id	sid	tid	token	lemma	pos
ejpam-4500	1	1	european	european	PROPN
ejpam-4500	1	2	journal	journal	PROPN
ejpam-4500	1	3	of	of	ADP
ejpam-4500	1	4	pure	pure	ADJ
ejpam-4500	1	5	and	and	CCONJ
ejpam-4500	1	6	applied	apply	VERB
ejpam-4500	1	7	mathematics	mathematic	NOUN
ejpam-4500	1	8	vol	vol	NOUN
ejpam-4500	1	9	.	.	PROPN
ejpam-4500	2	1	15	15	NUM
ejpam-4500	2	2	,	,	PUNCT
ejpam-4500	2	3	no	no	INTJ
ejpam-4500	2	4	.	.	NOUN
ejpam-4500	2	5	4	4	NUM
ejpam-4500	2	6	,	,	PUNCT
ejpam-4500	2	7	2022	2022	NUM
ejpam-4500	2	8	,	,	PUNCT
ejpam-4500	2	9	1705	1705	NUM
ejpam-4500	2	10	-	-	SYM
ejpam-4500	2	11	1715	1715	NUM
ejpam-4500	2	12	issn	issn	PROPN
ejpam-4500	2	13	1307	1307	NUM
ejpam-4500	2	14	-	-	SYM
ejpam-4500	2	15	5543	5543	NUM
ejpam-4500	2	16	–	–	PUNCT
ejpam-4500	2	17	ejpam.com	ejpam.com	X
ejpam-4500	2	18	published	publish	VERB
ejpam-4500	2	19	by	by	ADP
ejpam-4500	2	20	new	new	PROPN
ejpam-4500	2	21	york	york	PROPN
ejpam-4500	2	22	business	business	PROPN
ejpam-4500	2	23	global	global	ADJ
ejpam-4500	2	24	locating	locate	VERB
ejpam-4500	2	25	hop	hop	NOUN
ejpam-4500	2	26	sets	set	NOUN
ejpam-4500	2	27	in	in	ADP
ejpam-4500	2	28	a	a	DET
ejpam-4500	2	29	graph	graph	NOUN
ejpam-4500	2	30	ethel	ethel	PROPN
ejpam-4500	2	31	mae	mae	PROPN
ejpam-4500	2	32	a.	a.	PROPN
ejpam-4500	2	33	pagcu1,∗	pagcu1,∗	NOUN
ejpam-4500	2	34	,	,	PUNCT
ejpam-4500	2	35	gina	gina	PROPN
ejpam-4500	2	36	a.	a.	PROPN
ejpam-4500	2	37	malacas1,2	malacas1,2	PROPN
ejpam-4500	2	38	,	,	PUNCT
ejpam-4500	2	39	sergio	sergio	PROPN
ejpam-4500	2	40	r.	r.	PROPN
ejpam-4500	2	41	canoy	canoy	PROPN
ejpam-4500	2	42	,	,	PUNCT
ejpam-4500	2	43	jr.1,2	jr.1,2	ADJ
ejpam-4500	2	44	1	1	NUM
ejpam-4500	2	45	department	department	NOUN
ejpam-4500	2	46	of	of	ADP
ejpam-4500	2	47	mathematics	mathematic	NOUN
ejpam-4500	2	48	and	and	CCONJ
ejpam-4500	2	49	statistics	statistic	NOUN
ejpam-4500	2	50	,	,	PUNCT
ejpam-4500	2	51	college	college	NOUN
ejpam-4500	2	52	of	of	ADP
ejpam-4500	2	53	science	science	NOUN
ejpam-4500	2	54	and	and	CCONJ
ejpam-4500	2	55	mathematics	mathematic	NOUN
ejpam-4500	2	56	,	,	PUNCT
ejpam-4500	2	57	mindanao	mindanao	PROPN
ejpam-4500	2	58	state	state	PROPN
ejpam-4500	2	59	university	university	PROPN
ejpam-4500	2	60	-	-	PUNCT
ejpam-4500	2	61	iligan	iligan	PROPN
ejpam-4500	2	62	institute	institute	PROPN
ejpam-4500	2	63	of	of	ADP
ejpam-4500	2	64	technology	technology	PROPN
ejpam-4500	2	65	,	,	PUNCT
ejpam-4500	2	66	9200	9200	NUM
ejpam-4500	2	67	tibanga	tibanga	NOUN
ejpam-4500	2	68	,	,	PUNCT
ejpam-4500	2	69	iligan	iligan	ADJ
ejpam-4500	2	70	city	city	PROPN
ejpam-4500	2	71	,	,	PUNCT
ejpam-4500	2	72	philippines	philippine	NOUN
ejpam-4500	2	73	2	2	NUM
ejpam-4500	2	74	center	center	NOUN
ejpam-4500	2	75	for	for	ADP
ejpam-4500	2	76	graph	graph	NOUN
ejpam-4500	2	77	theory	theory	NOUN
ejpam-4500	2	78	,	,	PUNCT
ejpam-4500	2	79	algebra	algebra	NOUN
ejpam-4500	2	80	,	,	PUNCT
ejpam-4500	2	81	and	and	CCONJ
ejpam-4500	2	82	analysis	analysis	NOUN
ejpam-4500	2	83	,	,	PUNCT
ejpam-4500	2	84	premier	premier	PROPN
ejpam-4500	2	85	research	research	PROPN
ejpam-4500	2	86	institute	institute	PROPN
ejpam-4500	2	87	in	in	ADP
ejpam-4500	2	88	science	science	NOUN
ejpam-4500	2	89	and	and	CCONJ
ejpam-4500	2	90	mathematics	mathematic	NOUN
ejpam-4500	2	91	,	,	PUNCT
ejpam-4500	2	92	mindanao	mindanao	PROPN
ejpam-4500	2	93	state	state	PROPN
ejpam-4500	2	94	university	university	PROPN
ejpam-4500	2	95	-	-	PUNCT
ejpam-4500	2	96	iligan	iligan	PROPN
ejpam-4500	2	97	institute	institute	PROPN
ejpam-4500	2	98	of	of	ADP
ejpam-4500	2	99	technology	technology	PROPN
ejpam-4500	2	100	,	,	PUNCT
ejpam-4500	2	101	9200	9200	NUM
ejpam-4500	2	102	tibanga	tibanga	NOUN
ejpam-4500	2	103	,	,	PUNCT
ejpam-4500	2	104	iligan	iligan	ADJ
ejpam-4500	2	105	city	city	PROPN
ejpam-4500	2	106	,	,	PUNCT
ejpam-4500	2	107	philippines	philippine	NOUN
ejpam-4500	2	108	abstract	abstract	ADJ
ejpam-4500	2	109	.	.	PUNCT
ejpam-4500	3	1	let	let	VERB
ejpam-4500	3	2	g	g	PRON
ejpam-4500	3	3	be	be	AUX
ejpam-4500	3	4	a	a	DET
ejpam-4500	3	5	connected	connected	ADJ
ejpam-4500	3	6	graph	graph	NOUN
ejpam-4500	3	7	with	with	ADP
ejpam-4500	3	8	vertex	vertex	NOUN
ejpam-4500	3	9	set	set	VERB
ejpam-4500	3	10	v	v	NOUN
ejpam-4500	3	11	(	(	PUNCT
ejpam-4500	3	12	g	g	NOUN
ejpam-4500	3	13	)	)	PUNCT
ejpam-4500	3	14	and	and	CCONJ
ejpam-4500	3	15	edge	edge	VERB
ejpam-4500	3	16	set	set	VERB
ejpam-4500	3	17	e(g	e(g	PROPN
ejpam-4500	3	18	)	)	PUNCT
ejpam-4500	3	19	.	.	PUNCT
ejpam-4500	4	1	the	the	DET
ejpam-4500	4	2	open	open	ADJ
ejpam-4500	4	3	hop	hop	NOUN
ejpam-4500	4	4	neighborhood	neighborhood	NOUN
ejpam-4500	4	5	of	of	ADP
ejpam-4500	4	6	vertex	vertex	NOUN
ejpam-4500	4	7	v	v	ADP
ejpam-4500	4	8	∈	∈	PROPN
ejpam-4500	4	9	v	v	NOUN
ejpam-4500	4	10	(	(	PUNCT
ejpam-4500	4	11	g	g	NOUN
ejpam-4500	4	12	)	)	PUNCT
ejpam-4500	4	13	is	be	AUX
ejpam-4500	4	14	the	the	DET
ejpam-4500	4	15	set	set	NOUN
ejpam-4500	4	16	ng(v	ng(v	PUNCT
ejpam-4500	4	17	,	,	PUNCT
ejpam-4500	4	18	2	2	X
ejpam-4500	4	19	)	)	PUNCT
ejpam-4500	4	20	=	=	PRON
ejpam-4500	4	21	{	{	PUNCT
ejpam-4500	4	22	w	w	NOUN
ejpam-4500	4	23	∈	∈	PROPN
ejpam-4500	4	24	v	v	ADP
ejpam-4500	4	25	(	(	PUNCT
ejpam-4500	4	26	g	g	NOUN
ejpam-4500	4	27	)	)	PUNCT
ejpam-4500	4	28	:	:	PUNCT
ejpam-4500	4	29	dg(v	dg(v	X
ejpam-4500	4	30	,	,	PUNCT
ejpam-4500	4	31	w	w	NOUN
ejpam-4500	4	32	)	)	PUNCT
ejpam-4500	4	33	=	=	SYM
ejpam-4500	4	34	2	2	NUM
ejpam-4500	4	35	}	}	PUNCT
ejpam-4500	4	36	,	,	PUNCT
ejpam-4500	4	37	where	where	SCONJ
ejpam-4500	4	38	dg(v	dg(v	X
ejpam-4500	4	39	,	,	PUNCT
ejpam-4500	4	40	w	w	NOUN
ejpam-4500	4	41	)	)	PUNCT
ejpam-4500	4	42	denotes	denote	VERB
ejpam-4500	4	43	the	the	DET
ejpam-4500	4	44	distance	distance	NOUN
ejpam-4500	4	45	between	between	ADP
ejpam-4500	4	46	v	v	NOUN
ejpam-4500	4	47	and	and	CCONJ
ejpam-4500	4	48	w.	w.	PROPN
ejpam-4500	4	49	a	a	DET
ejpam-4500	4	50	non	non	ADJ
ejpam-4500	4	51	-	-	ADJ
ejpam-4500	4	52	empty	empty	ADJ
ejpam-4500	4	53	set	set	NOUN
ejpam-4500	4	54	s	s	PROPN
ejpam-4500	4	55	⊆	⊆	NUM
ejpam-4500	4	56	v	v	NOUN
ejpam-4500	4	57	(	(	PUNCT
ejpam-4500	4	58	g	g	NOUN
ejpam-4500	4	59	)	)	PUNCT
ejpam-4500	4	60	is	be	AUX
ejpam-4500	4	61	a	a	DET
ejpam-4500	4	62	locating	locate	VERB
ejpam-4500	4	63	hop	hop	NOUN
ejpam-4500	4	64	set	set	NOUN
ejpam-4500	4	65	of	of	ADP
ejpam-4500	4	66	g	g	PROPN
ejpam-4500	4	67	if	if	SCONJ
ejpam-4500	4	68	ng(u	ng(u	NOUN
ejpam-4500	4	69	,	,	PUNCT
ejpam-4500	4	70	2	2	X
ejpam-4500	4	71	)	)	PUNCT
ejpam-4500	4	72	∩	∩	NOUN
ejpam-4500	4	73	s	s	PART
ejpam-4500	4	74	̸=	̸=	PROPN
ejpam-4500	4	75	ng(v	ng(v	PUNCT
ejpam-4500	4	76	,	,	PUNCT
ejpam-4500	4	77	2	2	X
ejpam-4500	4	78	)	)	PUNCT
ejpam-4500	4	79	∩	∩	NOUN
ejpam-4500	4	80	s	s	PART
ejpam-4500	4	81	for	for	ADP
ejpam-4500	4	82	every	every	DET
ejpam-4500	4	83	pair	pair	NOUN
ejpam-4500	4	84	of	of	ADP
ejpam-4500	4	85	distinct	distinct	ADJ
ejpam-4500	4	86	vertices	vertex	NOUN
ejpam-4500	4	87	u	u	NOUN
ejpam-4500	4	88	,	,	PUNCT
ejpam-4500	4	89	v	v	NOUN
ejpam-4500	4	90	∈	∈	PROPN
ejpam-4500	4	91	v	v	NOUN
ejpam-4500	4	92	(	(	PUNCT
ejpam-4500	4	93	g	g	NOUN
ejpam-4500	4	94	)	)	PUNCT
ejpam-4500	4	95	\	\	PUNCT
ejpam-4500	5	1	s.	s.	PROPN
ejpam-4500	5	2	the	the	DET
ejpam-4500	5	3	smallest	small	ADJ
ejpam-4500	5	4	cardinality	cardinality	NOUN
ejpam-4500	5	5	of	of	ADP
ejpam-4500	5	6	a	a	DET
ejpam-4500	5	7	locating	locate	VERB
ejpam-4500	5	8	hop	hop	NOUN
ejpam-4500	5	9	set	set	NOUN
ejpam-4500	5	10	of	of	ADP
ejpam-4500	5	11	g	g	NOUN
ejpam-4500	5	12	,	,	PUNCT
ejpam-4500	5	13	denoted	denote	VERB
ejpam-4500	5	14	by	by	ADP
ejpam-4500	5	15	lhn(g	lhn(g	PROPN
ejpam-4500	5	16	)	)	PUNCT
ejpam-4500	5	17	is	be	AUX
ejpam-4500	5	18	called	call	VERB
ejpam-4500	5	19	the	the	DET
ejpam-4500	5	20	locating	locate	VERB
ejpam-4500	5	21	hop	hop	NOUN
ejpam-4500	5	22	number	number	NOUN
ejpam-4500	5	23	of	of	ADP
ejpam-4500	5	24	g.	g.	PROPN
ejpam-4500	5	25	this	this	DET
ejpam-4500	5	26	study	study	NOUN
ejpam-4500	5	27	focuses	focus	VERB
ejpam-4500	5	28	mainly	mainly	ADV
ejpam-4500	5	29	on	on	ADP
ejpam-4500	5	30	the	the	DET
ejpam-4500	5	31	concept	concept	NOUN
ejpam-4500	5	32	of	of	ADP
ejpam-4500	5	33	locating	locate	VERB
ejpam-4500	5	34	hop	hop	NOUN
ejpam-4500	5	35	set	set	VERB
ejpam-4500	5	36	in	in	ADP
ejpam-4500	5	37	graphs	graph	NOUN
ejpam-4500	5	38	.	.	PUNCT
ejpam-4500	6	1	characterizations	characterization	NOUN
ejpam-4500	6	2	of	of	ADP
ejpam-4500	6	3	locating	locate	VERB
ejpam-4500	6	4	hop	hop	NOUN
ejpam-4500	6	5	sets	set	NOUN
ejpam-4500	6	6	in	in	ADP
ejpam-4500	6	7	the	the	DET
ejpam-4500	6	8	join	join	NOUN
ejpam-4500	6	9	and	and	CCONJ
ejpam-4500	6	10	corona	corona	NOUN
ejpam-4500	6	11	of	of	ADP
ejpam-4500	6	12	two	two	NUM
ejpam-4500	6	13	graphs	graph	NOUN
ejpam-4500	6	14	are	be	AUX
ejpam-4500	6	15	given	give	VERB
ejpam-4500	6	16	and	and	CCONJ
ejpam-4500	6	17	bounds	bound	NOUN
ejpam-4500	6	18	for	for	ADP
ejpam-4500	6	19	the	the	DET
ejpam-4500	6	20	corresponding	corresponding	ADJ
ejpam-4500	6	21	locating	locate	VERB
ejpam-4500	6	22	hop	hop	NOUN
ejpam-4500	6	23	numbers	number	NOUN
ejpam-4500	6	24	of	of	ADP
ejpam-4500	6	25	these	these	DET
ejpam-4500	6	26	graphs	graph	NOUN
ejpam-4500	6	27	are	be	AUX
ejpam-4500	6	28	determined	determine	VERB
ejpam-4500	6	29	.	.	PUNCT
ejpam-4500	7	1	2020	2020	NUM
ejpam-4500	7	2	mathematics	mathematic	NOUN
ejpam-4500	7	3	subject	subject	NOUN
ejpam-4500	7	4	classifications	classification	NOUN
ejpam-4500	7	5	:	:	PUNCT
ejpam-4500	7	6	05c69	05c69	X
ejpam-4500	7	7	key	key	ADJ
ejpam-4500	7	8	words	word	NOUN
ejpam-4500	7	9	and	and	CCONJ
ejpam-4500	7	10	phrases	phrase	NOUN
ejpam-4500	7	11	:	:	PUNCT
ejpam-4500	7	12	locating	locate	VERB
ejpam-4500	7	13	hop	hop	NOUN
ejpam-4500	7	14	set	set	NOUN
ejpam-4500	7	15	,	,	PUNCT
ejpam-4500	7	16	strictly	strictly	ADV
ejpam-4500	7	17	locating	locate	VERB
ejpam-4500	7	18	hop	hop	NOUN
ejpam-4500	7	19	set	set	NOUN
ejpam-4500	7	20	,	,	PUNCT
ejpam-4500	7	21	join	join	NOUN
ejpam-4500	7	22	,	,	PUNCT
ejpam-4500	7	23	corona	corona	PROPN
ejpam-4500	7	24	1	1	NUM
ejpam-4500	7	25	.	.	PUNCT
ejpam-4500	8	1	introduction	introduction	NOUN
ejpam-4500	8	2	let	let	VERB
ejpam-4500	8	3	g	g	NOUN
ejpam-4500	8	4	=	=	SYM
ejpam-4500	8	5	(	(	PUNCT
ejpam-4500	8	6	v	v	NOUN
ejpam-4500	8	7	(	(	PUNCT
ejpam-4500	8	8	g	g	NOUN
ejpam-4500	8	9	)	)	PUNCT
ejpam-4500	8	10	,	,	PUNCT
ejpam-4500	8	11	e(g	e(g	PROPN
ejpam-4500	8	12	)	)	PUNCT
ejpam-4500	8	13	)	)	PUNCT
ejpam-4500	8	14	be	be	AUX
ejpam-4500	8	15	a	a	DET
ejpam-4500	8	16	simple	simple	ADJ
ejpam-4500	8	17	graph	graph	NOUN
ejpam-4500	8	18	and	and	CCONJ
ejpam-4500	8	19	v	v	ADP
ejpam-4500	8	20	∈	∈	PROPN
ejpam-4500	8	21	v	v	NOUN
ejpam-4500	8	22	(	(	PUNCT
ejpam-4500	8	23	g	g	NOUN
ejpam-4500	8	24	)	)	PUNCT
ejpam-4500	8	25	.	.	PUNCT
ejpam-4500	9	1	the	the	DET
ejpam-4500	9	2	set	set	NOUN
ejpam-4500	9	3	of	of	ADP
ejpam-4500	9	4	neighbors	neighbor	NOUN
ejpam-4500	9	5	of	of	ADP
ejpam-4500	9	6	a	a	DET
ejpam-4500	9	7	vertex	vertex	NOUN
ejpam-4500	9	8	u	u	NOUN
ejpam-4500	9	9	in	in	ADP
ejpam-4500	9	10	g	g	NOUN
ejpam-4500	9	11	,	,	PUNCT
ejpam-4500	9	12	denoted	denote	VERB
ejpam-4500	9	13	by	by	ADP
ejpam-4500	9	14	ng(u	ng(u	NOUN
ejpam-4500	9	15	)	)	PUNCT
ejpam-4500	9	16	,	,	PUNCT
ejpam-4500	9	17	is	be	AUX
ejpam-4500	9	18	called	call	VERB
ejpam-4500	9	19	the	the	DET
ejpam-4500	9	20	open	open	ADJ
ejpam-4500	9	21	neighborhood	neighborhood	NOUN
ejpam-4500	9	22	of	of	ADP
ejpam-4500	9	23	u	u	PROPN
ejpam-4500	9	24	in	in	ADP
ejpam-4500	9	25	g.	g.	PROPN
ejpam-4500	9	26	the	the	DET
ejpam-4500	9	27	closed	close	VERB
ejpam-4500	9	28	neighborhood	neighborhood	NOUN
ejpam-4500	9	29	of	of	ADP
ejpam-4500	9	30	u	u	NOUN
ejpam-4500	9	31	in	in	ADP
ejpam-4500	9	32	g	g	PROPN
ejpam-4500	9	33	is	be	AUX
ejpam-4500	9	34	the	the	DET
ejpam-4500	9	35	set	set	NOUN
ejpam-4500	9	36	ng[u	ng[u	PROPN
ejpam-4500	9	37	]	]	X
ejpam-4500	9	38	=	=	SYM
ejpam-4500	9	39	ng(u	ng(u	PROPN
ejpam-4500	9	40	)	)	PUNCT
ejpam-4500	9	41	∪	∪	NOUN
ejpam-4500	9	42	{	{	PUNCT
ejpam-4500	9	43	u	u	NOUN
ejpam-4500	9	44	}	}	PUNCT
ejpam-4500	9	45	.	.	PUNCT
ejpam-4500	10	1	the	the	DET
ejpam-4500	10	2	degree	degree	NOUN
ejpam-4500	10	3	of	of	ADP
ejpam-4500	10	4	a	a	DET
ejpam-4500	10	5	vertex	vertex	NOUN
ejpam-4500	10	6	v	v	NOUN
ejpam-4500	10	7	in	in	ADP
ejpam-4500	10	8	a	a	DET
ejpam-4500	10	9	graph	graph	NOUN
ejpam-4500	10	10	g	g	NOUN
ejpam-4500	10	11	,	,	PUNCT
ejpam-4500	10	12	denoted	denote	VERB
ejpam-4500	10	13	by	by	ADP
ejpam-4500	10	14	degg(v	degg(v	PROPN
ejpam-4500	10	15	)	)	PUNCT
ejpam-4500	10	16	,	,	PUNCT
ejpam-4500	10	17	is	be	AUX
ejpam-4500	10	18	the	the	DET
ejpam-4500	10	19	number	number	NOUN
ejpam-4500	10	20	of	of	ADP
ejpam-4500	10	21	edges	edge	NOUN
ejpam-4500	10	22	incident	incident	NOUN
ejpam-4500	10	23	with	with	ADP
ejpam-4500	10	24	v	v	NOUN
ejpam-4500	10	25	in	in	ADP
ejpam-4500	10	26	g	g	PROPN
ejpam-4500	10	27	and	and	CCONJ
ejpam-4500	10	28	the	the	DET
ejpam-4500	10	29	minimum	minimum	NOUN
ejpam-4500	10	30	degree	degree	NOUN
ejpam-4500	10	31	δ(g	δ(g	ADV
ejpam-4500	10	32	)	)	PUNCT
ejpam-4500	10	33	of	of	ADP
ejpam-4500	10	34	the	the	DET
ejpam-4500	10	35	vertices	vertex	NOUN
ejpam-4500	10	36	of	of	ADP
ejpam-4500	10	37	g	g	PROPN
ejpam-4500	10	38	is	be	AUX
ejpam-4500	10	39	the	the	DET
ejpam-4500	10	40	minimum	minimum	ADJ
ejpam-4500	10	41	degree	degree	NOUN
ejpam-4500	10	42	of	of	ADP
ejpam-4500	10	43	g.	g.	PROPN
ejpam-4500	10	44	the	the	DET
ejpam-4500	10	45	open	open	ADJ
ejpam-4500	10	46	hop	hop	NOUN
ejpam-4500	10	47	neighborhood	neighborhood	NOUN
ejpam-4500	10	48	of	of	ADP
ejpam-4500	10	49	vertex	vertex	NOUN
ejpam-4500	10	50	v	v	NOUN
ejpam-4500	10	51	is	be	AUX
ejpam-4500	10	52	the	the	DET
ejpam-4500	10	53	set	set	NOUN
ejpam-4500	10	54	ng(v	ng(v	PUNCT
ejpam-4500	10	55	,	,	PUNCT
ejpam-4500	10	56	2	2	X
ejpam-4500	10	57	)	)	PUNCT
ejpam-4500	10	58	=	=	PRON
ejpam-4500	10	59	{	{	PUNCT
ejpam-4500	10	60	w	w	NOUN
ejpam-4500	10	61	∈	∈	PROPN
ejpam-4500	10	62	v	v	ADP
ejpam-4500	10	63	(	(	PUNCT
ejpam-4500	10	64	g	g	NOUN
ejpam-4500	10	65	)	)	PUNCT
ejpam-4500	10	66	:	:	PUNCT
ejpam-4500	10	67	dg(v	dg(v	X
ejpam-4500	10	68	,	,	PUNCT
ejpam-4500	10	69	w	w	NOUN
ejpam-4500	10	70	)	)	PUNCT
ejpam-4500	10	71	=	=	SYM
ejpam-4500	10	72	2	2	NUM
ejpam-4500	10	73	}	}	PUNCT
ejpam-4500	10	74	,	,	PUNCT
ejpam-4500	10	75	where	where	SCONJ
ejpam-4500	10	76	dg(v	dg(v	X
ejpam-4500	10	77	,	,	PUNCT
ejpam-4500	10	78	w	w	NOUN
ejpam-4500	10	79	)	)	PUNCT
ejpam-4500	10	80	denotes	denote	VERB
ejpam-4500	10	81	the	the	DET
ejpam-4500	10	82	distance	distance	NOUN
ejpam-4500	10	83	between	between	ADP
ejpam-4500	10	84	v	v	NOUN
ejpam-4500	10	85	and	and	CCONJ
ejpam-4500	10	86	w.	w.	NOUN
ejpam-4500	10	87	the	the	DET
ejpam-4500	10	88	closed	close	VERB
ejpam-4500	10	89	hop	hop	NOUN
ejpam-4500	10	90	neighborhood	neighborhood	NOUN
ejpam-4500	10	91	of	of	ADP
ejpam-4500	10	92	vertex	vertex	NOUN
ejpam-4500	10	93	v	v	NOUN
ejpam-4500	10	94	is	be	AUX
ejpam-4500	10	95	the	the	DET
ejpam-4500	10	96	set	set	NOUN
ejpam-4500	10	97	ng[v	ng[v	PROPN
ejpam-4500	10	98	,	,	PUNCT
ejpam-4500	10	99	2	2	NUM
ejpam-4500	10	100	]	]	PUNCT
ejpam-4500	10	101	=	=	PUNCT
ejpam-4500	10	102	ng(v	ng(v	X
ejpam-4500	10	103	,	,	PUNCT
ejpam-4500	10	104	2	2	X
ejpam-4500	10	105	)	)	PUNCT
ejpam-4500	10	106	∪	∪	NOUN
ejpam-4500	10	107	{	{	PUNCT
ejpam-4500	10	108	v	v	NOUN
ejpam-4500	10	109	}	}	PUNCT
ejpam-4500	10	110	.	.	PUNCT
ejpam-4500	11	1	the	the	DET
ejpam-4500	11	2	concept	concept	NOUN
ejpam-4500	11	3	of	of	ADP
ejpam-4500	11	4	hop	hop	NOUN
ejpam-4500	11	5	neighborhood	neighborhood	NOUN
ejpam-4500	11	6	was	be	AUX
ejpam-4500	11	7	used	use	VERB
ejpam-4500	11	8	in	in	ADP
ejpam-4500	11	9	[	[	X
ejpam-4500	11	10	10	10	NUM
ejpam-4500	11	11	]	]	PUNCT
ejpam-4500	11	12	to	to	PART
ejpam-4500	11	13	define	define	VERB
ejpam-4500	11	14	and	and	CCONJ
ejpam-4500	11	15	investigate	investigate	VERB
ejpam-4500	11	16	the	the	DET
ejpam-4500	11	17	concept	concept	NOUN
ejpam-4500	11	18	of	of	ADP
ejpam-4500	11	19	hop	hop	NOUN
ejpam-4500	11	20	domination	domination	NOUN
ejpam-4500	11	21	.	.	PUNCT
ejpam-4500	12	1	hop	hop	PROPN
ejpam-4500	12	2	domination	domination	NOUN
ejpam-4500	12	3	and	and	CCONJ
ejpam-4500	12	4	some	some	PRON
ejpam-4500	12	5	of	of	ADP
ejpam-4500	12	6	its	its	PRON
ejpam-4500	12	7	variants	variant	NOUN
ejpam-4500	12	8	had	have	AUX
ejpam-4500	12	9	been	be	AUX
ejpam-4500	12	10	studied	study	VERB
ejpam-4500	12	11	also	also	ADV
ejpam-4500	12	12	in	in	ADP
ejpam-4500	12	13	[	[	X
ejpam-4500	12	14	6	6	NUM
ejpam-4500	12	15	]	]	PUNCT
ejpam-4500	12	16	,	,	PUNCT
ejpam-4500	12	17	[	[	X
ejpam-4500	12	18	7	7	NUM
ejpam-4500	12	19	]	]	PUNCT
ejpam-4500	12	20	,	,	PUNCT
ejpam-4500	12	21	[	[	X
ejpam-4500	12	22	9	9	NUM
ejpam-4500	12	23	]	]	PUNCT
ejpam-4500	12	24	,	,	PUNCT
ejpam-4500	13	1	[	[	X
ejpam-4500	13	2	12	12	NUM
ejpam-4500	13	3	]	]	PUNCT
ejpam-4500	13	4	,	,	PUNCT
ejpam-4500	13	5	and	and	CCONJ
ejpam-4500	13	6	[	[	X
ejpam-4500	13	7	13	13	NUM
ejpam-4500	13	8	]	]	PUNCT
ejpam-4500	13	9	.	.	PUNCT
ejpam-4500	14	1	∗corresponding	∗corresponde	VERB
ejpam-4500	14	2	author	author	NOUN
ejpam-4500	14	3	.	.	PUNCT
ejpam-4500	15	1	doi	doi	NOUN
ejpam-4500	15	2	:	:	PUNCT
ejpam-4500	15	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4500	https://doi.org/10.29020/nybg.ejpam.v15i4.4500	NUM
ejpam-4500	15	4	email	email	NOUN
ejpam-4500	15	5	addresses	address	NOUN
ejpam-4500	15	6	:	:	PUNCT
ejpam-4500	15	7	ethelmae.pagcu@g.msuiit.edu.ph	ethelmae.pagcu@g.msuiit.edu.ph	PROPN
ejpam-4500	15	8	(	(	PUNCT
ejpam-4500	15	9	em	em	PRON
ejpam-4500	15	10	.	.	PUNCT
ejpam-4500	16	1	pagcu	pagcu	NOUN
ejpam-4500	16	2	)	)	PUNCT
ejpam-4500	16	3	,	,	PUNCT
ejpam-4500	16	4	gina.malacas@g.msuiit.edu.ph	gina.malacas@g.msuiit.edu.ph	PROPN
ejpam-4500	16	5	(	(	PUNCT
ejpam-4500	16	6	g.	g.	PROPN
ejpam-4500	16	7	malacas	malacas	PROPN
ejpam-4500	16	8	)	)	PUNCT
ejpam-4500	16	9	,	,	PUNCT
ejpam-4500	16	10	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4500	16	11	(	(	PUNCT
ejpam-4500	16	12	s.	s.	PROPN
ejpam-4500	16	13	canoy	canoy	PROPN
ejpam-4500	16	14	,	,	PUNCT
ejpam-4500	16	15	jr	jr	PROPN
ejpam-4500	16	16	.	.	PUNCT
ejpam-4500	16	17	)	)	PUNCT
ejpam-4500	16	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4500	16	19	1705	1705	NUM
ejpam-4500	17	1	©	©	PROPN
ejpam-4500	17	2	2022	2022	NUM
ejpam-4500	17	3	ejpam	ejpam	VERB
ejpam-4500	17	4	all	all	DET
ejpam-4500	17	5	rights	right	NOUN
ejpam-4500	17	6	reserved	reserve	VERB
ejpam-4500	17	7	.	.	PUNCT
ejpam-4500	18	1	e.m	e.m	PROPN
ejpam-4500	18	2	.	.	PROPN
ejpam-4500	18	3	a.	a.	NOUN
ejpam-4500	18	4	pagcu	pagcu	PROPN
ejpam-4500	18	5	,	,	PUNCT
ejpam-4500	18	6	g.	g.	PROPN
ejpam-4500	18	7	a.	a.	NOUN
ejpam-4500	18	8	malacas	malacas	PROPN
ejpam-4500	18	9	,	,	PUNCT
ejpam-4500	18	10	s.	s.	PROPN
ejpam-4500	18	11	r.	r.	PROPN
ejpam-4500	18	12	canoy	canoy	PROPN
ejpam-4500	18	13	,	,	PUNCT
ejpam-4500	18	14	jr	jr	PROPN
ejpam-4500	18	15	.	.	PROPN
ejpam-4500	18	16	/	/	SYM
ejpam-4500	18	17	eur	eur	PROPN
ejpam-4500	18	18	.	.	PUNCT
ejpam-4500	19	1	j.	j.	PROPN
ejpam-4500	19	2	pure	pure	PROPN
ejpam-4500	19	3	appl	appl	PROPN
ejpam-4500	19	4	.	.	PROPN
ejpam-4500	19	5	math	math	PROPN
ejpam-4500	19	6	,	,	PUNCT
ejpam-4500	19	7	15	15	NUM
ejpam-4500	19	8	(	(	PUNCT
ejpam-4500	19	9	4	4	NUM
ejpam-4500	19	10	)	)	PUNCT
ejpam-4500	19	11	(	(	PUNCT
ejpam-4500	19	12	2022	2022	NUM
ejpam-4500	19	13	)	)	PUNCT
ejpam-4500	19	14	,	,	PUNCT
ejpam-4500	19	15	1705	1705	NUM
ejpam-4500	19	16	-	-	SYM
ejpam-4500	19	17	1715	1715	NUM
ejpam-4500	19	18	1706	1706	NUM
ejpam-4500	19	19	the	the	DET
ejpam-4500	19	20	concept	concept	NOUN
ejpam-4500	19	21	of	of	ADP
ejpam-4500	19	22	locating	locate	VERB
ejpam-4500	19	23	set	set	NOUN
ejpam-4500	19	24	was	be	AUX
ejpam-4500	19	25	first	first	ADV
ejpam-4500	19	26	introduced	introduce	VERB
ejpam-4500	19	27	by	by	ADP
ejpam-4500	19	28	slater	slater	NOUN
ejpam-4500	19	29	(	(	PUNCT
ejpam-4500	19	30	for	for	ADP
ejpam-4500	19	31	which	which	PRON
ejpam-4500	19	32	a	a	DET
ejpam-4500	19	33	protection	protection	NOUN
ejpam-4500	19	34	device	device	NOUN
ejpam-4500	19	35	can	can	AUX
ejpam-4500	19	36	determine	determine	VERB
ejpam-4500	19	37	the	the	DET
ejpam-4500	19	38	distance	distance	NOUN
ejpam-4500	19	39	to	to	ADP
ejpam-4500	19	40	an	an	DET
ejpam-4500	19	41	intruder	intruder	NOUN
ejpam-4500	19	42	)	)	PUNCT
ejpam-4500	19	43	in	in	ADP
ejpam-4500	19	44	1975	1975	NUM
ejpam-4500	19	45	(	(	PUNCT
ejpam-4500	19	46	see	see	VERB
ejpam-4500	19	47	[	[	X
ejpam-4500	19	48	16	16	NUM
ejpam-4500	19	49	]	]	SYM
ejpam-4500	19	50	)	)	PUNCT
ejpam-4500	19	51	.	.	PUNCT
ejpam-4500	20	1	omega	omega	NOUN
ejpam-4500	20	2	and	and	CCONJ
ejpam-4500	20	3	canoy	canoy	ADJ
ejpam-4500	20	4	in	in	ADP
ejpam-4500	20	5	[	[	X
ejpam-4500	20	6	11	11	NUM
ejpam-4500	20	7	]	]	PUNCT
ejpam-4500	20	8	studied	study	VERB
ejpam-4500	20	9	the	the	DET
ejpam-4500	20	10	locating	locating	NOUN
ejpam-4500	20	11	sets	set	NOUN
ejpam-4500	20	12	in	in	ADP
ejpam-4500	20	13	graphs	graph	NOUN
ejpam-4500	20	14	and	and	CCONJ
ejpam-4500	20	15	characterized	characterize	VERB
ejpam-4500	20	16	the	the	DET
ejpam-4500	20	17	locating	locating	NOUN
ejpam-4500	20	18	sets	set	NOUN
ejpam-4500	20	19	in	in	ADP
ejpam-4500	20	20	the	the	DET
ejpam-4500	20	21	join	join	NOUN
ejpam-4500	20	22	and	and	CCONJ
ejpam-4500	20	23	corona	corona	NOUN
ejpam-4500	20	24	of	of	ADP
ejpam-4500	20	25	graphs	graph	NOUN
ejpam-4500	20	26	where	where	SCONJ
ejpam-4500	20	27	they	they	PRON
ejpam-4500	20	28	also	also	ADV
ejpam-4500	20	29	determined	determine	VERB
ejpam-4500	20	30	the	the	DET
ejpam-4500	20	31	locating	locate	VERB
ejpam-4500	20	32	numbers	number	NOUN
ejpam-4500	20	33	of	of	ADP
ejpam-4500	20	34	these	these	DET
ejpam-4500	20	35	graphs	graph	NOUN
ejpam-4500	20	36	.	.	PUNCT
ejpam-4500	21	1	a	a	DET
ejpam-4500	21	2	set	set	NOUN
ejpam-4500	21	3	s	s	NOUN
ejpam-4500	21	4	⊆	⊆	NUM
ejpam-4500	21	5	v	v	NOUN
ejpam-4500	21	6	(	(	PUNCT
ejpam-4500	21	7	g	g	NOUN
ejpam-4500	21	8	)	)	PUNCT
ejpam-4500	21	9	is	be	AUX
ejpam-4500	21	10	a	a	DET
ejpam-4500	21	11	locating	locating	NOUN
ejpam-4500	21	12	set	set	VERB
ejpam-4500	21	13	if	if	SCONJ
ejpam-4500	21	14	for	for	ADP
ejpam-4500	21	15	every	every	DET
ejpam-4500	21	16	two	two	NUM
ejpam-4500	21	17	distinct	distinct	ADJ
ejpam-4500	21	18	vertices	vertex	NOUN
ejpam-4500	21	19	u	u	NOUN
ejpam-4500	21	20	,	,	PUNCT
ejpam-4500	21	21	v	v	NOUN
ejpam-4500	21	22	∈	∈	PROPN
ejpam-4500	21	23	v	v	NOUN
ejpam-4500	21	24	(	(	PUNCT
ejpam-4500	21	25	g	g	NOUN
ejpam-4500	21	26	)	)	PUNCT
ejpam-4500	21	27	\	\	PROPN
ejpam-4500	21	28	s	s	PROPN
ejpam-4500	21	29	,	,	PUNCT
ejpam-4500	21	30	ng(u	ng(u	NOUN
ejpam-4500	21	31	)	)	PUNCT
ejpam-4500	21	32	∩	∩	NOUN
ejpam-4500	21	33	s	s	PART
ejpam-4500	21	34	̸=	̸=	PROPN
ejpam-4500	21	35	ng(v	ng(v	NUM
ejpam-4500	21	36	)	)	PUNCT
ejpam-4500	21	37	∩	∩	PROPN
ejpam-4500	21	38	s.	s.	PROPN
ejpam-4500	21	39	a	a	DET
ejpam-4500	21	40	set	set	NOUN
ejpam-4500	21	41	s	s	PROPN
ejpam-4500	21	42	⊆	⊆	NUM
ejpam-4500	21	43	v	v	NOUN
ejpam-4500	21	44	(	(	PUNCT
ejpam-4500	21	45	g	g	NOUN
ejpam-4500	21	46	)	)	PUNCT
ejpam-4500	21	47	is	be	AUX
ejpam-4500	21	48	strictly	strictly	ADV
ejpam-4500	21	49	locating	locate	VERB
ejpam-4500	21	50	if	if	SCONJ
ejpam-4500	21	51	it	it	PRON
ejpam-4500	21	52	is	be	AUX
ejpam-4500	21	53	locating	locate	VERB
ejpam-4500	21	54	and	and	CCONJ
ejpam-4500	21	55	ng(u	ng(u	NOUN
ejpam-4500	21	56	)	)	PUNCT
ejpam-4500	21	57	∩	∩	NOUN
ejpam-4500	21	58	s	s	PART
ejpam-4500	21	59	̸=	̸=	PROPN
ejpam-4500	21	60	s	s	PART
ejpam-4500	21	61	for	for	ADP
ejpam-4500	21	62	all	all	DET
ejpam-4500	21	63	u	u	NOUN
ejpam-4500	21	64	∈	∈	PROPN
ejpam-4500	21	65	v	v	NOUN
ejpam-4500	21	66	(	(	PUNCT
ejpam-4500	21	67	g	g	NOUN
ejpam-4500	21	68	)	)	PUNCT
ejpam-4500	21	69	\	\	PUNCT
ejpam-4500	22	1	s.	s.	PROPN
ejpam-4500	22	2	the	the	DET
ejpam-4500	22	3	minimum	minimum	ADJ
ejpam-4500	22	4	cardinality	cardinality	NOUN
ejpam-4500	22	5	of	of	ADP
ejpam-4500	22	6	a	a	DET
ejpam-4500	22	7	locating	locating	NOUN
ejpam-4500	22	8	set	set	VERB
ejpam-4500	22	9	in	in	ADP
ejpam-4500	22	10	g	g	NOUN
ejpam-4500	22	11	,	,	PUNCT
ejpam-4500	22	12	denoted	denote	VERB
ejpam-4500	22	13	by	by	ADP
ejpam-4500	22	14	ln(g	ln(g	NOUN
ejpam-4500	22	15	)	)	PUNCT
ejpam-4500	22	16	,	,	PUNCT
ejpam-4500	22	17	is	be	AUX
ejpam-4500	22	18	called	call	VERB
ejpam-4500	22	19	the	the	DET
ejpam-4500	22	20	locating	locate	VERB
ejpam-4500	22	21	number	number	NOUN
ejpam-4500	22	22	of	of	ADP
ejpam-4500	22	23	g.	g.	PROPN
ejpam-4500	22	24	the	the	DET
ejpam-4500	22	25	minimum	minimum	ADJ
ejpam-4500	22	26	cardinality	cardinality	NOUN
ejpam-4500	22	27	of	of	ADP
ejpam-4500	22	28	a	a	DET
ejpam-4500	22	29	strictly	strictly	ADV
ejpam-4500	22	30	locating	locate	VERB
ejpam-4500	22	31	set	set	VERB
ejpam-4500	22	32	in	in	ADP
ejpam-4500	22	33	g	g	NOUN
ejpam-4500	22	34	,	,	PUNCT
ejpam-4500	22	35	denoted	denote	VERB
ejpam-4500	22	36	by	by	ADP
ejpam-4500	22	37	sln(g	sln(g	PROPN
ejpam-4500	22	38	)	)	PUNCT
ejpam-4500	22	39	,	,	PUNCT
ejpam-4500	22	40	is	be	AUX
ejpam-4500	22	41	the	the	DET
ejpam-4500	22	42	strict	strict	ADJ
ejpam-4500	22	43	locating	locating	NOUN
ejpam-4500	22	44	number	number	NOUN
ejpam-4500	22	45	of	of	ADP
ejpam-4500	22	46	g.	g.	PROPN
ejpam-4500	22	47	any	any	DET
ejpam-4500	22	48	locating	locating	NOUN
ejpam-4500	22	49	(	(	PUNCT
ejpam-4500	22	50	resp	resp	NOUN
ejpam-4500	22	51	.	.	PUNCT
ejpam-4500	23	1	strictly	strictly	ADV
ejpam-4500	23	2	locating	locate	VERB
ejpam-4500	23	3	)	)	PUNCT
ejpam-4500	23	4	set	set	VERB
ejpam-4500	23	5	with	with	ADP
ejpam-4500	23	6	cardinality	cardinality	NOUN
ejpam-4500	23	7	equal	equal	ADJ
ejpam-4500	23	8	to	to	ADP
ejpam-4500	23	9	ln(g	ln(g	NUM
ejpam-4500	23	10	)	)	PUNCT
ejpam-4500	23	11	(	(	PUNCT
ejpam-4500	23	12	resp	resp	NOUN
ejpam-4500	23	13	.	.	PUNCT
ejpam-4500	24	1	sln(g	sln(g	NOUN
ejpam-4500	24	2	)	)	PUNCT
ejpam-4500	24	3	)	)	PUNCT
ejpam-4500	25	1	,	,	PUNCT
ejpam-4500	25	2	is	be	AUX
ejpam-4500	25	3	called	call	VERB
ejpam-4500	25	4	a	a	DET
ejpam-4500	25	5	minimum	minimum	ADJ
ejpam-4500	25	6	locating	locating	NOUN
ejpam-4500	25	7	set	set	ADJ
ejpam-4500	25	8	or	or	CCONJ
ejpam-4500	25	9	ln	ln	ADV
ejpam-4500	25	10	-	-	PUNCT
ejpam-4500	25	11	set	set	ADJ
ejpam-4500	25	12	(	(	PUNCT
ejpam-4500	25	13	resp	resp	NOUN
ejpam-4500	25	14	.	.	PUNCT
ejpam-4500	26	1	minimum	minimum	NOUN
ejpam-4500	26	2	strictly	strictly	ADV
ejpam-4500	26	3	locating	locate	VERB
ejpam-4500	26	4	set	set	ADJ
ejpam-4500	26	5	or	or	CCONJ
ejpam-4500	26	6	sln	sln	NOUN
ejpam-4500	26	7	-	-	PUNCT
ejpam-4500	26	8	set	set	NOUN
ejpam-4500	26	9	)	)	PUNCT
ejpam-4500	26	10	.	.	PUNCT
ejpam-4500	27	1	in	in	ADP
ejpam-4500	27	2	1987	1987	NUM
ejpam-4500	27	3	,	,	PUNCT
ejpam-4500	27	4	slater	slater	NOUN
ejpam-4500	27	5	in	in	ADP
ejpam-4500	27	6	[	[	X
ejpam-4500	27	7	17	17	NUM
ejpam-4500	27	8	]	]	PUNCT
ejpam-4500	27	9	further	far	ADV
ejpam-4500	27	10	investigated	investigate	VERB
ejpam-4500	27	11	locating	locate	VERB
ejpam-4500	27	12	set	set	VERB
ejpam-4500	27	13	with	with	ADP
ejpam-4500	27	14	another	another	DET
ejpam-4500	27	15	concept	concept	NOUN
ejpam-4500	27	16	called	call	VERB
ejpam-4500	27	17	domination	domination	NOUN
ejpam-4500	27	18	.	.	PUNCT
ejpam-4500	28	1	a	a	DET
ejpam-4500	28	2	set	set	NOUN
ejpam-4500	28	3	d	d	NOUN
ejpam-4500	28	4	⊆	⊆	NUM
ejpam-4500	28	5	v	v	ADP
ejpam-4500	28	6	(	(	PUNCT
ejpam-4500	28	7	g	g	NOUN
ejpam-4500	28	8	)	)	PUNCT
ejpam-4500	28	9	is	be	AUX
ejpam-4500	28	10	a	a	DET
ejpam-4500	28	11	dominating	dominating	NOUN
ejpam-4500	28	12	set	set	NOUN
ejpam-4500	28	13	of	of	ADP
ejpam-4500	28	14	g	g	PROPN
ejpam-4500	28	15	if	if	SCONJ
ejpam-4500	28	16	∪x∈dn	∪x∈dn	PROPN
ejpam-4500	28	17	[	[	X
ejpam-4500	28	18	x	x	X
ejpam-4500	28	19	]	]	X
ejpam-4500	28	20	=	=	SYM
ejpam-4500	28	21	v	v	NOUN
ejpam-4500	28	22	(	(	PUNCT
ejpam-4500	28	23	g	g	NOUN
ejpam-4500	28	24	)	)	PUNCT
ejpam-4500	28	25	.	.	PUNCT
ejpam-4500	29	1	the	the	DET
ejpam-4500	29	2	domination	domination	NOUN
ejpam-4500	29	3	number	number	NOUN
ejpam-4500	29	4	of	of	ADP
ejpam-4500	29	5	g	g	NOUN
ejpam-4500	29	6	,	,	PUNCT
ejpam-4500	29	7	denoted	denote	VERB
ejpam-4500	29	8	by	by	ADP
ejpam-4500	29	9	γ(g	γ(g	PROPN
ejpam-4500	29	10	)	)	PUNCT
ejpam-4500	29	11	,	,	PUNCT
ejpam-4500	29	12	is	be	AUX
ejpam-4500	29	13	the	the	DET
ejpam-4500	29	14	minimum	minimum	ADJ
ejpam-4500	29	15	cardinality	cardinality	NOUN
ejpam-4500	29	16	of	of	ADP
ejpam-4500	29	17	a	a	DET
ejpam-4500	29	18	dominating	dominating	NOUN
ejpam-4500	29	19	set	set	NOUN
ejpam-4500	29	20	of	of	ADP
ejpam-4500	29	21	g.	g.	PROPN
ejpam-4500	29	22	eventually	eventually	ADV
ejpam-4500	29	23	,	,	PUNCT
ejpam-4500	29	24	the	the	DET
ejpam-4500	29	25	concept	concept	NOUN
ejpam-4500	29	26	of	of	ADP
ejpam-4500	29	27	locating	locate	VERB
ejpam-4500	29	28	dominating	dominating	NOUN
ejpam-4500	29	29	set	set	NOUN
ejpam-4500	29	30	was	be	AUX
ejpam-4500	29	31	introduced	introduce	VERB
ejpam-4500	29	32	and	and	CCONJ
ejpam-4500	29	33	is	be	AUX
ejpam-4500	29	34	one	one	NUM
ejpam-4500	29	35	of	of	ADP
ejpam-4500	29	36	the	the	DET
ejpam-4500	29	37	widely	widely	ADV
ejpam-4500	29	38	studied	study	VERB
ejpam-4500	29	39	topics	topic	NOUN
ejpam-4500	29	40	nowadays	nowadays	ADV
ejpam-4500	29	41	(	(	PUNCT
ejpam-4500	29	42	see	see	VERB
ejpam-4500	29	43	[	[	X
ejpam-4500	29	44	14	14	NUM
ejpam-4500	29	45	]	]	PUNCT
ejpam-4500	29	46	,	,	PUNCT
ejpam-4500	29	47	[	[	X
ejpam-4500	29	48	15	15	NUM
ejpam-4500	29	49	]	]	NUM
ejpam-4500	29	50	)	)	PUNCT
ejpam-4500	29	51	.	.	PUNCT
ejpam-4500	30	1	a	a	DET
ejpam-4500	30	2	locating	locating	NOUN
ejpam-4500	30	3	subset	subset	NOUN
ejpam-4500	30	4	s	s	VERB
ejpam-4500	30	5	⊆	⊆	NUM
ejpam-4500	30	6	v	v	NOUN
ejpam-4500	30	7	(	(	PUNCT
ejpam-4500	30	8	g	g	NOUN
ejpam-4500	30	9	)	)	PUNCT
ejpam-4500	30	10	which	which	PRON
ejpam-4500	30	11	is	be	AUX
ejpam-4500	30	12	also	also	ADV
ejpam-4500	30	13	a	a	DET
ejpam-4500	30	14	dominating	dominating	NOUN
ejpam-4500	30	15	set	set	NOUN
ejpam-4500	30	16	is	be	AUX
ejpam-4500	30	17	called	call	VERB
ejpam-4500	30	18	locating	locate	VERB
ejpam-4500	30	19	-	-	PUNCT
ejpam-4500	30	20	dominating	dominating	NOUN
ejpam-4500	30	21	set	set	NOUN
ejpam-4500	30	22	(	(	PUNCT
ejpam-4500	30	23	ld	ld	NOUN
ejpam-4500	30	24	-	-	PUNCT
ejpam-4500	30	25	set	set	NOUN
ejpam-4500	30	26	)	)	PUNCT
ejpam-4500	30	27	in	in	ADP
ejpam-4500	30	28	a	a	DET
ejpam-4500	30	29	graph	graph	NOUN
ejpam-4500	30	30	g.	g.	NOUN
ejpam-4500	30	31	a	a	DET
ejpam-4500	30	32	strictly	strictly	ADV
ejpam-4500	30	33	locating	locate	VERB
ejpam-4500	30	34	subset	subset	NOUN
ejpam-4500	30	35	s	s	PROPN
ejpam-4500	30	36	of	of	ADP
ejpam-4500	30	37	v	v	NOUN
ejpam-4500	30	38	(	(	PUNCT
ejpam-4500	30	39	g	g	NOUN
ejpam-4500	30	40	)	)	PUNCT
ejpam-4500	30	41	which	which	PRON
ejpam-4500	30	42	is	be	AUX
ejpam-4500	30	43	also	also	ADV
ejpam-4500	30	44	a	a	DET
ejpam-4500	30	45	dominating	dominating	NOUN
ejpam-4500	30	46	set	set	NOUN
ejpam-4500	30	47	is	be	AUX
ejpam-4500	30	48	called	call	VERB
ejpam-4500	30	49	strictly	strictly	ADV
ejpam-4500	30	50	locating	locate	VERB
ejpam-4500	30	51	-	-	PUNCT
ejpam-4500	30	52	dominating	dominating	NOUN
ejpam-4500	30	53	set	set	NOUN
ejpam-4500	30	54	(	(	PUNCT
