id	sid	tid	token	lemma	pos
ejpam-4770	1	1	european	european	PROPN
ejpam-4770	1	2	journal	journal	PROPN
ejpam-4770	1	3	of	of	ADP
ejpam-4770	1	4	pure	pure	ADJ
ejpam-4770	1	5	and	and	CCONJ
ejpam-4770	1	6	applied	apply	VERB
ejpam-4770	1	7	mathematics	mathematic	NOUN
ejpam-4770	1	8	vol	vol	NOUN
ejpam-4770	1	9	.	.	PUNCT
ejpam-4770	2	1	16	16	NUM
ejpam-4770	2	2	,	,	PUNCT
ejpam-4770	2	3	no	no	INTJ
ejpam-4770	2	4	.	.	NOUN
ejpam-4770	2	5	3	3	NUM
ejpam-4770	2	6	,	,	PUNCT
ejpam-4770	2	7	2023	2023	NUM
ejpam-4770	2	8	,	,	PUNCT
ejpam-4770	2	9	1464	1464	NUM
ejpam-4770	2	10	-	-	SYM
ejpam-4770	2	11	1479	1479	NUM
ejpam-4770	2	12	issn	issn	PROPN
ejpam-4770	2	13	1307	1307	NUM
ejpam-4770	2	14	-	-	SYM
ejpam-4770	2	15	5543	5543	NUM
ejpam-4770	2	16	–	–	PUNCT
ejpam-4770	3	1	ejpam.com	ejpam.com	X
ejpam-4770	3	2	published	publish	VERB
ejpam-4770	3	3	by	by	ADP
ejpam-4770	3	4	new	new	PROPN
ejpam-4770	3	5	york	york	PROPN
ejpam-4770	3	6	business	business	PROPN
ejpam-4770	3	7	global	global	ADJ
ejpam-4770	3	8	1	1	NUM
ejpam-4770	3	9	-	-	PUNCT
ejpam-4770	3	10	movable	movable	ADJ
ejpam-4770	3	11	2	2	NUM
ejpam-4770	3	12	-	-	PUNCT
ejpam-4770	3	13	resolving	resolve	VERB
ejpam-4770	3	14	hop	hop	NOUN
ejpam-4770	3	15	domination	domination	NOUN
ejpam-4770	3	16	in	in	ADP
ejpam-4770	3	17	graphs	graph	NOUN
ejpam-4770	3	18	angelica	angelica	PROPN
ejpam-4770	3	19	mae	mae	PROPN
ejpam-4770	3	20	mahistrado1	mahistrado1	PROPN
ejpam-4770	3	21	,	,	PUNCT
ejpam-4770	3	22	helen	helen	PROPN
ejpam-4770	3	23	rara1,∗	rara1,∗	VERB
ejpam-4770	3	24	1	1	NUM
ejpam-4770	3	25	department	department	NOUN
ejpam-4770	3	26	of	of	ADP
ejpam-4770	3	27	mathematics	mathematic	NOUN
ejpam-4770	3	28	and	and	CCONJ
ejpam-4770	3	29	statistics	statistic	NOUN
ejpam-4770	3	30	,	,	PUNCT
ejpam-4770	3	31	college	college	NOUN
ejpam-4770	3	32	of	of	ADP
ejpam-4770	3	33	science	science	NOUN
ejpam-4770	3	34	and	and	CCONJ
ejpam-4770	3	35	mathematics	mathematic	NOUN
ejpam-4770	3	36	,	,	PUNCT
ejpam-4770	3	37	center	center	NOUN
ejpam-4770	3	38	of	of	ADP
ejpam-4770	3	39	graph	graph	NOUN
ejpam-4770	3	40	theory	theory	NOUN
ejpam-4770	3	41	,	,	PUNCT
ejpam-4770	3	42	algebra	algebra	NOUN
ejpam-4770	3	43	,	,	PUNCT
ejpam-4770	3	44	and	and	CCONJ
ejpam-4770	3	45	analysis	analysis	NOUN
ejpam-4770	3	46	-	-	PUNCT
ejpam-4770	3	47	premier	premier	NOUN
ejpam-4770	3	48	research	research	NOUN
ejpam-4770	3	49	institute	institute	PROPN
ejpam-4770	3	50	of	of	ADP
ejpam-4770	3	51	science	science	NOUN
ejpam-4770	3	52	and	and	CCONJ
ejpam-4770	3	53	mathematics	mathematic	NOUN
ejpam-4770	3	54	,	,	PUNCT
ejpam-4770	3	55	mindanao	mindanao	PROPN
ejpam-4770	3	56	state	state	PROPN
ejpam-4770	3	57	university	university	PROPN
ejpam-4770	3	58	-	-	PUNCT
ejpam-4770	3	59	iligan	iligan	PROPN
ejpam-4770	3	60	institute	institute	PROPN
ejpam-4770	3	61	of	of	ADP
ejpam-4770	3	62	technology	technology	PROPN
ejpam-4770	3	63	,	,	PUNCT
ejpam-4770	3	64	9200	9200	NUM
ejpam-4770	3	65	iligan	iligan	ADJ
ejpam-4770	3	66	city	city	NOUN
ejpam-4770	3	67	,	,	PUNCT
ejpam-4770	3	68	philippines	philippine	NOUN
ejpam-4770	3	69	abstract	abstract	ADJ
ejpam-4770	3	70	.	.	PUNCT
ejpam-4770	4	1	let	let	VERB
ejpam-4770	4	2	g	g	PRON
ejpam-4770	4	3	be	be	AUX
ejpam-4770	4	4	a	a	DET
ejpam-4770	4	5	connected	connected	ADJ
ejpam-4770	4	6	graph	graph	NOUN
ejpam-4770	4	7	.	.	PUNCT
ejpam-4770	5	1	a	a	DET
ejpam-4770	5	2	set	set	NOUN
ejpam-4770	5	3	s	s	NOUN
ejpam-4770	5	4	of	of	ADP
ejpam-4770	5	5	vertices	vertex	NOUN
ejpam-4770	5	6	in	in	ADP
ejpam-4770	5	7	g	g	PROPN
ejpam-4770	5	8	is	be	AUX
ejpam-4770	5	9	a	a	DET
ejpam-4770	5	10	1	1	NUM
ejpam-4770	5	11	-	-	PUNCT
ejpam-4770	5	12	movable	movable	ADJ
ejpam-4770	5	13	2	2	NUM
ejpam-4770	5	14	-	-	PUNCT
ejpam-4770	5	15	resolving	resolve	VERB
ejpam-4770	5	16	hop	hop	NOUN
ejpam-4770	5	17	dominating	dominating	NOUN
ejpam-4770	5	18	set	set	NOUN
ejpam-4770	5	19	of	of	ADP
ejpam-4770	5	20	g	g	PROPN
ejpam-4770	5	21	if	if	SCONJ
ejpam-4770	5	22	s	s	VERB
ejpam-4770	5	23	is	be	AUX
ejpam-4770	5	24	a	a	DET
ejpam-4770	5	25	2	2	NUM
ejpam-4770	5	26	-	-	PUNCT
ejpam-4770	5	27	resolving	resolve	VERB
ejpam-4770	5	28	hop	hop	NOUN
ejpam-4770	5	29	dominating	dominating	NOUN
ejpam-4770	5	30	set	set	VERB
ejpam-4770	5	31	in	in	ADP
ejpam-4770	5	32	g	g	PROPN
ejpam-4770	5	33	and	and	CCONJ
ejpam-4770	5	34	for	for	SCONJ
ejpam-4770	5	35	every	every	DET
ejpam-4770	5	36	v	v	NUM
ejpam-4770	5	37	∈	∈	PROPN
ejpam-4770	5	38	s	s	NOUN
ejpam-4770	5	39	,	,	PUNCT
ejpam-4770	5	40	either	either	CCONJ
ejpam-4770	5	41	s\{v	s\{v	VERB
ejpam-4770	5	42	}	}	PUNCT
ejpam-4770	5	43	is	be	AUX
ejpam-4770	5	44	a	a	DET
ejpam-4770	5	45	2	2	NUM
ejpam-4770	5	46	-	-	PUNCT
ejpam-4770	5	47	resolving	resolve	VERB
ejpam-4770	5	48	hop	hop	NOUN
ejpam-4770	5	49	dominating	dominating	NOUN
ejpam-4770	5	50	set	set	NOUN
ejpam-4770	5	51	of	of	ADP
ejpam-4770	5	52	g	g	NOUN
ejpam-4770	5	53	or	or	CCONJ
ejpam-4770	5	54	there	there	ADV
ejpam-4770	5	55	exists	exist	VERB
ejpam-4770	5	56	a	a	DET
ejpam-4770	5	57	vertex	vertex	NOUN
ejpam-4770	5	58	u	u	NOUN
ejpam-4770	5	59	∈	∈	PROPN
ejpam-4770	5	60	(	(	PUNCT
ejpam-4770	5	61	(	(	PUNCT
ejpam-4770	5	62	v	v	NOUN
ejpam-4770	5	63	(	(	PUNCT
ejpam-4770	5	64	g)\s	g)\s	NOUN
ejpam-4770	5	65	)	)	PUNCT
ejpam-4770	5	66	∩ng(v	∩ng(v	PROPN
ejpam-4770	5	67	)	)	PUNCT
ejpam-4770	5	68	)	)	PUNCT
ejpam-4770	5	69	such	such	ADJ
ejpam-4770	5	70	that	that	SCONJ
ejpam-4770	5	71	(	(	PUNCT
ejpam-4770	5	72	s\{v	s\{v	VERB
ejpam-4770	5	73	}	}	PUNCT
ejpam-4770	5	74	)	)	PUNCT
ejpam-4770	5	75	∪	∪	ADP
ejpam-4770	5	76	{	{	PUNCT
ejpam-4770	5	77	u	u	NOUN
ejpam-4770	5	78	}	}	PUNCT
ejpam-4770	5	79	is	be	AUX
ejpam-4770	5	80	a	a	DET
ejpam-4770	5	81	2	2	NUM
ejpam-4770	5	82	-	-	PUNCT
ejpam-4770	5	83	resolving	resolve	VERB
ejpam-4770	5	84	hop	hop	NOUN
ejpam-4770	5	85	dominating	dominating	NOUN
ejpam-4770	5	86	set	set	NOUN
ejpam-4770	5	87	of	of	ADP
ejpam-4770	5	88	g.	g.	PROPN
ejpam-4770	5	89	the	the	DET
ejpam-4770	5	90	1	1	NUM
ejpam-4770	5	91	-	-	PUNCT
ejpam-4770	5	92	movable	movable	ADJ
ejpam-4770	5	93	2	2	NUM
ejpam-4770	5	94	-	-	PUNCT
ejpam-4770	5	95	resolving	resolve	VERB
ejpam-4770	5	96	hop	hop	NOUN
ejpam-4770	5	97	domination	domination	NOUN
ejpam-4770	5	98	number	number	NOUN
ejpam-4770	5	99	of	of	ADP
ejpam-4770	5	100	g	g	NOUN
ejpam-4770	5	101	,	,	PUNCT
ejpam-4770	5	102	denoted	denote	VERB
ejpam-4770	5	103	by	by	ADP
ejpam-4770	5	104	γ1	γ1	PROPN
ejpam-4770	5	105	m2rh(g	m2rh(g	PROPN
ejpam-4770	5	106	)	)	PUNCT
ejpam-4770	5	107	is	be	AUX
ejpam-4770	5	108	the	the	DET
ejpam-4770	5	109	smallest	small	ADJ
ejpam-4770	5	110	cardinality	cardinality	NOUN
ejpam-4770	5	111	of	of	ADP
ejpam-4770	5	112	a	a	DET
ejpam-4770	5	113	1	1	NUM
ejpam-4770	5	114	-	-	PUNCT
ejpam-4770	5	115	movable	movable	ADJ
ejpam-4770	5	116	2resolving	2resolving	NUM
ejpam-4770	5	117	hop	hop	NOUN
ejpam-4770	5	118	dominating	dominating	NOUN
ejpam-4770	5	119	set	set	NOUN
ejpam-4770	5	120	of	of	ADP
ejpam-4770	5	121	g.	g.	PROPN
ejpam-4770	5	122	in	in	ADP
ejpam-4770	5	123	this	this	DET
ejpam-4770	5	124	paper	paper	NOUN
ejpam-4770	5	125	,	,	PUNCT
ejpam-4770	5	126	we	we	PRON
ejpam-4770	5	127	investigate	investigate	VERB
ejpam-4770	5	128	the	the	DET
ejpam-4770	5	129	concept	concept	NOUN
ejpam-4770	5	130	and	and	CCONJ
ejpam-4770	5	131	study	study	VERB
ejpam-4770	5	132	it	it	PRON
ejpam-4770	5	133	for	for	ADP
ejpam-4770	5	134	graphs	graph	NOUN
ejpam-4770	5	135	resulting	result	VERB
ejpam-4770	5	136	from	from	ADP
ejpam-4770	5	137	some	some	DET
ejpam-4770	5	138	binary	binary	ADJ
ejpam-4770	5	139	operations	operation	NOUN
ejpam-4770	5	140	.	.	PUNCT
ejpam-4770	6	1	specifically	specifically	ADV
ejpam-4770	6	2	,	,	PUNCT
ejpam-4770	6	3	we	we	PRON
ejpam-4770	6	4	characterize	characterize	VERB
ejpam-4770	6	5	the	the	DET
ejpam-4770	6	6	1	1	NUM
ejpam-4770	6	7	-	-	PUNCT
ejpam-4770	6	8	movable	movable	ADJ
ejpam-4770	6	9	2	2	NUM
ejpam-4770	6	10	-	-	PUNCT
ejpam-4770	6	11	resolving	resolve	VERB
ejpam-4770	6	12	hop	hop	NOUN
ejpam-4770	6	13	dominating	dominating	NOUN
ejpam-4770	6	14	sets	set	NOUN
ejpam-4770	6	15	in	in	ADP
ejpam-4770	6	16	the	the	DET
ejpam-4770	6	17	join	join	NOUN
ejpam-4770	6	18	,	,	PUNCT
ejpam-4770	6	19	corona	corona	NOUN
ejpam-4770	6	20	and	and	CCONJ
ejpam-4770	6	21	lexicographic	lexicographic	ADJ
ejpam-4770	6	22	products	product	NOUN
ejpam-4770	6	23	of	of	ADP
ejpam-4770	6	24	graphs	graph	NOUN
ejpam-4770	6	25	,	,	PUNCT
ejpam-4770	6	26	and	and	CCONJ
ejpam-4770	6	27	determine	determine	VERB
ejpam-4770	6	28	the	the	DET
ejpam-4770	6	29	bounds	bound	NOUN
ejpam-4770	6	30	of	of	ADP
ejpam-4770	6	31	the	the	DET
ejpam-4770	6	32	1	1	NUM
ejpam-4770	6	33	-	-	PUNCT
ejpam-4770	6	34	movable	movable	ADJ
ejpam-4770	6	35	2	2	NUM
ejpam-4770	6	36	-	-	PUNCT
ejpam-4770	6	37	resolving	resolve	VERB
ejpam-4770	6	38	hop	hop	NOUN
ejpam-4770	6	39	domination	domination	NOUN
ejpam-4770	6	40	number	number	NOUN
ejpam-4770	6	41	of	of	ADP
ejpam-4770	6	42	each	each	PRON
ejpam-4770	6	43	of	of	ADP
ejpam-4770	6	44	these	these	DET
ejpam-4770	6	45	graphs	graph	NOUN
ejpam-4770	6	46	.	.	PUNCT
ejpam-4770	7	1	2020	2020	NUM
ejpam-4770	7	2	mathematics	mathematic	NOUN
ejpam-4770	7	3	subject	subject	NOUN
ejpam-4770	7	4	classifications	classification	NOUN
ejpam-4770	7	5	:	:	PUNCT
ejpam-4770	7	6	05c69	05c69	X
ejpam-4770	7	7	key	key	ADJ
ejpam-4770	7	8	words	word	NOUN
ejpam-4770	7	9	and	and	CCONJ
ejpam-4770	7	10	phrases	phrase	NOUN
ejpam-4770	7	11	:	:	PUNCT
ejpam-4770	7	12	1	1	NUM
ejpam-4770	7	13	-	-	NUM
ejpam-4770	7	14	movable	movable	ADJ
ejpam-4770	7	15	2	2	NUM
ejpam-4770	7	16	-	-	PUNCT
ejpam-4770	7	17	resolving	resolve	VERB
ejpam-4770	7	18	hop	hop	NOUN
ejpam-4770	7	19	dominating	dominating	NOUN
ejpam-4770	7	20	set	set	NOUN
ejpam-4770	7	21	,	,	PUNCT
ejpam-4770	7	22	1	1	NUM
ejpam-4770	7	23	-	-	PUNCT
ejpam-4770	7	24	movable	movable	ADJ
ejpam-4770	7	25	2	2	NUM
ejpam-4770	7	26	-	-	PUNCT
ejpam-4770	7	27	resolving	resolve	VERB
ejpam-4770	7	28	hop	hop	NOUN
ejpam-4770	7	29	domination	domination	NOUN
ejpam-4770	7	30	number	number	NOUN
ejpam-4770	7	31	,	,	PUNCT
ejpam-4770	7	32	join	join	NOUN
ejpam-4770	7	33	,	,	PUNCT
ejpam-4770	7	34	corona	corona	PROPN
ejpam-4770	7	35	,	,	PUNCT
ejpam-4770	7	36	edge	edge	NOUN
ejpam-4770	7	37	corona	corona	NOUN
ejpam-4770	7	38	,	,	PUNCT
ejpam-4770	7	39	lexicographic	lexicographic	ADJ
ejpam-4770	7	40	product	product	NOUN
ejpam-4770	7	41	1	1	NUM
ejpam-4770	7	42	.	.	PUNCT
ejpam-4770	7	43	introduction	introduction	NOUN
ejpam-4770	7	44	the	the	DET
ejpam-4770	7	45	concept	concept	NOUN
ejpam-4770	7	46	of	of	ADP
ejpam-4770	7	47	domination	domination	NOUN
ejpam-4770	7	48	was	be	AUX
ejpam-4770	7	49	formally	formally	ADV
ejpam-4770	7	50	studied	study	VERB
ejpam-4770	7	51	by	by	ADP
ejpam-4770	7	52	claude	claude	PROPN
ejpam-4770	7	53	berge	berge	PROPN
ejpam-4770	8	1	[	[	X
ejpam-4770	8	2	1	1	X
ejpam-4770	8	3	]	]	PUNCT
ejpam-4770	8	4	in	in	ADP
ejpam-4770	8	5	1958	1958	NUM
ejpam-4770	8	6	and	and	CCONJ
ejpam-4770	8	7	oystein	oystein	ADJ
ejpam-4770	8	8	ore	ore	NOUN
ejpam-4770	8	9	in	in	ADP
ejpam-4770	8	10	1962	1962	NUM
ejpam-4770	8	11	.	.	PUNCT
ejpam-4770	9	1	in	in	ADP
ejpam-4770	9	2	2015	2015	NUM
ejpam-4770	9	3	,	,	PUNCT
ejpam-4770	9	4	natarajan	natarajan	PROPN
ejpam-4770	9	5	and	and	CCONJ
ejpam-4770	9	6	ayyaswamy	ayyaswamy	PROPN
ejpam-4770	9	7	introduced	introduce	VERB
ejpam-4770	9	8	and	and	CCONJ
ejpam-4770	9	9	studied	study	VERB
ejpam-4770	9	10	the	the	DET
ejpam-4770	9	11	concept	concept	NOUN
ejpam-4770	9	12	of	of	ADP
ejpam-4770	9	13	hop	hop	NOUN
ejpam-4770	9	14	domination	domination	NOUN
ejpam-4770	9	15	[	[	X
ejpam-4770	9	16	14	14	NUM
ejpam-4770	9	17	]	]	PUNCT
ejpam-4770	9	18	.	.	PUNCT
ejpam-4770	10	1	on	on	ADP
ejpam-4770	10	2	the	the	DET
ejpam-4770	10	3	other	other	ADJ
ejpam-4770	10	4	hand	hand	NOUN
ejpam-4770	10	5	,	,	PUNCT
ejpam-4770	10	6	in	in	ADP
ejpam-4770	10	7	1975	1975	NUM
ejpam-4770	10	8	using	use	VERB
ejpam-4770	10	9	the	the	DET
ejpam-4770	10	10	term	term	NOUN
ejpam-4770	10	11	locating	locate	VERB
ejpam-4770	10	12	set	set	NOUN
ejpam-4770	10	13	,	,	PUNCT
ejpam-4770	10	14	the	the	DET
ejpam-4770	10	15	concept	concept	NOUN
ejpam-4770	10	16	of	of	ADP
ejpam-4770	10	17	resolving	resolve	VERB
ejpam-4770	10	18	sets	set	NOUN
ejpam-4770	10	19	for	for	ADP
ejpam-4770	10	20	a	a	DET
ejpam-4770	10	21	connected	connected	ADJ
ejpam-4770	10	22	graph	graph	NOUN
ejpam-4770	10	23	was	be	AUX
ejpam-4770	10	24	first	first	ADV
ejpam-4770	10	25	introduced	introduce	VERB
ejpam-4770	10	26	by	by	ADP
ejpam-4770	10	27	slater	slater	NOUN
ejpam-4770	10	28	[	[	X
ejpam-4770	10	29	17	17	NUM
ejpam-4770	10	30	]	]	PUNCT
ejpam-4770	10	31	.	.	PUNCT
ejpam-4770	11	1	these	these	DET
ejpam-4770	11	2	concepts	concept	NOUN
ejpam-4770	11	3	were	be	AUX
ejpam-4770	11	4	studied	study	VERB
ejpam-4770	11	5	much	much	ADV
ejpam-4770	11	6	earlier	early	ADV
ejpam-4770	11	7	in	in	ADP
ejpam-4770	11	8	the	the	DET
ejpam-4770	11	9	context	context	NOUN
ejpam-4770	11	10	of	of	ADP
ejpam-4770	11	11	the	the	DET
ejpam-4770	11	12	coin	coin	NOUN
ejpam-4770	11	13	-	-	PUNCT
ejpam-4770	11	14	weighing	weigh	VERB
ejpam-4770	11	15	problem	problem	NOUN
ejpam-4770	11	16	.	.	PUNCT
ejpam-4770	12	1	later	later	ADV
ejpam-4770	12	2	that	that	DET
ejpam-4770	12	3	year	year	NOUN
ejpam-4770	12	4	,	,	PUNCT
ejpam-4770	12	5	harary	harary	NOUN
ejpam-4770	12	6	and	and	CCONJ
ejpam-4770	12	7	melter	melter	NOUN
ejpam-4770	12	8	introduced	introduce	VERB
ejpam-4770	12	9	independently	independently	ADV
ejpam-4770	12	10	these	these	DET
ejpam-4770	12	11	concepts	concept	NOUN
ejpam-4770	12	12	,	,	PUNCT
ejpam-4770	12	13	but	but	CCONJ
ejpam-4770	12	14	with	with	ADP
ejpam-4770	12	15	different	different	ADJ
ejpam-4770	12	16	terminologies	terminology	NOUN
ejpam-4770	12	17	[	[	X
ejpam-4770	12	18	8	8	NUM
ejpam-4770	12	19	]	]	PUNCT
ejpam-4770	12	20	.	.	PUNCT
ejpam-4770	13	1	the	the	DET
ejpam-4770	13	2	term	term	NOUN
ejpam-4770	13	3	metric	metric	ADJ
ejpam-4770	13	4	dimension	dimension	NOUN
ejpam-4770	13	5	was	be	AUX
ejpam-4770	13	6	used	use	VERB
ejpam-4770	13	7	by	by	ADP
ejpam-4770	13	8	harary	harary	NOUN
ejpam-4770	13	9	and	and	CCONJ
ejpam-4770	13	10	melter	melter	NOUN
ejpam-4770	13	11	instead	instead	ADV
ejpam-4770	13	12	of	of	ADP
ejpam-4770	13	13	locating	locate	VERB
ejpam-4770	13	14	number	number	NOUN
ejpam-4770	13	15	.	.	PUNCT
ejpam-4770	14	1	recently	recently	ADV
ejpam-4770	14	2	,	,	PUNCT
ejpam-4770	14	3	2	2	NUM
ejpam-4770	14	4	-	-	PUNCT
ejpam-4770	14	5	resolving	resolve	VERB
ejpam-4770	14	6	hop	hop	NOUN
ejpam-4770	14	7	dominating	dominating	NOUN
ejpam-4770	14	8	sets	set	NOUN
ejpam-4770	14	9	in	in	ADP
ejpam-4770	14	10	graphs	graph	NOUN
ejpam-4770	14	11	was	be	AUX
ejpam-4770	14	12	studied	study	VERB
ejpam-4770	14	13	in	in	ADP
ejpam-4770	14	14	[	[	PUNCT
ejpam-4770	14	15	9	9	NUM
ejpam-4770	14	16	]	]	PUNCT
ejpam-4770	14	17	.	.	PUNCT
ejpam-4770	15	1	other	other	ADJ
ejpam-4770	15	2	variations	variation	NOUN
ejpam-4770	15	3	of	of	ADP
ejpam-4770	15	4	2	2	NUM
ejpam-4770	15	5	-	-	PUNCT
ejpam-4770	15	6	resolving	resolve	VERB
ejpam-4770	15	7	hop	hop	NOUN
ejpam-4770	15	8	dominating	dominating	NOUN
ejpam-4770	15	9	sets	set	NOUN
ejpam-4770	15	10	in	in	ADP
ejpam-4770	15	11	graphs	graph	NOUN
ejpam-4770	15	12	are	be	AUX
ejpam-4770	15	13	found	find	VERB
ejpam-4770	15	14	in	in	ADP
ejpam-4770	15	15	[	[	X
ejpam-4770	15	16	10	10	NUM
ejpam-4770	15	17	,	,	PUNCT
ejpam-4770	15	18	11	11	NUM
ejpam-4770	15	19	]	]	PUNCT
ejpam-4770	15	20	.	.	PUNCT
ejpam-4770	16	1	moreover	moreover	ADV
ejpam-4770	16	2	,	,	PUNCT
ejpam-4770	16	3	other	other	ADJ
ejpam-4770	16	4	variations	variation	NOUN
ejpam-4770	16	5	of	of	ADP
ejpam-4770	16	6	resolving	resolve	VERB
ejpam-4770	16	7	sets	set	NOUN
ejpam-4770	16	8	and	and	CCONJ
ejpam-4770	16	9	hop	hop	NOUN
ejpam-4770	16	10	dominating	dominating	NOUN
ejpam-4770	16	11	sets	set	NOUN
ejpam-4770	16	12	in	in	ADP
ejpam-4770	16	13	graphs	graph	NOUN
ejpam-4770	16	14	were	be	AUX
ejpam-4770	16	15	also	also	ADV
ejpam-4770	16	16	studied	study	VERB
ejpam-4770	16	17	in	in	ADP
ejpam-4770	16	18	[	[	X
ejpam-4770	16	19	4–7	4–7	X
ejpam-4770	16	20	,	,	PUNCT
ejpam-4770	16	21	12	12	NUM
ejpam-4770	16	22	,	,	PUNCT
ejpam-4770	16	23	13	13	NUM
ejpam-4770	16	24	]	]	PUNCT
ejpam-4770	16	25	.	.	PUNCT
ejpam-4770	17	1	∗corresponding	∗corresponde	VERB
ejpam-4770	17	2	author	author	NOUN
ejpam-4770	17	3	.	.	PUNCT
ejpam-4770	18	1	doi	doi	NOUN
ejpam-4770	18	2	:	:	PUNCT
ejpam-4770	18	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4770	https://doi.org/10.29020/nybg.ejpam.v16i3.4770	NOUN
ejpam-4770	18	4	email	email	NOUN
ejpam-4770	18	5	addresses	address	NOUN
ejpam-4770	18	6	:	:	PUNCT
ejpam-4770	18	7	angelicamae.mahistrado@g.msuiit.edu.ph	angelicamae.mahistrado@g.msuiit.edu.ph	PROPN
ejpam-4770	18	8	(	(	PUNCT
ejpam-4770	18	9	a.m.	a.m.	NOUN
ejpam-4770	18	10	mahistrado	mahistrado	PROPN
ejpam-4770	18	11	)	)	PUNCT
ejpam-4770	18	12	,	,	PUNCT
ejpam-4770	18	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4770	18	14	(	(	PUNCT
ejpam-4770	18	15	h.	h.	PROPN
ejpam-4770	18	16	rara	rara	PROPN
ejpam-4770	18	17	)	)	PUNCT
ejpam-4770	18	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4770	18	19	1464	1464	NUM
ejpam-4770	18	20	©	©	PROPN
ejpam-4770	18	21	2023	2023	NUM
ejpam-4770	18	22	ejpam	ejpam	NOUN
ejpam-4770	18	23	all	all	DET
ejpam-4770	18	24	rights	right	NOUN
ejpam-4770	18	25	reserved	reserve	VERB
ejpam-4770	18	26	.	.	PUNCT
ejpam-4770	19	1	a.m.	a.m.	PROPN
ejpam-4770	19	2	mahistrado	mahistrado	PROPN
ejpam-4770	19	3	,	,	PUNCT
ejpam-4770	19	4	h.	h.	PROPN
ejpam-4770	19	5	rara	rara	PROPN
ejpam-4770	19	6	/	/	SYM
ejpam-4770	19	7	eur	eur	PROPN
ejpam-4770	19	8	.	.	PUNCT
ejpam-4770	20	1	j.	j.	PROPN
ejpam-4770	20	2	pure	pure	PROPN
ejpam-4770	20	3	appl	appl	PROPN
ejpam-4770	20	4	.	.	PROPN
ejpam-4770	20	5	math	math	PROPN
ejpam-4770	20	6	,	,	PUNCT
ejpam-4770	20	7	16	16	NUM
ejpam-4770	20	8	(	(	PUNCT
ejpam-4770	20	9	3	3	NUM
ejpam-4770	20	10	)	)	PUNCT
ejpam-4770	20	11	(	(	PUNCT
ejpam-4770	20	12	2023	2023	NUM
ejpam-4770	20	13	)	)	PUNCT
ejpam-4770	20	14	,	,	PUNCT
ejpam-4770	20	15	1464	1464	NUM
ejpam-4770	20	16	-	-	SYM
ejpam-4770	20	17	1479	1479	NUM
ejpam-4770	20	18	1465	1465	NUM
ejpam-4770	20	19	2	2	NUM
ejpam-4770	20	20	.	.	PUNCT
ejpam-4770	20	21	terminology	terminology	NOUN
ejpam-4770	20	22	and	and	CCONJ
ejpam-4770	20	23	notation	notation	NOUN
ejpam-4770	20	24	in	in	ADP
ejpam-4770	20	25	this	this	DET
ejpam-4770	20	26	study	study	NOUN
ejpam-4770	20	27	,	,	PUNCT
ejpam-4770	20	28	we	we	PRON
ejpam-4770	20	29	consider	consider	VERB
ejpam-4770	20	30	finite	finite	ADJ
ejpam-4770	20	31	,	,	PUNCT
ejpam-4770	20	32	simple	simple	ADJ
ejpam-4770	20	33	,	,	PUNCT
ejpam-4770	20	34	connected	connect	VERB
ejpam-4770	20	35	,	,	PUNCT
ejpam-4770	20	36	undirected	undirected	ADJ
ejpam-4770	20	37	graphs	graph	NOUN
ejpam-4770	20	38	.	.	PUNCT
ejpam-4770	21	1	for	for	ADP
ejpam-4770	21	2	basic	basic	ADJ
ejpam-4770	21	3	graphtheoretic	graphtheoretic	ADJ
ejpam-4770	21	4	concepts	concept	NOUN
ejpam-4770	21	5	,	,	PUNCT
ejpam-4770	21	6	we	we	PRON
ejpam-4770	21	7	then	then	ADV
ejpam-4770	21	8	refer	refer	VERB
ejpam-4770	21	9	readers	reader	NOUN
ejpam-4770	21	10	to	to	ADP
ejpam-4770	21	11	[	[	X
ejpam-4770	21	12	2	2	NUM
ejpam-4770	21	13	]	]	PUNCT
ejpam-4770	21	14	and	and	CCONJ
ejpam-4770	21	15	[	[	X
ejpam-4770	21	16	3	3	NUM
ejpam-4770	21	17	]	]	PUNCT
ejpam-4770	21	18	.	.	PUNCT
ejpam-4770	22	1	the	the	DET
ejpam-4770	22	2	following	follow	VERB
ejpam-4770	22	3	concepts	concept	NOUN
ejpam-4770	22	4	are	be	AUX
ejpam-4770	22	5	found	find	VERB
ejpam-4770	22	6	in	in	ADP
ejpam-4770	22	7	[	[	X
ejpam-4770	22	8	2	2	NUM
ejpam-4770	22	9	]	]	PUNCT
ejpam-4770	22	10	,	,	PUNCT
ejpam-4770	22	11	[	[	X
ejpam-4770	22	12	14	14	NUM
ejpam-4770	22	13	]	]	PUNCT
ejpam-4770	22	14	,	,	PUNCT
ejpam-4770	22	15	and	and	CCONJ
ejpam-4770	22	16	[	[	X
ejpam-4770	22	17	16	16	NUM
ejpam-4770	22	18	]	]	X
ejpam-4770	22	19	,	,	PUNCT
ejpam-4770	22	20	respectively	respectively	ADV
ejpam-4770	22	21	.	.	PUNCT
ejpam-4770	23	1	let	let	VERB
ejpam-4770	23	2	g	g	PRON
ejpam-4770	23	3	be	be	AUX
ejpam-4770	23	4	a	a	DET
ejpam-4770	23	5	connected	connected	ADJ
ejpam-4770	23	6	graph	graph	NOUN
ejpam-4770	23	7	.	.	PUNCT
ejpam-4770	24	1	a	a	DET
ejpam-4770	24	2	vertex	vertex	NOUN
ejpam-4770	24	3	v	v	NOUN
ejpam-4770	24	4	in	in	ADP
ejpam-4770	24	5	g	g	PROPN
ejpam-4770	24	6	is	be	AUX
ejpam-4770	24	7	a	a	DET
ejpam-4770	24	8	hop	hop	NOUN
ejpam-4770	24	9	neighbor	neighbor	NOUN
ejpam-4770	24	10	of	of	ADP
ejpam-4770	24	11	vertex	vertex	NOUN
ejpam-4770	24	12	u	u	NOUN
ejpam-4770	24	13	in	in	ADP
ejpam-4770	24	14	g	g	PROPN
ejpam-4770	24	15	if	if	SCONJ
ejpam-4770	24	16	dg(u	dg(u	NOUN
ejpam-4770	24	17	,	,	PUNCT
ejpam-4770	24	18	v	v	NOUN
ejpam-4770	24	19	)	)	PUNCT
ejpam-4770	24	20	=	=	SYM
ejpam-4770	24	21	2	2	X
ejpam-4770	24	22	.	.	X
ejpam-4770	25	1	the	the	DET
ejpam-4770	25	2	set	set	NOUN
ejpam-4770	25	3	ng(u	ng(u	NOUN
ejpam-4770	25	4	,	,	PUNCT
ejpam-4770	25	5	2	2	NUM
ejpam-4770	25	6	)	)	PUNCT
ejpam-4770	25	7	=	=	PRON
ejpam-4770	25	8	{	{	PUNCT
ejpam-4770	25	9	v	v	NUM
ejpam-4770	25	10	∈	∈	NOUN
ejpam-4770	25	11	v	v	NOUN
ejpam-4770	25	12	(	(	PUNCT
ejpam-4770	25	13	g	g	NOUN
ejpam-4770	25	14	)	)	PUNCT
ejpam-4770	25	15	:	:	PUNCT
ejpam-4770	25	16	dg(v	dg(v	X
ejpam-4770	25	17	,	,	PUNCT
ejpam-4770	25	18	u	u	NOUN
ejpam-4770	25	19	)	)	PUNCT
ejpam-4770	25	20	=	=	SYM
ejpam-4770	25	21	2	2	X
ejpam-4770	25	22	}	}	PUNCT
ejpam-4770	25	23	is	be	AUX
ejpam-4770	25	24	called	call	VERB
ejpam-4770	25	25	the	the	DET
ejpam-4770	25	26	open	open	ADJ
ejpam-4770	25	27	hop	hop	NOUN
ejpam-4770	25	28	neighborhood	neighborhood	NOUN
ejpam-4770	25	29	of	of	ADP
ejpam-4770	25	30	u.	u.	PROPN
ejpam-4770	25	31	the	the	DET
ejpam-4770	25	32	closed	closed	ADJ
ejpam-4770	25	33	hop	hop	NOUN
ejpam-4770	25	34	neighborhood	neighborhood	NOUN
ejpam-4770	25	35	of	of	ADP
ejpam-4770	25	36	u	u	PROPN
ejpam-4770	25	37	in	in	ADP
ejpam-4770	25	38	g	g	PROPN
ejpam-4770	25	39	is	be	AUX
ejpam-4770	25	40	given	give	VERB
ejpam-4770	25	41	by	by	ADP
ejpam-4770	25	42	ng[u	ng[u	PROPN
ejpam-4770	25	43	,	,	PUNCT
ejpam-4770	25	44	2	2	NUM
ejpam-4770	25	45	]	]	PUNCT
ejpam-4770	26	1	=	=	SYM
ejpam-4770	26	2	ng(u	ng(u	PROPN
ejpam-4770	26	3	,	,	PUNCT
ejpam-4770	26	4	2)∪	2)∪	NUM
ejpam-4770	26	5	{	{	PUNCT
ejpam-4770	26	6	u	u	NOUN
ejpam-4770	26	7	}	}	PUNCT
ejpam-4770	26	8	.	.	PUNCT
ejpam-4770	27	1	the	the	DET
ejpam-4770	27	2	open	open	ADJ
ejpam-4770	27	3	hop	hop	NOUN
ejpam-4770	27	4	neighborhood	neighborhood	NOUN
ejpam-4770	27	5	of	of	ADP
ejpam-4770	27	6	x	x	PROPN
ejpam-4770	27	7	⊆	⊆	NUM
ejpam-4770	27	8	v	v	ADP
ejpam-4770	27	9	(	(	PUNCT
ejpam-4770	27	10	g	g	NOUN
ejpam-4770	27	11	)	)	PUNCT
ejpam-4770	27	12	is	be	AUX
ejpam-4770	27	13	the	the	DET
ejpam-4770	27	14	set	set	NOUN
ejpam-4770	27	15	ng(x	ng(x	NUM
ejpam-4770	27	16	,	,	PUNCT
ejpam-4770	27	17	2	2	X
ejpam-4770	27	18	)	)	PUNCT
ejpam-4770	27	19	=	=	NOUN
ejpam-4770	27	20	⋃	⋃	NOUN
ejpam-4770	27	21	u∈x	u∈x	ADJ
ejpam-4770	27	22	ng(u	ng(u	NOUN
ejpam-4770	27	23	,	,	PUNCT
ejpam-4770	27	24	2	2	NUM
ejpam-4770	27	25	)	)	PUNCT
ejpam-4770	27	26	.	.	PUNCT
ejpam-4770	28	1	the	the	DET
ejpam-4770	28	2	closed	closed	ADJ
ejpam-4770	28	3	hop	hop	NOUN
ejpam-4770	28	4	neighborhood	neighborhood	NOUN
ejpam-4770	28	5	of	of	ADP
ejpam-4770	28	6	x	x	PUNCT
ejpam-4770	28	7	in	in	ADP
ejpam-4770	28	8	g	g	PROPN
ejpam-4770	28	9	is	be	AUX
ejpam-4770	28	10	the	the	DET
ejpam-4770	28	11	set	set	PROPN
ejpam-4770	28	12	ng[x	ng[x	PROPN
ejpam-4770	28	13	,	,	PUNCT
ejpam-4770	28	14	2	2	NUM
ejpam-4770	28	15	]	]	PUNCT
ejpam-4770	28	16	=	=	SYM
ejpam-4770	28	17	ng(x	ng(x	X
ejpam-4770	28	18	,	,	PUNCT
ejpam-4770	28	19	2	2	NUM
ejpam-4770	28	20	)	)	PUNCT
ejpam-4770	28	21	∪x	∪x	NUM
ejpam-4770	28	22	.	.	PUNCT
ejpam-4770	29	1	a	a	DET
ejpam-4770	29	2	set	set	NOUN
ejpam-4770	29	3	s	s	NOUN
ejpam-4770	29	4	⊆	⊆	NUM
ejpam-4770	29	5	v	v	NOUN
ejpam-4770	29	6	(	(	PUNCT
ejpam-4770	29	7	g	g	NOUN
ejpam-4770	29	8	)	)	PUNCT
ejpam-4770	29	9	is	be	AUX
ejpam-4770	29	10	a	a	DET
ejpam-4770	29	11	hop	hop	NOUN
ejpam-4770	29	12	dominating	dominating	NOUN
ejpam-4770	29	13	set	set	NOUN
ejpam-4770	29	14	of	of	ADP
ejpam-4770	29	15	g	g	PROPN
ejpam-4770	29	16	if	if	SCONJ
ejpam-4770	29	17	ng[s	ng[	NOUN
ejpam-4770	29	18	,	,	PUNCT
ejpam-4770	29	19	2	2	NUM
ejpam-4770	29	20	]	]	PUNCT
ejpam-4770	29	21	=	=	SYM
ejpam-4770	29	22	v	v	NOUN
ejpam-4770	29	23	(	(	PUNCT
ejpam-4770	29	24	g	g	NOUN
ejpam-4770	29	25	)	)	PUNCT
ejpam-4770	29	26	,	,	PUNCT
ejpam-4770	29	27	that	that	ADV
ejpam-4770	29	28	is	is	ADV
ejpam-4770	29	29	,	,	PUNCT
ejpam-4770	29	30	for	for	ADP
ejpam-4770	29	31	every	every	DET
ejpam-4770	29	32	v	v	NUM
ejpam-4770	29	33	∈	∈	NOUN
ejpam-4770	29	34	v	v	NOUN
ejpam-4770	29	35	(	(	PUNCT
ejpam-4770	29	36	g)\s	g)\s	NOUN
ejpam-4770	29	37	,	,	PUNCT
ejpam-4770	29	38	there	there	PRON
ejpam-4770	29	39	exists	exist	VERB
ejpam-4770	29	40	u	u	PROPN
ejpam-4770	29	41	∈	∈	PROPN
ejpam-4770	29	42	s	s	VERB
ejpam-4770	29	43	such	such	ADJ
ejpam-4770	29	44	that	that	DET
ejpam-4770	29	45	dg(u	dg(u	ADJ
ejpam-4770	29	46	,	,	PUNCT
ejpam-4770	29	47	v	v	NOUN
ejpam-4770	29	48	)	)	PUNCT
ejpam-4770	30	1	=	=	SYM
ejpam-4770	30	2	2	2	X
ejpam-4770	30	3	.	.	PUNCT
ejpam-4770	31	1	the	the	DET
ejpam-4770	31	2	minimum	minimum	ADJ
ejpam-4770	31	3	cardinality	cardinality	NOUN
ejpam-4770	31	4	of	of	ADP
ejpam-4770	31	5	a	a	DET
ejpam-4770	31	6	hop	hop	NOUN
ejpam-4770	31	7	dominating	dominating	NOUN
ejpam-4770	31	8	set	set	NOUN
ejpam-4770	31	9	of	of	ADP
ejpam-4770	31	10	g	g	NOUN
ejpam-4770	31	11	,	,	PUNCT
ejpam-4770	31	12	denoted	denote	VERB
ejpam-4770	31	13	by	by	ADP
ejpam-4770	31	14	γh(g	γh(g	NOUN
ejpam-4770	31	15	)	)	PUNCT
ejpam-4770	31	16	,	,	PUNCT
ejpam-4770	31	17	is	be	AUX
ejpam-4770	31	18	called	call	VERB
ejpam-4770	31	19	the	the	DET
ejpam-4770	31	20	hop	hop	NOUN
ejpam-4770	31	21	domination	domination	NOUN
ejpam-4770	31	22	number	number	NOUN
ejpam-4770	31	23	of	of	ADP
ejpam-4770	31	24	g.	g.	PROPN
ejpam-4770	31	25	any	any	DET
ejpam-4770	31	26	hop	hop	NOUN
ejpam-4770	31	27	dominating	dominating	NOUN
ejpam-4770	31	28	set	set	VERB
ejpam-4770	31	29	with	with	ADP
ejpam-4770	31	30	cardinality	cardinality	NOUN
ejpam-4770	31	31	equal	equal	ADJ
ejpam-4770	31	32	to	to	ADP
ejpam-4770	31	33	γh(g	γh(g	NOUN
ejpam-4770	31	34	)	)	PUNCT
ejpam-4770	31	35	is	be	AUX
ejpam-4770	31	36	called	call	VERB
ejpam-4770	31	37	a	a	DET
ejpam-4770	31	38	γh	γh	ADV
ejpam-4770	31	39	-	-	PUNCT
ejpam-4770	31	40	set	set	NOUN
ejpam-4770	31	41	.	.	PUNCT
ejpam-4770	32	1	for	for	ADP
ejpam-4770	32	2	an	an	DET
ejpam-4770	32	3	ordered	order	VERB
ejpam-4770	32	4	set	set	NOUN
ejpam-4770	32	5	of	of	ADP
ejpam-4770	32	6	vertices	vertex	NOUN
ejpam-4770	32	7	w	w	NOUN
ejpam-4770	32	8	=	=	SYM
ejpam-4770	32	9	{	{	PUNCT
ejpam-4770	32	10	w1	w1	NOUN
ejpam-4770	32	11	,	,	PUNCT
ejpam-4770	32	12	w2	w2	NOUN
ejpam-4770	32	13	,	,	PUNCT
ejpam-4770	32	14	...	...	PUNCT
ejpam-4770	32	15	,	,	PUNCT
ejpam-4770	32	16	wk	wk	ADP
ejpam-4770	32	17	}	}	PUNCT
ejpam-4770	32	18	⊆	⊆	NUM
ejpam-4770	32	19	v	v	NOUN
ejpam-4770	32	20	(	(	PUNCT
ejpam-4770	32	21	g	g	NOUN
ejpam-4770	32	22	)	)	PUNCT
ejpam-4770	32	23	and	and	CCONJ
ejpam-4770	32	24	a	a	DET
ejpam-4770	32	25	vertex	vertex	NOUN
ejpam-4770	32	26	v	v	NOUN
ejpam-4770	32	27	in	in	ADP
ejpam-4770	32	28	g	g	NOUN
ejpam-4770	32	29	,	,	PUNCT
ejpam-4770	32	30	we	we	PRON
ejpam-4770	32	31	refer	refer	VERB
ejpam-4770	32	32	to	to	ADP
ejpam-4770	32	33	the	the	DET
ejpam-4770	32	34	k	k	NOUN
ejpam-4770	32	35	-	-	NOUN
ejpam-4770	32	36	vector	vector	NOUN
ejpam-4770	32	37	(	(	PUNCT
ejpam-4770	32	38	ordered	order	VERB
ejpam-4770	32	39	k	k	NOUN
ejpam-4770	32	40	-	-	PUNCT
ejpam-4770	32	41	tuple	tuple	NOUN
ejpam-4770	32	42	)	)	PUNCT
ejpam-4770	32	43	rg(v	rg(v	PROPN
ejpam-4770	32	44	/	/	SYM
ejpam-4770	32	45	w	w	NOUN
ejpam-4770	32	46	)	)	PUNCT
ejpam-4770	33	1	=	=	SYM
ejpam-4770	33	2	(	(	PUNCT
ejpam-4770	33	3	dg(v	dg(v	X
ejpam-4770	33	4	,	,	PUNCT
ejpam-4770	33	5	w1	w1	NOUN
ejpam-4770	33	6	)	)	PUNCT
ejpam-4770	33	7	,	,	PUNCT
ejpam-4770	33	8	dg(v	dg(v	X
ejpam-4770	33	9	,	,	PUNCT
ejpam-4770	33	10	w2	w2	NOUN
ejpam-4770	33	11	)	)	PUNCT
ejpam-4770	33	12	,	,	PUNCT
ejpam-4770	33	13	...	...	PUNCT
ejpam-4770	33	14	,	,	PUNCT
ejpam-4770	33	15	dg(v	dg(v	X
ejpam-4770	33	16	,	,	PUNCT
ejpam-4770	33	17	wk	wk	NOUN
ejpam-4770	33	18	)	)	PUNCT
ejpam-4770	33	19	)	)	PUNCT
ejpam-4770	34	1	as	as	ADP
ejpam-4770	34	2	the	the	DET
ejpam-4770	34	3	(	(	PUNCT
ejpam-4770	34	4	metric	metric	ADJ
ejpam-4770	34	5	)	)	PUNCT
ejpam-4770	34	6	representation	representation	NOUN
ejpam-4770	34	7	of	of	ADP
ejpam-4770	34	8	v	v	NOUN
ejpam-4770	34	9	with	with	ADP
ejpam-4770	34	10	respect	respect	NOUN
ejpam-4770	34	11	to	to	ADP
ejpam-4770	34	12	w	w	PROPN
ejpam-4770	34	13	.	.	PUNCT
ejpam-4770	35	1	the	the	DET
ejpam-4770	35	2	set	set	NOUN
ejpam-4770	35	3	w	w	NOUN
ejpam-4770	35	4	is	be	AUX
ejpam-4770	35	5	called	call	VERB
ejpam-4770	35	6	a	a	DET
ejpam-4770	35	7	resolving	resolving	NOUN
ejpam-4770	35	8	set	set	VERB
ejpam-4770	35	9	for	for	ADP
ejpam-4770	35	10	g	g	PROPN
ejpam-4770	35	11	if	if	SCONJ
ejpam-4770	35	12	distinct	distinct	ADJ
ejpam-4770	35	13	vertices	vertex	NOUN
ejpam-4770	35	14	have	have	VERB
ejpam-4770	35	15	distinct	distinct	ADJ
ejpam-4770	35	16	representations	representation	NOUN
ejpam-4770	35	17	with	with	ADP
ejpam-4770	35	18	respect	respect	NOUN
ejpam-4770	35	19	to	to	ADP
ejpam-4770	35	20	w	w	PROPN
ejpam-4770	35	21	.	.	PUNCT
ejpam-4770	36	1	hence	hence	ADV
ejpam-4770	36	2	,	,	PUNCT
ejpam-4770	36	3	if	if	SCONJ
ejpam-4770	36	4	w	w	NOUN
ejpam-4770	36	5	is	be	AUX
ejpam-4770	36	6	a	a	DET
ejpam-4770	36	7	resolving	resolving	NOUN
ejpam-4770	36	8	set	set	NOUN
ejpam-4770	36	9	of	of	ADP
ejpam-4770	36	10	cardinality	cardinality	PROPN
ejpam-4770	36	11	k	k	PROPN
ejpam-4770	36	12	for	for	ADP
ejpam-4770	36	13	a	a	DET
ejpam-4770	36	14	graph	graph	NOUN
ejpam-4770	36	15	g	g	NOUN
ejpam-4770	36	16	of	of	ADP
ejpam-4770	36	17	order	order	NOUN
ejpam-4770	36	18	n	n	CCONJ
ejpam-4770	36	19	,	,	PUNCT
ejpam-4770	36	20	then	then	ADV
ejpam-4770	36	21	the	the	DET
ejpam-4770	36	22	set	set	NOUN
ejpam-4770	36	23	{	{	PUNCT
ejpam-4770	36	24	rg(v	rg(v	NOUN
ejpam-4770	36	25	/	/	SYM
ejpam-4770	36	26	w	w	NOUN
ejpam-4770	36	27	)	)	PUNCT
ejpam-4770	36	28	:	:	PUNCT
ejpam-4770	36	29	v	v	X
ejpam-4770	36	30	∈	∈	PROPN
ejpam-4770	36	31	v	v	NOUN
ejpam-4770	36	32	(	(	PUNCT
ejpam-4770	36	33	g	g	NOUN
ejpam-4770	36	34	)	)	PUNCT
ejpam-4770	36	35	}	}	PUNCT
ejpam-4770	36	36	consists	consist	VERB
ejpam-4770	36	37	of	of	ADP
ejpam-4770	36	38	n	n	PRON
ejpam-4770	36	39	distinct	distinct	ADJ
ejpam-4770	36	40	k	k	NOUN
ejpam-4770	36	41	-	-	NOUN
ejpam-4770	36	42	vectors	vector	NOUN
ejpam-4770	36	43	.	.	PUNCT
ejpam-4770	37	1	a	a	DET
ejpam-4770	37	2	resolving	resolving	NOUN
ejpam-4770	37	3	set	set	NOUN
ejpam-4770	37	4	of	of	ADP
ejpam-4770	37	5	minimum	minimum	ADJ
ejpam-4770	37	6	cardinality	cardinality	NOUN
ejpam-4770	37	7	is	be	AUX
ejpam-4770	37	8	called	call	VERB
ejpam-4770	37	9	aminimum	aminimum	ADJ
ejpam-4770	37	10	resolving	resolving	NOUN
ejpam-4770	37	11	set	set	VERB
ejpam-4770	37	12	or	or	CCONJ
ejpam-4770	37	13	a	a	DET
ejpam-4770	37	14	basis	basis	NOUN
ejpam-4770	37	15	,	,	PUNCT
ejpam-4770	37	16	and	and	CCONJ
ejpam-4770	37	17	the	the	DET
ejpam-4770	37	18	cardinality	cardinality	NOUN
ejpam-4770	37	19	of	of	ADP
ejpam-4770	37	20	a	a	DET
ejpam-4770	37	21	basis	basis	NOUN
ejpam-4770	37	22	for	for	ADP
ejpam-4770	37	23	g	g	PROPN
ejpam-4770	37	24	is	be	AUX
ejpam-4770	37	25	the	the	DET
ejpam-4770	37	26	dimension	dimension	NOUN
ejpam-4770	37	27	dim(g	dim(g	PROPN
ejpam-4770	37	28	)	)	PUNCT
ejpam-4770	37	29	of	of	ADP
ejpam-4770	37	30	g.	g.	PROPN
ejpam-4770	37	31	an	an	DET
ejpam-4770	37	32	ordered	order	VERB
ejpam-4770	37	33	set	set	NOUN
ejpam-4770	37	34	of	of	ADP
ejpam-4770	37	35	vertices	vertex	NOUN
ejpam-4770	37	36	w	w	NOUN
ejpam-4770	37	37	=	=	SYM
ejpam-4770	37	38	{	{	PUNCT
ejpam-4770	37	39	w1	w1	NOUN
ejpam-4770	37	40	,	,	PUNCT
ejpam-4770	37	41	...	...	PUNCT
ejpam-4770	37	42	,	,	PUNCT
ejpam-4770	37	43	wk	wk	X
ejpam-4770	37	44	}	}	PUNCT
ejpam-4770	37	45	is	be	AUX
ejpam-4770	37	46	a	a	DET
ejpam-4770	37	47	k	k	NOUN
ejpam-4770	37	48	-	-	PUNCT
ejpam-4770	37	49	resolving	resolving	NOUN
ejpam-4770	37	50	set	set	NOUN
ejpam-4770	37	51	for	for	ADP
ejpam-4770	37	52	g	g	PROPN
ejpam-4770	37	53	if	if	SCONJ
ejpam-4770	37	54	,	,	PUNCT
ejpam-4770	37	55	for	for	ADP
ejpam-4770	37	56	any	any	DET
ejpam-4770	37	57	distinct	distinct	ADJ
ejpam-4770	37	58	vertices	vertex	NOUN
ejpam-4770	37	59	u	u	NOUN
ejpam-4770	37	60	,	,	PUNCT
ejpam-4770	37	61	v	v	NOUN
ejpam-4770	37	62	∈	∈	PROPN
ejpam-4770	37	63	v	v	NOUN
ejpam-4770	37	64	(	(	PUNCT
ejpam-4770	37	65	g	g	NOUN
ejpam-4770	37	66	)	)	PUNCT
ejpam-4770	37	67	,	,	PUNCT
ejpam-4770	37	68	the	the	DET
ejpam-4770	37	69	(	(	PUNCT
ejpam-4770	37	70	metric	metric	ADJ
ejpam-4770	37	71	)	)	PUNCT
ejpam-4770	37	72	representations	representation	NOUN
ejpam-4770	37	73	rg(u	rg(u	NOUN
ejpam-4770	37	74	/	/	SYM
ejpam-4770	37	75	w	w	NOUN
ejpam-4770	37	76	)	)	PUNCT
ejpam-4770	37	77	and	and	CCONJ
ejpam-4770	37	78	rg(v	rg(v	PROPN
ejpam-4770	37	79	/	/	SYM
ejpam-4770	37	80	w	w	NOUN
ejpam-4770	37	81	)	)	PUNCT
ejpam-4770	37	82	of	of	ADP
ejpam-4770	37	83	u	u	NOUN
ejpam-4770	37	84	and	and	CCONJ
ejpam-4770	37	85	v	v	NOUN
ejpam-4770	37	86	,	,	PUNCT
ejpam-4770	37	87	respectively	respectively	ADV
ejpam-4770	37	88	,	,	PUNCT
ejpam-4770	37	89	differ	differ	VERB
ejpam-4770	37	90	in	in	ADP
ejpam-4770	37	91	at	at	ADP
ejpam-4770	37	92	least	least	ADJ
ejpam-4770	37	93	k	k	NOUN
ejpam-4770	37	94	positions	position	NOUN
ejpam-4770	37	95	.	.	PUNCT
ejpam-4770	38	1	if	if	SCONJ
ejpam-4770	38	2	k	k	PROPN
ejpam-4770	38	3	=	=	SYM
ejpam-4770	38	4	1	1	NUM
ejpam-4770	38	5	,	,	PUNCT
ejpam-4770	38	6	then	then	ADV
ejpam-4770	38	7	the	the	DET
ejpam-4770	38	8	k	k	NOUN
ejpam-4770	38	9	-	-	PUNCT
ejpam-4770	38	10	resolving	resolving	ADJ
ejpam-4770	38	11	set	set	NOUN
ejpam-4770	38	12	is	be	AUX
ejpam-4770	38	13	called	call	VERB
ejpam-4770	38	14	a	a	DET
ejpam-4770	38	15	resolving	resolving	NOUN
ejpam-4770	38	16	set	set	VERB
ejpam-4770	38	17	for	for	ADP
ejpam-4770	38	18	g.	g.	PROPN
ejpam-4770	38	19	if	if	SCONJ
ejpam-4770	38	20	k	k	PROPN
ejpam-4770	38	21	=	=	SYM
ejpam-4770	38	22	2	2	NUM
ejpam-4770	38	23	,	,	PUNCT
ejpam-4770	38	24	then	then	ADV
ejpam-4770	38	25	the	the	DET
ejpam-4770	38	26	k	k	NOUN
ejpam-4770	38	27	-	-	PUNCT
ejpam-4770	38	28	resolving	resolving	ADJ
ejpam-4770	38	29	set	set	NOUN
ejpam-4770	38	30	is	be	AUX
ejpam-4770	38	31	called	call	VERB
ejpam-4770	38	32	a	a	DET
ejpam-4770	38	33	2	2	NUM
ejpam-4770	38	34	-	-	PUNCT
ejpam-4770	38	35	resolving	resolving	NOUN
ejpam-4770	38	36	set	set	NOUN
ejpam-4770	38	37	for	for	ADP
ejpam-4770	38	38	g.	g.	PROPN
ejpam-4770	38	39	if	if	SCONJ
ejpam-4770	38	40	g	g	PROPN
ejpam-4770	38	41	has	have	VERB
ejpam-4770	38	42	a	a	DET
ejpam-4770	38	43	k	k	ADJ
ejpam-4770	38	44	-	-	ADJ
ejpam-4770	38	45	resolving	resolving	ADJ
ejpam-4770	38	46	set	set	NOUN
ejpam-4770	38	47	,	,	PUNCT
ejpam-4770	38	48	the	the	DET
ejpam-4770	38	49	minimum	minimum	ADJ
ejpam-4770	38	50	cardinality	cardinality	PROPN
ejpam-4770	38	51	dimk(g	dimk(g	PROPN
ejpam-4770	38	52	)	)	PUNCT
ejpam-4770	38	53	of	of	ADP
ejpam-4770	38	54	a	a	DET
ejpam-4770	38	55	k	k	NOUN
ejpam-4770	38	56	-	-	PUNCT
ejpam-4770	38	57	resolving	resolving	ADJ
ejpam-4770	38	58	set	set	NOUN
ejpam-4770	38	59	is	be	AUX
ejpam-4770	38	60	called	call	VERB
ejpam-4770	38	61	the	the	DET
ejpam-4770	38	62	k	k	ADJ
ejpam-4770	38	63	-	-	ADJ
ejpam-4770	38	64	metric	metric	ADJ
ejpam-4770	38	65	dimension	dimension	NOUN
ejpam-4770	38	66	of	of	ADP
ejpam-4770	38	67	g.	g.	PROPN
ejpam-4770	38	68	a	a	DET
ejpam-4770	38	69	set	set	NOUN
ejpam-4770	38	70	s	s	NOUN
ejpam-4770	38	71	of	of	ADP
ejpam-4770	38	72	vertices	vertex	NOUN
ejpam-4770	38	73	in	in	ADP
ejpam-4770	38	74	g	g	PROPN
ejpam-4770	38	75	is	be	AUX
ejpam-4770	38	76	a	a	DET
ejpam-4770	38	77	1	1	NUM
ejpam-4770	38	78	-	-	PUNCT
ejpam-4770	38	79	movable	movable	ADJ
ejpam-4770	38	80	2	2	NUM
ejpam-4770	38	81	-	-	PUNCT
ejpam-4770	38	82	resolving	resolve	VERB
ejpam-4770	38	83	hop	hop	NOUN
ejpam-4770	38	84	dominating	dominating	NOUN
ejpam-4770	38	85	set	set	NOUN
ejpam-4770	38	86	of	of	ADP
ejpam-4770	38	87	g	g	PROPN
ejpam-4770	38	88	if	if	SCONJ
ejpam-4770	38	89	s	s	VERB
ejpam-4770	38	90	is	be	AUX
ejpam-4770	38	91	a	a	DET
ejpam-4770	38	92	2	2	NUM
ejpam-4770	38	93	-	-	PUNCT
ejpam-4770	38	94	resolving	resolve	VERB
ejpam-4770	38	95	hop	hop	NOUN
ejpam-4770	38	96	dominating	dominating	NOUN
ejpam-4770	38	97	set	set	VERB
ejpam-4770	38	98	in	in	ADP
ejpam-4770	38	99	g	g	PROPN
ejpam-4770	38	100	and	and	CCONJ
ejpam-4770	38	101	for	for	SCONJ
ejpam-4770	38	102	every	every	DET
ejpam-4770	38	103	v	v	NUM
ejpam-4770	38	104	∈	∈	PROPN
ejpam-4770	38	105	s	s	NOUN
ejpam-4770	38	106	,	,	PUNCT
ejpam-4770	38	107	either	either	CCONJ
ejpam-4770	38	108	s\{v	s\{v	VERB
ejpam-4770	38	109	}	}	PUNCT
ejpam-4770	38	110	is	be	AUX
ejpam-4770	38	111	a	a	DET
ejpam-4770	38	112	2	2	NUM
ejpam-4770	38	113	-	-	PUNCT
ejpam-4770	38	114	resolving	resolve	VERB
ejpam-4770	38	115	hop	hop	NOUN
ejpam-4770	38	116	dominating	dominating	NOUN
ejpam-4770	38	117	set	set	NOUN
ejpam-4770	38	118	of	of	ADP
ejpam-4770	38	119	g	g	NOUN
ejpam-4770	38	120	or	or	CCONJ
ejpam-4770	38	121	there	there	ADV
ejpam-4770	38	122	exists	exist	VERB
ejpam-4770	38	123	a	a	DET
ejpam-4770	38	124	vertex	vertex	NOUN
ejpam-4770	38	125	u	u	NOUN
ejpam-4770	38	126	∈	∈	PROPN
ejpam-4770	38	127	(	(	PUNCT
ejpam-4770	38	128	(	(	PUNCT
ejpam-4770	38	129	v	v	NOUN
ejpam-4770	38	130	(	(	PUNCT
ejpam-4770	38	131	g)\s	g)\s	NOUN
ejpam-4770	38	132	)	)	PUNCT
ejpam-4770	38	133	∩	∩	NOUN
ejpam-4770	38	134	ng(v	ng(v	NUM
ejpam-4770	38	135	)	)	PUNCT
ejpam-4770	38	136	)	)	PUNCT
ejpam-4770	38	137	such	such	ADJ
ejpam-4770	38	138	that	that	SCONJ
ejpam-4770	38	139	(	(	PUNCT
ejpam-4770	38	140	s\{v	s\{v	VERB
ejpam-4770	38	141	}	}	PUNCT
ejpam-4770	38	142	)	)	PUNCT
ejpam-4770	38	143	∪	∪	ADP
ejpam-4770	38	144	{	{	PUNCT
ejpam-4770	38	145	u	u	NOUN
ejpam-4770	38	146	}	}	PUNCT
ejpam-4770	38	147	is	be	AUX
ejpam-4770	38	148	a	a	DET
ejpam-4770	38	149	2	2	NUM
ejpam-4770	38	150	-	-	PUNCT
ejpam-4770	38	151	resolving	resolve	VERB
ejpam-4770	38	152	hop	hop	NOUN
ejpam-4770	38	153	dominating	dominating	NOUN
ejpam-4770	38	154	set	set	NOUN
ejpam-4770	38	155	of	of	ADP
ejpam-4770	38	156	g.	g.	PROPN
ejpam-4770	38	157	the	the	DET
ejpam-4770	38	158	1	1	NUM
ejpam-4770	38	159	-	-	PUNCT
ejpam-4770	38	160	movable	movable	ADJ
ejpam-4770	38	161	2	2	NUM
ejpam-4770	38	162	-	-	PUNCT
ejpam-4770	38	163	resolving	resolve	VERB
ejpam-4770	38	164	hop	hop	NOUN
ejpam-4770	38	165	domination	domination	NOUN
ejpam-4770	38	166	number	number	NOUN
ejpam-4770	38	167	of	of	ADP
