id	sid	tid	token	lemma	pos
ejpam-5241	1	1	european	european	PROPN
ejpam-5241	1	2	journal	journal	PROPN
ejpam-5241	1	3	of	of	ADP
ejpam-5241	1	4	pure	pure	ADJ
ejpam-5241	1	5	and	and	CCONJ
ejpam-5241	1	6	applied	apply	VERB
ejpam-5241	1	7	mathematics	mathematic	NOUN
ejpam-5241	1	8	vol	vol	NOUN
ejpam-5241	1	9	.	.	PROPN
ejpam-5241	2	1	17	17	NUM
ejpam-5241	2	2	,	,	PUNCT
ejpam-5241	2	3	no	no	INTJ
ejpam-5241	2	4	.	.	NOUN
ejpam-5241	2	5	3	3	NUM
ejpam-5241	2	6	,	,	PUNCT
ejpam-5241	2	7	2024	2024	NUM
ejpam-5241	2	8	,	,	PUNCT
ejpam-5241	2	9	1618	1618	NUM
ejpam-5241	2	10	-	-	SYM
ejpam-5241	2	11	1636	1636	NUM
ejpam-5241	2	12	issn	issn	PROPN
ejpam-5241	2	13	1307	1307	NUM
ejpam-5241	2	14	-	-	SYM
ejpam-5241	2	15	5543	5543	NUM
ejpam-5241	2	16	–	–	PUNCT
ejpam-5241	3	1	ejpam.com	ejpam.com	X
ejpam-5241	3	2	published	publish	VERB
ejpam-5241	3	3	by	by	ADP
ejpam-5241	3	4	new	new	PROPN
ejpam-5241	3	5	york	york	PROPN
ejpam-5241	3	6	business	business	PROPN
ejpam-5241	3	7	global	global	PROPN
ejpam-5241	3	8	closed	close	VERB
ejpam-5241	3	9	geodetic	geodetic	ADJ
ejpam-5241	3	10	hop	hop	NOUN
ejpam-5241	3	11	domination	domination	NOUN
ejpam-5241	3	12	in	in	ADP
ejpam-5241	3	13	graphs	graph	NOUN
ejpam-5241	3	14	niña	niña	ADJ
ejpam-5241	3	15	jeane	jeane	PROPN
ejpam-5241	3	16	a.	a.	PROPN
ejpam-5241	3	17	adolfo1,2,∗	adolfo1,2,∗	PROPN
ejpam-5241	3	18	,	,	PUNCT
ejpam-5241	3	19	imelda	imelda	PROPN
ejpam-5241	3	20	s.	s.	PROPN
ejpam-5241	3	21	aniversario1,2	aniversario1,2	PROPN
ejpam-5241	3	22	,	,	PUNCT
ejpam-5241	3	23	ferdinand	ferdinand	PROPN
ejpam-5241	4	1	p.	p.	PROPN
ejpam-5241	5	1	jamil1,2	jamil1,2	PROPN
ejpam-5241	5	2	1	1	NUM
ejpam-5241	5	3	department	department	NOUN
ejpam-5241	5	4	of	of	ADP
ejpam-5241	5	5	mathematics	mathematic	NOUN
ejpam-5241	5	6	and	and	CCONJ
ejpam-5241	5	7	statistics	statistic	NOUN
ejpam-5241	5	8	,	,	PUNCT
ejpam-5241	5	9	college	college	NOUN
ejpam-5241	5	10	of	of	ADP
ejpam-5241	5	11	science	science	NOUN
ejpam-5241	5	12	and	and	CCONJ
ejpam-5241	5	13	mathematics	mathematics	PROPN
ejpam-5241	5	14	2	2	NUM
ejpam-5241	5	15	center	center	NOUN
ejpam-5241	5	16	for	for	ADP
ejpam-5241	5	17	mathematical	mathematical	ADJ
ejpam-5241	5	18	and	and	CCONJ
ejpam-5241	5	19	theoretical	theoretical	ADJ
ejpam-5241	5	20	physical	physical	ADJ
ejpam-5241	5	21	sciences	science	NOUN
ejpam-5241	5	22	,	,	PUNCT
ejpam-5241	5	23	premier	premier	PROPN
ejpam-5241	5	24	research	research	PROPN
ejpam-5241	5	25	institute	institute	PROPN
ejpam-5241	5	26	of	of	ADP
ejpam-5241	5	27	science	science	PROPN
ejpam-5241	5	28	and	and	CCONJ
ejpam-5241	5	29	mathematics	mathematic	NOUN
ejpam-5241	5	30	msu	msu	PROPN
ejpam-5241	5	31	-	-	PUNCT
ejpam-5241	5	32	iligan	iligan	PROPN
ejpam-5241	5	33	institute	institute	PROPN
ejpam-5241	5	34	of	of	ADP
ejpam-5241	5	35	technology	technology	PROPN
ejpam-5241	5	36	,	,	PUNCT
ejpam-5241	5	37	9200	9200	NUM
ejpam-5241	5	38	iligan	iligan	ADJ
ejpam-5241	5	39	city	city	NOUN
ejpam-5241	5	40	,	,	PUNCT
ejpam-5241	5	41	philippines	philippine	NOUN
ejpam-5241	5	42	abstract	abstract	ADJ
ejpam-5241	5	43	.	.	PUNCT
ejpam-5241	6	1	let	let	VERB
ejpam-5241	6	2	g	g	PRON
ejpam-5241	6	3	be	be	AUX
ejpam-5241	6	4	a	a	DET
ejpam-5241	6	5	simple	simple	ADJ
ejpam-5241	6	6	,	,	PUNCT
ejpam-5241	6	7	undirected	undirected	ADJ
ejpam-5241	6	8	and	and	CCONJ
ejpam-5241	6	9	connected	connected	ADJ
ejpam-5241	6	10	graph	graph	NOUN
ejpam-5241	6	11	.	.	PUNCT
ejpam-5241	7	1	a	a	DET
ejpam-5241	7	2	subset	subset	NOUN
ejpam-5241	7	3	s	s	VERB
ejpam-5241	7	4	⊆	⊆	NUM
ejpam-5241	7	5	v	v	NOUN
ejpam-5241	7	6	(	(	PUNCT
ejpam-5241	7	7	g	g	NOUN
ejpam-5241	7	8	)	)	PUNCT
ejpam-5241	7	9	is	be	AUX
ejpam-5241	7	10	a	a	DET
ejpam-5241	7	11	geodetic	geodetic	ADJ
ejpam-5241	7	12	cover	cover	NOUN
ejpam-5241	7	13	of	of	ADP
ejpam-5241	7	14	g	g	PROPN
ejpam-5241	7	15	if	if	SCONJ
ejpam-5241	7	16	ig[s	ig[	NOUN
ejpam-5241	7	17	]	]	X
ejpam-5241	7	18	=	=	SYM
ejpam-5241	7	19	v	v	X
ejpam-5241	7	20	(	(	PUNCT
ejpam-5241	7	21	g	g	NOUN
ejpam-5241	7	22	)	)	PUNCT
ejpam-5241	7	23	,	,	PUNCT
ejpam-5241	7	24	where	where	SCONJ
ejpam-5241	7	25	ig[s	ig[s	PROPN
ejpam-5241	7	26	]	]	PUNCT
ejpam-5241	7	27	is	be	AUX
ejpam-5241	7	28	the	the	DET
ejpam-5241	7	29	set	set	NOUN
ejpam-5241	7	30	of	of	ADP
ejpam-5241	7	31	all	all	DET
ejpam-5241	7	32	vertices	vertex	NOUN
ejpam-5241	7	33	of	of	ADP
ejpam-5241	7	34	g	g	NOUN
ejpam-5241	7	35	lying	lie	VERB
ejpam-5241	7	36	on	on	ADP
ejpam-5241	7	37	any	any	DET
ejpam-5241	7	38	geodesic	geodesic	NOUN
ejpam-5241	7	39	between	between	ADP
ejpam-5241	7	40	two	two	NUM
ejpam-5241	7	41	vertices	vertex	NOUN
ejpam-5241	7	42	in	in	ADP
ejpam-5241	7	43	s.	s.	PROPN
ejpam-5241	7	44	a	a	DET
ejpam-5241	7	45	geodetic	geodetic	ADJ
ejpam-5241	7	46	cover	cover	NOUN
ejpam-5241	7	47	s	s	NOUN
ejpam-5241	7	48	of	of	ADP
ejpam-5241	7	49	g	g	PROPN
ejpam-5241	7	50	is	be	AUX
ejpam-5241	7	51	a	a	DET
ejpam-5241	7	52	closed	closed	ADJ
ejpam-5241	7	53	geodetic	geodetic	ADJ
ejpam-5241	7	54	cover	cover	NOUN
ejpam-5241	7	55	if	if	SCONJ
ejpam-5241	7	56	the	the	DET
ejpam-5241	7	57	vertices	vertex	NOUN
ejpam-5241	7	58	in	in	ADP
ejpam-5241	7	59	s	s	NOUN
ejpam-5241	7	60	are	be	AUX
ejpam-5241	7	61	sequentially	sequentially	ADV
ejpam-5241	7	62	selected	select	VERB
ejpam-5241	7	63	as	as	SCONJ
ejpam-5241	7	64	follows	follow	VERB
ejpam-5241	7	65	:	:	PUNCT
ejpam-5241	7	66	select	select	VERB
ejpam-5241	7	67	a	a	DET
ejpam-5241	7	68	vertex	vertex	NOUN
ejpam-5241	7	69	v1	v1	NOUN
ejpam-5241	7	70	and	and	CCONJ
ejpam-5241	7	71	let	let	VERB
ejpam-5241	7	72	s1	s1	PROPN
ejpam-5241	7	73	=	=	SYM
ejpam-5241	7	74	{	{	PUNCT
ejpam-5241	7	75	v1	v1	NOUN
ejpam-5241	7	76	}	}	PUNCT
ejpam-5241	7	77	.	.	PUNCT
ejpam-5241	8	1	if	if	SCONJ
ejpam-5241	8	2	g	g	PROPN
ejpam-5241	8	3	is	be	AUX
ejpam-5241	8	4	nontrivial	nontrivial	ADJ
ejpam-5241	8	5	,	,	PUNCT
ejpam-5241	8	6	select	select	VERB
ejpam-5241	8	7	a	a	DET
ejpam-5241	8	8	vertex	vertex	NOUN
ejpam-5241	8	9	v2	v2	NOUN
ejpam-5241	8	10	̸=	̸=	PROPN
ejpam-5241	8	11	v1	v1	NOUN
ejpam-5241	8	12	and	and	CCONJ
ejpam-5241	8	13	let	let	VERB
ejpam-5241	8	14	s2	s2	VERB
ejpam-5241	8	15	=	=	SYM
ejpam-5241	8	16	{	{	PUNCT
ejpam-5241	8	17	v1	v1	PROPN
ejpam-5241	8	18	,	,	PUNCT
ejpam-5241	8	19	v2	v2	PROPN
ejpam-5241	8	20	}	}	PUNCT
ejpam-5241	8	21	.	.	PUNCT
ejpam-5241	9	1	where	where	SCONJ
ejpam-5241	9	2	possible	possible	ADJ
ejpam-5241	9	3	,	,	PUNCT
ejpam-5241	9	4	for	for	ADP
ejpam-5241	9	5	i	i	PRON
ejpam-5241	9	6	≥	≥	NOUN
ejpam-5241	9	7	3	3	NUM
ejpam-5241	9	8	,	,	PUNCT
ejpam-5241	9	9	successively	successively	ADV
ejpam-5241	9	10	select	select	VERB
ejpam-5241	9	11	vertex	vertex	NOUN
ejpam-5241	9	12	vi	vi	PROPN
ejpam-5241	9	13	/∈	/∈	NOUN
ejpam-5241	9	14	ig[si−1	ig[si−1	PROPN
ejpam-5241	9	15	]	]	PUNCT
ejpam-5241	9	16	and	and	CCONJ
ejpam-5241	9	17	let	let	VERB
ejpam-5241	9	18	si	si	X
ejpam-5241	9	19	=	=	ADJ
ejpam-5241	9	20	{	{	PUNCT
ejpam-5241	9	21	v1	v1	PROPN
ejpam-5241	9	22	,	,	PUNCT
ejpam-5241	9	23	v2	v2	PROPN
ejpam-5241	9	24	,	,	PUNCT
ejpam-5241	9	25	...	...	PUNCT
ejpam-5241	9	26	,	,	PUNCT
ejpam-5241	9	27	vi	vi	ADJ
ejpam-5241	9	28	}	}	PUNCT
ejpam-5241	9	29	.	.	PUNCT
ejpam-5241	10	1	then	then	ADV
ejpam-5241	10	2	there	there	PRON
ejpam-5241	10	3	exists	exist	VERB
ejpam-5241	10	4	a	a	DET
ejpam-5241	10	5	positive	positive	ADJ
ejpam-5241	10	6	integer	integer	NOUN
ejpam-5241	10	7	k	k	PROPN
ejpam-5241	10	8	such	such	ADJ
ejpam-5241	10	9	that	that	SCONJ
ejpam-5241	10	10	sk	sk	PROPN
ejpam-5241	10	11	=	=	PUNCT
ejpam-5241	10	12	s.	s.	PROPN
ejpam-5241	10	13	a	a	DET
ejpam-5241	10	14	geodetic	geodetic	ADJ
ejpam-5241	10	15	cover	cover	NOUN
ejpam-5241	10	16	s	s	NOUN
ejpam-5241	10	17	of	of	ADP
ejpam-5241	10	18	g	g	PROPN
ejpam-5241	10	19	is	be	AUX
ejpam-5241	10	20	a	a	DET
ejpam-5241	10	21	geodetic	geodetic	ADJ
ejpam-5241	10	22	hop	hop	NOUN
ejpam-5241	10	23	dominating	dominating	NOUN
ejpam-5241	10	24	set	set	NOUN
ejpam-5241	10	25	if	if	SCONJ
ejpam-5241	10	26	every	every	DET
ejpam-5241	10	27	vertex	vertex	NOUN
ejpam-5241	10	28	in	in	ADP
ejpam-5241	10	29	v	v	NOUN
ejpam-5241	10	30	(	(	PUNCT
ejpam-5241	10	31	g	g	NOUN
ejpam-5241	10	32	)	)	PUNCT
ejpam-5241	10	33	\s	\s	NOUN
ejpam-5241	10	34	is	be	AUX
ejpam-5241	10	35	of	of	ADP
ejpam-5241	10	36	distance	distance	NOUN
ejpam-5241	10	37	2	2	NUM
ejpam-5241	10	38	from	from	ADP
ejpam-5241	10	39	a	a	DET
ejpam-5241	10	40	vertex	vertex	NOUN
ejpam-5241	10	41	in	in	ADP
ejpam-5241	10	42	s.	s.	PROPN
ejpam-5241	10	43	a	a	DET
ejpam-5241	10	44	geodetic	geodetic	ADJ
ejpam-5241	10	45	hop	hop	NOUN
ejpam-5241	10	46	dominating	dominating	NOUN
ejpam-5241	10	47	set	set	NOUN
ejpam-5241	10	48	s	s	VERB
ejpam-5241	10	49	is	be	AUX
ejpam-5241	10	50	a	a	DET
ejpam-5241	10	51	closed	closed	ADJ
ejpam-5241	10	52	geodetic	geodetic	ADJ
ejpam-5241	10	53	hop	hop	NOUN
ejpam-5241	10	54	dominating	dominating	NOUN
ejpam-5241	10	55	set	set	NOUN
ejpam-5241	10	56	if	if	SCONJ
ejpam-5241	10	57	s	s	NOUN
ejpam-5241	10	58	is	be	AUX
ejpam-5241	10	59	a	a	DET
ejpam-5241	10	60	closed	closed	ADJ
ejpam-5241	10	61	geodetic	geodetic	ADJ
ejpam-5241	10	62	cover	cover	NOUN
ejpam-5241	10	63	of	of	ADP
ejpam-5241	10	64	g.	g.	PROPN
ejpam-5241	10	65	the	the	DET
ejpam-5241	10	66	minimum	minimum	ADJ
ejpam-5241	10	67	cardinality	cardinality	NOUN
ejpam-5241	10	68	of	of	ADP
ejpam-5241	10	69	a	a	DET
ejpam-5241	10	70	(	(	PUNCT
ejpam-5241	10	71	closed	closed	ADJ
ejpam-5241	10	72	)	)	PUNCT
ejpam-5241	10	73	geodetic	geodetic	ADJ
ejpam-5241	10	74	hop	hop	NOUN
ejpam-5241	10	75	dominating	dominating	NOUN
ejpam-5241	10	76	set	set	NOUN
ejpam-5241	10	77	of	of	ADP
ejpam-5241	10	78	g	g	PROPN
ejpam-5241	10	79	is	be	AUX
ejpam-5241	10	80	the	the	DET
ejpam-5241	10	81	(	(	PUNCT
ejpam-5241	10	82	closed	closed	ADJ
ejpam-5241	10	83	)	)	PUNCT
ejpam-5241	10	84	geodetic	geodetic	ADJ
ejpam-5241	10	85	hop	hop	NOUN
ejpam-5241	10	86	domination	domination	NOUN
ejpam-5241	10	87	number	number	NOUN
ejpam-5241	10	88	of	of	ADP
ejpam-5241	10	89	g.	g.	PROPN
ejpam-5241	10	90	this	this	DET
ejpam-5241	10	91	study	study	NOUN
ejpam-5241	10	92	initiates	initiate	VERB
ejpam-5241	10	93	the	the	DET
ejpam-5241	10	94	study	study	NOUN
ejpam-5241	10	95	of	of	ADP
ejpam-5241	10	96	the	the	DET
ejpam-5241	10	97	closed	closed	ADJ
ejpam-5241	10	98	geodetic	geodetic	ADJ
ejpam-5241	10	99	hop	hop	NOUN
ejpam-5241	10	100	domination	domination	NOUN
ejpam-5241	10	101	.	.	PUNCT
ejpam-5241	11	1	first	first	ADV
ejpam-5241	11	2	,	,	PUNCT
ejpam-5241	11	3	it	it	PRON
ejpam-5241	11	4	characterizes	characterize	VERB
ejpam-5241	11	5	all	all	DET
ejpam-5241	11	6	graphs	graph	NOUN
ejpam-5241	11	7	g	g	ADP
ejpam-5241	11	8	of	of	ADP
ejpam-5241	11	9	order	order	NOUN
ejpam-5241	11	10	n	n	CCONJ
ejpam-5241	11	11	whose	whose	DET
ejpam-5241	11	12	closed	close	VERB
ejpam-5241	11	13	geodetic	geodetic	ADJ
ejpam-5241	11	14	hop	hop	NOUN
ejpam-5241	11	15	domination	domination	NOUN
ejpam-5241	11	16	numbers	number	NOUN
ejpam-5241	11	17	are	be	AUX
ejpam-5241	11	18	2	2	NUM
ejpam-5241	11	19	or	or	CCONJ
ejpam-5241	11	20	n	n	CCONJ
ejpam-5241	11	21	,	,	PUNCT
ejpam-5241	11	22	and	and	CCONJ
ejpam-5241	11	23	determines	determine	VERB
ejpam-5241	11	24	the	the	DET
ejpam-5241	11	25	closed	closed	ADJ
ejpam-5241	11	26	geodetic	geodetic	ADJ
ejpam-5241	11	27	hop	hop	NOUN
ejpam-5241	11	28	domination	domination	NOUN
ejpam-5241	11	29	number	number	NOUN
ejpam-5241	11	30	of	of	ADP
ejpam-5241	11	31	paths	path	NOUN
ejpam-5241	11	32	,	,	PUNCT
ejpam-5241	11	33	cycles	cycle	NOUN
ejpam-5241	11	34	and	and	CCONJ
ejpam-5241	11	35	multigraphs	multigraph	NOUN
ejpam-5241	11	36	.	.	PUNCT
ejpam-5241	12	1	next	next	ADV
ejpam-5241	12	2	,	,	PUNCT
ejpam-5241	12	3	it	it	PRON
ejpam-5241	12	4	shows	show	VERB
ejpam-5241	12	5	that	that	SCONJ
ejpam-5241	12	6	any	any	DET
ejpam-5241	12	7	positive	positive	ADJ
ejpam-5241	12	8	integers	integer	NOUN
ejpam-5241	12	9	a	a	PRON
ejpam-5241	12	10	and	and	CCONJ
ejpam-5241	12	11	b	b	NOUN
ejpam-5241	12	12	with	with	ADP
ejpam-5241	12	13	2	2	NUM
ejpam-5241	12	14	≤	≤	NOUN
ejpam-5241	12	15	a	a	DET
ejpam-5241	12	16	≤	≤	NUM
ejpam-5241	12	17	b	b	NOUN
ejpam-5241	12	18	are	be	AUX
ejpam-5241	12	19	realizable	realizable	ADJ
ejpam-5241	12	20	as	as	ADP
ejpam-5241	12	21	the	the	DET
ejpam-5241	12	22	closed	closed	ADJ
ejpam-5241	12	23	geodetic	geodetic	ADJ
ejpam-5241	12	24	number	number	NOUN
ejpam-5241	12	25	and	and	CCONJ
ejpam-5241	12	26	closed	close	VERB
ejpam-5241	12	27	geodetic	geodetic	ADJ
ejpam-5241	12	28	hop	hop	NOUN
ejpam-5241	12	29	domination	domination	NOUN
ejpam-5241	12	30	number	number	NOUN
ejpam-5241	12	31	of	of	ADP
ejpam-5241	12	32	a	a	DET
ejpam-5241	12	33	connected	connected	ADJ
ejpam-5241	12	34	graph	graph	NOUN
ejpam-5241	12	35	.	.	PUNCT
ejpam-5241	13	1	also	also	ADV
ejpam-5241	13	2	,	,	PUNCT
ejpam-5241	13	3	every	every	DET
ejpam-5241	13	4	positive	positive	ADJ
ejpam-5241	13	5	integer	integer	NOUN
ejpam-5241	13	6	n	n	CCONJ
ejpam-5241	13	7	,	,	PUNCT
ejpam-5241	13	8	m	m	PROPN
ejpam-5241	13	9	and	and	CCONJ
ejpam-5241	13	10	k	k	X
ejpam-5241	13	11	with	with	ADP
ejpam-5241	13	12	4	4	NUM
ejpam-5241	13	13	≤	≤	NUM
ejpam-5241	13	14	m	m	VERB
ejpam-5241	13	15	≤	≤	NOUN
ejpam-5241	13	16	k	k	NOUN
ejpam-5241	13	17	and	and	CCONJ
ejpam-5241	13	18	2k−m+2	2k−m+2	NUM
ejpam-5241	13	19	≤	≤	NOUN
ejpam-5241	13	20	n	n	CCONJ
ejpam-5241	13	21	are	be	AUX
ejpam-5241	13	22	realizable	realizable	ADJ
ejpam-5241	13	23	as	as	ADP
ejpam-5241	13	24	the	the	DET
ejpam-5241	13	25	order	order	NOUN
ejpam-5241	13	26	,	,	PUNCT
ejpam-5241	13	27	geodetic	geodetic	ADJ
ejpam-5241	13	28	hop	hop	NOUN
ejpam-5241	13	29	domination	domination	NOUN
ejpam-5241	13	30	number	number	NOUN
ejpam-5241	13	31	and	and	CCONJ
ejpam-5241	13	32	closed	close	VERB
ejpam-5241	13	33	geodetic	geodetic	ADJ
ejpam-5241	13	34	hop	hop	NOUN
ejpam-5241	13	35	domination	domination	NOUN
ejpam-5241	13	36	number	number	NOUN
ejpam-5241	13	37	,	,	PUNCT
ejpam-5241	13	38	respectively	respectively	ADV
ejpam-5241	13	39	of	of	ADP
ejpam-5241	13	40	a	a	DET
ejpam-5241	13	41	connected	connected	ADJ
ejpam-5241	13	42	graph	graph	NOUN
ejpam-5241	13	43	.	.	PUNCT
ejpam-5241	14	1	furthermore	furthermore	ADV
ejpam-5241	14	2	,	,	PUNCT
ejpam-5241	14	3	the	the	DET
ejpam-5241	14	4	study	study	NOUN
ejpam-5241	14	5	characterizes	characterize	VERB
ejpam-5241	14	6	the	the	DET
ejpam-5241	14	7	closed	closed	ADJ
ejpam-5241	14	8	geodetic	geodetic	ADJ
ejpam-5241	14	9	hop	hop	NOUN
ejpam-5241	14	10	dominating	dominating	NOUN
ejpam-5241	14	11	sets	set	NOUN
ejpam-5241	14	12	of	of	ADP
ejpam-5241	14	13	graphs	graph	NOUN
ejpam-5241	14	14	resulting	result	VERB
ejpam-5241	14	15	from	from	ADP
ejpam-5241	14	16	the	the	DET
ejpam-5241	14	17	join	join	NOUN
ejpam-5241	14	18	,	,	PUNCT
ejpam-5241	14	19	corona	corona	NOUN
ejpam-5241	14	20	and	and	CCONJ
ejpam-5241	14	21	edge	edge	NOUN
ejpam-5241	14	22	corona	corona	NOUN
ejpam-5241	14	23	of	of	ADP
ejpam-5241	14	24	graphs	graph	NOUN
ejpam-5241	14	25	.	.	PUNCT
ejpam-5241	15	1	2020	2020	NUM
ejpam-5241	15	2	mathematics	mathematic	NOUN
ejpam-5241	15	3	subject	subject	NOUN
ejpam-5241	15	4	classifications	classification	NOUN
ejpam-5241	15	5	:	:	PUNCT
ejpam-5241	15	6	05c69	05c69	X
ejpam-5241	15	7	key	key	ADJ
ejpam-5241	15	8	words	word	NOUN
ejpam-5241	15	9	and	and	CCONJ
ejpam-5241	15	10	phrases	phrase	NOUN
ejpam-5241	15	11	:	:	PUNCT
ejpam-5241	15	12	closed	close	VERB
ejpam-5241	15	13	geodetic	geodetic	ADJ
ejpam-5241	15	14	cover	cover	NOUN
ejpam-5241	15	15	,	,	PUNCT
ejpam-5241	15	16	hop	hop	NOUN
ejpam-5241	15	17	dominating	dominating	NOUN
ejpam-5241	15	18	set	set	NOUN
ejpam-5241	15	19	,	,	PUNCT
ejpam-5241	15	20	geodetic	geodetic	ADJ
ejpam-5241	15	21	hop	hop	NOUN
ejpam-5241	15	22	dominating	dominating	NOUN
ejpam-5241	15	23	set	set	NOUN
ejpam-5241	15	24	,	,	PUNCT
ejpam-5241	15	25	closed	close	VERB
ejpam-5241	15	26	geodetic	geodetic	ADJ
ejpam-5241	15	27	hop	hop	NOUN
ejpam-5241	15	28	dominating	dominating	NOUN
ejpam-5241	15	29	set	set	NOUN
ejpam-5241	15	30	,	,	PUNCT
ejpam-5241	15	31	closed	close	VERB
ejpam-5241	15	32	geodetic	geodetic	ADJ
ejpam-5241	15	33	hop	hop	NOUN
ejpam-5241	15	34	domination	domination	NOUN
ejpam-5241	15	35	number	number	NOUN
ejpam-5241	15	36	,	,	PUNCT
ejpam-5241	15	37	join	join	NOUN
ejpam-5241	15	38	,	,	PUNCT
ejpam-5241	15	39	corona	corona	PROPN
ejpam-5241	15	40	,	,	PUNCT
ejpam-5241	15	41	edge	edge	NOUN
ejpam-5241	15	42	corona	corona	NOUN
ejpam-5241	15	43	∗corresponding	∗corresponde	VERB
ejpam-5241	15	44	author	author	NOUN
ejpam-5241	15	45	.	.	PUNCT
ejpam-5241	16	1	doi	doi	NOUN
ejpam-5241	16	2	:	:	PUNCT
ejpam-5241	16	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5241	https://doi.org/10.29020/nybg.ejpam.v17i3.5241	VERB
ejpam-5241	16	4	email	email	NOUN
ejpam-5241	16	5	addresses	address	NOUN
ejpam-5241	16	6	:	:	PUNCT
ejpam-5241	16	7	ninajeane.adolfo@g.msuiit.edu.ph	ninajeane.adolfo@g.msuiit.edu.ph	PROPN
ejpam-5241	16	8	(	(	PUNCT
ejpam-5241	16	9	n.	n.	PROPN
ejpam-5241	16	10	adolfo	adolfo	PROPN
ejpam-5241	16	11	)	)	PUNCT
ejpam-5241	16	12	,	,	PUNCT
ejpam-5241	16	13	imelda.aniversario@g.msuiit.edu.ph	imelda.aniversario@g.msuiit.edu.ph	PROPN
ejpam-5241	16	14	(	(	PUNCT
ejpam-5241	16	15	i.	i.	PROPN
ejpam-5241	16	16	aniversario	aniversario	PROPN
ejpam-5241	16	17	)	)	PUNCT
ejpam-5241	16	18	,	,	PUNCT
ejpam-5241	16	19	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-5241	16	20	(	(	PUNCT
ejpam-5241	16	21	f.	f.	PROPN
ejpam-5241	16	22	jamil	jamil	PROPN
ejpam-5241	16	23	)	)	PUNCT
ejpam-5241	16	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5241	16	25	1618	1618	NUM
ejpam-5241	17	1	©	©	ADP
ejpam-5241	17	2	2024	2024	NUM
ejpam-5241	17	3	ejpam	ejpam	NOUN
ejpam-5241	17	4	all	all	DET
ejpam-5241	17	5	rights	right	NOUN
ejpam-5241	17	6	reserved	reserve	VERB
ejpam-5241	17	7	.	.	PUNCT
ejpam-5241	18	1	a.	a.	PROPN
ejpam-5241	18	2	adolfo	adolfo	PROPN
ejpam-5241	18	3	,	,	PUNCT
ejpam-5241	18	4	i.	i.	PROPN
ejpam-5241	18	5	aniversario	aniversario	PROPN
ejpam-5241	18	6	,	,	PUNCT
ejpam-5241	18	7	f.	f.	PROPN
ejpam-5241	18	8	jamil	jamil	PROPN
ejpam-5241	18	9	/	/	SYM
ejpam-5241	18	10	eur	eur	PROPN
ejpam-5241	18	11	.	.	PUNCT
ejpam-5241	19	1	j.	j.	PROPN
ejpam-5241	19	2	pure	pure	PROPN
ejpam-5241	19	3	appl	appl	PROPN
ejpam-5241	19	4	.	.	PROPN
ejpam-5241	19	5	math	math	PROPN
ejpam-5241	19	6	,	,	PUNCT
ejpam-5241	19	7	17	17	NUM
ejpam-5241	19	8	(	(	PUNCT
ejpam-5241	19	9	3	3	NUM
ejpam-5241	19	10	)	)	PUNCT
ejpam-5241	19	11	(	(	PUNCT
ejpam-5241	19	12	2024	2024	NUM
ejpam-5241	19	13	)	)	PUNCT
ejpam-5241	19	14	,	,	PUNCT
ejpam-5241	19	15	1618	1618	NUM
ejpam-5241	19	16	-	-	SYM
ejpam-5241	19	17	1636	1636	NUM
ejpam-5241	19	18	1619	1619	NUM
ejpam-5241	19	19	1	1	NUM
ejpam-5241	19	20	.	.	PUNCT
ejpam-5241	20	1	introduction	introduction	NOUN
ejpam-5241	20	2	f.	f.	PROPN
ejpam-5241	20	3	harary	harary	PROPN
ejpam-5241	20	4	in	in	ADP
ejpam-5241	20	5	[	[	X
ejpam-5241	20	6	9	9	NUM
ejpam-5241	20	7	]	]	PUNCT
ejpam-5241	20	8	introduced	introduce	VERB
ejpam-5241	20	9	two	two	NUM
ejpam-5241	20	10	categories	category	NOUN
ejpam-5241	20	11	of	of	ADP
ejpam-5241	20	12	graphical	graphical	ADJ
ejpam-5241	20	13	games	game	NOUN
ejpam-5241	20	14	called	call	VERB
ejpam-5241	20	15	the	the	DET
ejpam-5241	20	16	achievement	achievement	NOUN
ejpam-5241	20	17	and	and	CCONJ
ejpam-5241	20	18	avoidance	avoidance	NOUN
ejpam-5241	20	19	games	game	NOUN
ejpam-5241	20	20	from	from	ADP
ejpam-5241	20	21	which	which	PRON
ejpam-5241	20	22	the	the	DET
ejpam-5241	20	23	concept	concept	NOUN
ejpam-5241	20	24	of	of	ADP
ejpam-5241	20	25	closed	closed	ADJ
ejpam-5241	20	26	geodetic	geodetic	ADJ
ejpam-5241	20	27	number	number	NOUN
ejpam-5241	20	28	evolved	evolve	VERB
ejpam-5241	20	29	.	.	PUNCT
ejpam-5241	21	1	the	the	DET
ejpam-5241	21	2	closed	closed	ADJ
ejpam-5241	21	3	geodetic	geodetic	ADJ
ejpam-5241	21	4	sets	set	NOUN
ejpam-5241	21	5	and	and	CCONJ
ejpam-5241	21	6	closed	close	VERB
ejpam-5241	21	7	geodetic	geodetic	ADJ
ejpam-5241	21	8	numbers	number	NOUN
ejpam-5241	21	9	of	of	ADP
ejpam-5241	21	10	connected	connected	ADJ
ejpam-5241	21	11	graphs	graph	NOUN
ejpam-5241	21	12	,	,	PUNCT
ejpam-5241	21	13	which	which	PRON
ejpam-5241	21	14	can	can	AUX
ejpam-5241	21	15	find	find	VERB
ejpam-5241	21	16	applications	application	NOUN
ejpam-5241	21	17	in	in	ADP
ejpam-5241	21	18	location	location	NOUN
ejpam-5241	21	19	theory	theory	NOUN
ejpam-5241	21	20	and	and	CCONJ
ejpam-5241	21	21	convexity	convexity	NOUN
ejpam-5241	21	22	theory	theory	NOUN
ejpam-5241	21	23	,	,	PUNCT
ejpam-5241	21	24	have	have	AUX
ejpam-5241	21	25	been	be	AUX
ejpam-5241	21	26	extensively	extensively	ADV
ejpam-5241	21	27	studied	study	VERB
ejpam-5241	21	28	in	in	ADP
ejpam-5241	21	29	[	[	X
ejpam-5241	21	30	1	1	NUM
ejpam-5241	21	31	,	,	PUNCT
ejpam-5241	21	32	2	2	NUM
ejpam-5241	21	33	,	,	PUNCT
ejpam-5241	21	34	6	6	NUM
ejpam-5241	21	35	,	,	PUNCT
ejpam-5241	21	36	7	7	NUM
ejpam-5241	21	37	]	]	PUNCT
ejpam-5241	21	38	.	.	PUNCT
ejpam-5241	22	1	the	the	DET
ejpam-5241	22	2	hop	hop	NOUN
ejpam-5241	22	3	domination	domination	NOUN
ejpam-5241	22	4	in	in	ADP
ejpam-5241	22	5	graphs	graph	NOUN
ejpam-5241	22	6	is	be	AUX
ejpam-5241	22	7	introduced	introduce	VERB
ejpam-5241	22	8	in	in	ADP
ejpam-5241	22	9	[	[	X
ejpam-5241	22	10	14	14	NUM
ejpam-5241	22	11	]	]	PUNCT
ejpam-5241	22	12	by	by	ADP
ejpam-5241	22	13	s.k	s.k	PROPN
ejpam-5241	22	14	.	.	PROPN
ejpam-5241	22	15	ayyaswamy	ayyaswamy	PROPN
ejpam-5241	22	16	and	and	CCONJ
ejpam-5241	22	17	c.natarajan	c.natarajan	X
ejpam-5241	22	18	.	.	PUNCT
ejpam-5241	23	1	accordingly	accordingly	ADV
ejpam-5241	23	2	,	,	PUNCT
ejpam-5241	23	3	this	this	DET
ejpam-5241	23	4	graph	graph	NOUN
ejpam-5241	23	5	theoretic	theoretic	ADJ
ejpam-5241	23	6	concept	concept	NOUN
ejpam-5241	23	7	originated	originate	VERB
ejpam-5241	23	8	from	from	ADP
ejpam-5241	23	9	the	the	DET
ejpam-5241	23	10	second	second	ADJ
ejpam-5241	23	11	electron	electron	NOUN
ejpam-5241	23	12	affinity	affinity	NOUN
ejpam-5241	23	13	in	in	ADP
ejpam-5241	23	14	inorganic	inorganic	ADJ
ejpam-5241	23	15	chemistry	chemistry	NOUN
ejpam-5241	23	16	.	.	PUNCT
ejpam-5241	24	1	it	it	PRON
ejpam-5241	24	2	has	have	AUX
ejpam-5241	24	3	attracted	attract	VERB
ejpam-5241	24	4	relatively	relatively	ADV
ejpam-5241	24	5	much	much	ADJ
ejpam-5241	24	6	attention	attention	NOUN
ejpam-5241	24	7	and	and	CCONJ
ejpam-5241	24	8	several	several	ADJ
ejpam-5241	24	9	further	further	ADJ
ejpam-5241	24	10	studies	study	NOUN
ejpam-5241	24	11	including	include	VERB
ejpam-5241	24	12	investigations	investigation	NOUN
ejpam-5241	24	13	on	on	ADP
ejpam-5241	24	14	some	some	PRON
ejpam-5241	24	15	of	of	ADP
ejpam-5241	24	16	its	its	PRON
ejpam-5241	24	17	variations	variation	NOUN
ejpam-5241	24	18	can	can	AUX
ejpam-5241	24	19	be	be	AUX
ejpam-5241	24	20	found	find	VERB
ejpam-5241	24	21	in	in	ADP
ejpam-5241	24	22	the	the	DET
ejpam-5241	24	23	existing	exist	VERB
ejpam-5241	24	24	literature	literature	NOUN
ejpam-5241	24	25	(	(	PUNCT
ejpam-5241	24	26	see	see	VERB
ejpam-5241	24	27	[	[	X
ejpam-5241	24	28	4	4	NUM
ejpam-5241	24	29	,	,	PUNCT
ejpam-5241	24	30	5	5	NUM
ejpam-5241	24	31	,	,	PUNCT
ejpam-5241	24	32	12–17	12–17	NUM
ejpam-5241	24	33	]	]	PUNCT
ejpam-5241	24	34	)	)	PUNCT
ejpam-5241	24	35	.	.	PUNCT
ejpam-5241	25	1	in	in	ADP
ejpam-5241	25	2	this	this	DET
ejpam-5241	25	3	present	present	ADJ
ejpam-5241	25	4	paper	paper	NOUN
ejpam-5241	25	5	,	,	PUNCT
ejpam-5241	25	6	inspired	inspire	VERB
ejpam-5241	25	7	by	by	ADP
ejpam-5241	25	8	the	the	DET
ejpam-5241	25	9	above	above	ADV
ejpam-5241	25	10	-	-	PUNCT
ejpam-5241	25	11	mentioned	mention	VERB
ejpam-5241	25	12	concepts	concept	NOUN
ejpam-5241	25	13	,	,	PUNCT
ejpam-5241	25	14	we	we	PRON
ejpam-5241	25	15	introduce	introduce	VERB
ejpam-5241	25	16	and	and	CCONJ
ejpam-5241	25	17	initiate	initiate	VERB
ejpam-5241	25	18	the	the	DET
ejpam-5241	25	19	study	study	NOUN
ejpam-5241	25	20	of	of	ADP
ejpam-5241	25	21	closed	closed	ADJ
ejpam-5241	25	22	geodetic	geodetic	ADJ
ejpam-5241	25	23	hop	hop	NOUN
ejpam-5241	25	24	domination	domination	NOUN
ejpam-5241	25	25	in	in	ADP
ejpam-5241	25	26	graphs	graph	NOUN
ejpam-5241	25	27	.	.	PUNCT
ejpam-5241	26	1	all	all	DET
ejpam-5241	26	2	graphs	graph	NOUN
ejpam-5241	26	3	considered	consider	VERB
ejpam-5241	26	4	in	in	ADP
ejpam-5241	26	5	this	this	DET
ejpam-5241	26	6	study	study	NOUN
ejpam-5241	26	7	are	be	AUX
ejpam-5241	26	8	simple	simple	ADJ
ejpam-5241	26	9	,	,	PUNCT
ejpam-5241	26	10	undirected	undirected	ADJ
ejpam-5241	26	11	and	and	CCONJ
ejpam-5241	26	12	connected	connected	ADJ
ejpam-5241	26	13	.	.	PUNCT
ejpam-5241	27	1	all	all	DET
ejpam-5241	27	2	graph	graph	NOUN
ejpam-5241	27	3	terminologies	terminology	NOUN
ejpam-5241	27	4	which	which	PRON
ejpam-5241	27	5	are	be	AUX
ejpam-5241	27	6	not	not	PART
ejpam-5241	27	7	defined	define	VERB
ejpam-5241	27	8	but	but	CCONJ
ejpam-5241	27	9	are	be	AUX
ejpam-5241	27	10	used	use	VERB
ejpam-5241	27	11	here	here	ADV
ejpam-5241	27	12	are	be	AUX
ejpam-5241	27	13	adopted	adopt	VERB
ejpam-5241	27	14	from	from	ADP
ejpam-5241	27	15	[	[	X
ejpam-5241	27	16	6	6	NUM
ejpam-5241	27	17	]	]	PUNCT
ejpam-5241	27	18	.	.	PUNCT
ejpam-5241	28	1	as	as	ADP
ejpam-5241	28	2	usual	usual	ADJ
ejpam-5241	28	3	,	,	PUNCT
ejpam-5241	28	4	we	we	PRON
ejpam-5241	28	5	write	write	VERB
ejpam-5241	28	6	g	g	PROPN
ejpam-5241	28	7	=	=	SYM
ejpam-5241	28	8	(	(	PUNCT
ejpam-5241	28	9	v	v	NOUN
ejpam-5241	28	10	(	(	PUNCT
ejpam-5241	28	11	g	g	NOUN
ejpam-5241	28	12	)	)	PUNCT
ejpam-5241	28	13	,	,	PUNCT
ejpam-5241	28	14	e(g	e(g	PROPN
ejpam-5241	28	15	)	)	PUNCT
ejpam-5241	28	16	)	)	PUNCT
ejpam-5241	28	17	for	for	ADP
ejpam-5241	28	18	a	a	DET
ejpam-5241	28	19	graph	graph	NOUN
ejpam-5241	28	20	g	g	PROPN
ejpam-5241	28	21	where	where	SCONJ
ejpam-5241	28	22	v	v	NOUN
ejpam-5241	28	23	(	(	PUNCT
ejpam-5241	28	24	g	g	NOUN
ejpam-5241	28	25	)	)	PUNCT
ejpam-5241	28	26	and	and	CCONJ
ejpam-5241	28	27	e(g	e(g	PROPN
ejpam-5241	28	28	)	)	PUNCT
ejpam-5241	28	29	are	be	AUX
ejpam-5241	28	30	the	the	DET
ejpam-5241	28	31	vertex	vertex	NOUN
ejpam-5241	28	32	set	set	NOUN
ejpam-5241	28	33	and	and	CCONJ
ejpam-5241	28	34	edge	edge	NOUN
ejpam-5241	28	35	set	set	NOUN
ejpam-5241	28	36	,	,	PUNCT
ejpam-5241	28	37	respectively	respectively	ADV
ejpam-5241	28	38	,	,	PUNCT
ejpam-5241	28	39	of	of	ADP
ejpam-5241	28	40	g.	g.	NOUN
ejpam-5241	28	41	for	for	ADP
ejpam-5241	28	42	s	s	PROPN
ejpam-5241	28	43	⊆	⊆	NUM
ejpam-5241	28	44	v	v	NOUN
ejpam-5241	28	45	(	(	PUNCT
ejpam-5241	28	46	g	g	NOUN
ejpam-5241	28	47	)	)	PUNCT
ejpam-5241	28	48	,	,	PUNCT
ejpam-5241	28	49	|s|	|s|	PROPN
ejpam-5241	28	50	is	be	AUX
ejpam-5241	28	51	the	the	DET
ejpam-5241	28	52	cardinality	cardinality	NOUN
ejpam-5241	28	53	of	of	ADP
ejpam-5241	28	54	s.	s.	PROPN
ejpam-5241	28	55	in	in	ADP
ejpam-5241	28	56	particular	particular	ADJ
ejpam-5241	28	57	,	,	PUNCT
ejpam-5241	28	58	|v	|v	PROPN
ejpam-5241	28	59	(	(	PUNCT
ejpam-5241	28	60	g)|	g)|	PROPN
ejpam-5241	28	61	is	be	AUX
ejpam-5241	28	62	the	the	DET
ejpam-5241	28	63	order	order	NOUN
ejpam-5241	28	64	of	of	ADP
ejpam-5241	28	65	g.	g.	PROPN
ejpam-5241	28	66	let	let	VERB
ejpam-5241	28	67	g	g	NOUN
ejpam-5241	28	68	and	and	CCONJ
ejpam-5241	28	69	h	h	NOUN
ejpam-5241	28	70	be	be	VERB
ejpam-5241	28	71	two	two	NUM
ejpam-5241	28	72	graphs	graph	NOUN
ejpam-5241	28	73	with	with	ADP
ejpam-5241	28	74	disjoint	disjoint	ADJ
ejpam-5241	28	75	vertex	vertex	NOUN
ejpam-5241	28	76	sets	set	NOUN
ejpam-5241	28	77	.	.	PUNCT
ejpam-5241	29	1	the	the	DET
ejpam-5241	29	2	join	join	NOUN
ejpam-5241	29	3	of	of	ADP
ejpam-5241	29	4	g	g	PROPN
ejpam-5241	29	5	and	and	CCONJ
ejpam-5241	29	6	h	h	NOUN
ejpam-5241	29	7	,	,	PUNCT
ejpam-5241	29	8	denoted	denote	VERB
ejpam-5241	29	9	by	by	ADP
ejpam-5241	29	10	g+h	g+h	PROPN
ejpam-5241	29	11	,	,	PUNCT
ejpam-5241	29	12	is	be	AUX
ejpam-5241	29	13	the	the	DET
ejpam-5241	29	14	graph	graph	NOUN
ejpam-5241	29	15	with	with	ADP
ejpam-5241	29	16	vertex	vertex	NOUN
ejpam-5241	29	17	-	-	PUNCT
ejpam-5241	29	18	set	set	VERB
ejpam-5241	29	19	v	v	NOUN
ejpam-5241	29	20	(	(	PUNCT
ejpam-5241	29	21	g+h	g+h	NOUN
ejpam-5241	29	22	)	)	PUNCT
ejpam-5241	29	23	=	=	SYM
ejpam-5241	29	24	v	v	X
ejpam-5241	29	25	(	(	PUNCT
ejpam-5241	29	26	g)∪̇v	g)∪̇v	X
ejpam-5241	29	27	(	(	PUNCT
ejpam-5241	29	28	h	h	NOUN
ejpam-5241	29	29	)	)	PUNCT
ejpam-5241	29	30	and	and	CCONJ
ejpam-5241	29	31	edge	edge	NOUN
ejpam-5241	29	32	-	-	PUNCT
ejpam-5241	29	33	set	set	VERB
ejpam-5241	29	34	e(g+h	e(g+h	NUM
ejpam-5241	29	35	)	)	PUNCT
ejpam-5241	29	36	=	=	PUNCT
ejpam-5241	30	1	e(g)∪̇e(h)∪̇	e(g)∪̇e(h)∪̇	NOUN
ejpam-5241	30	2	{	{	PUNCT
ejpam-5241	30	3	uv	uv	NOUN
ejpam-5241	30	4	:	:	PUNCT
ejpam-5241	30	5	u	u	PROPN
ejpam-5241	30	6	∈	∈	PROPN
ejpam-5241	30	7	v	v	ADP
ejpam-5241	30	8	(	(	PUNCT
ejpam-5241	30	9	g	g	NOUN
ejpam-5241	30	10	)	)	PUNCT
ejpam-5241	30	11	,	,	PUNCT
ejpam-5241	30	12	v	v	X
ejpam-5241	30	13	∈	∈	PROPN
ejpam-5241	30	14	v	v	NOUN
ejpam-5241	30	15	(	(	PUNCT
ejpam-5241	30	16	h	h	NOUN
ejpam-5241	30	17	)	)	PUNCT
ejpam-5241	30	18	}	}	PUNCT
ejpam-5241	30	19	.	.	PUNCT
ejpam-5241	31	1	the	the	DET
ejpam-5241	31	2	corona	corona	NOUN
ejpam-5241	31	3	g	g	PROPN
ejpam-5241	31	4	◦	◦	NOUN
ejpam-5241	31	5	h	h	NOUN
ejpam-5241	31	6	of	of	ADP
ejpam-5241	31	7	g	g	PROPN
ejpam-5241	31	8	and	and	CCONJ
ejpam-5241	31	9	h	h	NOUN
ejpam-5241	31	10	is	be	AUX
ejpam-5241	31	11	the	the	DET
ejpam-5241	31	12	graph	graph	NOUN
ejpam-5241	31	13	obtained	obtain	VERB
ejpam-5241	31	14	by	by	ADP
ejpam-5241	31	15	taking	take	VERB
ejpam-5241	31	16	one	one	NUM
ejpam-5241	31	17	copy	copy	NOUN
ejpam-5241	31	18	of	of	ADP
ejpam-5241	31	19	g	g	PROPN
ejpam-5241	31	20	and	and	CCONJ
ejpam-5241	31	21	|v	|v	PROPN
ejpam-5241	31	22	(	(	PUNCT
ejpam-5241	31	23	g)|	g)|	NOUN
ejpam-5241	31	24	copies	copy	NOUN
ejpam-5241	31	25	of	of	ADP
ejpam-5241	31	26	h	h	NOUN
ejpam-5241	31	27	,	,	PUNCT
ejpam-5241	31	28	and	and	CCONJ
ejpam-5241	31	29	then	then	ADV
ejpam-5241	31	30	joining	join	VERB
ejpam-5241	31	31	the	the	DET
ejpam-5241	31	32	ith	ith	PROPN
ejpam-5241	31	33	vertex	vertex	NOUN
ejpam-5241	31	34	of	of	ADP
ejpam-5241	31	35	g	g	NOUN
ejpam-5241	31	36	to	to	ADP
ejpam-5241	31	37	every	every	DET
ejpam-5241	31	38	vertex	vertex	NOUN
ejpam-5241	31	39	of	of	ADP
ejpam-5241	31	40	the	the	DET
ejpam-5241	31	41	ith	ith	PROPN
ejpam-5241	31	42	copy	copy	NOUN
ejpam-5241	31	43	of	of	ADP
ejpam-5241	31	44	h.	h.	PROPN
ejpam-5241	31	45	the	the	DET
ejpam-5241	31	46	edge	edge	NOUN
ejpam-5241	31	47	corona	corona	PROPN
ejpam-5241	31	48	g	g	PROPN
ejpam-5241	31	49	⋄	⋄	PROPN
ejpam-5241	31	50	h	h	NOUN
ejpam-5241	31	51	of	of	ADP
ejpam-5241	31	52	g	g	PROPN
ejpam-5241	31	53	and	and	CCONJ
ejpam-5241	31	54	h	h	NOUN
ejpam-5241	31	55	is	be	AUX
ejpam-5241	31	56	the	the	DET
ejpam-5241	31	57	graph	graph	NOUN
ejpam-5241	31	58	obtained	obtain	VERB
ejpam-5241	31	59	by	by	ADP
ejpam-5241	31	60	taking	take	VERB
ejpam-5241	31	61	one	one	NUM
ejpam-5241	31	62	copy	copy	NOUN
ejpam-5241	31	63	of	of	ADP
ejpam-5241	31	64	g	g	PROPN
ejpam-5241	31	65	and	and	CCONJ
ejpam-5241	31	66	|e(g)|	|e(g)|	ADJ
ejpam-5241	31	67	copies	copy	NOUN
ejpam-5241	31	68	of	of	ADP
ejpam-5241	31	69	h	h	NOUN
ejpam-5241	31	70	and	and	CCONJ
ejpam-5241	31	71	joining	join	VERB
ejpam-5241	31	72	each	each	PRON
ejpam-5241	31	73	of	of	ADP
ejpam-5241	31	74	the	the	DET
ejpam-5241	31	75	end	end	NOUN
ejpam-5241	31	76	vertices	vertice	VERB
ejpam-5241	31	77	u	u	NOUN
ejpam-5241	31	78	and	and	CCONJ
ejpam-5241	31	79	v	v	NOUN
ejpam-5241	31	80	of	of	ADP
ejpam-5241	31	81	each	each	DET
ejpam-5241	31	82	edge	edge	NOUN
ejpam-5241	31	83	uv	uv	NOUN
ejpam-5241	31	84	of	of	ADP
ejpam-5241	31	85	g	g	NOUN
ejpam-5241	31	86	to	to	ADP
ejpam-5241	31	87	every	every	DET
ejpam-5241	31	88	vertex	vertex	NOUN
ejpam-5241	31	89	of	of	ADP
ejpam-5241	31	90	the	the	DET
ejpam-5241	31	91	copy	copy	NOUN
ejpam-5241	31	92	huv	huv	PROPN
ejpam-5241	31	93	of	of	ADP
ejpam-5241	31	94	h.	h.	PROPN
ejpam-5241	31	95	for	for	ADP
ejpam-5241	31	96	vertices	vertex	NOUN
ejpam-5241	31	97	u	u	NOUN
ejpam-5241	31	98	and	and	CCONJ
ejpam-5241	31	99	v	v	NOUN
ejpam-5241	31	100	in	in	ADP
ejpam-5241	31	101	g	g	PROPN
ejpam-5241	31	102	,	,	PUNCT
ejpam-5241	31	103	the	the	DET
ejpam-5241	31	104	distance	distance	NOUN
ejpam-5241	31	105	dg(u	dg(u	X
ejpam-5241	31	106	,	,	PUNCT
ejpam-5241	31	107	v	v	NOUN
ejpam-5241	31	108	)	)	PUNCT
ejpam-5241	31	109	between	between	ADP
ejpam-5241	31	110	u	u	NOUN
ejpam-5241	31	111	and	and	CCONJ
ejpam-5241	31	112	v	v	NOUN
ejpam-5241	31	113	is	be	AUX
ejpam-5241	31	114	the	the	DET
ejpam-5241	31	115	length	length	NOUN
ejpam-5241	31	116	of	of	ADP
ejpam-5241	31	117	a	a	DET
ejpam-5241	31	118	shortest	short	ADJ
ejpam-5241	31	119	path	path	NOUN
ejpam-5241	31	120	in	in	ADP
ejpam-5241	31	121	g	g	NOUN
ejpam-5241	31	122	joining	join	VERB
ejpam-5241	31	123	u	u	NOUN
ejpam-5241	31	124	and	and	CCONJ
ejpam-5241	31	125	v.	v.	ADP
ejpam-5241	31	126	any	any	DET
ejpam-5241	31	127	path	path	NOUN
ejpam-5241	31	128	joining	join	VERB
ejpam-5241	31	129	u	u	NOUN
ejpam-5241	31	130	and	and	CCONJ
ejpam-5241	31	131	v	v	ADP
ejpam-5241	31	132	of	of	ADP
ejpam-5241	31	133	length	length	NOUN
ejpam-5241	31	134	dg(u	dg(u	ADJ
ejpam-5241	31	135	,	,	PUNCT
ejpam-5241	31	136	v	v	NOUN
ejpam-5241	31	137	)	)	PUNCT
ejpam-5241	31	138	is	be	AUX
ejpam-5241	31	139	called	call	VERB
ejpam-5241	31	140	a	a	DET
ejpam-5241	31	141	u	u	NOUN
ejpam-5241	31	142	-	-	NOUN
ejpam-5241	31	143	v	v	ADJ
ejpam-5241	31	144	geodesic	geodesic	NOUN
ejpam-5241	31	145	.	.	PUNCT
ejpam-5241	32	1	the	the	DET
ejpam-5241	32	2	diameter	diameter	NOUN
ejpam-5241	32	3	diam(g	diam(g	PROPN
ejpam-5241	32	4	)	)	PUNCT
ejpam-5241	32	5	of	of	ADP
ejpam-5241	32	6	a	a	DET
ejpam-5241	32	7	graph	graph	NOUN
ejpam-5241	32	8	g	g	NOUN
ejpam-5241	32	9	is	be	AUX
ejpam-5241	32	10	the	the	DET
ejpam-5241	32	11	length	length	NOUN
ejpam-5241	32	12	of	of	ADP
ejpam-5241	32	13	any	any	DET
ejpam-5241	32	14	longest	long	ADJ
ejpam-5241	32	15	geodesic	geodesic	NOUN
ejpam-5241	32	16	of	of	ADP
ejpam-5241	32	17	g.	g.	NOUN
ejpam-5241	32	18	for	for	ADP
ejpam-5241	32	19	every	every	DET
ejpam-5241	32	20	two	two	NUM
ejpam-5241	32	21	vertices	vertex	NOUN
ejpam-5241	32	22	u	u	NOUN
ejpam-5241	32	23	and	and	CCONJ
ejpam-5241	32	24	v	v	NOUN
ejpam-5241	32	25	of	of	ADP
ejpam-5241	32	26	a	a	DET
ejpam-5241	32	27	graph	graph	NOUN
ejpam-5241	32	28	g	g	NOUN
ejpam-5241	32	29	,	,	PUNCT
ejpam-5241	32	30	the	the	DET
ejpam-5241	32	31	interval	interval	NOUN
ejpam-5241	32	32	ig[u	ig[u	PROPN
ejpam-5241	32	33	,	,	PUNCT
ejpam-5241	32	34	v	v	NOUN
ejpam-5241	32	35	]	]	PUNCT
ejpam-5241	32	36	refers	refer	VERB
ejpam-5241	32	37	the	the	DET
ejpam-5241	32	38	set	set	NOUN
ejpam-5241	32	39	of	of	ADP
ejpam-5241	32	40	all	all	DET
ejpam-5241	32	41	vertices	vertex	NOUN
ejpam-5241	32	42	lying	lie	VERB
ejpam-5241	32	43	in	in	ADP
ejpam-5241	32	44	some	some	DET
ejpam-5241	32	45	u	u	NOUN
ejpam-5241	32	46	-	-	NOUN
ejpam-5241	32	47	v	v	ADJ
ejpam-5241	32	48	geodesic	geodesic	NOUN
ejpam-5241	32	49	.	.	PUNCT
ejpam-5241	33	1	a	a	DET
ejpam-5241	33	2	vertex	vertex	NOUN
ejpam-5241	33	3	is	be	AUX
ejpam-5241	33	4	called	call	VERB
ejpam-5241	33	5	an	an	DET
ejpam-5241	33	6	end	end	NOUN
ejpam-5241	33	7	-	-	PUNCT
ejpam-5241	33	8	vertex	vertex	NOUN
ejpam-5241	33	9	or	or	CCONJ
ejpam-5241	33	10	a	a	DET
ejpam-5241	33	11	leaf	leaf	NOUN
ejpam-5241	33	12	if	if	SCONJ
ejpam-5241	33	13	its	its	PRON
ejpam-5241	33	14	degree	degree	NOUN
ejpam-5241	33	15	is	be	AUX
ejpam-5241	33	16	1	1	NUM
ejpam-5241	33	17	.	.	PUNCT
ejpam-5241	34	1	the	the	DET
ejpam-5241	34	2	set	set	NOUN
ejpam-5241	34	3	of	of	ADP
ejpam-5241	34	4	all	all	DET
ejpam-5241	34	5	end	end	NOUN
ejpam-5241	34	6	-	-	PUNCT
ejpam-5241	34	7	vertices	vertex	NOUN
ejpam-5241	34	8	of	of	ADP
ejpam-5241	34	9	g	g	PROPN
ejpam-5241	34	10	is	be	AUX
ejpam-5241	34	11	denoted	denote	VERB
ejpam-5241	34	12	by	by	ADP
ejpam-5241	34	13	l(g	l(g	NOUN
ejpam-5241	34	14	)	)	PUNCT
ejpam-5241	34	15	.	.	PUNCT
ejpam-5241	35	1	a	a	DET
ejpam-5241	35	2	vertex	vertex	NOUN
ejpam-5241	35	3	v	v	NOUN
ejpam-5241	35	4	in	in	ADP
ejpam-5241	35	5	a	a	DET
ejpam-5241	35	6	connected	connected	ADJ
ejpam-5241	35	7	graph	graph	NOUN
ejpam-5241	35	8	g	g	PROPN
ejpam-5241	35	9	is	be	AUX
ejpam-5241	35	10	an	an	DET
ejpam-5241	35	11	support	support	NOUN
ejpam-5241	35	12	vertex	vertex	NOUN
ejpam-5241	35	13	if	if	SCONJ
ejpam-5241	35	14	v	v	NOUN
ejpam-5241	35	15	is	be	AUX
ejpam-5241	35	16	adjacent	adjacent	ADJ
ejpam-5241	35	17	to	to	ADP
ejpam-5241	35	18	a	a	DET
ejpam-5241	35	19	leaf	leaf	NOUN
ejpam-5241	35	20	vertex	vertex	NOUN
ejpam-5241	35	21	of	of	ADP
ejpam-5241	35	22	g.	g.	PROPN
ejpam-5241	35	23	a	a	DET
ejpam-5241	35	24	vertex	vertex	NOUN
ejpam-5241	35	25	v	v	NOUN
ejpam-5241	35	26	in	in	ADP
ejpam-5241	35	27	a	a	DET
ejpam-5241	35	28	connected	connected	ADJ
ejpam-5241	35	29	graph	graph	NOUN
ejpam-5241	35	30	g	g	PROPN
ejpam-5241	35	31	is	be	AUX
ejpam-5241	35	32	an	an	DET
ejpam-5241	35	33	extreme	extreme	ADJ
ejpam-5241	35	34	vertex	vertex	NOUN
ejpam-5241	35	35	if	if	SCONJ
ejpam-5241	35	36	for	for	ADP
ejpam-5241	35	37	every	every	DET
ejpam-5241	35	38	pair	pair	NOUN
ejpam-5241	35	39	of	of	ADP
ejpam-5241	35	40	distinct	distinct	ADJ
ejpam-5241	35	41	vertices	vertex	NOUN
ejpam-5241	35	42	u	u	NOUN
ejpam-5241	35	43	and	and	CCONJ
ejpam-5241	35	44	w	w	NOUN
ejpam-5241	35	45	with	with	ADP
ejpam-5241	35	46	{	{	PUNCT
ejpam-5241	35	47	uv	uv	NOUN
ejpam-5241	35	48	,	,	PUNCT
ejpam-5241	35	49	wv	wv	PROPN
ejpam-5241	35	50	}	}	PUNCT
ejpam-5241	35	51	⊆	⊆	NUM
ejpam-5241	35	52	e(g	e(g	PROPN
ejpam-5241	35	53	)	)	PUNCT
ejpam-5241	35	54	,	,	PUNCT
ejpam-5241	35	55	uw	uw	PROPN
ejpam-5241	35	56	∈	∈	PROPN
ejpam-5241	35	57	e(g	e(g	PROPN
ejpam-5241	35	58	)	)	PUNCT
ejpam-5241	35	59	.	.	PUNCT
ejpam-5241	36	1	the	the	DET
ejpam-5241	36	2	set	set	NOUN
ejpam-5241	36	3	of	of	ADP
ejpam-5241	36	4	all	all	DET
ejpam-5241	36	5	extreme	extreme	ADJ
ejpam-5241	36	6	vertices	vertex	NOUN
ejpam-5241	36	7	in	in	ADP
ejpam-5241	36	8	g	g	PROPN
ejpam-5241	36	9	is	be	AUX
ejpam-5241	36	10	denoted	denote	VERB
ejpam-5241	36	11	by	by	ADP
ejpam-5241	36	12	ext(g	ext(g	PROPN
ejpam-5241	36	13	)	)	PUNCT
ejpam-5241	36	14	.	.	PUNCT
ejpam-5241	37	1	a	a	DET
ejpam-5241	37	2	vertex	vertex	NOUN
ejpam-5241	37	3	v	v	NOUN
ejpam-5241	37	4	in	in	ADP
ejpam-5241	37	5	a	a	DET
ejpam-5241	37	6	connected	connected	ADJ
ejpam-5241	37	7	graph	graph	NOUN
ejpam-5241	37	8	g	g	PROPN
ejpam-5241	37	9	is	be	AUX
ejpam-5241	37	10	a	a	DET
ejpam-5241	37	11	dominating	dominating	NOUN
ejpam-5241	37	12	vertex	vertex	NOUN
ejpam-5241	37	13	if	if	SCONJ
ejpam-5241	37	14	uv	uv	PROPN
ejpam-5241	37	15	∈	∈	PROPN
ejpam-5241	37	16	e(g	e(g	PROPN
ejpam-5241	37	17	)	)	PUNCT
ejpam-5241	37	18	for	for	ADP
ejpam-5241	37	19	all	all	PRON
ejpam-5241	37	20	u	u	PROPN
ejpam-5241	37	21	∈	∈	PROPN
ejpam-5241	37	22	v	v	NOUN
ejpam-5241	37	23	(	(	PUNCT
ejpam-5241	37	24	g	g	NOUN
ejpam-5241	37	25	)	)	PUNCT
ejpam-5241	37	26	\	\	NOUN
ejpam-5241	37	27	{	{	PUNCT
ejpam-5241	37	28	v	v	NOUN
ejpam-5241	37	29	}	}	PUNCT
ejpam-5241	37	30	.	.	PUNCT
ejpam-5241	38	1	dom(g	dom(g	ADV
ejpam-5241	38	2	)	)	PUNCT
ejpam-5241	39	1	is	be	AUX
ejpam-5241	39	2	the	the	DET
ejpam-5241	39	3	set	set	NOUN
ejpam-5241	39	4	of	of	ADP
ejpam-5241	39	5	all	all	DET
ejpam-5241	39	6	dominating	dominating	NOUN
ejpam-5241	39	7	vertices	vertex	NOUN
ejpam-5241	39	8	in	in	ADP
ejpam-5241	39	9	g.	g.	PROPN
ejpam-5241	39	10	for	for	ADP
ejpam-5241	39	11	s	s	PROPN
ejpam-5241	39	12	⊆	⊆	NUM
ejpam-5241	39	13	v	v	NOUN
ejpam-5241	39	14	(	(	PUNCT
ejpam-5241	39	15	g	g	NOUN
ejpam-5241	39	16	)	)	PUNCT
ejpam-5241	39	17	,	,	PUNCT
ejpam-5241	39	18	the	the	DET
ejpam-5241	39	19	2	2	NUM
ejpam-5241	39	20	-	-	PUNCT
ejpam-5241	39	21	path	path	NOUN
ejpam-5241	39	22	closure	closure	NOUN
ejpam-5241	39	23	p2[s]g	p2[s]g	PROPN
ejpam-5241	39	24	of	of	ADP
ejpam-5241	39	25	s	s	PROPN
ejpam-5241	39	26	is	be	AUX
ejpam-5241	39	27	the	the	DET
ejpam-5241	39	28	set	set	NOUN
ejpam-5241	39	29	p2[s]g	p2[s]g	PROPN
ejpam-5241	39	30	=	=	SYM
ejpam-5241	39	31	s∪{w	s∪{w	PROPN
ejpam-5241	40	1	∈	∈	PROPN
ejpam-5241	40	2	v	v	ADP
ejpam-5241	40	3	(	(	PUNCT
ejpam-5241	40	4	g	g	NOUN
ejpam-5241	40	5	)	)	PUNCT
ejpam-5241	40	6	:	:	PUNCT
ejpam-5241	40	7	w	w	X
ejpam-5241	40	8	∈	∈	PROPN
ejpam-5241	40	9	ig[u	ig[u	PROPN
ejpam-5241	40	10	,	,	PUNCT
ejpam-5241	40	11	v	v	NOUN
ejpam-5241	40	12	]	]	PUNCT
ejpam-5241	40	13	for	for	ADP
ejpam-5241	40	14	some	some	DET
ejpam-5241	40	15	u	u	NOUN
ejpam-5241	40	16	,	,	PUNCT
ejpam-5241	40	17	v	v	PROPN
ejpam-5241	40	18	∈	∈	NOUN
ejpam-5241	40	19	s	s	PART
ejpam-5241	40	20	with	with	ADP
ejpam-5241	40	21	dg(u	dg(u	ADJ
ejpam-5241	40	22	,	,	PUNCT
ejpam-5241	40	23	v	v	NOUN
ejpam-5241	40	24	)	)	PUNCT
ejpam-5241	40	25	=	=	SYM
ejpam-5241	40	26	2	2	NUM
ejpam-5241	40	27	}	}	PUNCT
ejpam-5241	40	28	.	.	PUNCT
ejpam-5241	41	1	a	a	DET
ejpam-5241	41	2	set	set	NOUN
ejpam-5241	41	3	s	s	PART
ejpam-5241	41	4	is	be	AUX
ejpam-5241	41	5	called	call	VERB
ejpam-5241	41	6	2	2	NUM
ejpam-5241	41	7	-	-	PUNCT
ejpam-5241	41	8	path	path	NOUN
ejpam-5241	41	9	closure	closure	NOUN
ejpam-5241	41	10	absorbing	absorb	VERB
ejpam-5241	41	11	if	if	SCONJ
ejpam-5241	41	12	p2[s]g	p2[s]g	PROPN
ejpam-5241	41	13	=	=	SYM
ejpam-5241	41	14	v	v	PROPN
ejpam-5241	41	15	(	(	PUNCT
ejpam-5241	41	16	g	g	NOUN
ejpam-5241	41	17	)	)	PUNCT
ejpam-5241	42	1	[	[	X
ejpam-5241	42	2	7	7	NUM
ejpam-5241	42	3	]	]	PUNCT
ejpam-5241	42	4	.	.	PUNCT
ejpam-5241	43	1	we	we	PRON
ejpam-5241	43	2	denote	denote	VERB
ejpam-5241	43	3	by	by	ADP
ejpam-5241	43	4	ρ2(g	ρ2(g	NOUN
ejpam-5241	43	5	)	)	PUNCT
ejpam-5241	43	6	the	the	DET
ejpam-5241	43	7	minimum	minimum	ADJ
ejpam-5241	43	8	cardinality	cardinality	NOUN
ejpam-5241	43	9	of	of	ADP
ejpam-5241	43	10	a	a	DET
ejpam-5241	43	11	2	2	NUM
ejpam-5241	43	12	-	-	PUNCT
ejpam-5241	43	13	path	path	NOUN
ejpam-5241	43	14	closure	closure	NOUN
ejpam-5241	43	15	a.	a.	PROPN
ejpam-5241	43	16	adolfo	adolfo	PROPN
ejpam-5241	43	17	,	,	PUNCT
ejpam-5241	43	18	i.	i.	PROPN
ejpam-5241	43	19	aniversario	aniversario	PROPN
ejpam-5241	43	20	,	,	PUNCT
ejpam-5241	43	21	f.	f.	PROPN
ejpam-5241	43	22	jamil	jamil	PROPN
ejpam-5241	43	23	/	/	SYM
ejpam-5241	43	24	eur	eur	PROPN
ejpam-5241	43	25	.	.	PUNCT
ejpam-5241	44	1	j.	j.	PROPN
ejpam-5241	44	2	pure	pure	PROPN
ejpam-5241	44	3	appl	appl	PROPN
ejpam-5241	44	4	.	.	PROPN
ejpam-5241	44	5	math	math	PROPN
ejpam-5241	44	6	,	,	PUNCT
ejpam-5241	44	7	17	17	NUM
ejpam-5241	44	8	(	(	PUNCT
ejpam-5241	44	9	3	3	NUM
ejpam-5241	44	10	)	)	PUNCT
ejpam-5241	44	11	(	(	PUNCT
ejpam-5241	44	12	2024	2024	NUM
ejpam-5241	44	13	)	)	PUNCT
ejpam-5241	44	14	,	,	PUNCT
ejpam-5241	44	15	1618	1618	NUM
ejpam-5241	44	16	-	-	SYM
ejpam-5241	44	17	1636	1636	NUM
ejpam-5241	44	18	1620	1620	NUM
ejpam-5241	44	19	absorbing	absorb	VERB
ejpam-5241	44	20	set	set	NOUN
ejpam-5241	44	21	of	of	ADP
ejpam-5241	44	22	g.	g.	PROPN
ejpam-5241	44	23	a	a	DET
ejpam-5241	44	24	set	set	NOUN
ejpam-5241	44	25	s	s	PROPN
ejpam-5241	44	26	⊆	⊆	NUM
ejpam-5241	44	27	v	v	NOUN
ejpam-5241	44	28	(	(	PUNCT
ejpam-5241	44	29	g	g	NOUN
ejpam-5241	44	30	)	)	PUNCT
ejpam-5241	44	31	is	be	AUX
ejpam-5241	44	32	a	a	DET
ejpam-5241	44	33	pointwise	pointwise	ADJ
ejpam-5241	44	34	non	non	ADJ
ejpam-5241	44	35	-	-	ADJ
ejpam-5241	44	36	dominating	dominating	ADJ
ejpam-5241	44	37	set	set	NOUN
ejpam-5241	44	38	of	of	ADP
ejpam-5241	44	39	g	g	PROPN
ejpam-5241	44	40	if	if	SCONJ
ejpam-5241	44	41	for	for	ADP
ejpam-5241	44	42	each	each	PRON
ejpam-5241	44	43	v	v	NUM
ejpam-5241	44	44	∈	∈	PROPN
ejpam-5241	44	45	v	v	NOUN
ejpam-5241	44	46	(	(	PUNCT
ejpam-5241	44	47	g	g	NOUN
ejpam-5241	44	48	)	)	PUNCT
ejpam-5241	44	49	\	\	PROPN
ejpam-5241	45	1	s	s	X
ejpam-5241	45	2	,	,	PUNCT
ejpam-5241	45	3	there	there	PRON
ejpam-5241	45	4	exists	exist	VERB
ejpam-5241	45	5	u	u	PROPN
ejpam-5241	45	6	∈	∈	PROPN
ejpam-5241	45	7	s	s	VERB
ejpam-5241	45	8	such	such	ADJ
ejpam-5241	45	9	that	that	DET
ejpam-5241	45	10	uv	uv	NOUN
ejpam-5241	45	11	/∈	/∈	PUNCT
ejpam-5241	45	12	e(g	e(g	PROPN
ejpam-5241	45	13	)	)	PUNCT
ejpam-5241	45	14	.	.	PUNCT
ejpam-5241	46	1	a	a	DET
ejpam-5241	46	2	pointwise	pointwise	ADJ
ejpam-5241	46	3	non	non	ADJ
ejpam-5241	46	4	-	-	ADJ
ejpam-5241	46	5	dominating	dominating	ADJ
ejpam-5241	46	6	set	set	NOUN
ejpam-5241	46	7	s	s	PROPN
ejpam-5241	46	8	⊆	⊆	NUM
ejpam-5241	46	9	v	v	NOUN
ejpam-5241	46	10	(	(	PUNCT
ejpam-5241	46	11	g	g	NOUN
ejpam-5241	46	12	)	)	PUNCT
ejpam-5241	46	13	of	of	ADP
ejpam-5241	46	14	a	a	DET
ejpam-5241	46	15	graph	graph	NOUN
ejpam-5241	46	16	g	g	NOUN
ejpam-5241	46	17	is	be	AUX
ejpam-5241	46	18	a	a	DET
ejpam-5241	46	19	2	2	NUM
ejpam-5241	46	20	-	-	PUNCT
ejpam-5241	46	21	path	path	NOUN
ejpam-5241	46	22	closure	closure	NOUN
ejpam-5241	46	23	absorbing	absorb	VERB
ejpam-5241	46	24	pointwise	pointwise	PROPN
ejpam-5241	46	25	non	non	ADJ
ejpam-5241	46	26	-	-	ADJ
ejpam-5241	46	27	dominating	dominating	ADJ
ejpam-5241	46	28	set	set	NOUN
ejpam-5241	46	29	if	if	SCONJ
ejpam-5241	46	30	it	it	PRON
ejpam-5241	46	31	is	be	AUX
ejpam-5241	46	32	a	a	DET
ejpam-5241	46	33	2	2	NUM
ejpam-5241	46	34	-	-	PUNCT
ejpam-5241	46	35	path	path	NOUN
ejpam-5241	46	36	closure	closure	NOUN
ejpam-5241	46	37	absorbing	absorb	VERB
ejpam-5241	46	38	set	set	NOUN
ejpam-5241	46	39	.	.	PUNCT
ejpam-5241	47	1	the	the	DET
ejpam-5241	47	2	minimum	minimum	ADJ
ejpam-5241	47	3	cardinality	cardinality	NOUN
ejpam-5241	47	4	of	of	ADP
ejpam-5241	47	5	a	a	DET
ejpam-5241	47	6	2	2	NUM
ejpam-5241	47	7	-	-	PUNCT
ejpam-5241	47	8	path	path	NOUN
ejpam-5241	47	9	closure	closure	NOUN
ejpam-5241	47	10	absorbing	absorb	VERB
ejpam-5241	47	11	pointwise	pointwise	PROPN
ejpam-5241	47	12	non	non	ADJ
ejpam-5241	47	13	-	-	ADJ
ejpam-5241	47	14	dominating	dominating	ADJ
ejpam-5241	47	15	set	set	NOUN
ejpam-5241	47	16	in	in	ADP
ejpam-5241	47	17	g	g	PROPN
ejpam-5241	47	18	is	be	AUX
ejpam-5241	47	19	denoted	denote	VERB
ejpam-5241	47	20	by	by	ADP
ejpam-5241	47	21	ρ2pnd(g	ρ2pnd(g	PROPN
ejpam-5241	47	22	)	)	PUNCT
ejpam-5241	47	23	a	a	DET
ejpam-5241	47	24	clique	clique	NOUN
ejpam-5241	47	25	in	in	ADP
ejpam-5241	47	26	g	g	PROPN
ejpam-5241	47	27	is	be	AUX
ejpam-5241	47	28	a	a	DET
ejpam-5241	47	29	complete	complete	ADJ
ejpam-5241	47	30	subgraph	subgraph	NOUN
ejpam-5241	47	31	of	of	ADP
ejpam-5241	47	32	g.	g.	PROPN
ejpam-5241	47	33	a	a	DET
ejpam-5241	47	34	maximal	maximal	ADJ
ejpam-5241	47	35	clique	clique	NOUN
ejpam-5241	47	36	is	be	AUX
ejpam-5241	47	37	a	a	DET
ejpam-5241	47	38	clique	clique	NOUN
ejpam-5241	47	39	which	which	PRON
ejpam-5241	47	40	is	be	AUX
ejpam-5241	47	41	not	not	PART
ejpam-5241	47	42	a	a	DET
ejpam-5241	47	43	proper	proper	ADJ
ejpam-5241	47	44	subgraph	subgraph	NOUN
ejpam-5241	47	45	of	of	ADP
ejpam-5241	47	46	a	a	DET
ejpam-5241	47	47	larger	large	ADJ
ejpam-5241	47	48	clique	clique	NOUN
ejpam-5241	47	49	.	.	PUNCT
ejpam-5241	48	1	the	the	DET
ejpam-5241	48	2	lower	low	ADJ
ejpam-5241	48	3	clique	clique	NOUN
ejpam-5241	48	4	number	number	NOUN
ejpam-5241	48	5	ωl(g	ωl(g	NUM
ejpam-5241	48	6	)	)	PUNCT
ejpam-5241	48	7	is	be	AUX
ejpam-5241	48	8	the	the	DET
ejpam-5241	48	9	minimum	minimum	ADJ
ejpam-5241	48	10	size	size	NOUN
ejpam-5241	48	11	of	of	ADP
ejpam-5241	48	12	all	all	DET
ejpam-5241	48	13	maximal	maximal	ADJ
ejpam-5241	48	14	cliques	clique	NOUN
ejpam-5241	48	15	of	of	ADP
ejpam-5241	48	16	g.	g.	PROPN
ejpam-5241	48	17	for	for	ADP
ejpam-5241	48	18	s	s	PROPN
ejpam-5241	48	19	⊆	⊆	NUM
ejpam-5241	48	20	v	v	NOUN
ejpam-5241	48	21	(	(	PUNCT
ejpam-5241	48	22	g	g	NOUN
ejpam-5241	48	23	)	)	PUNCT
ejpam-5241	48	24	,	,	PUNCT
ejpam-5241	48	25	the	the	DET
ejpam-5241	48	26	geodetic	geodetic	ADJ
ejpam-5241	48	27	closure	closure	NOUN
ejpam-5241	48	28	ig[s	ig[	NOUN
ejpam-5241	48	29	]	]	PUNCT
ejpam-5241	48	30	is	be	AUX
ejpam-5241	48	31	the	the	DET
ejpam-5241	48	32	union	union	NOUN
ejpam-5241	48	33	of	of	ADP
ejpam-5241	48	34	intervals	interval	NOUN
ejpam-5241	48	35	between	between	ADP
ejpam-5241	48	36	all	all	DET
ejpam-5241	48	37	pairs	pair	NOUN
ejpam-5241	48	38	of	of	ADP
ejpam-5241	48	39	vertices	vertex	NOUN
ejpam-5241	48	40	from	from	ADP
ejpam-5241	48	41	s	s	PROPN
ejpam-5241	48	42	,	,	PUNCT
ejpam-5241	48	43	that	that	ADV
ejpam-5241	48	44	is	is	ADV
ejpam-5241	48	45	,	,	PUNCT
ejpam-5241	48	46	ig[s	ig[s	PROPN
