id	sid	tid	token	lemma	pos
ejpam-6074	1	1	european	european	PROPN
ejpam-6074	1	2	journal	journal	PROPN
ejpam-6074	1	3	of	of	ADP
ejpam-6074	1	4	pure	pure	ADJ
ejpam-6074	1	5	and	and	CCONJ
ejpam-6074	1	6	applied	applied	ADJ
ejpam-6074	1	7	mathematics	mathematic	NOUN
ejpam-6074	1	8	2025	2025	NUM
ejpam-6074	1	9	,	,	PUNCT
ejpam-6074	1	10	vol	vol	NOUN
ejpam-6074	1	11	.	.	PROPN
ejpam-6074	1	12	18	18	NUM
ejpam-6074	1	13	,	,	PUNCT
ejpam-6074	1	14	issue	issue	NOUN
ejpam-6074	1	15	2	2	NUM
ejpam-6074	1	16	,	,	PUNCT
ejpam-6074	1	17	article	article	NOUN
ejpam-6074	1	18	number	number	NOUN
ejpam-6074	1	19	6074	6074	NUM
ejpam-6074	1	20	issn	issn	VERB
ejpam-6074	1	21	1307	1307	NUM
ejpam-6074	1	22	-	-	SYM
ejpam-6074	1	23	5543	5543	NUM
ejpam-6074	1	24	–	–	PUNCT
ejpam-6074	1	25	ejpam.com	ejpam.com	X
ejpam-6074	1	26	published	publish	VERB
ejpam-6074	1	27	by	by	ADP
ejpam-6074	1	28	new	new	PROPN
ejpam-6074	1	29	york	york	PROPN
ejpam-6074	1	30	business	business	PROPN
ejpam-6074	1	31	global	global	ADJ
ejpam-6074	1	32	2	2	NUM
ejpam-6074	1	33	-	-	PUNCT
ejpam-6074	1	34	step	step	NOUN
ejpam-6074	1	35	movability	movability	NOUN
ejpam-6074	1	36	of	of	ADP
ejpam-6074	1	37	hop	hop	NOUN
ejpam-6074	1	38	dominating	dominating	NOUN
ejpam-6074	1	39	sets	set	NOUN
ejpam-6074	1	40	in	in	ADP
ejpam-6074	1	41	graphs	graph	NOUN
ejpam-6074	1	42	roger	roger	PROPN
ejpam-6074	1	43	l.	l.	PROPN
ejpam-6074	1	44	estrella1,∗	estrella1,∗	PROPN
ejpam-6074	1	45	,	,	PUNCT
ejpam-6074	1	46	gina	gina	PROPN
ejpam-6074	1	47	m.	m.	PROPN
ejpam-6074	1	48	malacas1,2	malacas1,2	PROPN
ejpam-6074	1	49	,	,	PUNCT
ejpam-6074	1	50	sergio	sergio	PROPN
ejpam-6074	1	51	r.	r.	PROPN
ejpam-6074	1	52	canoy	canoy	PROPN
ejpam-6074	1	53	,	,	PUNCT
ejpam-6074	1	54	jr.1,2	jr.1,2	ADJ
ejpam-6074	1	55	1	1	NUM
ejpam-6074	1	56	department	department	NOUN
ejpam-6074	1	57	of	of	ADP
ejpam-6074	1	58	mathematics	mathematic	NOUN
ejpam-6074	1	59	and	and	CCONJ
ejpam-6074	1	60	statistics	statistic	NOUN
ejpam-6074	1	61	,	,	PUNCT
ejpam-6074	1	62	college	college	NOUN
ejpam-6074	1	63	of	of	ADP
ejpam-6074	1	64	science	science	NOUN
ejpam-6074	1	65	and	and	CCONJ
ejpam-6074	1	66	mathematics	mathematic	NOUN
ejpam-6074	1	67	,	,	PUNCT
ejpam-6074	1	68	msu	msu	PROPN
ejpam-6074	1	69	-	-	PUNCT
ejpam-6074	1	70	iligan	iligan	PROPN
ejpam-6074	1	71	institute	institute	PROPN
ejpam-6074	1	72	of	of	ADP
ejpam-6074	1	73	technology	technology	PROPN
ejpam-6074	1	74	,	,	PUNCT
ejpam-6074	1	75	9200	9200	NUM
ejpam-6074	1	76	iligan	iligan	ADJ
ejpam-6074	1	77	city	city	NOUN
ejpam-6074	1	78	,	,	PUNCT
ejpam-6074	1	79	philippines	philippine	NOUN
ejpam-6074	1	80	2	2	NUM
ejpam-6074	1	81	center	center	NOUN
ejpam-6074	1	82	for	for	ADP
ejpam-6074	1	83	mathematical	mathematical	ADJ
ejpam-6074	1	84	and	and	CCONJ
ejpam-6074	1	85	theoretical	theoretical	ADJ
ejpam-6074	1	86	physical	physical	ADJ
ejpam-6074	1	87	sciencesprism	sciencesprism	NOUN
ejpam-6074	1	88	,	,	PUNCT
ejpam-6074	1	89	msu	msu	PROPN
ejpam-6074	1	90	-	-	PUNCT
ejpam-6074	1	91	iligan	iligan	PROPN
ejpam-6074	1	92	institute	institute	PROPN
ejpam-6074	1	93	of	of	ADP
ejpam-6074	1	94	technology	technology	PROPN
ejpam-6074	1	95	,	,	PUNCT
ejpam-6074	1	96	9200	9200	NUM
ejpam-6074	1	97	iligan	iligan	ADJ
ejpam-6074	1	98	city	city	NOUN
ejpam-6074	1	99	,	,	PUNCT
ejpam-6074	1	100	philippines	philippine	NOUN
ejpam-6074	1	101	abstract	abstract	ADJ
ejpam-6074	1	102	.	.	PUNCT
ejpam-6074	2	1	let	let	VERB
ejpam-6074	2	2	g	g	PRON
ejpam-6074	2	3	be	be	AUX
ejpam-6074	2	4	an	an	DET
ejpam-6074	2	5	undirected	undirected	ADJ
ejpam-6074	2	6	connected	connected	ADJ
ejpam-6074	2	7	graph	graph	NOUN
ejpam-6074	2	8	with	with	ADP
ejpam-6074	2	9	vertex	vertex	NOUN
ejpam-6074	2	10	and	and	CCONJ
ejpam-6074	2	11	edge	edge	NOUN
ejpam-6074	2	12	sets	set	NOUN
ejpam-6074	2	13	v	v	ADP
ejpam-6074	2	14	(	(	PUNCT
ejpam-6074	2	15	g	g	NOUN
ejpam-6074	2	16	)	)	PUNCT
ejpam-6074	2	17	and	and	CCONJ
ejpam-6074	2	18	e(g	e(g	PROPN
ejpam-6074	2	19	)	)	PUNCT
ejpam-6074	2	20	,	,	PUNCT
ejpam-6074	2	21	respectively	respectively	ADV
ejpam-6074	2	22	.	.	PUNCT
ejpam-6074	3	1	a	a	DET
ejpam-6074	3	2	hop	hop	NOUN
ejpam-6074	3	3	dominating	dominating	NOUN
ejpam-6074	3	4	set	set	NOUN
ejpam-6074	3	5	s	s	PROPN
ejpam-6074	3	6	in	in	ADP
ejpam-6074	3	7	g	g	PROPN
ejpam-6074	3	8	is	be	AUX
ejpam-6074	3	9	2	2	NUM
ejpam-6074	3	10	-	-	PUNCT
ejpam-6074	3	11	step	step	NOUN
ejpam-6074	3	12	movable	movable	ADJ
ejpam-6074	3	13	hop	hop	NOUN
ejpam-6074	3	14	dominating	dominating	NOUN
ejpam-6074	3	15	if	if	SCONJ
ejpam-6074	3	16	for	for	ADP
ejpam-6074	3	17	each	each	DET
ejpam-6074	3	18	v	v	NUM
ejpam-6074	3	19	∈	∈	PROPN
ejpam-6074	3	20	s	s	NOUN
ejpam-6074	3	21	,	,	PUNCT
ejpam-6074	3	22	s	s	NOUN
ejpam-6074	3	23	\	\	X
ejpam-6074	3	24	{	{	PUNCT
ejpam-6074	3	25	v	v	NOUN
ejpam-6074	3	26	}	}	PUNCT
ejpam-6074	3	27	or	or	CCONJ
ejpam-6074	3	28	[	[	X
ejpam-6074	3	29	s	s	X
ejpam-6074	3	30	\	\	X
ejpam-6074	3	31	{	{	PUNCT
ejpam-6074	3	32	v	v	NOUN
ejpam-6074	3	33	}	}	PUNCT
ejpam-6074	3	34	]	]	PUNCT
ejpam-6074	3	35	∪	∪	X
ejpam-6074	3	36	{	{	PUNCT
ejpam-6074	3	37	w	w	NOUN
ejpam-6074	3	38	}	}	PUNCT
ejpam-6074	3	39	for	for	ADP
ejpam-6074	3	40	some	some	DET
ejpam-6074	3	41	w	w	NOUN
ejpam-6074	3	42	∈	∈	PROPN
ejpam-6074	4	1	[	[	X
ejpam-6074	4	2	v	v	X
ejpam-6074	4	3	(	(	PUNCT
ejpam-6074	4	4	g	g	NOUN
ejpam-6074	4	5	)	)	PUNCT
ejpam-6074	4	6	\	\	PUNCT
ejpam-6074	4	7	s	s	X
ejpam-6074	4	8	]	]	X
ejpam-6074	4	9	∩	∩	ADJ
ejpam-6074	4	10	n2	n2	ADJ
ejpam-6074	4	11	g(v	g(v	PROPN
ejpam-6074	4	12	)	)	PUNCT
ejpam-6074	4	13	is	be	AUX
ejpam-6074	4	14	a	a	DET
ejpam-6074	4	15	hop	hop	NOUN
ejpam-6074	4	16	dominating	dominating	NOUN
ejpam-6074	4	17	set	set	VERB
ejpam-6074	4	18	in	in	ADP
ejpam-6074	4	19	g.	g.	PROPN
ejpam-6074	4	20	the	the	DET
ejpam-6074	4	21	minimum	minimum	ADJ
ejpam-6074	4	22	cardinality	cardinality	NOUN
ejpam-6074	4	23	of	of	ADP
ejpam-6074	4	24	a	a	DET
ejpam-6074	4	25	2	2	NUM
ejpam-6074	4	26	-	-	PUNCT
ejpam-6074	4	27	step	step	NOUN
ejpam-6074	4	28	movable	movable	ADJ
ejpam-6074	4	29	hop	hop	NOUN
ejpam-6074	4	30	dominating	dominating	NOUN
ejpam-6074	4	31	set	set	NOUN
ejpam-6074	4	32	in	in	ADP
ejpam-6074	4	33	g	g	NOUN
ejpam-6074	4	34	,	,	PUNCT
ejpam-6074	4	35	denoted	denote	VERB
ejpam-6074	4	36	by	by	ADP
ejpam-6074	4	37	γ2	γ2	ADJ
ejpam-6074	4	38	mh(g	mh(g	NOUN
ejpam-6074	4	39	)	)	PUNCT
ejpam-6074	4	40	,	,	PUNCT
ejpam-6074	4	41	is	be	AUX
ejpam-6074	4	42	called	call	VERB
ejpam-6074	4	43	the	the	DET
ejpam-6074	4	44	2	2	NUM
ejpam-6074	4	45	-	-	PUNCT
ejpam-6074	4	46	step	step	NOUN
ejpam-6074	4	47	movable	movable	ADJ
ejpam-6074	4	48	hop	hop	NOUN
ejpam-6074	4	49	domination	domination	NOUN
ejpam-6074	4	50	number	number	NOUN
ejpam-6074	4	51	of	of	ADP
ejpam-6074	4	52	g.	g.	PROPN
ejpam-6074	4	53	in	in	ADP
ejpam-6074	4	54	this	this	DET
ejpam-6074	4	55	paper	paper	NOUN
ejpam-6074	4	56	,	,	PUNCT
ejpam-6074	4	57	we	we	PRON
ejpam-6074	4	58	characterize	characterize	VERB
ejpam-6074	4	59	those	those	DET
ejpam-6074	4	60	graphs	graph	NOUN
ejpam-6074	4	61	which	which	PRON
ejpam-6074	4	62	admit	admit	VERB
ejpam-6074	4	63	a	a	DET
ejpam-6074	4	64	2	2	NUM
ejpam-6074	4	65	-	-	PUNCT
ejpam-6074	4	66	step	step	NOUN
ejpam-6074	4	67	movable	movable	ADJ
ejpam-6074	4	68	hop	hop	NOUN
ejpam-6074	4	69	dominating	dominating	NOUN
ejpam-6074	4	70	set	set	NOUN
ejpam-6074	4	71	.	.	PUNCT
ejpam-6074	5	1	we	we	PRON
ejpam-6074	5	2	give	give	VERB
ejpam-6074	5	3	bounds	bound	NOUN
ejpam-6074	5	4	on	on	ADP
ejpam-6074	5	5	the	the	DET
ejpam-6074	5	6	2	2	NUM
ejpam-6074	5	7	-	-	PUNCT
ejpam-6074	5	8	step	step	NOUN
ejpam-6074	5	9	movable	movable	ADJ
ejpam-6074	5	10	hop	hop	NOUN
ejpam-6074	5	11	domination	domination	NOUN
ejpam-6074	5	12	number	number	NOUN
ejpam-6074	5	13	and	and	CCONJ
ejpam-6074	5	14	give	give	VERB
ejpam-6074	5	15	necessary	necessary	ADJ
ejpam-6074	5	16	and	and	CCONJ
ejpam-6074	5	17	sufficient	sufficient	ADJ
ejpam-6074	5	18	conditions	condition	NOUN
ejpam-6074	5	19	for	for	ADP
ejpam-6074	5	20	those	those	DET
ejpam-6074	5	21	graphs	graph	NOUN
ejpam-6074	5	22	that	that	PRON
ejpam-6074	5	23	attain	attain	VERB
ejpam-6074	5	24	these	these	DET
ejpam-6074	5	25	bounds	bound	NOUN
ejpam-6074	5	26	.	.	PUNCT
ejpam-6074	6	1	we	we	PRON
ejpam-6074	6	2	also	also	ADV
ejpam-6074	6	3	characterize	characterize	VERB
ejpam-6074	6	4	the	the	DET
ejpam-6074	6	5	2	2	NUM
ejpam-6074	6	6	-	-	PUNCT
ejpam-6074	6	7	step	step	NOUN
ejpam-6074	6	8	movable	movable	ADJ
ejpam-6074	6	9	hop	hop	NOUN
ejpam-6074	6	10	dominating	dominating	NOUN
ejpam-6074	6	11	sets	set	NOUN
ejpam-6074	6	12	in	in	ADP
ejpam-6074	6	13	the	the	DET
ejpam-6074	6	14	shadow	shadow	NOUN
ejpam-6074	6	15	graph	graph	NOUN
ejpam-6074	6	16	and	and	CCONJ
ejpam-6074	6	17	determine	determine	VERB
ejpam-6074	6	18	the	the	DET
ejpam-6074	6	19	2	2	NUM
ejpam-6074	6	20	-	-	PUNCT
ejpam-6074	6	21	step	step	NOUN
ejpam-6074	6	22	movable	movable	ADJ
ejpam-6074	6	23	hop	hop	NOUN
ejpam-6074	6	24	domination	domination	NOUN
ejpam-6074	6	25	numbers	number	NOUN
ejpam-6074	6	26	of	of	ADP
ejpam-6074	6	27	the	the	DET
ejpam-6074	6	28	shadow	shadow	NOUN
ejpam-6074	6	29	graph	graph	NOUN
ejpam-6074	6	30	and	and	CCONJ
ejpam-6074	6	31	complementary	complementary	ADJ
ejpam-6074	6	32	prism	prism	NOUN
ejpam-6074	6	33	.	.	PUNCT
ejpam-6074	7	1	2020	2020	NUM
ejpam-6074	7	2	mathematics	mathematic	NOUN
ejpam-6074	7	3	subject	subject	NOUN
ejpam-6074	7	4	classifications	classification	NOUN
ejpam-6074	7	5	:	:	PUNCT
ejpam-6074	7	6	05c69	05c69	X
ejpam-6074	7	7	key	key	ADJ
ejpam-6074	7	8	words	word	NOUN
ejpam-6074	7	9	and	and	CCONJ
ejpam-6074	7	10	phrases	phrase	NOUN
ejpam-6074	7	11	:	:	PUNCT
ejpam-6074	7	12	hop	hop	NOUN
ejpam-6074	7	13	domination	domination	NOUN
ejpam-6074	7	14	,	,	PUNCT
ejpam-6074	7	15	2	2	NUM
ejpam-6074	7	16	-	-	PUNCT
ejpam-6074	7	17	step	step	NOUN
ejpam-6074	7	18	movable	movable	ADJ
ejpam-6074	7	19	hop	hop	NOUN
ejpam-6074	7	20	dominating	dominating	NOUN
ejpam-6074	7	21	,	,	PUNCT
ejpam-6074	7	22	2	2	NUM
ejpam-6074	7	23	-	-	PUNCT
ejpam-6074	7	24	step	step	NOUN
ejpam-6074	7	25	movable	movable	ADJ
ejpam-6074	7	26	hop	hop	NOUN
ejpam-6074	7	27	domination	domination	NOUN
ejpam-6074	7	28	number	number	NOUN
ejpam-6074	7	29	1	1	NUM
ejpam-6074	7	30	.	.	PUNCT
ejpam-6074	8	1	introduction	introduction	NOUN
ejpam-6074	8	2	movability	movability	NOUN
ejpam-6074	8	3	of	of	ADP
ejpam-6074	8	4	dominating	dominating	NOUN
ejpam-6074	8	5	sets	set	NOUN
ejpam-6074	8	6	was	be	AUX
ejpam-6074	8	7	introduced	introduce	VERB
ejpam-6074	8	8	and	and	CCONJ
ejpam-6074	8	9	studied	study	VERB
ejpam-6074	8	10	by	by	ADP
ejpam-6074	8	11	blair	blair	PROPN
ejpam-6074	8	12	et	et	PROPN
ejpam-6074	8	13	al	al	PROPN
ejpam-6074	8	14	.	.	PUNCT
ejpam-6074	9	1	in	in	ADP
ejpam-6074	9	2	[	[	X
ejpam-6074	9	3	1	1	NUM
ejpam-6074	9	4	]	]	PUNCT
ejpam-6074	9	5	.	.	PUNCT
ejpam-6074	10	1	apparently	apparently	ADV
ejpam-6074	10	2	,	,	PUNCT
ejpam-6074	10	3	this	this	PRON
ejpam-6074	10	4	is	be	AUX
ejpam-6074	10	5	a	a	DET
ejpam-6074	10	6	variation	variation	NOUN
ejpam-6074	10	7	on	on	ADP
ejpam-6074	10	8	dominating	dominating	NOUN
ejpam-6074	10	9	sets	set	NOUN
ejpam-6074	10	10	in	in	ADP
ejpam-6074	10	11	which	which	PRON
ejpam-6074	10	12	vertices	vertice	VERB
ejpam-6074	10	13	in	in	ADP
ejpam-6074	10	14	a	a	DET
ejpam-6074	10	15	dominating	dominating	NOUN
ejpam-6074	10	16	set	set	NOUN
ejpam-6074	10	17	are	be	AUX
ejpam-6074	10	18	either	either	CCONJ
ejpam-6074	10	19	removed	remove	VERB
ejpam-6074	10	20	or	or	CCONJ
ejpam-6074	10	21	replaced	replace	VERB
ejpam-6074	10	22	.	.	PUNCT
ejpam-6074	11	1	a	a	DET
ejpam-6074	11	2	motivation	motivation	NOUN
ejpam-6074	11	3	of	of	ADP
ejpam-6074	11	4	this	this	DET
ejpam-6074	11	5	study	study	NOUN
ejpam-6074	11	6	can	can	AUX
ejpam-6074	11	7	be	be	AUX
ejpam-6074	11	8	seen	see	VERB
ejpam-6074	11	9	,	,	PUNCT
ejpam-6074	11	10	for	for	ADP
ejpam-6074	11	11	example	example	NOUN
ejpam-6074	11	12	,	,	PUNCT
ejpam-6074	11	13	in	in	ADP
ejpam-6074	11	14	a	a	DET
ejpam-6074	11	15	network	network	NOUN
ejpam-6074	11	16	with	with	ADP
ejpam-6074	11	17	sensors	sensor	NOUN
ejpam-6074	11	18	located	locate	VERB
ejpam-6074	11	19	at	at	ADP
ejpam-6074	11	20	some	some	DET
ejpam-6074	11	21	nodes	node	NOUN
ejpam-6074	11	22	or	or	CCONJ
ejpam-6074	11	23	vertices	vertex	NOUN
ejpam-6074	11	24	to	to	PART
ejpam-6074	11	25	serve	serve	VERB
ejpam-6074	11	26	their	their	PRON
ejpam-6074	11	27	purpose	purpose	NOUN
ejpam-6074	11	28	(	(	PUNCT
ejpam-6074	11	29	e.g.	e.g.	ADV
ejpam-6074	11	30	monitor	monitor	VERB
ejpam-6074	11	31	activities	activity	NOUN
ejpam-6074	11	32	in	in	ADP
ejpam-6074	11	33	the	the	DET
ejpam-6074	11	34	network	network	NOUN
ejpam-6074	11	35	)	)	PUNCT
ejpam-6074	11	36	.	.	PUNCT
ejpam-6074	12	1	it	it	PRON
ejpam-6074	12	2	may	may	AUX
ejpam-6074	12	3	happen	happen	VERB
ejpam-6074	12	4	that	that	SCONJ
ejpam-6074	12	5	malfunctioning	malfunctioning	NOUN
ejpam-6074	12	6	of	of	ADP
ejpam-6074	12	7	some	some	PRON
ejpam-6074	12	8	of	of	ADP
ejpam-6074	12	9	these	these	DET
ejpam-6074	12	10	sensors	sensor	NOUN
ejpam-6074	12	11	occurs	occur	VERB
ejpam-6074	12	12	due	due	ADJ
ejpam-6074	12	13	to	to	ADP
ejpam-6074	12	14	loss	loss	NOUN
ejpam-6074	12	15	of	of	ADP
ejpam-6074	12	16	battery	battery	NOUN
ejpam-6074	12	17	supply	supply	NOUN
ejpam-6074	12	18	or	or	CCONJ
ejpam-6074	12	19	destruction	destruction	NOUN
ejpam-6074	12	20	by	by	ADP
ejpam-6074	12	21	natural	natural	ADJ
ejpam-6074	12	22	calamities	calamity	NOUN
ejpam-6074	12	23	.	.	PUNCT
ejpam-6074	13	1	when	when	SCONJ
ejpam-6074	13	2	such	such	DET
ejpam-6074	13	3	a	a	DET
ejpam-6074	13	4	case	case	NOUN
ejpam-6074	13	5	happens	happen	VERB
ejpam-6074	13	6	,	,	PUNCT
ejpam-6074	13	7	a	a	DET
ejpam-6074	13	8	new	new	ADJ
ejpam-6074	13	9	nearby	nearby	ADJ
ejpam-6074	13	10	location	location	NOUN
ejpam-6074	13	11	for	for	ADP
ejpam-6074	13	12	a	a	DET
ejpam-6074	13	13	sensor	sensor	NOUN
ejpam-6074	13	14	can	can	AUX
ejpam-6074	13	15	be	be	AUX
ejpam-6074	13	16	chosen	choose	VERB
ejpam-6074	13	17	appropriately	appropriately	ADV
ejpam-6074	13	18	so	so	SCONJ
ejpam-6074	13	19	as	as	SCONJ
ejpam-6074	13	20	to	to	PART
ejpam-6074	13	21	preserve	preserve	VERB
ejpam-6074	13	22	the	the	DET
ejpam-6074	13	23	desired	desire	VERB
ejpam-6074	13	24	activity	activity	NOUN
ejpam-6074	13	25	,	,	PUNCT
ejpam-6074	13	26	connectivity	connectivity	NOUN
ejpam-6074	13	27	,	,	PUNCT
ejpam-6074	13	28	or	or	CCONJ
ejpam-6074	13	29	security	security	NOUN
ejpam-6074	13	30	these	these	DET
ejpam-6074	13	31	sensors	sensor	NOUN
ejpam-6074	13	32	are	be	AUX
ejpam-6074	13	33	purposely	purposely	ADV
ejpam-6074	13	34	designed	design	VERB
ejpam-6074	13	35	∗corresponding	∗corresponde	VERB
ejpam-6074	13	36	author	author	NOUN
ejpam-6074	13	37	.	.	PUNCT
ejpam-6074	14	1	doi	doi	NOUN
ejpam-6074	14	2	:	:	PUNCT
ejpam-6074	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6074	https://doi.org/10.29020/nybg.ejpam.v18i2.6074	PROPN
ejpam-6074	14	4	email	email	NOUN
ejpam-6074	14	5	addresses	address	VERB
ejpam-6074	14	6	:	:	PUNCT
ejpam-6074	14	7	roger.estrella@g.msuiit.edu.ph	roger.estrella@g.msuiit.edu.ph	PROPN
ejpam-6074	14	8	(	(	PUNCT
ejpam-6074	14	9	r.	r.	PROPN
ejpam-6074	14	10	estrella	estrella	PROPN
ejpam-6074	14	11	)	)	PUNCT
ejpam-6074	14	12	gina.malacas@g.msuiit.edu.ph	gina.malacas@g.msuiit.edu.ph	PROPN
ejpam-6074	14	13	(	(	PUNCT
ejpam-6074	14	14	g.	g.	PROPN
ejpam-6074	14	15	malacas	malacas	PROPN
ejpam-6074	14	16	)	)	PUNCT
ejpam-6074	14	17	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-6074	14	18	(	(	PUNCT
ejpam-6074	14	19	s.	s.	PROPN
ejpam-6074	14	20	canoy	canoy	PROPN
ejpam-6074	14	21	)	)	PUNCT
ejpam-6074	14	22	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6074	15	1	1	1	NUM
ejpam-6074	15	2	copyright	copyright	NOUN
ejpam-6074	15	3	:	:	PUNCT
ejpam-6074	15	4	©	©	PROPN
ejpam-6074	15	5	2025	2025	NUM
ejpam-6074	15	6	the	the	DET
ejpam-6074	15	7	author(s	author(s	NOUN
ejpam-6074	15	8	)	)	PUNCT
ejpam-6074	15	9	.	.	PUNCT
ejpam-6074	16	1	(	(	PUNCT
ejpam-6074	16	2	cc	cc	NOUN
ejpam-6074	16	3	by	by	ADP
ejpam-6074	16	4	-	-	PUNCT
ejpam-6074	16	5	nc	nc	PROPN
ejpam-6074	16	6	4.0	4.0	NUM
ejpam-6074	16	7	)	)	PUNCT
ejpam-6074	16	8	r.	r.	PROPN
ejpam-6074	16	9	estrella	estrella	PROPN
ejpam-6074	16	10	,	,	PUNCT
ejpam-6074	16	11	gina	gina	PROPN
ejpam-6074	16	12	m.	m.	PROPN
ejpam-6074	16	13	malacas	malacas	PROPN
ejpam-6074	16	14	,	,	PUNCT
ejpam-6074	16	15	s.	s.	PROPN
ejpam-6074	16	16	canoy	canoy	PROPN
ejpam-6074	16	17	jr	jr	PROPN
ejpam-6074	16	18	.	.	PROPN
ejpam-6074	16	19	/	/	SYM
ejpam-6074	16	20	eur	eur	PROPN
ejpam-6074	16	21	.	.	PUNCT
ejpam-6074	17	1	j.	j.	PROPN
ejpam-6074	17	2	pure	pure	PROPN
ejpam-6074	17	3	appl	appl	PROPN
ejpam-6074	17	4	.	.	PROPN
ejpam-6074	17	5	math	math	PROPN
ejpam-6074	17	6	,	,	PUNCT
ejpam-6074	17	7	18	18	NUM
ejpam-6074	17	8	(	(	PUNCT
ejpam-6074	17	9	2	2	NUM
ejpam-6074	17	10	)	)	PUNCT
ejpam-6074	17	11	(	(	PUNCT
ejpam-6074	17	12	2025	2025	NUM
ejpam-6074	17	13	)	)	PUNCT
ejpam-6074	17	14	,	,	PUNCT
ejpam-6074	17	15	6074	6074	NUM
ejpam-6074	17	16	2	2	NUM
ejpam-6074	17	17	of	of	ADP
ejpam-6074	17	18	15	15	NUM
ejpam-6074	17	19	in	in	ADP
ejpam-6074	17	20	the	the	DET
ejpam-6074	17	21	network	network	NOUN
ejpam-6074	17	22	.	.	PUNCT
ejpam-6074	18	1	movability	movability	NOUN
ejpam-6074	18	2	of	of	ADP
ejpam-6074	18	3	different	different	ADJ
ejpam-6074	18	4	types	type	NOUN
ejpam-6074	18	5	of	of	ADP
ejpam-6074	18	6	dominating	dominating	NOUN
ejpam-6074	18	7	sets	set	NOUN
ejpam-6074	18	8	had	have	AUX
ejpam-6074	18	9	been	be	AUX
ejpam-6074	18	10	considered	consider	VERB
ejpam-6074	18	11	in	in	ADP
ejpam-6074	18	12	[	[	X
ejpam-6074	18	13	2	2	NUM
ejpam-6074	18	14	]	]	PUNCT
ejpam-6074	18	15	,	,	PUNCT
ejpam-6074	18	16	[	[	X
ejpam-6074	18	17	3	3	NUM
ejpam-6074	18	18	]	]	PUNCT
ejpam-6074	18	19	,	,	PUNCT
ejpam-6074	18	20	[	[	X
ejpam-6074	18	21	4	4	NUM
ejpam-6074	18	22	]	]	PUNCT
ejpam-6074	18	23	,	,	PUNCT
ejpam-6074	18	24	[	[	X
ejpam-6074	18	25	5	5	NUM
ejpam-6074	18	26	]	]	PUNCT
ejpam-6074	18	27	,	,	PUNCT
ejpam-6074	18	28	[	[	X
ejpam-6074	18	29	6	6	NUM
ejpam-6074	18	30	]	]	PUNCT
ejpam-6074	18	31	,	,	PUNCT
ejpam-6074	18	32	and	and	CCONJ
ejpam-6074	18	33	[	[	X
ejpam-6074	18	34	7	7	NUM
ejpam-6074	18	35	]	]	PUNCT
ejpam-6074	18	36	.	.	PUNCT
ejpam-6074	19	1	hop	hop	PROPN
ejpam-6074	19	2	domination	domination	PROPN
ejpam-6074	19	3	,	,	PUNCT
ejpam-6074	19	4	a	a	DET
ejpam-6074	19	5	kind	kind	NOUN
ejpam-6074	19	6	of	of	ADP
ejpam-6074	19	7	domination	domination	NOUN
ejpam-6074	19	8	introduced	introduce	VERB
ejpam-6074	19	9	by	by	ADP
ejpam-6074	19	10	natarajan	natarajan	PROPN
ejpam-6074	19	11	et	et	PROPN
ejpam-6074	19	12	al	al	PROPN
ejpam-6074	19	13	.	.	PUNCT
ejpam-6074	20	1	in	in	ADP
ejpam-6074	20	2	[	[	X
ejpam-6074	20	3	8	8	NUM
ejpam-6074	20	4	]	]	PUNCT
ejpam-6074	20	5	,	,	PUNCT
ejpam-6074	20	6	has	have	AUX
ejpam-6074	20	7	also	also	ADV
ejpam-6074	20	8	gained	gain	VERB
ejpam-6074	20	9	popularity	popularity	NOUN
ejpam-6074	20	10	and	and	CCONJ
ejpam-6074	20	11	interest	interest	NOUN
ejpam-6074	20	12	among	among	ADP
ejpam-6074	20	13	the	the	DET
ejpam-6074	20	14	researchers	researcher	NOUN
ejpam-6074	20	15	in	in	ADP
ejpam-6074	20	16	the	the	DET
ejpam-6074	20	17	field	field	NOUN
ejpam-6074	20	18	.	.	PUNCT
ejpam-6074	21	1	through	through	ADP
ejpam-6074	21	2	the	the	DET
ejpam-6074	21	3	years	year	NOUN
ejpam-6074	21	4	,	,	PUNCT
ejpam-6074	21	5	a	a	DET
ejpam-6074	21	6	great	great	ADJ
ejpam-6074	21	7	number	number	NOUN
ejpam-6074	21	8	of	of	ADP
ejpam-6074	21	9	variants	variant	NOUN
ejpam-6074	21	10	of	of	ADP
ejpam-6074	21	11	hop	hop	NOUN
ejpam-6074	21	12	domination	domination	NOUN
ejpam-6074	21	13	have	have	AUX
ejpam-6074	21	14	already	already	ADV
ejpam-6074	21	15	been	be	AUX
ejpam-6074	21	16	considered	consider	VERB
ejpam-6074	21	17	and	and	CCONJ
ejpam-6074	21	18	studied	study	VERB
ejpam-6074	21	19	(	(	PUNCT
ejpam-6074	21	20	see	see	VERB
ejpam-6074	21	21	,	,	PUNCT
ejpam-6074	21	22	for	for	ADP
ejpam-6074	21	23	example	example	NOUN
ejpam-6074	21	24	,	,	PUNCT
ejpam-6074	22	1	[	[	X
ejpam-6074	22	2	9	9	NUM
ejpam-6074	22	3	]	]	PUNCT
ejpam-6074	22	4	,	,	PUNCT
ejpam-6074	22	5	[	[	X
ejpam-6074	22	6	10	10	NUM
ejpam-6074	22	7	]	]	PUNCT
ejpam-6074	22	8	,	,	PUNCT
ejpam-6074	22	9	[	[	X
ejpam-6074	22	10	11	11	NUM
ejpam-6074	22	11	]	]	PUNCT
ejpam-6074	22	12	,	,	PUNCT
ejpam-6074	22	13	[	[	X
ejpam-6074	22	14	12	12	NUM
ejpam-6074	22	15	]	]	PUNCT
ejpam-6074	22	16	,	,	PUNCT
ejpam-6074	22	17	[	[	X
ejpam-6074	22	18	13	13	NUM
ejpam-6074	22	19	]	]	PUNCT
ejpam-6074	22	20	,	,	PUNCT
ejpam-6074	22	21	[	[	X
ejpam-6074	22	22	14	14	NUM
ejpam-6074	22	23	]	]	PUNCT
ejpam-6074	22	24	,	,	PUNCT
ejpam-6074	22	25	[	[	X
ejpam-6074	22	26	15	15	NUM
ejpam-6074	22	27	]	]	PUNCT
ejpam-6074	22	28	,	,	PUNCT
ejpam-6074	22	29	[	[	X
ejpam-6074	22	30	16	16	NUM
ejpam-6074	22	31	]	]	PUNCT
ejpam-6074	22	32	,	,	PUNCT
ejpam-6074	23	1	[	[	X
ejpam-6074	23	2	17	17	NUM
ejpam-6074	23	3	]	]	PUNCT
ejpam-6074	23	4	,	,	PUNCT
ejpam-6074	23	5	[	[	X
ejpam-6074	23	6	18	18	NUM
ejpam-6074	23	7	]	]	PUNCT
ejpam-6074	23	8	,	,	PUNCT
ejpam-6074	23	9	and	and	CCONJ
ejpam-6074	23	10	[	[	X
ejpam-6074	23	11	19	19	NUM
ejpam-6074	23	12	]	]	NUM
ejpam-6074	23	13	)	)	PUNCT
ejpam-6074	23	14	.	.	PUNCT
ejpam-6074	24	1	since	since	SCONJ
ejpam-6074	24	2	hop	hop	PROPN
ejpam-6074	24	3	domination	domination	NOUN
ejpam-6074	24	4	and	and	CCONJ
ejpam-6074	24	5	domination	domination	NOUN
ejpam-6074	24	6	have	have	VERB
ejpam-6074	24	7	similar	similar	ADJ
ejpam-6074	24	8	applications	application	NOUN
ejpam-6074	24	9	in	in	ADP
ejpam-6074	24	10	networks	network	NOUN
ejpam-6074	24	11	,	,	PUNCT
ejpam-6074	24	12	it	it	PRON
ejpam-6074	24	13	is	be	AUX
ejpam-6074	24	14	also	also	ADV
ejpam-6074	24	15	worthwhile	worthwhile	ADJ
ejpam-6074	24	16	to	to	PART
ejpam-6074	24	17	consider	consider	VERB
ejpam-6074	24	18	movability	movability	NOUN
ejpam-6074	24	19	of	of	ADP
ejpam-6074	24	20	hop	hop	NOUN
ejpam-6074	24	21	dominating	dominating	NOUN
ejpam-6074	24	22	sets	set	NOUN
ejpam-6074	24	23	in	in	ADP
ejpam-6074	24	24	graphs	graph	NOUN
ejpam-6074	24	25	.	.	PUNCT
ejpam-6074	25	1	in	in	ADP
ejpam-6074	25	2	this	this	DET
ejpam-6074	25	3	paper	paper	NOUN
ejpam-6074	25	4	,	,	PUNCT
ejpam-6074	25	5	we	we	PRON
ejpam-6074	25	6	introduce	introduce	VERB
ejpam-6074	25	7	2	2	NUM
ejpam-6074	25	8	-	-	PUNCT
ejpam-6074	25	9	step	step	NOUN
ejpam-6074	25	10	movability	movability	NOUN
ejpam-6074	25	11	of	of	ADP
ejpam-6074	25	12	hop	hop	NOUN
ejpam-6074	25	13	dominating	dominating	NOUN
ejpam-6074	25	14	sets	set	NOUN
ejpam-6074	25	15	.	.	PUNCT
ejpam-6074	26	1	since	since	SCONJ
ejpam-6074	26	2	these	these	DET
ejpam-6074	26	3	types	type	NOUN
ejpam-6074	26	4	of	of	ADP
ejpam-6074	26	5	sets	set	NOUN
ejpam-6074	26	6	need	need	AUX
ejpam-6074	26	7	not	not	PART
ejpam-6074	26	8	be	be	AUX
ejpam-6074	26	9	present	present	ADJ
ejpam-6074	26	10	in	in	ADP
ejpam-6074	26	11	some	some	DET
ejpam-6074	26	12	graphs	graph	NOUN
ejpam-6074	26	13	,	,	PUNCT
ejpam-6074	26	14	we	we	PRON
ejpam-6074	26	15	characterize	characterize	VERB
ejpam-6074	26	16	those	those	DET
ejpam-6074	26	17	graphs	graph	NOUN
ejpam-6074	26	18	that	that	PRON
ejpam-6074	26	19	admit	admit	VERB
ejpam-6074	26	20	such	such	ADJ
ejpam-6074	26	21	sets	set	NOUN
ejpam-6074	26	22	.	.	PUNCT
ejpam-6074	27	1	we	we	PRON
ejpam-6074	27	2	also	also	ADV
ejpam-6074	27	3	give	give	VERB
ejpam-6074	27	4	bounds	bound	NOUN
ejpam-6074	27	5	on	on	ADP
ejpam-6074	27	6	the	the	DET
ejpam-6074	27	7	2	2	NUM
ejpam-6074	27	8	-	-	PUNCT
ejpam-6074	27	9	step	step	NOUN
ejpam-6074	27	10	movable	movable	ADJ
ejpam-6074	27	11	hop	hop	NOUN
ejpam-6074	27	12	domination	domination	NOUN
ejpam-6074	27	13	number	number	NOUN
ejpam-6074	27	14	and	and	CCONJ
ejpam-6074	27	15	determine	determine	VERB
ejpam-6074	27	16	the	the	DET
ejpam-6074	27	17	values	value	NOUN
ejpam-6074	27	18	of	of	ADP
ejpam-6074	27	19	the	the	DET
ejpam-6074	27	20	parameter	parameter	NOUN
ejpam-6074	27	21	in	in	ADP
ejpam-6074	27	22	some	some	DET
ejpam-6074	27	23	known	know	VERB
ejpam-6074	27	24	graphs	graph	NOUN
ejpam-6074	27	25	including	include	VERB
ejpam-6074	27	26	the	the	DET
ejpam-6074	27	27	shadow	shadow	NOUN
ejpam-6074	27	28	graph	graph	NOUN
ejpam-6074	27	29	and	and	CCONJ
ejpam-6074	27	30	complementary	complementary	ADJ
ejpam-6074	27	31	prism	prism	NOUN
ejpam-6074	27	32	.	.	PUNCT
ejpam-6074	28	1	2	2	X
ejpam-6074	28	2	.	.	X
ejpam-6074	28	3	terminology	terminology	NOUN
ejpam-6074	28	4	and	and	CCONJ
ejpam-6074	28	5	notation	notation	NOUN
ejpam-6074	28	6	let	let	VERB
ejpam-6074	28	7	g	g	PROPN
ejpam-6074	28	8	=	=	SYM
ejpam-6074	28	9	v	v	PROPN
ejpam-6074	28	10	(	(	PUNCT
ejpam-6074	28	11	g	g	NOUN
ejpam-6074	28	12	)	)	PUNCT
ejpam-6074	28	13	,	,	PUNCT
ejpam-6074	28	14	e(g	e(g	PROPN
ejpam-6074	28	15	)	)	PUNCT
ejpam-6074	28	16	)	)	PUNCT
ejpam-6074	28	17	be	be	AUX
ejpam-6074	28	18	an	an	DET
ejpam-6074	28	19	undirected	undirected	ADJ
ejpam-6074	28	20	graph	graph	NOUN
ejpam-6074	28	21	.	.	PUNCT
ejpam-6074	29	1	for	for	ADP
ejpam-6074	29	2	any	any	DET
ejpam-6074	29	3	two	two	NUM
ejpam-6074	29	4	vertices	vertex	NOUN
ejpam-6074	29	5	u	u	NOUN
ejpam-6074	29	6	and	and	CCONJ
ejpam-6074	29	7	v	v	NOUN
ejpam-6074	29	8	of	of	ADP
ejpam-6074	29	9	g	g	NOUN
ejpam-6074	29	10	,	,	PUNCT
ejpam-6074	29	11	the	the	DET
ejpam-6074	29	12	distance	distance	NOUN
ejpam-6074	29	13	dg(u	dg(u	X
ejpam-6074	29	14	,	,	PUNCT
ejpam-6074	29	15	v	v	NOUN
ejpam-6074	29	16	)	)	PUNCT
ejpam-6074	29	17	is	be	AUX
ejpam-6074	29	18	the	the	DET
ejpam-6074	29	19	length	length	NOUN
ejpam-6074	29	20	of	of	ADP
ejpam-6074	29	21	a	a	DET
ejpam-6074	29	22	shortest	short	ADJ
ejpam-6074	29	23	path	path	NOUN
ejpam-6074	29	24	joining	join	VERB
ejpam-6074	29	25	u	u	NOUN
ejpam-6074	29	26	and	and	CCONJ
ejpam-6074	29	27	v.	v.	ADP
ejpam-6074	29	28	any	any	DET
ejpam-6074	29	29	u	u	NOUN
ejpam-6074	29	30	-	-	NOUN
ejpam-6074	29	31	v	v	ADJ
ejpam-6074	29	32	path	path	NOUN
ejpam-6074	29	33	of	of	ADP
ejpam-6074	29	34	length	length	NOUN
ejpam-6074	29	35	dg(u	dg(u	PROPN
ejpam-6074	29	36	,	,	PUNCT
ejpam-6074	29	37	v	v	NOUN
ejpam-6074	29	38	)	)	PUNCT
ejpam-6074	29	39	is	be	AUX
ejpam-6074	29	40	called	call	VERB
ejpam-6074	29	41	a	a	DET
ejpam-6074	29	42	u	u	NOUN
ejpam-6074	29	43	-	-	NOUN
ejpam-6074	29	44	v	v	ADJ
ejpam-6074	29	45	geodesic	geodesic	NOUN
ejpam-6074	29	46	.	.	PUNCT
ejpam-6074	30	1	the	the	DET
ejpam-6074	30	2	interval	interval	NOUN
ejpam-6074	30	3	ig	ig	PROPN
ejpam-6074	31	1	[	[	X
ejpam-6074	31	2	u	u	NOUN
ejpam-6074	31	3	,	,	PUNCT
ejpam-6074	31	4	v	v	NOUN
ejpam-6074	31	5	]	]	PUNCT
ejpam-6074	31	6	consists	consist	VERB
ejpam-6074	31	7	of	of	ADP
ejpam-6074	31	8	u	u	NOUN
ejpam-6074	31	9	,	,	PUNCT
ejpam-6074	31	10	v	v	NOUN
ejpam-6074	31	11	,	,	PUNCT
ejpam-6074	31	12	and	and	CCONJ
ejpam-6074	31	13	all	all	DET
ejpam-6074	31	14	vertices	vertex	NOUN
ejpam-6074	31	15	lying	lie	VERB
ejpam-6074	31	16	on	on	ADP
ejpam-6074	31	17	a	a	DET
ejpam-6074	31	18	u	u	NOUN
ejpam-6074	31	19	-	-	NOUN
ejpam-6074	31	20	v	v	ADJ
ejpam-6074	31	21	geodesic	geodesic	NOUN
ejpam-6074	31	22	.	.	PUNCT
ejpam-6074	32	1	the	the	DET
ejpam-6074	32	2	interval	interval	NOUN
ejpam-6074	32	3	ig(u	ig(u	NOUN
ejpam-6074	32	4	,	,	PUNCT
ejpam-6074	32	5	v	v	NOUN
ejpam-6074	32	6	)	)	PUNCT
ejpam-6074	32	7	=	=	PUNCT
ejpam-6074	33	1	ig	ig	PROPN
ejpam-6074	34	1	[	[	X
ejpam-6074	34	2	u	u	NOUN
ejpam-6074	34	3	,	,	PUNCT
ejpam-6074	34	4	v	v	ADP
ejpam-6074	34	5	]	]	PUNCT
ejpam-6074	34	6	\	\	NOUN
ejpam-6074	34	7	{	{	PUNCT
ejpam-6074	34	8	u	u	NOUN
ejpam-6074	34	9	,	,	PUNCT
ejpam-6074	34	10	v	v	NOUN
ejpam-6074	34	11	}	}	PUNCT
ejpam-6074	34	12	.	.	PUNCT
ejpam-6074	35	1	vertices	vertice	VERB
ejpam-6074	35	2	u	u	NOUN
ejpam-6074	35	3	and	and	CCONJ
ejpam-6074	35	4	v	v	NOUN
ejpam-6074	35	5	are	be	AUX
ejpam-6074	35	6	adjacent	adjacent	ADJ
ejpam-6074	35	7	(	(	PUNCT
ejpam-6074	35	8	or	or	CCONJ
ejpam-6074	35	9	neighbors	neighbor	NOUN
ejpam-6074	35	10	)	)	PUNCT
ejpam-6074	35	11	if	if	SCONJ
ejpam-6074	35	12	uv	uv	PROPN
ejpam-6074	35	13	∈	∈	PROPN
ejpam-6074	35	14	e(g	e(g	PROPN
ejpam-6074	35	15	)	)	PUNCT
ejpam-6074	35	16	.	.	PUNCT
ejpam-6074	36	1	the	the	DET
ejpam-6074	36	2	set	set	NOUN
ejpam-6074	36	3	of	of	ADP
ejpam-6074	36	4	neighbors	neighbor	NOUN
ejpam-6074	36	5	of	of	ADP
ejpam-6074	36	6	a	a	DET
ejpam-6074	36	7	vertex	vertex	NOUN
ejpam-6074	36	8	u	u	NOUN
ejpam-6074	36	9	in	in	ADP
ejpam-6074	36	10	g	g	NOUN
ejpam-6074	36	11	,	,	PUNCT
ejpam-6074	36	12	denoted	denote	VERB
ejpam-6074	36	13	by	by	ADP
ejpam-6074	36	14	ng(u	ng(u	NOUN
ejpam-6074	36	15	)	)	PUNCT
ejpam-6074	36	16	,	,	PUNCT
ejpam-6074	36	17	is	be	AUX
ejpam-6074	36	18	called	call	VERB
ejpam-6074	36	19	the	the	DET
ejpam-6074	36	20	open	open	ADJ
ejpam-6074	36	21	neighborhood	neighborhood	NOUN
ejpam-6074	36	22	of	of	ADP
ejpam-6074	36	23	u.	u.	VERB
ejpam-6074	36	24	the	the	DET
ejpam-6074	36	25	closed	closed	ADJ
ejpam-6074	36	26	neighborhood	neighborhood	NOUN
ejpam-6074	36	27	of	of	ADP
ejpam-6074	36	28	u	u	NOUN
ejpam-6074	36	29	is	be	AUX
ejpam-6074	36	30	the	the	DET
ejpam-6074	36	31	set	set	NOUN
ejpam-6074	36	32	ng[u	ng[u	PROPN
ejpam-6074	36	33	]	]	X
ejpam-6074	36	34	=	=	SYM
ejpam-6074	36	35	ng(u	ng(u	PROPN
ejpam-6074	36	36	)	)	PUNCT
ejpam-6074	36	37	∪	∪	NOUN
ejpam-6074	36	38	{	{	PUNCT
ejpam-6074	36	39	u	u	NOUN
ejpam-6074	36	40	}	}	PUNCT
ejpam-6074	36	41	.	.	PUNCT
ejpam-6074	37	1	if	if	SCONJ
ejpam-6074	37	2	x	x	PROPN
ejpam-6074	37	3	⊆	⊆	NUM
ejpam-6074	37	4	v	v	X
ejpam-6074	37	5	(	(	PUNCT
ejpam-6074	37	6	g	g	NOUN
ejpam-6074	37	7	)	)	PUNCT
ejpam-6074	37	8	,	,	PUNCT
ejpam-6074	37	9	the	the	DET
ejpam-6074	37	10	open	open	ADJ
ejpam-6074	37	11	neighborhood	neighborhood	NOUN
ejpam-6074	37	12	of	of	ADP
ejpam-6074	37	13	x	x	SYM
ejpam-6074	37	14	is	be	AUX
ejpam-6074	37	15	the	the	DET
ejpam-6074	37	16	set	set	NOUN
ejpam-6074	37	17	ng(x	ng(x	NUM
ejpam-6074	37	18	)	)	PUNCT
ejpam-6074	38	1	=	=	SYM
ejpam-6074	38	2	⋃	⋃	NOUN
ejpam-6074	38	3	u∈x	u∈x	NOUN
ejpam-6074	38	4	ng(u	ng(u	NOUN
ejpam-6074	38	5	)	)	PUNCT
ejpam-6074	38	6	.	.	PUNCT
ejpam-6074	39	1	the	the	DET
ejpam-6074	39	2	closed	closed	ADJ
ejpam-6074	39	3	neighborhood	neighborhood	NOUN
ejpam-6074	39	4	of	of	ADP
ejpam-6074	39	5	x	x	SYM
ejpam-6074	39	6	is	be	AUX
ejpam-6074	39	7	the	the	DET
ejpam-6074	39	8	set	set	NOUN
ejpam-6074	39	9	ng[x	ng[x	PROPN
ejpam-6074	39	10	]	]	X
ejpam-6074	39	11	=	=	PUNCT
ejpam-6074	39	12	ng(x	ng(x	X
ejpam-6074	39	13	)	)	PUNCT
ejpam-6074	40	1	∪x	∪x	PROPN
ejpam-6074	40	2	.	.	PUNCT
ejpam-6074	41	1	a	a	DET
ejpam-6074	41	2	set	set	NOUN
ejpam-6074	41	3	d	d	NOUN
ejpam-6074	41	4	⊆	⊆	NUM
ejpam-6074	41	5	v	v	ADP
ejpam-6074	41	6	(	(	PUNCT
ejpam-6074	41	7	g	g	NOUN
ejpam-6074	41	8	)	)	PUNCT
ejpam-6074	41	9	is	be	AUX
ejpam-6074	41	10	a	a	DET
ejpam-6074	41	11	dominating	dominating	NOUN
ejpam-6074	41	12	set	set	NOUN
ejpam-6074	41	13	(	(	PUNCT
ejpam-6074	41	14	resp	resp	NOUN
ejpam-6074	41	15	.	.	PUNCT
ejpam-6074	42	1	total	total	ADJ
ejpam-6074	42	2	dominating	dominating	NOUN
ejpam-6074	42	3	set	set	NOUN
ejpam-6074	42	4	)	)	PUNCT
ejpam-6074	42	5	of	of	ADP
ejpam-6074	42	6	g	g	PROPN
ejpam-6074	42	7	if	if	SCONJ
ejpam-6074	42	8	for	for	ADP
ejpam-6074	42	9	every	every	PRON
ejpam-6074	42	10	v	v	NUM
ejpam-6074	42	11	∈	∈	NOUN
ejpam-6074	42	12	v	v	NOUN
ejpam-6074	42	13	(	(	PUNCT
ejpam-6074	42	14	g	g	NOUN
ejpam-6074	42	15	)	)	PUNCT
ejpam-6074	42	16	\	\	PUNCT
ejpam-6074	43	1	d	d	X
ejpam-6074	43	2	(	(	PUNCT
ejpam-6074	43	3	resp	resp	NOUN
ejpam-6074	43	4	.	.	PUNCT
ejpam-6074	44	1	v	v	ADP
ejpam-6074	44	2	∈	∈	PROPN
ejpam-6074	44	3	v	v	NOUN
ejpam-6074	44	4	(	(	PUNCT
ejpam-6074	44	5	g	g	NOUN
ejpam-6074	44	6	)	)	PUNCT
ejpam-6074	44	7	)	)	PUNCT
ejpam-6074	45	1	,	,	PUNCT
ejpam-6074	45	2	there	there	PRON
ejpam-6074	45	3	exists	exist	VERB
ejpam-6074	45	4	u	u	NOUN
ejpam-6074	45	5	∈	∈	PROPN
ejpam-6074	45	6	d	d	ADP
ejpam-6074	45	7	such	such	ADJ
ejpam-6074	45	8	that	that	DET
ejpam-6074	45	9	uv	uv	PROPN
ejpam-6074	45	10	∈	∈	PROPN
ejpam-6074	45	11	e(g	e(g	PROPN
ejpam-6074	45	12	)	)	PUNCT
ejpam-6074	45	13	,	,	PUNCT
ejpam-6074	45	14	that	that	ADV
ejpam-6074	45	15	is	is	ADV
ejpam-6074	45	16	,	,	PUNCT
ejpam-6074	45	17	ng[d	ng[d	PROPN
ejpam-6074	45	18	]	]	PUNCT
ejpam-6074	45	19	=	=	SYM
ejpam-6074	45	20	v	v	X
ejpam-6074	45	21	(	(	PUNCT
ejpam-6074	45	22	g	g	NOUN
ejpam-6074	45	23	)	)	PUNCT
ejpam-6074	45	24	(	(	PUNCT
ejpam-6074	45	25	resp	resp	NOUN
ejpam-6074	45	26	.	.	PUNCT
ejpam-6074	45	27	ng(d	ng(d	PUNCT
ejpam-6074	45	28	)	)	PUNCT
ejpam-6074	45	29	=	=	SYM
ejpam-6074	45	30	v	v	X
ejpam-6074	45	31	(	(	PUNCT
ejpam-6074	45	32	g	g	NOUN
ejpam-6074	45	33	)	)	PUNCT
ejpam-6074	45	34	)	)	PUNCT
ejpam-6074	45	35	.	.	PUNCT
ejpam-6074	46	1	the	the	DET
ejpam-6074	46	2	domination	domination	NOUN
ejpam-6074	46	3	number	number	NOUN
ejpam-6074	46	4	(	(	PUNCT
ejpam-6074	46	5	resp	resp	NOUN
ejpam-6074	46	6	.	.	PUNCT
ejpam-6074	47	1	total	total	ADJ
ejpam-6074	47	2	domination	domination	NOUN
ejpam-6074	47	3	number	number	NOUN
ejpam-6074	47	4	)	)	PUNCT
ejpam-6074	47	5	of	of	ADP
ejpam-6074	47	6	g	g	NOUN
ejpam-6074	47	7	,	,	PUNCT
ejpam-6074	47	8	denoted	denote	VERB
ejpam-6074	47	9	by	by	ADP
ejpam-6074	47	10	γ(g	γ(g	PROPN
ejpam-6074	47	11	)	)	PUNCT
ejpam-6074	47	12	(	(	PUNCT
ejpam-6074	47	13	resp	resp	NOUN
ejpam-6074	47	14	.	.	PUNCT
ejpam-6074	47	15	γt(g	γt(g	PUNCT
ejpam-6074	47	16	)	)	PUNCT
ejpam-6074	47	17	)	)	PUNCT
ejpam-6074	47	18	,	,	PUNCT
ejpam-6074	47	19	is	be	AUX
ejpam-6074	47	20	the	the	DET
ejpam-6074	47	21	minimum	minimum	ADJ
ejpam-6074	47	22	cardinality	cardinality	NOUN
ejpam-6074	47	23	of	of	ADP
ejpam-6074	47	24	a	a	DET
ejpam-6074	47	25	dominating	dominating	NOUN
ejpam-6074	47	26	(	(	PUNCT
ejpam-6074	47	27	resp	resp	NOUN
ejpam-6074	47	28	.	.	PUNCT
ejpam-6074	48	1	total	total	ADJ
ejpam-6074	48	2	dominating	dominating	NOUN
ejpam-6074	48	3	)	)	PUNCT
ejpam-6074	48	4	set	set	VERB
ejpam-6074	48	5	in	in	ADP
ejpam-6074	48	6	g.	g.	PROPN
ejpam-6074	48	7	any	any	DET
ejpam-6074	48	8	dominating	dominating	NOUN
ejpam-6074	48	9	(	(	PUNCT
ejpam-6074	48	10	resp	resp	NOUN
ejpam-6074	48	11	.	.	PUNCT
ejpam-6074	49	1	total	total	ADJ
ejpam-6074	49	2	dominating	dominating	NOUN
ejpam-6074	49	3	)	)	PUNCT
ejpam-6074	49	4	set	set	VERB
ejpam-6074	49	5	in	in	ADP
ejpam-6074	49	6	g	g	PROPN
ejpam-6074	49	7	with	with	ADP
ejpam-6074	49	8	cardinality	cardinality	PROPN
ejpam-6074	49	9	γ(g	γ(g	PROPN
ejpam-6074	49	10	)	)	PUNCT
ejpam-6074	49	11	(	(	PUNCT
ejpam-6074	49	12	resp	resp	NOUN
ejpam-6074	49	13	.	.	PUNCT
ejpam-6074	49	14	γt(g	γt(g	PUNCT
ejpam-6074	49	15	)	)	PUNCT
ejpam-6074	49	16	)	)	PUNCT
ejpam-6074	49	17	,	,	PUNCT
ejpam-6074	49	18	is	be	AUX
ejpam-6074	49	19	called	call	VERB
ejpam-6074	49	20	a	a	DET
ejpam-6074	49	21	γ	γ	NOUN
ejpam-6074	49	22	-	-	PUNCT
ejpam-6074	49	23	set	set	ADJ
ejpam-6074	49	24	(	(	PUNCT
ejpam-6074	49	25	resp	resp	NOUN
ejpam-6074	49	26	.	.	PUNCT
ejpam-6074	50	1	γt	γt	NOUN
ejpam-6074	50	2	-	-	PUNCT
ejpam-6074	50	3	set	set	NOUN
ejpam-6074	50	4	)	)	PUNCT
ejpam-6074	50	5	in	in	ADP
ejpam-6074	50	6	g.	g.	PROPN
ejpam-6074	51	1	if	if	SCONJ
ejpam-6074	51	2	γ(g	γ(g	PROPN
ejpam-6074	51	3	)	)	PUNCT
ejpam-6074	51	4	=	=	SYM
ejpam-6074	51	5	1	1	NUM
ejpam-6074	51	6	and	and	CCONJ
ejpam-6074	51	7	{	{	PUNCT
ejpam-6074	51	8	v	v	NOUN
ejpam-6074	51	9	}	}	PUNCT
ejpam-6074	51	10	is	be	AUX
ejpam-6074	51	11	a	a	DET
ejpam-6074	51	12	dominating	dominating	NOUN
ejpam-6074	51	13	set	set	NOUN
ejpam-6074	51	14	in	in	ADP
ejpam-6074	51	15	g	g	PROPN
ejpam-6074	51	16	,	,	PUNCT
ejpam-6074	51	17	then	then	ADV
ejpam-6074	51	18	we	we	PRON
ejpam-6074	51	19	call	call	VERB
ejpam-6074	51	20	v	v	ADP
ejpam-6074	51	21	a	a	DET
ejpam-6074	51	22	dominating	dominating	NOUN
ejpam-6074	51	23	vertex	vertex	NOUN
ejpam-6074	51	24	in	in	ADP
ejpam-6074	51	25	g.	g.	PROPN
ejpam-6074	51	26	a	a	DET
ejpam-6074	51	27	vertex	vertex	NOUN
ejpam-6074	51	28	v	v	NOUN
ejpam-6074	51	29	in	in	ADP
ejpam-6074	51	30	g	g	PROPN
ejpam-6074	51	31	is	be	AUX
ejpam-6074	51	32	a	a	DET
ejpam-6074	51	33	hop	hop	NOUN
ejpam-6074	51	34	neighbor	neighbor	NOUN
ejpam-6074	51	35	of	of	ADP
ejpam-6074	51	36	vertex	vertex	NOUN
ejpam-6074	51	37	u	u	NOUN
ejpam-6074	51	38	in	in	ADP
ejpam-6074	51	39	g	g	PROPN
ejpam-6074	51	40	if	if	SCONJ
ejpam-6074	51	41	dg(u	dg(u	NOUN
ejpam-6074	51	42	,	,	PUNCT
ejpam-6074	51	43	v	v	NOUN
ejpam-6074	51	44	)	)	PUNCT
ejpam-6074	51	45	=	=	SYM
ejpam-6074	52	1	2	2	X
ejpam-6074	52	2	.	.	X
ejpam-6074	52	3	the	the	DET
ejpam-6074	52	4	set	set	ADJ
ejpam-6074	52	5	n2	n2	ADJ
ejpam-6074	52	6	g(u	g(u	PROPN
ejpam-6074	52	7	)	)	PUNCT
ejpam-6074	52	8	=	=	PRON
ejpam-6074	52	9	{	{	PUNCT
ejpam-6074	52	10	v	v	NUM
ejpam-6074	52	11	∈	∈	NOUN
ejpam-6074	52	12	v	v	NOUN
ejpam-6074	52	13	(	(	PUNCT
ejpam-6074	52	14	g	g	NOUN
ejpam-6074	52	15	)	)	PUNCT
ejpam-6074	52	16	:	:	PUNCT
ejpam-6074	52	17	dg(v	dg(v	X
ejpam-6074	52	18	,	,	PUNCT
ejpam-6074	52	19	u	u	NOUN
ejpam-6074	52	20	)	)	PUNCT
ejpam-6074	52	21	=	=	SYM
ejpam-6074	52	22	2	2	X
ejpam-6074	52	23	}	}	PUNCT
ejpam-6074	52	24	is	be	AUX
ejpam-6074	52	25	called	call	VERB
ejpam-6074	52	26	the	the	DET
ejpam-6074	52	27	open	open	ADJ
ejpam-6074	52	28	hop	hop	NOUN
ejpam-6074	52	29	neighborhood	neighborhood	NOUN
ejpam-6074	52	30	of	of	ADP
ejpam-6074	52	31	u.	u.	PROPN
ejpam-6074	52	32	the	the	DET
ejpam-6074	52	33	closed	closed	ADJ
ejpam-6074	52	34	hop	hop	NOUN
ejpam-6074	52	35	neighborhood	neighborhood	NOUN
ejpam-6074	52	36	of	of	ADP
ejpam-6074	52	37	u	u	NOUN
ejpam-6074	52	38	is	be	AUX
ejpam-6074	52	39	given	give	VERB
ejpam-6074	52	40	by	by	ADP
ejpam-6074	52	41	n2	n2	PROPN
ejpam-6074	52	42	g[u	g[u	PROPN
ejpam-6074	52	43	]	]	X
ejpam-6074	52	44	=	=	SYM
ejpam-6074	52	45	n2	n2	ADJ
ejpam-6074	52	46	g(u	g(u	PROPN
ejpam-6074	52	47	)	)	PUNCT
ejpam-6074	52	48	∪	∪	NOUN
ejpam-6074	52	49	{	{	PUNCT
ejpam-6074	52	50	u	u	NOUN
ejpam-6074	52	51	}	}	PUNCT
ejpam-6074	52	52	.	.	PUNCT
ejpam-6074	53	1	the	the	DET
ejpam-6074	53	2	open	open	ADJ
ejpam-6074	53	3	hop	hop	NOUN
ejpam-6074	53	4	neighborhood	neighborhood	NOUN
ejpam-6074	53	5	of	of	ADP
ejpam-6074	53	6	x	x	PROPN
ejpam-6074	53	7	⊆	⊆	NUM
ejpam-6074	53	8	v	v	ADP
ejpam-6074	53	9	(	(	PUNCT
ejpam-6074	53	10	g	g	NOUN
ejpam-6074	53	11	)	)	PUNCT
ejpam-6074	53	12	is	be	AUX
ejpam-6074	53	13	the	the	DET
ejpam-6074	53	14	set	set	ADJ
ejpam-6074	53	15	n2	n2	ADJ
ejpam-6074	53	16	g(x	g(x	NOUN
ejpam-6074	53	17	)	)	PUNCT
ejpam-6074	54	1	=	=	SYM
ejpam-6074	54	2	⋃	⋃	NOUN
ejpam-6074	54	3	u∈x	u∈x	ADJ
ejpam-6074	54	4	n2	n2	NOUN
ejpam-6074	54	5	g(u	g(u	PROPN
ejpam-6074	54	6	)	)	PUNCT
ejpam-6074	54	7	.	.	PUNCT
ejpam-6074	55	1	the	the	DET
ejpam-6074	55	2	closed	closed	ADJ
ejpam-6074	55	3	hop	hop	NOUN
ejpam-6074	55	4	neighborhood	neighborhood	NOUN
ejpam-6074	55	5	of	of	ADP
ejpam-6074	55	6	x	x	SYM
ejpam-6074	55	7	is	be	AUX
ejpam-6074	55	8	the	the	DET
ejpam-6074	55	9	set	set	ADJ
ejpam-6074	55	10	n2	n2	NOUN
ejpam-6074	55	11	g[x	g[x	PROPN
ejpam-6074	55	12	]	]	X
ejpam-6074	55	13	=	=	SYM
ejpam-6074	55	14	n2	n2	PROPN
ejpam-6074	55	15	g(x	g(x	NOUN
ejpam-6074	55	16	)	)	PUNCT
ejpam-6074	55	17	∪x	∪x	NUM
ejpam-6074	55	18	.	.	PUNCT
ejpam-6074	56	1	a	a	DET
ejpam-6074	56	2	set	set	NOUN
ejpam-6074	56	3	s	s	NOUN
ejpam-6074	56	4	⊆	⊆	NUM
ejpam-6074	56	5	v	v	NOUN
ejpam-6074	56	6	(	(	PUNCT
ejpam-6074	56	7	g	g	NOUN
ejpam-6074	56	8	)	)	PUNCT
ejpam-6074	56	9	is	be	AUX
ejpam-6074	56	10	a	a	DET
ejpam-6074	56	11	hop	hop	NOUN
ejpam-6074	56	12	dominating	dominating	NOUN
ejpam-6074	56	13	set	set	VERB
ejpam-6074	56	14	in	in	ADP
ejpam-6074	56	15	g	g	PROPN
ejpam-6074	56	16	if	if	SCONJ
ejpam-6074	56	17	n2	n2	ADJ
ejpam-6074	56	18	g[s	g[s	PROPN
ejpam-6074	56	19	]	]	X
ejpam-6074	56	20	=	=	SYM
ejpam-6074	56	21	v	v	NOUN
ejpam-6074	56	22	(	(	PUNCT
ejpam-6074	56	23	g	g	NOUN
ejpam-6074	56	24	)	)	PUNCT
ejpam-6074	56	25	,	,	PUNCT
ejpam-6074	56	26	that	that	ADV
ejpam-6074	56	27	is	is	ADV
ejpam-6074	56	28	,	,	PUNCT
ejpam-6074	56	29	for	for	ADP
ejpam-6074	56	30	every	every	DET
ejpam-6074	56	31	v	v	NUM
ejpam-6074	56	32	∈	∈	NOUN
ejpam-6074	56	33	v	v	NOUN
ejpam-6074	56	34	(	(	PUNCT
ejpam-6074	56	35	g)\s	g)\s	NOUN
ejpam-6074	56	36	,	,	PUNCT
ejpam-6074	56	37	there	there	PRON
ejpam-6074	56	38	exists	exist	VERB
ejpam-6074	56	39	u	u	PROPN
ejpam-6074	56	40	∈	∈	PROPN
ejpam-6074	56	41	s	s	VERB
ejpam-6074	56	42	such	such	ADJ
ejpam-6074	56	43	that	that	DET
ejpam-6074	56	44	dg(u	dg(u	ADJ
ejpam-6074	56	45	,	,	PUNCT
ejpam-6074	56	46	v	v	NOUN
ejpam-6074	56	47	)	)	PUNCT
ejpam-6074	57	1	=	=	SYM
ejpam-6074	57	2	2	2	X
ejpam-6074	57	3	.	.	PUNCT
ejpam-6074	58	1	the	the	DET
ejpam-6074	58	2	minimum	minimum	ADJ
ejpam-6074	58	3	cardinality	cardinality	NOUN
ejpam-6074	58	4	among	among	ADP
ejpam-6074	58	5	all	all	DET
ejpam-6074	58	6	hop	hop	NOUN
ejpam-6074	58	7	dominating	dominating	NOUN
ejpam-6074	58	8	sets	set	NOUN
ejpam-6074	58	9	in	in	ADP
ejpam-6074	58	10	g	g	NOUN
ejpam-6074	58	11	,	,	PUNCT
ejpam-6074	58	12	denoted	denote	VERB
ejpam-6074	58	13	by	by	ADP
ejpam-6074	58	14	γh(g	γh(g	NOUN
ejpam-6074	58	15	)	)	PUNCT
ejpam-6074	58	16	,	,	PUNCT
ejpam-6074	58	17	is	be	AUX
ejpam-6074	58	18	called	call	VERB
ejpam-6074	58	19	the	the	DET
ejpam-6074	58	20	hop	hop	NOUN
ejpam-6074	58	21	domination	domination	NOUN
ejpam-6074	58	22	number	number	NOUN
ejpam-6074	58	23	of	of	ADP
ejpam-6074	58	24	g.	g.	PROPN
ejpam-6074	58	25	any	any	DET
ejpam-6074	58	26	hop	hop	NOUN
ejpam-6074	58	27	dominating	dominating	NOUN
ejpam-6074	58	28	set	set	VERB
ejpam-6074	58	29	with	with	ADP
ejpam-6074	58	30	cardinality	cardinality	NOUN
ejpam-6074	58	31	equal	equal	ADJ
ejpam-6074	58	32	to	to	ADP
ejpam-6074	58	33	γh(g	γh(g	NOUN
ejpam-6074	58	34	)	)	PUNCT
ejpam-6074	58	35	is	be	AUX
ejpam-6074	58	36	called	call	VERB
ejpam-6074	58	37	a	a	DET
ejpam-6074	58	38	γh	γh	ADV
ejpam-6074	58	39	-	-	PUNCT
ejpam-6074	58	40	set	set	NOUN
ejpam-6074	58	41	.	.	PUNCT
ejpam-6074	59	1	a	a	DET
ejpam-6074	59	2	hop	hop	NOUN
ejpam-6074	59	3	dominating	dominating	NOUN
ejpam-6074	59	4	set	set	NOUN
ejpam-6074	59	5	s	s	PART
ejpam-6074	59	6	is	be	AUX
ejpam-6074	59	7	2	2	NUM
ejpam-6074	59	8	-	-	PUNCT
ejpam-6074	59	9	step	step	NOUN
ejpam-6074	59	10	movable	movable	ADJ
ejpam-6074	59	11	hop	hop	NOUN
ejpam-6074	59	12	dominating	dominating	NOUN
ejpam-6074	59	13	if	if	SCONJ
ejpam-6074	59	14	for	for	ADP
ejpam-6074	59	15	each	each	DET
ejpam-6074	59	16	v	v	NUM
ejpam-6074	59	17	∈	∈	PROPN
ejpam-6074	59	18	s	s	NOUN
ejpam-6074	59	19	,	,	PUNCT
ejpam-6074	59	20	s	s	NOUN
ejpam-6074	59	21	\	\	X
ejpam-6074	59	22	{	{	PUNCT
ejpam-6074	59	23	v	v	NOUN
ejpam-6074	59	24	}	}	PUNCT
ejpam-6074	59	25	is	be	AUX
ejpam-6074	59	26	hop	hop	NOUN
ejpam-6074	59	27	dominating	dominating	NOUN
ejpam-6074	59	28	or	or	CCONJ
ejpam-6074	59	29	there	there	ADV
ejpam-6074	59	30	exists	exist	VERB
ejpam-6074	59	31	w	w	PROPN
ejpam-6074	59	32	∈	∈	PROPN
ejpam-6074	59	33	(	(	PUNCT
ejpam-6074	59	34	v	v	NOUN
ejpam-6074	59	35	(	(	PUNCT
ejpam-6074	59	36	g	g	NOUN
ejpam-6074	59	37	)	)	PUNCT
ejpam-6074	59	38	\	\	PROPN
ejpam-6074	60	1	s	s	X
ejpam-6074	60	2	)	)	PUNCT
ejpam-6074	60	3	∩	∩	ADJ
ejpam-6074	60	4	n2	n2	ADJ
ejpam-6074	60	5	g(v	g(v	PROPN
ejpam-6074	60	6	)	)	PUNCT
ejpam-6074	60	7	such	such	ADJ
ejpam-6074	60	8	that	that	SCONJ
ejpam-6074	60	9	(	(	PUNCT
ejpam-6074	60	10	s	s	NOUN
ejpam-6074	60	11	\	\	X
ejpam-6074	60	12	{	{	PUNCT
ejpam-6074	60	13	v	v	NOUN
ejpam-6074	60	14	}	}	PUNCT
ejpam-6074	60	15	)	)	PUNCT
ejpam-6074	60	16	∪	∪	ADP
ejpam-6074	60	17	{	{	PUNCT
ejpam-6074	60	18	w	w	NOUN
ejpam-6074	60	19	}	}	PUNCT
ejpam-6074	60	20	is	be	AUX
ejpam-6074	60	21	hop	hop	PROPN