ejpam-4770	38	168	g	g	NOUN
ejpam-4770	38	169	,	,	PUNCT
ejpam-4770	38	170	denoted	denote	VERB
ejpam-4770	38	171	by	by	ADP
ejpam-4770	38	172	γ1m2rh(g	γ1m2rh(g	NOUN
ejpam-4770	38	173	)	)	PUNCT
ejpam-4770	38	174	is	be	AUX
ejpam-4770	38	175	the	the	DET
ejpam-4770	38	176	smallest	small	ADJ
ejpam-4770	38	177	cardinality	cardinality	NOUN
ejpam-4770	38	178	of	of	ADP
ejpam-4770	38	179	a	a	DET
ejpam-4770	38	180	1	1	NUM
ejpam-4770	38	181	-	-	PUNCT
ejpam-4770	38	182	movable	movable	ADJ
ejpam-4770	38	183	2	2	NUM
ejpam-4770	38	184	-	-	PUNCT
ejpam-4770	38	185	resolving	resolve	VERB
ejpam-4770	38	186	hop	hop	NOUN
ejpam-4770	38	187	dominating	dominating	NOUN
ejpam-4770	38	188	set	set	NOUN
ejpam-4770	38	189	of	of	ADP
ejpam-4770	38	190	g.	g.	PROPN
ejpam-4770	38	191	any	any	DET
ejpam-4770	38	192	1	1	NUM
ejpam-4770	38	193	-	-	PUNCT
ejpam-4770	38	194	movable	movable	ADJ
ejpam-4770	38	195	2	2	NUM
ejpam-4770	38	196	-	-	PUNCT
ejpam-4770	38	197	resolving	resolve	VERB
ejpam-4770	38	198	hop	hop	NOUN
ejpam-4770	38	199	dominating	dominating	NOUN
ejpam-4770	38	200	set	set	NOUN
ejpam-4770	38	201	of	of	ADP
ejpam-4770	38	202	cardinality	cardinality	PROPN
ejpam-4770	38	203	γ1m2rh(g	γ1m2rh(g	PRON
ejpam-4770	38	204	)	)	PUNCT
ejpam-4770	38	205	is	be	AUX
ejpam-4770	38	206	referred	refer	VERB
ejpam-4770	38	207	to	to	ADP
ejpam-4770	38	208	as	as	ADP
ejpam-4770	38	209	a	a	DET
ejpam-4770	38	210	γ1m2rh	γ1m2rh	PUNCT
ejpam-4770	38	211	-set	-set	PUNCT
ejpam-4770	38	212	of	of	ADP
ejpam-4770	38	213	g.	g.	PROPN
ejpam-4770	38	214	definition	definition	NOUN
ejpam-4770	38	215	1	1	NUM
ejpam-4770	38	216	.	.	PUNCT
ejpam-4770	39	1	[	[	X
ejpam-4770	39	2	6	6	NUM
ejpam-4770	39	3	]	]	X
ejpam-4770	39	4	letg	letg	NOUN
ejpam-4770	39	5	be	be	VERB
ejpam-4770	39	6	any	any	DET
ejpam-4770	39	7	nontrivial	nontrivial	ADJ
ejpam-4770	39	8	connected	connect	VERB
ejpam-4770	39	9	graph	graph	NOUN
ejpam-4770	39	10	and	and	CCONJ
ejpam-4770	39	11	s	s	VERB
ejpam-4770	39	12	⊆	⊆	NUM
ejpam-4770	39	13	v	v	NOUN
ejpam-4770	39	14	(	(	PUNCT
ejpam-4770	39	15	g	g	NOUN
ejpam-4770	39	16	)	)	PUNCT
ejpam-4770	39	17	.	.	PUNCT
ejpam-4770	40	1	a	a	DET
ejpam-4770	40	2	set	set	NOUN
ejpam-4770	40	3	s	s	NOUN
ejpam-4770	40	4	⊆	⊆	NUM
ejpam-4770	40	5	v	v	NOUN
ejpam-4770	40	6	(	(	PUNCT
ejpam-4770	40	7	g	g	NOUN
ejpam-4770	40	8	)	)	PUNCT
ejpam-4770	40	9	is	be	AUX
ejpam-4770	40	10	a	a	DET
ejpam-4770	40	11	2	2	NUM
ejpam-4770	40	12	-	-	PUNCT
ejpam-4770	40	13	locating	locate	VERB
ejpam-4770	40	14	set	set	NOUN
ejpam-4770	40	15	of	of	ADP
ejpam-4770	40	16	g	g	NOUN
ejpam-4770	40	17	if	if	SCONJ
ejpam-4770	40	18	it	it	PRON
ejpam-4770	40	19	satisfies	satisfy	VERB
ejpam-4770	40	20	the	the	DET
ejpam-4770	40	21	following	follow	VERB
ejpam-4770	40	22	conditions	condition	NOUN
ejpam-4770	40	23	:	:	PUNCT
ejpam-4770	40	24	(	(	PUNCT
ejpam-4770	40	25	i	i	NOUN
ejpam-4770	40	26	)	)	PUNCT
ejpam-4770	40	27	∣∣[(ng(x)\ng(y	∣∣[(ng(x)\ng(y	PROPN
ejpam-4770	40	28	)	)	PUNCT
ejpam-4770	40	29	)	)	PUNCT
ejpam-4770	41	1	∩s]∪	∩s]∪	VERB
ejpam-4770	41	2	[	[	PUNCT
ejpam-4770	41	3	(	(	PUNCT
ejpam-4770	41	4	ng(y)\ng(x	ng(y)\ng(x	NOUN
ejpam-4770	41	5	)	)	PUNCT
ejpam-4770	41	6	)	)	PUNCT
ejpam-4770	42	1	∩s	∩s	PROPN
ejpam-4770	42	2	]	]	PUNCT
ejpam-4770	42	3	∣∣	∣∣	NUM
ejpam-4770	42	4	≥	≥	NOUN
ejpam-4770	42	5	2	2	NUM
ejpam-4770	42	6	,	,	PUNCT
ejpam-4770	42	7	for	for	ADP
ejpam-4770	42	8	all	all	DET
ejpam-4770	42	9	x	x	NOUN
ejpam-4770	42	10	,	,	PUNCT
ejpam-4770	42	11	y	y	PROPN
ejpam-4770	42	12	∈	∈	PROPN
ejpam-4770	42	13	v	v	X
ejpam-4770	42	14	(	(	PUNCT
ejpam-4770	42	15	g)\s	g)\s	VERB
ejpam-4770	42	16	with	with	ADP
ejpam-4770	42	17	x	x	PROPN
ejpam-4770	42	18	̸=	̸=	PROPN
ejpam-4770	42	19	y.	y.	PROPN
ejpam-4770	42	20	(	(	PUNCT
ejpam-4770	42	21	ii	ii	PROPN
ejpam-4770	42	22	)	)	PUNCT
ejpam-4770	42	23	(	(	PUNCT
ejpam-4770	42	24	ng(v)\ng(w	ng(v)\ng(w	ADJ
ejpam-4770	42	25	)	)	PUNCT
ejpam-4770	42	26	)	)	PUNCT
ejpam-4770	42	27	∩	∩	PROPN
ejpam-4770	42	28	s	s	PART
ejpam-4770	42	29	̸=	̸=	PROPN
ejpam-4770	42	30	∅	∅	NOUN
ejpam-4770	42	31	or	or	CCONJ
ejpam-4770	42	32	(	(	PUNCT
ejpam-4770	42	33	ng(w)\ng[v	ng(w)\ng[v	PROPN
ejpam-4770	42	34	]	]	PUNCT
ejpam-4770	42	35	)	)	PUNCT
ejpam-4770	42	36	∩	∩	PROPN
ejpam-4770	42	37	s	s	PART
ejpam-4770	42	38	̸=	̸=	PROPN
ejpam-4770	42	39	∅	∅	NOUN
ejpam-4770	42	40	,	,	PUNCT
ejpam-4770	42	41	for	for	ADP
ejpam-4770	42	42	all	all	PRON
ejpam-4770	42	43	v	v	ADP
ejpam-4770	42	44	∈	∈	NOUN
ejpam-4770	42	45	s	s	NOUN
ejpam-4770	42	46	and	and	CCONJ
ejpam-4770	42	47	for	for	ADP
ejpam-4770	42	48	all	all	PRON
ejpam-4770	42	49	w	w	PROPN
ejpam-4770	42	50	∈	∈	PROPN
ejpam-4770	42	51	v	v	NOUN
ejpam-4770	42	52	(	(	PUNCT
ejpam-4770	42	53	g)\s	g)\s	NOUN
ejpam-4770	42	54	.	.	PUNCT
ejpam-4770	43	1	a.m.	a.m.	PROPN
ejpam-4770	43	2	mahistrado	mahistrado	PROPN
ejpam-4770	43	3	,	,	PUNCT
ejpam-4770	43	4	h.	h.	PROPN
ejpam-4770	43	5	rara	rara	PROPN
ejpam-4770	43	6	/	/	SYM
ejpam-4770	43	7	eur	eur	PROPN
ejpam-4770	43	8	.	.	PUNCT
ejpam-4770	44	1	j.	j.	PROPN
ejpam-4770	44	2	pure	pure	PROPN
ejpam-4770	44	3	appl	appl	PROPN
ejpam-4770	44	4	.	.	PROPN
ejpam-4770	44	5	math	math	PROPN
ejpam-4770	44	6	,	,	PUNCT
ejpam-4770	44	7	16	16	NUM
ejpam-4770	44	8	(	(	PUNCT
ejpam-4770	44	9	3	3	NUM
ejpam-4770	44	10	)	)	PUNCT
ejpam-4770	44	11	(	(	PUNCT
ejpam-4770	44	12	2023	2023	NUM
ejpam-4770	44	13	)	)	PUNCT
ejpam-4770	44	14	,	,	PUNCT
ejpam-4770	44	15	1464	1464	NUM
ejpam-4770	44	16	-	-	SYM
ejpam-4770	44	17	1479	1479	NUM
ejpam-4770	44	18	1466	1466	NUM
ejpam-4770	44	19	the	the	DET
ejpam-4770	44	20	2	2	NUM
ejpam-4770	44	21	-	-	PUNCT
ejpam-4770	44	22	locating	locate	VERB
ejpam-4770	44	23	number	number	NOUN
ejpam-4770	44	24	of	of	ADP
ejpam-4770	44	25	g	g	NOUN
ejpam-4770	44	26	,	,	PUNCT
ejpam-4770	44	27	denoted	denote	VERB
ejpam-4770	44	28	by	by	ADP
ejpam-4770	44	29	ln2(g	ln2(g	NOUN
ejpam-4770	44	30	)	)	PUNCT
ejpam-4770	44	31	,	,	PUNCT
ejpam-4770	44	32	is	be	AUX
ejpam-4770	44	33	the	the	DET
ejpam-4770	44	34	smallest	small	ADJ
ejpam-4770	44	35	cardinality	cardinality	NOUN
ejpam-4770	44	36	of	of	ADP
ejpam-4770	44	37	a	a	DET
ejpam-4770	44	38	2	2	NUM
ejpam-4770	44	39	-	-	PUNCT
ejpam-4770	44	40	locating	locate	VERB
ejpam-4770	44	41	set	set	NOUN
ejpam-4770	44	42	of	of	ADP
ejpam-4770	44	43	g.	g.	PROPN
ejpam-4770	44	44	a	a	DET
ejpam-4770	44	45	2	2	NUM
ejpam-4770	44	46	-	-	PUNCT
ejpam-4770	44	47	locating	locate	VERB
ejpam-4770	44	48	set	set	NOUN
ejpam-4770	44	49	of	of	ADP
ejpam-4770	44	50	g	g	NOUN
ejpam-4770	44	51	of	of	ADP
ejpam-4770	44	52	cardinality	cardinality	PROPN
ejpam-4770	44	53	ln2(g	ln2(g	PROPN
ejpam-4770	44	54	)	)	PUNCT
ejpam-4770	44	55	is	be	AUX
ejpam-4770	44	56	referred	refer	VERB
ejpam-4770	44	57	to	to	ADP
ejpam-4770	44	58	as	as	ADP
ejpam-4770	44	59	an	an	DET
ejpam-4770	44	60	ln2	ln2	NOUN
ejpam-4770	44	61	-	-	PUNCT
ejpam-4770	44	62	set	set	NOUN
ejpam-4770	44	63	of	of	ADP
ejpam-4770	44	64	g.	g.	PROPN
ejpam-4770	44	65	definition	definition	NOUN
ejpam-4770	44	66	2	2	NUM
ejpam-4770	44	67	.	.	PUNCT
ejpam-4770	45	1	[	[	X
ejpam-4770	45	2	15	15	NUM
ejpam-4770	45	3	]	]	X
ejpam-4770	45	4	a	a	DET
ejpam-4770	45	5	set	set	NOUN
ejpam-4770	45	6	d	d	NOUN
ejpam-4770	45	7	⊆	⊆	NUM
ejpam-4770	45	8	v	v	ADP
ejpam-4770	45	9	(	(	PUNCT
ejpam-4770	45	10	g	g	NOUN
ejpam-4770	45	11	)	)	PUNCT
ejpam-4770	45	12	is	be	AUX
ejpam-4770	45	13	a	a	DET
ejpam-4770	45	14	point	point	NOUN
ejpam-4770	45	15	-	-	PUNCT
ejpam-4770	45	16	wise	wise	ADJ
ejpam-4770	45	17	non	non	ADJ
ejpam-4770	45	18	-	-	ADJ
ejpam-4770	45	19	dominating	dominating	ADJ
ejpam-4770	45	20	set	set	NOUN
ejpam-4770	45	21	of	of	ADP
ejpam-4770	45	22	g	g	PROPN
ejpam-4770	45	23	if	if	SCONJ
ejpam-4770	45	24	for	for	ADP
ejpam-4770	45	25	each	each	DET
ejpam-4770	45	26	v	v	NUM
ejpam-4770	45	27	∈	∈	PROPN
ejpam-4770	45	28	v	v	NOUN
ejpam-4770	45	29	(	(	PUNCT
ejpam-4770	45	30	g)\d	g)\d	NOUN
ejpam-4770	45	31	,	,	PUNCT
ejpam-4770	45	32	there	there	PRON
ejpam-4770	45	33	exists	exist	VERB
ejpam-4770	45	34	u	u	NOUN
ejpam-4770	45	35	∈	∈	PROPN
ejpam-4770	45	36	d	d	ADP
ejpam-4770	45	37	such	such	ADJ
ejpam-4770	45	38	that	that	DET
ejpam-4770	45	39	v	v	NOUN
ejpam-4770	45	40	/∈	/∈	PUNCT
ejpam-4770	45	41	ng(u	ng(u	NOUN
ejpam-4770	45	42	)	)	PUNCT
ejpam-4770	45	43	.	.	PUNCT
ejpam-4770	46	1	the	the	DET
ejpam-4770	46	2	smallest	small	ADJ
ejpam-4770	46	3	cardinality	cardinality	NOUN
ejpam-4770	46	4	of	of	ADP
ejpam-4770	46	5	a	a	DET
ejpam-4770	46	6	pointwise	pointwise	ADJ
ejpam-4770	46	7	non	non	ADJ
ejpam-4770	46	8	-	-	ADJ
ejpam-4770	46	9	dominating	dominating	ADJ
ejpam-4770	46	10	set	set	NOUN
ejpam-4770	46	11	of	of	ADP
ejpam-4770	46	12	g	g	NOUN
ejpam-4770	46	13	,	,	PUNCT
ejpam-4770	46	14	denoted	denote	VERB
ejpam-4770	46	15	by	by	ADP
ejpam-4770	46	16	pnd(g	pnd(g	PROPN
ejpam-4770	46	17	)	)	PUNCT
ejpam-4770	46	18	,	,	PUNCT
ejpam-4770	46	19	is	be	AUX
ejpam-4770	46	20	called	call	VERB
ejpam-4770	46	21	the	the	DET
ejpam-4770	46	22	point	point	NOUN
ejpam-4770	46	23	-	-	PUNCT
ejpam-4770	46	24	wise	wise	ADJ
ejpam-4770	46	25	non	non	ADJ
ejpam-4770	46	26	-	-	ADJ
ejpam-4770	46	27	domination	domination	ADJ
ejpam-4770	46	28	number	number	NOUN
ejpam-4770	46	29	of	of	ADP
ejpam-4770	46	30	g.	g.	PROPN
ejpam-4770	46	31	any	any	DET
ejpam-4770	46	32	point	point	NOUN
ejpam-4770	46	33	-	-	PUNCT
ejpam-4770	46	34	wise	wise	ADJ
ejpam-4770	46	35	non	non	ADJ
ejpam-4770	46	36	-	-	ADJ
ejpam-4770	46	37	dominating	dominating	ADJ
ejpam-4770	46	38	set	set	NOUN
ejpam-4770	46	39	d	d	NOUN
ejpam-4770	46	40	of	of	ADP
ejpam-4770	46	41	g	g	NOUN
ejpam-4770	46	42	with	with	ADP
ejpam-4770	46	43	|d|	|d|	PROPN
ejpam-4770	46	44	=	=	SYM
ejpam-4770	46	45	pnd(g	pnd(g	PROPN
ejpam-4770	46	46	)	)	PUNCT
ejpam-4770	46	47	,	,	PUNCT
ejpam-4770	46	48	is	be	AUX
ejpam-4770	46	49	called	call	VERB
ejpam-4770	46	50	a	a	DET
ejpam-4770	46	51	pnd	pnd	NOUN
ejpam-4770	46	52	-	-	PUNCT
ejpam-4770	46	53	set	set	NOUN
ejpam-4770	46	54	of	of	ADP
ejpam-4770	46	55	g.	g.	PROPN
ejpam-4770	46	56	definition	definition	NOUN
ejpam-4770	46	57	3	3	NUM
ejpam-4770	46	58	.	.	PUNCT
ejpam-4770	47	1	[	[	X
ejpam-4770	47	2	9	9	NUM
ejpam-4770	47	3	]	]	SYM
ejpam-4770	47	4	a	a	DET
ejpam-4770	47	5	2	2	NUM
ejpam-4770	47	6	-	-	PUNCT
ejpam-4770	47	7	locating	locate	VERB
ejpam-4770	47	8	set	set	NOUN
ejpam-4770	47	9	s	s	PROPN
ejpam-4770	47	10	⊆	⊆	NUM
ejpam-4770	47	11	v	v	NOUN
ejpam-4770	47	12	(	(	PUNCT
ejpam-4770	47	13	g	g	NOUN
ejpam-4770	47	14	)	)	PUNCT
ejpam-4770	47	15	which	which	PRON
ejpam-4770	47	16	is	be	AUX
ejpam-4770	47	17	point	point	ADV
ejpam-4770	47	18	-	-	PUNCT
ejpam-4770	47	19	wise	wise	ADJ
ejpam-4770	47	20	non	non	ADJ
ejpam-4770	47	21	-	-	ADJ
ejpam-4770	47	22	dominating	dominating	NOUN
ejpam-4770	47	23	is	be	AUX
ejpam-4770	47	24	called	call	VERB
ejpam-4770	47	25	a	a	DET
ejpam-4770	47	26	2	2	NUM
ejpam-4770	47	27	-	-	PUNCT
ejpam-4770	47	28	locating	locate	VERB
ejpam-4770	47	29	point	point	NOUN
ejpam-4770	47	30	-	-	PUNCT
ejpam-4770	47	31	wise	wise	ADJ
ejpam-4770	47	32	non	non	ADJ
ejpam-4770	47	33	-	-	ADJ
ejpam-4770	47	34	dominating	dominating	ADJ
ejpam-4770	47	35	set	set	NOUN
ejpam-4770	47	36	in	in	ADP
ejpam-4770	47	37	g.	g.	PROPN
ejpam-4770	47	38	the	the	DET
ejpam-4770	47	39	minimum	minimum	ADJ
ejpam-4770	47	40	cardinality	cardinality	NOUN
ejpam-4770	47	41	of	of	ADP
ejpam-4770	47	42	a	a	DET
ejpam-4770	47	43	2	2	NUM
ejpam-4770	47	44	-	-	PUNCT
ejpam-4770	47	45	locating	locate	VERB
ejpam-4770	47	46	point	point	NOUN
ejpam-4770	47	47	-	-	PUNCT
ejpam-4770	47	48	wise	wise	ADJ
ejpam-4770	47	49	non	non	ADJ
ejpam-4770	47	50	-	-	ADJ
ejpam-4770	47	51	dominating	dominating	ADJ
ejpam-4770	47	52	set	set	NOUN
ejpam-4770	47	53	in	in	ADP
ejpam-4770	47	54	g	g	NOUN
ejpam-4770	47	55	,	,	PUNCT
ejpam-4770	47	56	denoted	denote	VERB
ejpam-4770	47	57	by	by	ADP
ejpam-4770	47	58	lnpnd	lnpnd	ADJ
ejpam-4770	47	59	2	2	NUM
ejpam-4770	47	60	(	(	PUNCT
ejpam-4770	47	61	g	g	NOUN
ejpam-4770	47	62	)	)	PUNCT
ejpam-4770	47	63	is	be	AUX
ejpam-4770	47	64	called	call	VERB
ejpam-4770	47	65	the	the	DET
ejpam-4770	47	66	2	2	NUM
ejpam-4770	47	67	-	-	PUNCT
ejpam-4770	47	68	locating	locate	VERB
ejpam-4770	47	69	point	point	NOUN
ejpam-4770	47	70	-	-	PUNCT
ejpam-4770	47	71	wise	wise	ADJ
ejpam-4770	47	72	non	non	ADJ
ejpam-4770	47	73	-	-	ADJ
ejpam-4770	47	74	domination	domination	ADJ
ejpam-4770	47	75	number	number	NOUN
ejpam-4770	47	76	of	of	ADP
ejpam-4770	47	77	g.	g.	PROPN
ejpam-4770	47	78	any	any	DET
ejpam-4770	47	79	2	2	NUM
ejpam-4770	47	80	-	-	PUNCT
ejpam-4770	47	81	locating	locate	VERB
ejpam-4770	47	82	point	point	NOUN
ejpam-4770	47	83	-	-	PUNCT
ejpam-4770	47	84	wise	wise	ADJ
ejpam-4770	47	85	non	non	ADJ
ejpam-4770	47	86	-	-	ADJ
ejpam-4770	47	87	dominating	dominating	ADJ
ejpam-4770	47	88	set	set	NOUN
ejpam-4770	47	89	of	of	ADP
ejpam-4770	47	90	cardinality	cardinality	PROPN
ejpam-4770	47	91	lnpnd	lnpnd	PROPN
ejpam-4770	47	92	2	2	NUM
ejpam-4770	47	93	(	(	PUNCT
ejpam-4770	47	94	g	g	NOUN
ejpam-4770	47	95	)	)	PUNCT
ejpam-4770	47	96	is	be	AUX
ejpam-4770	47	97	then	then	ADV
ejpam-4770	47	98	referred	refer	VERB
ejpam-4770	47	99	to	to	ADP
ejpam-4770	47	100	as	as	ADP
ejpam-4770	47	101	a	a	DET
ejpam-4770	47	102	lnpnd	lnpnd	ADJ
ejpam-4770	47	103	2	2	NUM
ejpam-4770	47	104	(	(	PUNCT
ejpam-4770	47	105	g)-set	g)-set	VERB
ejpam-4770	47	106	in	in	ADP
ejpam-4770	47	107	g.	g.	PROPN
ejpam-4770	47	108	definition	definition	NOUN
ejpam-4770	47	109	4	4	NUM
ejpam-4770	47	110	.	.	PUNCT
ejpam-4770	48	1	[	[	X
ejpam-4770	48	2	6	6	NUM
ejpam-4770	48	3	]	]	PUNCT
ejpam-4770	48	4	let	let	VERB
ejpam-4770	48	5	g	g	NOUN
ejpam-4770	48	6	be	be	AUX
ejpam-4770	48	7	any	any	DET
ejpam-4770	48	8	nontrivial	nontrivial	ADJ
ejpam-4770	48	9	connected	connect	VERB
ejpam-4770	48	10	graph	graph	NOUN
ejpam-4770	48	11	and	and	CCONJ
ejpam-4770	48	12	s	s	VERB
ejpam-4770	48	13	⊆	⊆	NUM
ejpam-4770	48	14	v	v	NOUN
ejpam-4770	48	15	(	(	PUNCT
ejpam-4770	48	16	g	g	NOUN
ejpam-4770	48	17	)	)	PUNCT
ejpam-4770	48	18	.	.	PUNCT
ejpam-4770	49	1	s	s	PART
ejpam-4770	49	2	is	be	AUX
ejpam-4770	49	3	a	a	DET
ejpam-4770	49	4	(	(	PUNCT
ejpam-4770	49	5	2	2	NUM
ejpam-4770	49	6	,	,	PUNCT
ejpam-4770	49	7	2)locating	2)locating	NUM
ejpam-4770	49	8	(	(	PUNCT
ejpam-4770	49	9	(	(	PUNCT
ejpam-4770	49	10	2	2	NUM
ejpam-4770	49	11	,	,	PUNCT
ejpam-4770	49	12	1)-locating	1)-locating	NUM
ejpam-4770	49	13	,	,	PUNCT
ejpam-4770	49	14	respectively	respectively	ADV
ejpam-4770	49	15	)	)	PUNCT
ejpam-4770	49	16	set	set	VERB
ejpam-4770	49	17	in	in	ADP
ejpam-4770	49	18	g	g	PROPN
ejpam-4770	49	19	if	if	SCONJ
ejpam-4770	49	20	s	s	NOUN
ejpam-4770	49	21	is	be	AUX
ejpam-4770	49	22	2	2	NUM
ejpam-4770	49	23	-	-	PUNCT
ejpam-4770	49	24	locating	locate	VERB
ejpam-4770	49	25	and	and	CCONJ
ejpam-4770	49	26	|ng(y)∩	|ng(y)∩	NOUN
ejpam-4770	49	27	s|	s|	VERB
ejpam-4770	49	28	≤	≤	NUM
ejpam-4770	49	29	|s|	|s|	PROPN
ejpam-4770	49	30	−	−	PROPN
ejpam-4770	49	31	2	2	NUM
ejpam-4770	49	32	(	(	PUNCT
ejpam-4770	49	33	|ng(y)∩s|	|ng(y)∩s|	NOUN
ejpam-4770	49	34	≤	≤	X
ejpam-4770	49	35	|s|−	|s|−	NOUN
ejpam-4770	49	36	1	1	NUM
ejpam-4770	49	37	,	,	PUNCT
ejpam-4770	49	38	respectively	respectively	ADV
ejpam-4770	49	39	)	)	PUNCT
ejpam-4770	49	40	,	,	PUNCT
ejpam-4770	49	41	for	for	ADP
ejpam-4770	49	42	all	all	DET
ejpam-4770	49	43	y	y	PROPN
ejpam-4770	49	44	∈	∈	PROPN
ejpam-4770	49	45	v	v	NOUN
ejpam-4770	49	46	(	(	PUNCT
ejpam-4770	49	47	g	g	NOUN
ejpam-4770	49	48	)	)	PUNCT
ejpam-4770	49	49	.	.	PUNCT
ejpam-4770	50	1	the	the	DET
ejpam-4770	50	2	(	(	PUNCT
ejpam-4770	50	3	2	2	NUM
ejpam-4770	50	4	,	,	PUNCT
ejpam-4770	50	5	2)-locating	2)-locating	NUM
ejpam-4770	50	6	(	(	PUNCT
ejpam-4770	50	7	(	(	PUNCT
ejpam-4770	50	8	2	2	NUM
ejpam-4770	50	9	,	,	PUNCT
ejpam-4770	50	10	1)-locating	1)-locating	NUM
ejpam-4770	50	11	,	,	PUNCT
ejpam-4770	50	12	respectively	respectively	ADV
ejpam-4770	50	13	)	)	PUNCT
ejpam-4770	50	14	number	number	NOUN
ejpam-4770	50	15	of	of	ADP
ejpam-4770	50	16	g	g	NOUN
ejpam-4770	50	17	,	,	PUNCT
ejpam-4770	50	18	denoted	denote	VERB
ejpam-4770	50	19	by	by	ADP
ejpam-4770	50	20	ln(2,2)(g	ln(2,2)(g	NOUN
ejpam-4770	50	21	)	)	PUNCT
ejpam-4770	50	22	(	(	PUNCT
ejpam-4770	50	23	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4770	50	24	)	)	PUNCT
ejpam-4770	50	25	,	,	PUNCT
ejpam-4770	50	26	respectively	respectively	ADV
ejpam-4770	50	27	)	)	PUNCT
ejpam-4770	50	28	,	,	PUNCT
ejpam-4770	50	29	is	be	AUX
ejpam-4770	50	30	the	the	DET
ejpam-4770	50	31	smallest	small	ADJ
ejpam-4770	50	32	cardinality	cardinality	NOUN
ejpam-4770	50	33	of	of	ADP
ejpam-4770	50	34	a	a	DET
ejpam-4770	50	35	(	(	PUNCT
ejpam-4770	50	36	2	2	NUM
ejpam-4770	50	37	,	,	PUNCT
ejpam-4770	50	38	2)-locating	2)-locating	NUM
ejpam-4770	50	39	(	(	PUNCT
ejpam-4770	50	40	(	(	PUNCT
ejpam-4770	50	41	2	2	NUM
ejpam-4770	50	42	,	,	PUNCT
ejpam-4770	50	43	1)-locating	1)-locating	NUM
ejpam-4770	50	44	,	,	PUNCT
ejpam-4770	50	45	respectively	respectively	ADV
ejpam-4770	50	46	)	)	PUNCT
ejpam-4770	50	47	set	set	VERB
ejpam-4770	50	48	in	in	ADP
ejpam-4770	50	49	g.	g.	PROPN
ejpam-4770	50	50	a	a	PRON
ejpam-4770	50	51	(	(	PUNCT
ejpam-4770	50	52	2	2	NUM
ejpam-4770	50	53	,	,	PUNCT
ejpam-4770	50	54	2)-locating	2)-locating	NUM
ejpam-4770	50	55	(	(	PUNCT
ejpam-4770	50	56	(	(	PUNCT
ejpam-4770	50	57	2	2	NUM
ejpam-4770	50	58	,	,	PUNCT
ejpam-4770	50	59	1)-locating	1)-locating	NUM
ejpam-4770	50	60	,	,	PUNCT
ejpam-4770	50	61	respectively	respectively	ADV
ejpam-4770	50	62	)	)	PUNCT
ejpam-4770	50	63	set	set	VERB
ejpam-4770	50	64	in	in	ADP
ejpam-4770	50	65	g	g	NOUN
ejpam-4770	50	66	of	of	ADP
ejpam-4770	50	67	cardinality	cardinality	NOUN
ejpam-4770	50	68	ln(2,2)(g	ln(2,2)(g	PROPN
ejpam-4770	50	69	)	)	PUNCT
ejpam-4770	50	70	(	(	PUNCT
ejpam-4770	50	71	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4770	50	72	)	)	PUNCT
ejpam-4770	50	73	,	,	PUNCT
ejpam-4770	50	74	respectively	respectively	ADV
ejpam-4770	50	75	)	)	PUNCT
ejpam-4770	50	76	is	be	AUX
ejpam-4770	50	77	referred	refer	VERB
ejpam-4770	50	78	to	to	ADP
ejpam-4770	50	79	as	as	ADP
ejpam-4770	50	80	an	an	DET
ejpam-4770	50	81	ln(2,2)-set	ln(2,2)-set	NOUN
ejpam-4770	50	82	(	(	PUNCT
ejpam-4770	50	83	ln(2,1)-set	ln(2,1)-set	PROPN
ejpam-4770	50	84	,	,	PUNCT
ejpam-4770	50	85	respectively	respectively	ADV
ejpam-4770	50	86	)	)	PUNCT
ejpam-4770	50	87	in	in	ADP
ejpam-4770	50	88	g.	g.	PROPN
ejpam-4770	50	89	definition	definition	NOUN
ejpam-4770	50	90	5	5	NUM
ejpam-4770	50	91	.	.	PUNCT
ejpam-4770	51	1	[	[	X
ejpam-4770	51	2	9	9	NUM
ejpam-4770	51	3	]	]	X
ejpam-4770	51	4	a	a	PRON
ejpam-4770	51	5	(	(	PUNCT
ejpam-4770	51	6	2,2)-locating	2,2)-locating	NUM
ejpam-4770	51	7	(	(	PUNCT
ejpam-4770	51	8	(	(	PUNCT
ejpam-4770	51	9	2,1)-locating	2,1)-locating	NUM
ejpam-4770	51	10	,	,	PUNCT
ejpam-4770	51	11	respectively	respectively	ADV
ejpam-4770	51	12	)	)	PUNCT
ejpam-4770	51	13	set	set	VERB
ejpam-4770	51	14	s	s	PROPN
ejpam-4770	51	15	⊆	⊆	NUM
ejpam-4770	51	16	v	v	NOUN
ejpam-4770	51	17	(	(	PUNCT
ejpam-4770	51	18	g	g	NOUN
ejpam-4770	51	19	)	)	PUNCT
ejpam-4770	51	20	which	which	PRON
ejpam-4770	51	21	is	be	AUX
ejpam-4770	51	22	a	a	DET
ejpam-4770	51	23	point	point	NOUN
ejpam-4770	51	24	-	-	PUNCT
ejpam-4770	51	25	wise	wise	ADJ
ejpam-4770	51	26	non	non	ADJ
ejpam-4770	51	27	-	-	ADJ
ejpam-4770	51	28	dominating	dominating	NOUN
ejpam-4770	51	29	is	be	AUX
ejpam-4770	51	30	called	call	VERB
ejpam-4770	51	31	a	a	DET
ejpam-4770	51	32	(	(	PUNCT
ejpam-4770	51	33	2,2)-locating	2,2)-locating	NUM
ejpam-4770	51	34	point	point	ADV
ejpam-4770	51	35	-	-	PUNCT
ejpam-4770	51	36	wise	wise	ADJ
ejpam-4770	51	37	non	non	ADJ
ejpam-4770	51	38	-	-	ADJ
ejpam-4770	51	39	dominating	dominating	ADJ
ejpam-4770	51	40	(	(	PUNCT
ejpam-4770	51	41	(	(	PUNCT
ejpam-4770	51	42	2,1)locating	2,1)locating	NUM
ejpam-4770	51	43	point	point	NOUN
ejpam-4770	51	44	-	-	PUNCT
ejpam-4770	51	45	wise	wise	ADJ
ejpam-4770	51	46	non	non	ADJ
ejpam-4770	51	47	-	-	ADJ
ejpam-4770	51	48	dominating	dominating	ADJ
ejpam-4770	51	49	,	,	PUNCT
ejpam-4770	51	50	respectively	respectively	ADV
ejpam-4770	51	51	)	)	PUNCT
ejpam-4770	51	52	set	set	VERB
ejpam-4770	51	53	in	in	ADP
ejpam-4770	51	54	g.	g.	PROPN
ejpam-4770	51	55	the	the	DET
ejpam-4770	51	56	minimum	minimum	ADJ
ejpam-4770	51	57	cardinality	cardinality	NOUN
ejpam-4770	51	58	of	of	ADP
ejpam-4770	51	59	a	a	DET
ejpam-4770	51	60	(	(	PUNCT
ejpam-4770	51	61	2,2)-locating	2,2)-locating	NUM
ejpam-4770	51	62	point	point	ADV
ejpam-4770	51	63	-	-	PUNCT
ejpam-4770	51	64	wise	wise	ADJ
ejpam-4770	51	65	non	non	ADJ
ejpam-4770	51	66	-	-	ADJ
ejpam-4770	51	67	dominating	dominating	ADJ
ejpam-4770	51	68	(	(	PUNCT
ejpam-4770	51	69	(	(	PUNCT
ejpam-4770	51	70	2,1)-locating	2,1)-locating	NUM
ejpam-4770	51	71	point	point	NOUN
ejpam-4770	51	72	-	-	PUNCT
ejpam-4770	51	73	wise	wise	ADJ
ejpam-4770	51	74	non	non	ADJ
ejpam-4770	51	75	-	-	ADJ
ejpam-4770	51	76	dominating	dominating	ADJ
ejpam-4770	51	77	,	,	PUNCT
ejpam-4770	51	78	respectively	respectively	ADV
ejpam-4770	51	79	)	)	PUNCT
ejpam-4770	51	80	set	set	VERB
ejpam-4770	51	81	in	in	ADP
ejpam-4770	51	82	g	g	NOUN
ejpam-4770	51	83	,	,	PUNCT
ejpam-4770	51	84	denoted	denote	VERB
ejpam-4770	51	85	by	by	ADP
ejpam-4770	51	86	lnpnd	lnpnd	ADJ
ejpam-4770	51	87	(	(	PUNCT
ejpam-4770	51	88	2,2)(g	2,2)(g	NUM
ejpam-4770	51	89	)	)	PUNCT
ejpam-4770	51	90	(	(	PUNCT
ejpam-4770	51	91	lnpnd	lnpnd	ADJ
ejpam-4770	51	92	(	(	PUNCT
ejpam-4770	51	93	2,1)(g),respectively	2,1)(g),respectively	NUM
ejpam-4770	51	94	)	)	PUNCT
ejpam-4770	51	95	is	be	AUX
ejpam-4770	51	96	called	call	VERB
ejpam-4770	51	97	the	the	DET
ejpam-4770	51	98	(	(	PUNCT
ejpam-4770	51	99	2,2)locating	2,2)locating	NUM
ejpam-4770	51	100	point	point	NOUN
ejpam-4770	51	101	-	-	PUNCT
ejpam-4770	51	102	wise	wise	ADJ
ejpam-4770	51	103	non	non	ADJ
ejpam-4770	51	104	-	-	NOUN
ejpam-4770	51	105	domination	domination	ADJ
ejpam-4770	51	106	(	(	PUNCT
ejpam-4770	51	107	(	(	PUNCT
ejpam-4770	51	108	2,1)-locating	2,1)-locating	NUM
ejpam-4770	51	109	point	point	NOUN
ejpam-4770	51	110	-	-	PUNCT
ejpam-4770	51	111	wise	wise	ADJ
ejpam-4770	51	112	non	non	ADJ
ejpam-4770	51	113	-	-	ADJ
ejpam-4770	51	114	domination	domination	ADJ
ejpam-4770	51	115	)	)	PUNCT
ejpam-4770	51	116	number	number	NOUN
ejpam-4770	51	117	of	of	ADP
ejpam-4770	51	118	g.	g.	PROPN
ejpam-4770	51	119	any	any	PRON
ejpam-4770	51	120	(	(	PUNCT
ejpam-4770	51	121	2,2)-locating	2,2)-locating	NUM
ejpam-4770	51	122	point	point	ADV
ejpam-4770	51	123	-	-	PUNCT
ejpam-4770	51	124	wise	wise	ADJ
ejpam-4770	51	125	non	non	ADJ
ejpam-4770	51	126	-	-	ADJ
ejpam-4770	51	127	dominating	dominating	ADJ
ejpam-4770	51	128	(	(	PUNCT
ejpam-4770	51	129	(	(	PUNCT
ejpam-4770	51	130	2,1)-locating	2,1)-locating	NUM
ejpam-4770	51	131	point	point	NOUN
ejpam-4770	51	132	-	-	PUNCT
ejpam-4770	51	133	wise	wise	ADJ
ejpam-4770	51	134	non	non	ADJ
ejpam-4770	51	135	-	-	ADJ
ejpam-4770	51	136	dominating	dominating	ADJ
ejpam-4770	51	137	,	,	PUNCT
ejpam-4770	51	138	respectively	respectively	ADV
ejpam-4770	51	139	)	)	PUNCT
ejpam-4770	51	140	set	set	NOUN
ejpam-4770	51	141	of	of	ADP
ejpam-4770	51	142	cardinality	cardinality	PROPN
ejpam-4770	51	143	lnpnd	lnpnd	ADV
ejpam-4770	51	144	(	(	PUNCT
ejpam-4770	51	145	2,2)(g	2,2)(g	NUM
ejpam-4770	51	146	)	)	PUNCT
ejpam-4770	51	147	(	(	PUNCT
ejpam-4770	51	148	lnpnd	lnpnd	ADJ
ejpam-4770	51	149	(	(	PUNCT
ejpam-4770	51	150	2,1)(g	2,1)(g	NUM
ejpam-4770	51	151	)	)	PUNCT
ejpam-4770	51	152	,	,	PUNCT
ejpam-4770	51	153	respectively	respectively	ADV
ejpam-4770	51	154	)	)	PUNCT
ejpam-4770	51	155	is	be	AUX
ejpam-4770	51	156	then	then	ADV
ejpam-4770	51	157	referred	refer	VERB
ejpam-4770	51	158	to	to	ADP
ejpam-4770	51	159	as	as	ADP
ejpam-4770	51	160	a	a	DET
ejpam-4770	51	161	lnpnd	lnpnd	ADJ
ejpam-4770	51	162	(	(	PUNCT
ejpam-4770	51	163	2,2)-set	2,2)-set	NUM
ejpam-4770	51	164	(	(	PUNCT
ejpam-4770	51	165	ln	ln	ADJ
ejpam-4770	51	166	pnd	pnd	NOUN
ejpam-4770	51	167	(	(	PUNCT
ejpam-4770	51	168	2,1)-set	2,1)-set	NUM
ejpam-4770	51	169	)	)	PUNCT
ejpam-4770	51	170	in	in	ADP
ejpam-4770	51	171	g.	g.	PROPN
ejpam-4770	51	172	definition	definition	NOUN
ejpam-4770	51	173	6	6	NUM
ejpam-4770	51	174	.	.	PUNCT
ejpam-4770	52	1	a	a	DET
ejpam-4770	52	2	set	set	NOUN
ejpam-4770	52	3	s	s	NOUN
ejpam-4770	52	4	⊆	⊆	NUM
ejpam-4770	52	5	v	v	NOUN
ejpam-4770	52	6	(	(	PUNCT
ejpam-4770	52	7	g	g	NOUN
ejpam-4770	52	8	)	)	PUNCT
ejpam-4770	52	9	is	be	AUX
ejpam-4770	52	10	a	a	DET
ejpam-4770	52	11	1	1	NUM
ejpam-4770	52	12	-	-	PUNCT
ejpam-4770	52	13	movable	movable	ADJ
ejpam-4770	52	14	2	2	NUM
ejpam-4770	52	15	-	-	PUNCT
ejpam-4770	52	16	locating	locate	VERB
ejpam-4770	52	17	point	point	NOUN
ejpam-4770	52	18	-	-	PUNCT
ejpam-4770	52	19	wise	wise	ADJ
ejpam-4770	52	20	non	non	ADJ
ejpam-4770	52	21	-	-	ADJ
ejpam-4770	52	22	dominating	dominating	ADJ
ejpam-4770	52	23	set	set	NOUN
ejpam-4770	52	24	in	in	ADP
ejpam-4770	52	25	g	g	PROPN
ejpam-4770	52	26	if	if	SCONJ
ejpam-4770	52	27	s	s	VERB
ejpam-4770	52	28	is	be	AUX
ejpam-4770	52	29	a	a	DET
ejpam-4770	52	30	2	2	NUM
ejpam-4770	52	31	-	-	PUNCT
ejpam-4770	52	32	locating	locate	VERB
ejpam-4770	52	33	point	point	NOUN
ejpam-4770	52	34	-	-	PUNCT
ejpam-4770	52	35	wise	wise	ADJ
ejpam-4770	52	36	non	non	ADJ
ejpam-4770	52	37	-	-	ADJ
ejpam-4770	52	38	dominating	dominating	ADJ
ejpam-4770	52	39	set	set	NOUN
ejpam-4770	52	40	in	in	ADP
ejpam-4770	52	41	g	g	PROPN
ejpam-4770	52	42	and	and	CCONJ
ejpam-4770	52	43	for	for	ADP
ejpam-4770	52	44	every	every	DET
ejpam-4770	52	45	v	v	NUM
ejpam-4770	52	46	∈	∈	PROPN
ejpam-4770	52	47	s	s	NOUN
ejpam-4770	52	48	,	,	PUNCT
ejpam-4770	52	49	either	either	CCONJ
ejpam-4770	52	50	s\{v	s\{v	VERB
ejpam-4770	52	51	}	}	PUNCT
ejpam-4770	52	52	is	be	AUX
ejpam-4770	52	53	a	a	DET
ejpam-4770	52	54	2	2	NUM
ejpam-4770	52	55	-	-	PUNCT
ejpam-4770	52	56	locating	locate	VERB
ejpam-4770	52	57	point	point	NOUN
ejpam-4770	52	58	-	-	PUNCT
ejpam-4770	52	59	wise	wise	ADJ
ejpam-4770	52	60	non	non	ADJ
ejpam-4770	52	61	-	-	ADJ
ejpam-4770	52	62	dominating	dominating	ADJ
ejpam-4770	52	63	set	set	NOUN
ejpam-4770	52	64	or	or	CCONJ
ejpam-4770	52	65	there	there	PRON
ejpam-4770	52	66	exists	exist	VERB
ejpam-4770	52	67	a	a	DET
ejpam-4770	52	68	vertex	vertex	NOUN
ejpam-4770	52	69	u	u	NOUN
ejpam-4770	52	70	∈	∈	PROPN
ejpam-4770	52	71	(	(	PUNCT
ejpam-4770	52	72	(	(	PUNCT
ejpam-4770	52	73	v	v	NOUN
ejpam-4770	52	74	(	(	PUNCT
ejpam-4770	52	75	g)\s	g)\s	NOUN
ejpam-4770	52	76	)	)	PUNCT
ejpam-4770	52	77	∩	∩	NOUN
ejpam-4770	52	78	ng(v	ng(v	NUM
ejpam-4770	52	79	)	)	PUNCT
ejpam-4770	52	80	)	)	PUNCT
ejpam-4770	52	81	such	such	ADJ
ejpam-4770	52	82	that	that	SCONJ
ejpam-4770	52	83	(	(	PUNCT
ejpam-4770	52	84	s\{v	s\{v	VERB
ejpam-4770	52	85	}	}	PUNCT
ejpam-4770	52	86	)	)	PUNCT
ejpam-4770	52	87	∪	∪	ADP
ejpam-4770	52	88	{	{	PUNCT
ejpam-4770	52	89	u	u	NOUN
ejpam-4770	52	90	}	}	PUNCT
ejpam-4770	52	91	is	be	AUX
ejpam-4770	52	92	a	a	DET
ejpam-4770	52	93	2	2	NUM
ejpam-4770	52	94	-	-	PUNCT
ejpam-4770	52	95	locating	locate	VERB
ejpam-4770	52	96	point	point	NOUN
ejpam-4770	52	97	-	-	PUNCT
ejpam-4770	52	98	wise	wise	ADJ
ejpam-4770	52	99	non	non	ADJ
ejpam-4770	52	100	-	-	ADJ
ejpam-4770	52	101	dominating	dominating	ADJ
ejpam-4770	52	102	set	set	NOUN
ejpam-4770	52	103	of	of	ADP
ejpam-4770	52	104	g.	g.	PROPN
ejpam-4770	52	105	the	the	DET
ejpam-4770	52	106	1	1	NUM
ejpam-4770	52	107	-	-	PUNCT
ejpam-4770	52	108	movable	movable	ADJ
ejpam-4770	52	109	2	2	NUM
ejpam-4770	52	110	-	-	PUNCT
ejpam-4770	52	111	locating	locate	VERB
ejpam-4770	52	112	point	point	NOUN
ejpam-4770	52	113	-	-	PUNCT
ejpam-4770	52	114	wise	wise	ADJ
ejpam-4770	52	115	non	non	ADJ
ejpam-4770	52	116	-	-	ADJ
ejpam-4770	52	117	domination	domination	ADJ
ejpam-4770	52	118	number	number	NOUN
ejpam-4770	52	119	of	of	ADP
ejpam-4770	52	120	g	g	NOUN
ejpam-4770	52	121	,	,	PUNCT
ejpam-4770	52	122	denoted	denote	VERB
ejpam-4770	52	123	by	by	ADP
ejpam-4770	52	124	mlnpnd	mlnpnd	NOUN
ejpam-4770	52	125	2	2	NUM
ejpam-4770	52	126	(	(	PUNCT
ejpam-4770	52	127	g	g	NOUN
ejpam-4770	52	128	)	)	PUNCT
ejpam-4770	52	129	is	be	AUX
ejpam-4770	52	130	the	the	DET
ejpam-4770	52	131	smallest	small	ADJ
ejpam-4770	52	132	cardinality	cardinality	NOUN
ejpam-4770	52	133	of	of	ADP
ejpam-4770	52	134	a	a	DET
ejpam-4770	52	135	1	1	NUM
ejpam-4770	52	136	-	-	PUNCT
ejpam-4770	52	137	movable	movable	ADJ
ejpam-4770	52	138	2	2	NUM
ejpam-4770	52	139	-	-	PUNCT
ejpam-4770	52	140	locating	locate	VERB
ejpam-4770	52	141	point	point	NOUN
ejpam-4770	52	142	-	-	PUNCT
ejpam-4770	52	143	wise	wise	ADJ
ejpam-4770	52	144	non	non	ADJ
ejpam-4770	52	145	-	-	ADJ
ejpam-4770	52	146	dominating	dominating	ADJ
ejpam-4770	52	147	set	set	NOUN
ejpam-4770	52	148	of	of	ADP
ejpam-4770	52	149	g.	g.	PROPN
ejpam-4770	52	150	any	any	DET
ejpam-4770	52	151	1	1	NUM
ejpam-4770	52	152	-	-	PUNCT
ejpam-4770	52	153	movable	movable	ADJ
ejpam-4770	52	154	2	2	NUM
ejpam-4770	52	155	-	-	PUNCT
ejpam-4770	52	156	locating	locate	VERB
ejpam-4770	52	157	point	point	NOUN
ejpam-4770	52	158	-	-	PUNCT
ejpam-4770	52	159	wise	wise	ADJ
ejpam-4770	52	160	non	non	ADJ
ejpam-4770	52	161	-	-	ADJ
ejpam-4770	52	162	dominating	dominating	ADJ
ejpam-4770	52	163	set	set	NOUN
ejpam-4770	52	164	of	of	ADP
ejpam-4770	52	165	cardinality	cardinality	PROPN
ejpam-4770	52	166	mlnpnd	mlnpnd	NOUN
ejpam-4770	52	167	2	2	NUM
ejpam-4770	52	168	(	(	PUNCT
ejpam-4770	52	169	g	g	NOUN
ejpam-4770	52	170	)	)	PUNCT
ejpam-4770	52	171	is	be	AUX
ejpam-4770	52	172	referred	refer	VERB
ejpam-4770	52	173	to	to	ADP
ejpam-4770	52	174	as	as	ADP
ejpam-4770	52	175	a	a	DET
ejpam-4770	52	176	mlnpnd	mlnpnd	NOUN
ejpam-4770	52	177	2	2	NUM
ejpam-4770	52	178	-set	-set	PUNCT
ejpam-4770	52	179	of	of	ADP
ejpam-4770	52	180	g.	g.	PROPN
ejpam-4770	52	181	definition	definition	NOUN
ejpam-4770	52	182	7	7	NUM
ejpam-4770	52	183	.	.	PUNCT
ejpam-4770	53	1	a	a	DET
ejpam-4770	53	2	set	set	NOUN
ejpam-4770	53	3	s	s	NOUN
ejpam-4770	53	4	⊆	⊆	NUM
ejpam-4770	53	5	v	v	NOUN
ejpam-4770	53	6	(	(	PUNCT
ejpam-4770	53	7	g	g	NOUN
ejpam-4770	53	8	)	)	PUNCT
ejpam-4770	53	9	is	be	AUX
ejpam-4770	53	10	a	a	DET
ejpam-4770	53	11	1	1	NUM
ejpam-4770	53	12	-	-	PUNCT
ejpam-4770	53	13	movable	movable	ADJ
ejpam-4770	53	14	(	(	PUNCT
ejpam-4770	53	15	2	2	NUM
ejpam-4770	53	16	,	,	PUNCT
ejpam-4770	53	17	2)-locating	2)-locating	NUM
ejpam-4770	53	18	point	point	NOUN
ejpam-4770	53	19	-	-	PUNCT
ejpam-4770	53	20	wise	wise	ADJ
ejpam-4770	53	21	non	non	ADJ
ejpam-4770	53	22	-	-	ADJ
ejpam-4770	53	23	dominating	dominating	ADJ
ejpam-4770	53	24	(	(	PUNCT
ejpam-4770	53	25	(	(	PUNCT
ejpam-4770	53	26	2	2	NUM
ejpam-4770	53	27	,	,	PUNCT
ejpam-4770	53	28	1)-locating	1)-locating	NUM
ejpam-4770	53	29	point	point	NOUN
ejpam-4770	53	30	-	-	PUNCT
ejpam-4770	53	31	wise	wise	ADJ
ejpam-4770	53	32	non	non	ADJ
ejpam-4770	53	33	-	-	ADJ
ejpam-4770	53	34	dominating	dominating	ADJ
ejpam-4770	53	35	,	,	PUNCT
ejpam-4770	53	36	respectively	respectively	ADV
ejpam-4770	53	37	)	)	PUNCT
ejpam-4770	53	38	in	in	ADP
ejpam-4770	53	39	g	g	PROPN
ejpam-4770	53	40	if	if	SCONJ
ejpam-4770	53	41	s	s	VERB
ejpam-4770	53	42	is	be	AUX
ejpam-4770	53	43	a	a	DET
ejpam-4770	53	44	(	(	PUNCT
ejpam-4770	53	45	2	2	NUM
ejpam-4770	53	46	,	,	PUNCT
ejpam-4770	53	47	2)-locating	2)-locating	NUM
ejpam-4770	53	48	pointwise	pointwise	PROPN
ejpam-4770	53	49	non	non	ADJ
ejpam-4770	53	50	-	-	ADJ
ejpam-4770	53	51	dominating	dominating	ADJ
ejpam-4770	53	52	(	(	PUNCT
ejpam-4770	53	53	(	(	PUNCT
ejpam-4770	53	54	2	2	NUM
ejpam-4770	53	55	,	,	PUNCT
ejpam-4770	53	56	1)-locating	1)-locating	NUM
ejpam-4770	53	57	point	point	NOUN
ejpam-4770	53	58	-	-	PUNCT
ejpam-4770	53	59	wise	wise	ADJ
ejpam-4770	53	60	non	non	ADJ
ejpam-4770	53	61	-	-	ADJ
ejpam-4770	53	62	dominating	dominating	ADJ
ejpam-4770	53	63	,	,	PUNCT
ejpam-4770	53	64	respectively	respectively	ADV
ejpam-4770	53	65	)	)	PUNCT
ejpam-4770	53	66	set	set	VERB
ejpam-4770	53	67	in	in	ADP
ejpam-4770	53	68	g	g	PROPN
ejpam-4770	53	69	and	and	CCONJ
ejpam-4770	53	70	a.m.	a.m.	PROPN
ejpam-4770	53	71	mahistrado	mahistrado	PROPN
ejpam-4770	53	72	,	,	PUNCT
ejpam-4770	53	73	h.	h.	PROPN
ejpam-4770	53	74	rara	rara	PROPN
ejpam-4770	53	75	/	/	SYM
ejpam-4770	53	76	eur	eur	PROPN
ejpam-4770	53	77	.	.	PUNCT
ejpam-4770	54	1	j.	j.	PROPN
ejpam-4770	54	2	pure	pure	PROPN
ejpam-4770	54	3	appl	appl	PROPN
ejpam-4770	54	4	.	.	PROPN
ejpam-4770	54	5	math	math	PROPN
ejpam-4770	54	6	,	,	PUNCT
ejpam-4770	54	7	16	16	NUM
ejpam-4770	54	8	(	(	PUNCT
ejpam-4770	54	9	3	3	NUM
ejpam-4770	54	10	)	)	PUNCT
ejpam-4770	54	11	(	(	PUNCT
ejpam-4770	54	12	2023	2023	NUM
ejpam-4770	54	13	)	)	PUNCT
ejpam-4770	54	14	,	,	PUNCT
ejpam-4770	54	15	1464	1464	NUM
ejpam-4770	54	16	-	-	SYM
ejpam-4770	54	17	1479	1479	NUM
ejpam-4770	54	18	1467	1467	NUM
ejpam-4770	54	19	for	for	ADP
ejpam-4770	54	20	every	every	DET
ejpam-4770	54	21	v	v	NOUN
ejpam-4770	54	22	∈	∈	PROPN
ejpam-4770	54	23	s	s	NOUN
ejpam-4770	54	24	,	,	PUNCT
ejpam-4770	54	25	either	either	CCONJ
ejpam-4770	54	26	s\{v	s\{v	VERB
ejpam-4770	54	27	}	}	PUNCT
ejpam-4770	54	28	is	be	AUX
ejpam-4770	54	29	a	a	DET
ejpam-4770	54	30	2	2	NUM
ejpam-4770	54	31	-	-	PUNCT
ejpam-4770	54	32	locating	locate	VERB
ejpam-4770	54	33	point	point	NOUN
ejpam-4770	54	34	-	-	PUNCT
ejpam-4770	54	35	wise	wise	ADJ
ejpam-4770	54	36	non	non	ADJ
ejpam-4770	54	37	-	-	ADJ
ejpam-4770	54	38	dominating	dominating	ADJ
ejpam-4770	54	39	set	set	NOUN
ejpam-4770	54	40	or	or	CCONJ
ejpam-4770	54	41	there	there	PRON
ejpam-4770	54	42	exists	exist	VERB
ejpam-4770	54	43	a	a	DET
ejpam-4770	54	44	vertex	vertex	NOUN
ejpam-4770	54	45	u	u	NOUN
ejpam-4770	54	46	∈	∈	PROPN
ejpam-4770	54	47	(	(	PUNCT
ejpam-4770	54	48	(	(	PUNCT
ejpam-4770	54	49	v	v	NOUN
ejpam-4770	54	50	(	(	PUNCT
ejpam-4770	54	51	g)\s	g)\s	NOUN
ejpam-4770	54	52	)	)	PUNCT
ejpam-4770	54	53	∩ng(v	∩ng(v	PROPN
ejpam-4770	54	54	)	)	PUNCT
ejpam-4770	54	55	)	)	PUNCT
ejpam-4770	54	56	such	such	ADJ
ejpam-4770	54	57	that	that	SCONJ
ejpam-4770	54	58	(	(	PUNCT
ejpam-4770	54	59	s\{v	s\{v	VERB
ejpam-4770	54	60	}	}	PUNCT
ejpam-4770	54	61	)	)	PUNCT
ejpam-4770	54	62	∪	∪	ADP
ejpam-4770	54	63	{	{	PUNCT
ejpam-4770	54	64	u	u	NOUN
ejpam-4770	54	65	}	}	PUNCT
ejpam-4770	54	66	is	be	AUX
ejpam-4770	54	67	(	(	PUNCT
ejpam-4770	54	68	2	2	NUM
ejpam-4770	54	69	,	,	PUNCT
ejpam-4770	54	70	2)-locating	2)-locating	NUM
ejpam-4770	54	71	pointwise	pointwise	PROPN
ejpam-4770	54	72	non	non	ADJ
ejpam-4770	54	73	-	-	ADJ
ejpam-4770	54	74	dominating	dominating	ADJ
ejpam-4770	54	75	(	(	PUNCT
ejpam-4770	54	76	(	(	PUNCT
ejpam-4770	54	77	2	2	NUM
ejpam-4770	54	78	,	,	PUNCT
ejpam-4770	54	79	1)-locating	1)-locating	NUM
ejpam-4770	54	80	point	point	NOUN
ejpam-4770	54	81	-	-	PUNCT
ejpam-4770	54	82	wise	wise	ADJ
ejpam-4770	54	83	non	non	ADJ
ejpam-4770	54	84	-	-	ADJ
ejpam-4770	54	85	dominating	dominating	ADJ
ejpam-4770	54	86	,	,	PUNCT
ejpam-4770	54	87	respectively	respectively	ADV
ejpam-4770	54	88	)	)	PUNCT
ejpam-4770	54	89	set	set	VERB
ejpam-4770	54	90	in	in	ADP
ejpam-4770	54	91	g.	g.	PROPN
ejpam-4770	54	92	the	the	DET
ejpam-4770	54	93	1	1	NUM
ejpam-4770	54	94	-	-	PUNCT
ejpam-4770	54	95	movable	movable	NOUN
ejpam-4770	54	96	(	(	PUNCT
ejpam-4770	54	97	2,2)-locating	2,2)-locating	NUM
ejpam-4770	54	98	point	point	ADV
ejpam-4770	54	99	-	-	PUNCT
ejpam-4770	54	100	wise	wise	ADJ
ejpam-4770	54	101	non	non	ADJ
ejpam-4770	54	102	-	-	NOUN
ejpam-4770	54	103	domination	domination	ADJ
ejpam-4770	54	104	(	(	PUNCT
ejpam-4770	54	105	(	(	PUNCT
ejpam-4770	54	106	2,1)-locating	2,1)-locating	NUM
ejpam-4770	54	107	point	point	NOUN
ejpam-4770	54	108	-	-	PUNCT
ejpam-4770	54	109	wise	wise	ADJ
ejpam-4770	54	110	nondomination	nondomination	NOUN
ejpam-4770	54	111	)	)	PUNCT
ejpam-4770	54	112	number	number	NOUN
ejpam-4770	54	113	of	of	ADP
ejpam-4770	54	114	g	g	NOUN
ejpam-4770	54	115	,	,	PUNCT
ejpam-4770	54	116	denoted	denote	VERB
ejpam-4770	54	117	by	by	ADP
ejpam-4770	54	118	mlnpnd	mlnpnd	NOUN
ejpam-4770	54	119	(	(	PUNCT
ejpam-4770	54	120	2,2)(g	2,2)(g	NUM
ejpam-4770	54	121	)	)	PUNCT
ejpam-4770	54	122	(	(	PUNCT
ejpam-4770	54	123	mlnpnd	mlnpnd	NOUN
ejpam-4770	54	124	(	(	PUNCT
ejpam-4770	54	125	2,1)(g),respectively	2,1)(g),respectively	NUM
ejpam-4770	54	126	)	)	PUNCT
ejpam-4770	54	127	is	be	AUX
ejpam-4770	54	128	s	s	PRON
ejpam-4770	54	129	the	the	DET
ejpam-4770	54	130	smallest	small	ADJ
ejpam-4770	54	131	cardinality	cardinality	NOUN
ejpam-4770	54	132	of	of	ADP
ejpam-4770	54	133	a	a	DET
ejpam-4770	54	134	1	1	NUM
ejpam-4770	54	135	-	-	PUNCT
ejpam-4770	54	136	movable	movable	NOUN
ejpam-4770	54	137	called	call	VERB
ejpam-4770	54	138	the	the	DET
ejpam-4770	54	139	(	(	PUNCT
ejpam-4770	54	140	2,2)-locating	2,2)-locating	NUM
ejpam-4770	54	141	point	point	ADV
ejpam-4770	54	142	-	-	PUNCT
ejpam-4770	54	143	wise	wise	ADJ
ejpam-4770	54	144	non	non	ADJ
ejpam-4770	54	145	-	-	ADJ
ejpam-4770	54	146	dominating	dominating	ADJ
ejpam-4770	54	147	(	(	PUNCT
ejpam-4770	54	148	(	(	PUNCT
ejpam-4770	54	149	2,1)-locating	2,1)-locating	NUM
ejpam-4770	54	150	point	point	NOUN
ejpam-4770	54	151	-	-	PUNCT
ejpam-4770	54	152	wise	wise	ADJ
ejpam-4770	54	153	non	non	ADJ
ejpam-4770	54	154	-	-	ADJ
ejpam-4770	54	155	dominating	dominating	ADJ
ejpam-4770	54	156	)	)	PUNCT
ejpam-4770	54	157	number	number	NOUN
ejpam-4770	54	158	set	set	VERB
ejpam-4770	54	159	of	of	ADP
ejpam-4770	54	160	g.	g.	PROPN
ejpam-4770	54	161	any	any	DET
ejpam-4770	54	162	1	1	NUM
ejpam-4770	54	163	-	-	PUNCT
ejpam-4770	54	164	movable	movable	NOUN
ejpam-4770	54	165	(	(	PUNCT
ejpam-4770	54	166	2,2)-locating	2,2)-locating	NUM
ejpam-4770	54	167	point	point	ADV
ejpam-4770	54	168	-	-	PUNCT
ejpam-4770	54	169	wise	wise	ADJ
ejpam-4770	54	170	non	non	ADJ
ejpam-4770	54	171	-	-	ADJ
ejpam-4770	54	172	dominating	dominating	ADJ
ejpam-4770	54	173	(	(	PUNCT
ejpam-4770	54	174	(	(	PUNCT
ejpam-4770	54	175	2,1)-locating	2,1)-locating	NUM
ejpam-4770	54	176	point	point	NOUN
ejpam-4770	54	177	-	-	PUNCT
ejpam-4770	54	178	wise	wise	ADJ
ejpam-4770	54	179	non	non	ADJ
ejpam-4770	54	180	-	-	ADJ
ejpam-4770	54	181	dominating	dominating	ADJ
ejpam-4770	54	182	,	,	PUNCT
ejpam-4770	54	183	respectively	respectively	ADV
ejpam-4770	54	184	)	)	PUNCT
ejpam-4770	54	185	set	set	NOUN
ejpam-4770	54	186	of	of	ADP
ejpam-4770	54	187	cardinality	cardinality	PROPN
ejpam-4770	54	188	mlnpnd	mlnpnd	NOUN
ejpam-4770	54	189	(	(	PUNCT
ejpam-4770	54	190	2,2)(g	2,2)(g	NUM
ejpam-4770	54	191	)	)	PUNCT
ejpam-4770	54	192	(	(	PUNCT
ejpam-4770	54	193	mlnpnd	mlnpnd	NOUN
ejpam-4770	54	194	(	(	PUNCT
ejpam-4770	54	195	2,1)(g	2,1)(g	NUM
ejpam-4770	54	196	)	)	PUNCT
ejpam-4770	54	197	,	,	PUNCT
ejpam-4770	54	198	respectively	respectively	ADV
ejpam-4770	54	199	)	)	PUNCT
ejpam-4770	54	200	is	be	AUX
ejpam-4770	54	201	then	then	ADV
ejpam-4770	54	202	referred	refer	VERB
ejpam-4770	54	203	to	to	ADP
ejpam-4770	54	204	as	as	ADP
ejpam-4770	54	205	a	a	DET
ejpam-4770	54	206	mlnpnd	mlnpnd	NOUN
ejpam-4770	54	207	(	(	PUNCT
ejpam-4770	54	208	2,2)-set	2,2)-set	NUM
ejpam-4770	54	209	(	(	PUNCT