ejpam-5241	48	47	]	]	X
ejpam-5241	48	48	=	=	SYM
ejpam-5241	48	49	⋃	⋃	NOUN
ejpam-5241	48	50	{	{	PUNCT
ejpam-5241	48	51	ig[u	ig[u	PROPN
ejpam-5241	48	52	,	,	PUNCT
ejpam-5241	48	53	v	v	NOUN
ejpam-5241	48	54	]	]	X
ejpam-5241	48	55	:	:	PUNCT
ejpam-5241	48	56	u	u	NOUN
ejpam-5241	48	57	,	,	PUNCT
ejpam-5241	48	58	v	v	NOUN
ejpam-5241	48	59	∈	∈	NOUN
ejpam-5241	48	60	s	s	PART
ejpam-5241	48	61	}	}	PUNCT
ejpam-5241	48	62	.	.	PUNCT
ejpam-5241	49	1	s	s	PART
ejpam-5241	49	2	is	be	AUX
ejpam-5241	49	3	a	a	DET
ejpam-5241	49	4	geodetic	geodetic	ADJ
ejpam-5241	49	5	set	set	NOUN
ejpam-5241	49	6	provided	provide	VERB
ejpam-5241	49	7	ig[s	ig[	NOUN
ejpam-5241	49	8	]	]	X
ejpam-5241	49	9	=	=	SYM
ejpam-5241	49	10	v	v	X
ejpam-5241	49	11	(	(	PUNCT
ejpam-5241	49	12	g	g	NOUN
ejpam-5241	49	13	)	)	PUNCT
ejpam-5241	49	14	.	.	PUNCT
ejpam-5241	50	1	the	the	DET
ejpam-5241	50	2	minimum	minimum	PROPN
ejpam-5241	50	3	cardinality	cardinality	PROPN
ejpam-5241	50	4	gn(g	gn(g	NOUN
ejpam-5241	50	5	)	)	PUNCT
ejpam-5241	50	6	of	of	ADP
ejpam-5241	50	7	a	a	DET
ejpam-5241	50	8	geodetic	geodetic	ADJ
ejpam-5241	50	9	set	set	NOUN
ejpam-5241	50	10	is	be	AUX
ejpam-5241	50	11	the	the	DET
ejpam-5241	50	12	geodetic	geodetic	ADJ
ejpam-5241	50	13	number	number	NOUN
ejpam-5241	50	14	of	of	ADP
ejpam-5241	50	15	g.	g.	PROPN
ejpam-5241	50	16	a	a	DET
ejpam-5241	50	17	geodetic	geodetic	ADJ
ejpam-5241	50	18	set	set	NOUN
ejpam-5241	50	19	of	of	ADP
ejpam-5241	50	20	cardinality	cardinality	PROPN
ejpam-5241	50	21	gn(g	gn(g	PUNCT
ejpam-5241	50	22	)	)	PUNCT
ejpam-5241	50	23	is	be	AUX
ejpam-5241	50	24	a	a	DET
ejpam-5241	50	25	geodetic	geodetic	ADJ
ejpam-5241	50	26	basis	basis	NOUN
ejpam-5241	50	27	.	.	PUNCT
ejpam-5241	51	1	the	the	DET
ejpam-5241	51	2	introduction	introduction	NOUN
ejpam-5241	51	3	and	and	CCONJ
ejpam-5241	51	4	further	further	ADJ
ejpam-5241	51	5	studies	study	NOUN
ejpam-5241	51	6	on	on	ADP
ejpam-5241	51	7	geodetic	geodetic	ADJ
ejpam-5241	51	8	sets	set	NOUN
ejpam-5241	51	9	and	and	CCONJ
ejpam-5241	51	10	geodetic	geodetic	ADJ
ejpam-5241	51	11	numbers	number	NOUN
ejpam-5241	51	12	can	can	AUX
ejpam-5241	51	13	be	be	AUX
ejpam-5241	51	14	found	find	VERB
ejpam-5241	51	15	in	in	ADP
ejpam-5241	51	16	[	[	X
ejpam-5241	51	17	6–10	6–10	NOUN
ejpam-5241	51	18	]	]	X
ejpam-5241	51	19	.	.	PUNCT
ejpam-5241	52	1	a	a	DET
ejpam-5241	52	2	geodetic	geodetic	ADJ
ejpam-5241	52	3	set	set	NOUN
ejpam-5241	52	4	s	s	NOUN
ejpam-5241	52	5	of	of	ADP
ejpam-5241	52	6	g	g	PROPN
ejpam-5241	52	7	is	be	AUX
ejpam-5241	52	8	a	a	DET
ejpam-5241	52	9	closed	closed	ADJ
ejpam-5241	52	10	geodetic	geodetic	ADJ
ejpam-5241	52	11	cover	cover	NOUN
ejpam-5241	52	12	of	of	ADP
ejpam-5241	52	13	g	g	PROPN
ejpam-5241	52	14	if	if	SCONJ
ejpam-5241	52	15	s	s	NOUN
ejpam-5241	52	16	is	be	AUX
ejpam-5241	52	17	obtained	obtain	VERB
ejpam-5241	52	18	as	as	ADP
ejpam-5241	52	19	follows	follow	VERB
ejpam-5241	52	20	:	:	PUNCT
ejpam-5241	52	21	choose	choose	VERB
ejpam-5241	52	22	v1	v1	PROPN
ejpam-5241	52	23	∈	∈	PROPN
ejpam-5241	52	24	v	v	NOUN
ejpam-5241	52	25	(	(	PUNCT
ejpam-5241	52	26	g	g	NOUN
ejpam-5241	52	27	)	)	PUNCT
ejpam-5241	52	28	and	and	CCONJ
ejpam-5241	52	29	put	put	VERB
ejpam-5241	52	30	s1	s1	NOUN
ejpam-5241	52	31	=	=	SYM
ejpam-5241	52	32	{	{	PUNCT
ejpam-5241	52	33	v1	v1	NOUN
ejpam-5241	52	34	}	}	PUNCT
ejpam-5241	52	35	.	.	PUNCT
ejpam-5241	53	1	where	where	SCONJ
ejpam-5241	53	2	possible	possible	ADJ
ejpam-5241	53	3	,	,	PUNCT
ejpam-5241	53	4	choose	choose	VERB
ejpam-5241	53	5	v2	v2	PROPN
ejpam-5241	53	6	∈	∈	PROPN
ejpam-5241	53	7	v	v	NOUN
ejpam-5241	53	8	(	(	PUNCT
ejpam-5241	53	9	g	g	NOUN
ejpam-5241	53	10	)	)	PUNCT
ejpam-5241	53	11	\	\	NOUN
ejpam-5241	53	12	{	{	PUNCT
ejpam-5241	53	13	v1	v1	NOUN
ejpam-5241	53	14	}	}	PUNCT
ejpam-5241	53	15	and	and	CCONJ
ejpam-5241	53	16	put	put	VERB
ejpam-5241	53	17	s2	s2	NOUN
ejpam-5241	53	18	=	=	SYM
ejpam-5241	53	19	{	{	PUNCT
ejpam-5241	53	20	v1	v1	PROPN
ejpam-5241	53	21	,	,	PUNCT
ejpam-5241	53	22	v2	v2	PROPN
ejpam-5241	53	23	}	}	PUNCT
ejpam-5241	53	24	.	.	PUNCT
ejpam-5241	54	1	for	for	ADP
ejpam-5241	54	2	i	i	PRON
ejpam-5241	54	3	≥	≥	NOUN
ejpam-5241	54	4	3	3	NUM
ejpam-5241	54	5	,	,	PUNCT
ejpam-5241	54	6	choose	choose	VERB
ejpam-5241	54	7	vi	vi	PROPN
ejpam-5241	54	8	∈	∈	PROPN
ejpam-5241	54	9	v	v	NOUN
ejpam-5241	54	10	(	(	PUNCT
ejpam-5241	54	11	g	g	NOUN
ejpam-5241	54	12	)	)	PUNCT
ejpam-5241	54	13	\	\	PROPN
ejpam-5241	54	14	ig[si−1	ig[si−1	NOUN
ejpam-5241	54	15	]	]	PUNCT
ejpam-5241	54	16	,	,	PUNCT
ejpam-5241	54	17	where	where	SCONJ
ejpam-5241	54	18	sk	sk	VERB
ejpam-5241	54	19	=	=	PUNCT
ejpam-5241	54	20	{	{	PUNCT
ejpam-5241	54	21	v1	v1	PROPN
ejpam-5241	54	22	,	,	PUNCT
ejpam-5241	54	23	v2	v2	PROPN
ejpam-5241	54	24	,	,	PUNCT
ejpam-5241	54	25	.	.	PUNCT
ejpam-5241	54	26	.	.	PUNCT
ejpam-5241	55	1	.	.	PUNCT
ejpam-5241	56	1	,	,	PUNCT
ejpam-5241	56	2	vi	vi	NOUN
ejpam-5241	56	3	}	}	PUNCT
ejpam-5241	56	4	,	,	PUNCT
ejpam-5241	56	5	and	and	CCONJ
ejpam-5241	56	6	there	there	PRON
ejpam-5241	56	7	exists	exist	VERB
ejpam-5241	56	8	a	a	DET
ejpam-5241	56	9	positive	positive	ADJ
ejpam-5241	56	10	integer	integer	NOUN
ejpam-5241	56	11	k	k	PROPN
ejpam-5241	56	12	for	for	ADP
ejpam-5241	56	13	which	which	PRON
ejpam-5241	56	14	sk	sk	ADP
ejpam-5241	56	15	=	=	PUNCT
ejpam-5241	56	16	s.	s.	PROPN
ejpam-5241	56	17	the	the	DET
ejpam-5241	56	18	closed	closed	ADJ
ejpam-5241	56	19	geodetic	geodetic	ADJ
ejpam-5241	56	20	number	number	NOUN
ejpam-5241	56	21	of	of	ADP
ejpam-5241	56	22	g	g	NOUN
ejpam-5241	56	23	,	,	PUNCT
ejpam-5241	56	24	denoted	denote	VERB
ejpam-5241	56	25	cgn(g	cgn(g	PROPN
ejpam-5241	56	26	)	)	PUNCT
ejpam-5241	56	27	,	,	PUNCT
ejpam-5241	56	28	is	be	AUX
ejpam-5241	56	29	the	the	DET
ejpam-5241	56	30	smallest	small	ADJ
ejpam-5241	56	31	positive	positive	ADJ
ejpam-5241	56	32	integer	integer	NOUN
ejpam-5241	56	33	k	k	PROPN
ejpam-5241	56	34	for	for	ADP
ejpam-5241	56	35	which	which	PRON
ejpam-5241	56	36	ig[sk	ig[sk	X
ejpam-5241	56	37	]	]	X
ejpam-5241	56	38	=	=	SYM
ejpam-5241	56	39	v	v	X
ejpam-5241	56	40	(	(	PUNCT
ejpam-5241	56	41	g	g	NOUN
ejpam-5241	56	42	)	)	PUNCT
ejpam-5241	56	43	,	,	PUNCT
ejpam-5241	56	44	where	where	SCONJ
ejpam-5241	56	45	sk	sk	NOUN
ejpam-5241	56	46	is	be	AUX
ejpam-5241	56	47	obtained	obtain	VERB
ejpam-5241	56	48	as	as	ADP
ejpam-5241	56	49	illustrated	illustrate	VERB
ejpam-5241	56	50	above	above	ADV
ejpam-5241	56	51	.	.	PUNCT
ejpam-5241	57	1	if	if	SCONJ
ejpam-5241	57	2	c∗(g	c∗(g	NOUN
ejpam-5241	57	3	)	)	PUNCT
ejpam-5241	57	4	is	be	AUX
ejpam-5241	57	5	the	the	DET
ejpam-5241	57	6	collection	collection	NOUN
ejpam-5241	57	7	of	of	ADP
ejpam-5241	57	8	all	all	DET
ejpam-5241	57	9	closed	closed	ADJ
ejpam-5241	57	10	geodetic	geodetic	ADJ
ejpam-5241	57	11	covers	cover	NOUN
ejpam-5241	57	12	of	of	ADP
ejpam-5241	57	13	g	g	NOUN
ejpam-5241	57	14	,	,	PUNCT
ejpam-5241	57	15	then	then	ADV
ejpam-5241	57	16	cgn(g	cgn(g	NUM
ejpam-5241	57	17	)	)	PUNCT
ejpam-5241	57	18	=	=	NOUN
ejpam-5241	57	19	min{|s|	min{|s|	NOUN
ejpam-5241	57	20	:	:	PUNCT
ejpam-5241	57	21	s	s	X
ejpam-5241	57	22	∈	∈	PROPN
ejpam-5241	57	23	c∗(g	c∗(g	PROPN
ejpam-5241	57	24	)	)	PUNCT
ejpam-5241	57	25	}	}	PUNCT
ejpam-5241	57	26	.	.	PUNCT
ejpam-5241	58	1	any	any	DET
ejpam-5241	58	2	set	set	NOUN
ejpam-5241	58	3	s	s	NOUN
ejpam-5241	58	4	∈	∈	PROPN
ejpam-5241	58	5	c∗(g	c∗(g	PROPN
ejpam-5241	58	6	)	)	PUNCT
ejpam-5241	58	7	with	with	ADP
ejpam-5241	58	8	|s|	|s|	PROPN
ejpam-5241	58	9	=	=	SYM
ejpam-5241	58	10	cgn(g	cgn(g	PROPN
ejpam-5241	58	11	)	)	PUNCT
ejpam-5241	58	12	is	be	AUX
ejpam-5241	58	13	a	a	DET
ejpam-5241	58	14	closed	closed	ADJ
ejpam-5241	58	15	geodetic	geodetic	ADJ
ejpam-5241	58	16	basis	basis	NOUN
ejpam-5241	58	17	of	of	ADP
ejpam-5241	58	18	g.	g.	PROPN
ejpam-5241	58	19	a	a	DET
ejpam-5241	58	20	vertex	vertex	NOUN
ejpam-5241	58	21	v	v	NOUN
ejpam-5241	58	22	in	in	ADP
ejpam-5241	58	23	g	g	PROPN
ejpam-5241	58	24	is	be	AUX
ejpam-5241	58	25	a	a	DET
ejpam-5241	58	26	hop	hop	NOUN
ejpam-5241	58	27	neighbor	neighbor	NOUN
ejpam-5241	58	28	of	of	ADP
ejpam-5241	58	29	vertex	vertex	NOUN
ejpam-5241	58	30	u	u	NOUN
ejpam-5241	58	31	in	in	ADP
ejpam-5241	58	32	g	g	PROPN
ejpam-5241	58	33	if	if	SCONJ
ejpam-5241	58	34	dg(u	dg(u	NOUN
ejpam-5241	58	35	,	,	PUNCT
ejpam-5241	58	36	v	v	NOUN
ejpam-5241	58	37	)	)	PUNCT
ejpam-5241	58	38	=	=	SYM
ejpam-5241	58	39	2	2	X
ejpam-5241	58	40	.	.	X
ejpam-5241	59	1	the	the	DET
ejpam-5241	59	2	set	set	ADJ
ejpam-5241	59	3	n2	n2	ADJ
ejpam-5241	59	4	g(u	g(u	PROPN
ejpam-5241	59	5	)	)	PUNCT
ejpam-5241	59	6	=	=	PRON
ejpam-5241	59	7	{	{	PUNCT
ejpam-5241	59	8	v	v	NUM
ejpam-5241	59	9	∈	∈	NOUN
ejpam-5241	59	10	v	v	NOUN
ejpam-5241	59	11	(	(	PUNCT
ejpam-5241	59	12	g	g	NOUN
ejpam-5241	59	13	)	)	PUNCT
ejpam-5241	59	14	:	:	PUNCT
ejpam-5241	59	15	dg(v	dg(v	X
ejpam-5241	59	16	,	,	PUNCT
ejpam-5241	59	17	u	u	NOUN
ejpam-5241	59	18	)	)	PUNCT
ejpam-5241	59	19	=	=	SYM
ejpam-5241	59	20	2	2	X
ejpam-5241	59	21	}	}	PUNCT
ejpam-5241	59	22	is	be	AUX
ejpam-5241	59	23	called	call	VERB
ejpam-5241	59	24	the	the	DET
ejpam-5241	59	25	open	open	ADJ
ejpam-5241	59	26	hop	hop	NOUN
ejpam-5241	59	27	neighborhood	neighborhood	NOUN
ejpam-5241	59	28	of	of	ADP
ejpam-5241	59	29	u.	u.	PROPN
ejpam-5241	59	30	the	the	DET
ejpam-5241	59	31	closed	closed	ADJ
ejpam-5241	59	32	hop	hop	NOUN
ejpam-5241	59	33	neighborhood	neighborhood	NOUN
ejpam-5241	59	34	of	of	ADP
ejpam-5241	59	35	u	u	PROPN
ejpam-5241	59	36	in	in	ADP
ejpam-5241	59	37	g	g	PROPN
ejpam-5241	59	38	is	be	AUX
ejpam-5241	59	39	given	give	VERB
ejpam-5241	59	40	by	by	ADP
ejpam-5241	59	41	n2	n2	PROPN
ejpam-5241	59	42	g[u	g[u	PROPN
ejpam-5241	59	43	]	]	X
ejpam-5241	59	44	=	=	SYM
ejpam-5241	59	45	n2	n2	ADJ
ejpam-5241	59	46	g(u	g(u	PROPN
ejpam-5241	59	47	)	)	PUNCT
ejpam-5241	59	48	∪	∪	NOUN
ejpam-5241	59	49	{	{	PUNCT
ejpam-5241	59	50	u	u	NOUN
ejpam-5241	59	51	}	}	PUNCT
ejpam-5241	59	52	.	.	PUNCT
ejpam-5241	60	1	the	the	DET
ejpam-5241	60	2	open	open	ADJ
ejpam-5241	60	3	hop	hop	NOUN
ejpam-5241	60	4	neighborhood	neighborhood	NOUN
ejpam-5241	60	5	of	of	ADP
ejpam-5241	60	6	x	x	PROPN
ejpam-5241	60	7	⊆	⊆	NUM
ejpam-5241	60	8	v	v	ADP
ejpam-5241	60	9	(	(	PUNCT
ejpam-5241	60	10	g	g	NOUN
ejpam-5241	60	11	)	)	PUNCT
ejpam-5241	60	12	is	be	AUX
ejpam-5241	60	13	the	the	DET
ejpam-5241	60	14	set	set	ADJ
ejpam-5241	60	15	n2	n2	ADJ
ejpam-5241	60	16	g(x	g(x	NOUN
ejpam-5241	60	17	)	)	PUNCT
ejpam-5241	61	1	=	=	SYM
ejpam-5241	61	2	⋃	⋃	NOUN
ejpam-5241	61	3	u∈x	u∈x	ADJ
ejpam-5241	61	4	n2	n2	NOUN
ejpam-5241	61	5	g(u	g(u	PROPN
ejpam-5241	61	6	)	)	PUNCT
ejpam-5241	61	7	.	.	PUNCT
ejpam-5241	62	1	the	the	DET
ejpam-5241	62	2	closed	closed	ADJ
ejpam-5241	62	3	hop	hop	NOUN
ejpam-5241	62	4	neighborhood	neighborhood	NOUN
ejpam-5241	62	5	of	of	ADP
ejpam-5241	62	6	x	x	PUNCT
ejpam-5241	62	7	in	in	ADP
ejpam-5241	62	8	g	g	PROPN
ejpam-5241	62	9	is	be	AUX
ejpam-5241	62	10	the	the	DET
ejpam-5241	62	11	set	set	ADJ
ejpam-5241	62	12	n2	n2	NOUN
ejpam-5241	62	13	g[x	g[x	PROPN
ejpam-5241	62	14	]	]	X
ejpam-5241	62	15	=	=	SYM
ejpam-5241	62	16	n2	n2	ADJ
ejpam-5241	62	17	g(x	g(x	NOUN
ejpam-5241	62	18	)	)	PUNCT
ejpam-5241	62	19	∪	∪	NOUN
ejpam-5241	62	20	x.	x.	NOUN
ejpam-5241	62	21	let	let	VERB
ejpam-5241	62	22	g	g	NOUN
ejpam-5241	62	23	be	be	AUX
ejpam-5241	62	24	a	a	DET
ejpam-5241	62	25	connected	connected	ADJ
ejpam-5241	62	26	graph	graph	NOUN
ejpam-5241	62	27	.	.	PUNCT
ejpam-5241	63	1	a	a	DET
ejpam-5241	63	2	set	set	NOUN
ejpam-5241	63	3	s	s	NOUN
ejpam-5241	63	4	⊆	⊆	NUM
ejpam-5241	63	5	v	v	NOUN
ejpam-5241	63	6	(	(	PUNCT
ejpam-5241	63	7	g	g	NOUN
ejpam-5241	63	8	)	)	PUNCT
ejpam-5241	63	9	is	be	AUX
ejpam-5241	63	10	a	a	DET
ejpam-5241	63	11	hop	hop	NOUN
ejpam-5241	63	12	dominating	dominating	NOUN
ejpam-5241	63	13	set	set	NOUN
ejpam-5241	63	14	of	of	ADP
ejpam-5241	63	15	g	g	PROPN
ejpam-5241	63	16	if	if	SCONJ
ejpam-5241	63	17	for	for	ADP
ejpam-5241	63	18	every	every	PRON
ejpam-5241	63	19	v	v	NUM
ejpam-5241	63	20	∈	∈	NOUN
ejpam-5241	63	21	v	v	NOUN
ejpam-5241	63	22	(	(	PUNCT
ejpam-5241	63	23	g	g	NOUN
ejpam-5241	63	24	)	)	PUNCT
ejpam-5241	63	25	\	\	PROPN
ejpam-5241	64	1	s	s	X
ejpam-5241	64	2	,	,	PUNCT
ejpam-5241	64	3	there	there	PRON
ejpam-5241	64	4	exists	exist	VERB
ejpam-5241	64	5	u	u	PROPN
ejpam-5241	64	6	∈	∈	PROPN
ejpam-5241	64	7	s	s	VERB
ejpam-5241	64	8	such	such	ADJ
ejpam-5241	64	9	that	that	DET
ejpam-5241	64	10	dg(u	dg(u	ADJ
ejpam-5241	64	11	,	,	PUNCT
ejpam-5241	64	12	v	v	NOUN
ejpam-5241	64	13	)	)	PUNCT
ejpam-5241	64	14	=	=	SYM
ejpam-5241	64	15	2	2	X
ejpam-5241	64	16	.	.	X
ejpam-5241	65	1	in	in	ADP
ejpam-5241	65	2	particular	particular	ADJ
ejpam-5241	65	3	,	,	PUNCT
ejpam-5241	65	4	a	a	DET
ejpam-5241	65	5	set	set	NOUN
ejpam-5241	65	6	s	s	NOUN
ejpam-5241	65	7	⊆	⊆	NUM
ejpam-5241	65	8	v	v	NOUN
ejpam-5241	65	9	(	(	PUNCT
ejpam-5241	65	10	g	g	NOUN
ejpam-5241	65	11	)	)	PUNCT
ejpam-5241	65	12	is	be	AUX
ejpam-5241	65	13	a	a	DET
ejpam-5241	65	14	hop	hop	NOUN
ejpam-5241	65	15	dominating	dominating	NOUN
ejpam-5241	65	16	set	set	NOUN
ejpam-5241	65	17	if	if	SCONJ
ejpam-5241	65	18	n2	n2	ADJ
ejpam-5241	65	19	g[s	g[s	PROPN
ejpam-5241	65	20	]	]	X
ejpam-5241	65	21	=	=	SYM
ejpam-5241	65	22	v	v	NOUN
ejpam-5241	65	23	(	(	PUNCT
ejpam-5241	65	24	g	g	NOUN
ejpam-5241	65	25	)	)	PUNCT
ejpam-5241	65	26	.	.	PUNCT
ejpam-5241	66	1	the	the	DET
ejpam-5241	66	2	minimum	minimum	ADJ
ejpam-5241	66	3	cardinality	cardinality	NOUN
ejpam-5241	66	4	of	of	ADP
ejpam-5241	66	5	a	a	DET
ejpam-5241	66	6	hop	hop	NOUN
ejpam-5241	66	7	dominating	dominating	NOUN
ejpam-5241	66	8	set	set	NOUN
ejpam-5241	66	9	of	of	ADP
ejpam-5241	66	10	g	g	NOUN
ejpam-5241	66	11	,	,	PUNCT
ejpam-5241	66	12	denoted	denote	VERB
ejpam-5241	66	13	by	by	ADP
ejpam-5241	66	14	γh(g	γh(g	NOUN
ejpam-5241	66	15	)	)	PUNCT
ejpam-5241	66	16	,	,	PUNCT
ejpam-5241	66	17	is	be	AUX
ejpam-5241	66	18	called	call	VERB
ejpam-5241	66	19	the	the	DET
ejpam-5241	66	20	hop	hop	NOUN
ejpam-5241	66	21	domination	domination	NOUN
ejpam-5241	66	22	number	number	NOUN
ejpam-5241	66	23	of	of	ADP
ejpam-5241	66	24	g.	g.	PROPN
ejpam-5241	66	25	any	any	DET
ejpam-5241	66	26	hop	hop	NOUN
ejpam-5241	66	27	dominating	dominating	NOUN
ejpam-5241	66	28	set	set	VERB
ejpam-5241	66	29	with	with	ADP
ejpam-5241	66	30	cardinality	cardinality	NOUN
ejpam-5241	66	31	equals	equal	VERB
ejpam-5241	66	32	to	to	ADP
ejpam-5241	66	33	γh(g	γh(g	NOUN
ejpam-5241	66	34	)	)	PUNCT
ejpam-5241	66	35	is	be	AUX
ejpam-5241	66	36	called	call	VERB
ejpam-5241	66	37	a	a	DET
ejpam-5241	66	38	γh	γh	ADV
ejpam-5241	66	39	-	-	PUNCT
ejpam-5241	66	40	set	set	NOUN
ejpam-5241	66	41	of	of	ADP
ejpam-5241	66	42	g.	g.	PROPN
ejpam-5241	66	43	a	a	DET
ejpam-5241	66	44	subset	subset	NOUN
ejpam-5241	66	45	s	s	NOUN
ejpam-5241	66	46	of	of	ADP
ejpam-5241	66	47	vertex	vertex	NOUN
ejpam-5241	66	48	set	set	NOUN
ejpam-5241	66	49	of	of	ADP
ejpam-5241	66	50	g	g	PROPN
ejpam-5241	66	51	is	be	AUX
ejpam-5241	66	52	a	a	DET
ejpam-5241	66	53	geodetic	geodetic	ADJ
ejpam-5241	66	54	hop	hop	NOUN
ejpam-5241	66	55	dominating	dominating	NOUN
ejpam-5241	66	56	set	set	NOUN
ejpam-5241	66	57	if	if	SCONJ
ejpam-5241	66	58	it	it	PRON
ejpam-5241	66	59	is	be	AUX
ejpam-5241	66	60	both	both	CCONJ
ejpam-5241	66	61	a	a	DET
ejpam-5241	66	62	geodetic	geodetic	ADJ
ejpam-5241	66	63	and	and	CCONJ
ejpam-5241	66	64	a	a	DET
ejpam-5241	66	65	hop	hop	NOUN
ejpam-5241	66	66	dominating	dominating	NOUN
ejpam-5241	66	67	set	set	NOUN
ejpam-5241	66	68	.	.	PUNCT
ejpam-5241	67	1	the	the	DET
ejpam-5241	67	2	geodetic	geodetic	ADJ
ejpam-5241	67	3	hop	hop	NOUN
ejpam-5241	67	4	domination	domination	NOUN
ejpam-5241	67	5	number	number	NOUN
ejpam-5241	67	6	γhg(g	γhg(g	PROPN
ejpam-5241	67	7	)	)	PUNCT
ejpam-5241	67	8	of	of	ADP
ejpam-5241	67	9	g	g	PROPN
ejpam-5241	67	10	is	be	AUX
ejpam-5241	67	11	the	the	DET
ejpam-5241	67	12	minimum	minimum	ADJ
ejpam-5241	67	13	cardinality	cardinality	NOUN
ejpam-5241	67	14	among	among	ADP
ejpam-5241	67	15	all	all	DET
ejpam-5241	67	16	geodetic	geodetic	ADJ
ejpam-5241	67	17	hop	hop	NOUN
ejpam-5241	67	18	dominating	dominating	NOUN
ejpam-5241	67	19	sets	set	NOUN
ejpam-5241	67	20	in	in	ADP
ejpam-5241	67	21	g.	g.	PROPN
ejpam-5241	67	22	any	any	DET
ejpam-5241	67	23	geodetic	geodetic	ADJ
ejpam-5241	67	24	hop	hop	NOUN
ejpam-5241	67	25	dominating	dominating	NOUN
ejpam-5241	67	26	set	set	NOUN
ejpam-5241	67	27	of	of	ADP
ejpam-5241	67	28	g	g	PROPN
ejpam-5241	67	29	with	with	ADP
ejpam-5241	67	30	cardinality	cardinality	PROPN
ejpam-5241	67	31	γhg(g	γhg(g	PROPN
ejpam-5241	67	32	)	)	PUNCT
ejpam-5241	67	33	is	be	AUX
ejpam-5241	67	34	called	call	VERB
ejpam-5241	67	35	a	a	DET
ejpam-5241	67	36	γhg	γhg	NOUN
ejpam-5241	67	37	-	-	PUNCT
ejpam-5241	67	38	set	set	NOUN
ejpam-5241	67	39	of	of	ADP
ejpam-5241	67	40	g.	g.	PROPN
ejpam-5241	67	41	the	the	DET
ejpam-5241	67	42	geodetic	geodetic	ADJ
ejpam-5241	67	43	hop	hop	NOUN
ejpam-5241	67	44	dominating	dominating	NOUN
ejpam-5241	67	45	set	set	NOUN
ejpam-5241	67	46	was	be	AUX
ejpam-5241	67	47	first	first	ADV
ejpam-5241	67	48	introduced	introduce	VERB
ejpam-5241	67	49	by	by	ADP
ejpam-5241	67	50	anusha	anusha	PROPN
ejpam-5241	67	51	et	et	PROPN
ejpam-5241	67	52	al	al	PROPN
ejpam-5241	67	53	.	.	PUNCT
ejpam-5241	68	1	in	in	ADP
ejpam-5241	68	2	[	[	X
ejpam-5241	68	3	3	3	NUM
ejpam-5241	68	4	]	]	PUNCT
ejpam-5241	68	5	.	.	PUNCT
ejpam-5241	69	1	it	it	PRON
ejpam-5241	69	2	is	be	AUX
ejpam-5241	69	3	further	far	ADV
ejpam-5241	69	4	investigated	investigate	VERB
ejpam-5241	69	5	by	by	ADP
ejpam-5241	69	6	saromines	saromine	NOUN
ejpam-5241	69	7	et	et	PROPN
ejpam-5241	69	8	al	al	PROPN
ejpam-5241	69	9	.	.	PUNCT
ejpam-5241	70	1	in	in	ADP
ejpam-5241	70	2	[	[	X
ejpam-5241	70	3	18	18	NUM
ejpam-5241	70	4	,	,	PUNCT
ejpam-5241	70	5	19	19	NUM
ejpam-5241	70	6	]	]	PUNCT
ejpam-5241	70	7	.	.	PUNCT
ejpam-5241	71	1	the	the	DET
ejpam-5241	71	2	following	follow	VERB
ejpam-5241	71	3	results	result	NOUN
ejpam-5241	71	4	concerning	concern	VERB
ejpam-5241	71	5	geodetic	geodetic	ADJ
ejpam-5241	71	6	hop	hop	NOUN
ejpam-5241	71	7	domination	domination	NOUN
ejpam-5241	71	8	on	on	ADP
ejpam-5241	71	9	paths	path	NOUN
ejpam-5241	71	10	and	and	CCONJ
ejpam-5241	71	11	cycles	cycle	NOUN
ejpam-5241	71	12	are	be	AUX
ejpam-5241	71	13	found	find	VERB
ejpam-5241	71	14	in	in	ADP
ejpam-5241	71	15	[	[	X
ejpam-5241	71	16	19	19	NUM
ejpam-5241	71	17	]	]	PUNCT
ejpam-5241	71	18	.	.	PUNCT
ejpam-5241	72	1	proposition	proposition	NOUN
ejpam-5241	72	2	1	1	NUM
ejpam-5241	72	3	.	.	PUNCT
ejpam-5241	73	1	[	[	X
ejpam-5241	73	2	19	19	NUM
ejpam-5241	73	3	]	]	PUNCT
ejpam-5241	73	4	let	let	VERB
ejpam-5241	73	5	n	n	PRON
ejpam-5241	73	6	be	be	AUX
ejpam-5241	73	7	a	a	DET
ejpam-5241	73	8	positive	positive	ADJ
ejpam-5241	73	9	integer	integer	NOUN
ejpam-5241	73	10	.	.	PUNCT
ejpam-5241	74	1	a.	a.	PROPN
ejpam-5241	74	2	adolfo	adolfo	PROPN
ejpam-5241	74	3	,	,	PUNCT
ejpam-5241	74	4	i.	i.	PROPN
ejpam-5241	74	5	aniversario	aniversario	PROPN
ejpam-5241	74	6	,	,	PUNCT
ejpam-5241	74	7	f.	f.	PROPN
ejpam-5241	74	8	jamil	jamil	PROPN
ejpam-5241	74	9	/	/	SYM
ejpam-5241	74	10	eur	eur	PROPN
ejpam-5241	74	11	.	.	PUNCT
ejpam-5241	75	1	j.	j.	PROPN
ejpam-5241	75	2	pure	pure	PROPN
ejpam-5241	75	3	appl	appl	PROPN
ejpam-5241	75	4	.	.	PROPN
ejpam-5241	75	5	math	math	PROPN
ejpam-5241	75	6	,	,	PUNCT
ejpam-5241	75	7	17	17	NUM
ejpam-5241	75	8	(	(	PUNCT
ejpam-5241	75	9	3	3	NUM
ejpam-5241	75	10	)	)	PUNCT
ejpam-5241	75	11	(	(	PUNCT
ejpam-5241	75	12	2024	2024	NUM
ejpam-5241	75	13	)	)	PUNCT
ejpam-5241	75	14	,	,	PUNCT
ejpam-5241	75	15	1618	1618	NUM
ejpam-5241	75	16	-	-	SYM
ejpam-5241	75	17	1636	1636	NUM
ejpam-5241	75	18	1621	1621	NUM
ejpam-5241	75	19	(	(	PUNCT
ejpam-5241	75	20	i	i	NOUN
ejpam-5241	75	21	)	)	PUNCT
ejpam-5241	75	22	for	for	ADP
ejpam-5241	75	23	a	a	DET
ejpam-5241	75	24	path	path	NOUN
ejpam-5241	75	25	pn	pn	NOUN
ejpam-5241	75	26	on	on	ADP
ejpam-5241	75	27	n	n	PRON
ejpam-5241	75	28	vertices	vertex	NOUN
ejpam-5241	75	29	,	,	PUNCT
ejpam-5241	75	30	γhg(pn	γhg(pn	NOUN
ejpam-5241	75	31	)	)	PUNCT
ejpam-5241	75	32	=	=	PUNCT
ejpam-5241	75	33			VERB
ejpam-5241	76	1	n	n	CCONJ
ejpam-5241	76	2	if	if	SCONJ
ejpam-5241	76	3	n	n	NOUN
ejpam-5241	76	4	=	=	SYM
ejpam-5241	76	5	1	1	NUM
ejpam-5241	76	6	,	,	PUNCT
ejpam-5241	76	7	2	2	NUM
ejpam-5241	76	8	,	,	PUNCT
ejpam-5241	76	9	n+6	n+6	NOUN
ejpam-5241	76	10	3	3	NUM
ejpam-5241	76	11	if	if	SCONJ
ejpam-5241	76	12	n	n	PRON
ejpam-5241	76	13	≡	≡	PROPN
ejpam-5241	76	14	0(mod	0(mod	NOUN
ejpam-5241	77	1	3	3	X
ejpam-5241	77	2	)	)	PUNCT
ejpam-5241	77	3	,	,	PUNCT
ejpam-5241	78	1	n+2	n+2	PRON
ejpam-5241	78	2	3	3	NUM
ejpam-5241	78	3	if	if	SCONJ
ejpam-5241	78	4	n	n	PRON
ejpam-5241	78	5	≡	≡	PROPN
ejpam-5241	78	6	1(mod	1(mod	NUM
ejpam-5241	78	7	3	3	NUM
ejpam-5241	78	8	)	)	PUNCT
ejpam-5241	78	9	,	,	PUNCT
ejpam-5241	78	10	n+4	n+4	NUM
ejpam-5241	78	11	3	3	NUM
ejpam-5241	78	12	if	if	SCONJ
ejpam-5241	78	13	n	n	PRON
ejpam-5241	78	14	≡	≡	PROPN
ejpam-5241	78	15	2(mod	2(mod	NUM
ejpam-5241	78	16	3	3	X
ejpam-5241	78	17	)	)	PUNCT
ejpam-5241	78	18	(	(	PUNCT
ejpam-5241	78	19	ii	ii	NOUN
ejpam-5241	78	20	)	)	PUNCT
ejpam-5241	78	21	for	for	ADP
ejpam-5241	78	22	a	a	DET
ejpam-5241	78	23	cycle	cycle	NOUN
ejpam-5241	78	24	cn	cn	NOUN
ejpam-5241	78	25	on	on	ADP
ejpam-5241	78	26	n	n	PRON
ejpam-5241	78	27	vertices	vertex	NOUN
ejpam-5241	78	28	,	,	PUNCT
ejpam-5241	78	29	γhg(cn	γhg(cn	NOUN
ejpam-5241	78	30	)	)	PUNCT
ejpam-5241	78	31	=	=	PUNCT
ejpam-5241	78	32			NOUN
ejpam-5241	78	33	3	3	NUM
ejpam-5241	78	34	if	if	SCONJ
ejpam-5241	78	35	n	n	NOUN
ejpam-5241	78	36	=	=	SYM
ejpam-5241	78	37	3	3	NUM
ejpam-5241	78	38	,	,	PUNCT
ejpam-5241	78	39	4	4	NUM
ejpam-5241	78	40	,	,	PUNCT
ejpam-5241	78	41	5	5	NUM
ejpam-5241	78	42	,	,	PUNCT
ejpam-5241	78	43	n	n	PRON
ejpam-5241	78	44	3	3	NUM
ejpam-5241	78	45	if	if	SCONJ
ejpam-5241	78	46	n	n	PRON
ejpam-5241	78	47	≡	≡	PROPN
ejpam-5241	78	48	0(mod	0(mod	NOUN
ejpam-5241	78	49	3	3	X
ejpam-5241	78	50	)	)	PUNCT
ejpam-5241	78	51	,	,	PUNCT
ejpam-5241	79	1	n+2	n+2	PRON
ejpam-5241	79	2	3	3	NUM
ejpam-5241	79	3	if	if	SCONJ
ejpam-5241	79	4	n	n	PRON
ejpam-5241	79	5	≡	≡	PROPN
ejpam-5241	79	6	1(mod	1(mod	NUM
ejpam-5241	79	7	3	3	NUM
ejpam-5241	79	8	)	)	PUNCT
ejpam-5241	79	9	,	,	PUNCT
ejpam-5241	79	10	n+4	n+4	NUM
ejpam-5241	79	11	3	3	NUM
ejpam-5241	79	12	if	if	SCONJ
ejpam-5241	79	13	n	n	PRON
ejpam-5241	79	14	≡	≡	PROPN
ejpam-5241	79	15	2(mod	2(mod	NUM
ejpam-5241	79	16	3	3	X
ejpam-5241	79	17	)	)	PUNCT
ejpam-5241	79	18	.	.	PUNCT
ejpam-5241	80	1	2	2	X
ejpam-5241	80	2	.	.	X
ejpam-5241	80	3	results	result	NOUN
ejpam-5241	80	4	in	in	ADP
ejpam-5241	80	5	this	this	DET
ejpam-5241	80	6	section	section	NOUN
ejpam-5241	80	7	,	,	PUNCT
ejpam-5241	80	8	we	we	PRON
ejpam-5241	80	9	introduce	introduce	VERB
ejpam-5241	80	10	and	and	CCONJ
ejpam-5241	80	11	initiate	initiate	VERB
ejpam-5241	80	12	the	the	DET
ejpam-5241	80	13	study	study	NOUN
ejpam-5241	80	14	of	of	ADP
ejpam-5241	80	15	closed	closed	ADJ
ejpam-5241	80	16	geodetic	geodetic	ADJ
ejpam-5241	80	17	hop	hop	NOUN
ejpam-5241	80	18	domination	domination	NOUN
ejpam-5241	80	19	in	in	ADP
ejpam-5241	80	20	graphs	graph	NOUN
ejpam-5241	80	21	.	.	PUNCT
ejpam-5241	81	1	2.1	2.1	NUM
ejpam-5241	81	2	.	.	PUNCT
ejpam-5241	81	3	closed	close	VERB
ejpam-5241	81	4	geodetic	geodetic	ADJ
ejpam-5241	81	5	hop	hop	NOUN
ejpam-5241	81	6	domination	domination	NOUN
ejpam-5241	81	7	a	a	DET
ejpam-5241	81	8	subset	subset	NOUN
ejpam-5241	81	9	s	s	NOUN
ejpam-5241	81	10	of	of	ADP
ejpam-5241	81	11	vertices	vertex	NOUN
ejpam-5241	81	12	of	of	ADP
ejpam-5241	81	13	g	g	PROPN
ejpam-5241	81	14	is	be	AUX
ejpam-5241	81	15	a	a	DET
ejpam-5241	81	16	closed	closed	ADJ
ejpam-5241	81	17	geodetic	geodetic	ADJ
ejpam-5241	81	18	hop	hop	NOUN
ejpam-5241	81	19	dominating	dominating	NOUN
ejpam-5241	81	20	set	set	NOUN
ejpam-5241	82	1	if	if	SCONJ
ejpam-5241	82	2	it	it	PRON
ejpam-5241	82	3	is	be	AUX
ejpam-5241	82	4	both	both	CCONJ
ejpam-5241	82	5	a	a	DET
ejpam-5241	82	6	geodetic	geodetic	ADJ
ejpam-5241	82	7	hop	hop	NOUN
ejpam-5241	82	8	dominating	dominating	NOUN
ejpam-5241	82	9	set	set	NOUN
ejpam-5241	82	10	and	and	CCONJ
ejpam-5241	82	11	a	a	DET
ejpam-5241	82	12	closed	closed	ADJ
ejpam-5241	82	13	geodetic	geodetic	ADJ
ejpam-5241	82	14	cover	cover	NOUN
ejpam-5241	82	15	of	of	ADP
ejpam-5241	82	16	g.	g.	PROPN
ejpam-5241	82	17	the	the	DET
ejpam-5241	82	18	minimum	minimum	ADJ
ejpam-5241	82	19	cardinality	cardinality	NOUN
ejpam-5241	82	20	among	among	ADP
ejpam-5241	82	21	all	all	DET
ejpam-5241	82	22	closed	close	VERB
ejpam-5241	82	23	geodetic	geodetic	ADJ
ejpam-5241	82	24	hop	hop	NOUN
ejpam-5241	82	25	dominating	dominating	NOUN
ejpam-5241	82	26	sets	set	NOUN
ejpam-5241	82	27	in	in	ADP
ejpam-5241	82	28	g	g	NOUN
ejpam-5241	82	29	,	,	PUNCT
ejpam-5241	82	30	denoted	denote	VERB
ejpam-5241	82	31	by	by	ADP
ejpam-5241	82	32	γhcg(g	γhcg(g	NOUN
ejpam-5241	82	33	)	)	PUNCT
ejpam-5241	82	34	is	be	AUX
ejpam-5241	82	35	called	call	VERB
ejpam-5241	82	36	the	the	DET
ejpam-5241	82	37	closed	closed	ADJ
ejpam-5241	82	38	geodetic	geodetic	ADJ
ejpam-5241	82	39	hop	hop	NOUN
ejpam-5241	82	40	domination	domination	NOUN
ejpam-5241	82	41	number	number	NOUN
ejpam-5241	82	42	of	of	ADP
ejpam-5241	82	43	g.	g.	PROPN
ejpam-5241	82	44	a	a	DET
ejpam-5241	82	45	closed	close	VERB
ejpam-5241	82	46	geodetic	geodetic	ADJ
ejpam-5241	82	47	hop	hop	NOUN
ejpam-5241	82	48	dominating	dominating	NOUN
ejpam-5241	82	49	set	set	NOUN
ejpam-5241	82	50	s	s	NOUN
ejpam-5241	82	51	of	of	ADP
ejpam-5241	82	52	g	g	NOUN
ejpam-5241	82	53	with	with	ADP
ejpam-5241	82	54	|s|	|s|	PROPN
ejpam-5241	82	55	=	=	PUNCT
ejpam-5241	82	56	γhcg(g	γhcg(g	NOUN
ejpam-5241	82	57	)	)	PUNCT
ejpam-5241	82	58	is	be	AUX
ejpam-5241	82	59	called	call	VERB
ejpam-5241	82	60	a	a	DET
ejpam-5241	82	61	γhcg	γhcg	NOUN
ejpam-5241	82	62	-	-	PUNCT
ejpam-5241	82	63	set	set	NOUN
ejpam-5241	82	64	of	of	ADP
ejpam-5241	82	65	g.	g.	NOUN
ejpam-5241	82	66	we	we	PRON
ejpam-5241	82	67	remark	remark	VERB
ejpam-5241	82	68	that	that	SCONJ
ejpam-5241	82	69	not	not	PART
ejpam-5241	82	70	every	every	DET
ejpam-5241	82	71	graph	graph	NOUN
ejpam-5241	82	72	admits	admit	VERB
ejpam-5241	82	73	a	a	DET
ejpam-5241	82	74	closed	closed	ADJ
ejpam-5241	82	75	geodetic	geodetic	ADJ
ejpam-5241	82	76	hop	hop	NOUN
ejpam-5241	82	77	dominating	dominating	NOUN
ejpam-5241	82	78	set	set	NOUN
ejpam-5241	82	79	.	.	PUNCT
ejpam-5241	83	1	consider	consider	VERB
ejpam-5241	83	2	,	,	PUNCT
ejpam-5241	83	3	for	for	ADP
ejpam-5241	83	4	example	example	NOUN
ejpam-5241	83	5	,	,	PUNCT
ejpam-5241	83	6	the	the	DET
ejpam-5241	83	7	graph	graph	NOUN
ejpam-5241	83	8	g	g	PROPN
ejpam-5241	83	9	=	=	SYM
ejpam-5241	83	10	c12	c12	PROPN
ejpam-5241	83	11	.	.	PUNCT
ejpam-5241	84	1	it	it	PRON
ejpam-5241	84	2	is	be	AUX
ejpam-5241	84	3	easy	easy	ADJ
ejpam-5241	84	4	to	to	PART
ejpam-5241	84	5	verify	verify	VERB
ejpam-5241	84	6	that	that	SCONJ
ejpam-5241	84	7	every	every	DET
ejpam-5241	84	8	closed	closed	ADJ
ejpam-5241	84	9	geodetic	geodetic	ADJ
ejpam-5241	84	10	set	set	NOUN
ejpam-5241	84	11	of	of	ADP
ejpam-5241	84	12	g	g	PROPN
ejpam-5241	84	13	is	be	AUX
ejpam-5241	84	14	not	not	PART
ejpam-5241	84	15	a	a	DET
ejpam-5241	84	16	hop	hop	NOUN
ejpam-5241	84	17	dominating	dominating	NOUN
ejpam-5241	84	18	set	set	NOUN
ejpam-5241	84	19	.	.	PUNCT
ejpam-5241	85	1	observation	observation	NOUN
ejpam-5241	85	2	1	1	NUM
ejpam-5241	85	3	.	.	PUNCT
ejpam-5241	86	1	let	let	VERB
ejpam-5241	86	2	g	g	PRON
ejpam-5241	86	3	be	be	AUX
ejpam-5241	86	4	a	a	DET
ejpam-5241	86	5	connected	connected	ADJ
ejpam-5241	86	6	graph	graph	NOUN
ejpam-5241	86	7	.	.	PUNCT
ejpam-5241	87	1	if	if	SCONJ
ejpam-5241	87	2	v	v	INTJ
ejpam-5241	87	3	(	(	PUNCT
ejpam-5241	87	4	g	g	NOUN
ejpam-5241	87	5	)	)	PUNCT
ejpam-5241	87	6	is	be	AUX
ejpam-5241	87	7	a	a	DET
ejpam-5241	87	8	closed	closed	ADJ
ejpam-5241	87	9	geodetic	geodetic	ADJ
ejpam-5241	87	10	set	set	NOUN
ejpam-5241	87	11	,	,	PUNCT
ejpam-5241	87	12	then	then	ADV
ejpam-5241	87	13	g	g	PROPN
ejpam-5241	87	14	admits	admit	VERB
ejpam-5241	87	15	a	a	DET
ejpam-5241	87	16	closed	closed	ADJ
ejpam-5241	87	17	geodetic	geodetic	ADJ
ejpam-5241	87	18	hop	hop	NOUN
ejpam-5241	87	19	dominating	dominating	NOUN
ejpam-5241	87	20	set	set	NOUN
ejpam-5241	87	21	.	.	PUNCT
ejpam-5241	88	1	the	the	DET
ejpam-5241	88	2	following	following	NOUN
ejpam-5241	88	3	also	also	ADV
ejpam-5241	88	4	provides	provide	VERB
ejpam-5241	88	5	some	some	DET
ejpam-5241	88	6	other	other	ADJ
ejpam-5241	88	7	conditions	condition	NOUN
ejpam-5241	88	8	under	under	ADP
ejpam-5241	88	9	which	which	PRON
ejpam-5241	88	10	a	a	DET
ejpam-5241	88	11	graph	graph	NOUN
ejpam-5241	88	12	admits	admit	VERB
ejpam-5241	88	13	a	a	DET
ejpam-5241	88	14	closed	closed	ADJ
ejpam-5241	88	15	geodetic	geodetic	ADJ
ejpam-5241	88	16	hop	hop	NOUN
ejpam-5241	88	17	dominating	dominating	NOUN
ejpam-5241	88	18	set	set	NOUN
ejpam-5241	88	19	.	.	PUNCT
ejpam-5241	89	1	proposition	proposition	NOUN
ejpam-5241	89	2	2	2	NUM
ejpam-5241	89	3	.	.	PUNCT
ejpam-5241	90	1	if	if	SCONJ
ejpam-5241	90	2	g	g	PROPN
ejpam-5241	90	3	is	be	AUX
ejpam-5241	90	4	a	a	DET
ejpam-5241	90	5	connected	connected	ADJ
ejpam-5241	90	6	graph	graph	NOUN
ejpam-5241	90	7	with	with	ADP
ejpam-5241	90	8	diam(g	diam(g	NOUN
ejpam-5241	90	9	)	)	PUNCT
ejpam-5241	90	10	≤	≤	NOUN
ejpam-5241	90	11	2	2	NUM
ejpam-5241	90	12	,	,	PUNCT
ejpam-5241	90	13	then	then	ADV
ejpam-5241	90	14	g	g	PROPN
ejpam-5241	90	15	admits	admit	VERB
ejpam-5241	90	16	a	a	DET
ejpam-5241	90	17	closed	closed	ADJ
ejpam-5241	90	18	geodetic	geodetic	ADJ
ejpam-5241	90	19	hop	hop	NOUN
ejpam-5241	90	20	dominating	dominating	NOUN
ejpam-5241	90	21	set	set	NOUN
ejpam-5241	90	22	.	.	PUNCT
ejpam-5241	91	1	proof	proof	NOUN
ejpam-5241	91	2	.	.	PUNCT
ejpam-5241	92	1	if	if	SCONJ
ejpam-5241	92	2	diam(g	diam(g	NOUN
ejpam-5241	92	3	)	)	PUNCT
ejpam-5241	92	4	=	=	SYM
ejpam-5241	93	1	1	1	NUM
ejpam-5241	93	2	,	,	PUNCT
ejpam-5241	93	3	then	then	ADV
ejpam-5241	93	4	g	g	PROPN
ejpam-5241	93	5	is	be	AUX
ejpam-5241	93	6	complete	complete	ADJ
ejpam-5241	93	7	so	so	SCONJ
ejpam-5241	93	8	that	that	SCONJ
ejpam-5241	93	9	v	v	NOUN
ejpam-5241	93	10	(	(	PUNCT
ejpam-5241	93	11	g	g	NOUN
ejpam-5241	93	12	)	)	PUNCT
ejpam-5241	93	13	is	be	AUX
ejpam-5241	93	14	a	a	DET
ejpam-5241	93	15	closed	closed	ADJ
ejpam-5241	93	16	geodetic	geodetic	ADJ
ejpam-5241	93	17	set	set	NOUN
ejpam-5241	93	18	.	.	PUNCT
ejpam-5241	94	1	as	as	SCONJ
ejpam-5241	94	2	observed	observed	ADJ
ejpam-5241	94	3	above	above	ADV
ejpam-5241	94	4	,	,	PUNCT
ejpam-5241	94	5	g	g	PROPN
ejpam-5241	94	6	admits	admit	VERB
ejpam-5241	94	7	a	a	DET
ejpam-5241	94	8	closed	closed	ADJ
ejpam-5241	94	9	geodetic	geodetic	ADJ
ejpam-5241	94	10	hop	hop	NOUN
ejpam-5241	94	11	dominating	dominating	NOUN
ejpam-5241	94	12	set	set	NOUN
ejpam-5241	94	13	.	.	PUNCT
ejpam-5241	95	1	suppose	suppose	VERB
ejpam-5241	96	1	diam(g	diam(g	NOUN
ejpam-5241	96	2	)	)	PUNCT
ejpam-5241	96	3	=	=	SYM
ejpam-5241	97	1	2	2	X
ejpam-5241	97	2	.	.	PUNCT
ejpam-5241	97	3	then	then	ADV
ejpam-5241	97	4	g	g	PROPN
ejpam-5241	97	5	is	be	AUX
ejpam-5241	97	6	not	not	PART
ejpam-5241	97	7	complete	complete	ADJ
ejpam-5241	97	8	.	.	PUNCT
ejpam-5241	98	1	let	let	VERB
ejpam-5241	98	2	g1	g1	PROPN
ejpam-5241	98	3	be	be	AUX
ejpam-5241	98	4	a	a	DET
ejpam-5241	98	5	maximal	maximal	ADJ
ejpam-5241	98	6	clique	clique	NOUN
ejpam-5241	98	7	of	of	ADP
ejpam-5241	98	8	g.	g.	PROPN
ejpam-5241	98	9	let	let	VERB
ejpam-5241	98	10	v	v	NOUN
ejpam-5241	98	11	(	(	PUNCT
ejpam-5241	98	12	g1	g1	PROPN
ejpam-5241	98	13	)	)	PUNCT
ejpam-5241	98	14	=	=	SYM
ejpam-5241	98	15	sr	sr	PROPN
ejpam-5241	98	16	=	=	PUNCT
ejpam-5241	98	17	a.	a.	PROPN
ejpam-5241	98	18	adolfo	adolfo	PROPN
ejpam-5241	98	19	,	,	PUNCT
ejpam-5241	98	20	i.	i.	PROPN
ejpam-5241	98	21	aniversario	aniversario	PROPN
ejpam-5241	98	22	,	,	PUNCT
ejpam-5241	98	23	f.	f.	PROPN
ejpam-5241	98	24	jamil	jamil	PROPN
ejpam-5241	98	25	/	/	SYM
ejpam-5241	98	26	eur	eur	PROPN
ejpam-5241	98	27	.	.	PUNCT
ejpam-5241	99	1	j.	j.	PROPN
ejpam-5241	99	2	pure	pure	PROPN
ejpam-5241	99	3	appl	appl	PROPN
ejpam-5241	99	4	.	.	PROPN
ejpam-5241	99	5	math	math	PROPN
ejpam-5241	99	6	,	,	PUNCT
ejpam-5241	99	7	17	17	NUM
ejpam-5241	99	8	(	(	PUNCT
ejpam-5241	99	9	3	3	NUM
ejpam-5241	99	10	)	)	PUNCT
ejpam-5241	99	11	(	(	PUNCT
ejpam-5241	99	12	2024	2024	NUM
ejpam-5241	99	13	)	)	PUNCT
ejpam-5241	99	14	,	,	PUNCT
ejpam-5241	99	15	1618	1618	NUM
ejpam-5241	99	16	-	-	SYM
ejpam-5241	99	17	1636	1636	NUM
ejpam-5241	99	18	1622	1622	NUM
ejpam-5241	99	19	{	{	PUNCT
ejpam-5241	99	20	u1	u1	NOUN
ejpam-5241	99	21	,	,	PUNCT
ejpam-5241	99	22	u2	u2	NOUN
ejpam-5241	99	23	,	,	PUNCT
ejpam-5241	99	24	...	...	PUNCT
ejpam-5241	99	25	,	,	PUNCT
ejpam-5241	99	26	ur	ur	INTJ
ejpam-5241	99	27	}	}	PUNCT
ejpam-5241	99	28	.	.	PUNCT
ejpam-5241	100	1	since	since	SCONJ
ejpam-5241	100	2	g	g	PROPN
ejpam-5241	100	3	is	be	AUX
ejpam-5241	100	4	not	not	PART
ejpam-5241	100	5	complete	complete	ADJ
ejpam-5241	100	6	,	,	PUNCT
ejpam-5241	100	7	r	r	NOUN
ejpam-5241	100	8	<	<	X
ejpam-5241	100	9	|v	|v	X
ejpam-5241	100	10	(	(	PUNCT
ejpam-5241	100	11	g)|	g)|	NOUN
ejpam-5241	100	12	.	.	PUNCT
ejpam-5241	101	1	for	for	ADP
ejpam-5241	101	2	i	i	PRON
ejpam-5241	101	3	≥	≥	NOUN
ejpam-5241	101	4	1	1	NUM
ejpam-5241	101	5	,	,	PUNCT
ejpam-5241	101	6	choose	choose	VERB
ejpam-5241	101	7	ur+i	ur+i	ADP
ejpam-5241	101	8	∈	∈	PROPN
ejpam-5241	101	9	v	v	NOUN
ejpam-5241	101	10	(	(	PUNCT
ejpam-5241	101	11	g	g	NOUN
ejpam-5241	101	12	)	)	PUNCT
ejpam-5241	101	13	such	such	ADJ
ejpam-5241	101	14	that	that	SCONJ
ejpam-5241	101	15	ur+i	ur+i	PROPN
ejpam-5241	101	16	/∈	/∈	PUNCT
ejpam-5241	101	17	ig[sr+i−1	ig[sr+i−1	PROPN
ejpam-5241	101	18	]	]	X
ejpam-5241	101	19	where	where	SCONJ
ejpam-5241	101	20	sr+i−1	sr+i−1	PROPN
ejpam-5241	101	21	=	=	SYM
ejpam-5241	101	22	{	{	PUNCT
ejpam-5241	101	23	u1	u1	NOUN
ejpam-5241	101	24	,	,	PUNCT
ejpam-5241	101	25	u2	u2	PROPN
ejpam-5241	101	26	,	,	PUNCT
ejpam-5241	101	27	...	...	PUNCT
ejpam-5241	101	28	,	,	PUNCT
ejpam-5241	101	29	ur	ur	INTJ
ejpam-5241	101	30	,	,	PUNCT
ejpam-5241	101	31	ur+1	ur+1	INTJ
ejpam-5241	101	32	,	,	PUNCT
ejpam-5241	101	33	...	...	PUNCT
ejpam-5241	101	34	,	,	PUNCT
ejpam-5241	101	35	ur+i−1	ur+i−1	PROPN
ejpam-5241	101	36	}	}	PUNCT
ejpam-5241	101	37	.	.	PUNCT
ejpam-5241	102	1	since	since	SCONJ
ejpam-5241	102	2	v	v	NOUN
ejpam-5241	102	3	(	(	PUNCT
ejpam-5241	102	4	g	g	NOUN
ejpam-5241	102	5	)	)	PUNCT
ejpam-5241	102	6	is	be	AUX
ejpam-5241	102	7	finite	finite	ADJ
ejpam-5241	102	8	,	,	PUNCT
ejpam-5241	102	9	there	there	PRON
ejpam-5241	102	10	exists	exist	VERB
ejpam-5241	102	11	a	a	DET
ejpam-5241	102	12	smallest	small	ADJ
ejpam-5241	102	13	positive	positive	ADJ
ejpam-5241	102	14	integer	integer	NOUN
ejpam-5241	102	15	n	n	CCONJ
ejpam-5241	102	16	>	>	X
ejpam-5241	102	17	r	r	NOUN
ejpam-5241	102	18	for	for	ADP
ejpam-5241	102	19	which	which	PRON
ejpam-5241	102	20	ig[sn	ig[sn	NOUN
ejpam-5241	102	21	]	]	X
ejpam-5241	102	22	=	=	SYM
ejpam-5241	102	23	v	v	NOUN
ejpam-5241	102	24	(	(	PUNCT
ejpam-5241	102	25	g	g	NOUN
ejpam-5241	102	26	)	)	PUNCT
ejpam-5241	102	27	.	.	PUNCT
ejpam-5241	103	1	if	if	SCONJ
ejpam-5241	103	2	v	v	INTJ
ejpam-5241	103	3	(	(	PUNCT
ejpam-5241	103	4	g	g	NOUN
ejpam-5241	103	5	)	)	PUNCT
ejpam-5241	103	6	\	\	NOUN
ejpam-5241	103	7	sn	sn	PROPN
ejpam-5241	103	8	=	=	NOUN
ejpam-5241	103	9	∅	∅	NOUN
ejpam-5241	103	10	then	then	ADV
ejpam-5241	103	11	sn	sn	PROPN
ejpam-5241	104	1	=	=	SYM
ejpam-5241	104	2	v	v	PROPN
ejpam-5241	104	3	(	(	PUNCT
ejpam-5241	104	4	g	g	NOUN
ejpam-5241	104	5	)	)	PUNCT
ejpam-5241	104	6	.	.	PUNCT
ejpam-5241	105	1	suppose	suppose	VERB
ejpam-5241	106	1	v	v	X
ejpam-5241	106	2	(	(	PUNCT
ejpam-5241	106	3	g	g	NOUN
ejpam-5241	106	4	)	)	PUNCT
ejpam-5241	106	5	\	\	PROPN
ejpam-5241	107	1	sn	sn	PROPN
ejpam-5241	107	2	̸=	̸=	PROPN
ejpam-5241	107	3	∅	∅	NOUN
ejpam-5241	107	4	,	,	PUNCT
ejpam-5241	107	5	and	and	CCONJ
ejpam-5241	107	6	let	let	VERB
ejpam-5241	107	7	a	a	DET
ejpam-5241	107	8	∈	∈	PROPN
ejpam-5241	107	9	v	v	NOUN
ejpam-5241	107	10	(	(	PUNCT
ejpam-5241	107	11	g	g	NOUN
ejpam-5241	107	12	)	)	PUNCT
ejpam-5241	107	13	\	\	PROPN
ejpam-5241	107	14	sn	sn	PROPN
ejpam-5241	107	15	.	.	PUNCT
ejpam-5241	108	1	by	by	ADP
ejpam-5241	108	2	maximality	maximality	NOUN
ejpam-5241	108	3	of	of	ADP
ejpam-5241	108	4	g1	g1	PROPN
ejpam-5241	108	5	,	,	PUNCT
ejpam-5241	108	6	there	there	PRON
ejpam-5241	108	7	exists	exist	VERB
ejpam-5241	108	8	b	b	PROPN
ejpam-5241	108	9	in	in	ADP
ejpam-5241	108	10	sr	sr	PROPN
ejpam-5241	109	1	such	such	ADJ
ejpam-5241	109	2	that	that	PRON
ejpam-5241	109	3	dg(a	dg(a	PROPN
ejpam-5241	109	4	,	,	PUNCT
ejpam-5241	109	5	b	b	X
ejpam-5241	109	6	)	)	PUNCT
ejpam-5241	109	7	=	=	SYM
ejpam-5241	109	8	2	2	X
ejpam-5241	109	9	.	.	X
ejpam-5241	109	10	hence	hence	ADV
ejpam-5241	109	11	sn	sn	PROPN
ejpam-5241	109	12	is	be	AUX
ejpam-5241	109	13	a	a	DET
ejpam-5241	109	14	hop	hop	NOUN
ejpam-5241	109	15	dominating	dominating	NOUN
ejpam-5241	109	16	set	set	NOUN
ejpam-5241	109	17	of	of	ADP
ejpam-5241	109	18	g.	g.	PROPN
ejpam-5241	109	19	therefore	therefore	ADV
ejpam-5241	109	20	,	,	PUNCT
ejpam-5241	109	21	sn	sn	PROPN
ejpam-5241	109	22	is	be	AUX
ejpam-5241	109	23	a	a	DET
ejpam-5241	109	24	closed	closed	ADJ
ejpam-5241	109	25	geodetic	geodetic	ADJ
ejpam-5241	109	26	hop	hop	NOUN
ejpam-5241	109	27	dominating	dominating	NOUN
ejpam-5241	109	28	set	set	NOUN
ejpam-5241	109	29	of	of	ADP
ejpam-5241	109	30	g.	g.	PROPN
ejpam-5241	109	31	we	we	PRON
ejpam-5241	109	32	denote	denote	VERB
ejpam-5241	109	33	by	by	ADP
ejpam-5241	109	34	c	c	PROPN
ejpam-5241	109	35	∗	∗	NOUN
ejpam-5241	109	36	h	h	NOUN
ejpam-5241	109	37	the	the	DET
ejpam-5241	109	38	family	family	NOUN
ejpam-5241	109	39	of	of	ADP
ejpam-5241	109	40	all	all	DET
ejpam-5241	109	41	connected	connected	ADJ
ejpam-5241	109	42	graphs	graph	NOUN
ejpam-5241	109	43	that	that	PRON
ejpam-5241	109	44	admit	admit	VERB
ejpam-5241	109	45	a	a	DET
ejpam-5241	109	46	closed	closed	ADJ
ejpam-5241	109	47	geodetic	geodetic	ADJ
ejpam-5241	109	48	hop	hop	NOUN
ejpam-5241	109	49	dominating	dominating	NOUN
ejpam-5241	109	50	set	set	NOUN
ejpam-5241	109	51	.	.	PUNCT
ejpam-5241	110	1	since	since	SCONJ
ejpam-5241	110	2	closed	close	VERB
ejpam-5241	110	3	geodetic	geodetic	ADJ
ejpam-5241	110	4	hop	hop	NOUN
ejpam-5241	110	5	dominating	dominating	NOUN
ejpam-5241	110	6	sets	set	NOUN
ejpam-5241	110	7	are	be	AUX
ejpam-5241	110	8	themselves	themselves	PRON
ejpam-5241	110	9	geodetic	geodetic	ADJ
ejpam-5241	110	10	hop	hop	NOUN
ejpam-5241	110	11	dominating	dominating	NOUN
ejpam-5241	110	12	sets	set	NOUN
ejpam-5241	110	13	,	,	PUNCT
ejpam-5241	110	14	2	2	NUM
ejpam-5241	110	15	≤	≤	NUM
ejpam-5241	110	16	γhg(g	γhg(g	PROPN
ejpam-5241	110	17	)	)	PUNCT
ejpam-5241	110	18	≤	≤	NUM
ejpam-5241	110	19	γhcg(g	γhcg(g	NOUN
ejpam-5241	110	20	)	)	PUNCT
ejpam-5241	110	21	≤	≤	NOUN
ejpam-5241	111	1	n	n	CCONJ
ejpam-5241	111	2	(	(	PUNCT
ejpam-5241	111	3	1	1	NUM
ejpam-5241	111	4	)	)	PUNCT
ejpam-5241	111	5	for	for	ADP
ejpam-5241	111	6	all	all	DET
ejpam-5241	111	7	graphs	graph	NOUN
ejpam-5241	111	8	g	g	PROPN
ejpam-5241	111	9	∈	∈	PROPN
ejpam-5241	111	10	c	c	NOUN
ejpam-5241	111	11	∗	∗	NOUN
ejpam-5241	111	12	h	h	NOUN
ejpam-5241	111	13	.	.	PUNCT
ejpam-5241	112	1	theorem	theorem	ADJ
ejpam-5241	112	2	2	2	X
ejpam-5241	112	3	.	.	PUNCT
ejpam-5241	113	1	let	let	VERB
ejpam-5241	113	2	g	g	PROPN
ejpam-5241	113	3	∈	∈	PROPN
ejpam-5241	113	4	c	c	NOUN
ejpam-5241	113	5	∗	∗	NOUN
ejpam-5241	113	6	h	h	NOUN
ejpam-5241	113	7	.	.	PUNCT
ejpam-5241	114	1	then	then	ADV
ejpam-5241	114	2	γhcg(g	γhcg(g	NOUN
ejpam-5241	114	3	)	)	PUNCT
ejpam-5241	114	4	=	=	SYM
ejpam-5241	114	5	2	2	NUM
ejpam-5241	115	1	if	if	SCONJ
ejpam-5241	115	2	and	and	CCONJ
ejpam-5241	115	3	only	only	ADV
ejpam-5241	115	4	if	if	SCONJ
ejpam-5241	115	5	either	either	CCONJ
ejpam-5241	115	6	g	g	PROPN
ejpam-5241	115	7	=	=	SYM
ejpam-5241	115	8	k2	k2	PROPN
ejpam-5241	115	9	or	or	CCONJ
ejpam-5241	115	10	g	g	PROPN
ejpam-5241	115	11	has	have	VERB
ejpam-5241	115	12	a	a	DET
ejpam-5241	115	13	geodetic	geodetic	ADJ
ejpam-5241	115	14	set	set	NOUN
ejpam-5241	115	15	s	s	PART
ejpam-5241	115	16	=	=	PUNCT
ejpam-5241	115	17	{	{	PUNCT
ejpam-5241	115	18	u	u	NOUN
ejpam-5241	115	19	,	,	PUNCT
ejpam-5241	115	20	v	v	NOUN
ejpam-5241	115	21	}	}	PUNCT
ejpam-5241	115	22	such	such	ADJ
ejpam-5241	115	23	that	that	SCONJ
ejpam-5241	115	24	dg(u	dg(u	ADJ
ejpam-5241	115	25	,	,	PUNCT
ejpam-5241	115	26	v	v	NOUN
ejpam-5241	115	27	)	)	PUNCT
ejpam-5241	115	28	=	=	SYM
ejpam-5241	115	29	3	3	X
ejpam-5241	115	30	.	.	PUNCT
ejpam-5241	115	31	proof	proof	NOUN
ejpam-5241	115	32	.	.	PUNCT
ejpam-5241	116	1	suppose	suppose	VERB
ejpam-5241	116	2	that	that	SCONJ
ejpam-5241	116	3	γhcg(g	γhcg(g	NOUN
ejpam-5241	116	4	)	)	PUNCT
ejpam-5241	116	5	=	=	SYM
ejpam-5241	117	1	2	2	X
ejpam-5241	117	2	.	.	X
ejpam-5241	118	1	if	if	SCONJ
ejpam-5241	118	2	g	g	PROPN
ejpam-5241	118	3	=	=	SYM
ejpam-5241	118	4	k2	k2	PROPN
ejpam-5241	118	5	,	,	PUNCT
ejpam-5241	118	6	then	then	ADV
ejpam-5241	118	7	we	we	PRON
ejpam-5241	118	8	are	be	AUX
ejpam-5241	118	9	done	do	VERB
ejpam-5241	118	10	.	.	PUNCT
ejpam-5241	119	1	suppose	suppose	VERB
ejpam-5241	119	2	that	that	SCONJ
ejpam-5241	119	3	g	g	PROPN
ejpam-5241	119	4	̸=	̸=	PROPN
ejpam-5241	119	5	k2	k2	NOUN
ejpam-5241	119	6	.	.	PUNCT
ejpam-5241	120	1	let	let	VERB
ejpam-5241	120	2	s	s	PRON
ejpam-5241	120	3	=	=	PUNCT
ejpam-5241	120	4	{	{	PUNCT
ejpam-5241	120	5	u	u	NOUN
ejpam-5241	120	6	,	,	PUNCT
ejpam-5241	120	7	v	v	NOUN
ejpam-5241	120	8	}	}	PUNCT
ejpam-5241	120	9	be	be	AUX
ejpam-5241	120	10	a	a	DET
ejpam-5241	120	11	closed	closed	ADJ
ejpam-5241	120	12	geodetic	geodetic	ADJ
ejpam-5241	120	13	hop	hop	NOUN
ejpam-5241	120	14	dominating	dominating	NOUN
ejpam-5241	120	15	set	set	NOUN
ejpam-5241	120	16	of	of	ADP
ejpam-5241	120	17	g.	g.	PROPN
ejpam-5241	120	18	since	since	SCONJ
ejpam-5241	120	19	g	g	PROPN
ejpam-5241	120	20	̸=	̸=	PROPN
ejpam-5241	120	21	k2	k2	NOUN
ejpam-5241	120	22	,	,	PUNCT
ejpam-5241	120	23	v	v	NOUN
ejpam-5241	120	24	(	(	PUNCT
ejpam-5241	120	25	g	g	NOUN
ejpam-5241	120	26	)	)	PUNCT
ejpam-5241	120	27	\	\	PUNCT
ejpam-5241	121	1	s	s	PART
ejpam-5241	121	2	̸=	̸=	PROPN
ejpam-5241	121	3	∅	∅	NOUN
ejpam-5241	121	4	and	and	CCONJ
ejpam-5241	121	5	w	w	NOUN
ejpam-5241	121	6	∈	∈	PROPN
ejpam-5241	121	7	ig(u	ig(u	NOUN
ejpam-5241	121	8	,	,	PUNCT
ejpam-5241	121	9	v	v	NOUN
ejpam-5241	121	10	)	)	PUNCT
ejpam-5241	121	11	for	for	ADP
ejpam-5241	121	12	every	every	PRON
ejpam-5241	121	13	w	w	PROPN
ejpam-5241	121	14	∈	∈	PROPN
ejpam-5241	121	15	v	v	ADP
ejpam-5241	121	16	(	(	PUNCT
ejpam-5241	121	17	g	g	NOUN
ejpam-5241	121	18	)	)	PUNCT
ejpam-5241	121	19	\	\	PUNCT
ejpam-5241	122	1	s.	s.	PROPN
ejpam-5241	122	2	let	let	VERB
ejpam-5241	122	3	[	[	X
ejpam-5241	122	4	u	u	X
ejpam-5241	122	5	=	=	SYM
ejpam-5241	122	6	x1	x1	PROPN
ejpam-5241	122	7	,	,	PUNCT
ejpam-5241	122	8	x2	x2	PROPN
ejpam-5241	122	9	,	,	PUNCT
ejpam-5241	122	10	x3	x3	ADJ
ejpam-5241	122	11	,	,	PUNCT
ejpam-5241	122	12	.	.	PUNCT
ejpam-5241	122	13	.	.	PUNCT
ejpam-5241	123	1	.	.	PUNCT
ejpam-5241	124	1	,	,	PUNCT
ejpam-5241	124	2	xk	xk	PROPN
ejpam-5241	124	3	=	=	SYM
ejpam-5241	124	4	v	v	PROPN
ejpam-5241	124	5	]	]	PUNCT
ejpam-5241	124	6	be	be	AUX
ejpam-5241	124	7	a	a	DET
ejpam-5241	124	8	u	u	NOUN
ejpam-5241	124	9	-	-	NOUN
ejpam-5241	124	10	v	v	ADJ
ejpam-5241	124	11	geodesic	geodesic	NOUN
ejpam-5241	124	12	in	in	ADP
ejpam-5241	124	13	g.	g.	PROPN
ejpam-5241	125	1	then	then	ADV
ejpam-5241	125	2	k	k	PROPN
ejpam-5241	125	3	≥	≥	NUM
ejpam-5241	125	4	3	3	NUM
ejpam-5241	125	5	.	.	PUNCT
ejpam-5241	126	1	since	since	SCONJ
ejpam-5241	126	2	s	s	PROPN
ejpam-5241	126	3	is	be	AUX
ejpam-5241	126	4	a	a	DET
ejpam-5241	126	5	hop	hop	NOUN
ejpam-5241	126	6	dominating	dominating	NOUN
ejpam-5241	126	7	set	set	NOUN
ejpam-5241	126	8	,	,	PUNCT
ejpam-5241	126	9	in	in	ADP
ejpam-5241	126	10	particular	particular	ADJ
ejpam-5241	126	11	,	,	PUNCT
ejpam-5241	126	12	dg(x2	dg(x2	NOUN
ejpam-5241	126	13	,	,	PUNCT
ejpam-5241	126	14	v	v	NOUN
ejpam-5241	126	15	)	)	PUNCT
ejpam-5241	126	16	=	=	SYM
ejpam-5241	126	17	2	2	X
ejpam-5241	126	18	.	.	X
ejpam-5241	126	19	necessarily	necessarily	ADV
ejpam-5241	126	20	,	,	PUNCT
ejpam-5241	126	21	k	k	PROPN
ejpam-5241	126	22	=	=	SYM
ejpam-5241	126	23	4	4	NUM
ejpam-5241	126	24	and	and	CCONJ
ejpam-5241	126	25	dg(u	dg(u	NOUN
ejpam-5241	126	26	,	,	PUNCT
ejpam-5241	126	27	v	v	NOUN
ejpam-5241	126	28	)	)	PUNCT
ejpam-5241	126	29	=	=	SYM
ejpam-5241	126	30	3	3	X
ejpam-5241	126	31	.	.	PUNCT
ejpam-5241	127	1	clearly	clearly	ADV
ejpam-5241	127	2	,	,	PUNCT
ejpam-5241	127	3	if	if	SCONJ
ejpam-5241	127	4	g	g	PROPN
ejpam-5241	127	5	=	=	SYM
ejpam-5241	127	6	k2	k2	PROPN
ejpam-5241	127	7	,	,	PUNCT
ejpam-5241	127	8	then	then	ADV
ejpam-5241	127	9	γhcg(g	γhcg(g	NOUN
ejpam-5241	127	10	)	)	PUNCT
ejpam-5241	127	11	=	=	SYM
ejpam-5241	127	12	2	2	X
ejpam-5241	127	13	.	.	PUNCT
ejpam-5241	127	14	suppose	suppose	VERB
ejpam-5241	127	15	that	that	SCONJ
ejpam-5241	127	16	g	g	PROPN
ejpam-5241	127	17	has	have	VERB
ejpam-5241	127	18	a	a	DET
ejpam-5241	127	19	geodesic	geodesic	ADJ
ejpam-5241	127	20	set	set	NOUN
ejpam-5241	127	21	s	s	PART
ejpam-5241	127	22	=	=	PUNCT
ejpam-5241	127	23	{	{	PUNCT
ejpam-5241	127	24	u	u	NOUN
ejpam-5241	127	25	,	,	PUNCT
ejpam-5241	127	26	v	v	NOUN
ejpam-5241	127	27	}	}	PUNCT
ejpam-5241	127	28	with	with	ADP
ejpam-5241	127	29	dg(u	dg(u	ADJ
ejpam-5241	127	30	,	,	PUNCT
ejpam-5241	127	31	v	v	NOUN
ejpam-5241	127	32	)	)	PUNCT
ejpam-5241	127	33	=	=	SYM
ejpam-5241	128	1	3	3	X
ejpam-5241	128	2	.	.	PUNCT
ejpam-5241	129	1	then	then	ADV
ejpam-5241	129	2	s	s	VERB
ejpam-5241	129	3	is	be	AUX
ejpam-5241	129	4	a	a	DET
ejpam-5241	129	5	closed	closed	ADJ
ejpam-5241	129	6	geodetic	geodetic	ADJ
ejpam-5241	129	7	set	set	NOUN
ejpam-5241	129	8	of	of	ADP
ejpam-5241	129	9	g.	g.	PROPN
ejpam-5241	129	10	let	let	VERB
ejpam-5241	129	11	w	w	PROPN
ejpam-5241	129	12	∈	∈	PROPN
ejpam-5241	129	13	v	v	ADP
ejpam-5241	129	14	(	(	PUNCT
ejpam-5241	129	15	g	g	NOUN
ejpam-5241	129	16	)	)	PUNCT
ejpam-5241	129	17	\	\	PUNCT
ejpam-5241	130	1	s.	s.	PROPN
ejpam-5241	130	2	being	be	AUX
ejpam-5241	130	3	a	a	DET
ejpam-5241	130	4	geodetic	geodetic	ADJ
ejpam-5241	130	5	set	set	NOUN
ejpam-5241	130	6	,	,	PUNCT
ejpam-5241	130	7	there	there	PRON
ejpam-5241	130	8	exists	exist	VERB
ejpam-5241	130	9	a	a	DET
ejpam-5241	130	10	u	u	NOUN
ejpam-5241	130	11	-	-	NOUN
ejpam-5241	130	12	v	v	ADJ
ejpam-5241	130	13	geodesic	geodesic	NOUN
ejpam-5241	130	14	[	[	X
ejpam-5241	130	15	u	u	NOUN
ejpam-5241	130	16	,	,	PUNCT
ejpam-5241	130	17	x	x	PROPN
ejpam-5241	130	18	,	,	PUNCT
ejpam-5241	130	19	y	y	PROPN
ejpam-5241	130	20	,	,	PUNCT
ejpam-5241	130	21	v	v	ADP
ejpam-5241	130	22	]	]	PUNCT
ejpam-5241	130	23	on	on	ADP
ejpam-5241	130	24	which	which	PRON
ejpam-5241	130	25	w	w	NOUN
ejpam-5241	130	26	lies	lie	NOUN
ejpam-5241	130	27	.	.	PUNCT
ejpam-5241	131	1	if	if	SCONJ
ejpam-5241	131	2	w	w	PROPN
ejpam-5241	131	3	=	=	SYM
ejpam-5241	131	4	x	x	NOUN
ejpam-5241	131	5	,	,	PUNCT
ejpam-5241	131	6	then	then	ADV
ejpam-5241	131	7	dg(w	dg(w	NUM
ejpam-5241	131	8	,	,	PUNCT
ejpam-5241	131	9	v	v	NOUN
ejpam-5241	131	10	)	)	PUNCT
ejpam-5241	131	11	=	=	SYM
ejpam-5241	132	1	2	2	X
ejpam-5241	132	2	.	.	X
ejpam-5241	133	1	if	if	SCONJ
ejpam-5241	133	2	w	w	PROPN
ejpam-5241	133	3	=	=	SYM
ejpam-5241	133	4	y	y	PROPN
ejpam-5241	133	5	,	,	PUNCT
ejpam-5241	133	6	then	then	ADV
ejpam-5241	133	7	dg(u	dg(u	X
ejpam-5241	133	8	,	,	PUNCT
ejpam-5241	133	9	w	w	NOUN
ejpam-5241	133	10	)	)	PUNCT
ejpam-5241	133	11	=	=	SYM
ejpam-5241	133	12	2	2	X
ejpam-5241	133	13	.	.	PUNCT
ejpam-5241	133	14	accordingly	accordingly	ADV
ejpam-5241	133	15	,	,	PUNCT
ejpam-5241	133	16	s	s	VERB
ejpam-5241	133	17	is	be	AUX
ejpam-5241	133	18	a	a	DET
ejpam-5241	133	19	hop	hop	NOUN
ejpam-5241	133	20	dominating	dominating	NOUN
ejpam-5241	133	21	set	set	NOUN
ejpam-5241	133	22	of	of	ADP
ejpam-5241	133	23	g.	g.	PROPN
ejpam-5241	133	24	thus	thus	ADV
ejpam-5241	133	25	,	,	PUNCT
ejpam-5241	133	26	γhcg(g	γhcg(g	NOUN
ejpam-5241	133	27	)	)	PUNCT
ejpam-5241	133	28	≤	≤	NUM
ejpam-5241	133	29	|s|	|s|	PROPN
ejpam-5241	133	30	=	=	SYM
ejpam-5241	133	31	2	2	X
ejpam-5241	133	32	.	.	PUNCT
ejpam-5241	133	33	equation	equation	NOUN
ejpam-5241	133	34	1	1	NUM
