id	sid	tid	token	lemma	pos
ejpam-5251	1	1	european	european	PROPN
ejpam-5251	1	2	journal	journal	PROPN
ejpam-5251	1	3	of	of	ADP
ejpam-5251	1	4	pure	pure	ADJ
ejpam-5251	1	5	and	and	CCONJ
ejpam-5251	1	6	applied	apply	VERB
ejpam-5251	1	7	mathematics	mathematic	NOUN
ejpam-5251	1	8	vol	vol	NOUN
ejpam-5251	1	9	.	.	PROPN
ejpam-5251	2	1	17	17	NUM
ejpam-5251	2	2	,	,	PUNCT
ejpam-5251	2	3	no	no	INTJ
ejpam-5251	2	4	.	.	NOUN
ejpam-5251	2	5	3	3	NUM
ejpam-5251	2	6	,	,	PUNCT
ejpam-5251	2	7	2024	2024	NUM
ejpam-5251	2	8	,	,	PUNCT
ejpam-5251	2	9	1737	1737	NUM
ejpam-5251	2	10	-	-	SYM
ejpam-5251	2	11	1750	1750	NUM
ejpam-5251	2	12	issn	issn	PROPN
ejpam-5251	2	13	1307	1307	NUM
ejpam-5251	2	14	-	-	SYM
ejpam-5251	2	15	5543	5543	NUM
ejpam-5251	2	16	–	–	PUNCT
ejpam-5251	2	17	ejpam.com	ejpam.com	X
ejpam-5251	2	18	published	publish	VERB
ejpam-5251	2	19	by	by	ADP
ejpam-5251	2	20	new	new	PROPN
ejpam-5251	2	21	york	york	PROPN
ejpam-5251	2	22	business	business	PROPN
ejpam-5251	2	23	global	global	PROPN
ejpam-5251	2	24	on	on	ADP
ejpam-5251	2	25	minimal	minimal	ADJ
ejpam-5251	2	26	geodetic	geodetic	ADJ
ejpam-5251	2	27	hop	hop	NOUN
ejpam-5251	2	28	domination	domination	NOUN
ejpam-5251	2	29	in	in	ADP
ejpam-5251	2	30	graphs	graph	NOUN
ejpam-5251	2	31	dyjay	dyjay	VERB
ejpam-5251	2	32	catian1∗	catian1∗	PROPN
ejpam-5251	2	33	,	,	PUNCT
ejpam-5251	2	34	imelda	imelda	PROPN
ejpam-5251	2	35	s.	s.	PROPN
ejpam-5251	2	36	aniversario1	aniversario1	PROPN
ejpam-5251	2	37	,	,	PUNCT
ejpam-5251	3	1	ferdinand	ferdinand	PROPN
ejpam-5251	3	2	p.	p.	PROPN
ejpam-5251	3	3	jamil1	jamil1	NOUN
ejpam-5251	4	1	1	1	NUM
ejpam-5251	4	2	department	department	NOUN
ejpam-5251	4	3	of	of	ADP
ejpam-5251	4	4	mathematics	mathematic	NOUN
ejpam-5251	4	5	and	and	CCONJ
ejpam-5251	4	6	statistics	statistic	NOUN
ejpam-5251	4	7	,	,	PUNCT
ejpam-5251	4	8	college	college	NOUN
ejpam-5251	4	9	of	of	ADP
ejpam-5251	4	10	science	science	NOUN
ejpam-5251	4	11	and	and	CCONJ
ejpam-5251	4	12	mathematics	mathematic	NOUN
ejpam-5251	4	13	center	center	NOUN
ejpam-5251	4	14	for	for	ADP
ejpam-5251	4	15	mathematical	mathematical	ADJ
ejpam-5251	4	16	and	and	CCONJ
ejpam-5251	4	17	theoretical	theoretical	ADJ
ejpam-5251	4	18	physical	physical	ADJ
ejpam-5251	4	19	science	science	NOUN
ejpam-5251	4	20	,	,	PUNCT
ejpam-5251	4	21	prism	prism	NOUN
ejpam-5251	4	22	msu	msu	PROPN
ejpam-5251	4	23	-	-	PUNCT
ejpam-5251	4	24	iligan	iligan	PROPN
ejpam-5251	4	25	institute	institute	PROPN
ejpam-5251	4	26	of	of	ADP
ejpam-5251	4	27	technology	technology	PROPN
ejpam-5251	4	28	,	,	PUNCT
ejpam-5251	4	29	9200	9200	NUM
ejpam-5251	4	30	iligan	iligan	ADJ
ejpam-5251	4	31	city	city	NOUN
ejpam-5251	4	32	,	,	PUNCT
ejpam-5251	4	33	philippines	philippine	NOUN
ejpam-5251	4	34	abstract	abstract	ADJ
ejpam-5251	4	35	.	.	PUNCT
ejpam-5251	5	1	let	let	VERB
ejpam-5251	5	2	g	g	PRON
ejpam-5251	5	3	be	be	AUX
ejpam-5251	5	4	a	a	DET
ejpam-5251	5	5	nontrivial	nontrivial	ADJ
ejpam-5251	5	6	connected	connect	VERB
ejpam-5251	5	7	graph	graph	NOUN
ejpam-5251	5	8	with	with	ADP
ejpam-5251	5	9	vertex	vertex	NOUN
ejpam-5251	5	10	set	set	VERB
ejpam-5251	5	11	v	v	NOUN
ejpam-5251	5	12	(	(	PUNCT
ejpam-5251	5	13	g	g	NOUN
ejpam-5251	5	14	)	)	PUNCT
ejpam-5251	5	15	and	and	CCONJ
ejpam-5251	5	16	the	the	DET
ejpam-5251	5	17	edge	edge	NOUN
ejpam-5251	5	18	set	set	VERB
ejpam-5251	5	19	e(g	e(g	PROPN
ejpam-5251	5	20	)	)	PUNCT
ejpam-5251	5	21	.	.	PUNCT
ejpam-5251	6	1	a	a	DET
ejpam-5251	6	2	set	set	NOUN
ejpam-5251	6	3	s	s	NOUN
ejpam-5251	6	4	⊆	⊆	NUM
ejpam-5251	6	5	v	v	NOUN
ejpam-5251	6	6	(	(	PUNCT
ejpam-5251	6	7	g	g	NOUN
ejpam-5251	6	8	)	)	PUNCT
ejpam-5251	6	9	is	be	AUX
ejpam-5251	6	10	a	a	DET
ejpam-5251	6	11	geodetic	geodetic	ADJ
ejpam-5251	6	12	hop	hop	NOUN
ejpam-5251	6	13	dominating	dominating	NOUN
ejpam-5251	6	14	set	set	NOUN
ejpam-5251	6	15	of	of	ADP
ejpam-5251	6	16	g	g	PROPN
ejpam-5251	6	17	if	if	SCONJ
ejpam-5251	6	18	the	the	DET
ejpam-5251	6	19	following	follow	VERB
ejpam-5251	6	20	two	two	NUM
ejpam-5251	6	21	conditions	condition	NOUN
ejpam-5251	6	22	hold	hold	VERB
ejpam-5251	6	23	for	for	SCONJ
ejpam-5251	6	24	each	each	DET
ejpam-5251	6	25	x	x	SYM
ejpam-5251	6	26	∈	∈	PROPN
ejpam-5251	6	27	v	v	NOUN
ejpam-5251	6	28	(	(	PUNCT
ejpam-5251	6	29	g)\s	g)\s	NOUN
ejpam-5251	6	30	:	:	PUNCT
ejpam-5251	6	31	(	(	PUNCT
ejpam-5251	6	32	1	1	X
ejpam-5251	6	33	)	)	PUNCT
ejpam-5251	6	34	x	x	PUNCT
ejpam-5251	6	35	lies	lie	VERB
ejpam-5251	6	36	in	in	ADP
ejpam-5251	6	37	some	some	DET
ejpam-5251	6	38	u	u	NOUN
ejpam-5251	6	39	-	-	NOUN
ejpam-5251	6	40	v	v	ADJ
ejpam-5251	6	41	geodesic	geodesic	NOUN
ejpam-5251	6	42	in	in	ADP
ejpam-5251	6	43	g	g	PROPN
ejpam-5251	6	44	with	with	ADP
ejpam-5251	6	45	u	u	NOUN
ejpam-5251	6	46	,	,	PUNCT
ejpam-5251	6	47	v	v	ADP
ejpam-5251	6	48	∈	∈	PROPN
ejpam-5251	6	49	s	s	NOUN
ejpam-5251	6	50	,	,	PUNCT
ejpam-5251	6	51	and	and	CCONJ
ejpam-5251	6	52	(	(	PUNCT
ejpam-5251	6	53	2	2	X
ejpam-5251	6	54	)	)	PUNCT
ejpam-5251	6	55	x	x	X
ejpam-5251	6	56	is	be	AUX
ejpam-5251	6	57	of	of	ADP
ejpam-5251	6	58	distance	distance	NOUN
ejpam-5251	6	59	2	2	NUM
ejpam-5251	6	60	from	from	ADP
ejpam-5251	6	61	a	a	DET
ejpam-5251	6	62	vertex	vertex	NOUN
ejpam-5251	6	63	in	in	ADP
ejpam-5251	6	64	s.	s.	PROPN
ejpam-5251	6	65	the	the	DET
ejpam-5251	6	66	minimum	minimum	PROPN
ejpam-5251	6	67	cardinality	cardinality	PROPN
ejpam-5251	6	68	γhg(g	γhg(g	PROPN
ejpam-5251	6	69	)	)	PUNCT
ejpam-5251	6	70	of	of	ADP
ejpam-5251	6	71	a	a	DET
ejpam-5251	6	72	geodetic	geodetic	ADJ
ejpam-5251	6	73	hop	hop	NOUN
ejpam-5251	6	74	dominating	dominating	NOUN
ejpam-5251	6	75	set	set	NOUN
ejpam-5251	6	76	of	of	ADP
ejpam-5251	6	77	g	g	PROPN
ejpam-5251	6	78	is	be	AUX
ejpam-5251	6	79	the	the	DET
ejpam-5251	6	80	geodetic	geodetic	ADJ
ejpam-5251	6	81	hop	hop	NOUN
ejpam-5251	6	82	domination	domination	NOUN
ejpam-5251	6	83	number	number	NOUN
ejpam-5251	6	84	of	of	ADP
ejpam-5251	6	85	g.	g.	PROPN
ejpam-5251	6	86	a	a	DET
ejpam-5251	6	87	geodetic	geodetic	ADJ
ejpam-5251	6	88	hop	hop	NOUN
ejpam-5251	6	89	dominating	dominating	NOUN
ejpam-5251	6	90	set	set	NOUN
ejpam-5251	6	91	s	s	VERB
ejpam-5251	6	92	is	be	AUX
ejpam-5251	6	93	a	a	DET
ejpam-5251	6	94	minimal	minimal	ADJ
ejpam-5251	6	95	geodetic	geodetic	ADJ
ejpam-5251	6	96	hop	hop	NOUN
ejpam-5251	6	97	dominating	dominating	NOUN
ejpam-5251	6	98	set	set	NOUN
ejpam-5251	6	99	if	if	SCONJ
ejpam-5251	6	100	s	s	PRON
ejpam-5251	6	101	does	do	AUX
ejpam-5251	6	102	not	not	PART
ejpam-5251	6	103	contain	contain	VERB
ejpam-5251	6	104	a	a	DET
ejpam-5251	6	105	proper	proper	ADJ
ejpam-5251	6	106	subset	subset	NOUN
ejpam-5251	6	107	that	that	PRON
ejpam-5251	6	108	is	be	AUX
ejpam-5251	6	109	itself	itself	PRON
ejpam-5251	6	110	a	a	DET
ejpam-5251	6	111	geodetic	geodetic	ADJ
ejpam-5251	6	112	hop	hop	NOUN
ejpam-5251	6	113	dominating	dominating	NOUN
ejpam-5251	6	114	set	set	NOUN
ejpam-5251	6	115	.	.	PUNCT
ejpam-5251	7	1	the	the	DET
ejpam-5251	7	2	maximum	maximum	ADJ
ejpam-5251	7	3	cardinality	cardinality	NOUN
ejpam-5251	7	4	of	of	ADP
ejpam-5251	7	5	a	a	DET
ejpam-5251	7	6	minimal	minimal	ADJ
ejpam-5251	7	7	geodetic	geodetic	ADJ
ejpam-5251	7	8	hop	hop	NOUN
ejpam-5251	7	9	dominating	dominating	NOUN
ejpam-5251	7	10	set	set	NOUN
ejpam-5251	7	11	in	in	ADP
ejpam-5251	7	12	g	g	PROPN
ejpam-5251	7	13	is	be	AUX
ejpam-5251	7	14	the	the	DET
ejpam-5251	7	15	upper	upper	ADJ
ejpam-5251	7	16	geodetic	geodetic	ADJ
ejpam-5251	7	17	hop	hop	NOUN
ejpam-5251	7	18	domination	domination	NOUN
ejpam-5251	7	19	number	number	NOUN
ejpam-5251	7	20	of	of	ADP
ejpam-5251	7	21	g	g	NOUN
ejpam-5251	7	22	,	,	PUNCT
ejpam-5251	7	23	and	and	CCONJ
ejpam-5251	7	24	is	be	AUX
ejpam-5251	7	25	denoted	denote	VERB
ejpam-5251	7	26	by	by	ADP
ejpam-5251	7	27	γ+	γ+	X
ejpam-5251	7	28	hg(g	hg(g	NOUN
ejpam-5251	7	29	)	)	PUNCT
ejpam-5251	7	30	.	.	PUNCT
ejpam-5251	8	1	this	this	DET
ejpam-5251	8	2	paper	paper	NOUN
ejpam-5251	8	3	initiates	initiate	VERB
ejpam-5251	8	4	the	the	DET
ejpam-5251	8	5	study	study	NOUN
ejpam-5251	8	6	of	of	ADP
ejpam-5251	8	7	the	the	DET
ejpam-5251	8	8	minimal	minimal	ADJ
ejpam-5251	8	9	geodetic	geodetic	ADJ
ejpam-5251	8	10	hop	hop	NOUN
ejpam-5251	8	11	dominating	dominating	NOUN
ejpam-5251	8	12	set	set	NOUN
ejpam-5251	8	13	and	and	CCONJ
ejpam-5251	8	14	the	the	DET
ejpam-5251	8	15	corresponding	corresponding	ADJ
ejpam-5251	8	16	upper	upper	ADJ
ejpam-5251	8	17	geodetic	geodetic	ADJ
ejpam-5251	8	18	hop	hop	NOUN
ejpam-5251	8	19	domination	domination	NOUN
ejpam-5251	8	20	number	number	NOUN
ejpam-5251	8	21	of	of	ADP
ejpam-5251	8	22	nontrivial	nontrivial	ADJ
ejpam-5251	8	23	connected	connect	VERB
ejpam-5251	8	24	graphs	graph	NOUN
ejpam-5251	8	25	.	.	PUNCT
ejpam-5251	9	1	interestingly	interestingly	ADV
ejpam-5251	9	2	,	,	PUNCT
ejpam-5251	9	3	every	every	DET
ejpam-5251	9	4	pair	pair	NOUN
ejpam-5251	9	5	of	of	ADP
ejpam-5251	9	6	positive	positive	ADJ
ejpam-5251	9	7	integers	integer	NOUN
ejpam-5251	9	8	a	a	PRON
ejpam-5251	9	9	and	and	CCONJ
ejpam-5251	9	10	b	b	NOUN
ejpam-5251	9	11	with	with	ADP
ejpam-5251	9	12	2	2	NUM
ejpam-5251	9	13	≤	≤	NOUN
ejpam-5251	9	14	a	a	DET
ejpam-5251	9	15	≤	≤	NUM
ejpam-5251	9	16	b	b	NOUN
ejpam-5251	9	17	is	be	AUX
ejpam-5251	9	18	realizable	realizable	ADJ
ejpam-5251	9	19	as	as	ADP
ejpam-5251	9	20	the	the	DET
ejpam-5251	9	21	geodetic	geodetic	ADJ
ejpam-5251	9	22	domination	domination	NOUN
ejpam-5251	9	23	number	number	NOUN
ejpam-5251	9	24	and	and	CCONJ
ejpam-5251	9	25	the	the	DET
ejpam-5251	9	26	upper	upper	ADJ
ejpam-5251	9	27	geodetic	geodetic	ADJ
ejpam-5251	9	28	hop	hop	NOUN
ejpam-5251	9	29	domination	domination	NOUN
ejpam-5251	9	30	number	number	NOUN
ejpam-5251	9	31	,	,	PUNCT
ejpam-5251	9	32	respectively	respectively	ADV
ejpam-5251	9	33	,	,	PUNCT
ejpam-5251	9	34	of	of	ADP
ejpam-5251	9	35	some	some	DET
ejpam-5251	9	36	graph	graph	NOUN
ejpam-5251	9	37	.	.	PUNCT
ejpam-5251	10	1	furthermore	furthermore	ADV
ejpam-5251	10	2	,	,	PUNCT
ejpam-5251	10	3	this	this	DET
ejpam-5251	10	4	paper	paper	NOUN
ejpam-5251	10	5	investigates	investigate	VERB
ejpam-5251	10	6	the	the	DET
ejpam-5251	10	7	concept	concept	NOUN
ejpam-5251	10	8	in	in	ADP
ejpam-5251	10	9	the	the	DET
ejpam-5251	10	10	join	join	NOUN
ejpam-5251	10	11	,	,	PUNCT
ejpam-5251	10	12	corona	corona	NOUN
ejpam-5251	10	13	and	and	CCONJ
ejpam-5251	10	14	lexicographic	lexicographic	ADJ
ejpam-5251	10	15	product	product	NOUN
ejpam-5251	10	16	of	of	ADP
ejpam-5251	10	17	graphs	graph	NOUN
ejpam-5251	10	18	.	.	PUNCT
ejpam-5251	11	1	2020	2020	NUM
ejpam-5251	11	2	mathematics	mathematic	NOUN
ejpam-5251	11	3	subject	subject	NOUN
ejpam-5251	11	4	classifications	classification	NOUN
ejpam-5251	11	5	:	:	PUNCT
ejpam-5251	11	6	05c69	05c69	X
ejpam-5251	11	7	key	key	ADJ
ejpam-5251	11	8	words	word	NOUN
ejpam-5251	11	9	and	and	CCONJ
ejpam-5251	11	10	phrases	phrase	NOUN
ejpam-5251	11	11	:	:	PUNCT
ejpam-5251	11	12	minimal	minimal	ADJ
ejpam-5251	11	13	geodetic	geodetic	ADJ
ejpam-5251	11	14	hop	hop	NOUN
ejpam-5251	11	15	dominating	dominating	NOUN
ejpam-5251	11	16	set	set	NOUN
ejpam-5251	11	17	,	,	PUNCT
ejpam-5251	11	18	upper	upper	ADJ
ejpam-5251	11	19	geodetic	geodetic	ADJ
ejpam-5251	11	20	hop	hop	NOUN
ejpam-5251	11	21	dominating	dominating	NOUN
ejpam-5251	11	22	number	number	NOUN
ejpam-5251	11	23	,	,	PUNCT
ejpam-5251	11	24	2	2	NUM
ejpam-5251	11	25	-	-	PUNCT
ejpam-5251	11	26	path	path	NOUN
ejpam-5251	11	27	closure	closure	NOUN
ejpam-5251	11	28	absorbing	absorb	VERB
ejpam-5251	11	29	pointwise	pointwise	PROPN
ejpam-5251	11	30	non	non	ADJ
ejpam-5251	11	31	-	-	ADJ
ejpam-5251	11	32	dominating	dominating	ADJ
ejpam-5251	11	33	set	set	NOUN
ejpam-5251	11	34	1	1	NUM
ejpam-5251	11	35	.	.	PUNCT
ejpam-5251	11	36	introduction	introduction	NOUN
ejpam-5251	11	37	in	in	ADP
ejpam-5251	11	38	2021	2021	NUM
ejpam-5251	11	39	,	,	PUNCT
ejpam-5251	11	40	d.	d.	PROPN
ejpam-5251	11	41	anusha	anusha	VERB
ejpam-5251	11	42	et	et	PROPN
ejpam-5251	11	43	al	al	PROPN
ejpam-5251	11	44	.	.	PUNCT
ejpam-5251	12	1	[	[	X
ejpam-5251	12	2	17	17	NUM
ejpam-5251	12	3	]	]	PUNCT
ejpam-5251	12	4	introduced	introduce	VERB
ejpam-5251	12	5	the	the	DET
ejpam-5251	12	6	concept	concept	NOUN
ejpam-5251	12	7	of	of	ADP
ejpam-5251	12	8	geodetic	geodetic	ADJ
ejpam-5251	12	9	hop	hop	NOUN
ejpam-5251	12	10	domination	domination	NOUN
ejpam-5251	12	11	in	in	ADP
ejpam-5251	12	12	graphs	graph	NOUN
ejpam-5251	12	13	,	,	PUNCT
ejpam-5251	12	14	and	and	CCONJ
ejpam-5251	12	15	initially	initially	ADV
ejpam-5251	12	16	investigated	investigate	VERB
ejpam-5251	12	17	the	the	DET
ejpam-5251	12	18	concept	concept	NOUN
ejpam-5251	12	19	in	in	ADP
ejpam-5251	12	20	the	the	DET
ejpam-5251	12	21	complementary	complementary	ADJ
ejpam-5251	12	22	prism	prism	NOUN
ejpam-5251	12	23	of	of	ADP
ejpam-5251	12	24	graphs	graph	NOUN
ejpam-5251	12	25	.	.	PUNCT
ejpam-5251	13	1	further	further	ADJ
ejpam-5251	13	2	investigation	investigation	NOUN
ejpam-5251	13	3	of	of	ADP
ejpam-5251	13	4	the	the	DET
ejpam-5251	13	5	concept	concept	NOUN
ejpam-5251	13	6	was	be	AUX
ejpam-5251	13	7	done	do	VERB
ejpam-5251	13	8	by	by	ADP
ejpam-5251	13	9	d.	d.	PROPN
ejpam-5251	13	10	anusha	anusha	PROPN
ejpam-5251	14	1	[	[	X
ejpam-5251	14	2	3	3	X
ejpam-5251	14	3	]	]	PUNCT
ejpam-5251	14	4	in	in	ADP
ejpam-5251	14	5	2022	2022	NUM
ejpam-5251	14	6	,	,	PUNCT
ejpam-5251	14	7	by	by	ADP
ejpam-5251	14	8	c.j	c.j	PROPN
ejpam-5251	14	9	.	.	PROPN
ejpam-5251	14	10	saromines	saromine	NOUN
ejpam-5251	14	11	and	and	CCONJ
ejpam-5251	14	12	s.r	s.r	PROPN
ejpam-5251	14	13	.	.	PROPN
ejpam-5251	14	14	canoy	canoy	PROPN
ejpam-5251	14	15	jr	jr	PROPN
ejpam-5251	14	16	.	.	PUNCT
ejpam-5251	15	1	[	[	X
ejpam-5251	15	2	26	26	NUM
ejpam-5251	15	3	,	,	PUNCT
ejpam-5251	15	4	27	27	NUM
ejpam-5251	15	5	]	]	PUNCT
ejpam-5251	15	6	in	in	ADP
ejpam-5251	15	7	2023	2023	NUM
ejpam-5251	15	8	,	,	PUNCT
ejpam-5251	15	9	and	and	CCONJ
ejpam-5251	15	10	just	just	ADV
ejpam-5251	15	11	recently	recently	ADV
ejpam-5251	15	12	by	by	ADP
ejpam-5251	15	13	d.	d.	PROPN
ejpam-5251	15	14	anusha	anusha	PROPN
ejpam-5251	15	15	et	et	PROPN
ejpam-5251	15	16	al	al	PROPN
ejpam-5251	15	17	.	.	PUNCT
ejpam-5251	16	1	[	[	X
ejpam-5251	16	2	4	4	NUM
ejpam-5251	16	3	]	]	PUNCT
ejpam-5251	16	4	.	.	PUNCT
ejpam-5251	17	1	this	this	DET
ejpam-5251	17	2	present	present	ADJ
ejpam-5251	17	3	paper	paper	NOUN
ejpam-5251	17	4	introduces	introduce	NOUN
ejpam-5251	17	5	and	and	CCONJ
ejpam-5251	17	6	initiates	initiate	VERB
ejpam-5251	17	7	the	the	DET
ejpam-5251	17	8	study	study	NOUN
ejpam-5251	17	9	of	of	ADP
ejpam-5251	17	10	the	the	DET
ejpam-5251	17	11	concept	concept	NOUN
ejpam-5251	17	12	of	of	ADP
ejpam-5251	17	13	minimal	minimal	ADJ
ejpam-5251	17	14	geodetic	geodetic	ADJ
ejpam-5251	17	15	hop	hop	NOUN
ejpam-5251	17	16	domination	domination	NOUN
ejpam-5251	17	17	,	,	PUNCT
ejpam-5251	17	18	a	a	DET
ejpam-5251	17	19	natural	natural	ADJ
ejpam-5251	17	20	variation	variation	NOUN
ejpam-5251	17	21	of	of	ADP
ejpam-5251	17	22	the	the	DET
ejpam-5251	17	23	geodetic	geodetic	ADJ
ejpam-5251	17	24	hop	hop	NOUN
ejpam-5251	17	25	domination	domination	NOUN
ejpam-5251	17	26	.	.	PUNCT
ejpam-5251	18	1	throughout	throughout	ADP
ejpam-5251	18	2	this	this	DET
ejpam-5251	18	3	paper	paper	NOUN
ejpam-5251	18	4	,	,	PUNCT
ejpam-5251	18	5	all	all	DET
ejpam-5251	18	6	graphs	graph	NOUN
ejpam-5251	18	7	considered	consider	VERB
ejpam-5251	18	8	are	be	AUX
ejpam-5251	18	9	simple	simple	ADJ
ejpam-5251	18	10	and	and	CCONJ
ejpam-5251	18	11	undirected	undirected	ADJ
ejpam-5251	18	12	.	.	PUNCT
ejpam-5251	19	1	common	common	ADJ
ejpam-5251	19	2	graph	graph	NOUN
ejpam-5251	19	3	terminologies	terminology	NOUN
ejpam-5251	19	4	and	and	CCONJ
ejpam-5251	19	5	notations	notation	NOUN
ejpam-5251	19	6	used	use	VERB
ejpam-5251	19	7	here	here	ADV
ejpam-5251	19	8	are	be	AUX
ejpam-5251	19	9	adapted	adapt	VERB
ejpam-5251	19	10	from	from	ADP
ejpam-5251	19	11	[	[	X
ejpam-5251	19	12	6	6	NUM
ejpam-5251	19	13	,	,	PUNCT
ejpam-5251	19	14	11	11	NUM
ejpam-5251	19	15	]	]	PUNCT
ejpam-5251	19	16	.	.	PUNCT
ejpam-5251	20	1	given	give	VERB
ejpam-5251	20	2	two	two	NUM
ejpam-5251	20	3	graphs	graph	NOUN
ejpam-5251	20	4	g	g	NOUN
ejpam-5251	20	5	and	and	CCONJ
ejpam-5251	20	6	h	h	NOUN
ejpam-5251	20	7	with	with	ADP
ejpam-5251	20	8	disjoint	disjoint	ADJ
ejpam-5251	20	9	vertex	vertex	NOUN
ejpam-5251	20	10	sets	set	NOUN
ejpam-5251	20	11	,	,	PUNCT
ejpam-5251	20	12	the	the	DET
ejpam-5251	20	13	join	join	NOUN
ejpam-5251	20	14	of	of	ADP
ejpam-5251	20	15	g	g	PROPN
ejpam-5251	20	16	and	and	CCONJ
ejpam-5251	20	17	h	h	NOUN
ejpam-5251	20	18	is	be	AUX
ejpam-5251	20	19	the	the	DET
ejpam-5251	20	20	graph	graph	NOUN
ejpam-5251	20	21	g+h	g+h	PROPN
ejpam-5251	20	22	with	with	ADP
ejpam-5251	20	23	v	v	PROPN
ejpam-5251	20	24	(	(	PUNCT
ejpam-5251	20	25	g+h	g+h	NOUN
ejpam-5251	20	26	)	)	PUNCT
ejpam-5251	20	27	=	=	SYM
ejpam-5251	20	28	v	v	X
ejpam-5251	20	29	(	(	PUNCT
ejpam-5251	20	30	g	g	NOUN
ejpam-5251	20	31	)	)	PUNCT
ejpam-5251	20	32	∪	∪	NOUN
ejpam-5251	20	33	v	v	NOUN
ejpam-5251	20	34	(	(	PUNCT
ejpam-5251	20	35	h	h	NOUN
ejpam-5251	20	36	)	)	PUNCT
ejpam-5251	20	37	and	and	CCONJ
ejpam-5251	20	38	e(g+h	e(g+h	NUM
ejpam-5251	20	39	)	)	PUNCT
ejpam-5251	20	40	=	=	SYM
ejpam-5251	20	41	e(g	e(g	NOUN
ejpam-5251	20	42	)	)	PUNCT
ejpam-5251	20	43	∪	∪	ADP
ejpam-5251	20	44	e(h	e(h	PROPN
ejpam-5251	20	45	)	)	PUNCT
ejpam-5251	20	46	∪	∪	NOUN
ejpam-5251	20	47	{	{	PUNCT
ejpam-5251	20	48	uv	uv	NOUN
ejpam-5251	20	49	:	:	PUNCT
ejpam-5251	20	50	u	u	PROPN
ejpam-5251	20	51	∈	∈	PROPN
ejpam-5251	20	52	v	v	ADP
ejpam-5251	20	53	(	(	PUNCT
ejpam-5251	20	54	g	g	NOUN
ejpam-5251	20	55	)	)	PUNCT
ejpam-5251	20	56	,	,	PUNCT
ejpam-5251	20	57	v	v	X
ejpam-5251	20	58	∈	∈	PROPN
ejpam-5251	20	59	v	v	NOUN
ejpam-5251	20	60	(	(	PUNCT
ejpam-5251	20	61	h	h	NOUN
ejpam-5251	20	62	)	)	PUNCT
ejpam-5251	20	63	}	}	PUNCT
ejpam-5251	20	64	.	.	PUNCT
ejpam-5251	21	1	the	the	DET
ejpam-5251	21	2	corona	corona	NOUN
ejpam-5251	21	3	of	of	ADP
ejpam-5251	21	4	g	g	PROPN
ejpam-5251	21	5	and	and	CCONJ
ejpam-5251	21	6	h	h	NOUN
ejpam-5251	21	7	is	be	AUX
ejpam-5251	21	8	the	the	DET
ejpam-5251	21	9	graph	graph	NOUN
ejpam-5251	21	10	g	g	PROPN
ejpam-5251	21	11	◦	◦	NOUN
ejpam-5251	21	12	h	h	NOUN
ejpam-5251	21	13	obtained	obtain	VERB
ejpam-5251	21	14	by	by	ADP
ejpam-5251	21	15	taking	take	VERB
ejpam-5251	21	16	|v	|v	PROPN
ejpam-5251	21	17	(	(	PUNCT
ejpam-5251	21	18	g)|	g)|	NOUN
ejpam-5251	21	19	copies	copy	NOUN
ejpam-5251	21	20	of	of	ADP
ejpam-5251	21	21	h	h	NOUN
ejpam-5251	21	22	in	in	ADP
ejpam-5251	21	23	every	every	DET
ejpam-5251	21	24	vertex	vertex	NOUN
ejpam-5251	21	25	of	of	ADP
ejpam-5251	21	26	v	v	NOUN
ejpam-5251	21	27	(	(	PUNCT
ejpam-5251	21	28	g	g	NOUN
ejpam-5251	21	29	)	)	PUNCT
ejpam-5251	21	30	and	and	CCONJ
ejpam-5251	21	31	then	then	ADV
ejpam-5251	21	32	joining	join	VERB
ejpam-5251	21	33	the	the	DET
ejpam-5251	21	34	ith	ith	PROPN
ejpam-5251	21	35	vertex	vertex	NOUN
ejpam-5251	21	36	of	of	ADP
ejpam-5251	21	37	v	v	NOUN
ejpam-5251	21	38	(	(	PUNCT
ejpam-5251	21	39	g	g	NOUN
ejpam-5251	21	40	)	)	PUNCT
ejpam-5251	21	41	to	to	ADP
ejpam-5251	21	42	every	every	DET
ejpam-5251	21	43	vertex	vertex	NOUN
ejpam-5251	21	44	of	of	ADP
ejpam-5251	21	45	the	the	DET
ejpam-5251	21	46	ith	ith	PROPN
ejpam-5251	21	47	copy	copy	NOUN
ejpam-5251	21	48	of	of	ADP
ejpam-5251	21	49	h.	h.	PROPN
ejpam-5251	21	50	∗corresponding	∗corresponde	VERB
ejpam-5251	21	51	author	author	NOUN
ejpam-5251	21	52	.	.	PUNCT
ejpam-5251	22	1	doi	doi	NOUN
ejpam-5251	22	2	:	:	PUNCT
ejpam-5251	22	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5251	https://doi.org/10.29020/nybg.ejpam.v17i3.5251	NUM
ejpam-5251	22	4	email	email	NOUN
ejpam-5251	22	5	addresses	address	NOUN
ejpam-5251	22	6	:	:	PUNCT
ejpam-5251	22	7	dyjaybill.catian@g.msuiit.edu.ph	dyjaybill.catian@g.msuiit.edu.ph	PROPN
ejpam-5251	22	8	(	(	PUNCT
ejpam-5251	22	9	d.b	d.b	PROPN
ejpam-5251	22	10	.	.	PROPN
ejpam-5251	22	11	catian	catian	NOUN
ejpam-5251	22	12	)	)	PUNCT
ejpam-5251	22	13	,	,	PUNCT
ejpam-5251	22	14	imelda.aniversario@g.msuiit.edu.ph	imelda.aniversario@g.msuiit.edu.ph	PROPN
ejpam-5251	22	15	(	(	PUNCT
ejpam-5251	22	16	i.	i.	PROPN
ejpam-5251	22	17	aniversario	aniversario	PROPN
ejpam-5251	22	18	)	)	PUNCT
ejpam-5251	22	19	,	,	PUNCT
ejpam-5251	22	20	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-5251	22	21	(	(	PUNCT
ejpam-5251	22	22	f.	f.	PROPN
ejpam-5251	22	23	jamil	jamil	PROPN
ejpam-5251	22	24	)	)	PUNCT
ejpam-5251	22	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5251	22	26	1737	1737	NUM
ejpam-5251	22	27	©	©	ADP
ejpam-5251	22	28	2024	2024	NUM
ejpam-5251	22	29	ejpam	ejpam	NOUN
ejpam-5251	22	30	all	all	DET
ejpam-5251	22	31	rights	right	NOUN
ejpam-5251	22	32	reserved	reserve	VERB
ejpam-5251	22	33	.	.	PUNCT
ejpam-5251	23	1	d.	d.	PROPN
ejpam-5251	23	2	catian	catian	PROPN
ejpam-5251	23	3	,	,	PUNCT
ejpam-5251	23	4	i.	i.	PROPN
ejpam-5251	23	5	s.	s.	PROPN
ejpam-5251	23	6	aniversario	aniversario	PROPN
ejpam-5251	23	7	,	,	PUNCT
ejpam-5251	23	8	f.	f.	PROPN
ejpam-5251	23	9	p.	p.	PROPN
ejpam-5251	23	10	jamil	jamil	PROPN
ejpam-5251	23	11	/	/	SYM
ejpam-5251	23	12	eur	eur	PROPN
ejpam-5251	23	13	.	.	PUNCT
ejpam-5251	24	1	j.	j.	PROPN
ejpam-5251	24	2	pure	pure	PROPN
ejpam-5251	24	3	appl	appl	PROPN
ejpam-5251	24	4	.	.	PROPN
ejpam-5251	24	5	math	math	PROPN
ejpam-5251	24	6	,	,	PUNCT
ejpam-5251	24	7	17	17	NUM
ejpam-5251	24	8	(	(	PUNCT
ejpam-5251	24	9	3	3	NUM
ejpam-5251	24	10	)	)	PUNCT
ejpam-5251	24	11	(	(	PUNCT
ejpam-5251	24	12	2024	2024	NUM
ejpam-5251	24	13	)	)	PUNCT
ejpam-5251	24	14	,	,	PUNCT
ejpam-5251	24	15	1737	1737	NUM
ejpam-5251	24	16	-	-	SYM
ejpam-5251	24	17	1750	1750	NUM
ejpam-5251	24	18	1738	1738	NUM
ejpam-5251	24	19	the	the	DET
ejpam-5251	24	20	lexicographic	lexicographic	ADJ
ejpam-5251	24	21	product	product	NOUN
ejpam-5251	24	22	of	of	ADP
ejpam-5251	24	23	g	g	PROPN
ejpam-5251	24	24	and	and	CCONJ
ejpam-5251	24	25	h	h	NOUN
ejpam-5251	24	26	is	be	AUX
ejpam-5251	24	27	the	the	DET
ejpam-5251	24	28	graph	graph	NOUN
ejpam-5251	24	29	g[h	g[h	PROPN
ejpam-5251	24	30	]	]	PUNCT
ejpam-5251	24	31	with	with	ADP
ejpam-5251	24	32	v	v	NOUN
ejpam-5251	24	33	(	(	PUNCT
ejpam-5251	24	34	g[h	g[h	PROPN
ejpam-5251	24	35	]	]	PUNCT
ejpam-5251	24	36	)	)	PUNCT
ejpam-5251	24	37	=	=	SYM
ejpam-5251	24	38	v	v	X
ejpam-5251	24	39	(	(	PUNCT
ejpam-5251	24	40	g	g	NOUN
ejpam-5251	24	41	)	)	PUNCT
ejpam-5251	24	42	×	×	NOUN
ejpam-5251	24	43	v	v	NOUN
ejpam-5251	24	44	(	(	PUNCT
ejpam-5251	24	45	h	h	NOUN
ejpam-5251	24	46	)	)	PUNCT
ejpam-5251	24	47	and	and	CCONJ
ejpam-5251	24	48	(	(	PUNCT
ejpam-5251	24	49	u	u	NOUN
ejpam-5251	24	50	,	,	PUNCT
ejpam-5251	24	51	v)(w	v)(w	NOUN
ejpam-5251	24	52	,	,	PUNCT
ejpam-5251	24	53	z	z	NOUN
ejpam-5251	24	54	)	)	PUNCT
ejpam-5251	24	55	∈	∈	NOUN
ejpam-5251	24	56	e(g[h	e(g[h	NOUN
ejpam-5251	24	57	]	]	PUNCT
ejpam-5251	24	58	)	)	PUNCT
ejpam-5251	24	59	if	if	SCONJ
ejpam-5251	24	60	and	and	CCONJ
ejpam-5251	24	61	only	only	ADV
ejpam-5251	24	62	if	if	SCONJ
ejpam-5251	24	63	uw	uw	PROPN
ejpam-5251	24	64	∈	∈	PROPN
ejpam-5251	24	65	e(g	e(g	PROPN
ejpam-5251	24	66	)	)	PUNCT
ejpam-5251	24	67	or	or	CCONJ
ejpam-5251	24	68	u	u	X
ejpam-5251	24	69	=	=	PROPN
ejpam-5251	24	70	w	w	PROPN
ejpam-5251	24	71	and	and	CCONJ
ejpam-5251	24	72	vz	vz	PROPN
ejpam-5251	24	73	∈	∈	PROPN
ejpam-5251	24	74	e(h	e(h	PROPN
ejpam-5251	24	75	)	)	PUNCT
ejpam-5251	24	76	.	.	PUNCT
ejpam-5251	25	1	let	let	VERB
ejpam-5251	25	2	g	g	PRON
ejpam-5251	25	3	be	be	AUX
ejpam-5251	25	4	a	a	DET
ejpam-5251	25	5	connected	connected	ADJ
ejpam-5251	25	6	graph	graph	NOUN
ejpam-5251	25	7	.	.	PUNCT
ejpam-5251	26	1	for	for	ADP
ejpam-5251	26	2	any	any	DET
ejpam-5251	26	3	two	two	NUM
ejpam-5251	26	4	distinct	distinct	ADJ
ejpam-5251	26	5	u	u	NOUN
ejpam-5251	26	6	,	,	PUNCT
ejpam-5251	26	7	v	v	PROPN
ejpam-5251	26	8	∈	∈	PROPN
ejpam-5251	26	9	e(g	e(g	PROPN
ejpam-5251	26	10	)	)	PUNCT
ejpam-5251	26	11	,	,	PUNCT
ejpam-5251	26	12	a	a	DET
ejpam-5251	26	13	shortest	short	ADJ
ejpam-5251	26	14	path	path	NOUN
ejpam-5251	26	15	joining	join	VERB
ejpam-5251	26	16	u	u	NOUN
ejpam-5251	26	17	and	and	CCONJ
ejpam-5251	26	18	v	v	NOUN
ejpam-5251	26	19	is	be	AUX
ejpam-5251	26	20	called	call	VERB
ejpam-5251	26	21	a	a	DET
ejpam-5251	26	22	u	u	NOUN
ejpam-5251	26	23	-	-	NOUN
ejpam-5251	26	24	v	v	ADJ
ejpam-5251	26	25	geodesic	geodesic	NOUN
ejpam-5251	26	26	.	.	PUNCT
ejpam-5251	27	1	the	the	DET
ejpam-5251	27	2	length	length	NOUN
ejpam-5251	27	3	of	of	ADP
ejpam-5251	27	4	a	a	DET
ejpam-5251	27	5	u	u	NOUN
ejpam-5251	27	6	-	-	NOUN
ejpam-5251	27	7	v	v	ADJ
ejpam-5251	27	8	geodesic	geodesic	NOUN
ejpam-5251	27	9	is	be	AUX
ejpam-5251	27	10	called	call	VERB
ejpam-5251	27	11	the	the	DET
ejpam-5251	27	12	distance	distance	NOUN
ejpam-5251	27	13	between	between	ADP
ejpam-5251	27	14	u	u	NOUN
ejpam-5251	27	15	and	and	CCONJ
ejpam-5251	27	16	v	v	NOUN
ejpam-5251	27	17	,	,	PUNCT
ejpam-5251	27	18	which	which	PRON
ejpam-5251	27	19	is	be	AUX
ejpam-5251	27	20	denoted	denote	VERB
ejpam-5251	27	21	by	by	ADP
ejpam-5251	27	22	dg(u	dg(u	NOUN
ejpam-5251	27	23	,	,	PUNCT
ejpam-5251	27	24	v	v	NOUN
ejpam-5251	27	25	)	)	PUNCT
ejpam-5251	27	26	.	.	PUNCT
ejpam-5251	28	1	the	the	DET
ejpam-5251	28	2	diameter	diameter	NOUN
ejpam-5251	28	3	of	of	ADP
ejpam-5251	28	4	the	the	DET
ejpam-5251	28	5	graph	graph	NOUN
ejpam-5251	28	6	g	g	NOUN
ejpam-5251	28	7	,	,	PUNCT
ejpam-5251	28	8	denoted	denote	VERB
ejpam-5251	28	9	diam(g	diam(g	PROPN
ejpam-5251	28	10	)	)	PUNCT
ejpam-5251	28	11	,	,	PUNCT
ejpam-5251	28	12	is	be	AUX
ejpam-5251	28	13	the	the	DET
ejpam-5251	28	14	maximum	maximum	ADJ
ejpam-5251	28	15	distance	distance	NOUN
ejpam-5251	28	16	between	between	ADP
ejpam-5251	28	17	any	any	DET
ejpam-5251	28	18	pair	pair	NOUN
ejpam-5251	28	19	of	of	ADP
ejpam-5251	28	20	vertices	vertex	NOUN
ejpam-5251	28	21	in	in	ADP
ejpam-5251	28	22	g.	g.	PROPN
ejpam-5251	28	23	if	if	SCONJ
ejpam-5251	28	24	diam(g	diam(g	NOUN
ejpam-5251	28	25	)	)	PUNCT
ejpam-5251	28	26	=	=	SYM
ejpam-5251	28	27	1	1	NUM
ejpam-5251	28	28	,	,	PUNCT
ejpam-5251	28	29	then	then	ADV
ejpam-5251	28	30	g	g	PROPN
ejpam-5251	28	31	is	be	AUX
ejpam-5251	28	32	a	a	DET
ejpam-5251	28	33	complete	complete	ADJ
ejpam-5251	28	34	graph	graph	NOUN
ejpam-5251	28	35	.	.	PUNCT
ejpam-5251	29	1	a	a	DET
ejpam-5251	29	2	clique	clique	NOUN
ejpam-5251	29	3	of	of	ADP
ejpam-5251	29	4	a	a	DET
ejpam-5251	29	5	graph	graph	NOUN
ejpam-5251	29	6	g	g	NOUN
ejpam-5251	29	7	is	be	AUX
ejpam-5251	29	8	any	any	DET
ejpam-5251	29	9	complete	complete	ADJ
ejpam-5251	29	10	subgraph	subgraph	NOUN
ejpam-5251	29	11	of	of	ADP
ejpam-5251	29	12	g.	g.	PROPN
ejpam-5251	29	13	the	the	DET
ejpam-5251	29	14	clique	clique	ADJ
ejpam-5251	29	15	number	number	NOUN
ejpam-5251	29	16	of	of	ADP
ejpam-5251	29	17	g	g	PROPN
ejpam-5251	29	18	is	be	AUX
ejpam-5251	29	19	the	the	DET
ejpam-5251	29	20	maximum	maximum	ADJ
ejpam-5251	29	21	cardinality	cardinality	PROPN
ejpam-5251	29	22	ω(g	ω(g	NOUN
ejpam-5251	29	23	)	)	PUNCT
ejpam-5251	29	24	of	of	ADP
ejpam-5251	29	25	s	s	NOUN
ejpam-5251	29	26	⊆	⊆	NUM
ejpam-5251	29	27	v	v	NOUN
ejpam-5251	29	28	(	(	PUNCT
ejpam-5251	29	29	g	g	NOUN
ejpam-5251	29	30	)	)	PUNCT
ejpam-5251	29	31	for	for	ADP
ejpam-5251	29	32	which	which	PRON
ejpam-5251	29	33	⟨s⟩	⟨s⟩	VERB
ejpam-5251	29	34	is	be	AUX
ejpam-5251	29	35	a	a	DET
ejpam-5251	29	36	clique	clique	NOUN
ejpam-5251	29	37	.	.	PUNCT
ejpam-5251	30	1	by	by	ADP
ejpam-5251	30	2	the	the	DET
ejpam-5251	30	3	(	(	PUNCT
ejpam-5251	30	4	open	open	ADJ
ejpam-5251	30	5	)	)	PUNCT
ejpam-5251	30	6	neighborhood	neighborhood	NOUN
ejpam-5251	30	7	ng(v	ng(v	NOUN
ejpam-5251	30	8	)	)	PUNCT
ejpam-5251	30	9	of	of	ADP
ejpam-5251	30	10	a	a	DET
ejpam-5251	30	11	vertex	vertex	NOUN
ejpam-5251	30	12	v	v	NOUN
ejpam-5251	30	13	is	be	AUX
ejpam-5251	30	14	meant	mean	VERB
ejpam-5251	30	15	the	the	DET
ejpam-5251	30	16	set	set	NOUN
ejpam-5251	30	17	of	of	ADP
ejpam-5251	30	18	vertices	vertex	NOUN
ejpam-5251	30	19	that	that	PRON
ejpam-5251	30	20	are	be	AUX
ejpam-5251	30	21	adjacent	adjacent	ADJ
ejpam-5251	30	22	to	to	ADP
ejpam-5251	30	23	v	v	NOUN
ejpam-5251	30	24	,	,	PUNCT
ejpam-5251	30	25	that	that	ADV
ejpam-5251	30	26	is	is	ADV
ejpam-5251	30	27	,	,	PUNCT
ejpam-5251	30	28	ng(v	ng(v	PUNCT
ejpam-5251	30	29	)	)	PUNCT
ejpam-5251	30	30	=	=	SYM
ejpam-5251	30	31	{	{	PUNCT
ejpam-5251	30	32	u	u	NOUN
ejpam-5251	30	33	∈	∈	PROPN
ejpam-5251	30	34	v	v	NOUN
ejpam-5251	30	35	(	(	PUNCT
ejpam-5251	30	36	g	g	NOUN
ejpam-5251	30	37	)	)	PUNCT
ejpam-5251	30	38	:	:	PUNCT
ejpam-5251	30	39	uv	uv	PROPN
ejpam-5251	30	40	∈	∈	PROPN
ejpam-5251	30	41	e(g	e(g	PROPN
ejpam-5251	30	42	)	)	PUNCT
ejpam-5251	30	43	}	}	PUNCT
ejpam-5251	30	44	.	.	PUNCT
ejpam-5251	31	1	the	the	DET
ejpam-5251	31	2	closed	closed	ADJ
ejpam-5251	31	3	neighborhood	neighborhood	NOUN
ejpam-5251	31	4	of	of	ADP
ejpam-5251	31	5	vertex	vertex	NOUN
ejpam-5251	31	6	v	v	NOUN
ejpam-5251	31	7	is	be	AUX
ejpam-5251	31	8	ng[v	ng[v	X
ejpam-5251	31	9	]	]	X
ejpam-5251	31	10	=	=	SYM
ejpam-5251	31	11	ng(v	ng(v	X
ejpam-5251	31	12	)	)	PUNCT
ejpam-5251	31	13	∪	∪	ADP
ejpam-5251	31	14	{	{	PUNCT
ejpam-5251	31	15	v	v	NOUN
ejpam-5251	31	16	}	}	PUNCT
ejpam-5251	31	17	.	.	PUNCT
ejpam-5251	32	1	for	for	ADP
ejpam-5251	32	2	s	s	PROPN
ejpam-5251	32	3	⊆	⊆	NUM
ejpam-5251	32	4	v	v	NOUN
ejpam-5251	32	5	(	(	PUNCT
ejpam-5251	32	6	g	g	NOUN
ejpam-5251	32	7	)	)	PUNCT
ejpam-5251	32	8	,	,	PUNCT
ejpam-5251	32	9	ng(s	ng(s	NUM
ejpam-5251	32	10	)	)	PUNCT
ejpam-5251	32	11	=	=	SYM
ejpam-5251	32	12	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-5251	32	13	)	)	PUNCT
ejpam-5251	32	14	,	,	PUNCT
ejpam-5251	32	15	while	while	SCONJ
ejpam-5251	32	16	ng[s	ng[	NOUN
ejpam-5251	32	17	]	]	X
ejpam-5251	32	18	=	=	SYM
ejpam-5251	32	19	ng(s	ng(s	X
ejpam-5251	32	20	)	)	PUNCT
ejpam-5251	32	21	∪	∪	ADP
ejpam-5251	32	22	s.	s.	PROPN
ejpam-5251	32	23	a	a	DET
ejpam-5251	32	24	vertex	vertex	NOUN
ejpam-5251	32	25	v	v	NOUN
ejpam-5251	32	26	is	be	AUX
ejpam-5251	32	27	an	an	DET
ejpam-5251	32	28	extreme	extreme	ADJ
ejpam-5251	32	29	vertex	vertex	NOUN
ejpam-5251	32	30	if	if	SCONJ
ejpam-5251	32	31	the	the	DET
ejpam-5251	32	32	induced	induced	ADJ
ejpam-5251	32	33	subgraph	subgraph	NOUN
ejpam-5251	32	34	⟨ng(v)⟩	⟨ng(v)⟩	NOUN
ejpam-5251	32	35	is	be	AUX
ejpam-5251	32	36	a	a	DET
ejpam-5251	32	37	complete	complete	ADJ
ejpam-5251	32	38	graph	graph	NOUN
ejpam-5251	32	39	.	.	PUNCT
ejpam-5251	33	1	the	the	DET
ejpam-5251	33	2	symbol	symbol	NOUN
ejpam-5251	33	3	ext(g	ext(g	NOUN
ejpam-5251	33	4	)	)	PUNCT
ejpam-5251	33	5	denotes	denote	VERB
ejpam-5251	33	6	the	the	DET
ejpam-5251	33	7	set	set	NOUN
ejpam-5251	33	8	of	of	ADP
ejpam-5251	33	9	all	all	DET
ejpam-5251	33	10	extreme	extreme	ADJ
ejpam-5251	33	11	vertices	vertex	NOUN
ejpam-5251	33	12	in	in	ADP
ejpam-5251	33	13	g.	g.	PROPN
ejpam-5251	33	14	for	for	ADP
ejpam-5251	33	15	u	u	PROPN
ejpam-5251	33	16	,	,	PUNCT
ejpam-5251	33	17	v	v	PROPN
ejpam-5251	33	18	∈	∈	PROPN
ejpam-5251	33	19	v	v	NOUN
ejpam-5251	33	20	(	(	PUNCT
ejpam-5251	33	21	g	g	NOUN
ejpam-5251	33	22	)	)	PUNCT
ejpam-5251	33	23	,	,	PUNCT
ejpam-5251	33	24	the	the	DET
ejpam-5251	33	25	set	set	NOUN
ejpam-5251	33	26	ig(u	ig(u	NOUN
ejpam-5251	33	27	,	,	PUNCT
ejpam-5251	33	28	v	v	NOUN
ejpam-5251	33	29	)	)	PUNCT
ejpam-5251	33	30	refers	refer	VERB
ejpam-5251	33	31	to	to	ADP
ejpam-5251	33	32	the	the	DET
ejpam-5251	33	33	set	set	NOUN
ejpam-5251	33	34	consisting	consist	VERB
ejpam-5251	33	35	of	of	ADP
ejpam-5251	33	36	all	all	DET
ejpam-5251	33	37	the	the	DET
ejpam-5251	33	38	vertices	vertex	NOUN
ejpam-5251	33	39	lying	lie	VERB
ejpam-5251	33	40	in	in	ADP
ejpam-5251	33	41	any	any	DET
ejpam-5251	33	42	u	u	NOUN
ejpam-5251	33	43	−	−	PROPN
ejpam-5251	33	44	v	v	ADP
ejpam-5251	33	45	geodesic	geodesic	NOUN
ejpam-5251	33	46	of	of	ADP
ejpam-5251	33	47	g	g	PROPN
ejpam-5251	33	48	and	and	CCONJ
ejpam-5251	33	49	ig[u	ig[u	PROPN
ejpam-5251	33	50	,	,	PUNCT
ejpam-5251	33	51	v	v	NOUN
ejpam-5251	33	52	]	]	X
ejpam-5251	33	53	=	=	SYM
ejpam-5251	33	54	ig(u	ig(u	ADJ
ejpam-5251	33	55	,	,	PUNCT
ejpam-5251	33	56	v	v	NOUN
ejpam-5251	33	57	)	)	PUNCT
ejpam-5251	33	58	∪	∪	NOUN
ejpam-5251	33	59	{	{	PUNCT
ejpam-5251	33	60	u	u	NOUN
ejpam-5251	33	61	,	,	PUNCT
ejpam-5251	33	62	v	v	NOUN
ejpam-5251	33	63	}	}	PUNCT
ejpam-5251	33	64	.	.	PUNCT
ejpam-5251	34	1	for	for	ADP
ejpam-5251	34	2	a	a	DET
ejpam-5251	34	3	subset	subset	NOUN
ejpam-5251	34	4	s	s	VERB
ejpam-5251	34	5	⊆	⊆	NUM
ejpam-5251	34	6	v	v	NOUN
ejpam-5251	34	7	(	(	PUNCT
ejpam-5251	34	8	g	g	NOUN
ejpam-5251	34	9	)	)	PUNCT
ejpam-5251	34	10	,	,	PUNCT
ejpam-5251	34	11	the	the	DET
ejpam-5251	34	12	geodetic	geodetic	ADJ
ejpam-5251	34	13	closure	closure	NOUN
ejpam-5251	34	14	ig[s	ig[	NOUN
ejpam-5251	34	15	]	]	PUNCT
ejpam-5251	34	16	is	be	AUX
ejpam-5251	34	17	defined	define	VERB
ejpam-5251	34	18	by	by	ADP
ejpam-5251	34	19	ig[s	ig[s	PROPN
ejpam-5251	34	20	]	]	X
ejpam-5251	34	21	=	=	SYM
ejpam-5251	34	22	∪{ig[u	∪{ig[u	NOUN
ejpam-5251	34	23	,	,	PUNCT
ejpam-5251	34	24	v	v	NOUN
ejpam-5251	34	25	]	]	X
ejpam-5251	34	26	:	:	PUNCT
ejpam-5251	34	27	u	u	NOUN
ejpam-5251	34	28	,	,	PUNCT
ejpam-5251	34	29	v	v	NOUN
ejpam-5251	34	30	∈	∈	NOUN
ejpam-5251	34	31	s	s	PART
ejpam-5251	34	32	}	}	PUNCT
ejpam-5251	34	33	.	.	PUNCT
ejpam-5251	35	1	a	a	DET
ejpam-5251	35	2	geodetic	geodetic	ADJ
ejpam-5251	35	3	set	set	NOUN
ejpam-5251	35	4	is	be	AUX
ejpam-5251	35	5	any	any	DET
ejpam-5251	35	6	set	set	NOUN
ejpam-5251	35	7	s	s	NOUN
ejpam-5251	35	8	⊆	⊆	NUM
ejpam-5251	35	9	v	v	NOUN
ejpam-5251	35	10	(	(	PUNCT
ejpam-5251	35	11	g	g	NOUN
ejpam-5251	35	12	)	)	PUNCT
ejpam-5251	35	13	with	with	ADP
ejpam-5251	35	14	ig[s	ig[s	PROPN
ejpam-5251	35	15	]	]	X
ejpam-5251	35	16	=	=	SYM
ejpam-5251	35	17	v	v	X
ejpam-5251	35	18	(	(	PUNCT
ejpam-5251	35	19	g	g	NOUN
ejpam-5251	35	20	)	)	PUNCT
ejpam-5251	35	21	.	.	PUNCT
ejpam-5251	36	1	the	the	DET
ejpam-5251	36	2	minimum	minimum	ADJ
ejpam-5251	36	3	cardinality	cardinality	PROPN
ejpam-5251	36	4	g(g	g(g	PROPN
ejpam-5251	36	5	)	)	PUNCT
ejpam-5251	36	6	of	of	ADP
ejpam-5251	36	7	a	a	DET
ejpam-5251	36	8	geodetic	geodetic	ADJ
ejpam-5251	36	9	set	set	NOUN
ejpam-5251	36	10	is	be	AUX
ejpam-5251	36	11	the	the	DET
ejpam-5251	36	12	geodetic	geodetic	ADJ
ejpam-5251	36	13	number	number	NOUN
ejpam-5251	36	14	of	of	ADP
ejpam-5251	36	15	g.	g.	PROPN
ejpam-5251	36	16	a	a	DET
ejpam-5251	36	17	geodetic	geodetic	ADJ
ejpam-5251	36	18	set	set	NOUN
ejpam-5251	36	19	of	of	ADP
ejpam-5251	36	20	cardinality	cardinality	PROPN
ejpam-5251	36	21	g(g	g(g	PROPN
ejpam-5251	36	22	)	)	PUNCT
ejpam-5251	36	23	is	be	AUX
ejpam-5251	36	24	called	call	VERB
ejpam-5251	36	25	a	a	DET
ejpam-5251	36	26	geodetic	geodetic	ADJ
ejpam-5251	36	27	basis	basis	NOUN
ejpam-5251	36	28	.	.	PUNCT
ejpam-5251	37	1	a	a	DET
ejpam-5251	37	2	geodetic	geodetic	ADJ
ejpam-5251	37	3	set	set	NOUN
ejpam-5251	37	4	s	s	NOUN
ejpam-5251	37	5	in	in	ADP
ejpam-5251	37	6	g	g	PROPN
ejpam-5251	37	7	is	be	AUX
ejpam-5251	37	8	a	a	DET
ejpam-5251	37	9	minimal	minimal	ADJ
ejpam-5251	37	10	geodetic	geodetic	ADJ
ejpam-5251	37	11	set	set	NOUN
ejpam-5251	37	12	if	if	SCONJ
ejpam-5251	37	13	s	s	PRON
ejpam-5251	37	14	does	do	AUX
ejpam-5251	37	15	not	not	PART
ejpam-5251	37	16	have	have	VERB
ejpam-5251	37	17	a	a	DET
ejpam-5251	37	18	proper	proper	ADJ
ejpam-5251	37	19	subset	subset	NOUN
ejpam-5251	37	20	that	that	PRON
ejpam-5251	37	21	is	be	AUX
ejpam-5251	37	22	itself	itself	PRON
ejpam-5251	37	23	a	a	DET
ejpam-5251	37	24	geodetic	geodetic	ADJ
ejpam-5251	37	25	set	set	NOUN
ejpam-5251	37	26	in	in	ADP
ejpam-5251	37	27	g.	g.	PROPN
ejpam-5251	37	28	the	the	DET
ejpam-5251	37	29	maximum	maximum	ADJ
ejpam-5251	37	30	cardinality	cardinality	NOUN
ejpam-5251	37	31	of	of	ADP
ejpam-5251	37	32	a	a	DET
ejpam-5251	37	33	minimal	minimal	ADJ
ejpam-5251	37	34	geodetic	geodetic	ADJ
ejpam-5251	37	35	set	set	NOUN
ejpam-5251	37	36	in	in	ADP
ejpam-5251	37	37	g	g	PROPN
ejpam-5251	37	38	is	be	AUX
ejpam-5251	37	39	denoted	denote	VERB
ejpam-5251	37	40	by	by	ADP
ejpam-5251	37	41	g+(g	g+(g	NOUN
ejpam-5251	37	42	)	)	PUNCT
ejpam-5251	37	43	.	.	PUNCT
ejpam-5251	38	1	geodetic	geodetic	ADJ
ejpam-5251	38	2	sets	set	NOUN
ejpam-5251	38	3	and	and	CCONJ
ejpam-5251	38	4	geodetic	geodetic	ADJ
ejpam-5251	38	5	numbers	number	NOUN
ejpam-5251	38	6	of	of	ADP
ejpam-5251	38	7	graphs	graph	NOUN
ejpam-5251	38	8	are	be	AUX
ejpam-5251	38	9	,	,	PUNCT
ejpam-5251	38	10	in	in	ADP
ejpam-5251	38	11	fact	fact	NOUN
ejpam-5251	38	12	,	,	PUNCT
ejpam-5251	38	13	among	among	ADP
ejpam-5251	38	14	the	the	DET
ejpam-5251	38	15	very	very	ADV
ejpam-5251	38	16	well	well	ADV
ejpam-5251	38	17	-	-	PUNCT
ejpam-5251	38	18	studied	study	VERB
ejpam-5251	38	19	concepts	concept	NOUN
ejpam-5251	38	20	in	in	ADP
ejpam-5251	38	21	graph	graph	NOUN
ejpam-5251	38	22	theory	theory	NOUN
ejpam-5251	38	23	(	(	PUNCT
ejpam-5251	38	24	see	see	VERB
ejpam-5251	38	25	[	[	X
ejpam-5251	38	26	1	1	NUM
ejpam-5251	38	27	,	,	PUNCT
ejpam-5251	38	28	2	2	NUM
ejpam-5251	38	29	,	,	PUNCT
ejpam-5251	38	30	7	7	NUM