ejpam-4770	54	210	mlnpnd	mlnpnd	NOUN
ejpam-4770	54	211	(	(	PUNCT
ejpam-4770	54	212	2,1)-set	2,1)-set	NUM
ejpam-4770	54	213	)	)	PUNCT
ejpam-4770	54	214	in	in	ADP
ejpam-4770	54	215	g.	g.	PROPN
ejpam-4770	54	216	3	3	NUM
ejpam-4770	54	217	.	.	PUNCT
ejpam-4770	55	1	preliminary	preliminary	ADJ
ejpam-4770	55	2	results	result	NOUN
ejpam-4770	55	3	remark	remark	VERB
ejpam-4770	55	4	1	1	NUM
ejpam-4770	55	5	.	.	PUNCT
ejpam-4770	56	1	a	a	DET
ejpam-4770	56	2	1	1	NUM
ejpam-4770	56	3	-	-	PUNCT
ejpam-4770	56	4	movable	movable	ADJ
ejpam-4770	56	5	2	2	NUM
ejpam-4770	56	6	-	-	PUNCT
ejpam-4770	56	7	resolving	resolve	VERB
ejpam-4770	56	8	hop	hop	NOUN
ejpam-4770	56	9	dominating	dominating	NOUN
ejpam-4770	56	10	set	set	NOUN
ejpam-4770	56	11	does	do	AUX
ejpam-4770	56	12	not	not	PART
ejpam-4770	56	13	always	always	ADV
ejpam-4770	56	14	exist	exist	VERB
ejpam-4770	56	15	in	in	ADP
ejpam-4770	56	16	a	a	DET
ejpam-4770	56	17	graph	graph	NOUN
ejpam-4770	56	18	g.	g.	NOUN
ejpam-4770	56	19	example	example	NOUN
ejpam-4770	57	1	1	1	X
ejpam-4770	57	2	.	.	PUNCT
ejpam-4770	57	3	a	a	DET
ejpam-4770	57	4	complete	complete	ADJ
ejpam-4770	57	5	bipartite	bipartite	NOUN
ejpam-4770	57	6	graph	graph	NOUN
ejpam-4770	57	7	km	km	PROPN
ejpam-4770	57	8	,	,	PUNCT
ejpam-4770	57	9	n	n	PROPN
ejpam-4770	57	10	and	and	CCONJ
ejpam-4770	57	11	a	a	DET
ejpam-4770	57	12	complete	complete	ADJ
ejpam-4770	57	13	graph	graph	NOUN
ejpam-4770	57	14	kn	kn	PROPN
ejpam-4770	57	15	do	do	AUX
ejpam-4770	57	16	not	not	PART
ejpam-4770	57	17	admit	admit	VERB
ejpam-4770	57	18	1	1	NUM
ejpam-4770	57	19	-	-	PUNCT
ejpam-4770	57	20	movable	movable	ADJ
ejpam-4770	57	21	2	2	NUM
ejpam-4770	57	22	-	-	PUNCT
ejpam-4770	57	23	resolving	resolve	VERB
ejpam-4770	57	24	hop	hop	NOUN
ejpam-4770	57	25	dominating	dominating	NOUN
ejpam-4770	57	26	set	set	NOUN
ejpam-4770	57	27	.	.	PUNCT
ejpam-4770	58	1	remark	remark	PROPN
ejpam-4770	58	2	2	2	NUM
ejpam-4770	58	3	.	.	PUNCT
ejpam-4770	59	1	let	let	VERB
ejpam-4770	59	2	g	g	PRON
ejpam-4770	59	3	be	be	AUX
ejpam-4770	59	4	a	a	DET
ejpam-4770	59	5	nontrivial	nontrivial	ADJ
ejpam-4770	59	6	connected	connect	VERB
ejpam-4770	59	7	graph	graph	NOUN
ejpam-4770	59	8	.	.	PUNCT
ejpam-4770	60	1	if	if	SCONJ
ejpam-4770	60	2	s	s	PROPN
ejpam-4770	60	3	is	be	AUX
ejpam-4770	60	4	a	a	DET
ejpam-4770	60	5	2	2	NUM
ejpam-4770	60	6	-	-	PUNCT
ejpam-4770	60	7	resolving	resolving	NOUN
ejpam-4770	60	8	set	set	NOUN
ejpam-4770	60	9	in	in	ADP
ejpam-4770	60	10	g	g	NOUN
ejpam-4770	60	11	,	,	PUNCT
ejpam-4770	60	12	then	then	ADV
ejpam-4770	60	13	{	{	PUNCT
ejpam-4770	60	14	x	x	NOUN
ejpam-4770	60	15	,	,	PUNCT
ejpam-4770	60	16	y	y	PROPN
ejpam-4770	60	17	}	}	PUNCT
ejpam-4770	60	18	⊆	⊆	NUM
ejpam-4770	60	19	s	s	NOUN
ejpam-4770	60	20	for	for	ADP
ejpam-4770	60	21	every	every	DET
ejpam-4770	60	22	x	x	NOUN
ejpam-4770	60	23	,	,	PUNCT
ejpam-4770	60	24	y	y	PROPN
ejpam-4770	60	25	∈	∈	PROPN
ejpam-4770	60	26	v	v	ADP
ejpam-4770	60	27	(	(	PUNCT
ejpam-4770	60	28	g	g	NOUN
ejpam-4770	60	29	)	)	PUNCT
ejpam-4770	60	30	with	with	ADP
ejpam-4770	60	31	x	x	X
ejpam-4770	60	32	̸=	̸=	PROPN
ejpam-4770	60	33	y	y	PROPN
ejpam-4770	60	34	and	and	CCONJ
ejpam-4770	60	35	dg(x	dg(x	NUM
ejpam-4770	60	36	,	,	PUNCT
ejpam-4770	60	37	z	z	NOUN
ejpam-4770	60	38	)	)	PUNCT
ejpam-4770	60	39	=	=	SYM
ejpam-4770	60	40	dg(y	dg(y	ADJ
ejpam-4770	60	41	,	,	PUNCT
ejpam-4770	60	42	z	z	NOUN
ejpam-4770	60	43	)	)	PUNCT
ejpam-4770	60	44	for	for	ADP
ejpam-4770	60	45	each	each	DET
ejpam-4770	60	46	z	z	PROPN
ejpam-4770	60	47	∈	∈	PROPN
ejpam-4770	60	48	v	v	NOUN
ejpam-4770	60	49	(	(	PUNCT
ejpam-4770	60	50	g)\{x	g)\{x	PROPN
ejpam-4770	60	51	,	,	PUNCT
ejpam-4770	60	52	y	y	NOUN
ejpam-4770	60	53	}	}	PUNCT
ejpam-4770	60	54	.	.	PUNCT
ejpam-4770	61	1	proposition	proposition	NOUN
ejpam-4770	61	2	1	1	NUM
ejpam-4770	61	3	.	.	PUNCT
ejpam-4770	62	1	let	let	VERB
ejpam-4770	62	2	g	g	PRON
ejpam-4770	62	3	be	be	AUX
ejpam-4770	62	4	a	a	DET
ejpam-4770	62	5	nontrivial	nontrivial	ADJ
ejpam-4770	62	6	connected	connect	VERB
ejpam-4770	62	7	graph	graph	NOUN
ejpam-4770	62	8	.	.	PUNCT
ejpam-4770	63	1	then	then	ADV
ejpam-4770	63	2	g	g	PROPN
ejpam-4770	63	3	admits	admit	VERB
ejpam-4770	63	4	a	a	DET
ejpam-4770	63	5	1	1	NUM
ejpam-4770	63	6	-movable	-movable	ADJ
ejpam-4770	63	7	2	2	NUM
ejpam-4770	63	8	-	-	PUNCT
ejpam-4770	63	9	resolving	resolve	VERB
ejpam-4770	63	10	hop	hop	NOUN
ejpam-4770	63	11	dominating	dominating	NOUN
ejpam-4770	63	12	set	set	VERB
ejpam-4770	63	13	if	if	SCONJ
ejpam-4770	63	14	and	and	CCONJ
ejpam-4770	63	15	only	only	ADV
ejpam-4770	63	16	if	if	SCONJ
ejpam-4770	63	17	γ(g	γ(g	NOUN
ejpam-4770	63	18	)	)	PUNCT
ejpam-4770	63	19	̸=	̸=	PROPN
ejpam-4770	63	20	1	1	NUM
ejpam-4770	63	21	,	,	PUNCT
ejpam-4770	63	22	dim2(g	dim2(g	NOUN
ejpam-4770	63	23	)	)	PUNCT
ejpam-4770	63	24	̸=	̸=	PROPN
ejpam-4770	63	25	v	v	NOUN
ejpam-4770	63	26	(	(	PUNCT
ejpam-4770	63	27	g	g	NOUN
ejpam-4770	63	28	)	)	PUNCT
ejpam-4770	63	29	and	and	CCONJ
ejpam-4770	63	30	g	g	PROPN
ejpam-4770	63	31	is	be	AUX
ejpam-4770	63	32	a	a	DET
ejpam-4770	63	33	free	free	ADJ
ejpam-4770	63	34	-	-	PUNCT
ejpam-4770	63	35	equidistant	equidistant	ADJ
ejpam-4770	63	36	graph	graph	NOUN
ejpam-4770	63	37	.	.	PUNCT
ejpam-4770	64	1	proof	proof	NOUN
ejpam-4770	64	2	.	.	PUNCT
ejpam-4770	65	1	suppose	suppose	VERB
ejpam-4770	65	2	that	that	SCONJ
ejpam-4770	65	3	g	g	PROPN
ejpam-4770	65	4	admits	admit	VERB
ejpam-4770	65	5	a	a	DET
ejpam-4770	65	6	1	1	NUM
ejpam-4770	65	7	-	-	PUNCT
ejpam-4770	65	8	movable	movable	ADJ
ejpam-4770	65	9	2	2	NUM
ejpam-4770	65	10	-	-	PUNCT
ejpam-4770	65	11	resolving	resolve	VERB
ejpam-4770	65	12	hop	hop	NOUN
ejpam-4770	65	13	dominating	dominating	NOUN
ejpam-4770	65	14	set	set	NOUN
ejpam-4770	65	15	.	.	PUNCT
ejpam-4770	66	1	let	let	VERB
ejpam-4770	66	2	s	s	PRON
ejpam-4770	66	3	be	be	AUX
ejpam-4770	66	4	a	a	DET
ejpam-4770	66	5	1	1	NUM
ejpam-4770	66	6	-	-	PUNCT
ejpam-4770	66	7	movable	movable	ADJ
ejpam-4770	66	8	2	2	NUM
ejpam-4770	66	9	-	-	PUNCT
ejpam-4770	66	10	resolving	resolve	VERB
ejpam-4770	66	11	hop	hop	NOUN
ejpam-4770	66	12	dominating	dominating	NOUN
ejpam-4770	66	13	set	set	NOUN
ejpam-4770	66	14	of	of	ADP
ejpam-4770	66	15	g.	g.	PROPN
ejpam-4770	66	16	suppose	suppose	VERB
ejpam-4770	67	1	γ(g	γ(g	NOUN
ejpam-4770	67	2	)	)	PUNCT
ejpam-4770	67	3	=	=	SYM
ejpam-4770	68	1	1	1	X
ejpam-4770	68	2	.	.	PUNCT
ejpam-4770	68	3	let	let	VERB
ejpam-4770	68	4	a	a	PRON
ejpam-4770	68	5	=	=	SYM
ejpam-4770	68	6	{	{	PUNCT
ejpam-4770	68	7	x	x	PROPN
ejpam-4770	68	8	∈	∈	PROPN
ejpam-4770	68	9	v	v	NOUN
ejpam-4770	68	10	(	(	PUNCT
ejpam-4770	68	11	g	g	NOUN
ejpam-4770	68	12	)	)	PUNCT
ejpam-4770	68	13	:	:	PUNCT
ejpam-4770	68	14	{	{	PUNCT
ejpam-4770	68	15	x	x	X
ejpam-4770	68	16	}	}	PUNCT
ejpam-4770	68	17	is	be	AUX
ejpam-4770	68	18	a	a	DET
ejpam-4770	68	19	dominating	dominating	NOUN
ejpam-4770	68	20	set	set	NOUN
ejpam-4770	68	21	of	of	ADP
ejpam-4770	68	22	g	g	NOUN
ejpam-4770	68	23	}	}	PUNCT
ejpam-4770	68	24	.	.	PUNCT
ejpam-4770	69	1	then	then	ADV
ejpam-4770	69	2	a	a	DET
ejpam-4770	69	3	̸=	̸=	PROPN
ejpam-4770	69	4	∅	∅	NOUN
ejpam-4770	69	5	since	since	SCONJ
ejpam-4770	69	6	γ(g	γ(g	PROPN
ejpam-4770	69	7	)	)	PUNCT
ejpam-4770	69	8	=	=	PUNCT
ejpam-4770	70	1	1	1	X
ejpam-4770	70	2	.	.	PUNCT
ejpam-4770	70	3	since	since	SCONJ
ejpam-4770	70	4	s	s	PROPN
ejpam-4770	70	5	is	be	AUX
ejpam-4770	70	6	a	a	DET
ejpam-4770	70	7	hop	hop	NOUN
ejpam-4770	70	8	dominating	dominating	NOUN
ejpam-4770	70	9	set	set	NOUN
ejpam-4770	70	10	,	,	PUNCT
ejpam-4770	70	11	a	a	DET
ejpam-4770	70	12	⊆	⊆	NUM
ejpam-4770	70	13	s.	s.	PROPN
ejpam-4770	70	14	let	let	VERB
ejpam-4770	70	15	x	x	X
ejpam-4770	70	16	∈	∈	VERB
ejpam-4770	70	17	a.	a.	NOUN
ejpam-4770	70	18	then	then	ADV
ejpam-4770	70	19	s	s	VERB
ejpam-4770	70	20	\	\	X
ejpam-4770	70	21	{	{	PUNCT
ejpam-4770	70	22	x	x	NOUN
ejpam-4770	70	23	}	}	PUNCT
ejpam-4770	70	24	and	and	CCONJ
ejpam-4770	70	25	(	(	PUNCT
ejpam-4770	70	26	s	s	NOUN
ejpam-4770	70	27	\	\	X
ejpam-4770	70	28	{	{	PUNCT
ejpam-4770	70	29	x	x	NOUN
ejpam-4770	70	30	}	}	PUNCT
ejpam-4770	70	31	)	)	PUNCT
ejpam-4770	70	32	∪	∪	ADP
ejpam-4770	70	33	{	{	PUNCT
ejpam-4770	70	34	y	y	NOUN
ejpam-4770	70	35	}	}	PUNCT
ejpam-4770	70	36	for	for	ADP
ejpam-4770	70	37	each	each	DET
ejpam-4770	70	38	y	y	PROPN
ejpam-4770	70	39	∈	∈	PROPN
ejpam-4770	70	40	(	(	PUNCT
ejpam-4770	70	41	(	(	PUNCT
ejpam-4770	70	42	v	v	NOUN
ejpam-4770	70	43	(	(	PUNCT
ejpam-4770	70	44	g	g	NOUN
ejpam-4770	70	45	)	)	PUNCT
ejpam-4770	70	46	\	\	PROPN
ejpam-4770	71	1	s	s	X
ejpam-4770	71	2	)	)	PUNCT
ejpam-4770	71	3	∩ng(x	∩ng(x	NOUN
ejpam-4770	71	4	)	)	PUNCT
ejpam-4770	71	5	)	)	PUNCT
ejpam-4770	71	6	are	be	AUX
ejpam-4770	71	7	not	not	PART
ejpam-4770	71	8	hop	hop	ADJ
ejpam-4770	71	9	dominating	dominating	NOUN
ejpam-4770	71	10	sets	set	NOUN
ejpam-4770	71	11	of	of	ADP
ejpam-4770	71	12	g.	g.	PROPN
ejpam-4770	71	13	thus	thus	ADV
ejpam-4770	71	14	,	,	PUNCT
ejpam-4770	71	15	s	s	VERB
ejpam-4770	71	16	is	be	AUX
ejpam-4770	71	17	not	not	PART
ejpam-4770	71	18	a	a	DET
ejpam-4770	71	19	1	1	NUM
ejpam-4770	71	20	-	-	PUNCT
ejpam-4770	71	21	movable	movable	ADJ
ejpam-4770	71	22	2	2	NUM
ejpam-4770	71	23	-	-	PUNCT
ejpam-4770	71	24	resolving	resolve	VERB
ejpam-4770	71	25	hop	hop	NOUN
ejpam-4770	71	26	dominating	dominating	NOUN
ejpam-4770	71	27	set	set	NOUN
ejpam-4770	71	28	.	.	PUNCT
ejpam-4770	72	1	therefore	therefore	ADV
ejpam-4770	72	2	,	,	PUNCT
ejpam-4770	72	3	γ(g	γ(g	PROPN
ejpam-4770	72	4	)	)	PUNCT
ejpam-4770	72	5	̸=	̸=	PROPN
ejpam-4770	72	6	1	1	NUM
ejpam-4770	72	7	.	.	PUNCT
ejpam-4770	73	1	if	if	SCONJ
ejpam-4770	73	2	dim2(g	dim2(g	NOUN
ejpam-4770	73	3	)	)	PUNCT
ejpam-4770	73	4	=	=	SYM
ejpam-4770	73	5	v	v	NOUN
ejpam-4770	73	6	(	(	PUNCT
ejpam-4770	73	7	g	g	NOUN
ejpam-4770	73	8	)	)	PUNCT
ejpam-4770	73	9	,	,	PUNCT
ejpam-4770	73	10	then	then	ADV
ejpam-4770	73	11	v	v	X
ejpam-4770	73	12	(	(	PUNCT
ejpam-4770	73	13	g)\{z	g)\{z	NOUN
ejpam-4770	73	14	}	}	PUNCT
ejpam-4770	73	15	for	for	ADP
ejpam-4770	73	16	each	each	DET
ejpam-4770	73	17	z	z	PROPN
ejpam-4770	73	18	∈	∈	PROPN
ejpam-4770	73	19	v	v	ADP
ejpam-4770	73	20	(	(	PUNCT
ejpam-4770	73	21	g	g	NOUN
ejpam-4770	73	22	)	)	PUNCT
ejpam-4770	73	23	is	be	AUX
ejpam-4770	73	24	not	not	PART
ejpam-4770	73	25	a	a	DET
ejpam-4770	73	26	2	2	NUM
ejpam-4770	73	27	-	-	PUNCT
ejpam-4770	73	28	resolving	resolve	VERB
ejpam-4770	73	29	set	set	NOUN
ejpam-4770	73	30	.	.	PUNCT
ejpam-4770	74	1	thus	thus	ADV
ejpam-4770	74	2	,	,	PUNCT
ejpam-4770	74	3	s	s	VERB
ejpam-4770	74	4	is	be	AUX
ejpam-4770	74	5	not	not	PART
ejpam-4770	74	6	a	a	DET
ejpam-4770	74	7	1	1	NUM
ejpam-4770	74	8	-	-	PUNCT
ejpam-4770	74	9	movable	movable	ADJ
ejpam-4770	74	10	2	2	NUM
ejpam-4770	74	11	-	-	PUNCT
ejpam-4770	74	12	resolving	resolve	VERB
ejpam-4770	74	13	hop	hop	NOUN
ejpam-4770	74	14	dominating	dominating	NOUN
ejpam-4770	74	15	set	set	NOUN
ejpam-4770	74	16	.	.	PUNCT
ejpam-4770	75	1	therefore	therefore	ADV
ejpam-4770	75	2	,	,	PUNCT
ejpam-4770	75	3	dim2(g	dim2(g	NOUN
ejpam-4770	75	4	)	)	PUNCT
ejpam-4770	75	5	̸=	̸=	PROPN
ejpam-4770	75	6	v	v	NOUN
ejpam-4770	75	7	(	(	PUNCT
ejpam-4770	75	8	g	g	NOUN
ejpam-4770	75	9	)	)	PUNCT
ejpam-4770	75	10	.	.	PUNCT
ejpam-4770	76	1	if	if	SCONJ
ejpam-4770	76	2	g	g	PROPN
ejpam-4770	76	3	is	be	AUX
ejpam-4770	76	4	not	not	PART
ejpam-4770	76	5	a	a	DET
ejpam-4770	76	6	free	free	ADJ
ejpam-4770	76	7	-	-	PUNCT
ejpam-4770	76	8	equidistant	equidistant	ADJ
ejpam-4770	76	9	graph	graph	NOUN
ejpam-4770	76	10	,	,	PUNCT
ejpam-4770	76	11	then	then	ADV
ejpam-4770	76	12	there	there	PRON
ejpam-4770	76	13	exist	exist	VERB
ejpam-4770	76	14	a	a	DET
ejpam-4770	76	15	pair	pair	NOUN
ejpam-4770	76	16	of	of	ADP
ejpam-4770	76	17	vertices	vertex	NOUN
ejpam-4770	76	18	y	y	PROPN
ejpam-4770	76	19	,	,	PUNCT
ejpam-4770	76	20	w	w	PROPN
ejpam-4770	76	21	∈	∈	PROPN
ejpam-4770	76	22	v	v	ADP
ejpam-4770	76	23	(	(	PUNCT
ejpam-4770	76	24	g	g	NOUN
ejpam-4770	76	25	)	)	PUNCT
ejpam-4770	76	26	with	with	ADP
ejpam-4770	76	27	dg(w	dg(w	NOUN
ejpam-4770	76	28	,	,	PUNCT
ejpam-4770	76	29	z	z	NOUN
ejpam-4770	76	30	)	)	PUNCT
ejpam-4770	76	31	=	=	SYM
ejpam-4770	76	32	dg(y	dg(y	ADJ
ejpam-4770	76	33	,	,	PUNCT
ejpam-4770	76	34	z	z	NOUN
ejpam-4770	76	35	)	)	PUNCT
ejpam-4770	76	36	for	for	ADP
ejpam-4770	76	37	all	all	DET
ejpam-4770	76	38	z	z	NOUN
ejpam-4770	76	39	∈	∈	PROPN
ejpam-4770	76	40	v	v	NOUN
ejpam-4770	76	41	(	(	PUNCT
ejpam-4770	76	42	g)\{y	g)\{y	PROPN
ejpam-4770	76	43	,	,	PUNCT
ejpam-4770	76	44	w	w	PROPN
ejpam-4770	76	45	}	}	PUNCT
ejpam-4770	76	46	.	.	PUNCT
ejpam-4770	77	1	by	by	ADP
ejpam-4770	77	2	remark	remark	NOUN
ejpam-4770	77	3	2	2	NUM
ejpam-4770	77	4	,	,	PUNCT
ejpam-4770	77	5	y	y	PROPN
ejpam-4770	77	6	,	,	PUNCT
ejpam-4770	77	7	w	w	PROPN
ejpam-4770	77	8	∈	∈	PROPN
ejpam-4770	77	9	s.	s.	PROPN
ejpam-4770	77	10	hence	hence	ADV
ejpam-4770	77	11	,	,	PUNCT
ejpam-4770	77	12	rg(y/(s\{y	rg(y/(s\{y	PROPN
ejpam-4770	77	13	}	}	PUNCT
ejpam-4770	77	14	)	)	PUNCT
ejpam-4770	77	15	)	)	PUNCT
ejpam-4770	77	16	and	and	CCONJ
ejpam-4770	77	17	rg(w/(s\{y	rg(w/(s\{y	NOUN
ejpam-4770	77	18	}	}	PUNCT
ejpam-4770	77	19	)	)	PUNCT
ejpam-4770	77	20	)	)	PUNCT
ejpam-4770	77	21	differ	differ	VERB
ejpam-4770	77	22	in	in	ADP
ejpam-4770	77	23	at	at	ADP
ejpam-4770	77	24	most	most	ADV
ejpam-4770	77	25	one	one	NUM
ejpam-4770	77	26	position	position	NOUN
ejpam-4770	77	27	.	.	PUNCT
ejpam-4770	78	1	thus	thus	ADV
ejpam-4770	78	2	,	,	PUNCT
ejpam-4770	78	3	s	s	VERB
ejpam-4770	78	4	is	be	AUX
ejpam-4770	78	5	not	not	PART
ejpam-4770	78	6	a	a	DET
ejpam-4770	78	7	1	1	NUM
ejpam-4770	78	8	-	-	PUNCT
ejpam-4770	78	9	movable	movable	ADJ
ejpam-4770	78	10	2	2	NUM
ejpam-4770	78	11	-	-	PUNCT
ejpam-4770	78	12	resolving	resolve	VERB
ejpam-4770	78	13	hop	hop	NOUN
ejpam-4770	78	14	dominating	dominating	NOUN
ejpam-4770	78	15	set	set	NOUN
ejpam-4770	78	16	.	.	PUNCT
ejpam-4770	79	1	therefore	therefore	ADV
ejpam-4770	79	2	,	,	PUNCT
ejpam-4770	79	3	g	g	PROPN
ejpam-4770	79	4	is	be	AUX
ejpam-4770	79	5	a	a	DET
ejpam-4770	79	6	free	free	ADJ
ejpam-4770	79	7	-	-	PUNCT
ejpam-4770	79	8	equidistant	equidistant	ADJ
ejpam-4770	79	9	graph	graph	NOUN
ejpam-4770	79	10	.	.	PUNCT
ejpam-4770	80	1	conversely	conversely	ADV
ejpam-4770	80	2	,	,	PUNCT
ejpam-4770	80	3	suppose	suppose	VERB
ejpam-4770	80	4	that	that	SCONJ
ejpam-4770	80	5	γ(g	γ(g	PROPN
ejpam-4770	80	6	)	)	PUNCT
ejpam-4770	80	7	̸=	̸=	PROPN
ejpam-4770	80	8	1	1	NUM
ejpam-4770	80	9	,	,	PUNCT
ejpam-4770	80	10	dim2(g	dim2(g	NOUN
ejpam-4770	80	11	)	)	PUNCT
ejpam-4770	80	12	̸=	̸=	PROPN
ejpam-4770	80	13	v	v	NOUN
ejpam-4770	80	14	(	(	PUNCT
ejpam-4770	80	15	g	g	NOUN
ejpam-4770	80	16	)	)	PUNCT
ejpam-4770	80	17	and	and	CCONJ
ejpam-4770	80	18	g	g	PROPN
ejpam-4770	80	19	is	be	AUX
ejpam-4770	80	20	a	a	DET
ejpam-4770	80	21	free	free	ADJ
ejpam-4770	80	22	-	-	PUNCT
ejpam-4770	80	23	equidistant	equidistant	ADJ
ejpam-4770	80	24	graph	graph	NOUN
ejpam-4770	80	25	.	.	PUNCT
ejpam-4770	81	1	let	let	VERB
ejpam-4770	81	2	s	s	NOUN
ejpam-4770	81	3	=	=	X
ejpam-4770	81	4	v	v	ADJ
ejpam-4770	81	5	(	(	PUNCT
ejpam-4770	81	6	g	g	NOUN
ejpam-4770	81	7	)	)	PUNCT
ejpam-4770	81	8	.	.	PUNCT
ejpam-4770	82	1	then	then	ADV
ejpam-4770	82	2	s	s	VERB
ejpam-4770	82	3	is	be	AUX
ejpam-4770	82	4	a	a	DET
ejpam-4770	82	5	2	2	NUM
ejpam-4770	82	6	-	-	PUNCT
ejpam-4770	82	7	resolving	resolve	VERB
ejpam-4770	82	8	hop	hop	NOUN
ejpam-4770	82	9	dominating	dominating	NOUN
ejpam-4770	82	10	set	set	VERB
ejpam-4770	82	11	in	in	ADP
ejpam-4770	82	12	g.	g.	PROPN
ejpam-4770	82	13	for	for	ADP
ejpam-4770	82	14	each	each	DET
ejpam-4770	82	15	x	x	SYM
ejpam-4770	82	16	∈	∈	PROPN
ejpam-4770	82	17	s	s	PROPN
ejpam-4770	82	18	,	,	PUNCT
ejpam-4770	82	19	s	s	NOUN
ejpam-4770	82	20	\	\	X
ejpam-4770	82	21	{	{	PUNCT
ejpam-4770	82	22	x	x	X
ejpam-4770	82	23	}	}	PUNCT
ejpam-4770	82	24	is	be	AUX
ejpam-4770	82	25	a	a	DET
ejpam-4770	82	26	2	2	NUM
ejpam-4770	82	27	-	-	PUNCT
ejpam-4770	82	28	resolving	resolving	NOUN
ejpam-4770	82	29	set	set	NOUN
ejpam-4770	82	30	in	in	ADP
ejpam-4770	82	31	g	g	NOUN
ejpam-4770	82	32	since	since	SCONJ
ejpam-4770	82	33	dim2(g	dim2(g	NOUN
ejpam-4770	82	34	)	)	PUNCT
ejpam-4770	82	35	̸=	̸=	PROPN
ejpam-4770	82	36	v	v	NOUN
ejpam-4770	82	37	(	(	PUNCT
ejpam-4770	82	38	g	g	NOUN
ejpam-4770	82	39	)	)	PUNCT
ejpam-4770	82	40	and	and	CCONJ
ejpam-4770	82	41	g	g	PROPN
ejpam-4770	82	42	is	be	AUX
ejpam-4770	82	43	a	a	DET
ejpam-4770	82	44	free	free	ADJ
ejpam-4770	82	45	-	-	PUNCT
ejpam-4770	82	46	equidistant	equidistant	ADJ
ejpam-4770	82	47	graph	graph	NOUN
ejpam-4770	82	48	.	.	PUNCT
ejpam-4770	83	1	also	also	ADV
ejpam-4770	83	2	,	,	PUNCT
ejpam-4770	83	3	since	since	SCONJ
ejpam-4770	83	4	{	{	PUNCT
ejpam-4770	83	5	x	x	X
ejpam-4770	83	6	}	}	PUNCT
ejpam-4770	83	7	is	be	AUX
ejpam-4770	83	8	not	not	PART
ejpam-4770	83	9	a	a	DET
ejpam-4770	83	10	dominating	dominating	NOUN
ejpam-4770	83	11	set	set	NOUN
ejpam-4770	83	12	,	,	PUNCT
ejpam-4770	83	13	there	there	PRON
ejpam-4770	83	14	exists	exist	VERB
ejpam-4770	83	15	y	y	PROPN
ejpam-4770	83	16	∈	∈	PROPN
ejpam-4770	83	17	(	(	PUNCT
ejpam-4770	83	18	s	s	NOUN
ejpam-4770	83	19	\	\	X
ejpam-4770	83	20	{	{	PUNCT
ejpam-4770	83	21	x	x	NOUN
ejpam-4770	83	22	}	}	PUNCT
ejpam-4770	83	23	)	)	PUNCT
ejpam-4770	83	24	∩	∩	NOUN
ejpam-4770	83	25	ng(x	ng(x	NUM
ejpam-4770	83	26	,	,	PUNCT
ejpam-4770	83	27	2	2	NUM
ejpam-4770	83	28	)	)	PUNCT
ejpam-4770	83	29	.	.	PUNCT
ejpam-4770	84	1	hence	hence	ADV
ejpam-4770	84	2	,	,	PUNCT
ejpam-4770	84	3	s	s	NOUN
ejpam-4770	84	4	\	\	X
ejpam-4770	84	5	{	{	PUNCT
ejpam-4770	84	6	x	x	NOUN
ejpam-4770	84	7	}	}	PUNCT
ejpam-4770	84	8	is	be	AUX
ejpam-4770	84	9	a	a	DET
ejpam-4770	84	10	hop	hop	NOUN
ejpam-4770	84	11	dominating	dominating	NOUN
ejpam-4770	84	12	set	set	NOUN
ejpam-4770	84	13	of	of	ADP
ejpam-4770	84	14	g.	g.	PROPN
ejpam-4770	84	15	therefore	therefore	ADV
ejpam-4770	84	16	,	,	PUNCT
ejpam-4770	84	17	s	s	VERB
ejpam-4770	84	18	\	\	X
ejpam-4770	84	19	{	{	PUNCT
ejpam-4770	84	20	x	x	X
ejpam-4770	84	21	}	}	PUNCT
ejpam-4770	84	22	is	be	AUX
ejpam-4770	84	23	a	a	DET
ejpam-4770	84	24	2	2	NUM
ejpam-4770	84	25	-	-	PUNCT
ejpam-4770	84	26	resolving	resolve	VERB
ejpam-4770	84	27	hop	hop	NOUN
ejpam-4770	84	28	dominating	dominating	NOUN
ejpam-4770	84	29	a.m.	a.m.	PROPN
ejpam-4770	84	30	mahistrado	mahistrado	PROPN
ejpam-4770	84	31	,	,	PUNCT
ejpam-4770	84	32	h.	h.	PROPN
ejpam-4770	84	33	rara	rara	PROPN
ejpam-4770	84	34	/	/	SYM
ejpam-4770	84	35	eur	eur	PROPN
ejpam-4770	84	36	.	.	PUNCT
ejpam-4770	85	1	j.	j.	PROPN
ejpam-4770	85	2	pure	pure	PROPN
ejpam-4770	85	3	appl	appl	PROPN
ejpam-4770	85	4	.	.	PROPN
ejpam-4770	85	5	math	math	PROPN
ejpam-4770	85	6	,	,	PUNCT
ejpam-4770	85	7	16	16	NUM
ejpam-4770	85	8	(	(	PUNCT
ejpam-4770	85	9	3	3	NUM
ejpam-4770	85	10	)	)	PUNCT
ejpam-4770	85	11	(	(	PUNCT
ejpam-4770	85	12	2023	2023	NUM
ejpam-4770	85	13	)	)	PUNCT
ejpam-4770	85	14	,	,	PUNCT
ejpam-4770	85	15	1464	1464	NUM
ejpam-4770	85	16	-	-	SYM
ejpam-4770	85	17	1479	1479	NUM
ejpam-4770	85	18	1468	1468	NUM
ejpam-4770	85	19	set	set	VERB
ejpam-4770	85	20	in	in	ADP
ejpam-4770	85	21	g	g	NOUN
ejpam-4770	85	22	for	for	ADP
ejpam-4770	85	23	each	each	DET
ejpam-4770	85	24	x	x	SYM
ejpam-4770	85	25	∈	∈	PROPN
ejpam-4770	85	26	s.	s.	PROPN
ejpam-4770	85	27	it	it	PRON
ejpam-4770	85	28	follows	follow	VERB
ejpam-4770	85	29	that	that	SCONJ
ejpam-4770	85	30	s	s	VERB
ejpam-4770	85	31	is	be	AUX
ejpam-4770	85	32	a	a	DET
ejpam-4770	85	33	1	1	NUM
ejpam-4770	85	34	-	-	PUNCT
ejpam-4770	85	35	movable	movable	ADJ
ejpam-4770	85	36	2	2	NUM
ejpam-4770	85	37	-	-	PUNCT
ejpam-4770	85	38	resolving	resolve	VERB
ejpam-4770	85	39	hop	hop	NOUN
ejpam-4770	85	40	dominating	dominating	NOUN
ejpam-4770	85	41	set	set	VERB
ejpam-4770	85	42	in	in	ADP
ejpam-4770	85	43	g.	g.	PROPN
ejpam-4770	85	44	accordingly	accordingly	ADV
ejpam-4770	85	45	,	,	PUNCT
ejpam-4770	85	46	g	g	PROPN
ejpam-4770	85	47	admits	admit	VERB
ejpam-4770	85	48	1	1	NUM
ejpam-4770	85	49	-	-	PUNCT
ejpam-4770	85	50	movable	movable	ADJ
ejpam-4770	85	51	2	2	NUM
ejpam-4770	85	52	-	-	PUNCT
ejpam-4770	85	53	resolving	resolve	VERB
ejpam-4770	85	54	hop	hop	NOUN
ejpam-4770	85	55	dominating	dominating	NOUN
ejpam-4770	85	56	set	set	NOUN
ejpam-4770	85	57	.	.	PUNCT
ejpam-4770	86	1	remark	remark	PROPN
ejpam-4770	86	2	3	3	NUM
ejpam-4770	86	3	.	.	PUNCT
ejpam-4770	87	1	every	every	DET
ejpam-4770	87	2	1	1	NUM
ejpam-4770	87	3	-	-	PUNCT
ejpam-4770	87	4	movable	movable	ADJ
ejpam-4770	87	5	2	2	NUM
ejpam-4770	87	6	-	-	PUNCT
ejpam-4770	87	7	resolving	resolve	VERB
ejpam-4770	87	8	hop	hop	NOUN
ejpam-4770	87	9	dominating	dominating	NOUN
ejpam-4770	87	10	set	set	NOUN
ejpam-4770	87	11	in	in	ADP
ejpam-4770	87	12	g	g	PROPN
ejpam-4770	87	13	is	be	AUX
ejpam-4770	87	14	a	a	DET
ejpam-4770	87	15	2	2	NUM
ejpam-4770	87	16	-	-	PUNCT
ejpam-4770	87	17	resolving	resolve	VERB
ejpam-4770	87	18	hop	hop	NOUN
ejpam-4770	87	19	dominating	dominating	NOUN
ejpam-4770	87	20	set	set	VERB
ejpam-4770	87	21	in	in	ADP
ejpam-4770	87	22	g.	g.	PROPN
ejpam-4770	87	23	thus	thus	ADV
ejpam-4770	87	24	,	,	PUNCT
ejpam-4770	87	25	γ2rh(g	γ2rh(g	NOUN
ejpam-4770	87	26	)	)	PUNCT
ejpam-4770	87	27	≤	≤	NOUN
ejpam-4770	87	28	γ1m2rh(g	γ1m2rh(g	NUM
ejpam-4770	87	29	)	)	PUNCT
ejpam-4770	87	30	.	.	PUNCT
ejpam-4770	88	1	proposition	proposition	NOUN
ejpam-4770	88	2	2	2	NUM
ejpam-4770	88	3	.	.	PUNCT
ejpam-4770	88	4	(	(	PUNCT
ejpam-4770	88	5	i	i	NOUN
ejpam-4770	88	6	)	)	PUNCT
ejpam-4770	88	7	for	for	ADP
ejpam-4770	88	8	a	a	DET
ejpam-4770	88	9	path	path	NOUN
ejpam-4770	88	10	pn	pn	NOUN
ejpam-4770	88	11	on	on	ADP
ejpam-4770	88	12	n	n	PRON
ejpam-4770	88	13	vertices	vertex	NOUN
ejpam-4770	88	14	(	(	PUNCT
ejpam-4770	88	15	n	n	CCONJ
ejpam-4770	88	16	≥	≥	NOUN
ejpam-4770	88	17	4	4	NUM
ejpam-4770	88	18	)	)	PUNCT
ejpam-4770	88	19	,	,	PUNCT
ejpam-4770	88	20	γ1m2rh(pn	γ1m2rh(pn	NOUN
ejpam-4770	88	21	)	)	PUNCT
ejpam-4770	88	22	=	=	SYM
ejpam-4770	88	23	n.	n.	NOUN
ejpam-4770	88	24	(	(	PUNCT
ejpam-4770	88	25	ii	ii	PROPN
ejpam-4770	88	26	)	)	PUNCT
ejpam-4770	88	27	for	for	ADP
ejpam-4770	88	28	a	a	DET
ejpam-4770	88	29	cycle	cycle	NOUN
ejpam-4770	88	30	cn	cn	NOUN
ejpam-4770	88	31	on	on	ADP
ejpam-4770	88	32	n	n	PRON
ejpam-4770	88	33	vertices	vertex	NOUN
ejpam-4770	88	34	,	,	PUNCT
ejpam-4770	88	35	γ1m2rh(cn	γ1m2rh(cn	NOUN
ejpam-4770	88	36	)	)	PUNCT
ejpam-4770	88	37	=	=	SYM
ejpam-4770	89	1	3	3	VERB
ejpam-4770	89	2	,	,	PUNCT
ejpam-4770	89	3	if	if	SCONJ
ejpam-4770	89	4	n	n	NOUN
ejpam-4770	89	5	=	=	SYM
ejpam-4770	89	6	5	5	NUM
ejpam-4770	89	7	;	;	PUNCT
ejpam-4770	89	8	2n+	2n+	NUM
ejpam-4770	89	9	k	k	NOUN
ejpam-4770	89	10	3	3	NUM
ejpam-4770	89	11	,	,	PUNCT
ejpam-4770	89	12	if	if	SCONJ
ejpam-4770	89	13	n	n	ADV
ejpam-4770	89	14	=	=	SYM
ejpam-4770	89	15	k(mod	k(mod	PROPN
ejpam-4770	89	16	3	3	NUM
ejpam-4770	89	17	)	)	PUNCT
ejpam-4770	89	18	,	,	PUNCT
ejpam-4770	89	19	0	0	NUM
ejpam-4770	89	20	≤	≤	NUM
ejpam-4770	89	21	k	k	X
ejpam-4770	89	22	≤	≤	NUM
ejpam-4770	89	23	2	2	NUM
ejpam-4770	89	24	and	and	CCONJ
ejpam-4770	89	25	n	n	NOUN
ejpam-4770	89	26	>	>	X
ejpam-4770	89	27	5	5	NUM
ejpam-4770	89	28	.	.	PUNCT
ejpam-4770	90	1	proof	proof	NOUN
ejpam-4770	90	2	.	.	PUNCT
ejpam-4770	91	1	let	let	VERB
ejpam-4770	91	2	pn	pn	VERB
ejpam-4770	91	3	=	=	PUNCT
ejpam-4770	92	1	[	[	X
ejpam-4770	92	2	v1	v1	NOUN
ejpam-4770	92	3	,	,	PUNCT
ejpam-4770	92	4	v2	v2	PROPN
ejpam-4770	92	5	,	,	PUNCT
ejpam-4770	92	6	v3	v3	PROPN
ejpam-4770	92	7	,	,	PUNCT
ejpam-4770	92	8	.	.	PUNCT
ejpam-4770	92	9	.	.	PUNCT
ejpam-4770	92	10	.	.	PUNCT
ejpam-4770	93	1	vn	vn	PROPN
ejpam-4770	93	2	]	]	PUNCT
ejpam-4770	93	3	.	.	PUNCT
ejpam-4770	94	1	by	by	ADP
ejpam-4770	94	2	proposition	proposition	NOUN
ejpam-4770	94	3	1	1	NUM
ejpam-4770	94	4	,	,	PUNCT
ejpam-4770	94	5	v	v	PROPN
ejpam-4770	94	6	(	(	PUNCT
ejpam-4770	94	7	pn	pn	NOUN
ejpam-4770	94	8	)	)	PUNCT
ejpam-4770	94	9	is	be	AUX
ejpam-4770	94	10	a	a	DET
ejpam-4770	94	11	1	1	NUM
ejpam-4770	94	12	-	-	PUNCT
ejpam-4770	94	13	movable	movable	ADJ
ejpam-4770	94	14	2	2	NUM
ejpam-4770	94	15	-	-	PUNCT
ejpam-4770	94	16	resolving	resolve	VERB
ejpam-4770	94	17	hop	hop	NOUN
ejpam-4770	94	18	dominating	dominating	NOUN
ejpam-4770	94	19	set	set	NOUN
ejpam-4770	94	20	.	.	PUNCT
ejpam-4770	95	1	suppose	suppose	VERB
ejpam-4770	95	2	si	si	PROPN
ejpam-4770	95	3	=	=	SYM
ejpam-4770	95	4	v	v	PROPN
ejpam-4770	95	5	(	(	PUNCT
ejpam-4770	95	6	pn)\{vi1	pn)\{vi1	NOUN
ejpam-4770	95	7	,	,	PUNCT
ejpam-4770	95	8	vi2	vi2	INTJ
ejpam-4770	95	9	,	,	PUNCT
ejpam-4770	95	10	.	.	PUNCT
ejpam-4770	95	11	.	.	PUNCT
ejpam-4770	95	12	.	.	PUNCT
ejpam-4770	96	1	vik	vik	PROPN
ejpam-4770	96	2	}	}	PUNCT
ejpam-4770	96	3	is	be	AUX
ejpam-4770	96	4	a	a	DET
ejpam-4770	96	5	2	2	NUM
ejpam-4770	96	6	-	-	PUNCT
ejpam-4770	96	7	resolving	resolve	VERB
ejpam-4770	96	8	hop	hop	NOUN
ejpam-4770	96	9	dominating	dominating	NOUN
ejpam-4770	96	10	set	set	VERB
ejpam-4770	96	11	in	in	ADP
ejpam-4770	96	12	pn	pn	PROPN
ejpam-4770	96	13	for	for	ADP
ejpam-4770	96	14	1	1	NUM
ejpam-4770	96	15	≤	≤	NUM
ejpam-4770	96	16	k	k	PROPN
ejpam-4770	96	17	≤	≤	PROPN
ejpam-4770	96	18	n−	n−	NOUN
ejpam-4770	96	19	2	2	NUM
ejpam-4770	96	20	.	.	PUNCT
ejpam-4770	97	1	note	note	VERB
ejpam-4770	97	2	that	that	SCONJ
ejpam-4770	97	3	0	0	PUNCT
ejpam-4770	97	4	<	<	X
ejpam-4770	97	5	|npn(vim	|npn(vim	PROPN
ejpam-4770	97	6	,	,	PUNCT
ejpam-4770	97	7	2)|	2)|	NUM
ejpam-4770	97	8	≤	≤	NUM
ejpam-4770	97	9	2	2	NUM
ejpam-4770	97	10	for	for	ADP
ejpam-4770	97	11	each	each	DET
ejpam-4770	97	12	m	m	PROPN
ejpam-4770	97	13	∈	∈	NOUN
ejpam-4770	97	14	{	{	PUNCT
ejpam-4770	97	15	1	1	NUM
ejpam-4770	97	16	,	,	PUNCT
ejpam-4770	97	17	2	2	NUM
ejpam-4770	97	18	,	,	PUNCT
ejpam-4770	97	19	.	.	PUNCT
ejpam-4770	97	20	.	.	PUNCT
ejpam-4770	97	21	.	.	PUNCT
ejpam-4770	98	1	k	k	X
ejpam-4770	98	2	}	}	PUNCT
ejpam-4770	98	3	.	.	PUNCT
ejpam-4770	99	1	if	if	SCONJ
ejpam-4770	99	2	|npn(vim	|npn(vim	PROPN
ejpam-4770	99	3	,	,	PUNCT
ejpam-4770	99	4	2)|	2)|	NUM
ejpam-4770	99	5	=	=	SYM
ejpam-4770	99	6	1	1	NUM
ejpam-4770	99	7	,	,	PUNCT
ejpam-4770	99	8	then	then	ADV
ejpam-4770	99	9	si	si	PROPN
ejpam-4770	99	10	\{vj	\{vj	PROPN
ejpam-4770	99	11	}	}	PUNCT
ejpam-4770	99	12	is	be	AUX
ejpam-4770	99	13	not	not	PART
ejpam-4770	99	14	a	a	DET
ejpam-4770	99	15	hop	hop	NOUN
ejpam-4770	99	16	dominating	dominating	NOUN
ejpam-4770	99	17	set	set	NOUN
ejpam-4770	99	18	for	for	ADP
ejpam-4770	99	19	vj	vj	PROPN
ejpam-4770	99	20	∈	∈	PROPN
ejpam-4770	99	21	npn(vim	npn(vim	NOUN
ejpam-4770	99	22	,	,	PUNCT
ejpam-4770	99	23	2	2	NUM
ejpam-4770	99	24	)	)	PUNCT
ejpam-4770	99	25	.	.	PUNCT
ejpam-4770	100	1	suppose	suppose	VERB
ejpam-4770	101	1	|npn(vim	|npn(vim	PROPN
ejpam-4770	101	2	,	,	PUNCT
ejpam-4770	101	3	2)|	2)|	NUM
ejpam-4770	101	4	=	=	SYM
ejpam-4770	101	5	2	2	X
ejpam-4770	101	6	.	.	PUNCT
ejpam-4770	101	7	let	let	VERB
ejpam-4770	101	8	vj	vj	INTJ
ejpam-4770	101	9	,	,	PUNCT
ejpam-4770	101	10	vl	vl	PROPN
ejpam-4770	101	11	∈	∈	PROPN
ejpam-4770	101	12	npn(vim	npn(vim	NOUN
ejpam-4770	101	13	,	,	PUNCT
ejpam-4770	101	14	2	2	NUM
ejpam-4770	101	15	)	)	PUNCT
ejpam-4770	101	16	.	.	PUNCT
ejpam-4770	102	1	if	if	SCONJ
ejpam-4770	102	2	|npn(vj	|npn(vj	NOUN
ejpam-4770	102	3	,	,	PUNCT
ejpam-4770	102	4	2)|	2)|	NUM
ejpam-4770	102	5	=	=	SYM
ejpam-4770	102	6	1	1	NUM
ejpam-4770	102	7	or	or	CCONJ
ejpam-4770	102	8	|npn(vl	|npn(vl	NUM
ejpam-4770	102	9	,	,	PUNCT
ejpam-4770	102	10	2)|	2)|	NUM
ejpam-4770	102	11	=	=	SYM
ejpam-4770	102	12	1	1	NUM
ejpam-4770	102	13	,	,	PUNCT
ejpam-4770	102	14	then	then	ADV
ejpam-4770	102	15	si\{vj	si\{vj	NOUN
ejpam-4770	102	16	}	}	PUNCT
ejpam-4770	102	17	or	or	CCONJ
ejpam-4770	102	18	si\{vl	si\{vl	NOUN
ejpam-4770	102	19	}	}	PUNCT
ejpam-4770	102	20	is	be	AUX
ejpam-4770	102	21	not	not	PART
ejpam-4770	102	22	a	a	DET
ejpam-4770	102	23	hop	hop	NOUN
ejpam-4770	102	24	dominating	dominating	NOUN
ejpam-4770	102	25	set	set	VERB
ejpam-4770	102	26	in	in	ADP
ejpam-4770	102	27	pn	pn	PROPN
ejpam-4770	102	28	.	.	PROPN
ejpam-4770	103	1	on	on	ADP
ejpam-4770	103	2	the	the	DET
ejpam-4770	103	3	other	other	ADJ
ejpam-4770	103	4	hand	hand	NOUN
ejpam-4770	103	5	,	,	PUNCT
ejpam-4770	103	6	if	if	SCONJ
ejpam-4770	103	7	|npn(vj	|npn(vj	NOUN
ejpam-4770	103	8	,	,	PUNCT
ejpam-4770	103	9	2)|	2)|	NUM
ejpam-4770	103	10	=	=	SYM
ejpam-4770	103	11	2	2	NUM
ejpam-4770	103	12	or	or	CCONJ
ejpam-4770	103	13	|npn(vl	|npn(vl	NUM
ejpam-4770	103	14	,	,	PUNCT
ejpam-4770	103	15	2)|	2)|	NUM
ejpam-4770	103	16	=	=	SYM
ejpam-4770	103	17	2	2	NUM
ejpam-4770	103	18	,	,	PUNCT
ejpam-4770	103	19	then	then	ADV
ejpam-4770	103	20	si	si	PROPN
ejpam-4770	103	21	\	\	PROPN
ejpam-4770	103	22	{	{	PUNCT
ejpam-4770	103	23	vp	vp	NOUN
ejpam-4770	103	24	}	}	PUNCT
ejpam-4770	103	25	or	or	CCONJ
ejpam-4770	103	26	si	si	X
ejpam-4770	103	27	\	\	PROPN
ejpam-4770	103	28	{	{	PUNCT
ejpam-4770	103	29	vq	vq	NOUN
ejpam-4770	103	30	}	}	PUNCT
ejpam-4770	103	31	is	be	AUX
ejpam-4770	103	32	not	not	PART
ejpam-4770	103	33	a	a	DET
ejpam-4770	103	34	hop	hop	NOUN
ejpam-4770	103	35	dominating	dominating	NOUN
ejpam-4770	103	36	set	set	NOUN
ejpam-4770	103	37	where	where	SCONJ
ejpam-4770	103	38	vp	vp	PROPN
ejpam-4770	103	39	∈	∈	PROPN
ejpam-4770	103	40	npn(vj	npn(vj	NOUN
ejpam-4770	103	41	,	,	PUNCT
ejpam-4770	103	42	2	2	NUM
ejpam-4770	103	43	)	)	PUNCT
ejpam-4770	103	44	and	and	CCONJ
ejpam-4770	103	45	vq	vq	PROPN
ejpam-4770	103	46	∈	∈	PROPN
ejpam-4770	103	47	npn(vl	npn(vl	NOUN
ejpam-4770	103	48	,	,	PUNCT
ejpam-4770	103	49	2	2	NUM
ejpam-4770	103	50	)	)	PUNCT
ejpam-4770	103	51	.	.	PUNCT
ejpam-4770	104	1	thus	thus	ADV
ejpam-4770	104	2	,	,	PUNCT
ejpam-4770	104	3	si	si	X
ejpam-4770	104	4	is	be	AUX
ejpam-4770	104	5	not	not	PART
ejpam-4770	104	6	a	a	DET
ejpam-4770	104	7	1	1	NUM
ejpam-4770	104	8	-	-	PUNCT
ejpam-4770	104	9	movable	movable	ADJ
ejpam-4770	104	10	2	2	NUM
ejpam-4770	104	11	-	-	PUNCT
ejpam-4770	104	12	resolving	resolve	VERB
ejpam-4770	104	13	hop	hop	NOUN
ejpam-4770	104	14	dominating	dominating	NOUN
ejpam-4770	104	15	set	set	VERB
ejpam-4770	104	16	in	in	ADP
ejpam-4770	104	17	pn	pn	PROPN
ejpam-4770	104	18	.	.	PUNCT
ejpam-4770	105	1	therefore	therefore	ADV
ejpam-4770	105	2	,	,	PUNCT
ejpam-4770	105	3	γ	γ	PROPN
ejpam-4770	105	4	1	1	NUM
ejpam-4770	105	5	m2rh(pn	m2rh(pn	NUM
ejpam-4770	105	6	)	)	PUNCT
ejpam-4770	105	7	=	=	SYM
ejpam-4770	105	8	n.	n.	NOUN
ejpam-4770	105	9	(	(	PUNCT
ejpam-4770	105	10	ii	ii	NOUN
ejpam-4770	105	11	)	)	PUNCT
ejpam-4770	105	12	let	let	VERB
ejpam-4770	105	13	cn	cn	PROPN
ejpam-4770	105	14	=	=	PUNCT
ejpam-4770	106	1	[	[	X
ejpam-4770	106	2	v1	v1	NOUN
ejpam-4770	106	3	,	,	PUNCT
ejpam-4770	106	4	v2	v2	NOUN
ejpam-4770	106	5	,	,	PUNCT
ejpam-4770	106	6	.	.	PUNCT
ejpam-4770	106	7	.	.	PUNCT
ejpam-4770	106	8	.	.	PUNCT
ejpam-4770	107	1	,	,	PUNCT
ejpam-4770	107	2	vn	vn	X
ejpam-4770	107	3	]	]	PUNCT
ejpam-4770	107	4	and	and	CCONJ
ejpam-4770	107	5	s	s	AUX
ejpam-4770	107	6	be	be	AUX
ejpam-4770	107	7	a	a	DET
ejpam-4770	107	8	γ1m2rhset	γ1m2rhset	NOUN
ejpam-4770	107	9	of	of	ADP
ejpam-4770	107	10	cn	cn	PROPN
ejpam-4770	107	11	.	.	PUNCT
ejpam-4770	108	1	the	the	DET
ejpam-4770	108	2	case	case	NOUN
ejpam-4770	108	3	when	when	SCONJ
ejpam-4770	108	4	n	n	PROPN
ejpam-4770	108	5	=	=	SYM
ejpam-4770	108	6	5	5	NUM
ejpam-4770	108	7	can	can	AUX
ejpam-4770	108	8	be	be	AUX
ejpam-4770	108	9	verified	verify	VERB
ejpam-4770	108	10	.	.	PUNCT
ejpam-4770	109	1	next	next	ADV
ejpam-4770	109	2	,	,	PUNCT
ejpam-4770	109	3	let	let	VERB
ejpam-4770	109	4	n	n	PRON
ejpam-4770	109	5	>	>	X
ejpam-4770	109	6	5	5	NUM
ejpam-4770	109	7	and	and	CCONJ
ejpam-4770	109	8	n	n	PRON
ejpam-4770	109	9	≡	≡	PROPN
ejpam-4770	109	10	k(mod	k(mod	PROPN
ejpam-4770	109	11	3	3	X
ejpam-4770	109	12	)	)	PUNCT
ejpam-4770	109	13	where	where	SCONJ
ejpam-4770	109	14	0	0	NUM
ejpam-4770	109	15	≤	≤	NUM
ejpam-4770	110	1	k	k	X
ejpam-4770	110	2	≤	≤	ADJ
ejpam-4770	110	3	2	2	NUM
ejpam-4770	110	4	.	.	PUNCT
ejpam-4770	111	1	then	then	ADV
ejpam-4770	111	2	n	n	NOUN
ejpam-4770	111	3	=	=	NOUN
ejpam-4770	111	4	3r	3r	NUM
ejpam-4770	111	5	+	+	CCONJ
ejpam-4770	111	6	k.	k.	PROPN
ejpam-4770	112	1	hence	hence	ADV
ejpam-4770	112	2	,	,	PUNCT
ejpam-4770	112	3	r	r	NOUN
ejpam-4770	112	4	=	=	SYM
ejpam-4770	112	5	n−	n−	NOUN
ejpam-4770	112	6	k	k	NOUN
ejpam-4770	112	7	3	3	NUM
ejpam-4770	112	8	.	.	PUNCT
ejpam-4770	113	1	then	then	ADV
ejpam-4770	113	2	the	the	DET
ejpam-4770	113	3	set	set	NOUN
ejpam-4770	113	4	s	s	PART
ejpam-4770	113	5	=	=	NOUN
ejpam-4770	113	6	{	{	PUNCT
ejpam-4770	113	7	v1	v1	PROPN
ejpam-4770	113	8	,	,	PUNCT
ejpam-4770	113	9	v3	v3	PROPN
ejpam-4770	113	10	,	,	PUNCT
ejpam-4770	113	11	v4	v4	PROPN
ejpam-4770	113	12	,	,	PUNCT
ejpam-4770	113	13	v6	v6	NOUN
ejpam-4770	113	14	,	,	PUNCT
ejpam-4770	113	15	v7	v7	NUM
ejpam-4770	113	16	,	,	PUNCT
ejpam-4770	113	17	v9	v9	PROPN
ejpam-4770	113	18	,	,	PUNCT
ejpam-4770	113	19	v10	v10	NOUN
ejpam-4770	113	20	,	,	PUNCT
ejpam-4770	113	21	v12	v12	VERB
ejpam-4770	113	22	,	,	PUNCT
ejpam-4770	113	23	v13	v13	NOUN
ejpam-4770	113	24	,	,	PUNCT
ejpam-4770	113	25	.	.	PUNCT
ejpam-4770	113	26	.	.	PUNCT
ejpam-4770	113	27	.	.	PUNCT
ejpam-4770	114	1	,	,	PUNCT
ejpam-4770	114	2	v3r+k−3	v3r+k−3	PROPN
ejpam-4770	114	3	,	,	PUNCT
ejpam-4770	114	4	v3r+k−2	v3r+k−2	PROPN
ejpam-4770	114	5	,	,	PUNCT
ejpam-4770	114	6	.	.	PUNCT
ejpam-4770	114	7	.	.	PUNCT
ejpam-4770	115	1	.	.	PUNCT
ejpam-4770	116	1	,	,	PUNCT
ejpam-4770	116	2	v3r+k	v3r+k	PROPN
ejpam-4770	116	3	}	}	PUNCT
ejpam-4770	116	4	is	be	AUX
ejpam-4770	116	5	a	a	DET
ejpam-4770	116	6	γ1m2rhset	γ1m2rhset	PROPN
ejpam-4770	116	7	of	of	ADP
ejpam-4770	116	8	cn	cn	PROPN
ejpam-4770	116	9	.	.	PUNCT
ejpam-4770	117	1	therefore	therefore	ADV
ejpam-4770	117	2	,	,	PUNCT
ejpam-4770	117	3	|s|	|s|	PROPN
ejpam-4770	117	4	=	=	NOUN
ejpam-4770	117	5	3r	3r	NUM
ejpam-4770	118	1	+	+	CCONJ
ejpam-4770	119	1	k	k	NOUN
ejpam-4770	119	2	−	−	NOUN
ejpam-4770	119	3	r	r	NOUN
ejpam-4770	119	4	=	=	SYM
ejpam-4770	119	5	2n+	2n+	NUM
ejpam-4770	119	6	k	k	NOUN
ejpam-4770	119	7	3	3	NUM
ejpam-4770	119	8	.	.	PUNCT
ejpam-4770	120	1	now	now	ADV
ejpam-4770	120	2	,	,	PUNCT
ejpam-4770	120	3	consider	consider	VERB
ejpam-4770	120	4	the	the	DET
ejpam-4770	120	5	following	follow	VERB
ejpam-4770	120	6	results	result	NOUN
ejpam-4770	120	7	of	of	ADP
ejpam-4770	120	8	1	1	NUM
ejpam-4770	120	9	-	-	PUNCT
ejpam-4770	120	10	movable	movable	ADJ
ejpam-4770	120	11	2	2	NUM
ejpam-4770	120	12	-	-	PUNCT
ejpam-4770	120	13	locating	locate	VERB
ejpam-4770	120	14	point	point	NOUN
ejpam-4770	120	15	-	-	PUNCT
ejpam-4770	120	16	wise	wise	ADJ
ejpam-4770	120	17	non	non	ADJ
ejpam-4770	120	18	-	-	ADJ
ejpam-4770	120	19	dominating	dominating	ADJ
ejpam-4770	120	20	sets	set	NOUN
ejpam-4770	120	21	which	which	PRON
ejpam-4770	120	22	are	be	AUX
ejpam-4770	120	23	used	use	VERB
ejpam-4770	120	24	in	in	ADP
ejpam-4770	120	25	characterizing	characterize	VERB
ejpam-4770	120	26	the	the	DET
ejpam-4770	120	27	1	1	NUM
ejpam-4770	120	28	-	-	PUNCT
ejpam-4770	120	29	movable	movable	ADJ
ejpam-4770	120	30	2	2	NUM
ejpam-4770	120	31	-	-	PUNCT
ejpam-4770	120	32	resolving	resolve	VERB
ejpam-4770	120	33	hop	hop	NOUN
ejpam-4770	120	34	dominating	dominating	NOUN
ejpam-4770	120	35	sets	set	NOUN
ejpam-4770	120	36	in	in	ADP
ejpam-4770	120	37	some	some	DET
ejpam-4770	120	38	binary	binary	ADJ
ejpam-4770	120	39	operations	operation	NOUN
ejpam-4770	120	40	.	.	PUNCT
ejpam-4770	121	1	remark	remark	PROPN
ejpam-4770	121	2	4	4	NUM
ejpam-4770	121	3	.	.	PUNCT
ejpam-4770	122	1	a	a	DET
ejpam-4770	122	2	1	1	NUM
ejpam-4770	122	3	-	-	PUNCT
ejpam-4770	122	4	movable	movable	ADJ
ejpam-4770	122	5	2	2	NUM
ejpam-4770	122	6	-	-	PUNCT
ejpam-4770	122	7	locating	locate	VERB
ejpam-4770	122	8	point	point	NOUN
ejpam-4770	122	9	-	-	PUNCT
ejpam-4770	122	10	wise	wise	ADJ
ejpam-4770	122	11	non	non	ADJ
ejpam-4770	122	12	-	-	ADJ
ejpam-4770	122	13	dominating	dominating	ADJ
ejpam-4770	122	14	set	set	NOUN
ejpam-4770	122	15	does	do	AUX
ejpam-4770	122	16	not	not	PART
ejpam-4770	122	17	always	always	ADV
ejpam-4770	122	18	exist	exist	VERB
ejpam-4770	122	19	in	in	ADP
ejpam-4770	122	20	a	a	DET
ejpam-4770	122	21	graph	graph	NOUN
ejpam-4770	122	22	g.	g.	NOUN
ejpam-4770	122	23	example	example	NOUN
ejpam-4770	123	1	2	2	NUM
ejpam-4770	123	2	.	.	PUNCT
ejpam-4770	123	3	a	a	DET
ejpam-4770	123	4	complete	complete	ADJ
ejpam-4770	123	5	bipartite	bipartite	NOUN
ejpam-4770	123	6	graph	graph	NOUN
ejpam-4770	123	7	km	km	PROPN
ejpam-4770	123	8	,	,	PUNCT
ejpam-4770	123	9	n	n	PROPN
ejpam-4770	123	10	and	and	CCONJ
ejpam-4770	123	11	a	a	DET
ejpam-4770	123	12	complete	complete	ADJ
ejpam-4770	123	13	graph	graph	NOUN
ejpam-4770	123	14	kn	kn	PROPN
ejpam-4770	123	15	do	do	AUX
ejpam-4770	123	16	not	not	PART
ejpam-4770	123	17	admit	admit	VERB
ejpam-4770	123	18	1	1	NUM
ejpam-4770	123	19	-	-	PUNCT
ejpam-4770	123	20	movable	movable	ADJ
ejpam-4770	123	21	2	2	NUM
ejpam-4770	123	22	-	-	PUNCT
ejpam-4770	123	23	locating	locate	VERB
ejpam-4770	123	24	point	point	NOUN
ejpam-4770	123	25	-	-	PUNCT
ejpam-4770	123	26	wise	wise	ADJ
ejpam-4770	123	27	non	non	ADJ
ejpam-4770	123	28	-	-	ADJ
ejpam-4770	123	29	dominating	dominating	ADJ
ejpam-4770	123	30	set	set	NOUN
ejpam-4770	123	31	.	.	PUNCT
ejpam-4770	124	1	remark	remark	PROPN
ejpam-4770	124	2	5	5	NUM
ejpam-4770	124	3	.	.	PUNCT
ejpam-4770	125	1	let	let	VERB
ejpam-4770	125	2	g	g	PRON
ejpam-4770	125	3	be	be	AUX
ejpam-4770	125	4	a	a	DET
ejpam-4770	125	5	nontrivial	nontrivial	ADJ
ejpam-4770	125	6	connected	connect	VERB
ejpam-4770	125	7	graph	graph	NOUN
ejpam-4770	125	8	.	.	PUNCT
ejpam-4770	126	1	if	if	SCONJ
ejpam-4770	126	2	s	s	PROPN
ejpam-4770	126	3	is	be	AUX
ejpam-4770	126	4	a	a	DET
ejpam-4770	126	5	2	2	NUM
ejpam-4770	126	6	-	-	PUNCT
ejpam-4770	126	7	locating	locate	VERB
ejpam-4770	126	8	set	set	NOUN
ejpam-4770	126	9	in	in	ADP
ejpam-4770	126	10	g	g	NOUN
ejpam-4770	126	11	,	,	PUNCT
ejpam-4770	126	12	then	then	ADV
ejpam-4770	126	13	{	{	PUNCT
ejpam-4770	126	14	x	x	NOUN
ejpam-4770	126	15	,	,	PUNCT
ejpam-4770	126	16	y	y	PROPN
ejpam-4770	126	17	}	}	PUNCT
ejpam-4770	126	18	⊆	⊆	NUM
ejpam-4770	126	19	s	s	NOUN
ejpam-4770	126	20	for	for	ADP
ejpam-4770	126	21	every	every	DET
ejpam-4770	126	22	x	x	NOUN
ejpam-4770	126	23	,	,	PUNCT
ejpam-4770	126	24	y	y	PROPN
ejpam-4770	126	25	∈	∈	PROPN
ejpam-4770	126	26	v	v	ADP
ejpam-4770	126	27	(	(	PUNCT
ejpam-4770	126	28	g	g	NOUN
ejpam-4770	126	29	)	)	PUNCT
ejpam-4770	126	30	with	with	ADP
ejpam-4770	126	31	x	x	X
ejpam-4770	126	32	̸=	̸=	PROPN
ejpam-4770	126	33	y	y	PROPN
ejpam-4770	126	34	and	and	CCONJ
ejpam-4770	126	35	ng(x	ng(x	NUM
ejpam-4770	126	36	)	)	PUNCT
ejpam-4770	126	37	=	=	PUNCT
ejpam-4770	126	38	ng(y	ng(y	NOUN
ejpam-4770	126	39	)	)	PUNCT
ejpam-4770	126	40	.	.	PUNCT
ejpam-4770	127	1	a.m.	a.m.	PROPN
ejpam-4770	127	2	mahistrado	mahistrado	PROPN
ejpam-4770	127	3	,	,	PUNCT
ejpam-4770	127	4	h.	h.	PROPN
ejpam-4770	127	5	rara	rara	PROPN
ejpam-4770	127	6	/	/	SYM
ejpam-4770	127	7	eur	eur	PROPN
ejpam-4770	127	8	.	.	PUNCT
ejpam-4770	128	1	j.	j.	PROPN
ejpam-4770	128	2	pure	pure	PROPN
