id	sid	tid	token	lemma	pos
ejpam-6635	1	1	european	european	PROPN
ejpam-6635	1	2	journal	journal	PROPN
ejpam-6635	1	3	of	of	ADP
ejpam-6635	1	4	pure	pure	ADJ
ejpam-6635	1	5	and	and	CCONJ
ejpam-6635	1	6	applied	applied	ADJ
ejpam-6635	1	7	mathematics	mathematic	NOUN
ejpam-6635	1	8	2025	2025	NUM
ejpam-6635	1	9	,	,	PUNCT
ejpam-6635	1	10	vol	vol	NOUN
ejpam-6635	1	11	.	.	PROPN
ejpam-6635	1	12	18	18	NUM
ejpam-6635	1	13	,	,	PUNCT
ejpam-6635	1	14	issue	issue	NOUN
ejpam-6635	1	15	3	3	NUM
ejpam-6635	1	16	,	,	PUNCT
ejpam-6635	1	17	article	article	NOUN
ejpam-6635	1	18	number	number	NOUN
ejpam-6635	1	19	6635	6635	NUM
ejpam-6635	1	20	issn	issn	VERB
ejpam-6635	1	21	1307	1307	NUM
ejpam-6635	1	22	-	-	SYM
ejpam-6635	1	23	5543	5543	NUM
ejpam-6635	1	24	–	–	PUNCT
ejpam-6635	1	25	ejpam.com	ejpam.com	X
ejpam-6635	1	26	published	publish	VERB
ejpam-6635	1	27	by	by	ADP
ejpam-6635	2	1	new	new	PROPN
ejpam-6635	2	2	york	york	PROPN
ejpam-6635	2	3	business	business	PROPN
ejpam-6635	2	4	global	global	ADJ
ejpam-6635	2	5	secure	secure	PROPN
ejpam-6635	2	6	pointwise	pointwise	PROPN
ejpam-6635	2	7	non	non	ADJ
ejpam-6635	2	8	-	-	NOUN
ejpam-6635	2	9	domination	domination	NOUN
ejpam-6635	2	10	and	and	CCONJ
ejpam-6635	2	11	secure	secure	VERB
ejpam-6635	2	12	hop	hop	NOUN
ejpam-6635	2	13	domination	domination	NOUN
ejpam-6635	2	14	in	in	ADP
ejpam-6635	2	15	graphs	graph	NOUN
ejpam-6635	2	16	farene	farene	PROPN
ejpam-6635	2	17	loida	loida	PROPN
ejpam-6635	2	18	m.	m.	PROPN
ejpam-6635	2	19	alfeche1,∗	alfeche1,∗	PROPN
ejpam-6635	2	20	,	,	PUNCT
ejpam-6635	2	21	sergio	sergio	PROPN
ejpam-6635	2	22	r.	r.	PROPN
ejpam-6635	2	23	canoy	canoy	PROPN
ejpam-6635	2	24	,	,	PUNCT
ejpam-6635	2	25	jr.1,2	jr.1,2	ADJ
ejpam-6635	2	26	1	1	NUM
ejpam-6635	2	27	department	department	NOUN
ejpam-6635	2	28	of	of	ADP
ejpam-6635	2	29	mathematics	mathematic	NOUN
ejpam-6635	2	30	and	and	CCONJ
ejpam-6635	2	31	statistics	statistic	NOUN
ejpam-6635	2	32	,	,	PUNCT
ejpam-6635	2	33	college	college	NOUN
ejpam-6635	2	34	of	of	ADP
ejpam-6635	2	35	science	science	NOUN
ejpam-6635	2	36	and	and	CCONJ
ejpam-6635	2	37	mathematics	mathematic	NOUN
ejpam-6635	2	38	,	,	PUNCT
ejpam-6635	2	39	msu	msu	PROPN
ejpam-6635	2	40	-	-	PUNCT
ejpam-6635	2	41	iligan	iligan	PROPN
ejpam-6635	2	42	institute	institute	PROPN
ejpam-6635	2	43	of	of	ADP
ejpam-6635	2	44	technology	technology	PROPN
ejpam-6635	2	45	,	,	PUNCT
ejpam-6635	2	46	9200	9200	NUM
ejpam-6635	2	47	iligan	iligan	ADJ
ejpam-6635	2	48	city	city	NOUN
ejpam-6635	2	49	,	,	PUNCT
ejpam-6635	2	50	philippines	philippine	NOUN
ejpam-6635	2	51	2	2	NUM
ejpam-6635	2	52	center	center	NOUN
ejpam-6635	2	53	for	for	ADP
ejpam-6635	2	54	mathematical	mathematical	ADJ
ejpam-6635	2	55	and	and	CCONJ
ejpam-6635	2	56	theoretical	theoretical	ADJ
ejpam-6635	2	57	physical	physical	ADJ
ejpam-6635	2	58	sciencesprism	sciencesprism	NOUN
ejpam-6635	2	59	,	,	PUNCT
ejpam-6635	2	60	msu	msu	PROPN
ejpam-6635	2	61	-	-	PUNCT
ejpam-6635	2	62	iligan	iligan	PROPN
ejpam-6635	2	63	institute	institute	PROPN
ejpam-6635	2	64	of	of	ADP
ejpam-6635	2	65	technology	technology	PROPN
ejpam-6635	2	66	,	,	PUNCT
ejpam-6635	2	67	9200	9200	NUM
ejpam-6635	2	68	iligan	iligan	ADJ
ejpam-6635	2	69	city	city	NOUN
ejpam-6635	2	70	,	,	PUNCT
ejpam-6635	2	71	philippines	philippine	NOUN
ejpam-6635	2	72	abstract	abstract	ADJ
ejpam-6635	2	73	.	.	PUNCT
ejpam-6635	3	1	in	in	ADP
ejpam-6635	3	2	this	this	DET
ejpam-6635	3	3	paper	paper	NOUN
ejpam-6635	3	4	,	,	PUNCT
ejpam-6635	3	5	we	we	PRON
ejpam-6635	3	6	revisit	revisit	VERB
ejpam-6635	3	7	the	the	DET
ejpam-6635	3	8	concept	concept	NOUN
ejpam-6635	3	9	of	of	ADP
ejpam-6635	3	10	secure	secure	ADJ
ejpam-6635	3	11	hop	hop	NOUN
ejpam-6635	3	12	domination	domination	NOUN
ejpam-6635	3	13	in	in	ADP
ejpam-6635	3	14	graphs	graph	NOUN
ejpam-6635	3	15	and	and	CCONJ
ejpam-6635	3	16	define	define	VERB
ejpam-6635	3	17	a	a	DET
ejpam-6635	3	18	new	new	ADJ
ejpam-6635	3	19	concept	concept	NOUN
ejpam-6635	3	20	called	call	VERB
ejpam-6635	3	21	secure	secure	ADJ
ejpam-6635	3	22	pointwise	pointwise	PROPN
ejpam-6635	3	23	non	non	ADJ
ejpam-6635	3	24	-	-	NOUN
ejpam-6635	3	25	domination	domination	NOUN
ejpam-6635	3	26	.	.	PUNCT
ejpam-6635	4	1	a	a	DET
ejpam-6635	4	2	pointwise	pointwise	ADJ
ejpam-6635	4	3	non	non	ADJ
ejpam-6635	4	4	-	-	ADJ
ejpam-6635	4	5	dominating	dominating	ADJ
ejpam-6635	4	6	set	set	NOUN
ejpam-6635	4	7	s	s	VERB
ejpam-6635	4	8	is	be	AUX
ejpam-6635	4	9	a	a	DET
ejpam-6635	4	10	secure	secure	ADJ
ejpam-6635	4	11	pointwise	pointwise	ADJ
ejpam-6635	4	12	non	non	ADJ
ejpam-6635	4	13	-	-	ADJ
ejpam-6635	4	14	dominating	dominating	ADJ
ejpam-6635	4	15	set	set	NOUN
ejpam-6635	4	16	if	if	SCONJ
ejpam-6635	4	17	for	for	ADP
ejpam-6635	4	18	every	every	DET
ejpam-6635	4	19	u	u	PROPN
ejpam-6635	4	20	∈	∈	PROPN
ejpam-6635	4	21	v	v	ADP
ejpam-6635	4	22	(	(	PUNCT
ejpam-6635	4	23	g	g	NOUN
ejpam-6635	4	24	)	)	PUNCT
ejpam-6635	4	25	\	\	PROPN
ejpam-6635	5	1	s	s	X
ejpam-6635	5	2	,	,	PUNCT
ejpam-6635	5	3	there	there	PRON
ejpam-6635	5	4	exists	exist	VERB
ejpam-6635	5	5	v	v	ADP
ejpam-6635	5	6	∈	∈	PROPN
ejpam-6635	5	7	s	s	PART
ejpam-6635	5	8	\	\	NOUN
ejpam-6635	5	9	ng(u	ng(u	NOUN
ejpam-6635	5	10	)	)	PUNCT
ejpam-6635	5	11	such	such	ADJ
ejpam-6635	5	12	that	that	SCONJ
ejpam-6635	5	13	(	(	PUNCT
ejpam-6635	5	14	s	s	NOUN
ejpam-6635	5	15	\	\	X
ejpam-6635	5	16	{	{	PUNCT
ejpam-6635	5	17	v	v	NOUN
ejpam-6635	5	18	}	}	PUNCT
ejpam-6635	5	19	)	)	PUNCT
ejpam-6635	5	20	∪	∪	ADP
ejpam-6635	5	21	{	{	PUNCT
ejpam-6635	5	22	u	u	NOUN
ejpam-6635	5	23	}	}	PUNCT
ejpam-6635	5	24	is	be	AUX
ejpam-6635	5	25	a	a	DET
ejpam-6635	5	26	pointwise	pointwise	ADJ
ejpam-6635	5	27	non	non	ADJ
ejpam-6635	5	28	-	-	ADJ
ejpam-6635	5	29	dominating	dominating	ADJ
ejpam-6635	5	30	set	set	NOUN
ejpam-6635	5	31	.	.	PUNCT
ejpam-6635	6	1	the	the	DET
ejpam-6635	6	2	secure	secure	ADJ
ejpam-6635	6	3	pointwise	pointwise	PROPN
ejpam-6635	6	4	non	non	ADJ
ejpam-6635	6	5	-	-	ADJ
ejpam-6635	6	6	domination	domination	ADJ
ejpam-6635	6	7	number	number	NOUN
ejpam-6635	6	8	spnd(g	spnd(g	PROPN
ejpam-6635	6	9	)	)	PUNCT
ejpam-6635	6	10	of	of	ADP
ejpam-6635	6	11	g	g	PROPN
ejpam-6635	6	12	is	be	AUX
ejpam-6635	6	13	the	the	DET
ejpam-6635	6	14	smallest	small	ADJ
ejpam-6635	6	15	cardinality	cardinality	NOUN
ejpam-6635	6	16	of	of	ADP
ejpam-6635	6	17	a	a	DET
ejpam-6635	6	18	secure	secure	ADJ
ejpam-6635	6	19	pointwise	pointwise	ADJ
ejpam-6635	6	20	non	non	ADJ
ejpam-6635	6	21	-	-	ADJ
ejpam-6635	6	22	dominating	dominating	ADJ
ejpam-6635	6	23	set	set	NOUN
ejpam-6635	6	24	in	in	ADP
ejpam-6635	6	25	g.	g.	PROPN
ejpam-6635	6	26	in	in	ADP
ejpam-6635	6	27	this	this	DET
ejpam-6635	6	28	paper	paper	NOUN
ejpam-6635	6	29	,	,	PUNCT
ejpam-6635	6	30	we	we	PRON
ejpam-6635	6	31	give	give	VERB
ejpam-6635	6	32	bounds	bound	NOUN
ejpam-6635	6	33	on	on	ADP
ejpam-6635	6	34	the	the	DET
ejpam-6635	6	35	secure	secure	ADJ
ejpam-6635	6	36	pointwise	pointwise	PROPN
ejpam-6635	6	37	non	non	ADJ
ejpam-6635	6	38	-	-	ADJ
ejpam-6635	6	39	domination	domination	ADJ
ejpam-6635	6	40	number	number	NOUN
ejpam-6635	6	41	and	and	CCONJ
ejpam-6635	6	42	characterize	characterize	VERB
ejpam-6635	6	43	those	those	DET
ejpam-6635	6	44	graphs	graph	NOUN
ejpam-6635	6	45	which	which	PRON
ejpam-6635	6	46	attain	attain	VERB
ejpam-6635	6	47	these	these	DET
ejpam-6635	6	48	bounds	bound	NOUN
ejpam-6635	6	49	.	.	PUNCT
ejpam-6635	7	1	we	we	PRON
ejpam-6635	7	2	also	also	ADV
ejpam-6635	7	3	determine	determine	VERB
ejpam-6635	7	4	the	the	DET
ejpam-6635	7	5	secure	secure	ADJ
ejpam-6635	7	6	pointwise	pointwise	PROPN
ejpam-6635	7	7	non	non	ADJ
ejpam-6635	7	8	-	-	ADJ
ejpam-6635	7	9	domination	domination	ADJ
ejpam-6635	7	10	number	number	NOUN
ejpam-6635	7	11	of	of	ADP
ejpam-6635	7	12	some	some	DET
ejpam-6635	7	13	classes	class	NOUN
ejpam-6635	7	14	of	of	ADP
ejpam-6635	7	15	graphs	graph	NOUN
ejpam-6635	7	16	.	.	PUNCT
ejpam-6635	8	1	necessary	necessary	ADJ
ejpam-6635	8	2	and	and	CCONJ
ejpam-6635	8	3	sufficient	sufficient	ADJ
ejpam-6635	8	4	conditions	condition	NOUN
ejpam-6635	8	5	for	for	ADP
ejpam-6635	8	6	a	a	DET
ejpam-6635	8	7	subset	subset	NOUN
ejpam-6635	8	8	in	in	ADP
ejpam-6635	8	9	the	the	DET
ejpam-6635	8	10	join	join	NOUN
ejpam-6635	8	11	of	of	ADP
ejpam-6635	8	12	graphs	graph	NOUN
ejpam-6635	8	13	to	to	PART
ejpam-6635	8	14	be	be	AUX
ejpam-6635	8	15	a	a	DET
ejpam-6635	8	16	secure	secure	ADJ
ejpam-6635	8	17	hop	hop	NOUN
ejpam-6635	8	18	dominating	dominating	NOUN
ejpam-6635	8	19	set	set	NOUN
ejpam-6635	8	20	is	be	AUX
ejpam-6635	8	21	given	give	VERB
ejpam-6635	8	22	.	.	PUNCT
ejpam-6635	9	1	moreover	moreover	ADV
ejpam-6635	9	2	,	,	PUNCT
ejpam-6635	9	3	we	we	PRON
ejpam-6635	9	4	show	show	VERB
ejpam-6635	9	5	that	that	SCONJ
ejpam-6635	9	6	given	give	VERB
ejpam-6635	9	7	positive	positive	ADJ
ejpam-6635	9	8	integers	integer	NOUN
ejpam-6635	9	9	a	a	PRON
ejpam-6635	9	10	and	and	CCONJ
ejpam-6635	9	11	b	b	NOUN
ejpam-6635	9	12	with	with	ADP
ejpam-6635	9	13	2	2	NUM
ejpam-6635	9	14	≤	≤	NOUN
ejpam-6635	9	15	a	a	DET
ejpam-6635	9	16	≤	≤	NUM
ejpam-6635	9	17	b	b	NOUN
ejpam-6635	9	18	,	,	PUNCT
ejpam-6635	9	19	there	there	PRON
ejpam-6635	9	20	exists	exist	VERB
ejpam-6635	9	21	a	a	DET
ejpam-6635	9	22	connected	connected	ADJ
ejpam-6635	9	23	graph	graph	NOUN
ejpam-6635	9	24	such	such	ADJ
ejpam-6635	9	25	that	that	PRON
ejpam-6635	9	26	γh(g	γh(g	NOUN
ejpam-6635	9	27	)	)	PUNCT
ejpam-6635	9	28	=	=	PUNCT
ejpam-6635	9	29	a	a	PRON
ejpam-6635	9	30	and	and	CCONJ
ejpam-6635	9	31	γsh(g	γsh(g	NOUN
ejpam-6635	9	32	)	)	PUNCT
ejpam-6635	9	33	=	=	SYM
ejpam-6635	9	34	b	b	NOUN
ejpam-6635	9	35	,	,	PUNCT
ejpam-6635	9	36	where	where	SCONJ
ejpam-6635	9	37	γh(g	γh(g	NOUN
ejpam-6635	9	38	)	)	PUNCT
ejpam-6635	9	39	and	and	CCONJ
ejpam-6635	9	40	γsh(g	γsh(g	NOUN
ejpam-6635	9	41	)	)	PUNCT
ejpam-6635	9	42	are	be	AUX
ejpam-6635	9	43	the	the	DET
ejpam-6635	9	44	hop	hop	NOUN
ejpam-6635	9	45	domination	domination	NOUN
ejpam-6635	9	46	number	number	NOUN
ejpam-6635	9	47	and	and	CCONJ
ejpam-6635	9	48	secure	secure	VERB
ejpam-6635	9	49	hop	hop	NOUN
ejpam-6635	9	50	domination	domination	NOUN
ejpam-6635	9	51	number	number	NOUN
ejpam-6635	9	52	of	of	ADP
ejpam-6635	9	53	g	g	NOUN
ejpam-6635	9	54	,	,	PUNCT
ejpam-6635	9	55	respectively	respectively	ADV
ejpam-6635	9	56	.	.	PUNCT
ejpam-6635	10	1	2020	2020	NUM
ejpam-6635	10	2	mathematics	mathematic	NOUN
ejpam-6635	10	3	subject	subject	NOUN
ejpam-6635	10	4	classifications	classification	NOUN
ejpam-6635	10	5	:	:	PUNCT
ejpam-6635	10	6	05c69	05c69	X
ejpam-6635	10	7	key	key	ADJ
ejpam-6635	10	8	words	word	NOUN
ejpam-6635	10	9	and	and	CCONJ
ejpam-6635	10	10	phrases	phrase	NOUN
ejpam-6635	10	11	:	:	PUNCT
ejpam-6635	10	12	pointwise	pointwise	VERB
ejpam-6635	10	13	non	non	ADJ
ejpam-6635	10	14	-	-	ADJ
ejpam-6635	10	15	domination	domination	ADJ
ejpam-6635	10	16	number	number	NOUN
ejpam-6635	10	17	,	,	PUNCT
ejpam-6635	10	18	secure	secure	VERB
ejpam-6635	10	19	pointwise	pointwise	PROPN
ejpam-6635	10	20	non	non	ADJ
ejpam-6635	10	21	-	-	ADJ
ejpam-6635	10	22	domination	domination	ADJ
ejpam-6635	10	23	number	number	NOUN
ejpam-6635	10	24	,	,	PUNCT
ejpam-6635	10	25	hop	hop	NOUN
ejpam-6635	10	26	domination	domination	NOUN
ejpam-6635	10	27	,	,	PUNCT
ejpam-6635	10	28	secure	secure	VERB
ejpam-6635	10	29	hop	hop	NOUN
ejpam-6635	10	30	domination	domination	NOUN
ejpam-6635	10	31	number	number	NOUN
ejpam-6635	10	32	,	,	PUNCT
ejpam-6635	10	33	join	join	NOUN
ejpam-6635	10	34	of	of	ADP
ejpam-6635	10	35	graphs	graph	NOUN
ejpam-6635	10	36	1	1	NUM
ejpam-6635	10	37	.	.	PUNCT
ejpam-6635	10	38	introduction	introduction	NOUN
ejpam-6635	10	39	the	the	DET
ejpam-6635	10	40	concept	concept	NOUN
ejpam-6635	10	41	of	of	ADP
ejpam-6635	10	42	security	security	NOUN
ejpam-6635	10	43	in	in	ADP
ejpam-6635	10	44	graphs	graph	NOUN
ejpam-6635	10	45	could	could	AUX
ejpam-6635	10	46	provide	provide	VERB
ejpam-6635	10	47	a	a	DET
ejpam-6635	10	48	framework	framework	NOUN
ejpam-6635	10	49	for	for	ADP
ejpam-6635	10	50	modeling	model	VERB
ejpam-6635	10	51	a	a	DET
ejpam-6635	10	52	security	security	NOUN
ejpam-6635	10	53	system	system	NOUN
ejpam-6635	10	54	[	[	X
ejpam-6635	10	55	1	1	X
ejpam-6635	10	56	]	]	PUNCT
ejpam-6635	10	57	that	that	PRON
ejpam-6635	10	58	could	could	AUX
ejpam-6635	10	59	guarantee	guarantee	VERB
ejpam-6635	10	60	that	that	SCONJ
ejpam-6635	10	61	no	no	DET
ejpam-6635	10	62	area	area	NOUN
ejpam-6635	10	63	is	be	AUX
ejpam-6635	10	64	left	leave	VERB
ejpam-6635	10	65	unmonitored	unmonitored	ADJ
ejpam-6635	10	66	.	.	PUNCT
ejpam-6635	11	1	recently	recently	ADV
ejpam-6635	11	2	,	,	PUNCT
ejpam-6635	11	3	alfeche	alfeche	PROPN
ejpam-6635	11	4	et	et	PROPN
ejpam-6635	11	5	al	al	PROPN
ejpam-6635	11	6	.	.	PUNCT
ejpam-6635	12	1	[	[	X
ejpam-6635	12	2	2	2	NUM
ejpam-6635	12	3	]	]	PUNCT
ejpam-6635	12	4	studied	study	VERB
ejpam-6635	12	5	the	the	DET
ejpam-6635	12	6	secure	secure	ADJ
ejpam-6635	12	7	hop	hop	NOUN
ejpam-6635	12	8	dominating	dominating	NOUN
ejpam-6635	12	9	sets	set	NOUN
ejpam-6635	12	10	in	in	ADP
ejpam-6635	12	11	graphs	graph	NOUN
ejpam-6635	12	12	,	,	PUNCT
ejpam-6635	12	13	where	where	SCONJ
ejpam-6635	12	14	they	they	PRON
ejpam-6635	12	15	gave	give	VERB
ejpam-6635	12	16	bounds	bound	NOUN
ejpam-6635	12	17	on	on	ADP
ejpam-6635	12	18	the	the	DET
ejpam-6635	12	19	secure	secure	ADJ
ejpam-6635	12	20	hop	hop	NOUN
ejpam-6635	12	21	domination	domination	NOUN
ejpam-6635	12	22	number	number	NOUN
ejpam-6635	12	23	and	and	CCONJ
ejpam-6635	12	24	determine	determine	VERB
ejpam-6635	12	25	the	the	DET
ejpam-6635	12	26	secure	secure	ADJ
ejpam-6635	12	27	hop	hop	NOUN
ejpam-6635	12	28	domination	domination	NOUN
ejpam-6635	12	29	numbers	number	NOUN
ejpam-6635	12	30	of	of	ADP
ejpam-6635	12	31	the	the	DET
ejpam-6635	12	32	shadow	shadow	NOUN
ejpam-6635	12	33	graph	graph	NOUN
ejpam-6635	12	34	and	and	CCONJ
ejpam-6635	12	35	complementary	complementary	ADJ
ejpam-6635	12	36	prism	prism	NOUN
ejpam-6635	12	37	.	.	PUNCT
ejpam-6635	13	1	in	in	ADP
ejpam-6635	13	2	this	this	DET
ejpam-6635	13	3	paper	paper	NOUN
ejpam-6635	13	4	,	,	PUNCT
ejpam-6635	13	5	we	we	PRON
ejpam-6635	13	6	introduce	introduce	VERB
ejpam-6635	13	7	and	and	CCONJ
ejpam-6635	13	8	study	study	VERB
ejpam-6635	13	9	the	the	DET
ejpam-6635	13	10	concept	concept	NOUN
ejpam-6635	13	11	of	of	ADP
ejpam-6635	13	12	secure	secure	ADJ
ejpam-6635	13	13	pointwise	pointwise	PROPN
ejpam-6635	13	14	non	non	ADJ
ejpam-6635	13	15	-	-	ADJ
ejpam-6635	13	16	dominating	dominating	ADJ
ejpam-6635	13	17	set	set	NOUN
ejpam-6635	13	18	in	in	ADP
ejpam-6635	13	19	a	a	DET
ejpam-6635	13	20	graph	graph	NOUN
ejpam-6635	13	21	.	.	PUNCT
ejpam-6635	14	1	we	we	PRON
ejpam-6635	14	2	give	give	VERB
ejpam-6635	14	3	bounds	bound	NOUN
ejpam-6635	14	4	on	on	ADP
ejpam-6635	14	5	the	the	DET
ejpam-6635	14	6	parameter	parameter	NOUN
ejpam-6635	14	7	called	call	VERB
ejpam-6635	14	8	secure	secure	ADJ
ejpam-6635	14	9	pointwise	pointwise	PROPN
ejpam-6635	14	10	non	non	ADJ
ejpam-6635	14	11	-	-	ADJ
ejpam-6635	14	12	domination	domination	ADJ
ejpam-6635	14	13	number	number	NOUN
ejpam-6635	14	14	and	and	CCONJ
ejpam-6635	14	15	give	give	VERB
ejpam-6635	14	16	necessary	necessary	ADJ
ejpam-6635	14	17	and	and	CCONJ
ejpam-6635	14	18	sufficient	sufficient	ADJ
ejpam-6635	14	19	conditions	condition	NOUN
ejpam-6635	14	20	for	for	ADP
ejpam-6635	14	21	∗corresponding	∗corresponde	VERB
ejpam-6635	14	22	author	author	NOUN
ejpam-6635	14	23	.	.	PUNCT
ejpam-6635	15	1	doi	doi	NOUN
ejpam-6635	15	2	:	:	PUNCT
ejpam-6635	15	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6635	https://doi.org/10.29020/nybg.ejpam.v18i3.6635	ADJ
ejpam-6635	15	4	email	email	NOUN
ejpam-6635	15	5	addresses	address	NOUN
ejpam-6635	15	6	:	:	PUNCT
ejpam-6635	15	7	farene.alfeche@g.msuiit.edu.ph	farene.alfeche@g.msuiit.edu.ph	PROPN
ejpam-6635	15	8	(	(	PUNCT
ejpam-6635	15	9	f.l	f.l	PROPN
ejpam-6635	15	10	.	.	PROPN
ejpam-6635	15	11	alfeche	alfeche	PROPN
ejpam-6635	15	12	)	)	PUNCT
ejpam-6635	16	1	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-6635	16	2	(	(	PUNCT
ejpam-6635	16	3	s.	s.	PROPN
ejpam-6635	16	4	canoy	canoy	PROPN
ejpam-6635	16	5	)	)	PUNCT
ejpam-6635	16	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6635	17	1	1	1	NUM
ejpam-6635	17	2	copyright	copyright	NOUN
ejpam-6635	17	3	:	:	PUNCT
ejpam-6635	17	4	©	©	PROPN
ejpam-6635	17	5	2025	2025	NUM
ejpam-6635	17	6	the	the	DET
ejpam-6635	17	7	author(s	author(s	NOUN
ejpam-6635	17	8	)	)	PUNCT
ejpam-6635	17	9	.	.	PUNCT
ejpam-6635	18	1	(	(	PUNCT
ejpam-6635	18	2	cc	cc	NOUN
ejpam-6635	18	3	by	by	ADP
ejpam-6635	18	4	-	-	PUNCT
ejpam-6635	18	5	nc	nc	PROPN
ejpam-6635	18	6	4.0	4.0	NUM
ejpam-6635	18	7	)	)	PUNCT
ejpam-6635	18	8	f.	f.	PROPN
ejpam-6635	18	9	alfeche	alfeche	PROPN
ejpam-6635	18	10	,	,	PUNCT
ejpam-6635	18	11	s.	s.	PROPN
ejpam-6635	18	12	canoy	canoy	PROPN
ejpam-6635	18	13	jr	jr	PROPN
ejpam-6635	18	14	.	.	PROPN
ejpam-6635	18	15	/	/	SYM
ejpam-6635	18	16	eur	eur	PROPN
ejpam-6635	18	17	.	.	PUNCT
ejpam-6635	19	1	j.	j.	PROPN
ejpam-6635	19	2	pure	pure	PROPN
ejpam-6635	19	3	appl	appl	PROPN
ejpam-6635	19	4	.	.	PROPN
ejpam-6635	19	5	math	math	PROPN
ejpam-6635	19	6	,	,	PUNCT
ejpam-6635	19	7	18	18	NUM
ejpam-6635	19	8	(	(	PUNCT
ejpam-6635	19	9	3	3	NUM
ejpam-6635	19	10	)	)	PUNCT
ejpam-6635	19	11	(	(	PUNCT
ejpam-6635	19	12	2025	2025	NUM
ejpam-6635	19	13	)	)	PUNCT
ejpam-6635	19	14	,	,	PUNCT
ejpam-6635	19	15	6635	6635	NUM
ejpam-6635	19	16	2	2	NUM
ejpam-6635	19	17	of	of	ADP
ejpam-6635	19	18	11	11	NUM
ejpam-6635	19	19	those	those	DET
ejpam-6635	19	20	graphs	graph	NOUN
ejpam-6635	19	21	that	that	PRON
ejpam-6635	19	22	attain	attain	VERB
ejpam-6635	19	23	these	these	DET
ejpam-6635	19	24	bounds	bound	NOUN
ejpam-6635	19	25	.	.	PUNCT
ejpam-6635	20	1	furthermore	furthermore	ADV
ejpam-6635	20	2	,	,	PUNCT
ejpam-6635	20	3	we	we	PRON
ejpam-6635	20	4	use	use	VERB
ejpam-6635	20	5	this	this	DET
ejpam-6635	20	6	newly	newly	ADV
ejpam-6635	20	7	defined	define	VERB
ejpam-6635	20	8	concept	concept	NOUN
ejpam-6635	20	9	to	to	PART
ejpam-6635	20	10	characterize	characterize	VERB
ejpam-6635	20	11	the	the	DET
ejpam-6635	20	12	secure	secure	ADJ
ejpam-6635	20	13	hop	hop	NOUN
ejpam-6635	20	14	dominating	dominating	NOUN
ejpam-6635	20	15	sets	set	NOUN
ejpam-6635	20	16	in	in	ADP
ejpam-6635	20	17	the	the	DET
ejpam-6635	20	18	join	join	NOUN
ejpam-6635	20	19	of	of	ADP
ejpam-6635	20	20	graphs	graph	NOUN
ejpam-6635	20	21	.	.	PUNCT
ejpam-6635	21	1	other	other	ADJ
ejpam-6635	21	2	related	related	ADJ
ejpam-6635	21	3	studies	study	NOUN
ejpam-6635	21	4	could	could	AUX
ejpam-6635	21	5	be	be	AUX
ejpam-6635	21	6	found	find	VERB
ejpam-6635	21	7	in	in	ADP
ejpam-6635	21	8	[	[	X
ejpam-6635	21	9	3	3	NUM
ejpam-6635	21	10	]	]	PUNCT
ejpam-6635	21	11	,	,	PUNCT
ejpam-6635	21	12	[	[	X
ejpam-6635	21	13	4	4	NUM
ejpam-6635	21	14	]	]	PUNCT
ejpam-6635	21	15	,	,	PUNCT
ejpam-6635	21	16	[	[	X
ejpam-6635	21	17	5	5	NUM
ejpam-6635	21	18	]	]	PUNCT
ejpam-6635	21	19	,	,	PUNCT
ejpam-6635	21	20	[	[	X
ejpam-6635	21	21	6	6	NUM
ejpam-6635	21	22	]	]	PUNCT
ejpam-6635	21	23	,	,	PUNCT
ejpam-6635	21	24	[	[	X
ejpam-6635	21	25	7	7	NUM
ejpam-6635	21	26	]	]	PUNCT
ejpam-6635	21	27	,	,	PUNCT
ejpam-6635	21	28	[	[	X
ejpam-6635	21	29	8	8	NUM
ejpam-6635	21	30	]	]	PUNCT
ejpam-6635	21	31	,	,	PUNCT
ejpam-6635	21	32	[	[	X
ejpam-6635	21	33	9	9	NUM
ejpam-6635	21	34	]	]	PUNCT
ejpam-6635	21	35	,	,	PUNCT
ejpam-6635	21	36	[	[	X
ejpam-6635	21	37	10	10	NUM
ejpam-6635	21	38	]	]	PUNCT
ejpam-6635	21	39	,	,	PUNCT
ejpam-6635	21	40	[	[	X
ejpam-6635	21	41	11	11	NUM
ejpam-6635	21	42	]	]	PUNCT
ejpam-6635	21	43	,	,	PUNCT
ejpam-6635	21	44	[	[	X
ejpam-6635	21	45	12	12	NUM
ejpam-6635	21	46	]	]	PUNCT
ejpam-6635	21	47	,	,	PUNCT
ejpam-6635	21	48	[	[	X
ejpam-6635	21	49	13	13	NUM
ejpam-6635	21	50	]	]	PUNCT
ejpam-6635	21	51	,	,	PUNCT
ejpam-6635	21	52	[	[	X
ejpam-6635	21	53	14	14	NUM
ejpam-6635	21	54	]	]	PUNCT
ejpam-6635	21	55	,	,	PUNCT
ejpam-6635	21	56	[	[	X
ejpam-6635	21	57	15	15	NUM
ejpam-6635	21	58	]	]	PUNCT
ejpam-6635	21	59	,	,	PUNCT
ejpam-6635	22	1	[	[	X
ejpam-6635	22	2	16	16	NUM
ejpam-6635	22	3	]	]	PUNCT
ejpam-6635	22	4	,	,	PUNCT
ejpam-6635	23	1	[	[	X
ejpam-6635	23	2	17	17	NUM
ejpam-6635	23	3	]	]	PUNCT
ejpam-6635	23	4	,	,	PUNCT
ejpam-6635	23	5	and	and	CCONJ
ejpam-6635	23	6	[	[	X
ejpam-6635	23	7	18	18	NUM
ejpam-6635	23	8	]	]	SYM
ejpam-6635	23	9	.	.	PUNCT
ejpam-6635	24	1	2	2	X
ejpam-6635	24	2	.	.	X
ejpam-6635	24	3	terminology	terminology	NOUN
ejpam-6635	24	4	and	and	CCONJ
ejpam-6635	24	5	notation	notation	NOUN
ejpam-6635	24	6	let	let	VERB
ejpam-6635	24	7	g	g	PROPN
ejpam-6635	24	8	=	=	SYM
ejpam-6635	24	9	v	v	PROPN
ejpam-6635	24	10	(	(	PUNCT
ejpam-6635	24	11	g	g	NOUN
ejpam-6635	24	12	)	)	PUNCT
ejpam-6635	24	13	,	,	PUNCT
ejpam-6635	24	14	e(g	e(g	PROPN
ejpam-6635	24	15	)	)	PUNCT
ejpam-6635	24	16	)	)	PUNCT
ejpam-6635	24	17	be	be	AUX
ejpam-6635	24	18	an	an	DET
ejpam-6635	24	19	undirected	undirected	ADJ
ejpam-6635	24	20	graph	graph	NOUN
ejpam-6635	24	21	.	.	PUNCT
ejpam-6635	25	1	for	for	ADP
ejpam-6635	25	2	any	any	DET
ejpam-6635	25	3	two	two	NUM
ejpam-6635	25	4	vertices	vertex	NOUN
ejpam-6635	25	5	u	u	NOUN
ejpam-6635	25	6	and	and	CCONJ
ejpam-6635	25	7	v	v	NOUN
ejpam-6635	25	8	of	of	ADP
ejpam-6635	25	9	g	g	NOUN
ejpam-6635	25	10	,	,	PUNCT
ejpam-6635	25	11	the	the	DET
ejpam-6635	25	12	distance	distance	NOUN
ejpam-6635	25	13	dg(u	dg(u	X
ejpam-6635	25	14	,	,	PUNCT
ejpam-6635	25	15	v	v	NOUN
ejpam-6635	25	16	)	)	PUNCT
ejpam-6635	25	17	is	be	AUX
ejpam-6635	25	18	the	the	DET
ejpam-6635	25	19	length	length	NOUN
ejpam-6635	25	20	of	of	ADP
ejpam-6635	25	21	a	a	DET
ejpam-6635	25	22	shortest	short	ADJ
ejpam-6635	25	23	path	path	NOUN
ejpam-6635	25	24	joining	join	VERB
ejpam-6635	25	25	u	u	NOUN
ejpam-6635	25	26	and	and	CCONJ
ejpam-6635	25	27	v.	v.	ADP
ejpam-6635	25	28	any	any	DET
ejpam-6635	25	29	u	u	NOUN
ejpam-6635	25	30	-	-	NOUN
ejpam-6635	25	31	v	v	ADJ
ejpam-6635	25	32	path	path	NOUN
ejpam-6635	25	33	of	of	ADP
ejpam-6635	25	34	length	length	NOUN
ejpam-6635	25	35	dg(u	dg(u	PROPN
ejpam-6635	25	36	,	,	PUNCT
ejpam-6635	25	37	v	v	NOUN
ejpam-6635	25	38	)	)	PUNCT
ejpam-6635	25	39	is	be	AUX
ejpam-6635	25	40	called	call	VERB
ejpam-6635	25	41	a	a	DET
ejpam-6635	25	42	u	u	NOUN
ejpam-6635	25	43	-	-	NOUN
ejpam-6635	25	44	v	v	ADJ
ejpam-6635	25	45	geodesic	geodesic	NOUN
ejpam-6635	25	46	.	.	PUNCT
ejpam-6635	26	1	the	the	DET
ejpam-6635	26	2	interval	interval	NOUN
ejpam-6635	26	3	ig	ig	PROPN
ejpam-6635	27	1	[	[	X
ejpam-6635	27	2	u	u	NOUN
ejpam-6635	27	3	,	,	PUNCT
ejpam-6635	27	4	v	v	NOUN
ejpam-6635	27	5	]	]	PUNCT
ejpam-6635	27	6	consists	consist	VERB
ejpam-6635	27	7	of	of	ADP
ejpam-6635	27	8	u	u	NOUN
ejpam-6635	27	9	,	,	PUNCT
ejpam-6635	27	10	v	v	NOUN
ejpam-6635	27	11	,	,	PUNCT
ejpam-6635	27	12	and	and	CCONJ
ejpam-6635	27	13	all	all	DET
ejpam-6635	27	14	vertices	vertex	NOUN
ejpam-6635	27	15	lying	lie	VERB
ejpam-6635	27	16	on	on	ADP
ejpam-6635	27	17	a	a	DET
ejpam-6635	27	18	u	u	NOUN
ejpam-6635	27	19	-	-	NOUN
ejpam-6635	27	20	v	v	ADJ
ejpam-6635	27	21	geodesic	geodesic	NOUN
ejpam-6635	27	22	.	.	PUNCT
ejpam-6635	28	1	the	the	DET
ejpam-6635	28	2	interval	interval	NOUN
ejpam-6635	28	3	ig(u	ig(u	NOUN
ejpam-6635	28	4	,	,	PUNCT
ejpam-6635	28	5	v	v	NOUN
ejpam-6635	28	6	)	)	PUNCT
ejpam-6635	28	7	=	=	PUNCT
ejpam-6635	29	1	ig	ig	PROPN
ejpam-6635	30	1	[	[	X
ejpam-6635	30	2	u	u	NOUN
ejpam-6635	30	3	,	,	PUNCT
ejpam-6635	30	4	v	v	ADP
ejpam-6635	30	5	]	]	PUNCT
ejpam-6635	30	6	\	\	NOUN
ejpam-6635	30	7	{	{	PUNCT
ejpam-6635	30	8	u	u	NOUN
ejpam-6635	30	9	,	,	PUNCT
ejpam-6635	30	10	v	v	NOUN
ejpam-6635	30	11	}	}	PUNCT
ejpam-6635	30	12	.	.	PUNCT
ejpam-6635	31	1	vertices	vertice	VERB
ejpam-6635	31	2	u	u	NOUN
ejpam-6635	31	3	and	and	CCONJ
ejpam-6635	31	4	v	v	NOUN
ejpam-6635	31	5	are	be	AUX
ejpam-6635	31	6	adjacent	adjacent	ADJ
ejpam-6635	31	7	(	(	PUNCT
ejpam-6635	31	8	or	or	CCONJ
ejpam-6635	31	9	neighbors	neighbor	NOUN
ejpam-6635	31	10	)	)	PUNCT
ejpam-6635	31	11	if	if	SCONJ
ejpam-6635	31	12	uv	uv	PROPN
ejpam-6635	31	13	∈	∈	PROPN
ejpam-6635	31	14	e(g	e(g	PROPN
ejpam-6635	31	15	)	)	PUNCT
ejpam-6635	31	16	.	.	PUNCT
ejpam-6635	32	1	the	the	DET
ejpam-6635	32	2	set	set	NOUN
ejpam-6635	32	3	of	of	ADP
ejpam-6635	32	4	neighbors	neighbor	NOUN
ejpam-6635	32	5	of	of	ADP
ejpam-6635	32	6	a	a	DET
ejpam-6635	32	7	vertex	vertex	NOUN
ejpam-6635	32	8	u	u	NOUN
ejpam-6635	32	9	in	in	ADP
ejpam-6635	32	10	g	g	NOUN
ejpam-6635	32	11	,	,	PUNCT
ejpam-6635	32	12	denoted	denote	VERB
ejpam-6635	32	13	by	by	ADP
ejpam-6635	32	14	ng(u	ng(u	NOUN
ejpam-6635	32	15	)	)	PUNCT
ejpam-6635	32	16	,	,	PUNCT
ejpam-6635	32	17	is	be	AUX
ejpam-6635	32	18	called	call	VERB
ejpam-6635	32	19	the	the	DET
ejpam-6635	32	20	open	open	ADJ
ejpam-6635	32	21	neighborhood	neighborhood	NOUN
ejpam-6635	32	22	of	of	ADP
ejpam-6635	32	23	u.	u.	VERB
ejpam-6635	32	24	the	the	DET
ejpam-6635	32	25	closed	closed	ADJ
ejpam-6635	32	26	neighborhood	neighborhood	NOUN
ejpam-6635	32	27	of	of	ADP
ejpam-6635	32	28	u	u	NOUN
ejpam-6635	32	29	is	be	AUX
ejpam-6635	32	30	the	the	DET
ejpam-6635	32	31	set	set	NOUN
ejpam-6635	32	32	ng[u	ng[u	PROPN
ejpam-6635	32	33	]	]	X
ejpam-6635	32	34	=	=	SYM
ejpam-6635	32	35	ng(u	ng(u	PROPN
ejpam-6635	32	36	)	)	PUNCT
ejpam-6635	32	37	∪	∪	NOUN
ejpam-6635	32	38	{	{	PUNCT
ejpam-6635	32	39	u	u	NOUN
ejpam-6635	32	40	}	}	PUNCT
ejpam-6635	32	41	.	.	PUNCT
ejpam-6635	33	1	if	if	SCONJ
ejpam-6635	33	2	x	x	PROPN
ejpam-6635	33	3	⊆	⊆	NUM
ejpam-6635	33	4	v	v	X
ejpam-6635	33	5	(	(	PUNCT
ejpam-6635	33	6	g	g	NOUN
ejpam-6635	33	7	)	)	PUNCT
ejpam-6635	33	8	,	,	PUNCT
ejpam-6635	33	9	the	the	DET
ejpam-6635	33	10	open	open	ADJ
ejpam-6635	33	11	neighborhood	neighborhood	NOUN
ejpam-6635	33	12	of	of	ADP
ejpam-6635	33	13	x	x	SYM
ejpam-6635	33	14	is	be	AUX
ejpam-6635	33	15	the	the	DET
ejpam-6635	33	16	set	set	NOUN
ejpam-6635	33	17	ng(x	ng(x	NUM
ejpam-6635	33	18	)	)	PUNCT
ejpam-6635	34	1	=	=	SYM
ejpam-6635	34	2	⋃	⋃	NOUN
ejpam-6635	34	3	u∈x	u∈x	NOUN
ejpam-6635	34	4	ng(u	ng(u	NOUN
ejpam-6635	34	5	)	)	PUNCT
ejpam-6635	34	6	.	.	PUNCT
ejpam-6635	35	1	the	the	DET
ejpam-6635	35	2	closed	closed	ADJ
ejpam-6635	35	3	neighborhood	neighborhood	NOUN
ejpam-6635	35	4	of	of	ADP
ejpam-6635	35	5	x	x	SYM
ejpam-6635	35	6	is	be	AUX
ejpam-6635	35	7	the	the	DET
ejpam-6635	35	8	set	set	NOUN
ejpam-6635	35	9	ng[x	ng[x	PROPN
ejpam-6635	35	10	]	]	X
ejpam-6635	35	11	=	=	PUNCT
ejpam-6635	35	12	ng(x	ng(x	X
ejpam-6635	35	13	)	)	PUNCT
ejpam-6635	36	1	∪x	∪x	PROPN
ejpam-6635	36	2	.	.	PUNCT
ejpam-6635	37	1	a	a	DET
ejpam-6635	37	2	set	set	NOUN
ejpam-6635	37	3	d	d	NOUN
ejpam-6635	37	4	⊆	⊆	NUM
ejpam-6635	37	5	v	v	ADP
ejpam-6635	37	6	(	(	PUNCT
ejpam-6635	37	7	g	g	NOUN
ejpam-6635	37	8	)	)	PUNCT
ejpam-6635	37	9	is	be	AUX
ejpam-6635	37	10	a	a	DET
ejpam-6635	37	11	dominating	dominating	NOUN
ejpam-6635	37	12	set	set	VERB
ejpam-6635	37	13	in	in	ADP
ejpam-6635	37	14	g	g	PROPN
ejpam-6635	37	15	if	if	SCONJ
ejpam-6635	37	16	for	for	ADP
ejpam-6635	37	17	every	every	DET
ejpam-6635	37	18	v	v	NUM
ejpam-6635	37	19	∈	∈	NOUN
ejpam-6635	37	20	v	v	NOUN
ejpam-6635	37	21	(	(	PUNCT
ejpam-6635	37	22	g)\d	g)\d	NOUN
ejpam-6635	37	23	,	,	PUNCT
ejpam-6635	37	24	there	there	PRON
ejpam-6635	37	25	exists	exist	VERB
ejpam-6635	37	26	u	u	NOUN
ejpam-6635	37	27	∈	∈	PROPN
ejpam-6635	37	28	d	d	ADP
ejpam-6635	37	29	such	such	ADJ
ejpam-6635	37	30	that	that	DET
ejpam-6635	37	31	uv	uv	PROPN
ejpam-6635	37	32	∈	∈	PROPN
ejpam-6635	37	33	e(g	e(g	PROPN
ejpam-6635	37	34	)	)	PUNCT
ejpam-6635	37	35	,	,	PUNCT
