id	sid	tid	token	lemma	pos
ejpam-6075	1	1	european	european	PROPN
ejpam-6075	1	2	journal	journal	PROPN
ejpam-6075	1	3	of	of	ADP
ejpam-6075	1	4	pure	pure	ADJ
ejpam-6075	1	5	and	and	CCONJ
ejpam-6075	1	6	applied	applied	ADJ
ejpam-6075	1	7	mathematics	mathematic	NOUN
ejpam-6075	1	8	2025	2025	NUM
ejpam-6075	1	9	,	,	PUNCT
ejpam-6075	1	10	vol	vol	NOUN
ejpam-6075	1	11	.	.	PROPN
ejpam-6075	1	12	18	18	NUM
ejpam-6075	1	13	,	,	PUNCT
ejpam-6075	1	14	issue	issue	NOUN
ejpam-6075	1	15	2	2	NUM
ejpam-6075	1	16	,	,	PUNCT
ejpam-6075	1	17	article	article	NOUN
ejpam-6075	1	18	number	number	NOUN
ejpam-6075	1	19	6075	6075	NUM
ejpam-6075	1	20	issn	issn	PROPN
ejpam-6075	1	21	1307	1307	NUM
ejpam-6075	1	22	-	-	SYM
ejpam-6075	1	23	5543	5543	NUM
ejpam-6075	1	24	–	–	PUNCT
ejpam-6075	1	25	ejpam.com	ejpam.com	X
ejpam-6075	1	26	published	publish	VERB
ejpam-6075	1	27	by	by	ADP
ejpam-6075	1	28	new	new	PROPN
ejpam-6075	1	29	york	york	PROPN
ejpam-6075	1	30	business	business	PROPN
ejpam-6075	1	31	global	global	ADJ
ejpam-6075	1	32	secure	secure	ADJ
ejpam-6075	1	33	hop	hop	NOUN
ejpam-6075	1	34	dominating	dominating	NOUN
ejpam-6075	1	35	sets	set	NOUN
ejpam-6075	1	36	in	in	ADP
ejpam-6075	1	37	graphs	graph	NOUN
ejpam-6075	1	38	farene	farene	PROPN
ejpam-6075	1	39	loida	loida	PROPN
ejpam-6075	1	40	m.	m.	PROPN
ejpam-6075	1	41	alfeche1,∗	alfeche1,∗	PROPN
ejpam-6075	1	42	,	,	PUNCT
ejpam-6075	1	43	gina	gina	PROPN
ejpam-6075	1	44	a.	a.	PROPN
ejpam-6075	1	45	malacas1,2	malacas1,2	PROPN
ejpam-6075	1	46	,	,	PUNCT
ejpam-6075	1	47	sergio	sergio	PROPN
ejpam-6075	1	48	r.	r.	PROPN
ejpam-6075	1	49	canoy	canoy	PROPN
ejpam-6075	1	50	,	,	PUNCT
ejpam-6075	1	51	jr.1,2	jr.1,2	ADJ
ejpam-6075	1	52	1	1	NUM
ejpam-6075	1	53	department	department	NOUN
ejpam-6075	1	54	of	of	ADP
ejpam-6075	1	55	mathematics	mathematic	NOUN
ejpam-6075	1	56	and	and	CCONJ
ejpam-6075	1	57	statistics	statistic	NOUN
ejpam-6075	1	58	,	,	PUNCT
ejpam-6075	1	59	college	college	NOUN
ejpam-6075	1	60	of	of	ADP
ejpam-6075	1	61	science	science	NOUN
ejpam-6075	1	62	and	and	CCONJ
ejpam-6075	1	63	mathematics	mathematic	NOUN
ejpam-6075	1	64	,	,	PUNCT
ejpam-6075	1	65	msu	msu	PROPN
ejpam-6075	1	66	-	-	PUNCT
ejpam-6075	1	67	iligan	iligan	PROPN
ejpam-6075	1	68	institute	institute	PROPN
ejpam-6075	1	69	of	of	ADP
ejpam-6075	1	70	technology	technology	PROPN
ejpam-6075	1	71	,	,	PUNCT
ejpam-6075	1	72	9200	9200	NUM
ejpam-6075	1	73	iligan	iligan	ADJ
ejpam-6075	1	74	city	city	NOUN
ejpam-6075	1	75	,	,	PUNCT
ejpam-6075	1	76	philippines	philippine	NOUN
ejpam-6075	1	77	2	2	NUM
ejpam-6075	1	78	center	center	NOUN
ejpam-6075	1	79	for	for	ADP
ejpam-6075	1	80	mathematical	mathematical	ADJ
ejpam-6075	1	81	and	and	CCONJ
ejpam-6075	1	82	theoretical	theoretical	ADJ
ejpam-6075	1	83	physical	physical	ADJ
ejpam-6075	1	84	sciencesprism	sciencesprism	NOUN
ejpam-6075	1	85	,	,	PUNCT
ejpam-6075	1	86	msu	msu	PROPN
ejpam-6075	1	87	-	-	PUNCT
ejpam-6075	1	88	iligan	iligan	PROPN
ejpam-6075	1	89	institute	institute	PROPN
ejpam-6075	1	90	of	of	ADP
ejpam-6075	1	91	technology	technology	PROPN
ejpam-6075	1	92	,	,	PUNCT
ejpam-6075	1	93	9200	9200	NUM
ejpam-6075	1	94	iligan	iligan	ADJ
ejpam-6075	1	95	city	city	NOUN
ejpam-6075	1	96	,	,	PUNCT
ejpam-6075	1	97	philippines	philippine	NOUN
ejpam-6075	1	98	abstract	abstract	ADJ
ejpam-6075	1	99	.	.	PUNCT
ejpam-6075	2	1	let	let	VERB
ejpam-6075	2	2	g	g	PRON
ejpam-6075	2	3	be	be	AUX
ejpam-6075	2	4	an	an	DET
ejpam-6075	2	5	undirected	undirected	ADJ
ejpam-6075	2	6	(	(	PUNCT
ejpam-6075	2	7	simple	simple	ADJ
ejpam-6075	2	8	)	)	PUNCT
ejpam-6075	2	9	graph	graph	NOUN
ejpam-6075	2	10	with	with	ADP
ejpam-6075	2	11	vertex	vertex	NOUN
ejpam-6075	2	12	and	and	CCONJ
ejpam-6075	2	13	edge	edge	NOUN
ejpam-6075	2	14	sets	set	NOUN
ejpam-6075	2	15	v	v	ADP
ejpam-6075	2	16	(	(	PUNCT
ejpam-6075	2	17	g	g	NOUN
ejpam-6075	2	18	)	)	PUNCT
ejpam-6075	2	19	and	and	CCONJ
ejpam-6075	2	20	e(g	e(g	PROPN
ejpam-6075	2	21	)	)	PUNCT
ejpam-6075	2	22	,	,	PUNCT
ejpam-6075	2	23	respectively	respectively	ADV
ejpam-6075	2	24	.	.	PUNCT
ejpam-6075	3	1	a	a	DET
ejpam-6075	3	2	hop	hop	NOUN
ejpam-6075	3	3	dominating	dominating	NOUN
ejpam-6075	3	4	set	set	NOUN
ejpam-6075	3	5	s	s	PROPN
ejpam-6075	3	6	in	in	ADP
ejpam-6075	3	7	g	g	PROPN
ejpam-6075	3	8	is	be	AUX
ejpam-6075	3	9	secure	secure	ADJ
ejpam-6075	3	10	hop	hop	NOUN
ejpam-6075	3	11	dominating	dominate	VERB
ejpam-6075	3	12	if	if	SCONJ
ejpam-6075	3	13	for	for	ADP
ejpam-6075	3	14	each	each	DET
ejpam-6075	3	15	v	v	NUM
ejpam-6075	3	16	∈	∈	NOUN
ejpam-6075	3	17	v	v	NOUN
ejpam-6075	3	18	(	(	PUNCT
ejpam-6075	3	19	g)\s	g)\s	NOUN
ejpam-6075	3	20	,	,	PUNCT
ejpam-6075	3	21	there	there	PRON
ejpam-6075	3	22	exists	exist	VERB
ejpam-6075	3	23	w	w	PROPN
ejpam-6075	3	24	∈	∈	PROPN
ejpam-6075	3	25	s	s	PART
ejpam-6075	3	26	∩n2	∩n2	PROPN
ejpam-6075	3	27	g(v	g(v	PROPN
ejpam-6075	3	28	)	)	PUNCT
ejpam-6075	3	29	such	such	ADJ
ejpam-6075	3	30	that	that	SCONJ
ejpam-6075	3	31	(	(	PUNCT
ejpam-6075	3	32	s	s	NOUN
ejpam-6075	3	33	\	\	X
ejpam-6075	3	34	{	{	PUNCT
ejpam-6075	3	35	w})∪{v	w})∪{v	NOUN
ejpam-6075	3	36	}	}	PUNCT
ejpam-6075	3	37	is	be	AUX
ejpam-6075	3	38	hop	hop	NOUN
ejpam-6075	3	39	dominating	dominate	VERB
ejpam-6075	3	40	in	in	ADP
ejpam-6075	3	41	g.	g.	PROPN
ejpam-6075	3	42	the	the	DET
ejpam-6075	3	43	minimum	minimum	ADJ
ejpam-6075	3	44	cardinality	cardinality	NOUN
ejpam-6075	3	45	of	of	ADP
ejpam-6075	3	46	a	a	DET
ejpam-6075	3	47	secure	secure	ADJ
ejpam-6075	3	48	hop	hop	NOUN
ejpam-6075	3	49	dominating	dominating	NOUN
ejpam-6075	3	50	in	in	ADP
ejpam-6075	3	51	g	g	NOUN
ejpam-6075	3	52	,	,	PUNCT
ejpam-6075	3	53	denoted	denote	VERB
ejpam-6075	3	54	by	by	ADP
ejpam-6075	3	55	γsh(g	γsh(g	NOUN
ejpam-6075	3	56	)	)	PUNCT
ejpam-6075	3	57	,	,	PUNCT
ejpam-6075	3	58	is	be	AUX
ejpam-6075	3	59	called	call	VERB
ejpam-6075	3	60	the	the	DET
ejpam-6075	3	61	secure	secure	ADJ
ejpam-6075	3	62	hop	hop	NOUN
ejpam-6075	3	63	domination	domination	NOUN
ejpam-6075	3	64	number	number	NOUN
ejpam-6075	3	65	of	of	ADP
ejpam-6075	3	66	g.	g.	PROPN
ejpam-6075	3	67	in	in	ADP
ejpam-6075	3	68	this	this	DET
ejpam-6075	3	69	paper	paper	NOUN
ejpam-6075	3	70	,	,	PUNCT
ejpam-6075	3	71	we	we	PRON
ejpam-6075	3	72	show	show	VERB
ejpam-6075	3	73	that	that	SCONJ
ejpam-6075	3	74	the	the	DET
ejpam-6075	3	75	difference	difference	NOUN
ejpam-6075	3	76	γsh(g	γsh(g	NOUN
ejpam-6075	3	77	)	)	PUNCT
ejpam-6075	3	78	−	−	NOUN
ejpam-6075	3	79	γh(g	γh(g	NOUN
ejpam-6075	3	80	)	)	PUNCT
ejpam-6075	3	81	can	can	AUX
ejpam-6075	3	82	be	be	AUX
ejpam-6075	3	83	made	make	VERB
ejpam-6075	3	84	arbitrarily	arbitrarily	ADV
ejpam-6075	3	85	large	large	ADJ
ejpam-6075	3	86	,	,	PUNCT
ejpam-6075	3	87	where	where	SCONJ
ejpam-6075	3	88	γh(g	γh(g	NOUN
ejpam-6075	3	89	)	)	PUNCT
ejpam-6075	3	90	is	be	AUX
ejpam-6075	3	91	the	the	DET
ejpam-6075	3	92	hop	hop	NOUN
ejpam-6075	3	93	domination	domination	NOUN
ejpam-6075	3	94	number	number	NOUN
ejpam-6075	3	95	of	of	ADP
ejpam-6075	3	96	g.	g.	NOUN
ejpam-6075	3	97	we	we	PRON
ejpam-6075	3	98	give	give	VERB
ejpam-6075	3	99	bounds	bound	NOUN
ejpam-6075	3	100	on	on	ADP
ejpam-6075	3	101	the	the	DET
ejpam-6075	3	102	secure	secure	ADJ
ejpam-6075	3	103	hop	hop	NOUN
ejpam-6075	3	104	domination	domination	NOUN
ejpam-6075	3	105	number	number	NOUN
ejpam-6075	3	106	and	and	CCONJ
ejpam-6075	3	107	characterize	characterize	VERB
ejpam-6075	3	108	those	those	DET
ejpam-6075	3	109	graphs	graph	NOUN
ejpam-6075	3	110	which	which	PRON
ejpam-6075	3	111	attain	attain	VERB
ejpam-6075	3	112	these	these	DET
ejpam-6075	3	113	bounds	bound	NOUN
ejpam-6075	3	114	.	.	PUNCT
ejpam-6075	4	1	the	the	DET
ejpam-6075	4	2	value	value	NOUN
ejpam-6075	4	3	of	of	ADP
ejpam-6075	4	4	the	the	DET
ejpam-6075	4	5	newly	newly	ADV
ejpam-6075	4	6	defined	define	VERB
ejpam-6075	4	7	parameter	parameter	NOUN
ejpam-6075	4	8	is	be	AUX
ejpam-6075	4	9	determined	determine	VERB
ejpam-6075	4	10	for	for	ADP
ejpam-6075	4	11	some	some	DET
ejpam-6075	4	12	classes	class	NOUN
ejpam-6075	4	13	of	of	ADP
ejpam-6075	4	14	graphs	graph	NOUN
ejpam-6075	4	15	.	.	PUNCT
ejpam-6075	5	1	moreover	moreover	ADV
ejpam-6075	5	2	,	,	PUNCT
ejpam-6075	5	3	we	we	PRON
ejpam-6075	5	4	characterize	characterize	VERB
ejpam-6075	5	5	the	the	DET
ejpam-6075	5	6	secure	secure	ADJ
ejpam-6075	5	7	hop	hop	NOUN
ejpam-6075	5	8	dominating	dominating	NOUN
ejpam-6075	5	9	sets	set	NOUN
ejpam-6075	5	10	in	in	ADP
ejpam-6075	5	11	the	the	DET
ejpam-6075	5	12	shadow	shadow	NOUN
ejpam-6075	5	13	graph	graph	NOUN
ejpam-6075	5	14	and	and	CCONJ
ejpam-6075	5	15	complementary	complementary	ADJ
ejpam-6075	5	16	prism	prism	NOUN
ejpam-6075	5	17	and	and	CCONJ
ejpam-6075	5	18	determine	determine	VERB
ejpam-6075	5	19	the	the	DET
ejpam-6075	5	20	value	value	NOUN
ejpam-6075	5	21	of	of	ADP
ejpam-6075	5	22	the	the	DET
ejpam-6075	5	23	parameter	parameter	NOUN
ejpam-6075	5	24	for	for	ADP
ejpam-6075	5	25	each	each	PRON
ejpam-6075	5	26	of	of	ADP
ejpam-6075	5	27	these	these	DET
ejpam-6075	5	28	graphs	graph	NOUN
ejpam-6075	5	29	.	.	PUNCT
ejpam-6075	6	1	2020	2020	NUM
ejpam-6075	6	2	mathematics	mathematic	NOUN
ejpam-6075	6	3	subject	subject	NOUN
ejpam-6075	6	4	classifications	classification	NOUN
ejpam-6075	6	5	:	:	PUNCT
ejpam-6075	6	6	05c69	05c69	X
ejpam-6075	6	7	key	key	ADJ
ejpam-6075	6	8	words	word	NOUN
ejpam-6075	6	9	and	and	CCONJ
ejpam-6075	6	10	phrases	phrase	NOUN
ejpam-6075	6	11	:	:	PUNCT
ejpam-6075	6	12	hop	hop	NOUN
ejpam-6075	6	13	domination	domination	NOUN
ejpam-6075	6	14	,	,	PUNCT
ejpam-6075	6	15	secure	secure	VERB
ejpam-6075	6	16	hop	hop	NOUN
ejpam-6075	6	17	domination	domination	NOUN
ejpam-6075	6	18	number	number	NOUN
ejpam-6075	6	19	,	,	PUNCT
ejpam-6075	6	20	shadow	shadow	NOUN
ejpam-6075	6	21	graph	graph	NOUN
ejpam-6075	6	22	,	,	PUNCT
ejpam-6075	6	23	complementary	complementary	ADJ
ejpam-6075	6	24	prism	prism	NOUN
ejpam-6075	6	25	1	1	NUM
ejpam-6075	6	26	.	.	PUNCT
ejpam-6075	6	27	introduction	introduction	NOUN
ejpam-6075	6	28	in	in	ADP
ejpam-6075	6	29	2003	2003	NUM
ejpam-6075	6	30	,	,	PUNCT
ejpam-6075	6	31	cockayne	cockayne	NOUN
ejpam-6075	6	32	et	et	PROPN
ejpam-6075	6	33	al	al	PROPN
ejpam-6075	6	34	.	.	PUNCT
ejpam-6075	7	1	[	[	X
ejpam-6075	7	2	1	1	X
ejpam-6075	7	3	]	]	PUNCT
ejpam-6075	7	4	introduced	introduce	VERB
ejpam-6075	7	5	and	and	CCONJ
ejpam-6075	7	6	studied	study	VERB
ejpam-6075	7	7	secure	secure	ADJ
ejpam-6075	7	8	domination	domination	NOUN
ejpam-6075	7	9	,	,	PUNCT
ejpam-6075	7	10	a	a	DET
ejpam-6075	7	11	variant	variant	NOUN
ejpam-6075	7	12	of	of	ADP
ejpam-6075	7	13	the	the	DET
ejpam-6075	7	14	standard	standard	ADJ
ejpam-6075	7	15	domination	domination	NOUN
ejpam-6075	7	16	concept	concept	NOUN
ejpam-6075	7	17	.	.	PUNCT
ejpam-6075	8	1	as	as	SCONJ
ejpam-6075	8	2	used	use	VERB
ejpam-6075	8	3	to	to	PART
ejpam-6075	8	4	model	model	VERB
ejpam-6075	8	5	a	a	DET
ejpam-6075	8	6	protection	protection	NOUN
ejpam-6075	8	7	strategy	strategy	NOUN
ejpam-6075	8	8	in	in	ADP
ejpam-6075	8	9	a	a	DET
ejpam-6075	8	10	given	give	VERB
ejpam-6075	8	11	network	network	NOUN
ejpam-6075	8	12	,	,	PUNCT
ejpam-6075	8	13	a	a	DET
ejpam-6075	8	14	secure	secure	ADJ
ejpam-6075	8	15	dominating	dominating	NOUN
ejpam-6075	8	16	set	set	NOUN
ejpam-6075	8	17	may	may	AUX
ejpam-6075	8	18	be	be	AUX
ejpam-6075	8	19	viewed	view	VERB
ejpam-6075	8	20	as	as	ADP
ejpam-6075	8	21	one	one	NUM
ejpam-6075	8	22	consisting	consist	VERB
ejpam-6075	8	23	of	of	ADP
ejpam-6075	8	24	guards	guard	NOUN
ejpam-6075	8	25	that	that	PRON
ejpam-6075	8	26	protect	protect	VERB
ejpam-6075	8	27	the	the	DET
ejpam-6075	8	28	network	network	NOUN
ejpam-6075	8	29	from	from	ADP
ejpam-6075	8	30	possible	possible	ADJ
ejpam-6075	8	31	attacks	attack	NOUN
ejpam-6075	8	32	.	.	PUNCT
ejpam-6075	9	1	it	it	PRON
ejpam-6075	9	2	is	be	AUX
ejpam-6075	9	3	ensured	ensure	VERB
ejpam-6075	9	4	that	that	SCONJ
ejpam-6075	9	5	a	a	DET
ejpam-6075	9	6	guard	guard	NOUN
ejpam-6075	9	7	can	can	AUX
ejpam-6075	9	8	respond	respond	VERB
ejpam-6075	9	9	to	to	ADP
ejpam-6075	9	10	a	a	DET
ejpam-6075	9	11	certain	certain	ADJ
ejpam-6075	9	12	attack	attack	NOUN
ejpam-6075	9	13	in	in	ADP
ejpam-6075	9	14	some	some	DET
ejpam-6075	9	15	nearby	nearby	ADJ
ejpam-6075	9	16	vertex	vertex	NOUN
ejpam-6075	9	17	and	and	CCONJ
ejpam-6075	9	18	as	as	SCONJ
ejpam-6075	9	19	the	the	DET
ejpam-6075	9	20	guard	guard	NOUN
ejpam-6075	9	21	moves	move	VERB
ejpam-6075	9	22	to	to	ADP
ejpam-6075	9	23	this	this	DET
ejpam-6075	9	24	location	location	NOUN
ejpam-6075	9	25	to	to	PART
ejpam-6075	9	26	defend	defend	VERB
ejpam-6075	9	27	the	the	DET
ejpam-6075	9	28	attack	attack	NOUN
ejpam-6075	9	29	,	,	PUNCT
ejpam-6075	9	30	the	the	DET
ejpam-6075	9	31	protection	protection	NOUN
ejpam-6075	9	32	or	or	CCONJ
ejpam-6075	9	33	security	security	NOUN
ejpam-6075	9	34	of	of	ADP
ejpam-6075	9	35	the	the	DET
ejpam-6075	9	36	whole	whole	ADJ
ejpam-6075	9	37	network	network	NOUN
ejpam-6075	9	38	is	be	AUX
ejpam-6075	9	39	not	not	PART
ejpam-6075	9	40	compromised	compromise	VERB
ejpam-6075	9	41	.	.	PUNCT
ejpam-6075	10	1	the	the	DET
ejpam-6075	10	2	concept	concept	NOUN
ejpam-6075	10	3	and	and	CCONJ
ejpam-6075	10	4	some	some	PRON
ejpam-6075	10	5	of	of	ADP
ejpam-6075	10	6	its	its	PRON
ejpam-6075	10	7	variants	variant	NOUN
ejpam-6075	10	8	have	have	AUX
ejpam-6075	10	9	been	be	AUX
ejpam-6075	10	10	considered	consider	VERB
ejpam-6075	10	11	and	and	CCONJ
ejpam-6075	10	12	studied	study	VERB
ejpam-6075	10	13	in	in	ADP
ejpam-6075	10	14	[	[	X
ejpam-6075	10	15	2	2	NUM
ejpam-6075	10	16	]	]	PUNCT
ejpam-6075	10	17	,	,	PUNCT
ejpam-6075	10	18	[	[	X
ejpam-6075	10	19	3	3	NUM
ejpam-6075	10	20	]	]	PUNCT
ejpam-6075	10	21	,	,	PUNCT
ejpam-6075	10	22	[	[	X
ejpam-6075	10	23	4	4	NUM
ejpam-6075	10	24	]	]	PUNCT
ejpam-6075	10	25	,	,	PUNCT
ejpam-6075	10	26	[	[	X
ejpam-6075	10	27	5	5	NUM
ejpam-6075	10	28	]	]	PUNCT
ejpam-6075	10	29	,	,	PUNCT
ejpam-6075	10	30	[	[	X
ejpam-6075	10	31	6	6	NUM
ejpam-6075	10	32	]	]	PUNCT
ejpam-6075	10	33	,	,	PUNCT
ejpam-6075	10	34	[	[	X
ejpam-6075	10	35	7	7	NUM
ejpam-6075	10	36	]	]	PUNCT
ejpam-6075	10	37	,	,	PUNCT
ejpam-6075	10	38	[	[	X
ejpam-6075	10	39	8	8	NUM
ejpam-6075	10	40	]	]	PUNCT
ejpam-6075	10	41	,	,	PUNCT
ejpam-6075	11	1	[	[	X
ejpam-6075	11	2	9	9	NUM
ejpam-6075	11	3	]	]	PUNCT
ejpam-6075	11	4	,	,	PUNCT
ejpam-6075	11	5	and	and	CCONJ
ejpam-6075	11	6	[	[	X
ejpam-6075	11	7	10	10	NUM
ejpam-6075	11	8	]	]	PUNCT
ejpam-6075	11	9	.	.	PUNCT
ejpam-6075	12	1	another	another	DET
ejpam-6075	12	2	domination	domination	NOUN
ejpam-6075	12	3	-	-	PUNCT
ejpam-6075	12	4	related	relate	VERB
ejpam-6075	12	5	concept	concept	NOUN
ejpam-6075	12	6	was	be	AUX
ejpam-6075	12	7	introduced	introduce	VERB
ejpam-6075	12	8	by	by	ADP
ejpam-6075	12	9	natarajan	natarajan	PROPN
ejpam-6075	12	10	et	et	PROPN
ejpam-6075	12	11	al	al	PROPN
ejpam-6075	12	12	.	.	PUNCT
ejpam-6075	13	1	in	in	ADP
ejpam-6075	13	2	[	[	X
ejpam-6075	13	3	11	11	NUM
ejpam-6075	13	4	]	]	PUNCT
ejpam-6075	13	5	.	.	PUNCT
ejpam-6075	14	1	this	this	DET
ejpam-6075	14	2	parameter	parameter	NOUN
ejpam-6075	14	3	,	,	PUNCT
ejpam-6075	14	4	called	call	VERB
ejpam-6075	14	5	hop	hop	NOUN
ejpam-6075	14	6	domination	domination	NOUN
ejpam-6075	14	7	parameter	parameter	NOUN
ejpam-6075	14	8	,	,	PUNCT
ejpam-6075	14	9	and	and	CCONJ
ejpam-6075	14	10	some	some	PRON
ejpam-6075	14	11	of	of	ADP
ejpam-6075	14	12	its	its	PRON
ejpam-6075	14	13	variants	variant	NOUN
ejpam-6075	14	14	have	have	AUX
ejpam-6075	14	15	been	be	AUX
ejpam-6075	14	16	the	the	DET
ejpam-6075	14	17	∗corresponding	∗corresponde	VERB
ejpam-6075	14	18	author	author	NOUN
ejpam-6075	14	19	.	.	PUNCT
ejpam-6075	15	1	doi	doi	NOUN
ejpam-6075	15	2	:	:	PUNCT
ejpam-6075	15	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6075	https://doi.org/10.29020/nybg.ejpam.v18i2.6075	PROPN
ejpam-6075	15	4	email	email	NOUN
ejpam-6075	15	5	addresses	address	NOUN
ejpam-6075	15	6	:	:	PUNCT
ejpam-6075	15	7	farene.alfeche@g.msuiit.edu.ph	farene.alfeche@g.msuiit.edu.ph	PROPN
ejpam-6075	15	8	(	(	PUNCT
ejpam-6075	15	9	f.	f.	PROPN
ejpam-6075	15	10	l.	l.	PROPN
ejpam-6075	15	11	alfeche	alfeche	PROPN
ejpam-6075	15	12	)	)	PUNCT
ejpam-6075	15	13	gina.malacas@g.msuiit.edu.ph	gina.malacas@g.msuiit.edu.ph	PROPN
ejpam-6075	15	14	(	(	PUNCT
ejpam-6075	15	15	g.	g.	PROPN
ejpam-6075	15	16	a.	a.	PROPN
ejpam-6075	15	17	malacas	malacas	PROPN
ejpam-6075	15	18	)	)	PUNCT
ejpam-6075	15	19	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-6075	15	20	(	(	PUNCT
ejpam-6075	15	21	s.	s.	PROPN
ejpam-6075	15	22	r.	r.	PROPN
ejpam-6075	15	23	canoy	canoy	PROPN
ejpam-6075	15	24	)	)	PUNCT
ejpam-6075	15	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6075	16	1	1	1	NUM
ejpam-6075	16	2	copyright	copyright	NOUN
ejpam-6075	16	3	:	:	PUNCT
ejpam-6075	16	4	©	©	PROPN
ejpam-6075	16	5	2025	2025	NUM
ejpam-6075	16	6	the	the	DET
ejpam-6075	16	7	author(s	author(s	NOUN
ejpam-6075	16	8	)	)	PUNCT
ejpam-6075	16	9	.	.	PUNCT
ejpam-6075	17	1	(	(	PUNCT
ejpam-6075	17	2	cc	cc	NOUN
ejpam-6075	17	3	by	by	ADP
ejpam-6075	17	4	-	-	PUNCT
ejpam-6075	17	5	nc	nc	PROPN
ejpam-6075	17	6	4.0	4.0	NUM
ejpam-6075	17	7	)	)	PUNCT
ejpam-6075	17	8	f.	f.	PROPN
ejpam-6075	17	9	l.	l.	PROPN
ejpam-6075	17	10	alfeche	alfeche	PROPN
ejpam-6075	17	11	,	,	PUNCT
ejpam-6075	17	12	g.	g.	PROPN
ejpam-6075	17	13	a.	a.	PROPN
ejpam-6075	17	14	malacas	malacas	PROPN
ejpam-6075	17	15	,	,	PUNCT
ejpam-6075	17	16	s.	s.	PROPN
ejpam-6075	17	17	canoy	canoy	PROPN
ejpam-6075	17	18	jr	jr	PROPN
ejpam-6075	17	19	.	.	PROPN
ejpam-6075	17	20	/	/	SYM
ejpam-6075	17	21	eur	eur	PROPN
ejpam-6075	17	22	.	.	PUNCT
ejpam-6075	18	1	j.	j.	PROPN
ejpam-6075	18	2	pure	pure	PROPN
ejpam-6075	18	3	appl	appl	PROPN
ejpam-6075	18	4	.	.	PROPN
ejpam-6075	18	5	math	math	PROPN
ejpam-6075	18	6	,	,	PUNCT
ejpam-6075	18	7	18	18	NUM
ejpam-6075	18	8	(	(	PUNCT
ejpam-6075	18	9	2	2	NUM
ejpam-6075	18	10	)	)	PUNCT
ejpam-6075	18	11	(	(	PUNCT
ejpam-6075	18	12	2025	2025	NUM
ejpam-6075	18	13	)	)	PUNCT
ejpam-6075	18	14	,	,	PUNCT
ejpam-6075	18	15	6075	6075	NUM
ejpam-6075	18	16	2	2	NUM
ejpam-6075	18	17	of	of	ADP
ejpam-6075	18	18	14	14	NUM
ejpam-6075	18	19	subject	subject	NOUN
ejpam-6075	18	20	of	of	ADP
ejpam-6075	18	21	interest	interest	NOUN
ejpam-6075	18	22	in	in	ADP
ejpam-6075	18	23	a	a	DET
ejpam-6075	18	24	number	number	NOUN
ejpam-6075	18	25	of	of	ADP
ejpam-6075	18	26	recent	recent	ADJ
ejpam-6075	18	27	studies	study	NOUN
ejpam-6075	18	28	(	(	PUNCT
ejpam-6075	18	29	see	see	VERB
ejpam-6075	18	30	[	[	X
ejpam-6075	18	31	12	12	NUM
ejpam-6075	18	32	]	]	PUNCT
ejpam-6075	18	33	,	,	PUNCT
ejpam-6075	19	1	[	[	X
ejpam-6075	19	2	13	13	NUM
ejpam-6075	19	3	]	]	PUNCT
ejpam-6075	19	4	,	,	PUNCT
ejpam-6075	20	1	[	[	X
ejpam-6075	20	2	14	14	NUM
ejpam-6075	20	3	]	]	PUNCT
ejpam-6075	20	4	,	,	PUNCT
ejpam-6075	20	5	[	[	X
ejpam-6075	20	6	15	15	NUM
ejpam-6075	20	7	]	]	PUNCT
ejpam-6075	20	8	,	,	PUNCT
ejpam-6075	20	9	[	[	X
ejpam-6075	20	10	16	16	NUM
ejpam-6075	20	11	]	]	PUNCT
ejpam-6075	20	12	,	,	PUNCT
ejpam-6075	21	1	[	[	X
ejpam-6075	21	2	17	17	NUM
ejpam-6075	21	3	]	]	PUNCT
ejpam-6075	21	4	,	,	PUNCT
ejpam-6075	22	1	[	[	X
ejpam-6075	22	2	18	18	NUM
ejpam-6075	22	3	]	]	PUNCT
ejpam-6075	22	4	,	,	PUNCT
ejpam-6075	22	5	[	[	X
ejpam-6075	22	6	19	19	NUM
ejpam-6075	22	7	]	]	PUNCT
ejpam-6075	22	8	,	,	PUNCT
ejpam-6075	22	9	[	[	X
ejpam-6075	22	10	20	20	NUM
ejpam-6075	22	11	]	]	PUNCT
ejpam-6075	22	12	,	,	PUNCT
ejpam-6075	22	13	[	[	X
ejpam-6075	22	14	21	21	NUM
ejpam-6075	22	15	]	]	PUNCT
ejpam-6075	22	16	,	,	PUNCT
ejpam-6075	22	17	[	[	X
ejpam-6075	22	18	22	22	NUM
ejpam-6075	22	19	]	]	PUNCT
ejpam-6075	22	20	,	,	PUNCT
ejpam-6075	22	21	and	and	CCONJ
ejpam-6075	22	22	[	[	X
ejpam-6075	22	23	23	23	NUM
ejpam-6075	22	24	]	]	PUNCT
ejpam-6075	22	25	)	)	PUNCT
ejpam-6075	22	26	.	.	PUNCT
ejpam-6075	23	1	in	in	ADP
ejpam-6075	23	2	this	this	DET
ejpam-6075	23	3	paper	paper	NOUN
ejpam-6075	23	4	,	,	PUNCT
ejpam-6075	23	5	we	we	PRON
ejpam-6075	23	6	introduce	introduce	VERB
ejpam-6075	23	7	and	and	CCONJ
ejpam-6075	23	8	study	study	VERB
ejpam-6075	23	9	initially	initially	ADV
ejpam-6075	23	10	the	the	DET
ejpam-6075	23	11	new	new	ADJ
ejpam-6075	23	12	variant	variant	NOUN
ejpam-6075	23	13	secure	secure	ADJ
ejpam-6075	23	14	hop	hop	NOUN
ejpam-6075	23	15	domination	domination	NOUN
ejpam-6075	23	16	.	.	PUNCT
ejpam-6075	24	1	the	the	DET
ejpam-6075	24	2	motivation	motivation	NOUN
ejpam-6075	24	3	stems	stem	VERB
ejpam-6075	24	4	from	from	ADP
ejpam-6075	24	5	the	the	DET
ejpam-6075	24	6	fact	fact	NOUN
ejpam-6075	24	7	that	that	SCONJ
ejpam-6075	24	8	domination	domination	NOUN
ejpam-6075	24	9	and	and	CCONJ
ejpam-6075	24	10	hop	hop	NOUN
ejpam-6075	24	11	domination	domination	NOUN
ejpam-6075	24	12	have	have	AUX
ejpam-6075	24	13	many	many	ADJ
ejpam-6075	24	14	similar	similar	ADJ
ejpam-6075	24	15	applications	application	NOUN
ejpam-6075	24	16	in	in	ADP
ejpam-6075	24	17	networks	network	NOUN
ejpam-6075	24	18	.	.	PUNCT
ejpam-6075	25	1	it	it	PRON
ejpam-6075	25	2	is	be	AUX
ejpam-6075	25	3	easily	easily	ADV
ejpam-6075	25	4	observed	observe	VERB
ejpam-6075	25	5	from	from	ADP
ejpam-6075	25	6	its	its	PRON
ejpam-6075	25	7	definition	definition	NOUN
ejpam-6075	25	8	that	that	SCONJ
ejpam-6075	25	9	every	every	DET
ejpam-6075	25	10	graph	graph	NOUN
ejpam-6075	25	11	admits	admit	VERB
ejpam-6075	25	12	a	a	DET
ejpam-6075	25	13	secure	secure	ADJ
ejpam-6075	25	14	hop	hop	NOUN
ejpam-6075	25	15	dominating	dominating	NOUN
ejpam-6075	25	16	set	set	NOUN
ejpam-6075	25	17	;	;	PUNCT
ejpam-6075	25	18	in	in	ADP
ejpam-6075	25	19	fact	fact	NOUN
ejpam-6075	25	20	,	,	PUNCT
ejpam-6075	25	21	the	the	DET
ejpam-6075	25	22	vertex	vertex	NOUN
ejpam-6075	25	23	set	set	NOUN
ejpam-6075	25	24	of	of	ADP
ejpam-6075	25	25	a	a	DET
ejpam-6075	25	26	graph	graph	NOUN
ejpam-6075	25	27	is	be	AUX
ejpam-6075	25	28	such	such	DET
ejpam-6075	25	29	a	a	DET
ejpam-6075	25	30	set	set	NOUN
ejpam-6075	25	31	.	.	PUNCT
ejpam-6075	26	1	we	we	PRON
ejpam-6075	26	2	give	give	VERB
ejpam-6075	26	3	bounds	bound	NOUN
ejpam-6075	26	4	on	on	ADP
ejpam-6075	26	5	the	the	DET
ejpam-6075	26	6	parameter	parameter	NOUN
ejpam-6075	26	7	and	and	CCONJ
ejpam-6075	26	8	give	give	VERB
ejpam-6075	26	9	necessary	necessary	ADJ
ejpam-6075	26	10	and	and	CCONJ
ejpam-6075	26	11	sufficient	sufficient	ADJ
ejpam-6075	26	12	conditions	condition	NOUN
ejpam-6075	26	13	for	for	ADP
ejpam-6075	26	14	a	a	DET
ejpam-6075	26	15	hop	hop	NOUN
ejpam-6075	26	16	dominating	dominating	NOUN
ejpam-6075	26	17	set	set	NOUN
ejpam-6075	26	18	to	to	PART
ejpam-6075	26	19	be	be	AUX
ejpam-6075	26	20	secure	secure	ADJ
ejpam-6075	26	21	hop	hop	NOUN
ejpam-6075	26	22	dominating	dominating	NOUN
ejpam-6075	26	23	.	.	PUNCT
ejpam-6075	27	1	we	we	PRON
ejpam-6075	27	2	also	also	ADV
ejpam-6075	27	3	study	study	VERB
ejpam-6075	27	4	the	the	DET
ejpam-6075	27	5	newly	newly	ADV
ejpam-6075	27	6	defined	define	VERB
ejpam-6075	27	7	parameter	parameter	NOUN
ejpam-6075	27	8	in	in	ADP
ejpam-6075	27	9	the	the	DET
ejpam-6075	27	10	shadow	shadow	NOUN
ejpam-6075	27	11	graph	graph	NOUN
ejpam-6075	27	12	and	and	CCONJ
ejpam-6075	27	13	complementary	complementary	ADJ
ejpam-6075	27	14	prism	prism	NOUN
ejpam-6075	27	15	.	.	PUNCT
ejpam-6075	28	1	2	2	X
ejpam-6075	28	2	.	.	X
ejpam-6075	28	3	terminology	terminology	NOUN
ejpam-6075	28	4	and	and	CCONJ
ejpam-6075	28	5	notation	notation	NOUN
ejpam-6075	28	6	let	let	VERB
ejpam-6075	28	7	g	g	PROPN
ejpam-6075	28	8	=	=	SYM
ejpam-6075	28	9	v	v	PROPN
ejpam-6075	28	10	(	(	PUNCT
ejpam-6075	28	11	g	g	NOUN
ejpam-6075	28	12	)	)	PUNCT
ejpam-6075	28	13	,	,	PUNCT
ejpam-6075	28	14	e(g	e(g	PROPN
ejpam-6075	28	15	)	)	PUNCT
ejpam-6075	28	16	)	)	PUNCT
ejpam-6075	28	17	be	be	AUX
ejpam-6075	28	18	an	an	DET
ejpam-6075	28	19	undirected	undirected	ADJ
ejpam-6075	28	20	graph	graph	NOUN
ejpam-6075	28	21	.	.	PUNCT
ejpam-6075	29	1	for	for	ADP
ejpam-6075	29	2	any	any	DET
ejpam-6075	29	3	two	two	NUM
ejpam-6075	29	4	vertices	vertex	NOUN
ejpam-6075	29	5	u	u	NOUN
ejpam-6075	29	6	and	and	CCONJ
ejpam-6075	29	7	v	v	NOUN
ejpam-6075	29	8	of	of	ADP
ejpam-6075	29	9	g	g	NOUN
ejpam-6075	29	10	,	,	PUNCT
ejpam-6075	29	11	the	the	DET
ejpam-6075	29	12	distance	distance	NOUN
ejpam-6075	29	13	dg(u	dg(u	X
ejpam-6075	29	14	,	,	PUNCT
ejpam-6075	29	15	v	v	NOUN
ejpam-6075	29	16	)	)	PUNCT
ejpam-6075	29	17	is	be	AUX
ejpam-6075	29	18	the	the	DET
ejpam-6075	29	19	length	length	NOUN
ejpam-6075	29	20	of	of	ADP
ejpam-6075	29	21	a	a	DET
ejpam-6075	29	22	shortest	short	ADJ
ejpam-6075	29	23	path	path	NOUN
ejpam-6075	29	24	joining	join	VERB
ejpam-6075	29	25	u	u	NOUN
ejpam-6075	29	26	and	and	CCONJ
ejpam-6075	29	27	v.	v.	ADP
ejpam-6075	29	28	any	any	DET
ejpam-6075	29	29	u	u	NOUN
ejpam-6075	29	30	-	-	NOUN
ejpam-6075	29	31	v	v	ADJ
ejpam-6075	29	32	path	path	NOUN
ejpam-6075	29	33	of	of	ADP
ejpam-6075	29	34	length	length	NOUN
ejpam-6075	29	35	dg(u	dg(u	PROPN
ejpam-6075	29	36	,	,	PUNCT
ejpam-6075	29	37	v	v	NOUN
ejpam-6075	29	38	)	)	PUNCT
ejpam-6075	29	39	is	be	AUX
ejpam-6075	29	40	called	call	VERB
ejpam-6075	29	41	a	a	DET
ejpam-6075	29	42	u	u	NOUN
ejpam-6075	29	43	-	-	NOUN
ejpam-6075	29	44	v	v	ADJ
ejpam-6075	29	45	geodesic	geodesic	NOUN
ejpam-6075	29	46	.	.	PUNCT
ejpam-6075	30	1	the	the	DET
ejpam-6075	30	2	interval	interval	NOUN
ejpam-6075	30	3	ig	ig	PROPN
ejpam-6075	31	1	[	[	X
ejpam-6075	31	2	u	u	NOUN
ejpam-6075	31	3	,	,	PUNCT
ejpam-6075	31	4	v	v	NOUN
ejpam-6075	31	5	]	]	PUNCT
ejpam-6075	31	6	consists	consist	VERB
ejpam-6075	31	7	of	of	ADP
ejpam-6075	31	8	u	u	NOUN
ejpam-6075	31	9	,	,	PUNCT
ejpam-6075	31	10	v	v	NOUN
ejpam-6075	31	11	,	,	PUNCT
ejpam-6075	31	12	and	and	CCONJ
ejpam-6075	31	13	all	all	DET
ejpam-6075	31	14	vertices	vertex	NOUN
ejpam-6075	31	15	lying	lie	VERB
ejpam-6075	31	16	on	on	ADP
ejpam-6075	31	17	a	a	DET
ejpam-6075	31	18	u	u	NOUN
ejpam-6075	31	19	-	-	NOUN
ejpam-6075	31	20	v	v	ADJ
ejpam-6075	31	21	geodesic	geodesic	NOUN
ejpam-6075	31	22	.	.	PUNCT
ejpam-6075	32	1	the	the	DET
ejpam-6075	32	2	interval	interval	NOUN
ejpam-6075	32	3	ig(u	ig(u	NOUN
ejpam-6075	32	4	,	,	PUNCT
ejpam-6075	32	5	v	v	NOUN
ejpam-6075	32	6	)	)	PUNCT
ejpam-6075	32	7	=	=	PUNCT
ejpam-6075	33	1	ig	ig	PROPN
ejpam-6075	34	1	[	[	X
ejpam-6075	34	2	u	u	NOUN
ejpam-6075	34	3	,	,	PUNCT
ejpam-6075	34	4	v	v	ADP
ejpam-6075	34	5	]	]	PUNCT
ejpam-6075	34	6	\	\	NOUN
ejpam-6075	34	7	{	{	PUNCT
ejpam-6075	34	8	u	u	NOUN
ejpam-6075	34	9	,	,	PUNCT
ejpam-6075	34	10	v	v	NOUN
ejpam-6075	34	11	}	}	PUNCT
ejpam-6075	34	12	.	.	PUNCT
ejpam-6075	35	1	vertices	vertice	VERB
ejpam-6075	35	2	u	u	NOUN
ejpam-6075	35	3	and	and	CCONJ
ejpam-6075	35	4	v	v	NOUN
ejpam-6075	35	5	are	be	AUX
ejpam-6075	35	6	adjacent	adjacent	ADJ
ejpam-6075	35	7	(	(	PUNCT
ejpam-6075	35	8	or	or	CCONJ
ejpam-6075	35	9	neighbors	neighbor	NOUN
ejpam-6075	35	10	)	)	PUNCT
ejpam-6075	35	11	if	if	SCONJ
ejpam-6075	35	12	uv	uv	PROPN
ejpam-6075	35	13	∈	∈	PROPN
ejpam-6075	35	14	e(g	e(g	PROPN
ejpam-6075	35	15	)	)	PUNCT
ejpam-6075	35	16	.	.	PUNCT
ejpam-6075	36	1	the	the	DET
ejpam-6075	36	2	set	set	NOUN
ejpam-6075	36	3	of	of	ADP
ejpam-6075	36	4	neighbors	neighbor	NOUN
ejpam-6075	36	5	of	of	ADP
ejpam-6075	36	6	a	a	DET
ejpam-6075	36	7	vertex	vertex	NOUN
ejpam-6075	36	8	u	u	NOUN
ejpam-6075	36	9	in	in	ADP
ejpam-6075	36	10	g	g	NOUN
ejpam-6075	36	11	,	,	PUNCT
ejpam-6075	36	12	denoted	denote	VERB
ejpam-6075	36	13	by	by	ADP
ejpam-6075	36	14	ng(u	ng(u	NOUN
ejpam-6075	36	15	)	)	PUNCT
ejpam-6075	36	16	,	,	PUNCT
ejpam-6075	36	17	is	be	AUX
ejpam-6075	36	18	called	call	VERB
ejpam-6075	36	19	the	the	DET
ejpam-6075	36	20	open	open	ADJ
ejpam-6075	36	21	neighborhood	neighborhood	NOUN
ejpam-6075	36	22	of	of	ADP
ejpam-6075	36	23	u.	u.	VERB
ejpam-6075	36	24	the	the	DET
ejpam-6075	36	25	closed	closed	ADJ
ejpam-6075	36	26	neighborhood	neighborhood	NOUN
ejpam-6075	36	27	of	of	ADP
ejpam-6075	36	28	u	u	NOUN
ejpam-6075	36	29	is	be	AUX
ejpam-6075	36	30	the	the	DET
ejpam-6075	36	31	set	set	NOUN
ejpam-6075	36	32	ng[u	ng[u	PROPN
ejpam-6075	36	33	]	]	X
ejpam-6075	36	34	=	=	SYM
ejpam-6075	36	35	ng(u	ng(u	PROPN
ejpam-6075	36	36	)	)	PUNCT
ejpam-6075	36	37	∪	∪	NOUN
ejpam-6075	36	38	{	{	PUNCT
ejpam-6075	36	39	u	u	NOUN
ejpam-6075	36	40	}	}	PUNCT
ejpam-6075	36	41	.	.	PUNCT
ejpam-6075	37	1	if	if	SCONJ
ejpam-6075	37	2	x	x	PROPN
ejpam-6075	37	3	⊆	⊆	NUM
ejpam-6075	37	4	v	v	X
ejpam-6075	37	5	(	(	PUNCT
ejpam-6075	37	6	g	g	NOUN
ejpam-6075	37	7	)	)	PUNCT
ejpam-6075	37	8	,	,	PUNCT
ejpam-6075	37	9	the	the	DET
ejpam-6075	37	10	open	open	ADJ
ejpam-6075	37	11	neighborhood	neighborhood	NOUN
ejpam-6075	37	12	of	of	ADP
ejpam-6075	37	13	x	x	SYM
ejpam-6075	37	14	is	be	AUX
ejpam-6075	37	15	the	the	DET
ejpam-6075	37	16	set	set	NOUN
ejpam-6075	37	17	ng(x	ng(x	NUM
ejpam-6075	37	18	)	)	PUNCT
ejpam-6075	38	1	=	=	SYM
ejpam-6075	38	2	⋃	⋃	NOUN
ejpam-6075	38	3	u∈x	u∈x	NOUN
ejpam-6075	38	4	ng(u	ng(u	NOUN
ejpam-6075	38	5	)	)	PUNCT
ejpam-6075	38	6	.	.	PUNCT
ejpam-6075	39	1	the	the	DET
ejpam-6075	39	2	closed	closed	ADJ
ejpam-6075	39	3	neighborhood	neighborhood	NOUN
ejpam-6075	39	4	of	of	ADP
ejpam-6075	39	5	x	x	SYM
ejpam-6075	39	6	is	be	AUX
ejpam-6075	39	7	the	the	DET
ejpam-6075	39	8	set	set	NOUN
ejpam-6075	39	9	ng[x	ng[x	PROPN
ejpam-6075	39	10	]	]	X
ejpam-6075	39	11	=	=	PUNCT
ejpam-6075	39	12	ng(x	ng(x	X
ejpam-6075	39	13	)	)	PUNCT
ejpam-6075	40	1	∪x	∪x	PROPN
ejpam-6075	40	2	.	.	PUNCT
ejpam-6075	41	1	a	a	DET
ejpam-6075	41	2	set	set	NOUN
ejpam-6075	41	3	d	d	NOUN
ejpam-6075	41	4	⊆	⊆	NUM
ejpam-6075	41	5	v	v	ADP
ejpam-6075	41	6	(	(	PUNCT
ejpam-6075	41	7	g	g	NOUN
ejpam-6075	41	8	)	)	PUNCT
ejpam-6075	41	9	is	be	AUX
ejpam-6075	41	10	a	a	DET
ejpam-6075	41	11	dominating	dominating	NOUN
ejpam-6075	41	12	set	set	VERB
ejpam-6075	41	13	in	in	ADP
ejpam-6075	41	14	g	g	PROPN
ejpam-6075	41	15	if	if	SCONJ
ejpam-6075	41	16	for	for	ADP
ejpam-6075	41	17	every	every	DET
ejpam-6075	41	18	v	v	NUM
ejpam-6075	41	19	∈	∈	NOUN
ejpam-6075	41	20	v	v	NOUN
ejpam-6075	41	21	(	(	PUNCT
ejpam-6075	41	22	g)\d	g)\d	NOUN
ejpam-6075	41	23	,	,	PUNCT
ejpam-6075	41	24	there	there	PRON
ejpam-6075	41	25	exists	exist	VERB
ejpam-6075	41	26	u	u	NOUN
ejpam-6075	41	27	∈	∈	PROPN
ejpam-6075	41	28	d	d	ADP
ejpam-6075	41	29	such	such	ADJ
ejpam-6075	41	30	that	that	DET
ejpam-6075	41	31	uv	uv	PROPN
ejpam-6075	41	32	∈	∈	PROPN
ejpam-6075	41	33	e(g	e(g	PROPN
ejpam-6075	41	34	)	)	PUNCT
ejpam-6075	41	35	,	,	PUNCT
ejpam-6075	41	36	that	that	ADV
ejpam-6075	41	37	is	is	ADV
ejpam-6075	41	38	,	,	PUNCT
ejpam-6075	41	39	ng[d	ng[d	PROPN
ejpam-6075	41	40	]	]	PUNCT
ejpam-6075	41	41	=	=	SYM
ejpam-6075	41	42	v	v	X
ejpam-6075	41	43	(	(	PUNCT
ejpam-6075	41	44	g	g	NOUN
ejpam-6075	41	45	)	)	PUNCT
ejpam-6075	41	46	.	.	PUNCT
ejpam-6075	42	1	the	the	DET
ejpam-6075	42	2	domination	domination	NOUN
ejpam-6075	42	3	number	number	NOUN
ejpam-6075	42	4	of	of	ADP
ejpam-6075	42	5	g	g	NOUN
ejpam-6075	42	6	,	,	PUNCT
ejpam-6075	42	7	denoted	denote	VERB
ejpam-6075	42	8	by	by	ADP
ejpam-6075	42	9	γ(g	γ(g	PROPN
ejpam-6075	42	10	)	)	PUNCT
ejpam-6075	42	11	,	,	PUNCT
ejpam-6075	42	12	is	be	AUX
ejpam-6075	42	13	the	the	DET
ejpam-6075	42	14	minimum	minimum	ADJ
ejpam-6075	42	15	cardinality	cardinality	NOUN
ejpam-6075	42	16	of	of	ADP
ejpam-6075	42	17	a	a	DET
ejpam-6075	42	18	dominating	dominating	NOUN
ejpam-6075	42	19	set	set	VERB
ejpam-6075	42	20	in	in	ADP
ejpam-6075	42	21	g.	g.	PROPN
ejpam-6075	42	22	any	any	DET
ejpam-6075	42	23	dominating	dominating	NOUN
ejpam-6075	42	24	set	set	VERB
ejpam-6075	42	25	in	in	ADP
ejpam-6075	42	26	g	g	PROPN
ejpam-6075	42	27	with	with	ADP
ejpam-6075	42	28	cardinality	cardinality	PROPN
ejpam-6075	42	29	γ(g	γ(g	PROPN
ejpam-6075	42	30	)	)	PUNCT
ejpam-6075	42	31	,	,	PUNCT
ejpam-6075	42	32	is	be	AUX
ejpam-6075	42	33	called	call	VERB
ejpam-6075	42	34	a	a	DET
ejpam-6075	42	35	γ	γ	NOUN
ejpam-6075	42	36	-	-	PUNCT
ejpam-6075	42	37	set	set	NOUN
ejpam-6075	42	38	in	in	ADP
ejpam-6075	42	39	g.	g.	PROPN
ejpam-6075	42	40	if	if	SCONJ
ejpam-6075	42	41	γ(g	γ(g	PROPN
ejpam-6075	42	42	)	)	PUNCT
ejpam-6075	43	1	=	=	SYM
ejpam-6075	43	2	1	1	NUM
ejpam-6075	43	3	and	and	CCONJ
ejpam-6075	43	4	{	{	PUNCT
ejpam-6075	43	5	v	v	NOUN
ejpam-6075	43	6	}	}	PUNCT
ejpam-6075	43	7	is	be	AUX
ejpam-6075	43	8	a	a	DET
ejpam-6075	43	9	dominating	dominating	NOUN
ejpam-6075	43	10	set	set	NOUN
ejpam-6075	43	11	in	in	ADP
ejpam-6075	43	12	g	g	PROPN
ejpam-6075	43	13	,	,	PUNCT
ejpam-6075	43	14	then	then	ADV
ejpam-6075	43	15	we	we	PRON
ejpam-6075	43	16	call	call	VERB
ejpam-6075	43	17	v	v	ADP
ejpam-6075	43	18	a	a	DET
ejpam-6075	43	19	dominating	dominating	NOUN
ejpam-6075	43	20	vertex	vertex	NOUN
ejpam-6075	43	21	in	in	ADP
ejpam-6075	43	22	g.	g.	PROPN
ejpam-6075	43	23	a	a	DET
ejpam-6075	43	24	dominating	dominating	NOUN
ejpam-6075	43	25	set	set	NOUN
ejpam-6075	43	26	d	d	PROPN
ejpam-6075	43	27	⊆	⊆	NUM
ejpam-6075	43	28	v	v	ADP
ejpam-6075	43	29	(	(	PUNCT
ejpam-6075	43	30	g	g	NOUN
ejpam-6075	43	31	)	)	PUNCT
ejpam-6075	43	32	is	be	AUX
ejpam-6075	43	33	secure	secure	ADJ
ejpam-6075	43	34	dominating	dominating	NOUN
ejpam-6075	43	35	in	in	ADP
ejpam-6075	43	36	g	g	PROPN
ejpam-6075	43	37	if	if	SCONJ
ejpam-6075	43	38	for	for	ADP
ejpam-6075	43	39	every	every	DET
ejpam-6075	43	40	v	v	NUM
ejpam-6075	43	41	∈	∈	NOUN
ejpam-6075	43	42	v	v	NOUN
ejpam-6075	43	43	(	(	PUNCT
ejpam-6075	43	44	g	g	NOUN
ejpam-6075	43	45	)	)	PUNCT
ejpam-6075	43	46	\d	\d	NOUN
ejpam-6075	43	47	,	,	PUNCT
ejpam-6075	43	48	there	there	PRON
ejpam-6075	43	49	exists	exist	VERB
ejpam-6075	43	50	w	w	PROPN
ejpam-6075	43	51	∈	∈	PROPN
ejpam-6075	43	52	d	d	NOUN
ejpam-6075	43	53	∩	∩	NOUN
ejpam-6075	43	54	ng(v	ng(v	NOUN
ejpam-6075	43	55	)	)	PUNCT
ejpam-6075	43	56	such	such	ADJ
ejpam-6075	43	57	that	that	SCONJ
ejpam-6075	43	58	(	(	PUNCT
ejpam-6075	43	59	d	d	NOUN
ejpam-6075	43	60	\	\	X
ejpam-6075	43	61	{	{	PUNCT
ejpam-6075	43	62	w	w	NOUN
ejpam-6075	43	63	}	}	PUNCT
ejpam-6075	43	64	)	)	PUNCT
ejpam-6075	43	65	∪	∪	ADP
ejpam-6075	43	66	{	{	PUNCT
ejpam-6075	43	67	v	v	NOUN
ejpam-6075	43	68	}	}	PUNCT
ejpam-6075	43	69	is	be	AUX
ejpam-6075	43	70	a	a	DET
ejpam-6075	43	71	dominating	dominating	NOUN
ejpam-6075	43	72	set	set	VERB
ejpam-6075	43	73	in	in	ADP
ejpam-6075	43	74	g.	g.	PROPN
ejpam-6075	43	75	a	a	DET
ejpam-6075	43	76	vertex	vertex	NOUN
ejpam-6075	43	77	v	v	NOUN
ejpam-6075	43	78	in	in	ADP
ejpam-6075	43	79	g	g	PROPN
ejpam-6075	43	80	is	be	AUX
ejpam-6075	43	81	a	a	DET
ejpam-6075	43	82	hop	hop	NOUN
ejpam-6075	43	83	neighbor	neighbor	NOUN
ejpam-6075	43	84	of	of	ADP
ejpam-6075	43	85	vertex	vertex	NOUN
ejpam-6075	43	86	u	u	NOUN
ejpam-6075	43	87	in	in	ADP
ejpam-6075	43	88	g	g	PROPN
ejpam-6075	43	89	if	if	SCONJ
ejpam-6075	43	90	dg(u	dg(u	NOUN
ejpam-6075	43	91	,	,	PUNCT
ejpam-6075	43	92	v	v	NOUN
ejpam-6075	43	93	)	)	PUNCT
ejpam-6075	44	1	=	=	SYM
ejpam-6075	44	2	2	2	X
ejpam-6075	44	3	.	.	X
ejpam-6075	45	1	the	the	DET
ejpam-6075	45	2	set	set	ADJ
ejpam-6075	45	3	n2	n2	ADJ
ejpam-6075	45	4	g(u	g(u	PROPN
ejpam-6075	45	5	)	)	PUNCT
ejpam-6075	45	6	=	=	PRON
ejpam-6075	45	7	{	{	PUNCT
ejpam-6075	45	8	v	v	NUM
ejpam-6075	45	9	∈	∈	NOUN
ejpam-6075	45	10	v	v	NOUN
ejpam-6075	45	11	(	(	PUNCT
ejpam-6075	45	12	g	g	NOUN
ejpam-6075	45	13	)	)	PUNCT
ejpam-6075	45	14	:	:	PUNCT
ejpam-6075	45	15	dg(v	dg(v	X
ejpam-6075	45	16	,	,	PUNCT
ejpam-6075	45	17	u	u	NOUN
ejpam-6075	45	18	)	)	PUNCT
ejpam-6075	45	19	=	=	SYM
ejpam-6075	45	20	2	2	X
ejpam-6075	45	21	}	}	PUNCT
ejpam-6075	45	22	is	be	AUX
ejpam-6075	45	23	called	call	VERB
ejpam-6075	45	24	the	the	DET
ejpam-6075	45	25	open	open	ADJ
ejpam-6075	45	26	hop	hop	NOUN
ejpam-6075	45	27	neighborhood	neighborhood	NOUN
ejpam-6075	45	28	of	of	ADP
ejpam-6075	45	29	u.	u.	PROPN
ejpam-6075	45	30	the	the	DET
ejpam-6075	45	31	closed	closed	ADJ
ejpam-6075	45	32	hop	hop	NOUN
ejpam-6075	45	33	neighborhood	neighborhood	NOUN
ejpam-6075	45	34	of	of	ADP
ejpam-6075	45	35	u	u	NOUN
ejpam-6075	45	36	is	be	AUX
ejpam-6075	45	37	given	give	VERB
ejpam-6075	45	38	by	by	ADP
ejpam-6075	45	39	n2	n2	PROPN
ejpam-6075	45	40	g[u	g[u	PROPN
ejpam-6075	45	41	]	]	X
ejpam-6075	45	42	=	=	SYM
ejpam-6075	45	43	n2	n2	ADJ
ejpam-6075	45	44	g(u	g(u	PROPN
ejpam-6075	45	45	)	)	PUNCT
ejpam-6075	45	46	∪	∪	NOUN
ejpam-6075	45	47	{	{	PUNCT
ejpam-6075	45	48	u	u	NOUN
ejpam-6075	45	49	}	}	PUNCT
ejpam-6075	45	50	.	.	PUNCT
ejpam-6075	46	1	the	the	DET
ejpam-6075	46	2	open	open	ADJ
ejpam-6075	46	3	hop	hop	NOUN
ejpam-6075	46	4	neighborhood	neighborhood	NOUN
ejpam-6075	46	5	of	of	ADP
ejpam-6075	46	6	x	x	PROPN
ejpam-6075	46	7	⊆	⊆	NUM
ejpam-6075	46	8	v	v	ADP
ejpam-6075	46	9	(	(	PUNCT
ejpam-6075	46	10	g	g	NOUN
ejpam-6075	46	11	)	)	PUNCT
ejpam-6075	46	12	is	be	AUX
ejpam-6075	46	13	the	the	DET
ejpam-6075	46	14	set	set	ADJ
ejpam-6075	46	15	n2	n2	ADJ
ejpam-6075	46	16	g(x	g(x	NOUN
ejpam-6075	46	17	)	)	PUNCT
ejpam-6075	47	1	=	=	SYM
ejpam-6075	47	2	⋃	⋃	NOUN
ejpam-6075	47	3	u∈x	u∈x	ADJ
ejpam-6075	47	4	n2	n2	NOUN
ejpam-6075	47	5	g(u	g(u	PROPN
ejpam-6075	47	6	)	)	PUNCT
ejpam-6075	47	7	.	.	PUNCT
ejpam-6075	48	1	the	the	DET
ejpam-6075	48	2	closed	closed	ADJ
ejpam-6075	48	3	hop	hop	NOUN
ejpam-6075	48	4	neighborhood	neighborhood	NOUN
ejpam-6075	48	5	of	of	ADP
ejpam-6075	48	6	x	x	SYM
ejpam-6075	48	7	is	be	AUX
ejpam-6075	48	8	the	the	DET
ejpam-6075	48	9	set	set	ADJ
ejpam-6075	48	10	n2	n2	NOUN
ejpam-6075	48	11	g[x	g[x	PROPN
ejpam-6075	48	12	]	]	X
ejpam-6075	48	13	=	=	SYM
ejpam-6075	48	14	n2	n2	PROPN
ejpam-6075	48	15	g(x	g(x	NOUN
ejpam-6075	48	16	)	)	PUNCT
ejpam-6075	48	17	∪x	∪x	VERB
ejpam-6075	48	18	.	.	PUNCT
ejpam-6075	49	1	if	if	SCONJ
ejpam-6075	49	2	s	s	VERB
ejpam-6075	49	3	⊆	⊆	NUM
ejpam-6075	49	4	v	v	NOUN
ejpam-6075	49	5	(	(	PUNCT
ejpam-6075	49	6	g	g	NOUN
ejpam-6075	49	7	)	)	PUNCT
ejpam-6075	49	8	and	and	CCONJ
ejpam-6075	49	9	v	v	ADP
ejpam-6075	49	10	∈	∈	NOUN
ejpam-6075	49	11	s	s	NOUN
ejpam-6075	49	12	,	,	PUNCT
ejpam-6075	49	13	then	then	ADV
ejpam-6075	49	14	a	a	DET
ejpam-6075	49	15	vertex	vertex	NOUN
ejpam-6075	49	16	w	w	NOUN
ejpam-6075	49	17	∈	∈	PROPN
ejpam-6075	49	18	v	v	ADP
ejpam-6075	49	19	(	(	PUNCT
ejpam-6075	49	20	g	g	NOUN
ejpam-6075	49	21	)	)	PUNCT
ejpam-6075	49	22	\	\	PROPN
ejpam-6075	50	1	s	s	PART
ejpam-6075	50	2	is	be	AUX
ejpam-6075	50	3	an	an	DET
ejpam-6075	50	4	external	external	ADJ
ejpam-6075	50	5	private	private	ADJ
ejpam-6075	50	6	hop	hop	NOUN
ejpam-6075	50	7	neighbor	neighbor	NOUN
ejpam-6075	50	8	of	of	ADP
ejpam-6075	50	9	v	v	NOUN
ejpam-6075	50	10	if	if	SCONJ
ejpam-6075	50	11	n2	n2	ADJ
ejpam-6075	50	12	g(w	g(w	PROPN
ejpam-6075	50	13	)	)	PUNCT
ejpam-6075	50	14	∩	∩	NOUN
ejpam-6075	50	15	s	s	PART
ejpam-6075	50	16	=	=	PUNCT
ejpam-6075	50	17	{	{	PUNCT
ejpam-6075	50	18	v	v	NOUN
ejpam-6075	50	19	}	}	PUNCT
ejpam-6075	50	20	.	.	PUNCT
ejpam-6075	51	1	the	the	DET
ejpam-6075	51	2	set	set	NOUN
ejpam-6075	51	3	containing	contain	VERB
ejpam-6075	51	4	all	all	DET
ejpam-6075	51	5	the	the	DET
ejpam-6075	51	6	external	external	ADJ
ejpam-6075	51	7	private	private	ADJ
ejpam-6075	51	8	hop	hop	NOUN
ejpam-6075	51	9	neighbors	neighbor	NOUN
ejpam-6075	51	10	of	of	ADP
ejpam-6075	51	11	v	v	NOUN
ejpam-6075	51	12	with	with	ADP
ejpam-6075	51	13	respect	respect	NOUN
ejpam-6075	51	14	to	to	ADP
ejpam-6075	51	15	s	s	PRON
ejpam-6075	51	16	is	be	AUX
ejpam-6075	51	17	denoted	denote	VERB
ejpam-6075	51	18	by	by	ADP
ejpam-6075	51	19	ephn(v;s	ephn(v;s	NOUN
ejpam-6075	51	20	)	)	PUNCT
ejpam-6075	51	21	.	.	PUNCT
ejpam-6075	52	1	a	a	DET
ejpam-6075	52	2	set	set	NOUN
ejpam-6075	52	3	s	s	NOUN
ejpam-6075	52	4	⊆	⊆	NUM
ejpam-6075	52	5	v	v	NOUN
ejpam-6075	52	6	(	(	PUNCT
ejpam-6075	52	7	g	g	NOUN
ejpam-6075	52	8	)	)	PUNCT
ejpam-6075	52	9	is	be	AUX
ejpam-6075	52	10	a	a	DET
ejpam-6075	52	11	hop	hop	NOUN
ejpam-6075	52	12	dominating	dominating	NOUN
ejpam-6075	52	13	set	set	VERB
ejpam-6075	52	14	in	in	ADP
ejpam-6075	52	15	g	g	PROPN
ejpam-6075	52	16	if	if	SCONJ
ejpam-6075	52	17	n2	n2	ADJ
ejpam-6075	52	18	g[s	g[s	PROPN
ejpam-6075	52	19	]	]	X
ejpam-6075	52	20	=	=	SYM
ejpam-6075	52	21	v	v	NOUN
ejpam-6075	52	22	(	(	PUNCT
ejpam-6075	52	23	g	g	NOUN
ejpam-6075	52	24	)	)	PUNCT
ejpam-6075	52	25	,	,	PUNCT
ejpam-6075	52	26	that	that	ADV
ejpam-6075	52	27	is	is	ADV
ejpam-6075	52	28	,	,	PUNCT
ejpam-6075	52	29	for	for	ADP
ejpam-6075	52	30	every	every	DET
ejpam-6075	52	31	v	v	NUM
ejpam-6075	52	32	∈	∈	NOUN
ejpam-6075	52	33	v	v	NOUN
ejpam-6075	52	34	(	(	PUNCT
ejpam-6075	52	35	g)\s	g)\s	NOUN
ejpam-6075	52	36	,	,	PUNCT
ejpam-6075	52	37	there	there	PRON
ejpam-6075	52	38	exists	exist	VERB
ejpam-6075	52	39	u	u	PROPN
ejpam-6075	52	40	∈	∈	PROPN
ejpam-6075	52	41	s	s	VERB
ejpam-6075	52	42	such	such	ADJ
ejpam-6075	52	43	that	that	DET
ejpam-6075	52	44	dg(u	dg(u	ADJ
ejpam-6075	52	45	,	,	PUNCT
ejpam-6075	52	46	v	v	NOUN
ejpam-6075	52	47	)	)	PUNCT
ejpam-6075	53	1	=	=	SYM
ejpam-6075	53	2	2	2	X
ejpam-6075	53	3	.	.	PUNCT
ejpam-6075	54	1	the	the	DET
ejpam-6075	54	2	minimum	minimum	ADJ
ejpam-6075	54	3	cardinality	cardinality	NOUN
ejpam-6075	54	4	among	among	ADP
ejpam-6075	54	5	all	all	DET
ejpam-6075	54	6	hop	hop	NOUN
ejpam-6075	54	7	dominating	dominating	NOUN
ejpam-6075	54	8	sets	set	NOUN
ejpam-6075	54	9	in	in	ADP
ejpam-6075	54	10	g	g	NOUN
ejpam-6075	54	11	,	,	PUNCT
ejpam-6075	54	12	denoted	denote	VERB
ejpam-6075	54	13	by	by	ADP
ejpam-6075	54	14	γh(g	γh(g	NOUN
ejpam-6075	54	15	)	)	PUNCT
ejpam-6075	54	16	,	,	PUNCT
ejpam-6075	54	17	is	be	AUX
ejpam-6075	54	18	called	call	VERB
ejpam-6075	54	19	the	the	DET
ejpam-6075	54	20	hop	hop	NOUN
ejpam-6075	54	21	domination	domination	NOUN
ejpam-6075	54	22	number	number	NOUN
ejpam-6075	54	23	of	of	ADP
ejpam-6075	54	24	g.	g.	PROPN
ejpam-6075	54	25	any	any	DET
ejpam-6075	54	26	hop	hop	NOUN
ejpam-6075	54	27	dominating	dominating	NOUN
ejpam-6075	54	28	set	set	VERB
ejpam-6075	54	29	with	with	ADP
ejpam-6075	54	30	cardinality	cardinality	NOUN
ejpam-6075	54	31	equal	equal	ADJ
ejpam-6075	54	32	to	to	ADP
ejpam-6075	54	33	γh(g	γh(g	NOUN
ejpam-6075	54	34	)	)	PUNCT
ejpam-6075	54	35	is	be	AUX
ejpam-6075	54	36	called	call	VERB
ejpam-6075	54	37	a	a	DET
ejpam-6075	54	38	γh	γh	ADV
ejpam-6075	54	39	-	-	PUNCT
ejpam-6075	54	40	set	set	NOUN
ejpam-6075	54	41	.	.	PUNCT
ejpam-6075	55	1	a	a	DET
ejpam-6075	55	2	hop	hop	NOUN
ejpam-6075	55	3	dominating	dominating	NOUN
ejpam-6075	55	4	set	set	NOUN
ejpam-6075	55	5	s	s	VERB
ejpam-6075	55	6	is	be	AUX
ejpam-6075	55	7	secure	secure	ADJ
ejpam-6075	55	8	hop	hop	NOUN
ejpam-6075	55	9	dominating	dominate	VERB
ejpam-6075	55	10	if	if	SCONJ
ejpam-6075	55	11	for	for	ADP
ejpam-6075	55	12	each	each	DET
ejpam-6075	55	13	v	v	NUM
ejpam-6075	55	14	∈	∈	NOUN
ejpam-6075	55	15	v	v	NOUN
ejpam-6075	55	16	(	(	PUNCT
ejpam-6075	55	17	g)\s	g)\s	NOUN
