam-4821	335	4	of	of	ADP
ejpam-4821	335	5	g	g	PROPN
ejpam-4821	335	6	⋄	⋄	PROPN
ejpam-4821	335	7	h	h	NOUN
ejpam-4821	335	8	,	,	PUNCT
ejpam-4821	335	9	rg⋄h(x	rg⋄h(x	PROPN
ejpam-4821	335	10	/	/	SYM
ejpam-4821	335	11	c	c	NOUN
ejpam-4821	335	12	)	)	PUNCT
ejpam-4821	335	13	and	and	CCONJ
ejpam-4821	335	14	rg⋄h(y	rg⋄h(y	ADJ
ejpam-4821	335	15	/	/	SYM
ejpam-4821	335	16	c	c	NOUN
ejpam-4821	335	17	)	)	PUNCT
ejpam-4821	335	18	differ	differ	VERB
ejpam-4821	335	19	in	in	ADP
ejpam-4821	335	20	at	at	ADV
ejpam-4821	335	21	least	least	ADV
ejpam-4821	335	22	two	two	NUM
ejpam-4821	335	23	positions	position	NOUN
ejpam-4821	335	24	.	.	PUNCT
ejpam-4821	336	1	case	case	NOUN
ejpam-4821	336	2	2	2	NUM
ejpam-4821	336	3	:	:	PUNCT
ejpam-4821	336	4	x	x	SYM
ejpam-4821	336	5	∈	∈	NOUN
ejpam-4821	336	6	v	v	ADP
ejpam-4821	336	7	(	(	PUNCT
ejpam-4821	336	8	huv	huv	PROPN
ejpam-4821	336	9	)	)	PUNCT
ejpam-4821	336	10	\	\	PROPN
ejpam-4821	336	11	suv	suv	PROPN
ejpam-4821	336	12	or	or	CCONJ
ejpam-4821	336	13	x	x	PROPN
ejpam-4821	336	14	∈	∈	PROPN
ejpam-4821	336	15	suv	suv	PROPN
ejpam-4821	336	16	and	and	CCONJ
ejpam-4821	336	17	y	y	PROPN
ejpam-4821	336	18	=	=	PROPN
ejpam-4821	336	19	u	u	PROPN
ejpam-4821	336	20	for	for	ADP
ejpam-4821	336	21	some	some	DET
ejpam-4821	336	22	pendant	pendant	ADJ
ejpam-4821	336	23	edge	edge	NOUN
ejpam-4821	336	24	uv	uv	PROPN
ejpam-4821	336	25	∈	∈	PROPN
ejpam-4821	336	26	e(g	e(g	PROPN
ejpam-4821	336	27	)	)	PUNCT
ejpam-4821	336	28	and	and	CCONJ
ejpam-4821	336	29	u	u	NOUN
ejpam-4821	336	30	is	be	AUX
ejpam-4821	336	31	an	an	DET
ejpam-4821	336	32	endvertex	endvertex	NOUN
ejpam-4821	336	33	since	since	SCONJ
ejpam-4821	336	34	suv	suv	PROPN
ejpam-4821	336	35	is	be	AUX
ejpam-4821	336	36	a	a	DET
ejpam-4821	336	37	(	(	PUNCT
ejpam-4821	336	38	2,2)-locating	2,2)-locating	NUM
ejpam-4821	336	39	set	set	NOUN
ejpam-4821	336	40	,	,	PUNCT
ejpam-4821	336	41	there	there	PRON
ejpam-4821	336	42	exists	exist	VERB
ejpam-4821	336	43	a	a	DET
ejpam-4821	336	44	,	,	PUNCT
ejpam-4821	336	45	b	b	PROPN
ejpam-4821	336	46	∈	∈	PROPN
ejpam-4821	336	47	suv	suv	NOUN
ejpam-4821	336	48	\	\	PROPN
ejpam-4821	336	49	nhuv(x	nhuv(x	PROPN
ejpam-4821	336	50	)	)	PUNCT
ejpam-4821	336	51	but	but	CCONJ
ejpam-4821	336	52	a	a	PRON
ejpam-4821	336	53	,	,	PUNCT
ejpam-4821	336	54	b	b	PROPN
ejpam-4821	336	55	∈	∈	PROPN
ejpam-4821	336	56	ng⋄h(y	ng⋄h(y	NOUN
ejpam-4821	336	57	)	)	PUNCT
ejpam-4821	336	58	.	.	PUNCT
ejpam-4821	337	1	thus	thus	ADV
ejpam-4821	337	2	,	,	PUNCT
ejpam-4821	337	3	it	it	PRON
ejpam-4821	337	4	follows	follow	VERB
ejpam-4821	337	5	that	that	SCONJ
ejpam-4821	337	6	rg⋄h(x	rg⋄h(x	PROPN
ejpam-4821	337	7	/	/	SYM
ejpam-4821	337	8	c	c	NOUN
ejpam-4821	337	9	)	)	PUNCT
ejpam-4821	337	10	and	and	CCONJ
ejpam-4821	337	11	rg⋄h(y	rg⋄h(y	ADJ
ejpam-4821	337	12	/	/	SYM
ejpam-4821	337	13	c	c	NOUN
ejpam-4821	337	14	)	)	PUNCT
ejpam-4821	337	15	differ	differ	VERB
ejpam-4821	337	16	at	at	ADP
ejpam-4821	337	17	ath	ath	NOUN
ejpam-4821	337	18	and	and	CCONJ
ejpam-4821	337	19	bth	bth	PROPN
ejpam-4821	337	20	positions	position	NOUN
ejpam-4821	337	21	.	.	PUNCT
ejpam-4821	338	1	therefore	therefore	ADV
ejpam-4821	338	2	,	,	PUNCT
ejpam-4821	338	3	c	c	PROPN
ejpam-4821	338	4	is	be	AUX
ejpam-4821	338	5	a	a	DET
ejpam-4821	338	6	2	2	NUM
ejpam-4821	338	7	-	-	PUNCT
ejpam-4821	338	8	resolving	resolving	NOUN
ejpam-4821	338	9	set	set	NOUN
ejpam-4821	338	10	in	in	ADP
ejpam-4821	338	11	g	g	PROPN
ejpam-4821	338	12	⋄h	⋄h	PROPN
ejpam-4821	338	13	.	.	PUNCT
ejpam-4821	339	1	by	by	ADP
ejpam-4821	339	2	theorem	theorem	NOUN
ejpam-4821	339	3	7	7	NUM
ejpam-4821	339	4	,	,	PUNCT
ejpam-4821	339	5	c	c	PROPN
ejpam-4821	339	6	is	be	AUX
ejpam-4821	339	7	a	a	DET
ejpam-4821	339	8	2	2	NUM
ejpam-4821	339	9	-	-	PUNCT
ejpam-4821	339	10	locating	locate	VERB
ejpam-4821	339	11	set	set	NOUN
ejpam-4821	339	12	in	in	ADP
ejpam-4821	339	13	g.	g.	PROPN
ejpam-4821	339	14	corollary	corollary	PROPN
ejpam-4821	339	15	7	7	PROPN
ejpam-4821	339	16	.	.	PUNCT
ejpam-4821	340	1	let	let	VERB
ejpam-4821	340	2	g	g	NOUN
ejpam-4821	341	1	and	and	CCONJ
ejpam-4821	341	2	h	h	NOUN
ejpam-4821	341	3	be	be	VERB
ejpam-4821	341	4	any	any	DET
ejpam-4821	341	5	nontrivial	nontrivial	ADJ
ejpam-4821	341	6	connected	connect	VERB
ejpam-4821	341	7	graphs	graph	NOUN
ejpam-4821	341	8	where	where	SCONJ
ejpam-4821	341	9	g	g	PROPN
ejpam-4821	341	10	̸=	̸=	PROPN
ejpam-4821	341	11	p2	p2	VERB
ejpam-4821	341	12	with	with	ADP
ejpam-4821	341	13	|e(g)|	|e(g)|	PROPN
ejpam-4821	341	14	=	=	PROPN
ejpam-4821	341	15	m	m	NOUN
ejpam-4821	341	16	and	and	CCONJ
ejpam-4821	341	17	∆(h	∆(h	NOUN
ejpam-4821	341	18	)	)	PUNCT
ejpam-4821	341	19	≤	≤	NOUN
ejpam-4821	341	20	|v	|v	X
ejpam-4821	341	21	(	(	PUNCT
ejpam-4821	341	22	h)|	h)|	NOUN
ejpam-4821	341	23	−	−	PROPN
ejpam-4821	341	24	3	3	NUM
ejpam-4821	341	25	.	.	PUNCT
ejpam-4821	342	1	then	then	ADV
ejpam-4821	342	2	the	the	DET
ejpam-4821	342	3	following	following	ADJ
ejpam-4821	342	4	statements	statement	NOUN
ejpam-4821	342	5	hold	hold	VERB
ejpam-4821	342	6	.	.	PUNCT
ejpam-4821	343	1	(	(	PUNCT
ejpam-4821	343	2	i	i	NOUN
ejpam-4821	343	3	)	)	PUNCT
ejpam-4821	343	4	if	if	SCONJ
ejpam-4821	343	5	g	g	PROPN
ejpam-4821	343	6	is	be	AUX
ejpam-4821	343	7	a	a	DET
ejpam-4821	343	8	graph	graph	NOUN
ejpam-4821	343	9	with	with	ADP
ejpam-4821	343	10	no	no	DET
ejpam-4821	343	11	pendant	pendant	ADJ
ejpam-4821	343	12	edges	edge	NOUN
ejpam-4821	343	13	,	,	PUNCT
ejpam-4821	343	14	then	then	ADV
ejpam-4821	343	15	ln2(g	ln2(g	PROPN
ejpam-4821	343	16	⋄h	⋄h	PROPN
ejpam-4821	343	17	)	)	PUNCT
ejpam-4821	343	18	=	=	PUNCT
ejpam-4821	343	19	m	m	PUNCT
ejpam-4821	343	20	·	·	PUNCT
ejpam-4821	343	21	ln2(h	ln2(h	PROPN
ejpam-4821	343	22	)	)	PUNCT
ejpam-4821	343	23	.	.	PUNCT
ejpam-4821	344	1	(	(	PUNCT
ejpam-4821	344	2	ii	ii	NOUN
ejpam-4821	344	3	)	)	PUNCT
ejpam-4821	344	4	if	if	SCONJ
ejpam-4821	344	5	g	g	PROPN
ejpam-4821	344	6	is	be	AUX
ejpam-4821	344	7	a	a	DET
ejpam-4821	344	8	graph	graph	NOUN
ejpam-4821	344	9	with	with	ADP
ejpam-4821	344	10	k	k	PROPN
ejpam-4821	344	11	≥	≥	NUM
ejpam-4821	344	12	1	1	NUM
ejpam-4821	344	13	pendant	pendant	ADJ
ejpam-4821	344	14	edges	edge	NOUN
ejpam-4821	344	15	,	,	PUNCT
ejpam-4821	344	16	then	then	ADV
ejpam-4821	344	17	ln2(g	ln2(g	PROPN
ejpam-4821	344	18	⋄h	⋄h	PROPN
ejpam-4821	344	19	)	)	PUNCT
ejpam-4821	344	20	=	=	SYM
ejpam-4821	344	21	min	min	NOUN
ejpam-4821	344	22	{	{	PUNCT
ejpam-4821	344	23	(	(	PUNCT
ejpam-4821	344	24	m−	m−	PROPN
ejpam-4821	344	25	k	k	PROPN
ejpam-4821	344	26	)	)	PUNCT
ejpam-4821	344	27	ln2(h	ln2(h	PROPN
ejpam-4821	344	28	)	)	PUNCT
ejpam-4821	345	1	+	+	CCONJ
ejpam-4821	345	2	k	k	X
ejpam-4821	345	3	·	·	PUNCT
ejpam-4821	345	4	ln(2,1)(h	ln(2,1)(h	NUM
ejpam-4821	345	5	)	)	PUNCT
ejpam-4821	346	1	+	+	SYM
ejpam-4821	346	2	k	k	NOUN
ejpam-4821	346	3	,	,	PUNCT
ejpam-4821	346	4	(	(	PUNCT
ejpam-4821	346	5	m−	m−	PROPN
ejpam-4821	346	6	k	k	PROPN
ejpam-4821	346	7	)	)	PUNCT
ejpam-4821	346	8	ln2(h	ln2(h	PROPN
ejpam-4821	346	9	)	)	PUNCT
ejpam-4821	347	1	+	+	PROPN
ejpam-4821	347	2	k	k	X
ejpam-4821	347	3	·	·	PUNCT
ejpam-4821	347	4	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4821	347	5	)	)	PUNCT
ejpam-4821	347	6	}	}	PUNCT
ejpam-4821	347	7	and	and	CCONJ
ejpam-4821	347	8	ln2(g	ln2(g	DET
ejpam-4821	347	9	⋄	⋄	PROPN
ejpam-4821	347	10	h	h	NOUN
ejpam-4821	347	11	)	)	PUNCT
ejpam-4821	347	12	=	=	PRON
ejpam-4821	347	13	(	(	PUNCT
ejpam-4821	347	14	m	m	VERB
ejpam-4821	347	15	−	−	PROPN
ejpam-4821	347	16	k	k	NOUN
ejpam-4821	347	17	)	)	PUNCT
ejpam-4821	347	18	ln2(h	ln2(h	PROPN
ejpam-4821	347	19	)	)	PUNCT
ejpam-4821	348	1	+	+	CCONJ
ejpam-4821	348	2	k	k	PROPN
ejpam-4821	348	3	·	·	PUNCT
ejpam-4821	348	4	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4821	348	5	)	)	PUNCT
ejpam-4821	348	6	whenever	whenever	SCONJ
ejpam-4821	348	7	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4821	348	8	)	)	PUNCT
ejpam-4821	348	9	=	=	PUNCT
ejpam-4821	348	10	ln(2,1)(h	ln(2,1)(h	PRON
ejpam-4821	348	11	)	)	PUNCT
ejpam-4821	348	12	.	.	PUNCT
ejpam-4821	349	1	proof	proof	NOUN
ejpam-4821	349	2	.	.	PUNCT
ejpam-4821	350	1	(	(	PUNCT
ejpam-4821	350	2	i	i	NOUN
ejpam-4821	350	3	)	)	PUNCT
ejpam-4821	350	4	suppose	suppose	VERB
ejpam-4821	350	5	g	g	PROPN
ejpam-4821	350	6	is	be	AUX
ejpam-4821	350	7	a	a	DET
ejpam-4821	350	8	graph	graph	NOUN
ejpam-4821	350	9	with	with	ADP
ejpam-4821	350	10	no	no	DET
ejpam-4821	350	11	pendant	pendant	ADJ
ejpam-4821	350	12	edges	edge	NOUN
ejpam-4821	350	13	.	.	PUNCT
ejpam-4821	351	1	now	now	ADV
ejpam-4821	351	2	,	,	PUNCT
ejpam-4821	351	3	set	set	VERB
ejpam-4821	351	4	a	a	DET
ejpam-4821	351	5	=	=	NOUN
ejpam-4821	351	6	∅	∅	NOUN
ejpam-4821	351	7	and	and	CCONJ
ejpam-4821	351	8	let	let	VERB
ejpam-4821	351	9	suv	suv	PROPN
ejpam-4821	351	10	be	be	AUX
ejpam-4821	351	11	an	an	DET
ejpam-4821	351	12	ln2	ln2	ADJ
ejpam-4821	351	13	−	−	NOUN
ejpam-4821	351	14	set	set	NOUN
ejpam-4821	351	15	of	of	ADP
ejpam-4821	351	16	huv	huv	PROPN
ejpam-4821	351	17	for	for	ADP
ejpam-4821	351	18	all	all	DET
ejpam-4821	351	19	uv	uv	PROPN
ejpam-4821	351	20	∈	∈	PROPN
ejpam-4821	351	21	e(g	e(g	PROPN
ejpam-4821	351	22	)	)	PUNCT
ejpam-4821	351	23	.	.	PUNCT
ejpam-4821	352	1	then	then	ADV
ejpam-4821	352	2	c	c	X
ejpam-4821	352	3	=	=	SYM
ejpam-4821	352	4	a∪	a∪	PROPN
ejpam-4821	352	5	(	(	PUNCT
ejpam-4821	352	6	⋃	⋃	NOUN
ejpam-4821	352	7	uv∈e(g	uv∈e(g	NOUN
ejpam-4821	352	8	)	)	PUNCT
ejpam-4821	352	9	suv	suv	PROPN
ejpam-4821	352	10	)	)	PUNCT
ejpam-4821	352	11	is	be	AUX
ejpam-4821	352	12	a	a	DET
ejpam-4821	352	13	2	2	NUM
ejpam-4821	352	14	-	-	PUNCT
ejpam-4821	352	15	locating	locate	VERB
ejpam-4821	352	16	set	set	NOUN
ejpam-4821	352	17	in	in	ADP
ejpam-4821	352	18	g	g	NOUN
ejpam-4821	352	19	⋄h	⋄h	NOUN
ejpam-4821	352	20	by	by	ADP
ejpam-4821	352	21	theorem	theorem	NOUN
ejpam-4821	352	22	8	8	NUM
ejpam-4821	352	23	.	.	PUNCT
ejpam-4821	353	1	hence	hence	ADV
ejpam-4821	353	2	,	,	PUNCT
ejpam-4821	353	3	ln2(g	ln2(g	PROPN
ejpam-4821	353	4	⋄h	⋄h	PROPN
ejpam-4821	353	5	)	)	PUNCT
ejpam-4821	353	6	≤	≤	NOUN
ejpam-4821	353	7	|c|	|c|	PROPN
ejpam-4821	353	8	=	=	PUNCT
ejpam-4821	353	9	|a|+	|a|+	VERB
ejpam-4821	353	10	|e(g)||suv|	|e(g)||suv|	NUM
ejpam-4821	353	11	=	=	SYM
ejpam-4821	353	12	m(ln2(h	m(ln2(h	PROPN
ejpam-4821	353	13	)	)	PUNCT
ejpam-4821	353	14	)	)	PUNCT
ejpam-4821	353	15	.	.	PUNCT
ejpam-4821	354	1	next	next	ADV
ejpam-4821	354	2	,	,	PUNCT
ejpam-4821	354	3	let	let	VERB
ejpam-4821	354	4	c0	c0	NOUN
ejpam-4821	354	5	be	be	AUX
ejpam-4821	354	6	an	an	DET
ejpam-4821	354	7	ln2	ln2	ADJ
ejpam-4821	354	8	−	−	NOUN
ejpam-4821	354	9	set	set	NOUN
ejpam-4821	354	10	in	in	ADP
ejpam-4821	354	11	g	g	PROPN
ejpam-4821	354	12	⋄	⋄	PROPN
ejpam-4821	354	13	h.	h.	NOUN
ejpam-4821	354	14	then	then	ADV
ejpam-4821	354	15	by	by	ADP
ejpam-4821	354	16	theorem	theorem	NOUN
ejpam-4821	354	17	8	8	NUM
ejpam-4821	354	18	,	,	PUNCT
ejpam-4821	354	19	c0	c0	PROPN
ejpam-4821	354	20	=	=	SYM
ejpam-4821	354	21	a0	a0	PROPN
ejpam-4821	354	22	∪	∪	X
ejpam-4821	354	23	(	(	PUNCT
ejpam-4821	354	24	⋃	⋃	NOUN
ejpam-4821	354	25	uv∈e(g	uv∈e(g	NOUN
ejpam-4821	354	26	)	)	PUNCT
ejpam-4821	354	27	suv	suv	NOUN
ejpam-4821	354	28	)	)	PUNCT
ejpam-4821	354	29	where	where	SCONJ
ejpam-4821	354	30	a0	a0	PROPN
ejpam-4821	354	31	⊆	⊆	NUM
ejpam-4821	354	32	v	v	NOUN
ejpam-4821	354	33	(	(	PUNCT
ejpam-4821	354	34	g	g	NOUN
ejpam-4821	354	35	)	)	PUNCT
ejpam-4821	354	36	and	and	CCONJ
ejpam-4821	354	37	suv	suv	PROPN
ejpam-4821	354	38	is	be	AUX
ejpam-4821	354	39	a	a	DET
ejpam-4821	354	40	2	2	NUM
ejpam-4821	354	41	-	-	PUNCT
ejpam-4821	354	42	locating	locate	VERB
ejpam-4821	354	43	set	set	NOUN
ejpam-4821	354	44	of	of	ADP
ejpam-4821	354	45	huv	huv	PROPN
ejpam-4821	354	46	for	for	ADP
ejpam-4821	354	47	all	all	DET
ejpam-4821	354	48	uv	uv	PROPN
ejpam-4821	354	49	∈	∈	PROPN
ejpam-4821	354	50	e(g	e(g	PROPN
ejpam-4821	354	51	)	)	PUNCT
ejpam-4821	354	52	.	.	PUNCT
ejpam-4821	355	1	thus	thus	ADV
ejpam-4821	355	2	,	,	PUNCT
ejpam-4821	355	3	ln2(g	ln2(g	PROPN
ejpam-4821	355	4	⋄h	⋄h	PROPN
ejpam-4821	355	5	)	)	PUNCT
ejpam-4821	355	6	=	=	NOUN
ejpam-4821	355	7	|c0|	|c0|	NOUN
ejpam-4821	355	8	=	=	SYM
ejpam-4821	355	9	|a0|+	|a0|+	X
ejpam-4821	355	10	|	|	ADV
ejpam-4821	355	11	⋃	⋃	NOUN
ejpam-4821	355	12	uv∈e(g	uv∈e(g	NOUN
ejpam-4821	355	13	)	)	PUNCT
ejpam-4821	355	14	suv|	suv|	VERB
ejpam-4821	355	15	≥	≥	NUM
ejpam-4821	355	16	∑	∑	ADV
ejpam-4821	355	17	uv∈e(g	uv∈e(g	NUM
ejpam-4821	355	18	)	)	PUNCT
ejpam-4821	356	1	|suv|	|suv|	PROPN
ejpam-4821	356	2	≥	≥	NUM
ejpam-4821	356	3	m	m	PROPN
ejpam-4821	356	4	·	·	PUNCT
ejpam-4821	356	5	ln2(h	ln2(h	PROPN
ejpam-4821	356	6	)	)	PUNCT
ejpam-4821	356	7	.	.	PUNCT
ejpam-4821	357	1	therefore	therefore	ADV
ejpam-4821	357	2	,	,	PUNCT
ejpam-4821	357	3	ln2(g	ln2(g	PROPN
ejpam-4821	357	4	⋄h	⋄h	PROPN
ejpam-4821	357	5	)	)	PUNCT
ejpam-4821	357	6	=	=	PUNCT
ejpam-4821	358	1	m	m	PUNCT
ejpam-4821	358	2	·	·	PUNCT
ejpam-4821	358	3	ln2(h	ln2(h	PROPN
ejpam-4821	358	4	)	)	PUNCT
ejpam-4821	358	5	.	.	PUNCT
ejpam-4821	359	1	(	(	PUNCT
ejpam-4821	359	2	ii	ii	NOUN
ejpam-4821	359	3	)	)	PUNCT
ejpam-4821	359	4	let	let	VERB
ejpam-4821	359	5	g	g	NOUN
ejpam-4821	359	6	be	be	AUX