ejpam-5251	38	31	,	,	PUNCT
ejpam-5251	38	32	8	8	NUM
ejpam-5251	38	33	,	,	PUNCT
ejpam-5251	38	34	10	10	NUM
ejpam-5251	38	35	,	,	PUNCT
ejpam-5251	38	36	12	12	NUM
ejpam-5251	38	37	,	,	PUNCT
ejpam-5251	38	38	15	15	NUM
ejpam-5251	38	39	,	,	PUNCT
ejpam-5251	38	40	16	16	NUM
ejpam-5251	38	41	,	,	PUNCT
ejpam-5251	38	42	18	18	NUM
ejpam-5251	38	43	,	,	PUNCT
ejpam-5251	38	44	19	19	NUM
ejpam-5251	38	45	,	,	PUNCT
ejpam-5251	38	46	28	28	NUM
ejpam-5251	38	47	]	]	PUNCT
ejpam-5251	38	48	.	.	PUNCT
ejpam-5251	39	1	for	for	ADP
ejpam-5251	39	2	s	s	PROPN
ejpam-5251	39	3	⊆	⊆	NUM
ejpam-5251	39	4	v	v	NOUN
ejpam-5251	39	5	(	(	PUNCT
ejpam-5251	39	6	g	g	NOUN
ejpam-5251	39	7	)	)	PUNCT
ejpam-5251	39	8	,	,	PUNCT
ejpam-5251	39	9	the	the	DET
ejpam-5251	39	10	2	2	NUM
ejpam-5251	39	11	-	-	PUNCT
ejpam-5251	39	12	path	path	NOUN
ejpam-5251	39	13	closure	closure	NOUN
ejpam-5251	39	14	of	of	ADP
ejpam-5251	39	15	s	s	PRON
ejpam-5251	39	16	,	,	PUNCT
ejpam-5251	39	17	denoted	denote	VERB
ejpam-5251	39	18	by	by	ADP
ejpam-5251	39	19	p2[s]g	p2[s]g	PROPN
ejpam-5251	39	20	,	,	PUNCT
ejpam-5251	39	21	is	be	AUX
ejpam-5251	39	22	the	the	DET
ejpam-5251	39	23	set	set	NOUN
ejpam-5251	39	24	p2[s]g	p2[s]g	PROPN
ejpam-5251	39	25	=	=	SYM
ejpam-5251	39	26	s	s	X
ejpam-5251	39	27	∪	∪	X
ejpam-5251	39	28	{	{	PUNCT
ejpam-5251	39	29	w	w	NOUN
ejpam-5251	39	30	∈	∈	PROPN
ejpam-5251	39	31	v	v	ADP
ejpam-5251	39	32	(	(	PUNCT
ejpam-5251	39	33	g	g	NOUN
ejpam-5251	39	34	)	)	PUNCT
ejpam-5251	39	35	:	:	PUNCT
ejpam-5251	39	36	w	w	X
ejpam-5251	39	37	∈	∈	PROPN
ejpam-5251	39	38	ig[u	ig[u	PROPN
ejpam-5251	39	39	,	,	PUNCT
ejpam-5251	39	40	v	v	NOUN
ejpam-5251	39	41	]	]	X
ejpam-5251	39	42	϶	϶	PUNCT
ejpam-5251	39	43	u	u	NOUN
ejpam-5251	39	44	,	,	PUNCT
ejpam-5251	39	45	v	v	PROPN
ejpam-5251	39	46	∈	∈	NOUN
ejpam-5251	39	47	s	s	PART
ejpam-5251	39	48	with	with	ADP
ejpam-5251	39	49	dg(u	dg(u	ADJ
ejpam-5251	39	50	,	,	PUNCT
ejpam-5251	39	51	v	v	NOUN
ejpam-5251	39	52	)	)	PUNCT
ejpam-5251	39	53	=	=	SYM
ejpam-5251	40	1	2	2	X
ejpam-5251	40	2	}	}	PUNCT
ejpam-5251	40	3	a	a	DET
ejpam-5251	40	4	set	set	NOUN
ejpam-5251	40	5	s	s	PART
ejpam-5251	40	6	is	be	AUX
ejpam-5251	40	7	called	call	VERB
ejpam-5251	40	8	2	2	NUM
ejpam-5251	40	9	-	-	PUNCT
ejpam-5251	40	10	path	path	NOUN
ejpam-5251	40	11	closure	closure	NOUN
ejpam-5251	40	12	absorbing	absorb	VERB
ejpam-5251	40	13	if	if	SCONJ
ejpam-5251	40	14	p2[s]g	p2[s]g	PROPN
ejpam-5251	40	15	=	=	SYM
ejpam-5251	40	16	v	v	PROPN
ejpam-5251	40	17	(	(	PUNCT
ejpam-5251	40	18	g	g	NOUN
ejpam-5251	40	19	)	)	PUNCT
ejpam-5251	40	20	.	.	PUNCT
ejpam-5251	41	1	the	the	DET
ejpam-5251	41	2	minimum	minimum	ADJ
ejpam-5251	41	3	cardinality	cardinality	NOUN
ejpam-5251	41	4	of	of	ADP
ejpam-5251	41	5	a	a	DET
ejpam-5251	41	6	2	2	NUM
ejpam-5251	41	7	-	-	PUNCT
ejpam-5251	41	8	path	path	NOUN
ejpam-5251	41	9	closure	closure	NOUN
ejpam-5251	41	10	absorbing	absorb	VERB
ejpam-5251	41	11	set	set	NOUN
ejpam-5251	41	12	in	in	ADP
ejpam-5251	41	13	g	g	PROPN
ejpam-5251	41	14	is	be	AUX
ejpam-5251	41	15	denoted	denote	VERB
ejpam-5251	41	16	by	by	ADP
ejpam-5251	41	17	ρ2(g	ρ2(g	NOUN
ejpam-5251	41	18	)	)	PUNCT
ejpam-5251	41	19	.	.	PUNCT
ejpam-5251	42	1	a	a	DET
ejpam-5251	42	2	2	2	NUM
ejpam-5251	42	3	-	-	PUNCT
ejpam-5251	42	4	path	path	NOUN
ejpam-5251	42	5	closure	closure	NOUN
ejpam-5251	42	6	absorbing	absorb	VERB
ejpam-5251	42	7	set	set	NOUN
ejpam-5251	42	8	s	s	VERB
ejpam-5251	42	9	is	be	AUX
ejpam-5251	42	10	a	a	DET
ejpam-5251	42	11	minimal	minimal	ADJ
ejpam-5251	42	12	2	2	NUM
ejpam-5251	42	13	-	-	PUNCT
ejpam-5251	42	14	path	path	NOUN
ejpam-5251	42	15	closure	closure	NOUN
ejpam-5251	42	16	absorbing	absorb	VERB
ejpam-5251	42	17	set	set	NOUN
ejpam-5251	42	18	if	if	SCONJ
ejpam-5251	42	19	s	s	PRON
ejpam-5251	42	20	does	do	AUX
ejpam-5251	42	21	not	not	PART
ejpam-5251	42	22	contain	contain	VERB
ejpam-5251	42	23	a	a	DET
ejpam-5251	42	24	proper	proper	ADJ
ejpam-5251	42	25	subset	subset	NOUN
ejpam-5251	42	26	that	that	PRON
ejpam-5251	42	27	is	be	AUX
ejpam-5251	42	28	itself	itself	PRON
ejpam-5251	42	29	a	a	DET
ejpam-5251	42	30	2	2	NUM
ejpam-5251	42	31	-	-	PUNCT
ejpam-5251	42	32	path	path	NOUN
ejpam-5251	42	33	closure	closure	NOUN
ejpam-5251	42	34	absorbing	absorbing	NOUN
ejpam-5251	42	35	.	.	PUNCT
ejpam-5251	43	1	the	the	DET
ejpam-5251	43	2	maximum	maximum	ADJ
ejpam-5251	43	3	cardinality	cardinality	NOUN
ejpam-5251	43	4	of	of	ADP
ejpam-5251	43	5	a	a	DET
ejpam-5251	43	6	minimal	minimal	ADJ
ejpam-5251	43	7	2	2	NUM
ejpam-5251	43	8	-	-	PUNCT
ejpam-5251	43	9	path	path	NOUN
ejpam-5251	43	10	closure	closure	NOUN
ejpam-5251	43	11	absorbing	absorb	VERB
ejpam-5251	43	12	set	set	NOUN
ejpam-5251	43	13	in	in	ADP
ejpam-5251	43	14	g	g	PROPN
ejpam-5251	43	15	is	be	AUX
ejpam-5251	43	16	denoted	denote	VERB
ejpam-5251	43	17	by	by	ADP
ejpam-5251	43	18	ρ+2	ρ+2	PROPN
ejpam-5251	43	19	(	(	PUNCT
ejpam-5251	43	20	g	g	NOUN
ejpam-5251	43	21	)	)	PUNCT
ejpam-5251	43	22	.	.	PUNCT
ejpam-5251	44	1	the	the	DET
ejpam-5251	44	2	concept	concept	NOUN
ejpam-5251	44	3	of	of	ADP
ejpam-5251	44	4	2	2	NUM
ejpam-5251	44	5	-	-	PUNCT
ejpam-5251	44	6	path	path	NOUN
ejpam-5251	44	7	closure	closure	NOUN
ejpam-5251	44	8	absorbing	absorb	VERB
ejpam-5251	44	9	sets	set	NOUN
ejpam-5251	44	10	was	be	AUX
ejpam-5251	44	11	introduce	introduce	ADJ
ejpam-5251	44	12	in	in	ADP
ejpam-5251	44	13	[	[	X
ejpam-5251	44	14	15	15	NUM
ejpam-5251	44	15	,	,	PUNCT
ejpam-5251	44	16	18	18	NUM
ejpam-5251	44	17	,	,	PUNCT
ejpam-5251	44	18	19	19	NUM
ejpam-5251	44	19	]	]	PUNCT
ejpam-5251	44	20	.	.	PUNCT
ejpam-5251	45	1	the	the	DET
ejpam-5251	45	2	(	(	PUNCT
ejpam-5251	45	3	open	open	ADJ
ejpam-5251	45	4	)	)	PUNCT
ejpam-5251	45	5	hop	hop	NOUN
ejpam-5251	45	6	neighborhood	neighborhood	NOUN
ejpam-5251	45	7	of	of	ADP
ejpam-5251	45	8	a	a	DET
ejpam-5251	45	9	vertex	vertex	NOUN
ejpam-5251	45	10	v	v	NOUN
ejpam-5251	45	11	refers	refer	VERB
ejpam-5251	45	12	to	to	ADP
ejpam-5251	45	13	the	the	DET
ejpam-5251	45	14	set	set	ADJ
ejpam-5251	45	15	n2	n2	ADJ
ejpam-5251	45	16	g(v	g(v	PROPN
ejpam-5251	45	17	)	)	PUNCT
ejpam-5251	45	18	=	=	PRON
ejpam-5251	45	19	{	{	PUNCT
ejpam-5251	45	20	u	u	NOUN
ejpam-5251	45	21	∈	∈	PROPN
ejpam-5251	45	22	v	v	NOUN
ejpam-5251	45	23	(	(	PUNCT
ejpam-5251	45	24	g	g	NOUN
ejpam-5251	45	25	)	)	PUNCT
ejpam-5251	45	26	:	:	PUNCT
ejpam-5251	45	27	dg(u	dg(u	X
ejpam-5251	45	28	,	,	PUNCT
ejpam-5251	45	29	v	v	NOUN
ejpam-5251	45	30	)	)	PUNCT
ejpam-5251	45	31	=	=	SYM
ejpam-5251	45	32	2	2	NUM
ejpam-5251	45	33	}	}	PUNCT
ejpam-5251	45	34	.	.	PUNCT
ejpam-5251	46	1	the	the	DET
ejpam-5251	46	2	closed	closed	ADJ
ejpam-5251	46	3	hop	hop	NOUN
ejpam-5251	46	4	neighborhood	neighborhood	NOUN
ejpam-5251	46	5	of	of	ADP
ejpam-5251	46	6	a	a	DET
ejpam-5251	46	7	vertex	vertex	NOUN
ejpam-5251	46	8	v	v	NOUN
ejpam-5251	46	9	is	be	AUX
ejpam-5251	46	10	n2	n2	ADJ
ejpam-5251	46	11	g[v	g[v	NOUN
ejpam-5251	46	12	]	]	X
ejpam-5251	46	13	=	=	SYM
ejpam-5251	46	14	n2	n2	ADJ
ejpam-5251	46	15	g(v	g(v	PROPN
ejpam-5251	46	16	)	)	PUNCT
ejpam-5251	46	17	∪	∪	ADP
ejpam-5251	46	18	{	{	PUNCT
ejpam-5251	46	19	v	v	NOUN
ejpam-5251	46	20	}	}	PUNCT
ejpam-5251	46	21	.	.	PUNCT
ejpam-5251	47	1	for	for	ADP
ejpam-5251	47	2	s	s	PROPN
ejpam-5251	47	3	⊆	⊆	NUM
ejpam-5251	47	4	v	v	NOUN
ejpam-5251	47	5	(	(	PUNCT
ejpam-5251	47	6	g	g	NOUN
ejpam-5251	47	7	)	)	PUNCT
ejpam-5251	47	8	,	,	PUNCT
ejpam-5251	47	9	the	the	DET
ejpam-5251	47	10	(	(	PUNCT
ejpam-5251	47	11	open	open	ADJ
ejpam-5251	47	12	)	)	PUNCT
ejpam-5251	47	13	hop	hop	NOUN
ejpam-5251	47	14	neighborhood	neighborhood	NOUN
ejpam-5251	47	15	s	s	PART
ejpam-5251	47	16	is	be	AUX
ejpam-5251	47	17	the	the	DET
ejpam-5251	47	18	set	set	ADJ
ejpam-5251	47	19	n2	n2	ADJ
ejpam-5251	47	20	g(s	g(s	PROPN
ejpam-5251	47	21	)	)	PUNCT
ejpam-5251	47	22	=	=	SYM
ejpam-5251	47	23	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-5251	47	24	)	)	PUNCT
ejpam-5251	47	25	.	.	PUNCT
ejpam-5251	48	1	the	the	DET
ejpam-5251	48	2	closed	closed	ADJ
ejpam-5251	48	3	hop	hop	NOUN
ejpam-5251	48	4	neighborhood	neighborhood	NOUN
ejpam-5251	48	5	of	of	ADP
ejpam-5251	48	6	the	the	DET
ejpam-5251	48	7	set	set	NOUN
ejpam-5251	48	8	s	s	NOUN
ejpam-5251	48	9	is	be	AUX
ejpam-5251	48	10	n2	n2	ADJ
ejpam-5251	48	11	g[s	g[s	PROPN
ejpam-5251	48	12	]	]	PUNCT
ejpam-5251	48	13	=	=	SYM
ejpam-5251	48	14	n2	n2	ADJ
ejpam-5251	48	15	g(s	g(s	PROPN
ejpam-5251	48	16	)	)	PUNCT
ejpam-5251	48	17	∪	∪	ADP
ejpam-5251	48	18	s.	s.	PROPN
ejpam-5251	48	19	a	a	DET
ejpam-5251	48	20	set	set	NOUN
ejpam-5251	48	21	s	s	PROPN
ejpam-5251	48	22	⊆	⊆	NUM
ejpam-5251	48	23	v	v	NOUN
ejpam-5251	48	24	(	(	PUNCT
ejpam-5251	48	25	g	g	NOUN
ejpam-5251	48	26	)	)	PUNCT
ejpam-5251	48	27	is	be	AUX
ejpam-5251	48	28	called	call	VERB
ejpam-5251	48	29	a	a	DET
ejpam-5251	48	30	hop	hop	NOUN
ejpam-5251	48	31	dominating	dominating	NOUN
ejpam-5251	48	32	set	set	NOUN
ejpam-5251	48	33	if	if	SCONJ
ejpam-5251	48	34	n2	n2	ADJ
ejpam-5251	48	35	g[s	g[s	PROPN
ejpam-5251	48	36	]	]	X
ejpam-5251	48	37	=	=	SYM
ejpam-5251	48	38	v	v	NOUN
ejpam-5251	48	39	(	(	PUNCT
ejpam-5251	48	40	g	g	NOUN
ejpam-5251	48	41	)	)	PUNCT
ejpam-5251	48	42	.	.	PUNCT
ejpam-5251	49	1	the	the	DET
ejpam-5251	49	2	hop	hop	NOUN
ejpam-5251	49	3	domination	domination	NOUN
ejpam-5251	49	4	number	number	NOUN
ejpam-5251	49	5	of	of	ADP
ejpam-5251	49	6	g	g	NOUN
ejpam-5251	49	7	,	,	PUNCT
ejpam-5251	49	8	denoted	denote	VERB
ejpam-5251	49	9	by	by	ADP
ejpam-5251	49	10	γh(g	γh(g	NOUN
ejpam-5251	49	11	)	)	PUNCT
ejpam-5251	49	12	,	,	PUNCT
ejpam-5251	49	13	is	be	AUX
ejpam-5251	49	14	the	the	DET
ejpam-5251	49	15	minimum	minimum	ADJ
ejpam-5251	49	16	cardinality	cardinality	NOUN
ejpam-5251	49	17	among	among	ADP
ejpam-5251	49	18	all	all	DET
ejpam-5251	49	19	hop	hop	NOUN
ejpam-5251	49	20	dominating	dominating	NOUN
ejpam-5251	49	21	sets	set	NOUN
ejpam-5251	49	22	in	in	ADP
ejpam-5251	49	23	g.	g.	PROPN
ejpam-5251	49	24	a	a	DET
ejpam-5251	49	25	hop	hop	NOUN
ejpam-5251	49	26	dominating	dominating	NOUN
ejpam-5251	49	27	set	set	VERB
ejpam-5251	49	28	with	with	ADP
ejpam-5251	49	29	cardinality	cardinality	NOUN
ejpam-5251	49	30	equal	equal	ADJ
ejpam-5251	49	31	to	to	ADP
ejpam-5251	49	32	γh(g	γh(g	NOUN
ejpam-5251	49	33	)	)	PUNCT
ejpam-5251	49	34	is	be	AUX
ejpam-5251	49	35	called	call	VERB
ejpam-5251	49	36	a	a	DET
ejpam-5251	49	37	γh	γh	ADV
ejpam-5251	49	38	-	-	PUNCT
ejpam-5251	49	39	set	set	NOUN
ejpam-5251	49	40	of	of	ADP
ejpam-5251	49	41	g.	g.	PROPN
ejpam-5251	49	42	the	the	DET
ejpam-5251	49	43	authors	author	NOUN
ejpam-5251	49	44	refer	refer	VERB
ejpam-5251	49	45	to	to	ADP
ejpam-5251	49	46	[	[	X
ejpam-5251	49	47	4	4	NUM
ejpam-5251	49	48	,	,	PUNCT
ejpam-5251	49	49	5	5	NUM
ejpam-5251	49	50	,	,	PUNCT
ejpam-5251	49	51	9	9	NUM
ejpam-5251	49	52	,	,	PUNCT
ejpam-5251	49	53	13	13	NUM
ejpam-5251	49	54	,	,	PUNCT
ejpam-5251	49	55	14	14	NUM
ejpam-5251	49	56	,	,	PUNCT
ejpam-5251	49	57	20–25	20–25	NUM
ejpam-5251	49	58	]	]	PUNCT
ejpam-5251	49	59	for	for	ADP
ejpam-5251	49	60	the	the	DET
ejpam-5251	49	61	definitions	definition	NOUN
ejpam-5251	49	62	and	and	CCONJ
ejpam-5251	49	63	results	result	NOUN
ejpam-5251	49	64	on	on	ADP
ejpam-5251	49	65	hop	hop	NOUN
ejpam-5251	49	66	domination	domination	NOUN
ejpam-5251	49	67	which	which	PRON
ejpam-5251	49	68	are	be	AUX
ejpam-5251	49	69	essential	essential	ADJ
ejpam-5251	49	70	in	in	ADP
ejpam-5251	49	71	this	this	DET
ejpam-5251	49	72	study	study	NOUN
ejpam-5251	49	73	.	.	PUNCT
ejpam-5251	50	1	a	a	DET
ejpam-5251	50	2	subset	subset	NOUN
ejpam-5251	50	3	s	s	VERB
ejpam-5251	50	4	⊆	⊆	NUM
ejpam-5251	50	5	v	v	NOUN
ejpam-5251	50	6	(	(	PUNCT
ejpam-5251	50	7	g	g	NOUN
ejpam-5251	50	8	)	)	PUNCT
ejpam-5251	50	9	is	be	AUX
ejpam-5251	50	10	a	a	DET
ejpam-5251	50	11	geodetic	geodetic	ADJ
ejpam-5251	50	12	hop	hop	NOUN
ejpam-5251	50	13	dominating	dominating	NOUN
ejpam-5251	50	14	set	set	NOUN
ejpam-5251	50	15	if	if	SCONJ
ejpam-5251	50	16	s	s	VERB
ejpam-5251	50	17	is	be	AUX
ejpam-5251	50	18	both	both	PRON
ejpam-5251	50	19	a	a	DET
ejpam-5251	50	20	geodetic	geodetic	ADJ
ejpam-5251	50	21	and	and	CCONJ
ejpam-5251	50	22	a	a	DET
ejpam-5251	50	23	hop	hop	NOUN
ejpam-5251	50	24	dominating	dominating	NOUN
ejpam-5251	50	25	set	set	NOUN
ejpam-5251	50	26	of	of	ADP
ejpam-5251	50	27	g.	g.	PROPN
ejpam-5251	50	28	the	the	DET
ejpam-5251	50	29	geodetic	geodetic	ADJ
ejpam-5251	50	30	hop	hop	NOUN
ejpam-5251	50	31	domination	domination	NOUN
ejpam-5251	50	32	number	number	NOUN
ejpam-5251	50	33	γhg(g	γhg(g	PROPN
ejpam-5251	50	34	)	)	PUNCT
ejpam-5251	50	35	of	of	ADP
ejpam-5251	50	36	g	g	PROPN
ejpam-5251	50	37	is	be	AUX
ejpam-5251	50	38	the	the	DET
ejpam-5251	50	39	minimum	minimum	ADJ
ejpam-5251	50	40	cardinality	cardinality	NOUN
ejpam-5251	50	41	among	among	ADP
ejpam-5251	50	42	all	all	DET
ejpam-5251	50	43	geodetic	geodetic	ADJ
ejpam-5251	50	44	hop	hop	NOUN
ejpam-5251	50	45	dominating	dominating	NOUN
ejpam-5251	50	46	sets	set	NOUN
ejpam-5251	50	47	in	in	ADP
ejpam-5251	50	48	g.	g.	PROPN
ejpam-5251	50	49	any	any	DET
ejpam-5251	50	50	geodetic	geodetic	ADJ
ejpam-5251	50	51	hop	hop	NOUN
ejpam-5251	50	52	dominating	dominating	NOUN
ejpam-5251	50	53	set	set	NOUN
ejpam-5251	50	54	of	of	ADP
ejpam-5251	50	55	g	g	PROPN
ejpam-5251	50	56	with	with	ADP
ejpam-5251	50	57	cardinality	cardinality	PROPN
ejpam-5251	50	58	γhg(g	γhg(g	PROPN
ejpam-5251	50	59	)	)	PUNCT
ejpam-5251	50	60	is	be	AUX
ejpam-5251	50	61	called	call	VERB
ejpam-5251	50	62	a	a	DET
ejpam-5251	50	63	γhg	γhg	NOUN
ejpam-5251	50	64	-	-	PUNCT
ejpam-5251	50	65	set	set	NOUN
ejpam-5251	50	66	.	.	PUNCT
ejpam-5251	51	1	d.	d.	PROPN
ejpam-5251	51	2	catian	catian	PROPN
ejpam-5251	51	3	,	,	PUNCT
ejpam-5251	51	4	i.	i.	PROPN
ejpam-5251	51	5	s.	s.	PROPN
ejpam-5251	51	6	aniversario	aniversario	PROPN
ejpam-5251	51	7	,	,	PUNCT
ejpam-5251	51	8	f.	f.	PROPN
ejpam-5251	51	9	p.	p.	PROPN
ejpam-5251	51	10	jamil	jamil	PROPN
ejpam-5251	51	11	/	/	SYM
ejpam-5251	51	12	eur	eur	PROPN
ejpam-5251	51	13	.	.	PUNCT
ejpam-5251	52	1	j.	j.	PROPN
ejpam-5251	52	2	pure	pure	PROPN
ejpam-5251	52	3	appl	appl	PROPN
ejpam-5251	52	4	.	.	PROPN
ejpam-5251	52	5	math	math	PROPN
ejpam-5251	52	6	,	,	PUNCT
ejpam-5251	52	7	17	17	NUM
ejpam-5251	52	8	(	(	PUNCT
ejpam-5251	52	9	3	3	NUM
ejpam-5251	52	10	)	)	PUNCT
ejpam-5251	52	11	(	(	PUNCT
ejpam-5251	52	12	2024	2024	NUM
ejpam-5251	52	13	)	)	PUNCT
ejpam-5251	52	14	,	,	PUNCT
ejpam-5251	52	15	1737	1737	NUM
ejpam-5251	52	16	-	-	SYM
ejpam-5251	52	17	1750	1750	NUM
ejpam-5251	52	18	1739	1739	NUM
ejpam-5251	52	19	2	2	NUM
ejpam-5251	52	20	.	.	PUNCT
ejpam-5251	52	21	main	main	ADJ
ejpam-5251	52	22	results	result	NOUN
ejpam-5251	52	23	2.1	2.1	NUM
ejpam-5251	52	24	.	.	PUNCT
ejpam-5251	53	1	the	the	DET
ejpam-5251	53	2	minimal	minimal	ADJ
ejpam-5251	53	3	geodetic	geodetic	ADJ
ejpam-5251	53	4	hop	hop	NOUN
ejpam-5251	53	5	domination	domination	NOUN
ejpam-5251	53	6	in	in	ADP
ejpam-5251	53	7	graphs	graph	NOUN
ejpam-5251	53	8	let	let	VERB
ejpam-5251	53	9	g	g	PRON
ejpam-5251	53	10	be	be	AUX
ejpam-5251	53	11	a	a	DET
ejpam-5251	53	12	graph	graph	NOUN
ejpam-5251	53	13	.	.	PUNCT
ejpam-5251	54	1	a	a	DET
ejpam-5251	54	2	geodetic	geodetic	ADJ
ejpam-5251	54	3	hop	hop	NOUN
ejpam-5251	54	4	dominating	dominating	NOUN
ejpam-5251	54	5	set	set	NOUN
ejpam-5251	54	6	s	s	VERB
ejpam-5251	54	7	is	be	AUX
ejpam-5251	54	8	a	a	DET
ejpam-5251	54	9	minimal	minimal	ADJ
ejpam-5251	54	10	geodetic	geodetic	ADJ
ejpam-5251	54	11	hop	hop	NOUN
ejpam-5251	54	12	dominating	dominating	NOUN
ejpam-5251	54	13	set	set	NOUN
ejpam-5251	54	14	if	if	SCONJ
ejpam-5251	54	15	s	s	PRON
ejpam-5251	54	16	does	do	AUX
ejpam-5251	54	17	not	not	PART
ejpam-5251	54	18	contain	contain	VERB
ejpam-5251	54	19	a	a	DET
ejpam-5251	54	20	proper	proper	ADJ
ejpam-5251	54	21	subset	subset	NOUN
ejpam-5251	54	22	that	that	PRON
ejpam-5251	54	23	is	be	AUX
ejpam-5251	54	24	itself	itself	PRON
ejpam-5251	54	25	a	a	DET
ejpam-5251	54	26	geodetic	geodetic	ADJ
ejpam-5251	54	27	hop	hop	NOUN
ejpam-5251	54	28	dominating	dominating	NOUN
ejpam-5251	54	29	set	set	NOUN
ejpam-5251	54	30	.	.	PUNCT
ejpam-5251	55	1	the	the	DET
ejpam-5251	55	2	maximum	maximum	ADJ
ejpam-5251	55	3	cardinality	cardinality	NOUN
ejpam-5251	55	4	of	of	ADP
ejpam-5251	55	5	a	a	DET
ejpam-5251	55	6	minimal	minimal	ADJ
ejpam-5251	55	7	geodetic	geodetic	ADJ
ejpam-5251	55	8	hop	hop	NOUN
ejpam-5251	55	9	dominating	dominating	NOUN
ejpam-5251	55	10	set	set	NOUN
ejpam-5251	55	11	of	of	ADP
ejpam-5251	55	12	g	g	PROPN
ejpam-5251	55	13	is	be	AUX
ejpam-5251	55	14	the	the	DET
ejpam-5251	55	15	upper	upper	ADJ
ejpam-5251	55	16	geodetic	geodetic	ADJ
ejpam-5251	55	17	hop	hop	NOUN
ejpam-5251	55	18	domination	domination	NOUN
ejpam-5251	55	19	number	number	NOUN
ejpam-5251	55	20	of	of	ADP
ejpam-5251	55	21	g	g	NOUN
ejpam-5251	55	22	denoted	denote	VERB
ejpam-5251	55	23	by	by	ADP
ejpam-5251	55	24	γ+hg(g	γ+hg(g	PROPN
ejpam-5251	55	25	)	)	PUNCT
ejpam-5251	55	26	.	.	PUNCT
ejpam-5251	56	1	a	a	DET
ejpam-5251	56	2	minimal	minimal	ADJ
ejpam-5251	56	3	geodetic	geodetic	ADJ
ejpam-5251	56	4	hop	hop	NOUN
ejpam-5251	56	5	dominating	dominating	NOUN
ejpam-5251	56	6	set	set	VERB
ejpam-5251	56	7	with	with	ADP
ejpam-5251	56	8	cardinality	cardinality	PROPN
ejpam-5251	56	9	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	56	10	)	)	PUNCT
ejpam-5251	56	11	is	be	AUX
ejpam-5251	56	12	called	call	VERB
ejpam-5251	56	13	a	a	DET
ejpam-5251	56	14	γ+hg	γ+hg	NOUN
ejpam-5251	56	15	-	-	PUNCT
ejpam-5251	56	16	set	set	NOUN
ejpam-5251	56	17	.	.	PUNCT
ejpam-5251	57	1	every	every	DET
ejpam-5251	57	2	dominating	dominating	NOUN
ejpam-5251	57	3	vertex	vertex	NOUN
ejpam-5251	57	4	and	and	CCONJ
ejpam-5251	57	5	every	every	DET
ejpam-5251	57	6	extreme	extreme	ADJ
ejpam-5251	57	7	vertex	vertex	NOUN
ejpam-5251	57	8	in	in	ADP
ejpam-5251	57	9	g	g	PROPN
ejpam-5251	57	10	is	be	AUX
ejpam-5251	57	11	included	include	VERB
ejpam-5251	57	12	in	in	ADP
ejpam-5251	57	13	any	any	DET
ejpam-5251	57	14	minimal	minimal	ADJ
ejpam-5251	57	15	geodetic	geodetic	ADJ
ejpam-5251	57	16	hop	hop	NOUN
ejpam-5251	57	17	dominating	dominating	NOUN
ejpam-5251	57	18	set	set	NOUN
ejpam-5251	57	19	of	of	ADP
ejpam-5251	57	20	g.	g.	PROPN
ejpam-5251	57	21	proposition	proposition	PROPN
ejpam-5251	57	22	1	1	NUM
ejpam-5251	57	23	.	.	PUNCT
ejpam-5251	58	1	let	let	VERB
ejpam-5251	58	2	g	g	PRON
ejpam-5251	58	3	be	be	AUX
ejpam-5251	58	4	a	a	DET
ejpam-5251	58	5	nontrivial	nontrivial	ADJ
ejpam-5251	58	6	connected	connect	VERB
ejpam-5251	58	7	graph	graph	NOUN
ejpam-5251	58	8	of	of	ADP
ejpam-5251	58	9	order	order	NOUN
ejpam-5251	58	10	n.	n.	NOUN
ejpam-5251	58	11	then	then	ADV
ejpam-5251	58	12	2	2	NUM
ejpam-5251	58	13	≤	≤	NUM
ejpam-5251	58	14	γhg(g	γhg(g	PROPN
ejpam-5251	58	15	)	)	PUNCT
ejpam-5251	58	16	≤	≤	NUM
ejpam-5251	58	17	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	58	18	)	)	PUNCT
ejpam-5251	58	19	≤	≤	NOUN
ejpam-5251	58	20	n	n	CCONJ
ejpam-5251	58	21	in	in	ADP
ejpam-5251	58	22	particular	particular	ADJ
ejpam-5251	58	23	,	,	PUNCT
ejpam-5251	58	24	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	58	25	)	)	PUNCT
ejpam-5251	58	26	<	<	X
ejpam-5251	59	1	n	n	PROPN
ejpam-5251	59	2	if	if	SCONJ
ejpam-5251	59	3	g	g	PROPN
ejpam-5251	59	4	does	do	AUX
ejpam-5251	59	5	not	not	PART
ejpam-5251	59	6	have	have	VERB
ejpam-5251	59	7	any	any	DET
ejpam-5251	59	8	dominating	dominating	NOUN
ejpam-5251	59	9	vertex	vertex	NOUN
ejpam-5251	59	10	.	.	PUNCT
ejpam-5251	60	1	proof	proof	NOUN
ejpam-5251	60	2	.	.	PUNCT
ejpam-5251	61	1	since	since	SCONJ
ejpam-5251	61	2	a	a	DET
ejpam-5251	61	3	γhg	γhg	ADV
ejpam-5251	61	4	-	-	PUNCT
ejpam-5251	61	5	set	set	NOUN
ejpam-5251	61	6	is	be	AUX
ejpam-5251	61	7	a	a	DET
ejpam-5251	61	8	minimal	minimal	ADJ
ejpam-5251	61	9	geodetic	geodetic	ADJ
ejpam-5251	61	10	hop	hop	NOUN
ejpam-5251	61	11	dominating	dominating	NOUN
ejpam-5251	61	12	set	set	NOUN
ejpam-5251	61	13	,	,	PUNCT
ejpam-5251	61	14	γhg(g	γhg(g	PROPN
ejpam-5251	61	15	)	)	PUNCT
ejpam-5251	61	16	≤	≤	NUM
ejpam-5251	61	17	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	61	18	)	)	PUNCT
ejpam-5251	61	19	.	.	PUNCT
ejpam-5251	62	1	suppose	suppose	VERB
ejpam-5251	62	2	that	that	SCONJ
ejpam-5251	62	3	γ+hg(g	γ+hg(g	PROPN
ejpam-5251	62	4	)	)	PUNCT
ejpam-5251	62	5	=	=	SYM
ejpam-5251	63	1	n	n	PROPN
ejpam-5251	63	2	and	and	CCONJ
ejpam-5251	63	3	g	g	PROPN
ejpam-5251	63	4	has	have	VERB
ejpam-5251	63	5	no	no	DET
ejpam-5251	63	6	dominating	dominating	NOUN
ejpam-5251	63	7	vertex	vertex	NOUN
ejpam-5251	63	8	.	.	PUNCT
ejpam-5251	64	1	since	since	SCONJ
ejpam-5251	64	2	g	g	PROPN
ejpam-5251	64	3	is	be	AUX
ejpam-5251	64	4	not	not	PART
ejpam-5251	64	5	a	a	DET
ejpam-5251	64	6	complete	complete	ADJ
ejpam-5251	64	7	graph	graph	NOUN
ejpam-5251	64	8	,	,	PUNCT
ejpam-5251	64	9	g	g	PROPN
ejpam-5251	64	10	contains	contain	VERB
ejpam-5251	64	11	a	a	DET
ejpam-5251	64	12	geodesic	geodesic	NOUN
ejpam-5251	64	13	of	of	ADP
ejpam-5251	64	14	the	the	DET
ejpam-5251	64	15	form	form	NOUN
ejpam-5251	64	16	[	[	X
ejpam-5251	64	17	u	u	NOUN
ejpam-5251	64	18	,	,	PUNCT
ejpam-5251	64	19	w	w	PROPN
ejpam-5251	64	20	,	,	PUNCT
ejpam-5251	64	21	v	v	NOUN
ejpam-5251	64	22	]	]	PUNCT
ejpam-5251	64	23	.	.	PUNCT
ejpam-5251	65	1	since	since	SCONJ
ejpam-5251	65	2	w	w	PROPN
ejpam-5251	65	3	∈	∈	PROPN
ejpam-5251	65	4	ig(u	ig(u	NOUN
ejpam-5251	65	5	,	,	PUNCT
ejpam-5251	65	6	v	v	NOUN
ejpam-5251	65	7	)	)	PUNCT
ejpam-5251	65	8	,	,	PUNCT
ejpam-5251	65	9	s	s	NOUN
ejpam-5251	65	10	=	=	SYM
ejpam-5251	65	11	v	v	NOUN
ejpam-5251	65	12	(	(	PUNCT
ejpam-5251	65	13	g)\{w	g)\{w	NOUN
ejpam-5251	65	14	}	}	PUNCT
ejpam-5251	65	15	is	be	AUX
ejpam-5251	65	16	a	a	DET
ejpam-5251	65	17	geodetic	geodetic	ADJ
ejpam-5251	65	18	set	set	NOUN
ejpam-5251	65	19	of	of	ADP
ejpam-5251	65	20	g.	g.	PROPN
ejpam-5251	65	21	since	since	SCONJ
ejpam-5251	65	22	w	w	PROPN
ejpam-5251	65	23	is	be	AUX
ejpam-5251	65	24	a	a	DET
ejpam-5251	65	25	non	non	ADJ
ejpam-5251	65	26	-	-	ADJ
ejpam-5251	65	27	dominating	dominating	ADJ
ejpam-5251	65	28	vertex	vertex	NOUN
ejpam-5251	65	29	,	,	PUNCT
ejpam-5251	65	30	there	there	PRON
ejpam-5251	65	31	exists	exist	VERB
ejpam-5251	65	32	z	z	PROPN
ejpam-5251	65	33	∈	∈	PROPN
ejpam-5251	65	34	v	v	ADP
ejpam-5251	65	35	(	(	PUNCT
ejpam-5251	65	36	g	g	NOUN
ejpam-5251	65	37	)	)	PUNCT
ejpam-5251	65	38	such	such	ADJ
ejpam-5251	65	39	that	that	SCONJ
ejpam-5251	65	40	dg(w	dg(w	NOUN
ejpam-5251	65	41	,	,	PUNCT
ejpam-5251	65	42	z	z	NOUN
ejpam-5251	65	43	)	)	PUNCT
ejpam-5251	65	44	=	=	SYM
ejpam-5251	65	45	2	2	X
ejpam-5251	65	46	.	.	PUNCT
ejpam-5251	65	47	because	because	SCONJ
ejpam-5251	65	48	z	z	PROPN
ejpam-5251	65	49	∈	∈	PROPN
ejpam-5251	65	50	s	s	PROPN
ejpam-5251	65	51	,	,	PUNCT
ejpam-5251	65	52	s	s	PART
ejpam-5251	65	53	is	be	AUX
ejpam-5251	65	54	a	a	DET
ejpam-5251	65	55	hop	hop	NOUN
ejpam-5251	65	56	dominating	dominating	NOUN
ejpam-5251	65	57	set	set	NOUN
ejpam-5251	65	58	of	of	ADP
ejpam-5251	65	59	g.	g.	PROPN
ejpam-5251	65	60	thus	thus	ADV
ejpam-5251	65	61	,	,	PUNCT
ejpam-5251	65	62	s	s	VERB
ejpam-5251	65	63	is	be	AUX
ejpam-5251	65	64	a	a	DET
ejpam-5251	65	65	geodetic	geodetic	ADJ
ejpam-5251	65	66	hop	hop	NOUN
ejpam-5251	65	67	dominating	dominating	NOUN
ejpam-5251	65	68	set	set	NOUN
ejpam-5251	65	69	of	of	ADP
ejpam-5251	65	70	g.	g.	PROPN
ejpam-5251	65	71	since	since	SCONJ
ejpam-5251	65	72	v	v	PROPN
ejpam-5251	65	73	(	(	PUNCT
ejpam-5251	65	74	g	g	NOUN
ejpam-5251	65	75	)	)	PUNCT
ejpam-5251	65	76	is	be	AUX
ejpam-5251	65	77	a	a	DET
ejpam-5251	65	78	minimal	minimal	ADJ
ejpam-5251	65	79	geodetic	geodetic	ADJ
ejpam-5251	65	80	hop	hop	NOUN
ejpam-5251	65	81	dominating	dominating	NOUN
ejpam-5251	65	82	set	set	NOUN
ejpam-5251	65	83	,	,	PUNCT
ejpam-5251	65	84	this	this	PRON
ejpam-5251	65	85	is	be	AUX
ejpam-5251	65	86	impossible	impossible	ADJ
ejpam-5251	65	87	.	.	PUNCT
ejpam-5251	66	1	the	the	DET
ejpam-5251	66	2	contrapositive	contrapositive	NOUN
ejpam-5251	66	3	of	of	ADP
ejpam-5251	66	4	the	the	DET
ejpam-5251	66	5	second	second	ADJ
ejpam-5251	66	6	statement	statement	NOUN
ejpam-5251	66	7	in	in	ADP
ejpam-5251	66	8	proposition	proposition	NOUN
ejpam-5251	66	9	1	1	NUM
ejpam-5251	66	10	gives	give	VERB
ejpam-5251	66	11	the	the	DET
ejpam-5251	66	12	following	following	NOUN
ejpam-5251	66	13	:	:	PUNCT
ejpam-5251	66	14	corollary	corollary	ADJ
ejpam-5251	66	15	1	1	NUM
ejpam-5251	66	16	.	.	PUNCT
ejpam-5251	67	1	if	if	SCONJ
ejpam-5251	67	2	γ+hg(g	γ+hg(g	X
ejpam-5251	67	3	)	)	PUNCT
ejpam-5251	68	1	=	=	SYM
ejpam-5251	68	2	n	n	PROPN
ejpam-5251	68	3	for	for	ADP
ejpam-5251	68	4	a	a	DET
ejpam-5251	68	5	nontrivial	nontrivial	ADJ
ejpam-5251	68	6	connected	connect	VERB
ejpam-5251	68	7	graph	graph	NOUN
ejpam-5251	68	8	,	,	PUNCT
ejpam-5251	68	9	then	then	ADV
ejpam-5251	68	10	g	g	PROPN
ejpam-5251	68	11	contains	contain	VERB
ejpam-5251	68	12	at	at	ADV
ejpam-5251	68	13	least	least	ADV
ejpam-5251	68	14	one	one	NUM
ejpam-5251	68	15	dominating	dominating	NOUN
ejpam-5251	68	16	vertex	vertex	NOUN
ejpam-5251	68	17	.	.	PUNCT
ejpam-5251	69	1	theorem	theorem	NOUN
ejpam-5251	69	2	1	1	NUM
ejpam-5251	69	3	.	.	PUNCT
ejpam-5251	70	1	let	let	VERB
ejpam-5251	70	2	g	g	PRON
ejpam-5251	70	3	be	be	AUX
ejpam-5251	70	4	a	a	DET
ejpam-5251	70	5	nontrivial	nontrivial	ADJ
ejpam-5251	70	6	connected	connect	VERB
ejpam-5251	70	7	graph	graph	NOUN
ejpam-5251	70	8	of	of	ADP
ejpam-5251	70	9	order	order	NOUN
ejpam-5251	70	10	n.	n.	PROPN
ejpam-5251	70	11	then	then	ADV
ejpam-5251	70	12	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	70	13	)	)	PUNCT
ejpam-5251	71	1	=	=	SYM
ejpam-5251	72	1	n	n	NOUN
ejpam-5251	72	2	if	if	SCONJ
ejpam-5251	72	3	and	and	CCONJ
ejpam-5251	72	4	only	only	ADV
ejpam-5251	72	5	if	if	SCONJ
ejpam-5251	72	6	one	one	NUM
ejpam-5251	72	7	of	of	ADP
ejpam-5251	72	8	the	the	DET
ejpam-5251	72	9	following	follow	VERB
ejpam-5251	72	10	holds	hold	VERB
ejpam-5251	72	11	:	:	PUNCT
ejpam-5251	72	12	(	(	PUNCT
ejpam-5251	72	13	i.	i.	NOUN
ejpam-5251	72	14	)	)	PUNCT
ejpam-5251	73	1	g	g	PROPN
ejpam-5251	73	2	=	=	PROPN
ejpam-5251	73	3	kn	kn	PROPN
ejpam-5251	73	4	(	(	PUNCT
ejpam-5251	73	5	ii	ii	PROPN
ejpam-5251	73	6	.	.	PUNCT
ejpam-5251	73	7	)	)	PUNCT
ejpam-5251	74	1	g	g	PROPN
ejpam-5251	74	2	̸=	̸=	PROPN
ejpam-5251	74	3	kn	kn	PROPN
ejpam-5251	74	4	and	and	CCONJ
ejpam-5251	74	5	v	v	NOUN
ejpam-5251	74	6	(	(	PUNCT
ejpam-5251	74	7	g	g	NOUN
ejpam-5251	74	8	)	)	PUNCT
ejpam-5251	74	9	\	\	PART
ejpam-5251	75	1	s	s	PART
ejpam-5251	75	2	induces	induce	VERB
ejpam-5251	75	3	a	a	DET
ejpam-5251	75	4	disconnected	disconnected	ADJ
ejpam-5251	75	5	graph	graph	NOUN
ejpam-5251	75	6	of	of	ADP
ejpam-5251	75	7	complete	complete	ADJ
ejpam-5251	75	8	components	component	NOUN
ejpam-5251	75	9	where	where	SCONJ
ejpam-5251	75	10	s	s	AUX
ejpam-5251	75	11	⊊	⊊	VERB
ejpam-5251	75	12	v	v	NOUN
ejpam-5251	75	13	(	(	PUNCT
ejpam-5251	75	14	g	g	NOUN
ejpam-5251	75	15	)	)	PUNCT
ejpam-5251	75	16	is	be	AUX
ejpam-5251	75	17	the	the	DET
ejpam-5251	75	18	set	set	NOUN
ejpam-5251	75	19	of	of	ADP
ejpam-5251	75	20	all	all	DET
ejpam-5251	75	21	dominating	dominating	NOUN
ejpam-5251	75	22	vertices	vertex	NOUN
ejpam-5251	75	23	of	of	ADP
ejpam-5251	75	24	g.	g.	PROPN
ejpam-5251	75	25	proof	proof	NOUN
ejpam-5251	75	26	.	.	PUNCT
ejpam-5251	76	1	clearly	clearly	ADV
ejpam-5251	76	2	,	,	PUNCT
ejpam-5251	76	3	if	if	SCONJ
ejpam-5251	76	4	g	g	PROPN
ejpam-5251	76	5	=	=	SYM
ejpam-5251	76	6	kn	kn	PROPN
ejpam-5251	76	7	,	,	PUNCT
ejpam-5251	76	8	then	then	ADV
ejpam-5251	76	9	γ+hg(g	γ+hg(g	X
ejpam-5251	76	10	)	)	PUNCT
ejpam-5251	76	11	=	=	SYM
ejpam-5251	76	12	n.	n.	PROPN
ejpam-5251	76	13	suppose	suppose	VERB
ejpam-5251	76	14	g	g	PROPN
ejpam-5251	76	15	̸=	̸=	PROPN
ejpam-5251	76	16	kn	kn	PROPN
ejpam-5251	76	17	with	with	ADP
ejpam-5251	76	18	a	a	DET
ejpam-5251	76	19	nonempty	nonempty	ADJ
ejpam-5251	76	20	set	set	VERB
ejpam-5251	76	21	s	s	NOUN
ejpam-5251	76	22	of	of	ADP
ejpam-5251	76	23	dominating	dominating	NOUN
ejpam-5251	76	24	vertices	vertex	NOUN
ejpam-5251	76	25	of	of	ADP
ejpam-5251	76	26	g	g	PROPN
ejpam-5251	76	27	and	and	CCONJ
ejpam-5251	76	28	each	each	PRON
ejpam-5251	76	29	of	of	ADP
ejpam-5251	76	30	the	the	DET
ejpam-5251	76	31	components	component	NOUN
ejpam-5251	76	32	of	of	ADP
ejpam-5251	76	33	⟨v	⟨v	PROPN
ejpam-5251	76	34	(	(	PUNCT
ejpam-5251	76	35	g	g	NOUN
ejpam-5251	76	36	)	)	PUNCT
ejpam-5251	77	1	\s⟩	\s⟩	PROPN
ejpam-5251	77	2	is	be	AUX
ejpam-5251	77	3	complete	complete	ADJ
ejpam-5251	77	4	.	.	PUNCT
ejpam-5251	78	1	note	note	VERB
ejpam-5251	78	2	first	first	ADV
ejpam-5251	78	3	that	that	PRON
ejpam-5251	78	4	v	v	NOUN
ejpam-5251	78	5	(	(	PUNCT
ejpam-5251	78	6	g	g	NOUN
ejpam-5251	78	7	)	)	PUNCT
ejpam-5251	78	8	is	be	AUX
ejpam-5251	78	9	a	a	DET
ejpam-5251	78	10	geodetic	geodetic	ADJ
ejpam-5251	78	11	hop	hop	NOUN
ejpam-5251	78	12	dominating	dominating	NOUN
ejpam-5251	78	13	set	set	NOUN
ejpam-5251	78	14	of	of	ADP
ejpam-5251	78	15	g.	g.	PROPN
ejpam-5251	78	16	suppose	suppose	VERB
ejpam-5251	78	17	t	t	PROPN
ejpam-5251	78	18	⊆	⊆	NUM
ejpam-5251	78	19	v	v	NOUN
ejpam-5251	78	20	(	(	PUNCT
ejpam-5251	78	21	g	g	NOUN
ejpam-5251	78	22	)	)	PUNCT
ejpam-5251	78	23	is	be	AUX
ejpam-5251	78	24	a	a	DET
ejpam-5251	78	25	geodetic	geodetic	ADJ
ejpam-5251	78	26	hop	hop	NOUN
ejpam-5251	78	27	dominating	dominating	NOUN
ejpam-5251	78	28	set	set	NOUN
ejpam-5251	78	29	of	of	ADP
ejpam-5251	78	30	g.	g.	PROPN
ejpam-5251	78	31	by	by	ADP
ejpam-5251	78	32	the	the	DET
ejpam-5251	78	33	above	above	ADJ
ejpam-5251	78	34	remark	remark	NOUN
ejpam-5251	78	35	,	,	PUNCT
ejpam-5251	78	36	s	s	VERB
ejpam-5251	78	37	⊆	⊆	NUM
ejpam-5251	78	38	t	t	NOUN
ejpam-5251	78	39	.	.	PUNCT
ejpam-5251	79	1	let	let	VERB
ejpam-5251	79	2	c	c	PRON
ejpam-5251	79	3	be	be	AUX
ejpam-5251	79	4	a	a	DET
ejpam-5251	79	5	component	component	NOUN
ejpam-5251	79	6	of	of	ADP
ejpam-5251	79	7	⟨v	⟨v	PROPN
ejpam-5251	79	8	(	(	PUNCT
ejpam-5251	79	9	g	g	NOUN
ejpam-5251	79	10	)	)	PUNCT
ejpam-5251	79	11	\	\	PROPN
ejpam-5251	79	12	s⟩.	s⟩.	PROPN
ejpam-5251	79	13	we	we	PRON
ejpam-5251	79	14	claim	claim	VERB
ejpam-5251	79	15	that	that	SCONJ
ejpam-5251	79	16	v	v	X
ejpam-5251	79	17	(	(	PUNCT
ejpam-5251	79	18	c	c	NOUN
ejpam-5251	79	19	)	)	PUNCT
ejpam-5251	79	20	⊆	⊆	NUM
ejpam-5251	79	21	ext(g	ext(g	NOUN
ejpam-5251	79	22	)	)	PUNCT
ejpam-5251	79	23	.	.	PUNCT
ejpam-5251	80	1	let	let	VERB
ejpam-5251	80	2	x	x	SYM
ejpam-5251	80	3	∈	∈	PROPN
ejpam-5251	80	4	v	v	X
ejpam-5251	80	5	(	(	PUNCT
ejpam-5251	80	6	c	c	NOUN
ejpam-5251	80	7	)	)	PUNCT
ejpam-5251	80	8	,	,	PUNCT
ejpam-5251	80	9	and	and	CCONJ
ejpam-5251	80	10	let	let	VERB
ejpam-5251	80	11	u	u	NOUN
ejpam-5251	80	12	,	,	PUNCT
ejpam-5251	80	13	v	v	PROPN
ejpam-5251	80	14	∈	∈	PROPN
ejpam-5251	80	15	ng(x	ng(x	NUM
ejpam-5251	80	16	)	)	PUNCT
ejpam-5251	80	17	with	with	ADP
ejpam-5251	80	18	u	u	NOUN
ejpam-5251	80	19	̸=	̸=	PROPN
ejpam-5251	80	20	v.	v.	CCONJ
ejpam-5251	80	21	then	then	ADV
ejpam-5251	80	22	u	u	PROPN
ejpam-5251	80	23	,	,	PUNCT
ejpam-5251	80	24	v	v	PROPN
ejpam-5251	80	25	∈	∈	NOUN
ejpam-5251	80	26	s	s	PART
ejpam-5251	80	27	∪	∪	ADJ
ejpam-5251	80	28	v	v	NOUN
ejpam-5251	80	29	(	(	PUNCT
ejpam-5251	80	30	c	c	NOUN
ejpam-5251	80	31	)	)	PUNCT
ejpam-5251	80	32	.	.	PUNCT
ejpam-5251	81	1	if	if	SCONJ
ejpam-5251	81	2	u	u	NOUN
ejpam-5251	81	3	,	,	PUNCT
ejpam-5251	81	4	v	v	PROPN
ejpam-5251	81	5	∈	∈	PROPN
ejpam-5251	81	6	v	v	NOUN
ejpam-5251	81	7	(	(	PUNCT
ejpam-5251	81	8	c	c	NOUN
ejpam-5251	81	9	)	)	PUNCT
ejpam-5251	81	10	,	,	PUNCT
ejpam-5251	81	11	then	then	ADV
ejpam-5251	81	12	since	since	SCONJ
ejpam-5251	81	13	c	c	PROPN
ejpam-5251	81	14	is	be	AUX
ejpam-5251	81	15	complete	complete	ADJ
ejpam-5251	81	16	,	,	PUNCT
ejpam-5251	81	17	uv	uv	PROPN
ejpam-5251	81	18	∈	∈	PROPN
ejpam-5251	81	19	e(g	e(g	PROPN
ejpam-5251	81	20	)	)	PUNCT
ejpam-5251	81	21	.	.	PUNCT
ejpam-5251	82	1	if	if	SCONJ
ejpam-5251	82	2	u	u	PROPN
ejpam-5251	82	3	∈	∈	PROPN
ejpam-5251	82	4	s	s	X
ejpam-5251	82	5	or	or	CCONJ
ejpam-5251	82	6	v	v	ADP
ejpam-5251	82	7	∈	∈	PROPN
ejpam-5251	82	8	s	s	NOUN
ejpam-5251	82	9	,	,	PUNCT
ejpam-5251	82	10	then	then	ADV
ejpam-5251	82	11	uv	uv	PROPN
ejpam-5251	82	12	∈	∈	PROPN
ejpam-5251	82	13	e(g	e(g	PROPN
ejpam-5251	82	14	)	)	PUNCT
ejpam-5251	82	15	.	.	PUNCT
ejpam-5251	83	1	accordingly	accordingly	ADV
ejpam-5251	83	2	,	,	PUNCT
ejpam-5251	83	3	x	x	X
ejpam-5251	83	4	∈	∈	PROPN
ejpam-5251	83	5	ext(g	ext(g	PROPN
ejpam-5251	83	6	)	)	PUNCT
ejpam-5251	83	7	.	.	PUNCT
ejpam-5251	84	1	since	since	SCONJ
ejpam-5251	84	2	x	x	PRON
ejpam-5251	84	3	is	be	AUX
ejpam-5251	84	4	arbitrary	arbitrary	ADJ
ejpam-5251	84	5	,	,	PUNCT
ejpam-5251	84	6	v	v	ADJ
ejpam-5251	84	7	(	(	PUNCT
ejpam-5251	84	8	c	c	NOUN
ejpam-5251	84	9	)	)	PUNCT
ejpam-5251	84	10	⊆	⊆	NUM
ejpam-5251	84	11	ext(g	ext(g	NOUN
ejpam-5251	84	12	)	)	PUNCT
ejpam-5251	84	13	.	.	PUNCT
ejpam-5251	85	1	thus	thus	ADV
ejpam-5251	85	2	,	,	PUNCT
ejpam-5251	85	3	v	v	X
ejpam-5251	85	4	(	(	PUNCT
ejpam-5251	85	5	c	c	NOUN
ejpam-5251	85	6	)	)	PUNCT
ejpam-5251	85	7	⊆	⊆	NUM
ejpam-5251	85	8	t	t	NOUN
ejpam-5251	85	9	.	.	PUNCT
ejpam-5251	86	1	since	since	SCONJ
ejpam-5251	86	2	c	c	PROPN
ejpam-5251	86	3	is	be	AUX
ejpam-5251	86	4	arbitrary	arbitrary	ADJ
ejpam-5251	86	5	,	,	PUNCT
ejpam-5251	86	6	v	v	ADJ
ejpam-5251	86	7	(	(	PUNCT
ejpam-5251	86	8	g	g	NOUN
ejpam-5251	86	9	)	)	PUNCT
ejpam-5251	86	10	\	\	PUNCT
ejpam-5251	86	11	s	s	PART
ejpam-5251	86	12	⊆	⊆	NUM
ejpam-5251	86	13	t	t	NOUN
ejpam-5251	86	14	.	.	PUNCT
ejpam-5251	87	1	therefore	therefore	ADV
ejpam-5251	87	2	,	,	PUNCT
ejpam-5251	87	3	t	t	PROPN
ejpam-5251	87	4	=	=	SYM
ejpam-5251	87	5	v	v	PROPN
ejpam-5251	87	6	(	(	PUNCT
ejpam-5251	87	7	g	g	NOUN
ejpam-5251	87	8	)	)	PUNCT
ejpam-5251	87	9	.	.	PUNCT
ejpam-5251	88	1	this	this	PRON
ejpam-5251	88	2	means	mean	VERB
ejpam-5251	88	3	g	g	NOUN
ejpam-5251	88	4	does	do	AUX
ejpam-5251	88	5	not	not	PART
ejpam-5251	88	6	have	have	VERB
ejpam-5251	88	7	a	a	DET
ejpam-5251	88	8	proper	proper	ADJ
ejpam-5251	88	9	subset	subset	NOUN
ejpam-5251	88	10	that	that	PRON
ejpam-5251	88	11	is	be	AUX
ejpam-5251	88	12	itself	itself	PRON
ejpam-5251	88	13	a	a	DET
ejpam-5251	88	14	geodetic	geodetic	ADJ
ejpam-5251	88	15	hop	hop	NOUN
ejpam-5251	88	16	dominating	dominating	NOUN
ejpam-5251	88	17	set	set	NOUN
ejpam-5251	88	18	.	.	PUNCT
ejpam-5251	89	1	in	in	ADP
ejpam-5251	89	2	other	other	ADJ
ejpam-5251	89	3	words	word	NOUN
ejpam-5251	89	4	,	,	PUNCT
ejpam-5251	89	5	v	v	NOUN
ejpam-5251	89	6	(	(	PUNCT
ejpam-5251	89	7	g	g	NOUN
ejpam-5251	89	8	)	)	PUNCT
ejpam-5251	89	9	is	be	AUX
ejpam-5251	89	10	a	a	DET
ejpam-5251	89	11	minimal	minimal	ADJ
ejpam-5251	89	12	geodetic	geodetic	ADJ
ejpam-5251	89	13	hop	hop	NOUN
ejpam-5251	89	14	dominating	dominating	NOUN
ejpam-5251	89	15	set	set	NOUN
ejpam-5251	89	16	of	of	ADP
ejpam-5251	89	17	g.	g.	PROPN
ejpam-5251	89	18	therefore	therefore	ADV
ejpam-5251	89	19	,	,	PUNCT
ejpam-5251	89	20	γ+hg(g	γ+hg(g	X
ejpam-5251	89	21	)	)	PUNCT
ejpam-5251	90	1	=	=	VERB
ejpam-5251	90	2	n.	n.	NOUN
ejpam-5251	90	3	conversely	conversely	ADV
ejpam-5251	90	4	,	,	PUNCT
ejpam-5251	90	5	suppose	suppose	VERB
ejpam-5251	90	6	γ+hg(g	γ+hg(g	X
ejpam-5251	90	7	)	)	PUNCT
ejpam-5251	90	8	=	=	VERB
ejpam-5251	91	1	n.	n.	NOUN
ejpam-5251	91	2	if	if	SCONJ
ejpam-5251	91	3	g	g	PROPN
ejpam-5251	91	4	=	=	PROPN
ejpam-5251	91	5	kn	kn	PROPN
ejpam-5251	91	6	,	,	PUNCT
ejpam-5251	91	7	then	then	ADV
ejpam-5251	91	8	we	we	PRON
ejpam-5251	91	9	are	be	AUX
ejpam-5251	91	10	done	do	VERB
ejpam-5251	91	11	.	.	PUNCT
ejpam-5251	92	1	now	now	ADV
ejpam-5251	92	2	,	,	PUNCT
ejpam-5251	92	3	suppose	suppose	VERB
ejpam-5251	92	4	g	g	PROPN
ejpam-5251	92	5	̸=	̸=	PROPN
ejpam-5251	92	6	kn	kn	PROPN
ejpam-5251	92	7	.	.	PUNCT
ejpam-5251	93	1	by	by	ADP
ejpam-5251	93	2	corollary	corollary	ADJ
ejpam-5251	93	3	1	1	NUM
ejpam-5251	93	4	,	,	PUNCT
ejpam-5251	93	5	the	the	DET
ejpam-5251	93	6	set	set	NOUN
ejpam-5251	93	7	s	s	PROPN
ejpam-5251	93	8	⊆	⊆	NUM
ejpam-5251	93	9	v	v	NOUN
ejpam-5251	93	10	(	(	PUNCT
ejpam-5251	93	11	g	g	NOUN
ejpam-5251	93	12	)	)	PUNCT
ejpam-5251	93	13	consisting	consist	VERB
ejpam-5251	93	14	of	of	ADP
ejpam-5251	93	15	the	the	DET
ejpam-5251	93	16	dominating	dominating	NOUN
ejpam-5251	93	17	vertices	vertex	NOUN
ejpam-5251	93	18	of	of	ADP
ejpam-5251	93	19	g	g	PROPN
ejpam-5251	93	20	is	be	AUX
ejpam-5251	93	21	nonempty	nonempty	ADJ
ejpam-5251	93	22	.	.	PUNCT
ejpam-5251	94	1	suppose	suppose	VERB
ejpam-5251	94	2	that	that	PRON
ejpam-5251	94	3	⟨v	⟨v	NOUN
ejpam-5251	94	4	(	(	PUNCT
ejpam-5251	94	5	g	g	NOUN
ejpam-5251	94	6	)	)	PUNCT
ejpam-5251	94	7	\	\	PROPN
ejpam-5251	94	8	s⟩	s⟩	NOUN
ejpam-5251	94	9	has	have	VERB
ejpam-5251	94	10	a	a	DET
ejpam-5251	94	11	component	component	NOUN
ejpam-5251	94	12	c	c	NOUN
ejpam-5251	94	13	that	that	PRON
ejpam-5251	94	14	is	be	AUX
ejpam-5251	94	15	not	not	PART
ejpam-5251	94	16	complete	complete	ADJ
ejpam-5251	94	17	.	.	PUNCT
ejpam-5251	95	1	then	then	ADV
ejpam-5251	95	2	c	c	PROPN
ejpam-5251	95	3	contains	contain	VERB
ejpam-5251	95	4	a	a	DET
ejpam-5251	95	5	geodesic	geodesic	NOUN
ejpam-5251	95	6	of	of	ADP