ejpam-4500	30	55	sld	sld	NOUN
ejpam-4500	30	56	-	-	PUNCT
ejpam-4500	30	57	set	set	NOUN
ejpam-4500	30	58	)	)	PUNCT
ejpam-4500	30	59	in	in	ADP
ejpam-4500	30	60	a	a	DET
ejpam-4500	30	61	graph	graph	NOUN
ejpam-4500	30	62	g.	g.	NOUN
ejpam-4500	30	63	the	the	DET
ejpam-4500	30	64	locating	locate	VERB
ejpam-4500	30	65	-	-	PUNCT
ejpam-4500	30	66	domination	domination	NOUN
ejpam-4500	30	67	number	number	NOUN
ejpam-4500	30	68	or	or	CCONJ
ejpam-4500	30	69	l	l	NOUN
ejpam-4500	30	70	-	-	PUNCT
ejpam-4500	30	71	domination	domination	NOUN
ejpam-4500	30	72	number	number	NOUN
ejpam-4500	30	73	of	of	ADP
ejpam-4500	30	74	g	g	NOUN
ejpam-4500	30	75	,	,	PUNCT
ejpam-4500	30	76	denoted	denote	VERB
ejpam-4500	30	77	by	by	ADP
ejpam-4500	30	78	γl(g	γl(g	NUM
ejpam-4500	30	79	)	)	PUNCT
ejpam-4500	30	80	,	,	PUNCT
ejpam-4500	30	81	is	be	AUX
ejpam-4500	30	82	the	the	DET
ejpam-4500	30	83	minimum	minimum	ADJ
ejpam-4500	30	84	cardinality	cardinality	NOUN
ejpam-4500	30	85	of	of	ADP
ejpam-4500	30	86	a	a	DET
ejpam-4500	30	87	locating	locate	VERB
ejpam-4500	30	88	-	-	PUNCT
ejpam-4500	30	89	dominating	dominating	NOUN
ejpam-4500	30	90	set	set	NOUN
ejpam-4500	30	91	.	.	PUNCT
ejpam-4500	31	1	the	the	DET
ejpam-4500	31	2	minimum	minimum	ADJ
ejpam-4500	31	3	cardinality	cardinality	NOUN
ejpam-4500	31	4	of	of	ADP
ejpam-4500	31	5	a	a	DET
ejpam-4500	31	6	strictly	strictly	ADV
ejpam-4500	31	7	locating	locate	VERB
ejpam-4500	31	8	-	-	PUNCT
ejpam-4500	31	9	dominating	dominate	VERB
ejpam-4500	31	10	set	set	NOUN
ejpam-4500	31	11	of	of	ADP
ejpam-4500	31	12	g	g	NOUN
ejpam-4500	31	13	,	,	PUNCT
ejpam-4500	31	14	denoted	denote	VERB
ejpam-4500	31	15	by	by	ADP
ejpam-4500	31	16	γsl(g	γsl(g	NOUN
ejpam-4500	31	17	)	)	PUNCT
ejpam-4500	31	18	,	,	PUNCT
ejpam-4500	31	19	is	be	AUX
ejpam-4500	31	20	called	call	VERB
ejpam-4500	31	21	the	the	DET
ejpam-4500	31	22	sldomination	sldomination	NOUN
ejpam-4500	31	23	number	number	NOUN
ejpam-4500	31	24	of	of	ADP
ejpam-4500	31	25	g.	g.	PROPN
ejpam-4500	31	26	a	a	DET
ejpam-4500	31	27	locating	locate	VERB
ejpam-4500	31	28	-	-	PUNCT
ejpam-4500	31	29	dominating	dominate	VERB
ejpam-4500	31	30	(	(	PUNCT
ejpam-4500	31	31	resp	resp	NOUN
ejpam-4500	31	32	.	.	PUNCT
ejpam-4500	32	1	strictly	strictly	ADV
ejpam-4500	32	2	locating	locate	VERB
ejpam-4500	32	3	-	-	PUNCT
ejpam-4500	32	4	dominating	dominating	NOUN
ejpam-4500	32	5	)	)	PUNCT
ejpam-4500	32	6	set	set	VERB
ejpam-4500	32	7	with	with	ADP
ejpam-4500	32	8	cardinality	cardinality	NOUN
ejpam-4500	32	9	equal	equal	ADJ
ejpam-4500	32	10	to	to	ADP
ejpam-4500	32	11	γl(g	γl(g	NUM
ejpam-4500	32	12	)	)	PUNCT
ejpam-4500	32	13	(	(	PUNCT
ejpam-4500	33	1	resp	resp	NOUN
ejpam-4500	33	2	.	.	PUNCT
ejpam-4500	33	3	γsl(g))is	γsl(g))is	PROPN
ejpam-4500	33	4	called	call	VERB
ejpam-4500	33	5	a	a	DET
ejpam-4500	33	6	minimum	minimum	ADJ
ejpam-4500	33	7	locating	locating	NOUN
ejpam-4500	33	8	-	-	PUNCT
ejpam-4500	33	9	dominating	dominating	NOUN
ejpam-4500	33	10	set	set	NOUN
ejpam-4500	33	11	or	or	CCONJ
ejpam-4500	33	12	γl	γl	NOUN
ejpam-4500	33	13	-	-	PUNCT
ejpam-4500	33	14	set	set	VERB
ejpam-4500	33	15	(	(	PUNCT
ejpam-4500	33	16	minimum	minimum	NOUN
ejpam-4500	33	17	strictly	strictly	ADV
ejpam-4500	33	18	locating	locate	VERB
ejpam-4500	33	19	-	-	PUNCT
ejpam-4500	33	20	dominating	dominating	NOUN
ejpam-4500	33	21	set	set	NOUN
ejpam-4500	33	22	or	or	CCONJ
ejpam-4500	33	23	γsl	γsl	NOUN
ejpam-4500	33	24	-	-	PUNCT
ejpam-4500	33	25	set	set	NOUN
ejpam-4500	33	26	)	)	PUNCT
ejpam-4500	33	27	.	.	PUNCT
ejpam-4500	34	1	canoy	canoy	PROPN
ejpam-4500	34	2	et	et	PROPN
ejpam-4500	34	3	al	al	PROPN
ejpam-4500	34	4	.	.	PUNCT
ejpam-4500	35	1	[	[	X
ejpam-4500	35	2	8	8	NUM
ejpam-4500	35	3	]	]	PUNCT
ejpam-4500	35	4	characterized	characterize	VERB
ejpam-4500	35	5	the	the	DET
ejpam-4500	35	6	locating	locate	VERB
ejpam-4500	35	7	dominating	dominating	NOUN
ejpam-4500	35	8	sets	set	NOUN
ejpam-4500	35	9	in	in	ADP
ejpam-4500	35	10	the	the	DET
ejpam-4500	35	11	corona	corona	NOUN
ejpam-4500	35	12	and	and	CCONJ
ejpam-4500	35	13	composition	composition	NOUN
ejpam-4500	35	14	of	of	ADP
ejpam-4500	35	15	graphs	graph	NOUN
ejpam-4500	35	16	.	.	PUNCT
ejpam-4500	36	1	they	they	PRON
ejpam-4500	36	2	also	also	ADV
ejpam-4500	36	3	determined	determine	VERB
ejpam-4500	36	4	the	the	DET
ejpam-4500	36	5	locating	locate	VERB
ejpam-4500	36	6	-	-	PUNCT
ejpam-4500	36	7	domination	domination	NOUN
ejpam-4500	36	8	number	number	NOUN
ejpam-4500	36	9	of	of	ADP
ejpam-4500	36	10	these	these	DET
ejpam-4500	36	11	graphs	graph	NOUN
ejpam-4500	36	12	.	.	PUNCT
ejpam-4500	37	1	there	there	PRON
ejpam-4500	37	2	are	be	VERB
ejpam-4500	37	3	other	other	ADJ
ejpam-4500	37	4	studies	study	NOUN
ejpam-4500	37	5	involving	involve	VERB
ejpam-4500	37	6	the	the	DET
ejpam-4500	37	7	concept	concept	NOUN
ejpam-4500	37	8	of	of	ADP
ejpam-4500	37	9	locating	locate	VERB
ejpam-4500	37	10	set	set	VERB
ejpam-4500	37	11	and	and	CCONJ
ejpam-4500	37	12	locating	locate	VERB
ejpam-4500	37	13	dominating	dominating	NOUN
ejpam-4500	37	14	set	set	NOUN
ejpam-4500	37	15	(	(	PUNCT
ejpam-4500	37	16	see	see	VERB
ejpam-4500	37	17	[	[	X
ejpam-4500	37	18	4	4	NUM
ejpam-4500	37	19	]	]	PUNCT
ejpam-4500	37	20	,	,	PUNCT
ejpam-4500	37	21	[	[	X
ejpam-4500	37	22	5	5	NUM
ejpam-4500	37	23	]	]	PUNCT
ejpam-4500	37	24	,	,	PUNCT
ejpam-4500	37	25	[	[	X
ejpam-4500	37	26	8	8	NUM
ejpam-4500	37	27	]	]	PUNCT
ejpam-4500	37	28	,	,	PUNCT
ejpam-4500	37	29	[	[	X
ejpam-4500	37	30	10	10	NUM
ejpam-4500	37	31	]	]	PUNCT
ejpam-4500	37	32	,	,	PUNCT
ejpam-4500	37	33	and	and	CCONJ
ejpam-4500	37	34	[	[	X
ejpam-4500	37	35	11	11	NUM
ejpam-4500	37	36	]	]	NUM
ejpam-4500	37	37	)	)	PUNCT
ejpam-4500	37	38	.	.	PUNCT
ejpam-4500	38	1	a	a	DET
ejpam-4500	38	2	non	non	ADJ
ejpam-4500	38	3	-	-	ADJ
ejpam-4500	38	4	empty	empty	ADJ
ejpam-4500	38	5	set	set	NOUN
ejpam-4500	38	6	s	s	PROPN
ejpam-4500	38	7	⊆	⊆	NUM
ejpam-4500	38	8	v	v	NOUN
ejpam-4500	38	9	(	(	PUNCT
ejpam-4500	38	10	g	g	NOUN
ejpam-4500	38	11	)	)	PUNCT
ejpam-4500	38	12	is	be	AUX
ejpam-4500	38	13	a	a	DET
ejpam-4500	38	14	locating	locate	VERB
ejpam-4500	38	15	hop	hop	NOUN
ejpam-4500	38	16	set	set	NOUN
ejpam-4500	38	17	of	of	ADP
ejpam-4500	38	18	g	g	PROPN
ejpam-4500	38	19	if	if	SCONJ
ejpam-4500	38	20	ng(u	ng(u	NOUN
ejpam-4500	38	21	,	,	PUNCT
ejpam-4500	38	22	2)∩s	2)∩s	PROPN
ejpam-4500	38	23	̸=	̸=	PROPN
ejpam-4500	38	24	ng(v	ng(v	PUNCT
ejpam-4500	38	25	,	,	PUNCT
ejpam-4500	38	26	2)∩s	2)∩s	PROPN
ejpam-4500	38	27	for	for	ADP
ejpam-4500	38	28	every	every	DET
ejpam-4500	38	29	pair	pair	NOUN
ejpam-4500	38	30	of	of	ADP
ejpam-4500	38	31	distinct	distinct	ADJ
ejpam-4500	38	32	vertices	vertex	NOUN
ejpam-4500	38	33	u	u	NOUN
ejpam-4500	38	34	,	,	PUNCT
ejpam-4500	38	35	v	v	NOUN
ejpam-4500	38	36	∈	∈	PROPN
ejpam-4500	38	37	v	v	NOUN
ejpam-4500	38	38	(	(	PUNCT
ejpam-4500	38	39	g	g	NOUN
ejpam-4500	38	40	)	)	PUNCT
ejpam-4500	38	41	\s	\s	NOUN
ejpam-4500	38	42	.	.	PUNCT
ejpam-4500	39	1	a	a	DET
ejpam-4500	39	2	locating	locate	VERB
ejpam-4500	39	3	hop	hop	NOUN
ejpam-4500	39	4	set	set	NOUN
ejpam-4500	39	5	is	be	AUX
ejpam-4500	39	6	a	a	DET
ejpam-4500	39	7	strictly	strictly	ADV
ejpam-4500	39	8	locating	locate	VERB
ejpam-4500	39	9	hop	hop	NOUN
ejpam-4500	39	10	set	set	VERB
ejpam-4500	39	11	if	if	SCONJ
ejpam-4500	39	12	ng(v	ng(v	NOUN
ejpam-4500	39	13	,	,	PUNCT
ejpam-4500	39	14	2)∩	2)∩	NOUN
ejpam-4500	39	15	s	s	VERB
ejpam-4500	39	16	̸=	̸=	PROPN
ejpam-4500	39	17	s	s	PART
ejpam-4500	39	18	for	for	ADP
ejpam-4500	39	19	every	every	PRON
ejpam-4500	39	20	v	v	NUM
ejpam-4500	39	21	∈	∈	PROPN
ejpam-4500	39	22	v	v	NOUN
ejpam-4500	39	23	(	(	PUNCT
ejpam-4500	39	24	g	g	NOUN
ejpam-4500	39	25	)	)	PUNCT
ejpam-4500	39	26	\	\	PUNCT
ejpam-4500	40	1	s.	s.	PROPN
ejpam-4500	40	2	the	the	DET
ejpam-4500	40	3	smallest	small	ADJ
ejpam-4500	40	4	cardinality	cardinality	NOUN
ejpam-4500	40	5	of	of	ADP
ejpam-4500	40	6	a	a	DET
ejpam-4500	40	7	locating	locate	VERB
ejpam-4500	40	8	hop	hop	NOUN
ejpam-4500	40	9	set	set	NOUN
ejpam-4500	40	10	(	(	PUNCT
ejpam-4500	40	11	resp	resp	NOUN
ejpam-4500	40	12	.	.	PUNCT
ejpam-4500	41	1	strictly	strictly	ADV
ejpam-4500	41	2	locating	locate	VERB
ejpam-4500	41	3	hop	hop	NOUN
ejpam-4500	41	4	set	set	NOUN
ejpam-4500	41	5	)	)	PUNCT
ejpam-4500	41	6	of	of	ADP
ejpam-4500	41	7	g	g	NOUN
ejpam-4500	41	8	,	,	PUNCT
ejpam-4500	41	9	denoted	denote	VERB
ejpam-4500	41	10	by	by	ADP
ejpam-4500	41	11	lhn(g	lhn(g	PROPN
ejpam-4500	41	12	)	)	PUNCT
ejpam-4500	41	13	(	(	PUNCT
ejpam-4500	41	14	resp	resp	NOUN
ejpam-4500	41	15	.	.	PUNCT
ejpam-4500	42	1	slhn(g	slhn(g	X
ejpam-4500	42	2	)	)	PUNCT
ejpam-4500	42	3	)	)	PUNCT
ejpam-4500	43	1	is	be	AUX
ejpam-4500	43	2	called	call	VERB
ejpam-4500	43	3	the	the	DET
ejpam-4500	43	4	locating	locate	VERB
ejpam-4500	43	5	hop	hop	NOUN
ejpam-4500	43	6	(	(	PUNCT
ejpam-4500	43	7	resp	resp	NOUN
ejpam-4500	43	8	.	.	PUNCT
ejpam-4500	44	1	strictly	strictly	ADV
ejpam-4500	44	2	locating	locate	VERB
ejpam-4500	44	3	hop	hop	NOUN
ejpam-4500	44	4	)	)	PUNCT
ejpam-4500	44	5	number	number	NOUN
ejpam-4500	44	6	of	of	ADP
ejpam-4500	44	7	g.	g.	PROPN
ejpam-4500	44	8	any	any	DET
ejpam-4500	44	9	locating	locate	VERB
ejpam-4500	44	10	hop	hop	NOUN
ejpam-4500	44	11	set	set	NOUN
ejpam-4500	44	12	(	(	PUNCT
ejpam-4500	44	13	resp	resp	NOUN
ejpam-4500	44	14	.	.	PUNCT
ejpam-4500	45	1	strictly	strictly	ADV
ejpam-4500	45	2	locating	locate	VERB
ejpam-4500	45	3	hop	hop	NOUN
ejpam-4500	45	4	set	set	NOUN
ejpam-4500	45	5	)	)	PUNCT
ejpam-4500	45	6	with	with	ADP
ejpam-4500	45	7	cardinality	cardinality	NOUN
ejpam-4500	45	8	equal	equal	ADJ
ejpam-4500	45	9	to	to	ADP
ejpam-4500	45	10	lhn(g	lhn(g	PROPN
ejpam-4500	45	11	)	)	PUNCT
ejpam-4500	45	12	(	(	PUNCT
ejpam-4500	45	13	resp	resp	NOUN
ejpam-4500	45	14	.	.	PUNCT
ejpam-4500	46	1	slhn(g	slhn(g	X
ejpam-4500	46	2	)	)	PUNCT
ejpam-4500	46	3	)	)	PUNCT
ejpam-4500	47	1	is	be	AUX
ejpam-4500	47	2	called	call	VERB
ejpam-4500	47	3	a	a	DET
ejpam-4500	47	4	minimum	minimum	ADJ
ejpam-4500	47	5	locating	locating	NOUN
ejpam-4500	47	6	hop	hop	NOUN
ejpam-4500	47	7	set	set	NOUN
ejpam-4500	47	8	or	or	CCONJ
ejpam-4500	47	9	lhn	lhn	PROPN
ejpam-4500	47	10	-	-	PUNCT
ejpam-4500	47	11	set	set	VERB
ejpam-4500	47	12	(	(	PUNCT
ejpam-4500	47	13	resp	resp	NOUN
ejpam-4500	47	14	.	.	PUNCT
ejpam-4500	48	1	minimum	minimum	NOUN
ejpam-4500	48	2	strictly	strictly	ADV
ejpam-4500	48	3	locating	locate	VERB
ejpam-4500	48	4	hop	hop	NOUN
ejpam-4500	48	5	set	set	VERB
ejpam-4500	48	6	or	or	CCONJ
ejpam-4500	48	7	shln	shln	NOUN
ejpam-4500	48	8	-	-	PUNCT
ejpam-4500	48	9	set	set	NOUN
ejpam-4500	48	10	)	)	PUNCT
ejpam-4500	48	11	.	.	PUNCT
ejpam-4500	49	1	in	in	ADP
ejpam-4500	49	2	this	this	DET
ejpam-4500	49	3	paper	paper	NOUN
ejpam-4500	49	4	,	,	PUNCT
ejpam-4500	49	5	we	we	PRON
ejpam-4500	49	6	investigate	investigate	VERB
ejpam-4500	49	7	the	the	DET
ejpam-4500	49	8	concept	concept	NOUN
ejpam-4500	49	9	of	of	ADP
ejpam-4500	49	10	locating	locate	VERB
ejpam-4500	49	11	hop	hop	NOUN
ejpam-4500	49	12	set	set	VERB
ejpam-4500	49	13	in	in	ADP
ejpam-4500	49	14	the	the	DET
ejpam-4500	49	15	join	join	NOUN
ejpam-4500	49	16	and	and	CCONJ
ejpam-4500	49	17	corona	corona	NOUN
ejpam-4500	49	18	of	of	ADP
ejpam-4500	49	19	two	two	NUM
ejpam-4500	49	20	graphs	graph	NOUN
ejpam-4500	49	21	.	.	PUNCT
ejpam-4500	50	1	investigation	investigation	NOUN
ejpam-4500	50	2	of	of	ADP
ejpam-4500	50	3	several	several	ADJ
ejpam-4500	50	4	parameters	parameter	NOUN
ejpam-4500	50	5	in	in	ADP
ejpam-4500	50	6	graphs	graph	NOUN
ejpam-4500	50	7	under	under	ADP
ejpam-4500	50	8	some	some	DET
ejpam-4500	50	9	binary	binary	ADJ
ejpam-4500	50	10	operations	operation	NOUN
ejpam-4500	50	11	had	have	AUX
ejpam-4500	50	12	been	be	AUX
ejpam-4500	50	13	done	do	VERB
ejpam-4500	50	14	in	in	ADP
ejpam-4500	50	15	many	many	ADJ
ejpam-4500	50	16	studies	study	NOUN
ejpam-4500	50	17	(	(	PUNCT
ejpam-4500	50	18	see	see	VERB
ejpam-4500	50	19	[	[	X
ejpam-4500	50	20	1	1	NUM
ejpam-4500	50	21	]	]	PUNCT
ejpam-4500	50	22	,	,	PUNCT
ejpam-4500	50	23	[	[	X
ejpam-4500	50	24	2	2	NUM
ejpam-4500	50	25	]	]	PUNCT
ejpam-4500	50	26	,	,	PUNCT
ejpam-4500	50	27	[	[	X
ejpam-4500	50	28	3	3	NUM
ejpam-4500	50	29	]	]	NUM
ejpam-4500	50	30	)	)	PUNCT
ejpam-4500	50	31	.	.	PUNCT
ejpam-4500	51	1	a	a	DET
ejpam-4500	51	2	point	point	NOUN
ejpam-4500	51	3	determining	determine	VERB
ejpam-4500	51	4	graph	graph	NOUN
ejpam-4500	51	5	is	be	AUX
ejpam-4500	51	6	defined	define	VERB
ejpam-4500	51	7	in	in	ADP
ejpam-4500	51	8	[	[	X
ejpam-4500	51	9	18	18	NUM
ejpam-4500	51	10	]	]	PUNCT
ejpam-4500	51	11	as	as	ADP
ejpam-4500	51	12	a	a	DET
ejpam-4500	51	13	graph	graph	NOUN
ejpam-4500	51	14	in	in	ADP
ejpam-4500	51	15	which	which	PRON
ejpam-4500	51	16	distinct	distinct	ADJ
ejpam-4500	51	17	non	non	ADJ
ejpam-4500	51	18	-	-	ADJ
ejpam-4500	51	19	adjacent	adjacent	ADJ
ejpam-4500	51	20	vertices	vertex	NOUN
ejpam-4500	51	21	have	have	VERB
ejpam-4500	51	22	distinct	distinct	ADJ
ejpam-4500	51	23	neighborhoods	neighborhood	NOUN
ejpam-4500	51	24	.	.	PUNCT
ejpam-4500	52	1	e.m	e.m	PROPN
ejpam-4500	52	2	.	.	PROPN
ejpam-4500	52	3	a.	a.	NOUN
ejpam-4500	52	4	pagcu	pagcu	PROPN
ejpam-4500	52	5	,	,	PUNCT
ejpam-4500	52	6	g.	g.	PROPN
ejpam-4500	52	7	a.	a.	NOUN
ejpam-4500	52	8	malacas	malacas	PROPN
ejpam-4500	52	9	,	,	PUNCT
ejpam-4500	52	10	s.	s.	PROPN
ejpam-4500	52	11	r.	r.	PROPN
ejpam-4500	52	12	canoy	canoy	PROPN
ejpam-4500	52	13	,	,	PUNCT
ejpam-4500	52	14	jr	jr	PROPN
ejpam-4500	52	15	.	.	PROPN
ejpam-4500	52	16	/	/	SYM
ejpam-4500	52	17	eur	eur	PROPN
ejpam-4500	52	18	.	.	PUNCT
ejpam-4500	53	1	j.	j.	PROPN
ejpam-4500	53	2	pure	pure	PROPN
ejpam-4500	53	3	appl	appl	PROPN
ejpam-4500	53	4	.	.	PROPN
ejpam-4500	53	5	math	math	PROPN
ejpam-4500	53	6	,	,	PUNCT
ejpam-4500	53	7	15	15	NUM
ejpam-4500	53	8	(	(	PUNCT
ejpam-4500	53	9	4	4	NUM
ejpam-4500	53	10	)	)	PUNCT
ejpam-4500	53	11	(	(	PUNCT
ejpam-4500	53	12	2022	2022	NUM
ejpam-4500	53	13	)	)	PUNCT
ejpam-4500	53	14	,	,	PUNCT
ejpam-4500	53	15	1705	1705	NUM
ejpam-4500	53	16	-	-	SYM
ejpam-4500	53	17	1715	1715	NUM
ejpam-4500	53	18	1707	1707	NUM
ejpam-4500	53	19	2	2	NUM
ejpam-4500	53	20	.	.	PUNCT
ejpam-4500	53	21	preliminary	preliminary	ADJ
ejpam-4500	53	22	results	result	NOUN
ejpam-4500	53	23	proposition	proposition	NOUN
ejpam-4500	53	24	1	1	NUM
ejpam-4500	53	25	.	.	PUNCT
ejpam-4500	54	1	for	for	ADP
ejpam-4500	54	2	any	any	DET
ejpam-4500	54	3	graph	graph	NOUN
ejpam-4500	54	4	g	g	NOUN
ejpam-4500	54	5	of	of	ADP
ejpam-4500	54	6	order	order	NOUN
ejpam-4500	54	7	n	n	PRON
ejpam-4500	54	8	≥	≥	NOUN
ejpam-4500	54	9	2	2	NUM
ejpam-4500	54	10	,	,	PUNCT
ejpam-4500	54	11	1	1	NUM
ejpam-4500	54	12	≤	≤	NUM
ejpam-4500	54	13	lhn(g	lhn(g	PROPN
ejpam-4500	54	14	)	)	PUNCT
ejpam-4500	54	15	≤	≤	NUM
ejpam-4500	54	16	n−	n−	NOUN
ejpam-4500	54	17	1	1	NUM
ejpam-4500	54	18	.	.	PUNCT
ejpam-4500	55	1	proof	proof	NOUN
ejpam-4500	55	2	:	:	PUNCT
ejpam-4500	55	3	let	let	VERB
ejpam-4500	55	4	g	g	PRON
ejpam-4500	55	5	be	be	AUX
ejpam-4500	55	6	a	a	DET
ejpam-4500	55	7	connected	connected	ADJ
ejpam-4500	55	8	non	non	ADJ
ejpam-4500	55	9	-	-	ADJ
ejpam-4500	55	10	trivial	trivial	ADJ
ejpam-4500	55	11	graph	graph	NOUN
ejpam-4500	55	12	.	.	PUNCT
ejpam-4500	56	1	by	by	ADP
ejpam-4500	56	2	the	the	DET
ejpam-4500	56	3	definition	definition	NOUN
ejpam-4500	56	4	of	of	ADP
ejpam-4500	56	5	the	the	DET
ejpam-4500	56	6	locating	locate	VERB
ejpam-4500	56	7	hop	hop	NOUN
ejpam-4500	56	8	set	set	NOUN
ejpam-4500	56	9	,	,	PUNCT
ejpam-4500	56	10	lhn(g	lhn(g	PROPN
ejpam-4500	56	11	)	)	PUNCT
ejpam-4500	56	12	≥	≥	NOUN
ejpam-4500	56	13	1	1	NUM
ejpam-4500	56	14	.	.	PUNCT
ejpam-4500	57	1	let	let	VERB
ejpam-4500	57	2	v	v	NUM
ejpam-4500	57	3	∈	∈	PROPN
ejpam-4500	57	4	v	v	NOUN
ejpam-4500	57	5	(	(	PUNCT
ejpam-4500	57	6	g	g	NOUN
ejpam-4500	57	7	)	)	PUNCT
ejpam-4500	57	8	and	and	CCONJ
ejpam-4500	57	9	set	set	VERB
ejpam-4500	57	10	s	s	PART
ejpam-4500	57	11	=	=	X
ejpam-4500	57	12	v	v	ADJ
ejpam-4500	57	13	(	(	PUNCT
ejpam-4500	57	14	g	g	NOUN
ejpam-4500	57	15	)	)	PUNCT
ejpam-4500	57	16	\	\	NOUN
ejpam-4500	57	17	{	{	PUNCT
ejpam-4500	57	18	v	v	NOUN
ejpam-4500	57	19	}	}	PUNCT
ejpam-4500	57	20	.	.	PUNCT
ejpam-4500	58	1	then	then	ADV
ejpam-4500	58	2	s	s	VERB
ejpam-4500	58	3	is	be	AUX
ejpam-4500	58	4	a	a	DET
ejpam-4500	58	5	locating	locate	VERB
ejpam-4500	58	6	hop	hop	NOUN
ejpam-4500	58	7	set	set	NOUN
ejpam-4500	58	8	of	of	ADP
ejpam-4500	58	9	g.	g.	PROPN
ejpam-4500	58	10	hence	hence	ADV
ejpam-4500	58	11	,	,	PUNCT
ejpam-4500	58	12	lhn(g	lhn(g	PROPN
ejpam-4500	58	13	)	)	PUNCT
ejpam-4500	58	14	≤	≤	NUM
ejpam-4500	58	15	|s|	|s|	PROPN
ejpam-4500	58	16	=	=	SYM
ejpam-4500	58	17	n−	n−	NOUN
ejpam-4500	58	18	1	1	NUM
ejpam-4500	58	19	.	.	PUNCT
ejpam-4500	59	1	□	□	PUNCT
ejpam-4500	59	2	lemma	lemma	PROPN
ejpam-4500	59	3	1	1	X
ejpam-4500	59	4	.	.	PUNCT
ejpam-4500	60	1	let	let	VERB
ejpam-4500	60	2	g	g	PRON
ejpam-4500	60	3	be	be	AUX
ejpam-4500	60	4	a	a	DET
ejpam-4500	60	5	graph	graph	NOUN
ejpam-4500	60	6	with	with	ADP
ejpam-4500	60	7	n	n	ADP
ejpam-4500	60	8	vertices	vertex	NOUN
ejpam-4500	60	9	.	.	PUNCT
ejpam-4500	61	1	if	if	SCONJ
ejpam-4500	61	2	s	s	NOUN
ejpam-4500	61	3	is	be	AUX
ejpam-4500	61	4	a	a	DET
ejpam-4500	61	5	locating	locate	VERB
ejpam-4500	61	6	hop	hop	NOUN
ejpam-4500	61	7	set	set	NOUN
ejpam-4500	61	8	of	of	ADP
ejpam-4500	61	9	g	g	NOUN
ejpam-4500	61	10	,	,	PUNCT
ejpam-4500	61	11	then	then	ADV
ejpam-4500	61	12	n	n	NUM
ejpam-4500	61	13	≤	≤	NOUN
ejpam-4500	61	14	|s|+	|s|+	PROPN
ejpam-4500	61	15	2|s|	2|s|	NUM
ejpam-4500	61	16	.	.	PUNCT
ejpam-4500	62	1	in	in	ADP
ejpam-4500	62	2	particular	particular	ADJ
ejpam-4500	62	3	,	,	PUNCT
ejpam-4500	62	4	n	n	CCONJ
ejpam-4500	62	5	≤	≤	NOUN
ejpam-4500	62	6	lhn(g	lhn(g	NOUN
ejpam-4500	62	7	)	)	PUNCT
ejpam-4500	63	1	+	+	CCONJ
ejpam-4500	63	2	2lhn(g	2lhn(g	NUM
ejpam-4500	63	3	)	)	PUNCT
ejpam-4500	63	4	.	.	PUNCT
ejpam-4500	64	1	proof	proof	NOUN
ejpam-4500	64	2	:	:	PUNCT
ejpam-4500	64	3	let	let	VERB
ejpam-4500	64	4	g	g	PRON
ejpam-4500	64	5	be	be	AUX
ejpam-4500	64	6	a	a	DET
ejpam-4500	64	7	graph	graph	NOUN
ejpam-4500	64	8	of	of	ADP
ejpam-4500	64	9	order	order	NOUN
ejpam-4500	64	10	n	n	NOUN
ejpam-4500	64	11	and	and	CCONJ
ejpam-4500	64	12	s	s	VERB
ejpam-4500	64	13	is	be	AUX
ejpam-4500	64	14	a	a	DET
ejpam-4500	64	15	locating	locate	VERB
ejpam-4500	64	16	hop	hop	NOUN
ejpam-4500	64	17	set	set	VERB
ejpam-4500	64	18	in	in	ADP
ejpam-4500	64	19	g.	g.	PROPN
ejpam-4500	64	20	by	by	ADP
ejpam-4500	64	21	definition	definition	NOUN
ejpam-4500	64	22	of	of	ADP
ejpam-4500	64	23	locating	locate	VERB
ejpam-4500	64	24	hop	hop	NOUN
ejpam-4500	64	25	set	set	NOUN
ejpam-4500	64	26	,	,	PUNCT
ejpam-4500	64	27	the	the	DET
ejpam-4500	64	28	collection	collection	NOUN
ejpam-4500	64	29	{	{	PUNCT
ejpam-4500	64	30	ng(a	ng(a	NOUN
ejpam-4500	64	31	,	,	PUNCT
ejpam-4500	64	32	2	2	X
ejpam-4500	64	33	)	)	PUNCT
ejpam-4500	64	34	∩	∩	NOUN
ejpam-4500	64	35	s	s	PART
ejpam-4500	64	36	:	:	PUNCT
ejpam-4500	64	37	a	a	DET
ejpam-4500	64	38	∈	∈	PROPN
ejpam-4500	64	39	v	v	ADP
ejpam-4500	64	40	(	(	PUNCT
ejpam-4500	64	41	g	g	NOUN
ejpam-4500	64	42	)	)	PUNCT
ejpam-4500	64	43	\	\	PUNCT
ejpam-4500	65	1	s	s	X
ejpam-4500	65	2	}	}	PUNCT
ejpam-4500	65	3	contains	contain	VERB
ejpam-4500	65	4	exactly	exactly	ADV
ejpam-4500	65	5	|v	|v	ADJ
ejpam-4500	65	6	(	(	PUNCT
ejpam-4500	65	7	g	g	NOUN
ejpam-4500	65	8	)	)	PUNCT
ejpam-4500	65	9	\	\	PROPN
ejpam-4500	66	1	s|	s|	VERB
ejpam-4500	66	2	distinct	distinct	ADJ
ejpam-4500	66	3	subsets	subset	NOUN
ejpam-4500	66	4	of	of	ADP
ejpam-4500	66	5	s.	s.	PROPN
ejpam-4500	66	6	hence	hence	PROPN
ejpam-4500	66	7	,	,	PUNCT
ejpam-4500	66	8	|v	|v	PROPN
ejpam-4500	66	9	(	(	PUNCT
ejpam-4500	66	10	g)\s|	g)\s|	NOUN
ejpam-4500	66	11	=	=	PUNCT
ejpam-4500	66	12	n−|s|	n−|s|	NOUN
ejpam-4500	66	13	≤	≤	NOUN
ejpam-4500	66	14	2|s|	2|s|	NUM
ejpam-4500	66	15	,	,	PUNCT
ejpam-4500	66	16	i.e.	i.e.	X
ejpam-4500	66	17	,	,	PUNCT
ejpam-4500	66	18	n	n	DET
ejpam-4500	66	19	≤	≤	ADJ
ejpam-4500	66	20	|s|+2|s|	|s|+2|s|	PROPN
ejpam-4500	66	21	.	.	PUNCT
ejpam-4500	67	1	in	in	ADP
ejpam-4500	67	2	particular	particular	ADJ
ejpam-4500	67	3	,	,	PUNCT
ejpam-4500	67	4	if	if	SCONJ
ejpam-4500	67	5	s	s	VERB
ejpam-4500	67	6	is	be	AUX
ejpam-4500	67	7	an	an	DET
ejpam-4500	67	8	lhn	lhn	NOUN
ejpam-4500	67	9	-	-	PUNCT
ejpam-4500	67	10	set	set	NOUN
ejpam-4500	67	11	of	of	ADP
ejpam-4500	67	12	g	g	NOUN
ejpam-4500	67	13	,	,	PUNCT
ejpam-4500	67	14	then	then	ADV
ejpam-4500	67	15	n	n	CCONJ
ejpam-4500	67	16	≤	≤	NOUN
ejpam-4500	67	17	lhn(g	lhn(g	PROPN
ejpam-4500	67	18	)	)	PUNCT
ejpam-4500	68	1	+	+	CCONJ
ejpam-4500	68	2	2lhn(g	2lhn(g	NUM
ejpam-4500	68	3	)	)	PUNCT
ejpam-4500	68	4	.	.	PUNCT
ejpam-4500	69	1	□	□	PUNCT
ejpam-4500	69	2	theorem	theorem	NOUN
ejpam-4500	69	3	1	1	X
ejpam-4500	69	4	.	.	PUNCT
ejpam-4500	70	1	let	let	VERB
ejpam-4500	70	2	g	g	PRON
ejpam-4500	70	3	be	be	AUX
ejpam-4500	70	4	a	a	DET
ejpam-4500	70	5	non	non	ADJ
ejpam-4500	70	6	-	-	ADJ
ejpam-4500	70	7	trivial	trivial	ADJ
ejpam-4500	70	8	graph	graph	NOUN
ejpam-4500	70	9	.	.	PUNCT
ejpam-4500	71	1	then	then	ADV
ejpam-4500	71	2	lhn(g	lhn(g	NUM
ejpam-4500	71	3	)	)	PUNCT
ejpam-4500	71	4	=	=	SYM
ejpam-4500	72	1	n	n	CCONJ
ejpam-4500	72	2	−	−	PROPN
ejpam-4500	72	3	1	1	NUM
ejpam-4500	73	1	if	if	SCONJ
ejpam-4500	73	2	and	and	CCONJ
ejpam-4500	73	3	only	only	ADV
ejpam-4500	73	4	if	if	SCONJ
ejpam-4500	73	5	every	every	DET
ejpam-4500	73	6	component	component	NOUN
ejpam-4500	73	7	of	of	ADP
ejpam-4500	73	8	g	g	PROPN
ejpam-4500	73	9	is	be	AUX
ejpam-4500	73	10	complete	complete	ADJ
ejpam-4500	73	11	.	.	PUNCT
ejpam-4500	74	1	proof	proof	NOUN
ejpam-4500	74	2	:	:	PUNCT
ejpam-4500	74	3	suppose	suppose	VERB
ejpam-4500	74	4	that	that	SCONJ
ejpam-4500	74	5	lhn(g	lhn(g	PROPN
ejpam-4500	74	6	)	)	PUNCT
ejpam-4500	74	7	=	=	SYM
ejpam-4500	75	1	n	n	CCONJ
ejpam-4500	75	2	−	−	NUM
ejpam-4500	75	3	1	1	NUM
ejpam-4500	75	4	and	and	CCONJ
ejpam-4500	75	5	suppose	suppose	VERB
ejpam-4500	75	6	further	far	ADV
ejpam-4500	75	7	that	that	SCONJ
ejpam-4500	75	8	g	g	PROPN
ejpam-4500	75	9	has	have	VERB
ejpam-4500	75	10	a	a	DET
ejpam-4500	75	11	component	component	NOUN
ejpam-4500	75	12	h	h	NOUN
ejpam-4500	75	13	which	which	PRON
ejpam-4500	75	14	is	be	AUX
ejpam-4500	75	15	not	not	PART
ejpam-4500	75	16	complete	complete	ADJ
ejpam-4500	75	17	.	.	PUNCT
ejpam-4500	76	1	then	then	ADV
ejpam-4500	76	2	there	there	PRON
ejpam-4500	76	3	exist	exist	VERB
ejpam-4500	76	4	x	x	NOUN
ejpam-4500	76	5	,	,	PUNCT
ejpam-4500	76	6	y	y	PROPN
ejpam-4500	76	7	∈	∈	PROPN
ejpam-4500	76	8	v	v	ADP
ejpam-4500	76	9	(	(	PUNCT
ejpam-4500	76	10	h	h	NOUN
ejpam-4500	76	11	)	)	PUNCT
ejpam-4500	76	12	such	such	ADJ
ejpam-4500	76	13	that	that	SCONJ
ejpam-4500	76	14	dh(x	dh(x	NOUN
ejpam-4500	76	15	,	,	PUNCT
ejpam-4500	76	16	y	y	NOUN
ejpam-4500	76	17	)	)	PUNCT
ejpam-4500	76	18	=	=	SYM
ejpam-4500	77	1	dg(x	dg(x	X
ejpam-4500	77	2	,	,	PUNCT
ejpam-4500	77	3	y	y	NOUN
ejpam-4500	77	4	)	)	PUNCT
ejpam-4500	77	5	=	=	SYM
ejpam-4500	78	1	2	2	X
ejpam-4500	78	2	.	.	X
ejpam-4500	78	3	let	let	VERB
ejpam-4500	78	4	z	z	PROPN
ejpam-4500	78	5	∈	∈	PROPN
ejpam-4500	78	6	ng(x	ng(x	NUM
ejpam-4500	78	7	)	)	PUNCT
ejpam-4500	78	8	∩ng(y	∩ng(y	PROPN
ejpam-4500	78	9	)	)	PUNCT
ejpam-4500	78	10	and	and	CCONJ
ejpam-4500	78	11	s	s	NOUN
ejpam-4500	78	12	=	=	SYM
ejpam-4500	78	13	v	v	X
ejpam-4500	78	14	(	(	PUNCT
ejpam-4500	78	15	g	g	NOUN
ejpam-4500	78	16	)	)	PUNCT
ejpam-4500	78	17	\	\	NOUN
ejpam-4500	79	1	{	{	PUNCT
ejpam-4500	79	2	x	x	X
ejpam-4500	79	3	,	,	PUNCT
ejpam-4500	79	4	z	z	NOUN
ejpam-4500	79	5	}	}	PUNCT
ejpam-4500	79	6	.	.	PUNCT
ejpam-4500	80	1	since	since	SCONJ
ejpam-4500	80	2	y	y	PROPN
ejpam-4500	80	3	∈	∈	PROPN
ejpam-4500	80	4	ng(x	ng(x	NUM
ejpam-4500	80	5	,	,	PUNCT
ejpam-4500	80	6	2	2	NUM
ejpam-4500	80	7	)	)	PUNCT
ejpam-4500	80	8	\ng(z	\ng(z	NOUN
ejpam-4500	80	9	,	,	PUNCT
ejpam-4500	80	10	2	2	NUM
ejpam-4500	80	11	)	)	PUNCT
ejpam-4500	80	12	,	,	PUNCT
ejpam-4500	80	13	it	it	PRON
ejpam-4500	80	14	follows	follow	VERB
ejpam-4500	80	15	that	that	SCONJ
ejpam-4500	80	16	ng(x	ng(x	NUM
ejpam-4500	80	17	,	,	PUNCT
ejpam-4500	80	18	2)∩s	2)∩s	PROPN
ejpam-4500	80	19	̸=	̸=	PROPN
ejpam-4500	80	20	ng(z	ng(z	NUM
ejpam-4500	80	21	,	,	PUNCT
ejpam-4500	80	22	2)∩s	2)∩s	PROPN
ejpam-4500	80	23	.	.	PUNCT
ejpam-4500	81	1	thus	thus	ADV
ejpam-4500	81	2	,	,	PUNCT
ejpam-4500	81	3	s	s	VERB
ejpam-4500	81	4	is	be	AUX
ejpam-4500	81	5	a	a	DET
ejpam-4500	81	6	locating	locate	VERB
ejpam-4500	81	7	hop	hop	NOUN
ejpam-4500	81	8	set	set	NOUN
ejpam-4500	81	9	and	and	CCONJ
ejpam-4500	81	10	lhn(g	lhn(g	NUM
ejpam-4500	81	11	)	)	PUNCT
ejpam-4500	81	12	≤	≤	NUM
ejpam-4500	81	13	|s|	|s|	PROPN
ejpam-4500	81	14	=	=	SYM
ejpam-4500	81	15	n−2	n−2	PROPN
ejpam-4500	81	16	,	,	PUNCT
ejpam-4500	81	17	contrary	contrary	ADV
ejpam-4500	81	18	to	to	ADP
ejpam-4500	81	19	the	the	DET
ejpam-4500	81	20	assumption	assumption	NOUN
ejpam-4500	81	21	lhn(g	lhn(g	PROPN
ejpam-4500	81	22	)	)	PUNCT
ejpam-4500	82	1	=	=	SYM
ejpam-4500	82	2	n−1	n−1	PROPN
ejpam-4500	82	3	.	.	PUNCT
ejpam-4500	83	1	therefore	therefore	ADV
ejpam-4500	83	2	,	,	PUNCT
ejpam-4500	83	3	every	every	DET
ejpam-4500	83	4	component	component	NOUN
ejpam-4500	83	5	of	of	ADP
ejpam-4500	83	6	g	g	PROPN
ejpam-4500	83	7	is	be	AUX
ejpam-4500	83	8	complete	complete	ADJ
ejpam-4500	83	9	.	.	PUNCT
ejpam-4500	84	1	for	for	ADP
ejpam-4500	84	2	the	the	DET
ejpam-4500	84	3	converse	converse	NOUN
ejpam-4500	84	4	,	,	PUNCT
ejpam-4500	84	5	suppose	suppose	VERB
ejpam-4500	84	6	that	that	SCONJ
ejpam-4500	84	7	every	every	DET
ejpam-4500	84	8	component	component	NOUN
ejpam-4500	84	9	of	of	ADP
ejpam-4500	84	10	g	g	PROPN
ejpam-4500	84	11	is	be	AUX
ejpam-4500	84	12	complete	complete	ADJ
ejpam-4500	84	13	.	.	PUNCT
ejpam-4500	85	1	let	let	VERB
ejpam-4500	85	2	s	s	PRON
ejpam-4500	85	3	be	be	AUX
ejpam-4500	85	4	an	an	DET
ejpam-4500	85	5	lhn	lhn	NOUN
ejpam-4500	85	6	-	-	PUNCT
ejpam-4500	85	7	set	set	NOUN
ejpam-4500	85	8	of	of	ADP
ejpam-4500	85	9	g.	g.	PROPN
ejpam-4500	85	10	since	since	SCONJ
ejpam-4500	85	11	ng(u	ng(u	NOUN
ejpam-4500	85	12	,	,	PUNCT
ejpam-4500	85	13	2	2	NUM
ejpam-4500	85	14	)	)	PUNCT
ejpam-4500	85	15	∩	∩	NOUN
ejpam-4500	85	16	s	s	PART
ejpam-4500	85	17	=	=	NOUN
ejpam-4500	85	18	∅	∅	NOUN
ejpam-4500	85	19	∀u	∀u	NOUN
ejpam-4500	85	20	∈	∈	NOUN
ejpam-4500	85	21	v	v	NOUN
ejpam-4500	85	22	(	(	PUNCT
ejpam-4500	85	23	g	g	NOUN
ejpam-4500	85	24	)	)	PUNCT
ejpam-4500	85	25	,	,	PUNCT
ejpam-4500	85	26	v	v	X
ejpam-4500	85	27	(	(	PUNCT
ejpam-4500	85	28	g	g	NOUN
ejpam-4500	85	29	)	)	PUNCT
ejpam-4500	85	30	\	\	PROPN
ejpam-4500	86	1	s	s	AUX
ejpam-4500	86	2	can	can	AUX
ejpam-4500	86	3	not	not	PART
ejpam-4500	86	4	contain	contain	VERB
ejpam-4500	86	5	two	two	NUM
ejpam-4500	86	6	distinct	distinct	ADJ
ejpam-4500	86	7	vertices	vertex	NOUN
ejpam-4500	86	8	.	.	PUNCT
ejpam-4500	87	1	consequently	consequently	ADV
ejpam-4500	87	2	,	,	PUNCT
ejpam-4500	87	3	s	s	NOUN
ejpam-4500	87	4	=	=	SYM
ejpam-4500	87	5	v	v	X
ejpam-4500	87	6	(	(	PUNCT
ejpam-4500	87	7	g	g	NOUN
ejpam-4500	87	8	)	)	PUNCT
ejpam-4500	87	9	\	\	NOUN
ejpam-4500	87	10	{	{	PUNCT
ejpam-4500	87	11	v	v	NOUN
ejpam-4500	87	12	}	}	PUNCT
ejpam-4500	87	13	for	for	ADP
ejpam-4500	87	14	some	some	DET
ejpam-4500	87	15	vertex	vertex	NOUN
ejpam-4500	87	16	v	v	NOUN
ejpam-4500	87	17	of	of	ADP
ejpam-4500	87	18	g.	g.	PROPN
ejpam-4500	87	19	thus	thus	ADV
ejpam-4500	87	20	,	,	PUNCT
ejpam-4500	87	21	lhn(g	lhn(g	PROPN
ejpam-4500	87	22	)	)	PUNCT
ejpam-4500	87	23	=	=	SYM
ejpam-4500	87	24	|s|	|s|	NOUN
ejpam-4500	87	25	=	=	SYM
ejpam-4500	87	26	n−	n−	NOUN
ejpam-4500	87	27	1	1	NUM
ejpam-4500	87	28	.	.	PUNCT
ejpam-4500	88	1	□	□	PUNCT
ejpam-4500	88	2	corollary	corollary	ADJ
ejpam-4500	88	3	1	1	NUM
ejpam-4500	88	4	.	.	PUNCT
ejpam-4500	89	1	for	for	ADP
ejpam-4500	89	2	any	any	DET
ejpam-4500	89	3	positive	positive	ADJ
ejpam-4500	89	4	integer	integer	NOUN
ejpam-4500	89	5	n	n	PRON
ejpam-4500	89	6	≥	≥	NOUN
ejpam-4500	89	7	2	2	NUM
ejpam-4500	89	8	,	,	PUNCT
ejpam-4500	89	9	lhn(kn	lhn(kn	NOUN
ejpam-4500	89	10	)	)	PUNCT
ejpam-4500	89	11	=	=	SYM
ejpam-4500	89	12	lhn(kn	lhn(kn	NOUN
ejpam-4500	89	13	)	)	PUNCT
ejpam-4500	90	1	=	=	PUNCT
ejpam-4500	90	2	n−	n−	NOUN
ejpam-4500	90	3	1	1	NUM
ejpam-4500	90	4	.	.	PUNCT
ejpam-4500	90	5	proposition	proposition	NOUN
ejpam-4500	90	6	2	2	NUM
ejpam-4500	90	7	.	.	PUNCT
ejpam-4500	91	1	let	let	VERB
ejpam-4500	91	2	g	g	PRON
ejpam-4500	91	3	be	be	AUX
ejpam-4500	91	4	a	a	DET
ejpam-4500	91	5	graph	graph	NOUN
ejpam-4500	91	6	on	on	ADP
ejpam-4500	91	7	n	n	DET
ejpam-4500	91	8	vertices	vertex	NOUN
ejpam-4500	91	9	.	.	PUNCT
ejpam-4500	92	1	then	then	ADV
ejpam-4500	92	2	lhn(g	lhn(g	NUM
ejpam-4500	92	3	)	)	PUNCT
ejpam-4500	93	1	=	=	PUNCT
ejpam-4500	93	2	1	1	NUM
ejpam-4500	93	3	if	if	SCONJ
ejpam-4500	93	4	and	and	CCONJ
ejpam-4500	93	5	only	only	ADV
ejpam-4500	93	6	if	if	SCONJ
ejpam-4500	93	7	g	g	PROPN
ejpam-4500	93	8	∈	∈	PROPN
ejpam-4500	93	9	{	{	PUNCT
ejpam-4500	93	10	k1,k2	k1,k2	PROPN
ejpam-4500	93	11	,	,	PUNCT
ejpam-4500	93	12	p2	p2	NOUN
ejpam-4500	93	13	,	,	PUNCT
ejpam-4500	93	14	p3	p3	PROPN
ejpam-4500	93	15	}	}	PUNCT
ejpam-4500	93	16	.	.	PUNCT
ejpam-4500	94	1	proof	proof	NOUN
ejpam-4500	94	2	:	:	PUNCT
ejpam-4500	94	3	suppose	suppose	VERB
ejpam-4500	94	4	lhn(g	lhn(g	X
ejpam-4500	94	5	)	)	PUNCT
ejpam-4500	94	6	=	=	SYM
ejpam-4500	95	1	1	1	X
ejpam-4500	95	2	.	.	PUNCT
ejpam-4500	95	3	by	by	ADP
ejpam-4500	95	4	lemma	lemma	PROPN
ejpam-4500	95	5	1	1	NUM
ejpam-4500	95	6	,	,	PUNCT
ejpam-4500	95	7	n	n	PRON
ejpam-4500	95	8	≤	≤	NOUN
ejpam-4500	95	9	3	3	NUM
ejpam-4500	95	10	.	.	PUNCT
ejpam-4500	96	1	clearly	clearly	ADV
ejpam-4500	96	2	,	,	PUNCT
ejpam-4500	96	3	g	g	PROPN
ejpam-4500	96	4	=	=	PROPN
ejpam-4500	96	5	k1	k1	PROPN
ejpam-4500	96	6	if	if	SCONJ
ejpam-4500	96	7	n	n	NOUN
ejpam-4500	96	8	=	=	SYM
ejpam-4500	96	9	1	1	NUM
ejpam-4500	96	10	and	and	CCONJ
ejpam-4500	96	11	g	g	NOUN
ejpam-4500	96	12	=	=	PROPN
ejpam-4500	96	13	k2	k2	PROPN
ejpam-4500	96	14	=	=	NOUN
ejpam-4500	96	15	p2	p2	PROPN
ejpam-4500	96	16	or	or	CCONJ
ejpam-4500	96	17	g	g	NOUN
ejpam-4500	96	18	=	=	PROPN
ejpam-4500	96	19	k2	k2	PROPN
ejpam-4500	96	20	if	if	SCONJ
ejpam-4500	96	21	n	n	NOUN
ejpam-4500	96	22	=	=	SYM
ejpam-4500	96	23	2	2	X
ejpam-4500	96	24	.	.	PUNCT
ejpam-4500	96	25	suppose	suppose	VERB
ejpam-4500	96	26	n	n	PROPN
ejpam-4500	96	27	=	=	SYM
ejpam-4500	96	28	3	3	X
ejpam-4500	96	29	.	.	PUNCT
ejpam-4500	96	30	by	by	ADP
ejpam-4500	96	31	theorem	theorem	NOUN
ejpam-4500	96	32	1	1	NUM
ejpam-4500	96	33	,	,	PUNCT
ejpam-4500	96	34	lhn(k3	lhn(k3	PROPN
ejpam-4500	96	35	)	)	PUNCT
ejpam-4500	96	36	=	=	PUNCT
ejpam-4500	96	37	lhn(k1	lhn(k1	NOUN
ejpam-4500	96	38	∪	∪	ADJ
ejpam-4500	96	39	p2	p2	NOUN
ejpam-4500	96	40	)	)	PUNCT
ejpam-4500	96	41	=	=	SYM
ejpam-4500	97	1	lhn(k3	lhn(k3	PROPN
ejpam-4500	97	2	)	)	PUNCT
ejpam-4500	97	3	=	=	SYM
ejpam-4500	98	1	2	2	X
ejpam-4500	98	2	.	.	PUNCT
ejpam-4500	98	3	it	it	PRON
ejpam-4500	98	4	follows	follow	VERB
ejpam-4500	98	5	that	that	SCONJ
ejpam-4500	98	6	g	g	PROPN
ejpam-4500	98	7	=	=	PROPN
ejpam-4500	98	8	p3	p3	PROPN
ejpam-4500	98	9	.	.	PUNCT
ejpam-4500	99	1	thus	thus	ADV
ejpam-4500	99	2	,	,	PUNCT
ejpam-4500	99	3	g	g	PROPN
ejpam-4500	99	4	∈	∈	PROPN
ejpam-4500	99	5	{	{	PUNCT