ejpam-6635	37	36	that	that	ADV
ejpam-6635	37	37	is	is	ADV
ejpam-6635	37	38	,	,	PUNCT
ejpam-6635	37	39	ng[d	ng[d	PROPN
ejpam-6635	37	40	]	]	PUNCT
ejpam-6635	37	41	=	=	SYM
ejpam-6635	37	42	v	v	X
ejpam-6635	37	43	(	(	PUNCT
ejpam-6635	37	44	g	g	NOUN
ejpam-6635	37	45	)	)	PUNCT
ejpam-6635	37	46	.	.	PUNCT
ejpam-6635	38	1	the	the	DET
ejpam-6635	38	2	domination	domination	NOUN
ejpam-6635	38	3	number	number	NOUN
ejpam-6635	38	4	of	of	ADP
ejpam-6635	38	5	g	g	NOUN
ejpam-6635	38	6	,	,	PUNCT
ejpam-6635	38	7	denoted	denote	VERB
ejpam-6635	38	8	by	by	ADP
ejpam-6635	38	9	γ(g	γ(g	PROPN
ejpam-6635	38	10	)	)	PUNCT
ejpam-6635	38	11	,	,	PUNCT
ejpam-6635	38	12	is	be	AUX
ejpam-6635	38	13	the	the	DET
ejpam-6635	38	14	minimum	minimum	ADJ
ejpam-6635	38	15	cardinality	cardinality	NOUN
ejpam-6635	38	16	of	of	ADP
ejpam-6635	38	17	a	a	DET
ejpam-6635	38	18	dominating	dominating	NOUN
ejpam-6635	38	19	set	set	VERB
ejpam-6635	38	20	in	in	ADP
ejpam-6635	38	21	g.	g.	PROPN
ejpam-6635	38	22	any	any	DET
ejpam-6635	38	23	dominating	dominating	NOUN
ejpam-6635	38	24	set	set	VERB
ejpam-6635	38	25	in	in	ADP
ejpam-6635	38	26	g	g	PROPN
ejpam-6635	38	27	with	with	ADP
ejpam-6635	38	28	cardinality	cardinality	PROPN
ejpam-6635	38	29	γ(g	γ(g	PROPN
ejpam-6635	38	30	)	)	PUNCT
ejpam-6635	38	31	,	,	PUNCT
ejpam-6635	38	32	is	be	AUX
ejpam-6635	38	33	called	call	VERB
ejpam-6635	38	34	a	a	DET
ejpam-6635	38	35	γ	γ	NOUN
ejpam-6635	38	36	-	-	PUNCT
ejpam-6635	38	37	set	set	NOUN
ejpam-6635	38	38	in	in	ADP
ejpam-6635	38	39	g.	g.	PROPN
ejpam-6635	38	40	if	if	SCONJ
ejpam-6635	38	41	γ(g	γ(g	PROPN
ejpam-6635	38	42	)	)	PUNCT
ejpam-6635	39	1	=	=	SYM
ejpam-6635	39	2	1	1	NUM
ejpam-6635	39	3	and	and	CCONJ
ejpam-6635	39	4	{	{	PUNCT
ejpam-6635	39	5	v	v	NOUN
ejpam-6635	39	6	}	}	PUNCT
ejpam-6635	39	7	is	be	AUX
ejpam-6635	39	8	a	a	DET
ejpam-6635	39	9	dominating	dominating	NOUN
ejpam-6635	39	10	set	set	NOUN
ejpam-6635	39	11	in	in	ADP
ejpam-6635	39	12	g	g	PROPN
ejpam-6635	39	13	,	,	PUNCT
ejpam-6635	39	14	then	then	ADV
ejpam-6635	39	15	we	we	PRON
ejpam-6635	39	16	call	call	VERB
ejpam-6635	39	17	v	v	ADP
ejpam-6635	39	18	a	a	DET
ejpam-6635	39	19	dominating	dominating	NOUN
ejpam-6635	39	20	vertex	vertex	NOUN
ejpam-6635	39	21	in	in	ADP
ejpam-6635	39	22	g.	g.	PROPN
ejpam-6635	39	23	a	a	DET
ejpam-6635	39	24	dominating	dominating	NOUN
ejpam-6635	39	25	set	set	NOUN
ejpam-6635	39	26	d	d	PROPN
ejpam-6635	39	27	⊆	⊆	NUM
ejpam-6635	39	28	v	v	ADP
ejpam-6635	39	29	(	(	PUNCT
ejpam-6635	39	30	g	g	NOUN
ejpam-6635	39	31	)	)	PUNCT
ejpam-6635	39	32	is	be	AUX
ejpam-6635	39	33	secure	secure	ADJ
ejpam-6635	39	34	dominating	dominating	NOUN
ejpam-6635	39	35	in	in	ADP
ejpam-6635	39	36	g	g	PROPN
ejpam-6635	39	37	if	if	SCONJ
ejpam-6635	39	38	for	for	ADP
ejpam-6635	39	39	every	every	DET
ejpam-6635	39	40	v	v	NUM
ejpam-6635	39	41	∈	∈	NOUN
ejpam-6635	39	42	v	v	NOUN
ejpam-6635	39	43	(	(	PUNCT
ejpam-6635	39	44	g	g	NOUN
ejpam-6635	39	45	)	)	PUNCT
ejpam-6635	39	46	\d	\d	NOUN
ejpam-6635	39	47	,	,	PUNCT
ejpam-6635	39	48	there	there	PRON
ejpam-6635	39	49	exists	exist	VERB
ejpam-6635	39	50	w	w	PROPN
ejpam-6635	39	51	∈	∈	PROPN
ejpam-6635	39	52	d	d	NOUN
ejpam-6635	39	53	∩	∩	NOUN
ejpam-6635	39	54	ng(v	ng(v	NOUN
ejpam-6635	39	55	)	)	PUNCT
ejpam-6635	39	56	such	such	ADJ
ejpam-6635	39	57	that	that	SCONJ
ejpam-6635	39	58	(	(	PUNCT
ejpam-6635	39	59	d	d	NOUN
ejpam-6635	39	60	\	\	X
ejpam-6635	39	61	{	{	PUNCT
ejpam-6635	39	62	w	w	NOUN
ejpam-6635	39	63	}	}	PUNCT
ejpam-6635	39	64	)	)	PUNCT
ejpam-6635	39	65	∪	∪	ADP
ejpam-6635	39	66	{	{	PUNCT
ejpam-6635	39	67	v	v	NOUN
ejpam-6635	39	68	}	}	PUNCT
ejpam-6635	39	69	is	be	AUX
ejpam-6635	39	70	a	a	DET
ejpam-6635	39	71	dominating	dominating	NOUN
ejpam-6635	39	72	set	set	VERB
ejpam-6635	39	73	in	in	ADP
ejpam-6635	39	74	g.	g.	PROPN
ejpam-6635	39	75	a	a	DET
ejpam-6635	39	76	vertex	vertex	NOUN
ejpam-6635	39	77	v	v	NOUN
ejpam-6635	39	78	in	in	ADP
ejpam-6635	39	79	g	g	PROPN
ejpam-6635	39	80	is	be	AUX
ejpam-6635	39	81	a	a	DET
ejpam-6635	39	82	hop	hop	NOUN
ejpam-6635	39	83	neighbor	neighbor	NOUN
ejpam-6635	39	84	of	of	ADP
ejpam-6635	39	85	vertex	vertex	NOUN
ejpam-6635	39	86	u	u	NOUN
ejpam-6635	39	87	in	in	ADP
ejpam-6635	39	88	g	g	PROPN
ejpam-6635	39	89	if	if	SCONJ
ejpam-6635	39	90	dg(u	dg(u	NOUN
ejpam-6635	39	91	,	,	PUNCT
ejpam-6635	39	92	v	v	NOUN
ejpam-6635	39	93	)	)	PUNCT
ejpam-6635	40	1	=	=	SYM
ejpam-6635	40	2	2	2	X
ejpam-6635	40	3	.	.	X
ejpam-6635	41	1	the	the	DET
ejpam-6635	41	2	set	set	ADJ
ejpam-6635	41	3	n2	n2	ADJ
ejpam-6635	41	4	g(u	g(u	PROPN
ejpam-6635	41	5	)	)	PUNCT
ejpam-6635	41	6	=	=	PRON
ejpam-6635	41	7	{	{	PUNCT
ejpam-6635	41	8	v	v	NUM
ejpam-6635	41	9	∈	∈	NOUN
ejpam-6635	41	10	v	v	NOUN
ejpam-6635	41	11	(	(	PUNCT
ejpam-6635	41	12	g	g	NOUN
ejpam-6635	41	13	)	)	PUNCT
ejpam-6635	41	14	:	:	PUNCT
ejpam-6635	41	15	dg(v	dg(v	X
ejpam-6635	41	16	,	,	PUNCT
ejpam-6635	41	17	u	u	NOUN
ejpam-6635	41	18	)	)	PUNCT
ejpam-6635	41	19	=	=	SYM
ejpam-6635	41	20	2	2	X
ejpam-6635	41	21	}	}	PUNCT
ejpam-6635	41	22	is	be	AUX
ejpam-6635	41	23	called	call	VERB
ejpam-6635	41	24	the	the	DET
ejpam-6635	41	25	open	open	ADJ
ejpam-6635	41	26	hop	hop	NOUN
ejpam-6635	41	27	neighborhood	neighborhood	NOUN
ejpam-6635	41	28	of	of	ADP
ejpam-6635	41	29	u.	u.	PROPN
ejpam-6635	41	30	the	the	DET
ejpam-6635	41	31	closed	closed	ADJ
ejpam-6635	41	32	hop	hop	NOUN
ejpam-6635	41	33	neighborhood	neighborhood	NOUN
ejpam-6635	41	34	of	of	ADP
ejpam-6635	41	35	u	u	NOUN
ejpam-6635	41	36	is	be	AUX
ejpam-6635	41	37	given	give	VERB
ejpam-6635	41	38	by	by	ADP
ejpam-6635	41	39	n2	n2	PROPN
ejpam-6635	41	40	g[u	g[u	PROPN
ejpam-6635	41	41	]	]	X
ejpam-6635	41	42	=	=	SYM
ejpam-6635	41	43	n2	n2	ADJ
ejpam-6635	41	44	g(u	g(u	PROPN
ejpam-6635	41	45	)	)	PUNCT
ejpam-6635	41	46	∪	∪	NOUN
ejpam-6635	41	47	{	{	PUNCT
ejpam-6635	41	48	u	u	NOUN
ejpam-6635	41	49	}	}	PUNCT
ejpam-6635	41	50	.	.	PUNCT
ejpam-6635	42	1	the	the	DET
ejpam-6635	42	2	open	open	ADJ
ejpam-6635	42	3	hop	hop	NOUN
ejpam-6635	42	4	neighborhood	neighborhood	NOUN
ejpam-6635	42	5	of	of	ADP
ejpam-6635	42	6	x	x	PROPN
ejpam-6635	42	7	⊆	⊆	NUM
ejpam-6635	42	8	v	v	ADP
ejpam-6635	42	9	(	(	PUNCT
ejpam-6635	42	10	g	g	NOUN
ejpam-6635	42	11	)	)	PUNCT
ejpam-6635	42	12	is	be	AUX
ejpam-6635	42	13	the	the	DET
ejpam-6635	42	14	set	set	ADJ
ejpam-6635	42	15	n2	n2	ADJ
ejpam-6635	42	16	g(x	g(x	NOUN
ejpam-6635	42	17	)	)	PUNCT
ejpam-6635	43	1	=	=	SYM
ejpam-6635	43	2	⋃	⋃	NOUN
ejpam-6635	43	3	u∈x	u∈x	ADJ
ejpam-6635	43	4	n2	n2	NOUN
ejpam-6635	43	5	g(u	g(u	PROPN
ejpam-6635	43	6	)	)	PUNCT
ejpam-6635	43	7	.	.	PUNCT
ejpam-6635	44	1	the	the	DET
ejpam-6635	44	2	closed	closed	ADJ
ejpam-6635	44	3	hop	hop	NOUN
ejpam-6635	44	4	neighborhood	neighborhood	NOUN
ejpam-6635	44	5	of	of	ADP
ejpam-6635	44	6	x	x	SYM
ejpam-6635	44	7	is	be	AUX
ejpam-6635	44	8	the	the	DET
ejpam-6635	44	9	set	set	ADJ
ejpam-6635	44	10	n2	n2	NOUN
ejpam-6635	44	11	g[x	g[x	PROPN
ejpam-6635	44	12	]	]	X
ejpam-6635	44	13	=	=	SYM
ejpam-6635	44	14	n2	n2	PROPN
ejpam-6635	44	15	g(x	g(x	NOUN
ejpam-6635	44	16	)	)	PUNCT
ejpam-6635	44	17	∪x	∪x	VERB
ejpam-6635	44	18	.	.	PUNCT
ejpam-6635	45	1	if	if	SCONJ
ejpam-6635	45	2	s	s	VERB
ejpam-6635	45	3	⊆	⊆	NUM
ejpam-6635	45	4	v	v	NOUN
ejpam-6635	45	5	(	(	PUNCT
ejpam-6635	45	6	g	g	NOUN
ejpam-6635	45	7	)	)	PUNCT
ejpam-6635	45	8	and	and	CCONJ
ejpam-6635	45	9	v	v	ADP
ejpam-6635	45	10	∈	∈	NOUN
ejpam-6635	45	11	s	s	NOUN
ejpam-6635	45	12	,	,	PUNCT
ejpam-6635	45	13	then	then	ADV
ejpam-6635	45	14	a	a	DET
ejpam-6635	45	15	vertex	vertex	NOUN
ejpam-6635	45	16	w	w	NOUN
ejpam-6635	45	17	∈	∈	PROPN
ejpam-6635	45	18	v	v	ADP
ejpam-6635	45	19	(	(	PUNCT
ejpam-6635	45	20	g	g	NOUN
ejpam-6635	45	21	)	)	PUNCT
ejpam-6635	45	22	\	\	PROPN
ejpam-6635	46	1	s	s	PART
ejpam-6635	46	2	is	be	AUX
ejpam-6635	46	3	an	an	DET
ejpam-6635	46	4	external	external	ADJ
ejpam-6635	46	5	private	private	ADJ
ejpam-6635	46	6	hop	hop	NOUN
ejpam-6635	46	7	neighbor	neighbor	NOUN
ejpam-6635	46	8	of	of	ADP
ejpam-6635	46	9	v	v	NOUN
ejpam-6635	46	10	if	if	SCONJ
ejpam-6635	46	11	n2	n2	ADJ
ejpam-6635	46	12	g(w	g(w	PROPN
ejpam-6635	46	13	)	)	PUNCT
ejpam-6635	46	14	∩	∩	NOUN
ejpam-6635	46	15	s	s	PART
ejpam-6635	46	16	=	=	PUNCT
ejpam-6635	46	17	{	{	PUNCT
ejpam-6635	46	18	v	v	NOUN
ejpam-6635	46	19	}	}	PUNCT
ejpam-6635	46	20	.	.	PUNCT
ejpam-6635	47	1	the	the	DET
ejpam-6635	47	2	set	set	NOUN
ejpam-6635	47	3	containing	contain	VERB
ejpam-6635	47	4	all	all	DET
ejpam-6635	47	5	the	the	DET
ejpam-6635	47	6	external	external	ADJ
ejpam-6635	47	7	private	private	ADJ
ejpam-6635	47	8	hop	hop	NOUN
ejpam-6635	47	9	neighbors	neighbor	NOUN
ejpam-6635	47	10	of	of	ADP
ejpam-6635	47	11	v	v	NOUN
ejpam-6635	47	12	with	with	ADP
ejpam-6635	47	13	respect	respect	NOUN
ejpam-6635	47	14	to	to	ADP
ejpam-6635	47	15	s	s	PRON
ejpam-6635	47	16	is	be	AUX
ejpam-6635	47	17	denoted	denote	VERB
ejpam-6635	47	18	by	by	ADP
ejpam-6635	47	19	ephn(v;s	ephn(v;s	NOUN
ejpam-6635	47	20	)	)	PUNCT
ejpam-6635	47	21	.	.	PUNCT
ejpam-6635	48	1	a	a	DET
ejpam-6635	48	2	set	set	NOUN
ejpam-6635	48	3	s	s	NOUN
ejpam-6635	48	4	⊆	⊆	NUM
ejpam-6635	48	5	v	v	NOUN
ejpam-6635	48	6	(	(	PUNCT
ejpam-6635	48	7	g	g	NOUN
ejpam-6635	48	8	)	)	PUNCT
ejpam-6635	48	9	is	be	AUX
ejpam-6635	48	10	a	a	DET
ejpam-6635	48	11	hop	hop	NOUN
ejpam-6635	48	12	dominating	dominating	NOUN
ejpam-6635	48	13	set	set	VERB
ejpam-6635	48	14	in	in	ADP
ejpam-6635	48	15	g	g	PROPN
ejpam-6635	48	16	if	if	SCONJ
ejpam-6635	48	17	n2	n2	ADJ
ejpam-6635	48	18	g[s	g[s	PROPN
ejpam-6635	48	19	]	]	X
ejpam-6635	48	20	=	=	SYM
ejpam-6635	48	21	v	v	NOUN
ejpam-6635	48	22	(	(	PUNCT
ejpam-6635	48	23	g	g	NOUN
ejpam-6635	48	24	)	)	PUNCT
ejpam-6635	48	25	,	,	PUNCT
ejpam-6635	48	26	that	that	ADV
ejpam-6635	48	27	is	is	ADV
ejpam-6635	48	28	,	,	PUNCT
ejpam-6635	48	29	for	for	ADP
ejpam-6635	48	30	every	every	DET
ejpam-6635	48	31	v	v	NUM
ejpam-6635	48	32	∈	∈	NOUN
ejpam-6635	48	33	v	v	NOUN
ejpam-6635	48	34	(	(	PUNCT
ejpam-6635	48	35	g)\s	g)\s	NOUN
ejpam-6635	48	36	,	,	PUNCT
ejpam-6635	48	37	there	there	PRON
ejpam-6635	48	38	exists	exist	VERB
ejpam-6635	48	39	u	u	PROPN
ejpam-6635	48	40	∈	∈	PROPN
ejpam-6635	48	41	s	s	VERB
ejpam-6635	48	42	such	such	ADJ
ejpam-6635	48	43	that	that	DET
ejpam-6635	48	44	dg(u	dg(u	ADJ
ejpam-6635	48	45	,	,	PUNCT
ejpam-6635	48	46	v	v	NOUN
ejpam-6635	48	47	)	)	PUNCT
ejpam-6635	49	1	=	=	SYM
ejpam-6635	49	2	2	2	X
ejpam-6635	49	3	.	.	PUNCT
ejpam-6635	50	1	the	the	DET
ejpam-6635	50	2	minimum	minimum	ADJ
ejpam-6635	50	3	cardinality	cardinality	NOUN
ejpam-6635	50	4	among	among	ADP
ejpam-6635	50	5	all	all	DET
ejpam-6635	50	6	hop	hop	NOUN
ejpam-6635	50	7	dominating	dominating	NOUN
ejpam-6635	50	8	sets	set	NOUN
ejpam-6635	50	9	in	in	ADP
ejpam-6635	50	10	g	g	NOUN
ejpam-6635	50	11	,	,	PUNCT
ejpam-6635	50	12	denoted	denote	VERB
ejpam-6635	50	13	by	by	ADP
ejpam-6635	50	14	γh(g	γh(g	NOUN
ejpam-6635	50	15	)	)	PUNCT
ejpam-6635	50	16	,	,	PUNCT
ejpam-6635	50	17	is	be	AUX
ejpam-6635	50	18	called	call	VERB
ejpam-6635	50	19	the	the	DET
ejpam-6635	50	20	hop	hop	NOUN
ejpam-6635	50	21	domination	domination	NOUN
ejpam-6635	50	22	number	number	NOUN
ejpam-6635	50	23	of	of	ADP
ejpam-6635	50	24	g.	g.	PROPN
ejpam-6635	50	25	any	any	DET
ejpam-6635	50	26	hop	hop	NOUN
ejpam-6635	50	27	dominating	dominating	NOUN
ejpam-6635	50	28	set	set	VERB
ejpam-6635	50	29	with	with	ADP
ejpam-6635	50	30	cardinality	cardinality	NOUN
ejpam-6635	50	31	equal	equal	ADJ
ejpam-6635	50	32	to	to	ADP
ejpam-6635	50	33	γh(g	γh(g	NOUN
ejpam-6635	50	34	)	)	PUNCT
ejpam-6635	50	35	is	be	AUX
ejpam-6635	50	36	called	call	VERB
ejpam-6635	50	37	a	a	DET
ejpam-6635	50	38	γh	γh	ADV
ejpam-6635	50	39	-	-	PUNCT
ejpam-6635	50	40	set	set	NOUN
ejpam-6635	50	41	.	.	PUNCT
ejpam-6635	51	1	a	a	DET
ejpam-6635	51	2	set	set	NOUN
ejpam-6635	51	3	s	s	NOUN
ejpam-6635	51	4	⊆	⊆	NUM
ejpam-6635	51	5	v	v	NOUN
ejpam-6635	51	6	(	(	PUNCT
ejpam-6635	51	7	g	g	NOUN
ejpam-6635	51	8	)	)	PUNCT
ejpam-6635	51	9	is	be	AUX
ejpam-6635	51	10	a	a	DET
ejpam-6635	51	11	pointwise	pointwise	ADJ
ejpam-6635	51	12	non	non	ADJ
ejpam-6635	51	13	-	-	ADJ
ejpam-6635	51	14	dominating	dominating	ADJ
ejpam-6635	51	15	set	set	NOUN
ejpam-6635	51	16	of	of	ADP
ejpam-6635	51	17	g	g	PROPN
ejpam-6635	51	18	if	if	SCONJ
ejpam-6635	51	19	for	for	ADP
ejpam-6635	51	20	each	each	DET
ejpam-6635	51	21	v	v	NUM
ejpam-6635	51	22	∈	∈	PROPN
ejpam-6635	51	23	v	v	NOUN
ejpam-6635	51	24	(	(	PUNCT
ejpam-6635	51	25	g	g	NOUN
ejpam-6635	51	26	)	)	PUNCT
ejpam-6635	51	27	\s	\	NOUN
ejpam-6635	51	28	,	,	PUNCT
ejpam-6635	51	29	there	there	PRON
ejpam-6635	51	30	exists	exist	VERB
ejpam-6635	51	31	u	u	PROPN
ejpam-6635	51	32	∈	∈	PROPN
ejpam-6635	51	33	s	s	VERB
ejpam-6635	51	34	such	such	ADJ
ejpam-6635	51	35	that	that	DET
ejpam-6635	51	36	v	v	NOUN
ejpam-6635	51	37	/∈	/∈	PUNCT
ejpam-6635	51	38	ng(u	ng(u	NOUN
ejpam-6635	51	39	)	)	PUNCT
ejpam-6635	51	40	.	.	PUNCT
ejpam-6635	52	1	the	the	DET
ejpam-6635	52	2	smallest	small	ADJ
ejpam-6635	52	3	cardinality	cardinality	NOUN
ejpam-6635	52	4	of	of	ADP
ejpam-6635	52	5	a	a	DET
ejpam-6635	52	6	pointwise	pointwise	ADJ
ejpam-6635	52	7	non	non	ADJ
ejpam-6635	52	8	-	-	ADJ
ejpam-6635	52	9	dominating	dominating	ADJ
ejpam-6635	52	10	set	set	NOUN
ejpam-6635	52	11	of	of	ADP
ejpam-6635	52	12	g	g	NOUN
ejpam-6635	52	13	,	,	PUNCT
ejpam-6635	52	14	denoted	denote	VERB
ejpam-6635	52	15	pnd(g	pnd(g	ADP
ejpam-6635	52	16	)	)	PUNCT
ejpam-6635	52	17	,	,	PUNCT
ejpam-6635	52	18	is	be	AUX
ejpam-6635	52	19	called	call	VERB
ejpam-6635	52	20	the	the	DET
ejpam-6635	52	21	pointwise	pointwise	ADJ
ejpam-6635	52	22	non	non	ADJ
ejpam-6635	52	23	-	-	ADJ
ejpam-6635	52	24	domination	domination	ADJ
ejpam-6635	52	25	number	number	NOUN
ejpam-6635	52	26	of	of	ADP
ejpam-6635	52	27	g.	g.	PROPN
ejpam-6635	52	28	a	a	DET
ejpam-6635	52	29	pointwise	pointwise	ADJ
ejpam-6635	52	30	non	non	ADJ
ejpam-6635	52	31	-	-	ADJ
ejpam-6635	52	32	dominating	dominating	ADJ
ejpam-6635	52	33	set	set	NOUN
ejpam-6635	52	34	s	s	VERB
ejpam-6635	52	35	is	be	AUX
ejpam-6635	52	36	a	a	DET
ejpam-6635	52	37	secure	secure	ADJ
ejpam-6635	52	38	pointwise	pointwise	ADJ
ejpam-6635	52	39	non	non	ADJ
ejpam-6635	52	40	-	-	ADJ
ejpam-6635	52	41	dominating	dominating	ADJ
ejpam-6635	52	42	set	set	NOUN
ejpam-6635	52	43	if	if	SCONJ
ejpam-6635	52	44	for	for	ADP
ejpam-6635	52	45	every	every	DET
ejpam-6635	52	46	u	u	PROPN
ejpam-6635	52	47	∈	∈	PROPN
ejpam-6635	52	48	v	v	ADP
ejpam-6635	52	49	(	(	PUNCT
ejpam-6635	52	50	g	g	NOUN
ejpam-6635	52	51	)	)	PUNCT
ejpam-6635	52	52	\	\	PROPN
ejpam-6635	53	1	s	s	X
ejpam-6635	53	2	,	,	PUNCT
ejpam-6635	53	3	there	there	PRON
ejpam-6635	53	4	exists	exist	VERB
ejpam-6635	53	5	v	v	ADP
ejpam-6635	53	6	∈	∈	PROPN
ejpam-6635	53	7	s	s	PART
ejpam-6635	53	8	\	\	NOUN
ejpam-6635	53	9	ng(u	ng(u	NOUN
ejpam-6635	53	10	)	)	PUNCT
ejpam-6635	53	11	such	such	ADJ
ejpam-6635	53	12	that	that	SCONJ
ejpam-6635	53	13	(	(	PUNCT
ejpam-6635	53	14	s	s	NOUN
ejpam-6635	53	15	\	\	X
ejpam-6635	53	16	{	{	PUNCT
ejpam-6635	53	17	v	v	NOUN
ejpam-6635	53	18	}	}	PUNCT
ejpam-6635	53	19	)	)	PUNCT
ejpam-6635	53	20	∪	∪	ADP
ejpam-6635	53	21	{	{	PUNCT
ejpam-6635	53	22	u	u	NOUN
ejpam-6635	53	23	}	}	PUNCT
ejpam-6635	53	24	is	be	AUX
ejpam-6635	53	25	a	a	DET
ejpam-6635	53	26	pointwise	pointwise	ADJ
ejpam-6635	53	27	nondominating	nondominate	VERB
ejpam-6635	53	28	set	set	NOUN
ejpam-6635	53	29	.	.	PUNCT
ejpam-6635	54	1	the	the	DET
ejpam-6635	54	2	secure	secure	ADJ
ejpam-6635	54	3	pointwise	pointwise	PROPN
ejpam-6635	54	4	non	non	ADJ
ejpam-6635	54	5	-	-	ADJ
ejpam-6635	54	6	domination	domination	ADJ
ejpam-6635	54	7	number	number	NOUN
ejpam-6635	54	8	spnd(g	spnd(g	PROPN
ejpam-6635	54	9	)	)	PUNCT
ejpam-6635	54	10	ofg	ofg	PROPN
ejpam-6635	54	11	is	be	AUX
ejpam-6635	54	12	the	the	DET
ejpam-6635	54	13	smallest	small	ADJ
ejpam-6635	54	14	cardinality	cardinality	NOUN
ejpam-6635	54	15	of	of	ADP
ejpam-6635	54	16	a	a	DET
ejpam-6635	54	17	secure	secure	ADJ
ejpam-6635	54	18	pointwise	pointwise	ADJ
ejpam-6635	54	19	non	non	ADJ
ejpam-6635	54	20	-	-	ADJ
ejpam-6635	54	21	dominating	dominating	ADJ
ejpam-6635	54	22	set	set	NOUN
ejpam-6635	54	23	in	in	ADP
ejpam-6635	54	24	g.	g.	PROPN
ejpam-6635	54	25	a	a	DET
ejpam-6635	54	26	pointwise	pointwise	ADJ
ejpam-6635	54	27	(	(	PUNCT
ejpam-6635	54	28	secure	secure	VERB
ejpam-6635	54	29	pointwise	pointwise	PROPN
ejpam-6635	54	30	non	non	ADJ
ejpam-6635	54	31	-	-	ADJ
ejpam-6635	54	32	dominating	dominating	ADJ
ejpam-6635	54	33	)	)	PUNCT
ejpam-6635	54	34	set	set	VERB
ejpam-6635	54	35	in	in	ADP
ejpam-6635	54	36	g	g	NOUN
ejpam-6635	54	37	having	have	VERB
ejpam-6635	54	38	cardinality	cardinality	NOUN
ejpam-6635	54	39	equal	equal	ADJ
ejpam-6635	54	40	to	to	ADP
ejpam-6635	54	41	pnd(g	pnd(g	PROPN
ejpam-6635	54	42	)	)	PUNCT
ejpam-6635	54	43	(	(	PUNCT
ejpam-6635	54	44	resp	resp	NOUN
ejpam-6635	54	45	.	.	PUNCT
ejpam-6635	55	1	spnd(g	spnd(g	PROPN
ejpam-6635	55	2	)	)	PUNCT
ejpam-6635	55	3	)	)	PUNCT
ejpam-6635	55	4	is	be	AUX
ejpam-6635	55	5	called	call	VERB
ejpam-6635	55	6	a	a	DET
ejpam-6635	55	7	f.	f.	PROPN
ejpam-6635	55	8	alfeche	alfeche	PROPN
ejpam-6635	55	9	,	,	PUNCT
ejpam-6635	55	10	s.	s.	PROPN
ejpam-6635	55	11	canoy	canoy	PROPN
ejpam-6635	55	12	jr	jr	PROPN
ejpam-6635	55	13	.	.	PROPN
ejpam-6635	55	14	/	/	SYM
ejpam-6635	55	15	eur	eur	PROPN
ejpam-6635	55	16	.	.	PUNCT
ejpam-6635	56	1	j.	j.	PROPN
ejpam-6635	56	2	pure	pure	PROPN
ejpam-6635	56	3	appl	appl	PROPN
ejpam-6635	56	4	.	.	PROPN
ejpam-6635	56	5	math	math	PROPN
ejpam-6635	56	6	,	,	PUNCT
ejpam-6635	56	7	18	18	NUM
ejpam-6635	56	8	(	(	PUNCT
ejpam-6635	56	9	3	3	NUM
ejpam-6635	56	10	)	)	PUNCT
ejpam-6635	56	11	(	(	PUNCT
ejpam-6635	56	12	2025	2025	NUM
ejpam-6635	56	13	)	)	PUNCT
ejpam-6635	56	14	,	,	PUNCT
ejpam-6635	56	15	6635	6635	NUM
ejpam-6635	56	16	3	3	NUM
ejpam-6635	56	17	of	of	ADP
ejpam-6635	56	18	11	11	NUM
ejpam-6635	56	19	pnd	pnd	NOUN
ejpam-6635	56	20	-	-	PUNCT
ejpam-6635	56	21	set	set	VERB
ejpam-6635	56	22	(	(	PUNCT
ejpam-6635	56	23	resp	resp	NOUN
ejpam-6635	56	24	.	.	PUNCT
ejpam-6635	57	1	spnd	spnd	NOUN
ejpam-6635	57	2	-	-	PUNCT
ejpam-6635	57	3	set	set	NOUN
ejpam-6635	57	4	)	)	PUNCT
ejpam-6635	57	5	in	in	ADP
ejpam-6635	57	6	g.	g.	PROPN
ejpam-6635	57	7	a	a	DET
ejpam-6635	57	8	hop	hop	NOUN
ejpam-6635	57	9	dominating	dominating	NOUN
ejpam-6635	57	10	set	set	NOUN
ejpam-6635	57	11	s	s	VERB
ejpam-6635	57	12	is	be	AUX
ejpam-6635	57	13	secure	secure	ADJ
ejpam-6635	57	14	hop	hop	NOUN
ejpam-6635	57	15	dominating	dominate	VERB
ejpam-6635	57	16	if	if	SCONJ
ejpam-6635	57	17	for	for	ADP
ejpam-6635	57	18	each	each	DET
ejpam-6635	57	19	v	v	NUM
ejpam-6635	57	20	∈	∈	NOUN
ejpam-6635	57	21	v	v	NOUN
ejpam-6635	57	22	(	(	PUNCT
ejpam-6635	57	23	g)\s	g)\s	NOUN
ejpam-6635	57	24	,	,	PUNCT
ejpam-6635	57	25	there	there	PRON
ejpam-6635	57	26	exists	exist	VERB
ejpam-6635	57	27	w	w	PROPN
ejpam-6635	57	28	∈	∈	PROPN
ejpam-6635	57	29	s	s	PART
ejpam-6635	57	30	∩	∩	ADJ
ejpam-6635	57	31	n2	n2	ADJ
ejpam-6635	57	32	g(v	g(v	PROPN
ejpam-6635	57	33	)	)	PUNCT
ejpam-6635	57	34	such	such	ADJ
ejpam-6635	57	35	that	that	SCONJ
ejpam-6635	57	36	(	(	PUNCT
ejpam-6635	57	37	s	s	NOUN
ejpam-6635	57	38	\	\	X
ejpam-6635	57	39	{	{	PUNCT
ejpam-6635	57	40	w	w	NOUN
ejpam-6635	57	41	}	}	PUNCT
ejpam-6635	57	42	)	)	PUNCT
ejpam-6635	57	43	∪	∪	ADP
ejpam-6635	57	44	{	{	PUNCT
ejpam-6635	57	45	v	v	NOUN
ejpam-6635	57	46	}	}	PUNCT
ejpam-6635	57	47	is	be	AUX
ejpam-6635	57	48	a	a	DET
ejpam-6635	57	49	hop	hop	NOUN
ejpam-6635	57	50	dominating	dominating	NOUN
ejpam-6635	57	51	set	set	VERB
ejpam-6635	57	52	in	in	ADP
ejpam-6635	57	53	g.	g.	PROPN
ejpam-6635	57	54	the	the	DET
ejpam-6635	57	55	minimum	minimum	ADJ
ejpam-6635	57	56	cardinality	cardinality	NOUN
ejpam-6635	57	57	among	among	ADP
ejpam-6635	57	58	all	all	DET
ejpam-6635	57	59	secure	secure	ADJ
ejpam-6635	57	60	hop	hop	NOUN
ejpam-6635	57	61	dominating	dominating	NOUN
ejpam-6635	57	62	sets	set	NOUN
ejpam-6635	57	63	of	of	ADP
ejpam-6635	57	64	g	g	NOUN
ejpam-6635	57	65	,	,	PUNCT
ejpam-6635	57	66	denoted	denote	VERB
ejpam-6635	57	67	by	by	ADP
ejpam-6635	57	68	γsh(g	γsh(g	NOUN
ejpam-6635	57	69	)	)	PUNCT
ejpam-6635	57	70	,	,	PUNCT
ejpam-6635	57	71	is	be	AUX
ejpam-6635	57	72	called	call	VERB
ejpam-6635	57	73	the	the	DET
ejpam-6635	57	74	secure	secure	ADJ
ejpam-6635	57	75	hop	hop	NOUN
ejpam-6635	57	76	domination	domination	NOUN
ejpam-6635	57	77	number	number	NOUN
ejpam-6635	57	78	of	of	ADP
ejpam-6635	57	79	g.	g.	PROPN
ejpam-6635	57	80	any	any	DET
ejpam-6635	57	81	secure	secure	ADJ
ejpam-6635	57	82	hop	hop	NOUN
ejpam-6635	57	83	dominating	dominating	NOUN
ejpam-6635	57	84	set	set	VERB
ejpam-6635	57	85	with	with	ADP
ejpam-6635	57	86	cardinality	cardinality	NOUN
ejpam-6635	57	87	equal	equal	ADJ
ejpam-6635	57	88	to	to	ADP
ejpam-6635	57	89	γsh(g	γsh(g	NOUN
ejpam-6635	57	90	)	)	PUNCT
ejpam-6635	57	91	is	be	AUX
ejpam-6635	57	92	called	call	VERB
ejpam-6635	57	93	a	a	DET
ejpam-6635	57	94	γsh	γsh	NOUN
ejpam-6635	57	95	-	-	PUNCT
ejpam-6635	57	96	set	set	NOUN
ejpam-6635	57	97	.	.	PUNCT
ejpam-6635	58	1	the	the	DET
ejpam-6635	58	2	join	join	NOUN
ejpam-6635	58	3	of	of	ADP
ejpam-6635	58	4	graphs	graph	NOUN
ejpam-6635	58	5	g1	g1	PROPN
ejpam-6635	58	6	and	and	CCONJ
ejpam-6635	58	7	g2	g2	PROPN
ejpam-6635	58	8	,	,	PUNCT
ejpam-6635	58	9	denoted	denote	VERB
ejpam-6635	58	10	g1	g1	PROPN
ejpam-6635	58	11	+	+	CCONJ
ejpam-6635	58	12	g2	g2	PROPN
ejpam-6635	58	13	,	,	PUNCT
ejpam-6635	58	14	is	be	AUX
ejpam-6635	58	15	the	the	DET
ejpam-6635	58	16	graph	graph	NOUN
ejpam-6635	58	17	with	with	ADP
ejpam-6635	58	18	v	v	NOUN
ejpam-6635	58	19	(	(	PUNCT
ejpam-6635	58	20	g1	g1	PROPN
ejpam-6635	58	21	+	+	PROPN
ejpam-6635	58	22	g2	g2	PROPN
ejpam-6635	58	23	)	)	PUNCT
ejpam-6635	59	1	=	=	SYM
ejpam-6635	59	2	v	v	X
ejpam-6635	59	3	(	(	PUNCT
ejpam-6635	59	4	g1	g1	PROPN
ejpam-6635	59	5	)	)	PUNCT
ejpam-6635	59	6	∪	∪	NOUN
ejpam-6635	59	7	v	v	PROPN
ejpam-6635	59	8	(	(	PUNCT
ejpam-6635	59	9	g2	g2	PROPN
ejpam-6635	59	10	)	)	PUNCT
ejpam-6635	59	11	and	and	CCONJ
ejpam-6635	59	12	e(g1	e(g1	ADJ
ejpam-6635	59	13	+	+	X
ejpam-6635	59	14	g2	g2	NOUN
ejpam-6635	59	15	)	)	PUNCT
ejpam-6635	59	16	=	=	SYM
ejpam-6635	59	17	e(g1	e(g1	ADJ
ejpam-6635	59	18	)	)	PUNCT
ejpam-6635	59	19	∪	∪	ADP
ejpam-6635	59	20	e(g2	e(g2	ADV
ejpam-6635	59	21	)	)	PUNCT
ejpam-6635	59	22	∪	∪	NOUN
ejpam-6635	59	23	{	{	PUNCT
ejpam-6635	59	24	uv	uv	NOUN
ejpam-6635	59	25	:	:	PUNCT
ejpam-6635	59	26	u	u	PROPN
ejpam-6635	59	27	∈	∈	PROPN
ejpam-6635	59	28	v	v	NOUN
ejpam-6635	59	29	(	(	PUNCT
ejpam-6635	59	30	g1	g1	PROPN
ejpam-6635	59	31	)	)	PUNCT
ejpam-6635	59	32	and	and	CCONJ
ejpam-6635	59	33	v	v	ADP
ejpam-6635	59	34	∈	∈	PROPN
ejpam-6635	59	35	v	v	NOUN
ejpam-6635	59	36	(	(	PUNCT
ejpam-6635	59	37	g2	g2	PROPN
ejpam-6635	59	38	)	)	PUNCT
ejpam-6635	59	39	}	}	PUNCT
ejpam-6635	59	40	.	.	PUNCT
ejpam-6635	60	1	for	for	ADP
ejpam-6635	60	2	other	other	ADJ
ejpam-6635	60	3	graph	graph	NOUN
ejpam-6635	60	4	theoretic	theoretic	ADJ
ejpam-6635	60	5	terms	term	NOUN
ejpam-6635	60	6	not	not	PART
ejpam-6635	60	7	mentioned	mention	VERB
ejpam-6635	60	8	here	here	ADV
ejpam-6635	60	9	,	,	PUNCT
ejpam-6635	60	10	readers	reader	NOUN
ejpam-6635	60	11	may	may	AUX
ejpam-6635	60	12	refer	refer	VERB
ejpam-6635	60	13	to	to	ADP
ejpam-6635	60	14	[	[	X
ejpam-6635	60	15	19	19	NUM
ejpam-6635	60	16	]	]	PUNCT
ejpam-6635	60	17	and	and	CCONJ
ejpam-6635	60	18	[	[	X
ejpam-6635	60	19	20	20	NUM
ejpam-6635	60	20	]	]	PUNCT
ejpam-6635	60	21	.	.	PUNCT
ejpam-6635	61	1	3	3	X
ejpam-6635	61	2	.	.	X
ejpam-6635	61	3	results	result	NOUN
ejpam-6635	61	4	we	we	PRON
ejpam-6635	61	5	shall	shall	AUX
ejpam-6635	61	6	need	need	VERB
ejpam-6635	61	7	the	the	DET
ejpam-6635	61	8	following	follow	VERB
ejpam-6635	61	9	results	result	NOUN
ejpam-6635	61	10	.	.	PUNCT
ejpam-6635	62	1	theorem	theorem	NOUN
ejpam-6635	62	2	1	1	NUM
ejpam-6635	62	3	.	.	PUNCT
ejpam-6635	63	1	[	[	X
ejpam-6635	63	2	2	2	NUM
ejpam-6635	63	3	]	]	PUNCT
ejpam-6635	63	4	γsh(kn	γsh(kn	NUM
ejpam-6635	63	5	)	)	PUNCT
ejpam-6635	63	6	=	=	SYM
ejpam-6635	63	7	γsh(kn	γsh(kn	NOUN
ejpam-6635	63	8	)	)	PUNCT
ejpam-6635	63	9	=	=	SYM
ejpam-6635	64	1	n	n	CCONJ
ejpam-6635	64	2	for	for	ADP
ejpam-6635	64	3	every	every	DET
ejpam-6635	64	4	positive	positive	ADJ
ejpam-6635	64	5	integer	integer	NOUN
ejpam-6635	64	6	n.	n.	NOUN
ejpam-6635	64	7	theorem	theorem	VERB
ejpam-6635	64	8	2	2	NUM
ejpam-6635	64	9	.	.	PUNCT
ejpam-6635	65	1	[	[	X
ejpam-6635	65	2	21	21	NUM
ejpam-6635	65	3	]	]	PUNCT
ejpam-6635	65	4	let	let	VERB
ejpam-6635	65	5	g	g	PRON
ejpam-6635	65	6	be	be	AUX
ejpam-6635	65	7	a	a	DET
ejpam-6635	65	8	graph	graph	NOUN
ejpam-6635	65	9	of	of	ADP
ejpam-6635	65	10	order	order	NOUN
ejpam-6635	65	11	n.	n.	NOUN
ejpam-6635	65	12	then	then	ADV
ejpam-6635	65	13	each	each	PRON
ejpam-6635	65	14	of	of	ADP
ejpam-6635	65	15	the	the	DET
ejpam-6635	65	16	following	follow	VERB
ejpam-6635	65	17	holds	hold	VERB
ejpam-6635	65	18	:	:	PUNCT
ejpam-6635	65	19	(	(	PUNCT
ejpam-6635	65	20	i	i	NOUN
ejpam-6635	65	21	)	)	PUNCT
ejpam-6635	65	22	pnd(g	pnd(g	PROPN
ejpam-6635	65	23	)	)	PUNCT
ejpam-6635	65	24	=	=	SYM
ejpam-6635	65	25	1	1	NUM
ejpam-6635	65	26	if	if	SCONJ
ejpam-6635	65	27	and	and	CCONJ
ejpam-6635	65	28	only	only	ADV
ejpam-6635	65	29	if	if	SCONJ
ejpam-6635	65	30	g	g	PROPN
ejpam-6635	65	31	has	have	VERB
ejpam-6635	65	32	an	an	DET
ejpam-6635	65	33	isolated	isolated	ADJ
ejpam-6635	65	34	vertex	vertex	NOUN
ejpam-6635	65	35	.	.	PUNCT
ejpam-6635	66	1	(	(	PUNCT
ejpam-6635	66	2	ii	ii	NOUN
ejpam-6635	66	3	)	)	PUNCT
ejpam-6635	66	4	pnd(g	pnd(g	PROPN
ejpam-6635	66	5	)	)	PUNCT
ejpam-6635	66	6	=	=	SYM
ejpam-6635	67	1	n	n	NOUN
ejpam-6635	67	2	if	if	SCONJ
ejpam-6635	67	3	and	and	CCONJ
ejpam-6635	67	4	only	only	ADV
ejpam-6635	67	5	if	if	SCONJ
ejpam-6635	67	6	g	g	PROPN
ejpam-6635	67	7	=	=	PROPN
ejpam-6635	67	8	kn	kn	PROPN
ejpam-6635	67	9	.	.	PUNCT
ejpam-6635	68	1	it	it	PRON
ejpam-6635	68	2	should	should	AUX
ejpam-6635	68	3	be	be	AUX
ejpam-6635	68	4	noted	note	VERB
ejpam-6635	68	5	that	that	SCONJ
ejpam-6635	68	6	every	every	DET
ejpam-6635	68	7	graph	graph	NOUN
ejpam-6635	68	8	admits	admit	VERB
ejpam-6635	68	9	a	a	DET
ejpam-6635	68	10	secure	secure	ADJ
ejpam-6635	68	11	pointwise	pointwise	ADJ
ejpam-6635	68	12	non	non	ADJ
ejpam-6635	68	13	-	-	ADJ
ejpam-6635	68	14	dominating	dominating	ADJ
ejpam-6635	68	15	sets	set	NOUN
ejpam-6635	68	16	.	.	PUNCT
ejpam-6635	69	1	theorem	theorem	NOUN
ejpam-6635	69	2	3	3	X
ejpam-6635	69	3	.	.	PUNCT
ejpam-6635	70	1	let	let	VERB
ejpam-6635	70	2	g	g	PRON
ejpam-6635	70	3	be	be	AUX
ejpam-6635	70	4	a	a	DET
ejpam-6635	70	5	graph	graph	NOUN
ejpam-6635	70	6	of	of	ADP
ejpam-6635	70	7	order	order	NOUN
ejpam-6635	70	8	n.	n.	NOUN
ejpam-6635	70	9	then	then	ADV
ejpam-6635	71	1	1	1	NUM
ejpam-6635	71	2	≤	≤	NUM
ejpam-6635	71	3	pnd(g	pnd(g	ADP
ejpam-6635	71	4	)	)	PUNCT
ejpam-6635	71	5	≤	≤	NOUN
ejpam-6635	71	6	spnd(g	spnd(g	PROPN
ejpam-6635	71	7	)	)	PUNCT
ejpam-6635	71	8	≤	≤	PROPN
ejpam-6635	71	9	n.	n.	NOUN
ejpam-6635	71	10	moreover	moreover	ADV
ejpam-6635	71	11	,	,	PUNCT
ejpam-6635	71	12	each	each	PRON
ejpam-6635	71	13	of	of	ADP
ejpam-6635	71	14	the	the	DET
ejpam-6635	71	15	following	following	ADJ
ejpam-6635	71	16	statements	statement	NOUN
ejpam-6635	71	17	holds	hold	VERB
ejpam-6635	71	18	.	.	PUNCT
ejpam-6635	72	1	(	(	PUNCT
ejpam-6635	72	2	i	i	NOUN
ejpam-6635	72	3	)	)	PUNCT
ejpam-6635	72	4	spnd(g	spnd(g	PROPN
ejpam-6635	72	5	)	)	PUNCT
ejpam-6635	72	6	=	=	SYM
ejpam-6635	72	7	1	1	NUM
ejpam-6635	72	8	if	if	SCONJ
ejpam-6635	72	9	and	and	CCONJ
ejpam-6635	72	10	only	only	ADV