ejpam-6075	55	18	,	,	PUNCT
ejpam-6075	55	19	there	there	PRON
ejpam-6075	55	20	exists	exist	VERB
ejpam-6075	55	21	w	w	PROPN
ejpam-6075	55	22	∈	∈	PROPN
ejpam-6075	55	23	s	s	PART
ejpam-6075	55	24	∩	∩	ADJ
ejpam-6075	55	25	n2	n2	ADJ
ejpam-6075	55	26	g(v	g(v	PROPN
ejpam-6075	55	27	)	)	PUNCT
ejpam-6075	55	28	such	such	ADJ
ejpam-6075	55	29	that	that	SCONJ
ejpam-6075	55	30	(	(	PUNCT
ejpam-6075	55	31	s	s	NOUN
ejpam-6075	55	32	\	\	X
ejpam-6075	55	33	{	{	PUNCT
ejpam-6075	55	34	w	w	NOUN
ejpam-6075	55	35	}	}	PUNCT
ejpam-6075	55	36	)	)	PUNCT
ejpam-6075	55	37	∪	∪	ADP
ejpam-6075	55	38	{	{	PUNCT
ejpam-6075	55	39	v	v	NOUN
ejpam-6075	55	40	}	}	PUNCT
ejpam-6075	55	41	is	be	AUX
ejpam-6075	55	42	a	a	DET
ejpam-6075	55	43	hop	hop	NOUN
ejpam-6075	55	44	dominating	dominating	NOUN
ejpam-6075	55	45	set	set	VERB
ejpam-6075	55	46	in	in	ADP
ejpam-6075	55	47	g.	g.	PROPN
ejpam-6075	55	48	the	the	DET
ejpam-6075	55	49	minimum	minimum	ADJ
ejpam-6075	55	50	cardinality	cardinality	NOUN
ejpam-6075	55	51	among	among	ADP
ejpam-6075	55	52	all	all	DET
ejpam-6075	55	53	secure	secure	ADJ
ejpam-6075	55	54	hop	hop	NOUN
ejpam-6075	55	55	dominating	dominating	NOUN
ejpam-6075	55	56	sets	set	NOUN
ejpam-6075	55	57	of	of	ADP
ejpam-6075	55	58	g	g	NOUN
ejpam-6075	55	59	,	,	PUNCT
ejpam-6075	55	60	denoted	denote	VERB
ejpam-6075	55	61	by	by	ADP
ejpam-6075	55	62	γsh(g	γsh(g	NOUN
ejpam-6075	55	63	)	)	PUNCT
ejpam-6075	55	64	,	,	PUNCT
ejpam-6075	55	65	is	be	AUX
ejpam-6075	55	66	called	call	VERB
ejpam-6075	55	67	the	the	DET
ejpam-6075	55	68	secure	secure	ADJ
ejpam-6075	55	69	hop	hop	NOUN
ejpam-6075	55	70	domination	domination	NOUN
ejpam-6075	55	71	number	number	NOUN
ejpam-6075	55	72	of	of	ADP
ejpam-6075	55	73	g.	g.	PROPN
ejpam-6075	55	74	any	any	DET
ejpam-6075	55	75	secure	secure	ADJ
ejpam-6075	55	76	hop	hop	NOUN
ejpam-6075	55	77	dominating	dominating	NOUN
ejpam-6075	55	78	set	set	VERB
ejpam-6075	55	79	with	with	ADP
ejpam-6075	55	80	cardinality	cardinality	PROPN
ejpam-6075	55	81	f.	f.	PROPN
ejpam-6075	55	82	l.	l.	PROPN
ejpam-6075	55	83	alfeche	alfeche	PROPN
ejpam-6075	55	84	,	,	PUNCT
ejpam-6075	55	85	g.	g.	PROPN
ejpam-6075	55	86	a.	a.	PROPN
ejpam-6075	55	87	malacas	malacas	PROPN
ejpam-6075	55	88	,	,	PUNCT
ejpam-6075	56	1	s.	s.	PROPN
ejpam-6075	56	2	canoy	canoy	PROPN
ejpam-6075	56	3	jr	jr	PROPN
ejpam-6075	56	4	.	.	PROPN
ejpam-6075	56	5	/	/	SYM
ejpam-6075	56	6	eur	eur	PROPN
ejpam-6075	56	7	.	.	PUNCT
ejpam-6075	57	1	j.	j.	PROPN
ejpam-6075	57	2	pure	pure	PROPN
ejpam-6075	57	3	appl	appl	PROPN
ejpam-6075	57	4	.	.	PROPN
ejpam-6075	57	5	math	math	PROPN
ejpam-6075	57	6	,	,	PUNCT
ejpam-6075	57	7	18	18	NUM
ejpam-6075	57	8	(	(	PUNCT
ejpam-6075	57	9	2	2	NUM
ejpam-6075	57	10	)	)	PUNCT
ejpam-6075	57	11	(	(	PUNCT
ejpam-6075	57	12	2025	2025	NUM
ejpam-6075	57	13	)	)	PUNCT
ejpam-6075	57	14	,	,	PUNCT
ejpam-6075	57	15	6075	6075	NUM
ejpam-6075	57	16	3	3	NUM
ejpam-6075	57	17	of	of	ADP
ejpam-6075	57	18	14	14	NUM
ejpam-6075	57	19	equal	equal	ADJ
ejpam-6075	57	20	to	to	ADP
ejpam-6075	57	21	γsh(g	γsh(g	NOUN
ejpam-6075	57	22	)	)	PUNCT
ejpam-6075	57	23	is	be	AUX
ejpam-6075	57	24	called	call	VERB
ejpam-6075	57	25	a	a	DET
ejpam-6075	57	26	γsh	γsh	NOUN
ejpam-6075	57	27	-	-	PUNCT
ejpam-6075	57	28	set	set	NOUN
ejpam-6075	57	29	.	.	PUNCT
ejpam-6075	58	1	the	the	DET
ejpam-6075	58	2	complement	complement	NOUN
ejpam-6075	58	3	of	of	ADP
ejpam-6075	58	4	graph	graph	NOUN
ejpam-6075	58	5	g	g	NOUN
ejpam-6075	58	6	,	,	PUNCT
ejpam-6075	58	7	denoted	denote	VERB
ejpam-6075	58	8	by	by	ADP
ejpam-6075	58	9	g	g	NOUN
ejpam-6075	58	10	,	,	PUNCT
ejpam-6075	58	11	is	be	AUX
ejpam-6075	58	12	the	the	DET
ejpam-6075	58	13	graph	graph	NOUN
ejpam-6075	58	14	with	with	ADP
ejpam-6075	58	15	v	v	NOUN
ejpam-6075	58	16	(	(	PUNCT
ejpam-6075	58	17	g	g	NOUN
ejpam-6075	58	18	)	)	PUNCT
ejpam-6075	58	19	=	=	NOUN
ejpam-6075	58	20	v	v	X
ejpam-6075	58	21	(	(	PUNCT
ejpam-6075	58	22	g	g	NOUN
ejpam-6075	58	23	)	)	PUNCT
ejpam-6075	58	24	such	such	ADJ
ejpam-6075	58	25	that	that	SCONJ
ejpam-6075	58	26	vw	vw	PROPN
ejpam-6075	58	27	∈	∈	PROPN
ejpam-6075	58	28	e(g	e(g	PROPN
ejpam-6075	58	29	)	)	PUNCT
ejpam-6075	59	1	if	if	SCONJ
ejpam-6075	59	2	and	and	CCONJ
ejpam-6075	59	3	only	only	ADV
ejpam-6075	59	4	if	if	SCONJ
ejpam-6075	59	5	vw	vw	PROPN
ejpam-6075	59	6	/∈	/∈	PUNCT
ejpam-6075	59	7	e(g	e(g	PROPN
ejpam-6075	59	8	)	)	PUNCT
ejpam-6075	59	9	.	.	PUNCT
ejpam-6075	60	1	the	the	DET
ejpam-6075	60	2	shadow	shadow	NOUN
ejpam-6075	60	3	graph	graph	VERB
ejpam-6075	60	4	d2(g	d2(g	PROPN
ejpam-6075	60	5	)	)	PUNCT
ejpam-6075	60	6	of	of	ADP
ejpam-6075	60	7	graph	graph	NOUN
ejpam-6075	60	8	g	g	PROPN
ejpam-6075	60	9	is	be	AUX
ejpam-6075	60	10	constructed	construct	VERB
ejpam-6075	60	11	by	by	ADP
ejpam-6075	60	12	taking	take	VERB
ejpam-6075	60	13	two	two	NUM
ejpam-6075	60	14	copies	copy	NOUN
ejpam-6075	60	15	of	of	ADP
ejpam-6075	60	16	g	g	NOUN
ejpam-6075	60	17	,	,	PUNCT
ejpam-6075	60	18	say	say	VERB
ejpam-6075	60	19	g1	g1	PROPN
ejpam-6075	60	20	and	and	CCONJ
ejpam-6075	60	21	g2	g2	PROPN
ejpam-6075	60	22	,	,	PUNCT
ejpam-6075	60	23	and	and	CCONJ
ejpam-6075	60	24	then	then	ADV
ejpam-6075	60	25	joining	join	VERB
ejpam-6075	60	26	each	each	DET
ejpam-6075	60	27	vertex	vertex	NOUN
ejpam-6075	60	28	u	u	NOUN
ejpam-6075	60	29	∈	∈	PROPN
ejpam-6075	60	30	v	v	NOUN
ejpam-6075	60	31	(	(	PUNCT
ejpam-6075	60	32	g1	g1	PROPN
ejpam-6075	60	33	)	)	PUNCT
ejpam-6075	60	34	to	to	ADP
ejpam-6075	60	35	the	the	DET
ejpam-6075	60	36	neighbors	neighbor	NOUN
ejpam-6075	60	37	of	of	ADP
ejpam-6075	60	38	its	its	PRON
ejpam-6075	60	39	corresponding	correspond	VERB
ejpam-6075	60	40	vertex	vertex	NOUN
ejpam-6075	60	41	u′	u′	PROPN
ejpam-6075	60	42	∈	∈	PROPN
ejpam-6075	60	43	v	v	NOUN
ejpam-6075	60	44	(	(	PUNCT
ejpam-6075	60	45	g2	g2	PROPN
ejpam-6075	60	46	)	)	PUNCT
ejpam-6075	60	47	.	.	PUNCT
ejpam-6075	61	1	for	for	ADP
ejpam-6075	61	2	a	a	DET
ejpam-6075	61	3	graph	graph	NOUN
ejpam-6075	61	4	g	g	NOUN
ejpam-6075	61	5	,	,	PUNCT
ejpam-6075	61	6	the	the	DET
ejpam-6075	61	7	complementary	complementary	ADJ
ejpam-6075	61	8	prism	prism	NOUN
ejpam-6075	61	9	gg	gg	NOUN
ejpam-6075	61	10	is	be	AUX
ejpam-6075	61	11	the	the	DET
ejpam-6075	61	12	graph	graph	NOUN
ejpam-6075	61	13	formed	form	VERB
ejpam-6075	61	14	from	from	ADP
ejpam-6075	61	15	the	the	DET
ejpam-6075	61	16	disjoint	disjoint	PROPN
ejpam-6075	61	17	union	union	NOUN
ejpam-6075	61	18	of	of	ADP
ejpam-6075	61	19	g	g	PROPN
ejpam-6075	61	20	and	and	CCONJ
ejpam-6075	61	21	its	its	PRON
ejpam-6075	61	22	complement	complement	NOUN
ejpam-6075	61	23	g	g	NOUN
ejpam-6075	61	24	by	by	ADP
ejpam-6075	61	25	adding	add	VERB
ejpam-6075	61	26	a	a	DET
ejpam-6075	61	27	perfect	perfect	ADJ
ejpam-6075	61	28	matching	matching	NOUN
ejpam-6075	61	29	between	between	ADP
ejpam-6075	61	30	corresponding	corresponding	ADJ
ejpam-6075	61	31	vertices	vertex	NOUN
ejpam-6075	61	32	of	of	ADP
ejpam-6075	61	33	g	g	PROPN
ejpam-6075	61	34	and	and	CCONJ
ejpam-6075	61	35	g.	g.	PROPN
ejpam-6075	61	36	in	in	ADP
ejpam-6075	61	37	simple	simple	ADJ
ejpam-6075	61	38	terms	term	NOUN
ejpam-6075	61	39	,	,	PUNCT
ejpam-6075	61	40	the	the	DET
ejpam-6075	61	41	graph	graph	NOUN
ejpam-6075	61	42	gg	gg	NOUN
ejpam-6075	61	43	is	be	AUX
ejpam-6075	61	44	formed	form	VERB
ejpam-6075	61	45	from	from	ADP
ejpam-6075	61	46	g	g	PROPN
ejpam-6075	61	47	∪	∪	ADP
ejpam-6075	61	48	g	g	NOUN
ejpam-6075	61	49	by	by	ADP
ejpam-6075	61	50	adding	add	VERB
ejpam-6075	61	51	the	the	DET
ejpam-6075	61	52	edge	edge	NOUN
ejpam-6075	61	53	vv	vv	NOUN
ejpam-6075	61	54	for	for	ADP
ejpam-6075	61	55	every	every	DET
ejpam-6075	61	56	vertex	vertex	NOUN
ejpam-6075	61	57	v	v	ADP
ejpam-6075	61	58	∈	∈	NOUN
ejpam-6075	61	59	v	v	NOUN
ejpam-6075	61	60	(	(	PUNCT
ejpam-6075	61	61	g	g	NOUN
ejpam-6075	61	62	)	)	PUNCT
ejpam-6075	61	63	,	,	PUNCT
ejpam-6075	61	64	where	where	SCONJ
ejpam-6075	61	65	v	v	NOUN
ejpam-6075	61	66	is	be	AUX
ejpam-6075	61	67	the	the	DET
ejpam-6075	61	68	vertex	vertex	NOUN
ejpam-6075	61	69	of	of	ADP
ejpam-6075	61	70	g	g	PROPN
ejpam-6075	61	71	corresponding	correspond	VERB
ejpam-6075	61	72	to	to	ADP
ejpam-6075	61	73	vertex	vertex	VERB
ejpam-6075	61	74	v	v	NOUN
ejpam-6075	61	75	of	of	ADP
ejpam-6075	61	76	g.	g.	PROPN
ejpam-6075	61	77	for	for	ADP
ejpam-6075	61	78	other	other	ADJ
ejpam-6075	61	79	graph	graph	NOUN
ejpam-6075	61	80	theoretic	theoretic	ADJ
ejpam-6075	61	81	terms	term	NOUN
ejpam-6075	61	82	not	not	PART
ejpam-6075	61	83	mentioned	mention	VERB
ejpam-6075	61	84	here	here	ADV
ejpam-6075	61	85	,	,	PUNCT
ejpam-6075	61	86	readers	reader	NOUN
ejpam-6075	61	87	may	may	AUX
ejpam-6075	61	88	refer	refer	VERB
ejpam-6075	61	89	to	to	ADP
ejpam-6075	61	90	[	[	X
ejpam-6075	61	91	24	24	NUM
ejpam-6075	61	92	]	]	PUNCT
ejpam-6075	61	93	and	and	CCONJ
ejpam-6075	61	94	[	[	X
ejpam-6075	61	95	25	25	NUM
ejpam-6075	61	96	]	]	PUNCT
ejpam-6075	61	97	.	.	PUNCT
ejpam-6075	62	1	3	3	X
ejpam-6075	62	2	.	.	X
ejpam-6075	62	3	results	result	NOUN
ejpam-6075	62	4	given	give	VERB
ejpam-6075	62	5	a	a	DET
ejpam-6075	62	6	graph	graph	NOUN
ejpam-6075	62	7	g	g	NOUN
ejpam-6075	62	8	,	,	PUNCT
ejpam-6075	62	9	the	the	DET
ejpam-6075	62	10	vertex	vertex	NOUN
ejpam-6075	62	11	set	set	VERB
ejpam-6075	62	12	v	v	NOUN
ejpam-6075	62	13	(	(	PUNCT
ejpam-6075	62	14	g	g	NOUN
ejpam-6075	62	15	)	)	PUNCT
ejpam-6075	62	16	is	be	AUX
ejpam-6075	62	17	a	a	DET
ejpam-6075	62	18	secure	secure	ADJ
ejpam-6075	62	19	hop	hop	NOUN
ejpam-6075	62	20	dominating	dominating	NOUN
ejpam-6075	62	21	set	set	NOUN
ejpam-6075	62	22	of	of	ADP
ejpam-6075	62	23	g.	g.	PROPN
ejpam-6075	62	24	thus	thus	ADV
ejpam-6075	62	25	,	,	PUNCT
ejpam-6075	62	26	every	every	DET
ejpam-6075	62	27	graph	graph	NOUN
ejpam-6075	62	28	admits	admit	VERB
ejpam-6075	62	29	a	a	DET
ejpam-6075	62	30	secure	secure	ADJ
ejpam-6075	62	31	hop	hop	NOUN
ejpam-6075	62	32	dominating	dominating	NOUN
ejpam-6075	62	33	set	set	NOUN
ejpam-6075	62	34	.	.	PUNCT
ejpam-6075	63	1	remark	remark	PROPN
ejpam-6075	63	2	1	1	NUM
ejpam-6075	63	3	.	.	PUNCT
ejpam-6075	64	1	let	let	VERB
ejpam-6075	64	2	g1	g1	PROPN
ejpam-6075	64	3	,	,	PUNCT
ejpam-6075	64	4	g2	g2	PROPN
ejpam-6075	64	5	,	,	PUNCT
ejpam-6075	64	6	.	.	PUNCT
ejpam-6075	64	7	.	.	PUNCT
ejpam-6075	65	1	.	.	PUNCT
ejpam-6075	66	1	,	,	PUNCT
ejpam-6075	66	2	gk	gk	PROPN
ejpam-6075	66	3	be	be	AUX
ejpam-6075	66	4	the	the	DET
ejpam-6075	66	5	components	component	NOUN
ejpam-6075	66	6	of	of	ADP
ejpam-6075	66	7	a	a	DET
ejpam-6075	66	8	graph	graph	NOUN
ejpam-6075	67	1	g.	g.	NOUN
ejpam-6075	68	1	then	then	ADV
ejpam-6075	68	2	s	s	VERB
ejpam-6075	68	3	is	be	AUX
ejpam-6075	68	4	a	a	DET
ejpam-6075	68	5	hop	hop	NOUN
ejpam-6075	68	6	dominating	dominating	NOUN
ejpam-6075	68	7	set	set	VERB
ejpam-6075	68	8	in	in	ADP
ejpam-6075	68	9	g	g	PROPN
ejpam-6075	68	10	if	if	SCONJ
ejpam-6075	69	1	and	and	CCONJ
ejpam-6075	69	2	only	only	ADV
ejpam-6075	69	3	if	if	SCONJ
ejpam-6075	69	4	sj	sj	ADP
ejpam-6075	69	5	=	=	NOUN
ejpam-6075	69	6	s	s	PART
ejpam-6075	69	7	∩	∩	ADJ
ejpam-6075	69	8	v	v	NOUN
ejpam-6075	69	9	(	(	PUNCT
ejpam-6075	69	10	gj	gj	NOUN
ejpam-6075	69	11	)	)	PUNCT
ejpam-6075	69	12	is	be	AUX
ejpam-6075	69	13	a	a	DET
ejpam-6075	69	14	hop	hop	NOUN
ejpam-6075	69	15	dominating	dominating	NOUN
ejpam-6075	69	16	set	set	VERB
ejpam-6075	69	17	in	in	ADP
ejpam-6075	69	18	gj	gj	NOUN
ejpam-6075	69	19	for	for	ADP
ejpam-6075	69	20	each	each	DET
ejpam-6075	69	21	j	j	PROPN
ejpam-6075	69	22	∈	∈	PROPN
ejpam-6075	70	1	[	[	X
ejpam-6075	70	2	k	k	X
ejpam-6075	70	3	]	]	X
ejpam-6075	70	4	=	=	X
ejpam-6075	70	5	{	{	PUNCT
ejpam-6075	70	6	1	1	NUM
ejpam-6075	70	7	,	,	PUNCT
ejpam-6075	70	8	2	2	NUM
ejpam-6075	70	9	,	,	PUNCT
ejpam-6075	70	10	·	·	PUNCT
ejpam-6075	70	11	·	·	PUNCT
ejpam-6075	70	12	·	·	PUNCT
ejpam-6075	70	13	,	,	PUNCT
ejpam-6075	70	14	k	k	NOUN
ejpam-6075	70	15	}	}	PUNCT
ejpam-6075	70	16	.	.	PUNCT
ejpam-6075	71	1	moreover	moreover	ADV
ejpam-6075	71	2	,	,	PUNCT
ejpam-6075	71	3	γh(g	γh(g	NOUN
ejpam-6075	71	4	)	)	PUNCT
ejpam-6075	72	1	=	=	SYM
ejpam-6075	72	2	∑k	∑k	PROPN
ejpam-6075	72	3	j=1	j=1	PROPN
ejpam-6075	72	4	γh(gj	γh(gj	PROPN
ejpam-6075	72	5	)	)	PUNCT
ejpam-6075	72	6	.	.	PUNCT
ejpam-6075	73	1	theorem	theorem	NOUN
ejpam-6075	73	2	1	1	NUM
ejpam-6075	73	3	.	.	PUNCT
ejpam-6075	74	1	let	let	VERB
ejpam-6075	74	2	g1	g1	PROPN
ejpam-6075	74	3	,	,	PUNCT
ejpam-6075	74	4	g2	g2	PROPN
ejpam-6075	74	5	,	,	PUNCT
ejpam-6075	74	6	.	.	PUNCT
ejpam-6075	74	7	.	.	PUNCT
ejpam-6075	75	1	.	.	PUNCT
ejpam-6075	76	1	,	,	PUNCT
ejpam-6075	76	2	gk	gk	PROPN
ejpam-6075	76	3	be	be	AUX
ejpam-6075	76	4	the	the	DET
ejpam-6075	76	5	components	component	NOUN
ejpam-6075	76	6	of	of	ADP
ejpam-6075	76	7	g.	g.	PROPN
ejpam-6075	76	8	then	then	ADV
ejpam-6075	76	9	γsh(g	γsh(g	NOUN
ejpam-6075	76	10	)	)	PUNCT
ejpam-6075	76	11	=	=	SYM
ejpam-6075	77	1	∑k	∑k	PROPN
ejpam-6075	77	2	j=1	j=1	NOUN
ejpam-6075	77	3	γsh(gj	γsh(gj	X
ejpam-6075	77	4	)	)	PUNCT
ejpam-6075	77	5	.	.	PUNCT
ejpam-6075	78	1	proof	proof	NOUN
ejpam-6075	78	2	.	.	PUNCT
ejpam-6075	79	1	suppose	suppose	VERB
ejpam-6075	79	2	s	s	PRON
ejpam-6075	79	3	is	be	AUX
ejpam-6075	79	4	a	a	DET
ejpam-6075	79	5	secure	secure	ADJ
ejpam-6075	79	6	hop	hop	NOUN
ejpam-6075	79	7	dominating	dominating	NOUN
ejpam-6075	79	8	set	set	VERB
ejpam-6075	79	9	in	in	ADP
ejpam-6075	79	10	g.	g.	PROPN
ejpam-6075	79	11	then	then	ADV
ejpam-6075	79	12	,	,	PUNCT
ejpam-6075	79	13	by	by	ADP
ejpam-6075	79	14	remark	remark	NOUN
ejpam-6075	79	15	1	1	NUM
ejpam-6075	79	16	,	,	PUNCT
ejpam-6075	79	17	s	s	PART
ejpam-6075	79	18	=	=	SYM
ejpam-6075	79	19	∪j∈[k]sj	∪j∈[k]sj	PROPN
ejpam-6075	79	20	and	and	CCONJ
ejpam-6075	79	21	sj	sj	INTJ
ejpam-6075	79	22	=	=	NOUN
ejpam-6075	79	23	s	s	PROPN
ejpam-6075	79	24	∩	∩	ADJ
ejpam-6075	79	25	v	v	NOUN
ejpam-6075	79	26	(	(	PUNCT
ejpam-6075	79	27	gj	gj	NOUN
ejpam-6075	79	28	)	)	PUNCT
ejpam-6075	79	29	is	be	AUX
ejpam-6075	79	30	a	a	DET
ejpam-6075	79	31	hop	hop	NOUN
ejpam-6075	79	32	dominating	dominating	NOUN
ejpam-6075	79	33	set	set	VERB
ejpam-6075	79	34	in	in	ADP
ejpam-6075	79	35	gj	gj	NOUN
ejpam-6075	79	36	for	for	ADP
ejpam-6075	79	37	each	each	DET
ejpam-6075	79	38	j	j	PROPN
ejpam-6075	79	39	∈	∈	PROPN
ejpam-6075	80	1	[	[	X
ejpam-6075	80	2	k	k	X
ejpam-6075	80	3	]	]	X
ejpam-6075	80	4	.	.	PUNCT
ejpam-6075	81	1	for	for	ADP
ejpam-6075	81	2	j	j	PROPN
ejpam-6075	81	3	∈	∈	PROPN
ejpam-6075	81	4	[	[	X
ejpam-6075	81	5	k	k	X
ejpam-6075	81	6	]	]	X
ejpam-6075	81	7	,	,	PUNCT
ejpam-6075	81	8	let	let	VERB
ejpam-6075	81	9	x	x	PUNCT
ejpam-6075	81	10	∈	∈	PROPN
ejpam-6075	81	11	v	v	NOUN
ejpam-6075	81	12	(	(	PUNCT
ejpam-6075	81	13	gj)\sj	gj)\sj	NOUN
ejpam-6075	81	14	.	.	PUNCT
ejpam-6075	82	1	then	then	ADV
ejpam-6075	82	2	x	x	SYM
ejpam-6075	82	3	∈	∈	PROPN
ejpam-6075	82	4	v	v	X
ejpam-6075	82	5	(	(	PUNCT
ejpam-6075	82	6	g)\s	g)\s	NOUN
ejpam-6075	82	7	.	.	PUNCT
ejpam-6075	83	1	since	since	SCONJ
ejpam-6075	83	2	s	s	PROPN
ejpam-6075	83	3	is	be	AUX
ejpam-6075	83	4	a	a	DET
ejpam-6075	83	5	secure	secure	ADJ
ejpam-6075	83	6	hop	hop	NOUN
ejpam-6075	83	7	dominating	dominating	NOUN
ejpam-6075	83	8	set	set	NOUN
ejpam-6075	83	9	in	in	ADP
ejpam-6075	83	10	g	g	NOUN
ejpam-6075	83	11	,	,	PUNCT
ejpam-6075	83	12	there	there	PRON
ejpam-6075	83	13	exists	exist	VERB
ejpam-6075	83	14	y	y	PROPN
ejpam-6075	83	15	∈	∈	PROPN
ejpam-6075	83	16	s	s	VERB
ejpam-6075	83	17	∩n2	∩n2	PROPN
ejpam-6075	83	18	g(x	g(x	NOUN
ejpam-6075	83	19	)	)	PUNCT
ejpam-6075	83	20	such	such	ADJ
ejpam-6075	83	21	that	that	SCONJ
ejpam-6075	83	22	(	(	PUNCT
ejpam-6075	83	23	s	s	NOUN
ejpam-6075	83	24	\	\	X
ejpam-6075	83	25	{	{	PUNCT
ejpam-6075	83	26	y	y	NOUN
ejpam-6075	83	27	}	}	PUNCT
ejpam-6075	83	28	)	)	PUNCT
ejpam-6075	83	29	∪	∪	ADP
ejpam-6075	83	30	{	{	PUNCT
ejpam-6075	83	31	x	x	NOUN
ejpam-6075	83	32	}	}	PUNCT
ejpam-6075	83	33	=	=	SYM
ejpam-6075	84	1	[	[	X
ejpam-6075	84	2	(	(	PUNCT
ejpam-6075	84	3	sj	sj	INTJ
ejpam-6075	84	4	\	\	PROPN
ejpam-6075	84	5	{	{	PUNCT
ejpam-6075	84	6	y	y	NOUN
ejpam-6075	84	7	}	}	PUNCT
ejpam-6075	84	8	)	)	PUNCT
ejpam-6075	84	9	∪	∪	ADP
ejpam-6075	84	10	{	{	PUNCT
ejpam-6075	84	11	x	x	NOUN
ejpam-6075	84	12	}	}	PUNCT
ejpam-6075	84	13	]	]	PUNCT
ejpam-6075	84	14	∪	∪	ADP
ejpam-6075	84	15	[	[	PUNCT
ejpam-6075	84	16	∪i∈[k]\{j}si	∪i∈[k]\{j}si	NOUN
ejpam-6075	84	17	]	]	PUNCT
ejpam-6075	84	18	is	be	AUX
ejpam-6075	84	19	a	a	DET
ejpam-6075	84	20	hop	hop	NOUN
ejpam-6075	84	21	dominating	dominating	NOUN
ejpam-6075	84	22	dominating	dominating	NOUN
ejpam-6075	84	23	set	set	VERB
ejpam-6075	84	24	in	in	ADP
ejpam-6075	84	25	g.	g.	PROPN
ejpam-6075	84	26	thus	thus	ADV
ejpam-6075	84	27	,	,	PUNCT
ejpam-6075	84	28	(	(	PUNCT
ejpam-6075	84	29	sj	sj	INTJ
ejpam-6075	84	30	\	\	PROPN
ejpam-6075	84	31	{	{	PUNCT
ejpam-6075	84	32	y	y	NOUN
ejpam-6075	84	33	}	}	PUNCT
ejpam-6075	84	34	)	)	PUNCT
ejpam-6075	84	35	∪	∪	ADP
ejpam-6075	84	36	{	{	PUNCT
ejpam-6075	84	37	x	x	NOUN
ejpam-6075	84	38	}	}	PUNCT
ejpam-6075	84	39	is	be	AUX
ejpam-6075	84	40	a	a	DET
ejpam-6075	84	41	hop	hop	NOUN
ejpam-6075	84	42	dominating	dominating	NOUN
ejpam-6075	84	43	dominating	dominating	NOUN
ejpam-6075	84	44	set	set	VERB
ejpam-6075	84	45	in	in	ADP
ejpam-6075	84	46	gj	gj	NOUN
ejpam-6075	84	47	.	.	PUNCT
ejpam-6075	85	1	since	since	SCONJ
ejpam-6075	85	2	j	j	PROPN
ejpam-6075	85	3	was	be	AUX
ejpam-6075	85	4	arbitrarily	arbitrarily	ADV
ejpam-6075	85	5	chosen	choose	VERB
ejpam-6075	85	6	,	,	PUNCT
ejpam-6075	85	7	it	it	PRON
ejpam-6075	85	8	follows	follow	VERB
ejpam-6075	85	9	that	that	SCONJ
ejpam-6075	85	10	sj	sj	PROPN
ejpam-6075	85	11	is	be	AUX
ejpam-6075	85	12	a	a	DET
ejpam-6075	85	13	secure	secure	ADJ
ejpam-6075	85	14	hop	hop	NOUN
ejpam-6075	85	15	dominating	dominating	NOUN
ejpam-6075	85	16	set	set	VERB
ejpam-6075	85	17	in	in	ADP
ejpam-6075	85	18	gj	gj	NOUN
ejpam-6075	85	19	for	for	ADP
ejpam-6075	85	20	each	each	DET
ejpam-6075	85	21	j	j	PROPN
ejpam-6075	85	22	∈	∈	PROPN
ejpam-6075	86	1	[	[	X
ejpam-6075	86	2	k	k	X
ejpam-6075	86	3	]	]	X
ejpam-6075	86	4	.	.	PUNCT
ejpam-6075	87	1	therefore	therefore	ADV
ejpam-6075	87	2	,	,	PUNCT
ejpam-6075	87	3	γsh(g	γsh(g	SYM
ejpam-6075	87	4	)	)	PUNCT
ejpam-6075	87	5	=	=	SYM
ejpam-6075	87	6	|s|	|s|	PROPN
ejpam-6075	87	7	=	=	SYM
ejpam-6075	87	8	k∑	k∑	NOUN
ejpam-6075	87	9	j=1	j=1	PROPN
ejpam-6075	87	10	|sj	|sj	X
ejpam-6075	87	11	|	|	ADV
ejpam-6075	87	12	≥	≥	NOUN
ejpam-6075	87	13	k∑	k∑	VERB
ejpam-6075	87	14	j=1	j=1	NOUN
ejpam-6075	87	15	γsh(gj	γsh(gj	NUM
ejpam-6075	87	16	)	)	PUNCT
ejpam-6075	87	17	.	.	PUNCT
ejpam-6075	88	1	next	next	ADV
ejpam-6075	88	2	,	,	PUNCT
ejpam-6075	88	3	suppose	suppose	VERB
ejpam-6075	88	4	that	that	SCONJ
ejpam-6075	88	5	dj	dj	NOUN
ejpam-6075	88	6	is	be	AUX
ejpam-6075	88	7	a	a	DET
ejpam-6075	88	8	γsh	γsh	NOUN
ejpam-6075	88	9	-	-	PUNCT
ejpam-6075	88	10	set	set	VERB
ejpam-6075	88	11	in	in	ADP
ejpam-6075	88	12	gj	gj	NOUN
ejpam-6075	88	13	for	for	ADP
ejpam-6075	88	14	each	each	DET
ejpam-6075	88	15	j	j	PROPN
ejpam-6075	88	16	∈	∈	PROPN
ejpam-6075	89	1	[	[	X
ejpam-6075	89	2	k	k	X
ejpam-6075	89	3	]	]	X
ejpam-6075	89	4	.	.	PUNCT
ejpam-6075	90	1	since	since	SCONJ
ejpam-6075	90	2	each	each	DET
ejpam-6075	90	3	dj	dj	NOUN
ejpam-6075	90	4	is	be	AUX
ejpam-6075	90	5	a	a	DET
ejpam-6075	90	6	hop	hop	NOUN
ejpam-6075	90	7	dominating	dominating	NOUN
ejpam-6075	90	8	set	set	NOUN
ejpam-6075	90	9	of	of	ADP
ejpam-6075	90	10	gj	gj	NOUN
ejpam-6075	90	11	,	,	PUNCT
ejpam-6075	90	12	d	d	PROPN
ejpam-6075	90	13	=	=	SYM
ejpam-6075	90	14	∪j∈[k]dj	∪j∈[k]dj	PROPN
ejpam-6075	90	15	is	be	AUX
ejpam-6075	90	16	a	a	DET
ejpam-6075	90	17	hop	hop	NOUN
ejpam-6075	90	18	dominating	dominating	NOUN
ejpam-6075	90	19	set	set	VERB
ejpam-6075	90	20	in	in	ADP
ejpam-6075	90	21	g	g	NOUN
ejpam-6075	90	22	by	by	ADP
ejpam-6075	90	23	remark	remark	NOUN
ejpam-6075	90	24	1	1	NUM
ejpam-6075	90	25	.	.	PUNCT
ejpam-6075	91	1	let	let	VERB
ejpam-6075	91	2	v	v	NUM
ejpam-6075	91	3	∈	∈	PROPN
ejpam-6075	91	4	v	v	NOUN
ejpam-6075	91	5	(	(	PUNCT
ejpam-6075	91	6	g	g	NOUN
ejpam-6075	91	7	)	)	PUNCT
ejpam-6075	91	8	\	\	PROPN
ejpam-6075	92	1	d.	d.	PROPN
ejpam-6075	92	2	then	then	ADV
ejpam-6075	92	3	v	v	ADP
ejpam-6075	92	4	∈	∈	PROPN
ejpam-6075	92	5	v	v	NOUN
ejpam-6075	92	6	(	(	PUNCT
ejpam-6075	92	7	gt	gt	PROPN
ejpam-6075	92	8	)	)	PUNCT
ejpam-6075	92	9	\	\	PROPN
ejpam-6075	93	1	dt	dt	NOUN
ejpam-6075	94	1	for	for	ADP
ejpam-6075	94	2	a	a	DET
ejpam-6075	94	3	unique	unique	ADJ
ejpam-6075	94	4	t	t	NOUN
ejpam-6075	94	5	∈	∈	PROPN
ejpam-6075	95	1	[	[	X
ejpam-6075	95	2	k	k	X
ejpam-6075	95	3	]	]	X
ejpam-6075	95	4	.	.	PUNCT
ejpam-6075	96	1	since	since	SCONJ
ejpam-6075	96	2	dt	dt	PROPN
ejpam-6075	96	3	is	be	AUX
ejpam-6075	96	4	a	a	DET
ejpam-6075	96	5	secure	secure	ADJ
ejpam-6075	96	6	hop	hop	NOUN
ejpam-6075	96	7	dominating	dominating	NOUN
ejpam-6075	96	8	set	set	NOUN
ejpam-6075	96	9	in	in	ADP
ejpam-6075	96	10	gt	gt	PROPN
ejpam-6075	96	11	,	,	PUNCT
ejpam-6075	96	12	there	there	PRON
ejpam-6075	96	13	exists	exist	VERB
ejpam-6075	96	14	w	w	PROPN
ejpam-6075	96	15	∈	∈	PROPN
ejpam-6075	96	16	dt	dt	NOUN
ejpam-6075	96	17	∩	∩	PROPN
ejpam-6075	96	18	n2	n2	PROPN
ejpam-6075	96	19	gt	gt	PROPN
ejpam-6075	96	20	(	(	PUNCT
ejpam-6075	96	21	v	v	NOUN
ejpam-6075	96	22	)	)	PUNCT
ejpam-6075	96	23	such	such	ADJ
ejpam-6075	96	24	that	that	SCONJ
ejpam-6075	96	25	(	(	PUNCT
ejpam-6075	96	26	dt	dt	X
ejpam-6075	96	27	\	\	PROPN
ejpam-6075	96	28	{	{	PUNCT
ejpam-6075	96	29	w	w	NOUN
ejpam-6075	96	30	}	}	PUNCT
ejpam-6075	96	31	)	)	PUNCT
ejpam-6075	96	32	∪	∪	ADP
ejpam-6075	96	33	{	{	PUNCT
ejpam-6075	96	34	v	v	NOUN
ejpam-6075	96	35	}	}	PUNCT
ejpam-6075	96	36	is	be	AUX
ejpam-6075	96	37	a	a	DET
ejpam-6075	96	38	hop	hop	NOUN
ejpam-6075	96	39	dominating	dominating	NOUN
ejpam-6075	96	40	set	set	VERB
ejpam-6075	96	41	in	in	ADP
ejpam-6075	96	42	gt	gt	PROPN
ejpam-6075	96	43	.	.	PUNCT
ejpam-6075	97	1	by	by	ADP
ejpam-6075	97	2	remark	remark	NOUN
ejpam-6075	97	3	1	1	NUM
ejpam-6075	97	4	,	,	PUNCT
ejpam-6075	97	5	(	(	PUNCT
ejpam-6075	97	6	d	d	NOUN
ejpam-6075	97	7	\	\	X
ejpam-6075	97	8	{	{	PUNCT
ejpam-6075	97	9	w	w	NOUN
ejpam-6075	97	10	}	}	PUNCT
ejpam-6075	97	11	)	)	PUNCT
ejpam-6075	97	12	∪	∪	ADP
ejpam-6075	97	13	{	{	PUNCT
ejpam-6075	97	14	v	v	NOUN
ejpam-6075	97	15	}	}	PUNCT
ejpam-6075	97	16	=	=	SYM
ejpam-6075	98	1	[	[	X
ejpam-6075	98	2	(	(	PUNCT
ejpam-6075	98	3	dt	dt	PART
ejpam-6075	98	4	\	\	PROPN
ejpam-6075	98	5	{	{	PUNCT
ejpam-6075	98	6	w	w	NOUN
ejpam-6075	98	7	}	}	PUNCT
ejpam-6075	98	8	)	)	PUNCT
ejpam-6075	98	9	∪	∪	ADP
ejpam-6075	98	10	{	{	PUNCT
ejpam-6075	98	11	v	v	NOUN
ejpam-6075	98	12	}	}	PUNCT
ejpam-6075	98	13	]	]	PUNCT
ejpam-6075	98	14	∪	∪	ADP
ejpam-6075	98	15	[	[	X
ejpam-6075	98	16	∪i∈[k]\{t}di	∪i∈[k]\{t}di	X
ejpam-6075	98	17	]	]	X
ejpam-6075	98	18	f.	f.	PROPN
ejpam-6075	98	19	l.	l.	PROPN
ejpam-6075	98	20	alfeche	alfeche	PROPN
ejpam-6075	98	21	,	,	PUNCT
ejpam-6075	98	22	g.	g.	PROPN
ejpam-6075	98	23	a.	a.	PROPN
ejpam-6075	98	24	malacas	malacas	PROPN
ejpam-6075	98	25	,	,	PUNCT
ejpam-6075	98	26	s.	s.	PROPN
ejpam-6075	98	27	canoy	canoy	PROPN
ejpam-6075	98	28	jr	jr	PROPN
ejpam-6075	98	29	.	.	PROPN
ejpam-6075	98	30	/	/	SYM
ejpam-6075	98	31	eur	eur	PROPN
ejpam-6075	98	32	.	.	PUNCT
ejpam-6075	99	1	j.	j.	PROPN
ejpam-6075	99	2	pure	pure	PROPN
ejpam-6075	99	3	appl	appl	PROPN
ejpam-6075	99	4	.	.	PROPN
ejpam-6075	99	5	math	math	PROPN
ejpam-6075	99	6	,	,	PUNCT
ejpam-6075	99	7	18	18	NUM
ejpam-6075	99	8	(	(	PUNCT
ejpam-6075	99	9	2	2	NUM
ejpam-6075	99	10	)	)	PUNCT
ejpam-6075	99	11	(	(	PUNCT
ejpam-6075	99	12	2025	2025	NUM
ejpam-6075	99	13	)	)	PUNCT
ejpam-6075	99	14	,	,	PUNCT
ejpam-6075	99	15	6075	6075	NUM
ejpam-6075	99	16	4	4	NUM
ejpam-6075	99	17	of	of	ADP
ejpam-6075	99	18	14	14	NUM
ejpam-6075	99	19	is	be	AUX
ejpam-6075	99	20	a	a	DET
ejpam-6075	99	21	hop	hop	NOUN
ejpam-6075	99	22	dominating	dominating	NOUN
ejpam-6075	99	23	dominating	dominating	NOUN
ejpam-6075	99	24	set	set	VERB
ejpam-6075	99	25	in	in	ADP
ejpam-6075	99	26	g.	g.	PROPN
ejpam-6075	99	27	hence	hence	ADV
ejpam-6075	99	28	,	,	PUNCT
ejpam-6075	99	29	d	d	PROPN
ejpam-6075	99	30	is	be	AUX
ejpam-6075	99	31	a	a	DET
ejpam-6075	99	32	secure	secure	ADJ
ejpam-6075	99	33	hop	hop	NOUN
ejpam-6075	99	34	dominating	dominating	NOUN
ejpam-6075	99	35	set	set	VERB
ejpam-6075	99	36	in	in	ADP
ejpam-6075	99	37	g	g	NOUN
ejpam-6075	99	38	and	and	CCONJ
ejpam-6075	99	39	γsh(g	γsh(g	NOUN
ejpam-6075	99	40	)	)	PUNCT
ejpam-6075	99	41	≤	≤	PUNCT
ejpam-6075	100	1	|d|	|d|	PROPN
ejpam-6075	100	2	=	=	SYM
ejpam-6075	100	3	k∑	k∑	PROPN
ejpam-6075	101	1	j=1	j=1	NOUN
ejpam-6075	101	2	|dj	|dj	PUNCT
ejpam-6075	101	3	|	|	NOUN
ejpam-6075	101	4	=	=	SYM
ejpam-6075	101	5	k∑	k∑	NOUN
ejpam-6075	101	6	j=1	j=1	NOUN
ejpam-6075	101	7	γsh(gj	γsh(gj	NUM
ejpam-6075	101	8	)	)	PUNCT
ejpam-6075	101	9	.	.	PUNCT
ejpam-6075	102	1	therefore	therefore	ADV
ejpam-6075	102	2	,	,	PUNCT
ejpam-6075	102	3	the	the	DET
ejpam-6075	102	4	assertion	assertion	NOUN
ejpam-6075	102	5	holds	hold	VERB
ejpam-6075	102	6	.	.	PUNCT
ejpam-6075	103	1	theorem	theorem	NOUN
ejpam-6075	103	2	2	2	NUM
ejpam-6075	103	3	.	.	PUNCT
ejpam-6075	104	1	let	let	VERB
ejpam-6075	104	2	g	g	NOUN
ejpam-6075	104	3	be	be	AUX
ejpam-6075	104	4	any	any	DET
ejpam-6075	104	5	graph	graph	NOUN
ejpam-6075	104	6	.	.	PUNCT
ejpam-6075	105	1	then	then	ADV
ejpam-6075	105	2	γh(g	γh(g	PUNCT
ejpam-6075	105	3	)	)	PUNCT
ejpam-6075	105	4	≤	≤	NUM
ejpam-6075	105	5	γsh(g	γsh(g	NOUN
ejpam-6075	105	6	)	)	PUNCT
ejpam-6075	105	7	.	.	PUNCT
ejpam-6075	106	1	moreover	moreover	ADV
ejpam-6075	106	2	,	,	PUNCT
ejpam-6075	106	3	for	for	ADP
ejpam-6075	106	4	each	each	DET
ejpam-6075	106	5	positive	positive	ADJ
ejpam-6075	106	6	integer	integer	NOUN
ejpam-6075	106	7	n	n	CCONJ
ejpam-6075	106	8	,	,	PUNCT
ejpam-6075	106	9	there	there	PRON
ejpam-6075	106	10	exists	exist	VERB
ejpam-6075	106	11	a	a	DET
ejpam-6075	106	12	connected	connected	ADJ
ejpam-6075	106	13	graph	graph	NOUN
ejpam-6075	106	14	g	g	ADP
ejpam-6075	106	15	such	such	ADJ
ejpam-6075	106	16	that	that	SCONJ
ejpam-6075	106	17	γsh(g	γsh(g	NOUN
ejpam-6075	106	18	)	)	PUNCT
ejpam-6075	106	19	−	−	NOUN
ejpam-6075	106	20	γh(g	γh(g	NOUN
ejpam-6075	106	21	)	)	PUNCT
ejpam-6075	106	22	=	=	VERB
ejpam-6075	106	23	n.	n.	NOUN
ejpam-6075	106	24	in	in	ADP
ejpam-6075	106	25	particular	particular	ADJ
ejpam-6075	106	26	,	,	PUNCT
ejpam-6075	106	27	the	the	DET
ejpam-6075	106	28	difference	difference	NOUN
ejpam-6075	106	29	γsh(g)−	γsh(g)−	NOUN
ejpam-6075	106	30	γh(g	γh(g	NOUN
ejpam-6075	106	31	)	)	PUNCT
ejpam-6075	106	32	can	can	AUX
ejpam-6075	106	33	be	be	AUX
ejpam-6075	106	34	made	make	VERB
ejpam-6075	106	35	arbitrarily	arbitrarily	ADV
ejpam-6075	106	36	large	large	ADJ
ejpam-6075	106	37	.	.	PUNCT
ejpam-6075	107	1	since	since	SCONJ
ejpam-6075	107	2	every	every	DET
ejpam-6075	107	3	secure	secure	ADJ
ejpam-6075	107	4	hop	hop	NOUN
ejpam-6075	107	5	dominating	dominating	NOUN
ejpam-6075	107	6	set	set	NOUN
ejpam-6075	107	7	is	be	AUX
ejpam-6075	107	8	hop	hop	NOUN
ejpam-6075	107	9	dominating	dominating	NOUN
ejpam-6075	107	10	,	,	PUNCT
ejpam-6075	107	11	it	it	PRON
ejpam-6075	107	12	follows	follow	VERB
ejpam-6075	107	13	that	that	PRON
ejpam-6075	107	14	γh(g	γh(g	ADP
ejpam-6075	107	15	)	)	PUNCT
ejpam-6075	107	16	≤	≤	NUM
ejpam-6075	107	17	γsh(g	γsh(g	NOUN
ejpam-6075	107	18	)	)	PUNCT
ejpam-6075	107	19	.	.	PUNCT
ejpam-6075	108	1	next	next	ADV
ejpam-6075	108	2	,	,	PUNCT
ejpam-6075	108	3	let	let	VERB
ejpam-6075	108	4	n	n	PRON
ejpam-6075	108	5	be	be	AUX
ejpam-6075	108	6	a	a	DET
ejpam-6075	108	7	positive	positive	ADJ
ejpam-6075	108	8	integer	integer	NOUN
ejpam-6075	108	9	.	.	PUNCT
ejpam-6075	109	1	consider	consider	VERB
ejpam-6075	109	2	the	the	DET
ejpam-6075	109	3	graph	graph	NOUN
ejpam-6075	109	4	g	g	NOUN
ejpam-6075	109	5	in	in	ADP
ejpam-6075	109	6	figure	figure	NOUN
ejpam-6075	109	7	1	1	NUM
ejpam-6075	109	8	obtained	obtain	VERB
ejpam-6075	109	9	from	from	ADP
ejpam-6075	109	10	the	the	DET
ejpam-6075	109	11	complete	complete	ADJ
ejpam-6075	109	12	graph	graph	NOUN
ejpam-6075	109	13	kn+2	kn+2	PROPN
ejpam-6075	109	14	,	,	PUNCT
ejpam-6075	109	15	where	where	SCONJ
ejpam-6075	109	16	v	v	X
ejpam-6075	109	17	(	(	PUNCT
ejpam-6075	109	18	kn+2	kn+2	PROPN
ejpam-6075	109	19	)	)	PUNCT
ejpam-6075	109	20	=	=	SYM
ejpam-6075	109	21	{	{	PUNCT
ejpam-6075	109	22	z1	z1	PROPN
ejpam-6075	109	23	,	,	PUNCT
ejpam-6075	109	24	z2	z2	PROPN
ejpam-6075	109	25	,	,	PUNCT
ejpam-6075	109	26	·	·	PUNCT
ejpam-6075	109	27	·	·	PUNCT
ejpam-6075	109	28	·	·	PUNCT
ejpam-6075	109	29	,	,	PUNCT
ejpam-6075	109	30	zn+2	zn+2	NUM
ejpam-6075	109	31	}	}	PUNCT
ejpam-6075	109	32	,	,	PUNCT
ejpam-6075	109	33	by	by	ADP
ejpam-6075	109	34	adding	add	VERB
ejpam-6075	109	35	the	the	DET
ejpam-6075	109	36	edges	edge	NOUN
ejpam-6075	109	37	vw	vw	PROPN
ejpam-6075	109	38	and	and	CCONJ
ejpam-6075	109	39	wz1	wz1	PROPN
ejpam-6075	109	40	.	.	PUNCT
ejpam-6075	110	1	the	the	DET
ejpam-6075	110	2	set	set	NOUN
ejpam-6075	110	3	{	{	PUNCT
ejpam-6075	110	4	v	v	NOUN
ejpam-6075	110	5	,	,	PUNCT
ejpam-6075	110	6	w	w	NOUN
ejpam-6075	110	7	}	}	PUNCT
ejpam-6075	110	8	is	be	AUX
ejpam-6075	110	9	a	a	DET
ejpam-6075	110	10	γh	γh	ADV
ejpam-6075	110	11	-	-	PUNCT
ejpam-6075	110	12	set	set	NOUN
ejpam-6075	110	13	in	in	ADP
ejpam-6075	110	14	g.	g.	PROPN
ejpam-6075	110	15	thus	thus	ADV
ejpam-6075	110	16	,	,	PUNCT
ejpam-6075	110	17	γh(g	γh(g	NOUN
ejpam-6075	110	18	)	)	PUNCT
ejpam-6075	110	19	=	=	SYM
ejpam-6075	110	20	2	2	X
ejpam-6075	110	21	.	.	PUNCT
ejpam-6075	110	22	let	let	VERB
ejpam-6075	110	23	d	d	PRON
ejpam-6075	110	24	be	be	AUX
ejpam-6075	110	25	a	a	DET
ejpam-6075	110	26	γsh	γsh	NOUN
ejpam-6075	110	27	-	-	PUNCT
ejpam-6075	110	28	set	set	NOUN
ejpam-6075	110	29	in	in	ADP
ejpam-6075	110	30	g.	g.	PROPN
ejpam-6075	110	31	if	if	SCONJ
ejpam-6075	110	32	w	w	PROPN
ejpam-6075	110	33	/∈	/∈	PUNCT
ejpam-6075	111	1	d	d	NOUN
ejpam-6075	111	2	,	,	PUNCT
ejpam-6075	111	3	then	then	ADV
ejpam-6075	111	4	d	d	PROPN
ejpam-6075	111	5	=	=	PUNCT
ejpam-6075	111	6	{	{	PUNCT
ejpam-6075	111	7	v	v	NOUN
ejpam-6075	111	8	,	,	PUNCT
ejpam-6075	111	9	z2	z2	PROPN
ejpam-6075	111	10	,	,	PUNCT
ejpam-6075	111	11	·	·	PUNCT
ejpam-6075	111	12	·	·	PUNCT
ejpam-6075	111	13	·	·	PUNCT
ejpam-6075	111	14	,	,	PUNCT
ejpam-6075	111	15	zn+2	zn+2	NUM
ejpam-6075	111	16	}	}	PUNCT
ejpam-6075	111	17	or	or	CCONJ
ejpam-6075	111	18	d	d	NOUN
ejpam-6075	111	19	=	=	SYM
ejpam-6075	111	20	{	{	PUNCT
ejpam-6075	111	21	z1	z1	PROPN
ejpam-6075	111	22	,	,	PUNCT
ejpam-6075	111	23	z2	z2	PROPN
ejpam-6075	111	24	,	,	PUNCT
ejpam-6075	111	25	·	·	PUNCT
ejpam-6075	111	26	·	·	PUNCT
ejpam-6075	111	27	·	·	PUNCT
ejpam-6075	111	28	,	,	PUNCT
ejpam-6075	111	29	zn+2	zn+2	NUM
ejpam-6075	111	30	}	}	PUNCT
ejpam-6075	111	31	because	because	SCONJ
ejpam-6075	111	32	d	d	NOUN
ejpam-6075	111	33	is	be	AUX
ejpam-6075	111	34	a	a	DET
ejpam-6075	111	35	hop	hop	NOUN
ejpam-6075	111	36	dominating	dominating	NOUN
ejpam-6075	111	37	set	set	NOUN
ejpam-6075	111	38	.	.	PUNCT
ejpam-6075	112	1	hence	hence	ADV
ejpam-6075	112	2	,	,	PUNCT
ejpam-6075	112	3	|d|	|d|	PROPN
ejpam-6075	112	4	=	=	SYM
ejpam-6075	112	5	n	n	PROPN
ejpam-6075	112	6	+	+	NOUN
ejpam-6075	112	7	2	2	X
ejpam-6075	112	8	.	.	X
ejpam-6075	112	9	suppose	suppose	VERB
ejpam-6075	112	10	w	w	PROPN
ejpam-6075	112	11	∈	∈	PROPN
ejpam-6075	112	12	d	d	NOUN
ejpam-6075	112	13	and	and	CCONJ
ejpam-6075	112	14	let	let	VERB
ejpam-6075	112	15	zj	zj	PROPN
ejpam-6075	112	16	∈	∈	PROPN
ejpam-6075	112	17	v	v	X
ejpam-6075	112	18	(	(	PUNCT
ejpam-6075	112	19	g	g	NOUN
ejpam-6075	112	20	)	)	PUNCT
ejpam-6075	112	21	\	\	PUNCT
ejpam-6075	113	1	d	d	NOUN
ejpam-6075	113	2	for	for	ADP
ejpam-6075	113	3	some	some	DET
ejpam-6075	113	4	j	j	PROPN
ejpam-6075	113	5	∈	∈	PROPN
ejpam-6075	113	6	{	{	PUNCT
ejpam-6075	113	7	2	2	NUM
ejpam-6075	113	8	,	,	PUNCT
ejpam-6075	113	9	3	3	NUM
ejpam-6075	113	10	,	,	PUNCT
ejpam-6075	113	11	·	·	PUNCT
ejpam-6075	113	12	·	·	PUNCT
ejpam-6075	113	13	·	·	PUNCT
ejpam-6075	113	14	,	,	PUNCT
ejpam-6075	113	15	n	n	X
ejpam-6075	113	16	+	+	CCONJ
ejpam-6075	113	17	2	2	NUM
ejpam-6075	113	18	}	}	PUNCT
ejpam-6075	113	19	.	.	PUNCT
ejpam-6075	114	1	since	since	SCONJ
ejpam-6075	114	2	d	d	PROPN
ejpam-6075	114	3	is	be	AUX
ejpam-6075	114	4	secure	secure	ADJ
ejpam-6075	114	5	hop	hop	NOUN
ejpam-6075	114	6	dominating	dominating	NOUN
ejpam-6075	114	7	,	,	PUNCT
ejpam-6075	114	8	(	(	PUNCT
ejpam-6075	114	9	d	d	NOUN
ejpam-6075	114	10	\	\	X
ejpam-6075	114	11	{	{	PUNCT
ejpam-6075	114	12	w	w	NOUN
ejpam-6075	114	13	}	}	PUNCT
ejpam-6075	114	14	)	)	PUNCT
ejpam-6075	114	15	∪	∪	ADP
ejpam-6075	114	16	{	{	PUNCT
ejpam-6075	114	17	zj	zj	NOUN
ejpam-6075	114	18	}	}	PUNCT
ejpam-6075	114	19	is	be	AUX
ejpam-6075	114	20	hop	hop	PROPN
ejpam-6075	114	21	dominating	dominating	NOUN
ejpam-6075	114	22	.	.	PUNCT
ejpam-6075	115	1	note	note	VERB
ejpam-6075	115	2	that	that	SCONJ
ejpam-6075	115	3	n2	n2	ADJ
ejpam-6075	115	4	g(zj	g(zj	NOUN
ejpam-6075	115	5	)	)	PUNCT
ejpam-6075	115	6	∩	∩	NOUN
ejpam-6075	115	7	[	[	X
ejpam-6075	115	8	{	{	PUNCT
ejpam-6075	115	9	z2	z2	NOUN
ejpam-6075	115	10	,	,	PUNCT
ejpam-6075	115	11	z3	z3	PROPN
ejpam-6075	115	12	,	,	PUNCT
ejpam-6075	115	13	·	·	PUNCT
ejpam-6075	115	14	·	·	PUNCT
ejpam-6075	115	15	·	·	PUNCT
ejpam-6075	115	16	,	,	PUNCT
ejpam-6075	115	17	zn+2	zn+2	NUM
ejpam-6075	115	18	}	}	PUNCT
ejpam-6075	115	19	\	\	NOUN
ejpam-6075	115	20	{	{	PUNCT
ejpam-6075	115	21	zj	zj	NOUN
ejpam-6075	115	22	}	}	PUNCT
ejpam-6075	115	23	]	]	PUNCT
ejpam-6075	116	1	=	=	PUNCT
ejpam-6075	116	2	∅.	∅.	PRON
ejpam-6075	116	3	this	this	PRON
ejpam-6075	116	4	implies	imply	VERB
ejpam-6075	116	5	that	that	SCONJ
ejpam-6075	116	6	{	{	PUNCT
ejpam-6075	116	7	z2	z2	NOUN
ejpam-6075	116	8	,	,	PUNCT
ejpam-6075	116	9	z3	z3	PROPN
ejpam-6075	116	10	,	,	PUNCT
ejpam-6075	116	11	·	·	PUNCT
ejpam-6075	116	12	·	·	PUNCT
ejpam-6075	116	13	·	·	PUNCT
ejpam-6075	116	14	,	,	PUNCT
ejpam-6075	116	15	zn+2	zn+2	NUM
ejpam-6075	116	16	}	}	PUNCT
ejpam-6075	116	17	\	\	NOUN
ejpam-6075	116	18	{	{	PUNCT
ejpam-6075	116	19	zj	zj	PROPN
ejpam-6075	116	20	}	}	PUNCT
ejpam-6075	116	21	⊆	⊆	PROPN
ejpam-6075	116	22	d.	d.	PROPN
ejpam-6075	116	23	hence	hence	ADV
ejpam-6075	116	24	,	,	PUNCT
ejpam-6075	116	25	d	d	PROPN
ejpam-6075	116	26	=	=	PRON
ejpam-6075	116	27	{	{	PUNCT
ejpam-6075	116	28	v	v	NOUN
ejpam-6075	116	29	,	,	PUNCT
ejpam-6075	116	30	w	w	NOUN
ejpam-6075	116	31	}	}	PUNCT
ejpam-6075	116	32	∪	∪	ADJ
ejpam-6075	116	33	[	[	X
ejpam-6075	116	34	{	{	PUNCT
ejpam-6075	116	35	z2	z2	NOUN
ejpam-6075	116	36	,	,	PUNCT
ejpam-6075	116	37	·	·	PUNCT
ejpam-6075	116	38	·	·	PUNCT
ejpam-6075	116	39	·	·	PUNCT
ejpam-6075	116	40	,	,	PUNCT
ejpam-6075	116	41	zn+2	zn+2	NUM
ejpam-6075	116	42	}	}	PUNCT
ejpam-6075	116	43	\	\	NOUN
ejpam-6075	116	44	{	{	PUNCT
ejpam-6075	116	45	zj	zj	NOUN
ejpam-6075	116	46	}	}	PUNCT
ejpam-6075	116	47	]	]	PUNCT
ejpam-6075	116	48	or	or	CCONJ
ejpam-6075	116	49	d	d	AUX
ejpam-6075	116	50	=	=	SYM
ejpam-6075	116	51	{	{	PUNCT
ejpam-6075	116	52	w	w	NOUN
ejpam-6075	116	53	}	}	PUNCT
ejpam-6075	116	54	∪	∪	ADJ
ejpam-6075	116	55	[	[	X
ejpam-6075	116	56	{	{	PUNCT
ejpam-6075	116	57	z1	z1	ADJ
ejpam-6075	116	58	,	,	PUNCT
ejpam-6075	116	59	z2	z2	PROPN
ejpam-6075	116	60	,	,	PUNCT
ejpam-6075	116	61	·	·	PUNCT
ejpam-6075	116	62	·	·	PUNCT
ejpam-6075	116	63	·	·	PUNCT
ejpam-6075	116	64	,	,	PUNCT
ejpam-6075	116	65	zn+2	zn+2	NUM
ejpam-6075	116	66	}	}	PUNCT
ejpam-6075	116	67	\	\	NOUN
ejpam-6075	116	68	{	{	PUNCT
ejpam-6075	116	69	zj	zj	PROPN
ejpam-6075	116	70	}	}	PUNCT
ejpam-6075	116	71	]	]	PUNCT
ejpam-6075	116	72	.	.	PUNCT
ejpam-6075	117	1	it	it	PRON
ejpam-6075	117	2	follows	follow	VERB
ejpam-6075	117	3	that	that	SCONJ
ejpam-6075	117	4	|d|	|d|	PROPN
ejpam-6075	117	5	=	=	SYM
ejpam-6075	117	6	n	n	PROPN
ejpam-6075	117	7	+	+	NOUN
ejpam-6075	117	8	2	2	NUM
ejpam-6075	117	9	.	.	X
ejpam-6075	117	10	therefore	therefore	ADV
ejpam-6075	117	11	,	,	PUNCT
ejpam-6075	117	12	γsh(g	γsh(g	ADV
ejpam-6075	117	13	)	)	PUNCT
ejpam-6075	117	14	=	=	SYM
ejpam-6075	118	1	n	n	PROPN
ejpam-6075	118	2	+	+	CCONJ
ejpam-6075	118	3	2	2	NUM
ejpam-6075	118	4	and	and	CCONJ
ejpam-6075	118	5	γsh(g)−	γsh(g)−	NOUN
ejpam-6075	118	6	γh(g	γh(g	NOUN
ejpam-6075	118	7	)	)	PUNCT
ejpam-6075	118	8	=	=	VERB
ejpam-6075	118	9	n.	n.	NOUN
ejpam-6075	118	10	............	............	PUNCT
ejpam-6075	118	11	...........	...........	PUNCT
ejpam-6075	118	12	...........	...........	PUNCT
ejpam-6075	118	13	...........	...........	PUNCT
ejpam-6075	118	14	...........	...........	PUNCT
ejpam-6075	118	15	...........	...........	PUNCT
ejpam-6075	118	16	...........	...........	PUNCT
ejpam-6075	118	17	...........	...........	PUNCT
ejpam-6075	118	18	...........	...........	PUNCT
ejpam-6075	118	19	...........	...........	PUNCT
ejpam-6075	118	20	....................................	....................................	PUNCT
ejpam-6075	118	21	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-6075	118	22	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-6075	119	1	....................................	....................................	PUNCT
ejpam-6075	120	1	....................................................................................................................................................	....................................................................................................................................................	PUNCT
ejpam-6075	121	1	....................................................................................................................................................	....................................................................................................................................................	PUNCT
ejpam-6075	122	1	....................................	....................................	PUNCT
ejpam-6075	123	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-6075	124	1	....................................	....................................	PUNCT
ejpam-6075	125	1	....................................	....................................	PUNCT
ejpam-6075	126	1	............	............	PUNCT
ejpam-6075	127	1	...........	...........	PUNCT
ejpam-6075	128	1	...........	...........	PUNCT
ejpam-6075	129	1	...........	...........	PUNCT
ejpam-6075	130	1	...........	...........	PUNCT
ejpam-6075	131	1	...........	...........	PUNCT
ejpam-6075	132	1	...........	...........	PUNCT
ejpam-6075	133	1	...........	...........	PUNCT
ejpam-6075	134	1	...........	...........	PUNCT
ejpam-6075	135	1	...........	...........	PUNCT
ejpam-6075	136	1	....................................	....................................	PUNCT
ejpam-6075	137	1	....................................	....................................	PUNCT
ejpam-6075	138	1	.....................	.....................	PUNCT
ejpam-6075	139	1	....................	....................	PUNCT
ejpam-6075	140	1	....................	....................	PUNCT
ejpam-6075	141	1	....................	....................	PUNCT
ejpam-6075	142	1	....................	....................	PUNCT
ejpam-6075	143	1	....................	....................	PUNCT
ejpam-6075	144	1	....................	....................	PUNCT
ejpam-6075	145	1	....................	....................	PUNCT
ejpam-6075	146	1	....................	....................	PUNCT
ejpam-6075	147	1	....................	....................	PUNCT
ejpam-6075	148	1	........	........	PUNCT
ejpam-6075	149	1	....................................	....................................	PUNCT
ejpam-6075	150	1	....................................	....................................	PUNCT
ejpam-6075	151	1	.........................................................................................................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6075	152	1	.....................................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................................	PUNCT
ejpam-6075	153	1	....................................	....................................	PUNCT
ejpam-6075	154	1	....................................	....................................	PUNCT
ejpam-6075	155	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-6075	156	1	.....................................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................................	PUNCT
ejpam-6075	157	1	....................................	....................................	PUNCT
ejpam-6075	158	1	....................................	....................................	PUNCT
ejpam-6075	159	1	.....................................................................................................................................................................................................	.....................................................................................................................................................................................................	PUNCT
ejpam-6075	160	1	....................................	....................................	PUNCT
ejpam-6075	161	1	................................................................................................................................................................................	................................................................................................................................................................................	PUNCT
ejpam-6075	162	1	....................................	....................................	PUNCT
ejpam-6075	163	1	.........	.........	PUNCT
ejpam-6075	164	1	........	........	PUNCT
ejpam-6075	165	1	........	........	PUNCT
ejpam-6075	166	1	........	........	PUNCT
ejpam-6075	167	1	........	........	PUNCT
ejpam-6075	168	1	........	........	PUNCT
ejpam-6075	169	1	........	........	PUNCT
ejpam-6075	170	1	........	........	PUNCT
ejpam-6075	171	1	........	........	PUNCT
ejpam-6075	172	1	........	........	PUNCT
ejpam-6075	173	1	........	........	PUNCT
ejpam-6075	174	1	........	........	PUNCT
ejpam-6075	175	1	........	........	PUNCT
ejpam-6075	176	1	........	........	PUNCT
ejpam-6075	177	1	........	........	PUNCT
ejpam-6075	178	1	........	........	PUNCT
ejpam-6075	179	1	........	........	PUNCT
ejpam-6075	180	1	........	........	PUNCT
ejpam-6075	181	1	........	........	PUNCT
ejpam-6075	182	1	........	........	PUNCT
ejpam-6075	182	2	.	.	PUNCT
ejpam-6075	183	1	....................................	....................................	PUNCT