ejpam-4821	359	7	a	a	DET
ejpam-4821	359	8	graph	graph	NOUN
ejpam-4821	359	9	with	with	ADP
ejpam-4821	359	10	pendant	pendant	ADJ
ejpam-4821	359	11	edges	edge	NOUN
ejpam-4821	359	12	and	and	CCONJ
ejpam-4821	359	13	a	a	DET
ejpam-4821	359	14	⊆	⊆	NUM
ejpam-4821	359	15	v	v	NOUN
ejpam-4821	359	16	(	(	PUNCT
ejpam-4821	359	17	g	g	NOUN
ejpam-4821	359	18	)	)	PUNCT
ejpam-4821	359	19	consists	consist	VERB
ejpam-4821	359	20	of	of	ADP
ejpam-4821	359	21	pendant	pendant	ADJ
ejpam-4821	359	22	edges	edge	NOUN
ejpam-4821	359	23	in	in	ADP
ejpam-4821	359	24	a	a	DET
ejpam-4821	359	25	graph	graph	NOUN
ejpam-4821	359	26	g	g	NOUN
ejpam-4821	359	27	,	,	PUNCT
ejpam-4821	359	28	that	that	PRON
ejpam-4821	359	29	is	be	AUX
ejpam-4821	359	30	|a|	|a|	PROPN
ejpam-4821	359	31	=	=	PROPN
ejpam-4821	359	32	k.	k.	PROPN
ejpam-4821	359	33	by	by	ADP
ejpam-4821	359	34	theorem	theorem	NOUN
ejpam-4821	359	35	8	8	NUM
ejpam-4821	359	36	,	,	PUNCT
ejpam-4821	359	37	suv	suv	PROPN
ejpam-4821	359	38	is	be	AUX
ejpam-4821	359	39	a	a	DET
ejpam-4821	359	40	2	2	NUM
ejpam-4821	359	41	-	-	PUNCT
ejpam-4821	359	42	locating	locate	VERB
ejpam-4821	359	43	set	set	NOUN
ejpam-4821	359	44	of	of	ADP
ejpam-4821	359	45	huv	huv	PROPN
ejpam-4821	359	46	for	for	ADP
ejpam-4821	359	47	all	all	DET
ejpam-4821	359	48	uv	uv	PROPN
ejpam-4821	359	49	∈	∈	PROPN
ejpam-4821	359	50	e(g	e(g	PROPN
ejpam-4821	359	51	)	)	PUNCT
ejpam-4821	359	52	and	and	CCONJ
ejpam-4821	359	53	suv	suv	PROPN
ejpam-4821	359	54	is	be	AUX
ejpam-4821	359	55	a	a	DET
ejpam-4821	359	56	(	(	PUNCT
ejpam-4821	359	57	2,1)-locating	2,1)-locating	NUM
ejpam-4821	359	58	set	set	NOUN
ejpam-4821	359	59	of	of	ADP
ejpam-4821	359	60	huv	huv	PROPN
ejpam-4821	359	61	whenever	whenever	SCONJ
ejpam-4821	359	62	l(uv	l(uv	PROPN
ejpam-4821	359	63	)	)	PUNCT
ejpam-4821	359	64	⊆	⊆	NUM
ejpam-4821	359	65	a	a	PRON
ejpam-4821	359	66	and	and	CCONJ
ejpam-4821	359	67	suv	suv	PROPN
ejpam-4821	359	68	is	be	AUX
ejpam-4821	359	69	a	a	DET
ejpam-4821	359	70	(	(	PUNCT
ejpam-4821	359	71	2,2)-locating	2,2)-locating	NUM
ejpam-4821	359	72	set	set	NOUN
ejpam-4821	359	73	g.cañete	g.cañete	PROPN
ejpam-4821	359	74	,	,	PUNCT
ejpam-4821	359	75	h.	h.	PROPN
ejpam-4821	359	76	rara	rara	PROPN
ejpam-4821	359	77	,	,	PUNCT
ejpam-4821	359	78	a.m.	a.m.	PROPN
ejpam-4821	359	79	mahistrado	mahistrado	PROPN
ejpam-4821	359	80	/	/	SYM
ejpam-4821	359	81	eur	eur	PROPN
ejpam-4821	359	82	.	.	PUNCT
ejpam-4821	360	1	j.	j.	PROPN
ejpam-4821	360	2	pure	pure	PROPN
ejpam-4821	360	3	appl	appl	PROPN
ejpam-4821	360	4	.	.	PROPN
ejpam-4821	360	5	math	math	PROPN
ejpam-4821	360	6	,	,	PUNCT
ejpam-4821	360	7	16	16	NUM
ejpam-4821	360	8	(	(	PUNCT
ejpam-4821	360	9	3	3	NUM
ejpam-4821	360	10	)	)	PUNCT
ejpam-4821	360	11	(	(	PUNCT
ejpam-4821	360	12	2023	2023	NUM
ejpam-4821	360	13	)	)	PUNCT
ejpam-4821	360	14	,	,	PUNCT
ejpam-4821	360	15	1647	1647	NUM
ejpam-4821	360	16	-	-	SYM
ejpam-4821	360	17	1662	1662	NUM
ejpam-4821	360	18	1658	1658	NUM
ejpam-4821	360	19	of	of	ADP
ejpam-4821	360	20	huv	huv	PROPN
ejpam-4821	360	21	,	,	PUNCT
ejpam-4821	360	22	otherwise	otherwise	ADV
ejpam-4821	360	23	.	.	PUNCT
ejpam-4821	361	1	if	if	SCONJ
ejpam-4821	361	2	suv	suv	PROPN
ejpam-4821	361	3	is	be	AUX
ejpam-4821	361	4	a	a	DET
ejpam-4821	361	5	(	(	PUNCT
ejpam-4821	361	6	2,2)-locating	2,2)-locating	NUM
ejpam-4821	361	7	sets	set	NOUN
ejpam-4821	361	8	in	in	ADP
ejpam-4821	361	9	huv	huv	PROPN
ejpam-4821	361	10	,	,	PUNCT
ejpam-4821	361	11	then	then	ADV
ejpam-4821	361	12	(	(	PUNCT
ejpam-4821	361	13	m−	m−	PROPN
ejpam-4821	361	14	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	361	15	)	)	PUNCT
ejpam-4821	362	1	+	+	CCONJ
ejpam-4821	362	2	k	k	PROPN
ejpam-4821	362	3	·	·	PUNCT
ejpam-4821	362	4	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4821	362	5	)	)	PUNCT
ejpam-4821	362	6	≤	≤	NOUN
ejpam-4821	362	7	|c|	|c|	PROPN
ejpam-4821	362	8	=	=	PRON
ejpam-4821	362	9	ln2(g	ln2(g	PROPN
ejpam-4821	362	10	⋄h	⋄h	NOUN
ejpam-4821	362	11	)	)	PUNCT
ejpam-4821	362	12	.	.	PUNCT
ejpam-4821	363	1	if	if	SCONJ
ejpam-4821	363	2	suv	suv	PROPN
ejpam-4821	363	3	is	be	AUX
ejpam-4821	363	4	a	a	DET
ejpam-4821	363	5	(	(	PUNCT
ejpam-4821	363	6	2,2)-locating	2,2)-locating	NUM
ejpam-4821	363	7	sets	set	NOUN
ejpam-4821	363	8	in	in	ADP
ejpam-4821	363	9	huv	huv	PROPN
ejpam-4821	363	10	,	,	PUNCT
ejpam-4821	363	11	then	then	ADV
ejpam-4821	363	12	(	(	PUNCT
ejpam-4821	363	13	m−	m−	PROPN
ejpam-4821	363	14	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	363	15	)	)	PUNCT
ejpam-4821	364	1	+	+	CCONJ
ejpam-4821	364	2	k	k	X
ejpam-4821	364	3	·	·	PUNCT
ejpam-4821	364	4	ln(2,1)(h	ln(2,1)(h	NUM
ejpam-4821	364	5	)	)	PUNCT
ejpam-4821	365	1	+	+	CCONJ
ejpam-4821	365	2	k	k	PROPN
ejpam-4821	365	3	≤	≤	PROPN
ejpam-4821	365	4	|c|	|c|	PROPN
ejpam-4821	365	5	=	=	PRON
ejpam-4821	365	6	ln2(g	ln2(g	PROPN
ejpam-4821	365	7	⋄h	⋄h	NOUN
ejpam-4821	365	8	)	)	PUNCT
ejpam-4821	365	9	.	.	PUNCT
ejpam-4821	366	1	thus	thus	ADV
ejpam-4821	366	2	,	,	PUNCT
ejpam-4821	366	3	ln2(g	ln2(g	PROPN
ejpam-4821	366	4	⋄h	⋄h	PROPN
ejpam-4821	366	5	)	)	PUNCT
ejpam-4821	366	6	≥	≥	NOUN
ejpam-4821	366	7	min{(m−	min{(m−	PROPN
ejpam-4821	366	8	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	366	9	)	)	PUNCT
ejpam-4821	367	1	+	+	CCONJ
ejpam-4821	367	2	k	k	X
ejpam-4821	367	3	·	·	PUNCT
ejpam-4821	367	4	ln(2,1)(h	ln(2,1)(h	NUM
ejpam-4821	367	5	)	)	PUNCT
ejpam-4821	368	1	+	+	SYM
ejpam-4821	369	1	k	k	NOUN
ejpam-4821	369	2	,	,	PUNCT
ejpam-4821	369	3	(	(	PUNCT
ejpam-4821	369	4	m−	m−	PROPN
ejpam-4821	369	5	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	369	6	)	)	PUNCT
ejpam-4821	369	7	+	+	CCONJ
ejpam-4821	370	1	k	k	PROPN
ejpam-4821	370	2	·	·	PUNCT
ejpam-4821	370	3	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4821	370	4	)	)	PUNCT
ejpam-4821	370	5	}	}	PUNCT
ejpam-4821	370	6	.	.	PUNCT
ejpam-4821	371	1	let	let	VERB
ejpam-4821	371	2	(	(	PUNCT
ejpam-4821	371	3	m	m	VERB
ejpam-4821	371	4	−	−	PROPN
ejpam-4821	371	5	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	371	6	)	)	PUNCT
ejpam-4821	372	1	+	+	CCONJ
ejpam-4821	372	2	k	k	X
ejpam-4821	372	3	·	·	PUNCT
ejpam-4821	372	4	ln(2,1)(h	ln(2,1)(h	NUM
ejpam-4821	372	5	)	)	PUNCT
ejpam-4821	373	1	+	+	CCONJ
ejpam-4821	373	2	k	k	SYM
ejpam-4821	373	3	≤	≤	NOUN
ejpam-4821	373	4	(	(	PUNCT
ejpam-4821	373	5	m	m	NOUN
ejpam-4821	373	6	−	−	PROPN
ejpam-4821	373	7	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	373	8	)	)	PUNCT
ejpam-4821	374	1	+	+	CCONJ
ejpam-4821	374	2	k	k	PROPN
ejpam-4821	374	3	·	·	PUNCT
ejpam-4821	374	4	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4821	374	5	)	)	PUNCT
ejpam-4821	374	6	.	.	PUNCT
ejpam-4821	375	1	let	let	VERB
ejpam-4821	375	2	suv	suv	PROPN
ejpam-4821	375	3	be	be	AUX
ejpam-4821	375	4	the	the	DET
ejpam-4821	375	5	minimum	minimum	NOUN
ejpam-4821	375	6	(	(	PUNCT
ejpam-4821	375	7	2,1)-locating	2,1)-locating	NUM
ejpam-4821	375	8	set	set	NOUN
ejpam-4821	375	9	in	in	ADP
ejpam-4821	375	10	huv	huv	PROPN
ejpam-4821	375	11	whenever	whenever	SCONJ
ejpam-4821	375	12	l(uv	l(uv	PROPN
ejpam-4821	375	13	)	)	PUNCT
ejpam-4821	375	14	⊆	⊆	NUM
ejpam-4821	375	15	a	a	PRON
ejpam-4821	375	16	and	and	CCONJ
ejpam-4821	375	17	suv	suv	PROPN
ejpam-4821	375	18	be	be	AUX
ejpam-4821	375	19	the	the	DET
ejpam-4821	375	20	minimum	minimum	NOUN
ejpam-4821	375	21	(	(	PUNCT
ejpam-4821	375	22	2,2)-locating	2,2)-locating	NUM
ejpam-4821	375	23	set	set	NOUN
ejpam-4821	375	24	in	in	ADP
ejpam-4821	375	25	huv	huv	PROPN
ejpam-4821	375	26	,	,	PUNCT
ejpam-4821	375	27	otherwise	otherwise	ADV
ejpam-4821	375	28	.	.	PUNCT
ejpam-4821	376	1	then	then	ADV
ejpam-4821	376	2	,	,	PUNCT
ejpam-4821	376	3	c	c	PROPN
ejpam-4821	376	4	is	be	AUX
ejpam-4821	376	5	a	a	DET
ejpam-4821	376	6	2	2	NUM
ejpam-4821	376	7	-	-	PUNCT
ejpam-4821	376	8	locating	locate	VERB
ejpam-4821	376	9	set	set	NOUN
ejpam-4821	376	10	in	in	ADP
ejpam-4821	376	11	g	g	PROPN
ejpam-4821	376	12	⋄	⋄	PROPN
ejpam-4821	376	13	h	h	NOUN
ejpam-4821	376	14	by	by	ADP
ejpam-4821	376	15	corollary	corollary	ADJ
ejpam-4821	376	16	7	7	NUM
ejpam-4821	376	17	.	.	PUNCT
ejpam-4821	377	1	hence	hence	ADV
ejpam-4821	377	2	,	,	PUNCT
ejpam-4821	377	3	ln2(g	ln2(g	PROPN
ejpam-4821	377	4	⋄	⋄	PROPN
ejpam-4821	377	5	h	h	NOUN
ejpam-4821	377	6	)	)	PUNCT
ejpam-4821	377	7	≤	≤	NOUN
ejpam-4821	377	8	|c|	|c|	PROPN
ejpam-4821	377	9	=	=	PUNCT
ejpam-4821	377	10	(	(	PUNCT
ejpam-4821	377	11	m	m	VERB
ejpam-4821	377	12	−	−	PROPN
ejpam-4821	377	13	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	377	14	)	)	PUNCT
ejpam-4821	378	1	+	+	CCONJ
ejpam-4821	379	1	k	k	X
ejpam-4821	379	2	·	·	PUNCT
ejpam-4821	379	3	ln(2,1)(h	ln(2,1)(h	NUM
ejpam-4821	379	4	)	)	PUNCT
ejpam-4821	379	5	+	+	CCONJ
ejpam-4821	379	6	k.	k.	PROPN
ejpam-4821	379	7	similarly	similarly	ADV
ejpam-4821	379	8	,	,	PUNCT
ejpam-4821	379	9	if	if	SCONJ
ejpam-4821	379	10	(	(	PUNCT
ejpam-4821	379	11	m	m	NOUN
ejpam-4821	379	12	−	−	PROPN
ejpam-4821	379	13	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	379	14	)	)	PUNCT
ejpam-4821	379	15	+	+	CCONJ
ejpam-4821	379	16	k	k	PROPN
ejpam-4821	379	17	·	·	PUNCT
ejpam-4821	379	18	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4821	379	19	)	)	PUNCT
ejpam-4821	379	20	≤	≤	NOUN
ejpam-4821	379	21	(	(	PUNCT
ejpam-4821	379	22	m	m	NOUN
ejpam-4821	379	23	−	−	PROPN
ejpam-4821	379	24	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	379	25	)	)	PUNCT
ejpam-4821	380	1	+	+	CCONJ
ejpam-4821	381	1	k	k	X
ejpam-4821	381	2	·	·	PUNCT
ejpam-4821	381	3	ln(2,1)(h	ln(2,1)(h	NUM
ejpam-4821	381	4	)	)	PUNCT
ejpam-4821	381	5	+	+	CCONJ
ejpam-4821	382	1	k.	k.	PROPN
ejpam-4821	382	2	then	then	ADV
ejpam-4821	382	3	ln2(g	ln2(g	PROPN
ejpam-4821	382	4	⋄h	⋄h	PROPN
ejpam-4821	382	5	)	)	PUNCT
ejpam-4821	382	6	≤	≤	PROPN
ejpam-4821	382	7	|c|	|c|	PROPN
ejpam-4821	382	8	=	=	SYM
ejpam-4821	382	9	(	(	PUNCT
ejpam-4821	382	10	m−	m−	PROPN
ejpam-4821	382	11	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	382	12	)	)	PUNCT
ejpam-4821	382	13	+	+	CCONJ
ejpam-4821	382	14	k	k	PROPN
ejpam-4821	382	15	·	·	PUNCT
ejpam-4821	382	16	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4821	382	17	)	)	PUNCT
ejpam-4821	382	18	.	.	PUNCT
ejpam-4821	383	1	thus	thus	ADV
ejpam-4821	383	2	,	,	PUNCT
ejpam-4821	383	3	ln2(g	ln2(g	PROPN
ejpam-4821	383	4	⋄h	⋄h	PROPN
ejpam-4821	383	5	)	)	PUNCT
ejpam-4821	383	6	≤	≤	PUNCT
ejpam-4821	383	7	min{(m−	min{(m−	PROPN
ejpam-4821	383	8	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	383	9	)	)	PUNCT
ejpam-4821	384	1	+	+	CCONJ
ejpam-4821	384	2	k	k	X
ejpam-4821	384	3	·	·	PUNCT
ejpam-4821	384	4	ln(2,1)(h	ln(2,1)(h	NUM
ejpam-4821	384	5	)	)	PUNCT
ejpam-4821	385	1	+	+	SYM
ejpam-4821	386	1	k	k	NOUN
ejpam-4821	386	2	,	,	PUNCT
ejpam-4821	386	3	(	(	PUNCT
ejpam-4821	386	4	m−	m−	PROPN
ejpam-4821	386	5	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	386	6	)	)	PUNCT
ejpam-4821	386	7	+	+	CCONJ
ejpam-4821	387	1	k	k	PROPN
ejpam-4821	387	2	·	·	PUNCT
ejpam-4821	387	3	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4821	387	4	)	)	PUNCT
ejpam-4821	387	5	}	}	PUNCT
ejpam-4821	387	6	.	.	PUNCT
ejpam-4821	388	1	therefore	therefore	ADV
ejpam-4821	388	2	,	,	PUNCT
ejpam-4821	388	3	ln2(g	ln2(g	PROPN
ejpam-4821	388	4	⋄h	⋄h	PROPN
ejpam-4821	388	5	)	)	PUNCT
ejpam-4821	389	1	=	=	SYM
ejpam-4821	389	2	min{(m−	min{(m−	PROPN
ejpam-4821	389	3	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	389	4	)	)	PUNCT
ejpam-4821	389	5	+	+	CCONJ
ejpam-4821	389	6	k	k	X
ejpam-4821	389	7	·	·	PUNCT
ejpam-4821	389	8	ln(2,1)(h	ln(2,1)(h	NUM
ejpam-4821	389	9	)	)	PUNCT
ejpam-4821	390	1	+	+	SYM
ejpam-4821	391	1	k	k	NOUN
ejpam-4821	391	2	,	,	PUNCT
ejpam-4821	391	3	(	(	PUNCT
ejpam-4821	391	4	m−	m−	PROPN
ejpam-4821	391	5	k)ln2(h	k)ln2(h	PROPN
ejpam-4821	391	6	)	)	PUNCT
ejpam-4821	391	7	+	+	CCONJ
ejpam-4821	392	1	k	k	PROPN
ejpam-4821	392	2	·	·	PUNCT
ejpam-4821	392	3	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4821	392	4	)	)	PUNCT
ejpam-4821	392	5	}	}	PUNCT
ejpam-4821	392	6	.	.	PUNCT
ejpam-4821	393	1	8	8	X
ejpam-4821	393	2	.	.	NOUN
ejpam-4821	393	3	lexicographic	lexicographic	ADJ
ejpam-4821	393	4	product	product	NOUN
ejpam-4821	393	5	of	of	ADP
ejpam-4821	393	6	graphs	graph	NOUN
ejpam-4821	393	7	this	this	DET
ejpam-4821	393	8	section	section	NOUN
ejpam-4821	393	9	presents	present	VERB
ejpam-4821	393	10	characterizations	characterization	NOUN
ejpam-4821	393	11	on	on	ADP
ejpam-4821	393	12	the	the	DET
ejpam-4821	393	13	2	2	NUM
ejpam-4821	393	14	-	-	PUNCT
ejpam-4821	393	15	locating	locate	VERB
ejpam-4821	393	16	sets	set	NOUN
ejpam-4821	393	17	in	in	ADP
ejpam-4821	393	18	the	the	DET
ejpam-4821	393	19	lexicographic	lexicographic	ADJ
ejpam-4821	393	20	product	product	NOUN
ejpam-4821	393	21	of	of	ADP
ejpam-4821	393	22	graphs	graph	NOUN
ejpam-4821	393	23	.	.	PUNCT
ejpam-4821	394	1	theorem	theorem	VERB
ejpam-4821	394	2	9	9	NUM
ejpam-4821	394	3	.	.	PUNCT
ejpam-4821	395	1	[	[	X
ejpam-4821	395	2	6	6	NUM
ejpam-4821	395	3	]	]	PUNCT
ejpam-4821	395	4	let	let	VERB
ejpam-4821	395	5	g	g	NOUN
ejpam-4821	395	6	and	and	CCONJ
ejpam-4821	395	7	h	h	NOUN
ejpam-4821	395	8	be	be	AUX
ejpam-4821	395	9	nontrivial	nontrivial	ADJ