ejpam-6635	72	11	if	if	SCONJ
ejpam-6635	72	12	g	g	PROPN
ejpam-6635	72	13	=	=	PROPN
ejpam-6635	72	14	kn	kn	PROPN
ejpam-6635	72	15	.	.	PUNCT
ejpam-6635	72	16	(	(	PUNCT
ejpam-6635	72	17	ii	ii	NOUN
ejpam-6635	72	18	)	)	PUNCT
ejpam-6635	72	19	spnd(g	spnd(g	PROPN
ejpam-6635	72	20	)	)	PUNCT
ejpam-6635	72	21	=	=	SYM
ejpam-6635	72	22	2	2	NUM
ejpam-6635	72	23	if	if	SCONJ
ejpam-6635	72	24	and	and	CCONJ
ejpam-6635	72	25	only	only	ADV
ejpam-6635	72	26	if	if	SCONJ
ejpam-6635	72	27	the	the	DET
ejpam-6635	72	28	following	follow	VERB
ejpam-6635	72	29	conditions	condition	NOUN
ejpam-6635	72	30	hold	hold	VERB
ejpam-6635	72	31	:	:	PUNCT
ejpam-6635	72	32	(	(	PUNCT
ejpam-6635	72	33	j1	j1	PROPN
ejpam-6635	72	34	)	)	PUNCT
ejpam-6635	72	35	g	g	PROPN
ejpam-6635	72	36	̸=	̸=	PROPN
ejpam-6635	72	37	kn	kn	PROPN
ejpam-6635	72	38	;	;	PUNCT
ejpam-6635	72	39	(	(	PUNCT
ejpam-6635	72	40	j2	j2	PROPN
ejpam-6635	72	41	)	)	PUNCT
ejpam-6635	72	42	there	there	PRON
ejpam-6635	72	43	exist	exist	VERB
ejpam-6635	72	44	distinct	distinct	ADJ
ejpam-6635	72	45	vertices	vertex	NOUN
ejpam-6635	72	46	p	p	NOUN
ejpam-6635	72	47	,	,	PUNCT
ejpam-6635	72	48	q	q	X
ejpam-6635	72	49	such	such	ADJ
ejpam-6635	72	50	that	that	SCONJ
ejpam-6635	72	51	ng(p	ng(p	VERB
ejpam-6635	72	52	)	)	PUNCT
ejpam-6635	72	53	∩ng(q	∩ng(q	PROPN
ejpam-6635	72	54	)	)	PUNCT
ejpam-6635	72	55	=	=	NOUN
ejpam-6635	72	56	∅	∅	NOUN
ejpam-6635	72	57	;	;	PUNCT
ejpam-6635	72	58	and	and	CCONJ
ejpam-6635	72	59	(	(	PUNCT
ejpam-6635	72	60	j3	j3	PROPN
ejpam-6635	72	61	)	)	PUNCT
ejpam-6635	72	62	for	for	ADP
ejpam-6635	72	63	each	each	DET
ejpam-6635	72	64	x	x	SYM
ejpam-6635	72	65	∈	∈	PROPN
ejpam-6635	72	66	v	v	ADP
ejpam-6635	72	67	(	(	PUNCT
ejpam-6635	72	68	g	g	NOUN
ejpam-6635	72	69	)	)	PUNCT
ejpam-6635	72	70	\	\	NOUN
ejpam-6635	73	1	{	{	PUNCT
ejpam-6635	73	2	p	p	X
ejpam-6635	73	3	,	,	PUNCT
ejpam-6635	73	4	q	q	NOUN
ejpam-6635	73	5	}	}	PUNCT
ejpam-6635	73	6	,	,	PUNCT
ejpam-6635	73	7	either	either	CCONJ
ejpam-6635	73	8	xp	xp	INTJ
ejpam-6635	73	9	/∈	/∈	PUNCT
ejpam-6635	73	10	e(g	e(g	PROPN
ejpam-6635	73	11	)	)	PUNCT
ejpam-6635	73	12	and	and	CCONJ
ejpam-6635	73	13	ng(x	ng(x	NUM
ejpam-6635	73	14	)	)	PUNCT
ejpam-6635	73	15	∩	∩	NOUN
ejpam-6635	73	16	ng(q	ng(q	NOUN
ejpam-6635	73	17	)	)	PUNCT
ejpam-6635	73	18	=	=	SYM
ejpam-6635	73	19	∅	∅	NOUN
ejpam-6635	73	20	or	or	CCONJ
ejpam-6635	73	21	xq	xq	PROPN
ejpam-6635	73	22	/∈	/∈	PUNCT
ejpam-6635	73	23	e(g	e(g	PROPN
ejpam-6635	73	24	)	)	PUNCT
ejpam-6635	73	25	and	and	CCONJ
ejpam-6635	73	26	ng(x	ng(x	NUM
ejpam-6635	73	27	)	)	PUNCT
ejpam-6635	73	28	∩ng(p	∩ng(p	NOUN
ejpam-6635	73	29	)	)	PUNCT
ejpam-6635	73	30	=	=	PUNCT
ejpam-6635	73	31	∅.	∅.	PRON
ejpam-6635	73	32	(	(	PUNCT
ejpam-6635	73	33	iii	iii	NOUN
ejpam-6635	73	34	)	)	PUNCT
ejpam-6635	73	35	spnd(g	spnd(g	PROPN
ejpam-6635	73	36	)	)	PUNCT
ejpam-6635	73	37	=	=	SYM
ejpam-6635	74	1	n	n	NOUN
ejpam-6635	74	2	if	if	SCONJ
ejpam-6635	75	1	and	and	CCONJ
ejpam-6635	75	2	only	only	ADV
ejpam-6635	75	3	if	if	SCONJ
ejpam-6635	75	4	g	g	PROPN
ejpam-6635	75	5	=	=	PROPN
ejpam-6635	75	6	kn	kn	PROPN
ejpam-6635	75	7	.	.	PUNCT
ejpam-6635	75	8	proof	proof	NOUN
ejpam-6635	75	9	.	.	PUNCT
ejpam-6635	76	1	since	since	SCONJ
ejpam-6635	76	2	every	every	DET
ejpam-6635	76	3	secure	secure	ADJ
ejpam-6635	76	4	pointwise	pointwise	ADP
ejpam-6635	76	5	non	non	ADJ
ejpam-6635	76	6	-	-	ADJ
ejpam-6635	76	7	dominating	dominating	ADJ
ejpam-6635	76	8	set	set	NOUN
ejpam-6635	76	9	is	be	AUX
ejpam-6635	76	10	pointwise	pointwise	ADJ
ejpam-6635	76	11	non	non	ADJ
ejpam-6635	76	12	-	-	ADJ
ejpam-6635	76	13	dominating	dominating	ADJ
ejpam-6635	76	14	and	and	CCONJ
ejpam-6635	76	15	1	1	NUM
ejpam-6635	76	16	≤	≤	NUM
ejpam-6635	76	17	pnd(g	pnd(g	ADP
ejpam-6635	76	18	)	)	PUNCT
ejpam-6635	76	19	,	,	PUNCT
ejpam-6635	76	20	it	it	PRON
ejpam-6635	76	21	follows	follow	VERB
ejpam-6635	76	22	that	that	SCONJ
ejpam-6635	76	23	1	1	NUM
ejpam-6635	76	24	≤	≤	NUM
ejpam-6635	76	25	pnd(g	pnd(g	ADP
ejpam-6635	76	26	)	)	PUNCT
ejpam-6635	76	27	≤	≤	NOUN
ejpam-6635	76	28	spnd(g	spnd(g	PROPN
ejpam-6635	76	29	)	)	PUNCT
ejpam-6635	76	30	≤	≤	NOUN
ejpam-6635	76	31	n.	n.	NOUN
ejpam-6635	76	32	(	(	PUNCT
ejpam-6635	76	33	i	i	NOUN
ejpam-6635	76	34	)	)	PUNCT
ejpam-6635	76	35	suppose	suppose	VERB
ejpam-6635	76	36	spnd(g	spnd(g	X
ejpam-6635	76	37	)	)	PUNCT
ejpam-6635	76	38	=	=	SYM
ejpam-6635	77	1	1	1	X
ejpam-6635	77	2	.	.	PUNCT
ejpam-6635	77	3	then	then	ADV
ejpam-6635	77	4	pnd(g	pnd(g	ADP
ejpam-6635	77	5	)	)	PUNCT
ejpam-6635	77	6	=	=	SYM
ejpam-6635	77	7	1	1	X
ejpam-6635	77	8	.	.	PUNCT
ejpam-6635	77	9	by	by	ADP
ejpam-6635	77	10	theorem	theorem	NOUN
ejpam-6635	77	11	2	2	NUM
ejpam-6635	77	12	,	,	PUNCT
ejpam-6635	77	13	g	g	PROPN
ejpam-6635	77	14	has	have	VERB
ejpam-6635	77	15	an	an	DET
ejpam-6635	77	16	isolated	isolated	ADJ
ejpam-6635	77	17	vertex	vertex	NOUN
ejpam-6635	77	18	.	.	PUNCT
ejpam-6635	78	1	let	let	VERB
ejpam-6635	78	2	s	s	PRON
ejpam-6635	78	3	=	=	NOUN
ejpam-6635	78	4	{	{	PUNCT
ejpam-6635	78	5	v	v	NOUN
ejpam-6635	78	6	}	}	PUNCT
ejpam-6635	78	7	be	be	AUX
ejpam-6635	78	8	an	an	DET
ejpam-6635	78	9	spnd	spnd	NOUN
ejpam-6635	78	10	-	-	PUNCT
ejpam-6635	78	11	set	set	NOUN
ejpam-6635	78	12	in	in	ADP
ejpam-6635	78	13	g.	g.	PROPN
ejpam-6635	79	1	then	then	ADV
ejpam-6635	79	2	v	v	NOUN
ejpam-6635	79	3	is	be	AUX
ejpam-6635	79	4	an	an	DET
ejpam-6635	79	5	isolated	isolated	ADJ
ejpam-6635	79	6	vertex	vertex	NOUN
ejpam-6635	79	7	of	of	ADP
ejpam-6635	79	8	g	g	PROPN
ejpam-6635	79	9	(	(	PUNCT
ejpam-6635	79	10	otherwise	otherwise	ADV
ejpam-6635	79	11	s	s	VERB
ejpam-6635	79	12	is	be	AUX
ejpam-6635	79	13	not	not	PART
ejpam-6635	79	14	a	a	DET
ejpam-6635	79	15	pointwise	pointwise	ADJ
ejpam-6635	79	16	non	non	ADJ
ejpam-6635	79	17	-	-	ADJ
ejpam-6635	79	18	dominating	dominating	ADJ
ejpam-6635	79	19	set	set	NOUN
ejpam-6635	79	20	)	)	PUNCT
ejpam-6635	79	21	.	.	PUNCT
ejpam-6635	80	1	let	let	VERB
ejpam-6635	80	2	x	x	SYM
ejpam-6635	80	3	∈	∈	PROPN
ejpam-6635	80	4	v	v	X
ejpam-6635	80	5	(	(	PUNCT
ejpam-6635	80	6	g	g	NOUN
ejpam-6635	80	7	)	)	PUNCT
ejpam-6635	80	8	\	\	PUNCT
ejpam-6635	81	1	s.	s.	PROPN
ejpam-6635	81	2	since	since	SCONJ
ejpam-6635	81	3	s	s	PROPN
ejpam-6635	81	4	is	be	AUX
ejpam-6635	81	5	a	a	DET
ejpam-6635	81	6	secure	secure	ADJ
ejpam-6635	81	7	pointwise	pointwise	ADJ
ejpam-6635	81	8	non	non	ADJ
ejpam-6635	81	9	-	-	ADJ
ejpam-6635	81	10	dominating	dominating	ADJ
ejpam-6635	81	11	set	set	NOUN
ejpam-6635	81	12	,	,	PUNCT
ejpam-6635	81	13	(	(	PUNCT
ejpam-6635	81	14	s	s	X
ejpam-6635	81	15	\{v})∪{x	\{v})∪{x	NOUN
ejpam-6635	81	16	}	}	PUNCT
ejpam-6635	81	17	=	=	SYM
ejpam-6635	81	18	{	{	PUNCT
ejpam-6635	81	19	x	x	NOUN
ejpam-6635	81	20	}	}	PUNCT
ejpam-6635	81	21	is	be	AUX
ejpam-6635	81	22	a	a	DET
ejpam-6635	81	23	pointwise	pointwise	ADJ
ejpam-6635	81	24	non	non	ADJ
ejpam-6635	81	25	-	-	ADJ
ejpam-6635	81	26	dominating	dominating	ADJ
ejpam-6635	81	27	set	set	NOUN
ejpam-6635	81	28	.	.	PUNCT
ejpam-6635	82	1	this	this	PRON
ejpam-6635	82	2	implies	imply	VERB
ejpam-6635	82	3	that	that	SCONJ
ejpam-6635	82	4	x	x	PRON
ejpam-6635	82	5	is	be	AUX
ejpam-6635	82	6	an	an	DET
ejpam-6635	82	7	isolated	isolated	ADJ
ejpam-6635	82	8	vertex	vertex	NOUN
ejpam-6635	82	9	.	.	PUNCT
ejpam-6635	83	1	therefore	therefore	ADV
ejpam-6635	83	2	,	,	PUNCT
ejpam-6635	83	3	g	g	PROPN
ejpam-6635	83	4	=	=	SYM
ejpam-6635	83	5	kn	kn	PROPN
ejpam-6635	83	6	.	.	PUNCT
ejpam-6635	84	1	conversely	conversely	ADV
ejpam-6635	84	2	,	,	PUNCT
ejpam-6635	84	3	suppose	suppose	VERB
ejpam-6635	84	4	g	g	PROPN
ejpam-6635	84	5	=	=	PROPN
ejpam-6635	84	6	kn	kn	PROPN
ejpam-6635	84	7	.	.	PUNCT
ejpam-6635	84	8	choose	choose	VERB
ejpam-6635	84	9	any	any	DET
ejpam-6635	84	10	vertex	vertex	NOUN
ejpam-6635	84	11	u	u	NOUN
ejpam-6635	84	12	of	of	ADP
ejpam-6635	84	13	g.	g.	PROPN
ejpam-6635	84	14	then	then	ADV
ejpam-6635	84	15	{	{	PUNCT
ejpam-6635	84	16	u	u	NOUN
ejpam-6635	84	17	}	}	PUNCT
ejpam-6635	84	18	is	be	AUX
ejpam-6635	84	19	a	a	DET
ejpam-6635	84	20	secure	secure	ADJ
ejpam-6635	84	21	pointwise	pointwise	ADJ
ejpam-6635	84	22	non	non	ADJ
ejpam-6635	84	23	-	-	ADJ
ejpam-6635	84	24	dominating	dominating	ADJ
ejpam-6635	84	25	set	set	NOUN
ejpam-6635	84	26	in	in	ADP
ejpam-6635	84	27	g.	g.	PROPN
ejpam-6635	84	28	hence	hence	ADV
ejpam-6635	84	29	,	,	PUNCT
ejpam-6635	84	30	spnd(g	spnd(g	PROPN
ejpam-6635	84	31	)	)	PUNCT
ejpam-6635	84	32	=	=	SYM
ejpam-6635	85	1	1	1	X
ejpam-6635	85	2	.	.	PUNCT
ejpam-6635	85	3	f.	f.	PROPN
ejpam-6635	85	4	alfeche	alfeche	PROPN
ejpam-6635	85	5	,	,	PUNCT
ejpam-6635	85	6	s.	s.	PROPN
ejpam-6635	85	7	canoy	canoy	PROPN
ejpam-6635	85	8	jr	jr	PROPN
ejpam-6635	85	9	.	.	PROPN
ejpam-6635	85	10	/	/	SYM
ejpam-6635	85	11	eur	eur	PROPN
ejpam-6635	85	12	.	.	PUNCT
ejpam-6635	86	1	j.	j.	PROPN
ejpam-6635	86	2	pure	pure	PROPN
ejpam-6635	86	3	appl	appl	PROPN
ejpam-6635	86	4	.	.	PROPN
ejpam-6635	86	5	math	math	PROPN
ejpam-6635	86	6	,	,	PUNCT
ejpam-6635	86	7	18	18	NUM
ejpam-6635	86	8	(	(	PUNCT
ejpam-6635	86	9	3	3	NUM
ejpam-6635	86	10	)	)	PUNCT
ejpam-6635	86	11	(	(	PUNCT
ejpam-6635	86	12	2025	2025	NUM
ejpam-6635	86	13	)	)	PUNCT
ejpam-6635	86	14	,	,	PUNCT
ejpam-6635	86	15	6635	6635	NUM
ejpam-6635	86	16	4	4	NUM
ejpam-6635	86	17	of	of	ADP
ejpam-6635	86	18	11	11	NUM
ejpam-6635	86	19	(	(	PUNCT
ejpam-6635	86	20	ii	ii	NOUN
ejpam-6635	86	21	)	)	PUNCT
ejpam-6635	86	22	suppose	suppose	VERB
ejpam-6635	86	23	spnd(g	spnd(g	X
ejpam-6635	86	24	)	)	PUNCT
ejpam-6635	86	25	=	=	SYM
ejpam-6635	87	1	2	2	X
ejpam-6635	87	2	.	.	PUNCT
ejpam-6635	87	3	then	then	ADV
ejpam-6635	87	4	g	g	PROPN
ejpam-6635	87	5	̸=	̸=	PROPN
ejpam-6635	87	6	kn	kn	PROPN
ejpam-6635	87	7	.	.	PUNCT
ejpam-6635	88	1	let	let	VERB
ejpam-6635	88	2	d	d	NOUN
ejpam-6635	88	3	=	=	PRON
ejpam-6635	88	4	{	{	PUNCT
ejpam-6635	88	5	p	p	X
ejpam-6635	88	6	,	,	PUNCT
ejpam-6635	88	7	q	q	AUX
ejpam-6635	88	8	}	}	PUNCT
ejpam-6635	88	9	be	be	AUX
ejpam-6635	88	10	an	an	DET
ejpam-6635	88	11	spnd	spnd	NOUN
ejpam-6635	88	12	-	-	PUNCT
ejpam-6635	88	13	set	set	NOUN
ejpam-6635	88	14	in	in	ADP
ejpam-6635	88	15	g.	g.	PROPN
ejpam-6635	88	16	since	since	SCONJ
ejpam-6635	88	17	d	d	PROPN
ejpam-6635	88	18	=	=	PUNCT
ejpam-6635	88	19	{	{	PUNCT
ejpam-6635	88	20	p	p	X
ejpam-6635	88	21	,	,	PUNCT
ejpam-6635	88	22	q	q	X
ejpam-6635	88	23	}	}	PUNCT
ejpam-6635	88	24	is	be	AUX
ejpam-6635	88	25	a	a	DET
ejpam-6635	88	26	pointwise	pointwise	ADJ
ejpam-6635	88	27	non	non	ADJ
ejpam-6635	88	28	-	-	ADJ
ejpam-6635	88	29	dominating	dominating	ADJ
ejpam-6635	88	30	set	set	NOUN
ejpam-6635	88	31	,	,	PUNCT
ejpam-6635	88	32	ng(p	ng(p	ADJ
ejpam-6635	88	33	)	)	PUNCT
ejpam-6635	88	34	∩	∩	NOUN
ejpam-6635	88	35	ng(q	ng(q	NOUN
ejpam-6635	88	36	)	)	PUNCT
ejpam-6635	88	37	=	=	VERB
ejpam-6635	88	38	∅.	∅.	AUX
ejpam-6635	88	39	let	let	VERB
ejpam-6635	88	40	x	x	PUNCT
ejpam-6635	88	41	∈	∈	PROPN
ejpam-6635	88	42	v	v	X
ejpam-6635	88	43	(	(	PUNCT
ejpam-6635	88	44	g	g	NOUN
ejpam-6635	88	45	)	)	PUNCT
ejpam-6635	88	46	\	\	PROPN
ejpam-6635	88	47	d.	d.	PROPN
ejpam-6635	88	48	since	since	SCONJ
ejpam-6635	88	49	d	d	PROPN
ejpam-6635	88	50	is	be	AUX
ejpam-6635	88	51	secure	secure	ADJ
ejpam-6635	88	52	pointwise	pointwise	ADP
ejpam-6635	88	53	non	non	ADJ
ejpam-6635	88	54	-	-	ADJ
ejpam-6635	88	55	dominating	dominating	ADJ
ejpam-6635	88	56	,	,	PUNCT
ejpam-6635	88	57	xp	xp	NOUN
ejpam-6635	88	58	/∈	/∈	PUNCT
ejpam-6635	89	1	e(g	e(g	PROPN
ejpam-6635	89	2	)	)	PUNCT
ejpam-6635	89	3	and	and	CCONJ
ejpam-6635	89	4	dx	dx	PROPN
ejpam-6635	90	1	=	=	PUNCT
ejpam-6635	90	2	{	{	PUNCT
ejpam-6635	90	3	x	x	NOUN
ejpam-6635	90	4	,	,	PUNCT
ejpam-6635	90	5	q	q	X
ejpam-6635	90	6	}	}	PUNCT
ejpam-6635	90	7	is	be	AUX
ejpam-6635	90	8	pointwise	pointwise	NOUN
ejpam-6635	90	9	nondominating	nondominate	VERB
ejpam-6635	90	10	or	or	CCONJ
ejpam-6635	90	11	xq	xq	PROPN
ejpam-6635	90	12	/∈	/∈	PUNCT
ejpam-6635	90	13	e(g	e(g	PROPN
ejpam-6635	90	14	)	)	PUNCT
ejpam-6635	90	15	and	and	CCONJ
ejpam-6635	90	16	dx	dx	PROPN
ejpam-6635	90	17	=	=	PUNCT
ejpam-6635	90	18	{	{	PUNCT
ejpam-6635	90	19	x	x	X
ejpam-6635	90	20	,	,	PUNCT
ejpam-6635	90	21	p	p	X
ejpam-6635	90	22	}	}	PUNCT
ejpam-6635	90	23	is	be	AUX
ejpam-6635	90	24	pointwise	pointwise	PROPN
ejpam-6635	90	25	non	non	ADJ
ejpam-6635	90	26	-	-	ADJ
ejpam-6635	90	27	dominating	dominating	NOUN
ejpam-6635	90	28	.	.	PUNCT
ejpam-6635	91	1	thus	thus	ADV
ejpam-6635	91	2	,	,	PUNCT
ejpam-6635	91	3	xp	xp	INTJ
ejpam-6635	91	4	/∈	/∈	PUNCT
ejpam-6635	91	5	e(g	e(g	PROPN
ejpam-6635	91	6	)	)	PUNCT
ejpam-6635	91	7	and	and	CCONJ
ejpam-6635	91	8	ng(x	ng(x	NUM
ejpam-6635	91	9	)	)	PUNCT
ejpam-6635	92	1	∩ng(q	∩ng(q	PROPN
ejpam-6635	92	2	)	)	PUNCT
ejpam-6635	92	3	=	=	NOUN
ejpam-6635	92	4	∅	∅	NOUN
ejpam-6635	92	5	or	or	CCONJ
ejpam-6635	92	6	xq	xq	PROPN
ejpam-6635	92	7	/∈	/∈	PUNCT
ejpam-6635	92	8	e(g	e(g	PROPN
ejpam-6635	92	9	)	)	PUNCT
ejpam-6635	92	10	and	and	CCONJ
ejpam-6635	92	11	ng(x	ng(x	NUM
ejpam-6635	92	12	)	)	PUNCT
ejpam-6635	92	13	∩ng(p	∩ng(p	NOUN
ejpam-6635	92	14	)	)	PUNCT
ejpam-6635	92	15	=	=	PUNCT
ejpam-6635	92	16	∅.	∅.	VERB
ejpam-6635	92	17	hence	hence	ADV
ejpam-6635	92	18	,	,	PUNCT
ejpam-6635	92	19	conditions	condition	NOUN
ejpam-6635	92	20	(	(	PUNCT
ejpam-6635	92	21	j1	j1	PROPN
ejpam-6635	92	22	)	)	PUNCT
ejpam-6635	92	23	,	,	PUNCT
ejpam-6635	92	24	(	(	PUNCT
ejpam-6635	92	25	j2	j2	PROPN
ejpam-6635	92	26	)	)	PUNCT
ejpam-6635	92	27	,	,	PUNCT
ejpam-6635	92	28	and	and	CCONJ
ejpam-6635	92	29	(	(	PUNCT
ejpam-6635	92	30	j3	j3	PROPN
ejpam-6635	92	31	)	)	PUNCT
ejpam-6635	92	32	hold	hold	VERB
ejpam-6635	92	33	.	.	PUNCT
ejpam-6635	93	1	conversely	conversely	ADV
ejpam-6635	93	2	,	,	PUNCT
ejpam-6635	93	3	suppose	suppose	VERB
ejpam-6635	93	4	conditions	condition	NOUN
ejpam-6635	93	5	(	(	PUNCT
ejpam-6635	93	6	j1	j1	PROPN
ejpam-6635	93	7	)	)	PUNCT
ejpam-6635	93	8	,	,	PUNCT
ejpam-6635	93	9	(	(	PUNCT
ejpam-6635	93	10	j2	j2	PROPN
ejpam-6635	93	11	)	)	PUNCT
ejpam-6635	93	12	,	,	PUNCT
ejpam-6635	93	13	and	and	CCONJ
ejpam-6635	93	14	(	(	PUNCT
ejpam-6635	93	15	j3	j3	PROPN
ejpam-6635	93	16	)	)	PUNCT
ejpam-6635	93	17	hold	hold	VERB
ejpam-6635	93	18	.	.	PUNCT
ejpam-6635	94	1	by	by	ADP
ejpam-6635	94	2	(	(	PUNCT
ejpam-6635	94	3	j1	j1	PROPN
ejpam-6635	94	4	)	)	PUNCT
ejpam-6635	94	5	and	and	CCONJ
ejpam-6635	94	6	part	part	NOUN
ejpam-6635	94	7	(	(	PUNCT
ejpam-6635	94	8	i	i	NOUN
ejpam-6635	94	9	)	)	PUNCT
ejpam-6635	94	10	,	,	PUNCT
ejpam-6635	94	11	it	it	PRON
ejpam-6635	94	12	follows	follow	VERB
ejpam-6635	94	13	that	that	PRON
ejpam-6635	94	14	spnd(g	spnd(g	PROPN
ejpam-6635	94	15	)	)	PUNCT
ejpam-6635	94	16	≥	≥	NOUN
ejpam-6635	94	17	2	2	NUM
ejpam-6635	94	18	.	.	PUNCT
ejpam-6635	95	1	let	let	VERB
ejpam-6635	95	2	s	s	VERB
ejpam-6635	95	3	=	=	PUNCT
ejpam-6635	95	4	{	{	PUNCT
ejpam-6635	95	5	p	p	X
ejpam-6635	95	6	,	,	PUNCT
ejpam-6635	95	7	q	q	NOUN
ejpam-6635	95	8	}	}	PUNCT
ejpam-6635	95	9	.	.	PUNCT
ejpam-6635	96	1	by	by	ADP
ejpam-6635	96	2	(	(	PUNCT
ejpam-6635	96	3	j2	j2	PROPN
ejpam-6635	96	4	)	)	PUNCT
ejpam-6635	96	5	,	,	PUNCT
ejpam-6635	96	6	s	s	VERB
ejpam-6635	96	7	is	be	AUX
ejpam-6635	96	8	a	a	DET
ejpam-6635	96	9	pointwise	pointwise	ADJ
ejpam-6635	96	10	non	non	ADJ
ejpam-6635	96	11	-	-	ADJ
ejpam-6635	96	12	dominating	dominating	ADJ
ejpam-6635	96	13	set	set	NOUN
ejpam-6635	96	14	in	in	ADP
ejpam-6635	96	15	g.	g.	PROPN
ejpam-6635	96	16	next	next	ADV
ejpam-6635	96	17	,	,	PUNCT
ejpam-6635	96	18	let	let	VERB
ejpam-6635	96	19	x	x	PUNCT
ejpam-6635	96	20	∈	∈	PROPN
ejpam-6635	96	21	v	v	X
ejpam-6635	96	22	(	(	PUNCT
ejpam-6635	96	23	g	g	NOUN
ejpam-6635	96	24	)	)	PUNCT
ejpam-6635	96	25	\	\	PUNCT
ejpam-6635	97	1	s.	s.	PROPN
ejpam-6635	97	2	suppose	suppose	VERB
ejpam-6635	97	3	xp	xp	PROPN
ejpam-6635	97	4	/∈	/∈	PUNCT
ejpam-6635	97	5	e(g	e(g	PROPN
ejpam-6635	97	6	)	)	PUNCT
ejpam-6635	97	7	.	.	PUNCT
ejpam-6635	98	1	set	set	VERB
ejpam-6635	98	2	sx	sx	PROPN
ejpam-6635	98	3	=	=	PUNCT
ejpam-6635	98	4	(	(	PUNCT
ejpam-6635	98	5	s	s	X
ejpam-6635	98	6	\	\	X
ejpam-6635	98	7	{	{	PUNCT
ejpam-6635	98	8	p	p	NOUN
ejpam-6635	98	9	}	}	PUNCT
ejpam-6635	98	10	)	)	PUNCT
ejpam-6635	98	11	∪	∪	ADP
ejpam-6635	98	12	{	{	PUNCT
ejpam-6635	98	13	x	x	NOUN
ejpam-6635	98	14	}	}	PUNCT
ejpam-6635	98	15	=	=	SYM
ejpam-6635	98	16	{	{	PUNCT
ejpam-6635	98	17	x	x	NOUN
ejpam-6635	98	18	,	,	PUNCT
ejpam-6635	98	19	q	q	NOUN
ejpam-6635	98	20	}	}	PUNCT
ejpam-6635	98	21	.	.	PUNCT
ejpam-6635	99	1	by	by	ADP
ejpam-6635	99	2	(	(	PUNCT
ejpam-6635	99	3	j3	j3	PROPN
ejpam-6635	99	4	)	)	PUNCT
ejpam-6635	99	5	,	,	PUNCT
ejpam-6635	99	6	ng(x	ng(x	NUM
ejpam-6635	99	7	)	)	PUNCT
ejpam-6635	99	8	∩	∩	NOUN
ejpam-6635	99	9	ng(q	ng(q	NOUN
ejpam-6635	99	10	)	)	PUNCT
ejpam-6635	99	11	=	=	PUNCT
ejpam-6635	99	12	∅.	∅.	ADP
ejpam-6635	99	13	this	this	PRON
ejpam-6635	99	14	implies	imply	VERB
ejpam-6635	99	15	that	that	SCONJ
ejpam-6635	99	16	sx	sx	PROPN
ejpam-6635	99	17	is	be	AUX
ejpam-6635	99	18	pointwise	pointwise	ADJ
ejpam-6635	99	19	non	non	ADJ
ejpam-6635	99	20	-	-	ADJ
ejpam-6635	99	21	dominating	dominating	ADJ
ejpam-6635	99	22	.	.	PUNCT
ejpam-6635	100	1	if	if	SCONJ
ejpam-6635	100	2	xp	xp	PROPN
ejpam-6635	100	3	∈	∈	PROPN
ejpam-6635	100	4	e(g	e(g	PROPN
ejpam-6635	100	5	)	)	PUNCT
ejpam-6635	100	6	,	,	PUNCT
ejpam-6635	100	7	then	then	ADV
ejpam-6635	100	8	xq	xq	PROPN
ejpam-6635	100	9	/∈	/∈	PUNCT
ejpam-6635	100	10	e(g	e(g	PROPN
ejpam-6635	100	11	)	)	PUNCT
ejpam-6635	100	12	by	by	ADP
ejpam-6635	100	13	condition	condition	NOUN
ejpam-6635	100	14	(	(	PUNCT
ejpam-6635	100	15	j2	j2	PROPN
ejpam-6635	100	16	)	)	PUNCT
ejpam-6635	100	17	and	and	CCONJ
ejpam-6635	100	18	ng(x	ng(x	NUM
ejpam-6635	100	19	)	)	PUNCT
ejpam-6635	100	20	∩	∩	NOUN
ejpam-6635	100	21	ng(p	ng(p	X
ejpam-6635	100	22	)	)	PUNCT
ejpam-6635	100	23	=	=	NOUN
ejpam-6635	100	24	∅	∅	NOUN
ejpam-6635	100	25	by	by	ADP
ejpam-6635	100	26	(	(	PUNCT
ejpam-6635	100	27	j3	j3	PROPN
ejpam-6635	100	28	)	)	PUNCT
ejpam-6635	100	29	.	.	PUNCT
ejpam-6635	101	1	it	it	PRON
ejpam-6635	101	2	follows	follow	VERB
ejpam-6635	101	3	that	that	PRON
ejpam-6635	101	4	s′	s′	ADJ
ejpam-6635	101	5	x	x	X
ejpam-6635	101	6	=	=	SYM
ejpam-6635	101	7	(	(	PUNCT
ejpam-6635	101	8	s	s	NOUN
ejpam-6635	101	9	\	\	X
ejpam-6635	101	10	{	{	PUNCT
ejpam-6635	101	11	q	q	NOUN
ejpam-6635	101	12	}	}	PUNCT
ejpam-6635	101	13	)	)	PUNCT
ejpam-6635	101	14	∪	∪	ADP
ejpam-6635	101	15	{	{	PUNCT
ejpam-6635	101	16	x	x	NOUN
ejpam-6635	101	17	}	}	PUNCT
ejpam-6635	101	18	=	=	SYM
ejpam-6635	101	19	{	{	PUNCT
ejpam-6635	101	20	x	x	NOUN
ejpam-6635	101	21	,	,	PUNCT
ejpam-6635	101	22	p	p	X
ejpam-6635	101	23	}	}	PUNCT
ejpam-6635	101	24	is	be	AUX
ejpam-6635	101	25	pointwise	pointwise	PROPN
ejpam-6635	101	26	non	non	ADJ
ejpam-6635	101	27	-	-	ADJ
ejpam-6635	101	28	dominating	dominating	NOUN
ejpam-6635	101	29	in	in	ADP
ejpam-6635	101	30	g.	g.	PROPN
ejpam-6635	101	31	therefore	therefore	ADV
ejpam-6635	101	32	,	,	PUNCT
ejpam-6635	101	33	s	s	VERB
ejpam-6635	101	34	is	be	AUX
ejpam-6635	101	35	a	a	DET
ejpam-6635	101	36	secure	secure	ADJ
ejpam-6635	101	37	pointwise	pointwise	ADJ
ejpam-6635	101	38	non	non	ADJ
ejpam-6635	101	39	-	-	ADJ
ejpam-6635	101	40	dominating	dominating	ADJ
ejpam-6635	101	41	set	set	NOUN
ejpam-6635	101	42	in	in	ADP
ejpam-6635	101	43	g	g	PROPN
ejpam-6635	101	44	and	and	CCONJ
ejpam-6635	101	45	spnd(g	spnd(g	PROPN
ejpam-6635	101	46	)	)	PUNCT
ejpam-6635	101	47	=	=	SYM
ejpam-6635	101	48	|s|	|s|	NOUN
ejpam-6635	101	49	=	=	SYM
ejpam-6635	101	50	2	2	NUM
ejpam-6635	101	51	.	.	PUNCT
ejpam-6635	101	52	(	(	PUNCT
ejpam-6635	101	53	iii	iii	NOUN
ejpam-6635	101	54	)	)	PUNCT
ejpam-6635	101	55	suppose	suppose	VERB
ejpam-6635	101	56	spnd(g	spnd(g	X
ejpam-6635	101	57	)	)	PUNCT
ejpam-6635	101	58	=	=	VERB
ejpam-6635	101	59	n.	n.	NOUN
ejpam-6635	101	60	suppose	suppose	VERB
ejpam-6635	101	61	further	far	ADV
ejpam-6635	101	62	that	that	SCONJ
ejpam-6635	101	63	g	g	PROPN
ejpam-6635	101	64	̸=	̸=	PROPN
ejpam-6635	101	65	kn	kn	PROPN
ejpam-6635	101	66	.	.	PUNCT
ejpam-6635	102	1	then	then	ADV
ejpam-6635	102	2	there	there	PRON
ejpam-6635	102	3	exist	exist	VERB
ejpam-6635	102	4	non	non	ADJ
ejpam-6635	102	5	-	-	ADJ
ejpam-6635	102	6	adjacent	adjacent	ADJ
ejpam-6635	102	7	vertices	vertex	NOUN
ejpam-6635	102	8	x	x	PUNCT
ejpam-6635	102	9	and	and	CCONJ
ejpam-6635	102	10	y	y	PROPN
ejpam-6635	102	11	of	of	ADP
ejpam-6635	102	12	g.	g.	PROPN
ejpam-6635	102	13	let	let	VERB
ejpam-6635	102	14	s	s	VERB
ejpam-6635	102	15	=	=	NOUN
ejpam-6635	102	16	v	v	X
ejpam-6635	102	17	(	(	PUNCT
ejpam-6635	102	18	g)\{x	g)\{x	PROPN
ejpam-6635	102	19	}	}	PUNCT
ejpam-6635	102	20	.	.	PUNCT
ejpam-6635	103	1	since	since	SCONJ
ejpam-6635	103	2	y	y	PROPN
ejpam-6635	103	3	∈	∈	PROPN
ejpam-6635	103	4	s	s	PART
ejpam-6635	103	5	and	and	CCONJ
ejpam-6635	103	6	x	x	ADJ
ejpam-6635	103	7	/∈	/∈	PUNCT
ejpam-6635	103	8	ng(y	ng(y	NOUN
ejpam-6635	103	9	)	)	PUNCT
ejpam-6635	103	10	,	,	PUNCT
ejpam-6635	103	11	it	it	PRON
ejpam-6635	103	12	follows	follow	VERB
ejpam-6635	103	13	that	that	SCONJ
ejpam-6635	103	14	s	s	VERB
ejpam-6635	103	15	is	be	AUX
ejpam-6635	103	16	a	a	DET
ejpam-6635	103	17	pointwise	pointwise	ADJ
ejpam-6635	103	18	non	non	ADJ
ejpam-6635	103	19	-	-	ADJ
ejpam-6635	103	20	dominating	dominating	ADJ
ejpam-6635	103	21	set	set	NOUN
ejpam-6635	103	22	in	in	ADP
ejpam-6635	103	23	g.	g.	PROPN
ejpam-6635	103	24	moreover	moreover	ADV
ejpam-6635	103	25	,	,	PUNCT
ejpam-6635	103	26	because	because	SCONJ
ejpam-6635	103	27	v	v	X
ejpam-6635	103	28	(	(	PUNCT
ejpam-6635	103	29	g)\{y	g)\{y	VERB
ejpam-6635	103	30	}	}	PUNCT
ejpam-6635	103	31	is	be	AUX
ejpam-6635	103	32	also	also	ADV
ejpam-6635	103	33	pointwise	pointwise	ADJ
ejpam-6635	103	34	nondominating	nondominate	VERB
ejpam-6635	103	35	,	,	PUNCT
ejpam-6635	103	36	s	s	VERB
ejpam-6635	103	37	is	be	AUX
ejpam-6635	103	38	a	a	DET
ejpam-6635	103	39	secure	secure	ADJ
ejpam-6635	103	40	pointwise	pointwise	ADJ
ejpam-6635	103	41	non	non	ADJ
ejpam-6635	103	42	-	-	ADJ
ejpam-6635	103	43	dominating	dominating	ADJ
ejpam-6635	103	44	set	set	NOUN
ejpam-6635	103	45	in	in	ADP
ejpam-6635	103	46	g.	g.	PROPN
ejpam-6635	103	47	thus	thus	ADV
ejpam-6635	103	48	,	,	PUNCT
ejpam-6635	103	49	spnd(g	spnd(g	PROPN
ejpam-6635	103	50	)	)	PUNCT
ejpam-6635	103	51	≤	≤	NUM
ejpam-6635	103	52	|s|	|s|	PROPN
ejpam-6635	103	53	=	=	SYM
ejpam-6635	103	54	n−1	n−1	PROPN
ejpam-6635	103	55	,	,	PUNCT
ejpam-6635	103	56	a	a	DET
ejpam-6635	103	57	contradiction	contradiction	NOUN
ejpam-6635	103	58	.	.	PUNCT
ejpam-6635	104	1	therefore	therefore	ADV
ejpam-6635	104	2	,	,	PUNCT
ejpam-6635	104	3	g	g	PROPN
ejpam-6635	104	4	=	=	SYM
ejpam-6635	104	5	kn	kn	PROPN
ejpam-6635	104	6	.	.	PUNCT
ejpam-6635	105	1	the	the	DET
ejpam-6635	105	2	converse	converse	NOUN
ejpam-6635	105	3	is	be	AUX
ejpam-6635	105	4	clear	clear	ADJ
ejpam-6635	105	5	.	.	PUNCT
ejpam-6635	106	1	corollary	corollary	ADJ
ejpam-6635	106	2	1	1	NUM
ejpam-6635	106	3	.	.	PUNCT
ejpam-6635	107	1	let	let	VERB
ejpam-6635	107	2	n	n	PRON
ejpam-6635	107	3	be	be	AUX
ejpam-6635	107	4	a	a	DET
ejpam-6635	107	5	positive	positive	ADJ
ejpam-6635	107	6	integer	integer	NOUN
ejpam-6635	107	7	.	.	PUNCT
ejpam-6635	108	1	then	then	ADV
ejpam-6635	108	2	spnd(pn	spnd(pn	NOUN
ejpam-6635	108	3	)	)	PUNCT
ejpam-6635	108	4	=	=	SYM
ejpam-6635	108	5	{	{	PUNCT
ejpam-6635	108	6	1	1	NUM
ejpam-6635	108	7	if	if	SCONJ
ejpam-6635	108	8	n	n	CCONJ
ejpam-6635	108	9	=	=	SYM
ejpam-6635	108	10	1	1	NUM
ejpam-6635	108	11	2	2	NUM
ejpam-6635	108	12	if	if	SCONJ
ejpam-6635	108	13	n	n	PRON
ejpam-6635	108	14	≥	≥	NOUN
ejpam-6635	108	15	2	2	NUM
ejpam-6635	108	16	.	.	PUNCT
ejpam-6635	109	1	proof	proof	NOUN
ejpam-6635	109	2	.	.	PUNCT
ejpam-6635	110	1	let	let	VERB
ejpam-6635	110	2	pn	pn	VERB
ejpam-6635	110	3	=	=	PUNCT
ejpam-6635	111	1	[	[	X
ejpam-6635	111	2	v1	v1	NOUN
ejpam-6635	111	3	,	,	PUNCT
ejpam-6635	111	4	v2	v2	PROPN
ejpam-6635	111	5	,	,	PUNCT
ejpam-6635	111	6	·	·	PUNCT
ejpam-6635	111	7	·	·	PUNCT
ejpam-6635	111	8	·	·	PUNCT
ejpam-6635	111	9	,	,	PUNCT
ejpam-6635	111	10	vn	vn	X
ejpam-6635	111	11	]	]	PUNCT
ejpam-6635	111	12	.	.	PUNCT
ejpam-6635	112	1	by	by	ADP
ejpam-6635	112	2	theorem	theorem	NOUN
ejpam-6635	112	3	3(iii	3(iii	NUM
ejpam-6635	112	4	)	)	PUNCT
ejpam-6635	112	5	,	,	PUNCT
ejpam-6635	112	6	spnd(p1	spnd(p1	NOUN
ejpam-6635	112	7	)	)	PUNCT
ejpam-6635	112	8	=	=	SYM
ejpam-6635	112	9	1	1	NUM
ejpam-6635	112	10	and	and	CCONJ
ejpam-6635	112	11	spnd(p2	spnd(p2	ADJ
ejpam-6635	112	12	)	)	PUNCT
ejpam-6635	112	13	=	=	SYM
ejpam-6635	112	14	2	2	X
ejpam-6635	112	15	.	.	X
ejpam-6635	112	16	suppose	suppose	VERB
ejpam-6635	112	17	n	n	PRON
ejpam-6635	112	18	≥	≥	NUM
ejpam-6635	112	19	3	3	NUM
ejpam-6635	112	20	.	.	PUNCT
ejpam-6635	112	21	then	then	ADV
ejpam-6635	112	22	spnd(pn	spnd(pn	NOUN
ejpam-6635	112	23	)	)	PUNCT
ejpam-6635	112	24	≥	≥	NOUN
ejpam-6635	112	25	2	2	NUM
ejpam-6635	112	26	by	by	ADP
ejpam-6635	112	27	theorem	theorem	NOUN
ejpam-6635	112	28	3(i	3(i	NUM
ejpam-6635	112	29	)	)	PUNCT
ejpam-6635	112	30	.	.	PUNCT
ejpam-6635	113	1	let	let	VERB
ejpam-6635	113	2	p	p	NOUN
ejpam-6635	113	3	=	=	X
ejpam-6635	113	4	v1	v1	NOUN
ejpam-6635	113	5	and	and	CCONJ
ejpam-6635	113	6	q	q	NOUN
ejpam-6635	113	7	=	=	SYM
ejpam-6635	113	8	v2	v2	PROPN
ejpam-6635	113	9	.	.	PUNCT
ejpam-6635	114	1	then	then	ADV
ejpam-6635	114	2	npn(p	npn(p	PROPN
ejpam-6635	114	3	)	)	PUNCT
ejpam-6635	114	4	∩	∩	ADJ
ejpam-6635	114	5	npn(q	npn(q	NOUN
ejpam-6635	114	6	)	)	PUNCT
ejpam-6635	114	7	=	=	PUNCT
ejpam-6635	114	8	∅.	∅.	AUX
ejpam-6635	114	9	let	let	VERB
ejpam-6635	114	10	x	x	SYM
ejpam-6635	114	11	∈	∈	PROPN
ejpam-6635	114	12	v	v	NOUN
ejpam-6635	114	13	(	(	PUNCT
ejpam-6635	114	14	pn	pn	NOUN
ejpam-6635	114	15	)	)	PUNCT
ejpam-6635	114	16	\	\	NOUN
ejpam-6635	115	1	{	{	PUNCT
ejpam-6635	115	2	p	p	X
ejpam-6635	115	3	,	,	PUNCT
ejpam-6635	115	4	q	q	NOUN
ejpam-6635	115	5	}	}	PUNCT
ejpam-6635	115	6	.	.	PUNCT
ejpam-6635	116	1	if	if	SCONJ
ejpam-6635	116	2	x	x	PROPN
ejpam-6635	116	3	=	=	SYM
ejpam-6635	116	4	v3	v3	PROPN
ejpam-6635	116	5	,	,	PUNCT
ejpam-6635	116	6	then	then	ADV
ejpam-6635	116	7	xp	xp	INTJ
ejpam-6635	116	8	/∈	/∈	PUNCT
ejpam-6635	116	9	e(pn	e(pn	NUM
ejpam-6635	116	10	)	)	PUNCT
ejpam-6635	116	11	and	and	CCONJ
ejpam-6635	116	12	npn(q	npn(q	PROPN
ejpam-6635	116	13	)	)	PUNCT
ejpam-6635	116	14	∩npn(x	∩npn(x	NUM
ejpam-6635	116	15	)	)	PUNCT
ejpam-6635	116	16	=	=	PUNCT
ejpam-6635	116	17	∅.	∅.	VERB
ejpam-6635	116	18	if	if	SCONJ
ejpam-6635	116	19	x	x	PROPN
ejpam-6635	116	20	̸=	̸=	PROPN
ejpam-6635	116	21	v3	v3	PROPN
ejpam-6635	116	22	,	,	PUNCT
ejpam-6635	116	23	then	then	ADV
ejpam-6635	116	24	xq	xq	PROPN
ejpam-6635	116	25	/∈	/∈	PUNCT
ejpam-6635	116	26	e(pn	e(pn	NUM
ejpam-6635	116	27	)	)	PUNCT
ejpam-6635	116	28	and	and	CCONJ
ejpam-6635	116	29	npn(p	npn(p	NOUN
ejpam-6635	116	30	)	)	PUNCT
ejpam-6635	116	31	∩npn(x	∩npn(x	NUM
ejpam-6635	116	32	)	)	PUNCT
ejpam-6635	116	33	=	=	PUNCT
ejpam-6635	116	34	∅.	∅.	VERB
ejpam-6635	116	35	therefore	therefore	ADV
ejpam-6635	116	36	,	,	PUNCT
ejpam-6635	116	37	spnd(pn	spnd(pn	NOUN
ejpam-6635	116	38	)	)	PUNCT
ejpam-6635	116	39	=	=	SYM
ejpam-6635	116	40	2	2	NUM
ejpam-6635	116	41	by	by	ADP
ejpam-6635	116	42	theorem	theorem	ADJ
ejpam-6635	116	43	3(ii	3(ii	NUM
ejpam-6635	116	44	)	)	PUNCT
ejpam-6635	116	45	.	.	PUNCT
ejpam-6635	117	1	corollary	corollary	ADJ
ejpam-6635	117	2	2	2	NUM
ejpam-6635	117	3	.	.	PUNCT
ejpam-6635	118	1	let	let	VERB
ejpam-6635	118	2	n	n	PRON
ejpam-6635	118	3	be	be	AUX
ejpam-6635	118	4	a	a	DET
ejpam-6635	118	5	positive	positive	ADJ
ejpam-6635	118	6	integer	integer	NOUN
ejpam-6635	118	7	and	and	CCONJ
ejpam-6635	118	8	n	n	PRON