ejpam-6075	183	2	....................................	....................................	PUNCT
ejpam-6075	184	1	...........	...........	PUNCT
ejpam-6075	184	2	..........	..........	PUNCT
ejpam-6075	185	1	..........	..........	PUNCT
ejpam-6075	185	2	..........	..........	PUNCT
ejpam-6075	186	1	..........	..........	PUNCT
ejpam-6075	186	2	..........	..........	PUNCT
ejpam-6075	187	1	..........	..........	PUNCT
ejpam-6075	187	2	..........	..........	PUNCT
ejpam-6075	188	1	..........	..........	PUNCT
ejpam-6075	188	2	..........	..........	PUNCT
ejpam-6075	189	1	..........	..........	PUNCT
ejpam-6075	189	2	..........	..........	PUNCT
ejpam-6075	190	1	..........	..........	PUNCT
ejpam-6075	190	2	..........	..........	PUNCT
ejpam-6075	191	1	..........	..........	PUNCT
ejpam-6075	191	2	..........	..........	PUNCT
ejpam-6075	192	1	..........	..........	PUNCT
ejpam-6075	192	2	..........	..........	PUNCT
ejpam-6075	193	1	..........	..........	PUNCT
ejpam-6075	193	2	......	......	PUNCT
ejpam-6075	194	1	....................................	....................................	PUNCT
ejpam-6075	194	2	....................................	....................................	PUNCT
ejpam-6075	195	1	.....................	.....................	PUNCT
ejpam-6075	195	2	....................	....................	PUNCT
ejpam-6075	195	3	....................	....................	PUNCT
ejpam-6075	195	4	....................	....................	PUNCT
ejpam-6075	195	5	....................	....................	PUNCT
ejpam-6075	195	6	....................	....................	PUNCT
ejpam-6075	195	7	....................	....................	PUNCT
ejpam-6075	195	8	....................	....................	PUNCT
ejpam-6075	195	9	....................	....................	PUNCT
ejpam-6075	195	10	....................	....................	PUNCT
ejpam-6075	195	11	........	........	PUNCT
ejpam-6075	196	1	....................................	....................................	PUNCT
ejpam-6075	196	2	....................................	....................................	PUNCT
ejpam-6075	196	3	.........	.........	PUNCT
ejpam-6075	196	4	........	........	PUNCT
ejpam-6075	196	5	........	........	PUNCT
ejpam-6075	196	6	........	........	PUNCT
ejpam-6075	196	7	........	........	PUNCT
ejpam-6075	196	8	........	........	PUNCT
ejpam-6075	196	9	........	........	PUNCT
ejpam-6075	196	10	........	........	PUNCT
ejpam-6075	196	11	........	........	PUNCT
ejpam-6075	196	12	........	........	PUNCT
ejpam-6075	196	13	........	........	PUNCT
ejpam-6075	196	14	........	........	PUNCT
ejpam-6075	196	15	........	........	PUNCT
ejpam-6075	196	16	........	........	PUNCT
ejpam-6075	196	17	........	........	PUNCT
ejpam-6075	196	18	........	........	PUNCT
ejpam-6075	196	19	........	........	PUNCT
ejpam-6075	196	20	........	........	PUNCT
ejpam-6075	196	21	........	........	PUNCT
ejpam-6075	196	22	........	........	PUNCT
ejpam-6075	196	23	.	.	PUNCT
ejpam-6075	197	1	....................................	....................................	PUNCT
ejpam-6075	197	2	....................................	....................................	PUNCT
ejpam-6075	197	3	.	.	PUNCT
ejpam-6075	197	4	.	.	PUNCT
ejpam-6075	197	5	.	.	PUNCT
ejpam-6075	198	1	z4	z4	PROPN
ejpam-6075	198	2	z3z2	z3z2	PROPN
ejpam-6075	198	3	z1	z1	PROPN
ejpam-6075	198	4	zn+2	zn+2	NUM
ejpam-6075	198	5	z5	z5	X
ejpam-6075	198	6	v	v	ADP
ejpam-6075	198	7	w	w	PROPN
ejpam-6075	198	8	figure	figure	NOUN
ejpam-6075	198	9	1	1	NUM
ejpam-6075	198	10	:	:	PUNCT
ejpam-6075	198	11	graph	graph	VERB
ejpam-6075	198	12	g	g	NOUN
ejpam-6075	198	13	with	with	ADP
ejpam-6075	198	14	γsh(g)−	γsh(g)−	NOUN
ejpam-6075	198	15	γh(g	γh(g	NOUN
ejpam-6075	198	16	)	)	PUNCT
ejpam-6075	198	17	=	=	SYM
ejpam-6075	199	1	n	n	X
ejpam-6075	199	2	theorem	theorem	NOUN
ejpam-6075	199	3	3	3	X
ejpam-6075	199	4	.	.	PUNCT
ejpam-6075	200	1	let	let	VERB
ejpam-6075	200	2	g	g	NOUN
ejpam-6075	200	3	be	be	AUX
ejpam-6075	200	4	any	any	DET
ejpam-6075	200	5	graph	graph	NOUN
ejpam-6075	200	6	and	and	CCONJ
ejpam-6075	200	7	let	let	VERB
ejpam-6075	200	8	s	s	PRON
ejpam-6075	200	9	be	be	AUX
ejpam-6075	200	10	a	a	DET
ejpam-6075	200	11	hop	hop	NOUN
ejpam-6075	200	12	dominating	dominating	NOUN
ejpam-6075	200	13	set	set	VERB
ejpam-6075	200	14	in	in	ADP
ejpam-6075	200	15	g.	g.	PROPN
ejpam-6075	201	1	then	then	ADV
ejpam-6075	201	2	s	s	VERB
ejpam-6075	201	3	is	be	AUX
ejpam-6075	201	4	a	a	DET
ejpam-6075	201	5	secure	secure	ADJ
ejpam-6075	201	6	hop	hop	NOUN
ejpam-6075	201	7	dominating	dominating	NOUN
ejpam-6075	201	8	set	set	VERB
ejpam-6075	201	9	in	in	ADP
ejpam-6075	201	10	g	g	PROPN
ejpam-6075	201	11	if	if	SCONJ
ejpam-6075	201	12	and	and	CCONJ
ejpam-6075	201	13	only	only	ADV
ejpam-6075	201	14	if	if	SCONJ
ejpam-6075	201	15	for	for	ADP
ejpam-6075	201	16	each	each	PRON
ejpam-6075	201	17	v	v	NUM
ejpam-6075	201	18	∈	∈	PROPN
ejpam-6075	201	19	v	v	NOUN
ejpam-6075	201	20	(	(	PUNCT
ejpam-6075	201	21	g	g	NOUN
ejpam-6075	201	22	)	)	PUNCT
ejpam-6075	201	23	\	\	PROPN
ejpam-6075	202	1	s	s	VERB
ejpam-6075	203	1	there	there	PRON
ejpam-6075	203	2	exists	exist	VERB
ejpam-6075	203	3	w	w	PROPN
ejpam-6075	203	4	∈	∈	PROPN
ejpam-6075	203	5	s	s	PART
ejpam-6075	203	6	∩n2	∩n2	PROPN
ejpam-6075	203	7	g(v	g(v	PROPN
ejpam-6075	203	8	)	)	PUNCT
ejpam-6075	203	9	such	such	ADJ
ejpam-6075	203	10	that	that	DET
ejpam-6075	203	11	ephn(w;s	ephn(w;s	NOUN
ejpam-6075	203	12	)	)	PUNCT
ejpam-6075	203	13	⊆	⊆	NUM
ejpam-6075	203	14	n2	n2	ADJ
ejpam-6075	203	15	g[v	g[v	PROPN
ejpam-6075	203	16	]	]	PUNCT
ejpam-6075	203	17	.	.	PUNCT
ejpam-6075	204	1	proof	proof	NOUN
ejpam-6075	204	2	.	.	PUNCT
ejpam-6075	205	1	suppose	suppose	VERB
ejpam-6075	205	2	s	s	PRON
ejpam-6075	205	3	is	be	AUX
ejpam-6075	205	4	a	a	DET
ejpam-6075	205	5	secure	secure	ADJ
ejpam-6075	205	6	hop	hop	NOUN
ejpam-6075	205	7	dominating	dominating	NOUN
ejpam-6075	205	8	set	set	VERB
ejpam-6075	205	9	in	in	ADP
ejpam-6075	205	10	g.	g.	PROPN
ejpam-6075	205	11	let	let	VERB
ejpam-6075	205	12	v	v	NUM
ejpam-6075	205	13	∈	∈	PROPN
ejpam-6075	205	14	v	v	NOUN
ejpam-6075	205	15	(	(	PUNCT
ejpam-6075	205	16	g	g	NOUN
ejpam-6075	205	17	)	)	PUNCT
ejpam-6075	205	18	\	\	PUNCT
ejpam-6075	206	1	s.	s.	PROPN
ejpam-6075	206	2	since	since	SCONJ
ejpam-6075	206	3	s	s	PROPN
ejpam-6075	206	4	is	be	AUX
ejpam-6075	206	5	secure	secure	ADJ
ejpam-6075	206	6	hop	hop	NOUN
ejpam-6075	206	7	dominating	dominating	NOUN
ejpam-6075	206	8	,	,	PUNCT
ejpam-6075	206	9	there	there	PRON
ejpam-6075	206	10	exists	exist	VERB
ejpam-6075	206	11	w	w	PROPN
ejpam-6075	206	12	∈	∈	PROPN
ejpam-6075	206	13	s	s	PART
ejpam-6075	206	14	∩n2	∩n2	PROPN
ejpam-6075	206	15	g(v	g(v	PROPN
ejpam-6075	206	16	)	)	PUNCT
ejpam-6075	206	17	such	such	ADJ
ejpam-6075	206	18	that	that	PRON
ejpam-6075	206	19	sv	sv	PROPN
ejpam-6075	207	1	=	=	PUNCT
ejpam-6075	207	2	(	(	PUNCT
ejpam-6075	207	3	s	s	NOUN
ejpam-6075	207	4	\	\	X
ejpam-6075	207	5	{	{	PUNCT
ejpam-6075	207	6	w	w	NOUN
ejpam-6075	207	7	}	}	PUNCT
ejpam-6075	207	8	)	)	PUNCT
ejpam-6075	207	9	∪	∪	ADP
ejpam-6075	207	10	{	{	PUNCT
ejpam-6075	207	11	v	v	NOUN
ejpam-6075	207	12	}	}	PUNCT
ejpam-6075	207	13	is	be	AUX
ejpam-6075	207	14	hop	hop	NOUN
ejpam-6075	207	15	dominating	dominating	NOUN
ejpam-6075	207	16	.	.	PUNCT
ejpam-6075	208	1	let	let	VERB
ejpam-6075	208	2	z	z	NOUN
ejpam-6075	208	3	∈	∈	PROPN
ejpam-6075	208	4	ephn(w;s	ephn(w;s	PROPN
ejpam-6075	208	5	)	)	PUNCT
ejpam-6075	208	6	.	.	PUNCT
ejpam-6075	209	1	then	then	ADV
ejpam-6075	209	2	n2	n2	PROPN
ejpam-6075	209	3	g(z	g(z	PROPN
ejpam-6075	209	4	)	)	PUNCT
ejpam-6075	209	5	∩	∩	NOUN
ejpam-6075	209	6	s	s	PART
ejpam-6075	209	7	=	=	X
ejpam-6075	209	8	{	{	PUNCT
ejpam-6075	209	9	w	w	NOUN
ejpam-6075	209	10	}	}	PUNCT
ejpam-6075	209	11	.	.	PUNCT
ejpam-6075	210	1	since	since	SCONJ
ejpam-6075	210	2	sv	sv	PROPN
ejpam-6075	210	3	is	be	AUX
ejpam-6075	210	4	a	a	DET
ejpam-6075	210	5	hop	hop	NOUN
ejpam-6075	210	6	dominating	dominating	NOUN
ejpam-6075	210	7	set	set	NOUN
ejpam-6075	210	8	,	,	PUNCT
ejpam-6075	210	9	it	it	PRON
ejpam-6075	210	10	follows	follow	VERB
ejpam-6075	210	11	that	that	SCONJ
ejpam-6075	210	12	z	z	PROPN
ejpam-6075	210	13	∈	∈	PROPN
ejpam-6075	210	14	n2	n2	PROPN
ejpam-6075	210	15	g[v	g[v	PROPN
ejpam-6075	210	16	]	]	PUNCT
ejpam-6075	210	17	.	.	PUNCT
ejpam-6075	211	1	thus	thus	ADV
ejpam-6075	211	2	,	,	PUNCT
ejpam-6075	211	3	ephn(w;s	ephn(w;s	PROPN
ejpam-6075	211	4	)	)	PUNCT
ejpam-6075	211	5	⊆	⊆	NUM
ejpam-6075	211	6	n2	n2	ADJ
ejpam-6075	211	7	g[v	g[v	PROPN
ejpam-6075	211	8	]	]	PUNCT
ejpam-6075	211	9	.	.	PUNCT
ejpam-6075	212	1	for	for	ADP
ejpam-6075	212	2	the	the	DET
ejpam-6075	212	3	converse	converse	NOUN
ejpam-6075	212	4	,	,	PUNCT
ejpam-6075	212	5	suppose	suppose	VERB
ejpam-6075	212	6	that	that	SCONJ
ejpam-6075	212	7	the	the	DET
ejpam-6075	212	8	given	give	VERB
ejpam-6075	212	9	property	property	NOUN
ejpam-6075	212	10	holds	hold	NOUN
ejpam-6075	212	11	.	.	PUNCT
ejpam-6075	213	1	let	let	VERB
ejpam-6075	213	2	p	p	PRON
ejpam-6075	213	3	∈	∈	PROPN
ejpam-6075	213	4	v	v	ADP
ejpam-6075	213	5	(	(	PUNCT
ejpam-6075	213	6	g	g	NOUN
ejpam-6075	213	7	)	)	PUNCT
ejpam-6075	213	8	\	\	PUNCT
ejpam-6075	214	1	s.	s.	PROPN
ejpam-6075	214	2	then	then	ADV
ejpam-6075	214	3	by	by	ADP
ejpam-6075	214	4	assumption	assumption	NOUN
ejpam-6075	214	5	,	,	PUNCT
ejpam-6075	214	6	there	there	PRON
ejpam-6075	214	7	exists	exist	VERB
ejpam-6075	214	8	q	q	PROPN
ejpam-6075	214	9	∈	∈	PROPN
ejpam-6075	214	10	s	s	PART
ejpam-6075	214	11	∩	∩	ADJ
ejpam-6075	214	12	n2	n2	ADJ
ejpam-6075	214	13	g(p	g(p	PROPN
ejpam-6075	214	14	)	)	PUNCT
ejpam-6075	214	15	such	such	ADJ
ejpam-6075	214	16	that	that	SCONJ
ejpam-6075	214	17	ephn(q;s	ephn(q;	NOUN
ejpam-6075	214	18	)	)	PUNCT
ejpam-6075	214	19	⊆	⊆	NUM
ejpam-6075	214	20	n2	n2	NOUN
ejpam-6075	214	21	g[p	g[p	PROPN
ejpam-6075	214	22	]	]	PUNCT
ejpam-6075	214	23	.	.	PUNCT
ejpam-6075	215	1	let	let	VERB
ejpam-6075	215	2	sp	sp	ADP
ejpam-6075	215	3	=	=	PROPN
ejpam-6075	215	4	f.	f.	PROPN
ejpam-6075	215	5	l.	l.	PROPN
ejpam-6075	215	6	alfeche	alfeche	PROPN
ejpam-6075	215	7	,	,	PUNCT
ejpam-6075	215	8	g.	g.	PROPN
ejpam-6075	215	9	a.	a.	PROPN
ejpam-6075	215	10	malacas	malacas	PROPN
ejpam-6075	215	11	,	,	PUNCT
ejpam-6075	215	12	s.	s.	PROPN
ejpam-6075	215	13	canoy	canoy	PROPN
ejpam-6075	215	14	jr	jr	PROPN
ejpam-6075	215	15	.	.	PROPN
ejpam-6075	215	16	/	/	SYM
ejpam-6075	215	17	eur	eur	PROPN
ejpam-6075	215	18	.	.	PUNCT
ejpam-6075	216	1	j.	j.	PROPN
ejpam-6075	216	2	pure	pure	PROPN
ejpam-6075	216	3	appl	appl	PROPN
ejpam-6075	216	4	.	.	PROPN
ejpam-6075	216	5	math	math	PROPN
ejpam-6075	216	6	,	,	PUNCT
ejpam-6075	216	7	18	18	NUM
ejpam-6075	216	8	(	(	PUNCT
ejpam-6075	216	9	2	2	NUM
ejpam-6075	216	10	)	)	PUNCT
ejpam-6075	216	11	(	(	PUNCT
ejpam-6075	216	12	2025	2025	NUM
ejpam-6075	216	13	)	)	PUNCT
ejpam-6075	216	14	,	,	PUNCT
ejpam-6075	216	15	6075	6075	NUM
ejpam-6075	216	16	5	5	NUM
ejpam-6075	216	17	of	of	ADP
ejpam-6075	216	18	14	14	NUM
ejpam-6075	216	19	(	(	PUNCT
ejpam-6075	216	20	s	s	NOUN
ejpam-6075	216	21	\	\	X
ejpam-6075	216	22	{	{	PUNCT
ejpam-6075	216	23	q	q	NOUN
ejpam-6075	216	24	}	}	PUNCT
ejpam-6075	216	25	)	)	PUNCT
ejpam-6075	216	26	∪	∪	ADP
ejpam-6075	216	27	{	{	PUNCT
ejpam-6075	216	28	p	p	NOUN
ejpam-6075	216	29	}	}	PUNCT
ejpam-6075	216	30	and	and	CCONJ
ejpam-6075	216	31	let	let	VERB
ejpam-6075	216	32	x	x	SYM
ejpam-6075	216	33	∈	∈	PROPN
ejpam-6075	216	34	v	v	X
ejpam-6075	216	35	(	(	PUNCT
ejpam-6075	216	36	g	g	NOUN
ejpam-6075	216	37	)	)	PUNCT
ejpam-6075	216	38	\	\	PUNCT
ejpam-6075	217	1	s.	s.	PROPN
ejpam-6075	217	2	if	if	SCONJ
ejpam-6075	217	3	x	x	PROPN
ejpam-6075	217	4	=	=	SYM
ejpam-6075	217	5	q	q	ADJ
ejpam-6075	217	6	,	,	PUNCT
ejpam-6075	217	7	then	then	ADV
ejpam-6075	217	8	q	q	PROPN
ejpam-6075	217	9	∈	∈	PROPN
ejpam-6075	217	10	n2	n2	NOUN
ejpam-6075	217	11	g(p	g(p	PROPN
ejpam-6075	217	12	)	)	PUNCT
ejpam-6075	217	13	⊆	⊆	NUM
ejpam-6075	217	14	n2	n2	ADJ
ejpam-6075	217	15	g[sp	g[sp	PROPN
ejpam-6075	217	16	]	]	PUNCT
ejpam-6075	217	17	.	.	PUNCT
ejpam-6075	217	18	suppose	suppose	VERB
ejpam-6075	217	19	x	x	PUNCT
ejpam-6075	217	20	̸=	̸=	PROPN
ejpam-6075	217	21	q.	q.	VERB
ejpam-6075	217	22	if	if	SCONJ
ejpam-6075	217	23	x	x	X
ejpam-6075	217	24	/∈	/∈	PUNCT
ejpam-6075	217	25	ephn(q;s	ephn(q;	NOUN
ejpam-6075	217	26	)	)	PUNCT
ejpam-6075	217	27	,	,	PUNCT
ejpam-6075	217	28	then	then	ADV
ejpam-6075	217	29	there	there	PRON
ejpam-6075	217	30	exists	exist	VERB
ejpam-6075	217	31	y	y	PROPN
ejpam-6075	217	32	∈	∈	PROPN
ejpam-6075	217	33	(	(	PUNCT
ejpam-6075	217	34	s	s	NOUN
ejpam-6075	217	35	\	\	X
ejpam-6075	217	36	{	{	PUNCT
ejpam-6075	217	37	q	q	NOUN
ejpam-6075	217	38	}	}	PUNCT
ejpam-6075	217	39	)	)	PUNCT
ejpam-6075	217	40	∩	∩	NOUN
ejpam-6075	217	41	n2	n2	ADJ
ejpam-6075	217	42	g(x	g(x	NOUN
ejpam-6075	217	43	)	)	PUNCT
ejpam-6075	217	44	since	since	SCONJ
ejpam-6075	217	45	s	s	NOUN
ejpam-6075	217	46	is	be	AUX
ejpam-6075	217	47	a	a	DET
ejpam-6075	217	48	hop	hop	NOUN
ejpam-6075	217	49	dominating	dominating	NOUN
ejpam-6075	217	50	set	set	VERB
ejpam-6075	217	51	in	in	ADP
ejpam-6075	217	52	g.	g.	PROPN
ejpam-6075	217	53	hence	hence	ADV
ejpam-6075	217	54	,	,	PUNCT
ejpam-6075	217	55	x	x	SYM
ejpam-6075	217	56	∈	∈	PROPN
ejpam-6075	217	57	n2	n2	PROPN
ejpam-6075	217	58	g(y	g(y	PROPN
ejpam-6075	217	59	)	)	PUNCT
ejpam-6075	217	60	⊆	⊆	NUM
ejpam-6075	217	61	n2	n2	ADJ
ejpam-6075	217	62	g[sp	g[sp	PROPN
ejpam-6075	217	63	]	]	X
ejpam-6075	217	64	.	.	PUNCT
ejpam-6075	218	1	next	next	ADV
ejpam-6075	218	2	,	,	PUNCT
ejpam-6075	218	3	suppose	suppose	VERB
ejpam-6075	218	4	that	that	SCONJ
ejpam-6075	218	5	x	x	PROPN
ejpam-6075	218	6	∈	∈	PROPN
ejpam-6075	218	7	ephn(q;s	ephn(q;	NOUN
ejpam-6075	218	8	)	)	PUNCT
ejpam-6075	218	9	.	.	PUNCT
ejpam-6075	219	1	then	then	ADV
ejpam-6075	219	2	by	by	ADP
ejpam-6075	219	3	assumption	assumption	NOUN
ejpam-6075	219	4	,	,	PUNCT
ejpam-6075	219	5	x	x	SYM
ejpam-6075	219	6	∈	∈	PROPN
ejpam-6075	219	7	n2	n2	NOUN
ejpam-6075	219	8	g[p	g[p	PROPN
ejpam-6075	219	9	]	]	X
ejpam-6075	219	10	⊆	⊆	NUM
ejpam-6075	219	11	n2	n2	ADJ
ejpam-6075	219	12	g[sp	g[sp	PROPN
ejpam-6075	219	13	]	]	X
ejpam-6075	219	14	.	.	PUNCT
ejpam-6075	220	1	therefore	therefore	ADV
ejpam-6075	220	2	,	,	PUNCT
ejpam-6075	220	3	sp	sp	ADP
ejpam-6075	220	4	is	be	AUX
ejpam-6075	220	5	a	a	DET
ejpam-6075	220	6	hop	hop	NOUN
ejpam-6075	220	7	dominating	dominating	NOUN
ejpam-6075	220	8	set	set	VERB
ejpam-6075	220	9	in	in	ADP
ejpam-6075	220	10	g.	g.	PROPN
ejpam-6075	220	11	since	since	SCONJ
ejpam-6075	220	12	p	p	PROPN
ejpam-6075	220	13	was	be	AUX
ejpam-6075	220	14	arbitrarily	arbitrarily	ADV
ejpam-6075	220	15	chosen	choose	VERB
ejpam-6075	220	16	,	,	PUNCT
ejpam-6075	220	17	it	it	PRON
ejpam-6075	220	18	follows	follow	VERB
ejpam-6075	220	19	that	that	SCONJ
ejpam-6075	220	20	s	s	VERB
ejpam-6075	220	21	is	be	AUX
ejpam-6075	220	22	a	a	DET
ejpam-6075	220	23	secure	secure	ADJ
ejpam-6075	220	24	hop	hop	NOUN
ejpam-6075	220	25	dominating	dominating	NOUN
ejpam-6075	220	26	in	in	ADP
ejpam-6075	220	27	g.	g.	PROPN
ejpam-6075	220	28	corollary	corollary	NOUN
ejpam-6075	221	1	1	1	PROPN
ejpam-6075	221	2	.	.	PUNCT
ejpam-6075	222	1	let	let	VERB
ejpam-6075	222	2	g	g	PRON
ejpam-6075	222	3	be	be	AUX
ejpam-6075	222	4	a	a	DET
ejpam-6075	222	5	non	non	ADJ
ejpam-6075	222	6	-	-	ADJ
ejpam-6075	222	7	trivial	trivial	ADJ
ejpam-6075	222	8	graph	graph	NOUN
ejpam-6075	222	9	and	and	CCONJ
ejpam-6075	222	10	let	let	VERB
ejpam-6075	222	11	s	s	PRON
ejpam-6075	222	12	be	be	AUX
ejpam-6075	222	13	a	a	DET
ejpam-6075	222	14	hop	hop	NOUN
ejpam-6075	222	15	dominating	dominating	NOUN
ejpam-6075	222	16	set	set	VERB
ejpam-6075	222	17	in	in	ADP
ejpam-6075	222	18	g.	g.	PROPN
ejpam-6075	222	19	if	if	SCONJ
ejpam-6075	222	20	for	for	ADP
ejpam-6075	222	21	each	each	PRON
ejpam-6075	222	22	v	v	NUM
ejpam-6075	222	23	∈	∈	PROPN
ejpam-6075	222	24	v	v	NOUN
ejpam-6075	222	25	(	(	PUNCT
ejpam-6075	222	26	g	g	NOUN
ejpam-6075	222	27	)	)	PUNCT
ejpam-6075	222	28	\	\	PROPN
ejpam-6075	223	1	s	s	VERB
ejpam-6075	223	2	there	there	PRON
ejpam-6075	223	3	exists	exist	VERB
ejpam-6075	223	4	w	w	PROPN
ejpam-6075	223	5	∈	∈	PROPN
ejpam-6075	223	6	s	s	PART
ejpam-6075	223	7	∩n2	∩n2	NOUN
ejpam-6075	223	8	g(v	g(v	PROPN
ejpam-6075	223	9	)	)	PUNCT
ejpam-6075	223	10	with	with	ADP
ejpam-6075	223	11	|ephn(w;s)|	|ephn(w;s)|	NOUN
ejpam-6075	223	12	=	=	SYM
ejpam-6075	223	13	0	0	NUM
ejpam-6075	223	14	or	or	CCONJ
ejpam-6075	223	15	|ephn(w;s)|	|ephn(w;s)|	PRON
ejpam-6075	223	16	≥	≥	NOUN
ejpam-6075	223	17	1	1	NUM
ejpam-6075	223	18	such	such	ADJ
ejpam-6075	223	19	that	that	PRON
ejpam-6075	223	20	dg(v	dg(v	NOUN
ejpam-6075	223	21	,	,	PUNCT
ejpam-6075	223	22	p	p	NOUN
ejpam-6075	223	23	)	)	PUNCT
ejpam-6075	223	24	=	=	SYM
ejpam-6075	223	25	2	2	NUM
ejpam-6075	223	26	for	for	ADP
ejpam-6075	223	27	all	all	PRON
ejpam-6075	223	28	p	p	NOUN
ejpam-6075	223	29	∈	∈	PROPN
ejpam-6075	223	30	ephn(w;s	ephn(w;s	NOUN
ejpam-6075	223	31	)	)	PUNCT
ejpam-6075	223	32	\	\	NOUN
ejpam-6075	223	33	{	{	PUNCT
ejpam-6075	223	34	v	v	NOUN
ejpam-6075	223	35	}	}	PUNCT
ejpam-6075	223	36	,	,	PUNCT
ejpam-6075	223	37	then	then	ADV
ejpam-6075	223	38	s	s	VERB
ejpam-6075	223	39	is	be	AUX
ejpam-6075	223	40	a	a	DET
ejpam-6075	223	41	secure	secure	ADJ
ejpam-6075	223	42	hop	hop	NOUN
ejpam-6075	223	43	dominating	dominating	NOUN
ejpam-6075	223	44	set	set	VERB
ejpam-6075	223	45	in	in	ADP
ejpam-6075	223	46	g.	g.	PROPN
ejpam-6075	223	47	proof	proof	PROPN
ejpam-6075	223	48	.	.	PUNCT
ejpam-6075	224	1	suppose	suppose	VERB
ejpam-6075	224	2	s	s	PRON
ejpam-6075	224	3	satisfies	satisfie	NOUN
ejpam-6075	224	4	the	the	DET
ejpam-6075	224	5	given	give	VERB
ejpam-6075	224	6	property	property	NOUN
ejpam-6075	224	7	.	.	PUNCT
ejpam-6075	225	1	let	let	VERB
ejpam-6075	225	2	v	v	NUM
ejpam-6075	225	3	∈	∈	NOUN
ejpam-6075	225	4	v	v	NOUN
ejpam-6075	225	5	(	(	PUNCT
ejpam-6075	225	6	g)\s	g)\s	NOUN
ejpam-6075	225	7	.	.	PUNCT
ejpam-6075	226	1	by	by	ADP
ejpam-6075	226	2	assumption	assumption	NOUN
ejpam-6075	226	3	,	,	PUNCT
ejpam-6075	226	4	there	there	PRON
ejpam-6075	226	5	exists	exist	VERB
ejpam-6075	226	6	w	w	PROPN
ejpam-6075	226	7	∈	∈	PROPN
ejpam-6075	226	8	s	s	PART
ejpam-6075	226	9	∩	∩	ADJ
ejpam-6075	226	10	n2	n2	ADJ
ejpam-6075	226	11	g(v	g(v	X
ejpam-6075	226	12	)	)	PUNCT
ejpam-6075	226	13	satisfying	satisfy	VERB
ejpam-6075	226	14	the	the	DET
ejpam-6075	226	15	condition	condition	NOUN
ejpam-6075	226	16	.	.	PUNCT
ejpam-6075	227	1	if	if	SCONJ
ejpam-6075	227	2	|ephn(w;s)|	|ephn(w;s)|	PRON
ejpam-6075	227	3	=	=	SYM
ejpam-6075	227	4	0	0	NUM
ejpam-6075	227	5	,	,	PUNCT
ejpam-6075	227	6	then	then	ADV
ejpam-6075	227	7	ephn(w;s	ephn(w;s	PROPN
ejpam-6075	227	8	)	)	PUNCT
ejpam-6075	227	9	=	=	NOUN
ejpam-6075	227	10	∅	∅	NOUN
ejpam-6075	227	11	⊆	⊆	NUM
ejpam-6075	227	12	n2	n2	ADJ
ejpam-6075	227	13	g[v	g[v	NOUN
ejpam-6075	227	14	]	]	PUNCT
ejpam-6075	227	15	.	.	PUNCT
ejpam-6075	228	1	suppose	suppose	VERB
ejpam-6075	228	2	|ephn(w;s)|	|ephn(w;s)|	PRON
ejpam-6075	228	3	≥	≥	NOUN
ejpam-6075	228	4	1	1	NUM
ejpam-6075	228	5	.	.	PUNCT
ejpam-6075	229	1	then	then	ADV
ejpam-6075	229	2	dg(v	dg(v	PUNCT
ejpam-6075	229	3	,	,	PUNCT
ejpam-6075	229	4	p	p	NOUN
ejpam-6075	229	5	)	)	PUNCT
ejpam-6075	229	6	=	=	SYM
ejpam-6075	229	7	2	2	NUM
ejpam-6075	229	8	for	for	ADP
ejpam-6075	229	9	all	all	PRON
ejpam-6075	229	10	p	p	NOUN
ejpam-6075	229	11	∈	∈	PROPN
ejpam-6075	229	12	ephn(w;s	ephn(w;s	NOUN
ejpam-6075	229	13	)	)	PUNCT
ejpam-6075	229	14	\	\	NOUN
ejpam-6075	229	15	{	{	PUNCT
ejpam-6075	229	16	v	v	NOUN
ejpam-6075	229	17	}	}	PUNCT
ejpam-6075	229	18	by	by	ADP
ejpam-6075	229	19	assumption	assumption	NOUN
ejpam-6075	229	20	.	.	PUNCT
ejpam-6075	230	1	thus	thus	ADV
ejpam-6075	230	2	,	,	PUNCT
ejpam-6075	230	3	ephn(w;s	ephn(w;s	PROPN
ejpam-6075	230	4	)	)	PUNCT
ejpam-6075	230	5	⊆	⊆	NUM
ejpam-6075	230	6	n2	n2	ADJ
ejpam-6075	230	7	g[v	g[v	PROPN
ejpam-6075	230	8	]	]	PUNCT
ejpam-6075	230	9	.	.	PUNCT
ejpam-6075	231	1	therefore	therefore	ADV
ejpam-6075	231	2	,	,	PUNCT
ejpam-6075	231	3	s	s	VERB
ejpam-6075	231	4	is	be	AUX
ejpam-6075	231	5	a	a	DET
ejpam-6075	231	6	secure	secure	ADJ
ejpam-6075	231	7	hop	hop	NOUN
ejpam-6075	231	8	dominating	dominating	NOUN
ejpam-6075	231	9	set	set	VERB
ejpam-6075	231	10	by	by	ADP
ejpam-6075	231	11	theorem	theorem	NOUN
ejpam-6075	231	12	3	3	NUM
ejpam-6075	231	13	.	.	PUNCT
ejpam-6075	231	14	theorem	theorem	NOUN
ejpam-6075	231	15	4	4	NUM
ejpam-6075	231	16	.	.	PUNCT
ejpam-6075	231	17	γsh(kn	γsh(kn	NOUN
ejpam-6075	231	18	)	)	PUNCT
ejpam-6075	232	1	=	=	SYM
ejpam-6075	232	2	γsh(kn	γsh(kn	NOUN
ejpam-6075	232	3	)	)	PUNCT
ejpam-6075	232	4	=	=	SYM
ejpam-6075	233	1	n	n	CCONJ
ejpam-6075	233	2	for	for	ADP
ejpam-6075	233	3	every	every	DET
ejpam-6075	233	4	positive	positive	ADJ
ejpam-6075	233	5	integer	integer	NOUN
ejpam-6075	233	6	n.	n.	NOUN
ejpam-6075	233	7	proof	proof	NOUN
ejpam-6075	233	8	.	.	PUNCT
ejpam-6075	234	1	let	let	VERB
ejpam-6075	234	2	g	g	PROPN
ejpam-6075	234	3	∈	∈	PROPN
ejpam-6075	234	4	{	{	PUNCT
ejpam-6075	234	5	kn	kn	PROPN
ejpam-6075	234	6	,	,	PUNCT
ejpam-6075	234	7	kn	kn	PROPN
ejpam-6075	234	8	}	}	PUNCT
ejpam-6075	234	9	.	.	PUNCT
ejpam-6075	235	1	since	since	SCONJ
ejpam-6075	235	2	the	the	DET
ejpam-6075	235	3	only	only	ADJ
ejpam-6075	235	4	hop	hop	NOUN
ejpam-6075	235	5	dominating	dominating	NOUN
ejpam-6075	235	6	set	set	NOUN
ejpam-6075	235	7	in	in	ADP
ejpam-6075	235	8	g	g	PROPN
ejpam-6075	235	9	is	be	AUX
ejpam-6075	235	10	v	v	NOUN
ejpam-6075	235	11	(	(	PUNCT
ejpam-6075	235	12	g	g	NOUN
ejpam-6075	235	13	)	)	PUNCT
ejpam-6075	235	14	,	,	PUNCT
ejpam-6075	235	15	it	it	PRON
ejpam-6075	235	16	follows	follow	VERB
ejpam-6075	235	17	that	that	SCONJ
ejpam-6075	235	18	v	v	X
ejpam-6075	235	19	(	(	PUNCT
ejpam-6075	235	20	g	g	NOUN
ejpam-6075	235	21	)	)	PUNCT
ejpam-6075	235	22	is	be	AUX
ejpam-6075	235	23	the	the	DET
ejpam-6075	235	24	only	only	ADJ
ejpam-6075	235	25	secure	secure	ADJ
ejpam-6075	235	26	hop	hop	NOUN
ejpam-6075	235	27	dominating	dominating	NOUN
ejpam-6075	235	28	.	.	PUNCT
ejpam-6075	236	1	therefore	therefore	ADV
ejpam-6075	236	2	,	,	PUNCT
ejpam-6075	236	3	γsh(g	γsh(g	ADV
ejpam-6075	236	4	)	)	PUNCT
ejpam-6075	236	5	=	=	SYM
ejpam-6075	236	6	n.	n.	NOUN
ejpam-6075	236	7	lemma	lemma	PROPN
ejpam-6075	236	8	1	1	X
ejpam-6075	236	9	.	.	PUNCT
ejpam-6075	237	1	let	let	VERB
ejpam-6075	237	2	g	g	PRON
ejpam-6075	237	3	be	be	AUX
ejpam-6075	237	4	a	a	DET
ejpam-6075	237	5	non	non	ADJ
ejpam-6075	237	6	-	-	ADJ
ejpam-6075	237	7	trivial	trivial	ADJ
ejpam-6075	237	8	graph	graph	NOUN
ejpam-6075	237	9	and	and	CCONJ
ejpam-6075	237	10	let	let	VERB
ejpam-6075	237	11	s	s	PRON
ejpam-6075	237	12	=	=	PUNCT
ejpam-6075	237	13	{	{	PUNCT
ejpam-6075	237	14	p	p	X
ejpam-6075	237	15	,	,	PUNCT
ejpam-6075	237	16	q	q	AUX
ejpam-6075	237	17	}	}	PUNCT
ejpam-6075	237	18	be	be	AUX
ejpam-6075	237	19	a	a	DET
ejpam-6075	237	20	hop	hop	NOUN
ejpam-6075	237	21	dominating	dominating	NOUN
ejpam-6075	237	22	set	set	VERB
ejpam-6075	237	23	in	in	ADP
ejpam-6075	237	24	g.	g.	PROPN
ejpam-6075	237	25	then	then	ADV
ejpam-6075	237	26	ephn(p;s	ephn(p;s	NOUN
ejpam-6075	237	27	)	)	PUNCT
ejpam-6075	238	1	=	=	SYM
ejpam-6075	238	2	v	v	X
ejpam-6075	238	3	(	(	PUNCT
ejpam-6075	238	4	g	g	NOUN
ejpam-6075	238	5	)	)	PUNCT
ejpam-6075	238	6	\	\	PUNCT
ejpam-6075	238	7	(	(	PUNCT
ejpam-6075	238	8	n2	n2	ADJ
ejpam-6075	238	9	g[q	g[q	NOUN
ejpam-6075	238	10	]	]	PUNCT
ejpam-6075	238	11	∪	∪	X
ejpam-6075	238	12	{	{	PUNCT
ejpam-6075	238	13	p	p	NOUN
ejpam-6075	238	14	}	}	PUNCT
ejpam-6075	238	15	)	)	PUNCT
ejpam-6075	238	16	and	and	CCONJ
ejpam-6075	238	17	ephn(q;s	ephn(q;	NOUN
ejpam-6075	238	18	)	)	PUNCT
ejpam-6075	239	1	=	=	SYM
ejpam-6075	239	2	v	v	X
ejpam-6075	239	3	(	(	PUNCT
ejpam-6075	239	4	g	g	NOUN
ejpam-6075	239	5	)	)	PUNCT
ejpam-6075	239	6	\	\	PUNCT
ejpam-6075	239	7	(	(	PUNCT
ejpam-6075	239	8	n2	n2	NOUN
ejpam-6075	239	9	g[p	g[p	PROPN
ejpam-6075	239	10	]	]	PUNCT
ejpam-6075	239	11	∪	∪	X
ejpam-6075	239	12	{	{	PUNCT
ejpam-6075	239	13	q	q	NOUN
ejpam-6075	239	14	}	}	PUNCT
ejpam-6075	239	15	)	)	PUNCT
ejpam-6075	239	16	.	.	PUNCT
ejpam-6075	240	1	proof	proof	NOUN
ejpam-6075	240	2	.	.	PUNCT
ejpam-6075	241	1	note	note	VERB
ejpam-6075	241	2	that	that	SCONJ
ejpam-6075	241	3	since	since	SCONJ
ejpam-6075	241	4	s	s	NOUN
ejpam-6075	241	5	is	be	AUX
ejpam-6075	241	6	hop	hop	NOUN
ejpam-6075	241	7	dominating	dominating	NOUN
ejpam-6075	241	8	,	,	PUNCT
ejpam-6075	241	9	dg(p	dg(p	NOUN
ejpam-6075	241	10	,	,	PUNCT
ejpam-6075	241	11	q	q	X
ejpam-6075	241	12	)	)	PUNCT
ejpam-6075	241	13	̸=	̸=	PROPN
ejpam-6075	241	14	2	2	NUM
ejpam-6075	241	15	.	.	PUNCT
ejpam-6075	242	1	let	let	VERB
ejpam-6075	242	2	x	x	PUNCT
ejpam-6075	242	3	∈	∈	PROPN
ejpam-6075	242	4	ephn(p;s	ephn(p;s	NOUN
ejpam-6075	242	5	)	)	PUNCT
ejpam-6075	242	6	.	.	PUNCT
ejpam-6075	243	1	then	then	ADV
ejpam-6075	243	2	x	x	SYM
ejpam-6075	243	3	∈	∈	PROPN
ejpam-6075	243	4	v	v	ADP
ejpam-6075	243	5	(	(	PUNCT
ejpam-6075	243	6	g	g	NOUN
ejpam-6075	243	7	)	)	PUNCT
ejpam-6075	243	8	\	\	PROPN
ejpam-6075	243	9	s	s	PROPN
ejpam-6075	243	10	and	and	CCONJ
ejpam-6075	243	11	n2	n2	ADJ
ejpam-6075	243	12	g(x	g(x	NOUN
ejpam-6075	243	13	)	)	PUNCT
ejpam-6075	243	14	∩	∩	NOUN
ejpam-6075	243	15	s	s	PART
ejpam-6075	243	16	=	=	X
ejpam-6075	243	17	{	{	PUNCT
ejpam-6075	243	18	p	p	X
ejpam-6075	243	19	}	}	PUNCT
ejpam-6075	243	20	.	.	PUNCT
ejpam-6075	244	1	it	it	PRON
ejpam-6075	244	2	follows	follow	VERB
ejpam-6075	244	3	that	that	SCONJ
ejpam-6075	244	4	x	x	PUNCT
ejpam-6075	244	5	∈	∈	NOUN
ejpam-6075	244	6	v	v	ADP
ejpam-6075	244	7	(	(	PUNCT
ejpam-6075	244	8	g	g	NOUN
ejpam-6075	244	9	)	)	PUNCT
ejpam-6075	244	10	\	\	PUNCT
ejpam-6075	245	1	(	(	PUNCT
ejpam-6075	245	2	n2	n2	ADJ
ejpam-6075	245	3	g[q	g[q	NOUN
ejpam-6075	245	4	]	]	PUNCT
ejpam-6075	245	5	∪	∪	X
ejpam-6075	245	6	{	{	PUNCT
ejpam-6075	245	7	p	p	NOUN
ejpam-6075	245	8	}	}	PUNCT
ejpam-6075	245	9	)	)	PUNCT
ejpam-6075	245	10	.	.	PUNCT
ejpam-6075	246	1	hence	hence	ADV
ejpam-6075	246	2	,	,	PUNCT
ejpam-6075	246	3	ephn(p;s	ephn(p;s	NOUN
ejpam-6075	246	4	)	)	PUNCT
ejpam-6075	246	5	⊆	⊆	NUM
ejpam-6075	246	6	v	v	NOUN
ejpam-6075	246	7	(	(	PUNCT
ejpam-6075	246	8	g	g	NOUN
ejpam-6075	246	9	)	)	PUNCT
ejpam-6075	246	10	\	\	PUNCT
ejpam-6075	247	1	(	(	PUNCT
ejpam-6075	247	2	n2	n2	ADJ
ejpam-6075	247	3	g[q	g[q	NOUN
ejpam-6075	247	4	]	]	PUNCT
ejpam-6075	247	5	∪	∪	X
ejpam-6075	247	6	{	{	PUNCT
ejpam-6075	247	7	p	p	NOUN
ejpam-6075	247	8	}	}	PUNCT
ejpam-6075	247	9	)	)	PUNCT
ejpam-6075	247	10	.	.	PUNCT
ejpam-6075	248	1	now	now	ADV
ejpam-6075	248	2	,	,	PUNCT
ejpam-6075	248	3	let	let	VERB
ejpam-6075	248	4	z	z	NOUN
ejpam-6075	248	5	∈	∈	PROPN
ejpam-6075	248	6	v	v	ADP
ejpam-6075	248	7	(	(	PUNCT
ejpam-6075	248	8	g	g	NOUN
ejpam-6075	248	9	)	)	PUNCT
ejpam-6075	248	10	\	\	PUNCT
ejpam-6075	249	1	(	(	PUNCT
ejpam-6075	249	2	n2	n2	ADJ
ejpam-6075	249	3	g[q	g[q	NOUN
ejpam-6075	249	4	]	]	PUNCT
ejpam-6075	249	5	∪	∪	X
ejpam-6075	249	6	{	{	PUNCT
ejpam-6075	249	7	p	p	NOUN
ejpam-6075	249	8	}	}	PUNCT
ejpam-6075	249	9	)	)	PUNCT
ejpam-6075	249	10	.	.	PUNCT
ejpam-6075	250	1	then	then	ADV
ejpam-6075	250	2	z	z	PROPN
ejpam-6075	250	3	̸=	̸=	PROPN
ejpam-6075	250	4	p	p	NOUN
ejpam-6075	250	5	and	and	CCONJ
ejpam-6075	250	6	z	z	NOUN
ejpam-6075	250	7	/∈	/∈	PUNCT
ejpam-6075	250	8	n2	n2	ADJ
ejpam-6075	250	9	g[q	g[q	PROPN
ejpam-6075	250	10	]	]	PUNCT
ejpam-6075	250	11	.	.	PUNCT
ejpam-6075	251	1	since	since	SCONJ
ejpam-6075	251	2	s	s	PROPN
ejpam-6075	251	3	is	be	AUX
ejpam-6075	251	4	hop	hop	NOUN
ejpam-6075	251	5	dominating	dominating	NOUN
ejpam-6075	251	6	,	,	PUNCT
ejpam-6075	251	7	it	it	PRON
ejpam-6075	251	8	follows	follow	VERB
ejpam-6075	251	9	that	that	SCONJ
ejpam-6075	251	10	z	z	PROPN
ejpam-6075	251	11	∈	∈	PROPN
ejpam-6075	251	12	n2	n2	NOUN
ejpam-6075	251	13	g(p	g(p	PROPN
ejpam-6075	251	14	)	)	PUNCT
ejpam-6075	251	15	.	.	PUNCT
ejpam-6075	252	1	this	this	PRON
ejpam-6075	252	2	implies	imply	VERB
ejpam-6075	252	3	that	that	SCONJ
ejpam-6075	252	4	z	z	PROPN
ejpam-6075	252	5	∈	∈	PROPN
ejpam-6075	252	6	ephn(p;s	ephn(p;s	NOUN
ejpam-6075	252	7	)	)	PUNCT
ejpam-6075	252	8	.	.	PUNCT
ejpam-6075	253	1	thus	thus	ADV
ejpam-6075	253	2	,	,	PUNCT
ejpam-6075	253	3	v	v	INTJ
ejpam-6075	253	4	(	(	PUNCT
ejpam-6075	253	5	g	g	NOUN
ejpam-6075	253	6	)	)	PUNCT
ejpam-6075	253	7	\	\	PUNCT
ejpam-6075	253	8	(	(	PUNCT
ejpam-6075	253	9	n2	n2	ADJ
ejpam-6075	253	10	g[q	g[q	NOUN
ejpam-6075	253	11	]	]	PUNCT
ejpam-6075	253	12	∪	∪	X
ejpam-6075	253	13	{	{	PUNCT
ejpam-6075	253	14	p	p	NOUN
ejpam-6075	253	15	}	}	PUNCT
ejpam-6075	253	16	)	)	PUNCT
ejpam-6075	253	17	⊆	⊆	NUM
ejpam-6075	253	18	ephn(p;s	ephn(p;s	NOUN
ejpam-6075	253	19	)	)	PUNCT
ejpam-6075	253	20	,	,	PUNCT
ejpam-6075	253	21	showing	show	VERB
ejpam-6075	253	22	the	the	DET
ejpam-6075	253	23	desired	desire	VERB
ejpam-6075	253	24	equality	equality	NOUN
ejpam-6075	253	25	.	.	PUNCT
ejpam-6075	254	1	similarly	similarly	ADV
ejpam-6075	254	2	,	,	PUNCT
ejpam-6075	254	3	the	the	DET
ejpam-6075	254	4	second	second	ADJ
ejpam-6075	254	5	equality	equality	NOUN
ejpam-6075	254	6	also	also	ADV
ejpam-6075	254	7	holds	hold	VERB
ejpam-6075	254	8	.	.	PUNCT
ejpam-6075	255	1	theorem	theorem	NOUN
ejpam-6075	255	2	5	5	NUM
ejpam-6075	255	3	.	.	PUNCT
ejpam-6075	256	1	let	let	VERB
ejpam-6075	256	2	g	g	NOUN
ejpam-6075	256	3	be	be	AUX
ejpam-6075	256	4	any	any	DET
ejpam-6075	256	5	graph	graph	NOUN
ejpam-6075	256	6	of	of	ADP
ejpam-6075	256	7	order	order	NOUN
ejpam-6075	256	8	n.	n.	NOUN
ejpam-6075	256	9	then	then	ADV
ejpam-6075	256	10	1	1	NUM
ejpam-6075	256	11	≤	≤	NUM
ejpam-6075	256	12	γsh(g	γsh(g	NOUN
ejpam-6075	256	13	)	)	PUNCT
ejpam-6075	256	14	≤	≤	NUM
ejpam-6075	256	15	n.	n.	NOUN
ejpam-6075	256	16	moreover	moreover	ADV
ejpam-6075	256	17	,	,	PUNCT
ejpam-6075	256	18	each	each	PRON
ejpam-6075	256	19	of	of	ADP
ejpam-6075	256	20	the	the	DET
ejpam-6075	256	21	following	following	ADJ
ejpam-6075	256	22	statements	statement	NOUN
ejpam-6075	256	23	holds	hold	VERB
ejpam-6075	256	24	:	:	PUNCT
ejpam-6075	256	25	(	(	PUNCT
ejpam-6075	256	26	i	i	NOUN
ejpam-6075	256	27	)	)	PUNCT
ejpam-6075	256	28	γsh(g	γsh(g	NOUN
ejpam-6075	256	29	)	)	PUNCT
ejpam-6075	256	30	=	=	SYM
ejpam-6075	256	31	1	1	NUM
ejpam-6075	256	32	if	if	SCONJ
ejpam-6075	256	33	and	and	CCONJ
ejpam-6075	256	34	only	only	ADV
ejpam-6075	256	35	if	if	SCONJ
ejpam-6075	256	36	g	g	PROPN
ejpam-6075	256	37	=	=	PROPN
ejpam-6075	256	38	k1	k1	PROPN
ejpam-6075	256	39	.	.	PUNCT
ejpam-6075	256	40	(	(	PUNCT
ejpam-6075	256	41	ii	ii	NOUN
ejpam-6075	256	42	)	)	PUNCT
ejpam-6075	256	43	γsh(g	γsh(g	NOUN
ejpam-6075	256	44	)	)	PUNCT
ejpam-6075	256	45	=	=	SYM
ejpam-6075	256	46	2	2	NUM
ejpam-6075	256	47	if	if	SCONJ
ejpam-6075	256	48	and	and	CCONJ
ejpam-6075	256	49	only	only	ADV
ejpam-6075	256	50	if	if	SCONJ
ejpam-6075	256	51	there	there	PRON
ejpam-6075	256	52	exist	exist	VERB
ejpam-6075	256	53	two	two	NUM
ejpam-6075	256	54	distinct	distinct	ADJ
ejpam-6075	256	55	vertices	vertex	NOUN
ejpam-6075	256	56	v	v	ADP
ejpam-6075	256	57	,	,	PUNCT
ejpam-6075	256	58	w	w	PROPN
ejpam-6075	256	59	∈	∈	PROPN
ejpam-6075	256	60	v	v	ADP
ejpam-6075	256	61	(	(	PUNCT
ejpam-6075	256	62	g	g	NOUN
ejpam-6075	256	63	)	)	PUNCT
ejpam-6075	256	64	satisfying	satisfy	VERB
ejpam-6075	256	65	the	the	DET
ejpam-6075	256	66	following	follow	VERB
ejpam-6075	256	67	conditions	condition	NOUN
ejpam-6075	256	68	:	:	PUNCT
ejpam-6075	256	69	(	(	PUNCT
ejpam-6075	256	70	p1	p1	NOUN
ejpam-6075	256	71	)	)	PUNCT
ejpam-6075	256	72	n2	n2	PROPN
ejpam-6075	256	73	g[{v	g[{v	PROPN
ejpam-6075	256	74	,	,	PUNCT
ejpam-6075	256	75	w	w	NOUN
ejpam-6075	256	76	}	}	PUNCT
ejpam-6075	256	77	]	]	PUNCT
ejpam-6075	256	78	=	=	SYM
ejpam-6075	256	79	v	v	X
ejpam-6075	256	80	(	(	PUNCT
ejpam-6075	256	81	g	g	NOUN
ejpam-6075	256	82	)	)	PUNCT
ejpam-6075	256	83	and	and	CCONJ
ejpam-6075	256	84	n2	n2	ADJ
ejpam-6075	256	85	g(v	g(v	PROPN
ejpam-6075	256	86	)	)	PUNCT
ejpam-6075	256	87	∩n2	∩n2	PROPN
ejpam-6075	256	88	g(w	g(w	PROPN
ejpam-6075	256	89	)	)	PUNCT
ejpam-6075	257	1	=	=	PUNCT
ejpam-6075	257	2	∅.	∅.	X
ejpam-6075	257	3	(	(	PUNCT
ejpam-6075	257	4	p2	p2	PROPN
ejpam-6075	257	5	)	)	PUNCT
ejpam-6075	257	6	for	for	ADP
ejpam-6075	257	7	each	each	PRON
ejpam-6075	257	8	x	x	PROPN
ejpam-6075	257	9	/∈	/∈	PUNCT
ejpam-6075	257	10	{	{	PUNCT
ejpam-6075	257	11	v	v	NOUN
ejpam-6075	257	12	,	,	PUNCT
ejpam-6075	257	13	w	w	NOUN
ejpam-6075	257	14	}	}	PUNCT
ejpam-6075	257	15	such	such	ADJ
ejpam-6075	257	16	that	that	SCONJ
ejpam-6075	257	17	x	x	SYM
ejpam-6075	257	18	∈	∈	PROPN
ejpam-6075	257	19	n2	n2	NOUN
ejpam-6075	257	20	g(v	g(v	PROPN
ejpam-6075	257	21	)	)	PUNCT
ejpam-6075	257	22	(	(	PUNCT
ejpam-6075	257	23	or	or	CCONJ
ejpam-6075	257	24	x	x	PROPN
ejpam-6075	257	25	∈	∈	PROPN
ejpam-6075	257	26	n2	n2	NOUN
ejpam-6075	257	27	g(w	g(w	PROPN
ejpam-6075	257	28	)	)	PUNCT
ejpam-6075	257	29	)	)	PUNCT
ejpam-6075	257	30	,	,	PUNCT
ejpam-6075	257	31	it	it	PRON
ejpam-6075	257	32	holds	hold	VERB
ejpam-6075	257	33	that	that	SCONJ
ejpam-6075	257	34	v	v	NOUN
ejpam-6075	257	35	(	(	PUNCT
ejpam-6075	257	36	g	g	NOUN
ejpam-6075	257	37	)	)	PUNCT
ejpam-6075	257	38	\	\	PUNCT
ejpam-6075	258	1	(	(	PUNCT
ejpam-6075	258	2	n2	n2	PROPN
ejpam-6075	258	3	g[w	g[w	PROPN
ejpam-6075	258	4	]	]	PUNCT
ejpam-6075	258	5	∪	∪	X
ejpam-6075	258	6	{	{	PUNCT
ejpam-6075	258	7	v	v	NOUN
ejpam-6075	258	8	}	}	PUNCT
ejpam-6075	258	9	)	)	PUNCT
ejpam-6075	258	10	⊆	⊆	NUM
ejpam-6075	258	11	n2	n2	PROPN
ejpam-6075	258	12	g[x	g[x	PROPN
ejpam-6075	258	13	]	]	PUNCT
ejpam-6075	258	14	(	(	PUNCT
ejpam-6075	258	15	resp	resp	NOUN
ejpam-6075	258	16	.	.	PUNCT
ejpam-6075	259	1	v	v	X
ejpam-6075	259	2	(	(	PUNCT
ejpam-6075	259	3	g)\(n2	g)\(n2	PROPN
ejpam-6075	259	4	g[v	g[v	NOUN
ejpam-6075	259	5	]	]	PUNCT
ejpam-6075	259	6	∪	∪	X
ejpam-6075	259	7	{	{	PUNCT
ejpam-6075	259	8	w	w	NOUN
ejpam-6075	259	9	}	}	PUNCT
ejpam-6075	259	10	)	)	PUNCT
ejpam-6075	259	11	⊆	⊆	NUM
ejpam-6075	259	12	n2	n2	NOUN
ejpam-6075	259	13	g[x	g[x	PROPN
ejpam-6075	259	14	]	]	PUNCT
ejpam-6075	259	15	)	)	PUNCT
ejpam-6075	259	16	.	.	PUNCT
ejpam-6075	260	1	(	(	PUNCT
ejpam-6075	260	2	iii	iii	X
ejpam-6075	260	3	)	)	PUNCT
ejpam-6075	260	4	γsh(g	γsh(g	NOUN
ejpam-6075	260	5	)	)	PUNCT
ejpam-6075	260	6	=	=	SYM
ejpam-6075	261	1	n	n	NOUN
ejpam-6075	261	2	if	if	SCONJ
ejpam-6075	261	3	and	and	CCONJ
ejpam-6075	261	4	only	only	ADV
ejpam-6075	261	5	if	if	SCONJ
ejpam-6075	261	6	every	every	DET
ejpam-6075	261	7	component	component	NOUN
ejpam-6075	261	8	of	of	ADP
ejpam-6075	261	9	g	g	PROPN
ejpam-6075	261	10	is	be	AUX
ejpam-6075	261	11	complete	complete	ADJ
ejpam-6075	261	12	.	.	PUNCT
ejpam-6075	262	1	f.	f.	PROPN
ejpam-6075	262	2	l.	l.	PROPN
ejpam-6075	262	3	alfeche	alfeche	PROPN
ejpam-6075	262	4	,	,	PUNCT
ejpam-6075	262	5	g.	g.	PROPN
ejpam-6075	262	6	a.	a.	PROPN
ejpam-6075	262	7	malacas	malacas	PROPN
ejpam-6075	262	8	,	,	PUNCT
ejpam-6075	262	9	s.	s.	PROPN
ejpam-6075	262	10	canoy	canoy	PROPN
ejpam-6075	262	11	jr	jr	PROPN
ejpam-6075	262	12	.	.	PROPN
ejpam-6075	262	13	/	/	SYM
ejpam-6075	262	14	eur	eur	PROPN
ejpam-6075	262	15	.	.	PUNCT
ejpam-6075	263	1	j.	j.	PROPN
ejpam-6075	263	2	pure	pure	PROPN
ejpam-6075	263	3	appl	appl	PROPN
ejpam-6075	263	4	.	.	PROPN
ejpam-6075	263	5	math	math	PROPN
ejpam-6075	263	6	,	,	PUNCT
ejpam-6075	263	7	18	18	NUM
ejpam-6075	263	8	(	(	PUNCT
ejpam-6075	263	9	2	2	NUM
ejpam-6075	263	10	)	)	PUNCT
ejpam-6075	263	11	(	(	PUNCT
ejpam-6075	263	12	2025	2025	NUM
ejpam-6075	263	13	)	)	PUNCT
ejpam-6075	263	14	,	,	PUNCT
ejpam-6075	263	15	6075	6075	NUM
ejpam-6075	263	16	6	6	NUM
ejpam-6075	263	17	of	of	ADP
ejpam-6075	263	18	14	14	NUM
ejpam-6075	263	19	proof	proof	NOUN
ejpam-6075	263	20	.	.	PUNCT
ejpam-6075	264	1	clearly	clearly	ADV
ejpam-6075	264	2	,	,	PUNCT
ejpam-6075	264	3	1	1	NUM
ejpam-6075	264	4	≤	≤	NUM
ejpam-6075	264	5	γsh(g	γsh(g	NOUN
ejpam-6075	264	6	)	)	PUNCT
ejpam-6075	264	7	≤	≤	NUM
ejpam-6075	264	8	n.	n.	NOUN
ejpam-6075	264	9	(	(	PUNCT
ejpam-6075	264	10	i	i	NOUN
ejpam-6075	264	11	)	)	PUNCT
ejpam-6075	264	12	suppose	suppose	VERB
ejpam-6075	264	13	γsh(g	γsh(g	NOUN
ejpam-6075	264	14	)	)	PUNCT
ejpam-6075	264	15	=	=	SYM
ejpam-6075	264	16	1	1	X
ejpam-6075	264	17	,	,	PUNCT
ejpam-6075	264	18	say	say	VERB
ejpam-6075	264	19	s	s	X
ejpam-6075	264	20	=	=	VERB
ejpam-6075	264	21	{	{	PUNCT
ejpam-6075	264	22	v	v	NOUN
ejpam-6075	264	23	}	}	PUNCT
ejpam-6075	264	24	is	be	AUX
ejpam-6075	264	25	a	a	DET
ejpam-6075	264	26	γsh	γsh	NOUN
ejpam-6075	264	27	-	-	PUNCT
ejpam-6075	264	28	set	set	NOUN
ejpam-6075	264	29	in	in	ADP
ejpam-6075	264	30	g.	g.	PROPN
ejpam-6075	264	31	since	since	SCONJ
ejpam-6075	264	32	s	s	NOUN
ejpam-6075	264	33	can	can	AUX
ejpam-6075	264	34	not	not	PART
ejpam-6075	264	35	be	be	AUX
ejpam-6075	264	36	a	a	DET
ejpam-6075	264	37	hop	hop	NOUN
ejpam-6075	264	38	dominating	dominating	NOUN
ejpam-6075	264	39	set	set	NOUN
ejpam-6075	264	40	if	if	SCONJ
ejpam-6075	264	41	g	g	PROPN
ejpam-6075	264	42	is	be	AUX
ejpam-6075	264	43	non	non	ADJ
ejpam-6075	264	44	-	-	ADJ
ejpam-6075	264	45	trivial	trivial	ADJ
ejpam-6075	264	46	,	,	PUNCT
ejpam-6075	264	47	it	it	PRON
ejpam-6075	264	48	follows	follow	VERB
ejpam-6075	264	49	that	that	SCONJ
ejpam-6075	264	50	g	g	PROPN
ejpam-6075	264	51	=	=	PROPN
ejpam-6075	264	52	k1	k1	PROPN
ejpam-6075	264	53	.	.	PUNCT
ejpam-6075	265	1	conversely	conversely	ADV
ejpam-6075	265	2	,	,	PUNCT
ejpam-6075	265	3	if	if	SCONJ
ejpam-6075	265	4	g	g	PROPN
ejpam-6075	265	5	=	=	SYM
ejpam-6075	265	6	k1	k1	PROPN
ejpam-6075	265	7	,	,	PUNCT
ejpam-6075	265	8	then	then	ADV
ejpam-6075	265	9	γsh(g	γsh(g	NOUN
ejpam-6075	265	10	)	)	PUNCT
ejpam-6075	265	11	=	=	SYM
ejpam-6075	265	12	1	1	X
ejpam-6075	265	13	.	.	PUNCT
ejpam-6075	265	14	(	(	PUNCT
ejpam-6075	265	15	ii	ii	NOUN
ejpam-6075	265	16	)	)	PUNCT
ejpam-6075	265	17	suppose	suppose	VERB
ejpam-6075	265	18	γsh(g	γsh(g	NOUN
ejpam-6075	265	19	)	)	PUNCT
ejpam-6075	265	20	=	=	SYM
ejpam-6075	266	1	2	2	X
ejpam-6075	266	2	.	.	PUNCT
ejpam-6075	266	3	let	let	VERB
ejpam-6075	266	4	d	d	NOUN
ejpam-6075	266	5	=	=	PRON
ejpam-6075	266	6	{	{	PUNCT
ejpam-6075	266	7	v	v	NOUN
ejpam-6075	266	8	,	,	PUNCT
ejpam-6075	266	9	w	w	NOUN
ejpam-6075	266	10	}	}	PUNCT
ejpam-6075	266	11	be	be	AUX
ejpam-6075	266	12	a	a	DET
ejpam-6075	266	13	γsh	γsh	NOUN
ejpam-6075	266	14	-	-	PUNCT
ejpam-6075	266	15	set	set	NOUN
ejpam-6075	266	16	of	of	ADP
ejpam-6075	266	17	g.	g.	PROPN
ejpam-6075	266	18	since	since	SCONJ
ejpam-6075	266	19	d	d	PROPN
ejpam-6075	266	20	is	be	AUX
ejpam-6075	266	21	hop	hop	NOUN
ejpam-6075	266	22	dominating	dominating	NOUN
ejpam-6075	266	23	,	,	PUNCT
ejpam-6075	266	24	v	v	NOUN
ejpam-6075	266	25	(	(	PUNCT
ejpam-6075	266	26	g	g	NOUN
ejpam-6075	266	27	)	)	PUNCT
ejpam-6075	266	28	=	=	SYM
ejpam-6075	266	29	n2	n2	PROPN
ejpam-6075	266	30	g[{v	g[{v	PROPN
ejpam-6075	266	31	,	,	PUNCT
ejpam-6075	266	32	w	w	PROPN
ejpam-6075	266	33	}	}	PUNCT
ejpam-6075	266	34	]	]	PUNCT
ejpam-6075	266	35	.	.	PUNCT
ejpam-6075	267	1	suppose	suppose	VERB
ejpam-6075	267	2	p	p	X
ejpam-6075	267	3	∈	∈	PROPN
ejpam-6075	267	4	n2	n2	NOUN
ejpam-6075	267	5	g(v)∩n2	g(v)∩n2	PROPN
ejpam-6075	267	6	g(w	g(w	PROPN
ejpam-6075	267	7	)	)	PUNCT
ejpam-6075	267	8	.	.	PUNCT
ejpam-6075	268	1	since	since	SCONJ
ejpam-6075	268	2	d	d	PROPN
ejpam-6075	268	3	is	be	AUX
ejpam-6075	268	4	a	a	DET
ejpam-6075	268	5	secure	secure	ADJ
ejpam-6075	268	6	hop	hop	NOUN
ejpam-6075	268	7	dominating	dominating	NOUN
ejpam-6075	268	8	set	set	NOUN
ejpam-6075	268	9	,	,	PUNCT
ejpam-6075	268	10	we	we	PRON
ejpam-6075	268	11	may	may	AUX
ejpam-6075	268	12	assume	assume	VERB
ejpam-6075	268	13	that	that	SCONJ
ejpam-6075	268	14	sp	sp	ADP
ejpam-6075	268	15	=	=	PUNCT
ejpam-6075	268	16	(	(	PUNCT
ejpam-6075	268	17	d	d	NOUN
ejpam-6075	268	18	\	\	X
ejpam-6075	268	19	{	{	PUNCT
ejpam-6075	268	20	v	v	NOUN
ejpam-6075	268	21	}	}	PUNCT
ejpam-6075	268	22	)	)	PUNCT
ejpam-6075	268	23	∪	∪	ADP
ejpam-6075	268	24	{	{	PUNCT
ejpam-6075	268	25	p	p	NOUN
ejpam-6075	268	26	}	}	PUNCT
ejpam-6075	268	27	=	=	PUNCT
ejpam-6075	268	28	{	{	PUNCT
ejpam-6075	268	29	p	p	X
ejpam-6075	268	30	,	,	PUNCT
ejpam-6075	268	31	w	w	NOUN
ejpam-6075	268	32	}	}	PUNCT
ejpam-6075	268	33	is	be	AUX
ejpam-6075	268	34	hop	hop	NOUN
ejpam-6075	268	35	dominating	dominate	VERB
ejpam-6075	268	36	(	(	PUNCT
ejpam-6075	268	37	otherwise	otherwise	ADV
ejpam-6075	268	38	,	,	PUNCT
ejpam-6075	268	39	{	{	PUNCT
ejpam-6075	268	40	p	p	X
ejpam-6075	268	41	,	,	PUNCT
ejpam-6075	268	42	v	v	NOUN
ejpam-6075	268	43	}	}	PUNCT
ejpam-6075	268	44	is	be	AUX
ejpam-6075	268	45	hop	hop	NOUN
ejpam-6075	268	46	dominating	dominating	NOUN
ejpam-6075	268	47	)	)	PUNCT
ejpam-6075	268	48	.	.	PUNCT
ejpam-6075	269	1	let	let	VERB
ejpam-6075	269	2	q	q	PROPN
ejpam-6075	269	3	∈	∈	PROPN
ejpam-6075	269	4	ng(p	ng(p	NOUN
ejpam-6075	269	5	)	)	PUNCT
ejpam-6075	269	6	∩	∩	NOUN
ejpam-6075	269	7	ng(w	ng(w	NOUN
ejpam-6075	269	8	)	)	PUNCT
ejpam-6075	269	9	.	.	PUNCT
ejpam-6075	270	1	then	then	ADV
ejpam-6075	270	2	q	q	PROPN
ejpam-6075	270	3	/∈	/∈	PROPN
ejpam-6075	270	4	n2	n2	PROPN
ejpam-6075	270	5	g[sp	g[sp	PROPN
ejpam-6075	270	6	]	]	X
ejpam-6075	270	7	.	.	PUNCT
ejpam-6075	271	1	this	this	PRON
ejpam-6075	271	2	implies	imply	VERB
ejpam-6075	271	3	that	that	SCONJ
ejpam-6075	271	4	d	d	NOUN
ejpam-6075	271	5	is	be	AUX
ejpam-6075	271	6	not	not	PART
ejpam-6075	271	7	hop	hop	NOUN
ejpam-6075	271	8	dominating	dominating	NOUN
ejpam-6075	271	9	,	,	PUNCT
ejpam-6075	271	10	a	a	DET
ejpam-6075	271	11	contradiction	contradiction	NOUN
ejpam-6075	271	12	.	.	PUNCT
ejpam-6075	272	1	thus	thus	ADV
ejpam-6075	272	2	,	,	PUNCT
ejpam-6075	272	3	(	(	PUNCT
ejpam-6075	272	4	p1	p1	NOUN
ejpam-6075	272	5	)	)	PUNCT
ejpam-6075	272	6	holds	hold	VERB
ejpam-6075	272	7	.	.	PUNCT
ejpam-6075	273	1	next	next	ADV
ejpam-6075	273	2	,	,	PUNCT
ejpam-6075	273	3	let	let	VERB
ejpam-6075	273	4	x	x	PUNCT
ejpam-6075	273	5	∈	∈	PROPN
ejpam-6075	273	6	v	v	ADP
ejpam-6075	273	7	(	(	PUNCT
ejpam-6075	273	8	g	g	NOUN
ejpam-6075	273	9	)	)	PUNCT
ejpam-6075	273	10	\d	\d	NOUN
ejpam-6075	273	11	.	.	PUNCT
ejpam-6075	274	1	assume	assume	VERB
ejpam-6075	274	2	without	without	ADP
ejpam-6075	274	3	loss	loss	NOUN
ejpam-6075	274	4	of	of	ADP
ejpam-6075	274	5	generality	generality	NOUN
ejpam-6075	274	6	that	that	SCONJ
ejpam-6075	274	7	x	x	SYM
ejpam-6075	274	8	∈	∈	PROPN
ejpam-6075	274	9	n2	n2	NOUN
ejpam-6075	274	10	g(v	g(v	PROPN
ejpam-6075	274	11	)	)	PUNCT
ejpam-6075	274	12	(	(	PUNCT
ejpam-6075	274	13	hence	hence	ADV
ejpam-6075	274	14	,	,	PUNCT
ejpam-6075	274	15	x	x	PROPN
ejpam-6075	274	16	/∈	/∈	PUNCT
ejpam-6075	274	17	n2	n2	PROPN