ejpam-6074	60	22	r.	r.	PROPN
ejpam-6074	60	23	estrella	estrella	PROPN
ejpam-6074	60	24	,	,	PUNCT
ejpam-6074	60	25	gina	gina	PROPN
ejpam-6074	60	26	m.	m.	PROPN
ejpam-6074	60	27	malacas	malacas	PROPN
ejpam-6074	60	28	,	,	PUNCT
ejpam-6074	60	29	s.	s.	PROPN
ejpam-6074	60	30	canoy	canoy	PROPN
ejpam-6074	60	31	jr	jr	PROPN
ejpam-6074	60	32	.	.	PROPN
ejpam-6074	60	33	/	/	SYM
ejpam-6074	60	34	eur	eur	PROPN
ejpam-6074	60	35	.	.	PUNCT
ejpam-6074	61	1	j.	j.	PROPN
ejpam-6074	61	2	pure	pure	PROPN
ejpam-6074	61	3	appl	appl	PROPN
ejpam-6074	61	4	.	.	PROPN
ejpam-6074	61	5	math	math	PROPN
ejpam-6074	61	6	,	,	PUNCT
ejpam-6074	61	7	18	18	NUM
ejpam-6074	61	8	(	(	PUNCT
ejpam-6074	61	9	2	2	NUM
ejpam-6074	61	10	)	)	PUNCT
ejpam-6074	61	11	(	(	PUNCT
ejpam-6074	61	12	2025	2025	NUM
ejpam-6074	61	13	)	)	PUNCT
ejpam-6074	61	14	,	,	PUNCT
ejpam-6074	61	15	6074	6074	NUM
ejpam-6074	61	16	3	3	NUM
ejpam-6074	61	17	of	of	ADP
ejpam-6074	61	18	15	15	NUM
ejpam-6074	61	19	dominating	dominating	NOUN
ejpam-6074	61	20	in	in	ADP
ejpam-6074	61	21	g.	g.	PROPN
ejpam-6074	61	22	the	the	DET
ejpam-6074	61	23	minimum	minimum	ADJ
ejpam-6074	61	24	cardinality	cardinality	NOUN
ejpam-6074	61	25	among	among	ADP
ejpam-6074	61	26	all	all	DET
ejpam-6074	61	27	2	2	NUM
ejpam-6074	61	28	-	-	PUNCT
ejpam-6074	61	29	step	step	NOUN
ejpam-6074	61	30	movable	movable	ADJ
ejpam-6074	61	31	hop	hop	NOUN
ejpam-6074	61	32	dominating	dominating	NOUN
ejpam-6074	61	33	sets	set	NOUN
ejpam-6074	61	34	in	in	ADP
ejpam-6074	61	35	g	g	NOUN
ejpam-6074	61	36	,	,	PUNCT
ejpam-6074	61	37	denoted	denote	VERB
ejpam-6074	61	38	by	by	ADP
ejpam-6074	61	39	γ2mh(g	γ2mh(g	NOUN
ejpam-6074	61	40	)	)	PUNCT
ejpam-6074	61	41	,	,	PUNCT
ejpam-6074	61	42	is	be	AUX
ejpam-6074	61	43	called	call	VERB
ejpam-6074	61	44	the	the	DET
ejpam-6074	61	45	2	2	NUM
ejpam-6074	61	46	-	-	PUNCT
ejpam-6074	61	47	step	step	NOUN
ejpam-6074	61	48	movable	movable	ADJ
ejpam-6074	61	49	hop	hop	NOUN
ejpam-6074	61	50	domination	domination	NOUN
ejpam-6074	61	51	number	number	NOUN
ejpam-6074	61	52	of	of	ADP
ejpam-6074	61	53	g.	g.	PROPN
ejpam-6074	61	54	any	any	DET
ejpam-6074	61	55	2	2	NUM
ejpam-6074	61	56	-	-	PUNCT
ejpam-6074	61	57	step	step	NOUN
ejpam-6074	61	58	movable	movable	ADJ
ejpam-6074	61	59	hop	hop	NOUN
ejpam-6074	61	60	dominating	dominating	NOUN
ejpam-6074	61	61	set	set	VERB
ejpam-6074	61	62	with	with	ADP
ejpam-6074	61	63	cardinality	cardinality	NOUN
ejpam-6074	61	64	equal	equal	ADJ
ejpam-6074	61	65	to	to	ADP
ejpam-6074	61	66	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	61	67	)	)	PUNCT
ejpam-6074	61	68	is	be	AUX
ejpam-6074	61	69	called	call	VERB
ejpam-6074	61	70	a	a	DET
ejpam-6074	61	71	γ2mh	γ2mh	PROPN
ejpam-6074	61	72	-	-	PUNCT
ejpam-6074	61	73	set	set	NOUN
ejpam-6074	61	74	.	.	PUNCT
ejpam-6074	62	1	the	the	DET
ejpam-6074	62	2	shadow	shadow	NOUN
ejpam-6074	62	3	graph	graph	VERB
ejpam-6074	62	4	d2(g	d2(g	PROPN
ejpam-6074	62	5	)	)	PUNCT
ejpam-6074	62	6	of	of	ADP
ejpam-6074	62	7	graph	graph	NOUN
ejpam-6074	62	8	g	g	PROPN
ejpam-6074	62	9	is	be	AUX
ejpam-6074	62	10	constructed	construct	VERB
ejpam-6074	62	11	by	by	ADP
ejpam-6074	62	12	taking	take	VERB
ejpam-6074	62	13	two	two	NUM
ejpam-6074	62	14	copies	copy	NOUN
ejpam-6074	62	15	of	of	ADP
ejpam-6074	62	16	g	g	NOUN
ejpam-6074	62	17	,	,	PUNCT
ejpam-6074	62	18	say	say	VERB
ejpam-6074	62	19	g1	g1	PROPN
ejpam-6074	62	20	and	and	CCONJ
ejpam-6074	62	21	g2	g2	PROPN
ejpam-6074	62	22	,	,	PUNCT
ejpam-6074	62	23	and	and	CCONJ
ejpam-6074	62	24	then	then	ADV
ejpam-6074	62	25	joining	join	VERB
ejpam-6074	62	26	each	each	DET
ejpam-6074	62	27	vertex	vertex	NOUN
ejpam-6074	62	28	u	u	NOUN
ejpam-6074	62	29	∈	∈	PROPN
ejpam-6074	62	30	v	v	NOUN
ejpam-6074	62	31	(	(	PUNCT
ejpam-6074	62	32	g1	g1	PROPN
ejpam-6074	62	33	)	)	PUNCT
ejpam-6074	62	34	to	to	ADP
ejpam-6074	62	35	the	the	DET
ejpam-6074	62	36	neighbors	neighbor	NOUN
ejpam-6074	62	37	of	of	ADP
ejpam-6074	62	38	its	its	PRON
ejpam-6074	62	39	corresponding	correspond	VERB
ejpam-6074	62	40	vertex	vertex	NOUN
ejpam-6074	62	41	u′	u′	PROPN
ejpam-6074	62	42	∈	∈	PROPN
ejpam-6074	62	43	v	v	NOUN
ejpam-6074	62	44	(	(	PUNCT
ejpam-6074	62	45	g2	g2	PROPN
ejpam-6074	62	46	)	)	PUNCT
ejpam-6074	62	47	.	.	PUNCT
ejpam-6074	63	1	for	for	ADP
ejpam-6074	63	2	a	a	DET
ejpam-6074	63	3	graph	graph	NOUN
ejpam-6074	63	4	g	g	NOUN
ejpam-6074	63	5	,	,	PUNCT
ejpam-6074	63	6	the	the	DET
ejpam-6074	63	7	complementary	complementary	ADJ
ejpam-6074	63	8	prism	prism	NOUN
ejpam-6074	63	9	gg	gg	PROPN
ejpam-6074	63	10	,	,	PUNCT
ejpam-6074	63	11	is	be	AUX
ejpam-6074	63	12	the	the	DET
ejpam-6074	63	13	graph	graph	NOUN
ejpam-6074	63	14	formed	form	VERB
ejpam-6074	63	15	from	from	ADP
ejpam-6074	63	16	the	the	DET
ejpam-6074	63	17	disjoint	disjoint	PROPN
ejpam-6074	63	18	union	union	NOUN
ejpam-6074	63	19	of	of	ADP
ejpam-6074	63	20	g	g	PROPN
ejpam-6074	63	21	and	and	CCONJ
ejpam-6074	63	22	its	its	PRON
ejpam-6074	63	23	complement	complement	NOUN
ejpam-6074	63	24	g	g	NOUN
ejpam-6074	63	25	by	by	ADP
ejpam-6074	63	26	adding	add	VERB
ejpam-6074	63	27	a	a	DET
ejpam-6074	63	28	perfect	perfect	ADJ
ejpam-6074	63	29	matching	matching	NOUN
ejpam-6074	63	30	between	between	ADP
ejpam-6074	63	31	corresponding	corresponding	ADJ
ejpam-6074	63	32	vertices	vertex	NOUN
ejpam-6074	63	33	of	of	ADP
ejpam-6074	63	34	g	g	PROPN
ejpam-6074	63	35	and	and	CCONJ
ejpam-6074	63	36	g.	g.	NOUN
ejpam-6074	63	37	for	for	ADP
ejpam-6074	63	38	each	each	DET
ejpam-6074	63	39	v	v	NUM
ejpam-6074	63	40	∈	∈	PROPN
ejpam-6074	63	41	v	v	NOUN
ejpam-6074	63	42	(	(	PUNCT
ejpam-6074	63	43	g	g	NOUN
ejpam-6074	63	44	)	)	PUNCT
ejpam-6074	63	45	,	,	PUNCT
ejpam-6074	63	46	let	let	VERB
ejpam-6074	63	47	v	v	PART
ejpam-6074	63	48	denote	denote	VERB
ejpam-6074	63	49	the	the	DET
ejpam-6074	63	50	vertex	vertex	NOUN
ejpam-6074	63	51	in	in	ADP
ejpam-6074	63	52	g	g	NOUN
ejpam-6074	63	53	corresponding	correspond	VERB
ejpam-6074	63	54	to	to	ADP
ejpam-6074	63	55	v.	v.	PROPN
ejpam-6074	63	56	in	in	ADP
ejpam-6074	63	57	simple	simple	ADJ
ejpam-6074	63	58	terms	term	NOUN
ejpam-6074	63	59	,	,	PUNCT
ejpam-6074	63	60	the	the	DET
ejpam-6074	63	61	graph	graph	NOUN
ejpam-6074	63	62	gg	gg	NOUN
ejpam-6074	63	63	is	be	AUX
ejpam-6074	63	64	form	form	NOUN
ejpam-6074	63	65	from	from	ADP
ejpam-6074	63	66	g∪g	g∪g	NOUN
ejpam-6074	63	67	by	by	ADP
ejpam-6074	63	68	adding	add	VERB
ejpam-6074	63	69	the	the	DET
ejpam-6074	63	70	edge	edge	NOUN
ejpam-6074	63	71	vv	vv	NOUN
ejpam-6074	63	72	for	for	ADP
ejpam-6074	63	73	every	every	DET
ejpam-6074	63	74	vertex	vertex	NOUN
ejpam-6074	63	75	v	v	ADP
ejpam-6074	63	76	∈	∈	NOUN
ejpam-6074	63	77	v	v	NOUN
ejpam-6074	63	78	(	(	PUNCT
ejpam-6074	63	79	g	g	NOUN
ejpam-6074	63	80	)	)	PUNCT
ejpam-6074	63	81	.	.	PUNCT
ejpam-6074	64	1	3	3	X
ejpam-6074	64	2	.	.	X
ejpam-6074	64	3	results	result	VERB
ejpam-6074	64	4	our	our	PRON
ejpam-6074	64	5	first	first	ADJ
ejpam-6074	64	6	result	result	NOUN
ejpam-6074	64	7	characterizes	characterize	VERB
ejpam-6074	64	8	those	those	DET
ejpam-6074	64	9	connected	connect	VERB
ejpam-6074	64	10	graphs	graph	NOUN
ejpam-6074	64	11	which	which	PRON
ejpam-6074	64	12	admit	admit	VERB
ejpam-6074	64	13	a	a	DET
ejpam-6074	64	14	2	2	NUM
ejpam-6074	64	15	-	-	PUNCT
ejpam-6074	64	16	step	step	NOUN
ejpam-6074	64	17	movable	movable	ADJ
ejpam-6074	64	18	hop	hop	NOUN
ejpam-6074	64	19	dominating	dominating	NOUN
ejpam-6074	64	20	set	set	NOUN
ejpam-6074	64	21	.	.	PUNCT
ejpam-6074	65	1	theorem	theorem	NOUN
ejpam-6074	65	2	1	1	NUM
ejpam-6074	65	3	.	.	PUNCT
ejpam-6074	66	1	let	let	VERB
ejpam-6074	66	2	g	g	PRON
ejpam-6074	66	3	be	be	AUX
ejpam-6074	66	4	a	a	DET
ejpam-6074	66	5	connected	connected	ADJ
ejpam-6074	66	6	graph	graph	NOUN
ejpam-6074	66	7	.	.	PUNCT
ejpam-6074	67	1	then	then	ADV
ejpam-6074	67	2	g	g	PROPN
ejpam-6074	67	3	admits	admit	VERB
ejpam-6074	67	4	a	a	DET
ejpam-6074	67	5	2	2	NUM
ejpam-6074	67	6	-	-	PUNCT
ejpam-6074	67	7	step	step	NOUN
ejpam-6074	67	8	movable	movable	ADJ
ejpam-6074	67	9	hop	hop	NOUN
ejpam-6074	67	10	dominating	dominating	NOUN
ejpam-6074	67	11	set	set	VERB
ejpam-6074	67	12	if	if	SCONJ
ejpam-6074	67	13	and	and	CCONJ
ejpam-6074	67	14	only	only	ADV
ejpam-6074	67	15	if	if	SCONJ
ejpam-6074	67	16	γ(g	γ(g	NOUN
ejpam-6074	67	17	)	)	PUNCT
ejpam-6074	67	18	̸=	̸=	PROPN
ejpam-6074	67	19	1	1	NUM
ejpam-6074	67	20	.	.	PUNCT
ejpam-6074	68	1	proof	proof	NOUN
ejpam-6074	68	2	.	.	PUNCT
ejpam-6074	69	1	suppose	suppose	VERB
ejpam-6074	69	2	g	g	PROPN
ejpam-6074	69	3	admits	admit	VERB
ejpam-6074	69	4	a	a	DET
ejpam-6074	69	5	2	2	NUM
ejpam-6074	69	6	-	-	PUNCT
ejpam-6074	69	7	step	step	NOUN
ejpam-6074	69	8	movable	movable	ADJ
ejpam-6074	69	9	hop	hop	NOUN
ejpam-6074	69	10	dominating	dominating	NOUN
ejpam-6074	69	11	set	set	NOUN
ejpam-6074	69	12	,	,	PUNCT
ejpam-6074	69	13	say	say	VERB
ejpam-6074	69	14	s.	s.	PROPN
ejpam-6074	69	15	suppose	suppose	VERB
ejpam-6074	69	16	γ(g	γ(g	NOUN
ejpam-6074	69	17	)	)	PUNCT
ejpam-6074	70	1	=	=	SYM
ejpam-6074	70	2	1	1	NUM
ejpam-6074	70	3	,	,	PUNCT
ejpam-6074	70	4	say	say	VERB
ejpam-6074	70	5	v	v	NOUN
ejpam-6074	70	6	is	be	AUX
ejpam-6074	70	7	a	a	DET
ejpam-6074	70	8	dominating	dominating	NOUN
ejpam-6074	70	9	vertex	vertex	NOUN
ejpam-6074	70	10	in	in	ADP
ejpam-6074	70	11	g.	g.	PROPN
ejpam-6074	70	12	then	then	ADV
ejpam-6074	70	13	v	v	ADP
ejpam-6074	70	14	∈	∈	NOUN
ejpam-6074	70	15	s	s	PART
ejpam-6074	70	16	because	because	SCONJ
ejpam-6074	70	17	s	s	PROPN
ejpam-6074	70	18	is	be	AUX
ejpam-6074	70	19	a	a	DET
ejpam-6074	70	20	hop	hop	NOUN
ejpam-6074	70	21	dominating	dominating	NOUN
ejpam-6074	70	22	set	set	VERB
ejpam-6074	70	23	in	in	ADP
ejpam-6074	70	24	g.	g.	PROPN
ejpam-6074	70	25	since	since	SCONJ
ejpam-6074	70	26	every	every	DET
ejpam-6074	70	27	hop	hop	NOUN
ejpam-6074	70	28	dominating	dominating	NOUN
ejpam-6074	70	29	set	set	NOUN
ejpam-6074	70	30	contains	contain	VERB
ejpam-6074	70	31	all	all	DET
ejpam-6074	70	32	dominating	dominating	NOUN
ejpam-6074	70	33	vertices	vertex	NOUN
ejpam-6074	70	34	of	of	ADP
ejpam-6074	70	35	g	g	NOUN
ejpam-6074	70	36	where	where	SCONJ
ejpam-6074	70	37	v	v	NOUN
ejpam-6074	70	38	is	be	AUX
ejpam-6074	70	39	one	one	NUM
ejpam-6074	70	40	of	of	ADP
ejpam-6074	70	41	them	they	PRON
ejpam-6074	70	42	,	,	PUNCT
ejpam-6074	70	43	it	it	PRON
ejpam-6074	70	44	follows	follow	VERB
ejpam-6074	70	45	that	that	PRON
ejpam-6074	70	46	s	s	VERB
ejpam-6074	70	47	\	\	PROPN
ejpam-6074	70	48	{	{	PUNCT
ejpam-6074	70	49	v	v	NOUN
ejpam-6074	70	50	}	}	PUNCT
ejpam-6074	70	51	is	be	AUX
ejpam-6074	70	52	not	not	PART
ejpam-6074	70	53	a	a	DET
ejpam-6074	70	54	hop	hop	NOUN
ejpam-6074	70	55	dominating	dominating	NOUN
ejpam-6074	70	56	set	set	NOUN
ejpam-6074	70	57	.	.	PUNCT
ejpam-6074	71	1	also	also	ADV
ejpam-6074	71	2	,	,	PUNCT
ejpam-6074	71	3	since	since	SCONJ
ejpam-6074	71	4	n2	n2	ADJ
ejpam-6074	71	5	g(v	g(v	X
ejpam-6074	71	6	)	)	PUNCT
ejpam-6074	71	7	=	=	SYM
ejpam-6074	71	8	∅	∅	NOUN
ejpam-6074	71	9	,	,	PUNCT
ejpam-6074	71	10	there	there	PRON
ejpam-6074	71	11	exists	exist	VERB
ejpam-6074	71	12	no	no	DET
ejpam-6074	71	13	w	w	NOUN
ejpam-6074	71	14	∈	∈	PROPN
ejpam-6074	72	1	[	[	X
ejpam-6074	72	2	v	v	X
ejpam-6074	72	3	(	(	PUNCT
ejpam-6074	72	4	g	g	NOUN
ejpam-6074	72	5	)	)	PUNCT
ejpam-6074	72	6	\	\	PUNCT
ejpam-6074	72	7	s	s	X
ejpam-6074	72	8	]	]	X
ejpam-6074	72	9	∩n2	∩n2	PROPN
ejpam-6074	72	10	g(v	g(v	PROPN
ejpam-6074	72	11	)	)	PUNCT
ejpam-6074	72	12	such	such	ADJ
ejpam-6074	72	13	that	that	SCONJ
ejpam-6074	72	14	[	[	X
ejpam-6074	72	15	s	s	X
ejpam-6074	72	16	\	\	X
ejpam-6074	72	17	{	{	PUNCT
ejpam-6074	72	18	v	v	NOUN
ejpam-6074	72	19	}	}	PUNCT
ejpam-6074	72	20	]	]	PUNCT
ejpam-6074	72	21	∪	∪	X
ejpam-6074	72	22	{	{	PUNCT
ejpam-6074	72	23	w	w	NOUN
ejpam-6074	72	24	}	}	PUNCT
ejpam-6074	72	25	is	be	AUX
ejpam-6074	72	26	a	a	DET
ejpam-6074	72	27	hop	hop	NOUN
ejpam-6074	72	28	dominating	dominating	NOUN
ejpam-6074	72	29	set	set	VERB
ejpam-6074	72	30	in	in	ADP
ejpam-6074	72	31	g.	g.	PROPN
ejpam-6074	73	1	this	this	PRON
ejpam-6074	73	2	implies	imply	VERB
ejpam-6074	73	3	that	that	SCONJ
ejpam-6074	73	4	s	s	VERB
ejpam-6074	73	5	is	be	AUX
ejpam-6074	73	6	not	not	PART
ejpam-6074	73	7	a	a	DET
ejpam-6074	73	8	2	2	NUM
ejpam-6074	73	9	-	-	PUNCT
ejpam-6074	73	10	step	step	NOUN
ejpam-6074	73	11	movable	movable	ADJ
ejpam-6074	73	12	hop	hop	NOUN
ejpam-6074	73	13	dominating	dominating	NOUN
ejpam-6074	73	14	set	set	NOUN
ejpam-6074	73	15	,	,	PUNCT
ejpam-6074	73	16	contrary	contrary	ADV
ejpam-6074	73	17	to	to	ADP
ejpam-6074	73	18	our	our	PRON
ejpam-6074	73	19	assumption	assumption	NOUN
ejpam-6074	73	20	.	.	PUNCT
ejpam-6074	74	1	thus	thus	ADV
ejpam-6074	74	2	,	,	PUNCT
ejpam-6074	74	3	γ(g	γ(g	PROPN
ejpam-6074	74	4	)	)	PUNCT
ejpam-6074	74	5	̸=	̸=	PROPN
ejpam-6074	74	6	1	1	NUM
ejpam-6074	74	7	.	.	PUNCT
ejpam-6074	74	8	for	for	ADP
ejpam-6074	74	9	the	the	DET
ejpam-6074	74	10	converse	converse	NOUN
ejpam-6074	74	11	,	,	PUNCT
ejpam-6074	74	12	suppose	suppose	VERB
ejpam-6074	74	13	that	that	SCONJ
ejpam-6074	74	14	γ(g	γ(g	PROPN
ejpam-6074	74	15	)	)	PUNCT
ejpam-6074	74	16	̸=	̸=	PROPN
ejpam-6074	74	17	1	1	NUM
ejpam-6074	74	18	.	.	PUNCT
ejpam-6074	75	1	let	let	VERB
ejpam-6074	75	2	x	x	SYM
ejpam-6074	75	3	∈	∈	PROPN
ejpam-6074	75	4	v	v	X
ejpam-6074	75	5	(	(	PUNCT
ejpam-6074	75	6	g	g	NOUN
ejpam-6074	75	7	)	)	PUNCT
ejpam-6074	75	8	.	.	PUNCT
ejpam-6074	76	1	since	since	SCONJ
ejpam-6074	76	2	x	x	PRON
ejpam-6074	76	3	is	be	AUX
ejpam-6074	76	4	not	not	PART
ejpam-6074	76	5	a	a	DET
ejpam-6074	76	6	dominating	dominating	NOUN
ejpam-6074	76	7	vertex	vertex	NOUN
ejpam-6074	76	8	of	of	ADP
ejpam-6074	76	9	g	g	NOUN
ejpam-6074	76	10	,	,	PUNCT
ejpam-6074	76	11	there	there	PRON
ejpam-6074	76	12	exists	exist	VERB
ejpam-6074	76	13	y	y	PROPN
ejpam-6074	76	14	∈	∈	PROPN
ejpam-6074	76	15	n2	n2	NOUN
ejpam-6074	76	16	g(x	g(x	PROPN
ejpam-6074	76	17	)	)	PUNCT
ejpam-6074	76	18	.	.	PUNCT
ejpam-6074	77	1	it	it	PRON
ejpam-6074	77	2	follows	follow	VERB
ejpam-6074	77	3	that	that	SCONJ
ejpam-6074	77	4	v	v	ADP
ejpam-6074	77	5	(	(	PUNCT
ejpam-6074	77	6	g	g	NOUN
ejpam-6074	77	7	)	)	PUNCT
ejpam-6074	77	8	\	\	NOUN
ejpam-6074	77	9	{	{	PUNCT
ejpam-6074	77	10	x	x	NOUN
ejpam-6074	77	11	}	}	PUNCT
ejpam-6074	77	12	is	be	AUX
ejpam-6074	77	13	a	a	DET
ejpam-6074	77	14	hop	hop	NOUN
ejpam-6074	77	15	dominating	dominating	NOUN
ejpam-6074	77	16	set	set	VERB
ejpam-6074	77	17	in	in	ADP
ejpam-6074	77	18	g.	g.	PROPN
ejpam-6074	77	19	this	this	PRON
ejpam-6074	77	20	implies	imply	VERB
ejpam-6074	77	21	that	that	SCONJ
ejpam-6074	77	22	v	v	X
ejpam-6074	77	23	(	(	PUNCT
ejpam-6074	77	24	g	g	NOUN
ejpam-6074	77	25	)	)	PUNCT
ejpam-6074	77	26	is	be	AUX
ejpam-6074	77	27	a	a	DET
ejpam-6074	77	28	2	2	NUM
ejpam-6074	77	29	-	-	PUNCT
ejpam-6074	77	30	step	step	NOUN
ejpam-6074	77	31	movable	movable	ADJ
ejpam-6074	77	32	hop	hop	NOUN
ejpam-6074	77	33	dominating	dominating	NOUN
ejpam-6074	77	34	set	set	VERB
ejpam-6074	77	35	in	in	ADP
ejpam-6074	77	36	g.	g.	PROPN
ejpam-6074	77	37	remark	remark	PROPN
ejpam-6074	77	38	1	1	NUM
ejpam-6074	77	39	.	.	PUNCT
ejpam-6074	78	1	let	let	VERB
ejpam-6074	78	2	g1	g1	PROPN
ejpam-6074	78	3	,	,	PUNCT
ejpam-6074	78	4	g2	g2	PROPN
ejpam-6074	78	5	,	,	PUNCT
ejpam-6074	78	6	.	.	PUNCT
ejpam-6074	78	7	.	.	PUNCT
ejpam-6074	79	1	.	.	PUNCT
ejpam-6074	80	1	,	,	PUNCT
ejpam-6074	80	2	gk	gk	PROPN
ejpam-6074	80	3	be	be	AUX
ejpam-6074	80	4	the	the	DET
ejpam-6074	80	5	components	component	NOUN
ejpam-6074	80	6	of	of	ADP
ejpam-6074	80	7	a	a	DET
ejpam-6074	80	8	graph	graph	NOUN
ejpam-6074	81	1	g.	g.	NOUN
ejpam-6074	82	1	then	then	ADV
ejpam-6074	82	2	s	s	VERB
ejpam-6074	82	3	is	be	AUX
ejpam-6074	82	4	a	a	DET
ejpam-6074	82	5	hop	hop	NOUN
ejpam-6074	82	6	dominating	dominating	NOUN
ejpam-6074	82	7	set	set	VERB
ejpam-6074	82	8	in	in	ADP
ejpam-6074	82	9	g	g	PROPN
ejpam-6074	82	10	if	if	SCONJ
ejpam-6074	83	1	and	and	CCONJ
ejpam-6074	83	2	only	only	ADV
ejpam-6074	83	3	if	if	SCONJ
ejpam-6074	83	4	sj	sj	ADP
ejpam-6074	83	5	=	=	NOUN
ejpam-6074	83	6	s	s	PART
ejpam-6074	83	7	∩	∩	ADJ
ejpam-6074	83	8	v	v	NOUN
ejpam-6074	83	9	(	(	PUNCT
ejpam-6074	83	10	gj	gj	NOUN
ejpam-6074	83	11	)	)	PUNCT
ejpam-6074	83	12	is	be	AUX
ejpam-6074	83	13	a	a	DET
ejpam-6074	83	14	hop	hop	NOUN
ejpam-6074	83	15	dominating	dominating	NOUN
ejpam-6074	83	16	set	set	VERB
ejpam-6074	83	17	in	in	ADP
ejpam-6074	83	18	gj	gj	NOUN
ejpam-6074	83	19	for	for	ADP
ejpam-6074	83	20	each	each	DET
ejpam-6074	83	21	j	j	PROPN
ejpam-6074	83	22	∈	∈	PROPN
ejpam-6074	84	1	[	[	X
ejpam-6074	84	2	k	k	X
ejpam-6074	84	3	]	]	X
ejpam-6074	84	4	=	=	X
ejpam-6074	84	5	{	{	PUNCT
ejpam-6074	84	6	1	1	NUM
ejpam-6074	84	7	,	,	PUNCT
ejpam-6074	84	8	2	2	NUM
ejpam-6074	84	9	,	,	PUNCT
ejpam-6074	84	10	·	·	PUNCT
ejpam-6074	84	11	·	·	PUNCT
ejpam-6074	84	12	·	·	PUNCT
ejpam-6074	84	13	,	,	PUNCT
ejpam-6074	84	14	k	k	NOUN
ejpam-6074	84	15	}	}	PUNCT
ejpam-6074	84	16	.	.	PUNCT
ejpam-6074	85	1	moreover	moreover	ADV
ejpam-6074	85	2	,	,	PUNCT
ejpam-6074	85	3	γh(g	γh(g	NOUN
ejpam-6074	85	4	)	)	PUNCT
ejpam-6074	86	1	=	=	SYM
ejpam-6074	86	2	∑k	∑k	PROPN
ejpam-6074	86	3	j=1	j=1	PROPN
ejpam-6074	86	4	γh(gj	γh(gj	PROPN
ejpam-6074	86	5	)	)	PUNCT
ejpam-6074	86	6	.	.	PUNCT
ejpam-6074	87	1	theorem	theorem	NOUN
ejpam-6074	87	2	2	2	NUM
ejpam-6074	87	3	.	.	PUNCT
ejpam-6074	87	4	let	let	VERB
ejpam-6074	87	5	g1	g1	PROPN
ejpam-6074	87	6	,	,	PUNCT
ejpam-6074	87	7	g2	g2	PROPN
ejpam-6074	87	8	,	,	PUNCT
ejpam-6074	87	9	.	.	PUNCT
ejpam-6074	87	10	.	.	PUNCT
ejpam-6074	88	1	.	.	PUNCT
ejpam-6074	89	1	,	,	PUNCT
ejpam-6074	89	2	gk	gk	PROPN
ejpam-6074	89	3	be	be	AUX
ejpam-6074	89	4	the	the	DET
ejpam-6074	89	5	components	component	NOUN
ejpam-6074	89	6	of	of	ADP
ejpam-6074	89	7	g.	g.	PROPN
ejpam-6074	89	8	then	then	ADV
ejpam-6074	89	9	g	g	PROPN
ejpam-6074	89	10	admits	admit	VERB
ejpam-6074	89	11	a	a	DET
ejpam-6074	89	12	2	2	NUM
ejpam-6074	89	13	-	-	PUNCT
ejpam-6074	89	14	step	step	NOUN
ejpam-6074	89	15	movable	movable	ADJ
ejpam-6074	89	16	hop	hop	NOUN
ejpam-6074	89	17	dominating	dominating	NOUN
ejpam-6074	89	18	set	set	VERB
ejpam-6074	89	19	if	if	SCONJ
ejpam-6074	89	20	and	and	CCONJ
ejpam-6074	89	21	only	only	ADV
ejpam-6074	89	22	if	if	SCONJ
ejpam-6074	89	23	γ(gj	γ(gj	NUM
ejpam-6074	89	24	)	)	PUNCT
ejpam-6074	89	25	̸=	̸=	PROPN
ejpam-6074	89	26	1	1	NUM
ejpam-6074	89	27	for	for	ADP
ejpam-6074	89	28	every	every	DET
ejpam-6074	89	29	j	j	PROPN
ejpam-6074	89	30	∈	∈	PROPN
ejpam-6074	90	1	[	[	X
ejpam-6074	90	2	k	k	X
ejpam-6074	90	3	]	]	X
ejpam-6074	90	4	=	=	X
ejpam-6074	90	5	{	{	PUNCT
ejpam-6074	90	6	1	1	NUM
ejpam-6074	90	7	,	,	PUNCT
ejpam-6074	90	8	2	2	NUM
ejpam-6074	90	9	,	,	PUNCT
ejpam-6074	90	10	·	·	PUNCT
ejpam-6074	90	11	·	·	PUNCT
ejpam-6074	90	12	·	·	PUNCT
ejpam-6074	90	13	,	,	PUNCT
ejpam-6074	90	14	k	k	NOUN
ejpam-6074	90	15	}	}	PUNCT
ejpam-6074	90	16	.	.	PUNCT
ejpam-6074	91	1	in	in	ADP
ejpam-6074	91	2	this	this	DET
ejpam-6074	91	3	case	case	NOUN
ejpam-6074	91	4	,	,	PUNCT
ejpam-6074	91	5	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	91	6	)	)	PUNCT
ejpam-6074	91	7	=	=	SYM
ejpam-6074	92	1	∑k	∑k	PROPN
ejpam-6074	92	2	j=1	j=1	PROPN
ejpam-6074	92	3	γ	γ	PROPN
ejpam-6074	92	4	2	2	NUM
ejpam-6074	92	5	mh(gj	mh(gj	PROPN
ejpam-6074	92	6	)	)	PUNCT
ejpam-6074	92	7	.	.	PUNCT
ejpam-6074	93	1	proof	proof	NOUN
ejpam-6074	93	2	.	.	PUNCT
ejpam-6074	94	1	suppose	suppose	VERB
ejpam-6074	94	2	g	g	PROPN
ejpam-6074	94	3	admits	admit	VERB
ejpam-6074	94	4	a	a	DET
ejpam-6074	94	5	2	2	NUM
ejpam-6074	94	6	-	-	PUNCT
ejpam-6074	94	7	step	step	NOUN
ejpam-6074	94	8	movable	movable	ADJ
ejpam-6074	94	9	hop	hop	NOUN
ejpam-6074	94	10	dominating	dominating	NOUN
ejpam-6074	94	11	set	set	NOUN
ejpam-6074	94	12	,	,	PUNCT
ejpam-6074	94	13	say	say	VERB
ejpam-6074	94	14	s.	s.	PROPN
ejpam-6074	94	15	let	let	VERB
ejpam-6074	94	16	sj	sj	INTJ
ejpam-6074	94	17	=	=	NOUN
ejpam-6074	94	18	s	s	PART
ejpam-6074	94	19	∩	∩	ADJ
ejpam-6074	94	20	v	v	NOUN
ejpam-6074	94	21	(	(	PUNCT
ejpam-6074	94	22	gj	gj	NOUN
ejpam-6074	94	23	)	)	PUNCT
ejpam-6074	94	24	for	for	ADP
ejpam-6074	94	25	each	each	DET
ejpam-6074	94	26	j	j	PROPN
ejpam-6074	94	27	∈	∈	PROPN
ejpam-6074	95	1	[	[	X
ejpam-6074	95	2	k	k	X
ejpam-6074	95	3	]	]	X
ejpam-6074	95	4	.	.	PUNCT
ejpam-6074	96	1	by	by	ADP
ejpam-6074	96	2	remark	remark	NOUN
ejpam-6074	96	3	1	1	NUM
ejpam-6074	96	4	,	,	PUNCT
ejpam-6074	96	5	each	each	PRON
ejpam-6074	96	6	set	set	VERB
ejpam-6074	96	7	sj	sj	NOUN
ejpam-6074	96	8	is	be	AUX
ejpam-6074	96	9	a	a	DET
ejpam-6074	96	10	hop	hop	NOUN
ejpam-6074	96	11	dominating	dominating	NOUN
ejpam-6074	96	12	set	set	VERB
ejpam-6074	96	13	in	in	ADP
ejpam-6074	96	14	gj	gj	PROPN
ejpam-6074	96	15	.	.	PUNCT
ejpam-6074	97	1	for	for	ADP
ejpam-6074	97	2	an	an	DET
ejpam-6074	97	3	arbitrary	arbitrary	ADJ
ejpam-6074	97	4	j	j	PROPN
ejpam-6074	97	5	∈	∈	PROPN
ejpam-6074	97	6	[	[	X
ejpam-6074	97	7	k	k	X
ejpam-6074	97	8	]	]	X
ejpam-6074	97	9	,	,	PUNCT
ejpam-6074	97	10	let	let	VERB
ejpam-6074	97	11	x	x	X
ejpam-6074	97	12	∈	∈	PROPN
ejpam-6074	97	13	sj	sj	INTJ
ejpam-6074	97	14	.	.	PUNCT
ejpam-6074	98	1	then	then	ADV
ejpam-6074	98	2	x	x	SYM
ejpam-6074	98	3	∈	∈	PROPN
ejpam-6074	98	4	s.	s.	PROPN
ejpam-6074	98	5	since	since	SCONJ
ejpam-6074	98	6	s	s	PROPN
ejpam-6074	98	7	a	a	DET
ejpam-6074	98	8	2	2	NUM
ejpam-6074	98	9	-	-	PUNCT
ejpam-6074	98	10	step	step	NOUN
ejpam-6074	98	11	movable	movable	ADJ
ejpam-6074	98	12	hop	hop	NOUN
ejpam-6074	98	13	dominating	dominating	NOUN
ejpam-6074	98	14	set	set	VERB
ejpam-6074	98	15	in	in	ADP
ejpam-6074	98	16	g	g	PROPN
ejpam-6074	98	17	,	,	PUNCT
ejpam-6074	98	18	s	s	X
ejpam-6074	98	19	\{x	\{x	NOUN
ejpam-6074	98	20	}	}	PUNCT
ejpam-6074	98	21	or	or	CCONJ
ejpam-6074	98	22	[	[	X
ejpam-6074	98	23	s	s	X
ejpam-6074	98	24	\{x}]∪{y	\{x}]∪{y	NOUN
ejpam-6074	98	25	}	}	PUNCT
ejpam-6074	98	26	for	for	ADP
ejpam-6074	98	27	some	some	DET
ejpam-6074	98	28	y	y	PROPN
ejpam-6074	98	29	∈	∈	PROPN
ejpam-6074	99	1	[	[	X
ejpam-6074	99	2	v	v	X
ejpam-6074	99	3	(	(	PUNCT
ejpam-6074	99	4	g)\s]∩n2	g)\s]∩n2	NOUN
ejpam-6074	99	5	g(x	g(x	NOUN
ejpam-6074	99	6	)	)	PUNCT
ejpam-6074	99	7	,	,	PUNCT
ejpam-6074	99	8	is	be	AUX
ejpam-6074	99	9	a	a	DET
ejpam-6074	99	10	hop	hop	NOUN
ejpam-6074	99	11	dominating	dominating	NOUN
ejpam-6074	99	12	set	set	VERB
ejpam-6074	99	13	in	in	ADP
ejpam-6074	99	14	r.	r.	PROPN
ejpam-6074	99	15	estrella	estrella	PROPN
ejpam-6074	99	16	,	,	PUNCT
ejpam-6074	99	17	gina	gina	PROPN
ejpam-6074	99	18	m.	m.	PROPN
ejpam-6074	99	19	malacas	malacas	PROPN
ejpam-6074	99	20	,	,	PUNCT
ejpam-6074	99	21	s.	s.	PROPN
ejpam-6074	99	22	canoy	canoy	PROPN
ejpam-6074	99	23	jr	jr	PROPN
ejpam-6074	99	24	.	.	PROPN
ejpam-6074	99	25	/	/	SYM
ejpam-6074	99	26	eur	eur	PROPN
ejpam-6074	99	27	.	.	PUNCT
ejpam-6074	100	1	j.	j.	PROPN
ejpam-6074	100	2	pure	pure	PROPN
ejpam-6074	100	3	appl	appl	PROPN
ejpam-6074	100	4	.	.	PROPN
ejpam-6074	100	5	math	math	PROPN
ejpam-6074	100	6	,	,	PUNCT
ejpam-6074	100	7	18	18	NUM
ejpam-6074	100	8	(	(	PUNCT
ejpam-6074	100	9	2	2	NUM
ejpam-6074	100	10	)	)	PUNCT
ejpam-6074	100	11	(	(	PUNCT
ejpam-6074	100	12	2025	2025	NUM
ejpam-6074	100	13	)	)	PUNCT
ejpam-6074	100	14	,	,	PUNCT
ejpam-6074	100	15	6074	6074	NUM
ejpam-6074	100	16	4	4	NUM
ejpam-6074	100	17	of	of	ADP
ejpam-6074	100	18	15	15	NUM
ejpam-6074	100	19	g.	g.	NOUN
ejpam-6074	100	20	if	if	SCONJ
ejpam-6074	100	21	s	s	NOUN
ejpam-6074	100	22	\	\	X
ejpam-6074	100	23	{	{	PUNCT
ejpam-6074	100	24	x	x	NOUN
ejpam-6074	100	25	}	}	PUNCT
ejpam-6074	100	26	is	be	AUX
ejpam-6074	100	27	a	a	DET
ejpam-6074	100	28	hop	hop	NOUN
ejpam-6074	100	29	dominating	dominating	NOUN
ejpam-6074	100	30	set	set	NOUN
ejpam-6074	100	31	in	in	ADP
ejpam-6074	100	32	g	g	NOUN
ejpam-6074	100	33	,	,	PUNCT
ejpam-6074	100	34	then	then	ADV
ejpam-6074	100	35	sj	sj	INTJ
ejpam-6074	100	36	\	\	PROPN
ejpam-6074	100	37	{	{	PUNCT
ejpam-6074	100	38	x	x	X
ejpam-6074	100	39	}	}	PUNCT
ejpam-6074	100	40	is	be	AUX
ejpam-6074	100	41	a	a	DET
ejpam-6074	100	42	hop	hop	NOUN
ejpam-6074	100	43	dominating	dominating	NOUN
ejpam-6074	100	44	set	set	VERB
ejpam-6074	100	45	in	in	ADP
ejpam-6074	100	46	gj	gj	NOUN
ejpam-6074	100	47	by	by	ADP
ejpam-6074	100	48	remark	remark	NOUN
ejpam-6074	100	49	1	1	NUM
ejpam-6074	100	50	.	.	PUNCT
ejpam-6074	101	1	if	if	SCONJ
ejpam-6074	101	2	(	(	PUNCT
ejpam-6074	101	3	s	s	NOUN
ejpam-6074	101	4	\{x})∪{y	\{x})∪{y	NOUN
ejpam-6074	101	5	}	}	PUNCT
ejpam-6074	101	6	is	be	AUX
ejpam-6074	101	7	a	a	DET
ejpam-6074	101	8	hop	hop	NOUN
ejpam-6074	101	9	dominating	dominating	NOUN
ejpam-6074	101	10	set	set	VERB
ejpam-6074	101	11	in	in	ADP
ejpam-6074	101	12	g	g	NOUN
ejpam-6074	101	13	for	for	ADP
ejpam-6074	101	14	some	some	DET
ejpam-6074	101	15	y	y	PROPN
ejpam-6074	101	16	∈	∈	PROPN
ejpam-6074	101	17	(	(	PUNCT
ejpam-6074	101	18	v	v	NOUN
ejpam-6074	101	19	(	(	PUNCT
ejpam-6074	101	20	g)\s)∩n2	g)\s)∩n2	PROPN
ejpam-6074	101	21	g(x	g(x	NOUN
ejpam-6074	101	22	)	)	PUNCT
ejpam-6074	101	23	,	,	PUNCT
ejpam-6074	101	24	then	then	ADV
ejpam-6074	101	25	y	y	PROPN
ejpam-6074	101	26	∈	∈	PROPN
ejpam-6074	101	27	(	(	PUNCT
ejpam-6074	101	28	v	v	NOUN
ejpam-6074	101	29	(	(	PUNCT
ejpam-6074	101	30	gj)\sj)∩n2	gj)\sj)∩n2	PROPN
ejpam-6074	101	31	gj	gj	PROPN
ejpam-6074	101	32	(	(	PUNCT
ejpam-6074	101	33	x	x	NOUN
ejpam-6074	101	34	)	)	PUNCT
ejpam-6074	101	35	and	and	CCONJ
ejpam-6074	101	36	(	(	PUNCT
ejpam-6074	101	37	sj	sj	INTJ
ejpam-6074	101	38	\{x})∪{y	\{x})∪{y	NOUN
ejpam-6074	101	39	}	}	PUNCT
ejpam-6074	101	40	is	be	AUX
ejpam-6074	101	41	a	a	DET
ejpam-6074	101	42	hop	hop	NOUN
ejpam-6074	101	43	dominating	dominating	NOUN
ejpam-6074	101	44	set	set	VERB
ejpam-6074	101	45	in	in	ADP
ejpam-6074	101	46	gj	gj	NOUN
ejpam-6074	101	47	.	.	PUNCT
ejpam-6074	102	1	hence	hence	ADV
ejpam-6074	102	2	,	,	PUNCT
ejpam-6074	102	3	sj	sj	PROPN
ejpam-6074	102	4	is	be	AUX
ejpam-6074	102	5	a	a	DET
ejpam-6074	102	6	2	2	NUM
ejpam-6074	102	7	-	-	PUNCT
ejpam-6074	102	8	step	step	NOUN
ejpam-6074	102	9	movable	movable	ADJ
ejpam-6074	102	10	hop	hop	NOUN
ejpam-6074	102	11	dominating	dominating	NOUN
ejpam-6074	102	12	set	set	VERB
ejpam-6074	102	13	in	in	ADP
ejpam-6074	102	14	gj	gj	NOUN
ejpam-6074	102	15	.	.	PUNCT
ejpam-6074	103	1	by	by	ADP
ejpam-6074	103	2	theorem	theorem	NOUN
ejpam-6074	103	3	1	1	NUM
ejpam-6074	103	4	,	,	PUNCT
ejpam-6074	103	5	γ(gj	γ(gj	NUM
ejpam-6074	103	6	)	)	PUNCT
ejpam-6074	103	7	̸=	̸=	PROPN
ejpam-6074	103	8	1	1	NUM
ejpam-6074	103	9	.	.	PUNCT
ejpam-6074	104	1	note	note	VERB
ejpam-6074	104	2	that	that	SCONJ
ejpam-6074	104	3	if	if	SCONJ
ejpam-6074	104	4	,	,	PUNCT
ejpam-6074	104	5	in	in	ADP
ejpam-6074	104	6	particular	particular	ADJ
ejpam-6074	104	7	,	,	PUNCT
ejpam-6074	104	8	s	s	PART
ejpam-6074	104	9	is	be	AUX
ejpam-6074	104	10	a	a	DET
ejpam-6074	104	11	γ2mh	γ2mh	PROPN
ejpam-6074	104	12	-	-	PUNCT
ejpam-6074	104	13	set	set	VERB
ejpam-6074	104	14	in	in	ADP
ejpam-6074	104	15	g	g	NOUN
ejpam-6074	104	16	,	,	PUNCT
ejpam-6074	104	17	then	then	ADV
ejpam-6074	104	18	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	104	19	)	)	PUNCT
ejpam-6074	105	1	=	=	SYM
ejpam-6074	105	2	|s|	|s|	NOUN
ejpam-6074	105	3	=	=	SYM
ejpam-6074	105	4	|	|	PROPN
ejpam-6074	105	5	∪j∈[k	∪j∈[k	PROPN
ejpam-6074	105	6	]	]	X
ejpam-6074	105	7	sj	sj	INTJ
ejpam-6074	105	8	|	|	ADV
ejpam-6074	105	9	≥	≥	AUX
ejpam-6074	105	10	∑	∑	PROPN
ejpam-6074	105	11	j∈[k	j∈[k	PROPN
ejpam-6074	105	12	]	]	PUNCT
ejpam-6074	105	13	γ2mh(gj	γ2mh(gj	NUM
ejpam-6074	105	14	)	)	PUNCT
ejpam-6074	105	15	.	.	PUNCT
ejpam-6074	106	1	conversely	conversely	ADV
ejpam-6074	106	2	,	,	PUNCT
ejpam-6074	106	3	suppose	suppose	VERB
ejpam-6074	106	4	γ(gj	γ(gj	NUM
ejpam-6074	106	5	)	)	PUNCT
ejpam-6074	106	6	̸=	̸=	PROPN
ejpam-6074	106	7	1	1	NUM
ejpam-6074	106	8	for	for	ADP
ejpam-6074	106	9	each	each	DET
ejpam-6074	106	10	j	j	PROPN
ejpam-6074	106	11	∈	∈	PROPN
ejpam-6074	107	1	[	[	X
ejpam-6074	107	2	k	k	X
ejpam-6074	107	3	]	]	X
ejpam-6074	107	4	.	.	PUNCT
ejpam-6074	108	1	then	then	ADV
ejpam-6074	108	2	each	each	DET
ejpam-6074	108	3	gj	gj	NOUN
ejpam-6074	108	4	admits	admit	VERB
ejpam-6074	108	5	a	a	DET
ejpam-6074	108	6	2	2	NUM
ejpam-6074	108	7	-	-	PUNCT
ejpam-6074	108	8	step	step	NOUN
ejpam-6074	108	9	movable	movable	ADJ
ejpam-6074	108	10	hop	hop	NOUN
ejpam-6074	108	11	dominating	dominating	NOUN
ejpam-6074	108	12	set	set	NOUN
ejpam-6074	108	13	dj	dj	NOUN
ejpam-6074	108	14	by	by	ADP
ejpam-6074	108	15	theorem	theorem	NOUN
ejpam-6074	108	16	1	1	NUM
ejpam-6074	108	17	.	.	PUNCT
ejpam-6074	108	18	clearly	clearly	ADV
ejpam-6074	108	19	,	,	PUNCT
ejpam-6074	108	20	d	d	PROPN
ejpam-6074	108	21	=	=	SYM
ejpam-6074	108	22	∪j∈[k]dj	∪j∈[k]dj	PROPN
ejpam-6074	108	23	is	be	AUX
ejpam-6074	108	24	a	a	DET
ejpam-6074	108	25	2	2	NUM
ejpam-6074	108	26	-	-	PUNCT
ejpam-6074	108	27	step	step	NOUN
ejpam-6074	108	28	movable	movable	ADJ
ejpam-6074	108	29	hop	hop	NOUN
ejpam-6074	108	30	dominating	dominating	NOUN
ejpam-6074	108	31	set	set	VERB
ejpam-6074	108	32	in	in	ADP
ejpam-6074	108	33	g.	g.	PROPN
ejpam-6074	108	34	moreover	moreover	ADV
ejpam-6074	108	35	,	,	PUNCT
ejpam-6074	108	36	if	if	SCONJ
ejpam-6074	108	37	dj	dj	NOUN
ejpam-6074	108	38	is	be	AUX
ejpam-6074	108	39	a	a	DET
ejpam-6074	108	40	γ2mh	γ2mh	PROPN
ejpam-6074	108	41	-	-	PUNCT
ejpam-6074	108	42	set	set	VERB
ejpam-6074	108	43	in	in	ADP
ejpam-6074	108	44	gj	gj	NOUN
ejpam-6074	108	45	for	for	ADP
ejpam-6074	108	46	each	each	DET
ejpam-6074	108	47	j	j	PROPN
ejpam-6074	108	48	∈	∈	PROPN
ejpam-6074	109	1	[	[	X
ejpam-6074	109	2	k	k	X
ejpam-6074	109	3	]	]	X
ejpam-6074	109	4	,	,	PUNCT
ejpam-6074	109	5	then	then	ADV
ejpam-6074	109	6	we	we	PRON
ejpam-6074	109	7	have	have	VERB
ejpam-6074	109	8	γ2mh(g	γ2mh(g	NOUN
ejpam-6074	109	9	)	)	PUNCT
ejpam-6074	109	10	≤	≤	NUM
ejpam-6074	110	1	|d|	|d|	PROPN
ejpam-6074	110	2	=	=	PUNCT
ejpam-6074	111	1	|	|	ADV
ejpam-6074	111	2	∪j∈[k	∪j∈[k	ADJ
ejpam-6074	111	3	]	]	X
ejpam-6074	111	4	dj	dj	NOUN
ejpam-6074	112	1	|	|	NOUN
ejpam-6074	112	2	=	=	SYM
ejpam-6074	112	3	∑	∑	PUNCT
ejpam-6074	112	4	j∈[k	j∈[k	PROPN
ejpam-6074	112	5	]	]	PUNCT
ejpam-6074	112	6	γ2mh(gj	γ2mh(gj	NUM
ejpam-6074	112	7	)	)	PUNCT
ejpam-6074	112	8	.	.	PUNCT
ejpam-6074	113	1	therefore	therefore	ADV
ejpam-6074	113	2	,	,	PUNCT
ejpam-6074	113	3	the	the	DET
ejpam-6074	113	4	assertion	assertion	NOUN
ejpam-6074	113	5	holds	hold	VERB
ejpam-6074	113	6	.	.	PUNCT
ejpam-6074	114	1	corollary	corollary	ADJ
ejpam-6074	114	2	1	1	NUM
ejpam-6074	114	3	.	.	PUNCT
ejpam-6074	115	1	if	if	SCONJ
ejpam-6074	115	2	g	g	PROPN
ejpam-6074	115	3	admits	admit	VERB
ejpam-6074	115	4	a	a	DET
ejpam-6074	115	5	2	2	NUM
ejpam-6074	115	6	-	-	PUNCT
ejpam-6074	115	7	step	step	NOUN
ejpam-6074	115	8	movable	movable	ADJ
ejpam-6074	115	9	hop	hop	NOUN
ejpam-6074	115	10	dominating	dominating	NOUN
ejpam-6074	115	11	set	set	NOUN
ejpam-6074	115	12	,	,	PUNCT
ejpam-6074	115	13	then	then	ADV
ejpam-6074	115	14	|v	|v	PROPN
ejpam-6074	115	15	(	(	PUNCT
ejpam-6074	115	16	g)|	g)|	X
ejpam-6074	115	17	≥	≥	NOUN
ejpam-6074	115	18	4	4	NUM
ejpam-6074	115	19	.	.	PUNCT
ejpam-6074	115	20	proof	proof	NOUN
ejpam-6074	115	21	.	.	PUNCT
ejpam-6074	116	1	suppose	suppose	VERB
ejpam-6074	116	2	g	g	PROPN
ejpam-6074	116	3	admits	admit	VERB
ejpam-6074	116	4	a	a	DET
ejpam-6074	116	5	2	2	NUM
ejpam-6074	116	6	-	-	PUNCT
ejpam-6074	116	7	step	step	NOUN
ejpam-6074	116	8	movable	movable	ADJ
ejpam-6074	116	9	hop	hop	NOUN
ejpam-6074	116	10	dominating	dominating	NOUN
ejpam-6074	116	11	set	set	NOUN
ejpam-6074	116	12	.	.	PUNCT
ejpam-6074	117	1	let	let	VERB
ejpam-6074	117	2	g′	g′	NOUN
ejpam-6074	117	3	be	be	AUX
ejpam-6074	117	4	a	a	DET
ejpam-6074	117	5	component	component	NOUN
ejpam-6074	117	6	of	of	ADP
ejpam-6074	117	7	g.	g.	PROPN
ejpam-6074	117	8	then	then	ADV
ejpam-6074	117	9	γ(g′	γ(g′	NUM
ejpam-6074	117	10	)	)	PUNCT
ejpam-6074	117	11	̸=	̸=	PROPN
ejpam-6074	117	12	1	1	NUM
ejpam-6074	117	13	by	by	ADP
ejpam-6074	117	14	theorem	theorem	NOUN
ejpam-6074	117	15	2	2	NUM
ejpam-6074	117	16	.	.	PUNCT
ejpam-6074	118	1	it	it	PRON
ejpam-6074	118	2	follows	follow	VERB
ejpam-6074	118	3	that	that	DET
ejpam-6074	118	4	g′	g′	NOUN
ejpam-6074	118	5	/∈	/∈	PUNCT
ejpam-6074	119	1	{	{	PUNCT
ejpam-6074	119	2	k1,k2,k3	k1,k2,k3	ADJ
ejpam-6074	119	3	,	,	PUNCT
ejpam-6074	119	4	p3	p3	PROPN
ejpam-6074	119	5	}	}	PUNCT
ejpam-6074	119	6	.	.	PUNCT
ejpam-6074	120	1	thus	thus	ADV
ejpam-6074	120	2	,	,	PUNCT
ejpam-6074	120	3	4	4	NUM
ejpam-6074	120	4	≤	≤	NUM
ejpam-6074	120	5	|v	|v	X
ejpam-6074	120	6	(	(	PUNCT
ejpam-6074	120	7	g′)|	g′)|	PROPN
ejpam-6074	120	8	≤	≤	PROPN
ejpam-6074	120	9	|v	|v	X
ejpam-6074	120	10	(	(	PUNCT
ejpam-6074	120	11	g)|	g)|	NOUN
ejpam-6074	120	12	.	.	PUNCT
ejpam-6074	121	1	throughout	throughout	ADP
ejpam-6074	121	2	this	this	DET
ejpam-6074	121	3	section	section	NOUN
ejpam-6074	121	4	,	,	PUNCT
ejpam-6074	121	5	unless	unless	SCONJ
ejpam-6074	121	6	specified	specify	VERB
ejpam-6074	121	7	,	,	PUNCT
ejpam-6074	121	8	it	it	PRON
ejpam-6074	121	9	is	be	AUX
ejpam-6074	121	10	assumed	assume	VERB
ejpam-6074	121	11	that	that	SCONJ
ejpam-6074	121	12	every	every	DET
ejpam-6074	121	13	component	component	NOUN
ejpam-6074	121	14	of	of	ADP
ejpam-6074	121	15	a	a	DET
ejpam-6074	121	16	graph	graph	NOUN
ejpam-6074	121	17	does	do	AUX
ejpam-6074	121	18	not	not	PART
ejpam-6074	121	19	have	have	VERB
ejpam-6074	121	20	a	a	DET
ejpam-6074	121	21	dominating	dominating	NOUN
ejpam-6074	121	22	vertex	vertex	NOUN
ejpam-6074	121	23	,	,	PUNCT
ejpam-6074	121	24	i.e.	i.e.	X
ejpam-6074	121	25	,	,	PUNCT
ejpam-6074	121	26	every	every	DET
ejpam-6074	121	27	graph	graph	NOUN
ejpam-6074	121	28	admits	admit	VERB
ejpam-6074	121	29	a	a	DET
ejpam-6074	121	30	2	2	NUM
ejpam-6074	121	31	-	-	PUNCT
ejpam-6074	121	32	step	step	NOUN
ejpam-6074	121	33	movable	movable	ADJ
ejpam-6074	121	34	hop	hop	NOUN
ejpam-6074	121	35	dominating	dominating	NOUN
ejpam-6074	121	36	set	set	NOUN
ejpam-6074	121	37	.	.	PUNCT
ejpam-6074	122	1	remark	remark	PROPN
ejpam-6074	122	2	2	2	NUM
ejpam-6074	122	3	.	.	PUNCT
ejpam-6074	123	1	let	let	VERB
ejpam-6074	123	2	g	g	NOUN
ejpam-6074	123	3	be	be	AUX
ejpam-6074	123	4	any	any	DET
ejpam-6074	123	5	graph	graph	NOUN
ejpam-6074	123	6	.	.	PUNCT
ejpam-6074	124	1	then	then	ADV
ejpam-6074	124	2	γh(g	γh(g	NOUN
ejpam-6074	124	3	)	)	PUNCT
ejpam-6074	124	4	≤	≤	NUM
ejpam-6074	124	5	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	124	6	)	)	PUNCT
ejpam-6074	124	7	.	.	PUNCT
ejpam-6074	125	1	moreover	moreover	ADV
ejpam-6074	125	2	,	,	PUNCT
ejpam-6074	125	3	for	for	ADP
ejpam-6074	125	4	each	each	DET
ejpam-6074	125	5	positive	positive	ADJ
ejpam-6074	125	6	integer	integer	NOUN
ejpam-6074	125	7	n	n	CCONJ
ejpam-6074	125	8	,	,	PUNCT
ejpam-6074	125	9	there	there	PRON
ejpam-6074	125	10	exists	exist	VERB
ejpam-6074	125	11	a	a	DET
ejpam-6074	125	12	connected	connected	ADJ
ejpam-6074	125	13	graph	graph	NOUN
ejpam-6074	125	14	g	g	ADP
ejpam-6074	125	15	such	such	ADJ
ejpam-6074	125	16	that	that	SCONJ
ejpam-6074	125	17	γ2mh(g)−γh(g	γ2mh(g)−γh(g	NOUN
ejpam-6074	125	18	)	)	PUNCT
ejpam-6074	125	19	=	=	VERB
ejpam-6074	126	1	n.	n.	NOUN
ejpam-6074	126	2	in	in	ADP
ejpam-6074	126	3	other	other	ADJ
ejpam-6074	126	4	words	word	NOUN
ejpam-6074	126	5	,	,	PUNCT
ejpam-6074	126	6	the	the	DET
ejpam-6074	126	7	difference	difference	NOUN
ejpam-6074	126	8	γ2mh(g)−	γ2mh(g)−	PROPN
ejpam-6074	126	9	γh(g	γh(g	NOUN
ejpam-6074	126	10	)	)	PUNCT
ejpam-6074	126	11	can	can	AUX
ejpam-6074	126	12	be	be	AUX
ejpam-6074	126	13	made	make	VERB
ejpam-6074	126	14	arbitrarily	arbitrarily	ADV
ejpam-6074	126	15	large	large	ADJ
ejpam-6074	126	16	.	.	PUNCT
ejpam-6074	127	1	note	note	VERB
ejpam-6074	127	2	that	that	SCONJ
ejpam-6074	127	3	for	for	ADP
ejpam-6074	127	4	a	a	DET
ejpam-6074	127	5	graph	graph	NOUN
ejpam-6074	127	6	that	that	PRON
ejpam-6074	127	7	admits	admit	VERB
ejpam-6074	127	8	a	a	DET
ejpam-6074	127	9	2	2	NUM
ejpam-6074	127	10	-	-	PUNCT
ejpam-6074	127	11	step	step	NOUN
ejpam-6074	127	12	movable	movable	ADJ
ejpam-6074	127	13	hop	hop	NOUN
ejpam-6074	127	14	dominating	dominating	NOUN
ejpam-6074	127	15	set	set	NOUN
ejpam-6074	127	16	,	,	PUNCT
ejpam-6074	127	17	every	every	DET
ejpam-6074	127	18	2	2	NUM
ejpam-6074	127	19	-	-	PUNCT
ejpam-6074	127	20	step	step	NOUN
ejpam-6074	127	21	movable	movable	ADJ
ejpam-6074	127	22	hop	hop	NOUN
ejpam-6074	127	23	dominating	dominating	NOUN
ejpam-6074	127	24	set	set	NOUN
ejpam-6074	127	25	is	be	AUX
ejpam-6074	127	26	hop	hop	NOUN
ejpam-6074	127	27	dominating	dominating	NOUN
ejpam-6074	127	28	.	.	PUNCT
ejpam-6074	128	1	thus	thus	ADV
ejpam-6074	128	2	,	,	PUNCT
ejpam-6074	128	3	γh(g	γh(g	NOUN
ejpam-6074	128	4	)	)	PUNCT
ejpam-6074	128	5	≤	≤	NUM
ejpam-6074	128	6	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	128	7	)	)	PUNCT
ejpam-6074	128	8	.	.	PUNCT
ejpam-6074	129	1	to	to	PART
ejpam-6074	129	2	see	see	VERB
ejpam-6074	129	3	that	that	SCONJ
ejpam-6074	129	4	the	the	DET
ejpam-6074	129	5	second	second	ADJ
ejpam-6074	129	6	part	part	NOUN
ejpam-6074	129	7	of	of	ADP
ejpam-6074	129	8	remark	remark	NOUN
ejpam-6074	129	9	2	2	NUM
ejpam-6074	129	10	holds	hold	NOUN
ejpam-6074	129	11	,	,	PUNCT
ejpam-6074	129	12	let	let	VERB
ejpam-6074	129	13	n	n	PRON
ejpam-6074	129	14	be	be	AUX
ejpam-6074	129	15	a	a	DET
ejpam-6074	129	16	positive	positive	ADJ
ejpam-6074	129	17	integer	integer	NOUN
ejpam-6074	129	18	and	and	CCONJ
ejpam-6074	129	19	consider	consider	VERB
ejpam-6074	129	20	the	the	DET
ejpam-6074	129	21	graph	graph	NOUN
ejpam-6074	129	22	g	g	NOUN
ejpam-6074	129	23	in	in	ADP
ejpam-6074	129	24	figure	figure	NOUN
ejpam-6074	129	25	1	1	NUM
ejpam-6074	129	26	obtained	obtain	VERB
ejpam-6074	129	27	from	from	ADP
ejpam-6074	129	28	kn+2	kn+2	PRON
ejpam-6074	129	29	by	by	ADP
ejpam-6074	129	30	adding	add	VERB
ejpam-6074	129	31	the	the	DET
ejpam-6074	129	32	edges	edge	NOUN
ejpam-6074	129	33	ab	ab	PROPN
ejpam-6074	129	34	and	and	CCONJ
ejpam-6074	129	35	bx1	bx1	PROPN
ejpam-6074	129	36	,	,	PUNCT
ejpam-6074	130	1	where	where	SCONJ
ejpam-6074	130	2	v	v	X
ejpam-6074	130	3	(	(	PUNCT
ejpam-6074	130	4	kn+1	kn+1	PROPN
ejpam-6074	130	5	)	)	PUNCT
ejpam-6074	130	6	=	=	SYM
ejpam-6074	130	7	{	{	PUNCT
ejpam-6074	130	8	x1	x1	PROPN
ejpam-6074	130	9	,	,	PUNCT
ejpam-6074	130	10	x2	x2	PROPN
ejpam-6074	130	11	,	,	PUNCT
ejpam-6074	130	12	·	·	PUNCT
ejpam-6074	130	13	·	·	PUNCT
ejpam-6074	130	14	·	·	PUNCT
ejpam-6074	130	15	,	,	PUNCT
ejpam-6074	130	16	xn+2	xn+2	NUM
ejpam-6074	130	17	}	}	PUNCT
ejpam-6074	130	18	.	.	PUNCT
ejpam-6074	131	1	clearly	clearly	ADV
ejpam-6074	131	2	,	,	PUNCT
ejpam-6074	131	3	{	{	PUNCT
ejpam-6074	131	4	a	a	DET
ejpam-6074	131	5	,	,	PUNCT
ejpam-6074	131	6	b	b	NOUN
ejpam-6074	131	7	}	}	PUNCT
ejpam-6074	131	8	is	be	AUX
ejpam-6074	131	9	a	a	DET
ejpam-6074	131	10	γh	γh	ADV
ejpam-6074	131	11	-	-	PUNCT
ejpam-6074	131	12	set	set	VERB
ejpam-6074	131	13	ing	ing	NOUN
ejpam-6074	131	14	.	.	PUNCT
ejpam-6074	132	1	hence	hence	ADV
ejpam-6074	132	2	,	,	PUNCT
ejpam-6074	132	3	γh(g	γh(g	NOUN
ejpam-6074	132	4	)	)	PUNCT
ejpam-6074	132	5	=	=	SYM
ejpam-6074	132	6	2	2	X
ejpam-6074	132	7	.	.	X
ejpam-6074	132	8	let	let	VERB
ejpam-6074	132	9	s	s	PRON
ejpam-6074	132	10	be	be	AUX
ejpam-6074	132	11	a	a	DET
ejpam-6074	132	12	γ2mh	γ2mh	NOUN
ejpam-6074	132	13	-	-	PUNCT
ejpam-6074	132	14	set	set	VERB
ejpam-6074	132	15	in	in	ADP
ejpam-6074	132	16	g.	g.	PROPN
ejpam-6074	132	17	suppose	suppose	VERB
ejpam-6074	132	18	b	b	PROPN
ejpam-6074	132	19	/∈	/∈	PUNCT
ejpam-6074	132	20	s.	s.	PROPN
ejpam-6074	132	21	if	if	SCONJ
ejpam-6074	132	22	x1	x1	PROPN
ejpam-6074	132	23	∈	∈	PROPN
ejpam-6074	132	24	s	s	PART
ejpam-6074	132	25	,	,	PUNCT
ejpam-6074	132	26	then	then	ADV
ejpam-6074	132	27	s	s	VERB
ejpam-6074	132	28	=	=	PUNCT
ejpam-6074	132	29	{	{	PUNCT
ejpam-6074	132	30	x1	x1	PROPN
ejpam-6074	132	31	,	,	PUNCT
ejpam-6074	132	32	x2	x2	PROPN
ejpam-6074	132	33	,	,	PUNCT
ejpam-6074	132	34	·	·	PUNCT
ejpam-6074	132	35	·	·	PUNCT
ejpam-6074	132	36	·	·	PUNCT
ejpam-6074	132	37	,	,	PUNCT
ejpam-6074	132	38	xn+2	xn+2	X
ejpam-6074	132	39	}	}	PUNCT
ejpam-6074	132	40	is	be	AUX
ejpam-6074	132	41	a	a	DET
ejpam-6074	132	42	γ2mh	γ2mh	PROPN
ejpam-6074	132	43	-	-	PUNCT
ejpam-6074	132	44	set	set	VERB
ejpam-6074	132	45	in	in	ADP
ejpam-6074	132	46	g.	g.	PROPN
ejpam-6074	133	1	if	if	SCONJ
ejpam-6074	133	2	x1	x1	PROPN
ejpam-6074	133	3	/∈	/∈	PUNCT
ejpam-6074	134	1	s	s	X
ejpam-6074	134	2	,	,	PUNCT
ejpam-6074	134	3	then	then	ADV
ejpam-6074	134	4	s	s	VERB
ejpam-6074	134	5	=	=	PUNCT
ejpam-6074	134	6	{	{	PUNCT
ejpam-6074	134	7	a	a	NOUN
ejpam-6074	134	8	,	,	PUNCT
ejpam-6074	134	9	x2	x2	PROPN
ejpam-6074	134	10	,	,	PUNCT
ejpam-6074	134	11	·	·	PUNCT
ejpam-6074	134	12	·	·	PUNCT
ejpam-6074	134	13	·	·	PUNCT
ejpam-6074	134	14	,	,	PUNCT
ejpam-6074	134	15	xn+2	xn+2	NUM
ejpam-6074	134	16	}	}	PUNCT
ejpam-6074	134	17	.	.	PUNCT
ejpam-6074	135	1	suppose	suppose	VERB
ejpam-6074	135	2	b	b	X
ejpam-6074	135	3	∈	∈	PROPN
ejpam-6074	135	4	s.	s.	PROPN
ejpam-6074	135	5	suppose	suppose	VERB
ejpam-6074	135	6	|s∩{x2	|s∩{x2	PROPN
ejpam-6074	135	7	,	,	PUNCT
ejpam-6074	135	8	·	·	PUNCT
ejpam-6074	135	9	·	·	PUNCT
ejpam-6074	135	10	·	·	PUNCT
ejpam-6074	135	11	,	,	PUNCT
ejpam-6074	135	12	xn+2}|	xn+2}|	PUNCT
ejpam-6074	135	13	≤	≤	PROPN
ejpam-6074	135	14	n−1	n−1	PROPN
ejpam-6074	135	15	.	.	PUNCT
ejpam-6074	136	1	we	we	PRON
ejpam-6074	136	2	may	may	AUX
ejpam-6074	136	3	assume	assume	VERB
ejpam-6074	136	4	x2	x2	PROPN
ejpam-6074	136	5	,	,	PUNCT
ejpam-6074	136	6	x3	x3	PROPN
ejpam-6074	136	7	/∈	/∈	PUNCT
ejpam-6074	136	8	s.	s.	PROPN
ejpam-6074	136	9	since	since	SCONJ
ejpam-6074	136	10	for	for	ADP
ejpam-6074	136	11	each	each	DET
ejpam-6074	136	12	j	j	PROPN
ejpam-6074	136	13	∈	∈	PROPN
ejpam-6074	136	14	{	{	PUNCT
ejpam-6074	136	15	2	2	NUM
ejpam-6074	136	16	,	,	PUNCT
ejpam-6074	136	17	3	3	NUM
ejpam-6074	136	18	}	}	PUNCT
ejpam-6074	136	19	the	the	DET
ejpam-6074	136	20	set	set	NOUN
ejpam-6074	136	21	(	(	PUNCT
ejpam-6074	136	22	s	s	NOUN
ejpam-6074	136	23	\	\	X
ejpam-6074	136	24	{	{	PUNCT
ejpam-6074	136	25	b	b	NOUN
ejpam-6074	136	26	}	}	PUNCT
ejpam-6074	136	27	)	)	PUNCT
ejpam-6074	136	28	∪	∪	PROPN
ejpam-6074	136	29	{	{	PUNCT
ejpam-6074	136	30	xj	xj	NOUN
ejpam-6074	136	31	}	}	PUNCT
ejpam-6074	136	32	is	be	AUX
ejpam-6074	136	33	not	not	PART
ejpam-6074	136	34	hop	hop	NOUN
ejpam-6074	136	35	dominating	dominating	NOUN
ejpam-6074	136	36	,	,	PUNCT
ejpam-6074	136	37	it	it	PRON
ejpam-6074	136	38	follows	follow	VERB
ejpam-6074	136	39	that	that	SCONJ
ejpam-6074	136	40	s	s	VERB
ejpam-6074	136	41	is	be	AUX
ejpam-6074	136	42	not	not	PART
ejpam-6074	136	43	2	2	NUM
ejpam-6074	136	44	-	-	PUNCT
ejpam-6074	136	45	step	step	NOUN
ejpam-6074	136	46	hop	hop	NOUN
ejpam-6074	136	47	dominating	dominating	NOUN
ejpam-6074	136	48	,	,	PUNCT
ejpam-6074	136	49	a	a	DET
ejpam-6074	136	50	contradiction	contradiction	NOUN
ejpam-6074	136	51	.	.	PUNCT
ejpam-6074	137	1	r.	r.	PROPN
ejpam-6074	137	2	estrella	estrella	PROPN
ejpam-6074	137	3	,	,	PUNCT
ejpam-6074	137	4	gina	gina	PROPN
ejpam-6074	137	5	m.	m.	PROPN
ejpam-6074	137	6	malacas	malacas	PROPN
ejpam-6074	137	7	,	,	PUNCT
ejpam-6074	137	8	s.	s.	PROPN
ejpam-6074	137	9	canoy	canoy	PROPN
ejpam-6074	137	10	jr	jr	PROPN
ejpam-6074	137	11	.	.	PROPN
ejpam-6074	137	12	/	/	SYM
ejpam-6074	137	13	eur	eur	PROPN
ejpam-6074	137	14	.	.	PUNCT
ejpam-6074	138	1	j.	j.	PROPN
ejpam-6074	138	2	pure	pure	PROPN
ejpam-6074	138	3	appl	appl	PROPN
ejpam-6074	138	4	.	.	PROPN
ejpam-6074	138	5	math	math	PROPN
ejpam-6074	138	6	,	,	PUNCT
ejpam-6074	138	7	18	18	NUM
ejpam-6074	138	8	(	(	PUNCT
ejpam-6074	138	9	2	2	NUM
ejpam-6074	138	10	)	)	PUNCT
ejpam-6074	138	11	(	(	PUNCT
