id	sid	tid	token	lemma	pos
ejpam-4646	1	1	european	european	PROPN
ejpam-4646	1	2	journal	journal	PROPN
ejpam-4646	1	3	of	of	ADP
ejpam-4646	1	4	pure	pure	ADJ
ejpam-4646	1	5	and	and	CCONJ
ejpam-4646	1	6	applied	apply	VERB
ejpam-4646	1	7	mathematics	mathematic	NOUN
ejpam-4646	1	8	vol	vol	NOUN
ejpam-4646	1	9	.	.	PUNCT
ejpam-4646	2	1	16	16	NUM
ejpam-4646	2	2	,	,	PUNCT
ejpam-4646	2	3	no	no	INTJ
ejpam-4646	2	4	.	.	NOUN
ejpam-4646	2	5	1	1	NUM
ejpam-4646	2	6	,	,	PUNCT
ejpam-4646	2	7	2023	2023	NUM
ejpam-4646	2	8	,	,	PUNCT
ejpam-4646	2	9	5	5	NUM
ejpam-4646	2	10	-	-	SYM
ejpam-4646	2	11	17	17	NUM
ejpam-4646	2	12	issn	issn	PROPN
ejpam-4646	2	13	1307	1307	NUM
ejpam-4646	2	14	-	-	SYM
ejpam-4646	2	15	5543	5543	NUM
ejpam-4646	2	16	–	–	PUNCT
ejpam-4646	2	17	ejpam.com	ejpam.com	X
ejpam-4646	2	18	published	publish	VERB
ejpam-4646	2	19	by	by	ADP
ejpam-4646	2	20	new	new	PROPN
ejpam-4646	2	21	york	york	PROPN
ejpam-4646	2	22	business	business	PROPN
ejpam-4646	2	23	global	global	PROPN
ejpam-4646	2	24	geodetic	geodetic	ADJ
ejpam-4646	2	25	hop	hop	NOUN
ejpam-4646	2	26	dominating	dominating	NOUN
ejpam-4646	2	27	sets	set	NOUN
ejpam-4646	2	28	in	in	ADP
ejpam-4646	2	29	a	a	DET
ejpam-4646	2	30	graph	graph	NOUN
ejpam-4646	2	31	chrisley	chrisley	PROPN
ejpam-4646	2	32	jade	jade	PROPN
ejpam-4646	2	33	c.	c.	PROPN
ejpam-4646	2	34	saromines	saromine	VERB
ejpam-4646	2	35	1,∗	1,∗	PROPN
ejpam-4646	2	36	,	,	PUNCT
ejpam-4646	2	37	sergio	sergio	PROPN
ejpam-4646	2	38	r.	r.	PROPN
ejpam-4646	2	39	canoy	canoy	PROPN
ejpam-4646	2	40	,	,	PUNCT
ejpam-4646	2	41	jr.1	jr.1	PROPN
ejpam-4646	2	42	1	1	NUM
ejpam-4646	2	43	department	department	NOUN
ejpam-4646	2	44	of	of	ADP
ejpam-4646	2	45	mathematics	mathematic	NOUN
ejpam-4646	2	46	and	and	CCONJ
ejpam-4646	2	47	statistics	statistic	NOUN
ejpam-4646	2	48	,	,	PUNCT
ejpam-4646	2	49	college	college	NOUN
ejpam-4646	2	50	of	of	ADP
ejpam-4646	2	51	science	science	NOUN
ejpam-4646	2	52	and	and	CCONJ
ejpam-4646	2	53	mathematics	mathematic	NOUN
ejpam-4646	2	54	,	,	PUNCT
ejpam-4646	2	55	center	center	NOUN
ejpam-4646	2	56	for	for	ADP
ejpam-4646	2	57	graph	graph	NOUN
ejpam-4646	2	58	theory	theory	NOUN
ejpam-4646	2	59	,	,	PUNCT
ejpam-4646	2	60	algebra	algebra	NOUN
ejpam-4646	2	61	and	and	CCONJ
ejpam-4646	2	62	analysis	analysis	NOUN
ejpam-4646	2	63	-	-	PUNCT
ejpam-4646	2	64	prism	prism	NOUN
ejpam-4646	2	65	,	,	PUNCT
ejpam-4646	2	66	msu	msu	PROPN
ejpam-4646	2	67	-	-	PUNCT
ejpam-4646	2	68	iligan	iligan	PROPN
ejpam-4646	2	69	institute	institute	PROPN
ejpam-4646	2	70	of	of	ADP
ejpam-4646	2	71	technology	technology	PROPN
ejpam-4646	2	72	,	,	PUNCT
ejpam-4646	2	73	9200	9200	NUM
ejpam-4646	2	74	iligan	iligan	ADJ
ejpam-4646	2	75	city	city	NOUN
ejpam-4646	2	76	,	,	PUNCT
ejpam-4646	2	77	philippines	philippine	NOUN
ejpam-4646	2	78	abstract	abstract	ADJ
ejpam-4646	2	79	.	.	PUNCT
ejpam-4646	3	1	let	let	VERB
ejpam-4646	3	2	g	g	PRON
ejpam-4646	3	3	be	be	AUX
ejpam-4646	3	4	an	an	DET
ejpam-4646	3	5	undirected	undirected	ADJ
ejpam-4646	3	6	graph	graph	NOUN
ejpam-4646	3	7	with	with	ADP
ejpam-4646	3	8	vertex	vertex	NOUN
ejpam-4646	3	9	and	and	CCONJ
ejpam-4646	3	10	edge	edge	NOUN
ejpam-4646	3	11	sets	set	NOUN
ejpam-4646	3	12	v	v	ADP
ejpam-4646	3	13	(	(	PUNCT
ejpam-4646	3	14	g	g	NOUN
ejpam-4646	3	15	)	)	PUNCT
ejpam-4646	3	16	and	and	CCONJ
ejpam-4646	3	17	e(g	e(g	PROPN
ejpam-4646	3	18	)	)	PUNCT
ejpam-4646	3	19	,	,	PUNCT
ejpam-4646	3	20	respectively	respectively	ADV
ejpam-4646	3	21	.	.	PUNCT
ejpam-4646	4	1	a	a	DET
ejpam-4646	4	2	subset	subset	NOUN
ejpam-4646	4	3	s	s	NOUN
ejpam-4646	4	4	of	of	ADP
ejpam-4646	4	5	vertices	vertex	NOUN
ejpam-4646	4	6	of	of	ADP
ejpam-4646	4	7	g	g	PROPN
ejpam-4646	4	8	is	be	AUX
ejpam-4646	4	9	a	a	DET
ejpam-4646	4	10	geodetic	geodetic	ADJ
ejpam-4646	4	11	hop	hop	NOUN
ejpam-4646	4	12	dominating	dominating	NOUN
ejpam-4646	4	13	set	set	NOUN
ejpam-4646	4	14	if	if	SCONJ
ejpam-4646	4	15	it	it	PRON
ejpam-4646	4	16	is	be	AUX
ejpam-4646	4	17	both	both	CCONJ
ejpam-4646	4	18	a	a	DET
ejpam-4646	4	19	geodetic	geodetic	ADJ
ejpam-4646	4	20	and	and	CCONJ
ejpam-4646	4	21	a	a	DET
ejpam-4646	4	22	hop	hop	NOUN
ejpam-4646	4	23	dominating	dominating	NOUN
ejpam-4646	4	24	set	set	NOUN
ejpam-4646	4	25	.	.	PUNCT
ejpam-4646	5	1	the	the	DET
ejpam-4646	5	2	geodetic	geodetic	ADJ
ejpam-4646	5	3	hop	hop	NOUN
ejpam-4646	5	4	domination	domination	NOUN
ejpam-4646	5	5	number	number	NOUN
ejpam-4646	5	6	of	of	ADP
ejpam-4646	5	7	g	g	PROPN
ejpam-4646	5	8	,	,	PUNCT
ejpam-4646	5	9	γhg(g	γhg(g	PROPN
ejpam-4646	5	10	)	)	PUNCT
ejpam-4646	5	11	,	,	PUNCT
ejpam-4646	5	12	is	be	AUX
ejpam-4646	5	13	the	the	DET
ejpam-4646	5	14	minimum	minimum	ADJ
ejpam-4646	5	15	cardinality	cardinality	NOUN
ejpam-4646	5	16	among	among	ADP
ejpam-4646	5	17	all	all	DET
ejpam-4646	5	18	geodetic	geodetic	ADJ
ejpam-4646	5	19	hop	hop	NOUN
ejpam-4646	5	20	dominating	dominating	NOUN
ejpam-4646	5	21	sets	set	NOUN
ejpam-4646	5	22	in	in	ADP
ejpam-4646	5	23	g.	g.	PROPN
ejpam-4646	5	24	geodetic	geodetic	PROPN
ejpam-4646	5	25	hop	hop	NOUN
ejpam-4646	5	26	dominating	dominating	NOUN
ejpam-4646	5	27	sets	set	NOUN
ejpam-4646	5	28	in	in	ADP
ejpam-4646	5	29	a	a	DET
ejpam-4646	5	30	graph	graph	NOUN
ejpam-4646	5	31	resulting	result	VERB
ejpam-4646	5	32	from	from	ADP
ejpam-4646	5	33	some	some	DET
ejpam-4646	5	34	binary	binary	ADJ
ejpam-4646	5	35	operations	operation	NOUN
ejpam-4646	5	36	have	have	AUX
ejpam-4646	5	37	been	be	AUX
ejpam-4646	5	38	characterized	characterize	VERB
ejpam-4646	5	39	.	.	PUNCT
ejpam-4646	6	1	these	these	DET
ejpam-4646	6	2	characterizations	characterization	NOUN
ejpam-4646	6	3	have	have	AUX
ejpam-4646	6	4	been	be	AUX
ejpam-4646	6	5	used	use	VERB
ejpam-4646	6	6	to	to	PART
ejpam-4646	6	7	determine	determine	VERB
ejpam-4646	6	8	some	some	DET
ejpam-4646	6	9	tight	tight	ADJ
ejpam-4646	6	10	bounds	bound	NOUN
ejpam-4646	6	11	for	for	ADP
ejpam-4646	6	12	the	the	DET
ejpam-4646	6	13	geodetic	geodetic	ADJ
ejpam-4646	6	14	hop	hop	NOUN
ejpam-4646	6	15	domination	domination	NOUN
ejpam-4646	6	16	number	number	NOUN
ejpam-4646	6	17	of	of	ADP
ejpam-4646	6	18	each	each	PRON
ejpam-4646	6	19	of	of	ADP
ejpam-4646	6	20	the	the	DET
ejpam-4646	6	21	graphs	graph	NOUN
ejpam-4646	6	22	considered	consider	VERB
ejpam-4646	6	23	.	.	PUNCT
ejpam-4646	7	1	2020	2020	NUM
ejpam-4646	7	2	mathematics	mathematic	NOUN
ejpam-4646	7	3	subject	subject	NOUN
ejpam-4646	7	4	classifications	classification	NOUN
ejpam-4646	7	5	:	:	PUNCT
ejpam-4646	7	6	05c69	05c69	X
ejpam-4646	7	7	key	key	ADJ
ejpam-4646	7	8	words	word	NOUN
ejpam-4646	7	9	and	and	CCONJ
ejpam-4646	7	10	phrases	phrase	NOUN
ejpam-4646	7	11	:	:	PUNCT
ejpam-4646	7	12	geodetic	geodetic	ADJ
ejpam-4646	7	13	domination	domination	NOUN
ejpam-4646	7	14	,	,	PUNCT
ejpam-4646	7	15	hop	hop	NOUN
ejpam-4646	7	16	domination	domination	NOUN
ejpam-4646	7	17	,	,	PUNCT
ejpam-4646	7	18	corona	corona	PROPN
ejpam-4646	7	19	,	,	PUNCT
ejpam-4646	7	20	lexicographic	lexicographic	ADJ
ejpam-4646	7	21	1	1	NUM
ejpam-4646	7	22	.	.	PUNCT
ejpam-4646	8	1	introduction	introduction	NOUN
ejpam-4646	8	2	frank	frank	PROPN
ejpam-4646	8	3	harary	harary	PROPN
ejpam-4646	8	4	et	et	PROPN
ejpam-4646	8	5	al	al	PROPN
ejpam-4646	8	6	.	.	PUNCT
ejpam-4646	9	1	in	in	ADP
ejpam-4646	9	2	[	[	X
ejpam-4646	9	3	10	10	NUM
ejpam-4646	9	4	]	]	PUNCT
ejpam-4646	9	5	introduced	introduce	VERB
ejpam-4646	9	6	a	a	DET
ejpam-4646	9	7	graph	graph	NOUN
ejpam-4646	9	8	theoretical	theoretical	ADJ
ejpam-4646	9	9	parameter	parameter	NOUN
ejpam-4646	9	10	called	call	VERB
ejpam-4646	9	11	geodetic	geodetic	ADJ
ejpam-4646	9	12	number	number	NOUN
ejpam-4646	9	13	of	of	ADP
ejpam-4646	9	14	a	a	DET
ejpam-4646	9	15	graph	graph	NOUN
ejpam-4646	9	16	.	.	PUNCT
ejpam-4646	10	1	geodetic	geodetic	ADJ
ejpam-4646	10	2	sets	set	NOUN
ejpam-4646	10	3	and	and	CCONJ
ejpam-4646	10	4	geodetic	geodetic	ADJ
ejpam-4646	10	5	numbers	number	NOUN
ejpam-4646	10	6	are	be	AUX
ejpam-4646	10	7	studied	study	VERB
ejpam-4646	10	8	further	far	ADV
ejpam-4646	10	9	in	in	ADP
ejpam-4646	10	10	chartrand	chartrand	NOUN
ejpam-4646	11	1	[	[	X
ejpam-4646	11	2	7	7	NUM
ejpam-4646	11	3	]	]	PUNCT
ejpam-4646	11	4	.	.	PUNCT
ejpam-4646	12	1	in	in	ADP
ejpam-4646	12	2	2011	2011	NUM
ejpam-4646	12	3	,	,	PUNCT
ejpam-4646	12	4	h.	h.	PROPN
ejpam-4646	12	5	escuadro	escuadro	PROPN
ejpam-4646	12	6	et	et	PROPN
ejpam-4646	12	7	al	al	PROPN
ejpam-4646	12	8	.	.	PUNCT
ejpam-4646	13	1	(	(	PUNCT
ejpam-4646	13	2	see	see	VERB
ejpam-4646	13	3	[	[	X
ejpam-4646	13	4	8	8	NUM
ejpam-4646	13	5	]	]	PUNCT
ejpam-4646	13	6	)	)	PUNCT
ejpam-4646	13	7	introduced	introduce	VERB
ejpam-4646	13	8	the	the	DET
ejpam-4646	13	9	concept	concept	NOUN
ejpam-4646	13	10	of	of	ADP
ejpam-4646	13	11	geodetic	geodetic	ADJ
ejpam-4646	13	12	domination	domination	NOUN
ejpam-4646	13	13	in	in	ADP
ejpam-4646	13	14	graphs	graph	NOUN
ejpam-4646	13	15	.	.	PUNCT
ejpam-4646	14	1	after	after	ADP
ejpam-4646	14	2	their	their	PRON
ejpam-4646	14	3	introduction	introduction	NOUN
ejpam-4646	14	4	,	,	PUNCT
ejpam-4646	14	5	more	more	ADJ
ejpam-4646	14	6	studies	study	NOUN
ejpam-4646	14	7	have	have	AUX
ejpam-4646	14	8	been	be	AUX
ejpam-4646	14	9	done	do	VERB
ejpam-4646	14	10	on	on	ADP
ejpam-4646	14	11	the	the	DET
ejpam-4646	14	12	concepts	concept	NOUN
ejpam-4646	14	13	.	.	PUNCT
ejpam-4646	15	1	some	some	PRON
ejpam-4646	15	2	of	of	ADP
ejpam-4646	15	3	the	the	DET
ejpam-4646	15	4	studies	study	NOUN
ejpam-4646	15	5	dealing	deal	VERB
ejpam-4646	15	6	with	with	ADP
ejpam-4646	15	7	geodetic	geodetic	ADJ
ejpam-4646	15	8	sets	set	NOUN
ejpam-4646	15	9	,	,	PUNCT
ejpam-4646	15	10	geodetic	geodetic	ADJ
ejpam-4646	15	11	number	number	NOUN
ejpam-4646	15	12	,	,	PUNCT
ejpam-4646	15	13	and	and	CCONJ
ejpam-4646	15	14	geodetic	geodetic	ADJ
ejpam-4646	15	15	dominating	dominating	NOUN
ejpam-4646	15	16	sets	set	NOUN
ejpam-4646	15	17	can	can	AUX
ejpam-4646	15	18	be	be	AUX
ejpam-4646	15	19	found	find	VERB
ejpam-4646	15	20	in	in	ADP
ejpam-4646	15	21	[	[	X
ejpam-4646	15	22	4	4	NUM
ejpam-4646	15	23	]	]	PUNCT
ejpam-4646	15	24	,	,	PUNCT
ejpam-4646	15	25	[	[	X
ejpam-4646	15	26	5	5	NUM
ejpam-4646	15	27	]	]	PUNCT
ejpam-4646	15	28	,	,	PUNCT
ejpam-4646	15	29	[	[	X
ejpam-4646	15	30	6	6	NUM
ejpam-4646	15	31	]	]	PUNCT
ejpam-4646	15	32	,	,	PUNCT
ejpam-4646	15	33	[	[	X
ejpam-4646	15	34	7	7	NUM
ejpam-4646	15	35	]	]	PUNCT
ejpam-4646	15	36	,	,	PUNCT
ejpam-4646	15	37	[	[	X
ejpam-4646	15	38	8	8	NUM
ejpam-4646	15	39	]	]	PUNCT
ejpam-4646	15	40	,	,	PUNCT
ejpam-4646	15	41	[	[	X
ejpam-4646	15	42	9	9	NUM
ejpam-4646	15	43	]	]	PUNCT
ejpam-4646	15	44	,	,	PUNCT
ejpam-4646	15	45	[	[	X
ejpam-4646	15	46	10	10	NUM
ejpam-4646	15	47	]	]	PUNCT
ejpam-4646	15	48	,	,	PUNCT
ejpam-4646	15	49	[	[	X
ejpam-4646	15	50	14	14	NUM
ejpam-4646	15	51	]	]	PUNCT
ejpam-4646	15	52	,	,	PUNCT
ejpam-4646	15	53	and	and	CCONJ
ejpam-4646	15	54	[	[	X
ejpam-4646	15	55	24	24	NUM
ejpam-4646	15	56	]	]	PUNCT
ejpam-4646	15	57	.	.	PUNCT
ejpam-4646	16	1	the	the	DET
ejpam-4646	16	2	concept	concept	NOUN
ejpam-4646	16	3	of	of	ADP
ejpam-4646	16	4	hop	hop	NOUN
ejpam-4646	16	5	domination	domination	NOUN
ejpam-4646	16	6	in	in	ADP
ejpam-4646	16	7	graphs	graph	NOUN
ejpam-4646	16	8	was	be	AUX
ejpam-4646	16	9	introduced	introduce	VERB
ejpam-4646	16	10	and	and	CCONJ
ejpam-4646	16	11	initially	initially	ADV
ejpam-4646	16	12	investigated	investigate	VERB
ejpam-4646	16	13	by	by	ADP
ejpam-4646	16	14	natarajan	natarajan	PROPN
ejpam-4646	16	15	and	and	CCONJ
ejpam-4646	16	16	s.	s.	PROPN
ejpam-4646	16	17	k.	k.	PROPN
ejpam-4646	16	18	ayyaswamy	ayyaswamy	PROPN
ejpam-4646	17	1	[	[	X
ejpam-4646	17	2	19	19	NUM
ejpam-4646	17	3	]	]	PUNCT
ejpam-4646	17	4	.	.	PUNCT
ejpam-4646	18	1	the	the	DET
ejpam-4646	18	2	study	study	NOUN
ejpam-4646	18	3	was	be	AUX
ejpam-4646	18	4	then	then	ADV
ejpam-4646	18	5	followed	follow	VERB
ejpam-4646	18	6	by	by	ADP
ejpam-4646	18	7	numerous	numerous	ADJ
ejpam-4646	18	8	studies	study	NOUN
ejpam-4646	18	9	on	on	ADP
ejpam-4646	18	10	the	the	DET
ejpam-4646	18	11	topic	topic	NOUN
ejpam-4646	18	12	.	.	PUNCT
ejpam-4646	19	1	in	in	ADP
ejpam-4646	19	2	particular	particular	ADJ
ejpam-4646	19	3	,	,	PUNCT
ejpam-4646	19	4	a	a	DET
ejpam-4646	19	5	lot	lot	NOUN
ejpam-4646	19	6	of	of	ADP
ejpam-4646	19	7	variations	variation	NOUN
ejpam-4646	19	8	of	of	ADP
ejpam-4646	19	9	the	the	DET
ejpam-4646	19	10	concept	concept	NOUN
ejpam-4646	19	11	have	have	AUX
ejpam-4646	19	12	been	be	AUX
ejpam-4646	19	13	introduced	introduce	VERB
ejpam-4646	19	14	and	and	CCONJ
ejpam-4646	19	15	studied	study	VERB
ejpam-4646	19	16	(	(	PUNCT
ejpam-4646	19	17	see	see	VERB
ejpam-4646	19	18	[	[	X
ejpam-4646	19	19	2	2	NUM
ejpam-4646	19	20	]	]	PUNCT
ejpam-4646	19	21	,	,	PUNCT
ejpam-4646	19	22	[	[	X
ejpam-4646	19	23	3	3	NUM
ejpam-4646	19	24	]	]	PUNCT
ejpam-4646	19	25	,	,	PUNCT
ejpam-4646	19	26	[	[	X
ejpam-4646	19	27	11	11	NUM
ejpam-4646	19	28	]	]	PUNCT
ejpam-4646	19	29	,	,	PUNCT
ejpam-4646	20	1	[	[	X
ejpam-4646	20	2	12	12	NUM
ejpam-4646	20	3	]	]	PUNCT
ejpam-4646	20	4	,	,	PUNCT
ejpam-4646	20	5	[	[	X
ejpam-4646	20	6	13	13	NUM
ejpam-4646	20	7	]	]	PUNCT
ejpam-4646	20	8	,	,	PUNCT
ejpam-4646	20	9	[	[	X
ejpam-4646	20	10	15	15	NUM
ejpam-4646	20	11	]	]	PUNCT
ejpam-4646	20	12	,	,	PUNCT
ejpam-4646	20	13	[	[	X
ejpam-4646	20	14	16	16	NUM
ejpam-4646	20	15	]	]	PUNCT
ejpam-4646	20	16	,	,	PUNCT
ejpam-4646	20	17	[	[	X
ejpam-4646	20	18	18	18	NUM
ejpam-4646	20	19	]	]	PUNCT
ejpam-4646	20	20	,	,	PUNCT
ejpam-4646	20	21	[	[	X
ejpam-4646	20	22	20	20	NUM
ejpam-4646	20	23	]	]	PUNCT
ejpam-4646	20	24	,	,	PUNCT
ejpam-4646	20	25	[	[	X
ejpam-4646	20	26	21	21	NUM
ejpam-4646	20	27	]	]	PUNCT
ejpam-4646	20	28	,	,	PUNCT
ejpam-4646	20	29	[	[	X
ejpam-4646	20	30	17	17	NUM
ejpam-4646	20	31	]	]	PUNCT
ejpam-4646	20	32	,	,	PUNCT
ejpam-4646	21	1	[	[	X
ejpam-4646	21	2	22	22	NUM
ejpam-4646	21	3	]	]	PUNCT
ejpam-4646	21	4	,	,	PUNCT
ejpam-4646	21	5	and	and	CCONJ
ejpam-4646	21	6	[	[	X
ejpam-4646	21	7	23	23	NUM
ejpam-4646	21	8	]	]	PUNCT
ejpam-4646	21	9	)	)	PUNCT
ejpam-4646	21	10	.	.	PUNCT
ejpam-4646	22	1	recently	recently	ADV
ejpam-4646	22	2	,	,	PUNCT
ejpam-4646	22	3	anusha	anusha	VERB
ejpam-4646	22	4	and	and	CCONJ
ejpam-4646	22	5	robin	robin	PROPN
ejpam-4646	23	1	[	[	X
ejpam-4646	23	2	1	1	X
ejpam-4646	23	3	]	]	PUNCT
ejpam-4646	23	4	introduced	introduce	VERB
ejpam-4646	23	5	the	the	DET
ejpam-4646	23	6	concept	concept	NOUN
ejpam-4646	23	7	of	of	ADP
ejpam-4646	23	8	geodetic	geodetic	ADJ
ejpam-4646	23	9	hop	hop	NOUN
ejpam-4646	23	10	domination	domination	NOUN
ejpam-4646	23	11	and	and	CCONJ
ejpam-4646	23	12	studied	study	VERB
ejpam-4646	23	13	it	it	PRON
ejpam-4646	23	14	for	for	ADP
ejpam-4646	23	15	join	join	NOUN
ejpam-4646	23	16	and	and	CCONJ
ejpam-4646	23	17	corona	corona	NOUN
ejpam-4646	23	18	of	of	ADP
ejpam-4646	23	19	graphs	graph	NOUN
ejpam-4646	23	20	.	.	PUNCT
ejpam-4646	24	1	in	in	ADP
ejpam-4646	24	2	this	this	DET
ejpam-4646	24	3	present	present	ADJ
ejpam-4646	24	4	paper	paper	NOUN
ejpam-4646	24	5	,	,	PUNCT
ejpam-4646	24	6	we	we	PRON
ejpam-4646	24	7	revisit	revisit	VERB
ejpam-4646	24	8	the	the	DET
ejpam-4646	24	9	concept	concept	NOUN
ejpam-4646	24	10	of	of	ADP
ejpam-4646	24	11	geodetic	geodetic	ADJ
ejpam-4646	24	12	hop	hop	NOUN
ejpam-4646	24	13	domination	domination	NOUN
ejpam-4646	24	14	and	and	CCONJ
ejpam-4646	24	15	give	give	VERB
ejpam-4646	24	16	further	further	ADJ
ejpam-4646	24	17	results	result	NOUN
ejpam-4646	24	18	of	of	ADP
ejpam-4646	24	19	the	the	DET
ejpam-4646	24	20	new	new	ADJ
ejpam-4646	24	21	parameter	parameter	NOUN
ejpam-4646	24	22	.	.	PUNCT
ejpam-4646	25	1	∗corresponding	∗corresponde	VERB
ejpam-4646	25	2	author	author	NOUN
ejpam-4646	25	3	.	.	PUNCT
ejpam-4646	26	1	doi	doi	NOUN
ejpam-4646	26	2	:	:	PUNCT
ejpam-4646	26	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4646	https://doi.org/10.29020/nybg.ejpam.v16i1.4646	NOUN
ejpam-4646	26	4	email	email	NOUN
ejpam-4646	26	5	addresses	address	NOUN
ejpam-4646	26	6	:	:	PUNCT
ejpam-4646	26	7	chrisleyjade.saromines@g.msuiit.edu.ph	chrisleyjade.saromines@g.msuiit.edu.ph	PROPN
ejpam-4646	26	8	(	(	PUNCT
ejpam-4646	26	9	c.j	c.j	NOUN
ejpam-4646	26	10	.	.	PROPN
ejpam-4646	26	11	saromines	saromine	NOUN
ejpam-4646	26	12	)	)	PUNCT
ejpam-4646	26	13	,	,	PUNCT
ejpam-4646	26	14	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4646	26	15	(	(	PUNCT
ejpam-4646	26	16	s.	s.	PROPN
ejpam-4646	26	17	canoy	canoy	PROPN
ejpam-4646	26	18	,	,	PUNCT
ejpam-4646	26	19	jr	jr	PROPN
ejpam-4646	26	20	.	.	PUNCT
ejpam-4646	26	21	)	)	PUNCT
ejpam-4646	26	22	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4646	27	1	5	5	NUM
ejpam-4646	28	1	©	©	PROPN
ejpam-4646	28	2	2023	2023	NUM
ejpam-4646	28	3	ejpam	ejpam	NOUN
ejpam-4646	28	4	all	all	DET
ejpam-4646	28	5	rights	right	NOUN
ejpam-4646	28	6	reserved	reserve	VERB
ejpam-4646	28	7	.	.	PUNCT
ejpam-4646	29	1	c.j	c.j	PROPN
ejpam-4646	29	2	.	.	PROPN
ejpam-4646	29	3	saromines	saromines	PROPN
ejpam-4646	29	4	,	,	PUNCT
ejpam-4646	29	5	s.	s.	PROPN
ejpam-4646	29	6	canoy	canoy	PROPN
ejpam-4646	29	7	,	,	PUNCT
ejpam-4646	29	8	jr	jr	PROPN
ejpam-4646	29	9	.	.	PROPN
ejpam-4646	29	10	,	,	PUNCT
ejpam-4646	29	11	/	/	SYM
ejpam-4646	29	12	eur	eur	NOUN
ejpam-4646	29	13	.	.	PUNCT
ejpam-4646	30	1	j.	j.	PROPN
ejpam-4646	30	2	pure	pure	PROPN
ejpam-4646	30	3	appl	appl	PROPN
ejpam-4646	30	4	.	.	PROPN
ejpam-4646	30	5	math	math	PROPN
ejpam-4646	30	6	,	,	PUNCT
ejpam-4646	30	7	16	16	NUM
ejpam-4646	30	8	(	(	PUNCT
ejpam-4646	30	9	1	1	NUM
ejpam-4646	30	10	)	)	PUNCT
ejpam-4646	30	11	(	(	PUNCT
ejpam-4646	30	12	2023	2023	NUM
ejpam-4646	30	13	)	)	PUNCT
ejpam-4646	30	14	,	,	PUNCT
ejpam-4646	30	15	5	5	NUM
ejpam-4646	30	16	-	-	SYM
ejpam-4646	30	17	17	17	NUM
ejpam-4646	30	18	6	6	NUM
ejpam-4646	30	19	2	2	NUM
ejpam-4646	30	20	.	.	PUNCT
ejpam-4646	30	21	terminology	terminology	NOUN
ejpam-4646	30	22	and	and	CCONJ
ejpam-4646	30	23	notation	notation	NOUN
ejpam-4646	30	24	for	for	ADP
ejpam-4646	30	25	any	any	DET
ejpam-4646	30	26	two	two	NUM
ejpam-4646	30	27	vertices	vertex	NOUN
ejpam-4646	30	28	u	u	NOUN
ejpam-4646	30	29	and	and	CCONJ
ejpam-4646	30	30	v	v	NOUN
ejpam-4646	30	31	in	in	ADP
ejpam-4646	30	32	an	an	DET
ejpam-4646	30	33	undirected	undirected	ADJ
ejpam-4646	30	34	connected	connected	ADJ
ejpam-4646	30	35	graph	graph	NOUN
ejpam-4646	30	36	g	g	PROPN
ejpam-4646	30	37	,	,	PUNCT
ejpam-4646	30	38	the	the	DET
ejpam-4646	30	39	distance	distance	NOUN
ejpam-4646	30	40	dg(u	dg(u	X
ejpam-4646	30	41	,	,	PUNCT
ejpam-4646	30	42	v	v	NOUN
ejpam-4646	30	43	)	)	PUNCT
ejpam-4646	30	44	is	be	AUX
ejpam-4646	30	45	the	the	DET
ejpam-4646	30	46	length	length	NOUN
ejpam-4646	30	47	of	of	ADP
ejpam-4646	30	48	a	a	DET
ejpam-4646	30	49	shortest	short	ADJ
ejpam-4646	30	50	path	path	NOUN
ejpam-4646	30	51	joining	join	VERB
ejpam-4646	30	52	u	u	NOUN
ejpam-4646	30	53	and	and	CCONJ
ejpam-4646	30	54	v.	v.	ADP
ejpam-4646	30	55	any	any	DET
ejpam-4646	30	56	u	u	NOUN
ejpam-4646	30	57	-	-	NOUN
ejpam-4646	30	58	v	v	ADJ
ejpam-4646	30	59	path	path	NOUN
ejpam-4646	30	60	of	of	ADP
ejpam-4646	30	61	length	length	NOUN
ejpam-4646	30	62	dg(u	dg(u	PROPN
ejpam-4646	30	63	,	,	PUNCT
ejpam-4646	30	64	v	v	NOUN
ejpam-4646	30	65	)	)	PUNCT
ejpam-4646	30	66	is	be	AUX
ejpam-4646	30	67	called	call	VERB
ejpam-4646	30	68	a	a	DET
ejpam-4646	30	69	u	u	NOUN
ejpam-4646	30	70	-	-	NOUN
ejpam-4646	30	71	v	v	ADJ
ejpam-4646	30	72	geodesic	geodesic	NOUN
ejpam-4646	30	73	.	.	PUNCT
ejpam-4646	31	1	the	the	DET
ejpam-4646	31	2	interval	interval	NOUN
ejpam-4646	31	3	ig	ig	PROPN
ejpam-4646	32	1	[	[	X
ejpam-4646	32	2	u	u	NOUN
ejpam-4646	32	3	,	,	PUNCT
ejpam-4646	32	4	v	v	NOUN
ejpam-4646	32	5	]	]	PUNCT
ejpam-4646	32	6	consists	consist	VERB
ejpam-4646	32	7	u	u	NOUN
ejpam-4646	32	8	,	,	PUNCT
ejpam-4646	32	9	v	v	NOUN
ejpam-4646	32	10	and	and	CCONJ
ejpam-4646	32	11	all	all	DET
ejpam-4646	32	12	vertices	vertex	NOUN
ejpam-4646	32	13	lying	lie	VERB
ejpam-4646	32	14	on	on	ADP
ejpam-4646	32	15	a	a	DET
ejpam-4646	32	16	u	u	NOUN
ejpam-4646	32	17	-	-	NOUN
ejpam-4646	32	18	v	v	ADJ
ejpam-4646	32	19	geodesic	geodesic	NOUN
ejpam-4646	32	20	.	.	PUNCT
ejpam-4646	33	1	the	the	DET
ejpam-4646	33	2	interval	interval	NOUN
ejpam-4646	33	3	ig(u	ig(u	NOUN
ejpam-4646	33	4	,	,	PUNCT
ejpam-4646	33	5	v	v	NOUN
ejpam-4646	33	6	)	)	PUNCT
ejpam-4646	33	7	=	=	PUNCT
ejpam-4646	34	1	ig	ig	PROPN
ejpam-4646	35	1	[	[	X
ejpam-4646	35	2	u	u	NOUN
ejpam-4646	35	3	,	,	PUNCT
ejpam-4646	35	4	v	v	ADP
ejpam-4646	35	5	]	]	PUNCT
ejpam-4646	35	6	\	\	NOUN
ejpam-4646	35	7	{	{	PUNCT
ejpam-4646	35	8	u	u	NOUN
ejpam-4646	35	9	,	,	PUNCT
ejpam-4646	35	10	v	v	NOUN
ejpam-4646	35	11	}	}	PUNCT
ejpam-4646	35	12	.	.	PUNCT
ejpam-4646	36	1	the	the	DET
ejpam-4646	36	2	open	open	ADJ
ejpam-4646	36	3	neighborhood	neighborhood	NOUN
ejpam-4646	36	4	of	of	ADP
ejpam-4646	36	5	a	a	DET
ejpam-4646	36	6	vertex	vertex	NOUN
ejpam-4646	36	7	u	u	NOUN
ejpam-4646	36	8	is	be	AUX
ejpam-4646	36	9	the	the	DET
ejpam-4646	36	10	set	set	NOUN
ejpam-4646	36	11	ng(u	ng(u	NOUN
ejpam-4646	36	12	)	)	PUNCT
ejpam-4646	36	13	consisting	consist	VERB
ejpam-4646	36	14	of	of	ADP
ejpam-4646	36	15	all	all	DET
ejpam-4646	36	16	vertices	vertex	NOUN
ejpam-4646	36	17	v	v	NUM
ejpam-4646	36	18	which	which	PRON
ejpam-4646	36	19	are	be	AUX
ejpam-4646	36	20	adjacent	adjacent	ADJ
ejpam-4646	36	21	to	to	PART
ejpam-4646	36	22	u.	u.	VERB
ejpam-4646	36	23	the	the	DET
ejpam-4646	36	24	closed	closed	ADJ
ejpam-4646	36	25	neighborhood	neighborhood	NOUN
ejpam-4646	36	26	of	of	ADP
ejpam-4646	36	27	u	u	NOUN
ejpam-4646	36	28	is	be	AUX
ejpam-4646	36	29	ng[u	ng[u	PROPN
ejpam-4646	36	30	]	]	X
ejpam-4646	36	31	=	=	SYM
ejpam-4646	36	32	ng(u	ng(u	PROPN
ejpam-4646	36	33	)	)	PUNCT
ejpam-4646	36	34	∪	∪	NOUN
ejpam-4646	36	35	{	{	PUNCT
ejpam-4646	36	36	u	u	NOUN
ejpam-4646	36	37	}	}	PUNCT
ejpam-4646	36	38	.	.	PUNCT
ejpam-4646	37	1	for	for	ADP
ejpam-4646	37	2	any	any	DET
ejpam-4646	37	3	a	a	DET
ejpam-4646	37	4	⊆	⊆	NUM
ejpam-4646	37	5	v	v	NOUN
ejpam-4646	37	6	(	(	PUNCT
ejpam-4646	37	7	g	g	NOUN
ejpam-4646	37	8	)	)	PUNCT
ejpam-4646	37	9	,	,	PUNCT
ejpam-4646	37	10	ng(a	ng(a	X
ejpam-4646	37	11	)	)	PUNCT
ejpam-4646	37	12	=	=	PUNCT
ejpam-4646	37	13	⋃	⋃	NOUN
ejpam-4646	37	14	v∈a	v∈a	NOUN
ejpam-4646	37	15	ng(v	ng(v	PUNCT
ejpam-4646	37	16	)	)	PUNCT
ejpam-4646	37	17	is	be	AUX
ejpam-4646	37	18	called	call	VERB
ejpam-4646	37	19	the	the	DET
ejpam-4646	37	20	open	open	ADJ
ejpam-4646	37	21	neighborhood	neighborhood	NOUN
ejpam-4646	37	22	of	of	ADP
ejpam-4646	37	23	a	a	DET
ejpam-4646	37	24	andng[a	andng[a	NOUN
ejpam-4646	37	25	]	]	X
ejpam-4646	37	26	=	=	SYM
ejpam-4646	37	27	ng(a)∪a	ng(a)∪a	PROPN
ejpam-4646	37	28	is	be	AUX
ejpam-4646	37	29	called	call	VERB
ejpam-4646	37	30	the	the	DET
ejpam-4646	37	31	closed	closed	ADJ
ejpam-4646	37	32	neighborhood	neighborhood	NOUN
ejpam-4646	37	33	of	of	ADP
ejpam-4646	37	34	a.	a.	NOUN
ejpam-4646	37	35	the	the	DET
ejpam-4646	37	36	open	open	ADJ
ejpam-4646	37	37	hop	hop	NOUN
ejpam-4646	37	38	neighborhood	neighborhood	NOUN
ejpam-4646	37	39	of	of	ADP
ejpam-4646	37	40	a	a	DET
ejpam-4646	37	41	vertex	vertex	NOUN
ejpam-4646	37	42	u	u	NOUN
ejpam-4646	37	43	is	be	AUX
ejpam-4646	37	44	the	the	DET
ejpam-4646	37	45	set	set	ADJ
ejpam-4646	37	46	n2	n2	ADJ
ejpam-4646	37	47	g(u	g(u	PROPN
ejpam-4646	37	48	)	)	PUNCT
ejpam-4646	37	49	=	=	PRON
ejpam-4646	37	50	{	{	PUNCT
ejpam-4646	37	51	v	v	NUM
ejpam-4646	37	52	∈	∈	NOUN
ejpam-4646	37	53	v	v	NOUN
ejpam-4646	37	54	(	(	PUNCT
ejpam-4646	37	55	g	g	NOUN
ejpam-4646	37	56	)	)	PUNCT
ejpam-4646	37	57	:	:	PUNCT
ejpam-4646	37	58	dg(v	dg(v	X
ejpam-4646	37	59	,	,	PUNCT
ejpam-4646	37	60	u	u	NOUN
ejpam-4646	37	61	)	)	PUNCT
ejpam-4646	37	62	=	=	SYM
ejpam-4646	37	63	2	2	NUM
ejpam-4646	37	64	}	}	PUNCT
ejpam-4646	37	65	.	.	PUNCT
ejpam-4646	38	1	the	the	DET
ejpam-4646	38	2	closed	closed	ADJ
ejpam-4646	38	3	hop	hop	NOUN
ejpam-4646	38	4	neighborhood	neighborhood	NOUN
ejpam-4646	38	5	of	of	ADP
ejpam-4646	38	6	u	u	NOUN
ejpam-4646	38	7	is	be	AUX
ejpam-4646	38	8	n2	n2	ADJ
ejpam-4646	38	9	g[u	g[u	X
ejpam-4646	38	10	]	]	X
ejpam-4646	38	11	=	=	SYM
ejpam-4646	38	12	n2	n2	ADJ
ejpam-4646	38	13	g(u	g(u	PROPN
ejpam-4646	38	14	)	)	PUNCT
ejpam-4646	38	15	∪	∪	NOUN
ejpam-4646	38	16	{	{	PUNCT
ejpam-4646	38	17	u	u	NOUN
ejpam-4646	38	18	}	}	PUNCT
ejpam-4646	38	19	.	.	PUNCT
ejpam-4646	39	1	for	for	ADP
ejpam-4646	39	2	any	any	DET
ejpam-4646	39	3	a	a	DET
ejpam-4646	39	4	⊆	⊆	NUM
ejpam-4646	39	5	v	v	NOUN
ejpam-4646	39	6	(	(	PUNCT
ejpam-4646	39	7	g	g	NOUN
ejpam-4646	39	8	)	)	PUNCT
ejpam-4646	39	9	,	,	PUNCT
ejpam-4646	39	10	n2	n2	PROPN
ejpam-4646	39	11	g(a	g(a	PROPN
ejpam-4646	39	12	)	)	PUNCT
ejpam-4646	39	13	=	=	SYM
ejpam-4646	39	14	⋃	⋃	NOUN
ejpam-4646	39	15	v∈a	v∈a	NOUN
ejpam-4646	39	16	n2	n2	ADJ
ejpam-4646	39	17	g(v	g(v	PROPN
ejpam-4646	39	18	)	)	PUNCT
ejpam-4646	39	19	is	be	AUX
ejpam-4646	39	20	called	call	VERB
ejpam-4646	39	21	the	the	DET
ejpam-4646	39	22	open	open	ADJ
ejpam-4646	39	23	hop	hop	NOUN
ejpam-4646	39	24	neighborhood	neighborhood	NOUN
ejpam-4646	39	25	of	of	ADP
ejpam-4646	39	26	a	a	DET
ejpam-4646	39	27	and	and	CCONJ
ejpam-4646	39	28	n2	n2	ADJ
ejpam-4646	39	29	g[a	g[a	NOUN
ejpam-4646	39	30	]	]	X
ejpam-4646	39	31	=	=	SYM
ejpam-4646	39	32	n2	n2	PROPN
ejpam-4646	39	33	g(a)∪a	g(a)∪a	PROPN
ejpam-4646	39	34	is	be	AUX
ejpam-4646	39	35	called	call	VERB
ejpam-4646	39	36	the	the	DET
ejpam-4646	39	37	closed	closed	ADJ
ejpam-4646	39	38	hop	hop	NOUN
ejpam-4646	39	39	neighborhood	neighborhood	NOUN
ejpam-4646	39	40	of	of	ADP
ejpam-4646	39	41	a.	a.	NOUN
ejpam-4646	39	42	a	a	DET
ejpam-4646	39	43	set	set	NOUN
ejpam-4646	39	44	s	s	NOUN
ejpam-4646	39	45	⊆	⊆	NUM
ejpam-4646	39	46	v	v	NOUN
ejpam-4646	39	47	(	(	PUNCT
ejpam-4646	39	48	g	g	NOUN
ejpam-4646	39	49	)	)	PUNCT
ejpam-4646	39	50	is	be	AUX
ejpam-4646	39	51	a	a	DET
ejpam-4646	39	52	dominating	dominating	NOUN
ejpam-4646	39	53	set	set	VERB
ejpam-4646	39	54	in	in	ADP
ejpam-4646	39	55	g	g	PROPN
ejpam-4646	39	56	if	if	SCONJ
ejpam-4646	39	57	ng[s	ng[	NOUN
ejpam-4646	39	58	]	]	PUNCT
ejpam-4646	39	59	=	=	SYM
ejpam-4646	39	60	v	v	NOUN
ejpam-4646	39	61	(	(	PUNCT
ejpam-4646	39	62	g	g	NOUN
ejpam-4646	39	63	)	)	PUNCT
ejpam-4646	39	64	.	.	PUNCT
ejpam-4646	40	1	the	the	DET
ejpam-4646	40	2	smallest	small	ADJ
ejpam-4646	40	3	cardinality	cardinality	NOUN
ejpam-4646	40	4	of	of	ADP
ejpam-4646	40	5	a	a	DET
ejpam-4646	40	6	dominating	dominating	NOUN
ejpam-4646	40	7	set	set	NOUN
ejpam-4646	40	8	in	in	ADP
ejpam-4646	40	9	g	g	NOUN
ejpam-4646	40	10	,	,	PUNCT
ejpam-4646	40	11	denoted	denote	VERB
ejpam-4646	40	12	by	by	ADP
ejpam-4646	40	13	γ(g	γ(g	PROPN
ejpam-4646	40	14	)	)	PUNCT
ejpam-4646	40	15	is	be	AUX
ejpam-4646	40	16	called	call	VERB
ejpam-4646	40	17	the	the	DET
ejpam-4646	40	18	domination	domination	NOUN
ejpam-4646	40	19	number	number	NOUN
ejpam-4646	40	20	of	of	ADP
ejpam-4646	40	21	g.	g.	PROPN
ejpam-4646	40	22	the	the	DET
ejpam-4646	40	23	geodetic	geodetic	ADJ
ejpam-4646	40	24	closure	closure	NOUN
ejpam-4646	40	25	of	of	ADP
ejpam-4646	40	26	a	a	DET
ejpam-4646	40	27	set	set	NOUN
ejpam-4646	40	28	s	s	NOUN
ejpam-4646	40	29	⊆	⊆	NUM
ejpam-4646	40	30	v	v	NOUN
ejpam-4646	40	31	(	(	PUNCT
ejpam-4646	40	32	g	g	NOUN
ejpam-4646	40	33	)	)	PUNCT
ejpam-4646	40	34	,	,	PUNCT
ejpam-4646	40	35	denoted	denote	VERB
ejpam-4646	40	36	by	by	ADP
ejpam-4646	40	37	ig	ig	PROPN
ejpam-4646	41	1	[	[	X
ejpam-4646	41	2	s	s	X
ejpam-4646	41	3	]	]	X
ejpam-4646	41	4	,	,	PUNCT
ejpam-4646	41	5	is	be	AUX
ejpam-4646	41	6	the	the	DET
ejpam-4646	41	7	union	union	NOUN
ejpam-4646	41	8	of	of	ADP
ejpam-4646	41	9	the	the	DET
ejpam-4646	41	10	intervals	interval	NOUN
ejpam-4646	41	11	ig[u	ig[u	VERB
ejpam-4646	41	12	,	,	PUNCT
ejpam-4646	41	13	v	v	NOUN
ejpam-4646	41	14	]	]	X
ejpam-4646	41	15	,	,	PUNCT
ejpam-4646	41	16	where	where	SCONJ
ejpam-4646	41	17	u	u	NOUN
ejpam-4646	41	18	,	,	PUNCT
ejpam-4646	41	19	v	v	PROPN
ejpam-4646	41	20	∈	∈	PROPN
ejpam-4646	41	21	s.	s.	PROPN
ejpam-4646	41	22	set	set	VERB
ejpam-4646	41	23	s	s	VERB
ejpam-4646	41	24	is	be	AUX
ejpam-4646	41	25	geodetic	geodetic	ADJ
ejpam-4646	41	26	set	set	NOUN
ejpam-4646	41	27	in	in	ADP
ejpam-4646	41	28	g	g	PROPN
ejpam-4646	41	29	if	if	SCONJ
ejpam-4646	41	30	ig[s	ig[	NOUN
ejpam-4646	41	31	]	]	X
ejpam-4646	41	32	=	=	SYM
ejpam-4646	41	33	v	v	X
ejpam-4646	41	34	(	(	PUNCT
ejpam-4646	41	35	g	g	NOUN
ejpam-4646	41	36	)	)	PUNCT
ejpam-4646	41	37	.	.	PUNCT
ejpam-4646	42	1	the	the	DET
ejpam-4646	42	2	smallest	small	ADJ
ejpam-4646	42	3	cardinality	cardinality	NOUN
ejpam-4646	42	4	among	among	ADP
ejpam-4646	42	5	all	all	DET
ejpam-4646	42	6	geodetic	geodetic	ADJ
ejpam-4646	42	7	sets	set	NOUN
ejpam-4646	42	8	in	in	ADP
ejpam-4646	42	9	g	g	NOUN
ejpam-4646	42	10	,	,	PUNCT
ejpam-4646	42	11	denoted	denote	VERB
ejpam-4646	42	12	by	by	ADP
ejpam-4646	42	13	g(g	g(g	PROPN
ejpam-4646	42	14	)	)	PUNCT
ejpam-4646	42	15	,	,	PUNCT
ejpam-4646	42	16	is	be	AUX
ejpam-4646	42	17	called	call	VERB
ejpam-4646	42	18	the	the	DET
ejpam-4646	42	19	geodetic	geodetic	ADJ
ejpam-4646	42	20	number	number	NOUN
ejpam-4646	42	21	of	of	ADP
ejpam-4646	42	22	g.	g.	PROPN
ejpam-4646	42	23	a	a	DET
ejpam-4646	42	24	geodetic	geodetic	ADJ
ejpam-4646	42	25	set	set	NOUN
ejpam-4646	42	26	of	of	ADP
ejpam-4646	42	27	cardinality	cardinality	PROPN
ejpam-4646	42	28	g(g	g(g	PROPN
ejpam-4646	42	29	)	)	PUNCT
ejpam-4646	42	30	is	be	AUX
ejpam-4646	42	31	called	call	VERB
ejpam-4646	42	32	a	a	DET
ejpam-4646	42	33	g	g	NOUN
ejpam-4646	42	34	-	-	PUNCT
ejpam-4646	42	35	set	set	NOUN
ejpam-4646	42	36	of	of	ADP
ejpam-4646	42	37	g.	g.	PROPN
ejpam-4646	42	38	a	a	DET
ejpam-4646	42	39	set	set	NOUN
ejpam-4646	42	40	s	s	PROPN
ejpam-4646	42	41	⊆	⊆	NUM
ejpam-4646	42	42	v	v	NOUN
ejpam-4646	42	43	(	(	PUNCT
ejpam-4646	42	44	g	g	NOUN
ejpam-4646	42	45	)	)	PUNCT
ejpam-4646	42	46	is	be	AUX
ejpam-4646	42	47	a	a	DET
ejpam-4646	42	48	geodetic	geodetic	ADJ
ejpam-4646	42	49	dominating	dominating	NOUN
ejpam-4646	42	50	set	set	VERB
ejpam-4646	42	51	in	in	ADP
ejpam-4646	42	52	g	g	PROPN
ejpam-4646	42	53	if	if	SCONJ
ejpam-4646	42	54	it	it	PRON
ejpam-4646	42	55	is	be	AUX
ejpam-4646	42	56	both	both	CCONJ
ejpam-4646	42	57	a	a	DET
ejpam-4646	42	58	dominating	dominating	NOUN
ejpam-4646	42	59	and	and	CCONJ
ejpam-4646	42	60	a	a	DET
ejpam-4646	42	61	geodetic	geodetic	ADJ
ejpam-4646	42	62	set	set	NOUN
ejpam-4646	42	63	.	.	PUNCT
ejpam-4646	43	1	a	a	DET
ejpam-4646	43	2	set	set	NOUN
ejpam-4646	43	3	s	s	NOUN
ejpam-4646	43	4	⊆	⊆	NUM
ejpam-4646	43	5	v	v	NOUN
ejpam-4646	43	6	(	(	PUNCT
ejpam-4646	43	7	g	g	NOUN
ejpam-4646	43	8	)	)	PUNCT
ejpam-4646	43	9	is	be	AUX
ejpam-4646	43	10	a	a	DET
ejpam-4646	43	11	hop	hop	NOUN
ejpam-4646	43	12	dominating	dominating	NOUN
ejpam-4646	43	13	set	set	NOUN
ejpam-4646	43	14	if	if	SCONJ
ejpam-4646	43	15	n2	n2	ADJ
ejpam-4646	43	16	g[s	g[s	PROPN
ejpam-4646	43	17	]	]	X
ejpam-4646	43	18	=	=	SYM
ejpam-4646	43	19	v	v	NOUN
ejpam-4646	43	20	(	(	PUNCT
ejpam-4646	43	21	g	g	NOUN
ejpam-4646	43	22	)	)	PUNCT
ejpam-4646	43	23	.	.	PUNCT
ejpam-4646	44	1	the	the	DET
ejpam-4646	44	2	minimum	minimum	ADJ
ejpam-4646	44	3	cardinality	cardinality	NOUN
ejpam-4646	44	4	of	of	ADP
ejpam-4646	44	5	a	a	DET
ejpam-4646	44	6	hop	hop	NOUN
ejpam-4646	44	7	dominating	dominating	NOUN
ejpam-4646	44	8	set	set	NOUN
ejpam-4646	44	9	of	of	ADP
ejpam-4646	44	10	a	a	DET
ejpam-4646	44	11	graph	graph	NOUN
ejpam-4646	44	12	g	g	NOUN
ejpam-4646	44	13	,	,	PUNCT
ejpam-4646	44	14	denoted	denote	VERB
ejpam-4646	44	15	by	by	ADP
ejpam-4646	44	16	γh(g	γh(g	NOUN
ejpam-4646	44	17	)	)	PUNCT
ejpam-4646	44	18	,	,	PUNCT
ejpam-4646	44	19	is	be	AUX
ejpam-4646	44	20	called	call	VERB
ejpam-4646	44	21	the	the	DET
ejpam-4646	44	22	hop	hop	NOUN
ejpam-4646	44	23	domination	domination	NOUN
ejpam-4646	44	24	number	number	NOUN
ejpam-4646	44	25	of	of	ADP
ejpam-4646	44	26	g.	g.	PROPN
ejpam-4646	44	27	a	a	DET
ejpam-4646	44	28	subset	subset	NOUN
ejpam-4646	44	29	s	s	NOUN
ejpam-4646	44	30	of	of	ADP
ejpam-4646	44	31	v	v	NOUN
ejpam-4646	44	32	(	(	PUNCT
ejpam-4646	44	33	g	g	NOUN
ejpam-4646	44	34	)	)	PUNCT
ejpam-4646	44	35	is	be	AUX
ejpam-4646	44	36	a	a	DET
ejpam-4646	44	37	total	total	ADJ
ejpam-4646	44	38	hop	hop	NOUN
ejpam-4646	44	39	dominating	dominating	NOUN
ejpam-4646	44	40	set	set	NOUN
ejpam-4646	44	41	of	of	ADP
ejpam-4646	44	42	g	g	PROPN
ejpam-4646	44	43	if	if	SCONJ
ejpam-4646	44	44	for	for	ADP
ejpam-4646	44	45	every	every	DET
ejpam-4646	44	46	v	v	NUM
ejpam-4646	44	47	∈	∈	NOUN
ejpam-4646	44	48	v	v	NOUN
ejpam-4646	44	49	(	(	PUNCT
ejpam-4646	44	50	g	g	NOUN
ejpam-4646	44	51	)	)	PUNCT
ejpam-4646	44	52	,	,	PUNCT
ejpam-4646	44	53	there	there	PRON
ejpam-4646	44	54	exists	exist	VERB
ejpam-4646	44	55	u	u	PROPN
ejpam-4646	44	56	∈	∈	PROPN
ejpam-4646	44	57	s	s	VERB
ejpam-4646	44	58	such	such	ADJ
ejpam-4646	44	59	that	that	DET
ejpam-4646	44	60	dg(u	dg(u	ADJ
ejpam-4646	44	61	,	,	PUNCT
ejpam-4646	44	62	v	v	NOUN
ejpam-4646	44	63	)	)	PUNCT
ejpam-4646	45	1	=	=	SYM
ejpam-4646	45	2	2	2	X
ejpam-4646	45	3	.	.	X
ejpam-4646	45	4	the	the	DET
ejpam-4646	45	5	smallest	small	ADJ
ejpam-4646	45	6	cardinality	cardinality	NOUN
ejpam-4646	45	7	of	of	ADP
ejpam-4646	45	8	a	a	DET
ejpam-4646	45	9	total	total	ADJ
ejpam-4646	45	10	hop	hop	NOUN
ejpam-4646	45	11	dominating	dominating	NOUN
ejpam-4646	45	12	set	set	NOUN
ejpam-4646	45	13	of	of	ADP
ejpam-4646	45	14	g	g	NOUN
ejpam-4646	45	15	,	,	PUNCT
ejpam-4646	45	16	denoted	denote	VERB