ejpam-5241	133	35	completes	complete	VERB
ejpam-5241	133	36	the	the	DET
ejpam-5241	133	37	desired	desire	VERB
ejpam-5241	133	38	equality	equality	NOUN
ejpam-5241	133	39	.	.	PUNCT
ejpam-5241	134	1	lemma	lemma	PROPN
ejpam-5241	134	2	1	1	X
ejpam-5241	134	3	.	.	PUNCT
ejpam-5241	135	1	let	let	VERB
ejpam-5241	135	2	g	g	PROPN
ejpam-5241	135	3	∈	∈	PROPN
ejpam-5241	135	4	c	c	NOUN
ejpam-5241	135	5	∗	∗	NOUN
ejpam-5241	135	6	h	h	NOUN
ejpam-5241	135	7	of	of	ADP
ejpam-5241	135	8	order	order	NOUN
ejpam-5241	135	9	n.	n.	NOUN
ejpam-5241	135	10	if	if	SCONJ
ejpam-5241	135	11	γhcg(g	γhcg(g	NOUN
ejpam-5241	135	12	)	)	PUNCT
ejpam-5241	135	13	=	=	SYM
ejpam-5241	136	1	n	n	CCONJ
ejpam-5241	136	2	,	,	PUNCT
ejpam-5241	136	3	then	then	ADV
ejpam-5241	136	4	g	g	PROPN
ejpam-5241	136	5	has	have	VERB
ejpam-5241	136	6	a	a	DET
ejpam-5241	136	7	dominating	dominating	NOUN
ejpam-5241	136	8	vertex	vertex	NOUN
ejpam-5241	136	9	.	.	PUNCT
ejpam-5241	137	1	proof	proof	NOUN
ejpam-5241	137	2	.	.	PUNCT
ejpam-5241	138	1	this	this	PRON
ejpam-5241	138	2	is	be	AUX
ejpam-5241	138	3	clear	clear	ADJ
ejpam-5241	138	4	for	for	ADP
ejpam-5241	138	5	n	n	NOUN
ejpam-5241	138	6	=	=	SYM
ejpam-5241	138	7	1	1	NUM
ejpam-5241	138	8	,	,	PUNCT
ejpam-5241	138	9	2	2	NUM
ejpam-5241	138	10	.	.	X
ejpam-5241	139	1	let	let	VERB
ejpam-5241	139	2	n	n	PRON
ejpam-5241	139	3	≥	≥	NOUN
ejpam-5241	139	4	3	3	X
ejpam-5241	139	5	.	.	PUNCT
ejpam-5241	139	6	assume	assume	VERB
ejpam-5241	139	7	that	that	SCONJ
ejpam-5241	139	8	γhcg(g	γhcg(g	NOUN
ejpam-5241	139	9	)	)	PUNCT
ejpam-5241	140	1	=	=	VERB
ejpam-5241	140	2	n.	n.	NOUN
ejpam-5241	140	3	suppose	suppose	VERB
ejpam-5241	140	4	that	that	SCONJ
ejpam-5241	140	5	g	g	PROPN
ejpam-5241	140	6	does	do	AUX
ejpam-5241	140	7	not	not	PART
ejpam-5241	140	8	contain	contain	VERB
ejpam-5241	140	9	a	a	DET
ejpam-5241	140	10	dominating	dominating	NOUN
ejpam-5241	140	11	vertex	vertex	NOUN
ejpam-5241	140	12	.	.	PUNCT
ejpam-5241	141	1	the	the	DET
ejpam-5241	141	2	assumption	assumption	NOUN
ejpam-5241	141	3	implies	imply	VERB
ejpam-5241	141	4	that	that	SCONJ
ejpam-5241	141	5	there	there	PRON
ejpam-5241	141	6	exists	exist	VERB
ejpam-5241	141	7	a	a	DET
ejpam-5241	141	8	sequence	sequence	NOUN
ejpam-5241	141	9	of	of	ADP
ejpam-5241	141	10	sets	set	NOUN
ejpam-5241	141	11	of	of	ADP
ejpam-5241	141	12	vertices	vertex	NOUN
ejpam-5241	141	13	of	of	ADP
ejpam-5241	141	14	g	g	NOUN
ejpam-5241	141	15	,	,	PUNCT
ejpam-5241	141	16	say	say	VERB
ejpam-5241	141	17	sk	sk	INTJ
ejpam-5241	141	18	=	=	NOUN
ejpam-5241	141	19	{	{	PUNCT
ejpam-5241	141	20	v1	v1	PROPN
ejpam-5241	141	21	,	,	PUNCT
ejpam-5241	141	22	v2	v2	PROPN
ejpam-5241	141	23	,	,	PUNCT
ejpam-5241	141	24	.	.	PUNCT
ejpam-5241	141	25	.	.	PUNCT
ejpam-5241	142	1	.	.	PUNCT
ejpam-5241	143	1	,	,	PUNCT
ejpam-5241	143	2	vk	vk	ADP
ejpam-5241	143	3	}	}	PUNCT
ejpam-5241	143	4	,	,	PUNCT
ejpam-5241	143	5	k	k	PROPN
ejpam-5241	144	1	=	=	SYM
ejpam-5241	144	2	1	1	NUM
ejpam-5241	144	3	,	,	PUNCT
ejpam-5241	144	4	2	2	NUM
ejpam-5241	144	5	,	,	PUNCT
ejpam-5241	144	6	.	.	PUNCT
ejpam-5241	144	7	.	.	PUNCT
ejpam-5241	145	1	.	.	PUNCT
ejpam-5241	146	1	,	,	PUNCT
ejpam-5241	146	2	n	n	CCONJ
ejpam-5241	146	3	,	,	PUNCT
ejpam-5241	146	4	such	such	ADJ
ejpam-5241	146	5	that	that	DET
ejpam-5241	146	6	v1	v1	NOUN
ejpam-5241	146	7	̸=	̸=	PROPN
ejpam-5241	146	8	v2	v2	PROPN
ejpam-5241	146	9	and	and	CCONJ
ejpam-5241	146	10	vk	vk	INTJ
ejpam-5241	146	11	/∈	/∈	PUNCT
ejpam-5241	146	12	ig[sk−1	ig[sk−1	PROPN
ejpam-5241	146	13	]	]	PUNCT
ejpam-5241	146	14	for	for	ADP
ejpam-5241	146	15	all	all	DET
ejpam-5241	146	16	k	k	PROPN
ejpam-5241	146	17	≥	≥	NUM
ejpam-5241	146	18	3	3	NUM
ejpam-5241	146	19	.	.	PUNCT
ejpam-5241	147	1	now	now	ADV
ejpam-5241	147	2	,	,	PUNCT
ejpam-5241	147	3	since	since	SCONJ
ejpam-5241	147	4	g	g	PROPN
ejpam-5241	147	5	is	be	AUX
ejpam-5241	147	6	not	not	PART
ejpam-5241	147	7	complete	complete	ADJ
ejpam-5241	147	8	and	and	CCONJ
ejpam-5241	147	9	n	n	PRON
ejpam-5241	147	10	≥	≥	NOUN
ejpam-5241	147	11	3	3	NUM
ejpam-5241	147	12	,	,	PUNCT
ejpam-5241	147	13	g	g	PROPN
ejpam-5241	147	14	has	have	AUX
ejpam-5241	147	15	vertices	vertice	VERB
ejpam-5241	147	16	u	u	NOUN
ejpam-5241	147	17	and	and	CCONJ
ejpam-5241	147	18	v	v	ADP
ejpam-5241	147	19	such	such	ADJ
ejpam-5241	147	20	that	that	DET
ejpam-5241	147	21	dg(u	dg(u	ADJ
ejpam-5241	147	22	,	,	PUNCT
ejpam-5241	147	23	v	v	NOUN
ejpam-5241	147	24	)	)	PUNCT
ejpam-5241	147	25	=	=	SYM
ejpam-5241	147	26	2	2	X
ejpam-5241	147	27	.	.	X
ejpam-5241	147	28	let	let	VERB
ejpam-5241	147	29	[	[	X
ejpam-5241	147	30	u	u	NOUN
ejpam-5241	147	31	,	,	PUNCT
ejpam-5241	147	32	w	w	PROPN
ejpam-5241	147	33	,	,	PUNCT
ejpam-5241	147	34	v	v	NOUN
ejpam-5241	147	35	]	]	PUNCT
ejpam-5241	147	36	be	be	AUX
ejpam-5241	147	37	a	a	DET
ejpam-5241	147	38	u	u	NOUN
ejpam-5241	147	39	-	-	NOUN
ejpam-5241	147	40	v	v	ADJ
ejpam-5241	147	41	geodesic	geodesic	NOUN
ejpam-5241	147	42	in	in	ADP
ejpam-5241	147	43	g.	g.	NOUN
ejpam-5241	147	44	for	for	ADP
ejpam-5241	147	45	some	some	DET
ejpam-5241	147	46	distinct	distinct	ADJ
ejpam-5241	147	47	i	i	PROPN
ejpam-5241	147	48	,	,	PUNCT
ejpam-5241	147	49	j	j	PROPN
ejpam-5241	147	50	,	,	PUNCT
ejpam-5241	147	51	k	k	PROPN
ejpam-5241	147	52	∈	∈	PROPN
ejpam-5241	147	53	{	{	PUNCT
ejpam-5241	147	54	1	1	NUM
ejpam-5241	147	55	,	,	PUNCT
ejpam-5241	147	56	2	2	NUM
ejpam-5241	147	57	,	,	PUNCT
ejpam-5241	147	58	.	.	PUNCT
ejpam-5241	147	59	.	.	PUNCT
ejpam-5241	148	1	.	.	PUNCT
ejpam-5241	149	1	,	,	PUNCT
ejpam-5241	149	2	n	n	CCONJ
ejpam-5241	149	3	}	}	PUNCT
ejpam-5241	149	4	,	,	PUNCT
ejpam-5241	149	5	we	we	PRON
ejpam-5241	149	6	have	have	VERB
ejpam-5241	149	7	u	u	NOUN
ejpam-5241	149	8	=	=	NOUN
ejpam-5241	149	9	vi	vi	PROPN
ejpam-5241	149	10	,	,	PUNCT
ejpam-5241	149	11	w	w	NOUN
ejpam-5241	149	12	=	=	PUNCT
ejpam-5241	149	13	vj	vj	PROPN
ejpam-5241	149	14	and	and	CCONJ
ejpam-5241	149	15	vk	vk	INTJ
ejpam-5241	149	16	=	=	PUNCT
ejpam-5241	149	17	v.	v.	X
ejpam-5241	149	18	without	without	ADP
ejpam-5241	149	19	loss	loss	NOUN
ejpam-5241	149	20	of	of	ADP
ejpam-5241	149	21	generality	generality	NOUN
ejpam-5241	149	22	,	,	PUNCT
ejpam-5241	149	23	assume	assume	VERB
ejpam-5241	149	24	i	i	PRON
ejpam-5241	149	25	<	<	X
ejpam-5241	149	26	k.	k.	PROPN
ejpam-5241	149	27	since	since	SCONJ
ejpam-5241	149	28	w	w	PROPN
ejpam-5241	149	29	∈	∈	PROPN
ejpam-5241	149	30	ig[u	ig[u	PROPN
ejpam-5241	149	31	,	,	PUNCT
ejpam-5241	149	32	v	v	NOUN
ejpam-5241	149	33	]	]	PUNCT
ejpam-5241	149	34	and	and	CCONJ
ejpam-5241	149	35	vj	vj	PROPN
ejpam-5241	149	36	/∈	/∈	PROPN
ejpam-5241	149	37	ig[sj−1	ig[sj−1	PROPN
ejpam-5241	149	38	]	]	PUNCT
ejpam-5241	149	39	,	,	PUNCT
ejpam-5241	150	1	j	j	PROPN
ejpam-5241	150	2	<	<	X
ejpam-5241	150	3	k.	k.	PROPN
ejpam-5241	150	4	define	define	VERB
ejpam-5241	150	5	tl	tl	PROPN
ejpam-5241	150	6	=	=	PUNCT
ejpam-5241	150	7	{	{	PUNCT
ejpam-5241	150	8	x1	x1	PROPN
ejpam-5241	150	9	,	,	PUNCT
ejpam-5241	150	10	x2	x2	PROPN
ejpam-5241	150	11	,	,	PUNCT
ejpam-5241	150	12	.	.	PUNCT
ejpam-5241	150	13	.	.	PUNCT
ejpam-5241	150	14	.	.	PUNCT
ejpam-5241	151	1	,	,	PUNCT
ejpam-5241	151	2	xl	xl	PROPN
ejpam-5241	151	3	}	}	PUNCT
ejpam-5241	151	4	for	for	ADP
ejpam-5241	151	5	l	l	NOUN
ejpam-5241	151	6	=	=	SYM
ejpam-5241	151	7	1	1	NUM
ejpam-5241	151	8	,	,	PUNCT
ejpam-5241	151	9	2	2	NUM
ejpam-5241	151	10	,	,	PUNCT
ejpam-5241	151	11	.	.	PUNCT
ejpam-5241	151	12	.	.	PUNCT
ejpam-5241	152	1	.	.	PUNCT
ejpam-5241	153	1	,	,	PUNCT
ejpam-5241	153	2	m	m	VERB
ejpam-5241	153	3	with	with	ADP
ejpam-5241	153	4	k	k	PROPN
ejpam-5241	153	5	≤	≤	NUM
ejpam-5241	153	6	m	m	VERB
ejpam-5241	153	7	≤	≤	NOUN
ejpam-5241	153	8	n	n	CCONJ
ejpam-5241	153	9	−	−	PROPN
ejpam-5241	153	10	1	1	NUM
ejpam-5241	153	11	such	such	ADJ
ejpam-5241	153	12	that	that	PRON
ejpam-5241	153	13	•	•	NOUN
ejpam-5241	153	14	xl	xl	PROPN
ejpam-5241	153	15	=	=	PUNCT
ejpam-5241	153	16	vl	vl	PROPN
ejpam-5241	153	17	for	for	ADP
ejpam-5241	153	18	all	all	DET
ejpam-5241	153	19	l	l	NOUN
ejpam-5241	153	20	∈	∈	NOUN
ejpam-5241	153	21	{	{	PUNCT
ejpam-5241	153	22	1	1	NUM
ejpam-5241	153	23	,	,	PUNCT
ejpam-5241	153	24	2	2	NUM
ejpam-5241	153	25	,	,	PUNCT
ejpam-5241	153	26	.	.	PUNCT
ejpam-5241	153	27	.	.	PUNCT
ejpam-5241	154	1	.	.	PUNCT
ejpam-5241	155	1	,	,	PUNCT
ejpam-5241	155	2	j	j	PROPN
ejpam-5241	155	3	−	−	PROPN
ejpam-5241	155	4	1	1	NUM
ejpam-5241	155	5	}	}	PUNCT
ejpam-5241	155	6	;	;	PUNCT
ejpam-5241	155	7	•	•	X
ejpam-5241	155	8	xl	xl	PROPN
ejpam-5241	155	9	=	=	PUNCT
ejpam-5241	155	10	vl+1	vl+1	PROPN
ejpam-5241	155	11	for	for	ADP
ejpam-5241	155	12	all	all	DET
ejpam-5241	155	13	l	l	NOUN
ejpam-5241	155	14	∈	∈	PROPN
ejpam-5241	155	15	{	{	PUNCT
ejpam-5241	155	16	j	j	PROPN
ejpam-5241	155	17	,	,	PUNCT
ejpam-5241	155	18	j	j	PROPN
ejpam-5241	155	19	+	+	PROPN
ejpam-5241	155	20	1	1	NUM
ejpam-5241	155	21	,	,	PUNCT
ejpam-5241	155	22	.	.	PUNCT
ejpam-5241	155	23	.	.	PUNCT
ejpam-5241	155	24	.	.	PUNCT
ejpam-5241	156	1	,	,	PUNCT
ejpam-5241	156	2	m	m	VERB
ejpam-5241	156	3	}	}	PUNCT
ejpam-5241	156	4	.	.	PUNCT
ejpam-5241	157	1	a.	a.	PROPN
ejpam-5241	157	2	adolfo	adolfo	PROPN
ejpam-5241	157	3	,	,	PUNCT
ejpam-5241	157	4	i.	i.	PROPN
ejpam-5241	157	5	aniversario	aniversario	PROPN
ejpam-5241	157	6	,	,	PUNCT
ejpam-5241	157	7	f.	f.	PROPN
ejpam-5241	157	8	jamil	jamil	PROPN
ejpam-5241	157	9	/	/	SYM
ejpam-5241	157	10	eur	eur	PROPN
ejpam-5241	157	11	.	.	PUNCT
ejpam-5241	158	1	j.	j.	PROPN
ejpam-5241	158	2	pure	pure	PROPN
ejpam-5241	158	3	appl	appl	PROPN
ejpam-5241	158	4	.	.	PROPN
ejpam-5241	158	5	math	math	PROPN
ejpam-5241	158	6	,	,	PUNCT
ejpam-5241	158	7	17	17	NUM
ejpam-5241	158	8	(	(	PUNCT
ejpam-5241	158	9	3	3	NUM
ejpam-5241	158	10	)	)	PUNCT
ejpam-5241	158	11	(	(	PUNCT
ejpam-5241	158	12	2024	2024	NUM
ejpam-5241	158	13	)	)	PUNCT
ejpam-5241	158	14	,	,	PUNCT
ejpam-5241	158	15	1618	1618	NUM
ejpam-5241	158	16	-	-	SYM
ejpam-5241	158	17	1636	1636	NUM
ejpam-5241	158	18	1623	1623	NUM
ejpam-5241	158	19	then	then	ADV
ejpam-5241	158	20	•	•	ADP
ejpam-5241	158	21	ig[tl	ig[tl	X
ejpam-5241	158	22	]	]	PUNCT
ejpam-5241	158	23	=	=	PUNCT
ejpam-5241	159	1	ig[sl	ig[sl	X
ejpam-5241	159	2	]	]	X
ejpam-5241	159	3	=	=	PUNCT
ejpam-5241	159	4	sl	sl	PROPN
ejpam-5241	159	5	=	=	PUNCT
ejpam-5241	159	6	tl	tl	PROPN
ejpam-5241	159	7	for	for	ADP
ejpam-5241	159	8	all	all	DET
ejpam-5241	159	9	l	l	NOUN
ejpam-5241	159	10	∈	∈	NOUN
ejpam-5241	159	11	{	{	PUNCT
ejpam-5241	159	12	1	1	NUM
ejpam-5241	159	13	,	,	PUNCT
ejpam-5241	159	14	2	2	NUM
ejpam-5241	159	15	,	,	PUNCT
ejpam-5241	159	16	.	.	PUNCT
ejpam-5241	159	17	.	.	PUNCT
ejpam-5241	160	1	.	.	PUNCT
ejpam-5241	161	1	,	,	PUNCT
ejpam-5241	162	1	k	k	PROPN
ejpam-5241	163	1	−	−	PROPN
ejpam-5241	163	2	2	2	NUM
ejpam-5241	163	3	}	}	PUNCT
ejpam-5241	163	4	;	;	PUNCT
ejpam-5241	163	5	•	•	NUM
ejpam-5241	163	6	ig[tk−1	ig[tk−1	NOUN
ejpam-5241	163	7	]	]	X
ejpam-5241	163	8	=	=	PUNCT
ejpam-5241	163	9	tk−1	tk−1	ADV
ejpam-5241	163	10	∪	∪	ADJ
ejpam-5241	163	11	{	{	PUNCT
ejpam-5241	163	12	w	w	NOUN
ejpam-5241	163	13	}	}	PUNCT
ejpam-5241	163	14	=	=	PUNCT
ejpam-5241	163	15	sk	sk	NOUN
ejpam-5241	163	16	;	;	PUNCT
ejpam-5241	163	17	and	and	CCONJ
ejpam-5241	163	18	•	•	ADP
ejpam-5241	163	19	ig[tl	ig[tl	X
ejpam-5241	163	20	]	]	PUNCT
ejpam-5241	163	21	=	=	SYM
ejpam-5241	163	22	sl+1	sl+1	PROPN
ejpam-5241	163	23	for	for	ADP
ejpam-5241	163	24	all	all	DET
ejpam-5241	163	25	l	l	NOUN
ejpam-5241	163	26	∈	∈	PROPN
ejpam-5241	163	27	{	{	PUNCT
ejpam-5241	163	28	k	k	NOUN
ejpam-5241	163	29	,	,	PUNCT
ejpam-5241	163	30	k	k	PROPN
ejpam-5241	163	31	+	+	PROPN
ejpam-5241	163	32	1	1	NUM
ejpam-5241	163	33	,	,	PUNCT
ejpam-5241	163	34	.	.	PUNCT
ejpam-5241	163	35	.	.	PUNCT
ejpam-5241	163	36	.	.	PUNCT
ejpam-5241	164	1	,	,	PUNCT
ejpam-5241	164	2	m	m	VERB
ejpam-5241	164	3	}	}	PUNCT
ejpam-5241	164	4	.	.	PUNCT
ejpam-5241	165	1	this	this	PRON
ejpam-5241	165	2	means	mean	VERB
ejpam-5241	165	3	that	that	SCONJ
ejpam-5241	165	4	tm	tm	PROPN
ejpam-5241	165	5	=	=	PROPN
ejpam-5241	165	6	v	v	PROPN
ejpam-5241	165	7	(	(	PUNCT
ejpam-5241	165	8	g	g	NOUN
ejpam-5241	165	9	)	)	PUNCT
ejpam-5241	165	10	\	\	NOUN
ejpam-5241	165	11	{	{	PUNCT
ejpam-5241	165	12	w	w	NOUN
ejpam-5241	165	13	}	}	PUNCT
ejpam-5241	165	14	is	be	AUX
ejpam-5241	165	15	a	a	DET
ejpam-5241	165	16	closed	closed	ADJ
ejpam-5241	165	17	geodetic	geodetic	ADJ
ejpam-5241	165	18	set	set	NOUN
ejpam-5241	165	19	of	of	ADP
ejpam-5241	165	20	g.	g.	PROPN
ejpam-5241	165	21	finally	finally	ADV
ejpam-5241	165	22	,	,	PUNCT
ejpam-5241	165	23	since	since	SCONJ
ejpam-5241	165	24	w	w	NOUN
ejpam-5241	165	25	is	be	AUX
ejpam-5241	165	26	not	not	PART
ejpam-5241	165	27	a	a	DET
ejpam-5241	165	28	dominating	dominating	NOUN
ejpam-5241	165	29	vertex	vertex	NOUN
ejpam-5241	165	30	of	of	ADP
ejpam-5241	165	31	g	g	NOUN
ejpam-5241	165	32	,	,	PUNCT
ejpam-5241	165	33	there	there	PRON
ejpam-5241	165	34	exists	exist	VERB
ejpam-5241	165	35	z	z	PROPN
ejpam-5241	165	36	∈	∈	PROPN
ejpam-5241	165	37	v	v	ADP
ejpam-5241	165	38	(	(	PUNCT
ejpam-5241	165	39	g	g	NOUN
ejpam-5241	165	40	)	)	PUNCT
ejpam-5241	165	41	\	\	NOUN
ejpam-5241	165	42	{	{	PUNCT
ejpam-5241	165	43	w	w	NOUN
ejpam-5241	165	44	}	}	PUNCT
ejpam-5241	165	45	=	=	PUNCT
ejpam-5241	165	46	tm	tm	PROPN
ejpam-5241	165	47	such	such	ADJ
ejpam-5241	165	48	that	that	PRON
ejpam-5241	165	49	dg(w	dg(w	NOUN
ejpam-5241	165	50	,	,	PUNCT
ejpam-5241	165	51	z	z	NOUN
ejpam-5241	165	52	)	)	PUNCT
ejpam-5241	165	53	=	=	SYM
ejpam-5241	165	54	2	2	X
ejpam-5241	165	55	.	.	PUNCT
ejpam-5241	166	1	thus	thus	ADV
ejpam-5241	166	2	,	,	PUNCT
ejpam-5241	166	3	tm	tm	PRON
ejpam-5241	166	4	is	be	AUX
ejpam-5241	166	5	a	a	DET
ejpam-5241	166	6	hop	hop	NOUN
ejpam-5241	166	7	dominating	dominating	NOUN
ejpam-5241	166	8	set	set	NOUN
ejpam-5241	166	9	of	of	ADP
ejpam-5241	166	10	g.	g.	PROPN
ejpam-5241	166	11	hence	hence	ADV
ejpam-5241	166	12	,	,	PUNCT
ejpam-5241	166	13	γhcg(g	γhcg(g	NOUN
ejpam-5241	166	14	)	)	PUNCT
ejpam-5241	166	15	≤	≤	NUM
ejpam-5241	166	16	|tm|	|tm|	NOUN
ejpam-5241	167	1	=	=	PUNCT
ejpam-5241	167	2	m	m	VERB
ejpam-5241	167	3	<	<	X
ejpam-5241	167	4	n	n	CCONJ
ejpam-5241	167	5	,	,	PUNCT
ejpam-5241	167	6	a	a	DET
ejpam-5241	167	7	contradiction	contradiction	NOUN
ejpam-5241	167	8	.	.	PUNCT
ejpam-5241	168	1	therefore	therefore	ADV
ejpam-5241	168	2	,	,	PUNCT
ejpam-5241	168	3	g	g	PROPN
ejpam-5241	168	4	contains	contain	VERB
ejpam-5241	168	5	a	a	DET
ejpam-5241	168	6	dominating	dominating	NOUN
ejpam-5241	168	7	vertex	vertex	NOUN
ejpam-5241	168	8	.	.	PUNCT
ejpam-5241	169	1	if	if	SCONJ
ejpam-5241	169	2	g	g	PROPN
ejpam-5241	169	3	∈	∈	PROPN
ejpam-5241	169	4	c	c	NOUN
ejpam-5241	169	5	∗	∗	NOUN
ejpam-5241	169	6	h	h	NOUN
ejpam-5241	169	7	,	,	PUNCT
ejpam-5241	169	8	then	then	ADV
ejpam-5241	169	9	a	a	DET
ejpam-5241	169	10	closed	closed	ADJ
ejpam-5241	169	11	geodetic	geodetic	ADJ
ejpam-5241	169	12	hop	hop	NOUN
ejpam-5241	169	13	dominating	dominating	NOUN
ejpam-5241	169	14	set	set	NOUN
ejpam-5241	169	15	of	of	ADP
ejpam-5241	169	16	g	g	PROPN
ejpam-5241	169	17	contains	contain	VERB
ejpam-5241	169	18	the	the	DET
ejpam-5241	169	19	extreme	extreme	ADJ
ejpam-5241	169	20	vertices	vertex	NOUN
ejpam-5241	169	21	.	.	PUNCT
ejpam-5241	170	1	it	it	PRON
ejpam-5241	170	2	also	also	ADV
ejpam-5241	170	3	contains	contain	VERB
ejpam-5241	170	4	all	all	DET
ejpam-5241	170	5	dominating	dominating	NOUN
ejpam-5241	170	6	vertices	vertex	NOUN
ejpam-5241	170	7	.	.	PUNCT
ejpam-5241	171	1	theorem	theorem	NOUN
ejpam-5241	171	2	3	3	X
ejpam-5241	171	3	.	.	PUNCT
ejpam-5241	172	1	let	let	VERB
ejpam-5241	172	2	g	g	PROPN
ejpam-5241	172	3	∈	∈	PROPN
ejpam-5241	172	4	c	c	NOUN
ejpam-5241	172	5	∗	∗	NOUN
ejpam-5241	172	6	h	h	NOUN
ejpam-5241	172	7	of	of	ADP
ejpam-5241	172	8	order	order	NOUN
ejpam-5241	172	9	n.	n.	NOUN
ejpam-5241	172	10	then	then	ADV
ejpam-5241	172	11	γhcg(g	γhcg(g	PROPN
ejpam-5241	172	12	)	)	PUNCT
ejpam-5241	172	13	=	=	SYM
ejpam-5241	173	1	n	n	NOUN
ejpam-5241	173	2	if	if	SCONJ
ejpam-5241	173	3	and	and	CCONJ
ejpam-5241	173	4	only	only	ADV
ejpam-5241	173	5	if	if	SCONJ
ejpam-5241	173	6	either	either	CCONJ
ejpam-5241	173	7	(	(	PUNCT
ejpam-5241	173	8	i	i	NOUN
ejpam-5241	173	9	)	)	PUNCT
ejpam-5241	173	10	g	g	PROPN
ejpam-5241	173	11	=	=	SYM
ejpam-5241	173	12	kn	kn	PROPN
ejpam-5241	173	13	;	;	PUNCT
ejpam-5241	173	14	or	or	CCONJ
ejpam-5241	173	15	(	(	PUNCT
ejpam-5241	173	16	ii	ii	NOUN
ejpam-5241	173	17	)	)	PUNCT
ejpam-5241	173	18	g	g	PROPN
ejpam-5241	173	19	̸=	̸=	PROPN
ejpam-5241	173	20	kn	kn	PROPN
ejpam-5241	173	21	such	such	ADJ
ejpam-5241	173	22	that	that	SCONJ
ejpam-5241	173	23	the	the	DET
ejpam-5241	173	24	set	set	NOUN
ejpam-5241	173	25	s	s	NOUN
ejpam-5241	173	26	of	of	ADP
ejpam-5241	173	27	dominating	dominating	NOUN
ejpam-5241	173	28	vertices	vertex	NOUN
ejpam-5241	173	29	is	be	AUX
ejpam-5241	173	30	nonempty	nonempty	ADJ
ejpam-5241	173	31	and	and	CCONJ
ejpam-5241	173	32	each	each	PRON
ejpam-5241	173	33	of	of	ADP
ejpam-5241	173	34	the	the	DET
ejpam-5241	173	35	components	component	NOUN
ejpam-5241	173	36	of	of	ADP
ejpam-5241	173	37	⟨v	⟨v	PROPN
ejpam-5241	173	38	(	(	PUNCT
ejpam-5241	173	39	g	g	NOUN
ejpam-5241	173	40	)	)	PUNCT
ejpam-5241	173	41	\	\	PROPN
ejpam-5241	173	42	s⟩	s⟩	NOUN
ejpam-5241	173	43	is	be	AUX
ejpam-5241	173	44	complete	complete	ADJ
ejpam-5241	173	45	.	.	PUNCT
ejpam-5241	174	1	proof	proof	NOUN
ejpam-5241	174	2	.	.	PUNCT
ejpam-5241	175	1	if	if	SCONJ
ejpam-5241	175	2	g	g	PROPN
ejpam-5241	175	3	=	=	SYM
ejpam-5241	175	4	kn	kn	PROPN
ejpam-5241	175	5	,	,	PUNCT
ejpam-5241	175	6	then	then	ADV
ejpam-5241	175	7	v	v	X
ejpam-5241	175	8	(	(	PUNCT
ejpam-5241	175	9	g	g	NOUN
ejpam-5241	175	10	)	)	PUNCT
ejpam-5241	175	11	is	be	AUX
ejpam-5241	175	12	the	the	DET
ejpam-5241	175	13	unique	unique	ADJ
ejpam-5241	175	14	closed	closed	ADJ
ejpam-5241	175	15	geodetic	geodetic	ADJ
ejpam-5241	175	16	hop	hop	NOUN
ejpam-5241	175	17	dominating	dominating	NOUN
ejpam-5241	175	18	set	set	NOUN
ejpam-5241	175	19	of	of	ADP
ejpam-5241	175	20	g.	g.	PROPN
ejpam-5241	175	21	thus	thus	ADV
ejpam-5241	175	22	,	,	PUNCT
ejpam-5241	175	23	γhcg(g	γhcg(g	NOUN
ejpam-5241	175	24	)	)	PUNCT
ejpam-5241	175	25	=	=	SYM
ejpam-5241	176	1	n.	n.	NOUN
ejpam-5241	176	2	suppose	suppose	VERB
ejpam-5241	176	3	that	that	SCONJ
ejpam-5241	176	4	g	g	PROPN
ejpam-5241	176	5	̸=	̸=	PROPN
ejpam-5241	176	6	kn	kn	PROPN
ejpam-5241	176	7	.	.	PUNCT
ejpam-5241	177	1	first	first	ADV
ejpam-5241	177	2	,	,	PUNCT
ejpam-5241	177	3	assume	assume	VERB
ejpam-5241	177	4	γhcg(g	γhcg(g	NOUN
ejpam-5241	177	5	)	)	PUNCT
ejpam-5241	177	6	=	=	VERB
ejpam-5241	178	1	n.	n.	NOUN
ejpam-5241	178	2	by	by	ADP
ejpam-5241	178	3	lemma	lemma	PROPN
ejpam-5241	178	4	1	1	NUM
ejpam-5241	178	5	,	,	PUNCT
ejpam-5241	178	6	the	the	DET
ejpam-5241	178	7	set	set	NOUN
ejpam-5241	178	8	s	s	NOUN
ejpam-5241	178	9	of	of	ADP
ejpam-5241	178	10	dominating	dominating	NOUN
ejpam-5241	178	11	vertices	vertex	NOUN
ejpam-5241	178	12	of	of	ADP
ejpam-5241	178	13	g	g	PROPN
ejpam-5241	178	14	is	be	AUX
ejpam-5241	178	15	nonempty	nonempty	ADJ
ejpam-5241	178	16	.	.	PUNCT
ejpam-5241	179	1	let	let	VERB
ejpam-5241	179	2	c	c	PRON
ejpam-5241	179	3	be	be	AUX
ejpam-5241	179	4	a	a	DET
ejpam-5241	179	5	component	component	NOUN
ejpam-5241	179	6	of	of	ADP
ejpam-5241	179	7	⟨v	⟨v	PROPN
ejpam-5241	179	8	(	(	PUNCT
ejpam-5241	179	9	g	g	NOUN
ejpam-5241	179	10	)	)	PUNCT
ejpam-5241	179	11	\	\	PROPN
ejpam-5241	180	1	s⟩.	s⟩.	PROPN
ejpam-5241	180	2	we	we	PRON
ejpam-5241	180	3	claim	claim	VERB
ejpam-5241	180	4	that	that	SCONJ
ejpam-5241	180	5	c	c	PROPN
ejpam-5241	180	6	is	be	AUX
ejpam-5241	180	7	complete	complete	ADJ
ejpam-5241	180	8	.	.	PUNCT
ejpam-5241	181	1	let	let	VERB
ejpam-5241	181	2	x	x	SYM
ejpam-5241	181	3	∈	∈	PROPN
ejpam-5241	181	4	v	v	X
ejpam-5241	181	5	(	(	PUNCT
ejpam-5241	181	6	c	c	NOUN
ejpam-5241	181	7	)	)	PUNCT
ejpam-5241	181	8	and	and	CCONJ
ejpam-5241	181	9	let	let	VERB
ejpam-5241	181	10	u	u	NOUN
ejpam-5241	181	11	,	,	PUNCT
ejpam-5241	181	12	v	v	NOUN
ejpam-5241	181	13	∈	∈	NOUN
ejpam-5241	181	14	nc(x	nc(x	ADV
ejpam-5241	181	15	)	)	PUNCT
ejpam-5241	181	16	.	.	PUNCT
ejpam-5241	182	1	suppose	suppose	VERB
ejpam-5241	182	2	,	,	PUNCT
ejpam-5241	182	3	to	to	ADP
ejpam-5241	182	4	the	the	DET
ejpam-5241	182	5	contrary	contrary	NOUN
ejpam-5241	182	6	,	,	PUNCT
ejpam-5241	182	7	that	that	SCONJ
ejpam-5241	182	8	uv	uv	NOUN
ejpam-5241	182	9	/∈	/∈	PUNCT
ejpam-5241	182	10	e(c	e(c	NUM
ejpam-5241	182	11	)	)	PUNCT
ejpam-5241	182	12	.	.	PUNCT
ejpam-5241	183	1	following	follow	VERB
ejpam-5241	183	2	a	a	DET
ejpam-5241	183	3	similar	similar	ADJ
ejpam-5241	183	4	proof	proof	NOUN
ejpam-5241	183	5	to	to	ADP
ejpam-5241	183	6	that	that	PRON
ejpam-5241	183	7	of	of	ADP
ejpam-5241	183	8	lemma	lemma	PROPN
ejpam-5241	183	9	1	1	NUM
ejpam-5241	183	10	,	,	PUNCT
ejpam-5241	183	11	t	t	NOUN
ejpam-5241	183	12	=	=	SYM
ejpam-5241	183	13	v	v	PROPN
ejpam-5241	183	14	(	(	PUNCT
ejpam-5241	183	15	g)\{x	g)\{x	PROPN
ejpam-5241	183	16	}	}	PUNCT
ejpam-5241	183	17	is	be	AUX
ejpam-5241	183	18	a	a	DET
ejpam-5241	183	19	closed	closed	ADJ
ejpam-5241	183	20	geodetic	geodetic	ADJ
ejpam-5241	183	21	hop	hop	NOUN
ejpam-5241	183	22	dominating	dominating	NOUN
ejpam-5241	183	23	set	set	NOUN
ejpam-5241	183	24	of	of	ADP
ejpam-5241	183	25	g	g	PROPN
ejpam-5241	183	26	,	,	PUNCT
ejpam-5241	183	27	a	a	DET
ejpam-5241	183	28	contradiction	contradiction	NOUN
ejpam-5241	183	29	.	.	PUNCT
ejpam-5241	184	1	thus	thus	ADV
ejpam-5241	184	2	,	,	PUNCT
ejpam-5241	184	3	uv	uv	PROPN
ejpam-5241	184	4	∈	∈	PROPN
ejpam-5241	184	5	e(g	e(g	PROPN
ejpam-5241	184	6	)	)	PUNCT
ejpam-5241	184	7	,	,	PUNCT
ejpam-5241	184	8	showing	show	VERB
ejpam-5241	184	9	that	that	SCONJ
ejpam-5241	184	10	c	c	PROPN
ejpam-5241	184	11	is	be	AUX
ejpam-5241	184	12	complete	complete	ADJ
ejpam-5241	184	13	.	.	PUNCT
ejpam-5241	185	1	conversely	conversely	ADV
ejpam-5241	185	2	,	,	PUNCT
ejpam-5241	185	3	suppose	suppose	VERB
ejpam-5241	185	4	that	that	SCONJ
ejpam-5241	185	5	g	g	PROPN
ejpam-5241	185	6	is	be	AUX
ejpam-5241	185	7	as	as	SCONJ
ejpam-5241	185	8	described	describe	VERB
ejpam-5241	185	9	in	in	ADP
ejpam-5241	185	10	condition	condition	NOUN
ejpam-5241	185	11	(	(	PUNCT
ejpam-5241	185	12	ii	ii	NOUN
ejpam-5241	185	13	)	)	PUNCT
ejpam-5241	185	14	.	.	PUNCT
ejpam-5241	186	1	let	let	VERB
ejpam-5241	186	2	t	t	PROPN
ejpam-5241	186	3	⊆	⊆	NUM
ejpam-5241	186	4	v	v	NOUN
ejpam-5241	186	5	(	(	PUNCT
ejpam-5241	186	6	g	g	NOUN
ejpam-5241	186	7	)	)	PUNCT
ejpam-5241	186	8	be	be	AUX
ejpam-5241	186	9	a	a	DET
ejpam-5241	186	10	closed	closed	ADJ
ejpam-5241	186	11	geodetic	geodetic	ADJ
ejpam-5241	186	12	hop	hop	NOUN
ejpam-5241	186	13	dominating	dominating	NOUN
ejpam-5241	186	14	set	set	NOUN
ejpam-5241	186	15	of	of	ADP
ejpam-5241	186	16	g.	g.	PROPN
ejpam-5241	186	17	by	by	ADP
ejpam-5241	186	18	the	the	DET
ejpam-5241	186	19	preceding	precede	VERB
ejpam-5241	186	20	remark	remark	NOUN
ejpam-5241	186	21	,	,	PUNCT
ejpam-5241	186	22	s	s	VERB
ejpam-5241	186	23	⊆	⊆	NUM
ejpam-5241	186	24	t	t	NOUN
ejpam-5241	186	25	.	.	PUNCT
ejpam-5241	187	1	let	let	VERB
ejpam-5241	187	2	c	c	PRON
ejpam-5241	187	3	be	be	AUX
ejpam-5241	187	4	a	a	DET
ejpam-5241	187	5	component	component	NOUN
ejpam-5241	187	6	of	of	ADP
ejpam-5241	187	7	g∗	g∗	PROPN
ejpam-5241	187	8	=	=	SYM
ejpam-5241	187	9	⟨v	⟨v	NUM
ejpam-5241	187	10	(	(	PUNCT
ejpam-5241	187	11	g	g	NOUN
ejpam-5241	187	12	)	)	PUNCT
ejpam-5241	187	13	\	\	PROPN
ejpam-5241	188	1	s⟩.	s⟩.	PROPN
ejpam-5241	188	2	let	let	VERB
ejpam-5241	188	3	x	x	SYM
ejpam-5241	188	4	∈	∈	PROPN
ejpam-5241	188	5	v	v	X
ejpam-5241	188	6	(	(	PUNCT
ejpam-5241	188	7	c	c	NOUN
ejpam-5241	188	8	)	)	PUNCT
ejpam-5241	188	9	and	and	CCONJ
ejpam-5241	188	10	u	u	NOUN
ejpam-5241	188	11	,	,	PUNCT
ejpam-5241	188	12	v	v	PROPN
ejpam-5241	188	13	∈	∈	PROPN
ejpam-5241	188	14	ng(x	ng(x	NUM
ejpam-5241	188	15	)	)	PUNCT
ejpam-5241	188	16	.	.	PUNCT
ejpam-5241	189	1	if	if	SCONJ
ejpam-5241	189	2	u	u	NOUN
ejpam-5241	189	3	,	,	PUNCT
ejpam-5241	189	4	v	v	PROPN
ejpam-5241	189	5	∈	∈	PROPN
ejpam-5241	189	6	v	v	NOUN
ejpam-5241	189	7	(	(	PUNCT
ejpam-5241	189	8	c	c	NOUN
ejpam-5241	189	9	)	)	PUNCT
ejpam-5241	189	10	,	,	PUNCT
ejpam-5241	189	11	then	then	ADV
ejpam-5241	189	12	uv	uv	PROPN
ejpam-5241	189	13	∈	∈	PROPN
ejpam-5241	189	14	e(g	e(g	PROPN
ejpam-5241	189	15	)	)	PUNCT
ejpam-5241	189	16	since	since	SCONJ
ejpam-5241	189	17	c	c	PROPN
ejpam-5241	189	18	is	be	AUX
ejpam-5241	189	19	complete	complete	ADJ
ejpam-5241	189	20	.	.	PUNCT
ejpam-5241	190	1	suppose	suppose	VERB
ejpam-5241	190	2	that	that	SCONJ
ejpam-5241	190	3	u	u	PROPN
ejpam-5241	190	4	/∈	/∈	NOUN
ejpam-5241	190	5	v	v	INTJ
ejpam-5241	190	6	(	(	PUNCT
ejpam-5241	190	7	c	c	NOUN
ejpam-5241	190	8	)	)	PUNCT
ejpam-5241	190	9	.	.	PUNCT
ejpam-5241	191	1	then	then	ADV
ejpam-5241	191	2	u	u	PROPN
ejpam-5241	191	3	∈	∈	PROPN
ejpam-5241	191	4	s	s	NOUN
ejpam-5241	191	5	,	,	PUNCT
ejpam-5241	191	6	i.e.	i.e.	X
ejpam-5241	191	7	,	,	PUNCT
ejpam-5241	191	8	u	u	NOUN
ejpam-5241	191	9	is	be	AUX
ejpam-5241	191	10	a	a	DET
ejpam-5241	191	11	dominating	dominating	NOUN
ejpam-5241	191	12	vertex	vertex	NOUN
ejpam-5241	191	13	in	in	ADP
ejpam-5241	191	14	g.	g.	PROPN
ejpam-5241	191	15	thus	thus	ADV
ejpam-5241	191	16	,	,	PUNCT
ejpam-5241	191	17	uv	uv	PROPN
ejpam-5241	191	18	∈	∈	PROPN
ejpam-5241	191	19	e(g	e(g	PROPN
ejpam-5241	191	20	)	)	PUNCT
ejpam-5241	191	21	.	.	PUNCT
ejpam-5241	192	1	this	this	PRON
ejpam-5241	192	2	shows	show	VERB
ejpam-5241	192	3	that	that	SCONJ
ejpam-5241	192	4	x	x	SYM
ejpam-5241	192	5	∈	∈	PROPN
ejpam-5241	192	6	ext(g	ext(g	PROPN
ejpam-5241	192	7	)	)	PUNCT
ejpam-5241	192	8	⊆	⊆	NUM
ejpam-5241	192	9	t	t	NOUN
ejpam-5241	192	10	.	.	PUNCT
ejpam-5241	193	1	thus	thus	ADV
ejpam-5241	193	2	,	,	PUNCT
ejpam-5241	193	3	v	v	X
ejpam-5241	193	4	(	(	PUNCT
ejpam-5241	193	5	c	c	NOUN
ejpam-5241	193	6	)	)	PUNCT
ejpam-5241	193	7	⊆	⊆	NUM
ejpam-5241	193	8	t	t	NOUN
ejpam-5241	193	9	.	.	PUNCT
ejpam-5241	194	1	since	since	SCONJ
ejpam-5241	194	2	c	c	PROPN
ejpam-5241	194	3	is	be	AUX
ejpam-5241	194	4	arbitrary	arbitrary	ADJ
ejpam-5241	194	5	,	,	PUNCT
ejpam-5241	194	6	v	v	ADJ
ejpam-5241	194	7	(	(	PUNCT
ejpam-5241	194	8	g	g	NOUN
ejpam-5241	194	9	)	)	PUNCT
ejpam-5241	194	10	=	=	SYM
ejpam-5241	194	11	s	s	NOUN
ejpam-5241	194	12	∪	∪	X
ejpam-5241	194	13	(	(	PUNCT
ejpam-5241	194	14	∪c	∪c	NUM
ejpam-5241	194	15	component	component	NOUN
ejpam-5241	194	16	of	of	ADP
ejpam-5241	194	17	g∗	g∗	PROPN
ejpam-5241	194	18	v	v	NOUN
ejpam-5241	194	19	(	(	PUNCT
ejpam-5241	194	20	c	c	NOUN
ejpam-5241	194	21	)	)	PUNCT
ejpam-5241	194	22	)	)	PUNCT
ejpam-5241	195	1	=	=	PUNCT
ejpam-5241	196	1	t.	t.	NOUN
ejpam-5241	196	2	since	since	SCONJ
ejpam-5241	196	3	t	t	PROPN
ejpam-5241	196	4	is	be	AUX
ejpam-5241	196	5	arbitrary	arbitrary	ADJ
ejpam-5241	196	6	,	,	PUNCT
ejpam-5241	196	7	γhcg(g	γhcg(g	NOUN
ejpam-5241	196	8	)	)	PUNCT
ejpam-5241	196	9	=	=	SYM
ejpam-5241	196	10	|v	|v	PROPN
ejpam-5241	196	11	(	(	PUNCT
ejpam-5241	196	12	g)|	g)|	NOUN
ejpam-5241	196	13	=	=	PUNCT
ejpam-5241	196	14	n.	n.	NOUN
ejpam-5241	196	15	the	the	DET
ejpam-5241	196	16	star	star	NOUN
ejpam-5241	196	17	graph	graph	NOUN
ejpam-5241	196	18	k1,n	k1,n	PROPN
ejpam-5241	196	19	is	be	AUX
ejpam-5241	196	20	an	an	DET
ejpam-5241	196	21	example	example	NOUN
ejpam-5241	196	22	of	of	ADP
ejpam-5241	196	23	the	the	DET
ejpam-5241	196	24	infinite	infinite	ADJ
ejpam-5241	196	25	family	family	NOUN
ejpam-5241	196	26	of	of	ADP
ejpam-5241	196	27	graphs	graph	NOUN
ejpam-5241	196	28	described	describe	VERB
ejpam-5241	196	29	in	in	ADP
ejpam-5241	196	30	theorem	theorem	ADJ
ejpam-5241	196	31	3(ii	3(ii	NUM
ejpam-5241	196	32	)	)	PUNCT
ejpam-5241	196	33	.	.	PUNCT
ejpam-5241	197	1	a.	a.	PROPN
ejpam-5241	197	2	adolfo	adolfo	PROPN
ejpam-5241	197	3	,	,	PUNCT
ejpam-5241	197	4	i.	i.	PROPN
ejpam-5241	197	5	aniversario	aniversario	PROPN
ejpam-5241	197	6	,	,	PUNCT
ejpam-5241	197	7	f.	f.	PROPN
ejpam-5241	197	8	jamil	jamil	PROPN
ejpam-5241	197	9	/	/	SYM
ejpam-5241	197	10	eur	eur	PROPN
ejpam-5241	197	11	.	.	PUNCT
ejpam-5241	198	1	j.	j.	PROPN
ejpam-5241	198	2	pure	pure	PROPN
ejpam-5241	198	3	appl	appl	PROPN
ejpam-5241	198	4	.	.	PROPN
ejpam-5241	198	5	math	math	PROPN
ejpam-5241	198	6	,	,	PUNCT
ejpam-5241	198	7	17	17	NUM
ejpam-5241	198	8	(	(	PUNCT
ejpam-5241	198	9	3	3	NUM
ejpam-5241	198	10	)	)	PUNCT
ejpam-5241	198	11	(	(	PUNCT
ejpam-5241	198	12	2024	2024	NUM
ejpam-5241	198	13	)	)	PUNCT
ejpam-5241	198	14	,	,	PUNCT
ejpam-5241	198	15	1618	1618	NUM
ejpam-5241	198	16	-	-	SYM
ejpam-5241	198	17	1636	1636	NUM
ejpam-5241	198	18	1624	1624	NUM
ejpam-5241	198	19	2.2	2.2	NUM
ejpam-5241	198	20	.	.	PUNCT
ejpam-5241	199	1	for	for	ADP
ejpam-5241	199	2	paths	path	NOUN
ejpam-5241	199	3	pn	pn	PROPN
ejpam-5241	199	4	,	,	PUNCT
ejpam-5241	199	5	cycles	cycle	NOUN
ejpam-5241	199	6	cn	cn	ADJ
ejpam-5241	199	7	and	and	CCONJ
ejpam-5241	199	8	multipartite	multipartite	ADJ
ejpam-5241	199	9	graphs	graph	NOUN
ejpam-5241	199	10	since	since	SCONJ
ejpam-5241	199	11	every	every	DET
ejpam-5241	199	12	geodetic	geodetic	ADJ
ejpam-5241	199	13	hop	hop	NOUN
ejpam-5241	199	14	dominating	dominating	NOUN
ejpam-5241	199	15	set	set	NOUN
ejpam-5241	199	16	of	of	ADP
ejpam-5241	199	17	pn	pn	PROPN
ejpam-5241	199	18	is	be	AUX
ejpam-5241	199	19	a	a	DET
ejpam-5241	199	20	closed	closed	ADJ
ejpam-5241	199	21	geodetic	geodetic	ADJ
ejpam-5241	199	22	hop	hop	NOUN
ejpam-5241	199	23	dominating	dominating	NOUN
ejpam-5241	199	24	set	set	NOUN
ejpam-5241	199	25	of	of	ADP
ejpam-5241	199	26	pn	pn	PROPN
ejpam-5241	199	27	,	,	PUNCT
ejpam-5241	199	28	we	we	PRON
ejpam-5241	199	29	have	have	VERB
ejpam-5241	199	30	the	the	DET
ejpam-5241	199	31	following	following	NOUN
ejpam-5241	199	32	:	:	PUNCT
ejpam-5241	199	33	proposition	proposition	NOUN
ejpam-5241	199	34	3	3	NUM
ejpam-5241	199	35	.	.	X
ejpam-5241	199	36	for	for	ADP
ejpam-5241	199	37	a	a	DET
ejpam-5241	199	38	path	path	NOUN
ejpam-5241	199	39	pn	pn	NOUN
ejpam-5241	199	40	on	on	ADP
ejpam-5241	199	41	n	n	PRON
ejpam-5241	199	42	vertices	vertex	NOUN
ejpam-5241	199	43	,	,	PUNCT
ejpam-5241	199	44	γhcg(pn	γhcg(pn	NOUN
ejpam-5241	199	45	)	)	PUNCT
ejpam-5241	199	46	=	=	PUNCT
ejpam-5241	199	47			NOUN
ejpam-5241	200	1	n	n	CCONJ
ejpam-5241	200	2	if	if	SCONJ
ejpam-5241	200	3	n	n	NOUN
ejpam-5241	200	4	=	=	SYM
ejpam-5241	200	5	1	1	NUM
ejpam-5241	200	6	,	,	PUNCT
ejpam-5241	200	7	2	2	NUM
ejpam-5241	200	8	,	,	PUNCT
ejpam-5241	200	9	n+6	n+6	NOUN
ejpam-5241	200	10	3	3	NUM
ejpam-5241	200	11	if	if	SCONJ
ejpam-5241	200	12	n	n	PRON
ejpam-5241	200	13	≡	≡	PROPN
ejpam-5241	200	14	0(mod	0(mod	NOUN
ejpam-5241	201	1	3	3	X
ejpam-5241	201	2	)	)	PUNCT
ejpam-5241	201	3	,	,	PUNCT
ejpam-5241	202	1	n+2	n+2	PRON
ejpam-5241	202	2	3	3	NUM
ejpam-5241	202	3	if	if	SCONJ
ejpam-5241	202	4	n	n	PRON
ejpam-5241	202	5	≡	≡	PROPN
ejpam-5241	202	6	1(mod	1(mod	NUM
ejpam-5241	202	7	3	3	NUM
ejpam-5241	202	8	)	)	PUNCT
ejpam-5241	202	9	,	,	PUNCT
ejpam-5241	202	10	n+4	n+4	NUM
ejpam-5241	202	11	3	3	NUM
ejpam-5241	202	12	if	if	SCONJ
ejpam-5241	202	13	n	n	PRON
ejpam-5241	202	14	≡	≡	PROPN
ejpam-5241	202	15	2(mod	2(mod	NUM
ejpam-5241	202	16	3	3	X
ejpam-5241	202	17	)	)	PUNCT
ejpam-5241	202	18	proposition	proposition	NOUN
ejpam-5241	202	19	4	4	NUM
ejpam-5241	202	20	.	.	PUNCT
ejpam-5241	203	1	a	a	DET
ejpam-5241	203	2	cycle	cycle	NOUN
ejpam-5241	203	3	graph	graph	NOUN
ejpam-5241	203	4	cn	cn	NOUN
ejpam-5241	203	5	of	of	ADP
ejpam-5241	203	6	order	order	NOUN
ejpam-5241	203	7	n	n	PRON
ejpam-5241	203	8	admits	admit	VERB
ejpam-5241	203	9	a	a	DET
ejpam-5241	203	10	closed	closed	ADJ
ejpam-5241	203	11	geodetic	geodetic	ADJ
ejpam-5241	203	12	hop	hop	NOUN
ejpam-5241	203	13	dominating	dominating	NOUN
ejpam-5241	203	14	set	set	NOUN
ejpam-5241	203	15	if	if	SCONJ
ejpam-5241	203	16	and	and	CCONJ
ejpam-5241	203	17	only	only	ADV
ejpam-5241	203	18	if	if	SCONJ
ejpam-5241	203	19	n	n	X
ejpam-5241	203	20	<	<	X
ejpam-5241	203	21	12	12	NUM
ejpam-5241	203	22	.	.	PUNCT
ejpam-5241	204	1	moreover	moreover	ADV
ejpam-5241	204	2	precisely	precisely	ADV
ejpam-5241	204	3	,	,	PUNCT
ejpam-5241	204	4	γhcg(cn	γhcg(cn	NOUN
ejpam-5241	204	5	)	)	PUNCT
ejpam-5241	204	6	=	=	PUNCT
ejpam-5241	205	1			NOUN
ejpam-5241	205	2	3	3	NUM
ejpam-5241	205	3	if	if	SCONJ
ejpam-5241	205	4	n	n	NOUN
ejpam-5241	205	5	=	=	SYM
ejpam-5241	205	6	3	3	NUM
ejpam-5241	205	7	,	,	PUNCT
ejpam-5241	205	8	4	4	NUM
ejpam-5241	205	9	,	,	PUNCT
ejpam-5241	205	10	5	5	NUM
ejpam-5241	205	11	n	n	SYM
ejpam-5241	205	12	3	3	NUM
ejpam-5241	205	13	if	if	SCONJ
ejpam-5241	205	14	n	n	NOUN
ejpam-5241	205	15	=	=	SYM
ejpam-5241	205	16	6	6	NUM
ejpam-5241	205	17	,	,	PUNCT
ejpam-5241	205	18	9	9	NUM
ejpam-5241	205	19	n+2	n+2	SYM
ejpam-5241	205	20	3	3	NUM
ejpam-5241	205	21	if	if	SCONJ
ejpam-5241	205	22	n	n	NOUN
ejpam-5241	205	23	=	=	SYM
ejpam-5241	205	24	7	7	NUM
ejpam-5241	205	25	,	,	PUNCT
ejpam-5241	205	26	10	10	NUM
ejpam-5241	205	27	n+4	n+4	NUM
ejpam-5241	205	28	3	3	NUM
ejpam-5241	205	29	if	if	SCONJ
ejpam-5241	205	30	n	n	NOUN
ejpam-5241	205	31	=	=	SYM
ejpam-5241	205	32	8	8	NUM
ejpam-5241	205	33	,	,	PUNCT
ejpam-5241	205	34	11	11	NUM
ejpam-5241	205	35	(	(	PUNCT
ejpam-5241	205	36	2	2	NUM
ejpam-5241	205	37	)	)	PUNCT
ejpam-5241	205	38	proof	proof	NOUN
ejpam-5241	205	39	.	.	PUNCT
ejpam-5241	206	1	the	the	DET
ejpam-5241	206	2	case	case	NOUN
ejpam-5241	206	3	where	where	SCONJ
ejpam-5241	206	4	3	3	NUM
ejpam-5241	206	5	≤	≤	NOUN
ejpam-5241	206	6	n	n	PRON
ejpam-5241	206	7	≤	≤	NUM
ejpam-5241	206	8	11	11	NUM
ejpam-5241	206	9	can	can	AUX
ejpam-5241	206	10	be	be	AUX
ejpam-5241	206	11	readily	readily	ADV
ejpam-5241	206	12	verified	verify	VERB
ejpam-5241	206	13	.	.	PUNCT
ejpam-5241	206	14	suppose	suppose	VERB
ejpam-5241	206	15	that	that	SCONJ
ejpam-5241	206	16	n	n	PROPN
ejpam-5241	206	17	≥	≥	NUM
ejpam-5241	206	18	12	12	NUM
ejpam-5241	206	19	.	.	PUNCT
ejpam-5241	207	1	let	let	VERB
ejpam-5241	207	2	p	p	NOUN
ejpam-5241	207	3	=	=	PUNCT
ejpam-5241	208	1	[	[	X
ejpam-5241	208	2	x1	x1	PROPN
ejpam-5241	208	3	,	,	PUNCT
ejpam-5241	208	4	x2	x2	PROPN
ejpam-5241	208	5	,	,	PUNCT
ejpam-5241	208	6	...	...	PUNCT
ejpam-5241	208	7	,	,	PUNCT
ejpam-5241	208	8	xk	xk	PROPN
ejpam-5241	208	9	]	]	X
ejpam-5241	208	10	,	,	PUNCT
ejpam-5241	208	11	k	k	X
ejpam-5241	208	12	=	=	PUNCT
ejpam-5241	208	13	⌈n2	⌈n2	NOUN
ejpam-5241	208	14	⌉	⌉	NOUN
ejpam-5241	208	15	,	,	PUNCT
ejpam-5241	208	16	be	be	AUX
ejpam-5241	208	17	a	a	DET
ejpam-5241	208	18	path	path	NOUN
ejpam-5241	208	19	in	in	ADP
ejpam-5241	208	20	cn	cn	PROPN
ejpam-5241	208	21	and	and	CCONJ
ejpam-5241	208	22	v	v	ADP
ejpam-5241	208	23	∈	∈	PROPN
ejpam-5241	208	24	v	v	NOUN
ejpam-5241	208	25	(	(	PUNCT
ejpam-5241	208	26	cn	cn	PROPN
ejpam-5241	208	27	)	)	PUNCT
ejpam-5241	208	28	\	\	PROPN
ejpam-5241	208	29	v	v	X
ejpam-5241	208	30	(	(	PUNCT
ejpam-5241	208	31	p	p	NOUN
ejpam-5241	208	32	)	)	PUNCT
ejpam-5241	208	33	.	.	PUNCT
ejpam-5241	209	1	then	then	ADV
ejpam-5241	209	2	m	m	VERB
ejpam-5241	209	3	=	=	PUNCT
ejpam-5241	209	4	{	{	PUNCT
ejpam-5241	209	5	x1	x1	PROPN
ejpam-5241	209	6	,	,	PUNCT
ejpam-5241	209	7	x2	x2	PROPN
ejpam-5241	209	8	,	,	PUNCT
ejpam-5241	209	9	...	...	PUNCT
ejpam-5241	209	10	,	,	PUNCT
ejpam-5241	209	11	xk	xk	PROPN
ejpam-5241	209	12	,	,	PUNCT
ejpam-5241	209	13	v	v	NOUN
ejpam-5241	209	14	}	}	PUNCT
ejpam-5241	209	15	is	be	AUX
ejpam-5241	209	16	a	a	DET
ejpam-5241	209	17	closed	closed	ADJ
ejpam-5241	209	18	geodetic	geodetic	ADJ
ejpam-5241	209	19	cover	cover	NOUN
ejpam-5241	209	20	of	of	ADP
ejpam-5241	209	21	cn	cn	NOUN
ejpam-5241	209	22	with	with	ADP
ejpam-5241	209	23	|m	|m	NOUN
ejpam-5241	209	24	|	|	NOUN
ejpam-5241	209	25	=	=	SYM
ejpam-5241	209	26	⌈n2	⌈n2	NOUN
ejpam-5241	209	27	⌉	⌉	X
ejpam-5241	209	28	+	+	NOUN
ejpam-5241	209	29	1	1	X
ejpam-5241	209	30	.	.	PUNCT
ejpam-5241	209	31	since	since	SCONJ
ejpam-5241	209	32	n	n	PROPN
ejpam-5241	209	33	≥	≥	NOUN
ejpam-5241	209	34	12	12	NUM
ejpam-5241	209	35	,	,	PUNCT
ejpam-5241	209	36	|v	|v	PROPN
ejpam-5241	209	37	(	(	PUNCT
ejpam-5241	209	38	cn)\v	cn)\v	PROPN
ejpam-5241	209	39	(	(	PUNCT
ejpam-5241	209	40	p	p	NOUN
ejpam-5241	209	41	)	)	PUNCT
ejpam-5241	209	42	|	|	ADV
ejpam-5241	209	43	≥	≥	NOUN
ejpam-5241	209	44	6	6	NUM
ejpam-5241	209	45	.	.	PUNCT
ejpam-5241	210	1	thus	thus	ADV
ejpam-5241	210	2	,	,	PUNCT
ejpam-5241	210	3	cn	cn	PROPN
ejpam-5241	210	4	has	have	VERB
ejpam-5241	210	5	at	at	ADV
ejpam-5241	210	6	least	least	ADV
ejpam-5241	210	7	2	2	NUM
ejpam-5241	210	8	adjacent	adjacent	ADJ
ejpam-5241	210	9	vertices	vertex	NOUN
ejpam-5241	210	10	which	which	PRON
ejpam-5241	210	11	are	be	AUX
ejpam-5241	210	12	not	not	PART
ejpam-5241	210	13	hop	hop	ADV
ejpam-5241	210	14	dominated	dominate	VERB
ejpam-5241	210	15	by	by	ADP
ejpam-5241	210	16	v	v	NOUN
ejpam-5241	210	17	(	(	PUNCT
ejpam-5241	210	18	p	p	NOUN
ejpam-5241	210	19	)	)	PUNCT
ejpam-5241	210	20	.	.	PUNCT
ejpam-5241	211	1	consequently	consequently	ADV
ejpam-5241	211	2	,	,	PUNCT
ejpam-5241	211	3	cn	cn	PROPN
ejpam-5241	211	4	has	have	VERB
ejpam-5241	211	5	at	at	ADV
ejpam-5241	211	6	least	least	ADV
ejpam-5241	211	7	one	one	NUM
ejpam-5241	211	8	vertex	vertex	NOUN
ejpam-5241	211	9	which	which	PRON
ejpam-5241	211	10	is	be	AUX
ejpam-5241	211	11	not	not	PART
ejpam-5241	211	12	hop	hop	ADV
ejpam-5241	211	13	dominated	dominate	VERB
ejpam-5241	211	14	by	by	ADP
ejpam-5241	211	15	m	m	PROPN
ejpam-5241	211	16	.	.	PUNCT
ejpam-5241	212	1	this	this	PRON
ejpam-5241	212	2	means	mean	VERB
ejpam-5241	212	3	that	that	SCONJ
ejpam-5241	212	4	m	m	NOUN
ejpam-5241	212	5	is	be	AUX
ejpam-5241	212	6	not	not	PART
ejpam-5241	212	7	a	a	DET
ejpam-5241	212	8	hop	hop	NOUN
ejpam-5241	212	9	dominating	dominating	NOUN
ejpam-5241	212	10	set	set	NOUN
ejpam-5241	212	11	of	of	ADP
ejpam-5241	212	12	cn	cn	PROPN
ejpam-5241	212	13	(	(	PUNCT
ejpam-5241	212	14	see	see	VERB
ejpam-5241	212	15	,	,	PUNCT
ejpam-5241	212	16	for	for	ADP
ejpam-5241	212	17	example	example	NOUN
ejpam-5241	212	18	,	,	PUNCT
ejpam-5241	212	19	figure	figure	NOUN
ejpam-5241	212	20	1	1	NUM
ejpam-5241	212	21	)	)	PUNCT
ejpam-5241	212	22	.	.	PUNCT
ejpam-5241	213	1	we	we	PRON
ejpam-5241	213	2	claim	claim	VERB
ejpam-5241	213	3	that	that	SCONJ
ejpam-5241	213	4	every	every	DET
ejpam-5241	213	5	closed	closed	ADJ
ejpam-5241	213	6	geodetic	geodetic	ADJ
ejpam-5241	213	7	cover	cover	NOUN
ejpam-5241	213	8	s	s	NOUN
ejpam-5241	213	9	of	of	ADP
ejpam-5241	213	10	cn	cn	PROPN
ejpam-5241	213	11	is	be	AUX
ejpam-5241	213	12	contained	contain	VERB
ejpam-5241	213	13	in	in	ADP
ejpam-5241	213	14	a	a	DET
ejpam-5241	213	15	closed	closed	ADJ
ejpam-5241	213	16	geodetic	geodetic	ADJ
ejpam-5241	213	17	cover	cover	NOUN
ejpam-5241	213	18	m	m	NOUN
ejpam-5241	213	19	of	of	ADP
ejpam-5241	213	20	cn	cn	PROPN
ejpam-5241	213	21	as	as	SCONJ
ejpam-5241	213	22	constructed	construct	VERB
ejpam-5241	213	23	above	above	ADV
ejpam-5241	213	24	with	with	ADP
ejpam-5241	213	25	|m	|m	NOUN
ejpam-5241	213	26	|	|	NOUN
ejpam-5241	213	27	=	=	SYM
ejpam-5241	213	28	⌈n2	⌈n2	NOUN
ejpam-5241	213	29	⌉+	⌉+	NOUN
ejpam-5241	214	1	1	1	X
ejpam-5241	214	2	.	.	PUNCT
ejpam-5241	215	1	let	let	AUX
ejpam-5241	215	2	s	s	PRON
ejpam-5241	215	3	=	=	NOUN
ejpam-5241	215	4	sk	sk	X
ejpam-5241	215	5	=	=	NOUN
ejpam-5241	215	6	{	{	PUNCT
ejpam-5241	215	7	v1	v1	PROPN
ejpam-5241	215	8	,	,	PUNCT
ejpam-5241	215	9	v2	v2	PROPN
ejpam-5241	215	10	,	,	PUNCT
ejpam-5241	215	11	...	...	PUNCT
ejpam-5241	215	12	,	,	PUNCT
ejpam-5241	215	13	vk	vk	PART
ejpam-5241	215	14	}	}	PUNCT
ejpam-5241	215	15	be	be	AUX
ejpam-5241	215	16	a	a	DET
ejpam-5241	215	17	closed	closed	ADJ
ejpam-5241	215	18	geodetic	geodetic	ADJ
ejpam-5241	215	19	cover	cover	NOUN
ejpam-5241	215	20	of	of	ADP
ejpam-5241	215	21	cn	cn	PROPN
ejpam-5241	215	22	.	.	PROPN
ejpam-5241	215	23	note	note	VERB
ejpam-5241	215	24	that	that	SCONJ
ejpam-5241	215	25	here	here	ADV
ejpam-5241	215	26	,	,	PUNCT
ejpam-5241	215	27	ig[sj	ig[sj	X
ejpam-5241	215	28	]	]	PUNCT
ejpam-5241	215	29	̸=	̸=	PROPN
ejpam-5241	215	30	v	v	ADP
ejpam-5241	215	31	(	(	PUNCT
ejpam-5241	215	32	cn	cn	PROPN
ejpam-5241	215	33	)	)	PUNCT
ejpam-5241	215	34	for	for	ADP
ejpam-5241	215	35	all	all	DET
ejpam-5241	215	36	j	j	PROPN
ejpam-5241	215	37	∈	∈	PROPN
ejpam-5241	215	38	{	{	PUNCT
ejpam-5241	215	39	1	1	NUM
ejpam-5241	215	40	,	,	PUNCT
ejpam-5241	215	41	...	...	PUNCT
ejpam-5241	215	42	,	,	PUNCT
ejpam-5241	215	43	k	k	PROPN
ejpam-5241	215	44	−	−	PROPN
ejpam-5241	215	45	1	1	NUM
ejpam-5241	215	46	}	}	PUNCT
ejpam-5241	215	47	and	and	CCONJ
ejpam-5241	215	48	ig[sk	ig[sk	X
ejpam-5241	215	49	]	]	X
ejpam-5241	215	50	=	=	SYM
ejpam-5241	215	51	v	v	X
ejpam-5241	215	52	(	(	PUNCT
ejpam-5241	215	53	cn	cn	PROPN
ejpam-5241	215	54	)	)	PUNCT
ejpam-5241	215	55	.	.	PUNCT
ejpam-5241	216	1	if	if	SCONJ
ejpam-5241	216	2	k	k	PROPN
ejpam-5241	216	3	=	=	VERB
ejpam-5241	216	4	⌈n2	⌈n2	NOUN
ejpam-5241	216	5	⌉+1	⌉+1	PROPN
ejpam-5241	216	6	,	,	PUNCT
ejpam-5241	216	7	then	then	ADV
ejpam-5241	216	8	by	by	ADP
ejpam-5241	216	9	relabelling	relabelle	VERB
ejpam-5241	216	10	of	of	ADP
ejpam-5241	216	11	vertices	vertex	NOUN
ejpam-5241	216	12	where	where	SCONJ
ejpam-5241	216	13	necessary	necessary	ADJ
ejpam-5241	216	14	,	,	PUNCT
ejpam-5241	216	15	sk	sk	X
ejpam-5241	216	16	is	be	AUX
ejpam-5241	216	17	the	the	DET
ejpam-5241	216	18	desired	desire	VERB
ejpam-5241	216	19	m	m	NOUN
ejpam-5241	216	20	.	.	PUNCT
ejpam-5241	217	1	if	if	SCONJ
ejpam-5241	217	2	k	k	PROPN
ejpam-5241	217	3	=	=	SYM
ejpam-5241	217	4	2	2	NUM
ejpam-5241	217	5	,	,	PUNCT
ejpam-5241	217	6	then	then	ADV
ejpam-5241	217	7	dcn(v1	dcn(v1	PROPN
ejpam-5241	217	8	,	,	PUNCT
ejpam-5241	217	9	vk	vk	X
ejpam-5241	217	10	)	)	PUNCT
ejpam-5241	217	11	=	=	NOUN
ejpam-5241	217	12	⌈n2	⌈n2	NOUN
ejpam-5241	217	13	⌉.	⌉.	ADV
ejpam-5241	217	14	take	take	VERB
ejpam-5241	217	15	m	m	NOUN
ejpam-5241	217	16	=	=	PUNCT
ejpam-5241	217	17	{	{	PUNCT
ejpam-5241	217	18	x1	x1	PROPN
ejpam-5241	217	19	,	,	PUNCT
ejpam-5241	217	20	x2	x2	PROPN
ejpam-5241	217	21	,	,	PUNCT
ejpam-5241	217	22	...	...	PUNCT
ejpam-5241	217	23	,	,	PUNCT
ejpam-5241	217	24	xj	xj	NOUN
ejpam-5241	217	25	}	}	PUNCT
ejpam-5241	217	26	,	,	PUNCT
ejpam-5241	217	27	j	j	PROPN
ejpam-5241	217	28	=	=	PUNCT
ejpam-5241	217	29	⌈n2	⌈n2	NOUN
ejpam-5241	217	30	⌉	⌉	X
ejpam-5241	217	31	+	+	PUNCT
ejpam-5241	217	32	1	1	NUM
ejpam-5241	217	33	where	where	SCONJ
ejpam-5241	217	34	p	p	NOUN
ejpam-5241	217	35	=	=	PUNCT
ejpam-5241	218	1	[	[	X
ejpam-5241	218	2	x1	x1	PROPN
ejpam-5241	218	3	,	,	PUNCT
ejpam-5241	218	4	x2	x2	PROPN
ejpam-5241	218	5	,	,	PUNCT
ejpam-5241	218	6	...	...	PUNCT
ejpam-5241	218	7	,	,	PUNCT
ejpam-5241	218	8	xj	xj	PROPN
ejpam-5241	218	9	]	]	PUNCT
ejpam-5241	218	10	is	be	AUX
ejpam-5241	218	11	a	a	DET
ejpam-5241	218	12	v1	v1	NOUN
ejpam-5241	218	13	-	-	PUNCT
ejpam-5241	218	14	vk	vk	NOUN
ejpam-5241	218	15	geodesic	geodesic	NOUN
ejpam-5241	218	16	in	in	ADP
ejpam-5241	218	17	cn	cn	PROPN
ejpam-5241	218	18	.	.	PUNCT
ejpam-5241	219	1	then	then	ADV
ejpam-5241	219	2	m	m	PROPN
ejpam-5241	219	3	is	be	AUX
ejpam-5241	219	4	a	a	DET
ejpam-5241	219	5	closed	closed	ADJ
ejpam-5241	219	6	geodetic	geodetic	ADJ
ejpam-5241	219	7	cover	cover	NOUN
ejpam-5241	219	8	of	of	ADP
ejpam-5241	219	9	cn	cn	NOUN
ejpam-5241	219	10	with	with	ADP
ejpam-5241	219	11	|m	|m	NOUN
ejpam-5241	219	12	|	|	ADV
ejpam-5241	219	13	=	=	SYM
ejpam-5241	219	14	⌈n2	⌈n2	NOUN
ejpam-5241	219	15	⌉+1	⌉+1	NUM
ejpam-5241	219	16	and	and	CCONJ
ejpam-5241	219	17	s	s	VERB
ejpam-5241	219	18	⊆	⊆	NUM
ejpam-5241	219	19	m	m	NOUN
ejpam-5241	219	20	.	.	PUNCT
ejpam-5241	220	1	now	now	ADV
ejpam-5241	220	2	assume	assume	VERB
ejpam-5241	220	3	2	2	NUM
ejpam-5241	220	4	<	<	X
ejpam-5241	220	5	k	k	X
ejpam-5241	220	6	<	<	X
ejpam-5241	220	7	⌈n2	⌈n2	NOUN
ejpam-5241	220	8	⌉+1	⌉+1	PROPN
ejpam-5241	220	9	.	.	PUNCT
ejpam-5241	221	1	choose	choose	VERB
ejpam-5241	221	2	v	v	NUM
ejpam-5241	221	3	∈	∈	PROPN
ejpam-5241	221	4	v	v	NOUN
ejpam-5241	221	5	(	(	PUNCT
ejpam-5241	221	6	cn	cn	PROPN
ejpam-5241	221	7	)	)	PUNCT
ejpam-5241	221	8	and	and	CCONJ
ejpam-5241	221	9	a	a	DET
ejpam-5241	221	10	v	v	NOUN
ejpam-5241	221	11	-	-	ADJ
ejpam-5241	221	12	vk−1	vk−1	NOUN
ejpam-5241	221	13	geodesic	geodesic	NOUN
ejpam-5241	221	14	p	p	NOUN
ejpam-5241	221	15	=	=	PUNCT
ejpam-5241	222	1	[	[	X
ejpam-5241	222	2	x1	x1	PROPN
ejpam-5241	222	3	,	,	PUNCT
ejpam-5241	222	4	x2	x2	PROPN
ejpam-5241	222	5	,	,	PUNCT
ejpam-5241	222	6	...	...	PUNCT
ejpam-5241	222	7	,	,	PUNCT
ejpam-5241	222	8	xm	xm	PROPN
ejpam-5241	222	9	]	]	X
ejpam-5241	222	10	,	,	PUNCT
ejpam-5241	222	11	where	where	SCONJ
ejpam-5241	222	12	m	m	VERB
ejpam-5241	222	13	=	=	VERB
ejpam-5241	222	14	⌈n2	⌈n2	NOUN
ejpam-5241	222	15	⌉	⌉	VERB
ejpam-5241	222	16	such	such	ADJ
ejpam-5241	222	17	that	that	SCONJ
ejpam-5241	222	18	dcn(v	dcn(v	PROPN
ejpam-5241	222	19	,	,	PUNCT
ejpam-5241	222	20	vk−1	vk−1	NOUN
ejpam-5241	222	21	)	)	PUNCT
ejpam-5241	222	22	=	=	SYM
ejpam-5241	222	23	⌈n2	⌈n2	NOUN
ejpam-5241	222	24	⌉	⌉	PRON
ejpam-5241	222	25	−	−	PROPN
ejpam-5241	222	26	1	1	NUM
ejpam-5241	222	27	and	and	CCONJ
ejpam-5241	222	28	vk	vk	NOUN
ejpam-5241	222	29	/∈	/∈	NOUN
ejpam-5241	223	1	v	v	NOUN
ejpam-5241	223	2	(	(	PUNCT
ejpam-5241	223	3	p	p	NOUN
ejpam-5241	223	4	)	)	PUNCT
ejpam-5241	223	5	.	.	PUNCT
ejpam-5241	224	1	define	define	VERB
ejpam-5241	224	2	m	m	NOUN
ejpam-5241	224	3	=	=	PUNCT
ejpam-5241	224	4	{	{	PUNCT
ejpam-5241	224	5	x1	x1	PROPN
ejpam-5241	224	6	,	,	PUNCT
ejpam-5241	224	7	x2	x2	PROPN
ejpam-5241	224	8	,	,	PUNCT
ejpam-5241	224	9	...	...	PUNCT
ejpam-5241	224	10	,	,	PUNCT
ejpam-5241	224	11	xm	xm	PROPN
ejpam-5241	224	12	,	,	PUNCT
ejpam-5241	224	13	vk	vk	PROPN
ejpam-5241	224	14	}	}	PUNCT
ejpam-5241	224	15	.	.	PUNCT
ejpam-5241	225	1	consequently	consequently	ADV
ejpam-5241	225	2	,	,	PUNCT
ejpam-5241	225	3	m	m	VERB
ejpam-5241	225	4	is	be	AUX
ejpam-5241	225	5	a	a	DET
ejpam-5241	225	6	closed	closed	ADJ
ejpam-5241	225	7	geodetic	geodetic	ADJ
ejpam-5241	225	8	cover	cover	NOUN
ejpam-5241	225	9	of	of	ADP
ejpam-5241	225	10	cn	cn	NOUN
ejpam-5241	225	11	with	with	ADP
ejpam-5241	225	12	|m	|m	NOUN
ejpam-5241	225	13	|	|	NOUN
ejpam-5241	225	14	=	=	SYM
ejpam-5241	225	15	⌈n2	⌈n2	NOUN
ejpam-5241	225	16	⌉	⌉	X
ejpam-5241	225	17	+	+	CCONJ
ejpam-5241	225	18	1	1	NUM
ejpam-5241	225	19	as	as	SCONJ
ejpam-5241	225	20	described	describe	VERB
ejpam-5241	225	21	above	above	ADV
ejpam-5241	225	22	.	.	PUNCT
ejpam-5241	226	1	now	now	ADV
ejpam-5241	226	2	,	,	PUNCT
ejpam-5241	226	3	let	let	VERB
ejpam-5241	226	4	j	j	PROPN
ejpam-5241	226	5	∈	∈	PROPN
ejpam-5241	226	6	{	{	PUNCT
ejpam-5241	226	7	1	1	NUM
ejpam-5241	226	8	,	,	PUNCT
ejpam-5241	226	9	2	2	NUM
ejpam-5241	226	10	,	,	PUNCT
ejpam-5241	226	11	...	...	PUNCT
ejpam-5241	226	12	,	,	PUNCT
ejpam-5241	226	13	k	k	PROPN
ejpam-5241	226	14	−	−	PROPN
ejpam-5241	227	1	1	1	NUM
ejpam-5241	227	2	}	}	PUNCT
ejpam-5241	227	3	.	.	PUNCT
ejpam-5241	228	1	then	then	ADV
ejpam-5241	228	2	dcn(vj	dcn(vj	VERB
ejpam-5241	228	3	,	,	PUNCT
ejpam-5241	228	4	vk−1	vk−1	NOUN
ejpam-5241	228	5	)	)	PUNCT
ejpam-5241	228	6	≤	≤	NUM
ejpam-5241	228	7	⌈n2	⌈n2	NOUN
ejpam-5241	228	8	⌉	⌉	PRON
ejpam-5241	228	9	−	−	PROPN
ejpam-5241	228	10	1	1	NUM
ejpam-5241	228	11	.	.	PUNCT
ejpam-5241	229	1	by	by	ADP
ejpam-5241	229	2	the	the	DET
ejpam-5241	229	3	choice	choice	NOUN
ejpam-5241	229	4	of	of	ADP
ejpam-5241	229	5	p	p	NOUN
ejpam-5241	229	6	,	,	PUNCT
ejpam-5241	229	7	vj	vj	INTJ
ejpam-5241	229	8	∈	∈	PROPN
ejpam-5241	229	9	v	v	NOUN
ejpam-5241	229	10	(	(	PUNCT
ejpam-5241	229	11	p	p	NOUN
ejpam-5241	229	12	)	)	PUNCT
ejpam-5241	229	13	.	.	PUNCT
ejpam-5241	230	1	thus	thus	ADV
ejpam-5241	230	2	,	,	PUNCT
ejpam-5241	230	3	s	s	VERB
ejpam-5241	230	4	⊆	⊆	NUM
ejpam-5241	230	5	m	m	NOUN
ejpam-5241	230	6	.	.	PUNCT
ejpam-5241	231	1	therefore	therefore	ADV
ejpam-5241	231	2	,	,	PUNCT
ejpam-5241	231	3	being	be	AUX
ejpam-5241	231	4	a	a	DET
ejpam-5241	231	5	subset	subset	NOUN
ejpam-5241	231	6	of	of	ADP
ejpam-5241	231	7	a	a	DET
ejpam-5241	231	8	non	non	ADJ
ejpam-5241	231	9	-	-	ADJ
ejpam-5241	231	10	hop	hop	ADJ
ejpam-5241	231	11	dominating	dominating	NOUN
ejpam-5241	231	12	set	set	NOUN
ejpam-5241	231	13	,	,	PUNCT
ejpam-5241	231	14	any	any	DET
ejpam-5241	231	15	closed	closed	ADJ
ejpam-5241	231	16	geodetic	geodetic	ADJ
ejpam-5241	231	17	set	set	NOUN
ejpam-5241	231	18	s	s	PART
ejpam-5241	231	19	is	be	AUX
ejpam-5241	231	20	not	not	PART
ejpam-5241	231	21	a	a	DET
ejpam-5241	231	22	hop	hop	NOUN