ejpam-6074	138	12	2025	2025	NUM
ejpam-6074	138	13	)	)	PUNCT
ejpam-6074	138	14	,	,	PUNCT
ejpam-6074	138	15	6074	6074	NUM
ejpam-6074	138	16	5	5	NUM
ejpam-6074	138	17	of	of	ADP
ejpam-6074	138	18	15	15	NUM
ejpam-6074	138	19	............	............	PUNCT
ejpam-6074	138	20	...........	...........	PUNCT
ejpam-6074	138	21	...........	...........	PUNCT
ejpam-6074	138	22	...........	...........	PUNCT
ejpam-6074	138	23	...........	...........	PUNCT
ejpam-6074	138	24	...........	...........	PUNCT
ejpam-6074	138	25	...........	...........	PUNCT
ejpam-6074	138	26	...........	...........	PUNCT
ejpam-6074	138	27	...........	...........	PUNCT
ejpam-6074	138	28	...........	...........	PUNCT
ejpam-6074	138	29	....................................	....................................	PUNCT
ejpam-6074	138	30	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-6074	138	31	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-6074	139	1	....................................	....................................	PUNCT
ejpam-6074	139	2	...................................................................................................................................................	...................................................................................................................................................	PUNCT
ejpam-6074	140	1	....................................	....................................	PUNCT
ejpam-6074	140	2	....................................	....................................	PUNCT
ejpam-6074	140	3	............	............	PUNCT
ejpam-6074	140	4	...........	...........	PUNCT
ejpam-6074	141	1	...........	...........	PUNCT
ejpam-6074	141	2	...........	...........	PUNCT
ejpam-6074	141	3	...........	...........	PUNCT
ejpam-6074	141	4	...........	...........	PUNCT
ejpam-6074	141	5	...........	...........	PUNCT
ejpam-6074	141	6	...........	...........	PUNCT
ejpam-6074	141	7	...........	...........	PUNCT
ejpam-6074	141	8	...........	...........	PUNCT
ejpam-6074	141	9	....................................	....................................	PUNCT
ejpam-6074	141	10	....................................	....................................	PUNCT
ejpam-6074	141	11	.....................	.....................	PUNCT
ejpam-6074	141	12	....................	....................	PUNCT
ejpam-6074	141	13	....................	....................	PUNCT
ejpam-6074	141	14	....................	....................	PUNCT
ejpam-6074	141	15	....................	....................	PUNCT
ejpam-6074	141	16	....................	....................	PUNCT
ejpam-6074	141	17	....................	....................	PUNCT
ejpam-6074	141	18	....................	....................	PUNCT
ejpam-6074	141	19	....................	....................	PUNCT
ejpam-6074	141	20	....................	....................	PUNCT
ejpam-6074	141	21	........	........	PUNCT
ejpam-6074	142	1	....................................	....................................	PUNCT
ejpam-6074	142	2	....................................	....................................	PUNCT
ejpam-6074	143	1	.........................................................................................................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6074	143	2	.....................................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................................	PUNCT
ejpam-6074	143	3	....................................	....................................	PUNCT
ejpam-6074	143	4	....................................	....................................	PUNCT
ejpam-6074	144	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-6074	144	2	.....................................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................................	PUNCT
ejpam-6074	145	1	....................................	....................................	PUNCT
ejpam-6074	145	2	....................................	....................................	PUNCT
ejpam-6074	146	1	.....................................................................................................................................................................................................	.....................................................................................................................................................................................................	PUNCT
ejpam-6074	146	2	....................................	....................................	PUNCT
ejpam-6074	146	3	................................................................................................................................................................................	................................................................................................................................................................................	PUNCT
ejpam-6074	146	4	....................................	....................................	PUNCT
ejpam-6074	147	1	.........	.........	PUNCT
ejpam-6074	147	2	........	........	PUNCT
ejpam-6074	147	3	........	........	PUNCT
ejpam-6074	147	4	........	........	PUNCT
ejpam-6074	147	5	........	........	PUNCT
ejpam-6074	147	6	........	........	PUNCT
ejpam-6074	147	7	........	........	PUNCT
ejpam-6074	147	8	........	........	PUNCT
ejpam-6074	147	9	........	........	PUNCT
ejpam-6074	147	10	........	........	PUNCT
ejpam-6074	147	11	........	........	PUNCT
ejpam-6074	147	12	........	........	PUNCT
ejpam-6074	147	13	........	........	PUNCT
ejpam-6074	147	14	........	........	PUNCT
ejpam-6074	147	15	........	........	PUNCT
ejpam-6074	147	16	........	........	PUNCT
ejpam-6074	147	17	........	........	PUNCT
ejpam-6074	147	18	........	........	PUNCT
ejpam-6074	147	19	........	........	PUNCT
ejpam-6074	147	20	........	........	PUNCT
ejpam-6074	147	21	.	.	PUNCT
ejpam-6074	148	1	....................................	....................................	PUNCT
ejpam-6074	148	2	....................................	....................................	PUNCT
ejpam-6074	149	1	...........	...........	PUNCT
ejpam-6074	149	2	..........	..........	PUNCT
ejpam-6074	150	1	..........	..........	PUNCT
ejpam-6074	150	2	..........	..........	PUNCT
ejpam-6074	151	1	..........	..........	PUNCT
ejpam-6074	151	2	..........	..........	PUNCT
ejpam-6074	152	1	..........	..........	PUNCT
ejpam-6074	152	2	..........	..........	PUNCT
ejpam-6074	153	1	..........	..........	PUNCT
ejpam-6074	153	2	..........	..........	PUNCT
ejpam-6074	154	1	..........	..........	PUNCT
ejpam-6074	154	2	..........	..........	PUNCT
ejpam-6074	155	1	..........	..........	PUNCT
ejpam-6074	155	2	..........	..........	PUNCT
ejpam-6074	156	1	..........	..........	PUNCT
ejpam-6074	156	2	..........	..........	PUNCT
ejpam-6074	157	1	..........	..........	PUNCT
ejpam-6074	157	2	..........	..........	PUNCT
ejpam-6074	158	1	..........	..........	PUNCT
ejpam-6074	158	2	......	......	PUNCT
ejpam-6074	159	1	....................................	....................................	PUNCT
ejpam-6074	159	2	....................................	....................................	PUNCT
ejpam-6074	160	1	.....................	.....................	PUNCT
ejpam-6074	160	2	....................	....................	PUNCT
ejpam-6074	160	3	....................	....................	PUNCT
ejpam-6074	160	4	....................	....................	PUNCT
ejpam-6074	160	5	....................	....................	PUNCT
ejpam-6074	160	6	....................	....................	PUNCT
ejpam-6074	160	7	....................	....................	PUNCT
ejpam-6074	160	8	....................	....................	PUNCT
ejpam-6074	160	9	....................	....................	PUNCT
ejpam-6074	160	10	....................	....................	PUNCT
ejpam-6074	160	11	........	........	PUNCT
ejpam-6074	161	1	....................................	....................................	PUNCT
ejpam-6074	161	2	....................................	....................................	PUNCT
ejpam-6074	161	3	.........	.........	PUNCT
ejpam-6074	161	4	........	........	PUNCT
ejpam-6074	161	5	........	........	PUNCT
ejpam-6074	161	6	........	........	PUNCT
ejpam-6074	161	7	........	........	PUNCT
ejpam-6074	161	8	........	........	PUNCT
ejpam-6074	161	9	........	........	PUNCT
ejpam-6074	161	10	........	........	PUNCT
ejpam-6074	161	11	........	........	PUNCT
ejpam-6074	161	12	........	........	PUNCT
ejpam-6074	161	13	........	........	PUNCT
ejpam-6074	161	14	........	........	PUNCT
ejpam-6074	161	15	........	........	PUNCT
ejpam-6074	161	16	........	........	PUNCT
ejpam-6074	161	17	........	........	PUNCT
ejpam-6074	161	18	........	........	PUNCT
ejpam-6074	161	19	........	........	PUNCT
ejpam-6074	161	20	........	........	PUNCT
ejpam-6074	161	21	........	........	PUNCT
ejpam-6074	161	22	........	........	PUNCT
ejpam-6074	161	23	.	.	PUNCT
ejpam-6074	162	1	....................................	....................................	PUNCT
ejpam-6074	162	2	....................................	....................................	PUNCT
ejpam-6074	163	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-6074	163	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-6074	164	1	....................................	....................................	PUNCT
ejpam-6074	164	2	.	.	PUNCT
ejpam-6074	164	3	.	.	PUNCT
ejpam-6074	165	1	.	.	PUNCT
ejpam-6074	166	1	x1	x1	INTJ
ejpam-6074	166	2	x2x3	x2x3	PUNCT
ejpam-6074	167	1	x4	x4	PROPN
ejpam-6074	167	2	x5	x5	PROPN
ejpam-6074	167	3	xn+2	xn+2	PROPN
ejpam-6074	167	4	b	b	PROPN
ejpam-6074	167	5	a	a	DET
ejpam-6074	167	6	figure	figure	NOUN
ejpam-6074	167	7	1	1	NUM
ejpam-6074	167	8	:	:	PUNCT
ejpam-6074	167	9	graph	graph	VERB
ejpam-6074	167	10	g	g	NOUN
ejpam-6074	167	11	with	with	ADP
ejpam-6074	167	12	γ2	γ2	PROPN
ejpam-6074	167	13	mh(g)−	mh(g)−	NOUN
ejpam-6074	167	14	γh(g	γh(g	NOUN
ejpam-6074	167	15	)	)	PUNCT
ejpam-6074	167	16	=	=	SYM
ejpam-6074	167	17	n	n	PRON
ejpam-6074	167	18	thus	thus	ADV
ejpam-6074	167	19	,	,	PUNCT
ejpam-6074	167	20	|s	|s	PROPN
ejpam-6074	167	21	∩	∩	NOUN
ejpam-6074	167	22	{	{	PUNCT
ejpam-6074	167	23	x2	x2	PROPN
ejpam-6074	167	24	,	,	PUNCT
ejpam-6074	167	25	·	·	PUNCT
ejpam-6074	167	26	·	·	PUNCT
ejpam-6074	167	27	·	·	PUNCT
ejpam-6074	167	28	,	,	PUNCT
ejpam-6074	167	29	xn+2}|	xn+2}|	PUNCT
ejpam-6074	168	1	=	=	PUNCT
ejpam-6074	168	2	n.	n.	PROPN
ejpam-6074	168	3	moreover	moreover	ADV
ejpam-6074	168	4	,	,	PUNCT
ejpam-6074	168	5	|s	|s	PROPN
ejpam-6074	168	6	∩	∩	NOUN
ejpam-6074	168	7	{	{	PUNCT
ejpam-6074	168	8	a	a	X
ejpam-6074	168	9	,	,	PUNCT
ejpam-6074	168	10	x1}|	x1}|	PROPN
ejpam-6074	168	11	=	=	SYM
ejpam-6074	168	12	1	1	X
ejpam-6074	168	13	.	.	PUNCT
ejpam-6074	169	1	therefore	therefore	ADV
ejpam-6074	169	2	,	,	PUNCT
ejpam-6074	169	3	in	in	ADP
ejpam-6074	169	4	any	any	DET
ejpam-6074	169	5	case	case	NOUN
ejpam-6074	169	6	,	,	PUNCT
ejpam-6074	169	7	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	169	8	)	)	PUNCT
ejpam-6074	169	9	=	=	SYM
ejpam-6074	169	10	n+	n+	PUNCT
ejpam-6074	169	11	2	2	X
ejpam-6074	169	12	.	.	PUNCT
ejpam-6074	169	13	accordingly	accordingly	ADV
ejpam-6074	169	14	,	,	PUNCT
ejpam-6074	169	15	γ2mh(g)−	γ2mh(g)−	PROPN
ejpam-6074	169	16	γh(g	γh(g	NOUN
ejpam-6074	169	17	)	)	PUNCT
ejpam-6074	169	18	=	=	SYM
ejpam-6074	169	19	n.	n.	NOUN
ejpam-6074	169	20	theorem	theorem	NOUN
ejpam-6074	169	21	3	3	X
ejpam-6074	169	22	.	.	PUNCT
ejpam-6074	170	1	let	let	VERB
ejpam-6074	170	2	g	g	NOUN
ejpam-6074	170	3	be	be	AUX
ejpam-6074	170	4	any	any	DET
ejpam-6074	170	5	graph	graph	NOUN
ejpam-6074	170	6	of	of	ADP
ejpam-6074	170	7	order	order	NOUN
ejpam-6074	170	8	n	n	PRON
ejpam-6074	170	9	≥	≥	NOUN
ejpam-6074	170	10	4	4	NUM
ejpam-6074	170	11	and	and	CCONJ
ejpam-6074	170	12	let	let	VERB
ejpam-6074	170	13	s	s	PRON
ejpam-6074	170	14	be	be	AUX
ejpam-6074	170	15	a	a	DET
ejpam-6074	170	16	hop	hop	NOUN
ejpam-6074	170	17	dominating	dominating	NOUN
ejpam-6074	170	18	set	set	VERB
ejpam-6074	170	19	in	in	ADP
ejpam-6074	170	20	g.	g.	PROPN
ejpam-6074	171	1	then	then	ADV
ejpam-6074	171	2	s	s	VERB
ejpam-6074	171	3	is	be	AUX
ejpam-6074	171	4	a	a	DET
ejpam-6074	171	5	2	2	NUM
ejpam-6074	171	6	-	-	PUNCT
ejpam-6074	171	7	step	step	NOUN
ejpam-6074	171	8	movable	movable	ADJ
ejpam-6074	171	9	hop	hop	NOUN
ejpam-6074	171	10	dominating	dominating	NOUN
ejpam-6074	171	11	set	set	VERB
ejpam-6074	171	12	in	in	ADP
ejpam-6074	171	13	g	g	PROPN
ejpam-6074	171	14	if	if	SCONJ
ejpam-6074	171	15	and	and	CCONJ
ejpam-6074	171	16	only	only	ADV
ejpam-6074	171	17	if	if	SCONJ
ejpam-6074	171	18	for	for	ADP
ejpam-6074	171	19	each	each	DET
ejpam-6074	171	20	v	v	NOUN
ejpam-6074	171	21	∈	∈	NOUN
ejpam-6074	171	22	s	s	VERB
ejpam-6074	171	23	such	such	ADJ
ejpam-6074	171	24	that	that	PRON
ejpam-6074	171	25	s	s	VERB
ejpam-6074	171	26	\	\	PROPN
ejpam-6074	171	27	{	{	PUNCT
ejpam-6074	171	28	v	v	NOUN
ejpam-6074	171	29	}	}	PUNCT
ejpam-6074	171	30	is	be	AUX
ejpam-6074	171	31	not	not	PART
ejpam-6074	171	32	hop	hop	NOUN
ejpam-6074	171	33	dominating	dominating	NOUN
ejpam-6074	171	34	,	,	PUNCT
ejpam-6074	171	35	it	it	PRON
ejpam-6074	171	36	holds	hold	VERB
ejpam-6074	171	37	that	that	SCONJ
ejpam-6074	171	38	there	there	PRON
ejpam-6074	171	39	exists	exist	VERB
ejpam-6074	171	40	w	w	PROPN
ejpam-6074	171	41	∈	∈	PROPN
ejpam-6074	171	42	(	(	PUNCT
ejpam-6074	171	43	v	v	NOUN
ejpam-6074	171	44	(	(	PUNCT
ejpam-6074	171	45	g	g	NOUN
ejpam-6074	171	46	)	)	PUNCT
ejpam-6074	171	47	\s)∩n2	\s)∩n2	NOUN
ejpam-6074	171	48	g(v	g(v	PROPN
ejpam-6074	171	49	)	)	PUNCT
ejpam-6074	171	50	such	such	ADJ
ejpam-6074	171	51	that	that	PRON
ejpam-6074	171	52	ephn(v;s	ephn(v;s	NOUN
ejpam-6074	171	53	)	)	PUNCT
ejpam-6074	171	54	⊆	⊆	NUM
ejpam-6074	171	55	n2	n2	NOUN
ejpam-6074	171	56	g[w	g[w	PROPN
ejpam-6074	171	57	]	]	PUNCT
ejpam-6074	171	58	.	.	PUNCT
ejpam-6074	172	1	proof	proof	NOUN
ejpam-6074	172	2	.	.	PUNCT
ejpam-6074	173	1	suppose	suppose	VERB
ejpam-6074	173	2	s	s	NOUN
ejpam-6074	173	3	is	be	AUX
ejpam-6074	173	4	a	a	DET
ejpam-6074	173	5	2	2	NUM
ejpam-6074	173	6	-	-	PUNCT
ejpam-6074	173	7	step	step	NOUN
ejpam-6074	173	8	movable	movable	ADJ
ejpam-6074	173	9	hop	hop	NOUN
ejpam-6074	173	10	dominating	dominating	NOUN
ejpam-6074	173	11	set	set	VERB
ejpam-6074	173	12	in	in	ADP
ejpam-6074	173	13	g.	g.	PROPN
ejpam-6074	173	14	let	let	VERB
ejpam-6074	173	15	v	v	NUM
ejpam-6074	173	16	∈	∈	NOUN
ejpam-6074	173	17	s	s	VERB
ejpam-6074	173	18	such	such	ADJ
ejpam-6074	173	19	that	that	PRON
ejpam-6074	173	20	s	s	VERB
ejpam-6074	173	21	\	\	PROPN
ejpam-6074	173	22	{	{	PUNCT
ejpam-6074	173	23	v	v	NOUN
ejpam-6074	173	24	}	}	PUNCT
ejpam-6074	173	25	is	be	AUX
ejpam-6074	173	26	not	not	PART
ejpam-6074	173	27	hop	hop	NOUN
ejpam-6074	173	28	dominating	dominating	NOUN
ejpam-6074	173	29	.	.	PUNCT
ejpam-6074	174	1	since	since	SCONJ
ejpam-6074	174	2	s	s	PROPN
ejpam-6074	174	3	is	be	AUX
ejpam-6074	174	4	2	2	NUM
ejpam-6074	174	5	-	-	PUNCT
ejpam-6074	174	6	step	step	NOUN
ejpam-6074	174	7	movable	movable	ADJ
ejpam-6074	174	8	hop	hop	NOUN
ejpam-6074	174	9	dominating	dominating	NOUN
ejpam-6074	174	10	,	,	PUNCT
ejpam-6074	174	11	there	there	PRON
ejpam-6074	174	12	exists	exist	VERB
ejpam-6074	174	13	w	w	PROPN
ejpam-6074	174	14	∈	∈	PROPN
ejpam-6074	174	15	(	(	PUNCT
ejpam-6074	174	16	v	v	NOUN
ejpam-6074	174	17	(	(	PUNCT
ejpam-6074	174	18	g	g	NOUN
ejpam-6074	174	19	)	)	PUNCT
ejpam-6074	174	20	\	\	PROPN
ejpam-6074	174	21	s	s	X
ejpam-6074	174	22	)	)	PUNCT
ejpam-6074	174	23	∩	∩	ADJ
ejpam-6074	174	24	n2	n2	ADJ
ejpam-6074	174	25	g(v	g(v	PROPN
ejpam-6074	174	26	)	)	PUNCT
ejpam-6074	175	1	such	such	ADJ
ejpam-6074	175	2	that	that	PRON
ejpam-6074	175	3	sw	sw	PROPN
ejpam-6074	175	4	=	=	PUNCT
ejpam-6074	175	5	(	(	PUNCT
ejpam-6074	175	6	s	s	NOUN
ejpam-6074	175	7	\	\	X
ejpam-6074	175	8	{	{	PUNCT
ejpam-6074	175	9	v	v	NOUN
ejpam-6074	175	10	}	}	PUNCT
ejpam-6074	175	11	)	)	PUNCT
ejpam-6074	175	12	∪	∪	ADP
ejpam-6074	175	13	{	{	PUNCT
ejpam-6074	175	14	w	w	NOUN
ejpam-6074	175	15	}	}	PUNCT
ejpam-6074	175	16	is	be	AUX
ejpam-6074	175	17	a	a	DET
ejpam-6074	175	18	hop	hop	NOUN
ejpam-6074	175	19	dominating	dominating	NOUN
ejpam-6074	175	20	set	set	VERB
ejpam-6074	175	21	in	in	ADP
ejpam-6074	175	22	g.	g.	PROPN
ejpam-6074	175	23	now	now	ADV
ejpam-6074	175	24	let	let	VERB
ejpam-6074	175	25	z	z	PROPN
ejpam-6074	175	26	∈	∈	PROPN
ejpam-6074	175	27	ephn(v;s	ephn(v;s	NOUN
ejpam-6074	175	28	)	)	PUNCT
ejpam-6074	175	29	.	.	PUNCT
ejpam-6074	176	1	then	then	ADV
ejpam-6074	176	2	n2	n2	PROPN
ejpam-6074	176	3	g(z	g(z	PROPN
ejpam-6074	176	4	)	)	PUNCT
ejpam-6074	176	5	∩	∩	NOUN
ejpam-6074	176	6	s	s	PART
ejpam-6074	176	7	=	=	PUNCT
ejpam-6074	176	8	{	{	PUNCT
ejpam-6074	176	9	v	v	NOUN
ejpam-6074	176	10	}	}	PUNCT
ejpam-6074	176	11	.	.	PUNCT
ejpam-6074	177	1	since	since	SCONJ
ejpam-6074	177	2	sw	sw	PROPN
ejpam-6074	177	3	is	be	AUX
ejpam-6074	177	4	a	a	DET
ejpam-6074	177	5	hop	hop	NOUN
ejpam-6074	177	6	dominating	dominating	NOUN
ejpam-6074	177	7	set	set	NOUN
ejpam-6074	177	8	in	in	ADP
ejpam-6074	177	9	g	g	PROPN
ejpam-6074	177	10	,	,	PUNCT
ejpam-6074	177	11	it	it	PRON
ejpam-6074	177	12	follows	follow	VERB
ejpam-6074	177	13	that	that	SCONJ
ejpam-6074	177	14	z	z	PROPN
ejpam-6074	177	15	∈	∈	PROPN
ejpam-6074	177	16	n2	n2	PROPN
ejpam-6074	177	17	g[w	g[w	PROPN
ejpam-6074	177	18	]	]	PUNCT
ejpam-6074	177	19	.	.	PUNCT
ejpam-6074	178	1	thus	thus	ADV
ejpam-6074	178	2	,	,	PUNCT
ejpam-6074	178	3	ephn(v;s	ephn(v;s	NUM
ejpam-6074	178	4	)	)	PUNCT
ejpam-6074	178	5	⊆	⊆	NUM
ejpam-6074	178	6	n2	n2	NOUN
ejpam-6074	178	7	g[w	g[w	PROPN
ejpam-6074	178	8	]	]	PUNCT
ejpam-6074	178	9	.	.	PUNCT
ejpam-6074	179	1	for	for	ADP
ejpam-6074	179	2	the	the	DET
ejpam-6074	179	3	converse	converse	NOUN
ejpam-6074	179	4	,	,	PUNCT
ejpam-6074	179	5	suppose	suppose	VERB
ejpam-6074	179	6	that	that	SCONJ
ejpam-6074	179	7	the	the	DET
ejpam-6074	179	8	given	give	VERB
ejpam-6074	179	9	property	property	NOUN
ejpam-6074	179	10	holds	hold	NOUN
ejpam-6074	179	11	.	.	PUNCT
ejpam-6074	180	1	let	let	VERB
ejpam-6074	180	2	v	v	NUM
ejpam-6074	180	3	∈	∈	NOUN
ejpam-6074	180	4	s	s	VERB
ejpam-6074	180	5	such	such	ADJ
ejpam-6074	180	6	that	that	PRON
ejpam-6074	180	7	s	s	VERB
ejpam-6074	180	8	\	\	PROPN
ejpam-6074	180	9	{	{	PUNCT
ejpam-6074	180	10	v	v	NOUN
ejpam-6074	180	11	}	}	PUNCT
ejpam-6074	180	12	is	be	AUX
ejpam-6074	180	13	not	not	PART
ejpam-6074	180	14	hop	hop	NOUN
ejpam-6074	180	15	dominating	dominating	NOUN
ejpam-6074	180	16	.	.	PUNCT
ejpam-6074	181	1	then	then	ADV
ejpam-6074	181	2	by	by	ADP
ejpam-6074	181	3	assumption	assumption	NOUN
ejpam-6074	181	4	,	,	PUNCT
ejpam-6074	181	5	there	there	PRON
ejpam-6074	181	6	exists	exist	VERB
ejpam-6074	181	7	w	w	PROPN
ejpam-6074	181	8	∈	∈	PROPN
ejpam-6074	181	9	(	(	PUNCT
ejpam-6074	181	10	v	v	NOUN
ejpam-6074	181	11	(	(	PUNCT
ejpam-6074	181	12	g	g	NOUN
ejpam-6074	181	13	)	)	PUNCT
ejpam-6074	181	14	\	\	PROPN
ejpam-6074	181	15	s	s	X
ejpam-6074	181	16	)	)	PUNCT
ejpam-6074	181	17	∩	∩	ADJ
ejpam-6074	181	18	n2	n2	ADJ
ejpam-6074	181	19	g(v	g(v	PROPN
ejpam-6074	181	20	)	)	PUNCT
ejpam-6074	181	21	such	such	ADJ
ejpam-6074	181	22	that	that	PRON
ejpam-6074	181	23	ephn(v;s	ephn(v;s	NOUN
ejpam-6074	181	24	)	)	PUNCT
ejpam-6074	181	25	⊆	⊆	NUM
ejpam-6074	181	26	n2	n2	NOUN
ejpam-6074	181	27	g[w	g[w	PROPN
ejpam-6074	181	28	]	]	PUNCT
ejpam-6074	181	29	.	.	PUNCT
ejpam-6074	182	1	let	let	VERB
ejpam-6074	182	2	sw	sw	PROPN
ejpam-6074	182	3	=	=	PUNCT
ejpam-6074	182	4	(	(	PUNCT
ejpam-6074	182	5	s	s	NOUN
ejpam-6074	182	6	\	\	X
ejpam-6074	182	7	{	{	PUNCT
ejpam-6074	182	8	v})∪	v})∪	PROPN
ejpam-6074	182	9	{	{	PUNCT
ejpam-6074	182	10	w	w	NOUN
ejpam-6074	182	11	}	}	PUNCT
ejpam-6074	182	12	and	and	CCONJ
ejpam-6074	182	13	let	let	VERB
ejpam-6074	182	14	x	x	SYM
ejpam-6074	182	15	∈	∈	PROPN
ejpam-6074	182	16	v	v	X
ejpam-6074	182	17	(	(	PUNCT
ejpam-6074	182	18	g	g	NOUN
ejpam-6074	182	19	)	)	PUNCT
ejpam-6074	182	20	\sw	\sw	PROPN
ejpam-6074	182	21	.	.	PUNCT
ejpam-6074	183	1	if	if	SCONJ
ejpam-6074	183	2	x	x	X
ejpam-6074	183	3	=	=	SYM
ejpam-6074	183	4	v	v	NOUN
ejpam-6074	183	5	,	,	PUNCT
ejpam-6074	183	6	then	then	ADV
ejpam-6074	183	7	x	x	SYM
ejpam-6074	183	8	∈	∈	PROPN
ejpam-6074	183	9	n2	n2	NOUN
ejpam-6074	183	10	g(w	g(w	PROPN
ejpam-6074	183	11	)	)	PUNCT
ejpam-6074	183	12	.	.	PUNCT
ejpam-6074	184	1	suppose	suppose	VERB
ejpam-6074	184	2	x	x	X
ejpam-6074	184	3	̸=	̸=	PROPN
ejpam-6074	184	4	v.	v.	ADP
ejpam-6074	184	5	if	if	SCONJ
ejpam-6074	184	6	x	x	X
ejpam-6074	184	7	/∈	/∈	PUNCT
ejpam-6074	184	8	ephn(v;s	ephn(v;s	NUM
ejpam-6074	184	9	)	)	PUNCT
ejpam-6074	184	10	,	,	PUNCT
ejpam-6074	184	11	then	then	ADV
ejpam-6074	184	12	there	there	PRON
ejpam-6074	184	13	exists	exist	VERB
ejpam-6074	184	14	u	u	PROPN
ejpam-6074	184	15	∈	∈	PROPN
ejpam-6074	184	16	(	(	PUNCT
ejpam-6074	184	17	s\{v})∩n2	s\{v})∩n2	NOUN
ejpam-6074	184	18	g(x	g(x	NOUN
ejpam-6074	184	19	)	)	PUNCT
ejpam-6074	184	20	since	since	SCONJ
ejpam-6074	184	21	s	s	NOUN
ejpam-6074	184	22	is	be	AUX
ejpam-6074	184	23	a	a	DET
ejpam-6074	184	24	hop	hop	NOUN
ejpam-6074	184	25	dominating	dominating	NOUN
ejpam-6074	184	26	set	set	VERB
ejpam-6074	184	27	in	in	ADP
ejpam-6074	184	28	g.	g.	PROPN
ejpam-6074	184	29	hence	hence	ADV
ejpam-6074	184	30	,	,	PUNCT
ejpam-6074	184	31	x	x	PROPN
ejpam-6074	184	32	∈	∈	PROPN
ejpam-6074	184	33	n2	n2	PROPN
ejpam-6074	184	34	g(sw	g(sw	PROPN
ejpam-6074	184	35	)	)	PUNCT
ejpam-6074	184	36	.	.	PUNCT
ejpam-6074	185	1	next	next	ADV
ejpam-6074	185	2	,	,	PUNCT
ejpam-6074	185	3	suppose	suppose	VERB
ejpam-6074	185	4	that	that	SCONJ
ejpam-6074	185	5	x	x	PUNCT
ejpam-6074	185	6	∈	∈	PROPN
ejpam-6074	185	7	ephn(v;s	ephn(v;s	NOUN
ejpam-6074	185	8	)	)	PUNCT
ejpam-6074	185	9	.	.	PUNCT
ejpam-6074	186	1	then	then	ADV
ejpam-6074	186	2	x	x	SYM
ejpam-6074	186	3	∈	∈	PROPN
ejpam-6074	186	4	n2	n2	NOUN
ejpam-6074	186	5	g(w	g(w	PROPN
ejpam-6074	186	6	)	)	PUNCT
ejpam-6074	186	7	because	because	SCONJ
ejpam-6074	186	8	ephn(v;s	ephn(v;s	NUM
ejpam-6074	186	9	)	)	PUNCT
ejpam-6074	186	10	⊆	⊆	NUM
ejpam-6074	186	11	n2	n2	NOUN
ejpam-6074	186	12	g[w	g[w	PROPN
ejpam-6074	186	13	]	]	PUNCT
ejpam-6074	186	14	and	and	CCONJ
ejpam-6074	186	15	x	x	SYM
ejpam-6074	186	16	̸=	̸=	PROPN
ejpam-6074	186	17	w.	w.	PROPN
ejpam-6074	186	18	therefore	therefore	ADV
ejpam-6074	186	19	,	,	PUNCT
ejpam-6074	186	20	sw	sw	PROPN
ejpam-6074	186	21	is	be	AUX
ejpam-6074	186	22	a	a	DET
ejpam-6074	186	23	hop	hop	NOUN
ejpam-6074	186	24	dominating	dominating	NOUN
ejpam-6074	186	25	set	set	VERB
ejpam-6074	186	26	in	in	ADP
ejpam-6074	186	27	g.	g.	PROPN
ejpam-6074	186	28	since	since	SCONJ
ejpam-6074	186	29	this	this	PRON
ejpam-6074	186	30	is	be	AUX
ejpam-6074	186	31	true	true	ADJ
ejpam-6074	186	32	for	for	SCONJ
ejpam-6074	186	33	every	every	DET
ejpam-6074	186	34	v	v	NOUN
ejpam-6074	186	35	∈	∈	NOUN
ejpam-6074	186	36	s	s	VERB
ejpam-6074	186	37	such	such	ADJ
ejpam-6074	186	38	that	that	PRON
ejpam-6074	186	39	s	s	VERB
ejpam-6074	186	40	\	\	PROPN
ejpam-6074	186	41	{	{	PUNCT
ejpam-6074	186	42	v	v	NOUN
ejpam-6074	186	43	}	}	PUNCT
ejpam-6074	186	44	is	be	AUX
ejpam-6074	186	45	not	not	PART
ejpam-6074	186	46	hop	hop	NOUN
ejpam-6074	186	47	dominating	dominating	NOUN
ejpam-6074	186	48	,	,	PUNCT
ejpam-6074	186	49	it	it	PRON
ejpam-6074	186	50	follows	follow	VERB
ejpam-6074	186	51	that	that	SCONJ
ejpam-6074	186	52	s	s	VERB
ejpam-6074	186	53	is	be	AUX
ejpam-6074	186	54	a	a	DET
ejpam-6074	186	55	2	2	NUM
ejpam-6074	186	56	-	-	PUNCT
ejpam-6074	186	57	step	step	NOUN
ejpam-6074	186	58	movable	movable	ADJ
ejpam-6074	186	59	hop	hop	NOUN
ejpam-6074	186	60	dominating	dominating	NOUN
ejpam-6074	186	61	set	set	VERB
ejpam-6074	186	62	in	in	ADP
ejpam-6074	186	63	g.	g.	PROPN
ejpam-6074	186	64	corollary	corollary	PROPN
ejpam-6074	186	65	2	2	PROPN
ejpam-6074	186	66	.	.	PUNCT
ejpam-6074	187	1	let	let	VERB
ejpam-6074	187	2	g	g	PRON
ejpam-6074	187	3	be	be	AUX
ejpam-6074	187	4	a	a	DET
ejpam-6074	187	5	non	non	ADJ
ejpam-6074	187	6	-	-	ADJ
ejpam-6074	187	7	trivial	trivial	ADJ
ejpam-6074	187	8	graph	graph	NOUN
ejpam-6074	187	9	and	and	CCONJ
ejpam-6074	187	10	let	let	VERB
ejpam-6074	187	11	s	s	PRON
ejpam-6074	187	12	be	be	AUX
ejpam-6074	187	13	a	a	DET
ejpam-6074	187	14	hop	hop	NOUN
ejpam-6074	187	15	dominating	dominating	NOUN
ejpam-6074	187	16	set	set	VERB
ejpam-6074	187	17	in	in	ADP
ejpam-6074	187	18	g.	g.	PROPN
ejpam-6074	187	19	if	if	SCONJ
ejpam-6074	187	20	each	each	PRON
ejpam-6074	187	21	v	v	ADP
ejpam-6074	187	22	∈	∈	NOUN
ejpam-6074	187	23	s	s	PART
ejpam-6074	187	24	satisfies	satisfie	NOUN
ejpam-6074	187	25	the	the	DET
ejpam-6074	187	26	property	property	NOUN
ejpam-6074	187	27	that	that	PRON
ejpam-6074	187	28	|ephn(v;s)|	|ephn(v;s)|	PROPN
ejpam-6074	187	29	≤	≤	ADV
ejpam-6074	187	30	1	1	NUM
ejpam-6074	187	31	or	or	CCONJ
ejpam-6074	187	32	|ephn(v;s)|	|ephn(v;s)|	X
ejpam-6074	187	33	≥	≥	NOUN
ejpam-6074	187	34	2	2	NUM
ejpam-6074	187	35	such	such	ADJ
ejpam-6074	187	36	that	that	SCONJ
ejpam-6074	187	37	there	there	PRON
ejpam-6074	187	38	exists	exist	VERB
ejpam-6074	187	39	q	q	PROPN
ejpam-6074	187	40	∈	∈	PROPN
ejpam-6074	187	41	ephn(v;s	ephn(v;s	NOUN
ejpam-6074	187	42	)	)	PUNCT
ejpam-6074	187	43	with	with	ADP
ejpam-6074	187	44	the	the	DET
ejpam-6074	187	45	property	property	NOUN
ejpam-6074	187	46	that	that	PRON
ejpam-6074	187	47	dg(q	dg(q	NOUN
ejpam-6074	187	48	,	,	PUNCT
ejpam-6074	187	49	w	w	NOUN
ejpam-6074	187	50	)	)	PUNCT
ejpam-6074	187	51	=	=	SYM
ejpam-6074	187	52	2	2	NUM
ejpam-6074	187	53	for	for	ADP
ejpam-6074	187	54	every	every	DET
ejpam-6074	187	55	w	w	PROPN
ejpam-6074	187	56	∈	∈	PROPN
ejpam-6074	187	57	ephn(v;s	ephn(v;s	NOUN
ejpam-6074	187	58	)	)	PUNCT
ejpam-6074	187	59	\	\	NOUN
ejpam-6074	188	1	{	{	PUNCT
ejpam-6074	188	2	q	q	NOUN
ejpam-6074	188	3	}	}	PUNCT
ejpam-6074	188	4	,	,	PUNCT
ejpam-6074	188	5	then	then	ADV
ejpam-6074	188	6	s	s	VERB
ejpam-6074	188	7	is	be	AUX
ejpam-6074	188	8	2	2	NUM
ejpam-6074	188	9	-	-	PUNCT
ejpam-6074	188	10	step	step	NOUN
ejpam-6074	188	11	movable	movable	ADJ
ejpam-6074	188	12	hop	hop	NOUN
ejpam-6074	188	13	dominating	dominating	NOUN
ejpam-6074	188	14	in	in	ADP
ejpam-6074	188	15	g.	g.	PROPN
ejpam-6074	188	16	proof	proof	PROPN
ejpam-6074	188	17	.	.	PUNCT
ejpam-6074	189	1	suppose	suppose	VERB
ejpam-6074	189	2	s	s	PRON
ejpam-6074	189	3	satisfies	satisfie	NOUN
ejpam-6074	189	4	the	the	DET
ejpam-6074	189	5	given	give	VERB
ejpam-6074	189	6	property	property	NOUN
ejpam-6074	189	7	.	.	PUNCT
ejpam-6074	190	1	let	let	VERB
ejpam-6074	190	2	v	v	NUM
ejpam-6074	190	3	∈	∈	PROPN
ejpam-6074	190	4	s	s	PART
ejpam-6074	190	5	and	and	CCONJ
ejpam-6074	190	6	suppose	suppose	VERB
ejpam-6074	190	7	s	s	VERB
ejpam-6074	190	8	\	\	PROPN
ejpam-6074	190	9	{	{	PUNCT
ejpam-6074	190	10	v	v	NOUN
ejpam-6074	190	11	}	}	PUNCT
ejpam-6074	190	12	is	be	AUX
ejpam-6074	190	13	not	not	PART
ejpam-6074	190	14	hop	hop	NOUN
ejpam-6074	190	15	dominating	dominating	NOUN
ejpam-6074	190	16	.	.	PUNCT
ejpam-6074	191	1	since	since	SCONJ
ejpam-6074	191	2	γ(h	γ(h	NOUN
ejpam-6074	191	3	)	)	PUNCT
ejpam-6074	191	4	̸=	̸=	PROPN
ejpam-6074	191	5	1	1	NUM
ejpam-6074	191	6	for	for	ADP
ejpam-6074	191	7	every	every	DET
ejpam-6074	191	8	component	component	NOUN
ejpam-6074	191	9	h	h	NOUN
ejpam-6074	191	10	of	of	ADP
ejpam-6074	191	11	g	g	PROPN
ejpam-6074	191	12	,	,	PUNCT
ejpam-6074	191	13	|n2	|n2	PROPN
ejpam-6074	191	14	g(v)|	g(v)|	NOUN
ejpam-6074	191	15	̸=	̸=	PROPN
ejpam-6074	191	16	0	0	NUM
ejpam-6074	191	17	.	.	PUNCT
ejpam-6074	192	1	suppose	suppose	VERB
ejpam-6074	192	2	n2	n2	ADJ
ejpam-6074	192	3	g(v)∩(v	g(v)∩(v	X
ejpam-6074	192	4	(	(	PUNCT
ejpam-6074	192	5	g)\s	g)\s	NOUN
ejpam-6074	192	6	)	)	PUNCT
ejpam-6074	192	7	=	=	NOUN
ejpam-6074	193	1	∅	∅	NOUN
ejpam-6074	193	2	,	,	PUNCT
ejpam-6074	193	3	i.e.	i.e.	X
ejpam-6074	193	4	,	,	PUNCT
ejpam-6074	193	5	n2	n2	ADJ
ejpam-6074	193	6	g(v	g(v	X
ejpam-6074	193	7	)	)	PUNCT
ejpam-6074	193	8	⊆	⊆	NUM
ejpam-6074	193	9	s	s	NOUN
ejpam-6074	193	10	\{v	\{v	ADJ
ejpam-6074	193	11	}	}	PUNCT
ejpam-6074	193	12	.	.	PUNCT
ejpam-6074	194	1	this	this	PRON
ejpam-6074	194	2	and	and	CCONJ
ejpam-6074	194	3	the	the	DET
ejpam-6074	194	4	fact	fact	NOUN
ejpam-6074	194	5	that	that	SCONJ
ejpam-6074	194	6	s	s	VERB
ejpam-6074	194	7	is	be	AUX
ejpam-6074	194	8	hop	hop	NOUN
ejpam-6074	194	9	dominating	dominating	NOUN
ejpam-6074	194	10	imply	imply	ADV
ejpam-6074	194	11	that	that	PRON
ejpam-6074	194	12	s	s	VERB
ejpam-6074	194	13	\	\	PROPN
ejpam-6074	194	14	{	{	PUNCT
ejpam-6074	194	15	v	v	NOUN
ejpam-6074	194	16	}	}	PUNCT
ejpam-6074	194	17	is	be	AUX
ejpam-6074	194	18	hop	hop	NOUN
ejpam-6074	194	19	dominating	dominating	NOUN
ejpam-6074	194	20	,	,	PUNCT
ejpam-6074	194	21	a	a	DET
ejpam-6074	194	22	contradiction	contradiction	NOUN
ejpam-6074	194	23	.	.	PUNCT
ejpam-6074	195	1	thus	thus	ADV
ejpam-6074	195	2	,	,	PUNCT
ejpam-6074	195	3	n2	n2	ADJ
ejpam-6074	195	4	g(v	g(v	X
ejpam-6074	195	5	)	)	PUNCT
ejpam-6074	195	6	∩	∩	NOUN
ejpam-6074	195	7	(	(	PUNCT
ejpam-6074	195	8	v	v	NOUN
ejpam-6074	195	9	(	(	PUNCT
ejpam-6074	195	10	g	g	NOUN
ejpam-6074	195	11	)	)	PUNCT
ejpam-6074	195	12	\	\	PROPN
ejpam-6074	196	1	s	s	X
ejpam-6074	196	2	)	)	PUNCT
ejpam-6074	196	3	̸=	̸=	PROPN
ejpam-6074	196	4	∅.	∅.	ADV
ejpam-6074	196	5	if	if	SCONJ
ejpam-6074	196	6	|ephn(v;s)|	|ephn(v;s)|	PROPN
ejpam-6074	196	7	=	=	SYM
ejpam-6074	196	8	0	0	PROPN
ejpam-6074	196	9	,	,	PUNCT
ejpam-6074	196	10	then	then	ADV
ejpam-6074	196	11	ephn(v;s	ephn(v;s	VERB
ejpam-6074	196	12	)	)	PUNCT
ejpam-6074	196	13	⊆	⊆	NUM
ejpam-6074	196	14	n2	n2	NOUN
ejpam-6074	196	15	g[u	g[u	PROPN
ejpam-6074	196	16	]	]	PUNCT
ejpam-6074	196	17	for	for	ADP
ejpam-6074	196	18	each	each	DET
ejpam-6074	196	19	u	u	PROPN
ejpam-6074	196	20	∈	∈	PROPN
ejpam-6074	196	21	n2	n2	ADJ
ejpam-6074	196	22	g(v	g(v	PROPN
ejpam-6074	196	23	)	)	PUNCT
ejpam-6074	196	24	∩	∩	NOUN
ejpam-6074	196	25	(	(	PUNCT
ejpam-6074	196	26	v	v	NOUN
ejpam-6074	196	27	(	(	PUNCT
ejpam-6074	196	28	g	g	NOUN
ejpam-6074	196	29	)	)	PUNCT
ejpam-6074	196	30	\	\	PROPN
ejpam-6074	196	31	s	s	X
ejpam-6074	196	32	)	)	PUNCT
ejpam-6074	196	33	.	.	PUNCT
ejpam-6074	197	1	suppose	suppose	VERB
ejpam-6074	197	2	|ephn(v;s)|	|ephn(v;s)|	PROPN
ejpam-6074	197	3	=	=	NOUN
ejpam-6074	197	4	1	1	NUM
ejpam-6074	197	5	,	,	PUNCT
ejpam-6074	197	6	say	say	VERB
ejpam-6074	197	7	xv	xv	PROPN
ejpam-6074	197	8	∈	∈	PROPN
ejpam-6074	197	9	ephn(v;s	ephn(v;s	NOUN
ejpam-6074	197	10	)	)	PUNCT
ejpam-6074	197	11	.	.	PUNCT
ejpam-6074	198	1	then	then	ADV
ejpam-6074	198	2	xv	xv	PROPN
ejpam-6074	198	3	∈	∈	PROPN
ejpam-6074	198	4	(	(	PUNCT
ejpam-6074	198	5	v	v	NOUN
ejpam-6074	198	6	(	(	PUNCT
ejpam-6074	198	7	g	g	NOUN
ejpam-6074	198	8	)	)	PUNCT
ejpam-6074	198	9	\	\	PROPN
ejpam-6074	198	10	s	s	X
ejpam-6074	198	11	)	)	PUNCT
ejpam-6074	198	12	∩	∩	ADJ
ejpam-6074	198	13	n2	n2	ADJ
ejpam-6074	198	14	g(v	g(v	PROPN
ejpam-6074	198	15	)	)	PUNCT
ejpam-6074	198	16	and	and	CCONJ
ejpam-6074	198	17	ephn(v;s	ephn(v;s	NUM
ejpam-6074	198	18	)	)	PUNCT
ejpam-6074	198	19	=	=	PRON
ejpam-6074	198	20	{	{	PUNCT
ejpam-6074	198	21	xv	xv	PROPN
ejpam-6074	198	22	}	}	PUNCT
ejpam-6074	198	23	⊆	⊆	NUM
ejpam-6074	198	24	n2	n2	PROPN
ejpam-6074	198	25	g[xv	g[xv	PROPN
ejpam-6074	198	26	]	]	PUNCT
ejpam-6074	198	27	.	.	PUNCT
ejpam-6074	199	1	finally	finally	ADV
ejpam-6074	199	2	,	,	PUNCT
ejpam-6074	199	3	suppose	suppose	VERB
ejpam-6074	199	4	|ephn(v;s)|	|ephn(v;s)|	PROPN
ejpam-6074	199	5	≥	≥	NOUN
ejpam-6074	199	6	2	2	NUM
ejpam-6074	199	7	such	such	ADJ
ejpam-6074	199	8	that	that	SCONJ
ejpam-6074	199	9	there	there	PRON
ejpam-6074	199	10	exists	exist	VERB
ejpam-6074	199	11	q	q	PROPN
ejpam-6074	199	12	∈	∈	PROPN
ejpam-6074	199	13	ephn(v	ephn(v	NOUN
ejpam-6074	199	14	:	:	PUNCT
ejpam-6074	199	15	s	s	X
ejpam-6074	199	16	)	)	PUNCT
ejpam-6074	199	17	such	such	ADJ
ejpam-6074	199	18	that	that	PRON
ejpam-6074	199	19	dg(q	dg(q	NOUN
ejpam-6074	199	20	,	,	PUNCT
ejpam-6074	199	21	w	w	NOUN
ejpam-6074	199	22	)	)	PUNCT
ejpam-6074	199	23	=	=	SYM
ejpam-6074	199	24	2	2	NUM
ejpam-6074	199	25	for	for	ADP
ejpam-6074	199	26	every	every	DET
ejpam-6074	199	27	w	w	PROPN
ejpam-6074	199	28	∈	∈	PROPN
ejpam-6074	199	29	ephn(v;s	ephn(v;s	NOUN
ejpam-6074	199	30	)	)	PUNCT
ejpam-6074	199	31	\	\	NOUN
ejpam-6074	199	32	{	{	PUNCT
ejpam-6074	199	33	q	q	NOUN
ejpam-6074	199	34	}	}	PUNCT
ejpam-6074	199	35	.	.	PUNCT
ejpam-6074	200	1	then	then	ADV
ejpam-6074	200	2	q	q	PROPN
ejpam-6074	200	3	∈	∈	PROPN
ejpam-6074	200	4	(	(	PUNCT
ejpam-6074	200	5	v	v	NOUN
ejpam-6074	200	6	(	(	PUNCT
ejpam-6074	200	7	g	g	NOUN
ejpam-6074	200	8	)	)	PUNCT
ejpam-6074	200	9	\	\	PROPN
ejpam-6074	200	10	s	s	X
ejpam-6074	200	11	)	)	PUNCT
ejpam-6074	200	12	∩	∩	ADJ
ejpam-6074	200	13	n2	n2	ADJ
ejpam-6074	200	14	g(v	g(v	PROPN
ejpam-6074	200	15	)	)	PUNCT
ejpam-6074	200	16	.	.	PUNCT
ejpam-6074	201	1	r.	r.	PROPN
ejpam-6074	201	2	estrella	estrella	PROPN
ejpam-6074	201	3	,	,	PUNCT
ejpam-6074	201	4	gina	gina	PROPN
ejpam-6074	201	5	m.	m.	PROPN
ejpam-6074	201	6	malacas	malacas	PROPN
ejpam-6074	201	7	,	,	PUNCT
ejpam-6074	201	8	s.	s.	PROPN
ejpam-6074	201	9	canoy	canoy	PROPN
ejpam-6074	201	10	jr	jr	PROPN
ejpam-6074	201	11	.	.	PROPN
ejpam-6074	201	12	/	/	SYM
ejpam-6074	201	13	eur	eur	PROPN
ejpam-6074	201	14	.	.	PUNCT
ejpam-6074	202	1	j.	j.	PROPN
ejpam-6074	202	2	pure	pure	PROPN
ejpam-6074	202	3	appl	appl	PROPN
ejpam-6074	202	4	.	.	PROPN
ejpam-6074	202	5	math	math	PROPN
ejpam-6074	202	6	,	,	PUNCT
ejpam-6074	202	7	18	18	NUM
ejpam-6074	202	8	(	(	PUNCT
ejpam-6074	202	9	2	2	NUM
ejpam-6074	202	10	)	)	PUNCT
ejpam-6074	202	11	(	(	PUNCT
ejpam-6074	202	12	2025	2025	NUM
ejpam-6074	202	13	)	)	PUNCT
ejpam-6074	202	14	,	,	PUNCT
ejpam-6074	202	15	6074	6074	NUM
ejpam-6074	202	16	6	6	NUM
ejpam-6074	202	17	of	of	ADP
ejpam-6074	202	18	15	15	NUM
ejpam-6074	202	19	moreover	moreover	ADV
ejpam-6074	202	20	,	,	PUNCT
ejpam-6074	202	21	since	since	SCONJ
ejpam-6074	202	22	dg(q	dg(q	NUM
ejpam-6074	202	23	,	,	PUNCT
ejpam-6074	202	24	w	w	NOUN
ejpam-6074	202	25	)	)	PUNCT
ejpam-6074	202	26	=	=	SYM
ejpam-6074	202	27	2	2	NUM
ejpam-6074	202	28	for	for	ADP
ejpam-6074	202	29	every	every	DET
ejpam-6074	202	30	w	w	PROPN
ejpam-6074	202	31	∈	∈	PROPN
ejpam-6074	202	32	ephn(v;s	ephn(v;s	NOUN
ejpam-6074	202	33	)	)	PUNCT
ejpam-6074	202	34	\	\	NOUN
ejpam-6074	202	35	{	{	PUNCT
ejpam-6074	202	36	q	q	NOUN
ejpam-6074	202	37	}	}	PUNCT
ejpam-6074	203	1	,	,	PUNCT
ejpam-6074	203	2	it	it	PRON
ejpam-6074	203	3	follows	follow	VERB
ejpam-6074	203	4	that	that	SCONJ
ejpam-6074	203	5	ephn(v;s	ephn(v;s	NOUN
ejpam-6074	203	6	)	)	PUNCT
ejpam-6074	203	7	⊆	⊆	NUM
ejpam-6074	203	8	n2	n2	NOUN
ejpam-6074	203	9	g[q	g[q	NOUN
ejpam-6074	203	10	]	]	PUNCT
ejpam-6074	203	11	.	.	PUNCT
ejpam-6074	204	1	therefore	therefore	ADV
ejpam-6074	204	2	,	,	PUNCT
ejpam-6074	204	3	s	s	VERB
ejpam-6074	204	4	is	be	AUX
ejpam-6074	204	5	a	a	DET
ejpam-6074	204	6	2	2	NUM
ejpam-6074	204	7	-	-	PUNCT
ejpam-6074	204	8	step	step	NOUN
ejpam-6074	204	9	movable	movable	ADJ
ejpam-6074	204	10	hop	hop	NOUN
ejpam-6074	204	11	dominating	dominating	NOUN
ejpam-6074	204	12	set	set	VERB
ejpam-6074	204	13	in	in	ADP
ejpam-6074	204	14	g	g	NOUN
ejpam-6074	204	15	by	by	ADP
ejpam-6074	204	16	theorem	theorem	ADJ
ejpam-6074	204	17	3	3	NUM
ejpam-6074	204	18	.	.	PUNCT
ejpam-6074	204	19	theorem	theorem	NOUN
ejpam-6074	204	20	4	4	NUM
ejpam-6074	204	21	.	.	PUNCT
ejpam-6074	205	1	let	let	VERB
ejpam-6074	205	2	g	g	PRON
ejpam-6074	205	3	be	be	AUX
ejpam-6074	205	4	a	a	DET
ejpam-6074	205	5	graph	graph	NOUN
ejpam-6074	205	6	of	of	ADP
ejpam-6074	205	7	order	order	NOUN
ejpam-6074	205	8	n	n	PRON
ejpam-6074	205	9	≥	≥	NOUN
ejpam-6074	205	10	4	4	NUM
ejpam-6074	205	11	.	.	PUNCT
ejpam-6074	206	1	then	then	ADV
ejpam-6074	206	2	2	2	NUM
ejpam-6074	206	3	≤	≤	NUM
ejpam-6074	206	4	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	206	5	)	)	PUNCT
ejpam-6074	206	6	≤	≤	NOUN
ejpam-6074	206	7	n	n	CCONJ
ejpam-6074	206	8	−	−	PROPN
ejpam-6074	206	9	2	2	NUM
ejpam-6074	206	10	.	.	PUNCT
ejpam-6074	207	1	moreover	moreover	ADV
ejpam-6074	207	2	,	,	PUNCT
ejpam-6074	207	3	each	each	PRON
ejpam-6074	207	4	of	of	ADP
ejpam-6074	207	5	the	the	DET
ejpam-6074	207	6	following	follow	VERB
ejpam-6074	207	7	holds	hold	VERB
ejpam-6074	207	8	:	:	PUNCT
ejpam-6074	207	9	(	(	PUNCT
ejpam-6074	207	10	i	i	NOUN
ejpam-6074	207	11	)	)	PUNCT
ejpam-6074	207	12	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	207	13	)	)	PUNCT
ejpam-6074	207	14	=	=	SYM
ejpam-6074	207	15	2	2	NUM
ejpam-6074	207	16	if	if	SCONJ
ejpam-6074	207	17	and	and	CCONJ
ejpam-6074	207	18	only	only	ADV
ejpam-6074	207	19	if	if	SCONJ
ejpam-6074	207	20	there	there	PRON
ejpam-6074	207	21	exist	exist	VERB
ejpam-6074	207	22	distinct	distinct	ADJ
ejpam-6074	207	23	vertices	vertex	NOUN
ejpam-6074	207	24	p	p	X
ejpam-6074	207	25	,	,	PUNCT
ejpam-6074	207	26	q	q	NOUN
ejpam-6074	207	27	,	,	PUNCT
ejpam-6074	207	28	vp	vp	PROPN
ejpam-6074	207	29	,	,	PUNCT
ejpam-6074	207	30	vq	vq	PROPN
ejpam-6074	207	31	∈	∈	PROPN
ejpam-6074	207	32	v	v	ADP
ejpam-6074	207	33	(	(	PUNCT
ejpam-6074	207	34	g	g	NOUN
ejpam-6074	207	35	)	)	PUNCT
ejpam-6074	207	36	satisfying	satisfy	VERB
ejpam-6074	207	37	the	the	DET
ejpam-6074	207	38	following	follow	VERB
ejpam-6074	207	39	conditions	condition	NOUN
ejpam-6074	207	40	:	:	PUNCT
ejpam-6074	207	41	(	(	PUNCT
ejpam-6074	207	42	i1	i1	PROPN
ejpam-6074	207	43	)	)	PUNCT
ejpam-6074	207	44	n2	n2	PROPN
ejpam-6074	207	45	g[{p	g[{p	PROPN
ejpam-6074	207	46	,	,	PUNCT
ejpam-6074	207	47	q	q	NOUN
ejpam-6074	207	48	}	}	PUNCT
ejpam-6074	207	49	]	]	PUNCT
ejpam-6074	207	50	=	=	SYM
ejpam-6074	207	51	v	v	X
ejpam-6074	207	52	(	(	PUNCT
ejpam-6074	207	53	g	g	NOUN
ejpam-6074	207	54	)	)	PUNCT
ejpam-6074	207	55	,	,	PUNCT
ejpam-6074	207	56	i.e.	i.e.	X
ejpam-6074	207	57	,	,	PUNCT
ejpam-6074	207	58	{	{	PUNCT
ejpam-6074	207	59	p	p	X
ejpam-6074	207	60	,	,	PUNCT
ejpam-6074	207	61	q	q	ADJ
ejpam-6074	207	62	}	}	PUNCT
ejpam-6074	207	63	is	be	AUX
ejpam-6074	207	64	hop	hop	NOUN
ejpam-6074	207	65	dominating	dominate	VERB
ejpam-6074	207	66	in	in	ADP
ejpam-6074	207	67	g.	g.	PROPN
ejpam-6074	207	68	(	(	PUNCT
ejpam-6074	207	69	i2	i2	PROPN
ejpam-6074	207	70	)	)	PUNCT
ejpam-6074	207	71	dg(p	dg(p	NOUN
ejpam-6074	207	72	,	,	PUNCT
ejpam-6074	207	73	vp	vp	NOUN
ejpam-6074	207	74	)	)	PUNCT
ejpam-6074	207	75	=	=	SYM
ejpam-6074	207	76	dg(q	dg(q	PROPN
ejpam-6074	207	77	,	,	PUNCT
ejpam-6074	207	78	vq	vq	NOUN
ejpam-6074	207	79	)	)	PUNCT
ejpam-6074	207	80	=	=	SYM
ejpam-6074	207	81	2	2	NUM
ejpam-6074	207	82	,	,	PUNCT
ejpam-6074	207	83	v	v	NOUN
ejpam-6074	207	84	(	(	PUNCT
ejpam-6074	207	85	g	g	NOUN
ejpam-6074	207	86	)	)	PUNCT
ejpam-6074	207	87	\	\	PUNCT
ejpam-6074	208	1	(	(	PUNCT
ejpam-6074	208	2	n2	n2	ADJ
ejpam-6074	208	3	g[q]∪	g[q]∪	NOUN
ejpam-6074	208	4	{	{	PUNCT
ejpam-6074	208	5	p	p	NOUN
ejpam-6074	208	6	}	}	PUNCT
ejpam-6074	208	7	)	)	PUNCT
ejpam-6074	208	8	⊆	⊆	NUM
ejpam-6074	208	9	n2	n2	NOUN
ejpam-6074	208	10	g[vp	g[vp	PROPN
ejpam-6074	208	11	]	]	X
ejpam-6074	208	12	,	,	PUNCT
ejpam-6074	208	13	and	and	CCONJ
ejpam-6074	208	14	v	v	X
ejpam-6074	208	15	(	(	PUNCT
ejpam-6074	208	16	g	g	NOUN
ejpam-6074	208	17	)	)	PUNCT
ejpam-6074	208	18	\	\	PUNCT
ejpam-6074	209	1	(	(	PUNCT
ejpam-6074	209	2	n2	n2	PROPN
ejpam-6074	209	3	g[p]∪	g[p]∪	PROPN
ejpam-6074	209	4	{	{	PUNCT
ejpam-6074	209	5	q	q	NOUN
ejpam-6074	209	6	}	}	PUNCT
ejpam-6074	209	7	)	)	PUNCT
ejpam-6074	209	8	⊆	⊆	NUM
ejpam-6074	209	9	n2	n2	NOUN
ejpam-6074	209	10	g[vq	g[vq	PROPN
ejpam-6074	209	11	]	]	PUNCT
ejpam-6074	209	12	.	.	PUNCT
ejpam-6074	210	1	(	(	PUNCT
ejpam-6074	210	2	ii	ii	NOUN
ejpam-6074	210	3	)	)	PUNCT
ejpam-6074	210	4	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	210	5	)	)	PUNCT
ejpam-6074	211	1	=	=	PUNCT
ejpam-6074	211	2	n−	n−	NOUN
ejpam-6074	211	3	2	2	NUM
ejpam-6074	211	4	if	if	SCONJ
ejpam-6074	211	5	and	and	CCONJ
ejpam-6074	211	6	only	only	ADV
ejpam-6074	211	7	if	if	SCONJ
ejpam-6074	211	8	g	g	PROPN
ejpam-6074	211	9	satisfies	satisfy	VERB
ejpam-6074	211	10	the	the	DET
ejpam-6074	211	11	following	follow	VERB
ejpam-6074	211	12	conditions	condition	NOUN
ejpam-6074	211	13	:	:	PUNCT
ejpam-6074	211	14	(	(	PUNCT
ejpam-6074	211	15	j1	j1	PROPN
ejpam-6074	211	16	)	)	PUNCT
ejpam-6074	211	17	there	there	PRON
ejpam-6074	211	18	exist	exist	VERB
ejpam-6074	211	19	distinct	distinct	ADJ
ejpam-6074	211	20	vertices	vertex	NOUN
ejpam-6074	211	21	v	v	NOUN
ejpam-6074	211	22	and	and	CCONJ
ejpam-6074	211	23	w	w	NOUN
ejpam-6074	211	24	of	of	ADP
ejpam-6074	211	25	g	g	NOUN
ejpam-6074	211	26	such	such	ADJ
ejpam-6074	211	27	that	that	PRON
ejpam-6074	211	28	dg(v	dg(v	ADJ
ejpam-6074	211	29	,	,	PUNCT
ejpam-6074	211	30	w	w	NOUN
ejpam-6074	211	31	)	)	PUNCT
ejpam-6074	211	32	=	=	SYM
ejpam-6074	211	33	2	2	NUM
ejpam-6074	212	1	whenever	whenever	SCONJ
ejpam-6074	212	2	|ephn(x;v	|ephn(x;v	X
ejpam-6074	212	3	(	(	PUNCT
ejpam-6074	212	4	g	g	NOUN
ejpam-6074	212	5	)	)	PUNCT
ejpam-6074	212	6	\	\	NOUN
ejpam-6074	212	7	{	{	PUNCT
ejpam-6074	212	8	v	v	NOUN
ejpam-6074	212	9	,	,	PUNCT
ejpam-6074	212	10	w})|	w})|	NOUN
ejpam-6074	212	11	=	=	SYM
ejpam-6074	212	12	2	2	NUM
ejpam-6074	212	13	for	for	ADP
ejpam-6074	212	14	some	some	PRON
ejpam-6074	212	15	x	x	NOUN
ejpam-6074	212	16	/∈	/∈	PUNCT
ejpam-6074	212	17	{	{	PUNCT
ejpam-6074	212	18	v	v	NOUN
ejpam-6074	212	19	,	,	PUNCT
ejpam-6074	212	20	w	w	NOUN
ejpam-6074	212	21	}	}	PUNCT
ejpam-6074	212	22	;	;	PUNCT
ejpam-6074	212	23	and	and	CCONJ
ejpam-6074	212	24	(	(	PUNCT
ejpam-6074	212	25	j2	j2	PROPN
ejpam-6074	212	26	)	)	PUNCT
ejpam-6074	212	27	for	for	ADP
ejpam-6074	212	28	each	each	DET
ejpam-6074	212	29	hop	hop	NOUN
ejpam-6074	212	30	dominating	dominating	NOUN
ejpam-6074	212	31	set	set	NOUN
ejpam-6074	212	32	s	s	PRON
ejpam-6074	212	33	in	in	ADP
ejpam-6074	212	34	g	g	NOUN
ejpam-6074	212	35	with	with	ADP
ejpam-6074	212	36	|s|	|s|	NOUN
ejpam-6074	212	37	<	<	X
ejpam-6074	212	38	n	n	CCONJ
ejpam-6074	212	39	−	−	PROPN
ejpam-6074	212	40	2	2	NUM
ejpam-6074	212	41	,	,	PUNCT
ejpam-6074	212	42	|ephn(p;s)|	|ephn(p;s)|	X
ejpam-6074	212	43	≥	≥	NOUN
ejpam-6074	212	44	2	2	NUM
ejpam-6074	212	45	for	for	ADP
ejpam-6074	212	46	some	some	DET
ejpam-6074	212	47	p	p	NOUN
ejpam-6074	212	48	∈	∈	PROPN
ejpam-6074	212	49	s	s	NOUN
ejpam-6074	212	50	and	and	CCONJ
ejpam-6074	212	51	there	there	PRON
ejpam-6074	212	52	exists	exist	VERB
ejpam-6074	212	53	no	no	DET
ejpam-6074	212	54	q	q	NOUN
ejpam-6074	212	55	∈	∈	PROPN
ejpam-6074	212	56	ephn(p;s	ephn(p;s	NOUN
ejpam-6074	212	57	)	)	PUNCT
ejpam-6074	212	58	such	such	ADJ
ejpam-6074	212	59	that	that	DET
ejpam-6074	212	60	dg(q	dg(q	NOUN
ejpam-6074	212	61	,	,	PUNCT
ejpam-6074	212	62	s	s	PART
ejpam-6074	212	63	)	)	PUNCT
ejpam-6074	212	64	=	=	SYM
ejpam-6074	212	65	2	2	NUM
ejpam-6074	212	66	for	for	ADP
ejpam-6074	212	67	all	all	DET
ejpam-6074	212	68	s	s	PART
ejpam-6074	212	69	∈	∈	NOUN
ejpam-6074	212	70	ephn(p;s	ephn(p;s	NOUN
ejpam-6074	212	71	)	)	PUNCT
ejpam-6074	212	72	\	\	NOUN
ejpam-6074	213	1	{	{	PUNCT
ejpam-6074	213	2	q	q	NOUN
ejpam-6074	213	3	}	}	PUNCT
ejpam-6074	213	4	.	.	PUNCT
ejpam-6074	214	1	proof	proof	NOUN
ejpam-6074	214	2	.	.	PUNCT
ejpam-6074	215	1	since	since	SCONJ
ejpam-6074	215	2	γh(g	γh(g	NOUN
ejpam-6074	215	3	)	)	PUNCT
ejpam-6074	215	4	≥	≥	NOUN
ejpam-6074	215	5	2	2	NUM
ejpam-6074	215	6	,	,	PUNCT
ejpam-6074	215	7	it	it	PRON
ejpam-6074	215	8	follows	follow	VERB
ejpam-6074	215	9	from	from	ADP