ejpam-4500	99	6	k1,k2	k1,k2	PROPN
ejpam-4500	99	7	,	,	PUNCT
ejpam-4500	99	8	p2	p2	NOUN
ejpam-4500	99	9	,	,	PUNCT
ejpam-4500	99	10	p3	p3	PROPN
ejpam-4500	99	11	}	}	PUNCT
ejpam-4500	99	12	.	.	PUNCT
ejpam-4500	100	1	the	the	DET
ejpam-4500	100	2	converse	converse	NOUN
ejpam-4500	100	3	is	be	AUX
ejpam-4500	100	4	clear	clear	ADJ
ejpam-4500	100	5	.	.	PUNCT
ejpam-4500	101	1	□	□	PUNCT
ejpam-4500	101	2	proposition	proposition	NOUN
ejpam-4500	101	3	3	3	X
ejpam-4500	101	4	.	.	PUNCT
ejpam-4500	102	1	let	let	VERB
ejpam-4500	102	2	g	g	PRON
ejpam-4500	102	3	be	be	AUX
ejpam-4500	102	4	a	a	DET
ejpam-4500	102	5	connected	connected	ADJ
ejpam-4500	102	6	graph	graph	NOUN
ejpam-4500	102	7	of	of	ADP
ejpam-4500	102	8	order	order	NOUN
ejpam-4500	102	9	n.	n.	NOUN
ejpam-4500	102	10	if	if	SCONJ
ejpam-4500	102	11	lhn(g	lhn(g	PROPN
ejpam-4500	102	12	)	)	PUNCT
ejpam-4500	103	1	=	=	SYM
ejpam-4500	103	2	2	2	NUM
ejpam-4500	103	3	,	,	PUNCT
ejpam-4500	103	4	then	then	ADV
ejpam-4500	103	5	3	3	NUM
ejpam-4500	103	6	≤	≤	NOUN
ejpam-4500	103	7	|v	|v	X
ejpam-4500	103	8	(	(	PUNCT
ejpam-4500	103	9	g)|	g)|	VERB
ejpam-4500	103	10	≤	≤	ADV
ejpam-4500	103	11	6	6	NUM
ejpam-4500	103	12	.	.	PUNCT
ejpam-4500	104	1	proof	proof	NOUN
ejpam-4500	104	2	:	:	PUNCT
ejpam-4500	104	3	suppose	suppose	VERB
ejpam-4500	104	4	that	that	SCONJ
ejpam-4500	104	5	lhn(g	lhn(g	PROPN
ejpam-4500	104	6	)	)	PUNCT
ejpam-4500	104	7	=	=	SYM
ejpam-4500	105	1	2	2	X
ejpam-4500	105	2	.	.	PUNCT
ejpam-4500	105	3	by	by	ADP
ejpam-4500	105	4	lemma	lemma	PROPN
ejpam-4500	105	5	1	1	NUM
ejpam-4500	105	6	,	,	PUNCT
ejpam-4500	105	7	n	n	PRON
ejpam-4500	105	8	≤	≤	NOUN
ejpam-4500	105	9	lhn(g	lhn(g	NOUN
ejpam-4500	105	10	)	)	PUNCT
ejpam-4500	106	1	+	+	CCONJ
ejpam-4500	107	1	2lhn(g	2lhn(g	X
ejpam-4500	107	2	)	)	PUNCT
ejpam-4500	107	3	=	=	SYM
ejpam-4500	107	4	2	2	NUM
ejpam-4500	107	5	+	+	NUM
ejpam-4500	107	6	22	22	NUM
ejpam-4500	107	7	=	=	SYM
ejpam-4500	107	8	6	6	NUM
ejpam-4500	107	9	.	.	PUNCT
ejpam-4500	107	10	by	by	ADP
ejpam-4500	107	11	proposition	proposition	NOUN
ejpam-4500	107	12	2	2	NUM
ejpam-4500	107	13	,	,	PUNCT
ejpam-4500	107	14	it	it	PRON
ejpam-4500	107	15	follows	follow	VERB
ejpam-4500	107	16	that	that	SCONJ
ejpam-4500	107	17	3	3	NUM
ejpam-4500	107	18	≤	≤	NOUN
ejpam-4500	107	19	|v	|v	X
ejpam-4500	107	20	(	(	PUNCT
ejpam-4500	107	21	g)|	g)|	VERB
ejpam-4500	107	22	≤	≤	ADJ
ejpam-4500	107	23	6	6	NUM
ejpam-4500	107	24	.	.	PUNCT
ejpam-4500	108	1	□	□	PUNCT
ejpam-4500	108	2	proposition	proposition	NOUN
ejpam-4500	108	3	4	4	NUM
ejpam-4500	108	4	.	.	PUNCT
ejpam-4500	109	1	let	let	VERB
ejpam-4500	109	2	g	g	PRON
ejpam-4500	109	3	be	be	AUX
ejpam-4500	109	4	a	a	DET
ejpam-4500	109	5	connected	connected	ADJ
ejpam-4500	109	6	graph	graph	NOUN
ejpam-4500	109	7	of	of	ADP
ejpam-4500	109	8	order	order	NOUN
ejpam-4500	109	9	n	n	NOUN
ejpam-4500	109	10	=	=	SYM
ejpam-4500	109	11	4	4	X
ejpam-4500	109	12	.	.	PUNCT
ejpam-4500	109	13	then	then	ADV
ejpam-4500	109	14	lhn(g	lhn(g	NUM
ejpam-4500	109	15	)	)	PUNCT
ejpam-4500	110	1	=	=	SYM
ejpam-4500	110	2	2	2	NUM
ejpam-4500	110	3	if	if	SCONJ
ejpam-4500	110	4	and	and	CCONJ
ejpam-4500	110	5	only	only	ADV
ejpam-4500	110	6	if	if	SCONJ
ejpam-4500	110	7	g	g	PROPN
ejpam-4500	110	8	̸=	̸=	PROPN
ejpam-4500	110	9	k4	k4	NOUN
ejpam-4500	110	10	.	.	PUNCT
ejpam-4500	111	1	proof	proof	NOUN
ejpam-4500	111	2	:	:	PUNCT
ejpam-4500	111	3	let	let	VERB
ejpam-4500	111	4	lhn(g	lhn(g	PRON
ejpam-4500	111	5	)	)	PUNCT
ejpam-4500	111	6	=	=	SYM
ejpam-4500	112	1	2	2	X
ejpam-4500	112	2	.	.	PUNCT
ejpam-4500	112	3	then	then	ADV
ejpam-4500	112	4	by	by	ADP
ejpam-4500	112	5	corollary	corollary	ADJ
ejpam-4500	112	6	1	1	NUM
ejpam-4500	112	7	,	,	PUNCT
ejpam-4500	112	8	g	g	PROPN
ejpam-4500	112	9	̸=	̸=	PROPN
ejpam-4500	112	10	k4	k4	NOUN
ejpam-4500	112	11	.	.	PUNCT
ejpam-4500	113	1	for	for	ADP
ejpam-4500	113	2	the	the	DET
ejpam-4500	113	3	converse	converse	NOUN
ejpam-4500	113	4	,	,	PUNCT
ejpam-4500	113	5	suppose	suppose	VERB
ejpam-4500	113	6	that	that	SCONJ
ejpam-4500	113	7	g	g	PROPN
ejpam-4500	113	8	̸=	̸=	PROPN
ejpam-4500	113	9	k4	k4	NOUN
ejpam-4500	113	10	.	.	PUNCT
ejpam-4500	114	1	since	since	SCONJ
ejpam-4500	114	2	n	n	NOUN
ejpam-4500	114	3	=	=	SYM
ejpam-4500	114	4	4	4	NUM
ejpam-4500	114	5	,	,	PUNCT
ejpam-4500	114	6	by	by	ADP
ejpam-4500	114	7	proposition	proposition	NOUN
ejpam-4500	114	8	2	2	NUM
ejpam-4500	114	9	,	,	PUNCT
ejpam-4500	114	10	lhn(g	lhn(g	PROPN
ejpam-4500	114	11	)	)	PUNCT
ejpam-4500	114	12	≥	≥	NOUN
ejpam-4500	114	13	2	2	NUM
ejpam-4500	114	14	.	.	PUNCT
ejpam-4500	114	15	choose	choose	VERB
ejpam-4500	114	16	any	any	DET
ejpam-4500	114	17	u	u	NOUN
ejpam-4500	114	18	,	,	PUNCT
ejpam-4500	114	19	v	v	NOUN
ejpam-4500	114	20	∈	∈	PROPN
ejpam-4500	114	21	v	v	NOUN
ejpam-4500	114	22	(	(	PUNCT
ejpam-4500	114	23	g	g	NOUN
ejpam-4500	114	24	)	)	PUNCT
ejpam-4500	114	25	such	such	ADJ
ejpam-4500	114	26	that	that	SCONJ
ejpam-4500	114	27	dg(u	dg(u	ADJ
ejpam-4500	114	28	,	,	PUNCT
ejpam-4500	114	29	v	v	NOUN
ejpam-4500	114	30	)	)	PUNCT
ejpam-4500	114	31	=	=	SYM
ejpam-4500	115	1	2	2	X
ejpam-4500	115	2	.	.	X
ejpam-4500	115	3	let	let	VERB
ejpam-4500	115	4	w	w	PROPN
ejpam-4500	115	5	∈	∈	PROPN
ejpam-4500	115	6	ng(u	ng(u	NOUN
ejpam-4500	115	7	)	)	PUNCT
ejpam-4500	115	8	∩	∩	NOUN
ejpam-4500	115	9	ng(v	ng(v	NUM
ejpam-4500	115	10	)	)	PUNCT
ejpam-4500	115	11	and	and	CCONJ
ejpam-4500	115	12	let	let	VERB
ejpam-4500	115	13	s	s	PRON
ejpam-4500	115	14	∈	∈	VERB
ejpam-4500	115	15	v	v	ADP
ejpam-4500	115	16	(	(	PUNCT
ejpam-4500	115	17	g	g	NOUN
ejpam-4500	115	18	)	)	PUNCT
ejpam-4500	115	19	\	\	NOUN
ejpam-4500	115	20	{	{	PUNCT
ejpam-4500	115	21	u	u	NOUN
ejpam-4500	115	22	,	,	PUNCT
ejpam-4500	115	23	v	v	NOUN
ejpam-4500	115	24	,	,	PUNCT
ejpam-4500	115	25	w	w	NOUN
ejpam-4500	115	26	}	}	PUNCT
ejpam-4500	115	27	.	.	PUNCT
ejpam-4500	116	1	since	since	SCONJ
ejpam-4500	116	2	u	u	PROPN
ejpam-4500	116	3	∈	∈	PROPN
ejpam-4500	116	4	ng(v	ng(v	PUNCT
ejpam-4500	116	5	,	,	PUNCT
ejpam-4500	116	6	2	2	NUM
ejpam-4500	116	7	)	)	PUNCT
ejpam-4500	116	8	\ng(w	\ng(w	NOUN
ejpam-4500	116	9	,	,	PUNCT
ejpam-4500	116	10	2	2	NUM
ejpam-4500	116	11	)	)	PUNCT
ejpam-4500	116	12	,	,	PUNCT
ejpam-4500	116	13	it	it	PRON
ejpam-4500	116	14	follows	follow	VERB
ejpam-4500	116	15	that	that	PRON
ejpam-4500	116	16	s	s	VERB
ejpam-4500	116	17	=	=	PUNCT
ejpam-4500	116	18	{	{	PUNCT
ejpam-4500	116	19	u	u	NOUN
ejpam-4500	116	20	,	,	PUNCT
ejpam-4500	116	21	s	s	PART
ejpam-4500	116	22	}	}	PUNCT
ejpam-4500	116	23	is	be	AUX
ejpam-4500	116	24	a	a	DET
ejpam-4500	116	25	locating	locating	NOUN
ejpam-4500	116	26	set	set	NOUN
ejpam-4500	116	27	of	of	ADP
ejpam-4500	116	28	g.	g.	PROPN
ejpam-4500	116	29	consequently	consequently	ADV
ejpam-4500	116	30	,	,	PUNCT
ejpam-4500	116	31	lhn(g	lhn(g	PROPN
ejpam-4500	116	32	)	)	PUNCT
ejpam-4500	116	33	=	=	SYM
ejpam-4500	116	34	|s|	|s|	NOUN
ejpam-4500	116	35	=	=	SYM
ejpam-4500	116	36	2	2	NUM
ejpam-4500	116	37	.	.	PUNCT
ejpam-4500	116	38	□	□	PUNCT
ejpam-4500	116	39	e.m	e.m	PROPN
ejpam-4500	116	40	.	.	PROPN
ejpam-4500	116	41	a.	a.	NOUN
ejpam-4500	116	42	pagcu	pagcu	PROPN
ejpam-4500	116	43	,	,	PUNCT
ejpam-4500	116	44	g.	g.	PROPN
ejpam-4500	116	45	a.	a.	NOUN
ejpam-4500	116	46	malacas	malacas	PROPN
ejpam-4500	116	47	,	,	PUNCT
ejpam-4500	116	48	s.	s.	PROPN
ejpam-4500	116	49	r.	r.	PROPN
ejpam-4500	116	50	canoy	canoy	PROPN
ejpam-4500	116	51	,	,	PUNCT
ejpam-4500	116	52	jr	jr	PROPN
ejpam-4500	116	53	.	.	PROPN
ejpam-4500	116	54	/	/	SYM
ejpam-4500	116	55	eur	eur	PROPN
ejpam-4500	116	56	.	.	PUNCT
ejpam-4500	117	1	j.	j.	PROPN
ejpam-4500	117	2	pure	pure	PROPN
ejpam-4500	117	3	appl	appl	PROPN
ejpam-4500	117	4	.	.	PROPN
ejpam-4500	117	5	math	math	PROPN
ejpam-4500	117	6	,	,	PUNCT
ejpam-4500	117	7	15	15	NUM
ejpam-4500	117	8	(	(	PUNCT
ejpam-4500	117	9	4	4	NUM
ejpam-4500	117	10	)	)	PUNCT
ejpam-4500	117	11	(	(	PUNCT
ejpam-4500	117	12	2022	2022	NUM
ejpam-4500	117	13	)	)	PUNCT
ejpam-4500	117	14	,	,	PUNCT
ejpam-4500	117	15	1705	1705	NUM
ejpam-4500	117	16	-	-	SYM
ejpam-4500	117	17	1715	1715	NUM
ejpam-4500	117	18	1708	1708	NUM
ejpam-4500	117	19	proposition	proposition	NOUN
ejpam-4500	117	20	5	5	NUM
ejpam-4500	117	21	.	.	PUNCT
ejpam-4500	118	1	let	let	VERB
ejpam-4500	118	2	g	g	PRON
ejpam-4500	118	3	be	be	AUX
ejpam-4500	118	4	a	a	DET
ejpam-4500	118	5	connected	connected	ADJ
ejpam-4500	118	6	graph	graph	NOUN
ejpam-4500	118	7	of	of	ADP
ejpam-4500	118	8	order	order	NOUN
ejpam-4500	118	9	n	n	NOUN
ejpam-4500	118	10	=	=	SYM
ejpam-4500	118	11	5	5	NUM
ejpam-4500	118	12	.	.	PUNCT
ejpam-4500	118	13	then	then	ADV
ejpam-4500	118	14	lhn(g	lhn(g	NUM
ejpam-4500	118	15	)	)	PUNCT
ejpam-4500	119	1	=	=	SYM
ejpam-4500	119	2	2	2	NUM
ejpam-4500	119	3	if	if	SCONJ
ejpam-4500	119	4	and	and	CCONJ
ejpam-4500	119	5	only	only	ADV
ejpam-4500	119	6	if	if	SCONJ
ejpam-4500	119	7	there	there	PRON
ejpam-4500	119	8	exist	exist	VERB
ejpam-4500	119	9	distinct	distinct	ADJ
ejpam-4500	119	10	vertices	vertex	NOUN
ejpam-4500	119	11	x	x	PUNCT
ejpam-4500	119	12	and	and	CCONJ
ejpam-4500	119	13	y	y	PROPN
ejpam-4500	119	14	of	of	ADP
ejpam-4500	119	15	g	g	PROPN
ejpam-4500	119	16	satisfying	satisfy	VERB
ejpam-4500	119	17	one	one	NUM
ejpam-4500	119	18	of	of	ADP
ejpam-4500	119	19	the	the	DET
ejpam-4500	119	20	following	follow	VERB
ejpam-4500	119	21	properties	property	NOUN
ejpam-4500	119	22	:	:	PUNCT
ejpam-4500	119	23	(	(	PUNCT
ejpam-4500	119	24	i	i	NOUN
ejpam-4500	119	25	)	)	PUNCT
ejpam-4500	119	26	|ng(x	|ng(x	PUNCT
ejpam-4500	119	27	,	,	PUNCT
ejpam-4500	119	28	2	2	X
ejpam-4500	119	29	)	)	PUNCT
ejpam-4500	119	30	∩ng(y	∩ng(y	PROPN
ejpam-4500	119	31	,	,	PUNCT
ejpam-4500	119	32	2)|	2)|	NUM
ejpam-4500	119	33	=	=	SYM
ejpam-4500	119	34	0	0	NUM
ejpam-4500	119	35	and	and	CCONJ
ejpam-4500	119	36	|ng(x	|ng(x	PRON
ejpam-4500	119	37	,	,	PUNCT
ejpam-4500	119	38	2	2	X
ejpam-4500	119	39	)	)	PUNCT
ejpam-4500	119	40	\	\	NOUN
ejpam-4500	119	41	{	{	PUNCT
ejpam-4500	119	42	y}|	y}|	NOUN
ejpam-4500	119	43	=	=	SYM
ejpam-4500	119	44	|ng(y	|ng(y	NOUN
ejpam-4500	119	45	,	,	PUNCT
ejpam-4500	119	46	2	2	NUM
ejpam-4500	119	47	)	)	PUNCT
ejpam-4500	119	48	\	\	NOUN
ejpam-4500	119	49	{	{	PUNCT
ejpam-4500	119	50	x}|	x}|	X
ejpam-4500	119	51	=	=	SYM
ejpam-4500	119	52	1	1	X
ejpam-4500	119	53	.	.	PUNCT
ejpam-4500	119	54	(	(	PUNCT
ejpam-4500	119	55	ii	ii	NOUN
ejpam-4500	119	56	)	)	PUNCT
ejpam-4500	119	57	|ng(x	|ng(x	X
ejpam-4500	119	58	,	,	PUNCT
ejpam-4500	119	59	2)∩ng(y	2)∩ng(y	NUM
ejpam-4500	119	60	,	,	PUNCT
ejpam-4500	119	61	2)|	2)|	NUM
ejpam-4500	119	62	=	=	SYM
ejpam-4500	119	63	1	1	NUM
ejpam-4500	119	64	and	and	CCONJ
ejpam-4500	119	65	[	[	X
ejpam-4500	119	66	(	(	PUNCT
ejpam-4500	119	67	|ng(x	|ng(x	ADV
ejpam-4500	119	68	,	,	PUNCT
ejpam-4500	119	69	2)\{y}|	2)\{y}|	NUM
ejpam-4500	119	70	=	=	SYM
ejpam-4500	119	71	|ng(y	|ng(y	PROPN
ejpam-4500	119	72	,	,	PUNCT
ejpam-4500	119	73	2)\{x}|	2)\{x}|	NUM
ejpam-4500	119	74	=	=	SYM
ejpam-4500	119	75	2	2	NUM
ejpam-4500	119	76	)	)	PUNCT
ejpam-4500	119	77	or	or	CCONJ
ejpam-4500	119	78	(	(	PUNCT
ejpam-4500	119	79	|ng(x	|ng(x	PROPN
ejpam-4500	119	80	,	,	PUNCT
ejpam-4500	119	81	2)\	2)\	NUM
ejpam-4500	119	82	{	{	PUNCT
ejpam-4500	119	83	y}|	y}|	NOUN
ejpam-4500	119	84	=	=	SYM
ejpam-4500	119	85	2	2	NUM
ejpam-4500	119	86	and	and	CCONJ
ejpam-4500	119	87	|ng(y	|ng(y	ADP
ejpam-4500	119	88	,	,	PUNCT
ejpam-4500	119	89	2)\{x}|	2)\{x}|	NUM
ejpam-4500	119	90	=	=	SYM
ejpam-4500	119	91	1	1	NUM
ejpam-4500	119	92	)	)	PUNCT
ejpam-4500	119	93	or	or	CCONJ
ejpam-4500	119	94	(	(	PUNCT
ejpam-4500	119	95	|ng(x	|ng(x	ADV
ejpam-4500	119	96	,	,	PUNCT
ejpam-4500	119	97	2)\{y}|	2)\{y}|	NUM
ejpam-4500	119	98	=	=	SYM
ejpam-4500	119	99	1	1	NUM
ejpam-4500	119	100	and	and	CCONJ
ejpam-4500	119	101	|ng(y	|ng(y	ADP
ejpam-4500	119	102	,	,	PUNCT
ejpam-4500	119	103	2)\{x}|	2)\{x}|	NUM
ejpam-4500	119	104	=	=	SYM
ejpam-4500	119	105	2	2	NUM
ejpam-4500	119	106	)	)	PUNCT
ejpam-4500	119	107	]	]	PUNCT
ejpam-4500	119	108	.	.	PUNCT
ejpam-4500	120	1	proof	proof	NOUN
ejpam-4500	120	2	:	:	PUNCT
ejpam-4500	120	3	suppose	suppose	VERB
ejpam-4500	120	4	that	that	SCONJ
ejpam-4500	120	5	lhn(g	lhn(g	PROPN
ejpam-4500	120	6	)	)	PUNCT
ejpam-4500	120	7	=	=	SYM
ejpam-4500	121	1	2	2	X
ejpam-4500	121	2	.	.	PUNCT
ejpam-4500	121	3	then	then	ADV
ejpam-4500	121	4	there	there	PRON
ejpam-4500	121	5	exist	exist	VERB
ejpam-4500	121	6	distinct	distinct	ADJ
ejpam-4500	121	7	vertices	vertex	NOUN
ejpam-4500	121	8	x	x	X
ejpam-4500	121	9	,	,	PUNCT
ejpam-4500	121	10	y	y	PROPN
ejpam-4500	121	11	∈	∈	PROPN
ejpam-4500	121	12	v	v	ADP
ejpam-4500	121	13	(	(	PUNCT
ejpam-4500	121	14	g	g	NOUN
ejpam-4500	121	15	)	)	PUNCT
ejpam-4500	121	16	such	such	ADJ
ejpam-4500	121	17	that	that	DET
ejpam-4500	121	18	s	s	PART
ejpam-4500	121	19	=	=	X
ejpam-4500	121	20	{	{	PUNCT
ejpam-4500	121	21	x	x	PROPN
ejpam-4500	121	22	,	,	PUNCT
ejpam-4500	121	23	y	y	PRON
ejpam-4500	121	24	}	}	PUNCT
ejpam-4500	121	25	is	be	AUX
ejpam-4500	121	26	a	a	DET
ejpam-4500	121	27	minimum	minimum	ADJ
ejpam-4500	121	28	locating	locate	VERB
ejpam-4500	121	29	hop	hop	NOUN
ejpam-4500	121	30	set	set	NOUN
ejpam-4500	121	31	of	of	ADP
ejpam-4500	121	32	g.	g.	PROPN
ejpam-4500	121	33	hence	hence	ADV
ejpam-4500	121	34	,	,	PUNCT
ejpam-4500	121	35	|ng(x	|ng(x	X
ejpam-4500	121	36	,	,	PUNCT
ejpam-4500	121	37	2)∩ng(y	2)∩ng(y	NUM
ejpam-4500	121	38	,	,	PUNCT
ejpam-4500	121	39	2)|	2)|	NUM
ejpam-4500	121	40	≤	≤	NUM
ejpam-4500	121	41	1	1	NUM
ejpam-4500	121	42	.	.	PUNCT
ejpam-4500	122	1	suppose	suppose	VERB
ejpam-4500	122	2	|ng(x	|ng(x	NOUN
ejpam-4500	122	3	,	,	PUNCT
ejpam-4500	122	4	2	2	X
ejpam-4500	122	5	)	)	PUNCT
ejpam-4500	122	6	∩	∩	NOUN
ejpam-4500	122	7	ng(y	ng(y	ADP
ejpam-4500	122	8	,	,	PUNCT
ejpam-4500	122	9	2)|	2)|	NUM
ejpam-4500	122	10	=	=	SYM
ejpam-4500	122	11	0	0	X
ejpam-4500	122	12	.	.	PUNCT
ejpam-4500	123	1	since	since	SCONJ
ejpam-4500	123	2	s	s	PROPN
ejpam-4500	123	3	is	be	AUX
ejpam-4500	123	4	a	a	DET
ejpam-4500	123	5	locating	locate	VERB
ejpam-4500	123	6	hop	hop	NOUN
ejpam-4500	123	7	set	set	NOUN
ejpam-4500	123	8	,	,	PUNCT
ejpam-4500	123	9	|ng(x	|ng(x	X
ejpam-4500	123	10	,	,	PUNCT
ejpam-4500	123	11	2	2	X
ejpam-4500	123	12	)	)	PUNCT
ejpam-4500	123	13	\	\	NOUN
ejpam-4500	123	14	{	{	PUNCT
ejpam-4500	123	15	y}|	y}|	NOUN
ejpam-4500	123	16	≤	≤	NUM
ejpam-4500	123	17	1	1	NUM
ejpam-4500	123	18	.	.	PUNCT
ejpam-4500	123	19	suppose	suppose	VERB
ejpam-4500	123	20	|ng(x	|ng(x	NOUN
ejpam-4500	123	21	,	,	PUNCT
ejpam-4500	123	22	2	2	X
ejpam-4500	123	23	)	)	PUNCT
ejpam-4500	123	24	\	\	NOUN
ejpam-4500	123	25	{	{	PUNCT
ejpam-4500	123	26	y}|	y}|	NOUN
ejpam-4500	123	27	=	=	SYM
ejpam-4500	123	28	0	0	X
ejpam-4500	123	29	.	.	PUNCT
ejpam-4500	124	1	then	then	ADV
ejpam-4500	124	2	|ng(y	|ng(y	NOUN
ejpam-4500	124	3	,	,	PUNCT
ejpam-4500	124	4	2	2	NUM
ejpam-4500	124	5	)	)	PUNCT
ejpam-4500	124	6	\	\	NOUN
ejpam-4500	124	7	{	{	PUNCT
ejpam-4500	124	8	x}|	x}|	X
ejpam-4500	124	9	=	=	SYM
ejpam-4500	124	10	1	1	NUM
ejpam-4500	124	11	since	since	SCONJ
ejpam-4500	124	12	s	s	NOUN
ejpam-4500	124	13	is	be	AUX
ejpam-4500	124	14	a	a	DET
ejpam-4500	124	15	locating	locate	VERB
ejpam-4500	124	16	hop	hop	NOUN
ejpam-4500	124	17	set	set	NOUN
ejpam-4500	124	18	.	.	PUNCT
ejpam-4500	125	1	this	this	PRON
ejpam-4500	125	2	implies	imply	VERB
ejpam-4500	125	3	that	that	SCONJ
ejpam-4500	125	4	there	there	PRON
ejpam-4500	125	5	exist	exist	VERB
ejpam-4500	125	6	at	at	ADV
ejpam-4500	125	7	least	least	ADV
ejpam-4500	125	8	two	two	NUM
ejpam-4500	125	9	vertices	vertex	NOUN
ejpam-4500	125	10	say	say	VERB
ejpam-4500	125	11	z	z	NOUN
ejpam-4500	125	12	and	and	CCONJ
ejpam-4500	125	13	w	w	ADP
ejpam-4500	125	14	such	such	ADJ
ejpam-4500	125	15	that	that	PRON
ejpam-4500	125	16	z	z	NOUN
ejpam-4500	125	17	,	,	PUNCT
ejpam-4500	125	18	w	w	PROPN
ejpam-4500	125	19	/∈	/∈	PUNCT
ejpam-4500	125	20	ng(x	ng(x	NUM
ejpam-4500	125	21	,	,	PUNCT
ejpam-4500	125	22	2	2	X
ejpam-4500	125	23	)	)	PUNCT
ejpam-4500	125	24	∪	∪	ADP
ejpam-4500	125	25	ng(y	ng(y	NOUN
ejpam-4500	125	26	,	,	PUNCT
ejpam-4500	125	27	2	2	NUM
ejpam-4500	125	28	)	)	PUNCT
ejpam-4500	125	29	.	.	PUNCT
ejpam-4500	126	1	consequently	consequently	ADV
ejpam-4500	126	2	,	,	PUNCT
ejpam-4500	126	3	ng(z	ng(z	PROPN
ejpam-4500	126	4	,	,	PUNCT
ejpam-4500	126	5	2	2	NUM
ejpam-4500	126	6	)	)	PUNCT
ejpam-4500	126	7	=	=	NOUN
ejpam-4500	126	8	ng(w	ng(w	NOUN
ejpam-4500	126	9	,	,	PUNCT
ejpam-4500	126	10	2	2	X
ejpam-4500	126	11	)	)	PUNCT
ejpam-4500	126	12	=	=	NOUN
ejpam-4500	126	13	∅	∅	NOUN
ejpam-4500	126	14	,	,	PUNCT
ejpam-4500	126	15	contrary	contrary	ADJ
ejpam-4500	126	16	to	to	ADP
ejpam-4500	126	17	our	our	PRON
ejpam-4500	126	18	assumption	assumption	NOUN
ejpam-4500	126	19	that	that	SCONJ
ejpam-4500	126	20	s	s	VERB
ejpam-4500	126	21	is	be	AUX
ejpam-4500	126	22	a	a	DET
ejpam-4500	126	23	locating	locate	VERB
ejpam-4500	126	24	hop	hop	NOUN
ejpam-4500	126	25	set	set	NOUN
ejpam-4500	126	26	.	.	PUNCT
ejpam-4500	127	1	thus	thus	ADV
ejpam-4500	127	2	,	,	PUNCT
ejpam-4500	127	3	|ng(x	|ng(x	X
ejpam-4500	127	4	,	,	PUNCT
ejpam-4500	127	5	2	2	X
ejpam-4500	127	6	)	)	PUNCT
ejpam-4500	127	7	\	\	NOUN
ejpam-4500	127	8	{	{	PUNCT
ejpam-4500	127	9	y}|	y}|	NOUN
ejpam-4500	127	10	=	=	SYM
ejpam-4500	127	11	1	1	X
ejpam-4500	127	12	.	.	PUNCT
ejpam-4500	127	13	similarly	similarly	ADV
ejpam-4500	127	14	,	,	PUNCT
ejpam-4500	127	15	|ng(y	|ng(y	ADV
ejpam-4500	127	16	,	,	PUNCT
ejpam-4500	127	17	2	2	NUM
ejpam-4500	127	18	)	)	PUNCT
ejpam-4500	127	19	\	\	NOUN
ejpam-4500	127	20	{	{	PUNCT
ejpam-4500	127	21	x}|	x}|	X
ejpam-4500	127	22	=	=	SYM
ejpam-4500	127	23	1	1	X
ejpam-4500	127	24	.	.	PUNCT
ejpam-4500	128	1	hence	hence	ADV
ejpam-4500	128	2	,	,	PUNCT
ejpam-4500	128	3	(	(	PUNCT
ejpam-4500	128	4	i	i	NOUN
ejpam-4500	128	5	)	)	PUNCT
ejpam-4500	128	6	holds	hold	VERB
ejpam-4500	128	7	.	.	PUNCT
ejpam-4500	128	8	suppose	suppose	VERB
ejpam-4500	128	9	that	that	SCONJ
ejpam-4500	128	10	|ng(x	|ng(x	PUNCT
ejpam-4500	128	11	,	,	PUNCT
ejpam-4500	128	12	2	2	X
ejpam-4500	128	13	)	)	PUNCT
ejpam-4500	128	14	∩	∩	NOUN
ejpam-4500	128	15	ng(y	ng(y	ADP
ejpam-4500	128	16	,	,	PUNCT
ejpam-4500	128	17	2)|	2)|	NUM
ejpam-4500	128	18	=	=	SYM
ejpam-4500	128	19	1	1	X
ejpam-4500	128	20	.	.	PUNCT
ejpam-4500	128	21	let	let	VERB
ejpam-4500	128	22	a	a	DET
ejpam-4500	128	23	∈	∈	PROPN
ejpam-4500	128	24	v	v	NOUN
ejpam-4500	128	25	(	(	PUNCT
ejpam-4500	128	26	g	g	NOUN
ejpam-4500	128	27	)	)	PUNCT
ejpam-4500	128	28	such	such	ADJ
ejpam-4500	128	29	that	that	DET
ejpam-4500	128	30	dg(x	dg(x	NOUN
ejpam-4500	128	31	,	,	PUNCT
ejpam-4500	128	32	a	a	X
ejpam-4500	128	33	)	)	PUNCT
ejpam-4500	128	34	=	=	SYM
ejpam-4500	128	35	2	2	NUM
ejpam-4500	128	36	and	and	CCONJ
ejpam-4500	128	37	dg(y	dg(y	ADJ
ejpam-4500	128	38	,	,	PUNCT
ejpam-4500	128	39	a	a	PRON
ejpam-4500	128	40	)	)	PUNCT
ejpam-4500	128	41	=	=	SYM
ejpam-4500	128	42	2	2	NUM
ejpam-4500	128	43	and	and	CCONJ
ejpam-4500	128	44	let	let	VERB
ejpam-4500	128	45	b	b	X
ejpam-4500	128	46	,	,	PUNCT
ejpam-4500	128	47	c	c	PROPN
ejpam-4500	128	48	∈	∈	PROPN
ejpam-4500	128	49	v	v	ADP
ejpam-4500	128	50	(	(	PUNCT
ejpam-4500	128	51	g	g	NOUN
ejpam-4500	128	52	)	)	PUNCT
ejpam-4500	128	53	\	\	NOUN
ejpam-4500	129	1	{	{	PUNCT
ejpam-4500	129	2	x	x	NOUN
ejpam-4500	129	3	,	,	PUNCT
ejpam-4500	129	4	y	y	PROPN
ejpam-4500	129	5	,	,	PUNCT
ejpam-4500	129	6	a	a	PRON
ejpam-4500	129	7	}	}	PUNCT
ejpam-4500	129	8	.	.	PUNCT
ejpam-4500	130	1	then	then	ADV
ejpam-4500	130	2	b	b	X
ejpam-4500	130	3	,	,	PUNCT
ejpam-4500	130	4	c	c	PROPN
ejpam-4500	130	5	/∈	/∈	PUNCT
ejpam-4500	130	6	ng(x	ng(x	NUM
ejpam-4500	130	7	,	,	PUNCT
ejpam-4500	130	8	2	2	X
ejpam-4500	130	9	)	)	PUNCT
ejpam-4500	130	10	∩	∩	NOUN
ejpam-4500	130	11	ng(y	ng(y	NOUN
ejpam-4500	130	12	,	,	PUNCT
ejpam-4500	130	13	2	2	NUM
ejpam-4500	130	14	)	)	PUNCT
ejpam-4500	130	15	.	.	PUNCT
ejpam-4500	131	1	since	since	SCONJ
ejpam-4500	131	2	the	the	DET
ejpam-4500	131	3	subset	subset	NOUN
ejpam-4500	131	4	of	of	ADP
ejpam-4500	131	5	s	s	PROPN
ejpam-4500	131	6	are	be	AUX
ejpam-4500	131	7	∅	∅	NOUN
ejpam-4500	131	8	,	,	PUNCT
ejpam-4500	131	9	{	{	PUNCT
ejpam-4500	131	10	x	x	NOUN
ejpam-4500	131	11	,	,	PUNCT
ejpam-4500	131	12	y	y	PROPN
ejpam-4500	131	13	}	}	PUNCT
ejpam-4500	131	14	,	,	PUNCT
ejpam-4500	131	15	{	{	PUNCT
ejpam-4500	131	16	x	x	X
ejpam-4500	131	17	}	}	PUNCT
ejpam-4500	131	18	,	,	PUNCT
ejpam-4500	131	19	{	{	PUNCT
ejpam-4500	131	20	y	y	NOUN
ejpam-4500	131	21	}	}	PUNCT
ejpam-4500	131	22	and	and	CCONJ
ejpam-4500	131	23	since	since	SCONJ
ejpam-4500	131	24	ng(a	ng(a	NOUN
ejpam-4500	131	25	,	,	PUNCT
ejpam-4500	131	26	2	2	X
ejpam-4500	131	27	)	)	PUNCT
ejpam-4500	131	28	∩	∩	NOUN
ejpam-4500	131	29	s	s	PART
ejpam-4500	131	30	is	be	AUX
ejpam-4500	131	31	{	{	PUNCT
ejpam-4500	131	32	x	x	NOUN
ejpam-4500	131	33	,	,	PUNCT
ejpam-4500	131	34	y	y	PROPN
ejpam-4500	131	35	}	}	PUNCT
ejpam-4500	131	36	,	,	PUNCT
ejpam-4500	131	37	the	the	DET
ejpam-4500	131	38	remaining	remain	VERB
ejpam-4500	131	39	two	two	NUM
ejpam-4500	131	40	sets	set	NOUN
ejpam-4500	131	41	ng(b	ng(b	NOUN
ejpam-4500	131	42	,	,	PUNCT
ejpam-4500	131	43	2)∩s	2)∩s	PROPN
ejpam-4500	131	44	and	and	CCONJ
ejpam-4500	131	45	ng(c	ng(c	NUM
ejpam-4500	131	46	,	,	PUNCT
ejpam-4500	131	47	2)∩s	2)∩s	PROPN
ejpam-4500	131	48	are	be	AUX
ejpam-4500	131	49	{	{	PUNCT
ejpam-4500	131	50	x	x	NOUN
ejpam-4500	131	51	}	}	PUNCT
ejpam-4500	131	52	and	and	CCONJ
ejpam-4500	131	53	{	{	PUNCT
ejpam-4500	131	54	y	y	NOUN
ejpam-4500	131	55	}	}	PUNCT
ejpam-4500	131	56	or	or	CCONJ
ejpam-4500	131	57	{	{	PUNCT
ejpam-4500	131	58	x	x	NOUN
ejpam-4500	131	59	}	}	PUNCT
ejpam-4500	131	60	and	and	CCONJ
ejpam-4500	131	61	∅	∅	NOUN
ejpam-4500	131	62	or	or	CCONJ
ejpam-4500	131	63	{	{	PUNCT
ejpam-4500	131	64	y	y	NOUN
ejpam-4500	131	65	}	}	PUNCT
ejpam-4500	131	66	and	and	CCONJ
ejpam-4500	131	67	∅	∅	NOUN
ejpam-4500	131	68	,	,	PUNCT
ejpam-4500	131	69	respectively	respectively	ADV
ejpam-4500	131	70	.	.	PUNCT
ejpam-4500	132	1	thus	thus	ADV
ejpam-4500	132	2	,	,	PUNCT
ejpam-4500	132	3	|ng(x	|ng(x	X
ejpam-4500	132	4	,	,	PUNCT
ejpam-4500	132	5	2	2	X
ejpam-4500	132	6	)	)	PUNCT
ejpam-4500	132	7	\	\	NOUN
ejpam-4500	132	8	{	{	PUNCT
ejpam-4500	132	9	y}|	y}|	NOUN
ejpam-4500	132	10	=	=	SYM
ejpam-4500	132	11	|ng(y	|ng(y	NOUN
ejpam-4500	132	12	,	,	PUNCT
ejpam-4500	132	13	2	2	NUM
ejpam-4500	132	14	)	)	PUNCT
ejpam-4500	132	15	\	\	NOUN
ejpam-4500	132	16	{	{	PUNCT
ejpam-4500	132	17	x}|	x}|	X
ejpam-4500	132	18	=	=	SYM
ejpam-4500	132	19	2	2	NUM
ejpam-4500	132	20	or	or	CCONJ
ejpam-4500	132	21	|ng(x	|ng(x	ADP
ejpam-4500	132	22	,	,	PUNCT
ejpam-4500	132	23	2	2	X
ejpam-4500	132	24	)	)	PUNCT
ejpam-4500	132	25	\	\	NOUN
ejpam-4500	133	1	{	{	PUNCT
ejpam-4500	133	2	y}|	y}|	NOUN
ejpam-4500	133	3	=	=	SYM
ejpam-4500	133	4	2	2	NUM
ejpam-4500	133	5	and	and	CCONJ
ejpam-4500	133	6	|ng(y	|ng(y	NOUN
ejpam-4500	133	7	,	,	PUNCT
ejpam-4500	133	8	2	2	NUM
ejpam-4500	133	9	)	)	PUNCT
ejpam-4500	133	10	\	\	NOUN
ejpam-4500	133	11	{	{	PUNCT
ejpam-4500	133	12	x}|	x}|	X
ejpam-4500	133	13	=	=	SYM
ejpam-4500	133	14	1	1	NUM
ejpam-4500	133	15	or	or	CCONJ
ejpam-4500	133	16	|ng(x	|ng(x	ADP
ejpam-4500	133	17	,	,	PUNCT
ejpam-4500	133	18	2	2	X
ejpam-4500	133	19	)	)	PUNCT
ejpam-4500	133	20	\	\	NOUN
ejpam-4500	133	21	{	{	PUNCT
ejpam-4500	133	22	y}|	y}|	NOUN
ejpam-4500	133	23	=	=	SYM
ejpam-4500	133	24	1	1	NUM
ejpam-4500	133	25	and	and	CCONJ
ejpam-4500	133	26	|ng(y	|ng(y	NOUN
ejpam-4500	133	27	,	,	PUNCT
ejpam-4500	133	28	2	2	NUM
ejpam-4500	133	29	)	)	PUNCT
ejpam-4500	133	30	\	\	NOUN
ejpam-4500	133	31	{	{	PUNCT
ejpam-4500	133	32	x}|	x}|	X
ejpam-4500	133	33	=	=	SYM
ejpam-4500	133	34	2	2	X
ejpam-4500	133	35	.	.	PUNCT
ejpam-4500	133	36	therefore	therefore	ADV
ejpam-4500	133	37	,	,	PUNCT
ejpam-4500	133	38	(	(	PUNCT
ejpam-4500	133	39	ii	ii	NOUN
ejpam-4500	133	40	)	)	PUNCT
ejpam-4500	133	41	holds	hold	VERB
ejpam-4500	133	42	.	.	PUNCT
ejpam-4500	134	1	for	for	ADP
ejpam-4500	134	2	the	the	DET
ejpam-4500	134	3	converse	converse	NOUN
ejpam-4500	134	4	,	,	PUNCT
ejpam-4500	134	5	suppose	suppose	VERB
ejpam-4500	134	6	there	there	PRON
ejpam-4500	134	7	exist	exist	VERB
ejpam-4500	134	8	distinct	distinct	ADJ
ejpam-4500	134	9	vertices	vertex	NOUN
ejpam-4500	134	10	x	x	X
ejpam-4500	134	11	,	,	PUNCT
ejpam-4500	134	12	y	y	PROPN
ejpam-4500	134	13	∈	∈	PROPN
ejpam-4500	134	14	v	v	ADP
ejpam-4500	134	15	(	(	PUNCT
ejpam-4500	134	16	g	g	NOUN
ejpam-4500	134	17	)	)	PUNCT
ejpam-4500	134	18	satisfying	satisfying	NOUN
ejpam-4500	134	19	(	(	PUNCT
ejpam-4500	134	20	i	i	NOUN
ejpam-4500	134	21	)	)	PUNCT
ejpam-4500	134	22	or	or	CCONJ
ejpam-4500	134	23	(	(	PUNCT
ejpam-4500	134	24	ii	ii	NOUN
ejpam-4500	134	25	)	)	PUNCT
ejpam-4500	134	26	.	.	PUNCT
ejpam-4500	135	1	let	let	VERB
ejpam-4500	135	2	s	s	VERB
ejpam-4500	135	3	=	=	PUNCT
ejpam-4500	135	4	{	{	PUNCT
ejpam-4500	135	5	x	x	PROPN
ejpam-4500	135	6	,	,	PUNCT
ejpam-4500	135	7	y	y	PROPN
ejpam-4500	135	8	}	}	PUNCT
ejpam-4500	135	9	.	.	PUNCT
ejpam-4500	136	1	then	then	ADV
ejpam-4500	136	2	s	s	VERB
ejpam-4500	136	3	is	be	AUX
ejpam-4500	136	4	a	a	DET
ejpam-4500	136	5	minimum	minimum	ADJ
ejpam-4500	136	6	locating	locating	NOUN
ejpam-4500	136	7	hop	hop	NOUN
ejpam-4500	136	8	set	set	VERB
ejpam-4500	136	9	in	in	ADP
ejpam-4500	136	10	g.	g.	PROPN
ejpam-4500	136	11	therefore	therefore	ADV
ejpam-4500	136	12	,	,	PUNCT
ejpam-4500	136	13	lhn(g	lhn(g	PROPN
ejpam-4500	136	14	)	)	PUNCT
ejpam-4500	136	15	=	=	SYM
ejpam-4500	136	16	2	2	X
ejpam-4500	136	17	.	.	PUNCT
ejpam-4500	136	18	□	□	PUNCT
ejpam-4500	136	19	proposition	proposition	NOUN
ejpam-4500	136	20	6	6	NUM
ejpam-4500	136	21	.	.	PUNCT
ejpam-4500	137	1	let	let	VERB
ejpam-4500	137	2	g	g	PRON
ejpam-4500	137	3	be	be	AUX
ejpam-4500	137	4	a	a	DET
ejpam-4500	137	5	connected	connected	ADJ
ejpam-4500	137	6	graph	graph	NOUN
ejpam-4500	137	7	of	of	ADP
ejpam-4500	137	8	order	order	NOUN
ejpam-4500	137	9	n	n	PRON
ejpam-4500	137	10	≥	≥	NOUN
ejpam-4500	137	11	3	3	NUM
ejpam-4500	137	12	.	.	PUNCT
ejpam-4500	138	1	if	if	SCONJ
ejpam-4500	138	2	lhn(g	lhn(g	PROPN
ejpam-4500	138	3	)	)	PUNCT
ejpam-4500	138	4	<	<	X
ejpam-4500	138	5	slhn(g	slhn(g	PROPN
ejpam-4500	138	6	)	)	PUNCT
ejpam-4500	138	7	,	,	PUNCT
ejpam-4500	138	8	then	then	ADV
ejpam-4500	138	9	1	1	NUM
ejpam-4500	138	10	+	+	NUM
ejpam-4500	138	11	lhn(g	lhn(g	NUM
ejpam-4500	138	12	)	)	PUNCT
ejpam-4500	139	1	=	=	SYM
ejpam-4500	139	2	slhn(g	slhn(g	PROPN
ejpam-4500	139	3	)	)	PUNCT
ejpam-4500	139	4	.	.	PUNCT
ejpam-4500	140	1	proof	proof	NOUN
ejpam-4500	140	2	:	:	PUNCT
ejpam-4500	140	3	let	let	VERB
ejpam-4500	140	4	s	s	PRON
ejpam-4500	140	5	be	be	AUX
ejpam-4500	140	6	a	a	DET
ejpam-4500	140	7	minimum	minimum	ADJ
ejpam-4500	140	8	locating	locating	NOUN
ejpam-4500	140	9	hop	hop	NOUN
ejpam-4500	140	10	set	set	VERB
ejpam-4500	140	11	in	in	ADP
ejpam-4500	140	12	g.	g.	PROPN
ejpam-4500	141	1	then	then	ADV
ejpam-4500	141	2	s	s	VERB
ejpam-4500	141	3	is	be	AUX
ejpam-4500	141	4	not	not	PART
ejpam-4500	141	5	a	a	DET
ejpam-4500	141	6	strictly	strictly	ADV
ejpam-4500	141	7	locating	locate	VERB
ejpam-4500	141	8	hop	hop	NOUN
ejpam-4500	141	9	set	set	VERB
ejpam-4500	141	10	ing	ing	NOUN
ejpam-4500	141	11	.	.	PUNCT
ejpam-4500	142	1	hence	hence	ADV
ejpam-4500	142	2	,	,	PUNCT
ejpam-4500	142	3	there	there	PRON
ejpam-4500	142	4	exists	exist	VERB
ejpam-4500	142	5	a	a	DET
ejpam-4500	142	6	vertex	vertex	NOUN
ejpam-4500	142	7	u	u	NOUN
ejpam-4500	142	8	∈	∈	PROPN
ejpam-4500	142	9	v	v	NOUN
ejpam-4500	142	10	(	(	PUNCT
ejpam-4500	142	11	g)\s	g)\s	VERB
ejpam-4500	142	12	such	such	ADJ
ejpam-4500	142	13	thatng(u	thatng(u	PROPN
ejpam-4500	142	14	,	,	PUNCT
ejpam-4500	142	15	2)∩s	2)∩s	PROPN
ejpam-4500	142	16	=	=	PROPN
ejpam-4500	142	17	s.	s.	PROPN
ejpam-4500	142	18	let	let	VERB
ejpam-4500	142	19	s∗	s∗	PROPN
ejpam-4500	142	20	=	=	SYM
ejpam-4500	142	21	s∪{u	s∪{u	PROPN
ejpam-4500	142	22	}	}	PUNCT
ejpam-4500	142	23	and	and	CCONJ
ejpam-4500	142	24	let	let	VERB
ejpam-4500	142	25	z	z	NOUN
ejpam-4500	142	26	∈	∈	PROPN
ejpam-4500	142	27	v	v	ADP
ejpam-4500	142	28	(	(	PUNCT
ejpam-4500	142	29	g	g	NOUN
ejpam-4500	142	30	)	)	PUNCT
ejpam-4500	142	31	\	\	VERB
ejpam-4500	143	1	s∗.	s∗.	ADV
ejpam-4500	143	2	then	then	ADV
ejpam-4500	143	3	z	z	PROPN
ejpam-4500	143	4	̸=	̸=	PROPN
ejpam-4500	143	5	u.	u.	VERB
ejpam-4500	143	6	since	since	SCONJ
ejpam-4500	143	7	s	s	PROPN
ejpam-4500	143	8	is	be	AUX
ejpam-4500	143	9	a	a	DET
ejpam-4500	143	10	locating	locate	VERB
ejpam-4500	143	11	hop	hop	NOUN
ejpam-4500	143	12	set	set	VERB
ejpam-4500	143	13	and	and	CCONJ
ejpam-4500	143	14	ng(u	ng(u	NOUN
ejpam-4500	143	15	,	,	PUNCT
ejpam-4500	143	16	2	2	X
ejpam-4500	143	17	)	)	PUNCT
ejpam-4500	143	18	∩	∩	NOUN
ejpam-4500	143	19	s	s	PART
ejpam-4500	143	20	=	=	SYM
ejpam-4500	143	21	s	s	PROPN
ejpam-4500	143	22	,	,	PUNCT
ejpam-4500	143	23	ng(z	ng(z	NUM
ejpam-4500	143	24	,	,	PUNCT
ejpam-4500	143	25	2	2	NUM
ejpam-4500	143	26	)	)	PUNCT
ejpam-4500	143	27	∩	∩	NOUN
ejpam-4500	143	28	s	s	PART
ejpam-4500	143	29	̸=	̸=	PROPN
ejpam-4500	143	30	s.	s.	PROPN
ejpam-4500	143	31	this	this	PRON
ejpam-4500	143	32	implies	imply	VERB
ejpam-4500	143	33	that	that	SCONJ
ejpam-4500	143	34	there	there	PRON
ejpam-4500	143	35	exists	exist	VERB
ejpam-4500	143	36	w	w	PROPN
ejpam-4500	143	37	∈	∈	PROPN
ejpam-4500	143	38	s	s	VERB
ejpam-4500	143	39	such	such	ADJ
ejpam-4500	143	40	that	that	PRON
ejpam-4500	143	41	w	w	PROPN
ejpam-4500	143	42	/∈	/∈	PROPN
ejpam-4500	143	43	ng(z	ng(z	PROPN
ejpam-4500	143	44	,	,	PUNCT
ejpam-4500	143	45	2	2	NUM
ejpam-4500	143	46	)	)	PUNCT
ejpam-4500	143	47	.	.	PUNCT
ejpam-4500	144	1	since	since	SCONJ
ejpam-4500	144	2	u	u	PROPN
ejpam-4500	144	3	/∈	/∈	PROPN
ejpam-4500	144	4	s	s	PART
ejpam-4500	144	5	,	,	PUNCT
ejpam-4500	144	6	w	w	PROPN
ejpam-4500	144	7	̸=	̸=	PROPN
ejpam-4500	144	8	u.	u.	PROPN
ejpam-4500	144	9	thus	thus	ADV
ejpam-4500	144	10	,	,	PUNCT
ejpam-4500	144	11	ng(z	ng(z	NUM
ejpam-4500	144	12	,	,	PUNCT
ejpam-4500	144	13	2	2	NUM
ejpam-4500	144	14	)	)	PUNCT
ejpam-4500	144	15	∩	∩	NOUN
ejpam-4500	144	16	s∗	s∗	PROPN
ejpam-4500	144	17	̸=	̸=	PROPN
ejpam-4500	144	18	s∗.	s∗.	ADJ
ejpam-4500	144	19	this	this	PRON
ejpam-4500	144	20	implies	imply	VERB
ejpam-4500	144	21	that	that	SCONJ
ejpam-4500	144	22	s∗	s∗	PROPN
ejpam-4500	144	23	is	be	AUX
ejpam-4500	144	24	a	a	DET
ejpam-4500	144	25	strictly	strictly	ADV
ejpam-4500	144	26	locating	locate	VERB
ejpam-4500	144	27	hop	hop	NOUN
ejpam-4500	144	28	set	set	VERB
ejpam-4500	144	29	in	in	ADP
ejpam-4500	144	30	g.	g.	PROPN
ejpam-4500	144	31	hence	hence	ADV
ejpam-4500	144	32	,	,	PUNCT
ejpam-4500	144	33	slhn(g	slhn(g	PROPN
ejpam-4500	144	34	)	)	PUNCT
ejpam-4500	144	35	≤	≤	NOUN
ejpam-4500	144	36	1	1	NUM
ejpam-4500	145	1	+	+	NUM
ejpam-4500	145	2	lhn(g	lhn(g	NUM
ejpam-4500	145	3	)	)	PUNCT
ejpam-4500	145	4	.	.	PUNCT
ejpam-4500	146	1	since	since	SCONJ
ejpam-4500	146	2	lhn(g	lhn(g	PROPN
ejpam-4500	146	3	)	)	PUNCT
ejpam-4500	146	4	<	<	X
ejpam-4500	146	5	slhn(g	slhn(g	PROPN
ejpam-4500	146	6	)	)	PUNCT
ejpam-4500	146	7	,	,	PUNCT
ejpam-4500	146	8	1	1	NUM
ejpam-4500	146	9	+	+	NUM
ejpam-4500	146	10	lhn(g	lhn(g	NUM
ejpam-4500	146	11	)	)	PUNCT
ejpam-4500	146	12	≤	≤	NOUN
ejpam-4500	146	13	slhn(g	slhn(g	ADV
ejpam-4500	146	14	)	)	PUNCT
ejpam-4500	146	15	.	.	PUNCT
ejpam-4500	147	1	hence	hence	ADV