ejpam-4646	45	17	by	by	ADP
ejpam-4646	45	18	γth(g	γth(g	NOUN
ejpam-4646	45	19	)	)	PUNCT
ejpam-4646	45	20	is	be	AUX
ejpam-4646	45	21	called	call	VERB
ejpam-4646	45	22	the	the	DET
ejpam-4646	45	23	total	total	ADJ
ejpam-4646	45	24	hop	hop	NOUN
ejpam-4646	45	25	domination	domination	NOUN
ejpam-4646	45	26	number	number	NOUN
ejpam-4646	45	27	of	of	ADP
ejpam-4646	45	28	g.	g.	PROPN
ejpam-4646	45	29	any	any	DET
ejpam-4646	45	30	total	total	ADJ
ejpam-4646	45	31	hop	hop	NOUN
ejpam-4646	45	32	dominating	dominating	NOUN
ejpam-4646	45	33	set	set	NOUN
ejpam-4646	45	34	of	of	ADP
ejpam-4646	45	35	g	g	PROPN
ejpam-4646	45	36	with	with	ADP
ejpam-4646	45	37	cardinality	cardinality	PROPN
ejpam-4646	45	38	γth(g	γth(g	NOUN
ejpam-4646	45	39	)	)	PUNCT
ejpam-4646	45	40	is	be	AUX
ejpam-4646	45	41	called	call	VERB
ejpam-4646	45	42	a	a	DET
ejpam-4646	45	43	γth	γth	NOUN
ejpam-4646	45	44	-	-	PUNCT
ejpam-4646	45	45	set	set	NOUN
ejpam-4646	45	46	.	.	PUNCT
ejpam-4646	46	1	a	a	DET
ejpam-4646	46	2	subset	subset	NOUN
ejpam-4646	46	3	s	s	NOUN
ejpam-4646	46	4	of	of	ADP
ejpam-4646	46	5	vertices	vertex	NOUN
ejpam-4646	46	6	of	of	ADP
ejpam-4646	46	7	g	g	PROPN
ejpam-4646	46	8	is	be	AUX
ejpam-4646	46	9	a	a	DET
ejpam-4646	46	10	geodetic	geodetic	ADJ
ejpam-4646	46	11	hop	hop	NOUN
ejpam-4646	46	12	dominating	dominating	NOUN
ejpam-4646	46	13	set	set	NOUN
ejpam-4646	46	14	if	if	SCONJ
ejpam-4646	46	15	it	it	PRON
ejpam-4646	46	16	is	be	AUX
ejpam-4646	46	17	both	both	CCONJ
ejpam-4646	46	18	a	a	DET
ejpam-4646	46	19	geodetic	geodetic	ADJ
ejpam-4646	46	20	and	and	CCONJ
ejpam-4646	46	21	a	a	DET
ejpam-4646	46	22	hop	hop	NOUN
ejpam-4646	46	23	dominating	dominating	NOUN
ejpam-4646	46	24	set	set	NOUN
ejpam-4646	46	25	.	.	PUNCT
ejpam-4646	47	1	the	the	DET
ejpam-4646	47	2	geodetic	geodetic	ADJ
ejpam-4646	47	3	hop	hop	NOUN
ejpam-4646	47	4	domination	domination	NOUN
ejpam-4646	47	5	number	number	NOUN
ejpam-4646	47	6	γhg(g	γhg(g	PROPN
ejpam-4646	47	7	)	)	PUNCT
ejpam-4646	47	8	of	of	ADP
ejpam-4646	47	9	g	g	PROPN
ejpam-4646	47	10	is	be	AUX
ejpam-4646	47	11	the	the	DET
ejpam-4646	47	12	minimum	minimum	ADJ
ejpam-4646	47	13	cardinality	cardinality	NOUN
ejpam-4646	47	14	among	among	ADP
ejpam-4646	47	15	all	all	DET
ejpam-4646	47	16	geodetic	geodetic	ADJ
ejpam-4646	47	17	hop	hop	NOUN
ejpam-4646	47	18	dominating	dominating	NOUN
ejpam-4646	47	19	sets	set	NOUN
ejpam-4646	47	20	in	in	ADP
ejpam-4646	47	21	g.	g.	PROPN
ejpam-4646	47	22	any	any	DET
ejpam-4646	47	23	geodetic	geodetic	ADJ
ejpam-4646	47	24	hop	hop	NOUN
ejpam-4646	47	25	dominating	dominating	NOUN
ejpam-4646	47	26	set	set	NOUN
ejpam-4646	47	27	of	of	ADP
ejpam-4646	47	28	g	g	PROPN
ejpam-4646	47	29	with	with	ADP
ejpam-4646	47	30	cardinality	cardinality	PROPN
ejpam-4646	47	31	γhg(g	γhg(g	PROPN
ejpam-4646	47	32	)	)	PUNCT
ejpam-4646	47	33	is	be	AUX
ejpam-4646	47	34	called	call	VERB
ejpam-4646	47	35	a	a	DET
ejpam-4646	47	36	γhg	γhg	NOUN
ejpam-4646	47	37	-	-	PUNCT
ejpam-4646	47	38	set	set	NOUN
ejpam-4646	47	39	.	.	PUNCT
ejpam-4646	48	1	a	a	DET
ejpam-4646	48	2	set	set	NOUN
ejpam-4646	48	3	s	s	NOUN
ejpam-4646	48	4	⊆	⊆	NUM
ejpam-4646	48	5	v	v	NOUN
ejpam-4646	48	6	(	(	PUNCT
ejpam-4646	48	7	g	g	NOUN
ejpam-4646	48	8	)	)	PUNCT
ejpam-4646	48	9	of	of	ADP
ejpam-4646	48	10	a	a	DET
ejpam-4646	48	11	graph	graph	NOUN
ejpam-4646	48	12	g	g	NOUN
ejpam-4646	48	13	is	be	AUX
ejpam-4646	48	14	called	call	VERB
ejpam-4646	48	15	a	a	DET
ejpam-4646	48	16	2	2	NUM
ejpam-4646	48	17	-	-	PUNCT
ejpam-4646	48	18	path	path	NOUN
ejpam-4646	48	19	closure	closure	NOUN
ejpam-4646	48	20	absorbing	absorb	VERB
ejpam-4646	48	21	if	if	SCONJ
ejpam-4646	48	22	for	for	ADP
ejpam-4646	48	23	each	each	DET
ejpam-4646	48	24	x	x	SYM
ejpam-4646	48	25	∈	∈	PROPN
ejpam-4646	48	26	v	v	X
ejpam-4646	48	27	(	(	PUNCT
ejpam-4646	48	28	g)\s	g)\s	VERB
ejpam-4646	48	29	there	there	ADV
ejpam-4646	48	30	exist	exist	VERB
ejpam-4646	48	31	u	u	NOUN
ejpam-4646	48	32	,	,	PUNCT
ejpam-4646	48	33	v	v	PROPN
ejpam-4646	48	34	∈	∈	NOUN
ejpam-4646	48	35	s	s	VERB
ejpam-4646	48	36	such	such	ADJ
ejpam-4646	48	37	that	that	DET
ejpam-4646	48	38	dg(u	dg(u	ADJ
ejpam-4646	48	39	,	,	PUNCT
ejpam-4646	48	40	v	v	NOUN
ejpam-4646	48	41	)	)	PUNCT
ejpam-4646	48	42	=	=	SYM
ejpam-4646	48	43	2	2	NUM
ejpam-4646	48	44	and	and	CCONJ
ejpam-4646	48	45	x	x	PROPN
ejpam-4646	48	46	∈	∈	PROPN
ejpam-4646	48	47	ig(u	ig(u	NOUN
ejpam-4646	48	48	,	,	PUNCT
ejpam-4646	48	49	v	v	NOUN
ejpam-4646	48	50	)	)	PUNCT
ejpam-4646	48	51	.	.	PUNCT
ejpam-4646	49	1	the	the	DET
ejpam-4646	49	2	minimum	minimum	ADJ
ejpam-4646	49	3	cardinality	cardinality	NOUN
ejpam-4646	49	4	of	of	ADP
ejpam-4646	49	5	a	a	DET
ejpam-4646	49	6	2	2	NUM
ejpam-4646	49	7	-	-	PUNCT
ejpam-4646	49	8	path	path	NOUN
ejpam-4646	49	9	closure	closure	NOUN
ejpam-4646	49	10	absorbing	absorb	VERB
ejpam-4646	49	11	set	set	NOUN
ejpam-4646	49	12	in	in	ADP
ejpam-4646	49	13	g	g	PROPN
ejpam-4646	49	14	is	be	AUX
ejpam-4646	49	15	denoted	denote	VERB
ejpam-4646	49	16	by	by	ADP
ejpam-4646	49	17	ρ2(g	ρ2(g	NOUN
ejpam-4646	49	18	)	)	PUNCT
ejpam-4646	49	19	.	.	PUNCT
ejpam-4646	50	1	any	any	DET
ejpam-4646	50	2	2	2	NUM
ejpam-4646	50	3	-	-	PUNCT
ejpam-4646	50	4	path	path	NOUN
ejpam-4646	50	5	closure	closure	NOUN
ejpam-4646	50	6	absorbing	absorb	VERB
ejpam-4646	50	7	set	set	NOUN
ejpam-4646	50	8	of	of	ADP
ejpam-4646	50	9	g	g	NOUN
ejpam-4646	50	10	with	with	ADP
ejpam-4646	50	11	cardinality	cardinality	PROPN
ejpam-4646	50	12	ρ2(g	ρ2(g	NUM
ejpam-4646	50	13	)	)	PUNCT
ejpam-4646	50	14	is	be	AUX
ejpam-4646	50	15	called	call	VERB
ejpam-4646	50	16	a	a	DET
ejpam-4646	50	17	ρ2	ρ2	NOUN
ejpam-4646	50	18	-	-	PUNCT
ejpam-4646	50	19	set	set	NOUN
ejpam-4646	50	20	.	.	PUNCT
ejpam-4646	51	1	a	a	DET
ejpam-4646	51	2	set	set	NOUN
ejpam-4646	51	3	d	d	NOUN
ejpam-4646	51	4	⊆	⊆	NUM
ejpam-4646	51	5	v	v	ADP
ejpam-4646	51	6	(	(	PUNCT
ejpam-4646	51	7	g	g	NOUN
ejpam-4646	51	8	)	)	PUNCT
ejpam-4646	51	9	is	be	AUX
ejpam-4646	51	10	a	a	DET
ejpam-4646	51	11	pointwise	pointwise	ADJ
ejpam-4646	51	12	non	non	ADJ
ejpam-4646	51	13	-	-	ADJ
ejpam-4646	51	14	dominating	dominating	ADJ
ejpam-4646	51	15	set	set	NOUN
ejpam-4646	51	16	of	of	ADP
ejpam-4646	51	17	g	g	PROPN
ejpam-4646	51	18	if	if	SCONJ
ejpam-4646	51	19	for	for	ADP
ejpam-4646	51	20	each	each	PRON
ejpam-4646	51	21	v	v	NUM
ejpam-4646	51	22	∈	∈	PROPN
ejpam-4646	51	23	v	v	NOUN
ejpam-4646	51	24	(	(	PUNCT
ejpam-4646	51	25	g	g	NOUN
ejpam-4646	51	26	)	)	PUNCT
ejpam-4646	51	27	\	\	PROPN
ejpam-4646	52	1	s	s	X
ejpam-4646	52	2	,	,	PUNCT
ejpam-4646	52	3	there	there	PRON
ejpam-4646	52	4	exists	exist	VERB
ejpam-4646	52	5	u	u	PROPN
ejpam-4646	52	6	∈	∈	PROPN
ejpam-4646	52	7	s	s	VERB
ejpam-4646	52	8	such	such	ADJ
ejpam-4646	52	9	that	that	DET
ejpam-4646	52	10	v	v	NOUN
ejpam-4646	52	11	/∈	/∈	PUNCT
ejpam-4646	52	12	ng(u	ng(u	NOUN
ejpam-4646	52	13	)	)	PUNCT
ejpam-4646	52	14	.	.	PUNCT
ejpam-4646	53	1	the	the	DET
ejpam-4646	53	2	smallest	small	ADJ
ejpam-4646	53	3	cardinality	cardinality	NOUN
ejpam-4646	53	4	of	of	ADP
ejpam-4646	53	5	a	a	DET
ejpam-4646	53	6	pointwise	pointwise	ADJ
ejpam-4646	53	7	non	non	ADJ
ejpam-4646	53	8	-	-	ADJ
ejpam-4646	53	9	dominating	dominating	ADJ
ejpam-4646	53	10	set	set	NOUN
ejpam-4646	53	11	of	of	ADP
ejpam-4646	53	12	g	g	NOUN
ejpam-4646	53	13	,	,	PUNCT
ejpam-4646	53	14	denoted	denote	VERB
ejpam-4646	53	15	by	by	ADP
ejpam-4646	53	16	pnd(g	pnd(g	PROPN
ejpam-4646	53	17	)	)	PUNCT
ejpam-4646	53	18	,	,	PUNCT
ejpam-4646	53	19	is	be	AUX
ejpam-4646	53	20	called	call	VERB
ejpam-4646	53	21	the	the	DET
ejpam-4646	53	22	pointwise	pointwise	ADJ
ejpam-4646	53	23	non	non	ADJ
ejpam-4646	53	24	-	-	ADJ
ejpam-4646	53	25	domination	domination	ADJ
ejpam-4646	53	26	number	number	NOUN
ejpam-4646	53	27	of	of	ADP
ejpam-4646	53	28	g.	g.	PROPN
ejpam-4646	53	29	a	a	DET
ejpam-4646	53	30	pointwise	pointwise	ADJ
ejpam-4646	53	31	non	non	ADJ
ejpam-4646	53	32	-	-	ADJ
ejpam-4646	53	33	dominating	dominating	ADJ
ejpam-4646	53	34	set	set	NOUN
ejpam-4646	53	35	s	s	PROPN
ejpam-4646	53	36	⊆	⊆	NUM
ejpam-4646	53	37	v	v	NOUN
ejpam-4646	53	38	(	(	PUNCT
ejpam-4646	53	39	g	g	NOUN
ejpam-4646	53	40	)	)	PUNCT
ejpam-4646	53	41	of	of	ADP
ejpam-4646	53	42	a	a	DET
ejpam-4646	53	43	graph	graph	NOUN
ejpam-4646	53	44	g	g	NOUN
ejpam-4646	53	45	is	be	AUX
ejpam-4646	53	46	called	call	VERB
ejpam-4646	53	47	a	a	DET
ejpam-4646	53	48	2	2	NUM
ejpam-4646	53	49	-	-	PUNCT
ejpam-4646	53	50	path	path	NOUN
ejpam-4646	53	51	closure	closure	NOUN
ejpam-4646	53	52	absorbing	absorb	VERB
ejpam-4646	53	53	pointwise	pointwise	PROPN
ejpam-4646	53	54	non	non	ADJ
ejpam-4646	53	55	-	-	ADJ
ejpam-4646	53	56	dominating	dominating	ADJ
ejpam-4646	53	57	set	set	NOUN
ejpam-4646	53	58	if	if	SCONJ
ejpam-4646	53	59	it	it	PRON
ejpam-4646	53	60	is	be	AUX
ejpam-4646	53	61	a	a	DET
ejpam-4646	53	62	2	2	NUM
ejpam-4646	53	63	-	-	PUNCT
ejpam-4646	53	64	path	path	NOUN
ejpam-4646	53	65	closure	closure	NOUN
ejpam-4646	53	66	absorbing	absorb	VERB
ejpam-4646	53	67	set	set	NOUN
ejpam-4646	53	68	.	.	PUNCT
ejpam-4646	54	1	the	the	DET
ejpam-4646	54	2	minimum	minimum	ADJ
ejpam-4646	54	3	cardinality	cardinality	NOUN
ejpam-4646	54	4	of	of	ADP
ejpam-4646	54	5	a	a	DET
ejpam-4646	54	6	2	2	NUM
ejpam-4646	54	7	-	-	PUNCT
ejpam-4646	54	8	path	path	NOUN
ejpam-4646	54	9	closure	closure	NOUN
ejpam-4646	54	10	absorbing	absorb	VERB
ejpam-4646	54	11	pointwise	pointwise	PROPN
ejpam-4646	54	12	non	non	ADJ
ejpam-4646	54	13	-	-	ADJ
ejpam-4646	54	14	dominating	dominating	ADJ
ejpam-4646	54	15	set	set	NOUN
ejpam-4646	54	16	in	in	ADP
ejpam-4646	54	17	g	g	PROPN
ejpam-4646	54	18	is	be	AUX
ejpam-4646	54	19	denoted	denote	VERB
ejpam-4646	54	20	by	by	ADP
ejpam-4646	54	21	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4646	54	22	)	)	PUNCT
ejpam-4646	54	23	.	.	PUNCT
ejpam-4646	55	1	any	any	DET
ejpam-4646	55	2	2	2	NUM
ejpam-4646	55	3	-	-	PUNCT
ejpam-4646	55	4	path	path	NOUN
ejpam-4646	55	5	closure	closure	NOUN
ejpam-4646	55	6	absorbing	absorb	VERB
ejpam-4646	55	7	pointwise	pointwise	PROPN
ejpam-4646	55	8	non	non	ADJ
ejpam-4646	55	9	-	-	ADJ
ejpam-4646	55	10	dominating	dominating	ADJ
ejpam-4646	55	11	set	set	NOUN
ejpam-4646	55	12	of	of	ADP
ejpam-4646	55	13	g	g	PROPN
ejpam-4646	55	14	c.j	c.j	PROPN
ejpam-4646	55	15	.	.	PROPN
ejpam-4646	55	16	saromines	saromines	PROPN
ejpam-4646	55	17	,	,	PUNCT
ejpam-4646	55	18	s.	s.	PROPN
ejpam-4646	55	19	canoy	canoy	PROPN
ejpam-4646	55	20	,	,	PUNCT
ejpam-4646	55	21	jr	jr	PROPN
ejpam-4646	55	22	.	.	PROPN
ejpam-4646	55	23	,	,	PUNCT
ejpam-4646	55	24	/	/	SYM
ejpam-4646	55	25	eur	eur	NOUN
ejpam-4646	55	26	.	.	PUNCT
ejpam-4646	56	1	j.	j.	PROPN
ejpam-4646	56	2	pure	pure	PROPN
ejpam-4646	56	3	appl	appl	PROPN
ejpam-4646	56	4	.	.	PROPN
ejpam-4646	56	5	math	math	PROPN
ejpam-4646	56	6	,	,	PUNCT
ejpam-4646	56	7	16	16	NUM
ejpam-4646	56	8	(	(	PUNCT
ejpam-4646	56	9	1	1	NUM
ejpam-4646	56	10	)	)	PUNCT
ejpam-4646	56	11	(	(	PUNCT
ejpam-4646	56	12	2023	2023	NUM
ejpam-4646	56	13	)	)	PUNCT
ejpam-4646	56	14	,	,	PUNCT
ejpam-4646	56	15	5	5	NUM
ejpam-4646	56	16	-	-	SYM
ejpam-4646	56	17	17	17	NUM
ejpam-4646	56	18	7	7	NUM
ejpam-4646	56	19	with	with	ADP
ejpam-4646	56	20	cardinality	cardinality	PROPN
ejpam-4646	56	21	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4646	56	22	)	)	PUNCT
ejpam-4646	56	23	is	be	AUX
ejpam-4646	56	24	called	call	VERB
ejpam-4646	56	25	a	a	DET
ejpam-4646	56	26	ρ2pnd	ρ2pnd	ADV
ejpam-4646	56	27	-	-	PUNCT
ejpam-4646	56	28	set	set	NOUN
ejpam-4646	56	29	.	.	PUNCT
ejpam-4646	57	1	let	let	VERB
ejpam-4646	57	2	kn	kn	PROPN
ejpam-4646	57	3	be	be	AUX
ejpam-4646	57	4	the	the	DET
ejpam-4646	57	5	complete	complete	ADJ
ejpam-4646	57	6	graph	graph	NOUN
ejpam-4646	57	7	of	of	ADP
ejpam-4646	57	8	order	order	NOUN
ejpam-4646	57	9	n	n	PRON
ejpam-4646	57	10	≥	≥	NOUN
ejpam-4646	57	11	3	3	NUM
ejpam-4646	57	12	and	and	CCONJ
ejpam-4646	57	13	ω	ω	NUM
ejpam-4646	57	14	a	a	DET
ejpam-4646	57	15	family	family	NOUN
ejpam-4646	57	16	of	of	ADP
ejpam-4646	57	17	complete	complete	ADJ
ejpam-4646	57	18	proper	proper	ADJ
ejpam-4646	57	19	subgraphs	subgraph	NOUN
ejpam-4646	57	20	of	of	ADP
ejpam-4646	57	21	kn	kn	PROPN
ejpam-4646	57	22	.	.	PUNCT
ejpam-4646	58	1	we	we	PRON
ejpam-4646	58	2	say	say	VERB
ejpam-4646	58	3	that	that	SCONJ
ejpam-4646	58	4	ω	ω	PROPN
ejpam-4646	58	5	is	be	AUX
ejpam-4646	58	6	an	an	DET
ejpam-4646	58	7	independent	independent	ADJ
ejpam-4646	58	8	set	set	NOUN
ejpam-4646	58	9	if	if	SCONJ
ejpam-4646	58	10	no	no	DET
ejpam-4646	58	11	two	two	NUM
ejpam-4646	58	12	distinct	distinct	ADJ
ejpam-4646	58	13	subgraphs	subgraph	NOUN
ejpam-4646	58	14	in	in	ADP
ejpam-4646	58	15	ω	ω	NUM
ejpam-4646	58	16	have	have	VERB
ejpam-4646	58	17	common	common	ADJ
ejpam-4646	58	18	vertex	vertex	NOUN
ejpam-4646	58	19	.	.	PUNCT
ejpam-4646	59	1	the	the	DET
ejpam-4646	59	2	graph	graph	NOUN
ejpam-4646	59	3	g	g	NOUN
ejpam-4646	59	4	of	of	ADP
ejpam-4646	59	5	order	order	NOUN
ejpam-4646	59	6	n	n	PRON
ejpam-4646	59	7	obtained	obtain	VERB
ejpam-4646	59	8	from	from	ADP
ejpam-4646	59	9	kn	kn	PROPN
ejpam-4646	59	10	by	by	ADP
ejpam-4646	59	11	deleting	delete	VERB
ejpam-4646	59	12	the	the	DET
ejpam-4646	59	13	edges	edge	NOUN
ejpam-4646	59	14	in	in	ADP
ejpam-4646	59	15	ω	ω	PROPN
ejpam-4646	59	16	is	be	AUX
ejpam-4646	59	17	denoted	denote	VERB
ejpam-4646	59	18	kn	kn	PROPN
ejpam-4646	59	19	\	\	PROPN
ejpam-4646	59	20	e(ω	e(ω	PROPN
ejpam-4646	59	21	)	)	PUNCT
ejpam-4646	59	22	.	.	PUNCT
ejpam-4646	60	1	hence	hence	ADV
ejpam-4646	60	2	,	,	PUNCT
ejpam-4646	60	3	xy	xy	PROPN
ejpam-4646	60	4	∈	∈	PROPN
ejpam-4646	60	5	e(g	e(g	PROPN
ejpam-4646	60	6	)	)	PUNCT
ejpam-4646	61	1	if	if	SCONJ
ejpam-4646	61	2	and	and	CCONJ
ejpam-4646	61	3	only	only	ADV
ejpam-4646	61	4	if	if	SCONJ
ejpam-4646	61	5	xy	xy	PROPN
ejpam-4646	61	6	is	be	AUX
ejpam-4646	61	7	not	not	PART
ejpam-4646	61	8	an	an	DET
ejpam-4646	61	9	edge	edge	NOUN
ejpam-4646	61	10	in	in	ADP
ejpam-4646	61	11	any	any	DET
ejpam-4646	61	12	subgraph	subgraph	NOUN
ejpam-4646	61	13	in	in	ADP
ejpam-4646	61	14	ω	ω	PROPN
ejpam-4646	61	15	.	.	PUNCT
ejpam-4646	62	1	let	let	VERB
ejpam-4646	62	2	g	g	NOUN
ejpam-4646	62	3	and	and	CCONJ
ejpam-4646	62	4	h	h	NOUN
ejpam-4646	62	5	be	be	VERB
ejpam-4646	62	6	two	two	NUM
ejpam-4646	62	7	graphs	graph	NOUN
ejpam-4646	62	8	.	.	PUNCT
ejpam-4646	63	1	the	the	DET
ejpam-4646	63	2	corona	corona	NOUN
ejpam-4646	63	3	g	g	PROPN
ejpam-4646	63	4	◦	◦	NOUN
ejpam-4646	63	5	h	h	NOUN
ejpam-4646	63	6	is	be	AUX
ejpam-4646	63	7	the	the	DET
ejpam-4646	63	8	graph	graph	NOUN
ejpam-4646	63	9	obtained	obtain	VERB
ejpam-4646	63	10	by	by	ADP
ejpam-4646	63	11	taking	take	VERB
ejpam-4646	63	12	one	one	NUM
ejpam-4646	63	13	copy	copy	NOUN
ejpam-4646	63	14	of	of	ADP
ejpam-4646	63	15	g	g	PROPN
ejpam-4646	63	16	and	and	CCONJ
ejpam-4646	63	17	|v	|v	PROPN
ejpam-4646	63	18	(	(	PUNCT
ejpam-4646	63	19	g)|	g)|	NOUN
ejpam-4646	63	20	copies	copy	NOUN
ejpam-4646	63	21	of	of	ADP
ejpam-4646	63	22	h	h	NOUN
ejpam-4646	63	23	,	,	PUNCT
ejpam-4646	63	24	and	and	CCONJ
ejpam-4646	63	25	then	then	ADV
ejpam-4646	63	26	joining	join	VERB
ejpam-4646	63	27	the	the	DET
ejpam-4646	63	28	ith	ith	PROPN
ejpam-4646	63	29	vertex	vertex	NOUN
ejpam-4646	63	30	of	of	ADP
ejpam-4646	63	31	g	g	NOUN
ejpam-4646	63	32	to	to	ADP
ejpam-4646	63	33	every	every	DET
ejpam-4646	63	34	vertex	vertex	NOUN
ejpam-4646	63	35	of	of	ADP
ejpam-4646	63	36	the	the	DET
ejpam-4646	63	37	ith	ith	PROPN
ejpam-4646	63	38	copy	copy	NOUN
ejpam-4646	63	39	of	of	ADP
ejpam-4646	63	40	h.	h.	PROPN
ejpam-4646	63	41	we	we	PRON
ejpam-4646	63	42	denote	denote	VERB
ejpam-4646	63	43	by	by	ADP
ejpam-4646	63	44	hv	hv	PROPN
ejpam-4646	63	45	the	the	DET
ejpam-4646	63	46	copy	copy	NOUN
ejpam-4646	63	47	of	of	ADP
ejpam-4646	63	48	h	h	NOUN
ejpam-4646	63	49	in	in	ADP
ejpam-4646	63	50	g	g	PROPN
ejpam-4646	63	51	◦	◦	NOUN
ejpam-4646	63	52	h	h	NOUN
ejpam-4646	63	53	corresponding	correspond	VERB
ejpam-4646	63	54	to	to	ADP
ejpam-4646	63	55	the	the	DET
ejpam-4646	63	56	vertex	vertex	NOUN
ejpam-4646	63	57	v	v	ADP
ejpam-4646	63	58	∈	∈	PROPN
ejpam-4646	63	59	v	v	NOUN
ejpam-4646	63	60	(	(	PUNCT
ejpam-4646	63	61	g	g	NOUN
ejpam-4646	63	62	)	)	PUNCT
ejpam-4646	63	63	and	and	CCONJ
ejpam-4646	63	64	write	write	VERB
ejpam-4646	63	65	v	v	PRON
ejpam-4646	63	66	+	+	CCONJ
ejpam-4646	63	67	hv	hv	NOUN
ejpam-4646	63	68	for	for	ADP
ejpam-4646	63	69	⟨v⟩	⟨v⟩	PROPN
ejpam-4646	64	1	+	+	PROPN
ejpam-4646	64	2	hv	hv	PROPN
ejpam-4646	64	3	.	.	PUNCT
ejpam-4646	65	1	the	the	DET
ejpam-4646	65	2	lexicographic	lexicographic	ADJ
ejpam-4646	65	3	product	product	NOUN
ejpam-4646	65	4	g[h	g[h	PROPN
ejpam-4646	65	5	]	]	PUNCT
ejpam-4646	65	6	is	be	AUX
ejpam-4646	65	7	the	the	DET
ejpam-4646	65	8	graph	graph	NOUN
ejpam-4646	65	9	with	with	ADP
ejpam-4646	65	10	vertex	vertex	NOUN
ejpam-4646	65	11	set	set	VERB
ejpam-4646	65	12	v	v	NOUN
ejpam-4646	65	13	(	(	PUNCT
ejpam-4646	65	14	g[h	g[h	PROPN
ejpam-4646	65	15	]	]	PUNCT
ejpam-4646	65	16	)	)	PUNCT
ejpam-4646	65	17	=	=	SYM
ejpam-4646	65	18	v	v	X
ejpam-4646	65	19	(	(	PUNCT
ejpam-4646	65	20	g)×	g)×	NOUN
ejpam-4646	65	21	v	v	NOUN
ejpam-4646	65	22	(	(	PUNCT
ejpam-4646	65	23	h	h	NOUN
ejpam-4646	65	24	)	)	PUNCT
ejpam-4646	65	25	and	and	CCONJ
ejpam-4646	65	26	(	(	PUNCT
ejpam-4646	65	27	v	v	NOUN
ejpam-4646	65	28	,	,	PUNCT
ejpam-4646	65	29	a)(u	a)(u	ADJ
ejpam-4646	65	30	,	,	PUNCT
ejpam-4646	65	31	b	b	X
ejpam-4646	65	32	)	)	PUNCT
ejpam-4646	65	33	∈	∈	NOUN
ejpam-4646	65	34	e(g[h	e(g[h	NOUN
ejpam-4646	65	35	]	]	PUNCT
ejpam-4646	65	36	)	)	PUNCT
ejpam-4646	66	1	if	if	SCONJ
ejpam-4646	66	2	and	and	CCONJ
ejpam-4646	66	3	only	only	ADV
ejpam-4646	66	4	if	if	SCONJ
ejpam-4646	66	5	either	either	DET
ejpam-4646	66	6	uv	uv	PROPN
ejpam-4646	66	7	∈	∈	PROPN
ejpam-4646	66	8	e(g	e(g	PROPN
ejpam-4646	66	9	)	)	PUNCT
ejpam-4646	66	10	or	or	CCONJ
ejpam-4646	66	11	u	u	X
ejpam-4646	66	12	=	=	PROPN
ejpam-4646	66	13	v	v	PROPN
ejpam-4646	66	14	and	and	CCONJ
ejpam-4646	66	15	ab	ab	PROPN
ejpam-4646	66	16	∈	∈	PROPN
ejpam-4646	66	17	e(h	e(h	PROPN
ejpam-4646	66	18	)	)	PUNCT
ejpam-4646	66	19	.	.	PUNCT
ejpam-4646	67	1	note	note	VERB
ejpam-4646	67	2	that	that	SCONJ
ejpam-4646	67	3	any	any	DET
ejpam-4646	67	4	non	non	ADJ
ejpam-4646	67	5	-	-	ADJ
ejpam-4646	67	6	empty	empty	ADJ
ejpam-4646	67	7	set	set	NOUN
ejpam-4646	67	8	c	c	NOUN
ejpam-4646	67	9	⊆	⊆	NUM
ejpam-4646	67	10	v	v	NOUN
ejpam-4646	67	11	(	(	PUNCT
ejpam-4646	67	12	g)×v	g)×v	PROPN
ejpam-4646	67	13	(	(	PUNCT
ejpam-4646	67	14	h	h	NOUN
ejpam-4646	67	15	)	)	PUNCT
ejpam-4646	67	16	can	can	AUX
ejpam-4646	67	17	be	be	AUX
ejpam-4646	67	18	written	write	VERB
ejpam-4646	67	19	as	as	ADP
ejpam-4646	67	20	c	c	NOUN
ejpam-4646	67	21	=	=	PUNCT
ejpam-4646	67	22	⋃	⋃	PROPN
ejpam-4646	67	23	x∈s	x∈s	NOUN
ejpam-4646	68	1	[	[	X
ejpam-4646	68	2	{	{	PUNCT
ejpam-4646	68	3	x	x	NOUN
ejpam-4646	68	4	}	}	PUNCT
ejpam-4646	68	5	×	×	PROPN
ejpam-4646	68	6	tx	tx	PROPN
ejpam-4646	68	7	]	]	X
ejpam-4646	68	8	,	,	PUNCT
ejpam-4646	68	9	where	where	SCONJ
ejpam-4646	68	10	s	s	VERB
ejpam-4646	68	11	⊆	⊆	NUM
ejpam-4646	68	12	v	v	NOUN
ejpam-4646	68	13	(	(	PUNCT
ejpam-4646	68	14	g	g	NOUN
ejpam-4646	68	15	)	)	PUNCT
ejpam-4646	68	16	and	and	CCONJ
ejpam-4646	68	17	tx	tx	VERB
ejpam-4646	68	18	⊆	⊆	NUM
ejpam-4646	68	19	v	v	NOUN
ejpam-4646	68	20	(	(	PUNCT
ejpam-4646	68	21	h	h	NOUN
ejpam-4646	68	22	)	)	PUNCT
ejpam-4646	68	23	for	for	ADP
ejpam-4646	68	24	each	each	DET
ejpam-4646	68	25	x	x	PROPN
ejpam-4646	68	26	∈	∈	PROPN
ejpam-4646	68	27	s.	s.	PROPN
ejpam-4646	68	28	3	3	X
ejpam-4646	68	29	.	.	PROPN
ejpam-4646	68	30	results	result	NOUN
ejpam-4646	68	31	remark	remark	VERB
ejpam-4646	68	32	1	1	NUM
ejpam-4646	68	33	.	.	PUNCT
ejpam-4646	69	1	let	let	VERB
ejpam-4646	69	2	g	g	PRON
ejpam-4646	69	3	be	be	AUX
ejpam-4646	69	4	a	a	DET
ejpam-4646	69	5	connected	connected	ADJ
ejpam-4646	69	6	graph	graph	NOUN
ejpam-4646	69	7	of	of	ADP
ejpam-4646	69	8	order	order	NOUN
ejpam-4646	69	9	n.	n.	NOUN
ejpam-4646	69	10	if	if	SCONJ
ejpam-4646	69	11	s	s	VERB
ejpam-4646	69	12	is	be	AUX
ejpam-4646	69	13	a	a	DET
ejpam-4646	69	14	geodetic	geodetic	ADJ
ejpam-4646	69	15	hop	hop	NOUN
ejpam-4646	69	16	dominating	dominating	NOUN
ejpam-4646	69	17	set	set	NOUN
ejpam-4646	69	18	then	then	ADV
ejpam-4646	69	19	s	s	VERB
ejpam-4646	69	20	is	be	AUX
ejpam-4646	69	21	a	a	DET
ejpam-4646	69	22	hop	hop	NOUN
ejpam-4646	69	23	dominating	dominating	NOUN
ejpam-4646	69	24	set	set	NOUN
ejpam-4646	69	25	.	.	PUNCT
ejpam-4646	70	1	in	in	ADP
ejpam-4646	70	2	particular	particular	ADJ
ejpam-4646	70	3	,	,	PUNCT
ejpam-4646	70	4	γh(g	γh(g	NOUN
ejpam-4646	70	5	)	)	PUNCT
ejpam-4646	70	6	≤	≤	NUM
ejpam-4646	70	7	γhg(g	γhg(g	PROPN
ejpam-4646	70	8	)	)	PUNCT
ejpam-4646	70	9	.	.	PUNCT
ejpam-4646	71	1	theorem	theorem	NOUN
ejpam-4646	71	2	1	1	X
ejpam-4646	71	3	.	.	PUNCT
ejpam-4646	72	1	let	let	VERB
ejpam-4646	72	2	g	g	PRON
ejpam-4646	72	3	be	be	AUX
ejpam-4646	72	4	a	a	DET
ejpam-4646	72	5	connected	connected	ADJ
ejpam-4646	72	6	graph	graph	NOUN
ejpam-4646	72	7	of	of	ADP
ejpam-4646	72	8	order	order	NOUN
ejpam-4646	72	9	n	n	PRON
ejpam-4646	72	10	≥	≥	NOUN
ejpam-4646	72	11	2	2	NUM
ejpam-4646	72	12	.	.	PUNCT
ejpam-4646	73	1	then	then	ADV
ejpam-4646	73	2	γhg(g	γhg(g	PROPN
ejpam-4646	73	3	)	)	PUNCT
ejpam-4646	74	1	=	=	NOUN
ejpam-4646	75	1	n	n	NOUN
ejpam-4646	75	2	if	if	SCONJ
ejpam-4646	75	3	and	and	CCONJ
ejpam-4646	75	4	only	only	ADV
ejpam-4646	75	5	if	if	SCONJ
ejpam-4646	75	6	one	one	NUM
ejpam-4646	75	7	of	of	ADP
ejpam-4646	75	8	the	the	DET
ejpam-4646	75	9	following	follow	VERB
ejpam-4646	75	10	holds	hold	VERB
ejpam-4646	75	11	:	:	PUNCT
ejpam-4646	75	12	(	(	PUNCT
ejpam-4646	75	13	i	i	NOUN
ejpam-4646	75	14	)	)	PUNCT
ejpam-4646	75	15	g	g	PROPN
ejpam-4646	75	16	=	=	SYM
ejpam-4646	75	17	kn	kn	PROPN
ejpam-4646	75	18	(	(	PUNCT
ejpam-4646	75	19	ii	ii	NOUN
ejpam-4646	75	20	)	)	PUNCT
ejpam-4646	75	21	g	g	PROPN
ejpam-4646	75	22	̸=	̸=	PROPN
ejpam-4646	75	23	kn	kn	PROPN
ejpam-4646	75	24	and	and	CCONJ
ejpam-4646	75	25	there	there	PRON
ejpam-4646	75	26	exist	exist	VERB
ejpam-4646	75	27	dominating	dominating	NOUN
ejpam-4646	75	28	vertices	vertex	NOUN
ejpam-4646	75	29	v1	v1	NOUN
ejpam-4646	75	30	,	,	PUNCT
ejpam-4646	75	31	v2	v2	PROPN
ejpam-4646	75	32	,	,	PUNCT
ejpam-4646	75	33	...	...	PUNCT
ejpam-4646	75	34	,	,	PUNCT
ejpam-4646	75	35	vk	vk	VERB
ejpam-4646	75	36	such	such	ADJ
ejpam-4646	75	37	that	that	DET
ejpam-4646	75	38	h1	h1	PROPN
ejpam-4646	75	39	=	=	SYM
ejpam-4646	75	40	g	g	PROPN
ejpam-4646	75	41	\	\	PROPN
ejpam-4646	75	42	v1	v1	PROPN
ejpam-4646	75	43	,	,	PUNCT
ejpam-4646	75	44	h2	h2	NOUN
ejpam-4646	75	45	=	=	PUNCT
ejpam-4646	75	46	h1	h1	VERB
ejpam-4646	75	47	\	\	PROPN
ejpam-4646	75	48	v2	v2	PROPN
ejpam-4646	75	49	,	,	PUNCT
ejpam-4646	75	50	.	.	PUNCT
ejpam-4646	75	51	.	.	PUNCT
ejpam-4646	75	52	.	.	PUNCT
ejpam-4646	76	1	,	,	PUNCT
ejpam-4646	76	2	hk−1	hk−1	NOUN
ejpam-4646	76	3	=	=	PUNCT
ejpam-4646	76	4	hk−2	hk−2	PROPN
ejpam-4646	76	5	\	\	NOUN
ejpam-4646	76	6	vk−1	vk−1	NOUN
ejpam-4646	76	7	are	be	AUX
ejpam-4646	76	8	connected	connect	VERB
ejpam-4646	76	9	graphs	graph	NOUN
ejpam-4646	76	10	and	and	CCONJ
ejpam-4646	76	11	hk	hk	PROPN
ejpam-4646	76	12	=	=	PROPN
ejpam-4646	76	13	hk−1	hk−1	PROPN
ejpam-4646	76	14	\	\	PROPN
ejpam-4646	76	15	vk	vk	PROPN
ejpam-4646	76	16	is	be	AUX
ejpam-4646	76	17	the	the	DET
ejpam-4646	76	18	union	union	NOUN
ejpam-4646	76	19	of	of	ADP
ejpam-4646	76	20	atleast	atleast	ADJ
ejpam-4646	76	21	2	2	NUM
ejpam-4646	76	22	complete	complete	ADJ
ejpam-4646	76	23	components	component	NOUN
ejpam-4646	76	24	.	.	PUNCT
ejpam-4646	77	1	proof	proof	NOUN
ejpam-4646	77	2	.	.	PUNCT
ejpam-4646	78	1	suppose	suppose	VERB
ejpam-4646	78	2	γhg(g	γhg(g	NOUN
ejpam-4646	78	3	)	)	PUNCT
ejpam-4646	78	4	=	=	SYM
ejpam-4646	79	1	n	n	NOUN
ejpam-4646	80	1	and	and	CCONJ
ejpam-4646	80	2	suppose	suppose	VERB
ejpam-4646	80	3	that	that	SCONJ
ejpam-4646	80	4	g	g	PROPN
ejpam-4646	80	5	̸=	̸=	PROPN
ejpam-4646	80	6	kn	kn	PROPN
ejpam-4646	80	7	.	.	PUNCT
ejpam-4646	81	1	then	then	ADV
ejpam-4646	81	2	there	there	PRON
ejpam-4646	81	3	exist	exist	VERB
ejpam-4646	81	4	x	x	NOUN
ejpam-4646	81	5	,	,	PUNCT
ejpam-4646	81	6	y	y	PROPN
ejpam-4646	81	7	∈	∈	PROPN
ejpam-4646	81	8	v	v	ADP
ejpam-4646	81	9	(	(	PUNCT
ejpam-4646	81	10	g	g	NOUN
ejpam-4646	81	11	)	)	PUNCT
ejpam-4646	81	12	such	such	ADJ
ejpam-4646	81	13	that	that	DET
ejpam-4646	81	14	dg(x	dg(x	PROPN
ejpam-4646	81	15	,	,	PUNCT
ejpam-4646	81	16	y	y	NOUN
ejpam-4646	81	17	)	)	PUNCT
ejpam-4646	81	18	=	=	SYM
ejpam-4646	82	1	2	2	X
ejpam-4646	82	2	.	.	PUNCT
ejpam-4646	82	3	let	let	VERB
ejpam-4646	82	4	v1	v1	VERB
ejpam-4646	82	5	∈	∈	NOUN
ejpam-4646	82	6	ng(x	ng(x	NUM
ejpam-4646	82	7	)	)	PUNCT
ejpam-4646	82	8	∩	∩	NOUN
ejpam-4646	82	9	ng(y	ng(y	NOUN
ejpam-4646	82	10	)	)	PUNCT
ejpam-4646	82	11	.	.	PUNCT
ejpam-4646	83	1	suppose	suppose	VERB
ejpam-4646	83	2	there	there	PRON
ejpam-4646	83	3	exists	exist	VERB
ejpam-4646	83	4	z	z	PROPN
ejpam-4646	83	5	∈	∈	PROPN
ejpam-4646	83	6	v	v	ADP
ejpam-4646	83	7	(	(	PUNCT
ejpam-4646	83	8	g	g	NOUN
ejpam-4646	83	9	)	)	PUNCT
ejpam-4646	83	10	\	\	NOUN
ejpam-4646	83	11	{	{	PUNCT
ejpam-4646	83	12	v1	v1	NOUN
ejpam-4646	83	13	}	}	PUNCT
ejpam-4646	83	14	such	such	ADJ
ejpam-4646	83	15	that	that	DET
ejpam-4646	83	16	v1z	v1z	NOUN
ejpam-4646	83	17	/∈	/∈	PUNCT
ejpam-4646	83	18	e(g	e(g	PROPN
ejpam-4646	83	19	)	)	PUNCT
ejpam-4646	83	20	.	.	PUNCT
ejpam-4646	84	1	we	we	PRON
ejpam-4646	84	2	may	may	AUX
ejpam-4646	84	3	pick	pick	VERB
ejpam-4646	84	4	z	z	PROPN
ejpam-4646	84	5	so	so	SCONJ
ejpam-4646	84	6	that	that	SCONJ
ejpam-4646	84	7	dg(v1	dg(v1	VERB
ejpam-4646	84	8	,	,	PUNCT
ejpam-4646	84	9	z	z	NOUN
ejpam-4646	84	10	)	)	PUNCT
ejpam-4646	84	11	=	=	SYM
ejpam-4646	85	1	2	2	X
ejpam-4646	85	2	.	.	PUNCT
ejpam-4646	85	3	then	then	ADV
ejpam-4646	85	4	v	v	X
ejpam-4646	85	5	(	(	PUNCT
ejpam-4646	85	6	g	g	NOUN
ejpam-4646	85	7	)	)	PUNCT
ejpam-4646	85	8	\	\	NOUN
ejpam-4646	85	9	{	{	PUNCT
ejpam-4646	85	10	v1	v1	NOUN
ejpam-4646	85	11	}	}	PUNCT
ejpam-4646	85	12	is	be	AUX
ejpam-4646	85	13	a	a	DET
ejpam-4646	85	14	geodetic	geodetic	ADJ
ejpam-4646	85	15	hop	hop	NOUN
ejpam-4646	85	16	dominating	dominating	NOUN
ejpam-4646	85	17	set	set	NOUN
ejpam-4646	85	18	of	of	ADP
ejpam-4646	85	19	g	g	PROPN
ejpam-4646	85	20	,	,	PUNCT
ejpam-4646	85	21	contrary	contrary	ADJ
ejpam-4646	85	22	to	to	ADP
ejpam-4646	85	23	our	our	PRON
ejpam-4646	85	24	assumption	assumption	NOUN
ejpam-4646	85	25	that	that	SCONJ
ejpam-4646	85	26	γhg(g	γhg(g	PROPN
ejpam-4646	85	27	)	)	PUNCT
ejpam-4646	86	1	=	=	VERB
ejpam-4646	86	2	n.	n.	PROPN
ejpam-4646	86	3	thus	thus	ADV
ejpam-4646	86	4	,	,	PUNCT
ejpam-4646	86	5	ng	ng	PROPN
ejpam-4646	87	1	[	[	X
ejpam-4646	87	2	v1	v1	X
ejpam-4646	87	3	]	]	X
ejpam-4646	87	4	=	=	SYM
ejpam-4646	87	5	v	v	X
ejpam-4646	87	6	(	(	PUNCT
ejpam-4646	87	7	g	g	NOUN
ejpam-4646	87	8	)	)	PUNCT
ejpam-4646	87	9	.	.	PUNCT
ejpam-4646	88	1	next	next	ADV
ejpam-4646	88	2	,	,	PUNCT
ejpam-4646	88	3	let	let	VERB
ejpam-4646	88	4	h1	h1	VERB
ejpam-4646	88	5	=	=	SYM
ejpam-4646	88	6	g	g	PROPN
ejpam-4646	88	7	\	\	PROPN
ejpam-4646	88	8	v1	v1	PROPN
ejpam-4646	88	9	.	.	PUNCT
ejpam-4646	88	10	suppose	suppose	VERB
ejpam-4646	88	11	that	that	SCONJ
ejpam-4646	88	12	h1	h1	PROPN
ejpam-4646	88	13	is	be	AUX
ejpam-4646	88	14	disconnected	disconnect	VERB
ejpam-4646	88	15	and	and	CCONJ
ejpam-4646	88	16	suppose	suppose	VERB
ejpam-4646	88	17	that	that	SCONJ
ejpam-4646	88	18	h1	h1	PROPN
ejpam-4646	88	19	has	have	VERB
ejpam-4646	88	20	a	a	DET
ejpam-4646	88	21	component	component	NOUN
ejpam-4646	88	22	h	h	NOUN
ejpam-4646	88	23	′	′	NOUN
ejpam-4646	88	24	1	1	NUM
ejpam-4646	89	1	that	that	PRON
ejpam-4646	89	2	is	be	AUX
ejpam-4646	89	3	not	not	PART
ejpam-4646	89	4	complete	complete	ADJ
ejpam-4646	89	5	.	.	PUNCT
ejpam-4646	90	1	then	then	ADV
ejpam-4646	90	2	there	there	PRON
ejpam-4646	90	3	exists	exist	VERB
ejpam-4646	90	4	s	s	PROPN
ejpam-4646	90	5	,	,	PUNCT
ejpam-4646	90	6	t	t	PROPN
ejpam-4646	90	7	∈	∈	PROPN
ejpam-4646	90	8	v	v	X
ejpam-4646	90	9	(	(	PUNCT
ejpam-4646	90	10	h	h	NOUN
ejpam-4646	90	11	′	′	NOUN
ejpam-4646	90	12	1	1	NUM
ejpam-4646	90	13	)	)	PUNCT
ejpam-4646	90	14	such	such	ADJ
ejpam-4646	90	15	that	that	SCONJ
ejpam-4646	90	16	d	d	NOUN
ejpam-4646	90	17	h	h	NOUN
ejpam-4646	91	1	′	′	NOUN
ejpam-4646	91	2	1	1	NUM
ejpam-4646	91	3	(	(	PUNCT
ejpam-4646	91	4	s	s	PROPN
ejpam-4646	91	5	,	,	PUNCT
ejpam-4646	91	6	t	t	PROPN
ejpam-4646	91	7	)	)	PUNCT
ejpam-4646	91	8	=	=	SYM
ejpam-4646	91	9	dh1(s	dh1(s	PROPN
ejpam-4646	91	10	,	,	PUNCT
ejpam-4646	91	11	t	t	PROPN
ejpam-4646	91	12	)	)	PUNCT
ejpam-4646	91	13	=	=	SYM
ejpam-4646	91	14	dg(s	dg(s	NOUN
ejpam-4646	91	15	,	,	PUNCT
ejpam-4646	91	16	t	t	PROPN
ejpam-4646	91	17	)	)	PUNCT
ejpam-4646	91	18	=	=	SYM
ejpam-4646	92	1	2	2	X
ejpam-4646	92	2	.	.	X
ejpam-4646	92	3	let	let	VERB
ejpam-4646	92	4	r	r	NOUN
ejpam-4646	92	5	∈	∈	PROPN
ejpam-4646	92	6	ng(s	ng(s	PRON
ejpam-4646	92	7	)	)	PUNCT
ejpam-4646	92	8	∩	∩	NOUN
ejpam-4646	92	9	ng(t	ng(t	NUM
ejpam-4646	92	10	)	)	PUNCT
ejpam-4646	92	11	.	.	PUNCT
ejpam-4646	93	1	then	then	ADV
ejpam-4646	93	2	v	v	X
ejpam-4646	93	3	(	(	PUNCT
ejpam-4646	93	4	g	g	NOUN
ejpam-4646	93	5	)	)	PUNCT
ejpam-4646	93	6	\	\	NOUN
ejpam-4646	94	1	{	{	PUNCT
ejpam-4646	94	2	r	r	NOUN
ejpam-4646	94	3	}	}	PUNCT
ejpam-4646	94	4	is	be	AUX
ejpam-4646	94	5	a	a	DET
ejpam-4646	94	6	geodetic	geodetic	ADJ
ejpam-4646	94	7	hop	hop	NOUN
ejpam-4646	94	8	dominating	dominating	NOUN
ejpam-4646	94	9	set	set	NOUN
ejpam-4646	94	10	of	of	ADP
ejpam-4646	94	11	g	g	PROPN
ejpam-4646	94	12	,	,	PUNCT
ejpam-4646	94	13	a	a	DET
ejpam-4646	94	14	contradiction	contradiction	NOUN
ejpam-4646	94	15	.	.	PUNCT
ejpam-4646	95	1	therefore	therefore	ADV
ejpam-4646	95	2	,	,	PUNCT
ejpam-4646	95	3	all	all	DET
ejpam-4646	95	4	components	component	NOUN
ejpam-4646	95	5	of	of	ADP
ejpam-4646	95	6	h1	h1	PROPN
ejpam-4646	95	7	are	be	AUX
ejpam-4646	95	8	complete	complete	ADJ
ejpam-4646	95	9	.	.	PUNCT
ejpam-4646	96	1	suppose	suppose	VERB
ejpam-4646	96	2	h1	h1	PROPN
ejpam-4646	96	3	is	be	AUX
ejpam-4646	96	4	connected	connect	VERB
ejpam-4646	96	5	.	.	PUNCT
ejpam-4646	97	1	suppose	suppose	VERB
ejpam-4646	97	2	further	far	ADV
ejpam-4646	97	3	that	that	DET
ejpam-4646	97	4	dh1(x	dh1(x	NOUN
ejpam-4646	97	5	,	,	PUNCT
ejpam-4646	97	6	y	y	PROPN
ejpam-4646	97	7	)	)	PUNCT
ejpam-4646	97	8	≥	≥	NOUN
ejpam-4646	97	9	3	3	NUM
ejpam-4646	97	10	,	,	PUNCT
ejpam-4646	97	11	say	say	VERB
ejpam-4646	97	12	[	[	X
ejpam-4646	97	13	x1	x1	ADJ
ejpam-4646	97	14	,	,	PUNCT
ejpam-4646	97	15	x2	x2	PROPN
ejpam-4646	97	16	,	,	PUNCT
ejpam-4646	97	17	...	...	PUNCT
ejpam-4646	97	18	,	,	PUNCT
ejpam-4646	97	19	xk	xk	PROPN
ejpam-4646	97	20	]	]	X
ejpam-4646	97	21	,	,	PUNCT
ejpam-4646	97	22	where	where	SCONJ
ejpam-4646	97	23	x1	x1	ADJ
ejpam-4646	97	24	=	=	PUNCT
ejpam-4646	97	25	x	x	X
ejpam-4646	97	26	and	and	CCONJ
ejpam-4646	97	27	xk	xk	PROPN
ejpam-4646	97	28	=	=	SYM
ejpam-4646	97	29	y	y	PROPN
ejpam-4646	97	30	,	,	PUNCT
ejpam-4646	97	31	be	be	AUX
ejpam-4646	97	32	an	an	DET
ejpam-4646	97	33	x	x	NOUN
ejpam-4646	97	34	-	-	ADJ
ejpam-4646	97	35	y	y	PROPN
ejpam-4646	97	36	geodesic	geodesic	ADJ
ejpam-4646	97	37	inh	inh	PROPN
ejpam-4646	97	38	.	.	PUNCT
ejpam-4646	98	1	then	then	ADV
ejpam-4646	98	2	v	v	INTJ
ejpam-4646	98	3	(	(	PUNCT
ejpam-4646	98	4	g)\{x2	g)\{x2	PROPN
ejpam-4646	98	5	}	}	PUNCT
ejpam-4646	98	6	is	be	AUX
ejpam-4646	98	7	a	a	DET
ejpam-4646	98	8	geodetic	geodetic	ADJ
ejpam-4646	98	9	hop	hop	NOUN
ejpam-4646	98	10	dominating	dominating	NOUN
ejpam-4646	98	11	set	set	NOUN
ejpam-4646	98	12	,	,	PUNCT
ejpam-4646	98	13	a	a	DET
ejpam-4646	98	14	contradiction	contradiction	NOUN
ejpam-4646	98	15	.	.	PUNCT
ejpam-4646	99	1	thus	thus	ADV
ejpam-4646	99	2	,	,	PUNCT
ejpam-4646	99	3	dh(x	dh(x	X
ejpam-4646	99	4	,	,	PUNCT
ejpam-4646	99	5	y	y	NOUN
ejpam-4646	99	6	)	)	PUNCT
ejpam-4646	99	7	=	=	SYM
ejpam-4646	99	8	2	2	X
ejpam-4646	99	9	.	.	PUNCT
ejpam-4646	99	10	let	let	VERB
ejpam-4646	99	11	v2	v2	VERB
ejpam-4646	99	12	∈	∈	PROPN
ejpam-4646	99	13	nh1(x)∩nh2(y	nh1(x)∩nh2(y	NOUN
ejpam-4646	99	14	)	)	PUNCT
ejpam-4646	99	15	.	.	PUNCT
ejpam-4646	100	1	suppose	suppose	VERB
ejpam-4646	100	2	there	there	PRON
ejpam-4646	100	3	exists	exist	VERB
ejpam-4646	100	4	p	p	PROPN
ejpam-4646	100	5	∈	∈	PROPN
ejpam-4646	100	6	v	v	ADP
ejpam-4646	100	7	(	(	PUNCT
ejpam-4646	100	8	h1	h1	PROPN
ejpam-4646	100	9	)	)	PUNCT
ejpam-4646	101	1	such	such	ADJ
ejpam-4646	101	2	that	that	SCONJ
ejpam-4646	101	3	dh1(v2	dh1(v2	NOUN
ejpam-4646	101	4	,	,	PUNCT
ejpam-4646	101	5	p	p	NOUN
ejpam-4646	101	6	)	)	PUNCT
ejpam-4646	101	7	=	=	SYM
ejpam-4646	101	8	2	2	X
ejpam-4646	101	9	.	.	PUNCT
ejpam-4646	101	10	then	then	ADV
ejpam-4646	101	11	v	v	X
ejpam-4646	101	12	(	(	PUNCT
ejpam-4646	101	13	g	g	NOUN
ejpam-4646	101	14	)	)	PUNCT
ejpam-4646	101	15	\	\	NOUN
ejpam-4646	102	1	{	{	PUNCT
ejpam-4646	102	2	v2	v2	NOUN
ejpam-4646	102	3	}	}	PUNCT
ejpam-4646	102	4	is	be	AUX
ejpam-4646	102	5	geodetic	geodetic	ADJ
ejpam-4646	102	6	hop	hop	NOUN
ejpam-4646	102	7	dominating	dominating	NOUN
ejpam-4646	102	8	set	set	NOUN
ejpam-4646	102	9	of	of	ADP
ejpam-4646	102	10	g	g	PROPN
ejpam-4646	102	11	,	,	PUNCT
ejpam-4646	102	12	a	a	DET
ejpam-4646	102	13	contradiction	contradiction	NOUN
ejpam-4646	102	14	.	.	PUNCT
ejpam-4646	103	1	thus	thus	ADV
ejpam-4646	103	2	,	,	PUNCT
ejpam-4646	103	3	nh1(v2	nh1(v2	ADJ
ejpam-4646	103	4	)	)	PUNCT
ejpam-4646	103	5	=	=	SYM