ejpam-6074	215	10	remark	remark	NOUN
ejpam-6074	215	11	2	2	NUM
ejpam-6074	215	12	that	that	SCONJ
ejpam-6074	215	13	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	215	14	)	)	PUNCT
ejpam-6074	215	15	≥	≥	NOUN
ejpam-6074	216	1	2	2	NUM
ejpam-6074	216	2	.	.	PUNCT
ejpam-6074	217	1	next	next	ADV
ejpam-6074	217	2	,	,	PUNCT
ejpam-6074	217	3	let	let	VERB
ejpam-6074	217	4	v	v	NUM
ejpam-6074	217	5	∈	∈	PROPN
ejpam-6074	217	6	v	v	NOUN
ejpam-6074	217	7	(	(	PUNCT
ejpam-6074	217	8	g	g	NOUN
ejpam-6074	217	9	)	)	PUNCT
ejpam-6074	217	10	.	.	PUNCT
ejpam-6074	218	1	since	since	SCONJ
ejpam-6074	218	2	γ(g	γ(g	PROPN
ejpam-6074	218	3	)	)	PUNCT
ejpam-6074	218	4	̸=	̸=	PROPN
ejpam-6074	218	5	1	1	NUM
ejpam-6074	218	6	,	,	PUNCT
ejpam-6074	218	7	|n2	|n2	PROPN
ejpam-6074	218	8	g(v)|	g(v)|	PROPN
ejpam-6074	218	9	≥	≥	NOUN
ejpam-6074	218	10	1	1	NUM
ejpam-6074	218	11	.	.	PUNCT
ejpam-6074	218	12	let	let	VERB
ejpam-6074	218	13	z	z	NOUN
ejpam-6074	218	14	∈	∈	PROPN
ejpam-6074	218	15	n2	n2	ADJ
ejpam-6074	218	16	g(v	g(v	PROPN
ejpam-6074	218	17	)	)	PUNCT
ejpam-6074	218	18	and	and	CCONJ
ejpam-6074	218	19	let	let	VERB
ejpam-6074	218	20	w	w	PROPN
ejpam-6074	218	21	∈	∈	PROPN
ejpam-6074	218	22	ng(v	ng(v	NOUN
ejpam-6074	218	23	)	)	PUNCT
ejpam-6074	218	24	∩ng(w	∩ng(w	PROPN
ejpam-6074	218	25	)	)	PUNCT
ejpam-6074	218	26	.	.	PUNCT
ejpam-6074	219	1	set	set	VERB
ejpam-6074	219	2	s	s	PART
ejpam-6074	219	3	=	=	X
ejpam-6074	219	4	v	v	PROPN
ejpam-6074	219	5	(	(	PUNCT
ejpam-6074	219	6	g)\{v	g)\{v	PROPN
ejpam-6074	219	7	,	,	PUNCT
ejpam-6074	219	8	w	w	NOUN
ejpam-6074	219	9	}	}	PUNCT
ejpam-6074	219	10	.	.	PUNCT
ejpam-6074	220	1	then	then	ADV
ejpam-6074	220	2	s	s	VERB
ejpam-6074	220	3	is	be	AUX
ejpam-6074	220	4	a	a	DET
ejpam-6074	220	5	hop	hop	NOUN
ejpam-6074	220	6	dominating	dominating	NOUN
ejpam-6074	220	7	set	set	VERB
ejpam-6074	220	8	in	in	ADP
ejpam-6074	220	9	g.	g.	PROPN
ejpam-6074	220	10	let	let	VERB
ejpam-6074	220	11	x	x	PROPN
ejpam-6074	220	12	∈	∈	PROPN
ejpam-6074	220	13	s.	s.	PROPN
ejpam-6074	220	14	if	if	SCONJ
ejpam-6074	220	15	x	x	PROPN
ejpam-6074	220	16	/∈	/∈	PUNCT
ejpam-6074	220	17	n2	n2	PROPN
ejpam-6074	220	18	g(v)∪n2	g(v)∪n2	PROPN
ejpam-6074	220	19	g(w	g(w	PROPN
ejpam-6074	220	20	)	)	PUNCT
ejpam-6074	220	21	,	,	PUNCT
ejpam-6074	220	22	then	then	ADV
ejpam-6074	220	23	let	let	VERB
ejpam-6074	220	24	s1	s1	PROPN
ejpam-6074	220	25	=	=	SYM
ejpam-6074	220	26	s	s	PART
ejpam-6074	220	27	\	\	X
ejpam-6074	220	28	{	{	PUNCT
ejpam-6074	220	29	x	x	NOUN
ejpam-6074	220	30	}	}	PUNCT
ejpam-6074	220	31	=	=	SYM
ejpam-6074	220	32	v	v	NOUN
ejpam-6074	220	33	(	(	PUNCT
ejpam-6074	220	34	g	g	NOUN
ejpam-6074	220	35	)	)	PUNCT
ejpam-6074	220	36	\	\	NOUN
ejpam-6074	221	1	{	{	PUNCT
ejpam-6074	221	2	x	x	NOUN
ejpam-6074	221	3	,	,	PUNCT
ejpam-6074	221	4	v	v	NOUN
ejpam-6074	221	5	,	,	PUNCT
ejpam-6074	221	6	w	w	NOUN
ejpam-6074	221	7	}	}	PUNCT
ejpam-6074	221	8	.	.	PUNCT
ejpam-6074	222	1	clearly	clearly	ADV
ejpam-6074	222	2	,	,	PUNCT
ejpam-6074	222	3	s1	s1	PROPN
ejpam-6074	222	4	is	be	AUX
ejpam-6074	222	5	hop	hop	NOUN
ejpam-6074	222	6	dominating	dominate	VERB
ejpam-6074	222	7	in	in	ADP
ejpam-6074	222	8	g.	g.	PROPN
ejpam-6074	222	9	suppose	suppose	VERB
ejpam-6074	222	10	x	x	X
ejpam-6074	222	11	∈	∈	PROPN
ejpam-6074	222	12	n2	n2	ADJ
ejpam-6074	222	13	g(v	g(v	PROPN
ejpam-6074	222	14	)	)	PUNCT
ejpam-6074	222	15	∪	∪	ADP
ejpam-6074	222	16	n2	n2	ADJ
ejpam-6074	222	17	g(w	g(w	PROPN
ejpam-6074	222	18	)	)	PUNCT
ejpam-6074	222	19	.	.	PUNCT
ejpam-6074	223	1	if	if	SCONJ
ejpam-6074	223	2	x	x	PROPN
ejpam-6074	223	3	∈	∈	PROPN
ejpam-6074	223	4	n2	n2	NOUN
ejpam-6074	223	5	g(w	g(w	PROPN
ejpam-6074	223	6	)	)	PUNCT
ejpam-6074	223	7	\	\	PROPN
ejpam-6074	223	8	n2	n2	ADJ
ejpam-6074	223	9	g(v	g(v	PROPN
ejpam-6074	223	10	)	)	PUNCT
ejpam-6074	223	11	or	or	CCONJ
ejpam-6074	223	12	x	x	PUNCT
ejpam-6074	223	13	∈	∈	PROPN
ejpam-6074	223	14	n2	n2	ADJ
ejpam-6074	223	15	g(v	g(v	PROPN
ejpam-6074	223	16	)	)	PUNCT
ejpam-6074	223	17	∩	∩	NOUN
ejpam-6074	223	18	n2	n2	NOUN
ejpam-6074	223	19	g(w	g(w	PROPN
ejpam-6074	223	20	)	)	PUNCT
ejpam-6074	223	21	,	,	PUNCT
ejpam-6074	223	22	then	then	ADV
ejpam-6074	223	23	x	x	X
ejpam-6074	223	24	̸=	̸=	PROPN
ejpam-6074	223	25	z	z	NOUN
ejpam-6074	223	26	because	because	SCONJ
ejpam-6074	223	27	zw	zw	PROPN
ejpam-6074	223	28	∈	∈	PROPN
ejpam-6074	223	29	e(g	e(g	PROPN
ejpam-6074	223	30	)	)	PUNCT
ejpam-6074	223	31	.	.	PUNCT
ejpam-6074	224	1	then	then	ADV
ejpam-6074	224	2	(	(	PUNCT
ejpam-6074	224	3	s	s	NOUN
ejpam-6074	224	4	\	\	X
ejpam-6074	224	5	{	{	PUNCT
ejpam-6074	224	6	x	x	NOUN
ejpam-6074	224	7	}	}	PUNCT
ejpam-6074	224	8	)	)	PUNCT
ejpam-6074	224	9	∪	∪	ADP
ejpam-6074	224	10	{	{	PUNCT
ejpam-6074	224	11	w	w	NOUN
ejpam-6074	224	12	}	}	PUNCT
ejpam-6074	224	13	=	=	SYM
ejpam-6074	224	14	v	v	NOUN
ejpam-6074	224	15	(	(	PUNCT
ejpam-6074	224	16	g	g	NOUN
ejpam-6074	224	17	)	)	PUNCT
ejpam-6074	224	18	\	\	NOUN
ejpam-6074	225	1	{	{	PUNCT
ejpam-6074	225	2	x	x	NOUN
ejpam-6074	225	3	,	,	PUNCT
ejpam-6074	225	4	v	v	NOUN
ejpam-6074	225	5	}	}	PUNCT
ejpam-6074	225	6	is	be	AUX
ejpam-6074	225	7	hop	hop	NOUN
ejpam-6074	225	8	dominating	dominate	VERB
ejpam-6074	225	9	in	in	ADP
ejpam-6074	225	10	g	g	PROPN
ejpam-6074	225	11	because	because	SCONJ
ejpam-6074	225	12	x	x	PROPN
ejpam-6074	225	13	∈	∈	PROPN
ejpam-6074	225	14	n2	n2	PROPN
ejpam-6074	225	15	g(w	g(w	PROPN
ejpam-6074	225	16	)	)	PUNCT
ejpam-6074	225	17	and	and	CCONJ
ejpam-6074	225	18	v	v	ADP
ejpam-6074	225	19	∈	∈	PROPN
ejpam-6074	225	20	n2	n2	NOUN
ejpam-6074	225	21	g(z	g(z	PROPN
ejpam-6074	225	22	)	)	PUNCT
ejpam-6074	225	23	.	.	PUNCT
ejpam-6074	226	1	if	if	SCONJ
ejpam-6074	226	2	x	x	X
ejpam-6074	226	3	∈	∈	PROPN
ejpam-6074	226	4	n2	n2	NOUN
ejpam-6074	226	5	g(v	g(v	PROPN
ejpam-6074	226	6	)	)	PUNCT
ejpam-6074	226	7	\n2	\n2	PROPN
ejpam-6074	226	8	g(w	g(w	PROPN
ejpam-6074	226	9	)	)	PUNCT
ejpam-6074	226	10	,	,	PUNCT
ejpam-6074	226	11	then	then	ADV
ejpam-6074	226	12	(	(	PUNCT
ejpam-6074	226	13	s	s	NOUN
ejpam-6074	226	14	\	\	X
ejpam-6074	226	15	{	{	PUNCT
ejpam-6074	226	16	x	x	NOUN
ejpam-6074	226	17	}	}	PUNCT
ejpam-6074	226	18	)	)	PUNCT
ejpam-6074	226	19	∪	∪	ADP
ejpam-6074	226	20	{	{	PUNCT
ejpam-6074	226	21	v	v	NOUN
ejpam-6074	226	22	}	}	PUNCT
ejpam-6074	226	23	=	=	SYM
ejpam-6074	226	24	v	v	NOUN
ejpam-6074	226	25	(	(	PUNCT
ejpam-6074	226	26	g	g	NOUN
ejpam-6074	226	27	)	)	PUNCT
ejpam-6074	226	28	\	\	NOUN
ejpam-6074	227	1	{	{	PUNCT
ejpam-6074	227	2	x	x	NOUN
ejpam-6074	227	3	,	,	PUNCT
ejpam-6074	227	4	w	w	NOUN
ejpam-6074	227	5	}	}	PUNCT
ejpam-6074	227	6	is	be	AUX
ejpam-6074	227	7	a	a	DET
ejpam-6074	227	8	hop	hop	NOUN
ejpam-6074	227	9	dominating	dominating	NOUN
ejpam-6074	227	10	in	in	ADP
ejpam-6074	227	11	g.	g.	PROPN
ejpam-6074	227	12	this	this	PRON
ejpam-6074	227	13	implies	imply	VERB
ejpam-6074	227	14	that	that	SCONJ
ejpam-6074	227	15	s	s	VERB
ejpam-6074	227	16	is	be	AUX
ejpam-6074	227	17	a	a	DET
ejpam-6074	227	18	2	2	NUM
ejpam-6074	227	19	-	-	PUNCT
ejpam-6074	227	20	step	step	NOUN
ejpam-6074	227	21	movable	movable	ADJ
ejpam-6074	227	22	hop	hop	NOUN
ejpam-6074	227	23	dominating	dominating	NOUN
ejpam-6074	227	24	set	set	VERB
ejpam-6074	227	25	in	in	ADP
ejpam-6074	227	26	g.	g.	PROPN
ejpam-6074	227	27	therefore	therefore	ADV
ejpam-6074	227	28	,	,	PUNCT
ejpam-6074	227	29	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	227	30	)	)	PUNCT
ejpam-6074	227	31	≤	≤	NUM
ejpam-6074	227	32	|s|	|s|	PROPN
ejpam-6074	227	33	=	=	SYM
ejpam-6074	227	34	n−	n−	NOUN
ejpam-6074	227	35	2	2	NUM
ejpam-6074	227	36	.	.	PUNCT
ejpam-6074	228	1	(	(	PUNCT
ejpam-6074	228	2	i	i	NOUN
ejpam-6074	228	3	)	)	PUNCT
ejpam-6074	228	4	suppose	suppose	VERB
ejpam-6074	228	5	γ2mh(g	γ2mh(g	NOUN
ejpam-6074	228	6	)	)	PUNCT
ejpam-6074	228	7	=	=	SYM
ejpam-6074	228	8	2	2	NUM
ejpam-6074	228	9	,	,	PUNCT
ejpam-6074	228	10	say	say	VERB
ejpam-6074	228	11	s	s	X
ejpam-6074	228	12	=	=	PUNCT
ejpam-6074	228	13	{	{	PUNCT
ejpam-6074	228	14	p	p	X
ejpam-6074	228	15	,	,	PUNCT
ejpam-6074	228	16	q	q	X
ejpam-6074	228	17	}	}	PUNCT
ejpam-6074	228	18	is	be	AUX
ejpam-6074	228	19	a	a	DET
ejpam-6074	228	20	γ2mh	γ2mh	PROPN
ejpam-6074	228	21	-	-	PUNCT
ejpam-6074	228	22	set	set	NOUN
ejpam-6074	228	23	of	of	ADP
ejpam-6074	228	24	g.	g.	PROPN
ejpam-6074	229	1	then	then	ADV
ejpam-6074	229	2	s	s	VERB
ejpam-6074	229	3	is	be	AUX
ejpam-6074	229	4	a	a	DET
ejpam-6074	229	5	hop	hop	NOUN
ejpam-6074	229	6	dominating	dominating	NOUN
ejpam-6074	229	7	set	set	NOUN
ejpam-6074	229	8	and	and	CCONJ
ejpam-6074	229	9	γh(g	γh(g	PUNCT
ejpam-6074	229	10	)	)	PUNCT
ejpam-6074	229	11	=	=	SYM
ejpam-6074	230	1	2	2	X
ejpam-6074	230	2	.	.	PUNCT
ejpam-6074	230	3	it	it	PRON
ejpam-6074	230	4	follows	follow	VERB
ejpam-6074	230	5	that	that	PRON
ejpam-6074	230	6	s	s	VERB
ejpam-6074	230	7	\	\	PROPN
ejpam-6074	230	8	{	{	PUNCT
ejpam-6074	230	9	p	p	NOUN
ejpam-6074	230	10	}	}	PUNCT
ejpam-6074	230	11	and	and	CCONJ
ejpam-6074	230	12	s	s	X
ejpam-6074	230	13	\	\	X
ejpam-6074	230	14	{	{	PUNCT
ejpam-6074	230	15	q	q	NOUN
ejpam-6074	230	16	}	}	PUNCT
ejpam-6074	230	17	are	be	AUX
ejpam-6074	230	18	not	not	PART
ejpam-6074	230	19	hop	hop	ADJ
ejpam-6074	230	20	dominating	dominating	NOUN
ejpam-6074	230	21	sets	set	NOUN
ejpam-6074	230	22	.	.	PUNCT
ejpam-6074	231	1	by	by	ADP
ejpam-6074	231	2	theorem	theorem	NOUN
ejpam-6074	231	3	3	3	NUM
ejpam-6074	231	4	,	,	PUNCT
ejpam-6074	231	5	there	there	PRON
ejpam-6074	231	6	exist	exist	VERB
ejpam-6074	231	7	vertices	vertex	NOUN
ejpam-6074	231	8	vp	vp	PROPN
ejpam-6074	231	9	∈	∈	PROPN
ejpam-6074	231	10	(	(	PUNCT
ejpam-6074	231	11	v	v	NOUN
ejpam-6074	231	12	(	(	PUNCT
ejpam-6074	231	13	g	g	NOUN
ejpam-6074	231	14	)	)	PUNCT
ejpam-6074	231	15	\	\	PROPN
ejpam-6074	232	1	s	s	X
ejpam-6074	232	2	)	)	PUNCT
ejpam-6074	232	3	∩	∩	ADJ
ejpam-6074	232	4	n2	n2	ADJ
ejpam-6074	232	5	g(p	g(p	PROPN
ejpam-6074	232	6	)	)	PUNCT
ejpam-6074	232	7	and	and	CCONJ
ejpam-6074	233	1	vq	vq	PROPN
ejpam-6074	233	2	∈	∈	PROPN
ejpam-6074	233	3	(	(	PUNCT
ejpam-6074	233	4	v	v	NOUN
ejpam-6074	233	5	(	(	PUNCT
ejpam-6074	233	6	g	g	NOUN
ejpam-6074	233	7	)	)	PUNCT
ejpam-6074	233	8	\	\	PROPN
ejpam-6074	234	1	s	s	X
ejpam-6074	234	2	)	)	PUNCT
ejpam-6074	234	3	∩	∩	ADJ
ejpam-6074	234	4	n2	n2	ADJ
ejpam-6074	234	5	g(q	g(q	NOUN
ejpam-6074	234	6	)	)	PUNCT
ejpam-6074	234	7	such	such	ADJ
ejpam-6074	234	8	that	that	DET
ejpam-6074	234	9	ephn(p;s	ephn(p;s	NOUN
ejpam-6074	234	10	)	)	PUNCT
ejpam-6074	234	11	⊆	⊆	NUM
ejpam-6074	234	12	n2	n2	NOUN
ejpam-6074	234	13	g[vp	g[vp	PROPN
ejpam-6074	234	14	]	]	X
ejpam-6074	234	15	and	and	CCONJ
ejpam-6074	234	16	ephn(q;s	ephn(q;	NOUN
ejpam-6074	234	17	)	)	PUNCT
ejpam-6074	234	18	⊆	⊆	NUM
ejpam-6074	234	19	n2	n2	NOUN
ejpam-6074	234	20	g[vq	g[vq	PROPN
ejpam-6074	234	21	]	]	PUNCT
ejpam-6074	234	22	.	.	PUNCT
ejpam-6074	235	1	now	now	ADV
ejpam-6074	235	2	let	let	VERB
ejpam-6074	235	3	a	a	DET
ejpam-6074	235	4	∈	∈	PROPN
ejpam-6074	235	5	ephn(p;s	ephn(p;s	NOUN
ejpam-6074	235	6	)	)	PUNCT
ejpam-6074	235	7	.	.	PUNCT
ejpam-6074	236	1	then	then	ADV
ejpam-6074	236	2	a	a	DET
ejpam-6074	236	3	∈	∈	PROPN
ejpam-6074	236	4	v	v	ADP
ejpam-6074	236	5	(	(	PUNCT
ejpam-6074	236	6	g	g	NOUN
ejpam-6074	236	7	)	)	PUNCT
ejpam-6074	236	8	\	\	NOUN
ejpam-6074	236	9	{	{	PUNCT
ejpam-6074	236	10	p	p	X
ejpam-6074	236	11	,	,	PUNCT
ejpam-6074	236	12	q	q	ADJ
ejpam-6074	236	13	}	}	PUNCT
ejpam-6074	236	14	and	and	CCONJ
ejpam-6074	236	15	n2	n2	PROPN
ejpam-6074	236	16	g(a)∩	g(a)∩	PROPN
ejpam-6074	236	17	{	{	PUNCT
ejpam-6074	236	18	p	p	X
ejpam-6074	236	19	,	,	PUNCT
ejpam-6074	236	20	q	q	NOUN
ejpam-6074	236	21	}	}	PUNCT
ejpam-6074	236	22	=	=	SYM
ejpam-6074	236	23	{	{	PUNCT
ejpam-6074	236	24	p	p	X
ejpam-6074	236	25	}	}	PUNCT
ejpam-6074	236	26	.	.	PUNCT
ejpam-6074	237	1	this	this	PRON
ejpam-6074	237	2	shows	show	VERB
ejpam-6074	237	3	that	that	SCONJ
ejpam-6074	237	4	a	a	DET
ejpam-6074	237	5	∈	∈	PROPN
ejpam-6074	237	6	v	v	NOUN
ejpam-6074	237	7	(	(	PUNCT
ejpam-6074	237	8	g	g	NOUN
ejpam-6074	237	9	)	)	PUNCT
ejpam-6074	237	10	\	\	PUNCT
ejpam-6074	237	11	(	(	PUNCT
ejpam-6074	237	12	n2	n2	ADJ
ejpam-6074	237	13	g[q]∪	g[q]∪	NOUN
ejpam-6074	237	14	{	{	PUNCT
ejpam-6074	237	15	p	p	NOUN
ejpam-6074	237	16	}	}	PUNCT
ejpam-6074	237	17	)	)	PUNCT
ejpam-6074	237	18	.	.	PUNCT
ejpam-6074	238	1	it	it	PRON
ejpam-6074	238	2	follows	follow	VERB
ejpam-6074	238	3	that	that	DET
ejpam-6074	238	4	ephn(p;s	ephn(p;s	NOUN
ejpam-6074	238	5	)	)	PUNCT
ejpam-6074	239	1	⊆	⊆	NUM
ejpam-6074	239	2	v	v	NOUN
ejpam-6074	239	3	(	(	PUNCT
ejpam-6074	239	4	g	g	NOUN
ejpam-6074	239	5	)	)	PUNCT
ejpam-6074	239	6	\	\	PUNCT
ejpam-6074	240	1	(	(	PUNCT
ejpam-6074	240	2	n2	n2	ADJ
ejpam-6074	240	3	g[q]∪	g[q]∪	NOUN
ejpam-6074	240	4	{	{	PUNCT
ejpam-6074	240	5	p	p	NOUN
ejpam-6074	240	6	}	}	PUNCT
ejpam-6074	240	7	)	)	PUNCT
ejpam-6074	240	8	.	.	PUNCT
ejpam-6074	241	1	next	next	ADV
ejpam-6074	241	2	,	,	PUNCT
ejpam-6074	241	3	let	let	VERB
ejpam-6074	241	4	b	b	X
ejpam-6074	241	5	∈	∈	PROPN
ejpam-6074	241	6	v	v	X
ejpam-6074	241	7	(	(	PUNCT
ejpam-6074	241	8	g	g	NOUN
ejpam-6074	241	9	)	)	PUNCT
ejpam-6074	241	10	\	\	PUNCT
ejpam-6074	242	1	(	(	PUNCT
ejpam-6074	242	2	n2	n2	ADJ
ejpam-6074	242	3	g[q]∪	g[q]∪	NOUN
ejpam-6074	242	4	{	{	PUNCT
ejpam-6074	242	5	p	p	NOUN
ejpam-6074	242	6	}	}	PUNCT
ejpam-6074	242	7	)	)	PUNCT
ejpam-6074	242	8	.	.	PUNCT
ejpam-6074	243	1	then	then	ADV
ejpam-6074	243	2	b	b	X
ejpam-6074	243	3	∈	∈	PROPN
ejpam-6074	243	4	v	v	ADP
ejpam-6074	243	5	(	(	PUNCT
ejpam-6074	243	6	g	g	NOUN
ejpam-6074	243	7	)	)	PUNCT
ejpam-6074	243	8	\n2	\n2	VERB
ejpam-6074	243	9	g(q	g(q	NOUN
ejpam-6074	243	10	)	)	PUNCT
ejpam-6074	243	11	.	.	PUNCT
ejpam-6074	244	1	since	since	SCONJ
ejpam-6074	244	2	s	s	PROPN
ejpam-6074	244	3	is	be	AUX
ejpam-6074	244	4	hop	hop	NOUN
ejpam-6074	244	5	dominating	dominating	NOUN
ejpam-6074	244	6	and	and	CCONJ
ejpam-6074	244	7	b	b	PROPN
ejpam-6074	244	8	/∈	/∈	PROPN
ejpam-6074	244	9	s	s	X
ejpam-6074	244	10	,	,	PUNCT
ejpam-6074	244	11	it	it	PRON
ejpam-6074	244	12	follows	follow	VERB
ejpam-6074	244	13	that	that	SCONJ
ejpam-6074	244	14	b	b	PROPN
ejpam-6074	244	15	∈	∈	PROPN
ejpam-6074	244	16	n2	n2	NOUN
ejpam-6074	244	17	g(p	g(p	PROPN
ejpam-6074	244	18	)	)	PUNCT
ejpam-6074	244	19	.	.	PUNCT
ejpam-6074	245	1	thus	thus	ADV
ejpam-6074	245	2	,	,	PUNCT
ejpam-6074	245	3	b	b	PROPN
ejpam-6074	245	4	∈	∈	PROPN
ejpam-6074	245	5	ephn(p;s	ephn(p;s	NOUN
ejpam-6074	245	6	)	)	PUNCT
ejpam-6074	245	7	,	,	PUNCT
ejpam-6074	245	8	showing	show	VERB
ejpam-6074	245	9	that	that	DET
ejpam-6074	245	10	ephn(p;s	ephn(p;s	NOUN
ejpam-6074	245	11	)	)	PUNCT
ejpam-6074	246	1	=	=	SYM
ejpam-6074	246	2	v	v	X
ejpam-6074	246	3	(	(	PUNCT
ejpam-6074	246	4	g	g	NOUN
ejpam-6074	246	5	)	)	PUNCT
ejpam-6074	246	6	\	\	PUNCT
ejpam-6074	246	7	(	(	PUNCT
ejpam-6074	246	8	n2	n2	ADJ
ejpam-6074	246	9	g[q	g[q	NOUN
ejpam-6074	246	10	]	]	PUNCT
ejpam-6074	246	11	∪	∪	X
ejpam-6074	246	12	{	{	PUNCT
ejpam-6074	246	13	p	p	NOUN
ejpam-6074	246	14	}	}	PUNCT
ejpam-6074	246	15	)	)	PUNCT
ejpam-6074	246	16	.	.	PUNCT
ejpam-6074	247	1	similarly	similarly	ADV
ejpam-6074	247	2	,	,	PUNCT
ejpam-6074	247	3	ephn(q;s	ephn(q;s	PRON
ejpam-6074	247	4	)	)	PUNCT
ejpam-6074	248	1	=	=	SYM
ejpam-6074	248	2	v	v	X
ejpam-6074	248	3	(	(	PUNCT
ejpam-6074	248	4	g	g	NOUN
ejpam-6074	248	5	)	)	PUNCT
ejpam-6074	248	6	\	\	PUNCT
ejpam-6074	248	7	(	(	PUNCT
ejpam-6074	248	8	n2	n2	NOUN
ejpam-6074	248	9	g[p	g[p	PROPN
ejpam-6074	248	10	]	]	PUNCT
ejpam-6074	248	11	∪	∪	X
ejpam-6074	248	12	{	{	PUNCT
ejpam-6074	248	13	q	q	NOUN
ejpam-6074	248	14	}	}	PUNCT
ejpam-6074	248	15	)	)	PUNCT
ejpam-6074	248	16	.	.	PUNCT
ejpam-6074	249	1	it	it	PRON
ejpam-6074	249	2	remains	remain	VERB
ejpam-6074	249	3	to	to	PART
ejpam-6074	249	4	show	show	VERB
ejpam-6074	249	5	that	that	SCONJ
ejpam-6074	249	6	vp	vp	PROPN
ejpam-6074	249	7	̸=	̸=	PROPN
ejpam-6074	249	8	vq	vq	PROPN
ejpam-6074	249	9	.	.	PROPN
ejpam-6074	250	1	to	to	ADP
ejpam-6074	250	2	this	this	DET
ejpam-6074	250	3	end	end	NOUN
ejpam-6074	250	4	,	,	PUNCT
ejpam-6074	250	5	suppose	suppose	VERB
ejpam-6074	251	1	vp	vp	PROPN
ejpam-6074	251	2	=	=	SYM
ejpam-6074	251	3	vq	vq	PROPN
ejpam-6074	251	4	.	.	PROPN
ejpam-6074	251	5	let	let	VERB
ejpam-6074	251	6	[	[	X
ejpam-6074	251	7	p	p	X
ejpam-6074	251	8	,	,	PUNCT
ejpam-6074	251	9	s	s	X
ejpam-6074	251	10	,	,	PUNCT
ejpam-6074	251	11	vp	vp	X
ejpam-6074	251	12	]	]	PUNCT
ejpam-6074	251	13	and	and	CCONJ
ejpam-6074	251	14	[	[	AUX
ejpam-6074	251	15	q	q	X
ejpam-6074	251	16	,	,	PUNCT
ejpam-6074	251	17	t	t	PROPN
ejpam-6074	251	18	,	,	PUNCT
ejpam-6074	251	19	vq	vq	PROPN
ejpam-6074	251	20	]	]	PUNCT
ejpam-6074	251	21	be	be	AUX
ejpam-6074	251	22	p	p	NOUN
ejpam-6074	251	23	-	-	PUNCT
ejpam-6074	251	24	vp	vp	NOUN
ejpam-6074	251	25	and	and	CCONJ
ejpam-6074	251	26	q	q	ADJ
ejpam-6074	251	27	-	-	PUNCT
ejpam-6074	251	28	vq	vq	ADJ
ejpam-6074	251	29	geodesics	geodesic	NOUN
ejpam-6074	251	30	,	,	PUNCT
ejpam-6074	251	31	respectively	respectively	ADV
ejpam-6074	251	32	.	.	PUNCT
ejpam-6074	252	1	since	since	SCONJ
ejpam-6074	252	2	s	s	PROPN
ejpam-6074	252	3	is	be	AUX
ejpam-6074	252	4	hop	hop	NOUN
ejpam-6074	252	5	dominating	dominating	NOUN
ejpam-6074	252	6	,	,	PUNCT
ejpam-6074	252	7	t	t	PROPN
ejpam-6074	252	8	̸=	̸=	PROPN
ejpam-6074	252	9	s.	s.	PROPN
ejpam-6074	252	10	it	it	PRON
ejpam-6074	252	11	follows	follow	VERB
ejpam-6074	252	12	that	that	SCONJ
ejpam-6074	252	13	t	t	PROPN
ejpam-6074	252	14	∈	∈	PROPN
ejpam-6074	252	15	ephn(p;s	ephn(p;s	NOUN
ejpam-6074	252	16	)	)	PUNCT
ejpam-6074	252	17	\n2	\n2	VERB
ejpam-6074	252	18	g[vp	g[vp	PROPN
ejpam-6074	252	19	]	]	X
ejpam-6074	252	20	,	,	PUNCT
ejpam-6074	252	21	a	a	DET
ejpam-6074	252	22	contradiction	contradiction	NOUN
ejpam-6074	252	23	.	.	PUNCT
ejpam-6074	253	1	therefore	therefore	ADV
ejpam-6074	253	2	,	,	PUNCT
ejpam-6074	253	3	p	p	X
ejpam-6074	253	4	,	,	PUNCT
ejpam-6074	253	5	q	q	ADJ
ejpam-6074	253	6	,	,	PUNCT
ejpam-6074	253	7	vp	vp	NOUN
ejpam-6074	253	8	,	,	PUNCT
ejpam-6074	253	9	and	and	CCONJ
ejpam-6074	253	10	vq	vq	NOUN
ejpam-6074	253	11	are	be	AUX
ejpam-6074	253	12	distinct	distinct	ADJ
ejpam-6074	253	13	vertices	vertex	NOUN
ejpam-6074	253	14	of	of	ADP
ejpam-6074	253	15	g	g	NOUN
ejpam-6074	253	16	satisfying	satisfy	VERB
ejpam-6074	253	17	conditions	condition	NOUN
ejpam-6074	253	18	(	(	PUNCT
ejpam-6074	253	19	i1	i1	PROPN
ejpam-6074	253	20	)	)	PUNCT
ejpam-6074	253	21	and	and	CCONJ
ejpam-6074	253	22	(	(	PUNCT
ejpam-6074	253	23	i2	i2	PROPN
ejpam-6074	253	24	)	)	PUNCT
ejpam-6074	253	25	.	.	PUNCT
ejpam-6074	254	1	for	for	ADP
ejpam-6074	254	2	the	the	DET
ejpam-6074	254	3	converse	converse	NOUN
ejpam-6074	254	4	,	,	PUNCT
ejpam-6074	254	5	suppose	suppose	VERB
ejpam-6074	254	6	there	there	PRON
ejpam-6074	254	7	exist	exist	VERB
ejpam-6074	254	8	distinct	distinct	ADJ
ejpam-6074	254	9	vertices	vertex	NOUN
ejpam-6074	254	10	p	p	X
ejpam-6074	254	11	,	,	PUNCT
ejpam-6074	254	12	q	q	NOUN
ejpam-6074	254	13	,	,	PUNCT
ejpam-6074	254	14	vp	vp	PROPN
ejpam-6074	254	15	,	,	PUNCT
ejpam-6074	254	16	vq	vq	PROPN
ejpam-6074	254	17	∈	∈	PROPN
ejpam-6074	254	18	v	v	ADP
ejpam-6074	254	19	(	(	PUNCT
ejpam-6074	254	20	g	g	NOUN
ejpam-6074	254	21	)	)	PUNCT
ejpam-6074	254	22	satisfying	satisfy	VERB
ejpam-6074	254	23	conditions	condition	NOUN
ejpam-6074	254	24	(	(	PUNCT
ejpam-6074	254	25	i1	i1	PROPN
ejpam-6074	254	26	)	)	PUNCT
ejpam-6074	254	27	and	and	CCONJ
ejpam-6074	254	28	(	(	PUNCT
ejpam-6074	254	29	i2	i2	PROPN
ejpam-6074	254	30	)	)	PUNCT
ejpam-6074	254	31	.	.	PUNCT
ejpam-6074	255	1	set	set	VERB
ejpam-6074	256	1	d	d	NOUN
ejpam-6074	256	2	=	=	PRON
ejpam-6074	256	3	{	{	PUNCT
ejpam-6074	256	4	p	p	X
ejpam-6074	256	5	,	,	PUNCT
ejpam-6074	256	6	q	q	NOUN
ejpam-6074	256	7	}	}	PUNCT
ejpam-6074	256	8	and	and	CCONJ
ejpam-6074	256	9	let	let	VERB
ejpam-6074	256	10	dp	dp	NOUN
ejpam-6074	256	11	=	=	SYM
ejpam-6074	256	12	(	(	PUNCT
ejpam-6074	256	13	d	d	NOUN
ejpam-6074	256	14	\	\	X
ejpam-6074	256	15	{	{	PUNCT
ejpam-6074	256	16	p	p	NOUN
ejpam-6074	256	17	}	}	PUNCT
ejpam-6074	256	18	)	)	PUNCT
ejpam-6074	256	19	∪	∪	ADP
ejpam-6074	256	20	{	{	PUNCT
ejpam-6074	256	21	vp	vp	NOUN
ejpam-6074	256	22	}	}	PUNCT
ejpam-6074	256	23	=	=	SYM
ejpam-6074	256	24	{	{	PUNCT
ejpam-6074	256	25	vp	vp	NOUN
ejpam-6074	256	26	,	,	PUNCT
ejpam-6074	256	27	q	q	NOUN
ejpam-6074	256	28	}	}	PUNCT
ejpam-6074	256	29	.	.	PUNCT
ejpam-6074	257	1	then	then	ADV
ejpam-6074	257	2	d	d	PROPN
ejpam-6074	257	3	r.	r.	PROPN
ejpam-6074	257	4	estrella	estrella	PROPN
ejpam-6074	257	5	,	,	PUNCT
ejpam-6074	257	6	gina	gina	PROPN
ejpam-6074	257	7	m.	m.	PROPN
ejpam-6074	257	8	malacas	malacas	PROPN
ejpam-6074	257	9	,	,	PUNCT
ejpam-6074	257	10	s.	s.	PROPN
ejpam-6074	257	11	canoy	canoy	PROPN
ejpam-6074	257	12	jr	jr	PROPN
ejpam-6074	257	13	.	.	PROPN
ejpam-6074	257	14	/	/	SYM
ejpam-6074	257	15	eur	eur	PROPN
ejpam-6074	257	16	.	.	PUNCT
ejpam-6074	258	1	j.	j.	PROPN
ejpam-6074	258	2	pure	pure	PROPN
ejpam-6074	258	3	appl	appl	PROPN
ejpam-6074	258	4	.	.	PROPN
ejpam-6074	258	5	math	math	PROPN
ejpam-6074	258	6	,	,	PUNCT
ejpam-6074	258	7	18	18	NUM
ejpam-6074	258	8	(	(	PUNCT
ejpam-6074	258	9	2	2	NUM
ejpam-6074	258	10	)	)	PUNCT
ejpam-6074	258	11	(	(	PUNCT
ejpam-6074	258	12	2025	2025	NUM
ejpam-6074	258	13	)	)	PUNCT
ejpam-6074	258	14	,	,	PUNCT
ejpam-6074	258	15	6074	6074	NUM
ejpam-6074	258	16	7	7	NUM
ejpam-6074	258	17	of	of	ADP
ejpam-6074	258	18	15	15	NUM
ejpam-6074	258	19	is	be	AUX
ejpam-6074	258	20	a	a	DET
ejpam-6074	258	21	hop	hop	NOUN
ejpam-6074	258	22	dominating	dominating	NOUN
ejpam-6074	258	23	set	set	VERB
ejpam-6074	258	24	by	by	ADP
ejpam-6074	258	25	condition	condition	NOUN
ejpam-6074	258	26	(	(	PUNCT
ejpam-6074	258	27	i1	i1	PROPN
ejpam-6074	258	28	)	)	PUNCT
ejpam-6074	258	29	.	.	PUNCT
ejpam-6074	259	1	let	let	VERB
ejpam-6074	259	2	v	v	NUM
ejpam-6074	259	3	∈	∈	PROPN
ejpam-6074	259	4	v	v	NOUN
ejpam-6074	259	5	(	(	PUNCT
ejpam-6074	259	6	g	g	NOUN
ejpam-6074	259	7	)	)	PUNCT
ejpam-6074	259	8	\dp	\dp	PROPN
ejpam-6074	259	9	.	.	PUNCT
ejpam-6074	260	1	if	if	SCONJ
ejpam-6074	260	2	v	v	NUM
ejpam-6074	260	3	=	=	SYM
ejpam-6074	260	4	p	p	NOUN
ejpam-6074	260	5	,	,	PUNCT
ejpam-6074	260	6	then	then	ADV
ejpam-6074	260	7	dg(v	dg(v	PUNCT
ejpam-6074	260	8	,	,	PUNCT
ejpam-6074	260	9	vp	vp	X
ejpam-6074	260	10	)	)	PUNCT
ejpam-6074	260	11	=	=	SYM
ejpam-6074	260	12	2	2	NUM
ejpam-6074	260	13	by	by	ADP
ejpam-6074	260	14	assumption	assumption	NOUN
ejpam-6074	260	15	.	.	PUNCT
ejpam-6074	261	1	so	so	ADV
ejpam-6074	261	2	suppose	suppose	VERB
ejpam-6074	261	3	v	v	ADP
ejpam-6074	261	4	̸=	̸=	PROPN
ejpam-6074	261	5	p.	p.	NOUN
ejpam-6074	261	6	if	if	SCONJ
ejpam-6074	261	7	v	v	PROPN
ejpam-6074	261	8	∈	∈	PROPN
ejpam-6074	261	9	n2	n2	NOUN
ejpam-6074	261	10	g[q	g[q	NOUN
ejpam-6074	261	11	]	]	PUNCT
ejpam-6074	261	12	∪	∪	X
ejpam-6074	261	13	{	{	PUNCT
ejpam-6074	261	14	p	p	NOUN
ejpam-6074	261	15	}	}	PUNCT
ejpam-6074	261	16	,	,	PUNCT
ejpam-6074	261	17	then	then	ADV
ejpam-6074	261	18	v	v	ADP
ejpam-6074	261	19	∈	∈	PROPN
ejpam-6074	261	20	n2	n2	NOUN
ejpam-6074	261	21	g(q	g(q	PROPN
ejpam-6074	261	22	)	)	PUNCT
ejpam-6074	261	23	because	because	SCONJ
ejpam-6074	261	24	v	v	NUM
ejpam-6074	261	25	̸=	̸=	PROPN
ejpam-6074	261	26	q.	q.	NOUN
ejpam-6074	261	27	if	if	SCONJ
ejpam-6074	261	28	v	v	NUM
ejpam-6074	261	29	∈	∈	PROPN
ejpam-6074	261	30	v	v	NOUN
ejpam-6074	261	31	(	(	PUNCT
ejpam-6074	261	32	g)\(n2	g)\(n2	PROPN
ejpam-6074	261	33	g[q]∪{p	g[q]∪{p	PROPN
ejpam-6074	261	34	}	}	PUNCT
ejpam-6074	261	35	)	)	PUNCT
ejpam-6074	261	36	,	,	PUNCT
ejpam-6074	261	37	then	then	ADV
ejpam-6074	261	38	v	v	ADP
ejpam-6074	261	39	∈	∈	PROPN
ejpam-6074	261	40	n2	n2	NOUN
ejpam-6074	261	41	g(vp	g(vp	PROPN
ejpam-6074	261	42	)	)	PUNCT
ejpam-6074	261	43	by	by	ADP
ejpam-6074	261	44	(	(	PUNCT
ejpam-6074	261	45	i2	i2	PROPN
ejpam-6074	261	46	)	)	PUNCT
ejpam-6074	261	47	.	.	PUNCT
ejpam-6074	262	1	this	this	PRON
ejpam-6074	262	2	shows	show	VERB
ejpam-6074	262	3	that	that	SCONJ
ejpam-6074	262	4	dp	dp	NOUN
ejpam-6074	262	5	is	be	AUX
ejpam-6074	262	6	a	a	DET
ejpam-6074	262	7	hop	hop	NOUN
ejpam-6074	262	8	dominating	dominating	NOUN
ejpam-6074	262	9	set	set	VERB
ejpam-6074	262	10	in	in	ADP
ejpam-6074	262	11	g.	g.	PROPN
ejpam-6074	262	12	similarly	similarly	ADV
ejpam-6074	262	13	,	,	PUNCT
ejpam-6074	262	14	dq	dq	PROPN
ejpam-6074	262	15	=	=	SYM
ejpam-6074	262	16	{	{	PUNCT
ejpam-6074	262	17	vq	vq	NOUN
ejpam-6074	262	18	,	,	PUNCT
ejpam-6074	262	19	p	p	X
ejpam-6074	262	20	}	}	PUNCT
ejpam-6074	262	21	is	be	AUX
ejpam-6074	262	22	a	a	DET
ejpam-6074	262	23	hop	hop	NOUN
ejpam-6074	262	24	dominating	dominating	NOUN
ejpam-6074	262	25	set	set	VERB
ejpam-6074	262	26	in	in	ADP
ejpam-6074	262	27	g.	g.	PROPN
ejpam-6074	262	28	therefore	therefore	ADV
ejpam-6074	262	29	,	,	PUNCT
ejpam-6074	262	30	d	d	X
ejpam-6074	262	31	is	be	AUX
ejpam-6074	262	32	a	a	DET
ejpam-6074	262	33	2	2	NUM
ejpam-6074	262	34	-	-	PUNCT
ejpam-6074	262	35	step	step	NOUN
ejpam-6074	262	36	movable	movable	ADJ
ejpam-6074	262	37	hop	hop	NOUN
ejpam-6074	262	38	dominating	dominating	NOUN
ejpam-6074	262	39	set	set	VERB
ejpam-6074	262	40	in	in	ADP
ejpam-6074	262	41	g.	g.	PROPN
ejpam-6074	262	42	by	by	ADP
ejpam-6074	262	43	remark	remark	NOUN
ejpam-6074	262	44	1	1	NUM
ejpam-6074	262	45	,	,	PUNCT
ejpam-6074	262	46	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	262	47	)	)	PUNCT
ejpam-6074	262	48	=	=	SYM
ejpam-6074	262	49	2	2	X
ejpam-6074	262	50	.	.	PUNCT
ejpam-6074	262	51	(	(	PUNCT
ejpam-6074	262	52	ii	ii	NOUN
ejpam-6074	262	53	)	)	PUNCT
ejpam-6074	262	54	suppose	suppose	VERB
ejpam-6074	262	55	γ2mh(g	γ2mh(g	NOUN
ejpam-6074	262	56	)	)	PUNCT
ejpam-6074	262	57	=	=	SYM
ejpam-6074	263	1	n	n	CCONJ
ejpam-6074	263	2	−	−	NOUN
ejpam-6074	264	1	2	2	X
ejpam-6074	264	2	.	.	PUNCT
ejpam-6074	264	3	let	let	VERB
ejpam-6074	264	4	d	d	NOUN
ejpam-6074	264	5	=	=	SYM
ejpam-6074	264	6	v	v	X
ejpam-6074	264	7	(	(	PUNCT
ejpam-6074	264	8	g	g	NOUN
ejpam-6074	264	9	)	)	PUNCT
ejpam-6074	264	10	\	\	NOUN
ejpam-6074	264	11	{	{	PUNCT
ejpam-6074	264	12	v	v	NOUN
ejpam-6074	264	13	,	,	PUNCT
ejpam-6074	264	14	w	w	NOUN
ejpam-6074	264	15	}	}	PUNCT
ejpam-6074	264	16	be	be	AUX
ejpam-6074	264	17	a	a	DET
ejpam-6074	264	18	γ2mh	γ2mh	NOUN
ejpam-6074	264	19	-	-	PUNCT
ejpam-6074	264	20	set	set	VERB
ejpam-6074	264	21	in	in	ADP
ejpam-6074	264	22	g.	g.	PROPN
ejpam-6074	264	23	suppose	suppose	VERB
ejpam-6074	264	24	there	there	PRON
ejpam-6074	264	25	exists	exist	VERB
ejpam-6074	264	26	z	z	NOUN
ejpam-6074	264	27	∈	∈	PROPN
ejpam-6074	265	1	d	d	ADP
ejpam-6074	265	2	such	such	ADJ
ejpam-6074	265	3	that	that	PRON
ejpam-6074	265	4	ephn(z;d	ephn(z;d	NOUN
ejpam-6074	265	5	)	)	PUNCT
ejpam-6074	265	6	=	=	PRON
ejpam-6074	265	7	{	{	PUNCT
ejpam-6074	265	8	v	v	NOUN
ejpam-6074	265	9	,	,	PUNCT
ejpam-6074	265	10	w	w	NOUN
ejpam-6074	265	11	}	}	PUNCT
ejpam-6074	265	12	.	.	PUNCT
ejpam-6074	266	1	suppose	suppose	VERB
ejpam-6074	266	2	further	far	ADV
ejpam-6074	266	3	that	that	PRON
ejpam-6074	266	4	dg(v	dg(v	PUNCT
ejpam-6074	266	5	,	,	PUNCT
ejpam-6074	266	6	w	w	NOUN
ejpam-6074	266	7	)	)	PUNCT
ejpam-6074	266	8	̸=	̸=	PROPN
ejpam-6074	266	9	2	2	NUM
ejpam-6074	266	10	.	.	PUNCT
ejpam-6074	267	1	then	then	ADV
ejpam-6074	267	2	d\{z	d\{z	NOUN
ejpam-6074	267	3	}	}	PUNCT
ejpam-6074	267	4	,	,	PUNCT
ejpam-6074	267	5	(	(	PUNCT
ejpam-6074	267	6	d\{z})∪{v	d\{z})∪{v	NOUN
ejpam-6074	267	7	}	}	PUNCT
ejpam-6074	267	8	,	,	PUNCT
ejpam-6074	267	9	and	and	CCONJ
ejpam-6074	267	10	(	(	PUNCT
ejpam-6074	267	11	d\{z})∪{w	d\{z})∪{w	PROPN
ejpam-6074	267	12	}	}	PUNCT
ejpam-6074	267	13	are	be	AUX
ejpam-6074	267	14	not	not	PART
ejpam-6074	267	15	hop	hop	ADJ
ejpam-6074	267	16	dominating	dominating	NOUN
ejpam-6074	267	17	sets	set	NOUN
ejpam-6074	267	18	.	.	PUNCT
ejpam-6074	268	1	this	this	PRON
ejpam-6074	268	2	implies	imply	VERB
ejpam-6074	268	3	that	that	SCONJ
ejpam-6074	268	4	d	d	NOUN
ejpam-6074	268	5	is	be	AUX
ejpam-6074	268	6	not	not	PART
ejpam-6074	268	7	a	a	DET
ejpam-6074	268	8	2	2	NUM
ejpam-6074	268	9	-	-	PUNCT
ejpam-6074	268	10	step	step	NOUN
ejpam-6074	268	11	movable	movable	ADJ
ejpam-6074	268	12	hop	hop	NOUN
ejpam-6074	268	13	dominating	dominating	NOUN
ejpam-6074	268	14	set	set	NOUN
ejpam-6074	268	15	,	,	PUNCT
ejpam-6074	268	16	contrary	contrary	ADV
ejpam-6074	268	17	to	to	ADP
ejpam-6074	268	18	our	our	PRON
ejpam-6074	268	19	assumption	assumption	NOUN
ejpam-6074	268	20	.	.	PUNCT
ejpam-6074	269	1	therefore	therefore	ADV
ejpam-6074	269	2	,	,	PUNCT
ejpam-6074	269	3	(	(	PUNCT
ejpam-6074	269	4	j1	j1	PROPN
ejpam-6074	269	5	)	)	PUNCT
ejpam-6074	269	6	holds	hold	VERB
ejpam-6074	269	7	.	.	PUNCT
ejpam-6074	270	1	let	let	VERB
ejpam-6074	270	2	s	s	PRON
ejpam-6074	270	3	be	be	AUX
ejpam-6074	270	4	a	a	DET
ejpam-6074	270	5	hop	hop	NOUN
ejpam-6074	270	6	dominating	dominating	NOUN
ejpam-6074	270	7	set	set	VERB
ejpam-6074	270	8	in	in	ADP
ejpam-6074	270	9	g	g	NOUN
ejpam-6074	270	10	with	with	ADP
ejpam-6074	270	11	|s|	|s|	NOUN
ejpam-6074	270	12	<	<	X
ejpam-6074	270	13	n	n	CCONJ
ejpam-6074	270	14	−	−	PROPN
ejpam-6074	270	15	2	2	NUM
ejpam-6074	270	16	.	.	PUNCT
ejpam-6074	270	17	since	since	SCONJ
ejpam-6074	270	18	γ1h(g	γ1h(g	NOUN
ejpam-6074	270	19	)	)	PUNCT
ejpam-6074	271	1	=	=	SYM
ejpam-6074	271	2	n	n	CCONJ
ejpam-6074	271	3	−	−	NUM
ejpam-6074	271	4	2	2	NUM
ejpam-6074	271	5	,	,	PUNCT
ejpam-6074	271	6	s	s	VERB
ejpam-6074	271	7	is	be	AUX
ejpam-6074	271	8	not	not	PART
ejpam-6074	271	9	2	2	NUM
ejpam-6074	271	10	-	-	PUNCT
ejpam-6074	271	11	step	step	NOUN
ejpam-6074	271	12	movable	movable	ADJ
ejpam-6074	271	13	hop	hop	NOUN
ejpam-6074	271	14	dominating	dominating	NOUN
ejpam-6074	271	15	in	in	ADP
ejpam-6074	271	16	g.	g.	PROPN
ejpam-6074	271	17	hence	hence	ADV
ejpam-6074	271	18	,	,	PUNCT
ejpam-6074	271	19	there	there	PRON
ejpam-6074	271	20	exists	exist	VERB
ejpam-6074	271	21	p	p	PROPN
ejpam-6074	271	22	∈	∈	PROPN
ejpam-6074	271	23	s	s	VERB
ejpam-6074	271	24	such	such	ADJ
ejpam-6074	271	25	that	that	SCONJ
ejpam-6074	271	26	none	none	NOUN
ejpam-6074	271	27	of	of	ADP
ejpam-6074	271	28	s	s	NOUN
ejpam-6074	271	29	\	\	X
ejpam-6074	271	30	{	{	PUNCT
ejpam-6074	271	31	p	p	X
ejpam-6074	271	32	}	}	PUNCT
ejpam-6074	271	33	and	and	CCONJ
ejpam-6074	271	34	the	the	DET
ejpam-6074	271	35	sets	set	NOUN
ejpam-6074	271	36	(	(	PUNCT
ejpam-6074	271	37	s	s	NOUN
ejpam-6074	271	38	\	\	X
ejpam-6074	271	39	{	{	PUNCT
ejpam-6074	271	40	p	p	NOUN
ejpam-6074	271	41	}	}	PUNCT
ejpam-6074	271	42	)	)	PUNCT
ejpam-6074	271	43	∪	∪	ADP
ejpam-6074	271	44	{	{	PUNCT
ejpam-6074	271	45	s	s	NOUN
ejpam-6074	271	46	}	}	PUNCT
ejpam-6074	271	47	for	for	ADP
ejpam-6074	271	48	s	s	X
ejpam-6074	271	49	∈	∈	PROPN
ejpam-6074	271	50	(	(	PUNCT
ejpam-6074	271	51	v	v	NOUN
ejpam-6074	271	52	(	(	PUNCT
ejpam-6074	271	53	g	g	NOUN
ejpam-6074	271	54	)	)	PUNCT
ejpam-6074	271	55	\	\	PROPN
ejpam-6074	271	56	s	s	X
ejpam-6074	271	57	)	)	PUNCT
ejpam-6074	271	58	∩	∩	ADJ
ejpam-6074	271	59	n2	n2	ADJ
ejpam-6074	271	60	g(p	g(p	PROPN
ejpam-6074	271	61	)	)	PUNCT
ejpam-6074	271	62	is	be	AUX
ejpam-6074	271	63	a	a	DET
ejpam-6074	271	64	hop	hop	NOUN
ejpam-6074	271	65	dominating	dominating	NOUN
ejpam-6074	271	66	set	set	VERB
ejpam-6074	271	67	in	in	ADP
ejpam-6074	271	68	g.	g.	PROPN
ejpam-6074	271	69	by	by	ADP
ejpam-6074	271	70	the	the	DET
ejpam-6074	271	71	contrapositive	contrapositive	NOUN
ejpam-6074	271	72	of	of	ADP
ejpam-6074	271	73	corollary	corollary	ADJ
ejpam-6074	271	74	2	2	NUM
ejpam-6074	271	75	,	,	PUNCT
ejpam-6074	271	76	this	this	PRON
ejpam-6074	271	77	implies	imply	VERB
ejpam-6074	271	78	that	that	DET
ejpam-6074	271	79	ephn(p;s	ephn(p;s	NOUN
ejpam-6074	271	80	)	)	PUNCT
ejpam-6074	271	81	≥	≥	NOUN
ejpam-6074	271	82	2	2	NUM
ejpam-6074	271	83	and	and	CCONJ
ejpam-6074	271	84	there	there	PRON
ejpam-6074	271	85	exists	exist	VERB
ejpam-6074	271	86	no	no	DET
ejpam-6074	271	87	q	q	NOUN
ejpam-6074	271	88	∈	∈	PROPN
ejpam-6074	271	89	ephn(p;s	ephn(p;s	NOUN
ejpam-6074	271	90	)	)	PUNCT
ejpam-6074	271	91	such	such	ADJ
ejpam-6074	271	92	that	that	DET
ejpam-6074	271	93	dg(q	dg(q	PROPN
ejpam-6074	271	94	,	,	PUNCT
ejpam-6074	271	95	t	t	PROPN
ejpam-6074	271	96	)	)	PUNCT
ejpam-6074	271	97	=	=	SYM
ejpam-6074	271	98	2	2	NUM
ejpam-6074	271	99	for	for	ADP
ejpam-6074	271	100	all	all	DET
ejpam-6074	271	101	t	t	NOUN
ejpam-6074	271	102	∈	∈	PROPN
ejpam-6074	271	103	ephn(p;s	ephn(p;s	NOUN
ejpam-6074	271	104	)	)	PUNCT
ejpam-6074	271	105	\	\	NOUN
ejpam-6074	271	106	{	{	PUNCT
ejpam-6074	271	107	q	q	NOUN
ejpam-6074	271	108	}	}	PUNCT
ejpam-6074	271	109	.	.	PUNCT
ejpam-6074	272	1	this	this	PRON
ejpam-6074	272	2	shows	show	VERB
ejpam-6074	272	3	that	that	SCONJ
ejpam-6074	272	4	(	(	PUNCT
ejpam-6074	272	5	j2	j2	PROPN
ejpam-6074	272	6	)	)	PUNCT
ejpam-6074	272	7	holds	hold	VERB
ejpam-6074	272	8	.	.	PUNCT
ejpam-6074	273	1	for	for	ADP
ejpam-6074	273	2	the	the	DET
ejpam-6074	273	3	converse	converse	NOUN
ejpam-6074	273	4	,	,	PUNCT
ejpam-6074	273	5	suppose	suppose	VERB
ejpam-6074	273	6	g	g	PROPN
ejpam-6074	273	7	satisfies	satisfie	NOUN
ejpam-6074	273	8	(	(	PUNCT
ejpam-6074	273	9	j1	j1	PROPN
ejpam-6074	273	10	)	)	PUNCT
ejpam-6074	273	11	and	and	CCONJ
ejpam-6074	273	12	(	(	PUNCT
ejpam-6074	273	13	j2	j2	PROPN
ejpam-6074	273	14	)	)	PUNCT
ejpam-6074	273	15	.	.	PUNCT
ejpam-6074	274	1	let	let	VERB
ejpam-6074	274	2	q	q	NOUN
ejpam-6074	274	3	=	=	SYM
ejpam-6074	274	4	v	v	X
ejpam-6074	274	5	(	(	PUNCT
ejpam-6074	274	6	g	g	NOUN
ejpam-6074	274	7	)	)	PUNCT
ejpam-6074	274	8	\	\	NOUN
ejpam-6074	274	9	{	{	PUNCT
ejpam-6074	274	10	v	v	NOUN
ejpam-6074	274	11	,	,	PUNCT
ejpam-6074	274	12	w	w	NOUN
ejpam-6074	274	13	}	}	PUNCT
ejpam-6074	274	14	.	.	PUNCT
ejpam-6074	275	1	then	then	ADV
ejpam-6074	275	2	q	q	X
ejpam-6074	275	3	is	be	AUX
ejpam-6074	275	4	a	a	DET
ejpam-6074	275	5	2	2	NUM
ejpam-6074	275	6	-	-	PUNCT
ejpam-6074	275	7	step	step	NOUN
ejpam-6074	275	8	hop	hop	NOUN
ejpam-6074	275	9	dominating	dominating	NOUN
ejpam-6074	275	10	set	set	VERB
ejpam-6074	275	11	in	in	ADP
ejpam-6074	275	12	g	g	NOUN
ejpam-6074	275	13	by	by	ADP
ejpam-6074	275	14	(	(	PUNCT
ejpam-6074	275	15	j1	j1	PROPN
ejpam-6074	275	16	)	)	PUNCT
ejpam-6074	275	17	and	and	CCONJ
ejpam-6074	275	18	corollary	corollary	ADJ
ejpam-6074	275	19	2	2	NUM
ejpam-6074	275	20	.	.	PUNCT
ejpam-6074	276	1	by	by	ADP
ejpam-6074	276	2	(	(	PUNCT
ejpam-6074	276	3	j2	j2	PROPN
ejpam-6074	276	4	)	)	PUNCT
ejpam-6074	276	5	,	,	PUNCT
ejpam-6074	276	6	it	it	PRON
ejpam-6074	276	7	follows	follow	VERB
ejpam-6074	276	8	that	that	SCONJ
ejpam-6074	276	9	q	q	NOUN
ejpam-6074	276	10	is	be	AUX
ejpam-6074	276	11	a	a	DET
ejpam-6074	276	12	γ2mh	γ2mh	PROPN
ejpam-6074	276	13	-	-	PUNCT
ejpam-6074	276	14	set	set	VERB
ejpam-6074	276	15	in	in	ADP
ejpam-6074	276	16	g.	g.	PROPN
ejpam-6074	276	17	thus	thus	ADV
ejpam-6074	276	18	,	,	PUNCT
ejpam-6074	276	19	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	276	20	)	)	PUNCT
ejpam-6074	277	1	=	=	SYM
ejpam-6074	277	2	|q|	|q|	VERB
ejpam-6074	277	3	=	=	SYM
ejpam-6074	277	4	n−	n−	NOUN
ejpam-6074	277	5	2	2	NUM
ejpam-6074	277	6	.	.	PUNCT
ejpam-6074	277	7	theorem	theorem	NOUN
ejpam-6074	277	8	5	5	NUM
ejpam-6074	277	9	.	.	PUNCT
ejpam-6074	278	1	let	let	VERB
ejpam-6074	278	2	n	n	PRON
ejpam-6074	278	3	be	be	AUX
ejpam-6074	278	4	any	any	DET
ejpam-6074	278	5	positive	positive	ADJ
ejpam-6074	278	6	integer	integer	NOUN
ejpam-6074	278	7	such	such	ADJ
ejpam-6074	278	8	that	that	SCONJ
ejpam-6074	278	9	n	n	CCONJ
ejpam-6074	278	10	≥	≥	NOUN
ejpam-6074	278	11	4	4	NUM
ejpam-6074	278	12	.	.	PUNCT
ejpam-6074	279	1	then	then	ADV
ejpam-6074	279	2	γ2mh(pn	γ2mh(pn	NOUN
ejpam-6074	279	3	)	)	PUNCT
ejpam-6074	279	4	=	=	SYM
ejpam-6074	279	5			NUM
ejpam-6074	280	1	⌊n	⌊n	NUM
ejpam-6074	280	2	3	3	NUM
ejpam-6074	280	3	⌋	⌋	NOUN
ejpam-6074	280	4	+	+	CCONJ
ejpam-6074	280	5	2	2	NUM
ejpam-6074	280	6	,	,	PUNCT
ejpam-6074	280	7	if	if	SCONJ
ejpam-6074	280	8	n	n	ADV
ejpam-6074	280	9	∈	∈	PROPN
ejpam-6074	280	10	{	{	PUNCT
ejpam-6074	280	11	5	5	NUM
ejpam-6074	280	12	,	,	PUNCT
ejpam-6074	280	13	6	6	NUM
ejpam-6074	280	14	,	,	PUNCT
ejpam-6074	280	15	7	7	NUM
ejpam-6074	280	16	,	,	PUNCT
ejpam-6074	280	17	9	9	NUM
ejpam-6074	280	18	,	,	PUNCT
ejpam-6074	280	19	10	10	NUM
ejpam-6074	280	20	}	}	SYM
ejpam-6074	280	21	2	2	NUM
ejpam-6074	280	22	t	t	NOUN
ejpam-6074	280	23	,	,	PUNCT
ejpam-6074	280	24	if	if	SCONJ
ejpam-6074	280	25	n	n	NOUN
ejpam-6074	280	26	=	=	SYM
ejpam-6074	280	27	4	4	NUM
ejpam-6074	280	28	t	t	NOUN
ejpam-6074	280	29	(	(	PUNCT
ejpam-6074	280	30	t	t	PROPN
ejpam-6074	280	31	≥	≥	PROPN
ejpam-6074	280	32	1	1	NUM
ejpam-6074	280	33	)	)	PUNCT
ejpam-6074	280	34	or	or	CCONJ
ejpam-6074	280	35	n	n	CCONJ
ejpam-6074	280	36	=	=	SYM
ejpam-6074	280	37	4t+	4t+	NUM
ejpam-6074	280	38	1	1	NUM
ejpam-6074	280	39	(	(	PUNCT
ejpam-6074	280	40	t	t	PROPN
ejpam-6074	280	41	≥	≥	NUM
ejpam-6074	280	42	3	3	NUM
ejpam-6074	280	43	)	)	PUNCT
ejpam-6074	280	44	or	or	CCONJ
ejpam-6074	280	45	n	n	CCONJ
ejpam-6074	280	46	=	=	SYM
ejpam-6074	280	47	4t+	4t+	NUM
ejpam-6074	280	48	2	2	NUM
ejpam-6074	280	49	(	(	PUNCT
ejpam-6074	280	50	t	t	PROPN
ejpam-6074	280	51	≥	≥	PROPN
ejpam-6074	280	52	3	3	NUM
ejpam-6074	280	53	)	)	PUNCT
ejpam-6074	280	54	2t+	2t+	NUM
ejpam-6074	280	55	1	1	NUM
ejpam-6074	280	56	,	,	PUNCT
ejpam-6074	280	57	if	if	SCONJ
ejpam-6074	280	58	n	n	ADV
ejpam-6074	280	59	=	=	SYM
ejpam-6074	280	60	4t+	4t+	NUM
ejpam-6074	280	61	3	3	NUM
ejpam-6074	280	62	(	(	PUNCT
ejpam-6074	280	63	t	t	PROPN
ejpam-6074	280	64	≥	≥	PROPN
ejpam-6074	280	65	2	2	NUM
ejpam-6074	280	66	)	)	PUNCT
ejpam-6074	280	67	.	.	PUNCT
ejpam-6074	281	1	proof	proof	NOUN
ejpam-6074	281	2	.	.	PUNCT
ejpam-6074	282	1	let	let	VERB
ejpam-6074	282	2	pn	pn	VERB
ejpam-6074	282	3	=	=	PUNCT
ejpam-6074	283	1	[	[	X
ejpam-6074	283	2	v1	v1	NOUN
ejpam-6074	283	3	,	,	PUNCT
ejpam-6074	283	4	v2	v2	NOUN
ejpam-6074	283	5	,	,	PUNCT
ejpam-6074	283	6	.	.	PUNCT
ejpam-6074	283	7	.	.	PUNCT
ejpam-6074	283	8	.	.	PUNCT
ejpam-6074	284	1	,	,	PUNCT
ejpam-6074	284	2	vn	vn	X
ejpam-6074	284	3	]	]	PUNCT
ejpam-6074	284	4	and	and	CCONJ
ejpam-6074	284	5	consider	consider	VERB
ejpam-6074	284	6	the	the	DET
ejpam-6074	284	7	following	follow	VERB
ejpam-6074	284	8	cases	case	NOUN
ejpam-6074	284	9	:	:	PUNCT
ejpam-6074	284	10	case	case	NOUN
ejpam-6074	284	11	1	1	NUM
ejpam-6074	284	12	.	.	PUNCT
ejpam-6074	285	1	n	n	NOUN
ejpam-6074	285	2	=	=	SYM
ejpam-6074	285	3	4	4	NUM
ejpam-6074	285	4	t.	t.	NOUN
ejpam-6074	285	5	clearly	clearly	ADV
ejpam-6074	285	6	,	,	PUNCT
ejpam-6074	285	7	if	if	SCONJ
ejpam-6074	285	8	n	n	CCONJ
ejpam-6074	285	9	=	=	SYM
ejpam-6074	285	10	4	4	NUM
ejpam-6074	285	11	,	,	PUNCT
ejpam-6074	285	12	then	then	ADV
ejpam-6074	285	13	γ2mh(p4	γ2mh(p4	NUM
ejpam-6074	285	14	)	)	PUNCT
ejpam-6074	285	15	=	=	SYM
ejpam-6074	286	1	2	2	X
ejpam-6074	286	2	.	.	X
ejpam-6074	287	1	if	if	SCONJ
ejpam-6074	287	2	n	n	NOUN
ejpam-6074	287	3	=	=	SYM
ejpam-6074	287	4	8	8	NUM
ejpam-6074	287	5	,	,	PUNCT
ejpam-6074	287	6	then	then	ADV
ejpam-6074	287	7	r	r	NOUN
ejpam-6074	287	8	=	=	PUNCT
ejpam-6074	287	9	{	{	PUNCT
ejpam-6074	287	10	v1	v1	NOUN
ejpam-6074	287	11	,	,	PUNCT
ejpam-6074	287	12	v4	v4	NOUN
ejpam-6074	287	13	,	,	PUNCT
ejpam-6074	287	14	v7	v7	NUM
ejpam-6074	287	15	,	,	PUNCT
ejpam-6074	287	16	v8	v8	PROPN
ejpam-6074	287	17	}	}	PUNCT
ejpam-6074	287	18	is	be	AUX
ejpam-6074	287	19	a	a	DET
ejpam-6074	287	20	γ2mhset	γ2mhset	NOUN
ejpam-6074	287	21	of	of	ADP
ejpam-6074	287	22	p8	p8	PROPN
ejpam-6074	287	23	.	.	PUNCT
ejpam-6074	288	1	hence	hence	ADV
ejpam-6074	288	2	,	,	PUNCT
ejpam-6074	288	3	γ2mh(p8	γ2mh(p8	PROPN
ejpam-6074	288	4	)	)	PUNCT
ejpam-6074	288	5	=	=	PUNCT
ejpam-6074	289	1	4	4	X
ejpam-6074	289	2	.	.	PUNCT
ejpam-6074	290	1	next	next	ADV
ejpam-6074	290	2	,	,	PUNCT
ejpam-6074	290	3	let	let	VERB
ejpam-6074	290	4	t	t	PROPN
ejpam-6074	290	5	≥	≥	PRON
ejpam-6074	290	6	3	3	NUM
ejpam-6074	290	7	.	.	PUNCT
ejpam-6074	291	1	for	for	ADP
ejpam-6074	291	2	each	each	DET
ejpam-6074	291	3	j	j	PROPN
ejpam-6074	291	4	∈	∈	PROPN
ejpam-6074	291	5	{	{	PUNCT
ejpam-6074	291	6	1	1	NUM
ejpam-6074	291	7	,	,	PUNCT
ejpam-6074	291	8	2	2	NUM
ejpam-6074	291	9	,	,	PUNCT
ejpam-6074	291	10	.	.	PUNCT
ejpam-6074	291	11	.	.	PUNCT
ejpam-6074	291	12	.	.	PUNCT
ejpam-6074	292	1	,	,	PUNCT
ejpam-6074	292	2	⌊	⌊	VERB
ejpam-6074	292	3	t−1	t−1	NOUN
ejpam-6074	292	4	2	2	NUM
ejpam-6074	292	5	⌋	⌋	NOUN
ejpam-6074	292	6	,	,	PUNCT
ejpam-6074	292	7	set	set	VERB
ejpam-6074	292	8	sj	sj	NOUN
ejpam-6074	292	9	=	=	SYM
ejpam-6074	292	10	{	{	PUNCT
ejpam-6074	292	11	v8j−1	v8j−1	PROPN
ejpam-6074	292	12	,	,	PUNCT
ejpam-6074	292	13	v8j	v8j	NOUN
ejpam-6074	292	14	,	,	PUNCT
ejpam-6074	292	15	v8j+1	v8j+1	PROPN
ejpam-6074	292	16	,	,	PUNCT
ejpam-6074	292	17	v8j+2	v8j+2	PROPN
ejpam-6074	292	18	}	}	PUNCT
ejpam-6074	292	19	.	.	PUNCT
ejpam-6074	293	1	let	let	VERB
ejpam-6074	293	2	s	s	PRON
ejpam-6074	293	3	=	=	NOUN
ejpam-6074	293	4	{	{	PUNCT
ejpam-6074	293	5	v1	v1	PROPN
ejpam-6074	293	6	,	,	PUNCT
ejpam-6074	293	7	v2	v2	NOUN
ejpam-6074	293	8	}	}	PUNCT
ejpam-6074	293	9	∪	∪	NOUN
ejpam-6074	293	10	(	(	PUNCT
ejpam-6074	293	11	⋃⌊	⋃⌊	PROPN
ejpam-6074	293	12	t−1	t−1	PROPN
ejpam-6074	293	13	2	2	NUM
ejpam-6074	293	14	⌋	⌋	NOUN
ejpam-6074	293	15	j=1	j=1	PROPN
ejpam-6074	293	16	sj	sj	PROPN
ejpam-6074	293	17	)	)	PUNCT
ejpam-6074	293	18	.	.	PUNCT
ejpam-6074	294	1	since	since	SCONJ
ejpam-6074	294	2	s	s	PROPN
ejpam-6074	294	3	is	be	AUX
ejpam-6074	294	4	hop	hop	NOUN
ejpam-6074	294	5	dominating	dominating	NOUN
ejpam-6074	294	6	and	and	CCONJ
ejpam-6074	294	7	|ephn(v;s)|	|ephn(v;s)|	X
ejpam-6074	294	8	≤	≤	NUM
ejpam-6074	294	9	1	1	NUM
ejpam-6074	294	10	for	for	ADP
ejpam-6074	294	11	each	each	DET
ejpam-6074	294	12	v	v	NUM
ejpam-6074	294	13	∈	∈	PROPN
ejpam-6074	294	14	s	s	NOUN
ejpam-6074	294	15	,	,	PUNCT
ejpam-6074	294	16	s	s	PART
ejpam-6074	294	17	is	be	AUX
ejpam-6074	294	18	a	a	DET
ejpam-6074	294	19	2	2	NUM
ejpam-6074	294	20	-	-	PUNCT
ejpam-6074	294	21	step	step	NOUN
ejpam-6074	294	22	movable	movable	ADJ
ejpam-6074	294	23	hop	hop	NOUN
ejpam-6074	294	24	dominating	dominating	NOUN
ejpam-6074	294	25	set	set	VERB
ejpam-6074	294	26	in	in	ADP
ejpam-6074	294	27	pn	pn	PROPN
ejpam-6074	294	28	by	by	ADP
ejpam-6074	294	29	corollary	corollary	ADJ
ejpam-6074	294	30	2	2	NUM
ejpam-6074	294	31	.	.	PUNCT
ejpam-6074	295	1	moreover	moreover	ADV
ejpam-6074	295	2	,	,	PUNCT
ejpam-6074	295	3	|s|	|s|	PROPN
ejpam-6074	295	4	=	=	SYM
ejpam-6074	295	5	2	2	NUM
ejpam-6074	295	6	+	+	NUM
ejpam-6074	295	7	∑⌊	∑⌊	NOUN
ejpam-6074	295	8	t−1	t−1	PROPN
ejpam-6074	295	9	2	2	NUM
ejpam-6074	295	10	⌋	⌋	NOUN
ejpam-6074	295	11	j=1	j=1	NOUN
ejpam-6074	295	12	|sj	|sj	X
ejpam-6074	295	13	|	|	NOUN
ejpam-6074	295	14	=	=	SYM
ejpam-6074	295	15	2	2	NUM
ejpam-6074	295	16	+	+	NUM
ejpam-6074	295	17	4	4	NUM
ejpam-6074	295	18	(	(	PUNCT
ejpam-6074	295	19	t−1	t−1	NOUN
ejpam-6074	295	20	2	2	NUM
ejpam-6074	295	21	)	)	PUNCT
ejpam-6074	295	22	=	=	SYM
ejpam-6074	295	23	2	2	NUM
ejpam-6074	295	24	t.	t.	NOUN
ejpam-6074	295	25	it	it	PRON
ejpam-6074	295	26	can	can	AUX
ejpam-6074	295	27	be	be	AUX
ejpam-6074	295	28	shown	show	VERB
ejpam-6074	295	29	that	that	SCONJ
ejpam-6074	295	30	if	if	SCONJ
ejpam-6074	295	31	s′	s′	ADJ
ejpam-6074	295	32	is	be	AUX
ejpam-6074	295	33	a	a	DET
ejpam-6074	295	34	hop	hop	NOUN
ejpam-6074	295	35	dominating	dominating	NOUN
ejpam-6074	295	36	set	set	VERB
ejpam-6074	295	37	in	in	ADP
ejpam-6074	295	38	pn	pn	PROPN
ejpam-6074	295	39	with	with	ADP
ejpam-6074	295	40	|s′|	|s′|	NOUN
ejpam-6074	295	41	<	<	X
ejpam-6074	295	42	|s|	|s|	PROPN
ejpam-6074	295	43	,	,	PUNCT
ejpam-6074	295	44	then	then	ADV
ejpam-6074	295	45	there	there	PRON
ejpam-6074	295	46	exists	exist	VERB
ejpam-6074	295	47	a	a	DET