ejpam-4770	128	3	appl	appl	PROPN
ejpam-4770	128	4	.	.	PROPN
ejpam-4770	128	5	math	math	PROPN
ejpam-4770	128	6	,	,	PUNCT
ejpam-4770	128	7	16	16	NUM
ejpam-4770	128	8	(	(	PUNCT
ejpam-4770	128	9	3	3	NUM
ejpam-4770	128	10	)	)	PUNCT
ejpam-4770	128	11	(	(	PUNCT
ejpam-4770	128	12	2023	2023	NUM
ejpam-4770	128	13	)	)	PUNCT
ejpam-4770	128	14	,	,	PUNCT
ejpam-4770	128	15	1464	1464	NUM
ejpam-4770	128	16	-	-	SYM
ejpam-4770	128	17	1479	1479	NUM
ejpam-4770	128	18	1469	1469	NUM
ejpam-4770	128	19	proposition	proposition	NOUN
ejpam-4770	128	20	3	3	NUM
ejpam-4770	128	21	.	.	PUNCT
ejpam-4770	129	1	let	let	VERB
ejpam-4770	129	2	g	g	PRON
ejpam-4770	129	3	be	be	AUX
ejpam-4770	129	4	a	a	DET
ejpam-4770	129	5	nontrivial	nontrivial	ADJ
ejpam-4770	129	6	connected	connect	VERB
ejpam-4770	129	7	graph	graph	NOUN
ejpam-4770	129	8	.	.	PUNCT
ejpam-4770	130	1	then	then	ADV
ejpam-4770	130	2	g	g	PROPN
ejpam-4770	130	3	admits	admit	VERB
ejpam-4770	130	4	a	a	DET
ejpam-4770	130	5	1	1	NUM
ejpam-4770	130	6	-	-	PUNCT
ejpam-4770	130	7	movable	movable	ADJ
ejpam-4770	130	8	2	2	NUM
ejpam-4770	130	9	-	-	PUNCT
ejpam-4770	130	10	locating	locate	VERB
ejpam-4770	130	11	set	set	NOUN
ejpam-4770	130	12	if	if	SCONJ
ejpam-4770	130	13	and	and	CCONJ
ejpam-4770	130	14	only	only	ADV
ejpam-4770	130	15	if	if	SCONJ
ejpam-4770	130	16	g	g	PROPN
ejpam-4770	130	17	is	be	AUX
ejpam-4770	130	18	a	a	DET
ejpam-4770	130	19	point	point	NOUN
ejpam-4770	130	20	determining	determine	VERB
ejpam-4770	130	21	graph	graph	NOUN
ejpam-4770	130	22	.	.	PUNCT
ejpam-4770	131	1	proof	proof	NOUN
ejpam-4770	131	2	.	.	PUNCT
ejpam-4770	132	1	let	let	VERB
ejpam-4770	132	2	s	s	PRON
ejpam-4770	132	3	be	be	AUX
ejpam-4770	132	4	a	a	DET
ejpam-4770	132	5	1	1	NUM
ejpam-4770	132	6	-	-	PUNCT
ejpam-4770	132	7	movable	movable	ADJ
ejpam-4770	132	8	2	2	NUM
ejpam-4770	132	9	-	-	PUNCT
ejpam-4770	132	10	locating	locate	VERB
ejpam-4770	132	11	set	set	NOUN
ejpam-4770	132	12	of	of	ADP
ejpam-4770	132	13	g.	g.	PROPN
ejpam-4770	132	14	suppose	suppose	VERB
ejpam-4770	132	15	g	g	PROPN
ejpam-4770	132	16	is	be	AUX
ejpam-4770	132	17	not	not	PART
ejpam-4770	132	18	a	a	DET
ejpam-4770	132	19	point	point	NOUN
ejpam-4770	132	20	determining	determine	VERB
ejpam-4770	132	21	graph	graph	NOUN
ejpam-4770	132	22	.	.	PUNCT
ejpam-4770	133	1	then	then	ADV
ejpam-4770	133	2	there	there	PRON
ejpam-4770	133	3	exist	exist	VERB
ejpam-4770	133	4	x	x	NOUN
ejpam-4770	133	5	,	,	PUNCT
ejpam-4770	133	6	y	y	PROPN
ejpam-4770	133	7	∈	∈	PROPN
ejpam-4770	133	8	v	v	ADP
ejpam-4770	133	9	(	(	PUNCT
ejpam-4770	133	10	g	g	NOUN
ejpam-4770	133	11	)	)	PUNCT
ejpam-4770	133	12	with	with	ADP
ejpam-4770	133	13	x	x	X
ejpam-4770	133	14	̸=	̸=	PROPN
ejpam-4770	133	15	y	y	PROPN
ejpam-4770	133	16	and	and	CCONJ
ejpam-4770	133	17	ng(x	ng(x	NUM
ejpam-4770	133	18	)	)	PUNCT
ejpam-4770	133	19	=	=	PUNCT
ejpam-4770	133	20	ng(y	ng(y	NOUN
ejpam-4770	133	21	)	)	PUNCT
ejpam-4770	133	22	.	.	PUNCT
ejpam-4770	134	1	this	this	PRON
ejpam-4770	134	2	implies	imply	VERB
ejpam-4770	134	3	that	that	SCONJ
ejpam-4770	134	4	x	x	X
ejpam-4770	134	5	,	,	PUNCT
ejpam-4770	134	6	y	y	PROPN
ejpam-4770	134	7	∈	∈	PROPN
ejpam-4770	134	8	s	s	X
ejpam-4770	134	9	by	by	ADP
ejpam-4770	134	10	remark	remark	NOUN
ejpam-4770	134	11	5	5	NUM
ejpam-4770	134	12	.	.	PUNCT
ejpam-4770	134	13	thus	thus	ADV
ejpam-4770	134	14	,	,	PUNCT
ejpam-4770	134	15	s	s	VERB
ejpam-4770	134	16	\	\	X
ejpam-4770	134	17	{	{	PUNCT
ejpam-4770	134	18	x	x	NOUN
ejpam-4770	134	19	}	}	PUNCT
ejpam-4770	134	20	and	and	CCONJ
ejpam-4770	134	21	(	(	PUNCT
ejpam-4770	134	22	s	s	NOUN
ejpam-4770	134	23	\	\	X
ejpam-4770	134	24	{	{	PUNCT
ejpam-4770	134	25	x	x	NOUN
ejpam-4770	134	26	}	}	PUNCT
ejpam-4770	134	27	)	)	PUNCT
ejpam-4770	134	28	∪	∪	ADP
ejpam-4770	134	29	{	{	PUNCT
ejpam-4770	134	30	z	z	NOUN
ejpam-4770	134	31	}	}	PUNCT
ejpam-4770	134	32	are	be	AUX
ejpam-4770	134	33	not	not	PART
ejpam-4770	134	34	2	2	NUM
ejpam-4770	134	35	-	-	PUNCT
ejpam-4770	134	36	locating	locate	VERB
ejpam-4770	134	37	sets	set	NOUN
ejpam-4770	134	38	where	where	SCONJ
ejpam-4770	134	39	z	z	PROPN
ejpam-4770	134	40	∈	∈	PROPN
ejpam-4770	134	41	(	(	PUNCT
ejpam-4770	134	42	v	v	NOUN
ejpam-4770	134	43	(	(	PUNCT
ejpam-4770	134	44	g	g	NOUN
ejpam-4770	134	45	)	)	PUNCT
ejpam-4770	134	46	\	\	PROPN
ejpam-4770	134	47	s	s	X
ejpam-4770	134	48	)	)	PUNCT
ejpam-4770	134	49	∩ng(x	∩ng(x	NOUN
ejpam-4770	134	50	)	)	PUNCT
ejpam-4770	134	51	.	.	PUNCT
ejpam-4770	135	1	thus	thus	ADV
ejpam-4770	135	2	,	,	PUNCT
ejpam-4770	135	3	g	g	PROPN
ejpam-4770	135	4	is	be	AUX
ejpam-4770	135	5	a	a	DET
ejpam-4770	135	6	point	point	NOUN
ejpam-4770	135	7	determining	determine	VERB
ejpam-4770	135	8	graph	graph	NOUN
ejpam-4770	135	9	.	.	PUNCT
ejpam-4770	136	1	conversely	conversely	ADV
ejpam-4770	136	2	,	,	PUNCT
ejpam-4770	136	3	suppose	suppose	VERB
ejpam-4770	136	4	g	g	PROPN
ejpam-4770	136	5	is	be	AUX
ejpam-4770	136	6	a	a	DET
ejpam-4770	136	7	point	point	NOUN
ejpam-4770	136	8	determining	determine	VERB
ejpam-4770	136	9	graph	graph	NOUN
ejpam-4770	136	10	.	.	PUNCT
ejpam-4770	137	1	let	let	VERB
ejpam-4770	137	2	s	s	NOUN
ejpam-4770	137	3	=	=	X
ejpam-4770	137	4	v	v	ADJ
ejpam-4770	137	5	(	(	PUNCT
ejpam-4770	137	6	g	g	NOUN
ejpam-4770	137	7	)	)	PUNCT
ejpam-4770	137	8	.	.	PUNCT
ejpam-4770	138	1	then	then	ADV
ejpam-4770	138	2	s	s	VERB
ejpam-4770	138	3	is	be	AUX
ejpam-4770	138	4	a	a	DET
ejpam-4770	138	5	2	2	NUM
ejpam-4770	138	6	-	-	PUNCT
ejpam-4770	138	7	locating	locate	VERB
ejpam-4770	138	8	set	set	NOUN
ejpam-4770	138	9	of	of	ADP
ejpam-4770	138	10	g.	g.	PROPN
ejpam-4770	138	11	since	since	SCONJ
ejpam-4770	138	12	g	g	PROPN
ejpam-4770	138	13	is	be	AUX
ejpam-4770	138	14	a	a	DET
ejpam-4770	138	15	point	point	NOUN
ejpam-4770	138	16	determining	determine	VERB
ejpam-4770	138	17	graph	graph	NOUN
ejpam-4770	138	18	,	,	PUNCT
ejpam-4770	138	19	s	s	NOUN
ejpam-4770	138	20	\	\	X
ejpam-4770	138	21	{	{	PUNCT
ejpam-4770	138	22	x	x	X
ejpam-4770	138	23	}	}	PUNCT
ejpam-4770	138	24	is	be	AUX
ejpam-4770	138	25	a	a	DET
ejpam-4770	138	26	2	2	NUM
ejpam-4770	138	27	-	-	PUNCT
ejpam-4770	138	28	locating	locate	VERB
ejpam-4770	138	29	set	set	NOUN
ejpam-4770	138	30	for	for	ADP
ejpam-4770	138	31	all	all	DET
ejpam-4770	138	32	x	x	PROPN
ejpam-4770	138	33	∈	∈	PROPN
ejpam-4770	138	34	s.	s.	PROPN
ejpam-4770	138	35	therefore	therefore	ADV
ejpam-4770	138	36	,	,	PUNCT
ejpam-4770	138	37	g	g	PROPN
ejpam-4770	138	38	admits	admit	VERB
ejpam-4770	138	39	a	a	DET
ejpam-4770	138	40	1	1	NUM
ejpam-4770	138	41	-	-	PUNCT
ejpam-4770	138	42	movable	movable	ADJ
ejpam-4770	138	43	2	2	NUM
ejpam-4770	138	44	-	-	PUNCT
ejpam-4770	138	45	locating	locate	VERB
ejpam-4770	138	46	set	set	NOUN
ejpam-4770	138	47	.	.	PUNCT
ejpam-4770	139	1	proposition	proposition	NOUN
ejpam-4770	139	2	4	4	NUM
ejpam-4770	139	3	.	.	PUNCT
ejpam-4770	140	1	let	let	VERB
ejpam-4770	140	2	g	g	PRON
ejpam-4770	140	3	be	be	AUX
ejpam-4770	140	4	a	a	DET
ejpam-4770	140	5	nontrivial	nontrivial	ADJ
ejpam-4770	140	6	connected	connect	VERB
ejpam-4770	140	7	graph	graph	NOUN
ejpam-4770	140	8	.	.	PUNCT
ejpam-4770	141	1	then	then	ADV
ejpam-4770	141	2	g	g	PROPN
ejpam-4770	141	3	admits	admit	VERB
ejpam-4770	141	4	a	a	DET
ejpam-4770	141	5	1	1	NUM
ejpam-4770	141	6	-	-	PUNCT
ejpam-4770	141	7	movable	movable	ADJ
ejpam-4770	141	8	2	2	NUM
ejpam-4770	141	9	-	-	PUNCT
ejpam-4770	141	10	locating	locate	VERB
ejpam-4770	141	11	point	point	NOUN
ejpam-4770	141	12	-	-	PUNCT
ejpam-4770	141	13	wise	wise	ADJ
ejpam-4770	141	14	non	non	ADJ
ejpam-4770	141	15	-	-	ADJ
ejpam-4770	141	16	dominating	dominating	ADJ
ejpam-4770	141	17	set	set	NOUN
ejpam-4770	141	18	if	if	SCONJ
ejpam-4770	141	19	and	and	CCONJ
ejpam-4770	141	20	only	only	ADV
ejpam-4770	141	21	if	if	SCONJ
ejpam-4770	141	22	g	g	PROPN
ejpam-4770	141	23	is	be	AUX
ejpam-4770	141	24	a	a	DET
ejpam-4770	141	25	point	point	NOUN
ejpam-4770	141	26	determining	determine	VERB
ejpam-4770	141	27	graph	graph	NOUN
ejpam-4770	141	28	where	where	SCONJ
ejpam-4770	141	29	γ(g	γ(g	NOUN
ejpam-4770	141	30	)	)	PUNCT
ejpam-4770	141	31	̸=	̸=	PROPN
ejpam-4770	141	32	1	1	NUM
ejpam-4770	141	33	.	.	PUNCT
ejpam-4770	142	1	proof	proof	NOUN
ejpam-4770	142	2	.	.	PUNCT
ejpam-4770	143	1	let	let	VERB
ejpam-4770	143	2	s	s	PRON
ejpam-4770	143	3	be	be	AUX
ejpam-4770	143	4	a	a	DET
ejpam-4770	143	5	1	1	NUM
ejpam-4770	143	6	-	-	PUNCT
ejpam-4770	143	7	movable	movable	ADJ
ejpam-4770	143	8	2	2	NUM
ejpam-4770	143	9	-	-	PUNCT
ejpam-4770	143	10	locating	locate	VERB
ejpam-4770	143	11	point	point	NOUN
ejpam-4770	143	12	-	-	PUNCT
ejpam-4770	143	13	wise	wise	ADJ
ejpam-4770	143	14	non	non	ADJ
ejpam-4770	143	15	-	-	ADJ
ejpam-4770	143	16	dominating	dominating	ADJ
ejpam-4770	143	17	set	set	NOUN
ejpam-4770	143	18	of	of	ADP
ejpam-4770	143	19	g.	g.	PROPN
ejpam-4770	143	20	suppose	suppose	VERB
ejpam-4770	144	1	γ(g	γ(g	NOUN
ejpam-4770	144	2	)	)	PUNCT
ejpam-4770	144	3	=	=	SYM
ejpam-4770	144	4	1	1	X
ejpam-4770	144	5	.	.	X
ejpam-4770	144	6	set	set	VERB
ejpam-4770	144	7	a	a	DET
ejpam-4770	144	8	=	=	X
ejpam-4770	144	9	{	{	PUNCT
ejpam-4770	144	10	x	x	PROPN
ejpam-4770	144	11	∈	∈	PROPN
ejpam-4770	144	12	v	v	NOUN
ejpam-4770	144	13	(	(	PUNCT
ejpam-4770	144	14	g	g	NOUN
ejpam-4770	144	15	)	)	PUNCT
ejpam-4770	144	16	:	:	PUNCT
ejpam-4770	144	17	{	{	PUNCT
ejpam-4770	144	18	x	x	X
ejpam-4770	144	19	}	}	PUNCT
ejpam-4770	144	20	is	be	AUX
ejpam-4770	144	21	a	a	DET
ejpam-4770	144	22	dominating	dominating	NOUN
ejpam-4770	144	23	set	set	NOUN
ejpam-4770	144	24	of	of	ADP
ejpam-4770	144	25	g	g	NOUN
ejpam-4770	144	26	}	}	PUNCT
ejpam-4770	144	27	.	.	PUNCT
ejpam-4770	145	1	then	then	ADV
ejpam-4770	145	2	a	a	DET
ejpam-4770	145	3	̸=	̸=	PROPN
ejpam-4770	145	4	∅	∅	NOUN
ejpam-4770	145	5	since	since	SCONJ
ejpam-4770	145	6	γ(g	γ(g	PROPN
ejpam-4770	145	7	)	)	PUNCT
ejpam-4770	145	8	=	=	PUNCT
ejpam-4770	146	1	1	1	X
ejpam-4770	146	2	.	.	PUNCT
ejpam-4770	146	3	since	since	SCONJ
ejpam-4770	146	4	s	s	PROPN
ejpam-4770	146	5	is	be	AUX
ejpam-4770	146	6	a	a	DET
ejpam-4770	146	7	point	point	NOUN
ejpam-4770	146	8	-	-	PUNCT
ejpam-4770	146	9	wise	wise	ADJ
ejpam-4770	146	10	non	non	ADJ
ejpam-4770	146	11	-	-	ADJ
ejpam-4770	146	12	dominating	dominating	ADJ
ejpam-4770	146	13	set	set	NOUN
ejpam-4770	146	14	,	,	PUNCT
ejpam-4770	146	15	a	a	DET
ejpam-4770	146	16	⊆	⊆	NUM
ejpam-4770	146	17	s.	s.	PROPN
ejpam-4770	146	18	let	let	VERB
ejpam-4770	146	19	x	x	X
ejpam-4770	146	20	∈	∈	PROPN
ejpam-4770	146	21	a.	a.	NOUN
ejpam-4770	146	22	then	then	ADV
ejpam-4770	146	23	s\{x	s\{x	PROPN
ejpam-4770	146	24	}	}	PUNCT
ejpam-4770	146	25	and	and	CCONJ
ejpam-4770	146	26	(	(	PUNCT
ejpam-4770	146	27	s\{x	s\{x	PROPN
ejpam-4770	146	28	}	}	PUNCT
ejpam-4770	146	29	)	)	PUNCT
ejpam-4770	146	30	∪	∪	ADP
ejpam-4770	146	31	{	{	PUNCT
ejpam-4770	146	32	y	y	NOUN
ejpam-4770	146	33	}	}	PUNCT
ejpam-4770	146	34	for	for	ADP
ejpam-4770	146	35	each	each	DET
ejpam-4770	146	36	y	y	PROPN
ejpam-4770	146	37	∈	∈	PROPN
ejpam-4770	146	38	v	v	NOUN
ejpam-4770	146	39	(	(	PUNCT
ejpam-4770	146	40	g)\s	g)\s	NOUN
ejpam-4770	146	41	∩	∩	NOUN
ejpam-4770	146	42	ng(x	ng(x	NUM
ejpam-4770	146	43	)	)	PUNCT
ejpam-4770	146	44	are	be	AUX
ejpam-4770	146	45	not	not	PART
ejpam-4770	146	46	point	point	ADV
ejpam-4770	146	47	-	-	PUNCT
ejpam-4770	146	48	wise	wise	ADJ
ejpam-4770	146	49	non	non	ADJ
ejpam-4770	146	50	-	-	ADJ
ejpam-4770	146	51	dominating	dominating	ADJ
ejpam-4770	146	52	sets	set	NOUN
ejpam-4770	146	53	of	of	ADP
ejpam-4770	146	54	g.	g.	PROPN
ejpam-4770	146	55	thus	thus	ADV
ejpam-4770	146	56	,	,	PUNCT
ejpam-4770	146	57	s	s	VERB
ejpam-4770	146	58	is	be	AUX
ejpam-4770	146	59	not	not	PART
ejpam-4770	146	60	a	a	DET
ejpam-4770	146	61	1	1	NUM
ejpam-4770	146	62	-	-	PUNCT
ejpam-4770	146	63	movable	movable	ADJ
ejpam-4770	146	64	2	2	NUM
ejpam-4770	146	65	-	-	PUNCT
ejpam-4770	146	66	locating	locate	VERB
ejpam-4770	146	67	point	point	NOUN
ejpam-4770	146	68	-	-	PUNCT
ejpam-4770	146	69	wise	wise	ADJ
ejpam-4770	146	70	non	non	ADJ
ejpam-4770	146	71	-	-	ADJ
ejpam-4770	146	72	dominating	dominating	ADJ
ejpam-4770	146	73	set	set	NOUN
ejpam-4770	146	74	.	.	PUNCT
ejpam-4770	147	1	therefore	therefore	ADV
ejpam-4770	147	2	,	,	PUNCT
ejpam-4770	147	3	γ(g	γ(g	PROPN
ejpam-4770	147	4	)	)	PUNCT
ejpam-4770	147	5	̸=	̸=	PROPN
ejpam-4770	147	6	1	1	NUM
ejpam-4770	147	7	.	.	PUNCT
ejpam-4770	147	8	by	by	ADP
ejpam-4770	147	9	proposition	proposition	NOUN
ejpam-4770	147	10	3	3	NUM
ejpam-4770	147	11	,	,	PUNCT
ejpam-4770	147	12	g	g	PROPN
ejpam-4770	147	13	is	be	AUX
ejpam-4770	147	14	a	a	DET
ejpam-4770	147	15	point	point	NOUN
ejpam-4770	147	16	determining	determine	VERB
ejpam-4770	147	17	graph	graph	NOUN
ejpam-4770	147	18	.	.	PUNCT
ejpam-4770	148	1	conversely	conversely	ADV
ejpam-4770	148	2	,	,	PUNCT
ejpam-4770	148	3	suppose	suppose	VERB
ejpam-4770	148	4	g	g	PROPN
ejpam-4770	148	5	is	be	AUX
ejpam-4770	148	6	a	a	DET
ejpam-4770	148	7	point	point	NOUN
ejpam-4770	148	8	determining	determine	VERB
ejpam-4770	148	9	graph	graph	NOUN
ejpam-4770	148	10	where	where	SCONJ
ejpam-4770	148	11	γ(g	γ(g	NOUN
ejpam-4770	148	12	)	)	PUNCT
ejpam-4770	148	13	̸=	̸=	PROPN
ejpam-4770	148	14	1	1	NUM
ejpam-4770	148	15	.	.	PUNCT
ejpam-4770	149	1	then	then	ADV
ejpam-4770	149	2	by	by	ADP
ejpam-4770	149	3	proposition	proposition	NOUN
ejpam-4770	149	4	3	3	NUM
ejpam-4770	149	5	,	,	PUNCT
ejpam-4770	149	6	s	s	PART
ejpam-4770	149	7	=	=	SYM
ejpam-4770	149	8	v	v	X
ejpam-4770	149	9	(	(	PUNCT
ejpam-4770	149	10	g	g	NOUN
ejpam-4770	149	11	)	)	PUNCT
ejpam-4770	149	12	is	be	AUX
ejpam-4770	149	13	a	a	DET
ejpam-4770	149	14	1	1	NUM
ejpam-4770	149	15	-	-	PUNCT
ejpam-4770	149	16	movable	movable	ADJ
ejpam-4770	149	17	2	2	NUM
ejpam-4770	149	18	-	-	PUNCT
ejpam-4770	149	19	locating	locate	VERB
ejpam-4770	149	20	set	set	NOUN
ejpam-4770	149	21	.	.	PUNCT
ejpam-4770	150	1	thus	thus	ADV
ejpam-4770	150	2	,	,	PUNCT
ejpam-4770	150	3	s	s	VERB
ejpam-4770	150	4	is	be	AUX
ejpam-4770	150	5	a	a	DET
ejpam-4770	150	6	1	1	NUM
ejpam-4770	150	7	-	-	PUNCT
ejpam-4770	150	8	movable	movable	ADJ
ejpam-4770	150	9	2	2	NUM
ejpam-4770	150	10	-	-	PUNCT
ejpam-4770	150	11	locating	locate	VERB
ejpam-4770	150	12	point	point	NOUN
ejpam-4770	150	13	-	-	PUNCT
ejpam-4770	150	14	wise	wise	ADJ
ejpam-4770	150	15	non	non	ADJ
ejpam-4770	150	16	-	-	ADJ
ejpam-4770	150	17	dominating	dominating	ADJ
ejpam-4770	150	18	set	set	NOUN
ejpam-4770	150	19	of	of	ADP
ejpam-4770	150	20	g.	g.	PROPN
ejpam-4770	150	21	accordingly	accordingly	ADV
ejpam-4770	150	22	,	,	PUNCT
ejpam-4770	150	23	g	g	PROPN
ejpam-4770	150	24	admits	admit	VERB
ejpam-4770	150	25	a	a	DET
ejpam-4770	150	26	1	1	NUM
ejpam-4770	150	27	-	-	PUNCT
ejpam-4770	150	28	movable	movable	ADJ
ejpam-4770	150	29	2	2	NUM
ejpam-4770	150	30	-	-	PUNCT
ejpam-4770	150	31	locating	locate	VERB
ejpam-4770	150	32	pointwise	pointwise	ADJ
ejpam-4770	150	33	non	non	ADJ
ejpam-4770	150	34	-	-	ADJ
ejpam-4770	150	35	dominating	dominating	ADJ
ejpam-4770	150	36	set	set	NOUN
ejpam-4770	150	37	.	.	PUNCT
ejpam-4770	151	1	proposition	proposition	NOUN
ejpam-4770	151	2	5	5	NUM
ejpam-4770	151	3	.	.	PUNCT
ejpam-4770	152	1	let	let	VERB
ejpam-4770	152	2	g	g	PRON
ejpam-4770	152	3	be	be	AUX
ejpam-4770	152	4	a	a	DET
ejpam-4770	152	5	nontrivial	nontrivial	ADJ
ejpam-4770	152	6	connected	connect	VERB
ejpam-4770	152	7	graph	graph	NOUN
ejpam-4770	152	8	of	of	ADP
ejpam-4770	152	9	order	order	NOUN
ejpam-4770	152	10	n	n	PRON
ejpam-4770	152	11	≥	≥	NOUN
ejpam-4770	152	12	4	4	NUM
ejpam-4770	152	13	.	.	PUNCT
ejpam-4770	153	1	then	then	ADV
ejpam-4770	153	2	(	(	PUNCT
ejpam-4770	153	3	i	i	NOUN
ejpam-4770	153	4	)	)	PUNCT
ejpam-4770	153	5	mlnpnd	mlnpnd	NOUN
ejpam-4770	153	6	2	2	NUM
ejpam-4770	153	7	(	(	PUNCT
ejpam-4770	153	8	pn	pn	NOUN
ejpam-4770	153	9	)	)	PUNCT
ejpam-4770	153	10	=	=	SYM
ejpam-4770	154	1	n	n	PROPN
ejpam-4770	154	2	,	,	PUNCT
ejpam-4770	154	3	if	if	SCONJ
ejpam-4770	154	4	n	n	NOUN
ejpam-4770	154	5	=	=	SYM
ejpam-4770	154	6	4	4	NUM
ejpam-4770	154	7	,	,	PUNCT
ejpam-4770	154	8	5	5	NUM
ejpam-4770	154	9	;	;	PUNCT
ejpam-4770	154	10	2n+	2n+	NUM
ejpam-4770	154	11	k	k	NOUN
ejpam-4770	154	12	3	3	NUM
ejpam-4770	154	13	,	,	PUNCT
ejpam-4770	154	14	if	if	SCONJ
ejpam-4770	154	15	n	n	ADV
ejpam-4770	154	16	=	=	SYM
ejpam-4770	154	17	k(mod	k(mod	PROPN
ejpam-4770	154	18	3	3	NUM
ejpam-4770	154	19	)	)	PUNCT
ejpam-4770	154	20	,	,	PUNCT
ejpam-4770	154	21	0	0	NUM
ejpam-4770	154	22	≤	≤	NUM
ejpam-4770	154	23	k	k	X
ejpam-4770	154	24	≤	≤	NUM
ejpam-4770	154	25	2	2	NUM
ejpam-4770	154	26	and	and	CCONJ
ejpam-4770	154	27	n	n	NOUN
ejpam-4770	154	28	>	>	X
ejpam-4770	154	29	5	5	NUM
ejpam-4770	154	30	;	;	PUNCT
ejpam-4770	154	31	(	(	PUNCT
ejpam-4770	154	32	ii	ii	NOUN
ejpam-4770	154	33	)	)	PUNCT
ejpam-4770	154	34	mlnpnd	mlnpnd	NOUN
ejpam-4770	154	35	(	(	PUNCT
ejpam-4770	154	36	2,1)(pn	2,1)(pn	NUM
ejpam-4770	154	37	)	)	PUNCT
ejpam-4770	154	38	=	=	SYM
ejpam-4770	154	39	mlnpnd	mlnpnd	NOUN
ejpam-4770	154	40	(	(	PUNCT
ejpam-4770	154	41	2,2)(pn	2,2)(pn	NUM
ejpam-4770	154	42	)	)	PUNCT
ejpam-4770	154	43	=	=	SYM
ejpam-4770	155	1	n	n	PROPN
ejpam-4770	155	2	,	,	PUNCT
ejpam-4770	155	3	if	if	SCONJ
ejpam-4770	155	4	n	n	NOUN
ejpam-4770	155	5	=	=	SYM
ejpam-4770	155	6	5	5	NUM
ejpam-4770	155	7	;	;	PUNCT
ejpam-4770	155	8	2n+	2n+	NUM
ejpam-4770	155	9	k	k	NOUN
ejpam-4770	155	10	3	3	NUM
ejpam-4770	155	11	,	,	PUNCT
ejpam-4770	155	12	if	if	SCONJ
ejpam-4770	155	13	n	n	ADV
ejpam-4770	155	14	=	=	SYM
ejpam-4770	155	15	k(mod	k(mod	PROPN
ejpam-4770	155	16	3	3	NUM
ejpam-4770	155	17	)	)	PUNCT
ejpam-4770	155	18	,	,	PUNCT
ejpam-4770	155	19	0	0	NUM
ejpam-4770	155	20	≤	≤	NUM
ejpam-4770	155	21	k	k	X
ejpam-4770	155	22	≤	≤	NUM
ejpam-4770	155	23	2	2	NUM
ejpam-4770	155	24	and	and	CCONJ
ejpam-4770	155	25	n	n	NOUN
ejpam-4770	155	26	>	>	X
ejpam-4770	155	27	5	5	NUM
ejpam-4770	155	28	;	;	PUNCT
ejpam-4770	155	29	(	(	PUNCT
ejpam-4770	155	30	iii	iii	X
ejpam-4770	155	31	)	)	PUNCT
ejpam-4770	155	32	mlnpnd	mlnpnd	NOUN
ejpam-4770	155	33	2	2	NUM
ejpam-4770	155	34	(	(	PUNCT
ejpam-4770	155	35	cn	cn	NOUN
ejpam-4770	155	36	)	)	PUNCT
ejpam-4770	155	37	=	=	PUNCT
ejpam-4770	155	38	3	3	NOUN
ejpam-4770	155	39	,	,	PUNCT
ejpam-4770	155	40	if	if	SCONJ
ejpam-4770	155	41	n	n	NOUN
ejpam-4770	155	42	=	=	SYM
ejpam-4770	155	43	5	5	NUM
ejpam-4770	155	44	;	;	PUNCT
ejpam-4770	155	45	2n+	2n+	NUM
ejpam-4770	155	46	k	k	NOUN
ejpam-4770	155	47	3	3	NUM
ejpam-4770	155	48	,	,	PUNCT
ejpam-4770	155	49	if	if	SCONJ
ejpam-4770	155	50	n	n	ADV
ejpam-4770	155	51	=	=	SYM
ejpam-4770	155	52	k(mod	k(mod	PROPN
ejpam-4770	155	53	3	3	NUM
ejpam-4770	155	54	)	)	PUNCT
ejpam-4770	155	55	,	,	PUNCT
ejpam-4770	155	56	0	0	NUM
ejpam-4770	155	57	≤	≤	NUM
ejpam-4770	155	58	k	k	X
ejpam-4770	155	59	≤	≤	NUM
ejpam-4770	155	60	2	2	NUM
ejpam-4770	155	61	and	and	CCONJ
ejpam-4770	155	62	n	n	NOUN
ejpam-4770	155	63	>	>	X
ejpam-4770	155	64	5	5	NUM
ejpam-4770	155	65	;	;	PUNCT
ejpam-4770	155	66	a.m.	a.m.	PROPN
ejpam-4770	155	67	mahistrado	mahistrado	PROPN
ejpam-4770	155	68	,	,	PUNCT
ejpam-4770	155	69	h.	h.	PROPN
ejpam-4770	155	70	rara	rara	PROPN
ejpam-4770	155	71	/	/	SYM
ejpam-4770	155	72	eur	eur	PROPN
ejpam-4770	155	73	.	.	PUNCT
ejpam-4770	156	1	j.	j.	PROPN
ejpam-4770	156	2	pure	pure	PROPN
ejpam-4770	156	3	appl	appl	PROPN
ejpam-4770	156	4	.	.	PROPN
ejpam-4770	156	5	math	math	PROPN
ejpam-4770	156	6	,	,	PUNCT
ejpam-4770	156	7	16	16	NUM
ejpam-4770	156	8	(	(	PUNCT
ejpam-4770	156	9	3	3	NUM
ejpam-4770	156	10	)	)	PUNCT
ejpam-4770	156	11	(	(	PUNCT
ejpam-4770	156	12	2023	2023	NUM
ejpam-4770	156	13	)	)	PUNCT
ejpam-4770	156	14	,	,	PUNCT
ejpam-4770	156	15	1464	1464	NUM
ejpam-4770	156	16	-	-	SYM
ejpam-4770	156	17	1479	1479	NUM
ejpam-4770	156	18	1470	1470	NUM
ejpam-4770	156	19	(	(	PUNCT
ejpam-4770	156	20	iv	iv	X
ejpam-4770	156	21	)	)	PUNCT
ejpam-4770	156	22	mlnpnd	mlnpnd	NOUN
ejpam-4770	156	23	(	(	PUNCT
ejpam-4770	156	24	2,1)(cn	2,1)(cn	NUM
ejpam-4770	156	25	)	)	PUNCT
ejpam-4770	156	26	=	=	SYM
ejpam-4770	157	1	3	3	NOUN
ejpam-4770	157	2	,	,	PUNCT
ejpam-4770	157	3	if	if	SCONJ
ejpam-4770	157	4	n	n	NOUN
ejpam-4770	157	5	=	=	SYM
ejpam-4770	157	6	5	5	NUM
ejpam-4770	157	7	;	;	PUNCT
ejpam-4770	157	8	2n+	2n+	NUM
ejpam-4770	157	9	k	k	NOUN
ejpam-4770	157	10	3	3	NUM
ejpam-4770	157	11	,	,	PUNCT
ejpam-4770	157	12	if	if	SCONJ
ejpam-4770	157	13	n	n	ADV
ejpam-4770	157	14	=	=	SYM
ejpam-4770	157	15	k(mod	k(mod	PROPN
ejpam-4770	157	16	3	3	NUM
ejpam-4770	157	17	)	)	PUNCT
ejpam-4770	157	18	,	,	PUNCT
ejpam-4770	157	19	0	0	NUM
ejpam-4770	157	20	≤	≤	NUM
ejpam-4770	157	21	k	k	X
ejpam-4770	157	22	≤	≤	NUM
ejpam-4770	157	23	2	2	NUM
ejpam-4770	157	24	and	and	CCONJ
ejpam-4770	157	25	n	n	NOUN
ejpam-4770	157	26	>	>	X
ejpam-4770	157	27	5	5	NUM
ejpam-4770	157	28	;	;	PUNCT
ejpam-4770	157	29	(	(	PUNCT
ejpam-4770	157	30	v	v	NOUN
ejpam-4770	157	31	)	)	PUNCT
ejpam-4770	157	32	mlnpnd	mlnpnd	NOUN
ejpam-4770	157	33	(	(	PUNCT
ejpam-4770	157	34	2,2)(cn	2,2)(cn	NUM
ejpam-4770	157	35	)	)	PUNCT
ejpam-4770	157	36	=	=	SYM
ejpam-4770	157	37	5	5	NOUN
ejpam-4770	157	38	,	,	PUNCT
ejpam-4770	157	39	if	if	SCONJ
ejpam-4770	157	40	n	n	NOUN
ejpam-4770	157	41	=	=	SYM
ejpam-4770	157	42	5	5	NUM
ejpam-4770	157	43	;	;	PUNCT
ejpam-4770	157	44	2n+	2n+	NUM
ejpam-4770	157	45	k	k	NOUN
ejpam-4770	157	46	3	3	NUM
ejpam-4770	157	47	,	,	PUNCT
ejpam-4770	157	48	if	if	SCONJ
ejpam-4770	157	49	n	n	ADV
ejpam-4770	157	50	=	=	SYM
ejpam-4770	157	51	k(mod	k(mod	PROPN
ejpam-4770	157	52	3	3	NUM
ejpam-4770	157	53	)	)	PUNCT
ejpam-4770	157	54	,	,	PUNCT
ejpam-4770	157	55	0	0	NUM
ejpam-4770	157	56	≤	≤	NUM
ejpam-4770	157	57	k	k	X
ejpam-4770	157	58	≤	≤	NUM
ejpam-4770	157	59	2	2	NUM
ejpam-4770	157	60	and	and	CCONJ
ejpam-4770	157	61	n	n	NOUN
ejpam-4770	157	62	>	>	X
ejpam-4770	157	63	5	5	NUM
ejpam-4770	157	64	.	.	PUNCT
ejpam-4770	157	65	proof	proof	NOUN
ejpam-4770	157	66	.	.	PUNCT
ejpam-4770	158	1	(	(	PUNCT
ejpam-4770	158	2	i	i	NOUN
ejpam-4770	158	3	)	)	PUNCT
ejpam-4770	158	4	let	let	VERB
ejpam-4770	158	5	pn	pn	NOUN
ejpam-4770	158	6	=	=	PUNCT
ejpam-4770	159	1	[	[	X
ejpam-4770	159	2	v1	v1	NOUN
ejpam-4770	159	3	,	,	PUNCT
ejpam-4770	159	4	v2	v2	NOUN
ejpam-4770	159	5	,	,	PUNCT
ejpam-4770	159	6	.	.	PUNCT
ejpam-4770	159	7	.	.	PUNCT
ejpam-4770	159	8	.	.	PUNCT
ejpam-4770	160	1	,	,	PUNCT
ejpam-4770	160	2	vn	vn	X
ejpam-4770	160	3	]	]	PUNCT
ejpam-4770	160	4	and	and	CCONJ
ejpam-4770	160	5	s	s	AUX
ejpam-4770	160	6	be	be	AUX
ejpam-4770	160	7	an	an	DET
ejpam-4770	160	8	mlnpnd	mlnpnd	NOUN
ejpam-4770	160	9	2	2	NUM
ejpam-4770	160	10	set	set	NOUN
ejpam-4770	160	11	of	of	ADP
ejpam-4770	160	12	pn	pn	PROPN
ejpam-4770	160	13	.	.	PUNCT
ejpam-4770	161	1	the	the	DET
ejpam-4770	161	2	case	case	NOUN
ejpam-4770	161	3	where	where	SCONJ
ejpam-4770	161	4	n	n	NOUN
ejpam-4770	161	5	=	=	SYM
ejpam-4770	161	6	4	4	NUM
ejpam-4770	161	7	,	,	PUNCT
ejpam-4770	161	8	5	5	NUM
ejpam-4770	161	9	can	can	AUX
ejpam-4770	161	10	be	be	AUX
ejpam-4770	161	11	verified	verify	VERB
ejpam-4770	161	12	.	.	PUNCT
ejpam-4770	162	1	next	next	ADV
ejpam-4770	162	2	,	,	PUNCT
ejpam-4770	162	3	let	let	VERB
ejpam-4770	162	4	n	n	PRON
ejpam-4770	162	5	>	>	X
ejpam-4770	162	6	5	5	NUM
ejpam-4770	162	7	and	and	CCONJ
ejpam-4770	162	8	n	n	PRON
ejpam-4770	162	9	≡	≡	PROPN
ejpam-4770	162	10	k(mod	k(mod	PROPN
ejpam-4770	162	11	3	3	X
ejpam-4770	162	12	)	)	PUNCT
ejpam-4770	162	13	where	where	SCONJ
ejpam-4770	162	14	0	0	NUM
ejpam-4770	162	15	≤	≤	NUM
ejpam-4770	163	1	k	k	X
ejpam-4770	163	2	≤	≤	ADJ
ejpam-4770	163	3	2	2	NUM
ejpam-4770	163	4	.	.	PUNCT
ejpam-4770	164	1	then	then	ADV
ejpam-4770	164	2	n	n	NOUN
ejpam-4770	164	3	=	=	NOUN
ejpam-4770	164	4	3r	3r	NUM
ejpam-4770	164	5	+	+	CCONJ
ejpam-4770	164	6	k.	k.	PROPN
ejpam-4770	165	1	hence	hence	ADV
ejpam-4770	165	2	,	,	PUNCT
ejpam-4770	165	3	r	r	NOUN
ejpam-4770	165	4	=	=	SYM
ejpam-4770	165	5	n−	n−	NOUN
ejpam-4770	165	6	k	k	NOUN
ejpam-4770	165	7	3	3	NUM
ejpam-4770	165	8	.	.	PUNCT
ejpam-4770	166	1	then	then	ADV
ejpam-4770	166	2	the	the	DET
ejpam-4770	166	3	set	set	NOUN
ejpam-4770	166	4	s	s	PART
ejpam-4770	166	5	=	=	NOUN
ejpam-4770	166	6	{	{	PUNCT
ejpam-4770	166	7	v1	v1	PROPN
ejpam-4770	166	8	,	,	PUNCT
ejpam-4770	166	9	v3	v3	PROPN
ejpam-4770	166	10	,	,	PUNCT
ejpam-4770	166	11	v4	v4	PROPN
ejpam-4770	166	12	,	,	PUNCT
ejpam-4770	166	13	v6	v6	NOUN
ejpam-4770	166	14	,	,	PUNCT
ejpam-4770	166	15	v7	v7	NUM
ejpam-4770	166	16	,	,	PUNCT
ejpam-4770	166	17	v9	v9	PROPN
ejpam-4770	166	18	,	,	PUNCT
ejpam-4770	166	19	v10	v10	NOUN
ejpam-4770	166	20	,	,	PUNCT
ejpam-4770	166	21	v12	v12	VERB
ejpam-4770	166	22	,	,	PUNCT
ejpam-4770	166	23	v13	v13	NOUN
ejpam-4770	166	24	,	,	PUNCT
ejpam-4770	166	25	.	.	PUNCT
ejpam-4770	166	26	.	.	PUNCT
ejpam-4770	166	27	.	.	PUNCT
ejpam-4770	167	1	,	,	PUNCT
ejpam-4770	167	2	v3r+k−3	v3r+k−3	PROPN
ejpam-4770	167	3	,	,	PUNCT
ejpam-4770	167	4	v3r+k−2	v3r+k−2	PROPN
ejpam-4770	167	5	,	,	PUNCT
ejpam-4770	167	6	.	.	PUNCT
ejpam-4770	167	7	.	.	PUNCT
ejpam-4770	168	1	.	.	PUNCT
ejpam-4770	169	1	,	,	PUNCT
ejpam-4770	169	2	v3r+k	v3r+k	PROPN
ejpam-4770	169	3	}	}	PUNCT
ejpam-4770	169	4	is	be	AUX
ejpam-4770	169	5	an	an	DET
ejpam-4770	169	6	mlnpnd	mlnpnd	NOUN
ejpam-4770	169	7	2	2	NUM
ejpam-4770	169	8	set	set	NOUN
ejpam-4770	169	9	of	of	ADP
ejpam-4770	169	10	pn	pn	PROPN
ejpam-4770	169	11	.	.	PROPN
ejpam-4770	170	1	therefore	therefore	ADV
ejpam-4770	170	2	,	,	PUNCT
ejpam-4770	170	3	|s|	|s|	PROPN
ejpam-4770	170	4	=	=	NOUN
ejpam-4770	170	5	3r	3r	NUM
ejpam-4770	170	6	+	+	CCONJ
ejpam-4770	171	1	k	k	NOUN
ejpam-4770	171	2	−	−	NOUN
ejpam-4770	171	3	r	r	NOUN
ejpam-4770	171	4	=	=	SYM
ejpam-4770	171	5	2n+	2n+	NUM
ejpam-4770	171	6	k	k	NOUN
ejpam-4770	171	7	3	3	NUM
ejpam-4770	171	8	.	.	PUNCT
ejpam-4770	172	1	the	the	DET
ejpam-4770	172	2	proofs	proof	NOUN
ejpam-4770	172	3	of	of	ADP
ejpam-4770	172	4	(	(	PUNCT
ejpam-4770	172	5	ii	ii	NOUN
ejpam-4770	172	6	)	)	PUNCT
ejpam-4770	172	7	,	,	PUNCT
ejpam-4770	172	8	(	(	PUNCT
ejpam-4770	172	9	iii	iii	NOUN
ejpam-4770	172	10	)	)	PUNCT
ejpam-4770	172	11	,	,	PUNCT
ejpam-4770	172	12	(	(	PUNCT
ejpam-4770	172	13	iv	iv	X
ejpam-4770	172	14	)	)	PUNCT
ejpam-4770	172	15	and	and	CCONJ
ejpam-4770	172	16	(	(	PUNCT
ejpam-4770	172	17	v	v	NOUN
ejpam-4770	172	18	)	)	PUNCT
ejpam-4770	172	19	are	be	AUX
ejpam-4770	172	20	similar	similar	ADJ
ejpam-4770	172	21	to	to	ADP
ejpam-4770	172	22	(	(	PUNCT
ejpam-4770	172	23	i	i	NOUN
ejpam-4770	172	24	)	)	PUNCT
ejpam-4770	172	25	.	.	PUNCT
ejpam-4770	173	1	remark	remark	PROPN
ejpam-4770	173	2	6	6	NUM
ejpam-4770	173	3	.	.	PUNCT
ejpam-4770	174	1	let	let	VERB
ejpam-4770	174	2	g	g	PRON
ejpam-4770	174	3	be	be	AUX
ejpam-4770	174	4	a	a	DET
ejpam-4770	174	5	nontrivial	nontrivial	ADJ
ejpam-4770	174	6	connected	connect	VERB
ejpam-4770	174	7	graph	graph	NOUN
ejpam-4770	174	8	.	.	PUNCT
ejpam-4770	175	1	then	then	ADV
ejpam-4770	175	2	g	g	PROPN
ejpam-4770	175	3	admits	admit	VERB
ejpam-4770	175	4	a	a	DET
ejpam-4770	175	5	1	1	NUM
ejpam-4770	175	6	-	-	PUNCT
ejpam-4770	175	7	movable	movable	ADJ
ejpam-4770	175	8	(	(	PUNCT
ejpam-4770	175	9	2	2	NUM
ejpam-4770	175	10	,	,	PUNCT
ejpam-4770	175	11	1)locating	1)locating	NUM
ejpam-4770	175	12	point	point	ADV
ejpam-4770	175	13	-	-	PUNCT
ejpam-4770	175	14	wise	wise	ADJ
ejpam-4770	175	15	non	non	ADJ
ejpam-4770	175	16	-	-	ADJ
ejpam-4770	175	17	dominating	dominating	ADJ
ejpam-4770	175	18	set	set	NOUN
ejpam-4770	175	19	if	if	SCONJ
ejpam-4770	175	20	and	and	CCONJ
ejpam-4770	175	21	only	only	ADV
ejpam-4770	175	22	if	if	SCONJ
ejpam-4770	175	23	∆(g	∆(g	NOUN
ejpam-4770	175	24	)	)	PUNCT
ejpam-4770	175	25	≤	≤	NOUN
ejpam-4770	175	26	|v	|v	X
ejpam-4770	175	27	(	(	PUNCT
ejpam-4770	175	28	g)||	g)||	NOUN
ejpam-4770	175	29	−	−	NOUN
ejpam-4770	175	30	2	2	X
ejpam-4770	175	31	.	.	X
ejpam-4770	175	32	remark	remark	NOUN
ejpam-4770	175	33	7	7	NUM
ejpam-4770	175	34	.	.	PUNCT
ejpam-4770	176	1	let	let	VERB
ejpam-4770	176	2	g	g	PRON
ejpam-4770	176	3	be	be	AUX
ejpam-4770	176	4	a	a	DET
ejpam-4770	176	5	nontrivial	nontrivial	ADJ
ejpam-4770	176	6	connected	connect	VERB
ejpam-4770	176	7	graph	graph	NOUN
ejpam-4770	176	8	.	.	PUNCT
ejpam-4770	177	1	then	then	ADV
ejpam-4770	177	2	g	g	PROPN
ejpam-4770	177	3	admits	admit	VERB
ejpam-4770	177	4	a	a	DET
ejpam-4770	177	5	1	1	NUM
ejpam-4770	177	6	-	-	PUNCT
ejpam-4770	177	7	movable	movable	ADJ
ejpam-4770	177	8	(	(	PUNCT
ejpam-4770	177	9	2	2	NUM
ejpam-4770	177	10	,	,	PUNCT
ejpam-4770	177	11	2)locating	2)locating	NUM
ejpam-4770	177	12	point	point	NOUN
ejpam-4770	177	13	-	-	PUNCT
ejpam-4770	177	14	wise	wise	ADJ
ejpam-4770	177	15	non	non	ADJ
ejpam-4770	177	16	-	-	ADJ
ejpam-4770	177	17	dominating	dominating	ADJ
ejpam-4770	177	18	set	set	NOUN
ejpam-4770	177	19	if	if	SCONJ
ejpam-4770	177	20	and	and	CCONJ
ejpam-4770	177	21	only	only	ADV
ejpam-4770	177	22	if	if	SCONJ
ejpam-4770	177	23	∆(g	∆(g	NOUN
ejpam-4770	177	24	)	)	PUNCT
ejpam-4770	177	25	≤	≤	NOUN
ejpam-4770	177	26	|v	|v	X
ejpam-4770	177	27	(	(	PUNCT
ejpam-4770	177	28	g)||	g)||	NOUN
ejpam-4770	177	29	−	−	NOUN
ejpam-4770	177	30	3	3	X
ejpam-4770	177	31	.	.	PUNCT
ejpam-4770	178	1	we	we	PRON
ejpam-4770	178	2	now	now	ADV
ejpam-4770	178	3	characterize	characterize	VERB
ejpam-4770	178	4	the	the	DET
ejpam-4770	178	5	1	1	NUM
ejpam-4770	178	6	-	-	PUNCT
ejpam-4770	178	7	movable	movable	ADJ
ejpam-4770	178	8	2	2	NUM
ejpam-4770	178	9	-	-	PUNCT
ejpam-4770	178	10	resolving	resolve	VERB
ejpam-4770	178	11	hop	hop	NOUN
ejpam-4770	178	12	dominating	dominating	NOUN
ejpam-4770	178	13	sets	set	NOUN
ejpam-4770	178	14	in	in	ADP
ejpam-4770	178	15	some	some	DET
ejpam-4770	178	16	graphs	graph	NOUN
ejpam-4770	178	17	under	under	ADP
ejpam-4770	178	18	some	some	DET
ejpam-4770	178	19	binary	binary	ADJ
ejpam-4770	178	20	operations	operation	NOUN
ejpam-4770	178	21	.	.	PUNCT
ejpam-4770	179	1	4	4	X
ejpam-4770	179	2	.	.	X
ejpam-4770	179	3	join	join	VERB
ejpam-4770	179	4	of	of	ADP
ejpam-4770	179	5	graphs	graph	NOUN
ejpam-4770	179	6	as	as	ADP
ejpam-4770	179	7	a	a	DET
ejpam-4770	179	8	consequence	consequence	NOUN
ejpam-4770	179	9	of	of	ADP
ejpam-4770	179	10	proposition	proposition	NOUN
ejpam-4770	179	11	1	1	NUM
ejpam-4770	179	12	the	the	DET
ejpam-4770	179	13	next	next	ADJ
ejpam-4770	179	14	result	result	NOUN
ejpam-4770	179	15	follows	follow	VERB
ejpam-4770	179	16	.	.	PUNCT
ejpam-4770	180	1	corollary	corollary	ADJ
ejpam-4770	180	2	1	1	NUM
ejpam-4770	180	3	.	.	PUNCT
ejpam-4770	181	1	a	a	DET
ejpam-4770	181	2	graph	graph	NOUN
ejpam-4770	181	3	g	g	NOUN
ejpam-4770	181	4	does	do	AUX
ejpam-4770	181	5	not	not	PART
ejpam-4770	181	6	admit	admit	VERB
ejpam-4770	181	7	a	a	DET
ejpam-4770	181	8	1	1	NUM
ejpam-4770	181	9	-	-	PUNCT
ejpam-4770	181	10	movable	movable	ADJ
ejpam-4770	181	11	2	2	NUM
ejpam-4770	181	12	-	-	PUNCT
ejpam-4770	181	13	resolving	resolve	VERB
ejpam-4770	181	14	hop	hop	NOUN
ejpam-4770	181	15	dominating	dominating	NOUN
ejpam-4770	181	16	set	set	VERB
ejpam-4770	181	17	if	if	SCONJ
ejpam-4770	181	18	and	and	CCONJ
ejpam-4770	181	19	only	only	ADV
ejpam-4770	181	20	if	if	SCONJ
ejpam-4770	181	21	g	g	NOUN
ejpam-4770	181	22	=	=	PROPN
ejpam-4770	181	23	k1	k1	PROPN
ejpam-4770	182	1	+	+	NOUN
ejpam-4770	182	2	h	h	NOUN
ejpam-4770	182	3	for	for	ADP
ejpam-4770	182	4	any	any	DET
ejpam-4770	182	5	nontrivial	nontrivial	ADJ
ejpam-4770	182	6	connected	connect	VERB
ejpam-4770	182	7	graph	graph	NOUN
ejpam-4770	182	8	h.	h.	PROPN
ejpam-4770	182	9	theorem	theorem	PROPN
ejpam-4770	182	10	1	1	NUM
ejpam-4770	182	11	.	.	PUNCT
ejpam-4770	183	1	[	[	X
ejpam-4770	183	2	9	9	NUM
ejpam-4770	183	3	]	]	PUNCT
ejpam-4770	183	4	let	let	VERB
ejpam-4770	183	5	g	g	NOUN
ejpam-4770	183	6	and	and	CCONJ
ejpam-4770	183	7	h	h	NOUN
ejpam-4770	183	8	be	be	AUX
ejpam-4770	183	9	nontrivial	nontrivial	ADJ
ejpam-4770	183	10	connected	connect	VERB
ejpam-4770	183	11	graphs	graph	NOUN
ejpam-4770	183	12	with	with	ADP
ejpam-4770	183	13	γ(g	γ(g	NOUN
ejpam-4770	183	14	)	)	PUNCT
ejpam-4770	183	15	̸=	̸=	PROPN
ejpam-4770	183	16	1	1	NUM
ejpam-4770	183	17	and	and	CCONJ
ejpam-4770	183	18	γ(h	γ(h	NOUN
ejpam-4770	183	19	)	)	PUNCT
ejpam-4770	183	20	̸=	̸=	PROPN
ejpam-4770	183	21	1	1	NUM
ejpam-4770	183	22	.	.	PUNCT
ejpam-4770	184	1	a	a	DET
ejpam-4770	184	2	set	set	NOUN
ejpam-4770	184	3	s	s	NOUN
ejpam-4770	184	4	⊆	⊆	NUM
ejpam-4770	184	5	v	v	NOUN
ejpam-4770	184	6	(	(	PUNCT
ejpam-4770	184	7	g	g	PROPN
ejpam-4770	184	8	+	+	NOUN
ejpam-4770	184	9	h	h	NOUN
ejpam-4770	184	10	)	)	PUNCT
ejpam-4770	184	11	is	be	AUX
ejpam-4770	184	12	a	a	DET
ejpam-4770	184	13	2	2	NUM
ejpam-4770	184	14	-	-	PUNCT
ejpam-4770	184	15	resolving	resolve	VERB
ejpam-4770	184	16	hop	hop	NOUN
ejpam-4770	184	17	dominating	dominating	NOUN
ejpam-4770	184	18	set	set	NOUN
ejpam-4770	184	19	of	of	ADP
ejpam-4770	184	20	g	g	PROPN
ejpam-4770	185	1	+	+	CCONJ
ejpam-4770	185	2	h	h	NOUN
ejpam-4770	185	3	if	if	SCONJ
ejpam-4770	185	4	and	and	CCONJ
ejpam-4770	185	5	only	only	ADV
ejpam-4770	185	6	if	if	SCONJ
ejpam-4770	185	7	s	s	VERB
ejpam-4770	185	8	=	=	PUNCT
ejpam-4770	185	9	sg	sg	X
ejpam-4770	185	10	∪	∪	NOUN
ejpam-4770	185	11	sh	sh	PROPN
ejpam-4770	185	12	where	where	SCONJ
ejpam-4770	185	13	sg	sg	PROPN
ejpam-4770	185	14	=	=	SYM
ejpam-4770	185	15	v	v	PROPN
ejpam-4770	185	16	(	(	PUNCT
ejpam-4770	185	17	g	g	NOUN
ejpam-4770	185	18	)	)	PUNCT
ejpam-4770	185	19	∩	∩	NOUN
ejpam-4770	185	20	s	s	NOUN
ejpam-4770	185	21	and	and	CCONJ
ejpam-4770	185	22	sh	sh	PROPN
ejpam-4770	185	23	=	=	SYM
ejpam-4770	185	24	v	v	PROPN
ejpam-4770	185	25	(	(	PUNCT
ejpam-4770	185	26	h	h	NOUN
ejpam-4770	185	27	)	)	PUNCT
ejpam-4770	185	28	∩	∩	NOUN
ejpam-4770	185	29	s	s	NOUN
ejpam-4770	185	30	are	be	AUX
ejpam-4770	185	31	2	2	NUM
ejpam-4770	185	32	-	-	PUNCT
ejpam-4770	185	33	locating	locate	VERB
ejpam-4770	185	34	point	point	NOUN
ejpam-4770	185	35	-	-	PUNCT
ejpam-4770	185	36	wise	wise	ADJ
ejpam-4770	185	37	non	non	ADJ
ejpam-4770	185	38	-	-	ADJ
ejpam-4770	185	39	dominating	dominating	ADJ
ejpam-4770	185	40	sets	set	NOUN
ejpam-4770	185	41	of	of	ADP
ejpam-4770	185	42	g	g	PROPN
ejpam-4770	185	43	and	and	CCONJ
ejpam-4770	185	44	h	h	NOUN
ejpam-4770	185	45	,	,	PUNCT
ejpam-4770	185	46	respectively	respectively	ADV
ejpam-4770	185	47	where	where	SCONJ
ejpam-4770	185	48	sg	sg	PROPN
ejpam-4770	185	49	or	or	CCONJ
ejpam-4770	185	50	sh	sh	PROPN
ejpam-4770	185	51	is	be	AUX
ejpam-4770	185	52	a	a	DET
ejpam-4770	185	53	(	(	PUNCT
ejpam-4770	185	54	2	2	NUM
ejpam-4770	185	55	,	,	PUNCT
ejpam-4770	185	56	2)-locating	2)-locating	NUM
ejpam-4770	185	57	point	point	NOUN
ejpam-4770	185	58	-	-	PUNCT
ejpam-4770	185	59	wise	wise	ADJ
ejpam-4770	185	60	non	non	ADJ
ejpam-4770	185	61	-	-	ADJ
ejpam-4770	185	62	dominating	dominating	ADJ
ejpam-4770	185	63	set	set	NOUN
ejpam-4770	185	64	or	or	CCONJ
ejpam-4770	185	65	sg	sg	PROPN
ejpam-4770	185	66	and	and	CCONJ
ejpam-4770	185	67	sh	sh	PROPN
ejpam-4770	185	68	are	be	AUX
ejpam-4770	185	69	(	(	PUNCT
ejpam-4770	185	70	2	2	NUM
ejpam-4770	185	71	,	,	PUNCT
ejpam-4770	185	72	1)-locating	1)-locating	NUM
ejpam-4770	185	73	point	point	NOUN
ejpam-4770	185	74	-	-	PUNCT
ejpam-4770	185	75	wise	wise	ADJ
ejpam-4770	185	76	non	non	ADJ
ejpam-4770	185	77	-	-	ADJ
ejpam-4770	185	78	dominating	dominating	ADJ
ejpam-4770	185	79	sets	set	NOUN
ejpam-4770	185	80	.	.	PUNCT
ejpam-4770	186	1	a.m.	a.m.	PROPN
ejpam-4770	186	2	mahistrado	mahistrado	PROPN
ejpam-4770	186	3	,	,	PUNCT
ejpam-4770	186	4	h.	h.	PROPN
ejpam-4770	186	5	rara	rara	PROPN
ejpam-4770	186	6	/	/	SYM
ejpam-4770	186	7	eur	eur	PROPN
ejpam-4770	186	8	.	.	PUNCT
ejpam-4770	187	1	j.	j.	PROPN
ejpam-4770	187	2	pure	pure	PROPN
ejpam-4770	187	3	appl	appl	PROPN
ejpam-4770	187	4	.	.	PROPN
ejpam-4770	187	5	math	math	PROPN
ejpam-4770	187	6	,	,	PUNCT
ejpam-4770	187	7	16	16	NUM
ejpam-4770	187	8	(	(	PUNCT
ejpam-4770	187	9	3	3	NUM
ejpam-4770	187	10	)	)	PUNCT
ejpam-4770	187	11	(	(	PUNCT
ejpam-4770	187	12	2023	2023	NUM
ejpam-4770	187	13	)	)	PUNCT
ejpam-4770	187	14	,	,	PUNCT
ejpam-4770	187	15	1464	1464	NUM
ejpam-4770	187	16	-	-	SYM
ejpam-4770	187	17	1479	1479	NUM
ejpam-4770	187	18	1471	1471	NUM
ejpam-4770	187	19	theorem	theorem	NOUN
ejpam-4770	187	20	2	2	NUM
ejpam-4770	187	21	.	.	PUNCT
ejpam-4770	188	1	let	let	VERB
ejpam-4770	188	2	g	g	NOUN
ejpam-4770	188	3	and	and	CCONJ
ejpam-4770	188	4	h	h	NOUN
ejpam-4770	188	5	be	be	AUX
ejpam-4770	188	6	nontrivial	nontrivial	ADJ
ejpam-4770	188	7	connected	connect	VERB
ejpam-4770	188	8	graphs	graph	NOUN
ejpam-4770	188	9	with	with	ADP
ejpam-4770	188	10	γ(g	γ(g	NOUN
ejpam-4770	188	11	)	)	PUNCT
ejpam-4770	188	12	̸=	̸=	PROPN
ejpam-4770	188	13	1	1	NUM
ejpam-4770	188	14	and	and	CCONJ
ejpam-4770	188	15	γ(h	γ(h	NOUN
ejpam-4770	188	16	)	)	PUNCT
ejpam-4770	188	17	̸=	̸=	PROPN
ejpam-4770	188	18	1	1	NUM
ejpam-4770	188	19	.	.	PUNCT
ejpam-4770	189	1	a	a	DET
ejpam-4770	189	2	set	set	NOUN
ejpam-4770	189	3	s	s	NOUN
ejpam-4770	189	4	⊆	⊆	NUM
ejpam-4770	189	5	v	v	NOUN
ejpam-4770	189	6	(	(	PUNCT
ejpam-4770	189	7	g	g	PROPN
ejpam-4770	189	8	+	+	NOUN
ejpam-4770	189	9	h	h	NOUN
ejpam-4770	189	10	)	)	PUNCT
ejpam-4770	189	11	is	be	AUX
ejpam-4770	189	12	a	a	DET
ejpam-4770	189	13	1	1	NUM
ejpam-4770	189	14	-	-	PUNCT
ejpam-4770	189	15	movable	movable	ADJ
ejpam-4770	189	16	2	2	NUM
ejpam-4770	189	17	-	-	PUNCT
ejpam-4770	189	18	resolving	resolve	VERB
ejpam-4770	189	19	hop	hop	NOUN
ejpam-4770	189	20	dominating	dominating	NOUN
ejpam-4770	189	21	set	set	NOUN
ejpam-4770	189	22	of	of	ADP
ejpam-4770	189	23	g+h	g+h	PROPN
ejpam-4770	189	24	if	if	SCONJ
ejpam-4770	189	25	and	and	CCONJ
ejpam-4770	189	26	only	only	ADV
ejpam-4770	189	27	if	if	SCONJ
ejpam-4770	189	28	s	s	X
ejpam-4770	189	29	=	=	PUNCT
ejpam-4770	189	30	sg∪sh	sg∪sh	PROPN
ejpam-4770	189	31	where	where	SCONJ
ejpam-4770	189	32	sg	sg	PROPN
ejpam-4770	189	33	=	=	SYM
ejpam-4770	189	34	v	v	PROPN
ejpam-4770	189	35	(	(	PUNCT
ejpam-4770	189	36	g)∩s	g)∩s	PROPN
ejpam-4770	189	37	and	and	CCONJ
ejpam-4770	189	38	sh	sh	PROPN
ejpam-4770	189	39	=	=	SYM
ejpam-4770	189	40	v	v	PROPN
ejpam-4770	189	41	(	(	PUNCT
ejpam-4770	189	42	h)∩s	h)∩s	PROPN
ejpam-4770	189	43	are	be	AUX
ejpam-4770	189	44	1	1	NUM
ejpam-4770	189	45	-	-	PUNCT
ejpam-4770	189	46	movable	movable	ADJ
ejpam-4770	189	47	2	2	NUM
ejpam-4770	189	48	-	-	PUNCT
ejpam-4770	189	49	locating	locate	VERB
ejpam-4770	189	50	point	point	NOUN
ejpam-4770	189	51	-	-	PUNCT
ejpam-4770	189	52	wise	wise	ADJ
ejpam-4770	189	53	non	non	ADJ
ejpam-4770	189	54	-	-	ADJ
ejpam-4770	189	55	dominating	dominating	ADJ
ejpam-4770	189	56	sets	set	NOUN
ejpam-4770	189	57	of	of	ADP
ejpam-4770	189	58	g	g	PROPN
ejpam-4770	189	59	and	and	CCONJ
ejpam-4770	189	60	h	h	NOUN
ejpam-4770	189	61	,	,	PUNCT
ejpam-4770	189	62	respectively	respectively	ADV
ejpam-4770	189	63	where	where	SCONJ
ejpam-4770	189	64	sg	sg	PROPN
ejpam-4770	189	65	or	or	CCONJ
ejpam-4770	189	66	sh	sh	PROPN
ejpam-4770	189	67	is	be	AUX
ejpam-4770	189	68	a	a	DET
ejpam-4770	189	69	1	1	NUM
ejpam-4770	189	70	-	-	PUNCT
ejpam-4770	189	71	movable	movable	ADJ
ejpam-4770	189	72	(	(	PUNCT
ejpam-4770	189	73	2	2	NUM
ejpam-4770	189	74	,	,	PUNCT
ejpam-4770	189	75	2)-locating	2)-locating	NUM