ejpam-4646	103	6	v	v	X
ejpam-4646	103	7	(	(	PUNCT
ejpam-4646	103	8	h1	h1	PROPN
ejpam-4646	103	9	)	)	PUNCT
ejpam-4646	103	10	and	and	CCONJ
ejpam-4646	103	11	ng	ng	PROPN
ejpam-4646	104	1	[	[	X
ejpam-4646	104	2	v2	v2	X
ejpam-4646	104	3	]	]	X
ejpam-4646	104	4	=	=	SYM
ejpam-4646	104	5	v	v	NOUN
ejpam-4646	104	6	(	(	PUNCT
ejpam-4646	104	7	g	g	NOUN
ejpam-4646	104	8	)	)	PUNCT
ejpam-4646	104	9	.	.	PUNCT
ejpam-4646	105	1	c.j	c.j	PROPN
ejpam-4646	105	2	.	.	PROPN
ejpam-4646	105	3	saromines	saromines	PROPN
ejpam-4646	105	4	,	,	PUNCT
ejpam-4646	105	5	s.	s.	PROPN
ejpam-4646	105	6	canoy	canoy	PROPN
ejpam-4646	105	7	,	,	PUNCT
ejpam-4646	105	8	jr	jr	PROPN
ejpam-4646	105	9	.	.	PROPN
ejpam-4646	105	10	,	,	PUNCT
ejpam-4646	105	11	/	/	SYM
ejpam-4646	105	12	eur	eur	NOUN
ejpam-4646	105	13	.	.	PUNCT
ejpam-4646	106	1	j.	j.	PROPN
ejpam-4646	106	2	pure	pure	PROPN
ejpam-4646	106	3	appl	appl	PROPN
ejpam-4646	106	4	.	.	PROPN
ejpam-4646	106	5	math	math	PROPN
ejpam-4646	106	6	,	,	PUNCT
ejpam-4646	106	7	16	16	NUM
ejpam-4646	106	8	(	(	PUNCT
ejpam-4646	106	9	1	1	NUM
ejpam-4646	106	10	)	)	PUNCT
ejpam-4646	106	11	(	(	PUNCT
ejpam-4646	106	12	2023	2023	NUM
ejpam-4646	106	13	)	)	PUNCT
ejpam-4646	106	14	,	,	PUNCT
ejpam-4646	106	15	5	5	NUM
ejpam-4646	106	16	-	-	SYM
ejpam-4646	106	17	17	17	NUM
ejpam-4646	106	18	8	8	NUM
ejpam-4646	106	19	continuing	continue	VERB
ejpam-4646	106	20	in	in	ADP
ejpam-4646	106	21	this	this	DET
ejpam-4646	106	22	manner	manner	NOUN
ejpam-4646	107	1	,	,	PUNCT
ejpam-4646	107	2	there	there	PRON
ejpam-4646	107	3	exists	exist	VERB
ejpam-4646	107	4	a	a	DET
ejpam-4646	107	5	finite	finite	ADJ
ejpam-4646	107	6	sequence	sequence	NOUN
ejpam-4646	107	7	of	of	ADP
ejpam-4646	107	8	dominating	dominating	NOUN
ejpam-4646	107	9	vertices	vertex	NOUN
ejpam-4646	107	10	v1	v1	NOUN
ejpam-4646	107	11	,	,	PUNCT
ejpam-4646	107	12	v2	v2	PROPN
ejpam-4646	107	13	,	,	PUNCT
ejpam-4646	107	14	...	...	PUNCT
ejpam-4646	107	15	,	,	PUNCT
ejpam-4646	107	16	vk	vk	VERB
ejpam-4646	107	17	such	such	ADJ
ejpam-4646	107	18	that	that	DET
ejpam-4646	107	19	h1	h1	PROPN
ejpam-4646	107	20	=	=	SYM
ejpam-4646	107	21	g	g	PROPN
ejpam-4646	107	22	\	\	PROPN
ejpam-4646	107	23	v1	v1	PROPN
ejpam-4646	107	24	,	,	PUNCT
ejpam-4646	107	25	h2	h2	NOUN
ejpam-4646	107	26	=	=	PUNCT
ejpam-4646	107	27	h1	h1	VERB
ejpam-4646	107	28	\	\	PROPN
ejpam-4646	107	29	v2	v2	PROPN
ejpam-4646	107	30	,	,	PUNCT
ejpam-4646	107	31	.	.	PUNCT
ejpam-4646	107	32	.	.	PUNCT
ejpam-4646	108	1	.	.	PUNCT
ejpam-4646	109	1	,	,	PUNCT
ejpam-4646	109	2	hk−1	hk−1	NOUN
ejpam-4646	109	3	=	=	PUNCT
ejpam-4646	109	4	hk−2	hk−2	PROPN
ejpam-4646	109	5	\	\	NOUN
ejpam-4646	109	6	vk−1	vk−1	NOUN
ejpam-4646	109	7	are	be	AUX
ejpam-4646	109	8	connected	connect	VERB
ejpam-4646	109	9	graphs	graph	NOUN
ejpam-4646	109	10	and	and	CCONJ
ejpam-4646	109	11	hk	hk	PROPN
ejpam-4646	109	12	=	=	PROPN
ejpam-4646	109	13	hk−1	hk−1	PROPN
ejpam-4646	109	14	\	\	PROPN
ejpam-4646	109	15	vk	vk	PROPN
ejpam-4646	109	16	is	be	AUX
ejpam-4646	109	17	the	the	DET
ejpam-4646	109	18	union	union	NOUN
ejpam-4646	109	19	of	of	ADP
ejpam-4646	109	20	at	at	ADV
ejpam-4646	109	21	least	least	ADV
ejpam-4646	109	22	2	2	NUM
ejpam-4646	109	23	complete	complete	ADJ
ejpam-4646	109	24	components	component	NOUN
ejpam-4646	109	25	.	.	PUNCT
ejpam-4646	110	1	for	for	ADP
ejpam-4646	110	2	the	the	DET
ejpam-4646	110	3	converse	converse	NOUN
ejpam-4646	110	4	,	,	PUNCT
ejpam-4646	110	5	suppose	suppose	VERB
ejpam-4646	110	6	that	that	SCONJ
ejpam-4646	110	7	g	g	PROPN
ejpam-4646	110	8	=	=	PROPN
ejpam-4646	110	9	kn	kn	PROPN
ejpam-4646	110	10	.	.	PUNCT
ejpam-4646	111	1	then	then	ADV
ejpam-4646	111	2	,	,	PUNCT
ejpam-4646	111	3	clearly	clearly	ADV
ejpam-4646	111	4	,	,	PUNCT
ejpam-4646	111	5	γgh(g	γgh(g	NOUN
ejpam-4646	111	6	)	)	PUNCT
ejpam-4646	111	7	=	=	SYM
ejpam-4646	112	1	n.	n.	NOUN
ejpam-4646	112	2	let	let	VERB
ejpam-4646	112	3	v1	v1	NOUN
ejpam-4646	112	4	,	,	PUNCT
ejpam-4646	112	5	v2	v2	PROPN
ejpam-4646	112	6	,	,	PUNCT
ejpam-4646	112	7	...	...	PUNCT
ejpam-4646	112	8	,	,	PUNCT
ejpam-4646	112	9	vk	vk	AUX
ejpam-4646	112	10	be	be	AUX
ejpam-4646	112	11	dominating	dominate	VERB
ejpam-4646	112	12	vertices	vertex	NOUN
ejpam-4646	112	13	such	such	ADJ
ejpam-4646	112	14	that	that	SCONJ
ejpam-4646	112	15	h1	h1	PROPN
ejpam-4646	112	16	=	=	SYM
ejpam-4646	112	17	g	g	PROPN
ejpam-4646	112	18	\	\	PROPN
ejpam-4646	112	19	v1	v1	PROPN
ejpam-4646	112	20	,	,	PUNCT
ejpam-4646	112	21	...	...	PUNCT
ejpam-4646	112	22	,	,	PUNCT
ejpam-4646	112	23	hk−1	hk−1	NOUN
ejpam-4646	112	24	=	=	PUNCT
ejpam-4646	112	25	hk−2	hk−2	PROPN
ejpam-4646	112	26	\	\	NOUN
ejpam-4646	112	27	vk−1	vk−1	NOUN
ejpam-4646	112	28	are	be	AUX
ejpam-4646	112	29	connected	connect	VERB
ejpam-4646	112	30	and	and	CCONJ
ejpam-4646	112	31	hk	hk	PROPN
ejpam-4646	112	32	=	=	PROPN
ejpam-4646	112	33	hk−1	hk−1	PROPN
ejpam-4646	112	34	\	\	PROPN
ejpam-4646	112	35	vk	vk	PROPN
ejpam-4646	112	36	is	be	AUX
ejpam-4646	112	37	the	the	DET
ejpam-4646	112	38	union	union	NOUN
ejpam-4646	112	39	of	of	ADP
ejpam-4646	112	40	at	at	ADV
ejpam-4646	112	41	least	least	ADV
ejpam-4646	112	42	two	two	NUM
ejpam-4646	112	43	complete	complete	ADJ
ejpam-4646	112	44	graphs	graph	NOUN
ejpam-4646	112	45	.	.	PUNCT
ejpam-4646	113	1	let	let	VERB
ejpam-4646	113	2	s	s	PRON
ejpam-4646	113	3	be	be	AUX
ejpam-4646	113	4	a	a	DET
ejpam-4646	113	5	γhg	γhg	NOUN
ejpam-4646	113	6	-	-	PUNCT
ejpam-4646	113	7	set	set	NOUN
ejpam-4646	113	8	of	of	ADP
ejpam-4646	113	9	g.	g.	PROPN
ejpam-4646	113	10	then	then	ADV
ejpam-4646	113	11	v1	v1	VERB
ejpam-4646	113	12	,	,	PUNCT
ejpam-4646	113	13	v2	v2	PROPN
ejpam-4646	113	14	,	,	PUNCT
ejpam-4646	113	15	...	...	PUNCT
ejpam-4646	113	16	,	,	PUNCT
ejpam-4646	113	17	vk	vk	PROPN
ejpam-4646	113	18	∈	∈	PROPN
ejpam-4646	113	19	s.	s.	PROPN
ejpam-4646	113	20	let	let	VERB
ejpam-4646	113	21	v	v	ADP
ejpam-4646	113	22	∈	∈	PROPN
ejpam-4646	113	23	v	v	NOUN
ejpam-4646	113	24	(	(	PUNCT
ejpam-4646	113	25	g	g	NOUN
ejpam-4646	113	26	)	)	PUNCT
ejpam-4646	113	27	\	\	NOUN
ejpam-4646	113	28	{	{	PUNCT
ejpam-4646	113	29	v1	v1	NOUN
ejpam-4646	113	30	,	,	PUNCT
ejpam-4646	113	31	v2	v2	PROPN
ejpam-4646	113	32	,	,	PUNCT
ejpam-4646	113	33	...	...	PUNCT
ejpam-4646	113	34	,	,	PUNCT
ejpam-4646	113	35	vk	vk	ADP
ejpam-4646	113	36	}	}	PUNCT
ejpam-4646	113	37	.	.	PUNCT
ejpam-4646	114	1	suppose	suppose	VERB
ejpam-4646	114	2	v	v	ADP
ejpam-4646	114	3	∈	∈	PROPN
ejpam-4646	114	4	s.	s.	PROPN
ejpam-4646	114	5	since	since	SCONJ
ejpam-4646	114	6	s	s	PROPN
ejpam-4646	114	7	is	be	AUX
ejpam-4646	114	8	a	a	DET
ejpam-4646	114	9	hop	hop	NOUN
ejpam-4646	114	10	dominating	dominating	NOUN
ejpam-4646	114	11	set	set	NOUN
ejpam-4646	114	12	,	,	PUNCT
ejpam-4646	114	13	there	there	PRON
ejpam-4646	114	14	exists	exist	VERB
ejpam-4646	114	15	w	w	PROPN
ejpam-4646	114	16	∈	∈	PROPN
ejpam-4646	114	17	s	s	PART
ejpam-4646	114	18	∩	∩	ADJ
ejpam-4646	114	19	n2	n2	ADJ
ejpam-4646	114	20	g(v	g(v	PROPN
ejpam-4646	114	21	)	)	PUNCT
ejpam-4646	114	22	.	.	PUNCT
ejpam-4646	115	1	also	also	ADV
ejpam-4646	115	2	,	,	PUNCT
ejpam-4646	115	3	since	since	SCONJ
ejpam-4646	115	4	s	s	NOUN
ejpam-4646	115	5	is	be	AUX
ejpam-4646	115	6	a	a	DET
ejpam-4646	115	7	geodetic	geodetic	ADJ
ejpam-4646	115	8	set	set	NOUN
ejpam-4646	115	9	,	,	PUNCT
ejpam-4646	115	10	there	there	PRON
ejpam-4646	115	11	exists	exist	VERB
ejpam-4646	115	12	p	p	PRON
ejpam-4646	115	13	,	,	PUNCT
ejpam-4646	115	14	q	q	PROPN
ejpam-4646	115	15	∈	∈	PROPN
ejpam-4646	115	16	s	s	VERB
ejpam-4646	115	17	such	such	ADJ
ejpam-4646	115	18	that	that	SCONJ
ejpam-4646	115	19	[	[	X
ejpam-4646	115	20	p	p	X
ejpam-4646	115	21	,	,	PUNCT
ejpam-4646	115	22	v	v	NOUN
ejpam-4646	115	23	,	,	PUNCT
ejpam-4646	115	24	q	q	X
ejpam-4646	115	25	]	]	X
ejpam-4646	115	26	is	be	AUX
ejpam-4646	115	27	a	a	DET
ejpam-4646	115	28	p	p	NOUN
ejpam-4646	115	29	-	-	PUNCT
ejpam-4646	115	30	q	q	NOUN
ejpam-4646	115	31	geodesic	geodesic	NOUN
ejpam-4646	115	32	.	.	PUNCT
ejpam-4646	116	1	since	since	SCONJ
ejpam-4646	116	2	p	p	NOUN
ejpam-4646	116	3	,	,	PUNCT
ejpam-4646	116	4	v	v	NOUN
ejpam-4646	116	5	and	and	CCONJ
ejpam-4646	116	6	q	q	NOUN
ejpam-4646	116	7	are	be	AUX
ejpam-4646	116	8	not	not	PART
ejpam-4646	116	9	dominating	dominate	VERB
ejpam-4646	116	10	vertices	vertex	NOUN
ejpam-4646	116	11	,	,	PUNCT
ejpam-4646	116	12	p	p	X
ejpam-4646	116	13	,	,	PUNCT
ejpam-4646	116	14	v	v	NOUN
ejpam-4646	116	15	,	,	PUNCT
ejpam-4646	116	16	q	q	PROPN
ejpam-4646	116	17	∈	∈	PROPN
ejpam-4646	116	18	v	v	NOUN
ejpam-4646	116	19	(	(	PUNCT
ejpam-4646	116	20	hk	hk	PROPN
ejpam-4646	116	21	\	\	PROPN
ejpam-4646	116	22	vk	vk	PROPN
ejpam-4646	116	23	)	)	PUNCT
ejpam-4646	116	24	.	.	PUNCT
ejpam-4646	117	1	it	it	PRON
ejpam-4646	117	2	follows	follow	VERB
ejpam-4646	117	3	that	that	SCONJ
ejpam-4646	117	4	the	the	DET
ejpam-4646	117	5	component	component	NOUN
ejpam-4646	117	6	of	of	ADP
ejpam-4646	117	7	hk	hk	PROPN
ejpam-4646	117	8	\	\	PROPN
ejpam-4646	117	9	vk	vk	NOUN
ejpam-4646	117	10	containing	contain	VERB
ejpam-4646	117	11	p	p	NOUN
ejpam-4646	117	12	,	,	PUNCT
ejpam-4646	117	13	v	v	NOUN
ejpam-4646	117	14	and	and	CCONJ
ejpam-4646	117	15	q	q	NOUN
ejpam-4646	117	16	is	be	AUX
ejpam-4646	117	17	not	not	PART
ejpam-4646	117	18	complete	complete	ADJ
ejpam-4646	117	19	,	,	PUNCT
ejpam-4646	117	20	contrary	contrary	ADJ
ejpam-4646	117	21	to	to	ADP
ejpam-4646	117	22	our	our	PRON
ejpam-4646	117	23	assumption	assumption	NOUN
ejpam-4646	117	24	.	.	PUNCT
ejpam-4646	118	1	therefore	therefore	ADV
ejpam-4646	118	2	,	,	PUNCT
ejpam-4646	118	3	v	v	PROPN
ejpam-4646	118	4	∈	∈	PROPN
ejpam-4646	118	5	s.	s.	PROPN
ejpam-4646	118	6	accordingly	accordingly	ADV
ejpam-4646	118	7	,	,	PUNCT
ejpam-4646	118	8	s	s	VERB
ejpam-4646	118	9	=	=	SYM
ejpam-4646	118	10	v	v	X
ejpam-4646	118	11	(	(	PUNCT
ejpam-4646	118	12	g	g	NOUN
ejpam-4646	118	13	)	)	PUNCT
ejpam-4646	118	14	and	and	CCONJ
ejpam-4646	118	15	γhg(g	γhg(g	NUM
ejpam-4646	118	16	)	)	PUNCT
ejpam-4646	118	17	=	=	VERB
ejpam-4646	118	18	n.	n.	NOUN
ejpam-4646	118	19	proposition	proposition	NOUN
ejpam-4646	118	20	1	1	X
ejpam-4646	118	21	.	.	PUNCT
ejpam-4646	119	1	let	let	VERB
ejpam-4646	119	2	n	n	PRON
ejpam-4646	119	3	be	be	AUX
ejpam-4646	119	4	a	a	DET
ejpam-4646	119	5	positive	positive	ADJ
ejpam-4646	119	6	integer	integer	NOUN
ejpam-4646	119	7	.	.	PUNCT
ejpam-4646	120	1	(	(	PUNCT
ejpam-4646	120	2	i	i	NOUN
ejpam-4646	120	3	)	)	PUNCT
ejpam-4646	120	4	for	for	ADP
ejpam-4646	120	5	a	a	DET
ejpam-4646	120	6	path	path	NOUN
ejpam-4646	120	7	pn	pn	NOUN
ejpam-4646	120	8	on	on	ADP
ejpam-4646	120	9	n	n	PRON
ejpam-4646	120	10	vertices	vertex	NOUN
ejpam-4646	120	11	,	,	PUNCT
ejpam-4646	120	12	γhg(pn	γhg(pn	NOUN
ejpam-4646	120	13	)	)	PUNCT
ejpam-4646	120	14	=	=	PUNCT
ejpam-4646	120	15			NOUN
ejpam-4646	120	16	n	n	CCONJ
ejpam-4646	120	17	,	,	PUNCT
ejpam-4646	120	18	if	if	SCONJ
ejpam-4646	120	19	n	n	CCONJ
ejpam-4646	120	20	=	=	SYM
ejpam-4646	120	21	1	1	NUM
ejpam-4646	120	22	,	,	PUNCT
ejpam-4646	120	23	2	2	NUM
ejpam-4646	120	24	.	.	X
ejpam-4646	120	25	n+6	n+6	NUM
ejpam-4646	120	26	3	3	NUM
ejpam-4646	120	27	,	,	PUNCT
ejpam-4646	120	28	if	if	SCONJ
ejpam-4646	120	29	n	n	PRON
ejpam-4646	120	30	≡	≡	PROPN
ejpam-4646	120	31	0(mod3	0(mod3	NUM
ejpam-4646	120	32	)	)	PUNCT
ejpam-4646	120	33	,	,	PUNCT
ejpam-4646	120	34	n+2	n+2	PRON
ejpam-4646	120	35	3	3	NUM
ejpam-4646	120	36	,	,	PUNCT
ejpam-4646	120	37	if	if	SCONJ
ejpam-4646	120	38	n	n	PRON
ejpam-4646	120	39	≡	≡	PROPN
ejpam-4646	120	40	1(mod3	1(mod3	NUM
ejpam-4646	120	41	)	)	PUNCT
ejpam-4646	120	42	,	,	PUNCT
ejpam-4646	120	43	n+4	n+4	NUM
ejpam-4646	120	44	3	3	NUM
ejpam-4646	120	45	,	,	PUNCT
ejpam-4646	120	46	if	if	SCONJ
ejpam-4646	120	47	n	n	PRON
ejpam-4646	120	48	≡	≡	PROPN
ejpam-4646	120	49	2(mod3	2(mod3	NUM
ejpam-4646	120	50	)	)	PUNCT
ejpam-4646	120	51	,	,	PUNCT
ejpam-4646	120	52	(	(	PUNCT
ejpam-4646	120	53	ii	ii	NOUN
ejpam-4646	120	54	)	)	PUNCT
ejpam-4646	120	55	for	for	ADP
ejpam-4646	120	56	a	a	DET
ejpam-4646	120	57	cycle	cycle	NOUN
ejpam-4646	120	58	cn	cn	NOUN
ejpam-4646	120	59	on	on	ADP
ejpam-4646	120	60	n	n	PRON
ejpam-4646	120	61	vertices	vertex	NOUN
ejpam-4646	120	62	,	,	PUNCT
ejpam-4646	120	63	γhg(cn	γhg(cn	NOUN
ejpam-4646	120	64	)	)	PUNCT
ejpam-4646	120	65	=	=	PUNCT
ejpam-4646	120	66			NOUN
ejpam-4646	120	67	3	3	NUM
ejpam-4646	120	68	,	,	PUNCT
ejpam-4646	120	69	if	if	SCONJ
ejpam-4646	120	70	n	n	NOUN
ejpam-4646	120	71	=	=	SYM
ejpam-4646	120	72	3	3	NUM
ejpam-4646	120	73	,	,	PUNCT
ejpam-4646	120	74	4	4	NUM
ejpam-4646	120	75	,	,	PUNCT
ejpam-4646	120	76	5	5	NUM
ejpam-4646	120	77	n	n	PRON
ejpam-4646	120	78	3	3	NUM
ejpam-4646	120	79	,	,	PUNCT
ejpam-4646	120	80	if	if	SCONJ
ejpam-4646	120	81	n	n	PRON
ejpam-4646	120	82	≡	≡	PROPN
ejpam-4646	120	83	0(mod3	0(mod3	NUM
ejpam-4646	120	84	)	)	PUNCT
ejpam-4646	120	85	,	,	PUNCT
ejpam-4646	121	1	n+2	n+2	PRON
ejpam-4646	121	2	3	3	NUM
ejpam-4646	121	3	,	,	PUNCT
ejpam-4646	121	4	if	if	SCONJ
ejpam-4646	121	5	n	n	PRON
ejpam-4646	121	6	≡	≡	PROPN
ejpam-4646	121	7	1(mod3	1(mod3	NUM
ejpam-4646	121	8	)	)	PUNCT
ejpam-4646	121	9	,	,	PUNCT
ejpam-4646	121	10	n+4	n+4	NUM
ejpam-4646	121	11	3	3	NUM
ejpam-4646	121	12	,	,	PUNCT
ejpam-4646	121	13	if	if	SCONJ
ejpam-4646	121	14	n	n	PRON
ejpam-4646	121	15	≡	≡	PROPN
ejpam-4646	121	16	2(mod3	2(mod3	NUM
ejpam-4646	121	17	)	)	PUNCT
ejpam-4646	121	18	,	,	PUNCT
ejpam-4646	121	19	proof	proof	NOUN
ejpam-4646	121	20	.	.	PUNCT
ejpam-4646	122	1	(	(	PUNCT
ejpam-4646	122	2	i	i	NOUN
ejpam-4646	122	3	)	)	PUNCT
ejpam-4646	122	4	let	let	VERB
ejpam-4646	122	5	pn	pn	NOUN
ejpam-4646	122	6	=	=	PUNCT
ejpam-4646	123	1	[	[	X
ejpam-4646	123	2	v1	v1	NOUN
ejpam-4646	123	3	,	,	PUNCT
ejpam-4646	123	4	v2	v2	PROPN
ejpam-4646	123	5	,	,	PUNCT
ejpam-4646	123	6	...	...	PUNCT
ejpam-4646	123	7	,	,	PUNCT
ejpam-4646	123	8	vn	vn	X
ejpam-4646	123	9	]	]	PUNCT
ejpam-4646	123	10	and	and	CCONJ
ejpam-4646	123	11	s	s	AUX
ejpam-4646	123	12	be	be	AUX
ejpam-4646	123	13	γhg	γhg	VERB
ejpam-4646	123	14	-	-	PUNCT
ejpam-4646	123	15	set	set	NOUN
ejpam-4646	123	16	of	of	ADP
ejpam-4646	123	17	pn	pn	PROPN
ejpam-4646	123	18	.	.	PUNCT
ejpam-4646	124	1	since	since	SCONJ
ejpam-4646	124	2	s	s	PROPN
ejpam-4646	124	3	is	be	AUX
ejpam-4646	124	4	a	a	DET
ejpam-4646	124	5	geodetic	geodetic	ADJ
ejpam-4646	124	6	set	set	NOUN
ejpam-4646	124	7	,	,	PUNCT
ejpam-4646	124	8	v1	v1	PROPN
ejpam-4646	124	9	,	,	PUNCT
ejpam-4646	124	10	vn	vn	PROPN
ejpam-4646	124	11	∈	∈	PROPN
ejpam-4646	124	12	s.	s.	PROPN
ejpam-4646	124	13	consider	consider	VERB
ejpam-4646	124	14	the	the	DET
ejpam-4646	124	15	following	follow	VERB
ejpam-4646	124	16	cases	case	NOUN
ejpam-4646	124	17	:	:	PUNCT
ejpam-4646	124	18	case	case	NOUN
ejpam-4646	124	19	1	1	NUM
ejpam-4646	124	20	.	.	PUNCT
ejpam-4646	124	21	n	n	PROPN
ejpam-4646	124	22	≡	≡	PROPN
ejpam-4646	124	23	0(mod3	0(mod3	PROPN
ejpam-4646	124	24	)	)	PUNCT
ejpam-4646	124	25	let	let	VERB
ejpam-4646	124	26	n	n	NOUN
ejpam-4646	124	27	=	=	NOUN
ejpam-4646	124	28	3r	3r	NUM
ejpam-4646	124	29	,	,	PUNCT
ejpam-4646	124	30	for	for	ADP
ejpam-4646	124	31	some	some	DET
ejpam-4646	124	32	positive	positive	ADJ
ejpam-4646	124	33	integer	integer	NOUN
ejpam-4646	124	34	r.	r.	PROPN
ejpam-4646	124	35	then	then	ADV
ejpam-4646	124	36	s1	s1	PROPN
ejpam-4646	124	37	=	=	PUNCT
ejpam-4646	124	38	{	{	PUNCT
ejpam-4646	124	39	v1	v1	PROPN
ejpam-4646	124	40	,	,	PUNCT
ejpam-4646	124	41	v4	v4	NOUN
ejpam-4646	124	42	,	,	PUNCT
ejpam-4646	124	43	...	...	PUNCT
ejpam-4646	124	44	,	,	PUNCT
ejpam-4646	124	45	v3r−2	v3r−2	PROPN
ejpam-4646	124	46	,	,	PUNCT
ejpam-4646	124	47	v3r−1	v3r−1	PROPN
ejpam-4646	124	48	,	,	PUNCT
ejpam-4646	124	49	v3r	v3r	NOUN
ejpam-4646	124	50	}	}	PUNCT
ejpam-4646	124	51	and	and	CCONJ
ejpam-4646	124	52	s2	s2	VERB
ejpam-4646	124	53	=	=	SYM
ejpam-4646	124	54	{	{	PUNCT
ejpam-4646	124	55	v3r	v3r	NOUN
ejpam-4646	124	56	,	,	PUNCT
ejpam-4646	124	57	v3r−3	v3r−3	PROPN
ejpam-4646	124	58	,	,	PUNCT
ejpam-4646	124	59	...	...	PUNCT
ejpam-4646	124	60	,	,	PUNCT
ejpam-4646	124	61	v3	v3	PROPN
ejpam-4646	124	62	,	,	PUNCT
ejpam-4646	124	63	v2	v2	PROPN
ejpam-4646	124	64	,	,	PUNCT
ejpam-4646	124	65	v1	v1	NOUN
ejpam-4646	124	66	}	}	PUNCT
ejpam-4646	124	67	are	be	AUX
ejpam-4646	124	68	the	the	DET
ejpam-4646	124	69	only	only	ADJ
ejpam-4646	124	70	γhg	γhg	NOUN
ejpam-4646	124	71	-	-	PUNCT
ejpam-4646	124	72	sets	set	NOUN
ejpam-4646	124	73	of	of	ADP
ejpam-4646	124	74	pn	pn	PROPN
ejpam-4646	124	75	.	.	PROPN
ejpam-4646	125	1	hence	hence	ADV
ejpam-4646	125	2	,	,	PUNCT
ejpam-4646	125	3	γhg(pn	γhg(pn	NOUN
ejpam-4646	125	4	)	)	PUNCT
ejpam-4646	125	5	=	=	SYM
ejpam-4646	125	6	|s1|	|s1|	NOUN
ejpam-4646	125	7	=	=	SYM
ejpam-4646	125	8	n+6	n+6	NUM
ejpam-4646	125	9	3	3	NUM
ejpam-4646	125	10	.	.	PUNCT
ejpam-4646	126	1	case	case	NOUN
ejpam-4646	126	2	2	2	NUM
ejpam-4646	126	3	.	.	X
ejpam-4646	127	1	n	n	PROPN
ejpam-4646	127	2	≡	≡	PROPN
ejpam-4646	127	3	1(mod3	1(mod3	NUM
ejpam-4646	127	4	)	)	PUNCT
ejpam-4646	127	5	let	let	VERB
ejpam-4646	127	6	n	n	NOUN
ejpam-4646	127	7	=	=	SYM
ejpam-4646	127	8	3t+	3t+	NUM
ejpam-4646	127	9	1	1	NUM
ejpam-4646	127	10	,	,	PUNCT
ejpam-4646	127	11	for	for	ADP
ejpam-4646	127	12	some	some	DET
ejpam-4646	127	13	non	non	ADJ
ejpam-4646	127	14	-	-	ADJ
ejpam-4646	127	15	negative	negative	ADJ
ejpam-4646	127	16	integer	integer	NOUN
ejpam-4646	127	17	t.	t.	PROPN
ejpam-4646	127	18	then	then	ADV
ejpam-4646	127	19	s3	s3	PROPN
ejpam-4646	127	20	=	=	SYM
ejpam-4646	127	21	{	{	PUNCT
ejpam-4646	127	22	v1	v1	PROPN
ejpam-4646	127	23	,	,	PUNCT
ejpam-4646	127	24	v4	v4	NOUN
ejpam-4646	127	25	,	,	PUNCT
ejpam-4646	127	26	...	...	PUNCT
ejpam-4646	127	27	,	,	PUNCT
ejpam-4646	127	28	v3t+1	v3t+1	X
ejpam-4646	127	29	}	}	PUNCT
ejpam-4646	127	30	is	be	AUX
ejpam-4646	127	31	the	the	DET
ejpam-4646	127	32	unique	unique	ADJ
ejpam-4646	127	33	γhg	γhg	NOUN
ejpam-4646	127	34	-	-	PUNCT
ejpam-4646	127	35	set	set	NOUN
ejpam-4646	127	36	of	of	ADP
ejpam-4646	127	37	pn	pn	PROPN
ejpam-4646	127	38	.	.	PROPN
ejpam-4646	128	1	hence	hence	ADV
ejpam-4646	128	2	,	,	PUNCT
ejpam-4646	128	3	γhg(pn	γhg(pn	ADJ
ejpam-4646	128	4	)	)	PUNCT
ejpam-4646	128	5	=	=	SYM
ejpam-4646	128	6	|s3|	|s3|	NOUN
ejpam-4646	128	7	=	=	PUNCT
ejpam-4646	129	1	n+2	n+2	NUM
ejpam-4646	129	2	3	3	NUM
ejpam-4646	129	3	.	.	PUNCT
ejpam-4646	130	1	case	case	NOUN
ejpam-4646	130	2	3	3	NUM
ejpam-4646	130	3	.	.	X
ejpam-4646	131	1	n	n	PROPN
ejpam-4646	131	2	≡	≡	PROPN
ejpam-4646	131	3	2(mod3	2(mod3	NUM
ejpam-4646	131	4	)	)	PUNCT
ejpam-4646	131	5	let	let	VERB
ejpam-4646	131	6	n	n	NOUN
ejpam-4646	131	7	=	=	SYM
ejpam-4646	131	8	3s+	3s+	NUM
ejpam-4646	131	9	2	2	NUM
ejpam-4646	131	10	,	,	PUNCT
ejpam-4646	131	11	for	for	ADP
ejpam-4646	131	12	some	some	DET
ejpam-4646	131	13	non	non	ADJ
ejpam-4646	131	14	-	-	ADJ
ejpam-4646	131	15	negative	negative	ADJ
ejpam-4646	131	16	integer	integer	NOUN
ejpam-4646	131	17	s.	s.	PROPN
ejpam-4646	131	18	then	then	ADV
ejpam-4646	131	19	s4	s4	VERB
ejpam-4646	131	20	=	=	SYM
ejpam-4646	131	21	{	{	PUNCT
ejpam-4646	131	22	v1	v1	PROPN
ejpam-4646	131	23	,	,	PUNCT
ejpam-4646	131	24	v4	v4	NOUN
ejpam-4646	131	25	,	,	PUNCT
ejpam-4646	131	26	...	...	PUNCT
ejpam-4646	131	27	,	,	PUNCT
ejpam-4646	131	28	v3s+1	v3s+1	ADJ
ejpam-4646	131	29	,	,	PUNCT
ejpam-4646	131	30	v3s+2	v3s+2	NOUN
ejpam-4646	131	31	}	}	PUNCT
ejpam-4646	131	32	and	and	CCONJ
ejpam-4646	131	33	s5	s5	PROPN
ejpam-4646	131	34	=	=	PUNCT
ejpam-4646	131	35	{	{	PUNCT
ejpam-4646	131	36	v3s+2	v3s+2	PROPN
ejpam-4646	131	37	,	,	PUNCT
ejpam-4646	131	38	v3s−1	v3s−1	PROPN
ejpam-4646	131	39	,	,	PUNCT
ejpam-4646	131	40	...	...	PUNCT
ejpam-4646	131	41	,	,	PUNCT
ejpam-4646	131	42	v2	v2	PROPN
ejpam-4646	131	43	,	,	PUNCT
ejpam-4646	131	44	v1	v1	NOUN
ejpam-4646	131	45	}	}	PUNCT
ejpam-4646	131	46	are	be	AUX
ejpam-4646	131	47	the	the	DET
ejpam-4646	131	48	only	only	ADJ
ejpam-4646	131	49	γhg	γhg	NOUN
ejpam-4646	131	50	-	-	PUNCT
ejpam-4646	131	51	sets	set	NOUN
ejpam-4646	131	52	of	of	ADP
ejpam-4646	131	53	pn	pn	PROPN
ejpam-4646	131	54	.	.	PROPN
ejpam-4646	132	1	hence	hence	ADV
ejpam-4646	132	2	,	,	PUNCT
ejpam-4646	132	3	γhg(pn	γhg(pn	ADJ
ejpam-4646	132	4	)	)	PUNCT
ejpam-4646	132	5	=	=	SYM
ejpam-4646	133	1	|s4|	|s4|	NOUN
ejpam-4646	133	2	=	=	PUNCT
ejpam-4646	133	3	n+4	n+4	NUM
ejpam-4646	133	4	3	3	NUM
ejpam-4646	133	5	.	.	PUNCT
ejpam-4646	134	1	c.j	c.j	PROPN
ejpam-4646	134	2	.	.	PROPN
ejpam-4646	134	3	saromines	saromines	PROPN
ejpam-4646	134	4	,	,	PUNCT
ejpam-4646	134	5	s.	s.	PROPN
ejpam-4646	134	6	canoy	canoy	PROPN
ejpam-4646	134	7	,	,	PUNCT
ejpam-4646	134	8	jr	jr	PROPN
ejpam-4646	134	9	.	.	PROPN
ejpam-4646	134	10	,	,	PUNCT
ejpam-4646	134	11	/	/	SYM
ejpam-4646	134	12	eur	eur	NOUN
ejpam-4646	134	13	.	.	PUNCT
ejpam-4646	135	1	j.	j.	PROPN
ejpam-4646	135	2	pure	pure	PROPN
ejpam-4646	135	3	appl	appl	PROPN
ejpam-4646	135	4	.	.	PROPN
ejpam-4646	135	5	math	math	PROPN
ejpam-4646	135	6	,	,	PUNCT
ejpam-4646	135	7	16	16	NUM
ejpam-4646	135	8	(	(	PUNCT
ejpam-4646	135	9	1	1	NUM
ejpam-4646	135	10	)	)	PUNCT
ejpam-4646	135	11	(	(	PUNCT
ejpam-4646	135	12	2023	2023	NUM
ejpam-4646	135	13	)	)	PUNCT
ejpam-4646	135	14	,	,	PUNCT
ejpam-4646	135	15	5	5	NUM
ejpam-4646	135	16	-	-	SYM
ejpam-4646	135	17	17	17	NUM
ejpam-4646	135	18	9	9	NUM
ejpam-4646	135	19	(	(	PUNCT
ejpam-4646	135	20	ii	ii	NOUN
ejpam-4646	135	21	)	)	PUNCT
ejpam-4646	135	22	let	let	VERB
ejpam-4646	135	23	cn	cn	PROPN
ejpam-4646	135	24	=	=	PUNCT
ejpam-4646	136	1	[	[	X
ejpam-4646	136	2	v1	v1	NOUN
ejpam-4646	136	3	,	,	PUNCT
ejpam-4646	136	4	v2	v2	PROPN
ejpam-4646	136	5	,	,	PUNCT
ejpam-4646	136	6	...	...	PUNCT
ejpam-4646	136	7	,	,	PUNCT
ejpam-4646	136	8	vn	vn	INTJ
ejpam-4646	136	9	,	,	PUNCT
ejpam-4646	136	10	v1	v1	PROPN
ejpam-4646	136	11	]	]	PUNCT
ejpam-4646	136	12	and	and	CCONJ
ejpam-4646	136	13	let	let	VERB
ejpam-4646	136	14	d	d	PART
ejpam-4646	136	15	be	be	AUX
ejpam-4646	136	16	γhg	γhg	VERB
ejpam-4646	136	17	-	-	PUNCT
ejpam-4646	136	18	set	set	NOUN
ejpam-4646	136	19	of	of	ADP
ejpam-4646	136	20	cn	cn	PROPN
ejpam-4646	136	21	.	.	PUNCT
ejpam-4646	137	1	by	by	ADP
ejpam-4646	137	2	circularity	circularity	NOUN
ejpam-4646	137	3	property	property	NOUN
ejpam-4646	137	4	of	of	ADP
ejpam-4646	137	5	cn	cn	PROPN
ejpam-4646	137	6	,	,	PUNCT
ejpam-4646	137	7	we	we	PRON
ejpam-4646	137	8	may	may	AUX
ejpam-4646	137	9	assume	assume	VERB
ejpam-4646	137	10	that	that	SCONJ
ejpam-4646	137	11	v1	v1	PROPN
ejpam-4646	137	12	∈	∈	PROPN
ejpam-4646	137	13	d.	d.	NOUN
ejpam-4646	137	14	consider	consider	VERB
ejpam-4646	137	15	the	the	DET
ejpam-4646	137	16	following	follow	VERB
ejpam-4646	137	17	cases	case	NOUN
ejpam-4646	137	18	:	:	PUNCT
ejpam-4646	137	19	case	case	NOUN
ejpam-4646	137	20	1	1	NUM
ejpam-4646	137	21	.	.	PUNCT
ejpam-4646	137	22	n	n	PROPN
ejpam-4646	137	23	≡	≡	PROPN
ejpam-4646	137	24	0(mod3	0(mod3	PROPN
ejpam-4646	137	25	)	)	PUNCT
ejpam-4646	137	26	let	let	VERB
ejpam-4646	137	27	n	n	NOUN
ejpam-4646	137	28	=	=	NOUN
ejpam-4646	137	29	3r	3r	NUM
ejpam-4646	137	30	for	for	ADP
ejpam-4646	137	31	some	some	DET
ejpam-4646	137	32	positive	positive	ADJ
ejpam-4646	137	33	integer	integer	NOUN
ejpam-4646	137	34	r.	r.	NOUN
ejpam-4646	138	1	then	then	ADV
ejpam-4646	138	2	d	d	PROPN
ejpam-4646	138	3	=	=	PUNCT
ejpam-4646	138	4	{	{	PUNCT
ejpam-4646	138	5	v1	v1	PROPN
ejpam-4646	138	6	,	,	PUNCT
ejpam-4646	138	7	v4	v4	NOUN
ejpam-4646	138	8	,	,	PUNCT
ejpam-4646	138	9	...	...	PUNCT
ejpam-4646	138	10	,	,	PUNCT
ejpam-4646	138	11	v3r−2	v3r−2	PROPN
ejpam-4646	138	12	}	}	PUNCT
ejpam-4646	138	13	.	.	PUNCT
ejpam-4646	139	1	hence	hence	ADV
ejpam-4646	139	2	,	,	PUNCT
ejpam-4646	139	3	γhg(pn	γhg(pn	ADJ
ejpam-4646	139	4	)	)	PUNCT
ejpam-4646	139	5	=	=	SYM
ejpam-4646	139	6	|d|	|d|	PROPN
ejpam-4646	139	7	=	=	SYM
ejpam-4646	139	8	n	n	PRON
ejpam-4646	139	9	3	3	NUM
ejpam-4646	139	10	.	.	PUNCT
ejpam-4646	140	1	case	case	NOUN
ejpam-4646	140	2	2	2	NUM
ejpam-4646	140	3	.	.	X
ejpam-4646	141	1	n	n	PROPN
ejpam-4646	141	2	≡	≡	PROPN
ejpam-4646	141	3	1(mod3	1(mod3	NUM
ejpam-4646	141	4	)	)	PUNCT
ejpam-4646	141	5	let	let	VERB
ejpam-4646	141	6	n	n	NOUN
ejpam-4646	141	7	=	=	SYM
ejpam-4646	141	8	3t+	3t+	NUM
ejpam-4646	141	9	1	1	NUM
ejpam-4646	141	10	for	for	ADP
ejpam-4646	141	11	some	some	DET
ejpam-4646	141	12	non	non	ADJ
ejpam-4646	141	13	-	-	ADJ
ejpam-4646	141	14	negative	negative	ADJ
ejpam-4646	141	15	integer	integer	NOUN
ejpam-4646	141	16	t.	t.	NOUN
ejpam-4646	142	1	then	then	ADV
ejpam-4646	142	2	d	d	PROPN
ejpam-4646	142	3	=	=	PUNCT
ejpam-4646	142	4	{	{	PUNCT
ejpam-4646	142	5	v1	v1	PROPN
ejpam-4646	142	6	,	,	PUNCT
ejpam-4646	142	7	v4	v4	NOUN
ejpam-4646	142	8	,	,	PUNCT
ejpam-4646	142	9	...	...	PUNCT
ejpam-4646	142	10	,	,	PUNCT
ejpam-4646	142	11	v3t+1	v3t+1	PROPN
ejpam-4646	142	12	}	}	PUNCT
ejpam-4646	142	13	.	.	PUNCT
ejpam-4646	143	1	hence	hence	ADV
ejpam-4646	143	2	,	,	PUNCT
ejpam-4646	143	3	γhg(cn	γhg(cn	NOUN
ejpam-4646	143	4	)	)	PUNCT
ejpam-4646	143	5	=	=	SYM
ejpam-4646	144	1	|d|	|d|	PROPN
ejpam-4646	144	2	=	=	SYM
ejpam-4646	145	1	n+2	n+2	NUM
ejpam-4646	145	2	3	3	NUM
ejpam-4646	145	3	.	.	PUNCT
ejpam-4646	146	1	case	case	NOUN
ejpam-4646	146	2	3	3	NUM
ejpam-4646	146	3	.	.	X
ejpam-4646	147	1	n	n	PROPN
ejpam-4646	147	2	≡	≡	PROPN
ejpam-4646	147	3	2(mod3	2(mod3	NUM
ejpam-4646	147	4	)	)	PUNCT
ejpam-4646	147	5	let	let	VERB
ejpam-4646	147	6	n	n	NOUN
ejpam-4646	147	7	=	=	SYM
ejpam-4646	147	8	3s+	3s+	NUM
ejpam-4646	147	9	1	1	NUM
ejpam-4646	147	10	for	for	ADP
ejpam-4646	147	11	some	some	DET
ejpam-4646	147	12	non	non	ADJ
ejpam-4646	147	13	-	-	ADJ
ejpam-4646	147	14	negative	negative	ADJ
ejpam-4646	147	15	integer	integer	NOUN
ejpam-4646	147	16	s.	s.	PROPN
ejpam-4646	148	1	then	then	ADV
ejpam-4646	148	2	d	d	X
ejpam-4646	148	3	=	=	PUNCT
ejpam-4646	148	4	{	{	PUNCT
ejpam-4646	148	5	v1	v1	PROPN
ejpam-4646	148	6	,	,	PUNCT
ejpam-4646	148	7	v4	v4	NOUN
ejpam-4646	148	8	,	,	PUNCT
ejpam-4646	148	9	...	...	PUNCT
ejpam-4646	148	10	,	,	PUNCT
ejpam-4646	148	11	v3s+1	v3s+1	ADJ
ejpam-4646	148	12	,	,	PUNCT
ejpam-4646	148	13	v3s+2	v3s+2	NOUN
ejpam-4646	148	14	}	}	PUNCT
ejpam-4646	148	15	.	.	PUNCT
ejpam-4646	149	1	hence	hence	ADV
ejpam-4646	149	2	,	,	PUNCT
ejpam-4646	149	3	γhg(cn	γhg(cn	NOUN
ejpam-4646	149	4	)	)	PUNCT
ejpam-4646	149	5	=	=	SYM
ejpam-4646	149	6	|d|	|d|	PROPN
ejpam-4646	149	7	=	=	SYM
ejpam-4646	150	1	n+4	n+4	NUM
ejpam-4646	150	2	3	3	X
ejpam-4646	150	3	.	.	PUNCT
ejpam-4646	151	1	remark	remark	NOUN
ejpam-4646	151	2	2	2	NUM
ejpam-4646	151	3	.	.	PUNCT
ejpam-4646	152	1	if	if	SCONJ
ejpam-4646	152	2	pn	pn	PROPN
ejpam-4646	152	3	=	=	PUNCT
ejpam-4646	153	1	[	[	X
ejpam-4646	153	2	v1	v1	NOUN
ejpam-4646	153	3	,	,	PUNCT
ejpam-4646	153	4	v2	v2	PROPN
ejpam-4646	153	5	,	,	PUNCT
ejpam-4646	153	6	...	...	PUNCT
ejpam-4646	153	7	,	,	PUNCT
ejpam-4646	153	8	vn	vn	X
ejpam-4646	153	9	]	]	PUNCT
ejpam-4646	153	10	and	and	CCONJ
ejpam-4646	153	11	s	s	X
ejpam-4646	153	12	is	be	AUX
ejpam-4646	153	13	a	a	DET
ejpam-4646	153	14	geodetic	geodetic	ADJ
ejpam-4646	153	15	set	set	NOUN
ejpam-4646	153	16	of	of	ADP
ejpam-4646	153	17	pn	pn	PROPN
ejpam-4646	153	18	,	,	PUNCT
ejpam-4646	153	19	then	then	ADV
ejpam-4646	153	20	{	{	PUNCT
ejpam-4646	153	21	v1	v1	PROPN
ejpam-4646	153	22	,	,	PUNCT
ejpam-4646	153	23	vn	vn	X
ejpam-4646	153	24	}	}	PUNCT
ejpam-4646	153	25	⊆	⊆	NUM
ejpam-4646	153	26	s.	s.	PROPN
ejpam-4646	153	27	theorem	theorem	VERB
ejpam-4646	153	28	2	2	X
ejpam-4646	153	29	.	.	PUNCT
ejpam-4646	154	1	let	let	VERB
ejpam-4646	154	2	kn	kn	PROPN
ejpam-4646	154	3	be	be	AUX
ejpam-4646	154	4	the	the	DET
ejpam-4646	154	5	complete	complete	ADJ
ejpam-4646	154	6	graph	graph	NOUN
ejpam-4646	154	7	of	of	ADP
ejpam-4646	154	8	order	order	NOUN
ejpam-4646	154	9	n	n	PRON
ejpam-4646	154	10	≥	≥	NOUN
ejpam-4646	154	11	3	3	NUM
ejpam-4646	154	12	and	and	CCONJ
ejpam-4646	154	13	ω	ω	NUM
ejpam-4646	154	14	an	an	DET
ejpam-4646	154	15	independent	independent	ADJ
ejpam-4646	154	16	family	family	NOUN
ejpam-4646	154	17	of	of	ADP
ejpam-4646	154	18	complete	complete	ADJ
ejpam-4646	154	19	proper	proper	ADJ
ejpam-4646	154	20	subgraph	subgraph	NOUN
ejpam-4646	154	21	of	of	ADP
ejpam-4646	154	22	kn	kn	PROPN
ejpam-4646	154	23	,	,	PUNCT
ejpam-4646	154	24	each	each	PRON
ejpam-4646	154	25	of	of	ADP
ejpam-4646	154	26	order	order	NOUN
ejpam-4646	154	27	at	at	ADV
ejpam-4646	154	28	least	least	ADJ
ejpam-4646	154	29	2	2	NUM
ejpam-4646	154	30	.	.	PUNCT
ejpam-4646	155	1	if	if	SCONJ
ejpam-4646	155	2	g	g	PROPN
ejpam-4646	155	3	=	=	PROPN
ejpam-4646	155	4	kn	kn	PROPN
ejpam-4646	155	5	\	\	PROPN
ejpam-4646	155	6	e(ω	e(ω	PROPN
ejpam-4646	155	7	)	)	PUNCT
ejpam-4646	155	8	,	,	PUNCT
ejpam-4646	155	9	then	then	ADV
ejpam-4646	155	10	γhg(g	γhg(g	PROPN
ejpam-4646	155	11	)	)	PUNCT
ejpam-4646	155	12	=	=	SYM
ejpam-4646	156	1			PROPN
ejpam-4646	156	2	n	n	CCONJ
ejpam-4646	156	3	,	,	PUNCT
ejpam-4646	156	4	if	if	SCONJ
ejpam-4646	156	5	|ω|	|ω|	ADP
ejpam-4646	156	6	=	=	SYM
ejpam-4646	156	7	1	1	NUM
ejpam-4646	156	8	|ω|	|ω|	NUM
ejpam-4646	156	9	−	−	PROPN
ejpam-4646	156	10	2	2	NUM
ejpam-4646	156	11	+	+	CCONJ
ejpam-4646	156	12	n−	n−	NOUN
ejpam-4646	156	13	∑	∑	PUNCT
ejpam-4646	156	14	kq∈ω	kq∈ω	PRON
ejpam-4646	156	15	q	q	X
ejpam-4646	157	1	+	+	NOUN
ejpam-4646	157	2	min	min	NOUN
ejpam-4646	157	3	{	{	PUNCT
ejpam-4646	157	4	4	4	NUM
ejpam-4646	157	5	,	,	PUNCT
ejpam-4646	157	6	p+	p+	VERB
ejpam-4646	157	7	1	1	NUM
ejpam-4646	157	8	}	}	PUNCT
ejpam-4646	157	9	,	,	PUNCT
ejpam-4646	157	10	if	if	SCONJ
ejpam-4646	157	11	|ω|	|ω|	ADP
ejpam-4646	157	12	≥	≥	NOUN
ejpam-4646	157	13	2	2	NUM
ejpam-4646	157	14	where	where	SCONJ
ejpam-4646	157	15	p	p	NOUN
ejpam-4646	157	16	=	=	NOUN
ejpam-4646	157	17	min	min	PROPN
ejpam-4646	157	18	{	{	PUNCT
ejpam-4646	157	19	q	q	NOUN
ejpam-4646	157	20	:	:	PUNCT
ejpam-4646	157	21	kq	kq	PROPN
ejpam-4646	157	22	∈	∈	PROPN
ejpam-4646	157	23	ω	ω	PROPN
ejpam-4646	157	24	}	}	PUNCT
ejpam-4646	157	25	.	.	PUNCT
ejpam-4646	158	1	proof	proof	NOUN
ejpam-4646	158	2	.	.	PUNCT
ejpam-4646	159	1	suppose	suppose	VERB
ejpam-4646	159	2	that	that	SCONJ
ejpam-4646	159	3	s	s	VERB
ejpam-4646	159	4	is	be	AUX
ejpam-4646	159	5	a	a	DET
ejpam-4646	159	6	γhg	γhg	NOUN
ejpam-4646	159	7	-	-	PUNCT
ejpam-4646	159	8	set	set	NOUN
ejpam-4646	159	9	of	of	ADP
ejpam-4646	159	10	g	g	NOUN
ejpam-4646	159	11	and	and	CCONJ
ejpam-4646	159	12	let	let	VERB
ejpam-4646	159	13	ω	ω	PROPN
ejpam-4646	159	14	=	=	PRON
ejpam-4646	159	15	{	{	PUNCT
ejpam-4646	159	16	kp	kp	INTJ
ejpam-4646	159	17	}	}	PUNCT
ejpam-4646	159	18	.	.	PUNCT
ejpam-4646	160	1	if	if	SCONJ
ejpam-4646	160	2	kp	kp	PROPN
ejpam-4646	160	3	=	=	SYM
ejpam-4646	160	4	kn	kn	PROPN
ejpam-4646	160	5	,	,	PUNCT
ejpam-4646	160	6	then	then	ADV
ejpam-4646	160	7	we	we	PRON
ejpam-4646	160	8	are	be	AUX
ejpam-4646	160	9	done	do	VERB
ejpam-4646	160	10	.	.	PUNCT
ejpam-4646	161	1	if	if	SCONJ
ejpam-4646	161	2	kp	kp	PROPN
ejpam-4646	161	3	̸=	̸=	PROPN
ejpam-4646	161	4	kn	kn	PROPN
ejpam-4646	161	5	,	,	PUNCT
ejpam-4646	161	6	then	then	ADV
ejpam-4646	161	7	there	there	PRON
ejpam-4646	161	8	exist	exist	VERB
ejpam-4646	161	9	dominating	dominating	NOUN
ejpam-4646	161	10	vertices	vertex	NOUN
ejpam-4646	161	11	v1	v1	NOUN
ejpam-4646	161	12	,	,	PUNCT
ejpam-4646	161	13	v2	v2	PROPN
ejpam-4646	161	14	,	,	PUNCT
ejpam-4646	161	15	...	...	PUNCT
ejpam-4646	161	16	,	,	PUNCT
ejpam-4646	161	17	vk	vk	VERB
ejpam-4646	161	18	such	such	ADJ
ejpam-4646	161	19	that	that	DET
ejpam-4646	161	20	h1	h1	PROPN
ejpam-4646	161	21	=	=	SYM
ejpam-4646	161	22	g\v1	g\v1	PROPN
ejpam-4646	161	23	,	,	PUNCT
ejpam-4646	161	24	h2	h2	NOUN
ejpam-4646	161	25	=	=	PUNCT
ejpam-4646	161	26	h1	h1	VERB
ejpam-4646	161	27	\	\	PROPN
ejpam-4646	161	28	v2	v2	PROPN
ejpam-4646	161	29	,	,	PUNCT
ejpam-4646	161	30	.	.	PUNCT
ejpam-4646	161	31	.	.	PUNCT
ejpam-4646	162	1	.	.	PUNCT
ejpam-4646	163	1	,	,	PUNCT
ejpam-4646	163	2	hk−1	hk−1	NOUN
ejpam-4646	163	3	=	=	PUNCT
ejpam-4646	163	4	hk−2	hk−2	PROPN
ejpam-4646	163	5	\	\	NOUN
ejpam-4646	163	6	vk−1	vk−1	NOUN
ejpam-4646	163	7	are	be	AUX
ejpam-4646	163	8	connected	connect	VERB
ejpam-4646	163	9	graphs	graph	NOUN
ejpam-4646	163	10	and	and	CCONJ
ejpam-4646	163	11	hk	hk	PROPN
ejpam-4646	163	12	=	=	PROPN
ejpam-4646	163	13	hk−1	hk−1	PROPN
ejpam-4646	163	14	\	\	PROPN
ejpam-4646	163	15	vk	vk	PROPN
ejpam-4646	163	16	is	be	AUX
ejpam-4646	163	17	the	the	DET
ejpam-4646	163	18	union	union	NOUN
ejpam-4646	163	19	of	of	ADP
ejpam-4646	163	20	at	at	ADV
ejpam-4646	163	21	least	least	ADV
ejpam-4646	163	22	2	2	NUM
ejpam-4646	163	23	complete	complete	ADJ
ejpam-4646	163	24	components	component	NOUN
ejpam-4646	163	25	.	.	PUNCT
ejpam-4646	164	1	by	by	ADP
ejpam-4646	164	2	theorem	theorem	NOUN
ejpam-4646	164	3	2	2	NUM
ejpam-4646	164	4	,	,	PUNCT
ejpam-4646	164	5	γhg(g	γhg(g	PROPN
ejpam-4646	164	6	)	)	PUNCT
ejpam-4646	164	7	=	=	VERB
ejpam-4646	164	8	n.	n.	NOUN
ejpam-4646	164	9	suppose	suppose	VERB
ejpam-4646	164	10	|ω|	|ω|	NUM
ejpam-4646	164	11	≥	≥	PRON
ejpam-4646	164	12	2	2	NUM
ejpam-4646	164	13	.	.	PUNCT
ejpam-4646	165	1	let	let	VERB
ejpam-4646	165	2	d1	d1	PROPN
ejpam-4646	165	3	=	=	SYM
ejpam-4646	165	4	v	v	PROPN
ejpam-4646	165	5	(	(	PUNCT
ejpam-4646	165	6	g	g	NOUN
ejpam-4646	165	7	)	)	PUNCT
ejpam-4646	165	8	\	\	NOUN
ejpam-4646	166	1	⋃	⋃	SCONJ
ejpam-4646	166	2	kq∈ω	kq∈ω	PROPN
ejpam-4646	166	3	v	v	X
ejpam-4646	166	4	(	(	PUNCT
ejpam-4646	166	5	kq	kq	PROPN
ejpam-4646	166	6	)	)	PUNCT
ejpam-4646	166	7	and	and	CCONJ
ejpam-4646	166	8	let	let	VERB