ejpam-6075	274	18	g(w	g(w	PROPN
ejpam-6075	274	19	)	)	PUNCT
ejpam-6075	274	20	)	)	PUNCT
ejpam-6075	274	21	.	.	PUNCT
ejpam-6075	275	1	since	since	SCONJ
ejpam-6075	275	2	d	d	PROPN
ejpam-6075	275	3	is	be	AUX
ejpam-6075	275	4	a	a	DET
ejpam-6075	275	5	secure	secure	ADJ
ejpam-6075	275	6	hop	hop	NOUN
ejpam-6075	275	7	dominating	dominating	NOUN
ejpam-6075	275	8	set	set	NOUN
ejpam-6075	275	9	in	in	ADP
ejpam-6075	275	10	g	g	PROPN
ejpam-6075	275	11	,	,	PUNCT
ejpam-6075	275	12	it	it	PRON
ejpam-6075	275	13	follows	follow	VERB
ejpam-6075	275	14	that	that	PRON
ejpam-6075	275	15	dx	dx	PROPN
ejpam-6075	276	1	=	=	PUNCT
ejpam-6075	277	1	(	(	PUNCT
ejpam-6075	277	2	d	d	NOUN
ejpam-6075	277	3	\	\	X
ejpam-6075	277	4	{	{	PUNCT
ejpam-6075	277	5	v	v	NOUN
ejpam-6075	277	6	}	}	PUNCT
ejpam-6075	277	7	)	)	PUNCT
ejpam-6075	277	8	∪	∪	ADP
ejpam-6075	277	9	{	{	PUNCT
ejpam-6075	277	10	x	x	NOUN
ejpam-6075	277	11	}	}	PUNCT
ejpam-6075	277	12	=	=	SYM
ejpam-6075	277	13	{	{	PUNCT
ejpam-6075	277	14	w	w	PROPN
ejpam-6075	277	15	,	,	PUNCT
ejpam-6075	277	16	x	x	PRON
ejpam-6075	277	17	}	}	PUNCT
ejpam-6075	277	18	is	be	AUX
ejpam-6075	277	19	a	a	DET
ejpam-6075	277	20	hop	hop	NOUN
ejpam-6075	277	21	dominating	dominating	NOUN
ejpam-6075	277	22	set	set	VERB
ejpam-6075	277	23	in	in	ADP
ejpam-6075	277	24	g.	g.	PROPN
ejpam-6075	277	25	let	let	VERB
ejpam-6075	277	26	z	z	PROPN
ejpam-6075	277	27	∈	∈	PROPN
ejpam-6075	277	28	ephn(v;d	ephn(v;d	NOUN
ejpam-6075	277	29	)	)	PUNCT
ejpam-6075	277	30	.	.	PUNCT
ejpam-6075	278	1	then	then	ADV
ejpam-6075	278	2	n2	n2	PROPN
ejpam-6075	278	3	g(z	g(z	PROPN
ejpam-6075	278	4	)	)	PUNCT
ejpam-6075	278	5	∩d	∩d	VERB
ejpam-6075	278	6	=	=	PUNCT
ejpam-6075	278	7	{	{	PUNCT
ejpam-6075	278	8	v	v	NOUN
ejpam-6075	278	9	}	}	PUNCT
ejpam-6075	278	10	.	.	PUNCT
ejpam-6075	279	1	since	since	SCONJ
ejpam-6075	279	2	dx	dx	PROPN
ejpam-6075	279	3	is	be	AUX
ejpam-6075	279	4	hop	hop	PROPN
ejpam-6075	279	5	dominating	dominating	NOUN
ejpam-6075	279	6	,	,	PUNCT
ejpam-6075	279	7	we	we	PRON
ejpam-6075	279	8	must	must	AUX
ejpam-6075	279	9	have	have	VERB
ejpam-6075	279	10	z	z	NOUN
ejpam-6075	279	11	∈	∈	PROPN
ejpam-6075	279	12	n2	n2	PROPN
ejpam-6075	279	13	g[x	g[x	PROPN
ejpam-6075	279	14	]	]	PUNCT
ejpam-6075	279	15	.	.	PUNCT
ejpam-6075	280	1	hence	hence	ADV
ejpam-6075	280	2	,	,	PUNCT
ejpam-6075	280	3	ephn(v;d	ephn(v;d	PROPN
ejpam-6075	280	4	)	)	PUNCT
ejpam-6075	280	5	⊆	⊆	NUM
ejpam-6075	280	6	n2	n2	NOUN
ejpam-6075	280	7	g[x	g[x	PROPN
ejpam-6075	280	8	]	]	PUNCT
ejpam-6075	280	9	.	.	PUNCT
ejpam-6075	281	1	by	by	ADP
ejpam-6075	281	2	lemma	lemma	PROPN
ejpam-6075	281	3	1	1	NUM
ejpam-6075	281	4	,	,	PUNCT
ejpam-6075	281	5	(	(	PUNCT
ejpam-6075	281	6	p2	p2	NOUN
ejpam-6075	281	7	)	)	PUNCT
ejpam-6075	281	8	holds	hold	VERB
ejpam-6075	281	9	.	.	PUNCT
ejpam-6075	282	1	for	for	ADP
ejpam-6075	282	2	the	the	DET
ejpam-6075	282	3	converse	converse	NOUN
ejpam-6075	282	4	,	,	PUNCT
ejpam-6075	282	5	suppose	suppose	VERB
ejpam-6075	282	6	that	that	SCONJ
ejpam-6075	282	7	there	there	PRON
ejpam-6075	282	8	exist	exist	VERB
ejpam-6075	282	9	distinct	distinct	ADJ
ejpam-6075	282	10	vertices	vertex	NOUN
ejpam-6075	282	11	v	v	ADP
ejpam-6075	282	12	,	,	PUNCT
ejpam-6075	282	13	w	w	PROPN
ejpam-6075	282	14	∈	∈	PROPN
ejpam-6075	282	15	v	v	ADP
ejpam-6075	282	16	(	(	PUNCT
ejpam-6075	282	17	g	g	NOUN
ejpam-6075	282	18	)	)	PUNCT
ejpam-6075	282	19	satisfying	satisfy	VERB
ejpam-6075	282	20	properties	property	NOUN
ejpam-6075	282	21	(	(	PUNCT
ejpam-6075	282	22	p1	p1	NOUN
ejpam-6075	282	23	)	)	PUNCT
ejpam-6075	282	24	and	and	CCONJ
ejpam-6075	282	25	(	(	PUNCT
ejpam-6075	282	26	p2	p2	PROPN
ejpam-6075	282	27	)	)	PUNCT
ejpam-6075	282	28	.	.	PUNCT
ejpam-6075	283	1	set	set	NOUN
ejpam-6075	283	2	s	s	PART
ejpam-6075	283	3	=	=	PUNCT
ejpam-6075	283	4	{	{	PUNCT
ejpam-6075	283	5	v	v	NOUN
ejpam-6075	283	6	,	,	PUNCT
ejpam-6075	283	7	w	w	NOUN
ejpam-6075	283	8	}	}	PUNCT
ejpam-6075	283	9	.	.	PUNCT
ejpam-6075	284	1	then	then	ADV
ejpam-6075	284	2	s	s	VERB
ejpam-6075	284	3	is	be	AUX
ejpam-6075	284	4	a	a	DET
ejpam-6075	284	5	hop	hop	NOUN
ejpam-6075	284	6	dominating	dominating	NOUN
ejpam-6075	284	7	set	set	VERB
ejpam-6075	284	8	by	by	ADP
ejpam-6075	284	9	(	(	PUNCT
ejpam-6075	284	10	p1	p1	PROPN
ejpam-6075	284	11	)	)	PUNCT
ejpam-6075	284	12	.	.	PUNCT
ejpam-6075	285	1	let	let	VERB
ejpam-6075	285	2	x	x	SYM
ejpam-6075	285	3	∈	∈	PROPN
ejpam-6075	285	4	v	v	X
ejpam-6075	285	5	(	(	PUNCT
ejpam-6075	285	6	g	g	NOUN
ejpam-6075	285	7	)	)	PUNCT
ejpam-6075	285	8	\	\	PUNCT
ejpam-6075	286	1	s.	s.	PROPN
ejpam-6075	286	2	by	by	ADP
ejpam-6075	286	3	(	(	PUNCT
ejpam-6075	286	4	p1	p1	PROPN
ejpam-6075	286	5	)	)	PUNCT
ejpam-6075	286	6	,	,	PUNCT
ejpam-6075	286	7	x	x	PUNCT
ejpam-6075	286	8	∈	∈	PROPN
ejpam-6075	286	9	n2	n2	ADJ
ejpam-6075	286	10	g(v	g(v	PROPN
ejpam-6075	286	11	)	)	PUNCT
ejpam-6075	286	12	\	\	PROPN
ejpam-6075	286	13	n2	n2	PROPN
ejpam-6075	286	14	g(w	g(w	PROPN
ejpam-6075	286	15	)	)	PUNCT
ejpam-6075	286	16	or	or	CCONJ
ejpam-6075	286	17	x	x	PROPN
ejpam-6075	286	18	∈	∈	PROPN
ejpam-6075	286	19	n2	n2	PROPN
ejpam-6075	286	20	g(w	g(w	PROPN
ejpam-6075	286	21	)	)	PUNCT
ejpam-6075	286	22	\	\	PROPN
ejpam-6075	286	23	n2	n2	ADJ
ejpam-6075	286	24	g(v	g(v	PROPN
ejpam-6075	286	25	)	)	PUNCT
ejpam-6075	286	26	.	.	PUNCT
ejpam-6075	287	1	if	if	SCONJ
ejpam-6075	287	2	x	x	X
ejpam-6075	287	3	∈	∈	PROPN
ejpam-6075	287	4	n2	n2	NOUN
ejpam-6075	287	5	g(v	g(v	PROPN
ejpam-6075	287	6	)	)	PUNCT
ejpam-6075	287	7	\	\	PROPN
ejpam-6075	287	8	n2	n2	PROPN
ejpam-6075	287	9	g(w	g(w	PROPN
ejpam-6075	287	10	)	)	PUNCT
ejpam-6075	287	11	(	(	PUNCT
ejpam-6075	287	12	x	x	SYM
ejpam-6075	287	13	∈	∈	PROPN
ejpam-6075	287	14	n2	n2	NOUN
ejpam-6075	287	15	g(w	g(w	PROPN
ejpam-6075	287	16	)	)	PUNCT
ejpam-6075	287	17	\	\	PROPN
ejpam-6075	287	18	n2	n2	ADJ
ejpam-6075	287	19	g(v	g(v	PROPN
ejpam-6075	287	20	)	)	PUNCT
ejpam-6075	287	21	)	)	PUNCT
ejpam-6075	287	22	,	,	PUNCT
ejpam-6075	287	23	then	then	ADV
ejpam-6075	287	24	v	v	X
ejpam-6075	287	25	(	(	PUNCT
ejpam-6075	287	26	g	g	NOUN
ejpam-6075	287	27	)	)	PUNCT
ejpam-6075	287	28	\	\	PUNCT
ejpam-6075	288	1	(	(	PUNCT
ejpam-6075	288	2	n2	n2	PROPN
ejpam-6075	288	3	g[w	g[w	PROPN
ejpam-6075	288	4	]	]	PUNCT
ejpam-6075	288	5	∪	∪	X
ejpam-6075	288	6	{	{	PUNCT
ejpam-6075	288	7	v	v	NOUN
ejpam-6075	288	8	}	}	PUNCT
ejpam-6075	288	9	)	)	PUNCT
ejpam-6075	288	10	⊆	⊆	NUM
ejpam-6075	288	11	n2	n2	PROPN
ejpam-6075	288	12	g[x	g[x	PROPN
ejpam-6075	288	13	]	]	PUNCT
ejpam-6075	288	14	(	(	PUNCT
ejpam-6075	288	15	resp	resp	NOUN
ejpam-6075	288	16	.	.	PUNCT
ejpam-6075	289	1	v	v	X
ejpam-6075	289	2	(	(	PUNCT
ejpam-6075	289	3	g	g	NOUN
ejpam-6075	289	4	)	)	PUNCT
ejpam-6075	289	5	\	\	PUNCT
ejpam-6075	290	1	(	(	PUNCT
ejpam-6075	290	2	n2	n2	ADJ
ejpam-6075	290	3	g[v	g[v	PROPN
ejpam-6075	290	4	]	]	PUNCT
ejpam-6075	290	5	∪	∪	X
ejpam-6075	290	6	{	{	PUNCT
ejpam-6075	290	7	w	w	NOUN
ejpam-6075	290	8	}	}	PUNCT
ejpam-6075	290	9	)	)	PUNCT
ejpam-6075	290	10	⊆	⊆	NUM
ejpam-6075	290	11	n2	n2	NOUN
ejpam-6075	290	12	g[x	g[x	PROPN
ejpam-6075	290	13	]	]	PUNCT
ejpam-6075	290	14	)	)	PUNCT
ejpam-6075	290	15	by	by	ADP
ejpam-6075	290	16	(	(	PUNCT
ejpam-6075	290	17	p2	p2	PROPN
ejpam-6075	290	18	)	)	PUNCT
ejpam-6075	290	19	.	.	PUNCT
ejpam-6075	291	1	by	by	ADP
ejpam-6075	291	2	lemma	lemma	PROPN
ejpam-6075	291	3	1	1	NUM
ejpam-6075	291	4	and	and	CCONJ
ejpam-6075	291	5	theorem	theorem	VERB
ejpam-6075	291	6	3	3	NUM
ejpam-6075	291	7	,	,	PUNCT
ejpam-6075	291	8	s	s	VERB
ejpam-6075	291	9	is	be	AUX
ejpam-6075	291	10	a	a	DET
ejpam-6075	291	11	secure	secure	ADJ
ejpam-6075	291	12	hop	hop	NOUN
ejpam-6075	291	13	dominating	dominating	NOUN
ejpam-6075	291	14	set	set	VERB
ejpam-6075	291	15	in	in	ADP
ejpam-6075	291	16	g.	g.	PROPN
ejpam-6075	291	17	since	since	SCONJ
ejpam-6075	291	18	g	g	PROPN
ejpam-6075	291	19	is	be	AUX
ejpam-6075	291	20	non	non	ADJ
ejpam-6075	291	21	-	-	ADJ
ejpam-6075	291	22	trivial	trivial	ADJ
ejpam-6075	291	23	,	,	PUNCT
ejpam-6075	291	24	γsh(g	γsh(g	NOUN
ejpam-6075	291	25	)	)	PUNCT
ejpam-6075	291	26	=	=	SYM
ejpam-6075	291	27	|s|	|s|	NOUN
ejpam-6075	291	28	=	=	SYM
ejpam-6075	291	29	2	2	NUM
ejpam-6075	291	30	.	.	PUNCT
ejpam-6075	291	31	(	(	PUNCT
ejpam-6075	291	32	iii	iii	NOUN
ejpam-6075	291	33	)	)	PUNCT
ejpam-6075	291	34	suppose	suppose	VERB
ejpam-6075	291	35	γsh(g	γsh(g	NOUN
ejpam-6075	291	36	)	)	PUNCT
ejpam-6075	291	37	=	=	SYM
ejpam-6075	291	38	n.	n.	NOUN
ejpam-6075	291	39	suppose	suppose	VERB
ejpam-6075	291	40	there	there	PRON
ejpam-6075	291	41	exists	exist	VERB
ejpam-6075	291	42	a	a	DET
ejpam-6075	291	43	component	component	NOUN
ejpam-6075	291	44	of	of	ADP
ejpam-6075	291	45	h	h	NOUN
ejpam-6075	291	46	of	of	ADP
ejpam-6075	291	47	g	g	PROPN
ejpam-6075	291	48	that	that	PRON
ejpam-6075	291	49	is	be	AUX
ejpam-6075	291	50	not	not	PART
ejpam-6075	291	51	complete	complete	ADJ
ejpam-6075	291	52	.	.	PUNCT
ejpam-6075	292	1	then	then	ADV
ejpam-6075	292	2	there	there	PRON
ejpam-6075	292	3	exists	exist	VERB
ejpam-6075	292	4	v	v	ADP
ejpam-6075	292	5	∈	∈	PROPN
ejpam-6075	292	6	v	v	NOUN
ejpam-6075	292	7	(	(	PUNCT
ejpam-6075	292	8	h	h	NOUN
ejpam-6075	292	9	)	)	PUNCT
ejpam-6075	292	10	⊆	⊆	NUM
ejpam-6075	292	11	v	v	NOUN
ejpam-6075	292	12	(	(	PUNCT
ejpam-6075	292	13	g	g	NOUN
ejpam-6075	292	14	)	)	PUNCT
ejpam-6075	292	15	such	such	ADJ
ejpam-6075	292	16	that	that	DET
ejpam-6075	292	17	n2	n2	ADJ
ejpam-6075	292	18	h(v	h(v	PROPN
ejpam-6075	292	19	)	)	PUNCT
ejpam-6075	292	20	=	=	SYM
ejpam-6075	292	21	n2	n2	ADJ
ejpam-6075	292	22	g(v	g(v	PROPN
ejpam-6075	292	23	)	)	PUNCT
ejpam-6075	292	24	̸=	̸=	NOUN
ejpam-6075	292	25	∅	∅	NOUN
ejpam-6075	292	26	,	,	PUNCT
ejpam-6075	292	27	say	say	VERB
ejpam-6075	292	28	w	w	PROPN
ejpam-6075	292	29	∈	∈	PROPN
ejpam-6075	292	30	n2	n2	NOUN
ejpam-6075	292	31	h(v	h(v	PROPN
ejpam-6075	292	32	)	)	PUNCT
ejpam-6075	292	33	.	.	PUNCT
ejpam-6075	293	1	set	set	VERB
ejpam-6075	293	2	s	s	PART
ejpam-6075	293	3	=	=	X
ejpam-6075	293	4	v	v	ADJ
ejpam-6075	293	5	(	(	PUNCT
ejpam-6075	293	6	g	g	NOUN
ejpam-6075	293	7	)	)	PUNCT
ejpam-6075	293	8	\	\	NOUN
ejpam-6075	293	9	{	{	PUNCT
ejpam-6075	293	10	w	w	NOUN
ejpam-6075	293	11	}	}	PUNCT
ejpam-6075	293	12	.	.	PUNCT
ejpam-6075	294	1	then	then	ADV
ejpam-6075	294	2	clearly	clearly	ADV
ejpam-6075	294	3	,	,	PUNCT
ejpam-6075	294	4	s	s	VERB
ejpam-6075	294	5	is	be	AUX
ejpam-6075	294	6	a	a	DET
ejpam-6075	294	7	hop	hop	NOUN
ejpam-6075	294	8	dominating	dominating	NOUN
ejpam-6075	294	9	set	set	VERB
ejpam-6075	294	10	in	in	ADP
ejpam-6075	294	11	g.	g.	PROPN
ejpam-6075	294	12	since	since	SCONJ
ejpam-6075	294	13	sw	sw	PROPN
ejpam-6075	294	14	=	=	PUNCT
ejpam-6075	294	15	(	(	PUNCT
ejpam-6075	294	16	s	s	NOUN
ejpam-6075	294	17	\	\	X
ejpam-6075	294	18	{	{	PUNCT
ejpam-6075	294	19	v	v	NOUN
ejpam-6075	294	20	}	}	PUNCT
ejpam-6075	294	21	)	)	PUNCT
ejpam-6075	294	22	∪	∪	ADP
ejpam-6075	294	23	{	{	PUNCT
ejpam-6075	294	24	w	w	NOUN
ejpam-6075	294	25	}	}	PUNCT
ejpam-6075	294	26	=	=	SYM
ejpam-6075	294	27	v	v	NOUN
ejpam-6075	294	28	(	(	PUNCT
ejpam-6075	294	29	g	g	NOUN
ejpam-6075	294	30	)	)	PUNCT
ejpam-6075	294	31	\	\	NOUN
ejpam-6075	294	32	{	{	PUNCT
ejpam-6075	294	33	v	v	NOUN
ejpam-6075	294	34	}	}	PUNCT
ejpam-6075	294	35	is	be	AUX
ejpam-6075	294	36	also	also	ADV
ejpam-6075	294	37	hop	hop	NOUN
ejpam-6075	294	38	dominating	dominating	NOUN
ejpam-6075	294	39	,	,	PUNCT
ejpam-6075	294	40	it	it	PRON
ejpam-6075	294	41	follows	follow	VERB
ejpam-6075	294	42	that	that	SCONJ
ejpam-6075	294	43	s	s	VERB
ejpam-6075	294	44	is	be	AUX
ejpam-6075	294	45	a	a	DET
ejpam-6075	294	46	secure	secure	ADJ
ejpam-6075	294	47	hop	hop	NOUN
ejpam-6075	294	48	dominating	dominating	NOUN
ejpam-6075	294	49	set	set	NOUN
ejpam-6075	294	50	.	.	PUNCT
ejpam-6075	295	1	this	this	PRON
ejpam-6075	295	2	implies	imply	VERB
ejpam-6075	295	3	that	that	SCONJ
ejpam-6075	295	4	γsh(g	γsh(g	NOUN
ejpam-6075	295	5	)	)	PUNCT
ejpam-6075	295	6	≤	≤	NUM
ejpam-6075	295	7	|s|	|s|	PROPN
ejpam-6075	295	8	=	=	PUNCT
ejpam-6075	295	9	n	n	CCONJ
ejpam-6075	295	10	−	−	PROPN
ejpam-6075	295	11	1	1	NUM
ejpam-6075	295	12	,	,	PUNCT
ejpam-6075	295	13	a	a	DET
ejpam-6075	295	14	contradiction	contradiction	NOUN
ejpam-6075	295	15	.	.	PUNCT
ejpam-6075	296	1	therefore	therefore	ADV
ejpam-6075	296	2	,	,	PUNCT
ejpam-6075	296	3	every	every	DET
ejpam-6075	296	4	component	component	NOUN
ejpam-6075	296	5	of	of	ADP
ejpam-6075	296	6	g	g	PROPN
ejpam-6075	296	7	is	be	AUX
ejpam-6075	296	8	complete	complete	ADJ
ejpam-6075	296	9	.	.	PUNCT
ejpam-6075	297	1	for	for	ADP
ejpam-6075	297	2	the	the	DET
ejpam-6075	297	3	converse	converse	NOUN
ejpam-6075	297	4	,	,	PUNCT
ejpam-6075	297	5	suppose	suppose	VERB
ejpam-6075	297	6	that	that	SCONJ
ejpam-6075	297	7	every	every	DET
ejpam-6075	297	8	component	component	NOUN
ejpam-6075	297	9	of	of	ADP
ejpam-6075	297	10	g	g	PROPN
ejpam-6075	297	11	is	be	AUX
ejpam-6075	297	12	complete	complete	ADJ
ejpam-6075	297	13	.	.	PUNCT
ejpam-6075	298	1	let	let	VERB
ejpam-6075	298	2	g1	g1	PROPN
ejpam-6075	298	3	,	,	PUNCT
ejpam-6075	298	4	g2	g2	PROPN
ejpam-6075	298	5	,	,	PUNCT
ejpam-6075	298	6	.	.	PUNCT
ejpam-6075	298	7	.	.	PUNCT
ejpam-6075	299	1	.	.	PUNCT
ejpam-6075	300	1	,	,	PUNCT
ejpam-6075	300	2	gk	gk	PROPN
ejpam-6075	300	3	be	be	AUX
ejpam-6075	300	4	the	the	DET
ejpam-6075	300	5	components	component	NOUN
ejpam-6075	300	6	of	of	ADP
ejpam-6075	300	7	g.	g.	PROPN
ejpam-6075	300	8	by	by	ADP
ejpam-6075	300	9	assumption	assumption	NOUN
ejpam-6075	300	10	and	and	CCONJ
ejpam-6075	300	11	theorem	theorem	VERB
ejpam-6075	300	12	4	4	NUM
ejpam-6075	300	13	,	,	PUNCT
ejpam-6075	300	14	γsh(gj	γsh(gj	NUM
ejpam-6075	300	15	)	)	PUNCT
ejpam-6075	301	1	=	=	PUNCT
ejpam-6075	301	2	|v	|v	X
ejpam-6075	301	3	(	(	PUNCT
ejpam-6075	301	4	gj)|	gj)|	PROPN
ejpam-6075	301	5	for	for	ADP
ejpam-6075	301	6	each	each	DET
ejpam-6075	301	7	j	j	PROPN
ejpam-6075	301	8	∈	∈	PROPN
ejpam-6075	302	1	[	[	X
ejpam-6075	302	2	k	k	X
ejpam-6075	302	3	]	]	X
ejpam-6075	302	4	=	=	X
ejpam-6075	302	5	{	{	PUNCT
ejpam-6075	302	6	1	1	NUM
ejpam-6075	302	7	,	,	PUNCT
ejpam-6075	302	8	2	2	NUM
ejpam-6075	302	9	,	,	PUNCT
ejpam-6075	302	10	·	·	PUNCT
ejpam-6075	302	11	·	·	PUNCT
ejpam-6075	302	12	·	·	PUNCT
ejpam-6075	302	13	,	,	PUNCT
ejpam-6075	302	14	k	k	NOUN
ejpam-6075	302	15	}	}	PUNCT
ejpam-6075	302	16	.	.	PUNCT
ejpam-6075	303	1	thus	thus	ADV
ejpam-6075	303	2	,	,	PUNCT
ejpam-6075	303	3	γsh(g	γsh(g	NOUN
ejpam-6075	303	4	)	)	PUNCT
ejpam-6075	303	5	=	=	SYM
ejpam-6075	304	1	∑k	∑k	PROPN
ejpam-6075	304	2	j=1	j=1	NOUN
ejpam-6075	304	3	γsh(gj	γsh(gj	X
ejpam-6075	304	4	)	)	PUNCT
ejpam-6075	304	5	=	=	SYM
ejpam-6075	304	6	n	n	X
ejpam-6075	304	7	by	by	ADP
ejpam-6075	304	8	theorem	theorem	NOUN
ejpam-6075	304	9	1	1	NUM
ejpam-6075	304	10	.	.	PUNCT
ejpam-6075	304	11	lemma	lemma	PROPN
ejpam-6075	304	12	2	2	X
ejpam-6075	304	13	.	.	PUNCT
ejpam-6075	305	1	let	let	VERB
ejpam-6075	305	2	g	g	PRON
ejpam-6075	305	3	be	be	AUX
ejpam-6075	305	4	a	a	DET
ejpam-6075	305	5	graph	graph	NOUN
ejpam-6075	305	6	of	of	ADP
ejpam-6075	305	7	order	order	NOUN
ejpam-6075	305	8	n	n	PRON
ejpam-6075	305	9	≥	≥	NUM
ejpam-6075	305	10	3	3	NUM
ejpam-6075	305	11	such	such	ADJ
ejpam-6075	305	12	that	that	PRON
ejpam-6075	305	13	γ(g	γ(g	PROPN
ejpam-6075	305	14	)	)	PUNCT
ejpam-6075	306	1	=	=	PUNCT
ejpam-6075	306	2	1	1	X
ejpam-6075	306	3	.	.	PUNCT
ejpam-6075	307	1	if	if	SCONJ
ejpam-6075	307	2	|d(g)|	|d(g)|	NOUN
ejpam-6075	307	3	≥	≥	NOUN
ejpam-6075	307	4	2	2	NUM
ejpam-6075	307	5	,	,	PUNCT
ejpam-6075	307	6	where	where	SCONJ
ejpam-6075	307	7	d(g	d(g	NOUN
ejpam-6075	307	8	)	)	PUNCT
ejpam-6075	307	9	=	=	PRON
ejpam-6075	307	10	{	{	PUNCT
ejpam-6075	307	11	v	v	NUM
ejpam-6075	307	12	∈	∈	NOUN
ejpam-6075	307	13	v	v	NOUN
ejpam-6075	307	14	(	(	PUNCT
ejpam-6075	307	15	g	g	NOUN
ejpam-6075	307	16	)	)	PUNCT
ejpam-6075	307	17	:	:	PUNCT
ejpam-6075	308	1	ng[v	ng[v	ADV
ejpam-6075	308	2	]	]	X
ejpam-6075	308	3	=	=	SYM
ejpam-6075	308	4	v	v	X
ejpam-6075	308	5	(	(	PUNCT
ejpam-6075	308	6	g	g	NOUN
ejpam-6075	308	7	)	)	PUNCT
ejpam-6075	308	8	}	}	PUNCT
ejpam-6075	308	9	,	,	PUNCT
ejpam-6075	308	10	then	then	ADV
ejpam-6075	308	11	γsh(g	γsh(g	NOUN
ejpam-6075	308	12	)	)	PUNCT
ejpam-6075	308	13	≥	≥	NOUN
ejpam-6075	308	14	3	3	NUM
ejpam-6075	308	15	.	.	PUNCT
ejpam-6075	308	16	proof	proof	NOUN
ejpam-6075	308	17	.	.	PUNCT
ejpam-6075	309	1	if	if	SCONJ
ejpam-6075	309	2	g	g	PROPN
ejpam-6075	309	3	=	=	SYM
ejpam-6075	309	4	kn	kn	PROPN
ejpam-6075	309	5	,	,	PUNCT
ejpam-6075	309	6	then	then	ADV
ejpam-6075	309	7	γsh(g	γsh(g	NOUN
ejpam-6075	309	8	)	)	PUNCT
ejpam-6075	309	9	=	=	SYM
ejpam-6075	309	10	n	n	X
ejpam-6075	309	11	≥	≥	NOUN
ejpam-6075	309	12	3	3	NUM
ejpam-6075	309	13	.	.	PUNCT
ejpam-6075	310	1	so	so	ADV
ejpam-6075	310	2	suppose	suppose	VERB
ejpam-6075	310	3	g	g	PROPN
ejpam-6075	310	4	̸=	̸=	PROPN
ejpam-6075	310	5	kn	kn	PROPN
ejpam-6075	310	6	and	and	CCONJ
ejpam-6075	310	7	let	let	VERB
ejpam-6075	310	8	s	s	PRON
ejpam-6075	310	9	be	be	AUX
ejpam-6075	310	10	a	a	DET
ejpam-6075	310	11	γsh	γsh	NOUN
ejpam-6075	310	12	-	-	PUNCT
ejpam-6075	310	13	set	set	NOUN
ejpam-6075	310	14	in	in	ADP
ejpam-6075	310	15	g.	g.	PROPN
ejpam-6075	310	16	since	since	SCONJ
ejpam-6075	310	17	s	s	PROPN
ejpam-6075	310	18	is	be	AUX
ejpam-6075	310	19	a	a	DET
ejpam-6075	310	20	hop	hop	NOUN
ejpam-6075	310	21	dominating	dominating	NOUN
ejpam-6075	310	22	set	set	NOUN
ejpam-6075	310	23	,	,	PUNCT
ejpam-6075	310	24	d(g	d(g	PROPN
ejpam-6075	310	25	)	)	PUNCT
ejpam-6075	310	26	⊆	⊆	NUM
ejpam-6075	310	27	s.	s.	PROPN
ejpam-6075	310	28	hence	hence	ADV
ejpam-6075	310	29	,	,	PUNCT
ejpam-6075	310	30	if	if	SCONJ
ejpam-6075	310	31	|d(g)|	|d(g)|	NOUN
ejpam-6075	310	32	≥	≥	NOUN
ejpam-6075	310	33	3	3	NUM
ejpam-6075	310	34	,	,	PUNCT
ejpam-6075	310	35	then	then	ADV
ejpam-6075	310	36	γsh(g	γsh(g	NOUN
ejpam-6075	310	37	)	)	PUNCT
ejpam-6075	310	38	=	=	PUNCT
ejpam-6075	310	39	|s|	|s|	NOUN
ejpam-6075	310	40	≥	≥	NOUN
ejpam-6075	310	41	3	3	NUM
ejpam-6075	310	42	.	.	PUNCT
ejpam-6075	310	43	suppose	suppose	VERB
ejpam-6075	310	44	|d(g)|	|d(g)|	NOUN
ejpam-6075	310	45	=	=	SYM
ejpam-6075	310	46	2	2	X
ejpam-6075	310	47	.	.	PUNCT
ejpam-6075	310	48	since	since	SCONJ
ejpam-6075	310	49	|n2	|n2	PROPN
ejpam-6075	310	50	g(v)|	g(v)|	NOUN
ejpam-6075	311	1	=	=	NOUN
ejpam-6075	311	2	0	0	NUM
ejpam-6075	311	3	for	for	ADP
ejpam-6075	311	4	every	every	DET
ejpam-6075	311	5	v	v	NOUN
ejpam-6075	311	6	∈	∈	PROPN
ejpam-6075	311	7	d(g	d(g	PROPN
ejpam-6075	311	8	)	)	PUNCT
ejpam-6075	311	9	and	and	CCONJ
ejpam-6075	311	10	s	s	VERB
ejpam-6075	311	11	is	be	AUX
ejpam-6075	311	12	a	a	DET
ejpam-6075	311	13	hop	hop	NOUN
ejpam-6075	311	14	dominating	dominating	NOUN
ejpam-6075	311	15	set	set	NOUN
ejpam-6075	311	16	,	,	PUNCT
ejpam-6075	311	17	it	it	PRON
ejpam-6075	311	18	follows	follow	VERB
ejpam-6075	311	19	that	that	PRON
ejpam-6075	311	20	s	s	VERB
ejpam-6075	311	21	̸=	̸=	PROPN
ejpam-6075	311	22	d(g	d(g	PROPN
ejpam-6075	311	23	)	)	PUNCT
ejpam-6075	311	24	.	.	PUNCT
ejpam-6075	312	1	this	this	PRON
ejpam-6075	312	2	implies	imply	VERB
ejpam-6075	312	3	that	that	SCONJ
ejpam-6075	312	4	2	2	X
ejpam-6075	312	5	=	=	SYM
ejpam-6075	312	6	|d(g)|	|d(g)|	PROPN
ejpam-6075	312	7	<	<	X
ejpam-6075	312	8	|s|	|s|	NOUN
ejpam-6075	312	9	=	=	PUNCT
ejpam-6075	312	10	γsh(g	γsh(g	NOUN
ejpam-6075	312	11	)	)	PUNCT
ejpam-6075	312	12	.	.	PUNCT
ejpam-6075	313	1	this	this	PRON
ejpam-6075	313	2	proves	prove	VERB
ejpam-6075	313	3	the	the	DET
ejpam-6075	313	4	assertion	assertion	NOUN
ejpam-6075	313	5	.	.	PUNCT
ejpam-6075	314	1	theorem	theorem	ADJ
ejpam-6075	314	2	6	6	NUM
ejpam-6075	314	3	.	.	PUNCT
ejpam-6075	315	1	let	let	VERB
ejpam-6075	315	2	g	g	PRON
ejpam-6075	315	3	be	be	AUX
ejpam-6075	315	4	a	a	DET
ejpam-6075	315	5	non	non	ADJ
ejpam-6075	315	6	-	-	ADJ
ejpam-6075	315	7	trivial	trivial	ADJ
ejpam-6075	315	8	graph	graph	NOUN
ejpam-6075	315	9	of	of	ADP
ejpam-6075	315	10	order	order	NOUN
ejpam-6075	315	11	n	n	PRON
ejpam-6075	315	12	such	such	ADJ
ejpam-6075	315	13	that	that	PRON
ejpam-6075	315	14	γ(g	γ(g	PROPN
ejpam-6075	315	15	)	)	PUNCT
ejpam-6075	315	16	=	=	PUNCT
ejpam-6075	316	1	1	1	X
ejpam-6075	316	2	.	.	PUNCT
ejpam-6075	316	3	then	then	ADV
ejpam-6075	316	4	γsh(g	γsh(g	NOUN
ejpam-6075	316	5	)	)	PUNCT
ejpam-6075	316	6	=	=	SYM
ejpam-6075	316	7	2	2	NUM
ejpam-6075	316	8	if	if	SCONJ
ejpam-6075	316	9	and	and	CCONJ
ejpam-6075	316	10	if	if	SCONJ
ejpam-6075	316	11	g	g	NOUN
ejpam-6075	316	12	=	=	SYM
ejpam-6075	316	13	k1,n−1	k1,n−1	PROPN
ejpam-6075	316	14	,	,	PUNCT
ejpam-6075	316	15	that	that	ADV
ejpam-6075	316	16	is	is	ADV
ejpam-6075	316	17	,	,	PUNCT
ejpam-6075	316	18	g	g	PROPN
ejpam-6075	316	19	has	have	VERB
ejpam-6075	316	20	a	a	DET
ejpam-6075	316	21	unique	unique	ADJ
ejpam-6075	316	22	dominating	dominating	NOUN
ejpam-6075	316	23	vertex	vertex	NOUN
ejpam-6075	316	24	v	v	NOUN
ejpam-6075	316	25	and	and	CCONJ
ejpam-6075	316	26	|ng(x)|	|ng(x)|	NOUN
ejpam-6075	316	27	=	=	SYM
ejpam-6075	316	28	1	1	NUM
ejpam-6075	316	29	for	for	ADP
ejpam-6075	316	30	x	x	PROPN
ejpam-6075	316	31	∈	∈	PROPN
ejpam-6075	316	32	v	v	ADP
ejpam-6075	316	33	(	(	PUNCT
ejpam-6075	316	34	g	g	NOUN
ejpam-6075	316	35	)	)	PUNCT
ejpam-6075	316	36	\	\	NOUN
ejpam-6075	316	37	{	{	PUNCT
ejpam-6075	316	38	v	v	NOUN
ejpam-6075	316	39	}	}	PUNCT
ejpam-6075	316	40	.	.	PUNCT
ejpam-6075	317	1	f.	f.	PROPN
ejpam-6075	317	2	l.	l.	PROPN
ejpam-6075	317	3	alfeche	alfeche	PROPN
ejpam-6075	317	4	,	,	PUNCT
ejpam-6075	317	5	g.	g.	PROPN
ejpam-6075	317	6	a.	a.	PROPN
ejpam-6075	317	7	malacas	malacas	PROPN
ejpam-6075	317	8	,	,	PUNCT
ejpam-6075	317	9	s.	s.	PROPN
ejpam-6075	317	10	canoy	canoy	PROPN
ejpam-6075	317	11	jr	jr	PROPN
ejpam-6075	317	12	.	.	PROPN
ejpam-6075	317	13	/	/	SYM
ejpam-6075	317	14	eur	eur	PROPN
ejpam-6075	317	15	.	.	PUNCT
ejpam-6075	318	1	j.	j.	PROPN
ejpam-6075	318	2	pure	pure	PROPN
ejpam-6075	318	3	appl	appl	PROPN
ejpam-6075	318	4	.	.	PROPN
ejpam-6075	318	5	math	math	PROPN
ejpam-6075	318	6	,	,	PUNCT
ejpam-6075	318	7	18	18	NUM
ejpam-6075	318	8	(	(	PUNCT
ejpam-6075	318	9	2	2	NUM
ejpam-6075	318	10	)	)	PUNCT
ejpam-6075	318	11	(	(	PUNCT
ejpam-6075	318	12	2025	2025	NUM
ejpam-6075	318	13	)	)	PUNCT
ejpam-6075	318	14	,	,	PUNCT
ejpam-6075	318	15	6075	6075	NUM
ejpam-6075	318	16	7	7	NUM
ejpam-6075	318	17	of	of	ADP
ejpam-6075	318	18	14	14	NUM
ejpam-6075	318	19	proof	proof	NOUN
ejpam-6075	318	20	.	.	PUNCT
ejpam-6075	319	1	suppose	suppose	VERB
ejpam-6075	319	2	γsh(g	γsh(g	NOUN
ejpam-6075	319	3	)	)	PUNCT
ejpam-6075	319	4	=	=	SYM
ejpam-6075	320	1	2	2	X
ejpam-6075	320	2	.	.	X
ejpam-6075	321	1	if	if	SCONJ
ejpam-6075	321	2	n	n	NOUN
ejpam-6075	321	3	=	=	SYM
ejpam-6075	321	4	2	2	NUM
ejpam-6075	321	5	,	,	PUNCT
ejpam-6075	321	6	then	then	ADV
ejpam-6075	321	7	g	g	PROPN
ejpam-6075	321	8	=	=	PROPN
ejpam-6075	321	9	k2	k2	PROPN
ejpam-6075	321	10	=	=	PROPN
ejpam-6075	321	11	k1,1	k1,1	PROPN
ejpam-6075	321	12	.	.	PUNCT
ejpam-6075	321	13	suppose	suppose	VERB
ejpam-6075	321	14	n	n	PRON
ejpam-6075	321	15	≥	≥	X
ejpam-6075	321	16	3	3	NUM
ejpam-6075	321	17	and	and	CCONJ
ejpam-6075	321	18	let	let	VERB
ejpam-6075	321	19	s	s	PRON
ejpam-6075	321	20	be	be	AUX
ejpam-6075	321	21	a	a	DET
ejpam-6075	321	22	γsh	γsh	NOUN
ejpam-6075	321	23	-	-	PUNCT
ejpam-6075	321	24	set	set	VERB
ejpam-6075	321	25	in	in	ADP
ejpam-6075	321	26	g.	g.	PROPN
ejpam-6075	321	27	by	by	ADP
ejpam-6075	321	28	the	the	DET
ejpam-6075	321	29	contrapositive	contrapositive	NOUN
ejpam-6075	321	30	of	of	ADP
ejpam-6075	321	31	lemma	lemma	PROPN
ejpam-6075	321	32	2	2	NUM
ejpam-6075	321	33	,	,	PUNCT
ejpam-6075	321	34	|d(g)|	|d(g)|	NOUN
ejpam-6075	321	35	=	=	SYM
ejpam-6075	321	36	1	1	NUM
ejpam-6075	321	37	,	,	PUNCT
ejpam-6075	321	38	where	where	SCONJ
ejpam-6075	321	39	d(g	d(g	NOUN
ejpam-6075	321	40	)	)	PUNCT
ejpam-6075	321	41	=	=	PRON
ejpam-6075	322	1	{	{	PUNCT
ejpam-6075	322	2	u	u	NOUN
ejpam-6075	322	3	∈	∈	PROPN
ejpam-6075	322	4	v	v	NOUN
ejpam-6075	322	5	(	(	PUNCT
ejpam-6075	322	6	g	g	NOUN
ejpam-6075	322	7	)	)	PUNCT
ejpam-6075	322	8	:	:	PUNCT
ejpam-6075	323	1	ng[u	ng[u	PROPN
ejpam-6075	323	2	]	]	X
ejpam-6075	323	3	=	=	SYM
ejpam-6075	323	4	v	v	NOUN
ejpam-6075	323	5	(	(	PUNCT
ejpam-6075	323	6	g	g	NOUN
ejpam-6075	323	7	)	)	PUNCT
ejpam-6075	323	8	}	}	PUNCT
ejpam-6075	323	9	that	that	ADV
ejpam-6075	323	10	is	be	AUX
ejpam-6075	323	11	,	,	PUNCT
ejpam-6075	323	12	g	g	PROPN
ejpam-6075	323	13	has	have	VERB
ejpam-6075	323	14	a	a	DET
ejpam-6075	323	15	unique	unique	ADJ
ejpam-6075	323	16	dominating	dominating	NOUN
ejpam-6075	323	17	vertex	vertex	NOUN
ejpam-6075	323	18	,	,	PUNCT
ejpam-6075	323	19	say	say	VERB
ejpam-6075	323	20	v.	v.	ADP
ejpam-6075	323	21	this	this	PRON
ejpam-6075	323	22	implies	imply	VERB
ejpam-6075	323	23	that	that	PRON
ejpam-6075	323	24	s	s	VERB
ejpam-6075	323	25	=	=	PUNCT
ejpam-6075	323	26	{	{	PUNCT
ejpam-6075	323	27	v	v	NOUN
ejpam-6075	323	28	,	,	PUNCT
ejpam-6075	323	29	w	w	NOUN
ejpam-6075	323	30	}	}	PUNCT
ejpam-6075	323	31	for	for	ADP
ejpam-6075	323	32	some	some	DET
ejpam-6075	323	33	w	w	PROPN
ejpam-6075	323	34	∈	∈	PROPN
ejpam-6075	323	35	v	v	ADP
ejpam-6075	323	36	(	(	PUNCT
ejpam-6075	323	37	g	g	NOUN
ejpam-6075	323	38	)	)	PUNCT
ejpam-6075	323	39	\	\	NOUN
ejpam-6075	323	40	{	{	PUNCT
ejpam-6075	323	41	v	v	NOUN
ejpam-6075	323	42	}	}	PUNCT
ejpam-6075	323	43	.	.	PUNCT
ejpam-6075	324	1	note	note	VERB
ejpam-6075	324	2	that	that	SCONJ
ejpam-6075	324	3	since	since	SCONJ
ejpam-6075	324	4	s	s	NOUN
ejpam-6075	324	5	is	be	AUX
ejpam-6075	324	6	a	a	DET
ejpam-6075	324	7	hop	hop	NOUN
ejpam-6075	324	8	dominating	dominating	NOUN
ejpam-6075	324	9	set	set	NOUN
ejpam-6075	324	10	,	,	PUNCT
ejpam-6075	324	11	|ng(w)|	|ng(w)|	NOUN
ejpam-6075	324	12	=	=	NOUN
ejpam-6075	324	13	1	1	X
ejpam-6075	324	14	.	.	PUNCT
ejpam-6075	324	15	suppose	suppose	VERB
ejpam-6075	324	16	there	there	PRON
ejpam-6075	324	17	exists	exist	VERB
ejpam-6075	324	18	x	x	X
ejpam-6075	324	19	∈	∈	PROPN
ejpam-6075	324	20	v	v	X
ejpam-6075	324	21	(	(	PUNCT
ejpam-6075	324	22	g	g	NOUN
ejpam-6075	324	23	)	)	PUNCT
ejpam-6075	324	24	\	\	PUNCT
ejpam-6075	324	25	s	s	PART
ejpam-6075	324	26	with	with	ADP
ejpam-6075	324	27	|ng(x)|	|ng(x)|	NOUN
ejpam-6075	324	28	≥	≥	NOUN
ejpam-6075	324	29	2	2	NUM
ejpam-6075	324	30	.	.	PUNCT
ejpam-6075	325	1	since	since	SCONJ
ejpam-6075	325	2	s	s	PROPN
ejpam-6075	325	3	is	be	AUX
ejpam-6075	325	4	a	a	DET
ejpam-6075	325	5	secure	secure	ADJ
ejpam-6075	325	6	hop	hop	NOUN
ejpam-6075	325	7	dominating	dominating	NOUN
ejpam-6075	325	8	set	set	NOUN
ejpam-6075	325	9	and	and	CCONJ
ejpam-6075	325	10	v	v	NOUN
ejpam-6075	325	11	is	be	AUX
ejpam-6075	325	12	a	a	DET
ejpam-6075	325	13	dominating	dominating	NOUN
ejpam-6075	325	14	vertex	vertex	NOUN
ejpam-6075	325	15	,	,	PUNCT
ejpam-6075	325	16	it	it	PRON
ejpam-6075	325	17	follows	follow	VERB
ejpam-6075	325	18	that	that	SCONJ
ejpam-6075	325	19	x	x	SYM
ejpam-6075	325	20	∈	∈	PROPN
ejpam-6075	325	21	n2	n2	NOUN
ejpam-6075	325	22	g(w	g(w	PROPN
ejpam-6075	325	23	)	)	PUNCT
ejpam-6075	325	24	and	and	CCONJ
ejpam-6075	325	25	sx	sx	PROPN
ejpam-6075	325	26	=	=	PUNCT
ejpam-6075	325	27	(	(	PUNCT
ejpam-6075	325	28	s	s	NOUN
ejpam-6075	325	29	\	\	X
ejpam-6075	325	30	{	{	PUNCT
ejpam-6075	325	31	w	w	NOUN
ejpam-6075	325	32	}	}	PUNCT
ejpam-6075	325	33	)	)	PUNCT
ejpam-6075	325	34	∪	∪	ADP
ejpam-6075	325	35	{	{	PUNCT
ejpam-6075	325	36	x	x	NOUN
ejpam-6075	325	37	}	}	PUNCT
ejpam-6075	325	38	=	=	SYM
ejpam-6075	325	39	{	{	PUNCT
ejpam-6075	325	40	v	v	NOUN
ejpam-6075	325	41	,	,	PUNCT
ejpam-6075	325	42	x	x	PRON
ejpam-6075	325	43	}	}	PUNCT
ejpam-6075	325	44	is	be	AUX
ejpam-6075	325	45	a	a	DET
ejpam-6075	325	46	hop	hop	NOUN
ejpam-6075	325	47	dominating	dominating	NOUN
ejpam-6075	325	48	set	set	VERB
ejpam-6075	325	49	in	in	ADP
ejpam-6075	325	50	g.	g.	PROPN
ejpam-6075	325	51	this	this	PRON
ejpam-6075	325	52	,	,	PUNCT
ejpam-6075	325	53	however	however	ADV
ejpam-6075	325	54	,	,	PUNCT
ejpam-6075	325	55	is	be	AUX
ejpam-6075	325	56	not	not	PART
ejpam-6075	325	57	possible	possible	ADJ
ejpam-6075	325	58	because	because	SCONJ
ejpam-6075	325	59	a	a	DET
ejpam-6075	325	60	vertex	vertex	NOUN
ejpam-6075	325	61	y	y	PROPN
ejpam-6075	325	62	∈	∈	PROPN
ejpam-6075	325	63	ng(x	ng(x	NUM
ejpam-6075	325	64	)	)	PUNCT
ejpam-6075	325	65	\	\	NOUN
ejpam-6075	326	1	{	{	PUNCT
ejpam-6075	326	2	v	v	NOUN
ejpam-6075	326	3	}	}	PUNCT
ejpam-6075	326	4	is	be	AUX
ejpam-6075	326	5	not	not	PART
ejpam-6075	326	6	in	in	ADP
ejpam-6075	326	7	n2	n2	PROPN
ejpam-6075	326	8	g[sx	g[sx	PROPN
ejpam-6075	326	9	]	]	PUNCT
ejpam-6075	326	10	.	.	PUNCT
ejpam-6075	327	1	therefore	therefore	ADV
ejpam-6075	327	2	,	,	PUNCT
ejpam-6075	327	3	|ng(x)|	|ng(x)|	NOUN
ejpam-6075	327	4	=	=	SYM
ejpam-6075	327	5	1	1	NUM
ejpam-6075	327	6	for	for	ADP
ejpam-6075	327	7	every	every	DET
ejpam-6075	327	8	x	x	SYM
ejpam-6075	327	9	∈	∈	PROPN
ejpam-6075	327	10	v	v	ADP
ejpam-6075	327	11	(	(	PUNCT
ejpam-6075	327	12	g	g	NOUN
ejpam-6075	327	13	)	)	PUNCT
ejpam-6075	327	14	\	\	NOUN
ejpam-6075	328	1	{	{	PUNCT
ejpam-6075	328	2	v	v	NOUN
ejpam-6075	328	3	}	}	PUNCT
ejpam-6075	328	4	.	.	PUNCT
ejpam-6075	329	1	accordingly	accordingly	ADV
ejpam-6075	329	2	,	,	PUNCT
ejpam-6075	329	3	g	g	PROPN
ejpam-6075	329	4	=	=	PUNCT
ejpam-6075	329	5	k1,n−1	k1,n−1	PROPN
ejpam-6075	329	6	.	.	PUNCT
ejpam-6075	330	1	for	for	ADP
ejpam-6075	330	2	the	the	DET
ejpam-6075	330	3	converse	converse	NOUN
ejpam-6075	330	4	,	,	PUNCT
ejpam-6075	330	5	suppose	suppose	VERB
ejpam-6075	330	6	that	that	SCONJ
ejpam-6075	330	7	g	g	PROPN
ejpam-6075	330	8	=	=	SYM
ejpam-6075	330	9	k1,n−1	k1,n−1	PROPN
ejpam-6075	330	10	.	.	PUNCT
ejpam-6075	331	1	then	then	ADV
ejpam-6075	331	2	γsh(g	γsh(g	NOUN
ejpam-6075	331	3	)	)	PUNCT
ejpam-6075	331	4	≥	≥	NOUN
ejpam-6075	331	5	2	2	NUM
ejpam-6075	331	6	by	by	ADP
ejpam-6075	331	7	theorem	theorem	NOUN
ejpam-6075	331	8	5(i	5(i	NUM
ejpam-6075	331	9	)	)	PUNCT
ejpam-6075	331	10	.	.	PUNCT
ejpam-6075	332	1	let	let	VERB
ejpam-6075	332	2	v0	v0	PROPN
ejpam-6075	332	3	∈	∈	PROPN
ejpam-6075	332	4	v	v	X
ejpam-6075	332	5	(	(	PUNCT
ejpam-6075	332	6	g	g	NOUN
ejpam-6075	332	7	)	)	PUNCT
ejpam-6075	332	8	be	be	AUX
ejpam-6075	332	9	such	such	ADJ
ejpam-6075	332	10	that	that	DET
ejpam-6075	332	11	|ng(v0)|	|ng(v0)|	NOUN
ejpam-6075	332	12	=	=	PUNCT
ejpam-6075	332	13	n−	n−	NOUN
ejpam-6075	332	14	1	1	NUM
ejpam-6075	332	15	and	and	CCONJ
ejpam-6075	332	16	let	let	VERB
ejpam-6075	332	17	q	q	PROPN
ejpam-6075	332	18	∈	∈	PROPN
ejpam-6075	332	19	v	v	ADP
ejpam-6075	332	20	(	(	PUNCT
ejpam-6075	332	21	g	g	NOUN
ejpam-6075	332	22	)	)	PUNCT
ejpam-6075	332	23	\	\	NOUN
ejpam-6075	332	24	{	{	PUNCT
ejpam-6075	332	25	v0	v0	NOUN
ejpam-6075	332	26	}	}	PUNCT
ejpam-6075	332	27	.	.	PUNCT
ejpam-6075	333	1	then	then	ADV
ejpam-6075	333	2	v0	v0	PROPN
ejpam-6075	333	3	and	and	CCONJ
ejpam-6075	333	4	q	q	AUX
ejpam-6075	333	5	satisfy	satisfy	VERB
ejpam-6075	333	6	the	the	DET
ejpam-6075	333	7	properties	property	NOUN
ejpam-6075	333	8	(	(	PUNCT
ejpam-6075	333	9	p1	p1	PROPN
ejpam-6075	333	10	)	)	PUNCT
ejpam-6075	333	11	and	and	CCONJ
ejpam-6075	333	12	(	(	PUNCT
ejpam-6075	333	13	p2	p2	PROPN
ejpam-6075	333	14	)	)	PUNCT
ejpam-6075	333	15	of	of	ADP
ejpam-6075	333	16	theorem	theorem	NOUN
ejpam-6075	333	17	5(ii	5(ii	NUM
ejpam-6075	333	18	)	)	PUNCT
ejpam-6075	333	19	.	.	PUNCT
ejpam-6075	334	1	therefore	therefore	ADV
ejpam-6075	334	2	,	,	PUNCT
ejpam-6075	334	3	γsh(g	γsh(g	NOUN
ejpam-6075	334	4	)	)	PUNCT
ejpam-6075	334	5	=	=	SYM
ejpam-6075	334	6	2	2	X
ejpam-6075	334	7	.	.	NOUN
ejpam-6075	334	8	remark	remark	NOUN
ejpam-6075	334	9	2	2	NUM
ejpam-6075	334	10	.	.	PUNCT
ejpam-6075	335	1	there	there	PRON
ejpam-6075	335	2	are	be	VERB
ejpam-6075	335	3	graphs	graph	NOUN
ejpam-6075	335	4	g	g	NOUN
ejpam-6075	335	5	with	with	ADP
ejpam-6075	335	6	γsh(g	γsh(g	NOUN
ejpam-6075	335	7	)	)	PUNCT
ejpam-6075	335	8	=	=	SYM
ejpam-6075	335	9	2	2	NUM
ejpam-6075	335	10	such	such	ADJ
ejpam-6075	335	11	that	that	PRON
ejpam-6075	335	12	γ(g	γ(g	PROPN
ejpam-6075	335	13	)	)	PUNCT
ejpam-6075	335	14	̸=	̸=	PROPN
ejpam-6075	335	15	1	1	NUM
ejpam-6075	335	16	.	.	PUNCT
ejpam-6075	335	17	to	to	PART
ejpam-6075	335	18	see	see	VERB
ejpam-6075	335	19	this	this	PRON
ejpam-6075	335	20	,	,	PUNCT
ejpam-6075	335	21	consider	consider	VERB
ejpam-6075	335	22	g	g	PROPN
ejpam-6075	335	23	∈	∈	PROPN
ejpam-6075	335	24	{	{	PUNCT
ejpam-6075	335	25	p4	p4	ADJ
ejpam-6075	335	26	,	,	PUNCT
ejpam-6075	335	27	c4	c4	NOUN
ejpam-6075	335	28	,	,	PUNCT
ejpam-6075	335	29	h	h	NOUN
ejpam-6075	335	30	}	}	PUNCT
ejpam-6075	335	31	in	in	ADP
ejpam-6075	335	32	figure	figure	NOUN
ejpam-6075	335	33	2	2	NUM
ejpam-6075	335	34	.	.	PUNCT
ejpam-6075	335	35	clearly	clearly	ADV
ejpam-6075	335	36	,	,	PUNCT
ejpam-6075	335	37	γ(g	γ(g	PROPN
ejpam-6075	335	38	)	)	PUNCT
ejpam-6075	335	39	=	=	SYM
ejpam-6075	335	40	2	2	NUM
ejpam-6075	335	41	̸=	̸=	PROPN
ejpam-6075	335	42	1	1	NUM
ejpam-6075	335	43	.	.	PUNCT
ejpam-6075	336	1	it	it	PRON
ejpam-6075	336	2	can	can	AUX
ejpam-6075	336	3	be	be	AUX
ejpam-6075	336	4	verified	verify	VERB
ejpam-6075	336	5	easily	easily	ADV
ejpam-6075	336	6	that	that	SCONJ
ejpam-6075	336	7	the	the	DET
ejpam-6075	336	8	blackened	blacken	VERB
ejpam-6075	336	9	vertices	vertex	NOUN
ejpam-6075	336	10	form	form	VERB
ejpam-6075	336	11	a	a	DET
ejpam-6075	336	12	γsh	γsh	NOUN
ejpam-6075	336	13	-	-	PUNCT
ejpam-6075	336	14	set	set	NOUN
ejpam-6075	336	15	in	in	ADP
ejpam-6075	336	16	g.	g.	PROPN
ejpam-6075	336	17	.........	.........	PUNCT
ejpam-6075	337	1	........	........	PUNCT
ejpam-6075	337	2	........	........	PUNCT
ejpam-6075	337	3	........	........	PUNCT
ejpam-6075	337	4	........	........	PUNCT
ejpam-6075	337	5	........	........	PUNCT
ejpam-6075	337	6	........	........	PUNCT
ejpam-6075	337	7	........	........	PUNCT
ejpam-6075	337	8	........	........	PUNCT
ejpam-6075	337	9	...	...	PUNCT
ejpam-6075	338	1	....................................	....................................	PUNCT
ejpam-6075	338	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-6075	339	1	.........	.........	PUNCT
ejpam-6075	339	2	........	........	PUNCT
ejpam-6075	339	3	........	........	PUNCT
ejpam-6075	339	4	........	........	PUNCT
ejpam-6075	339	5	........	........	PUNCT
ejpam-6075	339	6	........	........	PUNCT
ejpam-6075	339	7	........	........	PUNCT
ejpam-6075	339	8	........	........	PUNCT
ejpam-6075	339	9	........	........	PUNCT
ejpam-6075	339	10	...	...	PUNCT
ejpam-6075	340	1	....................................	....................................	PUNCT
ejpam-6075	340	2	....................................	....................................	PUNCT
ejpam-6075	340	3	.........	.........	PUNCT
ejpam-6075	340	4	........	........	PUNCT
ejpam-6075	340	5	........	........	PUNCT
ejpam-6075	340	6	........	........	PUNCT
ejpam-6075	340	7	........	........	PUNCT
ejpam-6075	340	8	........	........	PUNCT
ejpam-6075	340	9	........	........	PUNCT
ejpam-6075	340	10	........	........	PUNCT
ejpam-6075	340	11	........	........	PUNCT
ejpam-6075	340	12	...	...	PUNCT
ejpam-6075	341	1	....................................	....................................	PUNCT
ejpam-6075	341	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-6075	342	1	.........	.........	PUNCT
ejpam-6075	342	2	........	........	PUNCT
ejpam-6075	342	3	........	........	PUNCT
ejpam-6075	342	4	........	........	PUNCT
ejpam-6075	342	5	........	........	PUNCT
ejpam-6075	342	6	........	........	PUNCT
ejpam-6075	342	7	........	........	PUNCT
ejpam-6075	342	8	........	........	PUNCT
ejpam-6075	342	9	........	........	PUNCT
ejpam-6075	342	10	...	...	PUNCT
ejpam-6075	343	1	....................................	....................................	PUNCT
ejpam-6075	343	2	............................................................................	............................................................................	PUNCT
ejpam-6075	343	3	........................................................................	........................................................................	PUNCT
ejpam-6075	344	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-6075	344	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-6075	345	1	....................................	....................................	PUNCT
ejpam-6075	345	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-6075	346	1	....................................	....................................	PUNCT
ejpam-6075	346	2	....................................	....................................	PUNCT
ejpam-6075	347	1	...........	...........	PUNCT
ejpam-6075	347	2	..........	..........	PUNCT
ejpam-6075	348	1	..........	..........	PUNCT
ejpam-6075	348	2	..........	..........	PUNCT
ejpam-6075	349	1	..........	..........	PUNCT
ejpam-6075	349	2	..........	..........	PUNCT
ejpam-6075	350	1	..........	..........	PUNCT
ejpam-6075	350	2	..........	..........	PUNCT
ejpam-6075	351	1	..........	..........	PUNCT
ejpam-6075	351	2	..	..	PUNCT
ejpam-6075	351	3	....................................	....................................	PUNCT
ejpam-6075	352	1	....................................	....................................	PUNCT
ejpam-6075	352	2	.........	.........	PUNCT
ejpam-6075	352	3	........	........	PUNCT
ejpam-6075	352	4	........	........	PUNCT
ejpam-6075	352	5	........	........	PUNCT
ejpam-6075	352	6	........	........	PUNCT
ejpam-6075	352	7	........	........	PUNCT
ejpam-6075	352	8	........	........	PUNCT
ejpam-6075	352	9	........	........	PUNCT
ejpam-6075	352	10	........	........	PUNCT
ejpam-6075	352	11	...	...	PUNCT
ejpam-6075	353	1	....................................	....................................	PUNCT
ejpam-6075	353	2	....................................	....................................	PUNCT
ejpam-6075	354	1	p4	p4	ADJ
ejpam-6075	354	2	c4	c4	NOUN
ejpam-6075	354	3	h	h	NOUN
ejpam-6075	354	4	•	•	ADJ
ejpam-6075	354	5	•	•	NUM
ejpam-6075	354	6	•	•	NUM
ejpam-6075	354	7	•	•	NUM
ejpam-6075	354	8	•	•	NOUN
ejpam-6075	354	9	•	•	NUM
ejpam-6075	354	10	figure	figure	NOUN
ejpam-6075	354	11	2	2	NUM
ejpam-6075	354	12	:	:	PUNCT
ejpam-6075	354	13	graph	graph	VERB
ejpam-6075	354	14	g	g	NOUN
ejpam-6075	354	15	with	with	ADP
ejpam-6075	354	16	γsh(g	γsh(g	NOUN
ejpam-6075	354	17	)	)	PUNCT
ejpam-6075	354	18	=	=	SYM
ejpam-6075	354	19	2	2	NUM
ejpam-6075	354	20	and	and	CCONJ
ejpam-6075	354	21	γ(g	γ(g	PROPN
ejpam-6075	354	22	)	)	PUNCT
ejpam-6075	355	1	=	=	PUNCT
ejpam-6075	355	2	2	2	NUM
ejpam-6075	355	3	the	the	DET
ejpam-6075	355	4	next	next	ADJ
ejpam-6075	355	5	result	result	NOUN
ejpam-6075	355	6	is	be	AUX
ejpam-6075	355	7	a	a	DET
ejpam-6075	355	8	consequence	consequence	NOUN
ejpam-6075	355	9	of	of	ADP
ejpam-6075	355	10	theorem	theorem	ADJ
ejpam-6075	355	11	1	1	NUM
ejpam-6075	355	12	,	,	PUNCT
ejpam-6075	355	13	theorem	theorem	VERB
ejpam-6075	355	14	6	6	NUM
ejpam-6075	355	15	,	,	PUNCT
ejpam-6075	355	16	and	and	CCONJ
ejpam-6075	355	17	theorem	theorem	VERB
ejpam-6075	355	18	5(ii	5(ii	NUM
ejpam-6075	355	19	)	)	PUNCT
ejpam-6075	355	20	.	.	PUNCT
ejpam-6075	356	1	corollary	corollary	ADJ
ejpam-6075	356	2	2	2	NUM
ejpam-6075	356	3	.	.	PUNCT
ejpam-6075	357	1	let	let	VERB
ejpam-6075	357	2	g	g	PRON
ejpam-6075	357	3	be	be	AUX
ejpam-6075	357	4	a	a	DET
ejpam-6075	357	5	graph	graph	NOUN
ejpam-6075	357	6	of	of	ADP
ejpam-6075	357	7	order	order	NOUN
ejpam-6075	357	8	n	n	PRON
ejpam-6075	357	9	where	where	SCONJ
ejpam-6075	357	10	3	3	NUM
ejpam-6075	357	11	≤	≤	NOUN
ejpam-6075	357	12	n	n	PRON
ejpam-6075	357	13	≤	≤	NOUN
ejpam-6075	357	14	4	4	NUM
ejpam-6075	357	15	.	.	PUNCT
ejpam-6075	358	1	if	if	SCONJ
ejpam-6075	358	2	γsh(g	γsh(g	NOUN
ejpam-6075	358	3	)	)	PUNCT
ejpam-6075	358	4	=	=	SYM
ejpam-6075	358	5	2	2	NUM
ejpam-6075	358	6	,	,	PUNCT
ejpam-6075	358	7	then	then	ADV
ejpam-6075	358	8	g	g	PROPN
ejpam-6075	358	9	∈	∈	PROPN
ejpam-6075	358	10	{	{	PUNCT
ejpam-6075	358	11	p3	p3	PROPN
ejpam-6075	358	12	,	,	PUNCT
ejpam-6075	358	13	p4	p4	ADJ
ejpam-6075	358	14	,	,	PUNCT
ejpam-6075	358	15	c4,k1,3	c4,k1,3	PROPN
ejpam-6075	358	16	}	}	PUNCT
ejpam-6075	358	17	.	.	PUNCT
ejpam-6075	359	1	proof	proof	NOUN
ejpam-6075	359	2	.	.	PUNCT
ejpam-6075	360	1	by	by	ADP
ejpam-6075	360	2	theorem	theorem	NOUN
ejpam-6075	360	3	1	1	NUM
ejpam-6075	360	4	and	and	CCONJ
ejpam-6075	360	5	theorem	theorem	VERB
ejpam-6075	360	6	5(ii	5(ii	NUM
ejpam-6075	360	7	)	)	PUNCT
ejpam-6075	360	8	,	,	PUNCT
ejpam-6075	360	9	none	none	NOUN
ejpam-6075	360	10	of	of	ADP
ejpam-6075	360	11	the	the	DET
ejpam-6075	360	12	disconnected	disconnected	ADJ
ejpam-6075	360	13	graphs	graph	NOUN
ejpam-6075	360	14	g	g	NOUN
ejpam-6075	360	15	satisfies	satisfy	VERB
ejpam-6075	360	16	γsh(g	γsh(g	NOUN
ejpam-6075	360	17	)	)	PUNCT
ejpam-6075	360	18	=	=	SYM
ejpam-6075	361	1	2	2	X
ejpam-6075	361	2	.	.	PUNCT
ejpam-6075	361	3	from	from	ADP
ejpam-6075	361	4	theorem	theorem	ADJ
ejpam-6075	361	5	6	6	NUM
ejpam-6075	361	6	,	,	PUNCT
ejpam-6075	361	7	it	it	PRON
ejpam-6075	361	8	follows	follow	VERB
ejpam-6075	361	9	that	that	PRON
ejpam-6075	361	10	γsh(p3	γsh(p3	PROPN
ejpam-6075	361	11	)	)	PUNCT
ejpam-6075	361	12	=	=	SYM
ejpam-6075	361	13	γsh(k1,3	γsh(k1,3	X
ejpam-6075	361	14	)	)	PUNCT
ejpam-6075	361	15	=	=	SYM
ejpam-6075	361	16	2	2	X
ejpam-6075	361	17	.	.	X
ejpam-6075	361	18	suppose	suppose	VERB
ejpam-6075	361	19	n	n	PROPN
ejpam-6075	361	20	=	=	SYM
ejpam-6075	361	21	4	4	X
ejpam-6075	361	22	.	.	PUNCT
ejpam-6075	361	23	as	as	SCONJ
ejpam-6075	361	24	seen	see	VERB
ejpam-6075	361	25	in	in	ADP
ejpam-6075	361	26	remark	remark	NOUN
ejpam-6075	361	27	2	2	NUM
ejpam-6075	361	28	,	,	PUNCT
ejpam-6075	361	29	γsh(p4	γsh(p4	NOUN
ejpam-6075	361	30	)	)	PUNCT
ejpam-6075	361	31	=	=	SYM
ejpam-6075	361	32	γsh(c4	γsh(c4	NOUN
ejpam-6075	361	33	)	)	PUNCT
ejpam-6075	361	34	=	=	SYM
ejpam-6075	362	1	2	2	X
ejpam-6075	362	2	.	.	X
ejpam-6075	362	3	if	if	SCONJ
ejpam-6075	362	4	g	g	PROPN
ejpam-6075	362	5	is	be	AUX
ejpam-6075	362	6	connected	connect	VERB
ejpam-6075	362	7	and	and	CCONJ
ejpam-6075	362	8	g	g	PROPN
ejpam-6075	362	9	/∈	/∈	PUNCT
ejpam-6075	362	10	{	{	PUNCT
ejpam-6075	362	11	p4	p4	ADJ
ejpam-6075	362	12	,	,	PUNCT
ejpam-6075	362	13	c4,k1,3	c4,k1,3	PROPN
ejpam-6075	362	14	}	}	PUNCT
ejpam-6075	362	15	,	,	PUNCT
ejpam-6075	362	16	then	then	ADV
ejpam-6075	362	17	γ(g	γ(g	PROPN
ejpam-6075	362	18	)	)	PUNCT
ejpam-6075	363	1	=	=	SYM
ejpam-6075	363	2	1	1	NUM
ejpam-6075	363	3	and	and	CCONJ
ejpam-6075	363	4	either	either	CCONJ
ejpam-6075	363	5	g	g	PROPN
ejpam-6075	363	6	has	have	VERB
ejpam-6075	363	7	more	more	ADJ
ejpam-6075	363	8	that	that	SCONJ
ejpam-6075	363	9	two	two	NUM