ejpam-4770	189	76	point	point	NOUN
ejpam-4770	189	77	-	-	PUNCT
ejpam-4770	189	78	wise	wise	ADJ
ejpam-4770	189	79	non	non	ADJ
ejpam-4770	189	80	-	-	ADJ
ejpam-4770	189	81	dominating	dominating	ADJ
ejpam-4770	189	82	set	set	NOUN
ejpam-4770	189	83	or	or	CCONJ
ejpam-4770	189	84	sg	sg	PROPN
ejpam-4770	189	85	and	and	CCONJ
ejpam-4770	189	86	sh	sh	PROPN
ejpam-4770	189	87	are	be	AUX
ejpam-4770	189	88	1	1	NUM
ejpam-4770	189	89	-	-	PUNCT
ejpam-4770	189	90	movable	movable	ADJ
ejpam-4770	189	91	(	(	PUNCT
ejpam-4770	189	92	2	2	NUM
ejpam-4770	189	93	,	,	PUNCT
ejpam-4770	189	94	1)-locating	1)-locating	NUM
ejpam-4770	189	95	point	point	NOUN
ejpam-4770	189	96	-	-	PUNCT
ejpam-4770	189	97	wise	wise	ADJ
ejpam-4770	189	98	non	non	ADJ
ejpam-4770	189	99	-	-	ADJ
ejpam-4770	189	100	dominating	dominating	ADJ
ejpam-4770	189	101	sets	set	NOUN
ejpam-4770	189	102	.	.	PUNCT
ejpam-4770	190	1	proof	proof	NOUN
ejpam-4770	190	2	.	.	PUNCT
ejpam-4770	191	1	suppose	suppose	VERB
ejpam-4770	191	2	that	that	SCONJ
ejpam-4770	191	3	s	s	VERB
ejpam-4770	191	4	⊆	⊆	NUM
ejpam-4770	191	5	v	v	NOUN
ejpam-4770	191	6	(	(	PUNCT
ejpam-4770	191	7	g	g	PROPN
ejpam-4770	191	8	+	+	NOUN
ejpam-4770	191	9	h	h	NOUN
ejpam-4770	191	10	)	)	PUNCT
ejpam-4770	191	11	is	be	AUX
ejpam-4770	191	12	a	a	DET
ejpam-4770	191	13	1	1	NUM
ejpam-4770	191	14	-	-	PUNCT
ejpam-4770	191	15	movable	movable	ADJ
ejpam-4770	191	16	2	2	NUM
ejpam-4770	191	17	-	-	PUNCT
ejpam-4770	191	18	resolving	resolve	VERB
ejpam-4770	191	19	hop	hop	NOUN
ejpam-4770	191	20	dominating	dominating	NOUN
ejpam-4770	191	21	set	set	NOUN
ejpam-4770	191	22	of	of	ADP
ejpam-4770	191	23	g	g	PROPN
ejpam-4770	191	24	+	+	CCONJ
ejpam-4770	191	25	h.	h.	PROPN
ejpam-4770	191	26	since	since	SCONJ
ejpam-4770	191	27	s	s	PROPN
ejpam-4770	191	28	is	be	AUX
ejpam-4770	191	29	2	2	NUM
ejpam-4770	191	30	-	-	PUNCT
ejpam-4770	191	31	resolving	resolve	VERB
ejpam-4770	191	32	hop	hop	NOUN
ejpam-4770	191	33	dominating	dominating	NOUN
ejpam-4770	191	34	set	set	VERB
ejpam-4770	191	35	by	by	ADP
ejpam-4770	191	36	theorem	theorem	NOUN
ejpam-4770	191	37	1	1	NUM
ejpam-4770	191	38	,	,	PUNCT
ejpam-4770	191	39	s	s	PART
ejpam-4770	191	40	=	=	PUNCT
ejpam-4770	191	41	sg	sg	X
ejpam-4770	191	42	∪	∪	NOUN
ejpam-4770	191	43	sh	sh	PROPN
ejpam-4770	191	44	where	where	SCONJ
ejpam-4770	191	45	sg	sg	PROPN
ejpam-4770	191	46	and	and	CCONJ
ejpam-4770	191	47	sh	sh	PROPN
ejpam-4770	191	48	are	be	AUX
ejpam-4770	191	49	2	2	NUM
ejpam-4770	191	50	-	-	PUNCT
ejpam-4770	191	51	locating	locate	VERB
ejpam-4770	191	52	point	point	NOUN
ejpam-4770	191	53	-	-	PUNCT
ejpam-4770	191	54	wise	wise	ADJ
ejpam-4770	191	55	non	non	ADJ
ejpam-4770	191	56	-	-	ADJ
ejpam-4770	191	57	dominating	dominating	ADJ
ejpam-4770	191	58	sets	set	NOUN
ejpam-4770	191	59	of	of	ADP
ejpam-4770	191	60	g	g	PROPN
ejpam-4770	191	61	and	and	CCONJ
ejpam-4770	191	62	h	h	NOUN
ejpam-4770	191	63	,	,	PUNCT
ejpam-4770	191	64	respectively	respectively	ADV
ejpam-4770	191	65	where	where	SCONJ
ejpam-4770	191	66	sg	sg	PROPN
ejpam-4770	191	67	or	or	CCONJ
ejpam-4770	191	68	sh	sh	PROPN
ejpam-4770	191	69	is	be	AUX
ejpam-4770	191	70	a	a	DET
ejpam-4770	191	71	(	(	PUNCT
ejpam-4770	191	72	2	2	NUM
ejpam-4770	191	73	,	,	PUNCT
ejpam-4770	191	74	2)-locating	2)-locating	NUM
ejpam-4770	191	75	(	(	PUNCT
ejpam-4770	191	76	point	point	NOUN
ejpam-4770	191	77	-	-	PUNCT
ejpam-4770	191	78	wise	wise	ADJ
ejpam-4770	191	79	non	non	ADJ
ejpam-4770	191	80	-	-	ADJ
ejpam-4770	191	81	dominating	dominating	ADJ
ejpam-4770	191	82	)	)	PUNCT
ejpam-4770	191	83	set	set	NOUN
ejpam-4770	191	84	or	or	CCONJ
ejpam-4770	191	85	sg	sg	PROPN
ejpam-4770	191	86	and	and	CCONJ
ejpam-4770	191	87	sh	sh	PROPN
ejpam-4770	191	88	are	be	AUX
ejpam-4770	191	89	(	(	PUNCT
ejpam-4770	191	90	2	2	NUM
ejpam-4770	191	91	,	,	PUNCT
ejpam-4770	191	92	1)-locating	1)-locating	NUM
ejpam-4770	191	93	(	(	PUNCT
ejpam-4770	191	94	point	point	NOUN
ejpam-4770	191	95	-	-	PUNCT
ejpam-4770	191	96	wise	wise	ADJ
ejpam-4770	191	97	non	non	ADJ
ejpam-4770	191	98	-	-	ADJ
ejpam-4770	191	99	dominating	dominating	ADJ
ejpam-4770	191	100	)	)	PUNCT
ejpam-4770	191	101	sets	set	NOUN
ejpam-4770	191	102	.	.	PUNCT
ejpam-4770	192	1	now	now	ADV
ejpam-4770	192	2	,	,	PUNCT
ejpam-4770	192	3	let	let	VERB
ejpam-4770	192	4	p	p	PRON
ejpam-4770	192	5	∈	∈	PROPN
ejpam-4770	192	6	sg	sg	PROPN
ejpam-4770	192	7	.	.	PUNCT
ejpam-4770	193	1	then	then	ADV
ejpam-4770	193	2	p	p	PROPN
ejpam-4770	193	3	∈	∈	PROPN
ejpam-4770	193	4	s.	s.	PROPN
ejpam-4770	193	5	thus	thus	ADV
ejpam-4770	193	6	,	,	PUNCT
ejpam-4770	193	7	s\{p	s\{p	X
ejpam-4770	193	8	}	}	PUNCT
ejpam-4770	193	9	=	=	SYM
ejpam-4770	193	10	(	(	PUNCT
ejpam-4770	193	11	sg\{p	sg\{p	NOUN
ejpam-4770	193	12	}	}	PUNCT
ejpam-4770	193	13	)	)	PUNCT
ejpam-4770	193	14	∪	∪	ADP
ejpam-4770	193	15	sh	sh	PROPN
ejpam-4770	193	16	or	or	CCONJ
ejpam-4770	193	17	(	(	PUNCT
ejpam-4770	193	18	s\{p	s\{p	NOUN
ejpam-4770	193	19	}	}	PUNCT
ejpam-4770	193	20	)	)	PUNCT
ejpam-4770	193	21	∪	∪	ADP
ejpam-4770	193	22	{	{	PUNCT
ejpam-4770	193	23	z	z	NOUN
ejpam-4770	193	24	}	}	PUNCT
ejpam-4770	193	25	=	=	SYM
ejpam-4770	194	1	[	[	X
ejpam-4770	194	2	(	(	PUNCT
ejpam-4770	194	3	sg\{p	sg\{p	NOUN
ejpam-4770	194	4	}	}	PUNCT
ejpam-4770	194	5	∪	∪	ADJ
ejpam-4770	194	6	{	{	PUNCT
ejpam-4770	194	7	z	z	NOUN
ejpam-4770	194	8	}	}	PUNCT
ejpam-4770	194	9	)	)	PUNCT
ejpam-4770	194	10	]	]	PUNCT
ejpam-4770	194	11	∪	∪	ADP
ejpam-4770	194	12	sh	sh	PROPN
ejpam-4770	194	13	for	for	ADP
ejpam-4770	194	14	some	some	DET
ejpam-4770	194	15	z	z	NOUN
ejpam-4770	194	16	∈	∈	PROPN
ejpam-4770	194	17	ng(p)∩(v	ng(p)∩(v	ADP
ejpam-4770	194	18	(	(	PUNCT
ejpam-4770	194	19	g)\sg	g)\sg	PROPN
ejpam-4770	194	20	)	)	PUNCT
ejpam-4770	194	21	or	or	CCONJ
ejpam-4770	194	22	(	(	PUNCT
ejpam-4770	194	23	s\{p})∪{q	s\{p})∪{q	NOUN
ejpam-4770	194	24	}	}	PUNCT
ejpam-4770	194	25	=	=	SYM
ejpam-4770	194	26	(	(	PUNCT
ejpam-4770	194	27	sg\{p})∪(sh∪{q	sg\{p})∪(sh∪{q	NOUN
ejpam-4770	194	28	}	}	PUNCT
ejpam-4770	194	29	)	)	PUNCT
ejpam-4770	194	30	for	for	ADP
ejpam-4770	194	31	some	some	DET
ejpam-4770	194	32	q	q	PROPN
ejpam-4770	194	33	∈	∈	PROPN
ejpam-4770	194	34	v	v	NOUN
ejpam-4770	194	35	(	(	PUNCT
ejpam-4770	194	36	h)\sh	h)\sh	PROPN
ejpam-4770	194	37	is	be	AUX
ejpam-4770	194	38	a	a	DET
ejpam-4770	194	39	2	2	NUM
ejpam-4770	194	40	-	-	PUNCT
ejpam-4770	194	41	resolving	resolve	VERB
ejpam-4770	194	42	hop	hop	NOUN
ejpam-4770	194	43	dominating	dominating	NOUN
ejpam-4770	194	44	set	set	NOUN
ejpam-4770	194	45	ing+h	ing+h	PROPN
ejpam-4770	194	46	.	.	PUNCT
ejpam-4770	195	1	hence	hence	ADV
ejpam-4770	195	2	,	,	PUNCT
ejpam-4770	195	3	by	by	ADP
ejpam-4770	195	4	theorem	theorem	NOUN
ejpam-4770	195	5	1	1	NUM
ejpam-4770	195	6	,	,	PUNCT
ejpam-4770	195	7	sg\{p	sg\{p	NUM
ejpam-4770	195	8	}	}	PUNCT
ejpam-4770	195	9	or	or	CCONJ
ejpam-4770	195	10	(	(	PUNCT
ejpam-4770	195	11	sg\{p})∪{z	sg\{p})∪{z	ADV
ejpam-4770	195	12	}	}	PUNCT
ejpam-4770	195	13	is	be	AUX
ejpam-4770	195	14	a	a	DET
ejpam-4770	195	15	2	2	NUM
ejpam-4770	195	16	-	-	PUNCT
ejpam-4770	195	17	locating	locate	VERB
ejpam-4770	195	18	point	point	NOUN
ejpam-4770	195	19	-	-	PUNCT
ejpam-4770	195	20	wise	wise	ADJ
ejpam-4770	195	21	non	non	ADJ
ejpam-4770	195	22	-	-	ADJ
ejpam-4770	195	23	dominating	dominating	ADJ
ejpam-4770	195	24	set	set	NOUN
ejpam-4770	195	25	of	of	ADP
ejpam-4770	195	26	g.	g.	PROPN
ejpam-4770	195	27	this	this	PRON
ejpam-4770	195	28	shows	show	VERB
ejpam-4770	195	29	that	that	SCONJ
ejpam-4770	195	30	sg	sg	PROPN
ejpam-4770	195	31	is	be	AUX
ejpam-4770	195	32	a	a	DET
ejpam-4770	195	33	1	1	NUM
ejpam-4770	195	34	-	-	PUNCT
ejpam-4770	195	35	movable	movable	ADJ
ejpam-4770	195	36	2	2	NUM
ejpam-4770	195	37	-	-	PUNCT
ejpam-4770	195	38	locating	locate	VERB
ejpam-4770	195	39	point	point	NOUN
ejpam-4770	195	40	-	-	PUNCT
ejpam-4770	195	41	wise	wise	ADJ
ejpam-4770	195	42	non	non	ADJ
ejpam-4770	195	43	-	-	ADJ
ejpam-4770	195	44	dominating	dominating	ADJ
ejpam-4770	195	45	set	set	NOUN
ejpam-4770	195	46	of	of	ADP
ejpam-4770	195	47	g.	g.	PROPN
ejpam-4770	195	48	similarly	similarly	ADV
ejpam-4770	195	49	,	,	PUNCT
ejpam-4770	195	50	sh	sh	PROPN
ejpam-4770	195	51	is	be	AUX
ejpam-4770	195	52	a	a	DET
ejpam-4770	195	53	1	1	NUM
ejpam-4770	195	54	-	-	PUNCT
ejpam-4770	195	55	movable	movable	ADJ
ejpam-4770	195	56	2	2	NUM
ejpam-4770	195	57	-	-	PUNCT
ejpam-4770	195	58	locating	locate	VERB
ejpam-4770	195	59	point	point	NOUN
ejpam-4770	195	60	-	-	PUNCT
ejpam-4770	195	61	wise	wise	ADJ
ejpam-4770	195	62	non	non	ADJ
ejpam-4770	195	63	-	-	ADJ
ejpam-4770	195	64	dominating	dominating	ADJ
ejpam-4770	195	65	set	set	NOUN
ejpam-4770	195	66	of	of	ADP
ejpam-4770	195	67	h.	h.	PROPN
ejpam-4770	195	68	therefore	therefore	ADV
ejpam-4770	195	69	,	,	PUNCT
ejpam-4770	195	70	sg	sg	PROPN
ejpam-4770	195	71	and	and	CCONJ
ejpam-4770	195	72	sh	sh	PROPN
ejpam-4770	195	73	are	be	AUX
ejpam-4770	195	74	1	1	NUM
ejpam-4770	195	75	-	-	PUNCT
ejpam-4770	195	76	movable	movable	ADJ
ejpam-4770	195	77	2	2	NUM
ejpam-4770	195	78	-	-	PUNCT
ejpam-4770	195	79	locating	locate	VERB
ejpam-4770	195	80	point	point	NOUN
ejpam-4770	195	81	-	-	PUNCT
ejpam-4770	195	82	wise	wise	ADJ
ejpam-4770	195	83	non	non	ADJ
ejpam-4770	195	84	-	-	ADJ
ejpam-4770	195	85	dominating	dominating	ADJ
ejpam-4770	195	86	sets	set	NOUN
ejpam-4770	195	87	of	of	ADP
ejpam-4770	195	88	g	g	PROPN
ejpam-4770	195	89	and	and	CCONJ
ejpam-4770	195	90	h	h	NOUN
ejpam-4770	195	91	,	,	PUNCT
ejpam-4770	195	92	respectively	respectively	ADV
ejpam-4770	195	93	where	where	SCONJ
ejpam-4770	195	94	sg	sg	PROPN
ejpam-4770	195	95	or	or	CCONJ
ejpam-4770	195	96	sh	sh	PROPN
ejpam-4770	195	97	is	be	AUX
ejpam-4770	195	98	a	a	DET
ejpam-4770	195	99	1	1	NUM
ejpam-4770	195	100	-	-	PUNCT
ejpam-4770	195	101	movable	movable	ADJ
ejpam-4770	195	102	(	(	PUNCT
ejpam-4770	195	103	2	2	NUM
ejpam-4770	195	104	,	,	PUNCT
ejpam-4770	195	105	2)-locating	2)-locating	NUM
ejpam-4770	195	106	(	(	PUNCT
ejpam-4770	195	107	point	point	NOUN
ejpam-4770	195	108	-	-	PUNCT
ejpam-4770	195	109	wise	wise	ADJ
ejpam-4770	195	110	non	non	ADJ
ejpam-4770	195	111	-	-	ADJ
ejpam-4770	195	112	dominating	dominating	ADJ
ejpam-4770	195	113	)	)	PUNCT
ejpam-4770	195	114	set	set	NOUN
ejpam-4770	195	115	or	or	CCONJ
ejpam-4770	195	116	sg	sg	PROPN
ejpam-4770	195	117	and	and	CCONJ
ejpam-4770	195	118	sh	sh	PROPN
ejpam-4770	195	119	are	be	AUX
ejpam-4770	195	120	1	1	NUM
ejpam-4770	195	121	-	-	PUNCT
ejpam-4770	195	122	movable	movable	ADJ
ejpam-4770	195	123	(	(	PUNCT
ejpam-4770	195	124	2	2	NUM
ejpam-4770	195	125	,	,	PUNCT
ejpam-4770	195	126	1)-locating	1)-locating	NUM
ejpam-4770	195	127	(	(	PUNCT
ejpam-4770	195	128	point	point	NOUN
ejpam-4770	195	129	-	-	PUNCT
ejpam-4770	195	130	wise	wise	ADJ
ejpam-4770	195	131	non	non	ADJ
ejpam-4770	195	132	-	-	ADJ
ejpam-4770	195	133	dominating	dominating	ADJ
ejpam-4770	195	134	)	)	PUNCT
ejpam-4770	195	135	sets	set	NOUN
ejpam-4770	195	136	.	.	PUNCT
ejpam-4770	196	1	conversely	conversely	ADV
ejpam-4770	196	2	,	,	PUNCT
ejpam-4770	196	3	suppose	suppose	VERB
ejpam-4770	196	4	that	that	SCONJ
ejpam-4770	196	5	sg	sg	PROPN
ejpam-4770	196	6	and	and	CCONJ
ejpam-4770	196	7	sh	sh	INTJ
ejpam-4770	196	8	satisfy	satisfy	VERB
ejpam-4770	196	9	the	the	DET
ejpam-4770	196	10	given	give	VERB
ejpam-4770	196	11	conditions	condition	NOUN
ejpam-4770	196	12	.	.	PUNCT
ejpam-4770	197	1	then	then	ADV
ejpam-4770	197	2	by	by	ADP
ejpam-4770	197	3	theorem	theorem	NOUN
ejpam-4770	197	4	1	1	NUM
ejpam-4770	197	5	,	,	PUNCT
ejpam-4770	197	6	s	s	PART
ejpam-4770	197	7	=	=	PUNCT
ejpam-4770	197	8	sg	sg	PROPN
ejpam-4770	197	9	∪	∪	NOUN
ejpam-4770	197	10	sh	sh	PROPN
ejpam-4770	197	11	is	be	AUX
ejpam-4770	197	12	a	a	DET
ejpam-4770	197	13	2	2	NUM
ejpam-4770	197	14	-	-	PUNCT
ejpam-4770	197	15	resolving	resolve	VERB
ejpam-4770	197	16	hop	hop	NOUN
ejpam-4770	197	17	dominating	dominating	NOUN
ejpam-4770	197	18	set	set	VERB
ejpam-4770	197	19	in	in	ADP
ejpam-4770	197	20	g	g	PROPN
ejpam-4770	197	21	+	+	CCONJ
ejpam-4770	197	22	h.	h.	PROPN
ejpam-4770	197	23	let	let	VERB
ejpam-4770	197	24	p	p	PROPN
ejpam-4770	197	25	∈	∈	PROPN
ejpam-4770	197	26	s.	s.	PROPN
ejpam-4770	197	27	if	if	SCONJ
ejpam-4770	197	28	p	p	PROPN
ejpam-4770	197	29	∈	∈	PROPN
ejpam-4770	197	30	sg	sg	PROPN
ejpam-4770	197	31	,	,	PUNCT
ejpam-4770	197	32	then	then	ADV
ejpam-4770	197	33	s\p	s\p	X
ejpam-4770	197	34	=	=	PUNCT
ejpam-4770	197	35	(	(	PUNCT
ejpam-4770	197	36	sg\{p})∪sh	sg\{p})∪sh	X
ejpam-4770	197	37	or	or	CCONJ
ejpam-4770	197	38	(	(	PUNCT
ejpam-4770	197	39	s\{p})∪{w	s\{p})∪{w	PROPN
ejpam-4770	197	40	}	}	PUNCT
ejpam-4770	197	41	=	=	SYM
ejpam-4770	197	42	[	[	PUNCT
ejpam-4770	197	43	(	(	PUNCT
ejpam-4770	197	44	sg\{p})∪{w	sg\{p})∪{w	NOUN
ejpam-4770	197	45	}	}	PUNCT
ejpam-4770	197	46	]	]	PUNCT
ejpam-4770	197	47	∪sh	∪sh	NOUN
ejpam-4770	197	48	for	for	ADP
ejpam-4770	197	49	some	some	DET
ejpam-4770	197	50	w	w	NOUN
ejpam-4770	197	51	∈	∈	PROPN
ejpam-4770	197	52	ng(p)∩	ng(p)∩	X
ejpam-4770	197	53	(	(	PUNCT
ejpam-4770	197	54	v	v	X
ejpam-4770	197	55	(	(	PUNCT
ejpam-4770	197	56	g)\sg	g)\sg	PROPN
ejpam-4770	197	57	)	)	PUNCT
ejpam-4770	197	58	is	be	AUX
ejpam-4770	197	59	a	a	DET
ejpam-4770	197	60	2	2	NUM
ejpam-4770	197	61	-	-	PUNCT
ejpam-4770	197	62	resolving	resolve	VERB
ejpam-4770	197	63	hop	hop	NOUN
ejpam-4770	197	64	dominating	dominating	NOUN
ejpam-4770	197	65	set	set	VERB
ejpam-4770	197	66	in	in	ADP
ejpam-4770	197	67	g+h	g+h	PROPN
ejpam-4770	197	68	.	.	PUNCT
ejpam-4770	198	1	similarly	similarly	ADV
ejpam-4770	198	2	,	,	PUNCT
ejpam-4770	198	3	suppose	suppose	VERB
ejpam-4770	198	4	that	that	SCONJ
ejpam-4770	198	5	p	p	PROPN
ejpam-4770	198	6	∈	∈	PROPN
ejpam-4770	198	7	sh	sh	INTJ
ejpam-4770	198	8	.	.	PUNCT
ejpam-4770	199	1	then	then	ADV
ejpam-4770	199	2	s\{p	s\{p	VERB
ejpam-4770	199	3	}	}	PUNCT
ejpam-4770	199	4	=	=	SYM
ejpam-4770	199	5	(	(	PUNCT
ejpam-4770	199	6	sh\{p})∪sg	sh\{p})∪sg	PROPN
ejpam-4770	199	7	or	or	CCONJ
ejpam-4770	199	8	(	(	PUNCT
ejpam-4770	199	9	s\{p})∪{w	s\{p})∪{w	PROPN
ejpam-4770	199	10	}	}	PUNCT
ejpam-4770	199	11	=	=	SYM
ejpam-4770	199	12	[	[	PUNCT
ejpam-4770	199	13	(	(	PUNCT
ejpam-4770	199	14	sh\{p})∪{w	sh\{p})∪{w	PROPN
ejpam-4770	199	15	}	}	PUNCT
ejpam-4770	199	16	]	]	PUNCT
ejpam-4770	199	17	∪sg	∪sg	VERB
ejpam-4770	199	18	for	for	ADP
ejpam-4770	199	19	some	some	DET
ejpam-4770	199	20	w	w	PROPN
ejpam-4770	199	21	∈	∈	PROPN
ejpam-4770	199	22	nh(p	nh(p	NOUN
ejpam-4770	199	23	)	)	PUNCT
ejpam-4770	199	24	∩	∩	NOUN
ejpam-4770	199	25	(	(	PUNCT
ejpam-4770	199	26	v	v	NOUN
ejpam-4770	199	27	(	(	PUNCT
ejpam-4770	199	28	h)\sh	h)\sh	PROPN
ejpam-4770	199	29	)	)	PUNCT
ejpam-4770	199	30	is	be	AUX
ejpam-4770	199	31	a	a	DET
ejpam-4770	199	32	2	2	NUM
ejpam-4770	199	33	-	-	PUNCT
ejpam-4770	199	34	resolving	resolve	VERB
ejpam-4770	199	35	hop	hop	NOUN
ejpam-4770	199	36	dominating	dominating	NOUN
ejpam-4770	199	37	set	set	VERB
ejpam-4770	199	38	in	in	ADP
ejpam-4770	199	39	g+h	g+h	PROPN
ejpam-4770	199	40	.	.	PUNCT
ejpam-4770	200	1	therefore	therefore	ADV
ejpam-4770	200	2	,	,	PUNCT
ejpam-4770	200	3	s	s	VERB
ejpam-4770	200	4	is	be	AUX
ejpam-4770	200	5	a	a	DET
ejpam-4770	200	6	1	1	NUM
ejpam-4770	200	7	-	-	PUNCT
ejpam-4770	200	8	movable	movable	ADJ
ejpam-4770	200	9	2	2	NUM
ejpam-4770	200	10	-	-	PUNCT
ejpam-4770	200	11	resolving	resolve	VERB
ejpam-4770	200	12	hop	hop	NOUN
ejpam-4770	200	13	dominating	dominating	NOUN
ejpam-4770	200	14	set	set	VERB
ejpam-4770	200	15	in	in	ADP
ejpam-4770	200	16	g+h	g+h	PROPN
ejpam-4770	200	17	.	.	PUNCT
ejpam-4770	201	1	corollary	corollary	ADJ
ejpam-4770	201	2	2	2	NUM
ejpam-4770	201	3	.	.	PUNCT
ejpam-4770	202	1	let	let	VERB
ejpam-4770	202	2	g	g	NOUN
ejpam-4770	202	3	and	and	CCONJ
ejpam-4770	202	4	h	h	NOUN
ejpam-4770	202	5	be	be	AUX
ejpam-4770	202	6	nontrivial	nontrivial	ADJ
ejpam-4770	202	7	connected	connect	VERB
ejpam-4770	202	8	graphs	graph	NOUN
ejpam-4770	202	9	with	with	ADP
ejpam-4770	202	10	γ(g	γ(g	NOUN
ejpam-4770	202	11	)	)	PUNCT
ejpam-4770	202	12	̸=	̸=	PROPN
ejpam-4770	202	13	1	1	NUM
ejpam-4770	202	14	and	and	CCONJ
ejpam-4770	202	15	γ(h	γ(h	NOUN
ejpam-4770	202	16	)	)	PUNCT
ejpam-4770	202	17	̸=	̸=	PROPN
ejpam-4770	202	18	1	1	NUM
ejpam-4770	202	19	.	.	PUNCT
ejpam-4770	203	1	then	then	ADV
ejpam-4770	203	2	γ1m2rh(g+h	γ1m2rh(g+h	PUNCT
ejpam-4770	203	3	)	)	PUNCT
ejpam-4770	204	1	=	=	NOUN
ejpam-4770	204	2	min{mlnpnd	min{mlnpnd	NOUN
ejpam-4770	204	3	(	(	PUNCT
ejpam-4770	204	4	2,2)(g	2,2)(g	NUM
ejpam-4770	204	5	)	)	PUNCT
ejpam-4770	205	1	+	+	ADJ
ejpam-4770	205	2	mlnpnd	mlnpnd	NOUN
ejpam-4770	205	3	(	(	PUNCT
ejpam-4770	205	4	2	2	NUM
ejpam-4770	205	5	)	)	PUNCT
ejpam-4770	205	6	(	(	PUNCT
ejpam-4770	205	7	h),mlnpnd	h),mlnpnd	NOUN
ejpam-4770	205	8	(	(	PUNCT
ejpam-4770	205	9	2	2	NUM
ejpam-4770	205	10	)	)	PUNCT
ejpam-4770	205	11	(	(	PUNCT
ejpam-4770	205	12	g	g	NOUN
ejpam-4770	205	13	)	)	PUNCT
ejpam-4770	205	14	+	+	ADJ
ejpam-4770	205	15	mlnpnd	mlnpnd	NOUN
ejpam-4770	205	16	(	(	PUNCT
ejpam-4770	205	17	2,2)(h	2,2)(h	NUM
ejpam-4770	205	18	)	)	PUNCT
ejpam-4770	205	19	,	,	PUNCT
ejpam-4770	205	20	mlnpnd	mlnpnd	NOUN
ejpam-4770	205	21	(	(	PUNCT
ejpam-4770	205	22	2,1)(g	2,1)(g	NUM
ejpam-4770	205	23	)	)	PUNCT
ejpam-4770	205	24	+	+	ADJ
ejpam-4770	205	25	mlnpnd	mlnpnd	NOUN
ejpam-4770	205	26	(	(	PUNCT
ejpam-4770	205	27	2,1)(h	2,1)(h	NUM
ejpam-4770	205	28	)	)	PUNCT
ejpam-4770	205	29	}	}	PUNCT
ejpam-4770	205	30	.	.	PUNCT
ejpam-4770	206	1	a.m.	a.m.	PROPN
ejpam-4770	206	2	mahistrado	mahistrado	PROPN
ejpam-4770	206	3	,	,	PUNCT
ejpam-4770	206	4	h.	h.	PROPN
ejpam-4770	206	5	rara	rara	PROPN
ejpam-4770	206	6	/	/	SYM
ejpam-4770	206	7	eur	eur	PROPN
ejpam-4770	206	8	.	.	PUNCT
ejpam-4770	207	1	j.	j.	PROPN
ejpam-4770	207	2	pure	pure	PROPN
ejpam-4770	207	3	appl	appl	PROPN
ejpam-4770	207	4	.	.	PROPN
ejpam-4770	207	5	math	math	PROPN
ejpam-4770	207	6	,	,	PUNCT
ejpam-4770	207	7	16	16	NUM
ejpam-4770	207	8	(	(	PUNCT
ejpam-4770	207	9	3	3	NUM
ejpam-4770	207	10	)	)	PUNCT
ejpam-4770	207	11	(	(	PUNCT
ejpam-4770	207	12	2023	2023	NUM
ejpam-4770	207	13	)	)	PUNCT
ejpam-4770	207	14	,	,	PUNCT
ejpam-4770	207	15	1464	1464	NUM
ejpam-4770	207	16	-	-	SYM
ejpam-4770	207	17	1479	1479	NUM
ejpam-4770	207	18	1472	1472	NUM
ejpam-4770	207	19	5	5	NUM
ejpam-4770	207	20	.	.	PUNCT
ejpam-4770	208	1	corona	corona	NOUN
ejpam-4770	208	2	of	of	ADP
ejpam-4770	208	3	graphs	graph	NOUN
ejpam-4770	208	4	theorem	theorem	VERB
ejpam-4770	208	5	3	3	NUM
ejpam-4770	208	6	.	.	PUNCT
ejpam-4770	209	1	[	[	X
ejpam-4770	209	2	9	9	NUM
ejpam-4770	209	3	]	]	PUNCT
ejpam-4770	209	4	let	let	VERB
ejpam-4770	209	5	g	g	NOUN
ejpam-4770	209	6	and	and	CCONJ
ejpam-4770	209	7	h	h	NOUN
ejpam-4770	209	8	be	be	AUX
ejpam-4770	209	9	nontrivial	nontrivial	ADJ
ejpam-4770	209	10	connected	connected	ADJ
ejpam-4770	209	11	graphs	graph	NOUN
ejpam-4770	209	12	.	.	PUNCT
ejpam-4770	210	1	a	a	DET
ejpam-4770	210	2	set	set	NOUN
ejpam-4770	210	3	s	s	NOUN
ejpam-4770	210	4	⊆	⊆	NUM
ejpam-4770	210	5	v	v	NOUN
ejpam-4770	210	6	(	(	PUNCT
ejpam-4770	210	7	g	g	PROPN
ejpam-4770	210	8	◦	◦	NOUN
ejpam-4770	210	9	h	h	NOUN
ejpam-4770	210	10	)	)	PUNCT
ejpam-4770	210	11	is	be	AUX
ejpam-4770	210	12	a	a	DET
ejpam-4770	210	13	2	2	NUM
ejpam-4770	210	14	-	-	PUNCT
ejpam-4770	210	15	resolving	resolve	VERB
ejpam-4770	210	16	hop	hop	NOUN
ejpam-4770	210	17	dominating	dominating	NOUN
ejpam-4770	210	18	set	set	NOUN
ejpam-4770	210	19	of	of	ADP
ejpam-4770	210	20	g	g	PROPN
ejpam-4770	210	21	◦	◦	NOUN
ejpam-4770	210	22	h	h	NOUN
ejpam-4770	210	23	if	if	SCONJ
ejpam-4770	211	1	and	and	CCONJ
ejpam-4770	211	2	only	only	ADV
ejpam-4770	211	3	if	if	SCONJ
ejpam-4770	211	4	s	s	VERB
ejpam-4770	211	5	=	=	NOUN
ejpam-4770	211	6	a	a	PRON
ejpam-4770	211	7	∪	∪	ADJ
ejpam-4770	211	8			PROPN
ejpam-4770	211	9	⋃	⋃	ADJ
ejpam-4770	211	10	v∈v	v∈v	NOUN
ejpam-4770	211	11	(	(	PUNCT
ejpam-4770	211	12	g)∩ng(a	g)∩ng(a	PROPN
ejpam-4770	212	1	)	)	PUNCT
ejpam-4770	212	2	sv	sv	NOUN
ejpam-4770	213	1			PROPN
ejpam-4770	213	2	∪	∪	VERB
ejpam-4770	213	3			PROPN
ejpam-4770	213	4	⋃	⋃	PROPN
ejpam-4770	213	5	w∈v	w∈v	PROPN
ejpam-4770	213	6	(	(	PUNCT
ejpam-4770	213	7	g)\ng(a	g)\ng(a	NOUN
ejpam-4770	213	8	)	)	PUNCT
ejpam-4770	213	9	dw	dw	NOUN
ejpam-4770	213	10			PROPN
ejpam-4770	213	11	where	where	SCONJ
ejpam-4770	213	12	(	(	PUNCT
ejpam-4770	213	13	i	i	NOUN
ejpam-4770	213	14	)	)	PUNCT
ejpam-4770	213	15	a	a	DET
ejpam-4770	213	16	⊆	⊆	NUM
ejpam-4770	213	17	v	v	NOUN
ejpam-4770	213	18	(	(	PUNCT
ejpam-4770	213	19	g	g	NOUN
ejpam-4770	213	20	)	)	PUNCT
ejpam-4770	213	21	such	such	ADJ
ejpam-4770	213	22	that	that	PRON
ejpam-4770	213	23	for	for	ADP
ejpam-4770	213	24	each	each	DET
ejpam-4770	213	25	w	w	PROPN
ejpam-4770	213	26	∈	∈	PROPN
ejpam-4770	213	27	v	v	NOUN
ejpam-4770	213	28	(	(	PUNCT
ejpam-4770	213	29	g)\a	g)\a	NOUN
ejpam-4770	213	30	,	,	PUNCT
ejpam-4770	213	31	there	there	PRON
ejpam-4770	213	32	exists	exist	VERB
ejpam-4770	213	33	x	x	X
ejpam-4770	213	34	∈	∈	PROPN
ejpam-4770	213	35	a	a	PRON
ejpam-4770	213	36	with	with	ADP
ejpam-4770	213	37	dg(w	dg(w	NOUN
ejpam-4770	213	38	,	,	PUNCT
ejpam-4770	213	39	x	x	X
ejpam-4770	213	40	)	)	PUNCT
ejpam-4770	213	41	=	=	SYM
ejpam-4770	213	42	2	2	NUM
ejpam-4770	213	43	or	or	CCONJ
ejpam-4770	213	44	there	there	PRON
ejpam-4770	213	45	exists	exist	VERB
ejpam-4770	213	46	y	y	PROPN
ejpam-4770	213	47	∈	∈	PROPN
ejpam-4770	213	48	v	v	ADP
ejpam-4770	213	49	(	(	PUNCT
ejpam-4770	213	50	g	g	NOUN
ejpam-4770	213	51	)	)	PUNCT
ejpam-4770	213	52	∩ng(w	∩ng(w	PROPN
ejpam-4770	213	53	)	)	PUNCT
ejpam-4770	213	54	with	with	ADP
ejpam-4770	213	55	v	v	NUM
ejpam-4770	213	56	(	(	PUNCT
ejpam-4770	213	57	hy	hy	NOUN
ejpam-4770	213	58	)	)	PUNCT
ejpam-4770	213	59	∩	∩	PROPN
ejpam-4770	213	60	s	s	PART
ejpam-4770	213	61	̸=	̸=	PROPN
ejpam-4770	213	62	∅	∅	NOUN
ejpam-4770	213	63	;	;	PUNCT
ejpam-4770	213	64	(	(	PUNCT
ejpam-4770	213	65	ii	ii	NOUN
ejpam-4770	213	66	)	)	PUNCT
ejpam-4770	213	67	sv	sv	VERB
ejpam-4770	214	1	⊆	⊆	NUM
ejpam-4770	214	2	v	v	ADP
ejpam-4770	214	3	(	(	PUNCT
ejpam-4770	214	4	hv	hv	X
ejpam-4770	214	5	)	)	PUNCT
ejpam-4770	214	6	is	be	AUX
ejpam-4770	214	7	a	a	DET
ejpam-4770	214	8	2	2	NUM
ejpam-4770	214	9	-	-	PUNCT
ejpam-4770	214	10	locating	locate	VERB
ejpam-4770	214	11	set	set	NOUN
ejpam-4770	214	12	of	of	ADP
ejpam-4770	214	13	hv	hv	PROPN
ejpam-4770	214	14	for	for	ADP
ejpam-4770	214	15	all	all	DET
ejpam-4770	214	16	v	v	ADP
ejpam-4770	214	17	∈	∈	NUM
ejpam-4770	214	18	v	v	NOUN
ejpam-4770	214	19	(	(	PUNCT
ejpam-4770	214	20	g	g	NOUN
ejpam-4770	214	21	)	)	PUNCT
ejpam-4770	214	22	∩ng(a	∩ng(a	NOUN
ejpam-4770	214	23	)	)	PUNCT
ejpam-4770	214	24	;	;	PUNCT
ejpam-4770	214	25	and	and	CCONJ
ejpam-4770	214	26	(	(	PUNCT
ejpam-4770	214	27	iii	iii	X
ejpam-4770	214	28	)	)	PUNCT
ejpam-4770	214	29	dw	dw	NOUN
ejpam-4770	214	30	⊆	⊆	NUM
ejpam-4770	214	31	v	v	NOUN
ejpam-4770	214	32	(	(	PUNCT
ejpam-4770	214	33	hw	hw	NOUN
ejpam-4770	214	34	)	)	PUNCT
ejpam-4770	214	35	is	be	AUX
ejpam-4770	214	36	a	a	DET
ejpam-4770	214	37	2	2	NUM
ejpam-4770	214	38	-	-	PUNCT
ejpam-4770	214	39	locating	locate	VERB
ejpam-4770	214	40	point	point	NOUN
ejpam-4770	214	41	-	-	PUNCT
ejpam-4770	214	42	wise	wise	ADJ
ejpam-4770	214	43	non	non	ADJ
ejpam-4770	214	44	-	-	ADJ
ejpam-4770	214	45	dominating	dominating	ADJ
ejpam-4770	214	46	set	set	NOUN
ejpam-4770	214	47	of	of	ADP
ejpam-4770	214	48	hw	hw	PRON
ejpam-4770	214	49	for	for	ADP
ejpam-4770	214	50	all	all	PRON
ejpam-4770	214	51	w	w	PROPN
ejpam-4770	214	52	∈	∈	PROPN
ejpam-4770	214	53	v	v	NOUN
ejpam-4770	214	54	(	(	PUNCT
ejpam-4770	214	55	g)\ng(a	g)\ng(a	NOUN
ejpam-4770	214	56	)	)	PUNCT
ejpam-4770	214	57	.	.	PUNCT
ejpam-4770	215	1	theorem	theorem	ADJ
ejpam-4770	215	2	4	4	NUM
ejpam-4770	215	3	.	.	PUNCT
ejpam-4770	216	1	let	let	VERB
ejpam-4770	216	2	g	g	NOUN
ejpam-4770	216	3	and	and	CCONJ
ejpam-4770	216	4	h	h	NOUN
ejpam-4770	216	5	be	be	AUX
ejpam-4770	216	6	nontrivial	nontrivial	ADJ
ejpam-4770	216	7	connected	connected	ADJ
ejpam-4770	216	8	graphs	graph	NOUN
ejpam-4770	216	9	.	.	PUNCT
ejpam-4770	217	1	then	then	ADV
ejpam-4770	217	2	s	s	VERB
ejpam-4770	217	3	⊆	⊆	NUM
ejpam-4770	217	4	v	v	NOUN
ejpam-4770	217	5	(	(	PUNCT
ejpam-4770	217	6	g	g	PROPN
ejpam-4770	217	7	◦	◦	NOUN
ejpam-4770	217	8	h	h	NOUN
ejpam-4770	217	9	)	)	PUNCT
ejpam-4770	217	10	is	be	AUX
ejpam-4770	217	11	a	a	DET
ejpam-4770	217	12	1	1	NUM
ejpam-4770	217	13	-	-	PUNCT
ejpam-4770	217	14	movable	movable	ADJ
ejpam-4770	217	15	2	2	NUM
ejpam-4770	217	16	-	-	PUNCT
ejpam-4770	217	17	resolving	resolve	VERB
ejpam-4770	217	18	hop	hop	NOUN
ejpam-4770	217	19	dominating	dominating	NOUN
ejpam-4770	217	20	set	set	NOUN
ejpam-4770	217	21	of	of	ADP
ejpam-4770	217	22	g	g	PROPN
ejpam-4770	217	23	◦	◦	NOUN
ejpam-4770	217	24	h	h	NOUN
ejpam-4770	217	25	if	if	SCONJ
ejpam-4770	218	1	and	and	CCONJ
ejpam-4770	218	2	only	only	ADV
ejpam-4770	218	3	if	if	SCONJ
ejpam-4770	218	4	s	s	ADP
ejpam-4770	218	5	∩	∩	ADJ
ejpam-4770	218	6	v	v	X
ejpam-4770	218	7	(	(	PUNCT
ejpam-4770	218	8	hv	hv	NOUN
ejpam-4770	218	9	)	)	PUNCT
ejpam-4770	218	10	̸=	̸=	PROPN
ejpam-4770	218	11	∅	∅	NOUN
ejpam-4770	218	12	and	and	CCONJ
ejpam-4770	218	13	s	s	VERB
ejpam-4770	218	14	=	=	NOUN
ejpam-4770	218	15	a	a	PRON
ejpam-4770	218	16	∪	∪	ADJ
ejpam-4770	218	17			PROPN
ejpam-4770	218	18	⋃	⋃	ADJ
ejpam-4770	218	19	v∈v	v∈v	NOUN
ejpam-4770	218	20	(	(	PUNCT
ejpam-4770	218	21	g)∩ng(a	g)∩ng(a	PROPN
ejpam-4770	218	22	)	)	PUNCT
ejpam-4770	218	23	sv	sv	NOUN
ejpam-4770	219	1			PROPN
ejpam-4770	219	2	∪	∪	VERB
ejpam-4770	219	3			PROPN
ejpam-4770	219	4	⋃	⋃	PROPN
ejpam-4770	219	5	w∈v	w∈v	PROPN
ejpam-4770	219	6	(	(	PUNCT
ejpam-4770	219	7	g)\ng(a	g)\ng(a	NOUN
ejpam-4770	219	8	)	)	PUNCT
ejpam-4770	219	9	dw	dw	NOUN
ejpam-4770	219	10			PROPN
ejpam-4770	219	11	where	where	SCONJ
ejpam-4770	219	12	(	(	PUNCT
ejpam-4770	219	13	i	i	NOUN
ejpam-4770	219	14	)	)	PUNCT
ejpam-4770	219	15	a	a	DET
ejpam-4770	219	16	⊆	⊆	NUM
ejpam-4770	219	17	v	v	NOUN
ejpam-4770	219	18	(	(	PUNCT
ejpam-4770	219	19	g	g	NOUN
ejpam-4770	219	20	)	)	PUNCT
ejpam-4770	219	21	(	(	PUNCT
ejpam-4770	219	22	ii	ii	NOUN
ejpam-4770	219	23	)	)	PUNCT
ejpam-4770	219	24	sv	sv	VERB
ejpam-4770	220	1	⊆	⊆	NUM
ejpam-4770	220	2	v	v	ADP
ejpam-4770	220	3	(	(	PUNCT
ejpam-4770	220	4	hv	hv	X
ejpam-4770	220	5	)	)	PUNCT
ejpam-4770	220	6	is	be	AUX
ejpam-4770	220	7	a	a	DET
ejpam-4770	220	8	1	1	NUM
ejpam-4770	220	9	-	-	PUNCT
ejpam-4770	220	10	movable	movable	ADJ
ejpam-4770	220	11	2	2	NUM
ejpam-4770	220	12	-	-	PUNCT
ejpam-4770	220	13	locating	locate	VERB
ejpam-4770	220	14	set	set	NOUN
ejpam-4770	220	15	of	of	ADP
ejpam-4770	220	16	hv	hv	PROPN
ejpam-4770	220	17	for	for	ADP
ejpam-4770	220	18	all	all	DET
ejpam-4770	220	19	v	v	ADP
ejpam-4770	220	20	∈	∈	NUM
ejpam-4770	220	21	v	v	NOUN
ejpam-4770	220	22	(	(	PUNCT
ejpam-4770	220	23	g	g	NOUN
ejpam-4770	220	24	)	)	PUNCT
ejpam-4770	220	25	∩ng(a	∩ng(a	NOUN
ejpam-4770	220	26	)	)	PUNCT
ejpam-4770	220	27	.	.	PUNCT
ejpam-4770	221	1	(	(	PUNCT
ejpam-4770	221	2	iii	iii	X
ejpam-4770	221	3	)	)	PUNCT
ejpam-4770	221	4	dw	dw	NOUN
ejpam-4770	221	5	⊆	⊆	NUM
ejpam-4770	221	6	v	v	NOUN
ejpam-4770	221	7	(	(	PUNCT
ejpam-4770	221	8	hw	hw	NOUN
ejpam-4770	221	9	)	)	PUNCT
ejpam-4770	221	10	is	be	AUX
ejpam-4770	221	11	a	a	DET
ejpam-4770	221	12	1	1	NUM
ejpam-4770	221	13	-	-	PUNCT
ejpam-4770	221	14	movable	movable	ADJ
ejpam-4770	221	15	2	2	NUM
ejpam-4770	221	16	-	-	PUNCT
ejpam-4770	221	17	locating	locate	VERB
ejpam-4770	221	18	point	point	NOUN
ejpam-4770	221	19	-	-	PUNCT
ejpam-4770	221	20	wise	wise	ADJ
ejpam-4770	221	21	non	non	ADJ
ejpam-4770	221	22	-	-	ADJ
ejpam-4770	221	23	dominating	dominating	ADJ
ejpam-4770	221	24	set	set	NOUN
ejpam-4770	221	25	of	of	ADP
ejpam-4770	221	26	hw	hw	PRON
ejpam-4770	221	27	for	for	ADP
ejpam-4770	221	28	all	all	DET
ejpam-4770	221	29	w	w	PROPN
ejpam-4770	221	30	∈	∈	PROPN
ejpam-4770	221	31	v	v	NOUN
ejpam-4770	221	32	(	(	PUNCT
ejpam-4770	221	33	g)\ng(a	g)\ng(a	NOUN
ejpam-4770	221	34	)	)	PUNCT
ejpam-4770	221	35	.	.	PUNCT
ejpam-4770	222	1	proof	proof	NOUN
ejpam-4770	222	2	.	.	PUNCT
ejpam-4770	223	1	suppose	suppose	VERB
ejpam-4770	223	2	that	that	SCONJ
ejpam-4770	223	3	s	s	VERB
ejpam-4770	223	4	⊆	⊆	NUM
ejpam-4770	223	5	v	v	NOUN
ejpam-4770	223	6	(	(	PUNCT
ejpam-4770	223	7	g	g	PROPN
ejpam-4770	223	8	◦	◦	NOUN
ejpam-4770	223	9	h	h	NOUN
ejpam-4770	223	10	)	)	PUNCT
ejpam-4770	223	11	is	be	AUX
ejpam-4770	223	12	a	a	DET
ejpam-4770	223	13	1	1	NUM
ejpam-4770	223	14	-	-	PUNCT
ejpam-4770	223	15	movable	movable	ADJ
ejpam-4770	223	16	2	2	NUM
ejpam-4770	223	17	-	-	PUNCT
ejpam-4770	223	18	resolving	resolve	VERB
ejpam-4770	223	19	hop	hop	NOUN
ejpam-4770	223	20	dominating	dominating	NOUN
ejpam-4770	223	21	set	set	NOUN
ejpam-4770	223	22	of	of	ADP
ejpam-4770	223	23	g	g	PROPN
ejpam-4770	223	24	◦	◦	NOUN
ejpam-4770	223	25	h.	h.	NOUN
ejpam-4770	224	1	then	then	ADV
ejpam-4770	224	2	s	s	VERB
ejpam-4770	224	3	is	be	AUX
ejpam-4770	224	4	a	a	DET
ejpam-4770	224	5	2	2	NUM
ejpam-4770	224	6	-	-	PUNCT
ejpam-4770	224	7	resolving	resolve	VERB
ejpam-4770	224	8	hop	hop	NOUN
ejpam-4770	224	9	dominating	dominating	NOUN
ejpam-4770	224	10	set	set	NOUN
ejpam-4770	224	11	.	.	PUNCT
ejpam-4770	225	1	let	let	VERB
ejpam-4770	225	2	a	a	DET
ejpam-4770	225	3	=	=	PUNCT
ejpam-4770	225	4	s∩v	s∩v	NOUN
ejpam-4770	225	5	(	(	PUNCT
ejpam-4770	225	6	g	g	NOUN
ejpam-4770	225	7	)	)	PUNCT
ejpam-4770	225	8	and	and	CCONJ
ejpam-4770	225	9	sv	sv	X
ejpam-4770	225	10	=	=	SYM
ejpam-4770	225	11	s∩v	s∩v	PROPN
ejpam-4770	225	12	(	(	PUNCT
ejpam-4770	225	13	hv	hv	PROPN
ejpam-4770	225	14	)	)	PUNCT
ejpam-4770	225	15	for	for	ADP
ejpam-4770	225	16	all	all	DET
ejpam-4770	225	17	v	v	ADP
ejpam-4770	225	18	∈	∈	NOUN
ejpam-4770	225	19	v	v	NOUN
ejpam-4770	225	20	(	(	PUNCT
ejpam-4770	225	21	g	g	NOUN
ejpam-4770	225	22	)	)	PUNCT
ejpam-4770	225	23	∩ng(a	∩ng(a	NOUN
ejpam-4770	225	24	)	)	PUNCT
ejpam-4770	225	25	.	.	PUNCT
ejpam-4770	226	1	by	by	ADP
ejpam-4770	226	2	theorem	theorem	NOUN
ejpam-4770	226	3	3	3	NUM
ejpam-4770	226	4	,	,	PUNCT
ejpam-4770	226	5	sv	sv	PROPN
ejpam-4770	226	6	is	be	AUX
ejpam-4770	226	7	a	a	DET
ejpam-4770	226	8	2	2	NUM
ejpam-4770	226	9	-	-	PUNCT
ejpam-4770	226	10	locating	locate	VERB
ejpam-4770	226	11	set	set	NOUN
ejpam-4770	226	12	of	of	ADP
ejpam-4770	226	13	hv	hv	PROPN
ejpam-4770	226	14	.	.	PUNCT
ejpam-4770	227	1	let	let	VERB
ejpam-4770	227	2	p	p	PROPN
ejpam-4770	227	3	∈	∈	PROPN
ejpam-4770	227	4	sv	sv	INTJ
ejpam-4770	227	5	.	.	PUNCT
ejpam-4770	228	1	since	since	SCONJ
ejpam-4770	228	2	s	s	PROPN
ejpam-4770	228	3	is	be	AUX
ejpam-4770	228	4	a	a	DET
ejpam-4770	228	5	1	1	NUM
ejpam-4770	228	6	-	-	PUNCT
ejpam-4770	228	7	movable	movable	ADJ
ejpam-4770	228	8	2	2	NUM
ejpam-4770	228	9	-	-	PUNCT
ejpam-4770	228	10	resolving	resolve	VERB
ejpam-4770	228	11	hop	hop	NOUN
ejpam-4770	228	12	dominating	dominating	NOUN
ejpam-4770	228	13	set	set	NOUN
ejpam-4770	228	14	and	and	CCONJ
ejpam-4770	228	15	p	p	NOUN
ejpam-4770	228	16	∈	∈	PROPN
ejpam-4770	228	17	s	s	X
ejpam-4770	228	18	,	,	PUNCT
ejpam-4770	228	19	either	either	CCONJ
ejpam-4770	228	20	s\{p	s\{p	NOUN
ejpam-4770	228	21	}	}	PUNCT
ejpam-4770	228	22	or	or	CCONJ
ejpam-4770	228	23	(	(	PUNCT
ejpam-4770	228	24	s\{p})∪{q	s\{p})∪{q	X
ejpam-4770	228	25	}	}	PUNCT
ejpam-4770	228	26	is	be	AUX
ejpam-4770	228	27	a	a	DET
ejpam-4770	228	28	2	2	NUM
ejpam-4770	228	29	-	-	PUNCT
ejpam-4770	228	30	resolving	resolve	VERB
ejpam-4770	228	31	hop	hop	NOUN
ejpam-4770	228	32	dominating	dominating	NOUN
ejpam-4770	228	33	set	set	VERB
ejpam-4770	228	34	in	in	ADP
ejpam-4770	228	35	g	g	PROPN
ejpam-4770	228	36	◦	◦	NOUN
ejpam-4770	228	37	h	h	NOUN
ejpam-4770	228	38	for	for	ADP
ejpam-4770	228	39	some	some	DET
ejpam-4770	228	40	q	q	NOUN
ejpam-4770	228	41	∈	∈	PROPN
ejpam-4770	228	42	(	(	PUNCT
ejpam-4770	228	43	v	v	NOUN
ejpam-4770	228	44	(	(	PUNCT
ejpam-4770	228	45	g	g	PROPN
ejpam-4770	228	46	◦	◦	NOUN
ejpam-4770	228	47	h)\s	h)\s	NOUN
ejpam-4770	228	48	)	)	PUNCT
ejpam-4770	228	49	∩	∩	PROPN
ejpam-4770	228	50	ng	ng	PROPN
ejpam-4770	228	51	◦	◦	NOUN
ejpam-4770	228	52	h(p	h(p	NOUN
ejpam-4770	228	53	)	)	PUNCT
ejpam-4770	228	54	.	.	PUNCT
ejpam-4770	229	1	now	now	ADV
ejpam-4770	229	2	,	,	PUNCT
ejpam-4770	229	3	note	note	VERB
ejpam-4770	229	4	that	that	SCONJ
ejpam-4770	229	5	s\{p	s\{p	VERB
ejpam-4770	229	6	}	}	PUNCT
ejpam-4770	229	7	=	=	PUNCT
ejpam-4770	229	8	a	a	DET
ejpam-4770	229	9	∪	∪	X
ejpam-4770	229	10	(	(	PUNCT
ejpam-4770	229	11	sv\{p	sv\{p	NUM
ejpam-4770	229	12	}	}	PUNCT
ejpam-4770	229	13	)	)	PUNCT
ejpam-4770	229	14	and	and	CCONJ
ejpam-4770	229	15	(	(	PUNCT
ejpam-4770	229	16	s\{p	s\{p	NOUN
ejpam-4770	229	17	}	}	PUNCT
ejpam-4770	229	18	)	)	PUNCT
ejpam-4770	229	19	∪	∪	ADP
ejpam-4770	229	20	{	{	PUNCT
ejpam-4770	229	21	q	q	NOUN
ejpam-4770	229	22	}	}	PUNCT
ejpam-4770	229	23	=	=	PUNCT
ejpam-4770	229	24	a	a	DET
ejpam-4770	229	25	∪	∪	X
ejpam-4770	229	26	(	(	PUNCT
ejpam-4770	229	27	(	(	PUNCT
ejpam-4770	229	28	sv\{p	sv\{p	NUM
ejpam-4770	229	29	}	}	PUNCT
ejpam-4770	229	30	)	)	PUNCT
ejpam-4770	229	31	∪	∪	ADP
ejpam-4770	229	32	{	{	PUNCT
ejpam-4770	229	33	q	q	NOUN
ejpam-4770	229	34	}	}	PUNCT
ejpam-4770	229	35	)	)	PUNCT
ejpam-4770	229	36	or	or	CCONJ
ejpam-4770	229	37	(	(	PUNCT
ejpam-4770	229	38	s\{p	s\{p	NOUN
ejpam-4770	229	39	}	}	PUNCT
ejpam-4770	229	40	)	)	PUNCT
ejpam-4770	229	41	∪	∪	ADP
ejpam-4770	229	42	{	{	PUNCT
ejpam-4770	229	43	q	q	NOUN
ejpam-4770	229	44	}	}	PUNCT
ejpam-4770	229	45	=	=	SYM
ejpam-4770	229	46	(	(	PUNCT
ejpam-4770	229	47	a	a	DET
ejpam-4770	229	48	∪	∪	ADJ
ejpam-4770	229	49	{	{	PUNCT
ejpam-4770	229	50	q	q	NOUN
ejpam-4770	229	51	}	}	PUNCT
ejpam-4770	229	52	)	)	PUNCT
ejpam-4770	229	53	∪	∪	ADP
ejpam-4770	229	54	(	(	PUNCT
ejpam-4770	229	55	sv\{p	sv\{p	NUM
ejpam-4770	229	56	}	}	PUNCT
ejpam-4770	229	57	)	)	PUNCT
ejpam-4770	229	58	.	.	PUNCT
ejpam-4770	230	1	hence	hence	ADV
ejpam-4770	230	2	,	,	PUNCT
ejpam-4770	230	3	either	either	CCONJ
ejpam-4770	230	4	sv\{p	sv\{p	NUM
ejpam-4770	230	5	}	}	PUNCT
ejpam-4770	230	6	or	or	CCONJ
ejpam-4770	230	7	(	(	PUNCT
ejpam-4770	230	8	sv\{p	sv\{p	NUM
ejpam-4770	230	9	}	}	PUNCT
ejpam-4770	230	10	)	)	PUNCT
ejpam-4770	230	11	∪	∪	ADP
ejpam-4770	230	12	{	{	PUNCT
ejpam-4770	230	13	q	q	NOUN
ejpam-4770	230	14	}	}	PUNCT
ejpam-4770	230	15	for	for	ADP
ejpam-4770	230	16	some	some	PRON
ejpam-4770	230	17	q	q	NOUN
ejpam-4770	230	18	∈	∈	PROPN
ejpam-4770	230	19	(	(	PUNCT
ejpam-4770	230	20	v	v	NOUN
ejpam-4770	230	21	(	(	PUNCT
ejpam-4770	230	22	hv)\sv)∩nhv(p	hv)\sv)∩nhv(p	PROPN
ejpam-4770	230	23	)	)	PUNCT
ejpam-4770	230	24	is	be	AUX
ejpam-4770	230	25	a	a	DET
ejpam-4770	230	26	2	2	NUM
ejpam-4770	230	27	-	-	PUNCT
ejpam-4770	230	28	locating	locate	VERB
ejpam-4770	230	29	set	set	NOUN
ejpam-4770	230	30	of	of	ADP
ejpam-4770	230	31	hv	hv	PROPN
ejpam-4770	230	32	.	.	PUNCT
ejpam-4770	231	1	thus	thus	ADV
ejpam-4770	231	2	,	,	PUNCT
ejpam-4770	231	3	sv	sv	PROPN
ejpam-4770	231	4	is	be	AUX
ejpam-4770	231	5	a	a	DET
ejpam-4770	231	6	1	1	NUM
ejpam-4770	231	7	-	-	PUNCT
ejpam-4770	231	8	movable	movable	ADJ
ejpam-4770	231	9	2	2	NUM
ejpam-4770	231	10	-	-	PUNCT
ejpam-4770	231	11	locating	locate	VERB
ejpam-4770	231	12	set	set	NOUN
ejpam-4770	231	13	of	of	ADP
ejpam-4770	231	14	hv	hv	PROPN
ejpam-4770	231	15	.	.	PUNCT
ejpam-4770	232	1	finally	finally	ADV
ejpam-4770	232	2	,	,	PUNCT
ejpam-4770	232	3	suppose	suppose	VERB
ejpam-4770	232	4	w	w	ADP
ejpam-4770	232	5	∈	∈	PROPN
ejpam-4770	232	6	v	v	ADP
ejpam-4770	232	7	(	(	PUNCT
ejpam-4770	232	8	g)\ng(a	g)\ng(a	NOUN
ejpam-4770	232	9	)	)	PUNCT
ejpam-4770	232	10	.	.	PUNCT
ejpam-4770	233	1	then	then	ADV
ejpam-4770	233	2	by	by	ADP
ejpam-4770	233	3	similar	similar	ADJ
ejpam-4770	233	4	argument	argument	NOUN
ejpam-4770	233	5	,	,	PUNCT
ejpam-4770	233	6	dw	dw	PROPN
ejpam-4770	233	7	is	be	AUX
ejpam-4770	233	8	a	a	DET
ejpam-4770	233	9	1	1	NUM
ejpam-4770	233	10	-	-	PUNCT
ejpam-4770	233	11	movable	movable	ADJ
ejpam-4770	233	12	2	2	NUM
ejpam-4770	233	13	-	-	PUNCT
ejpam-4770	233	14	locating	locate	VERB
ejpam-4770	233	15	point	point	NOUN
ejpam-4770	233	16	-	-	PUNCT
ejpam-4770	233	17	wise	wise	ADJ
ejpam-4770	233	18	non	non	ADJ
ejpam-4770	233	19	-	-	ADJ
ejpam-4770	233	20	dominating	dominating	ADJ
ejpam-4770	233	21	set	set	NOUN
ejpam-4770	233	22	of	of	ADP
ejpam-4770	233	23	hw	hw	PRON
ejpam-4770	233	24	.	.	PUNCT
ejpam-4770	234	1	thus	thus	ADV
ejpam-4770	234	2	,	,	PUNCT
ejpam-4770	234	3	(	(	PUNCT
ejpam-4770	234	4	ii	ii	NOUN
ejpam-4770	234	5	)	)	PUNCT
ejpam-4770	234	6	follows	follow	VERB
ejpam-4770	234	7	.	.	PUNCT
ejpam-4770	235	1	conversely	conversely	ADV
ejpam-4770	235	2	,	,	PUNCT
ejpam-4770	235	3	suppose	suppose	VERB
ejpam-4770	235	4	that	that	SCONJ
ejpam-4770	235	5	s	s	VERB
ejpam-4770	235	6	is	be	AUX
ejpam-4770	235	7	a	a	DET
ejpam-4770	235	8	set	set	NOUN
ejpam-4770	235	9	as	as	SCONJ
ejpam-4770	235	10	described	describe	VERB
ejpam-4770	235	11	and	and	CCONJ
ejpam-4770	235	12	satisfies	satisfy	VERB
ejpam-4770	235	13	the	the	DET
ejpam-4770	235	14	given	give	VERB
ejpam-4770	235	15	conditions	condition	NOUN
ejpam-4770	235	16	.	.	PUNCT
ejpam-4770	236	1	then	then	ADV
ejpam-4770	236	2	by	by	ADP
ejpam-4770	236	3	theorem	theorem	NOUN
ejpam-4770	236	4	3	3	NUM
ejpam-4770	236	5	,	,	PUNCT
ejpam-4770	236	6	s	s	VERB
ejpam-4770	236	7	is	be	AUX
ejpam-4770	236	8	a	a	DET
ejpam-4770	236	9	2	2	NUM
ejpam-4770	236	10	-	-	PUNCT
ejpam-4770	236	11	resolving	resolve	VERB
ejpam-4770	236	12	hop	hop	NOUN
ejpam-4770	236	13	dominating	dominating	NOUN
ejpam-4770	236	14	set	set	NOUN
ejpam-4770	236	15	.	.	PUNCT
ejpam-4770	237	1	let	let	VERB
ejpam-4770	237	2	x	x	PUNCT
ejpam-4770	237	3	∈	∈	NOUN
ejpam-4770	237	4	s	s	PART
ejpam-4770	237	5	and	and	CCONJ
ejpam-4770	237	6	let	let	VERB
ejpam-4770	237	7	v	v	NUM
ejpam-4770	237	8	∈	∈	PROPN
ejpam-4770	237	9	v	v	NOUN
ejpam-4770	237	10	(	(	PUNCT
ejpam-4770	237	11	g	g	NOUN
ejpam-4770	237	12	)	)	PUNCT
ejpam-4770	237	13	a.m.	a.m.	NOUN
ejpam-4770	237	14	mahistrado	mahistrado	PROPN
ejpam-4770	237	15	,	,	PUNCT
ejpam-4770	237	16	h.	h.	PROPN
ejpam-4770	237	17	rara	rara	PROPN
ejpam-4770	237	18	/	/	SYM
ejpam-4770	237	19	eur	eur	PROPN
ejpam-4770	237	20	.	.	PUNCT
ejpam-4770	238	1	j.	j.	PROPN
ejpam-4770	238	2	pure	pure	PROPN
ejpam-4770	238	3	appl	appl	PROPN
ejpam-4770	238	4	.	.	PROPN
ejpam-4770	238	5	math	math	PROPN
ejpam-4770	238	6	,	,	PUNCT
ejpam-4770	238	7	16	16	NUM
ejpam-4770	238	8	(	(	PUNCT
ejpam-4770	238	9	3	3	NUM
ejpam-4770	238	10	)	)	PUNCT
ejpam-4770	238	11	(	(	PUNCT
ejpam-4770	238	12	2023	2023	NUM
ejpam-4770	238	13	)	)	PUNCT
ejpam-4770	238	14	,	,	PUNCT
ejpam-4770	238	15	1464	1464	NUM
ejpam-4770	238	16	-	-	SYM
ejpam-4770	238	17	1479	1479	NUM
ejpam-4770	238	18	1473	1473	NUM
ejpam-4770	238	19	such	such	ADJ
ejpam-4770	238	20	that	that	SCONJ
ejpam-4770	238	21	x	x	SYM
ejpam-4770	238	22	∈	∈	PROPN
ejpam-4770	238	23	v	v	X
ejpam-4770	238	24	(	(	PUNCT
ejpam-4770	238	25	⟨v⟩+hv	⟨v⟩+hv	NOUN
ejpam-4770	238	26	)	)	PUNCT
ejpam-4770	238	27	.	.	PUNCT
ejpam-4770	239	1	if	if	SCONJ
ejpam-4770	239	2	x	x	X