ejpam-6074	295	48	vertex	vertex	NOUN
ejpam-6074	295	49	w	w	PROPN
ejpam-6074	295	50	∈	∈	PROPN
ejpam-6074	295	51	s′	s′	VERB
ejpam-6074	295	52	with	with	ADP
ejpam-6074	295	53	|ephn(w;s′)|	|ephn(w;s′)|	ADJ
ejpam-6074	295	54	=	=	SYM
ejpam-6074	295	55	2	2	X
ejpam-6074	295	56	.	.	PUNCT
ejpam-6074	296	1	this	this	PRON
ejpam-6074	296	2	implies	imply	VERB
ejpam-6074	296	3	that	that	SCONJ
ejpam-6074	296	4	s′	s′	ADJ
ejpam-6074	296	5	is	be	AUX
ejpam-6074	296	6	not	not	PART
ejpam-6074	296	7	a	a	DET
ejpam-6074	296	8	2	2	NUM
ejpam-6074	296	9	-	-	PUNCT
ejpam-6074	296	10	step	step	NOUN
ejpam-6074	296	11	movable	movable	ADJ
ejpam-6074	296	12	hop	hop	NOUN
ejpam-6074	296	13	dominating	dominating	NOUN
ejpam-6074	296	14	set	set	NOUN
ejpam-6074	296	15	.	.	PUNCT
ejpam-6074	297	1	r.	r.	PROPN
ejpam-6074	297	2	estrella	estrella	PROPN
ejpam-6074	297	3	,	,	PUNCT
ejpam-6074	297	4	gina	gina	PROPN
ejpam-6074	297	5	m.	m.	PROPN
ejpam-6074	297	6	malacas	malacas	PROPN
ejpam-6074	297	7	,	,	PUNCT
ejpam-6074	297	8	s.	s.	PROPN
ejpam-6074	297	9	canoy	canoy	PROPN
ejpam-6074	297	10	jr	jr	PROPN
ejpam-6074	297	11	.	.	PROPN
ejpam-6074	297	12	/	/	SYM
ejpam-6074	297	13	eur	eur	PROPN
ejpam-6074	297	14	.	.	PUNCT
ejpam-6074	298	1	j.	j.	PROPN
ejpam-6074	298	2	pure	pure	PROPN
ejpam-6074	298	3	appl	appl	PROPN
ejpam-6074	298	4	.	.	PROPN
ejpam-6074	298	5	math	math	PROPN
ejpam-6074	298	6	,	,	PUNCT
ejpam-6074	298	7	18	18	NUM
ejpam-6074	298	8	(	(	PUNCT
ejpam-6074	298	9	2	2	NUM
ejpam-6074	298	10	)	)	PUNCT
ejpam-6074	298	11	(	(	PUNCT
ejpam-6074	298	12	2025	2025	NUM
ejpam-6074	298	13	)	)	PUNCT
ejpam-6074	298	14	,	,	PUNCT
ejpam-6074	298	15	6074	6074	NUM
ejpam-6074	298	16	8	8	NUM
ejpam-6074	298	17	of	of	ADP
ejpam-6074	298	18	15	15	NUM
ejpam-6074	298	19	therefore	therefore	ADV
ejpam-6074	298	20	,	,	PUNCT
ejpam-6074	298	21	γ2mh(pn	γ2mh(pn	NOUN
ejpam-6074	298	22	)	)	PUNCT
ejpam-6074	298	23	=	=	PUNCT
ejpam-6074	298	24	|s|	|s|	NOUN
ejpam-6074	298	25	=	=	SYM
ejpam-6074	298	26	2	2	NUM
ejpam-6074	298	27	t.	t.	NOUN
ejpam-6074	298	28	case	case	NOUN
ejpam-6074	298	29	2	2	NUM
ejpam-6074	298	30	.	.	PUNCT
ejpam-6074	299	1	n	n	NOUN
ejpam-6074	299	2	=	=	SYM
ejpam-6074	299	3	4t+	4t+	NUM
ejpam-6074	299	4	1	1	NUM
ejpam-6074	299	5	or	or	CCONJ
ejpam-6074	299	6	n	n	NOUN
ejpam-6074	299	7	=	=	SYM
ejpam-6074	299	8	4t+	4t+	NUM
ejpam-6074	299	9	2	2	NUM
ejpam-6074	299	10	.	.	PUNCT
ejpam-6074	300	1	if	if	SCONJ
ejpam-6074	300	2	n	n	NOUN
ejpam-6074	300	3	=	=	SYM
ejpam-6074	300	4	5	5	NUM
ejpam-6074	300	5	,	,	PUNCT
ejpam-6074	300	6	then	then	ADV
ejpam-6074	300	7	s	s	VERB
ejpam-6074	300	8	=	=	NOUN
ejpam-6074	300	9	{	{	PUNCT
ejpam-6074	300	10	v1	v1	PROPN
ejpam-6074	300	11	,	,	PUNCT
ejpam-6074	300	12	v2	v2	PROPN
ejpam-6074	300	13	,	,	PUNCT
ejpam-6074	300	14	v5	v5	PROPN
ejpam-6074	300	15	}	}	PUNCT
ejpam-6074	300	16	is	be	AUX
ejpam-6074	300	17	a	a	DET
ejpam-6074	300	18	γ2mh	γ2mh	PROPN
ejpam-6074	300	19	-	-	PUNCT
ejpam-6074	300	20	set	set	VERB
ejpam-6074	300	21	in	in	ADP
ejpam-6074	300	22	p5	p5	NOUN
ejpam-6074	300	23	.	.	PUNCT
ejpam-6074	301	1	hence	hence	ADV
ejpam-6074	301	2	,	,	PUNCT
ejpam-6074	301	3	γ2mh(p5	γ2mh(p5	X
ejpam-6074	301	4	)	)	PUNCT
ejpam-6074	301	5	=	=	SYM
ejpam-6074	302	1	3	3	X
ejpam-6074	302	2	.	.	X
ejpam-6074	303	1	if	if	SCONJ
ejpam-6074	303	2	n	n	NOUN
ejpam-6074	303	3	=	=	SYM
ejpam-6074	303	4	6	6	NUM
ejpam-6074	303	5	,	,	PUNCT
ejpam-6074	303	6	then	then	ADV
ejpam-6074	303	7	s	s	VERB
ejpam-6074	303	8	=	=	NOUN
ejpam-6074	303	9	{	{	PUNCT
ejpam-6074	303	10	v1	v1	PROPN
ejpam-6074	303	11	,	,	PUNCT
ejpam-6074	303	12	v2	v2	PROPN
ejpam-6074	303	13	,	,	PUNCT
ejpam-6074	303	14	v5	v5	PROPN
ejpam-6074	303	15	,	,	PUNCT
ejpam-6074	303	16	v6	v6	NOUN
ejpam-6074	303	17	}	}	PUNCT
ejpam-6074	303	18	is	be	AUX
ejpam-6074	303	19	a	a	DET
ejpam-6074	303	20	γ2mh	γ2mh	PROPN
ejpam-6074	303	21	-	-	PUNCT
ejpam-6074	303	22	set	set	VERB
ejpam-6074	303	23	in	in	ADP
ejpam-6074	303	24	p6	p6	PROPN
ejpam-6074	303	25	.	.	PUNCT
ejpam-6074	304	1	thus	thus	ADV
ejpam-6074	304	2	,	,	PUNCT
ejpam-6074	304	3	γ2mh(p6	γ2mh(p6	PROPN
ejpam-6074	304	4	)	)	PUNCT
ejpam-6074	304	5	=	=	SYM
ejpam-6074	305	1	4	4	X
ejpam-6074	305	2	.	.	X
ejpam-6074	306	1	if	if	SCONJ
ejpam-6074	306	2	n	n	NOUN
ejpam-6074	306	3	=	=	SYM
ejpam-6074	306	4	9	9	NUM
ejpam-6074	306	5	,	,	PUNCT
ejpam-6074	306	6	then	then	ADV
ejpam-6074	306	7	s	s	VERB
ejpam-6074	306	8	=	=	NOUN
ejpam-6074	306	9	{	{	PUNCT
ejpam-6074	306	10	v1	v1	PROPN
ejpam-6074	306	11	,	,	PUNCT
ejpam-6074	306	12	v2	v2	PROPN
ejpam-6074	306	13	,	,	PUNCT
ejpam-6074	306	14	v5	v5	PROPN
ejpam-6074	306	15	,	,	PUNCT
ejpam-6074	306	16	v6	v6	NOUN
ejpam-6074	306	17	,	,	PUNCT
ejpam-6074	306	18	v7	v7	NOUN
ejpam-6074	306	19	}	}	PUNCT
ejpam-6074	306	20	is	be	AUX
ejpam-6074	306	21	a	a	DET
ejpam-6074	306	22	γ2mh	γ2mh	PROPN
ejpam-6074	306	23	-	-	PUNCT
ejpam-6074	306	24	set	set	VERB
ejpam-6074	306	25	in	in	ADP
ejpam-6074	306	26	p9	p9	PROPN
ejpam-6074	306	27	and	and	CCONJ
ejpam-6074	306	28	if	if	SCONJ
ejpam-6074	306	29	n	n	NOUN
ejpam-6074	306	30	=	=	SYM
ejpam-6074	306	31	10	10	NUM
ejpam-6074	306	32	,	,	PUNCT
ejpam-6074	306	33	then	then	ADV
ejpam-6074	306	34	s	s	VERB
ejpam-6074	306	35	=	=	NOUN
ejpam-6074	306	36	{	{	PUNCT
ejpam-6074	306	37	v1	v1	PROPN
ejpam-6074	306	38	,	,	PUNCT
ejpam-6074	306	39	v4	v4	NOUN
ejpam-6074	306	40	,	,	PUNCT
ejpam-6074	306	41	v7	v7	NUM
ejpam-6074	306	42	,	,	PUNCT
ejpam-6074	306	43	v8	v8	PROPN
ejpam-6074	306	44	,	,	PUNCT
ejpam-6074	306	45	v9	v9	PROPN
ejpam-6074	306	46	}	}	PUNCT
ejpam-6074	306	47	is	be	AUX
ejpam-6074	306	48	a	a	DET
ejpam-6074	306	49	γ2mhset	γ2mhset	NOUN
ejpam-6074	306	50	in	in	ADP
ejpam-6074	306	51	p10	p10	PROPN
ejpam-6074	306	52	.	.	PUNCT
ejpam-6074	307	1	hence	hence	ADV
ejpam-6074	307	2	,	,	PUNCT
ejpam-6074	307	3	γ2mh(p9	γ2mh(p9	ADV
ejpam-6074	307	4	)	)	PUNCT
ejpam-6074	307	5	=	=	SYM
ejpam-6074	307	6	γ2mh(p10	γ2mh(p10	NOUN
ejpam-6074	307	7	)	)	PUNCT
ejpam-6074	307	8	=	=	SYM
ejpam-6074	308	1	5	5	X
ejpam-6074	308	2	.	.	PUNCT
ejpam-6074	309	1	next	next	ADV
ejpam-6074	309	2	,	,	PUNCT
ejpam-6074	309	3	let	let	VERB
ejpam-6074	309	4	t	t	PROPN
ejpam-6074	309	5	≥	≥	PRON
ejpam-6074	309	6	3	3	X
ejpam-6074	309	7	.	.	PUNCT
ejpam-6074	310	1	let	let	VERB
ejpam-6074	310	2	sj	sj	INTJ
ejpam-6074	310	3	=	=	PRON
ejpam-6074	310	4	{	{	PUNCT
ejpam-6074	310	5	v4j+3	v4j+3	NOUN
ejpam-6074	310	6	,	,	PUNCT
ejpam-6074	310	7	v4j+4	v4j+4	NOUN
ejpam-6074	310	8	}	}	PUNCT
ejpam-6074	310	9	for	for	ADP
ejpam-6074	310	10	each	each	DET
ejpam-6074	310	11	j	j	PROPN
ejpam-6074	310	12	∈	∈	PROPN
ejpam-6074	310	13	{	{	PUNCT
ejpam-6074	310	14	1	1	NUM
ejpam-6074	310	15	,	,	PUNCT
ejpam-6074	310	16	.	.	PUNCT
ejpam-6074	310	17	.	.	PUNCT
ejpam-6074	311	1	.	.	PUNCT
ejpam-6074	312	1	,	,	PUNCT
ejpam-6074	312	2	t	t	NOUN
ejpam-6074	312	3	−	−	NOUN
ejpam-6074	312	4	1	1	NUM
ejpam-6074	312	5	}	}	PUNCT
ejpam-6074	312	6	.	.	PUNCT
ejpam-6074	313	1	let	let	VERB
ejpam-6074	313	2	s	s	AUX
ejpam-6074	313	3	=	=	NOUN
ejpam-6074	313	4	{	{	PUNCT
ejpam-6074	313	5	v1	v1	PROPN
ejpam-6074	313	6	,	,	PUNCT
ejpam-6074	313	7	v4	v4	NOUN
ejpam-6074	313	8	}	}	PUNCT
ejpam-6074	313	9	∪	∪	VERB
ejpam-6074	313	10	⋃t−1	⋃t−1	X
ejpam-6074	313	11	j=1	j=1	ADJ
ejpam-6074	313	12	sj	sj	INTJ
ejpam-6074	313	13	.	.	PUNCT
ejpam-6074	314	1	since	since	SCONJ
ejpam-6074	314	2	s	s	PROPN
ejpam-6074	314	3	is	be	AUX
ejpam-6074	314	4	hop	hop	NOUN
ejpam-6074	314	5	dominating	dominating	NOUN
ejpam-6074	314	6	and	and	CCONJ
ejpam-6074	314	7	|ephn(v;s)|	|ephn(v;s)|	X
ejpam-6074	314	8	≤	≤	NUM
ejpam-6074	314	9	1	1	NUM
ejpam-6074	314	10	for	for	ADP
ejpam-6074	314	11	each	each	DET
ejpam-6074	314	12	v	v	NUM
ejpam-6074	314	13	∈	∈	PROPN
ejpam-6074	314	14	s	s	NOUN
ejpam-6074	314	15	,	,	PUNCT
ejpam-6074	314	16	s	s	PART
ejpam-6074	314	17	is	be	AUX
ejpam-6074	314	18	a	a	DET
ejpam-6074	314	19	2	2	NUM
ejpam-6074	314	20	-	-	PUNCT
ejpam-6074	314	21	step	step	NOUN
ejpam-6074	314	22	movable	movable	ADJ
ejpam-6074	314	23	hop	hop	NOUN
ejpam-6074	314	24	dominating	dominating	NOUN
ejpam-6074	314	25	set	set	VERB
ejpam-6074	314	26	in	in	ADP
ejpam-6074	314	27	pn	pn	PROPN
ejpam-6074	314	28	by	by	ADP
ejpam-6074	314	29	corollary	corollary	ADJ
ejpam-6074	314	30	2	2	NUM
ejpam-6074	314	31	.	.	PUNCT
ejpam-6074	314	32	again	again	ADV
ejpam-6074	314	33	,	,	PUNCT
ejpam-6074	314	34	it	it	PRON
ejpam-6074	314	35	can	can	AUX
ejpam-6074	314	36	be	be	AUX
ejpam-6074	314	37	verified	verify	VERB
ejpam-6074	314	38	that	that	SCONJ
ejpam-6074	314	39	every	every	DET
ejpam-6074	314	40	hop	hop	NOUN
ejpam-6074	314	41	dominating	dominating	NOUN
ejpam-6074	314	42	set	set	NOUN
ejpam-6074	314	43	s′	s′	PUNCT
ejpam-6074	314	44	in	in	ADP
ejpam-6074	314	45	pn	pn	PROPN
ejpam-6074	314	46	with	with	ADP
ejpam-6074	314	47	|s′|	|s′|	NOUN
ejpam-6074	314	48	<	<	X
ejpam-6074	314	49	|s|	|s|	PROPN
ejpam-6074	314	50	has	have	VERB
ejpam-6074	314	51	a	a	DET
ejpam-6074	314	52	vertex	vertex	NOUN
ejpam-6074	314	53	w	w	NOUN
ejpam-6074	314	54	∈	∈	PROPN
ejpam-6074	314	55	s′	s′	VERB
ejpam-6074	314	56	with	with	ADP
ejpam-6074	314	57	|ephn(w;s′)|	|ephn(w;s′)|	ADJ
ejpam-6074	314	58	=	=	SYM
ejpam-6074	314	59	2	2	NUM
ejpam-6074	314	60	and	and	CCONJ
ejpam-6074	314	61	so	so	ADV
ejpam-6074	314	62	can	can	AUX
ejpam-6074	314	63	not	not	PART
ejpam-6074	314	64	be	be	AUX
ejpam-6074	314	65	a	a	DET
ejpam-6074	314	66	2	2	NUM
ejpam-6074	314	67	-	-	PUNCT
ejpam-6074	314	68	step	step	NOUN
ejpam-6074	314	69	movable	movable	ADJ
ejpam-6074	314	70	hop	hop	NOUN
ejpam-6074	314	71	dominating	dominating	NOUN
ejpam-6074	314	72	set	set	VERB
ejpam-6074	314	73	in	in	ADP
ejpam-6074	314	74	pn	pn	PROPN
ejpam-6074	314	75	.	.	PUNCT
ejpam-6074	314	76	therefore	therefore	ADV
ejpam-6074	314	77	,	,	PUNCT
ejpam-6074	314	78	γ2mh(pn	γ2mh(pn	NOUN
ejpam-6074	314	79	)	)	PUNCT
ejpam-6074	314	80	=	=	PUNCT
ejpam-6074	314	81	|s|	|s|	NOUN
ejpam-6074	314	82	=	=	SYM
ejpam-6074	314	83	2	2	NUM
ejpam-6074	314	84	+	+	CCONJ
ejpam-6074	314	85	t−1∑	t−1∑	NUM
ejpam-6074	314	86	j=1	j=1	NOUN
ejpam-6074	314	87	|sj	|sj	X
ejpam-6074	314	88	|	|	NOUN
ejpam-6074	314	89	=	=	SYM
ejpam-6074	314	90	2	2	NUM
ejpam-6074	314	91	+	+	SYM
ejpam-6074	314	92	2(t−	2(t−	NUM
ejpam-6074	314	93	1	1	NUM
ejpam-6074	314	94	)	)	PUNCT
ejpam-6074	314	95	=	=	SYM
ejpam-6074	314	96	2	2	NUM
ejpam-6074	314	97	t.	t.	NOUN
ejpam-6074	314	98	case	case	NOUN
ejpam-6074	314	99	3	3	NUM
ejpam-6074	314	100	:	:	PUNCT
ejpam-6074	314	101	n	n	PROPN
ejpam-6074	314	102	=	=	SYM
ejpam-6074	314	103	4t+	4t+	NUM
ejpam-6074	314	104	3	3	NUM
ejpam-6074	314	105	.	.	PUNCT
ejpam-6074	315	1	if	if	SCONJ
ejpam-6074	315	2	n	n	NOUN
ejpam-6074	315	3	=	=	SYM
ejpam-6074	315	4	7	7	NUM
ejpam-6074	315	5	,	,	PUNCT
ejpam-6074	315	6	then	then	ADV
ejpam-6074	315	7	s	s	VERB
ejpam-6074	315	8	=	=	NOUN
ejpam-6074	315	9	{	{	PUNCT
ejpam-6074	315	10	v1	v1	PROPN
ejpam-6074	315	11	,	,	PUNCT
ejpam-6074	315	12	v2	v2	PROPN
ejpam-6074	315	13	,	,	PUNCT
ejpam-6074	315	14	v5	v5	PROPN
ejpam-6074	315	15	,	,	PUNCT
ejpam-6074	315	16	v6	v6	NOUN
ejpam-6074	315	17	}	}	PUNCT
ejpam-6074	315	18	is	be	AUX
ejpam-6074	315	19	a	a	DET
ejpam-6074	315	20	γ2mh	γ2mh	PROPN
ejpam-6074	315	21	-	-	PUNCT
ejpam-6074	315	22	set	set	VERB
ejpam-6074	315	23	in	in	ADP
ejpam-6074	315	24	p7	p7	NOUN
ejpam-6074	315	25	.	.	PUNCT
ejpam-6074	316	1	thus	thus	ADV
ejpam-6074	316	2	,	,	PUNCT
ejpam-6074	316	3	γ2mh(p7	γ2mh(p7	PROPN
ejpam-6074	316	4	)	)	PUNCT
ejpam-6074	316	5	=	=	PUNCT
ejpam-6074	316	6	4	4	X
ejpam-6074	316	7	.	.	PUNCT
ejpam-6074	317	1	next	next	ADV
ejpam-6074	317	2	,	,	PUNCT
ejpam-6074	317	3	let	let	VERB
ejpam-6074	317	4	t	t	PROPN
ejpam-6074	317	5	≥	≥	NUM
ejpam-6074	317	6	2	2	NUM
ejpam-6074	317	7	anddj	anddj	NOUN
ejpam-6074	317	8	=	=	PUNCT
ejpam-6074	317	9	{	{	PUNCT
ejpam-6074	317	10	v4j+3	v4j+3	NOUN
ejpam-6074	317	11	,	,	PUNCT
ejpam-6074	317	12	v4j+4	v4j+4	NOUN
ejpam-6074	317	13	}	}	PUNCT
ejpam-6074	317	14	for	for	ADP
ejpam-6074	317	15	each	each	DET
ejpam-6074	317	16	j	j	PROPN
ejpam-6074	317	17	∈	∈	PROPN
ejpam-6074	317	18	{	{	PUNCT
ejpam-6074	317	19	1	1	NUM
ejpam-6074	317	20	,	,	PUNCT
ejpam-6074	317	21	2	2	NUM
ejpam-6074	317	22	,	,	PUNCT
ejpam-6074	317	23	.	.	PUNCT
ejpam-6074	317	24	.	.	PUNCT
ejpam-6074	318	1	.	.	PUNCT
ejpam-6074	319	1	,	,	PUNCT
ejpam-6074	319	2	t−1	t−1	NOUN
ejpam-6074	319	3	}	}	PUNCT
ejpam-6074	319	4	.	.	PUNCT
ejpam-6074	320	1	let	let	VERB
ejpam-6074	320	2	d	d	NOUN
ejpam-6074	320	3	=	=	SYM
ejpam-6074	320	4	{	{	PUNCT
ejpam-6074	320	5	v1	v1	PROPN
ejpam-6074	320	6	,	,	PUNCT
ejpam-6074	320	7	v4	v4	NOUN
ejpam-6074	320	8	,	,	PUNCT
ejpam-6074	320	9	v4t+3}∪	v4t+3}∪	X
ejpam-6074	320	10	⋃t−1	⋃t−1	X
ejpam-6074	321	1	j=1	j=1	ADJ
ejpam-6074	321	2	sj	sj	INTJ
ejpam-6074	321	3	.	.	PUNCT
ejpam-6074	322	1	by	by	ADP
ejpam-6074	322	2	corollary	corollary	ADJ
ejpam-6074	322	3	2	2	NUM
ejpam-6074	322	4	,	,	PUNCT
ejpam-6074	322	5	d	d	PRON
ejpam-6074	322	6	is	be	AUX
ejpam-6074	322	7	a	a	DET
ejpam-6074	322	8	2	2	NUM
ejpam-6074	322	9	-	-	PUNCT
ejpam-6074	322	10	step	step	NOUN
ejpam-6074	322	11	movable	movable	ADJ
ejpam-6074	322	12	hop	hop	NOUN
ejpam-6074	322	13	dominating	dominating	NOUN
ejpam-6074	322	14	set	set	VERB
ejpam-6074	322	15	in	in	ADP
ejpam-6074	322	16	pn	pn	PROPN
ejpam-6074	322	17	because	because	SCONJ
ejpam-6074	322	18	it	it	PRON
ejpam-6074	322	19	is	be	AUX
ejpam-6074	322	20	hop	hop	NOUN
ejpam-6074	322	21	dominating	dominating	NOUN
ejpam-6074	322	22	and	and	CCONJ
ejpam-6074	322	23	|ephn(v;d|	|ephn(v;d|	PROPN
ejpam-6074	322	24	≤	≤	ADV
ejpam-6074	322	25	1	1	NUM
ejpam-6074	322	26	for	for	ADP
ejpam-6074	322	27	each	each	DET
ejpam-6074	322	28	v	v	X
ejpam-6074	322	29	∈	∈	PROPN
ejpam-6074	322	30	d.	d.	NOUN
ejpam-6074	322	31	moreover	moreover	ADV
ejpam-6074	322	32	,	,	PUNCT
ejpam-6074	322	33	d	d	PROPN
ejpam-6074	322	34	is	be	AUX
ejpam-6074	322	35	a	a	DET
ejpam-6074	322	36	γ2mh	γ2mh	NOUN
ejpam-6074	322	37	-	-	PUNCT
ejpam-6074	322	38	set	set	NOUN
ejpam-6074	322	39	;	;	PUNCT
ejpam-6074	322	40	hence	hence	ADV
ejpam-6074	322	41	,	,	PUNCT
ejpam-6074	322	42	γ2mh(pn	γ2mh(pn	NOUN
ejpam-6074	322	43	)	)	PUNCT
ejpam-6074	322	44	=	=	PUNCT
ejpam-6074	322	45	|s|	|s|	NOUN
ejpam-6074	322	46	=	=	SYM
ejpam-6074	322	47	2	2	NUM
ejpam-6074	322	48	+	+	CCONJ
ejpam-6074	322	49	t−1∑	t−1∑	NUM
ejpam-6074	322	50	j=1	j=1	NOUN
ejpam-6074	322	51	|sj	|sj	X
ejpam-6074	322	52	|	|	NOUN
ejpam-6074	322	53	=	=	SYM
ejpam-6074	322	54	3	3	NUM
ejpam-6074	322	55	+	+	SYM
ejpam-6074	322	56	2(t−	2(t−	NUM
ejpam-6074	322	57	1	1	NUM
ejpam-6074	322	58	)	)	PUNCT
ejpam-6074	322	59	=	=	SYM
ejpam-6074	322	60	2t+	2t+	NUM
ejpam-6074	322	61	1	1	NUM
ejpam-6074	322	62	.	.	PUNCT
ejpam-6074	323	1	this	this	PRON
ejpam-6074	323	2	proves	prove	VERB
ejpam-6074	323	3	the	the	DET
ejpam-6074	323	4	assertion	assertion	NOUN
ejpam-6074	323	5	.	.	PUNCT
ejpam-6074	324	1	theorem	theorem	ADJ
ejpam-6074	324	2	6	6	NUM
ejpam-6074	324	3	.	.	PUNCT
ejpam-6074	325	1	let	let	VERB
ejpam-6074	325	2	n	n	PRON
ejpam-6074	325	3	be	be	AUX
ejpam-6074	325	4	any	any	DET
ejpam-6074	325	5	positive	positive	ADJ
ejpam-6074	325	6	integer	integer	NOUN
ejpam-6074	325	7	such	such	ADJ
ejpam-6074	325	8	that	that	SCONJ
ejpam-6074	325	9	n	n	CCONJ
ejpam-6074	325	10	≥	≥	NOUN
ejpam-6074	325	11	4	4	NUM
ejpam-6074	325	12	.	.	PUNCT
ejpam-6074	326	1	then	then	ADV
ejpam-6074	326	2	γ2mh(cn	γ2mh(cn	NOUN
ejpam-6074	326	3	)	)	PUNCT
ejpam-6074	326	4	=	=	PUNCT
ejpam-6074	326	5			PROPN
ejpam-6074	326	6	2	2	NUM
ejpam-6074	326	7	t	t	NOUN
ejpam-6074	326	8	,	,	PUNCT
ejpam-6074	326	9	if	if	SCONJ
ejpam-6074	326	10	n	n	NOUN
ejpam-6074	326	11	=	=	SYM
ejpam-6074	326	12	4	4	NUM
ejpam-6074	326	13	t	t	PROPN
ejpam-6074	326	14	,	,	PUNCT
ejpam-6074	326	15	t	t	PROPN
ejpam-6074	326	16	≥	≥	NUM
ejpam-6074	326	17	1	1	NUM
ejpam-6074	326	18	or	or	CCONJ
ejpam-6074	326	19	n	n	NOUN
ejpam-6074	326	20	=	=	SYM
ejpam-6074	326	21	4t+	4t+	NUM
ejpam-6074	326	22	1	1	NUM
ejpam-6074	326	23	,	,	PUNCT
ejpam-6074	326	24	t	t	VERB
ejpam-6074	326	25	≤	≤	NUM
ejpam-6074	326	26	3	3	NUM
ejpam-6074	326	27	or	or	CCONJ
ejpam-6074	326	28	n	n	NOUN
ejpam-6074	326	29	=	=	SYM
ejpam-6074	326	30	4t+	4t+	NUM
ejpam-6074	326	31	2	2	NUM
ejpam-6074	326	32	,	,	PUNCT
ejpam-6074	326	33	t	t	PROPN
ejpam-6074	326	34	≥	≥	NUM
ejpam-6074	326	35	1	1	NUM
ejpam-6074	326	36	2t−	2t−	NOUN
ejpam-6074	326	37	1	1	NUM
ejpam-6074	326	38	,	,	PUNCT
ejpam-6074	326	39	if	if	SCONJ
ejpam-6074	326	40	n	n	ADV
ejpam-6074	326	41	=	=	SYM
ejpam-6074	326	42	4t+	4t+	NUM
ejpam-6074	326	43	1	1	NUM
ejpam-6074	326	44	,	,	PUNCT
ejpam-6074	326	45	t	t	PROPN
ejpam-6074	326	46	≥	≥	NUM
ejpam-6074	326	47	4	4	NUM
ejpam-6074	326	48	2t+	2t+	NUM
ejpam-6074	326	49	1	1	NUM
ejpam-6074	326	50	,	,	PUNCT
ejpam-6074	326	51	if	if	SCONJ
ejpam-6074	326	52	n	n	ADV
ejpam-6074	326	53	=	=	SYM
ejpam-6074	326	54	4t+	4t+	NUM
ejpam-6074	326	55	3	3	NUM
ejpam-6074	326	56	,	,	PUNCT
ejpam-6074	326	57	t	t	PROPN
ejpam-6074	326	58	≥	≥	NUM
ejpam-6074	326	59	1	1	NUM
ejpam-6074	326	60	.	.	PUNCT
ejpam-6074	327	1	proof	proof	NOUN
ejpam-6074	327	2	.	.	PUNCT
ejpam-6074	328	1	let	let	VERB
ejpam-6074	328	2	cn	cn	PROPN
ejpam-6074	328	3	=	=	PUNCT
ejpam-6074	329	1	[	[	X
ejpam-6074	329	2	v1	v1	NOUN
ejpam-6074	329	3	,	,	PUNCT
ejpam-6074	329	4	v2	v2	NOUN
ejpam-6074	329	5	,	,	PUNCT
ejpam-6074	329	6	.	.	PUNCT
ejpam-6074	329	7	.	.	PUNCT
ejpam-6074	329	8	.	.	PUNCT
ejpam-6074	330	1	,	,	PUNCT
ejpam-6074	330	2	vn	vn	X
ejpam-6074	330	3	,	,	PUNCT
ejpam-6074	330	4	v1	v1	PROPN
ejpam-6074	330	5	]	]	PUNCT
ejpam-6074	330	6	,	,	PUNCT
ejpam-6074	330	7	where	where	SCONJ
ejpam-6074	330	8	n	n	PRON
ejpam-6074	330	9	≥	≥	X
ejpam-6074	330	10	4	4	NUM
ejpam-6074	330	11	.	.	PUNCT
ejpam-6074	331	1	consider	consider	VERB
ejpam-6074	331	2	the	the	DET
ejpam-6074	331	3	following	follow	VERB
ejpam-6074	331	4	cases	case	NOUN
ejpam-6074	331	5	:	:	PUNCT
ejpam-6074	331	6	case	case	NOUN
ejpam-6074	331	7	1	1	NUM
ejpam-6074	331	8	.	.	PUNCT
ejpam-6074	332	1	n	n	NOUN
ejpam-6074	332	2	=	=	SYM
ejpam-6074	332	3	4	4	NUM
ejpam-6074	332	4	t	t	NOUN
ejpam-6074	332	5	,	,	PUNCT
ejpam-6074	332	6	where	where	SCONJ
ejpam-6074	332	7	t	t	PROPN
ejpam-6074	332	8	≥	≥	PROPN
ejpam-6074	332	9	1	1	NUM
ejpam-6074	332	10	.	.	PUNCT
ejpam-6074	332	11	consider	consider	VERB
ejpam-6074	332	12	the	the	DET
ejpam-6074	332	13	following	follow	VERB
ejpam-6074	332	14	subcases	subcase	NOUN
ejpam-6074	332	15	:	:	PUNCT
ejpam-6074	332	16	r.	r.	PROPN
ejpam-6074	332	17	estrella	estrella	PROPN
ejpam-6074	332	18	,	,	PUNCT
ejpam-6074	332	19	gina	gina	PROPN
ejpam-6074	332	20	m.	m.	PROPN
ejpam-6074	332	21	malacas	malacas	PROPN
ejpam-6074	332	22	,	,	PUNCT
ejpam-6074	332	23	s.	s.	PROPN
ejpam-6074	332	24	canoy	canoy	PROPN
ejpam-6074	332	25	jr	jr	PROPN
ejpam-6074	332	26	.	.	PROPN
ejpam-6074	332	27	/	/	SYM
ejpam-6074	332	28	eur	eur	PROPN
ejpam-6074	332	29	.	.	PUNCT
ejpam-6074	333	1	j.	j.	PROPN
ejpam-6074	333	2	pure	pure	PROPN
ejpam-6074	333	3	appl	appl	PROPN
ejpam-6074	333	4	.	.	PROPN
ejpam-6074	333	5	math	math	PROPN
ejpam-6074	333	6	,	,	PUNCT
ejpam-6074	333	7	18	18	NUM
ejpam-6074	333	8	(	(	PUNCT
ejpam-6074	333	9	2	2	NUM
ejpam-6074	333	10	)	)	PUNCT
ejpam-6074	333	11	(	(	PUNCT
ejpam-6074	333	12	2025	2025	NUM
ejpam-6074	333	13	)	)	PUNCT
ejpam-6074	333	14	,	,	PUNCT
ejpam-6074	333	15	6074	6074	NUM
ejpam-6074	333	16	9	9	NUM
ejpam-6074	333	17	of	of	ADP
ejpam-6074	333	18	15	15	NUM
ejpam-6074	333	19	subcase	subcase	NOUN
ejpam-6074	333	20	1	1	NUM
ejpam-6074	333	21	:	:	PUNCT
ejpam-6074	333	22	t	t	PROPN
ejpam-6074	333	23	is	be	AUX
ejpam-6074	333	24	odd	odd	ADJ
ejpam-6074	333	25	.	.	PUNCT
ejpam-6074	334	1	if	if	SCONJ
ejpam-6074	334	2	n	n	NOUN
ejpam-6074	334	3	=	=	SYM
ejpam-6074	334	4	4	4	NUM
ejpam-6074	334	5	,	,	PUNCT
ejpam-6074	334	6	then	then	ADV
ejpam-6074	334	7	s	s	VERB
ejpam-6074	334	8	=	=	NOUN
ejpam-6074	334	9	{	{	PUNCT
ejpam-6074	334	10	v1	v1	PROPN
ejpam-6074	334	11	,	,	PUNCT
ejpam-6074	334	12	v2	v2	PROPN
ejpam-6074	334	13	}	}	PUNCT
ejpam-6074	334	14	is	be	AUX
ejpam-6074	334	15	a	a	DET
ejpam-6074	334	16	γ2mh	γ2mh	PROPN
ejpam-6074	334	17	-	-	PUNCT
ejpam-6074	334	18	set	set	VERB
ejpam-6074	334	19	in	in	ADP
ejpam-6074	334	20	c4	c4	NOUN
ejpam-6074	334	21	.	.	PUNCT
ejpam-6074	335	1	hence	hence	ADV
ejpam-6074	335	2	,	,	PUNCT
ejpam-6074	335	3	γ2mh(c4	γ2mh(c4	NOUN
ejpam-6074	335	4	)	)	PUNCT
ejpam-6074	335	5	=	=	SYM
ejpam-6074	336	1	2	2	X
ejpam-6074	336	2	.	.	PUNCT
ejpam-6074	337	1	next	next	ADV
ejpam-6074	337	2	,	,	PUNCT
ejpam-6074	337	3	suppose	suppose	VERB
ejpam-6074	337	4	that	that	SCONJ
ejpam-6074	337	5	t	t	PROPN
ejpam-6074	337	6	≥	≥	NUM
ejpam-6074	337	7	3	3	X
ejpam-6074	337	8	.	.	PUNCT
ejpam-6074	338	1	let	let	VERB
ejpam-6074	338	2	sj	sj	INTJ
ejpam-6074	338	3	=	=	PRON
ejpam-6074	338	4	{	{	PUNCT
ejpam-6074	338	5	v8j−1	v8j−1	PROPN
ejpam-6074	338	6	,	,	PUNCT
ejpam-6074	338	7	v8j	v8j	NOUN
ejpam-6074	338	8	,	,	PUNCT
ejpam-6074	338	9	v8j+1	v8j+1	PROPN
ejpam-6074	338	10	,	,	PUNCT
ejpam-6074	338	11	v8j+2	v8j+2	PROPN
ejpam-6074	338	12	}	}	PUNCT
ejpam-6074	338	13	for	for	ADP
ejpam-6074	338	14	j	j	PROPN
ejpam-6074	338	15	=	=	SYM
ejpam-6074	338	16	1	1	PROPN
ejpam-6074	338	17	,	,	PUNCT
ejpam-6074	338	18	.	.	PUNCT
ejpam-6074	338	19	.	.	PUNCT
ejpam-6074	339	1	.	.	PUNCT
ejpam-6074	340	1	,	,	PUNCT
ejpam-6074	340	2	t−1	t−1	PROPN
ejpam-6074	340	3	2	2	NUM
ejpam-6074	340	4	.	.	PUNCT
ejpam-6074	341	1	let	let	VERB
ejpam-6074	341	2	s	s	VERB
ejpam-6074	341	3	=	=	NOUN
ejpam-6074	341	4	{	{	PUNCT
ejpam-6074	341	5	v1	v1	PROPN
ejpam-6074	341	6	,	,	PUNCT
ejpam-6074	341	7	v2}∪	v2}∪	PROPN
ejpam-6074	341	8	(	(	PUNCT
ejpam-6074	341	9	⋃	⋃	PROPN
ejpam-6074	341	10	t−1	t−1	PROPN
ejpam-6074	341	11	2	2	NUM
ejpam-6074	341	12	j=1	j=1	NOUN
ejpam-6074	341	13	sj	sj	PROPN
ejpam-6074	341	14	)	)	PUNCT
ejpam-6074	341	15	.	.	PUNCT
ejpam-6074	342	1	then	then	ADV
ejpam-6074	342	2	s	s	VERB
ejpam-6074	342	3	is	be	AUX
ejpam-6074	342	4	a	a	DET
ejpam-6074	342	5	2	2	NUM
ejpam-6074	342	6	-	-	PUNCT
ejpam-6074	342	7	step	step	NOUN
ejpam-6074	342	8	movable	movable	ADJ
ejpam-6074	342	9	hop	hop	NOUN
ejpam-6074	342	10	dominating	dominating	NOUN
ejpam-6074	342	11	set	set	NOUN
ejpam-6074	342	12	in	in	ADP
ejpam-6074	342	13	cn	cn	PROPN
ejpam-6074	342	14	.	.	PUNCT
ejpam-6074	343	1	if	if	SCONJ
ejpam-6074	343	2	s′	s′	PRON
ejpam-6074	343	3	is	be	AUX
ejpam-6074	343	4	a	a	DET
ejpam-6074	343	5	hop	hop	NOUN
ejpam-6074	343	6	dominating	dominating	NOUN
ejpam-6074	343	7	set	set	VERB
ejpam-6074	343	8	with	with	ADP
ejpam-6074	343	9	|s′|	|s′|	NOUN
ejpam-6074	343	10	≤	≤	NUM
ejpam-6074	343	11	|s|	|s|	PROPN
ejpam-6074	343	12	,	,	PUNCT
ejpam-6074	343	13	then	then	ADV
ejpam-6074	343	14	∃	∃	PROPN
ejpam-6074	343	15	a	a	DET
ejpam-6074	343	16	vertex	vertex	NOUN
ejpam-6074	343	17	v	v	ADP
ejpam-6074	343	18	∈	∈	NOUN
ejpam-6074	343	19	s′	s′	VERB
ejpam-6074	343	20	with	with	ADP
ejpam-6074	343	21	|ephn(v;s′)|	|ephn(v;s′)|	PROPN
ejpam-6074	343	22	=	=	SYM
ejpam-6074	343	23	2	2	NUM
ejpam-6074	343	24	.	.	PUNCT
ejpam-6074	343	25	hence	hence	ADV
ejpam-6074	343	26	,	,	PUNCT
ejpam-6074	343	27	s′	s′	PROPN
ejpam-6074	343	28	is	be	AUX
ejpam-6074	343	29	not	not	PART
ejpam-6074	343	30	a	a	DET
ejpam-6074	343	31	2	2	NUM
ejpam-6074	343	32	-	-	PUNCT
ejpam-6074	343	33	step	step	NOUN
ejpam-6074	343	34	movable	movable	ADJ
ejpam-6074	343	35	hop	hop	NOUN
ejpam-6074	343	36	dominating	dominating	NOUN
ejpam-6074	343	37	set	set	NOUN
ejpam-6074	343	38	.	.	PUNCT
ejpam-6074	344	1	therefore	therefore	ADV
ejpam-6074	344	2	,	,	PUNCT
ejpam-6074	344	3	γ2mh(cn	γ2mh(cn	NOUN
ejpam-6074	344	4	)	)	PUNCT
ejpam-6074	344	5	=	=	PUNCT
ejpam-6074	344	6	|s|	|s|	NOUN
ejpam-6074	344	7	=	=	SYM
ejpam-6074	344	8	2	2	NUM
ejpam-6074	344	9	+	+	NUM
ejpam-6074	344	10	∑	∑	PROPN
ejpam-6074	344	11	t−1	t−1	PROPN
ejpam-6074	344	12	2	2	NUM
ejpam-6074	344	13	j=1	j=1	NOUN
ejpam-6074	344	14	|sj	|sj	X
ejpam-6074	344	15	|	|	NOUN
ejpam-6074	344	16	=	=	SYM
ejpam-6074	344	17	2	2	NUM
ejpam-6074	344	18	+	+	NOUN
ejpam-6074	344	19	4	4	NUM
ejpam-6074	344	20	(	(	PUNCT
ejpam-6074	344	21	t−1	t−1	NOUN
ejpam-6074	344	22	2	2	NUM
ejpam-6074	344	23	)	)	PUNCT
ejpam-6074	344	24	=	=	SYM
ejpam-6074	344	25	2	2	NUM
ejpam-6074	344	26	t.	t.	NOUN
ejpam-6074	344	27	subcase	subcase	NOUN
ejpam-6074	344	28	2	2	NUM
ejpam-6074	344	29	:	:	PUNCT
ejpam-6074	344	30	t	t	PROPN
ejpam-6074	344	31	is	be	AUX
ejpam-6074	344	32	even	even	ADV
ejpam-6074	344	33	.	.	PUNCT
ejpam-6074	345	1	let	let	VERB
ejpam-6074	345	2	sj	sj	INTJ
ejpam-6074	345	3	=	=	VERB
ejpam-6074	345	4	{	{	PUNCT
ejpam-6074	345	5	v8j−7	v8j−7	NOUN
ejpam-6074	345	6	,	,	PUNCT
ejpam-6074	345	7	v8j−6	v8j−6	PROPN
ejpam-6074	345	8	,	,	PUNCT
ejpam-6074	345	9	v8j−5	v8j−5	NOUN
ejpam-6074	345	10	,	,	PUNCT
ejpam-6074	345	11	v8j−4	v8j−4	PROPN
ejpam-6074	345	12	}	}	PUNCT
ejpam-6074	345	13	for	for	ADP
ejpam-6074	345	14	j	j	PROPN
ejpam-6074	345	15	=	=	SYM
ejpam-6074	345	16	1	1	PROPN
ejpam-6074	345	17	,	,	PUNCT
ejpam-6074	345	18	.	.	PUNCT
ejpam-6074	345	19	.	.	PUNCT
ejpam-6074	346	1	.	.	PUNCT
ejpam-6074	347	1	,	,	PUNCT
ejpam-6074	347	2	t	t	PROPN
ejpam-6074	347	3	2	2	NUM
ejpam-6074	347	4	.	.	PUNCT
ejpam-6074	348	1	let	let	VERB
ejpam-6074	348	2	s	s	VERB
ejpam-6074	348	3	=	=	VERB
ejpam-6074	348	4	∪	∪	X
ejpam-6074	348	5	(	(	PUNCT
ejpam-6074	348	6	⋃	⋃	PROPN
ejpam-6074	348	7	t	t	NOUN
ejpam-6074	348	8	2	2	NUM
ejpam-6074	348	9	j=1	j=1	NOUN
ejpam-6074	348	10	sj	sj	PROPN
ejpam-6074	348	11	)	)	PUNCT
ejpam-6074	348	12	.	.	PUNCT
ejpam-6074	349	1	then	then	ADV
ejpam-6074	349	2	s	s	VERB
ejpam-6074	349	3	is	be	AUX
ejpam-6074	349	4	a	a	DET
ejpam-6074	349	5	γ2mh	γ2mh	PROPN
ejpam-6074	349	6	-	-	PUNCT
ejpam-6074	349	7	set	set	NOUN
ejpam-6074	349	8	in	in	ADP
ejpam-6074	349	9	cn	cn	PROPN
ejpam-6074	349	10	and	and	CCONJ
ejpam-6074	349	11	γ2mh(cn	γ2mh(cn	NOUN
ejpam-6074	349	12	)	)	PUNCT
ejpam-6074	349	13	=	=	SYM
ejpam-6074	349	14	|s|	|s|	NOUN
ejpam-6074	349	15	=	=	SYM
ejpam-6074	349	16	(	(	PUNCT
ejpam-6074	349	17	∑	∑	PROPN
ejpam-6074	349	18	t	t	PROPN
ejpam-6074	349	19	2	2	NUM
ejpam-6074	349	20	j=1	j=1	NOUN
ejpam-6074	349	21	|sj	|sj	ADJ
ejpam-6074	349	22	|	|	NOUN
ejpam-6074	349	23	)	)	PUNCT
ejpam-6074	349	24	=	=	SYM
ejpam-6074	349	25	4	4	NUM
ejpam-6074	349	26	(	(	PUNCT
ejpam-6074	349	27	t2	t2	NOUN
ejpam-6074	349	28	)	)	PUNCT
ejpam-6074	349	29	=	=	SYM
ejpam-6074	349	30	2	2	NUM
ejpam-6074	349	31	t.	t.	NOUN
ejpam-6074	349	32	case	case	NOUN
ejpam-6074	349	33	2	2	NUM
ejpam-6074	349	34	.	.	PUNCT
ejpam-6074	350	1	n	n	NOUN
ejpam-6074	350	2	=	=	SYM
ejpam-6074	350	3	4t+	4t+	NUM
ejpam-6074	350	4	1	1	NUM
ejpam-6074	350	5	,	,	PUNCT
ejpam-6074	350	6	where	where	SCONJ
ejpam-6074	350	7	t	t	NOUN
ejpam-6074	350	8	≤	≤	NOUN
ejpam-6074	350	9	3	3	NUM
ejpam-6074	350	10	.	.	PUNCT
ejpam-6074	351	1	let	let	VERB
ejpam-6074	351	2	sj	sj	INTJ
ejpam-6074	351	3	=	=	PUNCT
ejpam-6074	351	4	{	{	PUNCT
ejpam-6074	351	5	v4j−3	v4j−3	PROPN
ejpam-6074	351	6	,	,	PUNCT
ejpam-6074	351	7	v4j−2	v4j−2	PROPN
ejpam-6074	351	8	}	}	PUNCT
ejpam-6074	351	9	for	for	ADP
ejpam-6074	351	10	j	j	PROPN
ejpam-6074	351	11	=	=	SYM
ejpam-6074	351	12	1	1	PROPN
ejpam-6074	351	13	,	,	PUNCT
ejpam-6074	351	14	.	.	PUNCT
ejpam-6074	351	15	.	.	PUNCT
ejpam-6074	352	1	.	.	PUNCT
ejpam-6074	353	1	,	,	PUNCT
ejpam-6074	353	2	t.	t.	PROPN
ejpam-6074	353	3	let	let	VERB
ejpam-6074	353	4	s	s	VERB
ejpam-6074	353	5	=	=	PUNCT
ejpam-6074	353	6	(	(	PUNCT
ejpam-6074	353	7	⋃t	⋃t	ADV
ejpam-6074	353	8	j=1	j=1	NOUN
ejpam-6074	353	9	sj	sj	PROPN
ejpam-6074	353	10	)	)	PUNCT
ejpam-6074	353	11	.	.	PUNCT
ejpam-6074	354	1	then	then	ADV
ejpam-6074	354	2	s	s	VERB
ejpam-6074	354	3	is	be	AUX
ejpam-6074	354	4	a	a	DET
ejpam-6074	354	5	γ2mh	γ2mh	PROPN
ejpam-6074	354	6	-	-	PUNCT
ejpam-6074	354	7	set	set	NOUN
ejpam-6074	354	8	in	in	ADP
ejpam-6074	354	9	cn	cn	PROPN
ejpam-6074	354	10	.	.	PUNCT
ejpam-6074	354	11	therefore	therefore	ADV
ejpam-6074	354	12	,	,	PUNCT
ejpam-6074	354	13	γ2mh(cn	γ2mh(cn	NOUN
ejpam-6074	354	14	)	)	PUNCT
ejpam-6074	354	15	=	=	SYM
ejpam-6074	354	16	|s|	|s|	NOUN
ejpam-6074	354	17	=	=	SYM
ejpam-6074	354	18	∑t	∑t	PROPN
ejpam-6074	354	19	j=1	j=1	NOUN
ejpam-6074	354	20	|sj	|sj	X
ejpam-6074	354	21	|	|	NOUN
ejpam-6074	354	22	=	=	SYM
ejpam-6074	354	23	2	2	NUM
ejpam-6074	354	24	t.	t.	NOUN
ejpam-6074	354	25	case	case	NOUN
ejpam-6074	354	26	3	3	NUM
ejpam-6074	354	27	.	.	PUNCT
ejpam-6074	355	1	n	n	NOUN
ejpam-6074	355	2	=	=	SYM
ejpam-6074	355	3	4t+	4t+	NUM
ejpam-6074	355	4	1	1	NUM
ejpam-6074	355	5	,	,	PUNCT
ejpam-6074	355	6	where	where	SCONJ
ejpam-6074	355	7	t	t	PROPN
ejpam-6074	355	8	≥	≥	NUM
ejpam-6074	355	9	4	4	NUM
ejpam-6074	355	10	.	.	PUNCT
ejpam-6074	356	1	let	let	VERB
ejpam-6074	356	2	sj	sj	INTJ
ejpam-6074	356	3	=	=	VERB
ejpam-6074	356	4	{	{	PUNCT
ejpam-6074	356	5	v4j+4	v4j+4	NOUN
ejpam-6074	356	6	,	,	PUNCT
ejpam-6074	356	7	v4j+5	v4j+5	NOUN
ejpam-6074	356	8	}	}	PUNCT
ejpam-6074	356	9	for	for	ADP
ejpam-6074	356	10	j	j	PROPN
ejpam-6074	356	11	=	=	SYM
ejpam-6074	356	12	1	1	PROPN
ejpam-6074	356	13	,	,	PUNCT
ejpam-6074	356	14	.	.	PUNCT
ejpam-6074	356	15	.	.	PUNCT
ejpam-6074	357	1	.	.	PUNCT
ejpam-6074	358	1	,	,	PUNCT
ejpam-6074	358	2	t	t	X
ejpam-6074	358	3	−	−	NOUN
ejpam-6074	359	1	3	3	X
ejpam-6074	359	2	.	.	PUNCT
ejpam-6074	360	1	let	let	VERB
ejpam-6074	360	2	s	s	AUX
ejpam-6074	360	3	=	=	NOUN
ejpam-6074	360	4	{	{	PUNCT
ejpam-6074	360	5	v1	v1	PROPN
ejpam-6074	360	6	,	,	PUNCT
ejpam-6074	360	7	v2	v2	PROPN
ejpam-6074	360	8	,	,	PUNCT
ejpam-6074	360	9	v5	v5	NOUN
ejpam-6074	360	10	,	,	PUNCT
ejpam-6074	360	11	vn−5	vn−5	PROPN
ejpam-6074	360	12	,	,	PUNCT
ejpam-6074	360	13	vn−2	vn−2	PROPN
ejpam-6074	360	14	}	}	PUNCT
ejpam-6074	360	15	∪	∪	X
ejpam-6074	360	16	(	(	PUNCT
ejpam-6074	360	17	⋃t−3	⋃t−3	X
ejpam-6074	360	18	j=1	j=1	PROPN
ejpam-6074	360	19	sj	sj	PROPN
ejpam-6074	360	20	)	)	PUNCT
ejpam-6074	360	21	.	.	PUNCT
ejpam-6074	361	1	then	then	ADV
ejpam-6074	361	2	s	s	VERB
ejpam-6074	361	3	is	be	AUX
ejpam-6074	361	4	a	a	DET
ejpam-6074	361	5	γ2mh	γ2mh	PROPN
ejpam-6074	361	6	-	-	PUNCT
ejpam-6074	361	7	set	set	NOUN
ejpam-6074	361	8	in	in	ADP
ejpam-6074	361	9	cn	cn	PROPN
ejpam-6074	361	10	and	and	CCONJ
ejpam-6074	361	11	γ2mh(cn	γ2mh(cn	NOUN
ejpam-6074	361	12	)	)	PUNCT
ejpam-6074	361	13	=	=	PUNCT
ejpam-6074	362	1	|s|	|s|	NOUN
ejpam-6074	362	2	=	=	SYM
ejpam-6074	362	3	4	4	NUM
ejpam-6074	362	4	+	+	CCONJ
ejpam-6074	362	5	∑t−3	∑t−3	VERB
ejpam-6074	362	6	j=1	j=1	NOUN
ejpam-6074	362	7	|sj	|sj	X
ejpam-6074	362	8	|	|	NOUN
ejpam-6074	362	9	=	=	SYM
ejpam-6074	362	10	5	5	NUM
ejpam-6074	362	11	+	+	NUM
ejpam-6074	362	12	2(t−	2(t−	NUM
ejpam-6074	362	13	3	3	NUM
ejpam-6074	362	14	)	)	PUNCT
ejpam-6074	362	15	=	=	PUNCT
ejpam-6074	363	1	2t−	2t−	ADP
ejpam-6074	363	2	1	1	NUM
ejpam-6074	363	3	.	.	PUNCT
ejpam-6074	363	4	case	case	NOUN
ejpam-6074	363	5	4	4	NUM
ejpam-6074	363	6	.	.	PUNCT
ejpam-6074	363	7	n	n	NOUN
ejpam-6074	363	8	=	=	SYM
ejpam-6074	363	9	4t+	4t+	NUM
ejpam-6074	363	10	2	2	NUM
ejpam-6074	363	11	.	.	PUNCT
ejpam-6074	364	1	if	if	SCONJ
ejpam-6074	364	2	n	n	NOUN
ejpam-6074	364	3	=	=	SYM
ejpam-6074	364	4	6	6	NUM
ejpam-6074	364	5	and	and	CCONJ
ejpam-6074	364	6	n	n	CCONJ
ejpam-6074	364	7	=	=	NUM
ejpam-6074	364	8	10	10	NUM
ejpam-6074	364	9	,	,	PUNCT
ejpam-6074	364	10	then	then	ADV
ejpam-6074	364	11	{	{	PUNCT
ejpam-6074	364	12	v1	v1	NOUN
ejpam-6074	364	13	,	,	PUNCT
ejpam-6074	364	14	v4	v4	NOUN
ejpam-6074	364	15	}	}	PUNCT
ejpam-6074	364	16	and	and	CCONJ
ejpam-6074	364	17	{	{	PUNCT
ejpam-6074	364	18	v1	v1	NOUN
ejpam-6074	364	19	,	,	PUNCT
ejpam-6074	364	20	v2	v2	PROPN
ejpam-6074	364	21	,	,	PUNCT
ejpam-6074	364	22	v6	v6	NOUN
ejpam-6074	364	23	,	,	PUNCT
ejpam-6074	364	24	v7	v7	VERB
ejpam-6074	364	25	}	}	PUNCT
ejpam-6074	364	26	are	be	AUX
ejpam-6074	364	27	γ2mh	γ2mh	NOUN
ejpam-6074	364	28	-	-	PUNCT
ejpam-6074	364	29	sets	set	NOUN
ejpam-6074	364	30	in	in	ADP
ejpam-6074	364	31	c4	c4	NOUN
ejpam-6074	364	32	and	and	CCONJ
ejpam-6074	364	33	c10	c10	VERB
ejpam-6074	364	34	,	,	PUNCT
ejpam-6074	364	35	respetively	respetively	ADV
ejpam-6074	364	36	.	.	PUNCT
ejpam-6074	365	1	hence	hence	ADV
ejpam-6074	365	2	,	,	PUNCT
ejpam-6074	365	3	γ2mh(c6	γ2mh(c6	PROPN
ejpam-6074	365	4	)	)	PUNCT
ejpam-6074	365	5	=	=	SYM
ejpam-6074	365	6	2	2	NUM
ejpam-6074	365	7	and	and	CCONJ
ejpam-6074	365	8	γ2mh(c10	γ2mh(c10	NUM
ejpam-6074	365	9	)	)	PUNCT
ejpam-6074	366	1	=	=	SYM
ejpam-6074	366	2	4	4	X
ejpam-6074	366	3	.	.	PUNCT
ejpam-6074	366	4	suppose	suppose	VERB
ejpam-6074	366	5	t	t	PROPN
ejpam-6074	366	6	≥	≥	NUM
ejpam-6074	366	7	3	3	X
ejpam-6074	366	8	.	.	PUNCT
ejpam-6074	367	1	let	let	VERB
ejpam-6074	367	2	sj	sj	INTJ
ejpam-6074	367	3	=	=	VERB
ejpam-6074	367	4	{	{	PUNCT
ejpam-6074	367	5	v4j+4	v4j+4	NOUN
ejpam-6074	367	6	,	,	PUNCT
ejpam-6074	367	7	v4j+5	v4j+5	NOUN
ejpam-6074	367	8	}	}	PUNCT
ejpam-6074	367	9	for	for	ADP
ejpam-6074	367	10	j	j	PROPN
ejpam-6074	367	11	=	=	SYM
ejpam-6074	367	12	1	1	PROPN
ejpam-6074	367	13	,	,	PUNCT
ejpam-6074	367	14	.	.	PUNCT
ejpam-6074	367	15	.	.	PUNCT
ejpam-6074	368	1	.	.	PUNCT
ejpam-6074	369	1	,	,	PUNCT
ejpam-6074	370	1	t−	t−	PROPN
ejpam-6074	370	2	2	2	X
ejpam-6074	370	3	.	.	PUNCT
ejpam-6074	371	1	let	let	VERB
ejpam-6074	371	2	s	s	VERB
ejpam-6074	371	3	=	=	NOUN
ejpam-6074	371	4	{	{	PUNCT
ejpam-6074	371	5	v1	v1	PROPN
ejpam-6074	371	6	,	,	PUNCT
ejpam-6074	371	7	v2	v2	PROPN
ejpam-6074	371	8	,	,	PUNCT
ejpam-6074	371	9	v5	v5	NOUN
ejpam-6074	371	10	,	,	PUNCT
ejpam-6074	371	11	vn−2}∪	vn−2}∪	PROPN
ejpam-6074	371	12	(	(	PUNCT
ejpam-6074	371	13	⋃t−2	⋃t−2	NOUN
ejpam-6074	371	14	j=1	j=1	PROPN
ejpam-6074	371	15	sj	sj	PROPN
ejpam-6074	371	16	)	)	PUNCT
ejpam-6074	371	17	.	.	PUNCT
ejpam-6074	372	1	then	then	ADV
ejpam-6074	372	2	s	s	VERB
ejpam-6074	372	3	is	be	AUX
ejpam-6074	372	4	a	a	DET
ejpam-6074	372	5	γ2mh	γ2mh	PROPN
ejpam-6074	372	6	-	-	PUNCT
ejpam-6074	372	7	set	set	NOUN
ejpam-6074	372	8	in	in	ADP
ejpam-6074	372	9	cn	cn	PROPN
ejpam-6074	372	10	and	and	CCONJ
ejpam-6074	372	11	γ2mh(cn	γ2mh(cn	NOUN
ejpam-6074	372	12	)	)	PUNCT
ejpam-6074	372	13	=	=	PUNCT
ejpam-6074	373	1	|s|	|s|	NOUN
ejpam-6074	373	2	=	=	SYM
ejpam-6074	373	3	4	4	NUM
ejpam-6074	373	4	+	+	NUM
ejpam-6074	373	5	∑t−2	∑t−2	NOUN
ejpam-6074	373	6	j=1	j=1	NOUN
ejpam-6074	373	7	|sj	|sj	X
ejpam-6074	374	1	|	|	NOUN
ejpam-6074	374	2	=	=	SYM
ejpam-6074	374	3	4	4	NUM
ejpam-6074	374	4	+	+	SYM
ejpam-6074	374	5	2(t−	2(t−	NUM
ejpam-6074	374	6	2	2	NUM
ejpam-6074	374	7	)	)	PUNCT
ejpam-6074	374	8	=	=	SYM
ejpam-6074	374	9	2	2	NUM
ejpam-6074	374	10	t.	t.	NOUN
ejpam-6074	374	11	case	case	NOUN
ejpam-6074	374	12	5	5	NUM
ejpam-6074	374	13	.	.	PUNCT
ejpam-6074	375	1	n	n	NOUN
ejpam-6074	375	2	=	=	SYM
ejpam-6074	375	3	4t+	4t+	NUM
ejpam-6074	375	4	3	3	X
ejpam-6074	375	5	.	.	PUNCT
ejpam-6074	376	1	let	let	VERB
ejpam-6074	376	2	sj	sj	INTJ
ejpam-6074	376	3	=	=	VERB
ejpam-6074	376	4	{	{	PUNCT
ejpam-6074	376	5	v4j+4	v4j+4	NOUN
ejpam-6074	376	6	,	,	PUNCT
ejpam-6074	376	7	v4j+5	v4j+5	NOUN
ejpam-6074	376	8	}	}	PUNCT
ejpam-6074	376	9	for	for	ADP
ejpam-6074	376	10	j	j	PROPN
ejpam-6074	376	11	=	=	SYM
ejpam-6074	376	12	1	1	PROPN
ejpam-6074	376	13	,	,	PUNCT
ejpam-6074	376	14	.	.	PUNCT
ejpam-6074	376	15	.	.	PUNCT
ejpam-6074	377	1	.	.	PUNCT
ejpam-6074	378	1	,	,	PUNCT
ejpam-6074	378	2	t	t	X
ejpam-6074	378	3	−	−	NOUN
ejpam-6074	379	1	1	1	X
ejpam-6074	379	2	.	.	PUNCT
ejpam-6074	380	1	let	let	VERB
ejpam-6074	380	2	s	s	VERB
ejpam-6074	380	3	=	=	NOUN
ejpam-6074	380	4	{	{	PUNCT
ejpam-6074	380	5	v1	v1	PROPN
ejpam-6074	380	6	,	,	PUNCT
ejpam-6074	380	7	v2	v2	PROPN
ejpam-6074	380	8	,	,	PUNCT
ejpam-6074	380	9	v5	v5	NOUN
ejpam-6074	380	10	}	}	PUNCT
ejpam-6074	380	11	∪	∪	X
ejpam-6074	380	12	(	(	PUNCT
ejpam-6074	380	13	⋃t−1	⋃t−1	X
ejpam-6074	380	14	j=1	j=1	NOUN
ejpam-6074	380	15	sj	sj	PROPN
ejpam-6074	380	16	)	)	PUNCT
ejpam-6074	380	17	.	.	PUNCT
ejpam-6074	381	1	then	then	ADV
ejpam-6074	381	2	s	s	VERB
ejpam-6074	381	3	is	be	AUX
ejpam-6074	381	4	a	a	DET
ejpam-6074	381	5	γ2mh	γ2mh	PROPN
ejpam-6074	381	6	-	-	PUNCT
ejpam-6074	381	7	set	set	NOUN
ejpam-6074	381	8	in	in	ADP
ejpam-6074	381	9	cn	cn	PROPN
ejpam-6074	381	10	and	and	CCONJ
ejpam-6074	381	11	γ2mh(cn	γ2mh(cn	NOUN
ejpam-6074	381	12	)	)	PUNCT
ejpam-6074	381	13	=	=	PUNCT
ejpam-6074	381	14	|s|	|s|	NOUN
ejpam-6074	381	15	=	=	SYM
ejpam-6074	381	16	4	4	NUM
ejpam-6074	381	17	+	+	NUM
ejpam-6074	381	18	∑t−1	∑t−1	VERB
ejpam-6074	381	19	j=1	j=1	NOUN
ejpam-6074	381	20	|sj	|sj	X
ejpam-6074	381	21	|	|	NOUN
ejpam-6074	381	22	=	=	SYM
ejpam-6074	381	23	3	3	NUM
ejpam-6074	381	24	+	+	SYM
ejpam-6074	381	25	2(t−	2(t−	NUM
ejpam-6074	381	26	1	1	NUM
ejpam-6074	381	27	)	)	PUNCT
ejpam-6074	381	28	=	=	SYM
ejpam-6074	381	29	2t+	2t+	NUM
ejpam-6074	381	30	1	1	NUM
ejpam-6074	381	31	.	.	PUNCT
ejpam-6074	382	1	if	if	SCONJ
ejpam-6074	382	2	g1	g1	PROPN
ejpam-6074	382	3	and	and	CCONJ
ejpam-6074	382	4	g2	g2	PROPN
ejpam-6074	382	5	are	be	AUX
ejpam-6074	382	6	the	the	DET
ejpam-6074	382	7	copies	copy	NOUN
ejpam-6074	382	8	of	of	ADP
ejpam-6074	382	9	graph	graph	NOUN
ejpam-6074	382	10	g	g	PROPN
ejpam-6074	382	11	in	in	ADP
ejpam-6074	382	12	the	the	DET
ejpam-6074	382	13	definition	definition	NOUN
ejpam-6074	382	14	of	of	ADP
ejpam-6074	382	15	the	the	DET
ejpam-6074	382	16	shadow	shadow	NOUN
ejpam-6074	382	17	graph	graph	VERB
ejpam-6074	382	18	d2(g	d2(g	PROPN
ejpam-6074	382	19	)	)	PUNCT
ejpam-6074	382	20	and	and	CCONJ
ejpam-6074	382	21	if	if	SCONJ
ejpam-6074	382	22	sg1	sg1	PROPN
ejpam-6074	382	23	⊆	⊆	PROPN
ejpam-6074	382	24	v	v	NOUN
ejpam-6074	382	25	(	(	PUNCT
ejpam-6074	382	26	g1	g1	PROPN
ejpam-6074	382	27	)	)	PUNCT
ejpam-6074	382	28	and	and	CCONJ
ejpam-6074	382	29	sg2	sg2	PROPN
ejpam-6074	382	30	⊆	⊆	NUM
ejpam-6074	382	31	v	v	PROPN
ejpam-6074	382	32	(	(	PUNCT
ejpam-6074	382	33	g2	g2	PROPN
ejpam-6074	382	34	)	)	PUNCT
ejpam-6074	382	35	,	,	PUNCT
ejpam-6074	382	36	then	then	ADV
ejpam-6074	382	37	the	the	DET
ejpam-6074	382	38	sets	set	NOUN
ejpam-6074	382	39	s′	s′	VERB
ejpam-6074	382	40	g1	g1	NOUN
ejpam-6074	382	41	and	and	CCONJ
ejpam-6074	382	42	s′	s′	ADJ
ejpam-6074	382	43	g2	g2	PROPN
ejpam-6074	382	44	are	be	AUX
ejpam-6074	382	45	the	the	DET
ejpam-6074	382	46	sets	set	NOUN
ejpam-6074	382	47	given	give	VERB
ejpam-6074	382	48	by	by	ADP
ejpam-6074	382	49	s′	s′	ADJ
ejpam-6074	382	50	g1	g1	NOUN
ejpam-6074	382	51	=	=	PUNCT
ejpam-6074	382	52	{	{	PUNCT
ejpam-6074	382	53	a′	a′	PROPN
ejpam-6074	382	54	∈	∈	PROPN
ejpam-6074	382	55	v	v	ADP
ejpam-6074	382	56	(	(	PUNCT
ejpam-6074	382	57	g2	g2	PROPN
ejpam-6074	382	58	)	)	PUNCT
ejpam-6074	382	59	:	:	PUNCT
ejpam-6074	382	60	a	a	DET
ejpam-6074	382	61	∈	∈	NOUN
ejpam-6074	382	62	sg1	sg1	NOUN
ejpam-6074	382	63	}	}	PUNCT
ejpam-6074	382	64	and	and	CCONJ
ejpam-6074	382	65	s′	s′	ADJ
ejpam-6074	382	66	g2	g2	PROPN
ejpam-6074	382	67	=	=	PRON
ejpam-6074	382	68	{	{	PUNCT
ejpam-6074	382	69	a	a	DET
ejpam-6074	382	70	∈	∈	PROPN
ejpam-6074	382	71	v	v	NOUN
ejpam-6074	382	72	(	(	PUNCT
ejpam-6074	382	73	g1	g1	PROPN
ejpam-6074	382	74	)	)	PUNCT
ejpam-6074	382	75	:	:	PUNCT
ejpam-6074	382	76	a	a	DET
ejpam-6074	382	77	′	′	NUM
ejpam-6074	382	78	∈	∈	PROPN
ejpam-6074	382	79	sg2	sg2	PROPN
ejpam-6074	382	80	}	}	PUNCT
ejpam-6074	382	81	.	.	PUNCT
ejpam-6074	383	1	r.	r.	PROPN
ejpam-6074	383	2	estrella	estrella	PROPN
ejpam-6074	383	3	,	,	PUNCT
ejpam-6074	383	4	gina	gina	PROPN
ejpam-6074	383	5	m.	m.	PROPN
ejpam-6074	383	6	malacas	malacas	PROPN
ejpam-6074	383	7	,	,	PUNCT
ejpam-6074	383	8	s.	s.	PROPN
ejpam-6074	383	9	canoy	canoy	PROPN
ejpam-6074	383	10	jr	jr	PROPN
ejpam-6074	383	11	.	.	PROPN
ejpam-6074	383	12	/	/	SYM
ejpam-6074	383	13	eur	eur	PROPN
ejpam-6074	383	14	.	.	PUNCT
ejpam-6074	384	1	j.	j.	PROPN
ejpam-6074	384	2	pure	pure	PROPN
ejpam-6074	384	3	appl	appl	PROPN
ejpam-6074	384	4	.	.	PROPN
ejpam-6074	384	5	math	math	PROPN
ejpam-6074	384	6	,	,	PUNCT
ejpam-6074	384	7	18	18	NUM
ejpam-6074	384	8	(	(	PUNCT
ejpam-6074	384	9	2	2	NUM
ejpam-6074	384	10	)	)	PUNCT
ejpam-6074	384	11	(	(	PUNCT
ejpam-6074	384	12	2025	2025	NUM
ejpam-6074	384	13	)	)	PUNCT
ejpam-6074	384	14	,	,	PUNCT
ejpam-6074	384	15	6074	6074	NUM
ejpam-6074	384	16	10	10	NUM
ejpam-6074	384	17	of	of	ADP
ejpam-6074	384	18	15	15	NUM
ejpam-6074	384	19	the	the	DET
ejpam-6074	384	20	next	next	ADJ
ejpam-6074	384	21	result	result	NOUN
ejpam-6074	384	22	is	be	AUX
ejpam-6074	384	23	found	find	VERB
ejpam-6074	384	24	in	in	ADP
ejpam-6074	384	25	[	[	X
ejpam-6074	384	26	20	20	NUM
ejpam-6074	384	27	]	]	PUNCT
ejpam-6074	384	28	.	.	PUNCT
ejpam-6074	385	1	theorem	theorem	ADJ
ejpam-6074	385	2	7	7	NUM
ejpam-6074	385	3	.	.	PUNCT
ejpam-6074	386	1	let	let	VERB
ejpam-6074	386	2	g	g	PRON
ejpam-6074	386	3	be	be	AUX
ejpam-6074	386	4	a	a	DET
ejpam-6074	386	5	non	non	ADJ
ejpam-6074	386	6	-	-	ADJ
ejpam-6074	386	7	trivial	trivial	ADJ
ejpam-6074	386	8	connected	connected	ADJ
ejpam-6074	386	9	graph	graph	NOUN
ejpam-6074	386	10	.	.	PUNCT
ejpam-6074	387	1	then	then	ADV
ejpam-6074	387	2	s	s	VERB
ejpam-6074	387	3	is	be	AUX
ejpam-6074	387	4	a	a	DET
ejpam-6074	387	5	hop	hop	NOUN
ejpam-6074	387	6	dominating	dominating	NOUN
ejpam-6074	387	7	set	set	VERB
ejpam-6074	387	8	in	in	ADP
ejpam-6074	387	9	d2(g	d2(g	PROPN
ejpam-6074	387	10	)	)	PUNCT
ejpam-6074	387	11	if	if	SCONJ
ejpam-6074	387	12	and	and	CCONJ
ejpam-6074	387	13	only	only	ADV
ejpam-6074	387	14	if	if	SCONJ
ejpam-6074	387	15	one	one	NUM
ejpam-6074	387	16	of	of	ADP
ejpam-6074	387	17	the	the	DET
ejpam-6074	387	18	following	follow	VERB
ejpam-6074	387	19	conditions	condition	NOUN
ejpam-6074	387	20	holds	hold	VERB
ejpam-6074	387	21	:	:	PUNCT
ejpam-6074	387	22	(	(	PUNCT
ejpam-6074	387	23	i	i	NOUN
ejpam-6074	387	24	)	)	PUNCT
ejpam-6074	387	25	s	s	VERB
ejpam-6074	387	26	is	be	AUX
ejpam-6074	387	27	a	a	DET
ejpam-6074	387	28	hop	hop	NOUN
ejpam-6074	387	29	dominating	dominating	NOUN
ejpam-6074	387	30	set	set	VERB
ejpam-6074	387	31	in	in	ADP
ejpam-6074	387	32	g1	g1	PROPN
ejpam-6074	387	33	.	.	PUNCT
ejpam-6074	388	1	(	(	PUNCT
ejpam-6074	388	2	ii	ii	X
ejpam-6074	388	3	)	)	PUNCT
ejpam-6074	388	4	s	s	VERB
ejpam-6074	388	5	is	be	AUX
ejpam-6074	388	6	a	a	DET
ejpam-6074	388	7	hop	hop	NOUN
ejpam-6074	388	8	dominating	dominating	NOUN
ejpam-6074	388	9	set	set	VERB
ejpam-6074	388	10	in	in	ADP
ejpam-6074	388	11	g2	g2	PROPN
ejpam-6074	388	12	.	.	PUNCT
ejpam-6074	389	1	(	(	PUNCT
ejpam-6074	389	2	iii	iii	X
ejpam-6074	389	3	)	)	PUNCT
ejpam-6074	389	4	s	s	PART
ejpam-6074	389	5	=	=	NOUN
ejpam-6074	389	6	sg1	sg1	NOUN
ejpam-6074	389	7	∪	∪	VERB
ejpam-6074	389	8	sg2	sg2	PROPN
ejpam-6074	389	9	such	such	ADJ
ejpam-6074	389	10	that	that	SCONJ
ejpam-6074	389	11	sg1	sg1	NOUN
ejpam-6074	389	12	∪	∪	ADP
ejpam-6074	389	13	s′	s′	ADJ
ejpam-6074	389	14	g2	g2	PROPN
ejpam-6074	389	15	and	and	CCONJ
ejpam-6074	389	16	s′	s′	ADJ
ejpam-6074	389	17	g1	g1	PROPN
ejpam-6074	389	18	∪	∪	ADP
ejpam-6074	389	19	sg2	sg2	PROPN
ejpam-6074	389	20	are	be	AUX
ejpam-6074	389	21	hop	hop	NOUN
ejpam-6074	389	22	dominating	dominating	NOUN
ejpam-6074	389	23	sets	set	NOUN
ejpam-6074	389	24	in	in	ADP
ejpam-6074	389	25	g1	g1	PROPN
ejpam-6074	389	26	and	and	CCONJ
ejpam-6074	389	27	g2	g2	PROPN
ejpam-6074	389	28	,	,	PUNCT
ejpam-6074	389	29	respectively	respectively	ADV
ejpam-6074	389	30	.	.	PUNCT
ejpam-6074	390	1	theorem	theorem	VERB
ejpam-6074	390	2	8	8	NUM
ejpam-6074	390	3	.	.	PUNCT
ejpam-6074	391	1	let	let	VERB
ejpam-6074	391	2	g	g	PRON
ejpam-6074	391	3	be	be	AUX
ejpam-6074	391	4	a	a	DET
ejpam-6074	391	5	non	non	ADJ
ejpam-6074	391	6	-	-	ADJ
ejpam-6074	391	7	trivial	trivial	ADJ
ejpam-6074	391	8	connected	connected	ADJ
ejpam-6074	391	9	graph	graph	NOUN
ejpam-6074	391	10	.	.	PUNCT
ejpam-6074	392	1	then	then	ADV
ejpam-6074	392	2	d2(g	d2(g	X
ejpam-6074	392	3	)	)	PUNCT
ejpam-6074	392	4	admits	admit	VERB
ejpam-6074	392	5	a	a	DET
ejpam-6074	392	6	2	2	NUM