ejpam-6635	118	9	≥	≥	NOUN
ejpam-6635	118	10	3	3	NUM
ejpam-6635	118	11	.	.	PUNCT
ejpam-6635	118	12	then	then	ADV
ejpam-6635	118	13	spnd(cn	spnd(cn	VERB
ejpam-6635	118	14	)	)	PUNCT
ejpam-6635	118	15	=	=	PUNCT
ejpam-6635	118	16	{	{	PUNCT
ejpam-6635	118	17	3	3	NUM
ejpam-6635	118	18	if	if	SCONJ
ejpam-6635	118	19	n	n	X
ejpam-6635	118	20	=	=	SYM
ejpam-6635	118	21	3	3	NUM
ejpam-6635	118	22	,	,	PUNCT
ejpam-6635	118	23	5	5	NUM
ejpam-6635	118	24	2	2	NUM
ejpam-6635	118	25	if	if	SCONJ
ejpam-6635	118	26	n	n	ADV
ejpam-6635	118	27	/∈	/∈	PUNCT
ejpam-6635	118	28	{	{	PUNCT
ejpam-6635	118	29	3	3	NUM
ejpam-6635	118	30	,	,	PUNCT
ejpam-6635	118	31	5	5	NUM
ejpam-6635	118	32	}	}	PUNCT
ejpam-6635	118	33	.	.	PUNCT
ejpam-6635	119	1	proof	proof	NOUN
ejpam-6635	119	2	.	.	PUNCT
ejpam-6635	120	1	let	let	VERB
ejpam-6635	120	2	cn	cn	PROPN
ejpam-6635	120	3	=	=	PUNCT
ejpam-6635	121	1	[	[	X
ejpam-6635	121	2	v1	v1	NOUN
ejpam-6635	121	3	,	,	PUNCT
ejpam-6635	121	4	v2	v2	PROPN
ejpam-6635	121	5	,	,	PUNCT
ejpam-6635	121	6	·	·	PUNCT
ejpam-6635	121	7	·	·	PUNCT
ejpam-6635	121	8	·	·	PUNCT
ejpam-6635	121	9	,	,	PUNCT
ejpam-6635	121	10	vn	vn	X
ejpam-6635	121	11	,	,	PUNCT
ejpam-6635	121	12	v1	v1	PROPN
ejpam-6635	121	13	]	]	PUNCT
ejpam-6635	121	14	.	.	PUNCT
ejpam-6635	122	1	by	by	ADP
ejpam-6635	122	2	theorem	theorem	NOUN
ejpam-6635	122	3	3(iii	3(iii	NUM
ejpam-6635	122	4	)	)	PUNCT
ejpam-6635	122	5	,	,	PUNCT
ejpam-6635	122	6	spnd(c3	spnd(c3	NOUN
ejpam-6635	122	7	)	)	PUNCT
ejpam-6635	122	8	=	=	SYM
ejpam-6635	122	9	3	3	X
ejpam-6635	122	10	.	.	X
ejpam-6635	122	11	suppose	suppose	VERB
ejpam-6635	122	12	n	n	PROPN
ejpam-6635	122	13	=	=	SYM
ejpam-6635	122	14	5	5	X
ejpam-6635	122	15	.	.	PUNCT
ejpam-6635	123	1	it	it	PRON
ejpam-6635	123	2	is	be	AUX
ejpam-6635	123	3	easy	easy	ADJ
ejpam-6635	123	4	to	to	PART
ejpam-6635	123	5	show	show	VERB
ejpam-6635	123	6	that	that	SCONJ
ejpam-6635	123	7	any	any	DET
ejpam-6635	123	8	set	set	NOUN
ejpam-6635	123	9	s	s	VERB
ejpam-6635	123	10	⊂	⊂	X
ejpam-6635	123	11	v	v	X
ejpam-6635	123	12	(	(	PUNCT
ejpam-6635	123	13	cn	cn	PROPN
ejpam-6635	123	14	)	)	PUNCT
ejpam-6635	123	15	with	with	ADP
ejpam-6635	123	16	|s|	|s|	PROPN
ejpam-6635	123	17	=	=	SYM
ejpam-6635	123	18	2	2	NUM
ejpam-6635	123	19	is	be	AUX
ejpam-6635	123	20	not	not	PART
ejpam-6635	123	21	secure	secure	ADJ
ejpam-6635	123	22	pointwise	pointwise	ADP
ejpam-6635	123	23	non	non	ADJ
ejpam-6635	123	24	-	-	ADJ
ejpam-6635	123	25	dominating	dominating	NOUN
ejpam-6635	123	26	.	.	PUNCT
ejpam-6635	124	1	since	since	SCONJ
ejpam-6635	124	2	{	{	PUNCT
ejpam-6635	124	3	v1	v1	NOUN
ejpam-6635	124	4	,	,	PUNCT
ejpam-6635	124	5	v2	v2	PROPN
ejpam-6635	124	6	,	,	PUNCT
ejpam-6635	124	7	v3	v3	PROPN
ejpam-6635	124	8	}	}	PUNCT
ejpam-6635	124	9	is	be	AUX
ejpam-6635	124	10	secure	secure	ADJ
ejpam-6635	124	11	pointwise	pointwise	ADP
ejpam-6635	124	12	non	non	ADJ
ejpam-6635	124	13	-	-	ADJ
ejpam-6635	124	14	dominating	dominating	ADJ
ejpam-6635	124	15	,	,	PUNCT
ejpam-6635	124	16	it	it	PRON
ejpam-6635	124	17	follows	follow	VERB
ejpam-6635	124	18	that	that	DET
ejpam-6635	124	19	spnd(c5	spnd(c5	NOUN
ejpam-6635	124	20	)	)	PUNCT
ejpam-6635	124	21	=	=	SYM
ejpam-6635	125	1	3	3	X
ejpam-6635	125	2	.	.	PUNCT
ejpam-6635	126	1	next	next	ADV
ejpam-6635	126	2	,	,	PUNCT
ejpam-6635	126	3	suppose	suppose	VERB
ejpam-6635	126	4	n	n	ADV
ejpam-6635	126	5	/∈	/∈	PUNCT
ejpam-6635	126	6	{	{	PUNCT
ejpam-6635	126	7	3	3	NUM
ejpam-6635	126	8	,	,	PUNCT
ejpam-6635	126	9	5	5	NUM
ejpam-6635	126	10	}	}	PUNCT
ejpam-6635	126	11	.	.	PUNCT
ejpam-6635	127	1	then	then	ADV
ejpam-6635	127	2	{	{	PUNCT
ejpam-6635	127	3	v1	v1	NOUN
ejpam-6635	127	4	,	,	PUNCT
ejpam-6635	127	5	v2	v2	PROPN
ejpam-6635	127	6	}	}	PUNCT
ejpam-6635	127	7	is	be	AUX
ejpam-6635	127	8	a	a	DET
ejpam-6635	127	9	secure	secure	ADJ
ejpam-6635	127	10	pointwise	pointwise	ADJ
ejpam-6635	127	11	nondominating	nondominate	VERB
ejpam-6635	127	12	set	set	NOUN
ejpam-6635	127	13	.	.	PUNCT
ejpam-6635	128	1	therefore	therefore	ADV
ejpam-6635	128	2	,	,	PUNCT
ejpam-6635	128	3	spnd(cn	spnd(cn	NOUN
ejpam-6635	128	4	)	)	PUNCT
ejpam-6635	128	5	=	=	SYM
ejpam-6635	128	6	2	2	X
ejpam-6635	128	7	.	.	X
ejpam-6635	128	8	theorem	theorem	NOUN
ejpam-6635	128	9	4	4	NUM
ejpam-6635	128	10	.	.	PUNCT
ejpam-6635	129	1	let	let	VERB
ejpam-6635	129	2	g1	g1	PROPN
ejpam-6635	129	3	,	,	PUNCT
ejpam-6635	129	4	g2	g2	PROPN
ejpam-6635	129	5	,	,	PUNCT
ejpam-6635	129	6	·	·	PUNCT
ejpam-6635	129	7	·	·	PUNCT
ejpam-6635	129	8	·	·	PUNCT
ejpam-6635	129	9	,	,	PUNCT
ejpam-6635	129	10	gk	gk	PROPN
ejpam-6635	129	11	be	be	AUX
ejpam-6635	129	12	the	the	DET
ejpam-6635	129	13	components	component	NOUN
ejpam-6635	129	14	of	of	ADP
ejpam-6635	129	15	g	g	PROPN
ejpam-6635	129	16	where	where	SCONJ
ejpam-6635	129	17	k	k	PROPN
ejpam-6635	129	18	≥	≥	NUM
ejpam-6635	129	19	2	2	NUM
ejpam-6635	129	20	and	and	CCONJ
ejpam-6635	129	21	at	at	ADV
ejpam-6635	129	22	least	least	ADV
ejpam-6635	129	23	one	one	NUM
ejpam-6635	129	24	component	component	NOUN
ejpam-6635	129	25	is	be	AUX
ejpam-6635	129	26	non	non	ADJ
ejpam-6635	129	27	-	-	ADJ
ejpam-6635	129	28	trivial	trivial	ADJ
ejpam-6635	129	29	.	.	PUNCT
ejpam-6635	130	1	then	then	ADV
ejpam-6635	130	2	each	each	PRON
ejpam-6635	130	3	of	of	ADP
ejpam-6635	130	4	the	the	DET
ejpam-6635	130	5	following	following	ADJ
ejpam-6635	130	6	statements	statement	NOUN
ejpam-6635	130	7	holds	hold	VERB
ejpam-6635	130	8	:	:	PUNCT
ejpam-6635	130	9	f.	f.	PROPN
ejpam-6635	130	10	alfeche	alfeche	PROPN
ejpam-6635	130	11	,	,	PUNCT
ejpam-6635	130	12	s.	s.	PROPN
ejpam-6635	130	13	canoy	canoy	PROPN
ejpam-6635	130	14	jr	jr	PROPN
ejpam-6635	130	15	.	.	PROPN
ejpam-6635	130	16	/	/	SYM
ejpam-6635	130	17	eur	eur	PROPN
ejpam-6635	130	18	.	.	PUNCT
ejpam-6635	131	1	j.	j.	PROPN
ejpam-6635	131	2	pure	pure	PROPN
ejpam-6635	131	3	appl	appl	PROPN
ejpam-6635	131	4	.	.	PROPN
ejpam-6635	131	5	math	math	PROPN
ejpam-6635	131	6	,	,	PUNCT
ejpam-6635	131	7	18	18	NUM
ejpam-6635	131	8	(	(	PUNCT
ejpam-6635	131	9	3	3	NUM
ejpam-6635	131	10	)	)	PUNCT
ejpam-6635	131	11	(	(	PUNCT
ejpam-6635	131	12	2025	2025	NUM
ejpam-6635	131	13	)	)	PUNCT
ejpam-6635	131	14	,	,	PUNCT
ejpam-6635	131	15	6635	6635	NUM
ejpam-6635	131	16	5	5	NUM
ejpam-6635	131	17	of	of	ADP
ejpam-6635	131	18	11	11	NUM
ejpam-6635	131	19	(	(	PUNCT
ejpam-6635	131	20	i	i	NOUN
ejpam-6635	131	21	)	)	PUNCT
ejpam-6635	131	22	if	if	SCONJ
ejpam-6635	131	23	spnd(gj	spnd(gj	VERB
ejpam-6635	131	24	)	)	PUNCT
ejpam-6635	131	25	=	=	SYM
ejpam-6635	131	26	2	2	NUM
ejpam-6635	131	27	for	for	ADP
ejpam-6635	131	28	some	some	DET
ejpam-6635	131	29	j	j	PROPN
ejpam-6635	131	30	∈	∈	PROPN
ejpam-6635	132	1	[	[	X
ejpam-6635	132	2	k	k	X
ejpam-6635	132	3	]	]	X
ejpam-6635	132	4	=	=	X
ejpam-6635	132	5	{	{	PUNCT
ejpam-6635	132	6	1	1	NUM
ejpam-6635	132	7	,	,	PUNCT
ejpam-6635	132	8	2	2	NUM
ejpam-6635	132	9	,	,	PUNCT
ejpam-6635	132	10	·	·	PUNCT
ejpam-6635	132	11	·	·	PUNCT
ejpam-6635	132	12	·	·	PUNCT
ejpam-6635	132	13	,	,	PUNCT
ejpam-6635	132	14	k	k	X
ejpam-6635	132	15	}	}	PUNCT
ejpam-6635	132	16	or	or	CCONJ
ejpam-6635	132	17	g	g	PROPN
ejpam-6635	132	18	has	have	VERB
ejpam-6635	132	19	two	two	NUM
ejpam-6635	132	20	trivial	trivial	ADJ
ejpam-6635	132	21	components	component	NOUN
ejpam-6635	132	22	,	,	PUNCT
ejpam-6635	132	23	then	then	ADV
ejpam-6635	132	24	spnd(g	spnd(g	PROPN
ejpam-6635	132	25	)	)	PUNCT
ejpam-6635	132	26	=	=	SYM
ejpam-6635	133	1	2	2	X
ejpam-6635	133	2	.	.	PUNCT
ejpam-6635	133	3	(	(	PUNCT
ejpam-6635	133	4	ii	ii	NOUN
ejpam-6635	133	5	)	)	PUNCT
ejpam-6635	133	6	if	if	SCONJ
ejpam-6635	133	7	k	k	PROPN
ejpam-6635	133	8	≥	≥	NUM
ejpam-6635	133	9	3	3	NUM
ejpam-6635	133	10	,	,	PUNCT
ejpam-6635	133	11	g	g	PROPN
ejpam-6635	133	12	has	have	VERB
ejpam-6635	133	13	at	at	ADP
ejpam-6635	133	14	most	most	ADV
ejpam-6635	133	15	one	one	NUM
ejpam-6635	133	16	trivial	trivial	ADJ
ejpam-6635	133	17	component	component	NOUN
ejpam-6635	133	18	,	,	PUNCT
ejpam-6635	133	19	and	and	CCONJ
ejpam-6635	133	20	pnd(gj	pnd(gj	NOUN
ejpam-6635	133	21	)	)	PUNCT
ejpam-6635	133	22	̸=	̸=	PROPN
ejpam-6635	133	23	2	2	NUM
ejpam-6635	133	24	for	for	ADP
ejpam-6635	133	25	all	all	DET
ejpam-6635	133	26	j	j	PROPN
ejpam-6635	133	27	∈	∈	PROPN
ejpam-6635	134	1	[	[	X
ejpam-6635	134	2	k	k	X
ejpam-6635	134	3	]	]	X
ejpam-6635	134	4	,	,	PUNCT
ejpam-6635	134	5	then	then	ADV
ejpam-6635	134	6	spnd(g	spnd(g	PROPN
ejpam-6635	134	7	)	)	PUNCT
ejpam-6635	134	8	=	=	SYM
ejpam-6635	135	1	3	3	X
ejpam-6635	135	2	.	.	PUNCT
ejpam-6635	135	3	(	(	PUNCT
ejpam-6635	135	4	iii	iii	X
ejpam-6635	135	5	)	)	PUNCT
ejpam-6635	135	6	if	if	SCONJ
ejpam-6635	135	7	k	k	PROPN
ejpam-6635	135	8	=	=	SYM
ejpam-6635	135	9	2	2	NUM
ejpam-6635	135	10	and	and	CCONJ
ejpam-6635	135	11	gj	gj	NOUN
ejpam-6635	135	12	is	be	AUX
ejpam-6635	135	13	complete	complete	ADJ
ejpam-6635	135	14	for	for	ADP
ejpam-6635	135	15	each	each	DET
ejpam-6635	135	16	j	j	PROPN
ejpam-6635	135	17	∈	∈	PROPN
ejpam-6635	135	18	{	{	PUNCT
ejpam-6635	135	19	1	1	NUM
ejpam-6635	135	20	,	,	PUNCT
ejpam-6635	135	21	2	2	NUM
ejpam-6635	135	22	}	}	PUNCT
ejpam-6635	135	23	,	,	PUNCT
ejpam-6635	135	24	then	then	ADV
ejpam-6635	135	25	spnd(g	spnd(g	PROPN
ejpam-6635	135	26	)	)	PUNCT
ejpam-6635	135	27	=	=	PUNCT
ejpam-6635	136	1			NOUN
ejpam-6635	136	2	2	2	NUM
ejpam-6635	136	3	if	if	SCONJ
ejpam-6635	136	4	g	g	PROPN
ejpam-6635	136	5	=	=	SYM
ejpam-6635	136	6	k2	k2	PROPN
ejpam-6635	136	7	∪km	∪km	PROPN
ejpam-6635	136	8	where	where	SCONJ
ejpam-6635	136	9	m	m	PROPN
ejpam-6635	136	10	≥	≥	VERB
ejpam-6635	136	11	1	1	NUM
ejpam-6635	136	12	3	3	NUM
ejpam-6635	136	13	if	if	SCONJ
ejpam-6635	136	14	g	g	NOUN
ejpam-6635	136	15	=	=	PUNCT
ejpam-6635	136	16	k3	k3	VERB
ejpam-6635	136	17	∪km	∪km	PROPN
ejpam-6635	136	18	where	where	SCONJ
ejpam-6635	136	19	m	m	PROPN
ejpam-6635	136	20	≥	≥	VERB
ejpam-6635	136	21	3	3	NUM
ejpam-6635	136	22	4	4	NUM
ejpam-6635	136	23	if	if	SCONJ
ejpam-6635	136	24	g	g	NOUN
ejpam-6635	136	25	=	=	PROPN
ejpam-6635	136	26	kr	kr	PROPN
ejpam-6635	136	27	∪km	∪km	PROPN
ejpam-6635	136	28	where	where	SCONJ
ejpam-6635	136	29	r	r	NOUN
ejpam-6635	136	30	,	,	PUNCT
ejpam-6635	136	31	m	m	VERB
ejpam-6635	136	32	≥	≥	NUM
ejpam-6635	136	33	4	4	NUM
ejpam-6635	136	34	m	m	NOUN
ejpam-6635	136	35	if	if	SCONJ
ejpam-6635	136	36	g	g	NOUN
ejpam-6635	136	37	=	=	PROPN
ejpam-6635	136	38	k1	k1	PROPN
ejpam-6635	136	39	∪km	∪km	PROPN
ejpam-6635	136	40	where	where	SCONJ
ejpam-6635	136	41	m	m	PROPN
ejpam-6635	136	42	≥	≥	NOUN
ejpam-6635	136	43	1	1	NUM
ejpam-6635	136	44	.	.	PUNCT
ejpam-6635	137	1	proof	proof	NOUN
ejpam-6635	137	2	.	.	PUNCT
ejpam-6635	138	1	(	(	PUNCT
ejpam-6635	138	2	i	i	NOUN
ejpam-6635	138	3	)	)	PUNCT
ejpam-6635	138	4	suppose	suppose	VERB
ejpam-6635	138	5	spnd(gj	spnd(gj	NOUN
ejpam-6635	138	6	)	)	PUNCT
ejpam-6635	138	7	=	=	SYM
ejpam-6635	138	8	2	2	NUM
ejpam-6635	138	9	for	for	ADP
ejpam-6635	138	10	some	some	DET
ejpam-6635	138	11	j	j	PROPN
ejpam-6635	138	12	∈	∈	PROPN
ejpam-6635	139	1	[	[	X
ejpam-6635	139	2	k	k	X
ejpam-6635	139	3	]	]	X
ejpam-6635	139	4	.	.	PUNCT
ejpam-6635	140	1	let	let	VERB
ejpam-6635	140	2	s	s	VERB
ejpam-6635	140	3	=	=	PUNCT
ejpam-6635	140	4	{	{	PUNCT
ejpam-6635	140	5	p	p	X
ejpam-6635	140	6	,	,	PUNCT
ejpam-6635	140	7	q	q	AUX
ejpam-6635	140	8	}	}	PUNCT
ejpam-6635	140	9	be	be	AUX
ejpam-6635	140	10	an	an	DET
ejpam-6635	140	11	spnd	spnd	NOUN
ejpam-6635	140	12	-	-	PUNCT
ejpam-6635	140	13	set	set	NOUN
ejpam-6635	140	14	in	in	ADP
ejpam-6635	140	15	gj	gj	NOUN
ejpam-6635	140	16	.	.	PUNCT
ejpam-6635	141	1	then	then	ADV
ejpam-6635	141	2	s	s	VERB
ejpam-6635	141	3	is	be	AUX
ejpam-6635	141	4	a	a	DET
ejpam-6635	141	5	pointwise	pointwise	ADJ
ejpam-6635	141	6	non	non	ADJ
ejpam-6635	141	7	-	-	ADJ
ejpam-6635	141	8	dominating	dominating	ADJ
ejpam-6635	141	9	set	set	NOUN
ejpam-6635	141	10	in	in	ADP
ejpam-6635	141	11	g.	g.	PROPN
ejpam-6635	141	12	let	let	VERB
ejpam-6635	141	13	x	x	SYM
ejpam-6635	141	14	∈	∈	PROPN
ejpam-6635	141	15	v	v	X
ejpam-6635	141	16	(	(	PUNCT
ejpam-6635	141	17	g	g	NOUN
ejpam-6635	141	18	)	)	PUNCT
ejpam-6635	141	19	\	\	PUNCT
ejpam-6635	141	20	s.	s.	PROPN
ejpam-6635	142	1	if	if	SCONJ
ejpam-6635	142	2	x	x	PROPN
ejpam-6635	142	3	∈	∈	PROPN
ejpam-6635	142	4	v	v	NOUN
ejpam-6635	142	5	(	(	PUNCT
ejpam-6635	142	6	gj	gj	PROPN
ejpam-6635	142	7	)	)	PUNCT
ejpam-6635	142	8	,	,	PUNCT
ejpam-6635	142	9	then	then	ADV
ejpam-6635	142	10	there	there	PRON
ejpam-6635	142	11	exists	exist	VERB
ejpam-6635	142	12	v	v	ADP
ejpam-6635	142	13	∈	∈	PROPN
ejpam-6635	142	14	s	s	PART
ejpam-6635	142	15	\	\	NOUN
ejpam-6635	142	16	ng(x	ng(x	NUM
ejpam-6635	142	17	)	)	PUNCT
ejpam-6635	142	18	,	,	PUNCT
ejpam-6635	142	19	say	say	VERB
ejpam-6635	142	20	v	v	ADP
ejpam-6635	142	21	=	=	SYM
ejpam-6635	142	22	p	p	NOUN
ejpam-6635	142	23	,	,	PUNCT
ejpam-6635	142	24	such	such	ADJ
ejpam-6635	142	25	that	that	SCONJ
ejpam-6635	142	26	(	(	PUNCT
ejpam-6635	142	27	s	s	X
ejpam-6635	142	28	\	\	X
ejpam-6635	142	29	{	{	PUNCT
ejpam-6635	142	30	p	p	NOUN
ejpam-6635	142	31	}	}	PUNCT
ejpam-6635	142	32	)	)	PUNCT
ejpam-6635	142	33	∪	∪	ADP
ejpam-6635	142	34	{	{	PUNCT
ejpam-6635	142	35	x	x	NOUN
ejpam-6635	142	36	}	}	PUNCT
ejpam-6635	142	37	=	=	SYM
ejpam-6635	142	38	{	{	PUNCT
ejpam-6635	142	39	x	x	NOUN
ejpam-6635	142	40	,	,	PUNCT
ejpam-6635	142	41	q	q	X
ejpam-6635	142	42	}	}	PUNCT
ejpam-6635	142	43	is	be	AUX
ejpam-6635	142	44	pointwise	pointwise	PROPN
ejpam-6635	142	45	non	non	ADJ
ejpam-6635	142	46	-	-	ADJ
ejpam-6635	142	47	dominating	dominating	NOUN
ejpam-6635	142	48	in	in	ADP
ejpam-6635	142	49	gj	gj	NOUN
ejpam-6635	142	50	because	because	SCONJ
ejpam-6635	142	51	s	s	NOUN
ejpam-6635	142	52	is	be	AUX
ejpam-6635	142	53	secure	secure	ADJ
ejpam-6635	142	54	pointwise	pointwise	ADP
ejpam-6635	142	55	non	non	ADJ
ejpam-6635	142	56	-	-	ADJ
ejpam-6635	142	57	dominating	dominating	NOUN
ejpam-6635	142	58	in	in	ADP
ejpam-6635	142	59	gj	gj	NOUN
ejpam-6635	142	60	.	.	PUNCT
ejpam-6635	143	1	hence	hence	ADV
ejpam-6635	143	2	,	,	PUNCT
ejpam-6635	143	3	{	{	PUNCT
ejpam-6635	143	4	x	x	NOUN
ejpam-6635	143	5	,	,	PUNCT
ejpam-6635	143	6	q	q	X
ejpam-6635	143	7	}	}	PUNCT
ejpam-6635	143	8	is	be	AUX
ejpam-6635	143	9	pointwise	pointwise	PROPN
ejpam-6635	143	10	non	non	ADJ
ejpam-6635	143	11	-	-	ADJ
ejpam-6635	143	12	dominating	dominating	NOUN
ejpam-6635	143	13	in	in	ADP
ejpam-6635	143	14	g.	g.	PROPN
ejpam-6635	143	15	suppose	suppose	VERB
ejpam-6635	143	16	x	x	X
ejpam-6635	143	17	∈	∈	PROPN
ejpam-6635	143	18	v	v	ADP
ejpam-6635	143	19	(	(	PUNCT
ejpam-6635	143	20	gi	gi	INTJ
ejpam-6635	143	21	)	)	PUNCT
ejpam-6635	143	22	for	for	ADP
ejpam-6635	143	23	i	i	PROPN
ejpam-6635	143	24	̸=	̸=	PROPN
ejpam-6635	143	25	j.	j.	PROPN
ejpam-6635	143	26	then	then	ADV
ejpam-6635	143	27	,	,	PUNCT
ejpam-6635	143	28	(	(	PUNCT
ejpam-6635	143	29	s	s	X
ejpam-6635	143	30	\	\	X
ejpam-6635	143	31	{	{	PUNCT
ejpam-6635	143	32	q	q	NOUN
ejpam-6635	143	33	}	}	PUNCT
ejpam-6635	143	34	)	)	PUNCT
ejpam-6635	143	35	∪	∪	ADP
ejpam-6635	143	36	{	{	PUNCT
ejpam-6635	143	37	x	x	NOUN
ejpam-6635	143	38	}	}	PUNCT
ejpam-6635	143	39	=	=	SYM
ejpam-6635	143	40	{	{	PUNCT
ejpam-6635	143	41	x	x	NOUN
ejpam-6635	143	42	,	,	PUNCT
ejpam-6635	143	43	p	p	X
ejpam-6635	143	44	}	}	PUNCT
ejpam-6635	143	45	is	be	AUX
ejpam-6635	143	46	pointwise	pointwise	PROPN
ejpam-6635	143	47	non	non	ADJ
ejpam-6635	143	48	-	-	ADJ
ejpam-6635	143	49	dominating	dominating	NOUN
ejpam-6635	143	50	in	in	ADP
ejpam-6635	143	51	g.	g.	PROPN
ejpam-6635	143	52	therefore	therefore	ADV
ejpam-6635	143	53	,	,	PUNCT
ejpam-6635	143	54	s	s	VERB
ejpam-6635	143	55	is	be	AUX
ejpam-6635	143	56	secure	secure	ADJ
ejpam-6635	144	1	pointwise	pointwise	ADP
ejpam-6635	144	2	non	non	ADJ
ejpam-6635	144	3	-	-	ADJ
ejpam-6635	144	4	dominating	dominating	NOUN
ejpam-6635	144	5	in	in	ADP
ejpam-6635	144	6	g.	g.	PROPN
ejpam-6635	144	7	this	this	PRON
ejpam-6635	144	8	implies	imply	VERB
ejpam-6635	144	9	that	that	SCONJ
ejpam-6635	144	10	spnd(g	spnd(g	PROPN
ejpam-6635	144	11	)	)	PUNCT
ejpam-6635	144	12	=	=	SYM
ejpam-6635	145	1	2	2	X
ejpam-6635	145	2	.	.	PUNCT
ejpam-6635	146	1	next	next	ADV
ejpam-6635	146	2	,	,	PUNCT
ejpam-6635	146	3	suppose	suppose	VERB
ejpam-6635	146	4	g	g	PROPN
ejpam-6635	146	5	has	have	VERB
ejpam-6635	146	6	two	two	NUM
ejpam-6635	146	7	trivial	trivial	ADJ
ejpam-6635	146	8	components	component	NOUN
ejpam-6635	146	9	,	,	PUNCT
ejpam-6635	146	10	say	say	VERB
ejpam-6635	146	11	g1	g1	PROPN
ejpam-6635	146	12	and	and	CCONJ
ejpam-6635	146	13	g2	g2	PROPN
ejpam-6635	146	14	.	.	PUNCT
ejpam-6635	147	1	then	then	ADV
ejpam-6635	147	2	d	d	X
ejpam-6635	147	3	=	=	SYM
ejpam-6635	147	4	v	v	PROPN
ejpam-6635	147	5	(	(	PUNCT
ejpam-6635	147	6	g1	g1	PROPN
ejpam-6635	147	7	)	)	PUNCT
ejpam-6635	147	8	∪	∪	NOUN
ejpam-6635	147	9	v	v	PROPN
ejpam-6635	147	10	(	(	PUNCT
ejpam-6635	147	11	g2	g2	PROPN
ejpam-6635	147	12	)	)	PUNCT
ejpam-6635	147	13	is	be	AUX
ejpam-6635	147	14	cleary	cleary	PROPN
ejpam-6635	147	15	an	an	DET
ejpam-6635	147	16	spnd	spnd	NOUN
ejpam-6635	147	17	-	-	PUNCT
ejpam-6635	147	18	set	set	NOUN
ejpam-6635	147	19	in	in	ADP
ejpam-6635	147	20	g.	g.	PROPN
ejpam-6635	147	21	hence	hence	ADV
ejpam-6635	147	22	,	,	PUNCT
ejpam-6635	147	23	spnd(g	spnd(g	PROPN
ejpam-6635	147	24	)	)	PUNCT
ejpam-6635	147	25	=	=	SYM
ejpam-6635	147	26	2	2	X
ejpam-6635	147	27	.	.	PUNCT
ejpam-6635	147	28	(	(	PUNCT
ejpam-6635	147	29	ii	ii	NOUN
ejpam-6635	147	30	)	)	PUNCT
ejpam-6635	147	31	suppose	suppose	VERB
ejpam-6635	147	32	k	k	PROPN
ejpam-6635	147	33	≥	≥	NUM
ejpam-6635	147	34	3	3	NUM
ejpam-6635	147	35	,	,	PUNCT
ejpam-6635	147	36	g	g	PROPN
ejpam-6635	147	37	has	have	VERB
ejpam-6635	147	38	at	at	ADP
ejpam-6635	147	39	most	most	ADV
ejpam-6635	147	40	one	one	NUM
ejpam-6635	147	41	trivial	trivial	ADJ
ejpam-6635	147	42	component	component	NOUN
ejpam-6635	147	43	,	,	PUNCT
ejpam-6635	147	44	and	and	CCONJ
ejpam-6635	147	45	pnd(gj	pnd(gj	NOUN
ejpam-6635	147	46	)	)	PUNCT
ejpam-6635	147	47	̸=	̸=	PROPN
ejpam-6635	147	48	2	2	NUM
ejpam-6635	147	49	for	for	ADP
ejpam-6635	147	50	all	all	DET
ejpam-6635	147	51	j	j	PROPN
ejpam-6635	147	52	∈	∈	PROPN
ejpam-6635	148	1	[	[	X
ejpam-6635	148	2	k	k	X
ejpam-6635	148	3	]	]	X
ejpam-6635	148	4	.	.	PUNCT
ejpam-6635	149	1	then	then	ADV
ejpam-6635	149	2	spnd(g	spnd(g	PROPN
ejpam-6635	149	3	)	)	PUNCT
ejpam-6635	149	4	≥	≥	NOUN
ejpam-6635	149	5	2	2	NUM
ejpam-6635	149	6	.	.	PUNCT
ejpam-6635	149	7	suppose	suppose	VERB
ejpam-6635	149	8	spnd(g	spnd(g	X
ejpam-6635	149	9	)	)	PUNCT
ejpam-6635	149	10	=	=	SYM
ejpam-6635	149	11	2	2	NUM
ejpam-6635	149	12	,	,	PUNCT
ejpam-6635	149	13	say	say	VERB
ejpam-6635	149	14	s	s	X
ejpam-6635	149	15	=	=	PUNCT
ejpam-6635	149	16	{	{	PUNCT
ejpam-6635	149	17	x	x	PROPN
ejpam-6635	149	18	,	,	PUNCT
ejpam-6635	149	19	y	y	PRON
ejpam-6635	149	20	}	}	PUNCT
ejpam-6635	149	21	is	be	AUX
ejpam-6635	149	22	an	an	DET
ejpam-6635	149	23	spnd	spnd	NOUN
ejpam-6635	149	24	-	-	PUNCT
ejpam-6635	149	25	set	set	NOUN
ejpam-6635	149	26	in	in	ADP
ejpam-6635	149	27	g.	g.	PROPN
ejpam-6635	149	28	since	since	SCONJ
ejpam-6635	149	29	pnd(gj	pnd(gj	PROPN
ejpam-6635	149	30	)	)	PUNCT
ejpam-6635	149	31	̸=	̸=	PROPN
ejpam-6635	149	32	2	2	NUM
ejpam-6635	149	33	for	for	ADP
ejpam-6635	149	34	all	all	DET
ejpam-6635	149	35	j	j	PROPN
ejpam-6635	149	36	∈	∈	PROPN
ejpam-6635	150	1	[	[	X
ejpam-6635	150	2	k	k	X
ejpam-6635	150	3	]	]	X
ejpam-6635	150	4	,	,	PUNCT
ejpam-6635	150	5	it	it	PRON
ejpam-6635	150	6	follows	follow	VERB
ejpam-6635	150	7	that	that	SCONJ
ejpam-6635	150	8	x	x	PUNCT
ejpam-6635	150	9	∈	∈	NOUN
ejpam-6635	150	10	v	v	ADP
ejpam-6635	150	11	(	(	PUNCT
ejpam-6635	150	12	gi	gi	NOUN
ejpam-6635	150	13	)	)	PUNCT
ejpam-6635	150	14	and	and	CCONJ
ejpam-6635	150	15	y	y	PROPN
ejpam-6635	150	16	∈	∈	PROPN
ejpam-6635	150	17	v	v	PROPN
ejpam-6635	150	18	(	(	PUNCT
ejpam-6635	150	19	gj	gj	NOUN
ejpam-6635	150	20	)	)	PUNCT
ejpam-6635	150	21	for	for	ADP
ejpam-6635	150	22	distinct	distinct	ADJ
ejpam-6635	150	23	indices	index	NOUN
ejpam-6635	150	24	i	i	PRON
ejpam-6635	150	25	,	,	PUNCT
ejpam-6635	150	26	j	j	PROPN
ejpam-6635	150	27	∈	∈	PROPN
ejpam-6635	151	1	[	[	X
ejpam-6635	151	2	k	k	X
ejpam-6635	151	3	]	]	X
ejpam-6635	151	4	.	.	PUNCT
ejpam-6635	152	1	since	since	SCONJ
ejpam-6635	152	2	g	g	PROPN
ejpam-6635	152	3	has	have	AUX
ejpam-6635	152	4	at	at	ADP
ejpam-6635	152	5	most	most	ADV
ejpam-6635	152	6	one	one	NUM
ejpam-6635	152	7	trivial	trivial	ADJ
ejpam-6635	152	8	component	component	NOUN
ejpam-6635	152	9	,	,	PUNCT
ejpam-6635	152	10	we	we	PRON
ejpam-6635	152	11	may	may	AUX
ejpam-6635	152	12	assume	assume	VERB
ejpam-6635	152	13	that	that	SCONJ
ejpam-6635	152	14	gi	gi	PROPN
ejpam-6635	152	15	is	be	AUX
ejpam-6635	152	16	a	a	DET
ejpam-6635	152	17	non	non	ADJ
ejpam-6635	152	18	-	-	ADJ
ejpam-6635	152	19	trivial	trivial	ADJ
ejpam-6635	152	20	graph	graph	NOUN
ejpam-6635	152	21	.	.	PUNCT
ejpam-6635	153	1	let	let	VERB
ejpam-6635	153	2	z	z	NOUN
ejpam-6635	153	3	∈	∈	PROPN
ejpam-6635	153	4	ng(x	ng(x	NUM
ejpam-6635	153	5	)	)	PUNCT
ejpam-6635	153	6	.	.	PUNCT
ejpam-6635	154	1	since	since	SCONJ
ejpam-6635	154	2	s	s	NOUN
ejpam-6635	154	3	is	be	AUX
ejpam-6635	154	4	secure	secure	ADJ
ejpam-6635	154	5	pointwise	pointwise	ADP
ejpam-6635	154	6	non	non	ADJ
ejpam-6635	154	7	-	-	ADJ
ejpam-6635	154	8	dominating	dominating	ADJ
ejpam-6635	154	9	,	,	PUNCT
ejpam-6635	154	10	(	(	PUNCT
ejpam-6635	154	11	s	s	NOUN
ejpam-6635	154	12	\	\	X
ejpam-6635	154	13	{	{	PUNCT
ejpam-6635	154	14	y	y	NOUN
ejpam-6635	154	15	}	}	PUNCT
ejpam-6635	154	16	)	)	PUNCT
ejpam-6635	154	17	∪	∪	ADP
ejpam-6635	154	18	{	{	PUNCT
ejpam-6635	154	19	z	z	NOUN
ejpam-6635	154	20	}	}	PUNCT
ejpam-6635	154	21	=	=	SYM
ejpam-6635	154	22	{	{	PUNCT
ejpam-6635	154	23	x	x	NOUN
ejpam-6635	154	24	,	,	PUNCT
ejpam-6635	154	25	z	z	NOUN
ejpam-6635	154	26	}	}	PUNCT
ejpam-6635	154	27	is	be	AUX
ejpam-6635	154	28	pointwise	pointwise	PROPN
ejpam-6635	154	29	non	non	ADJ
ejpam-6635	154	30	-	-	ADJ
ejpam-6635	154	31	dominating	dominating	NOUN
ejpam-6635	154	32	in	in	ADP
ejpam-6635	154	33	g.	g.	PROPN
ejpam-6635	154	34	hence	hence	ADV
ejpam-6635	154	35	,	,	PUNCT
ejpam-6635	154	36	{	{	PUNCT
ejpam-6635	154	37	x	x	NOUN
ejpam-6635	154	38	,	,	PUNCT
ejpam-6635	154	39	z	z	NOUN
ejpam-6635	154	40	}	}	PUNCT
ejpam-6635	154	41	is	be	AUX
ejpam-6635	154	42	pointwise	pointwise	PROPN
ejpam-6635	154	43	non	non	ADJ
ejpam-6635	154	44	-	-	ADJ
ejpam-6635	154	45	dominating	dominating	NOUN
ejpam-6635	154	46	in	in	ADP
ejpam-6635	154	47	gi	gi	NOUN
ejpam-6635	154	48	,	,	PUNCT
ejpam-6635	154	49	a	a	DET
ejpam-6635	154	50	contradiction	contradiction	NOUN
ejpam-6635	154	51	.	.	PUNCT
ejpam-6635	155	1	thus	thus	ADV
ejpam-6635	155	2	,	,	PUNCT
ejpam-6635	155	3	spnd(g	spnd(g	PROPN
ejpam-6635	155	4	)	)	PUNCT
ejpam-6635	155	5	≥	≥	NOUN
ejpam-6635	155	6	3	3	NUM
ejpam-6635	155	7	.	.	PUNCT
ejpam-6635	155	8	pick	pick	VERB
ejpam-6635	155	9	any	any	DET
ejpam-6635	155	10	aj	aj	PROPN
ejpam-6635	155	11	∈	∈	PROPN
ejpam-6635	155	12	v	v	PROPN
ejpam-6635	155	13	(	(	PUNCT
ejpam-6635	155	14	gj	gj	NOUN
ejpam-6635	155	15	)	)	PUNCT
ejpam-6635	155	16	for	for	ADP
ejpam-6635	155	17	j	j	PROPN
ejpam-6635	155	18	∈	∈	PROPN
ejpam-6635	155	19	{	{	PUNCT
ejpam-6635	155	20	1	1	NUM
ejpam-6635	155	21	,	,	PUNCT
ejpam-6635	155	22	2	2	NUM
ejpam-6635	155	23	,	,	PUNCT
ejpam-6635	155	24	3	3	NUM
ejpam-6635	155	25	}	}	PUNCT
ejpam-6635	155	26	and	and	CCONJ
ejpam-6635	155	27	setd	setd	NOUN
ejpam-6635	155	28	=	=	SYM
ejpam-6635	155	29	{	{	PUNCT
ejpam-6635	155	30	a1	a1	PROPN
ejpam-6635	155	31	,	,	PUNCT
ejpam-6635	155	32	a2	a2	PROPN
ejpam-6635	155	33	,	,	PUNCT
ejpam-6635	155	34	a3	a3	NOUN
ejpam-6635	155	35	}	}	PUNCT
ejpam-6635	155	36	.	.	PUNCT
ejpam-6635	156	1	then	then	ADV
ejpam-6635	156	2	clearly	clearly	ADV
ejpam-6635	156	3	,	,	PUNCT
ejpam-6635	156	4	d	d	PRON
ejpam-6635	156	5	is	be	AUX
ejpam-6635	156	6	a	a	DET
ejpam-6635	156	7	secure	secure	ADJ
ejpam-6635	156	8	pointwise	pointwise	ADJ
ejpam-6635	156	9	non	non	ADJ
ejpam-6635	156	10	-	-	ADJ
ejpam-6635	156	11	dominating	dominating	ADJ
ejpam-6635	156	12	set	set	NOUN
ejpam-6635	156	13	in	in	ADP
ejpam-6635	156	14	g.	g.	PROPN
ejpam-6635	156	15	therefore	therefore	ADV
ejpam-6635	156	16	,	,	PUNCT
ejpam-6635	156	17	spnd(g	spnd(g	PROPN
ejpam-6635	156	18	)	)	PUNCT
ejpam-6635	157	1	=	=	SYM
ejpam-6635	157	2	|d|	|d|	PROPN
ejpam-6635	157	3	=	=	SYM
ejpam-6635	157	4	3	3	X
ejpam-6635	157	5	.	.	PUNCT
ejpam-6635	157	6	(	(	PUNCT
ejpam-6635	157	7	iii	iii	NOUN
ejpam-6635	157	8	)	)	PUNCT
ejpam-6635	157	9	suppose	suppose	VERB
ejpam-6635	157	10	now	now	ADV
ejpam-6635	157	11	that	that	SCONJ
ejpam-6635	157	12	k	k	PROPN
ejpam-6635	157	13	=	=	SYM
ejpam-6635	157	14	2	2	NUM
ejpam-6635	157	15	and	and	CCONJ
ejpam-6635	157	16	gj	gj	NOUN
ejpam-6635	157	17	is	be	AUX
ejpam-6635	157	18	complete	complete	ADJ
ejpam-6635	157	19	for	for	ADP
ejpam-6635	157	20	each	each	DET
ejpam-6635	157	21	j	j	PROPN
ejpam-6635	157	22	∈	∈	PROPN
ejpam-6635	157	23	{	{	PUNCT
ejpam-6635	157	24	1	1	NUM
ejpam-6635	157	25	,	,	PUNCT
ejpam-6635	157	26	2	2	NUM
ejpam-6635	157	27	}	}	PUNCT
ejpam-6635	157	28	.	.	PUNCT
ejpam-6635	158	1	since	since	SCONJ
ejpam-6635	158	2	spnd(k2	spnd(k2	NOUN
ejpam-6635	158	3	)	)	PUNCT
ejpam-6635	158	4	=	=	SYM
ejpam-6635	158	5	2	2	NUM
ejpam-6635	158	6	,	,	PUNCT
ejpam-6635	158	7	it	it	PRON
ejpam-6635	158	8	follows	follow	VERB
ejpam-6635	158	9	from	from	ADP
ejpam-6635	158	10	(	(	PUNCT
ejpam-6635	158	11	i	i	NOUN
ejpam-6635	158	12	)	)	PUNCT
ejpam-6635	158	13	that	that	PRON
ejpam-6635	158	14	spnd(g	spnd(g	VERB
ejpam-6635	158	15	)	)	PUNCT
ejpam-6635	158	16	=	=	SYM
ejpam-6635	158	17	2	2	NUM
ejpam-6635	158	18	whenever	whenever	SCONJ
ejpam-6635	158	19	g	g	PROPN
ejpam-6635	158	20	=	=	SYM
ejpam-6635	158	21	k2	k2	PROPN
ejpam-6635	158	22	∪km	∪km	PROPN
ejpam-6635	158	23	for	for	ADP
ejpam-6635	158	24	m	m	PROPN
ejpam-6635	158	25	≥	≥	NOUN
ejpam-6635	158	26	1	1	NUM
ejpam-6635	158	27	.	.	PUNCT
ejpam-6635	159	1	next	next	ADV
ejpam-6635	159	2	,	,	PUNCT
ejpam-6635	159	3	suppose	suppose	VERB
ejpam-6635	159	4	g	g	PROPN
ejpam-6635	159	5	=	=	PUNCT
ejpam-6635	159	6	k3	k3	VERB
ejpam-6635	159	7	∪km	∪km	PROPN
ejpam-6635	159	8	where	where	SCONJ
ejpam-6635	159	9	m	m	PROPN
ejpam-6635	159	10	≥	≥	NOUN
ejpam-6635	159	11	3	3	NUM
ejpam-6635	159	12	.	.	PUNCT
ejpam-6635	160	1	clearly	clearly	ADV
ejpam-6635	160	2	,	,	PUNCT
ejpam-6635	160	3	spnd(g	spnd(g	PROPN
ejpam-6635	160	4	)	)	PUNCT
ejpam-6635	160	5	≥	≥	NOUN
ejpam-6635	160	6	3	3	NUM
ejpam-6635	160	7	.	.	PUNCT
ejpam-6635	161	1	since	since	SCONJ
ejpam-6635	161	2	s	s	PART
ejpam-6635	161	3	=	=	SYM
ejpam-6635	161	4	v	v	PROPN
ejpam-6635	161	5	(	(	PUNCT
ejpam-6635	161	6	k3	k3	PROPN
ejpam-6635	161	7	)	)	PUNCT
ejpam-6635	161	8	is	be	AUX
ejpam-6635	161	9	a	a	DET
ejpam-6635	161	10	secure	secure	ADJ
ejpam-6635	161	11	pointwise	pointwise	ADJ
ejpam-6635	161	12	non	non	ADJ
ejpam-6635	161	13	-	-	ADJ
ejpam-6635	161	14	dominating	dominating	ADJ
ejpam-6635	161	15	set	set	NOUN
ejpam-6635	161	16	in	in	ADP
ejpam-6635	161	17	g	g	PROPN
ejpam-6635	161	18	,	,	PUNCT
ejpam-6635	161	19	it	it	PRON
ejpam-6635	161	20	follows	follow	VERB
ejpam-6635	161	21	that	that	SCONJ
ejpam-6635	161	22	spnd(g	spnd(g	PROPN
ejpam-6635	161	23	)	)	PUNCT
ejpam-6635	161	24	=	=	PUNCT
ejpam-6635	161	25	|s|	|s|	NOUN
ejpam-6635	161	26	=	=	SYM
ejpam-6635	161	27	3	3	NUM
ejpam-6635	161	28	.	.	PUNCT
ejpam-6635	162	1	next	next	ADV
ejpam-6635	162	2	,	,	PUNCT
ejpam-6635	162	3	suppose	suppose	VERB
ejpam-6635	162	4	g	g	PROPN
ejpam-6635	162	5	=	=	SYM
ejpam-6635	162	6	kr	kr	PROPN
ejpam-6635	162	7	∪	∪	VERB