ejpam-4821	395	10	connected	connected	ADJ
ejpam-4821	395	11	graphs	graph	NOUN
ejpam-4821	395	12	.	.	PUNCT
ejpam-4821	396	1	then	then	ADV
ejpam-4821	396	2	w	w	NOUN
ejpam-4821	396	3	=	=	PUNCT
ejpam-4821	396	4	⋃	⋃	PROPN
ejpam-4821	396	5	x∈s	x∈s	NOUN
ejpam-4821	397	1	[	[	X
ejpam-4821	397	2	{	{	PUNCT
ejpam-4821	397	3	x	x	NOUN
ejpam-4821	397	4	}	}	PUNCT
ejpam-4821	397	5	×	×	PROPN
ejpam-4821	397	6	tx	tx	PROPN
ejpam-4821	397	7	]	]	X
ejpam-4821	397	8	,	,	PUNCT
ejpam-4821	397	9	where	where	SCONJ
ejpam-4821	397	10	s	s	VERB
ejpam-4821	397	11	⊆	⊆	NUM
ejpam-4821	397	12	v	v	NOUN
ejpam-4821	397	13	(	(	PUNCT
ejpam-4821	397	14	g	g	NOUN
ejpam-4821	397	15	)	)	PUNCT
ejpam-4821	397	16	and	and	CCONJ
ejpam-4821	397	17	tx	tx	VERB
ejpam-4821	397	18	⊆	⊆	NUM
ejpam-4821	397	19	v	v	NOUN
ejpam-4821	397	20	(	(	PUNCT
ejpam-4821	397	21	h	h	NOUN
ejpam-4821	397	22	)	)	PUNCT
ejpam-4821	397	23	for	for	ADP
ejpam-4821	397	24	each	each	DET
ejpam-4821	397	25	x	x	SYM
ejpam-4821	397	26	∈	∈	PROPN
ejpam-4821	397	27	s	s	NOUN
ejpam-4821	397	28	,	,	PUNCT
ejpam-4821	397	29	is	be	AUX
ejpam-4821	397	30	a	a	DET
ejpam-4821	397	31	2	2	NUM
ejpam-4821	397	32	-	-	PUNCT
ejpam-4821	397	33	resolving	resolving	NOUN
ejpam-4821	397	34	set	set	VERB
ejpam-4821	397	35	in	in	ADP
ejpam-4821	397	36	g[h	g[h	PROPN
ejpam-4821	397	37	]	]	PUNCT
ejpam-4821	397	38	if	if	SCONJ
ejpam-4821	397	39	and	and	CCONJ
ejpam-4821	397	40	only	only	ADV
ejpam-4821	397	41	if	if	SCONJ
ejpam-4821	397	42	(	(	PUNCT
ejpam-4821	397	43	i	i	NOUN
ejpam-4821	397	44	)	)	PUNCT
ejpam-4821	397	45	s	s	PART
ejpam-4821	397	46	=	=	SYM
ejpam-4821	397	47	v	v	NOUN
ejpam-4821	397	48	(	(	PUNCT
ejpam-4821	397	49	g	g	NOUN
ejpam-4821	397	50	)	)	PUNCT
ejpam-4821	397	51	;	;	PUNCT
ejpam-4821	397	52	(	(	PUNCT
ejpam-4821	397	53	ii	ii	NOUN
ejpam-4821	397	54	)	)	PUNCT
ejpam-4821	397	55	tx	tx	PROPN
ejpam-4821	397	56	is	be	AUX
ejpam-4821	397	57	a	a	DET
ejpam-4821	397	58	2	2	NUM
ejpam-4821	397	59	-	-	PUNCT
ejpam-4821	397	60	locating	locate	VERB
ejpam-4821	397	61	set	set	NOUN
ejpam-4821	397	62	in	in	ADP
ejpam-4821	397	63	h	h	NOUN
ejpam-4821	397	64	for	for	ADP
ejpam-4821	397	65	every	every	DET
ejpam-4821	397	66	x	x	SYM
ejpam-4821	397	67	∈	∈	PROPN
ejpam-4821	397	68	v	v	NOUN
ejpam-4821	397	69	(	(	PUNCT
ejpam-4821	397	70	g	g	NOUN
ejpam-4821	397	71	)	)	PUNCT
ejpam-4821	397	72	;	;	PUNCT
ejpam-4821	397	73	(	(	PUNCT
ejpam-4821	397	74	iii	iii	X
ejpam-4821	397	75	)	)	PUNCT
ejpam-4821	397	76	tx	tx	NOUN
ejpam-4821	398	1	and	and	CCONJ
ejpam-4821	398	2	ty	ty	INTJ
ejpam-4821	398	3	are	be	AUX
ejpam-4821	398	4	(	(	PUNCT
ejpam-4821	398	5	2,1)-locating	2,1)-locating	NUM
ejpam-4821	398	6	sets	set	NOUN
ejpam-4821	398	7	or	or	CCONJ
ejpam-4821	398	8	one	one	NUM
ejpam-4821	398	9	of	of	ADP
ejpam-4821	398	10	tx	tx	PROPN
ejpam-4821	398	11	and	and	CCONJ
ejpam-4821	398	12	ty	ty	PRON
ejpam-4821	398	13	is	be	AUX
ejpam-4821	398	14	a(2,2)-locating	a(2,2)-locate	VERB
ejpam-4821	398	15	set	set	VERB
ejpam-4821	398	16	in	in	ADP
ejpam-4821	398	17	h	h	NOUN
ejpam-4821	399	1	whenever	whenever	SCONJ
ejpam-4821	399	2	x	x	X
ejpam-4821	399	3	,	,	PUNCT
ejpam-4821	399	4	y	y	PROPN
ejpam-4821	399	5	∈	∈	PROPN
ejpam-4821	399	6	eq1(g	eq1(g	PROPN
ejpam-4821	399	7	)	)	PUNCT
ejpam-4821	399	8	;	;	PUNCT
ejpam-4821	399	9	and	and	CCONJ
ejpam-4821	399	10	g.cañete	g.cañete	PROPN
ejpam-4821	399	11	,	,	PUNCT
ejpam-4821	399	12	h.	h.	PROPN
ejpam-4821	399	13	rara	rara	PROPN
ejpam-4821	399	14	,	,	PUNCT
ejpam-4821	399	15	a.m.	a.m.	PROPN
ejpam-4821	399	16	mahistrado	mahistrado	PROPN
ejpam-4821	399	17	/	/	SYM
ejpam-4821	399	18	eur	eur	PROPN
ejpam-4821	399	19	.	.	PUNCT
ejpam-4821	400	1	j.	j.	PROPN
ejpam-4821	400	2	pure	pure	PROPN
ejpam-4821	400	3	appl	appl	PROPN
ejpam-4821	400	4	.	.	PROPN
ejpam-4821	400	5	math	math	PROPN
ejpam-4821	400	6	,	,	PUNCT
ejpam-4821	400	7	16	16	NUM
ejpam-4821	400	8	(	(	PUNCT
ejpam-4821	400	9	3	3	NUM
ejpam-4821	400	10	)	)	PUNCT
ejpam-4821	400	11	(	(	PUNCT
ejpam-4821	400	12	2023	2023	NUM
ejpam-4821	400	13	)	)	PUNCT
ejpam-4821	400	14	,	,	PUNCT
ejpam-4821	400	15	1647	1647	NUM
ejpam-4821	400	16	-	-	SYM
ejpam-4821	400	17	1662	1662	NUM
ejpam-4821	400	18	1659	1659	NUM
ejpam-4821	400	19	(	(	PUNCT
ejpam-4821	400	20	iv	iv	X
ejpam-4821	400	21	)	)	PUNCT
ejpam-4821	400	22	tx	tx	PROPN
ejpam-4821	400	23	and	and	CCONJ
ejpam-4821	400	24	ty	ty	INTJ
ejpam-4821	400	25	are	be	AUX
ejpam-4821	400	26	(	(	PUNCT
ejpam-4821	400	27	2	2	NUM
ejpam-4821	400	28	-	-	PUNCT
ejpam-4821	400	29	locating)dominating	locating)dominate	VERB
ejpam-4821	400	30	sets	set	NOUN
ejpam-4821	400	31	in	in	ADP
ejpam-4821	400	32	h	h	NOUN
ejpam-4821	400	33	or	or	CCONJ
ejpam-4821	400	34	one	one	NUM
ejpam-4821	400	35	of	of	ADP
ejpam-4821	400	36	tx	tx	PROPN
ejpam-4821	400	37	and	and	CCONJ
ejpam-4821	400	38	ty	ty	PRON
ejpam-4821	400	39	is	be	AUX
ejpam-4821	400	40	a	a	DET
ejpam-4821	400	41	2	2	NUM
ejpam-4821	400	42	-	-	PUNCT
ejpam-4821	400	43	dominating	dominating	NOUN
ejpam-4821	400	44	set	set	NOUN
ejpam-4821	400	45	whenever	whenever	SCONJ
ejpam-4821	400	46	x	x	X
ejpam-4821	400	47	,	,	PUNCT
ejpam-4821	400	48	y	y	PROPN
ejpam-4821	400	49	∈	∈	PROPN
ejpam-4821	400	50	eq2(g	eq2(g	VERB
ejpam-4821	400	51	)	)	PUNCT
ejpam-4821	400	52	.	.	PUNCT
ejpam-4821	401	1	theorem	theorem	ADJ
ejpam-4821	401	2	10	10	NUM
ejpam-4821	401	3	.	.	PUNCT
ejpam-4821	402	1	let	let	VERB
ejpam-4821	402	2	g	g	NOUN
ejpam-4821	402	3	and	and	CCONJ
ejpam-4821	402	4	h	h	NOUN
ejpam-4821	402	5	be	be	AUX
ejpam-4821	402	6	nontrivial	nontrivial	ADJ
ejpam-4821	402	7	connected	connect	VERB
ejpam-4821	402	8	graphs	graph	NOUN
ejpam-4821	402	9	with	with	ADP
ejpam-4821	402	10	∆(h	∆(h	NOUN
ejpam-4821	402	11	)	)	PUNCT
ejpam-4821	402	12	≤	≤	NOUN
ejpam-4821	402	13	|v	|v	X
ejpam-4821	402	14	(	(	PUNCT
ejpam-4821	402	15	h)|	h)|	NOUN
ejpam-4821	402	16	−	−	PROPN
ejpam-4821	402	17	3	3	NUM
ejpam-4821	402	18	.	.	PUNCT
ejpam-4821	403	1	then	then	ADV
ejpam-4821	403	2	w	w	PROPN
ejpam-4821	403	3	=	=	PUNCT
ejpam-4821	403	4	⋃	⋃	PROPN
ejpam-4821	403	5	x∈s	x∈s	NOUN
ejpam-4821	404	1	[	[	X
ejpam-4821	404	2	{	{	PUNCT
ejpam-4821	404	3	x}×tx	x}×tx	X
ejpam-4821	404	4	]	]	X
ejpam-4821	404	5	,	,	PUNCT
ejpam-4821	404	6	where	where	SCONJ
ejpam-4821	404	7	s	s	VERB
ejpam-4821	404	8	⊆	⊆	NUM
ejpam-4821	404	9	v	v	NOUN
ejpam-4821	404	10	(	(	PUNCT
ejpam-4821	404	11	g	g	NOUN
ejpam-4821	404	12	)	)	PUNCT
ejpam-4821	404	13	and	and	CCONJ
ejpam-4821	404	14	tx	tx	VERB
ejpam-4821	404	15	⊆	⊆	NUM
ejpam-4821	404	16	v	v	NOUN
ejpam-4821	404	17	(	(	PUNCT
ejpam-4821	404	18	h	h	NOUN
ejpam-4821	404	19	)	)	PUNCT
ejpam-4821	404	20	for	for	ADP
ejpam-4821	404	21	each	each	DET
ejpam-4821	404	22	x	x	SYM
ejpam-4821	404	23	∈	∈	PROPN
ejpam-4821	404	24	s	s	NOUN
ejpam-4821	404	25	,	,	PUNCT
ejpam-4821	404	26	is	be	AUX
ejpam-4821	404	27	a	a	DET
ejpam-4821	404	28	2	2	NUM
ejpam-4821	404	29	-	-	PUNCT
ejpam-4821	404	30	locating	locate	VERB
ejpam-4821	404	31	set	set	NOUN
ejpam-4821	404	32	in	in	ADP
ejpam-4821	404	33	g[h	g[h	PROPN
ejpam-4821	404	34	]	]	PUNCT
ejpam-4821	404	35	if	if	SCONJ
ejpam-4821	404	36	and	and	CCONJ
ejpam-4821	404	37	only	only	ADV
ejpam-4821	404	38	if	if	SCONJ
ejpam-4821	404	39	it	it	PRON
ejpam-4821	404	40	is	be	AUX
ejpam-4821	404	41	a	a	DET
ejpam-4821	404	42	2	2	NUM
ejpam-4821	404	43	-	-	PUNCT
ejpam-4821	404	44	resolving	resolve	VERB
ejpam-4821	404	45	set	set	NOUN
ejpam-4821	404	46	and	and	CCONJ
ejpam-4821	404	47	it	it	PRON
ejpam-4821	404	48	satisfies	satisfy	VERB
ejpam-4821	404	49	the	the	DET
ejpam-4821	404	50	following	following	NOUN
ejpam-4821	404	51	:	:	PUNCT
ejpam-4821	404	52	(	(	PUNCT
ejpam-4821	404	53	i	i	NOUN
ejpam-4821	404	54	)	)	PUNCT
ejpam-4821	404	55	s	s	PART
ejpam-4821	404	56	=	=	SYM
ejpam-4821	404	57	v	v	NOUN
ejpam-4821	404	58	(	(	PUNCT
ejpam-4821	404	59	g	g	NOUN
ejpam-4821	404	60	)	)	PUNCT
ejpam-4821	404	61	;	;	PUNCT
ejpam-4821	404	62	(	(	PUNCT
ejpam-4821	404	63	ii	ii	NOUN
ejpam-4821	404	64	)	)	PUNCT
ejpam-4821	404	65	tx	tx	PROPN
ejpam-4821	404	66	is	be	AUX
ejpam-4821	404	67	a	a	DET
ejpam-4821	404	68	2	2	NUM
ejpam-4821	404	69	-	-	PUNCT
ejpam-4821	404	70	locating	locate	VERB
ejpam-4821	404	71	set	set	NOUN
ejpam-4821	404	72	in	in	ADP
ejpam-4821	404	73	h	h	NOUN
ejpam-4821	404	74	for	for	ADP
ejpam-4821	404	75	every	every	DET
ejpam-4821	404	76	x	x	SYM
ejpam-4821	404	77	∈	∈	PROPN
ejpam-4821	404	78	v	v	NOUN
ejpam-4821	404	79	(	(	PUNCT
ejpam-4821	404	80	g	g	NOUN
ejpam-4821	404	81	)	)	PUNCT
ejpam-4821	404	82	;	;	PUNCT
ejpam-4821	404	83	(	(	PUNCT
ejpam-4821	404	84	iii	iii	X
ejpam-4821	404	85	)	)	PUNCT
ejpam-4821	404	86	tx	tx	NOUN
ejpam-4821	405	1	and	and	CCONJ
ejpam-4821	405	2	ty	ty	INTJ
ejpam-4821	405	3	is	be	AUX
ejpam-4821	405	4	a	a	DET
ejpam-4821	405	5	(	(	PUNCT
ejpam-4821	405	6	2	2	NUM
ejpam-4821	405	7	,	,	PUNCT
ejpam-4821	405	8	1)-locating	1)-locating	NUM
ejpam-4821	405	9	set	set	NOUN
ejpam-4821	405	10	or	or	CCONJ
ejpam-4821	405	11	one	one	NUM
ejpam-4821	405	12	of	of	ADP
ejpam-4821	405	13	tx	tx	PROPN
ejpam-4821	405	14	and	and	CCONJ
ejpam-4821	405	15	ty	ty	PRON
ejpam-4821	405	16	is	be	AUX
ejpam-4821	405	17	a	a	DET
ejpam-4821	405	18	(	(	PUNCT
ejpam-4821	405	19	2	2	NUM
ejpam-4821	405	20	,	,	PUNCT
ejpam-4821	405	21	2)-locating	2)-locating	NUM
ejpam-4821	405	22	set	set	VERB
ejpam-4821	405	23	in	in	ADP
ejpam-4821	405	24	h	h	NOUN
ejpam-4821	405	25	whenever	whenever	SCONJ
ejpam-4821	405	26	x	x	X
ejpam-4821	405	27	,	,	PUNCT
ejpam-4821	405	28	y	y	PROPN
ejpam-4821	405	29	∈	∈	PROPN
ejpam-4821	405	30	v	v	ADP
ejpam-4821	405	31	(	(	PUNCT
ejpam-4821	405	32	g	g	NOUN
ejpam-4821	405	33	)	)	PUNCT
ejpam-4821	405	34	with	with	ADP
ejpam-4821	405	35	ng[x	ng[x	PROPN
ejpam-4821	405	36	]	]	X
ejpam-4821	405	37	=	=	PUNCT
ejpam-4821	405	38	ng[y	ng[y	PROPN
ejpam-4821	405	39	]	]	X
ejpam-4821	405	40	;	;	PUNCT
ejpam-4821	405	41	and	and	CCONJ
ejpam-4821	405	42	(	(	PUNCT
ejpam-4821	405	43	iv	iv	X
ejpam-4821	405	44	)	)	PUNCT
ejpam-4821	405	45	tx	tx	PROPN
ejpam-4821	405	46	and	and	CCONJ
ejpam-4821	405	47	ty	ty	INTJ
ejpam-4821	405	48	are	be	AUX
ejpam-4821	405	49	(	(	PUNCT
ejpam-4821	405	50	2	2	NUM
ejpam-4821	405	51	−	−	NOUN
ejpam-4821	405	52	locating	locating	NOUN
ejpam-4821	405	53	)	)	PUNCT
ejpam-4821	405	54	dominating	dominating	NOUN
ejpam-4821	405	55	sets	set	NOUN
ejpam-4821	405	56	in	in	ADP
ejpam-4821	405	57	h	h	NOUN
ejpam-4821	405	58	or	or	CCONJ
ejpam-4821	405	59	one	one	NUM
ejpam-4821	405	60	of	of	ADP
ejpam-4821	405	61	tx	tx	PROPN
ejpam-4821	406	1	and	and	CCONJ
ejpam-4821	406	2	ty	ty	INTJ
ejpam-4821	406	3	is	be	AUX
ejpam-4821	406	4	a	a	DET
ejpam-4821	406	5	2dominating	2dominating	NUM
ejpam-4821	406	6	set	set	NOUN
ejpam-4821	406	7	whenever	whenever	SCONJ
ejpam-4821	406	8	x	x	X
ejpam-4821	406	9	,	,	PUNCT
ejpam-4821	406	10	y	y	PROPN
ejpam-4821	406	11	∈	∈	PROPN
ejpam-4821	406	12	v	v	ADP
ejpam-4821	406	13	(	(	PUNCT
ejpam-4821	406	14	g	g	NOUN
ejpam-4821	406	15	)	)	PUNCT
ejpam-4821	406	16	with	with	ADP
ejpam-4821	406	17	dg(x	dg(x	PROPN
ejpam-4821	406	18	,	,	PUNCT
ejpam-4821	406	19	y	y	NOUN
ejpam-4821	406	20	)	)	PUNCT
ejpam-4821	406	21	=	=	SYM
ejpam-4821	406	22	2	2	NUM
ejpam-4821	406	23	and	and	CCONJ
ejpam-4821	406	24	ng(x	ng(x	NUM
ejpam-4821	406	25	)	)	PUNCT
ejpam-4821	406	26	=	=	PUNCT
ejpam-4821	406	27	ng(y	ng(y	NOUN
ejpam-4821	406	28	)	)	PUNCT
ejpam-4821	406	29	.	.	PUNCT
ejpam-4821	407	1	proof	proof	NOUN
ejpam-4821	407	2	.	.	PUNCT
ejpam-4821	408	1	suppose	suppose	VERB
ejpam-4821	408	2	w	w	PROPN
ejpam-4821	408	3	=	=	PUNCT
ejpam-4821	408	4	⋃	⋃	PROPN
ejpam-4821	408	5	x∈s	x∈s	NOUN
ejpam-4821	408	6	[	[	PUNCT
ejpam-4821	408	7	{	{	PUNCT
ejpam-4821	408	8	x	x	NOUN
ejpam-4821	408	9	}	}	PUNCT
ejpam-4821	408	10	×	×	NOUN
ejpam-4821	408	11	tx	tx	PROPN
ejpam-4821	408	12	]	]	PUNCT
ejpam-4821	408	13	is	be	AUX
ejpam-4821	408	14	a	a	DET
ejpam-4821	408	15	2	2	NUM
ejpam-4821	408	16	-	-	PUNCT
ejpam-4821	408	17	locating	locate	VERB
ejpam-4821	408	18	set	set	NOUN
ejpam-4821	408	19	in	in	ADP
ejpam-4821	408	20	g[h	g[h	PROPN
ejpam-4821	408	21	]	]	PUNCT
ejpam-4821	408	22	.	.	PUNCT
ejpam-4821	409	1	suppose	suppose	VERB
ejpam-4821	409	2	there	there	PRON
ejpam-4821	409	3	exists	exist	VERB
ejpam-4821	409	4	x	x	X
ejpam-4821	409	5	∈	∈	PROPN
ejpam-4821	409	6	v	v	NOUN
ejpam-4821	409	7	(	(	PUNCT
ejpam-4821	409	8	g)\s	g)\s	NOUN
ejpam-4821	409	9	.	.	PUNCT
ejpam-4821	410	1	pick	pick	VERB
ejpam-4821	410	2	a	a	PRON
ejpam-4821	410	3	,	,	PUNCT
ejpam-4821	410	4	b	b	PROPN
ejpam-4821	410	5	∈	∈	PROPN
ejpam-4821	410	6	v	v	NOUN
ejpam-4821	410	7	(	(	PUNCT
ejpam-4821	410	8	h	h	NOUN
ejpam-4821	410	9	)	)	PUNCT
ejpam-4821	410	10	,	,	PUNCT
ejpam-4821	410	11	where	where	SCONJ
ejpam-4821	410	12	a	a	DET
ejpam-4821	410	13	̸=	̸=	PROPN
ejpam-4821	410	14	b.	b.	NOUN
ejpam-4821	410	15	then	then	ADV
ejpam-4821	410	16	(	(	PUNCT
ejpam-4821	410	17	x	x	X
ejpam-4821	410	18	,	,	PUNCT
ejpam-4821	410	19	a	a	PRON
ejpam-4821	410	20	)	)	PUNCT
ejpam-4821	410	21	,	,	PUNCT
ejpam-4821	410	22	(	(	PUNCT
ejpam-4821	410	23	x	x	NOUN
ejpam-4821	410	24	,	,	PUNCT
ejpam-4821	410	25	b	b	NOUN
ejpam-4821	410	26	)	)	PUNCT
ejpam-4821	410	27	/∈	/∈	PUNCT
ejpam-4821	411	1	w	w	NOUN
ejpam-4821	411	2	and	and	CCONJ
ejpam-4821	411	3	(	(	PUNCT