ejpam-5241	231	23	dominating	dominating	NOUN
ejpam-5241	231	24	set	set	NOUN
ejpam-5241	231	25	of	of	ADP
ejpam-5241	231	26	cn	cn	PROPN
ejpam-5241	231	27	.	.	PUNCT
ejpam-5241	232	1	thus	thus	ADV
ejpam-5241	232	2	,	,	PUNCT
ejpam-5241	232	3	cn	cn	PROPN
ejpam-5241	232	4	does	do	AUX
ejpam-5241	232	5	not	not	PART
ejpam-5241	232	6	admit	admit	VERB
ejpam-5241	232	7	a	a	DET
ejpam-5241	232	8	closed	closed	ADJ
ejpam-5241	232	9	geodetic	geodetic	ADJ
ejpam-5241	232	10	hop	hop	NOUN
ejpam-5241	232	11	dominating	dominating	NOUN
ejpam-5241	232	12	set	set	NOUN
ejpam-5241	232	13	.	.	PUNCT
ejpam-5241	233	1	a.	a.	PROPN
ejpam-5241	233	2	adolfo	adolfo	PROPN
ejpam-5241	233	3	,	,	PUNCT
ejpam-5241	233	4	i.	i.	PROPN
ejpam-5241	233	5	aniversario	aniversario	PROPN
ejpam-5241	233	6	,	,	PUNCT
ejpam-5241	233	7	f.	f.	PROPN
ejpam-5241	233	8	jamil	jamil	PROPN
ejpam-5241	233	9	/	/	SYM
ejpam-5241	233	10	eur	eur	PROPN
ejpam-5241	233	11	.	.	PUNCT
ejpam-5241	234	1	j.	j.	PROPN
ejpam-5241	234	2	pure	pure	PROPN
ejpam-5241	234	3	appl	appl	PROPN
ejpam-5241	234	4	.	.	PROPN
ejpam-5241	234	5	math	math	PROPN
ejpam-5241	234	6	,	,	PUNCT
ejpam-5241	234	7	17	17	NUM
ejpam-5241	234	8	(	(	PUNCT
ejpam-5241	234	9	3	3	NUM
ejpam-5241	234	10	)	)	PUNCT
ejpam-5241	234	11	(	(	PUNCT
ejpam-5241	234	12	2024	2024	NUM
ejpam-5241	234	13	)	)	PUNCT
ejpam-5241	234	14	,	,	PUNCT
ejpam-5241	234	15	1618	1618	NUM
ejpam-5241	234	16	-	-	SYM
ejpam-5241	234	17	1636	1636	NUM
ejpam-5241	234	18	1625	1625	NUM
ejpam-5241	234	19	....................................	....................................	PUNCT
ejpam-5241	234	20	........................................................................	........................................................................	PUNCT
ejpam-5241	235	1	....................................	....................................	PUNCT
ejpam-5241	235	2	....................................	....................................	PUNCT
ejpam-5241	236	1	..................	..................	PUNCT
ejpam-5241	236	2	.................	.................	PUNCT
ejpam-5241	236	3	.	.	PUNCT
ejpam-5241	237	1	......	......	PUNCT
ejpam-5241	237	2	..............................	..............................	PUNCT
ejpam-5241	238	1	....................................	....................................	PUNCT
ejpam-5241	238	2	....................................	....................................	PUNCT
ejpam-5241	239	1	...........	...........	PUNCT
ejpam-5241	239	2	..........	..........	PUNCT
ejpam-5241	240	1	..........	..........	PUNCT
ejpam-5241	240	2	.....	.....	PUNCT
ejpam-5241	241	1	....................................	....................................	PUNCT
ejpam-5241	241	2	....................................	....................................	PUNCT
ejpam-5241	242	1	....................................	....................................	PUNCT
ejpam-5241	242	2	.........	.........	PUNCT
ejpam-5241	242	3	........	........	PUNCT
ejpam-5241	242	4	........	........	PUNCT
ejpam-5241	242	5	........	........	PUNCT
ejpam-5241	242	6	...	...	PUNCT
ejpam-5241	243	1	....................................	....................................	PUNCT
ejpam-5241	243	2	..........	..........	PUNCT
ejpam-5241	244	1	.........	.........	PUNCT
ejpam-5241	244	2	.........	.........	PUNCT
ejpam-5241	245	1	........	........	PUNCT
ejpam-5241	245	2	....................................	....................................	PUNCT
ejpam-5241	246	1	....................................	....................................	PUNCT
ejpam-5241	246	2	....................................	....................................	PUNCT
ejpam-5241	246	3	.............	.............	PUNCT
ejpam-5241	246	4	............	............	PUNCT
ejpam-5241	246	5	...........	...........	PUNCT
ejpam-5241	246	6	....................................	....................................	PUNCT
ejpam-5241	246	7	....................................	....................................	PUNCT
ejpam-5241	247	1	......................................................................	......................................................................	PUNCT
ejpam-5241	247	2	..	..	PUNCT
ejpam-5241	247	3	........................................................................	........................................................................	PUNCT
ejpam-5241	247	4	........................................................................	........................................................................	PUNCT
ejpam-5241	247	5	••	••	NOUN
ejpam-5241	247	6	•	•	NUM
ejpam-5241	247	7	•	•	NUM
ejpam-5241	247	8	•	•	NUM
ejpam-5241	247	9	•	•	NUM
ejpam-5241	247	10	•	•	NOUN
ejpam-5241	247	11	•	•	NOUN
ejpam-5241	247	12	....................................	....................................	PUNCT
ejpam-5241	247	13	........................................................................	........................................................................	PUNCT
ejpam-5241	247	14	....................................	....................................	PUNCT
ejpam-5241	247	15	....................................	....................................	PUNCT
ejpam-5241	247	16	..................	..................	PUNCT
ejpam-5241	247	17	.................	.................	PUNCT
ejpam-5241	247	18	.	.	PUNCT
ejpam-5241	248	1	......	......	PUNCT
ejpam-5241	248	2	..............................	..............................	PUNCT
ejpam-5241	249	1	....................................	....................................	PUNCT
ejpam-5241	249	2	....................................	....................................	PUNCT
ejpam-5241	250	1	...........	...........	PUNCT
ejpam-5241	250	2	..........	..........	PUNCT
ejpam-5241	251	1	..........	..........	PUNCT
ejpam-5241	251	2	.....	.....	PUNCT
ejpam-5241	252	1	....................................	....................................	PUNCT
ejpam-5241	252	2	....................................	....................................	PUNCT
ejpam-5241	253	1	....................................	....................................	PUNCT
ejpam-5241	253	2	.........	.........	PUNCT
ejpam-5241	253	3	........	........	PUNCT
ejpam-5241	253	4	........	........	PUNCT
ejpam-5241	253	5	........	........	PUNCT
ejpam-5241	253	6	...	...	PUNCT
ejpam-5241	254	1	....................................	....................................	PUNCT
ejpam-5241	254	2	..........	..........	PUNCT
ejpam-5241	255	1	.........	.........	PUNCT
ejpam-5241	255	2	.........	.........	PUNCT
ejpam-5241	256	1	........	........	PUNCT
ejpam-5241	256	2	....................................	....................................	PUNCT
ejpam-5241	257	1	....................................	....................................	PUNCT
ejpam-5241	257	2	....................................	....................................	PUNCT
ejpam-5241	257	3	.............	.............	PUNCT
ejpam-5241	257	4	............	............	PUNCT
ejpam-5241	257	5	...........	...........	PUNCT
ejpam-5241	257	6	....................................	....................................	PUNCT
ejpam-5241	257	7	....................................	....................................	PUNCT
ejpam-5241	258	1	......................................................................	......................................................................	PUNCT
ejpam-5241	258	2	..	..	PUNCT
ejpam-5241	258	3	........................................................................	........................................................................	PUNCT
ejpam-5241	258	4	........................................................................	........................................................................	PUNCT
ejpam-5241	258	5	••	••	NOUN
ejpam-5241	258	6	•	•	NUM
ejpam-5241	258	7	•	•	NUM
ejpam-5241	258	8	•	•	NUM
ejpam-5241	258	9	•	•	NUM
ejpam-5241	258	10	•	•	NOUN
ejpam-5241	258	11	•	•	NOUN
ejpam-5241	258	12	....................................	....................................	PUNCT
ejpam-5241	258	13	........................................................................	........................................................................	PUNCT
ejpam-5241	258	14	....................................	....................................	PUNCT
ejpam-5241	258	15	....................................	....................................	PUNCT
ejpam-5241	258	16	..................	..................	PUNCT
ejpam-5241	258	17	.................	.................	PUNCT
ejpam-5241	258	18	.	.	PUNCT
ejpam-5241	259	1	......	......	PUNCT
ejpam-5241	259	2	..............................	..............................	PUNCT
ejpam-5241	260	1	....................................	....................................	PUNCT
ejpam-5241	260	2	....................................	....................................	PUNCT
ejpam-5241	261	1	...........	...........	PUNCT
ejpam-5241	261	2	..........	..........	PUNCT
ejpam-5241	262	1	..........	..........	PUNCT
ejpam-5241	262	2	.....	.....	PUNCT
ejpam-5241	263	1	....................................	....................................	PUNCT
ejpam-5241	263	2	....................................	....................................	PUNCT
ejpam-5241	264	1	....................................	....................................	PUNCT
ejpam-5241	264	2	.........	.........	PUNCT
ejpam-5241	264	3	........	........	PUNCT
ejpam-5241	264	4	........	........	PUNCT
ejpam-5241	264	5	........	........	PUNCT
ejpam-5241	264	6	...	...	PUNCT
ejpam-5241	265	1	....................................	....................................	PUNCT
ejpam-5241	265	2	..........	..........	PUNCT
ejpam-5241	266	1	.........	.........	PUNCT
ejpam-5241	266	2	.........	.........	PUNCT
ejpam-5241	267	1	........	........	PUNCT
ejpam-5241	267	2	....................................	....................................	PUNCT
ejpam-5241	268	1	....................................	....................................	PUNCT
ejpam-5241	268	2	....................................	....................................	PUNCT
ejpam-5241	268	3	.............	.............	PUNCT
ejpam-5241	268	4	............	............	PUNCT
ejpam-5241	268	5	...........	...........	PUNCT
ejpam-5241	268	6	....................................	....................................	PUNCT
ejpam-5241	268	7	....................................	....................................	PUNCT
ejpam-5241	269	1	......................................................................	......................................................................	PUNCT
ejpam-5241	269	2	..	..	PUNCT
ejpam-5241	269	3	........................................................................	........................................................................	PUNCT
ejpam-5241	269	4	........................................................................	........................................................................	PUNCT
ejpam-5241	269	5	••	••	NOUN
ejpam-5241	269	6	•	•	NUM
ejpam-5241	269	7	•	•	NUM
ejpam-5241	269	8	•	•	NUM
ejpam-5241	269	9	•	•	NUM
ejpam-5241	269	10	•	•	NOUN
ejpam-5241	269	11	•	•	NOUN
ejpam-5241	269	12	....................................	....................................	PUNCT
ejpam-5241	269	13	........................................................................	........................................................................	PUNCT
ejpam-5241	269	14	....................................	....................................	PUNCT
ejpam-5241	269	15	....................................	....................................	PUNCT
ejpam-5241	269	16	..................	..................	PUNCT
ejpam-5241	269	17	.................	.................	PUNCT
ejpam-5241	269	18	.	.	PUNCT
ejpam-5241	270	1	......	......	PUNCT
ejpam-5241	270	2	..............................	..............................	PUNCT
ejpam-5241	271	1	....................................	....................................	PUNCT
ejpam-5241	271	2	....................................	....................................	PUNCT
ejpam-5241	272	1	...........	...........	PUNCT
ejpam-5241	272	2	..........	..........	PUNCT
ejpam-5241	273	1	..........	..........	PUNCT
ejpam-5241	273	2	.....	.....	PUNCT
ejpam-5241	274	1	....................................	....................................	PUNCT
ejpam-5241	274	2	....................................	....................................	PUNCT
ejpam-5241	275	1	....................................	....................................	PUNCT
ejpam-5241	275	2	.........	.........	PUNCT
ejpam-5241	275	3	........	........	PUNCT
ejpam-5241	275	4	........	........	PUNCT
ejpam-5241	275	5	........	........	PUNCT
ejpam-5241	275	6	...	...	PUNCT
ejpam-5241	276	1	....................................	....................................	PUNCT
ejpam-5241	276	2	..........	..........	PUNCT
ejpam-5241	277	1	.........	.........	PUNCT
ejpam-5241	277	2	.........	.........	PUNCT
ejpam-5241	278	1	........	........	PUNCT
ejpam-5241	278	2	....................................	....................................	PUNCT
ejpam-5241	279	1	....................................	....................................	PUNCT
ejpam-5241	279	2	....................................	....................................	PUNCT
ejpam-5241	279	3	.............	.............	PUNCT
ejpam-5241	279	4	............	............	PUNCT
ejpam-5241	279	5	...........	...........	PUNCT
ejpam-5241	279	6	....................................	....................................	PUNCT
ejpam-5241	279	7	....................................	....................................	PUNCT
ejpam-5241	280	1	......................................................................	......................................................................	PUNCT
ejpam-5241	280	2	..	..	PUNCT
ejpam-5241	280	3	........................................................................	........................................................................	PUNCT
ejpam-5241	280	4	........................................................................	........................................................................	PUNCT
ejpam-5241	280	5	••	••	NOUN
ejpam-5241	280	6	•	•	NUM
ejpam-5241	280	7	•	•	NUM
ejpam-5241	280	8	•	•	NUM
ejpam-5241	280	9	•	•	NUM
ejpam-5241	280	10	•	•	NOUN
ejpam-5241	280	11	•	•	NOUN
ejpam-5241	280	12	....................................	....................................	PUNCT
ejpam-5241	280	13	........................................................................	........................................................................	PUNCT
ejpam-5241	280	14	....................................	....................................	PUNCT
ejpam-5241	280	15	....................................	....................................	PUNCT
ejpam-5241	280	16	..................	..................	PUNCT
ejpam-5241	280	17	.................	.................	PUNCT
ejpam-5241	280	18	.	.	PUNCT
ejpam-5241	281	1	......	......	PUNCT
ejpam-5241	281	2	..............................	..............................	PUNCT
ejpam-5241	282	1	....................................	....................................	PUNCT
ejpam-5241	282	2	....................................	....................................	PUNCT
ejpam-5241	283	1	...........	...........	PUNCT
ejpam-5241	283	2	..........	..........	PUNCT
ejpam-5241	284	1	..........	..........	PUNCT
ejpam-5241	284	2	.....	.....	PUNCT
ejpam-5241	285	1	....................................	....................................	PUNCT
ejpam-5241	285	2	....................................	....................................	PUNCT
ejpam-5241	286	1	....................................	....................................	PUNCT
ejpam-5241	286	2	.........	.........	PUNCT
ejpam-5241	286	3	........	........	PUNCT
ejpam-5241	286	4	........	........	PUNCT
ejpam-5241	286	5	........	........	PUNCT
ejpam-5241	286	6	...	...	PUNCT
ejpam-5241	287	1	....................................	....................................	PUNCT
ejpam-5241	287	2	..........	..........	PUNCT
ejpam-5241	288	1	.........	.........	PUNCT
ejpam-5241	288	2	.........	.........	PUNCT
ejpam-5241	289	1	........	........	PUNCT
ejpam-5241	289	2	....................................	....................................	PUNCT
ejpam-5241	290	1	....................................	....................................	PUNCT
ejpam-5241	290	2	....................................	....................................	PUNCT
ejpam-5241	290	3	.............	.............	PUNCT
ejpam-5241	290	4	............	............	PUNCT
ejpam-5241	290	5	...........	...........	PUNCT
ejpam-5241	290	6	....................................	....................................	PUNCT
ejpam-5241	290	7	....................................	....................................	PUNCT
ejpam-5241	291	1	......................................................................	......................................................................	PUNCT
ejpam-5241	291	2	..	..	PUNCT
ejpam-5241	291	3	........................................................................	........................................................................	PUNCT
ejpam-5241	291	4	........................................................................	........................................................................	PUNCT
ejpam-5241	291	5	••	••	NOUN
ejpam-5241	291	6	•	•	NUM
ejpam-5241	291	7	•	•	NUM
ejpam-5241	291	8	•	•	NUM
ejpam-5241	291	9	•	•	NUM
ejpam-5241	291	10	•	•	NOUN
ejpam-5241	291	11	•	•	NUM
ejpam-5241	291	12	figure	figure	NOUN
ejpam-5241	291	13	1	1	NUM
ejpam-5241	291	14	:	:	PUNCT
ejpam-5241	291	15	cycle	cycle	NOUN
ejpam-5241	291	16	graph	graph	NOUN
ejpam-5241	291	17	c13	c13	NOUN
ejpam-5241	291	18	illustrating	illustrate	VERB
ejpam-5241	291	19	the	the	DET
ejpam-5241	291	20	first	first	ADJ
ejpam-5241	291	21	part	part	NOUN
ejpam-5241	291	22	of	of	ADP
ejpam-5241	291	23	proof	proof	NOUN
ejpam-5241	291	24	of	of	ADP
ejpam-5241	291	25	proposition	proposition	NOUN
ejpam-5241	291	26	4	4	NUM
ejpam-5241	291	27	proposition	proposition	NOUN
ejpam-5241	291	28	5	5	NUM
ejpam-5241	291	29	.	.	PUNCT
ejpam-5241	292	1	let	let	VERB
ejpam-5241	292	2	p	p	PRON
ejpam-5241	292	3	≥	≥	NUM
ejpam-5241	292	4	2	2	NUM
ejpam-5241	292	5	,	,	PUNCT
ejpam-5241	292	6	2	2	NUM
ejpam-5241	292	7	≤	≤	NUM
ejpam-5241	292	8	n1	n1	ADJ
ejpam-5241	292	9	≤	≤	NOUN
ejpam-5241	292	10	n2	n2	ADJ
ejpam-5241	292	11	≤	≤	NUM
ejpam-5241	292	12	...	...	PUNCT
ejpam-5241	293	1	≤	≤	NUM
ejpam-5241	293	2	np	np	INTJ
ejpam-5241	293	3	and	and	CCONJ
ejpam-5241	293	4	g	g	PROPN
ejpam-5241	293	5	=	=	SYM
ejpam-5241	293	6	kn1,n2,	kn1,n2,	PROPN
ejpam-5241	293	7	...	...	PUNCT
ejpam-5241	293	8	,np	,np	PUNCT
ejpam-5241	293	9	with	with	ADP
ejpam-5241	293	10	partite	partite	ADJ
ejpam-5241	293	11	sets	set	NOUN
ejpam-5241	293	12	uni	uni	PROPN
ejpam-5241	293	13	,	,	PUNCT
ejpam-5241	293	14	i	i	NOUN
ejpam-5241	293	15	=	=	NOUN
ejpam-5241	293	16	1	1	NUM
ejpam-5241	293	17	,	,	PUNCT
ejpam-5241	293	18	2	2	NUM
ejpam-5241	293	19	,	,	PUNCT
ejpam-5241	293	20	.	.	PUNCT
ejpam-5241	293	21	.	.	PUNCT
ejpam-5241	293	22	.	.	PUNCT
ejpam-5241	294	1	,	,	PUNCT
ejpam-5241	294	2	p.	p.	NOUN
ejpam-5241	294	3	then	then	ADV
ejpam-5241	294	4	s	s	VERB
ejpam-5241	294	5	⊆	⊆	NUM
ejpam-5241	294	6	v	v	NOUN
ejpam-5241	294	7	(	(	PUNCT
ejpam-5241	294	8	g	g	NOUN
ejpam-5241	294	9	)	)	PUNCT
ejpam-5241	294	10	is	be	AUX
ejpam-5241	294	11	a	a	DET
ejpam-5241	294	12	closed	closed	ADJ
ejpam-5241	294	13	geodetic	geodetic	ADJ
ejpam-5241	294	14	hop	hop	NOUN
ejpam-5241	294	15	dominating	dominating	NOUN
ejpam-5241	294	16	set	set	NOUN
ejpam-5241	294	17	of	of	ADP
ejpam-5241	294	18	g	g	PROPN
ejpam-5241	295	1	if	if	SCONJ
ejpam-5241	295	2	and	and	CCONJ
ejpam-5241	295	3	only	only	ADV
ejpam-5241	295	4	if	if	SCONJ
ejpam-5241	295	5	for	for	ADP
ejpam-5241	295	6	some	some	DET
ejpam-5241	295	7	i	i	PROPN
ejpam-5241	295	8	,	,	PUNCT
ejpam-5241	295	9	s	s	PART
ejpam-5241	295	10	=	=	X
ejpam-5241	295	11	uni	uni	ADJ
ejpam-5241	295	12	∪	∪	X
ejpam-5241	295	13	(	(	PUNCT
ejpam-5241	295	14	∪p	∪p	NUM
ejpam-5241	295	15	k=1;k	k=1;k	PROPN
ejpam-5241	295	16	̸=i{xnk	̸=i{xnk	PROPN
ejpam-5241	295	17	}	}	PUNCT
ejpam-5241	295	18	)	)	PUNCT
ejpam-5241	295	19	,	,	PUNCT
ejpam-5241	295	20	(	(	PUNCT
ejpam-5241	295	21	3	3	X
ejpam-5241	295	22	)	)	PUNCT
ejpam-5241	295	23	where	where	SCONJ
ejpam-5241	295	24	xnk	xnk	PROPN
ejpam-5241	295	25	∈	∈	PROPN
ejpam-5241	295	26	unk	unk	NOUN
ejpam-5241	295	27	.	.	PUNCT
ejpam-5241	296	1	consequently	consequently	ADV
ejpam-5241	296	2	,	,	PUNCT
ejpam-5241	296	3	γhcg(kn1,n2,	γhcg(kn1,n2,	PROPN
ejpam-5241	296	4	...	...	PUNCT
ejpam-5241	296	5	,np	,np	PUNCT
ejpam-5241	296	6	)	)	PUNCT
ejpam-5241	297	1	=	=	SYM
ejpam-5241	297	2	n1+p−1	n1+p−1	ADJ
ejpam-5241	297	3	.	.	PUNCT
ejpam-5241	298	1	in	in	ADP
ejpam-5241	298	2	particular	particular	ADJ
ejpam-5241	298	3	,	,	PUNCT
ejpam-5241	298	4	γhcg(km	γhcg(km	NOUN
ejpam-5241	298	5	,	,	PUNCT
ejpam-5241	298	6	n	n	CCONJ
ejpam-5241	298	7	)	)	PUNCT
ejpam-5241	298	8	=	=	SYM
ejpam-5241	298	9	1	1	NUM
ejpam-5241	298	10	+	+	NOUN
ejpam-5241	298	11	min{m	min{m	NOUN
ejpam-5241	298	12	,	,	PUNCT
ejpam-5241	298	13	n	n	CCONJ
ejpam-5241	298	14	}	}	PUNCT
ejpam-5241	298	15	for	for	ADP
ejpam-5241	298	16	m	m	PROPN
ejpam-5241	298	17	,	,	PUNCT
ejpam-5241	298	18	n	n	PRON
ejpam-5241	298	19	≥	≥	NOUN
ejpam-5241	298	20	2	2	NUM
ejpam-5241	298	21	.	.	PUNCT
ejpam-5241	298	22	proof	proof	NOUN
ejpam-5241	298	23	.	.	PUNCT
ejpam-5241	299	1	clearly	clearly	ADV
ejpam-5241	299	2	,	,	PUNCT
ejpam-5241	299	3	if	if	SCONJ
ejpam-5241	299	4	s	s	VERB
ejpam-5241	299	5	⊆	⊆	NUM
ejpam-5241	299	6	v	v	NOUN
ejpam-5241	299	7	(	(	PUNCT
ejpam-5241	299	8	g	g	NOUN
ejpam-5241	299	9	)	)	PUNCT
ejpam-5241	299	10	satisfies	satisfy	VERB
ejpam-5241	299	11	equation	equation	NOUN
ejpam-5241	299	12	3	3	NUM
ejpam-5241	299	13	,	,	PUNCT
ejpam-5241	299	14	then	then	ADV
ejpam-5241	299	15	s	s	VERB
ejpam-5241	299	16	is	be	AUX
ejpam-5241	299	17	a	a	DET
ejpam-5241	299	18	closed	closed	ADJ
ejpam-5241	299	19	geodetic	geodetic	ADJ
ejpam-5241	299	20	hop	hop	NOUN
ejpam-5241	299	21	dominating	dominating	NOUN
ejpam-5241	299	22	set	set	NOUN
ejpam-5241	299	23	of	of	ADP
ejpam-5241	299	24	g.	g.	PROPN
ejpam-5241	299	25	conversely	conversely	ADV
ejpam-5241	299	26	,	,	PUNCT
ejpam-5241	299	27	let	let	VERB
ejpam-5241	299	28	s	s	PRON
ejpam-5241	299	29	be	be	AUX
ejpam-5241	299	30	a	a	DET
ejpam-5241	299	31	closed	closed	ADJ
ejpam-5241	299	32	geodetic	geodetic	ADJ
ejpam-5241	299	33	hop	hop	NOUN
ejpam-5241	299	34	dominating	dominating	NOUN
ejpam-5241	299	35	set	set	NOUN
ejpam-5241	299	36	of	of	ADP
ejpam-5241	299	37	g.	g.	PROPN
ejpam-5241	299	38	since	since	SCONJ
ejpam-5241	299	39	s	s	PROPN
ejpam-5241	299	40	is	be	AUX
ejpam-5241	299	41	a	a	DET
ejpam-5241	299	42	hop	hop	NOUN
ejpam-5241	299	43	dominating	dominating	NOUN
ejpam-5241	299	44	set	set	NOUN
ejpam-5241	299	45	,	,	PUNCT
ejpam-5241	299	46	s	s	PART
ejpam-5241	299	47	∩	∩	PROPN
ejpam-5241	299	48	unj	unj	NOUN
ejpam-5241	299	49	̸=	̸=	PROPN
ejpam-5241	299	50	∅	∅	NOUN
ejpam-5241	299	51	for	for	ADP
ejpam-5241	299	52	all	all	PRON
ejpam-5241	299	53	j	j	NOUN
ejpam-5241	299	54	=	=	SYM
ejpam-5241	299	55	1	1	NUM
ejpam-5241	299	56	,	,	PUNCT
ejpam-5241	299	57	2	2	NUM
ejpam-5241	299	58	,	,	PUNCT
ejpam-5241	299	59	...	...	PUNCT
ejpam-5241	299	60	,	,	PUNCT
ejpam-5241	299	61	p.	p.	NOUN
ejpam-5241	299	62	since	since	SCONJ
ejpam-5241	299	63	s	s	PROPN
ejpam-5241	299	64	is	be	AUX
ejpam-5241	299	65	a	a	DET
ejpam-5241	299	66	closed	closed	ADJ
ejpam-5241	299	67	geodetic	geodetic	ADJ
ejpam-5241	299	68	set	set	NOUN
ejpam-5241	299	69	,	,	PUNCT
ejpam-5241	299	70	uni	uni	PROPN
ejpam-5241	299	71	⊆	⊆	NUM
ejpam-5241	299	72	s	s	NOUN
ejpam-5241	299	73	for	for	ADP
ejpam-5241	299	74	some	some	DET
ejpam-5241	299	75	i	i	PROPN
ejpam-5241	299	76	and	and	CCONJ
ejpam-5241	299	77	|s	|s	PROPN
ejpam-5241	299	78	∩	∩	ADJ
ejpam-5241	299	79	unk	unk	NOUN
ejpam-5241	299	80	|	|	ADV
ejpam-5241	299	81	=	=	NOUN
ejpam-5241	299	82	1	1	NUM
ejpam-5241	299	83	for	for	ADP
ejpam-5241	299	84	all	all	DET
ejpam-5241	299	85	k	k	PROPN
ejpam-5241	299	86	̸=	̸=	PROPN
ejpam-5241	299	87	i.	i.	NOUN
ejpam-5241	299	88	the	the	DET
ejpam-5241	299	89	remaining	remain	VERB
ejpam-5241	299	90	statements	statement	NOUN
ejpam-5241	299	91	follow	follow	VERB
ejpam-5241	299	92	immediately	immediately	ADV
ejpam-5241	299	93	.	.	PUNCT
ejpam-5241	300	1	2.3	2.3	NUM
ejpam-5241	300	2	.	.	PUNCT
ejpam-5241	301	1	realization	realization	NOUN
ejpam-5241	301	2	problems	problem	NOUN
ejpam-5241	301	3	theorem	theorem	VERB
ejpam-5241	301	4	4	4	NUM
ejpam-5241	301	5	.	.	PUNCT
ejpam-5241	302	1	let	let	VERB
ejpam-5241	302	2	a	a	PRON
ejpam-5241	302	3	and	and	CCONJ
ejpam-5241	302	4	b	b	NOUN
ejpam-5241	302	5	be	be	AUX
ejpam-5241	302	6	positive	positive	ADJ
ejpam-5241	302	7	integers	integer	NOUN
ejpam-5241	302	8	such	such	ADJ
ejpam-5241	302	9	that	that	SCONJ
ejpam-5241	302	10	2	2	NUM
ejpam-5241	302	11	≤	≤	NUM
ejpam-5241	302	12	a	a	DET
ejpam-5241	302	13	≤	≤	PROPN
ejpam-5241	302	14	b.	b.	NOUN
ejpam-5241	303	1	then	then	ADV
ejpam-5241	303	2	there	there	PRON
ejpam-5241	303	3	exists	exist	VERB
ejpam-5241	303	4	a	a	DET
ejpam-5241	303	5	connected	connected	ADJ
ejpam-5241	303	6	graph	graph	NOUN
ejpam-5241	303	7	g	g	ADP
ejpam-5241	303	8	such	such	ADJ
ejpam-5241	303	9	that	that	DET
ejpam-5241	303	10	cgn(g	cgn(g	NOUN
ejpam-5241	303	11	)	)	PUNCT
ejpam-5241	303	12	=	=	SYM
ejpam-5241	303	13	a	a	PRON
ejpam-5241	303	14	and	and	CCONJ
ejpam-5241	303	15	γhcg(g	γhcg(g	NOUN
ejpam-5241	303	16	)	)	PUNCT
ejpam-5241	303	17	=	=	SYM
ejpam-5241	303	18	b.	b.	PROPN
ejpam-5241	303	19	proof	proof	NOUN
ejpam-5241	303	20	.	.	PUNCT
ejpam-5241	304	1	let	let	VERB
ejpam-5241	304	2	m	m	VERB
ejpam-5241	304	3	=	=	VERB
ejpam-5241	305	1	b	b	X
ejpam-5241	305	2	−	−	PROPN
ejpam-5241	305	3	a	a	DET
ejpam-5241	305	4	+	+	NOUN
ejpam-5241	305	5	1	1	NUM
ejpam-5241	305	6	.	.	X
ejpam-5241	305	7	consider	consider	VERB
ejpam-5241	305	8	the	the	DET
ejpam-5241	305	9	tree	tree	NOUN
ejpam-5241	305	10	g	g	NOUN
ejpam-5241	305	11	in	in	ADP
ejpam-5241	305	12	figure	figure	NOUN
ejpam-5241	305	13	2	2	NUM
ejpam-5241	305	14	below	below	ADV
ejpam-5241	305	15	obtained	obtain	VERB
ejpam-5241	305	16	from	from	ADP
ejpam-5241	305	17	the	the	DET
ejpam-5241	305	18	p3	p3	NOUN
ejpam-5241	305	19	m	m	PROPN
ejpam-5241	305	20	=	=	PUNCT
ejpam-5241	306	1	[	[	X
ejpam-5241	306	2	y1	y1	X
ejpam-5241	306	3	,	,	PUNCT
ejpam-5241	306	4	y2	y2	INTJ
ejpam-5241	306	5	,	,	PUNCT
ejpam-5241	306	6	.	.	PUNCT
ejpam-5241	306	7	.	.	PUNCT
ejpam-5241	306	8	.	.	PUNCT
ejpam-5241	307	1	,	,	PUNCT
ejpam-5241	307	2	y3	y3	PROPN
ejpam-5241	307	3	m	m	X
ejpam-5241	307	4	]	]	X
ejpam-5241	307	5	on	on	ADP
ejpam-5241	307	6	3	3	NUM
ejpam-5241	307	7	m	m	NOUN
ejpam-5241	307	8	vertices	vertex	NOUN
ejpam-5241	307	9	by	by	ADP
ejpam-5241	307	10	adding	add	VERB
ejpam-5241	307	11	(	(	PUNCT
ejpam-5241	307	12	a	a	DET
ejpam-5241	307	13	−	−	PROPN
ejpam-5241	307	14	1	1	NUM
ejpam-5241	307	15	)	)	PUNCT
ejpam-5241	307	16	pendant	pendant	ADJ
ejpam-5241	307	17	edges	edge	NOUN
ejpam-5241	307	18	xky1	xky1	PROPN
ejpam-5241	307	19	,	,	PUNCT
ejpam-5241	307	20	k	k	PROPN
ejpam-5241	308	1	=	=	SYM
ejpam-5241	308	2	1	1	NUM
ejpam-5241	308	3	,	,	PUNCT
ejpam-5241	308	4	2	2	NUM
ejpam-5241	308	5	,	,	PUNCT
ejpam-5241	308	6	.	.	PUNCT
ejpam-5241	308	7	.	.	PUNCT
ejpam-5241	309	1	.	.	PUNCT
ejpam-5241	310	1	,	,	PUNCT
ejpam-5241	310	2	a−	a−	PROPN
ejpam-5241	310	3	1	1	NUM
ejpam-5241	310	4	.	.	PUNCT
ejpam-5241	311	1	x1	x1	NUM
ejpam-5241	312	1	x2	x2	NOUN
ejpam-5241	312	2	x3	x3	PROPN
ejpam-5241	312	3	xa−1	xa−1	PROPN
ejpam-5241	312	4	y1	y1	PROPN
ejpam-5241	312	5	y2	y2	PROPN
ejpam-5241	312	6	y3	y3	PROPN
ejpam-5241	312	7	y4	y4	NOUN
ejpam-5241	312	8	y5	y5	PROPN
ejpam-5241	312	9	y6	y6	ADJ
ejpam-5241	312	10	y3(m−1	y3(m−1	PROPN
ejpam-5241	312	11	)	)	PUNCT
ejpam-5241	313	1	y3m−2	y3m−2	NOUN
ejpam-5241	313	2	y3m−1	y3m−1	PROPN
ejpam-5241	313	3	y3	y3	PROPN
ejpam-5241	313	4	m	m	PROPN
ejpam-5241	313	5	g	g	NOUN
ejpam-5241	313	6	:	:	PUNCT
ejpam-5241	313	7	figure	figure	NOUN
ejpam-5241	313	8	2	2	NUM
ejpam-5241	313	9	:	:	PUNCT
ejpam-5241	313	10	graph	graph	VERB
ejpam-5241	313	11	g	g	NOUN
ejpam-5241	313	12	complying	comply	VERB
ejpam-5241	313	13	with	with	ADP
ejpam-5241	313	14	the	the	DET
ejpam-5241	313	15	specifications	specification	NOUN
ejpam-5241	313	16	of	of	ADP
ejpam-5241	313	17	theorem	theorem	NOUN
ejpam-5241	313	18	4	4	NUM
ejpam-5241	313	19	a.	a.	NOUN
ejpam-5241	313	20	adolfo	adolfo	PROPN
ejpam-5241	313	21	,	,	PUNCT
ejpam-5241	313	22	i.	i.	PROPN
ejpam-5241	313	23	aniversario	aniversario	PROPN
ejpam-5241	313	24	,	,	PUNCT
ejpam-5241	313	25	f.	f.	PROPN
ejpam-5241	313	26	jamil	jamil	PROPN
ejpam-5241	313	27	/	/	SYM
ejpam-5241	313	28	eur	eur	PROPN
ejpam-5241	313	29	.	.	PUNCT
ejpam-5241	314	1	j.	j.	PROPN
ejpam-5241	314	2	pure	pure	PROPN
ejpam-5241	314	3	appl	appl	PROPN
ejpam-5241	314	4	.	.	PROPN
ejpam-5241	314	5	math	math	PROPN
ejpam-5241	314	6	,	,	PUNCT
ejpam-5241	314	7	17	17	NUM
ejpam-5241	314	8	(	(	PUNCT
ejpam-5241	314	9	3	3	NUM
ejpam-5241	314	10	)	)	PUNCT
ejpam-5241	314	11	(	(	PUNCT
ejpam-5241	314	12	2024	2024	NUM
ejpam-5241	314	13	)	)	PUNCT
ejpam-5241	314	14	,	,	PUNCT
ejpam-5241	314	15	1618	1618	NUM
ejpam-5241	314	16	-	-	SYM
ejpam-5241	314	17	1636	1636	NUM
ejpam-5241	314	18	1626	1626	NUM
ejpam-5241	314	19	then	then	ADV
ejpam-5241	314	20	set	set	VERB
ejpam-5241	314	21	ext(g	ext(g	NOUN
ejpam-5241	314	22	)	)	PUNCT
ejpam-5241	314	23	=	=	PRON
ejpam-5241	314	24	{	{	PUNCT
ejpam-5241	314	25	x1	x1	PROPN
ejpam-5241	314	26	,	,	PUNCT
ejpam-5241	314	27	x2	x2	PROPN
ejpam-5241	314	28	,	,	PUNCT
ejpam-5241	314	29	...	...	PUNCT
ejpam-5241	314	30	,	,	PUNCT
ejpam-5241	314	31	xa−1	xa−1	PROPN
ejpam-5241	314	32	,	,	PUNCT
ejpam-5241	314	33	y3	y3	PROPN
ejpam-5241	314	34	m	m	PROPN
ejpam-5241	314	35	}	}	PUNCT
ejpam-5241	314	36	is	be	AUX
ejpam-5241	314	37	a	a	DET
ejpam-5241	314	38	closed	closed	ADJ
ejpam-5241	314	39	geodetic	geodetic	ADJ
ejpam-5241	314	40	basis	basis	NOUN
ejpam-5241	314	41	of	of	ADP
ejpam-5241	314	42	g.	g.	PROPN
ejpam-5241	314	43	hence	hence	ADV
ejpam-5241	314	44	cgn(g	cgn(g	NUM
ejpam-5241	314	45	)	)	PUNCT
ejpam-5241	314	46	=	=	NOUN
ejpam-5241	315	1	a	a	DET
ejpam-5241	315	2	−	−	PROPN
ejpam-5241	315	3	1	1	NUM
ejpam-5241	315	4	+	+	SYM
ejpam-5241	315	5	1	1	NUM
ejpam-5241	315	6	=	=	SYM
ejpam-5241	315	7	a.	a.	NOUN
ejpam-5241	315	8	on	on	ADP
ejpam-5241	315	9	the	the	DET
ejpam-5241	315	10	other	other	ADJ
ejpam-5241	315	11	hand	hand	NOUN
ejpam-5241	315	12	,	,	PUNCT
ejpam-5241	315	13	the	the	DET
ejpam-5241	315	14	set	set	NOUN
ejpam-5241	315	15	{	{	PUNCT
ejpam-5241	315	16	x1	x1	PROPN
ejpam-5241	315	17	,	,	PUNCT
ejpam-5241	315	18	x2	x2	PROPN
ejpam-5241	315	19	,	,	PUNCT
ejpam-5241	315	20	...	...	PUNCT
ejpam-5241	315	21	,	,	PUNCT
ejpam-5241	315	22	xa−1	xa−1	PROPN
ejpam-5241	315	23	,	,	PUNCT
ejpam-5241	315	24	y3	y3	PROPN
ejpam-5241	315	25	,	,	PUNCT
ejpam-5241	315	26	y6	y6	ADJ
ejpam-5241	315	27	,	,	PUNCT
ejpam-5241	315	28	...	...	PUNCT
ejpam-5241	315	29	,	,	PUNCT
ejpam-5241	315	30	y3	y3	PROPN
ejpam-5241	315	31	m	m	PRON
ejpam-5241	315	32	}	}	PUNCT
ejpam-5241	315	33	is	be	AUX
ejpam-5241	315	34	a	a	DET
ejpam-5241	315	35	γhcg	γhcg	NOUN
ejpam-5241	315	36	-	-	PUNCT
ejpam-5241	315	37	set	set	NOUN
ejpam-5241	315	38	of	of	ADP
ejpam-5241	315	39	g.	g.	PROPN
ejpam-5241	315	40	hence	hence	ADV
ejpam-5241	315	41	γhcg(g	γhcg(g	PROPN
ejpam-5241	315	42	)	)	PUNCT
ejpam-5241	315	43	=	=	SYM
ejpam-5241	315	44	a−	a−	PROPN
ejpam-5241	315	45	1	1	NUM
ejpam-5241	315	46	+	+	NOUN
ejpam-5241	315	47	m	m	NOUN
ejpam-5241	315	48	=	=	ADJ
ejpam-5241	315	49	b.	b.	PROPN
ejpam-5241	315	50	theorem	theorem	VERB
ejpam-5241	315	51	5	5	NUM
ejpam-5241	315	52	.	.	PUNCT
ejpam-5241	316	1	if	if	SCONJ
ejpam-5241	316	2	n	n	CCONJ
ejpam-5241	316	3	,	,	PUNCT
ejpam-5241	316	4	m	m	PROPN
ejpam-5241	316	5	,	,	PUNCT
ejpam-5241	316	6	and	and	CCONJ
ejpam-5241	316	7	k	k	PROPN
ejpam-5241	316	8	are	be	AUX
ejpam-5241	316	9	integers	integer	NOUN
ejpam-5241	316	10	with	with	ADP
ejpam-5241	316	11	4	4	NUM
ejpam-5241	316	12	≤	≤	NUM
ejpam-5241	316	13	m	m	VERB
ejpam-5241	316	14	≤	≤	NOUN
ejpam-5241	316	15	k	k	NOUN
ejpam-5241	316	16	and	and	CCONJ
ejpam-5241	316	17	2k−m+	2k−m+	NUM
ejpam-5241	316	18	2	2	NUM
ejpam-5241	316	19	≤	≤	NOUN
ejpam-5241	316	20	n	n	CCONJ
ejpam-5241	316	21	,	,	PUNCT
ejpam-5241	316	22	then	then	ADV
ejpam-5241	316	23	there	there	PRON
ejpam-5241	316	24	exists	exist	VERB
ejpam-5241	316	25	a	a	DET
ejpam-5241	316	26	connected	connected	ADJ
ejpam-5241	316	27	graph	graph	NOUN
ejpam-5241	316	28	g	g	ADP
ejpam-5241	316	29	such	such	ADJ
ejpam-5241	316	30	that	that	SCONJ
ejpam-5241	316	31	|v	|v	PROPN
ejpam-5241	316	32	(	(	PUNCT
ejpam-5241	316	33	g)|	g)|	NOUN
ejpam-5241	316	34	=	=	PUNCT
ejpam-5241	316	35	n	n	CCONJ
ejpam-5241	316	36	,	,	PUNCT
ejpam-5241	316	37	γhg(g	γhg(g	PROPN
ejpam-5241	316	38	)	)	PUNCT
ejpam-5241	317	1	=	=	SYM
ejpam-5241	317	2	m	m	NOUN
ejpam-5241	317	3	and	and	CCONJ
ejpam-5241	317	4	γhcg(g	γhcg(g	NOUN
ejpam-5241	317	5	)	)	PUNCT
ejpam-5241	317	6	=	=	PUNCT
ejpam-5241	318	1	k.	k.	NOUN
ejpam-5241	318	2	proof	proof	NOUN
ejpam-5241	318	3	.	.	PUNCT
ejpam-5241	319	1	let	let	VERB
ejpam-5241	319	2	r	r	NOUN
ejpam-5241	319	3	=	=	PUNCT
ejpam-5241	319	4	k	k	NOUN
ejpam-5241	320	1	−	−	PROPN
ejpam-5241	320	2	m	m	VERB
ejpam-5241	321	1	+	+	NOUN
ejpam-5241	321	2	3	3	NUM
ejpam-5241	321	3	and	and	CCONJ
ejpam-5241	321	4	s	s	NOUN
ejpam-5241	321	5	=	=	SYM
ejpam-5241	321	6	n	n	PROPN
ejpam-5241	321	7	−	−	PROPN
ejpam-5241	322	1	k	k	NOUN
ejpam-5241	323	1	+	+	NOUN
ejpam-5241	323	2	1	1	X
ejpam-5241	323	3	.	.	PUNCT
ejpam-5241	323	4	let	let	VERB
ejpam-5241	323	5	u	u	PRON
ejpam-5241	323	6	=	=	NOUN
ejpam-5241	323	7	{	{	PUNCT
ejpam-5241	323	8	u1	u1	NOUN
ejpam-5241	323	9	,	,	PUNCT
ejpam-5241	323	10	u2	u2	NOUN
ejpam-5241	323	11	,	,	PUNCT
ejpam-5241	323	12	.	.	PUNCT
ejpam-5241	323	13	.	.	PUNCT
ejpam-5241	324	1	.	.	PUNCT
ejpam-5241	325	1	,	,	PUNCT
ejpam-5241	325	2	ur	ur	INTJ
ejpam-5241	325	3	}	}	PUNCT
ejpam-5241	325	4	and	and	CCONJ
ejpam-5241	325	5	w	w	NOUN
ejpam-5241	325	6	=	=	SYM
ejpam-5241	325	7	{	{	PUNCT
ejpam-5241	325	8	v1	v1	PROPN
ejpam-5241	325	9	,	,	PUNCT
ejpam-5241	325	10	v2	v2	PROPN
ejpam-5241	325	11	,	,	PUNCT
ejpam-5241	325	12	.	.	PUNCT
ejpam-5241	325	13	.	.	PUNCT
ejpam-5241	326	1	.	.	PUNCT
ejpam-5241	327	1	,	,	PUNCT
ejpam-5241	327	2	vs	vs	ADP
ejpam-5241	327	3	}	}	PUNCT
ejpam-5241	327	4	be	be	AUX
ejpam-5241	327	5	the	the	DET
ejpam-5241	327	6	partite	partite	ADJ
ejpam-5241	327	7	sets	set	NOUN
ejpam-5241	327	8	ofkr	ofkr	VERB
ejpam-5241	327	9	,	,	PUNCT
ejpam-5241	327	10	s.	s.	PROPN
ejpam-5241	327	11	obtaing	obtae	VERB
ejpam-5241	327	12	as	as	ADP
ejpam-5241	327	13	in	in	ADP
ejpam-5241	327	14	figure	figure	NOUN
ejpam-5241	327	15	3	3	NUM
ejpam-5241	327	16	by	by	ADP
ejpam-5241	327	17	adding	add	VERB
ejpam-5241	327	18	tokr	tokr	PROPN
ejpam-5241	327	19	,	,	PUNCT
ejpam-5241	327	20	s	s	PART
ejpam-5241	327	21	(	(	PUNCT
ejpam-5241	327	22	m−4	m−4	NOUN
ejpam-5241	327	23	)	)	PUNCT
ejpam-5241	327	24	new	new	ADJ
ejpam-5241	327	25	pendant	pendant	ADJ
ejpam-5241	327	26	edges	edge	NOUN
ejpam-5241	327	27	wjv1	wjv1	PROPN
ejpam-5241	327	28	,	,	PUNCT
ejpam-5241	327	29	j	j	PROPN
ejpam-5241	328	1	=	=	SYM
ejpam-5241	328	2	1	1	NUM
ejpam-5241	328	3	,	,	PUNCT
ejpam-5241	328	4	2	2	NUM
ejpam-5241	328	5	,	,	PUNCT
ejpam-5241	328	6	.	.	PUNCT
ejpam-5241	328	7	.	.	PUNCT
ejpam-5241	329	1	.	.	PUNCT
ejpam-5241	330	1	,	,	PUNCT
ejpam-5241	330	2	m	m	VERB
ejpam-5241	330	3	−	−	NOUN
ejpam-5241	331	1	4	4	NUM
ejpam-5241	331	2	.	.	PUNCT
ejpam-5241	331	3	then	then	ADV
ejpam-5241	331	4	|v	|v	PROPN
ejpam-5241	331	5	(	(	PUNCT
ejpam-5241	331	6	g)|	g)|	NOUN
ejpam-5241	331	7	=	=	SYM
ejpam-5241	331	8	r	r	NOUN
ejpam-5241	331	9	+	+	SYM
ejpam-5241	331	10	s	s	X
ejpam-5241	331	11	+	+	X
ejpam-5241	331	12	(	(	PUNCT
ejpam-5241	331	13	m	m	VERB
ejpam-5241	331	14	−	−	NOUN
ejpam-5241	331	15	4	4	NUM
ejpam-5241	331	16	)	)	PUNCT
ejpam-5241	331	17	=	=	VERB
ejpam-5241	331	18	n.	n.	VERB
ejpam-5241	331	19	the	the	DET
ejpam-5241	331	20	v1	v1	PROPN
ejpam-5241	331	21	v2	v2	PROPN
ejpam-5241	331	22	v3	v3	PROPN
ejpam-5241	331	23	v4	v4	PROPN
ejpam-5241	331	24	vs−2	vs−2	PROPN
ejpam-5241	331	25	vs−1	vs−1	PROPN
ejpam-5241	331	26	vs	vs	ADP
ejpam-5241	331	27	u1	u1	NOUN
ejpam-5241	331	28	u2	u2	PROPN
ejpam-5241	331	29	u3	u3	PROPN
ejpam-5241	331	30	ur−1	ur−1	PROPN
ejpam-5241	331	31	ur	ur	PROPN
ejpam-5241	331	32	w1	w1	PROPN
ejpam-5241	331	33	w2	w2	PROPN
ejpam-5241	331	34	w3	w3	PROPN
ejpam-5241	331	35	wm−4	wm−4	PROPN
ejpam-5241	331	36	figure	figure	NOUN
ejpam-5241	331	37	3	3	NUM
ejpam-5241	331	38	:	:	PUNCT
ejpam-5241	331	39	graph	graph	VERB
ejpam-5241	331	40	g	g	NOUN
ejpam-5241	331	41	complying	comply	VERB
ejpam-5241	331	42	with	with	ADP
ejpam-5241	331	43	the	the	DET
ejpam-5241	331	44	specifications	specification	NOUN
ejpam-5241	331	45	of	of	ADP
ejpam-5241	331	46	theorem	theorem	ADJ
ejpam-5241	331	47	5	5	NUM
ejpam-5241	331	48	vertices	vertex	NOUN
ejpam-5241	331	49	w1	w1	NOUN
ejpam-5241	331	50	,	,	PUNCT
ejpam-5241	331	51	w2	w2	NOUN
ejpam-5241	331	52	,	,	PUNCT
ejpam-5241	331	53	...	...	PUNCT
ejpam-5241	331	54	,	,	PUNCT
ejpam-5241	331	55	wm−4	wm−4	PROPN
ejpam-5241	331	56	are	be	AUX
ejpam-5241	331	57	extreme	extreme	ADJ
ejpam-5241	331	58	vertices	vertex	NOUN
ejpam-5241	331	59	,	,	PUNCT
ejpam-5241	331	60	thus	thus	ADV
ejpam-5241	331	61	are	be	AUX
ejpam-5241	331	62	in	in	ADP
ejpam-5241	331	63	any	any	DET
ejpam-5241	331	64	geodetic	geodetic	ADJ
ejpam-5241	331	65	cover	cover	NOUN
ejpam-5241	331	66	of	of	ADP
ejpam-5241	331	67	g.	g.	PROPN
ejpam-5241	331	68	since	since	SCONJ
ejpam-5241	331	69	the	the	DET
ejpam-5241	331	70	set	set	NOUN
ejpam-5241	331	71	{	{	PUNCT
ejpam-5241	331	72	w1	w1	NOUN
ejpam-5241	331	73	,	,	PUNCT
ejpam-5241	331	74	w2	w2	NOUN
ejpam-5241	331	75	,	,	PUNCT
ejpam-5241	331	76	...	...	PUNCT
ejpam-5241	331	77	,	,	PUNCT
ejpam-5241	331	78	wm−4	wm−4	PROPN
ejpam-5241	331	79	,	,	PUNCT
ejpam-5241	331	80	u1	u1	PROPN
ejpam-5241	331	81	,	,	PUNCT
ejpam-5241	331	82	ur	ur	INTJ
ejpam-5241	331	83	,	,	PUNCT
ejpam-5241	331	84	v1	v1	PROPN
ejpam-5241	331	85	,	,	PUNCT
ejpam-5241	331	86	vs	vs	ADP
ejpam-5241	331	87	}	}	PUNCT
ejpam-5241	331	88	is	be	AUX
ejpam-5241	331	89	a	a	DET
ejpam-5241	331	90	γhg	γhg	NOUN
ejpam-5241	331	91	-	-	PUNCT
ejpam-5241	331	92	set	set	NOUN
ejpam-5241	331	93	of	of	ADP
ejpam-5241	331	94	g	g	NOUN
ejpam-5241	331	95	,	,	PUNCT
ejpam-5241	331	96	it	it	PRON
ejpam-5241	331	97	follows	follow	VERB
ejpam-5241	331	98	that	that	SCONJ
ejpam-5241	331	99	γhg(g	γhg(g	PROPN
ejpam-5241	331	100	)	)	PUNCT
ejpam-5241	332	1	=	=	VERB
ejpam-5241	332	2	m.	m.	NOUN
ejpam-5241	332	3	since	since	SCONJ
ejpam-5241	332	4	the	the	DET
ejpam-5241	332	5	set	set	NOUN
ejpam-5241	332	6	{	{	PUNCT
ejpam-5241	332	7	v1	v1	NOUN
ejpam-5241	332	8	,	,	PUNCT
ejpam-5241	332	9	w1	w1	NOUN
ejpam-5241	332	10	,	,	PUNCT
ejpam-5241	332	11	w2	w2	NOUN
ejpam-5241	332	12	,	,	PUNCT
ejpam-5241	332	13	...	...	PUNCT
ejpam-5241	332	14	,	,	PUNCT
ejpam-5241	332	15	wm−4	wm−4	NOUN
ejpam-5241	332	16	,	,	PUNCT
ejpam-5241	332	17	u1	u1	PROPN
ejpam-5241	332	18	,	,	PUNCT
ejpam-5241	332	19	...	...	PUNCT
ejpam-5241	332	20	,	,	PUNCT
ejpam-5241	332	21	ur	ur	INTJ
ejpam-5241	332	22	}	}	PUNCT
ejpam-5241	332	23	is	be	AUX
ejpam-5241	332	24	a	a	DET
ejpam-5241	332	25	γhcg	γhcg	NOUN
ejpam-5241	332	26	-	-	PUNCT
ejpam-5241	332	27	set	set	NOUN
ejpam-5241	332	28	of	of	ADP
ejpam-5241	332	29	g	g	NOUN
ejpam-5241	332	30	,	,	PUNCT
ejpam-5241	332	31	we	we	PRON
ejpam-5241	332	32	have	have	VERB
ejpam-5241	332	33	γhcg(g	γhcg(g	NOUN
ejpam-5241	332	34	)	)	PUNCT
ejpam-5241	332	35	=	=	SYM
ejpam-5241	333	1	1+m−4+r	1+m−4+r	NUM
ejpam-5241	333	2	=	=	SYM
ejpam-5241	333	3	1	1	NUM
ejpam-5241	334	1	+	+	NOUN
ejpam-5241	334	2	m−	m−	PROPN
ejpam-5241	334	3	4	4	NUM
ejpam-5241	334	4	+	+	CCONJ
ejpam-5241	334	5	k	k	X
ejpam-5241	334	6	−m+	−m+	X
ejpam-5241	334	7	3	3	NUM
ejpam-5241	334	8	=	=	SYM
ejpam-5241	334	9	k.	k.	PROPN
ejpam-5241	334	10	2.4	2.4	NUM
ejpam-5241	334	11	.	.	PUNCT
ejpam-5241	335	1	in	in	ADP
ejpam-5241	335	2	the	the	DET
ejpam-5241	335	3	join	join	NOUN
ejpam-5241	335	4	of	of	ADP
ejpam-5241	335	5	graphs	graph	NOUN
ejpam-5241	335	6	since	since	SCONJ
ejpam-5241	335	7	diam(g+h	diam(g+h	ADJ
ejpam-5241	335	8	)	)	PUNCT
ejpam-5241	335	9	≤	≤	NUM
ejpam-5241	335	10	2	2	NUM
ejpam-5241	335	11	,	,	PUNCT
ejpam-5241	335	12	g+h	g+h	PROPN
ejpam-5241	335	13	∈	∈	PROPN
ejpam-5241	335	14	c	c	NOUN
ejpam-5241	335	15	∗	∗	NOUN
ejpam-5241	335	16	h	h	NOUN
ejpam-5241	335	17	for	for	ADP
ejpam-5241	335	18	any	any	DET
ejpam-5241	335	19	graphs	graph	NOUN
ejpam-5241	335	20	g	g	NOUN
ejpam-5241	335	21	and	and	CCONJ
ejpam-5241	335	22	h.	h.	PROPN
ejpam-5241	335	23	a	a	DET
ejpam-5241	335	24	set	set	NOUN
ejpam-5241	335	25	s	s	PROPN
ejpam-5241	335	26	⊆	⊆	NUM
ejpam-5241	335	27	v	v	NOUN
ejpam-5241	335	28	(	(	PUNCT
ejpam-5241	335	29	g	g	NOUN
ejpam-5241	335	30	)	)	PUNCT
ejpam-5241	335	31	is	be	AUX
ejpam-5241	335	32	a	a	DET
ejpam-5241	335	33	closed	closed	ADJ
ejpam-5241	335	34	2	2	NUM
ejpam-5241	335	35	-	-	PUNCT
ejpam-5241	335	36	path	path	NOUN
ejpam-5241	335	37	closure	closure	NOUN
ejpam-5241	335	38	absorbing	absorb	VERB
ejpam-5241	335	39	set	set	NOUN
ejpam-5241	335	40	of	of	ADP
ejpam-5241	335	41	g	g	PROPN
ejpam-5241	335	42	if	if	SCONJ
ejpam-5241	335	43	p2[s	p2[s	ADJ
ejpam-5241	335	44	]	]	X
ejpam-5241	335	45	=	=	SYM
ejpam-5241	335	46	v	v	X
ejpam-5241	335	47	(	(	PUNCT
ejpam-5241	335	48	g	g	NOUN
ejpam-5241	335	49	)	)	PUNCT
ejpam-5241	335	50	and	and	CCONJ
ejpam-5241	335	51	s	s	NOUN
ejpam-5241	335	52	=	=	PUNCT
ejpam-5241	335	53	sk	sk	NOUN
ejpam-5241	335	54	=	=	NOUN
ejpam-5241	335	55	{	{	PUNCT
ejpam-5241	335	56	v1	v1	PROPN
ejpam-5241	335	57	,	,	PUNCT
ejpam-5241	335	58	v2	v2	PROPN
ejpam-5241	335	59	,	,	PUNCT
ejpam-5241	335	60	...	...	PUNCT
ejpam-5241	335	61	,	,	PUNCT
ejpam-5241	335	62	vk	vk	ADP
ejpam-5241	335	63	}	}	PUNCT
ejpam-5241	335	64	where	where	SCONJ
ejpam-5241	335	65	v1	v1	VERB
ejpam-5241	335	66	̸=	̸=	PROPN
ejpam-5241	335	67	v2	v2	PROPN
ejpam-5241	335	68	and	and	CCONJ
ejpam-5241	335	69	vi	vi	NOUN
ejpam-5241	335	70	/∈	/∈	PUNCT
ejpam-5241	336	1	p2[si−1	p2[si−1	PROPN
ejpam-5241	336	2	]	]	PUNCT
ejpam-5241	336	3	for	for	ADP
ejpam-5241	336	4	3	3	NUM
ejpam-5241	336	5	≤	≤	NUM
ejpam-5241	336	6	i	i	PRON
ejpam-5241	336	7	≤	≤	PROPN
ejpam-5241	336	8	k.	k.	VERB
ejpam-5241	337	1	the	the	DET
ejpam-5241	337	2	minimum	minimum	ADJ
ejpam-5241	337	3	cardinality	cardinality	NOUN
ejpam-5241	337	4	of	of	ADP
ejpam-5241	337	5	a	a	DET
ejpam-5241	337	6	closed	closed	ADJ
ejpam-5241	337	7	2	2	NUM
ejpam-5241	337	8	-	-	PUNCT
ejpam-5241	337	9	path	path	NOUN
ejpam-5241	337	10	closure	closure	NOUN
ejpam-5241	337	11	absorbing	absorb	VERB
ejpam-5241	337	12	set	set	NOUN
ejpam-5241	337	13	in	in	ADP
ejpam-5241	337	14	g	g	PROPN
ejpam-5241	337	15	is	be	AUX
ejpam-5241	337	16	denoted	denote	VERB
ejpam-5241	337	17	by	by	ADP
ejpam-5241	337	18	ρc2(g	ρc2(g	NOUN
ejpam-5241	337	19	)	)	PUNCT
ejpam-5241	337	20	.	.	PUNCT
ejpam-5241	338	1	a	a	DET
ejpam-5241	338	2	2	2	NUM
ejpam-5241	338	3	-	-	PUNCT
ejpam-5241	338	4	path	path	NOUN
ejpam-5241	338	5	closure	closure	NOUN
ejpam-5241	338	6	absorbing	absorb	VERB
ejpam-5241	338	7	set	set	NOUN
ejpam-5241	338	8	of	of	ADP
ejpam-5241	338	9	g	g	NOUN
ejpam-5241	338	10	with	with	ADP
ejpam-5241	338	11	cardinality	cardinality	PROPN
ejpam-5241	338	12	ρc2(g	ρc2(g	PROPN
ejpam-5241	338	13	)	)	PUNCT
ejpam-5241	338	14	is	be	AUX
ejpam-5241	338	15	called	call	VERB
ejpam-5241	338	16	ρc2	ρc2	NOUN
ejpam-5241	338	17	-	-	PUNCT
ejpam-5241	338	18	set	set	NOUN
ejpam-5241	338	19	.	.	PUNCT
ejpam-5241	339	1	a	a	DET
ejpam-5241	339	2	set	set	NOUN
ejpam-5241	339	3	s	s	NOUN
ejpam-5241	339	4	⊆	⊆	NUM
ejpam-5241	339	5	v	v	NOUN
ejpam-5241	339	6	(	(	PUNCT
ejpam-5241	339	7	g	g	NOUN
ejpam-5241	339	8	)	)	PUNCT
ejpam-5241	339	9	is	be	AUX
ejpam-5241	339	10	a	a	DET
ejpam-5241	339	11	closed	closed	ADJ
ejpam-5241	339	12	2	2	NUM
ejpam-5241	339	13	-	-	PUNCT
ejpam-5241	339	14	path	path	NOUN
ejpam-5241	339	15	closure	closure	NOUN
ejpam-5241	339	16	absorbing	absorb	VERB
ejpam-5241	339	17	pointwise	pointwise	PROPN
ejpam-5241	339	18	non	non	ADJ
ejpam-5241	339	19	-	-	ADJ
ejpam-5241	339	20	dominating	dominating	ADJ
ejpam-5241	339	21	set	set	NOUN
ejpam-5241	339	22	of	of	ADP
ejpam-5241	339	23	g	g	NOUN
ejpam-5241	339	24	provided	provide	VERB
ejpam-5241	339	25	s	s	VERB
ejpam-5241	339	26	is	be	AUX
ejpam-5241	339	27	a	a	DET
ejpam-5241	339	28	closed	closed	ADJ
ejpam-5241	339	29	2	2	NUM
ejpam-5241	339	30	-	-	PUNCT
ejpam-5241	339	31	path	path	NOUN
ejpam-5241	339	32	closure	closure	NOUN
ejpam-5241	339	33	absorbing	absorb	VERB
ejpam-5241	339	34	set	set	NOUN
ejpam-5241	339	35	and	and	CCONJ
ejpam-5241	339	36	at	at	ADP
ejpam-5241	339	37	the	the	DET
ejpam-5241	339	38	same	same	ADJ
ejpam-5241	339	39	time	time	NOUN
ejpam-5241	339	40	pointwise	pointwise	VERB
ejpam-5241	339	41	non	non	ADJ
ejpam-5241	339	42	-	-	ADJ
ejpam-5241	339	43	dominating	dominating	ADJ
ejpam-5241	339	44	set	set	NOUN
ejpam-5241	339	45	of	of	ADP
ejpam-5241	339	46	g.	g.	PROPN
ejpam-5241	339	47	the	the	DET
ejpam-5241	339	48	minimum	minimum	ADJ
ejpam-5241	339	49	cardinality	cardinality	NOUN
ejpam-5241	339	50	of	of	ADP
ejpam-5241	339	51	a	a	DET
ejpam-5241	339	52	closed	closed	ADJ
ejpam-5241	339	53	2	2	NUM
ejpam-5241	339	54	-	-	PUNCT
ejpam-5241	339	55	path	path	NOUN
ejpam-5241	339	56	closure	closure	NOUN
ejpam-5241	339	57	absorbing	absorb	VERB
ejpam-5241	339	58	pointwise	pointwise	NOUN
ejpam-5241	339	59	nondominating	nondominate	VERB
ejpam-5241	339	60	set	set	NOUN
ejpam-5241	339	61	of	of	ADP
ejpam-5241	339	62	g	g	PROPN
ejpam-5241	339	63	is	be	AUX
ejpam-5241	339	64	denoted	denote	VERB
ejpam-5241	339	65	by	by	ADP
ejpam-5241	339	66	ρc2pnd(g	ρc2pnd(g	PROPN
ejpam-5241	339	67	)	)	PUNCT
ejpam-5241	339	68	.	.	PUNCT
ejpam-5241	340	1	a	a	DET
ejpam-5241	340	2	closed	closed	ADJ
ejpam-5241	340	3	2	2	NUM
ejpam-5241	340	4	-	-	PUNCT
ejpam-5241	340	5	path	path	NOUN
ejpam-5241	340	6	closure	closure	NOUN
ejpam-5241	340	7	absorbing	absorb	VERB
ejpam-5241	340	8	pointwise	pointwise	PROPN
ejpam-5241	340	9	non	non	ADJ
ejpam-5241	340	10	-	-	ADJ
ejpam-5241	340	11	dominating	dominating	ADJ
ejpam-5241	340	12	set	set	NOUN
ejpam-5241	340	13	of	of	ADP
ejpam-5241	340	14	g	g	PROPN
ejpam-5241	340	15	with	with	ADP
ejpam-5241	340	16	cardinality	cardinality	PROPN
ejpam-5241	340	17	ρc2pnd(g	ρc2pnd(g	PROPN
ejpam-5241	340	18	)	)	PUNCT
ejpam-5241	340	19	is	be	AUX
ejpam-5241	340	20	called	call	VERB
ejpam-5241	340	21	ρc2pnd	ρc2pnd	ADV
ejpam-5241	340	22	-	-	PUNCT
ejpam-5241	340	23	set	set	VERB
ejpam-5241	340	24	.	.	PUNCT
ejpam-5241	341	1	a.	a.	PROPN
ejpam-5241	341	2	adolfo	adolfo	PROPN
ejpam-5241	341	3	,	,	PUNCT
ejpam-5241	341	4	i.	i.	PROPN
ejpam-5241	341	5	aniversario	aniversario	PROPN
ejpam-5241	341	6	,	,	PUNCT
ejpam-5241	341	7	f.	f.	PROPN
ejpam-5241	341	8	jamil	jamil	PROPN
ejpam-5241	341	9	/	/	SYM
ejpam-5241	341	10	eur	eur	PROPN
ejpam-5241	341	11	.	.	PUNCT
ejpam-5241	342	1	j.	j.	PROPN
ejpam-5241	342	2	pure	pure	PROPN
ejpam-5241	342	3	appl	appl	PROPN
ejpam-5241	342	4	.	.	PROPN
ejpam-5241	342	5	math	math	PROPN
ejpam-5241	342	6	,	,	PUNCT
ejpam-5241	342	7	17	17	NUM
ejpam-5241	342	8	(	(	PUNCT
ejpam-5241	342	9	3	3	NUM
ejpam-5241	342	10	)	)	PUNCT
ejpam-5241	342	11	(	(	PUNCT
ejpam-5241	342	12	2024	2024	NUM
ejpam-5241	342	13	)	)	PUNCT
ejpam-5241	342	14	,	,	PUNCT
ejpam-5241	342	15	1618	1618	NUM
ejpam-5241	342	16	-	-	SYM
ejpam-5241	342	17	1636	1636	NUM
ejpam-5241	342	18	1627	1627	NUM
ejpam-5241	342	19	since	since	SCONJ
ejpam-5241	342	20	any	any	DET
ejpam-5241	342	21	closed	closed	ADJ
ejpam-5241	342	22	2	2	NUM
ejpam-5241	342	23	-	-	PUNCT