ejpam-6635	162	8	km	km	NOUN
ejpam-6635	162	9	where	where	SCONJ
ejpam-6635	162	10	r	r	NOUN
ejpam-6635	162	11	,	,	PUNCT
ejpam-6635	162	12	m	m	VERB
ejpam-6635	162	13	≥	≥	NOUN
ejpam-6635	162	14	4	4	NUM
ejpam-6635	162	15	.	.	PUNCT
ejpam-6635	163	1	clearly	clearly	ADV
ejpam-6635	163	2	,	,	PUNCT
ejpam-6635	163	3	spnd(g	spnd(g	PROPN
ejpam-6635	163	4	)	)	PUNCT
ejpam-6635	163	5	≥	≥	NOUN
ejpam-6635	163	6	3	3	NUM
ejpam-6635	164	1	.	.	PUNCT
ejpam-6635	164	2	suppose	suppose	VERB
ejpam-6635	164	3	spnd(g	spnd(g	X
ejpam-6635	164	4	)	)	PUNCT
ejpam-6635	164	5	=	=	SYM
ejpam-6635	165	1	3	3	X
ejpam-6635	165	2	,	,	PUNCT
ejpam-6635	165	3	say	say	VERB
ejpam-6635	165	4	q	q	X
ejpam-6635	165	5	=	=	PUNCT
ejpam-6635	165	6	{	{	PUNCT
ejpam-6635	165	7	x	x	PROPN
ejpam-6635	165	8	,	,	PUNCT
ejpam-6635	165	9	y	y	PROPN
ejpam-6635	165	10	,	,	PUNCT
ejpam-6635	165	11	z	z	NOUN
ejpam-6635	165	12	}	}	PUNCT
ejpam-6635	165	13	is	be	AUX
ejpam-6635	165	14	an	an	DET
ejpam-6635	165	15	spnd	spnd	NOUN
ejpam-6635	165	16	-	-	PUNCT
ejpam-6635	165	17	set	set	NOUN
ejpam-6635	165	18	in	in	ADP
ejpam-6635	165	19	g.	g.	PROPN
ejpam-6635	165	20	since	since	SCONJ
ejpam-6635	165	21	pnd(kr	pnd(kr	NOUN
ejpam-6635	165	22	)	)	PUNCT
ejpam-6635	166	1	=	=	SYM
ejpam-6635	166	2	r	r	NOUN
ejpam-6635	166	3	≥	≥	NUM
ejpam-6635	166	4	4	4	NUM
ejpam-6635	166	5	and	and	CCONJ
ejpam-6635	166	6	pnd(km	pnd(km	NOUN
ejpam-6635	166	7	)	)	PUNCT
ejpam-6635	166	8	=	=	SYM
ejpam-6635	166	9	m	m	VERB
ejpam-6635	166	10	≥	≥	NOUN
ejpam-6635	166	11	4	4	NUM
ejpam-6635	166	12	,	,	PUNCT
ejpam-6635	166	13	we	we	PRON
ejpam-6635	166	14	may	may	AUX
ejpam-6635	166	15	assume	assume	VERB
ejpam-6635	166	16	that	that	SCONJ
ejpam-6635	166	17	x	x	X
ejpam-6635	166	18	,	,	PUNCT
ejpam-6635	166	19	y	y	PROPN
ejpam-6635	166	20	∈	∈	PROPN
ejpam-6635	166	21	v	v	PROPN
ejpam-6635	166	22	(	(	PUNCT
ejpam-6635	166	23	kr	kr	PROPN
ejpam-6635	166	24	)	)	PUNCT
ejpam-6635	166	25	and	and	CCONJ
ejpam-6635	166	26	z	z	NOUN
ejpam-6635	166	27	∈	∈	PROPN
ejpam-6635	166	28	v	v	NOUN
ejpam-6635	166	29	(	(	PUNCT
ejpam-6635	166	30	km	km	PROPN
ejpam-6635	166	31	)	)	PUNCT
ejpam-6635	166	32	.	.	PUNCT
ejpam-6635	167	1	let	let	VERB
ejpam-6635	167	2	p	p	PRON
ejpam-6635	167	3	∈	∈	PROPN
ejpam-6635	167	4	v	v	X
ejpam-6635	167	5	(	(	PUNCT
ejpam-6635	167	6	kr	kr	PROPN
ejpam-6635	167	7	)	)	PUNCT
ejpam-6635	167	8	\	\	NOUN
ejpam-6635	167	9	{	{	PUNCT
ejpam-6635	167	10	x	x	NOUN
ejpam-6635	167	11	,	,	PUNCT
ejpam-6635	167	12	y	y	PROPN
ejpam-6635	167	13	}	}	PUNCT
ejpam-6635	167	14	.	.	PUNCT
ejpam-6635	168	1	since	since	SCONJ
ejpam-6635	168	2	q	q	PROPN
ejpam-6635	168	3	is	be	AUX
ejpam-6635	168	4	secure	secure	ADJ
ejpam-6635	168	5	pointwise	pointwise	PROPN
ejpam-6635	168	6	non	non	ADJ
ejpam-6635	168	7	-	-	ADJ
ejpam-6635	168	8	dominating	dominating	ADJ
ejpam-6635	168	9	,	,	PUNCT
ejpam-6635	168	10	it	it	PRON
ejpam-6635	168	11	follows	follow	VERB
ejpam-6635	168	12	that	that	SCONJ
ejpam-6635	168	13	(	(	PUNCT
ejpam-6635	168	14	q	q	NOUN
ejpam-6635	168	15	\	\	X
ejpam-6635	168	16	{	{	PUNCT
ejpam-6635	168	17	z	z	NOUN
ejpam-6635	168	18	}	}	PUNCT
ejpam-6635	168	19	)	)	PUNCT
ejpam-6635	168	20	∪	∪	ADP
ejpam-6635	168	21	{	{	PUNCT
ejpam-6635	168	22	p	p	NOUN
ejpam-6635	168	23	}	}	PUNCT
ejpam-6635	168	24	=	=	SYM
ejpam-6635	168	25	{	{	PUNCT
ejpam-6635	168	26	x	x	NOUN
ejpam-6635	168	27	,	,	PUNCT
ejpam-6635	168	28	y	y	PROPN
ejpam-6635	168	29	,	,	PUNCT
ejpam-6635	168	30	p	p	PRON
ejpam-6635	168	31	}	}	PUNCT
ejpam-6635	168	32	is	be	AUX
ejpam-6635	168	33	pointwise	pointwise	PROPN
ejpam-6635	168	34	non	non	ADJ
ejpam-6635	168	35	-	-	ADJ
ejpam-6635	168	36	dominating	dominating	NOUN
ejpam-6635	168	37	in	in	ADP
ejpam-6635	168	38	g	g	PROPN
ejpam-6635	168	39	(	(	PUNCT
ejpam-6635	168	40	and	and	CCONJ
ejpam-6635	168	41	in	in	ADP
ejpam-6635	168	42	kr	kr	NOUN
ejpam-6635	168	43	)	)	PUNCT
ejpam-6635	168	44	,	,	PUNCT
ejpam-6635	168	45	contrary	contrary	ADV
ejpam-6635	168	46	to	to	ADP
ejpam-6635	168	47	the	the	DET
ejpam-6635	168	48	fact	fact	NOUN
ejpam-6635	168	49	that	that	SCONJ
ejpam-6635	168	50	pnd(kr	pnd(kr	X
ejpam-6635	168	51	)	)	PUNCT
ejpam-6635	168	52	≥	≥	NOUN
ejpam-6635	168	53	4	4	NUM
ejpam-6635	168	54	.	.	PUNCT
ejpam-6635	169	1	thus	thus	ADV
ejpam-6635	169	2	,	,	PUNCT
ejpam-6635	169	3	spnd(g	spnd(g	PROPN
ejpam-6635	169	4	)	)	PUNCT
ejpam-6635	169	5	≥	≥	NOUN
ejpam-6635	169	6	4	4	NUM
ejpam-6635	169	7	.	.	PUNCT
ejpam-6635	169	8	choose	choose	VERB
ejpam-6635	169	9	any	any	DET
ejpam-6635	169	10	a	a	NOUN
ejpam-6635	169	11	,	,	PUNCT
ejpam-6635	169	12	b	b	PROPN
ejpam-6635	169	13	∈	∈	PROPN
ejpam-6635	169	14	v	v	NOUN
ejpam-6635	169	15	(	(	PUNCT
ejpam-6635	169	16	kr	kr	PROPN
ejpam-6635	169	17	)	)	PUNCT
ejpam-6635	169	18	and	and	CCONJ
ejpam-6635	169	19	c	c	X
ejpam-6635	169	20	,	,	PUNCT
ejpam-6635	169	21	d	d	PROPN
ejpam-6635	169	22	∈	∈	PROPN
ejpam-6635	169	23	v	v	NOUN
ejpam-6635	169	24	(	(	PUNCT
ejpam-6635	169	25	km	km	PROPN
ejpam-6635	169	26	)	)	PUNCT
ejpam-6635	169	27	.	.	PUNCT
ejpam-6635	170	1	then	then	ADV
ejpam-6635	170	2	r	r	NOUN
ejpam-6635	170	3	=	=	PUNCT
ejpam-6635	170	4	{	{	PUNCT
ejpam-6635	170	5	a	a	PRON
ejpam-6635	170	6	,	,	PUNCT
ejpam-6635	170	7	b	b	NOUN
ejpam-6635	170	8	,	,	PUNCT
ejpam-6635	170	9	c	c	NOUN
ejpam-6635	170	10	,	,	PUNCT
ejpam-6635	170	11	d	d	X
ejpam-6635	170	12	}	}	PUNCT
ejpam-6635	170	13	is	be	AUX
ejpam-6635	170	14	a	a	DET
ejpam-6635	170	15	secure	secure	ADJ
ejpam-6635	170	16	pointwise	pointwise	ADJ
ejpam-6635	170	17	non	non	ADJ
ejpam-6635	170	18	-	-	ADJ
ejpam-6635	170	19	dominating	dominating	ADJ
ejpam-6635	170	20	set	set	NOUN
ejpam-6635	170	21	in	in	ADP
ejpam-6635	170	22	g.	g.	PROPN
ejpam-6635	170	23	thus	thus	ADV
ejpam-6635	170	24	,	,	PUNCT
ejpam-6635	170	25	spnd(g	spnd(g	PROPN
ejpam-6635	170	26	)	)	PUNCT
ejpam-6635	170	27	=	=	SYM
ejpam-6635	170	28	4	4	X
ejpam-6635	170	29	.	.	PUNCT
ejpam-6635	170	30	f.	f.	PROPN
ejpam-6635	170	31	alfeche	alfeche	PROPN
ejpam-6635	170	32	,	,	PUNCT
ejpam-6635	170	33	s.	s.	PROPN
ejpam-6635	170	34	canoy	canoy	PROPN
ejpam-6635	170	35	jr	jr	PROPN
ejpam-6635	170	36	.	.	PROPN
ejpam-6635	170	37	/	/	SYM
ejpam-6635	170	38	eur	eur	PROPN
ejpam-6635	170	39	.	.	PUNCT
ejpam-6635	171	1	j.	j.	PROPN
ejpam-6635	171	2	pure	pure	PROPN
ejpam-6635	171	3	appl	appl	PROPN
ejpam-6635	171	4	.	.	PROPN
ejpam-6635	171	5	math	math	PROPN
ejpam-6635	171	6	,	,	PUNCT
ejpam-6635	171	7	18	18	NUM
ejpam-6635	171	8	(	(	PUNCT
ejpam-6635	171	9	3	3	NUM
ejpam-6635	171	10	)	)	PUNCT
ejpam-6635	171	11	(	(	PUNCT
ejpam-6635	171	12	2025	2025	NUM
ejpam-6635	171	13	)	)	PUNCT
ejpam-6635	171	14	,	,	PUNCT
ejpam-6635	171	15	6635	6635	NUM
ejpam-6635	171	16	6	6	NUM
ejpam-6635	171	17	of	of	ADP
ejpam-6635	171	18	11	11	NUM
ejpam-6635	171	19	finally	finally	ADV
ejpam-6635	171	20	,	,	PUNCT
ejpam-6635	171	21	suppose	suppose	VERB
ejpam-6635	171	22	g	g	PROPN
ejpam-6635	171	23	=	=	PROPN
ejpam-6635	171	24	k1	k1	PROPN
ejpam-6635	171	25	∪	∪	ADP
ejpam-6635	171	26	km	km	NOUN
ejpam-6635	171	27	where	where	SCONJ
ejpam-6635	171	28	m	m	VERB
ejpam-6635	171	29	≥	≥	NOUN
ejpam-6635	171	30	1	1	NUM
ejpam-6635	171	31	.	.	PUNCT
ejpam-6635	172	1	clearly	clearly	ADV
ejpam-6635	172	2	,	,	PUNCT
ejpam-6635	172	3	spnd(g	spnd(g	PROPN
ejpam-6635	172	4	)	)	PUNCT
ejpam-6635	173	1	=	=	PUNCT
ejpam-6635	173	2	m	m	NOUN
ejpam-6635	173	3	if	if	SCONJ
ejpam-6635	173	4	m	m	VERB
ejpam-6635	173	5	∈	∈	NOUN
ejpam-6635	173	6	{	{	PUNCT
ejpam-6635	173	7	1	1	NUM
ejpam-6635	173	8	,	,	PUNCT
ejpam-6635	173	9	2	2	NUM
ejpam-6635	173	10	}	}	PUNCT
ejpam-6635	173	11	.	.	PUNCT
ejpam-6635	174	1	suppose	suppose	VERB
ejpam-6635	174	2	m	m	PRON
ejpam-6635	174	3	≥	≥	NOUN
ejpam-6635	174	4	3	3	X
ejpam-6635	174	5	.	.	PUNCT
ejpam-6635	175	1	let	let	VERB
ejpam-6635	175	2	s	s	PRON
ejpam-6635	175	3	be	be	AUX
ejpam-6635	175	4	an	an	DET
ejpam-6635	175	5	spnd	spnd	NOUN
ejpam-6635	175	6	-	-	PUNCT
ejpam-6635	175	7	set	set	NOUN
ejpam-6635	175	8	in	in	ADP
ejpam-6635	175	9	g.	g.	PROPN
ejpam-6635	175	10	suppose	suppose	VERB
ejpam-6635	175	11	|s|	|s|	PROPN
ejpam-6635	175	12	<	<	X
ejpam-6635	175	13	m.	m.	NOUN
ejpam-6635	175	14	since	since	SCONJ
ejpam-6635	175	15	pnd(km	pnd(km	NOUN
ejpam-6635	175	16	)	)	PUNCT
ejpam-6635	176	1	=	=	SYM
ejpam-6635	176	2	m	m	PROPN
ejpam-6635	176	3	,	,	PUNCT
ejpam-6635	176	4	it	it	PRON
ejpam-6635	176	5	follows	follow	VERB
ejpam-6635	176	6	that	that	SCONJ
ejpam-6635	176	7	v	v	NOUN
ejpam-6635	176	8	(	(	PUNCT
ejpam-6635	176	9	k1	k1	NOUN
ejpam-6635	176	10	)	)	PUNCT
ejpam-6635	176	11	⊆	⊆	NUM
ejpam-6635	176	12	s.	s.	PROPN
ejpam-6635	176	13	this	this	PRON
ejpam-6635	176	14	implies	imply	VERB
ejpam-6635	176	15	that	that	SCONJ
ejpam-6635	176	16	|v	|v	PROPN
ejpam-6635	176	17	(	(	PUNCT
ejpam-6635	176	18	km)∩s|	km)∩s|	VERB
ejpam-6635	176	19	≤	≤	NUM
ejpam-6635	176	20	m−	m−	PROPN
ejpam-6635	176	21	2	2	NUM
ejpam-6635	176	22	.	.	PUNCT
ejpam-6635	176	23	let	let	VERB
ejpam-6635	176	24	w	w	NOUN
ejpam-6635	176	25	∈	∈	PROPN
ejpam-6635	176	26	v	v	X
ejpam-6635	176	27	(	(	PUNCT
ejpam-6635	176	28	km	km	NOUN
ejpam-6635	176	29	)	)	PUNCT
ejpam-6635	176	30	\s	\s	NOUN
ejpam-6635	176	31	and	and	CCONJ
ejpam-6635	176	32	let	let	VERB
ejpam-6635	176	33	v	v	NOUN
ejpam-6635	176	34	(	(	PUNCT
ejpam-6635	176	35	k1	k1	NOUN
ejpam-6635	176	36	)	)	PUNCT
ejpam-6635	176	37	=	=	PRON
ejpam-6635	176	38	{	{	PUNCT
ejpam-6635	176	39	q	q	X
ejpam-6635	176	40	}	}	PUNCT
ejpam-6635	176	41	.	.	PUNCT
ejpam-6635	177	1	since	since	SCONJ
ejpam-6635	177	2	s	s	NOUN
ejpam-6635	177	3	is	be	AUX
ejpam-6635	177	4	secure	secure	ADJ
ejpam-6635	177	5	pointwise	pointwise	ADP
ejpam-6635	177	6	non	non	ADJ
ejpam-6635	177	7	-	-	ADJ
ejpam-6635	177	8	dominating	dominating	NOUN
ejpam-6635	177	9	in	in	ADP
ejpam-6635	177	10	g	g	PROPN
ejpam-6635	177	11	,	,	PUNCT
ejpam-6635	177	12	sw	sw	PROPN
ejpam-6635	177	13	=	=	PUNCT
ejpam-6635	177	14	(	(	PUNCT
ejpam-6635	177	15	s	s	NOUN
ejpam-6635	177	16	\	\	X
ejpam-6635	177	17	{	{	PUNCT
ejpam-6635	177	18	q	q	NOUN
ejpam-6635	177	19	}	}	PUNCT
ejpam-6635	177	20	)	)	PUNCT
ejpam-6635	177	21	∪	∪	ADP
ejpam-6635	177	22	{	{	PUNCT
ejpam-6635	177	23	w	w	NOUN
ejpam-6635	177	24	}	}	PUNCT
ejpam-6635	177	25	is	be	AUX
ejpam-6635	177	26	pointwise	pointwise	PROPN
ejpam-6635	177	27	non	non	ADJ
ejpam-6635	177	28	-	-	ADJ
ejpam-6635	177	29	dominating	dominating	NOUN
ejpam-6635	177	30	in	in	ADP
ejpam-6635	177	31	g	g	PROPN
ejpam-6635	177	32	(	(	PUNCT
ejpam-6635	177	33	and	and	CCONJ
ejpam-6635	177	34	in	in	ADP
ejpam-6635	177	35	km	km	PROPN
ejpam-6635	177	36	)	)	PUNCT
ejpam-6635	177	37	,	,	PUNCT
ejpam-6635	177	38	a	a	DET
ejpam-6635	177	39	contradiction	contradiction	NOUN
ejpam-6635	177	40	because	because	SCONJ
ejpam-6635	177	41	pnd(km	pnd(km	NOUN
ejpam-6635	177	42	)	)	PUNCT
ejpam-6635	177	43	=	=	PUNCT
ejpam-6635	178	1	m	m	VERB
ejpam-6635	178	2	>	>	X
ejpam-6635	178	3	m−1	m−1	PROPN
ejpam-6635	178	4	≥	≥	NUM
ejpam-6635	178	5	|sw|	|sw|	PROPN
ejpam-6635	178	6	.	.	PUNCT
ejpam-6635	179	1	therefore	therefore	ADV
ejpam-6635	179	2	,	,	PUNCT
ejpam-6635	179	3	spnd(g	spnd(g	PROPN
ejpam-6635	179	4	)	)	PUNCT
ejpam-6635	179	5	≥	≥	NOUN
ejpam-6635	179	6	m.	m.	NOUN
ejpam-6635	179	7	since	since	SCONJ
ejpam-6635	179	8	v	v	PROPN
ejpam-6635	179	9	(	(	PUNCT
ejpam-6635	179	10	km	km	PROPN
ejpam-6635	179	11	)	)	PUNCT
ejpam-6635	179	12	is	be	AUX
ejpam-6635	179	13	a	a	DET
ejpam-6635	179	14	secure	secure	ADJ
ejpam-6635	179	15	pointwise	pointwise	ADJ
ejpam-6635	179	16	non	non	ADJ
ejpam-6635	179	17	-	-	ADJ
ejpam-6635	179	18	dominating	dominating	ADJ
ejpam-6635	179	19	set	set	NOUN
ejpam-6635	179	20	in	in	ADP
ejpam-6635	179	21	g	g	PROPN
ejpam-6635	179	22	,	,	PUNCT
ejpam-6635	179	23	it	it	PRON
ejpam-6635	179	24	follows	follow	VERB
ejpam-6635	179	25	that	that	SCONJ
ejpam-6635	179	26	spnd(g	spnd(g	PROPN
ejpam-6635	179	27	)	)	PUNCT
ejpam-6635	179	28	=	=	SYM
ejpam-6635	179	29	m.	m.	NOUN
ejpam-6635	179	30	given	give	VERB
ejpam-6635	179	31	a	a	DET
ejpam-6635	179	32	graph	graph	NOUN
ejpam-6635	179	33	g	g	NOUN
ejpam-6635	179	34	,	,	PUNCT
ejpam-6635	179	35	the	the	DET
ejpam-6635	179	36	vertex	vertex	NOUN
ejpam-6635	179	37	set	set	VERB
ejpam-6635	179	38	v	v	NOUN
ejpam-6635	179	39	(	(	PUNCT
ejpam-6635	179	40	g	g	NOUN
ejpam-6635	179	41	)	)	PUNCT
ejpam-6635	179	42	is	be	AUX
ejpam-6635	179	43	a	a	DET
ejpam-6635	179	44	secure	secure	ADJ
ejpam-6635	179	45	hop	hop	NOUN
ejpam-6635	179	46	dominating	dominating	NOUN
ejpam-6635	179	47	set	set	NOUN
ejpam-6635	179	48	of	of	ADP
ejpam-6635	179	49	g.	g.	PROPN
ejpam-6635	179	50	thus	thus	ADV
ejpam-6635	179	51	,	,	PUNCT
ejpam-6635	179	52	every	every	DET
ejpam-6635	179	53	graph	graph	NOUN
ejpam-6635	179	54	admits	admit	VERB
ejpam-6635	179	55	a	a	DET
ejpam-6635	179	56	secure	secure	ADJ
ejpam-6635	179	57	hop	hop	NOUN
ejpam-6635	179	58	dominating	dominating	NOUN
ejpam-6635	179	59	set	set	NOUN
ejpam-6635	179	60	.	.	PUNCT
ejpam-6635	180	1	theorem	theorem	VERB
ejpam-6635	180	2	5	5	NUM
ejpam-6635	180	3	.	.	PUNCT
ejpam-6635	181	1	[	[	X
ejpam-6635	181	2	22	22	NUM
ejpam-6635	181	3	]	]	PUNCT
ejpam-6635	181	4	let	let	VERB
ejpam-6635	181	5	g	g	NOUN
ejpam-6635	181	6	and	and	CCONJ
ejpam-6635	181	7	h	h	NOUN
ejpam-6635	181	8	be	be	VERB
ejpam-6635	181	9	any	any	DET
ejpam-6635	181	10	two	two	NUM
ejpam-6635	181	11	graphs	graph	NOUN
ejpam-6635	181	12	.	.	PUNCT
ejpam-6635	182	1	a	a	DET
ejpam-6635	182	2	set	set	NOUN
ejpam-6635	182	3	s	s	NOUN
ejpam-6635	182	4	⊆	⊆	NUM
ejpam-6635	182	5	v	v	NOUN
ejpam-6635	182	6	(	(	PUNCT
ejpam-6635	182	7	g+h	g+h	PROPN
ejpam-6635	182	8	)	)	PUNCT
ejpam-6635	182	9	is	be	AUX
ejpam-6635	182	10	hop	hop	NOUN
ejpam-6635	182	11	dominating	dominating	NOUN
ejpam-6635	182	12	set	set	VERB
ejpam-6635	182	13	in	in	ADP
ejpam-6635	182	14	g+h	g+h	PROPN
ejpam-6635	182	15	if	if	SCONJ
ejpam-6635	182	16	and	and	CCONJ
ejpam-6635	182	17	only	only	ADV
ejpam-6635	182	18	if	if	SCONJ
ejpam-6635	182	19	s	s	NOUN
ejpam-6635	182	20	=	=	PUNCT
ejpam-6635	182	21	sg	sg	PROPN
ejpam-6635	182	22	∪sh	∪sh	NOUN
ejpam-6635	182	23	,	,	PUNCT
ejpam-6635	182	24	where	where	SCONJ
ejpam-6635	182	25	sg	sg	PROPN
ejpam-6635	182	26	and	and	CCONJ
ejpam-6635	182	27	sh	sh	PROPN
ejpam-6635	182	28	are	be	AUX
ejpam-6635	182	29	pointwise	pointwise	PROPN
ejpam-6635	182	30	non	non	ADJ
ejpam-6635	182	31	-	-	ADJ
ejpam-6635	182	32	dominating	dominating	ADJ
ejpam-6635	182	33	sets	set	NOUN
ejpam-6635	182	34	in	in	ADP
ejpam-6635	182	35	g	g	PROPN
ejpam-6635	182	36	and	and	CCONJ
ejpam-6635	182	37	h	h	NOUN
ejpam-6635	182	38	,	,	PUNCT
ejpam-6635	182	39	respectively	respectively	ADV
ejpam-6635	182	40	.	.	PUNCT
ejpam-6635	183	1	corollary	corollary	ADJ
ejpam-6635	183	2	3	3	NUM
ejpam-6635	183	3	.	.	PUNCT
ejpam-6635	184	1	[	[	X
ejpam-6635	184	2	22	22	NUM
ejpam-6635	184	3	]	]	PUNCT
ejpam-6635	184	4	let	let	VERB
ejpam-6635	184	5	g	g	NOUN
ejpam-6635	184	6	and	and	CCONJ
ejpam-6635	184	7	h	h	NOUN
ejpam-6635	184	8	be	be	VERB
ejpam-6635	184	9	any	any	DET
ejpam-6635	184	10	two	two	NUM
ejpam-6635	184	11	graphs	graph	NOUN
ejpam-6635	184	12	.	.	PUNCT
ejpam-6635	185	1	then	then	ADV
ejpam-6635	185	2	γh(g+h	γh(g+h	NUM
ejpam-6635	185	3	)	)	PUNCT
ejpam-6635	185	4	=	=	SYM
ejpam-6635	185	5	pnd(g	pnd(g	PROPN
ejpam-6635	185	6	)	)	PUNCT
ejpam-6635	185	7	+	+	NUM
ejpam-6635	185	8	pnd(h	pnd(h	NUM
ejpam-6635	185	9	)	)	PUNCT
ejpam-6635	185	10	.	.	PUNCT
ejpam-6635	186	1	theorem	theorem	VERB
ejpam-6635	186	2	6	6	NUM
ejpam-6635	186	3	.	.	PUNCT
ejpam-6635	187	1	let	let	VERB
ejpam-6635	187	2	g	g	NOUN
ejpam-6635	188	1	and	and	CCONJ
ejpam-6635	188	2	h	h	NOUN
ejpam-6635	188	3	be	be	VERB
ejpam-6635	188	4	any	any	DET
ejpam-6635	188	5	graphs	graph	NOUN
ejpam-6635	188	6	.	.	PUNCT
ejpam-6635	189	1	then	then	ADV
ejpam-6635	189	2	s	s	VERB
ejpam-6635	189	3	⊆	⊆	NUM
ejpam-6635	189	4	v	v	NOUN
ejpam-6635	189	5	(	(	PUNCT
ejpam-6635	189	6	g+h	g+h	PROPN
ejpam-6635	189	7	)	)	PUNCT
ejpam-6635	189	8	is	be	AUX
ejpam-6635	189	9	a	a	DET
ejpam-6635	189	10	secure	secure	ADJ
ejpam-6635	189	11	hop	hop	NOUN
ejpam-6635	189	12	dominating	dominating	NOUN
ejpam-6635	189	13	set	set	VERB
ejpam-6635	189	14	if	if	SCONJ
ejpam-6635	189	15	and	and	CCONJ
ejpam-6635	189	16	only	only	ADV
ejpam-6635	189	17	if	if	SCONJ
ejpam-6635	189	18	s	s	VERB
ejpam-6635	189	19	=	=	PUNCT
ejpam-6635	189	20	sg	sg	PART
ejpam-6635	189	21	∪	∪	NOUN
ejpam-6635	189	22	sh	sh	PROPN
ejpam-6635	189	23	and	and	CCONJ
ejpam-6635	189	24	sg	sg	PROPN
ejpam-6635	189	25	and	and	CCONJ
ejpam-6635	189	26	sh	sh	PROPN
ejpam-6635	189	27	are	be	AUX
ejpam-6635	189	28	secure	secure	ADJ
ejpam-6635	189	29	pointwise	pointwise	PROPN
ejpam-6635	189	30	non	non	ADJ
ejpam-6635	189	31	-	-	ADJ
ejpam-6635	189	32	dominating	dominating	ADJ
ejpam-6635	189	33	sets	set	NOUN
ejpam-6635	189	34	in	in	ADP
ejpam-6635	189	35	g	g	PROPN
ejpam-6635	189	36	and	and	CCONJ
ejpam-6635	189	37	h	h	NOUN
ejpam-6635	189	38	,	,	PUNCT
ejpam-6635	189	39	respectively	respectively	ADV
ejpam-6635	189	40	.	.	PUNCT
ejpam-6635	190	1	proof	proof	NOUN
ejpam-6635	190	2	.	.	PUNCT
ejpam-6635	191	1	suppose	suppose	VERB
ejpam-6635	191	2	s	s	PRON
ejpam-6635	191	3	is	be	AUX
ejpam-6635	191	4	a	a	DET
ejpam-6635	191	5	secure	secure	ADJ
ejpam-6635	191	6	hop	hop	NOUN
ejpam-6635	191	7	dominating	dominating	NOUN
ejpam-6635	191	8	set	set	VERB
ejpam-6635	191	9	in	in	ADP
ejpam-6635	191	10	g+h	g+h	PROPN
ejpam-6635	191	11	.	.	PUNCT
ejpam-6635	192	1	since	since	SCONJ
ejpam-6635	192	2	s	s	PROPN
ejpam-6635	192	3	is	be	AUX
ejpam-6635	192	4	a	a	DET
ejpam-6635	192	5	hop	hop	NOUN
ejpam-6635	192	6	dominating	dominating	NOUN
ejpam-6635	192	7	set	set	NOUN
ejpam-6635	192	8	,	,	PUNCT
ejpam-6635	192	9	s	s	PART
ejpam-6635	192	10	=	=	PUNCT
ejpam-6635	192	11	sg	sg	X
ejpam-6635	192	12	∪	∪	NOUN
ejpam-6635	192	13	sh	sh	PROPN
ejpam-6635	192	14	where	where	SCONJ
ejpam-6635	192	15	sg	sg	PROPN
ejpam-6635	192	16	and	and	CCONJ
ejpam-6635	192	17	sh	sh	PROPN
ejpam-6635	192	18	are	be	AUX
ejpam-6635	192	19	pointwise	pointwise	PROPN
ejpam-6635	192	20	non	non	ADJ
ejpam-6635	192	21	-	-	ADJ
ejpam-6635	192	22	dominating	dominating	ADJ
ejpam-6635	192	23	sets	set	NOUN
ejpam-6635	192	24	in	in	ADP
ejpam-6635	192	25	g	g	PROPN
ejpam-6635	192	26	and	and	CCONJ
ejpam-6635	192	27	h	h	NOUN
ejpam-6635	192	28	,	,	PUNCT
ejpam-6635	192	29	respectively	respectively	ADV
ejpam-6635	192	30	,	,	PUNCT
ejpam-6635	192	31	by	by	ADP
ejpam-6635	192	32	theorem	theorem	NOUN
ejpam-6635	192	33	5	5	NUM
ejpam-6635	192	34	.	.	PUNCT
ejpam-6635	193	1	let	let	VERB
ejpam-6635	193	2	v	v	NUM
ejpam-6635	193	3	∈	∈	PROPN
ejpam-6635	193	4	v	v	NOUN
ejpam-6635	193	5	(	(	PUNCT
ejpam-6635	193	6	g	g	NOUN
ejpam-6635	193	7	)	)	PUNCT
ejpam-6635	193	8	\	\	PROPN
ejpam-6635	193	9	sg	sg	PROPN
ejpam-6635	193	10	.	.	PUNCT
ejpam-6635	194	1	then	then	ADV
ejpam-6635	194	2	v	v	ADP
ejpam-6635	194	3	∈	∈	PROPN
ejpam-6635	194	4	v	v	NOUN
ejpam-6635	194	5	(	(	PUNCT
ejpam-6635	194	6	g	g	PROPN
ejpam-6635	194	7	+	+	NOUN
ejpam-6635	194	8	h	h	NOUN
ejpam-6635	194	9	)	)	PUNCT
ejpam-6635	194	10	\	\	NOUN
ejpam-6635	195	1	s.	s.	PROPN
ejpam-6635	195	2	since	since	SCONJ
ejpam-6635	195	3	s	s	PROPN
ejpam-6635	195	4	is	be	AUX
ejpam-6635	195	5	a	a	DET
ejpam-6635	195	6	secure	secure	ADJ
ejpam-6635	195	7	hop	hop	NOUN
ejpam-6635	195	8	dominating	dominating	NOUN
ejpam-6635	195	9	set	set	NOUN
ejpam-6635	195	10	,	,	PUNCT
ejpam-6635	195	11	there	there	PRON
ejpam-6635	195	12	exists	exist	VERB
ejpam-6635	195	13	w	w	PROPN
ejpam-6635	195	14	∈	∈	PROPN
ejpam-6635	195	15	s	s	PART
ejpam-6635	195	16	\ng+h(v	\ng+h(v	NOUN
ejpam-6635	195	17	)	)	PUNCT
ejpam-6635	195	18	such	such	ADJ
ejpam-6635	195	19	that	that	PRON
ejpam-6635	195	20	sv	sv	PROPN
ejpam-6635	196	1	=	=	PUNCT
ejpam-6635	196	2	(	(	PUNCT
ejpam-6635	196	3	s	s	NOUN
ejpam-6635	196	4	\	\	X
ejpam-6635	196	5	{	{	PUNCT
ejpam-6635	196	6	w	w	NOUN
ejpam-6635	196	7	}	}	PUNCT
ejpam-6635	196	8	)	)	PUNCT
ejpam-6635	196	9	∪	∪	ADP
ejpam-6635	196	10	{	{	PUNCT
ejpam-6635	196	11	v	v	NOUN
ejpam-6635	196	12	}	}	PUNCT
ejpam-6635	196	13	is	be	AUX
ejpam-6635	196	14	a	a	DET
ejpam-6635	196	15	hop	hop	NOUN
ejpam-6635	196	16	dominating	dominating	NOUN
ejpam-6635	196	17	set	set	NOUN
ejpam-6635	196	18	.	.	PUNCT
ejpam-6635	197	1	note	note	VERB
ejpam-6635	197	2	that	that	SCONJ
ejpam-6635	197	3	since	since	SCONJ
ejpam-6635	197	4	w	w	PROPN
ejpam-6635	197	5	∈	∈	PROPN
ejpam-6635	197	6	s	s	PART
ejpam-6635	197	7	\	\	PROPN
ejpam-6635	197	8	ng+h(v	ng+h(v	PROPN
ejpam-6635	197	9	)	)	PUNCT
ejpam-6635	197	10	,	,	PUNCT
ejpam-6635	197	11	w	w	PROPN
ejpam-6635	197	12	∈	∈	PROPN
ejpam-6635	197	13	sg	sg	ADP
ejpam-6635	197	14	\	\	NOUN
ejpam-6635	197	15	ng(v	ng(v	PUNCT
ejpam-6635	197	16	)	)	PUNCT
ejpam-6635	197	17	.	.	PUNCT
ejpam-6635	198	1	hence	hence	ADV
ejpam-6635	198	2	,	,	PUNCT
ejpam-6635	198	3	sv	sv	PROPN
ejpam-6635	198	4	=	=	PUNCT
ejpam-6635	199	1	[	[	X
ejpam-6635	199	2	sg	sg	ADP
ejpam-6635	199	3	\	\	PROPN
ejpam-6635	199	4	{	{	PUNCT
ejpam-6635	199	5	w	w	NOUN
ejpam-6635	199	6	}	}	PUNCT
ejpam-6635	199	7	)	)	PUNCT
ejpam-6635	199	8	∪	∪	ADP
ejpam-6635	199	9	{	{	PUNCT
ejpam-6635	199	10	v	v	NOUN
ejpam-6635	199	11	}	}	PUNCT
ejpam-6635	199	12	]	]	PUNCT
ejpam-6635	199	13	∪	∪	ADP
ejpam-6635	199	14	sh	sh	PROPN
ejpam-6635	199	15	.	.	PUNCT
ejpam-6635	200	1	by	by	ADP
ejpam-6635	200	2	theorem	theorem	NOUN
ejpam-6635	200	3	5	5	NUM
ejpam-6635	200	4	,	,	PUNCT
ejpam-6635	200	5	(	(	PUNCT
ejpam-6635	200	6	sg	sg	ADP
ejpam-6635	200	7	\	\	PROPN
ejpam-6635	200	8	{	{	PUNCT
ejpam-6635	200	9	w	w	NOUN
ejpam-6635	200	10	}	}	PUNCT
ejpam-6635	200	11	)	)	PUNCT
ejpam-6635	200	12	∪	∪	ADP
ejpam-6635	200	13	{	{	PUNCT
ejpam-6635	200	14	v	v	NOUN
ejpam-6635	200	15	}	}	PUNCT
ejpam-6635	200	16	is	be	AUX
ejpam-6635	200	17	a	a	DET
ejpam-6635	200	18	pointwise	pointwise	ADJ
ejpam-6635	200	19	nondominating	nondominate	VERB
ejpam-6635	200	20	set	set	NOUN
ejpam-6635	200	21	because	because	SCONJ
ejpam-6635	200	22	sv	sv	PROPN
ejpam-6635	200	23	is	be	AUX
ejpam-6635	200	24	a	a	DET
ejpam-6635	200	25	hop	hop	NOUN
ejpam-6635	200	26	dominating	dominating	NOUN
ejpam-6635	200	27	set	set	NOUN
ejpam-6635	200	28	.	.	PUNCT
ejpam-6635	201	1	this	this	PRON
ejpam-6635	201	2	shows	show	VERB
ejpam-6635	201	3	that	that	SCONJ
ejpam-6635	201	4	sg	sg	PROPN
ejpam-6635	201	5	is	be	AUX
ejpam-6635	201	6	a	a	DET
ejpam-6635	201	7	secure	secure	ADJ
ejpam-6635	201	8	pointwise	pointwise	ADJ
ejpam-6635	201	9	non	non	ADJ
ejpam-6635	201	10	-	-	ADJ
ejpam-6635	201	11	dominating	dominating	ADJ
ejpam-6635	201	12	set	set	NOUN
ejpam-6635	201	13	in	in	ADP
ejpam-6635	201	14	g.	g.	PROPN
ejpam-6635	201	15	similarly	similarly	ADV
ejpam-6635	201	16	,	,	PUNCT
ejpam-6635	201	17	sh	sh	PROPN
ejpam-6635	201	18	is	be	AUX
ejpam-6635	201	19	a	a	DET
ejpam-6635	201	20	secure	secure	ADJ
ejpam-6635	201	21	pointwise	pointwise	ADJ
ejpam-6635	201	22	non	non	ADJ
ejpam-6635	201	23	-	-	ADJ
ejpam-6635	201	24	dominating	dominating	ADJ
ejpam-6635	201	25	set	set	NOUN
ejpam-6635	201	26	in	in	ADP
ejpam-6635	201	27	h.	h.	PROPN
ejpam-6635	201	28	for	for	ADP
ejpam-6635	201	29	the	the	DET
ejpam-6635	201	30	converse	converse	NOUN
ejpam-6635	201	31	,	,	PUNCT
ejpam-6635	201	32	suppose	suppose	VERB
ejpam-6635	201	33	that	that	SCONJ
ejpam-6635	201	34	s	s	VERB
ejpam-6635	201	35	=	=	PUNCT
ejpam-6635	201	36	sg	sg	PROPN
ejpam-6635	201	37	∪sh	∪sh	NOUN
ejpam-6635	201	38	and	and	CCONJ
ejpam-6635	201	39	sg	sg	PROPN
ejpam-6635	201	40	and	and	CCONJ
ejpam-6635	201	41	sh	sh	PROPN
ejpam-6635	201	42	are	be	AUX
ejpam-6635	201	43	secure	secure	ADJ
ejpam-6635	201	44	pointwise	pointwise	ADJ
ejpam-6635	201	45	nondominating	nondominate	VERB
ejpam-6635	201	46	sets	set	NOUN
ejpam-6635	201	47	in	in	ADP
ejpam-6635	201	48	g	g	PROPN
ejpam-6635	201	49	and	and	CCONJ
ejpam-6635	201	50	h	h	NOUN
ejpam-6635	201	51	,	,	PUNCT
ejpam-6635	201	52	respectively	respectively	ADV
ejpam-6635	201	53	.	.	PUNCT
ejpam-6635	202	1	then	then	ADV
ejpam-6635	202	2	sg	sg	PROPN
ejpam-6635	202	3	and	and	CCONJ
ejpam-6635	202	4	sh	sh	PROPN
ejpam-6635	202	5	are	be	AUX
ejpam-6635	202	6	pointwise	pointwise	PROPN
ejpam-6635	202	7	non	non	ADJ
ejpam-6635	202	8	-	-	ADJ
ejpam-6635	202	9	dominating	dominating	ADJ
ejpam-6635	202	10	sets	set	NOUN
ejpam-6635	202	11	,	,	PUNCT
ejpam-6635	202	12	s	s	VERB
ejpam-6635	202	13	is	be	AUX
ejpam-6635	202	14	a	a	DET
ejpam-6635	202	15	hop	hop	NOUN
ejpam-6635	202	16	dominating	dominating	NOUN
ejpam-6635	202	17	set	set	VERB
ejpam-6635	202	18	in	in	ADP
ejpam-6635	202	19	g+h	g+h	PROPN
ejpam-6635	202	20	by	by	ADP
ejpam-6635	202	21	theorem	theorem	NOUN
ejpam-6635	202	22	5	5	NUM
ejpam-6635	202	23	.	.	PUNCT
ejpam-6635	203	1	let	let	VERB
ejpam-6635	203	2	x	x	SYM
ejpam-6635	203	3	∈	∈	PROPN
ejpam-6635	203	4	v	v	X
ejpam-6635	203	5	(	(	PUNCT
ejpam-6635	203	6	g+h	g+h	NOUN
ejpam-6635	203	7	)	)	PUNCT
ejpam-6635	203	8	\	\	PUNCT
ejpam-6635	204	1	s.	s.	PROPN
ejpam-6635	204	2	we	we	PRON
ejpam-6635	204	3	may	may	AUX
ejpam-6635	204	4	assume	assume	VERB
ejpam-6635	204	5	that	that	SCONJ
ejpam-6635	204	6	x	x	PUNCT
ejpam-6635	204	7	∈	∈	NOUN
ejpam-6635	204	8	v	v	X
ejpam-6635	204	9	(	(	PUNCT
ejpam-6635	204	10	g	g	NOUN
ejpam-6635	204	11	)	)	PUNCT
ejpam-6635	204	12	.	.	PUNCT
ejpam-6635	205	1	then	then	ADV
ejpam-6635	205	2	x	x	X
ejpam-6635	205	3	/∈	/∈	PUNCT
ejpam-6635	206	1	sg	sg	PROPN
ejpam-6635	206	2	.	.	PUNCT
ejpam-6635	207	1	since	since	SCONJ
ejpam-6635	207	2	sg	sg	PROPN
ejpam-6635	207	3	is	be	AUX
ejpam-6635	207	4	a	a	DET
ejpam-6635	207	5	secure	secure	ADJ
ejpam-6635	207	6	pointwise	pointwise	ADJ
ejpam-6635	207	7	non	non	ADJ
ejpam-6635	207	8	-	-	ADJ
ejpam-6635	207	9	dominating	dominating	ADJ
ejpam-6635	207	10	set	set	NOUN
ejpam-6635	207	11	in	in	ADP
ejpam-6635	207	12	g	g	NOUN
ejpam-6635	207	13	,	,	PUNCT
ejpam-6635	207	14	there	there	PRON
ejpam-6635	207	15	exists	exist	VERB
ejpam-6635	207	16	y	y	PROPN
ejpam-6635	207	17	∈	∈	PROPN
ejpam-6635	207	18	s	s	PART
ejpam-6635	207	19	\ng(x	\ng(x	NOUN
ejpam-6635	207	20	)	)	PUNCT
ejpam-6635	207	21	such	such	ADJ
ejpam-6635	207	22	that	that	SCONJ
ejpam-6635	207	23	(	(	PUNCT
ejpam-6635	207	24	sg	sg	PROPN
ejpam-6635	207	25	\	\	PROPN
ejpam-6635	207	26	{	{	PUNCT
ejpam-6635	207	27	y})∪	y})∪	PROPN
ejpam-6635	207	28	{	{	PUNCT
ejpam-6635	207	29	x	x	NOUN
ejpam-6635	207	30	}	}	PUNCT
ejpam-6635	207	31	is	be	AUX
ejpam-6635	207	32	a	a	DET
ejpam-6635	207	33	pointwise	pointwise	ADJ
ejpam-6635	207	34	non	non	ADJ
ejpam-6635	207	35	-	-	ADJ
ejpam-6635	207	36	dominating	dominating	ADJ
ejpam-6635	207	37	set	set	NOUN
ejpam-6635	207	38	in	in	ADP
ejpam-6635	207	39	g.	g.	PROPN
ejpam-6635	207	40	it	it	PRON
ejpam-6635	207	41	follows	follow	VERB
ejpam-6635	207	42	from	from	ADP
ejpam-6635	207	43	theorem	theorem	ADJ
ejpam-6635	207	44	5	5	NUM
ejpam-6635	208	1	that	that	PRON
ejpam-6635	208	2	(	(	PUNCT
ejpam-6635	208	3	s	s	NOUN
ejpam-6635	208	4	\	\	X
ejpam-6635	208	5	{	{	PUNCT
ejpam-6635	208	6	y	y	NOUN
ejpam-6635	208	7	}	}	PUNCT
ejpam-6635	208	8	)	)	PUNCT
ejpam-6635	208	9	∪	∪	ADP
ejpam-6635	208	10	{	{	PUNCT
ejpam-6635	208	11	x	x	NOUN
ejpam-6635	208	12	}	}	PUNCT
ejpam-6635	208	13	=	=	SYM
ejpam-6635	208	14	[	[	X
ejpam-6635	208	15	(	(	PUNCT
ejpam-6635	208	16	sg	sg	PROPN
ejpam-6635	208	17	\	\	PROPN
ejpam-6635	208	18	{	{	PUNCT
ejpam-6635	208	19	y	y	NOUN
ejpam-6635	208	20	}	}	PUNCT
ejpam-6635	208	21	)	)	PUNCT
ejpam-6635	208	22	∪	∪	ADP
ejpam-6635	208	23	{	{	PUNCT
ejpam-6635	208	24	x	x	NOUN
ejpam-6635	208	25	}	}	PUNCT
ejpam-6635	208	26	]	]	PUNCT
ejpam-6635	208	27	∪	∪	NOUN
ejpam-6635	208	28	sh	sh	PROPN
ejpam-6635	208	29	is	be	AUX
ejpam-6635	208	30	a	a	DET
ejpam-6635	208	31	hop	hop	NOUN