ejpam-4646	166	9	d2	d2	PROPN
ejpam-4646	166	10	be	be	AUX
ejpam-4646	166	11	a	a	DET
ejpam-4646	166	12	smallest	small	ADJ
ejpam-4646	166	13	subset	subset	NOUN
ejpam-4646	166	14	of	of	ADP
ejpam-4646	166	15	s	s	PRON
ejpam-4646	166	16	such	such	ADJ
ejpam-4646	166	17	that	that	DET
ejpam-4646	166	18	v	v	NOUN
ejpam-4646	166	19	(	(	PUNCT
ejpam-4646	166	20	g	g	NOUN
ejpam-4646	166	21	)	)	PUNCT
ejpam-4646	166	22	\	\	PUNCT
ejpam-4646	166	23	s	s	PART
ejpam-4646	166	24	⊆	⊆	NUM
ejpam-4646	166	25	ig(d2	ig(d2	NOUN
ejpam-4646	166	26	)	)	PUNCT
ejpam-4646	166	27	.	.	PUNCT
ejpam-4646	167	1	since	since	SCONJ
ejpam-4646	167	2	g	g	PROPN
ejpam-4646	167	3	is	be	AUX
ejpam-4646	167	4	non	non	ADJ
ejpam-4646	167	5	-	-	ADJ
ejpam-4646	167	6	complete	complete	ADJ
ejpam-4646	167	7	,	,	PUNCT
ejpam-4646	167	8	there	there	PRON
ejpam-4646	167	9	exist	exist	VERB
ejpam-4646	167	10	u	u	NOUN
ejpam-4646	167	11	,	,	PUNCT
ejpam-4646	167	12	v	v	PROPN
ejpam-4646	167	13	∈	∈	NOUN
ejpam-4646	167	14	s	s	VERB
ejpam-4646	167	15	such	such	ADJ
ejpam-4646	167	16	that	that	DET
ejpam-4646	167	17	dg(u	dg(u	ADJ
ejpam-4646	167	18	,	,	PUNCT
ejpam-4646	167	19	v	v	NOUN
ejpam-4646	167	20	)	)	PUNCT
ejpam-4646	167	21	=	=	SYM
ejpam-4646	168	1	2	2	X
ejpam-4646	168	2	.	.	PUNCT
ejpam-4646	168	3	since	since	SCONJ
ejpam-4646	168	4	ω	ω	PROPN
ejpam-4646	168	5	is	be	AUX
ejpam-4646	168	6	an	an	DET
ejpam-4646	168	7	independent	independent	ADJ
ejpam-4646	168	8	set	set	NOUN
ejpam-4646	168	9	,	,	PUNCT
ejpam-4646	168	10	u	u	NOUN
ejpam-4646	168	11	,	,	PUNCT
ejpam-4646	168	12	v	v	NOUN
ejpam-4646	168	13	∈	∈	PROPN
ejpam-4646	168	14	v	v	NOUN
ejpam-4646	168	15	(	(	PUNCT
ejpam-4646	168	16	kq	kq	PROPN
ejpam-4646	168	17	)	)	PUNCT
ejpam-4646	168	18	for	for	ADP
ejpam-4646	168	19	a	a	DET
ejpam-4646	168	20	unique	unique	ADJ
ejpam-4646	168	21	kq	kq	PROPN
ejpam-4646	168	22	∈	∈	PROPN
ejpam-4646	168	23	ω	ω	PROPN
ejpam-4646	168	24	.	.	PUNCT
ejpam-4646	169	1	we	we	PRON
ejpam-4646	169	2	may	may	AUX
ejpam-4646	169	3	assume	assume	VERB
ejpam-4646	169	4	that	that	SCONJ
ejpam-4646	169	5	u	u	NOUN
ejpam-4646	169	6	,	,	PUNCT
ejpam-4646	169	7	v	v	PROPN
ejpam-4646	169	8	∈	∈	PROPN
ejpam-4646	169	9	d2	d2	NOUN
ejpam-4646	169	10	.	.	PUNCT
ejpam-4646	169	11	consider	consider	VERB
ejpam-4646	169	12	the	the	DET
ejpam-4646	169	13	following	follow	VERB
ejpam-4646	169	14	cases	case	NOUN
ejpam-4646	169	15	:	:	PUNCT
ejpam-4646	169	16	case	case	NOUN
ejpam-4646	169	17	1	1	NUM
ejpam-4646	169	18	.	.	PUNCT
ejpam-4646	170	1	p	p	X
ejpam-4646	170	2	<	<	X
ejpam-4646	170	3	4	4	NUM
ejpam-4646	170	4	.	.	PUNCT
ejpam-4646	171	1	then	then	ADV
ejpam-4646	171	2	v	v	X
ejpam-4646	171	3	(	(	PUNCT
ejpam-4646	171	4	g	g	NOUN
ejpam-4646	171	5	)	)	PUNCT
ejpam-4646	171	6	\	\	PUNCT
ejpam-4646	172	1	s	s	PART
ejpam-4646	172	2	⊆	⊆	NUM
ejpam-4646	172	3	ig(v	ig(v	X
ejpam-4646	172	4	(	(	PUNCT
ejpam-4646	172	5	kp	kp	PROPN
ejpam-4646	172	6	)	)	PUNCT
ejpam-4646	172	7	)	)	PUNCT
ejpam-4646	172	8	.	.	PUNCT
ejpam-4646	173	1	if	if	SCONJ
ejpam-4646	173	2	there	there	PRON
ejpam-4646	173	3	exists	exist	VERB
ejpam-4646	173	4	w	w	PROPN
ejpam-4646	173	5	∈	∈	PROPN
ejpam-4646	173	6	v	v	NOUN
ejpam-4646	173	7	(	(	PUNCT
ejpam-4646	173	8	kp	kp	PROPN
ejpam-4646	173	9	)	)	PUNCT
ejpam-4646	173	10	\	\	PROPN
ejpam-4646	174	1	s	s	X
ejpam-4646	174	2	,	,	PUNCT
ejpam-4646	174	3	then	then	ADV
ejpam-4646	174	4	there	there	PRON
ejpam-4646	174	5	exist	exist	VERB
ejpam-4646	174	6	x	x	NOUN
ejpam-4646	174	7	,	,	PUNCT
ejpam-4646	174	8	y	y	PROPN
ejpam-4646	174	9	∈	∈	PROPN
ejpam-4646	174	10	s	s	VERB
ejpam-4646	174	11	such	such	ADJ
ejpam-4646	174	12	that	that	SCONJ
ejpam-4646	174	13	[	[	X
ejpam-4646	174	14	x	x	X
ejpam-4646	174	15	,	,	PUNCT
ejpam-4646	174	16	w	w	PROPN
ejpam-4646	174	17	,	,	PUNCT
ejpam-4646	174	18	y	y	PROPN
ejpam-4646	174	19	]	]	X
ejpam-4646	174	20	is	be	AUX
ejpam-4646	174	21	an	an	DET
ejpam-4646	174	22	x	x	ADJ
ejpam-4646	174	23	-	-	NOUN
ejpam-4646	174	24	y	y	ADJ
ejpam-4646	174	25	geodesic	geodesic	NOUN
ejpam-4646	174	26	.	.	PUNCT
ejpam-4646	175	1	it	it	PRON
ejpam-4646	175	2	follows	follow	VERB
ejpam-4646	175	3	that	that	SCONJ
ejpam-4646	175	4	x	x	SYM
ejpam-4646	175	5	,	,	PUNCT
ejpam-4646	175	6	y	y	PROPN
ejpam-4646	175	7	∈	∈	PROPN
ejpam-4646	175	8	v	v	PROPN
ejpam-4646	175	9	(	(	PUNCT
ejpam-4646	175	10	kr	kr	PROPN
ejpam-4646	175	11	)	)	PUNCT
ejpam-4646	175	12	for	for	ADP
ejpam-4646	175	13	some	some	DET
ejpam-4646	175	14	kr	kr	PROPN
ejpam-4646	175	15	∈	∈	PROPN
ejpam-4646	175	16	ω\{kp	ω\{kp	NOUN
ejpam-4646	175	17	}	}	PUNCT
ejpam-4646	175	18	.	.	PUNCT
ejpam-4646	176	1	since	since	SCONJ
ejpam-4646	176	2	u	u	NOUN
ejpam-4646	176	3	,	,	PUNCT
ejpam-4646	176	4	v	v	NOUN
ejpam-4646	176	5	,	,	PUNCT
ejpam-4646	176	6	x	x	PRON
ejpam-4646	176	7	,	,	PUNCT
ejpam-4646	176	8	y	y	PROPN
ejpam-4646	176	9	∈	∈	PROPN
ejpam-4646	176	10	d2	d2	PROPN
ejpam-4646	176	11	,	,	PUNCT
ejpam-4646	176	12	|d2|	|d2|	NOUN
ejpam-4646	176	13	≥	≥	NUM
ejpam-4646	176	14	4	4	NUM
ejpam-4646	176	15	>	>	X
ejpam-4646	176	16	p	p	X
ejpam-4646	176	17	,	,	PUNCT
ejpam-4646	176	18	a	a	DET
ejpam-4646	176	19	contradiction	contradiction	NOUN
ejpam-4646	176	20	.	.	PUNCT
ejpam-4646	177	1	thus	thus	ADV
ejpam-4646	177	2	,	,	PUNCT
ejpam-4646	177	3	v	v	INTJ
ejpam-4646	177	4	(	(	PUNCT
ejpam-4646	177	5	kp	kp	PROPN
ejpam-4646	177	6	)	)	PUNCT
ejpam-4646	177	7	⊆	⊆	NUM
ejpam-4646	177	8	s	s	NOUN
ejpam-4646	177	9	and	and	CCONJ
ejpam-4646	177	10	d2	d2	PROPN
ejpam-4646	177	11	=	=	SYM
ejpam-4646	177	12	v	v	PROPN
ejpam-4646	177	13	(	(	PUNCT
ejpam-4646	177	14	kp	kp	PROPN
ejpam-4646	177	15	)	)	PUNCT
ejpam-4646	177	16	.	.	PUNCT
ejpam-4646	178	1	next	next	ADV
ejpam-4646	178	2	,	,	PUNCT
ejpam-4646	178	3	let	let	VERB
ejpam-4646	178	4	kq	kq	PROPN
ejpam-4646	178	5	∈	∈	PROPN
ejpam-4646	178	6	ω	ω	PROPN
ejpam-4646	178	7	\	\	PROPN
ejpam-4646	178	8	{	{	PUNCT
ejpam-4646	178	9	kp	kp	PROPN
ejpam-4646	178	10	}	}	PUNCT
ejpam-4646	178	11	.	.	PUNCT
ejpam-4646	179	1	since	since	SCONJ
ejpam-4646	179	2	s	s	PROPN
ejpam-4646	179	3	is	be	AUX
ejpam-4646	179	4	a	a	DET
ejpam-4646	179	5	hop	hop	NOUN
ejpam-4646	179	6	dominating	dominating	NOUN
ejpam-4646	179	7	set	set	NOUN
ejpam-4646	179	8	of	of	ADP
ejpam-4646	179	9	g	g	PROPN
ejpam-4646	179	10	,	,	PUNCT
ejpam-4646	179	11	s	s	X
ejpam-4646	179	12	∩	∩	ADJ
ejpam-4646	179	13	v	v	X
ejpam-4646	179	14	(	(	PUNCT
ejpam-4646	179	15	kq	kq	PROPN
ejpam-4646	179	16	)	)	PUNCT
ejpam-4646	179	17	̸=	̸=	PROPN
ejpam-4646	179	18	∅.	∅.	ADP
ejpam-4646	179	19	moreover	moreover	ADV
ejpam-4646	179	20	,	,	PUNCT
ejpam-4646	179	21	|s	|s	PROPN
ejpam-4646	179	22	∩	∩	ADJ
ejpam-4646	179	23	v	v	X
ejpam-4646	179	24	(	(	PUNCT
ejpam-4646	179	25	kq)|	kq)|	PROPN
ejpam-4646	179	26	=	=	PUNCT
ejpam-4646	179	27	1	1	NUM
ejpam-4646	179	28	since	since	SCONJ
ejpam-4646	179	29	s	s	NOUN
ejpam-4646	179	30	is	be	AUX
ejpam-4646	179	31	a	a	DET
ejpam-4646	179	32	γhg	γhg	NOUN
ejpam-4646	179	33	-	-	PUNCT
ejpam-4646	179	34	set	set	NOUN
ejpam-4646	179	35	of	of	ADP
ejpam-4646	179	36	g.	g.	PROPN
ejpam-4646	179	37	let	let	VERB
ejpam-4646	179	38	s	s	PRON
ejpam-4646	179	39	∩	∩	ADJ
ejpam-4646	179	40	v	v	X
ejpam-4646	179	41	(	(	PUNCT
ejpam-4646	179	42	kq	kq	PROPN
ejpam-4646	179	43	)	)	PUNCT
ejpam-4646	179	44	=	=	PRON
ejpam-4646	179	45	{	{	PUNCT
ejpam-4646	179	46	xq	xq	PROPN
ejpam-4646	179	47	}	}	PUNCT
ejpam-4646	179	48	for	for	ADP
ejpam-4646	179	49	each	each	DET
ejpam-4646	179	50	kq	kq	PROPN
ejpam-4646	179	51	∈	∈	PROPN
ejpam-4646	179	52	ω	ω	PROPN
ejpam-4646	179	53	\	\	PROPN
ejpam-4646	179	54	{	{	PUNCT
ejpam-4646	179	55	kp	kp	PROPN
ejpam-4646	179	56	}	}	PUNCT
ejpam-4646	179	57	.	.	PUNCT
ejpam-4646	180	1	note	note	VERB
ejpam-4646	180	2	that	that	SCONJ
ejpam-4646	180	3	if	if	SCONJ
ejpam-4646	180	4	d1	d1	PROPN
ejpam-4646	180	5	̸=	̸=	PROPN
ejpam-4646	180	6	∅	∅	NOUN
ejpam-4646	180	7	,	,	PUNCT
ejpam-4646	180	8	then	then	ADV
ejpam-4646	180	9	d1	d1	PROPN
ejpam-4646	180	10	contains	contain	VERB
ejpam-4646	180	11	all	all	DET
ejpam-4646	180	12	the	the	DET
ejpam-4646	180	13	dominating	dominating	NOUN
ejpam-4646	180	14	vertices	vertex	NOUN
ejpam-4646	180	15	of	of	ADP
ejpam-4646	180	16	g.	g.	NOUN
ejpam-4646	180	17	hence	hence	ADV
ejpam-4646	180	18	d1	d1	PROPN
ejpam-4646	180	19	⊆	⊆	NUM
ejpam-4646	180	20	s.	s.	PROPN
ejpam-4646	180	21	therefore	therefore	ADV
ejpam-4646	180	22	,	,	PUNCT
ejpam-4646	180	23	s	s	PART
ejpam-4646	180	24	=	=	X
ejpam-4646	180	25	d1	d1	PROPN
ejpam-4646	180	26	∪d2	∪d2	NOUN
ejpam-4646	180	27	∪	∪	VERB
ejpam-4646	180	28	⋃	⋃	SYM
ejpam-4646	180	29	q	q	ADJ
ejpam-4646	180	30	̸=p	̸=p	X
ejpam-4646	180	31	{	{	PUNCT
ejpam-4646	180	32	xq	xq	PROPN
ejpam-4646	180	33	}	}	PUNCT
ejpam-4646	180	34			PROPN
ejpam-4646	180	35	c.j	c.j	PROPN
ejpam-4646	180	36	.	.	PROPN
ejpam-4646	180	37	saromines	saromines	PROPN
ejpam-4646	180	38	,	,	PUNCT
ejpam-4646	180	39	s.	s.	PROPN
ejpam-4646	180	40	canoy	canoy	PROPN
ejpam-4646	180	41	,	,	PUNCT
ejpam-4646	180	42	jr	jr	PROPN
ejpam-4646	180	43	.	.	PROPN
ejpam-4646	180	44	,	,	PUNCT
ejpam-4646	180	45	/	/	SYM
ejpam-4646	180	46	eur	eur	NOUN
ejpam-4646	180	47	.	.	PUNCT
ejpam-4646	181	1	j.	j.	PROPN
ejpam-4646	181	2	pure	pure	PROPN
ejpam-4646	181	3	appl	appl	PROPN
ejpam-4646	181	4	.	.	PROPN
ejpam-4646	181	5	math	math	PROPN
ejpam-4646	181	6	,	,	PUNCT
ejpam-4646	181	7	16	16	NUM
ejpam-4646	181	8	(	(	PUNCT
ejpam-4646	181	9	1	1	NUM
ejpam-4646	181	10	)	)	PUNCT
ejpam-4646	181	11	(	(	PUNCT
ejpam-4646	181	12	2023	2023	NUM
ejpam-4646	181	13	)	)	PUNCT
ejpam-4646	181	14	,	,	PUNCT
ejpam-4646	181	15	5	5	NUM
ejpam-4646	181	16	-	-	SYM
ejpam-4646	181	17	17	17	NUM
ejpam-4646	181	18	10	10	NUM
ejpam-4646	181	19	and	and	CCONJ
ejpam-4646	181	20	γhg(g	γhg(g	NUM
ejpam-4646	181	21	)	)	PUNCT
ejpam-4646	181	22	=	=	NOUN
ejpam-4646	181	23	|s|	|s|	NOUN
ejpam-4646	181	24	=	=	SYM
ejpam-4646	181	25	n−	n−	PROPN
ejpam-4646	181	26	∑	∑	PUNCT
ejpam-4646	181	27	kq∈ω	kq∈ω	PRON
ejpam-4646	181	28	q	q	X
ejpam-4646	182	1	+	+	PROPN
ejpam-4646	182	2	p+	p+	AUX
ejpam-4646	182	3	|ω|	|ω|	NUM
ejpam-4646	182	4	−	−	PROPN
ejpam-4646	182	5	1	1	NUM
ejpam-4646	182	6	=	=	SYM
ejpam-4646	182	7	n−	n−	PROPN
ejpam-4646	182	8	∑	∑	PUNCT
ejpam-4646	182	9	kq∈ω	kq∈ω	DET
ejpam-4646	182	10	q	q	PROPN
ejpam-4646	182	11	+	+	PROPN
ejpam-4646	182	12	p+	p+	PROPN
ejpam-4646	182	13	1	1	NUM
ejpam-4646	182	14	+	+	NOUN
ejpam-4646	182	15	|ω|	|ω|	ADP
ejpam-4646	182	16	−	−	PROPN
ejpam-4646	182	17	2	2	NUM
ejpam-4646	182	18	.	.	PUNCT
ejpam-4646	182	19	case	case	NOUN
ejpam-4646	182	20	2	2	NUM
ejpam-4646	182	21	.	.	PUNCT
ejpam-4646	183	1	p	p	X
ejpam-4646	183	2	≥	≥	NUM
ejpam-4646	183	3	4	4	NUM
ejpam-4646	183	4	.	.	PUNCT
ejpam-4646	183	5	suppose	suppose	VERB
ejpam-4646	183	6	d2	d2	PROPN
ejpam-4646	183	7	=	=	PROPN
ejpam-4646	183	8	v	v	PROPN
ejpam-4646	183	9	(	(	PUNCT
ejpam-4646	183	10	kp	kp	PROPN
ejpam-4646	183	11	)	)	PUNCT
ejpam-4646	183	12	.	.	PUNCT
ejpam-4646	184	1	then	then	ADV
ejpam-4646	184	2	|s|	|s|	PROPN
ejpam-4646	184	3	=	=	SYM
ejpam-4646	184	4	n	n	CCONJ
ejpam-4646	184	5	−	−	NOUN
ejpam-4646	184	6	∑	∑	ADV
ejpam-4646	184	7	kq∈ω	kq∈ω	PROPN
ejpam-4646	184	8	q	q	NOUN
ejpam-4646	185	1	+	+	X
ejpam-4646	185	2	p	p	X
ejpam-4646	186	1	+	+	PROPN
ejpam-4646	186	2	|ω|	|ω|	ADP
ejpam-4646	186	3	−	−	PROPN
ejpam-4646	186	4	1	1	NUM
ejpam-4646	186	5	.	.	PUNCT
ejpam-4646	187	1	let	let	VERB
ejpam-4646	187	2	kt	kt	PROPN
ejpam-4646	187	3	∈	∈	PROPN
ejpam-4646	187	4	ω	ω	X
ejpam-4646	187	5	\	\	PROPN
ejpam-4646	187	6	{	{	PUNCT
ejpam-4646	187	7	kp	kp	PROPN
ejpam-4646	187	8	}	}	PUNCT
ejpam-4646	187	9	.	.	PUNCT
ejpam-4646	188	1	pick	pick	VERB
ejpam-4646	188	2	a	a	DET
ejpam-4646	188	3	,	,	PUNCT
ejpam-4646	188	4	b	b	PROPN
ejpam-4646	188	5	∈	∈	PROPN
ejpam-4646	188	6	v	v	NOUN
ejpam-4646	188	7	(	(	PUNCT
ejpam-4646	188	8	kt	kt	PROPN
ejpam-4646	188	9	)	)	PUNCT
ejpam-4646	188	10	with	with	ADP
ejpam-4646	188	11	a	a	DET
ejpam-4646	188	12	̸=	̸=	PROPN
ejpam-4646	188	13	b.	b.	NOUN
ejpam-4646	188	14	let	let	VERB
ejpam-4646	188	15	d	d	NOUN
ejpam-4646	188	16	′	′	NOUN
ejpam-4646	189	1	=	=	PUNCT
ejpam-4646	189	2	{	{	PUNCT
ejpam-4646	189	3	u	u	NOUN
ejpam-4646	189	4	,	,	PUNCT
ejpam-4646	189	5	v	v	NOUN
ejpam-4646	189	6	,	,	PUNCT
ejpam-4646	189	7	a	a	PRON
ejpam-4646	189	8	,	,	PUNCT
ejpam-4646	189	9	b	b	NOUN
ejpam-4646	189	10	}	}	PUNCT
ejpam-4646	189	11	.	.	PUNCT
ejpam-4646	190	1	then	then	ADV
ejpam-4646	190	2	v	v	X
ejpam-4646	190	3	(	(	PUNCT
ejpam-4646	190	4	g	g	NOUN
ejpam-4646	190	5	)	)	PUNCT
ejpam-4646	190	6	\	\	PUNCT
ejpam-4646	190	7	s	s	PART
ejpam-4646	190	8	⊆	⊆	NUM
ejpam-4646	190	9	i(d	i(d	NOUN
ejpam-4646	190	10	′	′	NUM
ejpam-4646	190	11	)	)	PUNCT
ejpam-4646	190	12	.	.	PUNCT
ejpam-4646	191	1	for	for	ADP
ejpam-4646	191	2	each	each	DET
ejpam-4646	191	3	kq	kq	PROPN
ejpam-4646	191	4	∈	∈	PROPN
ejpam-4646	191	5	ω	ω	PROPN
ejpam-4646	191	6	\	\	PROPN
ejpam-4646	191	7	{	{	PUNCT
ejpam-4646	191	8	kp	kp	PROPN
ejpam-4646	191	9	,	,	PUNCT
ejpam-4646	191	10	kt	kt	PROPN
ejpam-4646	191	11	}	}	PUNCT
ejpam-4646	191	12	,	,	PUNCT
ejpam-4646	191	13	pick	pick	VERB
ejpam-4646	191	14	yq	yq	PROPN
ejpam-4646	191	15	∈	∈	PROPN
ejpam-4646	191	16	v	v	PROPN
ejpam-4646	191	17	(	(	PUNCT
ejpam-4646	191	18	kq	kq	PROPN
ejpam-4646	191	19	)	)	PUNCT
ejpam-4646	191	20	.	.	PUNCT
ejpam-4646	192	1	let	let	VERB
ejpam-4646	192	2	s	s	PRON
ejpam-4646	192	3	′	′	NOUN
ejpam-4646	192	4	=	=	PUNCT
ejpam-4646	192	5	d1	d1	PROPN
ejpam-4646	192	6	∪	∪	ADJ
ejpam-4646	192	7	d	d	NOUN
ejpam-4646	192	8	′	′	NUM
ejpam-4646	192	9	∪	∪	NOUN
ejpam-4646	192	10	(	(	PUNCT
ejpam-4646	192	11	⋃	⋃	NOUN
ejpam-4646	192	12	q	q	ADJ
ejpam-4646	192	13	̸=p	̸=p	PROPN
ejpam-4646	192	14	,	,	PUNCT
ejpam-4646	192	15	t	t	PROPN
ejpam-4646	192	16	{	{	PUNCT
ejpam-4646	192	17	yq	yq	NOUN
ejpam-4646	192	18	}	}	PUNCT
ejpam-4646	192	19	)	)	PUNCT
ejpam-4646	192	20	.	.	PUNCT
ejpam-4646	193	1	then	then	ADV
ejpam-4646	193	2	s	s	VERB
ejpam-4646	193	3	′	′	NOUN
ejpam-4646	193	4	is	be	AUX
ejpam-4646	193	5	a	a	DET
ejpam-4646	193	6	geodetic	geodetic	ADJ
ejpam-4646	193	7	hop	hop	NOUN
ejpam-4646	193	8	dominating	dominating	NOUN
ejpam-4646	193	9	set	set	NOUN
ejpam-4646	193	10	of	of	ADP
ejpam-4646	193	11	g	g	PROPN
ejpam-4646	193	12	and	and	CCONJ
ejpam-4646	193	13	∣∣∣s′	∣∣∣s′	ADJ
ejpam-4646	193	14	∣∣∣	∣∣∣	ADJ
ejpam-4646	193	15	=	=	SYM
ejpam-4646	193	16	n−	n−	PROPN
ejpam-4646	193	17	∑	∑	PUNCT
ejpam-4646	193	18	kq∈ω	kq∈ω	DET
ejpam-4646	193	19	q	q	PUNCT
ejpam-4646	193	20	+	+	PROPN
ejpam-4646	193	21	4	4	NUM
ejpam-4646	193	22	+	+	NOUN
ejpam-4646	193	23	|ω|	|ω|	ADP
ejpam-4646	193	24	−	−	PROPN
ejpam-4646	193	25	2	2	NUM
ejpam-4646	193	26	<	<	X
ejpam-4646	193	27	n−	n−	PROPN
ejpam-4646	193	28	∑	∑	PUNCT
ejpam-4646	193	29	kq∈ω	kq∈ω	DET
ejpam-4646	193	30	q	q	PROPN
ejpam-4646	193	31	+	+	PROPN
ejpam-4646	193	32	p+	p+	ADJ
ejpam-4646	193	33	|ω|	|ω|	VERB
ejpam-4646	193	34	−	−	PROPN
ejpam-4646	193	35	1	1	NUM
ejpam-4646	193	36	.	.	PUNCT
ejpam-4646	194	1	this	this	PRON
ejpam-4646	194	2	is	be	AUX
ejpam-4646	194	3	a	a	DET
ejpam-4646	194	4	contradiction	contradiction	NOUN
ejpam-4646	194	5	to	to	ADP
ejpam-4646	194	6	the	the	DET
ejpam-4646	194	7	above	above	ADJ
ejpam-4646	194	8	assumption	assumption	NOUN
ejpam-4646	194	9	.	.	PUNCT
ejpam-4646	195	1	thus	thus	ADV
ejpam-4646	195	2	,	,	PUNCT
ejpam-4646	195	3	d	d	PROPN
ejpam-4646	195	4	̸=	̸=	PROPN
ejpam-4646	195	5	v	v	X
ejpam-4646	195	6	(	(	PUNCT
ejpam-4646	195	7	kp	kp	PROPN
ejpam-4646	195	8	)	)	PUNCT
ejpam-4646	195	9	.	.	PUNCT
ejpam-4646	196	1	using	use	VERB
ejpam-4646	196	2	the	the	DET
ejpam-4646	196	3	preceding	precede	VERB
ejpam-4646	196	4	arguments	argument	NOUN
ejpam-4646	196	5	,	,	PUNCT
ejpam-4646	196	6	we	we	PRON
ejpam-4646	196	7	have	have	VERB
ejpam-4646	196	8	γhg(g	γhg(g	NUM
ejpam-4646	196	9	)	)	PUNCT
ejpam-4646	197	1	=	=	SYM
ejpam-4646	197	2	|s|	|s|	NOUN
ejpam-4646	197	3	=	=	PUNCT
ejpam-4646	197	4	n−	n−	PROPN
ejpam-4646	197	5	∑	∑	PUNCT
ejpam-4646	197	6	kq∈ω	kq∈ω	DET
ejpam-4646	197	7	q	q	PUNCT
ejpam-4646	197	8	+	+	PROPN
ejpam-4646	197	9	4	4	NUM
ejpam-4646	197	10	+	+	NOUN
ejpam-4646	197	11	|ω|	|ω|	NUM
ejpam-4646	197	12	−	−	PROPN
ejpam-4646	197	13	2	2	NUM
ejpam-4646	197	14	.	.	PUNCT
ejpam-4646	198	1	this	this	PRON
ejpam-4646	198	2	proves	prove	VERB
ejpam-4646	198	3	the	the	DET
ejpam-4646	198	4	assertion	assertion	NOUN
ejpam-4646	198	5	.	.	PUNCT
ejpam-4646	199	1	corollary	corollary	ADJ
ejpam-4646	199	2	1	1	NUM
ejpam-4646	199	3	.	.	PUNCT
ejpam-4646	200	1	let	let	VERB
ejpam-4646	200	2	kn	kn	PROPN
ejpam-4646	200	3	be	be	AUX
ejpam-4646	200	4	the	the	DET
ejpam-4646	200	5	complete	complete	ADJ
ejpam-4646	200	6	graph	graph	NOUN
ejpam-4646	200	7	of	of	ADP
ejpam-4646	200	8	order	order	NOUN
ejpam-4646	200	9	n	n	PRON
ejpam-4646	200	10	≥	≥	NOUN
ejpam-4646	200	11	4	4	NUM
ejpam-4646	200	12	and	and	CCONJ
ejpam-4646	200	13	ω	ω	NUM
ejpam-4646	200	14	an	an	DET
ejpam-4646	200	15	independent	independent	ADJ
ejpam-4646	200	16	family	family	NOUN
ejpam-4646	200	17	of	of	ADP
ejpam-4646	200	18	complete	complete	ADJ
ejpam-4646	200	19	proper	proper	ADJ
ejpam-4646	200	20	subgraphs	subgraph	NOUN
ejpam-4646	200	21	of	of	ADP
ejpam-4646	200	22	kn	kn	PROPN
ejpam-4646	200	23	,	,	PUNCT
ejpam-4646	200	24	each	each	PRON
ejpam-4646	200	25	of	of	ADP
ejpam-4646	200	26	order	order	NOUN
ejpam-4646	200	27	at	at	ADV
ejpam-4646	200	28	least	least	ADJ
ejpam-4646	200	29	2	2	NUM
ejpam-4646	200	30	.	.	X
ejpam-4646	201	1	if	if	SCONJ
ejpam-4646	201	2	k2	k2	PROPN
ejpam-4646	201	3	∈	∈	PROPN
ejpam-4646	201	4	ω	ω	PROPN
ejpam-4646	201	5	and	and	CCONJ
ejpam-4646	201	6	g	g	NOUN
ejpam-4646	201	7	=	=	PROPN
ejpam-4646	201	8	kn	kn	PROPN
ejpam-4646	201	9	\e(ω	\e(ω	INTJ
ejpam-4646	201	10	)	)	PUNCT
ejpam-4646	201	11	,	,	PUNCT
ejpam-4646	201	12	then	then	ADV
ejpam-4646	201	13	γhg(g	γhg(g	PROPN
ejpam-4646	201	14	)	)	PUNCT
ejpam-4646	201	15	=	=	PRON
ejpam-4646	201	16	{	{	PUNCT
ejpam-4646	201	17	n	n	CCONJ
ejpam-4646	201	18	,	,	PUNCT
ejpam-4646	201	19	if	if	SCONJ
ejpam-4646	201	20	|ω|	|ω|	ADP
ejpam-4646	201	21	=	=	SYM
ejpam-4646	201	22	1	1	NUM
ejpam-4646	201	23	|ω|+	|ω|+	NOUN
ejpam-4646	201	24	1	1	NUM
ejpam-4646	201	25	+	+	CCONJ
ejpam-4646	201	26	n−	n−	PROPN
ejpam-4646	201	27	∑	∑	ADV
ejpam-4646	201	28	kq∈ω	kq∈ω	PROPN
ejpam-4646	201	29	,	,	PUNCT
ejpam-4646	201	30	if	if	SCONJ
ejpam-4646	201	31	|ω|	|ω|	ADP
ejpam-4646	201	32	≥	≥	NOUN
ejpam-4646	201	33	2	2	NUM
ejpam-4646	201	34	.	.	PUNCT
ejpam-4646	201	35	corollary	corollary	ADJ
ejpam-4646	201	36	2	2	NUM
ejpam-4646	201	37	.	.	PUNCT
ejpam-4646	202	1	let	let	VERB
ejpam-4646	202	2	kn	kn	PROPN
ejpam-4646	202	3	be	be	AUX
ejpam-4646	202	4	the	the	DET
ejpam-4646	202	5	complete	complete	ADJ
ejpam-4646	202	6	graph	graph	NOUN
ejpam-4646	202	7	of	of	ADP
ejpam-4646	202	8	order	order	NOUN
ejpam-4646	202	9	n	n	PRON
ejpam-4646	202	10	≥	≥	NOUN
ejpam-4646	202	11	4	4	NUM
ejpam-4646	202	12	.	.	PUNCT
ejpam-4646	203	1	if	if	SCONJ
ejpam-4646	203	2	g	g	PROPN
ejpam-4646	203	3	is	be	AUX
ejpam-4646	203	4	a	a	DET
ejpam-4646	203	5	graph	graph	NOUN
ejpam-4646	203	6	of	of	ADP
ejpam-4646	203	7	order	order	NOUN
ejpam-4646	203	8	n	n	PRON
ejpam-4646	203	9	obtained	obtain	VERB
ejpam-4646	203	10	from	from	ADP
ejpam-4646	203	11	kn	kn	PROPN
ejpam-4646	203	12	by	by	ADP
ejpam-4646	203	13	deleting	delete	VERB
ejpam-4646	203	14	an	an	DET
ejpam-4646	203	15	edge	edge	NOUN
ejpam-4646	203	16	,	,	PUNCT
ejpam-4646	203	17	then	then	ADV
ejpam-4646	203	18	γhg(g	γhg(g	PROPN
ejpam-4646	203	19	)	)	PUNCT
ejpam-4646	204	1	=	=	PRON
ejpam-4646	205	1	n	n	CCONJ
ejpam-4646	205	2	the	the	DET
ejpam-4646	205	3	next	next	ADJ
ejpam-4646	205	4	result	result	NOUN
ejpam-4646	205	5	is	be	AUX
ejpam-4646	205	6	a	a	DET
ejpam-4646	205	7	restatement	restatement	NOUN
ejpam-4646	205	8	of	of	ADP
ejpam-4646	205	9	the	the	DET
ejpam-4646	205	10	one	one	NOUN
ejpam-4646	205	11	obtained	obtain	VERB
ejpam-4646	205	12	in	in	ADP
ejpam-4646	205	13	[	[	X
ejpam-4646	205	14	15	15	NUM
ejpam-4646	205	15	]	]	PUNCT
ejpam-4646	205	16	.	.	PUNCT
ejpam-4646	206	1	c.j	c.j	PROPN
ejpam-4646	206	2	.	.	PROPN
ejpam-4646	206	3	saromines	saromines	PROPN
ejpam-4646	206	4	,	,	PUNCT
ejpam-4646	206	5	s.	s.	PROPN
ejpam-4646	206	6	canoy	canoy	PROPN
ejpam-4646	206	7	,	,	PUNCT
ejpam-4646	206	8	jr	jr	PROPN
ejpam-4646	206	9	.	.	PROPN
ejpam-4646	206	10	,	,	PUNCT
ejpam-4646	206	11	/	/	SYM
ejpam-4646	206	12	eur	eur	NOUN
ejpam-4646	206	13	.	.	PUNCT
ejpam-4646	207	1	j.	j.	PROPN
ejpam-4646	207	2	pure	pure	PROPN
ejpam-4646	207	3	appl	appl	PROPN
ejpam-4646	207	4	.	.	PROPN
ejpam-4646	207	5	math	math	PROPN
ejpam-4646	207	6	,	,	PUNCT
ejpam-4646	207	7	16	16	NUM
ejpam-4646	207	8	(	(	PUNCT
ejpam-4646	207	9	1	1	NUM
ejpam-4646	207	10	)	)	PUNCT
ejpam-4646	207	11	(	(	PUNCT
ejpam-4646	207	12	2023	2023	NUM
ejpam-4646	207	13	)	)	PUNCT
ejpam-4646	207	14	,	,	PUNCT
ejpam-4646	207	15	5	5	NUM
ejpam-4646	207	16	-	-	SYM
ejpam-4646	207	17	17	17	NUM
ejpam-4646	207	18	11	11	NUM
ejpam-4646	207	19	theorem	theorem	NOUN
ejpam-4646	207	20	3	3	X
ejpam-4646	207	21	.	.	PUNCT
ejpam-4646	208	1	let	let	VERB
ejpam-4646	208	2	g	g	NOUN
ejpam-4646	209	1	and	and	CCONJ
ejpam-4646	209	2	h	h	NOUN
ejpam-4646	209	3	be	be	VERB
ejpam-4646	209	4	any	any	DET
ejpam-4646	209	5	two	two	NUM
ejpam-4646	209	6	graphs	graph	NOUN
ejpam-4646	209	7	.	.	PUNCT
ejpam-4646	210	1	a	a	DET
ejpam-4646	210	2	set	set	NOUN
ejpam-4646	210	3	c	c	NOUN
ejpam-4646	210	4	⊆	⊆	NUM
ejpam-4646	210	5	v	v	NOUN
ejpam-4646	210	6	(	(	PUNCT
ejpam-4646	210	7	g	g	PROPN
ejpam-4646	210	8	◦	◦	NOUN
ejpam-4646	210	9	h	h	NOUN
ejpam-4646	210	10	)	)	PUNCT
ejpam-4646	210	11	is	be	AUX
ejpam-4646	210	12	a	a	DET
ejpam-4646	210	13	hop	hop	NOUN
ejpam-4646	210	14	dominating	dominating	NOUN
ejpam-4646	210	15	set	set	NOUN
ejpam-4646	210	16	of	of	ADP
ejpam-4646	210	17	g	g	PROPN
ejpam-4646	210	18	◦	◦	NOUN
ejpam-4646	210	19	h	h	NOUN
ejpam-4646	210	20	if	if	SCONJ
ejpam-4646	211	1	and	and	CCONJ
ejpam-4646	211	2	only	only	ADV
ejpam-4646	211	3	if	if	SCONJ
ejpam-4646	211	4	c	c	X
ejpam-4646	211	5	=	=	PUNCT
ejpam-4646	211	6	a	a	DET
ejpam-4646	211	7	∪	∪	X
ejpam-4646	211	8	(	(	PUNCT
ejpam-4646	211	9	∪v∈v	∪v∈v	X
ejpam-4646	211	10	(	(	PUNCT
ejpam-4646	211	11	g)sv	g)sv	PROPN
ejpam-4646	211	12	)	)	PUNCT
ejpam-4646	211	13	,	,	PUNCT
ejpam-4646	211	14	where	where	SCONJ
ejpam-4646	211	15	a	a	DET
ejpam-4646	211	16	⊆	⊆	NUM
ejpam-4646	211	17	v	v	NOUN
ejpam-4646	211	18	(	(	PUNCT
ejpam-4646	211	19	g	g	NOUN
ejpam-4646	211	20	)	)	PUNCT
ejpam-4646	211	21	and	and	CCONJ
ejpam-4646	211	22	sv	sv	X
ejpam-4646	211	23	⊆	⊆	NUM
ejpam-4646	211	24	v	v	X
ejpam-4646	211	25	(	(	PUNCT
ejpam-4646	211	26	hv	hv	PROPN
ejpam-4646	211	27	)	)	PUNCT
ejpam-4646	211	28	for	for	ADP
ejpam-4646	211	29	each	each	DET
ejpam-4646	211	30	v	v	NUM
ejpam-4646	211	31	∈	∈	PROPN
ejpam-4646	211	32	v	v	NOUN
ejpam-4646	211	33	(	(	PUNCT
ejpam-4646	211	34	g	g	NOUN
ejpam-4646	211	35	)	)	PUNCT
ejpam-4646	211	36	,	,	PUNCT
ejpam-4646	211	37	and	and	CCONJ
ejpam-4646	211	38	satisfies	satisfy	VERB
ejpam-4646	211	39	the	the	DET
ejpam-4646	211	40	following	follow	VERB
ejpam-4646	211	41	conditions	condition	NOUN
ejpam-4646	211	42	:	:	PUNCT
ejpam-4646	211	43	(	(	PUNCT
ejpam-4646	211	44	i	i	NOUN
ejpam-4646	211	45	)	)	PUNCT
ejpam-4646	211	46	for	for	ADP
ejpam-4646	211	47	each	each	DET
ejpam-4646	211	48	w	w	PROPN
ejpam-4646	211	49	∈	∈	PROPN
ejpam-4646	211	50	v	v	ADP
ejpam-4646	211	51	(	(	PUNCT
ejpam-4646	211	52	g	g	NOUN
ejpam-4646	211	53	)	)	PUNCT
ejpam-4646	211	54	\	\	PROPN
ejpam-4646	211	55	a	a	PRON
ejpam-4646	211	56	,	,	PUNCT
ejpam-4646	211	57	there	there	PRON
ejpam-4646	211	58	exists	exist	VERB
ejpam-4646	211	59	x	x	X
ejpam-4646	211	60	∈	∈	PROPN
ejpam-4646	211	61	a	a	PRON
ejpam-4646	211	62	with	with	ADP
ejpam-4646	211	63	dg(w	dg(w	NOUN
ejpam-4646	211	64	,	,	PUNCT
ejpam-4646	211	65	x	x	X
ejpam-4646	211	66	)	)	PUNCT
ejpam-4646	211	67	=	=	SYM
ejpam-4646	211	68	2	2	NUM
ejpam-4646	211	69	or	or	CCONJ
ejpam-4646	211	70	there	there	PRON
ejpam-4646	211	71	exists	exist	VERB
ejpam-4646	211	72	y	y	PROPN
ejpam-4646	211	73	∈	∈	PROPN
ejpam-4646	211	74	v	v	ADP
ejpam-4646	211	75	(	(	PUNCT
ejpam-4646	211	76	g	g	NOUN
ejpam-4646	211	77	)	)	PUNCT
ejpam-4646	211	78	∩ng(w	∩ng(w	PROPN
ejpam-4646	211	79	)	)	PUNCT
ejpam-4646	211	80	with	with	ADP
ejpam-4646	211	81	sy	sy	PROPN
ejpam-4646	211	82	̸=	̸=	PROPN
ejpam-4646	211	83	∅.	∅.	PROPN
ejpam-4646	211	84	(	(	PUNCT
ejpam-4646	211	85	ii	ii	NOUN
ejpam-4646	211	86	)	)	PUNCT
ejpam-4646	211	87	sv	sv	VERB
ejpam-4646	212	1	⊆	⊆	NUM
ejpam-4646	212	2	v	v	ADP
ejpam-4646	212	3	(	(	PUNCT
ejpam-4646	212	4	hv	hv	X
ejpam-4646	212	5	)	)	PUNCT
ejpam-4646	212	6	is	be	AUX
ejpam-4646	212	7	a	a	DET
ejpam-4646	212	8	pointwise	pointwise	ADJ
ejpam-4646	212	9	non	non	ADJ
ejpam-4646	212	10	-	-	ADJ
ejpam-4646	212	11	dominating	dominating	ADJ
ejpam-4646	212	12	set	set	NOUN
ejpam-4646	212	13	of	of	ADP
ejpam-4646	212	14	hv	hv	PROPN
ejpam-4646	212	15	for	for	ADP
ejpam-4646	212	16	each	each	PRON
ejpam-4646	212	17	v	v	NUM
ejpam-4646	212	18	∈	∈	PROPN
ejpam-4646	212	19	v	v	NOUN
ejpam-4646	212	20	(	(	PUNCT
ejpam-4646	212	21	g	g	NOUN
ejpam-4646	212	22	)	)	PUNCT
ejpam-4646	212	23	\ng(a	\ng(a	PROPN
ejpam-4646	212	24	)	)	PUNCT
ejpam-4646	212	25	.	.	PUNCT
ejpam-4646	213	1	theorem	theorem	ADJ
ejpam-4646	213	2	4	4	NUM
ejpam-4646	213	3	.	.	PUNCT
ejpam-4646	214	1	let	let	VERB
ejpam-4646	214	2	g	g	NOUN
ejpam-4646	214	3	and	and	CCONJ
ejpam-4646	214	4	h	h	NOUN
ejpam-4646	214	5	be	be	VERB
ejpam-4646	214	6	any	any	DET
ejpam-4646	214	7	two	two	NUM
ejpam-4646	214	8	graphs	graph	NOUN
ejpam-4646	214	9	.	.	PUNCT
ejpam-4646	215	1	a	a	DET
ejpam-4646	215	2	set	set	NOUN
ejpam-4646	215	3	c	c	NOUN
ejpam-4646	215	4	⊆	⊆	NUM
ejpam-4646	215	5	v	v	NOUN
ejpam-4646	215	6	(	(	PUNCT
ejpam-4646	215	7	g	g	PROPN
ejpam-4646	215	8	◦	◦	NOUN
ejpam-4646	215	9	h	h	NOUN
ejpam-4646	215	10	)	)	PUNCT
ejpam-4646	215	11	is	be	AUX
ejpam-4646	215	12	a	a	DET
ejpam-4646	215	13	geodetic	geodetic	ADJ
ejpam-4646	215	14	hop	hop	NOUN
ejpam-4646	215	15	dominating	dominating	NOUN
ejpam-4646	215	16	set	set	NOUN
ejpam-4646	215	17	of	of	ADP
ejpam-4646	215	18	g	g	PROPN
ejpam-4646	215	19	◦	◦	NOUN
ejpam-4646	215	20	h	h	NOUN
ejpam-4646	215	21	if	if	SCONJ
ejpam-4646	216	1	and	and	CCONJ
ejpam-4646	216	2	only	only	ADV
ejpam-4646	216	3	if	if	SCONJ
ejpam-4646	216	4	c	c	X
ejpam-4646	216	5	=	=	PUNCT
ejpam-4646	216	6	a	a	DET
ejpam-4646	216	7	∪	∪	X
ejpam-4646	216	8	(	(	PUNCT
ejpam-4646	216	9	∪v∈v	∪v∈v	X
ejpam-4646	216	10	(	(	PUNCT
ejpam-4646	216	11	g)sv	g)sv	PROPN
ejpam-4646	216	12	)	)	PUNCT
ejpam-4646	216	13	,	,	PUNCT
ejpam-4646	216	14	where	where	SCONJ
ejpam-4646	216	15	a	a	DET
ejpam-4646	216	16	⊆	⊆	NUM
ejpam-4646	216	17	v	v	NOUN
ejpam-4646	216	18	(	(	PUNCT
ejpam-4646	216	19	g	g	NOUN
ejpam-4646	216	20	)	)	PUNCT
ejpam-4646	216	21	and	and	CCONJ
ejpam-4646	216	22	sv	sv	X
ejpam-4646	216	23	⊆	⊆	NUM
ejpam-4646	216	24	v	v	X
ejpam-4646	216	25	(	(	PUNCT
ejpam-4646	216	26	hv	hv	PROPN
ejpam-4646	216	27	)	)	PUNCT
ejpam-4646	216	28	for	for	ADP
ejpam-4646	216	29	each	each	DET
ejpam-4646	216	30	v	v	NUM
ejpam-4646	216	31	∈	∈	PROPN
ejpam-4646	216	32	v	v	NOUN
ejpam-4646	216	33	(	(	PUNCT
ejpam-4646	216	34	g	g	NOUN
ejpam-4646	216	35	)	)	PUNCT
ejpam-4646	216	36	,	,	PUNCT
ejpam-4646	216	37	and	and	CCONJ
ejpam-4646	216	38	satisfies	satisfy	VERB
ejpam-4646	216	39	the	the	DET
ejpam-4646	216	40	following	follow	VERB
ejpam-4646	216	41	conditions	condition	NOUN
ejpam-4646	216	42	:	:	PUNCT
ejpam-4646	216	43	(	(	PUNCT
ejpam-4646	216	44	i	i	NOUN
ejpam-4646	216	45	)	)	PUNCT
ejpam-4646	216	46	sv	sv	VERB
ejpam-4646	217	1	⊆	⊆	NUM
ejpam-4646	217	2	v	v	X
ejpam-4646	217	3	(	(	PUNCT
ejpam-4646	217	4	hv	hv	X
ejpam-4646	217	5	)	)	PUNCT
ejpam-4646	217	6	is	be	AUX
ejpam-4646	217	7	a	a	DET
ejpam-4646	217	8	pointwise	pointwise	ADJ
ejpam-4646	217	9	non	non	ADJ
ejpam-4646	217	10	-	-	ADJ
ejpam-4646	217	11	dominating	dominating	ADJ
ejpam-4646	217	12	set	set	NOUN
ejpam-4646	217	13	of	of	ADP
ejpam-4646	217	14	hv	hv	PROPN
ejpam-4646	217	15	for	for	ADP
ejpam-4646	217	16	each	each	DET
ejpam-4646	217	17	v	v	NUM
ejpam-4646	217	18	∈	∈	PROPN
ejpam-4646	217	19	v	v	NOUN
ejpam-4646	217	20	(	(	PUNCT
ejpam-4646	217	21	g	g	NOUN
ejpam-4646	217	22	)	)	PUNCT
ejpam-4646	217	23	\ng(a	\ng(a	PROPN
ejpam-4646	217	24	)	)	PUNCT
ejpam-4646	217	25	.	.	PUNCT
ejpam-4646	218	1	(	(	PUNCT
ejpam-4646	218	2	ii	ii	NOUN
ejpam-4646	218	3	)	)	PUNCT
ejpam-4646	218	4	for	for	ADP
ejpam-4646	218	5	each	each	DET
ejpam-4646	218	6	w	w	PROPN
ejpam-4646	218	7	∈	∈	PROPN
ejpam-4646	218	8	v	v	ADP
ejpam-4646	218	9	(	(	PUNCT
ejpam-4646	218	10	g	g	NOUN
ejpam-4646	218	11	)	)	PUNCT
ejpam-4646	218	12	\a	\a	ADJ
ejpam-4646	218	13	,	,	PUNCT
ejpam-4646	218	14	one	one	NUM
ejpam-4646	218	15	of	of	ADP
ejpam-4646	218	16	the	the	DET
ejpam-4646	218	17	following	follow	VERB
ejpam-4646	218	18	condition	condition	NOUN
ejpam-4646	218	19	holds	hold	VERB
ejpam-4646	218	20	:	:	PUNCT
ejpam-4646	218	21	(	(	PUNCT
ejpam-4646	218	22	1	1	X
ejpam-4646	218	23	)	)	PUNCT
ejpam-4646	218	24	∃	∃	PROPN
ejpam-4646	218	25	a	a	PROPN
ejpam-4646	218	26	,	,	PUNCT
ejpam-4646	218	27	b	b	PROPN
ejpam-4646	218	28	∈	∈	PROPN
ejpam-4646	218	29	sw	sw	PROPN
ejpam-4646	218	30	with	with	ADP
ejpam-4646	218	31	dhw(a	dhw(a	PROPN
ejpam-4646	218	32	,	,	PUNCT
ejpam-4646	218	33	b	b	NOUN
ejpam-4646	218	34	)	)	PUNCT
ejpam-4646	218	35	̸=	̸=	PROPN
ejpam-4646	218	36	1	1	NUM
ejpam-4646	218	37	.	.	PUNCT
ejpam-4646	219	1	(	(	PUNCT
ejpam-4646	219	2	2	2	X
ejpam-4646	219	3	)	)	PUNCT
ejpam-4646	219	4	∃	∃	PROPN
ejpam-4646	219	5	x	x	NOUN
ejpam-4646	219	6	,	,	PUNCT
ejpam-4646	219	7	y	y	PROPN
ejpam-4646	219	8	∈	∈	PROPN
ejpam-4646	219	9	v	v	ADP
ejpam-4646	219	10	(	(	PUNCT
ejpam-4646	219	11	g	g	NOUN
ejpam-4646	219	12	)	)	PUNCT
ejpam-4646	219	13	with	with	ADP
ejpam-4646	219	14	w	w	PROPN
ejpam-4646	219	15	∈	∈	PROPN
ejpam-4646	219	16	ig(x	ig(x	X
ejpam-4646	219	17	,	,	PUNCT
ejpam-4646	219	18	y	y	NOUN
ejpam-4646	219	19	)	)	PUNCT
ejpam-4646	219	20	.	.	PUNCT
ejpam-4646	220	1	(	(	PUNCT
ejpam-4646	220	2	3	3	X
ejpam-4646	220	3	)	)	PUNCT
ejpam-4646	220	4	∃	∃	PROPN
ejpam-4646	220	5	s	s	PROPN
ejpam-4646	220	6	∈	∈	PROPN
ejpam-4646	220	7	sw	sw	PROPN
ejpam-4646	220	8	and	and	CCONJ
ejpam-4646	220	9	t	t	PROPN
ejpam-4646	220	10	∈	∈	PROPN
ejpam-4646	220	11	a.	a.	NOUN
ejpam-4646	220	12	(	(	PUNCT
ejpam-4646	220	13	iii	iii	X
ejpam-4646	220	14	)	)	PUNCT
ejpam-4646	220	15	sv	sv	PROPN
ejpam-4646	220	16	is	be	AUX
ejpam-4646	220	17	a	a	DET
ejpam-4646	220	18	2	2	NUM
ejpam-4646	220	19	-	-	PUNCT
ejpam-4646	220	20	path	path	NOUN
ejpam-4646	220	21	closure	closure	NOUN
ejpam-4646	220	22	absorbing	absorb	VERB
ejpam-4646	220	23	set	set	NOUN
ejpam-4646	220	24	in	in	ADP
ejpam-4646	220	25	hv	hv	PROPN
ejpam-4646	220	26	∀v	∀v	PROPN
ejpam-4646	220	27	∈	∈	PROPN
ejpam-4646	220	28	v	v	ADP
ejpam-4646	220	29	(	(	PUNCT
ejpam-4646	220	30	g	g	NOUN
ejpam-4646	220	31	)	)	PUNCT
ejpam-4646	220	32	.	.	PUNCT
ejpam-4646	221	1	proof	proof	NOUN
ejpam-4646	221	2	.	.	PUNCT
ejpam-4646	222	1	suppose	suppose	VERB
ejpam-4646	222	2	c	c	NOUN
ejpam-4646	222	3	is	be	AUX
ejpam-4646	222	4	a	a	DET
ejpam-4646	222	5	geodetic	geodetic	ADJ
ejpam-4646	222	6	hop	hop	NOUN
ejpam-4646	222	7	dominating	dominating	NOUN
ejpam-4646	222	8	set	set	NOUN
ejpam-4646	222	9	of	of	ADP
ejpam-4646	222	10	g	g	PROPN
ejpam-4646	222	11	◦	◦	NOUN
ejpam-4646	222	12	h.	h.	NOUN
ejpam-4646	222	13	let	let	VERB
ejpam-4646	222	14	a	a	DET
ejpam-4646	222	15	=	=	SYM
ejpam-4646	222	16	c	c	NOUN
ejpam-4646	222	17	∩	∩	X
ejpam-4646	222	18	v	v	X
ejpam-4646	222	19	(	(	PUNCT
ejpam-4646	222	20	g	g	NOUN
ejpam-4646	222	21	)	)	PUNCT
ejpam-4646	222	22	and	and	CCONJ
ejpam-4646	222	23	sv	sv	X
ejpam-4646	222	24	=	=	SYM
ejpam-4646	222	25	c	c	PROPN
ejpam-4646	222	26	∩	∩	X
ejpam-4646	222	27	v	v	X
ejpam-4646	222	28	(	(	PUNCT
ejpam-4646	222	29	hv	hv	PROPN
ejpam-4646	222	30	)	)	PUNCT
ejpam-4646	222	31	for	for	ADP
ejpam-4646	222	32	each	each	DET
ejpam-4646	222	33	v	v	NUM
ejpam-4646	222	34	∈	∈	PROPN
ejpam-4646	222	35	v	v	NOUN
ejpam-4646	222	36	(	(	PUNCT
ejpam-4646	222	37	g	g	NOUN
ejpam-4646	222	38	)	)	PUNCT
ejpam-4646	222	39	.	.	PUNCT
ejpam-4646	223	1	since	since	SCONJ
ejpam-4646	223	2	c	c	PROPN
ejpam-4646	223	3	is	be	AUX
ejpam-4646	223	4	a	a	DET
ejpam-4646	223	5	geodetic	geodetic	ADJ
ejpam-4646	223	6	set	set	NOUN
ejpam-4646	223	7	,	,	PUNCT
ejpam-4646	223	8	sv	sv	PROPN
ejpam-4646	223	9	̸=	̸=	PROPN
ejpam-4646	223	10	∅	∅	NOUN
ejpam-4646	223	11	for	for	ADP
ejpam-4646	223	12	each	each	DET
ejpam-4646	223	13	v	v	NUM
ejpam-4646	223	14	∈	∈	PROPN
ejpam-4646	223	15	v	v	NOUN
ejpam-4646	223	16	(	(	PUNCT
ejpam-4646	223	17	g	g	NOUN
ejpam-4646	223	18	)	)	PUNCT
ejpam-4646	223	19	.	.	PUNCT
ejpam-4646	224	1	by	by	ADP
ejpam-4646	224	2	theorem	theorem	NOUN
ejpam-4646	224	3	3	3	NUM
ejpam-4646	224	4	,	,	PUNCT
ejpam-4646	224	5	(	(	PUNCT
ejpam-4646	224	6	i	i	NOUN
ejpam-4646	224	7	)	)	PUNCT
ejpam-4646	224	8	holds	hold	VERB
ejpam-4646	224	9	.	.	PUNCT
ejpam-4646	225	1	let	let	VERB
ejpam-4646	225	2	w	w	NOUN
ejpam-4646	225	3	∈	∈	PROPN
ejpam-4646	225	4	v	v	ADP
ejpam-4646	225	5	(	(	PUNCT
ejpam-4646	225	6	g	g	NOUN
ejpam-4646	225	7	)	)	PUNCT
ejpam-4646	225	8	\	\	NOUN
ejpam-4646	225	9	a.	a.	NOUN
ejpam-4646	225	10	since	since	SCONJ
ejpam-4646	225	11	c	c	PROPN
ejpam-4646	225	12	is	be	AUX
ejpam-4646	225	13	a	a	DET
ejpam-4646	225	14	geodetic	geodetic	ADJ
ejpam-4646	225	15	set	set	NOUN
ejpam-4646	225	16	of	of	ADP
ejpam-4646	225	17	g	g	PROPN
ejpam-4646	225	18	◦	◦	NOUN