ejpam-5241	342	24	path	path	NOUN
ejpam-5241	342	25	closure	closure	NOUN
ejpam-5241	342	26	absorbing	absorb	VERB
ejpam-5241	342	27	pointwise	pointwise	PROPN
ejpam-5241	342	28	non	non	ADJ
ejpam-5241	342	29	-	-	ADJ
ejpam-5241	342	30	dominating	dominating	ADJ
ejpam-5241	342	31	set	set	NOUN
ejpam-5241	342	32	is	be	AUX
ejpam-5241	342	33	a	a	DET
ejpam-5241	342	34	2	2	NUM
ejpam-5241	342	35	-	-	PUNCT
ejpam-5241	342	36	path	path	NOUN
ejpam-5241	342	37	closure	closure	NOUN
ejpam-5241	342	38	absorbing	absorb	VERB
ejpam-5241	342	39	pointwise	pointwise	PROPN
ejpam-5241	342	40	non	non	ADJ
ejpam-5241	342	41	-	-	ADJ
ejpam-5241	342	42	dominating	dominating	ADJ
ejpam-5241	342	43	set	set	NOUN
ejpam-5241	342	44	and	and	CCONJ
ejpam-5241	342	45	a	a	DET
ejpam-5241	342	46	closed	closed	ADJ
ejpam-5241	342	47	2	2	NUM
ejpam-5241	342	48	-	-	PUNCT
ejpam-5241	342	49	path	path	NOUN
ejpam-5241	342	50	closure	closure	NOUN
ejpam-5241	342	51	absorbing	absorb	VERB
ejpam-5241	342	52	set	set	NOUN
ejpam-5241	342	53	,	,	PUNCT
ejpam-5241	342	54	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-5241	342	55	)	)	PUNCT
ejpam-5241	342	56	≤	≤	NOUN
ejpam-5241	342	57	ρc2pnd(g	ρc2pnd(g	PROPN
ejpam-5241	342	58	)	)	PUNCT
ejpam-5241	342	59	and	and	CCONJ
ejpam-5241	342	60	ρc2(g	ρc2(g	NUM
ejpam-5241	342	61	)	)	PUNCT
ejpam-5241	342	62	≤	≤	NOUN
ejpam-5241	342	63	ρc2pnd(g)for	ρc2pnd(g)for	ADP
ejpam-5241	342	64	all	all	DET
ejpam-5241	342	65	connected	connected	ADJ
ejpam-5241	342	66	graphs	graph	NOUN
ejpam-5241	342	67	.	.	PUNCT
ejpam-5241	343	1	example	example	NOUN
ejpam-5241	343	2	1	1	NUM
ejpam-5241	343	3	.	.	X
ejpam-5241	344	1	consider	consider	VERB
ejpam-5241	344	2	the	the	DET
ejpam-5241	344	3	graph	graph	NOUN
ejpam-5241	344	4	k5,6	k5,6	VERB
ejpam-5241	344	5	in	in	ADP
ejpam-5241	344	6	figure	figure	NOUN
ejpam-5241	344	7	4	4	NUM
ejpam-5241	344	8	,	,	PUNCT
ejpam-5241	344	9	the	the	DET
ejpam-5241	344	10	sets	set	NOUN
ejpam-5241	344	11	{	{	PUNCT
ejpam-5241	344	12	v1	v1	NOUN
ejpam-5241	344	13	,	,	PUNCT
ejpam-5241	344	14	v2	v2	PROPN
ejpam-5241	344	15	,	,	PUNCT
ejpam-5241	344	16	v3	v3	PROPN
ejpam-5241	344	17	,	,	PUNCT
ejpam-5241	344	18	v4	v4	PROPN
ejpam-5241	344	19	,	,	PUNCT
ejpam-5241	344	20	v5	v5	PROPN
ejpam-5241	344	21	}	}	PUNCT
ejpam-5241	344	22	,	,	PUNCT
ejpam-5241	344	23	{	{	PUNCT
ejpam-5241	344	24	v1	v1	NOUN
ejpam-5241	344	25	,	,	PUNCT
ejpam-5241	344	26	v3	v3	PROPN
ejpam-5241	344	27	,	,	PUNCT
ejpam-5241	344	28	u1	u1	NOUN
ejpam-5241	344	29	,	,	PUNCT
ejpam-5241	344	30	u2	u2	NOUN
ejpam-5241	344	31	}	}	PUNCT
ejpam-5241	344	32	,	,	PUNCT
ejpam-5241	344	33	and	and	CCONJ
ejpam-5241	344	34	{	{	PUNCT
ejpam-5241	344	35	u1	u1	NOUN
ejpam-5241	344	36	,	,	PUNCT
ejpam-5241	344	37	v1	v1	NOUN
ejpam-5241	344	38	,	,	PUNCT
ejpam-5241	344	39	v2	v2	PROPN
ejpam-5241	344	40	,	,	PUNCT
ejpam-5241	344	41	v3	v3	PROPN
ejpam-5241	344	42	,	,	PUNCT
ejpam-5241	344	43	v4	v4	PROPN
ejpam-5241	344	44	,	,	PUNCT
ejpam-5241	344	45	v5	v5	PROPN
ejpam-5241	344	46	}	}	PUNCT
ejpam-5241	344	47	are	be	AUX
ejpam-5241	344	48	ρ2c	ρ2c	NOUN
ejpam-5241	344	49	-	-	ADJ
ejpam-5241	344	50	set	set	ADJ
ejpam-5241	344	51	,	,	PUNCT
ejpam-5241	344	52	ρ2pnd	ρ2pnd	ADV
ejpam-5241	344	53	-	-	PUNCT
ejpam-5241	344	54	set	set	VERB
ejpam-5241	344	55	and	and	CCONJ
ejpam-5241	344	56	ρc2pnd	ρc2pnd	ADV
ejpam-5241	344	57	-	-	PUNCT
ejpam-5241	344	58	set	set	NOUN
ejpam-5241	344	59	of	of	ADP
ejpam-5241	344	60	k5,6	k5,6	PROPN
ejpam-5241	344	61	,	,	PUNCT
ejpam-5241	344	62	respectively	respectively	ADV
ejpam-5241	344	63	.	.	PUNCT
ejpam-5241	345	1	therefore	therefore	ADV
ejpam-5241	345	2	,	,	PUNCT
ejpam-5241	345	3	ρc2(k5,6	ρc2(k5,6	NOUN
ejpam-5241	345	4	)	)	PUNCT
ejpam-5241	345	5	=	=	SYM
ejpam-5241	345	6	5	5	NUM
ejpam-5241	345	7	ρ2pnd(k5,6	ρ2pnd(k5,6	NOUN
ejpam-5241	345	8	)	)	PUNCT
ejpam-5241	345	9	=	=	SYM
ejpam-5241	345	10	4	4	NUM
ejpam-5241	345	11	and	and	CCONJ
ejpam-5241	345	12	ρc2pnd(k5,6	ρc2pnd(k5,6	NOUN
ejpam-5241	345	13	)	)	PUNCT
ejpam-5241	345	14	=	=	SYM
ejpam-5241	346	1	6	6	X
ejpam-5241	346	2	.	.	X
ejpam-5241	346	3	k5,6	k5,6	NOUN
ejpam-5241	346	4	:	:	PUNCT
ejpam-5241	346	5	v1	v1	VERB
ejpam-5241	346	6	v2	v2	PROPN
ejpam-5241	346	7	v3	v3	PROPN
ejpam-5241	346	8	v4	v4	PROPN
ejpam-5241	346	9	v5	v5	PROPN
ejpam-5241	346	10	u1	u1	NOUN
ejpam-5241	346	11	u2	u2	PROPN
ejpam-5241	346	12	u3	u3	PROPN
ejpam-5241	346	13	u4	u4	PROPN
ejpam-5241	346	14	u5	u5	PROPN
ejpam-5241	346	15	u6	u6	PROPN
ejpam-5241	346	16	figure	figure	NOUN
ejpam-5241	346	17	4	4	NUM
ejpam-5241	346	18	:	:	PUNCT
ejpam-5241	346	19	the	the	DET
ejpam-5241	346	20	bipartite	bipartite	PROPN
ejpam-5241	346	21	graph	graph	NOUN
ejpam-5241	346	22	k5,6	k5,6	NOUN
ejpam-5241	346	23	observation	observation	NOUN
ejpam-5241	346	24	6	6	NUM
ejpam-5241	346	25	.	.	PUNCT
ejpam-5241	347	1	let	let	VERB
ejpam-5241	347	2	n	n	PRON
ejpam-5241	347	3	be	be	AUX
ejpam-5241	347	4	a	a	DET
ejpam-5241	347	5	positive	positive	ADJ
ejpam-5241	347	6	integer	integer	NOUN
ejpam-5241	347	7	.	.	PUNCT
ejpam-5241	348	1	then	then	ADV
ejpam-5241	348	2	(	(	PUNCT
ejpam-5241	348	3	i	i	NOUN
ejpam-5241	348	4	)	)	PUNCT
ejpam-5241	348	5	ρc2pnd(kn	ρc2pnd(kn	NOUN
ejpam-5241	348	6	)	)	PUNCT
ejpam-5241	348	7	=	=	SYM
ejpam-5241	348	8	n	n	NOUN
ejpam-5241	348	9	and	and	CCONJ
ejpam-5241	348	10	ρc2(kn	ρc2(kn	NUM
ejpam-5241	348	11	)	)	PUNCT
ejpam-5241	349	1	=	=	SYM
ejpam-5241	349	2	n	n	CCONJ
ejpam-5241	349	3	;	;	PUNCT
ejpam-5241	349	4	(	(	PUNCT
ejpam-5241	349	5	ii	ii	NOUN
ejpam-5241	349	6	)	)	PUNCT
ejpam-5241	349	7	ρc2pnd(pn	ρc2pnd(pn	PROPN
ejpam-5241	349	8	)	)	PUNCT
ejpam-5241	349	9	=	=	PRON
ejpam-5241	349	10	{	{	PUNCT
ejpam-5241	350	1	n	n	NOUN
ejpam-5241	350	2	if	if	SCONJ
ejpam-5241	350	3	n	n	NOUN
ejpam-5241	350	4	=	=	SYM
ejpam-5241	350	5	1	1	NUM
ejpam-5241	350	6	,	,	PUNCT
ejpam-5241	350	7	2	2	NUM
ejpam-5241	350	8	,	,	PUNCT
ejpam-5241	350	9	3	3	NUM
ejpam-5241	350	10	,	,	PUNCT
ejpam-5241	350	11	⌈n+1	⌈n+1	PROPN
ejpam-5241	350	12	2	2	NUM
ejpam-5241	350	13	⌉	⌉	NOUN
ejpam-5241	350	14	if	if	SCONJ
ejpam-5241	350	15	n	n	PRON
ejpam-5241	350	16	≥	≥	NOUN
ejpam-5241	350	17	4	4	NUM
ejpam-5241	350	18	,	,	PUNCT
ejpam-5241	350	19	and	and	CCONJ
ejpam-5241	350	20	ρc2(pn	ρc2(pn	PRON
ejpam-5241	350	21	)	)	PUNCT
ejpam-5241	351	1	=	=	NOUN
ejpam-5241	351	2	{	{	PUNCT
ejpam-5241	351	3	2	2	NUM
ejpam-5241	351	4	if	if	SCONJ
ejpam-5241	351	5	n	n	X
ejpam-5241	351	6	=	=	SYM
ejpam-5241	351	7	3	3	NUM
ejpam-5241	351	8	,	,	PUNCT
ejpam-5241	351	9	⌈n+1	⌈n+1	PROPN
ejpam-5241	351	10	2	2	NUM
ejpam-5241	351	11	⌉	⌉	NOUN
ejpam-5241	351	12	if	if	SCONJ
ejpam-5241	351	13	n	n	PRON
ejpam-5241	351	14	≥	≥	NOUN
ejpam-5241	351	15	4	4	NUM
ejpam-5241	351	16	;	;	PUNCT
ejpam-5241	351	17	(	(	PUNCT
ejpam-5241	351	18	iii	iii	X
ejpam-5241	351	19	)	)	PUNCT
ejpam-5241	351	20	ρc2pnd(cn	ρc2pnd(cn	PROPN
ejpam-5241	351	21	)	)	PUNCT
ejpam-5241	351	22	=	=	PRON
ejpam-5241	351	23	{	{	PUNCT
ejpam-5241	351	24	3	3	NUM
ejpam-5241	351	25	if	if	SCONJ
ejpam-5241	351	26	n	n	X
ejpam-5241	351	27	=	=	SYM
ejpam-5241	351	28	3	3	NUM
ejpam-5241	351	29	,	,	PUNCT
ejpam-5241	351	30	4	4	NUM
ejpam-5241	351	31	,	,	PUNCT
ejpam-5241	351	32	⌈n2	⌈n2	NOUN
ejpam-5241	351	33	⌉	⌉	PUNCT
ejpam-5241	351	34	if	if	SCONJ
ejpam-5241	351	35	n	n	PRON
ejpam-5241	351	36	≥	≥	NOUN
ejpam-5241	351	37	5	5	NUM
ejpam-5241	351	38	and	and	CCONJ
ejpam-5241	351	39	ρc2(cn	ρc2(cn	NUM
ejpam-5241	351	40	)	)	PUNCT
ejpam-5241	351	41	=	=	PRON
ejpam-5241	351	42	{	{	PUNCT
ejpam-5241	351	43	3	3	NUM
ejpam-5241	351	44	if	if	SCONJ
ejpam-5241	351	45	n	n	X
ejpam-5241	351	46	=	=	SYM
ejpam-5241	351	47	3	3	NUM
ejpam-5241	351	48	,	,	PUNCT
ejpam-5241	351	49	⌈n2	⌈n2	NOUN
ejpam-5241	351	50	⌉	⌉	PUNCT
ejpam-5241	351	51	if	if	SCONJ
ejpam-5241	351	52	n	n	PRON
ejpam-5241	351	53	≥	≥	NOUN
ejpam-5241	351	54	4	4	NUM
ejpam-5241	351	55	;	;	PUNCT
ejpam-5241	351	56	(	(	PUNCT
ejpam-5241	351	57	iv	iv	X
ejpam-5241	351	58	)	)	PUNCT
ejpam-5241	351	59	ρc2pnd(km	ρc2pnd(km	PROPN
ejpam-5241	351	60	,	,	PUNCT
ejpam-5241	351	61	n	n	CCONJ
ejpam-5241	351	62	)	)	PUNCT
ejpam-5241	351	63	=	=	PRON
ejpam-5241	351	64	{	{	PUNCT
ejpam-5241	351	65	m+	m+	NUM
ejpam-5241	351	66	n	n	NOUN
ejpam-5241	351	67	if	if	SCONJ
ejpam-5241	351	68	m	m	VERB
ejpam-5241	351	69	=	=	SYM
ejpam-5241	351	70	1	1	NUM
ejpam-5241	351	71	or	or	CCONJ
ejpam-5241	351	72	n	n	NOUN
ejpam-5241	351	73	=	=	SYM
ejpam-5241	351	74	1	1	NUM
ejpam-5241	351	75	min{m	min{m	NOUN
ejpam-5241	351	76	,	,	PUNCT
ejpam-5241	351	77	n}+	n}+	NOUN
ejpam-5241	351	78	1	1	NUM
ejpam-5241	351	79	if	if	SCONJ
ejpam-5241	351	80	m	m	PROPN
ejpam-5241	351	81	,	,	PUNCT
ejpam-5241	351	82	n	n	PRON
ejpam-5241	351	83	≥	≥	NOUN
ejpam-5241	351	84	2	2	NUM
ejpam-5241	351	85	lemma	lemma	PROPN
ejpam-5241	351	86	2	2	NUM
ejpam-5241	351	87	.	.	PUNCT
ejpam-5241	352	1	[	[	X
ejpam-5241	352	2	11	11	NUM
ejpam-5241	352	3	]	]	PUNCT
ejpam-5241	352	4	let	let	VERB
ejpam-5241	352	5	g	g	PRON
ejpam-5241	352	6	be	be	AUX
ejpam-5241	352	7	a	a	DET
ejpam-5241	352	8	connected	connected	ADJ
ejpam-5241	352	9	noncomplete	noncomplete	ADJ
ejpam-5241	352	10	graph	graph	NOUN
ejpam-5241	352	11	,	,	PUNCT
ejpam-5241	352	12	and	and	CCONJ
ejpam-5241	352	13	let	let	VERB
ejpam-5241	352	14	s	s	PRON
ejpam-5241	352	15	⊆	⊆	NUM
ejpam-5241	352	16	v	v	NOUN
ejpam-5241	352	17	(	(	PUNCT
ejpam-5241	352	18	g	g	NOUN
ejpam-5241	352	19	)	)	PUNCT
ejpam-5241	352	20	.	.	PUNCT
ejpam-5241	353	1	if	if	SCONJ
ejpam-5241	353	2	s	s	NOUN
ejpam-5241	353	3	is	be	AUX
ejpam-5241	353	4	a	a	DET
ejpam-5241	353	5	2	2	NUM
ejpam-5241	353	6	-	-	PUNCT
ejpam-5241	353	7	path	path	NOUN
ejpam-5241	353	8	closure	closure	NOUN
ejpam-5241	353	9	absorbing	absorb	VERB
ejpam-5241	353	10	set	set	NOUN
ejpam-5241	353	11	of	of	ADP
ejpam-5241	353	12	g	g	NOUN
ejpam-5241	353	13	,	,	PUNCT
ejpam-5241	353	14	then	then	ADV
ejpam-5241	353	15	⟨s⟩	⟨s⟩	PROPN
ejpam-5241	353	16	is	be	AUX
ejpam-5241	353	17	not	not	PART
ejpam-5241	353	18	complete	complete	ADJ
ejpam-5241	353	19	.	.	PUNCT
ejpam-5241	354	1	theorem	theorem	ADJ
ejpam-5241	354	2	7	7	NUM
ejpam-5241	354	3	.	.	PUNCT
ejpam-5241	355	1	let	let	VERB
ejpam-5241	355	2	g	g	PRON
ejpam-5241	355	3	be	be	AUX
ejpam-5241	355	4	a	a	DET
ejpam-5241	355	5	noncomplete	noncomplete	ADJ
ejpam-5241	355	6	connected	connect	VERB
ejpam-5241	355	7	graph	graph	NOUN
ejpam-5241	355	8	and	and	CCONJ
ejpam-5241	355	9	n	n	PRON
ejpam-5241	355	10	≥	≥	NOUN
ejpam-5241	355	11	1	1	NUM
ejpam-5241	355	12	.	.	PUNCT
ejpam-5241	356	1	then	then	ADV
ejpam-5241	356	2	s	s	VERB
ejpam-5241	356	3	⊆	⊆	NUM
ejpam-5241	356	4	v	v	NOUN
ejpam-5241	356	5	(	(	PUNCT
ejpam-5241	356	6	g+kn	g+kn	NOUN
ejpam-5241	356	7	)	)	PUNCT
ejpam-5241	356	8	is	be	AUX
ejpam-5241	356	9	a	a	DET
ejpam-5241	356	10	closed	closed	ADJ
ejpam-5241	356	11	geodetic	geodetic	ADJ
ejpam-5241	356	12	hop	hop	NOUN
ejpam-5241	356	13	dominating	dominating	NOUN
ejpam-5241	356	14	set	set	NOUN
ejpam-5241	356	15	of	of	ADP
ejpam-5241	356	16	g+kn	g+kn	NOUN
ejpam-5241	356	17	if	if	SCONJ
ejpam-5241	356	18	and	and	CCONJ
ejpam-5241	356	19	only	only	ADV
ejpam-5241	356	20	if	if	SCONJ
ejpam-5241	356	21	s	s	VERB
ejpam-5241	356	22	=	=	SYM
ejpam-5241	356	23	v	v	PROPN
ejpam-5241	356	24	(	(	PUNCT
ejpam-5241	356	25	kn	kn	PROPN
ejpam-5241	356	26	)	)	PUNCT
ejpam-5241	356	27	∪	∪	ADP
ejpam-5241	356	28	c	c	NOUN
ejpam-5241	356	29	,	,	PUNCT
ejpam-5241	356	30	where	where	SCONJ
ejpam-5241	356	31	c	c	PROPN
ejpam-5241	356	32	⊆	⊆	NUM
ejpam-5241	356	33	v	v	NOUN
ejpam-5241	356	34	(	(	PUNCT
ejpam-5241	356	35	g	g	NOUN
ejpam-5241	356	36	)	)	PUNCT
ejpam-5241	356	37	and	and	CCONJ
ejpam-5241	356	38	is	be	AUX
ejpam-5241	356	39	a	a	DET
ejpam-5241	356	40	closed	closed	ADJ
ejpam-5241	356	41	2	2	NUM
ejpam-5241	356	42	-	-	PUNCT
ejpam-5241	356	43	path	path	NOUN
ejpam-5241	356	44	closure	closure	NOUN
ejpam-5241	356	45	absorbing	absorb	VERB
ejpam-5241	356	46	pointwise	pointwise	PROPN
ejpam-5241	356	47	non	non	ADJ
ejpam-5241	356	48	-	-	ADJ
ejpam-5241	356	49	dominating	dominating	ADJ
ejpam-5241	356	50	set	set	NOUN
ejpam-5241	356	51	in	in	ADP
ejpam-5241	356	52	g.	g.	PROPN
ejpam-5241	356	53	a.	a.	PROPN
ejpam-5241	356	54	adolfo	adolfo	PROPN
ejpam-5241	356	55	,	,	PUNCT
ejpam-5241	356	56	i.	i.	PROPN
ejpam-5241	356	57	aniversario	aniversario	PROPN
ejpam-5241	356	58	,	,	PUNCT
ejpam-5241	356	59	f.	f.	PROPN
ejpam-5241	356	60	jamil	jamil	PROPN
ejpam-5241	356	61	/	/	SYM
ejpam-5241	356	62	eur	eur	PROPN
ejpam-5241	356	63	.	.	PUNCT
ejpam-5241	357	1	j.	j.	PROPN
ejpam-5241	357	2	pure	pure	PROPN
ejpam-5241	357	3	appl	appl	PROPN
ejpam-5241	357	4	.	.	PROPN
ejpam-5241	357	5	math	math	PROPN
ejpam-5241	357	6	,	,	PUNCT
ejpam-5241	357	7	17	17	NUM
ejpam-5241	357	8	(	(	PUNCT
ejpam-5241	357	9	3	3	NUM
ejpam-5241	357	10	)	)	PUNCT
ejpam-5241	357	11	(	(	PUNCT
ejpam-5241	357	12	2024	2024	NUM
ejpam-5241	357	13	)	)	PUNCT
ejpam-5241	357	14	,	,	PUNCT
ejpam-5241	357	15	1618	1618	NUM
ejpam-5241	357	16	-	-	SYM
ejpam-5241	357	17	1636	1636	NUM
ejpam-5241	357	18	1628	1628	NUM
ejpam-5241	357	19	proof	proof	NOUN
ejpam-5241	357	20	.	.	PUNCT
ejpam-5241	358	1	let	let	VERB
ejpam-5241	358	2	s	s	PRON
ejpam-5241	358	3	⊆	⊆	NUM
ejpam-5241	358	4	v	v	NOUN
ejpam-5241	358	5	(	(	PUNCT
ejpam-5241	358	6	g	g	PROPN
ejpam-5241	358	7	+	+	PROPN
ejpam-5241	358	8	kn	kn	PROPN
ejpam-5241	358	9	)	)	PUNCT
ejpam-5241	358	10	.	.	PUNCT
ejpam-5241	359	1	suppose	suppose	VERB
ejpam-5241	359	2	that	that	SCONJ
ejpam-5241	359	3	s	s	VERB
ejpam-5241	359	4	is	be	AUX
ejpam-5241	359	5	a	a	DET
ejpam-5241	359	6	closed	closed	ADJ
ejpam-5241	359	7	geodetic	geodetic	ADJ
ejpam-5241	359	8	hop	hop	NOUN
ejpam-5241	359	9	dominating	dominating	NOUN
ejpam-5241	359	10	set	set	NOUN
ejpam-5241	359	11	of	of	ADP
ejpam-5241	359	12	g	g	PROPN
ejpam-5241	359	13	+	+	CCONJ
ejpam-5241	359	14	kn	kn	PROPN
ejpam-5241	359	15	,	,	PUNCT
ejpam-5241	359	16	say	say	VERB
ejpam-5241	359	17	s	s	X
ejpam-5241	359	18	=	=	PUNCT
ejpam-5241	359	19	sk	sk	NOUN
ejpam-5241	359	20	=	=	PUNCT
ejpam-5241	359	21	{	{	PUNCT
ejpam-5241	359	22	x1	x1	PROPN
ejpam-5241	359	23	,	,	PUNCT
ejpam-5241	359	24	x2	x2	PROPN
ejpam-5241	359	25	,	,	PUNCT
ejpam-5241	359	26	.	.	PUNCT
ejpam-5241	359	27	.	.	PUNCT
ejpam-5241	359	28	.	.	PUNCT
ejpam-5241	360	1	,	,	PUNCT
ejpam-5241	360	2	xk	xk	PROPN
ejpam-5241	360	3	}	}	PUNCT
ejpam-5241	360	4	with	with	ADP
ejpam-5241	360	5	x1	x1	PROPN
ejpam-5241	360	6	̸=	̸=	PROPN
ejpam-5241	360	7	x2	x2	PROPN
ejpam-5241	360	8	and	and	CCONJ
ejpam-5241	360	9	for	for	ADP
ejpam-5241	360	10	k	k	PROPN
ejpam-5241	360	11	≥	≥	PROPN
ejpam-5241	360	12	3	3	NUM
ejpam-5241	360	13	,	,	PUNCT
ejpam-5241	360	14	xk	xk	PROPN
ejpam-5241	360	15	/∈	/∈	PUNCT
ejpam-5241	361	1	ig+kn	ig+kn	PROPN
ejpam-5241	362	1	[	[	X
ejpam-5241	362	2	sk−1	sk−1	X
ejpam-5241	362	3	]	]	PUNCT
ejpam-5241	362	4	.	.	PUNCT
ejpam-5241	363	1	since	since	SCONJ
ejpam-5241	363	2	v	v	X
ejpam-5241	363	3	(	(	PUNCT
ejpam-5241	363	4	kn	kn	PROPN
ejpam-5241	363	5	)	)	PUNCT
ejpam-5241	363	6	⊆	⊆	NUM
ejpam-5241	363	7	dom(g	dom(g	NOUN
ejpam-5241	363	8	+	+	NUM
ejpam-5241	363	9	kn	kn	PROPN
ejpam-5241	363	10	)	)	PUNCT
ejpam-5241	363	11	,	,	PUNCT
ejpam-5241	363	12	v	v	X
ejpam-5241	363	13	(	(	PUNCT
ejpam-5241	363	14	kn	kn	PROPN
ejpam-5241	363	15	)	)	PUNCT
ejpam-5241	363	16	⊆	⊆	NUM
ejpam-5241	363	17	s.	s.	PROPN
ejpam-5241	363	18	let	let	VERB
ejpam-5241	363	19	j	j	PROPN
ejpam-5241	363	20	=	=	SYM
ejpam-5241	363	21	|s	|s	PROPN
ejpam-5241	363	22	∩	∩	PROPN
ejpam-5241	363	23	v	v	NOUN
ejpam-5241	363	24	(	(	PUNCT
ejpam-5241	363	25	h)|	h)|	PROPN
ejpam-5241	363	26	.	.	PUNCT
ejpam-5241	364	1	write	write	PROPN
ejpam-5241	364	2	ai	ai	PROPN
ejpam-5241	364	3	=	=	PUNCT
ejpam-5241	364	4	{	{	PUNCT
ejpam-5241	364	5	xn1	xn1	X
ejpam-5241	364	6	,	,	PUNCT
ejpam-5241	364	7	xn2	xn2	PROPN
ejpam-5241	364	8	,	,	PUNCT
ejpam-5241	364	9	.	.	PUNCT
ejpam-5241	364	10	.	.	PUNCT
ejpam-5241	365	1	.	.	PUNCT
ejpam-5241	366	1	,	,	PUNCT
ejpam-5241	366	2	xni	xni	PROPN
ejpam-5241	366	3	}	}	PUNCT
ejpam-5241	366	4	for	for	ADP
ejpam-5241	366	5	i	i	PROPN
ejpam-5241	366	6	=	=	NOUN
ejpam-5241	366	7	1	1	NUM
ejpam-5241	366	8	,	,	PUNCT
ejpam-5241	366	9	2	2	NUM
ejpam-5241	366	10	,	,	PUNCT
ejpam-5241	366	11	.	.	PUNCT
ejpam-5241	366	12	.	.	PUNCT
ejpam-5241	366	13	.	.	PUNCT
ejpam-5241	367	1	,	,	PUNCT
ejpam-5241	367	2	j	j	PROPN
ejpam-5241	367	3	such	such	ADJ
ejpam-5241	367	4	that	that	SCONJ
ejpam-5241	367	5	n1	n1	PROPN
ejpam-5241	367	6	<	<	X
ejpam-5241	367	7	n2	n2	X
ejpam-5241	367	8	<	<	X
ejpam-5241	367	9	·	·	PUNCT
ejpam-5241	367	10	·	·	PUNCT
ejpam-5241	367	11	·	·	PUNCT
ejpam-5241	367	12	<	<	X
ejpam-5241	367	13	nj	nj	PROPN
ejpam-5241	367	14	.	.	PUNCT
ejpam-5241	368	1	first	first	ADV
ejpam-5241	368	2	,	,	PUNCT
ejpam-5241	368	3	we	we	PRON
ejpam-5241	368	4	claim	claim	VERB
ejpam-5241	368	5	that	that	SCONJ
ejpam-5241	368	6	c	c	AUX
ejpam-5241	368	7	=	=	SYM
ejpam-5241	368	8	aj	aj	PROPN
ejpam-5241	368	9	is	be	AUX
ejpam-5241	368	10	a	a	DET
ejpam-5241	368	11	closed	closed	ADJ
ejpam-5241	368	12	2	2	NUM
ejpam-5241	368	13	-	-	PUNCT
ejpam-5241	368	14	path	path	NOUN
ejpam-5241	368	15	closure	closure	NOUN
ejpam-5241	368	16	absorbing	absorb	VERB
ejpam-5241	368	17	set	set	NOUN
ejpam-5241	368	18	of	of	ADP
ejpam-5241	368	19	g.	g.	PROPN
ejpam-5241	368	20	suppose	suppose	VERB
ejpam-5241	368	21	that	that	SCONJ
ejpam-5241	368	22	for	for	ADP
ejpam-5241	368	23	some	some	DET
ejpam-5241	368	24	3	3	NUM
ejpam-5241	368	25	≤	≤	NUM
ejpam-5241	368	26	l	l	NOUN
ejpam-5241	368	27	≤	≤	PROPN
ejpam-5241	368	28	j	j	PROPN
ejpam-5241	368	29	,	,	PUNCT
ejpam-5241	368	30	xnl	xnl	PROPN
ejpam-5241	368	31	∈	∈	PROPN
ejpam-5241	368	32	p2[al−1	p2[al−1	NOUN
ejpam-5241	368	33	]	]	PUNCT
ejpam-5241	368	34	.	.	PUNCT
ejpam-5241	369	1	this	this	PRON
ejpam-5241	369	2	means	mean	VERB
ejpam-5241	369	3	that	that	SCONJ
ejpam-5241	369	4	there	there	PRON
ejpam-5241	369	5	exist	exist	VERB
ejpam-5241	369	6	r	r	NOUN
ejpam-5241	369	7	<	<	X
ejpam-5241	369	8	s	s	X
ejpam-5241	369	9	<	<	X
ejpam-5241	369	10	l	l	NOUN
ejpam-5241	369	11	such	such	ADJ
ejpam-5241	369	12	that	that	SCONJ
ejpam-5241	369	13	[	[	X
ejpam-5241	369	14	xnr	xnr	NUM
ejpam-5241	369	15	,	,	PUNCT
ejpam-5241	369	16	xnl	xnl	PROPN
ejpam-5241	369	17	,	,	PUNCT
ejpam-5241	369	18	xns	xns	PROPN
ejpam-5241	369	19	]	]	PUNCT
ejpam-5241	369	20	is	be	AUX
ejpam-5241	369	21	a	a	DET
ejpam-5241	369	22	geodesic	geodesic	NOUN
ejpam-5241	369	23	in	in	ADP
ejpam-5241	369	24	g.	g.	PROPN
ejpam-5241	369	25	since	since	SCONJ
ejpam-5241	369	26	diam(g+kn	diam(g+kn	NOUN
ejpam-5241	369	27	)	)	PUNCT
ejpam-5241	369	28	=	=	SYM
ejpam-5241	369	29	2	2	NUM
ejpam-5241	369	30	,	,	PUNCT
ejpam-5241	369	31	[	[	X
ejpam-5241	369	32	xnr	xnr	NUM
ejpam-5241	369	33	,	,	PUNCT
ejpam-5241	369	34	xnl	xnl	PROPN
ejpam-5241	369	35	,	,	PUNCT
ejpam-5241	369	36	xns	xns	PROPN
ejpam-5241	369	37	]	]	PUNCT
ejpam-5241	369	38	is	be	AUX
ejpam-5241	369	39	also	also	ADV
ejpam-5241	369	40	a	a	DET
ejpam-5241	369	41	geodesic	geodesic	NOUN
ejpam-5241	369	42	in	in	ADP
ejpam-5241	369	43	g+kn	g+kn	NOUN
ejpam-5241	369	44	.	.	PUNCT
ejpam-5241	370	1	thus	thus	ADV
ejpam-5241	370	2	,	,	PUNCT
ejpam-5241	370	3	xnl	xnl	PROPN
ejpam-5241	370	4	∈	∈	PROPN
ejpam-5241	370	5	ig+kn	ig+kn	X
ejpam-5241	371	1	[	[	X
ejpam-5241	371	2	snl−1	snl−1	NOUN
ejpam-5241	371	3	]	]	X
ejpam-5241	371	4	,	,	PUNCT
ejpam-5241	371	5	a	a	DET
ejpam-5241	371	6	contradiction	contradiction	NOUN
ejpam-5241	371	7	to	to	ADP
ejpam-5241	371	8	the	the	DET
ejpam-5241	371	9	definition	definition	NOUN
ejpam-5241	371	10	of	of	ADP
ejpam-5241	371	11	s	s	NOUN
ejpam-5241	371	12	=	=	PUNCT
ejpam-5241	371	13	sk	sk	PROPN
ejpam-5241	371	14	.	.	PROPN
ejpam-5241	371	15	hence	hence	ADV
ejpam-5241	371	16	,	,	PUNCT
ejpam-5241	371	17	xnl	xnl	PROPN
ejpam-5241	371	18	/∈	/∈	PUNCT
ejpam-5241	372	1	p2[al−1	p2[al−1	NOUN
ejpam-5241	372	2	]	]	PUNCT
ejpam-5241	372	3	for	for	ADP
ejpam-5241	372	4	each	each	DET
ejpam-5241	372	5	3	3	NUM
ejpam-5241	372	6	≤	≤	NUM
ejpam-5241	372	7	l	l	NOUN
ejpam-5241	372	8	≤	≤	NOUN
ejpam-5241	372	9	j.	j.	PROPN
ejpam-5241	372	10	let	let	VERB
ejpam-5241	372	11	x	x	SYM
ejpam-5241	372	12	∈	∈	PROPN
ejpam-5241	372	13	v	v	X
ejpam-5241	372	14	(	(	PUNCT
ejpam-5241	372	15	g	g	NOUN
ejpam-5241	372	16	)	)	PUNCT
ejpam-5241	372	17	\	\	PROPN
ejpam-5241	372	18	aj	aj	PROPN
ejpam-5241	372	19	.	.	PUNCT
ejpam-5241	373	1	there	there	PRON
ejpam-5241	373	2	exist	exist	VERB
ejpam-5241	373	3	a	a	DET
ejpam-5241	373	4	,	,	PUNCT
ejpam-5241	373	5	b	b	X
ejpam-5241	373	6	∈	∈	PROPN
ejpam-5241	373	7	{	{	PUNCT
ejpam-5241	373	8	1	1	NUM
ejpam-5241	373	9	,	,	PUNCT
ejpam-5241	373	10	2	2	NUM
ejpam-5241	373	11	,	,	PUNCT
ejpam-5241	373	12	.	.	PUNCT
ejpam-5241	373	13	.	.	PUNCT
ejpam-5241	374	1	.	.	PUNCT
ejpam-5241	375	1	,	,	PUNCT
ejpam-5241	375	2	k	k	X
ejpam-5241	375	3	}	}	PUNCT
ejpam-5241	375	4	such	such	ADJ
ejpam-5241	375	5	that	that	SCONJ
ejpam-5241	375	6	x	x	SYM
ejpam-5241	375	7	∈	∈	PROPN
ejpam-5241	375	8	ig+kn(xa	ig+kn(xa	PROPN
ejpam-5241	375	9	,	,	PUNCT
ejpam-5241	375	10	xb	xb	PROPN
ejpam-5241	375	11	)	)	PUNCT
ejpam-5241	375	12	.	.	PUNCT
ejpam-5241	376	1	necessarily	necessarily	ADV
ejpam-5241	376	2	,	,	PUNCT
ejpam-5241	376	3	xa	xa	PROPN
ejpam-5241	376	4	,	,	PUNCT
ejpam-5241	376	5	xb	xb	PROPN
ejpam-5241	376	6	∈	∈	PROPN
ejpam-5241	376	7	v	v	X
ejpam-5241	376	8	(	(	PUNCT
ejpam-5241	376	9	g)∩s	g)∩s	PROPN
ejpam-5241	376	10	=	=	PUNCT
ejpam-5241	376	11	aj	aj	PROPN
ejpam-5241	376	12	and	and	CCONJ
ejpam-5241	376	13	each	each	DET
ejpam-5241	376	14	xa	xa	PROPN
ejpam-5241	376	15	-	-	PUNCT
ejpam-5241	376	16	xb	xb	PROPN
ejpam-5241	376	17	geodesic	geodesic	NOUN
ejpam-5241	376	18	containing	contain	VERB
ejpam-5241	376	19	x	x	SYM
ejpam-5241	376	20	lies	lie	VERB
ejpam-5241	376	21	entirely	entirely	ADV
ejpam-5241	376	22	in	in	ADP
ejpam-5241	376	23	g.	g.	NOUN
ejpam-5241	376	24	since	since	SCONJ
ejpam-5241	376	25	diam(g	diam(g	PROPN
ejpam-5241	376	26	+	+	CCONJ
ejpam-5241	376	27	kn	kn	PROPN
ejpam-5241	376	28	)	)	PUNCT
ejpam-5241	376	29	=	=	SYM
ejpam-5241	376	30	2	2	NUM
ejpam-5241	376	31	,	,	PUNCT
ejpam-5241	376	32	dg(xa	dg(xa	NOUN
ejpam-5241	376	33	,	,	PUNCT
ejpam-5241	376	34	xb	xb	X
ejpam-5241	376	35	)	)	PUNCT
ejpam-5241	377	1	=	=	SYM
ejpam-5241	377	2	2	2	X
ejpam-5241	377	3	.	.	X
ejpam-5241	377	4	therefore	therefore	ADV
ejpam-5241	377	5	,	,	PUNCT
ejpam-5241	377	6	p2[aj	p2[aj	ADJ
ejpam-5241	377	7	]	]	PUNCT
ejpam-5241	377	8	=	=	SYM
ejpam-5241	377	9	v	v	X
ejpam-5241	377	10	(	(	PUNCT
ejpam-5241	377	11	g	g	NOUN
ejpam-5241	377	12	)	)	PUNCT
ejpam-5241	377	13	,	,	PUNCT
ejpam-5241	377	14	and	and	CCONJ
ejpam-5241	377	15	the	the	DET
ejpam-5241	377	16	first	first	ADJ
ejpam-5241	377	17	claim	claim	NOUN
ejpam-5241	377	18	is	be	AUX
ejpam-5241	377	19	done	do	VERB
ejpam-5241	377	20	.	.	PUNCT
ejpam-5241	378	1	we	we	PRON
ejpam-5241	378	2	next	next	ADJ
ejpam-5241	378	3	claim	claim	VERB
ejpam-5241	378	4	that	that	SCONJ
ejpam-5241	378	5	c	c	PROPN
ejpam-5241	378	6	is	be	AUX
ejpam-5241	378	7	a	a	DET
ejpam-5241	378	8	pointwise	pointwise	ADJ
ejpam-5241	378	9	nondominating	nondominate	VERB
ejpam-5241	378	10	set	set	NOUN
ejpam-5241	378	11	of	of	ADP
ejpam-5241	378	12	g.	g.	PROPN
ejpam-5241	378	13	let	let	VERB
ejpam-5241	378	14	x	x	SYM
ejpam-5241	378	15	∈	∈	PROPN
ejpam-5241	378	16	v	v	X
ejpam-5241	378	17	(	(	PUNCT
ejpam-5241	378	18	g	g	NOUN
ejpam-5241	378	19	)	)	PUNCT
ejpam-5241	378	20	\c	\c	NOUN
ejpam-5241	378	21	.	.	PUNCT
ejpam-5241	379	1	since	since	SCONJ
ejpam-5241	379	2	s	s	PROPN
ejpam-5241	379	3	is	be	AUX
ejpam-5241	379	4	a	a	DET
ejpam-5241	379	5	hop	hop	NOUN
ejpam-5241	379	6	dominating	dominating	NOUN
ejpam-5241	379	7	set	set	NOUN
ejpam-5241	379	8	of	of	ADP
ejpam-5241	379	9	g+kn	g+kn	NOUN
ejpam-5241	379	10	,	,	PUNCT
ejpam-5241	379	11	there	there	PRON
ejpam-5241	379	12	exists	exist	VERB
ejpam-5241	380	1	v	v	ADP
ejpam-5241	380	2	∈	∈	PROPN
ejpam-5241	380	3	s	s	VERB
ejpam-5241	380	4	such	such	ADJ
ejpam-5241	380	5	that	that	SCONJ
ejpam-5241	380	6	dg+kn(x	dg+kn(x	PROPN
ejpam-5241	380	7	,	,	PUNCT
ejpam-5241	380	8	v	v	NOUN
ejpam-5241	380	9	)	)	PUNCT
ejpam-5241	380	10	=	=	SYM
ejpam-5241	380	11	2	2	X
ejpam-5241	380	12	.	.	PUNCT
ejpam-5241	380	13	clearly	clearly	ADV
ejpam-5241	380	14	,	,	PUNCT
ejpam-5241	380	15	v	v	PROPN
ejpam-5241	380	16	∈	∈	PROPN
ejpam-5241	380	17	v	v	NOUN
ejpam-5241	380	18	(	(	PUNCT
ejpam-5241	380	19	g	g	NOUN
ejpam-5241	380	20	)	)	PUNCT
ejpam-5241	380	21	∩	∩	NOUN
ejpam-5241	380	22	s	s	PART
ejpam-5241	380	23	=	=	SYM
ejpam-5241	380	24	c	c	PROPN
ejpam-5241	380	25	and	and	CCONJ
ejpam-5241	380	26	dg(x	dg(x	NUM
ejpam-5241	380	27	,	,	PUNCT
ejpam-5241	380	28	v	v	NOUN
ejpam-5241	380	29	)	)	PUNCT
ejpam-5241	380	30	=	=	SYM
ejpam-5241	380	31	2	2	X
ejpam-5241	380	32	.	.	PUNCT
ejpam-5241	381	1	this	this	PRON
ejpam-5241	381	2	shows	show	VERB
ejpam-5241	381	3	that	that	SCONJ
ejpam-5241	381	4	the	the	DET
ejpam-5241	381	5	second	second	ADJ
ejpam-5241	381	6	claim	claim	NOUN
ejpam-5241	381	7	holds	hold	VERB
ejpam-5241	381	8	.	.	PUNCT
ejpam-5241	382	1	conversely	conversely	ADV
ejpam-5241	382	2	,	,	PUNCT
ejpam-5241	382	3	suppose	suppose	VERB
ejpam-5241	382	4	that	that	SCONJ
ejpam-5241	382	5	s	s	VERB
ejpam-5241	382	6	=	=	SYM
ejpam-5241	382	7	v	v	PROPN
ejpam-5241	382	8	(	(	PUNCT
ejpam-5241	382	9	kn	kn	PROPN
ejpam-5241	382	10	)	)	PUNCT
ejpam-5241	382	11	∪	∪	ADP
ejpam-5241	382	12	c	c	NOUN
ejpam-5241	382	13	,	,	PUNCT
ejpam-5241	382	14	where	where	SCONJ
ejpam-5241	382	15	c	c	PROPN
ejpam-5241	382	16	⊆	⊆	NUM
ejpam-5241	382	17	v	v	NOUN
ejpam-5241	382	18	(	(	PUNCT
ejpam-5241	382	19	g	g	NOUN
ejpam-5241	382	20	)	)	PUNCT
ejpam-5241	382	21	and	and	CCONJ
ejpam-5241	382	22	is	be	AUX
ejpam-5241	382	23	a	a	DET
ejpam-5241	382	24	closed	closed	ADJ
ejpam-5241	382	25	2	2	NUM
ejpam-5241	382	26	-	-	PUNCT
ejpam-5241	382	27	path	path	NOUN
ejpam-5241	382	28	closure	closure	NOUN
ejpam-5241	382	29	absorbing	absorb	VERB
ejpam-5241	382	30	pointwise	pointwise	PROPN
ejpam-5241	382	31	non	non	ADJ
ejpam-5241	382	32	-	-	ADJ
ejpam-5241	382	33	dominating	dominating	ADJ
ejpam-5241	382	34	set	set	NOUN
ejpam-5241	382	35	in	in	ADP
ejpam-5241	382	36	g.	g.	PROPN
ejpam-5241	382	37	let	let	VERB
ejpam-5241	382	38	k	k	PROPN
ejpam-5241	382	39	=	=	PROPN
ejpam-5241	382	40	|c|	|c|	PROPN
ejpam-5241	382	41	.	.	PUNCT
ejpam-5241	383	1	being	be	AUX
ejpam-5241	383	2	a	a	DET
ejpam-5241	383	3	closed	closed	ADJ
ejpam-5241	383	4	2	2	NUM
ejpam-5241	383	5	-	-	PUNCT
ejpam-5241	383	6	path	path	NOUN
ejpam-5241	383	7	closure	closure	NOUN
ejpam-5241	383	8	absorbing	absorb	VERB
ejpam-5241	383	9	set	set	NOUN
ejpam-5241	383	10	,	,	PUNCT
ejpam-5241	383	11	there	there	PRON
ejpam-5241	383	12	is	be	VERB
ejpam-5241	383	13	a	a	DET
ejpam-5241	383	14	sequence	sequence	NOUN
ejpam-5241	383	15	of	of	ADP
ejpam-5241	383	16	sets	set	NOUN
ejpam-5241	383	17	aj	aj	PROPN
ejpam-5241	383	18	=	=	SYM
ejpam-5241	383	19	{	{	PUNCT
ejpam-5241	383	20	v1	v1	PROPN
ejpam-5241	383	21	,	,	PUNCT
ejpam-5241	383	22	v2	v2	PROPN
ejpam-5241	383	23	,	,	PUNCT
ejpam-5241	383	24	.	.	PUNCT
ejpam-5241	383	25	.	.	PUNCT
ejpam-5241	384	1	.	.	PUNCT
ejpam-5241	385	1	,	,	PUNCT
ejpam-5241	385	2	vj	vj	INTJ
ejpam-5241	385	3	}	}	PUNCT
ejpam-5241	385	4	(	(	PUNCT
ejpam-5241	385	5	j	j	NOUN
ejpam-5241	385	6	=	=	SYM
ejpam-5241	385	7	1	1	NUM
ejpam-5241	385	8	,	,	PUNCT
ejpam-5241	385	9	2	2	NUM
ejpam-5241	385	10	,	,	PUNCT
ejpam-5241	385	11	.	.	PUNCT
ejpam-5241	385	12	.	.	PUNCT
ejpam-5241	385	13	.	.	PUNCT
ejpam-5241	386	1	,	,	PUNCT
ejpam-5241	386	2	k	k	X
ejpam-5241	386	3	)	)	PUNCT
ejpam-5241	386	4	such	such	ADJ
ejpam-5241	386	5	that	that	DET
ejpam-5241	386	6	v1	v1	NOUN
ejpam-5241	386	7	̸=	̸=	PROPN
ejpam-5241	386	8	v2	v2	PROPN
ejpam-5241	386	9	,	,	PUNCT
ejpam-5241	386	10	vj	vj	INTJ
ejpam-5241	386	11	/∈	/∈	PUNCT
ejpam-5241	386	12	p2[aj−1	p2[aj−1	NOUN
ejpam-5241	386	13	]	]	PUNCT
ejpam-5241	386	14	for	for	ADP
ejpam-5241	386	15	2	2	NUM
ejpam-5241	386	16	≤	≤	NUM
ejpam-5241	386	17	j	j	PROPN
ejpam-5241	386	18	≤	≤	PROPN
ejpam-5241	386	19	k	k	PROPN
ejpam-5241	386	20	and	and	CCONJ
ejpam-5241	386	21	p2[ak	p2[ak	NOUN
ejpam-5241	386	22	]	]	X
ejpam-5241	386	23	=	=	SYM
ejpam-5241	386	24	v	v	X
ejpam-5241	386	25	(	(	PUNCT
ejpam-5241	386	26	g	g	NOUN
ejpam-5241	386	27	)	)	PUNCT
ejpam-5241	386	28	.	.	PUNCT
ejpam-5241	387	1	for	for	ADP
ejpam-5241	387	2	i	i	PRON
ejpam-5241	387	3	=	=	NOUN
ejpam-5241	387	4	1	1	NUM
ejpam-5241	387	5	,	,	PUNCT
ejpam-5241	387	6	2	2	NUM
ejpam-5241	387	7	,	,	PUNCT
ejpam-5241	387	8	.	.	PUNCT
ejpam-5241	387	9	.	.	PUNCT
ejpam-5241	387	10	.	.	PUNCT
ejpam-5241	388	1	,	,	PUNCT
ejpam-5241	388	2	n+k	n+k	PROPN
ejpam-5241	388	3	,	,	PUNCT
ejpam-5241	388	4	write	write	VERB
ejpam-5241	388	5	si	si	X
ejpam-5241	388	6	=	=	PUNCT
ejpam-5241	388	7	{	{	PUNCT
ejpam-5241	388	8	x1	x1	PROPN
ejpam-5241	388	9	,	,	PUNCT
ejpam-5241	388	10	x2	x2	PROPN
ejpam-5241	388	11	,	,	PUNCT
ejpam-5241	388	12	.	.	PUNCT
ejpam-5241	388	13	.	.	PUNCT
ejpam-5241	389	1	.	.	PUNCT
ejpam-5241	390	1	,	,	PUNCT
ejpam-5241	390	2	xi	xi	ADP
ejpam-5241	390	3	}	}	PUNCT
ejpam-5241	390	4	,	,	PUNCT
ejpam-5241	390	5	where	where	SCONJ
ejpam-5241	390	6	v	v	X
ejpam-5241	390	7	(	(	PUNCT
ejpam-5241	390	8	kn	kn	PROPN
ejpam-5241	390	9	)	)	PUNCT
ejpam-5241	390	10	=	=	PRON
ejpam-5241	391	1	{	{	PUNCT
ejpam-5241	391	2	x1	x1	PROPN
ejpam-5241	391	3	,	,	PUNCT
ejpam-5241	391	4	x2	x2	PROPN
ejpam-5241	391	5	,	,	PUNCT
ejpam-5241	391	6	.	.	PUNCT
ejpam-5241	391	7	.	.	PUNCT
ejpam-5241	391	8	.	.	PUNCT
ejpam-5241	392	1	,	,	PUNCT
ejpam-5241	392	2	xn	xn	X
ejpam-5241	392	3	}	}	PUNCT
ejpam-5241	392	4	and	and	CCONJ
ejpam-5241	392	5	xn+j	xn+j	PROPN
ejpam-5241	392	6	=	=	PROPN
ejpam-5241	392	7	vj	vj	PROPN
ejpam-5241	392	8	for	for	ADP
ejpam-5241	392	9	all	all	PRON
ejpam-5241	392	10	j	j	NOUN
ejpam-5241	392	11	=	=	SYM
ejpam-5241	392	12	1	1	NUM
ejpam-5241	392	13	,	,	PUNCT
ejpam-5241	392	14	2	2	NUM
ejpam-5241	392	15	,	,	PUNCT
ejpam-5241	392	16	.	.	PUNCT
ejpam-5241	392	17	.	.	PUNCT
ejpam-5241	393	1	.	.	PUNCT
ejpam-5241	394	1	,	,	PUNCT
ejpam-5241	394	2	k.	k.	PROPN
ejpam-5241	394	3	observe	observe	VERB
ejpam-5241	394	4	that	that	SCONJ
ejpam-5241	394	5	•	•	NUM
ejpam-5241	394	6	ig+kn	ig+kn	X
ejpam-5241	395	1	[	[	X
ejpam-5241	395	2	si	si	X
ejpam-5241	395	3	]	]	X
ejpam-5241	395	4	=	=	PUNCT
ejpam-5241	395	5	si	si	X
ejpam-5241	395	6	for	for	ADP
ejpam-5241	395	7	all	all	DET
ejpam-5241	395	8	i	i	PRON
ejpam-5241	395	9	=	=	NOUN
ejpam-5241	395	10	1	1	NUM
ejpam-5241	395	11	,	,	PUNCT
ejpam-5241	395	12	2	2	NUM
ejpam-5241	395	13	,	,	PUNCT
ejpam-5241	395	14	.	.	PUNCT
ejpam-5241	395	15	.	.	PUNCT
ejpam-5241	396	1	.	.	PUNCT
ejpam-5241	397	1	,	,	PUNCT
ejpam-5241	397	2	n	n	CCONJ
ejpam-5241	397	3	;	;	PUNCT
ejpam-5241	397	4	•	•	X
ejpam-5241	397	5	xn+1	xn+1	X
ejpam-5241	397	6	/∈	/∈	PUNCT
ejpam-5241	397	7	ig+kn	ig+kn	X
ejpam-5241	398	1	[	[	X
ejpam-5241	398	2	sn	sn	X
ejpam-5241	398	3	]	]	PUNCT
ejpam-5241	398	4	and	and	CCONJ
ejpam-5241	398	5	xn+2	xn+2	NUM
ejpam-5241	398	6	/∈	/∈	PUNCT
ejpam-5241	398	7	ig+kn	ig+kn	PROPN
ejpam-5241	399	1	[	[	X
ejpam-5241	399	2	sn−1	sn−1	PROPN
ejpam-5241	399	3	]	]	X
ejpam-5241	399	4	;	;	PUNCT
ejpam-5241	399	5	•	•	X
ejpam-5241	399	6	xn+i	xn+i	PROPN
ejpam-5241	399	7	/∈	/∈	PUNCT
ejpam-5241	399	8	ig+kn	ig+kn	PROPN
ejpam-5241	400	1	[	[	X
ejpam-5241	400	2	sn+i−1	sn+i−1	X
ejpam-5241	400	3	]	]	X
ejpam-5241	400	4	=	=	SYM
ejpam-5241	400	5	v	v	X
ejpam-5241	400	6	(	(	PUNCT
ejpam-5241	400	7	kn	kn	PROPN
ejpam-5241	400	8	)	)	PUNCT
ejpam-5241	400	9	∪	∪	ADP
ejpam-5241	400	10	p2[ai−1	p2[ai−1	PROPN
ejpam-5241	400	11	]	]	PUNCT
ejpam-5241	400	12	for	for	ADP
ejpam-5241	400	13	all	all	DET
ejpam-5241	400	14	i	i	PRON
ejpam-5241	400	15	=	=	NOUN
ejpam-5241	400	16	1	1	NUM
ejpam-5241	400	17	,	,	PUNCT
ejpam-5241	400	18	2	2	NUM
ejpam-5241	400	19	,	,	PUNCT
ejpam-5241	400	20	.	.	PUNCT
ejpam-5241	400	21	.	.	PUNCT
ejpam-5241	400	22	.	.	PUNCT
ejpam-5241	401	1	,	,	PUNCT
ejpam-5241	401	2	k	k	NOUN
ejpam-5241	401	3	;	;	PUNCT
ejpam-5241	401	4	and	and	CCONJ
ejpam-5241	401	5	•	•	NUM
ejpam-5241	401	6	ig+kn	ig+kn	NOUN
ejpam-5241	402	1	[	[	X
ejpam-5241	402	2	s	s	X
ejpam-5241	402	3	]	]	X
ejpam-5241	402	4	=	=	SYM
ejpam-5241	402	5	v	v	X
ejpam-5241	402	6	(	(	PUNCT
ejpam-5241	402	7	g+kn	g+kn	NOUN
ejpam-5241	402	8	)	)	PUNCT
ejpam-5241	402	9	.	.	PUNCT
ejpam-5241	403	1	this	this	PRON
ejpam-5241	403	2	means	mean	VERB
ejpam-5241	403	3	that	that	SCONJ
ejpam-5241	403	4	s	s	VERB
ejpam-5241	403	5	is	be	AUX
ejpam-5241	403	6	a	a	DET
ejpam-5241	403	7	closed	closed	ADJ
ejpam-5241	403	8	geodetic	geodetic	ADJ
ejpam-5241	403	9	set	set	NOUN
ejpam-5241	403	10	of	of	ADP
ejpam-5241	403	11	g	g	PROPN
ejpam-5241	403	12	+	+	CCONJ
ejpam-5241	403	13	kn	kn	PROPN
ejpam-5241	403	14	.	.	PUNCT
ejpam-5241	404	1	finally	finally	ADV
ejpam-5241	404	2	,	,	PUNCT
ejpam-5241	404	3	let	let	VERB
ejpam-5241	404	4	x	x	PUNCT
ejpam-5241	404	5	∈	∈	PROPN
ejpam-5241	404	6	v	v	X
ejpam-5241	404	7	(	(	PUNCT
ejpam-5241	404	8	g	g	PROPN
ejpam-5241	404	9	+	+	PROPN
ejpam-5241	404	10	kn	kn	PROPN
ejpam-5241	404	11	)	)	PUNCT
ejpam-5241	404	12	\	\	PROPN
ejpam-5241	405	1	s.	s.	PROPN
ejpam-5241	405	2	then	then	ADV
ejpam-5241	405	3	x	x	PROPN
ejpam-5241	405	4	/∈	/∈	PROPN
ejpam-5241	405	5	c.	c.	NOUN
ejpam-5241	405	6	since	since	SCONJ
ejpam-5241	405	7	c	c	PROPN
ejpam-5241	405	8	is	be	AUX
ejpam-5241	405	9	a	a	DET
ejpam-5241	405	10	pointwise	pointwise	ADJ
ejpam-5241	405	11	non	non	ADJ
ejpam-5241	405	12	-	-	ADJ
ejpam-5241	405	13	dominating	dominating	ADJ
ejpam-5241	405	14	set	set	NOUN
ejpam-5241	405	15	,	,	PUNCT
ejpam-5241	405	16	there	there	PRON
ejpam-5241	405	17	exists	exist	VERB
ejpam-5241	405	18	y	y	PROPN
ejpam-5241	405	19	∈	∈	PROPN
ejpam-5241	405	20	c	c	PROPN
ejpam-5241	405	21	⊆	⊆	NUM
ejpam-5241	405	22	s	s	VERB
ejpam-5241	405	23	such	such	ADJ
ejpam-5241	405	24	that	that	PRON
ejpam-5241	405	25	dg+kn(x	dg+kn(x	PROPN
ejpam-5241	405	26	,	,	PUNCT
ejpam-5241	405	27	y	y	PROPN
ejpam-5241	405	28	)	)	PUNCT
ejpam-5241	405	29	=	=	SYM
ejpam-5241	405	30	dg(x	dg(x	X
ejpam-5241	405	31	,	,	PUNCT
ejpam-5241	405	32	y	y	NOUN
ejpam-5241	405	33	)	)	PUNCT
ejpam-5241	405	34	=	=	SYM
ejpam-5241	405	35	2	2	X
ejpam-5241	405	36	.	.	X
ejpam-5241	405	37	therefore	therefore	ADV
ejpam-5241	405	38	,	,	PUNCT
ejpam-5241	405	39	s	s	VERB
ejpam-5241	405	40	is	be	AUX
ejpam-5241	405	41	a	a	DET
ejpam-5241	405	42	closed	closed	ADJ
ejpam-5241	405	43	geodetic	geodetic	ADJ
ejpam-5241	405	44	hop	hop	NOUN
ejpam-5241	405	45	dominating	dominating	NOUN
ejpam-5241	405	46	set	set	NOUN
ejpam-5241	405	47	of	of	ADP
ejpam-5241	405	48	g+kn	g+kn	NOUN
ejpam-5241	405	49	.	.	PUNCT
ejpam-5241	406	1	corollary	corollary	ADJ
ejpam-5241	406	2	1	1	NUM
ejpam-5241	406	3	.	.	PUNCT
ejpam-5241	407	1	let	let	VERB
ejpam-5241	407	2	g	g	PRON
ejpam-5241	407	3	be	be	AUX
ejpam-5241	407	4	a	a	DET
ejpam-5241	407	5	noncomplete	noncomplete	ADJ
ejpam-5241	407	6	connected	connect	VERB
ejpam-5241	407	7	graph	graph	NOUN
ejpam-5241	407	8	and	and	CCONJ
ejpam-5241	407	9	n	n	PRON
ejpam-5241	407	10	≥	≥	NUM
ejpam-5241	407	11	1	1	NUM
ejpam-5241	407	12	.	.	PUNCT
ejpam-5241	408	1	then	then	ADV
ejpam-5241	408	2	γhcg(g+kn	γhcg(g+kn	NOUN
ejpam-5241	408	3	)	)	PUNCT
ejpam-5241	408	4	=	=	PUNCT
ejpam-5241	408	5	n+	n+	NUM
ejpam-5241	408	6	ρc2pnd(g	ρc2pnd(g	PROPN
ejpam-5241	408	7	)	)	PUNCT
ejpam-5241	408	8	.	.	PUNCT
ejpam-5241	409	1	example	example	NOUN
ejpam-5241	410	1	2	2	NUM
ejpam-5241	410	2	.	.	PUNCT
ejpam-5241	410	3	(	(	PUNCT
ejpam-5241	410	4	i	i	NOUN
ejpam-5241	410	5	)	)	PUNCT
ejpam-5241	410	6	γhcg(pn	γhcg(pn	PROPN
ejpam-5241	410	7	+	+	PROPN
ejpam-5241	410	8	kp	kp	NOUN
ejpam-5241	410	9	)	)	PUNCT
ejpam-5241	410	10	=	=	PRON
ejpam-5241	410	11	{	{	PUNCT
ejpam-5241	410	12	p+	p+	NOUN
ejpam-5241	410	13	3	3	NUM
ejpam-5241	410	14	if	if	SCONJ
ejpam-5241	410	15	n	n	NOUN
ejpam-5241	410	16	=	=	SYM
ejpam-5241	410	17	3	3	NUM
ejpam-5241	410	18	,	,	PUNCT
ejpam-5241	410	19	p+	p+	VERB
ejpam-5241	410	20	⌈n+1	⌈n+1	PROPN
ejpam-5241	410	21	2	2	NUM
ejpam-5241	410	22	⌉	⌉	NOUN
ejpam-5241	410	23	if	if	SCONJ
ejpam-5241	410	24	n	n	PRON
ejpam-5241	410	25	≥	≥	NOUN
ejpam-5241	410	26	4	4	NUM
ejpam-5241	410	27	,	,	PUNCT
ejpam-5241	410	28	(	(	PUNCT
ejpam-5241	410	29	ii	ii	NOUN
ejpam-5241	410	30	)	)	PUNCT
ejpam-5241	410	31	γhcg(cn	γhcg(cn	PROPN
ejpam-5241	410	32	+	+	PROPN
ejpam-5241	410	33	kp	kp	INTJ
ejpam-5241	410	34	)	)	PUNCT
ejpam-5241	410	35	=	=	PRON
ejpam-5241	410	36	{	{	PUNCT
ejpam-5241	410	37	p+	p+	NOUN
ejpam-5241	410	38	3	3	NUM
ejpam-5241	410	39	if	if	SCONJ
ejpam-5241	410	40	n	n	NOUN
ejpam-5241	410	41	=	=	SYM
ejpam-5241	410	42	3	3	NUM
ejpam-5241	410	43	,	,	PUNCT
ejpam-5241	410	44	4	4	NUM
ejpam-5241	410	45	,	,	PUNCT
ejpam-5241	410	46	p+	p+	VERB
ejpam-5241	410	47	⌈n2	⌈n2	NOUN
ejpam-5241	410	48	⌉	⌉	PUNCT
ejpam-5241	410	49	if	if	SCONJ
ejpam-5241	410	50	n	n	PRON
ejpam-5241	410	51	≥	≥	NOUN
ejpam-5241	410	52	5	5	NUM
ejpam-5241	410	53	.	.	PUNCT
ejpam-5241	410	54	a.	a.	PROPN
ejpam-5241	410	55	adolfo	adolfo	PROPN
ejpam-5241	410	56	,	,	PUNCT
ejpam-5241	410	57	i.	i.	PROPN
ejpam-5241	410	58	aniversario	aniversario	PROPN
ejpam-5241	410	59	,	,	PUNCT
ejpam-5241	410	60	f.	f.	PROPN
ejpam-5241	410	61	jamil	jamil	PROPN
ejpam-5241	410	62	/	/	SYM
ejpam-5241	410	63	eur	eur	PROPN
ejpam-5241	410	64	.	.	PUNCT
ejpam-5241	411	1	j.	j.	PROPN
ejpam-5241	411	2	pure	pure	PROPN
ejpam-5241	411	3	appl	appl	PROPN
ejpam-5241	411	4	.	.	PROPN
ejpam-5241	411	5	math	math	PROPN
ejpam-5241	411	6	,	,	PUNCT
ejpam-5241	411	7	17	17	NUM
ejpam-5241	411	8	(	(	PUNCT
ejpam-5241	411	9	3	3	NUM
ejpam-5241	411	10	)	)	PUNCT
ejpam-5241	411	11	(	(	PUNCT
ejpam-5241	411	12	2024	2024	NUM
ejpam-5241	411	13	)	)	PUNCT
ejpam-5241	411	14	,	,	PUNCT
ejpam-5241	411	15	1618	1618	NUM
ejpam-5241	411	16	-	-	SYM
ejpam-5241	411	17	1636	1636	NUM
ejpam-5241	411	18	1629	1629	NUM
ejpam-5241	411	19	theorem	theorem	NOUN
ejpam-5241	411	20	8	8	NUM
ejpam-5241	411	21	.	.	PUNCT
ejpam-5241	412	1	[	[	X
ejpam-5241	412	2	18	18	NUM
ejpam-5241	412	3	,	,	PUNCT
ejpam-5241	412	4	theorem	theorem	VERB
ejpam-5241	412	5	4	4	NUM
ejpam-5241	412	6	]	]	PUNCT
ejpam-5241	412	7	let	let	VERB
ejpam-5241	412	8	g	g	NOUN
ejpam-5241	412	9	and	and	CCONJ
ejpam-5241	412	10	h	h	NOUN
ejpam-5241	412	11	be	be	VERB
ejpam-5241	412	12	any	any	DET
ejpam-5241	412	13	graphs	graph	NOUN
ejpam-5241	412	14	.	.	PUNCT
ejpam-5241	413	1	a	a	DET
ejpam-5241	413	2	set	set	NOUN
ejpam-5241	413	3	s	s	NOUN
ejpam-5241	413	4	⊆	⊆	NUM
ejpam-5241	413	5	v	v	NOUN
ejpam-5241	413	6	(	(	PUNCT
ejpam-5241	413	7	g+h	g+h	NOUN
ejpam-5241	413	8	)	)	PUNCT
ejpam-5241	413	9	is	be	AUX
ejpam-5241	413	10	geodetic	geodetic	ADJ
ejpam-5241	413	11	hop	hop	NOUN
ejpam-5241	413	12	dominating	dominating	NOUN
ejpam-5241	413	13	set	set	NOUN
ejpam-5241	413	14	of	of	ADP
ejpam-5241	413	15	g+h	g+h	PROPN
ejpam-5241	413	16	if	if	SCONJ
ejpam-5241	413	17	and	and	CCONJ
ejpam-5241	413	18	only	only	ADV
ejpam-5241	413	19	if	if	SCONJ
ejpam-5241	413	20	s	s	NOUN
ejpam-5241	413	21	=	=	PUNCT
ejpam-5241	413	22	sg	sg	PROPN
ejpam-5241	413	23	∪sh	∪sh	NOUN
ejpam-5241	413	24	,	,	PUNCT
ejpam-5241	413	25	where	where	SCONJ
ejpam-5241	413	26	sg	sg	PROPN
ejpam-5241	413	27	and	and	CCONJ
ejpam-5241	413	28	sh	sh	PROPN
ejpam-5241	413	29	are	be	AUX
ejpam-5241	413	30	pointwise	pointwise	PROPN
ejpam-5241	413	31	non	non	ADJ
ejpam-5241	413	32	-	-	ADJ
ejpam-5241	413	33	dominating	dominating	ADJ
ejpam-5241	413	34	sets	set	NOUN
ejpam-5241	413	35	of	of	ADP
ejpam-5241	413	36	g	g	PROPN
ejpam-5241	413	37	and	and	CCONJ
ejpam-5241	413	38	h	h	NOUN
ejpam-5241	413	39	,	,	PUNCT
ejpam-5241	413	40	respectively	respectively	ADV
ejpam-5241	413	41	,	,	PUNCT
ejpam-5241	413	42	such	such	ADJ
ejpam-5241	413	43	that	that	SCONJ
ejpam-5241	413	44	(	(	PUNCT
ejpam-5241	413	45	i	i	NOUN
ejpam-5241	413	46	)	)	PUNCT
ejpam-5241	413	47	sg	sg	PROPN
ejpam-5241	413	48	is	be	AUX
ejpam-5241	413	49	a	a	DET
ejpam-5241	413	50	2	2	NUM
ejpam-5241	413	51	-	-	PUNCT
ejpam-5241	413	52	path	path	NOUN
ejpam-5241	413	53	closure	closure	NOUN
ejpam-5241	413	54	absorbing	absorb	VERB
ejpam-5241	413	55	set	set	NOUN
ejpam-5241	413	56	in	in	ADP
ejpam-5241	413	57	g	g	NOUN
ejpam-5241	413	58	whenever	whenever	SCONJ
ejpam-5241	413	59	⟨sh⟩	⟨sh⟩	PRON
ejpam-5241	413	60	is	be	AUX
ejpam-5241	413	61	a	a	DET
ejpam-5241	413	62	complete	complete	ADJ
ejpam-5241	413	63	subgraph	subgraph	NOUN
ejpam-5241	413	64	of	of	ADP
ejpam-5241	413	65	h	h	PROPN
ejpam-5241	413	66	and	and	CCONJ
ejpam-5241	413	67	(	(	PUNCT
ejpam-5241	413	68	ii	ii	NOUN
ejpam-5241	413	69	)	)	PUNCT
ejpam-5241	413	70	sh	sh	PROPN
ejpam-5241	413	71	is	be	AUX
ejpam-5241	413	72	a	a	DET
ejpam-5241	413	73	2	2	NUM
ejpam-5241	413	74	-	-	PUNCT
ejpam-5241	413	75	path	path	NOUN
ejpam-5241	413	76	closure	closure	NOUN
ejpam-5241	413	77	absorbing	absorb	VERB
ejpam-5241	413	78	set	set	NOUN
ejpam-5241	413	79	in	in	ADP
ejpam-5241	413	80	h	h	NOUN
ejpam-5241	413	81	whenever	whenever	SCONJ
ejpam-5241	413	82	⟨sg⟩	⟨sg⟩	PRON
ejpam-5241	413	83	is	be	AUX
ejpam-5241	413	84	a	a	DET
ejpam-5241	413	85	complete	complete	ADJ
ejpam-5241	413	86	subgraph	subgraph	NOUN
ejpam-5241	413	87	of	of	ADP
ejpam-5241	413	88	g.	g.	PROPN
ejpam-5241	413	89	part	part	NOUN
ejpam-5241	413	90	of	of	ADP
ejpam-5241	413	91	theorem	theorem	ADJ
ejpam-5241	413	92	9	9	NUM
ejpam-5241	413	93	asserts	assert	VERB
ejpam-5241	413	94	that	that	SCONJ
ejpam-5241	413	95	under	under	ADP
ejpam-5241	413	96	the	the	DET
ejpam-5241	413	97	same	same	ADJ
ejpam-5241	413	98	condition	condition	NOUN
ejpam-5241	413	99	,	,	PUNCT
ejpam-5241	413	100	s	s	PART
ejpam-5241	413	101	is	be	AUX
ejpam-5241	413	102	a	a	DET
ejpam-5241	413	103	hop	hop	NOUN
ejpam-5241	413	104	dominating	dominating	NOUN
ejpam-5241	413	105	set	set	NOUN
ejpam-5241	413	106	of	of	ADP
ejpam-5241	413	107	g+h	g+h	PROPN
ejpam-5241	414	1	if	if	SCONJ
ejpam-5241	414	2	and	and	CCONJ
ejpam-5241	414	3	only	only	ADV
ejpam-5241	414	4	if	if	SCONJ
ejpam-5241	414	5	sg	sg	PROPN
ejpam-5241	414	6	and	and	CCONJ
ejpam-5241	414	7	sh	sh	PROPN
ejpam-5241	414	8	are	be	AUX
ejpam-5241	414	9	pointwise	pointwise	PROPN
ejpam-5241	414	10	non	non	ADJ
ejpam-5241	414	11	-	-	ADJ
ejpam-5241	414	12	dominating	dominating	ADJ
ejpam-5241	414	13	sets	set	NOUN
ejpam-5241	414	14	of	of	ADP
ejpam-5241	414	15	g	g	NOUN
ejpam-5241	414	16	andh	andh	NOUN
ejpam-5241	414	17	,	,	PUNCT
ejpam-5241	414	18	respectively	respectively	ADV
ejpam-5241	414	19	.	.	PUNCT
ejpam-5241	415	1	theorem	theorem	VERB
ejpam-5241	415	2	9	9	NUM
ejpam-5241	415	3	.	.	PUNCT
ejpam-5241	416	1	let	let	VERB
ejpam-5241	416	2	g	g	NOUN
ejpam-5241	416	3	and	and	CCONJ
ejpam-5241	416	4	h	h	NOUN
ejpam-5241	416	5	be	be	AUX
ejpam-5241	416	6	connected	connect	VERB
ejpam-5241	416	7	noncomplete	noncomplete	ADJ
ejpam-5241	416	8	graphs	graph	NOUN
ejpam-5241	416	9	.	.	PUNCT
ejpam-5241	417	1	then	then	ADV
ejpam-5241	417	2	s	s	VERB
ejpam-5241	417	3	is	be	AUX
ejpam-5241	417	4	a	a	DET
ejpam-5241	417	5	closed	closed	ADJ
ejpam-5241	417	6	geodetic	geodetic	ADJ
ejpam-5241	417	7	hop	hop	NOUN
ejpam-5241	417	8	dominating	dominating	NOUN
ejpam-5241	417	9	set	set	NOUN
ejpam-5241	417	10	of	of	ADP
ejpam-5241	417	11	g	g	PROPN
ejpam-5241	417	12	if	if	SCONJ
ejpam-5241	417	13	and	and	CCONJ
ejpam-5241	417	14	only	only	ADV
ejpam-5241	417	15	if	if	SCONJ
ejpam-5241	417	16	s	s	VERB
ejpam-5241	417	17	=	=	PUNCT
ejpam-5241	417	18	sg	sg	X
ejpam-5241	417	19	∪	∪	NOUN
ejpam-5241	417	20	sh	sh	PROPN
ejpam-5241	417	21	where	where	SCONJ
ejpam-5241	417	22	sg	sg	PROPN
ejpam-5241	417	23	and	and	CCONJ
ejpam-5241	417	24	sh	sh	PROPN
ejpam-5241	417	25	are	be	AUX
ejpam-5241	417	26	pointwise	pointwise	PROPN
ejpam-5241	417	27	non	non	ADJ
ejpam-5241	417	28	-	-	ADJ
ejpam-5241	417	29	dominating	dominating	ADJ
ejpam-5241	417	30	sets	set	NOUN
ejpam-5241	417	31	of	of	ADP
ejpam-5241	417	32	g	g	PROPN
ejpam-5241	417	33	and	and	CCONJ
ejpam-5241	417	34	h	h	NOUN
ejpam-5241	417	35	,	,	PUNCT
ejpam-5241	417	36	respectively	respectively	ADV
ejpam-5241	417	37	,	,	PUNCT
ejpam-5241	417	38	such	such	ADJ
ejpam-5241	417	39	that	that	SCONJ
ejpam-5241	417	40	either	either	CCONJ
ejpam-5241	417	41	(	(	PUNCT
ejpam-5241	417	42	i	i	NOUN
ejpam-5241	417	43	)	)	PUNCT
ejpam-5241	417	44	⟨sg⟩	⟨sg⟩	PRON
ejpam-5241	417	45	is	be	AUX
ejpam-5241	417	46	complete	complete	ADJ
ejpam-5241	417	47	and	and	CCONJ
ejpam-5241	417	48	sh	sh	INTJ
ejpam-5241	417	49	is	be	AUX
ejpam-5241	417	50	a	a	DET
ejpam-5241	417	51	closed	closed	ADJ
ejpam-5241	417	52	2	2	NUM
ejpam-5241	417	53	-	-	PUNCT
ejpam-5241	417	54	path	path	NOUN
ejpam-5241	417	55	closure	closure	NOUN
ejpam-5241	417	56	absorbing	absorb	VERB
ejpam-5241	417	57	set	set	NOUN
ejpam-5241	417	58	of	of	ADP
ejpam-5241	417	59	h	h	NOUN
ejpam-5241	417	60	;	;	PUNCT
ejpam-5241	417	61	or	or	CCONJ
ejpam-5241	417	62	(	(	PUNCT
ejpam-5241	417	63	ii	ii	NOUN
ejpam-5241	417	64	)	)	PUNCT
ejpam-5241	417	65	⟨sh⟩	⟨sh⟩	NUM
ejpam-5241	417	66	is	be	AUX
ejpam-5241	417	67	complete	complete	ADJ
ejpam-5241	417	68	and	and	CCONJ
ejpam-5241	417	69	sg	sg	PROPN
ejpam-5241	417	70	is	be	AUX
ejpam-5241	417	71	a	a	DET
ejpam-5241	417	72	closed	closed	ADJ
ejpam-5241	417	73	2	2	NUM
ejpam-5241	417	74	-	-	PUNCT
ejpam-5241	417	75	path	path	NOUN
ejpam-5241	417	76	closure	closure	NOUN
ejpam-5241	417	77	absorbing	absorb	VERB
ejpam-5241	417	78	set	set	NOUN
ejpam-5241	417	79	of	of	ADP
ejpam-5241	417	80	g.	g.	PROPN
ejpam-5241	417	81	proof	proof	PROPN
ejpam-5241	417	82	.	.	PUNCT
ejpam-5241	418	1	suppose	suppose	VERB
ejpam-5241	418	2	that	that	SCONJ
ejpam-5241	418	3	s	s	VERB
ejpam-5241	418	4	is	be	AUX
ejpam-5241	418	5	a	a	DET
ejpam-5241	418	6	closed	closed	ADJ
ejpam-5241	418	7	geodetic	geodetic	ADJ
ejpam-5241	418	8	hop	hop	NOUN
ejpam-5241	418	9	dominating	dominating	NOUN
ejpam-5241	418	10	set	set	NOUN
ejpam-5241	418	11	of	of	ADP
ejpam-5241	418	12	g	g	PROPN
ejpam-5241	418	13	+	+	CCONJ
ejpam-5241	418	14	h.	h.	PROPN
ejpam-5241	418	15	then	then	ADV
ejpam-5241	418	16	sg	sg	PROPN
ejpam-5241	418	17	and	and	CCONJ
ejpam-5241	418	18	sh	sh	PROPN
ejpam-5241	418	19	are	be	AUX
ejpam-5241	418	20	pointwise	pointwise	PROPN
ejpam-5241	418	21	non	non	ADJ
ejpam-5241	418	22	-	-	ADJ
ejpam-5241	418	23	dominating	dominating	ADJ
ejpam-5241	418	24	sets	set	NOUN
ejpam-5241	418	25	of	of	ADP
ejpam-5241	418	26	g	g	PROPN
ejpam-5241	418	27	and	and	CCONJ
ejpam-5241	418	28	h	h	NOUN
ejpam-5241	418	29	,	,	PUNCT
ejpam-5241	418	30	respectively	respectively	ADV
ejpam-5241	418	31	.	.	PUNCT
ejpam-5241	419	1	since	since	SCONJ
ejpam-5241	419	2	s	s	PROPN
ejpam-5241	419	3	is	be	AUX
ejpam-5241	419	4	a	a	DET
ejpam-5241	419	5	closed	closed	ADJ
ejpam-5241	419	6	geodetic	geodetic	ADJ
ejpam-5241	419	7	set	set	NOUN
ejpam-5241	419	8	of	of	ADP
ejpam-5241	419	9	g+h	g+h	PROPN
ejpam-5241	419	10	,	,	PUNCT
ejpam-5241	419	11	there	there	PRON
ejpam-5241	419	12	is	be	VERB
ejpam-5241	419	13	a	a	DET
ejpam-5241	419	14	positive	positive	ADJ
ejpam-5241	419	15	integer	integer	NOUN
ejpam-5241	419	16	k	k	NOUN
ejpam-5241	419	17	and	and	CCONJ
ejpam-5241	419	18	sequence	sequence	NOUN
ejpam-5241	419	19	of	of	ADP
ejpam-5241	419	20	sets	set	NOUN
ejpam-5241	419	21	sj	sj	INTJ
ejpam-5241	419	22	=	=	PUNCT
ejpam-5241	419	23	{	{	PUNCT
ejpam-5241	419	24	x1	x1	PROPN
ejpam-5241	419	25	,	,	PUNCT
ejpam-5241	419	26	x2	x2	PROPN
ejpam-5241	419	27	,	,	PUNCT
ejpam-5241	419	28	.	.	PUNCT
ejpam-5241	419	29	.	.	PUNCT
ejpam-5241	420	1	.	.	PUNCT
ejpam-5241	421	1	,	,	PUNCT
ejpam-5241	421	2	xj	xj	PROPN
ejpam-5241	421	3	}	}	PUNCT
ejpam-5241	421	4	(	(	PUNCT
ejpam-5241	421	5	j	j	NOUN
ejpam-5241	421	6	=	=	SYM
ejpam-5241	421	7	1	1	NUM
ejpam-5241	421	8	,	,	PUNCT
ejpam-5241	421	9	2	2	NUM
ejpam-5241	421	10	,	,	PUNCT
ejpam-5241	421	11	.	.	PUNCT
ejpam-5241	421	12	.	.	PUNCT
ejpam-5241	422	1	.	.	PUNCT
ejpam-5241	423	1	,	,	PUNCT
ejpam-5241	423	2	k	k	X
ejpam-5241	423	3	)	)	PUNCT
ejpam-5241	423	4	such	such	ADJ
ejpam-5241	423	5	that	that	SCONJ
ejpam-5241	423	6	x1	x1	PROPN
ejpam-5241	423	7	̸=	̸=	PROPN
ejpam-5241	423	8	x2	x2	PROPN
ejpam-5241	423	9	,	,	PUNCT
ejpam-5241	423	10	ig+h	ig+h	PROPN
ejpam-5241	423	11	[	[	X
ejpam-5241	423	12	sk	sk	X
ejpam-5241	423	13	]	]	X
ejpam-5241	423	14	=	=	SYM
ejpam-5241	423	15	ig+h	ig+h	PROPN
ejpam-5241	424	1	[	[	X
ejpam-5241	424	2	s	s	X
ejpam-5241	424	3	]	]	X
ejpam-5241	424	4	=	=	SYM
ejpam-5241	424	5	v	v	X
ejpam-5241	424	6	(	(	PUNCT
ejpam-5241	424	7	g	g	NOUN
ejpam-5241	424	8	)	)	PUNCT
ejpam-5241	424	9	and	and	CCONJ