ejpam-6635	208	32	dominating	dominating	NOUN
ejpam-6635	208	33	set	set	VERB
ejpam-6635	208	34	in	in	ADP
ejpam-6635	208	35	g+h	g+h	PROPN
ejpam-6635	208	36	.	.	PUNCT
ejpam-6635	209	1	hence	hence	ADV
ejpam-6635	209	2	,	,	PUNCT
ejpam-6635	209	3	s	s	VERB
ejpam-6635	209	4	is	be	AUX
ejpam-6635	209	5	a	a	DET
ejpam-6635	209	6	secure	secure	ADJ
ejpam-6635	209	7	hop	hop	NOUN
ejpam-6635	209	8	dominating	dominating	NOUN
ejpam-6635	209	9	set	set	VERB
ejpam-6635	209	10	in	in	ADP
ejpam-6635	209	11	g+h	g+h	PROPN
ejpam-6635	209	12	.	.	PUNCT
ejpam-6635	210	1	corollary	corollary	ADJ
ejpam-6635	210	2	4	4	NUM
ejpam-6635	210	3	.	.	PUNCT
ejpam-6635	211	1	let	let	VERB
ejpam-6635	211	2	g	g	NOUN
ejpam-6635	211	3	and	and	CCONJ
ejpam-6635	211	4	h	h	NOUN
ejpam-6635	211	5	be	be	VERB
ejpam-6635	211	6	any	any	DET
ejpam-6635	211	7	graphs	graph	NOUN
ejpam-6635	211	8	.	.	PUNCT
ejpam-6635	212	1	then	then	ADV
ejpam-6635	212	2	γsh(g+h	γsh(g+h	NOUN
ejpam-6635	212	3	)	)	PUNCT
ejpam-6635	213	1	=	=	SYM
ejpam-6635	213	2	spnd(g	spnd(g	PROPN
ejpam-6635	213	3	)	)	PUNCT
ejpam-6635	213	4	+	+	NUM
ejpam-6635	213	5	spnd(h	spnd(h	NOUN
ejpam-6635	213	6	)	)	PUNCT
ejpam-6635	213	7	.	.	PUNCT
ejpam-6635	214	1	f.	f.	PROPN
ejpam-6635	214	2	alfeche	alfeche	PROPN
ejpam-6635	214	3	,	,	PUNCT
ejpam-6635	214	4	s.	s.	PROPN
ejpam-6635	214	5	canoy	canoy	PROPN
ejpam-6635	214	6	jr	jr	PROPN
ejpam-6635	214	7	.	.	PROPN
ejpam-6635	214	8	/	/	SYM
ejpam-6635	214	9	eur	eur	PROPN
ejpam-6635	214	10	.	.	PUNCT
ejpam-6635	215	1	j.	j.	PROPN
ejpam-6635	215	2	pure	pure	PROPN
ejpam-6635	215	3	appl	appl	PROPN
ejpam-6635	215	4	.	.	PROPN
ejpam-6635	215	5	math	math	PROPN
ejpam-6635	215	6	,	,	PUNCT
ejpam-6635	215	7	18	18	NUM
ejpam-6635	215	8	(	(	PUNCT
ejpam-6635	215	9	3	3	NUM
ejpam-6635	215	10	)	)	PUNCT
ejpam-6635	215	11	(	(	PUNCT
ejpam-6635	215	12	2025	2025	NUM
ejpam-6635	215	13	)	)	PUNCT
ejpam-6635	215	14	,	,	PUNCT
ejpam-6635	215	15	6635	6635	NUM
ejpam-6635	215	16	7	7	NUM
ejpam-6635	215	17	of	of	ADP
ejpam-6635	215	18	11	11	NUM
ejpam-6635	215	19	proof	proof	NOUN
ejpam-6635	215	20	.	.	PUNCT
ejpam-6635	216	1	suppose	suppose	VERB
ejpam-6635	216	2	dg	dg	PROPN
ejpam-6635	216	3	and	and	CCONJ
ejpam-6635	216	4	dh	dh	NOUN
ejpam-6635	216	5	are	be	AUX
ejpam-6635	216	6	spnd	spnd	NOUN
ejpam-6635	216	7	-	-	PUNCT
ejpam-6635	216	8	sets	set	NOUN
ejpam-6635	216	9	in	in	ADP
ejpam-6635	216	10	g	g	PROPN
ejpam-6635	216	11	and	and	CCONJ
ejpam-6635	216	12	h	h	NOUN
ejpam-6635	216	13	,	,	PUNCT
ejpam-6635	216	14	respectively	respectively	ADV
ejpam-6635	216	15	.	.	PUNCT
ejpam-6635	217	1	then	then	ADV
ejpam-6635	217	2	d	d	X
ejpam-6635	217	3	=	=	X
ejpam-6635	217	4	dg	dg	PROPN
ejpam-6635	217	5	∪dh	∪dh	PROPN
ejpam-6635	217	6	is	be	AUX
ejpam-6635	217	7	a	a	DET
ejpam-6635	217	8	secure	secure	ADJ
ejpam-6635	217	9	hop	hop	NOUN
ejpam-6635	217	10	dominating	dominating	NOUN
ejpam-6635	217	11	set	set	VERB
ejpam-6635	217	12	in	in	ADP
ejpam-6635	217	13	g+h	g+h	PROPN
ejpam-6635	217	14	by	by	ADP
ejpam-6635	217	15	theorem	theorem	NOUN
ejpam-6635	217	16	6	6	NUM
ejpam-6635	217	17	.	.	PUNCT
ejpam-6635	218	1	hence	hence	ADV
ejpam-6635	218	2	,	,	PUNCT
ejpam-6635	218	3	γsh(g+h	γsh(g+h	NOUN
ejpam-6635	218	4	)	)	PUNCT
ejpam-6635	218	5	≤	≤	NOUN
ejpam-6635	218	6	|d|	|d|	PROPN
ejpam-6635	218	7	=	=	PUNCT
ejpam-6635	218	8	|dg|+	|dg|+	ADP
ejpam-6635	218	9	|dh	|dh	NUM
ejpam-6635	218	10	|	|	ADV
ejpam-6635	218	11	=	=	SYM
ejpam-6635	218	12	spnd(g	spnd(g	PROPN
ejpam-6635	218	13	)	)	PUNCT
ejpam-6635	218	14	+	+	NUM
ejpam-6635	218	15	spnd(h	spnd(h	NOUN
ejpam-6635	218	16	)	)	PUNCT
ejpam-6635	218	17	.	.	PUNCT
ejpam-6635	219	1	next	next	ADV
ejpam-6635	219	2	,	,	PUNCT
ejpam-6635	219	3	let	let	VERB
ejpam-6635	219	4	s	s	PRON
ejpam-6635	219	5	be	be	AUX
ejpam-6635	219	6	an	an	DET
ejpam-6635	219	7	spnd	spnd	NOUN
ejpam-6635	219	8	-	-	PUNCT
ejpam-6635	219	9	set	set	NOUN
ejpam-6635	219	10	in	in	ADP
ejpam-6635	219	11	g	g	PROPN
ejpam-6635	219	12	+	+	CCONJ
ejpam-6635	219	13	h.	h.	PROPN
ejpam-6635	219	14	then	then	ADV
ejpam-6635	219	15	sg	sg	VERB
ejpam-6635	219	16	=	=	SYM
ejpam-6635	219	17	s	s	PROPN
ejpam-6635	219	18	∩	∩	ADJ
ejpam-6635	219	19	v	v	X
ejpam-6635	219	20	(	(	PUNCT
ejpam-6635	219	21	g	g	NOUN
ejpam-6635	219	22	)	)	PUNCT
ejpam-6635	219	23	and	and	CCONJ
ejpam-6635	219	24	sh	sh	INTJ
ejpam-6635	219	25	=	=	SYM
ejpam-6635	219	26	s	s	PROPN
ejpam-6635	219	27	∩	∩	ADJ
ejpam-6635	219	28	v	v	ADJ
ejpam-6635	219	29	(	(	PUNCT
ejpam-6635	219	30	h	h	NOUN
ejpam-6635	219	31	)	)	PUNCT
ejpam-6635	219	32	are	be	AUX
ejpam-6635	219	33	pointwise	pointwise	PROPN
ejpam-6635	219	34	non	non	ADJ
ejpam-6635	219	35	-	-	ADJ
ejpam-6635	219	36	dominating	dominating	ADJ
ejpam-6635	219	37	sets	set	NOUN
ejpam-6635	219	38	in	in	ADP
ejpam-6635	219	39	g	g	PROPN
ejpam-6635	219	40	and	and	CCONJ
ejpam-6635	219	41	h	h	NOUN
ejpam-6635	219	42	,	,	PUNCT
ejpam-6635	219	43	respectively	respectively	ADV
ejpam-6635	219	44	,	,	PUNCT
ejpam-6635	219	45	by	by	ADP
ejpam-6635	219	46	theorem	theorem	NOUN
ejpam-6635	219	47	6	6	NUM
ejpam-6635	219	48	.	.	PUNCT
ejpam-6635	220	1	it	it	PRON
ejpam-6635	220	2	follows	follow	VERB
ejpam-6635	220	3	that	that	SCONJ
ejpam-6635	220	4	γsh(g+h	γsh(g+h	NOUN
ejpam-6635	220	5	)	)	PUNCT
ejpam-6635	220	6	=	=	PUNCT
ejpam-6635	220	7	|s|	|s|	NOUN
ejpam-6635	220	8	=	=	PUNCT
ejpam-6635	220	9	|sg|+	|sg|+	PROPN
ejpam-6635	220	10	|sh	|sh	ADP
ejpam-6635	220	11	|	|	ADV
ejpam-6635	220	12	≥	≥	NOUN
ejpam-6635	220	13	spnd(g	spnd(g	PROPN
ejpam-6635	220	14	)	)	PUNCT
ejpam-6635	220	15	+	+	NUM
ejpam-6635	221	1	spnd(h	spnd(h	NOUN
ejpam-6635	221	2	)	)	PUNCT
ejpam-6635	221	3	.	.	PUNCT
ejpam-6635	222	1	this	this	PRON
ejpam-6635	222	2	establishes	establish	VERB
ejpam-6635	222	3	the	the	DET
ejpam-6635	222	4	desired	desire	VERB
ejpam-6635	222	5	equality	equality	NOUN
ejpam-6635	222	6	.	.	PUNCT
ejpam-6635	223	1	corollary	corollary	ADJ
ejpam-6635	223	2	5	5	NUM
ejpam-6635	223	3	.	.	PUNCT
ejpam-6635	224	1	each	each	PRON
ejpam-6635	224	2	of	of	ADP
ejpam-6635	224	3	the	the	DET
ejpam-6635	224	4	following	following	ADJ
ejpam-6635	224	5	statements	statement	NOUN
ejpam-6635	224	6	holds	hold	VERB
ejpam-6635	224	7	.	.	PUNCT
ejpam-6635	225	1	(	(	PUNCT
ejpam-6635	225	2	i	i	NOUN
ejpam-6635	225	3	)	)	PUNCT
ejpam-6635	225	4	γsh(k1,n	γsh(k1,n	PROPN
ejpam-6635	225	5	)	)	PUNCT
ejpam-6635	226	1	=	=	SYM
ejpam-6635	226	2	spnd(k1	spnd(k1	NOUN
ejpam-6635	226	3	)	)	PUNCT
ejpam-6635	226	4	+	+	CCONJ
ejpam-6635	226	5	spnd(kn	spnd(kn	NOUN
ejpam-6635	226	6	)	)	PUNCT
ejpam-6635	226	7	=	=	SYM
ejpam-6635	226	8	2	2	NUM
ejpam-6635	226	9	for	for	ADP
ejpam-6635	226	10	all	all	PRON
ejpam-6635	226	11	n	n	PRON
ejpam-6635	226	12	≥	≥	NOUN
ejpam-6635	226	13	1	1	NUM
ejpam-6635	226	14	.	.	PUNCT
ejpam-6635	226	15	(	(	PUNCT
ejpam-6635	226	16	ii	ii	NOUN
ejpam-6635	226	17	)	)	PUNCT
ejpam-6635	226	18	if	if	SCONJ
ejpam-6635	226	19	n	n	PRON
ejpam-6635	226	20	is	be	AUX
ejpam-6635	226	21	a	a	DET
ejpam-6635	226	22	positive	positive	ADJ
ejpam-6635	226	23	integer	integer	NOUN
ejpam-6635	226	24	,	,	PUNCT
ejpam-6635	226	25	then	then	ADV
ejpam-6635	226	26	γsh(fn	γsh(fn	ADP
ejpam-6635	226	27	)	)	PUNCT
ejpam-6635	227	1	=	=	SYM
ejpam-6635	227	2	γsh(k1	γsh(k1	PROPN
ejpam-6635	227	3	+	+	CCONJ
ejpam-6635	227	4	pn	pn	PROPN
ejpam-6635	227	5	)	)	PUNCT
ejpam-6635	227	6	=	=	PRON
ejpam-6635	227	7	{	{	PUNCT
ejpam-6635	227	8	2	2	NUM
ejpam-6635	227	9	if	if	SCONJ
ejpam-6635	227	10	n	n	NOUN
ejpam-6635	227	11	=	=	SYM
ejpam-6635	227	12	1	1	NUM
ejpam-6635	227	13	3	3	NUM
ejpam-6635	227	14	if	if	SCONJ
ejpam-6635	227	15	n	n	PRON
ejpam-6635	227	16	≥	≥	NOUN
ejpam-6635	227	17	2	2	NUM
ejpam-6635	227	18	.	.	PUNCT
ejpam-6635	227	19	(	(	PUNCT
ejpam-6635	227	20	iii	iii	X
ejpam-6635	227	21	)	)	PUNCT
ejpam-6635	227	22	if	if	SCONJ
ejpam-6635	227	23	n	n	PRON
ejpam-6635	227	24	is	be	AUX
ejpam-6635	227	25	a	a	DET
ejpam-6635	227	26	positive	positive	ADJ
ejpam-6635	227	27	integer	integer	NOUN
ejpam-6635	227	28	and	and	CCONJ
ejpam-6635	227	29	n	n	PRON
ejpam-6635	227	30	≥	≥	NOUN
ejpam-6635	227	31	3	3	NUM
ejpam-6635	227	32	,	,	PUNCT
ejpam-6635	227	33	then	then	ADV
ejpam-6635	227	34	γsh(wn	γsh(wn	NOUN
ejpam-6635	227	35	)	)	PUNCT
ejpam-6635	227	36	=	=	SYM
ejpam-6635	227	37	γsh(k1	γsh(k1	PROPN
ejpam-6635	227	38	+	+	CCONJ
ejpam-6635	227	39	cn	cn	PROPN
ejpam-6635	227	40	)	)	PUNCT
ejpam-6635	227	41	=	=	PRON
ejpam-6635	227	42	{	{	PUNCT
ejpam-6635	227	43	4	4	NUM
ejpam-6635	227	44	if	if	SCONJ
ejpam-6635	227	45	n	n	X
ejpam-6635	227	46	=	=	SYM
ejpam-6635	227	47	3	3	NUM
ejpam-6635	227	48	,	,	PUNCT
ejpam-6635	227	49	5	5	NUM
ejpam-6635	227	50	3	3	NUM
ejpam-6635	227	51	if	if	SCONJ
ejpam-6635	227	52	n	n	ADV
ejpam-6635	227	53	/∈	/∈	PUNCT
ejpam-6635	227	54	{	{	PUNCT
ejpam-6635	227	55	3	3	NUM
ejpam-6635	227	56	,	,	PUNCT
ejpam-6635	227	57	5	5	NUM
ejpam-6635	227	58	}	}	PUNCT
ejpam-6635	227	59	.	.	PUNCT
ejpam-6635	228	1	(	(	PUNCT
ejpam-6635	228	2	iv	iv	X
ejpam-6635	228	3	)	)	PUNCT
ejpam-6635	228	4	if	if	SCONJ
ejpam-6635	228	5	m	m	VERB
ejpam-6635	228	6	and	and	CCONJ
ejpam-6635	228	7	n	n	PRON
ejpam-6635	228	8	are	be	AUX
ejpam-6635	228	9	positive	positive	ADJ
ejpam-6635	228	10	integers	integer	NOUN
ejpam-6635	228	11	with	with	ADP
ejpam-6635	228	12	m	m	PROPN
ejpam-6635	228	13	≤	≤	NOUN
ejpam-6635	228	14	n	n	CCONJ
ejpam-6635	228	15	,	,	PUNCT
ejpam-6635	228	16	then	then	ADV
ejpam-6635	228	17	γsh(pm	γsh(pm	VERB
ejpam-6635	228	18	+	+	CCONJ
ejpam-6635	228	19	pn	pn	NOUN
ejpam-6635	228	20	)	)	PUNCT
ejpam-6635	228	21	=	=	SYM
ejpam-6635	228	22	spnd(pm	spnd(pm	NOUN
ejpam-6635	228	23	)	)	PUNCT
ejpam-6635	229	1	+	+	NUM
ejpam-6635	229	2	spnd(pn	spnd(pn	NOUN
ejpam-6635	229	3	)	)	PUNCT
ejpam-6635	229	4	=	=	PUNCT
ejpam-6635	230	1			NOUN
ejpam-6635	230	2	2	2	NUM
ejpam-6635	230	3	if	if	SCONJ
ejpam-6635	230	4	n	n	NOUN
ejpam-6635	230	5	=	=	SYM
ejpam-6635	230	6	1	1	NUM
ejpam-6635	230	7	3	3	NUM
ejpam-6635	230	8	if	if	SCONJ
ejpam-6635	230	9	m	m	VERB
ejpam-6635	230	10	=	=	SYM
ejpam-6635	230	11	1	1	NUM
ejpam-6635	230	12	and	and	CCONJ
ejpam-6635	230	13	n	n	CCONJ
ejpam-6635	230	14	=	=	SYM
ejpam-6635	230	15	2	2	NUM
ejpam-6635	230	16	4	4	NUM
ejpam-6635	230	17	if	if	SCONJ
ejpam-6635	230	18	m	m	VERB
ejpam-6635	230	19	≥	≥	NOUN
ejpam-6635	230	20	2	2	NUM
ejpam-6635	230	21	.	.	PUNCT
ejpam-6635	230	22	(	(	PUNCT
ejpam-6635	230	23	v	v	NOUN
ejpam-6635	230	24	)	)	PUNCT
ejpam-6635	230	25	if	if	SCONJ
ejpam-6635	230	26	m	m	VERB
ejpam-6635	230	27	and	and	CCONJ
ejpam-6635	230	28	n	n	PRON
ejpam-6635	230	29	are	be	AUX
ejpam-6635	230	30	positive	positive	ADJ
ejpam-6635	230	31	integers	integer	NOUN
ejpam-6635	230	32	with	with	ADP
ejpam-6635	230	33	3	3	NUM
ejpam-6635	230	34	≤	≤	NUM
ejpam-6635	230	35	m	m	VERB
ejpam-6635	230	36	≤	≤	NOUN
ejpam-6635	230	37	n	n	CCONJ
ejpam-6635	230	38	,	,	PUNCT
ejpam-6635	230	39	then	then	ADV
ejpam-6635	230	40	γsh(cm	γsh(cm	PROPN
ejpam-6635	230	41	+	+	CCONJ
ejpam-6635	230	42	cn	cn	ADJ
ejpam-6635	230	43	)	)	PUNCT
ejpam-6635	230	44	=	=	SYM
ejpam-6635	230	45	spnd(cm	spnd(cm	ADJ
ejpam-6635	230	46	)	)	PUNCT
ejpam-6635	230	47	+	+	CCONJ
ejpam-6635	230	48	spnd(cn	spnd(cn	NOUN
ejpam-6635	230	49	)	)	PUNCT
ejpam-6635	230	50	=	=	PUNCT
ejpam-6635	231	1			NOUN
ejpam-6635	231	2	6	6	NUM
ejpam-6635	231	3	if	if	SCONJ
ejpam-6635	231	4	n	n	NOUN
ejpam-6635	231	5	=	=	SYM
ejpam-6635	231	6	3	3	NUM
ejpam-6635	231	7	,	,	PUNCT
ejpam-6635	231	8	5	5	NUM
ejpam-6635	231	9	5	5	NUM
ejpam-6635	231	10	if	if	SCONJ
ejpam-6635	231	11	m	m	VERB
ejpam-6635	231	12	=	=	SYM
ejpam-6635	231	13	3	3	NUM
ejpam-6635	231	14	,	,	PUNCT
ejpam-6635	231	15	5	5	NUM
ejpam-6635	231	16	and	and	CCONJ
ejpam-6635	231	17	n	n	NUM
ejpam-6635	231	18	/∈	/∈	PUNCT
ejpam-6635	231	19	{	{	PUNCT
ejpam-6635	231	20	3	3	NUM
ejpam-6635	231	21	,	,	PUNCT
ejpam-6635	231	22	5	5	NUM
ejpam-6635	231	23	}	}	SYM
ejpam-6635	231	24	4	4	NUM
ejpam-6635	231	25	if	if	SCONJ
ejpam-6635	231	26	m	m	PRON
ejpam-6635	231	27	,	,	PUNCT
ejpam-6635	231	28	n	n	PROPN
ejpam-6635	231	29	/∈	/∈	PUNCT
ejpam-6635	231	30	{	{	PUNCT
ejpam-6635	231	31	3	3	NUM
ejpam-6635	231	32	,	,	PUNCT
ejpam-6635	231	33	5	5	NUM
ejpam-6635	231	34	}	}	PUNCT
ejpam-6635	231	35	.	.	PUNCT
ejpam-6635	232	1	(	(	PUNCT
ejpam-6635	232	2	v	v	NOUN
ejpam-6635	232	3	)	)	PUNCT
ejpam-6635	232	4	if	if	SCONJ
ejpam-6635	232	5	1	1	NUM
ejpam-6635	232	6	≤	≤	NUM
ejpam-6635	232	7	m1	m1	NOUN
ejpam-6635	232	8	≤	≤	NUM
ejpam-6635	232	9	m2	m2	PROPN
ejpam-6635	232	10	≤	≤	NOUN
ejpam-6635	232	11	·	·	PUNCT
ejpam-6635	232	12	·	·	PUNCT
ejpam-6635	232	13	·	·	PUNCT
ejpam-6635	233	1	≤	≤	NUM
ejpam-6635	233	2	mk	mk	PROPN
ejpam-6635	233	3	,	,	PUNCT
ejpam-6635	233	4	where	where	SCONJ
ejpam-6635	233	5	k	k	PROPN
ejpam-6635	233	6	≥	≥	NUM
ejpam-6635	233	7	2	2	NUM
ejpam-6635	233	8	,	,	PUNCT
ejpam-6635	233	9	then	then	ADV
ejpam-6635	233	10	γsh(km1,m2	γsh(km1,m2	NOUN
ejpam-6635	233	11	,	,	PUNCT
ejpam-6635	233	12	·	·	PUNCT
ejpam-6635	233	13	·	·	PUNCT
ejpam-6635	233	14	·	·	PUNCT
ejpam-6635	233	15	,	,	PUNCT
ejpam-6635	233	16	mk	mk	PROPN
ejpam-6635	233	17	)	)	PUNCT
ejpam-6635	233	18	=	=	PUNCT
ejpam-6635	234	1	k.	k.	PROPN
ejpam-6635	234	2	in	in	ADP
ejpam-6635	234	3	particular	particular	ADJ
ejpam-6635	234	4	,	,	PUNCT
ejpam-6635	234	5	γsh(km	γsh(km	NOUN
ejpam-6635	234	6	,	,	PUNCT
ejpam-6635	234	7	n	n	CCONJ
ejpam-6635	234	8	)	)	PUNCT
ejpam-6635	234	9	=	=	SYM
ejpam-6635	234	10	2	2	NUM
ejpam-6635	234	11	for	for	ADP
ejpam-6635	234	12	all	all	DET
ejpam-6635	234	13	m	m	PROPN
ejpam-6635	234	14	,	,	PUNCT
ejpam-6635	234	15	n	n	PRON
ejpam-6635	234	16	≥	≥	NOUN
ejpam-6635	234	17	2	2	NUM
ejpam-6635	234	18	.	.	PUNCT
ejpam-6635	235	1	proof	proof	NOUN
ejpam-6635	235	2	.	.	PUNCT
ejpam-6635	236	1	note	note	VERB
ejpam-6635	236	2	that	that	SCONJ
ejpam-6635	236	3	by	by	ADP
ejpam-6635	236	4	corollary	corollary	ADJ
ejpam-6635	236	5	4	4	NUM
ejpam-6635	236	6	,	,	PUNCT
ejpam-6635	236	7	theorem	theorem	VERB
ejpam-6635	236	8	3(i	3(i	NUM
ejpam-6635	236	9	)	)	PUNCT
ejpam-6635	236	10	,	,	PUNCT
ejpam-6635	236	11	corollary	corollary	ADJ
ejpam-6635	236	12	1	1	NUM
ejpam-6635	236	13	,	,	PUNCT
ejpam-6635	236	14	and	and	CCONJ
ejpam-6635	236	15	corollary	corollary	ADJ
ejpam-6635	236	16	2	2	NUM
ejpam-6635	236	17	,	,	PUNCT
ejpam-6635	236	18	statements	statement	NOUN
ejpam-6635	236	19	(	(	PUNCT
ejpam-6635	236	20	i	i	NOUN
ejpam-6635	236	21	)	)	PUNCT
ejpam-6635	236	22	,	,	PUNCT
ejpam-6635	236	23	(	(	PUNCT
ejpam-6635	236	24	ii	ii	NOUN
ejpam-6635	236	25	)	)	PUNCT
ejpam-6635	236	26	,	,	PUNCT
ejpam-6635	236	27	(	(	PUNCT
ejpam-6635	236	28	iii	iii	NOUN
ejpam-6635	236	29	)	)	PUNCT
ejpam-6635	236	30	,	,	PUNCT
ejpam-6635	236	31	(	(	PUNCT
ejpam-6635	236	32	iv	iv	X
ejpam-6635	236	33	)	)	PUNCT
ejpam-6635	236	34	,	,	PUNCT
ejpam-6635	236	35	and	and	CCONJ
ejpam-6635	236	36	(	(	PUNCT
ejpam-6635	236	37	v	v	NOUN
ejpam-6635	236	38	)	)	PUNCT
ejpam-6635	236	39	follow	follow	NOUN
ejpam-6635	236	40	.	.	PUNCT
ejpam-6635	237	1	by	by	ADP
ejpam-6635	237	2	repetitive	repetitive	ADJ
ejpam-6635	237	3	application	application	NOUN
ejpam-6635	237	4	of	of	ADP
ejpam-6635	237	5	corollary	corollary	ADJ
ejpam-6635	237	6	4	4	NUM
ejpam-6635	237	7	and	and	CCONJ
ejpam-6635	237	8	by	by	ADP
ejpam-6635	237	9	theorem	theorem	NOUN
ejpam-6635	237	10	4(i	4(i	NUM
ejpam-6635	237	11	)	)	PUNCT
ejpam-6635	237	12	,	,	PUNCT
ejpam-6635	237	13	we	we	PRON
ejpam-6635	237	14	have	have	VERB
ejpam-6635	237	15	γsh(km1,m2	γsh(km1,m2	NOUN
ejpam-6635	237	16	,	,	PUNCT
ejpam-6635	237	17	·	·	PUNCT
ejpam-6635	237	18	·	·	PUNCT
ejpam-6635	237	19	·	·	PUNCT
ejpam-6635	237	20	,	,	PUNCT
ejpam-6635	237	21	mk	mk	NOUN
ejpam-6635	237	22	)	)	PUNCT
ejpam-6635	238	1	=	=	PUNCT
ejpam-6635	238	2	∑	∑	PUNCT
ejpam-6635	238	3	j∈[k	j∈[k	PROPN
ejpam-6635	238	4	]	]	X
ejpam-6635	238	5	spnd(kmj	spnd(kmj	NOUN
ejpam-6635	238	6	)	)	PUNCT
ejpam-6635	239	1	=	=	PUNCT
ejpam-6635	239	2	k.	k.	PROPN
ejpam-6635	239	3	f.	f.	PROPN
ejpam-6635	239	4	alfeche	alfeche	PROPN
ejpam-6635	239	5	,	,	PUNCT
ejpam-6635	239	6	s.	s.	PROPN
ejpam-6635	239	7	canoy	canoy	PROPN
ejpam-6635	239	8	jr	jr	PROPN
ejpam-6635	239	9	.	.	PROPN
ejpam-6635	239	10	/	/	SYM
ejpam-6635	239	11	eur	eur	PROPN
ejpam-6635	239	12	.	.	PUNCT
ejpam-6635	240	1	j.	j.	PROPN
ejpam-6635	240	2	pure	pure	PROPN
ejpam-6635	240	3	appl	appl	PROPN
ejpam-6635	240	4	.	.	PROPN
ejpam-6635	240	5	math	math	PROPN
ejpam-6635	240	6	,	,	PUNCT
ejpam-6635	240	7	18	18	NUM
ejpam-6635	240	8	(	(	PUNCT
ejpam-6635	240	9	3	3	NUM
ejpam-6635	240	10	)	)	PUNCT
ejpam-6635	240	11	(	(	PUNCT
ejpam-6635	240	12	2025	2025	NUM
ejpam-6635	240	13	)	)	PUNCT
ejpam-6635	240	14	,	,	PUNCT
ejpam-6635	240	15	6635	6635	NUM
ejpam-6635	240	16	8	8	NUM
ejpam-6635	240	17	of	of	ADP
ejpam-6635	240	18	11	11	NUM
ejpam-6635	240	19	therefore	therefore	ADV
ejpam-6635	240	20	,	,	PUNCT
ejpam-6635	240	21	the	the	DET
ejpam-6635	240	22	assertions	assertion	NOUN
ejpam-6635	240	23	hold	hold	VERB
ejpam-6635	240	24	.	.	PUNCT
ejpam-6635	241	1	theorem	theorem	ADJ
ejpam-6635	241	2	7	7	NUM
ejpam-6635	241	3	.	.	PUNCT
ejpam-6635	241	4	let	let	VERB
ejpam-6635	241	5	a	a	PRON
ejpam-6635	241	6	and	and	CCONJ
ejpam-6635	241	7	b	b	NOUN
ejpam-6635	241	8	be	be	AUX
ejpam-6635	241	9	positive	positive	ADJ
ejpam-6635	241	10	integers	integer	NOUN
ejpam-6635	241	11	such	such	ADJ
ejpam-6635	241	12	that	that	SCONJ
ejpam-6635	241	13	2	2	NUM
ejpam-6635	241	14	≤	≤	NUM
ejpam-6635	241	15	a	a	DET
ejpam-6635	241	16	≤	≤	PROPN
ejpam-6635	241	17	b.	b.	NOUN
ejpam-6635	242	1	then	then	ADV
ejpam-6635	242	2	there	there	PRON
ejpam-6635	242	3	exists	exist	VERB
ejpam-6635	242	4	a	a	DET
ejpam-6635	242	5	connected	connected	ADJ
ejpam-6635	242	6	graph	graph	NOUN
ejpam-6635	242	7	g	g	ADP
ejpam-6635	242	8	such	such	ADJ
ejpam-6635	242	9	that	that	PRON
ejpam-6635	242	10	γh(g	γh(g	NOUN
ejpam-6635	242	11	)	)	PUNCT
ejpam-6635	242	12	=	=	PUNCT
ejpam-6635	242	13	a	a	PRON
ejpam-6635	242	14	and	and	CCONJ
ejpam-6635	242	15	γsh(g	γsh(g	NOUN
ejpam-6635	242	16	)	)	PUNCT
ejpam-6635	242	17	=	=	SYM
ejpam-6635	242	18	b.	b.	NOUN
ejpam-6635	242	19	proof	proof	NOUN
ejpam-6635	242	20	.	.	PUNCT
ejpam-6635	243	1	suppose	suppose	VERB
ejpam-6635	243	2	a	a	DET
ejpam-6635	243	3	=	=	X
ejpam-6635	243	4	b.	b.	NOUN
ejpam-6635	243	5	consider	consider	VERB
ejpam-6635	243	6	g	g	PROPN
ejpam-6635	243	7	=	=	SYM
ejpam-6635	243	8	ka	ka	PROPN
ejpam-6635	243	9	.	.	PROPN
ejpam-6635	243	10	then	then	ADV
ejpam-6635	243	11	γh(g	γh(g	NOUN
ejpam-6635	243	12	)	)	PUNCT
ejpam-6635	243	13	=	=	PUNCT
ejpam-6635	243	14	a	a	PRON
ejpam-6635	243	15	because	because	SCONJ
ejpam-6635	243	16	v	v	X
ejpam-6635	243	17	(	(	PUNCT
ejpam-6635	243	18	ka	ka	X
ejpam-6635	243	19	)	)	PUNCT
ejpam-6635	243	20	is	be	AUX
ejpam-6635	243	21	the	the	DET
ejpam-6635	243	22	only	only	ADJ
ejpam-6635	243	23	hop	hop	NOUN
ejpam-6635	243	24	dominating	dominating	NOUN
ejpam-6635	243	25	set	set	VERB
ejpam-6635	243	26	in	in	ADP
ejpam-6635	243	27	ka	ka	PROPN
ejpam-6635	243	28	.	.	PROPN
ejpam-6635	244	1	with	with	ADP
ejpam-6635	244	2	the	the	DET
ejpam-6635	244	3	same	same	ADJ
ejpam-6635	244	4	reason	reason	NOUN
ejpam-6635	244	5	,	,	PUNCT
ejpam-6635	244	6	γsh(g	γsh(g	X
ejpam-6635	244	7	)	)	PUNCT
ejpam-6635	244	8	=	=	SYM
ejpam-6635	244	9	a	a	PRON
ejpam-6635	244	10	(	(	PUNCT
ejpam-6635	244	11	also	also	ADV
ejpam-6635	244	12	by	by	ADP
ejpam-6635	244	13	theorem	theorem	NOUN
ejpam-6635	244	14	3(iii	3(iii	NUM
ejpam-6635	244	15	)	)	PUNCT
ejpam-6635	244	16	)	)	PUNCT
ejpam-6635	244	17	.	.	PUNCT
ejpam-6635	245	1	next	next	ADV
ejpam-6635	245	2	,	,	PUNCT
ejpam-6635	245	3	suppose	suppose	VERB
ejpam-6635	245	4	a	a	DET
ejpam-6635	245	5	<	<	X
ejpam-6635	245	6	b.	b.	NOUN
ejpam-6635	245	7	let	let	VERB
ejpam-6635	245	8	m	m	VERB
ejpam-6635	245	9	=	=	VERB
ejpam-6635	246	1	b	b	X
ejpam-6635	246	2	−	−	PROPN
ejpam-6635	246	3	a	a	PRON
ejpam-6635	246	4	and	and	CCONJ
ejpam-6635	246	5	let	let	VERB
ejpam-6635	246	6	g	g	NOUN
ejpam-6635	246	7	=	=	SYM
ejpam-6635	246	8	(	(	PUNCT
ejpam-6635	246	9	k1	k1	PROPN
ejpam-6635	246	10	∪km+1	∪km+1	PROPN
ejpam-6635	246	11	)	)	PUNCT
ejpam-6635	247	1	+	+	NOUN
ejpam-6635	247	2	ka−1	ka−1	PROPN
ejpam-6635	247	3	.	.	PUNCT
ejpam-6635	248	1	by	by	ADP
ejpam-6635	248	2	corollary	corollary	ADJ
ejpam-6635	248	3	3	3	NUM
ejpam-6635	248	4	and	and	CCONJ
ejpam-6635	248	5	theorem	theorem	VERB
ejpam-6635	248	6	2	2	NUM
ejpam-6635	248	7	,	,	PUNCT
ejpam-6635	248	8	γh(g	γh(g	NOUN
ejpam-6635	248	9	)	)	PUNCT
ejpam-6635	248	10	=	=	SYM
ejpam-6635	248	11	pnd(k1	pnd(k1	PROPN
ejpam-6635	248	12	∪km+1	∪km+1	X
ejpam-6635	248	13	)	)	PUNCT
ejpam-6635	248	14	+	+	CCONJ
ejpam-6635	248	15	pnd(ka−1	pnd(ka−1	NOUN
ejpam-6635	248	16	)	)	PUNCT
ejpam-6635	248	17	=	=	SYM
ejpam-6635	249	1	1	1	NUM
ejpam-6635	249	2	+	+	CCONJ
ejpam-6635	249	3	(	(	PUNCT
ejpam-6635	249	4	a−	a−	PROPN
ejpam-6635	249	5	1	1	NUM
ejpam-6635	249	6	)	)	PUNCT
ejpam-6635	249	7	=	=	SYM
ejpam-6635	249	8	a.	a.	NOUN
ejpam-6635	249	9	by	by	ADP
ejpam-6635	249	10	corollary	corollary	ADJ
ejpam-6635	249	11	4	4	NUM
ejpam-6635	249	12	,	,	PUNCT
ejpam-6635	249	13	and	and	CCONJ
ejpam-6635	249	14	theorem	theorem	VERB
ejpam-6635	249	15	3(iii	3(iii	NUM
ejpam-6635	249	16	)	)	PUNCT
ejpam-6635	249	17	,	,	PUNCT
ejpam-6635	249	18	we	we	PRON
ejpam-6635	249	19	have	have	VERB
ejpam-6635	249	20	γsh(g	γsh(g	NOUN
ejpam-6635	249	21	)	)	PUNCT
ejpam-6635	249	22	=	=	SYM
ejpam-6635	249	23	spnd(k1	spnd(k1	NOUN
ejpam-6635	249	24	∪km+1	∪km+1	NUM
ejpam-6635	249	25	)	)	PUNCT
ejpam-6635	249	26	+	+	SYM
ejpam-6635	249	27	spnd(ka−1	spnd(ka−1	ADJ
ejpam-6635	249	28	)	)	PUNCT
ejpam-6635	249	29	=	=	SYM
ejpam-6635	249	30	1	1	NUM
ejpam-6635	249	31	+	+	CCONJ
ejpam-6635	249	32	(	(	PUNCT
ejpam-6635	249	33	a−	a−	PROPN
ejpam-6635	249	34	1	1	NUM
ejpam-6635	249	35	)	)	PUNCT
ejpam-6635	249	36	=	=	SYM
ejpam-6635	249	37	(	(	PUNCT
ejpam-6635	249	38	m+	m+	NOUN
ejpam-6635	249	39	1	1	NUM
ejpam-6635	249	40	)	)	PUNCT
ejpam-6635	249	41	+	+	CCONJ
ejpam-6635	249	42	(	(	PUNCT
ejpam-6635	249	43	a−	a−	PROPN
ejpam-6635	249	44	1	1	NUM
ejpam-6635	249	45	)	)	PUNCT
ejpam-6635	249	46	=	=	SYM
ejpam-6635	250	1	b.	b.	PROPN
ejpam-6635	251	1	this	this	PRON
ejpam-6635	251	2	proves	prove	VERB
ejpam-6635	251	3	the	the	DET
ejpam-6635	251	4	assertion	assertion	NOUN
ejpam-6635	251	5	.	.	PUNCT
ejpam-6635	252	1	the	the	DET
ejpam-6635	252	2	next	next	ADJ
ejpam-6635	252	3	result	result	NOUN
ejpam-6635	252	4	is	be	AUX
ejpam-6635	252	5	found	find	VERB
ejpam-6635	252	6	in	in	ADP
ejpam-6635	252	7	[	[	X
ejpam-6635	252	8	22	22	NUM
ejpam-6635	252	9	]	]	PUNCT
ejpam-6635	252	10	.	.	PUNCT
ejpam-6635	253	1	theorem	theorem	ADJ
ejpam-6635	253	2	8	8	NUM
ejpam-6635	253	3	.	.	PUNCT
ejpam-6635	254	1	let	let	VERB
ejpam-6635	254	2	g	g	NOUN
ejpam-6635	254	3	and	and	CCONJ
ejpam-6635	254	4	h	h	NOUN
ejpam-6635	254	5	be	be	VERB
ejpam-6635	254	6	any	any	DET
ejpam-6635	254	7	two	two	NUM
ejpam-6635	254	8	graphs	graph	NOUN
ejpam-6635	254	9	.	.	PUNCT
ejpam-6635	255	1	a	a	DET
ejpam-6635	255	2	set	set	NOUN
ejpam-6635	255	3	c	c	NOUN
ejpam-6635	255	4	⊆	⊆	NUM
ejpam-6635	255	5	v	v	NOUN
ejpam-6635	255	6	(	(	PUNCT
ejpam-6635	255	7	g	g	PROPN
ejpam-6635	255	8	◦	◦	NOUN
ejpam-6635	255	9	h	h	NOUN
ejpam-6635	255	10	)	)	PUNCT
ejpam-6635	255	11	is	be	AUX
ejpam-6635	255	12	a	a	DET
ejpam-6635	255	13	hop	hop	NOUN
ejpam-6635	255	14	dominating	dominating	NOUN
ejpam-6635	255	15	set	set	NOUN
ejpam-6635	255	16	of	of	ADP
ejpam-6635	255	17	g	g	PROPN
ejpam-6635	255	18	◦	◦	NOUN
ejpam-6635	255	19	h	h	NOUN
ejpam-6635	255	20	if	if	SCONJ
ejpam-6635	256	1	and	and	CCONJ
ejpam-6635	256	2	only	only	ADV
ejpam-6635	256	3	if	if	SCONJ
ejpam-6635	256	4	c	c	X
ejpam-6635	256	5	=	=	PUNCT
ejpam-6635	256	6	a	a	DET
ejpam-6635	256	7	∪	∪	X
ejpam-6635	256	8	(	(	PUNCT
ejpam-6635	256	9	∪v∈v	∪v∈v	X
ejpam-6635	256	10	(	(	PUNCT
ejpam-6635	256	11	g)∩ng(a)sv	g)∩ng(a)sv	PROPN
ejpam-6635	256	12	)	)	PUNCT
ejpam-6635	256	13	)	)	PUNCT
ejpam-6635	256	14	∪	∪	ADV
ejpam-6635	256	15	(	(	PUNCT
ejpam-6635	256	16	∪w∈v	∪w∈v	PROPN
ejpam-6635	256	17	(	(	PUNCT
ejpam-6635	256	18	g)\ng(a)ew	g)\ng(a)ew	PROPN
ejpam-6635	256	19	)	)	PUNCT
ejpam-6635	256	20	;	;	PUNCT
ejpam-6635	256	21	where	where	SCONJ
ejpam-6635	256	22	(	(	PUNCT
ejpam-6635	256	23	i	i	NOUN
ejpam-6635	256	24	)	)	PUNCT
ejpam-6635	256	25	a	a	DET
ejpam-6635	256	26	⊆	⊆	NUM
ejpam-6635	256	27	v	v	NOUN
ejpam-6635	256	28	(	(	PUNCT
ejpam-6635	256	29	g	g	NOUN
ejpam-6635	256	30	)	)	PUNCT
ejpam-6635	256	31	such	such	ADJ
ejpam-6635	256	32	that	that	PRON
ejpam-6635	256	33	for	for	ADP
ejpam-6635	256	34	each	each	DET
ejpam-6635	256	35	w	w	PROPN
ejpam-6635	256	36	∈	∈	PROPN
ejpam-6635	256	37	v	v	ADP
ejpam-6635	256	38	(	(	PUNCT
ejpam-6635	256	39	g	g	NOUN
ejpam-6635	256	40	)	)	PUNCT
ejpam-6635	256	41	\a	\a	ADJ
ejpam-6635	256	42	,	,	PUNCT
ejpam-6635	256	43	there	there	PRON
ejpam-6635	256	44	exists	exist	VERB
ejpam-6635	256	45	x	x	X
ejpam-6635	256	46	∈	∈	PROPN
ejpam-6635	256	47	a	a	PRON
ejpam-6635	256	48	with	with	ADP
ejpam-6635	256	49	dg(w	dg(w	NOUN
ejpam-6635	256	50	,	,	PUNCT
ejpam-6635	256	51	x	x	X
ejpam-6635	256	52	)	)	PUNCT
ejpam-6635	256	53	=	=	SYM
ejpam-6635	256	54	2	2	NUM
ejpam-6635	256	55	or	or	CCONJ
ejpam-6635	256	56	there	there	PRON
ejpam-6635	256	57	exists	exist	VERB
ejpam-6635	256	58	y	y	PROPN
ejpam-6635	256	59	∈	∈	PROPN
ejpam-6635	256	60	ng(w	ng(w	NOUN
ejpam-6635	256	61	)	)	PUNCT
ejpam-6635	256	62	with	with	ADP
ejpam-6635	256	63	v	v	PROPN
ejpam-6635	256	64	(	(	PUNCT
ejpam-6635	256	65	hy	hy	NOUN
ejpam-6635	256	66	)	)	PUNCT
ejpam-6635	256	67	∩	∩	NOUN
ejpam-6635	256	68	c	c	PROPN
ejpam-6635	256	69	̸=	̸=	PROPN
ejpam-6635	256	70	∅	∅	NOUN
ejpam-6635	256	71	,	,	PUNCT
ejpam-6635	256	72	(	(	PUNCT
ejpam-6635	256	73	ii	ii	NOUN
ejpam-6635	256	74	)	)	PUNCT
ejpam-6635	256	75	sv	sv	VERB
ejpam-6635	257	1	⊆	⊆	NUM
ejpam-6635	257	2	v	v	X
ejpam-6635	257	3	(	(	PUNCT
ejpam-6635	257	4	hv	hv	PROPN
ejpam-6635	257	5	)	)	PUNCT
ejpam-6635	257	6	for	for	ADP
ejpam-6635	257	7	each	each	DET
ejpam-6635	257	8	v	v	ADP
ejpam-6635	257	9	∈	∈	PROPN
ejpam-6635	257	10	ng(a	ng(a	NOUN
ejpam-6635	257	11	)	)	PUNCT
ejpam-6635	257	12	,	,	PUNCT
ejpam-6635	257	13	and	and	CCONJ
ejpam-6635	257	14	(	(	PUNCT
ejpam-6635	257	15	iii	iii	NOUN
ejpam-6635	257	16	)	)	PUNCT
ejpam-6635	257	17	ew	ew	X
ejpam-6635	257	18	is	be	AUX
ejpam-6635	257	19	a	a	DET
ejpam-6635	257	20	pointwise	pointwise	ADJ
ejpam-6635	257	21	non	non	ADJ
ejpam-6635	257	22	-	-	ADJ
ejpam-6635	257	23	dominating	dominating	ADJ
ejpam-6635	257	24	set	set	NOUN
ejpam-6635	257	25	in	in	ADP
ejpam-6635	257	26	hw	hw	PRON
ejpam-6635	257	27	for	for	ADP
ejpam-6635	257	28	each	each	DET
ejpam-6635	257	29	w	w	PROPN
ejpam-6635	257	30	∈	∈	PROPN
ejpam-6635	257	31	v	v	ADP
ejpam-6635	257	32	(	(	PUNCT
ejpam-6635	257	33	g	g	NOUN
ejpam-6635	257	34	)	)	PUNCT
ejpam-6635	257	35	\ng(a	\ng(a	PROPN
ejpam-6635	257	36	)	)	PUNCT
ejpam-6635	257	37	.	.	PUNCT
ejpam-6635	258	1	theorem	theorem	NOUN
ejpam-6635	258	2	9	9	NUM
ejpam-6635	258	3	.	.	PUNCT
ejpam-6635	259	1	let	let	VERB
ejpam-6635	259	2	g	g	NOUN
ejpam-6635	259	3	and	and	CCONJ
ejpam-6635	259	4	h	h	NOUN
ejpam-6635	259	5	be	be	VERB
ejpam-6635	259	6	any	any	DET
ejpam-6635	259	7	two	two	NUM
ejpam-6635	259	8	non	non	ADJ
ejpam-6635	259	9	-	-	ADJ
ejpam-6635	259	10	trivial	trivial	ADJ
ejpam-6635	259	11	graphs	graph	NOUN
ejpam-6635	259	12	.	.	PUNCT
ejpam-6635	260	1	if	if	SCONJ
ejpam-6635	260	2	c	c	PROPN
ejpam-6635	260	3	=	=	SYM
ejpam-6635	260	4	a∪	a∪	PROPN
ejpam-6635	260	5	(	(	PUNCT
ejpam-6635	260	6	∪v∈v	∪v∈v	X
ejpam-6635	260	7	(	(	PUNCT
ejpam-6635	260	8	g)sv	g)sv	PROPN
ejpam-6635	260	9	)	)	PUNCT
ejpam-6635	260	10	)	)	PUNCT
ejpam-6635	260	11	,	,	PUNCT