ejpam-4646	225	19	h	h	NOUN
ejpam-4646	225	20	,	,	PUNCT
ejpam-4646	225	21	at	at	ADV
ejpam-4646	225	22	least	least	ADJ
ejpam-4646	225	23	one	one	NUM
ejpam-4646	225	24	of	of	ADP
ejpam-4646	225	25	the	the	DET
ejpam-4646	225	26	three	three	NUM
ejpam-4646	225	27	statements	statement	NOUN
ejpam-4646	225	28	in	in	ADP
ejpam-4646	225	29	(	(	PUNCT
ejpam-4646	225	30	ii	ii	NOUN
ejpam-4646	225	31	)	)	PUNCT
ejpam-4646	225	32	holds	hold	VERB
ejpam-4646	225	33	.	.	PUNCT
ejpam-4646	226	1	let	let	VERB
ejpam-4646	226	2	v	v	NUM
ejpam-4646	226	3	∈	∈	PROPN
ejpam-4646	226	4	v	v	NOUN
ejpam-4646	226	5	(	(	PUNCT
ejpam-4646	226	6	g	g	NOUN
ejpam-4646	226	7	)	)	PUNCT
ejpam-4646	226	8	.	.	PUNCT
ejpam-4646	227	1	let	let	VERB
ejpam-4646	227	2	p	p	PRON
ejpam-4646	227	3	∈	∈	PROPN
ejpam-4646	227	4	v	v	X
ejpam-4646	227	5	(	(	PUNCT
ejpam-4646	227	6	hv	hv	PROPN
ejpam-4646	227	7	)	)	PUNCT
ejpam-4646	227	8	\	\	PROPN
ejpam-4646	228	1	sv	sv	PROPN
ejpam-4646	228	2	.	.	PUNCT
ejpam-4646	229	1	since	since	SCONJ
ejpam-4646	229	2	c	c	PROPN
ejpam-4646	229	3	is	be	AUX
ejpam-4646	229	4	a	a	DET
ejpam-4646	229	5	geodetic	geodetic	ADJ
ejpam-4646	229	6	set	set	NOUN
ejpam-4646	229	7	,	,	PUNCT
ejpam-4646	229	8	there	there	PRON
ejpam-4646	229	9	exist	exist	VERB
ejpam-4646	229	10	s	s	PROPN
ejpam-4646	229	11	,	,	PUNCT
ejpam-4646	229	12	t	t	PROPN
ejpam-4646	229	13	∈	∈	PROPN
ejpam-4646	229	14	c	c	NOUN
ejpam-4646	229	15	such	such	ADJ
ejpam-4646	229	16	that	that	SCONJ
ejpam-4646	229	17	p	p	PROPN
ejpam-4646	229	18	∈	∈	PROPN
ejpam-4646	229	19	ig	ig	PROPN
ejpam-4646	229	20	◦	◦	NOUN
ejpam-4646	229	21	h(s	h(s	PROPN
ejpam-4646	229	22	,	,	PUNCT
ejpam-4646	229	23	t	t	PROPN
ejpam-4646	229	24	)	)	PUNCT
ejpam-4646	229	25	.	.	PUNCT
ejpam-4646	230	1	it	it	PRON
ejpam-4646	230	2	follows	follow	VERB
ejpam-4646	230	3	that	that	PRON
ejpam-4646	230	4	s	s	PROPN
ejpam-4646	230	5	,	,	PUNCT
ejpam-4646	230	6	t	t	PROPN
ejpam-4646	230	7	∈	∈	PROPN
ejpam-4646	230	8	sv	sv	PROPN
ejpam-4646	230	9	and	and	CCONJ
ejpam-4646	230	10	dhv(s	dhv(s	PROPN
ejpam-4646	230	11	,	,	PUNCT
ejpam-4646	230	12	t	t	PROPN
ejpam-4646	230	13	)	)	PUNCT
ejpam-4646	230	14	=	=	SYM
ejpam-4646	230	15	2	2	NUM
ejpam-4646	230	16	and	and	CCONJ
ejpam-4646	230	17	[	[	X
ejpam-4646	230	18	s	s	X
ejpam-4646	230	19	,	,	PUNCT
ejpam-4646	230	20	p	p	X
ejpam-4646	230	21	,	,	PUNCT
ejpam-4646	230	22	t	t	PROPN
ejpam-4646	230	23	]	]	PUNCT
ejpam-4646	230	24	is	be	AUX
ejpam-4646	230	25	an	an	DET
ejpam-4646	230	26	s	s	PROPN
ejpam-4646	230	27	-	-	PUNCT
ejpam-4646	230	28	t	t	NOUN
ejpam-4646	230	29	geodesic	geodesic	NOUN
ejpam-4646	230	30	in	in	ADP
ejpam-4646	230	31	hv	hv	PROPN
ejpam-4646	230	32	.	.	PUNCT
ejpam-4646	231	1	thus	thus	ADV
ejpam-4646	231	2	,	,	PUNCT
ejpam-4646	231	3	sv	sv	PROPN
ejpam-4646	231	4	is	be	AUX
ejpam-4646	231	5	a	a	DET
ejpam-4646	231	6	2	2	NUM
ejpam-4646	231	7	-	-	PUNCT
ejpam-4646	231	8	path	path	NOUN
ejpam-4646	231	9	closure	closure	NOUN
ejpam-4646	231	10	absorbing	absorb	VERB
ejpam-4646	231	11	set	set	NOUN
ejpam-4646	231	12	in	in	ADP
ejpam-4646	231	13	hv	hv	PROPN
ejpam-4646	231	14	,	,	PUNCT
ejpam-4646	231	15	showing	show	VERB
ejpam-4646	231	16	that	that	SCONJ
ejpam-4646	231	17	(	(	PUNCT
ejpam-4646	231	18	iii	iii	NOUN
ejpam-4646	231	19	)	)	PUNCT
ejpam-4646	231	20	holds	hold	VERB
ejpam-4646	231	21	.	.	PUNCT
ejpam-4646	232	1	conversely	conversely	ADV
ejpam-4646	232	2	,	,	PUNCT
ejpam-4646	232	3	suppose	suppose	VERB
ejpam-4646	232	4	c	c	NOUN
ejpam-4646	232	5	satisfies	satisfy	VERB
ejpam-4646	232	6	the	the	DET
ejpam-4646	232	7	given	give	VERB
ejpam-4646	232	8	conditions	condition	NOUN
ejpam-4646	232	9	.	.	PUNCT
ejpam-4646	233	1	let	let	VERB
ejpam-4646	233	2	v	v	NUM
ejpam-4646	233	3	∈	∈	PROPN
ejpam-4646	233	4	v	v	NOUN
ejpam-4646	233	5	(	(	PUNCT
ejpam-4646	233	6	g	g	NOUN
ejpam-4646	233	7	)	)	PUNCT
ejpam-4646	233	8	\a	\a	VERB
ejpam-4646	233	9	and	and	CCONJ
ejpam-4646	233	10	choose	choose	VERB
ejpam-4646	233	11	any	any	DET
ejpam-4646	233	12	y	y	PROPN
ejpam-4646	233	13	∈	∈	PROPN
ejpam-4646	233	14	ng(v	ng(v	NOUN
ejpam-4646	233	15	)	)	PUNCT
ejpam-4646	233	16	.	.	PUNCT
ejpam-4646	234	1	by	by	ADP
ejpam-4646	234	2	assumption	assumption	NOUN
ejpam-4646	234	3	,	,	PUNCT
ejpam-4646	234	4	sy	sy	ADP
ejpam-4646	234	5	̸=	̸=	PROPN
ejpam-4646	234	6	∅.	∅.	PRON
ejpam-4646	234	7	hence	hence	ADV
ejpam-4646	234	8	,	,	PUNCT
ejpam-4646	234	9	by	by	ADP
ejpam-4646	234	10	theorem	theorem	NOUN
ejpam-4646	234	11	3	3	NUM
ejpam-4646	234	12	,	,	PUNCT
ejpam-4646	234	13	c	c	PROPN
ejpam-4646	234	14	is	be	AUX
ejpam-4646	234	15	hop	hop	NOUN
ejpam-4646	234	16	dominating	dominate	VERB
ejpam-4646	234	17	set	set	NOUN
ejpam-4646	234	18	of	of	ADP
ejpam-4646	234	19	g	g	PROPN
ejpam-4646	234	20	◦	◦	NOUN
ejpam-4646	234	21	h.	h.	NOUN
ejpam-4646	234	22	let	let	VERB
ejpam-4646	234	23	z	z	PROPN
ejpam-4646	234	24	∈	∈	PROPN
ejpam-4646	234	25	v	v	NOUN
ejpam-4646	234	26	(	(	PUNCT
ejpam-4646	234	27	g	g	PROPN
ejpam-4646	234	28	◦	◦	NOUN
ejpam-4646	234	29	h	h	NOUN
ejpam-4646	234	30	)	)	PUNCT
ejpam-4646	234	31	\	\	NOUN
ejpam-4646	234	32	c	c	NOUN
ejpam-4646	234	33	and	and	CCONJ
ejpam-4646	234	34	let	let	VERB
ejpam-4646	234	35	w	w	PROPN
ejpam-4646	234	36	∈	∈	PROPN
ejpam-4646	234	37	v	v	ADP
ejpam-4646	234	38	(	(	PUNCT
ejpam-4646	234	39	g	g	NOUN
ejpam-4646	234	40	)	)	PUNCT
ejpam-4646	234	41	such	such	ADJ
ejpam-4646	234	42	that	that	SCONJ
ejpam-4646	234	43	z	z	PROPN
ejpam-4646	234	44	∈	∈	PROPN
ejpam-4646	234	45	v	v	NOUN
ejpam-4646	234	46	(	(	PUNCT
ejpam-4646	234	47	w	w	NOUN
ejpam-4646	234	48	+	+	NOUN
ejpam-4646	234	49	hw	hw	NOUN
ejpam-4646	234	50	)	)	PUNCT
ejpam-4646	234	51	.	.	PUNCT
ejpam-4646	235	1	consider	consider	VERB
ejpam-4646	235	2	the	the	DET
ejpam-4646	235	3	following	follow	VERB
ejpam-4646	235	4	cases	case	NOUN
ejpam-4646	235	5	:	:	PUNCT
ejpam-4646	235	6	case	case	NOUN
ejpam-4646	235	7	1	1	NUM
ejpam-4646	235	8	.	.	PUNCT
ejpam-4646	235	9	z	z	NOUN
ejpam-4646	236	1	=	=	SYM
ejpam-4646	236	2	w.	w.	PROPN
ejpam-4646	236	3	then	then	ADV
ejpam-4646	236	4	w	w	PROPN
ejpam-4646	236	5	∈	∈	PROPN
ejpam-4646	236	6	v	v	ADP
ejpam-4646	236	7	(	(	PUNCT
ejpam-4646	236	8	g	g	NOUN
ejpam-4646	236	9	)	)	PUNCT
ejpam-4646	236	10	\	\	NOUN
ejpam-4646	236	11	a.	a.	NOUN
ejpam-4646	236	12	suppose	suppose	VERB
ejpam-4646	236	13	condition	condition	NOUN
ejpam-4646	236	14	(	(	PUNCT
ejpam-4646	236	15	1	1	NUM
ejpam-4646	236	16	)	)	PUNCT
ejpam-4646	236	17	of	of	ADP
ejpam-4646	236	18	(	(	PUNCT
ejpam-4646	236	19	ii	ii	NOUN
ejpam-4646	236	20	)	)	PUNCT
ejpam-4646	236	21	holds	hold	VERB
ejpam-4646	236	22	.	.	PUNCT
ejpam-4646	237	1	then	then	ADV
ejpam-4646	237	2	a	a	DET
ejpam-4646	237	3	,	,	PUNCT
ejpam-4646	237	4	b	b	PROPN
ejpam-4646	237	5	∈	∈	PROPN
ejpam-4646	237	6	c	c	NOUN
ejpam-4646	237	7	and	and	CCONJ
ejpam-4646	237	8	z	z	PROPN
ejpam-4646	237	9	∈	∈	PROPN
ejpam-4646	237	10	ig	ig	PROPN
ejpam-4646	237	11	◦	◦	PROPN
ejpam-4646	237	12	h(a	h(a	PROPN
ejpam-4646	237	13	,	,	PUNCT
ejpam-4646	237	14	b	b	NOUN
ejpam-4646	237	15	)	)	PUNCT
ejpam-4646	237	16	.	.	PUNCT
ejpam-4646	238	1	suppose	suppose	VERB
ejpam-4646	238	2	(	(	PUNCT
ejpam-4646	238	3	2	2	X
ejpam-4646	238	4	)	)	PUNCT
ejpam-4646	238	5	holds	hold	VERB
ejpam-4646	238	6	.	.	PUNCT
ejpam-4646	239	1	let	let	VERB
ejpam-4646	239	2	p	p	PRON
ejpam-4646	239	3	∈	∈	PROPN
ejpam-4646	239	4	sx	sx	NOUN
ejpam-4646	239	5	and	and	CCONJ
ejpam-4646	239	6	q	q	PROPN
ejpam-4646	239	7	∈	∈	PROPN
ejpam-4646	240	1	sy	sy	PROPN
ejpam-4646	240	2	.	.	PUNCT
ejpam-4646	241	1	then	then	ADV
ejpam-4646	241	2	p	p	X
ejpam-4646	241	3	,	,	PUNCT
ejpam-4646	241	4	q	q	PROPN
ejpam-4646	241	5	∈	∈	PROPN
ejpam-4646	241	6	c	c	NOUN
ejpam-4646	241	7	and	and	CCONJ
ejpam-4646	241	8	z	z	PROPN
ejpam-4646	241	9	∈	∈	PROPN
ejpam-4646	241	10	ig	ig	PROPN
ejpam-4646	241	11	◦	◦	NOUN
ejpam-4646	241	12	h(p	h(p	NOUN
ejpam-4646	241	13	,	,	PUNCT
ejpam-4646	241	14	q	q	NOUN
ejpam-4646	241	15	)	)	PUNCT
ejpam-4646	241	16	.	.	PUNCT
ejpam-4646	242	1	next	next	ADV
ejpam-4646	242	2	,	,	PUNCT
ejpam-4646	242	3	suppose	suppose	VERB
ejpam-4646	242	4	that	that	SCONJ
ejpam-4646	242	5	(	(	PUNCT
ejpam-4646	242	6	3	3	X
ejpam-4646	242	7	)	)	PUNCT
ejpam-4646	242	8	holds	hold	VERB
ejpam-4646	242	9	.	.	PUNCT
ejpam-4646	243	1	then	then	ADV
ejpam-4646	243	2	s	s	PROPN
ejpam-4646	243	3	,	,	PUNCT
ejpam-4646	243	4	t	t	PROPN
ejpam-4646	243	5	∈	∈	PROPN
ejpam-4646	243	6	c	c	PROPN
ejpam-4646	243	7	and	and	CCONJ
ejpam-4646	243	8	z	z	PROPN
ejpam-4646	243	9	∈	∈	PROPN
ejpam-4646	243	10	ig	ig	PROPN
ejpam-4646	243	11	◦	◦	NOUN
ejpam-4646	243	12	h(s	h(s	PROPN
ejpam-4646	243	13	,	,	PUNCT
ejpam-4646	243	14	t	t	PROPN
ejpam-4646	243	15	)	)	PUNCT
ejpam-4646	243	16	.	.	PUNCT
ejpam-4646	244	1	case	case	NOUN
ejpam-4646	244	2	2	2	NUM
ejpam-4646	244	3	.	.	PUNCT
ejpam-4646	245	1	z	z	NOUN
ejpam-4646	245	2	̸=	̸=	PROPN
ejpam-4646	245	3	w.	w.	PROPN
ejpam-4646	245	4	c.j	c.j	PROPN
ejpam-4646	245	5	.	.	PROPN
ejpam-4646	245	6	saromines	saromines	PROPN
ejpam-4646	245	7	,	,	PUNCT
ejpam-4646	245	8	s.	s.	PROPN
ejpam-4646	245	9	canoy	canoy	PROPN
ejpam-4646	245	10	,	,	PUNCT
ejpam-4646	245	11	jr	jr	PROPN
ejpam-4646	245	12	.	.	PROPN
ejpam-4646	245	13	,	,	PUNCT
ejpam-4646	245	14	/	/	SYM
ejpam-4646	245	15	eur	eur	NOUN
ejpam-4646	245	16	.	.	PUNCT
ejpam-4646	246	1	j.	j.	PROPN
ejpam-4646	246	2	pure	pure	PROPN
ejpam-4646	246	3	appl	appl	PROPN
ejpam-4646	246	4	.	.	PROPN
ejpam-4646	246	5	math	math	PROPN
ejpam-4646	246	6	,	,	PUNCT
ejpam-4646	246	7	16	16	NUM
ejpam-4646	246	8	(	(	PUNCT
ejpam-4646	246	9	1	1	NUM
ejpam-4646	246	10	)	)	PUNCT
ejpam-4646	246	11	(	(	PUNCT
ejpam-4646	246	12	2023	2023	NUM
ejpam-4646	246	13	)	)	PUNCT
ejpam-4646	246	14	,	,	PUNCT
ejpam-4646	246	15	5	5	NUM
ejpam-4646	246	16	-	-	SYM
ejpam-4646	246	17	17	17	NUM
ejpam-4646	246	18	12	12	NUM
ejpam-4646	246	19	then	then	ADV
ejpam-4646	246	20	z	z	PROPN
ejpam-4646	246	21	∈	∈	PROPN
ejpam-4646	246	22	v	v	ADP
ejpam-4646	246	23	(	(	PUNCT
ejpam-4646	246	24	hw	hw	NOUN
ejpam-4646	246	25	)	)	PUNCT
ejpam-4646	246	26	\	\	PROPN
ejpam-4646	246	27	sw	sw	PROPN
ejpam-4646	246	28	.	.	PUNCT
ejpam-4646	247	1	by	by	ADP
ejpam-4646	247	2	(	(	PUNCT
ejpam-4646	247	3	iii	iii	NOUN
ejpam-4646	247	4	)	)	PUNCT
ejpam-4646	247	5	,	,	PUNCT
ejpam-4646	247	6	sw	sw	PROPN
ejpam-4646	247	7	is	be	AUX
ejpam-4646	247	8	a	a	DET
ejpam-4646	247	9	2	2	NUM
ejpam-4646	247	10	-	-	PUNCT
ejpam-4646	247	11	path	path	NOUN
ejpam-4646	247	12	closure	closure	NOUN
ejpam-4646	247	13	absorbing	absorb	VERB
ejpam-4646	247	14	set	set	NOUN
ejpam-4646	247	15	in	in	ADP
ejpam-4646	247	16	hw	hw	PRON
ejpam-4646	247	17	;	;	PUNCT
ejpam-4646	247	18	hence	hence	ADV
ejpam-4646	247	19	,	,	PUNCT
ejpam-4646	247	20	there	there	PRON
ejpam-4646	247	21	exists	exist	VERB
ejpam-4646	247	22	a	a	DET
ejpam-4646	247	23	,	,	PUNCT
ejpam-4646	247	24	b	b	PROPN
ejpam-4646	247	25	∈	∈	PROPN
ejpam-4646	247	26	sw	sw	NOUN
ejpam-4646	247	27	such	such	ADJ
ejpam-4646	247	28	that	that	SCONJ
ejpam-4646	247	29	[	[	X
ejpam-4646	247	30	a	a	X
ejpam-4646	247	31	,	,	PUNCT
ejpam-4646	247	32	z	z	PROPN
ejpam-4646	247	33	,	,	PUNCT
ejpam-4646	247	34	b	b	X
ejpam-4646	247	35	]	]	X
ejpam-4646	247	36	is	be	AUX
ejpam-4646	247	37	an	an	DET
ejpam-4646	247	38	a	a	PRON
ejpam-4646	247	39	-	-	PUNCT
ejpam-4646	247	40	b	b	NOUN
ejpam-4646	247	41	geodesic	geodesic	NOUN
ejpam-4646	247	42	in	in	ADP
ejpam-4646	247	43	hw	hw	PRON
ejpam-4646	247	44	.	.	PUNCT
ejpam-4646	248	1	therefore	therefore	ADV
ejpam-4646	248	2	,	,	PUNCT
ejpam-4646	248	3	a	a	DET
ejpam-4646	248	4	,	,	PUNCT
ejpam-4646	248	5	b	b	PROPN
ejpam-4646	248	6	∈	∈	PROPN
ejpam-4646	248	7	c	c	NOUN
ejpam-4646	248	8	and	and	CCONJ
ejpam-4646	248	9	[	[	X
ejpam-4646	248	10	a	a	X
ejpam-4646	248	11	,	,	PUNCT
ejpam-4646	248	12	z	z	PROPN
ejpam-4646	248	13	,	,	PUNCT
ejpam-4646	248	14	b	b	X
ejpam-4646	248	15	]	]	X
ejpam-4646	248	16	is	be	AUX
ejpam-4646	248	17	an	an	DET
ejpam-4646	248	18	a	a	PRON
ejpam-4646	248	19	-	-	PUNCT
ejpam-4646	248	20	b	b	NOUN
ejpam-4646	248	21	geodesic	geodesic	NOUN
ejpam-4646	248	22	in	in	ADP
ejpam-4646	248	23	g	g	PROPN
ejpam-4646	248	24	◦	◦	NOUN
ejpam-4646	248	25	h.	h.	NOUN
ejpam-4646	248	26	accordingly	accordingly	ADV
ejpam-4646	248	27	,	,	PUNCT
ejpam-4646	248	28	c	c	PROPN
ejpam-4646	248	29	is	be	AUX
ejpam-4646	248	30	a	a	DET
ejpam-4646	248	31	geodetic	geodetic	ADJ
ejpam-4646	248	32	hop	hop	NOUN
ejpam-4646	248	33	dominating	dominating	NOUN
ejpam-4646	248	34	set	set	NOUN
ejpam-4646	248	35	of	of	ADP
ejpam-4646	248	36	g	g	PROPN
ejpam-4646	248	37	◦	◦	NOUN
ejpam-4646	248	38	h.	h.	PROPN
ejpam-4646	248	39	corollary	corollary	ADJ
ejpam-4646	248	40	3	3	X
ejpam-4646	248	41	.	.	PUNCT
ejpam-4646	249	1	let	let	VERB
ejpam-4646	249	2	g	g	PRON
ejpam-4646	249	3	be	be	AUX
ejpam-4646	249	4	a	a	DET
ejpam-4646	249	5	connected	connected	ADJ
ejpam-4646	249	6	non	non	ADJ
ejpam-4646	249	7	-	-	ADJ
ejpam-4646	249	8	trivial	trivial	ADJ
ejpam-4646	249	9	graph	graph	NOUN
ejpam-4646	249	10	on	on	ADP
ejpam-4646	249	11	n	n	DET
ejpam-4646	249	12	vertices	vertex	NOUN
ejpam-4646	249	13	and	and	CCONJ
ejpam-4646	249	14	let	let	VERB
ejpam-4646	249	15	h	h	NOUN
ejpam-4646	249	16	be	be	AUX
ejpam-4646	249	17	any	any	DET
ejpam-4646	249	18	noncomplete	noncomplete	ADJ
ejpam-4646	249	19	graph	graph	NOUN
ejpam-4646	249	20	.	.	PUNCT
ejpam-4646	250	1	then	then	ADV
ejpam-4646	250	2	γhg(g	γhg(g	PROPN
ejpam-4646	250	3	◦	◦	NOUN
ejpam-4646	250	4	h	h	NOUN
ejpam-4646	250	5	)	)	PUNCT
ejpam-4646	250	6	=	=	SYM
ejpam-4646	250	7	min	min	NOUN
ejpam-4646	250	8	{	{	PUNCT
ejpam-4646	250	9	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	250	10	)	)	PUNCT
ejpam-4646	250	11	,	,	PUNCT
ejpam-4646	250	12	γ(h	γ(h	NOUN
ejpam-4646	250	13	)	)	PUNCT
ejpam-4646	250	14	+	+	NOUN
ejpam-4646	250	15	nρ2(h	nρ2(h	NUM
ejpam-4646	250	16	)	)	PUNCT
ejpam-4646	250	17	}	}	PUNCT
ejpam-4646	250	18	.	.	PUNCT
ejpam-4646	251	1	proof	proof	NOUN
ejpam-4646	251	2	.	.	PUNCT
ejpam-4646	252	1	for	for	ADP
ejpam-4646	252	2	each	each	DET
ejpam-4646	252	3	v	v	NUM
ejpam-4646	252	4	∈	∈	PROPN
ejpam-4646	252	5	v	v	NOUN
ejpam-4646	252	6	(	(	PUNCT
ejpam-4646	252	7	g	g	NOUN
ejpam-4646	252	8	)	)	PUNCT
ejpam-4646	252	9	,	,	PUNCT
ejpam-4646	252	10	let	let	VERB
ejpam-4646	252	11	sv	sv	INTJ
ejpam-4646	252	12	be	be	AUX
ejpam-4646	252	13	a	a	DET
ejpam-4646	252	14	ρ2pnd	ρ2pnd	ADV
ejpam-4646	252	15	-	-	PUNCT
ejpam-4646	252	16	set	set	NOUN
ejpam-4646	252	17	of	of	ADP
ejpam-4646	252	18	hv	hv	PROPN
ejpam-4646	252	19	.	.	PUNCT
ejpam-4646	253	1	then	then	ADV
ejpam-4646	253	2	c	c	X
ejpam-4646	254	1	=	=	PUNCT
ejpam-4646	254	2	∪v∈v	∪v∈v	X
ejpam-4646	254	3	(	(	PUNCT
ejpam-4646	254	4	g)sv	g)sv	PROPN
ejpam-4646	254	5	is	be	AUX
ejpam-4646	254	6	a	a	DET
ejpam-4646	254	7	geodetic	geodetic	ADJ
ejpam-4646	254	8	hop	hop	NOUN
ejpam-4646	254	9	dominating	dominating	NOUN
ejpam-4646	254	10	set	set	NOUN
ejpam-4646	254	11	of	of	ADP
ejpam-4646	254	12	g	g	PROPN
ejpam-4646	254	13	◦	◦	NOUN
ejpam-4646	254	14	h	h	NOUN
ejpam-4646	254	15	by	by	ADP
ejpam-4646	254	16	theorem	theorem	NOUN
ejpam-4646	254	17	4	4	NUM
ejpam-4646	254	18	.	.	PUNCT
ejpam-4646	255	1	next	next	ADV
ejpam-4646	255	2	,	,	PUNCT
ejpam-4646	255	3	let	let	VERB
ejpam-4646	255	4	a	a	PRON
ejpam-4646	255	5	be	be	AUX
ejpam-4646	255	6	a	a	DET
ejpam-4646	255	7	γ	γ	NOUN
ejpam-4646	255	8	-	-	PUNCT
ejpam-4646	255	9	set	set	NOUN
ejpam-4646	255	10	of	of	ADP
ejpam-4646	255	11	g.	g.	PROPN
ejpam-4646	255	12	for	for	ADP
ejpam-4646	255	13	each	each	DET
ejpam-4646	255	14	v	v	NUM
ejpam-4646	255	15	∈	∈	PROPN
ejpam-4646	255	16	v	v	NOUN
ejpam-4646	255	17	(	(	PUNCT
ejpam-4646	255	18	g	g	NOUN
ejpam-4646	255	19	)	)	PUNCT
ejpam-4646	255	20	,	,	PUNCT
ejpam-4646	255	21	let	let	VERB
ejpam-4646	255	22	tv	tv	NOUN
ejpam-4646	255	23	be	be	AUX
ejpam-4646	255	24	a	a	DET
ejpam-4646	255	25	ρ2	ρ2	NOUN
ejpam-4646	255	26	set	set	NOUN
ejpam-4646	255	27	of	of	ADP
ejpam-4646	255	28	hv	hv	PROPN
ejpam-4646	255	29	.	.	PUNCT
ejpam-4646	256	1	by	by	ADP
ejpam-4646	256	2	theorem	theorem	NOUN
ejpam-4646	256	3	4	4	NUM
ejpam-4646	256	4	,	,	PUNCT
ejpam-4646	256	5	c	c	NOUN
ejpam-4646	256	6	′	′	NOUN
ejpam-4646	257	1	=	=	PUNCT
ejpam-4646	257	2	a	a	DET
ejpam-4646	257	3	∪	∪	X
ejpam-4646	257	4	(	(	PUNCT
ejpam-4646	257	5	∪v∈v	∪v∈v	X
ejpam-4646	257	6	(	(	PUNCT
ejpam-4646	257	7	g)tv	g)tv	PROPN
ejpam-4646	257	8	)	)	PUNCT
ejpam-4646	257	9	is	be	AUX
ejpam-4646	257	10	a	a	DET
ejpam-4646	257	11	geodetic	geodetic	ADJ
ejpam-4646	257	12	hop	hop	NOUN
ejpam-4646	257	13	dominating	dominating	NOUN
ejpam-4646	257	14	set	set	NOUN
ejpam-4646	257	15	of	of	ADP
ejpam-4646	257	16	g	g	PROPN
ejpam-4646	257	17	◦	◦	NOUN
ejpam-4646	257	18	h.	h.	PROPN
ejpam-4646	257	19	thus	thus	ADV
ejpam-4646	257	20	,	,	PUNCT
ejpam-4646	257	21	γhg(g	γhg(g	PROPN
ejpam-4646	257	22	◦	◦	NOUN
ejpam-4646	257	23	h	h	NOUN
ejpam-4646	257	24	)	)	PUNCT
ejpam-4646	257	25	≤	≤	NUM
ejpam-4646	257	26	min	min	NOUN
ejpam-4646	257	27	{	{	PUNCT
ejpam-4646	257	28	|c|	|c|	PROPN
ejpam-4646	257	29	,	,	PUNCT
ejpam-4646	257	30	|c	|c	ADJ
ejpam-4646	257	31	′	′	NOUN
ejpam-4646	257	32	|	|	ADV
ejpam-4646	257	33	}	}	PUNCT
ejpam-4646	257	34	=	=	SYM
ejpam-4646	257	35	min	min	NOUN
ejpam-4646	257	36	{	{	PUNCT
ejpam-4646	257	37	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	257	38	)	)	PUNCT
ejpam-4646	257	39	,	,	PUNCT
ejpam-4646	257	40	γ(h	γ(h	NOUN
ejpam-4646	257	41	)	)	PUNCT
ejpam-4646	257	42	+	+	NOUN
ejpam-4646	257	43	nρ2(h	nρ2(h	NUM
ejpam-4646	257	44	)	)	PUNCT
ejpam-4646	257	45	}	}	PUNCT
ejpam-4646	257	46	.	.	PUNCT
ejpam-4646	258	1	let	let	VERB
ejpam-4646	258	2	rv	rv	PRON
ejpam-4646	258	3	be	be	AUX
ejpam-4646	258	4	a	a	DET
ejpam-4646	258	5	ρ2pnd	ρ2pnd	ADV
ejpam-4646	258	6	-	-	PUNCT
ejpam-4646	258	7	set	set	NOUN
ejpam-4646	258	8	of	of	ADP
ejpam-4646	258	9	hv	hv	PROPN
ejpam-4646	258	10	.	.	PUNCT
ejpam-4646	259	1	let	let	VERB
ejpam-4646	259	2	a1	a1	NOUN
ejpam-4646	259	3	=	=	SYM
ejpam-4646	259	4	v	v	NOUN
ejpam-4646	259	5	(	(	PUNCT
ejpam-4646	259	6	g	g	NOUN
ejpam-4646	259	7	)	)	PUNCT
ejpam-4646	259	8	\	\	NOUN
ejpam-4646	259	9	ng(a0	ng(a0	X
ejpam-4646	259	10	)	)	PUNCT
ejpam-4646	259	11	and	and	CCONJ
ejpam-4646	259	12	a2	a2	PROPN
ejpam-4646	259	13	=	=	SYM
ejpam-4646	259	14	ng(a0	ng(a0	NOUN
ejpam-4646	259	15	)	)	PUNCT
ejpam-4646	259	16	.	.	PUNCT
ejpam-4646	260	1	then	then	ADV
ejpam-4646	260	2	c0	c0	PROPN
ejpam-4646	260	3	=	=	SYM
ejpam-4646	260	4	a0	a0	PROPN
ejpam-4646	260	5	∪	∪	ADV
ejpam-4646	260	6	(	(	PUNCT
ejpam-4646	260	7	∪v∈v	∪v∈v	X
ejpam-4646	260	8	(	(	PUNCT
ejpam-4646	260	9	g)rv	g)rv	PROPN
ejpam-4646	260	10	)	)	PUNCT
ejpam-4646	260	11	is	be	AUX
ejpam-4646	260	12	a	a	DET
ejpam-4646	260	13	geodetic	geodetic	ADJ
ejpam-4646	260	14	hop	hop	NOUN
ejpam-4646	260	15	dominating	dominating	NOUN
ejpam-4646	260	16	set	set	NOUN
ejpam-4646	260	17	of	of	ADP
ejpam-4646	260	18	g	g	PROPN
ejpam-4646	260	19	◦	◦	NOUN
ejpam-4646	260	20	h	h	NOUN
ejpam-4646	260	21	by	by	ADP
ejpam-4646	260	22	theorem	theorem	NOUN
ejpam-4646	260	23	4	4	NUM
ejpam-4646	260	24	.	.	PUNCT
ejpam-4646	260	25	thus	thus	ADV
ejpam-4646	260	26	|c0|	|c0|	NOUN
ejpam-4646	260	27	=	=	SYM
ejpam-4646	260	28	|a0|+	|a0|+	NOUN
ejpam-4646	260	29	∑	∑	ADP
ejpam-4646	260	30	v∈a1	v∈a1	X
ejpam-4646	260	31	|rv|+	|rv|+	PROPN
ejpam-4646	260	32	∑	∑	PROPN
ejpam-4646	260	33	v∈a2	v∈a2	NOUN
ejpam-4646	260	34	|rv|	|rv|	PROPN
ejpam-4646	260	35	≥	≥	NUM
ejpam-4646	260	36	|a0|+	|a0|+	X
ejpam-4646	260	37	|a1|	|a1|	X
ejpam-4646	260	38	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4646	260	39	)	)	PUNCT
ejpam-4646	260	40	+	+	CCONJ
ejpam-4646	260	41	|a2|	|a2|	NOUN
ejpam-4646	260	42	ρ2(h	ρ2(h	NUM
ejpam-4646	260	43	)	)	PUNCT
ejpam-4646	260	44	.	.	PUNCT
ejpam-4646	261	1	suppose	suppose	VERB
ejpam-4646	261	2	γ(g	γ(g	NOUN
ejpam-4646	261	3	)	)	PUNCT
ejpam-4646	262	1	+	+	CCONJ
ejpam-4646	262	2	nρ2(h	nρ2(h	X
ejpam-4646	262	3	)	)	PUNCT
ejpam-4646	262	4	≤	≤	PUNCT
ejpam-4646	263	1	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	263	2	)	)	PUNCT
ejpam-4646	263	3	.	.	PUNCT
ejpam-4646	264	1	then	then	ADV
ejpam-4646	264	2	ρ2(h	ρ2(h	NUM
ejpam-4646	264	3	)	)	PUNCT
ejpam-4646	264	4	<	<	X
ejpam-4646	264	5	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4646	264	6	)	)	PUNCT
ejpam-4646	264	7	,	,	PUNCT
ejpam-4646	264	8	that	that	ADV
ejpam-4646	264	9	is	is	ADV
ejpam-4646	264	10	,	,	PUNCT
ejpam-4646	264	11	ρ2(h	ρ2(h	PROPN
ejpam-4646	264	12	)	)	PUNCT
ejpam-4646	264	13	+	+	CCONJ
ejpam-4646	264	14	1	1	NUM
ejpam-4646	264	15	≤	≤	NUM
ejpam-4646	264	16	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4646	264	17	)	)	PUNCT
ejpam-4646	264	18	.	.	PUNCT
ejpam-4646	265	1	it	it	PRON
ejpam-4646	265	2	follows	follow	VERB
ejpam-4646	265	3	that	that	SCONJ
ejpam-4646	265	4	|c0|	|c0|	NOUN
ejpam-4646	265	5	≥	≥	X
ejpam-4646	265	6	|a0|+	|a0|+	SYM
ejpam-4646	265	7	|a1|	|a1|	X
ejpam-4646	265	8	(	(	PUNCT
ejpam-4646	265	9	ρ2(h	ρ2(h	NUM
ejpam-4646	265	10	)	)	PUNCT
ejpam-4646	265	11	+	+	NOUN
ejpam-4646	265	12	1	1	X
ejpam-4646	265	13	)	)	PUNCT
ejpam-4646	265	14	+	+	CCONJ
ejpam-4646	265	15	|a2|	|a2|	NOUN
ejpam-4646	265	16	ρ2(h	ρ2(h	NUM
ejpam-4646	265	17	)	)	PUNCT
ejpam-4646	265	18	=	=	SYM
ejpam-4646	265	19	|a0|+	|a0|+	X
ejpam-4646	265	20	|a1|+	|a1|+	X
ejpam-4646	265	21	|a1|+	|a1|+	PRON
ejpam-4646	265	22	|a2|	|a2|	NOUN
ejpam-4646	265	23	ρ2(h	ρ2(h	NUM
ejpam-4646	265	24	)	)	PUNCT
ejpam-4646	265	25	=	=	SYM
ejpam-4646	265	26	|a0|+	|a0|+	SYM
ejpam-4646	265	27	|a1|+	|a1|+	X
ejpam-4646	265	28	nρ2(h	nρ2(h	PROPN
ejpam-4646	265	29	)	)	PUNCT
ejpam-4646	265	30	≥	≥	NOUN
ejpam-4646	265	31	γ(g	γ(g	PROPN
ejpam-4646	265	32	)	)	PUNCT
ejpam-4646	266	1	+	+	CCONJ
ejpam-4646	266	2	nρ2(h	nρ2(h	NUM
ejpam-4646	266	3	)	)	PUNCT
ejpam-4646	266	4	since	since	SCONJ
ejpam-4646	266	5	a0	a0	PROPN
ejpam-4646	266	6	∪a1	∪a1	PROPN
ejpam-4646	266	7	is	be	AUX
ejpam-4646	266	8	a	a	DET
ejpam-4646	266	9	dominating	dominating	NOUN
ejpam-4646	266	10	set	set	NOUN
ejpam-4646	266	11	of	of	ADP
ejpam-4646	266	12	g	g	PROPN
ejpam-4646	266	13	and	and	CCONJ
ejpam-4646	266	14	|a0	|a0	PROPN
ejpam-4646	267	1	+	+	X
ejpam-4646	267	2	a1|	a1|	NOUN
ejpam-4646	267	3	≤	≤	X
ejpam-4646	267	4	|a0|+	|a0|+	SYM
ejpam-4646	267	5	|a1|	|a1|	PROPN
ejpam-4646	267	6	.	.	PUNCT
ejpam-4646	268	1	suppose	suppose	VERB
ejpam-4646	268	2	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	268	3	)	)	PUNCT
ejpam-4646	268	4	<	<	X
ejpam-4646	268	5	γ(g	γ(g	PROPN
ejpam-4646	268	6	)	)	PUNCT
ejpam-4646	269	1	+	+	NOUN
ejpam-4646	269	2	nρ2(h	nρ2(h	NUM
ejpam-4646	269	3	)	)	PUNCT
ejpam-4646	269	4	.	.	PUNCT
ejpam-4646	270	1	then	then	ADV
ejpam-4646	270	2	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4646	270	3	)	)	PUNCT
ejpam-4646	270	4	=	=	SYM
ejpam-4646	271	1	ρ2(h	ρ2(h	NUM
ejpam-4646	271	2	)	)	PUNCT
ejpam-4646	271	3	.	.	PUNCT
ejpam-4646	272	1	thus	thus	ADV
ejpam-4646	272	2	,	,	PUNCT
ejpam-4646	272	3	|c0|	|c0|	NOUN
ejpam-4646	272	4	≥	≥	NOUN
ejpam-4646	272	5	|a0|+	|a0|+	X
ejpam-4646	272	6	|a1|	|a1|	X
ejpam-4646	272	7	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4646	272	8	)	)	PUNCT
ejpam-4646	273	1	+	+	CCONJ
ejpam-4646	273	2	|a2|	|a2|	NOUN
ejpam-4646	273	3	ρ2(h	ρ2(h	NUM
ejpam-4646	273	4	)	)	PUNCT
ejpam-4646	273	5	=	=	SYM
ejpam-4646	274	1	|a0|+	|a0|+	X
ejpam-4646	274	2	(	(	PUNCT
ejpam-4646	274	3	|a1|+	|a1|+	PRON
ejpam-4646	274	4	|a2|	|a2|	NOUN
ejpam-4646	274	5	)	)	PUNCT
ejpam-4646	274	6	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4646	274	7	)	)	PUNCT
ejpam-4646	274	8	=	=	SYM
ejpam-4646	275	1	|a0|+	|a0|+	SYM
ejpam-4646	275	2	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	275	3	)	)	PUNCT
ejpam-4646	275	4	≥	≥	NOUN
ejpam-4646	275	5	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	275	6	)	)	PUNCT
ejpam-4646	275	7	.	.	PUNCT
ejpam-4646	276	1	therefore	therefore	ADV
ejpam-4646	276	2	,	,	PUNCT
ejpam-4646	276	3	γhg(g	γhg(g	PROPN
ejpam-4646	276	4	◦	◦	NOUN
ejpam-4646	276	5	h	h	NOUN
ejpam-4646	276	6	)	)	PUNCT
ejpam-4646	276	7	=	=	NOUN
ejpam-4646	276	8	|c0|	|c0|	NOUN
ejpam-4646	276	9	≥	≥	NOUN
ejpam-4646	276	10	min	min	PROPN
ejpam-4646	276	11	{	{	PUNCT
ejpam-4646	276	12	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	276	13	)	)	PUNCT
ejpam-4646	276	14	,	,	PUNCT
ejpam-4646	276	15	γ(g	γ(g	PROPN
ejpam-4646	276	16	)	)	PUNCT
ejpam-4646	277	1	+	+	CCONJ
ejpam-4646	277	2	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	277	3	)	)	PUNCT
ejpam-4646	277	4	}	}	PUNCT
ejpam-4646	277	5	c.j	c.j	PROPN
ejpam-4646	277	6	.	.	PROPN
ejpam-4646	277	7	saromines	saromines	PROPN
ejpam-4646	277	8	,	,	PUNCT
ejpam-4646	277	9	s.	s.	PROPN
ejpam-4646	277	10	canoy	canoy	PROPN
ejpam-4646	277	11	,	,	PUNCT
ejpam-4646	277	12	jr	jr	PROPN
ejpam-4646	277	13	.	.	PROPN
ejpam-4646	277	14	,	,	PUNCT
ejpam-4646	277	15	/	/	SYM
ejpam-4646	277	16	eur	eur	NOUN
ejpam-4646	277	17	.	.	PUNCT
ejpam-4646	278	1	j.	j.	PROPN
ejpam-4646	278	2	pure	pure	PROPN
ejpam-4646	278	3	appl	appl	PROPN
ejpam-4646	278	4	.	.	PROPN
ejpam-4646	278	5	math	math	PROPN
ejpam-4646	278	6	,	,	PUNCT
ejpam-4646	278	7	16	16	NUM
ejpam-4646	278	8	(	(	PUNCT
ejpam-4646	278	9	1	1	NUM
ejpam-4646	278	10	)	)	PUNCT
ejpam-4646	278	11	(	(	PUNCT
ejpam-4646	278	12	2023	2023	NUM
ejpam-4646	278	13	)	)	PUNCT
ejpam-4646	278	14	,	,	PUNCT
ejpam-4646	278	15	5	5	NUM
ejpam-4646	278	16	-	-	SYM
ejpam-4646	278	17	17	17	NUM
ejpam-4646	278	18	13	13	NUM
ejpam-4646	278	19	accordingly	accordingly	ADV
ejpam-4646	278	20	,	,	PUNCT
ejpam-4646	278	21	γhg(g	γhg(g	PROPN
ejpam-4646	278	22	◦	◦	NOUN
ejpam-4646	278	23	h	h	NOUN
ejpam-4646	278	24	)	)	PUNCT
ejpam-4646	278	25	=	=	SYM
ejpam-4646	278	26	min	min	NOUN
ejpam-4646	278	27	{	{	PUNCT
ejpam-4646	278	28	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	278	29	)	)	PUNCT
ejpam-4646	278	30	,	,	PUNCT
ejpam-4646	278	31	γ(g	γ(g	PROPN
ejpam-4646	278	32	)	)	PUNCT
ejpam-4646	279	1	+	+	CCONJ
ejpam-4646	279	2	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	279	3	)	)	PUNCT
ejpam-4646	279	4	}	}	PUNCT
ejpam-4646	279	5	.	.	PUNCT
ejpam-4646	280	1	canoy	canoy	PROPN
ejpam-4646	280	2	et	et	PROPN
ejpam-4646	280	3	al	al	PROPN
ejpam-4646	280	4	.	.	PUNCT
ejpam-4646	281	1	in	in	ADP
ejpam-4646	281	2	[	[	X
ejpam-4646	281	3	15	15	NUM
ejpam-4646	281	4	]	]	PUNCT
ejpam-4646	281	5	obtained	obtain	VERB
ejpam-4646	281	6	the	the	DET
ejpam-4646	281	7	next	next	ADJ
ejpam-4646	281	8	result	result	NOUN
ejpam-4646	281	9	.	.	PUNCT
ejpam-4646	282	1	theorem	theorem	ADJ
ejpam-4646	282	2	5	5	NUM
ejpam-4646	282	3	.	.	PUNCT
ejpam-4646	283	1	let	let	VERB
ejpam-4646	283	2	g	g	NOUN
ejpam-4646	283	3	and	and	CCONJ
ejpam-4646	283	4	h	h	NOUN
ejpam-4646	283	5	be	be	AUX
ejpam-4646	283	6	connected	connect	VERB
ejpam-4646	283	7	non	non	ADJ
ejpam-4646	283	8	-	-	ADJ
ejpam-4646	283	9	trivial	trivial	ADJ
ejpam-4646	283	10	graphs	graph	NOUN
ejpam-4646	283	11	.	.	PUNCT
ejpam-4646	284	1	a	a	DET
ejpam-4646	284	2	subset	subset	NOUN
ejpam-4646	284	3	c	c	NOUN
ejpam-4646	284	4	=	=	PUNCT
ejpam-4646	284	5	⋃	⋃	PROPN
ejpam-4646	284	6	x∈s	x∈s	NOUN
ejpam-4646	285	1	[	[	X
ejpam-4646	285	2	x	x	X
ejpam-4646	285	3	×	×	PROPN
ejpam-4646	285	4	tx	tx	PROPN
ejpam-4646	285	5	]	]	PUNCT
ejpam-4646	285	6	of	of	ADP
ejpam-4646	285	7	v	v	NOUN
ejpam-4646	285	8	(	(	PUNCT
ejpam-4646	285	9	g[h	g[h	PROPN
ejpam-4646	285	10	]	]	PUNCT
ejpam-4646	285	11	)	)	PUNCT
ejpam-4646	285	12	,	,	PUNCT
ejpam-4646	285	13	where	where	SCONJ
ejpam-4646	285	14	s	s	VERB
ejpam-4646	285	15	⊆	⊆	NUM
ejpam-4646	285	16	v	v	NOUN
ejpam-4646	285	17	(	(	PUNCT
ejpam-4646	285	18	g	g	NOUN
ejpam-4646	285	19	)	)	PUNCT
ejpam-4646	285	20	and	and	CCONJ
ejpam-4646	285	21	tx	tx	VERB
ejpam-4646	285	22	⊆	⊆	NUM
ejpam-4646	285	23	v	v	NOUN
ejpam-4646	285	24	(	(	PUNCT
ejpam-4646	285	25	h	h	NOUN
ejpam-4646	285	26	)	)	PUNCT
ejpam-4646	285	27	for	for	ADP
ejpam-4646	285	28	each	each	DET
ejpam-4646	285	29	x	x	SYM
ejpam-4646	285	30	∈	∈	PROPN
ejpam-4646	285	31	s	s	NOUN
ejpam-4646	285	32	,	,	PUNCT
ejpam-4646	285	33	is	be	AUX
ejpam-4646	285	34	a	a	DET
ejpam-4646	285	35	hop	hop	NOUN
ejpam-4646	285	36	dominating	dominating	NOUN
ejpam-4646	285	37	set	set	NOUN
ejpam-4646	285	38	of	of	ADP
ejpam-4646	285	39	g[h	g[h	PROPN
ejpam-4646	285	40	]	]	PUNCT
ejpam-4646	285	41	if	if	SCONJ
ejpam-4646	285	42	and	and	CCONJ
ejpam-4646	285	43	only	only	ADV
ejpam-4646	285	44	if	if	SCONJ
ejpam-4646	285	45	the	the	DET
ejpam-4646	285	46	following	follow	VERB
ejpam-4646	285	47	conditions	condition	NOUN
ejpam-4646	285	48	hold	hold	VERB
ejpam-4646	285	49	:	:	PUNCT
ejpam-4646	285	50	(	(	PUNCT
ejpam-4646	285	51	i	i	NOUN
ejpam-4646	285	52	)	)	PUNCT
ejpam-4646	285	53	s	s	AUX
ejpam-4646	285	54	is	be	AUX
ejpam-4646	285	55	a	a	DET
ejpam-4646	285	56	hop	hop	NOUN
ejpam-4646	285	57	dominating	dominating	NOUN
ejpam-4646	285	58	set	set	NOUN
ejpam-4646	285	59	of	of	ADP
ejpam-4646	285	60	g	g	NOUN
ejpam-4646	285	61	;	;	PUNCT
ejpam-4646	285	62	(	(	PUNCT
ejpam-4646	285	63	ii	ii	NOUN
ejpam-4646	285	64	)	)	PUNCT
ejpam-4646	285	65	tx	tx	PROPN
ejpam-4646	285	66	is	be	AUX
ejpam-4646	285	67	a	a	DET
ejpam-4646	285	68	pointwise	pointwise	ADJ
ejpam-4646	285	69	non	non	ADJ
ejpam-4646	285	70	-	-	ADJ
ejpam-4646	285	71	dominating	dominating	ADJ
ejpam-4646	285	72	set	set	NOUN
ejpam-4646	285	73	of	of	ADP
ejpam-4646	285	74	h	h	NOUN
ejpam-4646	285	75	for	for	ADP
ejpam-4646	285	76	each	each	DET
ejpam-4646	285	77	x	x	SYM
ejpam-4646	285	78	∈	∈	PROPN
ejpam-4646	285	79	s	s	PART
ejpam-4646	285	80	\n2	\n2	ADJ
ejpam-4646	285	81	g(s	g(	NOUN
ejpam-4646	285	82	)	)	PUNCT
ejpam-4646	285	83	.	.	PUNCT
ejpam-4646	286	1	theorem	theorem	NOUN
ejpam-4646	286	2	6	6	NUM
ejpam-4646	286	3	.	.	PUNCT
ejpam-4646	287	1	let	let	VERB
ejpam-4646	287	2	g	g	NOUN
ejpam-4646	288	1	and	and	CCONJ
ejpam-4646	288	2	h	h	NOUN
ejpam-4646	288	3	be	be	AUX
ejpam-4646	288	4	connected	connect	VERB
ejpam-4646	288	5	non	non	ADJ
ejpam-4646	288	6	-	-	ADJ
ejpam-4646	288	7	trivial	trivial	ADJ
ejpam-4646	288	8	graphs	graph	NOUN
ejpam-4646	288	9	.	.	PUNCT
ejpam-4646	289	1	a	a	DET
ejpam-4646	289	2	subset	subset	NOUN
ejpam-4646	289	3	c	c	NOUN
ejpam-4646	289	4	=	=	PUNCT
ejpam-4646	289	5	⋃	⋃	PROPN
ejpam-4646	289	6	x∈s	x∈s	NOUN
ejpam-4646	289	7	[	[	X
ejpam-4646	289	8	x×tx	x×tx	X
ejpam-4646	289	9	]	]	X
ejpam-4646	289	10	of	of	ADP
ejpam-4646	289	11	v	v	NOUN
ejpam-4646	289	12	(	(	PUNCT
ejpam-4646	289	13	g[h	g[h	PROPN
ejpam-4646	289	14	]	]	PUNCT
ejpam-4646	289	15	)	)	PUNCT
ejpam-4646	289	16	,	,	PUNCT
ejpam-4646	289	17	where	where	SCONJ
ejpam-4646	289	18	s	s	VERB
ejpam-4646	289	19	⊆	⊆	NUM
ejpam-4646	289	20	v	v	NOUN
ejpam-4646	289	21	(	(	PUNCT
ejpam-4646	289	22	g	g	NOUN
ejpam-4646	289	23	)	)	PUNCT
ejpam-4646	289	24	and	and	CCONJ
ejpam-4646	289	25	tx	tx	VERB
ejpam-4646	289	26	⊆	⊆	NUM
ejpam-4646	289	27	v	v	NOUN
ejpam-4646	289	28	(	(	PUNCT
ejpam-4646	289	29	h	h	NOUN
ejpam-4646	289	30	)	)	PUNCT
ejpam-4646	289	31	for	for	ADP
ejpam-4646	289	32	each	each	DET
ejpam-4646	289	33	x	x	SYM
ejpam-4646	289	34	∈	∈	PROPN
ejpam-4646	289	35	s	s	NOUN
ejpam-4646	289	36	,	,	PUNCT
ejpam-4646	289	37	is	be	AUX
ejpam-4646	289	38	a	a	DET
ejpam-4646	289	39	geodetic	geodetic	ADJ
ejpam-4646	289	40	hop	hop	NOUN
ejpam-4646	289	41	dominating	dominating	NOUN
ejpam-4646	289	42	set	set	NOUN
ejpam-4646	289	43	of	of	ADP
ejpam-4646	289	44	g[h	g[h	PROPN
ejpam-4646	289	45	]	]	PUNCT
ejpam-4646	289	46	if	if	SCONJ
ejpam-4646	289	47	and	and	CCONJ
ejpam-4646	289	48	only	only	ADV
ejpam-4646	289	49	if	if	SCONJ
ejpam-4646	289	50	the	the	DET
ejpam-4646	289	51	following	follow	VERB
ejpam-4646	289	52	conditions	condition	NOUN
ejpam-4646	289	53	hold	hold	VERB
ejpam-4646	289	54	:	:	PUNCT
ejpam-4646	289	55	(	(	PUNCT
ejpam-4646	289	56	i	i	NOUN
ejpam-4646	289	57	)	)	PUNCT
ejpam-4646	289	58	s	s	AUX
ejpam-4646	289	59	is	be	AUX
ejpam-4646	289	60	a	a	DET
ejpam-4646	289	61	geodetic	geodetic	ADJ
ejpam-4646	289	62	hop	hop	NOUN
ejpam-4646	289	63	dominating	dominating	NOUN
ejpam-4646	289	64	set	set	NOUN
ejpam-4646	289	65	of	of	ADP
ejpam-4646	289	66	g	g	PROPN
ejpam-4646	289	67	,	,	PUNCT
ejpam-4646	289	68	(	(	PUNCT
ejpam-4646	289	69	ii	ii	NOUN
ejpam-4646	289	70	)	)	PUNCT
ejpam-4646	289	71	tx	tx	PROPN
ejpam-4646	289	72	is	be	AUX
ejpam-4646	289	73	a	a	DET
ejpam-4646	289	74	pointwise	pointwise	ADJ
ejpam-4646	289	75	non	non	ADJ
ejpam-4646	289	76	-	-	ADJ
ejpam-4646	289	77	dominating	dominating	ADJ
ejpam-4646	289	78	set	set	NOUN
ejpam-4646	289	79	of	of	ADP
ejpam-4646	289	80	h	h	NOUN
ejpam-4646	289	81	for	for	ADP
ejpam-4646	289	82	each	each	DET
ejpam-4646	289	83	x	x	SYM
ejpam-4646	289	84	∈	∈	PROPN
ejpam-4646	289	85	s	s	PART
ejpam-4646	289	86	\n2	\n2	ADJ
ejpam-4646	289	87	g(s	g(	NOUN
ejpam-4646	289	88	)	)	PUNCT
ejpam-4646	289	89	.	.	PUNCT
ejpam-4646	290	1	(	(	PUNCT
ejpam-4646	290	2	iii	iii	X
ejpam-4646	290	3	)	)	PUNCT
ejpam-4646	290	4	tx	tx	PROPN
ejpam-4646	290	5	is	be	AUX
ejpam-4646	290	6	a	a	DET
ejpam-4646	290	7	2	2	NUM
ejpam-4646	290	8	-	-	PUNCT
ejpam-4646	290	9	path	path	NOUN
ejpam-4646	290	10	closure	closure	NOUN
ejpam-4646	290	11	absorbing	absorb	VERB
ejpam-4646	290	12	set	set	NOUN
ejpam-4646	290	13	of	of	ADP
ejpam-4646	290	14	h	h	NOUN
ejpam-4646	290	15	for	for	ADP
ejpam-4646	290	16	each	each	DET
ejpam-4646	290	17	x	x	SYM
ejpam-4646	290	18	∈	∈	PROPN
ejpam-4646	290	19	s	s	PART
ejpam-4646	290	20	\	\	NOUN
ejpam-4646	290	21	ig(s	ig(s	NUM
ejpam-4646	290	22	)	)	PUNCT
ejpam-4646	290	23	.	.	PUNCT
ejpam-4646	291	1	proof	proof	NOUN
ejpam-4646	291	2	.	.	PUNCT
ejpam-4646	292	1	suppose	suppose	VERB
ejpam-4646	292	2	c	c	NOUN