ejpam-5241	424	10	xj	xj	PROPN
ejpam-5241	424	11	/∈	/∈	PUNCT
ejpam-5241	425	1	ig+h	ig+h	PRON
ejpam-5241	426	1	[	[	X
ejpam-5241	426	2	sj−1	sj−1	NOUN
ejpam-5241	426	3	]	]	PUNCT
ejpam-5241	426	4	for	for	ADP
ejpam-5241	426	5	3	3	NUM
ejpam-5241	426	6	≤	≤	NUM
ejpam-5241	426	7	j	j	PROPN
ejpam-5241	426	8	≤	≤	PROPN
ejpam-5241	426	9	k.	k.	PROPN
ejpam-5241	427	1	first	first	ADV
ejpam-5241	427	2	,	,	PUNCT
ejpam-5241	427	3	we	we	PRON
ejpam-5241	427	4	claim	claim	VERB
ejpam-5241	427	5	that	that	SCONJ
ejpam-5241	427	6	⟨sg⟩	⟨sg⟩	PRON
ejpam-5241	427	7	is	be	AUX
ejpam-5241	427	8	a	a	DET
ejpam-5241	427	9	complete	complete	ADJ
ejpam-5241	427	10	subgraph	subgraph	NOUN
ejpam-5241	427	11	of	of	ADP
ejpam-5241	427	12	g	g	PROPN
ejpam-5241	427	13	or	or	CCONJ
ejpam-5241	427	14	⟨sh⟩	⟨sh⟩	NOUN
ejpam-5241	427	15	is	be	AUX
ejpam-5241	427	16	a	a	DET
ejpam-5241	427	17	complete	complete	ADJ
ejpam-5241	427	18	subgraph	subgraph	NOUN
ejpam-5241	427	19	of	of	ADP
ejpam-5241	427	20	h.	h.	PROPN
ejpam-5241	427	21	suppose	suppose	VERB
ejpam-5241	427	22	this	this	DET
ejpam-5241	427	23	claim	claim	NOUN
ejpam-5241	427	24	is	be	AUX
ejpam-5241	427	25	false	false	ADJ
ejpam-5241	427	26	.	.	PUNCT
ejpam-5241	428	1	if	if	SCONJ
ejpam-5241	428	2	⟨sg⟩	⟨sg⟩	PRON
ejpam-5241	428	3	and	and	CCONJ
ejpam-5241	428	4	⟨sh⟩	⟨sh⟩	NOUN
ejpam-5241	428	5	are	be	AUX
ejpam-5241	428	6	noncomplete	noncomplete	ADJ
ejpam-5241	428	7	,	,	PUNCT
ejpam-5241	428	8	then	then	ADV
ejpam-5241	428	9	there	there	PRON
ejpam-5241	428	10	exist	exist	VERB
ejpam-5241	428	11	distinct	distinct	ADJ
ejpam-5241	428	12	integers	integer	NOUN
ejpam-5241	428	13	i	i	PRON
ejpam-5241	428	14	,	,	PUNCT
ejpam-5241	428	15	j	j	PROPN
ejpam-5241	428	16	,	,	PUNCT
ejpam-5241	428	17	l	l	PROPN
ejpam-5241	428	18	,	,	PUNCT
ejpam-5241	428	19	r	r	NOUN
ejpam-5241	428	20	such	such	ADJ
ejpam-5241	428	21	that	that	DET
ejpam-5241	428	22	xi	xi	PROPN
ejpam-5241	428	23	,	,	PUNCT
ejpam-5241	428	24	xj	xj	PROPN
ejpam-5241	428	25	∈	∈	PROPN
ejpam-5241	428	26	sg	sg	PROPN
ejpam-5241	428	27	with	with	ADP
ejpam-5241	428	28	dg(xi	dg(xi	PROPN
ejpam-5241	428	29	,	,	PUNCT
ejpam-5241	428	30	xj	xj	PROPN
ejpam-5241	428	31	)	)	PUNCT
ejpam-5241	428	32	=	=	SYM
ejpam-5241	428	33	2	2	NUM
ejpam-5241	428	34	and	and	CCONJ
ejpam-5241	428	35	xl	xl	PROPN
ejpam-5241	428	36	,	,	PUNCT
ejpam-5241	428	37	xr	xr	PROPN
ejpam-5241	428	38	∈	∈	PROPN
ejpam-5241	428	39	sh	sh	PROPN
ejpam-5241	428	40	with	with	ADP
ejpam-5241	428	41	dg(xl	dg(xl	NOUN
ejpam-5241	428	42	,	,	PUNCT
ejpam-5241	428	43	xr	xr	X
ejpam-5241	428	44	)	)	PUNCT
ejpam-5241	428	45	=	=	PUNCT
ejpam-5241	428	46	2	2	X
ejpam-5241	428	47	.	.	NOUN
ejpam-5241	428	48	without	without	ADP
ejpam-5241	428	49	loss	loss	NOUN
ejpam-5241	428	50	of	of	ADP
ejpam-5241	428	51	generality	generality	NOUN
ejpam-5241	428	52	,	,	PUNCT
ejpam-5241	428	53	assume	assume	VERB
ejpam-5241	428	54	that	that	SCONJ
ejpam-5241	428	55	l	l	NOUN
ejpam-5241	428	56	=	=	PUNCT
ejpam-5241	428	57	max{i	max{i	X
ejpam-5241	428	58	,	,	PUNCT
ejpam-5241	428	59	j	j	NOUN
ejpam-5241	428	60	,	,	PUNCT
ejpam-5241	428	61	l	l	NOUN
ejpam-5241	428	62	,	,	PUNCT
ejpam-5241	428	63	r	r	NOUN
ejpam-5241	428	64	}	}	PUNCT
ejpam-5241	428	65	.	.	PUNCT
ejpam-5241	429	1	since	since	SCONJ
ejpam-5241	429	2	xl	xl	PROPN
ejpam-5241	429	3	∈	∈	PROPN
ejpam-5241	429	4	ig+h(xi	ig+h(xi	PROPN
ejpam-5241	429	5	,	,	PUNCT
ejpam-5241	429	6	xj	xj	PROPN
ejpam-5241	429	7	)	)	PUNCT
ejpam-5241	429	8	,	,	PUNCT
ejpam-5241	429	9	xl	xl	PROPN
ejpam-5241	429	10	∈	∈	PROPN
ejpam-5241	429	11	ig+h	ig+h	PROPN
ejpam-5241	429	12	[	[	X
ejpam-5241	429	13	sl−1	sl−1	X
ejpam-5241	429	14	]	]	X
ejpam-5241	429	15	,	,	PUNCT
ejpam-5241	429	16	a	a	DET
ejpam-5241	429	17	contradiction	contradiction	NOUN
ejpam-5241	429	18	.	.	PUNCT
ejpam-5241	430	1	the	the	DET
ejpam-5241	430	2	claim	claim	NOUN
ejpam-5241	430	3	,	,	PUNCT
ejpam-5241	430	4	therefore	therefore	ADV
ejpam-5241	430	5	,	,	PUNCT
ejpam-5241	430	6	is	be	AUX
ejpam-5241	430	7	true	true	ADJ
ejpam-5241	430	8	.	.	PUNCT
ejpam-5241	431	1	next	next	ADV
ejpam-5241	431	2	,	,	PUNCT
ejpam-5241	431	3	suppose	suppose	VERB
ejpam-5241	431	4	⟨sg⟩	⟨sg⟩	PRON
ejpam-5241	431	5	is	be	AUX
ejpam-5241	431	6	a	a	DET
ejpam-5241	431	7	complete	complete	ADJ
ejpam-5241	431	8	subgraph	subgraph	NOUN
ejpam-5241	431	9	of	of	ADP
ejpam-5241	431	10	g.	g.	PROPN
ejpam-5241	431	11	write	write	VERB
ejpam-5241	431	12	sh	sh	PROPN
ejpam-5241	431	13	=	=	PUNCT
ejpam-5241	431	14	{	{	PUNCT
ejpam-5241	431	15	xn1	xn1	X
ejpam-5241	431	16	,	,	PUNCT
ejpam-5241	431	17	xn2	xn2	PROPN
ejpam-5241	431	18	,	,	PUNCT
ejpam-5241	431	19	.	.	PUNCT
ejpam-5241	431	20	.	.	PUNCT
ejpam-5241	431	21	.	.	PUNCT
ejpam-5241	432	1	,	,	PUNCT
ejpam-5241	432	2	xnl	xnl	PROPN
ejpam-5241	432	3	}	}	PUNCT
ejpam-5241	432	4	⊆	⊆	NUM
ejpam-5241	432	5	sk	sk	NOUN
ejpam-5241	432	6	with	with	ADP
ejpam-5241	432	7	n1	n1	PROPN
ejpam-5241	432	8	<	<	X
ejpam-5241	432	9	n2	n2	X
ejpam-5241	432	10	<	<	X
ejpam-5241	432	11	·	·	PUNCT
ejpam-5241	432	12	·	·	PUNCT
ejpam-5241	432	13	·	·	PUNCT
ejpam-5241	433	1	<	<	X
ejpam-5241	433	2	nl	nl	PROPN
ejpam-5241	433	3	,	,	PUNCT
ejpam-5241	433	4	and	and	CCONJ
ejpam-5241	433	5	let	let	VERB
ejpam-5241	433	6	aj	aj	PROPN
ejpam-5241	433	7	=	=	PRON
ejpam-5241	433	8	{	{	PUNCT
ejpam-5241	433	9	xn1	xn1	PROPN
ejpam-5241	433	10	,	,	PUNCT
ejpam-5241	433	11	xn2	xn2	PROPN
ejpam-5241	433	12	,	,	PUNCT
ejpam-5241	433	13	.	.	PUNCT
ejpam-5241	433	14	.	.	PUNCT
ejpam-5241	433	15	.	.	PUNCT
ejpam-5241	434	1	,	,	PUNCT
ejpam-5241	434	2	xnj	xnj	PROPN
ejpam-5241	434	3	}	}	PUNCT
ejpam-5241	434	4	for	for	ADP
ejpam-5241	434	5	each	each	PRON
ejpam-5241	434	6	j	j	PROPN
ejpam-5241	434	7	=	=	SYM
ejpam-5241	434	8	1	1	NUM
ejpam-5241	434	9	,	,	PUNCT
ejpam-5241	434	10	2	2	NUM
ejpam-5241	434	11	,	,	PUNCT
ejpam-5241	434	12	.	.	PUNCT
ejpam-5241	434	13	.	.	PUNCT
ejpam-5241	435	1	.	.	PUNCT
ejpam-5241	436	1	,	,	PUNCT
ejpam-5241	436	2	l.	l.	PROPN
ejpam-5241	436	3	as	as	SCONJ
ejpam-5241	436	4	shown	show	VERB
ejpam-5241	436	5	in	in	ADP
ejpam-5241	436	6	the	the	DET
ejpam-5241	436	7	proof	proof	NOUN
ejpam-5241	436	8	of	of	ADP
ejpam-5241	436	9	theorem	theorem	NOUN
ejpam-5241	436	10	7	7	NUM
ejpam-5241	436	11	,	,	PUNCT
ejpam-5241	436	12	xnj	xnj	PROPN
ejpam-5241	436	13	/∈	/∈	PUNCT
ejpam-5241	437	1	p2[aj−1	p2[aj−1	NOUN
ejpam-5241	437	2	]	]	PUNCT
ejpam-5241	437	3	for	for	ADP
ejpam-5241	437	4	3	3	NUM
ejpam-5241	437	5	≤	≤	NUM
ejpam-5241	437	6	j	j	PROPN
ejpam-5241	437	7	≤	≤	PROPN
ejpam-5241	437	8	l	l	NOUN
ejpam-5241	437	9	,	,	PUNCT
ejpam-5241	437	10	and	and	CCONJ
ejpam-5241	437	11	p2[al	p2[al	ADJ
ejpam-5241	437	12	]	]	X
ejpam-5241	437	13	=	=	SYM
ejpam-5241	437	14	v	v	X
ejpam-5241	437	15	(	(	PUNCT
ejpam-5241	437	16	h	h	NOUN
ejpam-5241	437	17	)	)	PUNCT
ejpam-5241	437	18	.	.	PUNCT
ejpam-5241	438	1	therefore	therefore	ADV
ejpam-5241	438	2	,	,	PUNCT
ejpam-5241	438	3	sh	sh	PROPN
ejpam-5241	438	4	is	be	AUX
ejpam-5241	438	5	a	a	DET
ejpam-5241	438	6	closed	closed	ADJ
ejpam-5241	438	7	2	2	NUM
ejpam-5241	438	8	-	-	PUNCT
ejpam-5241	438	9	path	path	NOUN
ejpam-5241	438	10	closure	closure	NOUN
ejpam-5241	438	11	absorbing	absorb	VERB
ejpam-5241	438	12	set	set	NOUN
ejpam-5241	438	13	of	of	ADP
ejpam-5241	438	14	h.	h.	NOUN
ejpam-5241	438	15	similarly	similarly	ADV
ejpam-5241	438	16	,	,	PUNCT
ejpam-5241	438	17	if	if	SCONJ
ejpam-5241	438	18	⟨sh⟩	⟨sh⟩	PRON
ejpam-5241	438	19	is	be	AUX
ejpam-5241	438	20	complete	complete	ADJ
ejpam-5241	438	21	,	,	PUNCT
ejpam-5241	438	22	then	then	ADV
ejpam-5241	438	23	sg	sg	PROPN
ejpam-5241	438	24	is	be	AUX
ejpam-5241	438	25	a	a	DET
ejpam-5241	438	26	closed	closed	ADJ
ejpam-5241	438	27	2	2	NUM
ejpam-5241	438	28	-	-	PUNCT
ejpam-5241	438	29	path	path	NOUN
ejpam-5241	438	30	closure	closure	NOUN
ejpam-5241	438	31	absorbing	absorb	VERB
ejpam-5241	438	32	set	set	NOUN
ejpam-5241	438	33	of	of	ADP
ejpam-5241	438	34	g.	g.	PROPN
ejpam-5241	438	35	in	in	ADP
ejpam-5241	438	36	view	view	NOUN
ejpam-5241	438	37	of	of	ADP
ejpam-5241	438	38	lemma	lemma	PROPN
ejpam-5241	438	39	2	2	NUM
ejpam-5241	438	40	,	,	PUNCT
ejpam-5241	438	41	conditions	condition	NOUN
ejpam-5241	438	42	(	(	PUNCT
ejpam-5241	438	43	i	i	NOUN
ejpam-5241	438	44	)	)	PUNCT
ejpam-5241	438	45	and	and	CCONJ
ejpam-5241	438	46	(	(	PUNCT
ejpam-5241	438	47	ii	ii	NOUN
ejpam-5241	438	48	)	)	PUNCT
ejpam-5241	438	49	can	can	AUX
ejpam-5241	438	50	not	not	PART
ejpam-5241	438	51	hold	hold	VERB
ejpam-5241	438	52	at	at	ADP
ejpam-5241	438	53	the	the	DET
ejpam-5241	438	54	same	same	ADJ
ejpam-5241	438	55	time	time	NOUN
ejpam-5241	438	56	.	.	PUNCT
ejpam-5241	439	1	conversely	conversely	ADV
ejpam-5241	439	2	,	,	PUNCT
ejpam-5241	439	3	suppose	suppose	VERB
ejpam-5241	439	4	that	that	SCONJ
ejpam-5241	439	5	sg	sg	PROPN
ejpam-5241	439	6	and	and	CCONJ
ejpam-5241	439	7	sh	sh	PROPN
ejpam-5241	439	8	are	be	AUX
ejpam-5241	439	9	pointwise	pointwise	PROPN
ejpam-5241	439	10	non	non	ADJ
ejpam-5241	439	11	-	-	ADJ
ejpam-5241	439	12	dominating	dominating	ADJ
ejpam-5241	439	13	sets	set	NOUN
ejpam-5241	439	14	of	of	ADP
ejpam-5241	439	15	g	g	PROPN
ejpam-5241	439	16	and	and	CCONJ
ejpam-5241	439	17	h	h	NOUN
ejpam-5241	439	18	,	,	PUNCT
ejpam-5241	439	19	respectively	respectively	ADV
ejpam-5241	439	20	.	.	PUNCT
ejpam-5241	440	1	then	then	ADV
ejpam-5241	440	2	s	s	VERB
ejpam-5241	440	3	=	=	PUNCT
ejpam-5241	440	4	sg	sg	PROPN
ejpam-5241	440	5	∪	∪	NOUN
ejpam-5241	440	6	sh	sh	PROPN
ejpam-5241	440	7	is	be	AUX
ejpam-5241	440	8	a	a	DET
ejpam-5241	440	9	hop	hop	NOUN
ejpam-5241	440	10	dominating	dominating	NOUN
ejpam-5241	440	11	set	set	NOUN
ejpam-5241	440	12	of	of	ADP
ejpam-5241	440	13	g+h	g+h	PROPN
ejpam-5241	440	14	.	.	PUNCT
ejpam-5241	441	1	suppose	suppose	VERB
ejpam-5241	441	2	further	far	ADV
ejpam-5241	441	3	that	that	DET
ejpam-5241	441	4	condition	condition	NOUN
ejpam-5241	441	5	(	(	PUNCT
ejpam-5241	441	6	i	i	NOUN
ejpam-5241	441	7	)	)	PUNCT
ejpam-5241	441	8	holds	hold	VERB
ejpam-5241	441	9	,	,	PUNCT
ejpam-5241	441	10	i.e.	i.e.	X
ejpam-5241	441	11	,	,	PUNCT
ejpam-5241	441	12	⟨sg⟩	⟨sg⟩	PRON
ejpam-5241	441	13	is	be	AUX
ejpam-5241	441	14	complete	complete	ADJ
ejpam-5241	441	15	and	and	CCONJ
ejpam-5241	441	16	sh	sh	INTJ
ejpam-5241	441	17	is	be	AUX
ejpam-5241	441	18	a	a	DET
ejpam-5241	441	19	closed	closed	ADJ
ejpam-5241	441	20	2	2	NUM
ejpam-5241	441	21	-	-	PUNCT
ejpam-5241	441	22	path	path	NOUN
ejpam-5241	441	23	closure	closure	NOUN
ejpam-5241	441	24	absorbing	absorb	VERB
ejpam-5241	441	25	set	set	NOUN
ejpam-5241	441	26	of	of	ADP
ejpam-5241	441	27	h.	h.	PROPN
ejpam-5241	441	28	let	let	VERB
ejpam-5241	441	29	k	k	PROPN
ejpam-5241	441	30	=	=	SYM
ejpam-5241	441	31	|sg|	|sg|	PROPN
ejpam-5241	441	32	=	=	SYM
ejpam-5241	441	33	k	k	PROPN
ejpam-5241	441	34	and	and	CCONJ
ejpam-5241	441	35	j	j	PROPN
ejpam-5241	441	36	=	=	PUNCT
ejpam-5241	441	37	|sh	|sh	VERB
ejpam-5241	441	38	|	|	ADV
ejpam-5241	441	39	.	.	PUNCT
ejpam-5241	442	1	there	there	PRON
ejpam-5241	442	2	is	be	VERB
ejpam-5241	442	3	a	a	DET
ejpam-5241	442	4	sequence	sequence	NOUN
ejpam-5241	442	5	of	of	ADP
ejpam-5241	442	6	sets	set	NOUN
ejpam-5241	442	7	ci	ci	NOUN
ejpam-5241	442	8	=	=	SYM
ejpam-5241	442	9	{	{	PUNCT
ejpam-5241	442	10	v1	v1	PROPN
ejpam-5241	442	11	,	,	PUNCT
ejpam-5241	442	12	v2	v2	PROPN
ejpam-5241	442	13	,	,	PUNCT
ejpam-5241	442	14	.	.	PUNCT
ejpam-5241	442	15	.	.	PUNCT
ejpam-5241	443	1	.	.	PUNCT
ejpam-5241	444	1	,	,	PUNCT
ejpam-5241	444	2	vi	vi	X
ejpam-5241	444	3	}	}	PUNCT
ejpam-5241	444	4	(	(	PUNCT
ejpam-5241	444	5	i	i	NOUN
ejpam-5241	444	6	=	=	NOUN
ejpam-5241	444	7	1	1	NUM
ejpam-5241	444	8	,	,	PUNCT
ejpam-5241	444	9	2	2	NUM
ejpam-5241	444	10	,	,	PUNCT
ejpam-5241	444	11	.	.	PUNCT
ejpam-5241	444	12	.	.	PUNCT
ejpam-5241	444	13	.	.	PUNCT
ejpam-5241	445	1	,	,	PUNCT
ejpam-5241	445	2	j	j	NOUN
ejpam-5241	445	3	)	)	PUNCT
ejpam-5241	445	4	such	such	ADJ
ejpam-5241	445	5	that	that	DET
ejpam-5241	445	6	v1	v1	NOUN
ejpam-5241	445	7	̸=	̸=	PROPN
ejpam-5241	445	8	v2	v2	PROPN
ejpam-5241	445	9	,	,	PUNCT
ejpam-5241	445	10	vi	vi	NOUN
ejpam-5241	445	11	/∈	/∈	PUNCT
ejpam-5241	446	1	p2[ci−1	p2[ci−1	PROPN
ejpam-5241	446	2	]	]	PUNCT
ejpam-5241	446	3	for	for	ADP
ejpam-5241	446	4	2	2	NUM
ejpam-5241	446	5	≤	≤	NUM
ejpam-5241	446	6	i	i	PRON
ejpam-5241	446	7	≤	≤	ADJ
ejpam-5241	446	8	j	j	PROPN
ejpam-5241	446	9	and	and	CCONJ
ejpam-5241	446	10	p2[cj	p2[cj	PROPN
ejpam-5241	446	11	]	]	PUNCT
ejpam-5241	446	12	=	=	SYM
ejpam-5241	446	13	v	v	X
ejpam-5241	446	14	(	(	PUNCT
ejpam-5241	446	15	h	h	NOUN
ejpam-5241	446	16	)	)	PUNCT
ejpam-5241	446	17	.	.	PUNCT
ejpam-5241	447	1	for	for	ADP
ejpam-5241	447	2	i	i	PRON
ejpam-5241	447	3	=	=	NOUN
ejpam-5241	447	4	1	1	NUM
ejpam-5241	447	5	,	,	PUNCT
ejpam-5241	447	6	2	2	NUM
ejpam-5241	447	7	,	,	PUNCT
ejpam-5241	447	8	.	.	PUNCT
ejpam-5241	447	9	.	.	PUNCT
ejpam-5241	447	10	.	.	PUNCT
ejpam-5241	448	1	,	,	PUNCT
ejpam-5241	449	1	k	k	PROPN
ejpam-5241	449	2	+	+	CCONJ
ejpam-5241	449	3	j	j	PROPN
ejpam-5241	449	4	,	,	PUNCT
ejpam-5241	449	5	write	write	VERB
ejpam-5241	449	6	si	si	X
ejpam-5241	449	7	=	=	PUNCT
ejpam-5241	449	8	{	{	PUNCT
ejpam-5241	449	9	x1	x1	PROPN
ejpam-5241	449	10	,	,	PUNCT
ejpam-5241	449	11	x2	x2	PROPN
ejpam-5241	449	12	,	,	PUNCT
ejpam-5241	449	13	.	.	PUNCT
ejpam-5241	449	14	.	.	PUNCT
ejpam-5241	450	1	.	.	PUNCT
ejpam-5241	451	1	,	,	PUNCT
ejpam-5241	451	2	xi	xi	ADP
ejpam-5241	451	3	}	}	PUNCT
ejpam-5241	451	4	,	,	PUNCT
ejpam-5241	451	5	where	where	SCONJ
ejpam-5241	451	6	sg	sg	ADV
ejpam-5241	451	7	=	=	PUNCT
ejpam-5241	451	8	{	{	PUNCT
ejpam-5241	451	9	x1	x1	PROPN
ejpam-5241	451	10	,	,	PUNCT
ejpam-5241	451	11	x2	x2	PROPN
ejpam-5241	451	12	,	,	PUNCT
ejpam-5241	451	13	.	.	PUNCT
ejpam-5241	451	14	.	.	PUNCT
ejpam-5241	452	1	.	.	PUNCT
ejpam-5241	453	1	,	,	PUNCT
ejpam-5241	453	2	xk	xk	PROPN
ejpam-5241	453	3	}	}	PUNCT
ejpam-5241	453	4	and	and	CCONJ
ejpam-5241	453	5	xk+i	xk+i	PROPN
ejpam-5241	453	6	=	=	SYM
ejpam-5241	453	7	vi	vi	PROPN
ejpam-5241	453	8	for	for	ADP
ejpam-5241	453	9	all	all	PRON
ejpam-5241	453	10	i	i	PRON
ejpam-5241	453	11	=	=	NOUN
ejpam-5241	453	12	1	1	NUM
ejpam-5241	453	13	,	,	PUNCT
ejpam-5241	453	14	2	2	NUM
ejpam-5241	453	15	,	,	PUNCT
ejpam-5241	453	16	.	.	PUNCT
ejpam-5241	453	17	.	.	PUNCT
ejpam-5241	454	1	.	.	PUNCT
ejpam-5241	455	1	,	,	PUNCT
ejpam-5241	455	2	j.	j.	PROPN
ejpam-5241	455	3	as	as	SCONJ
ejpam-5241	455	4	observed	observe	VERB
ejpam-5241	455	5	in	in	ADP
ejpam-5241	455	6	the	the	DET
ejpam-5241	455	7	proof	proof	NOUN
ejpam-5241	455	8	of	of	ADP
ejpam-5241	455	9	theorem	theorem	NOUN
ejpam-5241	455	10	7	7	NUM
ejpam-5241	455	11	,	,	PUNCT
ejpam-5241	455	12	s	s	VERB
ejpam-5241	455	13	is	be	AUX
ejpam-5241	455	14	a	a	DET
ejpam-5241	455	15	closed	closed	ADJ
ejpam-5241	455	16	geodetic	geodetic	ADJ
ejpam-5241	455	17	set	set	NOUN
ejpam-5241	455	18	of	of	ADP
ejpam-5241	455	19	g+h	g+h	PROPN
ejpam-5241	455	20	.	.	PUNCT
ejpam-5241	456	1	similarly	similarly	ADV
ejpam-5241	456	2	,	,	PUNCT
ejpam-5241	456	3	if	if	SCONJ
ejpam-5241	456	4	condition	condition	NOUN
ejpam-5241	456	5	(	(	PUNCT
ejpam-5241	456	6	ii	ii	NOUN
ejpam-5241	456	7	)	)	PUNCT
ejpam-5241	456	8	holds	hold	VERB
ejpam-5241	456	9	,	,	PUNCT
ejpam-5241	456	10	then	then	ADV
ejpam-5241	456	11	s	s	VERB
ejpam-5241	456	12	is	be	AUX
ejpam-5241	456	13	a	a	DET
ejpam-5241	456	14	closed	closed	ADJ
ejpam-5241	456	15	geodetic	geodetic	ADJ
ejpam-5241	456	16	set	set	NOUN
ejpam-5241	456	17	of	of	ADP
ejpam-5241	456	18	g+h	g+h	PROPN
ejpam-5241	456	19	.	.	PUNCT
ejpam-5241	457	1	a.	a.	PROPN
ejpam-5241	457	2	adolfo	adolfo	PROPN
ejpam-5241	457	3	,	,	PUNCT
ejpam-5241	457	4	i.	i.	PROPN
ejpam-5241	457	5	aniversario	aniversario	PROPN
ejpam-5241	457	6	,	,	PUNCT
ejpam-5241	457	7	f.	f.	PROPN
ejpam-5241	457	8	jamil	jamil	PROPN
ejpam-5241	457	9	/	/	SYM
ejpam-5241	457	10	eur	eur	PROPN
ejpam-5241	457	11	.	.	PUNCT
ejpam-5241	458	1	j.	j.	PROPN
ejpam-5241	458	2	pure	pure	PROPN
ejpam-5241	458	3	appl	appl	PROPN
ejpam-5241	458	4	.	.	PROPN
ejpam-5241	458	5	math	math	PROPN
ejpam-5241	458	6	,	,	PUNCT
ejpam-5241	458	7	17	17	NUM
ejpam-5241	458	8	(	(	PUNCT
ejpam-5241	458	9	3	3	NUM
ejpam-5241	458	10	)	)	PUNCT
ejpam-5241	458	11	(	(	PUNCT
ejpam-5241	458	12	2024	2024	NUM
ejpam-5241	458	13	)	)	PUNCT
ejpam-5241	458	14	,	,	PUNCT
ejpam-5241	458	15	1618	1618	NUM
ejpam-5241	458	16	-	-	SYM
ejpam-5241	458	17	1636	1636	NUM
ejpam-5241	458	18	1630	1630	NUM
ejpam-5241	458	19	lemma	lemma	PROPN
ejpam-5241	458	20	3	3	X
ejpam-5241	458	21	.	.	PUNCT
ejpam-5241	459	1	let	let	VERB
ejpam-5241	459	2	g	g	PRON
ejpam-5241	459	3	be	be	AUX
ejpam-5241	459	4	a	a	DET
ejpam-5241	459	5	connected	connected	ADJ
ejpam-5241	459	6	noncomplete	noncomplete	ADJ
ejpam-5241	459	7	graph	graph	NOUN
ejpam-5241	459	8	and	and	CCONJ
ejpam-5241	459	9	s	s	VERB
ejpam-5241	459	10	⊆	⊆	NUM
ejpam-5241	459	11	v	v	NOUN
ejpam-5241	459	12	(	(	PUNCT
ejpam-5241	459	13	g	g	NOUN
ejpam-5241	459	14	)	)	PUNCT
ejpam-5241	459	15	such	such	ADJ
ejpam-5241	459	16	that	that	SCONJ
ejpam-5241	459	17	⟨s⟩	⟨s⟩	PROPN
ejpam-5241	459	18	is	be	AUX
ejpam-5241	459	19	complete	complete	ADJ
ejpam-5241	459	20	.	.	PUNCT
ejpam-5241	460	1	then	then	ADV
ejpam-5241	460	2	⟨s⟩	⟨s⟩	PROPN
ejpam-5241	460	3	is	be	AUX
ejpam-5241	460	4	a	a	DET
ejpam-5241	460	5	maximal	maximal	ADJ
ejpam-5241	460	6	clique	clique	NOUN
ejpam-5241	460	7	if	if	SCONJ
ejpam-5241	460	8	and	and	CCONJ
ejpam-5241	460	9	only	only	ADV
ejpam-5241	460	10	if	if	SCONJ
ejpam-5241	460	11	s	s	NOUN
ejpam-5241	460	12	is	be	AUX
ejpam-5241	460	13	a	a	DET
ejpam-5241	460	14	pointwise	pointwise	ADJ
ejpam-5241	460	15	non	non	ADJ
ejpam-5241	460	16	-	-	ADJ
ejpam-5241	460	17	dominating	dominating	ADJ
ejpam-5241	460	18	set	set	NOUN
ejpam-5241	460	19	of	of	ADP
ejpam-5241	460	20	g.	g.	PROPN
ejpam-5241	460	21	proof	proof	PROPN
ejpam-5241	460	22	.	.	PUNCT
ejpam-5241	461	1	assume	assume	VERB
ejpam-5241	461	2	that	that	SCONJ
ejpam-5241	461	3	⟨s⟩	⟨s⟩	PROPN
ejpam-5241	461	4	is	be	AUX
ejpam-5241	461	5	a	a	DET
ejpam-5241	461	6	maximal	maximal	ADJ
ejpam-5241	461	7	clique	clique	NOUN
ejpam-5241	461	8	of	of	ADP
ejpam-5241	461	9	g.	g.	PROPN
ejpam-5241	461	10	let	let	VERB
ejpam-5241	461	11	v	v	NUM
ejpam-5241	461	12	∈	∈	PROPN
ejpam-5241	461	13	v	v	NOUN
ejpam-5241	461	14	(	(	PUNCT
ejpam-5241	461	15	g	g	NOUN
ejpam-5241	461	16	)	)	PUNCT
ejpam-5241	461	17	\	\	PUNCT
ejpam-5241	462	1	s.	s.	PROPN
ejpam-5241	462	2	suppose	suppose	VERB
ejpam-5241	462	3	that	that	SCONJ
ejpam-5241	462	4	uv	uv	PROPN
ejpam-5241	462	5	∈	∈	PROPN
ejpam-5241	462	6	e(g	e(g	PROPN
ejpam-5241	462	7	)	)	PUNCT
ejpam-5241	462	8	for	for	ADP
ejpam-5241	462	9	all	all	DET
ejpam-5241	462	10	u	u	PROPN
ejpam-5241	462	11	∈	∈	PROPN
ejpam-5241	462	12	s.	s.	PROPN
ejpam-5241	462	13	then	then	ADV
ejpam-5241	462	14	⟨s	⟨s	AUX
ejpam-5241	462	15	∪	∪	X
ejpam-5241	462	16	{	{	PUNCT
ejpam-5241	462	17	u}⟩	u}⟩	PROPN
ejpam-5241	462	18	is	be	AUX
ejpam-5241	462	19	a	a	DET
ejpam-5241	462	20	complete	complete	ADJ
ejpam-5241	462	21	subgraph	subgraph	NOUN
ejpam-5241	462	22	of	of	ADP
ejpam-5241	462	23	g	g	NOUN
ejpam-5241	462	24	,	,	PUNCT
ejpam-5241	462	25	contradicting	contradict	VERB
ejpam-5241	462	26	the	the	DET
ejpam-5241	462	27	maximality	maximality	NOUN
ejpam-5241	462	28	of	of	ADP
ejpam-5241	462	29	⟨s⟩.	⟨s⟩.	PROPN
ejpam-5241	462	30	thus	thus	ADV
ejpam-5241	462	31	,	,	PUNCT
ejpam-5241	462	32	there	there	PRON
ejpam-5241	462	33	exists	exist	VERB
ejpam-5241	462	34	u	u	PROPN
ejpam-5241	462	35	∈	∈	PROPN
ejpam-5241	462	36	s	s	X
ejpam-5241	462	37	for	for	ADP
ejpam-5241	462	38	which	which	PRON
ejpam-5241	462	39	dg(u	dg(u	ADJ
ejpam-5241	462	40	,	,	PUNCT
ejpam-5241	462	41	v	v	NOUN
ejpam-5241	462	42	)	)	PUNCT
ejpam-5241	462	43	≥	≥	NOUN
ejpam-5241	462	44	2	2	NUM
ejpam-5241	462	45	.	.	PUNCT
ejpam-5241	463	1	since	since	SCONJ
ejpam-5241	463	2	v	v	NOUN
ejpam-5241	463	3	is	be	AUX
ejpam-5241	463	4	arbitrary	arbitrary	ADJ
ejpam-5241	463	5	,	,	PUNCT
ejpam-5241	463	6	s	s	PART
ejpam-5241	463	7	is	be	AUX
ejpam-5241	463	8	pointwise	pointwise	ADJ
ejpam-5241	463	9	non	non	ADJ
ejpam-5241	463	10	-	-	ADJ
ejpam-5241	463	11	dominating	dominating	NOUN
ejpam-5241	463	12	.	.	PUNCT
ejpam-5241	464	1	conversely	conversely	ADV
ejpam-5241	464	2	,	,	PUNCT
ejpam-5241	464	3	suppose	suppose	VERB
ejpam-5241	464	4	that	that	SCONJ
ejpam-5241	464	5	s	s	VERB
ejpam-5241	464	6	is	be	AUX
ejpam-5241	464	7	pointwise	pointwise	ADJ
ejpam-5241	464	8	non	non	ADJ
ejpam-5241	464	9	-	-	ADJ
ejpam-5241	464	10	dominating	dominating	ADJ
ejpam-5241	464	11	set	set	NOUN
ejpam-5241	464	12	of	of	ADP
ejpam-5241	464	13	g.	g.	PROPN
ejpam-5241	464	14	let	let	VERB
ejpam-5241	464	15	c	c	PROPN
ejpam-5241	464	16	⊆	⊆	NUM
ejpam-5241	464	17	v	v	NOUN
ejpam-5241	464	18	(	(	PUNCT
ejpam-5241	464	19	g	g	NOUN
ejpam-5241	464	20	)	)	PUNCT
ejpam-5241	464	21	for	for	ADP
ejpam-5241	464	22	which	which	PRON
ejpam-5241	464	23	⟨c⟩	⟨c⟩	PROPN
ejpam-5241	464	24	is	be	AUX
ejpam-5241	464	25	a	a	DET
ejpam-5241	464	26	complete	complete	ADJ
ejpam-5241	464	27	subgraph	subgraph	NOUN
ejpam-5241	464	28	of	of	ADP
ejpam-5241	464	29	g	g	PROPN
ejpam-5241	464	30	and	and	CCONJ
ejpam-5241	464	31	s	s	PROPN
ejpam-5241	465	1	⊆	⊆	PROPN
ejpam-5241	465	2	c.	c.	NOUN
ejpam-5241	465	3	suppose	suppose	VERB
ejpam-5241	465	4	that	that	SCONJ
ejpam-5241	465	5	c	c	PROPN
ejpam-5241	465	6	\s	\s	PROPN
ejpam-5241	465	7	̸=	̸=	PROPN
ejpam-5241	465	8	∅	∅	NOUN
ejpam-5241	465	9	,	,	PUNCT
ejpam-5241	465	10	say	say	VERB
ejpam-5241	465	11	x	x	X
ejpam-5241	465	12	∈	∈	NOUN
ejpam-5241	465	13	c	c	NOUN
ejpam-5241	465	14	\s	\s	NOUN
ejpam-5241	465	15	.	.	PUNCT
ejpam-5241	466	1	since	since	SCONJ
ejpam-5241	466	2	s	s	NOUN
ejpam-5241	466	3	is	be	AUX
ejpam-5241	466	4	pointwise	pointwise	ADJ
ejpam-5241	466	5	non	non	ADJ
ejpam-5241	466	6	-	-	ADJ
ejpam-5241	466	7	dominating	dominating	ADJ
ejpam-5241	466	8	,	,	PUNCT
ejpam-5241	466	9	there	there	PRON
ejpam-5241	466	10	exists	exist	VERB
ejpam-5241	466	11	y	y	PROPN
ejpam-5241	466	12	∈	∈	PROPN
ejpam-5241	466	13	s	s	VERB
ejpam-5241	466	14	such	such	ADJ
ejpam-5241	466	15	that	that	PRON
ejpam-5241	467	1	xy	xy	PROPN
ejpam-5241	467	2	/∈	/∈	PUNCT
ejpam-5241	467	3	e(g	e(g	PROPN
ejpam-5241	467	4	)	)	PUNCT
ejpam-5241	467	5	.	.	PUNCT
ejpam-5241	468	1	however	however	ADV
ejpam-5241	468	2	,	,	PUNCT
ejpam-5241	468	3	y	y	PROPN
ejpam-5241	468	4	∈	∈	PROPN
ejpam-5241	468	5	c	c	PROPN
ejpam-5241	468	6	since	since	SCONJ
ejpam-5241	468	7	s	s	PROPN
ejpam-5241	468	8	⊆	⊆	NUM
ejpam-5241	468	9	c.	c.	NOUN
ejpam-5241	468	10	this	this	PRON
ejpam-5241	468	11	is	be	AUX
ejpam-5241	468	12	a	a	DET
ejpam-5241	468	13	contradiction	contradiction	NOUN
ejpam-5241	468	14	since	since	SCONJ
ejpam-5241	468	15	⟨c⟩	⟨c⟩	PROPN
ejpam-5241	468	16	is	be	AUX
ejpam-5241	468	17	complete	complete	ADJ
ejpam-5241	468	18	.	.	PUNCT
ejpam-5241	469	1	in	in	ADP
ejpam-5241	469	2	view	view	NOUN
ejpam-5241	469	3	of	of	ADP
ejpam-5241	469	4	lemma	lemma	PROPN
ejpam-5241	469	5	3	3	NUM
ejpam-5241	469	6	,	,	PUNCT
ejpam-5241	469	7	theorem	theorem	VERB
ejpam-5241	469	8	9	9	NUM
ejpam-5241	469	9	can	can	AUX
ejpam-5241	469	10	be	be	AUX
ejpam-5241	469	11	rephrased	rephrase	VERB
ejpam-5241	469	12	as	as	SCONJ
ejpam-5241	469	13	follows	follow	VERB
ejpam-5241	469	14	:	:	PUNCT
ejpam-5241	469	15	theorem	theorem	NOUN
ejpam-5241	469	16	10	10	NUM
ejpam-5241	469	17	.	.	PUNCT
ejpam-5241	470	1	let	let	VERB
ejpam-5241	470	2	g	g	NOUN
ejpam-5241	470	3	and	and	CCONJ
ejpam-5241	470	4	h	h	NOUN
ejpam-5241	470	5	be	be	AUX
ejpam-5241	470	6	connected	connect	VERB
ejpam-5241	470	7	noncomplete	noncomplete	ADJ
ejpam-5241	470	8	graphs	graph	NOUN
ejpam-5241	470	9	.	.	PUNCT
ejpam-5241	471	1	then	then	ADV
ejpam-5241	471	2	s	s	VERB
ejpam-5241	471	3	is	be	AUX
ejpam-5241	471	4	a	a	DET
ejpam-5241	471	5	closed	closed	ADJ
ejpam-5241	471	6	geodetic	geodetic	ADJ
ejpam-5241	471	7	hop	hop	NOUN
ejpam-5241	471	8	dominating	dominating	NOUN
ejpam-5241	471	9	set	set	NOUN
ejpam-5241	471	10	of	of	ADP
ejpam-5241	471	11	g	g	PROPN
ejpam-5241	471	12	if	if	SCONJ
ejpam-5241	471	13	and	and	CCONJ
ejpam-5241	471	14	only	only	ADV
ejpam-5241	471	15	if	if	SCONJ
ejpam-5241	471	16	s	s	VERB
ejpam-5241	471	17	=	=	PUNCT
ejpam-5241	471	18	sg	sg	X
ejpam-5241	471	19	∪	∪	NOUN
ejpam-5241	471	20	sh	sh	PROPN
ejpam-5241	471	21	where	where	SCONJ
ejpam-5241	471	22	sg	sg	PROPN
ejpam-5241	471	23	⊆	⊆	NUM
ejpam-5241	471	24	v	v	NOUN
ejpam-5241	471	25	(	(	PUNCT
ejpam-5241	471	26	g	g	NOUN
ejpam-5241	471	27	)	)	PUNCT
ejpam-5241	471	28	and	and	CCONJ
ejpam-5241	471	29	sh	sh	PROPN
ejpam-5241	471	30	⊆	⊆	NUM
ejpam-5241	471	31	v	v	ADP
ejpam-5241	471	32	(	(	PUNCT
ejpam-5241	471	33	h	h	NOUN
ejpam-5241	471	34	)	)	PUNCT
ejpam-5241	471	35	such	such	ADJ
ejpam-5241	471	36	that	that	SCONJ
ejpam-5241	471	37	either	either	CCONJ
ejpam-5241	471	38	(	(	PUNCT
ejpam-5241	471	39	i	i	NOUN
ejpam-5241	471	40	)	)	PUNCT
ejpam-5241	471	41	⟨sg⟩	⟨sg⟩	PRON
ejpam-5241	471	42	is	be	AUX
ejpam-5241	471	43	a	a	DET
ejpam-5241	471	44	maximal	maximal	ADJ
ejpam-5241	471	45	clique	clique	NOUN
ejpam-5241	471	46	of	of	ADP
ejpam-5241	471	47	g	g	PROPN
ejpam-5241	471	48	and	and	CCONJ
ejpam-5241	471	49	sh	sh	PROPN
ejpam-5241	471	50	is	be	AUX
ejpam-5241	471	51	a	a	DET
ejpam-5241	471	52	closed	closed	ADJ
ejpam-5241	471	53	2	2	NUM
ejpam-5241	471	54	-	-	PUNCT
ejpam-5241	471	55	path	path	NOUN
ejpam-5241	471	56	closure	closure	NOUN
ejpam-5241	471	57	absorbing	absorb	VERB
ejpam-5241	471	58	pointwise	pointwise	PROPN
ejpam-5241	471	59	non	non	ADJ
ejpam-5241	471	60	-	-	ADJ
ejpam-5241	471	61	dominating	dominating	ADJ
ejpam-5241	471	62	set	set	NOUN
ejpam-5241	471	63	of	of	ADP
ejpam-5241	471	64	h	h	NOUN
ejpam-5241	471	65	;	;	PUNCT
ejpam-5241	471	66	or	or	CCONJ
ejpam-5241	471	67	(	(	PUNCT
ejpam-5241	471	68	ii	ii	X
ejpam-5241	471	69	)	)	PUNCT
ejpam-5241	471	70	⟨sh⟩	⟨sh⟩	NUM
ejpam-5241	471	71	is	be	AUX
ejpam-5241	471	72	maximal	maximal	ADJ
ejpam-5241	471	73	clique	clique	NOUN
ejpam-5241	471	74	of	of	ADP
ejpam-5241	471	75	h	h	NOUN
ejpam-5241	471	76	and	and	CCONJ
ejpam-5241	471	77	sg	sg	PROPN
ejpam-5241	471	78	is	be	AUX
ejpam-5241	471	79	a	a	DET
ejpam-5241	471	80	closed	closed	ADJ
ejpam-5241	471	81	2	2	NUM
ejpam-5241	471	82	-	-	PUNCT
ejpam-5241	471	83	path	path	NOUN
ejpam-5241	471	84	closure	closure	NOUN
ejpam-5241	471	85	absorbing	absorb	VERB
ejpam-5241	471	86	pointwoise	pointwoise	ADJ
ejpam-5241	471	87	non	non	ADJ
ejpam-5241	471	88	-	-	ADJ
ejpam-5241	471	89	dominating	dominating	ADJ
ejpam-5241	471	90	set	set	NOUN
ejpam-5241	471	91	of	of	ADP
ejpam-5241	471	92	g.	g.	PROPN
ejpam-5241	471	93	corollary	corollary	PROPN
ejpam-5241	471	94	2	2	PROPN
ejpam-5241	471	95	.	.	PUNCT
ejpam-5241	472	1	let	let	VERB
ejpam-5241	472	2	g	g	NOUN
ejpam-5241	472	3	and	and	CCONJ
ejpam-5241	472	4	h	h	NOUN
ejpam-5241	472	5	be	be	AUX
ejpam-5241	472	6	connected	connect	VERB
ejpam-5241	472	7	noncomplete	noncomplete	ADJ
ejpam-5241	472	8	graphs	graph	NOUN
ejpam-5241	472	9	.	.	PUNCT
ejpam-5241	473	1	then	then	ADV
ejpam-5241	473	2	γhcg(g+h	γhcg(g+h	ADV
ejpam-5241	473	3	)	)	PUNCT
ejpam-5241	473	4	=	=	SYM
ejpam-5241	473	5	min{ρc2pnd(g	min{ρc2pnd(g	NOUN
ejpam-5241	473	6	)	)	PUNCT
ejpam-5241	473	7	+	+	NUM
ejpam-5241	473	8	ωl(h	ωl(h	NUM
ejpam-5241	473	9	)	)	PUNCT
ejpam-5241	473	10	,	,	PUNCT
ejpam-5241	473	11	ρc2pnd(h	ρc2pnd(h	PROPN
ejpam-5241	473	12	)	)	PUNCT
ejpam-5241	474	1	+	+	NUM
ejpam-5241	474	2	ωl(g	ωl(g	NUM
ejpam-5241	474	3	)	)	PUNCT
ejpam-5241	474	4	}	}	PUNCT
ejpam-5241	474	5	.	.	PUNCT
ejpam-5241	475	1	(	(	PUNCT
ejpam-5241	475	2	4	4	X
ejpam-5241	475	3	)	)	PUNCT
ejpam-5241	475	4	example	example	NOUN
ejpam-5241	475	5	3	3	NUM
ejpam-5241	475	6	.	.	PUNCT
ejpam-5241	476	1	(	(	PUNCT
ejpam-5241	476	2	i	i	NOUN
ejpam-5241	476	3	)	)	PUNCT
ejpam-5241	476	4	γhcg(pr+km	γhcg(pr+km	PROPN
ejpam-5241	476	5	,	,	PUNCT
ejpam-5241	476	6	n	n	CCONJ
ejpam-5241	476	7	)	)	PUNCT
ejpam-5241	476	8	=	=	PUNCT
ejpam-5241	477	1			NOUN
ejpam-5241	477	2	5	5	NUM
ejpam-5241	477	3	if	if	SCONJ
ejpam-5241	477	4	r	r	NOUN
ejpam-5241	477	5	=	=	SYM
ejpam-5241	477	6	3	3	NUM
ejpam-5241	477	7	and	and	CCONJ
ejpam-5241	477	8	m	m	PROPN
ejpam-5241	477	9	,	,	PUNCT
ejpam-5241	477	10	n	n	PROPN
ejpam-5241	477	11	≥	≥	NOUN
ejpam-5241	477	12	2	2	NUM
ejpam-5241	477	13	min{5,m+	min{5,m+	X
ejpam-5241	477	14	n+	n+	PUNCT
ejpam-5241	477	15	2	2	X
ejpam-5241	477	16	}	}	PUNCT
ejpam-5241	477	17	if	if	SCONJ
ejpam-5241	477	18	r	r	NOUN
ejpam-5241	477	19	=	=	SYM
ejpam-5241	477	20	3	3	NUM
ejpam-5241	477	21	and	and	CCONJ
ejpam-5241	477	22	m	m	PROPN
ejpam-5241	477	23	=	=	ADJ
ejpam-5241	477	24	1	1	NUM
ejpam-5241	477	25	or	or	CCONJ
ejpam-5241	477	26	n	n	CCONJ
ejpam-5241	477	27	=	=	SYM
ejpam-5241	477	28	1	1	NUM
ejpam-5241	477	29	min{⌈	min{⌈	NOUN
ejpam-5241	477	30	r+1	r+1	PROPN
ejpam-5241	477	31	2	2	NUM
ejpam-5241	477	32	⌉+	⌉+	SYM
ejpam-5241	477	33	2,m+	2,m+	NUM
ejpam-5241	477	34	n+	n+	PUNCT
ejpam-5241	477	35	2	2	X
ejpam-5241	477	36	}	}	PUNCT
ejpam-5241	477	37	if	if	SCONJ
ejpam-5241	477	38	r	r	NOUN
ejpam-5241	477	39	≥	≥	NUM
ejpam-5241	477	40	4	4	NUM
ejpam-5241	477	41	and	and	CCONJ
ejpam-5241	477	42	m	m	VERB
ejpam-5241	477	43	=	=	ADJ
ejpam-5241	477	44	1	1	NUM
ejpam-5241	477	45	or	or	CCONJ
ejpam-5241	477	46	n	n	CCONJ
ejpam-5241	477	47	=	=	SYM
ejpam-5241	477	48	1	1	NUM
ejpam-5241	477	49	min{⌈	min{⌈	NOUN
ejpam-5241	477	50	r+1	r+1	PROPN
ejpam-5241	477	51	2	2	NUM
ejpam-5241	477	52	⌉+	⌉+	SYM
ejpam-5241	477	53	2,min{m	2,min{m	NUM
ejpam-5241	477	54	,	,	PUNCT
ejpam-5241	477	55	n}+	n}+	NOUN
ejpam-5241	477	56	3	3	X
ejpam-5241	477	57	}	}	PUNCT
ejpam-5241	477	58	if	if	SCONJ
ejpam-5241	477	59	r	r	NOUN
ejpam-5241	477	60	≥	≥	NUM
ejpam-5241	477	61	4	4	NUM
ejpam-5241	477	62	and	and	CCONJ
ejpam-5241	477	63	m	m	PROPN
ejpam-5241	477	64	,	,	PUNCT
ejpam-5241	477	65	n	n	PRON
ejpam-5241	477	66	≥	≥	NOUN
ejpam-5241	477	67	2	2	NUM
ejpam-5241	477	68	,	,	PUNCT
ejpam-5241	477	69	(	(	PUNCT
ejpam-5241	477	70	ii	ii	NOUN
ejpam-5241	477	71	)	)	PUNCT
ejpam-5241	477	72	γhcg(cr	γhcg(cr	PROPN
ejpam-5241	477	73	+	+	PROPN
ejpam-5241	477	74	km	km	PROPN
ejpam-5241	477	75	,	,	PUNCT
ejpam-5241	477	76	n	n	CCONJ
ejpam-5241	477	77	)	)	PUNCT
ejpam-5241	477	78	=	=	PUNCT
ejpam-5241	477	79			NOUN
ejpam-5241	477	80	5	5	NUM
ejpam-5241	477	81	if	if	SCONJ
ejpam-5241	477	82	r	r	NOUN
ejpam-5241	477	83	=	=	SYM
ejpam-5241	477	84	4	4	NUM
ejpam-5241	477	85	and	and	CCONJ
ejpam-5241	477	86	m	m	PROPN
ejpam-5241	477	87	,	,	PUNCT
ejpam-5241	477	88	n	n	PROPN
ejpam-5241	477	89	≥	≥	NOUN
ejpam-5241	477	90	2	2	NUM
ejpam-5241	477	91	min{5,m+	min{5,m+	X
ejpam-5241	477	92	n+	n+	PUNCT
ejpam-5241	477	93	2	2	X
ejpam-5241	477	94	}	}	PUNCT
ejpam-5241	477	95	if	if	SCONJ
ejpam-5241	477	96	r	r	NOUN
ejpam-5241	477	97	=	=	SYM
ejpam-5241	477	98	4	4	NUM
ejpam-5241	477	99	and	and	CCONJ
ejpam-5241	477	100	m	m	VERB
ejpam-5241	477	101	=	=	ADJ
ejpam-5241	477	102	1	1	NUM
ejpam-5241	477	103	or	or	CCONJ
ejpam-5241	477	104	n	n	CCONJ
ejpam-5241	477	105	=	=	SYM
ejpam-5241	477	106	1	1	NUM
ejpam-5241	477	107	min{⌈	min{⌈	PROPN
ejpam-5241	477	108	r2⌉+	r2⌉+	PROPN
ejpam-5241	477	109	2,m+	2,m+	NUM
ejpam-5241	477	110	n+	n+	PUNCT
ejpam-5241	477	111	2	2	X
ejpam-5241	477	112	}	}	PUNCT
ejpam-5241	477	113	if	if	SCONJ
ejpam-5241	477	114	r	r	NOUN
ejpam-5241	477	115	≥	≥	NUM
ejpam-5241	477	116	5	5	NUM
ejpam-5241	477	117	and	and	CCONJ
ejpam-5241	477	118	m	m	VERB
ejpam-5241	477	119	=	=	ADJ
ejpam-5241	477	120	1	1	NUM
ejpam-5241	477	121	or	or	CCONJ
ejpam-5241	477	122	n	n	CCONJ
ejpam-5241	477	123	=	=	SYM
ejpam-5241	477	124	1	1	NUM
ejpam-5241	477	125	min{⌈	min{⌈	PROPN
ejpam-5241	477	126	r2⌉+	r2⌉+	NOUN
ejpam-5241	477	127	2,min{m	2,min{m	NUM
ejpam-5241	477	128	,	,	PUNCT
ejpam-5241	477	129	n}+	n}+	NOUN
ejpam-5241	477	130	3	3	X
ejpam-5241	477	131	}	}	PUNCT
ejpam-5241	477	132	if	if	SCONJ
ejpam-5241	477	133	r	r	NOUN
ejpam-5241	477	134	≥	≥	NUM
ejpam-5241	477	135	5	5	NUM
ejpam-5241	477	136	and	and	CCONJ
ejpam-5241	477	137	m	m	PROPN
ejpam-5241	477	138	,	,	PUNCT
ejpam-5241	477	139	n	n	PRON
ejpam-5241	477	140	≥	≥	NOUN
ejpam-5241	477	141	2	2	NUM
ejpam-5241	477	142	.	.	PUNCT
ejpam-5241	478	1	a.	a.	PROPN
ejpam-5241	478	2	adolfo	adolfo	PROPN
ejpam-5241	478	3	,	,	PUNCT
ejpam-5241	478	4	i.	i.	PROPN
ejpam-5241	478	5	aniversario	aniversario	PROPN
ejpam-5241	478	6	,	,	PUNCT
ejpam-5241	478	7	f.	f.	PROPN
ejpam-5241	478	8	jamil	jamil	PROPN
ejpam-5241	478	9	/	/	SYM
ejpam-5241	478	10	eur	eur	PROPN
ejpam-5241	478	11	.	.	PUNCT
ejpam-5241	479	1	j.	j.	PROPN
ejpam-5241	479	2	pure	pure	PROPN
ejpam-5241	479	3	appl	appl	PROPN
ejpam-5241	479	4	.	.	PROPN
ejpam-5241	479	5	math	math	PROPN
ejpam-5241	479	6	,	,	PUNCT
ejpam-5241	479	7	17	17	NUM
ejpam-5241	479	8	(	(	PUNCT
ejpam-5241	479	9	3	3	NUM
ejpam-5241	479	10	)	)	PUNCT
ejpam-5241	479	11	(	(	PUNCT
ejpam-5241	479	12	2024	2024	NUM
ejpam-5241	479	13	)	)	PUNCT
ejpam-5241	479	14	,	,	PUNCT
ejpam-5241	479	15	1618	1618	NUM
ejpam-5241	479	16	-	-	SYM
ejpam-5241	479	17	1636	1636	NUM
ejpam-5241	479	18	1631	1631	NUM
ejpam-5241	479	19	2.5	2.5	NUM
ejpam-5241	479	20	.	.	PUNCT
ejpam-5241	480	1	in	in	ADP
ejpam-5241	480	2	the	the	DET
ejpam-5241	480	3	corona	corona	NOUN
ejpam-5241	480	4	and	and	CCONJ
ejpam-5241	480	5	edge	edge	NOUN
ejpam-5241	480	6	corona	corona	NOUN
ejpam-5241	480	7	of	of	ADP
ejpam-5241	480	8	graphs	graph	NOUN
ejpam-5241	480	9	for	for	ADP
ejpam-5241	480	10	the	the	DET
ejpam-5241	480	11	purpose	purpose	NOUN
ejpam-5241	480	12	of	of	ADP
ejpam-5241	480	13	this	this	DET
ejpam-5241	480	14	section	section	NOUN
ejpam-5241	480	15	,	,	PUNCT
ejpam-5241	480	16	a	a	DET
ejpam-5241	480	17	sequence	sequence	NOUN
ejpam-5241	480	18	of	of	ADP
ejpam-5241	480	19	subsets	subset	NOUN
ejpam-5241	480	20	sk	sk	INTJ
ejpam-5241	480	21	=	=	PUNCT
ejpam-5241	480	22	{	{	PUNCT
ejpam-5241	480	23	v1	v1	PROPN
ejpam-5241	480	24	,	,	PUNCT
ejpam-5241	480	25	v2	v2	PROPN
ejpam-5241	480	26	,	,	PUNCT
ejpam-5241	480	27	.	.	PUNCT
ejpam-5241	480	28	.	.	PUNCT
ejpam-5241	480	29	.	.	PUNCT
ejpam-5241	481	1	,	,	PUNCT
ejpam-5241	481	2	xk	xk	PROPN
ejpam-5241	481	3	}	}	PUNCT
ejpam-5241	481	4	(	(	PUNCT
ejpam-5241	481	5	k	k	NOUN
ejpam-5241	481	6	=	=	SYM
ejpam-5241	481	7	1	1	NUM
ejpam-5241	481	8	,	,	PUNCT
ejpam-5241	481	9	2	2	NUM
ejpam-5241	481	10	,	,	PUNCT
ejpam-5241	481	11	.	.	PUNCT
ejpam-5241	481	12	.	.	PUNCT
ejpam-5241	482	1	.	.	PUNCT
ejpam-5241	483	1	,	,	PUNCT
ejpam-5241	483	2	n	n	CCONJ
ejpam-5241	483	3	)	)	PUNCT
ejpam-5241	483	4	of	of	ADP
ejpam-5241	483	5	v	v	NOUN
ejpam-5241	483	6	(	(	PUNCT
ejpam-5241	483	7	g	g	NOUN
ejpam-5241	483	8	)	)	PUNCT
ejpam-5241	483	9	is	be	AUX
ejpam-5241	483	10	said	say	VERB
ejpam-5241	483	11	to	to	PART
ejpam-5241	483	12	be	be	AUX
ejpam-5241	483	13	a	a	DET
ejpam-5241	483	14	closed	closed	ADJ
ejpam-5241	483	15	geodetic	geodetic	ADJ
ejpam-5241	483	16	sequence	sequence	NOUN
ejpam-5241	483	17	of	of	ADP
ejpam-5241	483	18	sets	set	NOUN
ejpam-5241	483	19	if	if	SCONJ
ejpam-5241	483	20	v1	v1	VERB
ejpam-5241	483	21	̸=	̸=	PROPN
ejpam-5241	483	22	v2	v2	PROPN
ejpam-5241	483	23	and	and	CCONJ
ejpam-5241	483	24	vk	vk	INTJ
ejpam-5241	483	25	/∈	/∈	PUNCT
ejpam-5241	483	26	ig[sk−1	ig[sk−1	PROPN
ejpam-5241	483	27	]	]	PUNCT
ejpam-5241	483	28	for	for	ADP
ejpam-5241	483	29	3	3	NUM
ejpam-5241	483	30	≤	≤	NUM
ejpam-5241	483	31	k	k	PROPN
ejpam-5241	483	32	≤	≤	PROPN
ejpam-5241	483	33	n.	n.	NOUN
ejpam-5241	483	34	a	a	DET
ejpam-5241	483	35	closed	closed	ADJ
ejpam-5241	483	36	geodetic	geodetic	ADJ
ejpam-5241	483	37	sequence	sequence	NOUN
ejpam-5241	483	38	of	of	ADP
ejpam-5241	483	39	sets	set	NOUN
ejpam-5241	483	40	sk	sk	INTJ
ejpam-5241	483	41	=	=	PUNCT
ejpam-5241	483	42	{	{	PUNCT
ejpam-5241	483	43	v1	v1	PROPN
ejpam-5241	483	44	,	,	PUNCT
ejpam-5241	483	45	v2	v2	PROPN
ejpam-5241	483	46	,	,	PUNCT
ejpam-5241	483	47	.	.	PUNCT
ejpam-5241	483	48	.	.	PUNCT
ejpam-5241	483	49	.	.	PUNCT
ejpam-5241	484	1	,	,	PUNCT
ejpam-5241	484	2	xk	xk	PROPN
ejpam-5241	484	3	}	}	PUNCT
ejpam-5241	484	4	(	(	PUNCT
ejpam-5241	484	5	k	k	NOUN
ejpam-5241	484	6	=	=	SYM
ejpam-5241	484	7	1	1	NUM
ejpam-5241	484	8	,	,	PUNCT
ejpam-5241	484	9	2	2	NUM
ejpam-5241	484	10	,	,	PUNCT
ejpam-5241	484	11	.	.	PUNCT
ejpam-5241	484	12	.	.	PUNCT
ejpam-5241	485	1	.	.	PUNCT
ejpam-5241	486	1	,	,	PUNCT
ejpam-5241	486	2	n	n	CCONJ
ejpam-5241	486	3	)	)	PUNCT
ejpam-5241	486	4	is	be	AUX
ejpam-5241	486	5	a	a	DET
ejpam-5241	486	6	maximal	maximal	ADJ
ejpam-5241	486	7	closed	closed	ADJ
ejpam-5241	486	8	geodetic	geodetic	ADJ
ejpam-5241	486	9	sequence	sequence	NOUN
ejpam-5241	486	10	if	if	SCONJ
ejpam-5241	486	11	ig[sn	ig[sn	NOUN
ejpam-5241	486	12	]	]	X
ejpam-5241	486	13	=	=	SYM
ejpam-5241	486	14	v	v	NOUN
ejpam-5241	486	15	(	(	PUNCT
ejpam-5241	486	16	g	g	NOUN
ejpam-5241	486	17	)	)	PUNCT
ejpam-5241	486	18	.	.	PUNCT
ejpam-5241	487	1	more	more	ADV
ejpam-5241	487	2	precisely	precisely	ADV
ejpam-5241	487	3	,	,	PUNCT
ejpam-5241	487	4	s	s	VERB
ejpam-5241	487	5	⊆	⊆	NUM
ejpam-5241	487	6	v	v	NOUN
ejpam-5241	487	7	(	(	PUNCT
ejpam-5241	487	8	g	g	NOUN
ejpam-5241	487	9	)	)	PUNCT
ejpam-5241	487	10	is	be	AUX
ejpam-5241	487	11	a	a	DET
ejpam-5241	487	12	closed	closed	ADJ
ejpam-5241	487	13	geodetic	geodetic	ADJ
ejpam-5241	487	14	set	set	NOUN
ejpam-5241	487	15	of	of	ADP
ejpam-5241	487	16	g	g	PROPN
ejpam-5241	487	17	if	if	SCONJ
ejpam-5241	488	1	and	and	CCONJ
ejpam-5241	488	2	only	only	ADV
ejpam-5241	488	3	if	if	SCONJ
ejpam-5241	488	4	there	there	PRON
ejpam-5241	488	5	exists	exist	VERB
ejpam-5241	488	6	a	a	DET
ejpam-5241	488	7	positive	positive	ADJ
ejpam-5241	488	8	integer	integer	NOUN
ejpam-5241	488	9	n	n	NOUN
ejpam-5241	488	10	and	and	CCONJ
ejpam-5241	488	11	a	a	DET
ejpam-5241	488	12	maximal	maximal	ADJ
ejpam-5241	488	13	closed	closed	ADJ
ejpam-5241	488	14	geodetic	geodetic	ADJ
ejpam-5241	488	15	sequence	sequence	NOUN
ejpam-5241	488	16	of	of	ADP
ejpam-5241	488	17	sets	set	NOUN
ejpam-5241	488	18	sk	sk	INTJ
ejpam-5241	488	19	=	=	PUNCT
ejpam-5241	488	20	{	{	PUNCT
ejpam-5241	488	21	v1	v1	PROPN
ejpam-5241	488	22	,	,	PUNCT
ejpam-5241	488	23	v2	v2	PROPN
ejpam-5241	488	24	,	,	PUNCT
ejpam-5241	488	25	.	.	PUNCT
ejpam-5241	488	26	.	.	PUNCT
ejpam-5241	489	1	.	.	PUNCT
ejpam-5241	490	1	,	,	PUNCT
ejpam-5241	490	2	xk	xk	PROPN
ejpam-5241	490	3	}	}	PUNCT
ejpam-5241	490	4	(	(	PUNCT
ejpam-5241	490	5	k	k	NOUN
ejpam-5241	490	6	=	=	SYM
ejpam-5241	490	7	1	1	NUM
ejpam-5241	490	8	,	,	PUNCT
ejpam-5241	490	9	2	2	NUM
ejpam-5241	490	10	,	,	PUNCT
ejpam-5241	490	11	.	.	PUNCT
ejpam-5241	490	12	.	.	PUNCT
ejpam-5241	491	1	.	.	PUNCT
ejpam-5241	492	1	,	,	PUNCT
ejpam-5241	493	1	n	n	CCONJ
ejpam-5241	493	2	)	)	PUNCT
ejpam-5241	494	1	such	such	ADJ
ejpam-5241	494	2	that	that	PRON
ejpam-5241	494	3	s	s	PART
ejpam-5241	494	4	=	=	SYM
ejpam-5241	494	5	sn	sn	X
ejpam-5241	494	6	.	.	PUNCT
ejpam-5241	495	1	parallel	parallel	ADJ
ejpam-5241	495	2	definitions	definition	NOUN
ejpam-5241	495	3	are	be	AUX
ejpam-5241	495	4	adopted	adopt	VERB
ejpam-5241	495	5	for	for	ADP
ejpam-5241	495	6	a	a	DET
ejpam-5241	495	7	closed	closed	ADJ
ejpam-5241	495	8	2	2	NUM
ejpam-5241	495	9	-	-	PUNCT
ejpam-5241	495	10	path	path	NOUN
ejpam-5241	495	11	closure	closure	NOUN
ejpam-5241	495	12	absorbing	absorb	VERB
ejpam-5241	495	13	sequence	sequence	NOUN
ejpam-5241	495	14	of	of	ADP
ejpam-5241	495	15	sets	set	NOUN
ejpam-5241	495	16	and	and	CCONJ
ejpam-5241	495	17	maximal	maximal	ADJ
ejpam-5241	495	18	closed	close	VERB
ejpam-5241	495	19	2	2	NUM
ejpam-5241	495	20	-	-	PUNCT
ejpam-5241	495	21	path	path	NOUN
ejpam-5241	495	22	closure	closure	NOUN
ejpam-5241	495	23	absorbing	absorb	VERB
ejpam-5241	495	24	sequence	sequence	NOUN
ejpam-5241	495	25	of	of	ADP
ejpam-5241	495	26	sets	set	NOUN
ejpam-5241	495	27	.	.	PUNCT
ejpam-5241	496	1	theorem	theorem	NOUN
ejpam-5241	496	2	11	11	NUM
ejpam-5241	496	3	.	.	PUNCT
ejpam-5241	497	1	let	let	VERB
ejpam-5241	497	2	g	g	NOUN
ejpam-5241	497	3	and	and	CCONJ
ejpam-5241	497	4	h	h	NOUN
ejpam-5241	497	5	be	be	AUX
ejpam-5241	497	6	connected	connect	VERB
ejpam-5241	497	7	graphs	graph	NOUN
ejpam-5241	497	8	where	where	SCONJ
ejpam-5241	497	9	g	g	PROPN
ejpam-5241	497	10	is	be	AUX
ejpam-5241	497	11	nontrivial	nontrivial	ADJ
ejpam-5241	497	12	,	,	PUNCT
ejpam-5241	497	13	and	and	CCONJ
ejpam-5241	497	14	let	let	VERB
ejpam-5241	497	15	s	s	PRON
ejpam-5241	497	16	⊆	⊆	NUM
ejpam-5241	497	17	v	v	NOUN
ejpam-5241	497	18	(	(	PUNCT
ejpam-5241	497	19	g	g	PROPN
ejpam-5241	497	20	◦	◦	NOUN
ejpam-5241	497	21	h	h	NOUN
ejpam-5241	497	22	)	)	PUNCT
ejpam-5241	497	23	.	.	PUNCT
ejpam-5241	498	1	then	then	ADV
ejpam-5241	498	2	s	s	VERB
ejpam-5241	498	3	is	be	AUX
ejpam-5241	498	4	a	a	DET
ejpam-5241	498	5	closed	closed	ADJ
ejpam-5241	498	6	geodetic	geodetic	ADJ
ejpam-5241	498	7	hop	hop	NOUN
ejpam-5241	498	8	dominating	dominating	NOUN
ejpam-5241	498	9	set	set	NOUN
ejpam-5241	498	10	of	of	ADP
ejpam-5241	498	11	g	g	PROPN
ejpam-5241	498	12	◦	◦	NOUN
ejpam-5241	498	13	h	h	NOUN
ejpam-5241	498	14	if	if	SCONJ
ejpam-5241	499	1	and	and	CCONJ
ejpam-5241	499	2	only	only	ADV
ejpam-5241	499	3	if	if	SCONJ
ejpam-5241	499	4	s	s	VERB
ejpam-5241	499	5	=	=	NOUN
ejpam-5241	499	6	a	a	DET
ejpam-5241	499	7	∪	∪	X
ejpam-5241	499	8	(	(	PUNCT
ejpam-5241	499	9	∪v∈v	∪v∈v	X
ejpam-5241	499	10	(	(	PUNCT
ejpam-5241	499	11	g)sv	g)sv	PROPN
ejpam-5241	499	12	)	)	PUNCT
ejpam-5241	499	13	,	,	PUNCT
ejpam-5241	499	14	(	(	PUNCT
ejpam-5241	499	15	5	5	X
ejpam-5241	499	16	)	)	PUNCT
ejpam-5241	499	17	where	where	SCONJ
ejpam-5241	499	18	a	a	DET
ejpam-5241	499	19	⊆	⊆	NUM
ejpam-5241	499	20	v	v	NOUN
ejpam-5241	499	21	(	(	PUNCT
ejpam-5241	499	22	g	g	NOUN
ejpam-5241	499	23	)	)	PUNCT
ejpam-5241	499	24	and	and	CCONJ
ejpam-5241	499	25	sv	sv	X
ejpam-5241	499	26	⊆	⊆	NUM
ejpam-5241	499	27	v	v	X
ejpam-5241	499	28	(	(	PUNCT
ejpam-5241	499	29	hv	hv	NOUN
ejpam-5241	499	30	)	)	PUNCT
ejpam-5241	499	31	satisfying	satisfy	VERB
ejpam-5241	499	32	the	the	DET
ejpam-5241	499	33	following	follow	VERB
ejpam-5241	499	34	conditions	condition	NOUN
ejpam-5241	499	35	:	:	PUNCT
ejpam-5241	499	36	(	(	PUNCT
ejpam-5241	499	37	i	i	NOUN
ejpam-5241	499	38	)	)	PUNCT
ejpam-5241	499	39	sv	sv	PROPN
ejpam-5241	499	40	is	be	AUX
ejpam-5241	499	41	a	a	DET
ejpam-5241	499	42	pointwise	pointwise	ADJ
ejpam-5241	499	43	non	non	ADJ
ejpam-5241	499	44	-	-	ADJ
ejpam-5241	499	45	dominating	dominating	ADJ
ejpam-5241	499	46	set	set	NOUN
ejpam-5241	499	47	of	of	ADP
ejpam-5241	499	48	hv	hv	PROPN
ejpam-5241	499	49	for	for	ADP
ejpam-5241	499	50	each	each	PRON
ejpam-5241	499	51	v	v	NUM
ejpam-5241	499	52	∈	∈	PROPN
ejpam-5241	499	53	v	v	NOUN
ejpam-5241	499	54	(	(	PUNCT
ejpam-5241	499	55	g	g	NOUN
ejpam-5241	499	56	)	)	PUNCT
ejpam-5241	499	57	\ng(a	\ng(a	PROPN
ejpam-5241	499	58	)	)	PUNCT
ejpam-5241	499	59	;	;	PUNCT
ejpam-5241	499	60	(	(	PUNCT
ejpam-5241	499	61	ii	ii	NOUN
ejpam-5241	499	62	)	)	PUNCT
ejpam-5241	499	63	sv	sv	PROPN
ejpam-5241	499	64	is	be	AUX
ejpam-5241	499	65	a	a	DET
ejpam-5241	499	66	closed	closed	ADJ
ejpam-5241	499	67	2	2	NUM
ejpam-5241	499	68	-	-	PUNCT
ejpam-5241	499	69	path	path	NOUN
ejpam-5241	499	70	closure	closure	NOUN
ejpam-5241	499	71	absorbing	absorb	VERB
ejpam-5241	499	72	set	set	NOUN
ejpam-5241	499	73	of	of	ADP
ejpam-5241	499	74	hv	hv	PROPN
ejpam-5241	499	75	;	;	PUNCT
ejpam-5241	499	76	and	and	CCONJ
ejpam-5241	499	77	(	(	PUNCT
ejpam-5241	499	78	iii	iii	X
ejpam-5241	499	79	)	)	PUNCT
ejpam-5241	499	80	the	the	DET
ejpam-5241	499	81	vertices	vertex	NOUN
ejpam-5241	499	82	in	in	ADP
ejpam-5241	499	83	a	a	DET
ejpam-5241	499	84	constitute	constitute	NOUN
ejpam-5241	499	85	a	a	DET
ejpam-5241	499	86	closed	closed	ADJ
ejpam-5241	499	87	geodetic	geodetic	ADJ
ejpam-5241	499	88	sequence	sequence	NOUN
ejpam-5241	499	89	of	of	ADP
ejpam-5241	499	90	sets	set	NOUN
ejpam-5241	499	91	of	of	ADP
ejpam-5241	499	92	g	g	NOUN
ejpam-5241	499	93	proof	proof	NOUN
ejpam-5241	499	94	.	.	PUNCT
ejpam-5241	500	1	assume	assume	VERB
ejpam-5241	500	2	s	s	PRON
ejpam-5241	500	3	is	be	AUX
ejpam-5241	500	4	a	a	DET
ejpam-5241	500	5	closed	closed	ADJ
ejpam-5241	500	6	geodetic	geodetic	ADJ
ejpam-5241	500	7	hop	hop	NOUN
ejpam-5241	500	8	dominating	dominating	NOUN
ejpam-5241	500	9	set	set	NOUN
ejpam-5241	500	10	of	of	ADP
ejpam-5241	500	11	g	g	PROPN
ejpam-5241	500	12	◦	◦	NOUN
ejpam-5241	500	13	h.	h.	NOUN
ejpam-5241	500	14	let	let	VERB
ejpam-5241	500	15	a	a	DET
ejpam-5241	500	16	=	=	X
ejpam-5241	500	17	s	s	NOUN
ejpam-5241	500	18	∩	∩	ADJ
ejpam-5241	500	19	v	v	X
ejpam-5241	500	20	(	(	PUNCT
ejpam-5241	500	21	g	g	NOUN
ejpam-5241	500	22	)	)	PUNCT
ejpam-5241	500	23	and	and	CCONJ
ejpam-5241	500	24	sv	sv	X
ejpam-5241	500	25	=	=	SYM
ejpam-5241	500	26	s∩v	s∩v	PROPN
ejpam-5241	500	27	(	(	PUNCT
ejpam-5241	500	28	hv	hv	PROPN
ejpam-5241	500	29	)	)	PUNCT
ejpam-5241	500	30	for	for	ADP
ejpam-5241	500	31	each	each	DET
ejpam-5241	500	32	v	v	NUM
ejpam-5241	500	33	∈	∈	PROPN
ejpam-5241	500	34	v	v	NOUN
ejpam-5241	500	35	(	(	PUNCT
ejpam-5241	500	36	g	g	NOUN
ejpam-5241	500	37	)	)	PUNCT
ejpam-5241	500	38	.	.	PUNCT
ejpam-5241	501	1	then	then	ADV
ejpam-5241	501	2	s	s	VERB
ejpam-5241	501	3	=	=	SYM
ejpam-5241	501	4	a∪	a∪	PROPN
ejpam-5241	501	5	(	(	PUNCT
ejpam-5241	501	6	∪v∈v	∪v∈v	X
ejpam-5241	501	7	(	(	PUNCT
ejpam-5241	501	8	g)sv	g)sv	PROPN
ejpam-5241	501	9	)	)	PUNCT
ejpam-5241	501	10	.	.	PUNCT
ejpam-5241	502	1	let	let	VERB
ejpam-5241	502	2	v	v	NUM
ejpam-5241	502	3	∈	∈	PROPN
ejpam-5241	502	4	v	v	NOUN
ejpam-5241	502	5	(	(	PUNCT
ejpam-5241	502	6	g)\ng(a	g)\ng(a	NOUN
ejpam-5241	502	7	)	)	PUNCT
ejpam-5241	502	8	,	,	PUNCT
ejpam-5241	502	9	and	and	CCONJ
ejpam-5241	502	10	let	let	VERB
ejpam-5241	502	11	u	u	PRON
ejpam-5241	502	12	∈	∈	PROPN
ejpam-5241	502	13	v	v	X
ejpam-5241	502	14	(	(	PUNCT
ejpam-5241	502	15	hv	hv	PROPN
ejpam-5241	502	16	)	)	PUNCT
ejpam-5241	502	17	\	\	PROPN
ejpam-5241	503	1	sv	sv	PROPN
ejpam-5241	503	2	.	.	PUNCT
ejpam-5241	504	1	since	since	SCONJ
ejpam-5241	504	2	s	s	PROPN
ejpam-5241	504	3	is	be	AUX
ejpam-5241	504	4	a	a	DET
ejpam-5241	504	5	hop	hop	NOUN
ejpam-5241	504	6	dominating	dominating	NOUN
ejpam-5241	504	7	set	set	NOUN
ejpam-5241	504	8	of	of	ADP
ejpam-5241	504	9	g	g	PROPN
ejpam-5241	504	10	◦	◦	NOUN
ejpam-5241	504	11	h	h	NOUN
ejpam-5241	504	12	,	,	PUNCT
ejpam-5241	504	13	there	there	PRON
ejpam-5241	504	14	exists	exist	VERB
ejpam-5241	504	15	w	w	PROPN
ejpam-5241	504	16	∈	∈	PROPN
ejpam-5241	504	17	s	s	VERB
ejpam-5241	504	18	such	such	ADJ
ejpam-5241	504	19	that	that	SCONJ
ejpam-5241	504	20	dg	dg	PROPN
ejpam-5241	504	21	◦	◦	PROPN
ejpam-5241	504	22	h(u	h(u	PROPN
ejpam-5241	504	23	,	,	PUNCT
ejpam-5241	504	24	w	w	NOUN
ejpam-5241	504	25	)	)	PUNCT
ejpam-5241	504	26	=	=	SYM
ejpam-5241	505	1	2	2	X
ejpam-5241	505	2	.	.	X
ejpam-5241	506	1	if	if	SCONJ
ejpam-5241	506	2	w	w	PROPN
ejpam-5241	506	3	∈	∈	PROPN
ejpam-5241	506	4	v	v	ADP
ejpam-5241	506	5	(	(	PUNCT
ejpam-5241	506	6	g	g	NOUN
ejpam-5241	506	7	)	)	PUNCT
ejpam-5241	506	8	,	,	PUNCT
ejpam-5241	506	9	then	then	ADV
ejpam-5241	506	10	w	w	PROPN
ejpam-5241	506	11	∈	∈	PROPN
ejpam-5241	506	12	a	a	PRON
ejpam-5241	506	13	and	and	CCONJ
ejpam-5241	506	14	wv	wv	PROPN
ejpam-5241	506	15	∈	∈	PROPN
ejpam-5241	506	16	e(g	e(g	PROPN
ejpam-5241	506	17	)	)	PUNCT
ejpam-5241	506	18	,	,	PUNCT
ejpam-5241	506	19	which	which	PRON
ejpam-5241	506	20	is	be	AUX
ejpam-5241	506	21	impossible	impossible	ADJ
ejpam-5241	506	22	.	.	PUNCT
ejpam-5241	507	1	thus	thus	ADV
ejpam-5241	507	2	,	,	PUNCT
ejpam-5241	507	3	w	w	PROPN
ejpam-5241	507	4	/∈	/∈	PROPN
ejpam-5241	507	5	v	v	NOUN
ejpam-5241	507	6	(	(	PUNCT
ejpam-5241	507	7	g	g	NOUN
ejpam-5241	507	8	)	)	PUNCT
ejpam-5241	508	1	so	so	SCONJ
ejpam-5241	508	2	that	that	SCONJ
ejpam-5241	508	3	w	w	PROPN
ejpam-5241	508	4	∈	∈	PROPN
ejpam-5241	508	5	sv	sv	ADP
ejpam-5241	508	6	.	.	PUNCT
ejpam-5241	509	1	in	in	ADP
ejpam-5241	509	2	this	this	DET
ejpam-5241	509	3	case	case	NOUN
ejpam-5241	509	4	,	,	PUNCT
ejpam-5241	509	5	dg	dg	PROPN
ejpam-5241	509	6	◦	◦	PROPN
ejpam-5241	509	7	h(u	h(u	PROPN
ejpam-5241	509	8	,	,	PUNCT
ejpam-5241	509	9	w	w	NOUN
ejpam-5241	509	10	)	)	PUNCT
ejpam-5241	509	11	=	=	SYM
ejpam-5241	509	12	dhv(u	dhv(u	PROPN
ejpam-5241	509	13	,	,	PUNCT
ejpam-5241	509	14	w	w	NOUN
ejpam-5241	509	15	)	)	PUNCT
ejpam-5241	509	16	=	=	SYM
ejpam-5241	510	1	2	2	X
ejpam-5241	510	2	.	.	PUNCT
ejpam-5241	510	3	this	this	PRON
ejpam-5241	510	4	means	mean	VERB
ejpam-5241	510	5	that	that	SCONJ
ejpam-5241	510	6	sv	sv	PROPN
ejpam-5241	510	7	is	be	AUX