ejpam-4500	147	2	,	,	PUNCT
ejpam-4500	147	3	1	1	NUM
ejpam-4500	147	4	+	+	NUM
ejpam-4500	147	5	lhn(g	lhn(g	NOUN
ejpam-4500	147	6	)	)	PUNCT
ejpam-4500	148	1	=	=	SYM
ejpam-4500	148	2	slhn(g	slhn(g	PROPN
ejpam-4500	148	3	)	)	PUNCT
ejpam-4500	148	4	.	.	PUNCT
ejpam-4500	149	1	□	□	PUNCT
ejpam-4500	149	2	3	3	X
ejpam-4500	149	3	.	.	X
ejpam-4500	149	4	locating	locate	VERB
ejpam-4500	149	5	hop	hop	NOUN
ejpam-4500	149	6	sets	set	NOUN
ejpam-4500	149	7	in	in	ADP
ejpam-4500	149	8	the	the	DET
ejpam-4500	149	9	join	join	NOUN
ejpam-4500	149	10	of	of	ADP
ejpam-4500	149	11	graphs	graph	NOUN
ejpam-4500	149	12	the	the	DET
ejpam-4500	149	13	join	join	NOUN
ejpam-4500	149	14	of	of	ADP
ejpam-4500	149	15	two	two	NUM
ejpam-4500	149	16	graphs	graph	NOUN
ejpam-4500	149	17	g	g	NOUN
ejpam-4500	149	18	and	and	CCONJ
ejpam-4500	149	19	h	h	NOUN
ejpam-4500	149	20	,	,	PUNCT
ejpam-4500	149	21	denoted	denote	VERB
ejpam-4500	149	22	by	by	ADP
ejpam-4500	149	23	g	g	PROPN
ejpam-4500	149	24	+	+	PROPN
ejpam-4500	149	25	h	h	NOUN
ejpam-4500	149	26	,	,	PUNCT
ejpam-4500	149	27	is	be	AUX
ejpam-4500	149	28	the	the	DET
ejpam-4500	149	29	graph	graph	NOUN
ejpam-4500	149	30	with	with	ADP
ejpam-4500	149	31	vertex	vertex	NOUN
ejpam-4500	149	32	-	-	PUNCT
ejpam-4500	149	33	set	set	VERB
ejpam-4500	149	34	v	v	NOUN
ejpam-4500	149	35	(	(	PUNCT
ejpam-4500	149	36	g+h	g+h	NOUN
ejpam-4500	149	37	)	)	PUNCT
ejpam-4500	149	38	=	=	SYM
ejpam-4500	149	39	v	v	NOUN
ejpam-4500	149	40	(	(	PUNCT
ejpam-4500	149	41	g)∪	g)∪	VERB
ejpam-4500	149	42	v	v	NUM
ejpam-4500	149	43	(	(	PUNCT
ejpam-4500	149	44	h	h	NOUN
ejpam-4500	149	45	)	)	PUNCT
ejpam-4500	149	46	and	and	CCONJ
ejpam-4500	149	47	edge	edge	NOUN
ejpam-4500	149	48	-	-	PUNCT
ejpam-4500	149	49	set	set	VERB
ejpam-4500	149	50	e(g+h	e(g+h	NUM
ejpam-4500	149	51	)	)	PUNCT
ejpam-4500	149	52	=	=	SYM
ejpam-4500	150	1	e(g)∪e(h)∪	e(g)∪e(h)∪	NOUN
ejpam-4500	150	2	{	{	PUNCT
ejpam-4500	150	3	uv	uv	NOUN
ejpam-4500	150	4	:	:	PUNCT
ejpam-4500	150	5	u	u	PROPN
ejpam-4500	150	6	∈	∈	PROPN
ejpam-4500	150	7	v	v	ADP
ejpam-4500	150	8	(	(	PUNCT
ejpam-4500	150	9	g	g	NOUN
ejpam-4500	150	10	)	)	PUNCT
ejpam-4500	150	11	,	,	PUNCT
ejpam-4500	150	12	v	v	X
ejpam-4500	150	13	∈	∈	PROPN
ejpam-4500	150	14	v	v	NOUN
ejpam-4500	150	15	(	(	PUNCT
ejpam-4500	150	16	h	h	NOUN
ejpam-4500	150	17	)	)	PUNCT
ejpam-4500	150	18	}	}	PUNCT
ejpam-4500	150	19	.	.	PUNCT
ejpam-4500	151	1	theorem	theorem	NOUN
ejpam-4500	151	2	2	2	NUM
ejpam-4500	151	3	.	.	PUNCT
ejpam-4500	152	1	let	let	VERB
ejpam-4500	152	2	g	g	NOUN
ejpam-4500	153	1	and	and	CCONJ
ejpam-4500	153	2	h	h	NOUN
ejpam-4500	153	3	be	be	AUX
ejpam-4500	153	4	connected	connect	VERB
ejpam-4500	153	5	non	non	ADJ
ejpam-4500	153	6	-	-	ADJ
ejpam-4500	153	7	trivial	trivial	ADJ
ejpam-4500	153	8	graphs	graph	NOUN
ejpam-4500	153	9	.	.	PUNCT
ejpam-4500	154	1	a	a	DET
ejpam-4500	154	2	set	set	NOUN
ejpam-4500	154	3	s	s	NOUN
ejpam-4500	154	4	⊆	⊆	NUM
ejpam-4500	154	5	v	v	NOUN
ejpam-4500	154	6	(	(	PUNCT
ejpam-4500	154	7	g	g	PROPN
ejpam-4500	154	8	+	+	NOUN
ejpam-4500	154	9	h	h	NOUN
ejpam-4500	154	10	)	)	PUNCT
ejpam-4500	154	11	is	be	AUX
ejpam-4500	154	12	a	a	DET
ejpam-4500	154	13	locating	locate	VERB
ejpam-4500	154	14	hop	hop	NOUN
ejpam-4500	154	15	set	set	VERB
ejpam-4500	154	16	in	in	ADP
ejpam-4500	154	17	g+h	g+h	PROPN
ejpam-4500	154	18	if	if	SCONJ
ejpam-4500	154	19	and	and	CCONJ
ejpam-4500	154	20	only	only	ADV
ejpam-4500	154	21	if	if	SCONJ
ejpam-4500	154	22	s1	s1	PROPN
ejpam-4500	154	23	=	=	SYM
ejpam-4500	154	24	v	v	PROPN
ejpam-4500	154	25	(	(	PUNCT
ejpam-4500	154	26	g	g	NOUN
ejpam-4500	154	27	)	)	PUNCT
ejpam-4500	154	28	∩	∩	PROPN
ejpam-4500	154	29	s	s	PART
ejpam-4500	154	30	and	and	CCONJ
ejpam-4500	154	31	s2	s2	PROPN
ejpam-4500	154	32	=	=	SYM
ejpam-4500	154	33	v	v	PROPN
ejpam-4500	154	34	(	(	PUNCT
ejpam-4500	154	35	h	h	NOUN
ejpam-4500	154	36	)	)	PUNCT
ejpam-4500	154	37	∩	∩	NOUN
ejpam-4500	154	38	s	s	PART
ejpam-4500	154	39	are	be	AUX
ejpam-4500	154	40	locating	locate	VERB
ejpam-4500	154	41	sets	set	NOUN
ejpam-4500	154	42	in	in	ADP
ejpam-4500	154	43	g	g	PROPN
ejpam-4500	154	44	and	and	CCONJ
ejpam-4500	154	45	h	h	NOUN
ejpam-4500	154	46	,	,	PUNCT
ejpam-4500	154	47	respectively	respectively	ADV
ejpam-4500	154	48	,	,	PUNCT
ejpam-4500	154	49	and	and	CCONJ
ejpam-4500	154	50	s1	s1	NOUN
ejpam-4500	154	51	or	or	CCONJ
ejpam-4500	154	52	s2	s2	NOUN
ejpam-4500	154	53	is	be	AUX
ejpam-4500	154	54	a	a	DET
ejpam-4500	154	55	strictly	strictly	ADV
ejpam-4500	154	56	locating	locate	VERB
ejpam-4500	154	57	set	set	NOUN
ejpam-4500	154	58	.	.	PUNCT
ejpam-4500	155	1	e.m	e.m	PROPN
ejpam-4500	155	2	.	.	PROPN
ejpam-4500	155	3	a.	a.	NOUN
ejpam-4500	155	4	pagcu	pagcu	PROPN
ejpam-4500	155	5	,	,	PUNCT
ejpam-4500	155	6	g.	g.	PROPN
ejpam-4500	155	7	a.	a.	NOUN
ejpam-4500	155	8	malacas	malacas	PROPN
ejpam-4500	155	9	,	,	PUNCT
ejpam-4500	155	10	s.	s.	PROPN
ejpam-4500	155	11	r.	r.	PROPN
ejpam-4500	155	12	canoy	canoy	PROPN
ejpam-4500	155	13	,	,	PUNCT
ejpam-4500	155	14	jr	jr	PROPN
ejpam-4500	155	15	.	.	PROPN
ejpam-4500	155	16	/	/	SYM
ejpam-4500	155	17	eur	eur	PROPN
ejpam-4500	155	18	.	.	PUNCT
ejpam-4500	156	1	j.	j.	PROPN
ejpam-4500	156	2	pure	pure	PROPN
ejpam-4500	156	3	appl	appl	PROPN
ejpam-4500	156	4	.	.	PROPN
ejpam-4500	156	5	math	math	PROPN
ejpam-4500	156	6	,	,	PUNCT
ejpam-4500	156	7	15	15	NUM
ejpam-4500	156	8	(	(	PUNCT
ejpam-4500	156	9	4	4	NUM
ejpam-4500	156	10	)	)	PUNCT
ejpam-4500	156	11	(	(	PUNCT
ejpam-4500	156	12	2022	2022	NUM
ejpam-4500	156	13	)	)	PUNCT
ejpam-4500	156	14	,	,	PUNCT
ejpam-4500	156	15	1705	1705	NUM
ejpam-4500	156	16	-	-	SYM
ejpam-4500	156	17	1715	1715	NUM
ejpam-4500	156	18	1709	1709	NUM
ejpam-4500	156	19	proof	proof	NOUN
ejpam-4500	156	20	:	:	PUNCT
ejpam-4500	156	21	suppose	suppose	VERB
ejpam-4500	156	22	that	that	SCONJ
ejpam-4500	156	23	s	s	VERB
ejpam-4500	156	24	is	be	AUX
ejpam-4500	156	25	a	a	DET
ejpam-4500	156	26	locating	locate	VERB
ejpam-4500	156	27	hop	hop	NOUN
ejpam-4500	156	28	set	set	VERB
ejpam-4500	156	29	in	in	ADP
ejpam-4500	156	30	g	g	PROPN
ejpam-4500	156	31	+	+	PROPN
ejpam-4500	156	32	h.	h.	PROPN
ejpam-4500	156	33	let	let	VERB
ejpam-4500	156	34	s1	s1	PROPN
ejpam-4500	156	35	⊆	⊆	NUM
ejpam-4500	156	36	v	v	NOUN
ejpam-4500	156	37	(	(	PUNCT
ejpam-4500	156	38	g	g	NOUN
ejpam-4500	156	39	)	)	PUNCT
ejpam-4500	156	40	and	and	CCONJ
ejpam-4500	156	41	s2	s2	VERB
ejpam-4500	156	42	⊆	⊆	NUM
ejpam-4500	156	43	v	v	NOUN
ejpam-4500	156	44	(	(	PUNCT
ejpam-4500	156	45	h	h	NOUN
ejpam-4500	156	46	)	)	PUNCT
ejpam-4500	156	47	.	.	PUNCT
ejpam-4500	157	1	suppose	suppose	VERB
ejpam-4500	157	2	s1	s1	NOUN
ejpam-4500	157	3	=	=	PUNCT
ejpam-4500	157	4	∅.	∅.	NOUN
ejpam-4500	157	5	then	then	ADV
ejpam-4500	157	6	for	for	ADP
ejpam-4500	157	7	any	any	DET
ejpam-4500	157	8	two	two	NUM
ejpam-4500	157	9	distinct	distinct	ADJ
ejpam-4500	157	10	vertices	vertex	NOUN
ejpam-4500	157	11	x	x	X
ejpam-4500	157	12	,	,	PUNCT
ejpam-4500	157	13	y	y	PROPN
ejpam-4500	157	14	∈	∈	PROPN
ejpam-4500	157	15	v	v	NOUN
ejpam-4500	157	16	(	(	PUNCT
ejpam-4500	157	17	g	g	NOUN
ejpam-4500	157	18	)	)	PUNCT
ejpam-4500	157	19	,	,	PUNCT
ejpam-4500	157	20	ng+h(x	ng+h(x	PROPN
ejpam-4500	157	21	,	,	PUNCT
ejpam-4500	157	22	2	2	NUM
ejpam-4500	157	23	)	)	PUNCT
ejpam-4500	157	24	∩	∩	NOUN
ejpam-4500	157	25	s	s	PART
ejpam-4500	157	26	=	=	SYM
ejpam-4500	157	27	ng+h(y	ng+h(y	NUM
ejpam-4500	157	28	,	,	PUNCT
ejpam-4500	157	29	2	2	X
ejpam-4500	157	30	)	)	PUNCT
ejpam-4500	157	31	∩	∩	NOUN
ejpam-4500	157	32	s	s	PART
ejpam-4500	157	33	=	=	SYM
ejpam-4500	157	34	∅	∅	NOUN
ejpam-4500	157	35	,	,	PUNCT
ejpam-4500	157	36	contrary	contrary	ADJ
ejpam-4500	157	37	to	to	ADP
ejpam-4500	157	38	our	our	PRON
ejpam-4500	157	39	assumption	assumption	NOUN
ejpam-4500	157	40	that	that	SCONJ
ejpam-4500	157	41	s	s	VERB
ejpam-4500	157	42	is	be	AUX
ejpam-4500	157	43	a	a	DET
ejpam-4500	157	44	locating	locate	VERB
ejpam-4500	157	45	hop	hop	NOUN
ejpam-4500	157	46	set	set	NOUN
ejpam-4500	157	47	.	.	PUNCT
ejpam-4500	158	1	thus	thus	ADV
ejpam-4500	158	2	,	,	PUNCT
ejpam-4500	158	3	s1	s1	PROPN
ejpam-4500	158	4	̸=	̸=	PROPN
ejpam-4500	158	5	∅.	∅.	PRON
ejpam-4500	158	6	similarly	similarly	ADV
ejpam-4500	158	7	,	,	PUNCT
ejpam-4500	158	8	s2	s2	VERB
ejpam-4500	158	9	̸=	̸=	PROPN
ejpam-4500	158	10	∅.	∅.	ADP
ejpam-4500	158	11	next	next	ADV
ejpam-4500	158	12	,	,	PUNCT
ejpam-4500	158	13	suppose	suppose	VERB
ejpam-4500	158	14	s1	s1	NOUN
ejpam-4500	158	15	or	or	CCONJ
ejpam-4500	158	16	s2	s2	NOUN
ejpam-4500	158	17	,	,	PUNCT
ejpam-4500	158	18	say	say	VERB
ejpam-4500	158	19	s1	s1	NOUN
ejpam-4500	158	20	is	be	AUX
ejpam-4500	158	21	not	not	PART
ejpam-4500	158	22	a	a	DET
ejpam-4500	158	23	locating	locating	NOUN
ejpam-4500	158	24	set	set	NOUN
ejpam-4500	158	25	.	.	PUNCT
ejpam-4500	159	1	then	then	ADV
ejpam-4500	159	2	there	there	PRON
ejpam-4500	159	3	exist	exist	VERB
ejpam-4500	159	4	u	u	NOUN
ejpam-4500	159	5	,	,	PUNCT
ejpam-4500	159	6	v	v	NOUN
ejpam-4500	159	7	∈	∈	PROPN
ejpam-4500	159	8	v	v	NOUN
ejpam-4500	159	9	(	(	PUNCT
ejpam-4500	159	10	g	g	NOUN
ejpam-4500	159	11	)	)	PUNCT
ejpam-4500	159	12	such	such	ADJ
ejpam-4500	159	13	that	that	SCONJ
ejpam-4500	159	14	ng(u	ng(u	NOUN
ejpam-4500	159	15	)	)	PUNCT
ejpam-4500	159	16	∩	∩	ADJ
ejpam-4500	159	17	s1	s1	NOUN
ejpam-4500	159	18	=	=	SYM
ejpam-4500	159	19	ng(v	ng(v	X
ejpam-4500	159	20	)	)	PUNCT
ejpam-4500	159	21	∩	∩	NOUN
ejpam-4500	159	22	s1	s1	NOUN
ejpam-4500	159	23	.	.	PUNCT
ejpam-4500	160	1	thus	thus	ADV
ejpam-4500	160	2	,	,	PUNCT
ejpam-4500	160	3	x	x	PUNCT
ejpam-4500	160	4	∈	∈	PROPN
ejpam-4500	160	5	[	[	X
ejpam-4500	160	6	v	v	X
ejpam-4500	160	7	(	(	PUNCT
ejpam-4500	160	8	g	g	NOUN
ejpam-4500	160	9	)	)	PUNCT
ejpam-4500	160	10	\	\	NOUN
ejpam-4500	160	11	ng(u	ng(u	NOUN
ejpam-4500	160	12	)	)	PUNCT
ejpam-4500	160	13	]	]	PUNCT
ejpam-4500	160	14	∩	∩	ADJ
ejpam-4500	160	15	s1	s1	NOUN
ejpam-4500	160	16	if	if	SCONJ
ejpam-4500	160	17	and	and	CCONJ
ejpam-4500	160	18	only	only	ADV
ejpam-4500	160	19	if	if	SCONJ
ejpam-4500	160	20	x	x	SYM
ejpam-4500	160	21	∈	∈	PROPN
ejpam-4500	160	22	[	[	X
ejpam-4500	160	23	v	v	X
ejpam-4500	160	24	(	(	PUNCT
ejpam-4500	160	25	g	g	NOUN
ejpam-4500	160	26	)	)	PUNCT
ejpam-4500	160	27	\	\	NOUN
ejpam-4500	160	28	ng(v	ng(v	PUNCT
ejpam-4500	160	29	)	)	PUNCT
ejpam-4500	160	30	]	]	PUNCT
ejpam-4500	160	31	∩	∩	PROPN
ejpam-4500	160	32	s1	s1	PROPN
ejpam-4500	160	33	.	.	PUNCT
ejpam-4500	161	1	this	this	PRON
ejpam-4500	161	2	implies	imply	VERB
ejpam-4500	161	3	that	that	SCONJ
ejpam-4500	161	4	[	[	X
ejpam-4500	161	5	v	v	X
ejpam-4500	161	6	(	(	PUNCT
ejpam-4500	161	7	g	g	NOUN
ejpam-4500	161	8	)	)	PUNCT
ejpam-4500	161	9	\	\	NOUN
ejpam-4500	161	10	ng(u	ng(u	NOUN
ejpam-4500	161	11	)	)	PUNCT
ejpam-4500	161	12	]	]	PUNCT
ejpam-4500	161	13	∩	∩	NOUN
ejpam-4500	161	14	s1	s1	NOUN
ejpam-4500	161	15	=	=	PUNCT
ejpam-4500	162	1	[	[	X
ejpam-4500	162	2	v	v	X
ejpam-4500	162	3	(	(	PUNCT
ejpam-4500	162	4	g	g	NOUN
ejpam-4500	162	5	)	)	PUNCT
ejpam-4500	162	6	\	\	NOUN
ejpam-4500	162	7	ng(v	ng(v	PUNCT
ejpam-4500	162	8	)	)	PUNCT
ejpam-4500	162	9	]	]	PUNCT
ejpam-4500	162	10	∩	∩	PROPN
ejpam-4500	162	11	s1	s1	PROPN
ejpam-4500	162	12	.	.	PUNCT
ejpam-4500	163	1	since	since	SCONJ
ejpam-4500	163	2	s2	s2	PROPN
ejpam-4500	163	3	∩ng+h(u	∩ng+h(u	SYM
ejpam-4500	163	4	,	,	PUNCT
ejpam-4500	163	5	2	2	X
ejpam-4500	163	6	)	)	PUNCT
ejpam-4500	163	7	=	=	NOUN
ejpam-4500	163	8	∅	∅	NOUN
ejpam-4500	163	9	and	and	CCONJ
ejpam-4500	163	10	s2	s2	PROPN
ejpam-4500	163	11	∩ng+h(v	∩ng+h(v	NOUN
ejpam-4500	163	12	,	,	PUNCT
ejpam-4500	163	13	2	2	X
ejpam-4500	163	14	)	)	PUNCT
ejpam-4500	164	1	=	=	NOUN
ejpam-4500	164	2	∅	∅	NOUN
ejpam-4500	164	3	,	,	PUNCT
ejpam-4500	164	4	it	it	PRON
ejpam-4500	164	5	follows	follow	VERB
ejpam-4500	164	6	that	that	SCONJ
ejpam-4500	164	7	ng+h(u	ng+h(u	PROPN
ejpam-4500	164	8	,	,	PUNCT
ejpam-4500	164	9	2	2	X
ejpam-4500	164	10	)	)	PUNCT
ejpam-4500	164	11	∩	∩	NOUN
ejpam-4500	164	12	s	s	PART
ejpam-4500	164	13	=	=	SYM
ejpam-4500	164	14	ng+h(u	ng+h(u	PROPN
ejpam-4500	164	15	,	,	PUNCT
ejpam-4500	164	16	2	2	NUM
ejpam-4500	164	17	)	)	PUNCT
ejpam-4500	164	18	∩	∩	ADJ
ejpam-4500	164	19	s1	s1	NOUN
ejpam-4500	164	20	=	=	PUNCT
ejpam-4500	165	1	[	[	X
ejpam-4500	165	2	v	v	X
ejpam-4500	165	3	(	(	PUNCT
ejpam-4500	165	4	g	g	NOUN
ejpam-4500	165	5	)	)	PUNCT
ejpam-4500	165	6	\ng(u	\ng(u	NOUN
ejpam-4500	165	7	)	)	PUNCT
ejpam-4500	165	8	]	]	PUNCT
ejpam-4500	165	9	∩	∩	NOUN
ejpam-4500	165	10	s1	s1	NOUN
ejpam-4500	165	11	=	=	PUNCT
ejpam-4500	166	1	[	[	X
ejpam-4500	166	2	v	v	X
ejpam-4500	166	3	(	(	PUNCT
ejpam-4500	166	4	g	g	NOUN
ejpam-4500	166	5	)	)	PUNCT
ejpam-4500	166	6	\ng(v	\ng(v	NOUN
ejpam-4500	166	7	)	)	PUNCT
ejpam-4500	166	8	]	]	PUNCT
ejpam-4500	167	1	∩	∩	NOUN
ejpam-4500	167	2	s1	s1	NOUN
ejpam-4500	167	3	=	=	SYM
ejpam-4500	167	4	ng+h(v	ng+h(v	PROPN
ejpam-4500	167	5	,	,	PUNCT
ejpam-4500	167	6	2	2	X
ejpam-4500	167	7	)	)	PUNCT
ejpam-4500	167	8	∩	∩	ADJ
ejpam-4500	167	9	s1	s1	NOUN
ejpam-4500	167	10	=	=	SYM
ejpam-4500	167	11	ng+h(v	ng+h(v	PROPN
ejpam-4500	167	12	,	,	PUNCT
ejpam-4500	167	13	2	2	X
ejpam-4500	167	14	)	)	PUNCT
ejpam-4500	167	15	∩	∩	NOUN
ejpam-4500	167	16	s.	s.	PROPN
ejpam-4500	167	17	thus	thus	ADV
ejpam-4500	167	18	,	,	PUNCT
ejpam-4500	167	19	s	s	VERB
ejpam-4500	167	20	is	be	AUX
ejpam-4500	167	21	not	not	PART
ejpam-4500	167	22	a	a	DET
ejpam-4500	167	23	locating	locate	VERB
ejpam-4500	167	24	hop	hop	NOUN
ejpam-4500	167	25	set	set	VERB
ejpam-4500	167	26	in	in	ADP
ejpam-4500	167	27	g	g	PROPN
ejpam-4500	167	28	+	+	CCONJ
ejpam-4500	167	29	h	h	NOUN
ejpam-4500	167	30	,	,	PUNCT
ejpam-4500	167	31	contrary	contrary	ADJ
ejpam-4500	167	32	to	to	ADP
ejpam-4500	167	33	our	our	PRON
ejpam-4500	167	34	assumption	assumption	NOUN
ejpam-4500	167	35	.	.	PUNCT
ejpam-4500	168	1	therefore	therefore	ADV
ejpam-4500	168	2	,	,	PUNCT
ejpam-4500	168	3	s1	s1	PROPN
ejpam-4500	168	4	and	and	CCONJ
ejpam-4500	168	5	s2	s2	PROPN
ejpam-4500	168	6	are	be	AUX
ejpam-4500	168	7	locating	locate	VERB
ejpam-4500	168	8	sets	set	NOUN
ejpam-4500	168	9	in	in	ADP
ejpam-4500	168	10	g	g	PROPN
ejpam-4500	168	11	and	and	CCONJ
ejpam-4500	168	12	h	h	NOUN
ejpam-4500	168	13	,	,	PUNCT
ejpam-4500	168	14	respectively	respectively	ADV
ejpam-4500	168	15	.	.	PUNCT
ejpam-4500	169	1	now	now	ADV
ejpam-4500	169	2	,	,	PUNCT
ejpam-4500	169	3	suppose	suppose	VERB
ejpam-4500	169	4	that	that	SCONJ
ejpam-4500	169	5	both	both	PRON
ejpam-4500	169	6	are	be	AUX
ejpam-4500	169	7	not	not	PART
ejpam-4500	169	8	strictly	strictly	ADV
ejpam-4500	169	9	locating	locate	VERB
ejpam-4500	169	10	sets	set	NOUN
ejpam-4500	169	11	.	.	PUNCT
ejpam-4500	170	1	then	then	ADV
ejpam-4500	170	2	there	there	PRON
ejpam-4500	170	3	exist	exist	VERB
ejpam-4500	170	4	p	p	PROPN
ejpam-4500	170	5	∈	∈	PROPN
ejpam-4500	170	6	v	v	NOUN
ejpam-4500	170	7	(	(	PUNCT
ejpam-4500	170	8	g)\s1	g)\s1	NOUN
ejpam-4500	170	9	and	and	CCONJ
ejpam-4500	170	10	q	q	NOUN
ejpam-4500	170	11	∈	∈	PROPN
ejpam-4500	170	12	v	v	NOUN
ejpam-4500	170	13	(	(	PUNCT
ejpam-4500	170	14	h)\s2	h)\s2	ADP
ejpam-4500	170	15	such	such	ADJ
ejpam-4500	170	16	that	that	DET
ejpam-4500	170	17	ng(p)∩s1	ng(p)∩s1	NOUN
ejpam-4500	170	18	=	=	SYM
ejpam-4500	170	19	s1	s1	PROPN
ejpam-4500	170	20	and	and	CCONJ
ejpam-4500	170	21	nh(q	nh(q	NOUN
ejpam-4500	170	22	)	)	PUNCT
ejpam-4500	170	23	∩	∩	ADJ
ejpam-4500	170	24	s2	s2	NOUN
ejpam-4500	170	25	=	=	SYM
ejpam-4500	170	26	s2	s2	PROPN
ejpam-4500	170	27	.	.	PUNCT
ejpam-4500	171	1	consequently	consequently	ADV
ejpam-4500	171	2	,	,	PUNCT
ejpam-4500	171	3	ng(p	ng(p	NOUN
ejpam-4500	171	4	,	,	PUNCT
ejpam-4500	171	5	2	2	X
ejpam-4500	171	6	)	)	PUNCT
ejpam-4500	171	7	∩	∩	ADJ
ejpam-4500	171	8	s1	s1	NOUN
ejpam-4500	171	9	=	=	SYM
ejpam-4500	171	10	∅	∅	NOUN
ejpam-4500	171	11	and	and	CCONJ
ejpam-4500	171	12	nh(q	nh(q	NOUN
ejpam-4500	171	13	,	,	PUNCT
ejpam-4500	171	14	2	2	X
ejpam-4500	171	15	)	)	PUNCT
ejpam-4500	171	16	∩	∩	ADJ
ejpam-4500	171	17	s2	s2	NOUN
ejpam-4500	171	18	=	=	PUNCT
ejpam-4500	171	19	∅.	∅.	ADP
ejpam-4500	171	20	this	this	PRON
ejpam-4500	171	21	implies	imply	VERB
ejpam-4500	171	22	that	that	SCONJ
ejpam-4500	171	23	ng+h(p	ng+h(p	NOUN
ejpam-4500	171	24	,	,	PUNCT
ejpam-4500	171	25	2)∩	2)∩	NOUN
ejpam-4500	171	26	s	s	PART
ejpam-4500	171	27	=	=	SYM
ejpam-4500	171	28	ng+h(q	ng+h(q	PROPN
ejpam-4500	171	29	,	,	PUNCT
ejpam-4500	171	30	2)∩	2)∩	PROPN
ejpam-4500	171	31	s	s	PART
ejpam-4500	171	32	=	=	NOUN
ejpam-4500	171	33	∅	∅	NOUN
ejpam-4500	171	34	,	,	PUNCT
ejpam-4500	171	35	contrary	contrary	ADJ
ejpam-4500	171	36	to	to	ADP
ejpam-4500	171	37	our	our	PRON
ejpam-4500	171	38	assumption	assumption	NOUN
ejpam-4500	171	39	that	that	SCONJ
ejpam-4500	171	40	s	s	VERB
ejpam-4500	171	41	is	be	AUX
ejpam-4500	171	42	a	a	DET
ejpam-4500	171	43	locating	locate	VERB
ejpam-4500	171	44	hop	hop	NOUN
ejpam-4500	171	45	set	set	NOUN
ejpam-4500	171	46	.	.	PUNCT
ejpam-4500	172	1	therefore	therefore	ADV
ejpam-4500	172	2	,	,	PUNCT
ejpam-4500	172	3	s1	s1	PROPN
ejpam-4500	172	4	is	be	AUX
ejpam-4500	172	5	a	a	DET
ejpam-4500	172	6	strictly	strictly	ADV
ejpam-4500	172	7	locating	locate	VERB
ejpam-4500	172	8	set	set	VERB
ejpam-4500	172	9	in	in	ADP
ejpam-4500	172	10	g	g	PROPN
ejpam-4500	172	11	or	or	CCONJ
ejpam-4500	172	12	s2	s2	PROPN
ejpam-4500	172	13	is	be	AUX
ejpam-4500	172	14	a	a	DET
ejpam-4500	172	15	strictly	strictly	ADV
ejpam-4500	172	16	locating	locate	VERB
ejpam-4500	172	17	set	set	VERB
ejpam-4500	172	18	in	in	ADP
ejpam-4500	172	19	h.	h.	PROPN
ejpam-4500	172	20	for	for	ADP
ejpam-4500	172	21	the	the	DET
ejpam-4500	172	22	converse	converse	NOUN
ejpam-4500	172	23	,	,	PUNCT
ejpam-4500	172	24	suppose	suppose	VERB
ejpam-4500	172	25	that	that	SCONJ
ejpam-4500	172	26	s1	s1	PROPN
ejpam-4500	172	27	and	and	CCONJ
ejpam-4500	172	28	s2	s2	PROPN
ejpam-4500	172	29	are	be	AUX
ejpam-4500	172	30	locating	locate	VERB
ejpam-4500	172	31	sets	set	NOUN
ejpam-4500	172	32	in	in	ADP
ejpam-4500	172	33	g	g	PROPN
ejpam-4500	172	34	and	and	CCONJ
ejpam-4500	172	35	h	h	NOUN
ejpam-4500	172	36	,	,	PUNCT
ejpam-4500	172	37	respectively	respectively	ADV
ejpam-4500	172	38	,	,	PUNCT
ejpam-4500	172	39	and	and	CCONJ
ejpam-4500	172	40	s1	s1	NOUN
ejpam-4500	172	41	or	or	CCONJ
ejpam-4500	172	42	s2	s2	NOUN
ejpam-4500	172	43	is	be	AUX
ejpam-4500	172	44	a	a	DET
ejpam-4500	172	45	strictly	strictly	ADV
ejpam-4500	172	46	locating	locate	VERB
ejpam-4500	172	47	set	set	NOUN
ejpam-4500	172	48	.	.	PUNCT
ejpam-4500	173	1	let	let	VERB
ejpam-4500	173	2	x	x	PRON
ejpam-4500	173	3	,	,	PUNCT
ejpam-4500	173	4	y	y	PROPN
ejpam-4500	173	5	∈	∈	PROPN
ejpam-4500	173	6	v	v	PROPN
ejpam-4500	173	7	(	(	PUNCT
ejpam-4500	173	8	g+h	g+h	NOUN
ejpam-4500	173	9	)	)	PUNCT
ejpam-4500	173	10	\s	\	VERB
ejpam-4500	173	11	with	with	ADP
ejpam-4500	173	12	x	x	X
ejpam-4500	173	13	̸=	̸=	PROPN
ejpam-4500	173	14	y.	y.	NOUN
ejpam-4500	173	15	if	if	SCONJ
ejpam-4500	173	16	x	x	PRON
ejpam-4500	173	17	,	,	PUNCT
ejpam-4500	173	18	y	y	PROPN
ejpam-4500	173	19	∈	∈	PROPN
ejpam-4500	173	20	v	v	NOUN
ejpam-4500	173	21	(	(	PUNCT
ejpam-4500	173	22	g	g	NOUN
ejpam-4500	173	23	)	)	PUNCT
ejpam-4500	173	24	,	,	PUNCT
ejpam-4500	173	25	then	then	ADV
ejpam-4500	173	26	ng(x	ng(x	NUM
ejpam-4500	173	27	)	)	PUNCT
ejpam-4500	173	28	∩	∩	NOUN
ejpam-4500	173	29	s1	s1	PROPN
ejpam-4500	173	30	̸=	̸=	PROPN
ejpam-4500	173	31	ng(y	ng(y	NOUN
ejpam-4500	173	32	)	)	PUNCT
ejpam-4500	173	33	∩	∩	ADJ
ejpam-4500	173	34	s1	s1	NOUN
ejpam-4500	173	35	.	.	PUNCT
ejpam-4500	174	1	moreover	moreover	ADV
ejpam-4500	174	2	,	,	PUNCT
ejpam-4500	174	3	ng+h(x	ng+h(x	PROPN
ejpam-4500	174	4	,	,	PUNCT
ejpam-4500	174	5	2	2	NUM
ejpam-4500	174	6	)	)	PUNCT
ejpam-4500	174	7	∩	∩	NOUN
ejpam-4500	174	8	s	s	PART
ejpam-4500	174	9	=	=	PUNCT
ejpam-4500	174	10	[	[	X
ejpam-4500	174	11	v	v	X
ejpam-4500	174	12	(	(	PUNCT
ejpam-4500	174	13	g	g	NOUN
ejpam-4500	174	14	)	)	PUNCT
ejpam-4500	174	15	\	\	NOUN
ejpam-4500	174	16	ng(x	ng(x	NUM
ejpam-4500	174	17	)	)	PUNCT
ejpam-4500	174	18	]	]	PUNCT
ejpam-4500	175	1	∩	∩	NOUN
ejpam-4500	175	2	s1	s1	PROPN
ejpam-4500	175	3	̸=	̸=	PROPN
ejpam-4500	175	4	[	[	X
ejpam-4500	175	5	v	v	X
ejpam-4500	175	6	(	(	PUNCT
ejpam-4500	175	7	g	g	NOUN
ejpam-4500	175	8	)	)	PUNCT
ejpam-4500	175	9	\ng(y	\ng(y	NOUN
ejpam-4500	175	10	)	)	PUNCT
ejpam-4500	175	11	]	]	PUNCT
ejpam-4500	175	12	∩	∩	NOUN
ejpam-4500	175	13	s1	s1	NOUN
ejpam-4500	175	14	=	=	SYM
ejpam-4500	175	15	ng+h(y	ng+h(y	NUM
ejpam-4500	175	16	,	,	PUNCT
ejpam-4500	175	17	2	2	X
ejpam-4500	175	18	)	)	PUNCT
ejpam-4500	175	19	∩	∩	NOUN
ejpam-4500	175	20	s.	s.	PROPN
ejpam-4500	175	21	similarly	similarly	ADV
ejpam-4500	175	22	,	,	PUNCT
ejpam-4500	175	23	if	if	SCONJ
ejpam-4500	175	24	x	x	X
ejpam-4500	175	25	,	,	PUNCT
ejpam-4500	175	26	y	y	PROPN
ejpam-4500	175	27	∈	∈	PROPN
ejpam-4500	175	28	v	v	PROPN
ejpam-4500	175	29	(	(	PUNCT
ejpam-4500	175	30	h	h	NOUN
ejpam-4500	175	31	)	)	PUNCT
ejpam-4500	175	32	,	,	PUNCT
ejpam-4500	175	33	then	then	ADV
ejpam-4500	175	34	ng+h(x	ng+h(x	PROPN
ejpam-4500	175	35	,	,	PUNCT
ejpam-4500	175	36	2	2	NUM
ejpam-4500	175	37	)	)	PUNCT
ejpam-4500	175	38	∩	∩	NOUN
ejpam-4500	175	39	s	s	PART
ejpam-4500	175	40	̸=	̸=	PROPN
ejpam-4500	175	41	ng+h(y	ng+h(y	NUM
ejpam-4500	175	42	,	,	PUNCT
ejpam-4500	175	43	2	2	X
ejpam-4500	175	44	)	)	PUNCT
ejpam-4500	175	45	∩	∩	NOUN
ejpam-4500	175	46	s.	s.	PROPN
ejpam-4500	175	47	suppose	suppose	VERB
ejpam-4500	175	48	that	that	SCONJ
ejpam-4500	175	49	x	x	PROPN
ejpam-4500	175	50	∈	∈	NOUN
ejpam-4500	175	51	v	v	X
ejpam-4500	175	52	(	(	PUNCT
ejpam-4500	175	53	g	g	NOUN
ejpam-4500	175	54	)	)	PUNCT
ejpam-4500	175	55	and	and	CCONJ
ejpam-4500	175	56	y	y	PROPN
ejpam-4500	175	57	∈	∈	PROPN
ejpam-4500	175	58	v	v	ADP
ejpam-4500	175	59	(	(	PUNCT
ejpam-4500	175	60	h	h	NOUN
ejpam-4500	175	61	)	)	PUNCT
ejpam-4500	175	62	and	and	CCONJ
ejpam-4500	175	63	suppose	suppose	VERB
ejpam-4500	175	64	that	that	SCONJ
ejpam-4500	175	65	s1	s1	PROPN
ejpam-4500	175	66	is	be	AUX
ejpam-4500	175	67	a	a	DET
ejpam-4500	175	68	strictly	strictly	ADV
ejpam-4500	175	69	locating	locate	VERB
ejpam-4500	175	70	set	set	VERB
ejpam-4500	175	71	in	in	ADP
ejpam-4500	175	72	g.	g.	PROPN
ejpam-4500	175	73	then	then	ADV
ejpam-4500	175	74	ng(x)∩s1	ng(x)∩s1	VERB
ejpam-4500	175	75	̸=	̸=	PROPN
ejpam-4500	175	76	s1	s1	NOUN
ejpam-4500	175	77	.	.	PUNCT
ejpam-4500	176	1	it	it	PRON
ejpam-4500	176	2	follows	follow	VERB
ejpam-4500	176	3	that	that	SCONJ
ejpam-4500	176	4	[	[	X
ejpam-4500	176	5	v	v	X
ejpam-4500	176	6	(	(	PUNCT
ejpam-4500	176	7	g)\ng(x)]∩s1	g)\ng(x)]∩s1	PROPN
ejpam-4500	176	8	=	=	PUNCT
ejpam-4500	176	9	ng+h(x)∩	ng+h(x)∩	X
ejpam-4500	176	10	s	s	X
ejpam-4500	176	11	̸=	̸=	PROPN
ejpam-4500	176	12	∅.	∅.	NOUN
ejpam-4500	176	13	since	since	SCONJ
ejpam-4500	176	14	s1	s1	PROPN
ejpam-4500	176	15	∩ng+h(y	∩ng+h(y	SYM
ejpam-4500	176	16	,	,	PUNCT
ejpam-4500	176	17	2	2	X
ejpam-4500	176	18	)	)	PUNCT
ejpam-4500	176	19	=	=	NOUN
ejpam-4500	176	20	∅	∅	NOUN
ejpam-4500	176	21	,	,	PUNCT
ejpam-4500	176	22	ng+h(x	ng+h(x	PROPN
ejpam-4500	176	23	,	,	PUNCT
ejpam-4500	176	24	2	2	NUM
ejpam-4500	176	25	)	)	PUNCT
ejpam-4500	176	26	∩	∩	NOUN
ejpam-4500	176	27	s	s	PART
ejpam-4500	176	28	̸=	̸=	PROPN
ejpam-4500	176	29	ng+h(y	ng+h(y	NUM
ejpam-4500	176	30	,	,	PUNCT
ejpam-4500	176	31	2	2	X
ejpam-4500	176	32	)	)	PUNCT
ejpam-4500	176	33	∩	∩	NOUN
ejpam-4500	176	34	s.	s.	PROPN
ejpam-4500	176	35	therefore	therefore	ADV
ejpam-4500	176	36	,	,	PUNCT
ejpam-4500	176	37	s	s	VERB
ejpam-4500	176	38	is	be	AUX
ejpam-4500	176	39	a	a	DET
ejpam-4500	176	40	locating	locate	VERB
ejpam-4500	176	41	hop	hop	NOUN
ejpam-4500	176	42	set	set	VERB
ejpam-4500	176	43	in	in	ADP
ejpam-4500	176	44	g+h	g+h	PROPN
ejpam-4500	176	45	.	.	PUNCT
ejpam-4500	177	1	□	□	PUNCT
ejpam-4500	177	2	corollary	corollary	ADJ
ejpam-4500	177	3	2	2	NUM
ejpam-4500	177	4	.	.	PUNCT
ejpam-4500	178	1	let	let	VERB
ejpam-4500	178	2	g	g	NOUN
ejpam-4500	178	3	and	and	CCONJ
ejpam-4500	178	4	h	h	NOUN
ejpam-4500	178	5	be	be	AUX
ejpam-4500	178	6	connected	connect	VERB
ejpam-4500	178	7	non	non	ADJ
ejpam-4500	178	8	-	-	ADJ
ejpam-4500	178	9	trivial	trivial	ADJ
ejpam-4500	178	10	graphs	graph	NOUN
ejpam-4500	178	11	.	.	PUNCT
ejpam-4500	179	1	then	then	ADV
ejpam-4500	179	2	lhn(g+h	lhn(g+h	NOUN
ejpam-4500	179	3	)	)	PUNCT
ejpam-4500	179	4	=	=	SYM
ejpam-4500	179	5	min{sln(h	min{sln(h	PROPN
ejpam-4500	179	6	)	)	PUNCT
ejpam-4500	179	7	+	+	NUM
ejpam-4500	179	8	ln(g	ln(g	NUM
ejpam-4500	179	9	)	)	PUNCT
ejpam-4500	179	10	,	,	PUNCT
ejpam-4500	179	11	sln(g	sln(g	PROPN
ejpam-4500	179	12	)	)	PUNCT
ejpam-4500	179	13	+	+	NUM
ejpam-4500	179	14	ln(h	ln(h	NUM
ejpam-4500	179	15	)	)	PUNCT
ejpam-4500	179	16	}	}	PUNCT
ejpam-4500	179	17	.	.	PUNCT
ejpam-4500	180	1	proof	proof	NOUN
ejpam-4500	180	2	:	:	PUNCT
ejpam-4500	180	3	let	let	VERB
ejpam-4500	180	4	s	s	PRON
ejpam-4500	180	5	be	be	AUX
ejpam-4500	180	6	a	a	DET
ejpam-4500	180	7	minimum	minimum	ADJ
ejpam-4500	180	8	locating	locating	NOUN
ejpam-4500	180	9	hop	hop	NOUN
ejpam-4500	180	10	set	set	VERB
ejpam-4500	180	11	in	in	ADP
ejpam-4500	180	12	g	g	PROPN
ejpam-4500	180	13	+	+	CCONJ
ejpam-4500	180	14	h.	h.	PROPN
ejpam-4500	180	15	let	let	VERB
ejpam-4500	180	16	s1	s1	PROPN
ejpam-4500	180	17	=	=	SYM
ejpam-4500	180	18	v	v	PROPN
ejpam-4500	180	19	(	(	PUNCT
ejpam-4500	180	20	g	g	NOUN
ejpam-4500	180	21	)	)	PUNCT
ejpam-4500	180	22	∩	∩	PROPN
ejpam-4500	180	23	s	s	PART
ejpam-4500	180	24	and	and	CCONJ
ejpam-4500	180	25	s2	s2	PROPN
ejpam-4500	180	26	=	=	SYM
ejpam-4500	180	27	v	v	PROPN
ejpam-4500	180	28	(	(	PUNCT
ejpam-4500	180	29	h	h	NOUN
ejpam-4500	180	30	)	)	PUNCT
ejpam-4500	180	31	∩	∩	NOUN
ejpam-4500	180	32	s.	s.	PROPN
ejpam-4500	180	33	by	by	ADP
ejpam-4500	180	34	theorem	theorem	NOUN
ejpam-4500	180	35	2	2	NUM
ejpam-4500	180	36	,	,	PUNCT
ejpam-4500	180	37	s1	s1	NOUN
ejpam-4500	180	38	and	and	CCONJ
ejpam-4500	180	39	s2	s2	PROPN
ejpam-4500	180	40	are	be	AUX
ejpam-4500	180	41	locating	locate	VERB
ejpam-4500	180	42	sets	set	NOUN
ejpam-4500	180	43	in	in	ADP
ejpam-4500	180	44	g	g	PROPN
ejpam-4500	180	45	and	and	CCONJ
ejpam-4500	180	46	h	h	NOUN
ejpam-4500	180	47	,	,	PUNCT
ejpam-4500	180	48	respectively	respectively	ADV
ejpam-4500	180	49	,	,	PUNCT
ejpam-4500	180	50	where	where	SCONJ
ejpam-4500	180	51	s1	s1	NOUN
ejpam-4500	180	52	or	or	CCONJ
ejpam-4500	180	53	s2	s2	NOUN
ejpam-4500	180	54	is	be	AUX
ejpam-4500	180	55	a	a	DET
ejpam-4500	180	56	strictly	strictly	ADV
ejpam-4500	180	57	locating	locate	VERB
ejpam-4500	180	58	set	set	NOUN
ejpam-4500	180	59	.	.	PUNCT
ejpam-4500	181	1	if	if	SCONJ
ejpam-4500	181	2	s1	s1	PROPN
ejpam-4500	181	3	is	be	AUX
ejpam-4500	181	4	strictly	strictly	ADV
ejpam-4500	181	5	locating	locate	VERB
ejpam-4500	181	6	set	set	NOUN
ejpam-4500	181	7	,	,	PUNCT
ejpam-4500	181	8	then	then	ADV
ejpam-4500	181	9	sln(g)+ln(h	sln(g)+ln(h	PROPN
ejpam-4500	181	10	)	)	PUNCT
ejpam-4500	181	11	≤	≤	NOUN
ejpam-4500	181	12	|s1|	|s1|	NOUN
ejpam-4500	181	13	+	+	NUM
ejpam-4500	181	14	|s2|	|s2|	NOUN
ejpam-4500	181	15	≤	≤	NUM
ejpam-4500	181	16	|s|	|s|	PROPN
ejpam-4500	181	17	=	=	SYM
ejpam-4500	181	18	lhn(g	lhn(g	PROPN
ejpam-4500	182	1	+	+	NUM
ejpam-4500	182	2	h	h	NOUN
ejpam-4500	182	3	)	)	PUNCT
ejpam-4500	182	4	.	.	PUNCT
ejpam-4500	183	1	if	if	SCONJ
ejpam-4500	183	2	s2	s2	PROPN
ejpam-4500	183	3	is	be	AUX
ejpam-4500	183	4	strictly	strictly	ADV
ejpam-4500	183	5	locating	locate	VERB
ejpam-4500	183	6	set	set	NOUN
ejpam-4500	183	7	,	,	PUNCT
ejpam-4500	183	8	then	then	ADV
ejpam-4500	183	9	sln(h	sln(h	VERB
ejpam-4500	183	10	)	)	PUNCT
ejpam-4500	183	11	+	+	NUM
ejpam-4500	183	12	ln(g	ln(g	X
ejpam-4500	183	13	)	)	PUNCT
ejpam-4500	183	14	≤	≤	NOUN
ejpam-4500	184	1	|s2|+|s1|	|s2|+|s1|	CCONJ
ejpam-4500	184	2	≤	≤	NUM
ejpam-4500	184	3	|s|	|s|	PROPN
ejpam-4500	184	4	=	=	PUNCT
ejpam-4500	184	5	lhn(g+h	lhn(g+h	NOUN
ejpam-4500	184	6	)	)	PUNCT
ejpam-4500	184	7	.	.	PUNCT
ejpam-4500	185	1	thus	thus	ADV
ejpam-4500	185	2	,	,	PUNCT
ejpam-4500	185	3	lhn(g+h	lhn(g+h	NOUN
ejpam-4500	185	4	)	)	PUNCT
ejpam-4500	185	5	≥	≥	NOUN
ejpam-4500	185	6	min{sln(h)+ln(g	min{sln(h)+ln(g	NOUN
ejpam-4500	185	7	)	)	PUNCT
ejpam-4500	185	8	,	,	PUNCT
ejpam-4500	185	9	sln(g)+ln(h	sln(g)+ln(h	PROPN
ejpam-4500	185	10	)	)	PUNCT
ejpam-4500	185	11	}	}	PUNCT
ejpam-4500	185	12	.	.	PUNCT
ejpam-4500	186	1	next	next	ADV
ejpam-4500	186	2	,	,	PUNCT
ejpam-4500	186	3	suppose	suppose	VERB
ejpam-4500	186	4	that	that	SCONJ
ejpam-4500	186	5	sln(g	sln(g	PROPN
ejpam-4500	186	6	)	)	PUNCT
ejpam-4500	186	7	+	+	CCONJ
ejpam-4500	186	8	ln(h	ln(h	X
ejpam-4500	186	9	)	)	PUNCT
ejpam-4500	186	10	≤	≤	NUM
ejpam-4500	186	11	sln(h	sln(h	VERB
ejpam-4500	186	12	)	)	PUNCT
ejpam-4500	186	13	+	+	NUM
ejpam-4500	186	14	ln(g	ln(g	NUM
ejpam-4500	186	15	)	)	PUNCT
ejpam-4500	186	16	.	.	PUNCT
ejpam-4500	187	1	let	let	VERB
ejpam-4500	187	2	s1	s1	NOUN
ejpam-4500	187	3	be	be	AUX
ejpam-4500	187	4	a	a	DET
ejpam-4500	187	5	minimum	minimum	NOUN
ejpam-4500	187	6	strictly	strictly	ADV
ejpam-4500	187	7	locating	locate	VERB
ejpam-4500	187	8	set	set	VERB
ejpam-4500	187	9	in	in	ADP
ejpam-4500	187	10	g	g	PROPN
ejpam-4500	187	11	and	and	CCONJ
ejpam-4500	187	12	s2	s2	PROPN
ejpam-4500	187	13	be	be	AUX
ejpam-4500	187	14	a	a	DET
ejpam-4500	187	15	minimum	minimum	ADJ
ejpam-4500	187	16	locating	locating	NOUN
ejpam-4500	187	17	set	set	VERB
ejpam-4500	187	18	in	in	ADP
ejpam-4500	187	19	h.	h.	PROPN
ejpam-4500	187	20	then	then	ADV
ejpam-4500	187	21	s	s	PART
ejpam-4500	187	22	=	=	SYM
ejpam-4500	187	23	s1	s1	PROPN
ejpam-4500	187	24	∪	∪	X
ejpam-4500	187	25	s2	s2	NOUN
ejpam-4500	187	26	is	be	AUX
ejpam-4500	187	27	a	a	DET
ejpam-4500	187	28	locating	locate	VERB
ejpam-4500	187	29	hop	hop	NOUN
ejpam-4500	187	30	set	set	VERB
ejpam-4500	187	31	by	by	ADP
ejpam-4500	187	32	theorem	theorem	NOUN
ejpam-4500	187	33	2	2	NUM
ejpam-4500	187	34	.	.	PUNCT
ejpam-4500	187	35	hence	hence	ADV
ejpam-4500	187	36	,	,	PUNCT
ejpam-4500	187	37	lhn(g+h	lhn(g+h	NOUN
ejpam-4500	187	38	)	)	PUNCT
ejpam-4500	187	39	≤	≤	NUM
ejpam-4500	187	40	|s|	|s|	PROPN
ejpam-4500	187	41	=	=	SYM
ejpam-4500	187	42	|s1|+|s2|	|s1|+|s2|	PROPN
ejpam-4500	187	43	=	=	PUNCT
ejpam-4500	187	44	sln(g)+ln(h	sln(g)+ln(h	PROPN
ejpam-4500	187	45	)	)	PUNCT
ejpam-4500	187	46	.	.	PUNCT
ejpam-4500	188	1	therefore	therefore	ADV
ejpam-4500	188	2	,	,	PUNCT
ejpam-4500	188	3	lhn(g+h	lhn(g+h	NOUN
ejpam-4500	188	4	)	)	PUNCT
ejpam-4500	188	5	=	=	SYM
ejpam-4500	188	6	min{sln(h	min{sln(h	PROPN
ejpam-4500	188	7	)	)	PUNCT
ejpam-4500	188	8	+	+	NUM
ejpam-4500	188	9	ln(g	ln(g	NUM
ejpam-4500	188	10	)	)	PUNCT
ejpam-4500	188	11	,	,	PUNCT
ejpam-4500	188	12	sln(g	sln(g	PROPN
ejpam-4500	188	13	)	)	PUNCT
ejpam-4500	188	14	+	+	NUM
ejpam-4500	188	15	ln(h	ln(h	NUM
ejpam-4500	188	16	)	)	PUNCT
ejpam-4500	188	17	}	}	PUNCT
ejpam-4500	188	18	.	.	PUNCT
ejpam-4500	189	1	□	□	PUNCT
ejpam-4500	189	2	theorem	theorem	ADJ
ejpam-4500	189	3	3	3	NUM
ejpam-4500	189	4	.	.	PUNCT
ejpam-4500	190	1	(	(	PUNCT
ejpam-4500	190	2	[	[	X
ejpam-4500	190	3	5],[11	5],[11	NOUN
ejpam-4500	190	4	]	]	PUNCT
ejpam-4500	190	5	)	)	PUNCT
ejpam-4500	190	6	let	let	VERB
ejpam-4500	190	7	g	g	PRON
ejpam-4500	190	8	be	be	AUX
ejpam-4500	190	9	a	a	DET
ejpam-4500	190	10	connected	connected	ADJ
ejpam-4500	190	11	graph	graph	NOUN
ejpam-4500	190	12	of	of	ADP
ejpam-4500	190	13	order	order	NOUN