ejpam-4646	292	3	is	be	AUX
ejpam-4646	292	4	a	a	DET
ejpam-4646	292	5	geodetic	geodetic	ADJ
ejpam-4646	292	6	hop	hop	NOUN
ejpam-4646	292	7	dominating	dominating	NOUN
ejpam-4646	292	8	set	set	NOUN
ejpam-4646	292	9	of	of	ADP
ejpam-4646	292	10	g	g	PROPN
ejpam-4646	293	1	[	[	X
ejpam-4646	293	2	h	h	X
ejpam-4646	293	3	]	]	X
ejpam-4646	293	4	.	.	PUNCT
ejpam-4646	294	1	by	by	ADP
ejpam-4646	294	2	theorem	theorem	NOUN
ejpam-4646	294	3	5	5	NUM
ejpam-4646	294	4	,	,	PUNCT
ejpam-4646	294	5	s	s	VERB
ejpam-4646	294	6	is	be	AUX
ejpam-4646	294	7	a	a	DET
ejpam-4646	294	8	hop	hop	NOUN
ejpam-4646	294	9	dominating	dominating	NOUN
ejpam-4646	294	10	set	set	NOUN
ejpam-4646	294	11	of	of	ADP
ejpam-4646	294	12	g	g	PROPN
ejpam-4646	294	13	and	and	CCONJ
ejpam-4646	294	14	(	(	PUNCT
ejpam-4646	294	15	ii	ii	NOUN
ejpam-4646	294	16	)	)	PUNCT
ejpam-4646	294	17	holds	hold	VERB
ejpam-4646	294	18	.	.	PUNCT
ejpam-4646	295	1	suppose	suppose	VERB
ejpam-4646	295	2	v	v	NUM
ejpam-4646	295	3	∈	∈	PROPN
ejpam-4646	295	4	v	v	NOUN
ejpam-4646	295	5	(	(	PUNCT
ejpam-4646	295	6	g	g	NOUN
ejpam-4646	295	7	)	)	PUNCT
ejpam-4646	295	8	\	\	PUNCT
ejpam-4646	296	1	s.	s.	PROPN
ejpam-4646	296	2	let	let	VERB
ejpam-4646	296	3	a	a	DET
ejpam-4646	296	4	∈	∈	PROPN
ejpam-4646	296	5	v	v	NOUN
ejpam-4646	296	6	(	(	PUNCT
ejpam-4646	296	7	h	h	NOUN
ejpam-4646	296	8	)	)	PUNCT
ejpam-4646	296	9	.	.	PUNCT
ejpam-4646	297	1	since	since	SCONJ
ejpam-4646	297	2	c	c	PROPN
ejpam-4646	297	3	is	be	AUX
ejpam-4646	297	4	a	a	DET
ejpam-4646	297	5	geodetic	geodetic	ADJ
ejpam-4646	297	6	set	set	NOUN
ejpam-4646	297	7	,	,	PUNCT
ejpam-4646	297	8	there	there	PRON
ejpam-4646	297	9	exist	exist	VERB
ejpam-4646	297	10	(	(	PUNCT
ejpam-4646	297	11	x	x	X
ejpam-4646	297	12	,	,	PUNCT
ejpam-4646	297	13	p	p	NOUN
ejpam-4646	297	14	)	)	PUNCT
ejpam-4646	297	15	,	,	PUNCT
ejpam-4646	297	16	(	(	PUNCT
ejpam-4646	297	17	y	y	NOUN
ejpam-4646	297	18	,	,	PUNCT
ejpam-4646	297	19	q	q	X
ejpam-4646	297	20	)	)	PUNCT
ejpam-4646	297	21	∈	∈	PROPN
ejpam-4646	297	22	c	c	NOUN
ejpam-4646	297	23	such	such	ADJ
ejpam-4646	297	24	that	that	DET
ejpam-4646	297	25	(	(	PUNCT
ejpam-4646	297	26	v	v	NOUN
ejpam-4646	297	27	,	,	PUNCT
ejpam-4646	297	28	a	a	PRON
ejpam-4646	297	29	)	)	PUNCT
ejpam-4646	297	30	∈	∈	PROPN
ejpam-4646	297	31	ig[h]((x	ig[h]((x	X
ejpam-4646	297	32	,	,	PUNCT
ejpam-4646	297	33	p	p	NOUN
ejpam-4646	297	34	)	)	PUNCT
ejpam-4646	297	35	,	,	PUNCT
ejpam-4646	297	36	(	(	PUNCT
ejpam-4646	297	37	y	y	NOUN
ejpam-4646	297	38	,	,	PUNCT
ejpam-4646	297	39	q	q	NOUN
ejpam-4646	297	40	)	)	PUNCT
ejpam-4646	297	41	)	)	PUNCT
ejpam-4646	297	42	.	.	PUNCT
ejpam-4646	298	1	then	then	ADV
ejpam-4646	298	2	x	x	X
ejpam-4646	298	3	,	,	PUNCT
ejpam-4646	298	4	y	y	PROPN
ejpam-4646	298	5	∈	∈	PROPN
ejpam-4646	298	6	s	s	X
ejpam-4646	298	7	and	and	CCONJ
ejpam-4646	298	8	v	v	ADP
ejpam-4646	298	9	∈	∈	NOUN
ejpam-4646	298	10	ig(x	ig(x	X
ejpam-4646	298	11	,	,	PUNCT
ejpam-4646	298	12	y	y	PROPN
ejpam-4646	298	13	)	)	PUNCT
ejpam-4646	298	14	.	.	PUNCT
ejpam-4646	299	1	this	this	PRON
ejpam-4646	299	2	shows	show	VERB
ejpam-4646	299	3	that	that	SCONJ
ejpam-4646	299	4	s	s	VERB
ejpam-4646	299	5	is	be	AUX
ejpam-4646	299	6	a	a	DET
ejpam-4646	299	7	geodetic	geodetic	ADJ
ejpam-4646	299	8	set	set	NOUN
ejpam-4646	299	9	of	of	ADP
ejpam-4646	299	10	g	g	NOUN
ejpam-4646	299	11	,	,	PUNCT
ejpam-4646	299	12	showing	show	VERB
ejpam-4646	299	13	that	that	SCONJ
ejpam-4646	299	14	(	(	PUNCT
ejpam-4646	299	15	i	i	NOUN
ejpam-4646	299	16	)	)	PUNCT
ejpam-4646	299	17	holds	hold	VERB
ejpam-4646	299	18	.	.	PUNCT
ejpam-4646	300	1	next	next	ADV
ejpam-4646	300	2	,	,	PUNCT
ejpam-4646	300	3	let	let	VERB
ejpam-4646	300	4	x	x	PUNCT
ejpam-4646	300	5	∈	∈	PROPN
ejpam-4646	300	6	s	s	PART
ejpam-4646	300	7	\	\	NOUN
ejpam-4646	300	8	ig(s	ig(s	NUM
ejpam-4646	300	9	)	)	PUNCT
ejpam-4646	300	10	.	.	PUNCT
ejpam-4646	301	1	if	if	SCONJ
ejpam-4646	301	2	tx	tx	PROPN
ejpam-4646	301	3	=	=	SYM
ejpam-4646	301	4	v	v	PROPN
ejpam-4646	301	5	(	(	PUNCT
ejpam-4646	301	6	h	h	NOUN
ejpam-4646	301	7	)	)	PUNCT
ejpam-4646	301	8	,	,	PUNCT
ejpam-4646	301	9	then	then	ADV
ejpam-4646	301	10	it	it	PRON
ejpam-4646	301	11	is	be	AUX
ejpam-4646	301	12	a	a	DET
ejpam-4646	301	13	2	2	NUM
ejpam-4646	301	14	-	-	PUNCT
ejpam-4646	301	15	path	path	NOUN
ejpam-4646	301	16	closure	closure	NOUN
ejpam-4646	301	17	absorbing	absorb	VERB
ejpam-4646	301	18	set	set	NOUN
ejpam-4646	301	19	of	of	ADP
ejpam-4646	301	20	h.	h.	PROPN
ejpam-4646	301	21	suppose	suppose	VERB
ejpam-4646	301	22	tx	tx	PROPN
ejpam-4646	301	23	̸=	̸=	PROPN
ejpam-4646	301	24	v	v	PROPN
ejpam-4646	301	25	(	(	PUNCT
ejpam-4646	301	26	h	h	NOUN
ejpam-4646	301	27	)	)	PUNCT
ejpam-4646	301	28	and	and	CCONJ
ejpam-4646	301	29	let	let	VERB
ejpam-4646	302	1	b	b	X
ejpam-4646	302	2	∈	∈	PROPN
ejpam-4646	302	3	v	v	X
ejpam-4646	302	4	(	(	PUNCT
ejpam-4646	302	5	h	h	NOUN
ejpam-4646	302	6	)	)	PUNCT
ejpam-4646	302	7	\	\	PROPN
ejpam-4646	302	8	tx	tx	PROPN
ejpam-4646	302	9	.	.	PUNCT
ejpam-4646	303	1	since	since	SCONJ
ejpam-4646	303	2	(	(	PUNCT
ejpam-4646	303	3	x	x	X
ejpam-4646	303	4	,	,	PUNCT
ejpam-4646	303	5	b	b	NOUN
ejpam-4646	303	6	)	)	PUNCT
ejpam-4646	303	7	/∈	/∈	PUNCT
ejpam-4646	304	1	c	c	NOUN
ejpam-4646	305	1	and	and	CCONJ
ejpam-4646	305	2	c	c	PROPN
ejpam-4646	305	3	is	be	AUX
ejpam-4646	305	4	a	a	DET
ejpam-4646	305	5	geodetic	geodetic	ADJ
ejpam-4646	305	6	set	set	NOUN
ejpam-4646	305	7	,	,	PUNCT
ejpam-4646	305	8	there	there	PRON
ejpam-4646	305	9	exist	exist	VERB
ejpam-4646	305	10	(	(	PUNCT
ejpam-4646	305	11	u	u	NOUN
ejpam-4646	305	12	,	,	PUNCT
ejpam-4646	305	13	k	k	NOUN
ejpam-4646	305	14	)	)	PUNCT
ejpam-4646	305	15	,	,	PUNCT
ejpam-4646	305	16	(	(	PUNCT
ejpam-4646	305	17	w	w	PROPN
ejpam-4646	305	18	,	,	PUNCT
ejpam-4646	305	19	t	t	PROPN
ejpam-4646	305	20	)	)	PUNCT
ejpam-4646	305	21	∈	∈	PROPN
ejpam-4646	305	22	c	c	NOUN
ejpam-4646	305	23	such	such	ADJ
ejpam-4646	305	24	that	that	PRON
ejpam-4646	305	25	(	(	PUNCT
ejpam-4646	305	26	x	x	NOUN
ejpam-4646	305	27	,	,	PUNCT
ejpam-4646	305	28	b	b	X
ejpam-4646	305	29	)	)	PUNCT
ejpam-4646	305	30	∈	∈	PROPN
ejpam-4646	305	31	ig[h]((u	ig[h]((u	NOUN
ejpam-4646	305	32	,	,	PUNCT
ejpam-4646	305	33	k	k	NOUN
ejpam-4646	305	34	)	)	PUNCT
ejpam-4646	305	35	,	,	PUNCT
ejpam-4646	305	36	(	(	PUNCT
ejpam-4646	305	37	w	w	PROPN
ejpam-4646	305	38	,	,	PUNCT
ejpam-4646	305	39	t	t	PROPN
ejpam-4646	305	40	)	)	PUNCT
ejpam-4646	305	41	)	)	PUNCT
ejpam-4646	305	42	.	.	PUNCT
ejpam-4646	306	1	since	since	SCONJ
ejpam-4646	306	2	x	x	PROPN
ejpam-4646	306	3	∈	∈	PROPN
ejpam-4646	306	4	s	s	PART
ejpam-4646	306	5	\	\	NOUN
ejpam-4646	306	6	ig(s	ig(s	X
ejpam-4646	306	7	)	)	PUNCT
ejpam-4646	306	8	,	,	PUNCT
ejpam-4646	306	9	u	u	NOUN
ejpam-4646	306	10	=	=	PROPN
ejpam-4646	306	11	w	w	PROPN
ejpam-4646	306	12	=	=	PUNCT
ejpam-4646	306	13	x	x	X
ejpam-4646	306	14	and	and	CCONJ
ejpam-4646	306	15	dg[h]((u	dg[h]((u	NOUN
ejpam-4646	306	16	,	,	PUNCT
ejpam-4646	306	17	k)(w	k)(w	PROPN
ejpam-4646	306	18	,	,	PUNCT
ejpam-4646	306	19	t	t	PROPN
ejpam-4646	306	20	)	)	PUNCT
ejpam-4646	306	21	)	)	PUNCT
ejpam-4646	307	1	=	=	PUNCT
ejpam-4646	307	2	2	2	X
ejpam-4646	307	3	.	.	PUNCT
ejpam-4646	307	4	because	because	SCONJ
ejpam-4646	307	5	(	(	PUNCT
ejpam-4646	307	6	x	x	X
ejpam-4646	307	7	,	,	PUNCT
ejpam-4646	307	8	b	b	X
ejpam-4646	307	9	)	)	PUNCT
ejpam-4646	307	10	∈	∈	PROPN
ejpam-4646	307	11	ig[h]((u	ig[h]((u	NOUN
ejpam-4646	307	12	,	,	PUNCT
ejpam-4646	307	13	k	k	NOUN
ejpam-4646	307	14	)	)	PUNCT
ejpam-4646	307	15	,	,	PUNCT
ejpam-4646	307	16	(	(	PUNCT
ejpam-4646	307	17	w	w	PROPN
ejpam-4646	307	18	,	,	PUNCT
ejpam-4646	307	19	t	t	PROPN
ejpam-4646	307	20	)	)	PUNCT
ejpam-4646	307	21	)	)	PUNCT
ejpam-4646	307	22	,	,	PUNCT
ejpam-4646	307	23	this	this	PRON
ejpam-4646	307	24	would	would	AUX
ejpam-4646	307	25	imply	imply	VERB
ejpam-4646	307	26	that	that	SCONJ
ejpam-4646	307	27	dh(k	dh(k	PROPN
ejpam-4646	307	28	,	,	PUNCT
ejpam-4646	307	29	t	t	PROPN
ejpam-4646	307	30	)	)	PUNCT
ejpam-4646	307	31	=	=	SYM
ejpam-4646	307	32	2	2	NUM
ejpam-4646	307	33	and	and	CCONJ
ejpam-4646	307	34	x	x	PROPN
ejpam-4646	307	35	∈	∈	PROPN
ejpam-4646	307	36	ih(k	ih(k	PROPN
ejpam-4646	307	37	,	,	PUNCT
ejpam-4646	307	38	t	t	PROPN
ejpam-4646	307	39	)	)	PUNCT
ejpam-4646	307	40	.	.	PUNCT
ejpam-4646	308	1	this	this	PRON
ejpam-4646	308	2	shows	show	VERB
ejpam-4646	308	3	that	that	SCONJ
ejpam-4646	308	4	tx	tx	PROPN
ejpam-4646	308	5	is	be	AUX
ejpam-4646	308	6	a	a	DET
ejpam-4646	308	7	2	2	NUM
ejpam-4646	308	8	-	-	PUNCT
ejpam-4646	308	9	path	path	NOUN
ejpam-4646	308	10	closure	closure	NOUN
ejpam-4646	308	11	absorbing	absorb	VERB
ejpam-4646	308	12	set	set	NOUN
ejpam-4646	308	13	of	of	ADP
ejpam-4646	308	14	h	h	NOUN
ejpam-4646	308	15	,	,	PUNCT
ejpam-4646	308	16	that	that	ADV
ejpam-4646	308	17	is	is	ADV
ejpam-4646	308	18	,	,	PUNCT
ejpam-4646	308	19	(	(	PUNCT
ejpam-4646	308	20	iii	iii	NOUN
ejpam-4646	308	21	)	)	PUNCT
ejpam-4646	308	22	holds	hold	VERB
ejpam-4646	308	23	.	.	PUNCT
ejpam-4646	309	1	conversely	conversely	ADV
ejpam-4646	309	2	,	,	PUNCT
ejpam-4646	309	3	suppose	suppose	VERB
ejpam-4646	309	4	c	c	NOUN
ejpam-4646	309	5	satisfies	satisfie	NOUN
ejpam-4646	309	6	(	(	PUNCT
ejpam-4646	309	7	i	i	NOUN
ejpam-4646	309	8	)	)	PUNCT
ejpam-4646	309	9	,	,	PUNCT
ejpam-4646	309	10	(	(	PUNCT
ejpam-4646	309	11	ii	ii	NOUN
ejpam-4646	309	12	)	)	PUNCT
ejpam-4646	309	13	and	and	CCONJ
ejpam-4646	309	14	(	(	PUNCT
ejpam-4646	309	15	iii	iii	NOUN
ejpam-4646	309	16	)	)	PUNCT
ejpam-4646	309	17	.	.	PUNCT
ejpam-4646	310	1	by	by	ADP
ejpam-4646	310	2	theorem	theorem	NOUN
ejpam-4646	310	3	5	5	NUM
ejpam-4646	310	4	,	,	PUNCT
ejpam-4646	310	5	s	s	VERB
ejpam-4646	310	6	is	be	AUX
ejpam-4646	310	7	a	a	DET
ejpam-4646	310	8	hop	hop	NOUN
ejpam-4646	310	9	dominating	dominating	NOUN
ejpam-4646	310	10	set	set	NOUN
ejpam-4646	310	11	of	of	ADP
ejpam-4646	310	12	g.	g.	PROPN
ejpam-4646	310	13	let	let	VERB
ejpam-4646	310	14	(	(	PUNCT
ejpam-4646	310	15	v	v	NOUN
ejpam-4646	310	16	,	,	PUNCT
ejpam-4646	310	17	p	p	NOUN
ejpam-4646	310	18	)	)	PUNCT
ejpam-4646	310	19	∈	∈	PROPN
ejpam-4646	310	20	v	v	NOUN
ejpam-4646	310	21	(	(	PUNCT
ejpam-4646	310	22	g[h	g[h	PROPN
ejpam-4646	310	23	]	]	PUNCT
ejpam-4646	310	24	)	)	PUNCT
ejpam-4646	310	25	\	\	PROPN
ejpam-4646	311	1	c.	c.	NOUN
ejpam-4646	311	2	consider	consider	VERB
ejpam-4646	311	3	the	the	DET
ejpam-4646	311	4	following	follow	VERB
ejpam-4646	311	5	cases	case	NOUN
ejpam-4646	311	6	:	:	PUNCT
ejpam-4646	311	7	case	case	NOUN
ejpam-4646	311	8	1	1	NUM
ejpam-4646	311	9	.	.	X
ejpam-4646	312	1	v	v	NOUN
ejpam-4646	312	2	/∈	/∈	PUNCT
ejpam-4646	312	3	s.	s.	PROPN
ejpam-4646	312	4	since	since	SCONJ
ejpam-4646	312	5	s	s	PROPN
ejpam-4646	312	6	is	be	AUX
ejpam-4646	312	7	a	a	DET
ejpam-4646	312	8	geodetic	geodetic	ADJ
ejpam-4646	312	9	set	set	NOUN
ejpam-4646	312	10	of	of	ADP
ejpam-4646	312	11	g	g	NOUN
ejpam-4646	312	12	,	,	PUNCT
ejpam-4646	312	13	there	there	PRON
ejpam-4646	312	14	exist	exist	VERB
ejpam-4646	312	15	u	u	NOUN
ejpam-4646	312	16	,	,	PUNCT
ejpam-4646	312	17	w	w	PROPN
ejpam-4646	312	18	∈	∈	PROPN
ejpam-4646	312	19	s	s	VERB
ejpam-4646	312	20	such	such	ADJ
ejpam-4646	312	21	that	that	PRON
ejpam-4646	312	22	v	v	NUM
ejpam-4646	312	23	∈	∈	PROPN
ejpam-4646	312	24	ig(u	ig(u	NOUN
ejpam-4646	312	25	,	,	PUNCT
ejpam-4646	312	26	w	w	NOUN
ejpam-4646	312	27	)	)	PUNCT
ejpam-4646	312	28	.	.	PUNCT
ejpam-4646	313	1	let	let	VERB
ejpam-4646	313	2	[	[	X
ejpam-4646	313	3	v1	v1	VERB
ejpam-4646	313	4	,	,	PUNCT
ejpam-4646	313	5	v2	v2	PROPN
ejpam-4646	313	6	,	,	PUNCT
ejpam-4646	313	7	...	...	PUNCT
ejpam-4646	313	8	,	,	PUNCT
ejpam-4646	313	9	vk	vk	ADP
ejpam-4646	313	10	]	]	PUNCT
ejpam-4646	313	11	,	,	PUNCT
ejpam-4646	313	12	where	where	SCONJ
ejpam-4646	313	13	v1	v1	NOUN
ejpam-4646	313	14	=	=	SYM
ejpam-4646	313	15	u	u	NOUN
ejpam-4646	313	16	and	and	CCONJ
ejpam-4646	313	17	vk	vk	PROPN
ejpam-4646	313	18	=	=	SYM
ejpam-4646	313	19	w	w	PROPN
ejpam-4646	313	20	,	,	PUNCT
ejpam-4646	313	21	a	a	DET
ejpam-4646	313	22	u	u	NOUN
ejpam-4646	313	23	-	-	NOUN
ejpam-4646	313	24	w	w	NOUN
ejpam-4646	313	25	geodesic	geodesic	NOUN
ejpam-4646	313	26	in	in	ADP
ejpam-4646	313	27	g.	g.	PROPN
ejpam-4646	313	28	let	let	VERB
ejpam-4646	313	29	v	v	VERB
ejpam-4646	313	30	=	=	PUNCT
ejpam-4646	313	31	vj	vj	INTJ
ejpam-4646	313	32	where	where	SCONJ
ejpam-4646	313	33	1	1	NUM
ejpam-4646	313	34	<	<	X
ejpam-4646	313	35	j	j	X
ejpam-4646	313	36	<	<	X
ejpam-4646	313	37	k.	k.	PROPN
ejpam-4646	313	38	let	let	VERB
ejpam-4646	313	39	s	s	PRON
ejpam-4646	313	40	∈	∈	PROPN
ejpam-4646	313	41	tu	tu	X
ejpam-4646	313	42	and	and	CCONJ
ejpam-4646	313	43	t	t	PROPN
ejpam-4646	313	44	∈	∈	PROPN
ejpam-4646	313	45	tw	tw	PROPN
ejpam-4646	313	46	.	.	PUNCT
ejpam-4646	314	1	then	then	ADV
ejpam-4646	314	2	[	[	X
ejpam-4646	314	3	(	(	PUNCT
ejpam-4646	314	4	v1	v1	NOUN
ejpam-4646	314	5	,	,	PUNCT
ejpam-4646	314	6	s	s	PART
ejpam-4646	314	7	)	)	PUNCT
ejpam-4646	314	8	,	,	PUNCT
ejpam-4646	314	9	(	(	PUNCT
ejpam-4646	314	10	v2	v2	NOUN
ejpam-4646	314	11	,	,	PUNCT
ejpam-4646	314	12	p	p	NOUN
ejpam-4646	314	13	)	)	PUNCT
ejpam-4646	314	14	,	,	PUNCT
ejpam-4646	314	15	...	...	PUNCT
ejpam-4646	314	16	,	,	PUNCT
ejpam-4646	314	17	(	(	PUNCT
ejpam-4646	314	18	vj	vj	INTJ
ejpam-4646	314	19	,	,	PUNCT
ejpam-4646	314	20	p	p	NOUN
ejpam-4646	314	21	)	)	PUNCT
ejpam-4646	314	22	,	,	PUNCT
ejpam-4646	314	23	...	...	PUNCT
ejpam-4646	314	24	,	,	PUNCT
ejpam-4646	314	25	(	(	PUNCT
ejpam-4646	314	26	vk−1	vk−1	NOUN
ejpam-4646	314	27	,	,	PUNCT
ejpam-4646	314	28	p	p	NOUN
ejpam-4646	314	29	)	)	PUNCT
ejpam-4646	314	30	,	,	PUNCT
ejpam-4646	314	31	(	(	PUNCT
ejpam-4646	314	32	vk	vk	X
ejpam-4646	314	33	,	,	PUNCT
ejpam-4646	314	34	t	t	PROPN
ejpam-4646	314	35	)	)	PUNCT
ejpam-4646	314	36	]	]	PUNCT
ejpam-4646	314	37	is	be	AUX
ejpam-4646	314	38	(	(	PUNCT
ejpam-4646	314	39	u	u	NOUN
ejpam-4646	314	40	,	,	PUNCT
ejpam-4646	314	41	s)-(w	s)-(w	PROPN
ejpam-4646	314	42	,	,	PUNCT
ejpam-4646	314	43	t	t	PROPN
ejpam-4646	314	44	)	)	PUNCT
ejpam-4646	314	45	geodesic	geodesic	NOUN
ejpam-4646	314	46	in	in	ADP
ejpam-4646	314	47	g[h	g[h	PROPN
ejpam-4646	314	48	]	]	PUNCT
ejpam-4646	314	49	containing	contain	VERB
ejpam-4646	314	50	(	(	PUNCT
ejpam-4646	314	51	v	v	NOUN
ejpam-4646	314	52	,	,	PUNCT
ejpam-4646	314	53	p	p	NOUN
ejpam-4646	314	54	)	)	PUNCT
ejpam-4646	314	55	.	.	PUNCT
ejpam-4646	315	1	case	case	NOUN
ejpam-4646	315	2	2	2	NUM
ejpam-4646	315	3	.	.	NOUN
ejpam-4646	315	4	v	v	NOUN
ejpam-4646	315	5	∈	∈	NOUN
ejpam-4646	315	6	s.	s.	PROPN
ejpam-4646	316	1	then	then	ADV
ejpam-4646	316	2	p	p	PROPN
ejpam-4646	316	3	/∈	/∈	PROPN
ejpam-4646	316	4	tv	tv	NOUN
ejpam-4646	316	5	.	.	PUNCT
ejpam-4646	317	1	if	if	SCONJ
ejpam-4646	317	2	v	v	NUM
ejpam-4646	317	3	∈	∈	PROPN
ejpam-4646	317	4	ig(s	ig(s	NUM
ejpam-4646	317	5	)	)	PUNCT
ejpam-4646	317	6	,	,	PUNCT
ejpam-4646	317	7	then	then	ADV
ejpam-4646	317	8	following	follow	VERB
ejpam-4646	317	9	the	the	DET
ejpam-4646	317	10	arguments	argument	NOUN
ejpam-4646	317	11	of	of	ADP
ejpam-4646	317	12	case	case	NOUN
ejpam-4646	317	13	1	1	NUM
ejpam-4646	317	14	,	,	PUNCT
ejpam-4646	317	15	there	there	PRON
ejpam-4646	317	16	exist	exist	VERB
ejpam-4646	317	17	(	(	PUNCT
ejpam-4646	317	18	x	x	X
ejpam-4646	317	19	,	,	PUNCT
ejpam-4646	317	20	a	a	PRON
ejpam-4646	317	21	)	)	PUNCT
ejpam-4646	317	22	,	,	PUNCT
ejpam-4646	317	23	(	(	PUNCT
ejpam-4646	317	24	y	y	PROPN
ejpam-4646	317	25	,	,	PUNCT
ejpam-4646	317	26	b	b	NOUN
ejpam-4646	317	27	)	)	PUNCT
ejpam-4646	317	28	∈	∈	PROPN
ejpam-4646	317	29	c	c	NOUN
ejpam-4646	317	30	such	such	ADJ
ejpam-4646	317	31	that	that	PRON
ejpam-4646	317	32	(	(	PUNCT
ejpam-4646	317	33	v	v	NOUN
ejpam-4646	317	34	,	,	PUNCT
ejpam-4646	317	35	p	p	NOUN
ejpam-4646	317	36	)	)	PUNCT
ejpam-4646	317	37	∈	∈	PROPN
ejpam-4646	317	38	ig[h]((x	ig[h]((x	NOUN
ejpam-4646	317	39	,	,	PUNCT
ejpam-4646	317	40	a	a	PRON
ejpam-4646	317	41	)	)	PUNCT
ejpam-4646	317	42	,	,	PUNCT
ejpam-4646	317	43	(	(	PUNCT
ejpam-4646	317	44	y	y	PROPN
ejpam-4646	317	45	,	,	PUNCT
ejpam-4646	317	46	b	b	NOUN
ejpam-4646	317	47	)	)	PUNCT
ejpam-4646	317	48	)	)	PUNCT
ejpam-4646	317	49	.	.	PUNCT
ejpam-4646	318	1	suppose	suppose	VERB
ejpam-4646	318	2	v	v	X
ejpam-4646	318	3	/∈	/∈	PUNCT
ejpam-4646	318	4	ig(s	ig(s	NUM
ejpam-4646	318	5	)	)	PUNCT
ejpam-4646	318	6	.	.	PUNCT
ejpam-4646	319	1	by	by	ADP
ejpam-4646	319	2	(	(	PUNCT
ejpam-4646	319	3	iii	iii	NOUN
ejpam-4646	319	4	)	)	PUNCT
ejpam-4646	319	5	,	,	PUNCT
ejpam-4646	319	6	c.j	c.j	PROPN
ejpam-4646	319	7	.	.	PROPN
ejpam-4646	319	8	saromines	saromines	PROPN
ejpam-4646	319	9	,	,	PUNCT
ejpam-4646	319	10	s.	s.	PROPN
ejpam-4646	319	11	canoy	canoy	PROPN
ejpam-4646	319	12	,	,	PUNCT
ejpam-4646	319	13	jr	jr	PROPN
ejpam-4646	319	14	.	.	PROPN
ejpam-4646	319	15	,	,	PUNCT
ejpam-4646	319	16	/	/	SYM
ejpam-4646	319	17	eur	eur	NOUN
ejpam-4646	319	18	.	.	PUNCT
ejpam-4646	320	1	j.	j.	PROPN
ejpam-4646	320	2	pure	pure	PROPN
ejpam-4646	320	3	appl	appl	PROPN
ejpam-4646	320	4	.	.	PROPN
ejpam-4646	320	5	math	math	PROPN
ejpam-4646	320	6	,	,	PUNCT
ejpam-4646	320	7	16	16	NUM
ejpam-4646	320	8	(	(	PUNCT
ejpam-4646	320	9	1	1	NUM
ejpam-4646	320	10	)	)	PUNCT
ejpam-4646	320	11	(	(	PUNCT
ejpam-4646	320	12	2023	2023	NUM
ejpam-4646	320	13	)	)	PUNCT
ejpam-4646	320	14	,	,	PUNCT
ejpam-4646	320	15	5	5	NUM
ejpam-4646	320	16	-	-	SYM
ejpam-4646	320	17	17	17	NUM
ejpam-4646	320	18	14	14	NUM
ejpam-4646	320	19	tv	tv	NOUN
ejpam-4646	320	20	is	be	AUX
ejpam-4646	320	21	a	a	DET
ejpam-4646	320	22	2	2	NUM
ejpam-4646	320	23	-	-	PUNCT
ejpam-4646	320	24	path	path	NOUN
ejpam-4646	320	25	closure	closure	NOUN
ejpam-4646	320	26	absorbing	absorb	VERB
ejpam-4646	320	27	set	set	NOUN
ejpam-4646	320	28	of	of	ADP
ejpam-4646	320	29	h.	h.	PROPN
ejpam-4646	320	30	this	this	PRON
ejpam-4646	320	31	implies	imply	VERB
ejpam-4646	320	32	that	that	SCONJ
ejpam-4646	320	33	there	there	PRON
ejpam-4646	320	34	exists	exist	VERB
ejpam-4646	320	35	c	c	NOUN
ejpam-4646	320	36	,	,	PUNCT
ejpam-4646	320	37	d	d	PROPN
ejpam-4646	320	38	∈	∈	PROPN
ejpam-4646	320	39	tv	tv	NOUN
ejpam-4646	320	40	such	such	ADJ
ejpam-4646	320	41	that	that	SCONJ
ejpam-4646	320	42	dh(c	dh(c	PROPN
ejpam-4646	320	43	,	,	PUNCT
ejpam-4646	320	44	d	d	NOUN
ejpam-4646	320	45	)	)	PUNCT
ejpam-4646	320	46	=	=	SYM
ejpam-4646	320	47	2	2	NUM
ejpam-4646	320	48	and	and	CCONJ
ejpam-4646	320	49	p	p	NOUN
ejpam-4646	320	50	∈	∈	PROPN
ejpam-4646	320	51	ih(c	ih(c	NOUN
ejpam-4646	320	52	,	,	PUNCT
ejpam-4646	320	53	d	d	NOUN
ejpam-4646	320	54	)	)	PUNCT
ejpam-4646	320	55	.	.	PUNCT
ejpam-4646	321	1	hence	hence	ADV
ejpam-4646	321	2	,	,	PUNCT
ejpam-4646	321	3	(	(	PUNCT
ejpam-4646	321	4	v	v	NOUN
ejpam-4646	321	5	,	,	PUNCT
ejpam-4646	321	6	c	c	NOUN
ejpam-4646	321	7	)	)	PUNCT
ejpam-4646	321	8	,	,	PUNCT
ejpam-4646	321	9	(	(	PUNCT
ejpam-4646	321	10	v	v	NOUN
ejpam-4646	321	11	,	,	PUNCT
ejpam-4646	321	12	d	d	NOUN
ejpam-4646	321	13	)	)	PUNCT
ejpam-4646	321	14	∈	∈	PROPN
ejpam-4646	321	15	c	c	NOUN
ejpam-4646	321	16	and	and	CCONJ
ejpam-4646	321	17	[	[	X
ejpam-4646	321	18	(	(	PUNCT
ejpam-4646	321	19	v	v	NOUN
ejpam-4646	321	20	,	,	PUNCT
ejpam-4646	321	21	c	c	NOUN
ejpam-4646	321	22	)	)	PUNCT
ejpam-4646	321	23	,	,	PUNCT
ejpam-4646	321	24	(	(	PUNCT
ejpam-4646	321	25	v	v	NOUN
ejpam-4646	321	26	,	,	PUNCT
ejpam-4646	321	27	p	p	NOUN
ejpam-4646	321	28	)	)	PUNCT
ejpam-4646	321	29	,	,	PUNCT
ejpam-4646	321	30	(	(	PUNCT
ejpam-4646	321	31	v	v	NOUN
ejpam-4646	321	32	,	,	PUNCT
ejpam-4646	321	33	d	d	NOUN
ejpam-4646	321	34	)	)	PUNCT
ejpam-4646	321	35	]	]	PUNCT
ejpam-4646	321	36	is	be	AUX
ejpam-4646	321	37	a	a	DET
ejpam-4646	321	38	(	(	PUNCT
ejpam-4646	321	39	v	v	NOUN
ejpam-4646	321	40	,	,	PUNCT
ejpam-4646	321	41	c)-(v	c)-(v	PROPN
ejpam-4646	321	42	,	,	PUNCT
ejpam-4646	321	43	d	d	NOUN
ejpam-4646	321	44	)	)	PUNCT
ejpam-4646	321	45	geodesic	geodesic	NOUN
ejpam-4646	321	46	in	in	ADP
ejpam-4646	321	47	g[h	g[h	PROPN
ejpam-4646	321	48	]	]	PUNCT
ejpam-4646	321	49	.	.	PUNCT
ejpam-4646	322	1	therefore	therefore	ADV
ejpam-4646	322	2	,	,	PUNCT
ejpam-4646	322	3	c	c	PROPN
ejpam-4646	322	4	is	be	AUX
ejpam-4646	322	5	a	a	DET
ejpam-4646	322	6	geodetic	geodetic	ADJ
ejpam-4646	322	7	hop	hop	NOUN
ejpam-4646	322	8	dominating	dominating	NOUN
ejpam-4646	322	9	set	set	NOUN
ejpam-4646	322	10	of	of	ADP
ejpam-4646	322	11	g[h	g[h	PROPN
ejpam-4646	322	12	]	]	PUNCT
ejpam-4646	322	13	.	.	PUNCT
ejpam-4646	323	1	corollary	corollary	ADJ
ejpam-4646	323	2	4	4	NUM
ejpam-4646	323	3	.	.	PUNCT
ejpam-4646	324	1	let	let	VERB
ejpam-4646	324	2	g	g	NOUN
ejpam-4646	324	3	and	and	CCONJ
ejpam-4646	324	4	h	h	NOUN
ejpam-4646	324	5	be	be	AUX
ejpam-4646	324	6	connected	connect	VERB
ejpam-4646	324	7	non	non	ADJ
ejpam-4646	324	8	-	-	ADJ
ejpam-4646	324	9	trivial	trivial	ADJ
ejpam-4646	324	10	graphs	graph	NOUN
ejpam-4646	324	11	.	.	PUNCT
ejpam-4646	325	1	then	then	ADV
ejpam-4646	325	2	γhg(g[h	γhg(g[h	NUM
ejpam-4646	325	3	]	]	PUNCT
ejpam-4646	325	4	)	)	PUNCT
ejpam-4646	325	5	≤	≤	NUM
ejpam-4646	325	6	γhg(g	γhg(g	PROPN
ejpam-4646	325	7	)	)	PUNCT
ejpam-4646	325	8	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4646	325	9	)	)	PUNCT
ejpam-4646	325	10	proof	proof	NOUN
ejpam-4646	325	11	.	.	PUNCT
ejpam-4646	326	1	let	let	VERB
ejpam-4646	326	2	s	s	PRON
ejpam-4646	326	3	be	be	AUX
ejpam-4646	326	4	a	a	DET
ejpam-4646	326	5	γhg	γhg	NOUN
ejpam-4646	326	6	-	-	PUNCT
ejpam-4646	326	7	set	set	NOUN
ejpam-4646	326	8	of	of	ADP
ejpam-4646	326	9	g	g	NOUN
ejpam-4646	326	10	and	and	CCONJ
ejpam-4646	326	11	let	let	VERB
ejpam-4646	326	12	d	d	PRON
ejpam-4646	326	13	be	be	AUX
ejpam-4646	326	14	a	a	DET
ejpam-4646	326	15	ρ2pnd	ρ2pnd	ADV
ejpam-4646	326	16	-	-	PUNCT
ejpam-4646	326	17	set	set	NOUN
ejpam-4646	326	18	of	of	ADP
ejpam-4646	326	19	h.	h.	NOUN
ejpam-4646	326	20	for	for	ADP
ejpam-4646	326	21	each	each	DET
ejpam-4646	326	22	x	x	SYM
ejpam-4646	326	23	∈	∈	PROPN
ejpam-4646	326	24	s	s	NOUN
ejpam-4646	326	25	,	,	PUNCT
ejpam-4646	326	26	let	let	VERB
ejpam-4646	326	27	tx	tx	VERB
ejpam-4646	326	28	=	=	PUNCT
ejpam-4646	326	29	d.	d.	PROPN
ejpam-4646	326	30	then	then	ADV
ejpam-4646	326	31	c	c	PROPN
ejpam-4646	327	1	=	=	PUNCT
ejpam-4646	327	2	⋃	⋃	PROPN
ejpam-4646	327	3	x∈s	x∈s	NOUN
ejpam-4646	327	4	(	(	PUNCT
ejpam-4646	327	5	{	{	PUNCT
ejpam-4646	327	6	x	x	NOUN
ejpam-4646	327	7	}	}	PUNCT
ejpam-4646	327	8	×	×	PROPN
ejpam-4646	327	9	tx	tx	PROPN
ejpam-4646	327	10	)	)	PUNCT
ejpam-4646	328	1	=	=	SYM
ejpam-4646	328	2	s	s	PART
ejpam-4646	328	3	×d	×d	NOUN
ejpam-4646	328	4	is	be	AUX
ejpam-4646	328	5	a	a	DET
ejpam-4646	328	6	geodetic	geodetic	ADJ
ejpam-4646	328	7	hop	hop	NOUN
ejpam-4646	328	8	dominating	dominating	NOUN
ejpam-4646	328	9	set	set	VERB
ejpam-4646	328	10	by	by	ADP
ejpam-4646	328	11	theorem	theorem	NOUN
ejpam-4646	328	12	6	6	NUM
ejpam-4646	328	13	.	.	PUNCT
ejpam-4646	329	1	therefore	therefore	ADV
ejpam-4646	329	2	,	,	PUNCT
ejpam-4646	329	3	γhg(g	γhg(g	PROPN
ejpam-4646	330	1	[	[	X
ejpam-4646	330	2	h	h	X
ejpam-4646	330	3	]	]	X
ejpam-4646	330	4	)	)	PUNCT
ejpam-4646	330	5	≤	≤	PROPN
ejpam-4646	330	6	|c|	|c|	PROPN
ejpam-4646	330	7	=	=	SYM
ejpam-4646	330	8	|s|	|s|	PROPN
ejpam-4646	330	9	|d|	|d|	PROPN
ejpam-4646	330	10	=	=	PUNCT
ejpam-4646	330	11	γhg(g)ρ2pnd(h	γhg(g)ρ2pnd(h	NUM
ejpam-4646	330	12	)	)	PUNCT
ejpam-4646	330	13	.	.	PUNCT
ejpam-4646	331	1	remark	remark	NOUN
ejpam-4646	331	2	3	3	NUM
ejpam-4646	331	3	.	.	PUNCT
ejpam-4646	331	4	strict	strict	ADJ
ejpam-4646	331	5	inequality	inequality	NOUN
ejpam-4646	331	6	in	in	ADP
ejpam-4646	331	7	corollary	corollary	ADJ
ejpam-4646	331	8	4	4	NUM
ejpam-4646	331	9	can	can	AUX
ejpam-4646	331	10	be	be	AUX
ejpam-4646	331	11	attained	attain	VERB
ejpam-4646	331	12	.	.	PUNCT
ejpam-4646	332	1	example	example	NOUN
ejpam-4646	332	2	1	1	X
ejpam-4646	332	3	.	.	X
ejpam-4646	333	1	consider	consider	VERB
ejpam-4646	333	2	the	the	DET
ejpam-4646	333	3	graph	graph	NOUN
ejpam-4646	333	4	p3	p3	PROPN
ejpam-4646	333	5	[	[	X
ejpam-4646	333	6	p3	p3	X
ejpam-4646	333	7	]	]	PUNCT
ejpam-4646	333	8	.	.	PUNCT
ejpam-4646	334	1	it	it	PRON
ejpam-4646	334	2	can	can	AUX
ejpam-4646	334	3	be	be	AUX
ejpam-4646	334	4	verified	verify	VERB
ejpam-4646	334	5	that	that	SCONJ
ejpam-4646	334	6	γhg(p3	γhg(p3	PROPN
ejpam-4646	334	7	[	[	X
ejpam-4646	334	8	p3	p3	PROPN
ejpam-4646	334	9	]	]	PUNCT
ejpam-4646	334	10	)	)	PUNCT
ejpam-4646	334	11	=	=	PUNCT
ejpam-4646	334	12	7	7	NUM
ejpam-4646	334	13	<	<	SYM
ejpam-4646	334	14	9	9	NUM
ejpam-4646	334	15	=	=	SYM
ejpam-4646	334	16	γhg(p3)ρ2pnd(p3	γhg(p3)ρ2pnd(p3	NOUN
ejpam-4646	334	17	)	)	PUNCT
ejpam-4646	334	18	.	.	PUNCT
ejpam-4646	335	1	....................................	....................................	PUNCT
ejpam-4646	335	2	....................................	....................................	PUNCT
ejpam-4646	336	1	....................................	....................................	PUNCT
ejpam-4646	336	2	....................................	....................................	PUNCT
ejpam-4646	337	1	....................................	....................................	PUNCT
ejpam-4646	337	2	....................................	....................................	PUNCT
ejpam-4646	338	1	....................................	....................................	PUNCT
ejpam-4646	338	2	....................................	....................................	PUNCT
ejpam-4646	339	1	....................................	....................................	PUNCT
ejpam-4646	339	2	.........	.........	PUNCT
ejpam-4646	339	3	........	........	PUNCT
ejpam-4646	339	4	........	........	PUNCT
ejpam-4646	339	5	........	........	PUNCT
ejpam-4646	339	6	........	........	PUNCT
ejpam-4646	339	7	........	........	PUNCT
ejpam-4646	339	8	........	........	PUNCT
ejpam-4646	339	9	........	........	PUNCT
ejpam-4646	339	10	........	........	PUNCT
ejpam-4646	339	11	........	........	PUNCT
ejpam-4646	339	12	........	........	PUNCT
ejpam-4646	339	13	........	........	PUNCT
ejpam-4646	339	14	.......	.......	PUNCT
ejpam-4646	339	15	.........	.........	PUNCT
ejpam-4646	339	16	........	........	PUNCT
ejpam-4646	339	17	........	........	PUNCT
ejpam-4646	339	18	........	........	PUNCT
ejpam-4646	339	19	........	........	PUNCT
ejpam-4646	339	20	........	........	PUNCT
ejpam-4646	339	21	........	........	PUNCT
ejpam-4646	339	22	........	........	PUNCT
ejpam-4646	339	23	........	........	PUNCT
ejpam-4646	339	24	........	........	PUNCT
ejpam-4646	339	25	........	........	PUNCT
ejpam-4646	339	26	........	........	PUNCT
ejpam-4646	339	27	.......	.......	PUNCT
ejpam-4646	339	28	.........	.........	PUNCT
ejpam-4646	339	29	........	........	PUNCT
ejpam-4646	339	30	........	........	PUNCT
ejpam-4646	339	31	........	........	PUNCT
ejpam-4646	339	32	........	........	PUNCT
ejpam-4646	339	33	........	........	PUNCT
ejpam-4646	339	34	........	........	PUNCT
ejpam-4646	339	35	........	........	PUNCT
ejpam-4646	339	36	........	........	PUNCT
ejpam-4646	339	37	........	........	PUNCT
ejpam-4646	339	38	........	........	PUNCT
ejpam-4646	339	39	........	........	PUNCT
ejpam-4646	339	40	.......	.......	PUNCT
ejpam-4646	339	41	............	............	PUNCT
ejpam-4646	339	42	...........	...........	PUNCT
ejpam-4646	339	43	...........	...........	PUNCT
ejpam-4646	339	44	...........	...........	PUNCT
ejpam-4646	339	45	...........	...........	PUNCT
ejpam-4646	339	46	...........	...........	PUNCT
ejpam-4646	339	47	...........	...........	PUNCT
ejpam-4646	339	48	...........	...........	PUNCT
ejpam-4646	339	49	...........	...........	PUNCT
ejpam-4646	339	50	...........	...........	PUNCT
ejpam-4646	339	51	...........	...........	PUNCT
ejpam-4646	339	52	...........	...........	PUNCT
ejpam-4646	339	53	...........	...........	PUNCT
ejpam-4646	339	54	........	........	PUNCT
ejpam-4646	339	55	...................	...................	PUNCT
ejpam-4646	340	1	..................	..................	PUNCT
ejpam-4646	340	2	..................	..................	PUNCT
ejpam-4646	341	1	..................	..................	PUNCT
ejpam-4646	341	2	..................	..................	PUNCT
ejpam-4646	342	1	..................	..................	PUNCT
ejpam-4646	342	2	..................	..................	PUNCT
ejpam-4646	343	1	..................	..................	PUNCT
ejpam-4646	343	2	..................	..................	PUNCT
ejpam-4646	344	1	..................	..................	PUNCT
ejpam-4646	344	2	..................	..................	PUNCT
ejpam-4646	345	1	..................	..................	PUNCT
ejpam-4646	345	2	..................	..................	PUNCT
ejpam-4646	346	1	...........	...........	PUNCT
ejpam-4646	346	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	347	1	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	347	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	348	1	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	348	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	349	1	................................................................................................................................................................................................................................................................	................................................................................................................................................................................................................................................................	PUNCT
ejpam-4646	349	2	............	............	PUNCT
ejpam-4646	349	3	...........	...........	PUNCT
ejpam-4646	349	4	...........	...........	PUNCT
ejpam-4646	349	5	...........	...........	PUNCT
ejpam-4646	349	6	...........	...........	PUNCT
ejpam-4646	349	7	...........	...........	PUNCT
ejpam-4646	349	8	...........	...........	PUNCT
ejpam-4646	349	9	...........	...........	PUNCT
ejpam-4646	349	10	...........	...........	PUNCT
ejpam-4646	349	11	...........	...........	PUNCT
ejpam-4646	349	12	...........	...........	PUNCT
ejpam-4646	349	13	...........	...........	PUNCT
ejpam-4646	349	14	...........	...........	PUNCT
ejpam-4646	349	15	..............................................................................................................................................................................................................................................................	..............................................................................................................................................................................................................................................................	PUNCT
ejpam-4646	349	16	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-4646	350	1	.........	.........	PUNCT
ejpam-4646	350	2	........	........	PUNCT
ejpam-4646	350	3	........	........	PUNCT
ejpam-4646	350	4	........	........	PUNCT
ejpam-4646	350	5	........	........	PUNCT
ejpam-4646	350	6	........	........	PUNCT
ejpam-4646	350	7	........	........	PUNCT
ejpam-4646	350	8	........	........	PUNCT
ejpam-4646	350	9	........	........	PUNCT
ejpam-4646	350	10	........	........	PUNCT
ejpam-4646	350	11	........	........	PUNCT
ejpam-4646	350	12	........	........	PUNCT
ejpam-4646	350	13	.......	.......	PUNCT
ejpam-4646	350	14	.........	.........	PUNCT
ejpam-4646	351	1	........	........	PUNCT
ejpam-4646	351	2	........	........	PUNCT
ejpam-4646	351	3	........	........	PUNCT
ejpam-4646	351	4	........	........	PUNCT
ejpam-4646	351	5	........	........	PUNCT
ejpam-4646	351	6	........	........	PUNCT
ejpam-4646	351	7	........	........	PUNCT
ejpam-4646	351	8	........	........	PUNCT
ejpam-4646	351	9	........	........	PUNCT
ejpam-4646	351	10	........	........	PUNCT
ejpam-4646	351	11	........	........	PUNCT
ejpam-4646	351	12	.......	.......	PUNCT
ejpam-4646	351	13	.........	.........	PUNCT
ejpam-4646	351	14	........	........	PUNCT
ejpam-4646	351	15	........	........	PUNCT
ejpam-4646	351	16	........	........	PUNCT
ejpam-4646	351	17	........	........	PUNCT
ejpam-4646	351	18	........	........	PUNCT
ejpam-4646	351	19	........	........	PUNCT
ejpam-4646	351	20	........	........	PUNCT
ejpam-4646	351	21	........	........	PUNCT
ejpam-4646	351	22	........	........	PUNCT
ejpam-4646	351	23	........	........	PUNCT
ejpam-4646	351	24	........	........	PUNCT
ejpam-4646	351	25	.......	.......	PUNCT
ejpam-4646	352	1	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-4646	352	2	......................................................................................................................................................................................................................................................	......................................................................................................................................................................................................................................................	PUNCT
ejpam-4646	353	1	........................................................................................................	........................................................................................................	PROPN