ejpam-5241	510	8	pointwise	pointwise	PROPN
ejpam-5241	510	9	non	non	ADJ
ejpam-5241	510	10	-	-	ADJ
ejpam-5241	510	11	dominating	dominating	NOUN
ejpam-5241	510	12	in	in	ADP
ejpam-5241	510	13	hv	hv	PROPN
ejpam-5241	510	14	,	,	PUNCT
ejpam-5241	510	15	showing	show	VERB
ejpam-5241	510	16	(	(	PUNCT
ejpam-5241	510	17	i	i	NOUN
ejpam-5241	510	18	)	)	PUNCT
ejpam-5241	510	19	.	.	PUNCT
ejpam-5241	511	1	to	to	PART
ejpam-5241	511	2	show	show	VERB
ejpam-5241	511	3	,	,	PUNCT
ejpam-5241	511	4	(	(	PUNCT
ejpam-5241	511	5	ii	ii	NOUN
ejpam-5241	511	6	)	)	PUNCT
ejpam-5241	511	7	,	,	PUNCT
ejpam-5241	511	8	let	let	VERB
ejpam-5241	511	9	v	v	NUM
ejpam-5241	511	10	∈	∈	PROPN
ejpam-5241	511	11	v	v	NOUN
ejpam-5241	511	12	(	(	PUNCT
ejpam-5241	511	13	g	g	NOUN
ejpam-5241	511	14	)	)	PUNCT
ejpam-5241	511	15	.	.	PUNCT
ejpam-5241	512	1	let	let	VERB
ejpam-5241	512	2	n	n	NOUN
ejpam-5241	512	3	=	=	SYM
ejpam-5241	512	4	|s|	|s|	PROPN
ejpam-5241	512	5	.	.	PUNCT
ejpam-5241	513	1	there	there	PRON
ejpam-5241	513	2	exists	exist	VERB
ejpam-5241	513	3	a	a	DET
ejpam-5241	513	4	closed	closed	ADJ
ejpam-5241	513	5	geodetic	geodetic	ADJ
ejpam-5241	513	6	sequence	sequence	NOUN
ejpam-5241	513	7	of	of	ADP
ejpam-5241	513	8	sets	set	NOUN
ejpam-5241	513	9	sk	sk	INTJ
ejpam-5241	513	10	=	=	PUNCT
ejpam-5241	513	11	{	{	PUNCT
ejpam-5241	513	12	x1	x1	PROPN
ejpam-5241	513	13	,	,	PUNCT
ejpam-5241	513	14	x2	x2	PROPN
ejpam-5241	513	15	,	,	PUNCT
ejpam-5241	513	16	.	.	PUNCT
ejpam-5241	513	17	.	.	PUNCT
ejpam-5241	514	1	.	.	PUNCT
ejpam-5241	515	1	,	,	PUNCT
ejpam-5241	515	2	xk	xk	PROPN
ejpam-5241	515	3	}	}	PUNCT
ejpam-5241	515	4	,	,	PUNCT
ejpam-5241	515	5	3	3	NUM
ejpam-5241	515	6	≤	≤	NUM
ejpam-5241	515	7	k	k	NOUN
ejpam-5241	515	8	≤	≤	PROPN
ejpam-5241	515	9	n	n	CCONJ
ejpam-5241	515	10	,	,	PUNCT
ejpam-5241	515	11	such	such	ADJ
ejpam-5241	515	12	that	that	SCONJ
ejpam-5241	515	13	ig	ig	PROPN
ejpam-5241	515	14	◦	◦	NOUN
ejpam-5241	515	15	h	h	NOUN
ejpam-5241	516	1	[	[	X
ejpam-5241	516	2	sn	sn	X
ejpam-5241	516	3	]	]	X
ejpam-5241	516	4	=	=	SYM
ejpam-5241	516	5	v	v	NOUN
ejpam-5241	516	6	(	(	PUNCT
ejpam-5241	516	7	g	g	PROPN
ejpam-5241	516	8	◦	◦	NOUN
ejpam-5241	516	9	h	h	NOUN
ejpam-5241	516	10	)	)	PUNCT
ejpam-5241	516	11	.	.	PUNCT
ejpam-5241	517	1	write	write	VERB
ejpam-5241	517	2	sv	sv	PROPN
ejpam-5241	518	1	=	=	PUNCT
ejpam-5241	518	2	{	{	PUNCT
ejpam-5241	518	3	xn1	xn1	X
ejpam-5241	518	4	,	,	PUNCT
ejpam-5241	518	5	xn2	xn2	PROPN
ejpam-5241	518	6	,	,	PUNCT
ejpam-5241	518	7	.	.	PUNCT
ejpam-5241	518	8	.	.	PUNCT
ejpam-5241	518	9	.	.	PUNCT
ejpam-5241	519	1	,	,	PUNCT
ejpam-5241	519	2	xnj	xnj	PROPN
ejpam-5241	519	3	}	}	PUNCT
ejpam-5241	519	4	with	with	ADP
ejpam-5241	519	5	n1	n1	PROPN
ejpam-5241	519	6	<	<	X
ejpam-5241	519	7	n2	n2	X
ejpam-5241	519	8	<	<	X
ejpam-5241	519	9	·	·	PUNCT
ejpam-5241	519	10	·	·	PUNCT
ejpam-5241	519	11	·	·	PUNCT
ejpam-5241	520	1	<	<	X
ejpam-5241	520	2	nj	nj	PROPN
ejpam-5241	520	3	.	.	PUNCT
ejpam-5241	521	1	define	define	VERB
ejpam-5241	521	2	ti	ti	NOUN
ejpam-5241	521	3	=	=	SYM
ejpam-5241	521	4	{	{	PUNCT
ejpam-5241	521	5	xn1	xn1	PROPN
ejpam-5241	521	6	,	,	PUNCT
ejpam-5241	521	7	xn2	xn2	PROPN
ejpam-5241	521	8	,	,	PUNCT
ejpam-5241	521	9	.	.	PUNCT
ejpam-5241	521	10	.	.	PUNCT
ejpam-5241	522	1	.	.	PUNCT
ejpam-5241	523	1	,	,	PUNCT
ejpam-5241	523	2	xni	xni	PROPN
ejpam-5241	523	3	}	}	PUNCT
ejpam-5241	523	4	for	for	ADP
ejpam-5241	523	5	i	i	PROPN
ejpam-5241	523	6	=	=	NOUN
ejpam-5241	523	7	1	1	NUM
ejpam-5241	523	8	,	,	PUNCT
ejpam-5241	523	9	2	2	NUM
ejpam-5241	523	10	,	,	PUNCT
ejpam-5241	523	11	.	.	PUNCT
ejpam-5241	523	12	.	.	PUNCT
ejpam-5241	524	1	.	.	PUNCT
ejpam-5241	525	1	,	,	PUNCT
ejpam-5241	525	2	j.	j.	PROPN
ejpam-5241	525	3	suppose	suppose	VERB
ejpam-5241	525	4	that	that	SCONJ
ejpam-5241	525	5	for	for	ADP
ejpam-5241	525	6	a	a	DET
ejpam-5241	525	7	<	<	X
ejpam-5241	525	8	b	b	X
ejpam-5241	525	9	<	<	X
ejpam-5241	525	10	c	c	X
ejpam-5241	525	11	,	,	PUNCT
ejpam-5241	525	12	[	[	X
ejpam-5241	525	13	xna	xna	X
ejpam-5241	525	14	,	,	PUNCT
ejpam-5241	525	15	xnc	xnc	PROPN
ejpam-5241	525	16	,	,	PUNCT
ejpam-5241	525	17	xnb	xnb	PROPN
ejpam-5241	525	18	]	]	X
ejpam-5241	525	19	is	be	AUX
ejpam-5241	525	20	a	a	DET
ejpam-5241	525	21	geodesic	geodesic	NOUN
ejpam-5241	525	22	in	in	ADP
ejpam-5241	525	23	hv	hv	PROPN
ejpam-5241	525	24	.	.	PUNCT
ejpam-5241	526	1	then	then	ADV
ejpam-5241	526	2	[	[	X
ejpam-5241	526	3	xna	xna	X
ejpam-5241	526	4	,	,	PUNCT
ejpam-5241	526	5	xnc	xnc	PROPN
ejpam-5241	526	6	,	,	PUNCT
ejpam-5241	526	7	xnb	xnb	PROPN
ejpam-5241	526	8	]	]	X
ejpam-5241	526	9	is	be	AUX
ejpam-5241	526	10	a	a	DET
ejpam-5241	526	11	geodesic	geodesic	NOUN
ejpam-5241	526	12	in	in	ADP
ejpam-5241	526	13	g	g	PROPN
ejpam-5241	526	14	◦	◦	NOUN
ejpam-5241	526	15	h	h	NOUN
ejpam-5241	526	16	so	so	SCONJ
ejpam-5241	526	17	that	that	SCONJ
ejpam-5241	526	18	xnc	xnc	PROPN
ejpam-5241	526	19	∈	∈	PROPN
ejpam-5241	526	20	ig	ig	PROPN
ejpam-5241	526	21	◦	◦	NOUN
ejpam-5241	526	22	h	h	NOUN
ejpam-5241	527	1	[	[	X
ejpam-5241	527	2	snb	snb	X
ejpam-5241	527	3	]	]	X
ejpam-5241	527	4	,	,	PUNCT
ejpam-5241	527	5	a	a	DET
ejpam-5241	527	6	contradiction	contradiction	NOUN
ejpam-5241	527	7	.	.	PUNCT
ejpam-5241	528	1	therefore	therefore	ADV
ejpam-5241	528	2	,	,	PUNCT
ejpam-5241	528	3	xni	xni	PROPN
ejpam-5241	528	4	/∈	/∈	PUNCT
ejpam-5241	528	5	p2[ti−1	p2[ti−1	PROPN
ejpam-5241	528	6	]	]	PUNCT
ejpam-5241	528	7	for	for	ADP
ejpam-5241	528	8	3	3	NUM
ejpam-5241	528	9	≤	≤	NUM
ejpam-5241	528	10	i	i	PRON
ejpam-5241	528	11	≤	≤	PROPN
ejpam-5241	528	12	j	j	PROPN
ejpam-5241	528	13	,	,	PUNCT
ejpam-5241	528	14	and	and	CCONJ
ejpam-5241	528	15	therefore	therefore	ADV
ejpam-5241	528	16	,	,	PUNCT
ejpam-5241	528	17	ti	ti	X
ejpam-5241	528	18	=	=	SYM
ejpam-5241	528	19	{	{	PUNCT
ejpam-5241	528	20	xn1	xn1	PROPN
ejpam-5241	528	21	,	,	PUNCT
ejpam-5241	528	22	xn2	xn2	PROPN
ejpam-5241	528	23	,	,	PUNCT
ejpam-5241	528	24	.	.	PUNCT
ejpam-5241	528	25	.	.	PUNCT
ejpam-5241	528	26	.	.	PUNCT
ejpam-5241	529	1	,	,	PUNCT
ejpam-5241	529	2	xni	xni	PROPN
ejpam-5241	529	3	}	}	PUNCT
ejpam-5241	529	4	,	,	PUNCT
ejpam-5241	529	5	i	i	PRON
ejpam-5241	529	6	=	=	NOUN
ejpam-5241	529	7	1	1	NUM
ejpam-5241	529	8	,	,	PUNCT
ejpam-5241	529	9	2	2	NUM
ejpam-5241	529	10	,	,	PUNCT
ejpam-5241	529	11	.	.	PUNCT
ejpam-5241	529	12	.	.	PUNCT
ejpam-5241	529	13	.	.	PUNCT
ejpam-5241	530	1	,	,	PUNCT
ejpam-5241	530	2	j	j	PROPN
ejpam-5241	530	3	,	,	PUNCT
ejpam-5241	530	4	is	be	AUX
ejpam-5241	530	5	a	a	DET
ejpam-5241	530	6	closed	closed	ADJ
ejpam-5241	530	7	2	2	NUM
ejpam-5241	530	8	-	-	PUNCT
ejpam-5241	530	9	path	path	NOUN
ejpam-5241	530	10	closure	closure	NOUN
ejpam-5241	530	11	absorbing	absorb	VERB
ejpam-5241	530	12	sequence	sequence	NOUN
ejpam-5241	530	13	of	of	ADP
ejpam-5241	530	14	sets	set	NOUN
ejpam-5241	530	15	in	in	ADP
ejpam-5241	530	16	hv	hv	PROPN
ejpam-5241	530	17	.	.	PUNCT
ejpam-5241	531	1	let	let	VERB
ejpam-5241	531	2	x	x	SYM
ejpam-5241	531	3	∈	∈	PROPN
ejpam-5241	531	4	v	v	ADP
ejpam-5241	531	5	(	(	PUNCT
ejpam-5241	531	6	hv	hv	NOUN
ejpam-5241	531	7	)	)	PUNCT
ejpam-5241	531	8	\	\	PROPN
ejpam-5241	531	9	tj	tj	NOUN
ejpam-5241	531	10	.	.	PUNCT
ejpam-5241	532	1	since	since	SCONJ
ejpam-5241	532	2	ig	ig	PRON
ejpam-5241	532	3	◦	◦	NOUN
ejpam-5241	532	4	h	h	NOUN
ejpam-5241	532	5	[	[	X
ejpam-5241	532	6	sn	sn	X
ejpam-5241	532	7	]	]	X
ejpam-5241	532	8	=	=	SYM
ejpam-5241	532	9	v	v	NOUN
ejpam-5241	532	10	(	(	PUNCT
ejpam-5241	532	11	g	g	PROPN
ejpam-5241	532	12	◦	◦	NOUN
ejpam-5241	532	13	h	h	NOUN
ejpam-5241	532	14	)	)	PUNCT
ejpam-5241	532	15	,	,	PUNCT
ejpam-5241	532	16	there	there	PRON
ejpam-5241	532	17	exist	exist	VERB
ejpam-5241	532	18	1	1	NUM
ejpam-5241	532	19	≤	≤	NOUN
ejpam-5241	532	20	a	a	PRON
ejpam-5241	532	21	,	,	PUNCT
ejpam-5241	532	22	b	b	PROPN
ejpam-5241	532	23	≤	≤	NUM
ejpam-5241	532	24	n	n	PRON
ejpam-5241	532	25	such	such	ADJ
ejpam-5241	532	26	that	that	SCONJ
ejpam-5241	532	27	x	x	SYM
ejpam-5241	532	28	∈	∈	PROPN
ejpam-5241	532	29	ig	ig	PROPN
ejpam-5241	532	30	◦	◦	NOUN
ejpam-5241	532	31	h(xa	h(xa	NOUN
ejpam-5241	532	32	,	,	PUNCT
ejpam-5241	532	33	xb	xb	PROPN
ejpam-5241	532	34	)	)	PUNCT
ejpam-5241	532	35	.	.	PUNCT
ejpam-5241	533	1	because	because	SCONJ
ejpam-5241	533	2	yv	yv	PROPN
ejpam-5241	533	3	∈	∈	PROPN
ejpam-5241	533	4	e(g	e(g	PROPN
ejpam-5241	533	5	◦	◦	NOUN
ejpam-5241	533	6	h	h	NOUN
ejpam-5241	533	7	for	for	ADP
ejpam-5241	533	8	all	all	DET
ejpam-5241	533	9	y	y	PROPN
ejpam-5241	533	10	∈	∈	PROPN
ejpam-5241	533	11	v	v	PROPN
ejpam-5241	533	12	(	(	PUNCT
ejpam-5241	533	13	hv	hv	PROPN
ejpam-5241	533	14	)	)	PUNCT
ejpam-5241	533	15	,	,	PUNCT
ejpam-5241	533	16	any	any	DET
ejpam-5241	533	17	xa	xa	PROPN
ejpam-5241	533	18	-	-	PUNCT
ejpam-5241	533	19	xb	xb	PROPN
ejpam-5241	533	20	geodesic	geodesic	NOUN
ejpam-5241	533	21	lies	lie	VERB
ejpam-5241	533	22	completely	completely	ADV
ejpam-5241	533	23	in	in	ADP
ejpam-5241	533	24	v	v	PROPN
ejpam-5241	533	25	(	(	PUNCT
ejpam-5241	533	26	hv	hv	PROPN
ejpam-5241	533	27	)	)	PUNCT
ejpam-5241	533	28	.	.	PUNCT
ejpam-5241	534	1	thus	thus	ADV
ejpam-5241	534	2	,	,	PUNCT
ejpam-5241	534	3	a	a	DET
ejpam-5241	534	4	,	,	PUNCT
ejpam-5241	534	5	b	b	PROPN
ejpam-5241	534	6	∈	∈	PROPN
ejpam-5241	534	7	{	{	PUNCT
ejpam-5241	534	8	n1	n1	NOUN
ejpam-5241	534	9	,	,	PUNCT
ejpam-5241	534	10	n2	n2	NOUN
ejpam-5241	534	11	,	,	PUNCT
ejpam-5241	534	12	.	.	PUNCT
ejpam-5241	534	13	.	.	PUNCT
ejpam-5241	534	14	.	.	PUNCT
ejpam-5241	535	1	,	,	PUNCT
ejpam-5241	535	2	nj	nj	PROPN
ejpam-5241	535	3	}	}	PUNCT
ejpam-5241	535	4	.	.	PUNCT
ejpam-5241	536	1	this	this	PRON
ejpam-5241	536	2	means	mean	VERB
ejpam-5241	536	3	that	that	SCONJ
ejpam-5241	536	4	p2[tj	p2[tj	NOUN
ejpam-5241	536	5	]	]	PUNCT
ejpam-5241	536	6	=	=	SYM
ejpam-5241	536	7	v	v	X
ejpam-5241	536	8	(	(	PUNCT
ejpam-5241	536	9	hv	hv	PROPN
ejpam-5241	536	10	)	)	PUNCT
ejpam-5241	536	11	and	and	CCONJ
ejpam-5241	536	12	tj	tj	X
ejpam-5241	536	13	=	=	NOUN
ejpam-5241	536	14	sv	sv	PROPN
ejpam-5241	536	15	is	be	AUX
ejpam-5241	536	16	a	a	DET
ejpam-5241	536	17	closed	closed	ADJ
ejpam-5241	536	18	2	2	NUM
ejpam-5241	536	19	-	-	PUNCT
ejpam-5241	536	20	path	path	NOUN
ejpam-5241	536	21	closure	closure	NOUN
ejpam-5241	536	22	absorbing	absorb	VERB
ejpam-5241	536	23	set	set	NOUN
ejpam-5241	536	24	of	of	ADP
ejpam-5241	536	25	hv	hv	PROPN
ejpam-5241	536	26	.	.	PUNCT
ejpam-5241	537	1	statement	statement	PROPN
ejpam-5241	537	2	(	(	PUNCT
ejpam-5241	537	3	iii	iii	NOUN
ejpam-5241	537	4	)	)	PUNCT
ejpam-5241	537	5	is	be	AUX
ejpam-5241	537	6	done	do	VERB
ejpam-5241	537	7	similarly	similarly	ADV
ejpam-5241	537	8	.	.	PUNCT
ejpam-5241	538	1	the	the	DET
ejpam-5241	538	2	sequence	sequence	NOUN
ejpam-5241	538	3	ai	ai	VERB
ejpam-5241	538	4	=	=	PUNCT
ejpam-5241	538	5	{	{	PUNCT
ejpam-5241	538	6	xk1	xk1	PROPN
ejpam-5241	538	7	,	,	PUNCT
ejpam-5241	538	8	xk2	xk2	NOUN
ejpam-5241	538	9	,	,	PUNCT
ejpam-5241	538	10	.	.	PUNCT
ejpam-5241	538	11	.	.	PUNCT
ejpam-5241	538	12	.	.	PUNCT
ejpam-5241	539	1	,	,	PUNCT
ejpam-5241	539	2	xki	xki	PROPN
ejpam-5241	539	3	}	}	PUNCT
ejpam-5241	539	4	,	,	PUNCT
ejpam-5241	539	5	i	i	PRON
ejpam-5241	539	6	=	=	NOUN
ejpam-5241	539	7	1	1	NUM
ejpam-5241	539	8	,	,	PUNCT
ejpam-5241	539	9	2	2	NUM
ejpam-5241	539	10	,	,	PUNCT
ejpam-5241	539	11	.	.	PUNCT
ejpam-5241	539	12	.	.	PUNCT
ejpam-5241	540	1	.	.	PUNCT
ejpam-5241	541	1	,	,	PUNCT
ejpam-5241	541	2	j	j	PROPN
ejpam-5241	541	3	,	,	PUNCT
ejpam-5241	541	4	such	such	ADJ
ejpam-5241	541	5	that	that	SCONJ
ejpam-5241	541	6	aj	aj	PROPN
ejpam-5241	541	7	=	=	PRON
ejpam-5241	541	8	a	a	PRON
ejpam-5241	541	9	is	be	AUX
ejpam-5241	541	10	a	a	DET
ejpam-5241	541	11	closed	closed	ADJ
ejpam-5241	541	12	geodetic	geodetic	ADJ
ejpam-5241	541	13	sequence	sequence	NOUN
ejpam-5241	541	14	of	of	ADP
ejpam-5241	541	15	sets	set	NOUN
ejpam-5241	541	16	of	of	ADP
ejpam-5241	541	17	g.	g.	PROPN
ejpam-5241	541	18	to	to	PART
ejpam-5241	541	19	prove	prove	VERB
ejpam-5241	541	20	the	the	DET
ejpam-5241	541	21	converse	converse	NOUN
ejpam-5241	541	22	,	,	PUNCT
ejpam-5241	541	23	assume	assume	VERB
ejpam-5241	541	24	that	that	SCONJ
ejpam-5241	541	25	equation	equation	NOUN
ejpam-5241	541	26	3	3	NUM
ejpam-5241	541	27	holds	hold	VERB
ejpam-5241	541	28	for	for	ADP
ejpam-5241	541	29	s	s	PRON
ejpam-5241	541	30	together	together	ADV
ejpam-5241	541	31	with	with	ADP
ejpam-5241	541	32	conditions	condition	NOUN
ejpam-5241	541	33	(	(	PUNCT
ejpam-5241	541	34	i	i	NOUN
ejpam-5241	541	35	)	)	PUNCT
ejpam-5241	541	36	,	,	PUNCT
ejpam-5241	541	37	(	(	PUNCT
ejpam-5241	541	38	ii	ii	NOUN
ejpam-5241	541	39	)	)	PUNCT
ejpam-5241	541	40	and	and	CCONJ
ejpam-5241	541	41	(	(	PUNCT
ejpam-5241	541	42	iii	iii	NOUN
ejpam-5241	541	43	)	)	PUNCT
ejpam-5241	541	44	.	.	PUNCT
ejpam-5241	542	1	let	let	VERB
ejpam-5241	542	2	n	n	NOUN
ejpam-5241	542	3	=	=	SYM
ejpam-5241	542	4	|s|	|s|	PROPN
ejpam-5241	542	5	,	,	PUNCT
ejpam-5241	542	6	j	j	PROPN
ejpam-5241	542	7	=	=	SYM
ejpam-5241	542	8	|a|	|a|	PROPN
ejpam-5241	542	9	,	,	PUNCT
ejpam-5241	542	10	and	and	CCONJ
ejpam-5241	542	11	for	for	ADP
ejpam-5241	542	12	each	each	DET
ejpam-5241	542	13	v	v	NUM
ejpam-5241	542	14	∈	∈	PROPN
ejpam-5241	542	15	v	v	NOUN
ejpam-5241	542	16	(	(	PUNCT
ejpam-5241	542	17	g	g	NOUN
ejpam-5241	542	18	)	)	PUNCT
ejpam-5241	542	19	,	,	PUNCT
ejpam-5241	542	20	let	let	VERB
ejpam-5241	542	21	sj	sj	PRON
ejpam-5241	542	22	v	v	VERB
ejpam-5241	542	23	=	=	PUNCT
ejpam-5241	542	24	{	{	PUNCT
ejpam-5241	542	25	x1v	x1v	PROPN
ejpam-5241	542	26	,	,	PUNCT
ejpam-5241	542	27	x2v	x2v	PROPN
ejpam-5241	542	28	,	,	PUNCT
ejpam-5241	542	29	.	.	PUNCT
ejpam-5241	542	30	.	.	PUNCT
ejpam-5241	542	31	.	.	PUNCT
ejpam-5241	543	1	,	,	PUNCT
ejpam-5241	543	2	x	x	X
ejpam-5241	543	3	j	j	PROPN
ejpam-5241	543	4	v	v	ADP
ejpam-5241	543	5	}	}	PUNCT
ejpam-5241	543	6	⊆	⊆	NUM
ejpam-5241	543	7	sv	sv	NOUN
ejpam-5241	543	8	,	,	PUNCT
ejpam-5241	543	9	a.	a.	PROPN
ejpam-5241	543	10	adolfo	adolfo	PROPN
ejpam-5241	543	11	,	,	PUNCT
ejpam-5241	543	12	i.	i.	PROPN
ejpam-5241	543	13	aniversario	aniversario	PROPN
ejpam-5241	543	14	,	,	PUNCT
ejpam-5241	543	15	f.	f.	PROPN
ejpam-5241	543	16	jamil	jamil	PROPN
ejpam-5241	543	17	/	/	SYM
ejpam-5241	543	18	eur	eur	PROPN
ejpam-5241	543	19	.	.	PUNCT
ejpam-5241	544	1	j.	j.	PROPN
ejpam-5241	544	2	pure	pure	PROPN
ejpam-5241	544	3	appl	appl	PROPN
ejpam-5241	544	4	.	.	PROPN
ejpam-5241	544	5	math	math	PROPN
ejpam-5241	544	6	,	,	PUNCT
ejpam-5241	544	7	17	17	NUM
ejpam-5241	544	8	(	(	PUNCT
ejpam-5241	544	9	3	3	NUM
ejpam-5241	544	10	)	)	PUNCT
ejpam-5241	544	11	(	(	PUNCT
ejpam-5241	544	12	2024	2024	NUM
ejpam-5241	544	13	)	)	PUNCT
ejpam-5241	544	14	,	,	PUNCT
ejpam-5241	544	15	1618	1618	NUM
ejpam-5241	544	16	-	-	SYM
ejpam-5241	544	17	1636	1636	NUM
ejpam-5241	544	18	1632	1632	NUM
ejpam-5241	544	19	j	j	NOUN
ejpam-5241	545	1	=	=	SYM
ejpam-5241	545	2	1	1	NUM
ejpam-5241	545	3	,	,	PUNCT
ejpam-5241	545	4	2	2	NUM
ejpam-5241	545	5	,	,	PUNCT
ejpam-5241	545	6	.	.	PUNCT
ejpam-5241	545	7	.	.	PUNCT
ejpam-5241	546	1	.	.	PUNCT
ejpam-5241	547	1	,	,	PUNCT
ejpam-5241	547	2	kv	kv	PROPN
ejpam-5241	547	3	,	,	PUNCT
ejpam-5241	547	4	be	be	AUX
ejpam-5241	547	5	a	a	DET
ejpam-5241	547	6	maximal	maximal	ADJ
ejpam-5241	547	7	closed	closed	ADJ
ejpam-5241	547	8	2	2	NUM
ejpam-5241	547	9	-	-	PUNCT
ejpam-5241	547	10	path	path	NOUN
ejpam-5241	547	11	closure	closure	NOUN
ejpam-5241	547	12	absorbing	absorb	VERB
ejpam-5241	547	13	sequence	sequence	NOUN
ejpam-5241	547	14	of	of	ADP
ejpam-5241	547	15	sets	set	NOUN
ejpam-5241	547	16	in	in	ADP
ejpam-5241	547	17	hv	hv	PROPN
ejpam-5241	547	18	.	.	PROPN
ejpam-5241	547	19	define	define	VERB
ejpam-5241	547	20	for	for	ADP
ejpam-5241	547	21	each	each	PRON
ejpam-5241	547	22	k	k	NOUN
ejpam-5241	547	23	=	=	SYM
ejpam-5241	547	24	1	1	NUM
ejpam-5241	547	25	,	,	PUNCT
ejpam-5241	547	26	2	2	NUM
ejpam-5241	547	27	,	,	PUNCT
ejpam-5241	547	28	.	.	PUNCT
ejpam-5241	547	29	.	.	PUNCT
ejpam-5241	548	1	.	.	PUNCT
ejpam-5241	549	1	,	,	PUNCT
ejpam-5241	549	2	n	n	CCONJ
ejpam-5241	549	3	,	,	PUNCT
ejpam-5241	549	4	sk	sk	X
ejpam-5241	549	5	=	=	PUNCT
ejpam-5241	549	6	{	{	PUNCT
ejpam-5241	549	7	x1	x1	PROPN
ejpam-5241	549	8	,	,	PUNCT
ejpam-5241	549	9	x2	x2	PROPN
ejpam-5241	549	10	,	,	PUNCT
ejpam-5241	549	11	.	.	PUNCT
ejpam-5241	549	12	.	.	PUNCT
ejpam-5241	550	1	.	.	PUNCT
ejpam-5241	551	1	,	,	PUNCT
ejpam-5241	551	2	xk	xk	ADJ
ejpam-5241	551	3	}	}	PUNCT
ejpam-5241	551	4	⊆	⊆	NUM
ejpam-5241	551	5	s	s	VERB
ejpam-5241	551	6	such	such	ADJ
ejpam-5241	551	7	that	that	SCONJ
ejpam-5241	551	8	•	•	NOUN
ejpam-5241	551	9	a	a	PRON
ejpam-5241	551	10	=	=	PUNCT
ejpam-5241	551	11	{	{	PUNCT
ejpam-5241	551	12	x1	x1	PROPN
ejpam-5241	551	13	,	,	PUNCT
ejpam-5241	551	14	x2	x2	PROPN
ejpam-5241	551	15	,	,	PUNCT
ejpam-5241	551	16	.	.	PUNCT
ejpam-5241	551	17	.	.	PUNCT
ejpam-5241	551	18	.	.	PUNCT
ejpam-5241	552	1	,	,	PUNCT
ejpam-5241	552	2	xj	xj	PROPN
ejpam-5241	552	3	}	}	PUNCT
ejpam-5241	552	4	;	;	PUNCT
ejpam-5241	552	5	•	•	X
ejpam-5241	552	6	if	if	SCONJ
ejpam-5241	552	7	for	for	ADP
ejpam-5241	552	8	i	i	PRON
ejpam-5241	552	9	<	<	X
ejpam-5241	552	10	k	k	X
ejpam-5241	552	11	,	,	PUNCT
ejpam-5241	552	12	xi	xi	PROPN
ejpam-5241	552	13	,	,	PUNCT
ejpam-5241	552	14	xk	xk	PROPN
ejpam-5241	552	15	∈	∈	PROPN
ejpam-5241	552	16	sv	sv	PROPN
ejpam-5241	552	17	,	,	PUNCT
ejpam-5241	552	18	say	say	VERB
ejpam-5241	552	19	xi	xi	INTJ
ejpam-5241	552	20	=	=	SYM
ejpam-5241	552	21	xsv	xsv	PROPN
ejpam-5241	552	22	and	and	CCONJ
ejpam-5241	552	23	xk	xk	PROPN
ejpam-5241	553	1	=	=	PUNCT
ejpam-5241	553	2	xrv	xrv	NOUN
ejpam-5241	553	3	,	,	PUNCT
ejpam-5241	553	4	then	then	ADV
ejpam-5241	553	5	s	s	VERB
ejpam-5241	553	6	<	<	X
ejpam-5241	553	7	r.	r.	PROPN
ejpam-5241	553	8	then	then	ADV
ejpam-5241	553	9	sk	sk	VERB
ejpam-5241	553	10	=	=	PUNCT
ejpam-5241	553	11	{	{	PUNCT
ejpam-5241	553	12	x1	x1	PROPN
ejpam-5241	553	13	,	,	PUNCT
ejpam-5241	553	14	x2	x2	PROPN
ejpam-5241	553	15	,	,	PUNCT
ejpam-5241	553	16	.	.	PUNCT
ejpam-5241	553	17	.	.	PUNCT
ejpam-5241	553	18	.	.	PUNCT
ejpam-5241	554	1	,	,	PUNCT
ejpam-5241	554	2	xk	xk	PROPN
ejpam-5241	554	3	}	}	PUNCT
ejpam-5241	554	4	(	(	PUNCT
ejpam-5241	554	5	k	k	NOUN
ejpam-5241	554	6	=	=	SYM
ejpam-5241	554	7	1	1	NUM
ejpam-5241	554	8	,	,	PUNCT
ejpam-5241	554	9	2	2	NUM
ejpam-5241	554	10	,	,	PUNCT
ejpam-5241	554	11	.	.	PUNCT
ejpam-5241	554	12	.	.	PUNCT
ejpam-5241	555	1	.	.	PUNCT
ejpam-5241	556	1	,	,	PUNCT
ejpam-5241	556	2	n	n	CCONJ
ejpam-5241	556	3	)	)	PUNCT
ejpam-5241	556	4	is	be	AUX
ejpam-5241	556	5	a	a	DET
ejpam-5241	556	6	closed	closed	ADJ
ejpam-5241	556	7	geodetic	geodetic	ADJ
ejpam-5241	556	8	sequence	sequence	NOUN
ejpam-5241	556	9	of	of	ADP
ejpam-5241	556	10	sets	set	NOUN
ejpam-5241	556	11	in	in	ADP
ejpam-5241	556	12	g	g	PROPN
ejpam-5241	556	13	◦	◦	NOUN
ejpam-5241	556	14	h.	h.	NOUN
ejpam-5241	556	15	let	let	VERB
ejpam-5241	556	16	w	w	PROPN
ejpam-5241	556	17	∈	∈	PROPN
ejpam-5241	556	18	v	v	NOUN
ejpam-5241	556	19	(	(	PUNCT
ejpam-5241	556	20	g	g	PROPN
ejpam-5241	556	21	◦	◦	NOUN
ejpam-5241	556	22	h	h	NOUN
ejpam-5241	556	23	)	)	PUNCT
ejpam-5241	556	24	\	\	PROPN
ejpam-5241	557	1	s	s	PROPN
ejpam-5241	557	2	,	,	PUNCT
ejpam-5241	557	3	and	and	CCONJ
ejpam-5241	557	4	let	let	VERB
ejpam-5241	557	5	v	v	NUM
ejpam-5241	557	6	∈	∈	PROPN
ejpam-5241	557	7	v	v	NOUN
ejpam-5241	557	8	(	(	PUNCT
ejpam-5241	557	9	g	g	NOUN
ejpam-5241	557	10	)	)	PUNCT
ejpam-5241	557	11	for	for	ADP
ejpam-5241	557	12	which	which	PRON
ejpam-5241	557	13	w	w	PROPN
ejpam-5241	557	14	∈	∈	PROPN
ejpam-5241	557	15	v	v	X
ejpam-5241	557	16	(	(	PUNCT
ejpam-5241	557	17	hv	hv	PROPN
ejpam-5241	557	18	+	+	PROPN
ejpam-5241	557	19	v	v	NOUN
ejpam-5241	557	20	)	)	PUNCT
ejpam-5241	557	21	.	.	PUNCT
ejpam-5241	558	1	if	if	SCONJ
ejpam-5241	558	2	w	w	PROPN
ejpam-5241	558	3	∈	∈	PROPN
ejpam-5241	558	4	v	v	ADP
ejpam-5241	558	5	(	(	PUNCT
ejpam-5241	558	6	hv	hv	PROPN
ejpam-5241	558	7	)	)	PUNCT
ejpam-5241	558	8	,	,	PUNCT
ejpam-5241	558	9	then	then	ADV
ejpam-5241	558	10	w	w	PROPN
ejpam-5241	558	11	∈	∈	PROPN
ejpam-5241	558	12	p2[sv	p2[sv	PROPN
ejpam-5241	558	13	]	]	X
ejpam-5241	558	14	=	=	PUNCT
ejpam-5241	558	15	ig	ig	PROPN
ejpam-5241	558	16	◦	◦	NOUN
ejpam-5241	558	17	h	h	NOUN
ejpam-5241	559	1	[	[	X
ejpam-5241	559	2	sv	sv	X
ejpam-5241	559	3	]	]	X
ejpam-5241	559	4	.	.	PUNCT
ejpam-5241	560	1	suppose	suppose	VERB
ejpam-5241	560	2	that	that	SCONJ
ejpam-5241	560	3	w	w	PROPN
ejpam-5241	560	4	=	=	PUNCT
ejpam-5241	560	5	v.	v.	CCONJ
ejpam-5241	560	6	let	let	VERB
ejpam-5241	560	7	z	z	NOUN
ejpam-5241	560	8	∈	∈	PROPN
ejpam-5241	560	9	v	v	ADP
ejpam-5241	560	10	(	(	PUNCT
ejpam-5241	560	11	g	g	NOUN
ejpam-5241	560	12	)	)	PUNCT
ejpam-5241	560	13	∩	∩	NOUN
ejpam-5241	560	14	ng(v	ng(v	NUM
ejpam-5241	560	15	)	)	PUNCT
ejpam-5241	560	16	.	.	PUNCT
ejpam-5241	561	1	pick	pick	VERB
ejpam-5241	561	2	u	u	PRON
ejpam-5241	561	3	∈	∈	PROPN
ejpam-5241	561	4	sv	sv	NOUN
ejpam-5241	561	5	and	and	CCONJ
ejpam-5241	561	6	y	y	PROPN
ejpam-5241	561	7	∈	∈	PROPN
ejpam-5241	561	8	sz	sz	PROPN
ejpam-5241	561	9	.	.	PUNCT
ejpam-5241	562	1	then	then	ADV
ejpam-5241	562	2	w	w	PROPN
ejpam-5241	562	3	∈	∈	PROPN
ejpam-5241	562	4	ig	ig	PROPN
ejpam-5241	562	5	◦	◦	NOUN
ejpam-5241	562	6	h	h	NOUN
ejpam-5241	563	1	[	[	X
ejpam-5241	563	2	u	u	NOUN
ejpam-5241	563	3	,	,	PUNCT
ejpam-5241	563	4	z	z	PROPN
ejpam-5241	563	5	]	]	X
ejpam-5241	563	6	⊆	⊆	NUM
ejpam-5241	563	7	ig	ig	PROPN
ejpam-5241	563	8	◦	◦	NOUN
ejpam-5241	563	9	h	h	NOUN
ejpam-5241	564	1	[	[	X
ejpam-5241	564	2	s	s	X
ejpam-5241	564	3	]	]	X
ejpam-5241	564	4	.	.	PUNCT
ejpam-5241	565	1	hence	hence	ADV
ejpam-5241	565	2	,	,	PUNCT
ejpam-5241	565	3	s	s	VERB
ejpam-5241	565	4	is	be	AUX
ejpam-5241	565	5	a	a	DET
ejpam-5241	565	6	closed	closed	ADJ
ejpam-5241	565	7	geodetic	geodetic	ADJ
ejpam-5241	565	8	set	set	NOUN
ejpam-5241	565	9	of	of	ADP
ejpam-5241	565	10	g	g	PROPN
ejpam-5241	565	11	◦	◦	NOUN
ejpam-5241	565	12	h.	h.	NOUN
ejpam-5241	565	13	finally	finally	ADV
ejpam-5241	565	14	,	,	PUNCT
ejpam-5241	565	15	we	we	PRON
ejpam-5241	565	16	show	show	VERB
ejpam-5241	565	17	s	s	VERB
ejpam-5241	565	18	is	be	AUX
ejpam-5241	565	19	a	a	DET
ejpam-5241	565	20	hop	hop	NOUN
ejpam-5241	565	21	dominating	dominating	NOUN
ejpam-5241	565	22	set	set	NOUN
ejpam-5241	565	23	of	of	ADP
ejpam-5241	565	24	g	g	PROPN
ejpam-5241	565	25	◦	◦	NOUN
ejpam-5241	565	26	h.	h.	NOUN
ejpam-5241	565	27	let	let	VERB
ejpam-5241	565	28	w	w	PROPN
ejpam-5241	565	29	∈	∈	PROPN
ejpam-5241	565	30	v	v	NOUN
ejpam-5241	565	31	(	(	PUNCT
ejpam-5241	565	32	g	g	PROPN
ejpam-5241	565	33	◦	◦	NOUN
ejpam-5241	565	34	h	h	NOUN
ejpam-5241	565	35	)	)	PUNCT
ejpam-5241	565	36	\	\	PROPN
ejpam-5241	566	1	s	s	PROPN
ejpam-5241	566	2	,	,	PUNCT
ejpam-5241	566	3	and	and	CCONJ
ejpam-5241	566	4	let	let	VERB
ejpam-5241	566	5	v	v	NUM
ejpam-5241	566	6	∈	∈	PROPN
ejpam-5241	566	7	v	v	NOUN
ejpam-5241	566	8	(	(	PUNCT
ejpam-5241	566	9	g	g	NOUN
ejpam-5241	566	10	)	)	PUNCT
ejpam-5241	566	11	for	for	ADP
ejpam-5241	566	12	which	which	PRON
ejpam-5241	566	13	w	w	PROPN
ejpam-5241	566	14	∈	∈	PROPN
ejpam-5241	566	15	v	v	X
ejpam-5241	566	16	(	(	PUNCT
ejpam-5241	566	17	hv	hv	PROPN
ejpam-5241	566	18	+	+	PROPN
ejpam-5241	566	19	v	v	NOUN
ejpam-5241	566	20	)	)	PUNCT
ejpam-5241	566	21	.	.	PUNCT
ejpam-5241	567	1	if	if	SCONJ
ejpam-5241	567	2	w	w	PROPN
ejpam-5241	567	3	=	=	SYM
ejpam-5241	567	4	v	v	NOUN
ejpam-5241	567	5	,	,	PUNCT
ejpam-5241	567	6	then	then	ADV
ejpam-5241	567	7	for	for	ADP
ejpam-5241	567	8	any	any	DET
ejpam-5241	567	9	z	z	PROPN
ejpam-5241	567	10	∈	∈	PROPN
ejpam-5241	567	11	ng(v	ng(v	NOUN
ejpam-5241	567	12	)	)	PUNCT
ejpam-5241	567	13	,	,	PUNCT
ejpam-5241	567	14	dg	dg	PROPN
ejpam-5241	567	15	◦	◦	PROPN
ejpam-5241	567	16	h(w	h(w	PROPN
ejpam-5241	567	17	,	,	PUNCT
ejpam-5241	567	18	y	y	NOUN
ejpam-5241	567	19	)	)	PUNCT
ejpam-5241	567	20	=	=	SYM
ejpam-5241	567	21	2	2	NUM
ejpam-5241	567	22	for	for	ADP
ejpam-5241	567	23	all	all	DET
ejpam-5241	567	24	y	y	PROPN
ejpam-5241	567	25	∈	∈	PROPN
ejpam-5241	567	26	sz	sz	PROPN
ejpam-5241	567	27	.	.	PUNCT
ejpam-5241	567	28	suppose	suppose	VERB
ejpam-5241	567	29	that	that	SCONJ
ejpam-5241	567	30	w	w	PROPN
ejpam-5241	567	31	∈	∈	PROPN
ejpam-5241	567	32	v	v	ADP
ejpam-5241	567	33	(	(	PUNCT
ejpam-5241	567	34	hv	hv	PROPN
ejpam-5241	567	35	)	)	PUNCT
ejpam-5241	567	36	.	.	PUNCT
ejpam-5241	568	1	if	if	SCONJ
ejpam-5241	568	2	v	v	NUM
ejpam-5241	568	3	∈	∈	PROPN
ejpam-5241	568	4	ng(a	ng(a	NOUN
ejpam-5241	568	5	)	)	PUNCT
ejpam-5241	568	6	,	,	PUNCT
ejpam-5241	568	7	then	then	ADV
ejpam-5241	568	8	dg	dg	VERB
ejpam-5241	568	9	◦	◦	NOUN
ejpam-5241	568	10	h(w	h(w	PROPN
ejpam-5241	568	11	,	,	PUNCT
ejpam-5241	568	12	y	y	NOUN
ejpam-5241	568	13	)	)	PUNCT
ejpam-5241	568	14	=	=	SYM
ejpam-5241	568	15	2	2	NUM
ejpam-5241	568	16	for	for	ADP
ejpam-5241	568	17	all	all	DET
ejpam-5241	568	18	y	y	PROPN
ejpam-5241	568	19	∈	∈	PROPN
ejpam-5241	568	20	a	a	DET
ejpam-5241	568	21	∩	∩	NOUN
ejpam-5241	568	22	ng(v	ng(v	NUM
ejpam-5241	568	23	)	)	PUNCT
ejpam-5241	568	24	.	.	PUNCT
ejpam-5241	569	1	if	if	SCONJ
ejpam-5241	569	2	v	v	NUM
ejpam-5241	569	3	/∈	/∈	PUNCT
ejpam-5241	569	4	ng(a	ng(a	NUM
ejpam-5241	569	5	)	)	PUNCT
ejpam-5241	569	6	,	,	PUNCT
ejpam-5241	569	7	then	then	ADV
ejpam-5241	569	8	since	since	SCONJ
ejpam-5241	569	9	sv	sv	PROPN
ejpam-5241	569	10	is	be	AUX
ejpam-5241	569	11	pointwise	pointwise	PROPN
ejpam-5241	569	12	non	non	ADJ
ejpam-5241	569	13	-	-	ADJ
ejpam-5241	569	14	dominating	dominating	ADJ
ejpam-5241	569	15	,	,	PUNCT
ejpam-5241	569	16	there	there	PRON
ejpam-5241	569	17	exists	exist	VERB
ejpam-5241	569	18	y	y	PROPN
ejpam-5241	569	19	∈	∈	PROPN
ejpam-5241	569	20	sv	sv	INTJ
ejpam-5241	569	21	for	for	ADP
ejpam-5241	569	22	which	which	PRON
ejpam-5241	569	23	wy	wy	PROPN
ejpam-5241	569	24	/∈	/∈	PUNCT
ejpam-5241	569	25	e(hv	e(hv	PROPN
ejpam-5241	569	26	)	)	PUNCT
ejpam-5241	569	27	.	.	PUNCT
ejpam-5241	570	1	then	then	ADV
ejpam-5241	570	2	dg	dg	VERB
ejpam-5241	570	3	◦	◦	PROPN
ejpam-5241	570	4	h(w	h(w	PROPN
ejpam-5241	570	5	,	,	PUNCT
ejpam-5241	570	6	y	y	NOUN
ejpam-5241	570	7	)	)	PUNCT
ejpam-5241	570	8	=	=	SYM
ejpam-5241	570	9	2	2	X
ejpam-5241	570	10	.	.	PUNCT
ejpam-5241	570	11	corollary	corollary	ADJ
ejpam-5241	570	12	3	3	X
ejpam-5241	570	13	.	.	PUNCT
ejpam-5241	571	1	let	let	VERB
ejpam-5241	571	2	g	g	NOUN
ejpam-5241	571	3	and	and	CCONJ
ejpam-5241	571	4	h	h	NOUN
ejpam-5241	571	5	be	be	AUX
ejpam-5241	571	6	connected	connect	VERB
ejpam-5241	571	7	graphs	graph	NOUN
ejpam-5241	571	8	where	where	SCONJ
ejpam-5241	571	9	g	g	PROPN
ejpam-5241	571	10	is	be	AUX
ejpam-5241	571	11	nontrivial	nontrivial	NOUN
ejpam-5241	571	12	of	of	ADP
ejpam-5241	571	13	order	order	NOUN
ejpam-5241	571	14	n.	n.	NOUN
ejpam-5241	571	15	then	then	ADV
ejpam-5241	571	16	n	n	CCONJ
ejpam-5241	571	17	·	·	PUNCT
ejpam-5241	571	18	ρ2(h	ρ2(h	X
ejpam-5241	571	19	)	)	PUNCT
ejpam-5241	571	20	≤	≤	NOUN
ejpam-5241	571	21	γhcg(g	γhcg(g	PROPN
ejpam-5241	571	22	◦	◦	NOUN
ejpam-5241	571	23	h	h	NOUN
ejpam-5241	571	24	)	)	PUNCT
ejpam-5241	571	25	≤	≤	NOUN
ejpam-5241	572	1	n	n	CCONJ
ejpam-5241	572	2	·	·	PUNCT
ejpam-5241	572	3	ρc2pnd(h	ρc2pnd(h	NUM
ejpam-5241	572	4	)	)	PUNCT
ejpam-5241	572	5	,	,	PUNCT
ejpam-5241	572	6	and	and	CCONJ
ejpam-5241	572	7	these	these	DET
ejpam-5241	572	8	bounds	bound	NOUN
ejpam-5241	572	9	are	be	AUX
ejpam-5241	572	10	sharp	sharp	ADJ
ejpam-5241	572	11	.	.	PUNCT
ejpam-5241	573	1	proof	proof	NOUN
ejpam-5241	573	2	.	.	PUNCT
ejpam-5241	574	1	let	let	VERB
ejpam-5241	574	2	s	s	PRON
ejpam-5241	574	3	⊆	⊆	NUM
ejpam-5241	574	4	v	v	NOUN
ejpam-5241	574	5	(	(	PUNCT
ejpam-5241	574	6	g	g	PROPN
ejpam-5241	574	7	◦	◦	NOUN
ejpam-5241	574	8	h	h	NOUN
ejpam-5241	574	9	)	)	PUNCT
ejpam-5241	574	10	be	be	VERB
ejpam-5241	574	11	a	a	DET
ejpam-5241	574	12	γhcg	γhcg	NOUN
ejpam-5241	574	13	-	-	PUNCT
ejpam-5241	574	14	set	set	NOUN
ejpam-5241	574	15	of	of	ADP
ejpam-5241	574	16	g	g	PROPN
ejpam-5241	574	17	◦	◦	NOUN
ejpam-5241	574	18	h.	h.	NOUN
ejpam-5241	574	19	by	by	ADP
ejpam-5241	574	20	theorem	theorem	NOUN
ejpam-5241	574	21	11	11	NUM
ejpam-5241	574	22	,	,	PUNCT
ejpam-5241	574	23	s	s	PART
ejpam-5241	574	24	=	=	PUNCT
ejpam-5241	574	25	a∪	a∪	PROPN
ejpam-5241	574	26	(	(	PUNCT
ejpam-5241	574	27	∪v∈v	∪v∈v	X
ejpam-5241	574	28	(	(	PUNCT
ejpam-5241	574	29	g)sv	g)sv	PROPN
ejpam-5241	574	30	)	)	PUNCT
ejpam-5241	574	31	,	,	PUNCT
ejpam-5241	574	32	where	where	SCONJ
ejpam-5241	574	33	sv	sv	PROPN
ejpam-5241	574	34	is	be	AUX
ejpam-5241	574	35	a	a	DET
ejpam-5241	574	36	closed	closed	ADJ
ejpam-5241	574	37	2	2	NUM
ejpam-5241	574	38	-	-	PUNCT
ejpam-5241	574	39	path	path	NOUN
ejpam-5241	574	40	closure	closure	NOUN
ejpam-5241	574	41	absorbing	absorb	VERB
ejpam-5241	574	42	set	set	NOUN
ejpam-5241	574	43	of	of	ADP
ejpam-5241	574	44	hv	hv	PROPN
ejpam-5241	574	45	.	.	PUNCT
ejpam-5241	575	1	thus	thus	ADV
ejpam-5241	575	2	,	,	PUNCT
ejpam-5241	575	3	n	n	PROPN
ejpam-5241	575	4	·	·	PUNCT
ejpam-5241	575	5	ρ2(h	ρ2(h	X
ejpam-5241	575	6	)	)	PUNCT
ejpam-5241	575	7	≤	≤	NOUN
ejpam-5241	575	8	∑	∑	PUNCT
ejpam-5241	575	9	v∈v	v∈v	NOUN
ejpam-5241	575	10	(	(	PUNCT
ejpam-5241	575	11	g	g	NOUN
ejpam-5241	575	12	)	)	PUNCT
ejpam-5241	575	13	|sv|	|sv|	PROPN
ejpam-5241	575	14	≤	≤	NUM
ejpam-5241	575	15	|s|	|s|	PROPN
ejpam-5241	575	16	=	=	PUNCT
ejpam-5241	575	17	γhcg(g	γhcg(g	PROPN
ejpam-5241	575	18	◦	◦	NOUN
ejpam-5241	575	19	h	h	NOUN
ejpam-5241	575	20	)	)	PUNCT
ejpam-5241	575	21	.	.	PUNCT
ejpam-5241	576	1	to	to	PART
ejpam-5241	576	2	get	get	VERB
ejpam-5241	576	3	the	the	DET
ejpam-5241	576	4	other	other	ADJ
ejpam-5241	576	5	inequality	inequality	NOUN
ejpam-5241	576	6	,	,	PUNCT
ejpam-5241	576	7	for	for	ADP
ejpam-5241	576	8	each	each	DET
ejpam-5241	576	9	v	v	NUM
ejpam-5241	576	10	∈	∈	PROPN
ejpam-5241	576	11	v	v	NOUN
ejpam-5241	576	12	(	(	PUNCT
ejpam-5241	576	13	g	g	NOUN
ejpam-5241	576	14	)	)	PUNCT
ejpam-5241	576	15	,	,	PUNCT
ejpam-5241	576	16	let	let	VERB
ejpam-5241	576	17	sv	sv	PROPN
ejpam-5241	576	18	⊆	⊆	NUM
ejpam-5241	576	19	v	v	X
ejpam-5241	576	20	(	(	PUNCT
ejpam-5241	576	21	hv	hv	NOUN
ejpam-5241	576	22	)	)	PUNCT
ejpam-5241	576	23	be	be	VERB
ejpam-5241	576	24	a	a	DET
ejpam-5241	576	25	closed	closed	ADJ
ejpam-5241	576	26	2	2	NUM
ejpam-5241	576	27	-	-	PUNCT
ejpam-5241	576	28	path	path	NOUN
ejpam-5241	576	29	closure	closure	NOUN
ejpam-5241	576	30	absorbing	absorb	VERB
ejpam-5241	576	31	pointwise	pointwise	PROPN
ejpam-5241	576	32	non	non	ADJ
ejpam-5241	576	33	-	-	ADJ
ejpam-5241	576	34	dominating	dominating	ADJ
ejpam-5241	576	35	set	set	NOUN
ejpam-5241	576	36	of	of	ADP
ejpam-5241	576	37	hv	hv	PROPN
ejpam-5241	576	38	.	.	PUNCT
ejpam-5241	577	1	by	by	ADP
ejpam-5241	577	2	theorem	theorem	NOUN
ejpam-5241	577	3	11	11	NUM
ejpam-5241	577	4	,	,	PUNCT
ejpam-5241	577	5	s	s	PART
ejpam-5241	577	6	=	=	SYM
ejpam-5241	577	7	∪v∈v	∪v∈v	X
ejpam-5241	577	8	(	(	PUNCT
ejpam-5241	577	9	g)sv	g)sv	PROPN
ejpam-5241	577	10	is	be	AUX
ejpam-5241	577	11	a	a	DET
ejpam-5241	577	12	closed	closed	ADJ
ejpam-5241	577	13	geodetic	geodetic	ADJ
ejpam-5241	577	14	hop	hop	NOUN
ejpam-5241	577	15	dominating	dominating	NOUN
ejpam-5241	577	16	set	set	NOUN
ejpam-5241	577	17	of	of	ADP
ejpam-5241	577	18	g	g	PROPN
ejpam-5241	577	19	◦	◦	NOUN
ejpam-5241	577	20	h.	h.	PROPN
ejpam-5241	577	21	hence	hence	ADV
ejpam-5241	577	22	,	,	PUNCT
ejpam-5241	577	23	γhcg(g	γhcg(g	PROPN
ejpam-5241	577	24	◦	◦	NOUN
ejpam-5241	577	25	h	h	NOUN
ejpam-5241	577	26	)	)	PUNCT
ejpam-5241	577	27	≤	≤	NUM
ejpam-5241	577	28	|s|	|s|	PROPN
ejpam-5241	577	29	=	=	PUNCT
ejpam-5241	577	30	n	n	PROPN
ejpam-5241	577	31	·	·	PUNCT
ejpam-5241	577	32	ρc2pnd(h	ρc2pnd(h	NUM
ejpam-5241	577	33	)	)	PUNCT
ejpam-5241	577	34	.	.	PUNCT
ejpam-5241	578	1	for	for	ADP
ejpam-5241	578	2	a	a	DET
ejpam-5241	578	3	graph	graph	NOUN
ejpam-5241	578	4	g	g	NOUN
ejpam-5241	578	5	,	,	PUNCT
ejpam-5241	578	6	let	let	VERB
ejpam-5241	578	7	τ(g	τ(g	NOUN
ejpam-5241	578	8	)	)	PUNCT
ejpam-5241	578	9	be	be	VERB
ejpam-5241	578	10	the	the	DET
ejpam-5241	578	11	set	set	NOUN
ejpam-5241	578	12	of	of	ADP
ejpam-5241	578	13	all	all	DET
ejpam-5241	578	14	support	support	NOUN
ejpam-5241	578	15	vertices	vertice	VERB
ejpam-5241	578	16	v	v	ADP
ejpam-5241	578	17	of	of	ADP
ejpam-5241	578	18	g	g	NOUN
ejpam-5241	578	19	for	for	ADP
ejpam-5241	578	20	which	which	PRON
ejpam-5241	578	21	ng(x	ng(x	NUM
ejpam-5241	578	22	)	)	PUNCT
ejpam-5241	579	1	=	=	PRON
ejpam-5241	579	2	{	{	PUNCT
ejpam-5241	579	3	v	v	NOUN
ejpam-5241	579	4	}	}	PUNCT
ejpam-5241	579	5	for	for	ADP
ejpam-5241	579	6	all	all	DET
ejpam-5241	579	7	x	x	SYM
ejpam-5241	579	8	∈	∈	NOUN
ejpam-5241	579	9	ng(v	ng(v	NOUN
ejpam-5241	579	10	)	)	PUNCT
ejpam-5241	579	11	}	}	PUNCT
ejpam-5241	579	12	.	.	PUNCT
ejpam-5241	580	1	in	in	ADP
ejpam-5241	580	2	particular	particular	ADJ
ejpam-5241	580	3	,	,	PUNCT
ejpam-5241	580	4	if	if	SCONJ
ejpam-5241	580	5	g	g	PROPN
ejpam-5241	580	6	=	=	SYM
ejpam-5241	580	7	k1,n	k1,n	PROPN
ejpam-5241	580	8	with	with	ADP
ejpam-5241	580	9	central	central	ADJ
ejpam-5241	580	10	vertex	vertex	NOUN
ejpam-5241	580	11	v	v	NOUN
ejpam-5241	580	12	,	,	PUNCT
ejpam-5241	580	13	then	then	ADV
ejpam-5241	580	14	τ(g	τ(g	NUM
ejpam-5241	580	15	)	)	PUNCT
ejpam-5241	580	16	=	=	PRON
ejpam-5241	580	17	{	{	PUNCT
ejpam-5241	580	18	v	v	NOUN
ejpam-5241	580	19	}	}	PUNCT
ejpam-5241	580	20	.	.	PUNCT
ejpam-5241	581	1	theorem	theorem	NOUN
ejpam-5241	581	2	12	12	NUM
ejpam-5241	581	3	.	.	PUNCT
ejpam-5241	582	1	let	let	VERB
ejpam-5241	582	2	g	g	PRON
ejpam-5241	582	3	be	be	AUX
ejpam-5241	582	4	a	a	DET
ejpam-5241	582	5	nontrivial	nontrivial	ADJ
ejpam-5241	582	6	connected	connect	VERB
ejpam-5241	582	7	graph	graph	NOUN
ejpam-5241	582	8	and	and	CCONJ
ejpam-5241	582	9	n	n	PRON
ejpam-5241	582	10	≥	≥	NOUN
ejpam-5241	582	11	1	1	NUM
ejpam-5241	582	12	,	,	PUNCT
ejpam-5241	582	13	and	and	CCONJ
ejpam-5241	582	14	let	let	VERB
ejpam-5241	582	15	s	s	PRON
ejpam-5241	582	16	⊆	⊆	NUM
ejpam-5241	582	17	v	v	NOUN
ejpam-5241	582	18	(	(	PUNCT
ejpam-5241	582	19	g	g	PROPN
ejpam-5241	582	20	⋄kn	⋄kn	PROPN
ejpam-5241	582	21	)	)	PUNCT
ejpam-5241	582	22	.	.	PUNCT
ejpam-5241	583	1	then	then	ADV
ejpam-5241	583	2	s	s	VERB
ejpam-5241	583	3	is	be	AUX
ejpam-5241	583	4	a	a	DET
ejpam-5241	583	5	closed	closed	ADJ
ejpam-5241	583	6	geodetic	geodetic	ADJ
ejpam-5241	583	7	hop	hop	NOUN
ejpam-5241	583	8	dominating	dominating	NOUN
ejpam-5241	583	9	set	set	NOUN
ejpam-5241	583	10	of	of	ADP
ejpam-5241	583	11	g	g	PROPN
ejpam-5241	583	12	⋄kn	⋄kn	PROPN
ejpam-5241	583	13	if	if	SCONJ
ejpam-5241	583	14	and	and	CCONJ
ejpam-5241	583	15	only	only	ADV
ejpam-5241	583	16	if	if	SCONJ
ejpam-5241	583	17	s	s	VERB
ejpam-5241	583	18	=	=	NOUN
ejpam-5241	583	19	a	a	DET
ejpam-5241	583	20	∪	∪	X
ejpam-5241	583	21	(	(	PUNCT
ejpam-5241	583	22	∪uv∈e(g)v	∪uv∈e(g)v	PROPN
ejpam-5241	583	23	(	(	PUNCT
ejpam-5241	583	24	huv	huv	PROPN
ejpam-5241	583	25	)	)	PUNCT
ejpam-5241	583	26	)	)	PUNCT
ejpam-5241	583	27	,	,	PUNCT
ejpam-5241	583	28	(	(	PUNCT
ejpam-5241	583	29	6	6	NUM
ejpam-5241	583	30	)	)	PUNCT
ejpam-5241	583	31	where	where	SCONJ
ejpam-5241	583	32	a	a	DET
ejpam-5241	583	33	⊆	⊆	NUM
ejpam-5241	583	34	v	v	NOUN
ejpam-5241	583	35	(	(	PUNCT
ejpam-5241	583	36	g	g	NOUN
ejpam-5241	583	37	)	)	PUNCT
ejpam-5241	583	38	such	such	ADJ
ejpam-5241	583	39	that	that	SCONJ
ejpam-5241	583	40	l(g	l(g	NOUN
ejpam-5241	583	41	)	)	PUNCT
ejpam-5241	583	42	∪	∪	ADP
ejpam-5241	583	43	τ(g	τ(g	PROPN
ejpam-5241	583	44	)	)	PUNCT
ejpam-5241	583	45	⊆	⊆	NUM
ejpam-5241	583	46	a	a	PRON
ejpam-5241	583	47	and	and	CCONJ
ejpam-5241	583	48	the	the	DET
ejpam-5241	583	49	elements	element	NOUN
ejpam-5241	583	50	of	of	ADP
ejpam-5241	583	51	a	a	DET
ejpam-5241	583	52	constitute	constitute	NOUN
ejpam-5241	583	53	a	a	DET
ejpam-5241	583	54	closed	closed	ADJ
ejpam-5241	583	55	geodetic	geodetic	ADJ
ejpam-5241	583	56	sequence	sequence	NOUN
ejpam-5241	583	57	of	of	ADP
ejpam-5241	583	58	sets	set	NOUN
ejpam-5241	583	59	of	of	ADP
ejpam-5241	583	60	g.	g.	PROPN
ejpam-5241	583	61	a.	a.	PROPN
ejpam-5241	583	62	adolfo	adolfo	PROPN
ejpam-5241	583	63	,	,	PUNCT
ejpam-5241	583	64	i.	i.	PROPN
ejpam-5241	583	65	aniversario	aniversario	PROPN
ejpam-5241	583	66	,	,	PUNCT
ejpam-5241	583	67	f.	f.	PROPN
ejpam-5241	583	68	jamil	jamil	PROPN
ejpam-5241	583	69	/	/	SYM
ejpam-5241	583	70	eur	eur	PROPN
ejpam-5241	583	71	.	.	PUNCT
ejpam-5241	584	1	j.	j.	PROPN
ejpam-5241	584	2	pure	pure	PROPN
ejpam-5241	584	3	appl	appl	PROPN
ejpam-5241	584	4	.	.	PROPN
ejpam-5241	584	5	math	math	PROPN
ejpam-5241	584	6	,	,	PUNCT
ejpam-5241	584	7	17	17	NUM
ejpam-5241	584	8	(	(	PUNCT
ejpam-5241	584	9	3	3	NUM
ejpam-5241	584	10	)	)	PUNCT
ejpam-5241	584	11	(	(	PUNCT
ejpam-5241	584	12	2024	2024	NUM
ejpam-5241	584	13	)	)	PUNCT
ejpam-5241	584	14	,	,	PUNCT
ejpam-5241	584	15	1618	1618	NUM
ejpam-5241	584	16	-	-	SYM
ejpam-5241	584	17	1636	1636	NUM
ejpam-5241	584	18	1633	1633	NUM
ejpam-5241	584	19	proof	proof	NOUN
ejpam-5241	584	20	.	.	PUNCT
ejpam-5241	585	1	put	put	VERB
ejpam-5241	585	2	h	h	NOUN
ejpam-5241	586	1	=	=	SYM
ejpam-5241	586	2	kn	kn	PROPN
ejpam-5241	586	3	.	.	PROPN
ejpam-5241	586	4	suppose	suppose	VERB
ejpam-5241	586	5	that	that	SCONJ
ejpam-5241	586	6	s	s	VERB
ejpam-5241	586	7	is	be	AUX
ejpam-5241	586	8	a	a	DET
ejpam-5241	586	9	closed	closed	ADJ
ejpam-5241	586	10	geodetic	geodetic	ADJ
ejpam-5241	586	11	hop	hop	NOUN
ejpam-5241	586	12	dominating	dominating	NOUN
ejpam-5241	586	13	set	set	NOUN
ejpam-5241	586	14	of	of	ADP
ejpam-5241	586	15	g	g	PROPN
ejpam-5241	586	16	⋄h	⋄h	PROPN
ejpam-5241	586	17	.	.	PUNCT
ejpam-5241	587	1	since	since	SCONJ
ejpam-5241	587	2	l(g	l(g	NOUN
ejpam-5241	587	3	)	)	PUNCT
ejpam-5241	587	4	∪	∪	NOUN
ejpam-5241	587	5	v	v	NOUN
ejpam-5241	587	6	(	(	PUNCT
ejpam-5241	587	7	huv	huv	PROPN
ejpam-5241	587	8	)	)	PUNCT
ejpam-5241	587	9	⊆	⊆	NUM
ejpam-5241	587	10	ext(g	ext(g	PROPN
ejpam-5241	587	11	⋄	⋄	PROPN
ejpam-5241	587	12	h	h	NOUN
ejpam-5241	587	13	)	)	PUNCT
ejpam-5241	587	14	,	,	PUNCT
ejpam-5241	587	15	l(g	l(g	PROPN
ejpam-5241	587	16	)	)	PUNCT
ejpam-5241	587	17	∪	∪	ADP
ejpam-5241	587	18	v	v	NOUN
ejpam-5241	587	19	(	(	PUNCT
ejpam-5241	587	20	huv	huv	PROPN
ejpam-5241	587	21	)	)	PUNCT
ejpam-5241	587	22	⊆	⊆	NUM
ejpam-5241	587	23	s	s	NOUN
ejpam-5241	587	24	for	for	ADP
ejpam-5241	587	25	each	each	DET
ejpam-5241	587	26	uv	uv	PROPN
ejpam-5241	587	27	∈	∈	PROPN
ejpam-5241	587	28	e(g	e(g	PROPN
ejpam-5241	587	29	)	)	PUNCT
ejpam-5241	587	30	.	.	PUNCT
ejpam-5241	588	1	let	let	VERB
ejpam-5241	588	2	a	a	DET
ejpam-5241	588	3	=	=	X
ejpam-5241	588	4	s	s	NOUN
ejpam-5241	588	5	∩	∩	ADJ
ejpam-5241	588	6	v	v	X
ejpam-5241	588	7	(	(	PUNCT
ejpam-5241	588	8	g	g	NOUN
ejpam-5241	588	9	)	)	PUNCT
ejpam-5241	588	10	.	.	PUNCT
ejpam-5241	589	1	since	since	SCONJ
ejpam-5241	589	2	the	the	DET
ejpam-5241	589	3	vertices	vertex	NOUN
ejpam-5241	589	4	in	in	ADP
ejpam-5241	589	5	s	s	NOUN
ejpam-5241	589	6	constitute	constitute	VERB
ejpam-5241	589	7	a	a	DET
ejpam-5241	589	8	closed	closed	ADJ
ejpam-5241	589	9	geodetic	geodetic	ADJ
ejpam-5241	589	10	sequence	sequence	NOUN
ejpam-5241	589	11	of	of	ADP
ejpam-5241	589	12	sets	set	NOUN
ejpam-5241	589	13	in	in	ADP
ejpam-5241	589	14	g	g	PROPN
ejpam-5241	589	15	⋄h	⋄h	PROPN
ejpam-5241	589	16	,	,	PUNCT
ejpam-5241	589	17	it	it	PRON
ejpam-5241	589	18	follows	follow	VERB
ejpam-5241	589	19	that	that	SCONJ
ejpam-5241	589	20	the	the	DET
ejpam-5241	589	21	vertices	vertex	NOUN
ejpam-5241	589	22	in	in	ADP
ejpam-5241	589	23	a	a	DET
ejpam-5241	589	24	constitute	constitute	NOUN
ejpam-5241	589	25	a	a	DET
ejpam-5241	589	26	closed	closed	ADJ
ejpam-5241	589	27	geodetic	geodetic	ADJ
ejpam-5241	589	28	sequence	sequence	NOUN
ejpam-5241	589	29	of	of	ADP
ejpam-5241	589	30	sets	set	NOUN
ejpam-5241	589	31	in	in	ADP
ejpam-5241	589	32	g.	g.	PROPN
ejpam-5241	589	33	let	let	VERB
ejpam-5241	589	34	w	w	PROPN
ejpam-5241	589	35	∈	∈	PROPN
ejpam-5241	589	36	τ(g	τ(g	PROPN
ejpam-5241	589	37	)	)	PUNCT
ejpam-5241	589	38	.	.	PUNCT
ejpam-5241	590	1	suppose	suppose	VERB
ejpam-5241	590	2	that	that	SCONJ
ejpam-5241	590	3	w	w	PROPN
ejpam-5241	590	4	/∈	/∈	NOUN
ejpam-5241	590	5	a.	a.	NOUN
ejpam-5241	590	6	since	since	SCONJ
ejpam-5241	590	7	s	s	PROPN
ejpam-5241	590	8	is	be	AUX
ejpam-5241	590	9	a	a	DET
ejpam-5241	590	10	hop	hop	NOUN
ejpam-5241	590	11	dominating	dominating	NOUN
ejpam-5241	590	12	set	set	NOUN
ejpam-5241	590	13	,	,	PUNCT
ejpam-5241	590	14	there	there	PRON
ejpam-5241	590	15	exists	exist	VERB
ejpam-5241	590	16	x	x	X
ejpam-5241	590	17	∈	∈	NOUN
ejpam-5241	590	18	s	s	VERB
ejpam-5241	590	19	such	such	ADJ
ejpam-5241	590	20	that	that	SCONJ
ejpam-5241	590	21	dg⋄h(w	dg⋄h(w	NOUN
ejpam-5241	590	22	,	,	PUNCT
ejpam-5241	590	23	x	x	NOUN
ejpam-5241	590	24	)	)	PUNCT
ejpam-5241	591	1	=	=	SYM
ejpam-5241	591	2	2	2	X
ejpam-5241	591	3	.	.	PUNCT
ejpam-5241	592	1	if	if	SCONJ
ejpam-5241	592	2	x	x	SYM
ejpam-5241	592	3	∈	∈	PROPN
ejpam-5241	592	4	v	v	X
ejpam-5241	592	5	(	(	PUNCT
ejpam-5241	592	6	g	g	NOUN
ejpam-5241	592	7	)	)	PUNCT
ejpam-5241	592	8	,	,	PUNCT
ejpam-5241	592	9	then	then	ADV
ejpam-5241	592	10	dg(x	dg(x	NUM
ejpam-5241	592	11	,	,	PUNCT
ejpam-5241	592	12	w	w	NOUN
ejpam-5241	592	13	)	)	PUNCT
ejpam-5241	592	14	=	=	SYM
ejpam-5241	592	15	2	2	X
ejpam-5241	592	16	.	.	PUNCT
ejpam-5241	592	17	thus	thus	ADV
ejpam-5241	592	18	,	,	PUNCT
ejpam-5241	592	19	g	g	PROPN
ejpam-5241	592	20	contains	contain	VERB
ejpam-5241	592	21	a	a	DET
ejpam-5241	592	22	geodesic	geodesic	NOUN
ejpam-5241	592	23	[	[	X
ejpam-5241	592	24	x	x	X
ejpam-5241	592	25	,	,	PUNCT
ejpam-5241	592	26	v	v	NOUN
ejpam-5241	592	27	,	,	PUNCT
ejpam-5241	592	28	w	w	NOUN
ejpam-5241	592	29	]	]	X
ejpam-5241	592	30	.	.	PUNCT
ejpam-5241	593	1	this	this	PRON
ejpam-5241	593	2	means	mean	VERB
ejpam-5241	593	3	that	that	SCONJ
ejpam-5241	593	4	there	there	PRON
ejpam-5241	593	5	exists	exist	VERB
ejpam-5241	593	6	v	v	ADP
ejpam-5241	593	7	∈	∈	NOUN
ejpam-5241	593	8	ng(w	ng(w	NOUN
ejpam-5241	593	9	)	)	PUNCT
ejpam-5241	593	10	with	with	ADP
ejpam-5241	593	11	ng(v	ng(v	NOUN
ejpam-5241	593	12	)	)	PUNCT
ejpam-5241	593	13	̸=	̸=	PROPN
ejpam-5241	593	14	{	{	PUNCT
ejpam-5241	593	15	w	w	PROPN
ejpam-5241	593	16	}	}	PUNCT
ejpam-5241	593	17	,	,	PUNCT
ejpam-5241	593	18	a	a	DET
ejpam-5241	593	19	contradiction	contradiction	NOUN
ejpam-5241	593	20	since	since	SCONJ
ejpam-5241	593	21	w	w	PROPN
ejpam-5241	593	22	∈	∈	PROPN
ejpam-5241	593	23	τ(g	τ(g	PROPN
ejpam-5241	593	24	)	)	PUNCT
ejpam-5241	593	25	.	.	PUNCT
ejpam-5241	594	1	suppose	suppose	VERB
ejpam-5241	594	2	there	there	PRON
ejpam-5241	594	3	exist	exist	VERB
ejpam-5241	594	4	uv	uv	PROPN
ejpam-5241	594	5	∈	∈	PROPN
ejpam-5241	594	6	e(g	e(g	PROPN
ejpam-5241	594	7	)	)	PUNCT
ejpam-5241	594	8	such	such	ADJ
ejpam-5241	594	9	that	that	SCONJ
ejpam-5241	594	10	x	x	SYM
ejpam-5241	594	11	∈	∈	PROPN
ejpam-5241	594	12	suv	suv	PROPN
ejpam-5241	594	13	.	.	PUNCT
ejpam-5241	595	1	then	then	ADV
ejpam-5241	595	2	either	either	CCONJ
ejpam-5241	595	3	wu	wu	PROPN
ejpam-5241	595	4	∈	∈	PROPN
ejpam-5241	595	5	e(g	e(g	PROPN
ejpam-5241	595	6	)	)	PUNCT
ejpam-5241	595	7	or	or	CCONJ
ejpam-5241	595	8	wv	wv	PROPN
ejpam-5241	595	9	∈	∈	PROPN
ejpam-5241	595	10	e(g	e(g	PROPN
ejpam-5241	595	11	)	)	PUNCT
ejpam-5241	595	12	.	.	PUNCT
ejpam-5241	596	1	assume	assume	VERB
ejpam-5241	596	2	wv	wv	PROPN
ejpam-5241	596	3	∈	∈	PROPN
ejpam-5241	596	4	e(g	e(g	PROPN
ejpam-5241	596	5	)	)	PUNCT
ejpam-5241	596	6	.	.	PUNCT
ejpam-5241	597	1	then	then	ADV
ejpam-5241	597	2	there	there	PRON
ejpam-5241	597	3	exists	exist	VERB
ejpam-5241	597	4	v	v	ADP
ejpam-5241	597	5	∈	∈	NOUN
ejpam-5241	597	6	ng(w	ng(w	NOUN
ejpam-5241	597	7	)	)	PUNCT
ejpam-5241	597	8	with	with	ADP
ejpam-5241	597	9	ng(v	ng(v	NOUN
ejpam-5241	597	10	)	)	PUNCT
ejpam-5241	597	11	̸=	̸=	PROPN
ejpam-5241	597	12	{	{	PUNCT
ejpam-5241	597	13	w	w	PROPN
ejpam-5241	597	14	}	}	PUNCT
ejpam-5241	597	15	,	,	PUNCT
ejpam-5241	597	16	a	a	DET
ejpam-5241	597	17	contradiction	contradiction	NOUN
ejpam-5241	597	18	.	.	PUNCT
ejpam-5241	598	1	hence	hence	ADV
ejpam-5241	598	2	,	,	PUNCT
ejpam-5241	598	3	τ(g	τ(g	PROPN
ejpam-5241	598	4	)	)	PUNCT
ejpam-5241	598	5	⊆	⊆	NUM
ejpam-5241	598	6	a.	a.	NOUN
ejpam-5241	598	7	conversely	conversely	ADV
ejpam-5241	598	8	,	,	PUNCT
ejpam-5241	598	9	suppose	suppose	VERB
ejpam-5241	598	10	that	that	SCONJ
ejpam-5241	598	11	s	s	VERB
ejpam-5241	598	12	is	be	AUX
ejpam-5241	598	13	as	as	SCONJ
ejpam-5241	598	14	described	describe	VERB
ejpam-5241	598	15	in	in	ADP
ejpam-5241	598	16	equation	equation	NOUN
ejpam-5241	598	17	3	3	NUM
ejpam-5241	598	18	together	together	ADV
ejpam-5241	598	19	with	with	ADP
ejpam-5241	598	20	the	the	DET
ejpam-5241	598	21	indicated	indicate	VERB
ejpam-5241	598	22	properties	property	NOUN
ejpam-5241	598	23	.	.	PUNCT
ejpam-5241	599	1	let	let	VERB
ejpam-5241	599	2	n	n	NOUN
ejpam-5241	599	3	=	=	PUNCT
ejpam-5241	599	4	|s|	|s|	PROPN
ejpam-5241	599	5	and	and	CCONJ
ejpam-5241	599	6	|a|	|a|	PROPN
ejpam-5241	599	7	=	=	PROPN
ejpam-5241	599	8	k.	k.	PROPN
ejpam-5241	599	9	for	for	ADP
ejpam-5241	599	10	each	each	DET
ejpam-5241	599	11	j	j	PROPN
ejpam-5241	599	12	=	=	SYM
ejpam-5241	599	13	1	1	NUM
ejpam-5241	599	14	,	,	PUNCT
ejpam-5241	599	15	2	2	NUM
ejpam-5241	599	16	,	,	PUNCT
ejpam-5241	599	17	.	.	PUNCT
ejpam-5241	599	18	.	.	PUNCT
ejpam-5241	600	1	.	.	PUNCT
ejpam-5241	601	1	,	,	PUNCT
ejpam-5241	601	2	k	k	NOUN
ejpam-5241	601	3	,	,	PUNCT
ejpam-5241	601	4	let	let	VERB
ejpam-5241	601	5	aj	aj	PROPN
ejpam-5241	601	6	=	=	PRON
ejpam-5241	601	7	{	{	PUNCT
ejpam-5241	601	8	x1	x1	PROPN
ejpam-5241	601	9	,	,	PUNCT
ejpam-5241	601	10	x2	x2	PROPN
ejpam-5241	601	11	,	,	PUNCT
ejpam-5241	601	12	.	.	PUNCT
ejpam-5241	601	13	.	.	PUNCT
ejpam-5241	602	1	.	.	PUNCT
ejpam-5241	603	1	,	,	PUNCT
ejpam-5241	603	2	xj	xj	PROPN
ejpam-5241	603	3	}	}	PUNCT
ejpam-5241	603	4	⊆	⊆	NUM
ejpam-5241	603	5	a	a	DET
ejpam-5241	603	6	be	be	AUX
ejpam-5241	603	7	a	a	DET
ejpam-5241	603	8	closed	closed	ADJ
ejpam-5241	603	9	geodetic	geodetic	ADJ
ejpam-5241	603	10	sequence	sequence	NOUN
ejpam-5241	603	11	ing	ing	ADJ
ejpam-5241	603	12	.	.	PUNCT
ejpam-5241	604	1	extend	extend	VERB
ejpam-5241	604	2	the	the	DET
ejpam-5241	604	3	sequence	sequence	NOUN
ejpam-5241	604	4	by	by	ADP
ejpam-5241	604	5	defining	define	VERB
ejpam-5241	604	6	for	for	ADP
ejpam-5241	604	7	each	each	DET
ejpam-5241	604	8	i	i	NOUN
ejpam-5241	604	9	=	=	NOUN
ejpam-5241	604	10	1	1	NUM
ejpam-5241	604	11	,	,	PUNCT
ejpam-5241	604	12	2	2	NUM
ejpam-5241	604	13	,	,	PUNCT
ejpam-5241	604	14	.	.	PUNCT
ejpam-5241	604	15	.	.	PUNCT
ejpam-5241	605	1	.	.	PUNCT
ejpam-5241	606	1	,	,	PUNCT
ejpam-5241	606	2	n	n	CCONJ
ejpam-5241	606	3	,	,	PUNCT
ejpam-5241	606	4	si	si	X
ejpam-5241	606	5	=	=	PUNCT
ejpam-5241	606	6	{	{	PUNCT
ejpam-5241	606	7	x1	x1	PROPN
ejpam-5241	606	8	,	,	PUNCT
ejpam-5241	606	9	x2	x2	PROPN
ejpam-5241	606	10	,	,	PUNCT
ejpam-5241	606	11	.	.	PUNCT
ejpam-5241	606	12	.	.	PUNCT
ejpam-5241	606	13	.	.	PUNCT
ejpam-5241	607	1	,	,	PUNCT
ejpam-5241	607	2	xk	xk	PROPN
ejpam-5241	607	3	,	,	PUNCT
ejpam-5241	607	4	xk+1	xk+1	PROPN
ejpam-5241	607	5	,	,	PUNCT
ejpam-5241	607	6	.	.	PUNCT
ejpam-5241	607	7	.	.	PUNCT
ejpam-5241	607	8	.	.	PUNCT
ejpam-5241	608	1	,	,	PUNCT
ejpam-5241	608	2	xi	xi	ADP
ejpam-5241	608	3	}	}	PUNCT
ejpam-5241	608	4	⊆	⊆	NUM
ejpam-5241	608	5	s.	s.	PROPN
ejpam-5241	608	6	this	this	PRON
ejpam-5241	608	7	means	mean	VERB
ejpam-5241	608	8	that	that	SCONJ
ejpam-5241	608	9	sn	sn	PROPN
ejpam-5241	608	10	\	\	PROPN
ejpam-5241	608	11	ak	ak	PROPN
ejpam-5241	608	12	=	=	SYM
ejpam-5241	608	13	∪uv∈e(g)v	∪uv∈e(g)v	PROPN
ejpam-5241	608	14	(	(	PUNCT
ejpam-5241	608	15	huv	huv	PROPN
ejpam-5241	608	16	)	)	PUNCT
ejpam-5241	608	17	.	.	PUNCT
ejpam-5241	609	1	thus	thus	ADV
ejpam-5241	609	2	,	,	PUNCT
ejpam-5241	609	3	si	si	PROPN
ejpam-5241	609	4	=	=	SYM
ejpam-5241	609	5	{	{	PUNCT
ejpam-5241	609	6	x1	x1	PROPN
ejpam-5241	609	7	,	,	PUNCT
ejpam-5241	609	8	x2	x2	PROPN
ejpam-5241	609	9	,	,	PUNCT
ejpam-5241	609	10	.	.	PUNCT
ejpam-5241	609	11	.	.	PUNCT
ejpam-5241	609	12	.	.	PUNCT
ejpam-5241	610	1	,	,	PUNCT
ejpam-5241	610	2	xk	xk	PROPN
ejpam-5241	610	3	,	,	PUNCT
ejpam-5241	610	4	xk+1	xk+1	PROPN
ejpam-5241	610	5	,	,	PUNCT
ejpam-5241	610	6	.	.	PUNCT
ejpam-5241	610	7	.	.	PUNCT
ejpam-5241	610	8	.	.	PUNCT
ejpam-5241	611	1	,	,	PUNCT
ejpam-5241	611	2	xi	xi	ADP
ejpam-5241	611	3	}	}	PUNCT
ejpam-5241	611	4	(	(	PUNCT
ejpam-5241	611	5	i	i	NOUN
ejpam-5241	611	6	=	=	NOUN
ejpam-5241	611	7	1	1	NUM
ejpam-5241	611	8	,	,	PUNCT