ejpam-4500	190	14	n	n	PRON
ejpam-4500	190	15	≥	≥	NOUN
ejpam-4500	190	16	2	2	NUM
ejpam-4500	190	17	.	.	PUNCT
ejpam-4500	191	1	if	if	SCONJ
ejpam-4500	191	2	ln(g	ln(g	NUM
ejpam-4500	191	3	)	)	PUNCT
ejpam-4500	192	1	<	<	X
ejpam-4500	192	2	sln(g	sln(g	PROPN
ejpam-4500	192	3	)	)	PUNCT
ejpam-4500	192	4	,	,	PUNCT
ejpam-4500	192	5	then	then	ADV
ejpam-4500	192	6	1	1	NUM
ejpam-4500	192	7	+	+	NUM
ejpam-4500	192	8	ln(g	ln(g	X
ejpam-4500	192	9	)	)	PUNCT
ejpam-4500	192	10	=	=	PUNCT
ejpam-4500	192	11	sln(g	sln(g	PROPN
ejpam-4500	192	12	)	)	PUNCT
ejpam-4500	192	13	.	.	PUNCT
ejpam-4500	193	1	e.m	e.m	PROPN
ejpam-4500	193	2	.	.	PROPN
ejpam-4500	193	3	a.	a.	NOUN
ejpam-4500	193	4	pagcu	pagcu	PROPN
ejpam-4500	193	5	,	,	PUNCT
ejpam-4500	193	6	g.	g.	PROPN
ejpam-4500	193	7	a.	a.	NOUN
ejpam-4500	193	8	malacas	malacas	PROPN
ejpam-4500	193	9	,	,	PUNCT
ejpam-4500	193	10	s.	s.	PROPN
ejpam-4500	193	11	r.	r.	PROPN
ejpam-4500	193	12	canoy	canoy	PROPN
ejpam-4500	193	13	,	,	PUNCT
ejpam-4500	193	14	jr	jr	PROPN
ejpam-4500	193	15	.	.	PROPN
ejpam-4500	193	16	/	/	SYM
ejpam-4500	193	17	eur	eur	PROPN
ejpam-4500	193	18	.	.	PUNCT
ejpam-4500	194	1	j.	j.	PROPN
ejpam-4500	194	2	pure	pure	PROPN
ejpam-4500	194	3	appl	appl	PROPN
ejpam-4500	194	4	.	.	PROPN
ejpam-4500	194	5	math	math	PROPN
ejpam-4500	194	6	,	,	PUNCT
ejpam-4500	194	7	15	15	NUM
ejpam-4500	194	8	(	(	PUNCT
ejpam-4500	194	9	4	4	NUM
ejpam-4500	194	10	)	)	PUNCT
ejpam-4500	194	11	(	(	PUNCT
ejpam-4500	194	12	2022	2022	NUM
ejpam-4500	194	13	)	)	PUNCT
ejpam-4500	194	14	,	,	PUNCT
ejpam-4500	194	15	1705	1705	NUM
ejpam-4500	194	16	-	-	SYM
ejpam-4500	194	17	1715	1715	NUM
ejpam-4500	194	18	1710	1710	NUM
ejpam-4500	194	19	corollary	corollary	NOUN
ejpam-4500	194	20	3	3	NUM
ejpam-4500	194	21	.	.	PUNCT
ejpam-4500	195	1	let	let	VERB
ejpam-4500	195	2	g	g	PRON
ejpam-4500	195	3	be	be	AUX
ejpam-4500	195	4	a	a	DET
ejpam-4500	195	5	connected	connected	ADJ
ejpam-4500	195	6	non	non	ADJ
ejpam-4500	195	7	-	-	ADJ
ejpam-4500	195	8	trivial	trivial	ADJ
ejpam-4500	195	9	graph	graph	NOUN
ejpam-4500	195	10	and	and	CCONJ
ejpam-4500	195	11	let	let	VERB
ejpam-4500	195	12	kn	kn	PROPN
ejpam-4500	195	13	be	be	AUX
ejpam-4500	195	14	a	a	DET
ejpam-4500	195	15	complete	complete	ADJ
ejpam-4500	195	16	graph	graph	NOUN
ejpam-4500	195	17	of	of	ADP
ejpam-4500	195	18	order	order	NOUN
ejpam-4500	195	19	n	n	PRON
ejpam-4500	195	20	≥	≥	NOUN
ejpam-4500	195	21	2	2	NUM
ejpam-4500	195	22	.	.	PUNCT
ejpam-4500	196	1	then	then	ADV
ejpam-4500	196	2	lhn(g+kn	lhn(g+kn	VERB
ejpam-4500	196	3	)	)	PUNCT
ejpam-4500	196	4	=	=	PUNCT
ejpam-4500	196	5	sln(g	sln(g	NOUN
ejpam-4500	196	6	)	)	PUNCT
ejpam-4500	197	1	+	+	CCONJ
ejpam-4500	197	2	n−	n−	NOUN
ejpam-4500	197	3	1	1	NUM
ejpam-4500	197	4	.	.	PUNCT
ejpam-4500	198	1	proof	proof	NOUN
ejpam-4500	198	2	:	:	PUNCT
ejpam-4500	198	3	note	note	VERB
ejpam-4500	198	4	that	that	SCONJ
ejpam-4500	198	5	ln(kn	ln(kn	NOUN
ejpam-4500	198	6	)	)	PUNCT
ejpam-4500	198	7	=	=	SYM
ejpam-4500	199	1	n	n	CCONJ
ejpam-4500	199	2	−	−	NUM
ejpam-4500	199	3	1	1	NUM
ejpam-4500	199	4	and	and	CCONJ
ejpam-4500	199	5	sln(kn	sln(kn	NOUN
ejpam-4500	199	6	)	)	PUNCT
ejpam-4500	200	1	=	=	VERB
ejpam-4500	200	2	n.	n.	NOUN
ejpam-4500	200	3	by	by	ADP
ejpam-4500	200	4	corollary	corollary	ADJ
ejpam-4500	200	5	2	2	NUM
ejpam-4500	200	6	,	,	PUNCT
ejpam-4500	200	7	lhn(g	lhn(g	NOUN
ejpam-4500	200	8	+	+	CCONJ
ejpam-4500	200	9	kn	kn	PROPN
ejpam-4500	200	10	)	)	PUNCT
ejpam-4500	200	11	=	=	SYM
ejpam-4500	200	12	min{sln(g	min{sln(g	PROPN
ejpam-4500	200	13	)	)	PUNCT
ejpam-4500	200	14	+	+	NUM
ejpam-4500	200	15	n	n	CCONJ
ejpam-4500	200	16	−	−	PROPN
ejpam-4500	200	17	1	1	NUM
ejpam-4500	200	18	,	,	PUNCT
ejpam-4500	200	19	ln(g	ln(g	PUNCT
ejpam-4500	200	20	)	)	PUNCT
ejpam-4500	200	21	+	+	NUM
ejpam-4500	200	22	n	n	CCONJ
ejpam-4500	200	23	}	}	PUNCT
ejpam-4500	200	24	and	and	CCONJ
ejpam-4500	200	25	by	by	ADP
ejpam-4500	200	26	theorem	theorem	ADJ
ejpam-4500	200	27	3	3	NUM
ejpam-4500	200	28	,	,	PUNCT
ejpam-4500	200	29	sln(g	sln(g	PROPN
ejpam-4500	200	30	)	)	PUNCT
ejpam-4500	200	31	−	−	PROPN
ejpam-4500	200	32	1	1	NUM
ejpam-4500	200	33	≤	≤	NOUN
ejpam-4500	200	34	ln(g	ln(g	NUM
ejpam-4500	200	35	)	)	PUNCT
ejpam-4500	200	36	.	.	PUNCT
ejpam-4500	201	1	therefore	therefore	ADV
ejpam-4500	201	2	,	,	PUNCT
ejpam-4500	201	3	lhn(g+kn	lhn(g+kn	NOUN
ejpam-4500	201	4	)	)	PUNCT
ejpam-4500	201	5	=	=	SYM
ejpam-4500	201	6	min{sln(g	min{sln(g	PROPN
ejpam-4500	201	7	)	)	PUNCT
ejpam-4500	202	1	+	+	NUM
ejpam-4500	202	2	n−	n−	NOUN
ejpam-4500	202	3	1	1	NUM
ejpam-4500	202	4	,	,	PUNCT
ejpam-4500	202	5	ln(g	ln(g	PUNCT
ejpam-4500	202	6	)	)	PUNCT
ejpam-4500	202	7	+	+	NUM
ejpam-4500	202	8	n	n	CCONJ
ejpam-4500	202	9	}	}	PUNCT
ejpam-4500	202	10	=	=	SYM
ejpam-4500	202	11	sln(g	sln(g	NOUN
ejpam-4500	202	12	)	)	PUNCT
ejpam-4500	203	1	+	+	CCONJ
ejpam-4500	203	2	n−	n−	NOUN
ejpam-4500	203	3	1	1	NUM
ejpam-4500	203	4	.	.	PUNCT
ejpam-4500	203	5	□	□	PUNCT
ejpam-4500	203	6	theorem	theorem	ADJ
ejpam-4500	203	7	4	4	NUM
ejpam-4500	203	8	.	.	PUNCT
ejpam-4500	204	1	let	let	VERB
ejpam-4500	204	2	g	g	PRON
ejpam-4500	204	3	be	be	AUX
ejpam-4500	204	4	a	a	DET
ejpam-4500	204	5	connected	connected	ADJ
ejpam-4500	204	6	non	non	ADJ
ejpam-4500	204	7	-	-	ADJ
ejpam-4500	204	8	trivial	trivial	ADJ
ejpam-4500	204	9	graph	graph	NOUN
ejpam-4500	204	10	and	and	CCONJ
ejpam-4500	204	11	let	let	VERB
ejpam-4500	205	1	k1	k1	NOUN
ejpam-4500	205	2	=	=	SYM
ejpam-4500	205	3	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4500	205	4	then	then	ADV
ejpam-4500	205	5	s	s	VERB
ejpam-4500	205	6	⊆	⊆	NUM
ejpam-4500	205	7	v	v	NOUN
ejpam-4500	205	8	(	(	PUNCT
ejpam-4500	205	9	g+k1	g+k1	NOUN
ejpam-4500	205	10	)	)	PUNCT
ejpam-4500	205	11	is	be	AUX
ejpam-4500	205	12	a	a	DET
ejpam-4500	205	13	locating	locate	VERB
ejpam-4500	205	14	hop	hop	NOUN
ejpam-4500	205	15	set	set	VERB
ejpam-4500	205	16	in	in	ADP
ejpam-4500	205	17	g+k1	g+k1	PROPN
ejpam-4500	205	18	if	if	SCONJ
ejpam-4500	205	19	and	and	CCONJ
ejpam-4500	205	20	only	only	ADV
ejpam-4500	205	21	if	if	SCONJ
ejpam-4500	205	22	v	v	NUM
ejpam-4500	205	23	/∈	/∈	PUNCT
ejpam-4500	205	24	s	s	PART
ejpam-4500	205	25	and	and	CCONJ
ejpam-4500	205	26	s	s	VERB
ejpam-4500	205	27	is	be	AUX
ejpam-4500	205	28	a	a	DET
ejpam-4500	205	29	strictly	strictly	ADV
ejpam-4500	205	30	locating	locate	VERB
ejpam-4500	205	31	set	set	VERB
ejpam-4500	205	32	in	in	ADP
ejpam-4500	205	33	g	g	PROPN
ejpam-4500	205	34	or	or	CCONJ
ejpam-4500	205	35	s	s	NOUN
ejpam-4500	205	36	=	=	PUNCT
ejpam-4500	205	37	{	{	PUNCT
ejpam-4500	205	38	v	v	NOUN
ejpam-4500	205	39	}	}	PUNCT
ejpam-4500	205	40	∪	∪	NOUN
ejpam-4500	205	41	s1	s1	NOUN
ejpam-4500	205	42	,	,	PUNCT
ejpam-4500	205	43	where	where	SCONJ
ejpam-4500	205	44	s1	s1	PROPN
ejpam-4500	205	45	is	be	AUX
ejpam-4500	205	46	a	a	DET
ejpam-4500	205	47	locating	locating	NOUN
ejpam-4500	205	48	set	set	VERB
ejpam-4500	205	49	in	in	ADP
ejpam-4500	205	50	g.	g.	PROPN
ejpam-4500	205	51	proof	proof	NOUN
ejpam-4500	205	52	:	:	PUNCT
ejpam-4500	205	53	let	let	VERB
ejpam-4500	205	54	s	s	PRON
ejpam-4500	205	55	⊆	⊆	NUM
ejpam-4500	205	56	v	v	NOUN
ejpam-4500	205	57	(	(	PUNCT
ejpam-4500	205	58	g	g	PROPN
ejpam-4500	205	59	+	+	CCONJ
ejpam-4500	205	60	k1	k1	NOUN
ejpam-4500	205	61	)	)	PUNCT
ejpam-4500	205	62	be	be	VERB
ejpam-4500	205	63	a	a	DET
ejpam-4500	205	64	locating	locate	VERB
ejpam-4500	205	65	hop	hop	NOUN
ejpam-4500	205	66	set	set	VERB
ejpam-4500	205	67	in	in	ADP
ejpam-4500	205	68	g	g	PROPN
ejpam-4500	205	69	+	+	CCONJ
ejpam-4500	205	70	k1	k1	NOUN
ejpam-4500	205	71	.	.	PUNCT
ejpam-4500	206	1	if	if	SCONJ
ejpam-4500	206	2	v	v	NUM
ejpam-4500	206	3	/∈	/∈	SYM
ejpam-4500	206	4	s	s	X
ejpam-4500	206	5	,	,	PUNCT
ejpam-4500	206	6	then	then	ADV
ejpam-4500	206	7	s	s	VERB
ejpam-4500	206	8	⊆	⊆	NUM
ejpam-4500	206	9	v	v	NOUN
ejpam-4500	206	10	(	(	PUNCT
ejpam-4500	206	11	g	g	NOUN
ejpam-4500	206	12	)	)	PUNCT
ejpam-4500	206	13	.	.	PUNCT
ejpam-4500	207	1	let	let	VERB
ejpam-4500	207	2	u	u	NOUN
ejpam-4500	207	3	,	,	PUNCT
ejpam-4500	207	4	s	s	PROPN
ejpam-4500	207	5	∈	∈	PROPN
ejpam-4500	207	6	v	v	ADP
ejpam-4500	207	7	(	(	PUNCT
ejpam-4500	207	8	g	g	NOUN
ejpam-4500	207	9	)	)	PUNCT
ejpam-4500	207	10	\	\	PUNCT
ejpam-4500	208	1	s.	s.	PROPN
ejpam-4500	208	2	then	then	ADV
ejpam-4500	208	3	ng+k1(u	ng+k1(u	SYM
ejpam-4500	208	4	,	,	PUNCT
ejpam-4500	208	5	2	2	NUM
ejpam-4500	208	6	)	)	PUNCT
ejpam-4500	208	7	∩	∩	NOUN
ejpam-4500	208	8	s	s	PART
ejpam-4500	208	9	̸=	̸=	PROPN
ejpam-4500	208	10	ng+k1(s	ng+k1(s	NUM
ejpam-4500	208	11	,	,	PUNCT
ejpam-4500	208	12	2	2	NUM
ejpam-4500	208	13	)	)	PUNCT
ejpam-4500	208	14	∩	∩	NOUN
ejpam-4500	208	15	s.	s.	PROPN
ejpam-4500	208	16	it	it	PRON
ejpam-4500	208	17	follows	follow	VERB
ejpam-4500	208	18	that	that	SCONJ
ejpam-4500	209	1	[	[	X
ejpam-4500	209	2	v	v	X
ejpam-4500	209	3	(	(	PUNCT
ejpam-4500	209	4	g	g	NOUN
ejpam-4500	209	5	)	)	PUNCT
ejpam-4500	209	6	\ng(u	\ng(u	NOUN
ejpam-4500	209	7	)	)	PUNCT
ejpam-4500	209	8	]	]	PUNCT
ejpam-4500	209	9	∩	∩	PROPN
ejpam-4500	209	10	s	s	PART
ejpam-4500	209	11	̸=	̸=	PROPN
ejpam-4500	209	12	[	[	PUNCT
ejpam-4500	209	13	v	v	X
ejpam-4500	209	14	(	(	PUNCT
ejpam-4500	209	15	g	g	NOUN
ejpam-4500	209	16	)	)	PUNCT
ejpam-4500	209	17	\ng(s	\ng(s	NUM
ejpam-4500	209	18	)	)	PUNCT
ejpam-4500	209	19	]	]	PUNCT
ejpam-4500	209	20	∩	∩	PROPN
ejpam-4500	209	21	s.	s.	PROPN
ejpam-4500	209	22	therefore	therefore	ADV
ejpam-4500	209	23	,	,	PUNCT
ejpam-4500	209	24	ng(u	ng(u	NOUN
ejpam-4500	209	25	)	)	PUNCT
ejpam-4500	209	26	∩	∩	NOUN
ejpam-4500	209	27	s	s	PART
ejpam-4500	209	28	=	=	PUNCT
ejpam-4500	209	29	[	[	X
ejpam-4500	209	30	v	v	X
ejpam-4500	209	31	(	(	PUNCT
ejpam-4500	209	32	g	g	NOUN
ejpam-4500	209	33	)	)	PUNCT
ejpam-4500	209	34	\ng+k1(u	\ng+k1(u	PROPN
ejpam-4500	209	35	,	,	PUNCT
ejpam-4500	209	36	2	2	NUM
ejpam-4500	209	37	)	)	PUNCT
ejpam-4500	209	38	]	]	PUNCT
ejpam-4500	209	39	∩	∩	PROPN
ejpam-4500	209	40	s	s	PART
ejpam-4500	209	41	̸=	̸=	PROPN
ejpam-4500	209	42	[	[	PUNCT
ejpam-4500	209	43	v	v	X
ejpam-4500	209	44	(	(	PUNCT
ejpam-4500	209	45	g	g	NOUN
ejpam-4500	209	46	)	)	PUNCT
ejpam-4500	209	47	\ng+k1(v	\ng+k1(v	NOUN
ejpam-4500	209	48	,	,	PUNCT
ejpam-4500	209	49	2	2	NUM
ejpam-4500	209	50	)	)	PUNCT
ejpam-4500	209	51	]	]	PUNCT
ejpam-4500	209	52	∩	∩	PROPN
ejpam-4500	209	53	s	s	PART
ejpam-4500	209	54	=	=	PUNCT
ejpam-4500	209	55	ng(v	ng(v	X
ejpam-4500	209	56	)	)	PUNCT
ejpam-4500	209	57	∩	∩	NOUN
ejpam-4500	209	58	s	s	PART
ejpam-4500	209	59	,	,	PUNCT
ejpam-4500	209	60	showing	show	VERB
ejpam-4500	209	61	that	that	SCONJ
ejpam-4500	209	62	s	s	VERB
ejpam-4500	209	63	is	be	AUX
ejpam-4500	209	64	a	a	DET
ejpam-4500	209	65	locating	locating	NOUN
ejpam-4500	209	66	set	set	VERB
ejpam-4500	209	67	in	in	ADP
ejpam-4500	209	68	g.	g.	PROPN
ejpam-4500	209	69	suppose	suppose	VERB
ejpam-4500	209	70	s	s	NOUN
ejpam-4500	209	71	is	be	AUX
ejpam-4500	209	72	not	not	PART
ejpam-4500	209	73	a	a	DET
ejpam-4500	209	74	strictly	strictly	ADV
ejpam-4500	209	75	locating	locate	VERB
ejpam-4500	209	76	set	set	VERB
ejpam-4500	209	77	in	in	ADP
ejpam-4500	209	78	g.	g.	PROPN
ejpam-4500	209	79	then	then	ADV
ejpam-4500	209	80	there	there	PRON
ejpam-4500	209	81	exists	exist	VERB
ejpam-4500	209	82	z	z	PROPN
ejpam-4500	209	83	∈	∈	PROPN
ejpam-4500	209	84	v	v	ADP
ejpam-4500	209	85	(	(	PUNCT
ejpam-4500	209	86	g	g	NOUN
ejpam-4500	209	87	)	)	PUNCT
ejpam-4500	209	88	\	\	PUNCT
ejpam-4500	210	1	s	s	VERB
ejpam-4500	210	2	such	such	ADJ
ejpam-4500	210	3	that	that	SCONJ
ejpam-4500	210	4	ng(z	ng(z	NUM
ejpam-4500	210	5	)	)	PUNCT
ejpam-4500	210	6	∩	∩	PROPN
ejpam-4500	210	7	s	s	PART
ejpam-4500	210	8	=	=	PUNCT
ejpam-4500	210	9	s.	s.	PROPN
ejpam-4500	210	10	this	this	PRON
ejpam-4500	210	11	implies	imply	VERB
ejpam-4500	210	12	that	that	SCONJ
ejpam-4500	210	13	ng(z	ng(z	NUM
ejpam-4500	210	14	,	,	PUNCT
ejpam-4500	210	15	2	2	NUM
ejpam-4500	210	16	)	)	PUNCT
ejpam-4500	210	17	∩	∩	NOUN
ejpam-4500	210	18	s	s	PART
ejpam-4500	210	19	=	=	NOUN
ejpam-4500	210	20	∅	∅	NOUN
ejpam-4500	210	21	=	=	PUNCT
ejpam-4500	210	22	ng(v	ng(v	X
ejpam-4500	210	23	,	,	PUNCT
ejpam-4500	210	24	2	2	X
ejpam-4500	210	25	)	)	PUNCT
ejpam-4500	210	26	∩	∩	NOUN
ejpam-4500	210	27	s	s	SYM
ejpam-4500	210	28	,	,	PUNCT
ejpam-4500	210	29	contrary	contrary	ADJ
ejpam-4500	210	30	to	to	ADP
ejpam-4500	210	31	our	our	PRON
ejpam-4500	210	32	assumption	assumption	NOUN
ejpam-4500	210	33	that	that	SCONJ
ejpam-4500	210	34	s	s	VERB
ejpam-4500	210	35	is	be	AUX
ejpam-4500	210	36	a	a	DET
ejpam-4500	210	37	locating	locate	VERB
ejpam-4500	210	38	hop	hop	NOUN
ejpam-4500	210	39	set	set	NOUN
ejpam-4500	210	40	.	.	PUNCT
ejpam-4500	211	1	hence	hence	ADV
ejpam-4500	211	2	,	,	PUNCT
ejpam-4500	211	3	s	s	VERB
ejpam-4500	211	4	is	be	AUX
ejpam-4500	211	5	a	a	DET
ejpam-4500	211	6	strictly	strictly	ADV
ejpam-4500	211	7	locating	locate	VERB
ejpam-4500	211	8	set	set	VERB
ejpam-4500	211	9	in	in	ADP
ejpam-4500	211	10	g.	g.	PROPN
ejpam-4500	211	11	next	next	ADV
ejpam-4500	211	12	,	,	PUNCT
ejpam-4500	211	13	suppose	suppose	VERB
ejpam-4500	211	14	that	that	SCONJ
ejpam-4500	211	15	s	s	VERB
ejpam-4500	211	16	=	=	X
ejpam-4500	211	17	{	{	PUNCT
ejpam-4500	211	18	v	v	NOUN
ejpam-4500	211	19	}	}	PUNCT
ejpam-4500	211	20	∪	∪	NOUN
ejpam-4500	211	21	s1	s1	NOUN
ejpam-4500	211	22	,	,	PUNCT
ejpam-4500	211	23	where	where	SCONJ
ejpam-4500	211	24	s1	s1	PROPN
ejpam-4500	211	25	=	=	SYM
ejpam-4500	211	26	v	v	PROPN
ejpam-4500	211	27	(	(	PUNCT
ejpam-4500	211	28	g	g	NOUN
ejpam-4500	211	29	)	)	PUNCT
ejpam-4500	211	30	∩	∩	PROPN
ejpam-4500	211	31	s.	s.	PROPN
ejpam-4500	211	32	then	then	ADV
ejpam-4500	211	33	s1	s1	PROPN
ejpam-4500	211	34	̸=	̸=	PROPN
ejpam-4500	211	35	∅	∅	NOUN
ejpam-4500	211	36	and	and	CCONJ
ejpam-4500	211	37	is	be	AUX
ejpam-4500	211	38	a	a	DET
ejpam-4500	211	39	locating	locating	NOUN
ejpam-4500	211	40	set	set	VERB
ejpam-4500	211	41	in	in	ADP
ejpam-4500	211	42	g.	g.	PROPN
ejpam-4500	211	43	for	for	ADP
ejpam-4500	211	44	the	the	DET
ejpam-4500	211	45	converse	converse	NOUN
ejpam-4500	211	46	,	,	PUNCT
ejpam-4500	211	47	suppose	suppose	VERB
ejpam-4500	211	48	v	v	ADP
ejpam-4500	211	49	/∈	/∈	PUNCT
ejpam-4500	211	50	s	s	PART
ejpam-4500	211	51	and	and	CCONJ
ejpam-4500	211	52	s	s	VERB
ejpam-4500	211	53	is	be	AUX
ejpam-4500	211	54	a	a	DET
ejpam-4500	211	55	strictly	strictly	ADV
ejpam-4500	211	56	locating	locate	VERB
ejpam-4500	211	57	set	set	VERB
ejpam-4500	211	58	in	in	ADP
ejpam-4500	211	59	g.	g.	PROPN
ejpam-4500	211	60	let	let	VERB
ejpam-4500	211	61	x	x	PRON
ejpam-4500	211	62	,	,	PUNCT
ejpam-4500	211	63	y	y	PROPN
ejpam-4500	211	64	∈	∈	PROPN
ejpam-4500	211	65	v	v	PROPN
ejpam-4500	211	66	(	(	PUNCT
ejpam-4500	211	67	g+k1	g+k1	NOUN
ejpam-4500	211	68	)	)	PUNCT
ejpam-4500	211	69	\	\	PROPN
ejpam-4500	211	70	s.	s.	PROPN
ejpam-4500	212	1	if	if	SCONJ
ejpam-4500	212	2	x	x	PRON
ejpam-4500	212	3	,	,	PUNCT
ejpam-4500	212	4	y	y	PROPN
ejpam-4500	212	5	∈	∈	PROPN
ejpam-4500	212	6	v	v	NOUN
ejpam-4500	212	7	(	(	PUNCT
ejpam-4500	212	8	g	g	NOUN
ejpam-4500	212	9	)	)	PUNCT
ejpam-4500	212	10	,	,	PUNCT
ejpam-4500	212	11	then	then	ADV
ejpam-4500	212	12	ng+k1(x	ng+k1(x	NOUN
ejpam-4500	212	13	,	,	PUNCT
ejpam-4500	212	14	2	2	X
ejpam-4500	212	15	)	)	PUNCT
ejpam-4500	212	16	∩	∩	NOUN
ejpam-4500	212	17	s	s	PART
ejpam-4500	212	18	=	=	PUNCT
ejpam-4500	213	1	[	[	X
ejpam-4500	213	2	v	v	X
ejpam-4500	213	3	(	(	PUNCT
ejpam-4500	213	4	g	g	NOUN
ejpam-4500	213	5	)	)	PUNCT
ejpam-4500	213	6	\ng(x	\ng(x	NOUN
ejpam-4500	213	7	)	)	PUNCT
ejpam-4500	213	8	]	]	PUNCT
ejpam-4500	214	1	∩	∩	PROPN
ejpam-4500	214	2	s	s	PART
ejpam-4500	214	3	̸=	̸=	PROPN
ejpam-4500	214	4	[	[	PUNCT
ejpam-4500	214	5	v	v	X
ejpam-4500	214	6	(	(	PUNCT
ejpam-4500	214	7	g	g	NOUN
ejpam-4500	214	8	)	)	PUNCT
ejpam-4500	214	9	\ng(y	\ng(y	NOUN
ejpam-4500	214	10	)	)	PUNCT
ejpam-4500	214	11	]	]	PUNCT
ejpam-4500	214	12	∩	∩	PROPN
ejpam-4500	214	13	s	s	X
ejpam-4500	214	14	=	=	SYM
ejpam-4500	214	15	ng+k1(y	ng+k1(y	NOUN
ejpam-4500	214	16	,	,	PUNCT
ejpam-4500	214	17	2	2	X
ejpam-4500	214	18	)	)	PUNCT
ejpam-4500	214	19	∩	∩	NOUN
ejpam-4500	214	20	s.	s.	PROPN
ejpam-4500	214	21	suppose	suppose	VERB
ejpam-4500	214	22	x	x	X
ejpam-4500	214	23	∈	∈	PROPN
ejpam-4500	214	24	v	v	X
ejpam-4500	214	25	(	(	PUNCT
ejpam-4500	214	26	g	g	NOUN
ejpam-4500	214	27	)	)	PUNCT
ejpam-4500	214	28	and	and	CCONJ
ejpam-4500	214	29	y	y	PROPN
ejpam-4500	214	30	=	=	PROPN
ejpam-4500	214	31	v.	v.	CCONJ
ejpam-4500	214	32	then	then	ADV
ejpam-4500	214	33	ng+k1(v	ng+k1(v	NOUN
ejpam-4500	214	34	,	,	PUNCT
ejpam-4500	214	35	2	2	X
ejpam-4500	214	36	)	)	PUNCT
ejpam-4500	214	37	∩	∩	NOUN
ejpam-4500	214	38	s	s	PART
ejpam-4500	214	39	=	=	X
ejpam-4500	214	40	∅.	∅.	NOUN
ejpam-4500	214	41	since	since	SCONJ
ejpam-4500	214	42	s	s	NOUN
ejpam-4500	214	43	is	be	AUX
ejpam-4500	214	44	a	a	DET
ejpam-4500	214	45	strictly	strictly	ADV
ejpam-4500	214	46	locating	locate	VERB
ejpam-4500	214	47	set	set	VERB
ejpam-4500	214	48	in	in	ADP
ejpam-4500	214	49	g	g	NOUN
ejpam-4500	214	50	,	,	PUNCT
ejpam-4500	214	51	ng(x	ng(x	NUM
ejpam-4500	214	52	)	)	PUNCT
ejpam-4500	214	53	∩	∩	NOUN
ejpam-4500	214	54	s	s	PART
ejpam-4500	214	55	̸=	̸=	PROPN
ejpam-4500	214	56	s.	s.	PROPN
ejpam-4500	214	57	then	then	ADV
ejpam-4500	214	58	ng+k1(x	ng+k1(x	NOUN
ejpam-4500	214	59	,	,	PUNCT
ejpam-4500	214	60	2	2	X
ejpam-4500	214	61	)	)	PUNCT
ejpam-4500	214	62	∩	∩	NOUN
ejpam-4500	214	63	s	s	PART
ejpam-4500	214	64	=	=	PUNCT
ejpam-4500	214	65	[	[	X
ejpam-4500	214	66	v	v	X
ejpam-4500	214	67	(	(	PUNCT
ejpam-4500	214	68	g	g	NOUN
ejpam-4500	214	69	)	)	PUNCT
ejpam-4500	214	70	\ng(x	\ng(x	NOUN
ejpam-4500	214	71	)	)	PUNCT
ejpam-4500	214	72	]	]	PUNCT
ejpam-4500	214	73	∩	∩	PROPN
ejpam-4500	214	74	s	s	PART
ejpam-4500	214	75	̸=	̸=	PROPN
ejpam-4500	214	76	[	[	PUNCT
ejpam-4500	214	77	v	v	X
ejpam-4500	214	78	(	(	PUNCT
ejpam-4500	214	79	g	g	NOUN
ejpam-4500	214	80	)	)	PUNCT
ejpam-4500	214	81	\ng(v	\ng(v	NOUN
ejpam-4500	214	82	)	)	PUNCT
ejpam-4500	214	83	]	]	PUNCT
ejpam-4500	215	1	∩	∩	PROPN
ejpam-4500	215	2	s	s	PART
ejpam-4500	215	3	=	=	ADJ
ejpam-4500	215	4	ng+k1(v	ng+k1(v	NOUN
ejpam-4500	215	5	,	,	PUNCT
ejpam-4500	215	6	2	2	X
ejpam-4500	215	7	)	)	PUNCT
ejpam-4500	215	8	∩	∩	NOUN
ejpam-4500	215	9	s.	s.	PROPN
ejpam-4500	215	10	therefore	therefore	ADV
ejpam-4500	215	11	,	,	PUNCT
ejpam-4500	215	12	s	s	VERB
ejpam-4500	215	13	is	be	AUX
ejpam-4500	215	14	a	a	DET
ejpam-4500	215	15	locating	locate	VERB
ejpam-4500	215	16	hop	hop	NOUN
ejpam-4500	215	17	set	set	VERB
ejpam-4500	215	18	in	in	ADP
ejpam-4500	215	19	g+k1	g+k1	PROPN
ejpam-4500	215	20	.	.	PUNCT
ejpam-4500	216	1	next	next	ADV
ejpam-4500	216	2	,	,	PUNCT
ejpam-4500	216	3	suppose	suppose	VERB
ejpam-4500	216	4	that	that	SCONJ
ejpam-4500	216	5	s	s	VERB
ejpam-4500	216	6	=	=	X
ejpam-4500	216	7	{	{	PUNCT
ejpam-4500	216	8	v	v	NOUN
ejpam-4500	216	9	}	}	PUNCT
ejpam-4500	216	10	∪	∪	NOUN
ejpam-4500	216	11	s1	s1	NOUN
ejpam-4500	216	12	,	,	PUNCT
ejpam-4500	216	13	where	where	SCONJ
ejpam-4500	216	14	s1	s1	PROPN
ejpam-4500	216	15	is	be	AUX
ejpam-4500	216	16	a	a	DET
ejpam-4500	216	17	locating	locating	NOUN
ejpam-4500	216	18	set	set	NOUN
ejpam-4500	216	19	of	of	ADP
ejpam-4500	216	20	g.	g.	PROPN
ejpam-4500	216	21	let	let	VERB
ejpam-4500	216	22	x	x	PRON
ejpam-4500	216	23	,	,	PUNCT
ejpam-4500	216	24	y	y	PROPN
ejpam-4500	216	25	∈	∈	PROPN
ejpam-4500	216	26	v	v	NOUN
ejpam-4500	216	27	(	(	PUNCT
ejpam-4500	216	28	g	g	PROPN
ejpam-4500	216	29	+	+	NOUN
ejpam-4500	216	30	k1	k1	NOUN
ejpam-4500	216	31	)	)	PUNCT
ejpam-4500	216	32	\	\	PUNCT
ejpam-4500	217	1	s	s	PART
ejpam-4500	217	2	with	with	ADP
ejpam-4500	217	3	x	x	PART
ejpam-4500	217	4	̸=	̸=	PROPN
ejpam-4500	217	5	y.	y.	PROPN
ejpam-4500	217	6	then	then	ADV
ejpam-4500	217	7	x	x	PRON
ejpam-4500	217	8	,	,	PUNCT
ejpam-4500	217	9	y	y	PROPN
ejpam-4500	217	10	∈	∈	PROPN
ejpam-4500	217	11	v	v	ADP
ejpam-4500	217	12	(	(	PUNCT
ejpam-4500	217	13	g	g	NOUN
ejpam-4500	217	14	)	)	PUNCT
ejpam-4500	217	15	\	\	NOUN
ejpam-4500	217	16	s1	s1	NOUN
ejpam-4500	217	17	and	and	CCONJ
ejpam-4500	217	18	ng(x	ng(x	NUM
ejpam-4500	217	19	)	)	PUNCT
ejpam-4500	217	20	∩	∩	NOUN
ejpam-4500	217	21	s1	s1	PROPN
ejpam-4500	217	22	̸=	̸=	PROPN
ejpam-4500	217	23	ng(y	ng(y	NOUN
ejpam-4500	217	24	)	)	PUNCT
ejpam-4500	217	25	∩	∩	ADJ
ejpam-4500	217	26	s1	s1	NOUN
ejpam-4500	217	27	.	.	PUNCT
ejpam-4500	218	1	thus	thus	ADV
ejpam-4500	218	2	,	,	PUNCT
ejpam-4500	218	3	ng+k1(x	ng+k1(x	NOUN
ejpam-4500	218	4	,	,	PUNCT
ejpam-4500	218	5	2	2	X
ejpam-4500	218	6	)	)	PUNCT
ejpam-4500	218	7	∩	∩	NOUN
ejpam-4500	218	8	s	s	PART
ejpam-4500	218	9	=	=	PUNCT
ejpam-4500	218	10	[	[	X
ejpam-4500	218	11	v	v	X
ejpam-4500	218	12	(	(	PUNCT
ejpam-4500	218	13	g	g	NOUN
ejpam-4500	218	14	)	)	PUNCT
ejpam-4500	218	15	\ng(x	\ng(x	NOUN
ejpam-4500	218	16	)	)	PUNCT
ejpam-4500	218	17	]	]	PUNCT
ejpam-4500	218	18	∩	∩	NOUN
ejpam-4500	218	19	s1	s1	PROPN
ejpam-4500	218	20	̸=	̸=	PROPN
ejpam-4500	218	21	[	[	X
ejpam-4500	218	22	v	v	X
ejpam-4500	218	23	(	(	PUNCT
ejpam-4500	218	24	g	g	NOUN
ejpam-4500	218	25	)	)	PUNCT
ejpam-4500	218	26	\ng(y	\ng(y	NOUN
ejpam-4500	218	27	)	)	PUNCT
ejpam-4500	218	28	]	]	PUNCT
ejpam-4500	218	29	∩	∩	NOUN
ejpam-4500	218	30	s1	s1	NOUN
ejpam-4500	218	31	=	=	SYM
ejpam-4500	218	32	ng+k1(y	ng+k1(y	NOUN
ejpam-4500	218	33	,	,	PUNCT
ejpam-4500	218	34	2	2	X
ejpam-4500	218	35	)	)	PUNCT
ejpam-4500	218	36	∩	∩	NOUN
ejpam-4500	218	37	s.	s.	PROPN
ejpam-4500	218	38	hence	hence	ADV
ejpam-4500	218	39	,	,	PUNCT
ejpam-4500	218	40	s	s	VERB
ejpam-4500	218	41	is	be	AUX
ejpam-4500	218	42	a	a	DET
ejpam-4500	218	43	locating	locate	VERB
ejpam-4500	218	44	hop	hop	NOUN
ejpam-4500	218	45	set	set	VERB
ejpam-4500	218	46	in	in	ADP
ejpam-4500	218	47	g+k1	g+k1	NOUN
ejpam-4500	218	48	.	.	PUNCT
ejpam-4500	219	1	□	□	PUNCT
ejpam-4500	219	2	corollary	corollary	ADJ
ejpam-4500	219	3	4	4	NUM
ejpam-4500	219	4	.	.	PUNCT
ejpam-4500	220	1	let	let	VERB
ejpam-4500	220	2	g	g	PRON
ejpam-4500	220	3	be	be	AUX
ejpam-4500	220	4	a	a	DET
ejpam-4500	220	5	connected	connected	ADJ
ejpam-4500	220	6	non	non	ADJ
ejpam-4500	220	7	-	-	ADJ
ejpam-4500	220	8	trivial	trivial	ADJ
ejpam-4500	220	9	graph	graph	NOUN
ejpam-4500	220	10	.	.	PUNCT
ejpam-4500	221	1	then	then	ADV
ejpam-4500	221	2	lhn(g+k1	lhn(g+k1	PROPN
ejpam-4500	221	3	)	)	PUNCT
ejpam-4500	221	4	=	=	PUNCT
ejpam-4500	221	5	sln(g	sln(g	PROPN
ejpam-4500	221	6	)	)	PUNCT
ejpam-4500	221	7	.	.	PUNCT
ejpam-4500	222	1	proof	proof	NOUN
ejpam-4500	222	2	:	:	PUNCT
ejpam-4500	222	3	by	by	ADP
ejpam-4500	222	4	theorem	theorem	ADJ
ejpam-4500	222	5	4	4	NUM
ejpam-4500	222	6	,	,	PUNCT
ejpam-4500	222	7	lhn(g+k1	lhn(g+k1	NOUN
ejpam-4500	222	8	)	)	PUNCT
ejpam-4500	222	9	=	=	SYM
ejpam-4500	222	10	min{sln(g	min{sln(g	PROPN
ejpam-4500	222	11	)	)	PUNCT
ejpam-4500	222	12	,	,	PUNCT
ejpam-4500	222	13	ln(g)+1	ln(g)+1	PROPN
ejpam-4500	222	14	}	}	PUNCT
ejpam-4500	222	15	.	.	PUNCT
ejpam-4500	223	1	by	by	ADP
ejpam-4500	223	2	theorem	theorem	ADJ
ejpam-4500	223	3	3	3	NUM
ejpam-4500	223	4	,	,	PUNCT
ejpam-4500	223	5	sln(g)−1	sln(g)−1	NOUN
ejpam-4500	223	6	≤	≤	NOUN
ejpam-4500	223	7	ln(g	ln(g	NUM
ejpam-4500	223	8	)	)	PUNCT
ejpam-4500	223	9	.	.	PUNCT
ejpam-4500	224	1	hence	hence	ADV
ejpam-4500	224	2	,	,	PUNCT
ejpam-4500	224	3	sln(g	sln(g	PROPN
ejpam-4500	224	4	)	)	PUNCT
ejpam-4500	224	5	≤	≤	NOUN
ejpam-4500	224	6	ln(g	ln(g	NUM
ejpam-4500	224	7	)	)	PUNCT
ejpam-4500	225	1	+	+	CCONJ
ejpam-4500	225	2	1	1	X
ejpam-4500	225	3	.	.	X
ejpam-4500	225	4	therefore	therefore	ADV
ejpam-4500	225	5	,	,	PUNCT
ejpam-4500	225	6	lhn(g+k1	lhn(g+k1	NOUN
ejpam-4500	225	7	)	)	PUNCT
ejpam-4500	225	8	=	=	PUNCT
ejpam-4500	225	9	sln(g	sln(g	PROPN
ejpam-4500	225	10	)	)	PUNCT
ejpam-4500	225	11	.	.	PUNCT
ejpam-4500	226	1	□	□	PUNCT
ejpam-4500	226	2	e.m	e.m	PROPN
ejpam-4500	226	3	.	.	PROPN
ejpam-4500	226	4	a.	a.	NOUN
ejpam-4500	226	5	pagcu	pagcu	PROPN
ejpam-4500	226	6	,	,	PUNCT
ejpam-4500	226	7	g.	g.	PROPN
ejpam-4500	226	8	a.	a.	NOUN
ejpam-4500	226	9	malacas	malacas	PROPN
ejpam-4500	226	10	,	,	PUNCT
ejpam-4500	226	11	s.	s.	PROPN
ejpam-4500	226	12	r.	r.	PROPN
ejpam-4500	226	13	canoy	canoy	PROPN
ejpam-4500	226	14	,	,	PUNCT
ejpam-4500	226	15	jr	jr	PROPN
ejpam-4500	226	16	.	.	PROPN
ejpam-4500	226	17	/	/	SYM
ejpam-4500	226	18	eur	eur	PROPN
ejpam-4500	226	19	.	.	PUNCT
ejpam-4500	227	1	j.	j.	PROPN
ejpam-4500	227	2	pure	pure	PROPN
ejpam-4500	227	3	appl	appl	PROPN
ejpam-4500	227	4	.	.	PROPN
ejpam-4500	227	5	math	math	PROPN
ejpam-4500	227	6	,	,	PUNCT
ejpam-4500	227	7	15	15	NUM
ejpam-4500	227	8	(	(	PUNCT
ejpam-4500	227	9	4	4	NUM
ejpam-4500	227	10	)	)	PUNCT
ejpam-4500	227	11	(	(	PUNCT
ejpam-4500	227	12	2022	2022	NUM
ejpam-4500	227	13	)	)	PUNCT
ejpam-4500	227	14	,	,	PUNCT
ejpam-4500	227	15	1705	1705	NUM
ejpam-4500	227	16	-	-	SYM
ejpam-4500	227	17	1715	1715	NUM
ejpam-4500	227	18	1711	1711	NUM
ejpam-4500	227	19	4	4	NUM
ejpam-4500	227	20	.	.	PUNCT
ejpam-4500	228	1	locating	locate	VERB
ejpam-4500	228	2	hop	hop	NOUN
ejpam-4500	228	3	sets	set	NOUN
ejpam-4500	228	4	in	in	ADP
ejpam-4500	228	5	the	the	DET
ejpam-4500	228	6	corona	corona	NOUN
ejpam-4500	228	7	of	of	ADP
ejpam-4500	228	8	graphs	graph	NOUN
ejpam-4500	228	9	the	the	DET
ejpam-4500	228	10	corona	corona	NOUN
ejpam-4500	228	11	of	of	ADP
ejpam-4500	228	12	two	two	NUM
ejpam-4500	228	13	graphs	graph	NOUN
ejpam-4500	228	14	g	g	NOUN
ejpam-4500	228	15	and	and	CCONJ
ejpam-4500	228	16	h	h	NOUN
ejpam-4500	228	17	,	,	PUNCT
ejpam-4500	228	18	denoted	denote	VERB
ejpam-4500	228	19	by	by	ADP
ejpam-4500	228	20	g	g	PROPN
ejpam-4500	228	21	◦	◦	NOUN
ejpam-4500	228	22	h	h	NOUN
ejpam-4500	228	23	,	,	PUNCT
ejpam-4500	228	24	is	be	AUX
ejpam-4500	228	25	the	the	DET
ejpam-4500	228	26	graph	graph	NOUN
ejpam-4500	228	27	obtained	obtain	VERB
ejpam-4500	228	28	by	by	ADP
ejpam-4500	228	29	taking	take	VERB
ejpam-4500	228	30	one	one	NUM
ejpam-4500	228	31	copy	copy	NOUN
ejpam-4500	228	32	of	of	ADP
ejpam-4500	228	33	g	g	NOUN
ejpam-4500	228	34	of	of	ADP
ejpam-4500	228	35	order	order	NOUN
ejpam-4500	228	36	n	n	NOUN
ejpam-4500	228	37	and	and	CCONJ
ejpam-4500	228	38	n	n	PRON
ejpam-4500	228	39	copies	copy	NOUN
ejpam-4500	228	40	of	of	ADP
ejpam-4500	228	41	h	h	NOUN
ejpam-4500	228	42	,	,	PUNCT
ejpam-4500	228	43	and	and	CCONJ
ejpam-4500	228	44	then	then	ADV
ejpam-4500	228	45	joining	join	VERB
ejpam-4500	228	46	the	the	DET
ejpam-4500	228	47	vertex	vertex	NOUN
ejpam-4500	228	48	vi	vi	NOUN
ejpam-4500	228	49	of	of	ADP
ejpam-4500	228	50	g	g	NOUN
ejpam-4500	228	51	to	to	ADP
ejpam-4500	228	52	every	every	DET
ejpam-4500	228	53	vertex	vertex	NOUN
ejpam-4500	228	54	of	of	ADP
ejpam-4500	228	55	the	the	DET
ejpam-4500	228	56	ith	ith	PROPN
ejpam-4500	228	57	copy	copy	NOUN
ejpam-4500	228	58	of	of	ADP
ejpam-4500	228	59	h.	h.	PROPN
ejpam-4500	228	60	for	for	ADP
ejpam-4500	228	61	every	every	DET
ejpam-4500	228	62	v	v	NUM
ejpam-4500	228	63	∈	∈	PROPN
ejpam-4500	228	64	v	v	NOUN
ejpam-4500	228	65	(	(	PUNCT
ejpam-4500	228	66	g	g	NOUN
ejpam-4500	228	67	)	)	PUNCT
ejpam-4500	228	68	,	,	PUNCT
ejpam-4500	228	69	denote	denote	VERB
ejpam-4500	228	70	by	by	ADP
ejpam-4500	228	71	hv	hv	PROPN
ejpam-4500	228	72	the	the	DET
ejpam-4500	228	73	copy	copy	NOUN
ejpam-4500	228	74	of	of	ADP
ejpam-4500	228	75	h	h	NOUN
ejpam-4500	228	76	whose	whose	DET
ejpam-4500	228	77	vertices	vertex	NOUN
ejpam-4500	228	78	are	be	AUX
ejpam-4500	228	79	joined	join	VERB
ejpam-4500	228	80	or	or	CCONJ
ejpam-4500	228	81	attached	attach	VERB
ejpam-4500	228	82	to	to	ADP
ejpam-4500	228	83	the	the	DET
ejpam-4500	228	84	vertex	vertex	NOUN
ejpam-4500	228	85	v.	v.	ADP
ejpam-4500	228	86	denote	denote	VERB
ejpam-4500	228	87	by	by	ADP
ejpam-4500	228	88	v	v	DET
ejpam-4500	228	89	+	+	NOUN
ejpam-4500	228	90	hv	hv	NOUN
ejpam-4500	228	91	the	the	DET
ejpam-4500	228	92	subgraph	subgraph	NOUN
ejpam-4500	228	93	of	of	ADP
ejpam-4500	228	94	the	the	DET
ejpam-4500	228	95	corona	corona	NOUN
ejpam-4500	228	96	g	g	PROPN
ejpam-4500	228	97	◦	◦	NOUN
ejpam-4500	228	98	h	h	NOUN
ejpam-4500	228	99	corresponding	correspond	VERB
ejpam-4500	228	100	to	to	ADP
ejpam-4500	228	101	the	the	DET
ejpam-4500	228	102	join	join	NOUN
ejpam-4500	228	103	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4500	228	104	.	.	PUNCT
ejpam-4500	229	1	theorem	theorem	VERB
ejpam-4500	229	2	5	5	NUM
ejpam-4500	229	3	.	.	PUNCT
ejpam-4500	230	1	let	let	VERB
ejpam-4500	230	2	g	g	PRON
ejpam-4500	230	3	be	be	AUX
ejpam-4500	230	4	a	a	DET
ejpam-4500	230	5	non	non	ADJ
ejpam-4500	230	6	-	-	ADJ
ejpam-4500	230	7	trivial	trivial	ADJ
ejpam-4500	230	8	connected	connected	ADJ
ejpam-4500	230	9	graph	graph	NOUN
ejpam-4500	230	10	and	and	CCONJ
ejpam-4500	230	11	let	let	VERB
ejpam-4500	230	12	h	h	NOUN
ejpam-4500	230	13	be	be	AUX
ejpam-4500	230	14	any	any	DET
ejpam-4500	230	15	non	non	ADJ
ejpam-4500	230	16	-	-	ADJ
ejpam-4500	230	17	trivial	trivial	ADJ
ejpam-4500	230	18	graph	graph	NOUN
ejpam-4500	230	19	.	.	PUNCT
ejpam-4500	231	1	then	then	ADV
ejpam-4500	231	2	s	s	VERB
ejpam-4500	231	3	⊆	⊆	NUM
ejpam-4500	231	4	v	v	NOUN
ejpam-4500	231	5	(	(	PUNCT
ejpam-4500	231	6	g	g	PROPN
ejpam-4500	231	7	◦	◦	NOUN
ejpam-4500	231	8	h	h	NOUN
ejpam-4500	231	9	)	)	PUNCT
ejpam-4500	231	10	is	be	AUX
ejpam-4500	231	11	a	a	DET
ejpam-4500	231	12	locating	locate	VERB
ejpam-4500	231	13	hop	hop	NOUN
ejpam-4500	231	14	set	set	NOUN
ejpam-4500	231	15	of	of	ADP
ejpam-4500	231	16	g	g	PROPN
ejpam-4500	231	17	◦	◦	NOUN
ejpam-4500	231	18	h	h	NOUN
ejpam-4500	231	19	if	if	SCONJ
ejpam-4500	232	1	and	and	CCONJ
ejpam-4500	232	2	only	only	ADV
ejpam-4500	232	3	if	if	SCONJ
ejpam-4500	232	4	s	s	VERB
ejpam-4500	232	5	=	=	PUNCT
ejpam-4500	232	6	a∪	a∪	NOUN
ejpam-4500	233	1	[	[	X
ejpam-4500	233	2	∪v∈v	∪v∈v	X
ejpam-4500	233	3	(	(	PUNCT
ejpam-4500	233	4	g)dv	g)dv	NOUN
ejpam-4500	233	5	]	]	PUNCT
ejpam-4500	233	6	and	and	CCONJ
ejpam-4500	233	7	(	(	PUNCT
ejpam-4500	233	8	i	i	NOUN
ejpam-4500	233	9	)	)	PUNCT
ejpam-4500	233	10	a	a	DET
ejpam-4500	233	11	⊆	⊆	NUM
ejpam-4500	233	12	v	v	NOUN
ejpam-4500	233	13	(	(	PUNCT
ejpam-4500	233	14	g	g	NOUN
ejpam-4500	233	15	)	)	PUNCT
ejpam-4500	233	16	such	such	ADJ
ejpam-4500	233	17	that	that	PRON
ejpam-4500	233	18	for	for	ADP
ejpam-4500	233	19	any	any	DET
ejpam-4500	233	20	two	two	NUM
ejpam-4500	233	21	distinct	distinct	ADJ
ejpam-4500	233	22	vertices	vertex	NOUN
ejpam-4500	233	23	v	v	ADP
ejpam-4500	233	24	,	,	PUNCT
ejpam-4500	233	25	w	w	PROPN
ejpam-4500	233	26	∈	∈	PROPN
ejpam-4500	233	27	v	v	ADP
ejpam-4500	233	28	(	(	PUNCT
ejpam-4500	233	29	g	g	NOUN
ejpam-4500	233	30	)	)	PUNCT
ejpam-4500	233	31	\	\	PROPN
ejpam-4500	233	32	a	a	PRON
ejpam-4500	233	33	,	,	PUNCT
ejpam-4500	233	34	ng(v	ng(v	PUNCT
ejpam-4500	233	35	)	)	PUNCT
ejpam-4500	233	36	̸=	̸=	PROPN
ejpam-4500	233	37	ng(w	ng(w	NOUN
ejpam-4500	233	38	)	)	PUNCT
ejpam-4500	233	39	or	or	CCONJ
ejpam-4500	233	40	ng(v	ng(v	PUNCT
ejpam-4500	233	41	,	,	PUNCT
ejpam-4500	233	42	2	2	X
ejpam-4500	233	43	)	)	PUNCT
ejpam-4500	233	44	∩a	∩a	PROPN
ejpam-4500	233	45	̸=	̸=	PROPN
ejpam-4500	233	46	ng(w	ng(w	NOUN
ejpam-4500	233	47	,	,	PUNCT
ejpam-4500	233	48	2	2	X
ejpam-4500	233	49	)	)	PUNCT
ejpam-4500	233	50	∩a	∩a	PROPN
ejpam-4500	233	51	;	;	PUNCT
ejpam-4500	233	52	(	(	PUNCT
ejpam-4500	233	53	ii	ii	X
ejpam-4500	233	54	)	)	PUNCT
ejpam-4500	233	55	dv	dv	PROPN
ejpam-4500	233	56	is	be	AUX