ejpam-4821	411	4	x	x	NOUN
ejpam-4821	411	5	,	,	PUNCT
ejpam-4821	411	6	a	a	PRON
ejpam-4821	411	7	)	)	PUNCT
ejpam-4821	411	8	̸=	̸=	PROPN
ejpam-4821	411	9	(	(	PUNCT
ejpam-4821	411	10	x	x	X
ejpam-4821	411	11	,	,	PUNCT
ejpam-4821	411	12	b	b	NOUN
ejpam-4821	411	13	)	)	PUNCT
ejpam-4821	411	14	.	.	PUNCT
ejpam-4821	412	1	since	since	SCONJ
ejpam-4821	412	2	x	x	PROPN
ejpam-4821	412	3	/∈	/∈	PROPN
ejpam-4821	412	4	s	s	PART
ejpam-4821	412	5	,	,	PUNCT
ejpam-4821	412	6	(	(	PUNCT
ejpam-4821	412	7	x	x	NOUN
ejpam-4821	412	8	,	,	PUNCT
ejpam-4821	412	9	r	r	NOUN
ejpam-4821	412	10	)	)	PUNCT
ejpam-4821	412	11	∈	∈	NOUN
ejpam-4821	412	12	v	v	NOUN
ejpam-4821	412	13	(	(	PUNCT
ejpam-4821	412	14	g[h	g[h	PROPN
ejpam-4821	412	15	]	]	PUNCT
ejpam-4821	412	16	)	)	PUNCT
ejpam-4821	412	17	\	\	PROPN
ejpam-4821	413	1	w	w	PROPN
ejpam-4821	413	2	.	.	PUNCT
ejpam-4821	414	1	note	note	VERB
ejpam-4821	414	2	that	that	SCONJ
ejpam-4821	414	3	(	(	PUNCT
ejpam-4821	414	4	z	z	X
ejpam-4821	414	5	,	,	PUNCT
ejpam-4821	414	6	c	c	NOUN
ejpam-4821	414	7	)	)	PUNCT
ejpam-4821	414	8	∈	∈	PROPN
ejpam-4821	414	9	ng[h](x	ng[h](x	PROPN
ejpam-4821	414	10	,	,	PUNCT
ejpam-4821	414	11	a	a	PRON
ejpam-4821	414	12	)	)	PUNCT
ejpam-4821	414	13	∪	∪	ADP
ejpam-4821	414	14	ng[h](x	ng[h](x	PROPN
ejpam-4821	414	15	,	,	PUNCT
ejpam-4821	414	16	b	b	NOUN
ejpam-4821	414	17	)	)	PUNCT
ejpam-4821	414	18	for	for	ADP
ejpam-4821	414	19	all	all	DET
ejpam-4821	414	20	z	z	NOUN
ejpam-4821	414	21	∈	∈	PROPN
ejpam-4821	414	22	ng(x	ng(x	NUM
ejpam-4821	414	23	)	)	PUNCT
ejpam-4821	414	24	.	.	PUNCT
ejpam-4821	415	1	thus	thus	ADV
ejpam-4821	415	2	,	,	PUNCT
ejpam-4821	415	3	ng[h](x	ng[h](x	PROPN
ejpam-4821	415	4	,	,	PUNCT
ejpam-4821	415	5	a	a	PRON
ejpam-4821	415	6	)	)	PUNCT
ejpam-4821	415	7	\ng[h](x	\ng[h](x	PROPN
ejpam-4821	415	8	,	,	PUNCT
ejpam-4821	415	9	b	b	NOUN
ejpam-4821	415	10	)	)	PUNCT
ejpam-4821	415	11	=	=	NOUN
ejpam-4821	415	12	∅	∅	NOUN
ejpam-4821	415	13	and	and	CCONJ
ejpam-4821	415	14	ng[h](x	ng[h](x	ADJ
ejpam-4821	415	15	,	,	PUNCT
ejpam-4821	415	16	b	b	NOUN
ejpam-4821	415	17	)	)	PUNCT
ejpam-4821	415	18	\ng[h](x	\ng[h](x	PROPN
ejpam-4821	415	19	,	,	PUNCT
ejpam-4821	415	20	a	a	PRON
ejpam-4821	415	21	)	)	PUNCT
ejpam-4821	415	22	=	=	PUNCT
ejpam-4821	415	23	∅.	∅.	ADP
ejpam-4821	415	24	this	this	PRON
ejpam-4821	415	25	implies	imply	VERB
ejpam-4821	415	26	that	that	SCONJ
ejpam-4821	415	27	w	w	NOUN
ejpam-4821	415	28	is	be	AUX
ejpam-4821	415	29	not	not	PART
ejpam-4821	415	30	a	a	DET
ejpam-4821	415	31	2	2	NUM
ejpam-4821	415	32	-	-	PUNCT
ejpam-4821	415	33	locating	locate	VERB
ejpam-4821	415	34	set	set	NOUN
ejpam-4821	415	35	of	of	ADP
ejpam-4821	415	36	g[h	g[h	PROPN
ejpam-4821	415	37	]	]	PUNCT
ejpam-4821	415	38	,	,	PUNCT
ejpam-4821	415	39	a	a	DET
ejpam-4821	415	40	contradiction	contradiction	NOUN
ejpam-4821	415	41	to	to	ADP
ejpam-4821	415	42	the	the	DET
ejpam-4821	415	43	assumption	assumption	NOUN
ejpam-4821	415	44	on	on	ADP
ejpam-4821	415	45	w	w	PROPN
ejpam-4821	415	46	.	.	PUNCT
ejpam-4821	416	1	therefore	therefore	ADV
ejpam-4821	416	2	,	,	PUNCT
ejpam-4821	416	3	s	s	VERB
ejpam-4821	416	4	=	=	SYM
ejpam-4821	416	5	v	v	X
ejpam-4821	416	6	(	(	PUNCT
ejpam-4821	416	7	g	g	NOUN
ejpam-4821	416	8	)	)	PUNCT
ejpam-4821	416	9	.	.	PUNCT
ejpam-4821	417	1	to	to	PART
ejpam-4821	417	2	prove	prove	VERB
ejpam-4821	417	3	(	(	PUNCT
ejpam-4821	417	4	ii	ii	NOUN
ejpam-4821	417	5	)	)	PUNCT
ejpam-4821	417	6	,	,	PUNCT
ejpam-4821	417	7	let	let	VERB
ejpam-4821	417	8	x	x	PUNCT
ejpam-4821	417	9	∈	∈	PROPN
ejpam-4821	417	10	v	v	X
ejpam-4821	417	11	(	(	PUNCT
ejpam-4821	417	12	g	g	NOUN
ejpam-4821	417	13	)	)	PUNCT
ejpam-4821	417	14	and	and	CCONJ
ejpam-4821	417	15	p	p	X
ejpam-4821	417	16	,	,	PUNCT
ejpam-4821	417	17	q	q	PROPN
ejpam-4821	417	18	∈	∈	PROPN
ejpam-4821	417	19	v	v	ADP
ejpam-4821	417	20	(	(	PUNCT
ejpam-4821	417	21	h	h	NOUN
ejpam-4821	417	22	)	)	PUNCT
ejpam-4821	417	23	where	where	SCONJ
ejpam-4821	417	24	p	p	PROPN
ejpam-4821	417	25	̸=	̸=	PROPN
ejpam-4821	417	26	q.	q.	NOUN
ejpam-4821	417	27	then	then	ADV
ejpam-4821	417	28	(	(	PUNCT
ejpam-4821	417	29	x	x	X
ejpam-4821	417	30	,	,	PUNCT
ejpam-4821	417	31	p	p	NOUN
ejpam-4821	417	32	)	)	PUNCT
ejpam-4821	417	33	̸=	̸=	PROPN
ejpam-4821	417	34	(	(	PUNCT
ejpam-4821	417	35	x	x	X
ejpam-4821	417	36	,	,	PUNCT
ejpam-4821	417	37	q	q	NOUN
ejpam-4821	417	38	)	)	PUNCT
ejpam-4821	417	39	.	.	PUNCT
ejpam-4821	418	1	if	if	SCONJ
ejpam-4821	418	2	p	p	X
ejpam-4821	418	3	,	,	PUNCT
ejpam-4821	418	4	q	q	NOUN
ejpam-4821	418	5	/∈	/∈	PUNCT
ejpam-4821	419	1	tx	tx	INTJ
ejpam-4821	419	2	or	or	CCONJ
ejpam-4821	419	3	[	[	X
ejpam-4821	419	4	p	p	X
ejpam-4821	419	5	∈	∈	PROPN
ejpam-4821	419	6	tx	tx	NOUN
ejpam-4821	419	7	and	and	CCONJ
ejpam-4821	419	8	q	q	NOUN
ejpam-4821	419	9	/∈	/∈	PUNCT
ejpam-4821	420	1	tx	tx	PROPN
ejpam-4821	420	2	]	]	PUNCT
ejpam-4821	420	3	,	,	PUNCT
ejpam-4821	420	4	then	then	ADV
ejpam-4821	420	5	(	(	PUNCT
ejpam-4821	420	6	x	x	X
ejpam-4821	420	7	,	,	PUNCT
ejpam-4821	420	8	p	p	NOUN
ejpam-4821	420	9	)	)	PUNCT
ejpam-4821	420	10	,	,	PUNCT
ejpam-4821	420	11	(	(	PUNCT
ejpam-4821	420	12	x	x	X
ejpam-4821	420	13	,	,	PUNCT
ejpam-4821	420	14	q	q	NOUN
ejpam-4821	420	15	)	)	PUNCT
ejpam-4821	420	16	/∈	/∈	PUNCT
ejpam-4821	421	1	w	w	NOUN
ejpam-4821	421	2	or	or	CCONJ
ejpam-4821	421	3	[	[	X
ejpam-4821	421	4	(	(	PUNCT
ejpam-4821	421	5	x	x	X
ejpam-4821	421	6	,	,	PUNCT
ejpam-4821	421	7	p	p	NOUN
ejpam-4821	421	8	)	)	PUNCT
ejpam-4821	421	9	∈	∈	PROPN
ejpam-4821	421	10	w	w	NOUN
ejpam-4821	421	11	and	and	CCONJ
ejpam-4821	421	12	(	(	PUNCT
ejpam-4821	421	13	x	x	NOUN
ejpam-4821	421	14	,	,	PUNCT
ejpam-4821	421	15	q	q	NOUN
ejpam-4821	421	16	)	)	PUNCT
ejpam-4821	421	17	/∈	/∈	PUNCT
ejpam-4821	422	1	w	w	NOUN
ejpam-4821	422	2	]	]	X
ejpam-4821	422	3	.	.	PUNCT
ejpam-4821	423	1	since	since	SCONJ
ejpam-4821	423	2	w	w	PROPN
ejpam-4821	423	3	is	be	AUX
ejpam-4821	423	4	a	a	DET
ejpam-4821	423	5	2	2	NUM
ejpam-4821	423	6	-	-	PUNCT
ejpam-4821	423	7	locating	locate	VERB
ejpam-4821	423	8	set	set	NOUN
ejpam-4821	423	9	in	in	ADP
ejpam-4821	423	10	g[h	g[h	PROPN
ejpam-4821	423	11	]	]	PUNCT
ejpam-4821	423	12	,	,	PUNCT
ejpam-4821	423	13	by	by	ADP
ejpam-4821	423	14	definition	definition	NOUN
ejpam-4821	423	15	of	of	ADP
ejpam-4821	423	16	g[h	g[h	PROPN
ejpam-4821	423	17	]	]	PUNCT
ejpam-4821	423	18	there	there	PRON
ejpam-4821	423	19	exist	exist	VERB
ejpam-4821	423	20	at	at	ADV
ejpam-4821	423	21	least	least	ADV
ejpam-4821	423	22	two	two	NUM
ejpam-4821	423	23	vertices	vertex	NOUN
ejpam-4821	423	24	(	(	PUNCT
ejpam-4821	423	25	x	x	X
ejpam-4821	423	26	,	,	PUNCT
ejpam-4821	423	27	r	r	NOUN
ejpam-4821	423	28	)	)	PUNCT
ejpam-4821	423	29	,	,	PUNCT
ejpam-4821	423	30	(	(	PUNCT
ejpam-4821	423	31	x	x	NOUN
ejpam-4821	423	32	,	,	PUNCT
ejpam-4821	423	33	s	s	PART
ejpam-4821	423	34	)	)	PUNCT
ejpam-4821	423	35	∈	∈	NOUN
ejpam-4821	423	36	v	v	ADP
ejpam-4821	423	37	(	(	PUNCT
ejpam-4821	423	38	h	h	NOUN
ejpam-4821	423	39	)	)	PUNCT
ejpam-4821	423	40	∩	∩	NOUN
ejpam-4821	423	41	tx	tx	VERB
ejpam-4821	423	42	such	such	ADJ
ejpam-4821	423	43	that	that	SCONJ
ejpam-4821	423	44	either	either	ADV
ejpam-4821	423	45	(	(	PUNCT
ejpam-4821	423	46	x	x	NOUN
ejpam-4821	423	47	,	,	PUNCT
ejpam-4821	423	48	r	r	NOUN
ejpam-4821	423	49	)	)	PUNCT
ejpam-4821	423	50	,	,	PUNCT
ejpam-4821	423	51	(	(	PUNCT
ejpam-4821	423	52	x	x	NOUN
ejpam-4821	423	53	,	,	PUNCT
ejpam-4821	423	54	s	s	PART
ejpam-4821	423	55	)	)	PUNCT
ejpam-4821	423	56	∈	∈	PROPN
ejpam-4821	423	57	nh((x	nh((x	NOUN
ejpam-4821	423	58	,	,	PUNCT
ejpam-4821	423	59	p))\nh((x	p))\nh((x	NOUN
ejpam-4821	423	60	,	,	PUNCT
ejpam-4821	423	61	q	q	NOUN
ejpam-4821	423	62	)	)	PUNCT
ejpam-4821	423	63	)	)	PUNCT
ejpam-4821	423	64	or	or	CCONJ
ejpam-4821	423	65	(	(	PUNCT
ejpam-4821	423	66	x	x	X
ejpam-4821	423	67	,	,	PUNCT
ejpam-4821	423	68	r	r	NOUN
ejpam-4821	423	69	)	)	PUNCT
ejpam-4821	423	70	,	,	PUNCT
ejpam-4821	423	71	(	(	PUNCT
ejpam-4821	423	72	x	x	NOUN
ejpam-4821	423	73	,	,	PUNCT
ejpam-4821	423	74	s	s	PART
ejpam-4821	423	75	)	)	PUNCT
ejpam-4821	423	76	∈	∈	PROPN
ejpam-4821	423	77	nh((x	nh((x	NOUN
ejpam-4821	423	78	,	,	PUNCT
ejpam-4821	423	79	q))\nh((x	q))\nh((x	NOUN
ejpam-4821	423	80	,	,	PUNCT
ejpam-4821	423	81	p	p	NOUN
ejpam-4821	423	82	)	)	PUNCT
ejpam-4821	423	83	)	)	PUNCT
ejpam-4821	423	84	or	or	CCONJ
ejpam-4821	423	85	(	(	PUNCT
ejpam-4821	423	86	x	x	NOUN
ejpam-4821	423	87	,	,	PUNCT
ejpam-4821	423	88	r	r	NOUN
ejpam-4821	423	89	)	)	PUNCT
ejpam-4821	423	90	∈	∈	NOUN
ejpam-4821	423	91	nh((x	nh((x	NOUN
ejpam-4821	423	92	,	,	PUNCT
ejpam-4821	423	93	p))\nh((x	p))\nh((x	NOUN
ejpam-4821	423	94	,	,	PUNCT
ejpam-4821	423	95	q	q	NOUN
ejpam-4821	423	96	)	)	PUNCT
ejpam-4821	423	97	)	)	PUNCT
ejpam-4821	423	98	and	and	CCONJ
ejpam-4821	423	99	(	(	PUNCT
ejpam-4821	423	100	x	x	NOUN
ejpam-4821	423	101	,	,	PUNCT
ejpam-4821	423	102	s	s	PART
ejpam-4821	423	103	)	)	PUNCT
ejpam-4821	423	104	∈	∈	PROPN
ejpam-4821	423	105	nh((x	nh((x	NOUN
ejpam-4821	423	106	,	,	PUNCT
ejpam-4821	423	107	q))\nh((x	q))\nh((x	NOUN
ejpam-4821	423	108	,	,	PUNCT
ejpam-4821	423	109	p	p	NOUN
ejpam-4821	423	110	)	)	PUNCT
ejpam-4821	423	111	)	)	PUNCT
ejpam-4821	423	112	.	.	PUNCT
ejpam-4821	424	1	similarly	similarly	ADV
ejpam-4821	424	2	,	,	PUNCT
ejpam-4821	424	3	if	if	SCONJ
ejpam-4821	424	4	(	(	PUNCT
ejpam-4821	424	5	x	x	NOUN
ejpam-4821	424	6	,	,	PUNCT
ejpam-4821	424	7	p	p	NOUN
ejpam-4821	424	8	)	)	PUNCT
ejpam-4821	424	9	∈	∈	PROPN
ejpam-4821	424	10	w	w	NOUN
ejpam-4821	424	11	and	and	CCONJ
ejpam-4821	424	12	(	(	PUNCT
ejpam-4821	424	13	x	x	NOUN
ejpam-4821	424	14	,	,	PUNCT
ejpam-4821	424	15	q	q	NOUN
ejpam-4821	424	16	)	)	PUNCT
ejpam-4821	424	17	/∈	/∈	PUNCT
ejpam-4821	425	1	w	w	NOUN
ejpam-4821	425	2	,	,	PUNCT
ejpam-4821	425	3	then	then	ADV
ejpam-4821	425	4	there	there	PRON
ejpam-4821	425	5	exists	exist	VERB
ejpam-4821	425	6	a	a	DET
ejpam-4821	425	7	vertex	vertex	NOUN
ejpam-4821	425	8	t	t	X
ejpam-4821	425	9	∈	∈	PROPN
ejpam-4821	425	10	v	v	ADP
ejpam-4821	425	11	(	(	PUNCT
ejpam-4821	425	12	h	h	NOUN
ejpam-4821	425	13	)	)	PUNCT
ejpam-4821	425	14	∩	∩	NOUN
ejpam-4821	425	15	tx	tx	VERB
ejpam-4821	425	16	such	such	ADJ
ejpam-4821	425	17	that	that	SCONJ
ejpam-4821	425	18	(	(	PUNCT
ejpam-4821	425	19	x	x	NOUN
ejpam-4821	425	20	,	,	PUNCT
ejpam-4821	425	21	t	t	PROPN
ejpam-4821	425	22	)	)	PUNCT
ejpam-4821	425	23	∈	∈	PROPN
ejpam-4821	425	24	nh((x	nh((x	NOUN
ejpam-4821	425	25	,	,	PUNCT
ejpam-4821	425	26	p))\nh((x	p))\nh((x	NOUN
ejpam-4821	425	27	,	,	PUNCT
ejpam-4821	425	28	q	q	NOUN
ejpam-4821	425	29	)	)	PUNCT
ejpam-4821	425	30	)	)	PUNCT
ejpam-4821	425	31	or	or	CCONJ
ejpam-4821	425	32	(	(	PUNCT
ejpam-4821	425	33	x	x	NOUN
ejpam-4821	425	34	,	,	PUNCT
ejpam-4821	425	35	t	t	PROPN
ejpam-4821	425	36	)	)	PUNCT
ejpam-4821	425	37	∈	∈	PROPN
ejpam-4821	425	38	nh((x	nh((x	NOUN
ejpam-4821	425	39	,	,	PUNCT
ejpam-4821	425	40	q))\nh((x	q))\nh((x	NOUN
ejpam-4821	425	41	,	,	PUNCT
ejpam-4821	425	42	p	p	NOUN
ejpam-4821	425	43	)	)	PUNCT
ejpam-4821	425	44	)	)	PUNCT
ejpam-4821	425	45	.	.	PUNCT
ejpam-4821	426	1	therefore	therefore	ADV
ejpam-4821	426	2	,	,	PUNCT
ejpam-4821	426	3	it	it	PRON
ejpam-4821	426	4	follows	follow	VERB
ejpam-4821	426	5	that	that	SCONJ
ejpam-4821	426	6	tx	tx	PROPN
ejpam-4821	426	7	is	be	AUX
ejpam-4821	426	8	a	a	DET
ejpam-4821	426	9	2	2	NUM
ejpam-4821	426	10	-	-	PUNCT
ejpam-4821	426	11	locating	locate	VERB
ejpam-4821	426	12	set	set	NOUN
ejpam-4821	426	13	of	of	ADP
ejpam-4821	426	14	h	h	NOUN
ejpam-4821	426	15	for	for	ADP
ejpam-4821	426	16	every	every	DET
ejpam-4821	426	17	x	x	SYM
ejpam-4821	426	18	∈	∈	PROPN
ejpam-4821	426	19	v	v	NOUN
ejpam-4821	426	20	(	(	PUNCT
ejpam-4821	426	21	g	g	NOUN
ejpam-4821	426	22	)	)	PUNCT
ejpam-4821	426	23	.	.	PUNCT
ejpam-4821	427	1	thus	thus	ADV
ejpam-4821	427	2	,	,	PUNCT
ejpam-4821	427	3	(	(	PUNCT
ejpam-4821	427	4	ii	ii	NOUN
ejpam-4821	427	5	)	)	PUNCT
ejpam-4821	427	6	follows	follow	VERB
ejpam-4821	427	7	.	.	PUNCT
ejpam-4821	428	1	to	to	PART
ejpam-4821	428	2	prove	prove	VERB
ejpam-4821	428	3	(	(	PUNCT
ejpam-4821	428	4	iii	iii	NOUN
ejpam-4821	428	5	)	)	PUNCT
ejpam-4821	428	6	,	,	PUNCT
ejpam-4821	428	7	let	let	VERB
ejpam-4821	428	8	x	x	PRON
ejpam-4821	428	9	,	,	PUNCT
ejpam-4821	428	10	y	y	PROPN
ejpam-4821	428	11	∈	∈	PROPN
ejpam-4821	428	12	v	v	ADP
ejpam-4821	428	13	(	(	PUNCT
ejpam-4821	428	14	g	g	NOUN
ejpam-4821	428	15	)	)	PUNCT
ejpam-4821	428	16	with	with	ADP
ejpam-4821	428	17	ng[x	ng[x	PROPN
ejpam-4821	428	18	]	]	X
ejpam-4821	428	19	=	=	PUNCT
ejpam-4821	428	20	ng[y	ng[y	PROPN
ejpam-4821	428	21	]	]	PUNCT
ejpam-4821	428	22	.	.	PUNCT
ejpam-4821	429	1	let	let	VERB
ejpam-4821	429	2	a	a	DET
ejpam-4821	429	3	,	,	PUNCT
ejpam-4821	429	4	b	b	PROPN
ejpam-4821	429	5	∈	∈	PROPN
ejpam-4821	429	6	v	v	NOUN
ejpam-4821	429	7	(	(	PUNCT
ejpam-4821	429	8	h	h	NOUN
ejpam-4821	429	9	)	)	PUNCT
ejpam-4821	429	10	,	,	PUNCT
ejpam-4821	429	11	a	a	DET
ejpam-4821	429	12	̸=	̸=	PROPN
ejpam-4821	429	13	b.	b.	NOUN
ejpam-4821	429	14	since	since	SCONJ
ejpam-4821	429	15	w	w	PROPN
ejpam-4821	429	16	is	be	AUX
ejpam-4821	429	17	a	a	DET
ejpam-4821	429	18	2	2	NUM
ejpam-4821	429	19	-	-	PUNCT
ejpam-4821	429	20	locating	locate	VERB