ejpam-6074	392	7	-	-	PUNCT
ejpam-6074	392	8	step	step	NOUN
ejpam-6074	392	9	movable	movable	ADJ
ejpam-6074	392	10	hop	hop	NOUN
ejpam-6074	392	11	dominating	dominating	NOUN
ejpam-6074	392	12	set	set	NOUN
ejpam-6074	392	13	.	.	PUNCT
ejpam-6074	393	1	moreover	moreover	ADV
ejpam-6074	393	2	,	,	PUNCT
ejpam-6074	393	3	a	a	DET
ejpam-6074	393	4	set	set	NOUN
ejpam-6074	393	5	s	s	NOUN
ejpam-6074	393	6	⊆	⊆	NUM
ejpam-6074	393	7	v	v	NOUN
ejpam-6074	393	8	(	(	PUNCT
ejpam-6074	393	9	d2(g	d2(g	PROPN
ejpam-6074	393	10	)	)	PUNCT
ejpam-6074	393	11	)	)	PUNCT
ejpam-6074	393	12	is	be	AUX
ejpam-6074	393	13	2	2	NUM
ejpam-6074	393	14	-	-	PUNCT
ejpam-6074	393	15	step	step	NOUN
ejpam-6074	393	16	movable	movable	ADJ
ejpam-6074	393	17	hop	hop	NOUN
ejpam-6074	393	18	dominating	dominating	NOUN
ejpam-6074	393	19	in	in	ADP
ejpam-6074	393	20	d2(g	d2(g	PROPN
ejpam-6074	393	21	)	)	PUNCT
ejpam-6074	393	22	if	if	SCONJ
ejpam-6074	394	1	and	and	CCONJ
ejpam-6074	394	2	only	only	ADV
ejpam-6074	394	3	if	if	SCONJ
ejpam-6074	394	4	one	one	NUM
ejpam-6074	394	5	of	of	ADP
ejpam-6074	394	6	the	the	DET
ejpam-6074	394	7	following	follow	VERB
ejpam-6074	394	8	conditions	condition	NOUN
ejpam-6074	394	9	holds	hold	VERB
ejpam-6074	394	10	:	:	PUNCT
ejpam-6074	394	11	(	(	PUNCT
ejpam-6074	394	12	i	i	NOUN
ejpam-6074	394	13	)	)	PUNCT
ejpam-6074	394	14	s	s	VERB
ejpam-6074	394	15	is	be	AUX
ejpam-6074	394	16	a	a	DET
ejpam-6074	394	17	2	2	NUM
ejpam-6074	394	18	-	-	PUNCT
ejpam-6074	394	19	step	step	NOUN
ejpam-6074	394	20	movable	movable	ADJ
ejpam-6074	394	21	hop	hop	NOUN
ejpam-6074	394	22	dominating	dominating	NOUN
ejpam-6074	394	23	set	set	VERB
ejpam-6074	394	24	in	in	ADP
ejpam-6074	394	25	g1	g1	PROPN
ejpam-6074	394	26	.	.	PUNCT
ejpam-6074	395	1	(	(	PUNCT
ejpam-6074	395	2	ii	ii	X
ejpam-6074	395	3	)	)	PUNCT
ejpam-6074	395	4	s	s	VERB
ejpam-6074	395	5	is	be	AUX
ejpam-6074	395	6	a	a	DET
ejpam-6074	395	7	2	2	NUM
ejpam-6074	395	8	-	-	PUNCT
ejpam-6074	395	9	step	step	NOUN
ejpam-6074	395	10	movable	movable	ADJ
ejpam-6074	395	11	hop	hop	NOUN
ejpam-6074	395	12	dominating	dominating	NOUN
ejpam-6074	395	13	set	set	VERB
ejpam-6074	395	14	in	in	ADP
ejpam-6074	395	15	g2	g2	PROPN
ejpam-6074	395	16	.	.	PUNCT
ejpam-6074	396	1	(	(	PUNCT
ejpam-6074	396	2	iii	iii	X
ejpam-6074	396	3	)	)	PUNCT
ejpam-6074	396	4	s	s	PART
ejpam-6074	396	5	=	=	X
ejpam-6074	396	6	sg1∪sg2	sg1∪sg2	PROPN
ejpam-6074	396	7	such	such	ADJ
ejpam-6074	396	8	that	that	SCONJ
ejpam-6074	396	9	sg1∪s′	sg1∪s′	NOUN
ejpam-6074	396	10	g2	g2	PROPN
ejpam-6074	396	11	and	and	CCONJ
ejpam-6074	396	12	s′	s′	NOUN
ejpam-6074	396	13	g1	g1	PROPN
ejpam-6074	396	14	∪sg2	∪sg2	PROPN
ejpam-6074	396	15	are	be	AUX
ejpam-6074	396	16	2	2	NUM
ejpam-6074	396	17	-	-	PUNCT
ejpam-6074	396	18	step	step	NOUN
ejpam-6074	396	19	movable	movable	ADJ
ejpam-6074	396	20	hop	hop	NOUN
ejpam-6074	396	21	dominating	dominating	NOUN
ejpam-6074	396	22	sets	set	NOUN
ejpam-6074	396	23	in	in	ADP
ejpam-6074	396	24	g1	g1	PROPN
ejpam-6074	396	25	and	and	CCONJ
ejpam-6074	396	26	g2	g2	PROPN
ejpam-6074	396	27	,	,	PUNCT
ejpam-6074	396	28	respectively	respectively	ADV
ejpam-6074	396	29	.	.	PUNCT
ejpam-6074	397	1	proof	proof	NOUN
ejpam-6074	397	2	.	.	PUNCT
ejpam-6074	398	1	since	since	SCONJ
ejpam-6074	398	2	g	g	PROPN
ejpam-6074	398	3	is	be	AUX
ejpam-6074	398	4	non	non	ADJ
ejpam-6074	398	5	-	-	ADJ
ejpam-6074	398	6	trivial	trivial	ADJ
ejpam-6074	398	7	and	and	CCONJ
ejpam-6074	398	8	connected	connected	ADJ
ejpam-6074	398	9	,	,	PUNCT
ejpam-6074	398	10	it	it	PRON
ejpam-6074	398	11	follows	follow	VERB
ejpam-6074	398	12	that	that	SCONJ
ejpam-6074	398	13	d2(g	d2(g	X
ejpam-6074	398	14	)	)	PUNCT
ejpam-6074	398	15	is	be	AUX
ejpam-6074	398	16	connected	connect	VERB
ejpam-6074	398	17	and	and	CCONJ
ejpam-6074	398	18	γ(d2(g	γ(d2(g	PROPN
ejpam-6074	398	19	)	)	PUNCT
ejpam-6074	398	20	)	)	PUNCT
ejpam-6074	399	1	̸=	̸=	PROPN
ejpam-6074	399	2	1	1	NUM
ejpam-6074	399	3	.	.	PUNCT
ejpam-6074	400	1	thus	thus	ADV
ejpam-6074	400	2	,	,	PUNCT
ejpam-6074	400	3	d2(g	d2(g	PROPN
ejpam-6074	400	4	)	)	PUNCT
ejpam-6074	400	5	admits	admit	VERB
ejpam-6074	400	6	a	a	DET
ejpam-6074	400	7	2	2	NUM
ejpam-6074	400	8	-	-	PUNCT
ejpam-6074	400	9	step	step	NOUN
ejpam-6074	400	10	movable	movable	ADJ
ejpam-6074	400	11	hop	hop	NOUN
ejpam-6074	400	12	dominating	dominating	NOUN
ejpam-6074	400	13	set	set	VERB
ejpam-6074	400	14	by	by	ADP
ejpam-6074	400	15	theorem	theorem	NOUN
ejpam-6074	400	16	2	2	NUM
ejpam-6074	400	17	.	.	PUNCT
ejpam-6074	401	1	let	let	VERB
ejpam-6074	401	2	s	s	PRON
ejpam-6074	401	3	be	be	AUX
ejpam-6074	401	4	a	a	DET
ejpam-6074	401	5	2	2	NUM
ejpam-6074	401	6	-	-	PUNCT
ejpam-6074	401	7	step	step	NOUN
ejpam-6074	401	8	movable	movable	ADJ
ejpam-6074	401	9	hop	hop	NOUN
ejpam-6074	401	10	dominating	dominating	NOUN
ejpam-6074	401	11	set	set	VERB
ejpam-6074	401	12	in	in	ADP
ejpam-6074	401	13	d2(g	d2(g	PROPN
ejpam-6074	401	14	)	)	PUNCT
ejpam-6074	401	15	.	.	PUNCT
ejpam-6074	402	1	set	set	VERB
ejpam-6074	402	2	sg1	sg1	NOUN
ejpam-6074	402	3	=	=	SYM
ejpam-6074	402	4	s	s	PROPN
ejpam-6074	402	5	∩	∩	ADJ
ejpam-6074	402	6	v	v	X
ejpam-6074	402	7	(	(	PUNCT
ejpam-6074	402	8	g1	g1	PROPN
ejpam-6074	402	9	)	)	PUNCT
ejpam-6074	402	10	and	and	CCONJ
ejpam-6074	402	11	sg2	sg2	PROPN
ejpam-6074	402	12	=	=	PROPN
ejpam-6074	402	13	s	s	PROPN
ejpam-6074	402	14	∩	∩	ADJ
ejpam-6074	402	15	v	v	X
ejpam-6074	402	16	(	(	PUNCT
ejpam-6074	402	17	g2	g2	PROPN
ejpam-6074	402	18	)	)	PUNCT
ejpam-6074	402	19	.	.	PUNCT
ejpam-6074	403	1	if	if	SCONJ
ejpam-6074	403	2	sg2	sg2	PROPN
ejpam-6074	403	3	=	=	SYM
ejpam-6074	403	4	∅	∅	NOUN
ejpam-6074	403	5	,	,	PUNCT
ejpam-6074	403	6	then	then	ADV
ejpam-6074	403	7	s	s	PART
ejpam-6074	403	8	=	=	NOUN
ejpam-6074	403	9	sg1	sg1	PROPN
ejpam-6074	403	10	is	be	AUX
ejpam-6074	403	11	a	a	DET
ejpam-6074	403	12	hop	hop	NOUN
ejpam-6074	403	13	dominating	dominating	NOUN
ejpam-6074	403	14	set	set	VERB
ejpam-6074	403	15	in	in	ADP
ejpam-6074	403	16	g1	g1	NOUN
ejpam-6074	403	17	by	by	ADP
ejpam-6074	403	18	theorem	theorem	NOUN
ejpam-6074	403	19	7(i	7(i	NUM
ejpam-6074	403	20	)	)	PUNCT
ejpam-6074	403	21	.	.	PUNCT
ejpam-6074	404	1	let	let	VERB
ejpam-6074	404	2	v	v	X
ejpam-6074	404	3	∈	∈	PROPN
ejpam-6074	404	4	sg1	sg1	NOUN
ejpam-6074	404	5	.	.	PUNCT
ejpam-6074	405	1	suppose	suppose	VERB
ejpam-6074	405	2	sg1	sg1	NOUN
ejpam-6074	405	3	\	\	PROPN
ejpam-6074	405	4	{	{	PUNCT
ejpam-6074	405	5	v	v	NOUN
ejpam-6074	405	6	}	}	PUNCT
ejpam-6074	405	7	is	be	AUX
ejpam-6074	405	8	not	not	PART
ejpam-6074	405	9	hop	hop	NOUN
ejpam-6074	405	10	dominating	dominate	VERB
ejpam-6074	405	11	in	in	ADP
ejpam-6074	405	12	d2(g	d2(g	NOUN
ejpam-6074	405	13	)	)	PUNCT
ejpam-6074	405	14	.	.	PUNCT
ejpam-6074	406	1	since	since	SCONJ
ejpam-6074	406	2	s	s	PROPN
ejpam-6074	406	3	is	be	AUX
ejpam-6074	406	4	a	a	DET
ejpam-6074	406	5	2	2	NUM
ejpam-6074	406	6	-	-	PUNCT
ejpam-6074	406	7	step	step	NOUN
ejpam-6074	406	8	movable	movable	ADJ
ejpam-6074	406	9	hop	hop	NOUN
ejpam-6074	406	10	dominating	dominating	NOUN
ejpam-6074	406	11	set	set	VERB
ejpam-6074	406	12	in	in	ADP
ejpam-6074	406	13	d2(g	d2(g	PROPN
ejpam-6074	406	14	)	)	PUNCT
ejpam-6074	406	15	,	,	PUNCT
ejpam-6074	406	16	there	there	PRON
ejpam-6074	406	17	exists	exist	VERB
ejpam-6074	406	18	w	w	PROPN
ejpam-6074	406	19	∈	∈	PROPN
ejpam-6074	406	20	v	v	ADP
ejpam-6074	406	21	(	(	PUNCT
ejpam-6074	406	22	d2(g	d2(g	PROPN
ejpam-6074	406	23	)	)	PUNCT
ejpam-6074	406	24	)	)	PUNCT
ejpam-6074	406	25	\	\	PROPN
ejpam-6074	407	1	s	s	X
ejpam-6074	407	2	)	)	PUNCT
ejpam-6074	407	3	∩n2	∩n2	PROPN
ejpam-6074	407	4	d2(g)(v	d2(g)(v	PROPN
ejpam-6074	407	5	)	)	PUNCT
ejpam-6074	407	6	such	such	ADJ
ejpam-6074	407	7	that	that	SCONJ
ejpam-6074	407	8	(	(	PUNCT
ejpam-6074	407	9	s	s	NOUN
ejpam-6074	407	10	\	\	X
ejpam-6074	407	11	{	{	PUNCT
ejpam-6074	407	12	v	v	NOUN
ejpam-6074	407	13	}	}	PUNCT
ejpam-6074	407	14	)	)	PUNCT
ejpam-6074	407	15	∪	∪	ADP
ejpam-6074	407	16	{	{	PUNCT
ejpam-6074	407	17	w	w	AUX
ejpam-6074	407	18	}	}	PUNCT
ejpam-6074	407	19	is	be	AUX
ejpam-6074	407	20	hop	hop	NOUN
ejpam-6074	407	21	dominating	dominate	VERB
ejpam-6074	407	22	in	in	ADP
ejpam-6074	407	23	d2(g	d2(g	NOUN
ejpam-6074	407	24	)	)	PUNCT
ejpam-6074	407	25	.	.	PUNCT
ejpam-6074	408	1	if	if	SCONJ
ejpam-6074	408	2	w	w	PROPN
ejpam-6074	408	3	∈	∈	PROPN
ejpam-6074	408	4	v	v	X
ejpam-6074	408	5	(	(	PUNCT
ejpam-6074	408	6	g1	g1	PROPN
ejpam-6074	408	7	)	)	PUNCT
ejpam-6074	408	8	,	,	PUNCT
ejpam-6074	408	9	then	then	ADV
ejpam-6074	408	10	(	(	PUNCT
ejpam-6074	408	11	s	s	NOUN
ejpam-6074	408	12	\	\	X
ejpam-6074	408	13	{	{	PUNCT
ejpam-6074	408	14	v	v	NOUN
ejpam-6074	408	15	}	}	PUNCT
ejpam-6074	408	16	)	)	PUNCT
ejpam-6074	408	17	∪	∪	ADP
ejpam-6074	408	18	{	{	PUNCT
ejpam-6074	408	19	w	w	NOUN
ejpam-6074	408	20	}	}	PUNCT
ejpam-6074	408	21	=	=	SYM
ejpam-6074	408	22	(	(	PUNCT
ejpam-6074	408	23	sg1	sg1	X
ejpam-6074	408	24	\	\	PROPN
ejpam-6074	408	25	{	{	PUNCT
ejpam-6074	408	26	v	v	NOUN
ejpam-6074	408	27	}	}	PUNCT
ejpam-6074	408	28	)	)	PUNCT
ejpam-6074	408	29	∪	∪	ADP
ejpam-6074	408	30	{	{	PUNCT
ejpam-6074	408	31	w	w	NOUN
ejpam-6074	408	32	}	}	PUNCT
ejpam-6074	408	33	is	be	AUX
ejpam-6074	408	34	hop	hop	NOUN
ejpam-6074	408	35	dominating	dominate	VERB
ejpam-6074	408	36	in	in	ADP
ejpam-6074	408	37	g1	g1	NOUN
ejpam-6074	408	38	by	by	ADP
ejpam-6074	408	39	theorem	theorem	NOUN
ejpam-6074	408	40	7(i	7(i	NUM
ejpam-6074	408	41	)	)	PUNCT
ejpam-6074	408	42	.	.	PUNCT
ejpam-6074	409	1	suppose	suppose	VERB
ejpam-6074	409	2	w	w	NOUN
ejpam-6074	409	3	=	=	PUNCT
ejpam-6074	409	4	u′	u′	PART
ejpam-6074	409	5	∈	∈	NOUN
ejpam-6074	409	6	v	v	NOUN
ejpam-6074	409	7	(	(	PUNCT
ejpam-6074	409	8	g2	g2	PROPN
ejpam-6074	409	9	)	)	PUNCT
ejpam-6074	409	10	.	.	PUNCT
ejpam-6074	410	1	then	then	ADV
ejpam-6074	410	2	u	u	PROPN
ejpam-6074	410	3	∈	∈	PROPN
ejpam-6074	410	4	v	v	NOUN
ejpam-6074	410	5	(	(	PUNCT
ejpam-6074	410	6	g1	g1	PROPN
ejpam-6074	410	7	)	)	PUNCT
ejpam-6074	410	8	and	and	CCONJ
ejpam-6074	410	9	dd2(g)(v	dd2(g)(v	PROPN
ejpam-6074	410	10	,	,	PUNCT
ejpam-6074	410	11	u	u	NOUN
ejpam-6074	410	12	′	′	NOUN
ejpam-6074	410	13	)	)	PUNCT
ejpam-6074	410	14	=	=	PUNCT
ejpam-6074	411	1	dd2(g)(v	dd2(g)(v	PROPN
ejpam-6074	411	2	,	,	PUNCT
ejpam-6074	411	3	u	u	NOUN
ejpam-6074	411	4	)	)	PUNCT
ejpam-6074	411	5	=	=	PUNCT
ejpam-6074	411	6	dg1(v	dg1(v	PROPN
ejpam-6074	411	7	,	,	PUNCT
ejpam-6074	411	8	u	u	NOUN
ejpam-6074	411	9	)	)	PUNCT
ejpam-6074	411	10	=	=	SYM
ejpam-6074	411	11	2	2	X
ejpam-6074	411	12	.	.	PUNCT
ejpam-6074	411	13	since	since	SCONJ
ejpam-6074	411	14	sg1	sg1	PROPN
ejpam-6074	411	15	\	\	PROPN
ejpam-6074	411	16	{	{	PUNCT
ejpam-6074	411	17	v	v	NOUN
ejpam-6074	411	18	}	}	PUNCT
ejpam-6074	411	19	is	be	AUX
ejpam-6074	411	20	not	not	PART
ejpam-6074	411	21	hop	hop	NOUN
ejpam-6074	411	22	dominating	dominate	VERB
ejpam-6074	411	23	in	in	ADP
ejpam-6074	411	24	d2(g	d2(g	PROPN
ejpam-6074	411	25	)	)	PUNCT
ejpam-6074	411	26	,	,	PUNCT
ejpam-6074	411	27	u	u	PROPN
ejpam-6074	411	28	∈	∈	PROPN
ejpam-6074	411	29	(	(	PUNCT
ejpam-6074	411	30	v	v	NOUN
ejpam-6074	411	31	(	(	PUNCT
ejpam-6074	411	32	g1	g1	PROPN
ejpam-6074	411	33	)	)	PUNCT
ejpam-6074	411	34	\	\	NOUN
ejpam-6074	411	35	{	{	PUNCT
ejpam-6074	411	36	v	v	NOUN
ejpam-6074	411	37	}	}	PUNCT
ejpam-6074	411	38	)	)	PUNCT
ejpam-6074	411	39	∩n2	∩n2	PROPN
ejpam-6074	411	40	g1	g1	PROPN
ejpam-6074	411	41	(	(	PUNCT
ejpam-6074	411	42	v	v	NOUN
ejpam-6074	411	43	)	)	PUNCT
ejpam-6074	411	44	.	.	PUNCT
ejpam-6074	412	1	also	also	ADV
ejpam-6074	412	2	,	,	PUNCT
ejpam-6074	412	3	since	since	SCONJ
ejpam-6074	412	4	(	(	PUNCT
ejpam-6074	412	5	sg1	sg1	PROPN
ejpam-6074	412	6	\	\	PROPN
ejpam-6074	412	7	{	{	PUNCT
ejpam-6074	412	8	v	v	NOUN
ejpam-6074	412	9	}	}	PUNCT
ejpam-6074	412	10	)	)	PUNCT
ejpam-6074	412	11	∪	∪	ADP
ejpam-6074	412	12	{	{	PUNCT
ejpam-6074	412	13	u′	u′	PROPN
ejpam-6074	412	14	}	}	PUNCT
ejpam-6074	412	15	is	be	AUX
ejpam-6074	412	16	hop	hop	NOUN
ejpam-6074	412	17	dominating	dominate	VERB
ejpam-6074	412	18	in	in	ADP
ejpam-6074	412	19	d2(g	d2(g	PROPN
ejpam-6074	412	20	)	)	PUNCT
ejpam-6074	412	21	,	,	PUNCT
ejpam-6074	412	22	(	(	PUNCT
ejpam-6074	412	23	sg1	sg1	X
ejpam-6074	412	24	\	\	PROPN
ejpam-6074	412	25	{	{	PUNCT
ejpam-6074	412	26	v	v	NOUN
ejpam-6074	412	27	}	}	PUNCT
ejpam-6074	412	28	)	)	PUNCT
ejpam-6074	412	29	∪	∪	ADP
ejpam-6074	412	30	{	{	PUNCT
ejpam-6074	412	31	u	u	NOUN
ejpam-6074	412	32	}	}	PUNCT
ejpam-6074	412	33	is	be	AUX
ejpam-6074	412	34	hop	hop	NOUN
ejpam-6074	412	35	dominating	dominate	VERB
ejpam-6074	412	36	in	in	ADP
ejpam-6074	412	37	g1	g1	NOUN
ejpam-6074	412	38	by	by	ADP
ejpam-6074	412	39	theorem	theorem	ADJ
ejpam-6074	412	40	7(iii	7(iii	NUM
ejpam-6074	412	41	)	)	PUNCT
ejpam-6074	412	42	.	.	PUNCT
ejpam-6074	413	1	therefore	therefore	ADV
ejpam-6074	413	2	,	,	PUNCT
ejpam-6074	413	3	s	s	PART
ejpam-6074	413	4	=	=	NOUN
ejpam-6074	413	5	sg1	sg1	NOUN
ejpam-6074	413	6	is	be	AUX
ejpam-6074	413	7	2	2	NUM
ejpam-6074	413	8	-	-	PUNCT
ejpam-6074	413	9	step	step	NOUN
ejpam-6074	413	10	movable	movable	ADJ
ejpam-6074	413	11	hop	hop	NOUN
ejpam-6074	413	12	dominating	dominating	NOUN
ejpam-6074	413	13	in	in	ADP
ejpam-6074	413	14	g1	g1	PROPN
ejpam-6074	413	15	.	.	PUNCT
ejpam-6074	414	1	similarly	similarly	ADV
ejpam-6074	414	2	,	,	PUNCT
ejpam-6074	414	3	s	s	PART
ejpam-6074	414	4	=	=	PUNCT
ejpam-6074	414	5	sg2	sg2	PROPN
ejpam-6074	414	6	is	be	AUX
ejpam-6074	414	7	2	2	NUM
ejpam-6074	414	8	-	-	PUNCT
ejpam-6074	414	9	step	step	NOUN
ejpam-6074	414	10	movable	movable	ADJ
ejpam-6074	414	11	hop	hop	NOUN
ejpam-6074	414	12	dominating	dominating	NOUN
ejpam-6074	414	13	in	in	ADP
ejpam-6074	414	14	g2	g2	PROPN
ejpam-6074	414	15	whenever	whenever	SCONJ
ejpam-6074	414	16	sg1	sg1	VERB
ejpam-6074	414	17	=	=	PRON
ejpam-6074	414	18	∅.	∅.	VERB
ejpam-6074	414	19	finally	finally	ADV
ejpam-6074	414	20	,	,	PUNCT
ejpam-6074	414	21	suppose	suppose	VERB
ejpam-6074	414	22	sg1	sg1	NOUN
ejpam-6074	414	23	̸=	̸=	PROPN
ejpam-6074	414	24	∅	∅	NOUN
ejpam-6074	414	25	and	and	CCONJ
ejpam-6074	414	26	sg2	sg2	PROPN
ejpam-6074	414	27	̸=	̸=	PROPN
ejpam-6074	414	28	∅.	∅.	ADV
ejpam-6074	414	29	by	by	ADP
ejpam-6074	414	30	theorem	theorem	ADJ
ejpam-6074	414	31	7(iii	7(iii	NUM
ejpam-6074	414	32	)	)	PUNCT
ejpam-6074	414	33	,	,	PUNCT
ejpam-6074	414	34	q	q	NOUN
ejpam-6074	415	1	=	=	PUNCT
ejpam-6074	415	2	sg1	sg1	NOUN
ejpam-6074	415	3	∪	∪	ADJ
ejpam-6074	415	4	s′	s′	ADJ
ejpam-6074	415	5	g2	g2	PROPN
ejpam-6074	415	6	and	and	CCONJ
ejpam-6074	415	7	r	r	NOUN
ejpam-6074	415	8	=	=	SYM
ejpam-6074	415	9	s′	s′	PUNCT
ejpam-6074	415	10	g1	g1	PROPN
ejpam-6074	415	11	∪	∪	ADP
ejpam-6074	415	12	sg2	sg2	PROPN
ejpam-6074	415	13	are	be	AUX
ejpam-6074	415	14	hop	hop	NOUN
ejpam-6074	415	15	dominating	dominating	NOUN
ejpam-6074	415	16	sets	set	NOUN
ejpam-6074	415	17	in	in	ADP
ejpam-6074	415	18	g1	g1	PROPN
ejpam-6074	415	19	and	and	CCONJ
ejpam-6074	415	20	g2	g2	PROPN
ejpam-6074	415	21	,	,	PUNCT
ejpam-6074	415	22	respectively	respectively	ADV
ejpam-6074	415	23	.	.	PUNCT
ejpam-6074	416	1	let	let	VERB
ejpam-6074	416	2	p	p	PRON
ejpam-6074	416	3	∈	∈	PROPN
ejpam-6074	416	4	q	q	NOUN
ejpam-6074	416	5	such	such	ADJ
ejpam-6074	416	6	that	that	SCONJ
ejpam-6074	416	7	q\{p	q\{p	NOUN
ejpam-6074	416	8	}	}	PUNCT
ejpam-6074	416	9	=	=	SYM
ejpam-6074	416	10	(	(	PUNCT
ejpam-6074	416	11	sg1\{p})∪s′	sg1\{p})∪s′	NOUN
ejpam-6074	416	12	g2	g2	PROPN
ejpam-6074	416	13	is	be	AUX
ejpam-6074	416	14	not	not	PART
ejpam-6074	416	15	hop	hop	NOUN
ejpam-6074	416	16	dominating	dominate	VERB
ejpam-6074	416	17	in	in	ADP
ejpam-6074	416	18	g1	g1	PROPN
ejpam-6074	416	19	.	.	PUNCT
ejpam-6074	417	1	then	then	ADV
ejpam-6074	417	2	s	s	AUX
ejpam-6074	417	3	\	\	PROPN
ejpam-6074	417	4	{	{	PUNCT
ejpam-6074	417	5	p	p	X
ejpam-6074	417	6	}	}	PUNCT
ejpam-6074	417	7	is	be	AUX
ejpam-6074	417	8	not	not	PART
ejpam-6074	417	9	hop	hop	NOUN
ejpam-6074	417	10	dominating	dominate	VERB
ejpam-6074	417	11	in	in	ADP
ejpam-6074	417	12	d2(g	d2(g	PROPN
ejpam-6074	417	13	)	)	PUNCT
ejpam-6074	417	14	by	by	ADP
ejpam-6074	417	15	theorem	theorem	NOUN
ejpam-6074	417	16	7	7	NUM
ejpam-6074	417	17	.	.	PUNCT
ejpam-6074	417	18	since	since	SCONJ
ejpam-6074	417	19	s	s	PROPN
ejpam-6074	417	20	is	be	AUX
ejpam-6074	417	21	2	2	NUM
ejpam-6074	417	22	-	-	PUNCT
ejpam-6074	417	23	step	step	NOUN
ejpam-6074	417	24	movable	movable	ADJ
ejpam-6074	417	25	hop	hop	NOUN
ejpam-6074	417	26	dominating	dominating	NOUN
ejpam-6074	417	27	in	in	ADP
ejpam-6074	417	28	d2(g	d2(g	PROPN
ejpam-6074	417	29	)	)	PUNCT
ejpam-6074	417	30	,	,	PUNCT
ejpam-6074	417	31	there	there	PRON
ejpam-6074	417	32	exists	exist	VERB
ejpam-6074	417	33	q	q	PROPN
ejpam-6074	417	34	∈	∈	PROPN
ejpam-6074	417	35	(	(	PUNCT
ejpam-6074	417	36	v	v	NOUN
ejpam-6074	417	37	(	(	PUNCT
ejpam-6074	417	38	d2(g	d2(g	PROPN
ejpam-6074	417	39	)	)	PUNCT
ejpam-6074	417	40	\	\	PART
ejpam-6074	417	41	s	s	X
ejpam-6074	417	42	)	)	PUNCT
ejpam-6074	417	43	∩n2	∩n2	PROPN
ejpam-6074	417	44	d2(g)(p	d2(g)(p	PROPN
ejpam-6074	417	45	)	)	PUNCT
ejpam-6074	417	46	such	such	ADJ
ejpam-6074	417	47	that	that	SCONJ
ejpam-6074	417	48	(	(	PUNCT
ejpam-6074	417	49	s	s	NOUN
ejpam-6074	417	50	\	\	X
ejpam-6074	417	51	{	{	PUNCT
ejpam-6074	417	52	p})∪{q	p})∪{q	PROPN
ejpam-6074	417	53	}	}	PUNCT
ejpam-6074	417	54	is	be	AUX
ejpam-6074	417	55	hop	hop	NOUN
ejpam-6074	417	56	dominating	dominate	VERB
ejpam-6074	417	57	in	in	ADP
ejpam-6074	417	58	d2(g	d2(g	NOUN
ejpam-6074	417	59	)	)	PUNCT
ejpam-6074	417	60	.	.	PUNCT
ejpam-6074	418	1	if	if	SCONJ
ejpam-6074	418	2	q	q	PROPN
ejpam-6074	418	3	∈	∈	PROPN
ejpam-6074	418	4	v	v	NOUN
ejpam-6074	418	5	(	(	PUNCT
ejpam-6074	418	6	g1	g1	PROPN
ejpam-6074	418	7	)	)	PUNCT
ejpam-6074	418	8	,	,	PUNCT
ejpam-6074	418	9	then	then	ADV
ejpam-6074	418	10	q	q	PROPN
ejpam-6074	418	11	∈	∈	PROPN
ejpam-6074	418	12	(	(	PUNCT
ejpam-6074	418	13	v	v	NOUN
ejpam-6074	418	14	(	(	PUNCT
ejpam-6074	418	15	(	(	PUNCT
ejpam-6074	418	16	g1	g1	X
ejpam-6074	418	17	)	)	PUNCT
ejpam-6074	418	18	\q)∩n2	\q)∩n2	NOUN
ejpam-6074	418	19	g1	g1	NOUN
ejpam-6074	418	20	(	(	PUNCT
ejpam-6074	418	21	p	p	NOUN
ejpam-6074	418	22	)	)	PUNCT
ejpam-6074	418	23	and	and	CCONJ
ejpam-6074	418	24	(	(	PUNCT
ejpam-6074	418	25	s\{p})∪{q	s\{p})∪{q	X
ejpam-6074	418	26	}	}	PUNCT
ejpam-6074	418	27	=	=	PUNCT
ejpam-6074	419	1	[	[	X
ejpam-6074	419	2	sg1\{p})∪{q}]∪sg2	sg1\{p})∪{q}]∪sg2	NOUN
ejpam-6074	419	3	.	.	PUNCT
ejpam-6074	420	1	hence	hence	ADV
ejpam-6074	420	2	,	,	PUNCT
ejpam-6074	420	3	[	[	X
ejpam-6074	420	4	sg1\{p})∪{q}]∪s′	sg1\{p})∪{q}]∪s′	PROPN
ejpam-6074	420	5	g2	g2	PROPN
ejpam-6074	420	6	=	=	PUNCT
ejpam-6074	420	7	(	(	PUNCT
ejpam-6074	420	8	q\{p})∪{q	q\{p})∪{q	X
ejpam-6074	420	9	}	}	PUNCT
ejpam-6074	420	10	is	be	AUX
ejpam-6074	420	11	hop	hop	NOUN
ejpam-6074	420	12	dominating	dominate	VERB
ejpam-6074	420	13	in	in	ADP
ejpam-6074	420	14	g1	g1	NOUN
ejpam-6074	420	15	by	by	ADP
ejpam-6074	420	16	theorem	theorem	ADJ
ejpam-6074	420	17	7(iii	7(iii	NUM
ejpam-6074	420	18	)	)	PUNCT
ejpam-6074	420	19	.	.	PUNCT
ejpam-6074	421	1	suppose	suppose	VERB
ejpam-6074	421	2	q	q	X
ejpam-6074	421	3	=	=	PUNCT
ejpam-6074	421	4	s′	s′	VERB
ejpam-6074	421	5	∈	∈	PROPN
ejpam-6074	421	6	v	v	NOUN
ejpam-6074	421	7	(	(	PUNCT
ejpam-6074	421	8	g2	g2	PROPN
ejpam-6074	421	9	)	)	PUNCT
ejpam-6074	421	10	.	.	PUNCT
ejpam-6074	422	1	by	by	ADP
ejpam-6074	422	2	assumption	assumption	NOUN
ejpam-6074	422	3	,	,	PUNCT
ejpam-6074	422	4	s	s	NOUN
ejpam-6074	422	5	∈	∈	PROPN
ejpam-6074	422	6	(	(	PUNCT
ejpam-6074	422	7	v	v	NOUN
ejpam-6074	422	8	(	(	PUNCT
ejpam-6074	422	9	g1	g1	PROPN
ejpam-6074	422	10	)	)	PUNCT
ejpam-6074	422	11	\	\	PROPN
ejpam-6074	422	12	q	q	X
ejpam-6074	422	13	)	)	PUNCT
ejpam-6074	422	14	∩	∩	ADJ
ejpam-6074	422	15	n2	n2	ADJ
ejpam-6074	422	16	g1	g1	PROPN
ejpam-6074	422	17	(	(	PUNCT
ejpam-6074	422	18	p	p	NOUN
ejpam-6074	422	19	)	)	PUNCT
ejpam-6074	422	20	and	and	CCONJ
ejpam-6074	422	21	(	(	PUNCT
ejpam-6074	422	22	s	s	X
ejpam-6074	422	23	\	\	X
ejpam-6074	422	24	{	{	PUNCT
ejpam-6074	422	25	p	p	NOUN
ejpam-6074	422	26	}	}	PUNCT
ejpam-6074	422	27	)	)	PUNCT
ejpam-6074	422	28	∪	∪	ADP
ejpam-6074	422	29	{	{	PUNCT
ejpam-6074	422	30	q	q	NOUN
ejpam-6074	422	31	}	}	PUNCT
ejpam-6074	422	32	=	=	SYM
ejpam-6074	422	33	(	(	PUNCT
ejpam-6074	422	34	sg1	sg1	X
ejpam-6074	422	35	\	\	PROPN
ejpam-6074	422	36	{	{	PUNCT
ejpam-6074	422	37	p	p	NOUN
ejpam-6074	422	38	}	}	PUNCT
ejpam-6074	422	39	)	)	PUNCT
ejpam-6074	422	40	∪	∪	NOUN
ejpam-6074	422	41	(	(	PUNCT
ejpam-6074	422	42	sg2	sg2	PROPN
ejpam-6074	422	43	∪	∪	PROPN
ejpam-6074	422	44	{	{	PUNCT
ejpam-6074	422	45	s′	s′	NOUN
ejpam-6074	422	46	}	}	PUNCT
ejpam-6074	422	47	.	.	PUNCT
ejpam-6074	423	1	it	it	PRON
ejpam-6074	423	2	follows	follow	VERB
ejpam-6074	423	3	from	from	ADP
ejpam-6074	423	4	theorem	theorem	ADJ
ejpam-6074	423	5	7(iii	7(iii	NOUN
ejpam-6074	423	6	)	)	PUNCT
ejpam-6074	423	7	that	that	SCONJ
ejpam-6074	423	8	(	(	PUNCT
ejpam-6074	423	9	q	q	SYM
ejpam-6074	423	10	\	\	PROPN
ejpam-6074	423	11	{	{	PUNCT
ejpam-6074	423	12	p	p	NOUN
ejpam-6074	423	13	}	}	PUNCT
ejpam-6074	423	14	)	)	PUNCT
ejpam-6074	423	15	∪	∪	ADP
ejpam-6074	423	16	{	{	PUNCT
ejpam-6074	423	17	s	s	NOUN
ejpam-6074	423	18	}	}	PUNCT
ejpam-6074	423	19	=	=	NOUN
ejpam-6074	424	1	[	[	X
ejpam-6074	424	2	sg1	sg1	X
ejpam-6074	424	3	\	\	PROPN
ejpam-6074	424	4	{	{	PUNCT
ejpam-6074	424	5	p	p	NOUN
ejpam-6074	424	6	}	}	PUNCT
ejpam-6074	424	7	)	)	PUNCT
ejpam-6074	424	8	∪	∪	ADP
ejpam-6074	424	9	{	{	PUNCT
ejpam-6074	424	10	s	s	NOUN
ejpam-6074	424	11	}	}	PUNCT
ejpam-6074	424	12	]	]	PUNCT
ejpam-6074	424	13	∪	∪	ADP
ejpam-6074	424	14	s′	s′	ADJ
ejpam-6074	424	15	g2	g2	PROPN
ejpam-6074	424	16	is	be	AUX
ejpam-6074	424	17	hop	hop	NOUN
ejpam-6074	424	18	dominating	dominate	VERB
ejpam-6074	424	19	in	in	ADP
ejpam-6074	424	20	r.	r.	PROPN
ejpam-6074	424	21	estrella	estrella	PROPN
ejpam-6074	424	22	,	,	PUNCT
ejpam-6074	424	23	gina	gina	PROPN
ejpam-6074	424	24	m.	m.	PROPN
ejpam-6074	424	25	malacas	malacas	PROPN
ejpam-6074	424	26	,	,	PUNCT
ejpam-6074	424	27	s.	s.	PROPN
ejpam-6074	424	28	canoy	canoy	PROPN
ejpam-6074	424	29	jr	jr	PROPN
ejpam-6074	424	30	.	.	PROPN
ejpam-6074	424	31	/	/	SYM
ejpam-6074	424	32	eur	eur	PROPN
ejpam-6074	424	33	.	.	PUNCT
ejpam-6074	425	1	j.	j.	PROPN
ejpam-6074	425	2	pure	pure	PROPN
ejpam-6074	425	3	appl	appl	PROPN
ejpam-6074	425	4	.	.	PROPN
ejpam-6074	425	5	math	math	PROPN
ejpam-6074	425	6	,	,	PUNCT
ejpam-6074	425	7	18	18	NUM
ejpam-6074	425	8	(	(	PUNCT
ejpam-6074	425	9	2	2	NUM
ejpam-6074	425	10	)	)	PUNCT
ejpam-6074	425	11	(	(	PUNCT
ejpam-6074	425	12	2025	2025	NUM
ejpam-6074	425	13	)	)	PUNCT
ejpam-6074	425	14	,	,	PUNCT
ejpam-6074	425	15	6074	6074	NUM
ejpam-6074	425	16	11	11	NUM
ejpam-6074	425	17	of	of	ADP
ejpam-6074	425	18	15	15	NUM
ejpam-6074	425	19	g1	g1	NOUN
ejpam-6074	425	20	.	.	PUNCT
ejpam-6074	426	1	thus	thus	ADV
ejpam-6074	426	2	,	,	PUNCT
ejpam-6074	426	3	q	q	PROPN
ejpam-6074	426	4	is	be	AUX
ejpam-6074	426	5	2	2	NUM
ejpam-6074	426	6	-	-	PUNCT
ejpam-6074	426	7	step	step	NOUN
ejpam-6074	426	8	movable	movable	ADJ
ejpam-6074	426	9	hop	hop	NOUN
ejpam-6074	426	10	dominating	dominating	NOUN
ejpam-6074	426	11	in	in	ADP
ejpam-6074	426	12	g1	g1	PROPN
ejpam-6074	426	13	.	.	PUNCT
ejpam-6074	427	1	similarly	similarly	ADV
ejpam-6074	427	2	,	,	PUNCT
ejpam-6074	427	3	r	r	NOUN
ejpam-6074	427	4	is	be	AUX
ejpam-6074	427	5	2	2	NUM
ejpam-6074	427	6	-	-	PUNCT
ejpam-6074	427	7	step	step	NOUN
ejpam-6074	427	8	movable	movable	ADJ
ejpam-6074	427	9	hop	hop	NOUN
ejpam-6074	427	10	dominating	dominating	NOUN
ejpam-6074	427	11	in	in	ADP
ejpam-6074	427	12	g2	g2	PROPN
ejpam-6074	427	13	.	.	PUNCT
ejpam-6074	428	1	therefore	therefore	ADV
ejpam-6074	428	2	,	,	PUNCT
ejpam-6074	428	3	(	(	PUNCT
ejpam-6074	428	4	i	i	NOUN
ejpam-6074	428	5	)	)	PUNCT
ejpam-6074	428	6	or	or	CCONJ
ejpam-6074	428	7	(	(	PUNCT
ejpam-6074	428	8	ii	ii	NOUN
ejpam-6074	428	9	)	)	PUNCT
ejpam-6074	428	10	or	or	CCONJ
ejpam-6074	428	11	(	(	PUNCT
ejpam-6074	428	12	iii	iii	NOUN
ejpam-6074	428	13	)	)	PUNCT
ejpam-6074	428	14	holds	hold	VERB
ejpam-6074	428	15	.	.	PUNCT
ejpam-6074	429	1	for	for	ADP
ejpam-6074	429	2	the	the	DET
ejpam-6074	429	3	converse	converse	NOUN
ejpam-6074	429	4	,	,	PUNCT
ejpam-6074	429	5	suppose	suppose	VERB
ejpam-6074	429	6	(	(	PUNCT
ejpam-6074	429	7	i	i	NOUN
ejpam-6074	429	8	)	)	PUNCT
ejpam-6074	429	9	holds	hold	VERB
ejpam-6074	429	10	.	.	PUNCT
ejpam-6074	430	1	then	then	ADV
ejpam-6074	430	2	s	s	AUX
ejpam-6074	430	3	is	be	AUX
ejpam-6074	430	4	hop	hop	NOUN
ejpam-6074	430	5	dominating	dominate	VERB
ejpam-6074	430	6	in	in	ADP
ejpam-6074	430	7	d2(g	d2(g	PROPN
ejpam-6074	430	8	)	)	PUNCT
ejpam-6074	430	9	by	by	ADP
ejpam-6074	430	10	theorem	theorem	NOUN
ejpam-6074	430	11	7	7	NUM
ejpam-6074	430	12	.	.	PUNCT
ejpam-6074	431	1	let	let	VERB
ejpam-6074	431	2	x	x	PUNCT
ejpam-6074	431	3	∈	∈	NOUN
ejpam-6074	431	4	s	s	VERB
ejpam-6074	431	5	such	such	ADJ
ejpam-6074	431	6	that	that	PRON
ejpam-6074	431	7	s	s	VERB
ejpam-6074	431	8	\	\	X
ejpam-6074	431	9	{	{	PUNCT
ejpam-6074	431	10	x	x	NOUN
ejpam-6074	431	11	}	}	PUNCT
ejpam-6074	431	12	is	be	AUX
ejpam-6074	431	13	not	not	PART
ejpam-6074	431	14	hop	hop	NOUN
ejpam-6074	431	15	dominating	dominate	VERB
ejpam-6074	431	16	in	in	ADP
ejpam-6074	431	17	d2(g	d2(g	NOUN
ejpam-6074	431	18	)	)	PUNCT
ejpam-6074	431	19	.	.	PUNCT
ejpam-6074	432	1	by	by	ADP
ejpam-6074	432	2	assumption	assumption	NOUN
ejpam-6074	432	3	,	,	PUNCT
ejpam-6074	432	4	there	there	PRON
ejpam-6074	432	5	exists	exist	VERB
ejpam-6074	432	6	y	y	PROPN
ejpam-6074	432	7	∈	∈	PROPN
ejpam-6074	432	8	(	(	PUNCT
ejpam-6074	432	9	v	v	NOUN
ejpam-6074	432	10	(	(	PUNCT
ejpam-6074	432	11	g1	g1	PROPN
ejpam-6074	432	12	)	)	PUNCT
ejpam-6074	432	13	\s)∩n2	\s)∩n2	PROPN
ejpam-6074	432	14	g1	g1	PROPN
ejpam-6074	432	15	(	(	PUNCT
ejpam-6074	432	16	x	x	X
ejpam-6074	432	17	)	)	PUNCT
ejpam-6074	432	18	such	such	ADJ
ejpam-6074	432	19	that	that	SCONJ
ejpam-6074	432	20	(	(	PUNCT
ejpam-6074	432	21	s	s	NOUN
ejpam-6074	432	22	\	\	X
ejpam-6074	432	23	{	{	PUNCT
ejpam-6074	432	24	x})∪{y	x})∪{y	PROPN
ejpam-6074	432	25	}	}	PUNCT
ejpam-6074	432	26	is	be	AUX
ejpam-6074	432	27	hop	hop	NOUN
ejpam-6074	432	28	dominating	dominate	VERB
ejpam-6074	432	29	in	in	ADP
ejpam-6074	432	30	g1	g1	PROPN
ejpam-6074	432	31	.	.	PUNCT
ejpam-6074	433	1	by	by	ADP
ejpam-6074	433	2	theorem	theorem	NOUN
ejpam-6074	433	3	7(i	7(i	NUM
ejpam-6074	433	4	)	)	PUNCT
ejpam-6074	433	5	,	,	PUNCT
ejpam-6074	433	6	(	(	PUNCT
ejpam-6074	433	7	s\{x})∪{y	s\{x})∪{y	VERB
ejpam-6074	433	8	}	}	PUNCT
ejpam-6074	433	9	is	be	AUX
ejpam-6074	433	10	hop	hop	PROPN
ejpam-6074	433	11	dominating	dominate	VERB
ejpam-6074	433	12	ind2(g	ind2(g	NOUN
ejpam-6074	433	13	)	)	PUNCT
ejpam-6074	433	14	.	.	PUNCT
ejpam-6074	434	1	note	note	VERB
ejpam-6074	434	2	that	that	SCONJ
ejpam-6074	434	3	since	since	SCONJ
ejpam-6074	434	4	dg1(x	dg1(x	PROPN
ejpam-6074	434	5	,	,	PUNCT
ejpam-6074	434	6	y	y	NOUN
ejpam-6074	434	7	)	)	PUNCT
ejpam-6074	434	8	=	=	SYM
ejpam-6074	434	9	dd2(g)(x	dd2(g)(x	PROPN
ejpam-6074	434	10	,	,	PUNCT
ejpam-6074	434	11	y	y	NOUN
ejpam-6074	434	12	)	)	PUNCT
ejpam-6074	434	13	=	=	SYM
ejpam-6074	435	1	2	2	NUM
ejpam-6074	435	2	,	,	PUNCT
ejpam-6074	435	3	y	y	PROPN
ejpam-6074	435	4	∈	∈	PROPN
ejpam-6074	435	5	(	(	PUNCT
ejpam-6074	435	6	v	v	NOUN
ejpam-6074	435	7	(	(	PUNCT
ejpam-6074	435	8	d2(g	d2(g	PROPN
ejpam-6074	435	9	)	)	PUNCT
ejpam-6074	435	10	)	)	PUNCT
ejpam-6074	435	11	\	\	PROPN
ejpam-6074	436	1	s	s	X
ejpam-6074	436	2	)	)	PUNCT
ejpam-6074	436	3	∩n2	∩n2	PROPN
ejpam-6074	436	4	d2(g)(x	d2(g)(x	PROPN
ejpam-6074	436	5	)	)	PUNCT
ejpam-6074	436	6	.	.	PUNCT
ejpam-6074	437	1	thus	thus	ADV
ejpam-6074	437	2	,	,	PUNCT
ejpam-6074	437	3	s	s	X
ejpam-6074	437	4	is	be	AUX
ejpam-6074	437	5	2	2	NUM
ejpam-6074	437	6	-	-	PUNCT
ejpam-6074	437	7	step	step	NOUN
ejpam-6074	437	8	movable	movable	ADJ
ejpam-6074	437	9	hop	hop	NOUN
ejpam-6074	437	10	dominating	dominating	NOUN
ejpam-6074	437	11	in	in	ADP
ejpam-6074	437	12	d2(g	d2(g	NOUN
ejpam-6074	437	13	)	)	PUNCT
ejpam-6074	437	14	.	.	PUNCT
ejpam-6074	438	1	the	the	DET
ejpam-6074	438	2	same	same	ADJ
ejpam-6074	438	3	conclusion	conclusion	NOUN
ejpam-6074	438	4	holds	hold	VERB
ejpam-6074	438	5	if	if	SCONJ
ejpam-6074	438	6	(	(	PUNCT
ejpam-6074	438	7	ii	ii	NOUN
ejpam-6074	438	8	)	)	PUNCT
ejpam-6074	438	9	holds	hold	VERB
ejpam-6074	438	10	.	.	PUNCT
ejpam-6074	439	1	finally	finally	ADV
ejpam-6074	439	2	,	,	PUNCT
ejpam-6074	439	3	suppose	suppose	VERB
ejpam-6074	439	4	s	s	PRON
ejpam-6074	439	5	satisfies	satisfie	NOUN
ejpam-6074	439	6	(	(	PUNCT
ejpam-6074	439	7	iii	iii	NOUN
ejpam-6074	439	8	)	)	PUNCT
ejpam-6074	439	9	.	.	PUNCT
ejpam-6074	440	1	let	let	VERB
ejpam-6074	440	2	v	v	NUM
ejpam-6074	440	3	∈	∈	NOUN
ejpam-6074	440	4	s	s	VERB
ejpam-6074	440	5	such	such	ADJ
ejpam-6074	440	6	that	that	PRON
ejpam-6074	440	7	s	s	VERB
ejpam-6074	440	8	\	\	PROPN
ejpam-6074	440	9	{	{	PUNCT
ejpam-6074	440	10	v	v	NOUN
ejpam-6074	440	11	}	}	PUNCT
ejpam-6074	440	12	is	be	AUX
ejpam-6074	440	13	not	not	PART
ejpam-6074	440	14	hop	hop	NOUN
ejpam-6074	440	15	dominating	dominate	VERB
ejpam-6074	440	16	in	in	ADP
ejpam-6074	440	17	d2(g	d2(g	PROPN
ejpam-6074	440	18	)	)	PUNCT
ejpam-6074	440	19	.	.	PUNCT
ejpam-6074	441	1	suppose	suppose	VERB
ejpam-6074	441	2	,	,	PUNCT
ejpam-6074	441	3	without	without	ADP
ejpam-6074	441	4	loss	loss	NOUN
ejpam-6074	441	5	of	of	ADP
ejpam-6074	441	6	generality	generality	NOUN
ejpam-6074	441	7	,	,	PUNCT
ejpam-6074	441	8	that	that	DET
ejpam-6074	441	9	v	v	NUM
ejpam-6074	441	10	∈	∈	PROPN
ejpam-6074	441	11	sg1	sg1	NOUN
ejpam-6074	441	12	.	.	PUNCT
ejpam-6074	442	1	then	then	ADV
ejpam-6074	442	2	v	v	X
ejpam-6074	442	3	∈	∈	PROPN
ejpam-6074	442	4	(	(	PUNCT
ejpam-6074	442	5	sg1	sg1	NOUN
ejpam-6074	442	6	∪	∪	ADJ
ejpam-6074	442	7	s′	s′	ADJ
ejpam-6074	442	8	g2	g2	PROPN
ejpam-6074	442	9	)	)	PUNCT
ejpam-6074	442	10	.	.	PUNCT
ejpam-6074	443	1	suppose	suppose	VERB
ejpam-6074	443	2	q	q	X
ejpam-6074	444	1	=	=	PUNCT
ejpam-6074	444	2	(	(	PUNCT
ejpam-6074	444	3	sg1	sg1	NOUN
ejpam-6074	444	4	∪	∪	ADP
ejpam-6074	444	5	s′	s′	ADJ
ejpam-6074	444	6	g2	g2	PROPN
ejpam-6074	444	7	)	)	PUNCT
ejpam-6074	444	8	\	\	PROPN
ejpam-6074	444	9	{	{	PUNCT
ejpam-6074	444	10	v	v	NOUN
ejpam-6074	444	11	}	}	PUNCT
ejpam-6074	444	12	=	=	SYM
ejpam-6074	444	13	(	(	PUNCT
ejpam-6074	444	14	sg1	sg1	X
ejpam-6074	444	15	\	\	PROPN
ejpam-6074	444	16	{	{	PUNCT
ejpam-6074	444	17	v	v	NOUN
ejpam-6074	444	18	}	}	PUNCT
ejpam-6074	444	19	)	)	PUNCT
ejpam-6074	444	20	∪	∪	ADP
ejpam-6074	444	21	s′	s′	ADJ
ejpam-6074	444	22	g2	g2	PROPN
ejpam-6074	444	23	is	be	AUX
ejpam-6074	444	24	hop	hop	NOUN
ejpam-6074	444	25	dominating	dominate	VERB
ejpam-6074	444	26	in	in	ADP
ejpam-6074	444	27	g1	g1	PROPN
ejpam-6074	444	28	.	.	PUNCT
ejpam-6074	445	1	let	let	VERB
ejpam-6074	445	2	p	p	NOUN
ejpam-6074	445	3	/∈	/∈	PUNCT
ejpam-6074	446	1	[	[	X
ejpam-6074	446	2	(	(	PUNCT
ejpam-6074	446	3	sg1	sg1	PROPN
ejpam-6074	446	4	\	\	PROPN
ejpam-6074	446	5	{	{	PUNCT
ejpam-6074	446	6	v	v	NOUN
ejpam-6074	446	7	}	}	PUNCT
ejpam-6074	446	8	)	)	PUNCT
ejpam-6074	446	9	∪	∪	ADP
ejpam-6074	446	10	sg2	sg2	PROPN
ejpam-6074	446	11	]	]	PUNCT
ejpam-6074	446	12	.	.	PUNCT
ejpam-6074	447	1	suppose	suppose	VERB
ejpam-6074	447	2	p	p	X
ejpam-6074	447	3	∈	∈	PROPN
ejpam-6074	447	4	v	v	NOUN
ejpam-6074	447	5	(	(	PUNCT
ejpam-6074	447	6	g1	g1	PROPN
ejpam-6074	447	7	)	)	PUNCT
ejpam-6074	447	8	.	.	PUNCT
ejpam-6074	448	1	if	if	SCONJ
ejpam-6074	448	2	p′	p′	NOUN
ejpam-6074	448	3	∈	∈	PROPN
ejpam-6074	448	4	sg2	sg2	PROPN
ejpam-6074	448	5	,	,	PUNCT
ejpam-6074	448	6	then	then	ADV
ejpam-6074	448	7	p′	p′	NOUN
ejpam-6074	448	8	∈	∈	PROPN
ejpam-6074	448	9	[	[	X
ejpam-6074	448	10	(	(	PUNCT
ejpam-6074	448	11	sg1	sg1	PROPN
ejpam-6074	448	12	\	\	PROPN
ejpam-6074	448	13	{	{	PUNCT
ejpam-6074	448	14	v	v	NOUN
ejpam-6074	448	15	}	}	PUNCT
ejpam-6074	448	16	)	)	PUNCT
ejpam-6074	448	17	∪	∪	ADP
ejpam-6074	448	18	sg2	sg2	PROPN
ejpam-6074	448	19	]	]	PUNCT
ejpam-6074	448	20	and	and	CCONJ
ejpam-6074	448	21	dd2(g)(p	dd2(g)(p	NOUN
ejpam-6074	448	22	,	,	PUNCT
ejpam-6074	448	23	p	p	NOUN
ejpam-6074	448	24	′	′	NOUN
ejpam-6074	448	25	)	)	PUNCT
ejpam-6074	448	26	=	=	SYM
ejpam-6074	448	27	2	2	X
ejpam-6074	448	28	.	.	X
ejpam-6074	448	29	if	if	SCONJ
ejpam-6074	448	30	p′	p′	PROPN
ejpam-6074	448	31	/∈	/∈	PUNCT
ejpam-6074	449	1	sg2	sg2	PROPN
ejpam-6074	449	2	,	,	PUNCT
ejpam-6074	449	3	then	then	ADV
ejpam-6074	449	4	p	p	PROPN
ejpam-6074	449	5	/∈	/∈	PROPN
ejpam-6074	449	6	q.	q.	PROPN
ejpam-6074	449	7	since	since	SCONJ
ejpam-6074	449	8	q	q	PROPN
ejpam-6074	449	9	is	be	AUX
ejpam-6074	449	10	hop	hop	NOUN
ejpam-6074	449	11	dominating	dominate	VERB
ejpam-6074	449	12	in	in	ADP
ejpam-6074	449	13	g1	g1	PROPN
ejpam-6074	449	14	,	,	PUNCT
ejpam-6074	449	15	there	there	PRON
ejpam-6074	449	16	exists	exist	VERB
ejpam-6074	449	17	q	q	PROPN
ejpam-6074	449	18	∈	∈	PROPN
ejpam-6074	449	19	q	q	NOUN
ejpam-6074	449	20	such	such	ADJ
ejpam-6074	449	21	that	that	SCONJ
ejpam-6074	449	22	dg1(p	dg1(p	PROPN
ejpam-6074	449	23	,	,	PUNCT
ejpam-6074	449	24	q	q	NOUN
ejpam-6074	449	25	)	)	PUNCT
ejpam-6074	449	26	=	=	SYM
ejpam-6074	449	27	dd2(g)(p	dd2(g)(p	NOUN
ejpam-6074	449	28	,	,	PUNCT
ejpam-6074	449	29	q	q	NOUN
ejpam-6074	449	30	)	)	PUNCT
ejpam-6074	450	1	=	=	SYM
ejpam-6074	450	2	2	2	X
ejpam-6074	450	3	.	.	X
ejpam-6074	451	1	if	if	SCONJ
ejpam-6074	451	2	q	q	X
ejpam-6074	451	3	∈	∈	PROPN
ejpam-6074	451	4	sg1	sg1	X
ejpam-6074	451	5	\	\	NOUN
ejpam-6074	451	6	{	{	PUNCT
ejpam-6074	451	7	v	v	NOUN
ejpam-6074	451	8	}	}	PUNCT
ejpam-6074	451	9	,	,	PUNCT
ejpam-6074	451	10	then	then	ADV
ejpam-6074	451	11	q	q	PROPN
ejpam-6074	451	12	∈	∈	PROPN
ejpam-6074	451	13	[	[	X
ejpam-6074	451	14	(	(	PUNCT
ejpam-6074	451	15	sg1	sg1	PROPN
ejpam-6074	451	16	\	\	PROPN
ejpam-6074	451	17	{	{	PUNCT
ejpam-6074	451	18	v})∪sg2	v})∪sg2	X
ejpam-6074	451	19	]	]	PUNCT
ejpam-6074	451	20	.	.	PUNCT
ejpam-6074	452	1	suppose	suppose	VERB
ejpam-6074	452	2	q	q	X
ejpam-6074	452	3	/∈	/∈	PUNCT
ejpam-6074	452	4	sg1	sg1	PROPN
ejpam-6074	452	5	\	\	PROPN
ejpam-6074	452	6	{	{	PUNCT
ejpam-6074	452	7	v	v	NOUN
ejpam-6074	452	8	}	}	PUNCT
ejpam-6074	452	9	.	.	PUNCT
ejpam-6074	453	1	then	then	ADV
ejpam-6074	453	2	q	q	PROPN
ejpam-6074	453	3	∈	∈	PROPN
ejpam-6074	453	4	s′	s′	VERB
ejpam-6074	453	5	g2	g2	PROPN
ejpam-6074	453	6	.	.	PUNCT
ejpam-6074	454	1	hence	hence	ADV
ejpam-6074	454	2	,	,	PUNCT
ejpam-6074	454	3	q′	q′	PUNCT
ejpam-6074	454	4	∈	∈	PROPN
ejpam-6074	454	5	sg2	sg2	PROPN
ejpam-6074	454	6	⊆	⊆	NUM
ejpam-6074	454	7	[	[	X
ejpam-6074	454	8	(	(	PUNCT
ejpam-6074	454	9	sg1	sg1	PROPN
ejpam-6074	454	10	\	\	PROPN
ejpam-6074	454	11	{	{	PUNCT
ejpam-6074	454	12	v	v	NOUN
ejpam-6074	454	13	}	}	PUNCT
ejpam-6074	454	14	)	)	PUNCT
ejpam-6074	454	15	∪	∪	ADP
ejpam-6074	454	16	sg2	sg2	PROPN
ejpam-6074	454	17	]	]	PUNCT
ejpam-6074	454	18	and	and	CCONJ
ejpam-6074	454	19	dd2(g)(p	dd2(g)(p	NOUN
ejpam-6074	454	20	,	,	PUNCT
ejpam-6074	454	21	q	q	NOUN
ejpam-6074	454	22	′	′	NOUN
ejpam-6074	454	23	)	)	PUNCT
ejpam-6074	454	24	=	=	SYM
ejpam-6074	454	25	dd2(g)(p	dd2(g)(p	NOUN
ejpam-6074	454	26	,	,	PUNCT
ejpam-6074	454	27	q	q	NOUN
ejpam-6074	454	28	)	)	PUNCT
ejpam-6074	454	29	=	=	SYM
ejpam-6074	454	30	2	2	X
ejpam-6074	454	31	.	.	PUNCT
ejpam-6074	454	32	this	this	PRON
ejpam-6074	454	33	implies	imply	VERB
ejpam-6074	454	34	that	that	SCONJ
ejpam-6074	454	35	s	s	VERB
ejpam-6074	454	36	\	\	PROPN
ejpam-6074	454	37	{	{	PUNCT
ejpam-6074	454	38	v	v	NOUN
ejpam-6074	454	39	}	}	PUNCT
ejpam-6074	454	40	=	=	SYM
ejpam-6074	455	1	[	[	X
ejpam-6074	455	2	(	(	PUNCT
ejpam-6074	455	3	sg1	sg1	PROPN
ejpam-6074	455	4	\	\	PROPN
ejpam-6074	455	5	{	{	PUNCT
ejpam-6074	455	6	v	v	NOUN
ejpam-6074	455	7	}	}	PUNCT
ejpam-6074	455	8	)	)	PUNCT
ejpam-6074	455	9	∪	∪	ADP
ejpam-6074	455	10	sg2	sg2	PROPN
ejpam-6074	455	11	]	]	PUNCT
ejpam-6074	455	12	is	be	AUX
ejpam-6074	455	13	hop	hop	PROPN
ejpam-6074	455	14	dominating	dominating	NOUN
ejpam-6074	455	15	,	,	PUNCT
ejpam-6074	455	16	a	a	DET
ejpam-6074	455	17	contradiction	contradiction	NOUN
ejpam-6074	455	18	.	.	PUNCT
ejpam-6074	456	1	now	now	ADV
ejpam-6074	456	2	,	,	PUNCT
ejpam-6074	456	3	since	since	SCONJ
ejpam-6074	456	4	sg1	sg1	PROPN
ejpam-6074	456	5	∪	∪	ADP
ejpam-6074	456	6	s′	s′	ADJ
ejpam-6074	456	7	g2	g2	PROPN
ejpam-6074	456	8	is	be	AUX
ejpam-6074	456	9	2	2	NUM
ejpam-6074	456	10	-	-	PUNCT
ejpam-6074	456	11	step	step	NOUN
ejpam-6074	456	12	movable	movable	ADJ
ejpam-6074	456	13	hop	hop	NOUN
ejpam-6074	456	14	dominating	dominating	NOUN
ejpam-6074	456	15	in	in	ADP
ejpam-6074	456	16	g1	g1	PROPN
ejpam-6074	456	17	,	,	PUNCT
ejpam-6074	456	18	there	there	PRON
ejpam-6074	456	19	exists	exist	VERB
ejpam-6074	456	20	t	t	PROPN
ejpam-6074	456	21	∈	∈	PROPN
ejpam-6074	457	1	[	[	X
ejpam-6074	457	2	v	v	X
ejpam-6074	457	3	(	(	PUNCT
ejpam-6074	457	4	g1	g1	PROPN
ejpam-6074	457	5	)	)	PUNCT
ejpam-6074	457	6	\	\	NOUN
ejpam-6074	458	1	(	(	PUNCT
ejpam-6074	458	2	sg1	sg1	NOUN
ejpam-6074	458	3	∪	∪	VERB
ejpam-6074	458	4	s′	s′	ADJ
ejpam-6074	458	5	g2	g2	PROPN
ejpam-6074	458	6	)	)	PUNCT
ejpam-6074	458	7	]	]	PUNCT
ejpam-6074	458	8	∩n2	∩n2	PROPN
ejpam-6074	458	9	g1	g1	PROPN
ejpam-6074	458	10	(	(	PUNCT
ejpam-6074	458	11	v	v	NOUN
ejpam-6074	458	12	)	)	PUNCT
ejpam-6074	458	13	such	such	ADJ
ejpam-6074	458	14	that	that	SCONJ
ejpam-6074	458	15	[	[	X
ejpam-6074	458	16	(	(	PUNCT
ejpam-6074	458	17	sg1	sg1	NOUN
ejpam-6074	458	18	∪	∪	ADJ
ejpam-6074	458	19	s′	s′	ADJ
ejpam-6074	458	20	g2	g2	PROPN
ejpam-6074	458	21	)	)	PUNCT
ejpam-6074	458	22	\	\	PROPN
ejpam-6074	459	1	{	{	PUNCT
ejpam-6074	459	2	v	v	NOUN
ejpam-6074	459	3	}	}	PUNCT
ejpam-6074	459	4	]	]	PUNCT
ejpam-6074	459	5	∪	∪	X
ejpam-6074	459	6	{	{	PUNCT
ejpam-6074	459	7	t	t	NOUN
ejpam-6074	459	8	}	}	PUNCT
ejpam-6074	459	9	is	be	AUX
ejpam-6074	459	10	hop	hop	NOUN
ejpam-6074	459	11	dominating	dominate	VERB
ejpam-6074	459	12	in	in	ADP
ejpam-6074	459	13	g1	g1	PROPN
ejpam-6074	459	14	.	.	PUNCT
ejpam-6074	460	1	by	by	ADP
ejpam-6074	460	2	theorem	theorem	NOUN
ejpam-6074	460	3	7	7	NUM
ejpam-6074	460	4	,	,	PUNCT
ejpam-6074	460	5	it	it	PRON
ejpam-6074	460	6	follows	follow	VERB
ejpam-6074	460	7	that	that	SCONJ
ejpam-6074	460	8	[	[	X
ejpam-6074	460	9	(	(	PUNCT
ejpam-6074	460	10	sg1	sg1	PROPN
ejpam-6074	460	11	\	\	PROPN
ejpam-6074	460	12	{	{	PUNCT
ejpam-6074	460	13	v	v	NOUN
ejpam-6074	460	14	}	}	PUNCT
ejpam-6074	460	15	)	)	PUNCT
ejpam-6074	460	16	∪	∪	ADP
ejpam-6074	460	17	{	{	PUNCT
ejpam-6074	460	18	t	t	PROPN
ejpam-6074	460	19	}	}	PUNCT
ejpam-6074	460	20	]	]	PUNCT
ejpam-6074	460	21	∪	∪	ADP
ejpam-6074	460	22	s′	s′	ADJ
ejpam-6074	460	23	g2	g2	PROPN
ejpam-6074	460	24	is	be	AUX
ejpam-6074	460	25	hop	hop	NOUN
ejpam-6074	460	26	dominating	dominate	VERB
ejpam-6074	460	27	in	in	ADP
ejpam-6074	460	28	d2(g	d2(g	NOUN
ejpam-6074	460	29	)	)	PUNCT
ejpam-6074	460	30	.	.	PUNCT
ejpam-6074	461	1	again	again	ADV
ejpam-6074	461	2	,	,	PUNCT
ejpam-6074	461	3	this	this	PRON
ejpam-6074	461	4	will	will	AUX
ejpam-6074	461	5	imply	imply	VERB
ejpam-6074	461	6	that	that	SCONJ
ejpam-6074	461	7	[	[	X
ejpam-6074	461	8	(	(	PUNCT
ejpam-6074	461	9	sg1	sg1	PROPN
ejpam-6074	461	10	\	\	PROPN
ejpam-6074	461	11	{	{	PUNCT
ejpam-6074	461	12	v	v	NOUN
ejpam-6074	461	13	}	}	PUNCT
ejpam-6074	461	14	)	)	PUNCT
ejpam-6074	461	15	∪	∪	ADP
ejpam-6074	461	16	{	{	PUNCT
ejpam-6074	461	17	t	t	PROPN
ejpam-6074	461	18	}	}	PUNCT
ejpam-6074	461	19	]	]	PUNCT
ejpam-6074	461	20	∪	∪	ADP
ejpam-6074	461	21	sg2	sg2	PROPN
ejpam-6074	461	22	is	be	AUX
ejpam-6074	461	23	hop	hop	NOUN
ejpam-6074	461	24	dominating	dominate	VERB
ejpam-6074	461	25	in	in	ADP
ejpam-6074	461	26	d2(g	d2(g	PROPN
ejpam-6074	461	27	)	)	PUNCT
ejpam-6074	461	28	,	,	PUNCT
ejpam-6074	461	29	showing	show	VERB
ejpam-6074	461	30	that	that	SCONJ
ejpam-6074	461	31	s	s	VERB
ejpam-6074	461	32	is	be	AUX
ejpam-6074	461	33	a	a	DET
ejpam-6074	461	34	2	2	NUM
ejpam-6074	461	35	-	-	PUNCT
ejpam-6074	461	36	step	step	NOUN
ejpam-6074	461	37	movable	movable	ADJ
ejpam-6074	461	38	hop	hop	NOUN
ejpam-6074	461	39	dominating	dominating	NOUN
ejpam-6074	461	40	set	set	VERB
ejpam-6074	461	41	in	in	ADP
ejpam-6074	461	42	d2(g	d2(g	PROPN
ejpam-6074	461	43	)	)	PUNCT
ejpam-6074	461	44	.	.	PUNCT
ejpam-6074	462	1	the	the	DET
ejpam-6074	462	2	next	next	ADJ
ejpam-6074	462	3	result	result	NOUN
ejpam-6074	462	4	is	be	AUX
ejpam-6074	462	5	a	a	DET
ejpam-6074	462	6	direct	direct	ADJ
ejpam-6074	462	7	consequence	consequence	NOUN
ejpam-6074	462	8	of	of	ADP
ejpam-6074	462	9	theorem	theorem	ADJ
ejpam-6074	462	10	8	8	NUM
ejpam-6074	462	11	.	.	PUNCT
ejpam-6074	462	12	corollary	corollary	ADJ
ejpam-6074	462	13	3	3	X
ejpam-6074	462	14	.	.	PUNCT
ejpam-6074	463	1	let	let	VERB
ejpam-6074	463	2	g	g	PRON
ejpam-6074	463	3	be	be	AUX
ejpam-6074	463	4	a	a	DET
ejpam-6074	463	5	non	non	ADJ
ejpam-6074	463	6	-	-	ADJ
ejpam-6074	463	7	trivial	trivial	ADJ
ejpam-6074	463	8	connected	connected	ADJ
ejpam-6074	463	9	graph	graph	NOUN
ejpam-6074	463	10	.	.	PUNCT
ejpam-6074	464	1	then	then	ADV
ejpam-6074	464	2	γ2mh(d2(g	γ2mh(d2(g	ADJ
ejpam-6074	464	3	)	)	PUNCT
ejpam-6074	464	4	)	)	PUNCT
ejpam-6074	465	1	=	=	SYM
ejpam-6074	465	2	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	465	3	)	)	PUNCT
ejpam-6074	465	4	.	.	PUNCT
ejpam-6074	466	1	proof	proof	NOUN
ejpam-6074	466	2	.	.	PUNCT
ejpam-6074	467	1	let	let	VERB
ejpam-6074	467	2	s	s	PRON
ejpam-6074	467	3	be	be	AUX
ejpam-6074	467	4	a	a	DET
ejpam-6074	467	5	γ2mh	γ2mh	NOUN
ejpam-6074	467	6	-	-	PUNCT
ejpam-6074	467	7	set	set	VERB
ejpam-6074	467	8	in	in	ADP
ejpam-6074	467	9	d2(g	d2(g	NOUN
ejpam-6074	467	10	)	)	PUNCT
ejpam-6074	467	11	.	.	PUNCT
ejpam-6074	468	1	if	if	SCONJ
ejpam-6074	468	2	s	s	VERB
ejpam-6074	468	3	⊆	⊆	NUM
ejpam-6074	468	4	v	v	NOUN
ejpam-6074	468	5	(	(	PUNCT
ejpam-6074	468	6	g1	g1	PROPN
ejpam-6074	468	7	)	)	PUNCT
ejpam-6074	468	8	or	or	CCONJ
ejpam-6074	468	9	s	s	PRON
ejpam-6074	468	10	⊆	⊆	NUM
ejpam-6074	468	11	v	v	NOUN
ejpam-6074	468	12	(	(	PUNCT
ejpam-6074	468	13	g2	g2	PROPN
ejpam-6074	468	14	)	)	PUNCT
ejpam-6074	468	15	,	,	PUNCT
ejpam-6074	468	16	then	then	ADV
ejpam-6074	468	17	s	s	VERB
ejpam-6074	468	18	is	be	AUX
ejpam-6074	468	19	a	a	DET
ejpam-6074	468	20	2	2	NUM
ejpam-6074	468	21	-	-	PUNCT
ejpam-6074	468	22	step	step	NOUN
ejpam-6074	468	23	movable	movable	ADJ
ejpam-6074	468	24	hop	hop	NOUN
ejpam-6074	468	25	dominating	dominating	NOUN
ejpam-6074	468	26	set	set	VERB
ejpam-6074	468	27	in	in	ADP
ejpam-6074	468	28	g1	g1	PROPN
ejpam-6074	468	29	or	or	CCONJ
ejpam-6074	468	30	in	in	ADP
ejpam-6074	468	31	g2	g2	PROPN
ejpam-6074	468	32	,	,	PUNCT
ejpam-6074	468	33	respectively	respectively	ADV
ejpam-6074	468	34	,	,	PUNCT
ejpam-6074	468	35	by	by	ADP
ejpam-6074	468	36	(	(	PUNCT
ejpam-6074	468	37	i	i	NOUN
ejpam-6074	468	38	)	)	PUNCT
ejpam-6074	468	39	and	and	CCONJ
ejpam-6074	468	40	(	(	PUNCT
ejpam-6074	468	41	ii	ii	NOUN
ejpam-6074	468	42	)	)	PUNCT
ejpam-6074	468	43	of	of	ADP
ejpam-6074	468	44	theorem	theorem	ADJ
ejpam-6074	468	45	8	8	NUM
ejpam-6074	468	46	.	.	PUNCT
ejpam-6074	469	1	hence	hence	ADV
ejpam-6074	469	2	,	,	PUNCT
ejpam-6074	469	3	γ2mh(d2(g	γ2mh(d2(g	ADJ
ejpam-6074	469	4	)	)	PUNCT
ejpam-6074	469	5	)	)	PUNCT
ejpam-6074	470	1	=	=	SYM
ejpam-6074	470	2	|s|	|s|	PROPN
ejpam-6074	470	3	≥	≥	NOUN
ejpam-6074	470	4	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	470	5	)	)	PUNCT
ejpam-6074	470	6	.	.	PUNCT
ejpam-6074	471	1	if	if	SCONJ
ejpam-6074	471	2	s	s	PRON
ejpam-6074	471	3	=	=	VERB
ejpam-6074	471	4	sg1	sg1	NOUN
ejpam-6074	471	5	∪sg2	∪sg2	PROPN
ejpam-6074	471	6	,	,	PUNCT
ejpam-6074	471	7	then	then	ADV
ejpam-6074	471	8	sg1	sg1	PROPN