ejpam-4770	239	3	=	=	SYM
ejpam-4770	239	4	v	v	NOUN
ejpam-4770	239	5	,	,	PUNCT
ejpam-4770	239	6	then	then	ADV
ejpam-4770	239	7	x	x	PART
ejpam-4770	239	8	∈	∈	NOUN
ejpam-4770	239	9	a.	a.	NOUN
ejpam-4770	239	10	by	by	ADP
ejpam-4770	239	11	theorem	theorem	ADJ
ejpam-4770	239	12	3	3	NUM
ejpam-4770	239	13	,	,	PUNCT
ejpam-4770	239	14	s\{x	s\{x	X
ejpam-4770	239	15	}	}	PUNCT
ejpam-4770	239	16	or	or	CCONJ
ejpam-4770	239	17	(	(	PUNCT
ejpam-4770	239	18	s\{x	s\{x	PROPN
ejpam-4770	239	19	}	}	PUNCT
ejpam-4770	239	20	)	)	PUNCT
ejpam-4770	239	21	∪{y	∪{y	PROPN
ejpam-4770	239	22	}	}	PUNCT
ejpam-4770	239	23	for	for	ADP
ejpam-4770	239	24	some	some	DET
ejpam-4770	239	25	y	y	PROPN
ejpam-4770	239	26	∈	∈	PROPN
ejpam-4770	239	27	(	(	PUNCT
ejpam-4770	239	28	v	v	NOUN
ejpam-4770	239	29	(	(	PUNCT
ejpam-4770	239	30	g	g	NOUN
ejpam-4770	239	31	◦	◦	NOUN
ejpam-4770	239	32	h)\s	h)\s	NOUN
ejpam-4770	239	33	)	)	PUNCT
ejpam-4770	239	34	∩ng	∩ng	VERB
ejpam-4770	239	35	◦	◦	NOUN
ejpam-4770	239	36	h(x	h(x	PROPN
ejpam-4770	239	37	)	)	PUNCT
ejpam-4770	239	38	is	be	AUX
ejpam-4770	239	39	a	a	DET
ejpam-4770	239	40	2	2	NUM
ejpam-4770	239	41	-	-	PUNCT
ejpam-4770	239	42	resolving	resolve	VERB
ejpam-4770	239	43	hop	hop	NOUN
ejpam-4770	239	44	dominating	dominating	NOUN
ejpam-4770	239	45	set	set	NOUN
ejpam-4770	239	46	.	.	PUNCT
ejpam-4770	240	1	next	next	ADV
ejpam-4770	240	2	,	,	PUNCT
ejpam-4770	240	3	suppose	suppose	VERB
ejpam-4770	240	4	that	that	SCONJ
ejpam-4770	240	5	x	x	X
ejpam-4770	240	6	̸=	̸=	PROPN
ejpam-4770	240	7	v.	v.	CCONJ
ejpam-4770	240	8	consider	consider	VERB
ejpam-4770	240	9	the	the	DET
ejpam-4770	240	10	following	follow	VERB
ejpam-4770	240	11	cases	case	NOUN
ejpam-4770	240	12	.	.	PUNCT
ejpam-4770	241	1	case	case	NOUN
ejpam-4770	241	2	1	1	NUM
ejpam-4770	241	3	:	:	SYM
ejpam-4770	241	4	v	v	NUM
ejpam-4770	241	5	∈	∈	PROPN
ejpam-4770	241	6	v	v	NOUN
ejpam-4770	241	7	(	(	PUNCT
ejpam-4770	241	8	g	g	NOUN
ejpam-4770	241	9	)	)	PUNCT
ejpam-4770	241	10	∩ng(a	∩ng(a	NOUN
ejpam-4770	241	11	)	)	PUNCT
ejpam-4770	241	12	then	then	ADV
ejpam-4770	241	13	x	x	SYM
ejpam-4770	241	14	∈	∈	PROPN
ejpam-4770	241	15	sv	sv	NOUN
ejpam-4770	241	16	and	and	CCONJ
ejpam-4770	241	17	s\{x	s\{x	PROPN
ejpam-4770	241	18	}	}	PUNCT
ejpam-4770	241	19	=	=	SYM
ejpam-4770	241	20	(	(	PUNCT
ejpam-4770	241	21	sv\{x})∪	sv\{x})∪	X
ejpam-4770	241	22	(	(	PUNCT
ejpam-4770	241	23	⋃	⋃	ADP
ejpam-4770	241	24	u∈v	u∈v	NOUN
ejpam-4770	241	25	(	(	PUNCT
ejpam-4770	241	26	g)\{v	g)\{v	PROPN
ejpam-4770	241	27	}	}	PUNCT
ejpam-4770	241	28	du	du	PROPN
ejpam-4770	241	29	)	)	PUNCT
ejpam-4770	241	30	∪a	∪a	X
ejpam-4770	241	31	or	or	CCONJ
ejpam-4770	241	32	(	(	PUNCT
ejpam-4770	241	33	s\{x})∪	s\{x})∪	PROPN
ejpam-4770	241	34	{	{	PUNCT
ejpam-4770	241	35	y	y	PROPN
ejpam-4770	241	36	}	}	PUNCT
ejpam-4770	241	37	for	for	ADP
ejpam-4770	241	38	some	some	DET
ejpam-4770	241	39	y	y	PROPN
ejpam-4770	241	40	∈	∈	PROPN
ejpam-4770	241	41	(	(	PUNCT
ejpam-4770	241	42	v	v	NOUN
ejpam-4770	241	43	(	(	PUNCT
ejpam-4770	241	44	g	g	PROPN
ejpam-4770	241	45	◦	◦	NOUN
ejpam-4770	241	46	h)\s	h)\s	NOUN
ejpam-4770	241	47	)	)	PUNCT
ejpam-4770	241	48	∩ng	∩ng	VERB
ejpam-4770	241	49	◦	◦	NOUN
ejpam-4770	241	50	h(x	h(x	PROPN
ejpam-4770	241	51	)	)	PUNCT
ejpam-4770	241	52	is	be	AUX
ejpam-4770	241	53	a	a	DET
ejpam-4770	241	54	2	2	NUM
ejpam-4770	241	55	-	-	PUNCT
ejpam-4770	241	56	resolving	resolve	VERB
ejpam-4770	241	57	hop	hop	NOUN
ejpam-4770	241	58	dominating	dominating	NOUN
ejpam-4770	241	59	set	set	NOUN
ejpam-4770	241	60	,	,	PUNCT
ejpam-4770	241	61	by	by	ADP
ejpam-4770	241	62	theorem	theorem	NOUN
ejpam-4770	241	63	3	3	NUM
ejpam-4770	241	64	.	.	NOUN
ejpam-4770	241	65	case	case	NOUN
ejpam-4770	241	66	2	2	NUM
ejpam-4770	241	67	:	:	PUNCT
ejpam-4770	241	68	v	v	NUM
ejpam-4770	241	69	∈	∈	PROPN
ejpam-4770	241	70	v	v	NOUN
ejpam-4770	241	71	(	(	PUNCT
ejpam-4770	241	72	g)\ng(a	g)\ng(a	NOUN
ejpam-4770	241	73	)	)	PUNCT
ejpam-4770	241	74	then	then	ADV
ejpam-4770	241	75	x	x	SYM
ejpam-4770	241	76	∈	∈	PROPN
ejpam-4770	241	77	dv	dv	PROPN
ejpam-4770	241	78	and	and	CCONJ
ejpam-4770	241	79	s\{x	s\{x	PROPN
ejpam-4770	241	80	}	}	PUNCT
ejpam-4770	241	81	=	=	SYM
ejpam-4770	241	82	(	(	PUNCT
ejpam-4770	241	83	dv\{x})∪	dv\{x})∪	PROPN
ejpam-4770	241	84	(	(	PUNCT
ejpam-4770	241	85	⋃	⋃	ADP
ejpam-4770	241	86	u∈v	u∈v	NOUN
ejpam-4770	241	87	(	(	PUNCT
ejpam-4770	241	88	g)\{v	g)\{v	PROPN
ejpam-4770	241	89	}	}	PUNCT
ejpam-4770	241	90	su	su	PROPN
ejpam-4770	241	91	)	)	PUNCT
ejpam-4770	241	92	∪a	∪a	X
ejpam-4770	241	93	or	or	CCONJ
ejpam-4770	241	94	(	(	PUNCT
ejpam-4770	241	95	s\{x})∪{y	s\{x})∪{y	PROPN
ejpam-4770	241	96	}	}	PUNCT
ejpam-4770	241	97	for	for	ADP
ejpam-4770	241	98	some	some	DET
ejpam-4770	241	99	y	y	PROPN
ejpam-4770	241	100	∈	∈	PROPN
ejpam-4770	241	101	(	(	PUNCT
ejpam-4770	241	102	v	v	NOUN
ejpam-4770	241	103	(	(	PUNCT
ejpam-4770	241	104	g	g	PROPN
ejpam-4770	241	105	◦	◦	NOUN
ejpam-4770	241	106	h)\s	h)\s	NOUN
ejpam-4770	241	107	)	)	PUNCT
ejpam-4770	241	108	∩ng	∩ng	VERB
ejpam-4770	241	109	◦	◦	NOUN
ejpam-4770	241	110	h(x	h(x	PROPN
ejpam-4770	241	111	)	)	PUNCT
ejpam-4770	241	112	is	be	AUX
ejpam-4770	241	113	a	a	DET
ejpam-4770	241	114	2	2	NUM
ejpam-4770	241	115	-	-	PUNCT
ejpam-4770	241	116	resolving	resolve	VERB
ejpam-4770	241	117	hop	hop	NOUN
ejpam-4770	241	118	dominating	dominating	NOUN
ejpam-4770	241	119	set	set	NOUN
ejpam-4770	241	120	,	,	PUNCT
ejpam-4770	241	121	by	by	ADP
ejpam-4770	241	122	theorem	theorem	NOUN
ejpam-4770	241	123	3	3	NUM
ejpam-4770	241	124	.	.	PUNCT
ejpam-4770	241	125	accordingly	accordingly	ADV
ejpam-4770	241	126	,	,	PUNCT
ejpam-4770	241	127	s	s	VERB
ejpam-4770	241	128	is	be	AUX
ejpam-4770	241	129	a	a	DET
ejpam-4770	241	130	1	1	NUM
ejpam-4770	241	131	-	-	PUNCT
ejpam-4770	241	132	movable	movable	ADJ
ejpam-4770	241	133	2	2	NUM
ejpam-4770	241	134	-	-	PUNCT
ejpam-4770	241	135	resolving	resolve	VERB
ejpam-4770	241	136	hop	hop	NOUN
ejpam-4770	241	137	dominating	dominating	NOUN
ejpam-4770	241	138	set	set	VERB
ejpam-4770	241	139	in	in	ADP
ejpam-4770	241	140	g	g	PROPN
ejpam-4770	241	141	◦	◦	NOUN
ejpam-4770	241	142	h.	h.	NOUN
ejpam-4770	241	143	corollary	corollary	ADJ
ejpam-4770	241	144	3	3	X
ejpam-4770	241	145	.	.	PUNCT
ejpam-4770	242	1	let	let	VERB
ejpam-4770	242	2	g	g	NOUN
ejpam-4770	242	3	and	and	CCONJ
ejpam-4770	242	4	h	h	NOUN
ejpam-4770	242	5	be	be	AUX
ejpam-4770	242	6	nontrivial	nontrivial	ADJ
ejpam-4770	242	7	connected	connect	VERB
ejpam-4770	242	8	graphs	graph	NOUN
ejpam-4770	242	9	where	where	SCONJ
ejpam-4770	242	10	|v	|v	PROPN
ejpam-4770	242	11	(	(	PUNCT
ejpam-4770	242	12	g)|	g)|	PROPN
ejpam-4770	242	13	=	=	NOUN
ejpam-4770	242	14	n.	n.	NOUN
ejpam-4770	242	15	then	then	ADV
ejpam-4770	242	16	γ1m2rh(g	γ1m2rh(g	ADP
ejpam-4770	242	17	◦	◦	NOUN
ejpam-4770	242	18	h	h	NOUN
ejpam-4770	242	19	)	)	PUNCT
ejpam-4770	242	20	≤	≤	NOUN
ejpam-4770	242	21	min{n	min{n	NOUN
ejpam-4770	242	22	·	·	SYM
ejpam-4770	242	23	mlnpnd	mlnpnd	NOUN
ejpam-4770	242	24	2	2	NUM
ejpam-4770	242	25	(	(	PUNCT
ejpam-4770	242	26	h	h	NOUN
ejpam-4770	242	27	)	)	PUNCT
ejpam-4770	242	28	,	,	PUNCT
ejpam-4770	242	29	γt(g	γt(g	PUNCT
ejpam-4770	242	30	)	)	PUNCT
ejpam-4770	243	1	+	+	CCONJ
ejpam-4770	243	2	n	n	CCONJ
ejpam-4770	243	3	·	·	SYM
ejpam-4770	243	4	mln2(h	mln2(h	NUM
ejpam-4770	243	5	)	)	PUNCT
ejpam-4770	243	6	}	}	PUNCT
ejpam-4770	243	7	.	.	PUNCT
ejpam-4770	244	1	proof	proof	NOUN
ejpam-4770	244	2	.	.	PUNCT
ejpam-4770	245	1	let	let	VERB
ejpam-4770	245	2	s	s	PRON
ejpam-4770	245	3	⊆	⊆	NUM
ejpam-4770	245	4	v	v	NOUN
ejpam-4770	245	5	(	(	PUNCT
ejpam-4770	245	6	g	g	PROPN
ejpam-4770	245	7	◦	◦	NOUN
ejpam-4770	245	8	h	h	NOUN
ejpam-4770	245	9	)	)	PUNCT
ejpam-4770	245	10	be	be	VERB
ejpam-4770	245	11	a	a	DET
ejpam-4770	245	12	1	1	NUM
ejpam-4770	245	13	-	-	PUNCT
ejpam-4770	245	14	movable	movable	ADJ
ejpam-4770	245	15	2	2	NUM
ejpam-4770	245	16	-	-	PUNCT
ejpam-4770	245	17	resolving	resolve	VERB
ejpam-4770	245	18	hop	hop	NOUN
ejpam-4770	245	19	dominating	dominating	NOUN
ejpam-4770	245	20	set	set	NOUN
ejpam-4770	245	21	of	of	ADP
ejpam-4770	245	22	g	g	PROPN
ejpam-4770	245	23	◦	◦	PROPN
ejpam-4770	245	24	h.	h.	PROPN
ejpam-4770	245	25	then	then	ADV
ejpam-4770	245	26	s	s	VERB
ejpam-4770	245	27	∩	∩	ADJ
ejpam-4770	245	28	v	v	X
ejpam-4770	245	29	(	(	PUNCT
ejpam-4770	245	30	hv	hv	NOUN
ejpam-4770	245	31	)	)	PUNCT
ejpam-4770	245	32	̸=	̸=	PROPN
ejpam-4770	245	33	∅	∅	NOUN
ejpam-4770	245	34	and	and	CCONJ
ejpam-4770	245	35	s	s	VERB
ejpam-4770	245	36	∩	∩	ADJ
ejpam-4770	245	37	v	v	X
ejpam-4770	245	38	(	(	PUNCT
ejpam-4770	245	39	hv	hv	X
ejpam-4770	245	40	)	)	PUNCT
ejpam-4770	245	41	is	be	AUX
ejpam-4770	245	42	a	a	DET
ejpam-4770	245	43	1	1	NUM
ejpam-4770	245	44	-	-	PUNCT
ejpam-4770	245	45	movable	movable	ADJ
ejpam-4770	245	46	2	2	NUM
ejpam-4770	245	47	-	-	PUNCT
ejpam-4770	245	48	locating	locate	VERB
ejpam-4770	245	49	set	set	NOUN
ejpam-4770	245	50	for	for	ADP
ejpam-4770	245	51	each	each	DET
ejpam-4770	245	52	v	v	NUM
ejpam-4770	245	53	∈	∈	PROPN
ejpam-4770	245	54	v	v	NOUN
ejpam-4770	245	55	(	(	PUNCT
ejpam-4770	245	56	g	g	NOUN
ejpam-4770	245	57	)	)	PUNCT
ejpam-4770	245	58	and	and	CCONJ
ejpam-4770	246	1	s	s	AUX
ejpam-4770	246	2	=	=	NOUN
ejpam-4770	246	3	a	a	PRON
ejpam-4770	246	4	∪	∪	ADJ
ejpam-4770	246	5			PROPN
ejpam-4770	246	6	⋃	⋃	ADJ
ejpam-4770	246	7	v∈v	v∈v	NOUN
ejpam-4770	246	8	(	(	PUNCT
ejpam-4770	246	9	g)∩ng(a	g)∩ng(a	PROPN
ejpam-4770	246	10	)	)	PUNCT
ejpam-4770	246	11	sv	sv	NOUN
ejpam-4770	247	1			PROPN
ejpam-4770	247	2	∪	∪	VERB
ejpam-4770	247	3			PROPN
ejpam-4770	247	4	⋃	⋃	PROPN
ejpam-4770	247	5	w∈v	w∈v	PROPN
ejpam-4770	247	6	(	(	PUNCT
ejpam-4770	247	7	g)\ng(a	g)\ng(a	NOUN
ejpam-4770	247	8	)	)	PUNCT
ejpam-4770	247	9	dw	dw	NOUN
ejpam-4770	247	10			PROPN
ejpam-4770	247	11	where	where	SCONJ
ejpam-4770	247	12	a	a	DET
ejpam-4770	247	13	⊆	⊆	NUM
ejpam-4770	247	14	v	v	NOUN
ejpam-4770	247	15	(	(	PUNCT
ejpam-4770	247	16	g	g	NOUN
ejpam-4770	247	17	)	)	PUNCT
ejpam-4770	247	18	and	and	CCONJ
ejpam-4770	247	19	sv	sv	PROPN
ejpam-4770	247	20	and	and	CCONJ
ejpam-4770	247	21	dw	dw	PROPN
ejpam-4770	247	22	satisfy	satisfy	VERB
ejpam-4770	247	23	the	the	DET
ejpam-4770	247	24	given	give	VERB
ejpam-4770	247	25	properties	property	NOUN
ejpam-4770	247	26	in	in	ADP
ejpam-4770	247	27	theorem	theorem	NOUN
ejpam-4770	247	28	4	4	NUM
ejpam-4770	247	29	.	.	PUNCT
ejpam-4770	248	1	consider	consider	VERB
ejpam-4770	248	2	the	the	DET
ejpam-4770	248	3	following	follow	VERB
ejpam-4770	248	4	cases	case	NOUN
ejpam-4770	248	5	for	for	ADP
ejpam-4770	248	6	set	set	ADJ
ejpam-4770	248	7	a.	a.	NOUN
ejpam-4770	248	8	case	case	NOUN
ejpam-4770	248	9	1	1	NUM
ejpam-4770	248	10	:	:	PUNCT
ejpam-4770	248	11	a	a	DET
ejpam-4770	248	12	=	=	NOUN
ejpam-4770	248	13	∅	∅	NOUN
ejpam-4770	248	14	let	let	VERB
ejpam-4770	248	15	dw	dw	NOUN
ejpam-4770	248	16	=	=	PUNCT
ejpam-4770	248	17	s∩v	s∩v	PROPN
ejpam-4770	248	18	(	(	PUNCT
ejpam-4770	248	19	hw	hw	NOUN
ejpam-4770	248	20	)	)	PUNCT
ejpam-4770	248	21	be	be	AUX
ejpam-4770	248	22	an	an	DET
ejpam-4770	248	23	mlnpnd	mlnpnd	NOUN
ejpam-4770	248	24	2	2	NUM
ejpam-4770	248	25	-set	-set	PUNCT
ejpam-4770	248	26	of	of	ADP
ejpam-4770	248	27	hw	hw	PRON
ejpam-4770	248	28	for	for	ADP
ejpam-4770	248	29	each	each	DET
ejpam-4770	248	30	w	w	PROPN
ejpam-4770	248	31	∈	∈	PROPN
ejpam-4770	248	32	v	v	ADP
ejpam-4770	248	33	(	(	PUNCT
ejpam-4770	248	34	g	g	NOUN
ejpam-4770	248	35	)	)	PUNCT
ejpam-4770	248	36	.	.	PUNCT
ejpam-4770	249	1	thus	thus	ADV
ejpam-4770	249	2	,	,	PUNCT
ejpam-4770	249	3	s	s	VERB
ejpam-4770	249	4	=	=	PUNCT
ejpam-4770	249	5	(	(	PUNCT
ejpam-4770	249	6	⋃	⋃	ADJ
ejpam-4770	249	7	v∈v	v∈v	NOUN
ejpam-4770	249	8	(	(	PUNCT
ejpam-4770	249	9	g	g	NOUN
ejpam-4770	249	10	)	)	PUNCT
ejpam-4770	249	11	dw	dw	PROPN
ejpam-4770	249	12	)	)	PUNCT
ejpam-4770	249	13	s	s	VERB
ejpam-4770	249	14	a	a	DET
ejpam-4770	249	15	1	1	NUM
ejpam-4770	249	16	-	-	PUNCT
ejpam-4770	249	17	movable	movable	ADJ
ejpam-4770	249	18	2	2	NUM
ejpam-4770	249	19	-	-	PUNCT
ejpam-4770	249	20	resolving	resolve	VERB
ejpam-4770	249	21	hop	hop	NOUN
ejpam-4770	249	22	dominating	dominating	NOUN
ejpam-4770	249	23	set	set	NOUN
ejpam-4770	249	24	of	of	ADP
ejpam-4770	249	25	g	g	PROPN
ejpam-4770	249	26	◦	◦	NOUN
ejpam-4770	249	27	h	h	NOUN
ejpam-4770	249	28	by	by	ADP
ejpam-4770	249	29	theorem	theorem	NOUN
ejpam-4770	249	30	4	4	NUM
ejpam-4770	249	31	.	.	PUNCT
ejpam-4770	249	32	implying	imply	VERB
ejpam-4770	249	33	that	that	SCONJ
ejpam-4770	249	34	,	,	PUNCT
ejpam-4770	249	35	γ1m2rh(g	γ1m2rh(g	PRON
ejpam-4770	249	36	◦	◦	NOUN
ejpam-4770	249	37	h	h	NOUN
ejpam-4770	249	38	)	)	PUNCT
ejpam-4770	249	39	≤	≤	NUM
ejpam-4770	249	40	|s|	|s|	PROPN
ejpam-4770	249	41	=	=	SYM
ejpam-4770	249	42	|v	|v	X
ejpam-4770	249	43	(	(	PUNCT
ejpam-4770	249	44	g)||dw|	g)||dw|	PROPN
ejpam-4770	249	45	≤	≤	NOUN
ejpam-4770	249	46	n	n	CCONJ
ejpam-4770	249	47	·	·	PUNCT
ejpam-4770	249	48	(	(	PUNCT
ejpam-4770	249	49	mlnpnd	mlnpnd	NOUN
ejpam-4770	249	50	2	2	NUM
ejpam-4770	249	51	(	(	PUNCT
ejpam-4770	249	52	h	h	NOUN
ejpam-4770	249	53	)	)	PUNCT
ejpam-4770	249	54	)	)	PUNCT
ejpam-4770	249	55	.	.	PUNCT
ejpam-4770	250	1	case	case	NOUN
ejpam-4770	250	2	2	2	NUM
ejpam-4770	250	3	:	:	PUNCT
ejpam-4770	250	4	a	a	PRON
ejpam-4770	250	5	is	be	AUX
ejpam-4770	250	6	a	a	DET
ejpam-4770	250	7	γt	γt	NOUN
ejpam-4770	250	8	-	-	NOUN
ejpam-4770	250	9	set	set	NOUN
ejpam-4770	250	10	of	of	ADP
ejpam-4770	250	11	g	g	PROPN
ejpam-4770	250	12	let	let	VERB
ejpam-4770	250	13	ng(a	ng(a	PRON
ejpam-4770	250	14	)	)	PUNCT
ejpam-4770	250	15	=	=	SYM
ejpam-4770	250	16	v	v	X
ejpam-4770	250	17	(	(	PUNCT
ejpam-4770	250	18	g	g	NOUN
ejpam-4770	250	19	)	)	PUNCT
ejpam-4770	250	20	.	.	PUNCT
ejpam-4770	251	1	sv	sv	X
ejpam-4770	252	1	=	=	SYM
ejpam-4770	252	2	s	s	PROPN
ejpam-4770	252	3	∩	∩	ADJ
ejpam-4770	252	4	v	v	X
ejpam-4770	252	5	(	(	PUNCT
ejpam-4770	252	6	hv	hv	NOUN
ejpam-4770	252	7	)	)	PUNCT
ejpam-4770	252	8	be	be	VERB
ejpam-4770	252	9	an	an	DET
ejpam-4770	252	10	mln2	mln2	NOUN
ejpam-4770	252	11	-	-	PUNCT
ejpam-4770	252	12	set	set	NOUN
ejpam-4770	252	13	of	of	ADP
ejpam-4770	252	14	hv	hv	PROPN
ejpam-4770	252	15	for	for	ADP
ejpam-4770	252	16	each	each	DET
ejpam-4770	252	17	v	v	NUM
ejpam-4770	252	18	∈	∈	PROPN
ejpam-4770	252	19	v	v	NOUN
ejpam-4770	252	20	(	(	PUNCT
ejpam-4770	252	21	g	g	NOUN
ejpam-4770	252	22	)	)	PUNCT
ejpam-4770	252	23	.	.	PUNCT
ejpam-4770	253	1	thus	thus	ADV
ejpam-4770	253	2	,	,	PUNCT
ejpam-4770	253	3	s	s	VERB
ejpam-4770	253	4	=	=	PUNCT
ejpam-4770	253	5	a	a	DET
ejpam-4770	253	6	∪	∪	X
ejpam-4770	253	7	(	(	PUNCT
ejpam-4770	253	8	⋃	⋃	NOUN
ejpam-4770	253	9	v∈v	v∈v	NOUN
ejpam-4770	253	10	(	(	PUNCT
ejpam-4770	253	11	g	g	NOUN
ejpam-4770	253	12	)	)	PUNCT
ejpam-4770	253	13	sv	sv	NOUN
ejpam-4770	253	14	)	)	PUNCT
ejpam-4770	253	15	s	s	VERB
ejpam-4770	253	16	a	a	DET
ejpam-4770	253	17	1	1	NUM
ejpam-4770	253	18	-	-	PUNCT
ejpam-4770	253	19	movable	movable	ADJ
ejpam-4770	253	20	2	2	NUM
ejpam-4770	253	21	-	-	PUNCT
ejpam-4770	253	22	resolving	resolve	VERB
ejpam-4770	253	23	hop	hop	NOUN
ejpam-4770	253	24	dominating	dominating	NOUN
ejpam-4770	253	25	set	set	NOUN
ejpam-4770	253	26	of	of	ADP
ejpam-4770	253	27	g	g	PROPN
ejpam-4770	253	28	◦	◦	NOUN
ejpam-4770	253	29	h	h	NOUN
ejpam-4770	253	30	by	by	ADP
ejpam-4770	253	31	theorem	theorem	NOUN
ejpam-4770	253	32	4	4	NUM
ejpam-4770	253	33	.	.	PUNCT
ejpam-4770	253	34	implying	imply	VERB
ejpam-4770	253	35	that	that	SCONJ
ejpam-4770	253	36	,	,	PUNCT
ejpam-4770	253	37	γ1m2rh(g	γ1m2rh(g	PRON
ejpam-4770	253	38	◦	◦	NOUN
ejpam-4770	253	39	h	h	NOUN
ejpam-4770	253	40	)	)	PUNCT
ejpam-4770	253	41	≤	≤	NUM
ejpam-4770	253	42	|s|	|s|	NOUN
ejpam-4770	253	43	=	=	SYM
ejpam-4770	253	44	|a|+	|a|+	NOUN
ejpam-4770	253	45	|v	|v	X
ejpam-4770	253	46	(	(	PUNCT
ejpam-4770	253	47	g)||sv|	g)||sv|	PROPN
ejpam-4770	253	48	≤	≤	NUM
ejpam-4770	253	49	γt(g	γt(g	PUNCT
ejpam-4770	253	50	)	)	PUNCT
ejpam-4770	253	51	+	+	CCONJ
ejpam-4770	253	52	n	n	X
ejpam-4770	253	53	·	·	PUNCT
ejpam-4770	253	54	(	(	PUNCT
ejpam-4770	253	55	mln2(h	mln2(h	X
ejpam-4770	253	56	)	)	PUNCT
ejpam-4770	253	57	)	)	PUNCT
ejpam-4770	253	58	.	.	PUNCT
ejpam-4770	254	1	a.m.	a.m.	PROPN
ejpam-4770	254	2	mahistrado	mahistrado	PROPN
ejpam-4770	254	3	,	,	PUNCT
ejpam-4770	254	4	h.	h.	PROPN
ejpam-4770	254	5	rara	rara	PROPN
ejpam-4770	254	6	/	/	SYM
ejpam-4770	254	7	eur	eur	PROPN
ejpam-4770	254	8	.	.	PUNCT
ejpam-4770	255	1	j.	j.	PROPN
ejpam-4770	255	2	pure	pure	PROPN
ejpam-4770	255	3	appl	appl	PROPN
ejpam-4770	255	4	.	.	PROPN
ejpam-4770	255	5	math	math	PROPN
ejpam-4770	255	6	,	,	PUNCT
ejpam-4770	255	7	16	16	NUM
ejpam-4770	255	8	(	(	PUNCT
ejpam-4770	255	9	3	3	NUM
ejpam-4770	255	10	)	)	PUNCT
ejpam-4770	255	11	(	(	PUNCT
ejpam-4770	255	12	2023	2023	NUM
ejpam-4770	255	13	)	)	PUNCT
ejpam-4770	255	14	,	,	PUNCT
ejpam-4770	255	15	1464	1464	NUM
ejpam-4770	255	16	-	-	SYM
ejpam-4770	255	17	1479	1479	NUM
ejpam-4770	255	18	1474	1474	NUM
ejpam-4770	255	19	6	6	NUM
ejpam-4770	255	20	.	.	PUNCT
ejpam-4770	255	21	edge	edge	NOUN
ejpam-4770	255	22	corona	corona	NOUN
ejpam-4770	255	23	of	of	ADP
ejpam-4770	255	24	graphs	graph	NOUN
ejpam-4770	255	25	theorem	theorem	VERB
ejpam-4770	255	26	5	5	NUM
ejpam-4770	255	27	.	.	PUNCT
ejpam-4770	256	1	let	let	VERB
ejpam-4770	256	2	g	g	PROPN
ejpam-4770	256	3	̸=	̸=	PROPN
ejpam-4770	256	4	p2	p2	PROPN
ejpam-4770	256	5	and	and	CCONJ
ejpam-4770	256	6	h	h	NOUN
ejpam-4770	256	7	be	be	VERB
ejpam-4770	256	8	any	any	DET
ejpam-4770	256	9	nontrivial	nontrivial	ADJ
ejpam-4770	256	10	connected	connect	VERB
ejpam-4770	256	11	graphs	graph	NOUN
ejpam-4770	256	12	.	.	PUNCT
ejpam-4770	257	1	a	a	DET
ejpam-4770	257	2	set	set	NOUN
ejpam-4770	257	3	c	c	NOUN
ejpam-4770	257	4	⊆	⊆	NUM
ejpam-4770	257	5	v	v	NOUN
ejpam-4770	257	6	(	(	PUNCT
ejpam-4770	257	7	g	g	PROPN
ejpam-4770	257	8	⋄h	⋄h	PROPN
ejpam-4770	257	9	)	)	PUNCT
ejpam-4770	257	10	is	be	AUX
ejpam-4770	257	11	a	a	DET
ejpam-4770	257	12	2	2	NUM
ejpam-4770	257	13	-	-	PUNCT
ejpam-4770	257	14	resolving	resolve	VERB
ejpam-4770	257	15	hop	hop	NOUN
ejpam-4770	257	16	dominating	dominating	NOUN
ejpam-4770	257	17	set	set	NOUN
ejpam-4770	257	18	of	of	ADP
ejpam-4770	257	19	g	g	PROPN
ejpam-4770	257	20	⋄h	⋄h	X
ejpam-4770	257	21	if	if	SCONJ
ejpam-4770	258	1	and	and	CCONJ
ejpam-4770	258	2	only	only	ADV
ejpam-4770	258	3	if	if	SCONJ
ejpam-4770	258	4	c	c	X
ejpam-4770	258	5	=	=	PUNCT
ejpam-4770	258	6	a	a	DET
ejpam-4770	258	7	∪	∪	ADJ
ejpam-4770	258	8			PROPN
ejpam-4770	258	9	⋃	⋃	ADJ
ejpam-4770	258	10	uv∈e(g	uv∈e(g	NOUN
ejpam-4770	258	11	)	)	PUNCT
ejpam-4770	258	12	suv	suv	NOUN
ejpam-4770	258	13			PROPN
ejpam-4770	259	1	where	where	SCONJ
ejpam-4770	259	2	(	(	PUNCT
ejpam-4770	259	3	i	i	NOUN
ejpam-4770	259	4	)	)	PUNCT
ejpam-4770	259	5	a	a	DET
ejpam-4770	259	6	⊆	⊆	NUM
ejpam-4770	259	7	v	v	NOUN
ejpam-4770	259	8	(	(	PUNCT
ejpam-4770	259	9	g	g	NOUN
ejpam-4770	259	10	)	)	PUNCT
ejpam-4770	259	11	;	;	PUNCT
ejpam-4770	259	12	(	(	PUNCT
ejpam-4770	259	13	ii	ii	X
ejpam-4770	259	14	)	)	PUNCT
ejpam-4770	259	15	suv	suv	PROPN
ejpam-4770	259	16	⊆	⊆	NUM
ejpam-4770	259	17	v	v	NOUN
ejpam-4770	259	18	(	(	PUNCT
ejpam-4770	259	19	huv	huv	PROPN
ejpam-4770	259	20	)	)	PUNCT
ejpam-4770	259	21	is	be	AUX
ejpam-4770	259	22	a	a	DET
ejpam-4770	259	23	2	2	NUM
ejpam-4770	259	24	-	-	PUNCT
ejpam-4770	259	25	locating	locate	VERB
ejpam-4770	259	26	set	set	NOUN
ejpam-4770	259	27	of	of	ADP
ejpam-4770	259	28	huv	huv	PROPN
ejpam-4770	259	29	for	for	ADP
ejpam-4770	259	30	all	all	DET
ejpam-4770	259	31	uv	uv	PROPN
ejpam-4770	259	32	∈	∈	PROPN
ejpam-4770	259	33	e(g	e(g	PROPN
ejpam-4770	259	34	)	)	PUNCT
ejpam-4770	259	35	or	or	CCONJ
ejpam-4770	259	36	if	if	SCONJ
ejpam-4770	259	37	uv	uv	NOUN
ejpam-4770	259	38	is	be	AUX
ejpam-4770	259	39	a	a	DET
ejpam-4770	259	40	pendant	pendant	ADJ
ejpam-4770	259	41	edge	edge	NOUN
ejpam-4770	259	42	,	,	PUNCT
ejpam-4770	259	43	then	then	ADV
ejpam-4770	259	44	suv	suv	PROPN
ejpam-4770	259	45	is	be	AUX
ejpam-4770	259	46	a	a	DET
ejpam-4770	259	47	(	(	PUNCT
ejpam-4770	259	48	2	2	NUM
ejpam-4770	259	49	,	,	PUNCT
ejpam-4770	259	50	1)-locating	1)-locating	NUM
ejpam-4770	259	51	set	set	NOUN
ejpam-4770	259	52	of	of	ADP
ejpam-4770	259	53	huv	huv	PROPN
ejpam-4770	259	54	whenever	whenever	SCONJ
ejpam-4770	259	55	l(⟨{u	l(⟨{u	PROPN
ejpam-4770	259	56	,	,	PUNCT
ejpam-4770	259	57	v}⟩	v}⟩	PROPN
ejpam-4770	259	58	)	)	PUNCT
ejpam-4770	259	59	⊆	⊆	NUM
ejpam-4770	259	60	a	a	PRON
ejpam-4770	259	61	and	and	CCONJ
ejpam-4770	259	62	suv	suv	PROPN
ejpam-4770	259	63	is	be	AUX
ejpam-4770	259	64	a	a	DET
ejpam-4770	259	65	(	(	PUNCT
ejpam-4770	259	66	2	2	NUM
ejpam-4770	259	67	,	,	PUNCT
ejpam-4770	259	68	2)-locating	2)-locating	NUM
ejpam-4770	259	69	set	set	NOUN
ejpam-4770	259	70	of	of	ADP
ejpam-4770	259	71	huv	huv	PROPN
ejpam-4770	259	72	otherwise	otherwise	ADV
ejpam-4770	259	73	.	.	PUNCT
ejpam-4770	260	1	theorem	theorem	VERB
ejpam-4770	260	2	6	6	NUM
ejpam-4770	260	3	.	.	PUNCT
ejpam-4770	261	1	let	let	VERB
ejpam-4770	261	2	g	g	NOUN
ejpam-4770	262	1	and	and	CCONJ
ejpam-4770	262	2	h	h	NOUN
ejpam-4770	262	3	be	be	VERB
ejpam-4770	262	4	any	any	DET
ejpam-4770	262	5	nontrivial	nontrivial	ADJ
ejpam-4770	262	6	connected	connect	VERB
ejpam-4770	262	7	graphs	graph	NOUN
ejpam-4770	262	8	where	where	SCONJ
ejpam-4770	262	9	γ(g	γ(g	NOUN
ejpam-4770	262	10	)	)	PUNCT
ejpam-4770	262	11	̸=	̸=	PROPN
ejpam-4770	262	12	1	1	NUM
ejpam-4770	262	13	and	and	CCONJ
ejpam-4770	262	14	∆(h	∆(h	NOUN
ejpam-4770	262	15	)	)	PUNCT
ejpam-4770	262	16	≤	≤	NOUN
ejpam-4770	262	17	|v	|v	X
ejpam-4770	262	18	(	(	PUNCT
ejpam-4770	262	19	h)|	h)|	NOUN
ejpam-4770	262	20	−	−	PROPN
ejpam-4770	262	21	3	3	NUM
ejpam-4770	262	22	.	.	PUNCT
ejpam-4770	263	1	a	a	DET
ejpam-4770	263	2	set	set	NOUN
ejpam-4770	263	3	c	c	NOUN
ejpam-4770	263	4	⊆	⊆	NUM
ejpam-4770	263	5	v	v	NOUN
ejpam-4770	263	6	(	(	PUNCT
ejpam-4770	263	7	g	g	PROPN
ejpam-4770	263	8	⋄h	⋄h	PROPN
ejpam-4770	263	9	)	)	PUNCT
ejpam-4770	263	10	is	be	AUX
ejpam-4770	263	11	a	a	DET
ejpam-4770	263	12	1	1	NUM
ejpam-4770	263	13	-	-	PUNCT
ejpam-4770	263	14	movable	movable	ADJ
ejpam-4770	263	15	2	2	NUM
ejpam-4770	263	16	-	-	PUNCT
ejpam-4770	263	17	resolving	resolve	VERB
ejpam-4770	263	18	hop	hop	NOUN
ejpam-4770	263	19	dominating	dominating	NOUN
ejpam-4770	263	20	set	set	NOUN
ejpam-4770	263	21	of	of	ADP
ejpam-4770	263	22	g	g	PROPN
ejpam-4770	263	23	⋄h	⋄h	X
ejpam-4770	263	24	if	if	SCONJ
ejpam-4770	264	1	and	and	CCONJ
ejpam-4770	264	2	only	only	ADV
ejpam-4770	264	3	if	if	SCONJ
ejpam-4770	264	4	c	c	X
ejpam-4770	264	5	=	=	PUNCT
ejpam-4770	264	6	a	a	DET
ejpam-4770	264	7	∪	∪	ADJ
ejpam-4770	264	8			PROPN
ejpam-4770	264	9	⋃	⋃	ADJ
ejpam-4770	264	10	uv∈e(g	uv∈e(g	NOUN
ejpam-4770	264	11	)	)	PUNCT
ejpam-4770	264	12	suv	suv	NOUN
ejpam-4770	264	13			PROPN
ejpam-4770	265	1	where	where	SCONJ
ejpam-4770	265	2	(	(	PUNCT
ejpam-4770	265	3	i	i	NOUN
ejpam-4770	265	4	)	)	PUNCT
ejpam-4770	265	5	a	a	DET
ejpam-4770	265	6	⊆	⊆	NUM
ejpam-4770	265	7	v	v	NOUN
ejpam-4770	265	8	(	(	PUNCT
ejpam-4770	265	9	g	g	NOUN
ejpam-4770	265	10	)	)	PUNCT
ejpam-4770	265	11	;	;	PUNCT
ejpam-4770	265	12	(	(	PUNCT
ejpam-4770	265	13	ii	ii	X
ejpam-4770	265	14	)	)	PUNCT
ejpam-4770	265	15	suv	suv	PROPN
ejpam-4770	265	16	⊆	⊆	NUM
ejpam-4770	265	17	v	v	NOUN
ejpam-4770	265	18	(	(	PUNCT
ejpam-4770	265	19	huv	huv	PROPN
ejpam-4770	265	20	)	)	PUNCT
ejpam-4770	265	21	is	be	AUX
ejpam-4770	265	22	a	a	DET
ejpam-4770	265	23	1	1	NUM
ejpam-4770	265	24	-	-	PUNCT
ejpam-4770	265	25	movable	movable	ADJ
ejpam-4770	265	26	2	2	NUM
ejpam-4770	265	27	-	-	PUNCT
ejpam-4770	265	28	locating	locate	VERB
ejpam-4770	265	29	set	set	NOUN
ejpam-4770	265	30	of	of	ADP
ejpam-4770	265	31	huv	huv	PROPN
ejpam-4770	265	32	for	for	ADP
ejpam-4770	265	33	all	all	DET
ejpam-4770	265	34	uv	uv	PROPN
ejpam-4770	265	35	∈	∈	PROPN
ejpam-4770	265	36	e(g	e(g	PROPN
ejpam-4770	265	37	)	)	PUNCT
ejpam-4770	265	38	or	or	CCONJ
ejpam-4770	265	39	if	if	SCONJ
ejpam-4770	265	40	uv	uv	NOUN
ejpam-4770	265	41	is	be	AUX
ejpam-4770	265	42	a	a	DET
ejpam-4770	265	43	pendant	pendant	ADJ
ejpam-4770	265	44	edge	edge	NOUN
ejpam-4770	265	45	,	,	PUNCT
ejpam-4770	265	46	then	then	ADV
ejpam-4770	265	47	suv	suv	PROPN
ejpam-4770	265	48	is	be	AUX
ejpam-4770	265	49	a	a	DET
ejpam-4770	265	50	1	1	NUM
ejpam-4770	265	51	-	-	PUNCT
ejpam-4770	265	52	movable	movable	ADJ
ejpam-4770	265	53	(	(	PUNCT
ejpam-4770	265	54	2	2	NUM
ejpam-4770	265	55	,	,	PUNCT
ejpam-4770	265	56	1)-locating	1)-locating	NUM
ejpam-4770	265	57	set	set	NOUN
ejpam-4770	265	58	of	of	ADP
ejpam-4770	265	59	huv	huv	PROPN
ejpam-4770	265	60	whenever	whenever	SCONJ
ejpam-4770	265	61	l(⟨{u	l(⟨{u	PROPN
ejpam-4770	265	62	,	,	PUNCT
ejpam-4770	265	63	v}⟩	v}⟩	PROPN
ejpam-4770	265	64	)	)	PUNCT
ejpam-4770	265	65	⊆	⊆	NUM
ejpam-4770	265	66	a	a	PRON
ejpam-4770	265	67	and	and	CCONJ
ejpam-4770	265	68	suv	suv	PROPN
ejpam-4770	265	69	is	be	AUX
ejpam-4770	265	70	a	a	DET
ejpam-4770	265	71	1	1	NUM
ejpam-4770	265	72	-	-	PUNCT
ejpam-4770	265	73	movable	movable	ADJ
ejpam-4770	265	74	(	(	PUNCT
ejpam-4770	265	75	2	2	NUM
ejpam-4770	265	76	,	,	PUNCT
ejpam-4770	265	77	2)-locating	2)-locating	NUM
ejpam-4770	265	78	set	set	NOUN
ejpam-4770	265	79	of	of	ADP
ejpam-4770	265	80	huv	huv	PROPN
ejpam-4770	265	81	otherwise	otherwise	ADV
ejpam-4770	265	82	.	.	PUNCT
ejpam-4770	266	1	proof	proof	NOUN
ejpam-4770	266	2	.	.	PUNCT
ejpam-4770	267	1	suppose	suppose	VERB
ejpam-4770	267	2	that	that	SCONJ
ejpam-4770	267	3	c	c	PROPN
ejpam-4770	267	4	⊆	⊆	NUM
ejpam-4770	267	5	v	v	NOUN
ejpam-4770	267	6	(	(	PUNCT
ejpam-4770	267	7	g	g	PROPN
ejpam-4770	267	8	⋄	⋄	PROPN
ejpam-4770	267	9	h	h	NOUN
ejpam-4770	267	10	)	)	PUNCT
ejpam-4770	267	11	is	be	AUX
ejpam-4770	267	12	a	a	DET
ejpam-4770	267	13	1	1	NUM
ejpam-4770	267	14	-	-	PUNCT
ejpam-4770	267	15	movable	movable	ADJ
ejpam-4770	267	16	2	2	NUM
ejpam-4770	267	17	-	-	PUNCT
ejpam-4770	267	18	resolving	resolve	VERB
ejpam-4770	267	19	hop	hop	NOUN
ejpam-4770	267	20	dominating	dominating	NOUN
ejpam-4770	267	21	set	set	NOUN
ejpam-4770	267	22	of	of	ADP
ejpam-4770	267	23	g	g	PROPN
ejpam-4770	267	24	⋄	⋄	PROPN
ejpam-4770	267	25	h.	h.	NOUN
ejpam-4770	268	1	then	then	ADV
ejpam-4770	268	2	c	c	PROPN
ejpam-4770	268	3	is	be	AUX
ejpam-4770	268	4	a	a	DET
ejpam-4770	268	5	2	2	NUM
ejpam-4770	268	6	-	-	PUNCT
ejpam-4770	268	7	resolving	resolve	VERB
ejpam-4770	268	8	hop	hop	NOUN
ejpam-4770	268	9	dominating	dominating	NOUN
ejpam-4770	268	10	set	set	NOUN
ejpam-4770	268	11	.	.	PUNCT
ejpam-4770	269	1	let	let	VERB
ejpam-4770	269	2	a	a	DET
ejpam-4770	269	3	=	=	SYM
ejpam-4770	269	4	c	c	NOUN
ejpam-4770	269	5	∩	∩	X
ejpam-4770	269	6	v	v	X
ejpam-4770	269	7	(	(	PUNCT
ejpam-4770	269	8	g	g	NOUN
ejpam-4770	269	9	)	)	PUNCT
ejpam-4770	269	10	and	and	CCONJ
ejpam-4770	269	11	suv	suv	PROPN
ejpam-4770	269	12	=	=	PROPN
ejpam-4770	269	13	c	c	PROPN
ejpam-4770	269	14	∩	∩	X
ejpam-4770	269	15	v	v	X
ejpam-4770	269	16	(	(	PUNCT
ejpam-4770	269	17	huv	huv	PROPN
ejpam-4770	269	18	)	)	PUNCT
ejpam-4770	269	19	for	for	ADP
ejpam-4770	269	20	all	all	DET
ejpam-4770	269	21	uv	uv	PROPN
ejpam-4770	269	22	∈	∈	PROPN
ejpam-4770	269	23	e(g	e(g	PROPN
ejpam-4770	269	24	)	)	PUNCT
ejpam-4770	269	25	.	.	PUNCT
ejpam-4770	270	1	then	then	ADV
ejpam-4770	270	2	c	c	X
ejpam-4770	270	3	=	=	PUNCT
ejpam-4770	270	4	a	a	DET
ejpam-4770	270	5	∪	∪	X
ejpam-4770	270	6	(	(	PUNCT
ejpam-4770	270	7	⋃	⋃	NOUN
ejpam-4770	270	8	uv∈e(g	uv∈e(g	NOUN
ejpam-4770	270	9	)	)	PUNCT
ejpam-4770	270	10	suv	suv	PROPN
ejpam-4770	270	11	)	)	PUNCT
ejpam-4770	270	12	where	where	SCONJ
ejpam-4770	270	13	a	a	DET
ejpam-4770	270	14	⊆	⊆	NUM
ejpam-4770	270	15	v	v	NOUN
ejpam-4770	270	16	(	(	PUNCT
ejpam-4770	270	17	g	g	NOUN
ejpam-4770	270	18	)	)	PUNCT
ejpam-4770	270	19	and	and	CCONJ
ejpam-4770	270	20	suv	suv	PROPN
ejpam-4770	270	21	⊆	⊆	NUM
ejpam-4770	270	22	v	v	NOUN
ejpam-4770	270	23	(	(	PUNCT
ejpam-4770	270	24	huv	huv	PROPN
ejpam-4770	270	25	)	)	PUNCT
ejpam-4770	270	26	for	for	ADP
ejpam-4770	270	27	all	all	DET
ejpam-4770	270	28	uv	uv	PROPN
ejpam-4770	270	29	∈	∈	PROPN
ejpam-4770	270	30	e(g	e(g	PROPN
ejpam-4770	270	31	)	)	PUNCT
ejpam-4770	270	32	.	.	PUNCT
ejpam-4770	271	1	by	by	ADP
ejpam-4770	271	2	theorem	theorem	NOUN
ejpam-4770	271	3	5	5	NUM
ejpam-4770	271	4	,	,	PUNCT
ejpam-4770	271	5	suv	suv	PROPN
ejpam-4770	271	6	is	be	AUX
ejpam-4770	271	7	a	a	DET
ejpam-4770	271	8	2	2	NUM
ejpam-4770	271	9	-	-	PUNCT
ejpam-4770	271	10	locating	locate	VERB
ejpam-4770	271	11	set	set	NOUN
ejpam-4770	271	12	of	of	ADP
ejpam-4770	271	13	huv	huv	PROPN
ejpam-4770	271	14	for	for	ADP
ejpam-4770	271	15	all	all	DET
ejpam-4770	271	16	uv	uv	PROPN
ejpam-4770	271	17	∈	∈	PROPN
ejpam-4770	271	18	e(g	e(g	PROPN
ejpam-4770	271	19	)	)	PUNCT
ejpam-4770	271	20	.	.	PUNCT
ejpam-4770	272	1	let	let	VERB
ejpam-4770	272	2	p	p	PROPN
ejpam-4770	272	3	∈	∈	PROPN
ejpam-4770	272	4	suv	suv	PROPN
ejpam-4770	272	5	.	.	PUNCT
ejpam-4770	273	1	since	since	SCONJ
ejpam-4770	273	2	c	c	PROPN
ejpam-4770	273	3	is	be	AUX
ejpam-4770	273	4	a	a	DET
ejpam-4770	273	5	1	1	NUM
ejpam-4770	273	6	-	-	PUNCT
ejpam-4770	273	7	movable	movable	ADJ
ejpam-4770	273	8	2	2	NUM
ejpam-4770	273	9	-	-	PUNCT
ejpam-4770	273	10	resolving	resolve	VERB
ejpam-4770	273	11	hop	hop	NOUN
ejpam-4770	273	12	dominating	dominating	NOUN
ejpam-4770	273	13	set	set	NOUN
ejpam-4770	273	14	and	and	CCONJ
ejpam-4770	273	15	p	p	NOUN
ejpam-4770	273	16	∈	∈	PROPN
ejpam-4770	273	17	c	c	NOUN
ejpam-4770	273	18	,	,	PUNCT
ejpam-4770	273	19	either	either	CCONJ
ejpam-4770	273	20	c\{p	c\{p	NOUN
ejpam-4770	273	21	}	}	PUNCT
ejpam-4770	273	22	or	or	CCONJ
ejpam-4770	273	23	(	(	PUNCT
ejpam-4770	273	24	c\{p	c\{p	NOUN
ejpam-4770	273	25	}	}	PUNCT
ejpam-4770	273	26	)	)	PUNCT
ejpam-4770	273	27	∪	∪	ADP
ejpam-4770	273	28	{	{	PUNCT
ejpam-4770	273	29	q	q	NOUN
ejpam-4770	273	30	}	}	PUNCT
ejpam-4770	273	31	is	be	AUX
ejpam-4770	273	32	a	a	DET
ejpam-4770	273	33	2	2	NUM
ejpam-4770	273	34	-	-	PUNCT
ejpam-4770	273	35	resolving	resolve	VERB
ejpam-4770	273	36	hop	hop	NOUN
ejpam-4770	273	37	dominating	dominating	NOUN
ejpam-4770	273	38	set	set	NOUN
ejpam-4770	273	39	of	of	ADP
ejpam-4770	273	40	g	g	PROPN
ejpam-4770	273	41	⋄	⋄	PROPN
ejpam-4770	273	42	h	h	NOUN
ejpam-4770	273	43	for	for	ADP
ejpam-4770	273	44	some	some	DET
ejpam-4770	273	45	q	q	NOUN
ejpam-4770	273	46	∈	∈	PROPN
ejpam-4770	273	47	(	(	PUNCT
ejpam-4770	273	48	v	v	NOUN
ejpam-4770	273	49	(	(	PUNCT
ejpam-4770	273	50	g	g	PROPN
ejpam-4770	273	51	⋄	⋄	PROPN
ejpam-4770	273	52	h)\c	h)\c	NOUN
ejpam-4770	273	53	)	)	PUNCT
ejpam-4770	273	54	∩	∩	NOUN
ejpam-4770	273	55	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4770	273	56	)	)	PUNCT
ejpam-4770	273	57	.	.	PUNCT
ejpam-4770	274	1	now	now	ADV
ejpam-4770	274	2	,	,	PUNCT
ejpam-4770	274	3	note	note	VERB
ejpam-4770	274	4	that	that	SCONJ
ejpam-4770	274	5	c\{p	c\{p	VERB
ejpam-4770	274	6	}	}	PUNCT
ejpam-4770	274	7	=	=	PUNCT
ejpam-4770	274	8	a	a	DET
ejpam-4770	274	9	∪	∪	ADJ
ejpam-4770	274	10	(	(	PUNCT
ejpam-4770	274	11	suv\{p	suv\{p	NUM
ejpam-4770	274	12	}	}	PUNCT
ejpam-4770	274	13	)	)	PUNCT
ejpam-4770	274	14	and	and	CCONJ
ejpam-4770	274	15	(	(	PUNCT
ejpam-4770	274	16	c\{p})∪	c\{p})∪	X
ejpam-4770	274	17	{	{	PUNCT
ejpam-4770	274	18	q	q	NOUN
ejpam-4770	274	19	}	}	PUNCT
ejpam-4770	274	20	=	=	SYM
ejpam-4770	274	21	a∪	a∪	X
ejpam-4770	274	22	(	(	PUNCT
ejpam-4770	274	23	(	(	PUNCT
ejpam-4770	274	24	suv\{p})∪	suv\{p})∪	X
ejpam-4770	274	25	{	{	PUNCT
ejpam-4770	274	26	q	q	NOUN
ejpam-4770	274	27	}	}	PUNCT
ejpam-4770	274	28	)	)	PUNCT
ejpam-4770	274	29	or	or	CCONJ
ejpam-4770	274	30	(	(	PUNCT
ejpam-4770	274	31	c\{p})∪	c\{p})∪	X
ejpam-4770	274	32	{	{	PUNCT
ejpam-4770	274	33	q	q	NOUN
ejpam-4770	274	34	}	}	PUNCT
ejpam-4770	274	35	=	=	SYM
ejpam-4770	274	36	(	(	PUNCT
ejpam-4770	274	37	a∪	a∪	X
ejpam-4770	274	38	{	{	PUNCT
ejpam-4770	274	39	q})∪	q})∪	PROPN
ejpam-4770	274	40	(	(	PUNCT
ejpam-4770	274	41	suv\{p	suv\{p	NUM
ejpam-4770	274	42	}	}	PUNCT
ejpam-4770	274	43	)	)	PUNCT
ejpam-4770	274	44	.	.	PUNCT
ejpam-4770	275	1	hence	hence	ADV
ejpam-4770	275	2	,	,	PUNCT
ejpam-4770	275	3	either	either	CCONJ
ejpam-4770	275	4	suv\{p	suv\{p	NOUN
ejpam-4770	275	5	}	}	PUNCT
ejpam-4770	275	6	or	or	CCONJ
ejpam-4770	275	7	(	(	PUNCT
ejpam-4770	275	8	suv\{p	suv\{p	NUM
ejpam-4770	275	9	}	}	PUNCT
ejpam-4770	275	10	)	)	PUNCT
ejpam-4770	275	11	∪	∪	ADP
ejpam-4770	275	12	{	{	PUNCT
ejpam-4770	275	13	q	q	NOUN
ejpam-4770	275	14	}	}	PUNCT
ejpam-4770	275	15	for	for	ADP
ejpam-4770	275	16	some	some	DET
ejpam-4770	275	17	q	q	NOUN
ejpam-4770	275	18	∈	∈	PROPN
ejpam-4770	275	19	(	(	PUNCT
ejpam-4770	275	20	v	v	NOUN
ejpam-4770	275	21	(	(	PUNCT
ejpam-4770	275	22	huv)\suv	huv)\suv	PROPN
ejpam-4770	275	23	)	)	PUNCT
ejpam-4770	275	24	∩	∩	PROPN
ejpam-4770	275	25	nhuv(p	nhuv(p	PROPN
ejpam-4770	275	26	)	)	PUNCT
ejpam-4770	275	27	is	be	AUX
ejpam-4770	275	28	a	a	DET
ejpam-4770	275	29	2	2	NUM
ejpam-4770	275	30	-	-	PUNCT
ejpam-4770	275	31	locating	locate	VERB
ejpam-4770	275	32	set	set	NOUN
ejpam-4770	275	33	of	of	ADP
ejpam-4770	275	34	huv	huv	PROPN
ejpam-4770	275	35	.	.	PUNCT
ejpam-4770	276	1	thus	thus	ADV
ejpam-4770	276	2	,	,	PUNCT
ejpam-4770	276	3	suv	suv	PROPN
ejpam-4770	276	4	is	be	AUX
ejpam-4770	276	5	a	a	DET
ejpam-4770	276	6	1	1	NUM
ejpam-4770	276	7	-	-	PUNCT
ejpam-4770	276	8	movable	movable	ADJ
ejpam-4770	276	9	2	2	NUM
ejpam-4770	276	10	-	-	PUNCT
ejpam-4770	276	11	locating	locate	VERB
ejpam-4770	276	12	set	set	NOUN
ejpam-4770	276	13	of	of	ADP
ejpam-4770	276	14	huv	huv	PROPN
ejpam-4770	276	15	.	.	PUNCT
ejpam-4770	277	1	next	next	ADV
ejpam-4770	277	2	,	,	PUNCT
ejpam-4770	277	3	suppose	suppose	VERB
ejpam-4770	277	4	that	that	SCONJ
ejpam-4770	277	5	uv	uv	NOUN
ejpam-4770	277	6	is	be	AUX
ejpam-4770	277	7	a	a	DET
ejpam-4770	277	8	pendant	pendant	ADJ
ejpam-4770	277	9	edge	edge	NOUN
ejpam-4770	277	10	and	and	CCONJ
ejpam-4770	277	11	suppose	suppose	VERB
ejpam-4770	277	12	u	u	PRON
ejpam-4770	277	13	is	be	AUX
ejpam-4770	277	14	an	an	DET
ejpam-4770	277	15	end	end	NOUN
ejpam-4770	277	16	-	-	PUNCT
ejpam-4770	277	17	vertex	vertex	NOUN
ejpam-4770	277	18	where	where	SCONJ
ejpam-4770	277	19	u	u	PROPN
ejpam-4770	277	20	∈	∈	PROPN
ejpam-4770	277	21	c.	c.	PROPN
ejpam-4770	277	22	since	since	SCONJ
ejpam-4770	277	23	suv	suv	PROPN
ejpam-4770	277	24	=	=	PROPN
ejpam-4770	277	25	c	c	PROPN
ejpam-4770	277	26	∩	∩	X
ejpam-4770	277	27	v	v	X
ejpam-4770	277	28	(	(	PUNCT
ejpam-4770	277	29	huv	huv	PROPN
ejpam-4770	277	30	)	)	PUNCT
ejpam-4770	277	31	⊆	⊆	NUM
ejpam-4770	277	32	c	c	NOUN
ejpam-4770	277	33	and	and	CCONJ
ejpam-4770	277	34	c	c	PROPN
ejpam-4770	277	35	is	be	AUX
ejpam-4770	277	36	a	a	DET
ejpam-4770	277	37	1	1	NUM
ejpam-4770	277	38	-	-	PUNCT
ejpam-4770	277	39	movable	movable	ADJ
ejpam-4770	277	40	2	2	NUM
ejpam-4770	277	41	-	-	PUNCT
ejpam-4770	277	42	resolving	resolving	NOUN
ejpam-4770	277	43	set	set	NOUN
ejpam-4770	277	44	it	it	PRON
ejpam-4770	277	45	follows	follow	VERB
ejpam-4770	277	46	by	by	ADP
ejpam-4770	277	47	theorem	theorem	NOUN
ejpam-4770	277	48	5	5	NUM
ejpam-4770	277	49	,	,	PUNCT
ejpam-4770	277	50	suv	suv	PROPN
ejpam-4770	277	51	is	be	AUX
ejpam-4770	277	52	a	a	DET
ejpam-4770	277	53	1movable	1movable	NUM
ejpam-4770	277	54	(	(	PUNCT
ejpam-4770	277	55	2	2	NUM
ejpam-4770	277	56	,	,	PUNCT
ejpam-4770	277	57	1)locating	1)locating	NUM
ejpam-4770	277	58	set	set	NOUN
ejpam-4770	277	59	of	of	ADP
ejpam-4770	277	60	huv	huv	PROPN
ejpam-4770	277	61	whenever	whenever	SCONJ
ejpam-4770	277	62	l(⟨{u	l(⟨{u	PROPN
ejpam-4770	277	63	,	,	PUNCT
ejpam-4770	277	64	v}⟩	v}⟩	PROPN
ejpam-4770	277	65	)	)	PUNCT
ejpam-4770	277	66	⊆	⊆	NUM
ejpam-4770	277	67	a	a	PRON
ejpam-4770	277	68	and	and	CCONJ
ejpam-4770	277	69	suv	suv	PROPN
ejpam-4770	277	70	is	be	AUX
ejpam-4770	277	71	a	a	DET
ejpam-4770	277	72	1	1	NUM
ejpam-4770	277	73	-	-	PUNCT
ejpam-4770	277	74	movable	movable	ADJ
ejpam-4770	277	75	(	(	PUNCT
ejpam-4770	277	76	2	2	NUM
ejpam-4770	277	77	,	,	PUNCT
ejpam-4770	277	78	2)-locating	2)-locating	NUM
ejpam-4770	277	79	set	set	NOUN
ejpam-4770	277	80	of	of	ADP
ejpam-4770	277	81	a.m.	a.m.	PROPN
ejpam-4770	277	82	mahistrado	mahistrado	PROPN
ejpam-4770	277	83	,	,	PUNCT
ejpam-4770	277	84	h.	h.	PROPN
ejpam-4770	277	85	rara	rara	PROPN
ejpam-4770	277	86	/	/	SYM
ejpam-4770	277	87	eur	eur	PROPN
ejpam-4770	277	88	.	.	PUNCT
ejpam-4770	278	1	j.	j.	PROPN
ejpam-4770	278	2	pure	pure	PROPN
ejpam-4770	278	3	appl	appl	PROPN
ejpam-4770	278	4	.	.	PROPN
ejpam-4770	278	5	math	math	PROPN
ejpam-4770	278	6	,	,	PUNCT
ejpam-4770	278	7	16	16	NUM
ejpam-4770	278	8	(	(	PUNCT
ejpam-4770	278	9	3	3	NUM
ejpam-4770	278	10	)	)	PUNCT
ejpam-4770	278	11	(	(	PUNCT
ejpam-4770	278	12	2023	2023	NUM
ejpam-4770	278	13	)	)	PUNCT
ejpam-4770	278	14	,	,	PUNCT
ejpam-4770	278	15	1464	1464	NUM
ejpam-4770	278	16	-	-	SYM
ejpam-4770	278	17	1479	1479	NUM
ejpam-4770	278	18	1475	1475	NUM
ejpam-4770	278	19	huv	huv	PROPN
ejpam-4770	278	20	otherwise	otherwise	ADV
ejpam-4770	278	21	.	.	PUNCT
ejpam-4770	279	1	thus	thus	ADV
ejpam-4770	279	2	,	,	PUNCT
ejpam-4770	279	3	(	(	PUNCT
ejpam-4770	279	4	ii	ii	NOUN
ejpam-4770	279	5	)	)	PUNCT
ejpam-4770	279	6	holds	hold	VERB
ejpam-4770	279	7	.	.	PUNCT
ejpam-4770	280	1	conversely	conversely	ADV
ejpam-4770	280	2	,	,	PUNCT
ejpam-4770	280	3	suppose	suppose	VERB
ejpam-4770	280	4	that	that	SCONJ
ejpam-4770	280	5	c	c	PROPN
ejpam-4770	280	6	is	be	AUX
ejpam-4770	280	7	a	a	DET
ejpam-4770	280	8	set	set	NOUN
ejpam-4770	280	9	as	as	SCONJ
ejpam-4770	280	10	described	describe	VERB
ejpam-4770	280	11	and	and	CCONJ
ejpam-4770	280	12	satisfies	satisfy	VERB
ejpam-4770	280	13	the	the	DET
ejpam-4770	280	14	given	give	VERB
ejpam-4770	280	15	conditions	condition	NOUN
ejpam-4770	280	16	.	.	PUNCT
ejpam-4770	281	1	by	by	ADP
ejpam-4770	281	2	theorem	theorem	NOUN
ejpam-4770	281	3	5	5	NUM
ejpam-4770	281	4	,	,	PUNCT
ejpam-4770	281	5	c	c	PROPN
ejpam-4770	281	6	is	be	AUX
ejpam-4770	281	7	2	2	NUM
ejpam-4770	281	8	-	-	PUNCT
ejpam-4770	281	9	resolving	resolve	VERB
ejpam-4770	281	10	hop	hop	NOUN
ejpam-4770	281	11	dominating	dominating	NOUN
ejpam-4770	281	12	set	set	NOUN
ejpam-4770	281	13	of	of	ADP
ejpam-4770	281	14	g	g	PROPN
ejpam-4770	281	15	⋄	⋄	PROPN
ejpam-4770	281	16	h.	h.	PROPN
ejpam-4770	281	17	let	let	VERB
ejpam-4770	281	18	p	p	PROPN
ejpam-4770	281	19	∈	∈	PROPN
ejpam-4770	281	20	c.	c.	NOUN
ejpam-4770	281	21	if	if	SCONJ
ejpam-4770	281	22	p	p	PROPN
ejpam-4770	281	23	∈	∈	PROPN
ejpam-4770	281	24	suv	suv	NOUN
ejpam-4770	281	25	,	,	PUNCT
ejpam-4770	281	26	then	then	ADV
ejpam-4770	281	27	by	by	ADP
ejpam-4770	281	28	assumption	assumption	NOUN
ejpam-4770	281	29	and	and	CCONJ
ejpam-4770	281	30	theorem	theorem	VERB
ejpam-4770	281	31	5	5	NUM
ejpam-4770	281	32	,	,	PUNCT
ejpam-4770	281	33	either	either	CCONJ
ejpam-4770	281	34	c\{p	c\{p	NOUN
ejpam-4770	281	35	}	}	PUNCT
ejpam-4770	281	36	=	=	PUNCT
ejpam-4770	281	37	a	a	DET
ejpam-4770	281	38	∪	∪	ADJ
ejpam-4770	281	39	(	(	PUNCT
ejpam-4770	281	40	suv\{p	suv\{p	NUM
ejpam-4770	281	41	}	}	PUNCT