ejpam-4821	429	21	set	set	NOUN
ejpam-4821	429	22	,	,	PUNCT
ejpam-4821	429	23	it	it	PRON
ejpam-4821	429	24	is	be	AUX
ejpam-4821	429	25	not	not	PART
ejpam-4821	429	26	possible	possible	ADJ
ejpam-4821	429	27	that	that	SCONJ
ejpam-4821	429	28	nh(a	nh(a	NUM
ejpam-4821	429	29	)	)	PUNCT
ejpam-4821	429	30	∩	∩	NOUN
ejpam-4821	429	31	tx	tx	PROPN
ejpam-4821	429	32	=	=	PUNCT
ejpam-4821	429	33	tx	tx	PROPN
ejpam-4821	429	34	and	and	CCONJ
ejpam-4821	429	35	nh(b	nh(b	NOUN
ejpam-4821	429	36	)	)	PUNCT
ejpam-4821	429	37	∩	∩	NOUN
ejpam-4821	430	1	ty	ty	INTJ
ejpam-4821	430	2	=	=	SYM
ejpam-4821	430	3	ty	ty	INTJ
ejpam-4821	430	4	.	.	PUNCT
ejpam-4821	431	1	if	if	SCONJ
ejpam-4821	431	2	tx	tx	PROPN
ejpam-4821	431	3	or	or	CCONJ
ejpam-4821	431	4	ty	ty	INTJ
ejpam-4821	431	5	is	be	AUX
ejpam-4821	431	6	(	(	PUNCT
ejpam-4821	431	7	2	2	NUM
ejpam-4821	431	8	,	,	PUNCT
ejpam-4821	431	9	2)-locating	2)-locating	NUM
ejpam-4821	431	10	,	,	PUNCT
ejpam-4821	431	11	then	then	ADV
ejpam-4821	431	12	we	we	PRON
ejpam-4821	431	13	are	be	AUX
ejpam-4821	431	14	done	do	VERB
ejpam-4821	431	15	.	.	PUNCT
ejpam-4821	432	1	otherwise	otherwise	ADV
ejpam-4821	432	2	,	,	PUNCT
ejpam-4821	432	3	tx	tx	PROPN
ejpam-4821	432	4	and	and	CCONJ
ejpam-4821	432	5	ty	ty	INTJ
ejpam-4821	432	6	are	be	AUX
ejpam-4821	432	7	(	(	PUNCT
ejpam-4821	432	8	2	2	NUM
ejpam-4821	432	9	,	,	PUNCT
ejpam-4821	432	10	1)-locating	1)-locating	NUM
ejpam-4821	432	11	.	.	PUNCT
ejpam-4821	433	1	to	to	PART
ejpam-4821	433	2	prove	prove	VERB
ejpam-4821	433	3	(	(	PUNCT
ejpam-4821	433	4	iv	iv	NUM
ejpam-4821	433	5	)	)	PUNCT
ejpam-4821	433	6	,	,	PUNCT
ejpam-4821	433	7	let	let	VERB
ejpam-4821	433	8	x	x	PRON
ejpam-4821	433	9	,	,	PUNCT
ejpam-4821	433	10	y	y	PROPN
ejpam-4821	433	11	∈	∈	PROPN
ejpam-4821	433	12	v	v	ADP
ejpam-4821	433	13	(	(	PUNCT
ejpam-4821	433	14	g	g	NOUN
ejpam-4821	433	15	)	)	PUNCT
ejpam-4821	433	16	where	where	SCONJ
ejpam-4821	433	17	dg(x	dg(x	NUM
ejpam-4821	433	18	,	,	PUNCT
ejpam-4821	433	19	y	y	NOUN
ejpam-4821	433	20	)	)	PUNCT
ejpam-4821	433	21	=	=	SYM
ejpam-4821	433	22	2	2	NUM
ejpam-4821	433	23	and	and	CCONJ
ejpam-4821	433	24	ng(x	ng(x	NUM
ejpam-4821	433	25	)	)	PUNCT
ejpam-4821	433	26	=	=	PUNCT
ejpam-4821	434	1	ng(y	ng(y	NOUN
ejpam-4821	434	2	)	)	PUNCT
ejpam-4821	434	3	.	.	PUNCT
ejpam-4821	435	1	let	let	VERB
ejpam-4821	435	2	a	a	DET
ejpam-4821	435	3	,	,	PUNCT
ejpam-4821	435	4	b	b	PROPN
ejpam-4821	435	5	∈	∈	PROPN
ejpam-4821	435	6	v	v	NOUN
ejpam-4821	435	7	(	(	PUNCT
ejpam-4821	435	8	h	h	NOUN
ejpam-4821	435	9	)	)	PUNCT
ejpam-4821	435	10	,	,	PUNCT
ejpam-4821	435	11	a	a	DET
ejpam-4821	435	12	̸=	̸=	PROPN
ejpam-4821	435	13	b.	b.	PROPN
ejpam-4821	435	14	suppose	suppose	VERB
ejpam-4821	435	15	one	one	NUM
ejpam-4821	435	16	of	of	ADP
ejpam-4821	435	17	tx	tx	PROPN
ejpam-4821	435	18	and	and	CCONJ
ejpam-4821	435	19	ty	ty	INTJ
ejpam-4821	435	20	,	,	PUNCT
ejpam-4821	435	21	say	say	VERB
ejpam-4821	435	22	tx	tx	PROPN
ejpam-4821	435	23	is	be	AUX
ejpam-4821	435	24	not	not	PART
ejpam-4821	435	25	a	a	DET
ejpam-4821	435	26	dominating	dominating	NOUN
ejpam-4821	435	27	set	set	NOUN
ejpam-4821	435	28	in	in	ADP
ejpam-4821	435	29	h.	h.	PROPN
ejpam-4821	435	30	pick	pick	VERB
ejpam-4821	435	31	a	a	DET
ejpam-4821	435	32	∈	∈	PROPN
ejpam-4821	435	33	v	v	NOUN
ejpam-4821	435	34	(	(	PUNCT
ejpam-4821	435	35	h)\nh	h)\nh	PROPN
ejpam-4821	436	1	[	[	X
ejpam-4821	436	2	tx	tx	X
ejpam-4821	436	3	]	]	PUNCT
ejpam-4821	436	4	and	and	CCONJ
ejpam-4821	436	5	let	let	VERB
ejpam-4821	436	6	b	b	X
ejpam-4821	436	7	∈	∈	PROPN
ejpam-4821	436	8	v	v	X
ejpam-4821	436	9	(	(	PUNCT
ejpam-4821	436	10	h)\ty	h)\ty	PROPN
ejpam-4821	436	11	.	.	PUNCT
ejpam-4821	437	1	since	since	SCONJ
ejpam-4821	437	2	dg[h]((x	dg[h]((x	PROPN
ejpam-4821	437	3	,	,	PUNCT
ejpam-4821	437	4	a	a	PRON
ejpam-4821	437	5	)	)	PUNCT
ejpam-4821	437	6	,	,	PUNCT
ejpam-4821	437	7	(	(	PUNCT
ejpam-4821	437	8	y	y	PROPN
ejpam-4821	437	9	,	,	PUNCT
ejpam-4821	437	10	b	b	NOUN
ejpam-4821	437	11	)	)	PUNCT
ejpam-4821	437	12	)	)	PUNCT
ejpam-4821	437	13	=	=	SYM
ejpam-4821	437	14	2	2	NUM
ejpam-4821	437	15	,	,	PUNCT
ejpam-4821	437	16	for	for	ADP
ejpam-4821	437	17	all	all	DET
ejpam-4821	437	18	(	(	PUNCT
ejpam-4821	437	19	y	y	PROPN
ejpam-4821	437	20	,	,	PUNCT
ejpam-4821	437	21	b	b	NOUN
ejpam-4821	437	22	)	)	PUNCT
ejpam-4821	437	23	,	,	PUNCT
ejpam-4821	437	24	it	it	PRON
ejpam-4821	437	25	follows	follow	VERB
ejpam-4821	437	26	that	that	PRON
ejpam-4821	437	27	|nh(b	|nh(b	NOUN
ejpam-4821	437	28	)	)	PUNCT
ejpam-4821	437	29	∩	∩	NOUN
ejpam-4821	437	30	ty|	ty|	PRON
ejpam-4821	437	31	≥	≥	NUM
ejpam-4821	437	32	2	2	NUM
ejpam-4821	437	33	,	,	PUNCT
ejpam-4821	437	34	i.e.	i.e.	X
ejpam-4821	437	35	,	,	PUNCT
ejpam-4821	437	36	ty	ty	INTJ
ejpam-4821	437	37	is	be	AUX
ejpam-4821	437	38	a	a	DET
ejpam-4821	437	39	2	2	NUM
ejpam-4821	437	40	-	-	PUNCT
ejpam-4821	437	41	dominating	dominating	NOUN
ejpam-4821	437	42	set	set	NOUN
ejpam-4821	437	43	.	.	PUNCT
ejpam-4821	438	1	conversely	conversely	ADV
ejpam-4821	438	2	,	,	PUNCT
ejpam-4821	438	3	let	let	VERB
ejpam-4821	438	4	w	w	NOUN
ejpam-4821	438	5	be	be	AUX
ejpam-4821	438	6	the	the	DET
ejpam-4821	438	7	set	set	NOUN
ejpam-4821	438	8	as	as	SCONJ
ejpam-4821	438	9	described	describe	VERB
ejpam-4821	438	10	and	and	CCONJ
ejpam-4821	438	11	satisfies	satisfy	VERB
ejpam-4821	438	12	the	the	DET
ejpam-4821	438	13	given	give	VERB
ejpam-4821	438	14	conditions	condition	NOUN
ejpam-4821	438	15	.	.	PUNCT
ejpam-4821	439	1	let	let	VERB
ejpam-4821	439	2	(	(	PUNCT
ejpam-4821	439	3	x	x	X
ejpam-4821	439	4	,	,	PUNCT
ejpam-4821	439	5	a	a	PRON
ejpam-4821	439	6	)	)	PUNCT
ejpam-4821	439	7	,	,	PUNCT
ejpam-4821	439	8	(	(	PUNCT
ejpam-4821	439	9	y	y	PROPN
ejpam-4821	439	10	,	,	PUNCT
ejpam-4821	439	11	b	b	NOUN
ejpam-4821	439	12	)	)	PUNCT
ejpam-4821	439	13	∈	∈	NOUN
ejpam-4821	439	14	v	v	NOUN
ejpam-4821	439	15	(	(	PUNCT
ejpam-4821	439	16	g[h	g[h	PROPN
ejpam-4821	439	17	]	]	PUNCT
ejpam-4821	439	18	)	)	PUNCT
ejpam-4821	439	19	,	,	PUNCT
ejpam-4821	439	20	(	(	PUNCT
ejpam-4821	439	21	x	x	X
ejpam-4821	439	22	,	,	PUNCT
ejpam-4821	439	23	a	a	PRON
ejpam-4821	439	24	)	)	PUNCT
ejpam-4821	439	25	̸=	̸=	PROPN
ejpam-4821	439	26	(	(	PUNCT
ejpam-4821	439	27	y	y	PROPN
ejpam-4821	439	28	,	,	PUNCT
ejpam-4821	439	29	b	b	NOUN
ejpam-4821	439	30	)	)	PUNCT
ejpam-4821	439	31	.	.	PUNCT
ejpam-4821	440	1	consider	consider	VERB
ejpam-4821	440	2	the	the	DET
ejpam-4821	440	3	following	follow	VERB
ejpam-4821	440	4	cases	case	NOUN
ejpam-4821	440	5	.	.	PUNCT
ejpam-4821	441	1	case	case	NOUN
ejpam-4821	441	2	1	1	NUM
ejpam-4821	441	3	.	.	PUNCT
ejpam-4821	441	4	x	x	NOUN
ejpam-4821	442	1	=	=	SYM
ejpam-4821	442	2	y	y	PROPN
ejpam-4821	442	3	suppose	suppose	VERB
ejpam-4821	442	4	(	(	PUNCT
ejpam-4821	442	5	x	x	X
ejpam-4821	442	6	,	,	PUNCT
ejpam-4821	442	7	a	a	PRON
ejpam-4821	442	8	)	)	PUNCT
ejpam-4821	442	9	,	,	PUNCT
ejpam-4821	442	10	(	(	PUNCT
ejpam-4821	442	11	y	y	NOUN
ejpam-4821	442	12	,	,	PUNCT
ejpam-4821	442	13	b	b	NOUN
ejpam-4821	442	14	)	)	PUNCT
ejpam-4821	442	15	/∈	/∈	PUNCT
ejpam-4821	443	1	w	w	INTJ
ejpam-4821	443	2	.	.	PUNCT
ejpam-4821	444	1	then	then	ADV
ejpam-4821	444	2	a	a	DET
ejpam-4821	444	3	̸=	̸=	PROPN
ejpam-4821	444	4	b	b	PROPN
ejpam-4821	444	5	and	and	CCONJ
ejpam-4821	444	6	a	a	DET
ejpam-4821	444	7	,	,	PUNCT
ejpam-4821	444	8	b	b	PROPN
ejpam-4821	444	9	/∈	/∈	PUNCT
ejpam-4821	445	1	tx	tx	PROPN
ejpam-4821	446	1	=	=	SYM
ejpam-4821	447	1	ty	ty	INTJ
ejpam-4821	447	2	.	.	PUNCT
ejpam-4821	448	1	by	by	ADP
ejpam-4821	448	2	(	(	PUNCT
ejpam-4821	448	3	ii	ii	NOUN
ejpam-4821	448	4	)	)	PUNCT
ejpam-4821	448	5	,	,	PUNCT
ejpam-4821	448	6	tx	tx	PROPN
ejpam-4821	448	7	is	be	AUX
ejpam-4821	448	8	a	a	DET
ejpam-4821	448	9	2	2	NUM
ejpam-4821	448	10	-	-	PUNCT
ejpam-4821	448	11	locating	locate	VERB
ejpam-4821	448	12	set	set	NOUN
ejpam-4821	448	13	.	.	PUNCT
ejpam-4821	449	1	on	on	ADP
ejpam-4821	449	2	the	the	DET
ejpam-4821	449	3	other	other	ADJ
ejpam-4821	449	4	hand	hand	NOUN
ejpam-4821	449	5	,	,	PUNCT
ejpam-4821	449	6	if	if	SCONJ
ejpam-4821	449	7	(	(	PUNCT
ejpam-4821	449	8	x	x	NOUN
ejpam-4821	449	9	,	,	PUNCT
ejpam-4821	449	10	a	a	PRON
ejpam-4821	449	11	)	)	PUNCT
ejpam-4821	449	12	∈	∈	PROPN
ejpam-4821	449	13	w	w	PROPN
ejpam-4821	449	14	,	,	PUNCT
ejpam-4821	449	15	(	(	PUNCT
ejpam-4821	449	16	y	y	PROPN
ejpam-4821	449	17	,	,	PUNCT
ejpam-4821	449	18	b	b	NOUN
ejpam-4821	449	19	)	)	PUNCT
ejpam-4821	449	20	/∈	/∈	PUNCT
ejpam-4821	450	1	w	w	NOUN
ejpam-4821	450	2	,	,	PUNCT
ejpam-4821	450	3	then	then	ADV
ejpam-4821	450	4	a	a	DET
ejpam-4821	450	5	∈	∈	PROPN
ejpam-4821	450	6	tx	tx	PROPN
ejpam-4821	450	7	,	,	PUNCT
ejpam-4821	450	8	b	b	PROPN
ejpam-4821	450	9	/∈	/∈	PROPN
ejpam-4821	451	1	ty	ty	INTJ
ejpam-4821	451	2	.	.	PUNCT
ejpam-4821	452	1	since	since	SCONJ
ejpam-4821	452	2	tx	tx	PROPN
ejpam-4821	452	3	is	be	AUX
ejpam-4821	452	4	a	a	DET
ejpam-4821	452	5	2	2	NUM
ejpam-4821	452	6	-	-	PUNCT
ejpam-4821	452	7	locating	locate	VERB
ejpam-4821	452	8	set	set	NOUN
ejpam-4821	452	9	,	,	PUNCT
ejpam-4821	452	10	there	there	PRON
ejpam-4821	452	11	exists	exist	VERB
ejpam-4821	452	12	(	(	PUNCT
ejpam-4821	452	13	x	x	X
ejpam-4821	452	14	,	,	PUNCT
ejpam-4821	452	15	s	s	PART
ejpam-4821	452	16	)	)	PUNCT
ejpam-4821	452	17	∈	∈	NOUN
ejpam-4821	452	18	v	v	ADP
ejpam-4821	452	19	(	(	PUNCT
ejpam-4821	452	20	h	h	NOUN
ejpam-4821	452	21	)	)	PUNCT
ejpam-4821	452	22	∩	∩	NOUN
ejpam-4821	452	23	tx	tx	VERB
ejpam-4821	452	24	such	such	ADJ
ejpam-4821	452	25	that	that	SCONJ
ejpam-4821	452	26	(	(	PUNCT
ejpam-4821	452	27	x	x	NOUN
ejpam-4821	452	28	,	,	PUNCT
ejpam-4821	452	29	s	s	PART
ejpam-4821	452	30	)	)	PUNCT
ejpam-4821	452	31	∈	∈	PROPN
ejpam-4821	452	32	nh((x	nh((x	NOUN
ejpam-4821	452	33	,	,	PUNCT
ejpam-4821	452	34	a))\nh((y	a))\nh((y	PROPN
ejpam-4821	452	35	,	,	PUNCT
ejpam-4821	452	36	b	b	NOUN
ejpam-4821	452	37	)	)	PUNCT
ejpam-4821	452	38	)	)	PUNCT
ejpam-4821	452	39	or	or	CCONJ
ejpam-4821	452	40	(	(	PUNCT
ejpam-4821	452	41	x	x	NOUN
ejpam-4821	452	42	,	,	PUNCT
ejpam-4821	452	43	s	s	PART
ejpam-4821	452	44	)	)	PUNCT
ejpam-4821	452	45	∈	∈	PROPN
ejpam-4821	452	46	nh((y	nh((y	NOUN
ejpam-4821	452	47	,	,	PUNCT
ejpam-4821	452	48	b))\nh((x	b))\nh((x	PROPN
ejpam-4821	452	49	,	,	PUNCT
ejpam-4821	452	50	a	a	PRON
ejpam-4821	452	51	)	)	PUNCT
ejpam-4821	452	52	)	)	PUNCT
ejpam-4821	452	53	.	.	PUNCT
ejpam-4821	453	1	thus	thus	ADV
ejpam-4821	453	2	,	,	PUNCT
ejpam-4821	453	3	it	it	PRON
ejpam-4821	453	4	follows	follow	VERB
ejpam-4821	453	5	that	that	SCONJ
ejpam-4821	453	6	w	w	NOUN
ejpam-4821	453	7	is	be	AUX
ejpam-4821	453	8	a	a	DET
ejpam-4821	453	9	2	2	NUM
ejpam-4821	453	10	-	-	PUNCT
ejpam-4821	453	11	locating	locate	VERB
ejpam-4821	453	12	set	set	NOUN
ejpam-4821	453	13	of	of	ADP
ejpam-4821	453	14	g[h	g[h	NOUN
ejpam-4821	453	15	]	]	PUNCT
ejpam-4821	453	16	.	.	PUNCT
ejpam-4821	454	1	g.cañete	g.cañete	PROPN
ejpam-4821	454	2	,	,	PUNCT
ejpam-4821	454	3	h.	h.	PROPN
ejpam-4821	454	4	rara	rara	PROPN
ejpam-4821	454	5	,	,	PUNCT
ejpam-4821	454	6	a.m.	a.m.	PROPN
ejpam-4821	454	7	mahistrado	mahistrado	PROPN
ejpam-4821	454	8	/	/	SYM
ejpam-4821	454	9	eur	eur	PROPN
ejpam-4821	454	10	.	.	PUNCT
ejpam-4821	455	1	j.	j.	PROPN
ejpam-4821	455	2	pure	pure	PROPN
ejpam-4821	455	3	appl	appl	PROPN
ejpam-4821	455	4	.	.	PROPN
ejpam-4821	455	5	math	math	PROPN
ejpam-4821	455	6	,	,	PUNCT
ejpam-4821	455	7	16	16	NUM
ejpam-4821	455	8	(	(	PUNCT
ejpam-4821	455	9	3	3	NUM
ejpam-4821	455	10	)	)	PUNCT
ejpam-4821	455	11	(	(	PUNCT
ejpam-4821	455	12	2023	2023	NUM
ejpam-4821	455	13	)	)	PUNCT
ejpam-4821	455	14	,	,	PUNCT
ejpam-4821	455	15	1647	1647	NUM
ejpam-4821	455	16	-	-	SYM
ejpam-4821	455	17	1662	1662	NUM
ejpam-4821	455	18	1660	1660	NUM
ejpam-4821	455	19	case	case	NOUN
ejpam-4821	455	20	2	2	NUM
ejpam-4821	455	21	.	.	PUNCT
ejpam-4821	455	22	x	x	X
ejpam-4821	456	1	̸=	̸=	PROPN
ejpam-4821	456	2	y.	y.	NOUN
ejpam-4821	456	3	subcase	subcase	VERB
ejpam-4821	456	4	2.1	2.1	NUM
ejpam-4821	456	5	xy	xy	PROPN
ejpam-4821	456	6	∈	∈	PROPN
ejpam-4821	456	7	e(g	e(g	PROPN
ejpam-4821	456	8	)	)	PUNCT
ejpam-4821	456	9	.	.	PUNCT
ejpam-4821	457	1	if	if	SCONJ
ejpam-4821	457	2	ng[x	ng[x	PROPN
ejpam-4821	457	3	]	]	PUNCT
ejpam-4821	457	4	̸=	̸=	PROPN
ejpam-4821	457	5	ng[y	ng[y	PROPN
ejpam-4821	457	6	]	]	PUNCT
ejpam-4821	457	7	,	,	PUNCT
ejpam-4821	457	8	then	then	ADV
ejpam-4821	457	9	we	we	PRON
ejpam-4821	457	10	are	be	AUX
ejpam-4821	457	11	done	do	VERB
ejpam-4821	457	12	.	.	PUNCT
ejpam-4821	458	1	suppose	suppose	VERB
ejpam-4821	458	2	ng[x	ng[x	PROPN
ejpam-4821	458	3	]	]	X
ejpam-4821	458	4	=	=	PUNCT
ejpam-4821	458	5	ng[y	ng[y	PROPN
ejpam-4821	458	6	]	]	PUNCT
ejpam-4821	458	7	,	,	PUNCT
ejpam-4821	458	8	then	then	ADV
ejpam-4821	458	9	by	by	ADP
ejpam-4821	458	10	(	(	PUNCT
ejpam-4821	458	11	iii	iii	NOUN
ejpam-4821	458	12	)	)	PUNCT
ejpam-4821	458	13	,	,	PUNCT
ejpam-4821	458	14	tx	tx	PROPN
ejpam-4821	458	15	and	and	CCONJ
ejpam-4821	458	16	ty	ty	INTJ
ejpam-4821	458	17	are	be	AUX
ejpam-4821	458	18	(	(	PUNCT
ejpam-4821	458	19	2	2	NUM
ejpam-4821	458	20	,	,	PUNCT
ejpam-4821	458	21	1)-locating	1)-locating	NUM
ejpam-4821	458	22	sets	set	NOUN
ejpam-4821	458	23	in	in	ADP
ejpam-4821	458	24	h	h	NOUN