ejpam-4646	353	2	................................................................................................................................................................................................................	................................................................................................................................................................................................................	PUNCT
ejpam-4646	354	1	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	354	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	355	1	....................................................................................................................	....................................................................................................................	PUNCT
ejpam-4646	355	2	...........	...........	PUNCT
ejpam-4646	356	1	...........	...........	PUNCT
ejpam-4646	356	2	...........	...........	PUNCT
ejpam-4646	356	3	...........	...........	PUNCT
ejpam-4646	356	4	...........	...........	PUNCT
ejpam-4646	356	5	...........	...........	PUNCT
ejpam-4646	356	6	...........	...........	PUNCT
ejpam-4646	356	7	...........	...........	PUNCT
ejpam-4646	356	8	...........	...........	PUNCT
ejpam-4646	356	9	...........	...........	PUNCT
ejpam-4646	356	10	...........	...........	PUNCT
ejpam-4646	356	11	...........	...........	PUNCT
ejpam-4646	356	12	........	........	PUNCT
ejpam-4646	356	13	...........................................................................................................................................................................	...........................................................................................................................................................................	PUNCT
ejpam-4646	356	14	..................	..................	PUNCT
ejpam-4646	356	15	..................	..................	PUNCT
ejpam-4646	357	1	..................	..................	PUNCT
ejpam-4646	357	2	..................	..................	PUNCT
ejpam-4646	358	1	..................	..................	PUNCT
ejpam-4646	358	2	..................	..................	PUNCT
ejpam-4646	359	1	..................	..................	PUNCT
ejpam-4646	359	2	..................	..................	PUNCT
ejpam-4646	360	1	..................	..................	PUNCT
ejpam-4646	360	2	..................	..................	PUNCT
ejpam-4646	361	1	..................	..................	PUNCT
ejpam-4646	361	2	..................	..................	PUNCT
ejpam-4646	361	3	...........	...........	PUNCT
ejpam-4646	361	4	............	............	PUNCT
ejpam-4646	361	5	...........	...........	PUNCT
ejpam-4646	361	6	...........	...........	PUNCT
ejpam-4646	361	7	...........	...........	PUNCT
ejpam-4646	361	8	...........	...........	PUNCT
ejpam-4646	361	9	...........	...........	PUNCT
ejpam-4646	361	10	...........	...........	PUNCT
ejpam-4646	361	11	...........	...........	PUNCT
ejpam-4646	361	12	...........	...........	PUNCT
ejpam-4646	361	13	...........	...........	PUNCT
ejpam-4646	361	14	...........	...........	PUNCT
ejpam-4646	361	15	...........	...........	PUNCT
ejpam-4646	361	16	...........	...........	PUNCT
ejpam-4646	362	1	........	........	PUNCT
ejpam-4646	362	2	figure	figure	NOUN
ejpam-4646	362	3	1	1	NUM
ejpam-4646	362	4	:	:	PUNCT
ejpam-4646	362	5	the	the	DET
ejpam-4646	362	6	lexicographic	lexicographic	ADJ
ejpam-4646	362	7	product	product	NOUN
ejpam-4646	362	8	p3[p3	p3[p3	NUM
ejpam-4646	362	9	]	]	X
ejpam-4646	362	10	corollary	corollary	ADJ
ejpam-4646	362	11	5	5	X
ejpam-4646	362	12	.	.	PUNCT
ejpam-4646	363	1	let	let	VERB
ejpam-4646	363	2	n	n	PRON
ejpam-4646	363	3	≥	≥	X
ejpam-4646	363	4	2	2	NUM
ejpam-4646	363	5	be	be	AUX
ejpam-4646	363	6	a	a	DET
ejpam-4646	363	7	positive	positive	ADJ
ejpam-4646	363	8	integer	integer	NOUN
ejpam-4646	363	9	and	and	CCONJ
ejpam-4646	363	10	let	let	VERB
ejpam-4646	363	11	h	h	NOUN
ejpam-4646	363	12	be	be	AUX
ejpam-4646	363	13	any	any	DET
ejpam-4646	363	14	connected	connected	ADJ
ejpam-4646	363	15	non	non	ADJ
ejpam-4646	363	16	-	-	ADJ
ejpam-4646	363	17	trivial	trivial	ADJ
ejpam-4646	363	18	graph	graph	NOUN
ejpam-4646	363	19	.	.	PUNCT
ejpam-4646	364	1	then	then	ADV
ejpam-4646	364	2	γhg	γhg	INTJ
ejpam-4646	364	3	(	(	PUNCT
ejpam-4646	364	4	kn	kn	PROPN
ejpam-4646	365	1	[	[	X
ejpam-4646	365	2	h	h	X
ejpam-4646	365	3	]	]	X
ejpam-4646	365	4	)	)	PUNCT
ejpam-4646	365	5	=	=	SYM
ejpam-4646	365	6	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	365	7	)	)	PUNCT
ejpam-4646	365	8	.	.	PUNCT
ejpam-4646	366	1	proof	proof	NOUN
ejpam-4646	366	2	.	.	PUNCT
ejpam-4646	367	1	let	let	VERB
ejpam-4646	367	2	c	c	NOUN
ejpam-4646	367	3	=	=	PUNCT
ejpam-4646	367	4	⋃	⋃	PROPN
ejpam-4646	367	5	x∈s	x∈s	NOUN
ejpam-4646	367	6	(	(	PUNCT
ejpam-4646	367	7	{	{	PUNCT
ejpam-4646	367	8	x	x	NOUN
ejpam-4646	367	9	}	}	PUNCT
ejpam-4646	367	10	×	×	PROPN
ejpam-4646	367	11	tx	tx	PROPN
ejpam-4646	367	12	)	)	PUNCT
ejpam-4646	367	13	be	be	AUX
ejpam-4646	367	14	a	a	DET
ejpam-4646	367	15	γhg	γhg	NOUN
ejpam-4646	367	16	-	-	PUNCT
ejpam-4646	367	17	set	set	NOUN
ejpam-4646	367	18	of	of	ADP
ejpam-4646	367	19	kn	kn	PROPN
ejpam-4646	368	1	[	[	X
ejpam-4646	368	2	h	h	X
ejpam-4646	368	3	]	]	X
ejpam-4646	368	4	.	.	PUNCT
ejpam-4646	369	1	then	then	ADV
ejpam-4646	369	2	s	s	VERB
ejpam-4646	369	3	=	=	SYM
ejpam-4646	369	4	v	v	PROPN
ejpam-4646	369	5	(	(	PUNCT
ejpam-4646	369	6	kn	kn	PROPN
ejpam-4646	369	7	)	)	PUNCT
ejpam-4646	369	8	by	by	ADP
ejpam-4646	369	9	theorem	theorem	NOUN
ejpam-4646	369	10	6(i	6(i	NUM
ejpam-4646	369	11	)	)	PUNCT
ejpam-4646	369	12	.	.	PUNCT
ejpam-4646	370	1	also	also	ADV
ejpam-4646	370	2	,	,	PUNCT
ejpam-4646	370	3	by	by	ADP
ejpam-4646	370	4	(	(	PUNCT
ejpam-4646	370	5	ii	ii	NOUN
ejpam-4646	370	6	)	)	PUNCT
ejpam-4646	370	7	and	and	CCONJ
ejpam-4646	370	8	(	(	PUNCT
ejpam-4646	370	9	iii	iii	NOUN
ejpam-4646	370	10	)	)	PUNCT
ejpam-4646	370	11	of	of	ADP
ejpam-4646	370	12	theorem	theorem	NOUN
ejpam-4646	370	13	6	6	NUM
ejpam-4646	370	14	,	,	PUNCT
ejpam-4646	370	15	tx	tx	PROPN
ejpam-4646	370	16	is	be	AUX
ejpam-4646	370	17	a	a	DET
ejpam-4646	370	18	pointwise	pointwise	ADJ
ejpam-4646	370	19	non	non	ADJ
ejpam-4646	370	20	-	-	ADJ
ejpam-4646	370	21	dominating	dominating	ADJ
ejpam-4646	370	22	and	and	CCONJ
ejpam-4646	370	23	2	2	NUM
ejpam-4646	370	24	-	-	PUNCT
ejpam-4646	370	25	path	path	NOUN
ejpam-4646	370	26	c.j	c.j	PROPN
ejpam-4646	370	27	.	.	PROPN
ejpam-4646	370	28	saromines	saromines	PROPN
ejpam-4646	370	29	,	,	PUNCT
ejpam-4646	370	30	s.	s.	PROPN
ejpam-4646	370	31	canoy	canoy	PROPN
ejpam-4646	370	32	,	,	PUNCT
ejpam-4646	370	33	jr	jr	PROPN
ejpam-4646	370	34	.	.	PROPN
ejpam-4646	370	35	,	,	PUNCT
ejpam-4646	370	36	/	/	SYM
ejpam-4646	370	37	eur	eur	NOUN
ejpam-4646	370	38	.	.	PUNCT
ejpam-4646	371	1	j.	j.	PROPN
ejpam-4646	371	2	pure	pure	PROPN
ejpam-4646	371	3	appl	appl	PROPN
ejpam-4646	371	4	.	.	PROPN
ejpam-4646	371	5	math	math	PROPN
ejpam-4646	371	6	,	,	PUNCT
ejpam-4646	371	7	16	16	NUM
ejpam-4646	371	8	(	(	PUNCT
ejpam-4646	371	9	1	1	NUM
ejpam-4646	371	10	)	)	PUNCT
ejpam-4646	371	11	(	(	PUNCT
ejpam-4646	371	12	2023	2023	NUM
ejpam-4646	371	13	)	)	PUNCT
ejpam-4646	371	14	,	,	PUNCT
ejpam-4646	371	15	5	5	NUM
ejpam-4646	371	16	-	-	SYM
ejpam-4646	371	17	17	17	NUM
ejpam-4646	371	18	15	15	NUM
ejpam-4646	371	19	closure	closure	NOUN
ejpam-4646	371	20	absorbing	absorb	VERB
ejpam-4646	371	21	set	set	NOUN
ejpam-4646	371	22	of	of	ADP
ejpam-4646	371	23	h	h	NOUN
ejpam-4646	371	24	for	for	ADP
ejpam-4646	371	25	every	every	DET
ejpam-4646	371	26	x	x	PROPN
ejpam-4646	371	27	∈	∈	PROPN
ejpam-4646	371	28	s.	s.	PROPN
ejpam-4646	372	1	thus	thus	ADV
ejpam-4646	372	2	,	,	PUNCT
ejpam-4646	372	3	γhg	γhg	PROPN
ejpam-4646	372	4	(	(	PUNCT
ejpam-4646	372	5	kn	kn	PROPN
ejpam-4646	373	1	[	[	X
ejpam-4646	373	2	h	h	X
ejpam-4646	373	3	]	]	X
ejpam-4646	373	4	)	)	PUNCT
ejpam-4646	373	5	=	=	SYM
ejpam-4646	373	6	|c|	|c|	PROPN
ejpam-4646	373	7	=	=	PUNCT
ejpam-4646	373	8	∑	∑	PROPN
ejpam-4646	373	9	x∈s	x∈s	PROPN
ejpam-4646	373	10	|tx|	|tx|	PROPN
ejpam-4646	373	11	≥	≥	NUM
ejpam-4646	373	12	|s|	|s|	PROPN
ejpam-4646	373	13	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4646	373	14	)	)	PUNCT
ejpam-4646	373	15	=	=	SYM
ejpam-4646	374	1	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	374	2	)	)	PUNCT
ejpam-4646	374	3	by	by	ADP
ejpam-4646	374	4	corollary	corollary	ADJ
ejpam-4646	374	5	4	4	NUM
ejpam-4646	374	6	,	,	PUNCT
ejpam-4646	374	7	γhg	γhg	NOUN
ejpam-4646	374	8	(	(	PUNCT
ejpam-4646	374	9	kn	kn	PROPN
ejpam-4646	375	1	[	[	X
ejpam-4646	375	2	h	h	X
ejpam-4646	375	3	]	]	X
ejpam-4646	375	4	)	)	PUNCT
ejpam-4646	375	5	=	=	SYM
ejpam-4646	375	6	nρ2pnd(h	nρ2pnd(h	PROPN
ejpam-4646	375	7	)	)	PUNCT
ejpam-4646	375	8	.	.	PUNCT
ejpam-4646	376	1	example	example	NOUN
ejpam-4646	377	1	2	2	NUM
ejpam-4646	377	2	.	.	X
ejpam-4646	377	3	consider	consider	VERB
ejpam-4646	377	4	the	the	DET
ejpam-4646	377	5	graph	graph	NOUN
ejpam-4646	377	6	k3	k3	VERB
ejpam-4646	377	7	[	[	X
ejpam-4646	377	8	p4	p4	ADJ
ejpam-4646	377	9	]	]	X
ejpam-4646	377	10	.	.	PUNCT
ejpam-4646	378	1	it	it	PRON
ejpam-4646	378	2	can	can	AUX
ejpam-4646	378	3	be	be	AUX
ejpam-4646	378	4	verified	verify	VERB
ejpam-4646	378	5	that	that	SCONJ
ejpam-4646	378	6	γhg(k3	γhg(k3	PROPN
ejpam-4646	379	1	[	[	X
ejpam-4646	379	2	p4	p4	ADJ
ejpam-4646	379	3	]	]	X
ejpam-4646	379	4	)	)	PUNCT
ejpam-4646	379	5	=	=	SYM
ejpam-4646	379	6	9	9	NUM
ejpam-4646	379	7	=	=	SYM
ejpam-4646	379	8	γhg(k3)ρ2pnd(p4	γhg(k3)ρ2pnd(p4	X
ejpam-4646	379	9	)	)	PUNCT
ejpam-4646	379	10	.	.	PUNCT
ejpam-4646	380	1	....................................	....................................	PUNCT
ejpam-4646	380	2	....................................	....................................	PUNCT
ejpam-4646	381	1	....................................	....................................	PUNCT
ejpam-4646	381	2	....................................	....................................	PUNCT
ejpam-4646	382	1	....................................	....................................	PUNCT
ejpam-4646	382	2	....................................	....................................	PUNCT
ejpam-4646	383	1	....................................	....................................	PUNCT
ejpam-4646	383	2	....................................	....................................	PUNCT
ejpam-4646	384	1	....................................	....................................	PUNCT
ejpam-4646	384	2	....................................	....................................	PUNCT
ejpam-4646	385	1	....................................	....................................	PUNCT
ejpam-4646	385	2	....................................	....................................	PUNCT
ejpam-4646	386	1	.........	.........	PUNCT
ejpam-4646	386	2	........	........	PUNCT
ejpam-4646	386	3	........	........	PUNCT
ejpam-4646	386	4	........	........	PUNCT
ejpam-4646	386	5	........	........	PUNCT
ejpam-4646	386	6	........	........	PUNCT
ejpam-4646	386	7	........	........	PUNCT
ejpam-4646	386	8	........	........	PUNCT
ejpam-4646	386	9	........	........	PUNCT
ejpam-4646	386	10	........	........	PUNCT
ejpam-4646	386	11	........	........	PUNCT
ejpam-4646	386	12	........	........	PUNCT
ejpam-4646	386	13	........	........	PUNCT
ejpam-4646	386	14	........	........	PUNCT
ejpam-4646	386	15	........	........	PUNCT
ejpam-4646	386	16	........	........	PUNCT
ejpam-4646	386	17	........	........	PUNCT
ejpam-4646	386	18	........	........	PUNCT
ejpam-4646	386	19	........	........	PUNCT
ejpam-4646	386	20	........	........	PUNCT
ejpam-4646	386	21	........	........	PUNCT
ejpam-4646	386	22	........	........	PUNCT
ejpam-4646	386	23	........	........	PUNCT
ejpam-4646	386	24	........	........	PUNCT
ejpam-4646	386	25	........	........	PUNCT
ejpam-4646	386	26	........	........	PUNCT
ejpam-4646	386	27	........	........	PUNCT
ejpam-4646	386	28	...	...	PUNCT
ejpam-4646	386	29	.........	.........	PUNCT
ejpam-4646	387	1	........	........	PUNCT
ejpam-4646	387	2	........	........	PUNCT
ejpam-4646	387	3	........	........	PUNCT
ejpam-4646	387	4	........	........	PUNCT
ejpam-4646	387	5	........	........	PUNCT
ejpam-4646	387	6	........	........	PUNCT
ejpam-4646	387	7	........	........	PUNCT
ejpam-4646	387	8	........	........	PUNCT
ejpam-4646	387	9	........	........	PUNCT
ejpam-4646	387	10	........	........	PUNCT
ejpam-4646	387	11	........	........	PUNCT
ejpam-4646	387	12	........	........	PUNCT
ejpam-4646	387	13	........	........	PUNCT
ejpam-4646	387	14	........	........	PUNCT
ejpam-4646	387	15	........	........	PUNCT
ejpam-4646	387	16	........	........	PUNCT
ejpam-4646	387	17	........	........	PUNCT
ejpam-4646	387	18	........	........	PUNCT
ejpam-4646	387	19	........	........	PUNCT
ejpam-4646	387	20	........	........	PUNCT
ejpam-4646	387	21	........	........	PUNCT
ejpam-4646	387	22	........	........	PUNCT
ejpam-4646	387	23	........	........	PUNCT
ejpam-4646	387	24	........	........	PUNCT
ejpam-4646	387	25	........	........	PUNCT
ejpam-4646	387	26	........	........	PUNCT
ejpam-4646	387	27	...	...	PUNCT
ejpam-4646	387	28	.........	.........	PUNCT
ejpam-4646	387	29	........	........	PUNCT
ejpam-4646	387	30	........	........	PUNCT
ejpam-4646	387	31	........	........	PUNCT
ejpam-4646	387	32	........	........	PUNCT
ejpam-4646	387	33	........	........	PUNCT
ejpam-4646	387	34	........	........	PUNCT
ejpam-4646	387	35	........	........	PUNCT
ejpam-4646	387	36	........	........	PUNCT
ejpam-4646	387	37	........	........	PUNCT
ejpam-4646	387	38	........	........	PUNCT
ejpam-4646	387	39	........	........	PUNCT
ejpam-4646	387	40	........	........	PUNCT
ejpam-4646	387	41	........	........	PUNCT
ejpam-4646	387	42	........	........	PUNCT
ejpam-4646	387	43	........	........	PUNCT
ejpam-4646	387	44	........	........	PUNCT
ejpam-4646	387	45	........	........	PUNCT
ejpam-4646	387	46	........	........	PUNCT
ejpam-4646	387	47	........	........	PUNCT
ejpam-4646	387	48	........	........	PUNCT
ejpam-4646	387	49	........	........	PUNCT
ejpam-4646	387	50	........	........	PUNCT
ejpam-4646	387	51	........	........	PUNCT
ejpam-4646	387	52	........	........	PUNCT
ejpam-4646	387	53	........	........	PUNCT
ejpam-4646	387	54	........	........	PUNCT
ejpam-4646	387	55	...	...	PUNCT
ejpam-4646	387	56	.........	.........	PUNCT
ejpam-4646	387	57	........	........	PUNCT
ejpam-4646	387	58	........	........	PUNCT
ejpam-4646	387	59	........	........	PUNCT
ejpam-4646	387	60	........	........	PUNCT
ejpam-4646	387	61	........	........	PUNCT
ejpam-4646	387	62	........	........	PUNCT
ejpam-4646	387	63	........	........	PUNCT
ejpam-4646	387	64	........	........	PUNCT
ejpam-4646	387	65	........	........	PUNCT
ejpam-4646	387	66	........	........	PUNCT
ejpam-4646	387	67	........	........	PUNCT
ejpam-4646	387	68	........	........	PUNCT
ejpam-4646	387	69	........	........	PUNCT
ejpam-4646	387	70	........	........	PUNCT
ejpam-4646	387	71	........	........	PUNCT
ejpam-4646	387	72	........	........	PUNCT
ejpam-4646	387	73	........	........	PUNCT
ejpam-4646	387	74	........	........	PUNCT
ejpam-4646	387	75	........	........	PUNCT
ejpam-4646	387	76	........	........	PUNCT
ejpam-4646	387	77	........	........	PUNCT
ejpam-4646	387	78	........	........	PUNCT
ejpam-4646	387	79	........	........	PUNCT
ejpam-4646	387	80	........	........	PUNCT
ejpam-4646	387	81	........	........	PUNCT
ejpam-4646	387	82	........	........	PUNCT
ejpam-4646	387	83	...	...	PUNCT
ejpam-4646	387	84	.........	.........	PUNCT
ejpam-4646	387	85	........	........	PUNCT
ejpam-4646	387	86	........	........	PUNCT
ejpam-4646	387	87	........	........	PUNCT
ejpam-4646	387	88	........	........	PUNCT
ejpam-4646	387	89	........	........	PUNCT
ejpam-4646	387	90	........	........	PUNCT
ejpam-4646	387	91	........	........	PUNCT
ejpam-4646	387	92	........	........	PUNCT
ejpam-4646	387	93	........	........	PUNCT
ejpam-4646	387	94	........	........	PUNCT
ejpam-4646	387	95	........	........	PUNCT
ejpam-4646	387	96	........	........	PUNCT
ejpam-4646	387	97	...	...	PUNCT
ejpam-4646	387	98	.........	.........	PUNCT
ejpam-4646	387	99	........	........	PUNCT
ejpam-4646	387	100	........	........	PUNCT
ejpam-4646	387	101	........	........	PUNCT
ejpam-4646	387	102	........	........	PUNCT
ejpam-4646	387	103	........	........	PUNCT
ejpam-4646	387	104	........	........	PUNCT
ejpam-4646	387	105	........	........	PUNCT
ejpam-4646	387	106	........	........	PUNCT
ejpam-4646	387	107	........	........	PUNCT
ejpam-4646	387	108	........	........	PUNCT
ejpam-4646	387	109	........	........	PUNCT
ejpam-4646	387	110	........	........	PUNCT
ejpam-4646	387	111	...	...	PUNCT
ejpam-4646	387	112	.........	.........	PUNCT
ejpam-4646	387	113	........	........	PUNCT
ejpam-4646	387	114	........	........	PUNCT
ejpam-4646	387	115	........	........	PUNCT
ejpam-4646	387	116	........	........	PUNCT
ejpam-4646	387	117	........	........	PUNCT
ejpam-4646	387	118	........	........	PUNCT
ejpam-4646	387	119	........	........	PUNCT
ejpam-4646	387	120	........	........	PUNCT
ejpam-4646	387	121	........	........	PUNCT
ejpam-4646	387	122	........	........	PUNCT
ejpam-4646	387	123	........	........	PUNCT
ejpam-4646	387	124	........	........	PUNCT
ejpam-4646	387	125	...	...	PUNCT
ejpam-4646	388	1	..............	..............	PUNCT
ejpam-4646	388	2	.............	.............	PUNCT
ejpam-4646	388	3	.............	.............	PUNCT
ejpam-4646	388	4	.............	.............	PUNCT
ejpam-4646	388	5	.............	.............	PUNCT
ejpam-4646	388	6	.............	.............	PUNCT
ejpam-4646	388	7	.............	.............	PUNCT
ejpam-4646	388	8	.............	.............	PUNCT
ejpam-4646	388	9	.............	.............	PUNCT
ejpam-4646	388	10	.............	.............	PUNCT
ejpam-4646	388	11	.............	.............	PUNCT
ejpam-4646	388	12	.............	.............	PUNCT
ejpam-4646	388	13	.............	.............	PUNCT
ejpam-4646	388	14	...	...	PUNCT
ejpam-4646	388	15	.....................	.....................	PUNCT
ejpam-4646	388	16	....................	....................	PUNCT
ejpam-4646	388	17	....................	....................	PUNCT
ejpam-4646	388	18	....................	....................	PUNCT
ejpam-4646	388	19	....................	....................	PUNCT
ejpam-4646	388	20	....................	....................	PUNCT
ejpam-4646	388	21	....................	....................	PUNCT
ejpam-4646	388	22	....................	....................	PUNCT
ejpam-4646	388	23	....................	....................	PUNCT
ejpam-4646	388	24	....................	....................	PUNCT
ejpam-4646	388	25	....................	....................	PUNCT
ejpam-4646	388	26	....................	....................	PUNCT
ejpam-4646	388	27	....................	....................	PUNCT
ejpam-4646	388	28	...........	...........	PUNCT
ejpam-4646	389	1	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	389	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	390	1	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	390	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	391	1	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	391	2	.............................................................................................................................................................................................................................................	.............................................................................................................................................................................................................................................	PUNCT
ejpam-4646	392	1	..............	..............	PUNCT
ejpam-4646	392	2	.............	.............	PUNCT
ejpam-4646	392	3	.............	.............	PUNCT
ejpam-4646	392	4	.............	.............	PUNCT
ejpam-4646	392	5	.............	.............	PUNCT
ejpam-4646	392	6	.............	.............	PUNCT
ejpam-4646	392	7	.............	.............	PUNCT
ejpam-4646	392	8	.............	.............	PUNCT
ejpam-4646	392	9	.............	.............	PUNCT
ejpam-4646	392	10	.............	.............	PUNCT
ejpam-4646	392	11	.............	.............	PUNCT
ejpam-4646	392	12	.............	.............	PUNCT
ejpam-4646	392	13	.............	.............	PUNCT
ejpam-4646	393	1	................................................................................................................................................................................................................................	................................................................................................................................................................................................................................	PUNCT
ejpam-4646	393	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4646	393	3	............................................................................................................	............................................................................................................	PUNCT
ejpam-4646	394	1	............................................................................................................	............................................................................................................	PUNCT
ejpam-4646	394	2	............................................................................................................	............................................................................................................	PUNCT
ejpam-4646	395	1	.............................................................................................................................................................................	.............................................................................................................................................................................	PUNCT
ejpam-4646	395	2	................................................................................................................................................................................................................................................................................	................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4646	396	1	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	396	2	................................................................................................................................................................................................................	................................................................................................................................................................................................................	PUNCT
ejpam-4646	397	1	........................................................................................................	........................................................................................................	PROPN
ejpam-4646	397	2	........................................................................................................	........................................................................................................	PROPN
ejpam-4646	398	1	...................................................................................................................	...................................................................................................................	PUNCT
ejpam-4646	398	2	..........	..........	PUNCT
ejpam-4646	399	1	..........	..........	PUNCT
ejpam-4646	399	2	..........	..........	PUNCT
ejpam-4646	400	1	..........	..........	PUNCT
ejpam-4646	400	2	..........	..........	PUNCT
ejpam-4646	401	1	..........	..........	PUNCT
ejpam-4646	401	2	..........	..........	PUNCT
ejpam-4646	402	1	..........	..........	PUNCT
ejpam-4646	402	2	..........	..........	PUNCT
ejpam-4646	403	1	..........	..........	PUNCT
ejpam-4646	403	2	..........	..........	PUNCT
ejpam-4646	404	1	..........	..........	PUNCT
ejpam-4646	404	2	..	..	PUNCT
ejpam-4646	405	1	..............................................................................................................................................................................................	..............................................................................................................................................................................................	PUNCT
ejpam-4646	405	2	................	................	PUNCT
ejpam-4646	406	1	................	................	PUNCT
ejpam-4646	406	2	................	................	PUNCT
ejpam-4646	407	1	................	................	PUNCT
ejpam-4646	407	2	................	................	PUNCT
ejpam-4646	408	1	................	................	PUNCT
ejpam-4646	408	2	................	................	PUNCT
ejpam-4646	409	1	................	................	PUNCT
ejpam-4646	409	2	................	................	PUNCT
ejpam-4646	410	1	................	................	PUNCT
ejpam-4646	410	2	................	................	PUNCT
ejpam-4646	410	3	................	................	PUNCT
ejpam-4646	410	4	............	............	PUNCT
ejpam-4646	410	5	...........	...........	PUNCT
ejpam-4646	410	6	..........	..........	PUNCT
ejpam-4646	411	1	..........	..........	PUNCT
ejpam-4646	411	2	..........	..........	PUNCT
ejpam-4646	412	1	..........	..........	PUNCT
ejpam-4646	412	2	..........	..........	PUNCT
ejpam-4646	413	1	..........	..........	PUNCT
ejpam-4646	413	2	..........	..........	PUNCT
ejpam-4646	414	1	..........	..........	PUNCT
ejpam-4646	414	2	..........	..........	PUNCT
ejpam-4646	415	1	..........	..........	PUNCT
ejpam-4646	415	2	..........	..........	PUNCT
ejpam-4646	416	1	..........	..........	PUNCT
ejpam-4646	416	2	..	..	PUNCT
ejpam-4646	416	3	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-4646	417	1	............................................................................................................	............................................................................................................	PUNCT
ejpam-4646	417	2	....................................	....................................	PUNCT
ejpam-4646	418	1	.........	.........	PUNCT
ejpam-4646	418	2	........	........	PUNCT
ejpam-4646	418	3	........	........	PUNCT
ejpam-4646	418	4	........	........	PUNCT
ejpam-4646	418	5	........	........	PUNCT
ejpam-4646	418	6	........	........	PUNCT
ejpam-4646	418	7	........	........	PUNCT
ejpam-4646	418	8	........	........	PUNCT
ejpam-4646	418	9	........	........	PUNCT
ejpam-4646	418	10	........	........	PUNCT
ejpam-4646	418	11	........	........	PUNCT
ejpam-4646	418	12	........	........	PUNCT
ejpam-4646	419	1	........	........	PUNCT
ejpam-4646	419	2	...	...	PUNCT
ejpam-4646	420	1	....................................	....................................	PUNCT
ejpam-4646	420	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	420	3	........................................................................	........................................................................	PUNCT
ejpam-4646	420	4	.............................................................................................................................................................................	.............................................................................................................................................................................	PUNCT
ejpam-4646	420	5	....................................	....................................	PUNCT
ejpam-4646	421	1	..............	..............	PUNCT
ejpam-4646	421	2	.............	.............	PUNCT
ejpam-4646	421	3	.............	.............	PUNCT
ejpam-4646	421	4	.............	.............	PUNCT
ejpam-4646	421	5	.............	.............	PUNCT
ejpam-4646	421	6	.............	.............	PUNCT
ejpam-4646	421	7	.............	.............	PUNCT
ejpam-4646	421	8	.............	.............	PUNCT
ejpam-4646	421	9	.............	.............	PUNCT
ejpam-4646	421	10	.............	.............	PUNCT
ejpam-4646	421	11	.............	.............	PUNCT
ejpam-4646	421	12	.............	.............	PUNCT
ejpam-4646	421	13	.............	.............	PUNCT
ejpam-4646	421	14	...	...	PUNCT
ejpam-4646	421	15	...	...	PUNCT
ejpam-4646	421	16	.................................	.................................	PUNCT
ejpam-4646	422	1	....................................	....................................	PUNCT
ejpam-4646	422	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4646	423	1	...............................................................................................................................................................................................................................................................................................................................................................................................	...............................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4646	423	2	................................................................................................................................................................................................................................................................................	................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4646	424	1	............................	............................	PUNCT
ejpam-4646	424	2	...........................	...........................	PUNCT
ejpam-4646	424	3	...........................	...........................	PUNCT
ejpam-4646	424	4	...........................	...........................	PUNCT
ejpam-4646	424	5	...........................	...........................	PUNCT
ejpam-4646	424	6	...........................	...........................	PUNCT
ejpam-4646	424	7	...........................	...........................	PUNCT
ejpam-4646	424	8	...........................	...........................	PUNCT
ejpam-4646	424	9	...........................	...........................	PUNCT
ejpam-4646	424	10	...........................	...........................	PUNCT
ejpam-4646	424	11	...........................	...........................	PUNCT
ejpam-4646	424	12	...........................	...........................	PUNCT
ejpam-4646	424	13	...........................	...........................	PUNCT
ejpam-4646	424	14	...........................	...........................	PUNCT
ejpam-4646	425	1	....	....	PUNCT
ejpam-4646	425	2	.....................	.....................	PUNCT
ejpam-4646	425	3	....................	....................	PUNCT
ejpam-4646	425	4	....................	....................	PUNCT
ejpam-4646	425	5	....................	....................	PUNCT
ejpam-4646	425	6	....................	....................	PUNCT
ejpam-4646	425	7	....................	....................	PUNCT
ejpam-4646	425	8	....................	....................	PUNCT
ejpam-4646	425	9	....................	....................	PUNCT
ejpam-4646	425	10	....................	....................	PUNCT
ejpam-4646	425	11	....................	....................	PUNCT
ejpam-4646	425	12	....................	....................	PUNCT
ejpam-4646	425	13	....................	....................	PUNCT
ejpam-4646	425	14	....................	....................	PUNCT
ejpam-4646	425	15	...........	...........	PUNCT
ejpam-4646	425	16	.........	.........	PUNCT
ejpam-4646	425	17	........	........	PUNCT
ejpam-4646	425	18	........	........	PUNCT
ejpam-4646	425	19	........	........	PUNCT
ejpam-4646	425	20	........	........	PUNCT
ejpam-4646	425	21	........	........	PUNCT
ejpam-4646	425	22	........	........	PUNCT
ejpam-4646	425	23	........	........	PUNCT
ejpam-4646	425	24	........	........	PUNCT
ejpam-4646	425	25	........	........	PUNCT
ejpam-4646	425	26	........	........	PUNCT
ejpam-4646	425	27	........	........	PUNCT
ejpam-4646	425	28	........	........	PUNCT
ejpam-4646	425	29	...	...	PUNCT
ejpam-4646	425	30	........................	........................	PUNCT
ejpam-4646	426	1	.......................	.......................	PUNCT
ejpam-4646	426	2	.......................	.......................	PUNCT
ejpam-4646	427	1	.......................	.......................	PUNCT
ejpam-4646	427	2	.......................	.......................	PUNCT
ejpam-4646	428	1	.......................	.......................	PUNCT
ejpam-4646	428	2	.......................	.......................	PUNCT
ejpam-4646	429	1	.......................	.......................	PUNCT
ejpam-4646	429	2	.......................	.......................	PUNCT
ejpam-4646	430	1	.......................	.......................	PUNCT
ejpam-4646	430	2	.......................	.......................	PUNCT
ejpam-4646	431	1	.......................	.......................	PUNCT