ejpam-4770	281	42	)	)	PUNCT
ejpam-4770	281	43	or	or	CCONJ
ejpam-4770	281	44	(	(	PUNCT
ejpam-4770	281	45	c\{p	c\{p	NOUN
ejpam-4770	281	46	}	}	PUNCT
ejpam-4770	281	47	)	)	PUNCT
ejpam-4770	281	48	∪	∪	ADP
ejpam-4770	281	49	{	{	PUNCT
ejpam-4770	281	50	q	q	NOUN
ejpam-4770	281	51	}	}	PUNCT
ejpam-4770	281	52	=	=	PUNCT
ejpam-4770	281	53	a	a	DET
ejpam-4770	281	54	∪	∪	X
ejpam-4770	281	55	(	(	PUNCT
ejpam-4770	281	56	(	(	PUNCT
ejpam-4770	281	57	suv\{p	suv\{p	NUM
ejpam-4770	281	58	}	}	PUNCT
ejpam-4770	281	59	)	)	PUNCT
ejpam-4770	281	60	∪	∪	ADP
ejpam-4770	281	61	{	{	PUNCT
ejpam-4770	281	62	q	q	NOUN
ejpam-4770	281	63	}	}	PUNCT
ejpam-4770	281	64	)	)	PUNCT
ejpam-4770	281	65	is	be	AUX
ejpam-4770	281	66	a	a	DET
ejpam-4770	281	67	2	2	NUM
ejpam-4770	281	68	-	-	PUNCT
ejpam-4770	281	69	resolving	resolve	VERB
ejpam-4770	281	70	hop	hop	NOUN
ejpam-4770	281	71	dominating	dominating	NOUN
ejpam-4770	281	72	set	set	NOUN
ejpam-4770	281	73	of	of	ADP
ejpam-4770	281	74	g	g	PROPN
ejpam-4770	281	75	⋄h	⋄h	NOUN
ejpam-4770	281	76	for	for	ADP
ejpam-4770	281	77	some	some	DET
ejpam-4770	281	78	q	q	NOUN
ejpam-4770	281	79	∈	∈	PROPN
ejpam-4770	281	80	(	(	PUNCT
ejpam-4770	281	81	v	v	NOUN
ejpam-4770	281	82	(	(	PUNCT
ejpam-4770	281	83	g	g	PROPN
ejpam-4770	281	84	⋄	⋄	PROPN
ejpam-4770	281	85	h)\c)∩ng⋄h(p	h)\c)∩ng⋄h(p	PROPN
ejpam-4770	281	86	)	)	PUNCT
ejpam-4770	281	87	.	.	PUNCT
ejpam-4770	282	1	therefore	therefore	ADV
ejpam-4770	282	2	,	,	PUNCT
ejpam-4770	282	3	c	c	PROPN
ejpam-4770	282	4	is	be	AUX
ejpam-4770	282	5	a	a	DET
ejpam-4770	282	6	1	1	NUM
ejpam-4770	282	7	-	-	PUNCT
ejpam-4770	282	8	movable	movable	ADJ
ejpam-4770	282	9	2	2	NUM
ejpam-4770	282	10	-	-	PUNCT
ejpam-4770	282	11	resolving	resolve	VERB
ejpam-4770	282	12	hop	hop	NOUN
ejpam-4770	282	13	dominating	dominating	NOUN
ejpam-4770	282	14	set	set	VERB
ejpam-4770	282	15	ofg⋄h	ofg⋄h	PROPN
ejpam-4770	282	16	.	.	PUNCT
ejpam-4770	283	1	corollary	corollary	ADJ
ejpam-4770	283	2	4	4	NUM
ejpam-4770	283	3	.	.	PUNCT
ejpam-4770	284	1	let	let	VERB
ejpam-4770	284	2	γ(g	γ(g	PRON
ejpam-4770	284	3	)	)	PUNCT
ejpam-4770	285	1	̸=	̸=	PROPN
ejpam-4770	285	2	1	1	NUM
ejpam-4770	285	3	and	and	CCONJ
ejpam-4770	285	4	h	h	DET
ejpam-4770	285	5	a	a	DET
ejpam-4770	285	6	nontrivial	nontrivial	ADJ
ejpam-4770	285	7	connected	connect	VERB
ejpam-4770	285	8	graph	graph	NOUN
ejpam-4770	285	9	with	with	ADP
ejpam-4770	285	10	|e(g)|	|e(g)|	PROPN
ejpam-4770	285	11	=	=	PROPN
ejpam-4770	285	12	p.	p.	NOUN
ejpam-4770	285	13	then	then	ADV
ejpam-4770	285	14	the	the	DET
ejpam-4770	285	15	following	follow	VERB
ejpam-4770	285	16	statements	statement	NOUN
ejpam-4770	285	17	hold	hold	VERB
ejpam-4770	285	18	.	.	PUNCT
ejpam-4770	286	1	(	(	PUNCT
ejpam-4770	286	2	i	i	NOUN
ejpam-4770	286	3	)	)	PUNCT
ejpam-4770	286	4	if	if	SCONJ
ejpam-4770	286	5	g	g	PROPN
ejpam-4770	286	6	is	be	AUX
ejpam-4770	286	7	a	a	DET
ejpam-4770	286	8	graph	graph	NOUN
ejpam-4770	286	9	with	with	ADP
ejpam-4770	286	10	no	no	DET
ejpam-4770	286	11	pendant	pendant	ADJ
ejpam-4770	286	12	edges	edge	NOUN
ejpam-4770	286	13	,	,	PUNCT
ejpam-4770	286	14	then	then	ADV
ejpam-4770	286	15	γ1m2rh(g	γ1m2rh(g	PROPN
ejpam-4770	286	16	⋄h	⋄h	PROPN
ejpam-4770	286	17	)	)	PUNCT
ejpam-4770	287	1	=	=	SYM
ejpam-4770	287	2	p	p	X
ejpam-4770	287	3	·	·	X
ejpam-4770	287	4	mln2(h	mln2(h	X
ejpam-4770	287	5	)	)	PUNCT
ejpam-4770	287	6	.	.	PUNCT
ejpam-4770	288	1	(	(	PUNCT
ejpam-4770	288	2	ii	ii	NOUN
ejpam-4770	288	3	)	)	PUNCT
ejpam-4770	288	4	if	if	SCONJ
ejpam-4770	288	5	g	g	PROPN
ejpam-4770	288	6	is	be	AUX
ejpam-4770	288	7	a	a	DET
ejpam-4770	288	8	graph	graph	NOUN
ejpam-4770	288	9	with	with	ADP
ejpam-4770	288	10	k	k	PROPN
ejpam-4770	288	11	≥	≥	NUM
ejpam-4770	288	12	1	1	NUM
ejpam-4770	288	13	pendant	pendant	ADJ
ejpam-4770	288	14	edges	edge	NOUN
ejpam-4770	288	15	,	,	PUNCT
ejpam-4770	288	16	then	then	ADV
ejpam-4770	288	17	γ1m2rh(g	γ1m2rh(g	PROPN
ejpam-4770	288	18	⋄h	⋄h	PROPN
ejpam-4770	288	19	)	)	PUNCT
ejpam-4770	289	1	=	=	NOUN
ejpam-4770	289	2	min	min	NOUN
ejpam-4770	289	3	{	{	PUNCT
ejpam-4770	289	4	(	(	PUNCT
ejpam-4770	289	5	p−	p−	NOUN
ejpam-4770	289	6	k	k	NOUN
ejpam-4770	289	7	)	)	PUNCT
ejpam-4770	289	8	mln2(h	mln2(h	X
ejpam-4770	289	9	)	)	PUNCT
ejpam-4770	289	10	+	+	CCONJ
ejpam-4770	289	11	k	k	X
ejpam-4770	289	12	·	·	PUNCT
ejpam-4770	289	13	mln(2,1)(h	mln(2,1)(h	PROPN
ejpam-4770	289	14	)	)	PUNCT
ejpam-4770	289	15	+	+	SYM
ejpam-4770	290	1	k	k	NOUN
ejpam-4770	290	2	,	,	PUNCT
ejpam-4770	290	3	(	(	PUNCT
ejpam-4770	290	4	p−	p−	NOUN
ejpam-4770	290	5	k	k	NOUN
ejpam-4770	290	6	)	)	PUNCT
ejpam-4770	290	7	mln2(h	mln2(h	X
ejpam-4770	290	8	)	)	PUNCT
ejpam-4770	290	9	+	+	CCONJ
ejpam-4770	290	10	k	k	PROPN
ejpam-4770	290	11	·	·	PUNCT
ejpam-4770	290	12	mln(2,2)(h	mln(2,2)(h	PROPN
ejpam-4770	290	13	)	)	PUNCT
ejpam-4770	290	14	}	}	PUNCT
ejpam-4770	290	15	and	and	CCONJ
ejpam-4770	290	16	γ1m2rh(g	γ1m2rh(g	DET
ejpam-4770	290	17	⋄h	⋄h	PROPN
ejpam-4770	290	18	)	)	PUNCT
ejpam-4770	290	19	=	=	PRON
ejpam-4770	291	1	(	(	PUNCT
ejpam-4770	291	2	p−	p−	NOUN
ejpam-4770	291	3	k	k	NOUN
ejpam-4770	291	4	)	)	PUNCT
ejpam-4770	291	5	mln2(h	mln2(h	X
ejpam-4770	291	6	)	)	PUNCT
ejpam-4770	292	1	+	+	CCONJ
ejpam-4770	292	2	k	k	PROPN
ejpam-4770	292	3	·	·	PUNCT
ejpam-4770	292	4	mln(2,2)(h	mln(2,2)(h	PROPN
ejpam-4770	292	5	)	)	PUNCT
ejpam-4770	292	6	whenever	whenever	SCONJ
ejpam-4770	292	7	mln(2,2)(h	mln(2,2)(h	PROPN
ejpam-4770	292	8	)	)	PUNCT
ejpam-4770	292	9	=	=	SYM
ejpam-4770	292	10	mln(2,1)(h	mln(2,1)(h	PROPN
ejpam-4770	292	11	)	)	PUNCT
ejpam-4770	292	12	.	.	PUNCT
ejpam-4770	293	1	7	7	X
ejpam-4770	293	2	.	.	NUM
ejpam-4770	293	3	lexicographic	lexicographic	ADJ
ejpam-4770	293	4	product	product	NOUN
ejpam-4770	293	5	of	of	ADP
ejpam-4770	293	6	graphs	graph	NOUN
ejpam-4770	293	7	theorem	theorem	VERB
ejpam-4770	293	8	7	7	NUM
ejpam-4770	293	9	.	.	PUNCT
ejpam-4770	294	1	[	[	X
ejpam-4770	294	2	9	9	NUM
ejpam-4770	294	3	]	]	PUNCT
ejpam-4770	294	4	let	let	VERB
ejpam-4770	294	5	g	g	NOUN
ejpam-4770	294	6	and	and	CCONJ
ejpam-4770	294	7	h	h	NOUN
ejpam-4770	294	8	be	be	AUX
ejpam-4770	294	9	nontrivial	nontrivial	ADJ
ejpam-4770	294	10	connected	connected	ADJ
ejpam-4770	294	11	graphs	graph	NOUN
ejpam-4770	294	12	.	.	PUNCT
ejpam-4770	295	1	then	then	ADV
ejpam-4770	295	2	w	w	NOUN
ejpam-4770	295	3	=	=	PUNCT
ejpam-4770	295	4	⋃	⋃	PROPN
ejpam-4770	295	5	x∈s	x∈s	NOUN
ejpam-4770	296	1	[	[	X
ejpam-4770	296	2	{	{	PUNCT
ejpam-4770	296	3	x	x	NOUN
ejpam-4770	296	4	}	}	PUNCT
ejpam-4770	296	5	×	×	PROPN
ejpam-4770	296	6	tx	tx	PROPN
ejpam-4770	296	7	]	]	X
ejpam-4770	296	8	,	,	PUNCT
ejpam-4770	296	9	where	where	SCONJ
ejpam-4770	296	10	s	s	VERB
ejpam-4770	296	11	⊆	⊆	NUM
ejpam-4770	296	12	v	v	NOUN
ejpam-4770	296	13	(	(	PUNCT
ejpam-4770	296	14	g	g	NOUN
ejpam-4770	296	15	)	)	PUNCT
ejpam-4770	296	16	and	and	CCONJ
ejpam-4770	296	17	tx	tx	VERB
ejpam-4770	296	18	⊆	⊆	NUM
ejpam-4770	296	19	v	v	NOUN
ejpam-4770	296	20	(	(	PUNCT
ejpam-4770	296	21	h	h	NOUN
ejpam-4770	296	22	)	)	PUNCT
ejpam-4770	296	23	for	for	ADP
ejpam-4770	296	24	each	each	DET
ejpam-4770	296	25	x	x	SYM
ejpam-4770	296	26	∈	∈	PROPN
ejpam-4770	296	27	s	s	NOUN
ejpam-4770	296	28	,	,	PUNCT
ejpam-4770	296	29	is	be	AUX
ejpam-4770	296	30	a	a	DET
ejpam-4770	296	31	2	2	NUM
ejpam-4770	296	32	-	-	PUNCT
ejpam-4770	296	33	resolving	resolve	VERB
ejpam-4770	296	34	hop	hop	NOUN
ejpam-4770	296	35	dominating	dominating	NOUN
ejpam-4770	296	36	set	set	VERB
ejpam-4770	296	37	in	in	ADP
ejpam-4770	296	38	g[h	g[h	PROPN
ejpam-4770	296	39	]	]	PUNCT
ejpam-4770	296	40	if	if	SCONJ
ejpam-4770	296	41	and	and	CCONJ
ejpam-4770	296	42	only	only	ADV
ejpam-4770	296	43	if	if	SCONJ
ejpam-4770	296	44	(	(	PUNCT
ejpam-4770	296	45	i	i	NOUN
ejpam-4770	296	46	)	)	PUNCT
ejpam-4770	296	47	s	s	PART
ejpam-4770	296	48	=	=	SYM
ejpam-4770	296	49	v	v	NOUN
ejpam-4770	296	50	(	(	PUNCT
ejpam-4770	296	51	g	g	NOUN
ejpam-4770	296	52	)	)	PUNCT
ejpam-4770	296	53	;	;	PUNCT
ejpam-4770	296	54	(	(	PUNCT
ejpam-4770	296	55	ii	ii	NOUN
ejpam-4770	296	56	)	)	PUNCT
ejpam-4770	296	57	tx	tx	PROPN
ejpam-4770	296	58	is	be	AUX
ejpam-4770	296	59	a	a	DET
ejpam-4770	296	60	2	2	NUM
ejpam-4770	296	61	-	-	PUNCT
ejpam-4770	296	62	locating	locate	VERB
ejpam-4770	296	63	set	set	NOUN
ejpam-4770	296	64	in	in	ADP
ejpam-4770	296	65	h	h	NOUN
ejpam-4770	296	66	for	for	ADP
ejpam-4770	296	67	every	every	DET
ejpam-4770	296	68	x	x	SYM
ejpam-4770	296	69	∈	∈	PROPN
ejpam-4770	296	70	v	v	ADP
ejpam-4770	296	71	(	(	PUNCT
ejpam-4770	296	72	g	g	NOUN
ejpam-4770	296	73	)	)	PUNCT
ejpam-4770	296	74	;	;	PUNCT
ejpam-4770	296	75	(	(	PUNCT
ejpam-4770	296	76	iii	iii	X
ejpam-4770	296	77	)	)	PUNCT
ejpam-4770	296	78	tx	tx	NOUN
ejpam-4770	297	1	or	or	CCONJ
ejpam-4770	297	2	ty	ty	INTJ
ejpam-4770	297	3	is	be	AUX
ejpam-4770	297	4	a	a	DET
ejpam-4770	297	5	(	(	PUNCT
ejpam-4770	297	6	2	2	NUM
ejpam-4770	297	7	,	,	PUNCT
ejpam-4770	297	8	1)-locating	1)-locating	NUM
ejpam-4770	297	9	set	set	NOUN
ejpam-4770	297	10	or	or	CCONJ
ejpam-4770	297	11	one	one	NUM
ejpam-4770	297	12	of	of	ADP
ejpam-4770	297	13	tx	tx	PROPN
ejpam-4770	297	14	and	and	CCONJ
ejpam-4770	297	15	ty	ty	PRON
ejpam-4770	297	16	is	be	AUX
ejpam-4770	297	17	a	a	DET
ejpam-4770	297	18	(	(	PUNCT
ejpam-4770	297	19	2	2	NUM
ejpam-4770	297	20	,	,	PUNCT
ejpam-4770	297	21	2)-locating	2)-locating	NUM
ejpam-4770	297	22	set	set	VERB
ejpam-4770	297	23	in	in	ADP
ejpam-4770	297	24	h	h	NOUN
ejpam-4770	297	25	whenever	whenever	SCONJ
ejpam-4770	297	26	x	x	X
ejpam-4770	297	27	,	,	PUNCT
ejpam-4770	297	28	y	y	PROPN
ejpam-4770	297	29	∈	∈	PROPN
ejpam-4770	297	30	eq1(g	eq1(g	PROPN
ejpam-4770	297	31	)	)	PUNCT
ejpam-4770	297	32	;	;	PUNCT
ejpam-4770	297	33	(	(	PUNCT
ejpam-4770	297	34	iv	iv	X
ejpam-4770	297	35	)	)	PUNCT
ejpam-4770	297	36	tx	tx	PROPN
ejpam-4770	298	1	and	and	CCONJ
ejpam-4770	298	2	ty	ty	INTJ
ejpam-4770	298	3	are	be	AUX
ejpam-4770	298	4	(	(	PUNCT
ejpam-4770	298	5	2	2	NUM
ejpam-4770	298	6	−	−	NOUN
ejpam-4770	298	7	locating	locating	NOUN
ejpam-4770	298	8	)	)	PUNCT
ejpam-4770	298	9	dominating	dominating	NOUN
ejpam-4770	298	10	sets	set	NOUN
ejpam-4770	298	11	in	in	ADP
ejpam-4770	298	12	h	h	NOUN
ejpam-4770	298	13	or	or	CCONJ
ejpam-4770	298	14	one	one	NUM
ejpam-4770	298	15	of	of	ADP
ejpam-4770	298	16	tx	tx	PROPN
ejpam-4770	299	1	and	and	CCONJ
ejpam-4770	299	2	ty	ty	PRON
ejpam-4770	299	3	is	be	AUX
ejpam-4770	299	4	a	a	DET
ejpam-4770	299	5	2	2	NUM
ejpam-4770	299	6	-	-	PUNCT
ejpam-4770	299	7	dominating	dominating	NOUN
ejpam-4770	299	8	set	set	NOUN
ejpam-4770	299	9	whenever	whenever	SCONJ
ejpam-4770	299	10	x	x	X
ejpam-4770	299	11	,	,	PUNCT
ejpam-4770	299	12	y	y	PROPN
ejpam-4770	299	13	∈	∈	PROPN
ejpam-4770	299	14	eq2(g	eq2(g	VERB
ejpam-4770	299	15	)	)	PUNCT
ejpam-4770	299	16	.	.	PUNCT
ejpam-4770	300	1	(	(	PUNCT
ejpam-4770	300	2	v	v	NOUN
ejpam-4770	300	3	)	)	PUNCT
ejpam-4770	300	4	tx	tx	PROPN
ejpam-4770	300	5	is	be	AUX
ejpam-4770	300	6	a	a	DET
ejpam-4770	300	7	2	2	NUM
ejpam-4770	300	8	-	-	PUNCT
ejpam-4770	300	9	locating	locate	VERB
ejpam-4770	300	10	point	point	NOUN
ejpam-4770	300	11	-	-	PUNCT
ejpam-4770	300	12	wise	wise	ADJ
ejpam-4770	300	13	non	non	ADJ
ejpam-4770	300	14	-	-	ADJ
ejpam-4770	300	15	dominating	dominating	ADJ
ejpam-4770	300	16	set	set	NOUN
ejpam-4770	300	17	in	in	ADP
ejpam-4770	300	18	h	h	NOUN
ejpam-4770	300	19	for	for	ADP
ejpam-4770	300	20	every	every	DET
ejpam-4770	300	21	x	x	SYM
ejpam-4770	300	22	∈	∈	PROPN
ejpam-4770	300	23	s	s	VERB
ejpam-4770	300	24	with	with	ADP
ejpam-4770	300	25	|ng(x	|ng(x	ADP
ejpam-4770	300	26	,	,	PUNCT
ejpam-4770	300	27	2	2	X
ejpam-4770	300	28	)	)	PUNCT
ejpam-4770	300	29	∩	∩	NOUN
ejpam-4770	300	30	s|	s|	VERB
ejpam-4770	300	31	=	=	SYM
ejpam-4770	300	32	0	0	X
ejpam-4770	300	33	.	.	PUNCT
ejpam-4770	300	34	theorem	theorem	NOUN
ejpam-4770	300	35	8	8	NUM
ejpam-4770	300	36	.	.	PUNCT
ejpam-4770	301	1	let	let	VERB
ejpam-4770	301	2	g	g	NOUN
ejpam-4770	301	3	and	and	CCONJ
ejpam-4770	301	4	h	h	NOUN
ejpam-4770	301	5	be	be	AUX
ejpam-4770	301	6	nontrivial	nontrivial	ADJ
ejpam-4770	301	7	connected	connect	VERB
ejpam-4770	301	8	graphs	graph	NOUN
ejpam-4770	301	9	with	with	ADP
ejpam-4770	301	10	△	△	X
ejpam-4770	301	11	(	(	PUNCT
ejpam-4770	301	12	h	h	NOUN
ejpam-4770	301	13	)	)	PUNCT
ejpam-4770	301	14	≤	≤	NOUN
ejpam-4770	301	15	|v	|v	X
ejpam-4770	301	16	(	(	PUNCT
ejpam-4770	301	17	h)|	h)|	NOUN
ejpam-4770	301	18	−	−	PROPN
ejpam-4770	301	19	3	3	NUM
ejpam-4770	301	20	.	.	PUNCT
ejpam-4770	302	1	then	then	ADV
ejpam-4770	302	2	w	w	PROPN
ejpam-4770	302	3	=	=	PUNCT
ejpam-4770	302	4	⋃	⋃	PROPN
ejpam-4770	302	5	x∈s	x∈s	NOUN
ejpam-4770	303	1	[	[	X
ejpam-4770	303	2	{	{	PUNCT
ejpam-4770	303	3	x	x	NOUN
ejpam-4770	303	4	}	}	PUNCT
ejpam-4770	303	5	×	×	PROPN
ejpam-4770	303	6	tx	tx	PROPN
ejpam-4770	303	7	]	]	X
ejpam-4770	303	8	,	,	PUNCT
ejpam-4770	303	9	where	where	SCONJ
ejpam-4770	303	10	s	s	VERB
ejpam-4770	303	11	⊆	⊆	NUM
ejpam-4770	303	12	v	v	NOUN
ejpam-4770	303	13	(	(	PUNCT
ejpam-4770	303	14	g	g	NOUN
ejpam-4770	303	15	)	)	PUNCT
ejpam-4770	303	16	and	and	CCONJ
ejpam-4770	303	17	tx	tx	VERB
ejpam-4770	303	18	⊆	⊆	NUM
ejpam-4770	303	19	v	v	NOUN
ejpam-4770	303	20	(	(	PUNCT
ejpam-4770	303	21	h	h	NOUN
ejpam-4770	303	22	)	)	PUNCT
ejpam-4770	303	23	for	for	ADP
ejpam-4770	303	24	each	each	DET
ejpam-4770	303	25	x	x	SYM
ejpam-4770	303	26	∈	∈	PROPN
ejpam-4770	303	27	s	s	NOUN
ejpam-4770	303	28	,	,	PUNCT
ejpam-4770	303	29	is	be	AUX
ejpam-4770	303	30	a	a	DET
ejpam-4770	303	31	1	1	NUM
ejpam-4770	303	32	-	-	PUNCT
ejpam-4770	303	33	movable	movable	ADJ
ejpam-4770	303	34	2	2	NUM
ejpam-4770	303	35	-	-	PUNCT
ejpam-4770	303	36	resolving	resolve	VERB
ejpam-4770	303	37	hop	hop	NOUN
ejpam-4770	303	38	dominating	dominating	NOUN
ejpam-4770	303	39	set	set	VERB
ejpam-4770	303	40	in	in	ADP
ejpam-4770	303	41	g[h	g[h	PROPN
ejpam-4770	303	42	]	]	PUNCT
ejpam-4770	303	43	if	if	SCONJ
ejpam-4770	303	44	and	and	CCONJ
ejpam-4770	303	45	only	only	ADV
ejpam-4770	303	46	if	if	SCONJ
ejpam-4770	303	47	(	(	PUNCT
ejpam-4770	303	48	i	i	NOUN
ejpam-4770	303	49	)	)	PUNCT
ejpam-4770	303	50	s	s	PART
ejpam-4770	303	51	=	=	SYM
ejpam-4770	303	52	v	v	NOUN
ejpam-4770	303	53	(	(	PUNCT
ejpam-4770	303	54	g	g	NOUN
ejpam-4770	303	55	)	)	PUNCT
ejpam-4770	303	56	;	;	PUNCT
ejpam-4770	303	57	(	(	PUNCT
ejpam-4770	303	58	ii	ii	NOUN
ejpam-4770	303	59	)	)	PUNCT
ejpam-4770	303	60	tx	tx	PROPN
ejpam-4770	303	61	is	be	AUX
ejpam-4770	303	62	a	a	DET
ejpam-4770	303	63	1	1	NUM
ejpam-4770	303	64	-	-	PUNCT
ejpam-4770	303	65	movable	movable	ADJ
ejpam-4770	303	66	2	2	NUM
ejpam-4770	303	67	-	-	PUNCT
ejpam-4770	303	68	locating	locate	VERB
ejpam-4770	303	69	set	set	NOUN
ejpam-4770	303	70	of	of	ADP
ejpam-4770	303	71	h	h	NOUN
ejpam-4770	303	72	for	for	ADP
ejpam-4770	303	73	every	every	DET
ejpam-4770	303	74	x	x	SYM
ejpam-4770	303	75	∈	∈	PROPN
ejpam-4770	303	76	v	v	ADP
ejpam-4770	303	77	(	(	PUNCT
ejpam-4770	303	78	g	g	NOUN
ejpam-4770	303	79	)	)	PUNCT
ejpam-4770	303	80	;	;	PUNCT
ejpam-4770	304	1	a.m.	a.m.	PROPN
ejpam-4770	304	2	mahistrado	mahistrado	PROPN
ejpam-4770	304	3	,	,	PUNCT
ejpam-4770	304	4	h.	h.	PROPN
ejpam-4770	304	5	rara	rara	PROPN
ejpam-4770	304	6	/	/	SYM
ejpam-4770	304	7	eur	eur	PROPN
ejpam-4770	304	8	.	.	PUNCT
ejpam-4770	305	1	j.	j.	PROPN
ejpam-4770	305	2	pure	pure	PROPN
ejpam-4770	305	3	appl	appl	PROPN
ejpam-4770	305	4	.	.	PROPN
ejpam-4770	305	5	math	math	PROPN
ejpam-4770	305	6	,	,	PUNCT
ejpam-4770	305	7	16	16	NUM
ejpam-4770	305	8	(	(	PUNCT
ejpam-4770	305	9	3	3	NUM
ejpam-4770	305	10	)	)	PUNCT
ejpam-4770	305	11	(	(	PUNCT
ejpam-4770	305	12	2023	2023	NUM
ejpam-4770	305	13	)	)	PUNCT
ejpam-4770	305	14	,	,	PUNCT
ejpam-4770	305	15	1464	1464	NUM
ejpam-4770	305	16	-	-	SYM
ejpam-4770	305	17	1479	1479	NUM
ejpam-4770	305	18	1476	1476	NUM
ejpam-4770	305	19	(	(	PUNCT
ejpam-4770	305	20	iii	iii	NOUN
ejpam-4770	305	21	)	)	PUNCT
ejpam-4770	305	22	tx\{p	tx\{p	NOUN
ejpam-4770	305	23	}	}	PUNCT
ejpam-4770	305	24	or	or	CCONJ
ejpam-4770	305	25	tx\{p}∪	tx\{p}∪	PRON
ejpam-4770	305	26	{	{	PUNCT
ejpam-4770	305	27	q	q	NOUN
ejpam-4770	305	28	}	}	PUNCT
ejpam-4770	305	29	is	be	AUX
ejpam-4770	305	30	a	a	DET
ejpam-4770	305	31	2	2	NUM
ejpam-4770	305	32	-	-	PUNCT
ejpam-4770	305	33	locating	locate	VERB
ejpam-4770	305	34	point	point	NOUN
ejpam-4770	305	35	-	-	PUNCT
ejpam-4770	305	36	wise	wise	ADJ
ejpam-4770	305	37	non	non	ADJ
ejpam-4770	305	38	-	-	ADJ
ejpam-4770	305	39	dominating	dominating	ADJ
ejpam-4770	305	40	set	set	NOUN
ejpam-4770	305	41	of	of	ADP
ejpam-4770	305	42	h	h	NOUN
ejpam-4770	305	43	for	for	ADP
ejpam-4770	305	44	every	every	DET
ejpam-4770	305	45	x	x	SYM
ejpam-4770	305	46	∈	∈	PROPN
ejpam-4770	305	47	s	s	VERB
ejpam-4770	305	48	with	with	ADP
ejpam-4770	305	49	|ng(x	|ng(x	ADP
ejpam-4770	305	50	,	,	PUNCT
ejpam-4770	305	51	2	2	X
ejpam-4770	305	52	)	)	PUNCT
ejpam-4770	305	53	∩	∩	NOUN
ejpam-4770	305	54	s|	s|	VERB
ejpam-4770	305	55	=	=	SYM
ejpam-4770	305	56	0	0	NUM
ejpam-4770	305	57	and	and	CCONJ
ejpam-4770	305	58	p	p	PROPN
ejpam-4770	305	59	∈	∈	PROPN
ejpam-4770	305	60	tx	tx	NOUN
ejpam-4770	305	61	and	and	CCONJ
ejpam-4770	305	62	for	for	ADP
ejpam-4770	305	63	some	some	DET
ejpam-4770	305	64	q	q	NOUN
ejpam-4770	305	65	∈	∈	PROPN
ejpam-4770	305	66	nh(p	nh(p	NUM
ejpam-4770	305	67	)	)	PUNCT
ejpam-4770	305	68	.	.	PUNCT
ejpam-4770	306	1	(	(	PUNCT
ejpam-4770	306	2	iv	iv	X
ejpam-4770	306	3	)	)	PUNCT
ejpam-4770	306	4	tx\{p	tx\{p	NUM
ejpam-4770	306	5	}	}	PUNCT
ejpam-4770	306	6	and	and	CCONJ
ejpam-4770	306	7	ty	ty	PRON
ejpam-4770	306	8	are	be	AUX
ejpam-4770	306	9	(	(	PUNCT
ejpam-4770	306	10	2	2	NUM
ejpam-4770	306	11	,	,	PUNCT
ejpam-4770	306	12	1)-locating	1)-locating	NUM
ejpam-4770	306	13	set	set	NOUN
ejpam-4770	306	14	or	or	CCONJ
ejpam-4770	306	15	one	one	NUM
ejpam-4770	306	16	of	of	ADP
ejpam-4770	306	17	tx\{p	tx\{p	NOUN
ejpam-4770	306	18	}	}	PUNCT
ejpam-4770	306	19	and	and	CCONJ
ejpam-4770	306	20	ty	ty	INTJ
ejpam-4770	306	21	is	be	AUX
ejpam-4770	306	22	a	a	DET
ejpam-4770	306	23	(	(	PUNCT
ejpam-4770	306	24	2	2	NUM
ejpam-4770	306	25	,	,	PUNCT
ejpam-4770	306	26	2)-locating	2)-locating	NUM
ejpam-4770	306	27	set	set	NOUN
ejpam-4770	306	28	of	of	ADP
ejpam-4770	306	29	h	h	NOUN
ejpam-4770	306	30	whenever	whenever	SCONJ
ejpam-4770	306	31	x	x	X
ejpam-4770	306	32	,	,	PUNCT
ejpam-4770	306	33	y	y	PROPN
ejpam-4770	306	34	∈	∈	PROPN
ejpam-4770	306	35	eq1(g	eq1(g	PROPN
ejpam-4770	306	36	)	)	PUNCT
ejpam-4770	306	37	and	and	CCONJ
ejpam-4770	306	38	for	for	ADP
ejpam-4770	306	39	each	each	DET
ejpam-4770	306	40	p	p	PROPN
ejpam-4770	306	41	∈	∈	PROPN
ejpam-4770	306	42	tx	tx	PROPN
ejpam-4770	306	43	;	;	PUNCT
ejpam-4770	306	44	(	(	PUNCT
ejpam-4770	306	45	v	v	NOUN
ejpam-4770	306	46	)	)	PUNCT
ejpam-4770	306	47	tx\{p	tx\{p	NUM
ejpam-4770	306	48	}	}	PUNCT
ejpam-4770	306	49	or	or	CCONJ
ejpam-4770	306	50	tx\{p}∪{q	tx\{p}∪{q	NUM
ejpam-4770	306	51	}	}	PUNCT
ejpam-4770	306	52	or	or	CCONJ
ejpam-4770	306	53	ty	ty	INTJ
ejpam-4770	306	54	is	be	AUX
ejpam-4770	306	55	(	(	PUNCT
ejpam-4770	306	56	2−	2−	NUM
ejpam-4770	306	57	locating	locating	NOUN
ejpam-4770	306	58	)	)	PUNCT
ejpam-4770	306	59	dominating	dominating	NOUN
ejpam-4770	306	60	sets	set	NOUN
ejpam-4770	306	61	in	in	ADP
ejpam-4770	306	62	h	h	NOUN
ejpam-4770	306	63	or	or	CCONJ
ejpam-4770	306	64	one	one	NUM
ejpam-4770	306	65	of	of	ADP
ejpam-4770	306	66	tx\{p	tx\{p	NOUN
ejpam-4770	306	67	}	}	PUNCT
ejpam-4770	306	68	and	and	CCONJ
ejpam-4770	306	69	ty	ty	INTJ
ejpam-4770	306	70	is	be	AUX
ejpam-4770	306	71	a	a	DET
ejpam-4770	306	72	2	2	NUM
ejpam-4770	306	73	-	-	PUNCT
ejpam-4770	306	74	dominating	dominating	NOUN
ejpam-4770	306	75	set	set	NOUN
ejpam-4770	306	76	whenever	whenever	SCONJ
ejpam-4770	306	77	x	x	X
ejpam-4770	306	78	,	,	PUNCT
ejpam-4770	306	79	y	y	PROPN
ejpam-4770	306	80	∈	∈	PROPN
ejpam-4770	306	81	eq2(g	eq2(g	VERB
ejpam-4770	306	82	)	)	PUNCT
ejpam-4770	306	83	and	and	CCONJ
ejpam-4770	306	84	for	for	ADP
ejpam-4770	306	85	each	each	DET
ejpam-4770	306	86	p	p	PROPN
ejpam-4770	306	87	∈	∈	PROPN
ejpam-4770	306	88	tx	tx	NOUN
ejpam-4770	306	89	and	and	CCONJ
ejpam-4770	306	90	for	for	ADP
ejpam-4770	306	91	some	some	DET
ejpam-4770	306	92	q	q	NOUN
ejpam-4770	306	93	∈	∈	PROPN
ejpam-4770	306	94	nh(p	nh(p	NUM
ejpam-4770	306	95	)	)	PUNCT
ejpam-4770	306	96	.	.	PUNCT
ejpam-4770	307	1	proof	proof	NOUN
ejpam-4770	307	2	.	.	PUNCT
ejpam-4770	308	1	suppose	suppose	VERB
ejpam-4770	308	2	w	w	NOUN
ejpam-4770	308	3	is	be	AUX
ejpam-4770	308	4	a	a	DET
ejpam-4770	308	5	1	1	NUM
ejpam-4770	308	6	-	-	PUNCT
ejpam-4770	308	7	movable	movable	ADJ
ejpam-4770	308	8	2	2	NUM
ejpam-4770	308	9	-	-	PUNCT
ejpam-4770	308	10	resolving	resolve	VERB
ejpam-4770	308	11	hop	hop	NOUN
ejpam-4770	308	12	dominating	dominating	NOUN
ejpam-4770	308	13	set	set	VERB
ejpam-4770	308	14	in	in	ADP
ejpam-4770	308	15	g[h	g[h	PROPN
ejpam-4770	308	16	]	]	PUNCT
ejpam-4770	308	17	.	.	PUNCT
ejpam-4770	309	1	then	then	ADV
ejpam-4770	309	2	by	by	ADP
ejpam-4770	309	3	theorem	theorem	NOUN
ejpam-4770	309	4	7	7	NUM
ejpam-4770	309	5	,	,	PUNCT
ejpam-4770	309	6	s	s	PART
ejpam-4770	309	7	=	=	SYM
ejpam-4770	309	8	v	v	X
ejpam-4770	309	9	(	(	PUNCT
ejpam-4770	309	10	g	g	NOUN
ejpam-4770	309	11	)	)	PUNCT
ejpam-4770	309	12	and	and	CCONJ
ejpam-4770	309	13	tx	tx	PROPN
ejpam-4770	309	14	is	be	AUX
ejpam-4770	309	15	a	a	DET
ejpam-4770	309	16	2	2	NUM
ejpam-4770	309	17	-	-	PUNCT
ejpam-4770	309	18	locating	locate	VERB
ejpam-4770	309	19	set	set	NOUN
ejpam-4770	309	20	of	of	ADP
ejpam-4770	309	21	h	h	NOUN
ejpam-4770	309	22	for	for	ADP
ejpam-4770	309	23	each	each	DET
ejpam-4770	309	24	x	x	SYM
ejpam-4770	309	25	∈	∈	PROPN
ejpam-4770	309	26	v	v	NOUN
ejpam-4770	309	27	(	(	PUNCT
ejpam-4770	309	28	g	g	NOUN
ejpam-4770	309	29	)	)	PUNCT
ejpam-4770	309	30	.	.	PUNCT
ejpam-4770	310	1	let	let	VERB
ejpam-4770	310	2	p	p	PROPN
ejpam-4770	310	3	∈	∈	PROPN
ejpam-4770	310	4	tx	tx	PROPN
ejpam-4770	310	5	.	.	PUNCT
ejpam-4770	311	1	then	then	ADV
ejpam-4770	311	2	(	(	PUNCT
ejpam-4770	311	3	x	x	X
ejpam-4770	311	4	,	,	PUNCT
ejpam-4770	311	5	p	p	NOUN
ejpam-4770	311	6	)	)	PUNCT
ejpam-4770	311	7	∈	∈	PROPN
ejpam-4770	311	8	w	w	NOUN
ejpam-4770	311	9	.	.	PUNCT
ejpam-4770	312	1	since	since	SCONJ
ejpam-4770	312	2	w	w	PROPN
ejpam-4770	312	3	is	be	AUX
ejpam-4770	312	4	a	a	DET
ejpam-4770	312	5	1	1	NUM
ejpam-4770	312	6	-	-	PUNCT
ejpam-4770	312	7	movable	movable	ADJ
ejpam-4770	312	8	2	2	NUM
ejpam-4770	312	9	-	-	PUNCT
ejpam-4770	312	10	resolving	resolve	VERB
ejpam-4770	312	11	hop	hop	NOUN
ejpam-4770	312	12	dominating	dominating	NOUN
ejpam-4770	312	13	set	set	NOUN
ejpam-4770	312	14	,	,	PUNCT
ejpam-4770	312	15	either	either	CCONJ
ejpam-4770	312	16	w\{(x	w\{(x	PROPN
ejpam-4770	312	17	,	,	PUNCT
ejpam-4770	312	18	p	p	NOUN
ejpam-4770	312	19	)	)	PUNCT
ejpam-4770	312	20	}	}	PUNCT
ejpam-4770	313	1	=	=	SYM
ejpam-4770	313	2			PROPN
ejpam-4770	313	3	⋃	⋃	PROPN
ejpam-4770	313	4	v∈s\{x	v∈s\{x	NOUN
ejpam-4770	313	5	}	}	PUNCT
ejpam-4770	313	6	(	(	PUNCT
ejpam-4770	313	7	{	{	PUNCT
ejpam-4770	313	8	v	v	NOUN
ejpam-4770	313	9	}	}	PUNCT
ejpam-4770	313	10	×	×	NOUN
ejpam-4770	313	11	tv	tv	NOUN
ejpam-4770	313	12	)	)	PUNCT
ejpam-4770	314	1			PROPN
ejpam-4770	314	2	∪	∪	ADV
ejpam-4770	314	3	[	[	X
ejpam-4770	314	4	{	{	PUNCT
ejpam-4770	314	5	x	x	NOUN
ejpam-4770	314	6	}	}	PUNCT
ejpam-4770	314	7	×	×	NOUN
ejpam-4770	314	8	(	(	PUNCT
ejpam-4770	314	9	tx\{p	tx\{p	NUM
ejpam-4770	314	10	}	}	PUNCT
ejpam-4770	314	11	)	)	PUNCT
ejpam-4770	314	12	]	]	PUNCT
ejpam-4770	314	13	or	or	CCONJ
ejpam-4770	314	14	(	(	PUNCT
ejpam-4770	314	15	w\{(x	w\{(x	PROPN
ejpam-4770	314	16	,	,	PUNCT
ejpam-4770	314	17	p	p	NOUN
ejpam-4770	314	18	)	)	PUNCT
ejpam-4770	314	19	}	}	PUNCT
ejpam-4770	314	20	)	)	PUNCT
ejpam-4770	314	21	∪	∪	X
ejpam-4770	314	22	{	{	PUNCT
ejpam-4770	314	23	(	(	PUNCT
ejpam-4770	314	24	x	x	NOUN
ejpam-4770	314	25	,	,	PUNCT
ejpam-4770	314	26	q	q	NOUN
ejpam-4770	314	27	)	)	PUNCT
ejpam-4770	314	28	}	}	PUNCT
ejpam-4770	314	29	=	=	SYM
ejpam-4770	315	1			PROPN
ejpam-4770	315	2	⋃	⋃	PROPN
ejpam-4770	315	3	z∈s\{x	z∈s\{x	PROPN
ejpam-4770	315	4	}	}	PUNCT
ejpam-4770	315	5	(	(	PUNCT
ejpam-4770	315	6	{	{	PUNCT
ejpam-4770	315	7	z	z	NOUN
ejpam-4770	315	8	}	}	PUNCT
ejpam-4770	315	9	×	×	PROPN
ejpam-4770	315	10	tz	tz	NOUN
ejpam-4770	315	11	)	)	PUNCT
ejpam-4770	315	12			PROPN
ejpam-4770	315	13	∪	∪	ADV
ejpam-4770	315	14	[	[	X
ejpam-4770	315	15	{	{	PUNCT
ejpam-4770	315	16	x	x	NOUN
ejpam-4770	315	17	}	}	PUNCT
ejpam-4770	315	18	×	×	NOUN
ejpam-4770	315	19	(	(	PUNCT
ejpam-4770	315	20	tx\{p	tx\{p	NOUN
ejpam-4770	315	21	}	}	PUNCT
ejpam-4770	315	22	∪	∪	ADJ
ejpam-4770	315	23	{	{	PUNCT
ejpam-4770	315	24	q	q	NOUN
ejpam-4770	315	25	}	}	PUNCT
ejpam-4770	315	26	)	)	PUNCT
ejpam-4770	315	27	]	]	PUNCT
ejpam-4770	315	28	for	for	ADP
ejpam-4770	315	29	some	some	DET
ejpam-4770	315	30	q	q	NOUN
ejpam-4770	315	31	∈	∈	PROPN
ejpam-4770	315	32	(	(	PUNCT
ejpam-4770	315	33	v	v	NOUN
ejpam-4770	315	34	(	(	PUNCT
ejpam-4770	315	35	h)\tx	h)\tx	NOUN
ejpam-4770	315	36	)	)	PUNCT
ejpam-4770	315	37	∩nh(p	∩nh(p	NOUN
ejpam-4770	315	38	)	)	PUNCT
ejpam-4770	315	39	or	or	CCONJ
ejpam-4770	315	40	(	(	PUNCT
ejpam-4770	315	41	w\{(x	w\{(x	PROPN
ejpam-4770	315	42	,	,	PUNCT
ejpam-4770	315	43	p	p	NOUN
ejpam-4770	315	44	)	)	PUNCT
ejpam-4770	315	45	}	}	PUNCT
ejpam-4770	315	46	)	)	PUNCT
ejpam-4770	315	47	∪	∪	X
ejpam-4770	315	48	{	{	PUNCT
ejpam-4770	315	49	(	(	PUNCT
ejpam-4770	315	50	y	y	PROPN
ejpam-4770	315	51	,	,	PUNCT
ejpam-4770	315	52	w	w	NOUN
ejpam-4770	315	53	)	)	PUNCT
ejpam-4770	315	54	}	}	PUNCT
ejpam-4770	315	55	=	=	SYM
ejpam-4770	316	1			PROPN
ejpam-4770	316	2	⋃	⋃	PROPN
ejpam-4770	316	3	a∈s\{(x	a∈s\{(x	NOUN
ejpam-4770	316	4	,	,	PUNCT
ejpam-4770	316	5	y	y	NOUN
ejpam-4770	316	6	)	)	PUNCT
ejpam-4770	316	7	}	}	PUNCT
ejpam-4770	316	8	(	(	PUNCT
ejpam-4770	316	9	{	{	PUNCT
ejpam-4770	316	10	a	a	PRON
ejpam-4770	316	11	}	}	PUNCT
ejpam-4770	316	12	×	×	NOUN
ejpam-4770	316	13	ta	ta	NOUN
ejpam-4770	316	14	)	)	PUNCT
ejpam-4770	316	15			PROPN
ejpam-4770	316	16	∪	∪	ADV
ejpam-4770	316	17	[	[	X
ejpam-4770	316	18	{	{	PUNCT
ejpam-4770	316	19	x	x	NOUN
ejpam-4770	316	20	}	}	PUNCT
ejpam-4770	316	21	×	×	NOUN
ejpam-4770	316	22	(	(	PUNCT
ejpam-4770	316	23	tx\{p	tx\{p	NUM
ejpam-4770	316	24	}	}	PUNCT
ejpam-4770	316	25	)	)	PUNCT
ejpam-4770	316	26	]	]	PUNCT
ejpam-4770	316	27	∪	∪	ADP
ejpam-4770	316	28	[	[	X
ejpam-4770	316	29	{	{	PUNCT
ejpam-4770	316	30	y	y	NOUN
ejpam-4770	316	31	}	}	PUNCT
ejpam-4770	316	32	×	×	NOUN
ejpam-4770	316	33	(	(	PUNCT
ejpam-4770	316	34	ty\{w	ty\{w	NUM
ejpam-4770	316	35	}	}	PUNCT
ejpam-4770	316	36	)	)	PUNCT
ejpam-4770	316	37	]	]	PUNCT
ejpam-4770	316	38	for	for	ADP
ejpam-4770	316	39	some	some	DET
ejpam-4770	316	40	y	y	PROPN
ejpam-4770	316	41	∈	∈	PROPN
ejpam-4770	316	42	v	v	PROPN
ejpam-4770	316	43	(	(	PUNCT
ejpam-4770	316	44	g)∩ng(x	g)∩ng(x	PROPN
ejpam-4770	316	45	)	)	PUNCT
ejpam-4770	316	46	and	and	CCONJ
ejpam-4770	316	47	w	w	PROPN
ejpam-4770	316	48	∈	∈	PROPN
ejpam-4770	316	49	v	v	X
ejpam-4770	316	50	(	(	PUNCT
ejpam-4770	316	51	h)\ty	h)\ty	PROPN
ejpam-4770	316	52	is	be	AUX
ejpam-4770	316	53	a	a	DET
ejpam-4770	316	54	2	2	NUM
ejpam-4770	316	55	-	-	PUNCT
ejpam-4770	316	56	resolving	resolve	VERB
ejpam-4770	316	57	hop	hop	NOUN
ejpam-4770	316	58	dominating	dominating	NOUN
ejpam-4770	316	59	set	set	NOUN
ejpam-4770	316	60	of	of	ADP
ejpam-4770	316	61	g[h	g[h	NOUN
ejpam-4770	316	62	]	]	PUNCT
ejpam-4770	316	63	.	.	PUNCT
ejpam-4770	317	1	by	by	ADP
ejpam-4770	317	2	theorem	theorem	NOUN
ejpam-4770	317	3	7	7	NUM
ejpam-4770	317	4	,	,	PUNCT
ejpam-4770	317	5	tx\{p	tx\{p	NUM
ejpam-4770	317	6	}	}	PUNCT
ejpam-4770	317	7	or	or	CCONJ
ejpam-4770	317	8	(	(	PUNCT
ejpam-4770	317	9	tx\p	tx\p	NUM
ejpam-4770	317	10	)	)	PUNCT
ejpam-4770	317	11	∪	∪	ADP
ejpam-4770	317	12	{	{	PUNCT
ejpam-4770	317	13	q	q	NOUN
ejpam-4770	317	14	}	}	PUNCT
ejpam-4770	317	15	is	be	AUX
ejpam-4770	317	16	a	a	DET
ejpam-4770	317	17	2	2	NUM
ejpam-4770	317	18	-	-	PUNCT
ejpam-4770	317	19	locating	locate	VERB
ejpam-4770	317	20	set	set	NOUN
ejpam-4770	317	21	of	of	ADP
ejpam-4770	317	22	h	h	NOUN
ejpam-4770	317	23	for	for	ADP
ejpam-4770	317	24	each	each	DET
ejpam-4770	317	25	p	p	PROPN
ejpam-4770	317	26	∈	∈	PROPN
ejpam-4770	317	27	tx	tx	NOUN
ejpam-4770	317	28	and	and	CCONJ
ejpam-4770	317	29	for	for	ADP
ejpam-4770	317	30	some	some	DET
ejpam-4770	317	31	q	q	NOUN
ejpam-4770	317	32	∈	∈	PROPN
ejpam-4770	317	33	(	(	PUNCT
ejpam-4770	317	34	v	v	NOUN
ejpam-4770	317	35	(	(	PUNCT
ejpam-4770	317	36	h)\tx	h)\tx	NOUN
ejpam-4770	317	37	)	)	PUNCT
ejpam-4770	317	38	∩nh(p	∩nh(p	NOUN
ejpam-4770	317	39	)	)	PUNCT
ejpam-4770	317	40	.	.	PUNCT
ejpam-4770	318	1	hence	hence	ADV
ejpam-4770	318	2	,	,	PUNCT
ejpam-4770	318	3	tx	tx	PROPN
ejpam-4770	318	4	is	be	AUX
ejpam-4770	318	5	a	a	DET
ejpam-4770	318	6	1	1	NUM
ejpam-4770	318	7	-	-	PUNCT
ejpam-4770	318	8	movable	movable	ADJ
ejpam-4770	318	9	2	2	NUM
ejpam-4770	318	10	-	-	PUNCT
ejpam-4770	318	11	locating	locate	VERB
ejpam-4770	318	12	set	set	NOUN
ejpam-4770	318	13	of	of	ADP
ejpam-4770	318	14	h	h	NOUN
ejpam-4770	318	15	for	for	ADP
ejpam-4770	318	16	each	each	DET
ejpam-4770	318	17	x	x	SYM
ejpam-4770	318	18	∈	∈	PROPN
ejpam-4770	318	19	v	v	ADP
ejpam-4770	318	20	(	(	PUNCT
ejpam-4770	318	21	g	g	NOUN
ejpam-4770	318	22	)	)	PUNCT
ejpam-4770	318	23	or	or	CCONJ
ejpam-4770	318	24	tx\{p	tx\{p	NUM
ejpam-4770	318	25	}	}	PUNCT
ejpam-4770	318	26	is	be	AUX
ejpam-4770	318	27	2	2	NUM
ejpam-4770	318	28	-	-	PUNCT
ejpam-4770	318	29	locating	locate	VERB
ejpam-4770	318	30	and	and	CCONJ
ejpam-4770	318	31	(	(	PUNCT
ejpam-4770	318	32	ii	ii	NOUN
ejpam-4770	318	33	)	)	PUNCT
ejpam-4770	318	34	holds	hold	VERB
ejpam-4770	318	35	.	.	PUNCT
ejpam-4770	319	1	if	if	SCONJ
ejpam-4770	319	2	(	(	PUNCT
ejpam-4770	319	3	iii	iii	NOUN
ejpam-4770	319	4	)	)	PUNCT
ejpam-4770	319	5	does	do	AUX
ejpam-4770	319	6	not	not	PART
ejpam-4770	319	7	hold	hold	VERB
ejpam-4770	319	8	,	,	PUNCT
ejpam-4770	319	9	then	then	ADV
ejpam-4770	319	10	w\{(x	w\{(x	PROPN
ejpam-4770	319	11	,	,	PUNCT
ejpam-4770	319	12	p	p	NOUN
ejpam-4770	319	13	)	)	PUNCT
ejpam-4770	319	14	}	}	PUNCT
ejpam-4770	319	15	and	and	CCONJ
ejpam-4770	319	16	(	(	PUNCT
ejpam-4770	319	17	w\{(x	w\{(x	PROPN
ejpam-4770	319	18	,	,	PUNCT
ejpam-4770	319	19	p	p	NOUN
ejpam-4770	319	20	)	)	PUNCT
ejpam-4770	319	21	}	}	PUNCT
ejpam-4770	319	22	∪	∪	X
ejpam-4770	319	23	{	{	PUNCT
ejpam-4770	319	24	(	(	PUNCT
ejpam-4770	319	25	y	y	PROPN
ejpam-4770	319	26	,	,	PUNCT
ejpam-4770	319	27	q	q	NOUN
ejpam-4770	319	28	)	)	PUNCT
ejpam-4770	319	29	}	}	PUNCT
ejpam-4770	319	30	)	)	PUNCT
ejpam-4770	319	31	are	be	AUX
ejpam-4770	319	32	not	not	PART
ejpam-4770	319	33	hop	hop	ADJ
ejpam-4770	319	34	dominating	dominating	NOUN
ejpam-4770	319	35	sets	set	NOUN
ejpam-4770	319	36	of	of	ADP
ejpam-4770	319	37	g[h	g[h	NOUN
ejpam-4770	319	38	]	]	PUNCT
ejpam-4770	319	39	for	for	ADP
ejpam-4770	319	40	all	all	DET
ejpam-4770	319	41	y	y	PROPN
ejpam-4770	319	42	∈	∈	PROPN
ejpam-4770	319	43	ng(x	ng(x	NUM
ejpam-4770	319	44	)	)	PUNCT
ejpam-4770	319	45	and	and	CCONJ
ejpam-4770	319	46	q	q	PROPN
ejpam-4770	319	47	∈	∈	PROPN
ejpam-4770	319	48	v	v	NOUN
ejpam-4770	319	49	(	(	PUNCT
ejpam-4770	319	50	h)\tx	h)\tx	NOUN
ejpam-4770	319	51	or	or	CCONJ
ejpam-4770	319	52	x	x	SYM
ejpam-4770	319	53	=	=	SYM
ejpam-4770	319	54	y	y	PROPN
ejpam-4770	319	55	and	and	CCONJ
ejpam-4770	319	56	q	q	PROPN
ejpam-4770	319	57	∈	∈	PROPN
ejpam-4770	319	58	nh(p	nh(p	NUM
ejpam-4770	319	59	)	)	PUNCT
ejpam-4770	319	60	.	.	PUNCT
ejpam-4770	320	1	this	this	PRON
ejpam-4770	320	2	is	be	AUX
ejpam-4770	320	3	a	a	DET
ejpam-4770	320	4	contradiction	contradiction	NOUN
ejpam-4770	320	5	to	to	ADP
ejpam-4770	320	6	w	w	NOUN
ejpam-4770	320	7	being	be	AUX
ejpam-4770	320	8	a	a	DET
ejpam-4770	320	9	1	1	NUM
ejpam-4770	320	10	-	-	PUNCT
ejpam-4770	320	11	movable	movable	ADJ
ejpam-4770	320	12	2	2	NUM
ejpam-4770	320	13	-	-	PUNCT
ejpam-4770	320	14	resolving	resolve	VERB
ejpam-4770	320	15	hop	hop	NOUN
ejpam-4770	320	16	dominating	dominating	NOUN
ejpam-4770	320	17	set	set	NOUN
ejpam-4770	320	18	of	of	ADP
ejpam-4770	320	19	g[h	g[h	NOUN
ejpam-4770	320	20	]	]	PUNCT
ejpam-4770	320	21	.	.	PUNCT
ejpam-4770	321	1	hence	hence	ADV
ejpam-4770	321	2	,	,	PUNCT
ejpam-4770	321	3	(	(	PUNCT
ejpam-4770	321	4	iii	iii	NOUN
ejpam-4770	321	5	)	)	PUNCT
ejpam-4770	321	6	holds	hold	VERB
ejpam-4770	321	7	.	.	PUNCT
ejpam-4770	322	1	to	to	PART
ejpam-4770	322	2	prove	prove	VERB
ejpam-4770	322	3	(	(	PUNCT
ejpam-4770	322	4	iv	iv	NUM
ejpam-4770	322	5	)	)	PUNCT
ejpam-4770	322	6	,	,	PUNCT
ejpam-4770	322	7	let	let	VERB
ejpam-4770	322	8	x	x	PRON
ejpam-4770	322	9	and	and	CCONJ
ejpam-4770	322	10	y	y	PROPN
ejpam-4770	322	11	be	be	AUX
ejpam-4770	322	12	adjacent	adjacent	ADJ
ejpam-4770	322	13	vertices	vertex	NOUN
ejpam-4770	322	14	of	of	ADP
ejpam-4770	322	15	g	g	NOUN
ejpam-4770	322	16	with	with	ADP
ejpam-4770	322	17	dg(x	dg(x	NUM
ejpam-4770	322	18	,	,	PUNCT
ejpam-4770	322	19	z	z	NOUN
ejpam-4770	322	20	)	)	PUNCT
ejpam-4770	322	21	=	=	SYM
ejpam-4770	322	22	dg(y	dg(y	ADJ
ejpam-4770	322	23	,	,	PUNCT
ejpam-4770	322	24	z	z	NOUN
ejpam-4770	322	25	)	)	PUNCT
ejpam-4770	322	26	for	for	ADP
ejpam-4770	322	27	all	all	DET
ejpam-4770	322	28	z	z	NOUN
ejpam-4770	322	29	∈	∈	PROPN
ejpam-4770	322	30	v	v	NOUN
ejpam-4770	322	31	(	(	PUNCT
ejpam-4770	322	32	g)\{x	g)\{x	PROPN
ejpam-4770	322	33	,	,	PUNCT
ejpam-4770	322	34	y	y	NOUN
ejpam-4770	322	35	}	}	PUNCT
ejpam-4770	322	36	.	.	PUNCT
ejpam-4770	323	1	let	let	VERB
ejpam-4770	323	2	p	p	PRON
ejpam-4770	323	3	,	,	PUNCT
ejpam-4770	323	4	w	w	PROPN
ejpam-4770	323	5	∈	∈	PROPN
ejpam-4770	323	6	v	v	ADP
ejpam-4770	323	7	(	(	PUNCT
ejpam-4770	323	8	h	h	NOUN
ejpam-4770	323	9	)	)	PUNCT
ejpam-4770	323	10	,	,	PUNCT
ejpam-4770	323	11	p	p	PROPN
ejpam-4770	323	12	̸=	̸=	PROPN
ejpam-4770	323	13	w.	w.	NOUN
ejpam-4770	323	14	suppose	suppose	VERB
ejpam-4770	323	15	(	(	PUNCT
ejpam-4770	323	16	iii	iii	X
ejpam-4770	323	17	)	)	PUNCT
ejpam-4770	323	18	does	do	AUX
ejpam-4770	323	19	not	not	PART
ejpam-4770	323	20	hold	hold	VERB
ejpam-4770	323	21	.	.	PUNCT
ejpam-4770	324	1	then	then	ADV
ejpam-4770	324	2	there	there	PRON
ejpam-4770	324	3	exist	exist	VERB
ejpam-4770	324	4	a	a	DET
ejpam-4770	324	5	∈	∈	PROPN
ejpam-4770	324	6	v	v	NOUN
ejpam-4770	324	7	(	(	PUNCT
ejpam-4770	324	8	h)\(tx\{p	h)\(tx\{p	NOUN
ejpam-4770	324	9	}	}	PUNCT
ejpam-4770	324	10	)	)	PUNCT
ejpam-4770	324	11	and	and	CCONJ
ejpam-4770	324	12	w	w	PROPN
ejpam-4770	324	13	∈	∈	PROPN
ejpam-4770	324	14	v	v	X
ejpam-4770	324	15	(	(	PUNCT
ejpam-4770	324	16	h)\ty	h)\ty	PROPN
ejpam-4770	324	17	such	such	ADJ
ejpam-4770	324	18	that	that	DET
ejpam-4770	324	19	nh(a	nh(a	NUM
ejpam-4770	324	20	)	)	PUNCT
ejpam-4770	324	21	∩	∩	NOUN
ejpam-4770	324	22	(	(	PUNCT
ejpam-4770	324	23	tx\{p	tx\{p	NUM
ejpam-4770	324	24	}	}	PUNCT
ejpam-4770	324	25	)	)	PUNCT
ejpam-4770	324	26	=	=	PUNCT
ejpam-4770	324	27	tx\{p	tx\{p	NOUN
ejpam-4770	324	28	}	}	PUNCT
ejpam-4770	324	29	and	and	CCONJ
ejpam-4770	324	30	nh(w)∩ty	nh(w)∩ty	NUM
ejpam-4770	324	31	=	=	PUNCT
ejpam-4770	324	32	ty	ty	INTJ
ejpam-4770	324	33	for	for	ADP
ejpam-4770	324	34	some	some	DET
ejpam-4770	324	35	adjacent	adjacent	ADJ
ejpam-4770	324	36	vertices	vertex	NOUN
ejpam-4770	324	37	x	x	PUNCT
ejpam-4770	324	38	and	and	CCONJ
ejpam-4770	324	39	y	y	PROPN
ejpam-4770	324	40	of	of	ADP
ejpam-4770	324	41	g	g	PROPN
ejpam-4770	324	42	and	and	CCONJ
ejpam-4770	324	43	for	for	ADP
ejpam-4770	324	44	some	some	DET
ejpam-4770	324	45	p	p	PROPN
ejpam-4770	324	46	∈	∈	PROPN
ejpam-4770	324	47	tx	tx	PROPN
ejpam-4770	324	48	.	.	PUNCT
ejpam-4770	325	1	hence	hence	ADV
ejpam-4770	325	2	,	,	PUNCT
ejpam-4770	325	3	both	both	DET
ejpam-4770	325	4	w\{(x	w\{(x	PROPN
ejpam-4770	325	5	,	,	PUNCT
ejpam-4770	325	6	p	p	NOUN
ejpam-4770	325	7	)	)	PUNCT
ejpam-4770	325	8	}	}	PUNCT
ejpam-4770	325	9	and	and	CCONJ
ejpam-4770	325	10	(	(	PUNCT
ejpam-4770	325	11	w\{(x	w\{(x	PROPN
ejpam-4770	325	12	,	,	PUNCT
ejpam-4770	325	13	p	p	NOUN
ejpam-4770	325	14	)	)	PUNCT
ejpam-4770	325	15	}	}	PUNCT
ejpam-4770	325	16	)	)	PUNCT
ejpam-4770	325	17	∪	∪	X
ejpam-4770	325	18	{	{	PUNCT
ejpam-4770	325	19	(	(	PUNCT
ejpam-4770	325	20	y	y	PROPN
ejpam-4770	325	21	,	,	PUNCT
ejpam-4770	325	22	w	w	NOUN
ejpam-4770	325	23	)	)	PUNCT
ejpam-4770	325	24	}	}	PUNCT
ejpam-4770	325	25	are	be	AUX
ejpam-4770	325	26	not	not	PART
ejpam-4770	325	27	2	2	NUM
ejpam-4770	325	28	-	-	PUNCT
ejpam-4770	325	29	resolving	resolve	VERB
ejpam-4770	325	30	sets	set	NOUN
ejpam-4770	325	31	,	,	PUNCT
ejpam-4770	325	32	a	a	DET
ejpam-4770	325	33	contradiction	contradiction	NOUN
ejpam-4770	325	34	.	.	PUNCT
ejpam-4770	326	1	thus	thus	ADV
ejpam-4770	326	2	,	,	PUNCT
ejpam-4770	326	3	(	(	PUNCT
ejpam-4770	326	4	iv	iv	X
ejpam-4770	326	5	)	)	PUNCT
ejpam-4770	326	6	holds	hold	NOUN
ejpam-4770	326	7	.	.	PUNCT
ejpam-4770	327	1	to	to	PART
ejpam-4770	327	2	prove	prove	VERB
ejpam-4770	327	3	(	(	PUNCT
ejpam-4770	327	4	v	v	NOUN
ejpam-4770	327	5	)	)	PUNCT
ejpam-4770	327	6	,	,	PUNCT
ejpam-4770	327	7	let	let	VERB
ejpam-4770	327	8	x	x	PRON
ejpam-4770	327	9	,	,	PUNCT
ejpam-4770	327	10	y	y	PROPN
ejpam-4770	327	11	∈	∈	PROPN
ejpam-4770	327	12	v	v	ADP
ejpam-4770	327	13	(	(	PUNCT
ejpam-4770	327	14	g	g	NOUN
ejpam-4770	327	15	)	)	PUNCT
ejpam-4770	327	16	where	where	SCONJ
ejpam-4770	327	17	dg(x	dg(x	NUM
ejpam-4770	327	18	,	,	PUNCT
ejpam-4770	327	19	y	y	NOUN
ejpam-4770	327	20	)	)	PUNCT
ejpam-4770	327	21	=	=	SYM
ejpam-4770	327	22	2	2	NUM
ejpam-4770	327	23	and	and	CCONJ
ejpam-4770	327	24	dg(x	dg(x	NUM
ejpam-4770	327	25	,	,	PUNCT
ejpam-4770	327	26	z	z	NOUN
ejpam-4770	327	27	)	)	PUNCT
ejpam-4770	327	28	=	=	SYM
ejpam-4770	327	29	dg(y	dg(y	ADJ
ejpam-4770	327	30	,	,	PUNCT
ejpam-4770	327	31	z	z	NOUN
ejpam-4770	327	32	)	)	PUNCT
ejpam-4770	327	33	for	for	ADP
ejpam-4770	327	34	all	all	DET
ejpam-4770	327	35	z	z	NOUN
ejpam-4770	327	36	∈	∈	PROPN
ejpam-4770	327	37	v	v	NOUN
ejpam-4770	327	38	(	(	PUNCT
ejpam-4770	327	39	g)\{x	g)\{x	PROPN
ejpam-4770	327	40	,	,	PUNCT
ejpam-4770	327	41	y	y	NOUN
ejpam-4770	327	42	}	}	PUNCT
ejpam-4770	327	43	.	.	PUNCT
ejpam-4770	328	1	let	let	VERB
ejpam-4770	328	2	p	p	PRON
ejpam-4770	328	3	,	,	PUNCT
ejpam-4770	328	4	w	w	PROPN
ejpam-4770	328	5	∈	∈	PROPN
ejpam-4770	328	6	v	v	ADP
ejpam-4770	328	7	(	(	PUNCT
ejpam-4770	328	8	h	h	NOUN
ejpam-4770	328	9	)	)	PUNCT
ejpam-4770	328	10	,	,	PUNCT
ejpam-4770	328	11	p	p	PROPN
ejpam-4770	328	12	̸=	̸=	PROPN
ejpam-4770	328	13	w.	w.	NOUN
ejpam-4770	328	14	suppose	suppose	VERB
ejpam-4770	328	15	one	one	NUM
ejpam-4770	328	16	of	of	ADP
ejpam-4770	328	17	tx\{p	tx\{p	NOUN
ejpam-4770	328	18	}	}	PUNCT
ejpam-4770	328	19	and	and	CCONJ
ejpam-4770	328	20	ty	ty	INTJ
ejpam-4770	328	21	,	,	PUNCT
ejpam-4770	328	22	say	say	VERB
ejpam-4770	328	23	tx\{p	tx\{p	NUM
ejpam-4770	328	24	}	}	PUNCT
ejpam-4770	328	25	a.m.	a.m.	NOUN
ejpam-4770	328	26	mahistrado	mahistrado	NOUN
ejpam-4770	328	27	,	,	PUNCT
ejpam-4770	328	28	h.	h.	PROPN
ejpam-4770	328	29	rara	rara	PROPN
ejpam-4770	328	30	/	/	SYM
ejpam-4770	328	31	eur	eur	PROPN