ejpam-6635	260	12	where	where	SCONJ
ejpam-6635	260	13	a	a	PRON
ejpam-6635	260	14	is	be	AUX
ejpam-6635	260	15	a	a	DET
ejpam-6635	260	16	secure	secure	ADJ
ejpam-6635	260	17	hop	hop	NOUN
ejpam-6635	260	18	dominating	dominating	NOUN
ejpam-6635	260	19	set	set	VERB
ejpam-6635	260	20	in	in	ADP
ejpam-6635	260	21	g	g	PROPN
ejpam-6635	260	22	and	and	CCONJ
ejpam-6635	260	23	sv	sv	PROPN
ejpam-6635	260	24	is	be	AUX
ejpam-6635	260	25	a	a	DET
ejpam-6635	260	26	secure	secure	ADJ
ejpam-6635	260	27	pointwise	pointwise	ADJ
ejpam-6635	260	28	non	non	ADJ
ejpam-6635	260	29	-	-	ADJ
ejpam-6635	260	30	dominating	dominating	ADJ
ejpam-6635	260	31	set	set	NOUN
ejpam-6635	260	32	in	in	ADP
ejpam-6635	260	33	hv	hv	PROPN
ejpam-6635	260	34	for	for	ADP
ejpam-6635	260	35	each	each	DET
ejpam-6635	260	36	v	v	NUM
ejpam-6635	260	37	∈	∈	PROPN
ejpam-6635	260	38	v	v	NOUN
ejpam-6635	260	39	(	(	PUNCT
ejpam-6635	260	40	g	g	NOUN
ejpam-6635	260	41	)	)	PUNCT
ejpam-6635	260	42	,	,	PUNCT
ejpam-6635	260	43	then	then	ADV
ejpam-6635	260	44	c	c	PROPN
ejpam-6635	260	45	is	be	AUX
ejpam-6635	260	46	a	a	DET
ejpam-6635	260	47	secure	secure	ADJ
ejpam-6635	260	48	hop	hop	NOUN
ejpam-6635	260	49	dominating	dominating	NOUN
ejpam-6635	260	50	set	set	VERB
ejpam-6635	260	51	in	in	ADP
ejpam-6635	260	52	g	g	PROPN
ejpam-6635	260	53	◦	◦	NOUN
ejpam-6635	260	54	h.	h.	NOUN
ejpam-6635	260	55	proof	proof	NOUN
ejpam-6635	260	56	.	.	PUNCT
ejpam-6635	261	1	by	by	ADP
ejpam-6635	261	2	theorem	theorem	NOUN
ejpam-6635	261	3	8	8	NUM
ejpam-6635	261	4	,	,	PUNCT
ejpam-6635	261	5	c	c	PROPN
ejpam-6635	261	6	is	be	AUX
ejpam-6635	261	7	a	a	DET
ejpam-6635	261	8	hop	hop	NOUN
ejpam-6635	261	9	dominating	dominating	NOUN
ejpam-6635	261	10	set	set	VERB
ejpam-6635	261	11	in	in	ADP
ejpam-6635	261	12	g	g	PROPN
ejpam-6635	261	13	◦	◦	NOUN
ejpam-6635	261	14	h.	h.	NOUN
ejpam-6635	261	15	let	let	VERB
ejpam-6635	261	16	x	x	SYM
ejpam-6635	261	17	∈	∈	PROPN
ejpam-6635	261	18	v	v	X
ejpam-6635	261	19	(	(	PUNCT
ejpam-6635	261	20	g	g	PROPN
ejpam-6635	261	21	◦	◦	NOUN
ejpam-6635	261	22	h	h	NOUN
ejpam-6635	261	23	)	)	PUNCT
ejpam-6635	261	24	\c	\c	NOUN
ejpam-6635	261	25	and	and	CCONJ
ejpam-6635	261	26	let	let	VERB
ejpam-6635	261	27	v	v	NUM
ejpam-6635	261	28	∈	∈	PROPN
ejpam-6635	261	29	v	v	NOUN
ejpam-6635	261	30	(	(	PUNCT
ejpam-6635	261	31	g	g	NOUN
ejpam-6635	261	32	)	)	PUNCT
ejpam-6635	261	33	such	such	ADJ
ejpam-6635	261	34	that	that	SCONJ
ejpam-6635	261	35	x	x	SYM
ejpam-6635	261	36	∈	∈	NOUN
ejpam-6635	261	37	v	v	NOUN
ejpam-6635	261	38	(	(	PUNCT
ejpam-6635	261	39	v	v	PROPN
ejpam-6635	261	40	+	+	PROPN
ejpam-6635	261	41	hv	hv	NOUN
ejpam-6635	261	42	)	)	PUNCT
ejpam-6635	261	43	.	.	PUNCT
ejpam-6635	262	1	consider	consider	VERB
ejpam-6635	262	2	the	the	DET
ejpam-6635	262	3	following	follow	VERB
ejpam-6635	262	4	cases	case	NOUN
ejpam-6635	262	5	:	:	PUNCT
ejpam-6635	262	6	case	case	NOUN
ejpam-6635	262	7	1	1	NUM
ejpam-6635	262	8	.	.	PUNCT
ejpam-6635	262	9	x	x	X
ejpam-6635	263	1	=	=	NOUN
ejpam-6635	264	1	v.	v.	CCONJ
ejpam-6635	264	2	then	then	ADV
ejpam-6635	264	3	x	x	SYM
ejpam-6635	264	4	∈	∈	PROPN
ejpam-6635	264	5	v	v	ADP
ejpam-6635	264	6	(	(	PUNCT
ejpam-6635	264	7	g	g	NOUN
ejpam-6635	264	8	)	)	PUNCT
ejpam-6635	264	9	\	\	PROPN
ejpam-6635	264	10	a.	a.	NOUN
ejpam-6635	264	11	since	since	SCONJ
ejpam-6635	264	12	a	a	PRON
ejpam-6635	264	13	is	be	AUX
ejpam-6635	264	14	secure	secure	ADJ
ejpam-6635	264	15	hop	hop	NOUN
ejpam-6635	264	16	dominating	dominating	NOUN
ejpam-6635	264	17	in	in	ADP
ejpam-6635	264	18	g	g	PROPN
ejpam-6635	264	19	,	,	PUNCT
ejpam-6635	264	20	(	(	PUNCT
ejpam-6635	264	21	a	a	DET
ejpam-6635	264	22	\	\	PROPN
ejpam-6635	264	23	{	{	PUNCT
ejpam-6635	264	24	y	y	NOUN
ejpam-6635	264	25	}	}	PUNCT
ejpam-6635	264	26	)	)	PUNCT
ejpam-6635	264	27	∪	∪	ADP
ejpam-6635	264	28	{	{	PUNCT
ejpam-6635	264	29	x	x	NOUN
ejpam-6635	264	30	}	}	PUNCT
ejpam-6635	264	31	is	be	AUX
ejpam-6635	264	32	hop	hop	NOUN
ejpam-6635	264	33	dominating	dominate	VERB
ejpam-6635	264	34	for	for	ADP
ejpam-6635	264	35	some	some	DET
ejpam-6635	264	36	y	y	PROPN
ejpam-6635	264	37	∈	∈	PROPN
ejpam-6635	264	38	a	a	DET
ejpam-6635	264	39	∩n2	∩n2	PROPN
ejpam-6635	264	40	g(x	g(x	NOUN
ejpam-6635	264	41	)	)	PUNCT
ejpam-6635	264	42	.	.	PUNCT
ejpam-6635	265	1	hence	hence	ADV
ejpam-6635	265	2	,	,	PUNCT
ejpam-6635	265	3	(	(	PUNCT
ejpam-6635	265	4	c	c	NOUN
ejpam-6635	265	5	\	\	PROPN
ejpam-6635	265	6	{	{	PUNCT
ejpam-6635	265	7	y	y	NOUN
ejpam-6635	265	8	}	}	PUNCT
ejpam-6635	265	9	)	)	PUNCT
ejpam-6635	265	10	∪	∪	ADP
ejpam-6635	265	11	{	{	PUNCT
ejpam-6635	265	12	x	x	NOUN
ejpam-6635	265	13	}	}	PUNCT
ejpam-6635	265	14	=	=	SYM
ejpam-6635	266	1	[	[	X
ejpam-6635	266	2	(	(	PUNCT
ejpam-6635	266	3	a	a	DET
ejpam-6635	266	4	\	\	PROPN
ejpam-6635	266	5	{	{	PUNCT
ejpam-6635	266	6	y	y	NOUN
ejpam-6635	266	7	}	}	PUNCT
ejpam-6635	266	8	)	)	PUNCT
ejpam-6635	266	9	∪	∪	ADP
ejpam-6635	266	10	{	{	PUNCT
ejpam-6635	266	11	x	x	NOUN
ejpam-6635	266	12	}	}	PUNCT
ejpam-6635	266	13	]	]	PUNCT
ejpam-6635	266	14	∪	∪	X
ejpam-6635	266	15	(	(	PUNCT
ejpam-6635	266	16	∪w∈v	∪w∈v	PROPN
ejpam-6635	266	17	(	(	PUNCT
ejpam-6635	266	18	g)sw	g)sw	PROPN
ejpam-6635	266	19	)	)	PUNCT
ejpam-6635	266	20	is	be	AUX
ejpam-6635	266	21	hop	hop	NOUN
ejpam-6635	266	22	dominating	dominate	VERB
ejpam-6635	266	23	in	in	ADP
ejpam-6635	266	24	g	g	PROPN
ejpam-6635	266	25	◦	◦	NOUN
ejpam-6635	266	26	h	h	NOUN
ejpam-6635	266	27	by	by	ADP
ejpam-6635	266	28	theorem	theorem	ADJ
ejpam-6635	266	29	8	8	NUM
ejpam-6635	266	30	.	.	PUNCT
ejpam-6635	266	31	case	case	NOUN
ejpam-6635	266	32	2	2	NUM
ejpam-6635	266	33	.	.	PUNCT
ejpam-6635	266	34	x	x	SYM
ejpam-6635	266	35	∈	∈	PROPN
ejpam-6635	266	36	v	v	ADP
ejpam-6635	266	37	(	(	PUNCT
ejpam-6635	266	38	hv	hv	PROPN
ejpam-6635	266	39	)	)	PUNCT
ejpam-6635	266	40	.	.	PUNCT
ejpam-6635	267	1	f.	f.	PROPN
ejpam-6635	267	2	alfeche	alfeche	PROPN
ejpam-6635	267	3	,	,	PUNCT
ejpam-6635	267	4	s.	s.	PROPN
ejpam-6635	267	5	canoy	canoy	PROPN
ejpam-6635	267	6	jr	jr	PROPN
ejpam-6635	267	7	.	.	PROPN
ejpam-6635	267	8	/	/	SYM
ejpam-6635	267	9	eur	eur	PROPN
ejpam-6635	267	10	.	.	PUNCT
ejpam-6635	268	1	j.	j.	PROPN
ejpam-6635	268	2	pure	pure	PROPN
ejpam-6635	268	3	appl	appl	PROPN
ejpam-6635	268	4	.	.	PROPN
ejpam-6635	268	5	math	math	PROPN
ejpam-6635	268	6	,	,	PUNCT
ejpam-6635	268	7	18	18	NUM
ejpam-6635	268	8	(	(	PUNCT
ejpam-6635	268	9	3	3	NUM
ejpam-6635	268	10	)	)	PUNCT
ejpam-6635	268	11	(	(	PUNCT
ejpam-6635	268	12	2025	2025	NUM
ejpam-6635	268	13	)	)	PUNCT
ejpam-6635	268	14	,	,	PUNCT
ejpam-6635	268	15	6635	6635	NUM
ejpam-6635	268	16	9	9	NUM
ejpam-6635	268	17	of	of	ADP
ejpam-6635	268	18	11	11	NUM
ejpam-6635	268	19	then	then	ADV
ejpam-6635	268	20	x	x	SYM
ejpam-6635	268	21	∈	∈	PROPN
ejpam-6635	268	22	v	v	ADP
ejpam-6635	268	23	(	(	PUNCT
ejpam-6635	268	24	hv	hv	PROPN
ejpam-6635	268	25	)	)	PUNCT
ejpam-6635	268	26	\	\	PROPN
ejpam-6635	269	1	sv	sv	PROPN
ejpam-6635	269	2	.	.	PUNCT
ejpam-6635	270	1	since	since	SCONJ
ejpam-6635	270	2	sv	sv	PROPN
ejpam-6635	270	3	is	be	AUX
ejpam-6635	270	4	secure	secure	ADJ
ejpam-6635	270	5	pointwise	pointwise	PROPN
ejpam-6635	270	6	non	non	ADJ
ejpam-6635	270	7	-	-	ADJ
ejpam-6635	270	8	dominating	dominating	NOUN
ejpam-6635	270	9	in	in	ADP
ejpam-6635	270	10	hv	hv	PROPN
ejpam-6635	270	11	,	,	PUNCT
ejpam-6635	270	12	there	there	PRON
ejpam-6635	270	13	exists	exist	VERB
ejpam-6635	270	14	p	p	PROPN
ejpam-6635	270	15	∈	∈	PROPN
ejpam-6635	270	16	sv	sv	ADP
ejpam-6635	270	17	\nhv(x	\nhv(x	NOUN
ejpam-6635	270	18	)	)	PUNCT
ejpam-6635	270	19	such	such	ADJ
ejpam-6635	270	20	that	that	SCONJ
ejpam-6635	270	21	(	(	PUNCT
ejpam-6635	270	22	sv	sv	PROPN
ejpam-6635	270	23	\	\	PROPN
ejpam-6635	270	24	{	{	PUNCT
ejpam-6635	270	25	p})∪{x	p})∪{x	NOUN
ejpam-6635	270	26	}	}	PUNCT
ejpam-6635	270	27	is	be	AUX
ejpam-6635	270	28	pointwise	pointwise	ADJ
ejpam-6635	270	29	non	non	ADJ
ejpam-6635	270	30	-	-	ADJ
ejpam-6635	270	31	dominating	dominating	NOUN
ejpam-6635	270	32	in	in	ADP
ejpam-6635	270	33	hv	hv	PROPN
ejpam-6635	270	34	.	.	PUNCT
ejpam-6635	271	1	therefore	therefore	ADV
ejpam-6635	271	2	,	,	PUNCT
ejpam-6635	271	3	by	by	ADP
ejpam-6635	271	4	theorem	theorem	NOUN
ejpam-6635	271	5	8	8	NUM
ejpam-6635	271	6	,	,	PUNCT
ejpam-6635	271	7	(	(	PUNCT
ejpam-6635	271	8	c	c	NOUN
ejpam-6635	271	9	\	\	X
ejpam-6635	271	10	{	{	PUNCT
ejpam-6635	271	11	p	p	NOUN
ejpam-6635	271	12	}	}	PUNCT
ejpam-6635	271	13	)	)	PUNCT
ejpam-6635	271	14	∪	∪	ADP
ejpam-6635	271	15	{	{	PUNCT
ejpam-6635	271	16	x	x	NOUN
ejpam-6635	271	17	}	}	PUNCT
ejpam-6635	271	18	=	=	PUNCT
ejpam-6635	271	19	a	a	DET
ejpam-6635	271	20	∪	∪	X
ejpam-6635	271	21	[	[	X
ejpam-6635	271	22	(	(	PUNCT
ejpam-6635	271	23	∪w∈v	∪w∈v	PROPN
ejpam-6635	271	24	(	(	PUNCT
ejpam-6635	271	25	g)\{v}sw	g)\{v}sw	NOUN
ejpam-6635	271	26	)	)	PUNCT
ejpam-6635	271	27	]	]	PUNCT
ejpam-6635	271	28	∪	∪	X
ejpam-6635	271	29	(	(	PUNCT
ejpam-6635	271	30	(	(	PUNCT
ejpam-6635	271	31	sv	sv	INTJ
ejpam-6635	271	32	\	\	PROPN
ejpam-6635	271	33	{	{	PUNCT
ejpam-6635	271	34	p	p	NOUN
ejpam-6635	271	35	}	}	PUNCT
ejpam-6635	271	36	)	)	PUNCT
ejpam-6635	271	37	∪	∪	ADP
ejpam-6635	271	38	{	{	PUNCT
ejpam-6635	271	39	x	x	NOUN
ejpam-6635	271	40	}	}	PUNCT
ejpam-6635	271	41	)	)	PUNCT
ejpam-6635	271	42	is	be	AUX
ejpam-6635	271	43	hop	hop	NOUN
ejpam-6635	271	44	dominating	dominate	VERB
ejpam-6635	271	45	in	in	ADP
ejpam-6635	271	46	g	g	PROPN
ejpam-6635	271	47	◦	◦	NOUN
ejpam-6635	271	48	h.	h.	PROPN
ejpam-6635	271	49	therefore	therefore	ADV
ejpam-6635	271	50	,	,	PUNCT
ejpam-6635	271	51	c	c	PROPN
ejpam-6635	271	52	is	be	AUX
ejpam-6635	271	53	a	a	DET
ejpam-6635	271	54	secure	secure	ADJ
ejpam-6635	271	55	hop	hop	NOUN
ejpam-6635	271	56	dominating	dominating	NOUN
ejpam-6635	271	57	set	set	VERB
ejpam-6635	271	58	in	in	ADP
ejpam-6635	271	59	g	g	PROPN
ejpam-6635	271	60	◦	◦	NOUN
ejpam-6635	271	61	h.	h.	NOUN
ejpam-6635	271	62	corollary	corollary	ADJ
ejpam-6635	271	63	6	6	NUM
ejpam-6635	271	64	.	.	PUNCT
ejpam-6635	272	1	let	let	VERB
ejpam-6635	272	2	g	g	NOUN
ejpam-6635	272	3	and	and	CCONJ
ejpam-6635	272	4	h	h	NOUN
ejpam-6635	272	5	be	be	VERB
ejpam-6635	272	6	any	any	DET
ejpam-6635	272	7	two	two	NUM
ejpam-6635	272	8	non	non	ADJ
ejpam-6635	272	9	-	-	ADJ
ejpam-6635	272	10	trivial	trivial	ADJ
ejpam-6635	272	11	graphs	graph	NOUN
ejpam-6635	272	12	.	.	PUNCT
ejpam-6635	273	1	then	then	ADV
ejpam-6635	273	2	γsh(g	γsh(g	ADP
ejpam-6635	273	3	◦	◦	NOUN
ejpam-6635	273	4	h	h	NOUN
ejpam-6635	273	5	)	)	PUNCT
ejpam-6635	273	6	≤	≤	NOUN
ejpam-6635	273	7	γsh(g	γsh(g	NOUN
ejpam-6635	273	8	)	)	PUNCT
ejpam-6635	274	1	+	+	CCONJ
ejpam-6635	274	2	|v	|v	X
ejpam-6635	274	3	(	(	PUNCT
ejpam-6635	274	4	g)|spnd(h	g)|spnd(h	NOUN
ejpam-6635	274	5	)	)	PUNCT
ejpam-6635	274	6	.	.	PUNCT
ejpam-6635	275	1	proof	proof	NOUN
ejpam-6635	275	2	.	.	PUNCT
ejpam-6635	276	1	let	let	VERB
ejpam-6635	276	2	a	a	DET
ejpam-6635	276	3	be	be	AUX
ejpam-6635	276	4	a	a	DET
ejpam-6635	276	5	γsh	γsh	NOUN
ejpam-6635	276	6	-	-	PUNCT
ejpam-6635	276	7	set	set	VERB
ejpam-6635	276	8	in	in	ADP
ejpam-6635	276	9	g	g	NOUN
ejpam-6635	276	10	and	and	CCONJ
ejpam-6635	276	11	let	let	VERB
ejpam-6635	276	12	sv	sv	INTJ
ejpam-6635	276	13	be	be	AUX
ejpam-6635	276	14	an	an	DET
ejpam-6635	276	15	spnd	spnd	NOUN
ejpam-6635	276	16	-	-	PUNCT
ejpam-6635	276	17	set	set	NOUN
ejpam-6635	276	18	in	in	ADP
ejpam-6635	276	19	hv	hv	PROPN
ejpam-6635	276	20	for	for	ADP
ejpam-6635	276	21	each	each	DET
ejpam-6635	276	22	v	v	NUM
ejpam-6635	276	23	∈	∈	PROPN
ejpam-6635	276	24	v	v	NOUN
ejpam-6635	276	25	(	(	PUNCT
ejpam-6635	276	26	g	g	NOUN
ejpam-6635	276	27	)	)	PUNCT
ejpam-6635	276	28	.	.	PUNCT
ejpam-6635	277	1	then	then	ADV
ejpam-6635	277	2	c	c	X
ejpam-6635	277	3	=	=	SYM
ejpam-6635	277	4	a∪	a∪	PROPN
ejpam-6635	277	5	(	(	PUNCT
ejpam-6635	277	6	∪v∈v	∪v∈v	X
ejpam-6635	277	7	(	(	PUNCT
ejpam-6635	277	8	g)sv	g)sv	PROPN
ejpam-6635	277	9	)	)	PUNCT
ejpam-6635	277	10	)	)	PUNCT
ejpam-6635	277	11	is	be	AUX
ejpam-6635	277	12	a	a	DET
ejpam-6635	277	13	secure	secure	ADJ
ejpam-6635	277	14	hop	hop	NOUN
ejpam-6635	277	15	dominating	dominating	NOUN
ejpam-6635	277	16	set	set	VERB
ejpam-6635	277	17	in	in	ADP
ejpam-6635	277	18	g	g	PROPN
ejpam-6635	277	19	◦	◦	NOUN
ejpam-6635	277	20	h	h	NOUN
ejpam-6635	277	21	by	by	ADP
ejpam-6635	277	22	theorem	theorem	NOUN
ejpam-6635	277	23	9	9	NUM
ejpam-6635	277	24	.	.	PUNCT
ejpam-6635	278	1	thus	thus	ADV
ejpam-6635	278	2	,	,	PUNCT
ejpam-6635	278	3	γsh(g	γsh(g	NOUN
ejpam-6635	278	4	◦	◦	NOUN
ejpam-6635	278	5	h	h	NOUN
ejpam-6635	278	6	)	)	PUNCT
ejpam-6635	278	7	≤	≤	NOUN
ejpam-6635	278	8	|c|	|c|	PROPN
ejpam-6635	278	9	=	=	PRON
ejpam-6635	278	10	|a|+	|a|+	VERB
ejpam-6635	278	11	∑	∑	PUNCT
ejpam-6635	278	12	v∈v	v∈v	NOUN
ejpam-6635	278	13	(	(	PUNCT
ejpam-6635	278	14	g	g	NOUN
ejpam-6635	278	15	)	)	PUNCT
ejpam-6635	278	16	|sv|	|sv|	PROPN
ejpam-6635	278	17	=	=	SYM
ejpam-6635	278	18	γsh(g	γsh(g	NOUN
ejpam-6635	278	19	)	)	PUNCT
ejpam-6635	278	20	+	+	CCONJ
ejpam-6635	278	21	∑	∑	PUNCT
ejpam-6635	278	22	v∈v	v∈v	NOUN
ejpam-6635	278	23	(	(	PUNCT
ejpam-6635	278	24	g	g	NOUN
ejpam-6635	278	25	)	)	PUNCT
ejpam-6635	278	26	spnd(h	spnd(h	NOUN
ejpam-6635	278	27	)	)	PUNCT
ejpam-6635	278	28	=	=	SYM
ejpam-6635	278	29	γsh(g	γsh(g	NOUN
ejpam-6635	278	30	)	)	PUNCT
ejpam-6635	278	31	+	+	CCONJ
ejpam-6635	278	32	|v	|v	X
ejpam-6635	278	33	(	(	PUNCT
ejpam-6635	278	34	g)|spnd(h	g)|spnd(h	NOUN
ejpam-6635	278	35	)	)	PUNCT
ejpam-6635	278	36	.	.	PUNCT
ejpam-6635	279	1	this	this	PRON
ejpam-6635	279	2	proves	prove	VERB
ejpam-6635	279	3	the	the	DET
ejpam-6635	279	4	assertion	assertion	NOUN
ejpam-6635	279	5	.	.	PUNCT
ejpam-6635	280	1	remark	remark	PROPN
ejpam-6635	280	2	1	1	NUM
ejpam-6635	280	3	.	.	PUNCT
ejpam-6635	281	1	the	the	DET
ejpam-6635	281	2	bound	bind	VERB
ejpam-6635	281	3	given	give	VERB
ejpam-6635	281	4	in	in	ADP
ejpam-6635	281	5	corollary	corollary	ADJ
ejpam-6635	281	6	6	6	NUM
ejpam-6635	281	7	is	be	AUX
ejpam-6635	281	8	sharp	sharp	ADJ
ejpam-6635	281	9	.	.	PUNCT
ejpam-6635	282	1	strict	strict	ADJ
ejpam-6635	282	2	inequality	inequality	NOUN
ejpam-6635	282	3	is	be	AUX
ejpam-6635	282	4	also	also	ADV
ejpam-6635	282	5	attainable	attainable	ADJ
ejpam-6635	282	6	.	.	PUNCT
ejpam-6635	283	1	to	to	PART
ejpam-6635	283	2	see	see	VERB
ejpam-6635	283	3	this	this	PRON
ejpam-6635	283	4	,	,	PUNCT
ejpam-6635	283	5	consider	consider	VERB
ejpam-6635	283	6	g1	g1	NOUN
ejpam-6635	283	7	=	=	SYM
ejpam-6635	283	8	k2	k2	PROPN
ejpam-6635	283	9	,	,	PUNCT
ejpam-6635	283	10	h1	h1	NOUN
ejpam-6635	283	11	=	=	SYM
ejpam-6635	283	12	k2	k2	PROPN
ejpam-6635	283	13	,	,	PUNCT
ejpam-6635	283	14	g2	g2	PROPN
ejpam-6635	283	15	=	=	PUNCT
ejpam-6635	283	16	k2	k2	PROPN
ejpam-6635	283	17	,	,	PUNCT
ejpam-6635	283	18	and	and	CCONJ
ejpam-6635	283	19	h2	h2	NOUN
ejpam-6635	283	20	=	=	SYM
ejpam-6635	283	21	k2	k2	PROPN
ejpam-6635	283	22	.	.	PUNCT
ejpam-6635	284	1	then	then	ADV
ejpam-6635	284	2	γsh(g1	γsh(g1	PROPN
ejpam-6635	284	3	◦	◦	NOUN
ejpam-6635	284	4	h1	h1	NOUN
ejpam-6635	284	5	)	)	PUNCT
ejpam-6635	285	1	=	=	PUNCT
ejpam-6635	286	1	γsh(k3	γsh(k3	X
ejpam-6635	286	2	∪k3	∪k3	NOUN
ejpam-6635	286	3	)	)	PUNCT
ejpam-6635	286	4	=	=	SYM
ejpam-6635	286	5	6	6	NUM
ejpam-6635	286	6	=	=	SYM
ejpam-6635	286	7	γsh(g1	γsh(g1	NOUN
ejpam-6635	286	8	)	)	PUNCT
ejpam-6635	286	9	+	+	SYM
ejpam-6635	286	10	2spnd(h1	2spnd(h1	NUM
ejpam-6635	286	11	)	)	PUNCT
ejpam-6635	286	12	and	and	CCONJ
ejpam-6635	286	13	γsh(g2	γsh(g2	PROPN
ejpam-6635	286	14	◦	◦	PROPN
ejpam-6635	286	15	h2	h2	NOUN
ejpam-6635	286	16	)	)	PUNCT
ejpam-6635	286	17	=	=	SYM
ejpam-6635	286	18	2	2	NUM
ejpam-6635	286	19	<	<	SYM
ejpam-6635	286	20	4	4	NUM
ejpam-6635	286	21	=	=	SYM
ejpam-6635	286	22	γsh(g2	γsh(g2	PROPN
ejpam-6635	286	23	)	)	PUNCT
ejpam-6635	286	24	+	+	NUM
ejpam-6635	286	25	2spnd(h2	2spnd(h2	NOUN
ejpam-6635	286	26	)	)	PUNCT
ejpam-6635	286	27	.	.	PUNCT
ejpam-6635	287	1	theorem	theorem	ADJ
ejpam-6635	287	2	10	10	NUM
ejpam-6635	287	3	.	.	PUNCT
ejpam-6635	288	1	let	let	VERB
ejpam-6635	288	2	g	g	PRON
ejpam-6635	288	3	be	be	AUX
ejpam-6635	288	4	a	a	DET
ejpam-6635	288	5	non	non	ADJ
ejpam-6635	288	6	-	-	ADJ
ejpam-6635	288	7	trivial	trivial	ADJ
ejpam-6635	288	8	connected	connected	ADJ
ejpam-6635	288	9	graph	graph	NOUN
ejpam-6635	288	10	with	with	ADP
ejpam-6635	288	11	δ(g	δ(g	PROPN
ejpam-6635	288	12	)	)	PUNCT
ejpam-6635	288	13	≥	≥	NOUN
ejpam-6635	288	14	2	2	NUM
ejpam-6635	288	15	and	and	CCONJ
ejpam-6635	288	16	let	let	VERB
ejpam-6635	288	17	h	h	NOUN
ejpam-6635	288	18	be	be	AUX
ejpam-6635	288	19	any	any	DET
ejpam-6635	288	20	graph	graph	NOUN
ejpam-6635	288	21	.	.	PUNCT
ejpam-6635	289	1	then	then	ADV
ejpam-6635	289	2	γsh(g	γsh(g	NOUN
ejpam-6635	289	3	◦	◦	NOUN
ejpam-6635	289	4	h	h	NOUN
ejpam-6635	289	5	)	)	PUNCT
ejpam-6635	289	6	≤	≤	NOUN
ejpam-6635	289	7	|v	|v	X
ejpam-6635	289	8	(	(	PUNCT
ejpam-6635	289	9	g)|	g)|	NOUN
ejpam-6635	289	10	.	.	PUNCT
ejpam-6635	290	1	proof	proof	NOUN
ejpam-6635	290	2	.	.	PUNCT
ejpam-6635	291	1	by	by	ADP
ejpam-6635	291	2	theorem	theorem	NOUN
ejpam-6635	291	3	8	8	NUM
ejpam-6635	291	4	,	,	PUNCT
ejpam-6635	291	5	c	c	NOUN
ejpam-6635	291	6	=	=	SYM
ejpam-6635	291	7	v	v	PROPN
ejpam-6635	291	8	(	(	PUNCT
ejpam-6635	291	9	g	g	NOUN
ejpam-6635	291	10	)	)	PUNCT
ejpam-6635	291	11	is	be	AUX
ejpam-6635	291	12	a	a	DET
ejpam-6635	291	13	hop	hop	NOUN
ejpam-6635	291	14	dominating	dominating	NOUN
ejpam-6635	291	15	set	set	VERB
ejpam-6635	291	16	in	in	ADP
ejpam-6635	291	17	g	g	PROPN
ejpam-6635	291	18	◦	◦	PROPN
ejpam-6635	291	19	h.	h.	PROPN
ejpam-6635	291	20	next	next	ADV
ejpam-6635	291	21	,	,	PUNCT
ejpam-6635	291	22	let	let	VERB
ejpam-6635	291	23	x	x	PUNCT
ejpam-6635	291	24	∈	∈	PROPN
ejpam-6635	291	25	v	v	X
ejpam-6635	291	26	(	(	PUNCT
ejpam-6635	291	27	g	g	PROPN
ejpam-6635	291	28	◦	◦	NOUN
ejpam-6635	291	29	h	h	NOUN
ejpam-6635	291	30	)	)	PUNCT
ejpam-6635	291	31	\	\	NOUN
ejpam-6635	291	32	c	c	NOUN
ejpam-6635	291	33	and	and	CCONJ
ejpam-6635	291	34	let	let	VERB
ejpam-6635	291	35	v	v	NUM
ejpam-6635	291	36	∈	∈	PROPN
ejpam-6635	291	37	v	v	NOUN
ejpam-6635	291	38	(	(	PUNCT
ejpam-6635	291	39	g	g	NOUN
ejpam-6635	291	40	)	)	PUNCT
ejpam-6635	291	41	such	such	ADJ
ejpam-6635	291	42	that	that	SCONJ
ejpam-6635	291	43	x	x	SYM
ejpam-6635	291	44	∈	∈	NOUN
ejpam-6635	291	45	v	v	NOUN
ejpam-6635	291	46	(	(	PUNCT
ejpam-6635	291	47	v	v	NOUN
ejpam-6635	291	48	+	+	CCONJ
ejpam-6635	291	49	hv	hv	PROPN
ejpam-6635	291	50	)	)	PUNCT
ejpam-6635	291	51	.	.	PUNCT
ejpam-6635	292	1	since	since	SCONJ
ejpam-6635	292	2	c	c	PROPN
ejpam-6635	292	3	=	=	SYM
ejpam-6635	292	4	v	v	PROPN
ejpam-6635	292	5	(	(	PUNCT
ejpam-6635	292	6	g	g	NOUN
ejpam-6635	292	7	)	)	PUNCT
ejpam-6635	292	8	,	,	PUNCT
ejpam-6635	292	9	it	it	PRON
ejpam-6635	292	10	follows	follow	VERB
ejpam-6635	292	11	that	that	SCONJ
ejpam-6635	292	12	x	x	PUNCT
ejpam-6635	292	13	∈	∈	NOUN
ejpam-6635	292	14	v	v	ADP
ejpam-6635	292	15	(	(	PUNCT
ejpam-6635	292	16	hv	hv	PROPN
ejpam-6635	292	17	)	)	PUNCT
ejpam-6635	292	18	\	\	PROPN
ejpam-6635	292	19	sv	sv	AUX
ejpam-6635	292	20	.	.	PROPN
ejpam-6635	292	21	pick	pick	VERB
ejpam-6635	292	22	any	any	DET
ejpam-6635	292	23	w	w	NOUN
ejpam-6635	292	24	∈	∈	PROPN
ejpam-6635	292	25	ng(v	ng(v	PUNCT
ejpam-6635	292	26	)	)	PUNCT
ejpam-6635	292	27	and	and	CCONJ
ejpam-6635	292	28	let	let	VERB
ejpam-6635	292	29	cx	cx	NOUN
ejpam-6635	292	30	=	=	PUNCT
ejpam-6635	293	1	[	[	X
ejpam-6635	293	2	v	v	X
ejpam-6635	293	3	(	(	PUNCT
ejpam-6635	293	4	g	g	NOUN
ejpam-6635	293	5	)	)	PUNCT
ejpam-6635	293	6	\	\	NOUN
ejpam-6635	293	7	{	{	PUNCT
ejpam-6635	293	8	w	w	NOUN
ejpam-6635	293	9	}	}	PUNCT
ejpam-6635	293	10	]	]	PUNCT
ejpam-6635	293	11	∪	∪	X
ejpam-6635	293	12	{	{	PUNCT
ejpam-6635	293	13	x	x	NOUN
ejpam-6635	293	14	}	}	PUNCT
ejpam-6635	293	15	.	.	PUNCT
ejpam-6635	294	1	let	let	VERB
ejpam-6635	294	2	p	p	PRON
ejpam-6635	294	3	∈	∈	PROPN
ejpam-6635	294	4	v	v	NOUN
ejpam-6635	294	5	(	(	PUNCT
ejpam-6635	294	6	g	g	PROPN
ejpam-6635	294	7	◦	◦	NOUN
ejpam-6635	294	8	h	h	NOUN
ejpam-6635	294	9	)	)	PUNCT
ejpam-6635	294	10	\	\	PROPN
ejpam-6635	294	11	cx	cx	PROPN
ejpam-6635	294	12	.	.	PUNCT
ejpam-6635	294	13	suppose	suppose	VERB
ejpam-6635	294	14	p	p	PROPN
ejpam-6635	294	15	=	=	PROPN
ejpam-6635	294	16	w.	w.	PROPN
ejpam-6635	294	17	then	then	ADV
ejpam-6635	294	18	x	x	SYM
ejpam-6635	294	19	∈	∈	PROPN
ejpam-6635	294	20	cx	cx	PROPN
ejpam-6635	294	21	∩	∩	PROPN
ejpam-6635	294	22	n2	n2	PROPN
ejpam-6635	294	23	g	g	PROPN
ejpam-6635	294	24	◦	◦	NOUN
ejpam-6635	294	25	h(p	h(p	NOUN
ejpam-6635	294	26	)	)	PUNCT
ejpam-6635	294	27	.	.	PUNCT
ejpam-6635	295	1	suppose	suppose	VERB
ejpam-6635	295	2	p	p	X
ejpam-6635	295	3	∈	∈	PROPN
ejpam-6635	295	4	v	v	NOUN
ejpam-6635	295	5	(	(	PUNCT
ejpam-6635	295	6	hz	hz	NOUN
ejpam-6635	295	7	)	)	PUNCT
ejpam-6635	295	8	for	for	ADP
ejpam-6635	295	9	some	some	DET
ejpam-6635	295	10	z	z	NOUN
ejpam-6635	295	11	∈	∈	PROPN
ejpam-6635	295	12	v	v	ADP
ejpam-6635	295	13	(	(	PUNCT
ejpam-6635	295	14	g	g	NOUN
ejpam-6635	295	15	)	)	PUNCT
ejpam-6635	295	16	.	.	PUNCT
ejpam-6635	296	1	if	if	SCONJ
ejpam-6635	296	2	z	z	NOUN
ejpam-6635	296	3	=	=	SYM
ejpam-6635	296	4	w	w	PROPN
ejpam-6635	296	5	,	,	PUNCT
ejpam-6635	296	6	then	then	ADV
ejpam-6635	296	7	v	v	ADP
ejpam-6635	296	8	∈	∈	PROPN
ejpam-6635	296	9	cx	cx	PROPN
ejpam-6635	296	10	∪	∪	ADP
ejpam-6635	296	11	ng	ng	PROPN
ejpam-6635	296	12	◦	◦	NOUN
ejpam-6635	296	13	h(p	h(p	NOUN
ejpam-6635	296	14	)	)	PUNCT
ejpam-6635	296	15	and	and	CCONJ
ejpam-6635	296	16	dg	dg	NOUN
ejpam-6635	296	17	◦	◦	PROPN
ejpam-6635	296	18	h(u	h(u	PROPN
ejpam-6635	296	19	,	,	PUNCT
ejpam-6635	296	20	p	p	X
ejpam-6635	296	21	)	)	PUNCT
ejpam-6635	296	22	=	=	SYM
ejpam-6635	296	23	2	2	X
ejpam-6635	296	24	.	.	X
ejpam-6635	296	25	suppose	suppose	VERB
ejpam-6635	296	26	z	z	PROPN
ejpam-6635	296	27	̸=	̸=	PROPN
ejpam-6635	296	28	w.	w.	PROPN
ejpam-6635	296	29	since	since	SCONJ
ejpam-6635	296	30	δ(g	δ(g	PROPN
ejpam-6635	296	31	)	)	PUNCT
ejpam-6635	296	32	≥	≥	NOUN
ejpam-6635	296	33	2	2	NUM
ejpam-6635	296	34	,	,	PUNCT
ejpam-6635	296	35	we	we	PRON
ejpam-6635	296	36	may	may	AUX
ejpam-6635	296	37	choose	choose	VERB
ejpam-6635	296	38	u	u	PROPN
ejpam-6635	296	39	∈	∈	PROPN
ejpam-6635	296	40	ng(z	ng(z	PROPN
ejpam-6635	296	41	)	)	PUNCT
ejpam-6635	296	42	\	\	PUNCT
ejpam-6635	296	43	{	{	PUNCT
ejpam-6635	296	44	w	w	NOUN
ejpam-6635	296	45	}	}	PUNCT
ejpam-6635	296	46	.	.	PUNCT
ejpam-6635	297	1	this	this	PRON
ejpam-6635	297	2	implies	imply	VERB
ejpam-6635	297	3	that	that	SCONJ
ejpam-6635	297	4	u	u	PROPN
ejpam-6635	297	5	∈	∈	PROPN
ejpam-6635	297	6	cx	cx	PROPN
ejpam-6635	297	7	and	and	CCONJ
ejpam-6635	297	8	dg	dg	PROPN
ejpam-6635	297	9	◦	◦	PROPN
ejpam-6635	297	10	h(u	h(u	PROPN
ejpam-6635	297	11	,	,	PUNCT
ejpam-6635	297	12	p	p	X
ejpam-6635	297	13	)	)	PUNCT
ejpam-6635	297	14	=	=	SYM
ejpam-6635	297	15	2	2	X
ejpam-6635	297	16	.	.	PUNCT
ejpam-6635	298	1	thus	thus	ADV
ejpam-6635	298	2	,	,	PUNCT
ejpam-6635	298	3	cx	cx	PROPN
ejpam-6635	298	4	is	be	AUX
ejpam-6635	298	5	hop	hop	NOUN
ejpam-6635	298	6	dominating	dominate	VERB
ejpam-6635	298	7	in	in	ADP
ejpam-6635	298	8	g	g	PROPN
ejpam-6635	298	9	◦	◦	PROPN
ejpam-6635	298	10	h.	h.	NOUN
ejpam-6635	298	11	since	since	SCONJ
ejpam-6635	298	12	x	x	PRON
ejpam-6635	298	13	was	be	AUX
ejpam-6635	298	14	arbitrarily	arbitrarily	ADV
ejpam-6635	298	15	chosen	choose	VERB
ejpam-6635	298	16	in	in	ADP
ejpam-6635	298	17	v	v	NUM
ejpam-6635	298	18	(	(	PUNCT
ejpam-6635	298	19	g	g	PROPN
ejpam-6635	298	20	◦	◦	NOUN
ejpam-6635	298	21	h	h	NOUN
ejpam-6635	298	22	)	)	PUNCT
ejpam-6635	298	23	\	\	NOUN
ejpam-6635	299	1	c	c	X
ejpam-6635	299	2	,	,	PUNCT
ejpam-6635	299	3	it	it	PRON
ejpam-6635	299	4	follows	follow	VERB
ejpam-6635	299	5	that	that	SCONJ
ejpam-6635	299	6	c	c	PROPN
ejpam-6635	299	7	is	be	AUX
ejpam-6635	299	8	a	a	DET
ejpam-6635	299	9	secure	secure	ADJ
ejpam-6635	299	10	hop	hop	NOUN
ejpam-6635	299	11	dominating	dominating	NOUN
ejpam-6635	299	12	set	set	VERB
ejpam-6635	299	13	in	in	ADP
ejpam-6635	299	14	g	g	PROPN
ejpam-6635	299	15	◦	◦	PROPN
ejpam-6635	299	16	h.	h.	PROPN
ejpam-6635	299	17	therefore	therefore	ADV
ejpam-6635	299	18	,	,	PUNCT
ejpam-6635	299	19	γsh(g	γsh(g	NOUN
ejpam-6635	299	20	◦	◦	NOUN
ejpam-6635	299	21	h	h	NOUN
ejpam-6635	299	22	)	)	PUNCT
ejpam-6635	299	23	≤	≤	NOUN
ejpam-6635	299	24	|v	|v	X
ejpam-6635	299	25	(	(	PUNCT
ejpam-6635	299	26	g)|	g)|	PROPN
ejpam-6635	299	27	.	.	PUNCT
ejpam-6635	299	28	f.	f.	PROPN
ejpam-6635	299	29	alfeche	alfeche	PROPN
ejpam-6635	299	30	,	,	PUNCT
ejpam-6635	299	31	s.	s.	PROPN
ejpam-6635	299	32	canoy	canoy	PROPN
ejpam-6635	299	33	jr	jr	PROPN
ejpam-6635	299	34	.	.	PROPN
ejpam-6635	299	35	/	/	SYM
ejpam-6635	299	36	eur	eur	PROPN
ejpam-6635	299	37	.	.	PUNCT
ejpam-6635	300	1	j.	j.	PROPN
ejpam-6635	300	2	pure	pure	PROPN
ejpam-6635	300	3	appl	appl	PROPN
ejpam-6635	300	4	.	.	PROPN
ejpam-6635	300	5	math	math	PROPN
ejpam-6635	300	6	,	,	PUNCT
ejpam-6635	300	7	18	18	NUM
ejpam-6635	300	8	(	(	PUNCT
ejpam-6635	300	9	3	3	NUM
ejpam-6635	300	10	)	)	PUNCT
ejpam-6635	300	11	(	(	PUNCT
ejpam-6635	300	12	2025	2025	NUM
ejpam-6635	300	13	)	)	PUNCT
ejpam-6635	300	14	,	,	PUNCT
ejpam-6635	300	15	6635	6635	NUM
ejpam-6635	300	16	10	10	NUM
ejpam-6635	300	17	of	of	ADP
ejpam-6635	300	18	11	11	NUM
ejpam-6635	300	19	4	4	NUM
ejpam-6635	300	20	.	.	PUNCT
ejpam-6635	301	1	conclusion	conclusion	NOUN
ejpam-6635	301	2	secure	secure	VERB
ejpam-6635	301	3	pointwise	pointwise	PROPN
ejpam-6635	301	4	non	non	ADJ
ejpam-6635	301	5	-	-	ADJ
ejpam-6635	301	6	domination	domination	NOUN
ejpam-6635	301	7	was	be	AUX
ejpam-6635	301	8	introduced	introduce	VERB
ejpam-6635	301	9	and	and	CCONJ
ejpam-6635	301	10	investigated	investigate	VERB
ejpam-6635	301	11	in	in	ADP
ejpam-6635	301	12	this	this	DET
ejpam-6635	301	13	study	study	NOUN
ejpam-6635	301	14	.	.	PUNCT
ejpam-6635	302	1	bounds	bound	NOUN
ejpam-6635	302	2	on	on	ADP
ejpam-6635	302	3	the	the	DET
ejpam-6635	302	4	secure	secure	ADJ
ejpam-6635	302	5	pointwise	pointwise	PROPN
ejpam-6635	302	6	non	non	ADJ
ejpam-6635	302	7	-	-	ADJ
ejpam-6635	302	8	domination	domination	ADJ
ejpam-6635	302	9	number	number	NOUN
ejpam-6635	302	10	were	be	AUX
ejpam-6635	302	11	established	establish	VERB
ejpam-6635	302	12	,	,	PUNCT
ejpam-6635	302	13	and	and	CCONJ
ejpam-6635	302	14	graphs	graph	NOUN
ejpam-6635	302	15	attaining	attain	VERB
ejpam-6635	302	16	these	these	DET
ejpam-6635	302	17	bounds	bound	NOUN
ejpam-6635	302	18	were	be	AUX
ejpam-6635	302	19	characterized	characterize	VERB
ejpam-6635	302	20	.	.	PUNCT
ejpam-6635	303	1	necessary	necessary	ADJ
ejpam-6635	303	2	and	and	CCONJ
ejpam-6635	303	3	sufficient	sufficient	ADJ
ejpam-6635	303	4	conditions	condition	NOUN
ejpam-6635	303	5	for	for	ADP
ejpam-6635	303	6	a	a	DET
ejpam-6635	303	7	subset	subset	NOUN
ejpam-6635	303	8	in	in	ADP
ejpam-6635	303	9	the	the	DET
ejpam-6635	303	10	join	join	NOUN
ejpam-6635	303	11	of	of	ADP
ejpam-6635	303	12	graphs	graph	NOUN
ejpam-6635	303	13	to	to	PART
ejpam-6635	303	14	be	be	AUX
ejpam-6635	303	15	a	a	DET
ejpam-6635	303	16	secure	secure	ADJ
ejpam-6635	303	17	pointwise	pointwise	ADJ
ejpam-6635	303	18	non	non	ADJ
ejpam-6635	303	19	-	-	ADJ
ejpam-6635	303	20	dominating	dominating	ADJ
ejpam-6635	303	21	set	set	NOUN
ejpam-6635	303	22	was	be	AUX
ejpam-6635	303	23	obtained	obtain	VERB
ejpam-6635	303	24	.	.	PUNCT
ejpam-6635	304	1	moreover	moreover	ADV
ejpam-6635	304	2	,	,	PUNCT
ejpam-6635	304	3	it	it	PRON
ejpam-6635	304	4	was	be	AUX
ejpam-6635	304	5	shown	show	VERB
ejpam-6635	304	6	that	that	SCONJ
ejpam-6635	304	7	given	give	VERB
ejpam-6635	304	8	positive	positive	ADJ