ejpam-6075	363	10	dominating	dominating	NOUN
ejpam-6075	363	11	vertices	vertex	NOUN
ejpam-6075	363	12	or	or	CCONJ
ejpam-6075	363	13	contains	contain	VERB
ejpam-6075	363	14	a	a	DET
ejpam-6075	363	15	single	single	ADJ
ejpam-6075	363	16	dominating	dominating	NOUN
ejpam-6075	363	17	vertex	vertex	NOUN
ejpam-6075	363	18	and	and	CCONJ
ejpam-6075	363	19	another	another	DET
ejpam-6075	363	20	vertex	vertex	NOUN
ejpam-6075	363	21	with	with	ADP
ejpam-6075	363	22	two	two	NUM
ejpam-6075	363	23	neighbors	neighbor	NOUN
ejpam-6075	363	24	.	.	PUNCT
ejpam-6075	364	1	thus	thus	ADV
ejpam-6075	364	2	,	,	PUNCT
ejpam-6075	364	3	γsh(g	γsh(g	NOUN
ejpam-6075	364	4	)	)	PUNCT
ejpam-6075	364	5	≥	≥	NOUN
ejpam-6075	364	6	3	3	NUM
ejpam-6075	364	7	by	by	ADP
ejpam-6075	364	8	theorem	theorem	NOUN
ejpam-6075	364	9	6	6	NUM
ejpam-6075	364	10	.	.	PUNCT
ejpam-6075	365	1	therefore	therefore	ADV
ejpam-6075	365	2	,	,	PUNCT
ejpam-6075	365	3	g	g	PROPN
ejpam-6075	365	4	∈	∈	PROPN
ejpam-6075	365	5	{	{	PUNCT
ejpam-6075	365	6	p3	p3	PROPN
ejpam-6075	365	7	,	,	PUNCT
ejpam-6075	365	8	p4	p4	ADJ
ejpam-6075	365	9	,	,	PUNCT
ejpam-6075	365	10	c4,k1,3	c4,k1,3	PROPN
ejpam-6075	365	11	}	}	PUNCT
ejpam-6075	365	12	.	.	PUNCT
ejpam-6075	366	1	proposition	proposition	NOUN
ejpam-6075	366	2	1	1	NUM
ejpam-6075	366	3	.	.	PUNCT
ejpam-6075	367	1	let	let	VERB
ejpam-6075	367	2	n	n	PRON
ejpam-6075	367	3	be	be	AUX
ejpam-6075	367	4	any	any	DET
ejpam-6075	367	5	positive	positive	ADJ
ejpam-6075	367	6	integer	integer	NOUN
ejpam-6075	367	7	.	.	PUNCT
ejpam-6075	368	1	then	then	ADV
ejpam-6075	368	2	γsh(pn	γsh(pn	NOUN
ejpam-6075	368	3	)	)	PUNCT
ejpam-6075	368	4	=	=	SYM
ejpam-6075	368	5			PROPN
ejpam-6075	368	6	n	n	NOUN
ejpam-6075	368	7	if	if	SCONJ
ejpam-6075	368	8	n	n	ADV
ejpam-6075	368	9	∈	∈	PROPN
ejpam-6075	368	10	{	{	PUNCT
ejpam-6075	368	11	1	1	NUM
ejpam-6075	368	12	,	,	PUNCT
ejpam-6075	368	13	2	2	NUM
ejpam-6075	368	14	}	}	SYM
ejpam-6075	368	15	2	2	NUM
ejpam-6075	368	16	if	if	SCONJ
ejpam-6075	368	17	n	n	NOUN
ejpam-6075	368	18	=	=	SYM
ejpam-6075	368	19	3	3	NUM
ejpam-6075	368	20	2	2	NUM
ejpam-6075	368	21	t	t	NOUN
ejpam-6075	368	22	if	if	SCONJ
ejpam-6075	368	23	n	n	NOUN
ejpam-6075	368	24	=	=	SYM
ejpam-6075	368	25	4	4	NUM
ejpam-6075	368	26	t	t	PROPN
ejpam-6075	368	27	,	,	PUNCT
ejpam-6075	368	28	t	t	PROPN
ejpam-6075	368	29	≥	≥	NUM
ejpam-6075	368	30	1	1	NUM
ejpam-6075	368	31	2t+	2t+	NUM
ejpam-6075	368	32	1	1	NUM
ejpam-6075	368	33	if	if	SCONJ
ejpam-6075	368	34	n	n	ADV
ejpam-6075	368	35	=	=	SYM
ejpam-6075	368	36	4t+	4t+	NUM
ejpam-6075	368	37	1	1	NUM
ejpam-6075	368	38	,	,	PUNCT
ejpam-6075	368	39	t	t	PROPN
ejpam-6075	368	40	≥	≥	NUM
ejpam-6075	368	41	1	1	NUM
ejpam-6075	368	42	2t+	2t+	NUM
ejpam-6075	368	43	2	2	NUM
ejpam-6075	368	44	if	if	SCONJ
ejpam-6075	368	45	n	n	ADV
ejpam-6075	368	46	=	=	SYM
ejpam-6075	368	47	4t+	4t+	NUM
ejpam-6075	368	48	2	2	NUM
ejpam-6075	368	49	,	,	PUNCT
ejpam-6075	368	50	t	t	PROPN
ejpam-6075	368	51	≥	≥	NUM
ejpam-6075	368	52	1	1	NUM
ejpam-6075	368	53	or	or	CCONJ
ejpam-6075	368	54	n	n	NOUN
ejpam-6075	368	55	=	=	SYM
ejpam-6075	368	56	4t+	4t+	NUM
ejpam-6075	368	57	3	3	NUM
ejpam-6075	368	58	,	,	PUNCT
ejpam-6075	368	59	t	t	PROPN
ejpam-6075	368	60	≥	≥	NUM
ejpam-6075	368	61	1	1	NUM
ejpam-6075	368	62	.	.	PUNCT
ejpam-6075	368	63	f.	f.	PROPN
ejpam-6075	368	64	l.	l.	PROPN
ejpam-6075	368	65	alfeche	alfeche	PROPN
ejpam-6075	368	66	,	,	PUNCT
ejpam-6075	368	67	g.	g.	PROPN
ejpam-6075	368	68	a.	a.	PROPN
ejpam-6075	368	69	malacas	malacas	PROPN
ejpam-6075	368	70	,	,	PUNCT
ejpam-6075	368	71	s.	s.	PROPN
ejpam-6075	368	72	canoy	canoy	PROPN
ejpam-6075	368	73	jr	jr	PROPN
ejpam-6075	368	74	.	.	PROPN
ejpam-6075	368	75	/	/	SYM
ejpam-6075	368	76	eur	eur	PROPN
ejpam-6075	368	77	.	.	PUNCT
ejpam-6075	369	1	j.	j.	PROPN
ejpam-6075	369	2	pure	pure	PROPN
ejpam-6075	369	3	appl	appl	PROPN
ejpam-6075	369	4	.	.	PROPN
ejpam-6075	369	5	math	math	PROPN
ejpam-6075	369	6	,	,	PUNCT
ejpam-6075	369	7	18	18	NUM
ejpam-6075	369	8	(	(	PUNCT
ejpam-6075	369	9	2	2	NUM
ejpam-6075	369	10	)	)	PUNCT
ejpam-6075	369	11	(	(	PUNCT
ejpam-6075	369	12	2025	2025	NUM
ejpam-6075	369	13	)	)	PUNCT
ejpam-6075	369	14	,	,	PUNCT
ejpam-6075	369	15	6075	6075	NUM
ejpam-6075	369	16	8	8	NUM
ejpam-6075	369	17	of	of	ADP
ejpam-6075	369	18	14	14	NUM
ejpam-6075	369	19	proof	proof	NOUN
ejpam-6075	369	20	.	.	PUNCT
ejpam-6075	370	1	let	let	VERB
ejpam-6075	370	2	pn	pn	VERB
ejpam-6075	370	3	=	=	PUNCT
ejpam-6075	371	1	[	[	X
ejpam-6075	371	2	v1	v1	NOUN
ejpam-6075	371	3	,	,	PUNCT
ejpam-6075	371	4	v2	v2	NOUN
ejpam-6075	371	5	,	,	PUNCT
ejpam-6075	371	6	.	.	PUNCT
ejpam-6075	371	7	.	.	PUNCT
ejpam-6075	371	8	.	.	PUNCT
ejpam-6075	372	1	,	,	PUNCT
ejpam-6075	372	2	vn	vn	X
ejpam-6075	372	3	]	]	PUNCT
ejpam-6075	372	4	.	.	PUNCT
ejpam-6075	373	1	then	then	ADV
ejpam-6075	373	2	γsh(pn	γsh(pn	NOUN
ejpam-6075	373	3	)	)	PUNCT
ejpam-6075	373	4	=	=	SYM
ejpam-6075	373	5	n	n	NOUN
ejpam-6075	373	6	for	for	ADP
ejpam-6075	373	7	n	n	PRON
ejpam-6075	373	8	∈	∈	NOUN
ejpam-6075	373	9	{	{	PUNCT
ejpam-6075	373	10	1	1	NUM
ejpam-6075	373	11	,	,	PUNCT
ejpam-6075	373	12	2	2	NUM
ejpam-6075	373	13	}	}	PUNCT
ejpam-6075	373	14	by	by	ADP
ejpam-6075	373	15	corollary	corollary	ADJ
ejpam-6075	373	16	4	4	NUM
ejpam-6075	373	17	,	,	PUNCT
ejpam-6075	373	18	and	and	CCONJ
ejpam-6075	373	19	γsh(p3	γsh(p3	PROPN
ejpam-6075	373	20	)	)	PUNCT
ejpam-6075	373	21	=	=	SYM
ejpam-6075	373	22	2	2	NUM
ejpam-6075	373	23	by	by	ADP
ejpam-6075	373	24	theorem	theorem	NOUN
ejpam-6075	373	25	6	6	NUM
ejpam-6075	373	26	.	.	PUNCT
ejpam-6075	373	27	suppose	suppose	VERB
ejpam-6075	373	28	n	n	PRON
ejpam-6075	373	29	≥	≥	X
ejpam-6075	373	30	4	4	NUM
ejpam-6075	373	31	and	and	CCONJ
ejpam-6075	373	32	consider	consider	VERB
ejpam-6075	373	33	the	the	DET
ejpam-6075	373	34	following	follow	VERB
ejpam-6075	373	35	cases	case	NOUN
ejpam-6075	373	36	:	:	PUNCT
ejpam-6075	373	37	case	case	NOUN
ejpam-6075	373	38	1	1	NUM
ejpam-6075	373	39	.	.	PUNCT
ejpam-6075	374	1	n	n	NOUN
ejpam-6075	374	2	=	=	SYM
ejpam-6075	374	3	4	4	NUM
ejpam-6075	374	4	t.	t.	NOUN
ejpam-6075	374	5	let	let	VERB
ejpam-6075	374	6	sj	sj	INTJ
ejpam-6075	374	7	=	=	PUNCT
ejpam-6075	374	8	{	{	PUNCT
ejpam-6075	374	9	v4j−3	v4j−3	PROPN
ejpam-6075	374	10	,	,	PUNCT
ejpam-6075	374	11	v4j−2	v4j−2	PROPN
ejpam-6075	374	12	}	}	PUNCT
ejpam-6075	374	13	for	for	ADP
ejpam-6075	374	14	each	each	DET
ejpam-6075	374	15	j	j	PROPN
ejpam-6075	374	16	∈	∈	PROPN
ejpam-6075	374	17	{	{	PUNCT
ejpam-6075	374	18	1	1	NUM
ejpam-6075	374	19	,	,	PUNCT
ejpam-6075	374	20	2	2	NUM
ejpam-6075	374	21	,	,	PUNCT
ejpam-6075	374	22	.	.	PUNCT
ejpam-6075	374	23	.	.	PUNCT
ejpam-6075	375	1	.	.	PUNCT
ejpam-6075	376	1	,	,	PUNCT
ejpam-6075	376	2	t	t	X
ejpam-6075	376	3	}	}	PUNCT
ejpam-6075	376	4	and	and	CCONJ
ejpam-6075	376	5	set	set	VERB
ejpam-6075	376	6	s	s	PART
ejpam-6075	376	7	=	=	PUNCT
ejpam-6075	376	8	∪t	∪t	X
ejpam-6075	376	9	j=1sj	j=1sj	NOUN
ejpam-6075	376	10	.	.	PUNCT
ejpam-6075	377	1	then	then	ADV
ejpam-6075	377	2	s	s	VERB
ejpam-6075	377	3	is	be	AUX
ejpam-6075	377	4	a	a	DET
ejpam-6075	377	5	secure	secure	ADJ
ejpam-6075	377	6	hop	hop	NOUN
ejpam-6075	377	7	dominating	dominating	NOUN
ejpam-6075	377	8	set	set	NOUN
ejpam-6075	377	9	and	and	CCONJ
ejpam-6075	377	10	|s|	|s|	PROPN
ejpam-6075	377	11	=	=	SYM
ejpam-6075	377	12	∑t	∑t	PROPN
ejpam-6075	377	13	j=1	j=1	NOUN
ejpam-6075	377	14	|sj	|sj	X
ejpam-6075	377	15	|	|	NOUN
ejpam-6075	377	16	=	=	SYM
ejpam-6075	377	17	2	2	NUM
ejpam-6075	377	18	t.	t.	NOUN
ejpam-6075	377	19	let	let	VERB
ejpam-6075	377	20	s′	s′	PROPN
ejpam-6075	377	21	be	be	AUX
ejpam-6075	377	22	a	a	DET
ejpam-6075	377	23	hop	hop	NOUN
ejpam-6075	377	24	dominating	dominating	NOUN
ejpam-6075	377	25	set	set	NOUN
ejpam-6075	377	26	such	such	ADJ
ejpam-6075	377	27	that	that	SCONJ
ejpam-6075	377	28	|s′|	|s′|	NOUN
ejpam-6075	377	29	<	<	X
ejpam-6075	377	30	|s|	|s|	PROPN
ejpam-6075	377	31	.	.	PUNCT
ejpam-6075	378	1	then	then	ADV
ejpam-6075	378	2	one	one	PRON
ejpam-6075	378	3	can	can	AUX
ejpam-6075	378	4	find	find	VERB
ejpam-6075	378	5	a	a	DET
ejpam-6075	378	6	vertex	vertex	NOUN
ejpam-6075	378	7	z	z	NOUN
ejpam-6075	378	8	∈	∈	PROPN
ejpam-6075	378	9	v	v	NOUN
ejpam-6075	378	10	(	(	PUNCT
ejpam-6075	378	11	pn	pn	NOUN
ejpam-6075	378	12	)	)	PUNCT
ejpam-6075	378	13	\	\	NOUN
ejpam-6075	378	14	s′	s′	VERB
ejpam-6075	378	15	such	such	ADJ
ejpam-6075	378	16	that	that	PRON
ejpam-6075	378	17	for	for	ADP
ejpam-6075	378	18	each	each	DET
ejpam-6075	378	19	v	v	NOUN
ejpam-6075	378	20	∈	∈	PROPN
ejpam-6075	378	21	s′	s′	VERB
ejpam-6075	378	22	∩n2	∩n2	PROPN
ejpam-6075	378	23	pn	pn	PROPN
ejpam-6075	378	24	(	(	PUNCT
ejpam-6075	378	25	z	z	NOUN
ejpam-6075	378	26	)	)	PUNCT
ejpam-6075	378	27	,	,	PUNCT
ejpam-6075	378	28	either	either	CCONJ
ejpam-6075	378	29	|ephn(v;s′)|	|ephn(v;s′)|	PROPN
ejpam-6075	378	30	=	=	SYM
ejpam-6075	378	31	1	1	NUM
ejpam-6075	378	32	and	and	CCONJ
ejpam-6075	378	33	v	v	NOUN
ejpam-6075	378	34	/∈	/∈	PUNCT
ejpam-6075	379	1	ephn(v	ephn(v	INTJ
ejpam-6075	379	2	;	;	PUNCT
ejpam-6075	379	3	s	s	X
ejpam-6075	379	4	)	)	PUNCT
ejpam-6075	379	5	or	or	CCONJ
ejpam-6075	379	6	|ephn(v;s′)|	|ephn(v;s′)|	PROPN
ejpam-6075	379	7	=	=	SYM
ejpam-6075	379	8	2	2	NUM
ejpam-6075	379	9	.	.	PUNCT
ejpam-6075	379	10	hence	hence	ADV
ejpam-6075	379	11	,	,	PUNCT
ejpam-6075	379	12	s′	s′	PROPN
ejpam-6075	379	13	is	be	AUX
ejpam-6075	379	14	not	not	PART
ejpam-6075	379	15	a	a	DET
ejpam-6075	379	16	secure	secure	ADJ
ejpam-6075	379	17	hop	hop	NOUN
ejpam-6075	379	18	dominating	dominating	NOUN
ejpam-6075	379	19	set	set	NOUN
ejpam-6075	379	20	.	.	PUNCT
ejpam-6075	380	1	thus	thus	ADV
ejpam-6075	380	2	,	,	PUNCT
ejpam-6075	380	3	s	s	VERB
ejpam-6075	380	4	is	be	AUX
ejpam-6075	380	5	a	a	DET
ejpam-6075	380	6	γsh	γsh	NOUN
ejpam-6075	380	7	-	-	PUNCT
ejpam-6075	380	8	set	set	VERB
ejpam-6075	380	9	in	in	ADP
ejpam-6075	380	10	pn	pn	PROPN
ejpam-6075	380	11	and	and	CCONJ
ejpam-6075	380	12	γsh(pn	γsh(pn	NOUN
ejpam-6075	380	13	)	)	PUNCT
ejpam-6075	380	14	=	=	PUNCT
ejpam-6075	380	15	|s|	|s|	NOUN
ejpam-6075	380	16	=	=	SYM
ejpam-6075	380	17	2	2	NUM
ejpam-6075	380	18	t.	t.	NOUN
ejpam-6075	380	19	case	case	NOUN
ejpam-6075	380	20	2	2	NUM
ejpam-6075	380	21	.	.	PUNCT
ejpam-6075	381	1	n	n	NOUN
ejpam-6075	381	2	=	=	SYM
ejpam-6075	381	3	4t+	4t+	NUM
ejpam-6075	381	4	1(t	1(t	NUM
ejpam-6075	381	5	≥	≥	NOUN
ejpam-6075	381	6	1	1	NUM
ejpam-6075	381	7	)	)	PUNCT
ejpam-6075	381	8	.	.	PUNCT
ejpam-6075	382	1	let	let	VERB
ejpam-6075	382	2	sj	sj	INTJ
ejpam-6075	382	3	=	=	VERB
ejpam-6075	382	4	{	{	PUNCT
ejpam-6075	382	5	v4j	v4j	X
ejpam-6075	382	6	,	,	PUNCT
ejpam-6075	382	7	v4j+1	v4j+1	PROPN
ejpam-6075	382	8	}	}	PUNCT
ejpam-6075	382	9	for	for	ADP
ejpam-6075	382	10	each	each	DET
ejpam-6075	382	11	j	j	PROPN
ejpam-6075	382	12	∈	∈	PROPN
ejpam-6075	382	13	{	{	PUNCT
ejpam-6075	382	14	1	1	NUM
ejpam-6075	382	15	,	,	PUNCT
ejpam-6075	382	16	2	2	NUM
ejpam-6075	382	17	,	,	PUNCT
ejpam-6075	382	18	.	.	PUNCT
ejpam-6075	382	19	.	.	PUNCT
ejpam-6075	383	1	.	.	PUNCT
ejpam-6075	384	1	,	,	PUNCT
ejpam-6075	384	2	t	t	PROPN
ejpam-6075	384	3	}	}	PUNCT
ejpam-6075	384	4	.	.	PUNCT
ejpam-6075	385	1	then	then	ADV
ejpam-6075	385	2	s	s	VERB
ejpam-6075	385	3	=	=	PUNCT
ejpam-6075	385	4	{	{	PUNCT
ejpam-6075	385	5	v1}∪[∪t	v1}∪[∪t	ADP
ejpam-6075	385	6	j=1sj	j=1sj	X
ejpam-6075	385	7	]	]	PUNCT
ejpam-6075	385	8	is	be	AUX
ejpam-6075	385	9	a	a	DET
ejpam-6075	385	10	hop	hop	NOUN
ejpam-6075	385	11	dominating	dominating	NOUN
ejpam-6075	385	12	set	set	VERB
ejpam-6075	385	13	in	in	ADP
ejpam-6075	385	14	pn	pn	PROPN
ejpam-6075	385	15	.	.	PUNCT
ejpam-6075	386	1	since	since	SCONJ
ejpam-6075	386	2	|ephn(v;s)|	|ephn(v;s)|	PROPN
ejpam-6075	386	3	≤	≤	ADV
ejpam-6075	386	4	1	1	NUM
ejpam-6075	386	5	for	for	ADP
ejpam-6075	386	6	every	every	DET
ejpam-6075	386	7	v	v	NUM
ejpam-6075	386	8	∈	∈	PROPN
ejpam-6075	386	9	s	s	NOUN
ejpam-6075	386	10	,	,	PUNCT
ejpam-6075	386	11	s	s	VERB
ejpam-6075	386	12	is	be	AUX
ejpam-6075	386	13	a	a	DET
ejpam-6075	386	14	secure	secure	ADJ
ejpam-6075	386	15	hop	hop	NOUN
ejpam-6075	386	16	dominating	dominating	NOUN
ejpam-6075	386	17	set	set	VERB
ejpam-6075	386	18	by	by	ADP
ejpam-6075	386	19	corollary	corollary	ADJ
ejpam-6075	386	20	1	1	NUM
ejpam-6075	386	21	.	.	PUNCT
ejpam-6075	387	1	following	follow	VERB
ejpam-6075	387	2	an	an	DET
ejpam-6075	387	3	argument	argument	NOUN
ejpam-6075	387	4	in	in	ADP
ejpam-6075	387	5	the	the	DET
ejpam-6075	387	6	preceding	precede	VERB
ejpam-6075	387	7	case	case	NOUN
ejpam-6075	387	8	,	,	PUNCT
ejpam-6075	387	9	any	any	DET
ejpam-6075	387	10	hop	hop	NOUN
ejpam-6075	387	11	dominating	dominating	NOUN
ejpam-6075	387	12	set	set	NOUN
ejpam-6075	387	13	s′	s′	VERB
ejpam-6075	387	14	with	with	ADP
ejpam-6075	387	15	|s′|	|s′|	NOUN
ejpam-6075	387	16	<	<	X
ejpam-6075	387	17	|s|	|s|	PROPN
ejpam-6075	387	18	is	be	AUX
ejpam-6075	387	19	not	not	PART
ejpam-6075	387	20	secure	secure	ADJ
ejpam-6075	387	21	hop	hop	NOUN
ejpam-6075	387	22	dominating	dominating	NOUN
ejpam-6075	387	23	.	.	PUNCT
ejpam-6075	388	1	therefore	therefore	ADV
ejpam-6075	388	2	,	,	PUNCT
ejpam-6075	388	3	γsh(pn	γsh(pn	NOUN
ejpam-6075	388	4	)	)	PUNCT
ejpam-6075	388	5	=	=	PUNCT
ejpam-6075	388	6	|s|	|s|	NOUN
ejpam-6075	388	7	=	=	SYM
ejpam-6075	388	8	1	1	NUM
ejpam-6075	388	9	+	+	NUM
ejpam-6075	388	10	∑t	∑t	NOUN
ejpam-6075	388	11	j=1	j=1	NOUN
ejpam-6075	388	12	|sj	|sj	X
ejpam-6075	388	13	|	|	NOUN
ejpam-6075	388	14	=	=	SYM
ejpam-6075	388	15	2t+1	2t+1	PROPN
ejpam-6075	388	16	.	.	PUNCT
ejpam-6075	389	1	case	case	NOUN
ejpam-6075	389	2	3	3	NUM
ejpam-6075	389	3	.	.	PUNCT
ejpam-6075	390	1	n	n	NOUN
ejpam-6075	390	2	=	=	SYM
ejpam-6075	390	3	4t+	4t+	NUM
ejpam-6075	390	4	2	2	NUM
ejpam-6075	390	5	or	or	CCONJ
ejpam-6075	390	6	4t+	4t+	NUM
ejpam-6075	390	7	3	3	NUM
ejpam-6075	390	8	.	.	PUNCT
ejpam-6075	391	1	consider	consider	VERB
ejpam-6075	391	2	the	the	DET
ejpam-6075	391	3	set	set	NOUN
ejpam-6075	391	4	sj	sj	NOUN
ejpam-6075	391	5	=	=	PUNCT
ejpam-6075	391	6	{	{	PUNCT
ejpam-6075	391	7	v4j−3	v4j−3	PROPN
ejpam-6075	391	8	,	,	PUNCT
ejpam-6075	391	9	v4j−2	v4j−2	PROPN
ejpam-6075	391	10	}	}	PUNCT
ejpam-6075	391	11	for	for	ADP
ejpam-6075	391	12	each	each	DET
ejpam-6075	391	13	j	j	PROPN
ejpam-6075	391	14	∈	∈	PROPN
ejpam-6075	391	15	{	{	PUNCT
ejpam-6075	391	16	1	1	NUM
ejpam-6075	391	17	,	,	PUNCT
ejpam-6075	391	18	2	2	NUM
ejpam-6075	391	19	,	,	PUNCT
ejpam-6075	391	20	.	.	PUNCT
ejpam-6075	391	21	.	.	PUNCT
ejpam-6075	392	1	.	.	PUNCT
ejpam-6075	393	1	,	,	PUNCT
ejpam-6075	393	2	t	t	PROPN
ejpam-6075	393	3	+	+	CCONJ
ejpam-6075	393	4	1	1	NUM
ejpam-6075	393	5	}	}	PUNCT
ejpam-6075	393	6	.	.	PUNCT
ejpam-6075	394	1	then	then	ADV
ejpam-6075	394	2	s	s	VERB
ejpam-6075	394	3	=	=	SYM
ejpam-6075	394	4	∪t+1	∪t+1	PROPN
ejpam-6075	394	5	j=1sj	j=1sj	NOUN
ejpam-6075	394	6	is	be	AUX
ejpam-6075	394	7	a	a	DET
ejpam-6075	394	8	γsh	γsh	NOUN
ejpam-6075	394	9	-	-	PUNCT
ejpam-6075	394	10	set	set	VERB
ejpam-6075	394	11	in	in	ADP
ejpam-6075	394	12	pn	pn	PROPN
ejpam-6075	394	13	.	.	PUNCT
ejpam-6075	394	14	therefore	therefore	ADV
ejpam-6075	394	15	,	,	PUNCT
ejpam-6075	394	16	γsh(pn	γsh(pn	NOUN
ejpam-6075	394	17	)	)	PUNCT
ejpam-6075	394	18	=	=	SYM
ejpam-6075	394	19	|s|	|s|	PROPN
ejpam-6075	394	20	=	=	SYM
ejpam-6075	394	21	∑t+1	∑t+1	PROPN
ejpam-6075	394	22	j=1	j=1	NOUN
ejpam-6075	394	23	|sj	|sj	X
ejpam-6075	394	24	|	|	NOUN
ejpam-6075	394	25	=	=	SYM
ejpam-6075	394	26	2(t+	2(t+	NUM
ejpam-6075	394	27	1	1	NUM
ejpam-6075	394	28	)	)	PUNCT
ejpam-6075	394	29	=	=	SYM
ejpam-6075	394	30	2t+	2t+	NUM
ejpam-6075	394	31	2	2	X
ejpam-6075	394	32	.	.	PUNCT
ejpam-6075	395	1	this	this	PRON
ejpam-6075	395	2	proves	prove	VERB
ejpam-6075	395	3	the	the	DET
ejpam-6075	395	4	assertion	assertion	NOUN
ejpam-6075	395	5	.	.	PUNCT
ejpam-6075	396	1	proposition	proposition	NOUN
ejpam-6075	396	2	2	2	NUM
ejpam-6075	396	3	.	.	PUNCT
ejpam-6075	397	1	let	let	VERB
ejpam-6075	397	2	n	n	PRON
ejpam-6075	397	3	be	be	AUX
ejpam-6075	397	4	any	any	DET
ejpam-6075	397	5	positive	positive	ADJ
ejpam-6075	397	6	integer	integer	NOUN
ejpam-6075	397	7	such	such	ADJ
ejpam-6075	397	8	that	that	SCONJ
ejpam-6075	397	9	n	n	NUM
ejpam-6075	397	10	≥	≥	NOUN
ejpam-6075	397	11	3	3	NUM
ejpam-6075	397	12	.	.	PUNCT
ejpam-6075	398	1	then	then	ADV
ejpam-6075	398	2	γsh(cn	γsh(cn	X
ejpam-6075	398	3	)	)	PUNCT
ejpam-6075	398	4	=	=	PUNCT
ejpam-6075	398	5			NUM
ejpam-6075	398	6	3	3	NUM
ejpam-6075	398	7	if	if	SCONJ
ejpam-6075	398	8	n	n	ADV
ejpam-6075	398	9	∈	∈	PROPN
ejpam-6075	398	10	{	{	PUNCT
ejpam-6075	398	11	3	3	NUM
ejpam-6075	398	12	,	,	PUNCT
ejpam-6075	398	13	5	5	NUM
ejpam-6075	398	14	}	}	SYM
ejpam-6075	398	15	2	2	NUM
ejpam-6075	398	16	t	t	NOUN
ejpam-6075	398	17	if	if	SCONJ
ejpam-6075	398	18	n	n	NOUN
ejpam-6075	398	19	=	=	SYM
ejpam-6075	398	20	4	4	NUM
ejpam-6075	398	21	t	t	PROPN
ejpam-6075	398	22	,	,	PUNCT
ejpam-6075	398	23	t	t	PROPN
ejpam-6075	398	24	≥	≥	NUM
ejpam-6075	398	25	1	1	NUM
ejpam-6075	398	26	or	or	CCONJ
ejpam-6075	398	27	n	n	NOUN
ejpam-6075	398	28	=	=	SYM
ejpam-6075	398	29	4t+	4t+	NUM
ejpam-6075	398	30	1	1	NUM
ejpam-6075	398	31	,	,	PUNCT
ejpam-6075	398	32	t	t	PROPN
ejpam-6075	398	33	≥	≥	NUM
ejpam-6075	398	34	2	2	NUM
ejpam-6075	398	35	or	or	CCONJ
ejpam-6075	398	36	n	n	NOUN
ejpam-6075	398	37	=	=	SYM
ejpam-6075	398	38	4t+	4t+	NUM
ejpam-6075	398	39	2	2	NUM
ejpam-6075	398	40	,	,	PUNCT
ejpam-6075	398	41	t	t	PROPN
ejpam-6075	398	42	≥	≥	NUM
ejpam-6075	398	43	1	1	NUM
ejpam-6075	398	44	2t+	2t+	NUM
ejpam-6075	398	45	1	1	NUM
ejpam-6075	398	46	n	n	NOUN
ejpam-6075	398	47	=	=	SYM
ejpam-6075	398	48	4t+	4t+	NUM
ejpam-6075	398	49	3	3	NUM
ejpam-6075	398	50	,	,	PUNCT
ejpam-6075	398	51	t	t	PROPN
ejpam-6075	398	52	≥	≥	NUM
ejpam-6075	398	53	1	1	NUM
ejpam-6075	398	54	.	.	PUNCT
ejpam-6075	399	1	proof	proof	NOUN
ejpam-6075	399	2	.	.	PUNCT
ejpam-6075	400	1	let	let	VERB
ejpam-6075	400	2	cn	cn	PROPN
ejpam-6075	400	3	=	=	PUNCT
ejpam-6075	401	1	[	[	X
ejpam-6075	401	2	v1	v1	NOUN
ejpam-6075	401	3	,	,	PUNCT
ejpam-6075	401	4	v2	v2	NOUN
ejpam-6075	401	5	,	,	PUNCT
ejpam-6075	401	6	.	.	PUNCT
ejpam-6075	401	7	.	.	PUNCT
ejpam-6075	401	8	.	.	PUNCT
ejpam-6075	402	1	,	,	PUNCT
ejpam-6075	402	2	vn	vn	X
ejpam-6075	402	3	,	,	PUNCT
ejpam-6075	402	4	v1	v1	PROPN
ejpam-6075	402	5	]	]	PUNCT
ejpam-6075	402	6	.	.	PUNCT
ejpam-6075	403	1	if	if	SCONJ
ejpam-6075	403	2	n	n	NUM
ejpam-6075	403	3	=	=	SYM
ejpam-6075	403	4	3	3	NUM
ejpam-6075	403	5	,	,	PUNCT
ejpam-6075	403	6	then	then	ADV
ejpam-6075	403	7	γsh(c3	γsh(c3	NOUN
ejpam-6075	403	8	)	)	PUNCT
ejpam-6075	404	1	=	=	SYM
ejpam-6075	404	2	γsh(k3	γsh(k3	X
ejpam-6075	404	3	)	)	PUNCT
ejpam-6075	404	4	=	=	SYM
ejpam-6075	404	5	3	3	NUM
ejpam-6075	404	6	by	by	ADP
ejpam-6075	404	7	corollary	corollary	ADJ
ejpam-6075	404	8	4	4	NUM
ejpam-6075	404	9	.	.	PUNCT
ejpam-6075	405	1	if	if	SCONJ
ejpam-6075	405	2	n	n	NOUN
ejpam-6075	405	3	=	=	SYM
ejpam-6075	405	4	5	5	NUM
ejpam-6075	405	5	,	,	PUNCT
ejpam-6075	405	6	then	then	ADV
ejpam-6075	405	7	d	d	X
ejpam-6075	405	8	=	=	PUNCT
ejpam-6075	405	9	{	{	PUNCT
ejpam-6075	405	10	v1	v1	PROPN
ejpam-6075	405	11	,	,	PUNCT
ejpam-6075	405	12	v2	v2	PROPN
ejpam-6075	405	13	,	,	PUNCT
ejpam-6075	405	14	v4	v4	PROPN
ejpam-6075	405	15	}	}	PUNCT
ejpam-6075	405	16	is	be	AUX
ejpam-6075	405	17	a	a	DET
ejpam-6075	405	18	γshset	γshset	NOUN
ejpam-6075	405	19	in	in	ADP
ejpam-6075	405	20	c5	c5	PROPN
ejpam-6075	405	21	.	.	PUNCT
ejpam-6075	406	1	hence	hence	ADV
ejpam-6075	406	2	,	,	PUNCT
ejpam-6075	406	3	γsh(c5	γsh(c5	ADJ
ejpam-6075	406	4	)	)	PUNCT
ejpam-6075	406	5	=	=	SYM
ejpam-6075	406	6	3	3	X
ejpam-6075	406	7	.	.	PUNCT
ejpam-6075	406	8	now	now	ADV
ejpam-6075	406	9	,	,	PUNCT
ejpam-6075	406	10	suppose	suppose	VERB
ejpam-6075	406	11	n	n	ADV
ejpam-6075	406	12	/∈	/∈	PUNCT
ejpam-6075	406	13	{	{	PUNCT
ejpam-6075	406	14	3	3	NUM
ejpam-6075	406	15	,	,	PUNCT
ejpam-6075	406	16	5	5	NUM
ejpam-6075	406	17	}	}	PUNCT
ejpam-6075	406	18	.	.	PUNCT
ejpam-6075	407	1	consider	consider	VERB
ejpam-6075	407	2	the	the	DET
ejpam-6075	407	3	following	follow	VERB
ejpam-6075	407	4	cases	case	NOUN
ejpam-6075	407	5	:	:	PUNCT
ejpam-6075	407	6	case	case	NOUN
ejpam-6075	407	7	1	1	NUM
ejpam-6075	407	8	.	.	PUNCT
ejpam-6075	408	1	n	n	NOUN
ejpam-6075	408	2	=	=	SYM
ejpam-6075	408	3	4	4	NUM
ejpam-6075	408	4	t	t	NOUN
ejpam-6075	408	5	or	or	CCONJ
ejpam-6075	408	6	n	n	NOUN
ejpam-6075	408	7	=	=	SYM
ejpam-6075	408	8	4t+	4t+	NUM
ejpam-6075	408	9	1	1	X
ejpam-6075	408	10	.	.	PUNCT
ejpam-6075	409	1	let	let	VERB
ejpam-6075	409	2	sj	sj	INTJ
ejpam-6075	409	3	=	=	PUNCT
ejpam-6075	409	4	{	{	PUNCT
ejpam-6075	409	5	v4j−3	v4j−3	PROPN
ejpam-6075	409	6	,	,	PUNCT
ejpam-6075	409	7	v4j−2	v4j−2	PROPN
ejpam-6075	409	8	}	}	PUNCT
ejpam-6075	409	9	for	for	ADP
ejpam-6075	409	10	each	each	DET
ejpam-6075	409	11	j	j	PROPN
ejpam-6075	409	12	∈	∈	PROPN
ejpam-6075	409	13	{	{	PUNCT
ejpam-6075	409	14	1	1	NUM
ejpam-6075	409	15	,	,	PUNCT
ejpam-6075	409	16	2	2	NUM
ejpam-6075	409	17	,	,	PUNCT
ejpam-6075	409	18	.	.	PUNCT
ejpam-6075	409	19	.	.	PUNCT
ejpam-6075	410	1	.	.	PUNCT
ejpam-6075	411	1	,	,	PUNCT
ejpam-6075	411	2	t	t	PROPN
ejpam-6075	411	3	}	}	PUNCT
ejpam-6075	411	4	.	.	PUNCT
ejpam-6075	412	1	then	then	ADV
ejpam-6075	412	2	s	s	VERB
ejpam-6075	412	3	=	=	SYM
ejpam-6075	412	4	∪t	∪t	NUM
ejpam-6075	412	5	j=1sj	j=1sj	NUM
ejpam-6075	412	6	is	be	AUX
ejpam-6075	412	7	γsh	γsh	NOUN
ejpam-6075	412	8	-	-	PUNCT
ejpam-6075	412	9	set	set	VERB
ejpam-6075	412	10	in	in	ADP
ejpam-6075	412	11	cn	cn	PROPN
ejpam-6075	412	12	.	.	PUNCT
ejpam-6075	413	1	it	it	PRON
ejpam-6075	413	2	follows	follow	VERB
ejpam-6075	413	3	that	that	PRON
ejpam-6075	413	4	γsh(cn	γsh(cn	NOUN
ejpam-6075	413	5	)	)	PUNCT
ejpam-6075	413	6	=	=	NOUN
ejpam-6075	413	7	|s|	|s|	NOUN
ejpam-6075	413	8	=	=	SYM
ejpam-6075	413	9	∑t	∑t	PROPN
ejpam-6075	413	10	j=1	j=1	NOUN
ejpam-6075	413	11	|sj	|sj	X
ejpam-6075	413	12	|	|	NOUN
ejpam-6075	413	13	=	=	SYM
ejpam-6075	413	14	2	2	NUM
ejpam-6075	413	15	t.	t.	PROPN
ejpam-6075	413	16	f.	f.	PROPN
ejpam-6075	413	17	l.	l.	PROPN
ejpam-6075	413	18	alfeche	alfeche	PROPN
ejpam-6075	413	19	,	,	PUNCT
ejpam-6075	413	20	g.	g.	PROPN
ejpam-6075	413	21	a.	a.	PROPN
ejpam-6075	413	22	malacas	malacas	PROPN
ejpam-6075	413	23	,	,	PUNCT
ejpam-6075	413	24	s.	s.	PROPN
ejpam-6075	413	25	canoy	canoy	PROPN
ejpam-6075	413	26	jr	jr	PROPN
ejpam-6075	413	27	.	.	PROPN
ejpam-6075	413	28	/	/	SYM
ejpam-6075	413	29	eur	eur	PROPN
ejpam-6075	413	30	.	.	PUNCT
ejpam-6075	414	1	j.	j.	PROPN
ejpam-6075	414	2	pure	pure	PROPN
ejpam-6075	414	3	appl	appl	PROPN
ejpam-6075	414	4	.	.	PROPN
ejpam-6075	414	5	math	math	PROPN
ejpam-6075	414	6	,	,	PUNCT
ejpam-6075	414	7	18	18	NUM
ejpam-6075	414	8	(	(	PUNCT
ejpam-6075	414	9	2	2	NUM
ejpam-6075	414	10	)	)	PUNCT
ejpam-6075	414	11	(	(	PUNCT
ejpam-6075	414	12	2025	2025	NUM
ejpam-6075	414	13	)	)	PUNCT
ejpam-6075	414	14	,	,	PUNCT
ejpam-6075	414	15	6075	6075	NUM
ejpam-6075	414	16	9	9	NUM
ejpam-6075	414	17	of	of	ADP
ejpam-6075	414	18	14	14	NUM
ejpam-6075	414	19	case	case	NOUN
ejpam-6075	414	20	2	2	NUM
ejpam-6075	414	21	.	.	PUNCT
ejpam-6075	415	1	n	n	NOUN
ejpam-6075	415	2	=	=	SYM
ejpam-6075	415	3	4t+	4t+	NUM
ejpam-6075	415	4	3	3	X
ejpam-6075	415	5	.	.	PUNCT
ejpam-6075	415	6	set	set	VERB
ejpam-6075	415	7	sj	sj	NOUN
ejpam-6075	415	8	=	=	PUNCT
ejpam-6075	415	9	{	{	PUNCT
ejpam-6075	415	10	v4j+3	v4j+3	NOUN
ejpam-6075	415	11	,	,	PUNCT
ejpam-6075	415	12	v4j+4	v4j+4	NOUN
ejpam-6075	415	13	}	}	PUNCT
ejpam-6075	415	14	,	,	PUNCT
ejpam-6075	415	15	j	j	PROPN
ejpam-6075	415	16	=	=	SYM
ejpam-6075	415	17	1	1	NUM
ejpam-6075	415	18	,	,	PUNCT
ejpam-6075	415	19	2	2	NUM
ejpam-6075	415	20	,	,	PUNCT
ejpam-6075	415	21	.	.	PUNCT
ejpam-6075	415	22	.	.	PUNCT
ejpam-6075	416	1	.	.	PUNCT
ejpam-6075	417	1	,	,	PUNCT
ejpam-6075	418	1	t−	t−	PROPN
ejpam-6075	418	2	1	1	X
ejpam-6075	418	3	.	.	PUNCT
ejpam-6075	419	1	then	then	ADV
ejpam-6075	419	2	s	s	VERB
ejpam-6075	419	3	=	=	SYM
ejpam-6075	419	4	{	{	PUNCT
ejpam-6075	419	5	v1	v1	PROPN
ejpam-6075	419	6	,	,	PUNCT
ejpam-6075	419	7	v2	v2	PROPN
ejpam-6075	419	8	,	,	PUNCT
ejpam-6075	419	9	vn	vn	NOUN
ejpam-6075	419	10	}	}	PUNCT
ejpam-6075	419	11	∪	∪	ADP
ejpam-6075	419	12	[	[	X
ejpam-6075	419	13	∪t−1	∪t−1	PROPN
ejpam-6075	419	14	j=1sj	j=1sj	NOUN
ejpam-6075	419	15	]	]	PUNCT
ejpam-6075	419	16	is	be	AUX
ejpam-6075	419	17	γsh	γsh	NOUN
ejpam-6075	419	18	-	-	PUNCT
ejpam-6075	419	19	set	set	VERB
ejpam-6075	419	20	in	in	ADP
ejpam-6075	419	21	cn	cn	PROPN
ejpam-6075	419	22	.	.	PUNCT
ejpam-6075	420	1	hence	hence	ADV
ejpam-6075	420	2	,	,	PUNCT
ejpam-6075	420	3	γsh(cn	γsh(cn	NUM
ejpam-6075	420	4	)	)	PUNCT
ejpam-6075	420	5	=	=	PUNCT
ejpam-6075	420	6	|s|	|s|	NOUN
ejpam-6075	420	7	=	=	SYM
ejpam-6075	420	8	3	3	NUM
ejpam-6075	421	1	+	+	NUM
ejpam-6075	421	2	∑t−1	∑t−1	NOUN
ejpam-6075	421	3	j=1	j=1	NOUN
ejpam-6075	421	4	|sj	|sj	X
ejpam-6075	421	5	|	|	NOUN
ejpam-6075	421	6	=	=	SYM
ejpam-6075	421	7	3	3	NUM
ejpam-6075	421	8	+	+	SYM
ejpam-6075	421	9	2(t−	2(t−	NUM
ejpam-6075	421	10	1	1	NUM
ejpam-6075	421	11	)	)	PUNCT
ejpam-6075	421	12	=	=	SYM
ejpam-6075	421	13	2t+	2t+	NUM
ejpam-6075	421	14	1	1	NUM
ejpam-6075	421	15	.	.	PUNCT
ejpam-6075	422	1	this	this	PRON
ejpam-6075	422	2	proves	prove	VERB
ejpam-6075	422	3	the	the	DET
ejpam-6075	422	4	theorem	theorem	NOUN
ejpam-6075	422	5	.	.	PUNCT
ejpam-6075	423	1	if	if	SCONJ
ejpam-6075	423	2	g1	g1	PROPN
ejpam-6075	423	3	and	and	CCONJ
ejpam-6075	423	4	g2	g2	PROPN
ejpam-6075	423	5	are	be	AUX
ejpam-6075	423	6	the	the	DET
ejpam-6075	423	7	copies	copy	NOUN
ejpam-6075	423	8	of	of	ADP
ejpam-6075	423	9	graph	graph	NOUN
ejpam-6075	423	10	g	g	PROPN
ejpam-6075	423	11	in	in	ADP
ejpam-6075	423	12	the	the	DET
ejpam-6075	423	13	definition	definition	NOUN
ejpam-6075	423	14	of	of	ADP
ejpam-6075	423	15	the	the	DET
ejpam-6075	423	16	shadow	shadow	NOUN
ejpam-6075	423	17	graph	graph	VERB
ejpam-6075	423	18	d2(g	d2(g	PROPN
ejpam-6075	423	19	)	)	PUNCT
ejpam-6075	423	20	and	and	CCONJ
ejpam-6075	423	21	if	if	SCONJ
ejpam-6075	423	22	sg1	sg1	PROPN
ejpam-6075	423	23	⊆	⊆	PROPN
ejpam-6075	423	24	v	v	NOUN
ejpam-6075	423	25	(	(	PUNCT
ejpam-6075	423	26	g1	g1	PROPN
ejpam-6075	423	27	)	)	PUNCT
ejpam-6075	423	28	and	and	CCONJ
ejpam-6075	423	29	sg2	sg2	PROPN
ejpam-6075	423	30	⊆	⊆	NUM
ejpam-6075	423	31	v	v	PROPN
ejpam-6075	423	32	(	(	PUNCT
ejpam-6075	423	33	g2	g2	PROPN
ejpam-6075	423	34	)	)	PUNCT
ejpam-6075	423	35	,	,	PUNCT
ejpam-6075	423	36	then	then	ADV
ejpam-6075	423	37	the	the	DET
ejpam-6075	423	38	sets	set	NOUN
ejpam-6075	423	39	s′	s′	VERB
ejpam-6075	423	40	g1	g1	NOUN
ejpam-6075	423	41	and	and	CCONJ
ejpam-6075	423	42	s′	s′	ADJ
ejpam-6075	423	43	g2	g2	PROPN
ejpam-6075	423	44	are	be	AUX
ejpam-6075	423	45	the	the	DET
ejpam-6075	423	46	sets	set	NOUN
ejpam-6075	423	47	given	give	VERB
ejpam-6075	423	48	by	by	ADP
ejpam-6075	423	49	s′	s′	ADJ
ejpam-6075	423	50	g1	g1	NOUN
ejpam-6075	423	51	=	=	PUNCT
ejpam-6075	423	52	{	{	PUNCT
ejpam-6075	423	53	a′	a′	PROPN
ejpam-6075	423	54	∈	∈	PROPN
ejpam-6075	423	55	v	v	ADP
ejpam-6075	423	56	(	(	PUNCT
ejpam-6075	423	57	g2	g2	PROPN
ejpam-6075	423	58	)	)	PUNCT
ejpam-6075	423	59	:	:	PUNCT
ejpam-6075	423	60	a	a	DET
ejpam-6075	423	61	∈	∈	NOUN
ejpam-6075	423	62	sg1	sg1	NOUN
ejpam-6075	423	63	}	}	PUNCT
ejpam-6075	423	64	and	and	CCONJ
ejpam-6075	423	65	s′	s′	ADJ
ejpam-6075	423	66	g2	g2	PROPN
ejpam-6075	423	67	=	=	PRON
ejpam-6075	423	68	{	{	PUNCT
ejpam-6075	423	69	a	a	DET
ejpam-6075	423	70	∈	∈	PROPN
ejpam-6075	423	71	v	v	NOUN
ejpam-6075	423	72	(	(	PUNCT
ejpam-6075	423	73	g1	g1	PROPN
ejpam-6075	423	74	)	)	PUNCT
ejpam-6075	423	75	:	:	PUNCT
ejpam-6075	423	76	a	a	DET
ejpam-6075	423	77	′	′	NUM
ejpam-6075	423	78	∈	∈	PROPN
ejpam-6075	423	79	sg2	sg2	PROPN
ejpam-6075	423	80	}	}	PUNCT
ejpam-6075	423	81	.	.	PUNCT
ejpam-6075	424	1	the	the	DET
ejpam-6075	424	2	next	next	ADJ
ejpam-6075	424	3	result	result	NOUN
ejpam-6075	424	4	is	be	AUX
ejpam-6075	424	5	obtained	obtain	VERB
ejpam-6075	424	6	by	by	ADP
ejpam-6075	424	7	hassan	hassan	PROPN
ejpam-6075	424	8	et	et	PROPN
ejpam-6075	424	9	al	al	PROPN
ejpam-6075	424	10	.	.	PUNCT
ejpam-6075	425	1	in	in	ADP
ejpam-6075	425	2	[	[	X
ejpam-6075	425	3	26	26	NUM
ejpam-6075	425	4	]	]	PUNCT
ejpam-6075	425	5	.	.	PUNCT
ejpam-6075	426	1	theorem	theorem	ADJ
ejpam-6075	426	2	7	7	NUM
ejpam-6075	426	3	.	.	PUNCT
ejpam-6075	427	1	let	let	VERB
ejpam-6075	427	2	g	g	PRON
ejpam-6075	427	3	be	be	AUX
ejpam-6075	427	4	a	a	DET
ejpam-6075	427	5	non	non	ADJ
ejpam-6075	427	6	-	-	ADJ
ejpam-6075	427	7	trivial	trivial	ADJ
ejpam-6075	427	8	connected	connected	ADJ
ejpam-6075	427	9	graph	graph	NOUN
ejpam-6075	427	10	.	.	PUNCT
ejpam-6075	428	1	then	then	ADV
ejpam-6075	428	2	s	s	VERB
ejpam-6075	428	3	is	be	AUX
ejpam-6075	428	4	a	a	DET
ejpam-6075	428	5	hop	hop	NOUN
ejpam-6075	428	6	dominating	dominating	NOUN
ejpam-6075	428	7	set	set	VERB
ejpam-6075	428	8	in	in	ADP
ejpam-6075	428	9	d2(g	d2(g	PROPN
ejpam-6075	428	10	)	)	PUNCT
ejpam-6075	428	11	if	if	SCONJ
ejpam-6075	428	12	and	and	CCONJ
ejpam-6075	428	13	only	only	ADV
ejpam-6075	428	14	if	if	SCONJ
ejpam-6075	428	15	one	one	NUM
ejpam-6075	428	16	of	of	ADP
ejpam-6075	428	17	the	the	DET
ejpam-6075	428	18	following	follow	VERB
ejpam-6075	428	19	conditions	condition	NOUN
ejpam-6075	428	20	holds	hold	VERB
ejpam-6075	428	21	:	:	PUNCT
ejpam-6075	428	22	(	(	PUNCT
ejpam-6075	428	23	i	i	NOUN
ejpam-6075	428	24	)	)	PUNCT
ejpam-6075	428	25	s	s	VERB
ejpam-6075	428	26	is	be	AUX
ejpam-6075	428	27	a	a	DET
ejpam-6075	428	28	hop	hop	NOUN
ejpam-6075	428	29	dominating	dominating	NOUN
ejpam-6075	428	30	set	set	VERB
ejpam-6075	428	31	in	in	ADP
ejpam-6075	428	32	g1	g1	PROPN
ejpam-6075	428	33	.	.	PUNCT
ejpam-6075	429	1	(	(	PUNCT
ejpam-6075	429	2	ii	ii	X
ejpam-6075	429	3	)	)	PUNCT
ejpam-6075	429	4	s	s	VERB
ejpam-6075	429	5	is	be	AUX
ejpam-6075	429	6	a	a	DET
ejpam-6075	429	7	hop	hop	NOUN
ejpam-6075	429	8	dominating	dominating	NOUN
ejpam-6075	429	9	set	set	VERB
ejpam-6075	429	10	in	in	ADP
ejpam-6075	429	11	g2	g2	PROPN
ejpam-6075	429	12	.	.	PUNCT
ejpam-6075	430	1	(	(	PUNCT
ejpam-6075	430	2	iii	iii	X
ejpam-6075	430	3	)	)	PUNCT
ejpam-6075	430	4	s	s	PART
ejpam-6075	430	5	=	=	NOUN
ejpam-6075	430	6	sg1	sg1	NOUN
ejpam-6075	430	7	∪	∪	VERB
ejpam-6075	430	8	sg2	sg2	PROPN
ejpam-6075	430	9	such	such	ADJ
ejpam-6075	430	10	that	that	SCONJ
ejpam-6075	430	11	sg1	sg1	NOUN
ejpam-6075	430	12	∪	∪	ADP
ejpam-6075	430	13	s′	s′	ADJ
ejpam-6075	430	14	g2	g2	PROPN
ejpam-6075	430	15	and	and	CCONJ
ejpam-6075	430	16	s′	s′	ADJ
ejpam-6075	430	17	g1	g1	PROPN
ejpam-6075	430	18	∪	∪	ADP
ejpam-6075	430	19	sg2	sg2	PROPN
ejpam-6075	430	20	are	be	AUX
ejpam-6075	430	21	hop	hop	NOUN
ejpam-6075	430	22	dominating	dominating	NOUN
ejpam-6075	430	23	sets	set	NOUN
ejpam-6075	430	24	in	in	ADP
ejpam-6075	430	25	g1	g1	PROPN
ejpam-6075	430	26	and	and	CCONJ
ejpam-6075	430	27	g2	g2	PROPN
ejpam-6075	430	28	,	,	PUNCT
ejpam-6075	430	29	respectively	respectively	ADV
ejpam-6075	430	30	.	.	PUNCT
ejpam-6075	431	1	theorem	theorem	VERB
ejpam-6075	431	2	8	8	NUM
ejpam-6075	431	3	.	.	PUNCT
ejpam-6075	432	1	let	let	VERB
ejpam-6075	432	2	g	g	PRON
ejpam-6075	432	3	be	be	AUX
ejpam-6075	432	4	a	a	DET
ejpam-6075	432	5	non	non	ADJ
ejpam-6075	432	6	-	-	ADJ
ejpam-6075	432	7	trivial	trivial	ADJ
ejpam-6075	432	8	connected	connected	ADJ
ejpam-6075	432	9	graph	graph	NOUN
ejpam-6075	432	10	.	.	PUNCT
ejpam-6075	433	1	then	then	ADV
ejpam-6075	433	2	a	a	DET
ejpam-6075	433	3	set	set	NOUN
ejpam-6075	433	4	s	s	NOUN
ejpam-6075	433	5	⊆	⊆	NUM
ejpam-6075	433	6	v	v	NOUN
ejpam-6075	433	7	(	(	PUNCT
ejpam-6075	433	8	d2(g	d2(g	PROPN
ejpam-6075	433	9	)	)	PUNCT
ejpam-6075	433	10	)	)	PUNCT
ejpam-6075	433	11	is	be	AUX
ejpam-6075	433	12	secure	secure	ADJ
ejpam-6075	433	13	hop	hop	NOUN
ejpam-6075	433	14	dominating	dominating	NOUN
ejpam-6075	433	15	in	in	ADP
ejpam-6075	433	16	d2(g	d2(g	PROPN
ejpam-6075	433	17	)	)	PUNCT
ejpam-6075	433	18	if	if	SCONJ
ejpam-6075	434	1	and	and	CCONJ
ejpam-6075	434	2	only	only	ADV
ejpam-6075	434	3	if	if	SCONJ
ejpam-6075	434	4	one	one	NUM
ejpam-6075	434	5	of	of	ADP
ejpam-6075	434	6	the	the	DET
ejpam-6075	434	7	following	follow	VERB
ejpam-6075	434	8	conditions	condition	NOUN
ejpam-6075	434	9	holds	hold	VERB
ejpam-6075	434	10	:	:	PUNCT
ejpam-6075	434	11	(	(	PUNCT
ejpam-6075	434	12	i	i	NOUN
ejpam-6075	434	13	)	)	PUNCT
ejpam-6075	434	14	s	s	VERB
ejpam-6075	434	15	is	be	AUX
ejpam-6075	434	16	a	a	DET
ejpam-6075	434	17	secure	secure	ADJ
ejpam-6075	434	18	hop	hop	NOUN
ejpam-6075	434	19	dominating	dominating	NOUN
ejpam-6075	434	20	set	set	VERB
ejpam-6075	434	21	in	in	ADP
ejpam-6075	434	22	g1	g1	PROPN
ejpam-6075	434	23	.	.	PUNCT
ejpam-6075	435	1	(	(	PUNCT
ejpam-6075	435	2	ii	ii	X
ejpam-6075	435	3	)	)	PUNCT
ejpam-6075	435	4	s	s	VERB
ejpam-6075	435	5	is	be	AUX
ejpam-6075	435	6	a	a	DET
ejpam-6075	435	7	secure	secure	ADJ
ejpam-6075	435	8	hop	hop	NOUN
ejpam-6075	435	9	dominating	dominating	NOUN
ejpam-6075	435	10	set	set	NOUN
ejpam-6075	435	11	in	in	ADP
ejpam-6075	435	12	g2	g2	PROPN
ejpam-6075	435	13	.	.	PUNCT
ejpam-6075	436	1	(	(	PUNCT
ejpam-6075	436	2	iii	iii	X
ejpam-6075	436	3	)	)	PUNCT
ejpam-6075	436	4	s	s	PART
ejpam-6075	436	5	=	=	NOUN
ejpam-6075	436	6	sg1	sg1	NOUN
ejpam-6075	436	7	∪	∪	VERB
ejpam-6075	436	8	sg2	sg2	PROPN
ejpam-6075	436	9	such	such	ADJ
ejpam-6075	436	10	that	that	SCONJ
ejpam-6075	436	11	sg1	sg1	NOUN
ejpam-6075	436	12	∪	∪	ADP
ejpam-6075	436	13	s′	s′	ADJ
ejpam-6075	436	14	g2	g2	PROPN
ejpam-6075	436	15	and	and	CCONJ
ejpam-6075	436	16	s′	s′	ADJ
ejpam-6075	436	17	g1	g1	PROPN
ejpam-6075	436	18	∪	∪	ADP
ejpam-6075	436	19	sg2	sg2	PROPN
ejpam-6075	436	20	are	be	AUX
ejpam-6075	436	21	secure	secure	ADJ
ejpam-6075	436	22	hop	hop	NOUN
ejpam-6075	436	23	dominating	dominating	NOUN
ejpam-6075	436	24	sets	set	NOUN
ejpam-6075	436	25	in	in	ADP
ejpam-6075	436	26	g1	g1	PROPN
ejpam-6075	436	27	and	and	CCONJ
ejpam-6075	436	28	g2	g2	PROPN
ejpam-6075	436	29	,	,	PUNCT
ejpam-6075	436	30	respectively	respectively	ADV
ejpam-6075	436	31	.	.	PUNCT
ejpam-6075	437	1	proof	proof	NOUN
ejpam-6075	437	2	.	.	PUNCT
ejpam-6075	438	1	let	let	VERB
ejpam-6075	438	2	s	s	PRON
ejpam-6075	438	3	be	be	AUX
ejpam-6075	438	4	a	a	DET
ejpam-6075	438	5	secure	secure	ADJ
ejpam-6075	438	6	hop	hop	NOUN
ejpam-6075	438	7	dominating	dominating	NOUN
ejpam-6075	438	8	set	set	VERB
ejpam-6075	438	9	in	in	ADP
ejpam-6075	438	10	d2(g	d2(g	PROPN
ejpam-6075	438	11	)	)	PUNCT
ejpam-6075	438	12	.	.	PUNCT
ejpam-6075	439	1	set	set	VERB
ejpam-6075	439	2	sg1	sg1	NOUN
ejpam-6075	439	3	=	=	SYM
ejpam-6075	439	4	s	s	PROPN
ejpam-6075	439	5	∩	∩	ADJ
ejpam-6075	439	6	v	v	X
ejpam-6075	439	7	(	(	PUNCT
ejpam-6075	439	8	g1	g1	PROPN
ejpam-6075	439	9	)	)	PUNCT
ejpam-6075	439	10	and	and	CCONJ
ejpam-6075	439	11	sg2	sg2	PROPN
ejpam-6075	439	12	=	=	PROPN
ejpam-6075	439	13	s	s	PROPN
ejpam-6075	439	14	∩	∩	ADJ
ejpam-6075	439	15	v	v	X
ejpam-6075	439	16	(	(	PUNCT
ejpam-6075	439	17	g2	g2	PROPN
ejpam-6075	439	18	)	)	PUNCT
ejpam-6075	439	19	.	.	PUNCT
ejpam-6075	440	1	if	if	SCONJ
ejpam-6075	440	2	sg2	sg2	PROPN
ejpam-6075	440	3	=	=	SYM
ejpam-6075	440	4	∅	∅	NOUN
ejpam-6075	440	5	,	,	PUNCT
ejpam-6075	440	6	then	then	ADV
ejpam-6075	440	7	s	s	PART
ejpam-6075	440	8	=	=	NOUN
ejpam-6075	440	9	sg1	sg1	PROPN
ejpam-6075	440	10	is	be	AUX
ejpam-6075	440	11	a	a	DET
ejpam-6075	440	12	hop	hop	NOUN
ejpam-6075	440	13	dominating	dominating	NOUN
ejpam-6075	440	14	set	set	VERB
ejpam-6075	440	15	in	in	ADP
ejpam-6075	440	16	g1	g1	NOUN
ejpam-6075	440	17	by	by	ADP
ejpam-6075	440	18	theorem	theorem	NOUN
ejpam-6075	440	19	7(i	7(i	NUM
ejpam-6075	440	20	)	)	PUNCT
ejpam-6075	440	21	.	.	PUNCT
ejpam-6075	441	1	let	let	VERB
ejpam-6075	441	2	x	x	SYM
ejpam-6075	441	3	∈	∈	PROPN
ejpam-6075	441	4	v	v	NOUN
ejpam-6075	441	5	(	(	PUNCT
ejpam-6075	441	6	g1	g1	PROPN
ejpam-6075	441	7	)	)	PUNCT
ejpam-6075	441	8	\	\	PROPN
ejpam-6075	441	9	sg1	sg1	NOUN
ejpam-6075	441	10	.	.	PUNCT
ejpam-6075	442	1	since	since	SCONJ
ejpam-6075	442	2	s	s	PROPN
ejpam-6075	442	3	is	be	AUX
ejpam-6075	442	4	a	a	DET
ejpam-6075	442	5	secure	secure	ADJ
ejpam-6075	442	6	hop	hop	NOUN
ejpam-6075	442	7	dominating	dominating	NOUN
ejpam-6075	442	8	set	set	VERB
ejpam-6075	442	9	in	in	ADP
ejpam-6075	442	10	d2(g	d2(g	PROPN
ejpam-6075	442	11	)	)	PUNCT
ejpam-6075	442	12	,	,	PUNCT
ejpam-6075	442	13	there	there	PRON
ejpam-6075	442	14	exists	exist	VERB
ejpam-6075	442	15	w	w	PROPN
ejpam-6075	442	16	∈	∈	PROPN
ejpam-6075	442	17	s	s	PART
ejpam-6075	442	18	∩n2	∩n2	PROPN
ejpam-6075	442	19	d2(g)(x	d2(g)(x	PROPN
ejpam-6075	442	20	)	)	PUNCT
ejpam-6075	442	21	such	such	ADJ
ejpam-6075	442	22	that	that	SCONJ
ejpam-6075	442	23	(	(	PUNCT
ejpam-6075	442	24	s	s	NOUN
ejpam-6075	442	25	\	\	X
ejpam-6075	442	26	{	{	PUNCT
ejpam-6075	442	27	w})∪{x	w})∪{x	NOUN
ejpam-6075	442	28	}	}	PUNCT
ejpam-6075	442	29	is	be	AUX
ejpam-6075	442	30	hop	hop	NOUN
ejpam-6075	442	31	dominating	dominate	VERB
ejpam-6075	442	32	in	in	ADP
ejpam-6075	442	33	d2(g	d2(g	NOUN
ejpam-6075	442	34	)	)	PUNCT
ejpam-6075	442	35	.	.	PUNCT
ejpam-6075	443	1	since	since	SCONJ
ejpam-6075	443	2	sg2	sg2	PROPN
ejpam-6075	443	3	=	=	SYM
ejpam-6075	443	4	∅	∅	NOUN
ejpam-6075	443	5	,	,	PUNCT
ejpam-6075	443	6	it	it	PRON
ejpam-6075	443	7	follows	follow	VERB
ejpam-6075	443	8	that	that	SCONJ
ejpam-6075	443	9	w	w	PROPN
ejpam-6075	443	10	∈	∈	PROPN
ejpam-6075	443	11	sg1	sg1	NOUN
ejpam-6075	443	12	.	.	PUNCT
ejpam-6075	444	1	thus	thus	ADV
ejpam-6075	444	2	,	,	PUNCT
ejpam-6075	444	3	(	(	PUNCT
ejpam-6075	444	4	s	s	NOUN
ejpam-6075	444	5	\	\	X
ejpam-6075	444	6	{	{	PUNCT
ejpam-6075	444	7	w	w	NOUN
ejpam-6075	444	8	}	}	PUNCT
ejpam-6075	444	9	)	)	PUNCT
ejpam-6075	444	10	∪	∪	ADP
ejpam-6075	444	11	{	{	PUNCT
ejpam-6075	444	12	x	x	NOUN
ejpam-6075	444	13	}	}	PUNCT
ejpam-6075	444	14	=	=	SYM
ejpam-6075	444	15	(	(	PUNCT
ejpam-6075	444	16	sg1	sg1	X
ejpam-6075	444	17	\	\	PROPN
ejpam-6075	444	18	{	{	PUNCT
ejpam-6075	444	19	w	w	NOUN
ejpam-6075	444	20	}	}	PUNCT
ejpam-6075	444	21	)	)	PUNCT
ejpam-6075	444	22	∪	∪	ADP
ejpam-6075	444	23	{	{	PUNCT
ejpam-6075	444	24	x	x	NOUN
ejpam-6075	444	25	}	}	PUNCT
ejpam-6075	444	26	is	be	AUX
ejpam-6075	444	27	hop	hop	NOUN
ejpam-6075	444	28	dominating	dominate	VERB
ejpam-6075	444	29	in	in	ADP
ejpam-6075	444	30	g1	g1	NOUN
ejpam-6075	444	31	by	by	ADP
ejpam-6075	444	32	theorem	theorem	NOUN
ejpam-6075	444	33	7(i	7(i	NUM
ejpam-6075	444	34	)	)	PUNCT
ejpam-6075	444	35	.	.	PUNCT
ejpam-6075	445	1	therefore	therefore	ADV
ejpam-6075	445	2	,	,	PUNCT
ejpam-6075	445	3	s	s	PART
ejpam-6075	445	4	=	=	NOUN
ejpam-6075	445	5	sg1	sg1	NOUN
ejpam-6075	445	6	is	be	AUX
ejpam-6075	445	7	secure	secure	ADJ
ejpam-6075	445	8	hop	hop	NOUN
ejpam-6075	445	9	dominating	dominating	NOUN
ejpam-6075	445	10	in	in	ADP
ejpam-6075	445	11	g1	g1	PROPN
ejpam-6075	445	12	.	.	PUNCT
ejpam-6075	446	1	similarly	similarly	ADV
ejpam-6075	446	2	,	,	PUNCT
ejpam-6075	446	3	s	s	VERB
ejpam-6075	446	4	=	=	PUNCT
ejpam-6075	446	5	sg2	sg2	PROPN
ejpam-6075	446	6	is	be	AUX
ejpam-6075	446	7	secure	secure	ADJ
ejpam-6075	446	8	hop	hop	NOUN
ejpam-6075	446	9	dominating	dominating	NOUN
ejpam-6075	446	10	in	in	ADP
ejpam-6075	446	11	g2	g2	PROPN
ejpam-6075	446	12	whenever	whenever	SCONJ
ejpam-6075	446	13	sg1	sg1	VERB
ejpam-6075	446	14	=	=	PRON
ejpam-6075	446	15	∅.	∅.	VERB
ejpam-6075	446	16	finally	finally	ADV
ejpam-6075	446	17	,	,	PUNCT
ejpam-6075	446	18	suppose	suppose	VERB
ejpam-6075	446	19	sg1	sg1	NOUN
ejpam-6075	446	20	̸=	̸=	PROPN
ejpam-6075	446	21	∅	∅	NOUN
ejpam-6075	446	22	and	and	CCONJ
ejpam-6075	446	23	sg2	sg2	PROPN
ejpam-6075	446	24	̸=	̸=	PROPN
ejpam-6075	446	25	∅.	∅.	ADV
ejpam-6075	446	26	by	by	ADP
ejpam-6075	446	27	theorem	theorem	ADJ
ejpam-6075	446	28	7(iii	7(iii	NUM
ejpam-6075	446	29	)	)	PUNCT
ejpam-6075	446	30	,	,	PUNCT
ejpam-6075	446	31	l	l	NOUN
ejpam-6075	446	32	=	=	SYM
ejpam-6075	446	33	sg1	sg1	NOUN
ejpam-6075	446	34	∪s′	∪s′	PROPN
ejpam-6075	446	35	g2	g2	PROPN
ejpam-6075	446	36	and	and	CCONJ
ejpam-6075	446	37	m	m	PROPN
ejpam-6075	446	38	=	=	NOUN
ejpam-6075	446	39	s′	s′	VERB
ejpam-6075	446	40	g1	g1	PROPN
ejpam-6075	446	41	∪sg2	∪sg2	PROPN
ejpam-6075	446	42	are	be	AUX
ejpam-6075	446	43	hop	hop	NOUN
ejpam-6075	446	44	dominating	dominating	NOUN
ejpam-6075	446	45	sets	set	NOUN
ejpam-6075	446	46	in	in	ADP
ejpam-6075	446	47	g1	g1	PROPN
ejpam-6075	446	48	and	and	CCONJ
ejpam-6075	446	49	g2	g2	PROPN
ejpam-6075	446	50	,	,	PUNCT
ejpam-6075	446	51	respectively	respectively	ADV
ejpam-6075	446	52	.	.	PUNCT
ejpam-6075	447	1	let	let	VERB
ejpam-6075	447	2	p	p	PRON
ejpam-6075	447	3	∈	∈	PROPN
ejpam-6075	447	4	v	v	NOUN
ejpam-6075	447	5	(	(	PUNCT
ejpam-6075	447	6	g1	g1	PROPN
ejpam-6075	447	7	)	)	PUNCT
ejpam-6075	447	8	\	\	PROPN
ejpam-6075	448	1	l.	l.	NOUN
ejpam-6075	448	2	since	since	SCONJ
ejpam-6075	448	3	s	s	PRON
ejpam-6075	448	4	secure	secure	ADJ
ejpam-6075	448	5	hop	hop	NOUN
ejpam-6075	448	6	dominating	dominating	NOUN
ejpam-6075	448	7	in	in	ADP
ejpam-6075	448	8	d2(g	d2(g	PROPN
ejpam-6075	448	9	)	)	PUNCT
ejpam-6075	448	10	,	,	PUNCT
ejpam-6075	448	11	there	there	PRON
ejpam-6075	448	12	exists	exist	VERB
ejpam-6075	448	13	q	q	PROPN
ejpam-6075	448	14	∈	∈	PROPN
ejpam-6075	448	15	s	s	PART
ejpam-6075	448	16	∩n2	∩n2	PROPN
ejpam-6075	448	17	d2(g)(p	d2(g)(p	NOUN
ejpam-6075	448	18	)	)	PUNCT
ejpam-6075	448	19	such	such	ADJ
ejpam-6075	448	20	that	that	PRON
ejpam-6075	448	21	sp	sp	ADP
ejpam-6075	448	22	=	=	PUNCT
ejpam-6075	448	23	(	(	PUNCT
ejpam-6075	448	24	s	s	NOUN
ejpam-6075	448	25	\	\	X
ejpam-6075	448	26	{	{	PUNCT
ejpam-6075	448	27	q	q	NOUN
ejpam-6075	448	28	}	}	PUNCT
ejpam-6075	448	29	)	)	PUNCT
ejpam-6075	448	30	∪	∪	ADP
ejpam-6075	448	31	{	{	PUNCT
ejpam-6075	448	32	p	p	NOUN
ejpam-6075	448	33	}	}	PUNCT
ejpam-6075	448	34	is	be	AUX
ejpam-6075	448	35	hop	hop	NOUN
ejpam-6075	448	36	dominating	dominate	VERB
ejpam-6075	448	37	in	in	ADP
ejpam-6075	448	38	d2(g	d2(g	PROPN
ejpam-6075	448	39	)	)	PUNCT
ejpam-6075	448	40	.	.	PUNCT
ejpam-6075	449	1	suppose	suppose	VERB
ejpam-6075	449	2	q	q	X
ejpam-6075	449	3	∈	∈	PROPN
ejpam-6075	449	4	sg1	sg1	NOUN
ejpam-6075	449	5	.	.	PUNCT
ejpam-6075	450	1	then	then	ADV
ejpam-6075	450	2	sp	sp	VERB
ejpam-6075	450	3	=	=	PUNCT
ejpam-6075	450	4	(	(	PUNCT
ejpam-6075	450	5	s	s	NOUN
ejpam-6075	450	6	\	\	X
ejpam-6075	450	7	{	{	PUNCT
ejpam-6075	450	8	q})∪	q})∪	PROPN
ejpam-6075	450	9	{	{	PUNCT
ejpam-6075	450	10	p	p	X
ejpam-6075	450	11	}	}	PUNCT
ejpam-6075	450	12	=	=	SYM
ejpam-6075	451	1	[	[	X
ejpam-6075	451	2	(	(	PUNCT
ejpam-6075	451	3	sg1	sg1	PROPN
ejpam-6075	451	4	\	\	NOUN
ejpam-6075	451	5	{	{	PUNCT
ejpam-6075	451	6	q})∪	q})∪	PROPN
ejpam-6075	451	7	{	{	PUNCT
ejpam-6075	451	8	p}]∪	p}]∪	NOUN