ejpam-4500	233	57	a	a	DET
ejpam-4500	233	58	locating	locating	NOUN
ejpam-4500	233	59	set	set	VERB
ejpam-4500	233	60	in	in	ADP
ejpam-4500	233	61	hv	hv	PROPN
ejpam-4500	233	62	for	for	ADP
ejpam-4500	233	63	each	each	PRON
ejpam-4500	233	64	v	v	NUM
ejpam-4500	233	65	∈	∈	PROPN
ejpam-4500	233	66	v	v	NOUN
ejpam-4500	233	67	(	(	PUNCT
ejpam-4500	233	68	g	g	NOUN
ejpam-4500	233	69	)	)	PUNCT
ejpam-4500	233	70	;	;	PUNCT
ejpam-4500	233	71	(	(	PUNCT
ejpam-4500	233	72	iii	iii	X
ejpam-4500	233	73	)	)	PUNCT
ejpam-4500	233	74	dw	dw	PROPN
ejpam-4500	233	75	is	be	AUX
ejpam-4500	233	76	a	a	DET
ejpam-4500	233	77	dominating	dominating	NOUN
ejpam-4500	233	78	set	set	NOUN
ejpam-4500	233	79	of	of	ADP
ejpam-4500	233	80	hw	hw	PRON
ejpam-4500	233	81	for	for	ADP
ejpam-4500	233	82	each	each	DET
ejpam-4500	233	83	w	w	PROPN
ejpam-4500	233	84	∈	∈	PROPN
ejpam-4500	233	85	v	v	ADP
ejpam-4500	233	86	(	(	PUNCT
ejpam-4500	233	87	g	g	NOUN
ejpam-4500	233	88	)	)	PUNCT
ejpam-4500	233	89	such	such	ADJ
ejpam-4500	233	90	that	that	SCONJ
ejpam-4500	233	91	ng(v	ng(v	PUNCT
ejpam-4500	233	92	)	)	PUNCT
ejpam-4500	233	93	=	=	SYM
ejpam-4500	233	94	{	{	PUNCT
ejpam-4500	233	95	w	w	NOUN
ejpam-4500	233	96	}	}	PUNCT
ejpam-4500	233	97	for	for	ADP
ejpam-4500	233	98	some	some	DET
ejpam-4500	233	99	v	v	ADP
ejpam-4500	233	100	∈	∈	PROPN
ejpam-4500	233	101	v	v	NOUN
ejpam-4500	233	102	(	(	PUNCT
ejpam-4500	233	103	g	g	NOUN
ejpam-4500	233	104	)	)	PUNCT
ejpam-4500	233	105	\a	\a	NUM
ejpam-4500	233	106	;	;	PUNCT
ejpam-4500	233	107	and	and	CCONJ
ejpam-4500	233	108	(	(	PUNCT
ejpam-4500	233	109	iv	iv	X
ejpam-4500	233	110	)	)	PUNCT
ejpam-4500	233	111	dv	dv	PROPN
ejpam-4500	233	112	or	or	CCONJ
ejpam-4500	233	113	dw	dw	PROPN
ejpam-4500	233	114	is	be	AUX
ejpam-4500	233	115	a	a	DET
ejpam-4500	233	116	strictly	strictly	ADV
ejpam-4500	233	117	locating	locate	VERB
ejpam-4500	233	118	set	set	VERB
ejpam-4500	233	119	for	for	ADP
ejpam-4500	233	120	each	each	DET
ejpam-4500	233	121	pair	pair	NOUN
ejpam-4500	233	122	of	of	ADP
ejpam-4500	233	123	distinct	distinct	ADJ
ejpam-4500	233	124	vertices	vertex	NOUN
ejpam-4500	233	125	v	v	NOUN
ejpam-4500	233	126	and	and	CCONJ
ejpam-4500	233	127	w	w	NOUN
ejpam-4500	233	128	of	of	ADP
ejpam-4500	233	129	g	g	NOUN
ejpam-4500	233	130	with	with	ADP
ejpam-4500	233	131	ng(v	ng(v	NOUN
ejpam-4500	233	132	)	)	PUNCT
ejpam-4500	234	1	∩a	∩a	PROPN
ejpam-4500	234	2	=	=	PUNCT
ejpam-4500	234	3	ng(w	ng(w	NOUN
ejpam-4500	234	4	)	)	PUNCT
ejpam-4500	234	5	∩a	∩a	PROPN
ejpam-4500	234	6	.	.	PUNCT
ejpam-4500	235	1	proof	proof	NOUN
ejpam-4500	235	2	:	:	PUNCT
ejpam-4500	235	3	suppose	suppose	VERB
ejpam-4500	235	4	s	s	NOUN
ejpam-4500	235	5	is	be	AUX
ejpam-4500	235	6	a	a	DET
ejpam-4500	235	7	locating	locate	VERB
ejpam-4500	235	8	hop	hop	NOUN
ejpam-4500	235	9	set	set	VERB
ejpam-4500	235	10	in	in	ADP
ejpam-4500	235	11	g	g	PROPN
ejpam-4500	235	12	◦	◦	NOUN
ejpam-4500	235	13	h.	h.	NOUN
ejpam-4500	235	14	let	let	VERB
ejpam-4500	235	15	a	a	DET
ejpam-4500	235	16	=	=	PUNCT
ejpam-4500	235	17	s∩v	s∩v	NOUN
ejpam-4500	235	18	(	(	PUNCT
ejpam-4500	235	19	g	g	NOUN
ejpam-4500	235	20	)	)	PUNCT
ejpam-4500	235	21	and	and	CCONJ
ejpam-4500	235	22	let	let	VERB
ejpam-4500	235	23	dv	dv	PROPN
ejpam-4500	235	24	=	=	PROPN
ejpam-4500	235	25	s∩v	s∩v	PROPN
ejpam-4500	235	26	(	(	PUNCT
ejpam-4500	235	27	hv	hv	PROPN
ejpam-4500	235	28	)	)	PUNCT
ejpam-4500	235	29	for	for	ADP
ejpam-4500	235	30	each	each	DET
ejpam-4500	235	31	v	v	NUM
ejpam-4500	235	32	∈	∈	PROPN
ejpam-4500	235	33	v	v	NOUN
ejpam-4500	235	34	(	(	PUNCT
ejpam-4500	235	35	g	g	NOUN
ejpam-4500	235	36	)	)	PUNCT
ejpam-4500	235	37	.	.	PUNCT
ejpam-4500	236	1	then	then	ADV
ejpam-4500	236	2	s	s	VERB
ejpam-4500	236	3	=	=	PUNCT
ejpam-4500	236	4	a	a	DET
ejpam-4500	236	5	∪	∪	ADJ
ejpam-4500	236	6	[	[	X
ejpam-4500	236	7	∪v∈v	∪v∈v	X
ejpam-4500	236	8	(	(	PUNCT
ejpam-4500	236	9	g)dv	g)dv	NOUN
ejpam-4500	236	10	]	]	PUNCT
ejpam-4500	236	11	.	.	PUNCT
ejpam-4500	237	1	let	let	VERB
ejpam-4500	237	2	v	v	NOUN
ejpam-4500	237	3	,	,	PUNCT
ejpam-4500	237	4	w	w	PROPN
ejpam-4500	237	5	∈	∈	PROPN
ejpam-4500	237	6	v	v	ADP
ejpam-4500	237	7	(	(	PUNCT
ejpam-4500	237	8	g	g	NOUN
ejpam-4500	237	9	)	)	PUNCT
ejpam-4500	237	10	\a	\a	VERB
ejpam-4500	237	11	with	with	ADP
ejpam-4500	237	12	v	v	NOUN
ejpam-4500	237	13	̸=	̸=	PROPN
ejpam-4500	237	14	w.	w.	NOUN
ejpam-4500	237	15	since	since	SCONJ
ejpam-4500	237	16	s	s	PROPN
ejpam-4500	237	17	is	be	AUX
ejpam-4500	237	18	a	a	DET
ejpam-4500	237	19	locating	locate	VERB
ejpam-4500	237	20	hop	hop	NOUN
ejpam-4500	237	21	set	set	VERB
ejpam-4500	237	22	in	in	ADP
ejpam-4500	237	23	g	g	PROPN
ejpam-4500	237	24	◦	◦	NOUN
ejpam-4500	237	25	h	h	NOUN
ejpam-4500	237	26	,	,	PUNCT
ejpam-4500	237	27	[	[	X
ejpam-4500	237	28	ng(v	ng(v	ADJ
ejpam-4500	237	29	,	,	PUNCT
ejpam-4500	237	30	2	2	X
ejpam-4500	237	31	)	)	PUNCT
ejpam-4500	237	32	∩a	∩a	NOUN
ejpam-4500	237	33	]	]	PUNCT
ejpam-4500	237	34	∪	∪	ADP
ejpam-4500	237	35	[	[	X
ejpam-4500	237	36	∪x∈ng(v)dx	∪x∈ng(v)dx	X
ejpam-4500	237	37	]	]	PUNCT
ejpam-4500	237	38	=	=	PUNCT
ejpam-4500	237	39	ng	ng	PROPN
ejpam-4500	237	40	◦	◦	NOUN
ejpam-4500	237	41	h(v	h(v	PROPN
ejpam-4500	238	1	,	,	PUNCT
ejpam-4500	238	2	2	2	NUM
ejpam-4500	238	3	)	)	PUNCT
ejpam-4500	238	4	∩	∩	NOUN
ejpam-4500	238	5	s	s	PART
ejpam-4500	238	6	̸=	̸=	PROPN
ejpam-4500	238	7	ng	ng	PROPN
ejpam-4500	238	8	◦	◦	PROPN
ejpam-4500	238	9	h(w	h(w	PROPN
ejpam-4500	238	10	,	,	PUNCT
ejpam-4500	238	11	2	2	X
ejpam-4500	238	12	)	)	PUNCT
ejpam-4500	238	13	∩	∩	NOUN
ejpam-4500	238	14	s	s	PART
ejpam-4500	238	15	=	=	X
ejpam-4500	238	16	[	[	X
ejpam-4500	238	17	ng(w	ng(w	NOUN
ejpam-4500	238	18	,	,	PUNCT
ejpam-4500	238	19	2	2	X
ejpam-4500	238	20	)	)	PUNCT
ejpam-4500	238	21	∩a	∩a	NOUN
ejpam-4500	238	22	]	]	PUNCT
ejpam-4500	238	23	∪	∪	ADP
ejpam-4500	238	24	[	[	PUNCT
ejpam-4500	238	25	∪y∈ng(w)dy	∪y∈ng(w)dy	NOUN
ejpam-4500	238	26	]	]	PUNCT
ejpam-4500	238	27	.	.	PUNCT
ejpam-4500	239	1	this	this	PRON
ejpam-4500	239	2	implies	imply	VERB
ejpam-4500	239	3	that	that	SCONJ
ejpam-4500	239	4	ng(v	ng(v	NOUN
ejpam-4500	239	5	,	,	PUNCT
ejpam-4500	239	6	2)∩a	2)∩a	NUM
ejpam-4500	239	7	̸=	̸=	PROPN
ejpam-4500	239	8	ng(w	ng(w	NOUN
ejpam-4500	239	9	,	,	PUNCT
ejpam-4500	239	10	2)∩a	2)∩a	NUM
ejpam-4500	239	11	or	or	CCONJ
ejpam-4500	239	12	ng(v	ng(v	PUNCT
ejpam-4500	239	13	)	)	PUNCT
ejpam-4500	239	14	̸=	̸=	PROPN
ejpam-4500	239	15	ng(w	ng(w	NOUN
ejpam-4500	239	16	)	)	PUNCT
ejpam-4500	239	17	,	,	PUNCT
ejpam-4500	239	18	showing	show	VERB
ejpam-4500	239	19	that	that	SCONJ
ejpam-4500	239	20	(	(	PUNCT
ejpam-4500	239	21	i	i	NOUN
ejpam-4500	239	22	)	)	PUNCT
ejpam-4500	239	23	holds	hold	VERB
ejpam-4500	239	24	.	.	PUNCT
ejpam-4500	240	1	next	next	ADV
ejpam-4500	240	2	,	,	PUNCT
ejpam-4500	240	3	let	let	VERB
ejpam-4500	240	4	v	v	NUM
ejpam-4500	240	5	∈	∈	PROPN
ejpam-4500	240	6	v	v	NOUN
ejpam-4500	240	7	(	(	PUNCT
ejpam-4500	240	8	g	g	NOUN
ejpam-4500	240	9	)	)	PUNCT
ejpam-4500	240	10	and	and	CCONJ
ejpam-4500	240	11	let	let	VERB
ejpam-4500	240	12	a	a	PRON
ejpam-4500	240	13	,	,	PUNCT
ejpam-4500	240	14	b	b	PROPN
ejpam-4500	240	15	∈	∈	PROPN
ejpam-4500	240	16	v	v	ADP
ejpam-4500	240	17	(	(	PUNCT
ejpam-4500	240	18	hv	hv	PROPN
ejpam-4500	240	19	)	)	PUNCT
ejpam-4500	240	20	\dv	\dv	PROPN
ejpam-4500	240	21	with	with	ADP
ejpam-4500	240	22	a	a	DET
ejpam-4500	240	23	̸=	̸=	PROPN
ejpam-4500	240	24	b.	b.	NOUN
ejpam-4500	240	25	since	since	SCONJ
ejpam-4500	240	26	s	s	PROPN
ejpam-4500	240	27	is	be	AUX
ejpam-4500	240	28	a	a	DET
ejpam-4500	240	29	locating	locate	VERB
ejpam-4500	240	30	hop	hop	NOUN
ejpam-4500	240	31	set	set	VERB
ejpam-4500	240	32	in	in	ADP
ejpam-4500	240	33	g	g	PROPN
ejpam-4500	240	34	◦	◦	NOUN
ejpam-4500	240	35	h	h	NOUN
ejpam-4500	240	36	,	,	PUNCT
ejpam-4500	240	37	(	(	PUNCT
ejpam-4500	240	38	[	[	X
ejpam-4500	240	39	v	v	X
ejpam-4500	240	40	(	(	PUNCT
ejpam-4500	240	41	hv	hv	NOUN
ejpam-4500	240	42	)	)	PUNCT
ejpam-4500	240	43	\nhv(a	\nhv(a	NOUN
ejpam-4500	240	44	)	)	PUNCT
ejpam-4500	240	45	]	]	PUNCT
ejpam-4500	240	46	∩dv	∩dv	NOUN
ejpam-4500	240	47	)	)	PUNCT
ejpam-4500	240	48	∪	∪	ADP
ejpam-4500	240	49	[	[	X
ejpam-4500	240	50	ng(v	ng(v	X
ejpam-4500	240	51	)	)	PUNCT
ejpam-4500	241	1	∩a	∩a	PROPN
ejpam-4500	241	2	]	]	PUNCT
ejpam-4500	242	1	=	=	PUNCT
ejpam-4500	242	2	ng	ng	PROPN
ejpam-4500	242	3	◦	◦	PROPN
ejpam-4500	242	4	h(a	h(a	PROPN
ejpam-4500	242	5	,	,	PUNCT
ejpam-4500	242	6	2	2	NUM
ejpam-4500	242	7	)	)	PUNCT
ejpam-4500	242	8	∩	∩	NOUN
ejpam-4500	242	9	s	s	PART
ejpam-4500	242	10	̸=	̸=	PROPN
ejpam-4500	242	11	ng	ng	PROPN
ejpam-4500	242	12	◦	◦	PROPN
ejpam-4500	242	13	h(b	h(b	PROPN
ejpam-4500	242	14	,	,	PUNCT
ejpam-4500	242	15	2	2	X
ejpam-4500	242	16	)	)	PUNCT
ejpam-4500	242	17	∩	∩	NOUN
ejpam-4500	242	18	s	s	PART
ejpam-4500	242	19	=	=	X
ejpam-4500	242	20	(	(	PUNCT
ejpam-4500	242	21	[	[	X
ejpam-4500	242	22	v	v	X
ejpam-4500	242	23	(	(	PUNCT
ejpam-4500	242	24	hv	hv	NOUN
ejpam-4500	242	25	)	)	PUNCT
ejpam-4500	242	26	\nhv(b	\nhv(b	PROPN
ejpam-4500	242	27	)	)	PUNCT
ejpam-4500	242	28	]	]	PUNCT
ejpam-4500	242	29	∩dv	∩dv	NOUN
ejpam-4500	242	30	)	)	PUNCT
ejpam-4500	242	31	∪	∪	ADP
ejpam-4500	242	32	[	[	NOUN
ejpam-4500	242	33	ng(w	ng(w	NOUN
ejpam-4500	242	34	)	)	PUNCT
ejpam-4500	242	35	∩a	∩a	PROPN
ejpam-4500	242	36	]	]	PUNCT
ejpam-4500	242	37	.	.	PUNCT
ejpam-4500	243	1	hence	hence	ADV
ejpam-4500	243	2	,	,	PUNCT
ejpam-4500	243	3	[	[	X
ejpam-4500	243	4	v	v	X
ejpam-4500	243	5	(	(	PUNCT
ejpam-4500	243	6	hv	hv	NOUN
ejpam-4500	243	7	)	)	PUNCT
ejpam-4500	243	8	\	\	PUNCT
ejpam-4500	243	9	nhv(a	nhv(a	PROPN
ejpam-4500	243	10	)	)	PUNCT
ejpam-4500	243	11	]	]	PUNCT
ejpam-4500	244	1	∩	∩	PROPN
ejpam-4500	244	2	dv	dv	PROPN
ejpam-4500	244	3	̸=	̸=	PROPN
ejpam-4500	244	4	[	[	X
ejpam-4500	244	5	v	v	X
ejpam-4500	244	6	(	(	PUNCT
ejpam-4500	244	7	hv	hv	NOUN
ejpam-4500	244	8	)	)	PUNCT
ejpam-4500	244	9	\	\	PUNCT
ejpam-4500	245	1	nhv(b	nhv(b	PROPN
ejpam-4500	245	2	)	)	PUNCT
ejpam-4500	245	3	]	]	PUNCT
ejpam-4500	246	1	∩	∩	PROPN
ejpam-4500	246	2	dv	dv	PROPN
ejpam-4500	246	3	.	.	PROPN
ejpam-4500	247	1	this	this	PRON
ejpam-4500	247	2	implies	imply	VERB
ejpam-4500	247	3	that	that	PRON
ejpam-4500	247	4	nhv(a	nhv(a	PROPN
ejpam-4500	247	5	)	)	PUNCT
ejpam-4500	247	6	∩	∩	PROPN
ejpam-4500	247	7	dv	dv	PROPN
ejpam-4500	247	8	̸=	̸=	PROPN
ejpam-4500	247	9	nhv(b	nhv(b	PROPN
ejpam-4500	247	10	)	)	PUNCT
ejpam-4500	247	11	∩	∩	PROPN
ejpam-4500	247	12	dv	dv	PROPN
ejpam-4500	247	13	,	,	PUNCT
ejpam-4500	247	14	showing	show	VERB
ejpam-4500	247	15	dv	dv	PROPN
ejpam-4500	247	16	is	be	AUX
ejpam-4500	247	17	a	a	DET
ejpam-4500	247	18	locating	locate	VERB
ejpam-4500	247	19	set	set	NOUN
ejpam-4500	247	20	of	of	ADP
ejpam-4500	247	21	hv	hv	PROPN
ejpam-4500	247	22	.	.	PUNCT
ejpam-4500	248	1	hence	hence	ADV
ejpam-4500	248	2	,	,	PUNCT
ejpam-4500	248	3	(	(	PUNCT
ejpam-4500	248	4	ii	ii	NOUN
ejpam-4500	248	5	)	)	PUNCT
ejpam-4500	248	6	holds	hold	VERB
ejpam-4500	248	7	.	.	PUNCT
ejpam-4500	249	1	to	to	PART
ejpam-4500	249	2	show	show	VERB
ejpam-4500	249	3	that	that	SCONJ
ejpam-4500	249	4	(	(	PUNCT
ejpam-4500	249	5	iii	iii	NOUN
ejpam-4500	249	6	)	)	PUNCT
ejpam-4500	249	7	holds	hold	NOUN
ejpam-4500	249	8	,	,	PUNCT
ejpam-4500	249	9	suppose	suppose	VERB
ejpam-4500	249	10	there	there	PRON
ejpam-4500	249	11	exists	exist	VERB
ejpam-4500	249	12	w	w	PROPN
ejpam-4500	249	13	∈	∈	PROPN
ejpam-4500	249	14	v	v	ADP
ejpam-4500	249	15	(	(	PUNCT
ejpam-4500	249	16	g	g	NOUN
ejpam-4500	249	17	)	)	PUNCT
ejpam-4500	249	18	such	such	ADJ
ejpam-4500	249	19	that	that	SCONJ
ejpam-4500	249	20	ng(v	ng(v	PUNCT
ejpam-4500	249	21	)	)	PUNCT
ejpam-4500	249	22	=	=	SYM
ejpam-4500	249	23	{	{	PUNCT
ejpam-4500	249	24	w	w	NOUN
ejpam-4500	249	25	}	}	PUNCT
ejpam-4500	249	26	for	for	ADP
ejpam-4500	249	27	some	some	DET
ejpam-4500	249	28	v	v	ADP
ejpam-4500	249	29	∈	∈	PROPN
ejpam-4500	249	30	v	v	NOUN
ejpam-4500	249	31	(	(	PUNCT
ejpam-4500	249	32	g	g	NOUN
ejpam-4500	249	33	)	)	PUNCT
ejpam-4500	249	34	\	\	NOUN
ejpam-4500	250	1	a.	a.	NOUN
ejpam-4500	251	1	if	if	SCONJ
ejpam-4500	251	2	dw	dw	PROPN
ejpam-4500	251	3	=	=	SYM
ejpam-4500	251	4	v	v	PROPN
ejpam-4500	251	5	(	(	PUNCT
ejpam-4500	251	6	hw	hw	NOUN
ejpam-4500	251	7	)	)	PUNCT
ejpam-4500	251	8	,	,	PUNCT
ejpam-4500	251	9	then	then	ADV
ejpam-4500	251	10	we	we	PRON
ejpam-4500	251	11	are	be	AUX
ejpam-4500	251	12	done	do	VERB
ejpam-4500	251	13	.	.	PUNCT
ejpam-4500	252	1	so	so	ADV
ejpam-4500	252	2	suppose	suppose	VERB
ejpam-4500	252	3	that	that	SCONJ
ejpam-4500	252	4	dw	dw	PROPN
ejpam-4500	252	5	̸=	̸=	PROPN
ejpam-4500	252	6	v	v	PROPN
ejpam-4500	252	7	(	(	PUNCT
ejpam-4500	252	8	hw	hw	NOUN
ejpam-4500	252	9	)	)	PUNCT
ejpam-4500	252	10	and	and	CCONJ
ejpam-4500	252	11	let	let	VERB
ejpam-4500	252	12	q	q	PROPN
ejpam-4500	252	13	∈	∈	PROPN
ejpam-4500	252	14	v	v	NOUN
ejpam-4500	252	15	(	(	PUNCT
ejpam-4500	252	16	hw	hw	NOUN
ejpam-4500	252	17	)	)	PUNCT
ejpam-4500	252	18	\dw	\dw	PROPN
ejpam-4500	252	19	.	.	PUNCT
ejpam-4500	252	20	then	then	ADV
ejpam-4500	252	21	by	by	ADP
ejpam-4500	252	22	assumption	assumption	NOUN
ejpam-4500	252	23	and	and	CCONJ
ejpam-4500	252	24	the	the	DET
ejpam-4500	252	25	fact	fact	NOUN
ejpam-4500	252	26	that	that	SCONJ
ejpam-4500	252	27	s	s	VERB
ejpam-4500	252	28	is	be	AUX
ejpam-4500	252	29	a	a	DET
ejpam-4500	252	30	locating	locate	VERB
ejpam-4500	252	31	hop	hop	NOUN
ejpam-4500	252	32	set	set	VERB
ejpam-4500	252	33	in	in	ADP
ejpam-4500	252	34	g	g	PROPN
ejpam-4500	252	35	◦	◦	NOUN
ejpam-4500	252	36	h	h	NOUN
ejpam-4500	252	37	,	,	PUNCT
ejpam-4500	252	38	dw	dw	NOUN
ejpam-4500	252	39	∪	∪	X
ejpam-4500	252	40	(	(	PUNCT
ejpam-4500	252	41	ng(w	ng(w	NOUN
ejpam-4500	252	42	)	)	PUNCT
ejpam-4500	252	43	∩a	∩a	NOUN
ejpam-4500	252	44	)	)	PUNCT
ejpam-4500	252	45	=	=	SYM
ejpam-4500	253	1	ng	ng	PROPN
ejpam-4500	253	2	◦	◦	NOUN
ejpam-4500	253	3	h(v	h(v	PROPN
ejpam-4500	253	4	,	,	PUNCT
ejpam-4500	253	5	2	2	NUM
ejpam-4500	253	6	)	)	PUNCT
ejpam-4500	253	7	∩	∩	PROPN
ejpam-4500	253	8	s	s	PART
ejpam-4500	253	9	e.m	e.m	PROPN
ejpam-4500	253	10	.	.	PROPN
ejpam-4500	253	11	a.	a.	NOUN
ejpam-4500	253	12	pagcu	pagcu	PROPN
ejpam-4500	253	13	,	,	PUNCT
ejpam-4500	253	14	g.	g.	PROPN
ejpam-4500	253	15	a.	a.	NOUN
ejpam-4500	253	16	malacas	malacas	PROPN
ejpam-4500	253	17	,	,	PUNCT
ejpam-4500	253	18	s.	s.	PROPN
ejpam-4500	253	19	r.	r.	PROPN
ejpam-4500	253	20	canoy	canoy	PROPN
ejpam-4500	253	21	,	,	PUNCT
ejpam-4500	253	22	jr	jr	PROPN
ejpam-4500	253	23	.	.	PROPN
ejpam-4500	253	24	/	/	SYM
ejpam-4500	253	25	eur	eur	PROPN
ejpam-4500	253	26	.	.	PUNCT
ejpam-4500	254	1	j.	j.	PROPN
ejpam-4500	254	2	pure	pure	PROPN
ejpam-4500	254	3	appl	appl	PROPN
ejpam-4500	254	4	.	.	PROPN
ejpam-4500	254	5	math	math	PROPN
ejpam-4500	254	6	,	,	PUNCT
ejpam-4500	254	7	15	15	NUM
ejpam-4500	254	8	(	(	PUNCT
ejpam-4500	254	9	4	4	NUM
ejpam-4500	254	10	)	)	PUNCT
ejpam-4500	254	11	(	(	PUNCT
ejpam-4500	254	12	2022	2022	NUM
ejpam-4500	254	13	)	)	PUNCT
ejpam-4500	254	14	,	,	PUNCT
ejpam-4500	254	15	1705	1705	NUM
ejpam-4500	254	16	-	-	SYM
ejpam-4500	254	17	1715	1715	NUM
ejpam-4500	254	18	1712	1712	NUM
ejpam-4500	254	19	̸=	̸=	PROPN
ejpam-4500	254	20	ng	ng	PROPN
ejpam-4500	254	21	◦	◦	PROPN
ejpam-4500	254	22	h(q	h(q	ADV
ejpam-4500	254	23	,	,	PUNCT
ejpam-4500	254	24	2	2	X
ejpam-4500	254	25	)	)	PUNCT
ejpam-4500	254	26	∩	∩	NOUN
ejpam-4500	254	27	s	s	PART
ejpam-4500	254	28	=	=	X
ejpam-4500	254	29	(	(	PUNCT
ejpam-4500	254	30	[	[	X
ejpam-4500	254	31	v	v	X
ejpam-4500	254	32	(	(	PUNCT
ejpam-4500	254	33	hw	hw	NOUN
ejpam-4500	254	34	)	)	PUNCT
ejpam-4500	254	35	\nhw(q	\nhw(q	NOUN
ejpam-4500	254	36	)	)	PUNCT
ejpam-4500	254	37	]	]	PUNCT
ejpam-4500	255	1	∩dw	∩dw	PROPN
ejpam-4500	255	2	)	)	PUNCT
ejpam-4500	255	3	∪	∪	ADP
ejpam-4500	255	4	[	[	NOUN
ejpam-4500	255	5	ng(w	ng(w	NOUN
ejpam-4500	255	6	)	)	PUNCT
ejpam-4500	255	7	∩a	∩a	PROPN
ejpam-4500	255	8	]	]	PUNCT
ejpam-4500	255	9	.	.	PUNCT
ejpam-4500	256	1	this	this	PRON
ejpam-4500	256	2	implies	imply	VERB
ejpam-4500	256	3	that	that	SCONJ
ejpam-4500	256	4	[	[	X
ejpam-4500	256	5	(	(	PUNCT
ejpam-4500	256	6	v	v	NOUN
ejpam-4500	256	7	(	(	PUNCT
ejpam-4500	256	8	hw	hw	NOUN
ejpam-4500	256	9	)	)	PUNCT
ejpam-4500	256	10	\	\	PROPN
ejpam-4500	256	11	nhw(q	nhw(q	PROPN
ejpam-4500	256	12	)	)	PUNCT
ejpam-4500	256	13	)	)	PUNCT
ejpam-4500	256	14	∩	∩	PROPN
ejpam-4500	256	15	dw	dw	X
ejpam-4500	256	16	]	]	X
ejpam-4500	256	17	̸=	̸=	PROPN
ejpam-4500	256	18	dw	dw	PROPN
ejpam-4500	256	19	,	,	PUNCT
ejpam-4500	256	20	that	that	ADV
ejpam-4500	256	21	is	is	ADV
ejpam-4500	256	22	,	,	PUNCT
ejpam-4500	256	23	nhw(q	nhw(q	PROPN
ejpam-4500	256	24	)	)	PUNCT
ejpam-4500	256	25	∩	∩	PROPN
ejpam-4500	256	26	dw	dw	PROPN
ejpam-4500	256	27	̸=	̸=	PROPN
ejpam-4500	256	28	∅.	∅.	ADP
ejpam-4500	256	29	this	this	DET
ejpam-4500	256	30	shows	show	VERB
ejpam-4500	256	31	that	that	SCONJ
ejpam-4500	256	32	dw	dw	PROPN
ejpam-4500	256	33	is	be	AUX
ejpam-4500	256	34	a	a	DET
ejpam-4500	256	35	dominating	dominating	NOUN
ejpam-4500	256	36	set	set	NOUN
ejpam-4500	256	37	of	of	ADP
ejpam-4500	256	38	hw	hw	PRON
ejpam-4500	256	39	.	.	PUNCT
ejpam-4500	257	1	finally	finally	ADV
ejpam-4500	257	2	,	,	PUNCT
ejpam-4500	257	3	let	let	VERB
ejpam-4500	257	4	v	v	ADP
ejpam-4500	257	5	,	,	PUNCT
ejpam-4500	257	6	w	w	PROPN
ejpam-4500	257	7	∈	∈	PROPN
ejpam-4500	257	8	v	v	ADP
ejpam-4500	257	9	(	(	PUNCT
ejpam-4500	257	10	g	g	NOUN
ejpam-4500	257	11	)	)	PUNCT
ejpam-4500	257	12	with	with	ADP
ejpam-4500	257	13	v	v	ADP
ejpam-4500	257	14	̸=	̸=	PROPN
ejpam-4500	257	15	w	w	NOUN
ejpam-4500	257	16	and	and	CCONJ
ejpam-4500	257	17	ng(w	ng(w	NOUN
ejpam-4500	257	18	)	)	PUNCT
ejpam-4500	257	19	∩	∩	NOUN
ejpam-4500	257	20	a	a	X
ejpam-4500	257	21	=	=	PUNCT
ejpam-4500	257	22	ng(v	ng(v	X
ejpam-4500	257	23	)	)	PUNCT
ejpam-4500	257	24	∩	∩	NOUN
ejpam-4500	257	25	a.	a.	NOUN
ejpam-4500	257	26	suppose	suppose	VERB
ejpam-4500	257	27	dv	dv	PROPN
ejpam-4500	257	28	and	and	CCONJ
ejpam-4500	257	29	dw	dw	PROPN
ejpam-4500	257	30	are	be	AUX
ejpam-4500	257	31	not	not	PART
ejpam-4500	257	32	strictly	strictly	ADV
ejpam-4500	257	33	locating	locate	VERB
ejpam-4500	257	34	sets	set	NOUN
ejpam-4500	257	35	of	of	ADP
ejpam-4500	257	36	hv	hv	PROPN
ejpam-4500	257	37	and	and	CCONJ
ejpam-4500	257	38	hw	hw	PROPN
ejpam-4500	257	39	,	,	PUNCT
ejpam-4500	257	40	respectively	respectively	ADV
ejpam-4500	257	41	.	.	PUNCT
ejpam-4500	258	1	then	then	ADV
ejpam-4500	258	2	there	there	PRON
ejpam-4500	258	3	exist	exist	VERB
ejpam-4500	258	4	x	x	SYM
ejpam-4500	258	5	∈	∈	PROPN
ejpam-4500	258	6	v	v	ADP
ejpam-4500	258	7	(	(	PUNCT
ejpam-4500	258	8	hv	hv	PROPN
ejpam-4500	258	9	)	)	PUNCT
ejpam-4500	258	10	\	\	PROPN
ejpam-4500	259	1	dv	dv	PROPN
ejpam-4500	259	2	and	and	CCONJ
ejpam-4500	259	3	y	y	PROPN
ejpam-4500	259	4	∈	∈	PROPN
ejpam-4500	259	5	v	v	ADP
ejpam-4500	259	6	(	(	PUNCT
ejpam-4500	259	7	hw	hw	NOUN
ejpam-4500	259	8	)	)	PUNCT
ejpam-4500	259	9	\	\	PROPN
ejpam-4500	260	1	dw	dw	PROPN
ejpam-4500	260	2	such	such	ADJ
ejpam-4500	260	3	that	that	SCONJ
ejpam-4500	260	4	nhv(x	nhv(x	PROPN
ejpam-4500	260	5	)	)	PUNCT
ejpam-4500	260	6	∩dv	∩dv	NOUN
ejpam-4500	260	7	=	=	SYM
ejpam-4500	260	8	dv	dv	PROPN
ejpam-4500	260	9	and	and	CCONJ
ejpam-4500	260	10	nhw(y	nhw(y	PROPN
ejpam-4500	260	11	)	)	PUNCT
ejpam-4500	260	12	∩dw	∩dw	PROPN
ejpam-4500	260	13	=	=	SYM
ejpam-4500	260	14	dw	dw	PROPN
ejpam-4500	260	15	.	.	PUNCT
ejpam-4500	261	1	it	it	PRON
ejpam-4500	261	2	follows	follow	VERB
ejpam-4500	261	3	that	that	SCONJ
ejpam-4500	261	4	[	[	X
ejpam-4500	261	5	v	v	X
ejpam-4500	261	6	(	(	PUNCT
ejpam-4500	261	7	hv	hv	NOUN
ejpam-4500	261	8	)	)	PUNCT
ejpam-4500	261	9	\nhv(x	\nhv(x	NOUN
ejpam-4500	261	10	)	)	PUNCT
ejpam-4500	261	11	]	]	PUNCT
ejpam-4500	261	12	∩dv	∩dv	NOUN
ejpam-4500	261	13	=	=	PUNCT
ejpam-4500	261	14	∅	∅	NOUN
ejpam-4500	261	15	and	and	CCONJ
ejpam-4500	261	16	[	[	X
ejpam-4500	261	17	v	v	X
ejpam-4500	261	18	(	(	PUNCT
ejpam-4500	261	19	hw	hw	NOUN
ejpam-4500	261	20	)	)	PUNCT
ejpam-4500	261	21	\nhw(y	\nhw(y	NOUN
ejpam-4500	261	22	)	)	PUNCT
ejpam-4500	261	23	]	]	PUNCT
ejpam-4500	261	24	∩dw	∩dw	PROPN
ejpam-4500	261	25	=	=	SYM
ejpam-4500	261	26	∅.	∅.	NOUN
ejpam-4500	261	27	this	this	PRON
ejpam-4500	261	28	would	would	AUX
ejpam-4500	261	29	imply	imply	VERB
ejpam-4500	261	30	that	that	PRON
ejpam-4500	261	31	ng	ng	PROPN
ejpam-4500	261	32	◦	◦	PROPN
ejpam-4500	261	33	h(x	h(x	PROPN
ejpam-4500	261	34	,	,	PUNCT
ejpam-4500	261	35	2	2	NUM
ejpam-4500	261	36	)	)	PUNCT
ejpam-4500	261	37	∩	∩	NOUN
ejpam-4500	261	38	s	s	PART
ejpam-4500	261	39	=	=	X
ejpam-4500	261	40	[	[	X
ejpam-4500	261	41	(	(	PUNCT
ejpam-4500	261	42	v	v	NOUN
ejpam-4500	261	43	(	(	PUNCT
ejpam-4500	261	44	hv	hv	NOUN
ejpam-4500	261	45	)	)	PUNCT
ejpam-4500	261	46	\nhv(x	\nhv(x	NOUN
ejpam-4500	261	47	)	)	PUNCT
ejpam-4500	261	48	)	)	PUNCT
ejpam-4500	261	49	∩dv	∩dv	NOUN
ejpam-4500	261	50	]	]	PUNCT
ejpam-4500	261	51	∪	∪	X
ejpam-4500	261	52	(	(	PUNCT
ejpam-4500	261	53	ng(v	ng(v	ADJ
ejpam-4500	261	54	)	)	PUNCT
ejpam-4500	261	55	∩a	∩a	NOUN
ejpam-4500	261	56	)	)	PUNCT
ejpam-4500	261	57	=	=	PUNCT
ejpam-4500	261	58	ng(v	ng(v	X
ejpam-4500	261	59	)	)	PUNCT
ejpam-4500	262	1	∩a	∩a	NOUN
ejpam-4500	262	2	=	=	PUNCT
ejpam-4500	262	3	ng(w	ng(w	PRON
ejpam-4500	262	4	)	)	PUNCT
ejpam-4500	262	5	∩a	∩a	NOUN
ejpam-4500	263	1	=	=	PUNCT
ejpam-4500	264	1	[	[	X
ejpam-4500	264	2	(	(	PUNCT
ejpam-4500	264	3	v	v	NOUN
ejpam-4500	264	4	(	(	PUNCT
ejpam-4500	264	5	hw	hw	NOUN
ejpam-4500	264	6	)	)	PUNCT
ejpam-4500	264	7	\nhw(y	\nhw(y	NOUN
ejpam-4500	264	8	)	)	PUNCT
ejpam-4500	264	9	)	)	PUNCT
ejpam-4500	264	10	∩dw	∩dw	VERB
ejpam-4500	264	11	]	]	PUNCT
ejpam-4500	264	12	∪	∪	X
ejpam-4500	264	13	(	(	PUNCT
ejpam-4500	264	14	ng(w	ng(w	NOUN
ejpam-4500	264	15	)	)	PUNCT
ejpam-4500	264	16	∩a	∩a	NOUN
ejpam-4500	264	17	)	)	PUNCT
ejpam-4500	265	1	=	=	SYM
ejpam-4500	265	2	ng	ng	PROPN
ejpam-4500	265	3	◦	◦	NOUN
ejpam-4500	265	4	h(y	h(y	ADV
ejpam-4500	265	5	,	,	PUNCT
ejpam-4500	265	6	2	2	X
ejpam-4500	265	7	)	)	PUNCT
ejpam-4500	265	8	∩	∩	NOUN
ejpam-4500	265	9	s	s	SYM
ejpam-4500	265	10	,	,	PUNCT
ejpam-4500	265	11	contrary	contrary	ADJ
ejpam-4500	265	12	to	to	ADP
ejpam-4500	265	13	the	the	DET
ejpam-4500	265	14	assumption	assumption	NOUN
ejpam-4500	265	15	that	that	SCONJ
ejpam-4500	265	16	s	s	VERB
ejpam-4500	265	17	is	be	AUX
ejpam-4500	265	18	a	a	DET
ejpam-4500	265	19	locating	locate	VERB
ejpam-4500	265	20	hop	hop	NOUN
ejpam-4500	265	21	set	set	NOUN
ejpam-4500	265	22	of	of	ADP
ejpam-4500	265	23	g	g	PROPN
ejpam-4500	265	24	◦	◦	NOUN
ejpam-4500	265	25	h.	h.	PROPN
ejpam-4500	265	26	thus	thus	ADV
ejpam-4500	265	27	,	,	PUNCT
ejpam-4500	265	28	(	(	PUNCT
ejpam-4500	265	29	iv	iv	X
ejpam-4500	265	30	)	)	PUNCT
ejpam-4500	265	31	holds	hold	NOUN
ejpam-4500	265	32	.	.	PUNCT
ejpam-4500	266	1	for	for	ADP
ejpam-4500	266	2	the	the	DET
ejpam-4500	266	3	converse	converse	NOUN
ejpam-4500	266	4	,	,	PUNCT
ejpam-4500	266	5	suppose	suppose	VERB
ejpam-4500	266	6	that	that	SCONJ
ejpam-4500	266	7	s	s	VERB
ejpam-4500	266	8	is	be	AUX
ejpam-4500	266	9	as	as	SCONJ
ejpam-4500	266	10	described	describe	VERB
ejpam-4500	266	11	and	and	CCONJ
ejpam-4500	266	12	satisfies	satisfie	NOUN
ejpam-4500	266	13	properties	property	NOUN
ejpam-4500	266	14	(	(	PUNCT
ejpam-4500	266	15	i)-(iv	i)-(iv	ADJ
ejpam-4500	266	16	)	)	PUNCT
ejpam-4500	266	17	.	.	PUNCT
ejpam-4500	267	1	let	let	VERB
ejpam-4500	267	2	a	a	DET
ejpam-4500	267	3	,	,	PUNCT
ejpam-4500	267	4	b	b	PROPN
ejpam-4500	267	5	∈	∈	PROPN
ejpam-4500	267	6	v	v	NOUN
ejpam-4500	267	7	(	(	PUNCT
ejpam-4500	267	8	g	g	PROPN
ejpam-4500	267	9	◦	◦	NOUN
ejpam-4500	267	10	h	h	NOUN
ejpam-4500	267	11	)	)	PUNCT
ejpam-4500	267	12	\	\	PROPN
ejpam-4500	268	1	s	s	PART
ejpam-4500	268	2	with	with	ADP
ejpam-4500	268	3	a	a	DET
ejpam-4500	268	4	̸=	̸=	PROPN
ejpam-4500	268	5	b	b	PROPN
ejpam-4500	268	6	and	and	CCONJ
ejpam-4500	268	7	let	let	VERB
ejpam-4500	268	8	v	v	NOUN
ejpam-4500	268	9	,	,	PUNCT
ejpam-4500	268	10	w	w	PROPN
ejpam-4500	268	11	∈	∈	PROPN
ejpam-4500	268	12	v	v	ADP
ejpam-4500	268	13	(	(	PUNCT
ejpam-4500	268	14	g	g	NOUN
ejpam-4500	268	15	)	)	PUNCT
ejpam-4500	268	16	such	such	ADJ
ejpam-4500	268	17	that	that	SCONJ
ejpam-4500	268	18	a	a	DET
ejpam-4500	268	19	∈	∈	PROPN
ejpam-4500	268	20	v	v	NOUN
ejpam-4500	268	21	(	(	PUNCT
ejpam-4500	268	22	v	v	NOUN
ejpam-4500	268	23	+	+	CCONJ
ejpam-4500	268	24	hv	hv	NOUN
ejpam-4500	268	25	)	)	PUNCT
ejpam-4500	268	26	and	and	CCONJ
ejpam-4500	268	27	b	b	X
ejpam-4500	268	28	∈	∈	PROPN
ejpam-4500	268	29	v	v	NOUN
ejpam-4500	268	30	(	(	PUNCT
ejpam-4500	268	31	w	w	NOUN
ejpam-4500	268	32	+	+	NOUN
ejpam-4500	268	33	hw	hw	NOUN
ejpam-4500	268	34	)	)	PUNCT
ejpam-4500	268	35	.	.	PUNCT
ejpam-4500	269	1	consider	consider	VERB
ejpam-4500	269	2	the	the	DET
ejpam-4500	269	3	following	follow	VERB
ejpam-4500	269	4	cases	case	NOUN
ejpam-4500	269	5	:	:	PUNCT
ejpam-4500	269	6	case	case	NOUN
ejpam-4500	269	7	1	1	NUM
ejpam-4500	269	8	:	:	SYM
ejpam-4500	269	9	v	v	NOUN
ejpam-4500	269	10	=	=	PUNCT
ejpam-4500	269	11	w.	w.	PROPN
ejpam-4500	269	12	suppose	suppose	VERB
ejpam-4500	269	13	a	a	PRON
ejpam-4500	269	14	,	,	PUNCT
ejpam-4500	269	15	b	b	PROPN
ejpam-4500	269	16	∈	∈	PROPN
ejpam-4500	269	17	v	v	ADP
ejpam-4500	269	18	(	(	PUNCT
ejpam-4500	269	19	hv	hv	PROPN
ejpam-4500	269	20	)	)	PUNCT
ejpam-4500	269	21	\dv	\dv	PROPN
ejpam-4500	269	22	.	.	PUNCT
ejpam-4500	270	1	by	by	ADP
ejpam-4500	270	2	(	(	PUNCT
ejpam-4500	270	3	ii	ii	NOUN
ejpam-4500	270	4	)	)	PUNCT
ejpam-4500	270	5	,	,	PUNCT
ejpam-4500	270	6	ng	ng	PROPN
ejpam-4500	270	7	◦	◦	PROPN
ejpam-4500	270	8	h(a	h(a	PROPN
ejpam-4500	270	9	,	,	PUNCT
ejpam-4500	270	10	2	2	NUM
ejpam-4500	270	11	)	)	PUNCT
ejpam-4500	270	12	∩	∩	NOUN
ejpam-4500	270	13	s	s	PART
ejpam-4500	270	14	̸=	̸=	PROPN
ejpam-4500	270	15	ng	ng	PROPN
ejpam-4500	270	16	◦	◦	PROPN
ejpam-4500	270	17	h(b	h(b	PROPN
ejpam-4500	270	18	,	,	PUNCT
ejpam-4500	270	19	2	2	NUM
ejpam-4500	270	20	)	)	PUNCT
ejpam-4500	270	21	∩	∩	NOUN
ejpam-4500	270	22	s.	s.	PROPN
ejpam-4500	270	23	suppose	suppose	VERB
ejpam-4500	270	24	a	a	DET
ejpam-4500	270	25	=	=	X
ejpam-4500	270	26	v	v	NOUN
ejpam-4500	270	27	and	and	CCONJ
ejpam-4500	270	28	b	b	NOUN
ejpam-4500	270	29	∈	∈	PROPN
ejpam-4500	270	30	v	v	ADP
ejpam-4500	270	31	(	(	PUNCT
ejpam-4500	270	32	hv	hv	PROPN
ejpam-4500	270	33	)	)	PUNCT
ejpam-4500	270	34	\dv	\dv	PROPN
ejpam-4500	270	35	.	.	PUNCT
ejpam-4500	271	1	pick	pick	VERB
ejpam-4500	271	2	any	any	DET
ejpam-4500	271	3	z	z	NOUN
ejpam-4500	271	4	∈	∈	PROPN
ejpam-4500	271	5	ng(v	ng(v	NOUN
ejpam-4500	271	6	)	)	PUNCT
ejpam-4500	271	7	.	.	PUNCT
ejpam-4500	272	1	since	since	SCONJ
ejpam-4500	272	2	dz	dz	PROPN
ejpam-4500	272	3	⊆	⊆	NUM
ejpam-4500	272	4	ng	ng	PROPN
ejpam-4500	272	5	◦	◦	PROPN
ejpam-4500	272	6	h(a	h(a	PROPN
ejpam-4500	272	7	,	,	PUNCT
ejpam-4500	272	8	2	2	NUM
ejpam-4500	272	9	)	)	PUNCT
ejpam-4500	272	10	\ng	\ng	PROPN
ejpam-4500	272	11	◦	◦	NOUN
ejpam-4500	272	12	h(b	h(b	PROPN
ejpam-4500	272	13	,	,	PUNCT
ejpam-4500	272	14	2	2	NUM
ejpam-4500	272	15	)	)	PUNCT
ejpam-4500	272	16	,	,	PUNCT
ejpam-4500	272	17	it	it	PRON
ejpam-4500	272	18	follows	follow	VERB
ejpam-4500	272	19	that	that	SCONJ
ejpam-4500	272	20	ng	ng	PROPN
ejpam-4500	272	21	◦	◦	PROPN
ejpam-4500	272	22	h(a	h(a	PROPN
ejpam-4500	272	23	,	,	PUNCT
ejpam-4500	272	24	2	2	NUM
ejpam-4500	272	25	)	)	PUNCT
ejpam-4500	272	26	∩	∩	NOUN
ejpam-4500	272	27	s	s	PART
ejpam-4500	272	28	̸=	̸=	PROPN
ejpam-4500	272	29	ng	ng	PROPN
ejpam-4500	272	30	◦	◦	PROPN
ejpam-4500	272	31	h(b	h(b	PROPN
ejpam-4500	272	32	,	,	PUNCT
ejpam-4500	272	33	2	2	NUM
ejpam-4500	272	34	)	)	PUNCT
ejpam-4500	272	35	∩	∩	ADJ
ejpam-4500	272	36	s.	s.	PROPN
ejpam-4500	272	37	case	case	NOUN
ejpam-4500	272	38	2	2	NUM
ejpam-4500	272	39	:	:	PUNCT
ejpam-4500	272	40	v	v	ADP
ejpam-4500	272	41	̸=	̸=	PROPN
ejpam-4500	272	42	w.	w.	NOUN
ejpam-4500	272	43	suppose	suppose	VERB
ejpam-4500	272	44	a	a	DET
ejpam-4500	272	45	=	=	X
ejpam-4500	272	46	v	v	NOUN
ejpam-4500	272	47	and	and	CCONJ
ejpam-4500	272	48	b	b	NOUN
ejpam-4500	272	49	=	=	SYM
ejpam-4500	272	50	w.	w.	PROPN
ejpam-4500	272	51	then	then	ADV
ejpam-4500	272	52	v	v	NOUN
ejpam-4500	272	53	,	,	PUNCT
ejpam-4500	272	54	w	w	PROPN
ejpam-4500	272	55	∈	∈	PROPN
ejpam-4500	272	56	v	v	ADP
ejpam-4500	272	57	(	(	PUNCT
ejpam-4500	272	58	g	g	NOUN
ejpam-4500	272	59	)	)	PUNCT
ejpam-4500	272	60	\	\	NOUN
ejpam-4500	272	61	a.	a.	NOUN
ejpam-4500	272	62	by	by	ADP
ejpam-4500	272	63	property	property	NOUN
ejpam-4500	272	64	(	(	PUNCT
ejpam-4500	272	65	i	i	NOUN
ejpam-4500	272	66	)	)	PUNCT
ejpam-4500	272	67	,	,	PUNCT
ejpam-4500	272	68	ng(v	ng(v	PUNCT
ejpam-4500	272	69	)	)	PUNCT
ejpam-4500	272	70	̸=	̸=	PROPN
ejpam-4500	272	71	ng(w	ng(w	NOUN
ejpam-4500	272	72	)	)	PUNCT
ejpam-4500	272	73	or	or	CCONJ
ejpam-4500	272	74	ng(v	ng(v	PUNCT
ejpam-4500	272	75	,	,	PUNCT
ejpam-4500	272	76	2	2	X
ejpam-4500	272	77	)	)	PUNCT
ejpam-4500	272	78	∩	∩	NOUN
ejpam-4500	272	79	a	a	DET
ejpam-4500	272	80	̸=	̸=	PROPN
ejpam-4500	272	81	ng(w	ng(w	NOUN
ejpam-4500	272	82	,	,	PUNCT
ejpam-4500	272	83	2	2	X
ejpam-4500	272	84	)	)	PUNCT
ejpam-4500	272	85	∩	∩	ADJ
ejpam-4500	272	86	a.	a.	NOUN
ejpam-4500	272	87	if	if	SCONJ
ejpam-4500	272	88	ng(v	ng(v	NOUN
ejpam-4500	272	89	,	,	PUNCT
ejpam-4500	272	90	2	2	X
ejpam-4500	272	91	)	)	PUNCT
ejpam-4500	272	92	∩	∩	NOUN
ejpam-4500	272	93	a	a	DET
ejpam-4500	272	94	̸=	̸=	PROPN
ejpam-4500	272	95	ng(w	ng(w	NOUN
ejpam-4500	272	96	,	,	PUNCT
ejpam-4500	272	97	2	2	X
ejpam-4500	272	98	)	)	PUNCT
ejpam-4500	272	99	∩	∩	NOUN
ejpam-4500	272	100	a	a	X
ejpam-4500	272	101	,	,	PUNCT
ejpam-4500	272	102	then	then	ADV
ejpam-4500	272	103	ng	ng	PROPN
ejpam-4500	272	104	◦	◦	PROPN
ejpam-4500	272	105	h(a	h(a	PROPN
ejpam-4500	272	106	,	,	PUNCT
ejpam-4500	272	107	2	2	NUM
ejpam-4500	272	108	)	)	PUNCT
ejpam-4500	272	109	∩	∩	NOUN
ejpam-4500	272	110	s	s	PART
ejpam-4500	272	111	̸=	̸=	PROPN
ejpam-4500	272	112	ng	ng	PROPN
ejpam-4500	272	113	◦	◦	PROPN
ejpam-4500	272	114	h(b	h(b	PROPN
ejpam-4500	272	115	,	,	PUNCT
ejpam-4500	272	116	2	2	NUM
ejpam-4500	272	117	)	)	PUNCT
ejpam-4500	272	118	∩	∩	NOUN
ejpam-4500	272	119	s.	s.	PROPN
ejpam-4500	272	120	suppose	suppose	VERB
ejpam-4500	272	121	ng(v	ng(v	NOUN
ejpam-4500	272	122	)	)	PUNCT
ejpam-4500	272	123	̸=	̸=	PROPN
ejpam-4500	272	124	ng(w	ng(w	NOUN
ejpam-4500	272	125	)	)	PUNCT
ejpam-4500	272	126	.	.	PUNCT
ejpam-4500	273	1	we	we	PRON
ejpam-4500	273	2	may	may	AUX
ejpam-4500	273	3	assume	assume	VERB
ejpam-4500	273	4	that	that	SCONJ
ejpam-4500	273	5	there	there	PRON
ejpam-4500	273	6	exists	exist	VERB
ejpam-4500	273	7	p	p	PROPN
ejpam-4500	273	8	∈	∈	PROPN
ejpam-4500	273	9	ng(v	ng(v	NOUN
ejpam-4500	273	10	)	)	PUNCT
ejpam-4500	273	11	\	\	NOUN
ejpam-4500	273	12	ng(w	ng(w	NOUN
ejpam-4500	273	13	)	)	PUNCT
ejpam-4500	273	14	.	.	PUNCT
ejpam-4500	274	1	then	then	ADV
ejpam-4500	274	2	dp	dp	VERB
ejpam-4500	274	3	⊆	⊆	NUM
ejpam-4500	274	4	ng	ng	PROPN
ejpam-4500	274	5	◦	◦	PROPN
ejpam-4500	274	6	h(a	h(a	PROPN
ejpam-4500	274	7	,	,	PUNCT
ejpam-4500	274	8	2	2	NUM
ejpam-4500	274	9	)	)	PUNCT
ejpam-4500	274	10	\ng	\ng	PROPN
ejpam-4500	274	11	◦	◦	NOUN
ejpam-4500	274	12	h(b	h(b	PROPN
ejpam-4500	274	13	,	,	PUNCT
ejpam-4500	274	14	2	2	NUM
ejpam-4500	274	15	)	)	PUNCT
ejpam-4500	274	16	.	.	PUNCT
ejpam-4500	275	1	hence	hence	ADV
ejpam-4500	275	2	,	,	PUNCT