ejpam-5251	95	7	the	the	DET
ejpam-5251	95	8	form	form	NOUN
ejpam-5251	95	9	[	[	X
ejpam-5251	95	10	u	u	NOUN
ejpam-5251	95	11	,	,	PUNCT
ejpam-5251	95	12	w	w	PROPN
ejpam-5251	95	13	,	,	PUNCT
ejpam-5251	95	14	v	v	NOUN
ejpam-5251	95	15	]	]	PUNCT
ejpam-5251	95	16	.	.	PUNCT
ejpam-5251	96	1	we	we	PRON
ejpam-5251	96	2	claim	claim	VERB
ejpam-5251	96	3	that	that	SCONJ
ejpam-5251	96	4	w	w	PROPN
ejpam-5251	96	5	=	=	SYM
ejpam-5251	96	6	v	v	PROPN
ejpam-5251	96	7	(	(	PUNCT
ejpam-5251	96	8	g	g	NOUN
ejpam-5251	96	9	)	)	PUNCT
ejpam-5251	96	10	\	\	NOUN
ejpam-5251	96	11	{	{	PUNCT
ejpam-5251	96	12	w	w	NOUN
ejpam-5251	96	13	}	}	PUNCT
ejpam-5251	96	14	is	be	AUX
ejpam-5251	96	15	a	a	DET
ejpam-5251	96	16	geodetic	geodetic	ADJ
ejpam-5251	96	17	hop	hop	NOUN
ejpam-5251	96	18	dominating	dominating	NOUN
ejpam-5251	96	19	set	set	NOUN
ejpam-5251	96	20	of	of	ADP
ejpam-5251	96	21	g.	g.	PROPN
ejpam-5251	96	22	since	since	SCONJ
ejpam-5251	96	23	d.	d.	PROPN
ejpam-5251	96	24	catian	catian	PROPN
ejpam-5251	96	25	,	,	PUNCT
ejpam-5251	96	26	i.	i.	PROPN
ejpam-5251	96	27	s.	s.	PROPN
ejpam-5251	96	28	aniversario	aniversario	PROPN
ejpam-5251	96	29	,	,	PUNCT
ejpam-5251	96	30	f.	f.	PROPN
ejpam-5251	96	31	p.	p.	PROPN
ejpam-5251	96	32	jamil	jamil	PROPN
ejpam-5251	96	33	/	/	SYM
ejpam-5251	96	34	eur	eur	PROPN
ejpam-5251	96	35	.	.	PUNCT
ejpam-5251	97	1	j.	j.	PROPN
ejpam-5251	97	2	pure	pure	PROPN
ejpam-5251	97	3	appl	appl	PROPN
ejpam-5251	97	4	.	.	PROPN
ejpam-5251	97	5	math	math	PROPN
ejpam-5251	97	6	,	,	PUNCT
ejpam-5251	97	7	17	17	NUM
ejpam-5251	97	8	(	(	PUNCT
ejpam-5251	97	9	3	3	NUM
ejpam-5251	97	10	)	)	PUNCT
ejpam-5251	97	11	(	(	PUNCT
ejpam-5251	97	12	2024	2024	NUM
ejpam-5251	97	13	)	)	PUNCT
ejpam-5251	97	14	,	,	PUNCT
ejpam-5251	97	15	1737	1737	NUM
ejpam-5251	97	16	-	-	SYM
ejpam-5251	97	17	1750	1750	NUM
ejpam-5251	97	18	1740	1740	NUM
ejpam-5251	97	19	w	w	PROPN
ejpam-5251	97	20	∈	∈	PROPN
ejpam-5251	97	21	ig(u	ig(u	NOUN
ejpam-5251	97	22	,	,	PUNCT
ejpam-5251	97	23	v	v	NOUN
ejpam-5251	97	24	)	)	PUNCT
ejpam-5251	97	25	,	,	PUNCT
ejpam-5251	97	26	w	w	PROPN
ejpam-5251	97	27	is	be	AUX
ejpam-5251	97	28	a	a	DET
ejpam-5251	97	29	geodetic	geodetic	ADJ
ejpam-5251	97	30	set	set	NOUN
ejpam-5251	97	31	of	of	ADP
ejpam-5251	97	32	g.	g.	PROPN
ejpam-5251	97	33	since	since	SCONJ
ejpam-5251	97	34	w	w	PROPN
ejpam-5251	97	35	/∈	/∈	PROPN
ejpam-5251	97	36	s	s	PART
ejpam-5251	97	37	,	,	PUNCT
ejpam-5251	97	38	there	there	PRON
ejpam-5251	97	39	exists	exist	VERB
ejpam-5251	97	40	z	z	PROPN
ejpam-5251	97	41	∈	∈	PROPN
ejpam-5251	97	42	v	v	ADP
ejpam-5251	97	43	(	(	PUNCT
ejpam-5251	97	44	g	g	NOUN
ejpam-5251	97	45	)	)	PUNCT
ejpam-5251	97	46	such	such	ADJ
ejpam-5251	97	47	that	that	PRON
ejpam-5251	97	48	wz	wz	VERB
ejpam-5251	97	49	/∈	/∈	PROPN
ejpam-5251	97	50	e(g	e(g	PROPN
ejpam-5251	97	51	)	)	PUNCT
ejpam-5251	97	52	.	.	PUNCT
ejpam-5251	98	1	necessarily	necessarily	ADV
ejpam-5251	98	2	,	,	PUNCT
ejpam-5251	98	3	z	z	PROPN
ejpam-5251	98	4	/∈	/∈	PUNCT
ejpam-5251	98	5	s.	s.	PROPN
ejpam-5251	98	6	pick	pick	PROPN
ejpam-5251	98	7	t	t	PROPN
ejpam-5251	98	8	∈	∈	PROPN
ejpam-5251	98	9	s.	s.	PROPN
ejpam-5251	99	1	then	then	ADV
ejpam-5251	99	2	[	[	X
ejpam-5251	99	3	w	w	PROPN
ejpam-5251	99	4	,	,	PUNCT
ejpam-5251	99	5	t	t	PROPN
ejpam-5251	99	6	,	,	PUNCT
ejpam-5251	99	7	z	z	X
ejpam-5251	99	8	]	]	X
ejpam-5251	99	9	is	be	AUX
ejpam-5251	99	10	a	a	DET
ejpam-5251	99	11	geodesic	geodesic	NOUN
ejpam-5251	99	12	in	in	ADP
ejpam-5251	99	13	g.	g.	PROPN
ejpam-5251	99	14	thus	thus	ADV
ejpam-5251	99	15	,	,	PUNCT
ejpam-5251	99	16	dg(w	dg(w	X
ejpam-5251	99	17	,	,	PUNCT
ejpam-5251	99	18	z	z	NOUN
ejpam-5251	99	19	)	)	PUNCT
ejpam-5251	99	20	=	=	SYM
ejpam-5251	99	21	2	2	X
ejpam-5251	99	22	.	.	PUNCT
ejpam-5251	100	1	this	this	PRON
ejpam-5251	100	2	means	mean	VERB
ejpam-5251	100	3	thatw	thatw	VERB
ejpam-5251	100	4	is	be	AUX
ejpam-5251	100	5	a	a	DET
ejpam-5251	100	6	geodetic	geodetic	ADJ
ejpam-5251	100	7	hop	hop	NOUN
ejpam-5251	100	8	dominating	dominating	NOUN
ejpam-5251	100	9	set	set	NOUN
ejpam-5251	100	10	of	of	ADP
ejpam-5251	100	11	g.	g.	PROPN
ejpam-5251	100	12	consequently	consequently	ADV
ejpam-5251	100	13	,	,	PUNCT
ejpam-5251	100	14	v	v	X
ejpam-5251	100	15	(	(	PUNCT
ejpam-5251	100	16	g	g	NOUN
ejpam-5251	100	17	)	)	PUNCT
ejpam-5251	100	18	is	be	AUX
ejpam-5251	100	19	not	not	PART
ejpam-5251	100	20	a	a	DET
ejpam-5251	100	21	minimal	minimal	ADJ
ejpam-5251	100	22	geodetic	geodetic	ADJ
ejpam-5251	100	23	hop	hop	NOUN
ejpam-5251	100	24	dominating	dominating	NOUN
ejpam-5251	100	25	set	set	NOUN
ejpam-5251	100	26	,	,	PUNCT
ejpam-5251	100	27	implying	imply	VERB
ejpam-5251	100	28	that	that	SCONJ
ejpam-5251	100	29	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	100	30	)	)	PUNCT
ejpam-5251	100	31	<	<	X
ejpam-5251	100	32	n	n	CCONJ
ejpam-5251	100	33	,	,	PUNCT
ejpam-5251	100	34	a	a	DET
ejpam-5251	100	35	contradiction	contradiction	NOUN
ejpam-5251	100	36	.	.	PUNCT
ejpam-5251	101	1	therefore	therefore	ADV
ejpam-5251	101	2	,	,	PUNCT
ejpam-5251	101	3	c	c	PROPN
ejpam-5251	101	4	is	be	AUX
ejpam-5251	101	5	complete	complete	ADJ
ejpam-5251	101	6	.	.	PUNCT
ejpam-5251	102	1	finally	finally	ADV
ejpam-5251	102	2	,	,	PUNCT
ejpam-5251	102	3	suppose	suppose	VERB
ejpam-5251	102	4	⟨v	⟨v	AUX
ejpam-5251	102	5	(	(	PUNCT
ejpam-5251	102	6	g	g	NOUN
ejpam-5251	102	7	)	)	PUNCT
ejpam-5251	102	8	\	\	NOUN
ejpam-5251	102	9	s⟩	s⟩	NOUN
ejpam-5251	103	1	=	=	SYM
ejpam-5251	103	2	c	c	NOUN
ejpam-5251	103	3	,	,	PUNCT
ejpam-5251	103	4	and	and	CCONJ
ejpam-5251	103	5	let	let	VERB
ejpam-5251	103	6	u	u	PRON
ejpam-5251	103	7	∈	∈	PROPN
ejpam-5251	103	8	v	v	X
ejpam-5251	103	9	(	(	PUNCT
ejpam-5251	103	10	c	c	NOUN
ejpam-5251	103	11	)	)	PUNCT
ejpam-5251	103	12	.	.	PUNCT
ejpam-5251	104	1	then	then	ADV
ejpam-5251	104	2	uv	uv	PROPN
ejpam-5251	104	3	∈	∈	PROPN
ejpam-5251	104	4	e(g	e(g	PROPN
ejpam-5251	104	5	)	)	PUNCT
ejpam-5251	105	1	for	for	ADP
ejpam-5251	105	2	each	each	DET
ejpam-5251	105	3	v	v	NUM
ejpam-5251	105	4	∈	∈	PROPN
ejpam-5251	105	5	v	v	NOUN
ejpam-5251	105	6	(	(	PUNCT
ejpam-5251	105	7	g	g	NOUN
ejpam-5251	105	8	)	)	PUNCT
ejpam-5251	105	9	\	\	PART
ejpam-5251	106	1	s	s	PART
ejpam-5251	106	2	=	=	SYM
ejpam-5251	106	3	v	v	NOUN
ejpam-5251	106	4	(	(	PUNCT
ejpam-5251	106	5	c	c	NOUN
ejpam-5251	106	6	)	)	PUNCT
ejpam-5251	106	7	with	with	ADP
ejpam-5251	106	8	u	u	NOUN
ejpam-5251	106	9	̸=	̸=	PROPN
ejpam-5251	106	10	v.	v.	CCONJ
ejpam-5251	106	11	also	also	ADV
ejpam-5251	106	12	,	,	PUNCT
ejpam-5251	106	13	uv	uv	PROPN
ejpam-5251	106	14	∈	∈	PROPN
ejpam-5251	106	15	e(g	e(g	PROPN
ejpam-5251	106	16	)	)	PUNCT
ejpam-5251	106	17	for	for	ADP
ejpam-5251	106	18	each	each	DET
ejpam-5251	106	19	(	(	PUNCT
ejpam-5251	106	20	dominating	dominating	NOUN
ejpam-5251	106	21	)	)	PUNCT
ejpam-5251	106	22	vertex	vertex	NOUN
ejpam-5251	106	23	v	v	ADP
ejpam-5251	106	24	∈	∈	NOUN
ejpam-5251	106	25	s.	s.	PROPN
ejpam-5251	106	26	hence	hence	ADV
ejpam-5251	106	27	,	,	PUNCT
ejpam-5251	106	28	u	u	PROPN
ejpam-5251	106	29	is	be	AUX
ejpam-5251	106	30	a	a	DET
ejpam-5251	106	31	dominating	dominating	NOUN
ejpam-5251	106	32	vertex	vertex	NOUN
ejpam-5251	106	33	of	of	ADP
ejpam-5251	106	34	g	g	PROPN
ejpam-5251	106	35	,	,	PUNCT
ejpam-5251	106	36	a	a	DET
ejpam-5251	106	37	contradiction	contradiction	NOUN
ejpam-5251	106	38	.	.	PUNCT
ejpam-5251	107	1	therefore	therefore	ADV
ejpam-5251	107	2	,	,	PUNCT
ejpam-5251	107	3	⟨v	⟨v	X
ejpam-5251	107	4	(	(	PUNCT
ejpam-5251	107	5	g	g	NOUN
ejpam-5251	107	6	)	)	PUNCT
ejpam-5251	107	7	\	\	PROPN
ejpam-5251	107	8	s⟩	s⟩	NOUN
ejpam-5251	107	9	is	be	AUX
ejpam-5251	107	10	a	a	DET
ejpam-5251	107	11	disconnected	disconnected	ADJ
ejpam-5251	107	12	graph	graph	NOUN
ejpam-5251	107	13	of	of	ADP
ejpam-5251	107	14	at	at	ADV
ejpam-5251	107	15	least	least	ADV
ejpam-5251	107	16	two	two	NUM
ejpam-5251	107	17	complete	complete	ADJ
ejpam-5251	107	18	components	component	NOUN
ejpam-5251	107	19	.	.	PUNCT
ejpam-5251	108	1	theorem	theorem	NOUN
ejpam-5251	108	2	2	2	NUM
ejpam-5251	108	3	.	.	PUNCT
ejpam-5251	109	1	let	let	VERB
ejpam-5251	109	2	g	g	PRON
ejpam-5251	109	3	be	be	AUX
ejpam-5251	109	4	a	a	DET
ejpam-5251	109	5	nontrivial	nontrivial	ADJ
ejpam-5251	109	6	graph	graph	NOUN
ejpam-5251	109	7	connected	connected	ADJ
ejpam-5251	109	8	graph	graph	NOUN
ejpam-5251	109	9	.	.	PUNCT
ejpam-5251	110	1	then	then	ADV
ejpam-5251	110	2	γ+hg(g	γ+hg(g	X
ejpam-5251	110	3	)	)	PUNCT
ejpam-5251	110	4	=	=	SYM
ejpam-5251	110	5	2	2	NUM
ejpam-5251	110	6	if	if	SCONJ
ejpam-5251	110	7	and	and	CCONJ
ejpam-5251	110	8	only	only	ADV
ejpam-5251	110	9	if	if	SCONJ
ejpam-5251	110	10	g	g	PROPN
ejpam-5251	110	11	satisfies	satisfy	VERB
ejpam-5251	110	12	the	the	DET
ejpam-5251	110	13	following	follow	VERB
ejpam-5251	110	14	graphs	graph	NOUN
ejpam-5251	110	15	:	:	PUNCT
ejpam-5251	110	16	(	(	PUNCT
ejpam-5251	110	17	i	i	NOUN
ejpam-5251	110	18	)	)	PUNCT
ejpam-5251	110	19	g	g	NOUN
ejpam-5251	110	20	=	=	NOUN
ejpam-5251	110	21	p2	p2	X
ejpam-5251	110	22	;	;	PUNCT
ejpam-5251	110	23	(	(	PUNCT
ejpam-5251	110	24	ii	ii	NOUN
ejpam-5251	110	25	)	)	PUNCT
ejpam-5251	110	26	g	g	PROPN
ejpam-5251	110	27	=	=	SYM
ejpam-5251	110	28	c6	c6	PROPN
ejpam-5251	110	29	;	;	PUNCT
ejpam-5251	110	30	(	(	PUNCT
ejpam-5251	110	31	iii	iii	X
ejpam-5251	110	32	)	)	PUNCT
ejpam-5251	110	33	g	g	NOUN
ejpam-5251	110	34	has	have	VERB
ejpam-5251	110	35	a	a	DET
ejpam-5251	110	36	geodetic	geodetic	ADJ
ejpam-5251	110	37	set	set	NOUN
ejpam-5251	110	38	s	s	PART
ejpam-5251	110	39	=	=	PUNCT
ejpam-5251	110	40	{	{	PUNCT
ejpam-5251	110	41	u	u	NOUN
ejpam-5251	110	42	,	,	PUNCT
ejpam-5251	110	43	v	v	NOUN
ejpam-5251	110	44	}	}	PUNCT
ejpam-5251	110	45	such	such	ADJ
ejpam-5251	110	46	that	that	SCONJ
ejpam-5251	110	47	dg(u	dg(u	ADJ
ejpam-5251	110	48	,	,	PUNCT
ejpam-5251	110	49	v	v	NOUN
ejpam-5251	110	50	)	)	PUNCT
ejpam-5251	110	51	=	=	SYM
ejpam-5251	110	52	3	3	NUM
ejpam-5251	110	53	and	and	CCONJ
ejpam-5251	110	54	u	u	NOUN
ejpam-5251	110	55	,	,	PUNCT
ejpam-5251	110	56	v	v	ADP
ejpam-5251	110	57	∈	∈	PROPN
ejpam-5251	110	58	ext(g	ext(g	PROPN
ejpam-5251	110	59	)	)	PUNCT
ejpam-5251	110	60	.	.	PUNCT
ejpam-5251	111	1	proof	proof	NOUN
ejpam-5251	111	2	.	.	PUNCT
ejpam-5251	112	1	it	it	PRON
ejpam-5251	112	2	is	be	AUX
ejpam-5251	112	3	easy	easy	ADJ
ejpam-5251	112	4	to	to	PART
ejpam-5251	112	5	verify	verify	VERB
ejpam-5251	112	6	that	that	SCONJ
ejpam-5251	112	7	if	if	SCONJ
ejpam-5251	112	8	g	g	PROPN
ejpam-5251	112	9	=	=	NOUN
ejpam-5251	112	10	p2	p2	PROPN
ejpam-5251	112	11	or	or	CCONJ
ejpam-5251	112	12	g	g	PROPN
ejpam-5251	112	13	=	=	PROPN
ejpam-5251	112	14	c6	c6	PROPN
ejpam-5251	112	15	,	,	PUNCT
ejpam-5251	112	16	then	then	ADV
ejpam-5251	112	17	γ+hg(g	γ+hg(g	X
ejpam-5251	112	18	)	)	PUNCT
ejpam-5251	112	19	=	=	SYM
ejpam-5251	112	20	2	2	X
ejpam-5251	112	21	.	.	PUNCT
ejpam-5251	112	22	suppose	suppose	VERB
ejpam-5251	112	23	that	that	SCONJ
ejpam-5251	112	24	g	g	PROPN
ejpam-5251	112	25	satisfies	satisfy	VERB
ejpam-5251	112	26	condition	condition	NOUN
ejpam-5251	112	27	(	(	PUNCT
ejpam-5251	112	28	iii	iii	NOUN
ejpam-5251	112	29	)	)	PUNCT
ejpam-5251	112	30	.	.	PUNCT
ejpam-5251	113	1	let	let	VERB
ejpam-5251	113	2	w	w	NOUN
ejpam-5251	113	3	∈	∈	PROPN
ejpam-5251	113	4	v	v	ADP
ejpam-5251	113	5	(	(	PUNCT
ejpam-5251	113	6	g	g	NOUN
ejpam-5251	113	7	)	)	PUNCT
ejpam-5251	113	8	\	\	PUNCT
ejpam-5251	114	1	s.	s.	PROPN
ejpam-5251	114	2	then	then	ADV
ejpam-5251	114	3	w	w	PROPN
ejpam-5251	114	4	lies	lie	NOUN
ejpam-5251	114	5	on	on	ADP
ejpam-5251	114	6	a	a	DET
ejpam-5251	114	7	u	u	NOUN
ejpam-5251	114	8	-	-	NOUN
ejpam-5251	114	9	v	v	ADJ
ejpam-5251	114	10	geodesic	geodesic	NOUN
ejpam-5251	114	11	.	.	PUNCT
ejpam-5251	115	1	thus	thus	ADV
ejpam-5251	115	2	,	,	PUNCT
ejpam-5251	115	3	either	either	CCONJ
ejpam-5251	115	4	dg(u	dg(u	NUM
ejpam-5251	115	5	,	,	PUNCT
ejpam-5251	115	6	w	w	NOUN
ejpam-5251	115	7	)	)	PUNCT
ejpam-5251	115	8	=	=	SYM
ejpam-5251	115	9	2	2	NUM
ejpam-5251	115	10	or	or	CCONJ
ejpam-5251	115	11	dg(w	dg(w	NOUN
ejpam-5251	115	12	,	,	PUNCT
ejpam-5251	115	13	v	v	NOUN
ejpam-5251	115	14	)	)	PUNCT
ejpam-5251	115	15	=	=	SYM
ejpam-5251	116	1	2	2	X
ejpam-5251	116	2	.	.	PUNCT
ejpam-5251	116	3	since	since	SCONJ
ejpam-5251	116	4	w	w	NOUN
ejpam-5251	116	5	is	be	AUX
ejpam-5251	116	6	arbitrary	arbitrary	ADJ
ejpam-5251	116	7	,	,	PUNCT
ejpam-5251	116	8	s	s	PART
ejpam-5251	116	9	is	be	AUX
ejpam-5251	116	10	a	a	DET
ejpam-5251	116	11	hop	hop	NOUN
ejpam-5251	116	12	dominating	dominating	NOUN
ejpam-5251	116	13	set	set	NOUN
ejpam-5251	116	14	of	of	ADP
ejpam-5251	116	15	g.	g.	PROPN
ejpam-5251	116	16	therefore	therefore	ADV
ejpam-5251	116	17	,	,	PUNCT
ejpam-5251	116	18	s	s	VERB
ejpam-5251	116	19	is	be	AUX
ejpam-5251	116	20	a	a	DET
ejpam-5251	116	21	(	(	PUNCT
ejpam-5251	116	22	minimal	minimal	ADJ
ejpam-5251	116	23	)	)	PUNCT
ejpam-5251	116	24	geodetic	geodetic	ADJ
ejpam-5251	116	25	hop	hop	NOUN
ejpam-5251	116	26	dominating	dominating	NOUN
ejpam-5251	116	27	set	set	NOUN
ejpam-5251	116	28	of	of	ADP
ejpam-5251	116	29	g.	g.	PROPN
ejpam-5251	116	30	now	now	ADV
ejpam-5251	116	31	,	,	PUNCT
ejpam-5251	116	32	s	s	VERB
ejpam-5251	116	33	⊆	⊆	NUM
ejpam-5251	116	34	t	t	NOUN
ejpam-5251	116	35	for	for	ADP
ejpam-5251	116	36	every	every	DET
ejpam-5251	116	37	geodetic	geodetic	ADJ
ejpam-5251	116	38	hop	hop	NOUN
ejpam-5251	116	39	dominating	dominating	NOUN
ejpam-5251	116	40	set	set	VERB
ejpam-5251	116	41	t	t	PROPN
ejpam-5251	116	42	of	of	ADP
ejpam-5251	116	43	g.	g.	PROPN
ejpam-5251	116	44	hence	hence	ADV
ejpam-5251	116	45	,	,	PUNCT
ejpam-5251	116	46	s	s	VERB
ejpam-5251	116	47	is	be	AUX
ejpam-5251	116	48	a	a	DET
ejpam-5251	116	49	γ+hg	γ+hg	NOUN
ejpam-5251	116	50	-	-	PUNCT
ejpam-5251	116	51	set	set	NOUN
ejpam-5251	116	52	of	of	ADP
ejpam-5251	116	53	g.	g.	PROPN
ejpam-5251	116	54	therefore	therefore	ADV
ejpam-5251	116	55	,	,	PUNCT
ejpam-5251	116	56	γ+hg(g	γ+hg(g	X
ejpam-5251	116	57	)	)	PUNCT
ejpam-5251	116	58	=	=	SYM
ejpam-5251	117	1	2	2	X
ejpam-5251	117	2	.	.	X
ejpam-5251	117	3	conversely	conversely	ADV
ejpam-5251	117	4	,	,	PUNCT
ejpam-5251	117	5	assume	assume	VERB
ejpam-5251	117	6	γ+hg(g	γ+hg(g	X
ejpam-5251	117	7	)	)	PUNCT
ejpam-5251	117	8	=	=	SYM
ejpam-5251	118	1	2	2	X
ejpam-5251	118	2	.	.	PUNCT
ejpam-5251	118	3	suppose	suppose	VERB
ejpam-5251	118	4	that	that	SCONJ
ejpam-5251	118	5	g	g	PROPN
ejpam-5251	118	6	/∈	/∈	PUNCT
ejpam-5251	118	7	{	{	PUNCT
ejpam-5251	118	8	p2	p2	PROPN
ejpam-5251	118	9	,	,	PUNCT
ejpam-5251	118	10	c6	c6	PROPN
ejpam-5251	118	11	}	}	PUNCT
ejpam-5251	118	12	.	.	PUNCT
ejpam-5251	119	1	let	let	VERB
ejpam-5251	119	2	s	s	PRON
ejpam-5251	119	3	=	=	PUNCT
ejpam-5251	119	4	{	{	PUNCT
ejpam-5251	119	5	u	u	NOUN
ejpam-5251	119	6	,	,	PUNCT
ejpam-5251	119	7	v	v	NOUN
ejpam-5251	119	8	}	}	PUNCT
ejpam-5251	119	9	be	be	AUX
ejpam-5251	119	10	a	a	DET
ejpam-5251	119	11	γ+hg	γ+hg	NOUN
ejpam-5251	119	12	-	-	PUNCT
ejpam-5251	119	13	set	set	NOUN
ejpam-5251	119	14	of	of	ADP
ejpam-5251	119	15	g.	g.	PROPN
ejpam-5251	119	16	since	since	SCONJ
ejpam-5251	119	17	g	g	PROPN
ejpam-5251	119	18	̸=	̸=	PROPN
ejpam-5251	119	19	p2	p2	NOUN
ejpam-5251	119	20	,	,	PUNCT
ejpam-5251	119	21	uv	uv	NOUN
ejpam-5251	119	22	/∈	/∈	PUNCT
ejpam-5251	119	23	e(g	e(g	PROPN
ejpam-5251	119	24	)	)	PUNCT
ejpam-5251	119	25	.	.	PUNCT
ejpam-5251	120	1	for	for	ADP
ejpam-5251	120	2	each	each	PRON
ejpam-5251	120	3	a	a	DET
ejpam-5251	120	4	∈	∈	PROPN
ejpam-5251	120	5	v	v	NOUN
ejpam-5251	120	6	(	(	PUNCT
ejpam-5251	120	7	g	g	NOUN
ejpam-5251	120	8	)	)	PUNCT
ejpam-5251	120	9	\	\	PROPN
ejpam-5251	120	10	s	s	X
ejpam-5251	120	11	,	,	PUNCT
ejpam-5251	120	12	a	a	DET
ejpam-5251	120	13	lies	lie	NOUN
ejpam-5251	120	14	on	on	ADP
ejpam-5251	120	15	a	a	DET
ejpam-5251	120	16	u	u	NOUN
ejpam-5251	120	17	-	-	NOUN
ejpam-5251	120	18	v	v	ADJ
ejpam-5251	120	19	geodesic	geodesic	NOUN
ejpam-5251	120	20	.	.	PUNCT
ejpam-5251	121	1	choose	choose	VERB
ejpam-5251	121	2	a	a	DET
ejpam-5251	121	3	∈	∈	PROPN
ejpam-5251	121	4	v	v	NOUN
ejpam-5251	121	5	(	(	PUNCT
ejpam-5251	121	6	g	g	NOUN
ejpam-5251	121	7	)	)	PUNCT
ejpam-5251	121	8	\	\	PUNCT
ejpam-5251	122	1	s	s	VERB
ejpam-5251	122	2	such	such	ADJ
ejpam-5251	122	3	that	that	SCONJ
ejpam-5251	122	4	ua	ua	PROPN
ejpam-5251	122	5	∈	∈	PROPN
ejpam-5251	122	6	e(g	e(g	PROPN
ejpam-5251	122	7	)	)	PUNCT
ejpam-5251	122	8	.	.	PUNCT
ejpam-5251	123	1	since	since	SCONJ
ejpam-5251	123	2	s	s	PROPN
ejpam-5251	123	3	is	be	AUX
ejpam-5251	123	4	a	a	DET
ejpam-5251	123	5	hop	hop	NOUN
ejpam-5251	123	6	dominating	dominating	NOUN
ejpam-5251	123	7	set	set	NOUN
ejpam-5251	123	8	of	of	ADP
ejpam-5251	123	9	g	g	NOUN
ejpam-5251	123	10	,	,	PUNCT
ejpam-5251	123	11	dg(a	dg(a	X
ejpam-5251	123	12	,	,	PUNCT
ejpam-5251	123	13	v	v	NOUN
ejpam-5251	123	14	)	)	PUNCT
ejpam-5251	123	15	=	=	SYM
ejpam-5251	123	16	2	2	X
ejpam-5251	123	17	.	.	X
ejpam-5251	123	18	necessarily	necessarily	ADV
ejpam-5251	123	19	,	,	PUNCT
ejpam-5251	123	20	dg(u	dg(u	X
ejpam-5251	123	21	,	,	PUNCT
ejpam-5251	123	22	v	v	NOUN
ejpam-5251	123	23	)	)	PUNCT
ejpam-5251	123	24	=	=	SYM
ejpam-5251	124	1	3	3	X
ejpam-5251	124	2	.	.	PUNCT
ejpam-5251	124	3	suppose	suppose	VERB
ejpam-5251	124	4	that	that	SCONJ
ejpam-5251	124	5	u	u	PROPN
ejpam-5251	124	6	/∈	/∈	PUNCT
ejpam-5251	124	7	ext(g	ext(g	PROPN
ejpam-5251	124	8	)	)	PUNCT
ejpam-5251	124	9	.	.	PUNCT
ejpam-5251	125	1	then	then	ADV
ejpam-5251	125	2	g	g	PROPN
ejpam-5251	125	3	contains	contain	VERB
ejpam-5251	125	4	a	a	DET
ejpam-5251	125	5	geodesic	geodesic	NOUN
ejpam-5251	125	6	[	[	X
ejpam-5251	125	7	x	x	X
ejpam-5251	125	8	,	,	PUNCT
ejpam-5251	125	9	u	u	NOUN
ejpam-5251	125	10	,	,	PUNCT
ejpam-5251	125	11	y	y	PROPN
ejpam-5251	125	12	]	]	PUNCT
ejpam-5251	125	13	containing	contain	VERB
ejpam-5251	125	14	u.	u.	NOUN
ejpam-5251	125	15	let	let	VERB
ejpam-5251	125	16	[	[	X
ejpam-5251	125	17	u	u	NOUN
ejpam-5251	125	18	,	,	PUNCT
ejpam-5251	125	19	y	y	PROPN
ejpam-5251	125	20	,	,	PUNCT
ejpam-5251	125	21	z	z	PROPN
ejpam-5251	125	22	,	,	PUNCT
ejpam-5251	125	23	v	v	PART
ejpam-5251	125	24	]	]	PUNCT
ejpam-5251	125	25	be	be	AUX
ejpam-5251	125	26	a	a	DET
ejpam-5251	125	27	u	u	NOUN
ejpam-5251	125	28	-	-	NOUN
ejpam-5251	125	29	v	v	ADJ
ejpam-5251	125	30	geodesic	geodesic	NOUN
ejpam-5251	125	31	containing	contain	VERB
ejpam-5251	125	32	y.	y.	NOUN
ejpam-5251	125	33	we	we	PRON
ejpam-5251	125	34	consider	consider	VERB
ejpam-5251	125	35	two	two	NUM
ejpam-5251	125	36	cases	case	NOUN
ejpam-5251	125	37	:	:	PUNCT
ejpam-5251	125	38	case	case	NOUN
ejpam-5251	125	39	1	1	NUM
ejpam-5251	125	40	:	:	PUNCT
ejpam-5251	125	41	suppose	suppose	VERB
ejpam-5251	125	42	degg(u	degg(u	NUM
ejpam-5251	125	43	)	)	PUNCT
ejpam-5251	125	44	≥	≥	NOUN
ejpam-5251	125	45	3	3	NUM
ejpam-5251	125	46	,	,	PUNCT
ejpam-5251	125	47	and	and	CCONJ
ejpam-5251	125	48	let	let	VERB
ejpam-5251	125	49	w	w	PROPN
ejpam-5251	125	50	∈	∈	PROPN
ejpam-5251	125	51	ng(u	ng(u	NOUN
ejpam-5251	125	52	)	)	PUNCT
ejpam-5251	125	53	\	\	NOUN
ejpam-5251	125	54	{	{	PUNCT
ejpam-5251	125	55	x	x	NOUN
ejpam-5251	125	56	,	,	PUNCT
ejpam-5251	125	57	y	y	PROPN
ejpam-5251	125	58	}	}	PUNCT
ejpam-5251	125	59	.	.	PUNCT
ejpam-5251	126	1	if	if	SCONJ
ejpam-5251	126	2	xz	xz	PROPN
ejpam-5251	126	3	∈	∈	PROPN
ejpam-5251	126	4	e(g	e(g	PROPN
ejpam-5251	126	5	)	)	PUNCT
ejpam-5251	126	6	,	,	PUNCT
ejpam-5251	126	7	then	then	ADV
ejpam-5251	126	8	a	a	DET
ejpam-5251	126	9	minimal	minimal	ADJ
ejpam-5251	126	10	geodetic	geodetic	ADJ
ejpam-5251	126	11	hop	hop	NOUN
ejpam-5251	126	12	dominating	dominating	NOUN
ejpam-5251	126	13	set	set	VERB
ejpam-5251	126	14	t	t	PROPN
ejpam-5251	126	15	of	of	ADP
ejpam-5251	126	16	g	g	PROPN
ejpam-5251	126	17	can	can	AUX
ejpam-5251	126	18	be	be	AUX
ejpam-5251	126	19	constructed	construct	VERB
ejpam-5251	126	20	containing	contain	VERB
ejpam-5251	126	21	x	x	PROPN
ejpam-5251	126	22	,	,	PUNCT
ejpam-5251	126	23	y	y	PROPN
ejpam-5251	126	24	,	,	PUNCT
ejpam-5251	126	25	z.	z.	PROPN
ejpam-5251	126	26	clearly	clearly	ADV
ejpam-5251	126	27	,	,	PUNCT
ejpam-5251	126	28	in	in	ADP
ejpam-5251	126	29	this	this	DET
ejpam-5251	126	30	case	case	NOUN
ejpam-5251	126	31	,	,	PUNCT
ejpam-5251	126	32	|t	|t	VERB
ejpam-5251	126	33	|	|	ADV
ejpam-5251	126	34	≥	≥	NOUN
ejpam-5251	126	35	3	3	NUM
ejpam-5251	126	36	.	.	PUNCT
ejpam-5251	127	1	on	on	ADP
ejpam-5251	127	2	the	the	DET
ejpam-5251	127	3	other	other	ADJ
ejpam-5251	127	4	hand	hand	NOUN
ejpam-5251	127	5	,	,	PUNCT
ejpam-5251	127	6	if	if	SCONJ
ejpam-5251	127	7	xz	xz	PROPN
ejpam-5251	127	8	/∈	/∈	PUNCT
ejpam-5251	127	9	e(g	e(g	PROPN
ejpam-5251	127	10	)	)	PUNCT
ejpam-5251	127	11	,	,	PUNCT
ejpam-5251	127	12	a	a	DET
ejpam-5251	127	13	minimal	minimal	ADJ
ejpam-5251	127	14	geodetic	geodetic	ADJ
ejpam-5251	127	15	hop	hop	NOUN
ejpam-5251	127	16	dominating	dominating	NOUN
ejpam-5251	127	17	set	set	NOUN
ejpam-5251	127	18	t	t	PROPN
ejpam-5251	127	19	can	can	AUX
ejpam-5251	127	20	be	be	AUX
ejpam-5251	127	21	constructed	construct	VERB
ejpam-5251	127	22	containing	contain	VERB
ejpam-5251	127	23	x	x	PROPN
ejpam-5251	127	24	,	,	PUNCT
ejpam-5251	127	25	z.	z.	PROPN
ejpam-5251	127	26	since	since	SCONJ
ejpam-5251	127	27	w	w	PROPN
ejpam-5251	127	28	/∈	/∈	PUNCT
ejpam-5251	128	1	ng[{x	ng[{x	ADJ
ejpam-5251	128	2	,	,	PUNCT
ejpam-5251	128	3	z	z	NOUN
ejpam-5251	128	4	}	}	PUNCT
ejpam-5251	128	5	]	]	PUNCT
ejpam-5251	128	6	,	,	PUNCT
ejpam-5251	128	7	|t	|t	PROPN
ejpam-5251	129	1	|	|	ADV
ejpam-5251	129	2	≥	≥	NOUN
ejpam-5251	129	3	3	3	NUM
ejpam-5251	129	4	.	.	PUNCT
ejpam-5251	129	5	either	either	CCONJ
ejpam-5251	129	6	subcase	subcase	PROPN
ejpam-5251	129	7	yields	yield	VERB
ejpam-5251	129	8	a	a	DET
ejpam-5251	129	9	contradiction	contradiction	NOUN
ejpam-5251	129	10	.	.	PUNCT
ejpam-5251	130	1	case	case	NOUN
ejpam-5251	130	2	2	2	NUM
ejpam-5251	130	3	:	:	PUNCT
ejpam-5251	130	4	suppose	suppose	VERB
ejpam-5251	130	5	that	that	SCONJ
ejpam-5251	130	6	degg(u	degg(u	PROPN
ejpam-5251	130	7	)	)	PUNCT
ejpam-5251	130	8	=	=	SYM
ejpam-5251	131	1	2	2	X
ejpam-5251	131	2	.	.	X
ejpam-5251	132	1	if	if	SCONJ
ejpam-5251	132	2	xz	xz	PROPN
ejpam-5251	132	3	∈	∈	PROPN
ejpam-5251	132	4	e(g	e(g	PROPN
ejpam-5251	132	5	)	)	PUNCT
ejpam-5251	132	6	,	,	PUNCT
ejpam-5251	132	7	then	then	ADV
ejpam-5251	132	8	t	t	PROPN
ejpam-5251	132	9	=	=	SYM
ejpam-5251	132	10	{	{	PUNCT
ejpam-5251	132	11	x	x	NOUN
ejpam-5251	132	12	,	,	PUNCT
ejpam-5251	132	13	y	y	PROPN
ejpam-5251	132	14	,	,	PUNCT
ejpam-5251	132	15	z	z	PROPN
ejpam-5251	132	16	,	,	PUNCT
ejpam-5251	132	17	v	v	NOUN
ejpam-5251	132	18	}	}	PUNCT
ejpam-5251	132	19	makes	make	VERB
ejpam-5251	132	20	a	a	DET
ejpam-5251	132	21	minimal	minimal	ADJ
ejpam-5251	132	22	geodetic	geodetic	ADJ
ejpam-5251	132	23	hop	hop	NOUN
ejpam-5251	132	24	dominating	dominating	NOUN
ejpam-5251	132	25	set	set	NOUN
ejpam-5251	132	26	of	of	ADP
ejpam-5251	132	27	g.	g.	PROPN
ejpam-5251	132	28	suppose	suppose	VERB
ejpam-5251	132	29	xz	xz	PROPN
ejpam-5251	132	30	/∈	/∈	PUNCT
ejpam-5251	132	31	e(g	e(g	PROPN
ejpam-5251	132	32	)	)	PUNCT
ejpam-5251	132	33	.	.	PUNCT
ejpam-5251	133	1	then	then	ADV
ejpam-5251	133	2	there	there	PRON
ejpam-5251	133	3	exists	exist	VERB
ejpam-5251	133	4	a	a	DET
ejpam-5251	133	5	u	u	NOUN
ejpam-5251	133	6	-	-	NOUN
ejpam-5251	133	7	v	v	NOUN
ejpam-5251	133	8	geodetic	geodetic	NOUN
ejpam-5251	133	9	in	in	ADP
ejpam-5251	133	10	g	g	NOUN
ejpam-5251	133	11	of	of	ADP
ejpam-5251	133	12	the	the	DET
ejpam-5251	133	13	form	form	NOUN
ejpam-5251	133	14	[	[	X
ejpam-5251	133	15	u	u	NOUN
ejpam-5251	133	16	,	,	PUNCT
ejpam-5251	133	17	x	x	PROPN
ejpam-5251	133	18	,	,	PUNCT
ejpam-5251	133	19	w	w	PROPN
ejpam-5251	133	20	,	,	PUNCT
ejpam-5251	133	21	v	v	NOUN
ejpam-5251	133	22	]	]	PUNCT
ejpam-5251	133	23	with	with	ADP
ejpam-5251	133	24	w	w	PROPN
ejpam-5251	133	25	̸=	̸=	PROPN
ejpam-5251	133	26	z.	z.	PROPN
ejpam-5251	133	27	consequently	consequently	ADV
ejpam-5251	133	28	,	,	PUNCT
ejpam-5251	133	29	|v	|v	PROPN
ejpam-5251	133	30	(	(	PUNCT
ejpam-5251	133	31	g)|	g)|	X
ejpam-5251	133	32	≥	≥	NOUN
ejpam-5251	133	33	6	6	NUM
ejpam-5251	133	34	.	.	PUNCT
ejpam-5251	133	35	suppose	suppose	VERB
ejpam-5251	133	36	that	that	SCONJ
ejpam-5251	133	37	|v	|v	PROPN
ejpam-5251	133	38	(	(	PUNCT
ejpam-5251	133	39	g)|	g)|	X
ejpam-5251	133	40	≥	≥	NOUN
ejpam-5251	133	41	7	7	NUM
ejpam-5251	133	42	.	.	PUNCT
ejpam-5251	133	43	then	then	ADV
ejpam-5251	133	44	a	a	DET
ejpam-5251	133	45	minimal	minimal	ADJ
ejpam-5251	133	46	geodetic	geodetic	ADJ
ejpam-5251	133	47	hop	hop	NOUN
ejpam-5251	133	48	dominating	dominating	NOUN
ejpam-5251	133	49	set	set	NOUN
ejpam-5251	133	50	can	can	AUX
ejpam-5251	133	51	be	be	AUX
ejpam-5251	133	52	constructed	construct	VERB
ejpam-5251	133	53	containing	contain	VERB
ejpam-5251	133	54	x	x	PROPN
ejpam-5251	133	55	and	and	CCONJ
ejpam-5251	133	56	y.	y.	NOUN
ejpam-5251	133	57	in	in	ADP
ejpam-5251	133	58	this	this	DET
ejpam-5251	133	59	case	case	NOUN
ejpam-5251	133	60	,	,	PUNCT
ejpam-5251	133	61	|t	|t	VERB
ejpam-5251	134	1	|	|	ADV
ejpam-5251	134	2	≥	≥	NOUN
ejpam-5251	134	3	3	3	NUM
ejpam-5251	134	4	.	.	PUNCT
ejpam-5251	135	1	finally	finally	ADV
ejpam-5251	135	2	,	,	PUNCT
ejpam-5251	135	3	suppose	suppose	VERB
ejpam-5251	135	4	that	that	SCONJ
ejpam-5251	135	5	|v	|v	PROPN
ejpam-5251	135	6	(	(	PUNCT
ejpam-5251	135	7	g)|	g)|	NOUN
ejpam-5251	135	8	=	=	NOUN
ejpam-5251	135	9	6	6	NUM
ejpam-5251	135	10	.	.	PUNCT
ejpam-5251	135	11	since	since	SCONJ
ejpam-5251	135	12	g	g	PROPN
ejpam-5251	135	13	̸=	̸=	PROPN
ejpam-5251	135	14	c6	c6	PROPN
ejpam-5251	135	15	,	,	PUNCT
ejpam-5251	135	16	g	g	PROPN
ejpam-5251	135	17	is	be	AUX
ejpam-5251	135	18	obtained	obtain	VERB
ejpam-5251	135	19	from	from	ADP
ejpam-5251	135	20	c6	c6	PROPN
ejpam-5251	135	21	by	by	ADP
ejpam-5251	135	22	adding	add	VERB
ejpam-5251	135	23	at	at	ADP
ejpam-5251	135	24	least	least	ADV
ejpam-5251	135	25	one	one	NUM
ejpam-5251	135	26	edge	edge	NOUN
ejpam-5251	135	27	to	to	PART
ejpam-5251	135	28	join	join	VERB
ejpam-5251	135	29	a	a	DET
ejpam-5251	135	30	pair	pair	NOUN
ejpam-5251	135	31	of	of	ADP
ejpam-5251	135	32	nonadjacent	nonadjacent	ADJ
ejpam-5251	135	33	vertices	vertex	NOUN
ejpam-5251	135	34	.	.	PUNCT
ejpam-5251	136	1	in	in	ADP
ejpam-5251	136	2	this	this	DET
ejpam-5251	136	3	case	case	NOUN
ejpam-5251	136	4	,	,	PUNCT
ejpam-5251	136	5	a	a	DET
ejpam-5251	136	6	minimal	minimal	ADJ
ejpam-5251	136	7	geodetic	geodetic	ADJ
ejpam-5251	136	8	hop	hop	NOUN
ejpam-5251	136	9	dominating	dominating	NOUN
ejpam-5251	136	10	set	set	NOUN
ejpam-5251	136	11	can	can	AUX
ejpam-5251	136	12	be	be	AUX
ejpam-5251	136	13	constructed	construct	VERB
ejpam-5251	136	14	with	with	ADP
ejpam-5251	136	15	|t	|t	PROPN
ejpam-5251	136	16	|	|	INTJ
ejpam-5251	136	17	≥	≥	NOUN
ejpam-5251	136	18	3	3	NUM
ejpam-5251	136	19	.	.	PUNCT
ejpam-5251	137	1	all	all	DET
ejpam-5251	137	2	possibilities	possibility	NOUN
ejpam-5251	137	3	yield	yield	VERB
ejpam-5251	137	4	to	to	ADP
ejpam-5251	137	5	contradiction	contradiction	NOUN
ejpam-5251	137	6	.	.	PUNCT
ejpam-5251	138	1	the	the	DET
ejpam-5251	138	2	above	above	ADJ
ejpam-5251	138	3	cases	case	NOUN
ejpam-5251	138	4	imply	imply	VERB
ejpam-5251	138	5	that	that	SCONJ
ejpam-5251	138	6	u	u	PROPN
ejpam-5251	138	7	∈	∈	PROPN
ejpam-5251	138	8	ext(g	ext(g	PROPN
ejpam-5251	138	9	)	)	PUNCT
ejpam-5251	138	10	.	.	PUNCT
ejpam-5251	139	1	similarly	similarly	ADV
ejpam-5251	139	2	,	,	PUNCT
ejpam-5251	139	3	v	v	ADP
ejpam-5251	139	4	∈	∈	PROPN
ejpam-5251	139	5	ext(g	ext(g	NOUN
ejpam-5251	139	6	)	)	PUNCT
ejpam-5251	139	7	proposition	proposition	NOUN
ejpam-5251	139	8	2	2	NUM
ejpam-5251	139	9	.	.	X
ejpam-5251	139	10	for	for	ADP
ejpam-5251	139	11	the	the	DET
ejpam-5251	139	12	complete	complete	ADJ
ejpam-5251	139	13	graph	graph	NOUN
ejpam-5251	139	14	kn	kn	PROPN
ejpam-5251	139	15	,	,	PUNCT
ejpam-5251	139	16	path	path	PROPN
ejpam-5251	139	17	pn	pn	PROPN
ejpam-5251	139	18	,	,	PUNCT
ejpam-5251	139	19	cycle	cycle	NOUN
ejpam-5251	139	20	cn	cn	PROPN
ejpam-5251	139	21	and	and	CCONJ
ejpam-5251	139	22	petersen	petersen	PROPN
ejpam-5251	139	23	graph	graph	NOUN
ejpam-5251	139	24	p	p	NOUN
ejpam-5251	139	25	,	,	PUNCT
ejpam-5251	139	26	and	and	CCONJ
ejpam-5251	139	27	for	for	ADP
ejpam-5251	139	28	k	k	PROPN
ejpam-5251	139	29	≥	≥	PROPN
ejpam-5251	139	30	1	1	NUM
ejpam-5251	139	31	,	,	PUNCT
ejpam-5251	139	32	(	(	PUNCT
ejpam-5251	139	33	i	i	NOUN
ejpam-5251	139	34	)	)	PUNCT
ejpam-5251	139	35	γ+hg(kn	γ+hg(kn	PUNCT
ejpam-5251	139	36	)	)	PUNCT
ejpam-5251	139	37	=	=	SYM
ejpam-5251	140	1	n	n	CCONJ
ejpam-5251	140	2	;	;	PUNCT
ejpam-5251	140	3	(	(	PUNCT
ejpam-5251	140	4	ii	ii	NOUN
ejpam-5251	140	5	)	)	PUNCT
ejpam-5251	140	6	γ+hg(pn	γ+hg(pn	NUM
ejpam-5251	140	7	)	)	PUNCT
ejpam-5251	140	8	=	=	SYM
ejpam-5251	140	9			PUNCT
ejpam-5251	141	1	n	n	NOUN
ejpam-5251	141	2	if	if	SCONJ
ejpam-5251	141	3	n	n	NOUN
ejpam-5251	141	4	=	=	SYM
ejpam-5251	141	5	1	1	NUM
ejpam-5251	141	6	,	,	PUNCT
ejpam-5251	141	7	2	2	NUM
ejpam-5251	141	8	,	,	PUNCT
ejpam-5251	141	9	3	3	NUM
ejpam-5251	141	10	2k	2k	NOUN
ejpam-5251	141	11	+	+	CCONJ
ejpam-5251	141	12	1	1	NUM
ejpam-5251	141	13	if	if	SCONJ
ejpam-5251	141	14	n	n	PRON
ejpam-5251	141	15	=	=	SYM
ejpam-5251	141	16	4k	4k	NOUN
ejpam-5251	141	17	+	+	NOUN
ejpam-5251	141	18	1	1	NUM
ejpam-5251	141	19	2	2	NUM
ejpam-5251	141	20	⌈n	⌈n	NOUN
ejpam-5251	141	21	4	4	NUM
ejpam-5251	141	22	⌉	⌉	SCONJ
ejpam-5251	141	23	otherwise	otherwise	ADV
ejpam-5251	141	24	d.	d.	PROPN
ejpam-5251	141	25	catian	catian	PROPN
ejpam-5251	141	26	,	,	PUNCT
ejpam-5251	141	27	i.	i.	PROPN
ejpam-5251	141	28	s.	s.	PROPN
ejpam-5251	141	29	aniversario	aniversario	PROPN
ejpam-5251	141	30	,	,	PUNCT
ejpam-5251	141	31	f.	f.	PROPN
ejpam-5251	141	32	p.	p.	PROPN
ejpam-5251	141	33	jamil	jamil	PROPN
ejpam-5251	141	34	/	/	SYM
ejpam-5251	141	35	eur	eur	PROPN
ejpam-5251	141	36	.	.	PUNCT
ejpam-5251	142	1	j.	j.	PROPN
ejpam-5251	142	2	pure	pure	PROPN
ejpam-5251	142	3	appl	appl	PROPN
ejpam-5251	142	4	.	.	PROPN
ejpam-5251	142	5	math	math	PROPN
ejpam-5251	142	6	,	,	PUNCT
ejpam-5251	142	7	17	17	NUM
ejpam-5251	142	8	(	(	PUNCT
ejpam-5251	142	9	3	3	NUM
ejpam-5251	142	10	)	)	PUNCT
ejpam-5251	142	11	(	(	PUNCT
ejpam-5251	142	12	2024	2024	NUM
ejpam-5251	142	13	)	)	PUNCT
ejpam-5251	142	14	,	,	PUNCT
ejpam-5251	142	15	1737	1737	NUM
ejpam-5251	142	16	-	-	SYM
ejpam-5251	142	17	1750	1750	NUM
ejpam-5251	142	18	1741	1741	NUM
ejpam-5251	142	19	(	(	PUNCT
ejpam-5251	142	20	iii	iii	NOUN
ejpam-5251	142	21	)	)	PUNCT
ejpam-5251	142	22	γ+hg(cn	γ+hg(cn	NUM
ejpam-5251	142	23	)	)	PUNCT
ejpam-5251	143	1	=	=	PRON
ejpam-5251	143	2			NUM
ejpam-5251	143	3	3	3	NUM
ejpam-5251	143	4	if	if	SCONJ
ejpam-5251	143	5	n	n	NOUN
ejpam-5251	143	6	=	=	SYM
ejpam-5251	143	7	3	3	NUM
ejpam-5251	143	8	,	,	PUNCT
ejpam-5251	143	9	4	4	NUM
ejpam-5251	143	10	,	,	PUNCT
ejpam-5251	143	11	5	5	NUM
ejpam-5251	143	12	2	2	NUM
ejpam-5251	143	13	if	if	SCONJ
ejpam-5251	143	14	n	n	NOUN
ejpam-5251	143	15	=	=	SYM
ejpam-5251	143	16	6	6	NUM
ejpam-5251	143	17	2k	2k	NUM
ejpam-5251	143	18	+	+	CCONJ
ejpam-5251	143	19	1	1	NUM
ejpam-5251	143	20	if	if	SCONJ
ejpam-5251	143	21	n	n	PRON
ejpam-5251	143	22	=	=	SYM
ejpam-5251	143	23	4k	4k	NOUN
ejpam-5251	143	24	+	+	NOUN
ejpam-5251	143	25	3	3	NUM
ejpam-5251	143	26	2	2	NUM
ejpam-5251	143	27	⌈n	⌈n	NOUN
ejpam-5251	143	28	4	4	NUM
ejpam-5251	143	29	⌉	⌉	PRON
ejpam-5251	143	30	otherwise	otherwise	ADV
ejpam-5251	143	31	(	(	PUNCT
ejpam-5251	143	32	iv	iv	X
ejpam-5251	143	33	)	)	PUNCT
ejpam-5251	143	34	γ+hg(p	γ+hg(p	NOUN
ejpam-5251	143	35	)	)	PUNCT
ejpam-5251	144	1	=	=	SYM
ejpam-5251	144	2	6	6	X
ejpam-5251	144	3	.	.	PUNCT
ejpam-5251	144	4	proof	proof	NOUN
ejpam-5251	144	5	.	.	PUNCT
ejpam-5251	145	1	since	since	SCONJ
ejpam-5251	145	2	γhg(kn	γhg(kn	NUM
ejpam-5251	145	3	)	)	PUNCT
ejpam-5251	145	4	=	=	SYM
ejpam-5251	145	5	n	n	CCONJ
ejpam-5251	145	6	,	,	PUNCT
ejpam-5251	145	7	proposition	proposition	NOUN
ejpam-5251	145	8	1	1	NUM
ejpam-5251	145	9	yields	yield	NOUN
ejpam-5251	145	10	γ+hg(kn	γ+hg(kn	NOUN
ejpam-5251	145	11	)	)	PUNCT
ejpam-5251	145	12	=	=	VERB
ejpam-5251	145	13	n.	n.	NOUN
ejpam-5251	145	14	let	let	VERB
ejpam-5251	145	15	pn	pn	VERB
ejpam-5251	145	16	=	=	PUNCT
ejpam-5251	146	1	[	[	X
ejpam-5251	146	2	x1	x1	PROPN
ejpam-5251	146	3	,	,	PUNCT
ejpam-5251	146	4	x2	x2	PROPN
ejpam-5251	146	5	,	,	PUNCT
ejpam-5251	146	6	.	.	PUNCT
ejpam-5251	146	7	.	.	PUNCT
ejpam-5251	147	1	.	.	PUNCT
ejpam-5251	148	1	,	,	PUNCT
ejpam-5251	148	2	xn	xn	PROPN
ejpam-5251	148	3	]	]	X
ejpam-5251	148	4	.	.	PUNCT
ejpam-5251	149	1	the	the	DET
ejpam-5251	149	2	case	case	NOUN
ejpam-5251	149	3	where	where	SCONJ
ejpam-5251	149	4	n	n	PROPN
ejpam-5251	149	5	=	=	SYM
ejpam-5251	149	6	1	1	NUM
ejpam-5251	149	7	,	,	PUNCT
ejpam-5251	149	8	2	2	NUM
ejpam-5251	149	9	,	,	PUNCT
ejpam-5251	149	10	3	3	NUM
ejpam-5251	149	11	is	be	AUX
ejpam-5251	149	12	trivial	trivial	ADJ
ejpam-5251	149	13	.	.	PUNCT
ejpam-5251	149	14	suppose	suppose	VERB
ejpam-5251	149	15	n	n	PRON
ejpam-5251	149	16	=	=	SYM
ejpam-5251	149	17	4k	4k	X
ejpam-5251	149	18	+	+	NOUN
ejpam-5251	149	19	1	1	NUM
ejpam-5251	149	20	,	,	PUNCT
ejpam-5251	149	21	where	where	SCONJ
ejpam-5251	149	22	k	k	PROPN
ejpam-5251	149	23	≥	≥	PROPN
ejpam-5251	149	24	1	1	NUM
ejpam-5251	149	25	.	.	PUNCT
ejpam-5251	150	1	since	since	SCONJ
ejpam-5251	150	2	s	s	PART
ejpam-5251	150	3	=	=	PUNCT
ejpam-5251	150	4	{	{	PUNCT
ejpam-5251	150	5	x1	x1	PROPN
ejpam-5251	150	6	,	,	PUNCT
ejpam-5251	150	7	x2	x2	PROPN
ejpam-5251	150	8	,	,	PUNCT
ejpam-5251	150	9	x5	x5	PROPN
ejpam-5251	150	10	,	,	PUNCT
ejpam-5251	150	11	x6	x6	PROPN
ejpam-5251	150	12	,	,	PUNCT
ejpam-5251	150	13	.	.	PUNCT
ejpam-5251	150	14	.	.	PUNCT
ejpam-5251	150	15	.	.	PUNCT
ejpam-5251	151	1	,	,	PUNCT
ejpam-5251	151	2	xn	xn	X
ejpam-5251	151	3	}	}	PUNCT
ejpam-5251	151	4	is	be	AUX
ejpam-5251	151	5	a	a	DET
ejpam-5251	151	6	minimal	minimal	ADJ
ejpam-5251	151	7	geodetic	geodetic	ADJ
ejpam-5251	151	8	hop	hop	NOUN
ejpam-5251	151	9	dominating	dominating	NOUN
ejpam-5251	151	10	set	set	NOUN
ejpam-5251	151	11	,	,	PUNCT
ejpam-5251	151	12	2k+1	2k+1	PROPN
ejpam-5251	151	13	=	=	SYM
ejpam-5251	151	14	|s|	|s|	PROPN
ejpam-5251	151	15	≤	≤	NUM
ejpam-5251	151	16	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	151	17	)	)	PUNCT
ejpam-5251	151	18	.	.	PUNCT
ejpam-5251	152	1	conversely	conversely	ADV
ejpam-5251	152	2	,	,	PUNCT
ejpam-5251	152	3	let	let	VERB
ejpam-5251	152	4	s	s	PRON
ejpam-5251	152	5	be	be	AUX
ejpam-5251	152	6	a	a	DET
ejpam-5251	152	7	γ+hg	γ+hg	NOUN
ejpam-5251	152	8	-	-	PUNCT
ejpam-5251	152	9	set	set	NOUN
ejpam-5251	152	10	of	of	ADP
ejpam-5251	152	11	g.	g.	PROPN
ejpam-5251	152	12	being	be	AUX
ejpam-5251	152	13	a	a	DET
ejpam-5251	152	14	geodetic	geodetic	ADJ
ejpam-5251	152	15	set	set	NOUN
ejpam-5251	152	16	,	,	PUNCT
ejpam-5251	152	17	x1	x1	PROPN
ejpam-5251	152	18	,	,	PUNCT
ejpam-5251	152	19	xn	xn	PROPN
ejpam-5251	152	20	∈	∈	PROPN
ejpam-5251	152	21	s.	s.	PROPN
ejpam-5251	152	22	for	for	ADP
ejpam-5251	152	23	every	every	DET
ejpam-5251	152	24	1	1	NUM
ejpam-5251	152	25	≤	≤	NUM
ejpam-5251	153	1	j	j	PROPN
ejpam-5251	153	2	≤	≤	PROPN
ejpam-5251	153	3	n−	n−	PROPN
ejpam-5251	153	4	3	3	NUM
ejpam-5251	153	5	,	,	PUNCT
ejpam-5251	153	6	s	s	NOUN
ejpam-5251	153	7	contains	contain	VERB
ejpam-5251	153	8	at	at	ADP
ejpam-5251	153	9	most	most	ADV
ejpam-5251	153	10	two	two	NUM
ejpam-5251	153	11	vertices	vertex	NOUN
ejpam-5251	153	12	in	in	ADP
ejpam-5251	153	13	xj	xj	PROPN
ejpam-5251	153	14	,	,	PUNCT
ejpam-5251	153	15	xj+1	xj+1	NUM
ejpam-5251	153	16	,	,	PUNCT
ejpam-5251	153	17	xj+2	xj+2	NUM
ejpam-5251	153	18	,	,	PUNCT
ejpam-5251	153	19	xj+3	xj+3	NUM
ejpam-5251	153	20	.	.	PUNCT
ejpam-5251	154	1	thus	thus	ADV
ejpam-5251	154	2	,	,	PUNCT
ejpam-5251	154	3	|s|	|s|	VERB
ejpam-5251	154	4	≤	≤	NUM
ejpam-5251	154	5	2k+1	2k+1	NOUN
ejpam-5251	154	6	.	.	PUNCT
ejpam-5251	155	1	hence	hence	ADV
ejpam-5251	155	2	,	,	PUNCT
ejpam-5251	155	3	γ+hg(pn	γ+hg(pn	PUNCT
ejpam-5251	155	4	)	)	PUNCT
ejpam-5251	155	5	=	=	SYM
ejpam-5251	155	6	2k	2k	NOUN
ejpam-5251	155	7	+	+	CCONJ
ejpam-5251	155	8	1	1	X
ejpam-5251	155	9	.	.	X
ejpam-5251	156	1	for	for	ADP
ejpam-5251	156	2	the	the	DET
ejpam-5251	156	3	third	third	ADJ
ejpam-5251	156	4	case	case	NOUN
ejpam-5251	156	5	,	,	PUNCT
ejpam-5251	156	6	assume	assume	VERB
ejpam-5251	156	7	n	n	PRON
ejpam-5251	156	8	̸=	̸=	PROPN
ejpam-5251	156	9	4k+1	4k+1	PROPN
ejpam-5251	156	10	.	.	PUNCT
ejpam-5251	157	1	if	if	SCONJ
ejpam-5251	157	2	n	n	NOUN
ejpam-5251	157	3	=	=	SYM
ejpam-5251	157	4	4k	4k	NUM
ejpam-5251	157	5	,	,	PUNCT
ejpam-5251	157	6	then	then	ADV
ejpam-5251	157	7	assume	assume	VERB
ejpam-5251	157	8	s	s	X
ejpam-5251	157	9	=	=	PUNCT
ejpam-5251	157	10	{	{	PUNCT
ejpam-5251	157	11	x1	x1	PROPN
ejpam-5251	157	12	,	,	PUNCT
ejpam-5251	157	13	x2	x2	PROPN
ejpam-5251	157	14	,	,	PUNCT
ejpam-5251	157	15	x5	x5	PROPN
ejpam-5251	157	16	,	,	PUNCT
ejpam-5251	157	17	x6	x6	PROPN
ejpam-5251	157	18	,	,	PUNCT
ejpam-5251	157	19	.	.	PUNCT
ejpam-5251	157	20	.	.	PUNCT
ejpam-5251	158	1	.	.	PUNCT
ejpam-5251	159	1	,	,	PUNCT
ejpam-5251	159	2	xn−3	xn−3	PROPN
ejpam-5251	159	3	,	,	PUNCT