ejpam-6074	471	9	∪s′	∪s′	PROPN
ejpam-6074	471	10	g2	g2	PROPN
ejpam-6074	471	11	and	and	CCONJ
ejpam-6074	471	12	s′	s′	NOUN
ejpam-6074	471	13	g1	g1	PROPN
ejpam-6074	471	14	∪sg2	∪sg2	PROPN
ejpam-6074	471	15	are	be	AUX
ejpam-6074	471	16	2	2	NUM
ejpam-6074	471	17	-	-	PUNCT
ejpam-6074	471	18	step	step	NOUN
ejpam-6074	471	19	movable	movable	ADJ
ejpam-6074	471	20	hop	hop	NOUN
ejpam-6074	471	21	dominating	dominating	NOUN
ejpam-6074	471	22	sets	set	NOUN
ejpam-6074	471	23	in	in	ADP
ejpam-6074	471	24	g1	g1	PROPN
ejpam-6074	471	25	and	and	CCONJ
ejpam-6074	471	26	g2	g2	PROPN
ejpam-6074	471	27	,	,	PUNCT
ejpam-6074	471	28	respectively	respectively	ADV
ejpam-6074	471	29	,	,	PUNCT
ejpam-6074	471	30	by	by	ADP
ejpam-6074	471	31	theorem	theorem	NOUN
ejpam-6074	471	32	8(iii	8(iii	NUM
ejpam-6074	471	33	)	)	PUNCT
ejpam-6074	471	34	.	.	PUNCT
ejpam-6074	472	1	thus	thus	ADV
ejpam-6074	472	2	,	,	PUNCT
ejpam-6074	472	3	γ2mh(d2(g	γ2mh(d2(g	ADJ
ejpam-6074	472	4	)	)	PUNCT
ejpam-6074	472	5	)	)	PUNCT
ejpam-6074	473	1	=	=	PUNCT
ejpam-6074	473	2	|sg1	|sg1	NOUN
ejpam-6074	473	3	∪	∪	VERB
ejpam-6074	473	4	sg2	sg2	PROPN
ejpam-6074	473	5	|	|	PROPN
ejpam-6074	473	6	=	=	PUNCT
ejpam-6074	473	7	|sg1	|sg1	NOUN
ejpam-6074	473	8	∪	∪	VERB
ejpam-6074	473	9	s′	s′	ADJ
ejpam-6074	473	10	g2	g2	PROPN
ejpam-6074	473	11	|	|	ADV
ejpam-6074	473	12	≥	≥	NOUN
ejpam-6074	473	13	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	473	14	)	)	PUNCT
ejpam-6074	473	15	.	.	PUNCT
ejpam-6074	474	1	next	next	ADV
ejpam-6074	474	2	,	,	PUNCT
ejpam-6074	474	3	suppose	suppose	VERB
ejpam-6074	474	4	q	q	X
ejpam-6074	474	5	is	be	AUX
ejpam-6074	474	6	a	a	DET
ejpam-6074	474	7	γ2mh	γ2mh	PROPN
ejpam-6074	474	8	-	-	PUNCT
ejpam-6074	474	9	set	set	VERB
ejpam-6074	474	10	in	in	ADP
ejpam-6074	474	11	g	g	NOUN
ejpam-6074	474	12	=	=	SYM
ejpam-6074	474	13	g1	g1	PROPN
ejpam-6074	474	14	.	.	PUNCT
ejpam-6074	475	1	then	then	ADV
ejpam-6074	475	2	q	q	X
ejpam-6074	475	3	is	be	AUX
ejpam-6074	475	4	2	2	NUM
ejpam-6074	475	5	-	-	PUNCT
ejpam-6074	475	6	step	step	NOUN
ejpam-6074	475	7	movable	movable	ADJ
ejpam-6074	475	8	hop	hop	NOUN
ejpam-6074	475	9	dominating	dominating	NOUN
ejpam-6074	475	10	set	set	VERB
ejpam-6074	475	11	in	in	ADP
ejpam-6074	475	12	d2(g	d2(g	PROPN
ejpam-6074	475	13	)	)	PUNCT
ejpam-6074	475	14	by	by	ADP
ejpam-6074	475	15	theorem	theorem	NOUN
ejpam-6074	475	16	8	8	NUM
ejpam-6074	475	17	.	.	PUNCT
ejpam-6074	476	1	hence	hence	ADV
ejpam-6074	476	2	,	,	PUNCT
ejpam-6074	476	3	γ2mh(d2(g	γ2mh(d2(g	ADJ
ejpam-6074	476	4	)	)	PUNCT
ejpam-6074	476	5	)	)	PUNCT
ejpam-6074	476	6	≤	≤	NUM
ejpam-6074	476	7	|q|	|q|	ADJ
ejpam-6074	476	8	=	=	PUNCT
ejpam-6074	476	9	γ2mh(g	γ2mh(g	PROPN
ejpam-6074	476	10	)	)	PUNCT
ejpam-6074	476	11	.	.	PUNCT
ejpam-6074	477	1	this	this	PRON
ejpam-6074	477	2	establishes	establish	VERB
ejpam-6074	477	3	the	the	DET
ejpam-6074	477	4	desired	desire	VERB
ejpam-6074	477	5	equality	equality	NOUN
ejpam-6074	477	6	.	.	PUNCT
ejpam-6074	478	1	theorem	theorem	NOUN
ejpam-6074	478	2	9	9	NUM
ejpam-6074	478	3	.	.	PUNCT
ejpam-6074	479	1	let	let	VERB
ejpam-6074	479	2	g	g	PRON
ejpam-6074	479	3	be	be	AUX
ejpam-6074	479	4	a	a	DET
ejpam-6074	479	5	non	non	ADJ
ejpam-6074	479	6	-	-	ADJ
ejpam-6074	479	7	trivial	trivial	ADJ
ejpam-6074	479	8	connected	connected	ADJ
ejpam-6074	479	9	graph	graph	NOUN
ejpam-6074	479	10	.	.	PUNCT
ejpam-6074	480	1	then	then	ADV
ejpam-6074	480	2	gg	gg	PROPN
ejpam-6074	480	3	admits	admit	VERB
ejpam-6074	480	4	a	a	DET
ejpam-6074	480	5	2	2	NUM
ejpam-6074	480	6	-	-	PUNCT
ejpam-6074	480	7	step	step	NOUN
ejpam-6074	480	8	movable	movable	ADJ
ejpam-6074	480	9	hop	hop	NOUN
ejpam-6074	480	10	dominating	dominating	NOUN
ejpam-6074	480	11	set	set	NOUN
ejpam-6074	480	12	and	and	CCONJ
ejpam-6074	480	13	2	2	NUM
ejpam-6074	480	14	≤	≤	NUM
ejpam-6074	480	15	γ2mh(gg	γ2mh(gg	NOUN
ejpam-6074	480	16	)	)	PUNCT
ejpam-6074	480	17	≤	≤	NUM
ejpam-6074	480	18	4	4	NUM
ejpam-6074	480	19	.	.	PUNCT
ejpam-6074	481	1	moreover	moreover	ADV
ejpam-6074	481	2	,	,	PUNCT
ejpam-6074	481	3	each	each	PRON
ejpam-6074	481	4	of	of	ADP
ejpam-6074	481	5	the	the	DET
ejpam-6074	481	6	following	following	ADJ
ejpam-6074	481	7	statements	statement	NOUN
ejpam-6074	481	8	hold	hold	VERB
ejpam-6074	481	9	:	:	PUNCT
ejpam-6074	481	10	(	(	PUNCT
ejpam-6074	481	11	i	i	NOUN
ejpam-6074	481	12	)	)	PUNCT
ejpam-6074	481	13	γ2mh(gg	γ2mh(gg	NOUN
ejpam-6074	481	14	)	)	PUNCT
ejpam-6074	481	15	=	=	SYM
ejpam-6074	481	16	2	2	NUM
ejpam-6074	481	17	if	if	SCONJ
ejpam-6074	481	18	and	and	CCONJ
ejpam-6074	481	19	only	only	ADV
ejpam-6074	481	20	if	if	SCONJ
ejpam-6074	481	21	γh(g	γh(g	NOUN
ejpam-6074	481	22	)	)	PUNCT
ejpam-6074	481	23	=	=	SYM
ejpam-6074	481	24	2	2	NUM
ejpam-6074	481	25	and	and	CCONJ
ejpam-6074	481	26	γh(g	γh(g	NOUN
ejpam-6074	481	27	)	)	PUNCT
ejpam-6074	481	28	=	=	SYM
ejpam-6074	482	1	2	2	X
ejpam-6074	482	2	.	.	PUNCT
ejpam-6074	482	3	(	(	PUNCT
ejpam-6074	482	4	ii	ii	NOUN
ejpam-6074	482	5	)	)	PUNCT
ejpam-6074	482	6	γ2mh(gg	γ2mh(gg	NOUN
ejpam-6074	482	7	)	)	PUNCT
ejpam-6074	482	8	=	=	SYM
ejpam-6074	482	9	3	3	NUM
ejpam-6074	482	10	if	if	SCONJ
ejpam-6074	482	11	and	and	CCONJ
ejpam-6074	482	12	only	only	ADV
ejpam-6074	482	13	if	if	SCONJ
ejpam-6074	482	14	one	one	NUM
ejpam-6074	482	15	of	of	ADP
ejpam-6074	482	16	the	the	DET
ejpam-6074	482	17	following	follow	VERB
ejpam-6074	482	18	conditions	condition	NOUN
ejpam-6074	482	19	holds	hold	VERB
ejpam-6074	482	20	.	.	PUNCT
ejpam-6074	483	1	(	(	PUNCT
ejpam-6074	483	2	a	a	NOUN
ejpam-6074	483	3	)	)	PUNCT
ejpam-6074	483	4	γh(g	γh(g	NOUN
ejpam-6074	483	5	)	)	PUNCT
ejpam-6074	483	6	=	=	SYM
ejpam-6074	483	7	2	2	NUM
ejpam-6074	483	8	and	and	CCONJ
ejpam-6074	483	9	γh(g	γh(g	NOUN
ejpam-6074	483	10	)	)	PUNCT
ejpam-6074	483	11	≥	≥	NOUN
ejpam-6074	483	12	3	3	NUM
ejpam-6074	483	13	or	or	CCONJ
ejpam-6074	483	14	γh(g	γh(g	NOUN
ejpam-6074	483	15	)	)	PUNCT
ejpam-6074	484	1	=	=	SYM
ejpam-6074	484	2	2	2	NUM
ejpam-6074	484	3	and	and	CCONJ
ejpam-6074	484	4	γh(g	γh(g	NOUN
ejpam-6074	484	5	)	)	PUNCT
ejpam-6074	484	6	≥	≥	NOUN
ejpam-6074	485	1	3	3	NUM
ejpam-6074	485	2	.	.	PUNCT
ejpam-6074	485	3	(	(	PUNCT
ejpam-6074	485	4	b	b	NOUN
ejpam-6074	485	5	)	)	PUNCT
ejpam-6074	485	6	γh(g	γh(g	NOUN
ejpam-6074	485	7	)	)	PUNCT
ejpam-6074	485	8	=	=	SYM
ejpam-6074	485	9	3	3	NUM
ejpam-6074	485	10	and	and	CCONJ
ejpam-6074	485	11	γh(g	γh(g	NOUN
ejpam-6074	485	12	)	)	PUNCT
ejpam-6074	485	13	≥	≥	NOUN
ejpam-6074	485	14	3	3	NUM
ejpam-6074	485	15	(	(	PUNCT
ejpam-6074	485	16	or	or	CCONJ
ejpam-6074	485	17	γh(g	γh(g	NOUN
ejpam-6074	485	18	)	)	PUNCT
ejpam-6074	485	19	≥	≥	NOUN
ejpam-6074	485	20	3	3	NUM
ejpam-6074	485	21	and	and	CCONJ
ejpam-6074	485	22	γh(g	γh(g	NOUN
ejpam-6074	485	23	)	)	PUNCT
ejpam-6074	486	1	=	=	SYM
ejpam-6074	486	2	3	3	NUM
ejpam-6074	486	3	)	)	PUNCT
ejpam-6074	486	4	.	.	PUNCT
ejpam-6074	487	1	r.	r.	PROPN
ejpam-6074	487	2	estrella	estrella	PROPN
ejpam-6074	487	3	,	,	PUNCT
ejpam-6074	487	4	gina	gina	PROPN
ejpam-6074	487	5	m.	m.	PROPN
ejpam-6074	487	6	malacas	malacas	PROPN
ejpam-6074	487	7	,	,	PUNCT
ejpam-6074	487	8	s.	s.	PROPN
ejpam-6074	487	9	canoy	canoy	PROPN
ejpam-6074	487	10	jr	jr	PROPN
ejpam-6074	487	11	.	.	PROPN
ejpam-6074	487	12	/	/	SYM
ejpam-6074	487	13	eur	eur	PROPN
ejpam-6074	487	14	.	.	PUNCT
ejpam-6074	488	1	j.	j.	PROPN
ejpam-6074	488	2	pure	pure	PROPN
ejpam-6074	488	3	appl	appl	PROPN
ejpam-6074	488	4	.	.	PROPN
ejpam-6074	488	5	math	math	PROPN
ejpam-6074	488	6	,	,	PUNCT
ejpam-6074	488	7	18	18	NUM
ejpam-6074	488	8	(	(	PUNCT
ejpam-6074	488	9	2	2	NUM
ejpam-6074	488	10	)	)	PUNCT
ejpam-6074	488	11	(	(	PUNCT
ejpam-6074	488	12	2025	2025	NUM
ejpam-6074	488	13	)	)	PUNCT
ejpam-6074	488	14	,	,	PUNCT
ejpam-6074	488	15	6074	6074	NUM
ejpam-6074	488	16	12	12	NUM
ejpam-6074	488	17	of	of	ADP
ejpam-6074	488	18	15	15	NUM
ejpam-6074	488	19	(	(	PUNCT
ejpam-6074	488	20	c	c	NOUN
ejpam-6074	488	21	)	)	PUNCT
ejpam-6074	488	22	there	there	PRON
ejpam-6074	488	23	exist	exist	VERB
ejpam-6074	488	24	vertices	vertex	NOUN
ejpam-6074	488	25	x	x	X
ejpam-6074	488	26	,	,	PUNCT
ejpam-6074	488	27	y	y	PROPN
ejpam-6074	488	28	,	,	PUNCT
ejpam-6074	488	29	z	z	PROPN
ejpam-6074	488	30	,	,	PUNCT
ejpam-6074	488	31	w	w	PROPN
ejpam-6074	488	32	∈	∈	PROPN
ejpam-6074	488	33	v	v	ADP
ejpam-6074	488	34	(	(	PUNCT
ejpam-6074	488	35	g	g	NOUN
ejpam-6074	488	36	)	)	PUNCT
ejpam-6074	488	37	such	such	ADJ
ejpam-6074	488	38	z	z	NOUN
ejpam-6074	488	39	,	,	PUNCT
ejpam-6074	488	40	w	w	PROPN
ejpam-6074	488	41	∈	∈	PROPN
ejpam-6074	488	42	n2	n2	PROPN
ejpam-6074	488	43	g[x	g[x	PROPN
ejpam-6074	488	44	]	]	PUNCT
ejpam-6074	488	45	∪	∪	ADP
ejpam-6074	488	46	n2	n2	ADJ
ejpam-6074	488	47	g[y	g[y	PROPN
ejpam-6074	488	48	[	[	X
ejpam-6074	488	49	,	,	PUNCT
ejpam-6074	488	50	z	z	PROPN
ejpam-6074	488	51	∈	∈	PROPN
ejpam-6074	488	52	ng[w	ng[w	PROPN
ejpam-6074	488	53	]	]	PUNCT
ejpam-6074	488	54	,	,	PUNCT
ejpam-6074	488	55	and	and	CCONJ
ejpam-6074	488	56	v	v	X
ejpam-6074	488	57	(	(	PUNCT
ejpam-6074	488	58	g	g	NOUN
ejpam-6074	488	59	)	)	PUNCT
ejpam-6074	488	60	\	\	PUNCT
ejpam-6074	489	1	[	[	X
ejpam-6074	489	2	ng(z	ng(z	NUM
ejpam-6074	489	3	)	)	PUNCT
ejpam-6074	489	4	∪ng(w	∪ng(w	PROPN
ejpam-6074	489	5	)	)	PUNCT
ejpam-6074	489	6	]	]	PUNCT
ejpam-6074	490	1	̸=	̸=	PROPN
ejpam-6074	490	2	∅.	∅.	X
ejpam-6074	490	3	(	(	PUNCT
ejpam-6074	490	4	d	d	X
ejpam-6074	490	5	)	)	PUNCT
ejpam-6074	490	6	there	there	PRON
ejpam-6074	490	7	exist	exist	VERB
ejpam-6074	490	8	vertices	vertex	NOUN
ejpam-6074	490	9	p	p	X
ejpam-6074	490	10	,	,	PUNCT
ejpam-6074	490	11	q	q	X
ejpam-6074	490	12	,	,	PUNCT
ejpam-6074	490	13	t	t	PROPN
ejpam-6074	490	14	,	,	PUNCT
ejpam-6074	490	15	s	s	PART
ejpam-6074	490	16	∈	∈	PROPN
ejpam-6074	490	17	v	v	ADP
ejpam-6074	490	18	(	(	PUNCT
ejpam-6074	490	19	g	g	NOUN
ejpam-6074	490	20	)	)	PUNCT
ejpam-6074	490	21	such	such	ADJ
ejpam-6074	490	22	that	that	DET
ejpam-6074	490	23	s	s	PROPN
ejpam-6074	490	24	∈	∈	PROPN
ejpam-6074	490	25	n2	n2	PROPN
ejpam-6074	490	26	g(t	g(t	PROPN
ejpam-6074	490	27	)	)	PUNCT
ejpam-6074	490	28	and	and	CCONJ
ejpam-6074	490	29	t	t	PROPN
ejpam-6074	490	30	,	,	PUNCT
ejpam-6074	490	31	s	s	PROPN
ejpam-6074	490	32	∈	∈	PROPN
ejpam-6074	490	33	n2	n2	NOUN
ejpam-6074	490	34	g	g	PROPN
ejpam-6074	491	1	[	[	X
ejpam-6074	491	2	{	{	PUNCT
ejpam-6074	491	3	p	p	X
ejpam-6074	491	4	,	,	PUNCT
ejpam-6074	491	5	q	q	NOUN
ejpam-6074	491	6	}	}	PUNCT
ejpam-6074	491	7	]	]	PUNCT
ejpam-6074	491	8	.	.	PUNCT
ejpam-6074	492	1	(	(	PUNCT
ejpam-6074	492	2	iii	iii	NOUN
ejpam-6074	492	3	)	)	PUNCT
ejpam-6074	492	4	γ2mh(gg	γ2mh(gg	NOUN
ejpam-6074	492	5	)	)	PUNCT
ejpam-6074	492	6	=	=	SYM
ejpam-6074	492	7	4	4	NUM
ejpam-6074	492	8	if	if	SCONJ
ejpam-6074	492	9	and	and	CCONJ
ejpam-6074	492	10	only	only	ADV
ejpam-6074	492	11	if	if	SCONJ
ejpam-6074	492	12	g	g	PROPN
ejpam-6074	492	13	does	do	AUX
ejpam-6074	492	14	not	not	PART
ejpam-6074	492	15	satisfy	satisfy	VERB
ejpam-6074	492	16	any	any	PRON
ejpam-6074	492	17	of	of	ADP
ejpam-6074	492	18	the	the	DET
ejpam-6074	492	19	properties	property	NOUN
ejpam-6074	492	20	in	in	ADP
ejpam-6074	492	21	(	(	PUNCT
ejpam-6074	492	22	i	i	NOUN
ejpam-6074	492	23	)	)	PUNCT
ejpam-6074	492	24	and	and	CCONJ
ejpam-6074	492	25	(	(	PUNCT
ejpam-6074	492	26	ii	ii	NOUN
ejpam-6074	492	27	)	)	PUNCT
ejpam-6074	492	28	.	.	PUNCT
ejpam-6074	493	1	proof	proof	NOUN
ejpam-6074	493	2	.	.	PUNCT
ejpam-6074	494	1	since	since	SCONJ
ejpam-6074	494	2	g	g	PROPN
ejpam-6074	494	3	is	be	AUX
ejpam-6074	494	4	non	non	ADJ
ejpam-6074	494	5	-	-	ADJ
ejpam-6074	494	6	trivial	trivial	ADJ
ejpam-6074	494	7	,	,	PUNCT
ejpam-6074	494	8	γ(gg	γ(gg	ADJ
ejpam-6074	494	9	)	)	PUNCT
ejpam-6074	494	10	̸=	̸=	PROPN
ejpam-6074	494	11	1	1	NUM
ejpam-6074	494	12	.	.	PUNCT
ejpam-6074	495	1	hence	hence	ADV
ejpam-6074	495	2	,	,	PUNCT
ejpam-6074	495	3	gg	gg	PROPN
ejpam-6074	495	4	admits	admit	VERB
ejpam-6074	495	5	a	a	DET
ejpam-6074	495	6	2	2	NUM
ejpam-6074	495	7	-	-	PUNCT
ejpam-6074	495	8	step	step	NOUN
ejpam-6074	495	9	movable	movable	ADJ
ejpam-6074	495	10	hop	hop	NOUN
ejpam-6074	495	11	dominating	dominating	NOUN
ejpam-6074	495	12	set	set	VERB
ejpam-6074	495	13	by	by	ADP
ejpam-6074	495	14	theorem	theorem	NOUN
ejpam-6074	495	15	1	1	NUM
ejpam-6074	495	16	.	.	PUNCT
ejpam-6074	495	17	note	note	VERB
ejpam-6074	495	18	that	that	SCONJ
ejpam-6074	495	19	{	{	PUNCT
ejpam-6074	495	20	v	v	NOUN
ejpam-6074	495	21	,	,	PUNCT
ejpam-6074	495	22	v	v	NOUN
ejpam-6074	495	23	}	}	PUNCT
ejpam-6074	495	24	is	be	AUX
ejpam-6074	495	25	a	a	DET
ejpam-6074	495	26	hop	hop	NOUN
ejpam-6074	495	27	dominating	dominating	NOUN
ejpam-6074	495	28	set	set	VERB
ejpam-6074	495	29	in	in	ADP
ejpam-6074	495	30	gg	gg	NOUN
ejpam-6074	495	31	for	for	ADP
ejpam-6074	495	32	each	each	DET
ejpam-6074	495	33	v	v	NUM
ejpam-6074	495	34	∈	∈	PROPN
ejpam-6074	495	35	v	v	NOUN
ejpam-6074	495	36	(	(	PUNCT
ejpam-6074	495	37	g	g	NOUN
ejpam-6074	495	38	)	)	PUNCT
ejpam-6074	495	39	.	.	PUNCT
ejpam-6074	496	1	thus	thus	ADV
ejpam-6074	496	2	,	,	PUNCT
ejpam-6074	496	3	{	{	PUNCT
ejpam-6074	496	4	v	v	NOUN
ejpam-6074	496	5	,	,	PUNCT
ejpam-6074	496	6	w	w	PROPN
ejpam-6074	496	7	,	,	PUNCT
ejpam-6074	496	8	v	v	NOUN
ejpam-6074	496	9	,	,	PUNCT
ejpam-6074	496	10	w	w	NOUN
ejpam-6074	496	11	}	}	PUNCT
ejpam-6074	496	12	is	be	AUX
ejpam-6074	496	13	a	a	DET
ejpam-6074	496	14	2	2	NUM
ejpam-6074	496	15	-	-	PUNCT
ejpam-6074	496	16	step	step	NOUN
ejpam-6074	496	17	movable	movable	ADJ
ejpam-6074	496	18	hop	hop	NOUN
ejpam-6074	496	19	dominating	dominating	NOUN
ejpam-6074	496	20	set	set	VERB
ejpam-6074	496	21	in	in	ADP
ejpam-6074	496	22	gg	gg	NOUN
ejpam-6074	496	23	for	for	ADP
ejpam-6074	496	24	each	each	DET
ejpam-6074	496	25	pair	pair	NOUN
ejpam-6074	496	26	of	of	ADP
ejpam-6074	496	27	distinct	distinct	ADJ
ejpam-6074	496	28	vertices	vertex	NOUN
ejpam-6074	496	29	v	v	NOUN
ejpam-6074	496	30	and	and	CCONJ
ejpam-6074	496	31	w	w	PROPN
ejpam-6074	496	32	of	of	ADP
ejpam-6074	496	33	g.	g.	PROPN
ejpam-6074	496	34	therefore	therefore	ADV
ejpam-6074	496	35	,	,	PUNCT
ejpam-6074	496	36	2	2	NUM
ejpam-6074	496	37	=	=	SYM
ejpam-6074	496	38	γh(gg	γh(gg	PROPN
ejpam-6074	496	39	)	)	PUNCT
ejpam-6074	496	40	≤	≤	NOUN
ejpam-6074	496	41	γ2mh(gg	γ2mh(gg	NOUN
ejpam-6074	496	42	)	)	PUNCT
ejpam-6074	496	43	≤	≤	NUM
ejpam-6074	496	44	4	4	NUM
ejpam-6074	496	45	.	.	PUNCT
ejpam-6074	497	1	(	(	PUNCT
ejpam-6074	497	2	i	i	NOUN
ejpam-6074	497	3	)	)	PUNCT
ejpam-6074	497	4	suppose	suppose	VERB
ejpam-6074	497	5	γ2mh(gg	γ2mh(gg	NOUN
ejpam-6074	497	6	)	)	PUNCT
ejpam-6074	497	7	=	=	SYM
ejpam-6074	497	8	2	2	NUM
ejpam-6074	497	9	,	,	PUNCT
ejpam-6074	497	10	say	say	VERB
ejpam-6074	497	11	s	s	X
ejpam-6074	497	12	=	=	PUNCT
ejpam-6074	497	13	{	{	PUNCT
ejpam-6074	497	14	p	p	X
ejpam-6074	497	15	,	,	PUNCT
ejpam-6074	497	16	q	q	X
ejpam-6074	497	17	}	}	PUNCT
ejpam-6074	497	18	is	be	AUX
ejpam-6074	497	19	a	a	DET
ejpam-6074	497	20	γ2mh	γ2mh	PROPN
ejpam-6074	497	21	-	-	PUNCT
ejpam-6074	497	22	set	set	VERB
ejpam-6074	497	23	in	in	ADP
ejpam-6074	497	24	gg	gg	NOUN
ejpam-6074	497	25	.	.	PUNCT
ejpam-6074	498	1	if	if	SCONJ
ejpam-6074	498	2	p	p	X
ejpam-6074	498	3	,	,	PUNCT
ejpam-6074	498	4	q	q	PROPN
ejpam-6074	498	5	∈	∈	PROPN
ejpam-6074	498	6	v	v	NOUN
ejpam-6074	498	7	(	(	PUNCT
ejpam-6074	498	8	g	g	NOUN
ejpam-6074	498	9	)	)	PUNCT
ejpam-6074	498	10	,	,	PUNCT
ejpam-6074	498	11	then	then	ADV
ejpam-6074	498	12	s	s	VERB
ejpam-6074	498	13	is	be	AUX
ejpam-6074	498	14	a	a	DET
ejpam-6074	498	15	hop	hop	NOUN
ejpam-6074	498	16	dominating	dominating	NOUN
ejpam-6074	498	17	set	set	NOUN
ejpam-6074	498	18	of	of	ADP
ejpam-6074	498	19	g.	g.	PROPN
ejpam-6074	498	20	if	if	SCONJ
ejpam-6074	498	21	p	p	X
ejpam-6074	498	22	,	,	PUNCT
ejpam-6074	498	23	q	q	PROPN
ejpam-6074	498	24	∈	∈	PROPN
ejpam-6074	498	25	v	v	NOUN
ejpam-6074	498	26	(	(	PUNCT
ejpam-6074	498	27	g	g	NOUN
ejpam-6074	498	28	)	)	PUNCT
ejpam-6074	498	29	,	,	PUNCT
ejpam-6074	498	30	then	then	ADV
ejpam-6074	498	31	s	s	VERB
ejpam-6074	498	32	is	be	AUX
ejpam-6074	498	33	a	a	DET
ejpam-6074	498	34	hop	hop	NOUN
ejpam-6074	498	35	dominating	dominating	NOUN
ejpam-6074	498	36	set	set	NOUN
ejpam-6074	498	37	of	of	ADP
ejpam-6074	498	38	g.	g.	PROPN
ejpam-6074	498	39	thus	thus	ADV
ejpam-6074	498	40	,	,	PUNCT
ejpam-6074	498	41	γh(g	γh(g	NOUN
ejpam-6074	498	42	)	)	PUNCT
ejpam-6074	498	43	=	=	SYM
ejpam-6074	498	44	2	2	NUM
ejpam-6074	498	45	or	or	CCONJ
ejpam-6074	498	46	γh(g	γh(g	NOUN
ejpam-6074	498	47	)	)	PUNCT
ejpam-6074	499	1	=	=	SYM
ejpam-6074	499	2	2	2	X
ejpam-6074	499	3	.	.	X
ejpam-6074	499	4	suppose	suppose	VERB
ejpam-6074	499	5	p	p	X
ejpam-6074	499	6	∈	∈	PROPN
ejpam-6074	499	7	v	v	ADP
ejpam-6074	499	8	(	(	PUNCT
ejpam-6074	499	9	g	g	NOUN
ejpam-6074	499	10	)	)	PUNCT
ejpam-6074	499	11	and	and	CCONJ
ejpam-6074	499	12	q	q	X
ejpam-6074	499	13	=	=	SYM
ejpam-6074	499	14	t	t	X
ejpam-6074	499	15	∈	∈	PROPN
ejpam-6074	499	16	v	v	ADP
ejpam-6074	499	17	(	(	PUNCT
ejpam-6074	499	18	g	g	NOUN
ejpam-6074	499	19	)	)	PUNCT
ejpam-6074	499	20	.	.	PUNCT
ejpam-6074	500	1	suppose	suppose	VERB
ejpam-6074	501	1	p	p	X
ejpam-6074	501	2	̸=	̸=	PROPN
ejpam-6074	501	3	t.	t.	NOUN
ejpam-6074	501	4	if	if	SCONJ
ejpam-6074	501	5	pt	pt	PROPN
ejpam-6074	501	6	∈	∈	PROPN
ejpam-6074	501	7	e(g	e(g	PROPN
ejpam-6074	501	8	)	)	PUNCT
ejpam-6074	501	9	,	,	PUNCT
ejpam-6074	501	10	then	then	ADV
ejpam-6074	501	11	p	p	PROPN
ejpam-6074	501	12	t	t	PROPN
ejpam-6074	501	13	/∈	/∈	PUNCT
ejpam-6074	501	14	e(g	e(g	PROPN
ejpam-6074	501	15	)	)	PUNCT
ejpam-6074	501	16	.	.	PUNCT
ejpam-6074	502	1	it	it	PRON
ejpam-6074	502	2	follows	follow	VERB
ejpam-6074	502	3	that	that	SCONJ
ejpam-6074	502	4	t	t	PROPN
ejpam-6074	502	5	∈	∈	PROPN
ejpam-6074	502	6	ngg(p	ngg(p	PROPN
ejpam-6074	502	7	)	)	PUNCT
ejpam-6074	502	8	∩	∩	NOUN
ejpam-6074	502	9	ngg(q	ngg(q	NOUN
ejpam-6074	502	10	)	)	PUNCT
ejpam-6074	502	11	.	.	PUNCT
ejpam-6074	503	1	if	if	SCONJ
ejpam-6074	503	2	pt	pt	PROPN
ejpam-6074	503	3	/∈	/∈	PROPN
ejpam-6074	503	4	e(g	e(g	PROPN
ejpam-6074	503	5	)	)	PUNCT
ejpam-6074	503	6	,	,	PUNCT
ejpam-6074	503	7	then	then	ADV
ejpam-6074	503	8	p	p	PROPN
ejpam-6074	503	9	t	t	PROPN
ejpam-6074	503	10	∈	∈	PROPN
ejpam-6074	503	11	e(g	e(g	PROPN
ejpam-6074	503	12	)	)	PUNCT
ejpam-6074	503	13	.	.	PUNCT
ejpam-6074	504	1	this	this	PRON
ejpam-6074	504	2	implies	imply	VERB
ejpam-6074	504	3	that	that	SCONJ
ejpam-6074	504	4	p	p	PROPN
ejpam-6074	504	5	∈	∈	PROPN
ejpam-6074	504	6	ngg(p	ngg(p	PROPN
ejpam-6074	504	7	)	)	PUNCT
ejpam-6074	504	8	∩	∩	NOUN
ejpam-6074	504	9	ngg(q	ngg(q	PROPN
ejpam-6074	504	10	)	)	PUNCT
ejpam-6074	504	11	.	.	PUNCT
ejpam-6074	505	1	thus	thus	ADV
ejpam-6074	505	2	,	,	PUNCT
ejpam-6074	505	3	s	s	VERB
ejpam-6074	505	4	is	be	AUX
ejpam-6074	505	5	not	not	PART
ejpam-6074	505	6	a	a	DET
ejpam-6074	505	7	hop	hop	NOUN
ejpam-6074	505	8	dominating	dominating	NOUN
ejpam-6074	505	9	set	set	VERB
ejpam-6074	505	10	in	in	ADP
ejpam-6074	505	11	d2(g	d2(g	PROPN
ejpam-6074	505	12	)	)	PUNCT
ejpam-6074	505	13	,	,	PUNCT
ejpam-6074	505	14	a	a	DET
ejpam-6074	505	15	contradiction	contradiction	NOUN
ejpam-6074	505	16	.	.	PUNCT
ejpam-6074	506	1	therefore	therefore	ADV
ejpam-6074	506	2	,	,	PUNCT
ejpam-6074	506	3	p	p	PROPN
ejpam-6074	506	4	=	=	PROPN
ejpam-6074	506	5	t	t	PROPN
ejpam-6074	506	6	,	,	PUNCT
ejpam-6074	506	7	i.e.	i.e.	X
ejpam-6074	506	8	,	,	PUNCT
ejpam-6074	506	9	s	s	VERB
ejpam-6074	506	10	=	=	PUNCT
ejpam-6074	506	11	{	{	PUNCT
ejpam-6074	506	12	p	p	X
ejpam-6074	506	13	,	,	PUNCT
ejpam-6074	506	14	p	p	NOUN
ejpam-6074	506	15	}	}	PUNCT
ejpam-6074	506	16	.	.	PUNCT
ejpam-6074	507	1	now	now	ADV
ejpam-6074	507	2	,	,	PUNCT
ejpam-6074	507	3	since	since	SCONJ
ejpam-6074	507	4	s	s	NOUN
ejpam-6074	507	5	is	be	AUX
ejpam-6074	507	6	2	2	NUM
ejpam-6074	507	7	-	-	PUNCT
ejpam-6074	507	8	step	step	NOUN
ejpam-6074	507	9	movable	movable	ADJ
ejpam-6074	507	10	hop	hop	NOUN
ejpam-6074	507	11	dominating	dominating	NOUN
ejpam-6074	507	12	in	in	ADP
ejpam-6074	507	13	d2(gg	d2(gg	PROPN
ejpam-6074	507	14	)	)	PUNCT
ejpam-6074	507	15	,	,	PUNCT
ejpam-6074	507	16	there	there	PRON
ejpam-6074	507	17	exists	exist	VERB
ejpam-6074	507	18	s	s	PART
ejpam-6074	507	19	∈	∈	PROPN
ejpam-6074	508	1	[	[	X
ejpam-6074	508	2	v	v	X
ejpam-6074	508	3	(	(	PUNCT
ejpam-6074	508	4	gg	gg	NOUN
ejpam-6074	508	5	)	)	PUNCT
ejpam-6074	508	6	\	\	PROPN
ejpam-6074	508	7	s	s	X
ejpam-6074	508	8	]	]	X
ejpam-6074	508	9	∩	∩	ADJ
ejpam-6074	508	10	n2	n2	PROPN
ejpam-6074	508	11	gg	gg	PROPN
ejpam-6074	508	12	(	(	PUNCT
ejpam-6074	508	13	p	p	NOUN
ejpam-6074	508	14	)	)	PUNCT
ejpam-6074	508	15	such	such	ADJ
ejpam-6074	508	16	that	that	SCONJ
ejpam-6074	508	17	(	(	PUNCT
ejpam-6074	508	18	s	s	VERB
ejpam-6074	508	19	\{p})∪{s	\{p})∪{s	NOUN
ejpam-6074	508	20	}	}	PUNCT
ejpam-6074	508	21	=	=	SYM
ejpam-6074	508	22	{	{	PUNCT
ejpam-6074	508	23	p	p	X
ejpam-6074	508	24	,	,	PUNCT
ejpam-6074	508	25	s	s	AUX
ejpam-6074	508	26	}	}	PUNCT
ejpam-6074	508	27	is	be	AUX
ejpam-6074	508	28	hop	hop	NOUN
ejpam-6074	508	29	dominating	dominate	VERB
ejpam-6074	508	30	in	in	ADP
ejpam-6074	508	31	gg	gg	PROPN
ejpam-6074	508	32	.	.	PUNCT
ejpam-6074	509	1	if	if	SCONJ
ejpam-6074	509	2	s	s	X
ejpam-6074	509	3	∈	∈	PROPN
ejpam-6074	509	4	v	v	ADP
ejpam-6074	509	5	(	(	PUNCT
ejpam-6074	509	6	g	g	NOUN
ejpam-6074	509	7	)	)	PUNCT
ejpam-6074	509	8	,	,	PUNCT
ejpam-6074	509	9	then	then	ADV
ejpam-6074	509	10	s	s	VERB
ejpam-6074	509	11	=	=	SYM
ejpam-6074	509	12	p	p	PROPN
ejpam-6074	509	13	,	,	PUNCT
ejpam-6074	509	14	a	a	DET
ejpam-6074	509	15	contradiction	contradiction	NOUN
ejpam-6074	509	16	.	.	PUNCT
ejpam-6074	510	1	thus	thus	ADV
ejpam-6074	510	2	,	,	PUNCT
ejpam-6074	510	3	s	s	VERB
ejpam-6074	510	4	∈	∈	PROPN
ejpam-6074	510	5	v	v	ADP
ejpam-6074	510	6	(	(	PUNCT
ejpam-6074	510	7	g	g	NOUN
ejpam-6074	510	8	)	)	PUNCT
ejpam-6074	510	9	and	and	CCONJ
ejpam-6074	510	10	{	{	PUNCT
ejpam-6074	510	11	p	p	X
ejpam-6074	510	12	,	,	PUNCT
ejpam-6074	510	13	s	s	AUX
ejpam-6074	510	14	}	}	PUNCT
ejpam-6074	510	15	is	be	AUX
ejpam-6074	510	16	a	a	DET
ejpam-6074	510	17	hop	hop	NOUN
ejpam-6074	510	18	dominating	dominating	NOUN
ejpam-6074	510	19	set	set	VERB
ejpam-6074	510	20	in	in	ADP
ejpam-6074	510	21	g.	g.	PROPN
ejpam-6074	510	22	this	this	PRON
ejpam-6074	510	23	implies	imply	VERB
ejpam-6074	510	24	that	that	SCONJ
ejpam-6074	510	25	γh(g	γh(g	NOUN
ejpam-6074	510	26	)	)	PUNCT
ejpam-6074	510	27	=	=	SYM
ejpam-6074	510	28	2	2	X
ejpam-6074	510	29	.	.	X
ejpam-6074	510	30	similarly	similarly	ADV
ejpam-6074	510	31	,	,	PUNCT
ejpam-6074	510	32	γh(g	γh(g	NOUN
ejpam-6074	510	33	)	)	PUNCT
ejpam-6074	510	34	=	=	SYM
ejpam-6074	510	35	2	2	X
ejpam-6074	510	36	.	.	X
ejpam-6074	510	37	for	for	ADP
ejpam-6074	510	38	the	the	DET
ejpam-6074	510	39	converse	converse	NOUN
ejpam-6074	510	40	,	,	PUNCT
ejpam-6074	510	41	suppose	suppose	VERB
ejpam-6074	510	42	γh(g	γh(g	NOUN
ejpam-6074	510	43	)	)	PUNCT
ejpam-6074	510	44	=	=	SYM
ejpam-6074	510	45	2	2	NUM
ejpam-6074	510	46	and	and	CCONJ
ejpam-6074	510	47	γh(g	γh(g	NOUN
ejpam-6074	510	48	)	)	PUNCT
ejpam-6074	510	49	=	=	SYM
ejpam-6074	511	1	2	2	X
ejpam-6074	511	2	.	.	PUNCT
ejpam-6074	511	3	let	let	VERB
ejpam-6074	511	4	d	d	NOUN
ejpam-6074	511	5	=	=	PRON
ejpam-6074	511	6	{	{	PUNCT
ejpam-6074	511	7	x	x	PROPN
ejpam-6074	511	8	,	,	PUNCT
ejpam-6074	511	9	y	y	PROPN
ejpam-6074	511	10	}	}	PUNCT
ejpam-6074	511	11	be	be	AUX
ejpam-6074	511	12	a	a	DET
ejpam-6074	511	13	γh	γh	ADV
ejpam-6074	511	14	-	-	PUNCT
ejpam-6074	511	15	set	set	NOUN
ejpam-6074	511	16	in	in	ADP
ejpam-6074	511	17	g.	g.	PROPN
ejpam-6074	511	18	note	note	VERB
ejpam-6074	511	19	that	that	SCONJ
ejpam-6074	511	20	whether	whether	SCONJ
ejpam-6074	511	21	xy	xy	PROPN
ejpam-6074	511	22	∈	∈	PROPN
ejpam-6074	511	23	e(g	e(g	PROPN
ejpam-6074	511	24	)	)	PUNCT
ejpam-6074	511	25	or	or	CCONJ
ejpam-6074	511	26	xy	xy	PROPN
ejpam-6074	511	27	/∈	/∈	PUNCT
ejpam-6074	512	1	e(g	e(g	PROPN
ejpam-6074	512	2	)	)	PUNCT
ejpam-6074	512	3	,	,	PUNCT
ejpam-6074	512	4	we	we	PRON
ejpam-6074	512	5	find	find	VERB
ejpam-6074	512	6	that	that	SCONJ
ejpam-6074	512	7	(	(	PUNCT
ejpam-6074	512	8	d	d	X
ejpam-6074	512	9	\	\	X
ejpam-6074	512	10	{	{	PUNCT
ejpam-6074	512	11	x	x	NOUN
ejpam-6074	512	12	}	}	PUNCT
ejpam-6074	512	13	)	)	PUNCT
ejpam-6074	512	14	∪	∪	ADP
ejpam-6074	512	15	{	{	PUNCT
ejpam-6074	512	16	y	y	NOUN
ejpam-6074	512	17	}	}	PUNCT
ejpam-6074	512	18	=	=	SYM
ejpam-6074	512	19	{	{	PUNCT
ejpam-6074	512	20	y	y	PROPN
ejpam-6074	512	21	,	,	PUNCT
ejpam-6074	512	22	y	y	PROPN
ejpam-6074	512	23	}	}	PUNCT
ejpam-6074	512	24	and	and	CCONJ
ejpam-6074	512	25	(	(	PUNCT
ejpam-6074	512	26	d	d	PROPN
ejpam-6074	512	27	\	\	X
ejpam-6074	512	28	{	{	PUNCT
ejpam-6074	512	29	y})∪{x	y})∪{x	NOUN
ejpam-6074	512	30	}	}	PUNCT
ejpam-6074	512	31	=	=	PUNCT
ejpam-6074	512	32	{	{	PUNCT
ejpam-6074	512	33	x	x	NOUN
ejpam-6074	512	34	,	,	PUNCT
ejpam-6074	512	35	x	x	PRON
ejpam-6074	512	36	}	}	PUNCT
ejpam-6074	512	37	are	be	AUX
ejpam-6074	512	38	hop	hop	NOUN
ejpam-6074	512	39	dominating	dominating	NOUN
ejpam-6074	512	40	sets	set	NOUN
ejpam-6074	512	41	.	.	PUNCT
ejpam-6074	513	1	this	this	PRON
ejpam-6074	513	2	implies	imply	VERB
ejpam-6074	513	3	that	that	SCONJ
ejpam-6074	513	4	d	d	NOUN
ejpam-6074	513	5	is	be	AUX
ejpam-6074	513	6	a	a	DET
ejpam-6074	513	7	2	2	NUM
ejpam-6074	513	8	-	-	PUNCT
ejpam-6074	513	9	step	step	NOUN
ejpam-6074	513	10	movable	movable	ADJ
ejpam-6074	513	11	hop	hop	NOUN
ejpam-6074	513	12	dominating	dominating	NOUN
ejpam-6074	513	13	set	set	VERB
ejpam-6074	513	14	in	in	ADP
ejpam-6074	513	15	gg	gg	PROPN
ejpam-6074	513	16	.	.	PUNCT
ejpam-6074	514	1	therefore	therefore	ADV
ejpam-6074	514	2	,	,	PUNCT
ejpam-6074	514	3	γ2mh(gg	γ2mh(gg	NOUN
ejpam-6074	514	4	)	)	PUNCT
ejpam-6074	514	5	=	=	SYM
ejpam-6074	514	6	2	2	X
ejpam-6074	514	7	.	.	PUNCT
ejpam-6074	514	8	(	(	PUNCT
ejpam-6074	514	9	ii	ii	NOUN
ejpam-6074	514	10	)	)	PUNCT
ejpam-6074	514	11	suppose	suppose	VERB
ejpam-6074	514	12	γ2mh(gg	γ2mh(gg	NOUN
ejpam-6074	514	13	)	)	PUNCT
ejpam-6074	514	14	=	=	SYM
ejpam-6074	515	1	3	3	X
ejpam-6074	515	2	.	.	PUNCT
ejpam-6074	515	3	if	if	SCONJ
ejpam-6074	515	4	γh(g	γh(g	NOUN
ejpam-6074	515	5	)	)	PUNCT
ejpam-6074	515	6	=	=	SYM
ejpam-6074	515	7	2	2	NUM
ejpam-6074	515	8	(	(	PUNCT
ejpam-6074	515	9	γh(g	γh(g	NOUN
ejpam-6074	515	10	)	)	PUNCT
ejpam-6074	515	11	=	=	SYM
ejpam-6074	515	12	2	2	NUM
ejpam-6074	515	13	)	)	PUNCT
ejpam-6074	515	14	,	,	PUNCT
ejpam-6074	515	15	then	then	ADV
ejpam-6074	515	16	γh(g	γh(g	PUNCT
ejpam-6074	515	17	)	)	PUNCT
ejpam-6074	515	18	≥	≥	NOUN
ejpam-6074	515	19	3	3	NUM
ejpam-6074	515	20	(	(	PUNCT
ejpam-6074	515	21	resp	resp	NOUN
ejpam-6074	515	22	.	.	PUNCT
ejpam-6074	515	23	γh(g	γh(g	NOUN
ejpam-6074	515	24	)	)	PUNCT
ejpam-6074	515	25	≥	≥	NOUN
ejpam-6074	515	26	3	3	NUM
ejpam-6074	515	27	)	)	PUNCT
ejpam-6074	515	28	by	by	ADP
ejpam-6074	515	29	(	(	PUNCT
ejpam-6074	515	30	i	i	NOUN
ejpam-6074	515	31	)	)	PUNCT
ejpam-6074	515	32	.	.	PUNCT
ejpam-6074	516	1	hence	hence	ADV
ejpam-6074	516	2	,	,	PUNCT
ejpam-6074	516	3	(	(	PUNCT
ejpam-6074	516	4	a	a	X
ejpam-6074	516	5	)	)	PUNCT
ejpam-6074	516	6	holds	hold	NOUN
ejpam-6074	516	7	.	.	PUNCT
ejpam-6074	517	1	next	next	ADV
ejpam-6074	517	2	,	,	PUNCT
ejpam-6074	517	3	suppose	suppose	VERB
ejpam-6074	517	4	γh(g	γh(g	NOUN
ejpam-6074	517	5	)	)	PUNCT
ejpam-6074	517	6	≥	≥	NOUN
ejpam-6074	517	7	3	3	NUM
ejpam-6074	517	8	and	and	CCONJ
ejpam-6074	517	9	γh(g	γh(g	NOUN
ejpam-6074	517	10	)	)	PUNCT
ejpam-6074	517	11	≥	≥	NOUN
ejpam-6074	518	1	3	3	NUM
ejpam-6074	518	2	.	.	PUNCT
ejpam-6074	519	1	if	if	SCONJ
ejpam-6074	519	2	γh(g	γh(g	NOUN
ejpam-6074	519	3	)	)	PUNCT
ejpam-6074	519	4	=	=	SYM
ejpam-6074	519	5	3	3	NUM
ejpam-6074	519	6	or	or	CCONJ
ejpam-6074	519	7	γh(g	γh(g	NOUN
ejpam-6074	519	8	)	)	PUNCT
ejpam-6074	519	9	=	=	SYM
ejpam-6074	519	10	3	3	NUM
ejpam-6074	519	11	,	,	PUNCT
ejpam-6074	519	12	then	then	ADV
ejpam-6074	519	13	(	(	PUNCT
ejpam-6074	519	14	b	b	X
ejpam-6074	519	15	)	)	PUNCT
ejpam-6074	519	16	holds	hold	VERB
ejpam-6074	519	17	.	.	PUNCT
ejpam-6074	519	18	suppose	suppose	VERB
ejpam-6074	519	19	γh(g	γh(g	NOUN
ejpam-6074	519	20	)	)	PUNCT
ejpam-6074	519	21	>	>	X
ejpam-6074	519	22	3	3	NUM
ejpam-6074	519	23	and	and	CCONJ
ejpam-6074	519	24	γh(g	γh(g	NOUN
ejpam-6074	519	25	)	)	PUNCT
ejpam-6074	519	26	>	>	X
ejpam-6074	520	1	3	3	X
ejpam-6074	520	2	.	.	PUNCT
ejpam-6074	520	3	let	let	VERB
ejpam-6074	520	4	s	s	VERB
ejpam-6074	520	5	=	=	PUNCT
ejpam-6074	520	6	{	{	PUNCT
ejpam-6074	520	7	x	x	PROPN
ejpam-6074	520	8	,	,	PUNCT
ejpam-6074	520	9	y	y	PROPN
ejpam-6074	520	10	,	,	PUNCT
ejpam-6074	520	11	t	t	PROPN
ejpam-6074	520	12	}	}	PUNCT
ejpam-6074	520	13	be	be	AUX
ejpam-6074	520	14	a	a	DET
ejpam-6074	520	15	γ2mh	γ2mh	NOUN
ejpam-6074	520	16	-	-	PUNCT
ejpam-6074	520	17	set	set	VERB
ejpam-6074	520	18	in	in	ADP
ejpam-6074	520	19	gg	gg	PROPN
ejpam-6074	520	20	.	.	PUNCT
ejpam-6074	521	1	by	by	ADP
ejpam-6074	521	2	assumption	assumption	NOUN
ejpam-6074	521	3	,	,	PUNCT
ejpam-6074	521	4	s	s	NOUN
ejpam-6074	521	5	∩	∩	ADJ
ejpam-6074	521	6	v	v	ADJ
ejpam-6074	521	7	(	(	PUNCT
ejpam-6074	521	8	g	g	NOUN
ejpam-6074	521	9	)	)	PUNCT
ejpam-6074	521	10	̸=	̸=	PROPN
ejpam-6074	521	11	∅	∅	NOUN
ejpam-6074	521	12	and	and	CCONJ
ejpam-6074	521	13	s	s	VERB
ejpam-6074	521	14	∩	∩	ADJ
ejpam-6074	521	15	v	v	ADJ
ejpam-6074	521	16	(	(	PUNCT
ejpam-6074	521	17	g	g	NOUN
ejpam-6074	521	18	)	)	PUNCT
ejpam-6074	521	19	̸=	̸=	PROPN
ejpam-6074	521	20	∅.	∅.	ADV
ejpam-6074	521	21	suppose	suppose	VERB
ejpam-6074	521	22	x	x	PRON
ejpam-6074	521	23	,	,	PUNCT
ejpam-6074	521	24	y	y	PROPN
ejpam-6074	521	25	∈	∈	PROPN
ejpam-6074	521	26	v	v	ADP
ejpam-6074	521	27	(	(	PUNCT
ejpam-6074	521	28	g	g	NOUN
ejpam-6074	521	29	)	)	PUNCT
ejpam-6074	521	30	and	and	CCONJ
ejpam-6074	521	31	t	t	X
ejpam-6074	521	32	=	=	PUNCT
ejpam-6074	521	33	z	z	PROPN
ejpam-6074	521	34	∈	∈	PROPN
ejpam-6074	521	35	v	v	NOUN
ejpam-6074	521	36	(	(	PUNCT
ejpam-6074	521	37	g	g	NOUN
ejpam-6074	521	38	)	)	PUNCT
ejpam-6074	521	39	.	.	PUNCT
ejpam-6074	522	1	since	since	SCONJ
ejpam-6074	522	2	z	z	PROPN
ejpam-6074	522	3	∈	∈	PROPN
ejpam-6074	522	4	ngg(z	ngg(z	PROPN
ejpam-6074	522	5	)	)	PUNCT
ejpam-6074	522	6	and	and	CCONJ
ejpam-6074	522	7	s	s	VERB
ejpam-6074	522	8	is	be	AUX
ejpam-6074	522	9	hop	hop	NOUN
ejpam-6074	522	10	dominating	dominate	VERB
ejpam-6074	522	11	in	in	ADP
ejpam-6074	522	12	gg	gg	PROPN
ejpam-6074	522	13	,	,	PUNCT
ejpam-6074	522	14	it	it	PRON
ejpam-6074	522	15	follows	follow	VERB
ejpam-6074	522	16	that	that	SCONJ
ejpam-6074	522	17	z	z	PROPN
ejpam-6074	522	18	∈	∈	PROPN
ejpam-6074	522	19	n2	n2	NOUN
ejpam-6074	522	20	g(x	g(x	NOUN
ejpam-6074	522	21	)	)	PUNCT
ejpam-6074	522	22	∪	∪	ADP
ejpam-6074	522	23	n2	n2	ADJ
ejpam-6074	522	24	g(y	g(y	PROPN
ejpam-6074	522	25	)	)	PUNCT
ejpam-6074	522	26	.	.	PUNCT
ejpam-6074	523	1	also	also	ADV
ejpam-6074	523	2	,	,	PUNCT
ejpam-6074	523	3	since	since	SCONJ
ejpam-6074	523	4	γh(g	γh(g	NOUN
ejpam-6074	523	5	)	)	PUNCT
ejpam-6074	523	6	>	>	X
ejpam-6074	523	7	3	3	NUM
ejpam-6074	523	8	and	and	CCONJ
ejpam-6074	523	9	s	s	NOUN
ejpam-6074	523	10	is	be	AUX
ejpam-6074	523	11	2	2	NUM
ejpam-6074	523	12	-	-	PUNCT
ejpam-6074	523	13	step	step	NOUN
ejpam-6074	523	14	movable	movable	ADJ
ejpam-6074	523	15	hop	hop	NOUN
ejpam-6074	523	16	dominating	dominating	NOUN
ejpam-6074	523	17	in	in	ADP
ejpam-6074	523	18	gg	gg	PROPN
ejpam-6074	523	19	,	,	PUNCT
ejpam-6074	523	20	it	it	PRON
ejpam-6074	523	21	follows	follow	VERB
ejpam-6074	523	22	that	that	SCONJ
ejpam-6074	523	23	(	(	PUNCT
ejpam-6074	523	24	s	s	NOUN
ejpam-6074	523	25	\	\	X
ejpam-6074	523	26	{	{	PUNCT
ejpam-6074	523	27	z	z	NOUN
ejpam-6074	523	28	}	}	PUNCT
ejpam-6074	523	29	)	)	PUNCT
ejpam-6074	523	30	∪	∪	ADP
ejpam-6074	523	31	{	{	PUNCT
ejpam-6074	523	32	w	w	NOUN
ejpam-6074	523	33	}	}	PUNCT
ejpam-6074	523	34	=	=	SYM
ejpam-6074	523	35	{	{	PUNCT
ejpam-6074	523	36	x	x	NOUN
ejpam-6074	523	37	,	,	PUNCT
ejpam-6074	523	38	y	y	PROPN
ejpam-6074	523	39	,	,	PUNCT
ejpam-6074	523	40	w	w	NOUN
ejpam-6074	523	41	}	}	PUNCT
ejpam-6074	523	42	is	be	AUX
ejpam-6074	523	43	hop	hop	NOUN
ejpam-6074	523	44	dominating	dominate	VERB
ejpam-6074	523	45	in	in	ADP
ejpam-6074	523	46	gg	gg	NOUN
ejpam-6074	523	47	for	for	ADP
ejpam-6074	523	48	some	some	DET
ejpam-6074	523	49	w	w	NOUN
ejpam-6074	523	50	∈	∈	PROPN
ejpam-6074	523	51	[	[	X
ejpam-6074	523	52	v	v	X
ejpam-6074	523	53	(	(	PUNCT
ejpam-6074	523	54	g	g	NOUN
ejpam-6074	523	55	)	)	PUNCT
ejpam-6074	523	56	\	\	NOUN
ejpam-6074	524	1	{	{	PUNCT
ejpam-6074	524	2	z	z	NOUN
ejpam-6074	524	3	}	}	PUNCT
ejpam-6074	524	4	]	]	PUNCT
ejpam-6074	524	5	∩	∩	PROPN
ejpam-6074	524	6	n2	n2	PROPN
ejpam-6074	524	7	g	g	PROPN
ejpam-6074	524	8	(	(	PUNCT
ejpam-6074	524	9	z	z	NOUN
ejpam-6074	524	10	)	)	PUNCT
ejpam-6074	524	11	.	.	PUNCT
ejpam-6074	525	1	this	this	PRON
ejpam-6074	525	2	implies	imply	VERB
ejpam-6074	525	3	that	that	SCONJ
ejpam-6074	525	4	w	w	PROPN
ejpam-6074	525	5	∈	∈	PROPN
ejpam-6074	525	6	n2	n2	NOUN
ejpam-6074	525	7	g(x	g(x	NOUN
ejpam-6074	525	8	)	)	PUNCT
ejpam-6074	525	9	∪	∪	ADP
ejpam-6074	525	10	n2	n2	ADJ
ejpam-6074	525	11	g(y	g(y	PROPN
ejpam-6074	525	12	)	)	PUNCT
ejpam-6074	525	13	,	,	PUNCT
ejpam-6074	525	14	z	z	NOUN
ejpam-6074	525	15	∈	∈	PROPN
ejpam-6074	525	16	ng(w	ng(w	NOUN
ejpam-6074	525	17	)	)	PUNCT
ejpam-6074	525	18	,	,	PUNCT
ejpam-6074	525	19	and	and	CCONJ
ejpam-6074	525	20	v	v	X
ejpam-6074	525	21	(	(	PUNCT
ejpam-6074	525	22	g	g	NOUN
ejpam-6074	525	23	)	)	PUNCT
ejpam-6074	525	24	\	\	PUNCT
ejpam-6074	526	1	[	[	X
ejpam-6074	526	2	ng(z	ng(z	NUM
ejpam-6074	526	3	)	)	PUNCT
ejpam-6074	526	4	∪ng(w	∪ng(w	PROPN
ejpam-6074	526	5	)	)	PUNCT
ejpam-6074	526	6	]	]	PUNCT
ejpam-6074	527	1	̸=	̸=	PROPN
ejpam-6074	527	2	∅.	∅.	ADP
ejpam-6074	527	3	this	this	DET
ejpam-6074	527	4	shows	show	VERB
ejpam-6074	527	5	that	that	SCONJ
ejpam-6074	527	6	(	(	PUNCT
ejpam-6074	527	7	c	c	X
ejpam-6074	527	8	)	)	PUNCT
ejpam-6074	527	9	holds	hold	VERB
ejpam-6074	527	10	.	.	PUNCT
ejpam-6074	528	1	suppose	suppose	VERB
ejpam-6074	528	2	x	x	PRON
ejpam-6074	528	3	,	,	PUNCT
ejpam-6074	528	4	y	y	PROPN
ejpam-6074	528	5	∈	∈	PROPN
ejpam-6074	528	6	v	v	ADP
ejpam-6074	528	7	(	(	PUNCT
ejpam-6074	528	8	g	g	NOUN
ejpam-6074	528	9	)	)	PUNCT
ejpam-6074	528	10	and	and	CCONJ
ejpam-6074	528	11	t	t	PROPN
ejpam-6074	528	12	∈	∈	PROPN
ejpam-6074	528	13	v	v	ADP
ejpam-6074	528	14	(	(	PUNCT
ejpam-6074	528	15	g	g	NOUN
ejpam-6074	528	16	)	)	PUNCT
ejpam-6074	528	17	.	.	PUNCT
ejpam-6074	529	1	let	let	VERB
ejpam-6074	529	2	x	x	PUNCT
ejpam-6074	529	3	=	=	PUNCT
ejpam-6074	529	4	p	p	PROPN
ejpam-6074	529	5	and	and	CCONJ
ejpam-6074	529	6	x	x	X
ejpam-6074	529	7	=	=	PUNCT
ejpam-6074	529	8	q.	q.	PROPN
ejpam-6074	529	9	since	since	SCONJ
ejpam-6074	529	10	tt	tt	PROPN
ejpam-6074	529	11	∈	∈	PROPN
ejpam-6074	529	12	e(gg	e(gg	PROPN
ejpam-6074	529	13	)	)	PUNCT
ejpam-6074	529	14	,	,	PUNCT
ejpam-6074	529	15	t	t	PROPN
ejpam-6074	529	16	∈	∈	PROPN
ejpam-6074	529	17	n2	n2	NOUN
ejpam-6074	529	18	g	g	PROPN
ejpam-6074	530	1	[	[	X
ejpam-6074	530	2	{	{	PUNCT
ejpam-6074	530	3	p	p	X
ejpam-6074	530	4	,	,	PUNCT
ejpam-6074	530	5	q	q	NOUN
ejpam-6074	530	6	}	}	PUNCT
ejpam-6074	530	7	]	]	PUNCT
ejpam-6074	530	8	because	because	SCONJ
ejpam-6074	530	9	s	s	NOUN
ejpam-6074	530	10	is	be	AUX
ejpam-6074	530	11	hop	hop	NOUN
ejpam-6074	530	12	dominating	dominate	VERB
ejpam-6074	530	13	in	in	ADP
ejpam-6074	530	14	gg	gg	PROPN
ejpam-6074	530	15	.	.	PUNCT
ejpam-6074	531	1	since	since	SCONJ
ejpam-6074	531	2	γh(g	γh(g	NOUN
ejpam-6074	531	3	)	)	PUNCT
ejpam-6074	531	4	>	>	X
ejpam-6074	531	5	3	3	NUM
ejpam-6074	531	6	and	and	CCONJ
ejpam-6074	531	7	s	s	NOUN
ejpam-6074	531	8	is	be	AUX
ejpam-6074	531	9	2	2	NUM
ejpam-6074	531	10	-	-	PUNCT
ejpam-6074	531	11	step	step	NOUN
ejpam-6074	531	12	movable	movable	ADJ
ejpam-6074	531	13	hop	hop	NOUN
ejpam-6074	531	14	dominating	dominating	NOUN
ejpam-6074	531	15	in	in	ADP
ejpam-6074	531	16	gg	gg	PROPN
ejpam-6074	531	17	,	,	PUNCT
ejpam-6074	531	18	there	there	PRON
ejpam-6074	531	19	exists	exist	VERB
ejpam-6074	531	20	s	s	PROPN
ejpam-6074	531	21	∈	∈	PROPN
ejpam-6074	531	22	n2	n2	PROPN
ejpam-6074	531	23	g(t	g(t	PROPN
ejpam-6074	531	24	)	)	PUNCT
ejpam-6074	531	25	such	such	ADJ
ejpam-6074	531	26	that	that	SCONJ
ejpam-6074	531	27	(	(	PUNCT
ejpam-6074	531	28	s	s	NOUN
ejpam-6074	531	29	\	\	X
ejpam-6074	531	30	{	{	PUNCT
ejpam-6074	531	31	t})∪	t})∪	PROPN
ejpam-6074	531	32	{	{	PUNCT
ejpam-6074	531	33	s	s	NOUN
ejpam-6074	531	34	}	}	PUNCT
ejpam-6074	531	35	=	=	SYM
ejpam-6074	531	36	{	{	PUNCT
ejpam-6074	531	37	p	p	X
ejpam-6074	531	38	,	,	PUNCT
ejpam-6074	531	39	q	q	ADJ
ejpam-6074	531	40	,	,	PUNCT
ejpam-6074	531	41	s	s	AUX
ejpam-6074	531	42	}	}	PUNCT
ejpam-6074	531	43	is	be	AUX
ejpam-6074	531	44	hop	hop	NOUN
ejpam-6074	531	45	dominating	dominate	VERB
ejpam-6074	531	46	in	in	ADP
ejpam-6074	531	47	gg	gg	PROPN
ejpam-6074	531	48	.	.	PUNCT
ejpam-6074	532	1	this	this	PRON
ejpam-6074	532	2	implies	imply	VERB
ejpam-6074	532	3	that	that	SCONJ
ejpam-6074	532	4	s	s	VERB
ejpam-6074	532	5	∈	∈	PROPN
ejpam-6074	532	6	n2	n2	NOUN
ejpam-6074	532	7	g	g	PROPN
ejpam-6074	533	1	[	[	X
ejpam-6074	533	2	{	{	PUNCT
ejpam-6074	533	3	p	p	X
ejpam-6074	533	4	,	,	PUNCT
ejpam-6074	533	5	q	q	NOUN
ejpam-6074	533	6	}	}	PUNCT
ejpam-6074	533	7	]	]	PUNCT
ejpam-6074	533	8	.	.	PUNCT
ejpam-6074	534	1	thus	thus	ADV
ejpam-6074	534	2	,	,	PUNCT
ejpam-6074	534	3	(	(	PUNCT
ejpam-6074	534	4	d	d	X
ejpam-6074	534	5	)	)	PUNCT
ejpam-6074	534	6	holds	hold	NOUN
ejpam-6074	534	7	.	.	PUNCT
ejpam-6074	535	1	for	for	ADP
ejpam-6074	535	2	the	the	DET
ejpam-6074	535	3	converse	converse	NOUN
ejpam-6074	535	4	,	,	PUNCT
ejpam-6074	535	5	suppose	suppose	VERB
ejpam-6074	535	6	(	(	PUNCT
ejpam-6074	535	7	a	a	PRON
ejpam-6074	535	8	)	)	PUNCT
ejpam-6074	535	9	holds	hold	VERB
ejpam-6074	535	10	.	.	PUNCT
ejpam-6074	536	1	let	let	VERB
ejpam-6074	536	2	q	q	NOUN
ejpam-6074	536	3	=	=	PUNCT
ejpam-6074	536	4	{	{	PUNCT
ejpam-6074	536	5	c	c	NOUN
ejpam-6074	536	6	,	,	PUNCT
ejpam-6074	536	7	d	d	AUX
ejpam-6074	536	8	}	}	PUNCT
ejpam-6074	536	9	be	be	AUX
ejpam-6074	536	10	a	a	DET
ejpam-6074	536	11	γh	γh	ADV
ejpam-6074	536	12	-	-	PUNCT
ejpam-6074	536	13	set	set	NOUN
ejpam-6074	536	14	of	of	ADP
ejpam-6074	536	15	g	g	NOUN
ejpam-6074	536	16	and	and	CCONJ
ejpam-6074	536	17	let	let	VERB
ejpam-6074	536	18	q∗	q∗	NOUN
ejpam-6074	536	19	=	=	SYM
ejpam-6074	536	20	{	{	PUNCT
ejpam-6074	536	21	c	c	NOUN
ejpam-6074	536	22	,	,	PUNCT
ejpam-6074	536	23	d	d	NOUN
ejpam-6074	536	24	,	,	PUNCT
ejpam-6074	536	25	d	d	NOUN
ejpam-6074	536	26	}	}	PUNCT
ejpam-6074	536	27	.	.	PUNCT
ejpam-6074	537	1	since	since	SCONJ
ejpam-6074	537	2	q∗	q∗	PROPN
ejpam-6074	537	3	\	\	PROPN
ejpam-6074	537	4	{	{	PUNCT
ejpam-6074	537	5	d	d	NOUN
ejpam-6074	537	6	}	}	PUNCT
ejpam-6074	537	7	=	=	SYM
ejpam-6074	537	8	{	{	PUNCT
ejpam-6074	537	9	c	c	NOUN
ejpam-6074	537	10	,	,	PUNCT
ejpam-6074	537	11	d	d	NOUN
ejpam-6074	537	12	}	}	PUNCT
ejpam-6074	537	13	,	,	PUNCT
ejpam-6074	537	14	q∗	q∗	PROPN
ejpam-6074	537	15	\	\	PROPN
ejpam-6074	537	16	{	{	PUNCT
ejpam-6074	537	17	c	c	NOUN
ejpam-6074	537	18	}	}	PUNCT
ejpam-6074	537	19	=	=	SYM
ejpam-6074	537	20	{	{	PUNCT
ejpam-6074	537	21	d	d	NOUN
ejpam-6074	537	22	,	,	PUNCT
ejpam-6074	537	23	d	d	NOUN
ejpam-6074	537	24	}	}	PUNCT
ejpam-6074	537	25	,	,	PUNCT
ejpam-6074	537	26	and	and	CCONJ
ejpam-6074	537	27	(	(	PUNCT
ejpam-6074	537	28	q∗	q∗	PROPN
ejpam-6074	537	29	\	\	PUNCT
ejpam-6074	537	30	{	{	PUNCT
ejpam-6074	537	31	d	d	NOUN
ejpam-6074	537	32	}	}	PUNCT
ejpam-6074	537	33	)	)	PUNCT
ejpam-6074	537	34	∪	∪	ADP
ejpam-6074	537	35	{	{	PUNCT
ejpam-6074	537	36	c	c	NOUN
ejpam-6074	537	37	}	}	PUNCT
ejpam-6074	537	38	=	=	SYM
ejpam-6074	537	39	{	{	PUNCT
ejpam-6074	537	40	c	c	NOUN
ejpam-6074	537	41	,	,	PUNCT
ejpam-6074	537	42	c	c	NOUN
ejpam-6074	537	43	}	}	PUNCT
ejpam-6074	537	44	are	be	AUX
ejpam-6074	537	45	hop	hop	NOUN
ejpam-6074	537	46	dominating	dominating	NOUN
ejpam-6074	537	47	sets	set	NOUN
ejpam-6074	537	48	in	in	ADP
ejpam-6074	537	49	gg	gg	PROPN
ejpam-6074	537	50	,	,	PUNCT
ejpam-6074	537	51	it	it	PRON
ejpam-6074	537	52	follows	follow	VERB
ejpam-6074	537	53	that	that	DET
ejpam-6074	537	54	q∗	q∗	NOUN
ejpam-6074	537	55	=	=	PUNCT
ejpam-6074	537	56	{	{	PUNCT
ejpam-6074	537	57	c	c	NOUN
ejpam-6074	537	58	,	,	PUNCT
ejpam-6074	537	59	d	d	NOUN
ejpam-6074	537	60	,	,	PUNCT
ejpam-6074	537	61	d	d	X
ejpam-6074	537	62	}	}	PUNCT
ejpam-6074	537	63	is	be	AUX
ejpam-6074	537	64	a	a	DET
ejpam-6074	537	65	γ2mh	γ2mh	PROPN
ejpam-6074	537	66	-	-	PUNCT
ejpam-6074	537	67	set	set	VERB
ejpam-6074	537	68	in	in	ADP
ejpam-6074	537	69	gg	gg	PROPN
ejpam-6074	537	70	.	.	PUNCT
ejpam-6074	538	1	hence	hence	ADV
ejpam-6074	538	2	,	,	PUNCT
ejpam-6074	538	3	γ2mh(gg	γ2mh(gg	NOUN
ejpam-6074	538	4	)	)	PUNCT
ejpam-6074	538	5	=	=	SYM
ejpam-6074	539	1	3	3	X
ejpam-6074	539	2	.	.	PUNCT
ejpam-6074	539	3	the	the	DET
ejpam-6074	539	4	same	same	ADJ
ejpam-6074	539	5	conclusion	conclusion	NOUN
ejpam-6074	539	6	holds	hold	VERB
ejpam-6074	539	7	if	if	SCONJ
ejpam-6074	539	8	γh(g	γh(g	NOUN
ejpam-6074	539	9	)	)	PUNCT
ejpam-6074	539	10	≥	≥	NOUN
ejpam-6074	539	11	3	3	NUM
ejpam-6074	539	12	and	and	CCONJ
ejpam-6074	539	13	γh(g	γh(g	NOUN
ejpam-6074	539	14	)	)	PUNCT
ejpam-6074	539	15	=	=	SYM
ejpam-6074	539	16	2	2	X
ejpam-6074	539	17	.	.	PUNCT
ejpam-6074	539	18	suppose	suppose	VERB
ejpam-6074	539	19	r.	r.	PROPN
ejpam-6074	539	20	estrella	estrella	PROPN
ejpam-6074	539	21	,	,	PUNCT
ejpam-6074	539	22	gina	gina	PROPN
ejpam-6074	539	23	m.	m.	PROPN
ejpam-6074	539	24	malacas	malacas	PROPN
ejpam-6074	539	25	,	,	PUNCT
ejpam-6074	539	26	s.	s.	PROPN
ejpam-6074	539	27	canoy	canoy	PROPN
ejpam-6074	539	28	jr	jr	PROPN
ejpam-6074	539	29	.	.	PROPN
ejpam-6074	539	30	/	/	SYM
ejpam-6074	539	31	eur	eur	PROPN
ejpam-6074	539	32	.	.	PUNCT
ejpam-6074	540	1	j.	j.	PROPN
ejpam-6074	540	2	pure	pure	PROPN
ejpam-6074	540	3	appl	appl	PROPN
ejpam-6074	540	4	.	.	PROPN
ejpam-6074	540	5	math	math	PROPN
ejpam-6074	540	6	,	,	PUNCT
ejpam-6074	540	7	18	18	NUM
ejpam-6074	540	8	(	(	PUNCT
ejpam-6074	540	9	2	2	NUM
ejpam-6074	540	10	)	)	PUNCT
ejpam-6074	540	11	(	(	PUNCT
ejpam-6074	540	12	2025	2025	NUM
ejpam-6074	540	13	)	)	PUNCT
ejpam-6074	540	14	,	,	PUNCT
ejpam-6074	540	15	6074	6074	NUM
ejpam-6074	540	16	13	13	NUM
ejpam-6074	540	17	of	of	ADP
ejpam-6074	540	18	15	15	NUM
ejpam-6074	540	19	(	(	PUNCT
ejpam-6074	540	20	b	b	NOUN
ejpam-6074	540	21	)	)	PUNCT
ejpam-6074	540	22	holds	hold	NOUN
ejpam-6074	540	23	,	,	PUNCT
ejpam-6074	540	24	i.e.	i.e.	X
ejpam-6074	540	25	,	,	PUNCT
ejpam-6074	540	26	γh(g	γh(g	NOUN
ejpam-6074	540	27	)	)	PUNCT
ejpam-6074	540	28	=	=	SYM
ejpam-6074	540	29	3	3	NUM
ejpam-6074	540	30	and	and	CCONJ
ejpam-6074	540	31	γh(g	γh(g	NOUN
ejpam-6074	540	32	)	)	PUNCT
ejpam-6074	540	33	≥	≥	NOUN
ejpam-6074	541	1	3	3	X
ejpam-6074	541	2	.	.	PUNCT
ejpam-6074	541	3	let	let	VERB
ejpam-6074	541	4	s	s	VERB
ejpam-6074	541	5	=	=	PUNCT
ejpam-6074	541	6	{	{	PUNCT
ejpam-6074	541	7	x	x	PROPN
ejpam-6074	541	8	,	,	PUNCT
ejpam-6074	541	9	y	y	PROPN
ejpam-6074	541	10	,	,	PUNCT
ejpam-6074	541	11	z	z	NOUN
ejpam-6074	541	12	}	}	PUNCT
ejpam-6074	541	13	be	be	AUX
ejpam-6074	541	14	a	a	DET
ejpam-6074	541	15	γh	γh	ADV
ejpam-6074	541	16	-	-	PUNCT
ejpam-6074	541	17	set	set	NOUN
ejpam-6074	541	18	in	in	ADP
ejpam-6074	541	19	g.	g.	PROPN
ejpam-6074	541	20	since	since	SCONJ
ejpam-6074	541	21	(	(	PUNCT
ejpam-6074	541	22	s	s	NOUN
ejpam-6074	541	23	\	\	X
ejpam-6074	541	24	{	{	PUNCT
ejpam-6074	541	25	x	x	NOUN
ejpam-6074	541	26	}	}	PUNCT
ejpam-6074	541	27	)	)	PUNCT
ejpam-6074	541	28	∪	∪	ADP
ejpam-6074	541	29	{	{	PUNCT
ejpam-6074	541	30	y	y	NOUN
ejpam-6074	541	31	}	}	PUNCT