ejpam-4770	328	32	.	.	PUNCT
ejpam-4770	329	1	j.	j.	PROPN
ejpam-4770	329	2	pure	pure	PROPN
ejpam-4770	329	3	appl	appl	PROPN
ejpam-4770	329	4	.	.	PROPN
ejpam-4770	329	5	math	math	PROPN
ejpam-4770	329	6	,	,	PUNCT
ejpam-4770	329	7	16	16	NUM
ejpam-4770	329	8	(	(	PUNCT
ejpam-4770	329	9	3	3	NUM
ejpam-4770	329	10	)	)	PUNCT
ejpam-4770	329	11	(	(	PUNCT
ejpam-4770	329	12	2023	2023	NUM
ejpam-4770	329	13	)	)	PUNCT
ejpam-4770	329	14	,	,	PUNCT
ejpam-4770	329	15	1464	1464	NUM
ejpam-4770	329	16	-	-	SYM
ejpam-4770	329	17	1479	1479	NUM
ejpam-4770	329	18	1477	1477	NUM
ejpam-4770	329	19	is	be	AUX
ejpam-4770	329	20	not	not	PART
ejpam-4770	329	21	a	a	DET
ejpam-4770	329	22	dominating	dominating	NOUN
ejpam-4770	329	23	set	set	VERB
ejpam-4770	329	24	in	in	ADP
ejpam-4770	329	25	h.	h.	PROPN
ejpam-4770	329	26	pick	pick	PROPN
ejpam-4770	329	27	p	p	PROPN
ejpam-4770	329	28	∈	∈	PROPN
ejpam-4770	329	29	v	v	NOUN
ejpam-4770	329	30	(	(	PUNCT
ejpam-4770	329	31	h)\nh	h)\nh	PROPN
ejpam-4770	330	1	[	[	X
ejpam-4770	330	2	tx	tx	X
ejpam-4770	330	3	]	]	PUNCT
ejpam-4770	330	4	and	and	CCONJ
ejpam-4770	330	5	let	let	VERB
ejpam-4770	330	6	w	w	PROPN
ejpam-4770	330	7	∈	∈	PROPN
ejpam-4770	330	8	v	v	X
ejpam-4770	330	9	(	(	PUNCT
ejpam-4770	330	10	h)\ty	h)\ty	PROPN
ejpam-4770	330	11	.	.	PUNCT
ejpam-4770	331	1	since	since	SCONJ
ejpam-4770	331	2	dg[h]((x	dg[h]((x	PROPN
ejpam-4770	331	3	,	,	PUNCT
ejpam-4770	331	4	a	a	PRON
ejpam-4770	331	5	)	)	PUNCT
ejpam-4770	331	6	,	,	PUNCT
ejpam-4770	331	7	(	(	PUNCT
ejpam-4770	331	8	y	y	NOUN
ejpam-4770	331	9	,	,	PUNCT
ejpam-4770	331	10	w	w	NOUN
ejpam-4770	331	11	)	)	PUNCT
ejpam-4770	331	12	)	)	PUNCT
ejpam-4770	331	13	=	=	SYM
ejpam-4770	331	14	2	2	NUM
ejpam-4770	331	15	,	,	PUNCT
ejpam-4770	331	16	for	for	ADP
ejpam-4770	331	17	all	all	PRON
ejpam-4770	331	18	(	(	PUNCT
ejpam-4770	331	19	y	y	PROPN
ejpam-4770	331	20	,	,	PUNCT
ejpam-4770	331	21	w	w	PROPN
ejpam-4770	331	22	)	)	PUNCT
ejpam-4770	331	23	,	,	PUNCT
ejpam-4770	331	24	it	it	PRON
ejpam-4770	331	25	follows	follow	VERB
ejpam-4770	331	26	that	that	PRON
ejpam-4770	331	27	|nh(b	|nh(b	NOUN
ejpam-4770	331	28	)	)	PUNCT
ejpam-4770	331	29	∩	∩	NOUN
ejpam-4770	331	30	ty|	ty|	PRON
ejpam-4770	331	31	≥	≥	NUM
ejpam-4770	331	32	2	2	NUM
ejpam-4770	331	33	,	,	PUNCT
ejpam-4770	331	34	that	that	ADV
ejpam-4770	331	35	is	is	ADV
ejpam-4770	331	36	,	,	PUNCT
ejpam-4770	331	37	ty	ty	INTJ
ejpam-4770	331	38	is	be	AUX
ejpam-4770	331	39	a	a	DET
ejpam-4770	331	40	2	2	NUM
ejpam-4770	331	41	-	-	PUNCT
ejpam-4770	331	42	dominating	dominating	NOUN
ejpam-4770	331	43	set	set	NOUN
ejpam-4770	331	44	.	.	PUNCT
ejpam-4770	332	1	thus	thus	ADV
ejpam-4770	332	2	,	,	PUNCT
ejpam-4770	332	3	(	(	PUNCT
ejpam-4770	332	4	v	v	NOUN
ejpam-4770	332	5	)	)	PUNCT
ejpam-4770	332	6	holds	hold	VERB
ejpam-4770	332	7	.	.	PUNCT
ejpam-4770	333	1	conversely	conversely	ADV
ejpam-4770	333	2	,	,	PUNCT
ejpam-4770	333	3	suppose	suppose	VERB
ejpam-4770	333	4	that	that	SCONJ
ejpam-4770	333	5	w	w	NOUN
ejpam-4770	333	6	satisfies	satisfie	NOUN
ejpam-4770	333	7	properties	property	NOUN
ejpam-4770	333	8	(	(	PUNCT
ejpam-4770	333	9	i	i	NOUN
ejpam-4770	333	10	)	)	PUNCT
ejpam-4770	333	11	to	to	ADP
ejpam-4770	333	12	(	(	PUNCT
ejpam-4770	333	13	v	v	NOUN
ejpam-4770	333	14	)	)	PUNCT
ejpam-4770	333	15	.	.	PUNCT
ejpam-4770	334	1	by	by	ADP
ejpam-4770	334	2	theorem	theorem	NOUN
ejpam-4770	334	3	7	7	NUM
ejpam-4770	334	4	,	,	PUNCT
ejpam-4770	334	5	w	w	PROPN
ejpam-4770	334	6	is	be	AUX
ejpam-4770	334	7	a	a	DET
ejpam-4770	334	8	2	2	NUM
ejpam-4770	334	9	-	-	PUNCT
ejpam-4770	334	10	resolving	resolve	VERB
ejpam-4770	334	11	hop	hop	NOUN
ejpam-4770	334	12	dominating	dominating	NOUN
ejpam-4770	334	13	set	set	NOUN
ejpam-4770	334	14	of	of	ADP
ejpam-4770	334	15	g[h	g[h	PROPN
ejpam-4770	334	16	]	]	PUNCT
ejpam-4770	334	17	.	.	PUNCT
ejpam-4770	335	1	let	let	VERB
ejpam-4770	335	2	x	x	SYM
ejpam-4770	335	3	∈	∈	PROPN
ejpam-4770	335	4	v	v	X
ejpam-4770	335	5	(	(	PUNCT
ejpam-4770	335	6	g	g	NOUN
ejpam-4770	335	7	)	)	PUNCT
ejpam-4770	335	8	and	and	CCONJ
ejpam-4770	335	9	p	p	PROPN
ejpam-4770	335	10	∈	∈	PROPN
ejpam-4770	335	11	tx	tx	PROPN
ejpam-4770	335	12	.	.	PUNCT
ejpam-4770	336	1	then	then	ADV
ejpam-4770	336	2	(	(	PUNCT
ejpam-4770	336	3	x	x	X
ejpam-4770	336	4	,	,	PUNCT
ejpam-4770	336	5	p	p	NOUN
ejpam-4770	336	6	)	)	PUNCT
ejpam-4770	336	7	∈	∈	PROPN
ejpam-4770	336	8	w	w	NOUN
ejpam-4770	336	9	and	and	CCONJ
ejpam-4770	336	10	w\{(x	w\{(x	PROPN
ejpam-4770	336	11	,	,	PUNCT
ejpam-4770	336	12	p	p	NOUN
ejpam-4770	336	13	)	)	PUNCT
ejpam-4770	336	14	}	}	PUNCT
ejpam-4770	336	15	=	=	SYM
ejpam-4770	336	16	(	(	PUNCT
ejpam-4770	336	17	⋃	⋃	NOUN
ejpam-4770	336	18	v∈s\{x	v∈s\{x	NOUN
ejpam-4770	336	19	}	}	PUNCT
ejpam-4770	336	20	(	(	PUNCT
ejpam-4770	336	21	{	{	PUNCT
ejpam-4770	336	22	v	v	NOUN
ejpam-4770	336	23	}	}	PUNCT
ejpam-4770	336	24	×	×	NOUN
ejpam-4770	336	25	tv	tv	NOUN
ejpam-4770	336	26	)	)	PUNCT
ejpam-4770	336	27	)	)	PUNCT
ejpam-4770	337	1	∪	∪	ADP
ejpam-4770	337	2	[	[	X
ejpam-4770	337	3	{	{	PUNCT
ejpam-4770	337	4	x	x	NOUN
ejpam-4770	337	5	}	}	PUNCT
ejpam-4770	337	6	×	×	NOUN
ejpam-4770	337	7	(	(	PUNCT
ejpam-4770	337	8	tx\{p	tx\{p	NUM
ejpam-4770	337	9	}	}	PUNCT
ejpam-4770	337	10	)	)	PUNCT
ejpam-4770	337	11	]	]	PUNCT
ejpam-4770	337	12	and	and	CCONJ
ejpam-4770	337	13	(	(	PUNCT
ejpam-4770	337	14	w\{(x	w\{(x	PROPN
ejpam-4770	337	15	,	,	PUNCT
ejpam-4770	337	16	p	p	NOUN
ejpam-4770	337	17	)	)	PUNCT
ejpam-4770	337	18	}	}	PUNCT
ejpam-4770	337	19	)	)	PUNCT
ejpam-4770	337	20	∪	∪	X
ejpam-4770	337	21	{	{	PUNCT
ejpam-4770	337	22	(	(	PUNCT
ejpam-4770	337	23	x	x	NOUN
ejpam-4770	337	24	,	,	PUNCT
ejpam-4770	337	25	q	q	NOUN
ejpam-4770	337	26	)	)	PUNCT
ejpam-4770	337	27	}	}	PUNCT
ejpam-4770	337	28	=	=	SYM
ejpam-4770	338	1			PROPN
ejpam-4770	338	2	⋃	⋃	PROPN
ejpam-4770	338	3	z∈s\{x	z∈s\{x	PROPN
ejpam-4770	338	4	}	}	PUNCT
ejpam-4770	338	5	(	(	PUNCT
ejpam-4770	338	6	{	{	PUNCT
ejpam-4770	338	7	z	z	NOUN
ejpam-4770	338	8	}	}	PUNCT
ejpam-4770	338	9	×	×	PROPN
ejpam-4770	338	10	tz	tz	NOUN
ejpam-4770	338	11	)	)	PUNCT
ejpam-4770	338	12			PROPN
ejpam-4770	338	13	∪	∪	ADV
ejpam-4770	338	14	[	[	X
ejpam-4770	338	15	{	{	PUNCT
ejpam-4770	338	16	x	x	NOUN
ejpam-4770	338	17	}	}	PUNCT
ejpam-4770	338	18	×	×	NOUN
ejpam-4770	338	19	(	(	PUNCT
ejpam-4770	338	20	tx\{p	tx\{p	NOUN
ejpam-4770	338	21	}	}	PUNCT
ejpam-4770	338	22	∪	∪	ADJ
ejpam-4770	338	23	{	{	PUNCT
ejpam-4770	338	24	q	q	NOUN
ejpam-4770	338	25	}	}	PUNCT
ejpam-4770	338	26	)	)	PUNCT
ejpam-4770	338	27	]	]	PUNCT
ejpam-4770	338	28	for	for	ADP
ejpam-4770	338	29	some	some	DET
ejpam-4770	338	30	q	q	NOUN
ejpam-4770	338	31	∈	∈	PROPN
ejpam-4770	338	32	(	(	PUNCT
ejpam-4770	338	33	v	v	NOUN
ejpam-4770	338	34	(	(	PUNCT
ejpam-4770	338	35	h)\tx	h)\tx	NOUN
ejpam-4770	338	36	)	)	PUNCT
ejpam-4770	338	37	∩nh(p	∩nh(p	NOUN
ejpam-4770	338	38	)	)	PUNCT
ejpam-4770	338	39	and	and	CCONJ
ejpam-4770	338	40	(	(	PUNCT
ejpam-4770	338	41	w\{(x	w\{(x	PROPN
ejpam-4770	338	42	,	,	PUNCT
ejpam-4770	338	43	p	p	NOUN
ejpam-4770	338	44	)	)	PUNCT
ejpam-4770	338	45	}	}	PUNCT
ejpam-4770	338	46	)	)	PUNCT
ejpam-4770	338	47	∪	∪	X
ejpam-4770	338	48	{	{	PUNCT
ejpam-4770	338	49	(	(	PUNCT
ejpam-4770	338	50	y	y	PROPN
ejpam-4770	338	51	,	,	PUNCT
ejpam-4770	338	52	w	w	NOUN
ejpam-4770	338	53	)	)	PUNCT
ejpam-4770	338	54	}	}	PUNCT
ejpam-4770	338	55	=	=	SYM
ejpam-4770	339	1			PROPN
ejpam-4770	339	2	⋃	⋃	PROPN
ejpam-4770	339	3	a∈s\{(x	a∈s\{(x	NOUN
ejpam-4770	339	4	,	,	PUNCT
ejpam-4770	339	5	y	y	NOUN
ejpam-4770	339	6	)	)	PUNCT
ejpam-4770	339	7	}	}	PUNCT
ejpam-4770	339	8	(	(	PUNCT
ejpam-4770	339	9	{	{	PUNCT
ejpam-4770	339	10	a	a	PRON
ejpam-4770	339	11	}	}	PUNCT
ejpam-4770	339	12	×	×	NOUN
ejpam-4770	339	13	ta	ta	NOUN
ejpam-4770	339	14	)	)	PUNCT
ejpam-4770	339	15			PROPN
ejpam-4770	339	16	∪	∪	ADV
ejpam-4770	339	17	[	[	X
ejpam-4770	339	18	{	{	PUNCT
ejpam-4770	339	19	x	x	NOUN
ejpam-4770	339	20	}	}	PUNCT
ejpam-4770	339	21	×	×	NOUN
ejpam-4770	339	22	(	(	PUNCT
ejpam-4770	339	23	tx\{p	tx\{p	NUM
ejpam-4770	339	24	}	}	PUNCT
ejpam-4770	339	25	)	)	PUNCT
ejpam-4770	339	26	]	]	PUNCT
ejpam-4770	339	27	∪	∪	ADP
ejpam-4770	339	28	[	[	X
ejpam-4770	339	29	{	{	PUNCT
ejpam-4770	339	30	y	y	NOUN
ejpam-4770	339	31	}	}	PUNCT
ejpam-4770	339	32	×	×	NOUN
ejpam-4770	339	33	(	(	PUNCT
ejpam-4770	339	34	ty\{w	ty\{w	NUM
ejpam-4770	339	35	}	}	PUNCT
ejpam-4770	339	36	)	)	PUNCT
ejpam-4770	339	37	]	]	PUNCT
ejpam-4770	339	38	for	for	ADP
ejpam-4770	339	39	some	some	DET
ejpam-4770	339	40	y	y	PROPN
ejpam-4770	339	41	∈	∈	PROPN
ejpam-4770	339	42	v	v	ADP
ejpam-4770	339	43	(	(	PUNCT
ejpam-4770	339	44	g	g	NOUN
ejpam-4770	339	45	)	)	PUNCT
ejpam-4770	339	46	∩ng(x	∩ng(x	NOUN
ejpam-4770	339	47	)	)	PUNCT
ejpam-4770	339	48	and	and	CCONJ
ejpam-4770	339	49	w	w	PROPN
ejpam-4770	339	50	∈	∈	PROPN
ejpam-4770	339	51	v	v	ADP
ejpam-4770	339	52	(	(	PUNCT
ejpam-4770	339	53	h)\ty	h)\ty	PROPN
ejpam-4770	339	54	.	.	PUNCT
ejpam-4770	339	55	by	by	ADP
ejpam-4770	339	56	(	(	PUNCT
ejpam-4770	339	57	i	i	NOUN
ejpam-4770	339	58	)	)	PUNCT
ejpam-4770	339	59	to	to	ADP
ejpam-4770	339	60	(	(	PUNCT
ejpam-4770	339	61	v	v	NOUN
ejpam-4770	339	62	)	)	PUNCT
ejpam-4770	339	63	,	,	PUNCT
ejpam-4770	339	64	for	for	ADP
ejpam-4770	339	65	every	every	DET
ejpam-4770	339	66	(	(	PUNCT
ejpam-4770	339	67	x	x	NOUN
ejpam-4770	339	68	,	,	PUNCT
ejpam-4770	339	69	p	p	NOUN
ejpam-4770	339	70	)	)	PUNCT
ejpam-4770	339	71	∈	∈	PROPN
ejpam-4770	339	72	w	w	ADP
ejpam-4770	339	73	either	either	CCONJ
ejpam-4770	339	74	w\{(x	w\{(x	PROPN
ejpam-4770	339	75	,	,	PUNCT
ejpam-4770	339	76	p	p	NOUN
ejpam-4770	339	77	)	)	PUNCT
ejpam-4770	339	78	}	}	PUNCT
ejpam-4770	339	79	is	be	AUX
ejpam-4770	339	80	a	a	DET
ejpam-4770	339	81	2	2	NUM
ejpam-4770	339	82	-	-	PUNCT
ejpam-4770	339	83	resolving	resolve	VERB
ejpam-4770	339	84	hop	hop	NOUN
ejpam-4770	339	85	dominating	dominating	NOUN
ejpam-4770	339	86	set	set	VERB
ejpam-4770	339	87	in	in	ADP
ejpam-4770	339	88	g[h	g[h	PROPN
ejpam-4770	339	89	]	]	PUNCT
ejpam-4770	339	90	or	or	CCONJ
ejpam-4770	339	91	there	there	PRON
ejpam-4770	339	92	exists	exist	VERB
ejpam-4770	339	93	(	(	PUNCT
ejpam-4770	339	94	y	y	NOUN
ejpam-4770	339	95	,	,	PUNCT
ejpam-4770	339	96	q	q	NOUN
ejpam-4770	339	97	)	)	PUNCT
ejpam-4770	339	98	∈	∈	PROPN
ejpam-4770	339	99	ng[h]((x	ng[h]((x	NOUN
ejpam-4770	339	100	,	,	PUNCT
ejpam-4770	339	101	p	p	NOUN
ejpam-4770	339	102	)	)	PUNCT
ejpam-4770	339	103	)	)	PUNCT
ejpam-4770	339	104	∩	∩	NOUN
ejpam-4770	339	105	(	(	PUNCT
ejpam-4770	339	106	v	v	NOUN
ejpam-4770	339	107	(	(	PUNCT
ejpam-4770	339	108	g[h])\w	g[h])\w	NOUN
ejpam-4770	339	109	)	)	PUNCT
ejpam-4770	339	110	such	such	ADJ
ejpam-4770	339	111	that	that	SCONJ
ejpam-4770	339	112	(	(	PUNCT
ejpam-4770	339	113	w\{(x	w\{(x	PROPN
ejpam-4770	339	114	,	,	PUNCT
ejpam-4770	339	115	p	p	NOUN
ejpam-4770	339	116	)	)	PUNCT
ejpam-4770	339	117	}	}	PUNCT
ejpam-4770	339	118	)	)	PUNCT
ejpam-4770	339	119	∪	∪	X
ejpam-4770	339	120	{	{	PUNCT
ejpam-4770	339	121	(	(	PUNCT
ejpam-4770	339	122	y	y	PROPN
ejpam-4770	339	123	,	,	PUNCT
ejpam-4770	339	124	q	q	NOUN
ejpam-4770	339	125	)	)	PUNCT
ejpam-4770	339	126	}	}	PUNCT
ejpam-4770	339	127	is	be	AUX
ejpam-4770	339	128	a	a	DET
ejpam-4770	339	129	2	2	NUM
ejpam-4770	339	130	-	-	PUNCT
ejpam-4770	339	131	resolving	resolve	VERB
ejpam-4770	339	132	hop	hop	NOUN
ejpam-4770	339	133	dominating	dominating	NOUN
ejpam-4770	339	134	set	set	VERB
ejpam-4770	339	135	in	in	ADP
ejpam-4770	339	136	g[h	g[h	PROPN
ejpam-4770	339	137	]	]	PUNCT
ejpam-4770	339	138	.	.	PUNCT
ejpam-4770	340	1	accordingly	accordingly	ADV
ejpam-4770	340	2	,	,	PUNCT
ejpam-4770	340	3	w	w	PROPN
ejpam-4770	340	4	is	be	AUX
ejpam-4770	340	5	a	a	DET
ejpam-4770	340	6	1	1	NUM
ejpam-4770	340	7	-	-	PUNCT
ejpam-4770	340	8	movable	movable	ADJ
ejpam-4770	340	9	2	2	NUM
ejpam-4770	340	10	-	-	PUNCT
ejpam-4770	340	11	resolving	resolve	VERB
ejpam-4770	340	12	hop	hop	NOUN
ejpam-4770	340	13	dominating	dominating	NOUN
ejpam-4770	340	14	set	set	VERB
ejpam-4770	340	15	in	in	ADP
ejpam-4770	340	16	g[h	g[h	PROPN
ejpam-4770	340	17	]	]	PUNCT
ejpam-4770	340	18	.	.	PUNCT
ejpam-4770	341	1	corollary	corollary	ADJ
ejpam-4770	341	2	5	5	NUM
ejpam-4770	341	3	.	.	PUNCT
ejpam-4770	342	1	let	let	VERB
ejpam-4770	342	2	g	g	NOUN
ejpam-4770	342	3	and	and	CCONJ
ejpam-4770	342	4	h	h	NOUN
ejpam-4770	342	5	be	be	AUX
ejpam-4770	342	6	nontrivial	nontrivial	ADJ
ejpam-4770	342	7	connected	connected	ADJ
ejpam-4770	342	8	graph	graph	NOUN
ejpam-4770	342	9	with	with	ADP
ejpam-4770	342	10	γ(g	γ(g	PROPN
ejpam-4770	342	11	)	)	PUNCT
ejpam-4770	342	12	̸=	̸=	PROPN
ejpam-4770	342	13	1	1	NUM
ejpam-4770	342	14	and	and	CCONJ
ejpam-4770	342	15	g	g	PROPN
ejpam-4770	342	16	is	be	AUX
ejpam-4770	342	17	freeequidistant	freeequidistant	ADJ
ejpam-4770	342	18	.	.	PUNCT
ejpam-4770	343	1	then	then	ADV
ejpam-4770	343	2	γ1m2rh(g[h	γ1m2rh(g[h	ADP
ejpam-4770	343	3	]	]	X
ejpam-4770	343	4	)	)	PUNCT
ejpam-4770	343	5	=	=	SYM
ejpam-4770	343	6	|v	|v	PROPN
ejpam-4770	343	7	(	(	PUNCT
ejpam-4770	343	8	g)|	g)|	PROPN
ejpam-4770	343	9	·	·	SYM
ejpam-4770	343	10	mln2(h	mln2(h	X
ejpam-4770	343	11	)	)	PUNCT
ejpam-4770	343	12	.	.	PUNCT
ejpam-4770	344	1	proof	proof	NOUN
ejpam-4770	344	2	.	.	PUNCT
ejpam-4770	345	1	let	let	VERB
ejpam-4770	345	2	s	s	PRON
ejpam-4770	345	3	=	=	X
ejpam-4770	345	4	v	v	ADJ
ejpam-4770	345	5	(	(	PUNCT
ejpam-4770	345	6	g	g	NOUN
ejpam-4770	345	7	)	)	PUNCT
ejpam-4770	345	8	and	and	CCONJ
ejpam-4770	345	9	let	let	VERB
ejpam-4770	345	10	rx	rx	AUX
ejpam-4770	345	11	be	be	AUX
ejpam-4770	345	12	an	an	DET
ejpam-4770	345	13	mln2	mln2	NOUN
ejpam-4770	345	14	-	-	PUNCT
ejpam-4770	345	15	set	set	NOUN
ejpam-4770	345	16	of	of	ADP
ejpam-4770	345	17	h	h	NOUN
ejpam-4770	345	18	for	for	ADP
ejpam-4770	345	19	each	each	DET
ejpam-4770	345	20	x	x	PROPN
ejpam-4770	345	21	∈	∈	PROPN
ejpam-4770	345	22	s.	s.	PROPN
ejpam-4770	345	23	since	since	SCONJ
ejpam-4770	345	24	γ(g	γ(g	PROPN
ejpam-4770	345	25	)	)	PUNCT
ejpam-4770	345	26	̸=	̸=	PROPN
ejpam-4770	345	27	1	1	NUM
ejpam-4770	345	28	,	,	PUNCT
ejpam-4770	345	29	x	x	SYM
ejpam-4770	345	30	∈	∈	NOUN
ejpam-4770	345	31	ng(s	ng(s	NOUN
ejpam-4770	345	32	,	,	PUNCT
ejpam-4770	345	33	2	2	NUM
ejpam-4770	345	34	)	)	PUNCT
ejpam-4770	345	35	for	for	ADP
ejpam-4770	345	36	each	each	DET
ejpam-4770	345	37	x	x	PROPN
ejpam-4770	345	38	∈	∈	PROPN
ejpam-4770	345	39	s.	s.	PROPN
ejpam-4770	345	40	by	by	ADP
ejpam-4770	345	41	theorem	theorem	ADJ
ejpam-4770	345	42	8	8	NUM
ejpam-4770	345	43	,	,	PUNCT
ejpam-4770	345	44	w	w	NOUN
ejpam-4770	345	45	=	=	PUNCT
ejpam-4770	345	46	⋃	⋃	PROPN
ejpam-4770	345	47	x∈s	x∈s	NOUN
ejpam-4770	346	1	[	[	X
ejpam-4770	346	2	{	{	PUNCT
ejpam-4770	346	3	x	x	ADJ
ejpam-4770	346	4	}	}	PUNCT
ejpam-4770	346	5	×rx	×rx	PROPN
ejpam-4770	346	6	]	]	PUNCT
ejpam-4770	346	7	is	be	AUX
ejpam-4770	346	8	a	a	DET
ejpam-4770	346	9	1	1	NUM
ejpam-4770	346	10	-	-	PUNCT
ejpam-4770	346	11	movable	movable	ADJ
ejpam-4770	346	12	2	2	NUM
ejpam-4770	346	13	-	-	PUNCT
ejpam-4770	346	14	resolving	resolve	VERB
ejpam-4770	346	15	hop	hop	NOUN
ejpam-4770	346	16	dominating	dominating	NOUN
ejpam-4770	346	17	set	set	VERB
ejpam-4770	346	18	in	in	ADP
ejpam-4770	346	19	g[h	g[h	PROPN
ejpam-4770	346	20	]	]	PUNCT
ejpam-4770	346	21	.	.	PUNCT
ejpam-4770	347	1	thus	thus	ADV
ejpam-4770	347	2	,	,	PUNCT
ejpam-4770	347	3	γ1m2rh(g[h	γ1m2rh(g[h	ADP
ejpam-4770	347	4	]	]	X
ejpam-4770	347	5	)	)	PUNCT
ejpam-4770	347	6	≤	≤	NOUN
ejpam-4770	347	7	|w	|w	NOUN
ejpam-4770	347	8	|	|	NOUN
ejpam-4770	347	9	=	=	SYM
ejpam-4770	347	10	|v	|v	PROPN
ejpam-4770	347	11	(	(	PUNCT
ejpam-4770	347	12	g)||rx|	g)||rx|	PROPN
ejpam-4770	347	13	=	=	SYM
ejpam-4770	347	14	|v	|v	X
ejpam-4770	347	15	(	(	PUNCT
ejpam-4770	347	16	g)|mln2(h	g)|mln2(h	NOUN
ejpam-4770	347	17	)	)	PUNCT
ejpam-4770	347	18	.	.	PUNCT
ejpam-4770	348	1	if	if	SCONJ
ejpam-4770	348	2	w0	w0	PROPN
ejpam-4770	348	3	=	=	PUNCT
ejpam-4770	348	4	⋃	⋃	PROPN
ejpam-4770	348	5	x∈s({x	x∈s({x	NOUN
ejpam-4770	348	6	}	}	SYM
ejpam-4770	348	7	×	×	PROPN
ejpam-4770	348	8	t	t	PROPN
ejpam-4770	348	9	)	)	PUNCT
ejpam-4770	348	10	is	be	AUX
ejpam-4770	348	11	a	a	DET
ejpam-4770	348	12	γ1m2rh	γ1m2rh	PUNCT
ejpam-4770	348	13	-set	-set	PUNCT
ejpam-4770	348	14	of	of	ADP
ejpam-4770	348	15	g[h	g[h	PROPN
ejpam-4770	348	16	]	]	PUNCT
ejpam-4770	348	17	,	,	PUNCT
ejpam-4770	348	18	then	then	ADV
ejpam-4770	348	19	s0	s0	PROPN
ejpam-4770	348	20	=	=	SYM
ejpam-4770	348	21	v	v	PROPN
ejpam-4770	348	22	(	(	PUNCT
ejpam-4770	348	23	g	g	NOUN
ejpam-4770	348	24	)	)	PUNCT
ejpam-4770	348	25	and	and	CCONJ
ejpam-4770	348	26	tx	tx	PROPN
ejpam-4770	348	27	is	be	AUX
ejpam-4770	348	28	a	a	DET
ejpam-4770	348	29	1	1	NUM
ejpam-4770	348	30	-	-	PUNCT
ejpam-4770	348	31	movable	movable	ADJ
ejpam-4770	348	32	2	2	NUM
ejpam-4770	348	33	-	-	PUNCT
ejpam-4770	348	34	locating	locate	VERB
ejpam-4770	348	35	set	set	NOUN
ejpam-4770	348	36	of	of	ADP
ejpam-4770	348	37	h	h	NOUN
ejpam-4770	348	38	for	for	ADP
ejpam-4770	348	39	each	each	DET
ejpam-4770	348	40	x	x	SYM
ejpam-4770	348	41	∈	∈	PROPN
ejpam-4770	348	42	v	v	ADP
ejpam-4770	348	43	(	(	PUNCT
ejpam-4770	348	44	g	g	NOUN
ejpam-4770	348	45	)	)	PUNCT
ejpam-4770	348	46	by	by	ADP
ejpam-4770	348	47	theorem	theorem	NOUN
ejpam-4770	348	48	8	8	NUM
ejpam-4770	348	49	.	.	PUNCT
ejpam-4770	349	1	hence	hence	ADV
ejpam-4770	349	2	,	,	PUNCT
ejpam-4770	349	3	γ1m2rh(g[h	γ1m2rh(g[h	ADP
ejpam-4770	349	4	]	]	X
ejpam-4770	349	5	)	)	PUNCT
ejpam-4770	349	6	=	=	NOUN
ejpam-4770	349	7	|w0|	|w0|	X
ejpam-4770	349	8	=	=	SYM
ejpam-4770	349	9	|v	|v	X
ejpam-4770	349	10	(	(	PUNCT
ejpam-4770	349	11	g)||tx|	g)||tx|	PROPN
ejpam-4770	349	12	≥	≥	NUM
ejpam-4770	349	13	|v	|v	PROPN
ejpam-4770	349	14	(	(	PUNCT
ejpam-4770	349	15	g)|mln2(h	g)|mln2(h	NOUN
ejpam-4770	349	16	)	)	PUNCT
ejpam-4770	349	17	.	.	PUNCT
ejpam-4770	350	1	therefore	therefore	ADV
ejpam-4770	350	2	,	,	PUNCT
ejpam-4770	350	3	γ1m2rh(g[h	γ1m2rh(g[h	ADP
ejpam-4770	350	4	]	]	X
ejpam-4770	350	5	)	)	PUNCT
ejpam-4770	350	6	=	=	SYM
ejpam-4770	350	7	|v	|v	PROPN
ejpam-4770	350	8	(	(	PUNCT
ejpam-4770	350	9	g)|	g)|	PROPN
ejpam-4770	350	10	·	·	SYM
ejpam-4770	350	11	mln2(h	mln2(h	NUM
ejpam-4770	350	12	)	)	PUNCT
ejpam-4770	350	13	.	.	PUNCT
ejpam-4770	351	1	8	8	X
ejpam-4770	351	2	.	.	X
ejpam-4770	351	3	conclusion	conclusion	NOUN
ejpam-4770	351	4	1	1	NUM
ejpam-4770	351	5	-	-	PUNCT
ejpam-4770	351	6	movable	movable	ADJ
ejpam-4770	351	7	2	2	NUM
ejpam-4770	351	8	-	-	PUNCT
ejpam-4770	351	9	resolving	resolve	VERB
ejpam-4770	351	10	hop	hop	NOUN
ejpam-4770	351	11	domination	domination	NOUN
ejpam-4770	351	12	,	,	PUNCT
ejpam-4770	351	13	a	a	DET
ejpam-4770	351	14	variant	variant	NOUN
ejpam-4770	351	15	of	of	ADP
ejpam-4770	351	16	2	2	NUM
ejpam-4770	351	17	-	-	PUNCT
ejpam-4770	351	18	resolving	resolve	VERB
ejpam-4770	351	19	hop	hop	NOUN
ejpam-4770	351	20	domination	domination	NOUN
ejpam-4770	351	21	,	,	PUNCT
ejpam-4770	351	22	has	have	AUX
ejpam-4770	351	23	been	be	AUX
ejpam-4770	351	24	introduced	introduce	VERB
ejpam-4770	351	25	and	and	CCONJ
ejpam-4770	351	26	studied	study	VERB
ejpam-4770	351	27	for	for	ADP
ejpam-4770	351	28	some	some	DET
ejpam-4770	351	29	graphs	graph	NOUN
ejpam-4770	351	30	and	and	CCONJ
ejpam-4770	351	31	graphs	graph	NOUN
ejpam-4770	351	32	resulting	result	VERB
ejpam-4770	351	33	from	from	ADP
ejpam-4770	351	34	the	the	DET
ejpam-4770	351	35	join	join	NOUN
ejpam-4770	351	36	,	,	PUNCT
ejpam-4770	351	37	corona	corona	NOUN
ejpam-4770	351	38	references	reference	NOUN
ejpam-4770	351	39	1478	1478	NUM
ejpam-4770	351	40	and	and	CCONJ
ejpam-4770	351	41	lexicographic	lexicographic	ADJ
ejpam-4770	351	42	product	product	NOUN
ejpam-4770	351	43	of	of	ADP
ejpam-4770	351	44	two	two	NUM
ejpam-4770	351	45	graphs	graph	NOUN
ejpam-4770	351	46	.	.	PUNCT
ejpam-4770	352	1	it	it	PRON
ejpam-4770	352	2	is	be	AUX
ejpam-4770	352	3	recommended	recommend	VERB
ejpam-4770	352	4	that	that	SCONJ
ejpam-4770	352	5	some	some	DET
ejpam-4770	352	6	bounds	bound	NOUN
ejpam-4770	352	7	on	on	ADP
ejpam-4770	352	8	the	the	DET
ejpam-4770	352	9	1	1	NUM
ejpam-4770	352	10	-	-	PUNCT
ejpam-4770	352	11	movable	movable	ADJ
ejpam-4770	352	12	2	2	NUM
ejpam-4770	352	13	-	-	PUNCT
ejpam-4770	352	14	resolving	resolve	VERB
ejpam-4770	352	15	hop	hop	NOUN
ejpam-4770	352	16	domination	domination	NOUN
ejpam-4770	352	17	be	be	AUX
ejpam-4770	352	18	determined	determine	VERB
ejpam-4770	352	19	and	and	CCONJ
ejpam-4770	352	20	that	that	SCONJ
ejpam-4770	352	21	the	the	DET
ejpam-4770	352	22	parameter	parameter	NOUN
ejpam-4770	352	23	can	can	AUX
ejpam-4770	352	24	be	be	AUX
ejpam-4770	352	25	investigated	investigate	VERB
ejpam-4770	352	26	further	far	ADV
ejpam-4770	352	27	for	for	ADP
ejpam-4770	352	28	graphs	graph	NOUN
ejpam-4770	352	29	under	under	ADP
ejpam-4770	352	30	other	other	ADJ
ejpam-4770	352	31	binary	binary	ADJ
ejpam-4770	352	32	operations	operation	NOUN
ejpam-4770	352	33	.	.	PUNCT
ejpam-4770	353	1	acknowledgements	acknowledgement	NOUN
ejpam-4770	353	2	the	the	DET
ejpam-4770	353	3	authors	author	NOUN
ejpam-4770	353	4	would	would	AUX
ejpam-4770	353	5	like	like	VERB
ejpam-4770	353	6	to	to	PART
ejpam-4770	353	7	thank	thank	VERB
ejpam-4770	353	8	the	the	DET
ejpam-4770	353	9	department	department	NOUN
ejpam-4770	353	10	of	of	ADP
ejpam-4770	353	11	science	science	NOUN
ejpam-4770	353	12	and	and	CCONJ
ejpam-4770	353	13	technology	technology	NOUN
ejpam-4770	353	14	accelerated	accelerate	VERB
ejpam-4770	353	15	science	science	NOUN
ejpam-4770	353	16	and	and	CCONJ
ejpam-4770	353	17	technology	technology	NOUN
ejpam-4770	353	18	human	human	ADJ
ejpam-4770	353	19	resource	resource	NOUN
ejpam-4770	353	20	development	development	NOUN
ejpam-4770	353	21	program	program	NOUN
ejpam-4770	353	22	(	(	PUNCT
ejpam-4770	353	23	dost	dost	NOUN
ejpam-4770	353	24	-	-	PUNCT
ejpam-4770	353	25	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-4770	353	26	,	,	PUNCT
ejpam-4770	353	27	msu	msu	PROPN
ejpam-4770	353	28	-	-	PUNCT
ejpam-4770	353	29	iligan	iligan	PROPN
ejpam-4770	353	30	institute	institute	PROPN
ejpam-4770	353	31	of	of	ADP
ejpam-4770	353	32	technology	technology	PROPN
ejpam-4770	353	33	.	.	PUNCT
ejpam-4770	354	1	references	reference	NOUN
ejpam-4770	354	2	[	[	X
ejpam-4770	354	3	1	1	NUM
ejpam-4770	354	4	]	]	PUNCT
ejpam-4770	354	5	c.	c.	PROPN
ejpam-4770	354	6	berge	berge	PROPN
ejpam-4770	354	7	.	.	PUNCT
ejpam-4770	355	1	theorie	theorie	PROPN
ejpam-4770	355	2	des	des	PROPN
ejpam-4770	355	3	graphes	graphes	PROPN
ejpam-4770	355	4	et	et	PROPN
ejpam-4770	355	5	ses	ses	PROPN
ejpam-4770	355	6	applications	application	NOUN
ejpam-4770	355	7	.	.	PUNCT
ejpam-4770	356	1	methuen	methuen	PROPN
ejpam-4770	356	2	(	(	PUNCT
ejpam-4770	356	3	london	london	PROPN
ejpam-4770	356	4	)	)	PUNCT
ejpam-4770	356	5	and	and	CCONJ
ejpam-4770	356	6	wiley	wiley	PROPN
ejpam-4770	356	7	(	(	PUNCT
ejpam-4770	356	8	new	new	PROPN
ejpam-4770	356	9	york	york	PROPN
ejpam-4770	356	10	)	)	PUNCT
ejpam-4770	356	11	,	,	PUNCT
ejpam-4770	356	12	1962	1962	NUM
ejpam-4770	356	13	.	.	PUNCT
ejpam-4770	357	1	[	[	X
ejpam-4770	357	2	2	2	X
ejpam-4770	357	3	]	]	PUNCT
ejpam-4770	357	4	j.	j.	PROPN
ejpam-4770	357	5	a.	a.	PROPN
ejpam-4770	357	6	bondy	bondy	PROPN
ejpam-4770	357	7	and	and	CCONJ
ejpam-4770	357	8	u.	u.	PROPN
ejpam-4770	357	9	s.	s.	PROPN
ejpam-4770	357	10	r.	r.	PROPN
ejpam-4770	357	11	murty	murty	PROPN
ejpam-4770	357	12	.	.	PUNCT
ejpam-4770	358	1	graph	graph	NOUN
ejpam-4770	358	2	theory	theory	NOUN
ejpam-4770	358	3	.	.	PUNCT
ejpam-4770	359	1	springer	springer	NOUN
ejpam-4770	359	2	,	,	PUNCT
ejpam-4770	359	3	2008	2008	NUM
ejpam-4770	359	4	.	.	PUNCT
ejpam-4770	360	1	[	[	X
ejpam-4770	360	2	3	3	NUM
ejpam-4770	360	3	]	]	X
ejpam-4770	360	4	f.	f.	PROPN
ejpam-4770	360	5	buckley	buckley	PROPN
ejpam-4770	360	6	and	and	CCONJ
ejpam-4770	360	7	f.	f.	PROPN
ejpam-4770	360	8	harary	harary	PROPN
ejpam-4770	360	9	.	.	PUNCT
ejpam-4770	361	1	distance	distance	NOUN
ejpam-4770	361	2	in	in	ADP
ejpam-4770	361	3	graphs	graph	NOUN
ejpam-4770	361	4	.	.	PUNCT
ejpam-4770	362	1	addison	addison	PROPN
ejpam-4770	362	2	-	-	PUNCT
ejpam-4770	362	3	wesley	wesley	PROPN
ejpam-4770	362	4	,	,	PUNCT
ejpam-4770	362	5	redwood	redwood	NOUN
ejpam-4770	362	6	city	city	NOUN
ejpam-4770	362	7	,	,	PUNCT
ejpam-4770	362	8	ca	ca	NOUN
ejpam-4770	362	9	,	,	PUNCT
ejpam-4770	362	10	1990	1990	NUM
ejpam-4770	362	11	.	.	PUNCT
ejpam-4770	363	1	[	[	X
ejpam-4770	363	2	4	4	X
ejpam-4770	363	3	]	]	X
ejpam-4770	363	4	j.	j.	PROPN
ejpam-4770	363	5	cabaro	cabaro	PROPN
ejpam-4770	363	6	and	and	CCONJ
ejpam-4770	363	7	h.	h.	PROPN
ejpam-4770	363	8	rara	rara	PROPN
ejpam-4770	363	9	.	.	PUNCT
ejpam-4770	364	1	on	on	ADP
ejpam-4770	364	2	2	2	NUM
ejpam-4770	364	3	-	-	PUNCT
ejpam-4770	364	4	resolving	resolve	VERB
ejpam-4770	364	5	sets	set	NOUN
ejpam-4770	364	6	in	in	ADP
ejpam-4770	364	7	the	the	DET
ejpam-4770	364	8	join	join	NOUN
ejpam-4770	364	9	,	,	PUNCT
ejpam-4770	364	10	and	and	CCONJ
ejpam-4770	364	11	corona	corona	NOUN
ejpam-4770	364	12	of	of	ADP
ejpam-4770	364	13	graphs	graph	NOUN
ejpam-4770	364	14	.	.	PUNCT
ejpam-4770	365	1	european	european	ADJ
ejpam-4770	365	2	journal	journal	PROPN
ejpam-4770	365	3	of	of	ADP
ejpam-4770	365	4	pure	pure	ADJ
ejpam-4770	365	5	and	and	CCONJ
ejpam-4770	365	6	applied	applied	ADJ
ejpam-4770	365	7	mathematics	mathematic	NOUN
ejpam-4770	365	8	,	,	PUNCT
ejpam-4770	365	9	14(3):773–782	14(3):773–782	PROPN
ejpam-4770	365	10	,	,	PUNCT
ejpam-4770	365	11	2021	2021	NUM
ejpam-4770	365	12	.	.	PUNCT
ejpam-4770	366	1	[	[	X
ejpam-4770	366	2	5	5	X
ejpam-4770	366	3	]	]	PUNCT
ejpam-4770	366	4	j.	j.	PROPN
ejpam-4770	366	5	cabaro	cabaro	PROPN
ejpam-4770	366	6	and	and	CCONJ
ejpam-4770	366	7	h.	h.	PROPN
ejpam-4770	366	8	rara	rara	PROPN
ejpam-4770	366	9	.	.	PUNCT
ejpam-4770	367	1	restrained	restrain	VERB
ejpam-4770	367	2	2	2	NUM
ejpam-4770	367	3	-	-	PUNCT
ejpam-4770	367	4	resolving	resolve	VERB
ejpam-4770	367	5	dominating	dominating	NOUN
ejpam-4770	367	6	sets	set	NOUN
ejpam-4770	367	7	in	in	ADP
ejpam-4770	367	8	the	the	DET
ejpam-4770	367	9	join	join	NOUN
ejpam-4770	367	10	and	and	CCONJ
ejpam-4770	367	11	corona	corona	PROPN
ejpam-4770	367	12	and	and	CCONJ
ejpam-4770	367	13	lexicographic	lexicographic	ADJ
ejpam-4770	367	14	product	product	NOUN
ejpam-4770	367	15	of	of	ADP
ejpam-4770	367	16	two	two	NUM
ejpam-4770	367	17	graphs	graph	NOUN
ejpam-4770	367	18	.	.	PUNCT
ejpam-4770	368	1	european	european	ADJ
ejpam-4770	368	2	journal	journal	PROPN
ejpam-4770	368	3	of	of	ADP
ejpam-4770	368	4	pure	pure	ADJ
ejpam-4770	368	5	and	and	CCONJ
ejpam-4770	368	6	applied	applied	ADJ
ejpam-4770	368	7	mathematics	mathematic	NOUN
ejpam-4770	368	8	,	,	PUNCT
ejpam-4770	368	9	15(3):1047–1053	15(3):1047–1053	NUM
ejpam-4770	368	10	,	,	PUNCT
ejpam-4770	368	11	2022	2022	NUM
ejpam-4770	368	12	.	.	PUNCT
ejpam-4770	369	1	[	[	X
ejpam-4770	369	2	6	6	NUM
ejpam-4770	369	3	]	]	PUNCT
ejpam-4770	369	4	j.	j.	PROPN
ejpam-4770	369	5	cabaro	cabaro	PROPN
ejpam-4770	369	6	and	and	CCONJ
ejpam-4770	369	7	h.	h.	PROPN
ejpam-4770	369	8	rara	rara	PROPN
ejpam-4770	369	9	.	.	PUNCT
ejpam-4770	370	1	on	on	ADP
ejpam-4770	370	2	2	2	NUM
ejpam-4770	370	3	-	-	PUNCT
ejpam-4770	370	4	resolving	resolve	VERB
ejpam-4770	370	5	dominating	dominating	NOUN
ejpam-4770	370	6	sets	set	NOUN
ejpam-4770	370	7	in	in	ADP
ejpam-4770	370	8	the	the	DET
ejpam-4770	370	9	join	join	NOUN
ejpam-4770	370	10	and	and	CCONJ
ejpam-4770	370	11	corona	corona	PROPN
ejpam-4770	370	12	and	and	CCONJ
ejpam-4770	370	13	lexicographic	lexicographic	ADJ
ejpam-4770	370	14	product	product	NOUN
ejpam-4770	370	15	of	of	ADP
ejpam-4770	370	16	graphs	graph	NOUN
ejpam-4770	370	17	.	.	PUNCT
ejpam-4770	371	1	european	european	ADJ
ejpam-4770	371	2	journal	journal	PROPN
ejpam-4770	371	3	of	of	ADP
ejpam-4770	371	4	pure	pure	ADJ
ejpam-4770	371	5	and	and	CCONJ
ejpam-4770	371	6	applied	applied	ADJ
ejpam-4770	371	7	mathematics	mathematic	NOUN
ejpam-4770	371	8	,	,	PUNCT
ejpam-4770	371	9	15(3):1417–1425	15(3):1417–1425	NUM
ejpam-4770	371	10	,	,	PUNCT
ejpam-4770	371	11	2022	2022	NUM
ejpam-4770	371	12	.	.	PUNCT
ejpam-4770	372	1	[	[	X
ejpam-4770	372	2	7	7	X
ejpam-4770	372	3	]	]	X
ejpam-4770	372	4	j.	j.	PROPN
ejpam-4770	372	5	cabaro	cabaro	PROPN
ejpam-4770	372	6	and	and	CCONJ
ejpam-4770	372	7	h.	h.	PROPN
ejpam-4770	372	8	rara	rara	PROPN
ejpam-4770	372	9	.	.	PUNCT
ejpam-4770	373	1	restrained	restrain	VERB
ejpam-4770	373	2	2	2	NUM
ejpam-4770	373	3	-	-	PUNCT
ejpam-4770	373	4	resolving	resolve	VERB
ejpam-4770	373	5	sets	set	NOUN
ejpam-4770	373	6	in	in	ADP
ejpam-4770	373	7	the	the	DET
ejpam-4770	373	8	join	join	NOUN
ejpam-4770	373	9	and	and	CCONJ
ejpam-4770	373	10	corona	corona	PROPN
ejpam-4770	373	11	and	and	CCONJ
ejpam-4770	373	12	lexicographic	lexicographic	ADJ
ejpam-4770	373	13	product	product	NOUN
ejpam-4770	373	14	of	of	ADP
ejpam-4770	373	15	graphs	graph	NOUN
ejpam-4770	373	16	.	.	PUNCT
ejpam-4770	374	1	european	european	ADJ
ejpam-4770	374	2	journal	journal	PROPN
ejpam-4770	374	3	of	of	ADP
ejpam-4770	374	4	pure	pure	ADJ
ejpam-4770	374	5	and	and	CCONJ
ejpam-4770	374	6	applied	applied	ADJ
ejpam-4770	374	7	mathematics	mathematic	NOUN
ejpam-4770	374	8	,	,	PUNCT
ejpam-4770	374	9	15(3):1229–1236	15(3):1229–1236	NUM
ejpam-4770	374	10	,	,	PUNCT
ejpam-4770	374	11	2022	2022	NUM
ejpam-4770	374	12	.	.	PUNCT
ejpam-4770	375	1	[	[	X
ejpam-4770	375	2	8	8	NUM
ejpam-4770	375	3	]	]	X
ejpam-4770	375	4	f.	f.	PROPN
ejpam-4770	375	5	harary	harary	PROPN
ejpam-4770	375	6	and	and	CCONJ
ejpam-4770	375	7	r.	r.	PROPN
ejpam-4770	375	8	melter	melter	NOUN
ejpam-4770	375	9	.	.	PUNCT
ejpam-4770	376	1	on	on	ADP
ejpam-4770	376	2	the	the	DET
ejpam-4770	376	3	metric	metric	ADJ
ejpam-4770	376	4	dimension	dimension	NOUN
ejpam-4770	376	5	of	of	ADP
ejpam-4770	376	6	a	a	DET
ejpam-4770	376	7	graph	graph	NOUN
ejpam-4770	376	8	.	.	PUNCT
ejpam-4770	376	9	ars	ars	PROPN
ejpam-4770	376	10	combinatoria	combinatoria	NOUN
ejpam-4770	376	11	,	,	PUNCT
ejpam-4770	376	12	2:191–195	2:191–195	NUM
ejpam-4770	376	13	,	,	PUNCT
ejpam-4770	376	14	1976	1976	NUM
ejpam-4770	376	15	.	.	PUNCT
ejpam-4770	377	1	[	[	X
ejpam-4770	377	2	9	9	NUM
ejpam-4770	377	3	]	]	PUNCT
ejpam-4770	377	4	a.	a.	NOUN
ejpam-4770	377	5	mahistrado	mahistrado	NOUN
ejpam-4770	377	6	and	and	CCONJ
ejpam-4770	377	7	h.	h.	PROPN
ejpam-4770	377	8	rara	rara	PROPN
ejpam-4770	377	9	.	.	PUNCT
ejpam-4770	378	1	on	on	ADP
ejpam-4770	378	2	2	2	NUM
ejpam-4770	378	3	-	-	PUNCT
ejpam-4770	378	4	resolving	resolve	VERB
ejpam-4770	378	5	hop	hop	NOUN
ejpam-4770	378	6	dominating	dominating	NOUN
ejpam-4770	378	7	sets	set	NOUN
ejpam-4770	378	8	in	in	ADP
ejpam-4770	378	9	the	the	DET
ejpam-4770	378	10	join	join	NOUN
ejpam-4770	378	11	and	and	CCONJ
ejpam-4770	378	12	corona	corona	PROPN
ejpam-4770	378	13	and	and	CCONJ
ejpam-4770	378	14	lexicographic	lexicographic	ADJ
ejpam-4770	378	15	product	product	NOUN
ejpam-4770	378	16	of	of	ADP
ejpam-4770	378	17	graphs	graph	NOUN
ejpam-4770	378	18	.	.	PUNCT
ejpam-4770	379	1	european	european	ADJ
ejpam-4770	379	2	journal	journal	PROPN
ejpam-4770	379	3	of	of	ADP
ejpam-4770	379	4	pure	pure	ADJ
ejpam-4770	379	5	and	and	CCONJ
ejpam-4770	379	6	applied	applied	ADJ
ejpam-4770	379	7	mathematics	mathematic	NOUN
ejpam-4770	379	8	,	,	PUNCT
ejpam-4770	379	9	15(4):1982–1997	15(4):1982–1997	NUM
ejpam-4770	379	10	,	,	PUNCT
ejpam-4770	379	11	2022	2022	NUM
ejpam-4770	379	12	.	.	PUNCT
ejpam-4770	380	1	[	[	X
ejpam-4770	380	2	10	10	NUM
ejpam-4770	380	3	]	]	PUNCT
ejpam-4770	380	4	a.	a.	NOUN
ejpam-4770	380	5	mahistrado	mahistrado	NOUN
ejpam-4770	380	6	and	and	CCONJ
ejpam-4770	380	7	h.	h.	PROPN
ejpam-4770	380	8	rara	rara	PROPN
ejpam-4770	380	9	.	.	PUNCT
ejpam-4770	381	1	restrained	restrain	VERB
ejpam-4770	381	2	2	2	NUM
ejpam-4770	381	3	-	-	PUNCT
ejpam-4770	381	4	resolving	resolve	VERB
ejpam-4770	381	5	hop	hop	NOUN
ejpam-4770	381	6	domination	domination	NOUN
ejpam-4770	381	7	in	in	ADP
ejpam-4770	381	8	graphs	graph	NOUN
ejpam-4770	381	9	.	.	PUNCT
ejpam-4770	382	1	european	european	ADJ
ejpam-4770	382	2	journal	journal	PROPN
ejpam-4770	382	3	of	of	ADP
ejpam-4770	382	4	pure	pure	ADJ
ejpam-4770	382	5	and	and	CCONJ
ejpam-4770	382	6	applied	applied	ADJ
ejpam-4770	382	7	mathematics	mathematic	NOUN
ejpam-4770	382	8	,	,	PUNCT
ejpam-4770	382	9	16(1):286–303	16(1):286–303	NUM
ejpam-4770	382	10	,	,	PUNCT
ejpam-4770	382	11	2023	2023	NUM
ejpam-4770	382	12	.	.	PUNCT
ejpam-4770	383	1	[	[	X
ejpam-4770	383	2	11	11	NUM
ejpam-4770	383	3	]	]	PUNCT
ejpam-4770	383	4	a.m.	a.m.	NOUN
ejpam-4770	383	5	mahistrado	mahistrado	NOUN
ejpam-4770	383	6	and	and	CCONJ
ejpam-4770	383	7	h.	h.	PROPN
ejpam-4770	383	8	rara	rara	PROPN
ejpam-4770	383	9	.	.	PUNCT
ejpam-4770	384	1	outer	outer	ADV
ejpam-4770	384	2	-	-	PUNCT
ejpam-4770	384	3	connected	connect	VERB
ejpam-4770	384	4	2	2	NUM
ejpam-4770	384	5	-	-	PUNCT
ejpam-4770	384	6	resolving	resolve	VERB
ejpam-4770	384	7	hop	hop	NOUN
ejpam-4770	384	8	domination	domination	NOUN
ejpam-4770	384	9	in	in	ADP
ejpam-4770	384	10	graphs	graph	NOUN
ejpam-4770	384	11	.	.	PUNCT
ejpam-4770	385	1	european	european	ADJ
ejpam-4770	385	2	journal	journal	PROPN
ejpam-4770	385	3	of	of	ADP
ejpam-4770	385	4	pure	pure	ADJ
ejpam-4770	385	5	and	and	CCONJ
ejpam-4770	385	6	applied	applied	ADJ
ejpam-4770	385	7	mathematics	mathematic	NOUN
ejpam-4770	385	8	,	,	PUNCT
ejpam-4770	385	9	16(2):1180–1195	16(2):1180–1195	NUM
ejpam-4770	385	10	,	,	PUNCT
ejpam-4770	385	11	2023	2023	NUM
ejpam-4770	385	12	.	.	PUNCT
ejpam-4770	386	1	references	reference	NOUN
ejpam-4770	386	2	1479	1479	NUM
ejpam-4770	387	1	[	[	X
ejpam-4770	387	2	12	12	NUM
ejpam-4770	387	3	]	]	PUNCT
ejpam-4770	387	4	j.	j.	PROPN
ejpam-4770	387	5	mohamad	mohamad	PROPN
ejpam-4770	387	6	and	and	CCONJ
ejpam-4770	387	7	h.	h.	PROPN
ejpam-4770	387	8	rara	rara	PROPN
ejpam-4770	387	9	.	.	PUNCT
ejpam-4770	388	1	on	on	ADP
ejpam-4770	388	2	resolving	resolve	VERB
ejpam-4770	388	3	hop	hop	NOUN
ejpam-4770	388	4	domination	domination	NOUN
ejpam-4770	388	5	in	in	ADP
ejpam-4770	388	6	graphs	graph	NOUN
ejpam-4770	388	7	.	.	PUNCT
ejpam-4770	389	1	european	european	ADJ
ejpam-4770	389	2	journal	journal	PROPN
ejpam-4770	389	3	of	of	ADP
ejpam-4770	389	4	pure	pure	ADJ
ejpam-4770	389	5	and	and	CCONJ
ejpam-4770	389	6	applied	applied	ADJ
ejpam-4770	389	7	mathematics	mathematic	NOUN
ejpam-4770	389	8	,	,	PUNCT
ejpam-4770	389	9	14(3):1015–1023	14(3):1015–1023	NUM
ejpam-4770	389	10	,	,	PUNCT
ejpam-4770	389	11	2021	2021	NUM
ejpam-4770	389	12	.	.	PUNCT
ejpam-4770	390	1	[	[	X
ejpam-4770	390	2	13	13	NUM
ejpam-4770	390	3	]	]	X
ejpam-4770	390	4	g.	g.	PROPN
ejpam-4770	390	5	monsanto	monsanto	PROPN
ejpam-4770	390	6	and	and	CCONJ
ejpam-4770	390	7	h.	h.	PROPN
ejpam-4770	390	8	rara	rara	PROPN
ejpam-4770	390	9	.	.	PUNCT
ejpam-4770	391	1	resolving	resolve	VERB
ejpam-4770	391	2	restrained	restrained	ADJ
ejpam-4770	391	3	domination	domination	NOUN
ejpam-4770	391	4	in	in	ADP
ejpam-4770	391	5	graphs	graph	NOUN
ejpam-4770	391	6	.	.	PUNCT
ejpam-4770	392	1	european	european	ADJ
ejpam-4770	392	2	journal	journal	PROPN
ejpam-4770	392	3	of	of	ADP
ejpam-4770	392	4	pure	pure	ADJ
ejpam-4770	392	5	and	and	CCONJ
ejpam-4770	392	6	applied	applied	ADJ
ejpam-4770	392	7	mathematics	mathematic	NOUN
ejpam-4770	392	8	,	,	PUNCT
ejpam-4770	392	9	4(3):829–841	4(3):829–841	NOUN
ejpam-4770	392	10	,	,	PUNCT
ejpam-4770	392	11	2021	2021	NUM
ejpam-4770	392	12	.	.	PUNCT
ejpam-4770	393	1	[	[	X
ejpam-4770	393	2	14	14	NUM
ejpam-4770	393	3	]	]	X
ejpam-4770	393	4	c.	c.	PROPN
ejpam-4770	393	5	natarajan	natarajan	PROPN
ejpam-4770	393	6	and	and	CCONJ
ejpam-4770	393	7	s.k	s.k	PROPN
ejpam-4770	393	8	.	.	PROPN
ejpam-4770	393	9	ayyaswamy	ayyaswamy	PROPN
ejpam-4770	393	10	.	.	PUNCT
ejpam-4770	394	1	hop	hop	PROPN
ejpam-4770	394	2	domination	domination	NOUN
ejpam-4770	394	3	in	in	ADP
ejpam-4770	394	4	graphs	graph	NOUN
ejpam-4770	394	5	-	-	PUNCT
ejpam-4770	394	6	ii	ii	NOUN
ejpam-4770	394	7	.	.	PUNCT
ejpam-4770	394	8	versita	versita	PROPN
ejpam-4770	394	9	,	,	PUNCT
ejpam-4770	394	10	23(2):187	23(2):187	NUM
ejpam-4770	394	11	–	–	PUNCT
ejpam-4770	394	12	199	199	NUM
ejpam-4770	394	13	,	,	PUNCT
ejpam-4770	394	14	2015	2015	NUM
ejpam-4770	394	15	.	.	PUNCT
ejpam-4770	395	1	[	[	X
ejpam-4770	395	2	15	15	NUM
ejpam-4770	395	3	]	]	X
ejpam-4770	395	4	jr	jr	PROPN
ejpam-4770	395	5	.	.	PROPN
ejpam-4770	395	6	r.	r.	PROPN
ejpam-4770	395	7	mollejon	mollejon	PROPN
ejpam-4770	395	8	s.	s.	PROPN
ejpam-4770	395	9	canoy	canoy	PROPN
ejpam-4770	395	10	and	and	CCONJ
ejpam-4770	395	11	j.g.canoy	j.g.canoy	PROPN
ejpam-4770	395	12	.	.	PUNCT
ejpam-4770	396	1	hop	hop	PROPN
ejpam-4770	396	2	dominating	dominating	NOUN
ejpam-4770	396	3	sets	set	NOUN
ejpam-4770	396	4	in	in	ADP
ejpam-4770	396	5	graphs	graph	NOUN
ejpam-4770	396	6	under	under	ADP
ejpam-4770	396	7	binary	binary	ADJ
ejpam-4770	396	8	operations	operation	NOUN
ejpam-4770	396	9	.	.	PUNCT
ejpam-4770	397	1	european	european	ADJ
ejpam-4770	397	2	journal	journal	PROPN
ejpam-4770	397	3	of	of	ADP
ejpam-4770	397	4	pure	pure	ADJ
ejpam-4770	397	5	and	and	CCONJ
ejpam-4770	397	6	applied	applied	ADJ
ejpam-4770	397	7	mathematics	mathematic	NOUN
ejpam-4770	397	8	,	,	PUNCT
ejpam-4770	397	9	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4770	397	10	,	,	PUNCT
ejpam-4770	397	11	2019	2019	NUM
ejpam-4770	397	12	.	.	PUNCT
ejpam-4770	398	1	[	[	X
ejpam-4770	398	2	16	16	X
ejpam-4770	398	3	]	]	X
ejpam-4770	398	4	v.	v.	ADP
ejpam-4770	398	5	saenpholphat	saenpholphat	PROPN
ejpam-4770	398	6	and	and	CCONJ
ejpam-4770	398	7	p.	p.	PROPN
ejpam-4770	398	8	zhang	zhang	PROPN
ejpam-4770	398	9	.	.	PUNCT
ejpam-4770	399	1	on	on	ADP
ejpam-4770	399	2	connected	connected	ADJ
ejpam-4770	399	3	resolvability	resolvability	NOUN
ejpam-4770	399	4	of	of	ADP
ejpam-4770	399	5	graphs	graph	NOUN
ejpam-4770	399	6	.	.	PUNCT
ejpam-4770	400	1	australian	australian	ADJ
ejpam-4770	400	2	journal	journal	NOUN
ejpam-4770	400	3	of	of	ADP
ejpam-4770	400	4	combinatorics	combinatoric	NOUN
ejpam-4770	400	5	,	,	PUNCT
ejpam-4770	400	6	28:26–37	28:26–37	NUM
ejpam-4770	400	7	,	,	PUNCT
ejpam-4770	400	8	2003	2003	NUM
ejpam-4770	400	9	.	.	PUNCT
ejpam-4770	401	1	[	[	X
ejpam-4770	401	2	17	17	NUM
ejpam-4770	401	3	]	]	PUNCT
ejpam-4770	401	4	p.	p.	PROPN
ejpam-4770	401	5	j.	j.	PROPN
ejpam-4770	401	6	slater	slater	PROPN
ejpam-4770	401	7	.	.	PUNCT
ejpam-4770	402	1	dominating	dominating	NOUN
ejpam-4770	402	2	and	and	CCONJ
ejpam-4770	402	3	reference	reference	NOUN
ejpam-4770	402	4	sets	set	NOUN
ejpam-4770	402	5	in	in	ADP
ejpam-4770	402	6	a	a	DET
ejpam-4770	402	7	graph	graph	NOUN
ejpam-4770	402	8	.	.	PUNCT
ejpam-4770	403	1	journal	journal	NOUN
ejpam-4770	403	2	of	of	ADP
ejpam-4770	403	3	mathematics	mathematic	NOUN
ejpam-4770	403	4	and	and	CCONJ
ejpam-4770	403	5	physical	physical	ADJ
ejpam-4770	403	6	science	science	NOUN
ejpam-4770	403	7	,	,	PUNCT
ejpam-4770	403	8	22(4):445–455	22(4):445–455	PROPN
ejpam-4770	403	9	.	.	PUNCT