ejpam-5251	159	4	xn	xn	PROPN
ejpam-5251	159	5	}	}	PUNCT
ejpam-5251	159	6	.	.	PUNCT
ejpam-5251	160	1	by	by	ADP
ejpam-5251	160	2	the	the	DET
ejpam-5251	160	3	same	same	ADJ
ejpam-5251	160	4	argument	argument	NOUN
ejpam-5251	160	5	provided	provide	VERB
ejpam-5251	160	6	above	above	ADV
ejpam-5251	160	7	,	,	PUNCT
ejpam-5251	160	8	we	we	PRON
ejpam-5251	160	9	have	have	VERB
ejpam-5251	160	10	s	s	AUX
ejpam-5251	160	11	be	be	AUX
ejpam-5251	160	12	a	a	DET
ejpam-5251	160	13	minimal	minimal	ADJ
ejpam-5251	160	14	geodetic	geodetic	ADJ
ejpam-5251	160	15	hop	hop	NOUN
ejpam-5251	160	16	dominating	dominating	NOUN
ejpam-5251	160	17	set	set	NOUN
ejpam-5251	160	18	so	so	SCONJ
ejpam-5251	160	19	that	that	PRON
ejpam-5251	160	20	s	s	VERB
ejpam-5251	160	21	is	be	AUX
ejpam-5251	160	22	a	a	DET
ejpam-5251	160	23	γ+hg	γ+hg	NOUN
ejpam-5251	160	24	-	-	PUNCT
ejpam-5251	160	25	set	set	NOUN
ejpam-5251	160	26	.	.	PUNCT
ejpam-5251	161	1	hence	hence	ADV
ejpam-5251	161	2	,	,	PUNCT
ejpam-5251	161	3	|s|	|s|	PROPN
ejpam-5251	161	4	=	=	SYM
ejpam-5251	161	5	4k	4k	X
ejpam-5251	161	6	2	2	NUM
ejpam-5251	161	7	=	=	SYM
ejpam-5251	161	8	2k	2k	NOUN
ejpam-5251	161	9	=	=	SYM
ejpam-5251	161	10	2	2	NUM
ejpam-5251	161	11	⌈	⌈	NOUN
ejpam-5251	161	12	n	n	PRON
ejpam-5251	161	13	4	4	NUM
ejpam-5251	161	14	⌉	⌉	NOUN
ejpam-5251	161	15	.	.	PUNCT
ejpam-5251	162	1	if	if	SCONJ
ejpam-5251	162	2	n	n	X
ejpam-5251	162	3	>	>	X
ejpam-5251	162	4	4k	4k	NUM
ejpam-5251	162	5	+	+	ADV
ejpam-5251	162	6	1	1	NUM
ejpam-5251	162	7	,	,	PUNCT
ejpam-5251	162	8	choose	choose	VERB
ejpam-5251	162	9	the	the	DET
ejpam-5251	162	10	set	set	NOUN
ejpam-5251	162	11	s	s	PART
ejpam-5251	162	12	=	=	PUNCT
ejpam-5251	162	13	{	{	PUNCT
ejpam-5251	162	14	x1	x1	PROPN
ejpam-5251	162	15	,	,	PUNCT
ejpam-5251	162	16	x2	x2	PROPN
ejpam-5251	162	17	,	,	PUNCT
ejpam-5251	162	18	x5	x5	PROPN
ejpam-5251	162	19	,	,	PUNCT
ejpam-5251	162	20	x6	x6	PROPN
ejpam-5251	162	21	,	,	PUNCT
ejpam-5251	162	22	.	.	PUNCT
ejpam-5251	162	23	.	.	PUNCT
ejpam-5251	163	1	.	.	PUNCT
ejpam-5251	164	1	,	,	PUNCT
ejpam-5251	164	2	xn−1	xn−1	PROPN
ejpam-5251	164	3	,	,	PUNCT
ejpam-5251	164	4	xn	xn	PROPN
ejpam-5251	164	5	}	}	PUNCT
ejpam-5251	164	6	to	to	PART
ejpam-5251	164	7	be	be	AUX
ejpam-5251	164	8	minimal	minimal	ADJ
ejpam-5251	164	9	geodetic	geodetic	ADJ
ejpam-5251	164	10	hop	hop	NOUN
ejpam-5251	164	11	dominating	dominating	NOUN
ejpam-5251	164	12	set	set	NOUN
ejpam-5251	164	13	.	.	PUNCT
ejpam-5251	165	1	by	by	ADP
ejpam-5251	165	2	the	the	DET
ejpam-5251	165	3	same	same	ADJ
ejpam-5251	165	4	argument	argument	NOUN
ejpam-5251	165	5	,	,	PUNCT
ejpam-5251	165	6	we	we	PRON
ejpam-5251	165	7	have	have	VERB
ejpam-5251	165	8	s	s	VERB
ejpam-5251	165	9	to	to	PART
ejpam-5251	165	10	be	be	AUX
ejpam-5251	165	11	a	a	DET
ejpam-5251	165	12	γ+hg	γ+hg	NOUN
ejpam-5251	165	13	-	-	PUNCT
ejpam-5251	165	14	set	set	VERB
ejpam-5251	165	15	with	with	ADP
ejpam-5251	165	16	|s|	|s|	NOUN
ejpam-5251	165	17	=	=	SYM
ejpam-5251	165	18	2	2	NUM
ejpam-5251	165	19	⌈	⌈	NOUN
ejpam-5251	165	20	n	n	PRON
ejpam-5251	165	21	4	4	NUM
ejpam-5251	165	22	⌉	⌉	NOUN
ejpam-5251	165	23	.	.	PUNCT
ejpam-5251	166	1	therefore	therefore	ADV
ejpam-5251	166	2	,	,	PUNCT
ejpam-5251	166	3	γ+hg(g	γ+hg(g	X
ejpam-5251	166	4	)	)	PUNCT
ejpam-5251	166	5	=	=	SYM
ejpam-5251	166	6	2	2	NUM
ejpam-5251	166	7	⌈	⌈	NOUN
ejpam-5251	166	8	n	n	PRON
ejpam-5251	166	9	4	4	NUM
ejpam-5251	166	10	⌉	⌉	X
ejpam-5251	166	11	.	.	PUNCT
ejpam-5251	167	1	let	let	VERB
ejpam-5251	167	2	g	g	NOUN
ejpam-5251	167	3	=	=	PUNCT
ejpam-5251	167	4	cn	cn	PROPN
ejpam-5251	167	5	=	=	PUNCT
ejpam-5251	168	1	[	[	X
ejpam-5251	168	2	v1	v1	NOUN
ejpam-5251	168	3	,	,	PUNCT
ejpam-5251	168	4	v2	v2	NOUN
ejpam-5251	168	5	,	,	PUNCT
ejpam-5251	168	6	.	.	PUNCT
ejpam-5251	168	7	.	.	PUNCT
ejpam-5251	168	8	.	.	PUNCT
ejpam-5251	169	1	,	,	PUNCT
ejpam-5251	169	2	vn	vn	X
ejpam-5251	169	3	,	,	PUNCT
ejpam-5251	169	4	v1	v1	PROPN
ejpam-5251	169	5	]	]	PUNCT
ejpam-5251	169	6	.	.	PUNCT
ejpam-5251	170	1	the	the	DET
ejpam-5251	170	2	first	first	ADJ
ejpam-5251	170	3	and	and	CCONJ
ejpam-5251	170	4	second	second	ADJ
ejpam-5251	170	5	case	case	NOUN
ejpam-5251	170	6	is	be	AUX
ejpam-5251	170	7	trivial	trivial	ADJ
ejpam-5251	170	8	.	.	PUNCT
ejpam-5251	171	1	let	let	VERB
ejpam-5251	171	2	k	k	PROPN
ejpam-5251	171	3	≥	≥	PROPN
ejpam-5251	171	4	1	1	NUM
ejpam-5251	171	5	.	.	PUNCT
ejpam-5251	172	1	for	for	ADP
ejpam-5251	172	2	the	the	DET
ejpam-5251	172	3	third	third	ADJ
ejpam-5251	172	4	case	case	NOUN
ejpam-5251	172	5	,	,	PUNCT
ejpam-5251	172	6	assume	assume	VERB
ejpam-5251	172	7	n	n	X
ejpam-5251	172	8	=	=	SYM
ejpam-5251	172	9	4k	4k	X
ejpam-5251	172	10	+	+	NOUN
ejpam-5251	172	11	3	3	X
ejpam-5251	172	12	.	.	PUNCT
ejpam-5251	172	13	suppose	suppose	VERB
ejpam-5251	172	14	s	s	X
ejpam-5251	172	15	=	=	SYM
ejpam-5251	172	16	{	{	PUNCT
ejpam-5251	172	17	v1	v1	PROPN
ejpam-5251	172	18	,	,	PUNCT
ejpam-5251	172	19	v2	v2	PROPN
ejpam-5251	172	20	,	,	PUNCT
ejpam-5251	172	21	v5	v5	PROPN
ejpam-5251	172	22	,	,	PUNCT
ejpam-5251	172	23	v6	v6	NOUN
ejpam-5251	172	24	,	,	PUNCT
ejpam-5251	172	25	.	.	PUNCT
ejpam-5251	172	26	.	.	PUNCT
ejpam-5251	173	1	.	.	PUNCT
ejpam-5251	174	1	,	,	PUNCT
ejpam-5251	174	2	vn−2	vn−2	PROPN
ejpam-5251	174	3	}	}	PUNCT
ejpam-5251	174	4	.	.	PUNCT
ejpam-5251	175	1	note	note	VERB
ejpam-5251	175	2	that	that	SCONJ
ejpam-5251	175	3	for	for	ADP
ejpam-5251	175	4	every	every	DET
ejpam-5251	175	5	vi	vi	NOUN
ejpam-5251	175	6	,	,	PUNCT
ejpam-5251	175	7	vi+1	vi+1	NOUN
ejpam-5251	175	8	/∈	/∈	PUNCT
ejpam-5251	175	9	s	s	VERB
ejpam-5251	175	10	where	where	SCONJ
ejpam-5251	175	11	i	i	PRON
ejpam-5251	175	12	≥	≥	VERB
ejpam-5251	175	13	3	3	NUM
ejpam-5251	175	14	,	,	PUNCT
ejpam-5251	175	15	there	there	PRON
ejpam-5251	175	16	exist	exist	VERB
ejpam-5251	175	17	vi−1	vi−1	PROPN
ejpam-5251	175	18	,	,	PUNCT
ejpam-5251	175	19	vi+2	vi+2	NUM
ejpam-5251	175	20	∈	∈	PROPN
ejpam-5251	175	21	s	s	VERB
ejpam-5251	175	22	such	such	ADJ
ejpam-5251	175	23	that	that	DET
ejpam-5251	175	24	vi	vi	NOUN
ejpam-5251	175	25	,	,	PUNCT
ejpam-5251	176	1	vi+1	vi+1	X
ejpam-5251	176	2	∈	∈	PROPN
ejpam-5251	176	3	ig(vi−1	ig(vi−1	PROPN
ejpam-5251	176	4	,	,	PUNCT
ejpam-5251	176	5	vi+2	vi+2	NUM
ejpam-5251	176	6	)	)	PUNCT
ejpam-5251	176	7	with	with	ADP
ejpam-5251	176	8	vi	vi	PROPN
ejpam-5251	176	9	∈	∈	PROPN
ejpam-5251	176	10	n2	n2	NOUN
ejpam-5251	176	11	g(vi+2	g(vi+2	PROPN
ejpam-5251	176	12	)	)	PUNCT
ejpam-5251	176	13	and	and	CCONJ
ejpam-5251	176	14	vi+1	vi+1	ADV
ejpam-5251	176	15	∈	∈	PROPN
ejpam-5251	176	16	n2	n2	NOUN
ejpam-5251	176	17	g(vi−1	g(vi−1	PROPN
ejpam-5251	176	18	)	)	PUNCT
ejpam-5251	176	19	so	so	SCONJ
ejpam-5251	176	20	that	that	PRON
ejpam-5251	176	21	s	s	VERB
ejpam-5251	176	22	is	be	AUX
ejpam-5251	176	23	both	both	PRON
ejpam-5251	176	24	a	a	DET
ejpam-5251	176	25	geodetic	geodetic	ADJ
ejpam-5251	176	26	set	set	NOUN
ejpam-5251	176	27	and	and	CCONJ
ejpam-5251	176	28	hop	hop	NOUN
ejpam-5251	176	29	dominating	dominating	NOUN
ejpam-5251	176	30	set	set	NOUN
ejpam-5251	176	31	.	.	PUNCT
ejpam-5251	177	1	thus	thus	ADV
ejpam-5251	177	2	,	,	PUNCT
ejpam-5251	177	3	s	s	VERB
ejpam-5251	177	4	is	be	AUX
ejpam-5251	177	5	a	a	DET
ejpam-5251	177	6	minimal	minimal	ADJ
ejpam-5251	177	7	geodetic	geodetic	ADJ
ejpam-5251	177	8	hop	hop	NOUN
ejpam-5251	177	9	dominating	dominating	NOUN
ejpam-5251	177	10	set	set	NOUN
ejpam-5251	177	11	so	so	SCONJ
ejpam-5251	177	12	that	that	SCONJ
ejpam-5251	177	13	|s|	|s|	NOUN
ejpam-5251	177	14	=	=	SYM
ejpam-5251	177	15	4k	4k	X
ejpam-5251	177	16	2	2	NUM
ejpam-5251	177	17	+	+	CCONJ
ejpam-5251	177	18	1	1	NUM
ejpam-5251	177	19	=	=	SYM
ejpam-5251	177	20	2k	2k	NOUN
ejpam-5251	177	21	+	+	CCONJ
ejpam-5251	177	22	1	1	NUM
ejpam-5251	177	23	≤	≤	NUM
ejpam-5251	177	24	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	177	25	)	)	PUNCT
ejpam-5251	177	26	.	.	PUNCT
ejpam-5251	178	1	conversely	conversely	ADV
ejpam-5251	178	2	,	,	PUNCT
ejpam-5251	178	3	by	by	ADP
ejpam-5251	178	4	the	the	DET
ejpam-5251	178	5	same	same	ADJ
ejpam-5251	178	6	argument	argument	NOUN
ejpam-5251	178	7	provided	provide	VERB
ejpam-5251	178	8	in	in	ADP
ejpam-5251	178	9	above	above	ADV
ejpam-5251	178	10	,	,	PUNCT
ejpam-5251	178	11	s	s	VERB
ejpam-5251	178	12	is	be	AUX
ejpam-5251	178	13	a	a	DET
ejpam-5251	178	14	minimal	minimal	ADJ
ejpam-5251	178	15	geodetic	geodetic	ADJ
ejpam-5251	178	16	hop	hop	NOUN
ejpam-5251	178	17	dominating	dominating	NOUN
ejpam-5251	178	18	set	set	NOUN
ejpam-5251	178	19	and	and	CCONJ
ejpam-5251	178	20	since	since	SCONJ
ejpam-5251	178	21	s	s	NOUN
ejpam-5251	178	22	is	be	AUX
ejpam-5251	178	23	arbitrary	arbitrary	ADJ
ejpam-5251	178	24	we	we	PRON
ejpam-5251	178	25	have	have	VERB
ejpam-5251	178	26	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	178	27	)	)	PUNCT
ejpam-5251	178	28	≤	≤	NUM
ejpam-5251	178	29	2k+1	2k+1	NOUN
ejpam-5251	178	30	.	.	PUNCT
ejpam-5251	179	1	therefore	therefore	ADV
ejpam-5251	179	2	,	,	PUNCT
ejpam-5251	179	3	γ+hg(g	γ+hg(g	X
ejpam-5251	179	4	)	)	PUNCT
ejpam-5251	180	1	=	=	SYM
ejpam-5251	180	2	2k+1	2k+1	X
ejpam-5251	180	3	.	.	PUNCT
ejpam-5251	181	1	for	for	ADP
ejpam-5251	181	2	the	the	DET
ejpam-5251	181	3	fourth	fourth	ADJ
ejpam-5251	181	4	case	case	NOUN
ejpam-5251	181	5	,	,	PUNCT
ejpam-5251	181	6	assume	assume	VERB
ejpam-5251	181	7	n	n	PRON
ejpam-5251	181	8	<	<	X
ejpam-5251	181	9	4k	4k	NUM
ejpam-5251	181	10	+	+	CCONJ
ejpam-5251	181	11	3	3	NUM
ejpam-5251	181	12	with	with	ADP
ejpam-5251	181	13	k	k	PROPN
ejpam-5251	181	14	≥	≥	NUM
ejpam-5251	181	15	2	2	NUM
ejpam-5251	181	16	.	.	PUNCT
ejpam-5251	182	1	suppose	suppose	VERB
ejpam-5251	182	2	s	s	X
ejpam-5251	182	3	=	=	SYM
ejpam-5251	182	4	{	{	PUNCT
ejpam-5251	182	5	v1	v1	PROPN
ejpam-5251	182	6	,	,	PUNCT
ejpam-5251	182	7	v2	v2	PROPN
ejpam-5251	182	8	,	,	PUNCT
ejpam-5251	182	9	v5	v5	PROPN
ejpam-5251	182	10	,	,	PUNCT
ejpam-5251	182	11	v6	v6	NOUN
ejpam-5251	182	12	,	,	PUNCT
ejpam-5251	182	13	.	.	PUNCT
ejpam-5251	182	14	.	.	PUNCT
ejpam-5251	183	1	.	.	PUNCT
ejpam-5251	184	1	,	,	PUNCT
ejpam-5251	184	2	vn−3	vn−3	PROPN
ejpam-5251	184	3	,	,	PUNCT
ejpam-5251	184	4	vn−2	vn−2	PROPN
ejpam-5251	184	5	}	}	PUNCT
ejpam-5251	184	6	.	.	PUNCT
ejpam-5251	185	1	the	the	DET
ejpam-5251	185	2	same	same	ADJ
ejpam-5251	185	3	argument	argument	NOUN
ejpam-5251	185	4	would	would	AUX
ejpam-5251	185	5	have	have	VERB
ejpam-5251	185	6	s	s	NOUN
ejpam-5251	185	7	to	to	PART
ejpam-5251	185	8	be	be	AUX
ejpam-5251	185	9	a	a	DET
ejpam-5251	185	10	minimal	minimal	ADJ
ejpam-5251	185	11	geodetic	geodetic	ADJ
ejpam-5251	185	12	hop	hop	NOUN
ejpam-5251	185	13	dominating	dominating	NOUN
ejpam-5251	185	14	set	set	NOUN
ejpam-5251	185	15	so	so	SCONJ
ejpam-5251	185	16	that	that	PRON
ejpam-5251	185	17	s	s	VERB
ejpam-5251	185	18	is	be	AUX
ejpam-5251	185	19	a	a	DET
ejpam-5251	185	20	γ+hg	γ+hg	NOUN
ejpam-5251	185	21	-	-	PUNCT
ejpam-5251	185	22	set	set	NOUN
ejpam-5251	185	23	.	.	PUNCT
ejpam-5251	186	1	it	it	PRON
ejpam-5251	186	2	follows	follow	VERB
ejpam-5251	186	3	that	that	SCONJ
ejpam-5251	186	4	|s|	|s|	NOUN
ejpam-5251	186	5	=	=	SYM
ejpam-5251	186	6	4k	4k	X
ejpam-5251	186	7	2	2	NUM
ejpam-5251	186	8	=	=	SYM
ejpam-5251	186	9	2k	2k	NOUN
ejpam-5251	186	10	=	=	SYM
ejpam-5251	186	11	2	2	NUM
ejpam-5251	186	12	⌈	⌈	NOUN
ejpam-5251	186	13	n	n	PRON
ejpam-5251	186	14	4	4	NUM
ejpam-5251	186	15	⌉	⌉	X
ejpam-5251	186	16	.	.	PUNCT
ejpam-5251	187	1	let	let	VERB
ejpam-5251	187	2	g	g	PRON
ejpam-5251	187	3	be	be	AUX
ejpam-5251	187	4	the	the	DET
ejpam-5251	187	5	petersen	petersen	NOUN
ejpam-5251	187	6	graph	graph	NOUN
ejpam-5251	187	7	shown	show	VERB
ejpam-5251	187	8	in	in	ADP
ejpam-5251	187	9	figure	figure	NOUN
ejpam-5251	187	10	1	1	NUM
ejpam-5251	187	11	.	.	PUNCT
ejpam-5251	188	1	a	a	DET
ejpam-5251	188	2	e	e	X
ejpam-5251	188	3	dc	dc	PROPN
ejpam-5251	188	4	b	b	PROPN
ejpam-5251	188	5	f	f	X
ejpam-5251	188	6	j	j	PROPN
ejpam-5251	188	7	ih	ih	PROPN
ejpam-5251	188	8	g	g	PROPN
ejpam-5251	188	9	figure	figure	NOUN
ejpam-5251	188	10	1	1	NUM
ejpam-5251	188	11	:	:	PUNCT
ejpam-5251	188	12	a	a	DET
ejpam-5251	188	13	petersen	petersen	NOUN
ejpam-5251	188	14	graph	graph	NOUN
ejpam-5251	188	15	then	then	ADV
ejpam-5251	188	16	s	s	VERB
ejpam-5251	188	17	=	=	PUNCT
ejpam-5251	188	18	{	{	PUNCT
ejpam-5251	188	19	a	a	X
ejpam-5251	188	20	,	,	PUNCT
ejpam-5251	188	21	c	c	NOUN
ejpam-5251	188	22	,	,	PUNCT
ejpam-5251	188	23	d	d	NOUN
ejpam-5251	188	24	,	,	PUNCT
ejpam-5251	188	25	f	f	PROPN
ejpam-5251	188	26	,	,	PUNCT
ejpam-5251	188	27	g	g	PROPN
ejpam-5251	188	28	,	,	PUNCT
ejpam-5251	188	29	j	j	PROPN
ejpam-5251	188	30	}	}	PUNCT
ejpam-5251	188	31	is	be	AUX
ejpam-5251	188	32	a	a	DET
ejpam-5251	188	33	γ+hg	γ+hg	NOUN
ejpam-5251	188	34	-	-	PUNCT
ejpam-5251	188	35	set	set	NOUN
ejpam-5251	188	36	.	.	PUNCT
ejpam-5251	189	1	hence	hence	ADV
ejpam-5251	189	2	,	,	PUNCT
ejpam-5251	189	3	γ	γ	X
ejpam-5251	189	4	+	+	X
ejpam-5251	189	5	hg(p	hg(p	NOUN
ejpam-5251	189	6	)	)	PUNCT
ejpam-5251	190	1	=	=	SYM
ejpam-5251	190	2	6	6	X
ejpam-5251	190	3	.	.	PUNCT
ejpam-5251	190	4	proposition	proposition	NOUN
ejpam-5251	190	5	3	3	NUM
ejpam-5251	190	6	.	.	PUNCT
ejpam-5251	191	1	let	let	VERB
ejpam-5251	191	2	g	g	PROPN
ejpam-5251	191	3	=	=	PROPN
ejpam-5251	191	4	km	km	PROPN
ejpam-5251	191	5	,	,	PUNCT
ejpam-5251	191	6	n	n	CCONJ
ejpam-5251	191	7	with	with	ADP
ejpam-5251	191	8	partite	partite	ADJ
ejpam-5251	191	9	sets	set	NOUN
ejpam-5251	191	10	u	u	NOUN
ejpam-5251	191	11	and	and	CCONJ
ejpam-5251	191	12	w	w	NOUN
ejpam-5251	191	13	with	with	ADP
ejpam-5251	191	14	|u	|u	ADJ
ejpam-5251	191	15	|	|	NOUN
ejpam-5251	191	16	=	=	SYM
ejpam-5251	191	17	m	m	NOUN
ejpam-5251	191	18	≥	≥	NOUN
ejpam-5251	191	19	2	2	NUM
ejpam-5251	191	20	and	and	CCONJ
ejpam-5251	192	1	|w	|w	ADJ
ejpam-5251	192	2	|	|	NOUN
ejpam-5251	192	3	=	=	SYM
ejpam-5251	192	4	n	n	X
ejpam-5251	192	5	≥	≥	NOUN
ejpam-5251	192	6	2	2	NUM
ejpam-5251	192	7	.	.	PUNCT
ejpam-5251	193	1	then	then	ADV
ejpam-5251	193	2	s	s	VERB
ejpam-5251	193	3	⊆	⊆	NUM
ejpam-5251	193	4	v	v	NOUN
ejpam-5251	193	5	(	(	PUNCT
ejpam-5251	193	6	g	g	NOUN
ejpam-5251	193	7	)	)	PUNCT
ejpam-5251	193	8	is	be	AUX
ejpam-5251	193	9	a	a	DET
ejpam-5251	193	10	minimal	minimal	ADJ
ejpam-5251	193	11	geodetic	geodetic	ADJ
ejpam-5251	193	12	hop	hop	NOUN
ejpam-5251	193	13	dominating	dominating	NOUN
ejpam-5251	193	14	set	set	NOUN
ejpam-5251	193	15	of	of	ADP
ejpam-5251	193	16	g	g	PROPN
ejpam-5251	193	17	if	if	SCONJ
ejpam-5251	194	1	and	and	CCONJ
ejpam-5251	194	2	only	only	ADV
ejpam-5251	194	3	if	if	SCONJ
ejpam-5251	194	4	s	s	NOUN
ejpam-5251	194	5	is	be	AUX
ejpam-5251	194	6	one	one	NUM
ejpam-5251	194	7	of	of	ADP
ejpam-5251	194	8	the	the	DET
ejpam-5251	194	9	following	following	NOUN
ejpam-5251	194	10	:	:	PUNCT
ejpam-5251	194	11	(	(	PUNCT
ejpam-5251	194	12	i	i	NOUN
ejpam-5251	194	13	)	)	PUNCT
ejpam-5251	194	14	s	s	PART
ejpam-5251	194	15	=	=	SYM
ejpam-5251	194	16	u	u	NOUN
ejpam-5251	194	17	∪	∪	X
ejpam-5251	194	18	{	{	PUNCT
ejpam-5251	194	19	w	w	NOUN
ejpam-5251	194	20	}	}	PUNCT
ejpam-5251	194	21	where	where	SCONJ
ejpam-5251	194	22	w	w	PROPN
ejpam-5251	194	23	∈	∈	PROPN
ejpam-5251	194	24	w	w	PROPN
ejpam-5251	194	25	d.	d.	PROPN
ejpam-5251	194	26	catian	catian	PROPN
ejpam-5251	194	27	,	,	PUNCT
ejpam-5251	194	28	i.	i.	PROPN
ejpam-5251	194	29	s.	s.	PROPN
ejpam-5251	194	30	aniversario	aniversario	PROPN
ejpam-5251	194	31	,	,	PUNCT
ejpam-5251	194	32	f.	f.	PROPN
ejpam-5251	194	33	p.	p.	PROPN
ejpam-5251	194	34	jamil	jamil	PROPN
ejpam-5251	194	35	/	/	SYM
ejpam-5251	194	36	eur	eur	PROPN
ejpam-5251	194	37	.	.	PUNCT
ejpam-5251	195	1	j.	j.	PROPN
ejpam-5251	195	2	pure	pure	PROPN
ejpam-5251	195	3	appl	appl	PROPN
ejpam-5251	195	4	.	.	PROPN
ejpam-5251	195	5	math	math	PROPN
ejpam-5251	195	6	,	,	PUNCT
ejpam-5251	195	7	17	17	NUM
ejpam-5251	195	8	(	(	PUNCT
ejpam-5251	195	9	3	3	NUM
ejpam-5251	195	10	)	)	PUNCT
ejpam-5251	195	11	(	(	PUNCT
ejpam-5251	195	12	2024	2024	NUM
ejpam-5251	195	13	)	)	PUNCT
ejpam-5251	195	14	,	,	PUNCT
ejpam-5251	195	15	1737	1737	NUM
ejpam-5251	195	16	-	-	SYM
ejpam-5251	195	17	1750	1750	NUM
ejpam-5251	195	18	1742	1742	NUM
ejpam-5251	195	19	(	(	PUNCT
ejpam-5251	195	20	ii	ii	NOUN
ejpam-5251	195	21	)	)	PUNCT
ejpam-5251	195	22	s	s	PART
ejpam-5251	196	1	=	=	NOUN
ejpam-5251	196	2	w	w	NOUN
ejpam-5251	196	3	∪	∪	X
ejpam-5251	196	4	{	{	PUNCT
ejpam-5251	196	5	u	u	NOUN
ejpam-5251	196	6	}	}	PUNCT
ejpam-5251	196	7	where	where	SCONJ
ejpam-5251	196	8	u	u	PROPN
ejpam-5251	196	9	∈	∈	PROPN
ejpam-5251	196	10	u	u	SYM
ejpam-5251	196	11	(	(	PUNCT
ejpam-5251	196	12	iii	iii	NOUN
ejpam-5251	196	13	)	)	PUNCT
ejpam-5251	196	14	s	s	PART
ejpam-5251	196	15	=	=	PUNCT
ejpam-5251	196	16	{	{	PUNCT
ejpam-5251	196	17	u	u	NOUN
ejpam-5251	196	18	,	,	PUNCT
ejpam-5251	196	19	v	v	NOUN
ejpam-5251	196	20	,	,	PUNCT
ejpam-5251	196	21	w	w	PROPN
ejpam-5251	196	22	,	,	PUNCT
ejpam-5251	196	23	z	z	NOUN
ejpam-5251	196	24	}	}	PUNCT
ejpam-5251	196	25	where	where	SCONJ
ejpam-5251	196	26	u	u	NOUN
ejpam-5251	196	27	,	,	PUNCT
ejpam-5251	196	28	v	v	ADP
ejpam-5251	196	29	∈	∈	PROPN
ejpam-5251	196	30	u	u	NOUN
ejpam-5251	196	31	and	and	CCONJ
ejpam-5251	196	32	w	w	PROPN
ejpam-5251	196	33	,	,	PUNCT
ejpam-5251	196	34	z	z	PROPN
ejpam-5251	196	35	∈	∈	PROPN
ejpam-5251	196	36	w	w	NOUN
ejpam-5251	196	37	,	,	PUNCT
ejpam-5251	196	38	in	in	ADP
ejpam-5251	196	39	case	case	NOUN
ejpam-5251	196	40	where	where	SCONJ
ejpam-5251	196	41	m	m	VERB
ejpam-5251	196	42	,	,	PUNCT
ejpam-5251	196	43	n	n	PRON
ejpam-5251	196	44	≥	≥	NOUN
ejpam-5251	196	45	3	3	NUM
ejpam-5251	196	46	.	.	PUNCT
ejpam-5251	197	1	proof	proof	NOUN
ejpam-5251	197	2	.	.	PUNCT
ejpam-5251	198	1	it	it	PRON
ejpam-5251	198	2	is	be	AUX
ejpam-5251	198	3	easy	easy	ADJ
ejpam-5251	198	4	to	to	PART
ejpam-5251	198	5	verify	verify	VERB
ejpam-5251	198	6	that	that	SCONJ
ejpam-5251	198	7	if	if	SCONJ
ejpam-5251	198	8	s	s	NOUN
ejpam-5251	198	9	is	be	AUX
ejpam-5251	198	10	any	any	PRON
ejpam-5251	198	11	of	of	ADP
ejpam-5251	198	12	the	the	DET
ejpam-5251	198	13	sets	set	NOUN
ejpam-5251	198	14	described	describe	VERB
ejpam-5251	198	15	in	in	ADP
ejpam-5251	198	16	(	(	PUNCT
ejpam-5251	198	17	i	i	NOUN
ejpam-5251	198	18	)	)	PUNCT
ejpam-5251	198	19	,	,	PUNCT
ejpam-5251	198	20	(	(	PUNCT
ejpam-5251	198	21	ii	ii	NOUN
ejpam-5251	198	22	)	)	PUNCT
ejpam-5251	198	23	and	and	CCONJ
ejpam-5251	198	24	(	(	PUNCT
ejpam-5251	198	25	iii	iii	NOUN
ejpam-5251	198	26	)	)	PUNCT
ejpam-5251	198	27	,	,	PUNCT
ejpam-5251	198	28	then	then	ADV
ejpam-5251	198	29	s	s	VERB
ejpam-5251	198	30	is	be	AUX
ejpam-5251	198	31	a	a	DET
ejpam-5251	198	32	minimal	minimal	ADJ
ejpam-5251	198	33	geodetic	geodetic	ADJ
ejpam-5251	198	34	hop	hop	NOUN
ejpam-5251	198	35	dominating	dominating	NOUN
ejpam-5251	198	36	set	set	NOUN
ejpam-5251	198	37	of	of	ADP
ejpam-5251	198	38	g.	g.	PROPN
ejpam-5251	198	39	conversely	conversely	ADV
ejpam-5251	198	40	,	,	PUNCT
ejpam-5251	198	41	suppose	suppose	VERB
ejpam-5251	198	42	s	s	NOUN
ejpam-5251	198	43	is	be	AUX
ejpam-5251	198	44	a	a	DET
ejpam-5251	198	45	minimal	minimal	ADJ
ejpam-5251	198	46	geodetic	geodetic	ADJ
ejpam-5251	198	47	hop	hop	NOUN
ejpam-5251	198	48	dominating	dominating	NOUN
ejpam-5251	198	49	set	set	NOUN
ejpam-5251	198	50	of	of	ADP
ejpam-5251	198	51	g.	g.	PROPN
ejpam-5251	198	52	being	be	AUX
ejpam-5251	198	53	a	a	DET
ejpam-5251	198	54	hop	hop	NOUN
ejpam-5251	198	55	dominating	dominating	NOUN
ejpam-5251	198	56	set	set	NOUN
ejpam-5251	198	57	,	,	PUNCT
ejpam-5251	198	58	s	s	PART
ejpam-5251	198	59	∩	∩	ADJ
ejpam-5251	198	60	u	u	ADJ
ejpam-5251	198	61	̸=	̸=	PROPN
ejpam-5251	198	62	∅	∅	NOUN
ejpam-5251	198	63	and	and	CCONJ
ejpam-5251	198	64	s	s	X
ejpam-5251	198	65	∩	∩	NOUN
ejpam-5251	198	66	w	w	PROPN
ejpam-5251	198	67	̸=	̸=	PROPN
ejpam-5251	198	68	∅.	∅.	ADV
ejpam-5251	198	69	suppose	suppose	VERB
ejpam-5251	198	70	that	that	SCONJ
ejpam-5251	198	71	u	u	PROPN
ejpam-5251	198	72	⊆	⊆	NUM
ejpam-5251	198	73	s.	s.	PROPN
ejpam-5251	198	74	note	note	VERB
ejpam-5251	198	75	that	that	SCONJ
ejpam-5251	198	76	if	if	SCONJ
ejpam-5251	198	77	w	w	PROPN
ejpam-5251	198	78	∈	∈	PROPN
ejpam-5251	198	79	s	s	PART
ejpam-5251	198	80	∩	∩	ADJ
ejpam-5251	198	81	w	w	NOUN
ejpam-5251	198	82	,	,	PUNCT
ejpam-5251	198	83	then	then	ADV
ejpam-5251	198	84	u	u	NOUN
ejpam-5251	198	85	∪	∪	X
ejpam-5251	198	86	{	{	PUNCT
ejpam-5251	198	87	w	w	NOUN
ejpam-5251	198	88	}	}	PUNCT
ejpam-5251	198	89	is	be	AUX
ejpam-5251	198	90	a	a	DET
ejpam-5251	198	91	geodetic	geodetic	ADJ
ejpam-5251	198	92	hop	hop	NOUN
ejpam-5251	198	93	dominating	dominating	NOUN
ejpam-5251	198	94	set	set	NOUN
ejpam-5251	198	95	of	of	ADP
ejpam-5251	198	96	g.	g.	PROPN
ejpam-5251	198	97	by	by	ADP
ejpam-5251	198	98	the	the	DET
ejpam-5251	198	99	minimality	minimality	NOUN
ejpam-5251	198	100	of	of	ADP
ejpam-5251	198	101	s	s	PROPN
ejpam-5251	198	102	,	,	PUNCT
ejpam-5251	198	103	s	s	PART
ejpam-5251	198	104	=	=	VERB
ejpam-5251	198	105	u	u	NOUN
ejpam-5251	198	106	∪	∪	X
ejpam-5251	198	107	{	{	PUNCT
ejpam-5251	198	108	w	w	NOUN
ejpam-5251	198	109	}	}	PUNCT
ejpam-5251	198	110	.	.	PUNCT
ejpam-5251	199	1	similarly	similarly	ADV
ejpam-5251	199	2	,	,	PUNCT
ejpam-5251	199	3	if	if	SCONJ
ejpam-5251	199	4	w	w	ADP
ejpam-5251	199	5	⊆	⊆	NUM
ejpam-5251	199	6	s	s	NOUN
ejpam-5251	199	7	,	,	PUNCT
ejpam-5251	199	8	then	then	ADV
ejpam-5251	199	9	s	s	VERB
ejpam-5251	199	10	=	=	SYM
ejpam-5251	199	11	w	w	PROPN
ejpam-5251	199	12	∪{u	∪{u	PROPN
ejpam-5251	199	13	}	}	PUNCT
ejpam-5251	199	14	,	,	PUNCT
ejpam-5251	199	15	where	where	SCONJ
ejpam-5251	199	16	u	u	PROPN
ejpam-5251	199	17	∈	∈	PROPN
ejpam-5251	199	18	u	u	NOUN
ejpam-5251	199	19	.	.	PUNCT
ejpam-5251	200	1	now	now	ADV
ejpam-5251	200	2	,	,	PUNCT
ejpam-5251	200	3	suppose	suppose	VERB
ejpam-5251	200	4	u	u	PRON
ejpam-5251	200	5	\s	\s	ADP
ejpam-5251	200	6	̸=	̸=	PROPN
ejpam-5251	200	7	∅	∅	NOUN
ejpam-5251	200	8	and	and	CCONJ
ejpam-5251	200	9	w	w	PROPN
ejpam-5251	200	10	\s	\s	PROPN
ejpam-5251	200	11	̸=	̸=	PROPN
ejpam-5251	200	12	∅.	∅.	ADV
ejpam-5251	200	13	since	since	SCONJ
ejpam-5251	200	14	s	s	NOUN
ejpam-5251	200	15	is	be	AUX
ejpam-5251	200	16	geodetic	geodetic	ADJ
ejpam-5251	200	17	,	,	PUNCT
ejpam-5251	200	18	|s	|s	PROPN
ejpam-5251	200	19	∩	∩	PROPN
ejpam-5251	200	20	u	u	NOUN
ejpam-5251	200	21	|	|	ADV
ejpam-5251	200	22	≥	≥	NOUN
ejpam-5251	200	23	2	2	NUM
ejpam-5251	200	24	and	and	CCONJ
ejpam-5251	200	25	|s	|s	PROPN
ejpam-5251	200	26	∩w	∩w	NOUN
ejpam-5251	201	1	|	|	CCONJ
ejpam-5251	201	2	≥	≥	NOUN
ejpam-5251	201	3	2	2	NUM
ejpam-5251	201	4	.	.	X
ejpam-5251	201	5	pick	pick	VERB
ejpam-5251	201	6	u	u	NOUN
ejpam-5251	201	7	,	,	PUNCT
ejpam-5251	201	8	v	v	PROPN
ejpam-5251	201	9	∈	∈	NOUN
ejpam-5251	201	10	s	s	PART
ejpam-5251	201	11	∩	∩	ADJ
ejpam-5251	201	12	u	u	NOUN
ejpam-5251	201	13	and	and	CCONJ
ejpam-5251	201	14	w	w	PROPN
ejpam-5251	201	15	,	,	PUNCT
ejpam-5251	201	16	z	z	PROPN
ejpam-5251	201	17	∈	∈	NOUN
ejpam-5251	201	18	s	s	VERB
ejpam-5251	201	19	∩w	∩w	NOUN
ejpam-5251	201	20	.	.	PUNCT
ejpam-5251	202	1	then	then	ADV
ejpam-5251	202	2	,	,	PUNCT
ejpam-5251	202	3	{	{	PUNCT
ejpam-5251	202	4	u	u	NOUN
ejpam-5251	202	5	,	,	PUNCT
ejpam-5251	202	6	v	v	NOUN
ejpam-5251	202	7	,	,	PUNCT
ejpam-5251	202	8	w	w	PROPN
ejpam-5251	202	9	,	,	PUNCT
ejpam-5251	202	10	z	z	NOUN
ejpam-5251	202	11	}	}	PUNCT
ejpam-5251	202	12	is	be	AUX
ejpam-5251	202	13	a	a	DET
ejpam-5251	202	14	minimal	minimal	ADJ
ejpam-5251	202	15	geodetic	geodetic	ADJ
ejpam-5251	202	16	hop	hop	NOUN
ejpam-5251	202	17	dominating	dominating	NOUN
ejpam-5251	202	18	set	set	NOUN
ejpam-5251	202	19	of	of	ADP
ejpam-5251	202	20	g.	g.	PROPN
ejpam-5251	202	21	thus	thus	ADV
ejpam-5251	202	22	,	,	PUNCT
ejpam-5251	202	23	s	s	VERB
ejpam-5251	202	24	=	=	PUNCT
ejpam-5251	202	25	{	{	PUNCT
ejpam-5251	202	26	u	u	NOUN
ejpam-5251	202	27	,	,	PUNCT
ejpam-5251	202	28	v	v	NOUN
ejpam-5251	202	29	,	,	PUNCT
ejpam-5251	202	30	w	w	PROPN
ejpam-5251	202	31	,	,	PUNCT
ejpam-5251	202	32	z	z	NOUN
ejpam-5251	202	33	}	}	PUNCT
ejpam-5251	202	34	.	.	PUNCT
ejpam-5251	203	1	corollary	corollary	ADJ
ejpam-5251	203	2	2	2	NUM
ejpam-5251	203	3	.	.	PUNCT
ejpam-5251	204	1	let	let	VERB
ejpam-5251	204	2	g	g	PROPN
ejpam-5251	204	3	=	=	PROPN
ejpam-5251	204	4	km	km	PROPN
ejpam-5251	204	5	,	,	PUNCT
ejpam-5251	204	6	n	n	CCONJ
ejpam-5251	204	7	where	where	SCONJ
ejpam-5251	204	8	m	m	VERB
ejpam-5251	204	9	,	,	PUNCT
ejpam-5251	204	10	n	n	PRON
ejpam-5251	204	11	≥	≥	NOUN
ejpam-5251	204	12	2	2	NUM
ejpam-5251	204	13	.	.	PUNCT
ejpam-5251	204	14	then	then	ADV
ejpam-5251	204	15	γ+hg(g	γ+hg(g	X
ejpam-5251	204	16	)	)	PUNCT
ejpam-5251	205	1	=	=	SYM
ejpam-5251	205	2	max{m	max{m	NOUN
ejpam-5251	205	3	,	,	PUNCT
ejpam-5251	205	4	n}+	n}+	NOUN
ejpam-5251	205	5	1	1	NUM
ejpam-5251	205	6	.	.	PUNCT
ejpam-5251	205	7	proof	proof	NOUN
ejpam-5251	205	8	.	.	PUNCT
ejpam-5251	206	1	if	if	SCONJ
ejpam-5251	206	2	n	n	NOUN
ejpam-5251	206	3	=	=	SYM
ejpam-5251	206	4	m	m	NOUN
ejpam-5251	206	5	=	=	SYM
ejpam-5251	206	6	2	2	NUM
ejpam-5251	206	7	,	,	PUNCT
ejpam-5251	206	8	then	then	ADV
ejpam-5251	206	9	γ+hg(g	γ+hg(g	X
ejpam-5251	206	10	)	)	PUNCT
ejpam-5251	206	11	=	=	SYM
ejpam-5251	206	12	3	3	NUM
ejpam-5251	206	13	=	=	SYM
ejpam-5251	206	14	1+max{m	1+max{m	NUM
ejpam-5251	206	15	,	,	PUNCT
ejpam-5251	206	16	n	n	CCONJ
ejpam-5251	206	17	}	}	PUNCT
ejpam-5251	206	18	.	.	PUNCT
ejpam-5251	207	1	if	if	SCONJ
ejpam-5251	207	2	n	n	NUM
ejpam-5251	207	3	≥	≥	VERB
ejpam-5251	207	4	3	3	NUM
ejpam-5251	207	5	or	or	CCONJ
ejpam-5251	207	6	m	m	PROPN
ejpam-5251	207	7	≥	≥	NOUN
ejpam-5251	207	8	3	3	NUM
ejpam-5251	207	9	,	,	PUNCT
ejpam-5251	207	10	then	then	ADV
ejpam-5251	207	11	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	207	12	)	)	PUNCT
ejpam-5251	207	13	≥	≥	NOUN
ejpam-5251	207	14	4	4	NUM
ejpam-5251	207	15	.	.	PUNCT
ejpam-5251	208	1	thus	thus	ADV
ejpam-5251	208	2	,	,	PUNCT
ejpam-5251	208	3	γ+hg(g	γ+hg(g	X
ejpam-5251	208	4	)	)	PUNCT
ejpam-5251	209	1	=	=	PUNCT
ejpam-5251	209	2	1	1	NUM
ejpam-5251	209	3	+	+	ADJ
ejpam-5251	209	4	max{m	max{m	NOUN
ejpam-5251	209	5	,	,	PUNCT
ejpam-5251	209	6	n	n	CCONJ
ejpam-5251	209	7	}	}	PUNCT
ejpam-5251	209	8	.	.	PUNCT
ejpam-5251	210	1	3	3	X
ejpam-5251	210	2	.	.	X
ejpam-5251	210	3	realization	realization	NOUN
ejpam-5251	210	4	problem	problem	NOUN
ejpam-5251	210	5	theorem	theorem	VERB
ejpam-5251	210	6	3	3	NUM
ejpam-5251	210	7	.	.	X
ejpam-5251	210	8	for	for	ADP
ejpam-5251	210	9	every	every	DET
ejpam-5251	210	10	pair	pair	NOUN
ejpam-5251	210	11	of	of	ADP
ejpam-5251	210	12	positive	positive	ADJ
ejpam-5251	210	13	integers	integer	NOUN
ejpam-5251	210	14	a	a	PRON
ejpam-5251	210	15	and	and	CCONJ
ejpam-5251	210	16	b	b	NOUN
ejpam-5251	210	17	with	with	ADP
ejpam-5251	210	18	2	2	NUM
ejpam-5251	210	19	≤	≤	NOUN
ejpam-5251	210	20	a	a	DET
ejpam-5251	210	21	≤	≤	NUM
ejpam-5251	210	22	b	b	NOUN
ejpam-5251	210	23	,	,	PUNCT
ejpam-5251	210	24	there	there	PRON
ejpam-5251	210	25	exists	exist	VERB
ejpam-5251	210	26	a	a	DET
ejpam-5251	210	27	connected	connected	ADJ
ejpam-5251	210	28	graph	graph	NOUN
ejpam-5251	210	29	g	g	ADP
ejpam-5251	210	30	such	such	ADJ
ejpam-5251	210	31	that	that	DET
ejpam-5251	210	32	γhg(g	γhg(g	PROPN
ejpam-5251	210	33	)	)	PUNCT
ejpam-5251	210	34	=	=	NOUN
ejpam-5251	210	35	a	a	PRON
ejpam-5251	210	36	and	and	CCONJ
ejpam-5251	210	37	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	210	38	)	)	PUNCT
ejpam-5251	210	39	=	=	SYM
ejpam-5251	210	40	b.	b.	PROPN
ejpam-5251	210	41	proof	proof	NOUN
ejpam-5251	210	42	.	.	PUNCT
ejpam-5251	211	1	if	if	SCONJ
ejpam-5251	211	2	a	a	DET
ejpam-5251	211	3	=	=	SYM
ejpam-5251	211	4	b	b	NOUN
ejpam-5251	211	5	,	,	PUNCT
ejpam-5251	211	6	then	then	ADV
ejpam-5251	211	7	take	take	VERB
ejpam-5251	211	8	g	g	PROPN
ejpam-5251	211	9	=	=	SYM
ejpam-5251	211	10	ka	ka	PROPN
ejpam-5251	211	11	.	.	PROPN
ejpam-5251	212	1	for	for	ADP
ejpam-5251	212	2	this	this	DET
ejpam-5251	212	3	graph	graph	NOUN
ejpam-5251	212	4	g	g	NOUN
ejpam-5251	212	5	,	,	PUNCT
ejpam-5251	212	6	γhg(g	γhg(g	PROPN
ejpam-5251	212	7	)	)	PUNCT
ejpam-5251	212	8	=	=	X
ejpam-5251	212	9	a	a	DET
ejpam-5251	212	10	=	=	SYM
ejpam-5251	212	11	b	b	PROPN
ejpam-5251	212	12	=	=	SYM
ejpam-5251	212	13	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	212	14	)	)	PUNCT
ejpam-5251	212	15	assume	assume	VERB
ejpam-5251	212	16	a	a	DET
ejpam-5251	212	17	<	<	X
ejpam-5251	212	18	b.	b.	PROPN
ejpam-5251	212	19	write	write	PROPN
ejpam-5251	212	20	b	b	PROPN
ejpam-5251	212	21	=	=	PUNCT
ejpam-5251	212	22	a	a	PROPN
ejpam-5251	212	23	+	+	X
ejpam-5251	212	24	k	k	NOUN
ejpam-5251	212	25	for	for	ADP
ejpam-5251	212	26	some	some	DET
ejpam-5251	212	27	k	k	PROPN
ejpam-5251	212	28	≥	≥	NUM
ejpam-5251	212	29	1	1	NUM
ejpam-5251	212	30	.	.	PUNCT
ejpam-5251	213	1	if	if	SCONJ
ejpam-5251	213	2	a	a	DET
ejpam-5251	213	3	=	=	SYM
ejpam-5251	213	4	2	2	NUM
ejpam-5251	213	5	,	,	PUNCT
ejpam-5251	213	6	then	then	ADV
ejpam-5251	213	7	we	we	PRON
ejpam-5251	213	8	consider	consider	VERB
ejpam-5251	213	9	the	the	DET
ejpam-5251	213	10	graph	graph	NOUN
ejpam-5251	213	11	g	g	PROPN
ejpam-5251	213	12	=	=	PUNCT
ejpam-5251	213	13	g1	g1	PROPN
ejpam-5251	213	14	in	in	ADP
ejpam-5251	213	15	figure	figure	NOUN
ejpam-5251	213	16	2	2	NUM
ejpam-5251	213	17	obtained	obtain	VERB
ejpam-5251	213	18	by	by	ADP
ejpam-5251	213	19	constructing	construct	VERB
ejpam-5251	213	20	k	k	PROPN
ejpam-5251	213	21	+	+	CCONJ
ejpam-5251	213	22	2	2	NUM
ejpam-5251	213	23	copies	copy	NOUN
ejpam-5251	213	24	of	of	ADP
ejpam-5251	213	25	p4	p4	ADJ
ejpam-5251	213	26	with	with	ADP
ejpam-5251	213	27	common	common	ADJ
ejpam-5251	213	28	end	end	NOUN
ejpam-5251	213	29	-	-	PUNCT
ejpam-5251	213	30	vertices	vertex	NOUN
ejpam-5251	213	31	.	.	PUNCT
ejpam-5251	214	1	u	u	NOUN
ejpam-5251	214	2	w1	w1	NOUN
ejpam-5251	214	3	z1	z1	PROPN
ejpam-5251	214	4	v	v	ADP
ejpam-5251	214	5	w2	w2	NOUN
ejpam-5251	214	6	z2	z2	PROPN
ejpam-5251	214	7	...	...	PUNCT
ejpam-5251	214	8	wk+2	wk+2	NUM
ejpam-5251	214	9	zk+2	zk+2	NOUN
ejpam-5251	214	10	figure	figure	NOUN
ejpam-5251	214	11	2	2	NUM
ejpam-5251	214	12	:	:	PUNCT
ejpam-5251	214	13	g1	g1	NOUN
ejpam-5251	214	14	:	:	PUNCT
ejpam-5251	214	15	a	a	DET
ejpam-5251	214	16	connected	connected	ADJ
ejpam-5251	214	17	graph	graph	NOUN
ejpam-5251	214	18	complying	comply	VERB
ejpam-5251	214	19	with	with	ADP
ejpam-5251	214	20	the	the	DET
ejpam-5251	214	21	specifications	specification	NOUN
ejpam-5251	214	22	of	of	ADP
ejpam-5251	214	23	theorem	theorem	NOUN
ejpam-5251	214	24	3	3	NUM
ejpam-5251	214	25	when	when	SCONJ
ejpam-5251	214	26	a	a	DET
ejpam-5251	214	27	=	=	SYM
ejpam-5251	214	28	2	2	NUM
ejpam-5251	214	29	let	let	VERB
ejpam-5251	214	30	s	s	VERB
ejpam-5251	214	31	=	=	PUNCT
ejpam-5251	214	32	{	{	PUNCT
ejpam-5251	214	33	u	u	NOUN
ejpam-5251	214	34	,	,	PUNCT
ejpam-5251	214	35	v	v	NOUN
ejpam-5251	214	36	}	}	PUNCT
ejpam-5251	214	37	and	and	CCONJ
ejpam-5251	214	38	t	t	NOUN
ejpam-5251	214	39	=	=	SYM
ejpam-5251	214	40	{	{	PUNCT
ejpam-5251	214	41	{	{	PUNCT
ejpam-5251	214	42	w2i−1	w2i−1	PROPN
ejpam-5251	214	43	,	,	PUNCT
ejpam-5251	214	44	z2i	z2i	PROPN
ejpam-5251	214	45	:	:	PUNCT
ejpam-5251	215	1	i	i	PRON
ejpam-5251	215	2	=	=	NOUN
ejpam-5251	215	3	1	1	NUM
ejpam-5251	215	4	,	,	PUNCT
ejpam-5251	215	5	2	2	NUM
ejpam-5251	215	6	,	,	PUNCT
ejpam-5251	215	7	3	3	NUM
ejpam-5251	215	8	,	,	PUNCT
ejpam-5251	215	9	.	.	PUNCT
ejpam-5251	215	10	.	.	PUNCT
ejpam-5251	215	11	.	.	PUNCT
ejpam-5251	216	1	,	,	PUNCT
ejpam-5251	216	2	k2	k2	NOUN
ejpam-5251	216	3	+	+	CCONJ
ejpam-5251	216	4	1	1	NUM
ejpam-5251	216	5	}	}	PUNCT
ejpam-5251	216	6	,	,	PUNCT
ejpam-5251	216	7	k	k	PROPN
ejpam-5251	216	8	is	be	AUX
ejpam-5251	216	9	even	even	ADV
ejpam-5251	216	10	;	;	PUNCT
ejpam-5251	216	11	{	{	PUNCT
ejpam-5251	216	12	w1	w1	NOUN
ejpam-5251	216	13	,	,	PUNCT
ejpam-5251	216	14	w2i+1	w2i+1	PROPN
ejpam-5251	216	15	,	,	PUNCT
ejpam-5251	216	16	z2i	z2i	NOUN
ejpam-5251	216	17	:	:	PUNCT
ejpam-5251	217	1	i	i	PRON
ejpam-5251	217	2	=	=	NOUN
ejpam-5251	217	3	1	1	NUM
ejpam-5251	217	4	,	,	PUNCT
ejpam-5251	217	5	2	2	NUM
ejpam-5251	217	6	,	,	PUNCT
ejpam-5251	217	7	3	3	NUM
ejpam-5251	217	8	,	,	PUNCT
ejpam-5251	217	9	.	.	PUNCT
ejpam-5251	217	10	.	.	PUNCT
ejpam-5251	217	11	.	.	PUNCT
ejpam-5251	218	1	,	,	PUNCT
ejpam-5251	218	2	⌊k+1	⌊k+1	X
ejpam-5251	218	3	2	2	NUM
ejpam-5251	218	4	⌋	⌋	NOUN
ejpam-5251	218	5	}	}	PUNCT
ejpam-5251	218	6	,	,	PUNCT
ejpam-5251	218	7	k	k	PROPN
ejpam-5251	218	8	is	be	AUX
ejpam-5251	218	9	odd	odd	ADJ
ejpam-5251	218	10	.	.	PUNCT
ejpam-5251	219	1	then	then	ADV
ejpam-5251	219	2	s	s	VERB
ejpam-5251	219	3	and	and	CCONJ
ejpam-5251	219	4	t	t	PROPN
ejpam-5251	219	5	are	be	AUX
ejpam-5251	219	6	γhg	γhg	ADV
ejpam-5251	219	7	-	-	PUNCT
ejpam-5251	219	8	set	set	VERB
ejpam-5251	219	9	and	and	CCONJ
ejpam-5251	219	10	γ+hg	γ+hg	NOUN
ejpam-5251	219	11	-	-	PUNCT
ejpam-5251	219	12	set	set	NOUN
ejpam-5251	219	13	of	of	ADP
ejpam-5251	219	14	g	g	NOUN
ejpam-5251	219	15	,	,	PUNCT
ejpam-5251	219	16	respectively	respectively	ADV
ejpam-5251	219	17	.	.	PUNCT
ejpam-5251	220	1	suppose	suppose	VERB
ejpam-5251	220	2	that	that	SCONJ
ejpam-5251	220	3	a	a	DET
ejpam-5251	220	4	≥	≥	NOUN
ejpam-5251	220	5	3	3	NUM
ejpam-5251	220	6	.	.	PUNCT
ejpam-5251	220	7	obtain	obtain	VERB
ejpam-5251	220	8	the	the	DET
ejpam-5251	220	9	graph	graph	NOUN
ejpam-5251	220	10	g	g	PROPN
ejpam-5251	220	11	=	=	PUNCT
ejpam-5251	220	12	g2	g2	PROPN
ejpam-5251	220	13	as	as	ADP
ejpam-5251	220	14	in	in	ADP
ejpam-5251	220	15	figure	figure	NOUN
ejpam-5251	220	16	3	3	NUM
ejpam-5251	220	17	from	from	ADP
ejpam-5251	220	18	g1	g1	NOUN
ejpam-5251	220	19	by	by	ADP
ejpam-5251	220	20	adding	add	VERB
ejpam-5251	220	21	to	to	ADP
ejpam-5251	220	22	g1	g1	PROPN
ejpam-5251	220	23	(	(	PUNCT
ejpam-5251	220	24	a−	a−	PROPN
ejpam-5251	220	25	2	2	NUM
ejpam-5251	220	26	)	)	PUNCT
ejpam-5251	220	27	pendant	pendant	ADJ
ejpam-5251	220	28	edges	edge	NOUN
ejpam-5251	220	29	vxj	vxj	NOUN
ejpam-5251	220	30	,	,	PUNCT
ejpam-5251	220	31	j	j	PROPN
ejpam-5251	220	32	=	=	SYM
ejpam-5251	220	33	1	1	NUM
ejpam-5251	220	34	,	,	PUNCT
ejpam-5251	220	35	2	2	NUM
ejpam-5251	220	36	,	,	PUNCT
ejpam-5251	220	37	.	.	PUNCT
ejpam-5251	220	38	.	.	PUNCT
ejpam-5251	221	1	.	.	PUNCT
ejpam-5251	222	1	,	,	PUNCT
ejpam-5251	222	2	a−	a−	PROPN
ejpam-5251	222	3	2	2	NUM
ejpam-5251	222	4	.	.	PUNCT
ejpam-5251	222	5	d.	d.	PROPN
ejpam-5251	222	6	catian	catian	PROPN
ejpam-5251	222	7	,	,	PUNCT
ejpam-5251	222	8	i.	i.	PROPN
ejpam-5251	222	9	s.	s.	PROPN
ejpam-5251	222	10	aniversario	aniversario	PROPN
ejpam-5251	222	11	,	,	PUNCT
ejpam-5251	222	12	f.	f.	PROPN
ejpam-5251	222	13	p.	p.	PROPN
ejpam-5251	222	14	jamil	jamil	PROPN
ejpam-5251	222	15	/	/	SYM
ejpam-5251	222	16	eur	eur	PROPN
ejpam-5251	222	17	.	.	PUNCT
ejpam-5251	223	1	j.	j.	PROPN
ejpam-5251	223	2	pure	pure	PROPN
ejpam-5251	223	3	appl	appl	PROPN
ejpam-5251	223	4	.	.	PROPN
ejpam-5251	223	5	math	math	PROPN
ejpam-5251	223	6	,	,	PUNCT
ejpam-5251	223	7	17	17	NUM
ejpam-5251	223	8	(	(	PUNCT
ejpam-5251	223	9	3	3	NUM
ejpam-5251	223	10	)	)	PUNCT
ejpam-5251	223	11	(	(	PUNCT
ejpam-5251	223	12	2024	2024	NUM
ejpam-5251	223	13	)	)	PUNCT
ejpam-5251	223	14	,	,	PUNCT
ejpam-5251	223	15	1737	1737	NUM
ejpam-5251	223	16	-	-	SYM
ejpam-5251	223	17	1750	1750	NUM
ejpam-5251	223	18	1743	1743	NUM
ejpam-5251	223	19	u	u	PROPN
ejpam-5251	223	20	w1	w1	NOUN
ejpam-5251	223	21	z1	z1	PROPN
ejpam-5251	223	22	v	v	ADP
ejpam-5251	223	23	w2	w2	NOUN
ejpam-5251	223	24	z2	z2	PROPN
ejpam-5251	223	25	...	...	PUNCT
ejpam-5251	223	26	wk+2	wk+2	VERB
ejpam-5251	223	27	zk+2	zk+2	NUM
ejpam-5251	224	1	x1	x1	NOUN
ejpam-5251	225	1	x2	x2	PROPN
ejpam-5251	225	2	...	...	PUNCT
ejpam-5251	226	1	xa−2	xa−2	NOUN
ejpam-5251	226	2	figure	figure	VERB
ejpam-5251	226	3	3	3	NUM
ejpam-5251	226	4	:	:	PUNCT
ejpam-5251	226	5	g2	g2	NOUN
ejpam-5251	226	6	:	:	PUNCT
ejpam-5251	226	7	a	a	DET
ejpam-5251	226	8	connected	connected	ADJ
ejpam-5251	226	9	graph	graph	NOUN
ejpam-5251	226	10	complying	comply	VERB
ejpam-5251	226	11	with	with	ADP
ejpam-5251	226	12	the	the	DET
ejpam-5251	226	13	specifications	specification	NOUN
ejpam-5251	226	14	of	of	ADP
ejpam-5251	226	15	theorem	theorem	NOUN
ejpam-5251	226	16	3	3	NUM
ejpam-5251	226	17	when	when	SCONJ
ejpam-5251	226	18	a	a	DET
ejpam-5251	226	19	≥	≥	NOUN
ejpam-5251	226	20	3	3	NUM
ejpam-5251	226	21	put	put	NOUN
ejpam-5251	226	22	s	s	PART
ejpam-5251	226	23	=	=	PUNCT
ejpam-5251	226	24	{	{	PUNCT
ejpam-5251	226	25	u	u	NOUN
ejpam-5251	226	26	,	,	PUNCT
ejpam-5251	226	27	v	v	PROPN
ejpam-5251	226	28	,	,	PUNCT
ejpam-5251	226	29	xi	xi	X
ejpam-5251	226	30	:	:	PUNCT
ejpam-5251	227	1	i	i	NOUN
ejpam-5251	227	2	=	=	NOUN
ejpam-5251	227	3	1	1	NUM
ejpam-5251	227	4	,	,	PUNCT
ejpam-5251	227	5	2	2	NUM
ejpam-5251	227	6	,	,	PUNCT
ejpam-5251	227	7	.	.	PUNCT
ejpam-5251	227	8	.	.	PUNCT
ejpam-5251	228	1	.	.	PUNCT
ejpam-5251	229	1	,	,	PUNCT
ejpam-5251	229	2	a−	a−	PROPN
ejpam-5251	229	3	2	2	NUM
ejpam-5251	229	4	}	}	PUNCT
ejpam-5251	229	5	and	and	CCONJ
ejpam-5251	229	6	t	t	NOUN
ejpam-5251	229	7	=	=	SYM
ejpam-5251	229	8	{	{	PUNCT
ejpam-5251	229	9	{	{	PUNCT
ejpam-5251	229	10	w2i−1	w2i−1	PROPN