ejpam-6074	541	32	=	=	SYM
ejpam-6074	541	33	{	{	PUNCT
ejpam-6074	541	34	y	y	PROPN
ejpam-6074	541	35	,	,	PUNCT
ejpam-6074	541	36	y	y	PROPN
ejpam-6074	541	37	,	,	PUNCT
ejpam-6074	541	38	z	z	NOUN
ejpam-6074	541	39	}	}	PUNCT
ejpam-6074	541	40	,	,	PUNCT
ejpam-6074	541	41	(	(	PUNCT
ejpam-6074	541	42	s	s	NOUN
ejpam-6074	541	43	\	\	X
ejpam-6074	541	44	{	{	PUNCT
ejpam-6074	541	45	y	y	NOUN
ejpam-6074	541	46	}	}	PUNCT
ejpam-6074	541	47	)	)	PUNCT
ejpam-6074	541	48	∪	∪	ADP
ejpam-6074	541	49	{	{	PUNCT
ejpam-6074	541	50	x	x	NOUN
ejpam-6074	541	51	}	}	PUNCT
ejpam-6074	541	52	=	=	SYM
ejpam-6074	541	53	{	{	PUNCT
ejpam-6074	541	54	x	x	NOUN
ejpam-6074	541	55	,	,	PUNCT
ejpam-6074	541	56	x	x	X
ejpam-6074	541	57	,	,	PUNCT
ejpam-6074	541	58	z	z	NOUN
ejpam-6074	541	59	}	}	PUNCT
ejpam-6074	541	60	,	,	PUNCT
ejpam-6074	541	61	and	and	CCONJ
ejpam-6074	541	62	(	(	PUNCT
ejpam-6074	541	63	s	s	NOUN
ejpam-6074	541	64	\	\	X
ejpam-6074	541	65	{	{	PUNCT
ejpam-6074	541	66	z	z	NOUN
ejpam-6074	541	67	}	}	PUNCT
ejpam-6074	541	68	)	)	PUNCT
ejpam-6074	541	69	∪	∪	ADP
ejpam-6074	541	70	{	{	PUNCT
ejpam-6074	541	71	y	y	NOUN
ejpam-6074	541	72	}	}	PUNCT
ejpam-6074	541	73	=	=	SYM
ejpam-6074	541	74	{	{	PUNCT
ejpam-6074	541	75	x	x	NOUN
ejpam-6074	541	76	,	,	PUNCT
ejpam-6074	541	77	y	y	PROPN
ejpam-6074	541	78	,	,	PUNCT
ejpam-6074	541	79	y	y	PROPN
ejpam-6074	541	80	}	}	PUNCT
ejpam-6074	541	81	are	be	AUX
ejpam-6074	541	82	hop	hop	NOUN
ejpam-6074	541	83	dominating	dominating	NOUN
ejpam-6074	541	84	sets	set	NOUN
ejpam-6074	541	85	ingg	ingg	NOUN
ejpam-6074	541	86	,	,	PUNCT
ejpam-6074	541	87	it	it	PRON
ejpam-6074	541	88	follows	follow	VERB
ejpam-6074	541	89	that	that	SCONJ
ejpam-6074	541	90	d	d	PROPN
ejpam-6074	541	91	is	be	AUX
ejpam-6074	541	92	a	a	DET
ejpam-6074	541	93	2	2	NUM
ejpam-6074	541	94	-	-	PUNCT
ejpam-6074	541	95	step	step	NOUN
ejpam-6074	541	96	movable	movable	ADJ
ejpam-6074	541	97	hop	hop	NOUN
ejpam-6074	541	98	dominating	dominating	NOUN
ejpam-6074	541	99	set	set	NOUN
ejpam-6074	541	100	ingg	ingg	NOUN
ejpam-6074	541	101	.	.	PUNCT
ejpam-6074	542	1	therefore	therefore	ADV
ejpam-6074	542	2	,	,	PUNCT
ejpam-6074	542	3	γ2mh(gg	γ2mh(gg	NOUN
ejpam-6074	542	4	)	)	PUNCT
ejpam-6074	542	5	=	=	SYM
ejpam-6074	542	6	3	3	X
ejpam-6074	542	7	.	.	PUNCT
ejpam-6074	543	1	this	this	DET
ejpam-6074	543	2	conclusion	conclusion	NOUN
ejpam-6074	543	3	also	also	ADV
ejpam-6074	543	4	holds	hold	VERB
ejpam-6074	543	5	if	if	SCONJ
ejpam-6074	543	6	γh(g	γh(g	NOUN
ejpam-6074	543	7	)	)	PUNCT
ejpam-6074	543	8	≥	≥	NOUN
ejpam-6074	543	9	3	3	NUM
ejpam-6074	543	10	and	and	CCONJ
ejpam-6074	543	11	γh(g	γh(g	PUNCT
ejpam-6074	543	12	)	)	PUNCT
ejpam-6074	543	13	=	=	SYM
ejpam-6074	544	1	3	3	X
ejpam-6074	544	2	.	.	PUNCT
ejpam-6074	545	1	next	next	ADV
ejpam-6074	545	2	,	,	PUNCT
ejpam-6074	545	3	suppose	suppose	VERB
ejpam-6074	545	4	(	(	PUNCT
ejpam-6074	545	5	c	c	NOUN
ejpam-6074	545	6	)	)	PUNCT
ejpam-6074	545	7	holds	hold	VERB
ejpam-6074	545	8	.	.	PUNCT
ejpam-6074	546	1	let	let	VERB
ejpam-6074	546	2	d	d	NOUN
ejpam-6074	546	3	=	=	PRON
ejpam-6074	546	4	{	{	PUNCT
ejpam-6074	546	5	x	x	PROPN
ejpam-6074	546	6	,	,	PUNCT
ejpam-6074	546	7	y	y	PROPN
ejpam-6074	546	8	,	,	PUNCT
ejpam-6074	546	9	z	z	NOUN
ejpam-6074	546	10	}	}	PUNCT
ejpam-6074	546	11	.	.	PUNCT
ejpam-6074	547	1	since	since	SCONJ
ejpam-6074	547	2	v	v	NOUN
ejpam-6074	547	3	(	(	PUNCT
ejpam-6074	547	4	g	g	NOUN
ejpam-6074	547	5	)	)	PUNCT
ejpam-6074	547	6	∪	∪	ADP
ejpam-6074	547	7	{	{	PUNCT
ejpam-6074	547	8	z	z	NOUN
ejpam-6074	547	9	}	}	PUNCT
ejpam-6074	547	10	⊆	⊆	NUM
ejpam-6074	547	11	n2	n2	ADJ
ejpam-6074	547	12	gg	gg	NOUN
ejpam-6074	547	13	(	(	PUNCT
ejpam-6074	547	14	{	{	PUNCT
ejpam-6074	547	15	x	x	NOUN
ejpam-6074	547	16	,	,	PUNCT
ejpam-6074	547	17	y	y	NOUN
ejpam-6074	547	18	}	}	PUNCT
ejpam-6074	547	19	)	)	PUNCT
ejpam-6074	547	20	and	and	CCONJ
ejpam-6074	547	21	v	v	ADP
ejpam-6074	547	22	∈	∈	PROPN
ejpam-6074	547	23	n2	n2	NOUN
ejpam-6074	547	24	gg	gg	NOUN
ejpam-6074	547	25	(	(	PUNCT
ejpam-6074	547	26	z	z	NOUN
ejpam-6074	547	27	)	)	PUNCT
ejpam-6074	547	28	for	for	ADP
ejpam-6074	547	29	all	all	PRON
ejpam-6074	547	30	v	v	ADP
ejpam-6074	547	31	∈	∈	NOUN
ejpam-6074	547	32	v	v	NOUN
ejpam-6074	547	33	(	(	PUNCT
ejpam-6074	547	34	g	g	NOUN
ejpam-6074	547	35	)	)	PUNCT
ejpam-6074	547	36	\	\	NOUN
ejpam-6074	547	37	{	{	PUNCT
ejpam-6074	547	38	z	z	NOUN
ejpam-6074	547	39	,	,	PUNCT
ejpam-6074	547	40	x	x	X
ejpam-6074	547	41	,	,	PUNCT
ejpam-6074	547	42	y	y	PROPN
ejpam-6074	547	43	}	}	PUNCT
ejpam-6074	547	44	it	it	PRON
ejpam-6074	547	45	follows	follow	VERB
ejpam-6074	547	46	that	that	SCONJ
ejpam-6074	547	47	d	d	NOUN
ejpam-6074	547	48	is	be	AUX
ejpam-6074	547	49	a	a	DET
ejpam-6074	547	50	hop	hop	NOUN
ejpam-6074	547	51	dominating	dominating	NOUN
ejpam-6074	547	52	set	set	VERB
ejpam-6074	547	53	in	in	ADP
ejpam-6074	547	54	gg	gg	PROPN
ejpam-6074	547	55	.	.	PUNCT
ejpam-6074	548	1	if	if	SCONJ
ejpam-6074	548	2	z	z	PROPN
ejpam-6074	548	3	∈	∈	PROPN
ejpam-6074	548	4	{	{	PUNCT
ejpam-6074	548	5	x	x	NOUN
ejpam-6074	548	6	,	,	PUNCT
ejpam-6074	548	7	y	y	PROPN
ejpam-6074	548	8	}	}	PUNCT
ejpam-6074	548	9	,	,	PUNCT
ejpam-6074	548	10	say	say	VERB
ejpam-6074	548	11	z	z	NOUN
ejpam-6074	548	12	=	=	SYM
ejpam-6074	548	13	y	y	PROPN
ejpam-6074	548	14	,	,	PUNCT
ejpam-6074	548	15	then	then	ADV
ejpam-6074	548	16	d	d	X
ejpam-6074	548	17	\	\	X
ejpam-6074	548	18	{	{	PUNCT
ejpam-6074	548	19	x	x	NOUN
ejpam-6074	548	20	}	}	PUNCT
ejpam-6074	548	21	=	=	SYM
ejpam-6074	548	22	{	{	PUNCT
ejpam-6074	548	23	y	y	PROPN
ejpam-6074	548	24	,	,	PUNCT
ejpam-6074	548	25	z	z	NOUN
ejpam-6074	548	26	}	}	PUNCT
ejpam-6074	548	27	is	be	AUX
ejpam-6074	548	28	hop	hop	NOUN
ejpam-6074	548	29	dominating	dominate	VERB
ejpam-6074	548	30	in	in	ADP
ejpam-6074	548	31	gg	gg	PROPN
ejpam-6074	548	32	.	.	PUNCT
ejpam-6074	548	33	suppose	suppose	VERB
ejpam-6074	548	34	z	z	NOUN
ejpam-6074	548	35	/∈	/∈	PUNCT
ejpam-6074	548	36	{	{	PUNCT
ejpam-6074	548	37	x	x	NOUN
ejpam-6074	548	38	,	,	PUNCT
ejpam-6074	548	39	y	y	PROPN
ejpam-6074	548	40	}	}	PUNCT
ejpam-6074	548	41	.	.	PUNCT
ejpam-6074	549	1	then	then	ADV
ejpam-6074	549	2	(	(	PUNCT
ejpam-6074	549	3	d	d	NOUN
ejpam-6074	549	4	\{x})∪{y	\{x})∪{y	NOUN
ejpam-6074	549	5	}	}	PUNCT
ejpam-6074	549	6	=	=	SYM
ejpam-6074	549	7	{	{	PUNCT
ejpam-6074	549	8	y	y	PROPN
ejpam-6074	549	9	,	,	PUNCT
ejpam-6074	549	10	y	y	PROPN
ejpam-6074	549	11	,	,	PUNCT
ejpam-6074	549	12	z	z	NOUN
ejpam-6074	549	13	}	}	PUNCT
ejpam-6074	549	14	,	,	PUNCT
ejpam-6074	549	15	(	(	PUNCT
ejpam-6074	549	16	d	d	NOUN
ejpam-6074	549	17	\{y})∪{x	\{y})∪{x	PROPN
ejpam-6074	549	18	}	}	PUNCT
ejpam-6074	549	19	=	=	SYM
ejpam-6074	549	20	{	{	PUNCT
ejpam-6074	549	21	x	x	NOUN
ejpam-6074	549	22	,	,	PUNCT
ejpam-6074	549	23	x	x	X
ejpam-6074	549	24	,	,	PUNCT
ejpam-6074	549	25	z	z	NOUN
ejpam-6074	549	26	}	}	PUNCT
ejpam-6074	549	27	,	,	PUNCT
ejpam-6074	549	28	and	and	CCONJ
ejpam-6074	549	29	(	(	PUNCT
ejpam-6074	549	30	d	d	PROPN
ejpam-6074	549	31	\{z})∪{w	\{z})∪{w	PROPN
ejpam-6074	549	32	}	}	PUNCT
ejpam-6074	549	33	=	=	SYM
ejpam-6074	549	34	{	{	PUNCT
ejpam-6074	549	35	x	x	NOUN
ejpam-6074	549	36	,	,	PUNCT
ejpam-6074	549	37	y	y	PROPN
ejpam-6074	549	38	,	,	PUNCT
ejpam-6074	549	39	w	w	NOUN
ejpam-6074	549	40	}	}	PUNCT
ejpam-6074	549	41	are	be	AUX
ejpam-6074	549	42	hop	hop	NOUN
ejpam-6074	549	43	dominating	dominate	VERB
ejpam-6074	549	44	in	in	ADP
ejpam-6074	549	45	gg	gg	PROPN
ejpam-6074	549	46	.	.	PUNCT
ejpam-6074	550	1	therefore	therefore	ADV
ejpam-6074	550	2	,	,	PUNCT
ejpam-6074	550	3	d	d	X
ejpam-6074	550	4	is	be	AUX
ejpam-6074	550	5	a	a	DET
ejpam-6074	550	6	γ2mh	γ2mh	PROPN
ejpam-6074	550	7	-	-	PUNCT
ejpam-6074	550	8	set	set	VERB
ejpam-6074	550	9	in	in	ADP
ejpam-6074	550	10	gg	gg	PROPN
ejpam-6074	550	11	.	.	PUNCT
ejpam-6074	551	1	hence	hence	ADV
ejpam-6074	551	2	,	,	PUNCT
ejpam-6074	551	3	γ2mh(gg	γ2mh(gg	NOUN
ejpam-6074	551	4	)	)	PUNCT
ejpam-6074	551	5	=	=	SYM
ejpam-6074	551	6	3	3	X
ejpam-6074	551	7	.	.	PUNCT
ejpam-6074	551	8	finally	finally	ADV
ejpam-6074	551	9	,	,	PUNCT
ejpam-6074	551	10	suppose	suppose	VERB
ejpam-6074	551	11	(	(	PUNCT
ejpam-6074	551	12	d	d	X
ejpam-6074	551	13	)	)	PUNCT
ejpam-6074	551	14	holds	hold	VERB
ejpam-6074	551	15	.	.	PUNCT
ejpam-6074	552	1	let	let	VERB
ejpam-6074	552	2	q	q	NOUN
ejpam-6074	553	1	=	=	PUNCT
ejpam-6074	553	2	{	{	PUNCT
ejpam-6074	553	3	p	p	X
ejpam-6074	553	4	,	,	PUNCT
ejpam-6074	553	5	q	q	X
ejpam-6074	553	6	,	,	PUNCT
ejpam-6074	553	7	t	t	PROPN
ejpam-6074	553	8	}	}	PUNCT
ejpam-6074	553	9	.	.	PUNCT
ejpam-6074	554	1	cleary	cleary	PROPN
ejpam-6074	554	2	,	,	PUNCT
ejpam-6074	554	3	q	q	PROPN
ejpam-6074	554	4	is	be	AUX
ejpam-6074	554	5	a	a	DET
ejpam-6074	554	6	hop	hop	NOUN
ejpam-6074	554	7	dominating	dominating	NOUN
ejpam-6074	554	8	set	set	VERB
ejpam-6074	554	9	in	in	ADP
ejpam-6074	554	10	gg	gg	PROPN
ejpam-6074	554	11	.	.	PUNCT
ejpam-6074	555	1	suppose	suppose	VERB
ejpam-6074	555	2	t	t	PROPN
ejpam-6074	555	3	∈	∈	PROPN
ejpam-6074	555	4	{	{	PUNCT
ejpam-6074	555	5	p	p	X
ejpam-6074	555	6	,	,	PUNCT
ejpam-6074	555	7	q	q	NOUN
ejpam-6074	555	8	}	}	PUNCT
ejpam-6074	555	9	,	,	PUNCT
ejpam-6074	555	10	say	say	VERB
ejpam-6074	555	11	t	t	PROPN
ejpam-6074	555	12	=	=	PUNCT
ejpam-6074	555	13	q.	q.	PROPN
ejpam-6074	555	14	then	then	ADV
ejpam-6074	555	15	q	q	X
ejpam-6074	555	16	\	\	PROPN
ejpam-6074	555	17	{	{	PUNCT
ejpam-6074	555	18	p	p	X
ejpam-6074	555	19	}	}	PUNCT
ejpam-6074	555	20	=	=	SYM
ejpam-6074	555	21	{	{	PUNCT
ejpam-6074	555	22	t	t	PROPN
ejpam-6074	555	23	,	,	PUNCT
ejpam-6074	555	24	q	q	PROPN
ejpam-6074	555	25	is	be	AUX
ejpam-6074	555	26	hop	hop	NOUN
ejpam-6074	555	27	dominating	dominate	VERB
ejpam-6074	555	28	in	in	ADP
ejpam-6074	555	29	gg	gg	PROPN
ejpam-6074	555	30	.	.	PUNCT
ejpam-6074	556	1	suppose	suppose	VERB
ejpam-6074	557	1	t	t	PROPN
ejpam-6074	557	2	/∈	/∈	PUNCT
ejpam-6074	557	3	{	{	PUNCT
ejpam-6074	557	4	p	p	X
ejpam-6074	557	5	,	,	PUNCT
ejpam-6074	557	6	q	q	NOUN
ejpam-6074	557	7	}	}	PUNCT
ejpam-6074	557	8	.	.	PUNCT
ejpam-6074	558	1	then	then	ADV
ejpam-6074	558	2	(	(	PUNCT
ejpam-6074	558	3	q\{p})∪{q	q\{p})∪{q	X
ejpam-6074	558	4	}	}	PUNCT
ejpam-6074	558	5	=	=	SYM
ejpam-6074	558	6	{	{	PUNCT
ejpam-6074	558	7	q	q	NOUN
ejpam-6074	558	8	,	,	PUNCT
ejpam-6074	558	9	q	q	NOUN
ejpam-6074	558	10	,	,	PUNCT
ejpam-6074	558	11	t	t	PROPN
ejpam-6074	558	12	}	}	PUNCT
ejpam-6074	558	13	,	,	PUNCT
ejpam-6074	558	14	(	(	PUNCT
ejpam-6074	558	15	q\{q})∪{p	q\{q})∪{p	X
ejpam-6074	558	16	}	}	PUNCT
ejpam-6074	558	17	=	=	SYM
ejpam-6074	558	18	{	{	PUNCT
ejpam-6074	558	19	p	p	X
ejpam-6074	558	20	,	,	PUNCT
ejpam-6074	558	21	p	p	X
ejpam-6074	558	22	,	,	PUNCT
ejpam-6074	558	23	t	t	PROPN
ejpam-6074	558	24	}	}	PUNCT
ejpam-6074	558	25	,	,	PUNCT
ejpam-6074	558	26	and	and	CCONJ
ejpam-6074	558	27	(	(	PUNCT
ejpam-6074	558	28	q\{t})∪{s	q\{t})∪{s	X
ejpam-6074	558	29	}	}	PUNCT
ejpam-6074	558	30	=	=	SYM
ejpam-6074	558	31	{	{	PUNCT
ejpam-6074	558	32	p	p	X
ejpam-6074	558	33	,	,	PUNCT
ejpam-6074	558	34	q	q	ADJ
ejpam-6074	558	35	,	,	PUNCT
ejpam-6074	558	36	s	s	AUX
ejpam-6074	558	37	}	}	PUNCT
ejpam-6074	558	38	are	be	AUX
ejpam-6074	558	39	hop	hop	NOUN
ejpam-6074	558	40	dominating	dominating	NOUN
ejpam-6074	558	41	sets	set	NOUN
ejpam-6074	558	42	in	in	ADP
ejpam-6074	558	43	gg	gg	PROPN
ejpam-6074	558	44	.	.	PUNCT
ejpam-6074	559	1	this	this	PRON
ejpam-6074	559	2	shows	show	VERB
ejpam-6074	559	3	that	that	SCONJ
ejpam-6074	559	4	q	q	NOUN
ejpam-6074	559	5	is	be	AUX
ejpam-6074	559	6	a	a	DET
ejpam-6074	559	7	γ2mh	γ2mh	PROPN
ejpam-6074	559	8	-	-	PUNCT
ejpam-6074	559	9	set	set	VERB
ejpam-6074	559	10	in	in	ADP
ejpam-6074	559	11	gg	gg	PROPN
ejpam-6074	559	12	.	.	PUNCT
ejpam-6074	560	1	thus	thus	ADV
ejpam-6074	560	2	,	,	PUNCT
ejpam-6074	560	3	γ2mh(gg	γ2mh(gg	NOUN
ejpam-6074	560	4	)	)	PUNCT
ejpam-6074	560	5	=	=	SYM
ejpam-6074	560	6	3	3	X
ejpam-6074	560	7	.	.	PUNCT
ejpam-6074	560	8	(	(	PUNCT
ejpam-6074	560	9	iii	iii	X
ejpam-6074	560	10	)	)	PUNCT
ejpam-6074	560	11	this	this	PRON
ejpam-6074	560	12	follows	follow	VERB
ejpam-6074	560	13	from	from	ADP
ejpam-6074	560	14	(	(	PUNCT
ejpam-6074	560	15	i	i	NOUN
ejpam-6074	560	16	)	)	PUNCT
ejpam-6074	560	17	and	and	CCONJ
ejpam-6074	560	18	(	(	PUNCT
ejpam-6074	560	19	ii	ii	NOUN
ejpam-6074	560	20	)	)	PUNCT
ejpam-6074	560	21	.	.	PUNCT
ejpam-6074	561	1	the	the	DET
ejpam-6074	561	2	next	next	ADJ
ejpam-6074	561	3	result	result	NOUN
ejpam-6074	561	4	follows	follow	VERB
ejpam-6074	561	5	from	from	ADP
ejpam-6074	561	6	theorem	theorem	ADJ
ejpam-6074	561	7	9	9	NUM
ejpam-6074	561	8	.	.	PUNCT
ejpam-6074	561	9	corollary	corollary	ADJ
ejpam-6074	561	10	4	4	NUM
ejpam-6074	561	11	.	.	PUNCT
ejpam-6074	562	1	let	let	VERB
ejpam-6074	562	2	n	n	PRON
ejpam-6074	562	3	be	be	AUX
ejpam-6074	562	4	a	a	DET
ejpam-6074	562	5	positive	positive	ADJ
ejpam-6074	562	6	integer	integer	NOUN
ejpam-6074	562	7	and	and	CCONJ
ejpam-6074	562	8	n	n	PRON
ejpam-6074	562	9	≥	≥	NOUN
ejpam-6074	562	10	2	2	NUM
ejpam-6074	562	11	.	.	PUNCT
ejpam-6074	562	12	then	then	ADV
ejpam-6074	562	13	γ2mh(knkn	γ2mh(knkn	VERB
ejpam-6074	562	14	)	)	PUNCT
ejpam-6074	563	1	=	=	PUNCT
ejpam-6074	564	1			NOUN
ejpam-6074	564	2	2	2	NUM
ejpam-6074	564	3	,	,	PUNCT
ejpam-6074	564	4	if	if	SCONJ
ejpam-6074	564	5	n	n	NOUN
ejpam-6074	564	6	=	=	SYM
ejpam-6074	564	7	2	2	NUM
ejpam-6074	564	8	3	3	NUM
ejpam-6074	564	9	,	,	PUNCT
ejpam-6074	564	10	if	if	SCONJ
ejpam-6074	564	11	n	n	NOUN
ejpam-6074	564	12	=	=	SYM
ejpam-6074	564	13	3	3	NUM
ejpam-6074	564	14	4	4	NUM
ejpam-6074	564	15	,	,	PUNCT
ejpam-6074	564	16	if	if	SCONJ
ejpam-6074	564	17	n	n	PRON
ejpam-6074	564	18	≥	≥	NOUN
ejpam-6074	564	19	4	4	NUM
ejpam-6074	564	20	.	.	NOUN
ejpam-6074	564	21	4	4	NUM
ejpam-6074	564	22	.	.	X
ejpam-6074	564	23	conclusion	conclusion	VERB
ejpam-6074	564	24	the	the	DET
ejpam-6074	564	25	concepts	concept	NOUN
ejpam-6074	564	26	of	of	ADP
ejpam-6074	564	27	2	2	NUM
ejpam-6074	564	28	-	-	PUNCT
ejpam-6074	564	29	step	step	NOUN
ejpam-6074	564	30	movability	movability	NOUN
ejpam-6074	564	31	of	of	ADP
ejpam-6074	564	32	hop	hop	NOUN
ejpam-6074	564	33	dominating	dominating	NOUN
ejpam-6074	564	34	sets	set	NOUN
ejpam-6074	564	35	as	as	ADV
ejpam-6074	564	36	well	well	ADV
ejpam-6074	564	37	as	as	ADP
ejpam-6074	564	38	the	the	DET
ejpam-6074	564	39	parameter	parameter	NOUN
ejpam-6074	564	40	2	2	NUM
ejpam-6074	564	41	-	-	PUNCT
ejpam-6074	564	42	step	step	NOUN
ejpam-6074	564	43	movable	movable	ADJ
ejpam-6074	564	44	hop	hop	NOUN
ejpam-6074	564	45	domination	domination	NOUN
ejpam-6074	564	46	number	number	NOUN
ejpam-6074	564	47	have	have	AUX
ejpam-6074	564	48	been	be	AUX
ejpam-6074	564	49	introduced	introduce	VERB
ejpam-6074	564	50	in	in	ADP
ejpam-6074	564	51	this	this	DET
ejpam-6074	564	52	paper	paper	NOUN
ejpam-6074	564	53	.	.	PUNCT
ejpam-6074	565	1	graphs	graph	NOUN
ejpam-6074	565	2	that	that	PRON
ejpam-6074	565	3	admit	admit	VERB
ejpam-6074	565	4	a	a	DET
ejpam-6074	565	5	2	2	NUM
ejpam-6074	565	6	-	-	PUNCT
ejpam-6074	565	7	step	step	NOUN
ejpam-6074	565	8	movable	movable	ADJ
ejpam-6074	565	9	hop	hop	NOUN
ejpam-6074	565	10	dominating	dominating	NOUN
ejpam-6074	565	11	set	set	NOUN
ejpam-6074	565	12	were	be	AUX
ejpam-6074	565	13	characterized	characterize	VERB
ejpam-6074	565	14	.	.	PUNCT
ejpam-6074	566	1	bounds	bound	NOUN
ejpam-6074	566	2	on	on	ADP
ejpam-6074	566	3	the	the	DET
ejpam-6074	566	4	2	2	NUM
ejpam-6074	566	5	-	-	PUNCT
ejpam-6074	566	6	step	step	NOUN
ejpam-6074	566	7	movable	movable	ADJ
ejpam-6074	566	8	hop	hop	NOUN
ejpam-6074	566	9	domination	domination	NOUN
ejpam-6074	566	10	number	number	NOUN
ejpam-6074	566	11	were	be	AUX
ejpam-6074	566	12	given	give	VERB
ejpam-6074	566	13	and	and	CCONJ
ejpam-6074	566	14	graphs	graph	NOUN
ejpam-6074	566	15	that	that	PRON
ejpam-6074	566	16	attained	attain	VERB
ejpam-6074	566	17	these	these	DET
ejpam-6074	566	18	bounds	bound	NOUN
ejpam-6074	566	19	were	be	AUX
ejpam-6074	566	20	characterized	characterize	VERB
ejpam-6074	566	21	.	.	PUNCT
ejpam-6074	567	1	it	it	PRON
ejpam-6074	567	2	was	be	AUX
ejpam-6074	567	3	shown	show	VERB
ejpam-6074	567	4	that	that	SCONJ
ejpam-6074	567	5	the	the	DET
ejpam-6074	567	6	difference	difference	NOUN
ejpam-6074	567	7	of	of	ADP
ejpam-6074	567	8	the	the	DET
ejpam-6074	567	9	2	2	NUM
ejpam-6074	567	10	-	-	PUNCT
ejpam-6074	567	11	step	step	NOUN
ejpam-6074	567	12	movable	movable	ADJ
ejpam-6074	567	13	hop	hop	NOUN
ejpam-6074	567	14	domination	domination	NOUN
ejpam-6074	567	15	number	number	NOUN
ejpam-6074	567	16	and	and	CCONJ
ejpam-6074	567	17	the	the	DET
ejpam-6074	567	18	hop	hop	NOUN
ejpam-6074	567	19	domination	domination	NOUN
ejpam-6074	567	20	can	can	AUX
ejpam-6074	567	21	be	be	AUX
ejpam-6074	567	22	made	make	VERB
ejpam-6074	567	23	arbitrarily	arbitrarily	ADV
ejpam-6074	567	24	large	large	ADJ
ejpam-6074	567	25	.	.	PUNCT
ejpam-6074	568	1	the	the	DET
ejpam-6074	568	2	2	2	NUM
ejpam-6074	568	3	-	-	PUNCT
ejpam-6074	568	4	step	step	NOUN
ejpam-6074	568	5	movability	movability	NOUN
ejpam-6074	568	6	of	of	ADP
ejpam-6074	568	7	hop	hop	NOUN
ejpam-6074	568	8	dominating	dominating	NOUN
ejpam-6074	568	9	sets	set	NOUN
ejpam-6074	568	10	in	in	ADP
ejpam-6074	568	11	the	the	DET
ejpam-6074	568	12	shadow	shadow	NOUN
ejpam-6074	568	13	graph	graph	NOUN
ejpam-6074	568	14	and	and	CCONJ
ejpam-6074	568	15	complementary	complementary	ADJ
ejpam-6074	568	16	prism	prism	NOUN
ejpam-6074	568	17	were	be	AUX
ejpam-6074	568	18	also	also	ADV
ejpam-6074	568	19	considered	consider	VERB
ejpam-6074	568	20	.	.	PUNCT
ejpam-6074	569	1	for	for	ADP
ejpam-6074	569	2	interested	interested	ADJ
ejpam-6074	569	3	readers	reader	NOUN
ejpam-6074	569	4	,	,	PUNCT
ejpam-6074	569	5	this	this	DET
ejpam-6074	569	6	newly	newly	ADV
ejpam-6074	569	7	defined	define	VERB
ejpam-6074	569	8	invariant	invariant	ADJ
ejpam-6074	569	9	may	may	AUX
ejpam-6074	569	10	be	be	AUX
ejpam-6074	569	11	studied	study	VERB
ejpam-6074	569	12	further	far	ADV
ejpam-6074	569	13	for	for	ADP
ejpam-6074	569	14	trees	tree	NOUN
ejpam-6074	569	15	and	and	CCONJ
ejpam-6074	569	16	graphs	graph	NOUN
ejpam-6074	569	17	under	under	ADP
ejpam-6074	569	18	binary	binary	ADJ
ejpam-6074	569	19	operations	operation	NOUN
ejpam-6074	569	20	and	and	CCONJ
ejpam-6074	569	21	even	even	ADV
ejpam-6074	569	22	for	for	ADP
ejpam-6074	569	23	its	its	PRON
ejpam-6074	569	24	complexity	complexity	NOUN
ejpam-6074	569	25	aspects	aspect	NOUN
ejpam-6074	569	26	.	.	PUNCT
ejpam-6074	570	1	acknowledgements	acknowledgement	NOUN
ejpam-6074	570	2	the	the	DET
ejpam-6074	570	3	authors	author	NOUN
ejpam-6074	570	4	would	would	AUX
ejpam-6074	570	5	like	like	VERB
ejpam-6074	570	6	to	to	PART
ejpam-6074	570	7	thank	thank	VERB
ejpam-6074	570	8	the	the	DET
ejpam-6074	570	9	referees	referee	NOUN
ejpam-6074	570	10	for	for	ADP
ejpam-6074	570	11	the	the	DET
ejpam-6074	570	12	invaluable	invaluable	ADJ
ejpam-6074	570	13	assistance	assistance	NOUN
ejpam-6074	570	14	they	they	PRON
ejpam-6074	570	15	gave	give	VERB
ejpam-6074	570	16	us	we	PRON
ejpam-6074	570	17	through	through	ADP
ejpam-6074	570	18	their	their	PRON
ejpam-6074	570	19	comments	comment	NOUN
ejpam-6074	570	20	and	and	CCONJ
ejpam-6074	570	21	suggestions	suggestion	NOUN
ejpam-6074	570	22	which	which	PRON
ejpam-6074	570	23	led	lead	VERB
ejpam-6074	570	24	to	to	ADP
ejpam-6074	570	25	the	the	DET
ejpam-6074	570	26	improvement	improvement	NOUN
ejpam-6074	570	27	of	of	ADP
ejpam-6074	570	28	the	the	DET
ejpam-6074	570	29	paper	paper	NOUN
ejpam-6074	570	30	.	.	PUNCT
ejpam-6074	571	1	the	the	DET
ejpam-6074	571	2	authors	author	NOUN
ejpam-6074	571	3	are	be	AUX
ejpam-6074	571	4	also	also	ADV
ejpam-6074	571	5	grateful	grateful	ADJ
ejpam-6074	571	6	to	to	ADP
ejpam-6074	571	7	the	the	DET
ejpam-6074	571	8	department	department	NOUN
ejpam-6074	571	9	of	of	ADP
ejpam-6074	571	10	science	science	NOUN
ejpam-6074	571	11	and	and	CCONJ
ejpam-6074	571	12	technology	technology	NOUN
ejpam-6074	571	13	accelerated	accelerate	VERB
ejpam-6074	571	14	science	science	NOUN
ejpam-6074	571	15	and	and	CCONJ
ejpam-6074	571	16	technology	technology	NOUN
ejpam-6074	571	17	human	human	ADJ
ejpam-6074	571	18	resource	resource	NOUN
ejpam-6074	571	19	development	development	NOUN
ejpam-6074	571	20	program	program	NOUN
ejpam-6074	571	21	(	(	PUNCT
ejpam-6074	571	22	dost	dost	NOUN
ejpam-6074	571	23	-	-	PUNCT
ejpam-6074	571	24	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-6074	571	25	and	and	CCONJ
ejpam-6074	571	26	msu	msu	PROPN
ejpam-6074	571	27	-	-	PUNCT
ejpam-6074	571	28	iligan	iligan	PROPN
ejpam-6074	571	29	institute	institute	PROPN
ejpam-6074	571	30	of	of	ADP
ejpam-6074	571	31	technology	technology	NOUN
ejpam-6074	571	32	for	for	ADP
ejpam-6074	571	33	funding	fund	VERB
ejpam-6074	571	34	this	this	DET
ejpam-6074	571	35	research	research	NOUN
ejpam-6074	571	36	.	.	PUNCT
ejpam-6074	572	1	r.	r.	PROPN
ejpam-6074	572	2	estrella	estrella	PROPN
ejpam-6074	572	3	,	,	PUNCT
ejpam-6074	572	4	gina	gina	PROPN
ejpam-6074	572	5	m.	m.	PROPN
ejpam-6074	572	6	malacas	malacas	PROPN
ejpam-6074	572	7	,	,	PUNCT
ejpam-6074	572	8	s.	s.	PROPN
ejpam-6074	572	9	canoy	canoy	PROPN
ejpam-6074	572	10	jr	jr	PROPN
ejpam-6074	572	11	.	.	PROPN
ejpam-6074	572	12	/	/	SYM
ejpam-6074	572	13	eur	eur	PROPN
ejpam-6074	572	14	.	.	PUNCT
ejpam-6074	573	1	j.	j.	PROPN
ejpam-6074	573	2	pure	pure	PROPN
ejpam-6074	573	3	appl	appl	PROPN
ejpam-6074	573	4	.	.	PROPN
ejpam-6074	573	5	math	math	PROPN
ejpam-6074	573	6	,	,	PUNCT
ejpam-6074	573	7	18	18	NUM
ejpam-6074	573	8	(	(	PUNCT
ejpam-6074	573	9	2	2	NUM
ejpam-6074	573	10	)	)	PUNCT
ejpam-6074	573	11	(	(	PUNCT
ejpam-6074	573	12	2025	2025	NUM
ejpam-6074	573	13	)	)	PUNCT
ejpam-6074	573	14	,	,	PUNCT
ejpam-6074	573	15	6074	6074	NUM
ejpam-6074	573	16	14	14	NUM
ejpam-6074	573	17	of	of	ADP
ejpam-6074	573	18	15	15	NUM
ejpam-6074	573	19	references	reference	NOUN
ejpam-6074	573	20	[	[	X
ejpam-6074	573	21	1	1	NUM
ejpam-6074	573	22	]	]	PUNCT
ejpam-6074	573	23	j.	j.	PROPN
ejpam-6074	573	24	blair	blair	PROPN
ejpam-6074	573	25	,	,	PUNCT
ejpam-6074	573	26	r.	r.	PROPN
ejpam-6074	573	27	gera	gera	PROPN
ejpam-6074	573	28	,	,	PUNCT
ejpam-6074	573	29	and	and	CCONJ
ejpam-6074	573	30	s.	s.	PROPN
ejpam-6074	573	31	horton	horton	PROPN
ejpam-6074	573	32	.	.	PUNCT
ejpam-6074	574	1	movable	movable	ADJ
ejpam-6074	574	2	dominating	dominating	NOUN
ejpam-6074	574	3	sensor	sensor	NOUN
ejpam-6074	574	4	sets	set	NOUN
ejpam-6074	574	5	in	in	ADP
ejpam-6074	574	6	networks	network	NOUN
ejpam-6074	574	7	.	.	PUNCT
ejpam-6074	575	1	journal	journal	NOUN
ejpam-6074	575	2	of	of	ADP
ejpam-6074	575	3	combinatorial	combinatorial	ADJ
ejpam-6074	575	4	mathematics	mathematic	NOUN
ejpam-6074	575	5	and	and	CCONJ
ejpam-6074	575	6	combinatorial	combinatorial	ADJ
ejpam-6074	575	7	computing	computing	NOUN
ejpam-6074	575	8	.	.	PUNCT
ejpam-6074	575	9	,	,	PUNCT
ejpam-6074	575	10	77:103–123	77:103–123	PROPN
ejpam-6074	575	11	,	,	PUNCT
ejpam-6074	575	12	2011	2011	NUM
ejpam-6074	575	13	.	.	PUNCT
ejpam-6074	576	1	[	[	X
ejpam-6074	576	2	2	2	NUM
ejpam-6074	576	3	]	]	PUNCT
ejpam-6074	576	4	l.	l.	PROPN
ejpam-6074	576	5	harutyunyan	harutyunyan	PROPN
ejpam-6074	576	6	.	.	PUNCT
ejpam-6074	577	1	1−movable	1−movable	ADJ
ejpam-6074	577	2	dominating	dominating	NOUN
ejpam-6074	577	3	set	set	VERB
ejpam-6074	577	4	in	in	ADP
ejpam-6074	577	5	wireless	wireless	ADJ
ejpam-6074	577	6	sensor	sensor	NOUN
ejpam-6074	577	7	networks	network	NOUN
ejpam-6074	577	8	.	.	PUNCT
ejpam-6074	578	1	2015	2015	NUM
ejpam-6074	578	2	8th	8th	NOUN
ejpam-6074	578	3	ifip	ifip	PROPN
ejpam-6074	578	4	wireless	wireless	NOUN
ejpam-6074	578	5	and	and	CCONJ
ejpam-6074	578	6	mobile	mobile	ADJ
ejpam-6074	578	7	networking	network	VERB
ejpam-6074	578	8	conference	conference	NOUN
ejpam-6074	578	9	(	(	PUNCT
ejpam-6074	578	10	wmnc	wmnc	PROPN
ejpam-6074	578	11	)	)	PUNCT
ejpam-6074	578	12	,	,	PUNCT
ejpam-6074	578	13	munich	munich	PROPN
ejpam-6074	578	14	,	,	PUNCT
ejpam-6074	578	15	germany	germany	PROPN
ejpam-6074	578	16	,	,	PUNCT
ejpam-6074	578	17	pages	page	NOUN
ejpam-6074	578	18	269–276	269–276	NUM
ejpam-6074	578	19	,	,	PUNCT
ejpam-6074	578	20	2015	2015	NUM
ejpam-6074	578	21	.	.	PUNCT
ejpam-6074	579	1	[	[	X
ejpam-6074	579	2	3	3	X
ejpam-6074	579	3	]	]	X
ejpam-6074	579	4	r.	r.	PROPN
ejpam-6074	579	5	hinampas	hinampas	PROPN
ejpam-6074	579	6	jr	jr	PROPN
ejpam-6074	579	7	and	and	CCONJ
ejpam-6074	579	8	s.	s.	PROPN
ejpam-6074	579	9	canoy	canoy	PROPN
ejpam-6074	579	10	jr	jr	PROPN
ejpam-6074	579	11	.	.	PROPN
ejpam-6074	579	12	1−movable	1−movable	NUM
ejpam-6074	579	13	domination	domination	NOUN
ejpam-6074	579	14	in	in	ADP
ejpam-6074	579	15	graphs	graph	NOUN
ejpam-6074	579	16	.	.	PUNCT
ejpam-6074	580	1	applied	apply	VERB
ejpam-6074	580	2	mathematical	mathematical	ADJ
ejpam-6074	580	3	sciences	sciences	PROPN
ejpam-6074	580	4	,	,	PUNCT
ejpam-6074	580	5	8(172):8565–8571	8(172):8565–8571	NUM
ejpam-6074	580	6	,	,	PUNCT
ejpam-6074	580	7	2014	2014	NUM
ejpam-6074	580	8	.	.	PUNCT
ejpam-6074	581	1	[	[	X
ejpam-6074	581	2	4	4	NUM
ejpam-6074	581	3	]	]	PUNCT
ejpam-6074	581	4	r.	r.	PROPN
ejpam-6074	581	5	hinampas	hinampas	PROPN
ejpam-6074	581	6	jr	jr	PROPN
ejpam-6074	581	7	and	and	CCONJ
ejpam-6074	581	8	s.	s.	PROPN
ejpam-6074	581	9	canoy	canoy	PROPN
ejpam-6074	581	10	jr	jr	PROPN
ejpam-6074	581	11	.	.	PROPN
ejpam-6074	581	12	1	1	NUM
ejpam-6074	581	13	-	-	PUNCT
ejpam-6074	581	14	movable	movable	ADJ
ejpam-6074	581	15	independent	independent	ADJ
ejpam-6074	581	16	domination	domination	NOUN
ejpam-6074	581	17	in	in	ADP
ejpam-6074	581	18	graphs	graph	NOUN
ejpam-6074	581	19	.	.	PUNCT
ejpam-6074	582	1	international	international	ADJ
ejpam-6074	582	2	journal	journal	PROPN
ejpam-6074	582	3	of	of	ADP
ejpam-6074	582	4	mathematical	mathematical	ADJ
ejpam-6074	582	5	analysis	analysis	NOUN
ejpam-6074	582	6	,	,	PUNCT
ejpam-6074	582	7	9(2):73–80	9(2):73–80	NUM
ejpam-6074	582	8	,	,	PUNCT
ejpam-6074	582	9	2015	2015	NUM
ejpam-6074	582	10	.	.	PUNCT
ejpam-6074	583	1	[	[	X
ejpam-6074	583	2	5	5	X
ejpam-6074	583	3	]	]	PUNCT
ejpam-6074	583	4	j.	j.	PROPN
ejpam-6074	583	5	lomarda	lomarda	PROPN
ejpam-6074	583	6	and	and	CCONJ
ejpam-6074	583	7	s.	s.	PROPN
ejpam-6074	583	8	canoy	canoy	PROPN
ejpam-6074	583	9	jr	jr	PROPN
ejpam-6074	583	10	.	.	PROPN
ejpam-6074	583	11	1−movable	1−movable	NUM
ejpam-6074	583	12	total	total	ADJ
ejpam-6074	583	13	dominating	dominating	NOUN
ejpam-6074	583	14	sets	set	NOUN
ejpam-6074	583	15	in	in	ADP
ejpam-6074	583	16	graphs	graph	NOUN
ejpam-6074	583	17	.	.	PUNCT
ejpam-6074	584	1	international	international	ADJ
ejpam-6074	584	2	journal	journal	PROPN
ejpam-6074	584	3	of	of	ADP
ejpam-6074	584	4	mathematical	mathematical	ADJ
ejpam-6074	584	5	analysis	analysis	NOUN
ejpam-6074	584	6	,	,	PUNCT
ejpam-6074	584	7	8(55):2703–2709	8(55):2703–2709	NUM
ejpam-6074	584	8	,	,	PUNCT
ejpam-6074	584	9	2014	2014	NUM
ejpam-6074	584	10	.	.	PUNCT
ejpam-6074	585	1	[	[	X
ejpam-6074	585	2	6	6	NUM
ejpam-6074	585	3	]	]	PUNCT
ejpam-6074	585	4	j.	j.	PROPN
ejpam-6074	585	5	lomarda	lomarda	PROPN
ejpam-6074	585	6	and	and	CCONJ
ejpam-6074	585	7	s.	s.	PROPN
ejpam-6074	585	8	canoy	canoy	PROPN
ejpam-6074	585	9	jr	jr	PROPN
ejpam-6074	585	10	.	.	PROPN
ejpam-6074	585	11	1−movable	1−movable	NUM
ejpam-6074	585	12	connected	connected	ADJ
ejpam-6074	585	13	dominating	dominating	NOUN
ejpam-6074	585	14	sets	set	NOUN
ejpam-6074	585	15	in	in	ADP
ejpam-6074	585	16	graphs	graph	NOUN
ejpam-6074	585	17	.	.	PUNCT
ejpam-6074	586	1	applied	apply	VERB
ejpam-6074	586	2	mathematical	mathematical	ADJ
ejpam-6074	586	3	sciences	science	NOUN
ejpam-6074	586	4	,	,	PUNCT
ejpam-6074	586	5	9(11):507–514	9(11):507–514	NUM
ejpam-6074	586	6	,	,	PUNCT
ejpam-6074	586	7	2015	2015	NUM
ejpam-6074	586	8	.	.	PUNCT
ejpam-6074	587	1	[	[	X
ejpam-6074	587	2	7	7	X
ejpam-6074	587	3	]	]	X
ejpam-6074	587	4	j.	j.	PROPN
ejpam-6074	587	5	lomarda	lomarda	PROPN
ejpam-6074	587	6	and	and	CCONJ
ejpam-6074	587	7	s.	s.	PROPN
ejpam-6074	587	8	canoy	canoy	PROPN
ejpam-6074	587	9	jr	jr	PROPN
ejpam-6074	587	10	.	.	PROPN
ejpam-6074	587	11	1−movable	1−movable	ADJ
ejpam-6074	587	12	total	total	ADJ
ejpam-6074	587	13	dominating	dominating	NOUN
ejpam-6074	587	14	,	,	PUNCT
ejpam-6074	587	15	connected	connect	VERB
ejpam-6074	587	16	dominating	dominating	NOUN
ejpam-6074	587	17	,	,	PUNCT
ejpam-6074	587	18	and	and	CCONJ
ejpam-6074	587	19	double	double	ADJ
ejpam-6074	587	20	dominating	dominating	NOUN
ejpam-6074	587	21	sets	set	NOUN
ejpam-6074	587	22	in	in	ADP
ejpam-6074	587	23	the	the	DET
ejpam-6074	587	24	composition	composition	NOUN
ejpam-6074	587	25	of	of	ADP
ejpam-6074	587	26	graphs	graph	NOUN
ejpam-6074	587	27	.	.	PUNCT
ejpam-6074	588	1	international	international	ADJ
ejpam-6074	588	2	journal	journal	PROPN
ejpam-6074	588	3	of	of	ADP
ejpam-6074	588	4	mathematical	mathematical	ADJ
ejpam-6074	588	5	analysis	analysis	NOUN
ejpam-6074	588	6	,	,	PUNCT
ejpam-6074	588	7	9(41):2037–2044	9(41):2037–2044	NUM
ejpam-6074	588	8	,	,	PUNCT
ejpam-6074	588	9	2015	2015	NUM
ejpam-6074	588	10	.	.	PUNCT
ejpam-6074	589	1	[	[	X
ejpam-6074	589	2	8	8	NUM
ejpam-6074	589	3	]	]	X
ejpam-6074	589	4	c.	c.	PROPN
ejpam-6074	589	5	natarajan	natarajan	PROPN
ejpam-6074	589	6	and	and	CCONJ
ejpam-6074	589	7	s.	s.	PROPN
ejpam-6074	589	8	ayyaswamy	ayyaswamy	PROPN
ejpam-6074	589	9	.	.	PUNCT
ejpam-6074	590	1	hop	hop	PROPN
ejpam-6074	590	2	domination	domination	NOUN
ejpam-6074	590	3	in	in	ADP
ejpam-6074	590	4	graphs	graphs	PROPN
ejpam-6074	590	5	ii	ii	PROPN
ejpam-6074	590	6	.	.	PUNCT
ejpam-6074	590	7	versita	versita	PROPN
ejpam-6074	590	8	,	,	PUNCT
ejpam-6074	590	9	23(2):187	23(2):187	NUM
ejpam-6074	590	10	–	–	PUNCT
ejpam-6074	590	11	199	199	NUM
ejpam-6074	590	12	,	,	PUNCT
ejpam-6074	590	13	2015	2015	NUM
ejpam-6074	590	14	.	.	PUNCT
ejpam-6074	591	1	[	[	X
ejpam-6074	591	2	9	9	NUM
ejpam-6074	591	3	]	]	PUNCT
ejpam-6074	591	4	s.	s.	PROPN
ejpam-6074	591	5	ayyaswamy	ayyaswamy	PROPN
ejpam-6074	591	6	,	,	PUNCT
ejpam-6074	591	7	b.	b.	PROPN
ejpam-6074	591	8	krishnakumari	krishnakumari	PROPN
ejpam-6074	591	9	,	,	PUNCT
ejpam-6074	591	10	b.	b.	PROPN
ejpam-6074	591	11	natarjan	natarjan	PROPN
ejpam-6074	591	12	,	,	PUNCT
ejpam-6074	591	13	and	and	CCONJ
ejpam-6074	591	14	y.	y.	PROPN
ejpam-6074	591	15	venkatakrishnan	venkatakrishnan	PROPN
ejpam-6074	591	16	.	.	PUNCT
ejpam-6074	592	1	bounds	bound	NOUN
ejpam-6074	592	2	on	on	ADP
ejpam-6074	592	3	the	the	DET
ejpam-6074	592	4	hop	hop	NOUN
ejpam-6074	592	5	domination	domination	NOUN
ejpam-6074	592	6	number	number	NOUN
ejpam-6074	592	7	of	of	ADP
ejpam-6074	592	8	a	a	DET
ejpam-6074	592	9	tree	tree	NOUN
ejpam-6074	592	10	.	.	PUNCT
ejpam-6074	593	1	proceedings	proceeding	NOUN
ejpam-6074	593	2	-	-	PUNCT
ejpam-6074	593	3	mathematical	mathematical	ADJ
ejpam-6074	593	4	sciences	science	NOUN
ejpam-6074	593	5	.	.	PUNCT
ejpam-6074	593	6	,	,	PUNCT
ejpam-6074	593	7	125(4):449–455	125(4):449–455	ADP
ejpam-6074	593	8	,	,	PUNCT
ejpam-6074	593	9	2015	2015	NUM
ejpam-6074	593	10	.	.	PUNCT
ejpam-6074	594	1	[	[	X
ejpam-6074	594	2	10	10	NUM
ejpam-6074	594	3	]	]	X
ejpam-6074	594	4	s.	s.	PROPN
ejpam-6074	594	5	ayyaswamy	ayyaswamy	PROPN
ejpam-6074	594	6	,	,	PUNCT
ejpam-6074	594	7	c.	c.	PROPN
ejpam-6074	594	8	natarajan	natarajan	PROPN
ejpam-6074	594	9	,	,	PUNCT
ejpam-6074	594	10	and	and	CCONJ
ejpam-6074	594	11	g.	g.	PROPN
ejpam-6074	594	12	sathiamoorphy	sathiamoorphy	PROPN
ejpam-6074	594	13	.	.	PUNCT
ejpam-6074	595	1	a	a	DET
ejpam-6074	595	2	note	note	NOUN
ejpam-6074	595	3	on	on	ADP
ejpam-6074	595	4	hop	hop	NOUN
ejpam-6074	595	5	domination	domination	NOUN
ejpam-6074	595	6	number	number	NOUN
ejpam-6074	595	7	of	of	ADP
ejpam-6074	595	8	some	some	DET
ejpam-6074	595	9	special	special	ADJ
ejpam-6074	595	10	families	family	NOUN
ejpam-6074	595	11	of	of	ADP
ejpam-6074	595	12	graphs	graph	NOUN
ejpam-6074	595	13	.	.	PUNCT
ejpam-6074	596	1	international	international	ADJ
ejpam-6074	596	2	journal	journal	NOUN
ejpam-6074	596	3	of	of	ADP
ejpam-6074	596	4	pure	pure	ADJ
ejpam-6074	596	5	and	and	CCONJ
ejpam-6074	596	6	applied	applied	ADJ
ejpam-6074	596	7	mathematics	mathematic	NOUN
ejpam-6074	596	8	.	.	PUNCT
ejpam-6074	596	9	,	,	PUNCT
ejpam-6074	596	10	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-6074	596	11	,	,	PUNCT
ejpam-6074	596	12	2018	2018	NUM
ejpam-6074	596	13	.	.	PUNCT
ejpam-6074	597	1	[	[	X
ejpam-6074	597	2	11	11	NUM
ejpam-6074	597	3	]	]	PUNCT
ejpam-6074	597	4	j.	j.	PROPN
ejpam-6074	597	5	hassan	hassan	PROPN
ejpam-6074	597	6	,	,	PUNCT
ejpam-6074	597	7	s.	s.	PROPN
ejpam-6074	597	8	canoy	canoy	PROPN
ejpam-6074	597	9	jr	jr	PROPN
ejpam-6074	597	10	.	.	PROPN
ejpam-6074	597	11	,	,	PUNCT
ejpam-6074	597	12	and	and	CCONJ
ejpam-6074	597	13	a.	a.	PROPN
ejpam-6074	597	14	aradais	aradais	PROPN
ejpam-6074	597	15	.	.	PUNCT
ejpam-6074	598	1	hop	hop	PROPN
ejpam-6074	598	2	independent	independent	ADJ
ejpam-6074	598	3	sets	set	NOUN
ejpam-6074	598	4	in	in	ADP
ejpam-6074	598	5	graphs	graph	NOUN
ejpam-6074	598	6	.	.	PUNCT
ejpam-6074	599	1	eur	eur	PROPN
ejpam-6074	599	2	.	.	PUNCT
ejpam-6074	600	1	j.	j.	PROPN
ejpam-6074	600	2	pure	pure	PROPN
ejpam-6074	600	3	appl	appl	PROPN
ejpam-6074	600	4	.	.	PUNCT
ejpam-6074	600	5	math	math	PROPN
ejpam-6074	600	6	.	.	PUNCT
ejpam-6074	600	7	,	,	PUNCT
ejpam-6074	600	8	15(2):467–477	15(2):467–477	PROPN
ejpam-6074	600	9	,	,	PUNCT
ejpam-6074	600	10	2022	2022	NUM
ejpam-6074	600	11	.	.	PUNCT
ejpam-6074	601	1	[	[	X
ejpam-6074	601	2	12	12	NUM
ejpam-6074	601	3	]	]	PUNCT
ejpam-6074	601	4	j.	j.	PROPN
ejpam-6074	601	5	hassan	hassan	PROPN
ejpam-6074	601	6	and	and	CCONJ
ejpam-6074	601	7	s.	s.	PROPN
ejpam-6074	601	8	canoy	canoy	PROPN
ejpam-6074	601	9	jr	jr	PROPN
ejpam-6074	601	10	.	.	PROPN
ejpam-6074	601	11	hop	hop	PROPN
ejpam-6074	601	12	independent	independent	ADJ
ejpam-6074	601	13	hop	hop	NOUN
ejpam-6074	601	14	domination	domination	NOUN
ejpam-6074	601	15	in	in	ADP
ejpam-6074	601	16	graphs	graph	NOUN
ejpam-6074	601	17	.	.	PUNCT
ejpam-6074	602	1	eur	eur	PROPN
ejpam-6074	602	2	.	.	PUNCT
ejpam-6074	603	1	j.	j.	PROPN
ejpam-6074	603	2	pure	pure	PROPN
ejpam-6074	603	3	appl	appl	PROPN
ejpam-6074	603	4	.	.	PUNCT
ejpam-6074	603	5	math	math	PROPN
ejpam-6074	603	6	.	.	PUNCT
ejpam-6074	603	7	,	,	PUNCT
ejpam-6074	603	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-6074	603	9	,	,	PUNCT
ejpam-6074	603	10	2022	2022	NUM
ejpam-6074	603	11	.	.	PUNCT
ejpam-6074	604	1	[	[	X
ejpam-6074	604	2	13	13	NUM
ejpam-6074	604	3	]	]	PUNCT
ejpam-6074	604	4	m.	m.	NOUN
ejpam-6074	604	5	henning	henning	PROPN
ejpam-6074	604	6	and	and	CCONJ
ejpam-6074	604	7	n.	n.	PROPN
ejpam-6074	604	8	rad	rad	PROPN
ejpam-6074	604	9	.	.	PROPN
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ejpam-6074	605	2	2	2	NUM
ejpam-6074	605	3	-	-	PUNCT
ejpam-6074	605	4	step	step	NOUN
ejpam-6074	605	5	and	and	CCONJ
ejpam-6074	605	6	hop	hop	NOUN
ejpam-6074	605	7	dominating	dominating	NOUN
ejpam-6074	605	8	sets	set	NOUN
ejpam-6074	605	9	in	in	ADP
ejpam-6074	605	10	graphs	graph	NOUN
ejpam-6074	605	11	.	.	PUNCT
ejpam-6074	606	1	graphs	graph	NOUN
ejpam-6074	606	2	and	and	CCONJ
ejpam-6074	606	3	combinatorics	combinatoric	NOUN
ejpam-6074	606	4	.	.	PUNCT
ejpam-6074	606	5	,	,	PUNCT
ejpam-6074	606	6	33(4):913–927	33(4):913–927	PROPN
ejpam-6074	606	7	,	,	PUNCT
ejpam-6074	606	8	2017	2017	NUM
ejpam-6074	606	9	.	.	PUNCT
ejpam-6074	607	1	[	[	X
ejpam-6074	607	2	14	14	NUM
ejpam-6074	607	3	]	]	X
ejpam-6074	607	4	s.	s.	PROPN
ejpam-6074	607	5	canoy	canoy	PROPN
ejpam-6074	607	6	jr	jr	PROPN
ejpam-6074	607	7	.	.	PROPN
ejpam-6074	607	8	,	,	PUNCT
ejpam-6074	607	9	r.	r.	PROPN
ejpam-6074	607	10	mollejon	mollejon	NOUN
ejpam-6074	607	11	,	,	PUNCT
ejpam-6074	607	12	and	and	CCONJ
ejpam-6074	607	13	j.	j.	PROPN
ejpam-6074	607	14	g.	g.	PROPN
ejpam-6074	607	15	canoy	canoy	PROPN
ejpam-6074	607	16	.	.	PUNCT
ejpam-6074	608	1	hop	hop	PROPN
ejpam-6074	608	2	dominating	dominating	NOUN
ejpam-6074	608	3	sets	set	NOUN
ejpam-6074	608	4	in	in	ADP
ejpam-6074	608	5	graphs	graph	NOUN
ejpam-6074	608	6	under	under	ADP
ejpam-6074	608	7	binary	binary	ADJ
ejpam-6074	608	8	operations	operation	NOUN
ejpam-6074	608	9	.	.	PUNCT
ejpam-6074	609	1	eur	eur	PROPN
ejpam-6074	609	2	.	.	PUNCT
ejpam-6074	610	1	j.	j.	PROPN
ejpam-6074	610	2	pure	pure	PROPN
ejpam-6074	610	3	appl	appl	PROPN
ejpam-6074	610	4	.	.	PUNCT
ejpam-6074	610	5	math	math	PROPN
ejpam-6074	610	6	.	.	PUNCT
ejpam-6074	610	7	,	,	PUNCT
ejpam-6074	611	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-6074	611	2	,	,	PUNCT
ejpam-6074	611	3	2019	2019	NUM
ejpam-6074	611	4	.	.	PUNCT
ejpam-6074	612	1	[	[	X
ejpam-6074	612	2	15	15	NUM
ejpam-6074	612	3	]	]	X
ejpam-6074	612	4	s.	s.	PROPN
ejpam-6074	612	5	canoy	canoy	PROPN
ejpam-6074	612	6	jr	jr	PROPN
ejpam-6074	612	7	.	.	PROPN
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ejpam-6074	612	9	g.	g.	PROPN
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ejpam-6074	612	11	.	.	PUNCT
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ejpam-6074	613	2	domination	domination	NOUN
ejpam-6074	613	3	,	,	PUNCT
ejpam-6074	613	4	hop	hop	NOUN
ejpam-6074	613	5	domination	domination	NOUN
ejpam-6074	613	6	,	,	PUNCT
ejpam-6074	613	7	and	and	CCONJ
ejpam-6074	613	8	global	global	ADJ
ejpam-6074	613	9	hop	hop	NOUN
ejpam-6074	613	10	domination	domination	NOUN
ejpam-6074	613	11	in	in	ADP
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ejpam-6074	613	13	.	.	PUNCT
ejpam-6074	614	1	eur	eur	PROPN
ejpam-6074	614	2	.	.	PUNCT
ejpam-6074	615	1	j.	j.	PROPN
ejpam-6074	615	2	pure	pure	PROPN
ejpam-6074	615	3	appl	appl	PROPN
ejpam-6074	615	4	.	.	PUNCT
ejpam-6074	615	5	math	math	PROPN
ejpam-6074	615	6	.	.	PUNCT
ejpam-6074	615	7	,	,	PUNCT
ejpam-6074	615	8	14:1415–1428	14:1415–1428	NUM
ejpam-6074	615	9	,	,	PUNCT
ejpam-6074	615	10	2021	2021	NUM
ejpam-6074	615	11	.	.	PUNCT
ejpam-6074	616	1	[	[	X
ejpam-6074	616	2	16	16	NUM
ejpam-6074	616	3	]	]	X
ejpam-6074	616	4	s.	s.	PROPN
ejpam-6074	616	5	canoy	canoy	PROPN
ejpam-6074	616	6	jr	jr	PROPN
ejpam-6074	616	7	.	.	PROPN
ejpam-6074	616	8	and	and	CCONJ
ejpam-6074	616	9	g.	g.	PROPN
ejpam-6074	616	10	salasalan	salasalan	NOUN
ejpam-6074	616	11	.	.	PUNCT
ejpam-6074	617	1	locating	locate	VERB
ejpam-6074	617	2	-	-	PUNCT
ejpam-6074	617	3	hop	hop	NOUN
ejpam-6074	617	4	domination	domination	NOUN
ejpam-6074	617	5	in	in	ADP
ejpam-6074	617	6	graphs	graph	NOUN
ejpam-6074	617	7	.	.	PUNCT
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ejpam-6074	618	2	mathematical	mathematical	PROPN
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ejpam-6074	618	4	.	.	PUNCT
ejpam-6074	618	5	,	,	PUNCT
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ejpam-6074	618	7	,	,	PUNCT
ejpam-6074	618	8	2022	2022	NUM
ejpam-6074	618	9	.	.	PUNCT
ejpam-6074	619	1	[	[	X
ejpam-6074	619	2	17	17	NUM
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ejpam-6074	619	9	.	.	PUNCT
ejpam-6074	620	1	connected	connect	VERB
ejpam-6074	620	2	hop	hop	NOUN
ejpam-6074	620	3	domination	domination	NOUN
ejpam-6074	620	4	in	in	ADP
ejpam-6074	620	5	graphs	graph	NOUN
ejpam-6074	620	6	under	under	ADP
ejpam-6074	620	7	some	some	DET
ejpam-6074	620	8	binary	binary	ADJ
ejpam-6074	620	9	operations	operation	NOUN
ejpam-6074	620	10	.	.	PUNCT
ejpam-6074	621	1	asian	asian	ADJ
ejpam-6074	621	2	-	-	PUNCT
ejpam-6074	621	3	eur	eur	NOUN
ejpam-6074	621	4	.	.	PUNCT
ejpam-6074	622	1	j.	j.	PROPN
ejpam-6074	622	2	math	math	PROPN
ejpam-6074	622	3	.	.	PROPN
ejpam-6074	622	4	,	,	PUNCT
ejpam-6074	622	5	11(5):1850075–1–1850075–11	11(5):1850075–1–1850075–11	NUM
ejpam-6074	622	6	,	,	PUNCT
ejpam-6074	622	7	2018	2018	NUM
ejpam-6074	622	8	.	.	PUNCT
ejpam-6074	623	1	[	[	X
ejpam-6074	623	2	18	18	NUM
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ejpam-6074	623	4	r.	r.	PROPN
ejpam-6074	623	5	rakim	rakim	PROPN
ejpam-6074	623	6	,	,	PUNCT
ejpam-6074	623	7	h.	h.	PROPN
ejpam-6074	623	8	rara	rara	PROPN
ejpam-6074	623	9	,	,	PUNCT
ejpam-6074	623	10	and	and	CCONJ
ejpam-6074	623	11	c.j	c.j	PROPN
ejpam-6074	623	12	.	.	PROPN
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ejpam-6074	623	14	.	.	PUNCT
ejpam-6074	624	1	perfect	perfect	ADJ
ejpam-6074	624	2	hop	hop	NOUN
ejpam-6074	624	3	domination	domination	NOUN
ejpam-6074	624	4	in	in	ADP
ejpam-6074	624	5	graphs	graph	NOUN
ejpam-6074	624	6	.	.	PUNCT
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ejpam-6074	625	2	mathematical	mathematical	ADJ
ejpam-6074	625	3	sciences	sciences	PROPN
ejpam-6074	625	4	,	,	PUNCT
ejpam-6074	625	5	12(13):635–649	12(13):635–649	NUM
ejpam-6074	625	6	,	,	PUNCT
ejpam-6074	625	7	2018	2018	NUM
ejpam-6074	625	8	.	.	PUNCT
ejpam-6074	626	1	[	[	X
ejpam-6074	626	2	19	19	NUM
ejpam-6074	626	3	]	]	X
ejpam-6074	626	4	g.	g.	NOUN
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ejpam-6074	626	6	and	and	CCONJ
ejpam-6074	626	7	s.	s.	PROPN
ejpam-6074	626	8	canoy	canoy	PROPN
ejpam-6074	626	9	jr	jr	PROPN
ejpam-6074	626	10	.	.	PROPN
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ejpam-6074	626	12	hop	hop	PROPN
ejpam-6074	626	13	domination	domination	PROPN
ejpam-6074	626	14	numbers	number	NOUN
ejpam-6074	626	15	of	of	ADP
ejpam-6074	626	16	graphs	graph	NOUN
ejpam-6074	626	17	.	.	PUNCT
ejpam-6074	627	1	eur	eur	PROPN
ejpam-6074	627	2	.	.	PUNCT
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ejpam-6074	628	6	m.	m.	PROPN
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ejpam-6074	628	8	,	,	PUNCT
ejpam-6074	628	9	s.	s.	PROPN
ejpam-6074	628	10	canoy	canoy	PROPN
ejpam-6074	628	11	jr	jr	PROPN
ejpam-6074	628	12	.	.	PROPN
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ejpam-6074	628	15	.	.	PUNCT
ejpam-6074	629	1	j.	j.	PROPN
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ejpam-6074	629	4	.	.	PROPN
ejpam-6074	629	5	math	math	PROPN
ejpam-6074	629	6	,	,	PUNCT
ejpam-6074	629	7	18	18	NUM
ejpam-6074	629	8	(	(	PUNCT
ejpam-6074	629	9	2	2	NUM
ejpam-6074	629	10	)	)	PUNCT
ejpam-6074	629	11	(	(	PUNCT
ejpam-6074	629	12	2025	2025	NUM
ejpam-6074	629	13	)	)	PUNCT
ejpam-6074	629	14	,	,	PUNCT
ejpam-6074	629	15	6074	6074	NUM
ejpam-6074	629	16	15	15	NUM
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ejpam-6074	629	18	15	15	NUM
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ejpam-6074	629	20	appl	appl	NOUN
ejpam-6074	629	21	.	.	PUNCT
ejpam-6074	629	22	math	math	PROPN
ejpam-6074	629	23	.	.	PUNCT
ejpam-6074	629	24	,	,	PUNCT
ejpam-6074	629	25	14(1):112–125	14(1):112–125	NUM
ejpam-6074	629	26	,	,	PUNCT
ejpam-6074	629	27	2021	2021	NUM
ejpam-6074	629	28	.	.	PUNCT
ejpam-6074	630	1	[	[	X
ejpam-6074	630	2	20	20	NUM
ejpam-6074	630	3	]	]	PUNCT
ejpam-6074	630	4	s.	s.	PROPN
ejpam-6074	630	5	canoy	canoy	PROPN
ejpam-6074	630	6	jr	jr	PROPN
ejpam-6074	630	7	.	.	PUNCT
ejpam-6074	630	8	j.	j.	PROPN
ejpam-6074	630	9	hassan	hassan	PROPN
ejpam-6074	630	10	and	and	CCONJ
ejpam-6074	630	11	c.j	c.j	PROPN
ejpam-6074	630	12	.	.	PROPN
ejpam-6074	630	13	saromines	saromine	NOUN
ejpam-6074	630	14	.	.	PUNCT
ejpam-6074	631	1	convex	convex	VERB
ejpam-6074	631	2	hop	hop	NOUN
ejpam-6074	631	3	domination	domination	NOUN
ejpam-6074	631	4	in	in	ADP
ejpam-6074	631	5	graphs	graph	NOUN
ejpam-6074	631	6	.	.	PUNCT
ejpam-6074	632	1	eur	eur	PROPN
ejpam-6074	632	2	.	.	PUNCT
ejpam-6074	633	1	j.	j.	PROPN
ejpam-6074	633	2	pure	pure	PROPN
ejpam-6074	633	3	appl	appl	PROPN
ejpam-6074	633	4	.	.	PUNCT
ejpam-6074	633	5	math	math	PROPN
ejpam-6074	633	6	.	.	PUNCT
ejpam-6074	633	7	,	,	PUNCT
ejpam-6074	633	8	16(1):319–335	16(1):319–335	NOUN
ejpam-6074	633	9	,	,	PUNCT
ejpam-6074	633	10	2023	2023	NUM
ejpam-6074	633	11	.	.	PUNCT