ejpam-4821	458	25	or	or	CCONJ
ejpam-4821	458	26	one	one	NUM
ejpam-4821	458	27	of	of	ADP
ejpam-4821	458	28	tx	tx	PROPN
ejpam-4821	458	29	and	and	CCONJ
ejpam-4821	458	30	ty	ty	PRON
ejpam-4821	458	31	is	be	AUX
ejpam-4821	458	32	a	a	DET
ejpam-4821	458	33	(	(	PUNCT
ejpam-4821	458	34	2	2	NUM
ejpam-4821	458	35	,	,	PUNCT
ejpam-4821	458	36	2)-locating	2)-locating	NUM
ejpam-4821	458	37	set	set	VERB
ejpam-4821	458	38	in	in	ADP
ejpam-4821	458	39	h.	h.	PROPN
ejpam-4821	458	40	subcase	subcase	PROPN
ejpam-4821	458	41	2.2	2.2	NUM
ejpam-4821	458	42	xy	xy	NOUN
ejpam-4821	458	43	/∈	/∈	PUNCT
ejpam-4821	459	1	e(g	e(g	NOUN
ejpam-4821	459	2	)	)	PUNCT
ejpam-4821	460	1	if	if	SCONJ
ejpam-4821	460	2	dg(x	dg(x	NUM
ejpam-4821	460	3	,	,	PUNCT
ejpam-4821	460	4	y	y	PROPN
ejpam-4821	460	5	)	)	PUNCT
ejpam-4821	460	6	>	>	X
ejpam-4821	461	1	2	2	NUM
ejpam-4821	461	2	,	,	PUNCT
ejpam-4821	461	3	then	then	ADV
ejpam-4821	461	4	we	we	PRON
ejpam-4821	461	5	are	be	AUX
ejpam-4821	461	6	done	do	VERB
ejpam-4821	461	7	.	.	PUNCT
ejpam-4821	462	1	suppose	suppose	VERB
ejpam-4821	462	2	dg(x	dg(x	PROPN
ejpam-4821	462	3	,	,	PUNCT
ejpam-4821	462	4	y	y	NOUN
ejpam-4821	462	5	)	)	PUNCT
ejpam-4821	462	6	=	=	SYM
ejpam-4821	462	7	2	2	NUM
ejpam-4821	462	8	and	and	CCONJ
ejpam-4821	462	9	ng(x	ng(x	NUM
ejpam-4821	462	10	)	)	PUNCT
ejpam-4821	462	11	=	=	PUNCT
ejpam-4821	462	12	ng(y	ng(y	NOUN
ejpam-4821	462	13	)	)	PUNCT
ejpam-4821	462	14	.	.	PUNCT
ejpam-4821	463	1	suppose	suppose	VERB
ejpam-4821	463	2	(	(	PUNCT
ejpam-4821	463	3	x	x	X
ejpam-4821	463	4	,	,	PUNCT
ejpam-4821	463	5	a	a	PRON
ejpam-4821	463	6	)	)	PUNCT
ejpam-4821	463	7	,	,	PUNCT
ejpam-4821	463	8	(	(	PUNCT
ejpam-4821	463	9	y	y	NOUN
ejpam-4821	463	10	,	,	PUNCT
ejpam-4821	463	11	b	b	NOUN
ejpam-4821	463	12	)	)	PUNCT
ejpam-4821	463	13	/∈	/∈	PUNCT
ejpam-4821	464	1	w	w	INTJ
ejpam-4821	464	2	.	.	PUNCT
ejpam-4821	465	1	then	then	ADV
ejpam-4821	465	2	a	a	DET
ejpam-4821	465	3	/∈	/∈	INTJ
ejpam-4821	465	4	tx	tx	NOUN
ejpam-4821	466	1	and	and	CCONJ
ejpam-4821	466	2	y	y	PROPN
ejpam-4821	466	3	/∈	/∈	PUNCT
ejpam-4821	467	1	ty	ty	INTJ
ejpam-4821	467	2	.	.	PUNCT
ejpam-4821	468	1	if	if	SCONJ
ejpam-4821	468	2	tx	tx	PROPN
ejpam-4821	468	3	and	and	CCONJ
ejpam-4821	468	4	ty	ty	PRON
ejpam-4821	468	5	are	be	AUX
ejpam-4821	468	6	both	both	PRON
ejpam-4821	468	7	dominating	dominate	VERB
ejpam-4821	468	8	,	,	PUNCT
ejpam-4821	468	9	then	then	ADV
ejpam-4821	468	10	there	there	PRON
ejpam-4821	468	11	exist	exist	VERB
ejpam-4821	468	12	at	at	ADV
ejpam-4821	468	13	least	least	ADV
ejpam-4821	468	14	two	two	NUM
ejpam-4821	468	15	vertices	vertex	NOUN
ejpam-4821	468	16	(	(	PUNCT
ejpam-4821	468	17	x	x	X
ejpam-4821	468	18	,	,	PUNCT
ejpam-4821	468	19	r	r	NOUN
ejpam-4821	468	20	)	)	PUNCT
ejpam-4821	468	21	,	,	PUNCT
ejpam-4821	468	22	(	(	PUNCT
ejpam-4821	468	23	x	x	NOUN
ejpam-4821	468	24	,	,	PUNCT
ejpam-4821	468	25	s	s	PART
ejpam-4821	468	26	)	)	PUNCT
ejpam-4821	468	27	∈	∈	NOUN
ejpam-4821	468	28	v	v	ADP
ejpam-4821	468	29	(	(	PUNCT
ejpam-4821	468	30	h	h	NOUN
ejpam-4821	468	31	)	)	PUNCT
ejpam-4821	468	32	∩	∩	NOUN
ejpam-4821	468	33	tx	tx	VERB
ejpam-4821	468	34	such	such	ADJ
ejpam-4821	468	35	that	that	SCONJ
ejpam-4821	468	36	either	either	ADV
ejpam-4821	468	37	(	(	PUNCT
ejpam-4821	468	38	x	x	NOUN
ejpam-4821	468	39	,	,	PUNCT
ejpam-4821	468	40	r	r	NOUN
ejpam-4821	468	41	)	)	PUNCT
ejpam-4821	468	42	,	,	PUNCT
ejpam-4821	468	43	(	(	PUNCT
ejpam-4821	468	44	x	x	NOUN
ejpam-4821	468	45	,	,	PUNCT
ejpam-4821	468	46	s	s	PART
ejpam-4821	468	47	)	)	PUNCT
ejpam-4821	468	48	∈	∈	PROPN
ejpam-4821	468	49	nh((x	nh((x	NOUN
ejpam-4821	468	50	,	,	PUNCT
ejpam-4821	468	51	p))\nh((x	p))\nh((x	NOUN
ejpam-4821	468	52	,	,	PUNCT
ejpam-4821	468	53	q	q	NOUN
ejpam-4821	468	54	)	)	PUNCT
ejpam-4821	468	55	)	)	PUNCT
ejpam-4821	468	56	or	or	CCONJ
ejpam-4821	468	57	(	(	PUNCT
ejpam-4821	468	58	x	x	X
ejpam-4821	468	59	,	,	PUNCT
ejpam-4821	468	60	r	r	NOUN
ejpam-4821	468	61	)	)	PUNCT
ejpam-4821	468	62	,	,	PUNCT
ejpam-4821	468	63	(	(	PUNCT
ejpam-4821	468	64	x	x	NOUN
ejpam-4821	468	65	,	,	PUNCT
ejpam-4821	468	66	s	s	PART
ejpam-4821	468	67	)	)	PUNCT
ejpam-4821	468	68	∈	∈	PROPN
ejpam-4821	468	69	nh((x	nh((x	NOUN
ejpam-4821	468	70	,	,	PUNCT
ejpam-4821	468	71	q))\nh((x	q))\nh((x	NOUN
ejpam-4821	468	72	,	,	PUNCT
ejpam-4821	468	73	p	p	NOUN
ejpam-4821	468	74	)	)	PUNCT
ejpam-4821	468	75	)	)	PUNCT
ejpam-4821	468	76	or	or	CCONJ
ejpam-4821	468	77	(	(	PUNCT
ejpam-4821	468	78	x	x	NOUN
ejpam-4821	468	79	,	,	PUNCT
ejpam-4821	468	80	r	r	NOUN
ejpam-4821	468	81	)	)	PUNCT
ejpam-4821	468	82	∈	∈	NOUN
ejpam-4821	468	83	nh((x	nh((x	NOUN
ejpam-4821	468	84	,	,	PUNCT
ejpam-4821	468	85	p))\nh((x	p))\nh((x	NOUN
ejpam-4821	468	86	,	,	PUNCT
ejpam-4821	468	87	q	q	NOUN
ejpam-4821	468	88	)	)	PUNCT
ejpam-4821	468	89	)	)	PUNCT
ejpam-4821	468	90	and	and	CCONJ
ejpam-4821	468	91	(	(	PUNCT
ejpam-4821	468	92	x	x	NOUN
ejpam-4821	468	93	,	,	PUNCT
ejpam-4821	468	94	s	s	PART
ejpam-4821	468	95	)	)	PUNCT
ejpam-4821	468	96	∈	∈	PROPN
ejpam-4821	468	97	nh((x	nh((x	NOUN
ejpam-4821	468	98	,	,	PUNCT
ejpam-4821	468	99	q))\nh((x	q))\nh((x	NOUN
ejpam-4821	468	100	,	,	PUNCT
ejpam-4821	468	101	p	p	NOUN
ejpam-4821	468	102	)	)	PUNCT
ejpam-4821	468	103	)	)	PUNCT
ejpam-4821	468	104	.	.	PUNCT
ejpam-4821	469	1	if	if	SCONJ
ejpam-4821	469	2	one	one	NUM
ejpam-4821	469	3	,	,	PUNCT
ejpam-4821	469	4	say	say	VERB
ejpam-4821	469	5	ty	ty	INTJ
ejpam-4821	469	6	,	,	PUNCT
ejpam-4821	469	7	is	be	AUX
ejpam-4821	469	8	a	a	DET
ejpam-4821	469	9	2	2	NUM
ejpam-4821	469	10	-	-	PUNCT
ejpam-4821	469	11	dominating	dominating	NOUN
ejpam-4821	469	12	set	set	NOUN
ejpam-4821	469	13	,	,	PUNCT
ejpam-4821	469	14	then	then	ADV
ejpam-4821	469	15	there	there	PRON
ejpam-4821	469	16	exist	exist	VERB
ejpam-4821	469	17	at	at	ADV
ejpam-4821	469	18	least	least	ADV
ejpam-4821	469	19	two	two	NUM
ejpam-4821	469	20	vertices	vertex	NOUN
ejpam-4821	469	21	r	r	NOUN
ejpam-4821	469	22	,	,	PUNCT
ejpam-4821	469	23	s	s	NOUN
ejpam-4821	469	24	∈	∈	PROPN
ejpam-4821	469	25	v	v	ADP
ejpam-4821	469	26	(	(	PUNCT
ejpam-4821	469	27	h	h	NOUN
ejpam-4821	469	28	)	)	PUNCT
ejpam-4821	469	29	∩	∩	NOUN
ejpam-4821	469	30	tx	tx	VERB
ejpam-4821	469	31	such	such	ADJ
ejpam-4821	469	32	that	that	SCONJ
ejpam-4821	469	33	either	either	ADV
ejpam-4821	469	34	(	(	PUNCT
ejpam-4821	469	35	x	x	NOUN
ejpam-4821	469	36	,	,	PUNCT
ejpam-4821	469	37	r	r	NOUN
ejpam-4821	469	38	)	)	PUNCT
ejpam-4821	469	39	,	,	PUNCT
ejpam-4821	469	40	(	(	PUNCT
ejpam-4821	469	41	x	x	NOUN
ejpam-4821	469	42	,	,	PUNCT
ejpam-4821	469	43	s	s	PART
ejpam-4821	469	44	)	)	PUNCT
ejpam-4821	469	45	∈	∈	PROPN
ejpam-4821	469	46	nh((x	nh((x	NOUN
ejpam-4821	469	47	,	,	PUNCT
ejpam-4821	469	48	p))\nh((x	p))\nh((x	NOUN
ejpam-4821	469	49	,	,	PUNCT
ejpam-4821	469	50	q	q	NOUN
ejpam-4821	469	51	)	)	PUNCT
ejpam-4821	469	52	)	)	PUNCT
ejpam-4821	469	53	or	or	CCONJ
ejpam-4821	469	54	(	(	PUNCT
ejpam-4821	469	55	x	x	X
ejpam-4821	469	56	,	,	PUNCT
ejpam-4821	469	57	r	r	NOUN
ejpam-4821	469	58	)	)	PUNCT
ejpam-4821	469	59	,	,	PUNCT
ejpam-4821	469	60	(	(	PUNCT
ejpam-4821	469	61	x	x	NOUN
ejpam-4821	469	62	,	,	PUNCT
ejpam-4821	469	63	s	s	PART
ejpam-4821	469	64	)	)	PUNCT
ejpam-4821	469	65	∈	∈	PROPN
ejpam-4821	469	66	nh((x	nh((x	NOUN
ejpam-4821	469	67	,	,	PUNCT
ejpam-4821	469	68	q))\nh((x	q))\nh((x	NOUN
ejpam-4821	469	69	,	,	PUNCT
ejpam-4821	469	70	p	p	NOUN
ejpam-4821	469	71	)	)	PUNCT
ejpam-4821	469	72	)	)	PUNCT
ejpam-4821	469	73	or	or	CCONJ
ejpam-4821	469	74	(	(	PUNCT
ejpam-4821	469	75	x	x	NOUN
ejpam-4821	469	76	,	,	PUNCT
ejpam-4821	469	77	r	r	NOUN
ejpam-4821	469	78	)	)	PUNCT
ejpam-4821	469	79	∈	∈	NOUN
ejpam-4821	469	80	nh((x	nh((x	NOUN
ejpam-4821	469	81	,	,	PUNCT
ejpam-4821	469	82	p))\nh((x	p))\nh((x	NOUN
ejpam-4821	469	83	,	,	PUNCT
ejpam-4821	469	84	q	q	NOUN
ejpam-4821	469	85	)	)	PUNCT
ejpam-4821	469	86	)	)	PUNCT
ejpam-4821	469	87	and	and	CCONJ
ejpam-4821	469	88	(	(	PUNCT
ejpam-4821	469	89	x	x	NOUN
ejpam-4821	469	90	,	,	PUNCT
ejpam-4821	469	91	s	s	PART
ejpam-4821	469	92	)	)	PUNCT
ejpam-4821	469	93	∈	∈	PROPN
ejpam-4821	469	94	nh((x	nh((x	NOUN
ejpam-4821	469	95	,	,	PUNCT
ejpam-4821	469	96	q))\nh((x	q))\nh((x	NOUN
ejpam-4821	469	97	,	,	PUNCT
ejpam-4821	469	98	p	p	NOUN
ejpam-4821	469	99	)	)	PUNCT
ejpam-4821	469	100	)	)	PUNCT
ejpam-4821	469	101	.	.	PUNCT
ejpam-4821	470	1	similarly	similarly	ADV
ejpam-4821	470	2	,	,	PUNCT
ejpam-4821	470	3	if	if	SCONJ
ejpam-4821	470	4	(	(	PUNCT
ejpam-4821	470	5	x	x	NOUN
ejpam-4821	470	6	,	,	PUNCT
ejpam-4821	470	7	a	a	PRON
ejpam-4821	470	8	)	)	PUNCT
ejpam-4821	470	9	∈	∈	PROPN
ejpam-4821	470	10	w	w	PROPN
ejpam-4821	470	11	,	,	PUNCT
ejpam-4821	470	12	(	(	PUNCT
ejpam-4821	470	13	y	y	PROPN
ejpam-4821	470	14	,	,	PUNCT
ejpam-4821	470	15	b	b	NOUN
ejpam-4821	470	16	)	)	PUNCT
ejpam-4821	470	17	/∈	/∈	PUNCT
ejpam-4821	471	1	w	w	NOUN
ejpam-4821	471	2	,	,	PUNCT
ejpam-4821	471	3	there	there	PRON
ejpam-4821	471	4	exists	exist	VERB
ejpam-4821	471	5	(	(	PUNCT
ejpam-4821	471	6	x	x	X
ejpam-4821	471	7	,	,	PUNCT
ejpam-4821	471	8	s	s	PART
ejpam-4821	471	9	)	)	PUNCT
ejpam-4821	471	10	∈	∈	NOUN
ejpam-4821	471	11	v	v	NOUN
ejpam-4821	471	12	(	(	PUNCT
ejpam-4821	471	13	h)∩tx	h)∩tx	PRON
ejpam-4821	471	14	such	such	ADJ
ejpam-4821	471	15	that	that	SCONJ
ejpam-4821	471	16	(	(	PUNCT
ejpam-4821	471	17	x	x	NOUN
ejpam-4821	471	18	,	,	PUNCT
ejpam-4821	471	19	s	s	PART
ejpam-4821	471	20	)	)	PUNCT
ejpam-4821	471	21	∈	∈	PROPN
ejpam-4821	471	22	nh((x	nh((x	NOUN
ejpam-4821	471	23	,	,	PUNCT
ejpam-4821	471	24	a))\nh((y	a))\nh((y	PROPN
ejpam-4821	471	25	,	,	PUNCT
ejpam-4821	471	26	b	b	NOUN
ejpam-4821	471	27	)	)	PUNCT
ejpam-4821	471	28	)	)	PUNCT
ejpam-4821	471	29	or	or	CCONJ
ejpam-4821	471	30	(	(	PUNCT
ejpam-4821	471	31	x	x	NOUN
ejpam-4821	471	32	,	,	PUNCT
ejpam-4821	471	33	s	s	PART
ejpam-4821	471	34	)	)	PUNCT
ejpam-4821	471	35	∈	∈	PROPN
ejpam-4821	471	36	nh((y	nh((y	NOUN
ejpam-4821	471	37	,	,	PUNCT
ejpam-4821	471	38	b))\nh((x	b))\nh((x	PROPN
ejpam-4821	471	39	,	,	PUNCT
ejpam-4821	471	40	a	a	PRON
ejpam-4821	471	41	)	)	PUNCT
ejpam-4821	471	42	)	)	PUNCT
ejpam-4821	471	43	.	.	PUNCT
ejpam-4821	472	1	accordingly	accordingly	ADV
ejpam-4821	472	2	,	,	PUNCT
ejpam-4821	472	3	w	w	PROPN
ejpam-4821	472	4	is	be	AUX
ejpam-4821	472	5	a	a	DET
ejpam-4821	472	6	2	2	NUM
ejpam-4821	472	7	-	-	PUNCT
ejpam-4821	472	8	locating	locate	VERB
ejpam-4821	472	9	set	set	NOUN
ejpam-4821	472	10	of	of	ADP
ejpam-4821	472	11	g[h	g[h	PROPN
ejpam-4821	472	12	]	]	PUNCT
ejpam-4821	472	13	.	.	PUNCT
ejpam-4821	473	1	corollary	corollary	ADJ
ejpam-4821	473	2	8	8	NUM
ejpam-4821	473	3	.	.	PUNCT
ejpam-4821	474	1	let	let	VERB
ejpam-4821	474	2	g	g	NOUN
ejpam-4821	474	3	and	and	CCONJ
ejpam-4821	474	4	h	h	NOUN
ejpam-4821	474	5	be	be	AUX
ejpam-4821	474	6	nontrivial	nontrivial	ADJ
ejpam-4821	474	7	connected	connect	VERB
ejpam-4821	474	8	graphs	graph	NOUN
ejpam-4821	474	9	with	with	ADP
ejpam-4821	474	10	∆(h	∆(h	NOUN
ejpam-4821	474	11	)	)	PUNCT
ejpam-4821	474	12	≤	≤	NOUN
ejpam-4821	474	13	|v	|v	X
ejpam-4821	474	14	(	(	PUNCT
ejpam-4821	474	15	h)|	h)|	NOUN
ejpam-4821	474	16	−	−	PROPN
ejpam-4821	474	17	3	3	X
ejpam-4821	474	18	.	.	PUNCT
ejpam-4821	475	1	if	if	SCONJ
ejpam-4821	475	2	g	g	PROPN
ejpam-4821	475	3	is	be	AUX
ejpam-4821	475	4	a	a	DET
ejpam-4821	475	5	totally	totally	ADV
ejpam-4821	475	6	point	point	NOUN
ejpam-4821	475	7	determining	determine	VERB
ejpam-4821	475	8	graph	graph	NOUN
ejpam-4821	475	9	,	,	PUNCT
ejpam-4821	475	10	then	then	ADV
ejpam-4821	475	11	ln2(g[h	ln2(g[h	ADV
ejpam-4821	475	12	]	]	X
ejpam-4821	475	13	)	)	PUNCT
ejpam-4821	475	14	=	=	SYM
ejpam-4821	475	15	|v	|v	PROPN
ejpam-4821	475	16	(	(	PUNCT
ejpam-4821	475	17	g)|	g)|	PROPN
ejpam-4821	475	18	·	·	SYM
ejpam-4821	475	19	ln2(h	ln2(h	PROPN
ejpam-4821	475	20	)	)	PUNCT
ejpam-4821	475	21	.	.	PUNCT
ejpam-4821	476	1	proof	proof	NOUN
ejpam-4821	476	2	.	.	PUNCT
ejpam-4821	477	1	supppose	supppose	VERB
ejpam-4821	477	2	that	that	SCONJ
ejpam-4821	477	3	g	g	PROPN
ejpam-4821	477	4	is	be	AUX
ejpam-4821	477	5	totally	totally	ADV
ejpam-4821	477	6	point	point	NOUN
ejpam-4821	477	7	determining	determine	VERB
ejpam-4821	477	8	graph	graph	NOUN
ejpam-4821	477	9	.	.	PUNCT
ejpam-4821	478	1	let	let	VERB
ejpam-4821	478	2	s	s	NOUN
ejpam-4821	478	3	=	=	X
ejpam-4821	478	4	v	v	ADJ
ejpam-4821	478	5	(	(	PUNCT
ejpam-4821	478	6	g	g	NOUN
ejpam-4821	478	7	)	)	PUNCT
ejpam-4821	478	8	and	and	CCONJ
ejpam-4821	478	9	let	let	VERB
ejpam-4821	478	10	tx	tx	PART
ejpam-4821	478	11	be	be	AUX
ejpam-4821	478	12	an	an	DET
ejpam-4821	478	13	ln2	ln2	NOUN
ejpam-4821	478	14	-	-	PUNCT
ejpam-4821	478	15	set	set	NOUN
ejpam-4821	478	16	of	of	ADP
ejpam-4821	478	17	h	h	NOUN
ejpam-4821	478	18	for	for	ADP
ejpam-4821	478	19	each	each	DET
ejpam-4821	478	20	x	x	SYM
ejpam-4821	478	21	∈	∈	PROPN
ejpam-4821	478	22	s.	s.	PROPN
ejpam-4821	478	23	by	by	ADP
ejpam-4821	478	24	theorem	theorem	ADJ
ejpam-4821	478	25	10	10	NUM
ejpam-4821	478	26	,	,	PUNCT
ejpam-4821	478	27	w	w	NOUN
ejpam-4821	478	28	=	=	PUNCT
ejpam-4821	478	29	⋃	⋃	PROPN
ejpam-4821	478	30	x∈s	x∈s	NOUN
ejpam-4821	479	1	[	[	X
ejpam-4821	479	2	{	{	PUNCT
ejpam-4821	479	3	x	x	NOUN
ejpam-4821	479	4	}	}	PUNCT