ejpam-5251	229	11	,	,	PUNCT
ejpam-5251	229	12	z2i	z2i	PROPN
ejpam-5251	229	13	,	,	PUNCT
ejpam-5251	229	14	xj	xj	PROPN
ejpam-5251	229	15	:	:	PUNCT
ejpam-5251	229	16	i	i	PRON
ejpam-5251	229	17	=	=	NOUN
ejpam-5251	229	18	1	1	NUM
ejpam-5251	229	19	,	,	PUNCT
ejpam-5251	229	20	2	2	NUM
ejpam-5251	229	21	,	,	PUNCT
ejpam-5251	229	22	3	3	NUM
ejpam-5251	229	23	,	,	PUNCT
ejpam-5251	229	24	.	.	PUNCT
ejpam-5251	229	25	.	.	PUNCT
ejpam-5251	229	26	.	.	PUNCT
ejpam-5251	230	1	,	,	PUNCT
ejpam-5251	230	2	k2	k2	NOUN
ejpam-5251	230	3	+	+	CCONJ
ejpam-5251	230	4	1	1	NUM
ejpam-5251	230	5	;	;	PUNCT
ejpam-5251	230	6	j	j	PROPN
ejpam-5251	230	7	=	=	SYM
ejpam-5251	230	8	1	1	NUM
ejpam-5251	230	9	,	,	PUNCT
ejpam-5251	230	10	2	2	NUM
ejpam-5251	230	11	,	,	PUNCT
ejpam-5251	230	12	.	.	PUNCT
ejpam-5251	230	13	.	.	PUNCT
ejpam-5251	231	1	.	.	PUNCT
ejpam-5251	232	1	,	,	PUNCT
ejpam-5251	232	2	a−	a−	PROPN
ejpam-5251	232	3	2	2	NUM
ejpam-5251	232	4	}	}	PUNCT
ejpam-5251	232	5	,	,	PUNCT
ejpam-5251	232	6	k	k	PROPN
ejpam-5251	232	7	is	be	AUX
ejpam-5251	232	8	even	even	ADV
ejpam-5251	232	9	;	;	PUNCT
ejpam-5251	232	10	{	{	PUNCT
ejpam-5251	232	11	w1	w1	NOUN
ejpam-5251	232	12	,	,	PUNCT
ejpam-5251	232	13	w2i+1	w2i+1	PROPN
ejpam-5251	232	14	,	,	PUNCT
ejpam-5251	232	15	z2i	z2i	PROPN
ejpam-5251	232	16	,	,	PUNCT
ejpam-5251	232	17	xj	xj	PROPN
ejpam-5251	232	18	:	:	PUNCT
ejpam-5251	233	1	i	i	PRON
ejpam-5251	233	2	=	=	NOUN
ejpam-5251	233	3	1	1	NUM
ejpam-5251	233	4	,	,	PUNCT
ejpam-5251	233	5	2	2	NUM
ejpam-5251	233	6	,	,	PUNCT
ejpam-5251	233	7	3	3	NUM
ejpam-5251	233	8	,	,	PUNCT
ejpam-5251	233	9	.	.	PUNCT
ejpam-5251	233	10	.	.	PUNCT
ejpam-5251	233	11	.	.	PUNCT
ejpam-5251	234	1	,	,	PUNCT
ejpam-5251	234	2	⌊k+1	⌊k+1	X
ejpam-5251	234	3	2	2	NUM
ejpam-5251	234	4	⌋	⌋	NUM
ejpam-5251	234	5	;	;	PUNCT
ejpam-5251	234	6	j	j	PROPN
ejpam-5251	234	7	=	=	SYM
ejpam-5251	234	8	1	1	NUM
ejpam-5251	234	9	,	,	PUNCT
ejpam-5251	234	10	2	2	NUM
ejpam-5251	234	11	,	,	PUNCT
ejpam-5251	234	12	.	.	PUNCT
ejpam-5251	234	13	.	.	PUNCT
ejpam-5251	235	1	.	.	PUNCT
ejpam-5251	236	1	,	,	PUNCT
ejpam-5251	236	2	a−	a−	PROPN
ejpam-5251	236	3	2	2	NUM
ejpam-5251	236	4	}	}	PUNCT
ejpam-5251	236	5	,	,	PUNCT
ejpam-5251	236	6	k	k	PROPN
ejpam-5251	236	7	is	be	AUX
ejpam-5251	236	8	odd	odd	ADJ
ejpam-5251	236	9	.	.	PUNCT
ejpam-5251	237	1	then	then	ADV
ejpam-5251	237	2	s	s	VERB
ejpam-5251	237	3	and	and	CCONJ
ejpam-5251	237	4	t	t	PROPN
ejpam-5251	237	5	are	be	AUX
ejpam-5251	237	6	γhg	γhg	ADV
ejpam-5251	237	7	-	-	PUNCT
ejpam-5251	237	8	set	set	VERB
ejpam-5251	237	9	and	and	CCONJ
ejpam-5251	237	10	γ+hg	γ+hg	NOUN
ejpam-5251	237	11	-	-	PUNCT
ejpam-5251	237	12	set	set	NOUN
ejpam-5251	237	13	of	of	ADP
ejpam-5251	237	14	g	g	NOUN
ejpam-5251	237	15	,	,	PUNCT
ejpam-5251	237	16	respectively	respectively	ADV
ejpam-5251	237	17	.	.	PUNCT
ejpam-5251	238	1	in	in	ADP
ejpam-5251	238	2	any	any	DET
ejpam-5251	238	3	case	case	NOUN
ejpam-5251	238	4	,	,	PUNCT
ejpam-5251	238	5	γhg(g	γhg(g	PROPN
ejpam-5251	238	6	)	)	PUNCT
ejpam-5251	238	7	=	=	SYM
ejpam-5251	239	1	a	a	PRON
ejpam-5251	239	2	and	and	CCONJ
ejpam-5251	239	3	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	239	4	)	)	PUNCT
ejpam-5251	240	1	=	=	PRON
ejpam-5251	240	2	a+	a+	PUNCT
ejpam-5251	241	1	k	k	PROPN
ejpam-5251	241	2	=	=	SYM
ejpam-5251	241	3	b	b	X
ejpam-5251	241	4	corollary	corollary	ADJ
ejpam-5251	241	5	3	3	NUM
ejpam-5251	241	6	.	.	PUNCT
ejpam-5251	242	1	the	the	DET
ejpam-5251	242	2	difference	difference	NOUN
ejpam-5251	242	3	between	between	ADP
ejpam-5251	242	4	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	242	5	)	)	PUNCT
ejpam-5251	242	6	and	and	CCONJ
ejpam-5251	242	7	γhg(g	γhg(g	PROPN
ejpam-5251	242	8	)	)	PUNCT
ejpam-5251	242	9	can	can	AUX
ejpam-5251	242	10	be	be	AUX
ejpam-5251	242	11	made	make	VERB
ejpam-5251	242	12	arbitrarily	arbitrarily	ADV
ejpam-5251	242	13	large	large	ADJ
ejpam-5251	242	14	.	.	PUNCT
ejpam-5251	243	1	4	4	X
ejpam-5251	243	2	.	.	X
ejpam-5251	243	3	in	in	ADP
ejpam-5251	243	4	the	the	DET
ejpam-5251	243	5	join	join	NOUN
ejpam-5251	243	6	of	of	ADP
ejpam-5251	243	7	graphs	graph	NOUN
ejpam-5251	243	8	for	for	ADP
ejpam-5251	243	9	the	the	DET
ejpam-5251	243	10	purposes	purpose	NOUN
ejpam-5251	243	11	of	of	ADP
ejpam-5251	243	12	the	the	DET
ejpam-5251	243	13	remaining	remain	VERB
ejpam-5251	243	14	sections	section	NOUN
ejpam-5251	243	15	,	,	PUNCT
ejpam-5251	243	16	we	we	PRON
ejpam-5251	243	17	define	define	VERB
ejpam-5251	243	18	the	the	DET
ejpam-5251	243	19	following	follow	VERB
ejpam-5251	243	20	variations	variation	NOUN
ejpam-5251	243	21	of	of	ADP
ejpam-5251	243	22	pointwise	pointwise	PROPN
ejpam-5251	243	23	non	non	ADJ
ejpam-5251	243	24	-	-	ADJ
ejpam-5251	243	25	dominating	dominating	ADJ
ejpam-5251	243	26	sets	set	NOUN
ejpam-5251	243	27	.	.	PUNCT
ejpam-5251	244	1	a	a	DET
ejpam-5251	244	2	pointwise	pointwise	ADJ
ejpam-5251	244	3	non	non	ADJ
ejpam-5251	244	4	-	-	ADJ
ejpam-5251	244	5	dominating	dominating	ADJ
ejpam-5251	244	6	set	set	NOUN
ejpam-5251	244	7	s	s	PROPN
ejpam-5251	244	8	⊆	⊆	NUM
ejpam-5251	244	9	v	v	NOUN
ejpam-5251	244	10	(	(	PUNCT
ejpam-5251	244	11	g	g	NOUN
ejpam-5251	244	12	)	)	PUNCT
ejpam-5251	244	13	is	be	AUX
ejpam-5251	244	14	a	a	DET
ejpam-5251	244	15	minimal	minimal	ADJ
ejpam-5251	244	16	pointwise	pointwise	ADJ
ejpam-5251	244	17	non	non	ADJ
ejpam-5251	244	18	-	-	ADJ
ejpam-5251	244	19	dominating	dominating	ADJ
ejpam-5251	244	20	set	set	NOUN
ejpam-5251	244	21	of	of	ADP
ejpam-5251	244	22	g	g	PROPN
ejpam-5251	244	23	if	if	SCONJ
ejpam-5251	244	24	s	s	PRON
ejpam-5251	244	25	does	do	AUX
ejpam-5251	244	26	not	not	PART
ejpam-5251	244	27	contain	contain	VERB
ejpam-5251	244	28	a	a	DET
ejpam-5251	244	29	proper	proper	ADJ
ejpam-5251	244	30	subset	subset	NOUN
ejpam-5251	244	31	which	which	PRON
ejpam-5251	244	32	is	be	AUX
ejpam-5251	244	33	itself	itself	PRON
ejpam-5251	244	34	a	a	DET
ejpam-5251	244	35	pointwise	pointwise	ADJ
ejpam-5251	244	36	non	non	ADJ
ejpam-5251	244	37	-	-	ADJ
ejpam-5251	244	38	dominating	dominating	ADJ
ejpam-5251	244	39	set	set	NOUN
ejpam-5251	244	40	in	in	ADP
ejpam-5251	244	41	g.	g.	PROPN
ejpam-5251	244	42	a	a	DET
ejpam-5251	244	43	set	set	NOUN
ejpam-5251	244	44	s	s	PROPN
ejpam-5251	244	45	⊆	⊆	NUM
ejpam-5251	244	46	v	v	NOUN
ejpam-5251	244	47	(	(	PUNCT
ejpam-5251	244	48	g	g	NOUN
ejpam-5251	244	49	)	)	PUNCT
ejpam-5251	244	50	is	be	AUX
ejpam-5251	244	51	a	a	DET
ejpam-5251	244	52	2	2	NUM
ejpam-5251	244	53	-	-	PUNCT
ejpam-5251	244	54	path	path	NOUN
ejpam-5251	244	55	closure	closure	NOUN
ejpam-5251	244	56	absorbing	absorb	VERB
ejpam-5251	244	57	pointwise	pointwise	PROPN
ejpam-5251	244	58	non	non	ADJ
ejpam-5251	244	59	-	-	ADJ
ejpam-5251	244	60	dominating	dominating	ADJ
ejpam-5251	244	61	set	set	NOUN
ejpam-5251	244	62	if	if	SCONJ
ejpam-5251	244	63	s	s	VERB
ejpam-5251	244	64	is	be	AUX
ejpam-5251	244	65	both	both	PRON
ejpam-5251	244	66	a	a	DET
ejpam-5251	244	67	2	2	NUM
ejpam-5251	244	68	-	-	PUNCT
ejpam-5251	244	69	path	path	NOUN
ejpam-5251	244	70	closure	closure	NOUN
ejpam-5251	244	71	absorbing	absorb	VERB
ejpam-5251	244	72	set	set	NOUN
ejpam-5251	244	73	and	and	CCONJ
ejpam-5251	244	74	a	a	DET
ejpam-5251	244	75	pointwise	pointwise	ADJ
ejpam-5251	244	76	non	non	ADJ
ejpam-5251	244	77	-	-	ADJ
ejpam-5251	244	78	dominating	dominating	ADJ
ejpam-5251	244	79	set	set	NOUN
ejpam-5251	244	80	in	in	ADP
ejpam-5251	244	81	g.	g.	PROPN
ejpam-5251	244	82	a	a	DET
ejpam-5251	244	83	2	2	NUM
ejpam-5251	244	84	-	-	PUNCT
ejpam-5251	244	85	path	path	NOUN
ejpam-5251	244	86	closure	closure	NOUN
ejpam-5251	244	87	absorbing	absorb	VERB
ejpam-5251	244	88	pointwise	pointwise	PROPN
ejpam-5251	244	89	non	non	ADJ
ejpam-5251	244	90	-	-	ADJ
ejpam-5251	244	91	dominating	dominating	ADJ
ejpam-5251	244	92	set	set	NOUN
ejpam-5251	244	93	s	s	NOUN
ejpam-5251	244	94	is	be	AUX
ejpam-5251	244	95	said	say	VERB
ejpam-5251	244	96	to	to	PART
ejpam-5251	244	97	be	be	AUX
ejpam-5251	244	98	a	a	DET
ejpam-5251	244	99	minimal	minimal	ADJ
ejpam-5251	244	100	2	2	NUM
ejpam-5251	244	101	-	-	PUNCT
ejpam-5251	244	102	path	path	NOUN
ejpam-5251	244	103	closure	closure	NOUN
ejpam-5251	244	104	absorbing	absorb	VERB
ejpam-5251	244	105	pointwise	pointwise	PROPN
ejpam-5251	244	106	non	non	ADJ
ejpam-5251	244	107	-	-	ADJ
ejpam-5251	244	108	dominating	dominating	ADJ
ejpam-5251	244	109	set	set	NOUN
ejpam-5251	244	110	whenever	whenever	SCONJ
ejpam-5251	244	111	s	s	VERB
ejpam-5251	244	112	does	do	AUX
ejpam-5251	244	113	not	not	PART
ejpam-5251	244	114	contain	contain	VERB
ejpam-5251	244	115	a	a	DET
ejpam-5251	244	116	proper	proper	ADJ
ejpam-5251	244	117	subset	subset	NOUN
ejpam-5251	244	118	which	which	PRON
ejpam-5251	244	119	is	be	AUX
ejpam-5251	244	120	itself	itself	PRON
ejpam-5251	244	121	a	a	DET
ejpam-5251	244	122	2	2	NUM
ejpam-5251	244	123	-	-	PUNCT
ejpam-5251	244	124	path	path	NOUN
ejpam-5251	244	125	closure	closure	NOUN
ejpam-5251	244	126	absorbing	absorb	VERB
ejpam-5251	244	127	pointwise	pointwise	PROPN
ejpam-5251	244	128	non	non	ADJ
ejpam-5251	244	129	-	-	ADJ
ejpam-5251	244	130	dominating	dominating	ADJ
ejpam-5251	244	131	set	set	NOUN
ejpam-5251	244	132	.	.	PUNCT
ejpam-5251	245	1	we	we	PRON
ejpam-5251	245	2	denote	denote	VERB
ejpam-5251	245	3	by	by	ADP
ejpam-5251	245	4	ρ+2pnd(g	ρ+2pnd(g	PROPN
ejpam-5251	245	5	)	)	PUNCT
ejpam-5251	245	6	the	the	DET
ejpam-5251	245	7	maximum	maximum	ADJ
ejpam-5251	245	8	cardinality	cardinality	NOUN
ejpam-5251	245	9	of	of	ADP
ejpam-5251	245	10	a	a	DET
ejpam-5251	245	11	minimal	minimal	ADJ
ejpam-5251	245	12	2	2	NUM
ejpam-5251	245	13	-	-	PUNCT
ejpam-5251	245	14	path	path	NOUN
ejpam-5251	245	15	closure	closure	NOUN
ejpam-5251	245	16	absorbing	absorb	VERB
ejpam-5251	245	17	pointwise	pointwise	PROPN
ejpam-5251	245	18	non	non	ADJ
ejpam-5251	245	19	-	-	ADJ
ejpam-5251	245	20	dominating	dominating	ADJ
ejpam-5251	245	21	set	set	NOUN
ejpam-5251	245	22	in	in	ADP
ejpam-5251	245	23	g.	g.	PROPN
ejpam-5251	245	24	a	a	DET
ejpam-5251	245	25	minimal	minimal	ADJ
ejpam-5251	245	26	2	2	NUM
ejpam-5251	245	27	-	-	PUNCT
ejpam-5251	245	28	path	path	NOUN
ejpam-5251	245	29	closure	closure	NOUN
ejpam-5251	245	30	absorbing	absorb	VERB
ejpam-5251	245	31	pointwise	pointwise	PROPN
ejpam-5251	245	32	non	non	ADJ
ejpam-5251	245	33	-	-	ADJ
ejpam-5251	245	34	dominating	dominating	ADJ
ejpam-5251	245	35	set	set	NOUN
ejpam-5251	245	36	s	s	PART
ejpam-5251	245	37	is	be	AUX
ejpam-5251	245	38	called	call	VERB
ejpam-5251	245	39	a	a	DET
ejpam-5251	245	40	ρ+2pnd	ρ+2pnd	NOUN
ejpam-5251	245	41	-	-	PUNCT
ejpam-5251	245	42	set	set	VERB
ejpam-5251	245	43	if	if	SCONJ
ejpam-5251	245	44	|s|	|s|	NOUN
ejpam-5251	245	45	=	=	SYM
ejpam-5251	245	46	ρ+2pnd(g	ρ+2pnd(g	PROPN
ejpam-5251	245	47	)	)	PUNCT
ejpam-5251	245	48	.	.	PUNCT
ejpam-5251	246	1	theorem	theorem	ADJ
ejpam-5251	246	2	4	4	NUM
ejpam-5251	246	3	.	.	PUNCT
ejpam-5251	247	1	[	[	X
ejpam-5251	247	2	26	26	NUM
ejpam-5251	247	3	]	]	PUNCT
ejpam-5251	247	4	let	let	VERB
ejpam-5251	247	5	g	g	NOUN
ejpam-5251	247	6	and	and	CCONJ
ejpam-5251	247	7	h	h	NOUN
ejpam-5251	247	8	be	be	VERB
ejpam-5251	247	9	any	any	DET
ejpam-5251	247	10	two	two	NUM
ejpam-5251	247	11	graphs	graph	NOUN
ejpam-5251	247	12	.	.	PUNCT
ejpam-5251	248	1	a	a	DET
ejpam-5251	248	2	set	set	NOUN
ejpam-5251	248	3	s	s	NOUN
ejpam-5251	248	4	⊆	⊆	NUM
ejpam-5251	248	5	v	v	NOUN
ejpam-5251	248	6	(	(	PUNCT
ejpam-5251	248	7	g	g	PROPN
ejpam-5251	248	8	+	+	NOUN
ejpam-5251	248	9	h	h	NOUN
ejpam-5251	248	10	)	)	PUNCT
ejpam-5251	248	11	is	be	AUX
ejpam-5251	248	12	a	a	DET
ejpam-5251	248	13	geodetic	geodetic	ADJ
ejpam-5251	248	14	hop	hop	NOUN
ejpam-5251	248	15	dominating	dominating	NOUN
ejpam-5251	248	16	set	set	NOUN
ejpam-5251	248	17	of	of	ADP
ejpam-5251	248	18	g	g	PROPN
ejpam-5251	249	1	+	+	CCONJ
ejpam-5251	249	2	h	h	NOUN
ejpam-5251	249	3	if	if	SCONJ
ejpam-5251	249	4	and	and	CCONJ
ejpam-5251	249	5	only	only	ADV
ejpam-5251	249	6	if	if	SCONJ
ejpam-5251	249	7	s	s	VERB
ejpam-5251	249	8	=	=	PUNCT
ejpam-5251	249	9	sg	sg	X
ejpam-5251	249	10	∪	∪	ADJ
ejpam-5251	249	11	sh	sh	PROPN
ejpam-5251	249	12	,	,	PUNCT
ejpam-5251	249	13	where	where	SCONJ
ejpam-5251	249	14	sg	sg	PROPN
ejpam-5251	249	15	and	and	CCONJ
ejpam-5251	249	16	sh	sh	PROPN
ejpam-5251	249	17	are	be	AUX
ejpam-5251	249	18	pointwise	pointwise	NUM
ejpam-5251	249	19	nondominating	nondominate	VERB
ejpam-5251	249	20	sets	set	NOUN
ejpam-5251	249	21	of	of	ADP
ejpam-5251	249	22	g	g	PROPN
ejpam-5251	249	23	and	and	CCONJ
ejpam-5251	249	24	h	h	NOUN
ejpam-5251	249	25	,	,	PUNCT
ejpam-5251	249	26	respectively	respectively	ADV
ejpam-5251	249	27	,	,	PUNCT
ejpam-5251	249	28	such	such	ADJ
ejpam-5251	249	29	that	that	SCONJ
ejpam-5251	249	30	i	i	PRON
ejpam-5251	249	31	)	)	PUNCT
ejpam-5251	249	32	sg	sg	PROPN
ejpam-5251	249	33	is	be	AUX
ejpam-5251	249	34	a	a	DET
ejpam-5251	249	35	2	2	NUM
ejpam-5251	249	36	-	-	PUNCT
ejpam-5251	249	37	path	path	NOUN
ejpam-5251	249	38	closure	closure	NOUN
ejpam-5251	249	39	absorbing	absorb	VERB
ejpam-5251	249	40	set	set	NOUN
ejpam-5251	249	41	in	in	ADP
ejpam-5251	249	42	g	g	NOUN
ejpam-5251	249	43	whenever	whenever	SCONJ
ejpam-5251	249	44	⟨sh⟩	⟨sh⟩	PRON
ejpam-5251	249	45	is	be	AUX
ejpam-5251	249	46	a	a	DET
ejpam-5251	249	47	complete	complete	ADJ
ejpam-5251	249	48	subgraph	subgraph	NOUN
ejpam-5251	249	49	of	of	ADP
ejpam-5251	249	50	h	h	PROPN
ejpam-5251	249	51	and	and	CCONJ
ejpam-5251	249	52	(	(	PUNCT
ejpam-5251	249	53	ii	ii	NOUN
ejpam-5251	249	54	)	)	PUNCT
ejpam-5251	249	55	sh	sh	PROPN
ejpam-5251	249	56	is	be	AUX
ejpam-5251	249	57	a	a	DET
ejpam-5251	249	58	2	2	NUM
ejpam-5251	249	59	-	-	PUNCT
ejpam-5251	249	60	path	path	NOUN
ejpam-5251	249	61	closure	closure	NOUN
ejpam-5251	249	62	absorbing	absorb	VERB
ejpam-5251	249	63	set	set	NOUN
ejpam-5251	249	64	in	in	ADP
ejpam-5251	249	65	h	h	NOUN
ejpam-5251	249	66	whenever	whenever	SCONJ
ejpam-5251	249	67	⟨sg⟩	⟨sg⟩	PRON
ejpam-5251	249	68	is	be	AUX
ejpam-5251	249	69	a	a	DET
ejpam-5251	249	70	complete	complete	ADJ
ejpam-5251	249	71	subgraph	subgraph	NOUN
ejpam-5251	249	72	of	of	ADP
ejpam-5251	249	73	g.	g.	PROPN
ejpam-5251	249	74	proposition	proposition	PROPN
ejpam-5251	249	75	4	4	NUM
ejpam-5251	249	76	.	.	PUNCT
ejpam-5251	250	1	let	let	VERB
ejpam-5251	250	2	g	g	NOUN
ejpam-5251	250	3	and	and	CCONJ
ejpam-5251	250	4	h	h	NOUN
ejpam-5251	250	5	be	be	AUX
ejpam-5251	250	6	connected	connect	VERB
ejpam-5251	250	7	graphs	graph	NOUN
ejpam-5251	250	8	,	,	PUNCT
ejpam-5251	250	9	and	and	CCONJ
ejpam-5251	250	10	let	let	VERB
ejpam-5251	250	11	s	s	PRON
ejpam-5251	250	12	⊆	⊆	NUM
ejpam-5251	250	13	g	g	NOUN
ejpam-5251	250	14	+	+	CCONJ
ejpam-5251	250	15	h.	h.	NOUN
ejpam-5251	250	16	if	if	SCONJ
ejpam-5251	250	17	s	s	PROPN
ejpam-5251	250	18	is	be	AUX
ejpam-5251	250	19	a	a	DET
ejpam-5251	250	20	minimal	minimal	ADJ
ejpam-5251	250	21	geodetic	geodetic	ADJ
ejpam-5251	250	22	hop	hop	NOUN
ejpam-5251	250	23	dominating	dominating	NOUN
ejpam-5251	250	24	set	set	NOUN
ejpam-5251	250	25	of	of	ADP
ejpam-5251	250	26	g+h	g+h	PROPN
ejpam-5251	250	27	,	,	PUNCT
ejpam-5251	250	28	then	then	ADV
ejpam-5251	250	29	s	s	VERB
ejpam-5251	250	30	=	=	PUNCT
ejpam-5251	250	31	sg	sg	X
ejpam-5251	250	32	∪	∪	ADJ
ejpam-5251	250	33	sh	sh	PROPN
ejpam-5251	250	34	,	,	PUNCT
ejpam-5251	250	35	where	where	SCONJ
ejpam-5251	250	36	sg	sg	ADP
ejpam-5251	250	37	⊆	⊆	NUM
ejpam-5251	250	38	v	v	NOUN
ejpam-5251	250	39	(	(	PUNCT
ejpam-5251	250	40	g	g	NOUN
ejpam-5251	250	41	)	)	PUNCT
ejpam-5251	250	42	and	and	CCONJ
ejpam-5251	250	43	sh	sh	PROPN
ejpam-5251	250	44	⊆	⊆	NUM
ejpam-5251	250	45	v	v	NOUN
ejpam-5251	250	46	(	(	PUNCT
ejpam-5251	250	47	h	h	NOUN
ejpam-5251	250	48	)	)	PUNCT
ejpam-5251	250	49	are	be	AUX
ejpam-5251	250	50	pointwise	pointwise	PROPN
ejpam-5251	250	51	non	non	ADJ
ejpam-5251	250	52	-	-	ADJ
ejpam-5251	250	53	dominating	dominating	ADJ
ejpam-5251	250	54	sets	set	NOUN
ejpam-5251	250	55	of	of	ADP
ejpam-5251	250	56	g	g	PROPN
ejpam-5251	250	57	and	and	CCONJ
ejpam-5251	250	58	h	h	NOUN
ejpam-5251	250	59	,	,	PUNCT
ejpam-5251	250	60	respectively	respectively	ADV
ejpam-5251	250	61	,	,	PUNCT
ejpam-5251	250	62	such	such	ADJ
ejpam-5251	250	63	that	that	SCONJ
ejpam-5251	250	64	(	(	PUNCT
ejpam-5251	250	65	i	i	NOUN
ejpam-5251	250	66	)	)	PUNCT
ejpam-5251	250	67	sg	sg	PROPN
ejpam-5251	250	68	is	be	AUX
ejpam-5251	250	69	a	a	DET
ejpam-5251	250	70	minimal	minimal	ADJ
ejpam-5251	250	71	2	2	NUM
ejpam-5251	250	72	-	-	PUNCT
ejpam-5251	250	73	path	path	NOUN
ejpam-5251	250	74	closure	closure	NOUN
ejpam-5251	250	75	absorbing	absorb	VERB
ejpam-5251	250	76	pointwise	pointwise	PROPN
ejpam-5251	250	77	non	non	ADJ
ejpam-5251	250	78	-	-	ADJ
ejpam-5251	250	79	dominating	dominating	ADJ
ejpam-5251	250	80	set	set	NOUN
ejpam-5251	250	81	in	in	ADP
ejpam-5251	250	82	g	g	NOUN
ejpam-5251	250	83	whenever	whenever	SCONJ
ejpam-5251	250	84	⟨sh⟩	⟨sh⟩	PRON
ejpam-5251	250	85	is	be	AUX
ejpam-5251	250	86	a	a	DET
ejpam-5251	250	87	complete	complete	ADJ
ejpam-5251	250	88	subgraph	subgraph	NOUN
ejpam-5251	250	89	of	of	ADP
ejpam-5251	250	90	h	h	NOUN
ejpam-5251	250	91	;	;	PUNCT
ejpam-5251	251	1	d.	d.	PROPN
ejpam-5251	251	2	catian	catian	PROPN
ejpam-5251	251	3	,	,	PUNCT
ejpam-5251	251	4	i.	i.	PROPN
ejpam-5251	251	5	s.	s.	PROPN
ejpam-5251	251	6	aniversario	aniversario	PROPN
ejpam-5251	251	7	,	,	PUNCT
ejpam-5251	251	8	f.	f.	PROPN
ejpam-5251	251	9	p.	p.	PROPN
ejpam-5251	251	10	jamil	jamil	PROPN
ejpam-5251	251	11	/	/	SYM
ejpam-5251	251	12	eur	eur	PROPN
ejpam-5251	251	13	.	.	PUNCT
ejpam-5251	252	1	j.	j.	PROPN
ejpam-5251	252	2	pure	pure	PROPN
ejpam-5251	252	3	appl	appl	PROPN
ejpam-5251	252	4	.	.	PROPN
ejpam-5251	252	5	math	math	PROPN
ejpam-5251	252	6	,	,	PUNCT
ejpam-5251	252	7	17	17	NUM
ejpam-5251	252	8	(	(	PUNCT
ejpam-5251	252	9	3	3	NUM
ejpam-5251	252	10	)	)	PUNCT
ejpam-5251	252	11	(	(	PUNCT
ejpam-5251	252	12	2024	2024	NUM
ejpam-5251	252	13	)	)	PUNCT
ejpam-5251	252	14	,	,	PUNCT
ejpam-5251	252	15	1737	1737	NUM
ejpam-5251	252	16	-	-	SYM
ejpam-5251	252	17	1750	1750	NUM
ejpam-5251	252	18	1744	1744	NUM
ejpam-5251	252	19	(	(	PUNCT
ejpam-5251	252	20	ii	ii	NOUN
ejpam-5251	252	21	)	)	PUNCT
ejpam-5251	252	22	sh	sh	PROPN
ejpam-5251	252	23	is	be	AUX
ejpam-5251	252	24	a	a	DET
ejpam-5251	252	25	minimal	minimal	ADJ
ejpam-5251	252	26	2	2	NUM
ejpam-5251	252	27	-	-	PUNCT
ejpam-5251	252	28	path	path	NOUN
ejpam-5251	252	29	closure	closure	NOUN
ejpam-5251	252	30	absorbing	absorb	VERB
ejpam-5251	252	31	pointwise	pointwise	PROPN
ejpam-5251	252	32	non	non	ADJ
ejpam-5251	252	33	-	-	ADJ
ejpam-5251	252	34	dominating	dominating	ADJ
ejpam-5251	252	35	set	set	NOUN
ejpam-5251	252	36	in	in	ADP
ejpam-5251	252	37	h	h	NOUN
ejpam-5251	252	38	whenever	whenever	SCONJ
ejpam-5251	252	39	⟨sg⟩	⟨sg⟩	PRON
ejpam-5251	252	40	is	be	AUX
ejpam-5251	252	41	a	a	DET
ejpam-5251	252	42	complete	complete	ADJ
ejpam-5251	252	43	subgraph	subgraph	NOUN
ejpam-5251	252	44	of	of	ADP
ejpam-5251	252	45	g.	g.	PROPN
ejpam-5251	252	46	proof	proof	PROPN
ejpam-5251	252	47	.	.	PUNCT
ejpam-5251	253	1	let	let	VERB
ejpam-5251	253	2	s	s	PRON
ejpam-5251	253	3	be	be	AUX
ejpam-5251	253	4	a	a	DET
ejpam-5251	253	5	minimal	minimal	ADJ
ejpam-5251	253	6	geodetic	geodetic	ADJ
ejpam-5251	253	7	hop	hop	NOUN
ejpam-5251	253	8	dominating	dominating	NOUN
ejpam-5251	253	9	set	set	NOUN
ejpam-5251	253	10	of	of	ADP
ejpam-5251	253	11	g	g	PROPN
ejpam-5251	253	12	+	+	CCONJ
ejpam-5251	253	13	h.	h.	PROPN
ejpam-5251	253	14	by	by	ADP
ejpam-5251	253	15	theorem	theorem	ADJ
ejpam-5251	253	16	4	4	NUM
ejpam-5251	253	17	,	,	PUNCT
ejpam-5251	253	18	s	s	PART
ejpam-5251	253	19	=	=	PUNCT
ejpam-5251	253	20	sg	sg	X
ejpam-5251	253	21	∪	∪	ADJ
ejpam-5251	253	22	sh	sh	PROPN
ejpam-5251	253	23	,	,	PUNCT
ejpam-5251	253	24	where	where	SCONJ
ejpam-5251	253	25	sg	sg	PROPN
ejpam-5251	253	26	and	and	CCONJ
ejpam-5251	253	27	sh	sh	PROPN
ejpam-5251	253	28	are	be	AUX
ejpam-5251	253	29	pointwise	pointwise	PROPN
ejpam-5251	253	30	non	non	ADJ
ejpam-5251	253	31	-	-	ADJ
ejpam-5251	253	32	dominating	dominating	ADJ
ejpam-5251	253	33	sets	set	NOUN
ejpam-5251	253	34	in	in	ADP
ejpam-5251	253	35	g	g	PROPN
ejpam-5251	253	36	and	and	CCONJ
ejpam-5251	253	37	h	h	NOUN
ejpam-5251	253	38	,	,	PUNCT
ejpam-5251	253	39	respectively	respectively	ADV
ejpam-5251	253	40	.	.	PUNCT
ejpam-5251	254	1	suppose	suppose	VERB
ejpam-5251	254	2	that	that	SCONJ
ejpam-5251	254	3	⟨sh⟩	⟨sh⟩	NOUN
ejpam-5251	254	4	is	be	AUX
ejpam-5251	254	5	a	a	DET
ejpam-5251	254	6	complete	complete	ADJ
ejpam-5251	254	7	subgraph	subgraph	NOUN
ejpam-5251	254	8	of	of	ADP
ejpam-5251	254	9	h.	h.	PROPN
ejpam-5251	254	10	by	by	ADP
ejpam-5251	254	11	theorem	theorem	NOUN
ejpam-5251	254	12	4	4	NUM
ejpam-5251	254	13	,	,	PUNCT
ejpam-5251	254	14	sg	sg	PROPN
ejpam-5251	254	15	is	be	AUX
ejpam-5251	254	16	a	a	DET
ejpam-5251	254	17	2path	2path	NUM
ejpam-5251	254	18	closure	closure	NOUN
ejpam-5251	254	19	absorbing	absorb	VERB
ejpam-5251	254	20	set	set	VERB
ejpam-5251	254	21	in	in	ADP
ejpam-5251	254	22	g.	g.	PROPN
ejpam-5251	254	23	let	let	AUX
ejpam-5251	254	24	s∗	s∗	PROPN
ejpam-5251	254	25	g	g	PROPN
ejpam-5251	254	26	⊆	⊆	NUM
ejpam-5251	254	27	v	v	NOUN
ejpam-5251	254	28	(	(	PUNCT
ejpam-5251	254	29	g	g	NOUN
ejpam-5251	254	30	)	)	PUNCT
ejpam-5251	254	31	be	be	AUX
ejpam-5251	254	32	a	a	DET
ejpam-5251	254	33	2	2	NUM
ejpam-5251	254	34	-	-	PUNCT
ejpam-5251	254	35	path	path	NOUN
ejpam-5251	254	36	closure	closure	NOUN
ejpam-5251	254	37	absorbing	absorb	VERB
ejpam-5251	254	38	set	set	NOUN
ejpam-5251	254	39	in	in	ADP
ejpam-5251	254	40	g	g	NOUN
ejpam-5251	254	41	with	with	ADP
ejpam-5251	254	42	s∗	s∗	PROPN
ejpam-5251	254	43	g	g	PROPN
ejpam-5251	254	44	⊆	⊆	NUM
ejpam-5251	254	45	sg	sg	NOUN
ejpam-5251	254	46	.	.	PUNCT
ejpam-5251	255	1	by	by	ADP
ejpam-5251	255	2	theorem	theorem	NOUN
ejpam-5251	255	3	4	4	NUM
ejpam-5251	255	4	,	,	PUNCT
ejpam-5251	255	5	s∗	s∗	PROPN
ejpam-5251	255	6	g∪sh	g∪sh	X
ejpam-5251	255	7	is	be	AUX
ejpam-5251	255	8	a	a	DET
ejpam-5251	255	9	geodetic	geodetic	ADJ
ejpam-5251	255	10	hop	hop	NOUN
ejpam-5251	255	11	dominating	dominating	NOUN
ejpam-5251	255	12	set	set	NOUN
ejpam-5251	255	13	of	of	ADP
ejpam-5251	255	14	g+h	g+h	PROPN
ejpam-5251	255	15	.	.	PUNCT
ejpam-5251	256	1	since	since	SCONJ
ejpam-5251	256	2	s∗	s∗	PROPN
ejpam-5251	256	3	g∪sh	g∪sh	ADP
ejpam-5251	256	4	⊆	⊆	NUM
ejpam-5251	256	5	s	s	NOUN
ejpam-5251	256	6	,	,	PUNCT
ejpam-5251	256	7	the	the	DET
ejpam-5251	256	8	minimality	minimality	NOUN
ejpam-5251	256	9	of	of	ADP
ejpam-5251	256	10	s	s	PRON
ejpam-5251	256	11	implies	imply	VERB
ejpam-5251	256	12	that	that	SCONJ
ejpam-5251	256	13	sg	sg	VERB
ejpam-5251	256	14	=	=	PUNCT
ejpam-5251	256	15	s∗	s∗	PROPN
ejpam-5251	256	16	g.	g.	PROPN
ejpam-5251	256	17	thus	thus	ADV
ejpam-5251	256	18	,	,	PUNCT
ejpam-5251	256	19	sg	sg	PROPN
ejpam-5251	256	20	is	be	AUX
ejpam-5251	256	21	a	a	DET
ejpam-5251	256	22	minimal	minimal	ADJ
ejpam-5251	256	23	2	2	NUM
ejpam-5251	256	24	-	-	PUNCT
ejpam-5251	256	25	path	path	NOUN
ejpam-5251	256	26	closure	closure	NOUN
ejpam-5251	256	27	absorbing	absorb	VERB
ejpam-5251	256	28	pointwise	pointwise	PROPN
ejpam-5251	256	29	non	non	ADJ
ejpam-5251	256	30	-	-	ADJ
ejpam-5251	256	31	dominating	dominating	ADJ
ejpam-5251	256	32	set	set	NOUN
ejpam-5251	256	33	in	in	ADP
ejpam-5251	256	34	g	g	PROPN
ejpam-5251	256	35	and	and	CCONJ
ejpam-5251	256	36	(	(	PUNCT
ejpam-5251	256	37	i	i	NOUN
ejpam-5251	256	38	)	)	PUNCT
ejpam-5251	256	39	holds	hold	VERB
ejpam-5251	256	40	.	.	PUNCT
ejpam-5251	257	1	similarly	similarly	ADV
ejpam-5251	257	2	,	,	PUNCT
ejpam-5251	257	3	if	if	SCONJ
ejpam-5251	257	4	⟨sg⟩	⟨sg⟩	PRON
ejpam-5251	257	5	is	be	AUX
ejpam-5251	257	6	complete	complete	ADJ
ejpam-5251	257	7	,	,	PUNCT
ejpam-5251	257	8	then	then	ADV
ejpam-5251	257	9	(	(	PUNCT
ejpam-5251	257	10	ii	ii	NOUN
ejpam-5251	257	11	)	)	PUNCT
ejpam-5251	257	12	holds	hold	VERB
ejpam-5251	257	13	.	.	PUNCT
ejpam-5251	258	1	lemma	lemma	PROPN
ejpam-5251	258	2	1	1	NUM
ejpam-5251	258	3	.	.	PUNCT
ejpam-5251	259	1	[	[	X
ejpam-5251	259	2	1	1	X
ejpam-5251	259	3	]	]	PUNCT
ejpam-5251	259	4	let	let	VERB
ejpam-5251	259	5	g	g	PRON
ejpam-5251	259	6	be	be	AUX
ejpam-5251	259	7	a	a	DET
ejpam-5251	259	8	connected	connected	ADJ
ejpam-5251	259	9	noncomplete	noncomplete	ADJ
ejpam-5251	259	10	graph	graph	NOUN
ejpam-5251	259	11	and	and	CCONJ
ejpam-5251	259	12	s	s	VERB
ejpam-5251	259	13	⊆	⊆	NUM
ejpam-5251	259	14	v	v	NOUN
ejpam-5251	259	15	(	(	PUNCT
ejpam-5251	259	16	g	g	NOUN
ejpam-5251	259	17	)	)	PUNCT
ejpam-5251	259	18	.	.	PUNCT
ejpam-5251	260	1	if	if	SCONJ
ejpam-5251	260	2	s	s	NOUN
ejpam-5251	260	3	is	be	AUX
ejpam-5251	260	4	a	a	DET
ejpam-5251	260	5	2	2	NUM
ejpam-5251	260	6	-	-	PUNCT
ejpam-5251	260	7	path	path	NOUN
ejpam-5251	260	8	closure	closure	NOUN
ejpam-5251	260	9	absorbing	absorb	VERB
ejpam-5251	260	10	set	set	NOUN
ejpam-5251	260	11	in	in	ADP
ejpam-5251	260	12	g	g	NOUN
ejpam-5251	260	13	,	,	PUNCT
ejpam-5251	260	14	then	then	ADV
ejpam-5251	260	15	⟨s⟩	⟨s⟩	PROPN
ejpam-5251	260	16	is	be	AUX
ejpam-5251	260	17	not	not	PART
ejpam-5251	260	18	complete	complete	ADJ
ejpam-5251	260	19	.	.	PUNCT
ejpam-5251	261	1	proposition	proposition	NOUN
ejpam-5251	261	2	5	5	NUM
ejpam-5251	261	3	.	.	PUNCT
ejpam-5251	262	1	let	let	VERB
ejpam-5251	262	2	g	g	NOUN
ejpam-5251	262	3	and	and	CCONJ
ejpam-5251	262	4	h	h	NOUN
ejpam-5251	262	5	be	be	AUX
ejpam-5251	262	6	connected	connect	VERB
ejpam-5251	262	7	graphs	graph	NOUN
ejpam-5251	262	8	,	,	PUNCT
ejpam-5251	262	9	and	and	CCONJ
ejpam-5251	262	10	let	let	VERB
ejpam-5251	262	11	s	s	PRON
ejpam-5251	262	12	⊆	⊆	NUM
ejpam-5251	262	13	g	g	NOUN
ejpam-5251	262	14	+	+	PROPN
ejpam-5251	262	15	h.	h.	PROPN
ejpam-5251	262	16	suppose	suppose	VERB
ejpam-5251	262	17	that	that	SCONJ
ejpam-5251	262	18	s	s	VERB
ejpam-5251	262	19	=	=	PUNCT
ejpam-5251	262	20	sg	sg	X
ejpam-5251	262	21	∪	∪	ADJ
ejpam-5251	262	22	sh	sh	PROPN
ejpam-5251	262	23	,	,	PUNCT
ejpam-5251	262	24	where	where	SCONJ
ejpam-5251	262	25	sg	sg	ADP
ejpam-5251	262	26	⊆	⊆	NUM
ejpam-5251	262	27	v	v	NOUN
ejpam-5251	262	28	(	(	PUNCT
ejpam-5251	262	29	g	g	NOUN
ejpam-5251	262	30	)	)	PUNCT
ejpam-5251	262	31	and	and	CCONJ
ejpam-5251	262	32	sh	sh	PROPN
ejpam-5251	262	33	⊆	⊆	NUM
ejpam-5251	262	34	v	v	NOUN
ejpam-5251	262	35	(	(	PUNCT
ejpam-5251	262	36	h	h	NOUN
ejpam-5251	262	37	)	)	PUNCT
ejpam-5251	262	38	are	be	AUX
ejpam-5251	262	39	pointwise	pointwise	PROPN
ejpam-5251	262	40	non	non	ADJ
ejpam-5251	262	41	-	-	ADJ
ejpam-5251	262	42	dominating	dominating	ADJ
ejpam-5251	262	43	sets	set	NOUN
ejpam-5251	262	44	of	of	ADP
ejpam-5251	262	45	g	g	PROPN
ejpam-5251	262	46	and	and	CCONJ
ejpam-5251	262	47	h	h	NOUN
ejpam-5251	262	48	,	,	PUNCT
ejpam-5251	262	49	respectively	respectively	ADV
ejpam-5251	262	50	,	,	PUNCT
ejpam-5251	262	51	such	such	ADJ
ejpam-5251	262	52	that	that	SCONJ
ejpam-5251	262	53	one	one	NUM
ejpam-5251	262	54	of	of	ADP
ejpam-5251	262	55	the	the	DET
ejpam-5251	262	56	following	follow	VERB
ejpam-5251	262	57	holds	hold	VERB
ejpam-5251	262	58	:	:	PUNCT
ejpam-5251	262	59	(	(	PUNCT
ejpam-5251	262	60	i	i	NOUN
ejpam-5251	262	61	)	)	PUNCT
ejpam-5251	262	62	⟨sh⟩	⟨sh⟩	PRON
ejpam-5251	262	63	is	be	AUX
ejpam-5251	262	64	a	a	DET
ejpam-5251	262	65	complete	complete	ADJ
ejpam-5251	262	66	subgraph	subgraph	NOUN
ejpam-5251	262	67	of	of	ADP
ejpam-5251	262	68	h	h	NOUN
ejpam-5251	262	69	and	and	CCONJ
ejpam-5251	262	70	sg	sg	PROPN
ejpam-5251	262	71	is	be	AUX
ejpam-5251	262	72	a	a	DET
ejpam-5251	262	73	minimal	minimal	ADJ
ejpam-5251	262	74	2	2	NUM
ejpam-5251	262	75	-	-	PUNCT
ejpam-5251	262	76	path	path	NOUN
ejpam-5251	262	77	closure	closure	NOUN
ejpam-5251	262	78	absorbing	absorb	VERB
ejpam-5251	262	79	pointwise	pointwise	PROPN
ejpam-5251	262	80	non	non	ADJ
ejpam-5251	262	81	-	-	ADJ
ejpam-5251	262	82	dominating	dominating	ADJ
ejpam-5251	262	83	set	set	NOUN
ejpam-5251	262	84	in	in	ADP
ejpam-5251	262	85	g.	g.	PROPN
ejpam-5251	262	86	(	(	PUNCT
ejpam-5251	262	87	ii	ii	PROPN
ejpam-5251	262	88	)	)	PUNCT
ejpam-5251	262	89	⟨sg⟩	⟨sg⟩	PRON
ejpam-5251	262	90	is	be	AUX
ejpam-5251	262	91	a	a	DET
ejpam-5251	262	92	complete	complete	ADJ
ejpam-5251	262	93	subgraph	subgraph	NOUN
ejpam-5251	262	94	of	of	ADP
ejpam-5251	262	95	g	g	PROPN
ejpam-5251	262	96	and	and	CCONJ
ejpam-5251	262	97	sh	sh	PROPN
ejpam-5251	262	98	is	be	AUX
ejpam-5251	262	99	a	a	DET
ejpam-5251	262	100	minimal	minimal	ADJ
ejpam-5251	262	101	2	2	NUM
ejpam-5251	262	102	-	-	PUNCT
ejpam-5251	262	103	path	path	NOUN
ejpam-5251	262	104	closure	closure	NOUN
ejpam-5251	262	105	absorbing	absorb	VERB
ejpam-5251	262	106	pointwise	pointwise	PROPN
ejpam-5251	262	107	non	non	ADJ
ejpam-5251	262	108	-	-	ADJ
ejpam-5251	262	109	dominating	dominating	ADJ
ejpam-5251	262	110	set	set	NOUN
ejpam-5251	262	111	in	in	ADP
ejpam-5251	262	112	h.	h.	PROPN
ejpam-5251	263	1	then	then	ADV
ejpam-5251	263	2	s	s	VERB
ejpam-5251	263	3	is	be	AUX
ejpam-5251	263	4	a	a	DET
ejpam-5251	263	5	minimal	minimal	ADJ
ejpam-5251	263	6	geodetic	geodetic	ADJ
ejpam-5251	263	7	hop	hop	NOUN
ejpam-5251	263	8	dominating	dominating	NOUN
ejpam-5251	263	9	set	set	NOUN
ejpam-5251	263	10	of	of	ADP
ejpam-5251	263	11	g+h	g+h	PROPN
ejpam-5251	263	12	.	.	PUNCT
ejpam-5251	264	1	proof	proof	NOUN
ejpam-5251	264	2	.	.	PUNCT
ejpam-5251	265	1	assume	assume	VERB
ejpam-5251	265	2	that	that	SCONJ
ejpam-5251	265	3	sg	sg	PROPN
ejpam-5251	265	4	and	and	CCONJ
ejpam-5251	265	5	sh	sh	PROPN
ejpam-5251	265	6	are	be	AUX
ejpam-5251	265	7	pointwise	pointwise	PROPN
ejpam-5251	265	8	non	non	ADJ
ejpam-5251	265	9	-	-	ADJ
ejpam-5251	265	10	dominating	dominating	ADJ
ejpam-5251	265	11	sets	set	NOUN
ejpam-5251	265	12	of	of	ADP
ejpam-5251	265	13	g	g	PROPN
ejpam-5251	265	14	and	and	CCONJ
ejpam-5251	265	15	h	h	NOUN
ejpam-5251	265	16	,	,	PUNCT
ejpam-5251	265	17	respectively	respectively	ADV
ejpam-5251	265	18	.	.	PUNCT
ejpam-5251	266	1	then	then	ADV
ejpam-5251	266	2	s	s	VERB
ejpam-5251	266	3	is	be	AUX
ejpam-5251	266	4	a	a	DET
ejpam-5251	266	5	hop	hop	NOUN
ejpam-5251	266	6	dominating	dominating	NOUN
ejpam-5251	266	7	set	set	VERB
ejpam-5251	266	8	in	in	ADP
ejpam-5251	266	9	g+h	g+h	PROPN
ejpam-5251	266	10	.	.	PUNCT
ejpam-5251	267	1	assume	assume	VERB
ejpam-5251	267	2	further	far	ADV
ejpam-5251	267	3	that	that	SCONJ
ejpam-5251	267	4	(	(	PUNCT
ejpam-5251	267	5	i	i	NOUN
ejpam-5251	267	6	)	)	PUNCT
ejpam-5251	267	7	holds	hold	VERB
ejpam-5251	267	8	for	for	SCONJ
ejpam-5251	267	9	s.	s.	PROPN
ejpam-5251	267	10	let	let	VERB
ejpam-5251	267	11	x	x	SYM
ejpam-5251	267	12	∈	∈	PROPN
ejpam-5251	267	13	v	v	X
ejpam-5251	267	14	(	(	PUNCT
ejpam-5251	267	15	g	g	PROPN
ejpam-5251	267	16	+	+	NOUN
ejpam-5251	267	17	h	h	NOUN
ejpam-5251	267	18	)	)	PUNCT
ejpam-5251	267	19	\	\	PUNCT
ejpam-5251	268	1	s.	s.	PROPN
ejpam-5251	268	2	suppose	suppose	VERB
ejpam-5251	268	3	that	that	SCONJ
ejpam-5251	268	4	x	x	PROPN
ejpam-5251	268	5	∈	∈	NOUN
ejpam-5251	268	6	v	v	ADP
ejpam-5251	268	7	(	(	PUNCT
ejpam-5251	268	8	g	g	NOUN
ejpam-5251	268	9	)	)	PUNCT
ejpam-5251	268	10	\	\	PUNCT
ejpam-5251	268	11	s.	s.	PROPN
ejpam-5251	268	12	since	since	SCONJ
ejpam-5251	268	13	sg	sg	PROPN
ejpam-5251	268	14	is	be	AUX
ejpam-5251	268	15	a	a	DET
ejpam-5251	268	16	2	2	NUM
ejpam-5251	268	17	-	-	PUNCT
ejpam-5251	268	18	path	path	NOUN
ejpam-5251	268	19	closure	closure	NOUN
ejpam-5251	268	20	absorbing	absorb	VERB
ejpam-5251	268	21	set	set	NOUN
ejpam-5251	268	22	in	in	ADP
ejpam-5251	268	23	g	g	NOUN
ejpam-5251	268	24	,	,	PUNCT
ejpam-5251	268	25	there	there	PRON
ejpam-5251	268	26	exists	exist	VERB
ejpam-5251	268	27	u	u	NOUN
ejpam-5251	268	28	,	,	PUNCT
ejpam-5251	268	29	v	v	NOUN
ejpam-5251	268	30	∈	∈	NOUN
ejpam-5251	268	31	sg	sg	NOUN
ejpam-5251	268	32	for	for	ADP
ejpam-5251	268	33	which	which	PRON
ejpam-5251	268	34	dg(u	dg(u	X
ejpam-5251	268	35	,	,	PUNCT
ejpam-5251	268	36	v	v	NOUN
ejpam-5251	268	37	)	)	PUNCT
ejpam-5251	268	38	=	=	SYM
ejpam-5251	268	39	2	2	NUM
ejpam-5251	268	40	and	and	CCONJ
ejpam-5251	268	41	x	x	PROPN
ejpam-5251	268	42	∈	∈	PROPN
ejpam-5251	268	43	ig(u	ig(u	NOUN
ejpam-5251	268	44	,	,	PUNCT
ejpam-5251	268	45	v	v	NOUN
ejpam-5251	268	46	)	)	PUNCT
ejpam-5251	268	47	.	.	PUNCT
ejpam-5251	269	1	observe	observe	VERB
ejpam-5251	269	2	that	that	SCONJ
ejpam-5251	269	3	dg+h(u	dg+h(u	PROPN
ejpam-5251	269	4	,	,	PUNCT
ejpam-5251	269	5	v	v	NOUN
ejpam-5251	269	6	)	)	PUNCT
ejpam-5251	269	7	=	=	SYM
ejpam-5251	269	8	dg(u	dg(u	X
ejpam-5251	269	9	,	,	PUNCT
ejpam-5251	269	10	v	v	NOUN
ejpam-5251	269	11	)	)	PUNCT
ejpam-5251	269	12	=	=	SYM
ejpam-5251	269	13	2	2	NUM
ejpam-5251	269	14	and	and	CCONJ
ejpam-5251	269	15	ig(u	ig(u	NOUN
ejpam-5251	269	16	,	,	PUNCT
ejpam-5251	269	17	v	v	NOUN
ejpam-5251	269	18	)	)	PUNCT
ejpam-5251	269	19	⊆	⊆	NUM
ejpam-5251	269	20	ig+h(u	ig+h(u	NOUN
ejpam-5251	269	21	,	,	PUNCT
ejpam-5251	269	22	v	v	NOUN
ejpam-5251	269	23	)	)	PUNCT
ejpam-5251	269	24	.	.	PUNCT
ejpam-5251	270	1	suppose	suppose	VERB
ejpam-5251	270	2	that	that	SCONJ
ejpam-5251	270	3	x	x	SYM
ejpam-5251	270	4	∈	∈	NOUN
ejpam-5251	270	5	v	v	ADP
ejpam-5251	270	6	(	(	PUNCT
ejpam-5251	270	7	h	h	NOUN
ejpam-5251	270	8	)	)	PUNCT
ejpam-5251	270	9	\	\	PUNCT
ejpam-5251	270	10	s.	s.	PROPN
ejpam-5251	270	11	by	by	ADP
ejpam-5251	270	12	lemma	lemma	PROPN
ejpam-5251	270	13	1	1	NUM
ejpam-5251	270	14	,	,	PUNCT
ejpam-5251	270	15	⟨sg⟩	⟨sg⟩	PRON
ejpam-5251	270	16	is	be	AUX
ejpam-5251	270	17	noncomplete	noncomplete	ADJ
ejpam-5251	270	18	.	.	PUNCT
ejpam-5251	271	1	thus	thus	ADV
ejpam-5251	271	2	,	,	PUNCT
ejpam-5251	271	3	there	there	PRON
ejpam-5251	271	4	exists	exist	VERB
ejpam-5251	271	5	u	u	NOUN
ejpam-5251	271	6	,	,	PUNCT
ejpam-5251	271	7	v	v	NOUN
ejpam-5251	271	8	∈	∈	PROPN
ejpam-5251	271	9	sg	sg	ADP
ejpam-5251	271	10	such	such	ADJ
ejpam-5251	271	11	that	that	DET
ejpam-5251	271	12	dg(u	dg(u	ADJ
ejpam-5251	271	13	,	,	PUNCT
ejpam-5251	271	14	v	v	NOUN
ejpam-5251	271	15	)	)	PUNCT
ejpam-5251	272	1	=	=	SYM
ejpam-5251	272	2	2	2	X
ejpam-5251	272	3	.	.	PUNCT
ejpam-5251	273	1	then	then	ADV
ejpam-5251	273	2	dg+h(u	dg+h(u	PROPN
ejpam-5251	273	3	,	,	PUNCT
ejpam-5251	273	4	v	v	NOUN
ejpam-5251	273	5	)	)	PUNCT
ejpam-5251	273	6	=	=	SYM
ejpam-5251	273	7	2	2	NUM
ejpam-5251	273	8	and	and	CCONJ
ejpam-5251	273	9	x	x	SYM
ejpam-5251	273	10	∈	∈	PROPN
ejpam-5251	273	11	ig+h(u	ig+h(u	PROPN
ejpam-5251	273	12	,	,	PUNCT
ejpam-5251	273	13	v	v	NOUN
ejpam-5251	273	14	)	)	PUNCT
ejpam-5251	273	15	.	.	PUNCT
ejpam-5251	274	1	since	since	SCONJ
ejpam-5251	274	2	x	x	PRON
ejpam-5251	274	3	is	be	AUX
ejpam-5251	274	4	arbitrary	arbitrary	ADJ
ejpam-5251	274	5	,	,	PUNCT
ejpam-5251	274	6	s	s	PART
ejpam-5251	274	7	is	be	AUX
ejpam-5251	274	8	a	a	DET
ejpam-5251	274	9	geodetic	geodetic	ADJ
ejpam-5251	274	10	set	set	NOUN
ejpam-5251	274	11	in	in	ADP
ejpam-5251	274	12	g+h	g+h	PROPN
ejpam-5251	274	13	.	.	PUNCT
ejpam-5251	275	1	therefore	therefore	ADV
ejpam-5251	275	2	,	,	PUNCT
ejpam-5251	275	3	s	s	VERB
ejpam-5251	275	4	is	be	AUX
ejpam-5251	275	5	a	a	DET
ejpam-5251	275	6	geodetic	geodetic	ADJ
ejpam-5251	275	7	hop	hop	NOUN
ejpam-5251	275	8	dominating	dominating	NOUN
ejpam-5251	275	9	set	set	VERB
ejpam-5251	275	10	in	in	ADP
ejpam-5251	275	11	g+h	g+h	PROPN
ejpam-5251	275	12	.	.	PUNCT
ejpam-5251	276	1	now	now	ADV
ejpam-5251	276	2	,	,	PUNCT
ejpam-5251	276	3	let	let	VERB
ejpam-5251	276	4	t	t	PROPN
ejpam-5251	276	5	⊆	⊆	NUM
ejpam-5251	276	6	v	v	NOUN
ejpam-5251	276	7	(	(	PUNCT
ejpam-5251	276	8	g	g	PROPN
ejpam-5251	276	9	+	+	NOUN
ejpam-5251	276	10	h	h	NOUN
ejpam-5251	276	11	)	)	PUNCT
ejpam-5251	276	12	be	be	VERB
ejpam-5251	276	13	a	a	DET
ejpam-5251	276	14	geodetic	geodetic	ADJ
ejpam-5251	276	15	hop	hop	NOUN
ejpam-5251	276	16	dominating	dominating	NOUN
ejpam-5251	276	17	set	set	VERB
ejpam-5251	276	18	in	in	ADP
ejpam-5251	276	19	g	g	PROPN
ejpam-5251	276	20	+	+	CCONJ
ejpam-5251	276	21	h	h	NOUN
ejpam-5251	276	22	with	with	ADP
ejpam-5251	276	23	t	t	PROPN
ejpam-5251	276	24	⊆	⊆	NUM
ejpam-5251	276	25	s.	s.	PROPN
ejpam-5251	276	26	write	write	VERB
ejpam-5251	276	27	t	t	PROPN
ejpam-5251	277	1	=	=	PUNCT
ejpam-5251	277	2	tg	tg	PROPN
ejpam-5251	277	3	∪	∪	ADP
ejpam-5251	277	4	th	th	PROPN
ejpam-5251	277	5	,	,	PUNCT
ejpam-5251	277	6	where	where	SCONJ
ejpam-5251	277	7	tg	tg	PROPN
ejpam-5251	277	8	=	=	SYM
ejpam-5251	277	9	t	t	PROPN
ejpam-5251	277	10	∩	∩	NOUN
ejpam-5251	277	11	v	v	X
ejpam-5251	277	12	(	(	PUNCT
ejpam-5251	277	13	g	g	NOUN
ejpam-5251	277	14	)	)	PUNCT
ejpam-5251	277	15	and	and	CCONJ
ejpam-5251	277	16	th	th	X
ejpam-5251	277	17	=	=	SYM
ejpam-5251	277	18	t	t	PROPN
ejpam-5251	277	19	∩	∩	ADJ
ejpam-5251	277	20	v	v	X
ejpam-5251	277	21	(	(	PUNCT
ejpam-5251	277	22	h	h	NOUN
ejpam-5251	277	23	)	)	PUNCT
ejpam-5251	277	24	.	.	PUNCT
ejpam-5251	278	1	then	then	ADV
ejpam-5251	278	2	tg	tg	PROPN
ejpam-5251	278	3	and	and	CCONJ
ejpam-5251	278	4	th	th	PROPN
ejpam-5251	278	5	are	be	AUX
ejpam-5251	278	6	pointwise	pointwise	PROPN
ejpam-5251	278	7	non	non	ADJ
ejpam-5251	278	8	-	-	ADJ
ejpam-5251	278	9	dominating	dominating	ADJ
ejpam-5251	278	10	sets	set	NOUN
ejpam-5251	278	11	in	in	ADP