ejpam-6635	304	9	integers	integer	NOUN
ejpam-6635	304	10	a	a	PRON
ejpam-6635	304	11	and	and	CCONJ
ejpam-6635	304	12	b	b	NOUN
ejpam-6635	304	13	with	with	ADP
ejpam-6635	304	14	2	2	NUM
ejpam-6635	304	15	≤	≤	NOUN
ejpam-6635	304	16	a	a	DET
ejpam-6635	304	17	≤	≤	NUM
ejpam-6635	304	18	b	b	NOUN
ejpam-6635	304	19	,	,	PUNCT
ejpam-6635	304	20	there	there	PRON
ejpam-6635	304	21	exists	exist	VERB
ejpam-6635	304	22	a	a	DET
ejpam-6635	304	23	connected	connected	ADJ
ejpam-6635	304	24	graph	graph	NOUN
ejpam-6635	304	25	such	such	ADJ
ejpam-6635	304	26	that	that	PRON
ejpam-6635	304	27	γh(g	γh(g	NOUN
ejpam-6635	304	28	)	)	PUNCT
ejpam-6635	304	29	=	=	PUNCT
ejpam-6635	304	30	a	a	PRON
ejpam-6635	304	31	and	and	CCONJ
ejpam-6635	304	32	γsh(g	γsh(g	NOUN
ejpam-6635	304	33	)	)	PUNCT
ejpam-6635	304	34	=	=	SYM
ejpam-6635	304	35	b	b	NOUN
ejpam-6635	304	36	,	,	PUNCT
ejpam-6635	304	37	where	where	SCONJ
ejpam-6635	304	38	γh(g	γh(g	NOUN
ejpam-6635	304	39	)	)	PUNCT
ejpam-6635	304	40	and	and	CCONJ
ejpam-6635	304	41	γsh(g	γsh(g	NOUN
ejpam-6635	304	42	)	)	PUNCT
ejpam-6635	304	43	are	be	AUX
ejpam-6635	304	44	the	the	DET
ejpam-6635	304	45	hop	hop	NOUN
ejpam-6635	304	46	domination	domination	NOUN
ejpam-6635	304	47	number	number	NOUN
ejpam-6635	304	48	and	and	CCONJ
ejpam-6635	304	49	secure	secure	VERB
ejpam-6635	304	50	hop	hop	NOUN
ejpam-6635	304	51	domination	domination	NOUN
ejpam-6635	304	52	number	number	NOUN
ejpam-6635	304	53	of	of	ADP
ejpam-6635	304	54	g	g	NOUN
ejpam-6635	304	55	,	,	PUNCT
ejpam-6635	304	56	respectively	respectively	ADV
ejpam-6635	304	57	.	.	PUNCT
ejpam-6635	305	1	secure	secure	VERB
ejpam-6635	305	2	pointwise	pointwise	PROPN
ejpam-6635	305	3	non	non	ADJ
ejpam-6635	305	4	-	-	ADJ
ejpam-6635	305	5	domination	domination	NOUN
ejpam-6635	305	6	may	may	AUX
ejpam-6635	305	7	be	be	AUX
ejpam-6635	305	8	used	use	VERB
ejpam-6635	305	9	to	to	PART
ejpam-6635	305	10	characterize	characterize	VERB
ejpam-6635	305	11	the	the	DET
ejpam-6635	305	12	secure	secure	ADJ
ejpam-6635	305	13	hop	hop	NOUN
ejpam-6635	305	14	dominating	dominating	NOUN
ejpam-6635	305	15	sets	set	NOUN
ejpam-6635	305	16	in	in	ADP
ejpam-6635	305	17	the	the	DET
ejpam-6635	305	18	corona	corona	NOUN
ejpam-6635	305	19	and	and	CCONJ
ejpam-6635	305	20	lexicographic	lexicographic	ADJ
ejpam-6635	305	21	product	product	NOUN
ejpam-6635	305	22	of	of	ADP
ejpam-6635	305	23	graphs	graph	NOUN
ejpam-6635	305	24	.	.	PUNCT
ejpam-6635	306	1	acknowledgements	acknowledgement	NOUN
ejpam-6635	306	2	the	the	DET
ejpam-6635	306	3	authors	author	NOUN
ejpam-6635	306	4	would	would	AUX
ejpam-6635	306	5	like	like	VERB
ejpam-6635	306	6	to	to	PART
ejpam-6635	306	7	thank	thank	VERB
ejpam-6635	306	8	the	the	DET
ejpam-6635	306	9	referees	referee	NOUN
ejpam-6635	306	10	for	for	ADP
ejpam-6635	306	11	their	their	PRON
ejpam-6635	306	12	comments	comment	NOUN
ejpam-6635	306	13	and	and	CCONJ
ejpam-6635	306	14	suggestions	suggestion	NOUN
ejpam-6635	306	15	which	which	PRON
ejpam-6635	306	16	led	lead	VERB
ejpam-6635	306	17	to	to	ADP
ejpam-6635	306	18	this	this	DET
ejpam-6635	306	19	much	much	ADV
ejpam-6635	306	20	improved	improved	ADJ
ejpam-6635	306	21	version	version	NOUN
ejpam-6635	306	22	of	of	ADP
ejpam-6635	306	23	the	the	DET
ejpam-6635	306	24	paper	paper	NOUN
ejpam-6635	306	25	.	.	PUNCT
ejpam-6635	307	1	moreover	moreover	ADV
ejpam-6635	307	2	,	,	PUNCT
ejpam-6635	307	3	the	the	DET
ejpam-6635	307	4	authors	author	NOUN
ejpam-6635	307	5	are	be	AUX
ejpam-6635	307	6	grateful	grateful	ADJ
ejpam-6635	307	7	to	to	ADP
ejpam-6635	307	8	the	the	DET
ejpam-6635	307	9	department	department	NOUN
ejpam-6635	307	10	of	of	ADP
ejpam-6635	307	11	science	science	NOUN
ejpam-6635	307	12	and	and	CCONJ
ejpam-6635	307	13	technology	technology	NOUN
ejpam-6635	307	14	accelerated	accelerate	VERB
ejpam-6635	307	15	science	science	NOUN
ejpam-6635	307	16	and	and	CCONJ
ejpam-6635	307	17	technology	technology	NOUN
ejpam-6635	307	18	human	human	ADJ
ejpam-6635	307	19	resource	resource	NOUN
ejpam-6635	307	20	development	development	NOUN
ejpam-6635	307	21	program	program	NOUN
ejpam-6635	307	22	(	(	PUNCT
ejpam-6635	307	23	dost	dost	NOUN
ejpam-6635	307	24	-	-	PUNCT
ejpam-6635	307	25	asthrdp)-philippines	asthrdp)-philippines	PROPN
ejpam-6635	307	26	and	and	CCONJ
ejpam-6635	307	27	the	the	DET
ejpam-6635	307	28	msu	msu	PROPN
ejpam-6635	307	29	-	-	PUNCT
ejpam-6635	307	30	iligan	iligan	PROPN
ejpam-6635	307	31	institute	institute	PROPN
ejpam-6635	307	32	of	of	ADP
ejpam-6635	307	33	technology	technology	PROPN
ejpam-6635	307	34	,	,	PUNCT
ejpam-6635	307	35	iligan	iligan	ADJ
ejpam-6635	307	36	city	city	NOUN
ejpam-6635	307	37	for	for	ADP
ejpam-6635	307	38	funding	fund	VERB
ejpam-6635	307	39	this	this	DET
ejpam-6635	307	40	research	research	NOUN
ejpam-6635	307	41	.	.	PUNCT
ejpam-6635	308	1	references	reference	NOUN
ejpam-6635	308	2	[	[	X
ejpam-6635	308	3	1	1	X
ejpam-6635	308	4	]	]	X
ejpam-6635	308	5	r.c	r.c	PROPN
ejpam-6635	308	6	brigham	brigham	PROPN
ejpam-6635	308	7	,	,	PUNCT
ejpam-6635	308	8	r.d	r.d	PROPN
ejpam-6635	308	9	.	.	PROPN
ejpam-6635	308	10	dutton	dutton	PROPN
ejpam-6635	308	11	,	,	PUNCT
ejpam-6635	308	12	and	and	CCONJ
ejpam-6635	308	13	s.t	s.t	PROPN
ejpam-6635	308	14	.	.	PROPN
ejpam-6635	308	15	hedetniemi	hedetniemi	PROPN
ejpam-6635	308	16	.	.	PUNCT
ejpam-6635	309	1	security	security	NOUN
ejpam-6635	309	2	in	in	ADP
ejpam-6635	309	3	graphs	graph	NOUN
ejpam-6635	309	4	.	.	PUNCT
ejpam-6635	310	1	discrete	discrete	ADJ
ejpam-6635	310	2	applied	apply	VERB
ejpam-6635	310	3	mathematics	mathematic	NOUN
ejpam-6635	310	4	,	,	PUNCT
ejpam-6635	310	5	155(13):1708–1714	155(13):1708–1714	NUM
ejpam-6635	310	6	,	,	PUNCT
ejpam-6635	310	7	2007	2007	NUM
ejpam-6635	310	8	.	.	PUNCT
ejpam-6635	311	1	[	[	X
ejpam-6635	311	2	2	2	NUM
ejpam-6635	311	3	]	]	X
ejpam-6635	311	4	f.l	f.l	PROPN
ejpam-6635	311	5	.	.	PROPN
ejpam-6635	311	6	alfeche	alfeche	PROPN
ejpam-6635	311	7	,	,	PUNCT
ejpam-6635	311	8	g.	g.	PROPN
ejpam-6635	311	9	malacas	malacas	PROPN
ejpam-6635	311	10	,	,	PUNCT
ejpam-6635	311	11	and	and	CCONJ
ejpam-6635	311	12	s.	s.	PROPN
ejpam-6635	311	13	canoy	canoy	PROPN
ejpam-6635	311	14	jr	jr	PROPN
ejpam-6635	311	15	.	.	PROPN
ejpam-6635	311	16	secure	secure	VERB
ejpam-6635	311	17	hop	hop	NOUN
ejpam-6635	311	18	dominating	dominating	NOUN
ejpam-6635	311	19	sets	set	NOUN
ejpam-6635	311	20	in	in	ADP
ejpam-6635	311	21	graphs	graph	NOUN
ejpam-6635	311	22	.	.	PUNCT
ejpam-6635	312	1	european	european	ADJ
ejpam-6635	312	2	journal	journal	PROPN
ejpam-6635	312	3	of	of	ADP
ejpam-6635	312	4	pure	pure	ADJ
ejpam-6635	312	5	and	and	CCONJ
ejpam-6635	312	6	applied	applied	ADJ
ejpam-6635	312	7	mathematics	mathematic	NOUN
ejpam-6635	312	8	,	,	PUNCT
ejpam-6635	312	9	16(3):article	16(3):article	NUM
ejpam-6635	312	10	number	number	NOUN
ejpam-6635	312	11	6075	6075	NUM
ejpam-6635	312	12	,	,	PUNCT
ejpam-6635	312	13	2025	2025	NUM
ejpam-6635	312	14	.	.	PUNCT
ejpam-6635	313	1	[	[	X
ejpam-6635	313	2	3	3	X
ejpam-6635	313	3	]	]	PUNCT
ejpam-6635	313	4	t.	t.	PROPN
ejpam-6635	313	5	araki	araki	PROPN
ejpam-6635	313	6	and	and	CCONJ
ejpam-6635	313	7	r.	r.	PROPN
ejpam-6635	313	8	yamanaka	yamanaka	PROPN
ejpam-6635	313	9	.	.	PUNCT
ejpam-6635	314	1	secure	secure	ADJ
ejpam-6635	314	2	domination	domination	NOUN
ejpam-6635	314	3	in	in	ADP
ejpam-6635	314	4	cographs	cograph	NOUN
ejpam-6635	314	5	.	.	PUNCT
ejpam-6635	315	1	discrete	discrete	ADJ
ejpam-6635	315	2	applied	apply	VERB
ejpam-6635	315	3	mathematics	mathematic	NOUN
ejpam-6635	315	4	,	,	PUNCT
ejpam-6635	315	5	262:179–184	262:179–184	NUM
ejpam-6635	315	6	,	,	PUNCT
ejpam-6635	315	7	2019	2019	NUM
ejpam-6635	315	8	.	.	PUNCT
ejpam-6635	316	1	[	[	X
ejpam-6635	316	2	4	4	X
ejpam-6635	316	3	]	]	PUNCT
ejpam-6635	316	4	s.	s.	PROPN
ejpam-6635	316	5	benecke	benecke	PROPN
ejpam-6635	316	6	,	,	PUNCT
ejpam-6635	316	7	e.	e.	PROPN
ejpam-6635	316	8	cockayne	cockayne	PROPN
ejpam-6635	316	9	,	,	PUNCT
ejpam-6635	316	10	and	and	CCONJ
ejpam-6635	316	11	c.	c.	PROPN
ejpam-6635	316	12	mynhardt	mynhardt	PROPN
ejpam-6635	316	13	.	.	PUNCT
ejpam-6635	317	1	secure	secure	ADJ
ejpam-6635	317	2	total	total	ADJ
ejpam-6635	317	3	domination	domination	NOUN
ejpam-6635	317	4	in	in	ADP
ejpam-6635	317	5	graphs	graph	NOUN
ejpam-6635	317	6	.	.	PUNCT
ejpam-6635	318	1	utilitas	utilitas	ADJ
ejpam-6635	318	2	math	math	NOUN
ejpam-6635	318	3	,	,	PUNCT
ejpam-6635	318	4	74:247–259	74:247–259	PROPN
ejpam-6635	318	5	,	,	PUNCT
ejpam-6635	318	6	2007	2007	NUM
ejpam-6635	318	7	.	.	PUNCT
ejpam-6635	319	1	[	[	X
ejpam-6635	319	2	5	5	NUM
ejpam-6635	319	3	]	]	X
ejpam-6635	319	4	a.g	a.g	PROPN
ejpam-6635	319	5	.	.	PROPN
ejpam-6635	319	6	cabaro	cabaro	PROPN
ejpam-6635	319	7	,	,	PUNCT
ejpam-6635	319	8	i.	i.	PROPN
ejpam-6635	319	9	anniversario	anniversario	PROPN
ejpam-6635	319	10	,	,	PUNCT
ejpam-6635	319	11	and	and	CCONJ
ejpam-6635	319	12	s.	s.	PROPN
ejpam-6635	319	13	canoy	canoy	PROPN
ejpam-6635	319	14	jr	jr	PROPN
ejpam-6635	319	15	.	.	PROPN
ejpam-6635	319	16	secure	secure	VERB
ejpam-6635	319	17	connected	connected	ADJ
ejpam-6635	319	18	domination	domination	NOUN
ejpam-6635	319	19	in	in	ADP
ejpam-6635	319	20	a	a	DET
ejpam-6635	319	21	graph	graph	NOUN
ejpam-6635	319	22	.	.	PUNCT
ejpam-6635	320	1	international	international	ADJ
ejpam-6635	320	2	journal	journal	PROPN
ejpam-6635	320	3	of	of	ADP
ejpam-6635	320	4	mathematical	mathematical	ADJ
ejpam-6635	320	5	analysis	analysis	NOUN
ejpam-6635	320	6	,	,	PUNCT
ejpam-6635	320	7	8(42):2065–2074	8(42):2065–2074	NUM
ejpam-6635	320	8	,	,	PUNCT
ejpam-6635	320	9	2014	2014	NUM
ejpam-6635	320	10	.	.	PUNCT
ejpam-6635	321	1	[	[	X
ejpam-6635	321	2	6	6	NUM
ejpam-6635	321	3	]	]	X
ejpam-6635	321	4	a.g	a.g	PROPN
ejpam-6635	321	5	.	.	PROPN
ejpam-6635	321	6	cabaro	cabaro	PROPN
ejpam-6635	321	7	and	and	CCONJ
ejpam-6635	321	8	s.	s.	PROPN
ejpam-6635	321	9	canoy	canoy	PROPN
ejpam-6635	321	10	jr	jr	PROPN
ejpam-6635	321	11	.	.	PROPN
ejpam-6635	321	12	secure	secure	VERB
ejpam-6635	321	13	connected	connected	ADJ
ejpam-6635	321	14	dominating	dominating	NOUN
ejpam-6635	321	15	sets	set	NOUN
ejpam-6635	321	16	in	in	ADP
ejpam-6635	321	17	the	the	DET
ejpam-6635	321	18	join	join	NOUN
ejpam-6635	321	19	and	and	CCONJ
ejpam-6635	321	20	composition	composition	NOUN
ejpam-6635	321	21	of	of	ADP
ejpam-6635	321	22	graphs	graph	NOUN
ejpam-6635	321	23	.	.	PUNCT
ejpam-6635	322	1	international	international	ADJ
ejpam-6635	322	2	journal	journal	PROPN
ejpam-6635	322	3	of	of	ADP
ejpam-6635	322	4	mathematical	mathematical	ADJ
ejpam-6635	322	5	analysis	analysis	NOUN
ejpam-6635	322	6	,	,	PUNCT
ejpam-6635	322	7	9(25):1241	9(25):1241	NUM
ejpam-6635	322	8	–	–	PUNCT
ejpam-6635	322	9	1248	1248	NUM
ejpam-6635	322	10	,	,	PUNCT
ejpam-6635	322	11	2015	2015	NUM
ejpam-6635	322	12	.	.	PUNCT
ejpam-6635	323	1	[	[	X
ejpam-6635	323	2	7	7	X
ejpam-6635	323	3	]	]	X
ejpam-6635	323	4	e.	e.	PROPN
ejpam-6635	323	5	castillano	castillano	PROPN
ejpam-6635	323	6	,	,	PUNCT
ejpam-6635	323	7	r.a	r.a	PROPN
ejpam-6635	323	8	.	.	PROPN
ejpam-6635	323	9	ugbinada	ugbinada	PROPN
ejpam-6635	323	10	,	,	PUNCT
ejpam-6635	323	11	and	and	CCONJ
ejpam-6635	323	12	s.	s.	PROPN
ejpam-6635	323	13	canoy	canoy	PROPN
ejpam-6635	323	14	jr	jr	PROPN
ejpam-6635	323	15	.	.	PUNCT
ejpam-6635	323	16	secure	secure	ADJ
ejpam-6635	323	17	domination	domination	NOUN
ejpam-6635	323	18	in	in	ADP
ejpam-6635	323	19	the	the	DET
ejpam-6635	323	20	joins	join	NOUN
ejpam-6635	323	21	of	of	ADP
ejpam-6635	323	22	graphs	graph	NOUN
ejpam-6635	323	23	.	.	PUNCT
ejpam-6635	324	1	applied	apply	VERB
ejpam-6635	324	2	mathematical	mathematical	ADJ
ejpam-6635	324	3	sciences	science	NOUN
ejpam-6635	324	4	,	,	PUNCT
ejpam-6635	324	5	8(105):5203–5211	8(105):5203–5211	NUM
ejpam-6635	324	6	,	,	PUNCT
ejpam-6635	324	7	2014	2014	NUM
ejpam-6635	324	8	.	.	PUNCT
ejpam-6635	325	1	[	[	X
ejpam-6635	325	2	8	8	NUM
ejpam-6635	325	3	]	]	X
ejpam-6635	325	4	e.	e.	PROPN
ejpam-6635	325	5	cockayne	cockayne	PROPN
ejpam-6635	325	6	.	.	PUNCT
ejpam-6635	326	1	irredundance	irredundance	NOUN
ejpam-6635	326	2	,	,	PUNCT
ejpam-6635	326	3	secure	secure	ADJ
ejpam-6635	326	4	domination	domination	NOUN
ejpam-6635	326	5	and	and	CCONJ
ejpam-6635	326	6	maximum	maximum	ADJ
ejpam-6635	326	7	degree	degree	NOUN
ejpam-6635	326	8	in	in	ADP
ejpam-6635	326	9	trees	tree	NOUN
ejpam-6635	326	10	.	.	PUNCT
ejpam-6635	327	1	discrete	discrete	ADJ
ejpam-6635	327	2	math	math	NOUN
ejpam-6635	327	3	,	,	PUNCT
ejpam-6635	327	4	307:12–17	307:12–17	NUM
ejpam-6635	327	5	,	,	PUNCT
ejpam-6635	327	6	2007	2007	NUM
ejpam-6635	327	7	.	.	PUNCT
ejpam-6635	328	1	[	[	X
ejpam-6635	328	2	9	9	NUM
ejpam-6635	328	3	]	]	X
ejpam-6635	328	4	e.	e.	PROPN
ejpam-6635	328	5	cockayne	cockayne	PROPN
ejpam-6635	328	6	,	,	PUNCT
ejpam-6635	328	7	o.	o.	PROPN
ejpam-6635	328	8	favaron	favaron	PROPN
ejpam-6635	328	9	,	,	PUNCT
ejpam-6635	328	10	and	and	CCONJ
ejpam-6635	328	11	c.m	c.m	PROPN
ejpam-6635	328	12	.	.	PROPN
ejpam-6635	328	13	mynhardt	mynhardt	PROPN
ejpam-6635	328	14	.	.	PUNCT
ejpam-6635	329	1	secure	secure	ADJ
ejpam-6635	329	2	domination	domination	NOUN
ejpam-6635	329	3	,	,	PUNCT
ejpam-6635	329	4	weak	weak	ADJ
ejpam-6635	329	5	roman	roman	ADJ
ejpam-6635	329	6	domination	domination	NOUN
ejpam-6635	329	7	and	and	CCONJ
ejpam-6635	329	8	forbidden	forbid	VERB
ejpam-6635	329	9	subgraphs	subgraph	NOUN
ejpam-6635	329	10	.	.	PUNCT
ejpam-6635	330	1	bull	bull	NOUN
ejpam-6635	330	2	.	.	PUNCT
ejpam-6635	330	3	inst	inst	PROPN
ejpam-6635	330	4	.	.	PUNCT
ejpam-6635	331	1	combin	combin	NOUN
ejpam-6635	331	2	.	.	PUNCT
ejpam-6635	332	1	appl	appl	PROPN
ejpam-6635	332	2	.	.	PROPN
ejpam-6635	332	3	,	,	PUNCT
ejpam-6635	332	4	39:87–100	39:87–100	NUM
ejpam-6635	332	5	,	,	PUNCT
ejpam-6635	332	6	2003	2003	NUM
ejpam-6635	332	7	.	.	PUNCT
ejpam-6635	333	1	[	[	X
ejpam-6635	333	2	10	10	NUM
ejpam-6635	333	3	]	]	X
ejpam-6635	333	4	e.	e.	PROPN
ejpam-6635	333	5	enriquez	enriquez	PROPN
ejpam-6635	333	6	and	and	CCONJ
ejpam-6635	333	7	s.	s.	PROPN
ejpam-6635	333	8	canoy	canoy	PROPN
ejpam-6635	333	9	jr	jr	PROPN
ejpam-6635	333	10	.	.	PUNCT
ejpam-6635	333	11	secure	secure	VERB
ejpam-6635	333	12	convex	convex	NOUN
ejpam-6635	333	13	domination	domination	NOUN
ejpam-6635	333	14	in	in	ADP
ejpam-6635	333	15	a	a	DET
ejpam-6635	333	16	graph	graph	NOUN
ejpam-6635	333	17	.	.	PUNCT
ejpam-6635	334	1	international	international	ADJ
ejpam-6635	334	2	journal	journal	PROPN
ejpam-6635	334	3	of	of	ADP
ejpam-6635	334	4	mathematical	mathematical	ADJ
ejpam-6635	334	5	analysis	analysis	NOUN
ejpam-6635	334	6	,	,	PUNCT
ejpam-6635	334	7	9(7):317–325	9(7):317–325	NUM
ejpam-6635	334	8	,	,	PUNCT
ejpam-6635	334	9	2015	2015	NUM
ejpam-6635	334	10	.	.	PUNCT
ejpam-6635	335	1	f.	f.	PROPN
ejpam-6635	335	2	alfeche	alfeche	PROPN
ejpam-6635	335	3	,	,	PUNCT
ejpam-6635	335	4	s.	s.	PROPN
ejpam-6635	335	5	canoy	canoy	PROPN
ejpam-6635	335	6	jr	jr	PROPN
ejpam-6635	335	7	.	.	PROPN
ejpam-6635	335	8	/	/	SYM
ejpam-6635	335	9	eur	eur	PROPN
ejpam-6635	335	10	.	.	PUNCT
ejpam-6635	336	1	j.	j.	PROPN
ejpam-6635	336	2	pure	pure	PROPN
ejpam-6635	336	3	appl	appl	PROPN
ejpam-6635	336	4	.	.	PROPN
ejpam-6635	336	5	math	math	PROPN
ejpam-6635	336	6	,	,	PUNCT
ejpam-6635	336	7	18	18	NUM
ejpam-6635	336	8	(	(	PUNCT
ejpam-6635	336	9	3	3	NUM
ejpam-6635	336	10	)	)	PUNCT
ejpam-6635	336	11	(	(	PUNCT
ejpam-6635	336	12	2025	2025	NUM
ejpam-6635	336	13	)	)	PUNCT
ejpam-6635	336	14	,	,	PUNCT
ejpam-6635	336	15	6635	6635	NUM
ejpam-6635	336	16	11	11	NUM
ejpam-6635	336	17	of	of	ADP
ejpam-6635	336	18	11	11	NUM
ejpam-6635	336	19	[	[	X
ejpam-6635	336	20	11	11	NUM
ejpam-6635	336	21	]	]	X
ejpam-6635	336	22	r.l	r.l	PROPN
ejpam-6635	336	23	.	.	PROPN
ejpam-6635	336	24	estrella	estrella	PROPN
ejpam-6635	336	25	,	,	PUNCT
ejpam-6635	336	26	g.	g.	PROPN
ejpam-6635	336	27	malacas	malacas	PROPN
ejpam-6635	336	28	,	,	PUNCT
ejpam-6635	336	29	and	and	CCONJ
ejpam-6635	336	30	s.	s.	PROPN
ejpam-6635	336	31	canoy	canoy	PROPN
ejpam-6635	336	32	jr	jr	PROPN
ejpam-6635	336	33	.	.	PROPN
ejpam-6635	336	34	secure	secure	VERB
ejpam-6635	336	35	hop	hop	NOUN
ejpam-6635	336	36	dominating	dominating	NOUN
ejpam-6635	336	37	sets	set	NOUN
ejpam-6635	336	38	in	in	ADP
ejpam-6635	336	39	graphs	graph	NOUN
ejpam-6635	336	40	.	.	PUNCT
ejpam-6635	337	1	european	european	ADJ
ejpam-6635	337	2	journal	journal	PROPN
ejpam-6635	337	3	of	of	ADP
ejpam-6635	337	4	pure	pure	ADJ
ejpam-6635	337	5	and	and	CCONJ
ejpam-6635	337	6	applied	applied	ADJ
ejpam-6635	337	7	mathematics	mathematic	NOUN
ejpam-6635	337	8	,	,	PUNCT
ejpam-6635	337	9	16(3):article	16(3):article	NUM
ejpam-6635	337	10	number	number	NOUN
ejpam-6635	337	11	6074	6074	NUM
ejpam-6635	337	12	,	,	PUNCT
ejpam-6635	337	13	2025	2025	NUM
ejpam-6635	337	14	.	.	PUNCT
ejpam-6635	338	1	[	[	X
ejpam-6635	338	2	12	12	NUM
ejpam-6635	338	3	]	]	PUNCT
ejpam-6635	338	4	j.	j.	PROPN
ejpam-6635	338	5	hassan	hassan	PROPN
ejpam-6635	338	6	and	and	CCONJ
ejpam-6635	338	7	s.	s.	PROPN
ejpam-6635	338	8	canoy	canoy	PROPN
ejpam-6635	338	9	jr	jr	PROPN
ejpam-6635	338	10	.	.	PROPN
ejpam-6635	338	11	hop	hop	PROPN
ejpam-6635	338	12	independent	independent	ADJ
ejpam-6635	338	13	hop	hop	NOUN
ejpam-6635	338	14	domination	domination	NOUN
ejpam-6635	338	15	in	in	ADP
ejpam-6635	338	16	graphs	graph	NOUN
ejpam-6635	338	17	.	.	PUNCT
ejpam-6635	339	1	eur	eur	PROPN
ejpam-6635	339	2	.	.	PUNCT
ejpam-6635	340	1	j.	j.	PROPN
ejpam-6635	340	2	pure	pure	PROPN
ejpam-6635	340	3	appl	appl	PROPN
ejpam-6635	340	4	.	.	PUNCT
ejpam-6635	340	5	math	math	PROPN
ejpam-6635	340	6	.	.	PUNCT
ejpam-6635	340	7	,	,	PUNCT
ejpam-6635	340	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-6635	340	9	,	,	PUNCT
ejpam-6635	340	10	2022	2022	NUM
ejpam-6635	340	11	.	.	PUNCT
ejpam-6635	341	1	[	[	X
ejpam-6635	341	2	13	13	NUM
ejpam-6635	341	3	]	]	PUNCT
ejpam-6635	341	4	j.	j.	PROPN
ejpam-6635	341	5	hassan	hassan	PROPN
ejpam-6635	341	6	,	,	PUNCT
ejpam-6635	341	7	s.	s.	PROPN
ejpam-6635	341	8	canoy	canoy	PROPN
ejpam-6635	341	9	jr	jr	PROPN
ejpam-6635	341	10	.	.	PROPN
ejpam-6635	341	11	,	,	PUNCT
ejpam-6635	341	12	and	and	CCONJ
ejpam-6635	341	13	a.	a.	PROPN
ejpam-6635	341	14	aradais	aradais	PROPN
ejpam-6635	341	15	.	.	PUNCT
ejpam-6635	342	1	hop	hop	PROPN
ejpam-6635	342	2	independent	independent	ADJ
ejpam-6635	342	3	sets	set	NOUN
ejpam-6635	342	4	in	in	ADP
ejpam-6635	342	5	graphs	graph	NOUN
ejpam-6635	342	6	.	.	PUNCT
ejpam-6635	343	1	eur	eur	PROPN
ejpam-6635	343	2	.	.	PUNCT
ejpam-6635	344	1	j.	j.	PROPN
ejpam-6635	344	2	pure	pure	PROPN
ejpam-6635	344	3	appl	appl	PROPN
ejpam-6635	344	4	.	.	PUNCT
ejpam-6635	344	5	math	math	PROPN
ejpam-6635	344	6	.	.	PUNCT
ejpam-6635	344	7	,	,	PUNCT
ejpam-6635	344	8	15(2):467–477	15(2):467–477	PROPN
ejpam-6635	344	9	,	,	PUNCT
ejpam-6635	344	10	2022	2022	NUM
ejpam-6635	344	11	.	.	PUNCT
ejpam-6635	345	1	[	[	X
ejpam-6635	345	2	14	14	NUM
ejpam-6635	345	3	]	]	X
ejpam-6635	345	4	s.	s.	PROPN
ejpam-6635	345	5	canoy	canoy	PROPN
ejpam-6635	345	6	jr	jr	PROPN
ejpam-6635	345	7	,	,	PUNCT
ejpam-6635	345	8	s.a	s.a	PROPN
ejpam-6635	345	9	.	.	PROPN
ejpam-6635	345	10	canoy	canoy	PROPN
ejpam-6635	345	11	,	,	PUNCT
ejpam-6635	345	12	and	and	CCONJ
ejpam-6635	345	13	m.	m.	NOUN
ejpam-6635	345	14	cruzate	cruzate	NOUN
ejpam-6635	345	15	.	.	PUNCT
ejpam-6635	346	1	secure	secure	ADJ
ejpam-6635	346	2	dominating	dominating	NOUN
ejpam-6635	346	3	sets	set	NOUN
ejpam-6635	346	4	in	in	ADP
ejpam-6635	346	5	the	the	DET
ejpam-6635	346	6	lexicographic	lexicographic	ADJ
ejpam-6635	346	7	product	product	NOUN
ejpam-6635	346	8	of	of	ADP
ejpam-6635	346	9	graphs	graph	NOUN
ejpam-6635	346	10	.	.	PUNCT
ejpam-6635	347	1	advances	advance	NOUN
ejpam-6635	347	2	and	and	CCONJ
ejpam-6635	347	3	applications	application	NOUN
ejpam-6635	347	4	in	in	ADP
ejpam-6635	347	5	discrete	discrete	ADJ
ejpam-6635	347	6	mathematics	mathematic	NOUN
ejpam-6635	347	7	,	,	PUNCT
ejpam-6635	347	8	20(1	20(1	NUM
ejpam-6635	347	9	)	)	PUNCT
ejpam-6635	347	10	,	,	PUNCT
ejpam-6635	347	11	2019	2019	NUM
ejpam-6635	347	12	.	.	PUNCT
ejpam-6635	348	1	[	[	X
ejpam-6635	348	2	15	15	NUM
ejpam-6635	348	3	]	]	X
ejpam-6635	348	4	s.	s.	PROPN
ejpam-6635	348	5	canoy	canoy	PROPN
ejpam-6635	348	6	jr	jr	PROPN
ejpam-6635	348	7	.	.	PROPN
ejpam-6635	348	8	and	and	CCONJ
ejpam-6635	348	9	g.	g.	PROPN
ejpam-6635	348	10	salasalan	salasalan	NOUN
ejpam-6635	348	11	.	.	PUNCT
ejpam-6635	349	1	locating	locate	VERB
ejpam-6635	349	2	-	-	PUNCT
ejpam-6635	349	3	hop	hop	NOUN
ejpam-6635	349	4	domination	domination	NOUN
ejpam-6635	349	5	in	in	ADP
ejpam-6635	349	6	graphs	graph	NOUN
ejpam-6635	349	7	.	.	PUNCT
ejpam-6635	350	1	kyungpook	kyungpook	PROPN
ejpam-6635	350	2	mathematical	mathematical	PROPN
ejpam-6635	350	3	journal	journal	PROPN
ejpam-6635	350	4	,	,	PUNCT
ejpam-6635	350	5	62(1):193–204	62(1):193–204	PROPN
ejpam-6635	350	6	,	,	PUNCT
ejpam-6635	350	7	2022	2022	NUM
ejpam-6635	350	8	.	.	PUNCT
ejpam-6635	351	1	[	[	X
ejpam-6635	351	2	16	16	NUM
ejpam-6635	351	3	]	]	X
ejpam-6635	351	4	s.r	s.r	PROPN
ejpam-6635	351	5	.	.	PROPN
ejpam-6635	351	6	canoy	canoy	PROPN
ejpam-6635	351	7	jr	jr	PROPN
ejpam-6635	351	8	and	and	CCONJ
ejpam-6635	351	9	j.	j.	PROPN
ejpam-6635	351	10	hassan	hassan	PROPN
ejpam-6635	351	11	.	.	PUNCT
ejpam-6635	352	1	weakly	weakly	ADJ
ejpam-6635	352	2	convex	convex	VERB
ejpam-6635	352	3	hop	hop	NOUN
ejpam-6635	352	4	dominating	dominating	NOUN
ejpam-6635	352	5	sets	set	NOUN
ejpam-6635	352	6	in	in	ADP
ejpam-6635	352	7	graphs	graph	NOUN
ejpam-6635	352	8	.	.	PUNCT
ejpam-6635	353	1	european	european	ADJ
ejpam-6635	353	2	journal	journal	PROPN
ejpam-6635	353	3	of	of	ADP
ejpam-6635	353	4	pure	pure	ADJ
ejpam-6635	353	5	and	and	CCONJ
ejpam-6635	353	6	applied	applied	ADJ
ejpam-6635	353	7	mathematics	mathematic	NOUN
ejpam-6635	353	8	,	,	PUNCT
ejpam-6635	353	9	16(2):1196–1211	16(2):1196–1211	NUM
ejpam-6635	353	10	,	,	PUNCT
ejpam-6635	353	11	2023	2023	NUM
ejpam-6635	353	12	.	.	PUNCT
ejpam-6635	354	1	[	[	X
ejpam-6635	354	2	17	17	NUM
ejpam-6635	354	3	]	]	X
ejpam-6635	354	4	w.	w.	PROPN
ejpam-6635	354	5	klostermeyer	klostermeyer	PROPN
ejpam-6635	354	6	and	and	CCONJ
ejpam-6635	354	7	c.	c.	PROPN
ejpam-6635	354	8	mynhardt	mynhardt	PROPN
ejpam-6635	354	9	.	.	PUNCT
ejpam-6635	355	1	secure	secure	ADJ
ejpam-6635	355	2	domination	domination	NOUN
ejpam-6635	355	3	and	and	CCONJ
ejpam-6635	355	4	secure	secure	VERB
ejpam-6635	355	5	total	total	ADJ
ejpam-6635	355	6	domination	domination	NOUN
ejpam-6635	355	7	in	in	ADP
ejpam-6635	355	8	graphs	graph	NOUN
ejpam-6635	355	9	.	.	PUNCT
ejpam-6635	356	1	discussiones	discussione	NOUN
ejpam-6635	356	2	mathematicae	mathematicae	PROPN
ejpam-6635	356	3	graph	graph	NOUN
ejpam-6635	356	4	theory	theory	NOUN
ejpam-6635	356	5	,	,	PUNCT
ejpam-6635	356	6	28:267–284	28:267–284	PROPN
ejpam-6635	356	7	,	,	PUNCT
ejpam-6635	356	8	2008	2008	NUM
ejpam-6635	356	9	.	.	PUNCT
ejpam-6635	357	1	[	[	X
ejpam-6635	357	2	18	18	NUM
ejpam-6635	357	3	]	]	X
ejpam-6635	357	4	g.	g.	NOUN
ejpam-6635	357	5	salasalan	salasalan	NOUN
ejpam-6635	357	6	and	and	CCONJ
ejpam-6635	357	7	s.	s.	PROPN
ejpam-6635	357	8	canoy	canoy	PROPN
ejpam-6635	357	9	jr	jr	PROPN
ejpam-6635	357	10	.	.	PUNCT
ejpam-6635	357	11	revisiting	revisit	VERB
ejpam-6635	357	12	domination	domination	NOUN
ejpam-6635	357	13	,	,	PUNCT
ejpam-6635	357	14	hop	hop	NOUN
ejpam-6635	357	15	domination	domination	NOUN
ejpam-6635	357	16	,	,	PUNCT
ejpam-6635	357	17	and	and	CCONJ
ejpam-6635	357	18	global	global	ADJ
ejpam-6635	357	19	hop	hop	NOUN
ejpam-6635	357	20	domination	domination	NOUN
ejpam-6635	357	21	in	in	ADP
ejpam-6635	357	22	graphs	graph	NOUN
ejpam-6635	357	23	.	.	PUNCT
ejpam-6635	358	1	european	european	ADJ
ejpam-6635	358	2	journal	journal	PROPN
ejpam-6635	358	3	of	of	ADP
ejpam-6635	358	4	pure	pure	ADJ
ejpam-6635	358	5	and	and	CCONJ
ejpam-6635	358	6	applied	applied	ADJ
ejpam-6635	358	7	mathematics	mathematic	NOUN
ejpam-6635	358	8	,	,	PUNCT
ejpam-6635	358	9	14(4):1415–1428	14(4):1415–1428	NUM
ejpam-6635	358	10	,	,	PUNCT
ejpam-6635	358	11	2021	2021	NUM
ejpam-6635	358	12	.	.	PUNCT
ejpam-6635	359	1	[	[	X
ejpam-6635	359	2	19	19	NUM
ejpam-6635	359	3	]	]	PUNCT
ejpam-6635	359	4	f.	f.	PROPN
ejpam-6635	359	5	buckey	buckey	PROPN
ejpam-6635	359	6	and	and	CCONJ
ejpam-6635	359	7	f.	f.	PROPN
ejpam-6635	359	8	harary	harary	PROPN
ejpam-6635	359	9	.	.	PUNCT
ejpam-6635	360	1	distance	distance	NOUN
ejpam-6635	360	2	in	in	ADP
ejpam-6635	360	3	graphs	graph	NOUN
ejpam-6635	360	4	.	.	PUNCT
ejpam-6635	361	1	addison	addison	PROPN
ejpam-6635	361	2	-	-	PUNCT
ejpam-6635	361	3	wesley	wesley	PROPN
ejpam-6635	361	4	,	,	PUNCT
ejpam-6635	361	5	redwood	redwood	NOUN
ejpam-6635	361	6	city	city	NOUN
ejpam-6635	361	7	,	,	PUNCT
ejpam-6635	361	8	california	california	PROPN
ejpam-6635	361	9	,	,	PUNCT
ejpam-6635	361	10	1990	1990	NUM
ejpam-6635	361	11	.	.	PUNCT
ejpam-6635	362	1	[	[	X
ejpam-6635	362	2	20	20	NUM
ejpam-6635	362	3	]	]	PUNCT
ejpam-6635	362	4	f.	f.	PROPN
ejpam-6635	362	5	harary	harary	PROPN
ejpam-6635	362	6	.	.	PUNCT
ejpam-6635	363	1	graph	graph	NOUN
ejpam-6635	363	2	theory	theory	NOUN
ejpam-6635	363	3	.	.	PUNCT
ejpam-6635	364	1	addison	addison	PROPN
ejpam-6635	364	2	-	-	PUNCT
ejpam-6635	364	3	wesley	wesley	PROPN
ejpam-6635	364	4	,	,	PUNCT
ejpam-6635	364	5	singapore	singapore	PROPN
ejpam-6635	364	6	,	,	PUNCT
ejpam-6635	364	7	1989	1989	NUM
ejpam-6635	364	8	.	.	PUNCT
ejpam-6635	365	1	[	[	X
ejpam-6635	365	2	21	21	NUM
ejpam-6635	365	3	]	]	PUNCT
ejpam-6635	365	4	s.	s.	PROPN
ejpam-6635	365	5	arriola	arriola	PROPN
ejpam-6635	365	6	and	and	CCONJ
ejpam-6635	365	7	s.	s.	PROPN
ejpam-6635	365	8	canoy	canoy	PROPN
ejpam-6635	365	9	jr	jr	PROPN
ejpam-6635	365	10	.	.	PUNCT
ejpam-6635	366	1	(	(	PUNCT
ejpam-6635	366	2	1,2)*-domination	1,2)*-domination	NUM
ejpam-6635	366	3	in	in	ADP
ejpam-6635	366	4	graphs	graph	NOUN
ejpam-6635	366	5	.	.	PUNCT
ejpam-6635	367	1	advances	advance	NOUN
ejpam-6635	367	2	and	and	CCONJ
ejpam-6635	367	3	applications	application	NOUN
ejpam-6635	367	4	in	in	ADP
ejpam-6635	367	5	discrete	discrete	ADJ
ejpam-6635	367	6	mathematics	mathematic	NOUN
ejpam-6635	367	7	,	,	PUNCT
ejpam-6635	367	8	18(2	18(2	NUM
ejpam-6635	367	9	)	)	PUNCT
ejpam-6635	367	10	,	,	PUNCT
ejpam-6635	367	11	2017	2017	NUM
ejpam-6635	367	12	.	.	PUNCT
ejpam-6635	368	1	[	[	X
ejpam-6635	368	2	22	22	NUM
ejpam-6635	368	3	]	]	X
ejpam-6635	368	4	s.	s.	PROPN
ejpam-6635	368	5	canoy	canoy	PROPN
ejpam-6635	368	6	jr	jr	PROPN
ejpam-6635	368	7	.	.	PROPN
ejpam-6635	368	8	,	,	PUNCT
ejpam-6635	368	9	r.	r.	PROPN
ejpam-6635	368	10	mollejon	mollejon	NOUN
ejpam-6635	368	11	,	,	PUNCT
ejpam-6635	368	12	and	and	CCONJ
ejpam-6635	368	13	j.g	j.g	PROPN
ejpam-6635	368	14	.	.	PROPN
ejpam-6635	368	15	canoy	canoy	PROPN
ejpam-6635	368	16	.	.	PUNCT
ejpam-6635	369	1	hop	hop	PROPN
ejpam-6635	369	2	dominating	dominating	NOUN
ejpam-6635	369	3	sets	set	NOUN
ejpam-6635	369	4	in	in	ADP
ejpam-6635	369	5	graphs	graph	NOUN
ejpam-6635	369	6	under	under	ADP
ejpam-6635	369	7	binary	binary	ADJ
ejpam-6635	369	8	operations	operation	NOUN
ejpam-6635	369	9	.	.	PUNCT
ejpam-6635	370	1	european	european	ADJ
ejpam-6635	370	2	journal	journal	PROPN
ejpam-6635	370	3	of	of	ADP
ejpam-6635	370	4	pure	pure	ADJ
ejpam-6635	370	5	and	and	CCONJ
ejpam-6635	370	6	applied	applied	ADJ
ejpam-6635	370	7	mathematics	mathematic	NOUN
ejpam-6635	370	8	,	,	PUNCT
ejpam-6635	370	9	12(4	12(4	NUM
ejpam-6635	370	10	)	)	PUNCT
ejpam-6635	370	11	,	,	PUNCT
ejpam-6635	370	12	2019	2019	NUM
ejpam-6635	370	13	.	.	PUNCT