ejpam-6075	451	9	sg2	sg2	PROPN
ejpam-6075	451	10	.	.	PUNCT
ejpam-6075	452	1	since	since	SCONJ
ejpam-6075	452	2	sp	sp	PROPN
ejpam-6075	452	3	is	be	AUX
ejpam-6075	452	4	hop	hop	NOUN
ejpam-6075	452	5	dominating	dominate	VERB
ejpam-6075	452	6	in	in	ADP
ejpam-6075	452	7	d2(g	d2(g	PROPN
ejpam-6075	452	8	)	)	PUNCT
ejpam-6075	452	9	,	,	PUNCT
ejpam-6075	452	10	it	it	PRON
ejpam-6075	452	11	follows	follow	VERB
ejpam-6075	452	12	from	from	ADP
ejpam-6075	452	13	theorem	theorem	ADJ
ejpam-6075	452	14	7(iii	7(iii	NOUN
ejpam-6075	452	15	)	)	PUNCT
ejpam-6075	452	16	that	that	SCONJ
ejpam-6075	453	1	[	[	X
ejpam-6075	453	2	(	(	PUNCT
ejpam-6075	453	3	sg1	sg1	PROPN
ejpam-6075	453	4	\	\	PROPN
ejpam-6075	453	5	{	{	PUNCT
ejpam-6075	453	6	q	q	NOUN
ejpam-6075	453	7	}	}	PUNCT
ejpam-6075	453	8	)	)	PUNCT
ejpam-6075	453	9	∪	∪	ADP
ejpam-6075	453	10	{	{	PUNCT
ejpam-6075	453	11	p	p	NOUN
ejpam-6075	453	12	}	}	PUNCT
ejpam-6075	453	13	]	]	PUNCT
ejpam-6075	453	14	∪	∪	ADP
ejpam-6075	453	15	s′	s′	ADJ
ejpam-6075	453	16	g2	g2	PROPN
ejpam-6075	453	17	=	=	PUNCT
ejpam-6075	454	1	[	[	X
ejpam-6075	454	2	(	(	PUNCT
ejpam-6075	454	3	sg1	sg1	NOUN
ejpam-6075	454	4	∪	∪	ADJ
ejpam-6075	454	5	s′	s′	ADJ
ejpam-6075	454	6	g2	g2	PROPN
ejpam-6075	454	7	)	)	PUNCT
ejpam-6075	454	8	\	\	PROPN
ejpam-6075	454	9	{	{	PUNCT
ejpam-6075	454	10	q	q	NOUN
ejpam-6075	454	11	}	}	PUNCT
ejpam-6075	454	12	]	]	PUNCT
ejpam-6075	454	13	)	)	PUNCT
ejpam-6075	454	14	∪	∪	ADP
ejpam-6075	454	15	{	{	PUNCT
ejpam-6075	454	16	p	p	ADJ
ejpam-6075	454	17	}	}	PUNCT
ejpam-6075	454	18	f.	f.	PROPN
ejpam-6075	454	19	l.	l.	PROPN
ejpam-6075	454	20	alfeche	alfeche	PROPN
ejpam-6075	454	21	,	,	PUNCT
ejpam-6075	454	22	g.	g.	PROPN
ejpam-6075	454	23	a.	a.	PROPN
ejpam-6075	454	24	malacas	malacas	PROPN
ejpam-6075	454	25	,	,	PUNCT
ejpam-6075	454	26	s.	s.	PROPN
ejpam-6075	454	27	canoy	canoy	PROPN
ejpam-6075	454	28	jr	jr	PROPN
ejpam-6075	454	29	.	.	PROPN
ejpam-6075	454	30	/	/	SYM
ejpam-6075	454	31	eur	eur	PROPN
ejpam-6075	454	32	.	.	PUNCT
ejpam-6075	455	1	j.	j.	PROPN
ejpam-6075	455	2	pure	pure	PROPN
ejpam-6075	455	3	appl	appl	PROPN
ejpam-6075	455	4	.	.	PROPN
ejpam-6075	455	5	math	math	PROPN
ejpam-6075	455	6	,	,	PUNCT
ejpam-6075	455	7	18	18	NUM
ejpam-6075	455	8	(	(	PUNCT
ejpam-6075	455	9	2	2	NUM
ejpam-6075	455	10	)	)	PUNCT
ejpam-6075	455	11	(	(	PUNCT
ejpam-6075	455	12	2025	2025	NUM
ejpam-6075	455	13	)	)	PUNCT
ejpam-6075	455	14	,	,	PUNCT
ejpam-6075	455	15	6075	6075	NUM
ejpam-6075	455	16	10	10	NUM
ejpam-6075	455	17	of	of	ADP
ejpam-6075	455	18	14	14	NUM
ejpam-6075	455	19	is	be	AUX
ejpam-6075	455	20	hop	hop	NOUN
ejpam-6075	455	21	dominating	dominate	VERB
ejpam-6075	455	22	in	in	ADP
ejpam-6075	455	23	g1	g1	PROPN
ejpam-6075	455	24	theorem	theorem	VERB
ejpam-6075	455	25	7(iii	7(iii	NUM
ejpam-6075	455	26	)	)	PUNCT
ejpam-6075	455	27	.	.	PUNCT
ejpam-6075	456	1	suppose	suppose	VERB
ejpam-6075	457	1	q	q	X
ejpam-6075	457	2	=	=	SYM
ejpam-6075	457	3	t′	t′	X
ejpam-6075	457	4	∈	∈	PROPN
ejpam-6075	457	5	sg2	sg2	PROPN
ejpam-6075	457	6	.	.	PUNCT
ejpam-6075	458	1	then	then	ADV
ejpam-6075	458	2	t	t	PROPN
ejpam-6075	458	3	∈	∈	PROPN
ejpam-6075	458	4	s′	s′	ADJ
ejpam-6075	458	5	g2	g2	PROPN
ejpam-6075	458	6	∩	∩	ADJ
ejpam-6075	458	7	n2	n2	PROPN
ejpam-6075	458	8	g1	g1	PROPN
ejpam-6075	458	9	(	(	PUNCT
ejpam-6075	458	10	p	p	NOUN
ejpam-6075	458	11	)	)	PUNCT
ejpam-6075	458	12	and	and	CCONJ
ejpam-6075	458	13	sp	sp	ADP
ejpam-6075	458	14	=	=	SYM
ejpam-6075	458	15	(	(	PUNCT
ejpam-6075	458	16	sg1	sg1	PROPN
ejpam-6075	458	17	∪	∪	VERB
ejpam-6075	458	18	{	{	PUNCT
ejpam-6075	458	19	p	p	NOUN
ejpam-6075	458	20	}	}	PUNCT
ejpam-6075	458	21	)	)	PUNCT
ejpam-6075	458	22	∪	∪	ADP
ejpam-6075	459	1	[	[	X
ejpam-6075	459	2	(	(	PUNCT
ejpam-6075	459	3	sg2	sg2	PROPN
ejpam-6075	459	4	\	\	PROPN
ejpam-6075	459	5	{	{	PUNCT
ejpam-6075	459	6	t′	t′	NUM
ejpam-6075	459	7	}	}	PUNCT
ejpam-6075	459	8	]	]	PUNCT
ejpam-6075	459	9	.	.	PUNCT
ejpam-6075	460	1	since	since	SCONJ
ejpam-6075	460	2	sp	sp	PROPN
ejpam-6075	460	3	is	be	AUX
ejpam-6075	460	4	hop	hop	NOUN
ejpam-6075	460	5	dominating	dominate	VERB
ejpam-6075	460	6	in	in	ADP
ejpam-6075	460	7	d2(g	d2(g	PROPN
ejpam-6075	460	8	)	)	PUNCT
ejpam-6075	460	9	,	,	PUNCT
ejpam-6075	460	10	(	(	PUNCT
ejpam-6075	460	11	sg1	sg1	PROPN
ejpam-6075	460	12	∪	∪	VERB
ejpam-6075	460	13	{	{	PUNCT
ejpam-6075	460	14	p	p	NOUN
ejpam-6075	460	15	}	}	PUNCT
ejpam-6075	460	16	)	)	PUNCT
ejpam-6075	460	17	∪	∪	ADP
ejpam-6075	460	18	[	[	X
ejpam-6075	460	19	(	(	PUNCT
ejpam-6075	460	20	s′	s′	VERB
ejpam-6075	460	21	g2	g2	PROPN
ejpam-6075	460	22	\	\	PROPN
ejpam-6075	460	23	{	{	PUNCT
ejpam-6075	460	24	t	t	PROPN
ejpam-6075	460	25	}	}	PUNCT
ejpam-6075	460	26	]	]	PUNCT
ejpam-6075	461	1	=	=	PUNCT
ejpam-6075	461	2	[	[	X
ejpam-6075	461	3	(	(	PUNCT
ejpam-6075	461	4	sg1	sg1	PROPN
ejpam-6075	461	5	\	\	PROPN
ejpam-6075	461	6	{	{	PUNCT
ejpam-6075	461	7	t	t	PROPN
ejpam-6075	461	8	}	}	PUNCT
ejpam-6075	461	9	)	)	PUNCT
ejpam-6075	461	10	∪	∪	ADP
ejpam-6075	461	11	{	{	PUNCT
ejpam-6075	461	12	p	p	NOUN
ejpam-6075	461	13	}	}	PUNCT
ejpam-6075	461	14	]	]	PUNCT
ejpam-6075	461	15	∪	∪	ADP
ejpam-6075	461	16	s′	s′	ADJ
ejpam-6075	461	17	g2	g2	PROPN
ejpam-6075	461	18	=	=	PUNCT
ejpam-6075	462	1	[	[	X
ejpam-6075	462	2	(	(	PUNCT
ejpam-6075	462	3	sg1	sg1	NOUN
ejpam-6075	462	4	∪	∪	ADJ
ejpam-6075	462	5	s′	s′	ADJ
ejpam-6075	462	6	g2	g2	PROPN
ejpam-6075	462	7	)	)	PUNCT
ejpam-6075	462	8	\	\	PROPN
ejpam-6075	462	9	{	{	PUNCT
ejpam-6075	462	10	t	t	PROPN
ejpam-6075	462	11	}	}	PUNCT
ejpam-6075	462	12	]	]	PUNCT
ejpam-6075	462	13	∪	∪	X
ejpam-6075	462	14	{	{	PUNCT
ejpam-6075	462	15	p	p	AUX
ejpam-6075	462	16	}	}	PUNCT
ejpam-6075	462	17	is	be	AUX
ejpam-6075	462	18	hop	hop	NOUN
ejpam-6075	462	19	dominating	dominate	VERB
ejpam-6075	462	20	in	in	ADP
ejpam-6075	462	21	g1	g1	NOUN
ejpam-6075	462	22	by	by	ADP
ejpam-6075	462	23	theorem	theorem	ADJ
ejpam-6075	462	24	7(iii	7(iii	NUM
ejpam-6075	462	25	)	)	PUNCT
ejpam-6075	462	26	.	.	PUNCT
ejpam-6075	463	1	thus	thus	ADV
ejpam-6075	463	2	,	,	PUNCT
ejpam-6075	463	3	l	l	NOUN
ejpam-6075	463	4	is	be	AUX
ejpam-6075	463	5	secure	secure	ADJ
ejpam-6075	463	6	hop	hop	NOUN
ejpam-6075	463	7	dominating	dominating	NOUN
ejpam-6075	463	8	in	in	ADP
ejpam-6075	463	9	g1	g1	PROPN
ejpam-6075	463	10	.	.	PUNCT
ejpam-6075	464	1	similarly	similarly	ADV
ejpam-6075	464	2	,	,	PUNCT
ejpam-6075	464	3	m	m	VERB
ejpam-6075	464	4	is	be	AUX
ejpam-6075	464	5	secure	secure	ADJ
ejpam-6075	464	6	hop	hop	NOUN
ejpam-6075	464	7	dominating	dominating	NOUN
ejpam-6075	464	8	in	in	ADP
ejpam-6075	464	9	g2	g2	PROPN
ejpam-6075	464	10	.	.	PUNCT
ejpam-6075	465	1	therefore	therefore	ADV
ejpam-6075	465	2	,	,	PUNCT
ejpam-6075	465	3	one	one	NUM
ejpam-6075	465	4	of	of	ADP
ejpam-6075	465	5	(	(	PUNCT
ejpam-6075	465	6	i	i	NOUN
ejpam-6075	465	7	)	)	PUNCT
ejpam-6075	465	8	,	,	PUNCT
ejpam-6075	465	9	(	(	PUNCT
ejpam-6075	465	10	ii	ii	NOUN
ejpam-6075	465	11	)	)	PUNCT
ejpam-6075	465	12	,	,	PUNCT
ejpam-6075	465	13	and	and	CCONJ
ejpam-6075	465	14	(	(	PUNCT
ejpam-6075	465	15	iii	iii	NOUN
ejpam-6075	465	16	)	)	PUNCT
ejpam-6075	465	17	holds	hold	VERB
ejpam-6075	465	18	.	.	PUNCT
ejpam-6075	466	1	for	for	ADP
ejpam-6075	466	2	the	the	DET
ejpam-6075	466	3	converse	converse	NOUN
ejpam-6075	466	4	,	,	PUNCT
ejpam-6075	466	5	suppose	suppose	VERB
ejpam-6075	466	6	(	(	PUNCT
ejpam-6075	466	7	i	i	NOUN
ejpam-6075	466	8	)	)	PUNCT
ejpam-6075	466	9	holds	hold	VERB
ejpam-6075	466	10	.	.	PUNCT
ejpam-6075	467	1	then	then	ADV
ejpam-6075	467	2	s	s	AUX
ejpam-6075	467	3	is	be	AUX
ejpam-6075	467	4	hop	hop	NOUN
ejpam-6075	467	5	dominating	dominate	VERB
ejpam-6075	467	6	in	in	ADP
ejpam-6075	467	7	d2(g	d2(g	PROPN
ejpam-6075	467	8	)	)	PUNCT
ejpam-6075	467	9	by	by	ADP
ejpam-6075	467	10	theorem	theorem	NOUN
ejpam-6075	467	11	7(i	7(i	NUM
ejpam-6075	467	12	)	)	PUNCT
ejpam-6075	467	13	.	.	PUNCT
ejpam-6075	468	1	let	let	VERB
ejpam-6075	468	2	z	z	NOUN
ejpam-6075	468	3	∈	∈	PROPN
ejpam-6075	468	4	v	v	X
ejpam-6075	468	5	(	(	PUNCT
ejpam-6075	468	6	d2(g	d2(g	PROPN
ejpam-6075	468	7	)	)	PUNCT
ejpam-6075	468	8	)	)	PUNCT
ejpam-6075	468	9	\	\	PUNCT
ejpam-6075	469	1	s.	s.	PROPN
ejpam-6075	469	2	suppose	suppose	VERB
ejpam-6075	469	3	z	z	PROPN
ejpam-6075	469	4	∈	∈	PROPN
ejpam-6075	469	5	v	v	PROPN
ejpam-6075	469	6	(	(	PUNCT
ejpam-6075	469	7	g1	g1	PROPN
ejpam-6075	469	8	)	)	PUNCT
ejpam-6075	469	9	.	.	PUNCT
ejpam-6075	470	1	since	since	SCONJ
ejpam-6075	470	2	s	s	NOUN
ejpam-6075	470	3	is	be	AUX
ejpam-6075	470	4	secure	secure	ADJ
ejpam-6075	470	5	hop	hop	NOUN
ejpam-6075	470	6	dominating	dominating	NOUN
ejpam-6075	470	7	in	in	ADP
ejpam-6075	470	8	g1	g1	PROPN
ejpam-6075	470	9	,	,	PUNCT
ejpam-6075	470	10	there	there	PRON
ejpam-6075	470	11	exists	exist	VERB
ejpam-6075	470	12	q	q	PROPN
ejpam-6075	470	13	∈	∈	PROPN
ejpam-6075	470	14	s	s	PART
ejpam-6075	470	15	∩	∩	ADJ
ejpam-6075	470	16	n2	n2	ADJ
ejpam-6075	470	17	g(z	g(z	PROPN
ejpam-6075	470	18	)	)	PUNCT
ejpam-6075	470	19	such	such	ADJ
ejpam-6075	470	20	that	that	SCONJ
ejpam-6075	470	21	(	(	PUNCT
ejpam-6075	470	22	s	s	NOUN
ejpam-6075	470	23	\	\	X
ejpam-6075	470	24	{	{	PUNCT
ejpam-6075	470	25	q	q	NOUN
ejpam-6075	470	26	}	}	PUNCT
ejpam-6075	470	27	)	)	PUNCT
ejpam-6075	470	28	∪	∪	ADP
ejpam-6075	470	29	{	{	PUNCT
ejpam-6075	470	30	z	z	NOUN
ejpam-6075	470	31	}	}	PUNCT
ejpam-6075	470	32	is	be	AUX
ejpam-6075	470	33	hop	hop	NOUN
ejpam-6075	470	34	dominating	dominate	VERB
ejpam-6075	470	35	in	in	ADP
ejpam-6075	470	36	g1	g1	PROPN
ejpam-6075	470	37	.	.	PUNCT
ejpam-6075	471	1	by	by	ADP
ejpam-6075	471	2	theorem	theorem	NOUN
ejpam-6075	471	3	7	7	NUM
ejpam-6075	471	4	,	,	PUNCT
ejpam-6075	471	5	(	(	PUNCT
ejpam-6075	471	6	s	s	NOUN
ejpam-6075	471	7	\	\	X
ejpam-6075	471	8	{	{	PUNCT
ejpam-6075	471	9	q	q	NOUN
ejpam-6075	471	10	}	}	PUNCT
ejpam-6075	471	11	)	)	PUNCT
ejpam-6075	471	12	∪	∪	ADP
ejpam-6075	471	13	{	{	PUNCT
ejpam-6075	471	14	z	z	NOUN
ejpam-6075	471	15	}	}	PUNCT
ejpam-6075	471	16	is	be	AUX
ejpam-6075	471	17	hop	hop	NOUN
ejpam-6075	471	18	dominating	dominate	VERB
ejpam-6075	471	19	in	in	ADP
ejpam-6075	471	20	d2(g	d2(g	NOUN
ejpam-6075	471	21	)	)	PUNCT
ejpam-6075	471	22	.	.	PUNCT
ejpam-6075	472	1	next	next	ADJ
ejpam-6075	472	2	suppose	suppose	VERB
ejpam-6075	472	3	z	z	NOUN
ejpam-6075	472	4	=	=	SYM
ejpam-6075	472	5	t′	t′	NUM
ejpam-6075	472	6	∈	∈	NOUN
ejpam-6075	472	7	v	v	NOUN
ejpam-6075	472	8	(	(	PUNCT
ejpam-6075	472	9	g2	g2	PROPN
ejpam-6075	472	10	)	)	PUNCT
ejpam-6075	472	11	.	.	PUNCT
ejpam-6075	473	1	if	if	SCONJ
ejpam-6075	473	2	t	t	PROPN
ejpam-6075	473	3	∈	∈	PROPN
ejpam-6075	473	4	s	s	PROPN
ejpam-6075	473	5	,	,	PUNCT
ejpam-6075	473	6	then	then	ADV
ejpam-6075	473	7	dd2(g)(t	dd2(g)(t	PROPN
ejpam-6075	473	8	,	,	PUNCT
ejpam-6075	473	9	t	t	NOUN
ejpam-6075	473	10	′	′	NUM
ejpam-6075	473	11	)	)	PUNCT
ejpam-6075	473	12	=	=	SYM
ejpam-6075	474	1	2	2	X
ejpam-6075	474	2	.	.	X
ejpam-6075	475	1	if	if	SCONJ
ejpam-6075	475	2	a	a	DET
ejpam-6075	475	3	∈	∈	PROPN
ejpam-6075	475	4	ephn(t;s	ephn(t;s	PROPN
ejpam-6075	475	5	)	)	PUNCT
ejpam-6075	475	6	,	,	PUNCT
ejpam-6075	475	7	then	then	ADV
ejpam-6075	475	8	dd2(g)(a	dd2(g)(a	PROPN
ejpam-6075	475	9	,	,	PUNCT
ejpam-6075	475	10	t	t	PROPN
ejpam-6075	475	11	)	)	PUNCT
ejpam-6075	475	12	=	=	PUNCT
ejpam-6075	476	1	dd2(g)(a	dd2(g)(a	PROPN
ejpam-6075	476	2	,	,	PUNCT
ejpam-6075	476	3	t	t	NOUN
ejpam-6075	476	4	′	′	NUM
ejpam-6075	476	5	)	)	PUNCT
ejpam-6075	476	6	=	=	SYM
ejpam-6075	477	1	2	2	X
ejpam-6075	477	2	.	.	PUNCT
ejpam-6075	478	1	this	this	PRON
ejpam-6075	478	2	implies	imply	VERB
ejpam-6075	478	3	that	that	SCONJ
ejpam-6075	478	4	ephn(t;s	ephn(t;s	PROPN
ejpam-6075	478	5	)	)	PUNCT
ejpam-6075	478	6	⊆	⊆	NUM
ejpam-6075	478	7	n2	n2	NOUN
ejpam-6075	478	8	d2(g)[t	d2(g)[t	PROPN
ejpam-6075	478	9	′	′	NOUN
ejpam-6075	478	10	]	]	PUNCT
ejpam-6075	478	11	.	.	PUNCT
ejpam-6075	479	1	hence	hence	ADV
ejpam-6075	479	2	,	,	PUNCT
ejpam-6075	479	3	(	(	PUNCT
ejpam-6075	479	4	s	s	NOUN
ejpam-6075	479	5	\	\	X
ejpam-6075	479	6	{	{	PUNCT
ejpam-6075	479	7	t	t	PROPN
ejpam-6075	479	8	}	}	PUNCT
ejpam-6075	479	9	)	)	PUNCT
ejpam-6075	479	10	∪	∪	ADP
ejpam-6075	479	11	{	{	PUNCT
ejpam-6075	479	12	t′	t′	NUM
ejpam-6075	479	13	}	}	PUNCT
ejpam-6075	479	14	is	be	AUX
ejpam-6075	479	15	a	a	DET
ejpam-6075	479	16	hop	hop	NOUN
ejpam-6075	479	17	dominating	dominating	NOUN
ejpam-6075	479	18	set	set	VERB
ejpam-6075	479	19	in	in	ADP
ejpam-6075	479	20	d2(g	d2(g	PROPN
ejpam-6075	479	21	)	)	PUNCT
ejpam-6075	479	22	.	.	PUNCT
ejpam-6075	480	1	suppose	suppose	VERB
ejpam-6075	481	1	t	t	PROPN
ejpam-6075	481	2	/∈	/∈	PUNCT
ejpam-6075	481	3	s.	s.	PROPN
ejpam-6075	482	1	since	since	SCONJ
ejpam-6075	482	2	s	s	PROPN
ejpam-6075	482	3	is	be	AUX
ejpam-6075	482	4	a	a	DET
ejpam-6075	482	5	secure	secure	ADJ
ejpam-6075	482	6	hop	hop	NOUN
ejpam-6075	482	7	dominating	dominating	NOUN
ejpam-6075	482	8	set	set	VERB
ejpam-6075	482	9	in	in	ADP
ejpam-6075	482	10	g1	g1	PROPN
ejpam-6075	482	11	,	,	PUNCT
ejpam-6075	482	12	there	there	PRON
ejpam-6075	482	13	exists	exist	VERB
ejpam-6075	482	14	s	s	PROPN
ejpam-6075	482	15	∈	∈	PROPN
ejpam-6075	482	16	s	s	PART
ejpam-6075	482	17	∩	∩	ADJ
ejpam-6075	482	18	n2	n2	ADJ
ejpam-6075	482	19	g1	g1	PROPN
ejpam-6075	482	20	(	(	PUNCT
ejpam-6075	482	21	t	t	NOUN
ejpam-6075	482	22	)	)	PUNCT
ejpam-6075	482	23	such	such	ADJ
ejpam-6075	482	24	that	that	DET
ejpam-6075	482	25	st	st	PROPN
ejpam-6075	482	26	=	=	X
ejpam-6075	482	27	(	(	PUNCT
ejpam-6075	482	28	s	s	NOUN
ejpam-6075	482	29	\	\	X
ejpam-6075	482	30	{	{	PUNCT
ejpam-6075	482	31	s	s	NOUN
ejpam-6075	482	32	}	}	PUNCT
ejpam-6075	482	33	)	)	PUNCT
ejpam-6075	482	34	∪	∪	ADP
ejpam-6075	482	35	{	{	PUNCT
ejpam-6075	482	36	t	t	NOUN
ejpam-6075	482	37	}	}	PUNCT
ejpam-6075	482	38	is	be	AUX
ejpam-6075	482	39	hop	hop	NOUN
ejpam-6075	482	40	dominating	dominate	VERB
ejpam-6075	482	41	in	in	ADP
ejpam-6075	482	42	g1	g1	PROPN
ejpam-6075	482	43	.	.	PUNCT
ejpam-6075	483	1	thus	thus	ADV
ejpam-6075	483	2	,	,	PUNCT
ejpam-6075	483	3	st	st	PROPN
ejpam-6075	483	4	is	be	AUX
ejpam-6075	483	5	hop	hop	NOUN
ejpam-6075	483	6	dominating	dominate	VERB
ejpam-6075	483	7	in	in	ADP
ejpam-6075	483	8	d2(g	d2(g	NOUN
ejpam-6075	483	9	)	)	PUNCT
ejpam-6075	483	10	.	.	PUNCT
ejpam-6075	484	1	set	set	VERB
ejpam-6075	484	2	st′	st′	PROPN
ejpam-6075	484	3	=	=	SYM
ejpam-6075	484	4	(	(	PUNCT
ejpam-6075	484	5	s	s	X
ejpam-6075	484	6	\	\	X
ejpam-6075	484	7	{	{	PUNCT
ejpam-6075	484	8	s	s	NOUN
ejpam-6075	484	9	}	}	PUNCT
ejpam-6075	484	10	)	)	PUNCT
ejpam-6075	484	11	∪	∪	ADP
ejpam-6075	484	12	{	{	PUNCT
ejpam-6075	484	13	t′	t′	NUM
ejpam-6075	484	14	}	}	PUNCT
ejpam-6075	484	15	and	and	CCONJ
ejpam-6075	484	16	let	let	VERB
ejpam-6075	484	17	p	p	PRON
ejpam-6075	484	18	∈	∈	PROPN
ejpam-6075	484	19	v	v	X
ejpam-6075	484	20	(	(	PUNCT
ejpam-6075	484	21	d2(g	d2(g	PROPN
ejpam-6075	484	22	)	)	PUNCT
ejpam-6075	484	23	)	)	PUNCT
ejpam-6075	484	24	\	\	PROPN
ejpam-6075	484	25	st′	st′	PROPN
ejpam-6075	484	26	.	.	PUNCT
ejpam-6075	485	1	then	then	ADV
ejpam-6075	485	2	p	p	X
ejpam-6075	485	3	/∈	/∈	PUNCT
ejpam-6075	485	4	s	s	VERB
ejpam-6075	485	5	\	\	X
ejpam-6075	485	6	{	{	PUNCT
ejpam-6075	485	7	s	s	NOUN
ejpam-6075	485	8	}	}	PUNCT
ejpam-6075	485	9	and	and	CCONJ
ejpam-6075	485	10	p	p	PRON
ejpam-6075	485	11	̸=	̸=	PROPN
ejpam-6075	485	12	t′.	t′.	NOUN
ejpam-6075	485	13	suppose	suppose	VERB
ejpam-6075	485	14	first	first	ADV
ejpam-6075	485	15	that	that	SCONJ
ejpam-6075	485	16	p	p	PROPN
ejpam-6075	485	17	∈	∈	PROPN
ejpam-6075	485	18	v	v	NOUN
ejpam-6075	485	19	(	(	PUNCT
ejpam-6075	485	20	g1	g1	PROPN
ejpam-6075	485	21	)	)	PUNCT
ejpam-6075	485	22	.	.	PUNCT
ejpam-6075	486	1	if	if	SCONJ
ejpam-6075	486	2	p	p	X
ejpam-6075	486	3	∈	∈	PROPN
ejpam-6075	486	4	{	{	PUNCT
ejpam-6075	486	5	s	s	PROPN
ejpam-6075	486	6	,	,	PUNCT
ejpam-6075	486	7	t	t	PROPN
ejpam-6075	486	8	}	}	PUNCT
ejpam-6075	486	9	,	,	PUNCT
ejpam-6075	486	10	then	then	ADV
ejpam-6075	486	11	p	p	PROPN
ejpam-6075	486	12	∈	∈	PROPN
ejpam-6075	486	13	n2	n2	NOUN
ejpam-6075	486	14	d2(g)(t	d2(g)(t	PROPN
ejpam-6075	486	15	′	′	NUM
ejpam-6075	486	16	)	)	PUNCT
ejpam-6075	486	17	.	.	PUNCT
ejpam-6075	487	1	suppose	suppose	VERB
ejpam-6075	487	2	p	p	X
ejpam-6075	487	3	/∈	/∈	PUNCT
ejpam-6075	487	4	{	{	PUNCT
ejpam-6075	487	5	s	s	PROPN
ejpam-6075	487	6	,	,	PUNCT
ejpam-6075	487	7	t	t	PROPN
ejpam-6075	487	8	}	}	PUNCT
ejpam-6075	487	9	.	.	PUNCT
ejpam-6075	488	1	since	since	SCONJ
ejpam-6075	488	2	st	st	PROPN
ejpam-6075	488	3	is	be	AUX
ejpam-6075	488	4	hop	hop	PROPN
ejpam-6075	488	5	dominating	dominating	NOUN
ejpam-6075	488	6	,	,	PUNCT
ejpam-6075	488	7	there	there	PRON
ejpam-6075	488	8	exists	exist	VERB
ejpam-6075	488	9	r	r	PROPN
ejpam-6075	488	10	∈	∈	PROPN
ejpam-6075	488	11	(	(	PUNCT
ejpam-6075	488	12	st	st	PROPN
ejpam-6075	488	13	\	\	PROPN
ejpam-6075	488	14	{	{	PUNCT
ejpam-6075	488	15	s	s	NOUN
ejpam-6075	488	16	}	}	PUNCT
ejpam-6075	488	17	)	)	PUNCT
ejpam-6075	488	18	∩	∩	ADJ
ejpam-6075	488	19	n2	n2	ADJ
ejpam-6075	488	20	g1	g1	PROPN
ejpam-6075	488	21	(	(	PUNCT
ejpam-6075	488	22	p	p	NOUN
ejpam-6075	488	23	)	)	PUNCT
ejpam-6075	488	24	.	.	PUNCT
ejpam-6075	489	1	it	it	PRON
ejpam-6075	489	2	follows	follow	VERB
ejpam-6075	489	3	that	that	SCONJ
ejpam-6075	489	4	r	r	NOUN
ejpam-6075	489	5	∈	∈	PROPN
ejpam-6075	489	6	st′	st′	PROPN
ejpam-6075	489	7	∩n2	∩n2	PROPN
ejpam-6075	489	8	d2(g)(p	d2(g)(p	PROPN
ejpam-6075	489	9	)	)	PUNCT
ejpam-6075	489	10	.	.	PUNCT
ejpam-6075	490	1	suppose	suppose	VERB
ejpam-6075	490	2	p	p	X
ejpam-6075	490	3	=	=	X
ejpam-6075	490	4	b′	b′	NUM
ejpam-6075	490	5	∈	∈	NOUN
ejpam-6075	490	6	v	v	NOUN
ejpam-6075	490	7	(	(	PUNCT
ejpam-6075	490	8	g2	g2	PROPN
ejpam-6075	490	9	)	)	PUNCT
ejpam-6075	490	10	.	.	PUNCT
ejpam-6075	491	1	by	by	ADP
ejpam-6075	491	2	considering	consider	VERB
ejpam-6075	491	3	b	b	PROPN
ejpam-6075	491	4	and	and	CCONJ
ejpam-6075	491	5	following	follow	VERB
ejpam-6075	491	6	the	the	DET
ejpam-6075	491	7	preceding	precede	VERB
ejpam-6075	491	8	arguments	argument	NOUN
ejpam-6075	491	9	,	,	PUNCT
ejpam-6075	491	10	it	it	PRON
ejpam-6075	491	11	can	can	AUX
ejpam-6075	491	12	be	be	AUX
ejpam-6075	491	13	shown	show	VERB
ejpam-6075	491	14	that	that	SCONJ
ejpam-6075	491	15	there	there	PRON
ejpam-6075	491	16	exists	exist	VERB
ejpam-6075	491	17	d	d	X
ejpam-6075	491	18	∈	∈	PROPN
ejpam-6075	491	19	st′	st′	PROPN
ejpam-6075	491	20	∩n2	∩n2	PROPN
ejpam-6075	491	21	d2(g)(p	d2(g)(p	PROPN
ejpam-6075	491	22	)	)	PUNCT
ejpam-6075	491	23	.	.	PUNCT
ejpam-6075	492	1	hence	hence	ADV
ejpam-6075	492	2	,	,	PUNCT
ejpam-6075	492	3	st′	st′	PROPN
ejpam-6075	492	4	is	be	AUX
ejpam-6075	492	5	hop	hop	NOUN
ejpam-6075	492	6	dominating	dominate	VERB
ejpam-6075	492	7	in	in	ADP
ejpam-6075	492	8	d2(g	d2(g	NOUN
ejpam-6075	492	9	)	)	PUNCT
ejpam-6075	492	10	.	.	PUNCT
ejpam-6075	493	1	therefore	therefore	ADV
ejpam-6075	493	2	,	,	PUNCT
ejpam-6075	493	3	s	s	VERB
ejpam-6075	493	4	is	be	AUX
ejpam-6075	493	5	a	a	DET
ejpam-6075	493	6	secure	secure	ADJ
ejpam-6075	493	7	hop	hop	NOUN
ejpam-6075	493	8	dominating	dominating	NOUN
ejpam-6075	493	9	set	set	VERB
ejpam-6075	493	10	in	in	ADP
ejpam-6075	493	11	d2(g	d2(g	PROPN
ejpam-6075	493	12	)	)	PUNCT
ejpam-6075	493	13	.	.	PUNCT
ejpam-6075	494	1	the	the	DET
ejpam-6075	494	2	same	same	ADJ
ejpam-6075	494	3	conclusion	conclusion	NOUN
ejpam-6075	494	4	holds	hold	VERB
ejpam-6075	494	5	if	if	SCONJ
ejpam-6075	494	6	(	(	PUNCT
ejpam-6075	494	7	ii	ii	NOUN
ejpam-6075	494	8	)	)	PUNCT
ejpam-6075	494	9	holds	hold	VERB
ejpam-6075	494	10	.	.	PUNCT
ejpam-6075	495	1	finally	finally	ADV
ejpam-6075	495	2	,	,	PUNCT
ejpam-6075	495	3	suppose	suppose	VERB
ejpam-6075	495	4	(	(	PUNCT
ejpam-6075	495	5	iii	iii	NOUN
ejpam-6075	495	6	)	)	PUNCT
ejpam-6075	495	7	holds	hold	VERB
ejpam-6075	495	8	.	.	PUNCT
ejpam-6075	496	1	then	then	ADV
ejpam-6075	496	2	,	,	PUNCT
ejpam-6075	496	3	by	by	ADP
ejpam-6075	496	4	theorem	theorem	NOUN
ejpam-6075	496	5	7(iii	7(iii	NUM
ejpam-6075	496	6	)	)	PUNCT
ejpam-6075	496	7	,	,	PUNCT
ejpam-6075	496	8	s	s	PART
ejpam-6075	496	9	=	=	PUNCT
ejpam-6075	496	10	sg1	sg1	PROPN
ejpam-6075	496	11	∪	∪	ADP
ejpam-6075	496	12	sg2	sg2	PROPN
ejpam-6075	496	13	is	be	AUX
ejpam-6075	496	14	hop	hop	PROPN
ejpam-6075	496	15	dominating	dominating	NOUN
ejpam-6075	496	16	.	.	PUNCT
ejpam-6075	497	1	let	let	VERB
ejpam-6075	497	2	x	x	SYM
ejpam-6075	497	3	∈	∈	PROPN
ejpam-6075	497	4	v	v	X
ejpam-6075	497	5	(	(	PUNCT
ejpam-6075	497	6	d2(g	d2(g	PROPN
ejpam-6075	497	7	)	)	PUNCT
ejpam-6075	497	8	)	)	PUNCT
ejpam-6075	497	9	\	\	PUNCT
ejpam-6075	498	1	s.	s.	PROPN
ejpam-6075	498	2	then	then	ADV
ejpam-6075	498	3	x	x	PROPN
ejpam-6075	498	4	/∈	/∈	PUNCT
ejpam-6075	498	5	sg1	sg1	PROPN
ejpam-6075	498	6	∪	∪	VERB
ejpam-6075	498	7	sg2	sg2	PROPN
ejpam-6075	498	8	.	.	PUNCT
ejpam-6075	499	1	we	we	PRON
ejpam-6075	499	2	may	may	AUX
ejpam-6075	499	3	assume	assume	VERB
ejpam-6075	499	4	that	that	SCONJ
ejpam-6075	499	5	x	x	SYM
ejpam-6075	499	6	∈	∈	PROPN
ejpam-6075	499	7	v	v	NOUN
ejpam-6075	499	8	(	(	PUNCT
ejpam-6075	499	9	g1	g1	PROPN
ejpam-6075	499	10	)	)	PUNCT
ejpam-6075	499	11	\	\	PROPN
ejpam-6075	499	12	sg1	sg1	NOUN
ejpam-6075	499	13	.	.	PUNCT
ejpam-6075	500	1	if	if	SCONJ
ejpam-6075	500	2	x′	x′	PROPN
ejpam-6075	500	3	∈	∈	PROPN
ejpam-6075	500	4	sg2	sg2	PROPN
ejpam-6075	500	5	,	,	PUNCT
ejpam-6075	500	6	then	then	ADV
ejpam-6075	500	7	x′	x′	PROPN
ejpam-6075	500	8	∈	∈	PROPN
ejpam-6075	500	9	s	s	VERB
ejpam-6075	500	10	∩n2	∩n2	PROPN
ejpam-6075	500	11	d2(g)(x	d2(g)(x	PROPN
ejpam-6075	500	12	)	)	PUNCT
ejpam-6075	500	13	and	and	CCONJ
ejpam-6075	500	14	(	(	PUNCT
ejpam-6075	500	15	s	s	X
ejpam-6075	500	16	\	\	X
ejpam-6075	500	17	{	{	PUNCT
ejpam-6075	500	18	x′	x′	NUM
ejpam-6075	500	19	}	}	PUNCT
ejpam-6075	500	20	)	)	PUNCT
ejpam-6075	500	21	∪	∪	ADP
ejpam-6075	500	22	{	{	PUNCT
ejpam-6075	500	23	x	x	NOUN
ejpam-6075	500	24	}	}	PUNCT
ejpam-6075	500	25	is	be	AUX
ejpam-6075	500	26	hop	hop	NOUN
ejpam-6075	500	27	dominating	dominate	VERB
ejpam-6075	500	28	in	in	ADP
ejpam-6075	500	29	d2(g	d2(g	PROPN
ejpam-6075	500	30	)	)	PUNCT
ejpam-6075	500	31	.	.	PUNCT
ejpam-6075	501	1	suppose	suppose	VERB
ejpam-6075	501	2	x′	x′	PROPN
ejpam-6075	501	3	/∈	/∈	PUNCT
ejpam-6075	502	1	sg2	sg2	PROPN
ejpam-6075	502	2	.	.	PUNCT
ejpam-6075	503	1	then	then	ADV
ejpam-6075	503	2	x	x	X
ejpam-6075	503	3	/∈	/∈	PUNCT
ejpam-6075	503	4	s′	s′	VERB
ejpam-6075	503	5	g2	g2	PROPN
ejpam-6075	503	6	.	.	PUNCT
ejpam-6075	504	1	this	this	PRON
ejpam-6075	504	2	implies	imply	VERB
ejpam-6075	504	3	that	that	SCONJ
ejpam-6075	504	4	x	x	X
ejpam-6075	504	5	/∈	/∈	PUNCT
ejpam-6075	504	6	v	v	X
ejpam-6075	504	7	(	(	PUNCT
ejpam-6075	504	8	g1	g1	PROPN
ejpam-6075	504	9	)	)	PUNCT
ejpam-6075	504	10	\	\	NOUN
ejpam-6075	505	1	(	(	PUNCT
ejpam-6075	505	2	sg1	sg1	NOUN
ejpam-6075	505	3	∪	∪	VERB
ejpam-6075	505	4	s′	s′	ADJ
ejpam-6075	505	5	g2	g2	PROPN
ejpam-6075	505	6	.	.	PUNCT
ejpam-6075	506	1	since	since	SCONJ
ejpam-6075	506	2	sg1	sg1	PROPN
ejpam-6075	506	3	∪	∪	ADP
ejpam-6075	506	4	s′	s′	ADJ
ejpam-6075	506	5	g2	g2	PROPN
ejpam-6075	506	6	is	be	AUX
ejpam-6075	506	7	secure	secure	ADJ
ejpam-6075	506	8	hop	hop	NOUN
ejpam-6075	506	9	dominating	dominating	NOUN
ejpam-6075	506	10	in	in	ADP
ejpam-6075	506	11	g1	g1	PROPN
ejpam-6075	506	12	,	,	PUNCT
ejpam-6075	506	13	there	there	PRON
ejpam-6075	506	14	exists	exist	VERB
ejpam-6075	506	15	y	y	PROPN
ejpam-6075	506	16	∈	∈	PROPN
ejpam-6075	506	17	(	(	PUNCT
ejpam-6075	506	18	sg1	sg1	NOUN
ejpam-6075	506	19	∪	∪	ADP
ejpam-6075	506	20	s′	s′	ADJ
ejpam-6075	506	21	g2	g2	PROPN
ejpam-6075	506	22	)	)	PUNCT
ejpam-6075	506	23	∩n2	∩n2	PROPN
ejpam-6075	506	24	g1	g1	PROPN
ejpam-6075	506	25	(	(	PUNCT
ejpam-6075	506	26	x	x	X
ejpam-6075	506	27	)	)	PUNCT
ejpam-6075	506	28	such	such	ADJ
ejpam-6075	506	29	that	that	SCONJ
ejpam-6075	506	30	[	[	X
ejpam-6075	506	31	(	(	PUNCT
ejpam-6075	506	32	sg1	sg1	NOUN
ejpam-6075	506	33	∪	∪	ADJ
ejpam-6075	506	34	s′	s′	ADJ
ejpam-6075	506	35	g2	g2	PROPN
ejpam-6075	506	36	)	)	PUNCT
ejpam-6075	506	37	\	\	PROPN
ejpam-6075	507	1	{	{	PUNCT
ejpam-6075	507	2	y	y	NOUN
ejpam-6075	507	3	}	}	PUNCT
ejpam-6075	507	4	]	]	PUNCT
ejpam-6075	507	5	∪	∪	X
ejpam-6075	507	6	{	{	PUNCT
ejpam-6075	507	7	x	x	NOUN
ejpam-6075	507	8	}	}	PUNCT
ejpam-6075	507	9	=	=	SYM
ejpam-6075	507	10	[	[	X
ejpam-6075	507	11	(	(	PUNCT
ejpam-6075	507	12	sg1	sg1	PROPN
ejpam-6075	507	13	\	\	PROPN
ejpam-6075	507	14	{	{	PUNCT
ejpam-6075	507	15	y	y	NOUN
ejpam-6075	507	16	}	}	PUNCT
ejpam-6075	507	17	)	)	PUNCT
ejpam-6075	507	18	∪	∪	ADP
ejpam-6075	507	19	{	{	PUNCT
ejpam-6075	507	20	x	x	NOUN
ejpam-6075	507	21	}	}	PUNCT
ejpam-6075	507	22	]	]	PUNCT
ejpam-6075	507	23	∪	∪	ADP
ejpam-6075	507	24	s′	s′	ADJ
ejpam-6075	507	25	g2	g2	PROPN
ejpam-6075	507	26	is	be	AUX
ejpam-6075	507	27	hop	hop	NOUN
ejpam-6075	507	28	dominating	dominate	VERB
ejpam-6075	507	29	in	in	ADP
ejpam-6075	507	30	g1	g1	PROPN
ejpam-6075	507	31	.	.	PUNCT
ejpam-6075	508	1	by	by	ADP
ejpam-6075	508	2	theorem	theorem	NOUN
ejpam-6075	508	3	7(iii	7(iii	NUM
ejpam-6075	508	4	)	)	PUNCT
ejpam-6075	508	5	,	,	PUNCT
ejpam-6075	508	6	[	[	X
ejpam-6075	508	7	(	(	PUNCT
ejpam-6075	508	8	sg1	sg1	PROPN
ejpam-6075	508	9	\	\	PROPN
ejpam-6075	508	10	{	{	PUNCT
ejpam-6075	508	11	y	y	NOUN
ejpam-6075	508	12	}	}	PUNCT
ejpam-6075	508	13	)	)	PUNCT
ejpam-6075	508	14	∪	∪	ADP
ejpam-6075	508	15	{	{	PUNCT
ejpam-6075	508	16	x	x	NOUN
ejpam-6075	508	17	}	}	PUNCT
ejpam-6075	508	18	]	]	PUNCT
ejpam-6075	508	19	∪	∪	ADP
ejpam-6075	508	20	sg2	sg2	PROPN
ejpam-6075	508	21	is	be	AUX
ejpam-6075	508	22	hop	hop	NOUN
ejpam-6075	508	23	dominating	dominate	VERB
ejpam-6075	508	24	in	in	ADP
ejpam-6075	508	25	g1	g1	PROPN
ejpam-6075	508	26	.	.	PUNCT
ejpam-6075	509	1	thus	thus	ADV
ejpam-6075	509	2	,	,	PUNCT
ejpam-6075	509	3	(	(	PUNCT
ejpam-6075	509	4	s	s	NOUN
ejpam-6075	509	5	\	\	X
ejpam-6075	509	6	{	{	PUNCT
ejpam-6075	509	7	y	y	NOUN
ejpam-6075	509	8	}	}	PUNCT
ejpam-6075	509	9	)	)	PUNCT
ejpam-6075	509	10	∪	∪	ADP
ejpam-6075	509	11	{	{	PUNCT
ejpam-6075	509	12	x	x	NOUN
ejpam-6075	509	13	}	}	PUNCT
ejpam-6075	509	14	=	=	SYM
ejpam-6075	510	1	[	[	X
ejpam-6075	510	2	(	(	PUNCT
ejpam-6075	510	3	sg1	sg1	PROPN
ejpam-6075	510	4	\	\	PROPN
ejpam-6075	510	5	{	{	PUNCT
ejpam-6075	510	6	y	y	NOUN
ejpam-6075	510	7	}	}	PUNCT
ejpam-6075	510	8	)	)	PUNCT
ejpam-6075	510	9	∪	∪	ADP
ejpam-6075	510	10	{	{	PUNCT
ejpam-6075	510	11	x	x	NOUN
ejpam-6075	510	12	}	}	PUNCT
ejpam-6075	510	13	]	]	PUNCT
ejpam-6075	510	14	∪	∪	ADP
ejpam-6075	510	15	sg2	sg2	PROPN
ejpam-6075	510	16	is	be	AUX
ejpam-6075	510	17	hop	hop	NOUN
ejpam-6075	510	18	dominating	dominate	VERB
ejpam-6075	510	19	in	in	ADP
ejpam-6075	510	20	d2(g	d2(g	NOUN
ejpam-6075	510	21	)	)	PUNCT
ejpam-6075	510	22	.	.	PUNCT
ejpam-6075	511	1	therefore	therefore	ADV
ejpam-6075	511	2	,	,	PUNCT
ejpam-6075	511	3	s	s	VERB
ejpam-6075	511	4	is	be	AUX
ejpam-6075	511	5	secure	secure	ADJ
ejpam-6075	511	6	hop	hop	NOUN
ejpam-6075	511	7	dominating	dominating	NOUN
ejpam-6075	511	8	in	in	ADP
ejpam-6075	511	9	d2(g	d2(g	NOUN
ejpam-6075	511	10	)	)	PUNCT
ejpam-6075	511	11	.	.	PUNCT
ejpam-6075	512	1	the	the	DET
ejpam-6075	512	2	next	next	ADJ
ejpam-6075	512	3	result	result	NOUN
ejpam-6075	512	4	is	be	AUX
ejpam-6075	512	5	a	a	DET
ejpam-6075	512	6	direct	direct	ADJ
ejpam-6075	512	7	consequence	consequence	NOUN
ejpam-6075	512	8	of	of	ADP
ejpam-6075	512	9	theorem	theorem	ADJ
ejpam-6075	512	10	8	8	NUM
ejpam-6075	512	11	.	.	PUNCT
ejpam-6075	512	12	corollary	corollary	ADJ
ejpam-6075	512	13	3	3	X
ejpam-6075	512	14	.	.	PUNCT
ejpam-6075	513	1	let	let	VERB
ejpam-6075	513	2	g	g	PRON
ejpam-6075	513	3	be	be	AUX
ejpam-6075	513	4	a	a	DET
ejpam-6075	513	5	non	non	ADJ
ejpam-6075	513	6	-	-	ADJ
ejpam-6075	513	7	trivial	trivial	ADJ
ejpam-6075	513	8	connected	connected	ADJ
ejpam-6075	513	9	graph	graph	NOUN
ejpam-6075	513	10	.	.	PUNCT
ejpam-6075	514	1	then	then	ADV
ejpam-6075	514	2	γsh(d2(g	γsh(d2(g	NUM
ejpam-6075	514	3	)	)	PUNCT
ejpam-6075	514	4	)	)	PUNCT
ejpam-6075	515	1	=	=	PUNCT
ejpam-6075	515	2	γsh(g	γsh(g	NOUN
ejpam-6075	515	3	)	)	PUNCT
ejpam-6075	515	4	.	.	PUNCT
ejpam-6075	516	1	proof	proof	NOUN
ejpam-6075	516	2	.	.	PUNCT
ejpam-6075	517	1	let	let	VERB
ejpam-6075	517	2	s	s	PRON
ejpam-6075	517	3	be	be	AUX
ejpam-6075	517	4	a	a	DET
ejpam-6075	517	5	γsh	γsh	NOUN
ejpam-6075	517	6	-	-	PUNCT
ejpam-6075	517	7	set	set	NOUN
ejpam-6075	517	8	of	of	ADP
ejpam-6075	517	9	g	g	NOUN
ejpam-6075	517	10	=	=	PUNCT
ejpam-6075	517	11	g1	g1	PROPN
ejpam-6075	517	12	.	.	PUNCT
ejpam-6075	518	1	then	then	ADV
ejpam-6075	518	2	s	s	VERB
ejpam-6075	518	3	is	be	AUX
ejpam-6075	518	4	a	a	DET
ejpam-6075	518	5	secure	secure	ADJ
ejpam-6075	518	6	hop	hop	NOUN
ejpam-6075	518	7	dominating	dominating	NOUN
ejpam-6075	518	8	set	set	NOUN
ejpam-6075	518	9	of	of	ADP
ejpam-6075	518	10	d2(g	d2(g	PROPN
ejpam-6075	518	11	)	)	PUNCT
ejpam-6075	518	12	by	by	ADP
ejpam-6075	518	13	theorem	theorem	NOUN
ejpam-6075	518	14	8	8	NUM
ejpam-6075	518	15	.	.	PUNCT
ejpam-6075	519	1	hence	hence	ADV
ejpam-6075	519	2	,	,	PUNCT
ejpam-6075	519	3	γsh(d2(g	γsh(d2(g	NUM
ejpam-6075	519	4	)	)	PUNCT
ejpam-6075	520	1	)	)	PUNCT
ejpam-6075	520	2	≤	≤	NUM
ejpam-6075	520	3	|s|	|s|	PROPN
ejpam-6075	520	4	=	=	PUNCT
ejpam-6075	520	5	γsh(g	γsh(g	NOUN
ejpam-6075	520	6	)	)	PUNCT
ejpam-6075	520	7	.	.	PUNCT
ejpam-6075	521	1	next	next	ADV
ejpam-6075	521	2	,	,	PUNCT
ejpam-6075	521	3	suppose	suppose	VERB
ejpam-6075	521	4	s′	s′	PRON
ejpam-6075	521	5	is	be	AUX
ejpam-6075	521	6	a	a	DET
ejpam-6075	521	7	γsh	γsh	NOUN
ejpam-6075	521	8	-	-	PUNCT
ejpam-6075	521	9	set	set	NOUN
ejpam-6075	521	10	of	of	ADP
ejpam-6075	521	11	d2(g	d2(g	PROPN
ejpam-6075	521	12	)	)	PUNCT
ejpam-6075	521	13	.	.	PUNCT
ejpam-6075	522	1	if	if	SCONJ
ejpam-6075	522	2	s′	s′	VERB
ejpam-6075	522	3	⊆	⊆	NUM
ejpam-6075	522	4	v	v	NOUN
ejpam-6075	522	5	(	(	PUNCT
ejpam-6075	522	6	g1	g1	PROPN
ejpam-6075	522	7	)	)	PUNCT
ejpam-6075	522	8	or	or	CCONJ
ejpam-6075	522	9	s′	s′	ADJ
ejpam-6075	522	10	⊆	⊆	NUM
ejpam-6075	522	11	v	v	NOUN
ejpam-6075	522	12	(	(	PUNCT
ejpam-6075	522	13	g2	g2	PROPN
ejpam-6075	522	14	)	)	PUNCT
ejpam-6075	522	15	,	,	PUNCT
ejpam-6075	522	16	then	then	ADV
ejpam-6075	522	17	s′	s′	ADJ
ejpam-6075	522	18	is	be	AUX
ejpam-6075	522	19	a	a	DET
ejpam-6075	522	20	secure	secure	ADJ
ejpam-6075	522	21	hop	hop	NOUN
ejpam-6075	522	22	dominating	dominating	NOUN
ejpam-6075	522	23	set	set	NOUN
ejpam-6075	522	24	of	of	ADP
ejpam-6075	522	25	g	g	NOUN
ejpam-6075	522	26	by	by	ADP
ejpam-6075	522	27	(	(	PUNCT
ejpam-6075	522	28	i	i	NOUN
ejpam-6075	522	29	)	)	PUNCT
ejpam-6075	522	30	and	and	CCONJ
ejpam-6075	522	31	(	(	PUNCT
ejpam-6075	522	32	ii	ii	NOUN
ejpam-6075	522	33	)	)	PUNCT
ejpam-6075	522	34	of	of	ADP
ejpam-6075	522	35	theorem	theorem	NOUN
ejpam-6075	522	36	8	8	NUM
ejpam-6075	522	37	.	.	PUNCT
ejpam-6075	523	1	it	it	PRON
ejpam-6075	523	2	follows	follow	VERB
ejpam-6075	523	3	that	that	SCONJ
ejpam-6075	523	4	γsh(g	γsh(g	NOUN
ejpam-6075	523	5	)	)	PUNCT
ejpam-6075	523	6	≤	≤	NOUN
ejpam-6075	523	7	|s′|	|s′|	NOUN
ejpam-6075	523	8	=	=	PUNCT
ejpam-6075	523	9	γsh(d2(g	γsh(d2(g	NUM
ejpam-6075	523	10	)	)	PUNCT
ejpam-6075	523	11	)	)	PUNCT
ejpam-6075	523	12	.	.	PUNCT
ejpam-6075	524	1	if	if	SCONJ
ejpam-6075	524	2	s′	s′	ADJ
ejpam-6075	524	3	=	=	NOUN
ejpam-6075	524	4	sg1	sg1	NOUN
ejpam-6075	524	5	∪	∪	PROPN
ejpam-6075	524	6	sg2	sg2	PROPN
ejpam-6075	524	7	,	,	PUNCT
ejpam-6075	524	8	then	then	ADV
ejpam-6075	524	9	sg1	sg1	NOUN
ejpam-6075	524	10	∪	∪	ADP
ejpam-6075	524	11	s′	s′	ADJ
ejpam-6075	524	12	g2	g2	PROPN
ejpam-6075	524	13	is	be	AUX
ejpam-6075	524	14	secure	secure	ADJ
ejpam-6075	524	15	hop	hop	NOUN
ejpam-6075	524	16	dominating	dominating	NOUN
ejpam-6075	524	17	in	in	ADP
ejpam-6075	524	18	g	g	PROPN
ejpam-6075	524	19	by	by	ADP
ejpam-6075	524	20	f.	f.	PROPN
ejpam-6075	524	21	l.	l.	PROPN
ejpam-6075	524	22	alfeche	alfeche	PROPN
ejpam-6075	524	23	,	,	PUNCT
ejpam-6075	524	24	g.	g.	PROPN
ejpam-6075	524	25	a.	a.	PROPN
ejpam-6075	524	26	malacas	malacas	PROPN
ejpam-6075	524	27	,	,	PUNCT
ejpam-6075	524	28	s.	s.	PROPN
ejpam-6075	524	29	canoy	canoy	PROPN
ejpam-6075	524	30	jr	jr	PROPN
ejpam-6075	524	31	.	.	PROPN
ejpam-6075	524	32	/	/	SYM
ejpam-6075	524	33	eur	eur	PROPN
ejpam-6075	524	34	.	.	PUNCT
ejpam-6075	525	1	j.	j.	PROPN
ejpam-6075	525	2	pure	pure	PROPN
ejpam-6075	525	3	appl	appl	PROPN
ejpam-6075	525	4	.	.	PROPN
ejpam-6075	525	5	math	math	PROPN
ejpam-6075	525	6	,	,	PUNCT
ejpam-6075	525	7	18	18	NUM
ejpam-6075	525	8	(	(	PUNCT
ejpam-6075	525	9	2	2	NUM
ejpam-6075	525	10	)	)	PUNCT
ejpam-6075	525	11	(	(	PUNCT
ejpam-6075	525	12	2025	2025	NUM
ejpam-6075	525	13	)	)	PUNCT
ejpam-6075	525	14	,	,	PUNCT
ejpam-6075	525	15	6075	6075	NUM
ejpam-6075	525	16	11	11	NUM
ejpam-6075	525	17	of	of	ADP
ejpam-6075	525	18	14	14	NUM
ejpam-6075	525	19	theorem	theorem	ADJ
ejpam-6075	525	20	8(iii	8(iii	NUM
ejpam-6075	525	21	)	)	PUNCT
ejpam-6075	525	22	.	.	PUNCT
ejpam-6075	526	1	hence	hence	ADV
ejpam-6075	526	2	,	,	PUNCT
ejpam-6075	526	3	γsh(g	γsh(g	NOUN
ejpam-6075	526	4	)	)	PUNCT
ejpam-6075	526	5	≤	≤	NUM
ejpam-6075	526	6	|sg1	|sg1	PROPN
ejpam-6075	526	7	∪	∪	ADP
ejpam-6075	526	8	s′	s′	ADJ
ejpam-6075	526	9	g2	g2	PROPN
ejpam-6075	526	10	|	|	ADV
ejpam-6075	526	11	=	=	PUNCT
ejpam-6075	526	12	|sg1	|sg1	NOUN
ejpam-6075	526	13	∪	∪	VERB
ejpam-6075	526	14	sg2	sg2	PROPN
ejpam-6075	526	15	|	|	PROPN
ejpam-6075	526	16	=	=	PUNCT
ejpam-6075	526	17	|s′|	|s′|	NOUN
ejpam-6075	526	18	=	=	PUNCT
ejpam-6075	526	19	γsh(d2(g	γsh(d2(g	NUM
ejpam-6075	526	20	)	)	PUNCT
ejpam-6075	526	21	)	)	PUNCT
ejpam-6075	526	22	.	.	PUNCT
ejpam-6075	527	1	this	this	PRON
ejpam-6075	527	2	establishes	establish	VERB
ejpam-6075	527	3	the	the	DET
ejpam-6075	527	4	desired	desire	VERB
ejpam-6075	527	5	equality	equality	NOUN
ejpam-6075	527	6	.	.	PUNCT
ejpam-6075	528	1	lemma	lemma	PROPN
ejpam-6075	528	2	3	3	X
ejpam-6075	528	3	.	.	PUNCT
ejpam-6075	529	1	let	let	VERB
ejpam-6075	529	2	g	g	PRON
ejpam-6075	529	3	be	be	AUX
ejpam-6075	529	4	a	a	DET
ejpam-6075	529	5	graph	graph	NOUN
ejpam-6075	529	6	.	.	PUNCT
ejpam-6075	530	1	then	then	ADV
ejpam-6075	530	2	s	s	VERB
ejpam-6075	530	3	=	=	SYM
ejpam-6075	530	4	{	{	PUNCT
ejpam-6075	530	5	x	x	PROPN
ejpam-6075	530	6	,	,	PUNCT
ejpam-6075	530	7	y	y	PROPN
ejpam-6075	530	8	}	}	PUNCT
ejpam-6075	530	9	,	,	PUNCT
ejpam-6075	530	10	where	where	SCONJ
ejpam-6075	530	11	x	x	X
ejpam-6075	530	12	,	,	PUNCT
ejpam-6075	530	13	y	y	PROPN
ejpam-6075	530	14	∈	∈	PROPN
ejpam-6075	530	15	v	v	NOUN
ejpam-6075	530	16	(	(	PUNCT
ejpam-6075	530	17	g	g	NOUN
ejpam-6075	530	18	)	)	PUNCT
ejpam-6075	530	19	,	,	PUNCT
ejpam-6075	530	20	is	be	AUX
ejpam-6075	530	21	a	a	DET
ejpam-6075	530	22	hop	hop	NOUN
ejpam-6075	530	23	dominating	dominating	NOUN
ejpam-6075	530	24	set	set	VERB
ejpam-6075	530	25	in	in	ADP
ejpam-6075	530	26	gg	gg	PROPN
ejpam-6075	530	27	if	if	SCONJ
ejpam-6075	530	28	and	and	CCONJ
ejpam-6075	530	29	only	only	ADV
ejpam-6075	530	30	if	if	SCONJ
ejpam-6075	530	31	x	x	X
ejpam-6075	530	32	=	=	SYM
ejpam-6075	530	33	y.	y.	NOUN
ejpam-6075	530	34	proof	proof	NOUN
ejpam-6075	530	35	.	.	PUNCT
ejpam-6075	531	1	suppose	suppose	VERB
ejpam-6075	531	2	s	s	PRON
ejpam-6075	531	3	is	be	AUX
ejpam-6075	531	4	a	a	DET
ejpam-6075	531	5	hop	hop	NOUN
ejpam-6075	531	6	dominating	dominating	NOUN
ejpam-6075	531	7	set	set	VERB
ejpam-6075	531	8	in	in	ADP
ejpam-6075	531	9	gg	gg	PROPN
ejpam-6075	531	10	.	.	PUNCT
ejpam-6075	531	11	suppose	suppose	VERB
ejpam-6075	531	12	x	x	PUNCT
ejpam-6075	531	13	̸=	̸=	PROPN
ejpam-6075	531	14	y.	y.	NOUN
ejpam-6075	531	15	if	if	SCONJ
ejpam-6075	531	16	xy	xy	PROPN
ejpam-6075	531	17	∈	∈	PROPN
ejpam-6075	531	18	e(g	e(g	PROPN
ejpam-6075	531	19	)	)	PUNCT
ejpam-6075	532	1	,	,	PUNCT
ejpam-6075	532	2	then	then	ADV
ejpam-6075	532	3	y	y	PROPN
ejpam-6075	532	4	/∈	/∈	PROPN
ejpam-6075	532	5	n2	n2	PROPN
ejpam-6075	532	6	gg	gg	PROPN
ejpam-6075	532	7	(	(	PUNCT
ejpam-6075	532	8	s	s	PROPN
ejpam-6075	532	9	)	)	PUNCT
ejpam-6075	532	10	because	because	SCONJ
ejpam-6075	532	11	yy	yy	PROPN
ejpam-6075	532	12	∈	∈	PROPN
ejpam-6075	532	13	e(gg	e(gg	PROPN
ejpam-6075	532	14	)	)	PUNCT
ejpam-6075	532	15	.	.	PUNCT
ejpam-6075	533	1	if	if	SCONJ
ejpam-6075	533	2	xy	xy	PROPN
ejpam-6075	533	3	/∈	/∈	PUNCT
ejpam-6075	533	4	e(g	e(g	PROPN
ejpam-6075	533	5	)	)	PUNCT
ejpam-6075	533	6	,	,	PUNCT
ejpam-6075	533	7	then	then	ADV
ejpam-6075	533	8	x	x	X
ejpam-6075	533	9	y	y	PROPN
ejpam-6075	533	10	∈	∈	PROPN
ejpam-6075	533	11	e(g	e(g	PROPN
ejpam-6075	533	12	)	)	PUNCT
ejpam-6075	533	13	.	.	PUNCT
ejpam-6075	534	1	thus	thus	ADV
ejpam-6075	534	2	,	,	PUNCT
ejpam-6075	534	3	x	x	PROPN
ejpam-6075	534	4	/∈	/∈	PUNCT
ejpam-6075	534	5	n2	n2	PROPN
ejpam-6075	534	6	gg	gg	PROPN
ejpam-6075	534	7	(	(	PUNCT
ejpam-6075	534	8	s	s	NOUN
ejpam-6075	534	9	)	)	PUNCT
ejpam-6075	534	10	.	.	PUNCT
ejpam-6075	535	1	in	in	ADP
ejpam-6075	535	2	both	both	DET
ejpam-6075	535	3	cases	case	NOUN
ejpam-6075	535	4	,	,	PUNCT
ejpam-6075	535	5	we	we	PRON
ejpam-6075	535	6	obtain	obtain	VERB
ejpam-6075	535	7	a	a	DET
ejpam-6075	535	8	contradiction	contradiction	NOUN
ejpam-6075	535	9	.	.	PUNCT
ejpam-6075	536	1	thus	thus	ADV
ejpam-6075	536	2	,	,	PUNCT
ejpam-6075	536	3	x	x	PUNCT
ejpam-6075	536	4	=	=	PUNCT
ejpam-6075	536	5	y.	y.	NOUN
ejpam-6075	536	6	for	for	ADP
ejpam-6075	536	7	the	the	DET
ejpam-6075	536	8	converse	converse	NOUN
ejpam-6075	536	9	,	,	PUNCT
ejpam-6075	536	10	suppose	suppose	VERB
ejpam-6075	536	11	x	x	X
ejpam-6075	536	12	=	=	PUNCT
ejpam-6075	536	13	y.	y.	NOUN
ejpam-6075	536	14	then	then	ADV
ejpam-6075	536	15	clearly	clearly	ADV
ejpam-6075	536	16	,	,	PUNCT
ejpam-6075	536	17	s	s	VERB
ejpam-6075	536	18	=	=	PUNCT
ejpam-6075	536	19	{	{	PUNCT
ejpam-6075	536	20	x	x	NOUN
ejpam-6075	536	21	,	,	PUNCT
ejpam-6075	536	22	x	x	PRON
ejpam-6075	536	23	}	}	PUNCT
ejpam-6075	536	24	is	be	AUX
ejpam-6075	536	25	a	a	DET
ejpam-6075	536	26	hop	hop	NOUN
ejpam-6075	536	27	dominating	dominating	NOUN
ejpam-6075	536	28	set	set	VERB
ejpam-6075	536	29	in	in	ADP
ejpam-6075	536	30	gg	gg	PROPN
ejpam-6075	536	31	.	.	PUNCT
ejpam-6075	537	1	theorem	theorem	PROPN
ejpam-6075	537	2	9	9	NUM
ejpam-6075	537	3	.	.	PUNCT
ejpam-6075	538	1	let	let	VERB
ejpam-6075	538	2	g	g	PRON
ejpam-6075	538	3	be	be	AUX
ejpam-6075	538	4	a	a	DET
ejpam-6075	538	5	graph	graph	NOUN
ejpam-6075	538	6	.	.	PUNCT
ejpam-6075	539	1	then	then	ADV
ejpam-6075	539	2	2	2	NUM
ejpam-6075	539	3	≤	≤	NOUN
ejpam-6075	539	4	γsh(gg	γsh(gg	ADJ
ejpam-6075	539	5	)	)	PUNCT
ejpam-6075	539	6	≤	≤	NUM
ejpam-6075	539	7	4	4	NUM
ejpam-6075	539	8	.	.	PUNCT
ejpam-6075	540	1	moreover	moreover	ADV
ejpam-6075	540	2	,	,	PUNCT
ejpam-6075	540	3	each	each	PRON
ejpam-6075	540	4	of	of	ADP
ejpam-6075	540	5	the	the	DET
ejpam-6075	540	6	following	following	ADJ
ejpam-6075	540	7	statements	statement	NOUN
ejpam-6075	540	8	hold	hold	VERB
ejpam-6075	540	9	:	:	PUNCT
ejpam-6075	540	10	(	(	PUNCT
ejpam-6075	540	11	i	i	NOUN
ejpam-6075	540	12	)	)	PUNCT
ejpam-6075	540	13	γsh(gg	γsh(gg	ADJ
ejpam-6075	540	14	)	)	PUNCT
ejpam-6075	541	1	=	=	SYM
ejpam-6075	541	2	2	2	NUM
ejpam-6075	541	3	if	if	SCONJ
ejpam-6075	541	4	and	and	CCONJ
ejpam-6075	541	5	only	only	ADV
ejpam-6075	541	6	if	if	SCONJ
ejpam-6075	541	7	g	g	PROPN
ejpam-6075	541	8	∈	∈	PROPN
ejpam-6075	541	9	{	{	PUNCT
ejpam-6075	541	10	k1,k2,k2	k1,k2,k2	ADV
ejpam-6075	541	11	}	}	PUNCT
ejpam-6075	541	12	.	.	PUNCT
ejpam-6075	542	1	(	(	PUNCT
ejpam-6075	542	2	ii	ii	NOUN
ejpam-6075	542	3	)	)	PUNCT
ejpam-6075	542	4	γsh(gg	γsh(gg	ADJ
ejpam-6075	542	5	)	)	PUNCT
ejpam-6075	542	6	=	=	SYM
ejpam-6075	542	7	3	3	NUM
ejpam-6075	542	8	if	if	SCONJ
ejpam-6075	542	9	and	and	CCONJ
ejpam-6075	542	10	only	only	ADV
ejpam-6075	542	11	if	if	SCONJ
ejpam-6075	542	12	g	g	PROPN
ejpam-6075	542	13	/∈	/∈	PUNCT
ejpam-6075	542	14	{	{	PUNCT
ejpam-6075	542	15	k2,k2	k2,k2	PROPN
ejpam-6075	542	16	}	}	PUNCT
ejpam-6075	542	17	and	and	CCONJ
ejpam-6075	542	18	one	one	NUM
ejpam-6075	542	19	of	of	ADP
ejpam-6075	542	20	the	the	DET
ejpam-6075	542	21	following	follow	VERB
ejpam-6075	542	22	conditions	condition	NOUN
ejpam-6075	542	23	holds	hold	VERB
ejpam-6075	542	24	:	:	PUNCT
ejpam-6075	542	25	(	(	PUNCT
ejpam-6075	542	26	i1	i1	PROPN
ejpam-6075	542	27	)	)	PUNCT
ejpam-6075	542	28	γh(g	γh(g	PUNCT
ejpam-6075	542	29	)	)	PUNCT
ejpam-6075	542	30	=	=	SYM
ejpam-6075	542	31	2	2	NUM
ejpam-6075	542	32	or	or	CCONJ
ejpam-6075	542	33	γh(g	γh(g	NOUN
ejpam-6075	542	34	)	)	PUNCT
ejpam-6075	542	35	=	=	SYM
ejpam-6075	542	36	2	2	X
ejpam-6075	542	37	.	.	PUNCT
ejpam-6075	542	38	(	(	PUNCT
ejpam-6075	542	39	i2	i2	PROPN
ejpam-6075	542	40	)	)	PUNCT
ejpam-6075	542	41	there	there	PRON
ejpam-6075	542	42	exists	exist	VERB
ejpam-6075	542	43	a	a	DET
ejpam-6075	542	44	secure	secure	ADJ
ejpam-6075	542	45	hop	hop	NOUN
ejpam-6075	542	46	dominating	dominating	NOUN
ejpam-6075	542	47	set	set	NOUN
ejpam-6075	542	48	s	s	NOUN
ejpam-6075	542	49	of	of	ADP
ejpam-6075	542	50	g	g	NOUN
ejpam-6075	542	51	with	with	ADP
ejpam-6075	542	52	|s|	|s|	NOUN
ejpam-6075	542	53	=	=	SYM
ejpam-6075	542	54	3	3	NUM
ejpam-6075	542	55	such	such	ADJ
ejpam-6075	542	56	that	that	DET
ejpam-6075	542	57	ephn(v;s	ephn(v;s	NUM
ejpam-6075	542	58	)	)	PUNCT
ejpam-6075	542	59	=	=	SYM
ejpam-6075	542	60	0	0	NUM
ejpam-6075	543	1	for	for	ADP
ejpam-6075	543	2	some	some	DET
ejpam-6075	543	3	v	v	ADP
ejpam-6075	543	4	∈	∈	PROPN
ejpam-6075	543	5	s	s	NOUN
ejpam-6075	543	6	or	or	CCONJ
ejpam-6075	543	7	a	a	DET
ejpam-6075	543	8	secure	secure	ADJ
ejpam-6075	543	9	hop	hop	NOUN
ejpam-6075	543	10	dominating	dominating	NOUN
ejpam-6075	543	11	set	set	NOUN
ejpam-6075	543	12	s	s	NOUN
ejpam-6075	543	13	of	of	ADP
ejpam-6075	543	14	g	g	NOUN
ejpam-6075	543	15	with	with	ADP
ejpam-6075	543	16	|s|	|s|	NOUN
ejpam-6075	543	17	=	=	SYM
ejpam-6075	543	18	3	3	NUM
ejpam-6075	543	19	such	such	ADJ
ejpam-6075	543	20	that	that	DET
ejpam-6075	543	21	ephn(v;s	ephn(v;s	NUM
ejpam-6075	543	22	)	)	PUNCT
ejpam-6075	543	23	=	=	SYM
ejpam-6075	543	24	0	0	NUM
ejpam-6075	543	25	for	for	ADP
ejpam-6075	543	26	some	some	PRON
ejpam-6075	543	27	v	v	ADP
ejpam-6075	543	28	∈	∈	PROPN
ejpam-6075	543	29	s.	s.	PROPN
ejpam-6075	543	30	(	(	PUNCT
ejpam-6075	543	31	i3	i3	PROPN
ejpam-6075	543	32	)	)	PUNCT
ejpam-6075	543	33	there	there	PRON
ejpam-6075	543	34	exist	exist	VERB
ejpam-6075	543	35	vertices	vertex	NOUN
ejpam-6075	543	36	x	x	X
ejpam-6075	543	37	,	,	PUNCT
ejpam-6075	543	38	y	y	PROPN
ejpam-6075	543	39	,	,	PUNCT
ejpam-6075	543	40	z,∈	z,∈	PROPN
ejpam-6075	543	41	v	v	NOUN
ejpam-6075	543	42	(	(	PUNCT
ejpam-6075	543	43	g	g	NOUN
ejpam-6075	543	44	)	)	PUNCT
ejpam-6075	543	45	such	such	ADJ
ejpam-6075	543	46	z	z	PROPN
ejpam-6075	543	47	∈	∈	PROPN
ejpam-6075	543	48	n2	n2	PROPN