ejpam-5251	278	12	g	g	PROPN
ejpam-5251	278	13	and	and	CCONJ
ejpam-5251	278	14	h	h	NOUN
ejpam-5251	278	15	,	,	PUNCT
ejpam-5251	278	16	respectively	respectively	ADV
ejpam-5251	278	17	,	,	PUNCT
ejpam-5251	278	18	by	by	ADP
ejpam-5251	278	19	theorem	theorem	NOUN
ejpam-5251	278	20	4	4	NUM
ejpam-5251	278	21	.	.	PUNCT
ejpam-5251	278	22	note	note	VERB
ejpam-5251	278	23	that	that	SCONJ
ejpam-5251	278	24	tg	tg	PROPN
ejpam-5251	278	25	⊆	⊆	NUM
ejpam-5251	278	26	sg	sg	NOUN
ejpam-5251	278	27	and	and	CCONJ
ejpam-5251	278	28	th	th	X
ejpam-5251	278	29	⊆	⊆	NUM
ejpam-5251	278	30	sh	sh	NOUN
ejpam-5251	278	31	.	.	PUNCT
ejpam-5251	279	1	since	since	SCONJ
ejpam-5251	279	2	⟨sh⟩	⟨sh⟩	NOUN
ejpam-5251	279	3	is	be	AUX
ejpam-5251	279	4	complete	complete	ADJ
ejpam-5251	279	5	,	,	PUNCT
ejpam-5251	279	6	⟨th⟩	⟨th⟩	NOUN
ejpam-5251	279	7	is	be	AUX
ejpam-5251	279	8	a	a	DET
ejpam-5251	279	9	complete	complete	ADJ
ejpam-5251	279	10	subgraph	subgraph	NOUN
ejpam-5251	279	11	of	of	ADP
ejpam-5251	279	12	h.	h.	PROPN
ejpam-5251	280	1	if	if	SCONJ
ejpam-5251	280	2	sh	sh	PROPN
ejpam-5251	280	3	\	\	PROPN
ejpam-5251	280	4	th	th	PROPN
ejpam-5251	280	5	̸=	̸=	PROPN
ejpam-5251	280	6	∅	∅	NOUN
ejpam-5251	280	7	and	and	CCONJ
ejpam-5251	280	8	x	x	PUNCT
ejpam-5251	280	9	∈	∈	PROPN
ejpam-5251	280	10	sh	sh	INTJ
ejpam-5251	280	11	\	\	PROPN
ejpam-5251	280	12	th	th	INTJ
ejpam-5251	280	13	,	,	PUNCT
ejpam-5251	280	14	then	then	ADV
ejpam-5251	280	15	xy	xy	PROPN
ejpam-5251	280	16	∈	∈	PROPN
ejpam-5251	280	17	e(g	e(g	PROPN
ejpam-5251	281	1	+	+	CCONJ
ejpam-5251	281	2	h	h	NOUN
ejpam-5251	281	3	)	)	PUNCT
ejpam-5251	281	4	for	for	ADP
ejpam-5251	281	5	all	all	DET
ejpam-5251	281	6	y	y	PROPN
ejpam-5251	281	7	∈	∈	PROPN
ejpam-5251	281	8	th	th	X
ejpam-5251	281	9	,	,	PUNCT
ejpam-5251	281	10	a	a	DET
ejpam-5251	281	11	contradiction	contradiction	NOUN
ejpam-5251	281	12	since	since	SCONJ
ejpam-5251	281	13	th	th	NUM
ejpam-5251	281	14	is	be	AUX
ejpam-5251	281	15	a	a	DET
ejpam-5251	281	16	pointwise	pointwise	ADJ
ejpam-5251	281	17	non	non	ADJ
ejpam-5251	281	18	-	-	ADJ
ejpam-5251	281	19	dominating	dominating	ADJ
ejpam-5251	281	20	set	set	NOUN
ejpam-5251	281	21	in	in	ADP
ejpam-5251	281	22	h.	h.	PROPN
ejpam-5251	281	23	thus	thus	ADV
ejpam-5251	281	24	,	,	PUNCT
ejpam-5251	281	25	sh	sh	PROPN
ejpam-5251	281	26	=	=	SYM
ejpam-5251	281	27	th	th	X
ejpam-5251	281	28	.	.	PUNCT
ejpam-5251	282	1	by	by	ADP
ejpam-5251	282	2	theorem	theorem	NOUN
ejpam-5251	282	3	4	4	NUM
ejpam-5251	282	4	,	,	PUNCT
ejpam-5251	282	5	tg	tg	PROPN
ejpam-5251	282	6	is	be	AUX
ejpam-5251	282	7	a	a	DET
ejpam-5251	282	8	2	2	NUM
ejpam-5251	282	9	-	-	PUNCT
ejpam-5251	282	10	path	path	NOUN
ejpam-5251	282	11	closure	closure	NOUN
ejpam-5251	282	12	absorbing	absorb	VERB
ejpam-5251	282	13	set	set	VERB
ejpam-5251	282	14	in	in	ADP
ejpam-5251	282	15	g.	g.	PROPN
ejpam-5251	282	16	since	since	SCONJ
ejpam-5251	282	17	tg	tg	PROPN
ejpam-5251	282	18	⊆	⊆	NUM
ejpam-5251	282	19	sg	sg	NOUN
ejpam-5251	282	20	,	,	PUNCT
ejpam-5251	282	21	the	the	DET
ejpam-5251	282	22	minimality	minimality	NOUN
ejpam-5251	282	23	of	of	ADP
ejpam-5251	282	24	sg	sg	PROPN
ejpam-5251	282	25	implies	imply	VERB
ejpam-5251	282	26	that	that	SCONJ
ejpam-5251	282	27	sg	sg	VERB
ejpam-5251	282	28	=	=	SYM
ejpam-5251	282	29	tg	tg	PROPN
ejpam-5251	282	30	.	.	PUNCT
ejpam-5251	283	1	therefore	therefore	ADV
ejpam-5251	283	2	,	,	PUNCT
ejpam-5251	283	3	s	s	PART
ejpam-5251	283	4	=	=	X
ejpam-5251	283	5	t	t	PROPN
ejpam-5251	283	6	and	and	CCONJ
ejpam-5251	283	7	s	s	VERB
ejpam-5251	283	8	is	be	AUX
ejpam-5251	283	9	a	a	DET
ejpam-5251	283	10	minimal	minimal	ADJ
ejpam-5251	283	11	geodetic	geodetic	ADJ
ejpam-5251	283	12	hop	hop	NOUN
ejpam-5251	283	13	dominating	dominating	NOUN
ejpam-5251	283	14	set	set	VERB
ejpam-5251	283	15	in	in	ADP
ejpam-5251	283	16	g+h	g+h	PROPN
ejpam-5251	283	17	.	.	PUNCT
ejpam-5251	284	1	similarly	similarly	ADV
ejpam-5251	284	2	,	,	PUNCT
ejpam-5251	284	3	if	if	SCONJ
ejpam-5251	284	4	condition	condition	NOUN
ejpam-5251	284	5	(	(	PUNCT
ejpam-5251	284	6	ii	ii	NOUN
ejpam-5251	284	7	)	)	PUNCT
ejpam-5251	284	8	holds	hold	VERB
ejpam-5251	284	9	,	,	PUNCT
ejpam-5251	284	10	then	then	ADV
ejpam-5251	284	11	s	s	VERB
ejpam-5251	284	12	is	be	AUX
ejpam-5251	284	13	a	a	DET
ejpam-5251	284	14	minimal	minimal	ADJ
ejpam-5251	284	15	geodetic	geodetic	ADJ
ejpam-5251	284	16	hop	hop	NOUN
ejpam-5251	284	17	dominating	dominating	NOUN
ejpam-5251	284	18	set	set	VERB
ejpam-5251	284	19	in	in	ADP
ejpam-5251	284	20	g+h	g+h	PROPN
ejpam-5251	284	21	.	.	PUNCT
ejpam-5251	285	1	corollary	corollary	ADJ
ejpam-5251	285	2	4	4	NUM
ejpam-5251	285	3	.	.	PUNCT
ejpam-5251	286	1	let	let	VERB
ejpam-5251	286	2	g	g	PRON
ejpam-5251	286	3	be	be	AUX
ejpam-5251	286	4	a	a	DET
ejpam-5251	286	5	nontrivial	nontrivial	ADJ
ejpam-5251	286	6	connected	connect	VERB
ejpam-5251	286	7	graphs	graph	NOUN
ejpam-5251	286	8	and	and	CCONJ
ejpam-5251	286	9	p	p	DET
ejpam-5251	286	10	≥	≥	NUM
ejpam-5251	286	11	1	1	NUM
ejpam-5251	286	12	,	,	PUNCT
ejpam-5251	286	13	and	and	CCONJ
ejpam-5251	286	14	let	let	VERB
ejpam-5251	286	15	s	s	PRON
ejpam-5251	286	16	⊆	⊆	NUM
ejpam-5251	286	17	v	v	NOUN
ejpam-5251	286	18	(	(	PUNCT
ejpam-5251	286	19	g+kp	g+kp	NOUN
ejpam-5251	286	20	)	)	PUNCT
ejpam-5251	286	21	.	.	PUNCT
ejpam-5251	287	1	then	then	ADV
ejpam-5251	287	2	s	s	VERB
ejpam-5251	287	3	is	be	AUX
ejpam-5251	287	4	a	a	DET
ejpam-5251	287	5	minimal	minimal	ADJ
ejpam-5251	287	6	geodetic	geodetic	ADJ
ejpam-5251	287	7	hop	hop	NOUN
ejpam-5251	287	8	dominating	dominating	NOUN
ejpam-5251	287	9	set	set	NOUN
ejpam-5251	287	10	of	of	ADP
ejpam-5251	287	11	g	g	PROPN
ejpam-5251	287	12	+	+	CCONJ
ejpam-5251	287	13	kp	kp	X
ejpam-5251	287	14	if	if	SCONJ
ejpam-5251	288	1	and	and	CCONJ
ejpam-5251	288	2	only	only	ADV
ejpam-5251	288	3	if	if	SCONJ
ejpam-5251	288	4	s	s	VERB
ejpam-5251	288	5	=	=	SYM
ejpam-5251	288	6	v	v	PROPN
ejpam-5251	288	7	(	(	PUNCT
ejpam-5251	288	8	kp	kp	PROPN
ejpam-5251	288	9	)	)	PUNCT
ejpam-5251	288	10	∪	∪	NOUN
ejpam-5251	288	11	sg	sg	ADP
ejpam-5251	288	12	where	where	SCONJ
ejpam-5251	288	13	sg	sg	PROPN
ejpam-5251	288	14	⊆	⊆	NUM
ejpam-5251	288	15	v	v	NOUN
ejpam-5251	288	16	(	(	PUNCT
ejpam-5251	288	17	g	g	NOUN
ejpam-5251	288	18	)	)	PUNCT
ejpam-5251	288	19	is	be	AUX
ejpam-5251	288	20	a	a	DET
ejpam-5251	288	21	minimal	minimal	ADJ
ejpam-5251	288	22	2	2	NUM
ejpam-5251	288	23	-	-	PUNCT
ejpam-5251	288	24	path	path	NOUN
ejpam-5251	288	25	closure	closure	NOUN
ejpam-5251	288	26	absorbing	absorb	VERB
ejpam-5251	288	27	pointwise	pointwise	PROPN
ejpam-5251	288	28	non	non	ADJ
ejpam-5251	288	29	-	-	ADJ
ejpam-5251	288	30	dominating	dominating	ADJ
ejpam-5251	288	31	set	set	NOUN
ejpam-5251	288	32	of	of	ADP
ejpam-5251	288	33	g.	g.	PROPN
ejpam-5251	288	34	more	more	ADV
ejpam-5251	288	35	precisely	precisely	ADV
ejpam-5251	288	36	,	,	PUNCT
ejpam-5251	288	37	γ+hg(g+kp	γ+hg(g+kp	NOUN
ejpam-5251	288	38	)	)	PUNCT
ejpam-5251	288	39	=	=	PRON
ejpam-5251	288	40	p+	p+	ADJ
ejpam-5251	288	41	ρ+2pnd(g	ρ+2pnd(g	PROPN
ejpam-5251	288	42	)	)	PUNCT
ejpam-5251	288	43	.	.	PUNCT
ejpam-5251	289	1	d.	d.	PROPN
ejpam-5251	289	2	catian	catian	PROPN
ejpam-5251	289	3	,	,	PUNCT
ejpam-5251	289	4	i.	i.	PROPN
ejpam-5251	289	5	s.	s.	PROPN
ejpam-5251	289	6	aniversario	aniversario	PROPN
ejpam-5251	289	7	,	,	PUNCT
ejpam-5251	289	8	f.	f.	PROPN
ejpam-5251	289	9	p.	p.	PROPN
ejpam-5251	289	10	jamil	jamil	PROPN
ejpam-5251	289	11	/	/	SYM
ejpam-5251	289	12	eur	eur	PROPN
ejpam-5251	289	13	.	.	PUNCT
ejpam-5251	290	1	j.	j.	PROPN
ejpam-5251	290	2	pure	pure	PROPN
ejpam-5251	290	3	appl	appl	PROPN
ejpam-5251	290	4	.	.	PROPN
ejpam-5251	290	5	math	math	PROPN
ejpam-5251	290	6	,	,	PUNCT
ejpam-5251	290	7	17	17	NUM
ejpam-5251	290	8	(	(	PUNCT
ejpam-5251	290	9	3	3	NUM
ejpam-5251	290	10	)	)	PUNCT
ejpam-5251	290	11	(	(	PUNCT
ejpam-5251	290	12	2024	2024	NUM
ejpam-5251	290	13	)	)	PUNCT
ejpam-5251	290	14	,	,	PUNCT
ejpam-5251	290	15	1737	1737	NUM
ejpam-5251	290	16	-	-	SYM
ejpam-5251	290	17	1750	1750	NUM
ejpam-5251	290	18	1745	1745	NUM
ejpam-5251	290	19	proof	proof	NOUN
ejpam-5251	290	20	.	.	PUNCT
ejpam-5251	291	1	if	if	SCONJ
ejpam-5251	291	2	g	g	PROPN
ejpam-5251	291	3	is	be	AUX
ejpam-5251	291	4	complete	complete	ADJ
ejpam-5251	291	5	,	,	PUNCT
ejpam-5251	291	6	then	then	ADV
ejpam-5251	291	7	g	g	PROPN
ejpam-5251	291	8	+	+	CCONJ
ejpam-5251	291	9	h	h	NOUN
ejpam-5251	291	10	is	be	AUX
ejpam-5251	291	11	complete	complete	ADJ
ejpam-5251	291	12	,	,	PUNCT
ejpam-5251	291	13	and	and	CCONJ
ejpam-5251	291	14	the	the	DET
ejpam-5251	291	15	assertion	assertion	NOUN
ejpam-5251	291	16	is	be	AUX
ejpam-5251	291	17	obvious	obvious	ADJ
ejpam-5251	291	18	.	.	PUNCT
ejpam-5251	292	1	suppose	suppose	VERB
ejpam-5251	292	2	that	that	SCONJ
ejpam-5251	292	3	g	g	PROPN
ejpam-5251	292	4	is	be	AUX
ejpam-5251	292	5	noncomplete	noncomplete	ADJ
ejpam-5251	292	6	.	.	PUNCT
ejpam-5251	293	1	put	put	VERB
ejpam-5251	293	2	h	h	NOUN
ejpam-5251	294	1	=	=	PUNCT
ejpam-5251	294	2	kp	kp	PROPN
ejpam-5251	294	3	,	,	PUNCT
ejpam-5251	294	4	and	and	CCONJ
ejpam-5251	294	5	let	let	VERB
ejpam-5251	294	6	sg	sg	VERB
ejpam-5251	294	7	=	=	SYM
ejpam-5251	294	8	s	s	PART
ejpam-5251	294	9	∩	∩	ADJ
ejpam-5251	294	10	v	v	X
ejpam-5251	294	11	(	(	PUNCT
ejpam-5251	294	12	g	g	NOUN
ejpam-5251	294	13	)	)	PUNCT
ejpam-5251	294	14	and	and	CCONJ
ejpam-5251	294	15	sh	sh	INTJ
ejpam-5251	294	16	=	=	SYM
ejpam-5251	294	17	s	s	PROPN
ejpam-5251	294	18	∩	∩	ADJ
ejpam-5251	294	19	v	v	ADJ
ejpam-5251	294	20	(	(	PUNCT
ejpam-5251	294	21	h	h	NOUN
ejpam-5251	294	22	)	)	PUNCT
ejpam-5251	294	23	=	=	NOUN
ejpam-5251	294	24	v	v	X
ejpam-5251	294	25	(	(	PUNCT
ejpam-5251	294	26	kp	kp	PROPN
ejpam-5251	294	27	)	)	PUNCT
ejpam-5251	294	28	.	.	PUNCT
ejpam-5251	295	1	assume	assume	VERB
ejpam-5251	295	2	s	s	PRON
ejpam-5251	295	3	is	be	AUX
ejpam-5251	295	4	a	a	DET
ejpam-5251	295	5	minimal	minimal	ADJ
ejpam-5251	295	6	geodetic	geodetic	ADJ
ejpam-5251	295	7	hop	hop	NOUN
ejpam-5251	295	8	dominating	dominating	NOUN
ejpam-5251	295	9	set	set	VERB
ejpam-5251	295	10	in	in	ADP
ejpam-5251	295	11	g	g	PROPN
ejpam-5251	295	12	+	+	CCONJ
ejpam-5251	296	1	kp	kp	PROPN
ejpam-5251	296	2	.	.	PUNCT
ejpam-5251	296	3	note	note	VERB
ejpam-5251	296	4	that	that	SCONJ
ejpam-5251	296	5	⟨sh⟩	⟨sh⟩	PRON
ejpam-5251	296	6	is	be	AUX
ejpam-5251	296	7	complete	complete	ADJ
ejpam-5251	296	8	and	and	CCONJ
ejpam-5251	296	9	sh	sh	INTJ
ejpam-5251	296	10	=	=	SYM
ejpam-5251	296	11	v	v	PROPN
ejpam-5251	296	12	(	(	PUNCT
ejpam-5251	296	13	kp	kp	PROPN
ejpam-5251	296	14	)	)	PUNCT
ejpam-5251	296	15	is	be	AUX
ejpam-5251	296	16	a	a	DET
ejpam-5251	296	17	pointwise	pointwise	ADJ
ejpam-5251	296	18	non	non	ADJ
ejpam-5251	296	19	-	-	ADJ
ejpam-5251	296	20	dominating	dominating	ADJ
ejpam-5251	296	21	set	set	NOUN
ejpam-5251	296	22	in	in	ADP
ejpam-5251	296	23	h.	h.	PROPN
ejpam-5251	296	24	thus	thus	ADV
ejpam-5251	296	25	,	,	PUNCT
ejpam-5251	296	26	sg	sg	PROPN
ejpam-5251	296	27	is	be	AUX
ejpam-5251	296	28	a	a	DET
ejpam-5251	296	29	minimal	minimal	ADJ
ejpam-5251	296	30	2	2	NUM
ejpam-5251	296	31	-	-	PUNCT
ejpam-5251	296	32	path	path	NOUN
ejpam-5251	296	33	closure	closure	NOUN
ejpam-5251	296	34	absorbing	absorb	VERB
ejpam-5251	296	35	pointwise	pointwise	PROPN
ejpam-5251	296	36	non	non	ADJ
ejpam-5251	296	37	-	-	ADJ
ejpam-5251	296	38	dominating	dominating	ADJ
ejpam-5251	296	39	set	set	NOUN
ejpam-5251	296	40	in	in	ADP
ejpam-5251	296	41	g	g	NOUN
ejpam-5251	296	42	by	by	ADP
ejpam-5251	296	43	proposition	proposition	NOUN
ejpam-5251	296	44	4	4	NUM
ejpam-5251	296	45	.	.	PUNCT
ejpam-5251	296	46	conversely	conversely	ADV
ejpam-5251	296	47	,	,	PUNCT
ejpam-5251	296	48	suppose	suppose	VERB
ejpam-5251	296	49	that	that	SCONJ
ejpam-5251	296	50	sg	sg	PROPN
ejpam-5251	296	51	is	be	AUX
ejpam-5251	296	52	a	a	DET
ejpam-5251	296	53	minimal	minimal	ADJ
ejpam-5251	296	54	2	2	NUM
ejpam-5251	296	55	-	-	PUNCT
ejpam-5251	296	56	path	path	NOUN
ejpam-5251	296	57	closure	closure	NOUN
ejpam-5251	296	58	absorbing	absorb	VERB
ejpam-5251	296	59	pointwise	pointwise	PROPN
ejpam-5251	296	60	non	non	ADJ
ejpam-5251	296	61	-	-	ADJ
ejpam-5251	296	62	dominating	dominating	ADJ
ejpam-5251	296	63	set	set	NOUN
ejpam-5251	296	64	in	in	ADP
ejpam-5251	296	65	g.	g.	NOUN
ejpam-5251	296	66	by	by	ADP
ejpam-5251	296	67	proposition	proposition	NOUN
ejpam-5251	296	68	5	5	NUM
ejpam-5251	296	69	,	,	PUNCT
ejpam-5251	296	70	s	s	PART
ejpam-5251	296	71	=	=	PUNCT
ejpam-5251	296	72	sg	sg	PROPN
ejpam-5251	296	73	∪	∪	NOUN
ejpam-5251	296	74	sh	sh	PROPN
ejpam-5251	296	75	is	be	AUX
ejpam-5251	296	76	a	a	DET
ejpam-5251	296	77	minimal	minimal	ADJ
ejpam-5251	296	78	geodetic	geodetic	ADJ
ejpam-5251	296	79	hop	hop	NOUN
ejpam-5251	296	80	dominating	dominating	NOUN
ejpam-5251	296	81	set	set	VERB
ejpam-5251	296	82	in	in	ADP
ejpam-5251	296	83	g+h	g+h	PROPN
ejpam-5251	296	84	.	.	PUNCT
ejpam-5251	297	1	proposition	proposition	NOUN
ejpam-5251	297	2	6	6	NUM
ejpam-5251	297	3	.	.	PUNCT
ejpam-5251	298	1	let	let	VERB
ejpam-5251	298	2	g	g	NOUN
ejpam-5251	298	3	and	and	CCONJ
ejpam-5251	298	4	h	h	NOUN
ejpam-5251	298	5	be	be	AUX
ejpam-5251	298	6	connected	connect	VERB
ejpam-5251	298	7	noncomplete	noncomplete	ADJ
ejpam-5251	298	8	graphs	graph	NOUN
ejpam-5251	298	9	.	.	PUNCT
ejpam-5251	299	1	then	then	ADV
ejpam-5251	299	2	γ+hg(g+h	γ+hg(g+h	NUM
ejpam-5251	299	3	)	)	PUNCT
ejpam-5251	299	4	≥	≥	NUM
ejpam-5251	299	5	max{ρ+2pnd(g	max{ρ+2pnd(g	PROPN
ejpam-5251	299	6	)	)	PUNCT
ejpam-5251	299	7	+	+	NUM
ejpam-5251	299	8	ω(h	ω(h	NUM
ejpam-5251	299	9	)	)	PUNCT
ejpam-5251	299	10	,	,	PUNCT
ejpam-5251	299	11	ρ+2pnd(h	ρ+2pnd(h	PROPN
ejpam-5251	299	12	)	)	PUNCT
ejpam-5251	300	1	+	+	NUM
ejpam-5251	300	2	ω(g	ω(g	NOUN
ejpam-5251	300	3	)	)	PUNCT
ejpam-5251	300	4	}	}	PUNCT
ejpam-5251	300	5	.	.	PUNCT
ejpam-5251	301	1	proof	proof	NOUN
ejpam-5251	301	2	.	.	PUNCT
ejpam-5251	302	1	let	let	VERB
ejpam-5251	302	2	sg	sg	ADP
ejpam-5251	302	3	⊆	⊆	NUM
ejpam-5251	302	4	v	v	NOUN
ejpam-5251	302	5	(	(	PUNCT
ejpam-5251	302	6	g	g	NOUN
ejpam-5251	302	7	)	)	PUNCT
ejpam-5251	302	8	be	be	AUX
ejpam-5251	302	9	a	a	DET
ejpam-5251	302	10	ρ+2pnd	ρ+2pnd	NOUN
ejpam-5251	302	11	-	-	PUNCT
ejpam-5251	302	12	set	set	NOUN
ejpam-5251	302	13	of	of	ADP
ejpam-5251	302	14	g	g	PROPN
ejpam-5251	302	15	and	and	CCONJ
ejpam-5251	302	16	sh	sh	PROPN
ejpam-5251	302	17	⊆	⊆	NUM
ejpam-5251	302	18	v	v	ADP
ejpam-5251	302	19	(	(	PUNCT
ejpam-5251	302	20	h	h	NOUN
ejpam-5251	302	21	)	)	PUNCT
ejpam-5251	302	22	be	be	VERB
ejpam-5251	302	23	ω	ω	NOUN
ejpam-5251	302	24	-	-	PUNCT
ejpam-5251	302	25	set	set	NOUN
ejpam-5251	302	26	of	of	ADP
ejpam-5251	302	27	h.	h.	PROPN
ejpam-5251	302	28	because	because	SCONJ
ejpam-5251	302	29	h	h	NOUN
ejpam-5251	302	30	is	be	AUX
ejpam-5251	302	31	noncomplete	noncomplete	ADJ
ejpam-5251	302	32	,	,	PUNCT
ejpam-5251	302	33	v	v	ADJ
ejpam-5251	302	34	(	(	PUNCT
ejpam-5251	302	35	h	h	NOUN
ejpam-5251	302	36	)	)	PUNCT
ejpam-5251	302	37	̸=	̸=	PROPN
ejpam-5251	302	38	sh	sh	INTJ
ejpam-5251	302	39	.	.	PUNCT
ejpam-5251	303	1	let	let	VERB
ejpam-5251	303	2	x	x	SYM
ejpam-5251	303	3	∈	∈	PROPN
ejpam-5251	303	4	v	v	ADP
ejpam-5251	303	5	(	(	PUNCT
ejpam-5251	303	6	h	h	NOUN
ejpam-5251	303	7	)	)	PUNCT
ejpam-5251	303	8	\sh	\sh	PROPN
ejpam-5251	303	9	.	.	PUNCT
ejpam-5251	304	1	since	since	SCONJ
ejpam-5251	304	2	⟨sh	⟨sh	NUM
ejpam-5251	304	3	∪{x}⟩	∪{x}⟩	NOUN
ejpam-5251	304	4	is	be	AUX
ejpam-5251	304	5	a	a	DET
ejpam-5251	304	6	not	not	PART
ejpam-5251	304	7	complete	complete	ADJ
ejpam-5251	304	8	,	,	PUNCT
ejpam-5251	304	9	there	there	PRON
ejpam-5251	304	10	exists	exist	VERB
ejpam-5251	304	11	y	y	PROPN
ejpam-5251	304	12	∈	∈	PROPN
ejpam-5251	304	13	sh	sh	INTJ
ejpam-5251	304	14	for	for	ADP
ejpam-5251	304	15	which	which	PRON
ejpam-5251	304	16	xy	xy	PROPN
ejpam-5251	304	17	/∈	/∈	PUNCT
ejpam-5251	304	18	e(h	e(h	PROPN
ejpam-5251	304	19	)	)	PUNCT
ejpam-5251	304	20	.	.	PUNCT
ejpam-5251	305	1	since	since	SCONJ
ejpam-5251	305	2	x	x	PRON
ejpam-5251	305	3	is	be	AUX
ejpam-5251	305	4	arbitrary	arbitrary	ADJ
ejpam-5251	305	5	,	,	PUNCT
ejpam-5251	305	6	sh	sh	PROPN
ejpam-5251	305	7	is	be	AUX
ejpam-5251	305	8	a	a	DET
ejpam-5251	305	9	pointwise	pointwise	ADJ
ejpam-5251	305	10	non	non	ADJ
ejpam-5251	305	11	-	-	ADJ
ejpam-5251	305	12	dominating	dominating	ADJ
ejpam-5251	305	13	set	set	NOUN
ejpam-5251	305	14	in	in	ADP
ejpam-5251	305	15	h.	h.	NOUN
ejpam-5251	305	16	by	by	ADP
ejpam-5251	305	17	proposition	proposition	NOUN
ejpam-5251	305	18	4	4	NUM
ejpam-5251	305	19	,	,	PUNCT
ejpam-5251	305	20	s	s	PART
ejpam-5251	305	21	=	=	PUNCT
ejpam-5251	305	22	sg	sg	PROPN
ejpam-5251	305	23	∪	∪	NOUN
ejpam-5251	305	24	sh	sh	PROPN
ejpam-5251	305	25	is	be	AUX
ejpam-5251	305	26	a	a	DET
ejpam-5251	305	27	minimal	minimal	ADJ
ejpam-5251	305	28	geodetic	geodetic	ADJ
ejpam-5251	305	29	hop	hop	NOUN
ejpam-5251	305	30	dominating	dominating	NOUN
ejpam-5251	305	31	set	set	VERB
ejpam-5251	305	32	in	in	ADP
ejpam-5251	305	33	g+h	g+h	PROPN
ejpam-5251	305	34	.	.	PUNCT
ejpam-5251	306	1	thus	thus	ADV
ejpam-5251	306	2	,	,	PUNCT
ejpam-5251	306	3	γ+hg(g+h	γ+hg(g+h	PROPN
ejpam-5251	306	4	)	)	PUNCT
ejpam-5251	306	5	≥	≥	NOUN
ejpam-5251	306	6	|s|	|s|	NOUN
ejpam-5251	306	7	=	=	SYM
ejpam-5251	306	8	ρ+hg(g	ρ+hg(g	PROPN
ejpam-5251	306	9	)	)	PUNCT
ejpam-5251	306	10	+	+	NUM
ejpam-5251	306	11	ω(h	ω(h	NUM
ejpam-5251	306	12	)	)	PUNCT
ejpam-5251	306	13	.	.	PUNCT
ejpam-5251	307	1	similarly	similarly	ADV
ejpam-5251	307	2	,	,	PUNCT
ejpam-5251	307	3	γ+hg(g+h	γ+hg(g+h	PROPN
ejpam-5251	307	4	)	)	PUNCT
ejpam-5251	307	5	≥	≥	PROPN
ejpam-5251	307	6	|s|	|s|	NOUN
ejpam-5251	307	7	=	=	PUNCT
ejpam-5251	307	8	ρ+hg(h	ρ+hg(h	PROPN
ejpam-5251	307	9	)	)	PUNCT
ejpam-5251	307	10	+	+	CCONJ
ejpam-5251	307	11	ω(g	ω(g	NOUN
ejpam-5251	307	12	)	)	PUNCT
ejpam-5251	307	13	.	.	PUNCT
ejpam-5251	308	1	since	since	SCONJ
ejpam-5251	308	2	γ+hg(p3	γ+hg(p3	PROPN
ejpam-5251	308	3	+	+	CCONJ
ejpam-5251	308	4	c3	c3	PROPN
ejpam-5251	308	5	)	)	PUNCT
ejpam-5251	308	6	=	=	SYM
ejpam-5251	308	7	5	5	NUM
ejpam-5251	308	8	=	=	SYM
ejpam-5251	308	9	ρ+2pnd(p3	ρ+2pnd(p3	PROPN
ejpam-5251	308	10	)	)	PUNCT
ejpam-5251	308	11	+	+	SYM
ejpam-5251	308	12	ω(p3	ω(p3	NOUN
ejpam-5251	308	13	)	)	PUNCT
ejpam-5251	308	14	,	,	PUNCT
ejpam-5251	308	15	the	the	DET
ejpam-5251	308	16	lower	lower	ADV
ejpam-5251	308	17	bound	bind	VERB
ejpam-5251	308	18	in	in	ADP
ejpam-5251	308	19	proposition	proposition	NOUN
ejpam-5251	308	20	6	6	NUM
ejpam-5251	308	21	is	be	AUX
ejpam-5251	308	22	sharp	sharp	ADJ
ejpam-5251	308	23	.	.	PUNCT
ejpam-5251	309	1	5	5	X
ejpam-5251	309	2	.	.	X
ejpam-5251	309	3	in	in	ADP
ejpam-5251	309	4	the	the	DET
ejpam-5251	309	5	corona	corona	NOUN
ejpam-5251	309	6	of	of	ADP
ejpam-5251	309	7	graphs	graph	NOUN
ejpam-5251	309	8	theorem	theorem	VERB
ejpam-5251	309	9	5	5	NUM
ejpam-5251	309	10	.	.	PUNCT
ejpam-5251	310	1	[	[	X
ejpam-5251	310	2	27	27	NUM
ejpam-5251	310	3	]	]	PUNCT
ejpam-5251	310	4	let	let	VERB
ejpam-5251	310	5	g	g	NOUN
ejpam-5251	310	6	and	and	CCONJ
ejpam-5251	310	7	h	h	NOUN
ejpam-5251	310	8	be	be	VERB
ejpam-5251	310	9	any	any	DET
ejpam-5251	310	10	two	two	NUM
ejpam-5251	310	11	graphs	graph	NOUN
ejpam-5251	310	12	.	.	PUNCT
ejpam-5251	311	1	a	a	DET
ejpam-5251	311	2	set	set	NOUN
ejpam-5251	311	3	s	s	NOUN
ejpam-5251	311	4	⊆	⊆	NUM
ejpam-5251	311	5	v	v	NOUN
ejpam-5251	311	6	(	(	PUNCT
ejpam-5251	311	7	g	g	PROPN
ejpam-5251	311	8	◦	◦	NOUN
ejpam-5251	311	9	h	h	NOUN
ejpam-5251	311	10	)	)	PUNCT
ejpam-5251	311	11	is	be	AUX
ejpam-5251	311	12	a	a	DET
ejpam-5251	311	13	geodetic	geodetic	ADJ
ejpam-5251	311	14	hop	hop	NOUN
ejpam-5251	311	15	dominating	dominating	NOUN
ejpam-5251	311	16	set	set	NOUN
ejpam-5251	311	17	of	of	ADP
ejpam-5251	311	18	g	g	PROPN
ejpam-5251	311	19	◦	◦	NOUN
ejpam-5251	311	20	h	h	NOUN
ejpam-5251	311	21	if	if	SCONJ
ejpam-5251	312	1	and	and	CCONJ
ejpam-5251	312	2	only	only	ADV
ejpam-5251	312	3	if	if	SCONJ
ejpam-5251	312	4	s	s	VERB
ejpam-5251	312	5	=	=	NOUN
ejpam-5251	312	6	a	a	DET
ejpam-5251	312	7	∪	∪	X
ejpam-5251	312	8	(	(	PUNCT
ejpam-5251	312	9	∪v∈v	∪v∈v	X
ejpam-5251	312	10	(	(	PUNCT
ejpam-5251	312	11	g)sv	g)sv	PROPN
ejpam-5251	312	12	)	)	PUNCT
ejpam-5251	312	13	,	,	PUNCT
ejpam-5251	312	14	where	where	SCONJ
ejpam-5251	312	15	a	a	DET
ejpam-5251	312	16	⊆	⊆	NUM
ejpam-5251	312	17	v	v	NOUN
ejpam-5251	312	18	(	(	PUNCT
ejpam-5251	312	19	g	g	NOUN
ejpam-5251	312	20	)	)	PUNCT
ejpam-5251	312	21	and	and	CCONJ
ejpam-5251	312	22	sv	sv	X
ejpam-5251	312	23	⊆	⊆	NUM
ejpam-5251	312	24	v	v	X
ejpam-5251	312	25	(	(	PUNCT
ejpam-5251	312	26	hv	hv	PROPN
ejpam-5251	312	27	)	)	PUNCT
ejpam-5251	312	28	for	for	ADP
ejpam-5251	312	29	each	each	DET
ejpam-5251	312	30	v	v	NUM
ejpam-5251	312	31	∈	∈	PROPN
ejpam-5251	312	32	v	v	NOUN
ejpam-5251	312	33	(	(	PUNCT
ejpam-5251	312	34	g	g	NOUN
ejpam-5251	312	35	)	)	PUNCT
ejpam-5251	312	36	,	,	PUNCT
ejpam-5251	312	37	and	and	CCONJ
ejpam-5251	312	38	satisfies	satisfy	VERB
ejpam-5251	312	39	the	the	DET
ejpam-5251	312	40	following	follow	VERB
ejpam-5251	312	41	conditions	condition	NOUN
ejpam-5251	312	42	:	:	PUNCT
ejpam-5251	312	43	(	(	PUNCT
ejpam-5251	312	44	i	i	NOUN
ejpam-5251	312	45	)	)	PUNCT
ejpam-5251	312	46	sv	sv	PROPN
ejpam-5251	312	47	is	be	AUX
ejpam-5251	312	48	a	a	DET
ejpam-5251	312	49	pointwise	pointwise	ADJ
ejpam-5251	312	50	non	non	ADJ
ejpam-5251	312	51	-	-	ADJ
ejpam-5251	312	52	dominating	dominating	ADJ
ejpam-5251	312	53	set	set	NOUN
ejpam-5251	312	54	in	in	ADP
ejpam-5251	312	55	hv	hv	PROPN
ejpam-5251	312	56	for	for	ADP
ejpam-5251	312	57	each	each	PRON
ejpam-5251	312	58	v	v	NUM
ejpam-5251	312	59	∈	∈	PROPN
ejpam-5251	312	60	v	v	NOUN
ejpam-5251	312	61	(	(	PUNCT
ejpam-5251	312	62	g	g	NOUN
ejpam-5251	312	63	)	)	PUNCT
ejpam-5251	312	64	\ng(a	\ng(a	PROPN
ejpam-5251	312	65	)	)	PUNCT
ejpam-5251	312	66	;	;	PUNCT
ejpam-5251	312	67	(	(	PUNCT
ejpam-5251	312	68	ii	ii	NOUN
ejpam-5251	312	69	)	)	PUNCT
ejpam-5251	312	70	for	for	ADP
ejpam-5251	312	71	each	each	DET
ejpam-5251	312	72	w	w	PROPN
ejpam-5251	312	73	∈	∈	PROPN
ejpam-5251	312	74	v	v	ADP
ejpam-5251	312	75	(	(	PUNCT
ejpam-5251	312	76	g	g	NOUN
ejpam-5251	312	77	)	)	PUNCT
ejpam-5251	312	78	\a	\a	ADJ
ejpam-5251	312	79	,	,	PUNCT
ejpam-5251	312	80	one	one	NUM
ejpam-5251	312	81	of	of	ADP
ejpam-5251	312	82	the	the	DET
ejpam-5251	312	83	following	following	NOUN
ejpam-5251	312	84	holds	hold	VERB
ejpam-5251	312	85	:	:	PUNCT
ejpam-5251	312	86	(	(	PUNCT
ejpam-5251	312	87	a	a	X
ejpam-5251	312	88	)	)	PUNCT
ejpam-5251	312	89	∃a	∃a	NOUN
ejpam-5251	312	90	,	,	PUNCT
ejpam-5251	312	91	b	b	PROPN
ejpam-5251	312	92	∈	∈	PROPN
ejpam-5251	312	93	sw	sw	PROPN
ejpam-5251	312	94	with	with	ADP
ejpam-5251	312	95	dhw(a	dhw(a	PROPN
ejpam-5251	312	96	,	,	PUNCT
ejpam-5251	312	97	b	b	NOUN
ejpam-5251	312	98	)	)	PUNCT
ejpam-5251	312	99	̸=	̸=	PROPN
ejpam-5251	312	100	1	1	NUM
ejpam-5251	312	101	;	;	PUNCT
ejpam-5251	312	102	(	(	PUNCT
ejpam-5251	312	103	b	b	X
ejpam-5251	312	104	)	)	PUNCT
ejpam-5251	312	105	∃x	∃x	NOUN
ejpam-5251	312	106	,	,	PUNCT
ejpam-5251	312	107	y	y	PROPN
ejpam-5251	312	108	∈	∈	PROPN
ejpam-5251	312	109	v	v	ADP
ejpam-5251	312	110	(	(	PUNCT
ejpam-5251	312	111	g	g	NOUN
ejpam-5251	312	112	)	)	PUNCT
ejpam-5251	312	113	with	with	ADP
ejpam-5251	312	114	w	w	PROPN
ejpam-5251	312	115	∈	∈	PROPN
ejpam-5251	312	116	ig(x	ig(x	X
ejpam-5251	312	117	,	,	PUNCT
ejpam-5251	312	118	y	y	NOUN
ejpam-5251	312	119	)	)	PUNCT
ejpam-5251	312	120	;	;	PUNCT
ejpam-5251	312	121	(	(	PUNCT
ejpam-5251	312	122	c	c	X
ejpam-5251	312	123	)	)	PUNCT
ejpam-5251	312	124	∃s	∃s	PROPN
ejpam-5251	312	125	∈	∈	PROPN
ejpam-5251	312	126	sw	sw	PROPN
ejpam-5251	312	127	and	and	CCONJ
ejpam-5251	312	128	t	t	PROPN
ejpam-5251	312	129	∈	∈	PROPN
ejpam-5251	312	130	a.	a.	NOUN
ejpam-5251	312	131	(	(	PUNCT
ejpam-5251	312	132	iii	iii	X
ejpam-5251	312	133	)	)	PUNCT
ejpam-5251	312	134	sv	sv	PROPN
ejpam-5251	312	135	is	be	AUX
ejpam-5251	312	136	a	a	DET
ejpam-5251	312	137	2	2	NUM
ejpam-5251	312	138	-	-	PUNCT
ejpam-5251	312	139	path	path	NOUN
ejpam-5251	312	140	closure	closure	NOUN
ejpam-5251	312	141	absorbing	absorb	VERB
ejpam-5251	312	142	set	set	NOUN
ejpam-5251	312	143	in	in	ADP
ejpam-5251	312	144	hv	hv	PROPN
ejpam-5251	312	145	for	for	ADP
ejpam-5251	312	146	all	all	PRON
ejpam-5251	312	147	v	v	ADP
ejpam-5251	312	148	∈	∈	NUM
ejpam-5251	312	149	v	v	NOUN
ejpam-5251	312	150	(	(	PUNCT
ejpam-5251	312	151	g	g	NOUN
ejpam-5251	312	152	)	)	PUNCT
ejpam-5251	312	153	.	.	PUNCT
ejpam-5251	313	1	observe	observe	VERB
ejpam-5251	313	2	that	that	SCONJ
ejpam-5251	313	3	if	if	SCONJ
ejpam-5251	313	4	g	g	PROPN
ejpam-5251	313	5	is	be	AUX
ejpam-5251	313	6	a	a	DET
ejpam-5251	313	7	nontrivial	nontrivial	ADJ
ejpam-5251	313	8	connected	connect	VERB
ejpam-5251	313	9	graph	graph	NOUN
ejpam-5251	313	10	,	,	PUNCT
ejpam-5251	313	11	then	then	ADV
ejpam-5251	313	12	condition	condition	NOUN
ejpam-5251	313	13	(	(	PUNCT
ejpam-5251	313	14	ii	ii	NOUN
ejpam-5251	313	15	)	)	PUNCT
ejpam-5251	313	16	in	in	ADP
ejpam-5251	313	17	theorem	theorem	NOUN
ejpam-5251	313	18	5	5	NUM
ejpam-5251	313	19	may	may	AUX
ejpam-5251	313	20	be	be	AUX
ejpam-5251	313	21	removed	remove	VERB
ejpam-5251	313	22	.	.	PUNCT
ejpam-5251	314	1	corollary	corollary	ADJ
ejpam-5251	314	2	5	5	NUM
ejpam-5251	314	3	.	.	PUNCT
ejpam-5251	315	1	let	let	VERB
ejpam-5251	315	2	g	g	NOUN
ejpam-5251	315	3	and	and	CCONJ
ejpam-5251	315	4	h	h	NOUN
ejpam-5251	315	5	be	be	VERB
ejpam-5251	315	6	two	two	NUM
ejpam-5251	315	7	graphs	graph	NOUN
ejpam-5251	315	8	,	,	PUNCT
ejpam-5251	315	9	where	where	SCONJ
ejpam-5251	315	10	g	g	PROPN
ejpam-5251	315	11	is	be	AUX
ejpam-5251	315	12	connected	connect	VERB
ejpam-5251	315	13	and	and	CCONJ
ejpam-5251	315	14	nontrivial	nontrivial	ADJ
ejpam-5251	315	15	.	.	PUNCT
ejpam-5251	316	1	a	a	DET
ejpam-5251	316	2	set	set	NOUN
ejpam-5251	316	3	s	s	NOUN
ejpam-5251	316	4	⊆	⊆	NUM
ejpam-5251	316	5	v	v	NOUN
ejpam-5251	316	6	(	(	PUNCT
ejpam-5251	316	7	g	g	PROPN
ejpam-5251	316	8	◦	◦	NOUN
ejpam-5251	316	9	h	h	NOUN
ejpam-5251	316	10	)	)	PUNCT
ejpam-5251	316	11	is	be	AUX
ejpam-5251	316	12	a	a	DET
ejpam-5251	316	13	geodetic	geodetic	ADJ
ejpam-5251	316	14	hop	hop	NOUN
ejpam-5251	316	15	dominating	dominating	NOUN
ejpam-5251	316	16	set	set	NOUN
ejpam-5251	316	17	of	of	ADP
ejpam-5251	316	18	g	g	PROPN
ejpam-5251	316	19	◦	◦	NOUN
ejpam-5251	316	20	h	h	NOUN
ejpam-5251	316	21	if	if	SCONJ
ejpam-5251	317	1	and	and	CCONJ
ejpam-5251	317	2	only	only	ADV
ejpam-5251	317	3	if	if	SCONJ
ejpam-5251	317	4	s	s	VERB
ejpam-5251	317	5	=	=	NOUN
ejpam-5251	317	6	a	a	DET
ejpam-5251	317	7	∪	∪	X
ejpam-5251	317	8	(	(	PUNCT
ejpam-5251	317	9	∪v∈v	∪v∈v	X
ejpam-5251	317	10	(	(	PUNCT
ejpam-5251	317	11	g)sv	g)sv	PROPN
ejpam-5251	317	12	)	)	PUNCT
ejpam-5251	317	13	,	,	PUNCT
ejpam-5251	317	14	where	where	SCONJ
ejpam-5251	317	15	a	a	DET
ejpam-5251	317	16	⊆	⊆	NUM
ejpam-5251	317	17	v	v	NOUN
ejpam-5251	317	18	(	(	PUNCT
ejpam-5251	317	19	g	g	NOUN
ejpam-5251	317	20	)	)	PUNCT
ejpam-5251	317	21	and	and	CCONJ
ejpam-5251	317	22	sv	sv	X
ejpam-5251	317	23	⊆	⊆	NUM
ejpam-5251	317	24	v	v	X
ejpam-5251	317	25	(	(	PUNCT
ejpam-5251	317	26	hv	hv	PROPN
ejpam-5251	317	27	)	)	PUNCT
ejpam-5251	317	28	for	for	ADP
ejpam-5251	317	29	each	each	DET
ejpam-5251	317	30	v	v	NUM
ejpam-5251	317	31	∈	∈	PROPN
ejpam-5251	317	32	v	v	NOUN
ejpam-5251	317	33	(	(	PUNCT
ejpam-5251	317	34	g	g	NOUN
ejpam-5251	317	35	)	)	PUNCT
ejpam-5251	317	36	,	,	PUNCT
ejpam-5251	317	37	and	and	CCONJ
ejpam-5251	317	38	satisfies	satisfy	VERB
ejpam-5251	317	39	the	the	DET
ejpam-5251	317	40	following	follow	VERB
ejpam-5251	317	41	conditions	condition	NOUN
ejpam-5251	317	42	:	:	PUNCT
ejpam-5251	317	43	d.	d.	PROPN
ejpam-5251	317	44	catian	catian	PROPN
ejpam-5251	317	45	,	,	PUNCT
ejpam-5251	317	46	i.	i.	PROPN
ejpam-5251	317	47	s.	s.	PROPN
ejpam-5251	317	48	aniversario	aniversario	PROPN
ejpam-5251	317	49	,	,	PUNCT
ejpam-5251	317	50	f.	f.	PROPN
ejpam-5251	317	51	p.	p.	PROPN
ejpam-5251	317	52	jamil	jamil	PROPN
ejpam-5251	317	53	/	/	SYM
ejpam-5251	317	54	eur	eur	PROPN
ejpam-5251	317	55	.	.	PUNCT
ejpam-5251	318	1	j.	j.	PROPN
ejpam-5251	318	2	pure	pure	PROPN
ejpam-5251	318	3	appl	appl	PROPN
ejpam-5251	318	4	.	.	PROPN
ejpam-5251	318	5	math	math	PROPN
ejpam-5251	318	6	,	,	PUNCT
ejpam-5251	318	7	17	17	NUM
ejpam-5251	318	8	(	(	PUNCT
ejpam-5251	318	9	3	3	NUM
ejpam-5251	318	10	)	)	PUNCT
ejpam-5251	318	11	(	(	PUNCT
ejpam-5251	318	12	2024	2024	NUM
ejpam-5251	318	13	)	)	PUNCT
ejpam-5251	318	14	,	,	PUNCT
ejpam-5251	318	15	1737	1737	NUM
ejpam-5251	318	16	-	-	SYM
ejpam-5251	318	17	1750	1750	NUM
ejpam-5251	318	18	1746	1746	NUM
ejpam-5251	318	19	(	(	PUNCT
ejpam-5251	318	20	i	i	NOUN
ejpam-5251	318	21	)	)	PUNCT
ejpam-5251	318	22	sv	sv	PROPN
ejpam-5251	318	23	is	be	AUX
ejpam-5251	318	24	a	a	DET
ejpam-5251	318	25	pointwise	pointwise	ADJ
ejpam-5251	318	26	non	non	ADJ
ejpam-5251	318	27	-	-	ADJ
ejpam-5251	318	28	dominating	dominating	ADJ
ejpam-5251	318	29	set	set	NOUN
ejpam-5251	318	30	in	in	ADP
ejpam-5251	318	31	hv	hv	PROPN
ejpam-5251	318	32	for	for	ADP
ejpam-5251	318	33	each	each	PRON
ejpam-5251	318	34	v	v	NUM
ejpam-5251	318	35	∈	∈	PROPN
ejpam-5251	318	36	v	v	NOUN
ejpam-5251	318	37	(	(	PUNCT
ejpam-5251	318	38	g	g	NOUN
ejpam-5251	318	39	)	)	PUNCT
ejpam-5251	318	40	\ng(a	\ng(a	PROPN
ejpam-5251	318	41	)	)	PUNCT
ejpam-5251	318	42	;	;	PUNCT
ejpam-5251	318	43	(	(	PUNCT
ejpam-5251	318	44	ii	ii	NOUN
ejpam-5251	318	45	)	)	PUNCT
ejpam-5251	318	46	sv	sv	PROPN
ejpam-5251	318	47	is	be	AUX
ejpam-5251	318	48	a	a	DET
ejpam-5251	318	49	2	2	NUM
ejpam-5251	318	50	-	-	PUNCT
ejpam-5251	318	51	path	path	NOUN
ejpam-5251	318	52	closure	closure	NOUN
ejpam-5251	318	53	absorbing	absorb	VERB
ejpam-5251	318	54	set	set	NOUN
ejpam-5251	318	55	in	in	ADP
ejpam-5251	318	56	hv	hv	PROPN
ejpam-5251	318	57	for	for	ADP
ejpam-5251	318	58	all	all	PRON
ejpam-5251	318	59	v	v	ADP
ejpam-5251	318	60	∈	∈	NUM
ejpam-5251	318	61	v	v	NOUN
ejpam-5251	318	62	(	(	PUNCT
ejpam-5251	318	63	g	g	NOUN
ejpam-5251	318	64	)	)	PUNCT
ejpam-5251	318	65	.	.	PUNCT
ejpam-5251	319	1	proof	proof	NOUN
ejpam-5251	319	2	.	.	PUNCT
ejpam-5251	320	1	the	the	DET
ejpam-5251	320	2	necessity	necessity	NOUN
ejpam-5251	320	3	part	part	NOUN
ejpam-5251	320	4	follows	follow	VERB
ejpam-5251	320	5	from	from	ADP
ejpam-5251	320	6	theorem	theorem	ADJ
ejpam-5251	320	7	5	5	NUM
ejpam-5251	320	8	.	.	PUNCT
ejpam-5251	320	9	suppose	suppose	VERB
ejpam-5251	320	10	that	that	SCONJ
ejpam-5251	320	11	(	(	PUNCT
ejpam-5251	320	12	i	i	NOUN
ejpam-5251	320	13	)	)	PUNCT
ejpam-5251	320	14	and	and	CCONJ
ejpam-5251	320	15	(	(	PUNCT
ejpam-5251	320	16	ii	ii	NOUN
ejpam-5251	320	17	)	)	PUNCT
ejpam-5251	320	18	hold	hold	VERB
ejpam-5251	320	19	for	for	ADP
ejpam-5251	320	20	s.	s.	PROPN
ejpam-5251	320	21	following	follow	VERB
ejpam-5251	320	22	the	the	DET
ejpam-5251	320	23	same	same	ADJ
ejpam-5251	320	24	proof	proof	NOUN
ejpam-5251	320	25	as	as	ADP
ejpam-5251	320	26	one	one	NUM
ejpam-5251	320	27	given	give	VERB
ejpam-5251	320	28	in	in	ADP
ejpam-5251	320	29	[	[	NOUN
ejpam-5251	320	30	9	9	NUM
ejpam-5251	320	31	]	]	PUNCT
ejpam-5251	320	32	for	for	ADP
ejpam-5251	320	33	theorem	theorem	ADJ
ejpam-5251	320	34	5	5	NUM
ejpam-5251	320	35	,	,	PUNCT
ejpam-5251	320	36	s	s	VERB
ejpam-5251	320	37	is	be	AUX
ejpam-5251	320	38	a	a	DET
ejpam-5251	320	39	hop	hop	NOUN
ejpam-5251	320	40	dominating	dominating	NOUN
ejpam-5251	320	41	set	set	VERB
ejpam-5251	320	42	in	in	ADP
ejpam-5251	320	43	g	g	PROPN
ejpam-5251	320	44	◦	◦	NOUN
ejpam-5251	320	45	h	h	NOUN
ejpam-5251	320	46	and	and	CCONJ
ejpam-5251	320	47	for	for	ADP
ejpam-5251	320	48	every	every	DET
ejpam-5251	320	49	w	w	PROPN
ejpam-5251	320	50	∈	∈	PROPN
ejpam-5251	320	51	v	v	ADP
ejpam-5251	320	52	(	(	PUNCT
ejpam-5251	320	53	hw	hw	NOUN
ejpam-5251	320	54	)	)	PUNCT
ejpam-5251	320	55	\	\	PROPN
ejpam-5251	320	56	sw	sw	PROPN
ejpam-5251	320	57	,	,	PUNCT
ejpam-5251	320	58	there	there	PRON
ejpam-5251	320	59	exist	exist	VERB
ejpam-5251	320	60	u	u	NOUN
ejpam-5251	320	61	,	,	PUNCT
ejpam-5251	320	62	v	v	PROPN
ejpam-5251	320	63	∈	∈	NOUN
ejpam-5251	320	64	s	s	VERB
ejpam-5251	320	65	such	such	ADJ
ejpam-5251	320	66	that	that	SCONJ
ejpam-5251	320	67	w	w	PROPN
ejpam-5251	320	68	∈	∈	PROPN
ejpam-5251	320	69	ig+h(u	ig+h(u	PROPN
ejpam-5251	320	70	,	,	PUNCT
ejpam-5251	320	71	v	v	NOUN
ejpam-5251	320	72	)	)	PUNCT
ejpam-5251	320	73	.	.	PUNCT
ejpam-5251	321	1	now	now	ADV
ejpam-5251	321	2	,	,	PUNCT
ejpam-5251	321	3	suppose	suppose	VERB
ejpam-5251	321	4	that	that	SCONJ
ejpam-5251	321	5	w	w	PROPN
ejpam-5251	321	6	∈	∈	PROPN
ejpam-5251	321	7	v	v	ADP
ejpam-5251	321	8	(	(	PUNCT
ejpam-5251	321	9	g	g	NOUN
ejpam-5251	321	10	)	)	PUNCT
ejpam-5251	321	11	\a	\a	ADJ
ejpam-5251	321	12	.	.	PUNCT
ejpam-5251	322	1	since	since	SCONJ
ejpam-5251	322	2	g	g	PROPN
ejpam-5251	322	3	is	be	AUX
ejpam-5251	322	4	nontrivial	nontrivial	ADJ
ejpam-5251	322	5	and	and	CCONJ
ejpam-5251	322	6	connected	connect	VERB
ejpam-5251	322	7	,	,	PUNCT
ejpam-5251	322	8	ng(w	ng(w	NOUN
ejpam-5251	322	9	)	)	PUNCT
ejpam-5251	322	10	̸=	̸=	NOUN
ejpam-5251	322	11	∅	∅	NOUN
ejpam-5251	322	12	,	,	PUNCT
ejpam-5251	322	13	say	say	VERB
ejpam-5251	322	14	z	z	PROPN
ejpam-5251	322	15	∈	∈	PROPN
ejpam-5251	322	16	ng(w	ng(w	NOUN
ejpam-5251	322	17	)	)	PUNCT
ejpam-5251	322	18	.	.	PUNCT
ejpam-5251	323	1	by	by	ADP
ejpam-5251	323	2	(	(	PUNCT
ejpam-5251	323	3	ii	ii	NOUN
ejpam-5251	323	4	)	)	PUNCT
ejpam-5251	323	5	,	,	PUNCT
ejpam-5251	323	6	sz	sz	PROPN
ejpam-5251	323	7	̸=	̸=	PROPN
ejpam-5251	323	8	∅	∅	NOUN
ejpam-5251	323	9	and	and	CCONJ
ejpam-5251	323	10	sw	sw	PROPN
ejpam-5251	323	11	̸=	̸=	PROPN
ejpam-5251	323	12	∅.	∅.	AUX
ejpam-5251	323	13	pick	pick	VERB
ejpam-5251	323	14	u	u	PROPN
ejpam-5251	323	15	∈	∈	PROPN
ejpam-5251	323	16	sz	sz	PROPN
ejpam-5251	323	17	and	and	CCONJ
ejpam-5251	323	18	v	v	ADP
ejpam-5251	323	19	∈	∈	PROPN
ejpam-5251	323	20	sw	sw	PROPN
ejpam-5251	323	21	.	.	PUNCT
ejpam-5251	324	1	then	then	ADV
ejpam-5251	324	2	w	w	PROPN
ejpam-5251	324	3	∈	∈	PROPN
ejpam-5251	324	4	ig	ig	PROPN
ejpam-5251	324	5	◦	◦	NOUN
ejpam-5251	324	6	h(u	h(u	PROPN
ejpam-5251	324	7	,	,	PUNCT
ejpam-5251	324	8	v	v	NOUN
ejpam-5251	324	9	)	)	PUNCT
ejpam-5251	324	10	.	.	PUNCT
ejpam-5251	325	1	proposition	proposition	NOUN
ejpam-5251	325	2	7	7	NUM
ejpam-5251	325	3	.	.	PUNCT
ejpam-5251	326	1	let	let	VERB
ejpam-5251	326	2	g	g	NOUN
ejpam-5251	326	3	and	and	CCONJ
ejpam-5251	326	4	h	h	NOUN
ejpam-5251	326	5	be	be	VERB
ejpam-5251	326	6	two	two	NUM
ejpam-5251	326	7	graphs	graph	NOUN
ejpam-5251	326	8	,	,	PUNCT
ejpam-5251	326	9	where	where	SCONJ
ejpam-5251	326	10	g	g	PROPN
ejpam-5251	326	11	is	be	AUX
ejpam-5251	326	12	connected	connect	VERB
ejpam-5251	326	13	of	of	ADP
ejpam-5251	326	14	order	order	NOUN
ejpam-5251	326	15	n	n	PRON
ejpam-5251	326	16	≥	≥	NOUN
ejpam-5251	326	17	2	2	NUM
ejpam-5251	326	18	.	.	PUNCT
ejpam-5251	327	1	then	then	ADV
ejpam-5251	327	2	γ+hg(g	γ+hg(g	PROPN
ejpam-5251	327	3	◦	◦	NOUN
ejpam-5251	327	4	h	h	NOUN
ejpam-5251	327	5	)	)	PUNCT
ejpam-5251	327	6	≥	≥	PROPN
ejpam-5251	327	7	n	n	CCONJ
ejpam-5251	327	8	·	·	PUNCT
ejpam-5251	327	9	ρ+2pnd(h	ρ+2pnd(h	NUM
ejpam-5251	327	10	)	)	PUNCT
ejpam-5251	327	11	,	,	PUNCT
ejpam-5251	327	12	and	and	CCONJ
ejpam-5251	327	13	this	this	DET
ejpam-5251	327	14	bound	bind	VERB
ejpam-5251	327	15	is	be	AUX
ejpam-5251	327	16	sharp	sharp	ADJ
ejpam-5251	327	17	.	.	PUNCT
ejpam-5251	328	1	proof	proof	NOUN
ejpam-5251	328	2	.	.	PUNCT
ejpam-5251	329	1	for	for	ADP
ejpam-5251	329	2	each	each	DET
ejpam-5251	329	3	v	v	NUM
ejpam-5251	329	4	∈	∈	PROPN
ejpam-5251	329	5	v	v	NOUN
ejpam-5251	329	6	(	(	PUNCT
ejpam-5251	329	7	g	g	NOUN
ejpam-5251	329	8	)	)	PUNCT
ejpam-5251	329	9	,	,	PUNCT
ejpam-5251	329	10	let	let	VERB
ejpam-5251	329	11	sv	sv	PROPN
ejpam-5251	329	12	⊆	⊆	NUM
ejpam-5251	329	13	v	v	X
ejpam-5251	329	14	(	(	PUNCT
ejpam-5251	329	15	hv	hv	NOUN
ejpam-5251	329	16	)	)	PUNCT
ejpam-5251	329	17	be	be	VERB
ejpam-5251	329	18	a	a	DET
ejpam-5251	329	19	ρ+2pnd	ρ+2pnd	NOUN
ejpam-5251	329	20	-	-	PUNCT
ejpam-5251	329	21	set	set	NOUN
ejpam-5251	329	22	of	of	ADP
ejpam-5251	329	23	h	h	NOUN
ejpam-5251	329	24	v.	v.	ADV
ejpam-5251	329	25	by	by	ADP
ejpam-5251	329	26	corollary	corollary	ADJ
ejpam-5251	329	27	5	5	NUM
ejpam-5251	329	28	,	,	PUNCT
ejpam-5251	329	29	∪v∈v	∪v∈v	X
ejpam-5251	329	30	(	(	PUNCT
ejpam-5251	329	31	g)sv	g)sv	PROPN
ejpam-5251	329	32	is	be	AUX
ejpam-5251	329	33	a	a	DET
ejpam-5251	329	34	geodetic	geodetic	ADJ
ejpam-5251	329	35	hop	hop	NOUN
ejpam-5251	329	36	dominating	dominating	NOUN
ejpam-5251	329	37	set	set	VERB
ejpam-5251	329	38	in	in	ADP
ejpam-5251	329	39	g	g	PROPN
ejpam-5251	329	40	◦	◦	NOUN
ejpam-5251	329	41	h.	h.	PROPN
ejpam-5251	329	42	let	let	AUX
ejpam-5251	329	43	t	t	PROPN
ejpam-5251	329	44	⊆	⊆	NUM
ejpam-5251	329	45	v	v	NOUN
ejpam-5251	329	46	(	(	PUNCT
ejpam-5251	329	47	g	g	PROPN
ejpam-5251	329	48	◦	◦	NOUN
ejpam-5251	329	49	h	h	NOUN
ejpam-5251	329	50	)	)	PUNCT
ejpam-5251	329	51	be	be	VERB
ejpam-5251	329	52	a	a	DET
ejpam-5251	329	53	geodetic	geodetic	ADJ
ejpam-5251	329	54	hop	hop	NOUN