ejpam-4821	479	5	×	×	PROPN
ejpam-4821	479	6	tx	tx	PROPN
ejpam-4821	479	7	]	]	PUNCT
ejpam-4821	479	8	is	be	AUX
ejpam-4821	479	9	a	a	DET
ejpam-4821	479	10	2	2	NUM
ejpam-4821	479	11	-	-	PUNCT
ejpam-4821	479	12	locating	locate	VERB
ejpam-4821	479	13	set	set	NOUN
ejpam-4821	479	14	of	of	ADP
ejpam-4821	479	15	g[h	g[h	NOUN
ejpam-4821	479	16	]	]	PUNCT
ejpam-4821	479	17	.	.	PUNCT
ejpam-4821	480	1	it	it	PRON
ejpam-4821	480	2	follows	follow	VERB
ejpam-4821	480	3	that	that	SCONJ
ejpam-4821	480	4	ln2(g[h	ln2(g[h	ADP
ejpam-4821	480	5	]	]	PUNCT
ejpam-4821	480	6	)	)	PUNCT
ejpam-4821	480	7	≤	≤	NOUN
ejpam-4821	480	8	|w	|w	NOUN
ejpam-4821	480	9	|	|	NOUN
ejpam-4821	480	10	=	=	SYM
ejpam-4821	480	11	|v	|v	PROPN
ejpam-4821	480	12	(	(	PUNCT
ejpam-4821	480	13	g)||tx|	g)||tx|	PROPN
ejpam-4821	480	14	=	=	SYM
ejpam-4821	480	15	|v	|v	PROPN
ejpam-4821	480	16	(	(	PUNCT
ejpam-4821	480	17	g)|	g)|	PROPN
ejpam-4821	480	18	·	·	SYM
ejpam-4821	480	19	ln2(h	ln2(h	PROPN
ejpam-4821	480	20	)	)	PUNCT
ejpam-4821	480	21	.	.	PUNCT
ejpam-4821	481	1	now	now	ADV
ejpam-4821	481	2	,	,	PUNCT
ejpam-4821	481	3	if	if	SCONJ
ejpam-4821	481	4	w0	w0	PROPN
ejpam-4821	481	5	=	=	PUNCT
ejpam-4821	481	6	⋃	⋃	PROPN
ejpam-4821	481	7	x∈s0	x∈s0	NOUN
ejpam-4821	482	1	[	[	X
ejpam-4821	482	2	{	{	PUNCT
ejpam-4821	482	3	x	x	NOUN
ejpam-4821	482	4	}	}	PUNCT
ejpam-4821	482	5	×	×	PROPN
ejpam-4821	482	6	tx	tx	PROPN
ejpam-4821	482	7	]	]	PUNCT
ejpam-4821	482	8	is	be	AUX
ejpam-4821	482	9	an	an	DET
ejpam-4821	482	10	ln2	ln2	NOUN
ejpam-4821	482	11	-	-	PUNCT
ejpam-4821	482	12	set	set	NOUN
ejpam-4821	482	13	of	of	ADP
ejpam-4821	482	14	g[h	g[h	PROPN
ejpam-4821	482	15	]	]	PUNCT
ejpam-4821	482	16	,	,	PUNCT
ejpam-4821	482	17	then	then	ADV
ejpam-4821	482	18	s0	s0	PROPN
ejpam-4821	482	19	=	=	SYM
ejpam-4821	482	20	v	v	PROPN
ejpam-4821	482	21	(	(	PUNCT
ejpam-4821	482	22	g	g	NOUN
ejpam-4821	482	23	)	)	PUNCT
ejpam-4821	482	24	and	and	CCONJ
ejpam-4821	482	25	tx	tx	PROPN
ejpam-4821	482	26	is	be	AUX
ejpam-4821	482	27	a	a	DET
ejpam-4821	482	28	2	2	NUM
ejpam-4821	482	29	-	-	PUNCT
ejpam-4821	482	30	locating	locate	VERB
ejpam-4821	482	31	set	set	NOUN
ejpam-4821	482	32	of	of	ADP
ejpam-4821	482	33	h	h	NOUN
ejpam-4821	482	34	for	for	ADP
ejpam-4821	482	35	each	each	DET
ejpam-4821	482	36	x	x	SYM
ejpam-4821	482	37	∈	∈	PROPN
ejpam-4821	482	38	v	v	ADP
ejpam-4821	482	39	(	(	PUNCT
ejpam-4821	482	40	g	g	NOUN
ejpam-4821	482	41	)	)	PUNCT
ejpam-4821	482	42	by	by	ADP
ejpam-4821	482	43	theorem	theorem	NOUN
ejpam-4821	482	44	10	10	NUM
ejpam-4821	482	45	.	.	PUNCT
ejpam-4821	483	1	hence	hence	ADV
ejpam-4821	483	2	,	,	PUNCT
ejpam-4821	483	3	ln2(g[h	ln2(g[h	ADV
ejpam-4821	483	4	]	]	PUNCT
ejpam-4821	483	5	)	)	PUNCT
ejpam-4821	483	6	=	=	VERB
ejpam-4821	483	7	|w0|	|w0|	X
ejpam-4821	483	8	=	=	SYM
ejpam-4821	483	9	|v	|v	X
ejpam-4821	483	10	(	(	PUNCT
ejpam-4821	483	11	g)||tx|	g)||tx|	PROPN
ejpam-4821	483	12	≥	≥	NUM
ejpam-4821	483	13	|v	|v	PROPN
ejpam-4821	483	14	(	(	PUNCT
ejpam-4821	483	15	g)|	g)|	PROPN
ejpam-4821	483	16	·	·	SYM
ejpam-4821	483	17	ln2(h	ln2(h	PROPN
ejpam-4821	483	18	)	)	PUNCT
ejpam-4821	483	19	.	.	PUNCT
ejpam-4821	484	1	therefore	therefore	ADV
ejpam-4821	484	2	,	,	PUNCT
ejpam-4821	484	3	ln2(g[h	ln2(g[h	ADJ
ejpam-4821	484	4	]	]	PUNCT
ejpam-4821	484	5	)	)	PUNCT
ejpam-4821	484	6	=	=	SYM
ejpam-4821	484	7	|v	|v	PROPN
ejpam-4821	484	8	(	(	PUNCT
ejpam-4821	484	9	g)|	g)|	PROPN
ejpam-4821	484	10	·	·	SYM
ejpam-4821	484	11	ln2(h	ln2(h	PROPN
ejpam-4821	484	12	)	)	PUNCT
ejpam-4821	484	13	.	.	PUNCT
ejpam-4821	485	1	9	9	X
ejpam-4821	485	2	.	.	X
ejpam-4821	485	3	conclusion	conclusion	NOUN
ejpam-4821	485	4	it	it	PRON
ejpam-4821	485	5	is	be	AUX
ejpam-4821	485	6	shown	show	VERB
ejpam-4821	485	7	that	that	SCONJ
ejpam-4821	485	8	the	the	DET
ejpam-4821	485	9	difference	difference	NOUN
ejpam-4821	485	10	of	of	ADP
ejpam-4821	485	11	the	the	DET
ejpam-4821	485	12	2	2	NUM
ejpam-4821	485	13	-	-	PUNCT
ejpam-4821	485	14	metric	metric	ADJ
ejpam-4821	485	15	dimension	dimension	NOUN
ejpam-4821	485	16	and	and	CCONJ
ejpam-4821	485	17	2	2	NUM
ejpam-4821	485	18	-	-	PUNCT
ejpam-4821	485	19	locating	locate	VERB
ejpam-4821	485	20	number	number	NOUN
ejpam-4821	485	21	can	can	AUX
ejpam-4821	485	22	be	be	AUX
ejpam-4821	485	23	made	make	VERB
ejpam-4821	485	24	arbitrarily	arbitrarily	ADV
ejpam-4821	485	25	large	large	ADJ
ejpam-4821	485	26	.	.	PUNCT
ejpam-4821	486	1	2	2	NUM
ejpam-4821	486	2	-	-	PUNCT
ejpam-4821	486	3	locating	locate	VERB
ejpam-4821	486	4	sets	set	NOUN
ejpam-4821	486	5	in	in	ADP
ejpam-4821	486	6	the	the	DET
ejpam-4821	486	7	join	join	NOUN
ejpam-4821	486	8	,	,	PUNCT
ejpam-4821	486	9	corona	corona	PROPN
ejpam-4821	486	10	,	,	PUNCT
ejpam-4821	486	11	edge	edge	NOUN
ejpam-4821	486	12	corona	corona	NOUN
ejpam-4821	486	13	,	,	PUNCT
ejpam-4821	486	14	and	and	CCONJ
ejpam-4821	486	15	lexicographic	lexicographic	ADJ
ejpam-4821	486	16	product	product	NOUN
ejpam-4821	486	17	of	of	ADP
ejpam-4821	486	18	two	two	NUM
ejpam-4821	486	19	graphs	graph	NOUN
ejpam-4821	486	20	have	have	AUX
ejpam-4821	486	21	been	be	AUX
ejpam-4821	486	22	characterized	characterize	VERB
ejpam-4821	486	23	.	.	PUNCT
ejpam-4821	487	1	from	from	ADP
ejpam-4821	487	2	these	these	DET
ejpam-4821	487	3	characterizations	characterization	NOUN
ejpam-4821	487	4	,	,	PUNCT
ejpam-4821	487	5	2	2	NUM
ejpam-4821	487	6	-	-	PUNCT
ejpam-4821	487	7	locating	locate	VERB
ejpam-4821	487	8	numbers	number	NOUN
ejpam-4821	487	9	have	have	AUX
ejpam-4821	487	10	been	be	AUX
ejpam-4821	487	11	determined	determine	VERB
ejpam-4821	487	12	.	.	PUNCT
ejpam-4821	488	1	this	this	DET
ejpam-4821	488	2	new	new	ADJ
ejpam-4821	488	3	invariant	invariant	NOUN
ejpam-4821	488	4	can	can	AUX
ejpam-4821	488	5	also	also	ADV
ejpam-4821	488	6	be	be	AUX
ejpam-4821	488	7	studied	study	VERB
ejpam-4821	488	8	for	for	ADP
ejpam-4821	488	9	graphs	graph	NOUN
ejpam-4821	488	10	under	under	ADP
ejpam-4821	488	11	other	other	ADJ
ejpam-4821	488	12	binary	binary	ADJ
ejpam-4821	488	13	operations	operation	NOUN
ejpam-4821	488	14	.	.	PUNCT
ejpam-4821	489	1	references	reference	NOUN
ejpam-4821	489	2	1661	1661	NUM
ejpam-4821	489	3	acknowledgements	acknowledgement	NOUN
ejpam-4821	489	4	the	the	DET
ejpam-4821	489	5	authors	author	NOUN
ejpam-4821	489	6	would	would	AUX
ejpam-4821	489	7	like	like	VERB
ejpam-4821	489	8	to	to	PART
ejpam-4821	489	9	thank	thank	VERB
ejpam-4821	489	10	the	the	DET
ejpam-4821	489	11	department	department	NOUN
ejpam-4821	489	12	of	of	ADP
ejpam-4821	489	13	science	science	NOUN
ejpam-4821	489	14	and	and	CCONJ
ejpam-4821	489	15	technology	technology	NOUN
ejpam-4821	489	16	accelerated	accelerate	VERB
ejpam-4821	489	17	science	science	NOUN
ejpam-4821	489	18	and	and	CCONJ
ejpam-4821	489	19	technology	technology	NOUN
ejpam-4821	489	20	human	human	ADJ
ejpam-4821	489	21	resource	resource	NOUN
ejpam-4821	489	22	development	development	NOUN
ejpam-4821	489	23	program	program	NOUN
ejpam-4821	489	24	(	(	PUNCT
ejpam-4821	489	25	dost	dost	NOUN
ejpam-4821	489	26	-	-	PUNCT
ejpam-4821	489	27	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-4821	489	28	,	,	PUNCT
ejpam-4821	489	29	msu	msu	PROPN
ejpam-4821	489	30	-	-	PUNCT
ejpam-4821	489	31	iligan	iligan	PROPN
ejpam-4821	489	32	institute	institute	PROPN
ejpam-4821	489	33	of	of	ADP
ejpam-4821	489	34	technology	technology	PROPN
ejpam-4821	489	35	.	.	PUNCT
ejpam-4821	490	1	references	reference	NOUN
ejpam-4821	490	2	[	[	X
ejpam-4821	490	3	1	1	NUM
ejpam-4821	490	4	]	]	PUNCT
ejpam-4821	490	5	r.	r.	PROPN
ejpam-4821	490	6	bailey	bailey	PROPN
ejpam-4821	490	7	,	,	PUNCT
ejpam-4821	490	8	j.	j.	PROPN
ejpam-4821	490	9	cáceres	cáceres	PROPN
ejpam-4821	490	10	,	,	PUNCT
ejpam-4821	490	11	j.	j.	PROPN
ejpam-4821	490	12	garijo	garijo	PROPN
ejpam-4821	490	13	,	,	PUNCT
ejpam-4821	490	14	a.	a.	PROPN
ejpam-4821	490	15	gonzález	gonzález	PROPN
ejpam-4821	490	16	,	,	PUNCT
ejpam-4821	490	17	a.	a.	NOUN
ejpam-4821	490	18	márquez	márquez	PROPN
ejpam-4821	490	19	,	,	PUNCT
ejpam-4821	490	20	k.	k.	PROPN
ejpam-4821	490	21	meagher	meagher	PROPN
ejpam-4821	490	22	,	,	PUNCT
ejpam-4821	490	23	and	and	CCONJ
ejpam-4821	490	24	m.l	m.l	PROPN
ejpam-4821	490	25	.	.	PROPN
ejpam-4821	490	26	puertas	puertas	PROPN
ejpam-4821	490	27	.	.	PUNCT
ejpam-4821	491	1	resolving	resolve	VERB
ejpam-4821	491	2	sets	set	NOUN
ejpam-4821	491	3	for	for	ADP
ejpam-4821	491	4	johnson	johnson	PROPN
ejpam-4821	491	5	and	and	CCONJ
ejpam-4821	491	6	kneser	kneser	NOUN
ejpam-4821	491	7	graphs	graph	NOUN
ejpam-4821	491	8	.	.	PUNCT
ejpam-4821	492	1	european	european	ADJ
ejpam-4821	492	2	journal	journal	PROPN
ejpam-4821	492	3	of	of	ADP
ejpam-4821	492	4	combinatorics	combinatoric	NOUN
ejpam-4821	492	5	,	,	PUNCT
ejpam-4821	492	6	34:736–751	34:736–751	NUM
ejpam-4821	492	7	,	,	PUNCT
ejpam-4821	492	8	2013	2013	NUM
ejpam-4821	492	9	.	.	PUNCT
ejpam-4821	493	1	[	[	X
ejpam-4821	493	2	2	2	NUM
ejpam-4821	493	3	]	]	PUNCT
ejpam-4821	493	4	r.	r.	PROPN
ejpam-4821	493	5	bailey	bailey	PROPN
ejpam-4821	493	6	and	and	CCONJ
ejpam-4821	493	7	i.	i.	PROPN
ejpam-4821	493	8	yero	yero	PROPN
ejpam-4821	493	9	.	.	PUNCT
ejpam-4821	494	1	error	error	NOUN
ejpam-4821	494	2	-	-	PUNCT
ejpam-4821	494	3	correcting	correct	VERB
ejpam-4821	494	4	codes	code	NOUN
ejpam-4821	494	5	from	from	ADP
ejpam-4821	494	6	k	k	ADJ
ejpam-4821	494	7	-	-	PUNCT
ejpam-4821	494	8	resolving	resolving	ADJ
ejpam-4821	494	9	sets	set	NOUN
ejpam-4821	494	10	.	.	PUNCT
ejpam-4821	495	1	discussiones	discussione	NOUN
ejpam-4821	495	2	mathematicae	mathematicae	VERB
ejpam-4821	495	3	,	,	PUNCT
ejpam-4821	495	4	graph	graph	NOUN
ejpam-4821	495	5	theory	theory	NOUN
ejpam-4821	495	6	,	,	PUNCT
ejpam-4821	495	7	39:341–355	39:341–355	PROPN
ejpam-4821	495	8	,	,	PUNCT
ejpam-4821	495	9	2019	2019	NUM
ejpam-4821	495	10	.	.	PUNCT
ejpam-4821	496	1	[	[	X
ejpam-4821	496	2	3	3	X
ejpam-4821	496	3	]	]	PUNCT
ejpam-4821	496	4	j.	j.	PROPN
ejpam-4821	496	5	a.	a.	PROPN
ejpam-4821	496	6	bondy	bondy	PROPN
ejpam-4821	496	7	and	and	CCONJ
ejpam-4821	496	8	u.	u.	PROPN
ejpam-4821	496	9	s.	s.	PROPN
ejpam-4821	496	10	r.	r.	PROPN
ejpam-4821	496	11	murty	murty	PROPN
ejpam-4821	496	12	.	.	PUNCT
ejpam-4821	497	1	graph	graph	NOUN
ejpam-4821	497	2	theory	theory	NOUN
ejpam-4821	497	3	.	.	PUNCT
ejpam-4821	498	1	springer	springer	NOUN
ejpam-4821	498	2	,	,	PUNCT
ejpam-4821	498	3	2008	2008	NUM
ejpam-4821	498	4	.	.	PUNCT
ejpam-4821	499	1	[	[	X
ejpam-4821	499	2	4	4	NUM
ejpam-4821	499	3	]	]	X
ejpam-4821	499	4	f.	f.	PROPN
ejpam-4821	499	5	buckley	buckley	PROPN
ejpam-4821	499	6	and	and	CCONJ
ejpam-4821	499	7	f.	f.	PROPN
ejpam-4821	499	8	harary	harary	PROPN
ejpam-4821	499	9	.	.	PUNCT
ejpam-4821	500	1	distance	distance	NOUN
ejpam-4821	500	2	in	in	ADP
ejpam-4821	500	3	graphs	graph	NOUN
ejpam-4821	500	4	.	.	PUNCT
ejpam-4821	501	1	addison	addison	PROPN
ejpam-4821	501	2	-	-	PUNCT
ejpam-4821	501	3	wesley	wesley	PROPN
ejpam-4821	501	4	,	,	PUNCT
ejpam-4821	501	5	redwood	redwood	NOUN
ejpam-4821	501	6	city	city	NOUN
ejpam-4821	501	7	,	,	PUNCT
ejpam-4821	501	8	ca	ca	NOUN
ejpam-4821	501	9	,	,	PUNCT
ejpam-4821	501	10	1990	1990	NUM
ejpam-4821	501	11	.	.	PUNCT
ejpam-4821	502	1	[	[	X
ejpam-4821	502	2	5	5	X
ejpam-4821	502	3	]	]	PUNCT
ejpam-4821	502	4	j.	j.	PROPN
ejpam-4821	502	5	cabaro	cabaro	PROPN
ejpam-4821	502	6	and	and	CCONJ
ejpam-4821	502	7	h.	h.	PROPN
ejpam-4821	502	8	rara	rara	PROPN
ejpam-4821	502	9	.	.	PUNCT
ejpam-4821	503	1	on	on	ADP
ejpam-4821	503	2	2	2	NUM
ejpam-4821	503	3	-	-	PUNCT
ejpam-4821	503	4	resolving	resolve	VERB
ejpam-4821	503	5	sets	set	NOUN
ejpam-4821	503	6	in	in	ADP
ejpam-4821	503	7	the	the	DET
ejpam-4821	503	8	join	join	NOUN
ejpam-4821	503	9	and	and	CCONJ
ejpam-4821	503	10	corona	corona	NOUN
ejpam-4821	503	11	of	of	ADP
ejpam-4821	503	12	graphs	graph	NOUN
ejpam-4821	503	13	.	.	PUNCT
ejpam-4821	504	1	european	european	ADJ
ejpam-4821	504	2	journal	journal	PROPN
ejpam-4821	504	3	of	of	ADP
ejpam-4821	504	4	pure	pure	ADJ
ejpam-4821	504	5	and	and	CCONJ
ejpam-4821	504	6	applied	applied	ADJ
ejpam-4821	504	7	mathematics	mathematic	NOUN
ejpam-4821	504	8	,	,	PUNCT
ejpam-4821	504	9	14(3):773–782	14(3):773–782	PROPN
ejpam-4821	504	10	,	,	PUNCT
ejpam-4821	504	11	2021	2021	NUM
ejpam-4821	504	12	.	.	PUNCT
ejpam-4821	505	1	[	[	X
ejpam-4821	505	2	6	6	NUM
ejpam-4821	505	3	]	]	PUNCT
ejpam-4821	505	4	j.	j.	PROPN
ejpam-4821	505	5	cabaro	cabaro	PROPN
ejpam-4821	505	6	and	and	CCONJ
ejpam-4821	505	7	h.	h.	PROPN
ejpam-4821	505	8	rara	rara	PROPN
ejpam-4821	505	9	.	.	PUNCT
ejpam-4821	506	1	on	on	ADP
ejpam-4821	506	2	2	2	NUM
ejpam-4821	506	3	-	-	PUNCT
ejpam-4821	506	4	resolving	resolve	VERB
ejpam-4821	506	5	dominating	dominating	NOUN
ejpam-4821	506	6	sets	set	NOUN
ejpam-4821	506	7	in	in	ADP
ejpam-4821	506	8	the	the	DET
ejpam-4821	506	9	join	join	NOUN
ejpam-4821	506	10	and	and	CCONJ
ejpam-4821	506	11	corona	corona	PROPN
ejpam-4821	506	12	and	and	CCONJ
ejpam-4821	506	13	lexicographic	lexicographic	ADJ
ejpam-4821	506	14	product	product	NOUN
ejpam-4821	506	15	of	of	ADP
ejpam-4821	506	16	graphs	graph	NOUN
ejpam-4821	506	17	.	.	PUNCT
ejpam-4821	507	1	european	european	ADJ