ejpam-6075	543	49	g[{x	g[{x	PROPN
ejpam-6075	543	50	,	,	PUNCT
ejpam-6075	543	51	y	y	PROPN
ejpam-6075	543	52	}	}	PUNCT
ejpam-6075	543	53	]	]	PUNCT
ejpam-6075	543	54	,	,	PUNCT
ejpam-6075	543	55	and	and	CCONJ
ejpam-6075	543	56	dg(v	dg(v	X
ejpam-6075	543	57	,	,	PUNCT
ejpam-6075	543	58	w	w	NOUN
ejpam-6075	543	59	)	)	PUNCT
ejpam-6075	543	60	=	=	SYM
ejpam-6075	543	61	2	2	NUM
ejpam-6075	543	62	for	for	ADP
ejpam-6075	543	63	all	all	DET
ejpam-6075	543	64	v	v	NOUN
ejpam-6075	543	65	,	,	PUNCT
ejpam-6075	544	1	w	w	PROPN
ejpam-6075	544	2	∈	∈	PROPN
ejpam-6075	544	3	v	v	ADP
ejpam-6075	544	4	(	(	PUNCT
ejpam-6075	544	5	g	g	NOUN
ejpam-6075	544	6	)	)	PUNCT
ejpam-6075	544	7	\n2	\n2	PROPN
ejpam-6075	544	8	g({x	g({x	PROPN
ejpam-6075	544	9	,	,	PUNCT
ejpam-6075	544	10	y	y	NOUN
ejpam-6075	544	11	}	}	PUNCT
ejpam-6075	544	12	)	)	PUNCT
ejpam-6075	544	13	,	,	PUNCT
ejpam-6075	544	14	where	where	SCONJ
ejpam-6075	544	15	v	v	ADP
ejpam-6075	544	16	̸=	̸=	PROPN
ejpam-6075	544	17	w.	w.	PROPN
ejpam-6075	544	18	(	(	PUNCT
ejpam-6075	544	19	i4	i4	PROPN
ejpam-6075	544	20	)	)	PUNCT
ejpam-6075	544	21	there	there	PRON
ejpam-6075	544	22	exist	exist	VERB
ejpam-6075	544	23	vertices	vertex	NOUN
ejpam-6075	544	24	x	x	X
ejpam-6075	544	25	,	,	PUNCT
ejpam-6075	544	26	y	y	PROPN
ejpam-6075	544	27	,	,	PUNCT
ejpam-6075	544	28	z	z	PROPN
ejpam-6075	544	29	∈	∈	PROPN
ejpam-6075	544	30	v	v	ADP
ejpam-6075	544	31	(	(	PUNCT
ejpam-6075	544	32	g	g	NOUN
ejpam-6075	544	33	)	)	PUNCT
ejpam-6075	544	34	such	such	ADJ
ejpam-6075	544	35	z	z	PROPN
ejpam-6075	544	36	∈	∈	PROPN
ejpam-6075	544	37	n2	n2	NOUN
ejpam-6075	544	38	g	g	PROPN
ejpam-6075	545	1	[	[	X
ejpam-6075	545	2	{	{	PUNCT
ejpam-6075	545	3	x	x	NOUN
ejpam-6075	545	4	,	,	PUNCT
ejpam-6075	545	5	y	y	PROPN
ejpam-6075	545	6	}	}	PUNCT
ejpam-6075	545	7	]	]	PUNCT
ejpam-6075	545	8	,	,	PUNCT
ejpam-6075	545	9	and	and	CCONJ
ejpam-6075	545	10	dg(v	dg(v	X
ejpam-6075	545	11	,	,	PUNCT
ejpam-6075	545	12	w	w	NOUN
ejpam-6075	545	13	)	)	PUNCT
ejpam-6075	545	14	=	=	SYM
ejpam-6075	545	15	2	2	NUM
ejpam-6075	545	16	for	for	ADP
ejpam-6075	545	17	all	all	DET
ejpam-6075	545	18	v	v	NOUN
ejpam-6075	545	19	,	,	PUNCT
ejpam-6075	545	20	w	w	PROPN
ejpam-6075	545	21	∈	∈	PROPN
ejpam-6075	545	22	v	v	ADP
ejpam-6075	545	23	(	(	PUNCT
ejpam-6075	545	24	g	g	NOUN
ejpam-6075	545	25	)	)	PUNCT
ejpam-6075	545	26	\n2	\n2	VERB
ejpam-6075	546	1	g	g	PROPN
ejpam-6075	547	1	[	[	X
ejpam-6075	547	2	{	{	PUNCT
ejpam-6075	547	3	x	x	NOUN
ejpam-6075	547	4	,	,	PUNCT
ejpam-6075	547	5	y	y	PROPN
ejpam-6075	547	6	}	}	PUNCT
ejpam-6075	547	7	]	]	PUNCT
ejpam-6075	547	8	,	,	PUNCT
ejpam-6075	547	9	where	where	SCONJ
ejpam-6075	547	10	v	v	ADP
ejpam-6075	547	11	̸=	̸=	PROPN
ejpam-6075	547	12	w	w	PROPN
ejpam-6075	547	13	(	(	PUNCT
ejpam-6075	547	14	iii	iii	NOUN
ejpam-6075	547	15	)	)	PUNCT
ejpam-6075	547	16	γsh(gg	γsh(gg	ADJ
ejpam-6075	547	17	)	)	PUNCT
ejpam-6075	547	18	=	=	SYM
ejpam-6075	547	19	4	4	NUM
ejpam-6075	547	20	if	if	SCONJ
ejpam-6075	547	21	and	and	CCONJ
ejpam-6075	547	22	only	only	ADV
ejpam-6075	547	23	if	if	SCONJ
ejpam-6075	547	24	g	g	PROPN
ejpam-6075	547	25	does	do	AUX
ejpam-6075	547	26	not	not	PART
ejpam-6075	547	27	satisfy	satisfy	VERB
ejpam-6075	547	28	any	any	PRON
ejpam-6075	547	29	of	of	ADP
ejpam-6075	547	30	the	the	DET
ejpam-6075	547	31	properties	property	NOUN
ejpam-6075	547	32	in	in	ADP
ejpam-6075	547	33	(	(	PUNCT
ejpam-6075	547	34	i	i	NOUN
ejpam-6075	547	35	)	)	PUNCT
ejpam-6075	547	36	and	and	CCONJ
ejpam-6075	547	37	(	(	PUNCT
ejpam-6075	547	38	ii	ii	NOUN
ejpam-6075	547	39	)	)	PUNCT
ejpam-6075	547	40	.	.	PUNCT
ejpam-6075	548	1	proof	proof	NOUN
ejpam-6075	548	2	.	.	PUNCT
ejpam-6075	549	1	since	since	SCONJ
ejpam-6075	549	2	gg	gg	PROPN
ejpam-6075	549	3	is	be	AUX
ejpam-6075	549	4	non	non	ADJ
ejpam-6075	549	5	-	-	ADJ
ejpam-6075	549	6	trivial	trivial	ADJ
ejpam-6075	549	7	,	,	PUNCT
ejpam-6075	549	8	it	it	PRON
ejpam-6075	549	9	follows	follow	VERB
ejpam-6075	549	10	that	that	SCONJ
ejpam-6075	549	11	2	2	NUM
ejpam-6075	549	12	≤	≤	NOUN
ejpam-6075	549	13	γsh(gg	γsh(gg	ADJ
ejpam-6075	549	14	)	)	PUNCT
ejpam-6075	549	15	.	.	PUNCT
ejpam-6075	550	1	since	since	SCONJ
ejpam-6075	550	2	{	{	PUNCT
ejpam-6075	550	3	v	v	NOUN
ejpam-6075	550	4	,	,	PUNCT
ejpam-6075	550	5	v	v	NOUN
ejpam-6075	550	6	}	}	PUNCT
ejpam-6075	550	7	is	be	AUX
ejpam-6075	550	8	a	a	DET
ejpam-6075	550	9	hop	hop	NOUN
ejpam-6075	550	10	dominating	dominating	NOUN
ejpam-6075	550	11	set	set	VERB
ejpam-6075	550	12	in	in	ADP
ejpam-6075	550	13	gg	gg	NOUN
ejpam-6075	550	14	for	for	ADP
ejpam-6075	550	15	each	each	DET
ejpam-6075	550	16	v	v	NUM
ejpam-6075	550	17	∈	∈	PROPN
ejpam-6075	550	18	v	v	NOUN
ejpam-6075	550	19	(	(	PUNCT
ejpam-6075	550	20	g	g	NOUN
ejpam-6075	550	21	)	)	PUNCT
ejpam-6075	550	22	,	,	PUNCT
ejpam-6075	550	23	{	{	PUNCT
ejpam-6075	550	24	v	v	NOUN
ejpam-6075	550	25	,	,	PUNCT
ejpam-6075	550	26	w	w	PROPN
ejpam-6075	550	27	,	,	PUNCT
ejpam-6075	550	28	v	v	NOUN
ejpam-6075	550	29	,	,	PUNCT
ejpam-6075	550	30	w	w	NOUN
ejpam-6075	550	31	}	}	PUNCT
ejpam-6075	550	32	is	be	AUX
ejpam-6075	550	33	a	a	DET
ejpam-6075	550	34	secure	secure	ADJ
ejpam-6075	550	35	hop	hop	NOUN
ejpam-6075	550	36	dominating	dominating	NOUN
ejpam-6075	550	37	set	set	VERB
ejpam-6075	550	38	in	in	ADP
ejpam-6075	550	39	gg	gg	NOUN
ejpam-6075	550	40	for	for	ADP
ejpam-6075	550	41	each	each	DET
ejpam-6075	550	42	pair	pair	NOUN
ejpam-6075	550	43	of	of	ADP
ejpam-6075	550	44	distinct	distinct	ADJ
ejpam-6075	550	45	vertices	vertex	NOUN
ejpam-6075	550	46	v	v	NOUN
ejpam-6075	550	47	and	and	CCONJ
ejpam-6075	550	48	w	w	PROPN
ejpam-6075	550	49	of	of	ADP
ejpam-6075	550	50	g.	g.	PROPN
ejpam-6075	550	51	therefore	therefore	ADV
ejpam-6075	550	52	,	,	PUNCT
ejpam-6075	550	53	2	2	NUM
ejpam-6075	550	54	≤	≤	NUM
ejpam-6075	550	55	γsh(gg	γsh(gg	ADJ
ejpam-6075	550	56	)	)	PUNCT
ejpam-6075	550	57	≤	≤	NUM
ejpam-6075	550	58	4	4	NUM
ejpam-6075	550	59	.	.	PUNCT
ejpam-6075	551	1	(	(	PUNCT
ejpam-6075	551	2	i	i	NOUN
ejpam-6075	551	3	)	)	PUNCT
ejpam-6075	551	4	suppose	suppose	VERB
ejpam-6075	551	5	γsh(gg	γsh(gg	ADJ
ejpam-6075	551	6	)	)	PUNCT
ejpam-6075	551	7	=	=	SYM
ejpam-6075	551	8	2	2	NUM
ejpam-6075	551	9	,	,	PUNCT
ejpam-6075	551	10	say	say	VERB
ejpam-6075	551	11	s	s	X
ejpam-6075	551	12	=	=	PUNCT
ejpam-6075	551	13	{	{	PUNCT
ejpam-6075	551	14	p	p	X
ejpam-6075	551	15	,	,	PUNCT
ejpam-6075	551	16	q	q	X
ejpam-6075	551	17	}	}	PUNCT
ejpam-6075	551	18	is	be	AUX
ejpam-6075	551	19	a	a	DET
ejpam-6075	551	20	γsh	γsh	NOUN
ejpam-6075	551	21	-	-	PUNCT
ejpam-6075	551	22	set	set	VERB
ejpam-6075	551	23	ingg	ingg	NOUN
ejpam-6075	551	24	.	.	PUNCT
ejpam-6075	552	1	supposeg	supposeg	PROPN
ejpam-6075	552	2	/∈	/∈	PUNCT
ejpam-6075	552	3	{	{	PUNCT
ejpam-6075	552	4	k1,k2,k2	k1,k2,k2	ADV
ejpam-6075	552	5	}	}	PUNCT
ejpam-6075	552	6	.	.	PUNCT
ejpam-6075	553	1	then	then	ADV
ejpam-6075	553	2	|v	|v	PROPN
ejpam-6075	553	3	(	(	PUNCT
ejpam-6075	553	4	g)|	g)|	X
ejpam-6075	553	5	≥	≥	NOUN
ejpam-6075	553	6	3	3	NUM
ejpam-6075	553	7	.	.	PUNCT
ejpam-6075	553	8	suppose	suppose	VERB
ejpam-6075	553	9	p	p	X
ejpam-6075	553	10	,	,	PUNCT
ejpam-6075	553	11	q	q	PROPN
ejpam-6075	553	12	∈	∈	PROPN
ejpam-6075	553	13	v	v	NOUN
ejpam-6075	553	14	(	(	PUNCT
ejpam-6075	553	15	g	g	NOUN
ejpam-6075	553	16	)	)	PUNCT
ejpam-6075	553	17	.	.	PUNCT
ejpam-6075	554	1	choose	choose	VERB
ejpam-6075	554	2	any	any	DET
ejpam-6075	554	3	s	s	PROPN
ejpam-6075	554	4	∈	∈	NOUN
ejpam-6075	554	5	v	v	NOUN
ejpam-6075	554	6	(	(	PUNCT
ejpam-6075	554	7	g	g	NOUN
ejpam-6075	554	8	)	)	PUNCT
ejpam-6075	554	9	\	\	PUNCT
ejpam-6075	555	1	s.	s.	PROPN
ejpam-6075	555	2	then	then	ADV
ejpam-6075	555	3	s	s	VERB
ejpam-6075	555	4	∈	∈	PROPN
ejpam-6075	555	5	v	v	NOUN
ejpam-6075	555	6	(	(	PUNCT
ejpam-6075	555	7	gg	gg	NOUN
ejpam-6075	555	8	)	)	PUNCT
ejpam-6075	555	9	\	\	PROPN
ejpam-6075	555	10	s.	s.	PROPN
ejpam-6075	555	11	since	since	SCONJ
ejpam-6075	555	12	s	s	PROPN
ejpam-6075	555	13	is	be	AUX
ejpam-6075	555	14	secure	secure	ADJ
ejpam-6075	555	15	hop	hop	NOUN
ejpam-6075	555	16	dominating	dominating	NOUN
ejpam-6075	555	17	in	in	ADP
ejpam-6075	555	18	gg	gg	PROPN
ejpam-6075	555	19	,	,	PUNCT
ejpam-6075	555	20	{	{	PUNCT
ejpam-6075	555	21	p	p	X
ejpam-6075	555	22	,	,	PUNCT
ejpam-6075	555	23	s	s	PART
ejpam-6075	555	24	}	}	PUNCT
ejpam-6075	555	25	or	or	CCONJ
ejpam-6075	555	26	{	{	PUNCT
ejpam-6075	555	27	q	q	NOUN
ejpam-6075	555	28	,	,	PUNCT
ejpam-6075	555	29	s	s	AUX
ejpam-6075	555	30	}	}	PUNCT
ejpam-6075	555	31	is	be	AUX
ejpam-6075	555	32	hop	hop	NOUN
ejpam-6075	555	33	dominating	dominate	VERB
ejpam-6075	555	34	in	in	ADP
ejpam-6075	555	35	gg	gg	PROPN
ejpam-6075	555	36	.	.	PUNCT
ejpam-6075	556	1	according	accord	VERB
ejpam-6075	556	2	to	to	ADP
ejpam-6075	556	3	lemma	lemma	PROPN
ejpam-6075	556	4	3	3	NUM
ejpam-6075	556	5	,	,	PUNCT
ejpam-6075	556	6	this	this	PRON
ejpam-6075	556	7	is	be	AUX
ejpam-6075	556	8	impossible	impossible	ADJ
ejpam-6075	556	9	.	.	PUNCT
ejpam-6075	557	1	similarly	similarly	ADV
ejpam-6075	557	2	,	,	PUNCT
ejpam-6075	557	3	we	we	PRON
ejpam-6075	557	4	arrived	arrive	VERB
ejpam-6075	557	5	at	at	ADP
ejpam-6075	557	6	a	a	DET
ejpam-6075	557	7	contradiction	contradiction	NOUN
ejpam-6075	557	8	if	if	SCONJ
ejpam-6075	557	9	p	p	X
ejpam-6075	557	10	,	,	PUNCT
ejpam-6075	557	11	q	q	PROPN
ejpam-6075	557	12	∈	∈	PROPN
ejpam-6075	557	13	v	v	NOUN
ejpam-6075	557	14	(	(	PUNCT
ejpam-6075	557	15	g	g	NOUN
ejpam-6075	557	16	)	)	PUNCT
ejpam-6075	557	17	.	.	PUNCT
ejpam-6075	558	1	suppose	suppose	VERB
ejpam-6075	558	2	now	now	ADV
ejpam-6075	558	3	that	that	SCONJ
ejpam-6075	558	4	p	p	PROPN
ejpam-6075	558	5	∈	∈	PROPN
ejpam-6075	558	6	v	v	ADP
ejpam-6075	558	7	(	(	PUNCT
ejpam-6075	558	8	g	g	NOUN
ejpam-6075	558	9	)	)	PUNCT
ejpam-6075	558	10	and	and	CCONJ
ejpam-6075	558	11	q	q	NOUN
ejpam-6075	558	12	=	=	SYM
ejpam-6075	558	13	c	c	X
ejpam-6075	558	14	∈	∈	PROPN
ejpam-6075	558	15	v	v	NOUN
ejpam-6075	558	16	(	(	PUNCT
ejpam-6075	558	17	g	g	NOUN
ejpam-6075	558	18	)	)	PUNCT
ejpam-6075	558	19	.	.	PUNCT
ejpam-6075	559	1	by	by	ADP
ejpam-6075	559	2	lemma	lemma	PROPN
ejpam-6075	559	3	3	3	NUM
ejpam-6075	559	4	,	,	PUNCT
ejpam-6075	559	5	p	p	NOUN
ejpam-6075	559	6	=	=	SYM
ejpam-6075	559	7	c	c	NOUN
ejpam-6075	559	8	,	,	PUNCT
ejpam-6075	559	9	i.e.	i.e.	X
ejpam-6075	559	10	,	,	PUNCT
ejpam-6075	559	11	s	s	VERB
ejpam-6075	559	12	=	=	PUNCT
ejpam-6075	559	13	{	{	PUNCT
ejpam-6075	559	14	p	p	X
ejpam-6075	559	15	,	,	PUNCT
ejpam-6075	559	16	p	p	X
ejpam-6075	559	17	}	}	PUNCT
ejpam-6075	559	18	.	.	PUNCT
ejpam-6075	560	1	let	let	VERB
ejpam-6075	560	2	z	z	NOUN
ejpam-6075	560	3	∈	∈	PROPN
ejpam-6075	560	4	v	v	ADP
ejpam-6075	560	5	(	(	PUNCT
ejpam-6075	560	6	g	g	NOUN
ejpam-6075	560	7	)	)	PUNCT
ejpam-6075	560	8	\	\	NOUN
ejpam-6075	561	1	{	{	PUNCT
ejpam-6075	561	2	p	p	X
ejpam-6075	561	3	}	}	PUNCT
ejpam-6075	561	4	.	.	PUNCT
ejpam-6075	562	1	then	then	ADV
ejpam-6075	562	2	,	,	PUNCT
ejpam-6075	562	3	by	by	ADP
ejpam-6075	562	4	lemma	lemma	PROPN
ejpam-6075	562	5	3	3	NUM
ejpam-6075	562	6	,	,	PUNCT
ejpam-6075	562	7	(	(	PUNCT
ejpam-6075	562	8	s	s	X
ejpam-6075	562	9	\	\	X
ejpam-6075	562	10	{	{	PUNCT
ejpam-6075	562	11	p	p	NOUN
ejpam-6075	562	12	}	}	PUNCT
ejpam-6075	562	13	)	)	PUNCT
ejpam-6075	562	14	∪	∪	ADP
ejpam-6075	562	15	{	{	PUNCT
ejpam-6075	562	16	z	z	NOUN
ejpam-6075	562	17	}	}	PUNCT
ejpam-6075	562	18	=	=	SYM
ejpam-6075	562	19	{	{	PUNCT
ejpam-6075	562	20	p	p	X
ejpam-6075	562	21	,	,	PUNCT
ejpam-6075	562	22	z	z	NOUN
ejpam-6075	562	23	}	}	PUNCT
ejpam-6075	562	24	is	be	AUX
ejpam-6075	562	25	a	a	DET
ejpam-6075	562	26	hop	hop	NOUN
ejpam-6075	562	27	dominating	dominating	NOUN
ejpam-6075	562	28	set	set	VERB
ejpam-6075	562	29	in	in	ADP
ejpam-6075	562	30	g.	g.	PROPN
ejpam-6075	562	31	suppose	suppose	VERB
ejpam-6075	562	32	g	g	PROPN
ejpam-6075	562	33	is	be	AUX
ejpam-6075	562	34	disconnected	disconnect	VERB
ejpam-6075	562	35	.	.	PUNCT
ejpam-6075	563	1	pick	pick	VERB
ejpam-6075	563	2	w	w	PROPN
ejpam-6075	563	3	∈	∈	PROPN
ejpam-6075	563	4	v	v	ADP
ejpam-6075	563	5	(	(	PUNCT
ejpam-6075	563	6	h	h	NOUN
ejpam-6075	563	7	)	)	PUNCT
ejpam-6075	563	8	where	where	SCONJ
ejpam-6075	563	9	h	h	NOUN
ejpam-6075	563	10	is	be	AUX
ejpam-6075	563	11	a	a	DET
ejpam-6075	563	12	component	component	NOUN
ejpam-6075	563	13	of	of	ADP
ejpam-6075	563	14	g	g	PROPN
ejpam-6075	563	15	such	such	ADJ
ejpam-6075	563	16	f.	f.	PROPN
ejpam-6075	563	17	l.	l.	PROPN
ejpam-6075	563	18	alfeche	alfeche	PROPN
ejpam-6075	563	19	,	,	PUNCT
ejpam-6075	563	20	g.	g.	PROPN
ejpam-6075	563	21	a.	a.	PROPN
ejpam-6075	563	22	malacas	malacas	PROPN
ejpam-6075	563	23	,	,	PUNCT
ejpam-6075	563	24	s.	s.	PROPN
ejpam-6075	563	25	canoy	canoy	PROPN
ejpam-6075	563	26	jr	jr	PROPN
ejpam-6075	563	27	.	.	PROPN
ejpam-6075	563	28	/	/	SYM
ejpam-6075	563	29	eur	eur	PROPN
ejpam-6075	563	30	.	.	PUNCT
ejpam-6075	564	1	j.	j.	PROPN
ejpam-6075	564	2	pure	pure	PROPN
ejpam-6075	564	3	appl	appl	PROPN
ejpam-6075	564	4	.	.	PROPN
ejpam-6075	564	5	math	math	PROPN
ejpam-6075	564	6	,	,	PUNCT
ejpam-6075	564	7	18	18	NUM
ejpam-6075	564	8	(	(	PUNCT
ejpam-6075	564	9	2	2	NUM
ejpam-6075	564	10	)	)	PUNCT
ejpam-6075	564	11	(	(	PUNCT
ejpam-6075	564	12	2025	2025	NUM
ejpam-6075	564	13	)	)	PUNCT
ejpam-6075	564	14	,	,	PUNCT
ejpam-6075	564	15	6075	6075	NUM
ejpam-6075	564	16	12	12	NUM
ejpam-6075	564	17	of	of	ADP
ejpam-6075	564	18	14	14	NUM
ejpam-6075	565	1	that	that	PRON
ejpam-6075	565	2	p	p	X
ejpam-6075	565	3	/∈	/∈	NOUN
ejpam-6075	566	1	v	v	INTJ
ejpam-6075	566	2	(	(	PUNCT
ejpam-6075	566	3	h	h	NOUN
ejpam-6075	566	4	)	)	PUNCT
ejpam-6075	566	5	.	.	PUNCT
ejpam-6075	567	1	then	then	ADV
ejpam-6075	567	2	(	(	PUNCT
ejpam-6075	567	3	s	s	X
ejpam-6075	567	4	\	\	X
ejpam-6075	567	5	{	{	PUNCT
ejpam-6075	567	6	p	p	NOUN
ejpam-6075	567	7	}	}	PUNCT
ejpam-6075	567	8	)	)	PUNCT
ejpam-6075	567	9	∪	∪	ADP
ejpam-6075	567	10	{	{	PUNCT
ejpam-6075	567	11	w	w	NOUN
ejpam-6075	567	12	}	}	PUNCT
ejpam-6075	567	13	=	=	SYM
ejpam-6075	567	14	{	{	PUNCT
ejpam-6075	567	15	p	p	X
ejpam-6075	567	16	,	,	PUNCT
ejpam-6075	567	17	w	w	NOUN
ejpam-6075	567	18	}	}	PUNCT
ejpam-6075	567	19	is	be	AUX
ejpam-6075	567	20	not	not	PART
ejpam-6075	567	21	a	a	DET
ejpam-6075	567	22	hop	hop	NOUN
ejpam-6075	567	23	dominating	dominating	NOUN
ejpam-6075	567	24	set	set	NOUN
ejpam-6075	567	25	,	,	PUNCT
ejpam-6075	567	26	a	a	DET
ejpam-6075	567	27	contradiction	contradiction	NOUN
ejpam-6075	567	28	.	.	PUNCT
ejpam-6075	568	1	hence	hence	ADV
ejpam-6075	568	2	,	,	PUNCT
ejpam-6075	568	3	g	g	PROPN
ejpam-6075	568	4	is	be	AUX
ejpam-6075	568	5	connected	connect	VERB
ejpam-6075	568	6	.	.	PUNCT
ejpam-6075	569	1	since	since	SCONJ
ejpam-6075	569	2	g	g	PROPN
ejpam-6075	569	3	/∈	/∈	PUNCT
ejpam-6075	569	4	{	{	PUNCT
ejpam-6075	569	5	k1,k2	k1,k2	PROPN
ejpam-6075	569	6	}	}	PUNCT
ejpam-6075	569	7	,	,	PUNCT
ejpam-6075	569	8	we	we	PRON
ejpam-6075	569	9	may	may	AUX
ejpam-6075	569	10	choose	choose	VERB
ejpam-6075	569	11	a	a	DET
ejpam-6075	569	12	vertex	vertex	NOUN
ejpam-6075	569	13	d	d	NOUN
ejpam-6075	569	14	such	such	ADJ
ejpam-6075	569	15	that	that	SCONJ
ejpam-6075	569	16	ng(p	ng(p	VERB
ejpam-6075	569	17	)	)	PUNCT
ejpam-6075	569	18	∩ng(d	∩ng(d	PROPN
ejpam-6075	569	19	)	)	PUNCT
ejpam-6075	569	20	̸=	̸=	PROPN
ejpam-6075	569	21	∅.	∅.	ADP
ejpam-6075	569	22	this	this	PRON
ejpam-6075	569	23	implies	imply	VERB
ejpam-6075	569	24	that	that	SCONJ
ejpam-6075	569	25	(	(	PUNCT
ejpam-6075	569	26	s	s	X
ejpam-6075	569	27	\	\	X
ejpam-6075	569	28	{	{	PUNCT
ejpam-6075	569	29	p	p	NOUN
ejpam-6075	569	30	}	}	PUNCT
ejpam-6075	569	31	)	)	PUNCT
ejpam-6075	569	32	∪	∪	ADP
ejpam-6075	569	33	{	{	PUNCT
ejpam-6075	569	34	d	d	NOUN
ejpam-6075	569	35	}	}	PUNCT
ejpam-6075	569	36	=	=	SYM
ejpam-6075	569	37	{	{	PUNCT
ejpam-6075	569	38	p	p	X
ejpam-6075	569	39	,	,	PUNCT
ejpam-6075	569	40	d	d	NOUN
ejpam-6075	569	41	}	}	PUNCT
ejpam-6075	569	42	is	be	AUX
ejpam-6075	569	43	not	not	PART
ejpam-6075	569	44	a	a	DET
ejpam-6075	569	45	hop	hop	NOUN
ejpam-6075	569	46	dominating	dominating	NOUN
ejpam-6075	569	47	set	set	NOUN
ejpam-6075	569	48	in	in	ADP
ejpam-6075	569	49	g	g	PROPN
ejpam-6075	569	50	,	,	PUNCT
ejpam-6075	569	51	a	a	DET
ejpam-6075	569	52	contradiction	contradiction	NOUN
ejpam-6075	569	53	.	.	PUNCT
ejpam-6075	570	1	therefore	therefore	ADV
ejpam-6075	570	2	,	,	PUNCT
ejpam-6075	570	3	g	g	PROPN
ejpam-6075	570	4	∈	∈	PROPN
ejpam-6075	570	5	{	{	PUNCT
ejpam-6075	570	6	k1,k2,k2	k1,k2,k2	ADV
ejpam-6075	570	7	}	}	PUNCT
ejpam-6075	570	8	.	.	PUNCT
ejpam-6075	571	1	for	for	ADP
ejpam-6075	571	2	the	the	DET
ejpam-6075	571	3	converse	converse	NOUN
ejpam-6075	571	4	,	,	PUNCT
ejpam-6075	571	5	suppose	suppose	VERB
ejpam-6075	571	6	first	first	ADV
ejpam-6075	571	7	that	that	SCONJ
ejpam-6075	571	8	g	g	PROPN
ejpam-6075	571	9	=	=	PROPN
ejpam-6075	571	10	k1	k1	PROPN
ejpam-6075	571	11	.	.	PUNCT
ejpam-6075	572	1	then	then	ADV
ejpam-6075	572	2	gg	gg	PROPN
ejpam-6075	572	3	=	=	SYM
ejpam-6075	572	4	k2	k2	PROPN
ejpam-6075	572	5	and	and	CCONJ
ejpam-6075	572	6	γsh(gg	γsh(gg	ADJ
ejpam-6075	572	7	)	)	PUNCT
ejpam-6075	573	1	=	=	SYM
ejpam-6075	573	2	2	2	X
ejpam-6075	573	3	.	.	X
ejpam-6075	574	1	if	if	SCONJ
ejpam-6075	574	2	g	g	PROPN
ejpam-6075	574	3	∈	∈	PROPN
ejpam-6075	574	4	{	{	PUNCT
ejpam-6075	574	5	k2,k2	k2,k2	PROPN
ejpam-6075	574	6	}	}	PUNCT
ejpam-6075	574	7	,	,	PUNCT
ejpam-6075	574	8	then	then	ADV
ejpam-6075	574	9	gg	gg	PROPN
ejpam-6075	574	10	=	=	PUNCT
ejpam-6075	574	11	p4	p4	ADJ
ejpam-6075	574	12	.	.	PUNCT
ejpam-6075	575	1	by	by	ADP
ejpam-6075	575	2	theorem	theorem	NOUN
ejpam-6075	575	3	1	1	NUM
ejpam-6075	575	4	,	,	PUNCT
ejpam-6075	575	5	γsh(gg	γsh(gg	ADJ
ejpam-6075	575	6	)	)	PUNCT
ejpam-6075	575	7	=	=	SYM
ejpam-6075	575	8	2	2	X
ejpam-6075	575	9	.	.	PUNCT
ejpam-6075	575	10	(	(	PUNCT
ejpam-6075	575	11	ii	ii	NOUN
ejpam-6075	575	12	)	)	PUNCT
ejpam-6075	575	13	suppose	suppose	VERB
ejpam-6075	575	14	γsh(gg	γsh(gg	ADJ
ejpam-6075	575	15	)	)	PUNCT
ejpam-6075	575	16	=	=	SYM
ejpam-6075	576	1	3	3	X
ejpam-6075	576	2	.	.	PUNCT
ejpam-6075	576	3	then	then	ADV
ejpam-6075	576	4	g	g	PROPN
ejpam-6075	576	5	/∈	/∈	PUNCT
ejpam-6075	576	6	{	{	PUNCT
ejpam-6075	576	7	k2,k2	k2,k2	PROPN
ejpam-6075	576	8	}	}	PUNCT
ejpam-6075	576	9	by	by	ADP
ejpam-6075	576	10	(	(	PUNCT
ejpam-6075	576	11	i	i	NOUN
ejpam-6075	576	12	)	)	PUNCT
ejpam-6075	576	13	.	.	PUNCT
ejpam-6075	577	1	if	if	SCONJ
ejpam-6075	577	2	γh(g	γh(g	NOUN
ejpam-6075	577	3	)	)	PUNCT
ejpam-6075	577	4	=	=	SYM
ejpam-6075	577	5	2	2	NUM
ejpam-6075	577	6	or	or	CCONJ
ejpam-6075	577	7	γh(g	γh(g	NOUN
ejpam-6075	577	8	)	)	PUNCT
ejpam-6075	577	9	=	=	SYM
ejpam-6075	577	10	2	2	NUM
ejpam-6075	577	11	,	,	PUNCT
ejpam-6075	577	12	then	then	ADV
ejpam-6075	577	13	(	(	PUNCT
ejpam-6075	577	14	i1	i1	PROPN
ejpam-6075	577	15	)	)	PUNCT
ejpam-6075	577	16	is	be	AUX
ejpam-6075	577	17	satisfied	satisfied	ADJ
ejpam-6075	577	18	.	.	PUNCT
ejpam-6075	578	1	suppose	suppose	VERB
ejpam-6075	578	2	γh(g	γh(g	NOUN
ejpam-6075	578	3	)	)	PUNCT
ejpam-6075	578	4	>	>	SYM
ejpam-6075	578	5	2	2	NUM
ejpam-6075	578	6	and	and	CCONJ
ejpam-6075	578	7	γh(g	γh(g	NOUN
ejpam-6075	578	8	)	)	PUNCT
ejpam-6075	578	9	>	>	X
ejpam-6075	579	1	2	2	X
ejpam-6075	579	2	.	.	PUNCT
ejpam-6075	579	3	let	let	VERB
ejpam-6075	579	4	d	d	NOUN
ejpam-6075	579	5	=	=	PRON
ejpam-6075	579	6	{	{	PUNCT
ejpam-6075	579	7	x	x	PROPN
ejpam-6075	579	8	,	,	PUNCT
ejpam-6075	579	9	y	y	PROPN
ejpam-6075	579	10	,	,	PUNCT
ejpam-6075	579	11	s	s	AUX
ejpam-6075	579	12	}	}	PUNCT
ejpam-6075	579	13	be	be	AUX
ejpam-6075	579	14	a	a	DET
ejpam-6075	579	15	γsh	γsh	NOUN
ejpam-6075	579	16	-	-	PUNCT
ejpam-6075	579	17	set	set	VERB
ejpam-6075	579	18	in	in	ADP
ejpam-6075	579	19	gg	gg	PROPN
ejpam-6075	579	20	.	.	PUNCT
ejpam-6075	580	1	we	we	PRON
ejpam-6075	580	2	may	may	AUX
ejpam-6075	580	3	assume	assume	VERB
ejpam-6075	580	4	that	that	SCONJ
ejpam-6075	580	5	d	d	PROPN
ejpam-6075	580	6	⊆	⊆	NUM
ejpam-6075	580	7	v	v	ADP
ejpam-6075	580	8	(	(	PUNCT
ejpam-6075	580	9	g	g	NOUN
ejpam-6075	580	10	)	)	PUNCT
ejpam-6075	580	11	.	.	PUNCT
ejpam-6075	581	1	then	then	ADV
ejpam-6075	581	2	d	d	X
ejpam-6075	581	3	is	be	AUX
ejpam-6075	581	4	a	a	DET
ejpam-6075	581	5	secure	secure	ADJ
ejpam-6075	581	6	hop	hop	NOUN
ejpam-6075	581	7	dominating	dominating	NOUN
ejpam-6075	581	8	set	set	VERB
ejpam-6075	581	9	in	in	ADP
ejpam-6075	581	10	g.	g.	PROPN
ejpam-6075	581	11	suppose	suppose	VERB
ejpam-6075	581	12	ephn(v;s	ephn(v;s	NUM
ejpam-6075	581	13	)	)	PUNCT
ejpam-6075	581	14	̸=	̸=	NOUN
ejpam-6075	581	15	0	0	NUM
ejpam-6075	581	16	for	for	ADP
ejpam-6075	581	17	all	all	PRON
ejpam-6075	581	18	v	v	NOUN
ejpam-6075	581	19	∈	∈	PROPN
ejpam-6075	581	20	d.	d.	NOUN
ejpam-6075	581	21	let	let	VERB
ejpam-6075	581	22	u′	u′	PRON
ejpam-6075	581	23	∈	∈	PROPN
ejpam-6075	581	24	v	v	ADP
ejpam-6075	581	25	(	(	PUNCT
ejpam-6075	581	26	g	g	NOUN
ejpam-6075	581	27	)	)	PUNCT
ejpam-6075	581	28	where	where	SCONJ
ejpam-6075	581	29	u	u	NOUN
ejpam-6075	581	30	/∈	/∈	PUNCT
ejpam-6075	581	31	{	{	PUNCT
ejpam-6075	581	32	x	x	NOUN
ejpam-6075	581	33	,	,	PUNCT
ejpam-6075	581	34	y	y	PROPN
ejpam-6075	581	35	,	,	PUNCT
ejpam-6075	581	36	s	s	PART
ejpam-6075	581	37	}	}	PUNCT
ejpam-6075	581	38	.	.	PUNCT
ejpam-6075	582	1	since	since	SCONJ
ejpam-6075	582	2	d	d	PROPN
ejpam-6075	582	3	is	be	AUX
ejpam-6075	582	4	secure	secure	ADJ
ejpam-6075	582	5	hop	hop	NOUN
ejpam-6075	582	6	dominating	dominating	NOUN
ejpam-6075	582	7	in	in	ADP
ejpam-6075	582	8	gg	gg	PROPN
ejpam-6075	582	9	,	,	PUNCT
ejpam-6075	582	10	there	there	PRON
ejpam-6075	582	11	exists	exist	VERB
ejpam-6075	582	12	w	w	PROPN
ejpam-6075	582	13	∈	∈	PROPN
ejpam-6075	582	14	d	d	PROPN
ejpam-6075	582	15	,	,	PUNCT
ejpam-6075	582	16	say	say	VERB
ejpam-6075	582	17	w	w	NOUN
ejpam-6075	582	18	=	=	SYM
ejpam-6075	582	19	x	x	NOUN
ejpam-6075	582	20	,	,	PUNCT
ejpam-6075	582	21	such	such	ADJ
ejpam-6075	582	22	that	that	SCONJ
ejpam-6075	582	23	(	(	PUNCT
ejpam-6075	582	24	d	d	NOUN
ejpam-6075	582	25	\	\	X
ejpam-6075	582	26	{	{	PUNCT
ejpam-6075	582	27	x	x	NOUN
ejpam-6075	582	28	}	}	PUNCT
ejpam-6075	582	29	)	)	PUNCT
ejpam-6075	582	30	∪	∪	ADP
ejpam-6075	582	31	{	{	PUNCT
ejpam-6075	582	32	u	u	NOUN
ejpam-6075	582	33	}	}	PUNCT
ejpam-6075	582	34	is	be	AUX
ejpam-6075	582	35	hop	hop	NOUN
ejpam-6075	582	36	dominating	dominate	VERB
ejpam-6075	582	37	in	in	ADP
ejpam-6075	582	38	gg	gg	PROPN
ejpam-6075	582	39	.	.	PUNCT
ejpam-6075	583	1	this	this	PRON
ejpam-6075	583	2	,	,	PUNCT
ejpam-6075	583	3	however	however	ADV
ejpam-6075	583	4	,	,	PUNCT
ejpam-6075	583	5	is	be	AUX
ejpam-6075	583	6	not	not	PART
ejpam-6075	583	7	possible	possible	ADJ
ejpam-6075	583	8	because	because	SCONJ
ejpam-6075	583	9	ephn(x;s	ephn(x;	VERB
ejpam-6075	583	10	)	)	PUNCT
ejpam-6075	583	11	̸=	̸=	PROPN
ejpam-6075	583	12	0	0	NUM
ejpam-6075	583	13	.	.	PUNCT
ejpam-6075	584	1	thus	thus	ADV
ejpam-6075	584	2	,	,	PUNCT
ejpam-6075	584	3	there	there	PRON
ejpam-6075	584	4	exists	exist	VERB
ejpam-6075	584	5	v	v	ADP
ejpam-6075	584	6	∈	∈	PROPN
ejpam-6075	584	7	d	d	NOUN
ejpam-6075	584	8	such	such	ADJ
ejpam-6075	584	9	that	that	PRON
ejpam-6075	584	10	ephn(v;s	ephn(v;s	NOUN
ejpam-6075	584	11	)	)	PUNCT
ejpam-6075	585	1	=	=	SYM
ejpam-6075	585	2	0	0	X
ejpam-6075	585	3	.	.	PUNCT
ejpam-6075	586	1	this	this	PRON
ejpam-6075	586	2	shows	show	VERB
ejpam-6075	586	3	that	that	SCONJ
ejpam-6075	586	4	(	(	PUNCT
ejpam-6075	586	5	i2	i2	NOUN
ejpam-6075	586	6	)	)	PUNCT
ejpam-6075	586	7	holds	hold	VERB
ejpam-6075	586	8	.	.	PUNCT
ejpam-6075	587	1	next	next	ADV
ejpam-6075	587	2	,	,	PUNCT
ejpam-6075	587	3	suppose	suppose	VERB
ejpam-6075	587	4	that	that	SCONJ
ejpam-6075	587	5	x	x	NOUN
ejpam-6075	587	6	,	,	PUNCT
ejpam-6075	587	7	y	y	PROPN
ejpam-6075	587	8	∈	∈	PROPN
ejpam-6075	587	9	v	v	ADP
ejpam-6075	587	10	(	(	PUNCT
ejpam-6075	587	11	g	g	NOUN
ejpam-6075	587	12	)	)	PUNCT
ejpam-6075	587	13	and	and	CCONJ
ejpam-6075	587	14	s	s	VERB
ejpam-6075	587	15	=	=	SYM
ejpam-6075	587	16	z	z	PROPN
ejpam-6075	587	17	∈	∈	PROPN
ejpam-6075	587	18	v	v	ADP
ejpam-6075	587	19	(	(	PUNCT
ejpam-6075	587	20	g	g	NOUN
ejpam-6075	587	21	)	)	PUNCT
ejpam-6075	587	22	.	.	PUNCT
ejpam-6075	588	1	if	if	SCONJ
ejpam-6075	588	2	{	{	PUNCT
ejpam-6075	588	3	x	x	NOUN
ejpam-6075	588	4	,	,	PUNCT
ejpam-6075	588	5	y	y	PRON
ejpam-6075	588	6	}	}	PUNCT
ejpam-6075	588	7	is	be	AUX
ejpam-6075	588	8	a	a	DET
ejpam-6075	588	9	hop	hop	NOUN
ejpam-6075	588	10	dominating	dominating	NOUN
ejpam-6075	588	11	set	set	NOUN
ejpam-6075	588	12	in	in	ADP
ejpam-6075	588	13	g	g	NOUN
ejpam-6075	588	14	,	,	PUNCT
ejpam-6075	588	15	then	then	ADV
ejpam-6075	588	16	γh(g	γh(g	PUNCT
ejpam-6075	588	17	)	)	PUNCT
ejpam-6075	588	18	=	=	SYM
ejpam-6075	588	19	2	2	NUM
ejpam-6075	588	20	and	and	CCONJ
ejpam-6075	588	21	we	we	PRON
ejpam-6075	588	22	find	find	VERB
ejpam-6075	588	23	that	that	SCONJ
ejpam-6075	588	24	(	(	PUNCT
ejpam-6075	588	25	i1	i1	PROPN
ejpam-6075	588	26	)	)	PUNCT
ejpam-6075	588	27	holds	hold	VERB
ejpam-6075	588	28	.	.	PUNCT
ejpam-6075	589	1	suppose	suppose	VERB
ejpam-6075	589	2	{	{	PUNCT
ejpam-6075	589	3	x	x	NOUN
ejpam-6075	589	4	,	,	PUNCT
ejpam-6075	589	5	y	y	NOUN
ejpam-6075	589	6	}	}	PUNCT
ejpam-6075	589	7	is	be	AUX
ejpam-6075	589	8	not	not	PART
ejpam-6075	589	9	a	a	DET
ejpam-6075	589	10	hop	hop	NOUN
ejpam-6075	589	11	dominating	dominating	NOUN
ejpam-6075	589	12	set	set	VERB
ejpam-6075	589	13	in	in	ADP
ejpam-6075	589	14	g.	g.	PROPN
ejpam-6075	589	15	since	since	SCONJ
ejpam-6075	589	16	zz	zz	PROPN
ejpam-6075	589	17	∈	∈	PROPN
ejpam-6075	589	18	e(gg	e(gg	PROPN
ejpam-6075	589	19	)	)	PUNCT
ejpam-6075	589	20	and	and	CCONJ
ejpam-6075	589	21	d	d	PROPN
ejpam-6075	589	22	is	be	AUX
ejpam-6075	589	23	a	a	DET
ejpam-6075	589	24	hop	hop	NOUN
ejpam-6075	589	25	dominating	dominating	NOUN
ejpam-6075	589	26	set	set	VERB
ejpam-6075	589	27	in	in	ADP
ejpam-6075	589	28	gg	gg	PROPN
ejpam-6075	589	29	,	,	PUNCT
ejpam-6075	589	30	it	it	PRON
ejpam-6075	589	31	follows	follow	VERB
ejpam-6075	589	32	that	that	SCONJ
ejpam-6075	589	33	z	z	PROPN
ejpam-6075	589	34	∈	∈	PROPN
ejpam-6075	589	35	n2	n2	PROPN
ejpam-6075	589	36	g({x	g({x	PROPN
ejpam-6075	589	37	,	,	PUNCT
ejpam-6075	589	38	y	y	NOUN
ejpam-6075	589	39	}	}	PUNCT
ejpam-6075	589	40	)	)	PUNCT
ejpam-6075	589	41	.	.	PUNCT
ejpam-6075	590	1	let	let	VERB
ejpam-6075	590	2	v	v	NUM
ejpam-6075	590	3	∈	∈	PROPN
ejpam-6075	590	4	v	v	NOUN
ejpam-6075	590	5	(	(	PUNCT
ejpam-6075	590	6	g	g	NOUN
ejpam-6075	590	7	)	)	PUNCT
ejpam-6075	590	8	\n2	\n2	PROPN
ejpam-6075	590	9	g({x	g({x	PROPN
ejpam-6075	590	10	,	,	PUNCT
ejpam-6075	590	11	y	y	NOUN
ejpam-6075	590	12	}	}	PUNCT
ejpam-6075	590	13	)	)	PUNCT
ejpam-6075	590	14	.	.	PUNCT
ejpam-6075	591	1	since	since	SCONJ
ejpam-6075	591	2	d	d	PROPN
ejpam-6075	591	3	is	be	AUX
ejpam-6075	591	4	a	a	DET
ejpam-6075	591	5	secure	secure	ADJ
ejpam-6075	591	6	hop	hop	NOUN
ejpam-6075	591	7	dominating	dominating	NOUN
ejpam-6075	591	8	set	set	NOUN
ejpam-6075	591	9	in	in	ADP
ejpam-6075	591	10	gg	gg	PROPN
ejpam-6075	591	11	,	,	PUNCT
ejpam-6075	591	12	dv	dv	PROPN
ejpam-6075	591	13	=	=	PUNCT
ejpam-6075	591	14	(	(	PUNCT
ejpam-6075	591	15	d	d	NOUN
ejpam-6075	591	16	\	\	X
ejpam-6075	591	17	{	{	PUNCT
ejpam-6075	591	18	z	z	NOUN
ejpam-6075	591	19	}	}	PUNCT
ejpam-6075	591	20	)	)	PUNCT
ejpam-6075	591	21	∪	∪	ADP
ejpam-6075	591	22	{	{	PUNCT
ejpam-6075	591	23	v	v	NOUN
ejpam-6075	591	24	}	}	PUNCT
ejpam-6075	591	25	)	)	PUNCT
ejpam-6075	592	1	=	=	PRON
ejpam-6075	592	2	{	{	PUNCT
ejpam-6075	592	3	x	x	NOUN
ejpam-6075	592	4	,	,	PUNCT
ejpam-6075	592	5	y	y	PROPN
ejpam-6075	592	6	,	,	PUNCT
ejpam-6075	592	7	v	v	NOUN
ejpam-6075	592	8	}	}	PUNCT
ejpam-6075	592	9	is	be	AUX
ejpam-6075	592	10	a	a	DET
ejpam-6075	592	11	hop	hop	NOUN
ejpam-6075	592	12	dominating	dominating	NOUN
ejpam-6075	592	13	set	set	VERB
ejpam-6075	592	14	in	in	ADP
ejpam-6075	592	15	gg	gg	PROPN
ejpam-6075	592	16	.	.	PUNCT
ejpam-6075	593	1	let	let	VERB
ejpam-6075	593	2	w	w	NOUN
ejpam-6075	593	3	∈	∈	PROPN
ejpam-6075	593	4	v	v	ADP
ejpam-6075	593	5	(	(	PUNCT
ejpam-6075	593	6	g	g	NOUN
ejpam-6075	593	7	)	)	PUNCT
ejpam-6075	593	8	\	\	PUNCT
ejpam-6075	594	1	[	[	X
ejpam-6075	594	2	n2	n2	ADJ
ejpam-6075	594	3	g({x	g({x	NOUN
ejpam-6075	594	4	,	,	PUNCT
ejpam-6075	594	5	y})∪	y})∪	PROPN
ejpam-6075	594	6	{	{	PUNCT
ejpam-6075	594	7	v	v	NOUN
ejpam-6075	594	8	}	}	PUNCT
ejpam-6075	594	9	]	]	PUNCT
ejpam-6075	594	10	.	.	PUNCT
ejpam-6075	595	1	since	since	SCONJ
ejpam-6075	595	2	dv	dv	PROPN
ejpam-6075	595	3	is	be	AUX
ejpam-6075	595	4	hop	hop	NOUN
ejpam-6075	595	5	dominating	dominate	VERB
ejpam-6075	595	6	in	in	ADP
ejpam-6075	595	7	gg	gg	PROPN
ejpam-6075	595	8	,	,	PUNCT
ejpam-6075	595	9	w	w	PROPN
ejpam-6075	595	10	∈	∈	PROPN
ejpam-6075	595	11	n2	n2	ADJ
ejpam-6075	595	12	g(v	g(v	PROPN
ejpam-6075	595	13	)	)	PUNCT
ejpam-6075	595	14	.	.	PUNCT
ejpam-6075	596	1	hence	hence	ADV
ejpam-6075	596	2	,	,	PUNCT
ejpam-6075	596	3	dg(v	dg(v	X
ejpam-6075	596	4	,	,	PUNCT
ejpam-6075	596	5	w	w	NOUN
ejpam-6075	596	6	)	)	PUNCT
ejpam-6075	596	7	=	=	SYM
ejpam-6075	596	8	2	2	NUM
ejpam-6075	596	9	for	for	ADP
ejpam-6075	596	10	any	any	DET
ejpam-6075	596	11	pair	pair	NOUN
ejpam-6075	596	12	of	of	ADP
ejpam-6075	596	13	distinct	distinct	ADJ
ejpam-6075	596	14	vertices	vertex	NOUN
ejpam-6075	596	15	v	v	ADP
ejpam-6075	596	16	,	,	PUNCT
ejpam-6075	596	17	w	w	PROPN
ejpam-6075	596	18	∈	∈	PROPN
ejpam-6075	596	19	v	v	ADP
ejpam-6075	596	20	(	(	PUNCT
ejpam-6075	596	21	g	g	NOUN
ejpam-6075	596	22	)	)	PUNCT
ejpam-6075	596	23	\n2	\n2	PROPN
ejpam-6075	596	24	g({x	g({x	PROPN
ejpam-6075	596	25	,	,	PUNCT
ejpam-6075	596	26	y	y	NOUN
ejpam-6075	596	27	}	}	PUNCT
ejpam-6075	596	28	)	)	PUNCT
ejpam-6075	596	29	.	.	PUNCT
ejpam-6075	597	1	this	this	PRON
ejpam-6075	597	2	shows	show	VERB
ejpam-6075	597	3	that	that	SCONJ
ejpam-6075	597	4	(	(	PUNCT
ejpam-6075	597	5	i3	i3	NOUN
ejpam-6075	597	6	)	)	PUNCT
ejpam-6075	597	7	holds	hold	VERB
ejpam-6075	597	8	.	.	PUNCT
ejpam-6075	598	1	similarly	similarly	ADV
ejpam-6075	598	2	,	,	PUNCT
ejpam-6075	598	3	(	(	PUNCT
ejpam-6075	598	4	i4	i4	PROPN
ejpam-6075	598	5	)	)	PUNCT
ejpam-6075	598	6	holds	hold	VERB
ejpam-6075	598	7	.	.	PUNCT
ejpam-6075	599	1	for	for	ADP
ejpam-6075	599	2	the	the	DET
ejpam-6075	599	3	converse	converse	NOUN
ejpam-6075	599	4	,	,	PUNCT
ejpam-6075	599	5	suppose	suppose	VERB
ejpam-6075	599	6	(	(	PUNCT
ejpam-6075	599	7	i1	i1	PROPN
ejpam-6075	599	8	)	)	PUNCT
ejpam-6075	599	9	holds	hold	VERB
ejpam-6075	599	10	.	.	PUNCT
ejpam-6075	600	1	note	note	VERB
ejpam-6075	600	2	that	that	SCONJ
ejpam-6075	600	3	since	since	SCONJ
ejpam-6075	600	4	g	g	PROPN
ejpam-6075	600	5	/∈	/∈	PUNCT
ejpam-6075	600	6	{	{	PUNCT
ejpam-6075	600	7	k1,k2,k2	k1,k2,k2	ADV
ejpam-6075	600	8	}	}	PUNCT
ejpam-6075	600	9	,	,	PUNCT
ejpam-6075	600	10	it	it	PRON
ejpam-6075	600	11	follows	follow	VERB
ejpam-6075	600	12	that	that	SCONJ
ejpam-6075	600	13	γsh(gg	γsh(gg	ADJ
ejpam-6075	600	14	)	)	PUNCT
ejpam-6075	600	15	≥	≥	NOUN
ejpam-6075	601	1	3	3	X
ejpam-6075	601	2	.	.	PUNCT
ejpam-6075	602	1	let	let	VERB
ejpam-6075	602	2	{	{	PUNCT
ejpam-6075	602	3	x	x	NOUN
ejpam-6075	602	4	,	,	PUNCT
ejpam-6075	602	5	y	y	PROPN
ejpam-6075	602	6	}	}	PUNCT
ejpam-6075	602	7	be	be	AUX
ejpam-6075	602	8	a	a	DET
ejpam-6075	602	9	γh	γh	ADV
ejpam-6075	602	10	-	-	PUNCT
ejpam-6075	602	11	set	set	NOUN
ejpam-6075	602	12	of	of	ADP
ejpam-6075	602	13	g	g	NOUN
ejpam-6075	602	14	and	and	CCONJ
ejpam-6075	602	15	let	let	VERB
ejpam-6075	602	16	q	q	NOUN
ejpam-6075	602	17	=	=	PUNCT
ejpam-6075	602	18	{	{	PUNCT
ejpam-6075	602	19	x	x	PROPN
ejpam-6075	602	20	,	,	PUNCT
ejpam-6075	602	21	y	y	PROPN
ejpam-6075	602	22	,	,	PUNCT
ejpam-6075	602	23	x	x	NOUN
ejpam-6075	602	24	}	}	PUNCT
ejpam-6075	602	25	.	.	PUNCT
ejpam-6075	603	1	then	then	ADV
ejpam-6075	603	2	clearly	clearly	ADV
ejpam-6075	603	3	,	,	PUNCT
ejpam-6075	603	4	q	q	X
ejpam-6075	603	5	is	be	AUX
ejpam-6075	603	6	a	a	DET
ejpam-6075	603	7	hop	hop	NOUN
ejpam-6075	603	8	dominating	dominating	NOUN
ejpam-6075	603	9	set	set	VERB
ejpam-6075	603	10	in	in	ADP
ejpam-6075	603	11	gg	gg	PROPN
ejpam-6075	603	12	.	.	PUNCT
ejpam-6075	604	1	let	let	VERB
ejpam-6075	604	2	z	z	NOUN
ejpam-6075	604	3	∈	∈	PROPN
ejpam-6075	604	4	v	v	PROPN
ejpam-6075	604	5	(	(	PUNCT
ejpam-6075	604	6	gg	gg	NOUN
ejpam-6075	604	7	)	)	PUNCT
ejpam-6075	604	8	\	\	PROPN
ejpam-6075	604	9	q.	q.	PROPN
ejpam-6075	604	10	suppose	suppose	VERB
ejpam-6075	604	11	z	z	PROPN
ejpam-6075	604	12	∈	∈	PROPN
ejpam-6075	604	13	v	v	ADP
ejpam-6075	604	14	(	(	PUNCT
ejpam-6075	604	15	g	g	NOUN
ejpam-6075	604	16	)	)	PUNCT
ejpam-6075	604	17	.	.	PUNCT
ejpam-6075	605	1	since	since	SCONJ
ejpam-6075	605	2	{	{	PUNCT
ejpam-6075	605	3	x	x	NOUN
ejpam-6075	605	4	,	,	PUNCT
ejpam-6075	605	5	y	y	PRON
ejpam-6075	605	6	}	}	PUNCT
ejpam-6075	605	7	is	be	AUX
ejpam-6075	605	8	hop	hop	NOUN
ejpam-6075	605	9	dominating	dominate	VERB
ejpam-6075	605	10	in	in	ADP
ejpam-6075	605	11	g	g	PROPN
ejpam-6075	605	12	,	,	PUNCT
ejpam-6075	605	13	z	z	PROPN
ejpam-6075	605	14	∈	∈	PROPN
ejpam-6075	605	15	n2	n2	PROPN
ejpam-6075	605	16	g({x	g({x	PROPN
ejpam-6075	605	17	,	,	PUNCT
ejpam-6075	605	18	y	y	NOUN
ejpam-6075	605	19	}	}	PUNCT
ejpam-6075	605	20	)	)	PUNCT
ejpam-6075	605	21	.	.	PUNCT
ejpam-6075	606	1	both	both	DET
ejpam-6075	606	2	sets	set	NOUN
ejpam-6075	606	3	(	(	PUNCT
ejpam-6075	606	4	q	q	NOUN
ejpam-6075	606	5	\	\	PROPN
ejpam-6075	606	6	{	{	PUNCT
ejpam-6075	606	7	y	y	NOUN
ejpam-6075	606	8	}	}	PUNCT
ejpam-6075	606	9	)	)	PUNCT
ejpam-6075	606	10	∪	∪	ADP
ejpam-6075	606	11	{	{	PUNCT
ejpam-6075	606	12	z	z	NOUN
ejpam-6075	606	13	}	}	PUNCT
ejpam-6075	606	14	and	and	CCONJ
ejpam-6075	606	15	(	(	PUNCT
ejpam-6075	606	16	q	q	NOUN
ejpam-6075	606	17	\	\	PROPN
ejpam-6075	606	18	{	{	PUNCT
ejpam-6075	606	19	x	x	NOUN
ejpam-6075	606	20	}	}	PUNCT
ejpam-6075	606	21	)	)	PUNCT
ejpam-6075	606	22	∪	∪	ADP
ejpam-6075	606	23	{	{	PUNCT
ejpam-6075	606	24	z	z	AUX
ejpam-6075	606	25	}	}	PUNCT
ejpam-6075	606	26	are	be	AUX
ejpam-6075	606	27	hop	hop	NOUN
ejpam-6075	606	28	dominating	dominate	VERB
ejpam-6075	606	29	in	in	ADP
ejpam-6075	606	30	gg	gg	PROPN
ejpam-6075	606	31	.	.	PUNCT
ejpam-6075	607	1	suppose	suppose	VERB
ejpam-6075	607	2	z	z	NOUN
ejpam-6075	607	3	=	=	PUNCT
ejpam-6075	607	4	s	s	PART
ejpam-6075	607	5	∈	∈	PROPN
ejpam-6075	607	6	v	v	NOUN
ejpam-6075	607	7	(	(	PUNCT
ejpam-6075	607	8	g	g	NOUN
ejpam-6075	607	9	)	)	PUNCT
ejpam-6075	607	10	.	.	PUNCT
ejpam-6075	608	1	if	if	SCONJ
ejpam-6075	608	2	s	s	VERB
ejpam-6075	608	3	=	=	SYM
ejpam-6075	608	4	y	y	PROPN
ejpam-6075	608	5	,	,	PUNCT
ejpam-6075	608	6	then	then	ADV
ejpam-6075	608	7	s	s	VERB
ejpam-6075	608	8	∈	∈	PROPN
ejpam-6075	608	9	n2	n2	PROPN
ejpam-6075	608	10	gg	gg	PROPN
ejpam-6075	608	11	(	(	PUNCT
ejpam-6075	608	12	x	x	NOUN
ejpam-6075	608	13	)	)	PUNCT
ejpam-6075	608	14	and	and	CCONJ
ejpam-6075	608	15	(	(	PUNCT
ejpam-6075	608	16	q\{x})∪{s	q\{x})∪{s	NOUN
ejpam-6075	608	17	}	}	PUNCT
ejpam-6075	608	18	=	=	SYM
ejpam-6075	608	19	{	{	PUNCT
ejpam-6075	608	20	y	y	PROPN
ejpam-6075	608	21	,	,	PUNCT
ejpam-6075	608	22	s	s	X
ejpam-6075	608	23	,	,	PUNCT
ejpam-6075	608	24	x	x	PRON
ejpam-6075	608	25	}	}	PUNCT
ejpam-6075	608	26	is	be	AUX
ejpam-6075	608	27	hop	hop	NOUN
ejpam-6075	608	28	dominating	dominate	VERB
ejpam-6075	608	29	in	in	ADP
ejpam-6075	608	30	gg	gg	PROPN
ejpam-6075	608	31	.	.	PUNCT
ejpam-6075	609	1	suppose	suppose	VERB
ejpam-6075	609	2	s	s	AUX
ejpam-6075	609	3	̸=	̸=	PROPN
ejpam-6075	609	4	y.	y.	PROPN
ejpam-6075	609	5	then	then	ADV
ejpam-6075	609	6	s	s	VERB
ejpam-6075	609	7	∈	∈	PROPN
ejpam-6075	609	8	n2	n2	PROPN
ejpam-6075	609	9	gg	gg	PROPN
ejpam-6075	609	10	(	(	PUNCT
ejpam-6075	609	11	y	y	NOUN
ejpam-6075	609	12	)	)	PUNCT
ejpam-6075	609	13	and	and	CCONJ
ejpam-6075	609	14	(	(	PUNCT
ejpam-6075	609	15	q	q	PROPN
ejpam-6075	609	16	\	\	PROPN
ejpam-6075	609	17	{	{	PUNCT
ejpam-6075	609	18	y	y	NOUN
ejpam-6075	609	19	}	}	PUNCT
ejpam-6075	609	20	)	)	PUNCT
ejpam-6075	609	21	∪	∪	ADP
ejpam-6075	609	22	{	{	PUNCT
ejpam-6075	609	23	s	s	NOUN
ejpam-6075	609	24	}	}	PUNCT
ejpam-6075	609	25	=	=	SYM
ejpam-6075	609	26	{	{	PUNCT
ejpam-6075	609	27	x	x	NOUN
ejpam-6075	609	28	,	,	PUNCT
ejpam-6075	609	29	s	s	X
ejpam-6075	609	30	,	,	PUNCT
ejpam-6075	609	31	x	x	PRON
ejpam-6075	609	32	}	}	PUNCT
ejpam-6075	609	33	is	be	AUX
ejpam-6075	609	34	hop	hop	NOUN
ejpam-6075	609	35	dominating	dominate	VERB
ejpam-6075	609	36	in	in	ADP
ejpam-6075	609	37	gg	gg	PROPN
ejpam-6075	609	38	.	.	PUNCT
ejpam-6075	610	1	hence	hence	ADV
ejpam-6075	610	2	,	,	PUNCT
ejpam-6075	610	3	q	q	PROPN
ejpam-6075	610	4	is	be	AUX
ejpam-6075	610	5	secure	secure	ADJ
ejpam-6075	610	6	hop	hop	NOUN
ejpam-6075	610	7	dominating	dominating	NOUN
ejpam-6075	610	8	in	in	ADP
ejpam-6075	610	9	gg	gg	NOUN
ejpam-6075	610	10	and	and	CCONJ
ejpam-6075	610	11	γsh(gg	γsh(gg	ADJ
ejpam-6075	610	12	)	)	PUNCT
ejpam-6075	611	1	=	=	SYM
ejpam-6075	611	2	|q|	|q|	VERB
ejpam-6075	611	3	=	=	SYM
ejpam-6075	611	4	3	3	X
ejpam-6075	611	5	.	.	PUNCT
ejpam-6075	611	6	the	the	DET
ejpam-6075	611	7	same	same	ADJ
ejpam-6075	611	8	conclusion	conclusion	NOUN
ejpam-6075	611	9	holds	hold	VERB
ejpam-6075	611	10	if	if	SCONJ
ejpam-6075	611	11	{	{	PUNCT
ejpam-6075	611	12	x	x	NOUN
ejpam-6075	611	13	,	,	PUNCT
ejpam-6075	611	14	y	y	PRON
ejpam-6075	611	15	}	}	PUNCT
ejpam-6075	611	16	is	be	AUX
ejpam-6075	611	17	a	a	DET
ejpam-6075	611	18	γh	γh	ADV
ejpam-6075	611	19	-	-	PUNCT
ejpam-6075	611	20	set	set	NOUN
ejpam-6075	611	21	in	in	ADP
ejpam-6075	611	22	g.	g.	PROPN
ejpam-6075	611	23	suppose	suppose	VERB
ejpam-6075	611	24	now	now	ADV
ejpam-6075	611	25	that	that	SCONJ
ejpam-6075	611	26	(	(	PUNCT
ejpam-6075	611	27	i2	i2	NOUN
ejpam-6075	611	28	)	)	PUNCT
ejpam-6075	611	29	holds	hold	VERB
ejpam-6075	611	30	.	.	PUNCT
ejpam-6075	612	1	we	we	PRON
ejpam-6075	612	2	may	may	AUX
ejpam-6075	612	3	assume	assume	VERB
ejpam-6075	612	4	that	that	SCONJ
ejpam-6075	612	5	there	there	PRON
ejpam-6075	612	6	exists	exist	VERB
ejpam-6075	612	7	a	a	DET
ejpam-6075	612	8	secure	secure	ADJ
ejpam-6075	612	9	hop	hop	NOUN
ejpam-6075	612	10	dominating	dominating	NOUN
ejpam-6075	612	11	set	set	NOUN
ejpam-6075	612	12	s	s	PART
ejpam-6075	612	13	=	=	PUNCT
ejpam-6075	612	14	{	{	PUNCT
ejpam-6075	612	15	a	a	DET
ejpam-6075	612	16	,	,	PUNCT
ejpam-6075	612	17	b	b	NOUN
ejpam-6075	612	18	,	,	PUNCT
ejpam-6075	612	19	c	c	NOUN
ejpam-6075	612	20	}	}	PUNCT
ejpam-6075	612	21	of	of	ADP
ejpam-6075	612	22	g	g	NOUN
ejpam-6075	612	23	with	with	ADP
ejpam-6075	612	24	|s|	|s|	NOUN
ejpam-6075	612	25	=	=	SYM
ejpam-6075	612	26	3	3	NUM
ejpam-6075	612	27	and	and	CCONJ
ejpam-6075	612	28	ephn(a;s	ephn(a;s	NOUN
ejpam-6075	612	29	)	)	PUNCT
ejpam-6075	612	30	=	=	SYM
ejpam-6075	613	1	0	0	X
ejpam-6075	613	2	.	.	PUNCT
ejpam-6075	613	3	clearly	clearly	ADV
ejpam-6075	613	4	,	,	PUNCT
ejpam-6075	613	5	s	s	VERB
ejpam-6075	613	6	is	be	AUX
ejpam-6075	613	7	hop	hop	NOUN
ejpam-6075	613	8	dominating	dominate	VERB
ejpam-6075	613	9	in	in	ADP
ejpam-6075	613	10	gg	gg	PROPN
ejpam-6075	613	11	.	.	PUNCT
ejpam-6075	614	1	moreover	moreover	ADV
ejpam-6075	614	2	,	,	PUNCT
ejpam-6075	614	3	because	because	SCONJ
ejpam-6075	614	4	of	of	ADP
ejpam-6075	614	5	the	the	DET
ejpam-6075	614	6	conditions	condition	NOUN
ejpam-6075	614	7	that	that	PRON
ejpam-6075	614	8	s	s	VERB
ejpam-6075	614	9	is	be	AUX
ejpam-6075	614	10	secure	secure	ADJ
ejpam-6075	614	11	hop	hop	NOUN
ejpam-6075	614	12	dominating	dominating	NOUN
ejpam-6075	614	13	in	in	ADP
ejpam-6075	614	14	g	g	PROPN
ejpam-6075	614	15	and	and	CCONJ
ejpam-6075	614	16	ephn(a;s	ephn(a;s	NOUN
ejpam-6075	614	17	)	)	PUNCT
ejpam-6075	614	18	=	=	SYM
ejpam-6075	614	19	0	0	NUM
ejpam-6075	614	20	,	,	PUNCT
ejpam-6075	614	21	s	s	VERB
ejpam-6075	614	22	is	be	AUX
ejpam-6075	614	23	hop	hop	NOUN
ejpam-6075	614	24	dominating	dominate	VERB
ejpam-6075	614	25	in	in	ADP
ejpam-6075	614	26	gg	gg	PROPN
ejpam-6075	614	27	.	.	PUNCT
ejpam-6075	615	1	hence	hence	ADV
ejpam-6075	615	2	,	,	PUNCT
ejpam-6075	615	3	γsh(gg	γsh(gg	ADJ
ejpam-6075	615	4	)	)	PUNCT
ejpam-6075	615	5	=	=	SYM
ejpam-6075	615	6	|s|	|s|	NOUN
ejpam-6075	615	7	=	=	SYM
ejpam-6075	615	8	3	3	X
ejpam-6075	615	9	.	.	PUNCT
ejpam-6075	615	10	suppose	suppose	VERB
ejpam-6075	615	11	(	(	PUNCT
ejpam-6075	615	12	i3	i3	NOUN
ejpam-6075	615	13	)	)	PUNCT
ejpam-6075	615	14	holds	hold	NOUN
ejpam-6075	615	15	,	,	PUNCT
ejpam-6075	615	16	i.e.	i.e.	X
ejpam-6075	615	17	,	,	PUNCT
ejpam-6075	615	18	there	there	PRON
ejpam-6075	615	19	exist	exist	VERB
ejpam-6075	615	20	vertices	vertex	NOUN
ejpam-6075	615	21	x	x	X
ejpam-6075	615	22	,	,	PUNCT
ejpam-6075	615	23	y	y	PROPN
ejpam-6075	615	24	,	,	PUNCT
ejpam-6075	615	25	z,∈	z,∈	PROPN
ejpam-6075	615	26	v	v	NOUN
ejpam-6075	615	27	(	(	PUNCT
ejpam-6075	615	28	g	g	NOUN
ejpam-6075	615	29	)	)	PUNCT
ejpam-6075	615	30	such	such	ADJ
ejpam-6075	615	31	z	z	PROPN
ejpam-6075	615	32	∈	∈	PROPN
ejpam-6075	615	33	n2	n2	PROPN
ejpam-6075	615	34	g[{x	g[{x	PROPN
ejpam-6075	615	35	,	,	PUNCT
ejpam-6075	615	36	y	y	PROPN
ejpam-6075	615	37	}	}	PUNCT
ejpam-6075	615	38	]	]	PUNCT
ejpam-6075	615	39	,	,	PUNCT
ejpam-6075	615	40	and	and	CCONJ
ejpam-6075	615	41	dg(v	dg(v	X
ejpam-6075	615	42	,	,	PUNCT
ejpam-6075	615	43	w	w	NOUN
ejpam-6075	615	44	)	)	PUNCT
ejpam-6075	615	45	=	=	SYM
ejpam-6075	615	46	2	2	NUM
ejpam-6075	615	47	for	for	ADP
ejpam-6075	615	48	all	all	DET
ejpam-6075	615	49	v	v	NOUN
ejpam-6075	615	50	,	,	PUNCT
ejpam-6075	615	51	w	w	PROPN
ejpam-6075	615	52	∈	∈	PROPN
ejpam-6075	615	53	v	v	ADP
ejpam-6075	615	54	(	(	PUNCT
ejpam-6075	615	55	g	g	NOUN
ejpam-6075	615	56	)	)	PUNCT
ejpam-6075	615	57	\n2	\n2	PROPN
ejpam-6075	615	58	g({x	g({x	PROPN
ejpam-6075	615	59	,	,	PUNCT
ejpam-6075	615	60	y	y	NOUN
ejpam-6075	615	61	}	}	PUNCT
ejpam-6075	615	62	)	)	PUNCT
ejpam-6075	615	63	,	,	PUNCT
ejpam-6075	615	64	where	where	SCONJ
ejpam-6075	615	65	v	v	AUX
ejpam-6075	615	66	̸=	̸=	PROPN
ejpam-6075	615	67	w.	w.	NOUN
ejpam-6075	615	68	let	let	VERB
ejpam-6075	615	69	r	r	NOUN
ejpam-6075	615	70	=	=	PRON
ejpam-6075	615	71	{	{	PUNCT
ejpam-6075	615	72	x	x	NOUN
ejpam-6075	615	73	,	,	PUNCT
ejpam-6075	615	74	y	y	PROPN
ejpam-6075	615	75	,	,	PUNCT
ejpam-6075	615	76	z	z	NOUN
ejpam-6075	615	77	}	}	PUNCT
ejpam-6075	615	78	.	.	PUNCT
ejpam-6075	616	1	then	then	ADV
ejpam-6075	616	2	r	r	NOUN
ejpam-6075	616	3	is	be	AUX
ejpam-6075	616	4	a	a	DET
ejpam-6075	616	5	hop	hop	NOUN
ejpam-6075	616	6	dominating	dominating	NOUN
ejpam-6075	616	7	set	set	VERB
ejpam-6075	616	8	in	in	ADP
ejpam-6075	616	9	gg	gg	PROPN
ejpam-6075	616	10	.	.	PUNCT
ejpam-6075	617	1	let	let	VERB
ejpam-6075	617	2	u	u	PRON
ejpam-6075	617	3	∈	∈	PROPN
ejpam-6075	617	4	v	v	X
ejpam-6075	617	5	(	(	PUNCT
ejpam-6075	617	6	gg	gg	NOUN
ejpam-6075	617	7	)	)	PUNCT