ejpam-5251	329	55	dominating	dominating	NOUN
ejpam-5251	329	56	set	set	VERB
ejpam-5251	329	57	in	in	ADP
ejpam-5251	329	58	g	g	PROPN
ejpam-5251	329	59	◦	◦	NOUN
ejpam-5251	329	60	h	h	NOUN
ejpam-5251	329	61	with	with	ADP
ejpam-5251	329	62	t	t	PROPN
ejpam-5251	329	63	⊆	⊆	NUM
ejpam-5251	329	64	s.	s.	PROPN
ejpam-5251	329	65	by	by	ADP
ejpam-5251	329	66	corollary	corollary	ADJ
ejpam-5251	329	67	5	5	NUM
ejpam-5251	329	68	and	and	CCONJ
ejpam-5251	329	69	since	since	SCONJ
ejpam-5251	329	70	t	t	PROPN
ejpam-5251	329	71	⊆	⊆	NUM
ejpam-5251	329	72	s	s	NOUN
ejpam-5251	329	73	,	,	PUNCT
ejpam-5251	329	74	t	t	NOUN
ejpam-5251	329	75	=	=	SYM
ejpam-5251	329	76	∪v∈v	∪v∈v	X
ejpam-5251	329	77	(	(	PUNCT
ejpam-5251	329	78	g)tv	g)tv	PROPN
ejpam-5251	329	79	,	,	PUNCT
ejpam-5251	329	80	where	where	SCONJ
ejpam-5251	329	81	tv	tv	NOUN
ejpam-5251	329	82	⊆	⊆	NUM
ejpam-5251	329	83	sv	sv	NOUN
ejpam-5251	329	84	is	be	AUX
ejpam-5251	329	85	a	a	DET
ejpam-5251	329	86	2	2	NUM
ejpam-5251	329	87	-	-	PUNCT
ejpam-5251	329	88	path	path	NOUN
ejpam-5251	329	89	closure	closure	NOUN
ejpam-5251	329	90	absorbing	absorb	VERB
ejpam-5251	329	91	pointwise	pointwise	PROPN
ejpam-5251	329	92	non	non	ADJ
ejpam-5251	329	93	-	-	ADJ
ejpam-5251	329	94	dominating	dominating	ADJ
ejpam-5251	329	95	set	set	NOUN
ejpam-5251	329	96	in	in	ADP
ejpam-5251	329	97	hv	hv	PROPN
ejpam-5251	329	98	for	for	ADP
ejpam-5251	329	99	each	each	DET
ejpam-5251	329	100	v	v	NUM
ejpam-5251	329	101	∈	∈	PROPN
ejpam-5251	329	102	v	v	NOUN
ejpam-5251	329	103	(	(	PUNCT
ejpam-5251	329	104	g	g	NOUN
ejpam-5251	329	105	)	)	PUNCT
ejpam-5251	329	106	.	.	PUNCT
ejpam-5251	330	1	by	by	ADP
ejpam-5251	330	2	the	the	DET
ejpam-5251	330	3	minimality	minimality	NOUN
ejpam-5251	330	4	of	of	ADP
ejpam-5251	330	5	sv	sv	PROPN
ejpam-5251	330	6	,	,	PUNCT
ejpam-5251	330	7	tv	tv	NOUN
ejpam-5251	330	8	=	=	PUNCT
ejpam-5251	330	9	sv	sv	PROPN
ejpam-5251	330	10	for	for	ADP
ejpam-5251	330	11	each	each	DET
ejpam-5251	330	12	v	v	NUM
ejpam-5251	330	13	∈	∈	PROPN
ejpam-5251	330	14	v	v	NOUN
ejpam-5251	330	15	(	(	PUNCT
ejpam-5251	330	16	g	g	NOUN
ejpam-5251	330	17	)	)	PUNCT
ejpam-5251	330	18	.	.	PUNCT
ejpam-5251	331	1	therefore	therefore	ADV
ejpam-5251	331	2	,	,	PUNCT
ejpam-5251	331	3	s	s	PART
ejpam-5251	331	4	=	=	X
ejpam-5251	331	5	t	t	PROPN
ejpam-5251	331	6	and	and	CCONJ
ejpam-5251	331	7	s	s	VERB
ejpam-5251	331	8	is	be	AUX
ejpam-5251	331	9	a	a	DET
ejpam-5251	331	10	minimal	minimal	ADJ
ejpam-5251	331	11	geodetic	geodetic	ADJ
ejpam-5251	331	12	hop	hop	NOUN
ejpam-5251	331	13	dominating	dominating	NOUN
ejpam-5251	331	14	set	set	VERB
ejpam-5251	331	15	in	in	ADP
ejpam-5251	331	16	g	g	PROPN
ejpam-5251	331	17	◦	◦	NOUN
ejpam-5251	331	18	h.	h.	PROPN
ejpam-5251	331	19	thus	thus	ADV
ejpam-5251	331	20	,	,	PUNCT
ejpam-5251	331	21	γ+hg(g	γ+hg(g	PROPN
ejpam-5251	331	22	◦	◦	NOUN
ejpam-5251	331	23	h	h	NOUN
ejpam-5251	331	24	)	)	PUNCT
ejpam-5251	331	25	≥	≥	NOUN
ejpam-5251	331	26	|s|	|s|	NOUN
ejpam-5251	331	27	=	=	SYM
ejpam-5251	331	28	n	n	CCONJ
ejpam-5251	331	29	·	·	PUNCT
ejpam-5251	331	30	ρ+2pnd(h	ρ+2pnd(h	NUM
ejpam-5251	331	31	)	)	PUNCT
ejpam-5251	331	32	.	.	PUNCT
ejpam-5251	332	1	further	far	ADV
ejpam-5251	332	2	,	,	PUNCT
ejpam-5251	332	3	since	since	SCONJ
ejpam-5251	332	4	γ+hg(p2	γ+hg(p2	PROPN
ejpam-5251	332	5	◦	◦	NOUN
ejpam-5251	332	6	p2	p2	NOUN
ejpam-5251	332	7	)	)	PUNCT
ejpam-5251	332	8	=	=	SYM
ejpam-5251	332	9	4	4	NUM
ejpam-5251	332	10	=	=	SYM
ejpam-5251	332	11	2ρ+2pnd(p2	2ρ+2pnd(p2	NUM
ejpam-5251	332	12	)	)	PUNCT
ejpam-5251	332	13	,	,	PUNCT
ejpam-5251	332	14	the	the	DET
ejpam-5251	332	15	given	give	VERB
ejpam-5251	332	16	bound	bind	VERB
ejpam-5251	332	17	is	be	AUX
ejpam-5251	332	18	sharp	sharp	ADJ
ejpam-5251	332	19	.	.	PUNCT
ejpam-5251	333	1	proposition	proposition	NOUN
ejpam-5251	333	2	8	8	NUM
ejpam-5251	333	3	.	.	PUNCT
ejpam-5251	334	1	let	let	VERB
ejpam-5251	334	2	g	g	NOUN
ejpam-5251	334	3	and	and	CCONJ
ejpam-5251	334	4	h	h	NOUN
ejpam-5251	334	5	be	be	VERB
ejpam-5251	334	6	any	any	DET
ejpam-5251	334	7	two	two	NUM
ejpam-5251	334	8	graphs	graph	NOUN
ejpam-5251	334	9	,	,	PUNCT
ejpam-5251	334	10	where	where	SCONJ
ejpam-5251	334	11	g	g	PROPN
ejpam-5251	334	12	is	be	AUX
ejpam-5251	334	13	connected	connect	VERB
ejpam-5251	334	14	and	and	CCONJ
ejpam-5251	334	15	nontrivial	nontrivial	ADJ
ejpam-5251	334	16	.	.	PUNCT
ejpam-5251	335	1	if	if	SCONJ
ejpam-5251	335	2	s	s	VERB
ejpam-5251	335	3	⊆	⊆	NUM
ejpam-5251	335	4	v	v	NOUN
ejpam-5251	335	5	(	(	PUNCT
ejpam-5251	335	6	g	g	PROPN
ejpam-5251	335	7	◦	◦	NOUN
ejpam-5251	335	8	h	h	NOUN
ejpam-5251	335	9	)	)	PUNCT
ejpam-5251	335	10	is	be	AUX
ejpam-5251	335	11	a	a	DET
ejpam-5251	335	12	minimal	minimal	ADJ
ejpam-5251	335	13	geodetic	geodetic	ADJ
ejpam-5251	335	14	hop	hop	NOUN
ejpam-5251	335	15	dominating	dominating	NOUN
ejpam-5251	335	16	set	set	VERB
ejpam-5251	335	17	in	in	ADP
ejpam-5251	335	18	g	g	PROPN
ejpam-5251	335	19	◦	◦	NOUN
ejpam-5251	335	20	h	h	NOUN
ejpam-5251	335	21	,	,	PUNCT
ejpam-5251	335	22	then	then	ADV
ejpam-5251	335	23	s	s	VERB
ejpam-5251	335	24	=	=	PUNCT
ejpam-5251	335	25	a	a	DET
ejpam-5251	335	26	∪	∪	X
ejpam-5251	335	27	(	(	PUNCT
ejpam-5251	335	28	∪v∈v	∪v∈v	X
ejpam-5251	335	29	(	(	PUNCT
ejpam-5251	335	30	g)sv	g)sv	PROPN
ejpam-5251	335	31	)	)	PUNCT
ejpam-5251	335	32	,	,	PUNCT
ejpam-5251	335	33	where	where	SCONJ
ejpam-5251	335	34	a	a	DET
ejpam-5251	335	35	⊆	⊆	NUM
ejpam-5251	335	36	v	v	NOUN
ejpam-5251	335	37	(	(	PUNCT
ejpam-5251	335	38	g	g	NOUN
ejpam-5251	335	39	)	)	PUNCT
ejpam-5251	335	40	and	and	CCONJ
ejpam-5251	335	41	sv	sv	X
ejpam-5251	335	42	⊆	⊆	NUM
ejpam-5251	335	43	v	v	X
ejpam-5251	335	44	(	(	PUNCT
ejpam-5251	335	45	hv	hv	PROPN
ejpam-5251	335	46	)	)	PUNCT
ejpam-5251	335	47	for	for	ADP
ejpam-5251	335	48	each	each	DET
ejpam-5251	335	49	v	v	NUM
ejpam-5251	335	50	∈	∈	PROPN
ejpam-5251	335	51	v	v	NOUN
ejpam-5251	335	52	(	(	PUNCT
ejpam-5251	335	53	g	g	NOUN
ejpam-5251	335	54	)	)	PUNCT
ejpam-5251	335	55	,	,	PUNCT
ejpam-5251	335	56	and	and	CCONJ
ejpam-5251	335	57	satisfies	satisfy	VERB
ejpam-5251	335	58	the	the	DET
ejpam-5251	335	59	following	follow	VERB
ejpam-5251	335	60	conditions	condition	NOUN
ejpam-5251	335	61	:	:	PUNCT
ejpam-5251	335	62	(	(	PUNCT
ejpam-5251	335	63	i	i	NOUN
ejpam-5251	335	64	)	)	PUNCT
ejpam-5251	335	65	sv	sv	PROPN
ejpam-5251	335	66	is	be	AUX
ejpam-5251	335	67	a	a	DET
ejpam-5251	335	68	minimal	minimal	ADJ
ejpam-5251	335	69	2	2	NUM
ejpam-5251	335	70	-	-	PUNCT
ejpam-5251	335	71	path	path	NOUN
ejpam-5251	335	72	closure	closure	NOUN
ejpam-5251	335	73	absorbing	absorb	VERB
ejpam-5251	335	74	pointwise	pointwise	PROPN
ejpam-5251	335	75	non	non	ADJ
ejpam-5251	335	76	-	-	ADJ
ejpam-5251	335	77	dominating	dominating	ADJ
ejpam-5251	335	78	set	set	NOUN
ejpam-5251	335	79	in	in	ADP
ejpam-5251	335	80	hv	hv	PROPN
ejpam-5251	335	81	for	for	ADP
ejpam-5251	335	82	each	each	PRON
ejpam-5251	335	83	v	v	NUM
ejpam-5251	335	84	∈	∈	PROPN
ejpam-5251	335	85	v	v	NOUN
ejpam-5251	335	86	(	(	PUNCT
ejpam-5251	335	87	g	g	NOUN
ejpam-5251	335	88	)	)	PUNCT
ejpam-5251	335	89	\ng(a	\ng(a	PROPN
ejpam-5251	335	90	)	)	PUNCT
ejpam-5251	335	91	;	;	PUNCT
ejpam-5251	335	92	(	(	PUNCT
ejpam-5251	335	93	ii	ii	NOUN
ejpam-5251	335	94	)	)	PUNCT
ejpam-5251	335	95	sv	sv	PROPN
ejpam-5251	335	96	is	be	AUX
ejpam-5251	335	97	a	a	DET
ejpam-5251	335	98	minimal	minimal	ADJ
ejpam-5251	335	99	2	2	NUM
ejpam-5251	335	100	-	-	PUNCT
ejpam-5251	335	101	path	path	NOUN
ejpam-5251	335	102	closure	closure	NOUN
ejpam-5251	335	103	absorbing	absorb	VERB
ejpam-5251	335	104	set	set	NOUN
ejpam-5251	335	105	in	in	ADP
ejpam-5251	335	106	hv	hv	PROPN
ejpam-5251	335	107	for	for	ADP
ejpam-5251	335	108	all	all	DET
ejpam-5251	335	109	v	v	ADP
ejpam-5251	335	110	∈	∈	NUM
ejpam-5251	335	111	v	v	NOUN
ejpam-5251	335	112	(	(	PUNCT
ejpam-5251	335	113	g	g	NOUN
ejpam-5251	335	114	)	)	PUNCT
ejpam-5251	335	115	∩ng(a	∩ng(a	NOUN
ejpam-5251	335	116	)	)	PUNCT
ejpam-5251	335	117	.	.	PUNCT
ejpam-5251	336	1	proof	proof	NOUN
ejpam-5251	336	2	.	.	PUNCT
ejpam-5251	337	1	in	in	ADP
ejpam-5251	337	2	view	view	NOUN
ejpam-5251	337	3	of	of	ADP
ejpam-5251	337	4	corollary	corollary	ADJ
ejpam-5251	337	5	5	5	NUM
ejpam-5251	337	6	,	,	PUNCT
ejpam-5251	337	7	we	we	PRON
ejpam-5251	337	8	are	be	AUX
ejpam-5251	337	9	left	leave	VERB
ejpam-5251	337	10	to	to	PART
ejpam-5251	337	11	work	work	VERB
ejpam-5251	337	12	only	only	ADV
ejpam-5251	337	13	on	on	ADP
ejpam-5251	337	14	the	the	DET
ejpam-5251	337	15	minimality	minimality	NOUN
ejpam-5251	337	16	part	part	NOUN
ejpam-5251	337	17	.	.	PUNCT
ejpam-5251	338	1	let	let	VERB
ejpam-5251	338	2	s	s	PRON
ejpam-5251	338	3	be	be	AUX
ejpam-5251	338	4	a	a	DET
ejpam-5251	338	5	minimal	minimal	ADJ
ejpam-5251	338	6	geodetic	geodetic	ADJ
ejpam-5251	338	7	hop	hop	NOUN
ejpam-5251	338	8	dominating	dominating	NOUN
ejpam-5251	338	9	set	set	VERB
ejpam-5251	338	10	in	in	ADP
ejpam-5251	338	11	g	g	PROPN
ejpam-5251	338	12	◦	◦	PROPN
ejpam-5251	338	13	h.	h.	PROPN
ejpam-5251	338	14	let	let	VERB
ejpam-5251	338	15	v	v	NUM
ejpam-5251	338	16	∈	∈	PROPN
ejpam-5251	338	17	v	v	NOUN
ejpam-5251	338	18	(	(	PUNCT
ejpam-5251	338	19	g	g	NOUN
ejpam-5251	338	20	)	)	PUNCT
ejpam-5251	338	21	\	\	NOUN
ejpam-5251	338	22	ng(a	ng(a	NOUN
ejpam-5251	338	23	)	)	PUNCT
ejpam-5251	338	24	.	.	PUNCT
ejpam-5251	339	1	let	let	VERB
ejpam-5251	339	2	d	d	NOUN
ejpam-5251	339	3	⊆	⊆	NUM
ejpam-5251	339	4	v	v	ADP
ejpam-5251	339	5	(	(	PUNCT
ejpam-5251	339	6	hv	hv	NOUN
ejpam-5251	339	7	)	)	PUNCT
ejpam-5251	339	8	be	be	VERB
ejpam-5251	339	9	a	a	DET
ejpam-5251	339	10	2	2	NUM
ejpam-5251	339	11	-	-	PUNCT
ejpam-5251	339	12	path	path	NOUN
ejpam-5251	339	13	closure	closure	NOUN
ejpam-5251	339	14	absorbing	absorb	VERB
ejpam-5251	339	15	pointwise	pointwise	PROPN
ejpam-5251	339	16	non	non	ADJ
ejpam-5251	339	17	-	-	ADJ
ejpam-5251	339	18	dominating	dominating	ADJ
ejpam-5251	339	19	set	set	NOUN
ejpam-5251	339	20	in	in	ADP
ejpam-5251	339	21	hv	hv	PROPN
ejpam-5251	339	22	with	with	ADP
ejpam-5251	339	23	d	d	PROPN
ejpam-5251	339	24	⊆	⊆	NUM
ejpam-5251	339	25	sv	sv	NOUN
ejpam-5251	339	26	.	.	PUNCT
ejpam-5251	340	1	then	then	ADV
ejpam-5251	340	2	t	t	PROPN
ejpam-5251	340	3	=	=	PUNCT
ejpam-5251	340	4	a∪	a∪	PROPN
ejpam-5251	340	5	(	(	PUNCT
ejpam-5251	340	6	∪u∈v	∪u∈v	PROPN
ejpam-5251	340	7	(	(	PUNCT
ejpam-5251	340	8	g)\{v}su	g)\{v}su	PROPN
ejpam-5251	340	9	)	)	PUNCT
ejpam-5251	340	10	∪d	∪d	NUM
ejpam-5251	340	11	is	be	AUX
ejpam-5251	340	12	a	a	DET
ejpam-5251	340	13	geodetic	geodetic	ADJ
ejpam-5251	340	14	hop	hop	NOUN
ejpam-5251	340	15	dominating	dominating	NOUN
ejpam-5251	340	16	set	set	NOUN
ejpam-5251	340	17	of	of	ADP
ejpam-5251	340	18	g	g	PROPN
ejpam-5251	340	19	◦	◦	NOUN
ejpam-5251	340	20	h.	h.	NOUN
ejpam-5251	340	21	since	since	SCONJ
ejpam-5251	340	22	t	t	PROPN
ejpam-5251	340	23	⊆	⊆	NUM
ejpam-5251	340	24	s	s	NOUN
ejpam-5251	340	25	,	,	PUNCT
ejpam-5251	340	26	the	the	DET
ejpam-5251	340	27	minimality	minimality	NOUN
ejpam-5251	340	28	of	of	ADP
ejpam-5251	340	29	s	s	PRON
ejpam-5251	340	30	implies	imply	VERB
ejpam-5251	340	31	that	that	SCONJ
ejpam-5251	340	32	t	t	PROPN
ejpam-5251	340	33	=	=	PUNCT
ejpam-5251	340	34	s.	s.	PROPN
ejpam-5251	340	35	necessarily	necessarily	ADV
ejpam-5251	340	36	,	,	PUNCT
ejpam-5251	340	37	sv	sv	PROPN
ejpam-5251	340	38	=	=	SYM
ejpam-5251	340	39	d	d	PROPN
ejpam-5251	340	40	,	,	PUNCT
ejpam-5251	340	41	showing	show	VERB
ejpam-5251	340	42	that	that	SCONJ
ejpam-5251	340	43	sv	sv	PROPN
ejpam-5251	340	44	is	be	AUX
ejpam-5251	340	45	a	a	DET
ejpam-5251	340	46	minimal	minimal	ADJ
ejpam-5251	340	47	2	2	NUM
ejpam-5251	340	48	-	-	PUNCT
ejpam-5251	340	49	path	path	NOUN
ejpam-5251	340	50	closure	closure	NOUN
ejpam-5251	340	51	absorbing	absorb	VERB
ejpam-5251	340	52	pointwise	pointwise	PROPN
ejpam-5251	340	53	non	non	ADJ
ejpam-5251	340	54	-	-	ADJ
ejpam-5251	340	55	dominating	dominating	ADJ
ejpam-5251	340	56	set	set	NOUN
ejpam-5251	340	57	in	in	ADP
ejpam-5251	340	58	hv	hv	PROPN
ejpam-5251	340	59	,	,	PUNCT
ejpam-5251	340	60	and	and	CCONJ
ejpam-5251	340	61	(	(	PUNCT
ejpam-5251	340	62	i	i	NOUN
ejpam-5251	340	63	)	)	PUNCT
ejpam-5251	340	64	holds	hold	VERB
ejpam-5251	340	65	.	.	PUNCT
ejpam-5251	341	1	similarly	similarly	ADV
ejpam-5251	341	2	,	,	PUNCT
ejpam-5251	341	3	(	(	PUNCT
ejpam-5251	341	4	ii	ii	NOUN
ejpam-5251	341	5	)	)	PUNCT
ejpam-5251	341	6	holds	hold	VERB
ejpam-5251	341	7	.	.	PUNCT
ejpam-5251	342	1	corollary	corollary	ADJ
ejpam-5251	342	2	6	6	NUM
ejpam-5251	342	3	.	.	PUNCT
ejpam-5251	343	1	let	let	VERB
ejpam-5251	343	2	g	g	NOUN
ejpam-5251	343	3	and	and	CCONJ
ejpam-5251	343	4	h	h	NOUN
ejpam-5251	343	5	be	be	VERB
ejpam-5251	343	6	two	two	NUM
ejpam-5251	343	7	graphs	graph	NOUN
ejpam-5251	343	8	,	,	PUNCT
ejpam-5251	343	9	where	where	SCONJ
ejpam-5251	343	10	g	g	PROPN
ejpam-5251	343	11	is	be	AUX
ejpam-5251	343	12	connected	connect	VERB
ejpam-5251	343	13	of	of	ADP
ejpam-5251	343	14	order	order	NOUN
ejpam-5251	343	15	n	n	PRON
ejpam-5251	343	16	≥	≥	NOUN
ejpam-5251	343	17	2	2	NUM
ejpam-5251	343	18	and	and	CCONJ
ejpam-5251	343	19	ρ+2pnd(h	ρ+2pnd(h	NUM
ejpam-5251	343	20	)	)	PUNCT
ejpam-5251	344	1	=	=	PUNCT
ejpam-5251	344	2	ρ+2	ρ+2	NUM
ejpam-5251	344	3	(	(	PUNCT
ejpam-5251	344	4	h	h	NOUN
ejpam-5251	344	5	)	)	PUNCT
ejpam-5251	344	6	.	.	PUNCT
ejpam-5251	345	1	then	then	ADV
ejpam-5251	345	2	γ+hg(g	γ+hg(g	PROPN
ejpam-5251	346	1	◦	◦	NOUN
ejpam-5251	346	2	h	h	NOUN
ejpam-5251	346	3	)	)	PUNCT
ejpam-5251	346	4	=	=	SYM
ejpam-5251	346	5	n	n	PART
ejpam-5251	346	6	·	·	PUNCT
ejpam-5251	346	7	ρ+2pnd(h	ρ+2pnd(h	NUM
ejpam-5251	346	8	)	)	PUNCT
ejpam-5251	346	9	.	.	PUNCT
ejpam-5251	347	1	in	in	ADP
ejpam-5251	347	2	particular	particular	ADJ
ejpam-5251	347	3	,	,	PUNCT
ejpam-5251	347	4	for	for	ADP
ejpam-5251	347	5	p	p	PRON
ejpam-5251	347	6	≥	≥	NUM
ejpam-5251	347	7	1	1	NUM
ejpam-5251	347	8	,	,	PUNCT
ejpam-5251	347	9	γ+hg(g	γ+hg(g	PROPN
ejpam-5251	347	10	◦	◦	NOUN
ejpam-5251	347	11	kp	kp	PROPN
ejpam-5251	347	12	)	)	PUNCT
ejpam-5251	347	13	=	=	SYM
ejpam-5251	347	14	np	np	PROPN
ejpam-5251	347	15	.	.	PROPN
ejpam-5251	347	16	d.	d.	PROPN
ejpam-5251	347	17	catian	catian	PROPN
ejpam-5251	347	18	,	,	PUNCT
ejpam-5251	347	19	i.	i.	PROPN
ejpam-5251	347	20	s.	s.	PROPN
ejpam-5251	347	21	aniversario	aniversario	PROPN
ejpam-5251	347	22	,	,	PUNCT
ejpam-5251	347	23	f.	f.	PROPN
ejpam-5251	347	24	p.	p.	PROPN
ejpam-5251	347	25	jamil	jamil	PROPN
ejpam-5251	347	26	/	/	SYM
ejpam-5251	347	27	eur	eur	PROPN
ejpam-5251	347	28	.	.	PUNCT
ejpam-5251	348	1	j.	j.	PROPN
ejpam-5251	348	2	pure	pure	PROPN
ejpam-5251	348	3	appl	appl	PROPN
ejpam-5251	348	4	.	.	PROPN
ejpam-5251	348	5	math	math	PROPN
ejpam-5251	348	6	,	,	PUNCT
ejpam-5251	348	7	17	17	NUM
ejpam-5251	348	8	(	(	PUNCT
ejpam-5251	348	9	3	3	NUM
ejpam-5251	348	10	)	)	PUNCT
ejpam-5251	348	11	(	(	PUNCT
ejpam-5251	348	12	2024	2024	NUM
ejpam-5251	348	13	)	)	PUNCT
ejpam-5251	348	14	,	,	PUNCT
ejpam-5251	348	15	1737	1737	NUM
ejpam-5251	348	16	-	-	SYM
ejpam-5251	348	17	1750	1750	NUM
ejpam-5251	348	18	1747	1747	NUM
ejpam-5251	348	19	proof	proof	NOUN
ejpam-5251	348	20	.	.	PUNCT
ejpam-5251	349	1	let	let	VERB
ejpam-5251	349	2	s	s	PRON
ejpam-5251	349	3	be	be	AUX
ejpam-5251	349	4	a	a	DET
ejpam-5251	349	5	γ+hg	γ+hg	NOUN
ejpam-5251	349	6	-	-	PUNCT
ejpam-5251	349	7	set	set	NOUN
ejpam-5251	349	8	of	of	ADP
ejpam-5251	349	9	g	g	PROPN
ejpam-5251	349	10	◦	◦	NOUN
ejpam-5251	349	11	h.	h.	NOUN
ejpam-5251	349	12	by	by	ADP
ejpam-5251	349	13	proposition	proposition	NOUN
ejpam-5251	349	14	8	8	NUM
ejpam-5251	349	15	,	,	PUNCT
ejpam-5251	349	16	s	s	PART
ejpam-5251	349	17	=	=	PUNCT
ejpam-5251	349	18	a∪	a∪	PROPN
ejpam-5251	349	19	(	(	PUNCT
ejpam-5251	349	20	∪v∈v	∪v∈v	X
ejpam-5251	349	21	(	(	PUNCT
ejpam-5251	349	22	g)sv	g)sv	PROPN
ejpam-5251	349	23	)	)	PUNCT
ejpam-5251	349	24	,	,	PUNCT
ejpam-5251	349	25	where	where	SCONJ
ejpam-5251	349	26	a	a	DET
ejpam-5251	349	27	⊆	⊆	NUM
ejpam-5251	349	28	v	v	NOUN
ejpam-5251	349	29	(	(	PUNCT
ejpam-5251	349	30	g	g	NOUN
ejpam-5251	349	31	)	)	PUNCT
ejpam-5251	349	32	and	and	CCONJ
ejpam-5251	349	33	sv	sv	X
ejpam-5251	349	34	⊆	⊆	NUM
ejpam-5251	349	35	v	v	X
ejpam-5251	349	36	(	(	PUNCT
ejpam-5251	349	37	hv	hv	PROPN
ejpam-5251	349	38	)	)	PUNCT
ejpam-5251	349	39	for	for	ADP
ejpam-5251	349	40	each	each	DET
ejpam-5251	349	41	v	v	NUM
ejpam-5251	349	42	∈	∈	PROPN
ejpam-5251	349	43	v	v	NOUN
ejpam-5251	349	44	(	(	PUNCT
ejpam-5251	349	45	g)such	g)such	NOUN
ejpam-5251	349	46	that	that	PRON
ejpam-5251	349	47	sv	sv	PROPN
ejpam-5251	349	48	is	be	AUX
ejpam-5251	349	49	a	a	DET
ejpam-5251	349	50	minimal	minimal	ADJ
ejpam-5251	349	51	2	2	NUM
ejpam-5251	349	52	-	-	PUNCT
ejpam-5251	349	53	path	path	NOUN
ejpam-5251	349	54	closure	closure	NOUN
ejpam-5251	349	55	absorbing	absorb	VERB
ejpam-5251	349	56	pointwise	pointwise	PROPN
ejpam-5251	349	57	non	non	ADJ
ejpam-5251	349	58	-	-	ADJ
ejpam-5251	349	59	dominating	dominating	ADJ
ejpam-5251	349	60	set	set	NOUN
ejpam-5251	349	61	in	in	ADP
ejpam-5251	349	62	hv	hv	PROPN
ejpam-5251	349	63	for	for	ADP
ejpam-5251	349	64	each	each	PRON
ejpam-5251	349	65	v	v	NUM
ejpam-5251	349	66	∈	∈	PROPN
ejpam-5251	349	67	v	v	NOUN
ejpam-5251	349	68	(	(	PUNCT
ejpam-5251	349	69	g	g	NOUN
ejpam-5251	349	70	)	)	PUNCT
ejpam-5251	349	71	\	\	NOUN
ejpam-5251	349	72	ng(a	ng(a	NOUN
ejpam-5251	349	73	)	)	PUNCT
ejpam-5251	349	74	and	and	CCONJ
ejpam-5251	349	75	sv	sv	PROPN
ejpam-5251	349	76	is	be	AUX
ejpam-5251	349	77	a	a	DET
ejpam-5251	349	78	minimal	minimal	ADJ
ejpam-5251	349	79	2	2	NUM
ejpam-5251	349	80	-	-	PUNCT
ejpam-5251	349	81	path	path	NOUN
ejpam-5251	349	82	closure	closure	NOUN
ejpam-5251	349	83	absorbing	absorb	VERB
ejpam-5251	349	84	set	set	NOUN
ejpam-5251	349	85	in	in	ADP
ejpam-5251	349	86	hv	hv	PROPN
ejpam-5251	349	87	for	for	ADP
ejpam-5251	349	88	all	all	DET
ejpam-5251	349	89	v	v	ADP
ejpam-5251	349	90	∈	∈	NUM
ejpam-5251	349	91	v	v	NOUN
ejpam-5251	349	92	(	(	PUNCT
ejpam-5251	349	93	g	g	NOUN
ejpam-5251	349	94	)	)	PUNCT
ejpam-5251	349	95	∩	∩	NOUN
ejpam-5251	349	96	ng(a	ng(a	NOUN
ejpam-5251	349	97	)	)	PUNCT
ejpam-5251	349	98	.	.	PUNCT
ejpam-5251	350	1	since	since	SCONJ
ejpam-5251	350	2	s	s	PROPN
ejpam-5251	350	3	is	be	AUX
ejpam-5251	350	4	a	a	DET
ejpam-5251	350	5	γ+hg	γ+hg	NOUN
ejpam-5251	350	6	-	-	PUNCT
ejpam-5251	350	7	set	set	NOUN
ejpam-5251	350	8	,	,	PUNCT
ejpam-5251	350	9	|sv|	|sv|	PROPN
ejpam-5251	350	10	=	=	SYM
ejpam-5251	350	11	ρ+2pnd(h	ρ+2pnd(h	PROPN
ejpam-5251	350	12	)	)	PUNCT
ejpam-5251	350	13	for	for	ADP
ejpam-5251	350	14	all	all	DET
ejpam-5251	350	15	v	v	ADP
ejpam-5251	350	16	∈	∈	NOUN
ejpam-5251	350	17	v	v	NOUN
ejpam-5251	350	18	(	(	PUNCT
ejpam-5251	350	19	g	g	NOUN
ejpam-5251	350	20	)	)	PUNCT
ejpam-5251	350	21	.	.	PUNCT
ejpam-5251	351	1	consequently	consequently	ADV
ejpam-5251	351	2	,	,	PUNCT
ejpam-5251	351	3	the	the	DET
ejpam-5251	351	4	minimality	minimality	NOUN
ejpam-5251	351	5	of	of	ADP
ejpam-5251	351	6	s	s	PRON
ejpam-5251	351	7	implies	imply	VERB
ejpam-5251	351	8	that	that	SCONJ
ejpam-5251	351	9	a	a	DET
ejpam-5251	351	10	=	=	X
ejpam-5251	351	11	∅.	∅.	NOUN
ejpam-5251	351	12	thus	thus	ADV
ejpam-5251	351	13	,	,	PUNCT
ejpam-5251	351	14	γ+hg(g	γ+hg(g	PROPN
ejpam-5251	351	15	◦	◦	NOUN
ejpam-5251	351	16	h	h	NOUN
ejpam-5251	351	17	)	)	PUNCT
ejpam-5251	351	18	=	=	SYM
ejpam-5251	352	1	|s|	|s|	PROPN
ejpam-5251	352	2	=	=	PUNCT
ejpam-5251	352	3	|v	|v	PROPN
ejpam-5251	352	4	(	(	PUNCT
ejpam-5251	352	5	g)|	g)|	NOUN
ejpam-5251	352	6	·	·	PUNCT
ejpam-5251	352	7	ρ+2pnd(h	ρ+2pnd(h	NUM
ejpam-5251	352	8	)	)	PUNCT
ejpam-5251	352	9	.	.	PUNCT
ejpam-5251	353	1	6	6	X
ejpam-5251	353	2	.	.	X
ejpam-5251	353	3	in	in	ADP
ejpam-5251	353	4	the	the	DET
ejpam-5251	353	5	lexicographic	lexicographic	ADJ
ejpam-5251	353	6	product	product	NOUN
ejpam-5251	353	7	of	of	ADP
ejpam-5251	353	8	graphs	graph	NOUN
ejpam-5251	353	9	theorem	theorem	VERB
ejpam-5251	353	10	6	6	NUM
ejpam-5251	353	11	.	.	PUNCT
ejpam-5251	354	1	[	[	X
ejpam-5251	354	2	27	27	NUM
ejpam-5251	354	3	]	]	PUNCT
ejpam-5251	354	4	let	let	VERB
ejpam-5251	354	5	g	g	PROPN
ejpam-5251	354	6	and	and	CCONJ
ejpam-5251	354	7	h	h	NOUN
ejpam-5251	354	8	be	be	AUX
ejpam-5251	354	9	connected	connect	VERB
ejpam-5251	354	10	nontrivial	nontrivial	ADJ
ejpam-5251	354	11	graphs	graph	NOUN
ejpam-5251	354	12	.	.	PUNCT
ejpam-5251	355	1	a	a	DET
ejpam-5251	355	2	subset	subset	NOUN
ejpam-5251	355	3	c	c	NOUN
ejpam-5251	355	4	=	=	SYM
ejpam-5251	355	5	∪x∈s	∪x∈s	PROPN
ejpam-5251	355	6	(	(	PUNCT
ejpam-5251	355	7	{	{	PUNCT
ejpam-5251	355	8	x	x	NOUN
ejpam-5251	355	9	}	}	PUNCT
ejpam-5251	355	10	×	×	PROPN
ejpam-5251	355	11	sx	sx	PROPN
ejpam-5251	355	12	)	)	PUNCT
ejpam-5251	355	13	⊆	⊆	NUM
ejpam-5251	355	14	v	v	NOUN
ejpam-5251	355	15	(	(	PUNCT
ejpam-5251	355	16	g[h	g[h	PROPN
ejpam-5251	355	17	]	]	PUNCT
ejpam-5251	355	18	)	)	PUNCT
ejpam-5251	355	19	,	,	PUNCT
ejpam-5251	355	20	where	where	SCONJ
ejpam-5251	355	21	s	s	VERB
ejpam-5251	355	22	⊆	⊆	NUM
ejpam-5251	355	23	v	v	NOUN
ejpam-5251	355	24	(	(	PUNCT
ejpam-5251	355	25	g	g	NOUN
ejpam-5251	355	26	)	)	PUNCT
ejpam-5251	355	27	and	and	CCONJ
ejpam-5251	355	28	sx	sx	VERB
ejpam-5251	355	29	⊆	⊆	NUM
ejpam-5251	355	30	v	v	NOUN
ejpam-5251	355	31	(	(	PUNCT
ejpam-5251	355	32	h	h	NOUN
ejpam-5251	355	33	)	)	PUNCT
ejpam-5251	355	34	,	,	PUNCT
ejpam-5251	355	35	is	be	AUX
ejpam-5251	355	36	a	a	DET
ejpam-5251	355	37	geodetic	geodetic	ADJ
ejpam-5251	355	38	hop	hop	NOUN
ejpam-5251	355	39	dominating	dominating	NOUN
ejpam-5251	355	40	set	set	VERB
ejpam-5251	355	41	in	in	ADP
ejpam-5251	355	42	g[h	g[h	PROPN
ejpam-5251	355	43	]	]	PUNCT
ejpam-5251	355	44	if	if	SCONJ
ejpam-5251	355	45	and	and	CCONJ
ejpam-5251	355	46	only	only	ADV
ejpam-5251	355	47	if	if	SCONJ
ejpam-5251	355	48	the	the	DET
ejpam-5251	355	49	following	follow	VERB
ejpam-5251	355	50	conditions	condition	NOUN
ejpam-5251	355	51	hold	hold	VERB
ejpam-5251	355	52	:	:	PUNCT
ejpam-5251	355	53	(	(	PUNCT
ejpam-5251	355	54	i	i	NOUN
ejpam-5251	355	55	)	)	PUNCT
ejpam-5251	355	56	s	s	AUX
ejpam-5251	355	57	is	be	AUX
ejpam-5251	355	58	a	a	DET
ejpam-5251	355	59	geodetic	geodetic	ADJ
ejpam-5251	355	60	hop	hop	NOUN
ejpam-5251	355	61	dominating	dominating	NOUN
ejpam-5251	355	62	set	set	NOUN
ejpam-5251	355	63	in	in	ADP
ejpam-5251	355	64	g	g	NOUN
ejpam-5251	355	65	;	;	PUNCT
ejpam-5251	355	66	(	(	PUNCT
ejpam-5251	355	67	ii	ii	NOUN
ejpam-5251	355	68	)	)	PUNCT
ejpam-5251	355	69	sx	sx	PROPN
ejpam-5251	355	70	is	be	AUX
ejpam-5251	355	71	a	a	DET
ejpam-5251	355	72	pointwise	pointwise	ADJ
ejpam-5251	355	73	non	non	ADJ
ejpam-5251	355	74	-	-	ADJ
ejpam-5251	355	75	dominating	dominating	ADJ
ejpam-5251	355	76	set	set	NOUN
ejpam-5251	355	77	in	in	ADP
ejpam-5251	355	78	h	h	NOUN
ejpam-5251	355	79	for	for	ADP
ejpam-5251	355	80	each	each	DET
ejpam-5251	355	81	x	x	SYM
ejpam-5251	355	82	∈	∈	PROPN
ejpam-5251	355	83	s	s	PART
ejpam-5251	355	84	\n2	\n2	ADJ
ejpam-5251	355	85	g(s	g(	NOUN
ejpam-5251	355	86	)	)	PUNCT
ejpam-5251	355	87	;	;	PUNCT
ejpam-5251	355	88	(	(	PUNCT
ejpam-5251	355	89	iii	iii	X
ejpam-5251	355	90	)	)	PUNCT
ejpam-5251	355	91	sx	sx	PROPN
ejpam-5251	355	92	is	be	AUX
ejpam-5251	355	93	a	a	DET
ejpam-5251	355	94	2	2	NUM
ejpam-5251	355	95	-	-	PUNCT
ejpam-5251	355	96	path	path	NOUN
ejpam-5251	355	97	closure	closure	NOUN
ejpam-5251	355	98	absorbing	absorb	VERB
ejpam-5251	355	99	set	set	VERB
ejpam-5251	355	100	in	in	ADP
ejpam-5251	355	101	h	h	NOUN
ejpam-5251	355	102	for	for	ADP
ejpam-5251	355	103	each	each	DET
ejpam-5251	355	104	x	x	SYM
ejpam-5251	355	105	∈	∈	PROPN
ejpam-5251	355	106	s	s	PART
ejpam-5251	355	107	\	\	NOUN
ejpam-5251	355	108	ig(s	ig(s	NUM
ejpam-5251	355	109	)	)	PUNCT
ejpam-5251	355	110	.	.	PUNCT
ejpam-5251	356	1	the	the	DET
ejpam-5251	356	2	following	following	NOUN
ejpam-5251	356	3	follows	follow	VERB
ejpam-5251	356	4	from	from	ADP
ejpam-5251	356	5	theorem	theorem	ADJ
ejpam-5251	356	6	6	6	NUM
ejpam-5251	356	7	.	.	PUNCT
ejpam-5251	356	8	corollary	corollary	ADJ
ejpam-5251	356	9	7	7	NUM
ejpam-5251	356	10	.	.	PUNCT
ejpam-5251	357	1	let	let	VERB
ejpam-5251	357	2	g	g	NOUN
ejpam-5251	357	3	and	and	CCONJ
ejpam-5251	357	4	h	h	NOUN
ejpam-5251	357	5	be	be	AUX
ejpam-5251	357	6	connected	connect	VERB
ejpam-5251	357	7	nontrivial	nontrivial	ADJ
ejpam-5251	357	8	graphs	graph	NOUN
ejpam-5251	357	9	.	.	PUNCT
ejpam-5251	358	1	let	let	VERB
ejpam-5251	358	2	c	c	NOUN
ejpam-5251	358	3	=	=	SYM
ejpam-5251	358	4	∪x∈s	∪x∈s	PROPN
ejpam-5251	358	5	(	(	PUNCT
ejpam-5251	358	6	{	{	PUNCT
ejpam-5251	358	7	x	x	NOUN
ejpam-5251	358	8	}	}	PUNCT
ejpam-5251	358	9	×	×	PROPN
ejpam-5251	358	10	sx	sx	PROPN
ejpam-5251	358	11	)	)	PUNCT
ejpam-5251	358	12	⊆	⊆	NUM
ejpam-5251	358	13	v	v	NOUN
ejpam-5251	358	14	(	(	PUNCT
ejpam-5251	358	15	g[h	g[h	PROPN
ejpam-5251	358	16	]	]	PUNCT
ejpam-5251	358	17	)	)	PUNCT
ejpam-5251	358	18	,	,	PUNCT
ejpam-5251	358	19	where	where	SCONJ
ejpam-5251	358	20	s	s	VERB
ejpam-5251	358	21	⊆	⊆	NUM
ejpam-5251	358	22	v	v	NOUN
ejpam-5251	358	23	(	(	PUNCT
ejpam-5251	358	24	g	g	NOUN
ejpam-5251	358	25	)	)	PUNCT
ejpam-5251	358	26	and	and	CCONJ
ejpam-5251	358	27	sx	sx	VERB
ejpam-5251	358	28	⊆	⊆	NUM
ejpam-5251	358	29	v	v	NOUN
ejpam-5251	358	30	(	(	PUNCT
ejpam-5251	358	31	h	h	NOUN
ejpam-5251	358	32	)	)	PUNCT
ejpam-5251	358	33	,	,	PUNCT
ejpam-5251	358	34	such	such	ADJ
ejpam-5251	358	35	that	that	SCONJ
ejpam-5251	358	36	the	the	DET
ejpam-5251	358	37	following	follow	VERB
ejpam-5251	358	38	conditions	condition	NOUN
ejpam-5251	358	39	hold	hold	VERB
ejpam-5251	358	40	:	:	PUNCT
ejpam-5251	358	41	(	(	PUNCT
ejpam-5251	358	42	i	i	NOUN
ejpam-5251	358	43	)	)	PUNCT
ejpam-5251	358	44	s	s	VERB
ejpam-5251	358	45	is	be	AUX
ejpam-5251	358	46	a	a	DET
ejpam-5251	358	47	minimal	minimal	ADJ
ejpam-5251	358	48	geodetic	geodetic	ADJ
ejpam-5251	358	49	hop	hop	NOUN
ejpam-5251	358	50	dominating	dominating	NOUN
ejpam-5251	358	51	set	set	NOUN
ejpam-5251	358	52	in	in	ADP
ejpam-5251	358	53	g	g	NOUN
ejpam-5251	358	54	;	;	PUNCT
ejpam-5251	358	55	(	(	PUNCT
ejpam-5251	358	56	ii	ii	NOUN
ejpam-5251	358	57	)	)	PUNCT
ejpam-5251	358	58	sx	sx	PROPN
ejpam-5251	358	59	is	be	AUX
ejpam-5251	358	60	a	a	DET
ejpam-5251	358	61	minimal	minimal	ADJ
ejpam-5251	358	62	pointwise	pointwise	ADJ
ejpam-5251	358	63	non	non	ADJ
ejpam-5251	358	64	-	-	ADJ
ejpam-5251	358	65	dominating	dominating	ADJ
ejpam-5251	358	66	set	set	NOUN
ejpam-5251	358	67	in	in	ADP
ejpam-5251	358	68	h	h	NOUN
ejpam-5251	358	69	for	for	ADP
ejpam-5251	358	70	each	each	DET
ejpam-5251	358	71	x	x	SYM
ejpam-5251	358	72	∈	∈	PROPN
ejpam-5251	358	73	s	s	PART
ejpam-5251	358	74	\n2	\n2	ADJ
ejpam-5251	358	75	g(s	g(	NOUN
ejpam-5251	358	76	)	)	PUNCT
ejpam-5251	358	77	;	;	PUNCT
ejpam-5251	358	78	(	(	PUNCT
ejpam-5251	358	79	iii	iii	X
ejpam-5251	358	80	)	)	PUNCT
ejpam-5251	358	81	sx	sx	PROPN
ejpam-5251	358	82	is	be	AUX
ejpam-5251	358	83	a	a	DET
ejpam-5251	358	84	minimal	minimal	ADJ
ejpam-5251	358	85	2	2	NUM
ejpam-5251	358	86	-	-	PUNCT
ejpam-5251	358	87	path	path	NOUN
ejpam-5251	358	88	closure	closure	NOUN
ejpam-5251	358	89	absorbing	absorb	VERB
ejpam-5251	358	90	set	set	VERB
ejpam-5251	358	91	in	in	ADP
ejpam-5251	358	92	h	h	NOUN
ejpam-5251	358	93	for	for	ADP
ejpam-5251	358	94	each	each	DET
ejpam-5251	358	95	x	x	SYM
ejpam-5251	358	96	∈	∈	PROPN
ejpam-5251	358	97	s	s	PART
ejpam-5251	358	98	\	\	NOUN
ejpam-5251	358	99	ig(s	ig(s	NUM
ejpam-5251	358	100	)	)	PUNCT
ejpam-5251	358	101	.	.	PUNCT
ejpam-5251	359	1	then	then	ADV
ejpam-5251	359	2	c	c	PROPN
ejpam-5251	359	3	is	be	AUX
ejpam-5251	359	4	minimal	minimal	ADJ
ejpam-5251	359	5	geodetic	geodetic	ADJ
ejpam-5251	359	6	hop	hop	NOUN
ejpam-5251	359	7	dominating	dominating	NOUN
ejpam-5251	359	8	set	set	VERB
ejpam-5251	359	9	in	in	ADP
ejpam-5251	359	10	g[h	g[h	PROPN
ejpam-5251	359	11	]	]	PUNCT
ejpam-5251	359	12	.	.	PUNCT
ejpam-5251	360	1	proof	proof	NOUN
ejpam-5251	360	2	.	.	PUNCT
ejpam-5251	361	1	by	by	ADP
ejpam-5251	361	2	theorem	theorem	NOUN
ejpam-5251	361	3	6	6	NUM
ejpam-5251	361	4	,	,	PUNCT
ejpam-5251	361	5	c	c	PROPN
ejpam-5251	361	6	is	be	AUX
ejpam-5251	361	7	a	a	DET
ejpam-5251	361	8	geodetic	geodetic	ADJ
ejpam-5251	361	9	hop	hop	NOUN
ejpam-5251	361	10	dominating	dominating	NOUN
ejpam-5251	361	11	set	set	VERB
ejpam-5251	361	12	in	in	ADP
ejpam-5251	361	13	g[h	g[h	PROPN
ejpam-5251	361	14	]	]	PUNCT
ejpam-5251	361	15	.	.	PUNCT
ejpam-5251	362	1	let	let	VERB
ejpam-5251	362	2	c∗	c∗	PROPN
ejpam-5251	362	3	⊆	⊆	NUM
ejpam-5251	362	4	c	c	NOUN
ejpam-5251	362	5	be	be	AUX
ejpam-5251	362	6	a	a	DET
ejpam-5251	362	7	geodetic	geodetic	ADJ
ejpam-5251	362	8	hop	hop	NOUN
ejpam-5251	362	9	dominating	dominating	NOUN
ejpam-5251	362	10	set	set	VERB
ejpam-5251	362	11	in	in	ADP
ejpam-5251	362	12	g[h	g[h	PROPN
ejpam-5251	362	13	]	]	PUNCT
ejpam-5251	362	14	.	.	PUNCT
ejpam-5251	363	1	by	by	ADP
ejpam-5251	363	2	theorem	theorem	NOUN
ejpam-5251	363	3	6	6	NUM
ejpam-5251	363	4	,	,	PUNCT
ejpam-5251	363	5	there	there	PRON
ejpam-5251	363	6	exist	exist	VERB
ejpam-5251	363	7	t	t	PROPN
ejpam-5251	363	8	⊆	⊆	NUM
ejpam-5251	363	9	v	v	NOUN
ejpam-5251	363	10	(	(	PUNCT
ejpam-5251	363	11	g	g	NOUN
ejpam-5251	363	12	)	)	PUNCT
ejpam-5251	363	13	and	and	CCONJ
ejpam-5251	363	14	tx	tx	VERB
ejpam-5251	363	15	⊆	⊆	NUM
ejpam-5251	363	16	v	v	NOUN
ejpam-5251	363	17	(	(	PUNCT
ejpam-5251	363	18	h	h	NOUN
ejpam-5251	363	19	)	)	PUNCT
ejpam-5251	363	20	for	for	ADP
ejpam-5251	363	21	each	each	DET
ejpam-5251	363	22	x	x	SYM
ejpam-5251	363	23	∈	∈	PROPN
ejpam-5251	363	24	t	t	NOUN
ejpam-5251	363	25	such	such	ADJ
ejpam-5251	363	26	that	that	DET
ejpam-5251	363	27	c∗	c∗	PROPN
ejpam-5251	363	28	=	=	PUNCT
ejpam-5251	363	29	∪x∈t	∪x∈t	NOUN
ejpam-5251	363	30	(	(	PUNCT
ejpam-5251	363	31	{	{	PUNCT
ejpam-5251	363	32	x	x	NOUN
ejpam-5251	363	33	}	}	PUNCT
ejpam-5251	363	34	×	×	PROPN
ejpam-5251	363	35	tx	tx	PROPN
ejpam-5251	363	36	)	)	PUNCT
ejpam-5251	363	37	.	.	PUNCT
ejpam-5251	364	1	moreover	moreover	ADV
ejpam-5251	364	2	,	,	PUNCT
ejpam-5251	364	3	t	t	PROPN
ejpam-5251	364	4	is	be	AUX
ejpam-5251	364	5	a	a	DET
ejpam-5251	364	6	geodetic	geodetic	ADJ
ejpam-5251	364	7	hop	hop	NOUN
ejpam-5251	364	8	dominating	dominating	NOUN
ejpam-5251	364	9	set	set	NOUN
ejpam-5251	364	10	in	in	ADP
ejpam-5251	364	11	g	g	PROPN
ejpam-5251	364	12	,	,	PUNCT
ejpam-5251	364	13	tx	tx	PROPN
ejpam-5251	364	14	is	be	AUX
ejpam-5251	364	15	a	a	DET
ejpam-5251	364	16	pointwise	pointwise	ADJ
ejpam-5251	364	17	non	non	ADJ
ejpam-5251	364	18	-	-	ADJ
ejpam-5251	364	19	dominating	dominating	ADJ
ejpam-5251	364	20	set	set	NOUN
ejpam-5251	364	21	in	in	ADP
ejpam-5251	364	22	h	h	NOUN
ejpam-5251	364	23	for	for	ADP
ejpam-5251	364	24	each	each	DET
ejpam-5251	364	25	x	x	SYM
ejpam-5251	364	26	∈	∈	PROPN
ejpam-5251	364	27	t	t	NOUN
ejpam-5251	364	28	\n2	\n2	VERB
ejpam-5251	364	29	g(t	g(t	PROPN
ejpam-5251	364	30	)	)	PUNCT
ejpam-5251	364	31	,	,	PUNCT
ejpam-5251	364	32	and	and	CCONJ
ejpam-5251	364	33	tx	tx	PROPN
ejpam-5251	364	34	is	be	AUX
ejpam-5251	364	35	a	a	DET
ejpam-5251	364	36	2	2	NUM
ejpam-5251	364	37	-	-	PUNCT
ejpam-5251	364	38	path	path	NOUN
ejpam-5251	364	39	closure	closure	NOUN
ejpam-5251	364	40	absorbing	absorb	VERB
ejpam-5251	364	41	set	set	VERB
ejpam-5251	364	42	in	in	ADP
ejpam-5251	364	43	h	h	NOUN
ejpam-5251	364	44	for	for	ADP
ejpam-5251	364	45	each	each	DET
ejpam-5251	364	46	x	x	SYM
ejpam-5251	364	47	∈	∈	PROPN
ejpam-5251	364	48	t	t	PROPN
ejpam-5251	364	49	\	\	PUNCT
ejpam-5251	364	50	ig(t	ig(t	PUNCT
ejpam-5251	364	51	)	)	PUNCT
ejpam-5251	364	52	.	.	PUNCT
ejpam-5251	365	1	since	since	SCONJ
ejpam-5251	365	2	c∗	c∗	PROPN
ejpam-5251	365	3	⊆	⊆	NUM
ejpam-5251	365	4	c	c	NOUN
ejpam-5251	365	5	,	,	PUNCT
ejpam-5251	365	6	t	t	PROPN
ejpam-5251	365	7	⊆	⊆	NUM
ejpam-5251	365	8	s	s	NOUN
ejpam-5251	365	9	and	and	CCONJ
ejpam-5251	365	10	tx	tx	VERB
ejpam-5251	365	11	⊆	⊆	NUM
ejpam-5251	365	12	sx	sx	NOUN
ejpam-5251	365	13	for	for	ADP
ejpam-5251	365	14	each	each	DET
ejpam-5251	365	15	x	x	SYM
ejpam-5251	365	16	∈	∈	PROPN
ejpam-5251	365	17	t	t	NOUN
ejpam-5251	365	18	.	.	PUNCT
ejpam-5251	366	1	the	the	DET
ejpam-5251	366	2	minimality	minimality	NOUN
ejpam-5251	366	3	of	of	ADP
ejpam-5251	366	4	s	s	PRON
ejpam-5251	366	5	implies	imply	VERB
ejpam-5251	366	6	that	that	SCONJ
ejpam-5251	366	7	t	t	PROPN
ejpam-5251	366	8	=	=	PUNCT
ejpam-5251	366	9	s.	s.	PROPN
ejpam-5251	366	10	consequently	consequently	ADV
ejpam-5251	366	11	,	,	PUNCT
ejpam-5251	366	12	the	the	DET
ejpam-5251	366	13	minimality	minimality	NOUN
ejpam-5251	366	14	of	of	ADP
ejpam-5251	366	15	sx	sx	PROPN
ejpam-5251	366	16	implies	imply	VERB
ejpam-5251	366	17	that	that	SCONJ
ejpam-5251	366	18	sx	sx	PROPN
ejpam-5251	366	19	=	=	PUNCT
ejpam-5251	366	20	tx	tx	PROPN
ejpam-5251	366	21	for	for	ADP
ejpam-5251	366	22	all	all	DET
ejpam-5251	366	23	x	x	SYM
ejpam-5251	366	24	∈	∈	PROPN
ejpam-5251	366	25	t	t	NOUN
ejpam-5251	366	26	\n2	\n2	VERB
ejpam-5251	366	27	g(t	g(t	PROPN
ejpam-5251	366	28	)	)	PUNCT
ejpam-5251	366	29	and	and	CCONJ
ejpam-5251	366	30	sx	sx	PROPN
ejpam-5251	366	31	=	=	PUNCT
ejpam-5251	366	32	tx	tx	PROPN
ejpam-5251	366	33	for	for	ADP
ejpam-5251	366	34	all	all	DET
ejpam-5251	366	35	x	x	SYM
ejpam-5251	366	36	∈	∈	PROPN
ejpam-5251	366	37	t	t	NOUN
ejpam-5251	366	38	\	\	PUNCT
ejpam-5251	366	39	ig(t	ig(t	PUNCT
ejpam-5251	366	40	)	)	PUNCT
ejpam-5251	366	41	.	.	PUNCT
ejpam-5251	367	1	hence	hence	ADV
ejpam-5251	367	2	,	,	PUNCT
ejpam-5251	367	3	c	c	NOUN
ejpam-5251	367	4	=	=	SYM
ejpam-5251	367	5	c∗	c∗	PROPN
ejpam-5251	367	6	,	,	PUNCT
ejpam-5251	367	7	showing	show	VERB
ejpam-5251	367	8	that	that	SCONJ
ejpam-5251	367	9	c	c	PROPN
ejpam-5251	367	10	is	be	AUX
ejpam-5251	367	11	a	a	DET
ejpam-5251	367	12	minimal	minimal	ADJ
ejpam-5251	367	13	geodetic	geodetic	ADJ
ejpam-5251	367	14	hop	hop	NOUN
ejpam-5251	367	15	dominating	dominating	NOUN
ejpam-5251	367	16	set	set	VERB
ejpam-5251	367	17	in	in	ADP
ejpam-5251	367	18	g[h	g[h	PROPN
ejpam-5251	367	19	]	]	PUNCT
ejpam-5251	367	20	.	.	PUNCT
ejpam-5251	368	1	corollary	corollary	ADJ
ejpam-5251	368	2	8	8	NUM
ejpam-5251	368	3	.	.	PUNCT
ejpam-5251	369	1	for	for	ADP
ejpam-5251	369	2	nontrivial	nontrivial	ADJ
ejpam-5251	369	3	connected	connect	VERB
ejpam-5251	369	4	graphs	graph	NOUN
ejpam-5251	369	5	g	g	NOUN
ejpam-5251	369	6	and	and	CCONJ
ejpam-5251	369	7	p	p	X
ejpam-5251	369	8	≥	≥	NUM
ejpam-5251	369	9	2	2	NUM
ejpam-5251	369	10	,	,	PUNCT
ejpam-5251	369	11	(	(	PUNCT
ejpam-5251	369	12	i	i	NOUN
ejpam-5251	369	13	)	)	PUNCT
ejpam-5251	369	14	γ+hg(g[kp	γ+hg(g[kp	NOUN
ejpam-5251	369	15	]	]	PUNCT
ejpam-5251	369	16	)	)	PUNCT
ejpam-5251	370	1	=	=	SYM
ejpam-5251	370	2	p	p	X
ejpam-5251	370	3	·	·	PUNCT
ejpam-5251	370	4	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	370	5	)	)	PUNCT
ejpam-5251	370	6	.	.	PUNCT
ejpam-5251	371	1	(	(	PUNCT
ejpam-5251	371	2	ii	ii	X
ejpam-5251	371	3	)	)	PUNCT
ejpam-5251	371	4	γ+hg(kp[g	γ+hg(kp[g	NOUN
ejpam-5251	371	5	]	]	X
ejpam-5251	371	6	)	)	PUNCT
ejpam-5251	372	1	=	=	SYM
ejpam-5251	372	2	p	p	X
ejpam-5251	372	3	·	·	PUNCT
ejpam-5251	372	4	ρ+2pnd(h	ρ+2pnd(h	NUM
ejpam-5251	372	5	)	)	PUNCT
ejpam-5251	372	6	.	.	PUNCT
ejpam-5251	373	1	references	reference	NOUN
ejpam-5251	373	2	1748	1748	NUM
ejpam-5251	373	3	proof	proof	NOUN
ejpam-5251	373	4	.	.	PUNCT
ejpam-5251	374	1	let	let	VERB
ejpam-5251	374	2	s	s	PRON
ejpam-5251	374	3	⊆	⊆	NUM
ejpam-5251	374	4	v	v	NOUN
ejpam-5251	374	5	(	(	PUNCT
ejpam-5251	374	6	g	g	NOUN
ejpam-5251	374	7	)	)	PUNCT
ejpam-5251	374	8	be	be	AUX
ejpam-5251	374	9	a	a	DET
ejpam-5251	374	10	γ+hg	γ+hg	NOUN
ejpam-5251	374	11	-	-	PUNCT
ejpam-5251	374	12	set	set	NOUN
ejpam-5251	374	13	of	of	ADP
ejpam-5251	374	14	g	g	NOUN
ejpam-5251	374	15	,	,	PUNCT
ejpam-5251	374	16	and	and	CCONJ
ejpam-5251	374	17	let	let	VERB
ejpam-5251	374	18	d	d	NOUN
ejpam-5251	374	19	=	=	SYM
ejpam-5251	374	20	v	v	PROPN
ejpam-5251	374	21	(	(	PUNCT
ejpam-5251	374	22	kp	kp	PROPN
ejpam-5251	374	23	)	)	PUNCT
ejpam-5251	374	24	.	.	PUNCT
ejpam-5251	375	1	then	then	ADV
ejpam-5251	375	2	c	c	X
ejpam-5251	375	3	=	=	SYM
ejpam-5251	375	4	∪x∈s	∪x∈s	PROPN
ejpam-5251	375	5	(	(	PUNCT
ejpam-5251	375	6	{	{	PUNCT
ejpam-5251	375	7	x	x	NOUN
ejpam-5251	375	8	}	}	PUNCT
ejpam-5251	375	9	×d	×d	NOUN
ejpam-5251	375	10	)	)	PUNCT
ejpam-5251	375	11	is	be	AUX
ejpam-5251	375	12	a	a	DET
ejpam-5251	375	13	minimal	minimal	ADJ
ejpam-5251	375	14	geodetic	geodetic	ADJ
ejpam-5251	375	15	hop	hop	NOUN
ejpam-5251	375	16	dominating	dominating	NOUN
ejpam-5251	375	17	set	set	VERB
ejpam-5251	375	18	in	in	ADP
ejpam-5251	375	19	g[kp	g[kp	PROPN
ejpam-5251	375	20	]	]	PUNCT
ejpam-5251	375	21	by	by	ADP
ejpam-5251	375	22	corollary	corollary	ADJ
ejpam-5251	375	23	7	7	NUM
ejpam-5251	375	24	.	.	PUNCT
ejpam-5251	376	1	thus	thus	ADV
ejpam-5251	376	2	,	,	PUNCT
ejpam-5251	376	3	γ+hg(g[kp	γ+hg(g[kp	NOUN
ejpam-5251	376	4	]	]	PUNCT
ejpam-5251	376	5	)	)	PUNCT
ejpam-5251	376	6	≥	≥	PROPN
ejpam-5251	376	7	|c|	|c|	PROPN
ejpam-5251	376	8	=	=	SYM
ejpam-5251	376	9	|s|	|s|	PROPN
ejpam-5251	376	10	·	·	PUNCT
ejpam-5251	376	11	|d|	|d|	PROPN
ejpam-5251	376	12	=	=	SYM
ejpam-5251	377	1	p	p	PROPN