ejpam-4646	431	2	.......................	.......................	PUNCT
ejpam-4646	431	3	.......................	.......................	PUNCT
ejpam-4646	431	4	...	...	PUNCT
ejpam-4646	432	1	.................	.................	PUNCT
ejpam-4646	432	2	................	................	PUNCT
ejpam-4646	433	1	................	................	PUNCT
ejpam-4646	433	2	................	................	PUNCT
ejpam-4646	434	1	................	................	PUNCT
ejpam-4646	434	2	................	................	PUNCT
ejpam-4646	435	1	................	................	PUNCT
ejpam-4646	435	2	................	................	PUNCT
ejpam-4646	436	1	................	................	PUNCT
ejpam-4646	436	2	................	................	PUNCT
ejpam-4646	437	1	................	................	PUNCT
ejpam-4646	437	2	................	................	PUNCT
ejpam-4646	437	3	................	................	PUNCT
ejpam-4646	437	4	............	............	PUNCT
ejpam-4646	437	5	...........	...........	PUNCT
ejpam-4646	437	6	..........	..........	PUNCT
ejpam-4646	438	1	..........	..........	PUNCT
ejpam-4646	438	2	..........	..........	PUNCT
ejpam-4646	439	1	..........	..........	PUNCT
ejpam-4646	439	2	..........	..........	PUNCT
ejpam-4646	440	1	..........	..........	PUNCT
ejpam-4646	440	2	..........	..........	PUNCT
ejpam-4646	441	1	..........	..........	PUNCT
ejpam-4646	441	2	..........	..........	PUNCT
ejpam-4646	442	1	..........	..........	PUNCT
ejpam-4646	442	2	..........	..........	PUNCT
ejpam-4646	443	1	..........	..........	PUNCT
ejpam-4646	443	2	..	..	PUNCT
ejpam-4646	443	3	......................................................................................................................................................................................................................................................................................................................................	......................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4646	443	4	.............................................................................................................................................................................................................................	.............................................................................................................................................................................................................................	PUNCT
ejpam-4646	444	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4646	444	2	figure	figure	NOUN
ejpam-4646	444	3	2	2	NUM
ejpam-4646	444	4	:	:	PUNCT
ejpam-4646	444	5	the	the	DET
ejpam-4646	444	6	lexicographic	lexicographic	ADJ
ejpam-4646	444	7	product	product	NOUN
ejpam-4646	444	8	k3[p4	k3[p4	PROPN
ejpam-4646	444	9	]	]	X
ejpam-4646	444	10	4	4	NUM
ejpam-4646	444	11	.	.	X
ejpam-4646	444	12	conclusion	conclusion	NOUN
ejpam-4646	444	13	this	this	DET
ejpam-4646	444	14	paper	paper	NOUN
ejpam-4646	444	15	investigated	investigate	VERB
ejpam-4646	444	16	the	the	DET
ejpam-4646	444	17	concept	concept	NOUN
ejpam-4646	444	18	of	of	ADP
ejpam-4646	444	19	geodetic	geodetic	ADJ
ejpam-4646	444	20	hop	hop	NOUN
ejpam-4646	444	21	domination	domination	NOUN
ejpam-4646	444	22	,	,	PUNCT
ejpam-4646	444	23	a	a	DET
ejpam-4646	444	24	variant	variant	NOUN
ejpam-4646	444	25	of	of	ADP
ejpam-4646	444	26	hop	hop	NOUN
ejpam-4646	444	27	domination	domination	NOUN
ejpam-4646	444	28	,	,	PUNCT
ejpam-4646	444	29	which	which	PRON
ejpam-4646	444	30	was	be	AUX
ejpam-4646	444	31	definedand	definedand	NOUN
ejpam-4646	444	32	studied	study	VERB
ejpam-4646	444	33	previously	previously	ADV
ejpam-4646	444	34	by	by	ADP
ejpam-4646	444	35	some	some	DET
ejpam-4646	444	36	authors	author	NOUN
ejpam-4646	444	37	.	.	PUNCT
ejpam-4646	445	1	some	some	DET
ejpam-4646	445	2	bounds	bound	NOUN
ejpam-4646	445	3	of	of	ADP
ejpam-4646	445	4	the	the	DET
ejpam-4646	445	5	parameter	parameter	NOUN
ejpam-4646	445	6	are	be	AUX
ejpam-4646	445	7	determined	determine	VERB
ejpam-4646	445	8	and	and	CCONJ
ejpam-4646	445	9	graphs	graph	NOUN
ejpam-4646	445	10	attaining	attain	VERB
ejpam-4646	445	11	these	these	DET
ejpam-4646	445	12	bounds	bound	NOUN
ejpam-4646	445	13	are	be	AUX
ejpam-4646	445	14	also	also	ADV
ejpam-4646	445	15	characterized	characterize	VERB
ejpam-4646	445	16	.	.	PUNCT
ejpam-4646	446	1	characterizations	characterization	NOUN
ejpam-4646	446	2	of	of	ADP
ejpam-4646	446	3	geodetic	geodetic	ADJ
ejpam-4646	446	4	hop	hop	NOUN
ejpam-4646	446	5	dominating	dominating	NOUN
ejpam-4646	446	6	sets	set	NOUN
ejpam-4646	446	7	in	in	ADP
ejpam-4646	446	8	the	the	DET
ejpam-4646	446	9	corona	corona	NOUN
ejpam-4646	446	10	and	and	CCONJ
ejpam-4646	446	11	lexicographic	lexicographic	ADJ
ejpam-4646	446	12	product	product	NOUN
ejpam-4646	446	13	of	of	ADP
ejpam-4646	446	14	two	two	NUM
ejpam-4646	446	15	graphs	graph	NOUN
ejpam-4646	446	16	are	be	AUX
ejpam-4646	446	17	given	give	VERB
ejpam-4646	446	18	.	.	PUNCT
ejpam-4646	447	1	these	these	DET
ejpam-4646	447	2	characterizations	characterization	NOUN
ejpam-4646	447	3	were	be	AUX
ejpam-4646	447	4	used	use	VERB
ejpam-4646	447	5	to	to	PART
ejpam-4646	447	6	obtain	obtain	VERB
ejpam-4646	447	7	exact	exact	ADJ
ejpam-4646	447	8	or	or	CCONJ
ejpam-4646	447	9	tight	tight	ADJ
ejpam-4646	447	10	bounds	bound	NOUN
ejpam-4646	447	11	for	for	ADP
ejpam-4646	447	12	the	the	DET
ejpam-4646	447	13	geodetic	geodetic	ADJ
ejpam-4646	447	14	hop	hop	NOUN
ejpam-4646	447	15	domination	domination	NOUN
ejpam-4646	447	16	number	number	NOUN
ejpam-4646	447	17	of	of	ADP
ejpam-4646	447	18	the	the	DET
ejpam-4646	447	19	corresponding	correspond	VERB
ejpam-4646	447	20	graphs	graph	NOUN
ejpam-4646	447	21	.	.	PUNCT
ejpam-4646	448	1	it	it	PRON
ejpam-4646	448	2	is	be	AUX
ejpam-4646	448	3	recommended	recommend	VERB
ejpam-4646	448	4	that	that	SCONJ
ejpam-4646	448	5	some	some	DET
ejpam-4646	448	6	other	other	ADJ
ejpam-4646	448	7	bounds	bound	NOUN
ejpam-4646	448	8	for	for	ADP
ejpam-4646	448	9	the	the	DET
ejpam-4646	448	10	geodetic	geodetic	ADJ
ejpam-4646	448	11	hop	hop	NOUN
ejpam-4646	448	12	domination	domination	NOUN
ejpam-4646	448	13	be	be	AUX
ejpam-4646	448	14	determined	determine	VERB
ejpam-4646	448	15	and	and	CCONJ
ejpam-4646	448	16	that	that	SCONJ
ejpam-4646	448	17	the	the	DET
ejpam-4646	448	18	parameter	parameter	NOUN
ejpam-4646	448	19	be	be	AUX
ejpam-4646	448	20	studied	study	VERB
ejpam-4646	448	21	for	for	ADP
ejpam-4646	448	22	other	other	ADJ
ejpam-4646	448	23	interesting	interesting	ADJ
ejpam-4646	448	24	graphs	graph	NOUN
ejpam-4646	448	25	.	.	PUNCT
ejpam-4646	449	1	acknowledgements	acknowledgement	NOUN
ejpam-4646	449	2	the	the	DET
ejpam-4646	449	3	authors	author	NOUN
ejpam-4646	449	4	are	be	AUX
ejpam-4646	449	5	very	very	ADV
ejpam-4646	449	6	much	much	ADV
ejpam-4646	449	7	grateful	grateful	ADJ
ejpam-4646	449	8	to	to	ADP
ejpam-4646	449	9	the	the	DET
ejpam-4646	449	10	referees	referee	NOUN
ejpam-4646	449	11	for	for	ADP
ejpam-4646	449	12	the	the	DET
ejpam-4646	449	13	corrections	correction	NOUN
ejpam-4646	449	14	and	and	CCONJ
ejpam-4646	449	15	suggestions	suggestion	NOUN
ejpam-4646	449	16	they	they	PRON
ejpam-4646	449	17	made	make	VERB
ejpam-4646	449	18	in	in	ADP
ejpam-4646	449	19	the	the	DET
ejpam-4646	449	20	initial	initial	ADJ
ejpam-4646	449	21	manuscript	manuscript	NOUN
ejpam-4646	449	22	.	.	PUNCT
ejpam-4646	450	1	the	the	DET
ejpam-4646	450	2	authors	author	NOUN
ejpam-4646	450	3	would	would	AUX
ejpam-4646	450	4	like	like	VERB
ejpam-4646	450	5	to	to	PART
ejpam-4646	450	6	thank	thank	VERB
ejpam-4646	450	7	the	the	DET
ejpam-4646	450	8	department	department	NOUN
ejpam-4646	450	9	of	of	ADP
ejpam-4646	450	10	science	science	NOUN
ejpam-4646	450	11	and	and	CCONJ
ejpam-4646	450	12	technology	technology	NOUN
ejpam-4646	450	13	accelerated	accelerate	VERB
ejpam-4646	450	14	science	science	NOUN
ejpam-4646	450	15	and	and	CCONJ
ejpam-4646	450	16	technology	technology	NOUN
ejpam-4646	450	17	human	human	ADJ
ejpam-4646	450	18	resource	resource	NOUN
ejpam-4646	450	19	development	development	NOUN
ejpam-4646	450	20	program	program	NOUN
ejpam-4646	450	21	(	(	PUNCT
ejpam-4646	450	22	dost	dost	NOUN
ejpam-4646	450	23	-	-	PUNCT
ejpam-4646	450	24	asthrdp)-philippines	asthrdp)-philippine	NOUN
ejpam-4646	450	25	,	,	PUNCT
ejpam-4646	450	26	and	and	CCONJ
ejpam-4646	450	27	msu	msu	PROPN
ejpam-4646	450	28	-	-	PUNCT
ejpam-4646	450	29	iligan	iligan	PROPN
ejpam-4646	450	30	institute	institute	PROPN
ejpam-4646	450	31	of	of	ADP
ejpam-4646	450	32	technology	technology	NOUN
ejpam-4646	450	33	for	for	ADP
ejpam-4646	450	34	funding	fund	VERB
ejpam-4646	450	35	this	this	DET
ejpam-4646	450	36	research	research	NOUN
ejpam-4646	450	37	.	.	PUNCT
ejpam-4646	451	1	references	reference	NOUN
ejpam-4646	451	2	16	16	NUM
ejpam-4646	451	3	references	reference	NOUN
ejpam-4646	451	4	[	[	X
ejpam-4646	451	5	1	1	NUM
ejpam-4646	451	6	]	]	PUNCT
ejpam-4646	451	7	d.	d.	NOUN
ejpam-4646	451	8	anusha	anusha	PROPN
ejpam-4646	451	9	and	and	CCONJ
ejpam-4646	451	10	s.	s.	PROPN
ejpam-4646	451	11	joseph	joseph	PROPN
ejpam-4646	451	12	robin	robin	PROPN
ejpam-4646	451	13	.	.	PUNCT
ejpam-4646	452	1	geodetic	geodetic	ADJ
ejpam-4646	452	2	hop	hop	NOUN
ejpam-4646	452	3	domination	domination	NOUN
ejpam-4646	452	4	in	in	ADP
ejpam-4646	452	5	join	join	NOUN
ejpam-4646	452	6	and	and	CCONJ
ejpam-4646	452	7	corona	corona	NOUN
ejpam-4646	452	8	of	of	ADP
ejpam-4646	452	9	graphs	graph	NOUN
ejpam-4646	452	10	.	.	PUNCT
ejpam-4646	453	1	journal	journal	NOUN
ejpam-4646	453	2	of	of	ADP
ejpam-4646	453	3	combinatorial	combinatorial	ADJ
ejpam-4646	453	4	mathematics	mathematic	NOUN
ejpam-4646	453	5	and	and	CCONJ
ejpam-4646	453	6	combinatorial	combinatorial	ADJ
ejpam-4646	453	7	computing	computing	NOUN
ejpam-4646	453	8	,	,	PUNCT
ejpam-4646	453	9	21(3):1117–1127	21(3):1117–1127	NUM
ejpam-4646	453	10	,	,	PUNCT
ejpam-4646	453	11	2011	2011	NUM
ejpam-4646	453	12	.	.	PUNCT
ejpam-4646	454	1	[	[	X
ejpam-4646	454	2	2	2	X
ejpam-4646	454	3	]	]	PUNCT
ejpam-4646	454	4	s.	s.	PROPN
ejpam-4646	454	5	arriola	arriola	PROPN
ejpam-4646	454	6	and	and	CCONJ
ejpam-4646	454	7	s.	s.	PROPN
ejpam-4646	454	8	canoy	canoy	PROPN
ejpam-4646	454	9	jr	jr	PROPN
ejpam-4646	454	10	.	.	PROPN
ejpam-4646	454	11	(	(	PUNCT
ejpam-4646	454	12	1	1	NUM
ejpam-4646	454	13	,	,	PUNCT
ejpam-4646	454	14	2)∗-domination	2)∗-domination	NOUN
ejpam-4646	454	15	in	in	ADP
ejpam-4646	454	16	graphs	graph	NOUN
ejpam-4646	454	17	.	.	PUNCT
ejpam-4646	455	1	advances	advance	NOUN
ejpam-4646	455	2	and	and	CCONJ
ejpam-4646	455	3	applications	application	NOUN
ejpam-4646	455	4	in	in	ADP
ejpam-4646	455	5	discrete	discrete	ADJ
ejpam-4646	455	6	mathematics	mathematic	NOUN
ejpam-4646	455	7	.	.	PUNCT
ejpam-4646	455	8	,	,	PUNCT
ejpam-4646	455	9	18(2):179–190	18(2):179–190	NUM
ejpam-4646	455	10	,	,	PUNCT
ejpam-4646	455	11	2017	2017	NUM
ejpam-4646	455	12	.	.	PUNCT
ejpam-4646	456	1	[	[	X
ejpam-4646	456	2	3	3	X
ejpam-4646	456	3	]	]	X
ejpam-4646	456	4	s.	s.	PROPN
ejpam-4646	456	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4646	456	6	,	,	PUNCT
ejpam-4646	456	7	b.	b.	PROPN
ejpam-4646	456	8	krishnakumari	krishnakumari	PROPN
ejpam-4646	456	9	,	,	PUNCT
ejpam-4646	456	10	b.	b.	PROPN
ejpam-4646	456	11	natarjan	natarjan	PROPN
ejpam-4646	456	12	,	,	PUNCT
ejpam-4646	456	13	and	and	CCONJ
ejpam-4646	456	14	y.	y.	PROPN
ejpam-4646	456	15	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4646	456	16	.	.	PUNCT
ejpam-4646	457	1	bounds	bound	NOUN
ejpam-4646	457	2	on	on	ADP
ejpam-4646	457	3	the	the	DET
ejpam-4646	457	4	hop	hop	NOUN
ejpam-4646	457	5	domination	domination	NOUN
ejpam-4646	457	6	number	number	NOUN
ejpam-4646	457	7	of	of	ADP
ejpam-4646	457	8	a	a	DET
ejpam-4646	457	9	tree	tree	NOUN
ejpam-4646	457	10	.	.	PUNCT
ejpam-4646	458	1	proceedings	proceeding	NOUN
ejpam-4646	458	2	-	-	PUNCT
ejpam-4646	458	3	mathematical	mathematical	ADJ
ejpam-4646	458	4	sciences	science	NOUN
ejpam-4646	458	5	,	,	PUNCT
ejpam-4646	458	6	125(4):449	125(4):449	NUM
ejpam-4646	458	7	–	–	PUNCT
ejpam-4646	458	8	455	455	NUM
ejpam-4646	458	9	,	,	PUNCT
ejpam-4646	458	10	2015	2015	NUM
ejpam-4646	458	11	.	.	PUNCT
ejpam-4646	459	1	[	[	X
ejpam-4646	459	2	4	4	X
ejpam-4646	459	3	]	]	PUNCT
ejpam-4646	459	4	g.	g.	NOUN
ejpam-4646	459	5	cagaanan	cagaanan	PROPN
ejpam-4646	459	6	and	and	CCONJ
ejpam-4646	459	7	s.	s.	PROPN
ejpam-4646	459	8	canoy	canoy	PROPN
ejpam-4646	459	9	jr	jr	PROPN
ejpam-4646	459	10	.	.	PROPN
ejpam-4646	459	11	on	on	ADP
ejpam-4646	459	12	the	the	DET
ejpam-4646	459	13	geodesic	geodesic	ADJ
ejpam-4646	459	14	and	and	CCONJ
ejpam-4646	459	15	hull	hull	NOUN
ejpam-4646	459	16	numbers	number	NOUN
ejpam-4646	459	17	of	of	ADP
ejpam-4646	459	18	the	the	DET
ejpam-4646	459	19	sum	sum	NOUN
ejpam-4646	459	20	of	of	ADP
ejpam-4646	459	21	graphs	graph	NOUN
ejpam-4646	459	22	.	.	PUNCT
ejpam-4646	460	1	congresus	congresus	PROPN
ejpam-4646	460	2	numerantium	numerantium	PROPN
ejpam-4646	460	3	,	,	PUNCT
ejpam-4646	460	4	161:97–104	161:97–104	NUM
ejpam-4646	460	5	,	,	PUNCT
ejpam-4646	460	6	2003	2003	NUM
ejpam-4646	460	7	.	.	PUNCT
ejpam-4646	461	1	[	[	X
ejpam-4646	461	2	5	5	X
ejpam-4646	461	3	]	]	PUNCT
ejpam-4646	461	4	g.	g.	NOUN
ejpam-4646	461	5	cagaanan	cagaanan	PROPN
ejpam-4646	461	6	and	and	CCONJ
ejpam-4646	461	7	s.	s.	PROPN
ejpam-4646	461	8	canoy	canoy	PROPN
ejpam-4646	461	9	jr	jr	PROPN
ejpam-4646	461	10	.	.	PROPN
ejpam-4646	461	11	on	on	ADP
ejpam-4646	461	12	the	the	DET
ejpam-4646	461	13	geodetic	geodetic	ADJ
ejpam-4646	461	14	bases	basis	NOUN
ejpam-4646	461	15	of	of	ADP
ejpam-4646	461	16	the	the	DET
ejpam-4646	461	17	composition	composition	NOUN
ejpam-4646	461	18	g[km	g[km	PROPN
ejpam-4646	461	19	]	]	PUNCT
ejpam-4646	461	20	.	.	PUNCT
ejpam-4646	461	21	ars	ars	PROPN
ejpam-4646	461	22	combinatoria	combinatoria	PROPN
ejpam-4646	461	23	,	,	PUNCT
ejpam-4646	461	24	79:33–45	79:33–45	NUM
ejpam-4646	461	25	,	,	PUNCT
ejpam-4646	461	26	2006	2006	NUM
ejpam-4646	461	27	.	.	PUNCT
ejpam-4646	462	1	[	[	X
ejpam-4646	462	2	6	6	NUM
ejpam-4646	462	3	]	]	PUNCT
ejpam-4646	462	4	g.	g.	NOUN
ejpam-4646	462	5	cagaanan	cagaanan	PROPN
ejpam-4646	462	6	and	and	CCONJ
ejpam-4646	462	7	s.	s.	PROPN
ejpam-4646	462	8	canoy	canoy	PROPN
ejpam-4646	462	9	jr	jr	PROPN
ejpam-4646	462	10	.	.	PROPN
ejpam-4646	462	11	bounds	bound	VERB
ejpam-4646	462	12	for	for	ADP
ejpam-4646	462	13	the	the	DET
ejpam-4646	462	14	geodetic	geodetic	ADJ
ejpam-4646	462	15	number	number	NOUN
ejpam-4646	462	16	of	of	ADP
ejpam-4646	462	17	the	the	DET
ejpam-4646	462	18	cartesian	cartesian	ADJ
ejpam-4646	462	19	product	product	NOUN
ejpam-4646	462	20	of	of	ADP
ejpam-4646	462	21	graphs	graph	NOUN
ejpam-4646	462	22	.	.	PUNCT
ejpam-4646	463	1	utilitas	utilitas	PROPN
ejpam-4646	463	2	matematica	matematica	PROPN
ejpam-4646	463	3	,	,	PUNCT
ejpam-4646	463	4	79:91–98	79:91–98	NUM
ejpam-4646	463	5	,	,	PUNCT
ejpam-4646	463	6	2009	2009	NUM
ejpam-4646	463	7	.	.	PUNCT
ejpam-4646	464	1	[	[	X
ejpam-4646	464	2	7	7	X
ejpam-4646	464	3	]	]	X
ejpam-4646	464	4	g.	g.	PROPN
ejpam-4646	464	5	chartrand	chartrand	PROPN
ejpam-4646	464	6	,	,	PUNCT
ejpam-4646	464	7	f.	f.	PROPN
ejpam-4646	464	8	harary	harary	PROPN
ejpam-4646	464	9	,	,	PUNCT
ejpam-4646	464	10	and	and	CCONJ
ejpam-4646	464	11	p.	p.	PROPN
ejpam-4646	464	12	zhang	zhang	PROPN
ejpam-4646	464	13	.	.	PUNCT
ejpam-4646	465	1	the	the	DET
ejpam-4646	465	2	geodetic	geodetic	ADJ
ejpam-4646	465	3	number	number	NOUN
ejpam-4646	465	4	of	of	ADP
ejpam-4646	465	5	a	a	DET
ejpam-4646	465	6	graph	graph	NOUN
ejpam-4646	465	7	.	.	PUNCT
ejpam-4646	466	1	networks	network	NOUN
ejpam-4646	466	2	:	:	PUNCT
ejpam-4646	466	3	an	an	DET
ejpam-4646	466	4	international	international	ADJ
ejpam-4646	466	5	journal	journal	NOUN
ejpam-4646	466	6	,	,	PUNCT
ejpam-4646	466	7	39(1):1–6	39(1):1–6	NUM
ejpam-4646	466	8	,	,	PUNCT
ejpam-4646	466	9	2002	2002	NUM
ejpam-4646	466	10	.	.	PUNCT
ejpam-4646	467	1	[	[	X
ejpam-4646	467	2	8	8	NUM
ejpam-4646	467	3	]	]	X
ejpam-4646	467	4	h.	h.	NOUN
ejpam-4646	467	5	escuardo	escuardo	PROPN
ejpam-4646	467	6	,	,	PUNCT
ejpam-4646	467	7	r.	r.	PROPN
ejpam-4646	467	8	gera	gera	PROPN
ejpam-4646	467	9	,	,	PUNCT
ejpam-4646	467	10	a.	a.	NOUN
ejpam-4646	467	11	hansberg	hansberg	PROPN
ejpam-4646	467	12	,	,	PUNCT
ejpam-4646	467	13	n.	n.	PROPN
ejpam-4646	467	14	jafari	jafari	PROPN
ejpam-4646	467	15	rad	rad	PROPN
ejpam-4646	467	16	,	,	PUNCT
ejpam-4646	467	17	and	and	CCONJ
ejpam-4646	467	18	l.	l.	PROPN
ejpam-4646	467	19	volkmann	volkmann	PROPN
ejpam-4646	467	20	.	.	PUNCT
ejpam-4646	468	1	geodetic	geodetic	ADJ
ejpam-4646	468	2	domination	domination	NOUN
ejpam-4646	468	3	in	in	ADP
ejpam-4646	468	4	graphs	graph	NOUN
ejpam-4646	468	5	.	.	PUNCT
ejpam-4646	469	1	j.	j.	PROPN
ejpam-4646	469	2	combin	combin	PROPN
ejpam-4646	469	3	.	.	PUNCT
ejpam-4646	470	1	math	math	NOUN
ejpam-4646	470	2	.	.	PUNCT
ejpam-4646	471	1	combin	combin	NOUN
ejpam-4646	471	2	.	.	PUNCT
ejpam-4646	472	1	comput	comput	NOUN
ejpam-4646	472	2	.	.	PUNCT
ejpam-4646	472	3	,	,	PUNCT
ejpam-4646	473	1	77(1):89–101	77(1):89–101	NUM
ejpam-4646	473	2	,	,	PUNCT
ejpam-4646	473	3	2022	2022	NUM
ejpam-4646	473	4	.	.	PUNCT
ejpam-4646	474	1	[	[	X
ejpam-4646	474	2	9	9	NUM
ejpam-4646	474	3	]	]	PUNCT
ejpam-4646	474	4	a.	a.	NOUN
ejpam-4646	474	5	hansberg	hansberg	PROPN
ejpam-4646	474	6	and	and	CCONJ
ejpam-4646	474	7	l.	l.	PROPN
ejpam-4646	474	8	volkmann	volkmann	PROPN
ejpam-4646	474	9	.	.	PUNCT
ejpam-4646	475	1	on	on	ADP
ejpam-4646	475	2	the	the	DET
ejpam-4646	475	3	geodetic	geodetic	ADJ
ejpam-4646	475	4	and	and	CCONJ
ejpam-4646	475	5	geodetic	geodetic	ADJ
ejpam-4646	475	6	domination	domination	NOUN
ejpam-4646	475	7	numbers	number	NOUN
ejpam-4646	475	8	of	of	ADP
ejpam-4646	475	9	a	a	DET
ejpam-4646	475	10	graph	graph	NOUN
ejpam-4646	475	11	,	,	PUNCT
ejpam-4646	475	12	.	.	PUNCT
ejpam-4646	476	1	discrete	discrete	ADJ
ejpam-4646	476	2	math	math	NOUN
ejpam-4646	476	3	,	,	PUNCT
ejpam-4646	476	4	310(1):2140–2146	310(1):2140–2146	PROPN
ejpam-4646	476	5	,	,	PUNCT
ejpam-4646	476	6	2010	2010	NUM
ejpam-4646	476	7	.	.	PUNCT
ejpam-4646	477	1	[	[	X
ejpam-4646	477	2	10	10	NUM
ejpam-4646	477	3	]	]	X
ejpam-4646	477	4	f.	f.	PROPN
ejpam-4646	477	5	harary	harary	PROPN
ejpam-4646	477	6	.	.	PUNCT
ejpam-4646	478	1	the	the	DET
ejpam-4646	478	2	geodetic	geodetic	ADJ
ejpam-4646	478	3	number	number	NOUN
ejpam-4646	478	4	of	of	ADP
ejpam-4646	478	5	a	a	DET
ejpam-4646	478	6	graph	graph	NOUN
ejpam-4646	478	7	.	.	PUNCT
ejpam-4646	479	1	mathl	mathl	NOUN
ejpam-4646	479	2	.	.	PUNCT
ejpam-4646	480	1	comput	comput	NOUN
ejpam-4646	480	2	.	.	PUNCT
ejpam-4646	481	1	modelling	modelling	NOUN
ejpam-4646	481	2	,	,	PUNCT
ejpam-4646	481	3	17(11):89–95	17(11):89–95	NUM
ejpam-4646	481	4	,	,	PUNCT
ejpam-4646	481	5	1993	1993	NUM
ejpam-4646	481	6	.	.	PUNCT
ejpam-4646	482	1	[	[	X
ejpam-4646	482	2	11	11	NUM
ejpam-4646	482	3	]	]	PUNCT
ejpam-4646	482	4	j.	j.	PROPN
ejpam-4646	482	5	hassan	hassan	PROPN
ejpam-4646	482	6	and	and	CCONJ
ejpam-4646	482	7	s.	s.	PROPN
ejpam-4646	482	8	canoy	canoy	PROPN
ejpam-4646	482	9	jr	jr	PROPN
ejpam-4646	482	10	.	.	PUNCT
ejpam-4646	483	1	grundy	grundy	PROPN
ejpam-4646	483	2	hop	hop	PROPN
ejpam-4646	483	3	domination	domination	PROPN
ejpam-4646	483	4	in	in	ADP
ejpam-4646	483	5	graphs	graph	NOUN
ejpam-4646	483	6	.	.	PUNCT
ejpam-4646	484	1	european	european	ADJ
ejpam-4646	484	2	journal	journal	PROPN
ejpam-4646	484	3	of	of	ADP
ejpam-4646	484	4	pure	pure	ADJ
ejpam-4646	484	5	and	and	CCONJ
ejpam-4646	484	6	applied	applied	ADJ
ejpam-4646	484	7	mathematics	mathematic	NOUN
ejpam-4646	484	8	,	,	PUNCT
ejpam-4646	484	9	15(4):1623–1636	15(4):1623–1636	NUM
ejpam-4646	484	10	,	,	PUNCT
ejpam-4646	484	11	2022	2022	NUM
ejpam-4646	484	12	.	.	PUNCT
ejpam-4646	485	1	[	[	X
ejpam-4646	485	2	12	12	NUM
ejpam-4646	485	3	]	]	PUNCT
ejpam-4646	485	4	j.	j.	PROPN
ejpam-4646	485	5	hassan	hassan	PROPN
ejpam-4646	485	6	and	and	CCONJ
ejpam-4646	485	7	s.	s.	PROPN
ejpam-4646	485	8	canoy	canoy	PROPN
ejpam-4646	485	9	jr	jr	PROPN
ejpam-4646	485	10	.	.	PROPN
ejpam-4646	485	11	hop	hop	PROPN
ejpam-4646	485	12	independent	independent	ADJ
ejpam-4646	485	13	hop	hop	NOUN
ejpam-4646	485	14	domination	domination	NOUN
ejpam-4646	485	15	in	in	ADP
ejpam-4646	485	16	graphs	graph	NOUN
ejpam-4646	485	17	.	.	PUNCT
ejpam-4646	486	1	european	european	ADJ
ejpam-4646	486	2	journal	journal	PROPN
ejpam-4646	486	3	of	of	ADP
ejpam-4646	486	4	pure	pure	ADJ
ejpam-4646	486	5	and	and	CCONJ
ejpam-4646	486	6	applied	applied	ADJ
ejpam-4646	486	7	mathematics	mathematic	NOUN
ejpam-4646	486	8	,	,	PUNCT
ejpam-4646	486	9	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-4646	486	10	,	,	PUNCT
ejpam-4646	486	11	2022	2022	NUM
ejpam-4646	486	12	.	.	PUNCT
ejpam-4646	487	1	[	[	X
ejpam-4646	487	2	13	13	NUM
ejpam-4646	487	3	]	]	PUNCT
ejpam-4646	487	4	m.	m.	NOUN
ejpam-4646	487	5	henning	henning	PROPN
ejpam-4646	487	6	and	and	CCONJ
ejpam-4646	487	7	n.	n.	PROPN
ejpam-4646	487	8	rad	rad	PROPN
ejpam-4646	487	9	.	.	PROPN
ejpam-4646	488	1	on	on	ADP
ejpam-4646	488	2	2	2	NUM
ejpam-4646	488	3	-	-	PUNCT
ejpam-4646	488	4	step	step	NOUN
ejpam-4646	488	5	and	and	CCONJ
ejpam-4646	488	6	hop	hop	NOUN
ejpam-4646	488	7	dominating	dominating	NOUN
ejpam-4646	488	8	sets	set	NOUN
ejpam-4646	488	9	in	in	ADP
ejpam-4646	488	10	graphs	graph	NOUN
ejpam-4646	488	11	.	.	PUNCT
ejpam-4646	489	1	graphs	graph	NOUN
ejpam-4646	489	2	and	and	CCONJ
ejpam-4646	489	3	combinatorics	combinatoric	NOUN
ejpam-4646	489	4	.	.	PUNCT
ejpam-4646	489	5	,	,	PUNCT
ejpam-4646	489	6	33(4):913–927	33(4):913–927	PROPN
ejpam-4646	489	7	,	,	PUNCT
ejpam-4646	489	8	2017	2017	NUM
ejpam-4646	489	9	.	.	PUNCT
ejpam-4646	490	1	[	[	X
ejpam-4646	490	2	14	14	NUM
ejpam-4646	490	3	]	]	X
ejpam-4646	490	4	s.	s.	PROPN
ejpam-4646	490	5	canoy	canoy	PROPN
ejpam-4646	490	6	jr	jr	PROPN
ejpam-4646	490	7	.	.	PROPN
ejpam-4646	490	8	,	,	PUNCT
ejpam-4646	490	9	g.	g.	PROPN
ejpam-4646	490	10	cagaanan	cagaanan	PROPN
ejpam-4646	490	11	,	,	PUNCT
ejpam-4646	490	12	and	and	CCONJ
ejpam-4646	490	13	s.	s.	PROPN
ejpam-4646	490	14	gervacio	gervacio	PROPN
ejpam-4646	490	15	.	.	PUNCT
ejpam-4646	491	1	convexity	convexity	PROPN
ejpam-4646	491	2	,	,	PUNCT
ejpam-4646	491	3	geodetic	geodetic	ADJ
ejpam-4646	491	4	and	and	CCONJ
ejpam-4646	491	5	hull	hull	NOUN
ejpam-4646	491	6	numbers	number	NOUN
ejpam-4646	491	7	of	of	ADP
ejpam-4646	491	8	the	the	DET
ejpam-4646	491	9	join	join	NOUN
ejpam-4646	491	10	of	of	ADP
ejpam-4646	491	11	graphs	graph	NOUN
ejpam-4646	491	12	.	.	PUNCT
ejpam-4646	492	1	utilitas	utilitas	PROPN
ejpam-4646	492	2	matematica	matematica	PROPN
ejpam-4646	492	3	,	,	PUNCT
ejpam-4646	492	4	71:143–159	71:143–159	PROPN
ejpam-4646	492	5	,	,	PUNCT
ejpam-4646	492	6	2006	2006	NUM
ejpam-4646	492	7	.	.	PUNCT
ejpam-4646	493	1	[	[	X
ejpam-4646	493	2	15	15	NUM
ejpam-4646	493	3	]	]	X
ejpam-4646	493	4	s.	s.	PROPN
ejpam-4646	493	5	canoy	canoy	PROPN
ejpam-4646	493	6	jr	jr	PROPN
ejpam-4646	493	7	.	.	PROPN
ejpam-4646	493	8	,	,	PUNCT
ejpam-4646	493	9	r.	r.	PROPN
ejpam-4646	493	10	mollejon	mollejon	NOUN
ejpam-4646	493	11	,	,	PUNCT
ejpam-4646	493	12	and	and	CCONJ
ejpam-4646	493	13	j.	j.	PROPN
ejpam-4646	493	14	g.	g.	PROPN
ejpam-4646	493	15	canoy	canoy	PROPN
ejpam-4646	493	16	.	.	PUNCT
ejpam-4646	494	1	hop	hop	PROPN
ejpam-4646	494	2	dominating	dominating	NOUN
ejpam-4646	494	3	sets	set	NOUN
ejpam-4646	494	4	in	in	ADP
ejpam-4646	494	5	graphs	graph	NOUN
ejpam-4646	494	6	under	under	ADP
ejpam-4646	494	7	binary	binary	ADJ
ejpam-4646	494	8	operations	operation	NOUN
ejpam-4646	494	9	.	.	PUNCT
ejpam-4646	495	1	european	european	ADJ
ejpam-4646	495	2	journal	journal	PROPN
ejpam-4646	495	3	of	of	ADP
ejpam-4646	495	4	pure	pure	ADJ
ejpam-4646	495	5	and	and	CCONJ
ejpam-4646	495	6	applied	applied	ADJ
ejpam-4646	495	7	mathematics	mathematic	NOUN
ejpam-4646	495	8	,	,	PUNCT
ejpam-4646	495	9	12(4):1455	12(4):1455	NUM
ejpam-4646	495	10	–	–	PUNCT
ejpam-4646	495	11	1463	1463	NUM
ejpam-4646	495	12	,	,	PUNCT
ejpam-4646	495	13	2019	2019	NUM
ejpam-4646	495	14	.	.	PUNCT
ejpam-4646	496	1	references	reference	NOUN
ejpam-4646	496	2	17	17	NUM
ejpam-4646	496	3	[	[	X
ejpam-4646	496	4	16	16	NUM
ejpam-4646	496	5	]	]	X
ejpam-4646	496	6	s.	s.	PROPN
ejpam-4646	496	7	canoy	canoy	PROPN
ejpam-4646	496	8	jr	jr	PROPN
ejpam-4646	496	9	.	.	PROPN
ejpam-4646	496	10	and	and	CCONJ
ejpam-4646	496	11	g.	g.	PROPN
ejpam-4646	496	12	salasalan	salasalan	NOUN
ejpam-4646	496	13	.	.	PUNCT
ejpam-4646	497	1	global	global	ADJ
ejpam-4646	497	2	hop	hop	PROPN
ejpam-4646	497	3	domination	domination	PROPN
ejpam-4646	497	4	numbers	number	NOUN
ejpam-4646	497	5	of	of	ADP
ejpam-4646	497	6	graphs	graph	NOUN
ejpam-4646	497	7	.	.	PUNCT
ejpam-4646	498	1	european	european	ADJ
ejpam-4646	498	2	journal	journal	PROPN
ejpam-4646	498	3	of	of	ADP
ejpam-4646	498	4	pure	pure	ADJ
ejpam-4646	498	5	and	and	CCONJ
ejpam-4646	498	6	applied	applied	ADJ
ejpam-4646	498	7	mathematics	mathematic	NOUN
ejpam-4646	498	8	,	,	PUNCT
ejpam-4646	498	9	14(1):112–125	14(1):112–125	NUM
ejpam-4646	498	10	,	,	PUNCT
ejpam-4646	498	11	2021	2021	NUM
ejpam-4646	498	12	.	.	PUNCT
ejpam-4646	499	1	[	[	X
ejpam-4646	499	2	17	17	NUM
ejpam-4646	499	3	]	]	X
ejpam-4646	499	4	s.	s.	PROPN
ejpam-4646	499	5	canoy	canoy	PROPN
ejpam-4646	499	6	jr	jr	PROPN
ejpam-4646	499	7	.	.	PROPN
ejpam-4646	499	8	and	and	CCONJ
ejpam-4646	499	9	g.	g.	PROPN
ejpam-4646	499	10	salasalan	salasalan	NOUN
ejpam-4646	499	11	.	.	PUNCT
ejpam-4646	500	1	locating	locate	VERB
ejpam-4646	500	2	-	-	PUNCT
ejpam-4646	500	3	hop	hop	NOUN
ejpam-4646	500	4	domination	domination	NOUN
ejpam-4646	500	5	in	in	ADP
ejpam-4646	500	6	graphs	graph	NOUN
ejpam-4646	500	7	.	.	PUNCT
ejpam-4646	501	1	kyungpook	kyungpook	PROPN
ejpam-4646	501	2	mathematical	mathematical	PROPN
ejpam-4646	501	3	journal	journal	PROPN
ejpam-4646	501	4	,	,	PUNCT
ejpam-4646	501	5	62:193–204	62:193–204	PROPN
ejpam-4646	501	6	,	,	PUNCT
ejpam-4646	501	7	2022	2022	NUM
ejpam-4646	501	8	.	.	PUNCT
ejpam-4646	502	1	[	[	X
ejpam-4646	502	2	18	18	NUM
ejpam-4646	502	3	]	]	X
ejpam-4646	502	4	s.	s.	PROPN
ejpam-4646	502	5	canoy	canoy	PROPN
ejpam-4646	502	6	jr	jr	PROPN
ejpam-4646	502	7	.	.	PROPN
ejpam-4646	502	8	and	and	CCONJ
ejpam-4646	502	9	g.	g.	PROPN
ejpam-4646	502	10	salasalan	salasalan	NOUN
ejpam-4646	502	11	.	.	PUNCT
ejpam-4646	503	1	a	a	DET
ejpam-4646	503	2	variant	variant	NOUN
ejpam-4646	503	3	of	of	ADP
ejpam-4646	503	4	hop	hop	NOUN
ejpam-4646	503	5	domination	domination	NOUN
ejpam-4646	503	6	in	in	ADP
ejpam-4646	503	7	a	a	DET
ejpam-4646	503	8	graph	graph	NOUN
ejpam-4646	503	9	.	.	PUNCT
ejpam-4646	504	1	european	european	ADJ
ejpam-4646	504	2	journal	journal	PROPN
ejpam-4646	504	3	of	of	ADP
ejpam-4646	504	4	pure	pure	ADJ
ejpam-4646	504	5	and	and	CCONJ
ejpam-4646	504	6	applied	applied	ADJ
ejpam-4646	504	7	mathematics	mathematic	NOUN
ejpam-4646	504	8	,	,	PUNCT
ejpam-4646	504	9	15(2):342–353	15(2):342–353	NUM
ejpam-4646	504	10	,	,	PUNCT
ejpam-4646	504	11	2022	2022	NUM
ejpam-4646	504	12	.	.	PUNCT
ejpam-4646	505	1	[	[	X
ejpam-4646	505	2	19	19	NUM
ejpam-4646	505	3	]	]	X
ejpam-4646	505	4	c.	c.	PROPN
ejpam-4646	505	5	natarajan	natarajan	PROPN
ejpam-4646	505	6	and	and	CCONJ
ejpam-4646	505	7	s.	s.	PROPN
ejpam-4646	505	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4646	505	9	.	.	PUNCT
ejpam-4646	506	1	hop	hop	PROPN
ejpam-4646	506	2	domination	domination	NOUN
ejpam-4646	506	3	in	in	ADP
ejpam-4646	506	4	graphs	graphs	PROPN
ejpam-4646	506	5	ii	ii	PROPN
ejpam-4646	506	6	.	.	PUNCT
ejpam-4646	506	7	versita	versita	PROPN
ejpam-4646	506	8	,	,	PUNCT
ejpam-4646	506	9	23(2):187	23(2):187	NUM
ejpam-4646	506	10	–	–	PUNCT
ejpam-4646	506	11	199	199	NUM
ejpam-4646	506	12	,	,	PUNCT
ejpam-4646	506	13	2015	2015	NUM
ejpam-4646	506	14	.	.	PUNCT
ejpam-4646	507	1	[	[	X
ejpam-4646	507	2	20	20	NUM
ejpam-4646	507	3	]	]	PUNCT
ejpam-4646	507	4	r.	r.	PROPN
ejpam-4646	507	5	rakim	rakim	PROPN
ejpam-4646	507	6	and	and	CCONJ
ejpam-4646	507	7	h.	h.	PROPN
ejpam-4646	507	8	rara	rara	PROPN
ejpam-4646	507	9	.	.	PUNCT
ejpam-4646	508	1	total	total	ADJ
ejpam-4646	508	2	perfect	perfect	ADJ
ejpam-4646	508	3	hop	hop	NOUN
ejpam-4646	508	4	domination	domination	NOUN
ejpam-4646	508	5	in	in	ADP
ejpam-4646	508	6	graphs	graph	NOUN
ejpam-4646	508	7	under	under	ADP
ejpam-4646	508	8	some	some	DET
ejpam-4646	508	9	binary	binary	ADJ
ejpam-4646	508	10	operations	operation	NOUN
ejpam-4646	508	11	.	.	PUNCT
ejpam-4646	509	1	european	european	ADJ
ejpam-4646	509	2	journal	journal	PROPN
ejpam-4646	509	3	of	of	ADP
ejpam-4646	509	4	pure	pure	ADJ
ejpam-4646	509	5	and	and	CCONJ
ejpam-4646	509	6	applied	applied	ADJ
ejpam-4646	509	7	mathematics	mathematic	NOUN
ejpam-4646	509	8	,	,	PUNCT
ejpam-4646	509	9	14(3):803–815	14(3):803–815	PROPN
ejpam-4646	509	10	,	,	PUNCT
ejpam-4646	509	11	2021	2021	NUM
ejpam-4646	509	12	.	.	PUNCT
ejpam-4646	510	1	[	[	X
ejpam-4646	510	2	21	21	NUM
ejpam-4646	510	3	]	]	X
ejpam-4646	510	4	r.	r.	PROPN
ejpam-4646	510	5	rakim	rakim	PROPN
ejpam-4646	510	6	,	,	PUNCT
ejpam-4646	510	7	h.	h.	PROPN
ejpam-4646	510	8	rara	rara	PROPN
ejpam-4646	510	9	,	,	PUNCT
ejpam-4646	510	10	and	and	CCONJ
ejpam-4646	510	11	c.j	c.j	PROPN
ejpam-4646	510	12	.	.	PROPN
ejpam-4646	510	13	saromines	saromine	NOUN
ejpam-4646	510	14	.	.	PUNCT
ejpam-4646	511	1	perfect	perfect	ADJ
ejpam-4646	511	2	hop	hop	NOUN
ejpam-4646	511	3	domination	domination	NOUN
ejpam-4646	511	4	in	in	ADP
ejpam-4646	511	5	graphs	graph	NOUN
ejpam-4646	511	6	.	.	PUNCT
ejpam-4646	512	1	applied	apply	VERB
ejpam-4646	512	2	mathematical	mathematical	ADJ
ejpam-4646	512	3	sciences	sciences	PROPN
ejpam-4646	512	4	,	,	PUNCT
ejpam-4646	512	5	12(13):635–649	12(13):635–649	NUM
ejpam-4646	512	6	,	,	PUNCT
ejpam-4646	512	7	2018	2018	NUM
ejpam-4646	512	8	.	.	PUNCT
ejpam-4646	513	1	[	[	X
ejpam-4646	513	2	22	22	NUM
ejpam-4646	513	3	]	]	X
ejpam-4646	513	4	g.	g.	NOUN
ejpam-4646	513	5	salasalan	salasalan	NOUN
ejpam-4646	513	6	and	and	CCONJ
ejpam-4646	513	7	s.	s.	PROPN
ejpam-4646	513	8	canoy	canoy	PROPN
ejpam-4646	513	9	jr	jr	PROPN
ejpam-4646	513	10	.	.	PUNCT
ejpam-4646	513	11	revisiting	revisit	VERB
ejpam-4646	513	12	domination	domination	NOUN
ejpam-4646	513	13	,	,	PUNCT
ejpam-4646	513	14	hop	hop	NOUN
ejpam-4646	513	15	domination	domination	NOUN
ejpam-4646	513	16	,	,	PUNCT
ejpam-4646	513	17	and	and	CCONJ
ejpam-4646	513	18	global	global	ADJ
ejpam-4646	513	19	hop	hop	NOUN
ejpam-4646	513	20	domination	domination	NOUN
ejpam-4646	513	21	in	in	ADP
ejpam-4646	513	22	graphs	graph	NOUN
ejpam-4646	513	23	.	.	PUNCT
ejpam-4646	514	1	european	european	ADJ
ejpam-4646	514	2	journal	journal	PROPN
ejpam-4646	514	3	of	of	ADP
ejpam-4646	514	4	pure	pure	ADJ
ejpam-4646	514	5	and	and	CCONJ
ejpam-4646	514	6	applied	applied	ADJ
ejpam-4646	514	7	mathematics	mathematic	NOUN
ejpam-4646	514	8	,	,	PUNCT
ejpam-4646	514	9	14(4):1415–1428	14(4):1415–1428	NUM
ejpam-4646	514	10	,	,	PUNCT
ejpam-4646	514	11	2021	2021	NUM
ejpam-4646	514	12	.	.	PUNCT
ejpam-4646	515	1	[	[	X
ejpam-4646	515	2	23	23	NUM
ejpam-4646	515	3	]	]	X
ejpam-4646	515	4	c.	c.	PROPN
ejpam-4646	515	5	j.	j.	PROPN
ejpam-4646	515	6	saromines	saromines	PROPN
ejpam-4646	515	7	and	and	CCONJ
ejpam-4646	515	8	s.	s.	PROPN
ejpam-4646	515	9	canoy	canoy	PROPN
ejpam-4646	515	10	jr	jr	PROPN
ejpam-4646	515	11	.	.	PUNCT
ejpam-4646	515	12	outer	outer	ADV
ejpam-4646	515	13	-	-	PUNCT
ejpam-4646	515	14	connected	connect	VERB
ejpam-4646	515	15	hop	hop	NOUN
ejpam-4646	515	16	dominating	dominating	NOUN
ejpam-4646	515	17	sets	set	NOUN
ejpam-4646	515	18	in	in	ADP
ejpam-4646	515	19	graphs	graph	NOUN
ejpam-4646	515	20	.	.	PUNCT
ejpam-4646	516	1	european	european	ADJ
ejpam-4646	516	2	journal	journal	PROPN
ejpam-4646	516	3	of	of	ADP
ejpam-4646	516	4	pure	pure	ADJ
ejpam-4646	516	5	and	and	CCONJ
ejpam-4646	516	6	applied	applied	ADJ
ejpam-4646	516	7	mathematics	mathematic	NOUN
ejpam-4646	516	8	,	,	PUNCT
ejpam-4646	516	9	15(4):1966–1981	15(4):1966–1981	NUM
ejpam-4646	516	10	,	,	PUNCT
ejpam-4646	516	11	2022	2022	NUM
ejpam-4646	516	12	.	.	PUNCT
ejpam-4646	517	1	[	[	X
ejpam-4646	517	2	24	24	NUM
ejpam-4646	517	3	]	]	PUNCT
ejpam-4646	517	4	t.	t.	NOUN
ejpam-4646	517	5	tacbobo	tacbobo	NOUN
ejpam-4646	517	6	,	,	PUNCT
ejpam-4646	517	7	f.	f.	PROPN
ejpam-4646	517	8	jamil	jamil	PROPN
ejpam-4646	517	9	,	,	PUNCT
ejpam-4646	517	10	and	and	CCONJ
ejpam-4646	517	11	s.	s.	PROPN
ejpam-4646	517	12	canoy	canoy	PROPN
ejpam-4646	517	13	jr	jr	PROPN
ejpam-4646	517	14	.	.	PROPN
ejpam-4646	517	15	monophonic	monophonic	ADJ
ejpam-4646	517	16	and	and	CCONJ
ejpam-4646	517	17	geodetic	geodetic	ADJ
ejpam-4646	517	18	domination	domination	NOUN
ejpam-4646	517	19	in	in	ADP
ejpam-4646	517	20	the	the	DET
ejpam-4646	517	21	join	join	NOUN
ejpam-4646	517	22	,	,	PUNCT
ejpam-4646	517	23	corona	corona	NOUN
ejpam-4646	517	24	and	and	CCONJ
ejpam-4646	517	25	composition	composition	NOUN
ejpam-4646	517	26	of	of	ADP
ejpam-4646	517	27	graphs	graph	NOUN
ejpam-4646	517	28	.	.	PUNCT
ejpam-4646	518	1	ars	ars	PROPN
ejpam-4646	518	2	combin	combin	PROPN
ejpam-4646	518	3	,	,	PUNCT
ejpam-4646	518	4	112(1):13–32	112(1):13–32	NUM
ejpam-4646	518	5	,	,	PUNCT
ejpam-4646	518	6	2013	2013	NUM
ejpam-4646	518	7	.	.	PUNCT