ejpam-4500	275	3	ng	ng	PROPN
ejpam-4500	275	4	◦	◦	PROPN
ejpam-4500	275	5	h(a	h(a	PROPN
ejpam-4500	275	6	,	,	PUNCT
ejpam-4500	275	7	2	2	NUM
ejpam-4500	275	8	)	)	PUNCT
ejpam-4500	275	9	∩	∩	NOUN
ejpam-4500	275	10	s	s	PART
ejpam-4500	275	11	̸=	̸=	PROPN
ejpam-4500	275	12	ng	ng	PROPN
ejpam-4500	275	13	◦	◦	PROPN
ejpam-4500	275	14	h(b	h(b	PROPN
ejpam-4500	275	15	,	,	PUNCT
ejpam-4500	275	16	2	2	NUM
ejpam-4500	275	17	)	)	PUNCT
ejpam-4500	275	18	∩	∩	NOUN
ejpam-4500	275	19	s.	s.	PROPN
ejpam-4500	275	20	next	next	ADV
ejpam-4500	275	21	,	,	PUNCT
ejpam-4500	275	22	suppose	suppose	VERB
ejpam-4500	275	23	that	that	SCONJ
ejpam-4500	275	24	a	a	DET
ejpam-4500	275	25	=	=	SYM
ejpam-4500	275	26	v	v	NOUN
ejpam-4500	275	27	and	and	CCONJ
ejpam-4500	275	28	b	b	NOUN
ejpam-4500	275	29	∈	∈	PROPN
ejpam-4500	275	30	v	v	NOUN
ejpam-4500	275	31	(	(	PUNCT
ejpam-4500	275	32	hw	hw	NOUN
ejpam-4500	275	33	)	)	PUNCT
ejpam-4500	275	34	\	\	PROPN
ejpam-4500	275	35	dw	dw	PROPN
ejpam-4500	275	36	(	(	PUNCT
ejpam-4500	275	37	or	or	CCONJ
ejpam-4500	275	38	b	b	X
ejpam-4500	275	39	=	=	SYM
ejpam-4500	275	40	w	w	PROPN
ejpam-4500	275	41	and	and	CCONJ
ejpam-4500	275	42	a	a	DET
ejpam-4500	275	43	∈	∈	PROPN
ejpam-4500	275	44	v	v	ADP
ejpam-4500	275	45	(	(	PUNCT
ejpam-4500	275	46	hv	hv	PROPN
ejpam-4500	275	47	)	)	PUNCT
ejpam-4500	275	48	\	\	PROPN
ejpam-4500	275	49	dv	dv	PROPN
ejpam-4500	275	50	)	)	PUNCT
ejpam-4500	275	51	.	.	PUNCT
ejpam-4500	276	1	if	if	SCONJ
ejpam-4500	276	2	|ng(v)|	|ng(v)|	PROPN
ejpam-4500	276	3	>	>	X
ejpam-4500	276	4	1	1	NUM
ejpam-4500	276	5	or	or	CCONJ
ejpam-4500	276	6	vw	vw	PRON
ejpam-4500	276	7	/∈	/∈	PUNCT
ejpam-4500	276	8	e(g	e(g	PROPN
ejpam-4500	276	9	)	)	PUNCT
ejpam-4500	276	10	,	,	PUNCT
ejpam-4500	276	11	pick	pick	VERB
ejpam-4500	276	12	any	any	DET
ejpam-4500	276	13	z	z	NOUN
ejpam-4500	276	14	∈	∈	PROPN
ejpam-4500	276	15	ng(v)\{w	ng(v)\{w	NOUN
ejpam-4500	276	16	}	}	PUNCT
ejpam-4500	276	17	.	.	PUNCT
ejpam-4500	277	1	then	then	ADV
ejpam-4500	277	2	dz	dz	PROPN
ejpam-4500	277	3	⊆	⊆	NUM
ejpam-4500	277	4	ng	ng	PROPN
ejpam-4500	277	5	◦	◦	PROPN
ejpam-4500	277	6	h(a	h(a	PROPN
ejpam-4500	277	7	,	,	PUNCT
ejpam-4500	277	8	2)\ng	2)\ng	NUM
ejpam-4500	277	9	◦	◦	NOUN
ejpam-4500	277	10	h(b	h(b	PROPN
ejpam-4500	277	11	,	,	PUNCT
ejpam-4500	277	12	2	2	NUM
ejpam-4500	277	13	)	)	PUNCT
ejpam-4500	277	14	.	.	PUNCT
ejpam-4500	278	1	it	it	PRON
ejpam-4500	278	2	follows	follow	VERB
ejpam-4500	278	3	that	that	SCONJ
ejpam-4500	278	4	ng	ng	PROPN
ejpam-4500	278	5	◦	◦	PROPN
ejpam-4500	278	6	h(a	h(a	PROPN
ejpam-4500	278	7	,	,	PUNCT
ejpam-4500	278	8	2)∩s	2)∩s	PROPN
ejpam-4500	278	9	̸=	̸=	PROPN
ejpam-4500	278	10	ng	ng	PROPN
ejpam-4500	278	11	◦	◦	PROPN
ejpam-4500	278	12	h(b	h(b	PROPN
ejpam-4500	278	13	,	,	PUNCT
ejpam-4500	278	14	2)∩s	2)∩s	PROPN
ejpam-4500	278	15	.	.	PUNCT
ejpam-4500	279	1	suppose	suppose	VERB
ejpam-4500	279	2	that	that	SCONJ
ejpam-4500	279	3	ng(v	ng(v	NOUN
ejpam-4500	279	4	)	)	PUNCT
ejpam-4500	279	5	=	=	SYM
ejpam-4500	279	6	{	{	PUNCT
ejpam-4500	279	7	w	w	NOUN
ejpam-4500	279	8	}	}	PUNCT
ejpam-4500	279	9	.	.	PUNCT
ejpam-4500	280	1	then	then	ADV
ejpam-4500	280	2	dw	dw	PROPN
ejpam-4500	280	3	is	be	AUX
ejpam-4500	280	4	a	a	DET
ejpam-4500	280	5	dominating	dominating	NOUN
ejpam-4500	280	6	set	set	VERB
ejpam-4500	280	7	by	by	ADP
ejpam-4500	280	8	(	(	PUNCT
ejpam-4500	280	9	iii	iii	NOUN
ejpam-4500	280	10	)	)	PUNCT
ejpam-4500	280	11	.	.	PUNCT
ejpam-4500	281	1	hence	hence	ADV
ejpam-4500	281	2	,	,	PUNCT
ejpam-4500	281	3	[	[	X
ejpam-4500	281	4	(	(	PUNCT
ejpam-4500	281	5	v	v	NOUN
ejpam-4500	281	6	(	(	PUNCT
ejpam-4500	281	7	hw	hw	NOUN
ejpam-4500	281	8	)	)	PUNCT
ejpam-4500	281	9	\nhw(b	\nhw(b	NOUN
ejpam-4500	281	10	)	)	PUNCT
ejpam-4500	281	11	)	)	PUNCT
ejpam-4500	281	12	∩dw	∩dw	VERB
ejpam-4500	281	13	]	]	PUNCT
ejpam-4500	281	14	̸=	̸=	PROPN
ejpam-4500	281	15	dw	dw	PROPN
ejpam-4500	281	16	.	.	PUNCT
ejpam-4500	282	1	this	this	PRON
ejpam-4500	282	2	implies	imply	VERB
ejpam-4500	282	3	that	that	SCONJ
ejpam-4500	282	4	ng	ng	PROPN
ejpam-4500	282	5	◦	◦	PROPN
ejpam-4500	282	6	h(a	h(a	PROPN
ejpam-4500	282	7	,	,	PUNCT
ejpam-4500	282	8	2	2	NUM
ejpam-4500	282	9	)	)	PUNCT
ejpam-4500	282	10	∩	∩	NOUN
ejpam-4500	282	11	s	s	PART
ejpam-4500	282	12	=	=	PUNCT
ejpam-4500	282	13	dw	dw	X
ejpam-4500	282	14	∪	∪	X
ejpam-4500	282	15	(	(	PUNCT
ejpam-4500	282	16	ng(w	ng(w	NOUN
ejpam-4500	282	17	)	)	PUNCT
ejpam-4500	282	18	∩a	∩a	PROPN
ejpam-4500	282	19	)	)	PUNCT
ejpam-4500	283	1	̸=	̸=	PROPN
ejpam-4500	283	2	[	[	X
ejpam-4500	283	3	(	(	PUNCT
ejpam-4500	283	4	v	v	NOUN
ejpam-4500	283	5	(	(	PUNCT
ejpam-4500	283	6	hw	hw	NOUN
ejpam-4500	283	7	)	)	PUNCT
ejpam-4500	283	8	\nhw(b	\nhw(b	NOUN
ejpam-4500	283	9	)	)	PUNCT
ejpam-4500	283	10	)	)	PUNCT
ejpam-4500	283	11	∩dw	∩dw	VERB
ejpam-4500	283	12	]	]	PUNCT
ejpam-4500	283	13	∪	∪	X
ejpam-4500	283	14	(	(	PUNCT
ejpam-4500	283	15	ng(w	ng(w	NOUN
ejpam-4500	283	16	)	)	PUNCT
ejpam-4500	283	17	∩a	∩a	NOUN
ejpam-4500	283	18	)	)	PUNCT
ejpam-4500	284	1	=	=	SYM
ejpam-4500	284	2	ng	ng	PROPN
ejpam-4500	284	3	◦	◦	PROPN
ejpam-4500	284	4	h(b	h(b	PROPN
ejpam-4500	284	5	,	,	PUNCT
ejpam-4500	284	6	2	2	NUM
ejpam-4500	284	7	)	)	PUNCT
ejpam-4500	284	8	∩	∩	NOUN
ejpam-4500	284	9	s.	s.	PROPN
ejpam-4500	284	10	finally	finally	ADV
ejpam-4500	284	11	,	,	PUNCT
ejpam-4500	284	12	suppose	suppose	VERB
ejpam-4500	284	13	that	that	SCONJ
ejpam-4500	284	14	a	a	DET
ejpam-4500	284	15	∈	∈	PROPN
ejpam-4500	284	16	v	v	NOUN
ejpam-4500	284	17	(	(	PUNCT
ejpam-4500	284	18	hv)\dv	hv)\dv	NOUN
ejpam-4500	284	19	and	and	CCONJ
ejpam-4500	284	20	b	b	PROPN
ejpam-4500	284	21	∈	∈	PROPN
ejpam-4500	284	22	v	v	NOUN
ejpam-4500	284	23	(	(	PUNCT
ejpam-4500	284	24	hw)\dw	hw)\dw	INTJ
ejpam-4500	284	25	.	.	PUNCT
ejpam-4500	285	1	if	if	SCONJ
ejpam-4500	285	2	[	[	X
ejpam-4500	285	3	v	v	X
ejpam-4500	285	4	(	(	PUNCT
ejpam-4500	285	5	hv)\nhv(a)]∩dv	hv)\nhv(a)]∩dv	NOUN
ejpam-4500	285	6	̸=	̸=	PROPN
ejpam-4500	285	7	∅	∅	NOUN
ejpam-4500	285	8	and	and	CCONJ
ejpam-4500	285	9	[	[	X
ejpam-4500	285	10	v	v	X
ejpam-4500	285	11	(	(	PUNCT
ejpam-4500	285	12	hw	hw	NOUN
ejpam-4500	285	13	)	)	PUNCT
ejpam-4500	285	14	\	\	PROPN
ejpam-4500	285	15	nhw(b	nhw(b	PROPN
ejpam-4500	285	16	)	)	PUNCT
ejpam-4500	285	17	]	]	PUNCT
ejpam-4500	285	18	∩	∩	PROPN
ejpam-4500	285	19	dw	dw	PROPN
ejpam-4500	285	20	̸=	̸=	PROPN
ejpam-4500	285	21	∅	∅	NOUN
ejpam-4500	285	22	,	,	PUNCT
ejpam-4500	285	23	then	then	ADV
ejpam-4500	285	24	ng	ng	PROPN
ejpam-4500	285	25	◦	◦	PROPN
ejpam-4500	285	26	h(a	h(a	PROPN
ejpam-4500	285	27	,	,	PUNCT
ejpam-4500	285	28	2	2	NUM
ejpam-4500	285	29	)	)	PUNCT
ejpam-4500	285	30	∩	∩	NOUN
ejpam-4500	285	31	s	s	PART
ejpam-4500	285	32	̸=	̸=	PROPN
ejpam-4500	285	33	ng	ng	PROPN
ejpam-4500	285	34	◦	◦	PROPN
ejpam-4500	285	35	h(b	h(b	PROPN
ejpam-4500	285	36	,	,	PUNCT
ejpam-4500	285	37	2	2	NUM
ejpam-4500	285	38	)	)	PUNCT
ejpam-4500	285	39	∩	∩	NOUN
ejpam-4500	285	40	s.	s.	PROPN
ejpam-4500	285	41	suppose	suppose	VERB
ejpam-4500	285	42	one	one	NUM
ejpam-4500	285	43	,	,	PUNCT
ejpam-4500	285	44	say	say	VERB
ejpam-4500	285	45	[	[	X
ejpam-4500	285	46	v	v	X
ejpam-4500	285	47	(	(	PUNCT
ejpam-4500	285	48	hv	hv	NOUN
ejpam-4500	285	49	)	)	PUNCT
ejpam-4500	285	50	\	\	PUNCT
ejpam-4500	286	1	nhw(a	nhw(a	PROPN
ejpam-4500	286	2	)	)	PUNCT
ejpam-4500	286	3	]	]	PUNCT
ejpam-4500	287	1	∩	∩	PROPN
ejpam-4500	287	2	dv	dv	PROPN
ejpam-4500	287	3	=	=	PROPN
ejpam-4500	287	4	∅.	∅.	PROPN
ejpam-4500	287	5	if	if	SCONJ
ejpam-4500	287	6	ng(v	ng(v	NOUN
ejpam-4500	287	7	)	)	PUNCT
ejpam-4500	287	8	∩	∩	NOUN
ejpam-4500	287	9	a	a	DET
ejpam-4500	287	10	̸=	̸=	PROPN
ejpam-4500	287	11	ng(w	ng(w	NOUN
ejpam-4500	287	12	)	)	PUNCT
ejpam-4500	287	13	∩	∩	NOUN
ejpam-4500	287	14	a	a	X
ejpam-4500	287	15	,	,	PUNCT
ejpam-4500	287	16	then	then	ADV
ejpam-4500	287	17	ng	ng	PROPN
ejpam-4500	287	18	◦	◦	PROPN
ejpam-4500	287	19	h(a	h(a	PROPN
ejpam-4500	287	20	,	,	PUNCT
ejpam-4500	287	21	2	2	NUM
ejpam-4500	287	22	)	)	PUNCT
ejpam-4500	287	23	∩	∩	NOUN
ejpam-4500	287	24	s	s	PART
ejpam-4500	287	25	̸=	̸=	PROPN
ejpam-4500	287	26	ng	ng	PROPN
ejpam-4500	287	27	◦	◦	PROPN
ejpam-4500	287	28	h(b	h(b	PROPN
ejpam-4500	287	29	,	,	PUNCT
ejpam-4500	287	30	2	2	NUM
ejpam-4500	287	31	)	)	PUNCT
ejpam-4500	287	32	∩	∩	NOUN
ejpam-4500	287	33	s.	s.	PROPN
ejpam-4500	287	34	if	if	SCONJ
ejpam-4500	287	35	ng(v	ng(v	NOUN
ejpam-4500	287	36	)	)	PUNCT
ejpam-4500	287	37	∩	∩	NOUN
ejpam-4500	287	38	a	a	PRON
ejpam-4500	287	39	=	=	NOUN
ejpam-4500	287	40	ng(w	ng(w	NOUN
ejpam-4500	287	41	)	)	PUNCT
ejpam-4500	287	42	∩	∩	NOUN
ejpam-4500	287	43	a	a	X
ejpam-4500	287	44	,	,	PUNCT
ejpam-4500	287	45	then	then	ADV
ejpam-4500	287	46	[	[	X
ejpam-4500	287	47	v	v	X
ejpam-4500	287	48	(	(	PUNCT
ejpam-4500	287	49	hw	hw	NOUN
ejpam-4500	287	50	)	)	PUNCT
ejpam-4500	287	51	\	\	PROPN
ejpam-4500	287	52	nhw(b	nhw(b	PROPN
ejpam-4500	287	53	)	)	PUNCT
ejpam-4500	287	54	]	]	PUNCT
ejpam-4500	288	1	∩	∩	PROPN
ejpam-4500	288	2	dw	dw	PROPN
ejpam-4500	288	3	̸=	̸=	PROPN
ejpam-4500	288	4	∅	∅	NOUN
ejpam-4500	288	5	by	by	ADP
ejpam-4500	288	6	(	(	PUNCT
ejpam-4500	288	7	iv	iv	NOUN
ejpam-4500	288	8	)	)	PUNCT
ejpam-4500	288	9	.	.	PUNCT
ejpam-4500	289	1	thus	thus	ADV
ejpam-4500	289	2	,	,	PUNCT
ejpam-4500	289	3	ng	ng	PROPN
ejpam-4500	289	4	◦	◦	PROPN
ejpam-4500	289	5	h(a	h(a	PROPN
ejpam-4500	289	6	,	,	PUNCT
ejpam-4500	289	7	2	2	NUM
ejpam-4500	289	8	)	)	PUNCT
ejpam-4500	289	9	∩	∩	NOUN
ejpam-4500	289	10	s	s	PART
ejpam-4500	289	11	̸=	̸=	PROPN
ejpam-4500	289	12	ng	ng	PROPN
ejpam-4500	289	13	◦	◦	PROPN
ejpam-4500	289	14	h(b	h(b	PROPN
ejpam-4500	289	15	,	,	PUNCT
ejpam-4500	289	16	2	2	NUM
ejpam-4500	289	17	)	)	PUNCT
ejpam-4500	289	18	∩	∩	NOUN
ejpam-4500	289	19	s.	s.	PROPN
ejpam-4500	289	20	accordingly	accordingly	ADV
ejpam-4500	289	21	,	,	PUNCT
ejpam-4500	289	22	s	s	VERB
ejpam-4500	289	23	is	be	AUX
ejpam-4500	289	24	a	a	DET
ejpam-4500	289	25	locating	locate	VERB
ejpam-4500	289	26	hop	hop	NOUN
ejpam-4500	289	27	set	set	NOUN
ejpam-4500	289	28	of	of	ADP
ejpam-4500	289	29	g	g	PROPN
ejpam-4500	289	30	◦	◦	NOUN
ejpam-4500	289	31	h.	h.	NOUN
ejpam-4500	289	32	□	□	PUNCT
ejpam-4500	289	33	the	the	DET
ejpam-4500	289	34	next	next	ADJ
ejpam-4500	289	35	result	result	NOUN
ejpam-4500	289	36	is	be	AUX
ejpam-4500	289	37	an	an	DET
ejpam-4500	289	38	immediate	immediate	ADJ
ejpam-4500	289	39	consequence	consequence	NOUN
ejpam-4500	289	40	of	of	ADP
ejpam-4500	289	41	theorem	theorem	NOUN
ejpam-4500	289	42	5	5	NUM
ejpam-4500	289	43	.	.	PUNCT
ejpam-4500	289	44	e.m	e.m	PROPN
ejpam-4500	289	45	.	.	PROPN
ejpam-4500	289	46	a.	a.	NOUN
ejpam-4500	289	47	pagcu	pagcu	PROPN
ejpam-4500	289	48	,	,	PUNCT
ejpam-4500	289	49	g.	g.	PROPN
ejpam-4500	289	50	a.	a.	NOUN
ejpam-4500	289	51	malacas	malacas	PROPN
ejpam-4500	289	52	,	,	PUNCT
ejpam-4500	289	53	s.	s.	PROPN
ejpam-4500	289	54	r.	r.	PROPN
ejpam-4500	289	55	canoy	canoy	PROPN
ejpam-4500	289	56	,	,	PUNCT
ejpam-4500	289	57	jr	jr	PROPN
ejpam-4500	289	58	.	.	PROPN
ejpam-4500	289	59	/	/	SYM
ejpam-4500	289	60	eur	eur	PROPN
ejpam-4500	289	61	.	.	PUNCT
ejpam-4500	290	1	j.	j.	PROPN
ejpam-4500	290	2	pure	pure	PROPN
ejpam-4500	290	3	appl	appl	PROPN
ejpam-4500	290	4	.	.	PROPN
ejpam-4500	290	5	math	math	PROPN
ejpam-4500	290	6	,	,	PUNCT
ejpam-4500	290	7	15	15	NUM
ejpam-4500	290	8	(	(	PUNCT
ejpam-4500	290	9	4	4	NUM
ejpam-4500	290	10	)	)	PUNCT
ejpam-4500	290	11	(	(	PUNCT
ejpam-4500	290	12	2022	2022	NUM
ejpam-4500	290	13	)	)	PUNCT
ejpam-4500	290	14	,	,	PUNCT
ejpam-4500	290	15	1705	1705	NUM
ejpam-4500	290	16	-	-	SYM
ejpam-4500	290	17	1715	1715	NUM
ejpam-4500	290	18	1713	1713	NUM
ejpam-4500	290	19	corollary	corollary	NOUN
ejpam-4500	290	20	5	5	NUM
ejpam-4500	290	21	.	.	PUNCT
ejpam-4500	291	1	let	let	VERB
ejpam-4500	291	2	g	g	PRON
ejpam-4500	291	3	be	be	AUX
ejpam-4500	291	4	a	a	DET
ejpam-4500	291	5	non	non	ADJ
ejpam-4500	291	6	-	-	ADJ
ejpam-4500	291	7	trivial	trivial	ADJ
ejpam-4500	291	8	connected	connected	ADJ
ejpam-4500	291	9	graph	graph	NOUN
ejpam-4500	291	10	of	of	ADP
ejpam-4500	291	11	order	order	NOUN
ejpam-4500	291	12	m	m	VERB
ejpam-4500	291	13	and	and	CCONJ
ejpam-4500	291	14	let	let	VERB
ejpam-4500	291	15	h	h	NOUN
ejpam-4500	291	16	be	be	AUX
ejpam-4500	291	17	any	any	DET
ejpam-4500	291	18	graph	graph	NOUN
ejpam-4500	291	19	.	.	PUNCT
ejpam-4500	292	1	then	then	ADV
ejpam-4500	292	2	the	the	DET
ejpam-4500	292	3	following	following	ADJ
ejpam-4500	292	4	statements	statement	NOUN
ejpam-4500	292	5	hold	hold	VERB
ejpam-4500	292	6	:	:	PUNCT
ejpam-4500	292	7	(	(	PUNCT
ejpam-4500	292	8	i	i	NOUN
ejpam-4500	292	9	)	)	PUNCT
ejpam-4500	292	10	m	m	VERB
ejpam-4500	292	11	·	·	PUNCT
ejpam-4500	292	12	ln(h	ln(h	NUM
ejpam-4500	292	13	)	)	PUNCT
ejpam-4500	292	14	≤	≤	NOUN
ejpam-4500	293	1	lhn(g	lhn(g	NUM
ejpam-4500	293	2	◦	◦	NOUN
ejpam-4500	293	3	h	h	NOUN
ejpam-4500	293	4	)	)	PUNCT
ejpam-4500	293	5	≤	≤	NUM
ejpam-4500	293	6	lhn(g	lhn(g	NUM
ejpam-4500	293	7	)	)	PUNCT
ejpam-4500	294	1	+	+	VERB
ejpam-4500	294	2	m	m	PROPN
ejpam-4500	294	3	·	·	PUNCT
ejpam-4500	294	4	γsl(h	γsl(h	PROPN
ejpam-4500	294	5	)	)	PUNCT
ejpam-4500	294	6	.	.	PUNCT
ejpam-4500	295	1	(	(	PUNCT
ejpam-4500	295	2	ii	ii	NOUN
ejpam-4500	295	3	)	)	PUNCT
ejpam-4500	295	4	if	if	SCONJ
ejpam-4500	295	5	δ(g	δ(g	PROPN
ejpam-4500	295	6	)	)	PUNCT
ejpam-4500	295	7	≥	≥	NOUN
ejpam-4500	295	8	2	2	NUM
ejpam-4500	295	9	,	,	PUNCT
ejpam-4500	295	10	then	then	ADV
ejpam-4500	295	11	lhn(g	lhn(g	PROPN
ejpam-4500	295	12	◦	◦	NOUN
ejpam-4500	295	13	h	h	NOUN
ejpam-4500	295	14	)	)	PUNCT
ejpam-4500	295	15	≤	≤	NUM
ejpam-4500	295	16	lhn(g	lhn(g	NUM
ejpam-4500	295	17	)	)	PUNCT
ejpam-4500	296	1	+	+	VERB
ejpam-4500	296	2	m	m	PROPN
ejpam-4500	296	3	·	·	PUNCT
ejpam-4500	296	4	sln(h	sln(h	ADJ
ejpam-4500	296	5	)	)	PUNCT
ejpam-4500	296	6	.	.	PUNCT
ejpam-4500	297	1	(	(	PUNCT
ejpam-4500	297	2	iii	iii	X
ejpam-4500	297	3	)	)	PUNCT
ejpam-4500	297	4	if	if	SCONJ
ejpam-4500	297	5	g	g	PROPN
ejpam-4500	297	6	is	be	AUX
ejpam-4500	297	7	point	point	NOUN
ejpam-4500	297	8	determining	determine	VERB
ejpam-4500	297	9	,	,	PUNCT
ejpam-4500	297	10	then	then	ADV
ejpam-4500	297	11	lhn(g	lhn(g	PROPN
ejpam-4500	297	12	◦	◦	NOUN
ejpam-4500	297	13	h	h	NOUN
ejpam-4500	297	14	)	)	PUNCT
ejpam-4500	297	15	≤	≤	NUM
ejpam-4500	297	16	m	m	VERB
ejpam-4500	297	17	·	·	PUNCT
ejpam-4500	297	18	γsl(h	γsl(h	PROPN
ejpam-4500	297	19	)	)	PUNCT
ejpam-4500	297	20	.	.	PUNCT
ejpam-4500	298	1	(	(	PUNCT
ejpam-4500	298	2	iv	iv	X
ejpam-4500	298	3	)	)	PUNCT
ejpam-4500	298	4	if	if	SCONJ
ejpam-4500	298	5	g	g	PROPN
ejpam-4500	298	6	is	be	AUX
ejpam-4500	298	7	point	point	NOUN
ejpam-4500	298	8	determining	determine	VERB
ejpam-4500	298	9	and	and	CCONJ
ejpam-4500	298	10	δ(g	δ(g	ADJ
ejpam-4500	298	11	)	)	PUNCT
ejpam-4500	298	12	≥	≥	NOUN
ejpam-4500	298	13	2	2	NUM
ejpam-4500	298	14	,	,	PUNCT
ejpam-4500	298	15	then	then	ADV
ejpam-4500	298	16	lhn(g	lhn(g	PROPN
ejpam-4500	298	17	◦	◦	NOUN
ejpam-4500	298	18	h	h	NOUN
ejpam-4500	298	19	)	)	PUNCT
ejpam-4500	298	20	≤	≤	NUM
ejpam-4500	298	21	m	m	VERB
ejpam-4500	298	22	·	·	PUNCT
ejpam-4500	298	23	sln(h	sln(h	ADJ
ejpam-4500	298	24	)	)	PUNCT
ejpam-4500	298	25	.	.	PUNCT
ejpam-4500	299	1	moreover	moreover	ADV
ejpam-4500	299	2	,	,	PUNCT
ejpam-4500	299	3	if	if	SCONJ
ejpam-4500	299	4	in	in	ADP
ejpam-4500	299	5	addition	addition	NOUN
ejpam-4500	299	6	,	,	PUNCT
ejpam-4500	299	7	ln(h	ln(h	PUNCT
ejpam-4500	299	8	)	)	PUNCT
ejpam-4500	300	1	=	=	PUNCT
ejpam-4500	300	2	sln(h	sln(h	VERB
ejpam-4500	300	3	)	)	PUNCT
ejpam-4500	300	4	,	,	PUNCT
ejpam-4500	300	5	then	then	ADV
ejpam-4500	300	6	lhn(g	lhn(g	PROPN
ejpam-4500	300	7	◦	◦	NOUN
ejpam-4500	300	8	h	h	NOUN
ejpam-4500	300	9	)	)	PUNCT
ejpam-4500	300	10	=	=	PUNCT
ejpam-4500	300	11	m	m	PROPN
ejpam-4500	300	12	·	·	PUNCT
ejpam-4500	300	13	ln(h	ln(h	PUNCT
ejpam-4500	300	14	)	)	PUNCT
ejpam-4500	301	1	=	=	PUNCT
ejpam-4500	301	2	m	m	AUX
ejpam-4500	301	3	·	·	PUNCT
ejpam-4500	301	4	sln(h	sln(h	ADJ
ejpam-4500	301	5	)	)	PUNCT
ejpam-4500	301	6	.	.	PUNCT
ejpam-4500	302	1	proof	proof	NOUN
ejpam-4500	302	2	:	:	PUNCT
ejpam-4500	302	3	let	let	VERB
ejpam-4500	302	4	s	s	PRON
ejpam-4500	302	5	be	be	AUX
ejpam-4500	302	6	a	a	DET
ejpam-4500	302	7	minimum	minimum	ADJ
ejpam-4500	302	8	locating	locating	NOUN
ejpam-4500	302	9	hop	hop	NOUN
ejpam-4500	302	10	set	set	NOUN
ejpam-4500	302	11	(	(	PUNCT
ejpam-4500	302	12	lhn	lhn	PROPN
ejpam-4500	302	13	-	-	PUNCT
ejpam-4500	302	14	set	set	NOUN
ejpam-4500	302	15	)	)	PUNCT
ejpam-4500	302	16	in	in	ADP
ejpam-4500	302	17	g.	g.	PROPN
ejpam-4500	302	18	then	then	ADV
ejpam-4500	302	19	s	s	VERB
ejpam-4500	302	20	=	=	PUNCT
ejpam-4500	302	21	a	a	DET
ejpam-4500	302	22	∪	∪	ADJ
ejpam-4500	302	23	[	[	X
ejpam-4500	302	24	∪v∈v	∪v∈v	X
ejpam-4500	302	25	(	(	PUNCT
ejpam-4500	302	26	g)dv	g)dv	NOUN
ejpam-4500	302	27	]	]	PUNCT
ejpam-4500	302	28	and	and	CCONJ
ejpam-4500	302	29	satisfies	satisfy	VERB
ejpam-4500	302	30	the	the	DET
ejpam-4500	302	31	conditions	condition	NOUN
ejpam-4500	302	32	in	in	ADP
ejpam-4500	302	33	theorem	theorem	NOUN
ejpam-4500	302	34	5	5	NUM
ejpam-4500	302	35	.	.	PUNCT
ejpam-4500	303	1	in	in	ADP
ejpam-4500	303	2	particular	particular	ADJ
ejpam-4500	303	3	,	,	PUNCT
ejpam-4500	303	4	dv	dv	PROPN
ejpam-4500	303	5	is	be	AUX
ejpam-4500	303	6	a	a	DET
ejpam-4500	303	7	(	(	PUNCT
ejpam-4500	303	8	minimum	minimum	NOUN
ejpam-4500	303	9	)	)	PUNCT
ejpam-4500	303	10	locating	locate	VERB
ejpam-4500	303	11	set	set	VERB
ejpam-4500	303	12	in	in	ADP
ejpam-4500	303	13	hv	hv	PROPN
ejpam-4500	303	14	for	for	ADP
ejpam-4500	303	15	each	each	DET
ejpam-4500	303	16	v	v	NUM
ejpam-4500	303	17	∈	∈	PROPN
ejpam-4500	303	18	v	v	NOUN
ejpam-4500	303	19	(	(	PUNCT
ejpam-4500	303	20	g	g	NOUN
ejpam-4500	303	21	)	)	PUNCT
ejpam-4500	303	22	.	.	PUNCT
ejpam-4500	304	1	hence	hence	ADV
ejpam-4500	304	2	,	,	PUNCT
ejpam-4500	304	3	m	m	PROPN
ejpam-4500	304	4	·	·	PUNCT
ejpam-4500	304	5	ln(h	ln(h	NUM
ejpam-4500	304	6	)	)	PUNCT
ejpam-4500	304	7	≤	≤	NOUN
ejpam-4500	304	8	|a|+	|a|+	VERB
ejpam-4500	304	9	∑	∑	PUNCT
ejpam-4500	304	10	v∈v	v∈v	NOUN
ejpam-4500	304	11	(	(	PUNCT
ejpam-4500	304	12	g	g	NOUN
ejpam-4500	304	13	)	)	PUNCT
ejpam-4500	304	14	|dv|	|dv|	NOUN
ejpam-4500	304	15	=	=	SYM
ejpam-4500	304	16	|s|	|s|	PROPN
ejpam-4500	304	17	=	=	PUNCT
ejpam-4500	304	18	lhn(g	lhn(g	PROPN
ejpam-4500	304	19	◦	◦	NOUN
ejpam-4500	304	20	h	h	NOUN
ejpam-4500	304	21	)	)	PUNCT
ejpam-4500	304	22	.	.	PUNCT
ejpam-4500	305	1	now	now	ADV
ejpam-4500	305	2	,	,	PUNCT
ejpam-4500	305	3	let	let	VERB
ejpam-4500	305	4	a1	a1	NOUN
ejpam-4500	305	5	be	be	AUX
ejpam-4500	305	6	a	a	DET
ejpam-4500	305	7	locating	locate	VERB
ejpam-4500	305	8	hop	hop	NOUN
ejpam-4500	305	9	set	set	VERB
ejpam-4500	305	10	in	in	ADP
ejpam-4500	305	11	g	g	NOUN
ejpam-4500	305	12	and	and	CCONJ
ejpam-4500	305	13	let	let	VERB
ejpam-4500	305	14	lv	lv	PROPN
ejpam-4500	305	15	be	be	AUX
ejpam-4500	305	16	a	a	DET
ejpam-4500	305	17	strictly	strictly	ADV
ejpam-4500	305	18	locating	locate	VERB
ejpam-4500	305	19	-	-	PUNCT
ejpam-4500	305	20	dominating	dominating	NOUN
ejpam-4500	305	21	set	set	NOUN
ejpam-4500	305	22	(	(	PUNCT
ejpam-4500	305	23	γsl	γsl	NOUN
ejpam-4500	305	24	-	-	PUNCT
ejpam-4500	305	25	set	set	NOUN
ejpam-4500	305	26	)	)	PUNCT
ejpam-4500	305	27	in	in	ADP
ejpam-4500	305	28	hv	hv	PROPN
ejpam-4500	305	29	for	for	ADP
ejpam-4500	305	30	each	each	DET
ejpam-4500	305	31	v	v	NUM
ejpam-4500	305	32	∈	∈	PROPN
ejpam-4500	305	33	v	v	NOUN
ejpam-4500	305	34	(	(	PUNCT
ejpam-4500	305	35	g	g	NOUN
ejpam-4500	305	36	)	)	PUNCT
ejpam-4500	305	37	.	.	PUNCT
ejpam-4500	306	1	then	then	ADV
ejpam-4500	306	2	s	s	VERB
ejpam-4500	306	3	=	=	NOUN
ejpam-4500	306	4	a1	a1	NOUN
ejpam-4500	306	5	∪	∪	ADV
ejpam-4500	306	6	[	[	X
ejpam-4500	306	7	∪v∈v	∪v∈v	VERB
ejpam-4500	306	8	(	(	PUNCT
ejpam-4500	306	9	g)lv	g)lv	NOUN
ejpam-4500	306	10	]	]	X
ejpam-4500	306	11	is	be	AUX
ejpam-4500	306	12	a	a	DET
ejpam-4500	306	13	locating	locate	VERB
ejpam-4500	306	14	hop	hop	NOUN
ejpam-4500	306	15	set	set	VERB
ejpam-4500	306	16	in	in	ADP
ejpam-4500	306	17	g	g	PROPN
ejpam-4500	306	18	◦	◦	NOUN
ejpam-4500	306	19	h	h	NOUN
ejpam-4500	306	20	by	by	ADP
ejpam-4500	306	21	theorem	theorem	NOUN
ejpam-4500	306	22	5	5	NUM
ejpam-4500	306	23	.	.	PUNCT
ejpam-4500	307	1	this	this	PRON
ejpam-4500	307	2	implies	imply	VERB
ejpam-4500	307	3	that	that	SCONJ
ejpam-4500	307	4	lhn(g	lhn(g	PROPN
ejpam-4500	307	5	◦	◦	NOUN
ejpam-4500	307	6	h	h	NOUN
ejpam-4500	307	7	)	)	PUNCT
ejpam-4500	307	8	≤	≤	NUM
ejpam-4500	307	9	|s|	|s|	PROPN
ejpam-4500	307	10	=	=	SYM
ejpam-4500	307	11	lhn(g	lhn(g	PROPN
ejpam-4500	307	12	)	)	PUNCT
ejpam-4500	308	1	+	+	CCONJ
ejpam-4500	308	2	m	m	VERB
ejpam-4500	308	3	·	·	PUNCT
ejpam-4500	308	4	γsl(h	γsl(h	PROPN
ejpam-4500	308	5	)	)	PUNCT
ejpam-4500	308	6	,	,	PUNCT
ejpam-4500	308	7	showing	show	VERB
ejpam-4500	308	8	that	that	SCONJ
ejpam-4500	308	9	(	(	PUNCT
ejpam-4500	308	10	i	i	NOUN
ejpam-4500	308	11	)	)	PUNCT
ejpam-4500	308	12	holds	hold	VERB
ejpam-4500	308	13	.	.	PUNCT
ejpam-4500	309	1	if	if	SCONJ
ejpam-4500	309	2	δ(g	δ(g	PROPN
ejpam-4500	309	3	)	)	PUNCT
ejpam-4500	309	4	≥	≥	NOUN
ejpam-4500	309	5	2	2	NUM
ejpam-4500	309	6	and	and	CCONJ
ejpam-4500	309	7	each	each	DET
ejpam-4500	309	8	lv	lv	PROPN
ejpam-4500	309	9	is	be	AUX
ejpam-4500	309	10	a	a	DET
ejpam-4500	309	11	minimum	minimum	NOUN
ejpam-4500	309	12	strictly	strictly	ADV
ejpam-4500	309	13	locating	locate	VERB
ejpam-4500	309	14	set	set	NOUN
ejpam-4500	309	15	(	(	PUNCT
ejpam-4500	309	16	slnset	slnset	NOUN
ejpam-4500	309	17	)	)	PUNCT
ejpam-4500	309	18	in	in	ADP
ejpam-4500	309	19	hv	hv	PROPN
ejpam-4500	309	20	,	,	PUNCT
ejpam-4500	309	21	then	then	ADV
ejpam-4500	309	22	s	s	VERB
ejpam-4500	309	23	is	be	AUX
ejpam-4500	309	24	a	a	DET
ejpam-4500	309	25	locating	locate	VERB
ejpam-4500	309	26	hop	hop	NOUN
ejpam-4500	309	27	set	set	VERB
ejpam-4500	309	28	in	in	ADP
ejpam-4500	309	29	g	g	PROPN
ejpam-4500	309	30	◦	◦	NOUN
ejpam-4500	309	31	h	h	NOUN
ejpam-4500	309	32	by	by	ADP
ejpam-4500	309	33	theorem	theorem	NOUN
ejpam-4500	309	34	5	5	NUM
ejpam-4500	309	35	.	.	PUNCT
ejpam-4500	309	36	thus	thus	ADV
ejpam-4500	309	37	,	,	PUNCT
ejpam-4500	309	38	(	(	PUNCT
ejpam-4500	309	39	ii	ii	NOUN
ejpam-4500	309	40	)	)	PUNCT
ejpam-4500	309	41	holds	hold	VERB
ejpam-4500	309	42	,	,	PUNCT
ejpam-4500	309	43	that	that	ADV
ejpam-4500	309	44	is	is	ADV
ejpam-4500	309	45	,	,	PUNCT
ejpam-4500	309	46	lhn(g	lhn(g	PROPN
ejpam-4500	309	47	◦	◦	NOUN
ejpam-4500	309	48	h	h	NOUN
ejpam-4500	309	49	)	)	PUNCT
ejpam-4500	309	50	≤	≤	NUM
ejpam-4500	309	51	|s|	|s|	PROPN
ejpam-4500	309	52	=	=	SYM
ejpam-4500	309	53	lhn(g	lhn(g	PROPN
ejpam-4500	309	54	)	)	PUNCT
ejpam-4500	310	1	+	+	VERB
ejpam-4500	310	2	m	m	NOUN
ejpam-4500	310	3	·	·	PUNCT
ejpam-4500	310	4	sln(h	sln(h	ADJ
ejpam-4500	310	5	)	)	PUNCT
ejpam-4500	310	6	.	.	PUNCT
ejpam-4500	311	1	suppose	suppose	VERB
ejpam-4500	311	2	g	g	PROPN
ejpam-4500	311	3	is	be	AUX
ejpam-4500	311	4	a	a	DET
ejpam-4500	311	5	point	point	NOUN
ejpam-4500	311	6	determining	determine	VERB
ejpam-4500	311	7	graph	graph	NOUN
ejpam-4500	311	8	.	.	PUNCT
ejpam-4500	312	1	for	for	ADP
ejpam-4500	312	2	each	each	DET
ejpam-4500	312	3	v	v	NUM
ejpam-4500	312	4	∈	∈	PROPN
ejpam-4500	312	5	v	v	NOUN
ejpam-4500	312	6	(	(	PUNCT
ejpam-4500	312	7	g	g	NOUN
ejpam-4500	312	8	)	)	PUNCT
ejpam-4500	312	9	,	,	PUNCT
ejpam-4500	312	10	let	let	VERB
ejpam-4500	312	11	tv	tv	NOUN
ejpam-4500	312	12	be	be	AUX
ejpam-4500	312	13	a	a	DET
ejpam-4500	312	14	minimum	minimum	NOUN
ejpam-4500	312	15	strictly	strictly	ADV
ejpam-4500	312	16	locating	locate	VERB
ejpam-4500	312	17	-	-	PUNCT
ejpam-4500	312	18	dominating	dominating	NOUN
ejpam-4500	312	19	set	set	NOUN
ejpam-4500	312	20	(	(	PUNCT
ejpam-4500	312	21	γsl	γsl	NOUN
ejpam-4500	312	22	-	-	PUNCT
ejpam-4500	312	23	set	set	NOUN
ejpam-4500	312	24	)	)	PUNCT
ejpam-4500	312	25	in	in	ADP
ejpam-4500	312	26	hv	hv	PROPN
ejpam-4500	312	27	.	.	PUNCT
ejpam-4500	313	1	then	then	ADV
ejpam-4500	313	2	s1	s1	PROPN
ejpam-4500	313	3	=	=	PUNCT
ejpam-4500	314	1	∪v∈v	∪v∈v	X
ejpam-4500	314	2	(	(	PUNCT
ejpam-4500	314	3	g)tv	g)tv	NOUN
ejpam-4500	314	4	is	be	AUX
ejpam-4500	314	5	a	a	DET
ejpam-4500	314	6	locating	locate	VERB
ejpam-4500	314	7	hop	hop	NOUN
ejpam-4500	314	8	set	set	VERB
ejpam-4500	314	9	in	in	ADP
ejpam-4500	314	10	g	g	PROPN
ejpam-4500	314	11	◦	◦	NOUN
ejpam-4500	314	12	h	h	NOUN
ejpam-4500	314	13	by	by	ADP
ejpam-4500	314	14	theorem	theorem	NOUN
ejpam-4500	314	15	5	5	NUM
ejpam-4500	314	16	.	.	PUNCT
ejpam-4500	315	1	this	this	PRON
ejpam-4500	315	2	implies	imply	VERB
ejpam-4500	315	3	that	that	SCONJ
ejpam-4500	315	4	lhn(g	lhn(g	PROPN
ejpam-4500	315	5	◦	◦	NOUN
ejpam-4500	315	6	h	h	NOUN
ejpam-4500	315	7	)	)	PUNCT
ejpam-4500	315	8	≤	≤	NUM
ejpam-4500	315	9	|s|	|s|	PROPN
ejpam-4500	315	10	=	=	PUNCT
ejpam-4500	315	11	m	m	PROPN
ejpam-4500	315	12	·	·	PUNCT
ejpam-4500	315	13	γsl(h	γsl(h	PROPN
ejpam-4500	315	14	)	)	PUNCT
ejpam-4500	315	15	,	,	PUNCT
ejpam-4500	315	16	showing	show	VERB
ejpam-4500	315	17	that	that	SCONJ
ejpam-4500	315	18	(	(	PUNCT
ejpam-4500	315	19	iii	iii	NOUN
ejpam-4500	315	20	)	)	PUNCT
ejpam-4500	315	21	holds	hold	VERB
ejpam-4500	315	22	.	.	PUNCT
ejpam-4500	316	1	moreover	moreover	ADV
ejpam-4500	316	2	,	,	PUNCT
ejpam-4500	316	3	if	if	SCONJ
ejpam-4500	316	4	we	we	PRON
ejpam-4500	316	5	impose	impose	VERB
ejpam-4500	316	6	that	that	PRON
ejpam-4500	316	7	δ(g	δ(g	PROPN
ejpam-4500	316	8	)	)	PUNCT
ejpam-4500	316	9	≥	≥	NOUN
ejpam-4500	316	10	2	2	NUM
ejpam-4500	316	11	,	,	PUNCT
ejpam-4500	316	12	then	then	ADV
ejpam-4500	316	13	each	each	DET
ejpam-4500	316	14	set	set	VERB
ejpam-4500	316	15	tv	tv	NOUN
ejpam-4500	316	16	can	can	AUX
ejpam-4500	316	17	be	be	AUX
ejpam-4500	316	18	taken	take	VERB
ejpam-4500	316	19	as	as	ADP
ejpam-4500	316	20	a	a	DET
ejpam-4500	316	21	strictly	strictly	ADV
ejpam-4500	316	22	locating	locate	VERB
ejpam-4500	316	23	set	set	NOUN
ejpam-4500	316	24	of	of	ADP
ejpam-4500	316	25	hv	hv	PROPN
ejpam-4500	316	26	.	.	PUNCT
ejpam-4500	317	1	now	now	ADV
ejpam-4500	317	2	,	,	PUNCT
ejpam-4500	317	3	s1	s1	PROPN
ejpam-4500	317	4	is	be	AUX
ejpam-4500	317	5	still	still	ADV
ejpam-4500	317	6	a	a	DET
ejpam-4500	317	7	locating	locate	VERB
ejpam-4500	317	8	hop	hop	NOUN
ejpam-4500	317	9	set	set	VERB
ejpam-4500	317	10	in	in	ADP
ejpam-4500	317	11	g	g	PROPN
ejpam-4500	317	12	◦	◦	NOUN
ejpam-4500	317	13	h	h	NOUN
ejpam-4500	317	14	by	by	ADP
ejpam-4500	317	15	theorem	theorem	NOUN
ejpam-4500	317	16	5	5	NUM
ejpam-4500	317	17	.	.	PUNCT
ejpam-4500	318	1	thus	thus	ADV
ejpam-4500	318	2	,	,	PUNCT
ejpam-4500	318	3	lhn(g	lhn(g	PROPN
ejpam-4500	318	4	◦	◦	NOUN
ejpam-4500	318	5	h	h	NOUN
ejpam-4500	318	6	)	)	PUNCT
ejpam-4500	318	7	≤	≤	NUM
ejpam-4500	318	8	m	m	VERB
ejpam-4500	318	9	·	·	PUNCT
ejpam-4500	318	10	sln(h	sln(h	VERB
ejpam-4500	318	11	)	)	PUNCT
ejpam-4500	318	12	.	.	PUNCT
ejpam-4500	319	1	suppose	suppose	VERB
ejpam-4500	319	2	now	now	ADV
ejpam-4500	319	3	that	that	SCONJ
ejpam-4500	319	4	,	,	PUNCT
ejpam-4500	319	5	in	in	ADP
ejpam-4500	319	6	addition	addition	NOUN
ejpam-4500	319	7	,	,	PUNCT
ejpam-4500	319	8	ln(h	ln(h	PUNCT
ejpam-4500	319	9	)	)	PUNCT
ejpam-4500	319	10	=	=	PUNCT
ejpam-4500	319	11	sln(h	sln(h	VERB
ejpam-4500	319	12	)	)	PUNCT
ejpam-4500	319	13	.	.	PUNCT
ejpam-4500	320	1	then	then	ADV
ejpam-4500	320	2	lhn(g	lhn(g	PROPN
ejpam-4500	320	3	◦	◦	NOUN
ejpam-4500	320	4	h	h	NOUN
ejpam-4500	320	5	)	)	PUNCT
ejpam-4500	320	6	≤	≤	NUM
ejpam-4500	320	7	m	m	VERB
ejpam-4500	320	8	·	·	PUNCT
ejpam-4500	320	9	sln(h	sln(h	ADJ
ejpam-4500	320	10	)	)	PUNCT
ejpam-4500	320	11	=	=	PUNCT
ejpam-4500	320	12	m	m	PROPN
ejpam-4500	320	13	·	·	PUNCT
ejpam-4500	320	14	ln(h	ln(h	NUM
ejpam-4500	320	15	)	)	PUNCT
ejpam-4500	320	16	.	.	PUNCT
ejpam-4500	321	1	combining	combine	VERB
ejpam-4500	321	2	this	this	PRON
ejpam-4500	321	3	with	with	ADP
ejpam-4500	321	4	an	an	DET
ejpam-4500	321	5	inequality	inequality	NOUN
ejpam-4500	321	6	in	in	ADP
ejpam-4500	321	7	(	(	PUNCT
ejpam-4500	321	8	i	i	NOUN
ejpam-4500	321	9	)	)	PUNCT
ejpam-4500	321	10	,	,	PUNCT
ejpam-4500	321	11	it	it	PRON
ejpam-4500	321	12	follows	follow	VERB
ejpam-4500	321	13	that	that	SCONJ
ejpam-4500	321	14	lhn(g	lhn(g	PROPN
ejpam-4500	321	15	◦	◦	NOUN
ejpam-4500	321	16	h	h	NOUN
ejpam-4500	321	17	)	)	PUNCT
ejpam-4500	321	18	=	=	PUNCT
ejpam-4500	321	19	m	m	PROPN
ejpam-4500	321	20	·	·	PUNCT
ejpam-4500	321	21	ln(h	ln(h	PUNCT
ejpam-4500	321	22	)	)	PUNCT
ejpam-4500	322	1	=	=	PUNCT
ejpam-4500	322	2	m	m	AUX
ejpam-4500	322	3	·	·	PUNCT
ejpam-4500	322	4	sln(h	sln(h	ADJ
ejpam-4500	322	5	)	)	PUNCT
ejpam-4500	322	6	.	.	PUNCT
ejpam-4500	323	1	□	□	PUNCT
ejpam-4500	323	2	corollary	corollary	ADJ
ejpam-4500	323	3	6	6	NUM
ejpam-4500	323	4	.	.	PUNCT
ejpam-4500	324	1	let	let	VERB
ejpam-4500	324	2	g	g	PRON
ejpam-4500	324	3	be	be	AUX
ejpam-4500	324	4	a	a	DET
ejpam-4500	324	5	cycle	cycle	NOUN
ejpam-4500	324	6	of	of	ADP
ejpam-4500	324	7	order	order	NOUN
ejpam-4500	324	8	m	m	VERB
ejpam-4500	324	9	=	=	SYM
ejpam-4500	324	10	4	4	NUM
ejpam-4500	324	11	and	and	CCONJ
ejpam-4500	324	12	h	h	NOUN
ejpam-4500	324	13	be	be	VERB
ejpam-4500	324	14	a	a	DET
ejpam-4500	324	15	non	non	ADJ
ejpam-4500	324	16	-	-	ADJ
ejpam-4500	324	17	trivial	trivial	ADJ
ejpam-4500	324	18	graph	graph	NOUN
ejpam-4500	324	19	.	.	PUNCT
ejpam-4500	325	1	then	then	ADV
ejpam-4500	325	2	lhn(g	lhn(g	PROPN
ejpam-4500	325	3	◦	◦	NOUN
ejpam-4500	325	4	h	h	NOUN
ejpam-4500	325	5	)	)	PUNCT
ejpam-4500	326	1	=	=	PRON
ejpam-4500	326	2	{	{	PUNCT
ejpam-4500	326	3	m	m	VERB
ejpam-4500	326	4	·	·	PUNCT
ejpam-4500	326	5	sln(h	sln(h	ADJ
ejpam-4500	326	6	)	)	PUNCT
ejpam-4500	326	7	+	+	CCONJ
ejpam-4500	326	8	2	2	NUM
ejpam-4500	326	9	if	if	SCONJ
ejpam-4500	326	10	ln(h	ln(h	VERB
ejpam-4500	326	11	)	)	PUNCT
ejpam-4500	326	12	=	=	PUNCT
ejpam-4500	326	13	sln(h	sln(h	ADJ
ejpam-4500	326	14	)	)	PUNCT
ejpam-4500	326	15	2sln(h	2sln(h	NOUN
ejpam-4500	326	16	)	)	PUNCT
ejpam-4500	326	17	+	+	NUM
ejpam-4500	326	18	2ln(h	2ln(h	NUM
ejpam-4500	326	19	)	)	PUNCT
ejpam-4500	327	1	+	+	CCONJ
ejpam-4500	327	2	2	2	NUM
ejpam-4500	327	3	if	if	SCONJ
ejpam-4500	327	4	ln(h	ln(h	VERB
ejpam-4500	327	5	)	)	PUNCT
ejpam-4500	327	6	<	<	X
ejpam-4500	328	1	sln(h	sln(h	PROPN
ejpam-4500	328	2	)	)	PUNCT
ejpam-4500	328	3	.	.	PUNCT
ejpam-4500	329	1	proof	proof	NOUN
ejpam-4500	329	2	:	:	PUNCT
ejpam-4500	329	3	let	let	VERB
ejpam-4500	329	4	c4	c4	NOUN
ejpam-4500	329	5	=	=	PUNCT
ejpam-4500	330	1	[	[	X
ejpam-4500	330	2	a	a	PRON
ejpam-4500	330	3	,	,	PUNCT
ejpam-4500	330	4	b	b	NOUN
ejpam-4500	330	5	,	,	PUNCT
ejpam-4500	330	6	c	c	NOUN
ejpam-4500	330	7	,	,	PUNCT
ejpam-4500	330	8	d	d	NOUN
ejpam-4500	330	9	,	,	PUNCT
ejpam-4500	330	10	a	a	PRON
ejpam-4500	330	11	]	]	PUNCT
ejpam-4500	330	12	and	and	CCONJ
ejpam-4500	330	13	let	let	VERB
ejpam-4500	330	14	s	s	PRON
ejpam-4500	330	15	be	be	AUX
ejpam-4500	330	16	a	a	DET
ejpam-4500	330	17	minimum	minimum	ADJ
ejpam-4500	330	18	locating	locating	NOUN
ejpam-4500	330	19	hop	hop	NOUN
ejpam-4500	330	20	set	set	VERB
ejpam-4500	330	21	in	in	ADP
ejpam-4500	330	22	c4	c4	PROPN
ejpam-4500	330	23	◦	◦	PROPN
ejpam-4500	330	24	h.	h.	PROPN
ejpam-4500	330	25	put	put	VERB
ejpam-4500	330	26	dv	dv	PROPN
ejpam-4500	330	27	=	=	PROPN
ejpam-4500	330	28	s	s	PROPN
ejpam-4500	330	29	∩	∩	ADJ
ejpam-4500	330	30	v	v	X