ejpam-5251	377	2	·	·	PUNCT
ejpam-5251	377	3	γ+hg(g	γ+hg(g	NOUN
ejpam-5251	377	4	)	)	PUNCT
ejpam-5251	377	5	.	.	PUNCT
ejpam-5251	378	1	to	to	PART
ejpam-5251	378	2	get	get	VERB
ejpam-5251	378	3	the	the	DET
ejpam-5251	378	4	other	other	ADJ
ejpam-5251	378	5	inequality	inequality	NOUN
ejpam-5251	378	6	,	,	PUNCT
ejpam-5251	378	7	let	let	VERB
ejpam-5251	378	8	c	c	NOUN
ejpam-5251	378	9	=	=	SYM
ejpam-5251	378	10	∪x∈s	∪x∈s	PROPN
ejpam-5251	378	11	(	(	PUNCT
ejpam-5251	378	12	{	{	PUNCT
ejpam-5251	378	13	x	x	NOUN
ejpam-5251	378	14	}	}	PUNCT
ejpam-5251	378	15	×	×	PROPN
ejpam-5251	378	16	sx	sx	PROPN
ejpam-5251	378	17	)	)	PUNCT
ejpam-5251	378	18	⊆	⊆	NUM
ejpam-5251	378	19	v	v	NOUN
ejpam-5251	378	20	(	(	PUNCT
ejpam-5251	378	21	g[h	g[h	PROPN
ejpam-5251	378	22	]	]	PUNCT
ejpam-5251	378	23	)	)	PUNCT
ejpam-5251	378	24	be	be	AUX
ejpam-5251	378	25	a	a	DET
ejpam-5251	378	26	γ+hg	γ+hg	NOUN
ejpam-5251	378	27	-	-	PUNCT
ejpam-5251	378	28	set	set	NOUN
ejpam-5251	378	29	of	of	ADP
ejpam-5251	378	30	g[kp	g[kp	PROPN
ejpam-5251	378	31	]	]	PUNCT
ejpam-5251	378	32	.	.	PUNCT
ejpam-5251	379	1	by	by	ADP
ejpam-5251	379	2	theorem	theorem	NOUN
ejpam-5251	379	3	6	6	NUM
ejpam-5251	379	4	and	and	CCONJ
ejpam-5251	379	5	the	the	DET
ejpam-5251	379	6	minimality	minimality	NOUN
ejpam-5251	379	7	of	of	ADP
ejpam-5251	379	8	c	c	PROPN
ejpam-5251	379	9	,	,	PUNCT
ejpam-5251	379	10	s	s	VERB
ejpam-5251	379	11	is	be	AUX
ejpam-5251	379	12	a	a	DET
ejpam-5251	379	13	minimal	minimal	ADJ
ejpam-5251	379	14	geodetic	geodetic	ADJ
ejpam-5251	379	15	hop	hop	NOUN
ejpam-5251	379	16	dominating	dominating	NOUN
ejpam-5251	379	17	set	set	VERB
ejpam-5251	379	18	in	in	ADP
ejpam-5251	379	19	g	g	PROPN
ejpam-5251	379	20	and	and	CCONJ
ejpam-5251	379	21	sx	sx	PROPN
ejpam-5251	379	22	=	=	PUNCT
ejpam-5251	379	23	v	v	PROPN
ejpam-5251	379	24	(	(	PUNCT
ejpam-5251	379	25	kp	kp	PROPN
ejpam-5251	379	26	)	)	PUNCT
ejpam-5251	379	27	for	for	ADP
ejpam-5251	379	28	all	all	DET
ejpam-5251	379	29	x	x	SYM
ejpam-5251	379	30	∈	∈	PROPN
ejpam-5251	379	31	s	s	PART
ejpam-5251	379	32	\n2	\n2	ADJ
ejpam-5251	379	33	g(s	g(	NOUN
ejpam-5251	379	34	)	)	PUNCT
ejpam-5251	379	35	and	and	CCONJ
ejpam-5251	379	36	for	for	ADP
ejpam-5251	379	37	all	all	DET
ejpam-5251	379	38	x	x	PART
ejpam-5251	379	39	∈	∈	PROPN
ejpam-5251	379	40	s	s	PART
ejpam-5251	379	41	\	\	NOUN
ejpam-5251	379	42	ig(s	ig(s	NUM
ejpam-5251	379	43	)	)	PUNCT
ejpam-5251	379	44	.	.	PUNCT
ejpam-5251	380	1	thus	thus	ADV
ejpam-5251	380	2	,	,	PUNCT
ejpam-5251	380	3	γ+hg(g[kp	γ+hg(g[kp	NOUN
ejpam-5251	380	4	]	]	PUNCT
ejpam-5251	380	5	)	)	PUNCT
ejpam-5251	381	1	=	=	SYM
ejpam-5251	381	2	|c|	|c|	PROPN
ejpam-5251	381	3	=	=	PUNCT
ejpam-5251	381	4	∑	∑	PROPN
ejpam-5251	381	5	x∈s	x∈s	NOUN
ejpam-5251	381	6	|sx|	|sx|	ADJ
ejpam-5251	381	7	≤	≤	PROPN
ejpam-5251	381	8	∑	∑	PUNCT
ejpam-5251	381	9	x∈s	x∈s	PROPN
ejpam-5251	381	10	|v	|v	PROPN
ejpam-5251	381	11	(	(	PUNCT
ejpam-5251	381	12	kp)|	kp)|	PROPN
ejpam-5251	381	13	=	=	PUNCT
ejpam-5251	381	14	p	p	PROPN
ejpam-5251	381	15	·	·	PUNCT
ejpam-5251	381	16	|s|	|s|	NOUN
ejpam-5251	381	17	≤	≤	PROPN
ejpam-5251	381	18	p	p	X
ejpam-5251	381	19	·	·	PUNCT
ejpam-5251	381	20	γ+hg(g	γ+hg(g	X
ejpam-5251	381	21	)	)	PUNCT
ejpam-5251	381	22	.	.	PUNCT
ejpam-5251	382	1	this	this	PRON
ejpam-5251	382	2	proves	prove	VERB
ejpam-5251	382	3	(	(	PUNCT
ejpam-5251	382	4	i	i	NOUN
ejpam-5251	382	5	)	)	PUNCT
ejpam-5251	382	6	.	.	PUNCT
ejpam-5251	383	1	to	to	PART
ejpam-5251	383	2	prove	prove	VERB
ejpam-5251	383	3	(	(	PUNCT
ejpam-5251	383	4	ii	ii	NOUN
ejpam-5251	383	5	)	)	PUNCT
ejpam-5251	383	6	,	,	PUNCT
ejpam-5251	383	7	let	let	VERB
ejpam-5251	383	8	c	c	NOUN
ejpam-5251	383	9	=	=	SYM
ejpam-5251	383	10	∪x∈s	∪x∈s	PROPN
ejpam-5251	383	11	(	(	PUNCT
ejpam-5251	383	12	{	{	PUNCT
ejpam-5251	383	13	x	x	NOUN
ejpam-5251	383	14	}	}	PUNCT
ejpam-5251	383	15	×	×	PROPN
ejpam-5251	383	16	tx	tx	PROPN
ejpam-5251	383	17	)	)	PUNCT
ejpam-5251	383	18	⊆	⊆	NUM
ejpam-5251	383	19	v	v	NOUN
ejpam-5251	383	20	(	(	PUNCT
ejpam-5251	383	21	kp[g	kp[g	NOUN
ejpam-5251	383	22	]	]	PUNCT
ejpam-5251	383	23	)	)	PUNCT
ejpam-5251	383	24	be	be	AUX
ejpam-5251	383	25	a	a	DET
ejpam-5251	383	26	γ+hg	γ+hg	NOUN
ejpam-5251	383	27	-	-	PUNCT
ejpam-5251	383	28	set	set	NOUN
ejpam-5251	383	29	of	of	ADP
ejpam-5251	383	30	kp[g	kp[g	NOUN
ejpam-5251	383	31	]	]	PUNCT
ejpam-5251	383	32	.	.	PUNCT
ejpam-5251	384	1	by	by	ADP
ejpam-5251	384	2	theorem	theorem	NOUN
ejpam-5251	384	3	6	6	NUM
ejpam-5251	384	4	,	,	PUNCT
ejpam-5251	384	5	s	s	PART
ejpam-5251	384	6	=	=	SYM
ejpam-5251	384	7	v	v	PROPN
ejpam-5251	384	8	(	(	PUNCT
ejpam-5251	384	9	kp	kp	PROPN
ejpam-5251	384	10	)	)	PUNCT
ejpam-5251	384	11	and	and	CCONJ
ejpam-5251	384	12	sx	sx	PROPN
ejpam-5251	384	13	is	be	AUX
ejpam-5251	384	14	a	a	DET
ejpam-5251	384	15	2	2	NUM
ejpam-5251	384	16	-	-	PUNCT
ejpam-5251	384	17	path	path	NOUN
ejpam-5251	384	18	closure	closure	NOUN
ejpam-5251	384	19	absorbing	absorb	VERB
ejpam-5251	384	20	pointwise	pointwise	PROPN
ejpam-5251	384	21	non	non	ADJ
ejpam-5251	384	22	-	-	ADJ
ejpam-5251	384	23	dominating	dominating	ADJ
ejpam-5251	384	24	set	set	NOUN
ejpam-5251	384	25	in	in	ADP
ejpam-5251	384	26	h.	h.	PROPN
ejpam-5251	384	27	moreover	moreover	ADV
ejpam-5251	384	28	,	,	PUNCT
ejpam-5251	384	29	by	by	ADP
ejpam-5251	384	30	the	the	DET
ejpam-5251	384	31	minimality	minimality	NOUN
ejpam-5251	384	32	of	of	ADP
ejpam-5251	384	33	c	c	PROPN
ejpam-5251	384	34	,	,	PUNCT
ejpam-5251	384	35	sx	sx	PROPN
ejpam-5251	384	36	is	be	AUX
ejpam-5251	384	37	a	a	DET
ejpam-5251	384	38	minimal	minimal	ADJ
ejpam-5251	384	39	2	2	NUM
ejpam-5251	384	40	-	-	PUNCT
ejpam-5251	384	41	path	path	NOUN
ejpam-5251	384	42	closure	closure	NOUN
ejpam-5251	384	43	absorbing	absorb	VERB
ejpam-5251	384	44	pointwise	pointwise	PROPN
ejpam-5251	384	45	non	non	ADJ
ejpam-5251	384	46	-	-	ADJ
ejpam-5251	384	47	dominating	dominating	ADJ
ejpam-5251	384	48	set	set	NOUN
ejpam-5251	384	49	in	in	ADP
ejpam-5251	384	50	h.	h.	PROPN
ejpam-5251	384	51	thus	thus	ADV
ejpam-5251	384	52	,	,	PUNCT
ejpam-5251	384	53	γ+hg(kp[g	γ+hg(kp[g	NOUN
ejpam-5251	384	54	]	]	X
ejpam-5251	384	55	)	)	PUNCT
ejpam-5251	385	1	=	=	SYM
ejpam-5251	385	2	|c|	|c|	PROPN
ejpam-5251	385	3	=	=	PUNCT
ejpam-5251	385	4	∑	∑	PUNCT
ejpam-5251	385	5	x∈v	x∈v	PROPN
ejpam-5251	385	6	(	(	PUNCT
ejpam-5251	385	7	g	g	NOUN
ejpam-5251	385	8	)	)	PUNCT
ejpam-5251	385	9	|sx|	|sx|	NUM
ejpam-5251	385	10	≤	≤	NOUN
ejpam-5251	386	1	p	p	X
ejpam-5251	386	2	·	·	PUNCT
ejpam-5251	386	3	ρ+2pnd(h	ρ+2pnd(h	NUM
ejpam-5251	386	4	)	)	PUNCT
ejpam-5251	386	5	.	.	PUNCT
ejpam-5251	387	1	to	to	PART
ejpam-5251	387	2	get	get	VERB
ejpam-5251	387	3	the	the	DET
ejpam-5251	387	4	other	other	ADJ
ejpam-5251	387	5	inequality	inequality	NOUN
ejpam-5251	387	6	,	,	PUNCT
ejpam-5251	387	7	d	d	PROPN
ejpam-5251	387	8	⊆	⊆	NUM
ejpam-5251	387	9	v	v	ADP
ejpam-5251	387	10	(	(	PUNCT
ejpam-5251	387	11	h	h	NOUN
ejpam-5251	387	12	)	)	PUNCT
ejpam-5251	387	13	be	be	VERB
ejpam-5251	387	14	a	a	DET
ejpam-5251	387	15	ρ+2pnd	ρ+2pnd	NOUN
ejpam-5251	387	16	-	-	PUNCT
ejpam-5251	387	17	set	set	NOUN
ejpam-5251	387	18	of	of	ADP
ejpam-5251	387	19	h.	h.	PROPN
ejpam-5251	387	20	then	then	ADV
ejpam-5251	387	21	c	c	X
ejpam-5251	388	1	=	=	PUNCT
ejpam-5251	388	2	∪v∈v	∪v∈v	X
ejpam-5251	388	3	(	(	PUNCT
ejpam-5251	388	4	kp	kp	PROPN
ejpam-5251	388	5	)	)	PUNCT
ejpam-5251	388	6	(	(	PUNCT
ejpam-5251	388	7	{	{	PUNCT
ejpam-5251	388	8	x	x	NOUN
ejpam-5251	388	9	}	}	PUNCT
ejpam-5251	388	10	×d	×d	NOUN
ejpam-5251	388	11	)	)	PUNCT
ejpam-5251	388	12	=	=	SYM
ejpam-5251	388	13	v	v	X
ejpam-5251	388	14	(	(	PUNCT
ejpam-5251	388	15	kp)×d	kp)×d	PROPN
ejpam-5251	388	16	is	be	AUX
ejpam-5251	388	17	a	a	DET
ejpam-5251	388	18	minimal	minimal	ADJ
ejpam-5251	388	19	geodetic	geodetic	ADJ
ejpam-5251	388	20	hop	hop	NOUN
ejpam-5251	388	21	dominating	dominating	NOUN
ejpam-5251	388	22	set	set	VERB
ejpam-5251	388	23	in	in	ADP
ejpam-5251	388	24	kp[g	kp[g	NOUN
ejpam-5251	388	25	]	]	PUNCT
ejpam-5251	388	26	.	.	PUNCT
ejpam-5251	389	1	therefore	therefore	ADV
ejpam-5251	389	2	,	,	PUNCT
ejpam-5251	389	3	γ+hg(kp[g	γ+hg(kp[g	NOUN
ejpam-5251	389	4	]	]	PUNCT
ejpam-5251	389	5	)	)	PUNCT
ejpam-5251	389	6	≥	≥	NOUN
ejpam-5251	389	7	|c|	|c|	PROPN
ejpam-5251	390	1	=	=	SYM
ejpam-5251	390	2	p	p	X
ejpam-5251	390	3	·	·	PUNCT
ejpam-5251	390	4	ρ+2pnd(h	ρ+2pnd(h	NUM
ejpam-5251	390	5	)	)	PUNCT
ejpam-5251	390	6	.	.	PUNCT
ejpam-5251	391	1	acknowledgements	acknowledgement	VERB
ejpam-5251	391	2	the	the	DET
ejpam-5251	391	3	first	first	ADJ
ejpam-5251	391	4	author	author	NOUN
ejpam-5251	391	5	would	would	AUX
ejpam-5251	391	6	like	like	VERB
ejpam-5251	391	7	to	to	PART
ejpam-5251	391	8	thank	thank	VERB
ejpam-5251	391	9	the	the	DET
ejpam-5251	391	10	dost	dost	NOUN
ejpam-5251	391	11	-	-	PUNCT
ejpam-5251	391	12	asthrd	asthrd	NOUN
ejpam-5251	391	13	program	program	NOUN
ejpam-5251	391	14	of	of	ADP
ejpam-5251	391	15	the	the	DET
ejpam-5251	391	16	department	department	PROPN
ejpam-5251	391	17	of	of	ADP
ejpam-5251	391	18	science	science	NOUN
ejpam-5251	391	19	and	and	CCONJ
ejpam-5251	391	20	technology	technology	NOUN
ejpam-5251	391	21	,	,	PUNCT
ejpam-5251	391	22	philippines	philippine	NOUN
ejpam-5251	391	23	,	,	PUNCT
ejpam-5251	391	24	for	for	ADP
ejpam-5251	391	25	fully	fully	ADV
ejpam-5251	391	26	supporting	support	VERB
ejpam-5251	391	27	his	his	PRON
ejpam-5251	391	28	research	research	NOUN
ejpam-5251	391	29	activities	activity	NOUN
ejpam-5251	391	30	for	for	ADP
ejpam-5251	391	31	this	this	DET
ejpam-5251	391	32	project	project	NOUN
ejpam-5251	391	33	.	.	PUNCT
ejpam-5251	392	1	moreover	moreover	ADV
ejpam-5251	392	2	,	,	PUNCT
ejpam-5251	392	3	the	the	DET
ejpam-5251	392	4	first	first	ADJ
ejpam-5251	392	5	author	author	NOUN
ejpam-5251	392	6	is	be	AUX
ejpam-5251	392	7	thankful	thankful	ADJ
ejpam-5251	392	8	and	and	CCONJ
ejpam-5251	392	9	references	reference	NOUN
ejpam-5251	392	10	[	[	X
ejpam-5251	392	11	1	1	NUM
ejpam-5251	392	12	]	]	X
ejpam-5251	392	13	i.s	i.s	PROPN
ejpam-5251	392	14	.	.	PROPN
ejpam-5251	392	15	aniversario	aniversario	PROPN
ejpam-5251	392	16	and	and	CCONJ
ejpam-5251	392	17	f.p	f.p	PROPN
ejpam-5251	392	18	.	.	PROPN
ejpam-5251	392	19	jamil	jamil	PROPN
ejpam-5251	392	20	.	.	PUNCT
ejpam-5251	393	1	the	the	DET
ejpam-5251	393	2	minimal	minimal	ADJ
ejpam-5251	393	3	closed	closed	ADJ
ejpam-5251	393	4	geodetic	geodetic	ADJ
ejpam-5251	393	5	numbers	number	NOUN
ejpam-5251	393	6	of	of	ADP
ejpam-5251	393	7	graphs	graph	NOUN
ejpam-5251	393	8	.	.	PUNCT
ejpam-5251	394	1	utilitas	utilitas	PROPN
ejpam-5251	394	2	mathematica	mathematica	PROPN
ejpam-5251	394	3	,	,	PUNCT
ejpam-5251	394	4	79	79	NUM
ejpam-5251	394	5	,	,	PUNCT
ejpam-5251	394	6	2009	2009	NUM
ejpam-5251	394	7	.	.	PUNCT
ejpam-5251	395	1	[	[	X
ejpam-5251	395	2	2	2	NUM
ejpam-5251	395	3	]	]	X
ejpam-5251	395	4	i.s	i.s	PROPN
ejpam-5251	395	5	.	.	PROPN
ejpam-5251	395	6	aniversario	aniversario	PROPN
ejpam-5251	395	7	,	,	PUNCT
ejpam-5251	395	8	f.p	f.p	PROPN
ejpam-5251	395	9	.	.	PROPN
ejpam-5251	395	10	jamil	jamil	PROPN
ejpam-5251	395	11	,	,	PUNCT
ejpam-5251	395	12	and	and	CCONJ
ejpam-5251	395	13	s.r	s.r	PROPN
ejpam-5251	395	14	.	.	PROPN
ejpam-5251	395	15	canoy	canoy	PROPN
ejpam-5251	395	16	.	.	PUNCT
ejpam-5251	396	1	the	the	DET
ejpam-5251	396	2	closed	closed	ADJ
ejpam-5251	396	3	geodetic	geodetic	ADJ
ejpam-5251	396	4	numbers	number	NOUN
ejpam-5251	396	5	of	of	ADP
ejpam-5251	396	6	graphs	graph	NOUN
ejpam-5251	396	7	.	.	PUNCT
ejpam-5251	397	1	utilitas	utilitas	PROPN
ejpam-5251	397	2	mathematica	mathematica	PROPN
ejpam-5251	397	3	,	,	PUNCT
ejpam-5251	397	4	74	74	NUM
ejpam-5251	397	5	,	,	PUNCT
ejpam-5251	397	6	2007	2007	NUM
ejpam-5251	397	7	.	.	PUNCT
ejpam-5251	398	1	[	[	X
ejpam-5251	398	2	3	3	X
ejpam-5251	398	3	]	]	X
ejpam-5251	398	4	d.	d.	PROPN
ejpam-5251	398	5	anusha	anusha	PROPN
ejpam-5251	398	6	.	.	PUNCT
ejpam-5251	399	1	geodetic	geodetic	ADJ
ejpam-5251	399	2	hop	hop	NOUN
ejpam-5251	399	3	domination	domination	NOUN
ejpam-5251	399	4	number	number	NOUN
ejpam-5251	399	5	in	in	ADP
ejpam-5251	399	6	join	join	NOUN
ejpam-5251	399	7	and	and	CCONJ
ejpam-5251	399	8	corona	corona	NOUN
ejpam-5251	399	9	of	of	ADP
ejpam-5251	399	10	graphs	graph	NOUN
ejpam-5251	399	11	.	.	PUNCT
ejpam-5251	400	1	advances	advance	NOUN
ejpam-5251	400	2	and	and	CCONJ
ejpam-5251	400	3	applications	application	NOUN
ejpam-5251	400	4	in	in	ADP
ejpam-5251	400	5	mathematical	mathematical	ADJ
ejpam-5251	400	6	sciences	science	NOUN
ejpam-5251	400	7	,	,	PUNCT
ejpam-5251	400	8	21(3):1117–1127	21(3):1117–1127	NUM
ejpam-5251	400	9	.	.	PUNCT
ejpam-5251	401	1	[	[	X
ejpam-5251	401	2	4	4	X
ejpam-5251	401	3	]	]	X
ejpam-5251	401	4	d.	d.	PROPN
ejpam-5251	401	5	anusha	anusha	PROPN
ejpam-5251	401	6	,	,	PUNCT
ejpam-5251	401	7	j.	j.	PROPN
ejpam-5251	401	8	john	john	PROPN
ejpam-5251	401	9	,	,	PUNCT
ejpam-5251	401	10	and	and	CCONJ
ejpam-5251	401	11	s.	s.	PROPN
ejpam-5251	401	12	joseph	joseph	PROPN
ejpam-5251	401	13	robin	robin	PROPN
ejpam-5251	401	14	.	.	PUNCT
ejpam-5251	402	1	further	further	ADJ
ejpam-5251	402	2	results	result	NOUN
ejpam-5251	402	3	on	on	ADP
ejpam-5251	402	4	the	the	DET
ejpam-5251	402	5	hop	hop	NOUN
ejpam-5251	402	6	domination	domination	NOUN
ejpam-5251	402	7	number	number	NOUN
ejpam-5251	402	8	of	of	ADP
ejpam-5251	402	9	a	a	DET
ejpam-5251	402	10	graph	graph	NOUN
ejpam-5251	402	11	.	.	PUNCT
ejpam-5251	403	1	boletim	boletim	PROPN
ejpam-5251	403	2	da	da	PROPN
ejpam-5251	403	3	sociedade	sociedade	PROPN
ejpam-5251	403	4	paranaense	paranaense	PROPN
ejpam-5251	403	5	de	de	PROPN
ejpam-5251	403	6	matemática	matemática	PROPN
ejpam-5251	403	7	,	,	PUNCT
ejpam-5251	403	8	42:1–12	42:1–12	NUM
ejpam-5251	403	9	,	,	PUNCT
ejpam-5251	403	10	2024	2024	NUM
ejpam-5251	403	11	.	.	PUNCT
ejpam-5251	404	1	[	[	X
ejpam-5251	404	2	5	5	NUM
ejpam-5251	404	3	]	]	X
ejpam-5251	404	4	s	s	VERB
ejpam-5251	404	5	ayyaswamy	ayyaswamy	PROPN
ejpam-5251	404	6	,	,	PUNCT
ejpam-5251	404	7	natarajan	natarajan	PROPN
ejpam-5251	404	8	chidambaram	chidambaram	PROPN
ejpam-5251	404	9	,	,	PUNCT
ejpam-5251	404	10	and	and	CCONJ
ejpam-5251	404	11	venkatakrishnan	venkatakrishnan	NOUN
ejpam-5251	404	12	yanamandram	yanamandram	PROPN
ejpam-5251	404	13	.	.	PUNCT
ejpam-5251	405	1	hop	hop	PROPN
ejpam-5251	405	2	domination	domination	NOUN
ejpam-5251	405	3	in	in	ADP
ejpam-5251	405	4	graphs	graph	NOUN
ejpam-5251	405	5	.	.	PUNCT
ejpam-5251	406	1	2022	2022	NUM
ejpam-5251	406	2	.	.	PUNCT
ejpam-5251	407	1	references	reference	NOUN
ejpam-5251	407	2	1749	1749	NUM
ejpam-5251	407	3	[	[	X
ejpam-5251	407	4	6	6	NUM
ejpam-5251	407	5	]	]	PUNCT
ejpam-5251	407	6	c.	c.	PROPN
ejpam-5251	407	7	berge	berge	PROPN
ejpam-5251	407	8	.	.	PUNCT
ejpam-5251	408	1	theory	theory	NOUN
ejpam-5251	408	2	of	of	ADP
ejpam-5251	408	3	graphs	graph	NOUN
ejpam-5251	408	4	and	and	CCONJ
ejpam-5251	408	5	applications	application	NOUN
ejpam-5251	408	6	.	.	PUNCT
ejpam-5251	409	1	methuen	methuen	PROPN
ejpam-5251	409	2	co.	co.	PROPN
ejpam-5251	409	3	ltd	ltd	PROPN
ejpam-5251	409	4	.	.	PROPN
ejpam-5251	409	5	london	london	PROPN
ejpam-5251	409	6	,	,	PUNCT
ejpam-5251	409	7	john	john	PROPN
ejpam-5251	409	8	wiley	wiley	PROPN
ejpam-5251	409	9	&	&	CCONJ
ejpam-5251	409	10	sons	sons	PROPN
ejpam-5251	409	11	inc	inc	PROPN
ejpam-5251	409	12	,	,	PUNCT
ejpam-5251	409	13	new	new	PROPN
ejpam-5251	409	14	york	york	PROPN
ejpam-5251	409	15	,	,	PUNCT
ejpam-5251	409	16	1962	1962	NUM
ejpam-5251	409	17	.	.	PUNCT
ejpam-5251	410	1	[	[	X
ejpam-5251	410	2	7	7	X
ejpam-5251	410	3	]	]	PUNCT
ejpam-5251	410	4	boštjan	boštjan	NOUN
ejpam-5251	410	5	brešar	brešar	PROPN
ejpam-5251	410	6	,	,	PUNCT
ejpam-5251	410	7	matjaž	matjaž	NOUN
ejpam-5251	410	8	kovše	kovše	PROPN
ejpam-5251	410	9	,	,	PUNCT
ejpam-5251	410	10	and	and	CCONJ
ejpam-5251	410	11	aleksandra	aleksandra	PROPN
ejpam-5251	410	12	tepeh	tepeh	PROPN
ejpam-5251	410	13	.	.	PUNCT
ejpam-5251	411	1	geodetic	geodetic	ADJ
ejpam-5251	411	2	sets	set	NOUN
ejpam-5251	411	3	in	in	ADP
ejpam-5251	411	4	graphs	graph	NOUN
ejpam-5251	411	5	,	,	PUNCT
ejpam-5251	411	6	pages	page	NOUN
ejpam-5251	411	7	197–218	197–218	NUM
ejpam-5251	411	8	.	.	PROPN
ejpam-5251	411	9	1	1	NUM
ejpam-5251	411	10	1970	1970	NUM
ejpam-5251	411	11	.	.	PUNCT
ejpam-5251	412	1	[	[	X
ejpam-5251	412	2	8	8	NUM
ejpam-5251	412	3	]	]	PUNCT
ejpam-5251	412	4	g.	g.	NOUN
ejpam-5251	412	5	cagaanan	cagaanan	PROPN
ejpam-5251	412	6	and	and	CCONJ
ejpam-5251	412	7	s.r	s.r	PROPN
ejpam-5251	412	8	.	.	PROPN
ejpam-5251	412	9	canoy	canoy	PROPN
ejpam-5251	412	10	jr	jr	PROPN
ejpam-5251	412	11	.	.	PROPN
ejpam-5251	413	1	on	on	ADP
ejpam-5251	413	2	the	the	DET
ejpam-5251	413	3	geodetic	geodetic	ADJ
ejpam-5251	413	4	covers	cover	NOUN
ejpam-5251	413	5	and	and	CCONJ
ejpam-5251	413	6	geodetic	geodetic	ADJ
ejpam-5251	413	7	bases	basis	NOUN
ejpam-5251	413	8	of	of	ADP
ejpam-5251	413	9	the	the	DET
ejpam-5251	413	10	composition	composition	NOUN
ejpam-5251	413	11	g[km	g[km	PROPN
ejpam-5251	413	12	]	]	PUNCT
ejpam-5251	413	13	.	.	PUNCT
ejpam-5251	413	14	ars	ars	PROPN
ejpam-5251	413	15	comb	comb	PROPN
ejpam-5251	413	16	.	.	PUNCT
ejpam-5251	413	17	,	,	PUNCT
ejpam-5251	413	18	79	79	NUM
ejpam-5251	413	19	,	,	PUNCT
ejpam-5251	413	20	2006	2006	NUM
ejpam-5251	413	21	.	.	PUNCT
ejpam-5251	414	1	[	[	X
ejpam-5251	414	2	9	9	NUM
ejpam-5251	414	3	]	]	X
ejpam-5251	414	4	s.r	s.r	PROPN
ejpam-5251	414	5	.	.	PROPN
ejpam-5251	414	6	canoy	canoy	PROPN
ejpam-5251	414	7	and	and	CCONJ
ejpam-5251	414	8	g.p	g.p	PROPN
ejpam-5251	414	9	.	.	PROPN
ejpam-5251	414	10	salasalan	salasalan	NOUN
ejpam-5251	414	11	.	.	PUNCT
ejpam-5251	415	1	a	a	DET
ejpam-5251	415	2	variant	variant	NOUN
ejpam-5251	415	3	of	of	ADP
ejpam-5251	415	4	hop	hop	NOUN
ejpam-5251	415	5	domination	domination	NOUN
ejpam-5251	415	6	in	in	ADP
ejpam-5251	415	7	graphs	graph	NOUN
ejpam-5251	415	8	.	.	PUNCT
ejpam-5251	416	1	european	european	ADJ
ejpam-5251	416	2	journal	journal	PROPN
ejpam-5251	416	3	of	of	ADP
ejpam-5251	416	4	pure	pure	ADJ
ejpam-5251	416	5	and	and	CCONJ
ejpam-5251	416	6	applied	applied	ADJ
ejpam-5251	416	7	mathematics	mathematic	NOUN
ejpam-5251	416	8	,	,	PUNCT
ejpam-5251	416	9	15(2):342–353	15(2):342–353	NUM
ejpam-5251	416	10	,	,	PUNCT
ejpam-5251	416	11	2022	2022	NUM
ejpam-5251	416	12	.	.	PUNCT
ejpam-5251	417	1	[	[	X
ejpam-5251	417	2	10	10	NUM
ejpam-5251	417	3	]	]	X
ejpam-5251	417	4	g.	g.	PROPN
ejpam-5251	417	5	chartrand	chartrand	PROPN
ejpam-5251	417	6	,	,	PUNCT
ejpam-5251	417	7	f.	f.	PROPN
ejpam-5251	417	8	harary	harary	PROPN
ejpam-5251	417	9	,	,	PUNCT
ejpam-5251	417	10	and	and	CCONJ
ejpam-5251	417	11	p.	p.	PROPN
ejpam-5251	417	12	zhang	zhang	PROPN
ejpam-5251	417	13	.	.	PUNCT
ejpam-5251	418	1	the	the	DET
ejpam-5251	418	2	geodetic	geodetic	ADJ
ejpam-5251	418	3	number	number	NOUN
ejpam-5251	418	4	of	of	ADP
ejpam-5251	418	5	a	a	DET
ejpam-5251	418	6	graph	graph	NOUN
ejpam-5251	418	7	.	.	PUNCT
ejpam-5251	419	1	networks	network	NOUN
ejpam-5251	419	2	:	:	PUNCT
ejpam-5251	419	3	an	an	DET
ejpam-5251	419	4	international	international	ADJ
ejpam-5251	419	5	journal	journal	NOUN
ejpam-5251	419	6	,	,	PUNCT
ejpam-5251	419	7	39(1):1–6	39(1):1–6	NUM
ejpam-5251	419	8	,	,	PUNCT
ejpam-5251	419	9	2002	2002	NUM
ejpam-5251	419	10	.	.	PUNCT
ejpam-5251	420	1	[	[	X
ejpam-5251	420	2	11	11	NUM
ejpam-5251	420	3	]	]	X
ejpam-5251	420	4	f.	f.	PROPN
ejpam-5251	420	5	harary	harary	PROPN
ejpam-5251	420	6	.	.	PUNCT
ejpam-5251	421	1	graph	graph	NOUN
ejpam-5251	421	2	theory	theory	NOUN
ejpam-5251	421	3	.	.	PUNCT
ejpam-5251	422	1	addison	addison	PROPN
ejpam-5251	422	2	-	-	PUNCT
ejpam-5251	422	3	wesley	wesley	PROPN
ejpam-5251	422	4	publishing	publishing	PROPN
ejpam-5251	422	5	company	company	NOUN
ejpam-5251	422	6	,	,	PUNCT
ejpam-5251	422	7	1991	1991	NUM
ejpam-5251	422	8	.	.	PUNCT
ejpam-5251	423	1	[	[	X
ejpam-5251	423	2	12	12	NUM
ejpam-5251	423	3	]	]	X
ejpam-5251	423	4	f.	f.	PROPN
ejpam-5251	423	5	harary	harary	PROPN
ejpam-5251	423	6	.	.	PUNCT
ejpam-5251	424	1	the	the	DET
ejpam-5251	424	2	geodetic	geodetic	ADJ
ejpam-5251	424	3	number	number	NOUN
ejpam-5251	424	4	of	of	ADP
ejpam-5251	424	5	a	a	DET
ejpam-5251	424	6	graph	graph	NOUN
ejpam-5251	424	7	.	.	PUNCT
ejpam-5251	425	1	mathl	mathl	NOUN
ejpam-5251	425	2	.	.	PUNCT
ejpam-5251	426	1	comput	comput	NOUN
ejpam-5251	426	2	.	.	PUNCT
ejpam-5251	427	1	modelling	modelling	NOUN
ejpam-5251	427	2	,	,	PUNCT
ejpam-5251	427	3	17(11):89–95	17(11):89–95	NUM
ejpam-5251	427	4	,	,	PUNCT
ejpam-5251	427	5	1993	1993	NUM
ejpam-5251	427	6	.	.	PUNCT
ejpam-5251	428	1	[	[	X
ejpam-5251	428	2	13	13	NUM
ejpam-5251	428	3	]	]	PUNCT
ejpam-5251	428	4	m.	m.	NOUN
ejpam-5251	428	5	henning	henning	PROPN
ejpam-5251	428	6	,	,	PUNCT
ejpam-5251	428	7	s.	s.	PROPN
ejpam-5251	428	8	pal	pal	PROPN
ejpam-5251	428	9	,	,	PUNCT
ejpam-5251	428	10	and	and	CCONJ
ejpam-5251	428	11	d.	d.	PROPN
ejpam-5251	428	12	pradhan	pradhan	PROPN
ejpam-5251	428	13	.	.	PUNCT
ejpam-5251	429	1	algorithm	algorithm	PROPN
ejpam-5251	429	2	and	and	CCONJ
ejpam-5251	429	3	hardness	hardness	NOUN
ejpam-5251	429	4	results	result	NOUN
ejpam-5251	429	5	on	on	ADP
ejpam-5251	429	6	hop	hop	NOUN
ejpam-5251	429	7	domination	domination	NOUN
ejpam-5251	429	8	in	in	ADP
ejpam-5251	429	9	graphs	graph	NOUN
ejpam-5251	429	10	.	.	PUNCT
ejpam-5251	430	1	information	information	NOUN
ejpam-5251	430	2	processing	processing	NOUN
ejpam-5251	430	3	letters	letter	NOUN
ejpam-5251	430	4	,	,	PUNCT
ejpam-5251	430	5	2019	2019	NUM
ejpam-5251	430	6	.	.	PUNCT
ejpam-5251	431	1	[	[	X
ejpam-5251	431	2	14	14	NUM
ejpam-5251	431	3	]	]	X
ejpam-5251	431	4	m.	m.	NOUN
ejpam-5251	431	5	henning	henning	PROPN
ejpam-5251	431	6	and	and	CCONJ
ejpam-5251	431	7	n.	n.	PROPN
ejpam-5251	431	8	jafari	jafari	PROPN
ejpam-5251	431	9	rad	rad	PROPN
ejpam-5251	431	10	.	.	PROPN
ejpam-5251	432	1	on	on	ADP
ejpam-5251	432	2	2	2	NUM
ejpam-5251	432	3	-	-	PUNCT
ejpam-5251	432	4	step	step	NOUN
ejpam-5251	432	5	and	and	CCONJ
ejpam-5251	432	6	hop	hop	NOUN
ejpam-5251	432	7	dominating	dominating	NOUN
ejpam-5251	432	8	sets	set	NOUN
ejpam-5251	432	9	in	in	ADP
ejpam-5251	432	10	graphs	graph	NOUN
ejpam-5251	432	11	.	.	PUNCT
ejpam-5251	433	1	graphs	graph	NOUN
ejpam-5251	433	2	and	and	CCONJ
ejpam-5251	433	3	combinatorics	combinatoric	NOUN
ejpam-5251	433	4	,	,	PUNCT
ejpam-5251	433	5	33:1–15	33:1–15	NUM
ejpam-5251	433	6	,	,	PUNCT
ejpam-5251	433	7	2017	2017	NUM
ejpam-5251	433	8	.	.	PUNCT
ejpam-5251	434	1	[	[	X
ejpam-5251	434	2	15	15	NUM
ejpam-5251	434	3	]	]	X
ejpam-5251	434	4	f.p	f.p	PROPN
ejpam-5251	434	5	.	.	PROPN
ejpam-5251	434	6	jamil	jamil	PROPN
ejpam-5251	434	7	,	,	PUNCT
ejpam-5251	434	8	i.s	i.s	PROPN
ejpam-5251	434	9	.	.	PROPN
ejpam-5251	434	10	aniversario	aniversario	PROPN
ejpam-5251	434	11	,	,	PUNCT
ejpam-5251	434	12	and	and	CCONJ
ejpam-5251	434	13	s.r	s.r	PROPN
ejpam-5251	434	14	.	.	PROPN
ejpam-5251	434	15	canoy	canoy	PROPN
ejpam-5251	434	16	.	.	PUNCT
ejpam-5251	435	1	the	the	DET
ejpam-5251	435	2	closed	closed	ADJ
ejpam-5251	435	3	geodetic	geodetic	ADJ
ejpam-5251	435	4	numbers	number	NOUN
ejpam-5251	435	5	of	of	ADP
ejpam-5251	435	6	the	the	DET
ejpam-5251	435	7	corona	corona	NOUN
ejpam-5251	435	8	and	and	CCONJ
ejpam-5251	435	9	composition	composition	NOUN
ejpam-5251	435	10	of	of	ADP
ejpam-5251	435	11	graphs	graph	NOUN
ejpam-5251	435	12	.	.	PUNCT
ejpam-5251	436	1	utilitas	utilitas	PROPN
ejpam-5251	436	2	mathematica	mathematica	PROPN
ejpam-5251	436	3	,	,	PUNCT
ejpam-5251	436	4	82	82	NUM
ejpam-5251	436	5	,	,	PUNCT
ejpam-5251	436	6	2010	2010	NUM
ejpam-5251	436	7	.	.	PUNCT
ejpam-5251	437	1	[	[	X
ejpam-5251	437	2	16	16	NUM
ejpam-5251	437	3	]	]	X
ejpam-5251	437	4	f.p	f.p	PROPN
ejpam-5251	437	5	.	.	PROPN
ejpam-5251	437	6	jamil	jamil	PROPN
ejpam-5251	437	7	and	and	CCONJ
ejpam-5251	437	8	h.	h.	PROPN
ejpam-5251	437	9	nuenay	nuenay	PROPN
ejpam-5251	437	10	-	-	PUNCT
ejpam-5251	437	11	maglanque	maglanque	ADJ
ejpam-5251	437	12	.	.	PUNCT
ejpam-5251	438	1	on	on	ADP
ejpam-5251	438	2	minimal	minimal	ADJ
ejpam-5251	438	3	geodetic	geodetic	ADJ
ejpam-5251	438	4	domination	domination	NOUN
ejpam-5251	438	5	in	in	ADP
ejpam-5251	438	6	graphs	graph	NOUN
ejpam-5251	438	7	.	.	PUNCT
ejpam-5251	439	1	discussiones	discussione	NOUN
ejpam-5251	439	2	mathematicae	mathematicae	PROPN
ejpam-5251	439	3	graph	graph	NOUN
ejpam-5251	439	4	theory	theory	NOUN
ejpam-5251	439	5	,	,	PUNCT
ejpam-5251	439	6	2015	2015	NUM
ejpam-5251	439	7	.	.	PUNCT
ejpam-5251	440	1	[	[	X
ejpam-5251	440	2	17	17	NUM
ejpam-5251	440	3	]	]	PUNCT
ejpam-5251	440	4	j.	j.	PROPN
ejpam-5251	440	5	john	john	PROPN
ejpam-5251	440	6	.	.	PUNCT
ejpam-5251	441	1	the	the	DET
ejpam-5251	441	2	geodetic	geodetic	ADJ
ejpam-5251	441	3	hop	hop	NOUN
ejpam-5251	441	4	domination	domination	NOUN
ejpam-5251	441	5	number	number	NOUN
ejpam-5251	441	6	of	of	ADP
ejpam-5251	441	7	complementary	complementary	ADJ
ejpam-5251	441	8	prisms	prism	NOUN
ejpam-5251	441	9	.	.	PUNCT
ejpam-5251	442	1	discrete	discrete	ADJ
ejpam-5251	442	2	mathematics	mathematic	NOUN
ejpam-5251	442	3	algorithms	algorithm	NOUN
ejpam-5251	442	4	and	and	CCONJ
ejpam-5251	442	5	applications	application	NOUN
ejpam-5251	442	6	,	,	PUNCT
ejpam-5251	442	7	13(12	13(12	NUM
ejpam-5251	442	8	)	)	PUNCT
ejpam-5251	442	9	,	,	PUNCT
ejpam-5251	442	10	2020	2020	NUM
ejpam-5251	442	11	.	.	PUNCT
ejpam-5251	443	1	[	[	X
ejpam-5251	443	2	18	18	NUM
ejpam-5251	443	3	]	]	X
ejpam-5251	443	4	s.r	s.r	PROPN
ejpam-5251	443	5	.	.	PROPN
ejpam-5251	443	6	canoy	canoy	PROPN
ejpam-5251	443	7	jr	jr	PROPN
ejpam-5251	443	8	and	and	CCONJ
ejpam-5251	443	9	g.	g.	PROPN
ejpam-5251	443	10	cagaanan	cagaanan	PROPN
ejpam-5251	443	11	.	.	PUNCT
ejpam-5251	444	1	on	on	ADP
ejpam-5251	444	2	the	the	DET
ejpam-5251	444	3	geodesic	geodesic	ADJ
ejpam-5251	444	4	and	and	CCONJ
ejpam-5251	444	5	hull	hull	NOUN
ejpam-5251	444	6	numbers	number	NOUN
ejpam-5251	444	7	of	of	ADP
ejpam-5251	444	8	the	the	DET
ejpam-5251	444	9	sum	sum	NOUN
ejpam-5251	444	10	of	of	ADP
ejpam-5251	444	11	graphs	graph	NOUN
ejpam-5251	444	12	.	.	PUNCT
ejpam-5251	445	1	congressus	congressus	PROPN
ejpam-5251	445	2	numerantium	numerantium	PROPN
ejpam-5251	445	3	,	,	PUNCT
ejpam-5251	445	4	2003	2003	NUM
ejpam-5251	445	5	.	.	PUNCT
ejpam-5251	446	1	[	[	X
ejpam-5251	446	2	19	19	NUM
ejpam-5251	446	3	]	]	X
ejpam-5251	446	4	s.r	s.r	PROPN
ejpam-5251	446	5	.	.	PROPN
ejpam-5251	446	6	canoy	canoy	PROPN
ejpam-5251	446	7	jr	jr	PROPN
ejpam-5251	446	8	.	.	PROPN
ejpam-5251	446	9	,	,	PUNCT
ejpam-5251	446	10	g.	g.	PROPN
ejpam-5251	446	11	cagaanan	cagaanan	PROPN
ejpam-5251	446	12	,	,	PUNCT
ejpam-5251	446	13	and	and	CCONJ
ejpam-5251	446	14	s.	s.	PROPN
ejpam-5251	446	15	gervacio	gervacio	PROPN
ejpam-5251	446	16	.	.	PUNCT
ejpam-5251	447	1	convexity	convexity	PROPN
ejpam-5251	447	2	,	,	PUNCT
ejpam-5251	447	3	geodetic	geodetic	ADJ
ejpam-5251	447	4	,	,	PUNCT
ejpam-5251	447	5	and	and	CCONJ
ejpam-5251	447	6	hull	hull	NOUN
ejpam-5251	447	7	numbers	number	NOUN
ejpam-5251	447	8	of	of	ADP
ejpam-5251	447	9	the	the	DET
ejpam-5251	447	10	join	join	NOUN
ejpam-5251	447	11	of	of	ADP
ejpam-5251	447	12	graphs	graph	NOUN
ejpam-5251	447	13	.	.	PUNCT
ejpam-5251	448	1	utilitas	utilitas	PROPN
ejpam-5251	448	2	mathematica	mathematica	PROPN
ejpam-5251	448	3	,	,	PUNCT
ejpam-5251	448	4	71	71	NUM
ejpam-5251	448	5	,	,	PUNCT
ejpam-5251	448	6	2006	2006	NUM
ejpam-5251	448	7	.	.	PUNCT
ejpam-5251	449	1	[	[	X
ejpam-5251	449	2	20	20	NUM
ejpam-5251	449	3	]	]	X
ejpam-5251	449	4	s.r	s.r	PROPN
ejpam-5251	449	5	.	.	PROPN
ejpam-5251	449	6	canoy	canoy	PROPN
ejpam-5251	449	7	jr	jr	PROPN
ejpam-5251	449	8	,	,	PUNCT
ejpam-5251	449	9	r.	r.	PROPN
ejpam-5251	449	10	mollejon	mollejon	NOUN
ejpam-5251	449	11	,	,	PUNCT
ejpam-5251	449	12	and	and	CCONJ
ejpam-5251	449	13	j.	j.	PROPN
ejpam-5251	449	14	canoy	canoy	PROPN
ejpam-5251	449	15	.	.	PUNCT
ejpam-5251	450	1	hop	hop	PROPN
ejpam-5251	450	2	dominating	dominating	NOUN
ejpam-5251	450	3	sets	set	NOUN
ejpam-5251	450	4	in	in	ADP
ejpam-5251	450	5	graphs	graph	NOUN
ejpam-5251	450	6	under	under	ADP
ejpam-5251	450	7	binary	binary	ADJ
ejpam-5251	450	8	operations	operation	NOUN
ejpam-5251	450	9	.	.	PUNCT
ejpam-5251	451	1	european	european	ADJ
ejpam-5251	451	2	journal	journal	PROPN
ejpam-5251	451	3	of	of	ADP
ejpam-5251	451	4	pure	pure	ADJ
ejpam-5251	451	5	and	and	CCONJ
ejpam-5251	451	6	applied	applied	ADJ
ejpam-5251	451	7	mathematics	mathematic	NOUN
ejpam-5251	451	8	,	,	PUNCT
ejpam-5251	451	9	11	11	NUM
ejpam-5251	451	10	,	,	PUNCT
ejpam-5251	451	11	2019	2019	NUM
ejpam-5251	451	12	.	.	PUNCT
ejpam-5251	452	1	[	[	X
ejpam-5251	452	2	21	21	NUM
ejpam-5251	452	3	]	]	X
ejpam-5251	452	4	c.	c.	PROPN
ejpam-5251	452	5	natajaran	natajaran	PROPN
ejpam-5251	452	6	and	and	CCONJ
ejpam-5251	452	7	s.k	s.k	PROPN
ejpam-5251	452	8	.	.	PROPN
ejpam-5251	452	9	ayyaswamy	ayyaswamy	PROPN
ejpam-5251	452	10	.	.	PUNCT
ejpam-5251	453	1	hop	hop	PROPN
ejpam-5251	453	2	domination	domination	NOUN
ejpam-5251	453	3	in	in	ADP
ejpam-5251	453	4	graphs	graph	NOUN
ejpam-5251	453	5	-	-	PUNCT
ejpam-5251	453	6	ii	ii	NOUN
ejpam-5251	453	7	.	.	PUNCT
ejpam-5251	454	1	analele	analele	PROPN
ejpam-5251	454	2	universitatii	universitatii	PROPN
ejpam-5251	454	3	“	"	PUNCT
ejpam-5251	454	4	ovidius	ovidius	PROPN
ejpam-5251	454	5	”	"	PUNCT
ejpam-5251	454	6	constanta	constanta	PROPN
ejpam-5251	454	7	seria	seria	PROPN
ejpam-5251	454	8	matematica	matematica	PROPN
ejpam-5251	454	9	,	,	PUNCT
ejpam-5251	454	10	2015	2015	NUM
ejpam-5251	454	11	.	.	PUNCT
ejpam-5251	455	1	[	[	X
ejpam-5251	455	2	22	22	NUM
ejpam-5251	455	3	]	]	X
ejpam-5251	455	4	y.	y.	NOUN
ejpam-5251	455	5	pabilona	pabilona	PROPN
ejpam-5251	455	6	and	and	CCONJ
ejpam-5251	455	7	h.	h.	PROPN
ejpam-5251	455	8	rara	rara	PROPN
ejpam-5251	455	9	.	.	PUNCT
ejpam-5251	456	1	connected	connect	VERB
ejpam-5251	456	2	hop	hop	NOUN
ejpam-5251	456	3	domination	domination	NOUN
ejpam-5251	456	4	in	in	ADP
ejpam-5251	456	5	graphs	graph	NOUN
ejpam-5251	456	6	under	under	ADP
ejpam-5251	456	7	some	some	DET
ejpam-5251	456	8	binary	binary	ADJ
ejpam-5251	456	9	operations	operation	NOUN
ejpam-5251	456	10	.	.	PUNCT
ejpam-5251	457	1	asian	asian	ADJ
ejpam-5251	457	2	-	-	PUNCT
ejpam-5251	457	3	european	european	ADJ
ejpam-5251	457	4	journal	journal	NOUN
ejpam-5251	457	5	of	of	ADP
ejpam-5251	457	6	mathematics	mathematic	NOUN
ejpam-5251	457	7	,	,	PUNCT
ejpam-5251	457	8	11	11	NUM
ejpam-5251	457	9	,	,	PUNCT
ejpam-5251	457	10	2017	2017	NUM
ejpam-5251	457	11	.	.	PUNCT
ejpam-5251	458	1	[	[	X
ejpam-5251	458	2	23	23	NUM
ejpam-5251	458	3	]	]	X
ejpam-5251	458	4	g.	g.	PROPN
ejpam-5251	458	5	salasalan	salasalan	NOUN
ejpam-5251	458	6	and	and	CCONJ
ejpam-5251	458	7	s.r	s.r	PROPN
ejpam-5251	458	8	.	.	PROPN
ejpam-5251	458	9	canoy	canoy	PROPN
ejpam-5251	458	10	jr	jr	PROPN
ejpam-5251	458	11	.	.	PROPN
ejpam-5251	458	12	global	global	PROPN
ejpam-5251	458	13	hop	hop	PROPN
ejpam-5251	458	14	domination	domination	PROPN
ejpam-5251	458	15	numbers	number	NOUN
ejpam-5251	458	16	of	of	ADP
ejpam-5251	458	17	graphs	graph	NOUN
ejpam-5251	458	18	.	.	PUNCT
ejpam-5251	459	1	european	european	ADJ
ejpam-5251	459	2	journal	journal	PROPN
ejpam-5251	459	3	of	of	ADP
ejpam-5251	459	4	pure	pure	ADJ
ejpam-5251	459	5	and	and	CCONJ
ejpam-5251	459	6	applied	applied	ADJ
ejpam-5251	459	7	mathematics	mathematic	NOUN
ejpam-5251	459	8	,	,	PUNCT
ejpam-5251	459	9	14:112–125	14:112–125	NUM
ejpam-5251	459	10	,	,	PUNCT
ejpam-5251	459	11	2021	2021	NUM
ejpam-5251	459	12	.	.	PUNCT
ejpam-5251	460	1	[	[	X
ejpam-5251	460	2	24	24	NUM
ejpam-5251	460	3	]	]	X
ejpam-5251	460	4	g.	g.	NOUN
ejpam-5251	460	5	salasalan	salasalan	NOUN
ejpam-5251	460	6	and	and	CCONJ
ejpam-5251	460	7	s.r	s.r	PROPN
ejpam-5251	460	8	.	.	PROPN
ejpam-5251	460	9	canoy	canoy	PROPN
ejpam-5251	460	10	jr	jr	PROPN
ejpam-5251	460	11	.	.	PUNCT
ejpam-5251	460	12	revisiting	revisit	VERB
ejpam-5251	460	13	domination	domination	NOUN
ejpam-5251	460	14	,	,	PUNCT
ejpam-5251	460	15	hop	hop	NOUN
ejpam-5251	460	16	domination	domination	NOUN
ejpam-5251	460	17	,	,	PUNCT
ejpam-5251	460	18	and	and	CCONJ
ejpam-5251	460	19	global	global	ADJ
ejpam-5251	460	20	hop	hop	NOUN
ejpam-5251	460	21	domination	domination	NOUN
ejpam-5251	460	22	in	in	ADP
ejpam-5251	460	23	graphs	graph	NOUN
ejpam-5251	460	24	.	.	PUNCT
ejpam-5251	461	1	european	european	ADJ
ejpam-5251	461	2	journal	journal	PROPN
ejpam-5251	461	3	of	of	ADP
ejpam-5251	461	4	pure	pure	ADJ
ejpam-5251	461	5	and	and	CCONJ
ejpam-5251	461	6	applied	applied	ADJ
ejpam-5251	461	7	mathematics	mathematic	NOUN
ejpam-5251	461	8	,	,	PUNCT
ejpam-5251	461	9	14:1415–1428	14:1415–1428	NUM
ejpam-5251	461	10	,	,	PUNCT
ejpam-5251	461	11	2021	2021	NUM
ejpam-5251	461	12	.	.	PUNCT
ejpam-5251	462	1	references	reference	NOUN
ejpam-5251	462	2	1750	1750	NUM
ejpam-5251	462	3	[	[	X
ejpam-5251	462	4	25	25	NUM
ejpam-5251	462	5	]	]	X
ejpam-5251	462	6	c.j	c.j	PROPN
ejpam-5251	462	7	.	.	PROPN
ejpam-5251	462	8	saromines	saromine	NOUN
ejpam-5251	462	9	and	and	CCONJ
ejpam-5251	462	10	s.r	s.r	PROPN
ejpam-5251	462	11	.	.	PROPN
ejpam-5251	462	12	canoy	canoy	PROPN
ejpam-5251	462	13	.	.	PUNCT
ejpam-5251	463	1	outer	outer	ADV
ejpam-5251	463	2	-	-	PUNCT
ejpam-5251	463	3	connected	connect	VERB
ejpam-5251	463	4	hop	hop	NOUN
ejpam-5251	463	5	dominating	dominating	NOUN
ejpam-5251	463	6	sets	set	NOUN
ejpam-5251	463	7	in	in	ADP
ejpam-5251	463	8	graphs	graph	NOUN
ejpam-5251	463	9	.	.	PUNCT
ejpam-5251	464	1	european	european	ADJ
ejpam-5251	464	2	journal	journal	PROPN
ejpam-5251	464	3	of	of	ADP
ejpam-5251	464	4	pure	pure	ADJ
ejpam-5251	464	5	and	and	CCONJ
ejpam-5251	464	6	applied	applied	ADJ
ejpam-5251	464	7	mathematics	mathematic	NOUN
ejpam-5251	464	8	,	,	PUNCT
ejpam-5251	464	9	15:1966–1981	15:1966–1981	NUM
ejpam-5251	464	10	,	,	PUNCT
ejpam-5251	464	11	2022	2022	NUM
ejpam-5251	464	12	.	.	PUNCT
ejpam-5251	465	1	[	[	X
ejpam-5251	465	2	26	26	NUM
ejpam-5251	465	3	]	]	X
ejpam-5251	465	4	c.j	c.j	PROPN
ejpam-5251	465	5	.	.	PROPN
ejpam-5251	465	6	saromines	saromine	NOUN
ejpam-5251	465	7	and	and	CCONJ
ejpam-5251	465	8	s.r	s.r	PROPN
ejpam-5251	465	9	.	.	PROPN
ejpam-5251	465	10	canoy	canoy	PROPN
ejpam-5251	465	11	.	.	PUNCT
ejpam-5251	466	1	another	another	DET
ejpam-5251	466	2	look	look	NOUN
ejpam-5251	466	3	at	at	ADP
ejpam-5251	466	4	geodetic	geodetic	ADJ
ejpam-5251	466	5	hop	hop	NOUN
ejpam-5251	466	6	domination	domination	NOUN
ejpam-5251	466	7	in	in	ADP
ejpam-5251	466	8	a	a	DET
ejpam-5251	466	9	graph	graph	NOUN
ejpam-5251	466	10	.	.	PUNCT
ejpam-5251	467	1	european	european	ADJ
ejpam-5251	467	2	journal	journal	PROPN
ejpam-5251	467	3	of	of	ADP
ejpam-5251	467	4	pure	pure	ADJ
ejpam-5251	467	5	and	and	CCONJ
ejpam-5251	467	6	applied	applied	ADJ
ejpam-5251	467	7	mathematics	mathematic	NOUN
ejpam-5251	467	8	,	,	PUNCT
ejpam-5251	467	9	2023	2023	NUM
ejpam-5251	467	10	.	.	PUNCT
ejpam-5251	468	1	[	[	X
ejpam-5251	468	2	27	27	NUM
ejpam-5251	468	3	]	]	X
ejpam-5251	468	4	c.j	c.j	PROPN
ejpam-5251	468	5	.	.	PROPN
ejpam-5251	468	6	saromines	saromine	NOUN
ejpam-5251	468	7	and	and	CCONJ
ejpam-5251	468	8	s.r	s.r	PROPN
ejpam-5251	468	9	.	.	PROPN
ejpam-5251	468	10	canoy	canoy	PROPN
ejpam-5251	468	11	.	.	PUNCT
ejpam-5251	469	1	geodetic	geodetic	ADJ
ejpam-5251	469	2	hop	hop	NOUN
ejpam-5251	469	3	dominating	dominating	NOUN
ejpam-5251	469	4	sets	set	NOUN
ejpam-5251	469	5	in	in	ADP
ejpam-5251	469	6	a	a	DET
ejpam-5251	469	7	graph	graph	NOUN
ejpam-5251	469	8	.	.	PUNCT
ejpam-5251	470	1	european	european	ADJ
ejpam-5251	470	2	journal	journal	PROPN
ejpam-5251	470	3	of	of	ADP
ejpam-5251	470	4	pure	pure	ADJ
ejpam-5251	470	5	and	and	CCONJ
ejpam-5251	470	6	applied	applied	ADJ
ejpam-5251	470	7	mathematics	mathematic	NOUN
ejpam-5251	470	8	,	,	PUNCT
ejpam-5251	470	9	2023	2023	NUM
ejpam-5251	470	10	.	.	PUNCT
ejpam-5251	471	1	[	[	X
ejpam-5251	471	2	28	28	NUM
ejpam-5251	471	3	]	]	X
ejpam-5251	471	4	t.	t.	NOUN
ejpam-5251	471	5	tacbobo	tacbobo	NOUN
ejpam-5251	471	6	,	,	PUNCT
ejpam-5251	471	7	f.p	f.p	PROPN
ejpam-5251	471	8	.	.	PROPN
ejpam-5251	471	9	jamil	jamil	PROPN
ejpam-5251	471	10	,	,	PUNCT
ejpam-5251	471	11	and	and	CCONJ
ejpam-5251	471	12	s.r	s.r	PROPN
ejpam-5251	471	13	.	.	PROPN
ejpam-5251	471	14	canoy	canoy	PROPN
ejpam-5251	471	15	jr	jr	PROPN
ejpam-5251	471	16	.	.	PROPN
ejpam-5251	471	17	monophonic	monophonic	ADJ
ejpam-5251	471	18	and	and	CCONJ
ejpam-5251	471	19	geodetic	geodetic	ADJ
ejpam-5251	471	20	dominations	domination	NOUN
ejpam-5251	471	21	in	in	ADP
ejpam-5251	471	22	the	the	DET
ejpam-5251	471	23	join	join	NOUN
ejpam-5251	471	24	,	,	PUNCT
ejpam-5251	471	25	corona	corona	NOUN
ejpam-5251	471	26	and	and	CCONJ
ejpam-5251	471	27	composition	composition	NOUN
ejpam-5251	471	28	of	of	ADP
ejpam-5251	471	29	graphs	graph	NOUN
ejpam-5251	471	30	.	.	PUNCT
ejpam-5251	472	1	ars	ar	NOUN
ejpam-5251	472	2	combinatoria	combinatoria	PROPN
ejpam-5251	472	3	,	,	PUNCT
ejpam-5251	472	4	112:13–31	112:13–31	NUM
ejpam-5251	472	5	,	,	PUNCT
ejpam-5251	472	6	2013	2013	NUM
ejpam-5251	472	7	.	.	PUNCT