ejpam-4821	507	2	journal	journal	PROPN
ejpam-4821	507	3	of	of	ADP
ejpam-4821	507	4	pure	pure	ADJ
ejpam-4821	507	5	and	and	CCONJ
ejpam-4821	507	6	applied	applied	ADJ
ejpam-4821	507	7	mathematics	mathematic	NOUN
ejpam-4821	507	8	,	,	PUNCT
ejpam-4821	507	9	15(3):1201–1210	15(3):1201–1210	NUM
ejpam-4821	507	10	,	,	PUNCT
ejpam-4821	507	11	2022	2022	NUM
ejpam-4821	507	12	.	.	PUNCT
ejpam-4821	508	1	[	[	X
ejpam-4821	508	2	7	7	X
ejpam-4821	508	3	]	]	X
ejpam-4821	508	4	s.	s.	PROPN
ejpam-4821	508	5	canoy	canoy	PROPN
ejpam-4821	508	6	jr	jr	PROPN
ejpam-4821	508	7	and	and	CCONJ
ejpam-4821	508	8	g.	g.	PROPN
ejpam-4821	508	9	malacas	malacas	PROPN
ejpam-4821	508	10	.	.	PUNCT
ejpam-4821	509	1	locating	locate	VERB
ejpam-4821	509	2	dominating	dominating	NOUN
ejpam-4821	509	3	sets	set	NOUN
ejpam-4821	509	4	in	in	ADP
ejpam-4821	509	5	graphs	graph	NOUN
ejpam-4821	509	6	.	.	PUNCT
ejpam-4821	510	1	applied	apply	VERB
ejpam-4821	510	2	mathematical	mathematical	ADJ
ejpam-4821	510	3	sciences	sciences	PROPN
ejpam-4821	510	4	,	,	PUNCT
ejpam-4821	510	5	8(88):4381–4388	8(88):4381–4388	NUM
ejpam-4821	510	6	,	,	PUNCT
ejpam-4821	510	7	2014	2014	NUM
ejpam-4821	510	8	.	.	PUNCT
ejpam-4821	511	1	[	[	X
ejpam-4821	511	2	8	8	X
ejpam-4821	511	3	]	]	X
ejpam-4821	511	4	s.	s.	PROPN
ejpam-4821	511	5	canoy	canoy	PROPN
ejpam-4821	511	6	jr	jr	PROPN
ejpam-4821	511	7	and	and	CCONJ
ejpam-4821	511	8	g.	g.	PROPN
ejpam-4821	511	9	malacas	malacas	PROPN
ejpam-4821	511	10	.	.	PUNCT
ejpam-4821	512	1	locating	locate	VERB
ejpam-4821	512	2	sets	set	NOUN
ejpam-4821	512	3	in	in	ADP
ejpam-4821	512	4	a	a	DET
ejpam-4821	512	5	graph	graph	NOUN
ejpam-4821	512	6	.	.	PUNCT
ejpam-4821	513	1	applied	apply	VERB
ejpam-4821	513	2	mathematical	mathematical	ADJ
ejpam-4821	513	3	sciences	science	NOUN
ejpam-4821	513	4	,	,	PUNCT
ejpam-4821	513	5	9:2957–2964	9:2957–2964	NUM
ejpam-4821	513	6	,	,	PUNCT
ejpam-4821	513	7	2015	2015	NUM
ejpam-4821	513	8	.	.	PUNCT
ejpam-4821	514	1	[	[	X
ejpam-4821	514	2	9	9	NUM
ejpam-4821	514	3	]	]	PUNCT
ejpam-4821	514	4	a.	a.	NOUN
ejpam-4821	514	5	mahistrado	mahistrado	NOUN
ejpam-4821	514	6	and	and	CCONJ
ejpam-4821	514	7	h.	h.	PROPN
ejpam-4821	514	8	rara	rara	PROPN
ejpam-4821	514	9	.	.	PUNCT
ejpam-4821	515	1	on	on	ADP
ejpam-4821	515	2	2	2	NUM
ejpam-4821	515	3	-	-	PUNCT
ejpam-4821	515	4	resolving	resolve	VERB
ejpam-4821	515	5	hop	hop	NOUN
ejpam-4821	515	6	dominating	dominating	NOUN
ejpam-4821	515	7	sets	set	NOUN
ejpam-4821	515	8	in	in	ADP
ejpam-4821	515	9	the	the	DET
ejpam-4821	515	10	join	join	NOUN
ejpam-4821	515	11	and	and	CCONJ
ejpam-4821	515	12	corona	corona	PROPN
ejpam-4821	515	13	and	and	CCONJ
ejpam-4821	515	14	lexicographic	lexicographic	ADJ
ejpam-4821	515	15	product	product	NOUN
ejpam-4821	515	16	of	of	ADP
ejpam-4821	515	17	graphs	graph	NOUN
ejpam-4821	515	18	.	.	PUNCT
ejpam-4821	516	1	european	european	ADJ
ejpam-4821	516	2	journal	journal	PROPN
ejpam-4821	516	3	of	of	ADP
ejpam-4821	516	4	pure	pure	ADJ
ejpam-4821	516	5	and	and	CCONJ
ejpam-4821	516	6	applied	applied	ADJ
ejpam-4821	516	7	mathematics	mathematic	NOUN
ejpam-4821	516	8	,	,	PUNCT
ejpam-4821	516	9	15(4):1982–1997	15(4):1982–1997	NUM
ejpam-4821	516	10	,	,	PUNCT
ejpam-4821	516	11	2022	2022	NUM
ejpam-4821	516	12	.	.	PUNCT
ejpam-4821	517	1	[	[	X
ejpam-4821	517	2	10	10	NUM
ejpam-4821	517	3	]	]	PUNCT
ejpam-4821	517	4	a.	a.	NOUN
ejpam-4821	517	5	mahistrado	mahistrado	NOUN
ejpam-4821	517	6	and	and	CCONJ
ejpam-4821	517	7	h.	h.	PROPN
ejpam-4821	517	8	rara	rara	PROPN
ejpam-4821	517	9	.	.	PUNCT
ejpam-4821	518	1	outer	outer	ADV
ejpam-4821	518	2	-	-	PUNCT
ejpam-4821	518	3	connected	connect	VERB
ejpam-4821	518	4	2	2	NUM
ejpam-4821	518	5	-	-	PUNCT
ejpam-4821	518	6	resolving	resolve	VERB
ejpam-4821	518	7	hop	hop	NOUN
ejpam-4821	518	8	domination	domination	NOUN
ejpam-4821	518	9	in	in	ADP
ejpam-4821	518	10	graphs	graph	NOUN
ejpam-4821	518	11	.	.	PUNCT
ejpam-4821	519	1	european	european	ADJ
ejpam-4821	519	2	journal	journal	PROPN
ejpam-4821	519	3	of	of	ADP
ejpam-4821	519	4	pure	pure	ADJ
ejpam-4821	519	5	and	and	CCONJ
ejpam-4821	519	6	applied	applied	ADJ
ejpam-4821	519	7	mathematics	mathematic	NOUN
ejpam-4821	519	8	,	,	PUNCT
ejpam-4821	519	9	16(2):1180–1195	16(2):1180–1195	NUM
ejpam-4821	519	10	,	,	PUNCT
ejpam-4821	519	11	2023	2023	NUM
ejpam-4821	519	12	.	.	PUNCT
ejpam-4821	520	1	[	[	X
ejpam-4821	520	2	11	11	NUM
ejpam-4821	520	3	]	]	PUNCT
ejpam-4821	520	4	a.	a.	NOUN
ejpam-4821	520	5	mahistrado	mahistrado	NOUN
ejpam-4821	520	6	and	and	CCONJ
ejpam-4821	520	7	h.	h.	PROPN
ejpam-4821	520	8	rara	rara	PROPN
ejpam-4821	520	9	.	.	PUNCT
ejpam-4821	521	1	restrained	restrain	VERB
ejpam-4821	521	2	2	2	NUM
ejpam-4821	521	3	-	-	PUNCT
ejpam-4821	521	4	resolving	resolve	VERB
ejpam-4821	521	5	hop	hop	NOUN
ejpam-4821	521	6	domination	domination	NOUN
ejpam-4821	521	7	in	in	ADP
ejpam-4821	521	8	graphs	graph	NOUN
ejpam-4821	521	9	.	.	PUNCT
ejpam-4821	522	1	european	european	ADJ
ejpam-4821	522	2	journal	journal	PROPN
ejpam-4821	522	3	of	of	ADP
ejpam-4821	522	4	pure	pure	ADJ
ejpam-4821	522	5	and	and	CCONJ
ejpam-4821	522	6	applied	applied	ADJ
ejpam-4821	522	7	mathematics	mathematic	NOUN
ejpam-4821	522	8	,	,	PUNCT
ejpam-4821	522	9	16(1):286–303	16(1):286–303	NUM
ejpam-4821	522	10	,	,	PUNCT
ejpam-4821	522	11	2023	2023	NUM
ejpam-4821	522	12	.	.	PUNCT
ejpam-4821	523	1	[	[	X
ejpam-4821	523	2	12	12	NUM
ejpam-4821	523	3	]	]	X
ejpam-4821	523	4	d.	d.	PROPN
ejpam-4821	523	5	managbanag	managbanag	PROPN
ejpam-4821	523	6	and	and	CCONJ
ejpam-4821	523	7	h.	h.	PROPN
ejpam-4821	523	8	rara	rara	PROPN
ejpam-4821	523	9	.	.	PUNCT
ejpam-4821	524	1	forcing	force	VERB
ejpam-4821	524	2	2	2	NUM
ejpam-4821	524	3	-	-	PUNCT
ejpam-4821	524	4	metric	metric	ADJ
ejpam-4821	524	5	dimension	dimension	NOUN
ejpam-4821	524	6	in	in	ADP
ejpam-4821	524	7	the	the	DET
ejpam-4821	524	8	join	join	NOUN
ejpam-4821	524	9	and	and	CCONJ
ejpam-4821	524	10	corona	corona	NOUN
ejpam-4821	524	11	of	of	ADP
ejpam-4821	524	12	graphs	graph	NOUN
ejpam-4821	524	13	.	.	PUNCT
ejpam-4821	525	1	european	european	ADJ
ejpam-4821	525	2	journal	journal	PROPN
ejpam-4821	525	3	of	of	ADP
ejpam-4821	525	4	pure	pure	ADJ
ejpam-4821	525	5	and	and	CCONJ
ejpam-4821	525	6	applied	applied	ADJ
ejpam-4821	525	7	mathematics	mathematic	NOUN
ejpam-4821	525	8	,	,	PUNCT
ejpam-4821	525	9	16(2):1068–1083	16(2):1068–1083	NUM
ejpam-4821	525	10	,	,	PUNCT
ejpam-4821	525	11	2023	2023	NUM
ejpam-4821	525	12	.	.	PUNCT
ejpam-4821	526	1	[	[	X
ejpam-4821	526	2	13	13	NUM
ejpam-4821	526	3	]	]	PUNCT
ejpam-4821	526	4	j.	j.	PROPN
ejpam-4821	526	5	s.	s.	PROPN
ejpam-4821	526	6	mohamad	mohamad	PROPN
ejpam-4821	526	7	and	and	CCONJ
ejpam-4821	526	8	h.	h.	PROPN
ejpam-4821	526	9	rara	rara	PROPN
ejpam-4821	526	10	.	.	PUNCT
ejpam-4821	527	1	on	on	ADP
ejpam-4821	527	2	resolving	resolve	VERB
ejpam-4821	527	3	hop	hop	NOUN
ejpam-4821	527	4	domination	domination	NOUN
ejpam-4821	527	5	in	in	ADP
ejpam-4821	527	6	graphs	graph	NOUN
ejpam-4821	527	7	.	.	PUNCT
ejpam-4821	528	1	european	european	ADJ
ejpam-4821	528	2	journal	journal	PROPN
ejpam-4821	528	3	of	of	ADP
ejpam-4821	528	4	pure	pure	ADJ
ejpam-4821	528	5	and	and	CCONJ
ejpam-4821	528	6	applied	applied	ADJ
ejpam-4821	528	7	mathematics	mathematic	NOUN
ejpam-4821	528	8	,	,	PUNCT
ejpam-4821	528	9	14(3):1015–1023	14(3):1015–1023	NUM
ejpam-4821	528	10	,	,	PUNCT
ejpam-4821	528	11	2021	2021	NUM
ejpam-4821	528	12	.	.	PUNCT
ejpam-4821	529	1	references	reference	NOUN
ejpam-4821	529	2	1662	1662	NUM
ejpam-4821	530	1	[	[	X
ejpam-4821	530	2	14	14	NUM
ejpam-4821	530	3	]	]	PUNCT
ejpam-4821	531	1	j.	j.	PROPN
ejpam-4821	531	2	s.	s.	PROPN
ejpam-4821	531	3	mohamad	mohamad	PROPN
ejpam-4821	531	4	and	and	CCONJ
ejpam-4821	531	5	h.	h.	PROPN
ejpam-4821	531	6	rara	rara	PROPN
ejpam-4821	531	7	.	.	PUNCT
ejpam-4821	532	1	1	1	NUM
ejpam-4821	532	2	-	-	PUNCT
ejpam-4821	532	3	movable	movable	ADJ
ejpam-4821	532	4	resolving	resolve	VERB
ejpam-4821	532	5	hop	hop	NOUN
ejpam-4821	532	6	domination	domination	NOUN
ejpam-4821	532	7	in	in	ADP
ejpam-4821	532	8	graphs	graph	NOUN
ejpam-4821	532	9	.	.	PUNCT
ejpam-4821	533	1	european	european	ADJ
ejpam-4821	533	2	journal	journal	PROPN
ejpam-4821	533	3	of	of	ADP
ejpam-4821	533	4	pure	pure	ADJ
ejpam-4821	533	5	and	and	CCONJ
ejpam-4821	533	6	applied	applied	ADJ
ejpam-4821	533	7	mathematics	mathematic	NOUN
ejpam-4821	533	8	,	,	PUNCT
ejpam-4821	533	9	16(1):418–429	16(1):418–429	PROPN
ejpam-4821	533	10	,	,	PUNCT
ejpam-4821	533	11	2023	2023	NUM
ejpam-4821	533	12	.	.	PUNCT
ejpam-4821	534	1	[	[	X
ejpam-4821	534	2	15	15	NUM
ejpam-4821	534	3	]	]	PUNCT
ejpam-4821	534	4	j.	j.	PROPN
ejpam-4821	534	5	s.	s.	PROPN
ejpam-4821	534	6	mohamad	mohamad	PROPN
ejpam-4821	534	7	and	and	CCONJ
ejpam-4821	534	8	h.	h.	PROPN
ejpam-4821	534	9	rara	rara	PROPN
ejpam-4821	534	10	.	.	PUNCT
ejpam-4821	535	1	strong	strong	ADJ
ejpam-4821	535	2	resolving	resolve	VERB
ejpam-4821	535	3	hop	hop	NOUN
ejpam-4821	535	4	domination	domination	NOUN
ejpam-4821	535	5	in	in	ADP
ejpam-4821	535	6	graphs	graph	NOUN
ejpam-4821	535	7	.	.	PUNCT
ejpam-4821	536	1	european	european	ADJ
ejpam-4821	536	2	journal	journal	PROPN
ejpam-4821	536	3	of	of	ADP
ejpam-4821	536	4	pure	pure	ADJ
ejpam-4821	536	5	and	and	CCONJ
ejpam-4821	536	6	applied	applied	ADJ
ejpam-4821	536	7	mathematics	mathematic	NOUN
ejpam-4821	536	8	,	,	PUNCT
ejpam-4821	536	9	16(1):131–143	16(1):131–143	PROPN
ejpam-4821	536	10	,	,	PUNCT
ejpam-4821	536	11	2023	2023	NUM
ejpam-4821	536	12	.	.	PUNCT
ejpam-4821	537	1	[	[	X
ejpam-4821	537	2	16	16	NUM
ejpam-4821	537	3	]	]	PUNCT
ejpam-4821	537	4	b.	b.	PROPN
ejpam-4821	537	5	omamalin	omamalin	PROPN
ejpam-4821	537	6	,	,	PUNCT
ejpam-4821	537	7	s.	s.	PROPN
ejpam-4821	537	8	canoy	canoy	PROPN
ejpam-4821	537	9	,	,	PUNCT
ejpam-4821	537	10	and	and	CCONJ
ejpam-4821	537	11	h.	h.	PROPN
ejpam-4821	537	12	rara	rara	PROPN
ejpam-4821	537	13	.	.	PUNCT
ejpam-4821	538	1	locating	locate	VERB
ejpam-4821	538	2	total	total	ADJ
ejpam-4821	538	3	dominating	dominating	NOUN
ejpam-4821	538	4	sets	set	NOUN
ejpam-4821	538	5	in	in	ADP
ejpam-4821	538	6	the	the	DET
ejpam-4821	538	7	join	join	NOUN
ejpam-4821	538	8	,	,	PUNCT
ejpam-4821	538	9	corona	corona	NOUN
ejpam-4821	538	10	and	and	CCONJ
ejpam-4821	538	11	composition	composition	NOUN
ejpam-4821	538	12	of	of	ADP
ejpam-4821	538	13	graphs	graph	NOUN
ejpam-4821	538	14	.	.	PUNCT
ejpam-4821	539	1	applied	apply	VERB
ejpam-4821	539	2	mathematical	mathematical	ADJ
ejpam-4821	539	3	scciences	sccience	NOUN
ejpam-4821	539	4	,	,	PUNCT
ejpam-4821	539	5	8(48):2363	8(48):2363	NOUN
ejpam-4821	539	6	–	–	PUNCT
ejpam-4821	539	7	2374	2374	NUM
ejpam-4821	539	8	,	,	PUNCT
ejpam-4821	539	9	2014	2014	NUM
ejpam-4821	539	10	.	.	PUNCT
ejpam-4821	540	1	[	[	X
ejpam-4821	540	2	17	17	NUM
ejpam-4821	540	3	]	]	X
ejpam-4821	540	4	v.	v.	ADP
ejpam-4821	540	5	saenpholphat	saenpholphat	PROPN
ejpam-4821	540	6	and	and	CCONJ
ejpam-4821	540	7	p.	p.	PROPN
ejpam-4821	540	8	zhang	zhang	PROPN
ejpam-4821	540	9	.	.	PUNCT
ejpam-4821	541	1	on	on	ADP
ejpam-4821	541	2	connected	connected	ADJ
ejpam-4821	541	3	resolvability	resolvability	NOUN
ejpam-4821	541	4	of	of	ADP
ejpam-4821	541	5	graphs	graph	NOUN
ejpam-4821	541	6	.	.	PUNCT
ejpam-4821	542	1	australian	australian	ADJ
ejpam-4821	542	2	journal	journal	NOUN
ejpam-4821	542	3	of	of	ADP
ejpam-4821	542	4	combinatorics	combinatoric	NOUN
ejpam-4821	542	5	,	,	PUNCT
ejpam-4821	542	6	28:26–37	28:26–37	NUM
ejpam-4821	542	7	,	,	PUNCT
ejpam-4821	542	8	2003	2003	NUM
ejpam-4821	542	9	.	.	PUNCT
ejpam-4821	543	1	[	[	X
ejpam-4821	543	2	18	18	NUM
ejpam-4821	543	3	]	]	X
ejpam-4821	543	4	s.	s.	PROPN
ejpam-4821	543	5	seo	seo	PROPN
ejpam-4821	543	6	and	and	CCONJ
ejpam-4821	543	7	p.	p.	PROPN
ejpam-4821	543	8	slater	slater	PROPN
ejpam-4821	543	9	.	.	PUNCT
ejpam-4821	544	1	open	open	ADJ
ejpam-4821	544	2	neighborhood	neighborhood	NOUN
ejpam-4821	544	3	locating	locate	VERB
ejpam-4821	544	4	-	-	PUNCT
ejpam-4821	544	5	dominating	dominating	NOUN
ejpam-4821	544	6	sets	set	NOUN
ejpam-4821	544	7	.	.	PUNCT
ejpam-4821	545	1	australian	australian	ADJ
ejpam-4821	545	2	journal	journal	NOUN
ejpam-4821	545	3	of	of	ADP
ejpam-4821	545	4	combinatorics	combinatoric	NOUN
ejpam-4821	545	5	,	,	PUNCT
ejpam-4821	545	6	46:109–119	46:109–119	PROPN
ejpam-4821	545	7	,	,	PUNCT
ejpam-4821	545	8	2010	2010	NUM
ejpam-4821	545	9	.	.	PUNCT
ejpam-4821	546	1	[	[	X
ejpam-4821	546	2	19	19	NUM
ejpam-4821	546	3	]	]	X
ejpam-4821	546	4	p.	p.	PROPN
ejpam-4821	546	5	slater	slater	PROPN
ejpam-4821	546	6	.	.	PUNCT
ejpam-4821	547	1	dominating	dominating	NOUN
ejpam-4821	547	2	and	and	CCONJ
ejpam-4821	547	3	reference	reference	NOUN
ejpam-4821	547	4	sets	set	NOUN
ejpam-4821	547	5	in	in	ADP
ejpam-4821	547	6	a	a	DET
ejpam-4821	547	7	graph	graph	NOUN
ejpam-4821	547	8	.	.	PUNCT
ejpam-4821	548	1	journal	journal	NOUN
ejpam-4821	548	2	of	of	ADP
ejpam-4821	548	3	mathematics	mathematic	NOUN
ejpam-4821	548	4	and	and	CCONJ
ejpam-4821	548	5	physical	physical	ADJ
ejpam-4821	548	6	science	science	NOUN
ejpam-4821	548	7	,	,	PUNCT
ejpam-4821	548	8	22(4):445–455	22(4):445–455	PROPN
ejpam-4821	548	9	.	.	PUNCT