ejpam-4500	330	31	(	(	PUNCT
ejpam-4500	330	32	hv	hv	PROPN
ejpam-4500	330	33	)	)	PUNCT
ejpam-4500	330	34	for	for	ADP
ejpam-4500	330	35	each	each	DET
ejpam-4500	330	36	v	v	PROPN
ejpam-4500	330	37	∈	∈	PROPN
ejpam-4500	330	38	c4	c4	NOUN
ejpam-4500	330	39	.	.	PUNCT
ejpam-4500	331	1	by	by	ADP
ejpam-4500	331	2	theorem	theorem	NOUN
ejpam-4500	331	3	5(i	5(i	NOUN
ejpam-4500	331	4	)	)	PUNCT
ejpam-4500	331	5	,	,	PUNCT
ejpam-4500	331	6	a	a	DET
ejpam-4500	331	7	=	=	X
ejpam-4500	331	8	s	s	NOUN
ejpam-4500	331	9	∩	∩	ADJ
ejpam-4500	331	10	v	v	NOUN
ejpam-4500	331	11	(	(	PUNCT
ejpam-4500	331	12	c4	c4	NOUN
ejpam-4500	331	13	)	)	PUNCT
ejpam-4500	331	14	̸=	̸=	PROPN
ejpam-4500	331	15	∅.	∅.	ADV
ejpam-4500	331	16	without	without	ADP
ejpam-4500	331	17	loss	loss	NOUN
ejpam-4500	331	18	of	of	ADP
ejpam-4500	331	19	generality	generality	NOUN
ejpam-4500	331	20	,	,	PUNCT
ejpam-4500	331	21	we	we	PRON
ejpam-4500	331	22	suppose	suppose	VERB
ejpam-4500	331	23	that	that	SCONJ
ejpam-4500	331	24	a	a	DET
ejpam-4500	331	25	∈	∈	PROPN
ejpam-4500	331	26	a.	a.	NOUN
ejpam-4500	331	27	suppose	suppose	VERB
ejpam-4500	331	28	further	far	ADV
ejpam-4500	331	29	that	that	DET
ejpam-4500	331	30	b	b	NOUN
ejpam-4500	331	31	,	,	PUNCT
ejpam-4500	331	32	d	d	NOUN
ejpam-4500	331	33	/∈	/∈	PUNCT
ejpam-4500	331	34	a.	a.	NOUN
ejpam-4500	331	35	since	since	SCONJ
ejpam-4500	331	36	nc4(b	nc4(b	NOUN
ejpam-4500	331	37	)	)	PUNCT
ejpam-4500	331	38	=	=	SYM
ejpam-4500	331	39	nc4(d	nc4(d	PROPN
ejpam-4500	331	40	)	)	PUNCT
ejpam-4500	331	41	and	and	CCONJ
ejpam-4500	331	42	nc4(b	nc4(b	PROPN
ejpam-4500	331	43	,	,	PUNCT
ejpam-4500	331	44	2	2	NUM
ejpam-4500	331	45	)	)	PUNCT
ejpam-4500	331	46	∩a	∩a	NOUN
ejpam-4500	331	47	=	=	SYM
ejpam-4500	331	48	nc4(d	nc4(d	PROPN
ejpam-4500	331	49	,	,	PUNCT
ejpam-4500	331	50	2	2	NUM
ejpam-4500	331	51	)	)	PUNCT
ejpam-4500	331	52	∩a	∩a	NOUN
ejpam-4500	331	53	=	=	VERB
ejpam-4500	331	54	∅	∅	NOUN
ejpam-4500	331	55	,	,	PUNCT
ejpam-4500	331	56	a	a	PRON
ejpam-4500	331	57	does	do	AUX
ejpam-4500	331	58	not	not	PART
ejpam-4500	331	59	satisfy	satisfy	VERB
ejpam-4500	331	60	theorem	theorem	VERB
ejpam-4500	331	61	5(i	5(i	NOUN
ejpam-4500	331	62	)	)	PUNCT
ejpam-4500	331	63	,	,	PUNCT
ejpam-4500	331	64	contrary	contrary	ADV
ejpam-4500	331	65	to	to	ADP
ejpam-4500	331	66	our	our	PRON
ejpam-4500	331	67	assumption	assumption	NOUN
ejpam-4500	331	68	that	that	SCONJ
ejpam-4500	331	69	s	s	VERB
ejpam-4500	331	70	is	be	AUX
ejpam-4500	331	71	a	a	DET
ejpam-4500	331	72	locating	locate	VERB
ejpam-4500	331	73	hop	hop	NOUN
ejpam-4500	331	74	set	set	VERB
ejpam-4500	331	75	in	in	ADP
ejpam-4500	331	76	c4	c4	PROPN
ejpam-4500	331	77	◦	◦	PROPN
ejpam-4500	331	78	h.	h.	PROPN
ejpam-4500	331	79	hence	hence	ADV
ejpam-4500	331	80	,	,	PUNCT
ejpam-4500	331	81	either	either	CCONJ
ejpam-4500	331	82	b	b	PROPN
ejpam-4500	331	83	∈	∈	PROPN
ejpam-4500	331	84	a	a	PRON
ejpam-4500	331	85	or	or	CCONJ
ejpam-4500	331	86	d	d	PROPN
ejpam-4500	331	87	∈	∈	PROPN
ejpam-4500	331	88	a	a	PRON
ejpam-4500	331	89	,	,	PUNCT
ejpam-4500	331	90	say	say	VERB
ejpam-4500	331	91	b	b	X
ejpam-4500	331	92	∈	∈	PROPN
ejpam-4500	331	93	a.	a.	NOUN
ejpam-4500	331	94	since	since	SCONJ
ejpam-4500	331	95	nc4(a	nc4(a	PROPN
ejpam-4500	331	96	)	)	PUNCT
ejpam-4500	331	97	∩	∩	NOUN
ejpam-4500	331	98	a	a	DET
ejpam-4500	331	99	=	=	SYM
ejpam-4500	331	100	nc4(c	nc4(c	PROPN
ejpam-4500	331	101	)	)	PUNCT
ejpam-4500	331	102	∩	∩	PROPN
ejpam-4500	331	103	a	a	X
ejpam-4500	331	104	,	,	PUNCT
ejpam-4500	331	105	da	da	PROPN
ejpam-4500	331	106	or	or	CCONJ
ejpam-4500	331	107	dc	dc	PROPN
ejpam-4500	331	108	,	,	PUNCT
ejpam-4500	331	109	say	say	VERB
ejpam-4500	331	110	da	da	PROPN
ejpam-4500	331	111	must	must	AUX
ejpam-4500	331	112	be	be	AUX
ejpam-4500	331	113	a	a	DET
ejpam-4500	331	114	minimum	minimum	NOUN
ejpam-4500	331	115	strictly	strictly	ADV
ejpam-4500	331	116	locating	locate	VERB
ejpam-4500	331	117	references	reference	NOUN
ejpam-4500	331	118	1714	1714	NUM
ejpam-4500	331	119	set	set	VERB
ejpam-4500	331	120	in	in	ADP
ejpam-4500	331	121	ha	ha	INTJ
ejpam-4500	331	122	.	.	PUNCT
ejpam-4500	332	1	it	it	PRON
ejpam-4500	332	2	follows	follow	VERB
ejpam-4500	332	3	that	that	SCONJ
ejpam-4500	332	4	dc	dc	PROPN
ejpam-4500	332	5	is	be	AUX
ejpam-4500	332	6	a	a	DET
ejpam-4500	332	7	minimum	minimum	NOUN
ejpam-4500	332	8	locatng	locatng	VERB
ejpam-4500	332	9	set	set	VERB
ejpam-4500	332	10	in	in	ADP
ejpam-4500	332	11	hc	hc	PRON
ejpam-4500	332	12	by	by	ADP
ejpam-4500	332	13	theorem	theorem	ADJ
ejpam-4500	332	14	5(iv	5(iv	NUM
ejpam-4500	332	15	)	)	PUNCT
ejpam-4500	332	16	and	and	CCONJ
ejpam-4500	332	17	the	the	DET
ejpam-4500	332	18	fact	fact	NOUN
ejpam-4500	332	19	that	that	SCONJ
ejpam-4500	332	20	s	s	VERB
ejpam-4500	332	21	is	be	AUX
ejpam-4500	332	22	an	an	DET
ejpam-4500	332	23	lhn	lhn	PROPN
ejpam-4500	332	24	-	-	PUNCT
ejpam-4500	332	25	set	set	NOUN
ejpam-4500	332	26	.	.	PUNCT
ejpam-4500	333	1	similarly	similarly	ADV
ejpam-4500	333	2	,	,	PUNCT
ejpam-4500	333	3	one	one	NUM
ejpam-4500	333	4	of	of	ADP
ejpam-4500	333	5	db	db	PROPN
ejpam-4500	333	6	and	and	CCONJ
ejpam-4500	333	7	dd	dd	VERB
ejpam-4500	333	8	is	be	AUX
ejpam-4500	333	9	a	a	DET
ejpam-4500	333	10	minimum	minimum	NOUN
ejpam-4500	333	11	strictly	strictly	ADV
ejpam-4500	333	12	locating	locate	VERB
ejpam-4500	333	13	set	set	VERB
ejpam-4500	333	14	and	and	CCONJ
ejpam-4500	333	15	the	the	DET
ejpam-4500	333	16	other	other	ADJ
ejpam-4500	333	17	a	a	DET
ejpam-4500	333	18	minimum	minimum	ADJ
ejpam-4500	333	19	locating	locating	NOUN
ejpam-4500	333	20	set	set	NOUN
ejpam-4500	333	21	.	.	PUNCT
ejpam-4500	334	1	since	since	SCONJ
ejpam-4500	334	2	s	s	PROPN
ejpam-4500	334	3	is	be	AUX
ejpam-4500	334	4	a	a	DET
ejpam-4500	334	5	minimum	minimum	ADJ
ejpam-4500	334	6	locating	locating	NOUN
ejpam-4500	334	7	hop	hop	NOUN
ejpam-4500	334	8	set	set	VERB
ejpam-4500	334	9	in	in	ADP
ejpam-4500	334	10	c4	c4	NOUN
ejpam-4500	334	11	◦	◦	PROPN
ejpam-4500	334	12	h	h	NOUN
ejpam-4500	334	13	,	,	PUNCT
ejpam-4500	334	14	|a|	|a|	PROPN
ejpam-4500	334	15	=	=	SYM
ejpam-4500	334	16	2	2	NUM
ejpam-4500	334	17	(	(	PUNCT
ejpam-4500	334	18	increasing	increase	VERB
ejpam-4500	334	19	the	the	DET
ejpam-4500	334	20	number	number	NOUN
ejpam-4500	334	21	of	of	ADP
ejpam-4500	334	22	elements	element	NOUN
ejpam-4500	334	23	of	of	ADP
ejpam-4500	334	24	a	a	PRON
ejpam-4500	334	25	will	will	AUX
ejpam-4500	334	26	not	not	PART
ejpam-4500	334	27	change	change	VERB
ejpam-4500	334	28	the	the	DET
ejpam-4500	334	29	above	above	ADJ
ejpam-4500	334	30	requirement	requirement	NOUN
ejpam-4500	334	31	for	for	ADP
ejpam-4500	334	32	the	the	DET
ejpam-4500	334	33	sets	set	NOUN
ejpam-4500	334	34	dv	dv	PROPN
ejpam-4500	334	35	)	)	PUNCT
ejpam-4500	334	36	,	,	PUNCT
ejpam-4500	334	37	and	and	CCONJ
ejpam-4500	334	38	two	two	NUM
ejpam-4500	334	39	subsets	subset	NOUN
ejpam-4500	334	40	of	of	ADP
ejpam-4500	334	41	s	s	PRON
ejpam-4500	334	42	in	in	ADP
ejpam-4500	334	43	copies	copy	NOUN
ejpam-4500	334	44	of	of	ADP
ejpam-4500	334	45	h	h	NOUN
ejpam-4500	334	46	are	be	AUX
ejpam-4500	334	47	strictly	strictly	ADV
ejpam-4500	334	48	locating	locate	VERB
ejpam-4500	334	49	sets	set	NOUN
ejpam-4500	334	50	.	.	PUNCT
ejpam-4500	335	1	therefore	therefore	ADV
ejpam-4500	335	2	,	,	PUNCT
ejpam-4500	335	3	lhn(c4	lhn(c4	ADP
ejpam-4500	335	4	◦	◦	NOUN
ejpam-4500	335	5	h	h	NOUN
ejpam-4500	335	6	)	)	PUNCT
ejpam-4500	335	7	=	=	PUNCT
ejpam-4500	335	8	|a|+	|a|+	NOUN
ejpam-4500	335	9	2ln(h	2ln(h	NUM
ejpam-4500	335	10	)	)	PUNCT
ejpam-4500	336	1	+	+	NUM
ejpam-4500	336	2	2sln(h	2sln(h	X
ejpam-4500	336	3	)	)	PUNCT
ejpam-4500	336	4	=	=	SYM
ejpam-4500	336	5	2ln(h	2ln(h	NUM
ejpam-4500	336	6	)	)	PUNCT
ejpam-4500	337	1	+	+	NUM
ejpam-4500	337	2	2sln(h	2sln(h	NOUN
ejpam-4500	337	3	)	)	PUNCT
ejpam-4500	337	4	+	+	NOUN
ejpam-4500	338	1	2	2	X
ejpam-4500	338	2	.	.	X
ejpam-4500	338	3	if	if	SCONJ
ejpam-4500	338	4	ln(h	ln(h	VERB
ejpam-4500	338	5	)	)	PUNCT
ejpam-4500	338	6	=	=	PUNCT
ejpam-4500	338	7	sln(h	sln(h	VERB
ejpam-4500	338	8	)	)	PUNCT
ejpam-4500	338	9	,	,	PUNCT
ejpam-4500	338	10	then	then	ADV
ejpam-4500	338	11	lhn(c4	lhn(c4	ADP
ejpam-4500	338	12	◦	◦	NOUN
ejpam-4500	338	13	h	h	NOUN
ejpam-4500	338	14	)	)	PUNCT
ejpam-4500	338	15	=	=	SYM
ejpam-4500	338	16	4ln(h	4ln(h	NUM
ejpam-4500	338	17	)	)	PUNCT
ejpam-4500	339	1	+	+	CCONJ
ejpam-4500	339	2	2	2	NUM
ejpam-4500	339	3	=	=	SYM
ejpam-4500	339	4	4sln(h	4sln(h	NUM
ejpam-4500	339	5	)	)	PUNCT
ejpam-4500	339	6	+	+	NOUN
ejpam-4500	339	7	2	2	X
ejpam-4500	339	8	.	.	X
ejpam-4500	339	9	□	□	SYM
ejpam-4500	339	10	5	5	NUM
ejpam-4500	339	11	.	.	X
ejpam-4500	339	12	conclusion	conclusion	NOUN
ejpam-4500	339	13	as	as	SCONJ
ejpam-4500	339	14	the	the	DET
ejpam-4500	339	15	concept	concept	NOUN
ejpam-4500	339	16	of	of	ADP
ejpam-4500	339	17	locating	locate	VERB
ejpam-4500	339	18	set	set	NOUN
ejpam-4500	339	19	plays	play	VERB
ejpam-4500	339	20	an	an	DET
ejpam-4500	339	21	important	important	ADJ
ejpam-4500	339	22	role	role	NOUN
ejpam-4500	339	23	in	in	ADP
ejpam-4500	339	24	the	the	DET
ejpam-4500	339	25	study	study	NOUN
ejpam-4500	339	26	of	of	ADP
ejpam-4500	339	27	locating	locate	VERB
ejpam-4500	339	28	domination	domination	NOUN
ejpam-4500	339	29	in	in	ADP
ejpam-4500	339	30	a	a	DET
ejpam-4500	339	31	graph	graph	NOUN
ejpam-4500	339	32	,	,	PUNCT
ejpam-4500	339	33	the	the	DET
ejpam-4500	339	34	concept	concept	NOUN
ejpam-4500	339	35	of	of	ADP
ejpam-4500	339	36	locating	locate	VERB
ejpam-4500	339	37	hop	hop	NOUN
ejpam-4500	339	38	set	set	NOUN
ejpam-4500	339	39	plays	play	VERB
ejpam-4500	339	40	a	a	DET
ejpam-4500	339	41	similar	similar	ADJ
ejpam-4500	339	42	important	important	ADJ
ejpam-4500	339	43	part	part	NOUN
ejpam-4500	339	44	in	in	ADP
ejpam-4500	339	45	the	the	DET
ejpam-4500	339	46	study	study	NOUN
ejpam-4500	339	47	of	of	ADP
ejpam-4500	339	48	locating	locate	VERB
ejpam-4500	339	49	hop	hop	NOUN
ejpam-4500	339	50	domination	domination	NOUN
ejpam-4500	339	51	.	.	PUNCT
ejpam-4500	340	1	locating	locate	VERB
ejpam-4500	340	2	hop	hop	NOUN
ejpam-4500	340	3	sets	set	NOUN
ejpam-4500	340	4	in	in	ADP
ejpam-4500	340	5	the	the	DET
ejpam-4500	340	6	join	join	NOUN
ejpam-4500	340	7	and	and	CCONJ
ejpam-4500	340	8	the	the	DET
ejpam-4500	340	9	corona	corona	NOUN
ejpam-4500	340	10	of	of	ADP
ejpam-4500	340	11	two	two	NUM
ejpam-4500	340	12	graphs	graph	NOUN
ejpam-4500	340	13	have	have	AUX
ejpam-4500	340	14	been	be	AUX
ejpam-4500	340	15	characterized	characterize	VERB
ejpam-4500	340	16	.	.	PUNCT
ejpam-4500	341	1	these	these	DET
ejpam-4500	341	2	type	type	NOUN
ejpam-4500	341	3	of	of	ADP
ejpam-4500	341	4	sets	set	NOUN
ejpam-4500	341	5	may	may	AUX
ejpam-4500	341	6	be	be	AUX
ejpam-4500	341	7	studied	study	VERB
ejpam-4500	341	8	also	also	ADV
ejpam-4500	341	9	in	in	ADP
ejpam-4500	341	10	other	other	ADJ
ejpam-4500	341	11	graphs	graph	NOUN
ejpam-4500	341	12	including	include	VERB
ejpam-4500	341	13	those	those	DET
ejpam-4500	341	14	graphs	graph	NOUN
ejpam-4500	341	15	which	which	PRON
ejpam-4500	341	16	can	can	AUX
ejpam-4500	341	17	be	be	AUX
ejpam-4500	341	18	obtained	obtain	VERB
ejpam-4500	341	19	by	by	ADP
ejpam-4500	341	20	applying	apply	VERB
ejpam-4500	341	21	other	other	ADJ
ejpam-4500	341	22	binary	binary	ADJ
ejpam-4500	341	23	operations	operation	NOUN
ejpam-4500	341	24	of	of	ADP
ejpam-4500	341	25	graphs	graph	NOUN
ejpam-4500	341	26	.	.	PUNCT
ejpam-4500	342	1	furthermore	furthermore	ADV
ejpam-4500	342	2	,	,	PUNCT
ejpam-4500	342	3	it	it	PRON
ejpam-4500	342	4	may	may	AUX
ejpam-4500	342	5	be	be	AUX
ejpam-4500	342	6	interesting	interesting	ADJ
ejpam-4500	342	7	to	to	PART
ejpam-4500	342	8	study	study	VERB
ejpam-4500	342	9	the	the	DET
ejpam-4500	342	10	relationship	relationship	NOUN
ejpam-4500	342	11	between	between	ADP
ejpam-4500	342	12	this	this	DET
ejpam-4500	342	13	new	new	ADJ
ejpam-4500	342	14	parameter	parameter	NOUN
ejpam-4500	342	15	and	and	CCONJ
ejpam-4500	342	16	other	other	ADJ
ejpam-4500	342	17	related	relate	VERB
ejpam-4500	342	18	known	know	VERB
ejpam-4500	342	19	graph	graph	NOUN
ejpam-4500	342	20	-	-	PUNCT
ejpam-4500	342	21	theoretic	theoretic	NOUN
ejpam-4500	342	22	parameters	parameter	NOUN
ejpam-4500	342	23	.	.	PUNCT
ejpam-4500	343	1	acknowledgements	acknowledgement	NOUN
ejpam-4500	343	2	this	this	DET
ejpam-4500	343	3	research	research	NOUN
ejpam-4500	343	4	is	be	AUX
ejpam-4500	343	5	funded	fund	VERB
ejpam-4500	343	6	by	by	ADP
ejpam-4500	343	7	the	the	DET
ejpam-4500	343	8	department	department	PROPN
ejpam-4500	343	9	of	of	ADP
ejpam-4500	343	10	science	science	NOUN
ejpam-4500	343	11	and	and	CCONJ
ejpam-4500	343	12	technology	technology	NOUN
ejpam-4500	343	13	-	-	PUNCT
ejpam-4500	343	14	accelerated	accelerate	VERB
ejpam-4500	343	15	science	science	NOUN
ejpam-4500	343	16	and	and	CCONJ
ejpam-4500	343	17	technology	technology	NOUN
ejpam-4500	343	18	human	human	ADJ
ejpam-4500	343	19	resource	resource	NOUN
ejpam-4500	343	20	development	development	NOUN
ejpam-4500	343	21	program	program	NOUN
ejpam-4500	343	22	(	(	PUNCT
ejpam-4500	343	23	dost	dost	NOUN
ejpam-4500	343	24	-	-	PUNCT
ejpam-4500	343	25	asthrdp	asthrdp	NOUN
ejpam-4500	343	26	)	)	PUNCT
ejpam-4500	343	27	and	and	CCONJ
ejpam-4500	343	28	the	the	DET
ejpam-4500	343	29	minadanao	minadanao	ADJ
ejpam-4500	343	30	state	state	PROPN
ejpam-4500	343	31	university	university	PROPN
ejpam-4500	343	32	-	-	PUNCT
ejpam-4500	343	33	iligan	iligan	PROPN
ejpam-4500	343	34	institute	institute	PROPN
ejpam-4500	343	35	of	of	ADP
ejpam-4500	343	36	technology	technology	PROPN
ejpam-4500	343	37	.	.	PUNCT
ejpam-4500	344	1	the	the	DET
ejpam-4500	344	2	authors	author	NOUN
ejpam-4500	344	3	would	would	AUX
ejpam-4500	344	4	like	like	VERB
ejpam-4500	344	5	to	to	PART
ejpam-4500	344	6	thank	thank	VERB
ejpam-4500	344	7	the	the	DET
ejpam-4500	344	8	reviewers	reviewer	NOUN
ejpam-4500	344	9	for	for	ADP
ejpam-4500	344	10	their	their	PRON
ejpam-4500	344	11	indispensable	indispensable	ADJ
ejpam-4500	344	12	comments	comment	NOUN
ejpam-4500	344	13	and	and	CCONJ
ejpam-4500	344	14	suggestions	suggestion	NOUN
ejpam-4500	344	15	that	that	PRON
ejpam-4500	344	16	led	lead	VERB
ejpam-4500	344	17	to	to	ADP
ejpam-4500	344	18	this	this	DET
ejpam-4500	344	19	improved	improve	VERB
ejpam-4500	344	20	version	version	NOUN
ejpam-4500	344	21	of	of	ADP
ejpam-4500	344	22	the	the	DET
ejpam-4500	344	23	paper	paper	NOUN
ejpam-4500	344	24	.	.	PUNCT
ejpam-4500	345	1	references	reference	NOUN
ejpam-4500	345	2	[	[	X
ejpam-4500	345	3	1	1	NUM
ejpam-4500	345	4	]	]	PUNCT
ejpam-4500	345	5	g.	g.	PROPN
ejpam-4500	345	6	cagaanan	cagaanan	PROPN
ejpam-4500	345	7	and	and	CCONJ
ejpam-4500	345	8	s.	s.	PROPN
ejpam-4500	345	9	canoy	canoy	PROPN
ejpam-4500	345	10	jr	jr	PROPN
ejpam-4500	345	11	.	.	PROPN
ejpam-4500	345	12	bounds	bound	VERB
ejpam-4500	345	13	for	for	ADP
ejpam-4500	345	14	the	the	DET
ejpam-4500	345	15	geodetic	geodetic	ADJ
ejpam-4500	345	16	number	number	NOUN
ejpam-4500	345	17	of	of	ADP
ejpam-4500	345	18	the	the	DET
ejpam-4500	345	19	cartesian	cartesian	ADJ
ejpam-4500	345	20	product	product	NOUN
ejpam-4500	345	21	of	of	ADP
ejpam-4500	345	22	graphs	graph	NOUN
ejpam-4500	345	23	.	.	PUNCT
ejpam-4500	346	1	utilitas	utilitas	PROPN
ejpam-4500	346	2	matematica	matematica	PROPN
ejpam-4500	346	3	,	,	PUNCT
ejpam-4500	346	4	79:91–98	79:91–98	NUM
ejpam-4500	346	5	,	,	PUNCT
ejpam-4500	346	6	2009	2009	NUM
ejpam-4500	346	7	.	.	PUNCT
ejpam-4500	347	1	[	[	X
ejpam-4500	347	2	2	2	X
ejpam-4500	347	3	]	]	PUNCT
ejpam-4500	347	4	t.	t.	PROPN
ejpam-4500	347	5	daniel	daniel	PROPN
ejpam-4500	347	6	and	and	CCONJ
ejpam-4500	347	7	s.	s.	PROPN
ejpam-4500	347	8	canoy	canoy	PROPN
ejpam-4500	347	9	jr	jr	PROPN
ejpam-4500	347	10	.	.	PROPN
ejpam-4500	347	11	clique	clique	PROPN
ejpam-4500	347	12	domination	domination	NOUN
ejpam-4500	347	13	in	in	ADP
ejpam-4500	347	14	a	a	DET
ejpam-4500	347	15	graph	graph	NOUN
ejpam-4500	347	16	.	.	PUNCT
ejpam-4500	348	1	applied	apply	VERB
ejpam-4500	348	2	mathematical	mathematical	ADJ
ejpam-4500	348	3	sciences	science	NOUN
ejpam-4500	348	4	,	,	PUNCT
ejpam-4500	348	5	9(116):5749–5755	9(116):5749–5755	NUM
ejpam-4500	348	6	,	,	PUNCT
ejpam-4500	348	7	2015	2015	NUM
ejpam-4500	348	8	.	.	PUNCT
ejpam-4500	349	1	[	[	X
ejpam-4500	349	2	3	3	X
ejpam-4500	349	3	]	]	X
ejpam-4500	349	4	r.	r.	NOUN
ejpam-4500	349	5	eballe	eballe	PROPN
ejpam-4500	349	6	and	and	CCONJ
ejpam-4500	349	7	s.	s.	PROPN
ejpam-4500	349	8	canoy	canoy	PROPN
ejpam-4500	349	9	jr	jr	PROPN
ejpam-4500	349	10	.	.	PROPN
ejpam-4500	349	11	steiner	steiner	PROPN
ejpam-4500	349	12	sets	set	NOUN
ejpam-4500	349	13	in	in	ADP
ejpam-4500	349	14	the	the	DET
ejpam-4500	349	15	join	join	NOUN
ejpam-4500	349	16	and	and	CCONJ
ejpam-4500	349	17	composition	composition	NOUN
ejpam-4500	349	18	of	of	ADP
ejpam-4500	349	19	graphs	graph	NOUN
ejpam-4500	349	20	.	.	PUNCT
ejpam-4500	350	1	applied	apply	VERB
ejpam-4500	350	2	mathematical	mathematical	ADJ
ejpam-4500	350	3	sciences	sciences	PROPN
ejpam-4500	350	4	,	,	PUNCT
ejpam-4500	350	5	170:65–73	170:65–73	NUM
ejpam-4500	350	6	,	,	PUNCT
ejpam-4500	350	7	2004	2004	NUM
ejpam-4500	350	8	.	.	PUNCT
ejpam-4500	351	1	[	[	X
ejpam-4500	351	2	4	4	X
ejpam-4500	351	3	]	]	PUNCT
ejpam-4500	351	4	b.	b.	NOUN
ejpam-4500	351	5	omamalin	omamalin	PROPN
ejpam-4500	351	6	,	,	PUNCT
ejpam-4500	351	7	s.	s.	PROPN
ejpam-4500	351	8	canoy	canoy	PROPN
ejpam-4500	351	9	jr	jr	PROPN
ejpam-4500	351	10	.	.	PROPN
ejpam-4500	351	11	and	and	CCONJ
ejpam-4500	351	12	h	h	PROPN
ejpam-4500	351	13	rara	rara	NOUN
ejpam-4500	351	14	.	.	PUNCT
ejpam-4500	352	1	locating	locate	VERB
ejpam-4500	352	2	total	total	ADJ
ejpam-4500	352	3	dominating	dominating	NOUN
ejpam-4500	352	4	sets	set	NOUN
ejpam-4500	352	5	in	in	ADP
ejpam-4500	352	6	the	the	DET
ejpam-4500	352	7	join	join	NOUN
ejpam-4500	352	8	,	,	PUNCT
ejpam-4500	352	9	corona	corona	NOUN
ejpam-4500	352	10	and	and	CCONJ
ejpam-4500	352	11	composition	composition	NOUN
ejpam-4500	352	12	of	of	ADP
ejpam-4500	352	13	graphs	graph	NOUN
ejpam-4500	352	14	.	.	PUNCT
ejpam-4500	353	1	applied	apply	VERB
ejpam-4500	353	2	mathematical	mathematical	ADJ
ejpam-4500	353	3	sciences	science	NOUN
ejpam-4500	353	4	,	,	PUNCT
ejpam-4500	353	5	8:2363–2374	8:2363–2374	NUM
ejpam-4500	353	6	,	,	PUNCT
ejpam-4500	353	7	2014	2014	NUM
ejpam-4500	353	8	.	.	PUNCT
ejpam-4500	354	1	[	[	X
ejpam-4500	354	2	5	5	X
ejpam-4500	354	3	]	]	PUNCT
ejpam-4500	354	4	s.	s.	PROPN
ejpam-4500	354	5	canoy	canoy	PROPN
ejpam-4500	354	6	jr	jr	PROPN
ejpam-4500	354	7	.	.	PROPN
ejpam-4500	354	8	and	and	CCONJ
ejpam-4500	354	9	g.	g.	PROPN
ejpam-4500	354	10	malacas	malacas	PROPN
ejpam-4500	354	11	.	.	PUNCT
ejpam-4500	355	1	determining	determine	VERB
ejpam-4500	355	2	the	the	DET
ejpam-4500	355	3	intruder	intruder	NOUN
ejpam-4500	355	4	’s	’s	PART
ejpam-4500	355	5	location	location	NOUN
ejpam-4500	355	6	in	in	ADP
ejpam-4500	355	7	a	a	DET
ejpam-4500	355	8	given	give	VERB
ejpam-4500	355	9	network	network	NOUN
ejpam-4500	355	10	:	:	PUNCT
ejpam-4500	355	11	locating	locate	VERB
ejpam-4500	355	12	-	-	PUNCT
ejpam-4500	355	13	dominating	dominating	NOUN
ejpam-4500	355	14	sets	set	NOUN
ejpam-4500	355	15	in	in	ADP
ejpam-4500	355	16	a	a	DET
ejpam-4500	355	17	graph	graph	NOUN
ejpam-4500	355	18	.	.	PUNCT
ejpam-4500	356	1	nrcp	nrcp	PROPN
ejpam-4500	356	2	research	research	PROPN
ejpam-4500	356	3	journal	journal	PROPN
ejpam-4500	356	4	,	,	PUNCT
ejpam-4500	356	5	8:0117–3294	8:0117–3294	NUM
ejpam-4500	356	6	,	,	PUNCT
ejpam-4500	356	7	2013	2013	NUM
ejpam-4500	356	8	.	.	PUNCT
ejpam-4500	357	1	references	reference	NOUN
ejpam-4500	357	2	1715	1715	NUM
ejpam-4500	357	3	[	[	X
ejpam-4500	357	4	6	6	NUM
ejpam-4500	357	5	]	]	PUNCT
ejpam-4500	357	6	s.	s.	PROPN
ejpam-4500	357	7	canoy	canoy	PROPN
ejpam-4500	357	8	jr	jr	PROPN
ejpam-4500	357	9	.	.	PROPN
ejpam-4500	357	10	and	and	CCONJ
ejpam-4500	357	11	g.	g.	PROPN
ejpam-4500	357	12	salasalan	salasalan	NOUN
ejpam-4500	357	13	.	.	PUNCT
ejpam-4500	358	1	a	a	DET
ejpam-4500	358	2	variant	variant	NOUN
ejpam-4500	358	3	of	of	ADP
ejpam-4500	358	4	hop	hop	NOUN
ejpam-4500	358	5	dominationin	dominationin	NOUN
ejpam-4500	358	6	graphs	graph	NOUN
ejpam-4500	358	7	.	.	PUNCT
ejpam-4500	359	1	eur	eur	PROPN
ejpam-4500	359	2	.	.	PUNCT
ejpam-4500	360	1	j.	j.	PROPN
ejpam-4500	360	2	pure	pure	PROPN
ejpam-4500	360	3	appl	appl	PROPN
ejpam-4500	360	4	.	.	PUNCT
ejpam-4500	360	5	math	math	PROPN
ejpam-4500	360	6	.	.	PUNCT
ejpam-4500	360	7	,	,	PUNCT
ejpam-4500	360	8	15(2):342–353	15(2):342–353	NUM
ejpam-4500	360	9	,	,	PUNCT
ejpam-4500	360	10	2021	2021	NUM
ejpam-4500	360	11	.	.	PUNCT
ejpam-4500	361	1	[	[	X
ejpam-4500	361	2	7	7	X
ejpam-4500	361	3	]	]	X
ejpam-4500	361	4	s.	s.	PROPN
ejpam-4500	361	5	canoy	canoy	PROPN
ejpam-4500	361	6	jr	jr	PROPN
ejpam-4500	361	7	.	.	PROPN
ejpam-4500	361	8	and	and	CCONJ
ejpam-4500	361	9	g.	g.	PROPN
ejpam-4500	361	10	salasalan	salasalan	NOUN
ejpam-4500	361	11	.	.	PUNCT
ejpam-4500	362	1	locating	locate	VERB
ejpam-4500	362	2	-	-	PUNCT
ejpam-4500	362	3	hop	hop	NOUN
ejpam-4500	362	4	domination	domination	NOUN
ejpam-4500	362	5	in	in	ADP
ejpam-4500	362	6	graphs	graph	NOUN
ejpam-4500	362	7	.	.	PUNCT
ejpam-4500	363	1	kyungpook	kyungpook	PROPN
ejpam-4500	363	2	mathematical	mathematical	PROPN
ejpam-4500	363	3	journal	journal	PROPN
ejpam-4500	363	4	,	,	PUNCT
ejpam-4500	363	5	62:193–204	62:193–204	PROPN
ejpam-4500	363	6	,	,	PUNCT
ejpam-4500	363	7	2022	2022	NUM
ejpam-4500	363	8	.	.	PUNCT
ejpam-4500	364	1	[	[	X
ejpam-4500	364	2	8	8	NUM
ejpam-4500	364	3	]	]	X
ejpam-4500	364	4	s.	s.	PROPN
ejpam-4500	364	5	canoy	canoy	PROPN
ejpam-4500	364	6	jr	jr	PROPN
ejpam-4500	364	7	.	.	PROPN
ejpam-4500	364	8	,	,	PUNCT
ejpam-4500	364	9	g.	g.	PROPN
ejpam-4500	364	10	malacas	malacas	PROPN
ejpam-4500	364	11	and	and	CCONJ
ejpam-4500	364	12	d.	d.	PROPN
ejpam-4500	364	13	tarepe	tarepe	PROPN
ejpam-4500	364	14	.	.	PUNCT
ejpam-4500	365	1	locating	locate	VERB
ejpam-4500	365	2	-	-	PUNCT
ejpam-4500	365	3	dominating	dominating	NOUN
ejpam-4500	365	4	sets	set	NOUN
ejpam-4500	365	5	in	in	ADP
ejpam-4500	365	6	graphs	graph	NOUN
ejpam-4500	365	7	.	.	PUNCT
ejpam-4500	366	1	applied	apply	VERB
ejpam-4500	366	2	mathematical	mathematical	ADJ
ejpam-4500	366	3	sciences	sciences	PROPN
ejpam-4500	366	4	,	,	PUNCT
ejpam-4500	366	5	8:4381–4388	8:4381–4388	NUM
ejpam-4500	366	6	,	,	PUNCT
ejpam-4500	366	7	2014	2014	NUM
ejpam-4500	366	8	.	.	PUNCT
ejpam-4500	367	1	[	[	X
ejpam-4500	367	2	9	9	NUM
ejpam-4500	367	3	]	]	PUNCT
ejpam-4500	367	4	s.	s.	PROPN
ejpam-4500	367	5	canoy	canoy	PROPN
ejpam-4500	367	6	jr	jr	PROPN
ejpam-4500	367	7	.	.	PROPN
ejpam-4500	367	8	,	,	PUNCT
ejpam-4500	367	9	r.	r.	PROPN
ejpam-4500	367	10	mollejon	mollejon	NOUN
ejpam-4500	367	11	and	and	CCONJ
ejpam-4500	367	12	j.g	j.g	PROPN
ejpam-4500	367	13	.	.	PROPN
ejpam-4500	367	14	canoy	canoy	PROPN
ejpam-4500	367	15	.	.	PUNCT
ejpam-4500	368	1	hop	hop	PROPN
ejpam-4500	368	2	dominating	dominating	NOUN
ejpam-4500	368	3	sets	set	NOUN
ejpam-4500	368	4	in	in	ADP
ejpam-4500	368	5	graphs	graph	NOUN
ejpam-4500	368	6	under	under	ADP
ejpam-4500	368	7	binary	binary	ADJ
ejpam-4500	368	8	operations	operation	NOUN
ejpam-4500	368	9	.	.	PUNCT
ejpam-4500	369	1	european	european	ADJ
ejpam-4500	369	2	journal	journal	PROPN
ejpam-4500	369	3	of	of	ADP
ejpam-4500	369	4	pure	pure	ADJ
ejpam-4500	369	5	and	and	CCONJ
ejpam-4500	369	6	applied	applied	ADJ
ejpam-4500	369	7	mathematics	mathematic	NOUN
ejpam-4500	369	8	,	,	PUNCT
ejpam-4500	369	9	12:1455–1463	12:1455–1463	NUM
ejpam-4500	369	10	,	,	PUNCT
ejpam-4500	369	11	2019	2019	NUM
ejpam-4500	369	12	.	.	PUNCT
ejpam-4500	370	1	[	[	X
ejpam-4500	370	2	10	10	NUM
ejpam-4500	370	3	]	]	X
ejpam-4500	370	4	c.	c.	PROPN
ejpam-4500	370	5	natarajan	natarajan	PROPN
ejpam-4500	370	6	and	and	CCONJ
ejpam-4500	370	7	s.	s.	PROPN
ejpam-4500	370	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4500	370	9	.	.	PUNCT
ejpam-4500	371	1	hop	hop	PROPN
ejpam-4500	371	2	domination	domination	NOUN
ejpam-4500	371	3	in	in	ADP
ejpam-4500	371	4	graphs	graph	NOUN
ejpam-4500	371	5	-	-	PUNCT
ejpam-4500	371	6	ii	ii	NOUN
ejpam-4500	371	7	.	.	PUNCT
ejpam-4500	371	8	versita	versita	PROPN
ejpam-4500	371	9	,	,	PUNCT
ejpam-4500	371	10	23(2):187	23(2):187	NUM
ejpam-4500	371	11	–	–	PUNCT
ejpam-4500	371	12	199	199	NUM
ejpam-4500	371	13	,	,	PUNCT
ejpam-4500	371	14	2015	2015	NUM
ejpam-4500	371	15	.	.	PUNCT
ejpam-4500	372	1	[	[	X
ejpam-4500	372	2	11	11	NUM
ejpam-4500	372	3	]	]	PUNCT
ejpam-4500	372	4	s.	s.	PROPN
ejpam-4500	372	5	omega	omega	PROPN
ejpam-4500	372	6	and	and	CCONJ
ejpam-4500	372	7	s.	s.	PROPN
ejpam-4500	372	8	canoy	canoy	PROPN
ejpam-4500	372	9	jr	jr	PROPN
ejpam-4500	372	10	.	.	PUNCT
ejpam-4500	372	11	locating	locate	VERB
ejpam-4500	372	12	sets	set	NOUN
ejpam-4500	372	13	in	in	ADP
ejpam-4500	372	14	a	a	DET
ejpam-4500	372	15	graph	graph	NOUN
ejpam-4500	372	16	.	.	PUNCT
ejpam-4500	373	1	applied	apply	VERB
ejpam-4500	373	2	mathematical	mathematical	ADJ
ejpam-4500	373	3	sciences	science	NOUN
ejpam-4500	373	4	,	,	PUNCT
ejpam-4500	373	5	9:2957–2964	9:2957–2964	NUM
ejpam-4500	373	6	,	,	PUNCT
ejpam-4500	373	7	2015	2015	NUM
ejpam-4500	373	8	.	.	PUNCT
ejpam-4500	374	1	[	[	X
ejpam-4500	374	2	12	12	NUM
ejpam-4500	374	3	]	]	X
ejpam-4500	374	4	g.	g.	NOUN
ejpam-4500	374	5	salasalan	salasalan	NOUN
ejpam-4500	374	6	and	and	CCONJ
ejpam-4500	374	7	s.	s.	PROPN
ejpam-4500	374	8	canoy	canoy	PROPN
ejpam-4500	374	9	jr	jr	PROPN
ejpam-4500	374	10	.	.	PROPN
ejpam-4500	374	11	global	global	PROPN
ejpam-4500	374	12	hop	hop	PROPN
ejpam-4500	374	13	domination	domination	PROPN
ejpam-4500	374	14	numbers	number	NOUN
ejpam-4500	374	15	of	of	ADP
ejpam-4500	374	16	graphs	graph	NOUN
ejpam-4500	374	17	.	.	PUNCT
ejpam-4500	375	1	eur	eur	PROPN
ejpam-4500	375	2	.	.	PUNCT
ejpam-4500	376	1	j.	j.	PROPN
ejpam-4500	376	2	pure	pure	PROPN
ejpam-4500	376	3	appl	appl	PROPN
ejpam-4500	376	4	.	.	PUNCT
ejpam-4500	376	5	math	math	PROPN
ejpam-4500	376	6	.	.	PUNCT
ejpam-4500	376	7	,	,	PUNCT
ejpam-4500	376	8	14(1):112–125	14(1):112–125	NUM
ejpam-4500	376	9	,	,	PUNCT
ejpam-4500	376	10	2021	2021	NUM
ejpam-4500	376	11	.	.	PUNCT
ejpam-4500	377	1	[	[	X
ejpam-4500	377	2	13	13	NUM
ejpam-4500	377	3	]	]	X
ejpam-4500	377	4	g.	g.	NOUN
ejpam-4500	377	5	salasalan	salasalan	NOUN
ejpam-4500	377	6	and	and	CCONJ
ejpam-4500	377	7	s.	s.	PROPN
ejpam-4500	377	8	canoy	canoy	PROPN
ejpam-4500	377	9	jr	jr	PROPN
ejpam-4500	377	10	.	.	PUNCT
ejpam-4500	377	11	revisiting	revisit	VERB
ejpam-4500	377	12	domination	domination	NOUN
ejpam-4500	377	13	,	,	PUNCT
ejpam-4500	377	14	hop	hop	NOUN
ejpam-4500	377	15	domination	domination	NOUN
ejpam-4500	377	16	,	,	PUNCT
ejpam-4500	377	17	and	and	CCONJ
ejpam-4500	377	18	global	global	ADJ
ejpam-4500	377	19	hop	hop	NOUN
ejpam-4500	377	20	domination	domination	NOUN
ejpam-4500	377	21	in	in	ADP
ejpam-4500	377	22	graphs	graph	NOUN
ejpam-4500	377	23	.	.	PUNCT
ejpam-4500	378	1	eur	eur	PROPN
ejpam-4500	378	2	.	.	PUNCT
ejpam-4500	379	1	j.	j.	PROPN
ejpam-4500	379	2	pure	pure	PROPN
ejpam-4500	379	3	appl	appl	PROPN
ejpam-4500	379	4	.	.	PUNCT
ejpam-4500	379	5	math	math	PROPN
ejpam-4500	379	6	.	.	PUNCT
ejpam-4500	379	7	,	,	PUNCT
ejpam-4500	380	1	14(4):1415–1428	14(4):1415–1428	NUM
ejpam-4500	380	2	,	,	PUNCT
ejpam-4500	380	3	2021	2021	NUM
ejpam-4500	380	4	.	.	PUNCT
ejpam-4500	381	1	[	[	X
ejpam-4500	381	2	14	14	NUM
ejpam-4500	381	3	]	]	X
ejpam-4500	381	4	s.j	s.j	PROPN
ejpam-4500	381	5	.	.	PROPN
ejpam-4500	381	6	seo	seo	PROPN
ejpam-4500	381	7	and	and	CCONJ
ejpam-4500	381	8	p.j	p.j	PROPN
ejpam-4500	381	9	.	.	PROPN
ejpam-4500	381	10	slater	slater	PROPN
ejpam-4500	381	11	.	.	PUNCT
ejpam-4500	382	1	open	open	ADJ
ejpam-4500	382	2	neighborhood	neighborhood	NOUN
ejpam-4500	382	3	locating	locate	VERB
ejpam-4500	382	4	-	-	PUNCT
ejpam-4500	382	5	dominating	dominating	NOUN
ejpam-4500	382	6	sets	set	NOUN
ejpam-4500	382	7	.	.	PUNCT
ejpam-4500	383	1	australasean	australasean	ADJ
ejpam-4500	383	2	journal	journal	PROPN
ejpam-4500	383	3	of	of	ADP
ejpam-4500	383	4	combinatorics	combinatoric	NOUN
ejpam-4500	383	5	,	,	PUNCT
ejpam-4500	383	6	46:109–119	46:109–119	PROPN
ejpam-4500	383	7	,	,	PUNCT
ejpam-4500	383	8	2010	2010	NUM
ejpam-4500	383	9	.	.	PUNCT
ejpam-4500	384	1	[	[	X
ejpam-4500	384	2	15	15	NUM
ejpam-4500	384	3	]	]	X
ejpam-4500	384	4	s.j	s.j	PROPN
ejpam-4500	384	5	.	.	PROPN
ejpam-4500	384	6	seo	seo	PROPN
ejpam-4500	384	7	and	and	CCONJ
ejpam-4500	384	8	p.j	p.j	PROPN
ejpam-4500	384	9	.	.	PROPN
ejpam-4500	384	10	slater	slater	PROPN
ejpam-4500	384	11	.	.	PUNCT
ejpam-4500	385	1	open	open	ADJ
ejpam-4500	385	2	neighborhood	neighborhood	NOUN
ejpam-4500	385	3	locating	locate	VERB
ejpam-4500	385	4	-	-	PUNCT
ejpam-4500	385	5	dominating	dominating	NOUN
ejpam-4500	385	6	in	in	ADP
ejpam-4500	385	7	trees	tree	NOUN
ejpam-4500	385	8	.	.	PUNCT
ejpam-4500	386	1	discrete	discrete	ADJ
ejpam-4500	386	2	applied	apply	VERB
ejpam-4500	386	3	mathematics	mathematic	NOUN
ejpam-4500	386	4	,	,	PUNCT
ejpam-4500	386	5	159:484–489	159:484–489	NUM
ejpam-4500	386	6	,	,	PUNCT
ejpam-4500	386	7	2011	2011	NUM
ejpam-4500	386	8	.	.	PUNCT
ejpam-4500	387	1	[	[	X
ejpam-4500	387	2	16	16	NUM
ejpam-4500	387	3	]	]	X
ejpam-4500	387	4	p.j	p.j	PROPN
ejpam-4500	387	5	.	.	PROPN
ejpam-4500	387	6	slater	slater	PROPN
ejpam-4500	387	7	.	.	PUNCT
ejpam-4500	388	1	leaves	leave	NOUN
ejpam-4500	388	2	of	of	ADP
ejpam-4500	388	3	trees	tree	NOUN
ejpam-4500	388	4	.	.	PUNCT
ejpam-4500	389	1	congressus	congressus	PROPN
ejpam-4500	389	2	numerantium	numerantium	PROPN
ejpam-4500	389	3	,	,	PUNCT
ejpam-4500	389	4	pages	page	NOUN
ejpam-4500	389	5	549–559	549–559	NUM
ejpam-4500	389	6	,	,	PUNCT
ejpam-4500	389	7	1975	1975	NUM
ejpam-4500	389	8	.	.	PUNCT
ejpam-4500	390	1	[	[	X
ejpam-4500	390	2	17	17	NUM
ejpam-4500	390	3	]	]	X
ejpam-4500	390	4	p.j	p.j	PROPN
ejpam-4500	390	5	.	.	PROPN
ejpam-4500	390	6	slater	slater	PROPN
ejpam-4500	390	7	.	.	PUNCT
ejpam-4500	391	1	domination	domination	NOUN
ejpam-4500	391	2	and	and	CCONJ
ejpam-4500	391	3	location	location	NOUN
ejpam-4500	391	4	in	in	ADP
ejpam-4500	391	5	acyclic	acyclic	ADJ
ejpam-4500	391	6	graphs	graph	NOUN
ejpam-4500	391	7	.	.	PUNCT
ejpam-4500	392	1	networks	network	NOUN
ejpam-4500	392	2	,	,	PUNCT
ejpam-4500	392	3	17:55–64	17:55–64	PROPN
ejpam-4500	392	4	,	,	PUNCT
ejpam-4500	392	5	1987	1987	NUM
ejpam-4500	392	6	.	.	PUNCT
ejpam-4500	393	1	[	[	X
ejpam-4500	393	2	18	18	NUM
ejpam-4500	393	3	]	]	X
ejpam-4500	393	4	d.p	d.p	PROPN
ejpam-4500	393	5	.	.	PROPN
ejpam-4500	393	6	summer	summer	NOUN
ejpam-4500	393	7	.	.	PUNCT
ejpam-4500	394	1	point	point	NOUN
ejpam-4500	394	2	determination	determination	NOUN
ejpam-4500	394	3	in	in	ADP
ejpam-4500	394	4	graphs∗.	graphs∗.	PROPN
ejpam-4500	394	5	discrete	discrete	ADJ
ejpam-4500	394	6	mathematics	mathematic	NOUN
ejpam-4500	394	7	,	,	PUNCT
ejpam-4500	394	8	north	north	NOUN
ejpam-4500	394	9	-	-	PUNCT
ejpam-4500	394	10	holland	holland	PROPN
ejpam-4500	394	11	publishing	publishing	PROPN
ejpam-4500	394	12	company	company	NOUN
ejpam-4500	394	13	,	,	PUNCT
ejpam-4500	394	14	pages	page	NOUN
ejpam-4500	394	15	179–187	179–187	NUM
ejpam-4500	394	16	,	,	PUNCT
ejpam-4500	394	17	1973	1973	NUM
ejpam-4500	394	18	.	.	PUNCT