ejpam-6075	617	8	\	\	PROPN
ejpam-6075	617	9	r.	r.	PROPN
ejpam-6075	617	10	clearly	clearly	ADV
ejpam-6075	617	11	,	,	PUNCT
ejpam-6075	617	12	if	if	SCONJ
ejpam-6075	617	13	u	u	NOUN
ejpam-6075	617	14	=	=	PROPN
ejpam-6075	617	15	k′	k′	PROPN
ejpam-6075	617	16	∈	∈	PROPN
ejpam-6075	617	17	v	v	NOUN
ejpam-6075	617	18	(	(	PUNCT
ejpam-6075	617	19	g	g	NOUN
ejpam-6075	617	20	)	)	PUNCT
ejpam-6075	617	21	,	,	PUNCT
ejpam-6075	617	22	then	then	ADV
ejpam-6075	617	23	(	(	PUNCT
ejpam-6075	617	24	r	r	NOUN
ejpam-6075	617	25	\	\	PUNCT
ejpam-6075	617	26	{	{	PUNCT
ejpam-6075	617	27	x	x	NOUN
ejpam-6075	617	28	}	}	PUNCT
ejpam-6075	617	29	)	)	PUNCT
ejpam-6075	617	30	∪	∪	ADP
ejpam-6075	617	31	{	{	PUNCT
ejpam-6075	617	32	u	u	NOUN
ejpam-6075	617	33	}	}	PUNCT
ejpam-6075	617	34	is	be	AUX
ejpam-6075	617	35	hop	hop	NOUN
ejpam-6075	617	36	dominating	dominate	VERB
ejpam-6075	617	37	if	if	SCONJ
ejpam-6075	617	38	k	k	PROPN
ejpam-6075	617	39	̸=	̸=	PROPN
ejpam-6075	617	40	x	x	PUNCT
ejpam-6075	617	41	and	and	CCONJ
ejpam-6075	617	42	(	(	PUNCT
ejpam-6075	617	43	r	r	NOUN
ejpam-6075	617	44	\	\	PROPN
ejpam-6075	617	45	{	{	PUNCT
ejpam-6075	617	46	y	y	NOUN
ejpam-6075	617	47	}	}	PUNCT
ejpam-6075	617	48	)	)	PUNCT
ejpam-6075	617	49	∪	∪	ADP
ejpam-6075	617	50	{	{	PUNCT
ejpam-6075	617	51	u	u	NOUN
ejpam-6075	617	52	}	}	PUNCT
ejpam-6075	617	53	is	be	AUX
ejpam-6075	617	54	hop	hop	NOUN
ejpam-6075	617	55	dominating	dominate	VERB
ejpam-6075	617	56	if	if	SCONJ
ejpam-6075	617	57	k	k	PROPN
ejpam-6075	617	58	̸=	̸=	PROPN
ejpam-6075	617	59	y.	y.	NOUN
ejpam-6075	617	60	suppose	suppose	VERB
ejpam-6075	617	61	u	u	PROPN
ejpam-6075	617	62	∈	∈	PROPN
ejpam-6075	617	63	v	v	ADP
ejpam-6075	617	64	(	(	PUNCT
ejpam-6075	617	65	g	g	NOUN
ejpam-6075	617	66	)	)	PUNCT
ejpam-6075	617	67	.	.	PUNCT
ejpam-6075	618	1	if	if	SCONJ
ejpam-6075	618	2	u	u	PROPN
ejpam-6075	618	3	∈	∈	PROPN
ejpam-6075	618	4	n2	n2	PROPN
ejpam-6075	618	5	g({x	g({x	PROPN
ejpam-6075	618	6	,	,	PUNCT
ejpam-6075	618	7	y	y	NOUN
ejpam-6075	618	8	}	}	PUNCT
ejpam-6075	618	9	)	)	PUNCT
ejpam-6075	618	10	,	,	PUNCT
ejpam-6075	618	11	say	say	VERB
ejpam-6075	618	12	u	u	PROPN
ejpam-6075	618	13	∈	∈	PROPN
ejpam-6075	618	14	n2	n2	NOUN
ejpam-6075	618	15	g(x	g(x	PROPN
ejpam-6075	618	16	)	)	PUNCT
ejpam-6075	618	17	,	,	PUNCT
ejpam-6075	618	18	then	then	ADV
ejpam-6075	618	19	(	(	PUNCT
ejpam-6075	618	20	r	r	NOUN
ejpam-6075	618	21	\	\	PUNCT
ejpam-6075	618	22	{	{	PUNCT
ejpam-6075	618	23	x	x	NOUN
ejpam-6075	618	24	}	}	PUNCT
ejpam-6075	618	25	)	)	PUNCT
ejpam-6075	618	26	∪	∪	ADP
ejpam-6075	618	27	{	{	PUNCT
ejpam-6075	618	28	u	u	NOUN
ejpam-6075	618	29	}	}	PUNCT
ejpam-6075	618	30	is	be	AUX
ejpam-6075	618	31	hop	hop	NOUN
ejpam-6075	618	32	dominating	dominate	VERB
ejpam-6075	618	33	in	in	ADP
ejpam-6075	618	34	gg	gg	PROPN
ejpam-6075	618	35	.	.	PUNCT
ejpam-6075	619	1	if	if	SCONJ
ejpam-6075	619	2	u	u	PROPN
ejpam-6075	619	3	/∈	/∈	PROPN
ejpam-6075	619	4	n2	n2	PROPN
ejpam-6075	619	5	g({x	g({x	PROPN
ejpam-6075	619	6	,	,	PUNCT
ejpam-6075	619	7	y	y	NOUN
ejpam-6075	619	8	}	}	PUNCT
ejpam-6075	619	9	)	)	PUNCT
ejpam-6075	619	10	,	,	PUNCT
ejpam-6075	619	11	then	then	ADV
ejpam-6075	619	12	(	(	PUNCT
ejpam-6075	619	13	r	r	NOUN
ejpam-6075	619	14	\	\	X
ejpam-6075	619	15	{	{	PUNCT
ejpam-6075	619	16	z	z	NOUN
ejpam-6075	619	17	}	}	PUNCT
ejpam-6075	619	18	)	)	PUNCT
ejpam-6075	619	19	∪	∪	ADP
ejpam-6075	619	20	{	{	PUNCT
ejpam-6075	619	21	u	u	NOUN
ejpam-6075	619	22	}	}	PUNCT
ejpam-6075	619	23	is	be	AUX
ejpam-6075	619	24	hop	hop	NOUN
ejpam-6075	619	25	dominating	dominate	VERB
ejpam-6075	619	26	in	in	ADP
ejpam-6075	619	27	gg	gg	NOUN
ejpam-6075	619	28	because	because	SCONJ
ejpam-6075	619	29	of	of	ADP
ejpam-6075	619	30	the	the	DET
ejpam-6075	619	31	additional	additional	ADJ
ejpam-6075	619	32	assumption	assumption	NOUN
ejpam-6075	619	33	that	that	PRON
ejpam-6075	619	34	dg(v	dg(v	NOUN
ejpam-6075	619	35	,	,	PUNCT
ejpam-6075	619	36	w	w	NOUN
ejpam-6075	619	37	)	)	PUNCT
ejpam-6075	619	38	=	=	SYM
ejpam-6075	619	39	2	2	NUM
ejpam-6075	619	40	for	for	ADP
ejpam-6075	619	41	all	all	DET
ejpam-6075	619	42	v	v	NOUN
ejpam-6075	619	43	,	,	PUNCT
ejpam-6075	619	44	w	w	PROPN
ejpam-6075	619	45	∈	∈	PROPN
ejpam-6075	619	46	v	v	ADP
ejpam-6075	619	47	(	(	PUNCT
ejpam-6075	619	48	g	g	NOUN
ejpam-6075	619	49	)	)	PUNCT
ejpam-6075	619	50	\n2	\n2	PROPN
ejpam-6075	620	1	g({x	g({x	PROPN
ejpam-6075	620	2	,	,	PUNCT
ejpam-6075	620	3	y	y	NOUN
ejpam-6075	620	4	}	}	PUNCT
ejpam-6075	620	5	)	)	PUNCT
ejpam-6075	620	6	,	,	PUNCT
ejpam-6075	620	7	where	where	SCONJ
ejpam-6075	620	8	v	v	ADP
ejpam-6075	620	9	̸=	̸=	PROPN
ejpam-6075	620	10	w.	w.	NOUN
ejpam-6075	620	11	hence	hence	ADV
ejpam-6075	620	12	,	,	PUNCT
ejpam-6075	620	13	r	r	NOUN
ejpam-6075	620	14	is	be	AUX
ejpam-6075	620	15	a	a	DET
ejpam-6075	620	16	secure	secure	ADJ
ejpam-6075	620	17	hop	hop	NOUN
ejpam-6075	620	18	dominating	dominating	NOUN
ejpam-6075	620	19	set	set	VERB
ejpam-6075	620	20	in	in	ADP
ejpam-6075	620	21	gg	gg	NOUN
ejpam-6075	620	22	and	and	CCONJ
ejpam-6075	620	23	γsh(gg	γsh(gg	ADJ
ejpam-6075	620	24	)	)	PUNCT
ejpam-6075	621	1	=	=	SYM
ejpam-6075	621	2	|r|	|r|	NOUN
ejpam-6075	621	3	=	=	SYM
ejpam-6075	621	4	3	3	X
ejpam-6075	621	5	.	.	PUNCT
ejpam-6075	621	6	the	the	DET
ejpam-6075	621	7	same	same	ADJ
ejpam-6075	621	8	conclusion	conclusion	NOUN
ejpam-6075	621	9	holds	hold	VERB
ejpam-6075	621	10	if	if	SCONJ
ejpam-6075	621	11	(	(	PUNCT
ejpam-6075	621	12	i4	i4	PROPN
ejpam-6075	621	13	)	)	PUNCT
ejpam-6075	621	14	is	be	AUX
ejpam-6075	621	15	assumed	assume	VERB
ejpam-6075	621	16	.	.	PUNCT
ejpam-6075	622	1	(	(	PUNCT
ejpam-6075	622	2	iii	iii	X
ejpam-6075	622	3	)	)	PUNCT
ejpam-6075	622	4	this	this	PRON
ejpam-6075	622	5	follows	follow	VERB
ejpam-6075	622	6	from	from	ADP
ejpam-6075	622	7	(	(	PUNCT
ejpam-6075	622	8	i	i	NOUN
ejpam-6075	622	9	)	)	PUNCT
ejpam-6075	622	10	and	and	CCONJ
ejpam-6075	622	11	(	(	PUNCT
ejpam-6075	622	12	ii	ii	NOUN
ejpam-6075	622	13	)	)	PUNCT
ejpam-6075	622	14	.	.	PUNCT
ejpam-6075	623	1	f.	f.	PROPN
ejpam-6075	623	2	l.	l.	PROPN
ejpam-6075	623	3	alfeche	alfeche	PROPN
ejpam-6075	623	4	,	,	PUNCT
ejpam-6075	623	5	g.	g.	PROPN
ejpam-6075	623	6	a.	a.	PROPN
ejpam-6075	623	7	malacas	malacas	PROPN
ejpam-6075	623	8	,	,	PUNCT
ejpam-6075	623	9	s.	s.	PROPN
ejpam-6075	623	10	canoy	canoy	PROPN
ejpam-6075	623	11	jr	jr	PROPN
ejpam-6075	623	12	.	.	PROPN
ejpam-6075	623	13	/	/	SYM
ejpam-6075	623	14	eur	eur	PROPN
ejpam-6075	623	15	.	.	PUNCT
ejpam-6075	624	1	j.	j.	PROPN
ejpam-6075	624	2	pure	pure	PROPN
ejpam-6075	624	3	appl	appl	PROPN
ejpam-6075	624	4	.	.	PROPN
ejpam-6075	624	5	math	math	PROPN
ejpam-6075	624	6	,	,	PUNCT
ejpam-6075	624	7	18	18	NUM
ejpam-6075	624	8	(	(	PUNCT
ejpam-6075	624	9	2	2	NUM
ejpam-6075	624	10	)	)	PUNCT
ejpam-6075	624	11	(	(	PUNCT
ejpam-6075	624	12	2025	2025	NUM
ejpam-6075	624	13	)	)	PUNCT
ejpam-6075	624	14	,	,	PUNCT
ejpam-6075	624	15	6075	6075	NUM
ejpam-6075	624	16	13	13	NUM
ejpam-6075	624	17	of	of	ADP
ejpam-6075	624	18	14	14	NUM
ejpam-6075	624	19	the	the	DET
ejpam-6075	624	20	next	next	ADJ
ejpam-6075	624	21	result	result	NOUN
ejpam-6075	624	22	follows	follow	VERB
ejpam-6075	624	23	from	from	ADP
ejpam-6075	624	24	theorem	theorem	ADJ
ejpam-6075	624	25	9	9	NUM
ejpam-6075	624	26	.	.	PUNCT
ejpam-6075	624	27	corollary	corollary	ADJ
ejpam-6075	624	28	4	4	NUM
ejpam-6075	624	29	.	.	PUNCT
ejpam-6075	625	1	let	let	VERB
ejpam-6075	625	2	n	n	PRON
ejpam-6075	625	3	be	be	AUX
ejpam-6075	625	4	a	a	DET
ejpam-6075	625	5	positive	positive	ADJ
ejpam-6075	625	6	integer	integer	NOUN
ejpam-6075	625	7	and	and	CCONJ
ejpam-6075	625	8	n	n	PRON
ejpam-6075	625	9	≥	≥	NOUN
ejpam-6075	625	10	2	2	NUM
ejpam-6075	625	11	.	.	PUNCT
ejpam-6075	626	1	then	then	ADV
ejpam-6075	626	2	γsh(knkn	γsh(knkn	NUM
ejpam-6075	626	3	)	)	PUNCT
ejpam-6075	627	1	=	=	SYM
ejpam-6075	628	1			NOUN
ejpam-6075	628	2	2	2	NUM
ejpam-6075	628	3	,	,	PUNCT
ejpam-6075	628	4	if	if	SCONJ
ejpam-6075	628	5	n	n	NOUN
ejpam-6075	628	6	=	=	SYM
ejpam-6075	628	7	2	2	NUM
ejpam-6075	628	8	3	3	NUM
ejpam-6075	628	9	,	,	PUNCT
ejpam-6075	628	10	if	if	SCONJ
ejpam-6075	628	11	n	n	NOUN
ejpam-6075	628	12	=	=	SYM
ejpam-6075	628	13	3	3	NUM
ejpam-6075	628	14	4	4	NUM
ejpam-6075	628	15	,	,	PUNCT
ejpam-6075	628	16	if	if	SCONJ
ejpam-6075	628	17	n	n	PRON
ejpam-6075	628	18	≥	≥	NOUN
ejpam-6075	628	19	4	4	NUM
ejpam-6075	628	20	.	.	NOUN
ejpam-6075	628	21	4	4	NUM
ejpam-6075	628	22	.	.	X
ejpam-6075	628	23	conclusion	conclusion	NOUN
ejpam-6075	628	24	secure	secure	VERB
ejpam-6075	628	25	hop	hop	NOUN
ejpam-6075	628	26	domination	domination	NOUN
ejpam-6075	628	27	was	be	AUX
ejpam-6075	628	28	introduced	introduce	VERB
ejpam-6075	628	29	and	and	CCONJ
ejpam-6075	628	30	initially	initially	ADV
ejpam-6075	628	31	investigated	investigate	VERB
ejpam-6075	628	32	in	in	ADP
ejpam-6075	628	33	this	this	DET
ejpam-6075	628	34	study	study	NOUN
ejpam-6075	628	35	.	.	PUNCT
ejpam-6075	629	1	bounds	bound	NOUN
ejpam-6075	629	2	on	on	ADP
ejpam-6075	629	3	the	the	DET
ejpam-6075	629	4	parameter	parameter	NOUN
ejpam-6075	629	5	were	be	AUX
ejpam-6075	629	6	given	give	VERB
ejpam-6075	629	7	and	and	CCONJ
ejpam-6075	629	8	graphs	graph	NOUN
ejpam-6075	629	9	which	which	PRON
ejpam-6075	629	10	attain	attain	VERB
ejpam-6075	629	11	these	these	DET
ejpam-6075	629	12	bounds	bound	NOUN
ejpam-6075	629	13	were	be	AUX
ejpam-6075	629	14	characterized	characterize	VERB
ejpam-6075	629	15	.	.	PUNCT
ejpam-6075	630	1	it	it	PRON
ejpam-6075	630	2	was	be	AUX
ejpam-6075	630	3	shown	show	VERB
ejpam-6075	630	4	that	that	SCONJ
ejpam-6075	630	5	the	the	DET
ejpam-6075	630	6	difference	difference	NOUN
ejpam-6075	630	7	of	of	ADP
ejpam-6075	630	8	the	the	DET
ejpam-6075	630	9	secure	secure	ADJ
ejpam-6075	630	10	hop	hop	NOUN
ejpam-6075	630	11	domination	domination	NOUN
ejpam-6075	630	12	number	number	NOUN
ejpam-6075	630	13	and	and	CCONJ
ejpam-6075	630	14	the	the	DET
ejpam-6075	630	15	hop	hop	NOUN
ejpam-6075	630	16	domination	domination	NOUN
ejpam-6075	630	17	number	number	NOUN
ejpam-6075	630	18	can	can	AUX
ejpam-6075	630	19	be	be	AUX
ejpam-6075	630	20	made	make	VERB
ejpam-6075	630	21	arbitrarily	arbitrarily	ADV
ejpam-6075	630	22	large	large	ADJ
ejpam-6075	630	23	.	.	PUNCT
ejpam-6075	631	1	a	a	DET
ejpam-6075	631	2	necessary	necessary	ADJ
ejpam-6075	631	3	and	and	CCONJ
ejpam-6075	631	4	sufficient	sufficient	ADJ
ejpam-6075	631	5	condition	condition	NOUN
ejpam-6075	631	6	for	for	ADP
ejpam-6075	631	7	a	a	DET
ejpam-6075	631	8	hop	hop	NOUN
ejpam-6075	631	9	dominating	dominating	NOUN
ejpam-6075	631	10	set	set	NOUN
ejpam-6075	631	11	to	to	PART
ejpam-6075	631	12	be	be	AUX
ejpam-6075	631	13	secure	secure	ADJ
ejpam-6075	631	14	hop	hop	NOUN
ejpam-6075	631	15	dominating	dominating	NOUN
ejpam-6075	631	16	was	be	AUX
ejpam-6075	631	17	obtained	obtain	VERB
ejpam-6075	631	18	.	.	PUNCT
ejpam-6075	632	1	moreover	moreover	ADV
ejpam-6075	632	2	,	,	PUNCT
ejpam-6075	632	3	the	the	DET
ejpam-6075	632	4	secure	secure	ADJ
ejpam-6075	632	5	hop	hop	NOUN
ejpam-6075	632	6	dominating	dominating	NOUN
ejpam-6075	632	7	sets	set	NOUN
ejpam-6075	632	8	in	in	ADP
ejpam-6075	632	9	the	the	DET
ejpam-6075	632	10	shadow	shadow	NOUN
ejpam-6075	632	11	graph	graph	NOUN
ejpam-6075	632	12	and	and	CCONJ
ejpam-6075	632	13	complementary	complementary	ADJ
ejpam-6075	632	14	prism	prism	NOUN
ejpam-6075	632	15	were	be	AUX
ejpam-6075	632	16	characterized	characterize	VERB
ejpam-6075	632	17	.	.	PUNCT
ejpam-6075	633	1	these	these	DET
ejpam-6075	633	2	characterizations	characterization	NOUN
ejpam-6075	633	3	were	be	AUX
ejpam-6075	633	4	used	use	VERB
ejpam-6075	633	5	to	to	PART
ejpam-6075	633	6	determine	determine	VERB
ejpam-6075	633	7	the	the	DET
ejpam-6075	633	8	values	value	NOUN
ejpam-6075	633	9	of	of	ADP
ejpam-6075	633	10	the	the	DET
ejpam-6075	633	11	parameter	parameter	NOUN
ejpam-6075	633	12	for	for	ADP
ejpam-6075	633	13	these	these	DET
ejpam-6075	633	14	graphs	graph	NOUN
ejpam-6075	633	15	.	.	PUNCT
ejpam-6075	634	1	the	the	DET
ejpam-6075	634	2	newly	newly	ADV
ejpam-6075	634	3	defined	define	VERB
ejpam-6075	634	4	parameter	parameter	NOUN
ejpam-6075	634	5	can	can	AUX
ejpam-6075	634	6	be	be	AUX
ejpam-6075	634	7	studied	study	VERB
ejpam-6075	634	8	further	far	ADV
ejpam-6075	634	9	for	for	ADP
ejpam-6075	634	10	trees	tree	NOUN
ejpam-6075	634	11	and	and	CCONJ
ejpam-6075	634	12	even	even	ADV
ejpam-6075	634	13	for	for	ADP
ejpam-6075	634	14	graphs	graph	NOUN
ejpam-6075	634	15	resulting	result	VERB
ejpam-6075	634	16	from	from	ADP
ejpam-6075	634	17	some	some	DET
ejpam-6075	634	18	binary	binary	ADJ
ejpam-6075	634	19	operations	operation	NOUN
ejpam-6075	634	20	.	.	PUNCT
ejpam-6075	635	1	moreover	moreover	ADV
ejpam-6075	635	2	,	,	PUNCT
ejpam-6075	635	3	it	it	PRON
ejpam-6075	635	4	may	may	AUX
ejpam-6075	635	5	be	be	AUX
ejpam-6075	635	6	interesting	interesting	ADJ
ejpam-6075	635	7	to	to	PART
ejpam-6075	635	8	consider	consider	VERB
ejpam-6075	635	9	and	and	CCONJ
ejpam-6075	635	10	investigate	investigate	VERB
ejpam-6075	635	11	the	the	DET
ejpam-6075	635	12	complexity	complexity	NOUN
ejpam-6075	635	13	of	of	ADP
ejpam-6075	635	14	the	the	DET
ejpam-6075	635	15	secure	secure	ADJ
ejpam-6075	635	16	hop	hop	NOUN
ejpam-6075	635	17	dominating	dominating	NOUN
ejpam-6075	635	18	set	set	NOUN
ejpam-6075	635	19	problem	problem	NOUN
ejpam-6075	635	20	.	.	PUNCT
ejpam-6075	636	1	acknowledgements	acknowledgement	NOUN
ejpam-6075	636	2	the	the	DET
ejpam-6075	636	3	authors	author	NOUN
ejpam-6075	636	4	would	would	AUX
ejpam-6075	636	5	like	like	VERB
ejpam-6075	636	6	to	to	PART
ejpam-6075	636	7	thank	thank	VERB
ejpam-6075	636	8	the	the	DET
ejpam-6075	636	9	referees	referee	NOUN
ejpam-6075	636	10	for	for	ADP
ejpam-6075	636	11	their	their	PRON
ejpam-6075	636	12	comments	comment	NOUN
ejpam-6075	636	13	and	and	CCONJ
ejpam-6075	636	14	suggestions	suggestion	NOUN
ejpam-6075	636	15	which	which	PRON
ejpam-6075	636	16	led	lead	VERB
ejpam-6075	636	17	to	to	ADP
ejpam-6075	636	18	this	this	DET
ejpam-6075	636	19	much	much	ADV
ejpam-6075	636	20	improved	improved	ADJ
ejpam-6075	636	21	version	version	NOUN
ejpam-6075	636	22	of	of	ADP
ejpam-6075	636	23	the	the	DET
ejpam-6075	636	24	paper	paper	NOUN
ejpam-6075	636	25	.	.	PUNCT
ejpam-6075	637	1	moreover	moreover	ADV
ejpam-6075	637	2	,	,	PUNCT
ejpam-6075	637	3	the	the	DET
ejpam-6075	637	4	authors	author	NOUN
ejpam-6075	637	5	are	be	AUX
ejpam-6075	637	6	grateful	grateful	ADJ
ejpam-6075	637	7	to	to	ADP
ejpam-6075	637	8	the	the	DET
ejpam-6075	637	9	department	department	NOUN
ejpam-6075	637	10	of	of	ADP
ejpam-6075	637	11	science	science	NOUN
ejpam-6075	637	12	and	and	CCONJ
ejpam-6075	637	13	technology	technology	NOUN
ejpam-6075	637	14	accelerated	accelerate	VERB
ejpam-6075	637	15	science	science	NOUN
ejpam-6075	637	16	and	and	CCONJ
ejpam-6075	637	17	technology	technology	NOUN
ejpam-6075	637	18	human	human	ADJ
ejpam-6075	637	19	resource	resource	NOUN
ejpam-6075	637	20	development	development	NOUN
ejpam-6075	637	21	program	program	NOUN
ejpam-6075	637	22	(	(	PUNCT
ejpam-6075	637	23	dost	dost	NOUN
ejpam-6075	637	24	-	-	PUNCT
ejpam-6075	637	25	asthrdp)-philippines	asthrdp)-philippines	PROPN
ejpam-6075	637	26	and	and	CCONJ
ejpam-6075	637	27	the	the	DET
ejpam-6075	637	28	msu	msu	PROPN
ejpam-6075	637	29	-	-	PUNCT
ejpam-6075	637	30	iligan	iligan	PROPN
ejpam-6075	637	31	institute	institute	PROPN
ejpam-6075	637	32	of	of	ADP
ejpam-6075	637	33	technology	technology	PROPN
ejpam-6075	637	34	,	,	PUNCT
ejpam-6075	637	35	iligan	iligan	ADJ
ejpam-6075	637	36	city	city	NOUN
ejpam-6075	637	37	for	for	ADP
ejpam-6075	637	38	funding	fund	VERB
ejpam-6075	637	39	this	this	DET
ejpam-6075	637	40	research	research	NOUN
ejpam-6075	637	41	.	.	PUNCT
ejpam-6075	638	1	references	reference	NOUN
ejpam-6075	638	2	[	[	X
ejpam-6075	638	3	1	1	NUM
ejpam-6075	638	4	]	]	PUNCT
ejpam-6075	638	5	e.	e.	PROPN
ejpam-6075	638	6	cockayne	cockayne	PROPN
ejpam-6075	638	7	,	,	PUNCT
ejpam-6075	638	8	o.	o.	PROPN
ejpam-6075	638	9	favaron	favaron	PROPN
ejpam-6075	638	10	,	,	PUNCT
ejpam-6075	638	11	and	and	CCONJ
ejpam-6075	638	12	c.m	c.m	PROPN
ejpam-6075	638	13	.	.	PROPN
ejpam-6075	638	14	mynhardt	mynhardt	PROPN
ejpam-6075	638	15	.	.	PUNCT
ejpam-6075	639	1	secure	secure	ADJ
ejpam-6075	639	2	domination	domination	NOUN
ejpam-6075	639	3	,	,	PUNCT
ejpam-6075	639	4	weak	weak	ADJ
ejpam-6075	639	5	roman	roman	ADJ
ejpam-6075	639	6	domination	domination	NOUN
ejpam-6075	639	7	and	and	CCONJ
ejpam-6075	639	8	forbidden	forbid	VERB
ejpam-6075	639	9	subgraphs	subgraph	NOUN
ejpam-6075	639	10	.	.	PUNCT
ejpam-6075	640	1	bull	bull	NOUN
ejpam-6075	640	2	.	.	PUNCT
ejpam-6075	640	3	inst	inst	PROPN
ejpam-6075	640	4	.	.	PUNCT
ejpam-6075	641	1	combin	combin	NOUN
ejpam-6075	641	2	.	.	PUNCT
ejpam-6075	642	1	appl	appl	PROPN
ejpam-6075	642	2	.	.	PROPN
ejpam-6075	642	3	,	,	PUNCT
ejpam-6075	642	4	39:87–100	39:87–100	NUM
ejpam-6075	642	5	,	,	PUNCT
ejpam-6075	642	6	2003	2003	NUM
ejpam-6075	642	7	.	.	PUNCT
ejpam-6075	643	1	[	[	X
ejpam-6075	643	2	2	2	X
ejpam-6075	643	3	]	]	PUNCT
ejpam-6075	643	4	t.	t.	PROPN
ejpam-6075	643	5	araki	araki	PROPN
ejpam-6075	643	6	and	and	CCONJ
ejpam-6075	643	7	r.	r.	PROPN
ejpam-6075	643	8	yamanaka	yamanaka	PROPN
ejpam-6075	643	9	.	.	PUNCT
ejpam-6075	644	1	secure	secure	ADJ
ejpam-6075	644	2	domination	domination	NOUN
ejpam-6075	644	3	in	in	ADP
ejpam-6075	644	4	cographs	cograph	NOUN
ejpam-6075	644	5	.	.	PUNCT
ejpam-6075	645	1	discrete	discrete	ADJ
ejpam-6075	645	2	applied	apply	VERB
ejpam-6075	645	3	mathematics	mathematic	NOUN
ejpam-6075	645	4	,	,	PUNCT
ejpam-6075	645	5	262:179–184	262:179–184	NUM
ejpam-6075	645	6	,	,	PUNCT
ejpam-6075	645	7	2019	2019	NUM
ejpam-6075	645	8	.	.	PUNCT
ejpam-6075	646	1	[	[	X
ejpam-6075	646	2	3	3	X
ejpam-6075	646	3	]	]	X
ejpam-6075	646	4	s.	s.	PROPN
ejpam-6075	646	5	benecke	benecke	PROPN
ejpam-6075	646	6	,	,	PUNCT
ejpam-6075	646	7	e.	e.	PROPN
ejpam-6075	646	8	cockayne	cockayne	PROPN
ejpam-6075	646	9	,	,	PUNCT
ejpam-6075	646	10	and	and	CCONJ
ejpam-6075	646	11	c.	c.	PROPN
ejpam-6075	646	12	mynhardt	mynhardt	PROPN
ejpam-6075	646	13	.	.	PUNCT
ejpam-6075	647	1	secure	secure	ADJ
ejpam-6075	647	2	total	total	ADJ
ejpam-6075	647	3	domination	domination	NOUN
ejpam-6075	647	4	in	in	ADP
ejpam-6075	647	5	graphs	graph	NOUN
ejpam-6075	647	6	.	.	PUNCT
ejpam-6075	648	1	utilitas	utilitas	ADJ
ejpam-6075	648	2	math	math	NOUN
ejpam-6075	648	3	.	.	PUNCT
ejpam-6075	648	4	,	,	PUNCT
ejpam-6075	649	1	74:247–259	74:247–259	PROPN
ejpam-6075	649	2	,	,	PUNCT
ejpam-6075	649	3	2007	2007	NUM
ejpam-6075	649	4	.	.	PUNCT
ejpam-6075	650	1	[	[	X
ejpam-6075	650	2	4	4	NUM
ejpam-6075	650	3	]	]	PUNCT
ejpam-6075	650	4	a.	a.	NOUN
ejpam-6075	650	5	cabaro	cabaro	NOUN
ejpam-6075	650	6	,	,	PUNCT
ejpam-6075	650	7	s.	s.	PROPN
ejpam-6075	650	8	canoy	canoy	PROPN
ejpam-6075	650	9	jr	jr	PROPN
ejpam-6075	650	10	,	,	PUNCT
ejpam-6075	650	11	and	and	CCONJ
ejpam-6075	650	12	i.	i.	PROPN
ejpam-6075	650	13	aniversario	aniversario	PROPN
ejpam-6075	650	14	.	.	PUNCT
ejpam-6075	651	1	secure	secure	VERB
ejpam-6075	651	2	connected	connected	ADJ
ejpam-6075	651	3	domination	domination	NOUN
ejpam-6075	651	4	in	in	ADP
ejpam-6075	651	5	a	a	DET
ejpam-6075	651	6	graph	graph	NOUN
ejpam-6075	651	7	.	.	PUNCT
ejpam-6075	652	1	international	international	ADJ
ejpam-6075	652	2	journal	journal	PROPN
ejpam-6075	652	3	of	of	ADP
ejpam-6075	652	4	mathematical	mathematical	ADJ
ejpam-6075	652	5	analysis	analysis	NOUN
ejpam-6075	652	6	,	,	PUNCT
ejpam-6075	652	7	8(42):2065–2074	8(42):2065–2074	NUM
ejpam-6075	652	8	,	,	PUNCT
ejpam-6075	652	9	2014	2014	NUM
ejpam-6075	652	10	.	.	PUNCT
ejpam-6075	653	1	[	[	X
ejpam-6075	653	2	5	5	X
ejpam-6075	653	3	]	]	PUNCT
ejpam-6075	653	4	e.	e.	PROPN
ejpam-6075	653	5	castillano	castillano	PROPN
ejpam-6075	653	6	,	,	PUNCT
ejpam-6075	653	7	r.a	r.a	PROPN
ejpam-6075	653	8	.	.	PROPN
ejpam-6075	653	9	ugbinada	ugbinada	PROPN
ejpam-6075	653	10	,	,	PUNCT
ejpam-6075	653	11	and	and	CCONJ
ejpam-6075	653	12	s.	s.	PROPN
ejpam-6075	653	13	canoy	canoy	PROPN
ejpam-6075	653	14	jr	jr	PROPN
ejpam-6075	653	15	.	.	PUNCT
ejpam-6075	653	16	secure	secure	ADJ
ejpam-6075	653	17	domination	domination	NOUN
ejpam-6075	653	18	in	in	ADP
ejpam-6075	653	19	the	the	DET
ejpam-6075	653	20	joins	join	NOUN
ejpam-6075	653	21	of	of	ADP
ejpam-6075	653	22	graphs	graph	NOUN
ejpam-6075	653	23	.	.	PUNCT
ejpam-6075	654	1	applied	apply	VERB
ejpam-6075	654	2	mathematical	mathematical	ADJ
ejpam-6075	654	3	sciences	science	NOUN
ejpam-6075	654	4	,	,	PUNCT
ejpam-6075	654	5	8(105):5203–5211	8(105):5203–5211	NUM
ejpam-6075	654	6	,	,	PUNCT
ejpam-6075	654	7	2014	2014	NUM
ejpam-6075	654	8	.	.	PUNCT
ejpam-6075	655	1	[	[	X
ejpam-6075	655	2	6	6	NUM
ejpam-6075	655	3	]	]	PUNCT
ejpam-6075	655	4	e.	e.	PROPN
ejpam-6075	655	5	cockayne	cockayne	PROPN
ejpam-6075	655	6	.	.	PUNCT
ejpam-6075	656	1	irredundance	irredundance	NOUN
ejpam-6075	656	2	,	,	PUNCT
ejpam-6075	656	3	secure	secure	ADJ
ejpam-6075	656	4	domination	domination	NOUN
ejpam-6075	656	5	and	and	CCONJ
ejpam-6075	656	6	maximum	maximum	ADJ
ejpam-6075	656	7	degree	degree	NOUN
ejpam-6075	656	8	in	in	ADP
ejpam-6075	656	9	trees	tree	NOUN
ejpam-6075	656	10	.	.	PUNCT
ejpam-6075	657	1	discrete	discrete	ADJ
ejpam-6075	657	2	math	math	NOUN
ejpam-6075	657	3	.	.	PUNCT
ejpam-6075	657	4	,	,	PUNCT
ejpam-6075	658	1	307:12–17	307:12–17	NUM
ejpam-6075	658	2	,	,	PUNCT
ejpam-6075	658	3	2007	2007	NUM
ejpam-6075	658	4	.	.	PUNCT
ejpam-6075	659	1	f.	f.	PROPN
ejpam-6075	659	2	l.	l.	PROPN
ejpam-6075	659	3	alfeche	alfeche	PROPN
ejpam-6075	659	4	,	,	PUNCT
ejpam-6075	659	5	g.	g.	PROPN
ejpam-6075	659	6	a.	a.	PROPN
ejpam-6075	659	7	malacas	malacas	PROPN
ejpam-6075	659	8	,	,	PUNCT
ejpam-6075	659	9	s.	s.	PROPN
ejpam-6075	659	10	canoy	canoy	PROPN
ejpam-6075	659	11	jr	jr	PROPN
ejpam-6075	659	12	.	.	PROPN
ejpam-6075	659	13	/	/	SYM
ejpam-6075	659	14	eur	eur	PROPN
ejpam-6075	659	15	.	.	PUNCT
ejpam-6075	660	1	j.	j.	PROPN
ejpam-6075	660	2	pure	pure	PROPN
ejpam-6075	660	3	appl	appl	PROPN
ejpam-6075	660	4	.	.	PROPN
ejpam-6075	660	5	math	math	PROPN
ejpam-6075	660	6	,	,	PUNCT
ejpam-6075	660	7	18	18	NUM
ejpam-6075	660	8	(	(	PUNCT
ejpam-6075	660	9	2	2	NUM
ejpam-6075	660	10	)	)	PUNCT
ejpam-6075	660	11	(	(	PUNCT
ejpam-6075	660	12	2025	2025	NUM
ejpam-6075	660	13	)	)	PUNCT
ejpam-6075	660	14	,	,	PUNCT
ejpam-6075	660	15	6075	6075	NUM
ejpam-6075	660	16	14	14	NUM
ejpam-6075	660	17	of	of	ADP
ejpam-6075	660	18	14	14	NUM
ejpam-6075	660	19	[	[	X
ejpam-6075	660	20	7	7	NUM
ejpam-6075	660	21	]	]	X
ejpam-6075	660	22	e.	e.	PROPN
ejpam-6075	660	23	cockayne	cockayne	PROPN
ejpam-6075	660	24	,	,	PUNCT
ejpam-6075	660	25	p.	p.	NOUN
ejpam-6075	660	26	grobler	grobler	NOUN
ejpam-6075	660	27	,	,	PUNCT
ejpam-6075	660	28	w.	w.	PROPN
ejpam-6075	660	29	grundlingh	grundlingh	PROPN
ejpam-6075	660	30	,	,	PUNCT
ejpam-6075	660	31	j.	j.	PROPN
ejpam-6075	660	32	munganga	munganga	PROPN
ejpam-6075	660	33	,	,	PUNCT
ejpam-6075	660	34	and	and	CCONJ
ejpam-6075	660	35	j.	j.	PROPN
ejpam-6075	660	36	van	van	PROPN
ejpam-6075	660	37	vuuren	vuuren	PROPN
ejpam-6075	660	38	.	.	PUNCT
ejpam-6075	661	1	protection	protection	NOUN
ejpam-6075	661	2	of	of	ADP
ejpam-6075	661	3	a	a	DET
ejpam-6075	661	4	graph	graph	NOUN
ejpam-6075	661	5	.	.	PUNCT
ejpam-6075	662	1	utilitas	utilitas	PROPN
ejpam-6075	662	2	math	math	NOUN
ejpam-6075	662	3	.	.	PUNCT
ejpam-6075	662	4	,	,	PUNCT
ejpam-6075	662	5	67:19–32	67:19–32	PROPN
ejpam-6075	662	6	,	,	PUNCT
ejpam-6075	662	7	2005	2005	NUM
ejpam-6075	662	8	.	.	PUNCT
ejpam-6075	663	1	[	[	X
ejpam-6075	663	2	8	8	NUM
ejpam-6075	663	3	]	]	X
ejpam-6075	663	4	e.	e.	PROPN
ejpam-6075	663	5	enriquez	enriquez	PROPN
ejpam-6075	663	6	and	and	CCONJ
ejpam-6075	663	7	s.	s.	PROPN
ejpam-6075	663	8	canoy	canoy	PROPN
ejpam-6075	663	9	jr	jr	PROPN
ejpam-6075	663	10	.	.	PUNCT
ejpam-6075	663	11	secure	secure	VERB
ejpam-6075	663	12	convex	convex	NOUN
ejpam-6075	663	13	domination	domination	NOUN
ejpam-6075	663	14	in	in	ADP
ejpam-6075	663	15	a	a	DET
ejpam-6075	663	16	graph	graph	NOUN
ejpam-6075	663	17	.	.	PUNCT
ejpam-6075	664	1	international	international	ADJ
ejpam-6075	664	2	journal	journal	PROPN
ejpam-6075	664	3	of	of	ADP
ejpam-6075	664	4	mathematical	mathematical	ADJ
ejpam-6075	664	5	analysis	analysis	NOUN
ejpam-6075	664	6	,	,	PUNCT
ejpam-6075	664	7	9(7):317–325	9(7):317–325	NUM
ejpam-6075	664	8	,	,	PUNCT
ejpam-6075	664	9	2015	2015	NUM
ejpam-6075	664	10	.	.	PUNCT
ejpam-6075	665	1	[	[	X
ejpam-6075	665	2	9	9	NUM
ejpam-6075	665	3	]	]	PUNCT
ejpam-6075	665	4	s.	s.	PROPN
ejpam-6075	665	5	canoy	canoy	PROPN
ejpam-6075	665	6	jr	jr	PROPN
ejpam-6075	665	7	,	,	PUNCT
ejpam-6075	665	8	s.a	s.a	PROPN
ejpam-6075	665	9	.	.	PROPN
ejpam-6075	665	10	canoy	canoy	PROPN
ejpam-6075	665	11	,	,	PUNCT
ejpam-6075	665	12	and	and	CCONJ
ejpam-6075	665	13	m.	m.	NOUN
ejpam-6075	665	14	cruzate	cruzate	NOUN
ejpam-6075	665	15	.	.	PUNCT
ejpam-6075	666	1	secure	secure	ADJ
ejpam-6075	666	2	dominating	dominating	NOUN
ejpam-6075	666	3	sets	set	NOUN
ejpam-6075	666	4	in	in	ADP
ejpam-6075	666	5	the	the	DET
ejpam-6075	666	6	lexicographic	lexicographic	ADJ
ejpam-6075	666	7	product	product	NOUN
ejpam-6075	666	8	of	of	ADP
ejpam-6075	666	9	graphs	graph	NOUN
ejpam-6075	666	10	.	.	PUNCT
ejpam-6075	667	1	advances	advance	NOUN
ejpam-6075	667	2	and	and	CCONJ
ejpam-6075	667	3	applications	application	NOUN
ejpam-6075	667	4	in	in	ADP
ejpam-6075	667	5	discrete	discrete	ADJ
ejpam-6075	667	6	mathematics	mathematic	NOUN
ejpam-6075	667	7	,	,	PUNCT
ejpam-6075	667	8	20(1	20(1	NUM
ejpam-6075	667	9	)	)	PUNCT
ejpam-6075	667	10	,	,	PUNCT
ejpam-6075	667	11	2019	2019	NUM
ejpam-6075	667	12	.	.	PUNCT
ejpam-6075	668	1	[	[	X
ejpam-6075	668	2	10	10	NUM
ejpam-6075	668	3	]	]	X
ejpam-6075	668	4	william	william	PROPN
ejpam-6075	668	5	f.	f.	PROPN
ejpam-6075	668	6	klostermeyer	klostermeyer	PROPN
ejpam-6075	668	7	and	and	CCONJ
ejpam-6075	668	8	c.	c.	PROPN
ejpam-6075	668	9	mynhardt	mynhardt	PROPN
ejpam-6075	668	10	.	.	PUNCT
ejpam-6075	669	1	secure	secure	ADJ
ejpam-6075	669	2	domination	domination	NOUN
ejpam-6075	669	3	and	and	CCONJ
ejpam-6075	669	4	secure	secure	VERB
ejpam-6075	669	5	total	total	ADJ
ejpam-6075	669	6	domination	domination	NOUN
ejpam-6075	669	7	in	in	ADP
ejpam-6075	669	8	graphs	graph	NOUN
ejpam-6075	669	9	.	.	PUNCT
ejpam-6075	670	1	discussiones	discussione	NOUN
ejpam-6075	670	2	mathematicae	mathematicae	PROPN
ejpam-6075	670	3	graph	graph	NOUN
ejpam-6075	670	4	theory	theory	NOUN
ejpam-6075	670	5	,	,	PUNCT
ejpam-6075	670	6	28:267–284	28:267–284	PROPN
ejpam-6075	670	7	,	,	PUNCT
ejpam-6075	670	8	2008	2008	NUM
ejpam-6075	670	9	.	.	PUNCT
ejpam-6075	671	1	[	[	X
ejpam-6075	671	2	11	11	NUM
ejpam-6075	671	3	]	]	X
ejpam-6075	671	4	c.	c.	PROPN
ejpam-6075	671	5	natarajan	natarajan	PROPN
ejpam-6075	671	6	and	and	CCONJ
ejpam-6075	671	7	s.	s.	PROPN
ejpam-6075	671	8	ayyaswamy	ayyaswamy	PROPN
ejpam-6075	671	9	.	.	PUNCT
ejpam-6075	672	1	hop	hop	PROPN
ejpam-6075	672	2	domination	domination	NOUN
ejpam-6075	672	3	in	in	ADP
ejpam-6075	672	4	graphs	graphs	PROPN
ejpam-6075	672	5	ii	ii	PROPN
ejpam-6075	672	6	.	.	PUNCT
ejpam-6075	672	7	versita	versita	PROPN
ejpam-6075	672	8	,	,	PUNCT
ejpam-6075	672	9	23(2):187	23(2):187	NUM
ejpam-6075	672	10	–	–	PUNCT
ejpam-6075	672	11	199	199	NUM
ejpam-6075	672	12	,	,	PUNCT
ejpam-6075	672	13	2015	2015	NUM
ejpam-6075	672	14	.	.	PUNCT
ejpam-6075	673	1	[	[	X
ejpam-6075	673	2	12	12	NUM
ejpam-6075	673	3	]	]	X
ejpam-6075	673	4	s.	s.	PROPN
ejpam-6075	673	5	ayyaswamy	ayyaswamy	PROPN
ejpam-6075	673	6	,	,	PUNCT
ejpam-6075	673	7	b.	b.	PROPN
ejpam-6075	673	8	krishnakumari	krishnakumari	PROPN
ejpam-6075	673	9	,	,	PUNCT
ejpam-6075	673	10	b.	b.	PROPN
ejpam-6075	673	11	natarjan	natarjan	PROPN
ejpam-6075	673	12	,	,	PUNCT
ejpam-6075	673	13	and	and	CCONJ
ejpam-6075	673	14	y.	y.	PROPN
ejpam-6075	673	15	venkatakrishnan	venkatakrishnan	PROPN
ejpam-6075	673	16	.	.	PUNCT
ejpam-6075	674	1	bounds	bound	NOUN
ejpam-6075	674	2	on	on	ADP
ejpam-6075	674	3	the	the	DET
ejpam-6075	674	4	hop	hop	NOUN
ejpam-6075	674	5	domination	domination	NOUN
ejpam-6075	674	6	number	number	NOUN
ejpam-6075	674	7	of	of	ADP
ejpam-6075	674	8	a	a	DET
ejpam-6075	674	9	tree	tree	NOUN
ejpam-6075	674	10	.	.	PUNCT
ejpam-6075	675	1	proceedings	proceeding	NOUN
ejpam-6075	675	2	-	-	PUNCT
ejpam-6075	675	3	mathematical	mathematical	ADJ
ejpam-6075	675	4	sciences	science	NOUN
ejpam-6075	675	5	.	.	PUNCT
ejpam-6075	675	6	,	,	PUNCT
ejpam-6075	675	7	125(4):449–455	125(4):449–455	ADP
ejpam-6075	675	8	,	,	PUNCT
ejpam-6075	675	9	2015	2015	NUM
ejpam-6075	675	10	.	.	PUNCT
ejpam-6075	676	1	[	[	X
ejpam-6075	676	2	13	13	NUM
ejpam-6075	676	3	]	]	PUNCT
ejpam-6075	676	4	s.	s.	PROPN
ejpam-6075	676	5	ayyaswamy	ayyaswamy	PROPN
ejpam-6075	676	6	,	,	PUNCT
ejpam-6075	676	7	c.	c.	PROPN
ejpam-6075	676	8	natarajan	natarajan	PROPN
ejpam-6075	676	9	,	,	PUNCT
ejpam-6075	676	10	and	and	CCONJ
ejpam-6075	676	11	g.	g.	PROPN
ejpam-6075	676	12	sathiamoorphy	sathiamoorphy	PROPN
ejpam-6075	676	13	.	.	PUNCT
ejpam-6075	677	1	a	a	DET
ejpam-6075	677	2	note	note	NOUN
ejpam-6075	677	3	on	on	ADP
ejpam-6075	677	4	hop	hop	NOUN
ejpam-6075	677	5	domination	domination	NOUN
ejpam-6075	677	6	number	number	NOUN
ejpam-6075	677	7	of	of	ADP
ejpam-6075	677	8	some	some	DET
ejpam-6075	677	9	special	special	ADJ
ejpam-6075	677	10	families	family	NOUN
ejpam-6075	677	11	of	of	ADP
ejpam-6075	677	12	graphs	graph	NOUN
ejpam-6075	677	13	.	.	PUNCT
ejpam-6075	678	1	international	international	ADJ
ejpam-6075	678	2	journal	journal	NOUN
ejpam-6075	678	3	of	of	ADP
ejpam-6075	678	4	pure	pure	ADJ
ejpam-6075	678	5	and	and	CCONJ
ejpam-6075	678	6	applied	applied	ADJ
ejpam-6075	678	7	mathematics	mathematic	NOUN
ejpam-6075	678	8	.	.	PUNCT
ejpam-6075	678	9	,	,	PUNCT
ejpam-6075	678	10	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-6075	678	11	,	,	PUNCT
ejpam-6075	678	12	2018	2018	NUM
ejpam-6075	678	13	.	.	PUNCT
ejpam-6075	679	1	[	[	X
ejpam-6075	679	2	14	14	NUM
ejpam-6075	679	3	]	]	PUNCT
ejpam-6075	679	4	j.	j.	PROPN
ejpam-6075	679	5	hassan	hassan	PROPN
ejpam-6075	679	6	and	and	CCONJ
ejpam-6075	679	7	s.	s.	PROPN
ejpam-6075	679	8	canoy	canoy	PROPN
ejpam-6075	679	9	jr	jr	PROPN
ejpam-6075	679	10	.	.	PROPN
ejpam-6075	679	11	hop	hop	PROPN
ejpam-6075	679	12	independent	independent	ADJ
ejpam-6075	679	13	hop	hop	NOUN
ejpam-6075	679	14	domination	domination	NOUN
ejpam-6075	679	15	in	in	ADP
ejpam-6075	679	16	graphs	graph	NOUN
ejpam-6075	679	17	.	.	PUNCT
ejpam-6075	680	1	eur	eur	PROPN
ejpam-6075	680	2	.	.	PUNCT
ejpam-6075	681	1	j.	j.	PROPN
ejpam-6075	681	2	pure	pure	PROPN
ejpam-6075	681	3	appl	appl	PROPN
ejpam-6075	681	4	.	.	PUNCT
ejpam-6075	681	5	math	math	PROPN
ejpam-6075	681	6	.	.	PUNCT
ejpam-6075	681	7	,	,	PUNCT
ejpam-6075	681	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-6075	681	9	,	,	PUNCT
ejpam-6075	681	10	2022	2022	NUM
ejpam-6075	681	11	.	.	PUNCT
ejpam-6075	682	1	[	[	X
ejpam-6075	682	2	15	15	NUM
ejpam-6075	682	3	]	]	X
ejpam-6075	682	4	j.	j.	PROPN
ejpam-6075	682	5	hassan	hassan	PROPN
ejpam-6075	682	6	,	,	PUNCT
ejpam-6075	682	7	s.	s.	PROPN
ejpam-6075	682	8	canoy	canoy	PROPN
ejpam-6075	682	9	jr	jr	PROPN
ejpam-6075	682	10	.	.	PROPN
ejpam-6075	682	11	,	,	PUNCT
ejpam-6075	682	12	and	and	CCONJ
ejpam-6075	682	13	a.	a.	PROPN
ejpam-6075	682	14	aradais	aradais	PROPN
ejpam-6075	682	15	.	.	PUNCT
ejpam-6075	683	1	hop	hop	PROPN
ejpam-6075	683	2	independent	independent	ADJ
ejpam-6075	683	3	sets	set	NOUN
ejpam-6075	683	4	in	in	ADP
ejpam-6075	683	5	graphs	graph	NOUN
ejpam-6075	683	6	.	.	PUNCT
ejpam-6075	684	1	eur	eur	PROPN
ejpam-6075	684	2	.	.	PUNCT
ejpam-6075	685	1	j.	j.	PROPN
ejpam-6075	685	2	pure	pure	PROPN
ejpam-6075	685	3	appl	appl	PROPN
ejpam-6075	685	4	.	.	PUNCT
ejpam-6075	685	5	math	math	PROPN
ejpam-6075	685	6	.	.	PUNCT
ejpam-6075	685	7	,	,	PUNCT
ejpam-6075	685	8	15(2):467–477	15(2):467–477	PROPN
ejpam-6075	685	9	,	,	PUNCT
ejpam-6075	685	10	2022	2022	NUM
ejpam-6075	685	11	.	.	PUNCT
ejpam-6075	686	1	[	[	X
ejpam-6075	686	2	16	16	NUM
ejpam-6075	686	3	]	]	X
ejpam-6075	686	4	m.	m.	NOUN
ejpam-6075	686	5	henning	henning	PROPN
ejpam-6075	686	6	and	and	CCONJ
ejpam-6075	686	7	n.	n.	PROPN
ejpam-6075	686	8	rad	rad	PROPN
ejpam-6075	686	9	.	.	PROPN
ejpam-6075	687	1	on	on	ADP
ejpam-6075	687	2	2	2	NUM
ejpam-6075	687	3	-	-	PUNCT
ejpam-6075	687	4	step	step	NOUN
ejpam-6075	687	5	and	and	CCONJ
ejpam-6075	687	6	hop	hop	NOUN
ejpam-6075	687	7	dominating	dominating	NOUN
ejpam-6075	687	8	sets	set	NOUN
ejpam-6075	687	9	in	in	ADP
ejpam-6075	687	10	graphs	graph	NOUN
ejpam-6075	687	11	.	.	PUNCT
ejpam-6075	688	1	graphs	graph	NOUN
ejpam-6075	688	2	and	and	CCONJ
ejpam-6075	688	3	combinatorics	combinatoric	NOUN
ejpam-6075	688	4	.	.	PUNCT
ejpam-6075	688	5	,	,	PUNCT
ejpam-6075	688	6	33(4):913–927	33(4):913–927	PROPN
ejpam-6075	688	7	,	,	PUNCT
ejpam-6075	688	8	2017	2017	NUM
ejpam-6075	688	9	.	.	PUNCT
ejpam-6075	689	1	[	[	X
ejpam-6075	689	2	17	17	NUM
ejpam-6075	689	3	]	]	X
ejpam-6075	689	4	s.	s.	PROPN
ejpam-6075	689	5	canoy	canoy	PROPN
ejpam-6075	689	6	jr	jr	PROPN
ejpam-6075	689	7	and	and	CCONJ
ejpam-6075	689	8	j.	j.	PROPN
ejpam-6075	689	9	hassan	hassan	PROPN
ejpam-6075	689	10	.	.	PUNCT
ejpam-6075	690	1	weakly	weakly	ADJ
ejpam-6075	690	2	convex	convex	VERB
ejpam-6075	690	3	hop	hop	NOUN
ejpam-6075	690	4	dominating	dominating	NOUN
ejpam-6075	690	5	sets	set	NOUN
ejpam-6075	690	6	in	in	ADP
ejpam-6075	690	7	graphs	graph	NOUN
ejpam-6075	690	8	.	.	PUNCT
ejpam-6075	691	1	european	european	ADJ
ejpam-6075	691	2	journal	journal	PROPN
ejpam-6075	691	3	of	of	ADP
ejpam-6075	691	4	pure	pure	ADJ
ejpam-6075	691	5	and	and	CCONJ
ejpam-6075	691	6	applied	applied	ADJ
ejpam-6075	691	7	mathematics	mathematic	NOUN
ejpam-6075	691	8	,	,	PUNCT
ejpam-6075	691	9	16(2):1196–1211	16(2):1196–1211	NUM
ejpam-6075	691	10	,	,	PUNCT
ejpam-6075	691	11	2023	2023	NUM
ejpam-6075	691	12	.	.	PUNCT
ejpam-6075	692	1	[	[	X
ejpam-6075	692	2	18	18	NUM
ejpam-6075	692	3	]	]	X
ejpam-6075	692	4	s.	s.	PROPN
ejpam-6075	692	5	canoy	canoy	PROPN
ejpam-6075	692	6	jr	jr	PROPN
ejpam-6075	692	7	.	.	PROPN
ejpam-6075	692	8	,	,	PUNCT
ejpam-6075	692	9	r.	r.	PROPN
ejpam-6075	692	10	mollejon	mollejon	NOUN
ejpam-6075	692	11	,	,	PUNCT
ejpam-6075	692	12	and	and	CCONJ
ejpam-6075	692	13	j.	j.	PROPN
ejpam-6075	692	14	g.	g.	PROPN
ejpam-6075	692	15	canoy	canoy	PROPN
ejpam-6075	692	16	.	.	PUNCT
ejpam-6075	693	1	hop	hop	PROPN
ejpam-6075	693	2	dominating	dominating	NOUN
ejpam-6075	693	3	sets	set	NOUN
ejpam-6075	693	4	in	in	ADP
ejpam-6075	693	5	graphs	graph	NOUN
ejpam-6075	693	6	under	under	ADP
ejpam-6075	693	7	binary	binary	ADJ
ejpam-6075	693	8	operations	operation	NOUN
ejpam-6075	693	9	.	.	PUNCT
ejpam-6075	694	1	eur	eur	PROPN
ejpam-6075	694	2	.	.	PUNCT
ejpam-6075	695	1	j.	j.	PROPN
ejpam-6075	695	2	pure	pure	PROPN
ejpam-6075	695	3	appl	appl	PROPN
ejpam-6075	695	4	.	.	PUNCT
ejpam-6075	695	5	math	math	PROPN
ejpam-6075	695	6	.	.	PUNCT
ejpam-6075	695	7	,	,	PUNCT
ejpam-6075	696	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-6075	696	2	,	,	PUNCT
ejpam-6075	696	3	2019	2019	NUM
ejpam-6075	696	4	.	.	PUNCT
ejpam-6075	697	1	[	[	X
ejpam-6075	697	2	19	19	NUM
ejpam-6075	697	3	]	]	X
ejpam-6075	697	4	s.	s.	PROPN
ejpam-6075	697	5	canoy	canoy	PROPN
ejpam-6075	697	6	jr	jr	PROPN
ejpam-6075	697	7	.	.	PROPN
ejpam-6075	697	8	and	and	CCONJ
ejpam-6075	697	9	g.	g.	PROPN
ejpam-6075	697	10	salasalan	salasalan	NOUN
ejpam-6075	697	11	.	.	PUNCT
ejpam-6075	698	1	revisiting	revisit	VERB
ejpam-6075	698	2	domination	domination	NOUN
ejpam-6075	698	3	,	,	PUNCT
ejpam-6075	698	4	hop	hop	NOUN
ejpam-6075	698	5	domination	domination	NOUN
ejpam-6075	698	6	,	,	PUNCT
ejpam-6075	698	7	and	and	CCONJ
ejpam-6075	698	8	global	global	ADJ
ejpam-6075	698	9	hop	hop	NOUN
ejpam-6075	698	10	domination	domination	NOUN
ejpam-6075	698	11	in	in	ADP
ejpam-6075	698	12	graphs	graph	NOUN
ejpam-6075	698	13	.	.	PUNCT
ejpam-6075	699	1	eur	eur	PROPN
ejpam-6075	699	2	.	.	PUNCT
ejpam-6075	700	1	j.	j.	PROPN
ejpam-6075	700	2	pure	pure	PROPN
ejpam-6075	700	3	appl	appl	PROPN
ejpam-6075	700	4	.	.	PUNCT
ejpam-6075	700	5	math	math	PROPN
ejpam-6075	700	6	.	.	PUNCT
ejpam-6075	700	7	,	,	PUNCT
ejpam-6075	700	8	14:1415–1428	14:1415–1428	NUM
ejpam-6075	700	9	,	,	PUNCT
ejpam-6075	700	10	2021	2021	NUM
ejpam-6075	700	11	.	.	PUNCT
ejpam-6075	701	1	[	[	X
ejpam-6075	701	2	20	20	NUM
ejpam-6075	701	3	]	]	PUNCT
ejpam-6075	701	4	s.	s.	PROPN
ejpam-6075	701	5	canoy	canoy	PROPN
ejpam-6075	701	6	jr	jr	PROPN
ejpam-6075	701	7	.	.	PROPN
ejpam-6075	701	8	and	and	CCONJ
ejpam-6075	701	9	g.	g.	PROPN
ejpam-6075	701	10	salasalan	salasalan	NOUN
ejpam-6075	701	11	.	.	PUNCT
ejpam-6075	702	1	locating	locate	VERB
ejpam-6075	702	2	-	-	PUNCT
ejpam-6075	702	3	hop	hop	NOUN
ejpam-6075	702	4	domination	domination	NOUN
ejpam-6075	702	5	in	in	ADP
ejpam-6075	702	6	graphs	graph	NOUN
ejpam-6075	702	7	.	.	PUNCT
ejpam-6075	703	1	kyungpook	kyungpook	PROPN
ejpam-6075	703	2	mathematical	mathematical	PROPN
ejpam-6075	703	3	journal	journal	PROPN
ejpam-6075	703	4	.	.	PUNCT
ejpam-6075	703	5	,	,	PUNCT
ejpam-6075	703	6	62:193–204	62:193–204	NUM
ejpam-6075	703	7	,	,	PUNCT
ejpam-6075	703	8	2022	2022	NUM
ejpam-6075	703	9	.	.	PUNCT
ejpam-6075	704	1	[	[	X
ejpam-6075	704	2	21	21	NUM
ejpam-6075	704	3	]	]	X
ejpam-6075	704	4	y.	y.	PROPN
ejpam-6075	704	5	pabilona	pabilona	PROPN
ejpam-6075	704	6	and	and	CCONJ
ejpam-6075	704	7	h.	h.	PROPN
ejpam-6075	704	8	rara	rara	PROPN
ejpam-6075	704	9	.	.	PUNCT
ejpam-6075	705	1	connected	connect	VERB
ejpam-6075	705	2	hop	hop	NOUN
ejpam-6075	705	3	domination	domination	NOUN
ejpam-6075	705	4	in	in	ADP
ejpam-6075	705	5	graphs	graph	NOUN
ejpam-6075	705	6	under	under	ADP
ejpam-6075	705	7	some	some	DET
ejpam-6075	705	8	binary	binary	ADJ
ejpam-6075	705	9	operations	operation	NOUN
ejpam-6075	705	10	.	.	PUNCT
ejpam-6075	706	1	asian	asian	ADJ
ejpam-6075	706	2	-	-	PUNCT
ejpam-6075	706	3	eur	eur	NOUN
ejpam-6075	706	4	.	.	PUNCT
ejpam-6075	707	1	j.	j.	PROPN
ejpam-6075	707	2	math	math	PROPN
ejpam-6075	707	3	.	.	PROPN
ejpam-6075	707	4	,	,	PUNCT
ejpam-6075	707	5	11(5):1850075–1–1850075–11	11(5):1850075–1–1850075–11	NUM
ejpam-6075	707	6	,	,	PUNCT
ejpam-6075	707	7	2018	2018	NUM
ejpam-6075	707	8	.	.	PUNCT
ejpam-6075	708	1	[	[	X
ejpam-6075	708	2	22	22	NUM
ejpam-6075	708	3	]	]	PUNCT
ejpam-6075	708	4	r.	r.	PROPN
ejpam-6075	708	5	rakim	rakim	PROPN
ejpam-6075	708	6	,	,	PUNCT
ejpam-6075	708	7	h.	h.	PROPN
ejpam-6075	708	8	rara	rara	PROPN
ejpam-6075	708	9	,	,	PUNCT
ejpam-6075	708	10	and	and	CCONJ
ejpam-6075	708	11	c.j	c.j	PROPN
ejpam-6075	708	12	.	.	PROPN
ejpam-6075	708	13	saromines	saromine	NOUN
ejpam-6075	708	14	.	.	PUNCT
ejpam-6075	709	1	perfect	perfect	ADJ
ejpam-6075	709	2	hop	hop	NOUN
ejpam-6075	709	3	domination	domination	NOUN
ejpam-6075	709	4	in	in	ADP
ejpam-6075	709	5	graphs	graph	NOUN
ejpam-6075	709	6	.	.	PUNCT
ejpam-6075	710	1	applied	apply	VERB
ejpam-6075	710	2	mathematical	mathematical	ADJ
ejpam-6075	710	3	sciences	sciences	PROPN
ejpam-6075	710	4	,	,	PUNCT
ejpam-6075	710	5	12(13):635–649	12(13):635–649	NUM
ejpam-6075	710	6	,	,	PUNCT
ejpam-6075	710	7	2018	2018	NUM
ejpam-6075	710	8	.	.	PUNCT
ejpam-6075	711	1	[	[	X
ejpam-6075	711	2	23	23	NUM
ejpam-6075	711	3	]	]	X
ejpam-6075	711	4	g.	g.	NOUN
ejpam-6075	711	5	salasalan	salasalan	PROPN
ejpam-6075	711	6	and	and	CCONJ
ejpam-6075	711	7	s.	s.	PROPN
ejpam-6075	711	8	canoy	canoy	PROPN
ejpam-6075	711	9	jr	jr	PROPN
ejpam-6075	711	10	.	.	PROPN
ejpam-6075	711	11	global	global	PROPN
ejpam-6075	711	12	hop	hop	PROPN
ejpam-6075	711	13	domination	domination	PROPN
ejpam-6075	711	14	numbers	number	NOUN
ejpam-6075	711	15	of	of	ADP
ejpam-6075	711	16	graphs	graph	NOUN
ejpam-6075	711	17	.	.	PUNCT
ejpam-6075	712	1	eur	eur	PROPN
ejpam-6075	712	2	.	.	PUNCT
ejpam-6075	713	1	j.	j.	PROPN
ejpam-6075	713	2	pure	pure	PROPN
ejpam-6075	713	3	appl	appl	PROPN
ejpam-6075	713	4	.	.	PUNCT
ejpam-6075	713	5	math	math	PROPN
ejpam-6075	713	6	.	.	PUNCT
ejpam-6075	713	7	,	,	PUNCT
ejpam-6075	713	8	14(1):112–125	14(1):112–125	NUM
ejpam-6075	713	9	,	,	PUNCT
ejpam-6075	713	10	2021	2021	NUM
ejpam-6075	713	11	.	.	PUNCT
ejpam-6075	714	1	[	[	X
ejpam-6075	714	2	24	24	NUM
ejpam-6075	714	3	]	]	PUNCT
ejpam-6075	714	4	f.	f.	PROPN
ejpam-6075	714	5	buckey	buckey	PROPN
ejpam-6075	714	6	and	and	CCONJ
ejpam-6075	714	7	f.	f.	PROPN
ejpam-6075	714	8	harary	harary	PROPN
ejpam-6075	714	9	.	.	PUNCT
ejpam-6075	715	1	distance	distance	NOUN
ejpam-6075	715	2	in	in	ADP
ejpam-6075	715	3	graphs	graph	NOUN
ejpam-6075	715	4	.	.	PUNCT
ejpam-6075	716	1	addison	addison	PROPN
ejpam-6075	716	2	-	-	PUNCT
ejpam-6075	716	3	wesley	wesley	PROPN
ejpam-6075	716	4	,	,	PUNCT
ejpam-6075	716	5	redwood	redwood	NOUN
ejpam-6075	716	6	city	city	NOUN
ejpam-6075	716	7	,	,	PUNCT
ejpam-6075	716	8	california	california	PROPN
ejpam-6075	716	9	,	,	PUNCT
ejpam-6075	716	10	1990	1990	NUM
ejpam-6075	716	11	.	.	PUNCT
ejpam-6075	717	1	[	[	X
ejpam-6075	717	2	25	25	NUM
ejpam-6075	717	3	]	]	PUNCT
ejpam-6075	717	4	f.	f.	PROPN
ejpam-6075	717	5	harary	harary	PROPN
ejpam-6075	717	6	.	.	PUNCT
ejpam-6075	718	1	graph	graph	NOUN
ejpam-6075	718	2	theory	theory	NOUN
ejpam-6075	718	3	.	.	PUNCT
ejpam-6075	719	1	addison	addison	PROPN
ejpam-6075	719	2	-	-	PUNCT
ejpam-6075	719	3	wesley	wesley	PROPN
ejpam-6075	719	4	,	,	PUNCT
ejpam-6075	719	5	singapore	singapore	PROPN
ejpam-6075	719	6	,	,	PUNCT
ejpam-6075	719	7	1989	1989	NUM
ejpam-6075	719	8	.	.	PUNCT
ejpam-6075	720	1	[	[	X
ejpam-6075	720	2	26	26	NUM
ejpam-6075	720	3	]	]	X
ejpam-6075	720	4	s.	s.	PROPN
ejpam-6075	720	5	canoy	canoy	PROPN
ejpam-6075	720	6	jr	jr	PROPN
ejpam-6075	720	7	.	.	PUNCT
ejpam-6075	720	8	j.	j.	PROPN
ejpam-6075	720	9	hassan	hassan	PROPN
ejpam-6075	720	10	and	and	CCONJ
ejpam-6075	720	11	c.j	c.j	PROPN
ejpam-6075	720	12	.	.	PROPN
ejpam-6075	720	13	saromines	saromine	NOUN
ejpam-6075	720	14	.	.	PUNCT
ejpam-6075	721	1	convex	convex	VERB
ejpam-6075	721	2	hop	hop	NOUN
ejpam-6075	721	3	domination	domination	NOUN
ejpam-6075	721	4	in	in	ADP
ejpam-6075	721	5	graphs	graph	NOUN
ejpam-6075	721	6	.	.	PUNCT
ejpam-6075	722	1	eur	eur	PROPN
ejpam-6075	722	2	.	.	PUNCT
ejpam-6075	723	1	j.	j.	PROPN
ejpam-6075	723	2	pure	pure	PROPN
ejpam-6075	723	3	appl	appl	PROPN
ejpam-6075	723	4	.	.	PUNCT
ejpam-6075	723	5	math	math	PROPN
ejpam-6075	723	6	.	.	PUNCT
ejpam-6075	723	7	,	,	PUNCT
ejpam-6075	723	8	16(1):319–335	16(1):319–335	NOUN
ejpam-6075	723	9	,	,	PUNCT
ejpam-6075	723	10	2023	2023	NUM
ejpam-6075	723	11	.	.	PUNCT