ejpam-5241	611	9	2	2	NUM
ejpam-5241	611	10	,	,	PUNCT
ejpam-5241	611	11	.	.	PUNCT
ejpam-5241	611	12	.	.	PUNCT
ejpam-5241	612	1	.	.	PUNCT
ejpam-5241	613	1	,	,	PUNCT
ejpam-5241	613	2	n	n	CCONJ
ejpam-5241	613	3	)	)	PUNCT
ejpam-5241	613	4	is	be	AUX
ejpam-5241	613	5	a	a	DET
ejpam-5241	613	6	closed	closed	ADJ
ejpam-5241	613	7	geodetic	geodetic	ADJ
ejpam-5241	613	8	sequence	sequence	NOUN
ejpam-5241	613	9	in	in	ADP
ejpam-5241	613	10	g	g	PROPN
ejpam-5241	613	11	⋄	⋄	PROPN
ejpam-5241	613	12	h.	h.	PROPN
ejpam-5241	613	13	let	let	VERB
ejpam-5241	613	14	w	w	PROPN
ejpam-5241	613	15	∈	∈	PROPN
ejpam-5241	613	16	v	v	ADP
ejpam-5241	613	17	(	(	PUNCT
ejpam-5241	613	18	g	g	NOUN
ejpam-5241	613	19	)	)	PUNCT
ejpam-5241	613	20	\	\	PROPN
ejpam-5241	613	21	a.	a.	NOUN
ejpam-5241	613	22	since	since	SCONJ
ejpam-5241	613	23	w	w	PROPN
ejpam-5241	613	24	/∈	/∈	PUNCT
ejpam-5241	613	25	l(g	l(g	NOUN
ejpam-5241	613	26	)	)	PUNCT
ejpam-5241	613	27	,	,	PUNCT
ejpam-5241	613	28	there	there	PRON
ejpam-5241	613	29	exist	exist	VERB
ejpam-5241	613	30	distinct	distinct	ADJ
ejpam-5241	613	31	x	x	NOUN
ejpam-5241	613	32	,	,	PUNCT
ejpam-5241	613	33	y	y	PROPN
ejpam-5241	613	34	∈	∈	PROPN
ejpam-5241	613	35	v	v	ADP
ejpam-5241	613	36	(	(	PUNCT
ejpam-5241	613	37	g	g	NOUN
ejpam-5241	613	38	)	)	PUNCT
ejpam-5241	613	39	∩ng(w	∩ng(w	PROPN
ejpam-5241	613	40	)	)	PUNCT
ejpam-5241	613	41	.	.	PUNCT
ejpam-5241	614	1	pick	pick	VERB
ejpam-5241	614	2	z	z	PROPN
ejpam-5241	614	3	∈	∈	PROPN
ejpam-5241	614	4	v	v	ADP
ejpam-5241	614	5	(	(	PUNCT
ejpam-5241	614	6	hxw	hxw	PROPN
ejpam-5241	614	7	)	)	PUNCT
ejpam-5241	614	8	and	and	CCONJ
ejpam-5241	614	9	t	t	PROPN
ejpam-5241	614	10	∈	∈	PROPN
ejpam-5241	614	11	v	v	X
ejpam-5241	614	12	(	(	PUNCT
ejpam-5241	614	13	hyw	hyw	PROPN
ejpam-5241	614	14	)	)	PUNCT
ejpam-5241	614	15	.	.	PUNCT
ejpam-5241	615	1	then	then	ADV
ejpam-5241	615	2	z	z	X
ejpam-5241	615	3	,	,	PUNCT
ejpam-5241	615	4	t	t	PROPN
ejpam-5241	615	5	∈	∈	PROPN
ejpam-5241	615	6	s	s	X
ejpam-5241	615	7	and	and	CCONJ
ejpam-5241	615	8	w	w	PROPN
ejpam-5241	615	9	∈	∈	PROPN
ejpam-5241	615	10	ig⋄h(z	ig⋄h(z	PROPN
ejpam-5241	615	11	,	,	PUNCT
ejpam-5241	615	12	y	y	PROPN
ejpam-5241	615	13	)	)	PUNCT
ejpam-5241	615	14	.	.	PUNCT
ejpam-5241	616	1	since	since	SCONJ
ejpam-5241	616	2	w	w	NOUN
ejpam-5241	616	3	is	be	AUX
ejpam-5241	616	4	arbitrary	arbitrary	ADJ
ejpam-5241	616	5	,	,	PUNCT
ejpam-5241	616	6	ig⋄h	ig⋄h	PROPN
ejpam-5241	617	1	[	[	X
ejpam-5241	617	2	s	s	X
ejpam-5241	617	3	]	]	X
ejpam-5241	617	4	=	=	SYM
ejpam-5241	617	5	v	v	X
ejpam-5241	617	6	(	(	PUNCT
ejpam-5241	617	7	g	g	PROPN
ejpam-5241	617	8	⋄h	⋄h	PROPN
ejpam-5241	617	9	)	)	PUNCT
ejpam-5241	617	10	and	and	CCONJ
ejpam-5241	617	11	s	s	VERB
ejpam-5241	617	12	is	be	AUX
ejpam-5241	617	13	a	a	DET
ejpam-5241	617	14	closed	closed	ADJ
ejpam-5241	617	15	geodetic	geodetic	ADJ
ejpam-5241	617	16	set	set	NOUN
ejpam-5241	617	17	of	of	ADP
ejpam-5241	617	18	g	g	PROPN
ejpam-5241	617	19	⋄h	⋄h	PROPN
ejpam-5241	617	20	.	.	PUNCT
ejpam-5241	618	1	to	to	PART
ejpam-5241	618	2	show	show	VERB
ejpam-5241	618	3	that	that	SCONJ
ejpam-5241	618	4	s	s	VERB
ejpam-5241	618	5	is	be	AUX
ejpam-5241	618	6	a	a	DET
ejpam-5241	618	7	hop	hop	NOUN
ejpam-5241	618	8	dominating	dominating	NOUN
ejpam-5241	618	9	set	set	NOUN
ejpam-5241	618	10	,	,	PUNCT
ejpam-5241	618	11	let	let	VERB
ejpam-5241	618	12	w	w	NOUN
ejpam-5241	618	13	∈	∈	PROPN
ejpam-5241	618	14	v	v	ADP
ejpam-5241	618	15	(	(	PUNCT
ejpam-5241	618	16	g	g	NOUN
ejpam-5241	618	17	)	)	PUNCT
ejpam-5241	618	18	\	\	PROPN
ejpam-5241	618	19	a.	a.	NOUN
ejpam-5241	618	20	since	since	SCONJ
ejpam-5241	618	21	w	w	PROPN
ejpam-5241	618	22	/∈	/∈	PUNCT
ejpam-5241	618	23	τ(g	τ(g	PROPN
ejpam-5241	618	24	)	)	PUNCT
ejpam-5241	618	25	,	,	PUNCT
ejpam-5241	618	26	there	there	PRON
ejpam-5241	618	27	exists	exist	VERB
ejpam-5241	618	28	v	v	ADP
ejpam-5241	618	29	∈	∈	PROPN
ejpam-5241	618	30	ng(w	ng(w	NOUN
ejpam-5241	618	31	)	)	PUNCT
ejpam-5241	618	32	such	such	ADJ
ejpam-5241	618	33	that	that	SCONJ
ejpam-5241	618	34	ng(v	ng(v	PUNCT
ejpam-5241	618	35	)	)	PUNCT
ejpam-5241	618	36	\	\	NOUN
ejpam-5241	618	37	{	{	PUNCT
ejpam-5241	618	38	w	w	NOUN
ejpam-5241	618	39	}	}	PUNCT
ejpam-5241	618	40	=	=	NOUN
ejpam-5241	618	41	̸	̸	ADJ
ejpam-5241	618	42	∅	∅	NOUN
ejpam-5241	618	43	,	,	PUNCT
ejpam-5241	618	44	say	say	VERB
ejpam-5241	618	45	u	u	PROPN
ejpam-5241	618	46	∈	∈	PROPN
ejpam-5241	618	47	ng(v	ng(v	PUNCT
ejpam-5241	618	48	)	)	PUNCT
ejpam-5241	618	49	\	\	NOUN
ejpam-5241	618	50	{	{	PUNCT
ejpam-5241	618	51	w	w	NOUN
ejpam-5241	618	52	}	}	PUNCT
ejpam-5241	618	53	.	.	PUNCT
ejpam-5241	619	1	pick	pick	VERB
ejpam-5241	619	2	z	z	PROPN
ejpam-5241	619	3	∈	∈	PROPN
ejpam-5241	619	4	suv	suv	PROPN
ejpam-5241	619	5	.	.	PUNCT
ejpam-5241	620	1	then	then	ADV
ejpam-5241	620	2	z	z	PROPN
ejpam-5241	620	3	∈	∈	PROPN
ejpam-5241	620	4	s	s	PART
ejpam-5241	620	5	and	and	CCONJ
ejpam-5241	620	6	dg⋄h(w	dg⋄h(w	VERB
ejpam-5241	620	7	,	,	PUNCT
ejpam-5241	620	8	z	z	NOUN
ejpam-5241	620	9	)	)	PUNCT
ejpam-5241	620	10	=	=	SYM
ejpam-5241	620	11	2	2	X
ejpam-5241	620	12	.	.	PUNCT
ejpam-5241	620	13	accordingly	accordingly	ADV
ejpam-5241	620	14	,	,	PUNCT
ejpam-5241	620	15	s	s	VERB
ejpam-5241	620	16	is	be	AUX
ejpam-5241	620	17	a	a	DET
ejpam-5241	620	18	hop	hop	NOUN
ejpam-5241	620	19	dominating	dominating	NOUN
ejpam-5241	620	20	set	set	NOUN
ejpam-5241	620	21	of	of	ADP
ejpam-5241	620	22	g	g	PROPN
ejpam-5241	620	23	⋄h	⋄h	PROPN
ejpam-5241	620	24	.	.	PUNCT
ejpam-5241	621	1	corollary	corollary	ADJ
ejpam-5241	621	2	4	4	NUM
ejpam-5241	621	3	.	.	PUNCT
ejpam-5241	622	1	let	let	VERB
ejpam-5241	622	2	g	g	PRON
ejpam-5241	622	3	be	be	AUX
ejpam-5241	622	4	a	a	DET
ejpam-5241	622	5	nontrivial	nontrivial	ADJ
ejpam-5241	622	6	connected	connect	VERB
ejpam-5241	622	7	graph	graph	NOUN
ejpam-5241	622	8	of	of	ADP
ejpam-5241	622	9	size	size	NOUN
ejpam-5241	622	10	n	n	PROPN
ejpam-5241	622	11	and	and	CCONJ
ejpam-5241	622	12	p	p	PRON
ejpam-5241	622	13	≥	≥	NUM
ejpam-5241	622	14	1	1	NUM
ejpam-5241	622	15	.	.	PUNCT
ejpam-5241	623	1	then	then	ADV
ejpam-5241	623	2	γhcg(g	γhcg(g	NUM
ejpam-5241	623	3	⋄kp	⋄kp	NOUN
ejpam-5241	623	4	)	)	PUNCT
ejpam-5241	624	1	=	=	SYM
ejpam-5241	624	2	np+	np+	NOUN
ejpam-5241	624	3	|l(g)|+	|l(g)|+	VERB
ejpam-5241	624	4	|τ(g)|	|τ(g)|	PROPN
ejpam-5241	624	5	.	.	PUNCT
ejpam-5241	625	1	(	(	PUNCT
ejpam-5241	625	2	7	7	X
ejpam-5241	625	3	)	)	PUNCT
ejpam-5241	625	4	in	in	ADP
ejpam-5241	625	5	particular	particular	ADJ
ejpam-5241	625	6	,	,	PUNCT
ejpam-5241	625	7	if	if	SCONJ
ejpam-5241	625	8	l(g	l(g	NOUN
ejpam-5241	625	9	)	)	PUNCT
ejpam-5241	625	10	=	=	SYM
ejpam-5241	625	11	∅	∅	NOUN
ejpam-5241	625	12	and	and	CCONJ
ejpam-5241	625	13	τ(g	τ(g	PROPN
ejpam-5241	625	14	)	)	PUNCT
ejpam-5241	626	1	=	=	NOUN
ejpam-5241	626	2	∅	∅	NOUN
ejpam-5241	626	3	,	,	PUNCT
ejpam-5241	626	4	then	then	ADV
ejpam-5241	626	5	γhcg(g	γhcg(g	ADJ
ejpam-5241	626	6	⋄kp	⋄kp	NOUN
ejpam-5241	626	7	)	)	PUNCT
ejpam-5241	626	8	=	=	SYM
ejpam-5241	627	1	np	np	PROPN
ejpam-5241	627	2	.	.	PUNCT
ejpam-5241	628	1	(	(	PUNCT
ejpam-5241	628	2	8)	8)	NUM
ejpam-5241	628	3	if	if	SCONJ
ejpam-5241	628	4	g	g	PROPN
ejpam-5241	628	5	=	=	SYM
ejpam-5241	628	6	k2	k2	PROPN
ejpam-5241	628	7	,	,	PUNCT
ejpam-5241	628	8	then	then	ADV
ejpam-5241	628	9	g	g	NOUN
ejpam-5241	628	10	⋄h	⋄h	PROPN
ejpam-5241	628	11	=	=	PROPN
ejpam-5241	628	12	k2	k2	PROPN
ejpam-5241	628	13	+	+	PROPN
ejpam-5241	628	14	h.	h.	PROPN
ejpam-5241	628	15	this	this	DET
ejpam-5241	628	16	case	case	NOUN
ejpam-5241	628	17	is	be	AUX
ejpam-5241	628	18	taken	take	VERB
ejpam-5241	628	19	in	in	ADP
ejpam-5241	628	20	theorem	theorem	ADJ
ejpam-5241	628	21	7	7	NUM
ejpam-5241	628	22	.	.	PUNCT
ejpam-5241	629	1	in	in	ADP
ejpam-5241	629	2	what	what	PRON
ejpam-5241	629	3	follows	follow	VERB
ejpam-5241	629	4	,	,	PUNCT
ejpam-5241	629	5	we	we	PRON
ejpam-5241	629	6	consider	consider	VERB
ejpam-5241	629	7	g	g	NOUN
ejpam-5241	629	8	of	of	ADP
ejpam-5241	629	9	order	order	NOUN
ejpam-5241	629	10	n	n	PRON
ejpam-5241	629	11	≥	≥	NOUN
ejpam-5241	629	12	3	3	NUM
ejpam-5241	629	13	.	.	PUNCT
ejpam-5241	629	14	theorem	theorem	VERB
ejpam-5241	629	15	13	13	NUM
ejpam-5241	629	16	.	.	PUNCT
ejpam-5241	630	1	let	let	VERB
ejpam-5241	630	2	g	g	NOUN
ejpam-5241	630	3	and	and	CCONJ
ejpam-5241	630	4	h	h	NOUN
ejpam-5241	630	5	be	be	AUX
ejpam-5241	630	6	connected	connect	VERB
ejpam-5241	630	7	graphs	graph	NOUN
ejpam-5241	630	8	where	where	SCONJ
ejpam-5241	630	9	|v	|v	PROPN
ejpam-5241	630	10	(	(	PUNCT
ejpam-5241	630	11	g)|	g)|	X
ejpam-5241	630	12	≥	≥	NUM
ejpam-5241	630	13	3	3	NUM
ejpam-5241	630	14	and	and	CCONJ
ejpam-5241	630	15	h	h	NOUN
ejpam-5241	630	16	is	be	AUX
ejpam-5241	630	17	not	not	PART
ejpam-5241	630	18	complete	complete	ADJ
ejpam-5241	630	19	,	,	PUNCT
ejpam-5241	630	20	and	and	CCONJ
ejpam-5241	630	21	let	let	VERB
ejpam-5241	630	22	s	s	PRON
ejpam-5241	630	23	⊆	⊆	NUM
ejpam-5241	630	24	v	v	NOUN
ejpam-5241	630	25	(	(	PUNCT
ejpam-5241	630	26	g	g	PROPN
ejpam-5241	630	27	⋄	⋄	PROPN
ejpam-5241	630	28	h	h	PROPN
ejpam-5241	630	29	)	)	PUNCT
ejpam-5241	630	30	.	.	PUNCT
ejpam-5241	631	1	then	then	ADV
ejpam-5241	631	2	s	s	VERB
ejpam-5241	631	3	is	be	AUX
ejpam-5241	631	4	a	a	DET
ejpam-5241	631	5	closed	closed	ADJ
ejpam-5241	631	6	geodetic	geodetic	ADJ
ejpam-5241	631	7	hop	hop	NOUN
ejpam-5241	631	8	dominating	dominating	NOUN
ejpam-5241	631	9	set	set	NOUN
ejpam-5241	631	10	of	of	ADP
ejpam-5241	631	11	g	g	PROPN
ejpam-5241	631	12	⋄	⋄	PROPN
ejpam-5241	631	13	h	h	NOUN
ejpam-5241	632	1	if	if	SCONJ
ejpam-5241	632	2	and	and	CCONJ
ejpam-5241	632	3	only	only	ADV
ejpam-5241	632	4	if	if	SCONJ
ejpam-5241	632	5	s	s	VERB
ejpam-5241	632	6	=	=	NOUN
ejpam-5241	632	7	a	a	DET
ejpam-5241	632	8	∪	∪	X
ejpam-5241	632	9	(	(	PUNCT
ejpam-5241	632	10	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-5241	632	11	)	)	PUNCT
ejpam-5241	632	12	,	,	PUNCT
ejpam-5241	632	13	(	(	PUNCT
ejpam-5241	632	14	9	9	X
ejpam-5241	632	15	)	)	PUNCT
ejpam-5241	632	16	where	where	SCONJ
ejpam-5241	632	17	a	a	DET
ejpam-5241	632	18	⊆	⊆	NUM
ejpam-5241	632	19	v	v	NOUN
ejpam-5241	632	20	(	(	PUNCT
ejpam-5241	632	21	g	g	NOUN
ejpam-5241	632	22	)	)	PUNCT
ejpam-5241	632	23	and	and	CCONJ
ejpam-5241	632	24	suv	suv	PROPN
ejpam-5241	632	25	⊆	⊆	NUM
ejpam-5241	632	26	v	v	NOUN
ejpam-5241	632	27	(	(	PUNCT
ejpam-5241	632	28	huv	huv	PROPN
ejpam-5241	632	29	)	)	PUNCT
ejpam-5241	632	30	satisfying	satisfy	VERB
ejpam-5241	632	31	the	the	DET
ejpam-5241	632	32	following	following	NOUN
ejpam-5241	632	33	:	:	PUNCT
ejpam-5241	632	34	(	(	PUNCT
ejpam-5241	632	35	i	i	NOUN
ejpam-5241	632	36	)	)	PUNCT
ejpam-5241	632	37	the	the	DET
ejpam-5241	632	38	elements	element	NOUN
ejpam-5241	632	39	in	in	ADP
ejpam-5241	632	40	a	a	DET
ejpam-5241	632	41	constitute	constitute	NOUN
ejpam-5241	632	42	a	a	DET
ejpam-5241	632	43	closed	closed	ADJ
ejpam-5241	632	44	geodetic	geodetic	ADJ
ejpam-5241	632	45	sequence	sequence	NOUN
ejpam-5241	632	46	of	of	ADP
ejpam-5241	632	47	sets	set	NOUN
ejpam-5241	632	48	of	of	ADP
ejpam-5241	632	49	g	g	NOUN
ejpam-5241	632	50	and	and	CCONJ
ejpam-5241	632	51	τ(g	τ(g	PROPN
ejpam-5241	632	52	)	)	PUNCT
ejpam-5241	633	1	⊆	⊆	NUM
ejpam-5241	633	2	a	a	PRON
ejpam-5241	633	3	;	;	PUNCT
ejpam-5241	633	4	(	(	PUNCT
ejpam-5241	633	5	ii	ii	X
ejpam-5241	633	6	)	)	PUNCT
ejpam-5241	633	7	suv	suv	PROPN
ejpam-5241	633	8	is	be	AUX
ejpam-5241	633	9	a	a	DET
ejpam-5241	633	10	closed	closed	ADJ
ejpam-5241	633	11	2	2	NUM
ejpam-5241	633	12	-	-	PUNCT
ejpam-5241	633	13	path	path	NOUN
ejpam-5241	633	14	closure	closure	NOUN
ejpam-5241	633	15	absorbing	absorb	VERB
ejpam-5241	633	16	set	set	NOUN
ejpam-5241	633	17	of	of	ADP
ejpam-5241	633	18	huv	huv	PROPN
ejpam-5241	633	19	for	for	ADP
ejpam-5241	633	20	each	each	DET
ejpam-5241	633	21	uv	uv	PROPN
ejpam-5241	633	22	∈	∈	PROPN
ejpam-5241	633	23	e(g	e(g	PROPN
ejpam-5241	633	24	)	)	PUNCT
ejpam-5241	633	25	.	.	PUNCT
ejpam-5241	634	1	a.	a.	PROPN
ejpam-5241	634	2	adolfo	adolfo	PROPN
ejpam-5241	634	3	,	,	PUNCT
ejpam-5241	634	4	i.	i.	PROPN
ejpam-5241	634	5	aniversario	aniversario	PROPN
ejpam-5241	634	6	,	,	PUNCT
ejpam-5241	634	7	f.	f.	PROPN
ejpam-5241	634	8	jamil	jamil	PROPN
ejpam-5241	634	9	/	/	SYM
ejpam-5241	634	10	eur	eur	PROPN
ejpam-5241	634	11	.	.	PUNCT
ejpam-5241	635	1	j.	j.	PROPN
ejpam-5241	635	2	pure	pure	PROPN
ejpam-5241	635	3	appl	appl	PROPN
ejpam-5241	635	4	.	.	PROPN
ejpam-5241	635	5	math	math	PROPN
ejpam-5241	635	6	,	,	PUNCT
ejpam-5241	635	7	17	17	NUM
ejpam-5241	635	8	(	(	PUNCT
ejpam-5241	635	9	3	3	NUM
ejpam-5241	635	10	)	)	PUNCT
ejpam-5241	635	11	(	(	PUNCT
ejpam-5241	635	12	2024	2024	NUM
ejpam-5241	635	13	)	)	PUNCT
ejpam-5241	635	14	,	,	PUNCT
ejpam-5241	635	15	1618	1618	NUM
ejpam-5241	635	16	-	-	SYM
ejpam-5241	635	17	1636	1636	NUM
ejpam-5241	635	18	1634	1634	NUM
ejpam-5241	635	19	proof	proof	NOUN
ejpam-5241	635	20	.	.	PUNCT
ejpam-5241	636	1	assume	assume	VERB
ejpam-5241	636	2	s	s	PRON
ejpam-5241	636	3	is	be	AUX
ejpam-5241	636	4	a	a	DET
ejpam-5241	636	5	closed	closed	ADJ
ejpam-5241	636	6	geodetic	geodetic	ADJ
ejpam-5241	636	7	set	set	NOUN
ejpam-5241	636	8	of	of	ADP
ejpam-5241	636	9	g	g	PROPN
ejpam-5241	636	10	◦	◦	PROPN
ejpam-5241	636	11	h.	h.	PROPN
ejpam-5241	636	12	let	let	VERB
ejpam-5241	636	13	a	a	DET
ejpam-5241	636	14	=	=	X
ejpam-5241	636	15	s	s	NOUN
ejpam-5241	636	16	∩	∩	ADJ
ejpam-5241	636	17	v	v	NOUN
ejpam-5241	636	18	(	(	PUNCT
ejpam-5241	636	19	g	g	NOUN
ejpam-5241	636	20	)	)	PUNCT
ejpam-5241	636	21	,	,	PUNCT
ejpam-5241	636	22	and	and	CCONJ
ejpam-5241	636	23	suv	suv	PROPN
ejpam-5241	636	24	=	=	PROPN
ejpam-5241	636	25	s	s	PROPN
ejpam-5241	636	26	∩	∩	ADJ
ejpam-5241	636	27	v	v	X
ejpam-5241	636	28	(	(	PUNCT
ejpam-5241	636	29	huv	huv	PROPN
ejpam-5241	636	30	)	)	PUNCT
ejpam-5241	636	31	for	for	ADP
ejpam-5241	636	32	each	each	DET
ejpam-5241	636	33	uv	uv	PROPN
ejpam-5241	636	34	∈	∈	PROPN
ejpam-5241	636	35	e(g	e(g	PROPN
ejpam-5241	636	36	)	)	PUNCT
ejpam-5241	636	37	.	.	PUNCT
ejpam-5241	637	1	then	then	ADV
ejpam-5241	637	2	s	s	VERB
ejpam-5241	637	3	=	=	PUNCT
ejpam-5241	637	4	a	a	DET
ejpam-5241	637	5	∪	∪	X
ejpam-5241	637	6	(	(	PUNCT
ejpam-5241	637	7	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-5241	637	8	)	)	PUNCT
ejpam-5241	637	9	.	.	PUNCT
ejpam-5241	638	1	at	at	ADP
ejpam-5241	638	2	this	this	PRON
ejpam-5241	638	3	far	far	ADV
ejpam-5241	638	4	,	,	PUNCT
ejpam-5241	638	5	showing	show	VERB
ejpam-5241	638	6	that	that	SCONJ
ejpam-5241	638	7	the	the	DET
ejpam-5241	638	8	elements	element	NOUN
ejpam-5241	638	9	of	of	ADP
ejpam-5241	638	10	a	a	PRON
ejpam-5241	638	11	and	and	CCONJ
ejpam-5241	638	12	suv	suv	PROPN
ejpam-5241	638	13	constitute	constitute	VERB
ejpam-5241	638	14	a	a	DET
ejpam-5241	638	15	closed	closed	ADJ
ejpam-5241	638	16	geodetic	geodetic	ADJ
ejpam-5241	638	17	sequence	sequence	NOUN
ejpam-5241	638	18	and	and	CCONJ
ejpam-5241	638	19	a	a	DET
ejpam-5241	638	20	closed	closed	ADJ
ejpam-5241	638	21	2	2	NUM
ejpam-5241	638	22	-	-	PUNCT
ejpam-5241	638	23	path	path	NOUN
ejpam-5241	638	24	closure	closure	NOUN
ejpam-5241	638	25	absorbing	absorb	VERB
ejpam-5241	638	26	sequence	sequence	NOUN
ejpam-5241	638	27	of	of	ADP
ejpam-5241	638	28	sets	set	NOUN
ejpam-5241	638	29	in	in	ADP
ejpam-5241	638	30	g	g	PROPN
ejpam-5241	638	31	and	and	CCONJ
ejpam-5241	638	32	huv	huv	PROPN
ejpam-5241	638	33	,	,	PUNCT
ejpam-5241	638	34	respectively	respectively	ADV
ejpam-5241	638	35	,	,	PUNCT
ejpam-5241	638	36	for	for	ADP
ejpam-5241	638	37	each	each	DET
ejpam-5241	638	38	uv	uv	PROPN
ejpam-5241	638	39	∈	∈	PROPN
ejpam-5241	638	40	e(g	e(g	PROPN
ejpam-5241	638	41	)	)	PUNCT
ejpam-5241	638	42	,	,	PUNCT
ejpam-5241	638	43	is	be	AUX
ejpam-5241	638	44	already	already	ADV
ejpam-5241	638	45	a	a	DET
ejpam-5241	638	46	routine	routine	NOUN
ejpam-5241	638	47	.	.	PUNCT
ejpam-5241	639	1	since	since	SCONJ
ejpam-5241	639	2	s	s	PROPN
ejpam-5241	639	3	is	be	AUX
ejpam-5241	639	4	a	a	DET
ejpam-5241	639	5	hop	hop	NOUN
ejpam-5241	639	6	dominating	dominating	NOUN
ejpam-5241	639	7	set	set	NOUN
ejpam-5241	639	8	,	,	PUNCT
ejpam-5241	639	9	τ(g	τ(g	PROPN
ejpam-5241	639	10	)	)	PUNCT
ejpam-5241	639	11	⊆	⊆	NUM
ejpam-5241	639	12	a.	a.	NOUN
ejpam-5241	639	13	thus	thus	ADV
ejpam-5241	639	14	,	,	PUNCT
ejpam-5241	639	15	(	(	PUNCT
ejpam-5241	639	16	i	i	NOUN
ejpam-5241	639	17	)	)	PUNCT
ejpam-5241	639	18	holds	hold	VERB
ejpam-5241	639	19	.	.	PUNCT
ejpam-5241	640	1	to	to	PART
ejpam-5241	640	2	completely	completely	ADV
ejpam-5241	640	3	show	show	VERB
ejpam-5241	640	4	(	(	PUNCT
ejpam-5241	640	5	ii	ii	NOUN
ejpam-5241	640	6	)	)	PUNCT
ejpam-5241	640	7	,	,	PUNCT
ejpam-5241	640	8	observe	observe	VERB
ejpam-5241	640	9	that	that	SCONJ
ejpam-5241	640	10	for	for	ADP
ejpam-5241	640	11	each	each	DET
ejpam-5241	640	12	z	z	NOUN
ejpam-5241	640	13	∈	∈	PROPN
ejpam-5241	640	14	v	v	NOUN
ejpam-5241	640	15	(	(	PUNCT
ejpam-5241	640	16	huv	huv	PROPN
ejpam-5241	640	17	)	)	PUNCT
ejpam-5241	640	18	,	,	PUNCT
ejpam-5241	640	19	every	every	DET
ejpam-5241	640	20	x	x	PROPN
ejpam-5241	640	21	-	-	PROPN
ejpam-5241	640	22	y	y	ADJ
ejpam-5241	640	23	geodesic	geodesic	NOUN
ejpam-5241	640	24	(	(	PUNCT
ejpam-5241	640	25	with	with	ADP
ejpam-5241	640	26	x	x	PUNCT
ejpam-5241	640	27	̸=	̸=	PROPN
ejpam-5241	640	28	z	z	PROPN
ejpam-5241	640	29	̸=	̸=	PROPN
ejpam-5241	640	30	y	y	PROPN
ejpam-5241	640	31	)	)	PUNCT
ejpam-5241	640	32	in	in	ADP
ejpam-5241	640	33	g	g	PROPN
ejpam-5241	640	34	⋄	⋄	PROPN
ejpam-5241	640	35	h	h	NOUN
ejpam-5241	640	36	containing	contain	VERB
ejpam-5241	640	37	z	z	NOUN
ejpam-5241	640	38	lies	lie	VERB
ejpam-5241	640	39	entirely	entirely	ADV
ejpam-5241	640	40	in	in	ADP
ejpam-5241	640	41	huv	huv	PROPN
ejpam-5241	640	42	.	.	PUNCT
ejpam-5241	641	1	thus	thus	ADV
ejpam-5241	641	2	,	,	PUNCT
ejpam-5241	641	3	since	since	SCONJ
ejpam-5241	641	4	ig⋄h	ig⋄h	PROPN
ejpam-5241	641	5	[	[	X
ejpam-5241	641	6	s	s	X
ejpam-5241	641	7	]	]	X
ejpam-5241	641	8	=	=	SYM
ejpam-5241	641	9	v	v	X
ejpam-5241	641	10	(	(	PUNCT
ejpam-5241	641	11	g	g	PROPN
ejpam-5241	641	12	⋄	⋄	PROPN
ejpam-5241	641	13	h	h	NOUN
ejpam-5241	641	14	)	)	PUNCT
ejpam-5241	641	15	,	,	PUNCT
ejpam-5241	641	16	p2[suv	p2[suv	PROPN
ejpam-5241	641	17	]	]	PUNCT
ejpam-5241	641	18	=	=	SYM
ejpam-5241	641	19	v	v	X
ejpam-5241	641	20	(	(	PUNCT
ejpam-5241	641	21	huv	huv	PROPN
ejpam-5241	641	22	)	)	PUNCT
ejpam-5241	641	23	.	.	PUNCT
ejpam-5241	642	1	this	this	PRON
ejpam-5241	642	2	makes	make	VERB
ejpam-5241	642	3	suv	suv	PROPN
ejpam-5241	642	4	a	a	DET
ejpam-5241	642	5	closed	closed	ADJ
ejpam-5241	642	6	2	2	NUM
ejpam-5241	642	7	-	-	PUNCT
ejpam-5241	642	8	path	path	NOUN
ejpam-5241	642	9	absorbing	absorb	VERB
ejpam-5241	642	10	set	set	NOUN
ejpam-5241	642	11	of	of	ADP
ejpam-5241	642	12	huv	huv	PROPN
ejpam-5241	642	13	.	.	PUNCT
ejpam-5241	643	1	conversely	conversely	ADV
ejpam-5241	643	2	,	,	PUNCT
ejpam-5241	643	3	suppose	suppose	VERB
ejpam-5241	643	4	that	that	SCONJ
ejpam-5241	643	5	s	s	VERB
ejpam-5241	643	6	is	be	AUX
ejpam-5241	643	7	as	as	SCONJ
ejpam-5241	643	8	given	give	VERB
ejpam-5241	643	9	in	in	ADP
ejpam-5241	643	10	equation	equation	NOUN
ejpam-5241	643	11	4	4	NUM
ejpam-5241	643	12	and	and	CCONJ
ejpam-5241	643	13	satisfies	satisfy	VERB
ejpam-5241	643	14	conditions	condition	NOUN
ejpam-5241	643	15	(	(	PUNCT
ejpam-5241	643	16	i	i	NOUN
ejpam-5241	643	17	)	)	PUNCT
ejpam-5241	643	18	and	and	CCONJ
ejpam-5241	643	19	(	(	PUNCT
ejpam-5241	643	20	ii	ii	NOUN
ejpam-5241	643	21	)	)	PUNCT
ejpam-5241	643	22	.	.	PUNCT
ejpam-5241	644	1	assume	assume	VERB
ejpam-5241	644	2	|s|	|s|	PROPN
ejpam-5241	644	3	=	=	SYM
ejpam-5241	644	4	n.	n.	NOUN
ejpam-5241	644	5	obtain	obtain	VERB
ejpam-5241	644	6	from	from	ADP
ejpam-5241	644	7	s	s	PROPN
ejpam-5241	644	8	a	a	DET
ejpam-5241	644	9	closed	closed	ADJ
ejpam-5241	644	10	geodetic	geodetic	ADJ
ejpam-5241	644	11	sequence	sequence	NOUN
ejpam-5241	644	12	of	of	ADP
ejpam-5241	644	13	sets	set	NOUN
ejpam-5241	644	14	in	in	ADP
ejpam-5241	644	15	g⋄h	g⋄h	NOUN
ejpam-5241	644	16	as	as	SCONJ
ejpam-5241	644	17	follows	follow	VERB
ejpam-5241	644	18	:	:	PUNCT
ejpam-5241	644	19	construct	construct	VERB
ejpam-5241	644	20	sk	sk	X
ejpam-5241	644	21	=	=	PUNCT
ejpam-5241	644	22	{	{	PUNCT
ejpam-5241	644	23	x1	x1	PROPN
ejpam-5241	644	24	,	,	PUNCT
ejpam-5241	644	25	x2	x2	PROPN
ejpam-5241	644	26	,	,	PUNCT
ejpam-5241	644	27	.	.	PUNCT
ejpam-5241	644	28	.	.	PUNCT
ejpam-5241	644	29	.	.	PUNCT
ejpam-5241	645	1	,	,	PUNCT
ejpam-5241	645	2	xk	xk	PROPN
ejpam-5241	645	3	}	}	PUNCT
ejpam-5241	645	4	for	for	ADP
ejpam-5241	645	5	k	k	PROPN
ejpam-5241	645	6	=	=	SYM
ejpam-5241	645	7	1	1	NUM
ejpam-5241	645	8	,	,	PUNCT
ejpam-5241	645	9	2	2	NUM
ejpam-5241	645	10	,	,	PUNCT
ejpam-5241	645	11	.	.	PUNCT
ejpam-5241	645	12	.	.	PUNCT
ejpam-5241	646	1	.	.	PUNCT
ejpam-5241	647	1	,	,	PUNCT
ejpam-5241	647	2	n	n	PRON
ejpam-5241	647	3	such	such	ADJ
ejpam-5241	647	4	that	that	SCONJ
ejpam-5241	647	5	sk	sk	VERB
ejpam-5241	647	6	for	for	ADP
ejpam-5241	647	7	k	k	PROPN
ejpam-5241	647	8	∈	∈	PROPN
ejpam-5241	647	9	{	{	PUNCT
ejpam-5241	647	10	1	1	NUM
ejpam-5241	647	11	,	,	PUNCT
ejpam-5241	647	12	2	2	NUM
ejpam-5241	647	13	,	,	PUNCT
ejpam-5241	647	14	.	.	PUNCT
ejpam-5241	647	15	.	.	PUNCT
ejpam-5241	648	1	.	.	PUNCT
ejpam-5241	649	1	,	,	PUNCT
ejpam-5241	649	2	|a|	|a|	NOUN
ejpam-5241	649	3	}	}	PUNCT
ejpam-5241	649	4	is	be	AUX
ejpam-5241	649	5	a	a	DET
ejpam-5241	649	6	closed	closed	ADJ
ejpam-5241	649	7	geodetic	geodetic	ADJ
ejpam-5241	649	8	sequence	sequence	NOUN
ejpam-5241	649	9	constituted	constitute	VERB
ejpam-5241	649	10	by	by	ADP
ejpam-5241	649	11	the	the	DET
ejpam-5241	649	12	vertices	vertex	NOUN
ejpam-5241	649	13	in	in	ADP
ejpam-5241	649	14	a	a	PRON
ejpam-5241	649	15	and	and	CCONJ
ejpam-5241	649	16	sn	sn	ADV
ejpam-5241	649	17	\a	\a	VERB
ejpam-5241	650	1	=	=	PUNCT
ejpam-5241	650	2	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-5241	650	3	.	.	PUNCT
ejpam-5241	651	1	then	then	ADV
ejpam-5241	651	2	sk	sk	VERB
ejpam-5241	651	3	,	,	PUNCT
ejpam-5241	651	4	k	k	PROPN
ejpam-5241	651	5	=	=	SYM
ejpam-5241	651	6	1	1	NUM
ejpam-5241	651	7	,	,	PUNCT
ejpam-5241	651	8	2	2	NUM
ejpam-5241	651	9	,	,	PUNCT
ejpam-5241	651	10	.	.	PUNCT
ejpam-5241	651	11	.	.	PUNCT
ejpam-5241	652	1	.	.	PUNCT
ejpam-5241	653	1	,	,	PUNCT
ejpam-5241	653	2	n	n	CCONJ
ejpam-5241	653	3	,	,	PUNCT
ejpam-5241	653	4	is	be	AUX
ejpam-5241	653	5	a	a	DET
ejpam-5241	653	6	closed	closed	ADJ
ejpam-5241	653	7	geodetic	geodetic	ADJ
ejpam-5241	653	8	sequence	sequence	NOUN
ejpam-5241	653	9	of	of	ADP
ejpam-5241	653	10	sets	set	NOUN
ejpam-5241	653	11	in	in	ADP
ejpam-5241	653	12	g	g	PROPN
ejpam-5241	653	13	⋄h	⋄h	PROPN
ejpam-5241	653	14	.	.	PUNCT
ejpam-5241	654	1	let	let	VERB
ejpam-5241	654	2	w	w	NOUN
ejpam-5241	654	3	∈	∈	PROPN
ejpam-5241	654	4	v	v	NOUN
ejpam-5241	654	5	(	(	PUNCT
ejpam-5241	654	6	g	g	PROPN
ejpam-5241	654	7	⋄h	⋄h	PROPN
ejpam-5241	654	8	)	)	PUNCT
ejpam-5241	654	9	\	\	PROPN
ejpam-5241	654	10	s	s	PART
ejpam-5241	654	11	and	and	CCONJ
ejpam-5241	654	12	let	let	VERB
ejpam-5241	654	13	uv	uv	PROPN
ejpam-5241	654	14	∈	∈	PROPN
ejpam-5241	654	15	e(g	e(g	PROPN
ejpam-5241	654	16	)	)	PUNCT
ejpam-5241	654	17	such	such	ADJ
ejpam-5241	654	18	that	that	SCONJ
ejpam-5241	654	19	w	w	PROPN
ejpam-5241	654	20	∈	∈	PROPN
ejpam-5241	654	21	v	v	NOUN
ejpam-5241	654	22	(	(	PUNCT
ejpam-5241	654	23	huv	huv	PROPN
ejpam-5241	654	24	+	+	NUM
ejpam-5241	654	25	uv	uv	NOUN
ejpam-5241	654	26	)	)	PUNCT
ejpam-5241	654	27	.	.	PUNCT
ejpam-5241	655	1	suppose	suppose	VERB
ejpam-5241	655	2	that	that	SCONJ
ejpam-5241	655	3	u	u	PRON
ejpam-5241	655	4	=	=	PROPN
ejpam-5241	655	5	w.	w.	PROPN
ejpam-5241	655	6	if	if	SCONJ
ejpam-5241	655	7	suv	suv	PROPN
ejpam-5241	655	8	=	=	SYM
ejpam-5241	655	9	v	v	PROPN
ejpam-5241	655	10	(	(	PUNCT
ejpam-5241	655	11	huv	huv	PROPN
ejpam-5241	655	12	)	)	PUNCT
ejpam-5241	655	13	,	,	PUNCT
ejpam-5241	655	14	then	then	ADV
ejpam-5241	655	15	since	since	SCONJ
ejpam-5241	655	16	huv	huv	PROPN
ejpam-5241	655	17	is	be	AUX
ejpam-5241	655	18	not	not	PART
ejpam-5241	655	19	complete	complete	ADJ
ejpam-5241	655	20	,	,	PUNCT
ejpam-5241	655	21	there	there	PRON
ejpam-5241	655	22	exist	exist	VERB
ejpam-5241	655	23	x	x	NOUN
ejpam-5241	655	24	,	,	PUNCT
ejpam-5241	655	25	y	y	PROPN
ejpam-5241	655	26	∈	∈	PROPN
ejpam-5241	655	27	suv	suv	PROPN
ejpam-5241	655	28	such	such	ADJ
ejpam-5241	655	29	that	that	PRON
ejpam-5241	655	30	xy	xy	PROPN
ejpam-5241	655	31	/∈	/∈	PUNCT
ejpam-5241	655	32	e(huv	e(huv	PROPN
ejpam-5241	655	33	)	)	PUNCT
ejpam-5241	655	34	.	.	PUNCT
ejpam-5241	656	1	then	then	ADV
ejpam-5241	656	2	dg⋄h(x	dg⋄h(x	PROPN
ejpam-5241	656	3	,	,	PUNCT
ejpam-5241	656	4	y	y	PROPN
ejpam-5241	656	5	)	)	PUNCT
ejpam-5241	656	6	=	=	SYM
ejpam-5241	656	7	2	2	NUM
ejpam-5241	656	8	and	and	CCONJ
ejpam-5241	656	9	w	w	PROPN
ejpam-5241	656	10	∈	∈	PROPN
ejpam-5241	656	11	ig⋄h(x	ig⋄h(x	NOUN
ejpam-5241	656	12	,	,	PUNCT
ejpam-5241	656	13	y	y	PROPN
ejpam-5241	656	14	)	)	PUNCT
ejpam-5241	656	15	.	.	PUNCT
ejpam-5241	657	1	suppose	suppose	VERB
ejpam-5241	657	2	that	that	SCONJ
ejpam-5241	657	3	suv	suv	PROPN
ejpam-5241	657	4	̸=	̸=	PROPN
ejpam-5241	657	5	v	v	PROPN
ejpam-5241	657	6	(	(	PUNCT
ejpam-5241	657	7	huv	huv	PROPN
ejpam-5241	657	8	)	)	PUNCT
ejpam-5241	657	9	.	.	PUNCT
ejpam-5241	658	1	since	since	SCONJ
ejpam-5241	658	2	suv	suv	PROPN
ejpam-5241	658	3	is	be	AUX
ejpam-5241	658	4	a	a	DET
ejpam-5241	658	5	2	2	NUM
ejpam-5241	658	6	-	-	PUNCT
ejpam-5241	658	7	path	path	NOUN
ejpam-5241	658	8	closure	closure	NOUN
ejpam-5241	658	9	absorbing	absorb	VERB
ejpam-5241	658	10	set	set	NOUN
ejpam-5241	658	11	of	of	ADP
ejpam-5241	658	12	huv	huv	PROPN
ejpam-5241	658	13	,	,	PUNCT
ejpam-5241	658	14	for	for	ADP
ejpam-5241	658	15	w	w	PROPN
ejpam-5241	658	16	∈	∈	PROPN
ejpam-5241	658	17	v	v	NOUN
ejpam-5241	658	18	(	(	PUNCT
ejpam-5241	658	19	huv)\suv	huv)\suv	PROPN
ejpam-5241	658	20	,	,	PUNCT
ejpam-5241	658	21	there	there	PRON
ejpam-5241	658	22	exist	exist	VERB
ejpam-5241	658	23	x	x	NOUN
ejpam-5241	658	24	,	,	PUNCT
ejpam-5241	658	25	y	y	PROPN
ejpam-5241	658	26	∈	∈	PROPN
ejpam-5241	658	27	suv	suv	PROPN
ejpam-5241	658	28	such	such	ADJ
ejpam-5241	658	29	that	that	SCONJ
ejpam-5241	658	30	[	[	X
ejpam-5241	658	31	x	x	X
ejpam-5241	658	32	,	,	PUNCT
ejpam-5241	658	33	w	w	PROPN
ejpam-5241	658	34	,	,	PUNCT
ejpam-5241	658	35	y	y	PROPN
ejpam-5241	658	36	]	]	X
ejpam-5241	658	37	is	be	AUX
ejpam-5241	658	38	a	a	DET
ejpam-5241	658	39	geodesic	geodesic	NOUN
ejpam-5241	658	40	in	in	ADP
ejpam-5241	658	41	huv	huv	PROPN
ejpam-5241	658	42	.	.	PUNCT
ejpam-5241	659	1	this	this	PRON
ejpam-5241	659	2	means	mean	VERB
ejpam-5241	659	3	that	that	SCONJ
ejpam-5241	659	4	dg⋄h(x	dg⋄h(x	PROPN
ejpam-5241	659	5	,	,	PUNCT
ejpam-5241	659	6	y	y	PROPN
ejpam-5241	659	7	)	)	PUNCT
ejpam-5241	659	8	=	=	SYM
ejpam-5241	659	9	2	2	NUM
ejpam-5241	659	10	and	and	CCONJ
ejpam-5241	659	11	w	w	PROPN
ejpam-5241	659	12	∈	∈	PROPN
ejpam-5241	659	13	ig⋄h(x	ig⋄h(x	NOUN
ejpam-5241	659	14	,	,	PUNCT
ejpam-5241	659	15	y	y	PROPN
ejpam-5241	659	16	)	)	PUNCT
ejpam-5241	659	17	.	.	PUNCT
ejpam-5241	660	1	the	the	DET
ejpam-5241	660	2	case	case	NOUN
ejpam-5241	660	3	where	where	SCONJ
ejpam-5241	660	4	w	w	NOUN
ejpam-5241	660	5	=	=	NOUN
ejpam-5241	660	6	v	v	NOUN
ejpam-5241	660	7	is	be	AUX
ejpam-5241	660	8	handled	handle	VERB
ejpam-5241	660	9	similarly	similarly	ADV
ejpam-5241	660	10	.	.	PUNCT
ejpam-5241	661	1	now	now	ADV
ejpam-5241	661	2	,	,	PUNCT
ejpam-5241	661	3	suppose	suppose	VERB
ejpam-5241	661	4	that	that	SCONJ
ejpam-5241	661	5	w	w	PROPN
ejpam-5241	661	6	∈	∈	PROPN
ejpam-5241	661	7	v	v	NOUN
ejpam-5241	661	8	(	(	PUNCT
ejpam-5241	661	9	huv	huv	PROPN
ejpam-5241	661	10	)	)	PUNCT
ejpam-5241	661	11	.	.	PUNCT
ejpam-5241	662	1	since	since	SCONJ
ejpam-5241	662	2	suv	suv	PROPN
ejpam-5241	662	3	is	be	AUX
ejpam-5241	662	4	2	2	NUM
ejpam-5241	662	5	-	-	PUNCT
ejpam-5241	662	6	path	path	NOUN
ejpam-5241	662	7	closure	closure	NOUN
ejpam-5241	662	8	absorbing	absorbing	NOUN
ejpam-5241	662	9	,	,	PUNCT
ejpam-5241	662	10	there	there	PRON
ejpam-5241	662	11	exist	exist	VERB
ejpam-5241	662	12	x	x	NOUN
ejpam-5241	662	13	,	,	PUNCT
ejpam-5241	662	14	y	y	PROPN
ejpam-5241	662	15	∈	∈	PROPN
ejpam-5241	662	16	suv	suv	PROPN
ejpam-5241	662	17	such	such	ADJ
ejpam-5241	662	18	that	that	SCONJ
ejpam-5241	662	19	dhuv(x	dhuv(x	PROPN
ejpam-5241	662	20	,	,	PUNCT
ejpam-5241	662	21	y	y	NOUN
ejpam-5241	662	22	)	)	PUNCT
ejpam-5241	662	23	=	=	SYM
ejpam-5241	662	24	2	2	NUM
ejpam-5241	662	25	and	and	CCONJ
ejpam-5241	662	26	w	w	PROPN
ejpam-5241	662	27	∈	∈	PROPN
ejpam-5241	662	28	ihuv(x	ihuv(x	PROPN
ejpam-5241	662	29	,	,	PUNCT
ejpam-5241	662	30	y	y	PROPN
ejpam-5241	662	31	)	)	PUNCT
ejpam-5241	662	32	.	.	PUNCT
ejpam-5241	663	1	this	this	PRON
ejpam-5241	663	2	means	mean	VERB
ejpam-5241	663	3	that	that	SCONJ
ejpam-5241	663	4	dg⋄h(x	dg⋄h(x	PROPN
ejpam-5241	663	5	,	,	PUNCT
ejpam-5241	663	6	y	y	PROPN
ejpam-5241	663	7	)	)	PUNCT
ejpam-5241	663	8	=	=	SYM
ejpam-5241	663	9	2	2	NUM
ejpam-5241	663	10	and	and	CCONJ
ejpam-5241	663	11	w	w	PROPN
ejpam-5241	663	12	∈	∈	PROPN
ejpam-5241	663	13	ig⋄h(x	ig⋄h(x	NOUN
ejpam-5241	663	14	,	,	PUNCT
ejpam-5241	663	15	y	y	PROPN
ejpam-5241	663	16	)	)	PUNCT
ejpam-5241	663	17	.	.	PUNCT
ejpam-5241	664	1	we	we	PRON
ejpam-5241	664	2	have	have	AUX
ejpam-5241	664	3	just	just	ADV
ejpam-5241	664	4	shown	show	VERB
ejpam-5241	664	5	that	that	SCONJ
ejpam-5241	664	6	s	s	NOUN
ejpam-5241	664	7	is	be	AUX
ejpam-5241	664	8	a	a	DET
ejpam-5241	664	9	closed	closed	ADJ
ejpam-5241	664	10	geodetic	geodetic	ADJ
ejpam-5241	664	11	set	set	NOUN
ejpam-5241	664	12	of	of	ADP
ejpam-5241	664	13	g	g	PROPN
ejpam-5241	664	14	⋄h	⋄h	PROPN
ejpam-5241	664	15	.	.	PUNCT
ejpam-5241	665	1	finally	finally	ADV
ejpam-5241	665	2	,	,	PUNCT
ejpam-5241	665	3	to	to	PART
ejpam-5241	665	4	show	show	VERB
ejpam-5241	665	5	that	that	SCONJ
ejpam-5241	665	6	s	s	VERB
ejpam-5241	665	7	is	be	AUX
ejpam-5241	665	8	a	a	DET
ejpam-5241	665	9	hop	hop	NOUN
ejpam-5241	665	10	dominating	dominating	NOUN
ejpam-5241	665	11	set	set	NOUN
ejpam-5241	665	12	,	,	PUNCT
ejpam-5241	665	13	let	let	VERB
ejpam-5241	665	14	w	w	NOUN
ejpam-5241	665	15	∈	∈	PROPN
ejpam-5241	665	16	v	v	NOUN
ejpam-5241	665	17	(	(	PUNCT
ejpam-5241	665	18	g⋄h)\s	g⋄h)\s	NOUN
ejpam-5241	665	19	.	.	PUNCT
ejpam-5241	666	1	if	if	SCONJ
ejpam-5241	666	2	w	w	PROPN
ejpam-5241	666	3	∈	∈	PROPN
ejpam-5241	666	4	v	v	ADP
ejpam-5241	666	5	(	(	PUNCT
ejpam-5241	666	6	g	g	NOUN
ejpam-5241	666	7	)	)	PUNCT
ejpam-5241	666	8	,	,	PUNCT
ejpam-5241	666	9	then	then	ADV
ejpam-5241	666	10	since	since	SCONJ
ejpam-5241	666	11	w	w	PROPN
ejpam-5241	666	12	/∈	/∈	PUNCT
ejpam-5241	666	13	τ(g	τ(g	PROPN
ejpam-5241	666	14	)	)	PUNCT
ejpam-5241	666	15	,	,	PUNCT
ejpam-5241	666	16	there	there	PRON
ejpam-5241	666	17	exists	exist	VERB
ejpam-5241	666	18	v	v	ADP
ejpam-5241	666	19	∈	∈	PROPN
ejpam-5241	666	20	ng(w	ng(w	NOUN
ejpam-5241	666	21	)	)	PUNCT
ejpam-5241	666	22	such	such	ADJ
ejpam-5241	666	23	that	that	SCONJ
ejpam-5241	666	24	ng(v	ng(v	PUNCT
ejpam-5241	666	25	)	)	PUNCT
ejpam-5241	666	26	\	\	NOUN
ejpam-5241	666	27	{	{	PUNCT
ejpam-5241	666	28	w	w	NOUN
ejpam-5241	666	29	}	}	PUNCT
ejpam-5241	666	30	=	=	NOUN
ejpam-5241	666	31	̸	̸	ADV
ejpam-5241	666	32	∅.	∅.	ADV
ejpam-5241	666	33	let	let	VERB
ejpam-5241	666	34	u	u	PRON
ejpam-5241	666	35	∈	∈	NOUN
ejpam-5241	666	36	ng(v	ng(v	PUNCT
ejpam-5241	666	37	)	)	PUNCT
ejpam-5241	666	38	\	\	NOUN
ejpam-5241	666	39	{	{	PUNCT
ejpam-5241	666	40	w	w	NOUN
ejpam-5241	666	41	}	}	PUNCT
ejpam-5241	666	42	.	.	PUNCT
ejpam-5241	667	1	pick	pick	VERB
ejpam-5241	667	2	z	z	PROPN
ejpam-5241	667	3	∈	∈	PROPN
ejpam-5241	667	4	suv	suv	PROPN
ejpam-5241	667	5	.	.	PUNCT
ejpam-5241	668	1	then	then	ADV
ejpam-5241	668	2	dg⋄h(w	dg⋄h(w	VERB
ejpam-5241	668	3	,	,	PUNCT
ejpam-5241	668	4	z	z	NOUN
ejpam-5241	668	5	)	)	PUNCT
ejpam-5241	668	6	=	=	SYM
ejpam-5241	668	7	2	2	X
ejpam-5241	668	8	.	.	PUNCT
ejpam-5241	668	9	suppose	suppose	VERB
ejpam-5241	668	10	that	that	SCONJ
ejpam-5241	668	11	w	w	PROPN
ejpam-5241	668	12	∈	∈	PROPN
ejpam-5241	668	13	v	v	NOUN
ejpam-5241	668	14	(	(	PUNCT
ejpam-5241	668	15	huv	huv	PROPN
ejpam-5241	668	16	)	)	PUNCT
ejpam-5241	668	17	for	for	ADP
ejpam-5241	668	18	some	some	DET
ejpam-5241	668	19	uv	uv	NOUN
ejpam-5241	668	20	∈	∈	PROPN
ejpam-5241	668	21	v	v	NOUN
ejpam-5241	668	22	(	(	PUNCT
ejpam-5241	668	23	g	g	NOUN
ejpam-5241	668	24	)	)	PUNCT
ejpam-5241	668	25	.	.	PUNCT
ejpam-5241	669	1	then	then	ADV
ejpam-5241	669	2	w	w	PROPN
ejpam-5241	669	3	∈	∈	PROPN
ejpam-5241	669	4	v	v	NOUN
ejpam-5241	669	5	(	(	PUNCT
ejpam-5241	669	6	huv)\suv	huv)\suv	PROPN
ejpam-5241	669	7	.	.	PUNCT
ejpam-5241	670	1	since	since	SCONJ
ejpam-5241	670	2	|v	|v	PROPN
ejpam-5241	670	3	(	(	PUNCT
ejpam-5241	670	4	g)|	g)|	X
ejpam-5241	670	5	≥	≥	NUM
ejpam-5241	670	6	3	3	NUM
ejpam-5241	670	7	and	and	CCONJ
ejpam-5241	670	8	g	g	NOUN
ejpam-5241	670	9	is	be	AUX
ejpam-5241	670	10	connected	connect	VERB
ejpam-5241	670	11	,	,	PUNCT
ejpam-5241	670	12	there	there	PRON
ejpam-5241	670	13	exists	exist	VERB
ejpam-5241	670	14	z	z	PROPN
ejpam-5241	670	15	∈	∈	PROPN
ejpam-5241	670	16	v	v	ADP
ejpam-5241	670	17	(	(	PUNCT
ejpam-5241	670	18	g	g	NOUN
ejpam-5241	670	19	)	)	PUNCT
ejpam-5241	670	20	such	such	ADJ
ejpam-5241	670	21	that	that	SCONJ
ejpam-5241	670	22	uz	uz	PROPN
ejpam-5241	670	23	or	or	CCONJ
ejpam-5241	670	24	vz	vz	NOUN
ejpam-5241	670	25	is	be	AUX
ejpam-5241	670	26	an	an	DET
ejpam-5241	670	27	edge	edge	NOUN
ejpam-5241	670	28	in	in	ADP
ejpam-5241	670	29	g.	g.	PROPN
ejpam-5241	670	30	let	let	VERB
ejpam-5241	670	31	uz	uz	PROPN
ejpam-5241	670	32	∈	∈	PROPN
ejpam-5241	670	33	e(g	e(g	PROPN
ejpam-5241	670	34	)	)	PUNCT
ejpam-5241	670	35	.	.	PUNCT
ejpam-5241	671	1	take	take	VERB
ejpam-5241	671	2	x	x	PUNCT
ejpam-5241	671	3	∈	∈	PROPN
ejpam-5241	671	4	suz	suz	NOUN
ejpam-5241	671	5	.	.	PUNCT
ejpam-5241	672	1	then	then	ADV
ejpam-5241	672	2	dg⋄h(x	dg⋄h(x	PROPN
ejpam-5241	672	3	,	,	PUNCT
ejpam-5241	672	4	w	w	PROPN
ejpam-5241	672	5	)	)	PUNCT
ejpam-5241	672	6	=	=	SYM
ejpam-5241	673	1	2	2	X
ejpam-5241	673	2	.	.	NOUN
ejpam-5241	673	3	same	same	ADJ
ejpam-5241	673	4	goes	go	VERB
ejpam-5241	673	5	for	for	ADP
ejpam-5241	673	6	the	the	DET
ejpam-5241	673	7	case	case	NOUN
ejpam-5241	673	8	where	where	SCONJ
ejpam-5241	673	9	vz	vz	PROPN
ejpam-5241	673	10	∈	∈	PROPN
ejpam-5241	673	11	e(g	e(g	PROPN
ejpam-5241	673	12	)	)	PUNCT
ejpam-5241	673	13	.	.	PUNCT
ejpam-5241	674	1	therefore	therefore	ADV
ejpam-5241	674	2	,	,	PUNCT
ejpam-5241	674	3	s	s	VERB
ejpam-5241	674	4	is	be	AUX
ejpam-5241	674	5	a	a	DET
ejpam-5241	674	6	hop	hop	NOUN
ejpam-5241	674	7	dominating	dominating	NOUN
ejpam-5241	674	8	set	set	NOUN
ejpam-5241	674	9	of	of	ADP
ejpam-5241	674	10	g	g	PROPN
ejpam-5241	674	11	⋄h	⋄h	PROPN
ejpam-5241	674	12	.	.	PUNCT
ejpam-5241	675	1	corollary	corollary	NOUN
ejpam-5241	675	2	5	5	NUM
ejpam-5241	675	3	.	.	PUNCT
ejpam-5241	676	1	let	let	VERB
ejpam-5241	676	2	g	g	NOUN
ejpam-5241	676	3	and	and	CCONJ
ejpam-5241	676	4	h	h	NOUN
ejpam-5241	676	5	be	be	AUX
ejpam-5241	676	6	connected	connect	VERB
ejpam-5241	676	7	graphs	graph	NOUN
ejpam-5241	676	8	where	where	SCONJ
ejpam-5241	676	9	g	g	PROPN
ejpam-5241	676	10	is	be	AUX
ejpam-5241	676	11	of	of	ADP
ejpam-5241	676	12	order	order	NOUN
ejpam-5241	676	13	n	n	PRON
ejpam-5241	676	14	≥	≥	NOUN
ejpam-5241	676	15	3	3	NUM
ejpam-5241	676	16	and	and	CCONJ
ejpam-5241	676	17	h	h	NOUN
ejpam-5241	676	18	is	be	AUX
ejpam-5241	676	19	not	not	PART
ejpam-5241	676	20	complete	complete	ADJ
ejpam-5241	676	21	.	.	PUNCT
ejpam-5241	677	1	then	then	ADV
ejpam-5241	677	2	γhcg(g	γhcg(g	VERB
ejpam-5241	677	3	⋄h	⋄h	PROPN
ejpam-5241	677	4	)	)	PUNCT
ejpam-5241	677	5	=	=	SYM
ejpam-5241	677	6	n	n	X
ejpam-5241	677	7	·	·	PUNCT
ejpam-5241	677	8	ρc2(h	ρc2(h	NUM
ejpam-5241	677	9	)	)	PUNCT
ejpam-5241	677	10	+	+	PUNCT
ejpam-5241	678	1	|τ(g)|	|τ(g)|	PROPN
ejpam-5241	678	2	.	.	PUNCT
ejpam-5241	679	1	(	(	PUNCT
ejpam-5241	679	2	10	10	NUM
ejpam-5241	679	3	)	)	PUNCT
ejpam-5241	679	4	3	3	NUM
ejpam-5241	679	5	.	.	X
ejpam-5241	679	6	conclusion	conclusion	NOUN
ejpam-5241	679	7	the	the	DET
ejpam-5241	679	8	concept	concept	NOUN
ejpam-5241	679	9	of	of	ADP
ejpam-5241	679	10	closed	closed	ADJ
ejpam-5241	679	11	geodetic	geodetic	ADJ
ejpam-5241	679	12	hop	hop	NOUN
ejpam-5241	679	13	domination	domination	NOUN
ejpam-5241	679	14	in	in	ADP
ejpam-5241	679	15	graphs	graph	NOUN
ejpam-5241	679	16	has	have	AUX
ejpam-5241	679	17	been	be	AUX
ejpam-5241	679	18	introduced	introduce	VERB
ejpam-5241	679	19	and	and	CCONJ
ejpam-5241	679	20	initially	initially	ADV
ejpam-5241	679	21	investigated	investigate	VERB
ejpam-5241	679	22	in	in	ADP
ejpam-5241	679	23	this	this	DET
ejpam-5241	679	24	study	study	NOUN
ejpam-5241	679	25	.	.	PUNCT
ejpam-5241	680	1	as	as	SCONJ
ejpam-5241	680	2	shown	show	VERB
ejpam-5241	680	3	,	,	PUNCT
ejpam-5241	680	4	not	not	PART
ejpam-5241	680	5	all	all	DET
ejpam-5241	680	6	graphs	graph	NOUN
ejpam-5241	680	7	admit	admit	VERB
ejpam-5241	680	8	this	this	DET
ejpam-5241	680	9	concept	concept	NOUN
ejpam-5241	680	10	.	.	PUNCT
ejpam-5241	681	1	some	some	DET
ejpam-5241	681	2	conditions	condition	NOUN
ejpam-5241	681	3	under	under	ADP
ejpam-5241	681	4	which	which	PRON
ejpam-5241	681	5	a	a	DET
ejpam-5241	681	6	graph	graph	NOUN
ejpam-5241	681	7	admits	admit	VERB
ejpam-5241	681	8	a	a	DET
ejpam-5241	681	9	closed	closed	ADJ
ejpam-5241	681	10	geodetic	geodetic	ADJ
ejpam-5241	681	11	hop	hop	NOUN
ejpam-5241	681	12	dominating	dominating	NOUN
ejpam-5241	681	13	set	set	NOUN
ejpam-5241	681	14	are	be	AUX
ejpam-5241	681	15	provided	provide	VERB
ejpam-5241	681	16	.	.	PUNCT
ejpam-5241	682	1	realizations	realization	NOUN
ejpam-5241	682	2	results	result	NOUN
ejpam-5241	682	3	involving	involve	VERB
ejpam-5241	682	4	closed	close	VERB
ejpam-5241	682	5	geodetic	geodetic	ADJ
ejpam-5241	682	6	number	number	NOUN
ejpam-5241	682	7	,	,	PUNCT
ejpam-5241	682	8	geodetic	geodetic	ADJ
ejpam-5241	682	9	hop	hop	NOUN
ejpam-5241	682	10	domination	domination	NOUN
ejpam-5241	682	11	number	number	NOUN
ejpam-5241	682	12	and	and	CCONJ
ejpam-5241	682	13	closed	close	VERB
ejpam-5241	682	14	geodetic	geodetic	ADJ
ejpam-5241	682	15	hop	hop	NOUN
ejpam-5241	682	16	domination	domination	NOUN
ejpam-5241	682	17	number	number	NOUN
ejpam-5241	682	18	are	be	AUX
ejpam-5241	682	19	also	also	ADV
ejpam-5241	682	20	provided	provide	VERB
ejpam-5241	682	21	.	.	PUNCT
ejpam-5241	683	1	the	the	DET
ejpam-5241	683	2	closed	closed	ADJ
ejpam-5241	683	3	geodetic	geodetic	ADJ
ejpam-5241	683	4	hop	hop	NOUN
ejpam-5241	683	5	dominating	dominating	NOUN
ejpam-5241	683	6	sets	set	NOUN
ejpam-5241	683	7	of	of	ADP
ejpam-5241	683	8	the	the	DET
ejpam-5241	683	9	join	join	NOUN
ejpam-5241	683	10	corona	corona	PROPN
ejpam-5241	683	11	,	,	PUNCT
ejpam-5241	683	12	and	and	CCONJ
ejpam-5241	683	13	edge	edge	NOUN
ejpam-5241	683	14	corona	corona	NOUN
ejpam-5241	683	15	of	of	ADP
ejpam-5241	683	16	two	two	NUM
ejpam-5241	683	17	graphs	graph	NOUN
ejpam-5241	683	18	have	have	AUX
ejpam-5241	683	19	been	be	AUX
ejpam-5241	683	20	obtained	obtain	VERB
ejpam-5241	683	21	.	.	PUNCT
ejpam-5241	684	1	these	these	DET
ejpam-5241	684	2	characterizations	characterization	NOUN
ejpam-5241	684	3	have	have	AUX
ejpam-5241	684	4	been	be	AUX
ejpam-5241	684	5	used	use	VERB
ejpam-5241	684	6	to	to	PART
ejpam-5241	684	7	obtain	obtain	VERB
ejpam-5241	684	8	bounds	bound	NOUN
ejpam-5241	684	9	or	or	CCONJ
ejpam-5241	684	10	exact	exact	ADJ
ejpam-5241	684	11	values	value	NOUN
ejpam-5241	684	12	of	of	ADP
ejpam-5241	684	13	the	the	DET
ejpam-5241	684	14	closed	closed	ADJ
ejpam-5241	684	15	references	reference	NOUN
ejpam-5241	684	16	1635	1635	NUM
ejpam-5241	684	17	geodetic	geodetic	ADJ
ejpam-5241	684	18	hop	hop	NOUN
ejpam-5241	684	19	domination	domination	NOUN
ejpam-5241	684	20	number	number	NOUN
ejpam-5241	684	21	of	of	ADP
ejpam-5241	684	22	each	each	PRON
ejpam-5241	684	23	of	of	ADP
ejpam-5241	684	24	these	these	DET
ejpam-5241	684	25	graphs	graph	NOUN
ejpam-5241	684	26	.	.	PUNCT
ejpam-5241	685	1	exploring	explore	VERB
ejpam-5241	685	2	necessary	necessary	ADJ
ejpam-5241	685	3	and	and	CCONJ
ejpam-5241	685	4	sufficient	sufficient	ADJ
ejpam-5241	685	5	conditions	condition	NOUN
ejpam-5241	685	6	for	for	ADP
ejpam-5241	685	7	a	a	DET
ejpam-5241	685	8	graph	graph	NOUN
ejpam-5241	685	9	to	to	PART
ejpam-5241	685	10	admit	admit	VERB
ejpam-5241	685	11	closed	closed	ADJ
ejpam-5241	685	12	geodetic	geodetic	ADJ
ejpam-5241	685	13	hop	hop	NOUN
ejpam-5241	685	14	dominating	dominating	NOUN
ejpam-5241	685	15	set	set	NOUN
ejpam-5241	685	16	may	may	AUX
ejpam-5241	685	17	be	be	AUX
ejpam-5241	685	18	interesting	interesting	ADJ
ejpam-5241	685	19	and	and	CCONJ
ejpam-5241	685	20	worthwhile	worthwhile	ADJ
ejpam-5241	685	21	to	to	PART
ejpam-5241	685	22	possibly	possibly	ADV
ejpam-5241	685	23	provide	provide	VERB
ejpam-5241	685	24	insightful	insightful	ADJ
ejpam-5241	685	25	results	result	NOUN
ejpam-5241	685	26	.	.	PUNCT
ejpam-5241	686	1	acknowledgements	acknowledgement	NOUN
ejpam-5241	686	2	the	the	DET
ejpam-5241	686	3	authors	author	NOUN
ejpam-5241	686	4	would	would	AUX
ejpam-5241	686	5	like	like	VERB
ejpam-5241	686	6	to	to	PART
ejpam-5241	686	7	thank	thank	VERB
ejpam-5241	686	8	the	the	DET
ejpam-5241	686	9	department	department	NOUN
ejpam-5241	686	10	of	of	ADP
ejpam-5241	686	11	science	science	NOUN
ejpam-5241	686	12	and	and	CCONJ
ejpam-5241	686	13	technology	technology	NOUN
ejpam-5241	686	14	accelerated	accelerate	VERB
ejpam-5241	686	15	science	science	NOUN
ejpam-5241	686	16	and	and	CCONJ
ejpam-5241	686	17	technology	technology	NOUN
ejpam-5241	686	18	human	human	ADJ
ejpam-5241	686	19	resource	resource	NOUN
ejpam-5241	686	20	development	development	NOUN
ejpam-5241	686	21	program	program	NOUN
ejpam-5241	686	22	(	(	PUNCT
ejpam-5241	686	23	dost	dost	NOUN
ejpam-5241	686	24	-	-	PUNCT
ejpam-5241	686	25	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-5241	686	26	,	,	PUNCT
ejpam-5241	686	27	and	and	CCONJ
ejpam-5241	686	28	msu	msu	PROPN
ejpam-5241	686	29	-	-	PUNCT
ejpam-5241	686	30	iligan	iligan	PROPN
ejpam-5241	686	31	institute	institute	PROPN
ejpam-5241	686	32	of	of	ADP
ejpam-5241	686	33	technology	technology	NOUN
ejpam-5241	686	34	for	for	ADP
ejpam-5241	686	35	funding	fund	VERB
ejpam-5241	686	36	this	this	DET
ejpam-5241	686	37	research	research	NOUN
ejpam-5241	686	38	.	.	PUNCT
ejpam-5241	687	1	references	reference	NOUN
ejpam-5241	687	2	[	[	X
ejpam-5241	687	3	1	1	NUM
ejpam-5241	687	4	]	]	X
ejpam-5241	687	5	i.	i.	NOUN
ejpam-5241	687	6	aniversario	aniversario	PROPN
ejpam-5241	687	7	,	,	PUNCT
ejpam-5241	687	8	f.	f.	PROPN
ejpam-5241	687	9	jamil	jamil	PROPN
ejpam-5241	687	10	,	,	PUNCT
ejpam-5241	687	11	and	and	CCONJ
ejpam-5241	687	12	s.	s.	PROPN
ejpam-5241	687	13	canoy	canoy	PROPN
ejpam-5241	687	14	jr	jr	PROPN
ejpam-5241	687	15	.	.	PUNCT
ejpam-5241	688	1	the	the	DET
ejpam-5241	688	2	closed	closed	ADJ
ejpam-5241	688	3	geodetic	geodetic	ADJ
ejpam-5241	688	4	numbers	number	NOUN
ejpam-5241	688	5	of	of	ADP
ejpam-5241	688	6	graphs	graph	NOUN
ejpam-5241	688	7	.	.	PUNCT
ejpam-5241	689	1	utilitas	utilitas	PROPN
ejpam-5241	689	2	mathematica	mathematica	PROPN
ejpam-5241	689	3	,	,	PUNCT
ejpam-5241	689	4	74:3–18	74:3–18	NUM
ejpam-5241	689	5	,	,	PUNCT
ejpam-5241	689	6	2007	2007	NUM
ejpam-5241	689	7	.	.	PUNCT
ejpam-5241	690	1	[	[	X
ejpam-5241	690	2	2	2	NUM
ejpam-5241	690	3	]	]	PUNCT
ejpam-5241	690	4	i.	i.	NOUN
ejpam-5241	690	5	aniversario	aniversario	PROPN
ejpam-5241	690	6	,	,	PUNCT
ejpam-5241	690	7	f.	f.	PROPN
ejpam-5241	690	8	jamil	jamil	PROPN
ejpam-5241	690	9	,	,	PUNCT
ejpam-5241	690	10	and	and	CCONJ
ejpam-5241	690	11	s.	s.	PROPN
ejpam-5241	690	12	canoy	canoy	PROPN
ejpam-5241	690	13	jr	jr	PROPN
ejpam-5241	690	14	.	.	PUNCT
ejpam-5241	691	1	the	the	DET
ejpam-5241	691	2	closed	closed	ADJ
ejpam-5241	691	3	geodetic	geodetic	ADJ
ejpam-5241	691	4	numbers	number	NOUN
ejpam-5241	691	5	of	of	ADP
ejpam-5241	691	6	the	the	DET
ejpam-5241	691	7	corona	corona	NOUN
ejpam-5241	691	8	and	and	CCONJ
ejpam-5241	691	9	composition	composition	NOUN
ejpam-5241	691	10	of	of	ADP
ejpam-5241	691	11	graphs	graph	NOUN
ejpam-5241	691	12	.	.	PUNCT
ejpam-5241	692	1	utilitas	utilitas	PROPN
ejpam-5241	692	2	mathematica	mathematica	PROPN
ejpam-5241	692	3	,	,	PUNCT
ejpam-5241	692	4	82	82	NUM
ejpam-5241	692	5	,	,	PUNCT
ejpam-5241	692	6	2010	2010	NUM
ejpam-5241	692	7	.	.	PUNCT
ejpam-5241	693	1	[	[	X
ejpam-5241	693	2	3	3	X
ejpam-5241	693	3	]	]	X
ejpam-5241	693	4	d.	d.	NOUN
ejpam-5241	693	5	anusha	anusha	PROPN
ejpam-5241	693	6	and	and	CCONJ
ejpam-5241	693	7	s.	s.	PROPN
ejpam-5241	693	8	joseph	joseph	PROPN
ejpam-5241	693	9	robin	robin	PROPN
ejpam-5241	693	10	.	.	PUNCT
ejpam-5241	694	1	geodetic	geodetic	ADJ
ejpam-5241	694	2	hop	hop	NOUN
ejpam-5241	694	3	domination	domination	NOUN
ejpam-5241	694	4	in	in	ADP
ejpam-5241	694	5	join	join	NOUN
ejpam-5241	694	6	and	and	CCONJ
ejpam-5241	694	7	corona	corona	NOUN
ejpam-5241	694	8	of	of	ADP
ejpam-5241	694	9	graphs	graph	NOUN
ejpam-5241	694	10	.	.	PUNCT
ejpam-5241	695	1	journal	journal	NOUN
ejpam-5241	695	2	of	of	ADP
ejpam-5241	695	3	combinatorial	combinatorial	ADJ
ejpam-5241	695	4	mathematics	mathematic	NOUN
ejpam-5241	695	5	and	and	CCONJ
ejpam-5241	695	6	combinatorial	combinatorial	ADJ
ejpam-5241	695	7	computing	computing	NOUN
ejpam-5241	695	8	,	,	PUNCT
ejpam-5241	695	9	21:1117–1127	21:1117–1127	NUM
ejpam-5241	695	10	,	,	PUNCT
ejpam-5241	695	11	2011	2011	NUM
ejpam-5241	695	12	.	.	PUNCT
ejpam-5241	696	1	[	[	X
ejpam-5241	696	2	4	4	X
ejpam-5241	696	3	]	]	PUNCT
ejpam-5241	696	4	s.	s.	PROPN
ejpam-5241	696	5	ayyaswamy	ayyaswamy	PROPN
ejpam-5241	696	6	,	,	PUNCT
ejpam-5241	696	7	b.	b.	PROPN
ejpam-5241	696	8	krishnakumari	krishnakumari	PROPN
ejpam-5241	696	9	,	,	PUNCT
ejpam-5241	696	10	c.	c.	PROPN
ejpam-5241	696	11	natarajan	natarajan	PROPN
ejpam-5241	696	12	,	,	PUNCT
ejpam-5241	696	13	and	and	CCONJ
ejpam-5241	696	14	y.	y.	PROPN
ejpam-5241	696	15	venkatakrishman	venkatakrishman	NOUN
ejpam-5241	696	16	.	.	PUNCT
ejpam-5241	697	1	bounds	bound	NOUN
ejpam-5241	697	2	on	on	ADP
ejpam-5241	697	3	the	the	DET
ejpam-5241	697	4	hop	hop	NOUN
ejpam-5241	697	5	domination	domination	NOUN
ejpam-5241	697	6	number	number	NOUN
ejpam-5241	697	7	of	of	ADP
ejpam-5241	697	8	a	a	DET
ejpam-5241	697	9	tree	tree	NOUN
ejpam-5241	697	10	.	.	PUNCT
ejpam-5241	698	1	proc	proc	NOUN
ejpam-5241	698	2	.	.	PUNCT
ejpam-5241	699	1	math	math	NOUN
ejpam-5241	699	2	.	.	PUNCT
ejpam-5241	700	1	sci	sci	PROPN
ejpam-5241	700	2	.	.	PROPN
ejpam-5241	700	3	,	,	PUNCT
ejpam-5241	700	4	125:449–455	125:449–455	NUM
ejpam-5241	700	5	,	,	PUNCT
ejpam-5241	700	6	2015	2015	NUM
ejpam-5241	700	7	.	.	PUNCT
ejpam-5241	701	1	[	[	X
ejpam-5241	701	2	5	5	NUM
ejpam-5241	701	3	]	]	X
ejpam-5241	701	4	m.a	m.a	PROPN
ejpam-5241	701	5	.	.	PROPN
ejpam-5241	701	6	bonsocan	bonsocan	PROPN
ejpam-5241	701	7	and	and	CCONJ
ejpam-5241	701	8	f.	f.	PROPN
ejpam-5241	701	9	jamil	jamil	PROPN
ejpam-5241	701	10	.	.	PUNCT
ejpam-5241	702	1	transversal	transversal	PROPN
ejpam-5241	702	2	hop	hop	PROPN
ejpam-5241	702	3	domination	domination	NOUN
ejpam-5241	702	4	in	in	ADP
ejpam-5241	702	5	graphs	graph	NOUN
ejpam-5241	702	6	.	.	PUNCT
ejpam-5241	703	1	european	european	ADJ
ejpam-5241	703	2	journal	journal	PROPN
ejpam-5241	703	3	of	of	ADP
ejpam-5241	703	4	pure	pure	ADJ
ejpam-5241	703	5	and	and	CCONJ
ejpam-5241	703	6	applied	applied	ADJ
ejpam-5241	703	7	mathematics	mathematic	NOUN
ejpam-5241	703	8	,	,	PUNCT
ejpam-5241	703	9	16(1):192–206	16(1):192–206	NUM
ejpam-5241	703	10	,	,	PUNCT
ejpam-5241	703	11	2023	2023	NUM
ejpam-5241	703	12	.	.	PUNCT
ejpam-5241	704	1	[	[	X
ejpam-5241	704	2	6	6	NUM
ejpam-5241	704	3	]	]	X
ejpam-5241	704	4	f.	f.	PROPN
ejpam-5241	704	5	buckley	buckley	PROPN
ejpam-5241	704	6	and	and	CCONJ
ejpam-5241	704	7	f.	f.	PROPN
ejpam-5241	704	8	harary	harary	PROPN
ejpam-5241	704	9	.	.	PUNCT
ejpam-5241	705	1	distance	distance	NOUN
ejpam-5241	705	2	in	in	ADP
ejpam-5241	705	3	graphs	graph	NOUN
ejpam-5241	705	4	.	.	PUNCT
ejpam-5241	706	1	addison	addison	PROPN
ejpam-5241	706	2	-	-	PUNCT
ejpam-5241	706	3	wesley	wesley	PROPN
ejpam-5241	706	4	publishing	publishing	PROPN
ejpam-5241	706	5	company	company	PROPN
ejpam-5241	706	6	,	,	PUNCT
ejpam-5241	706	7	inc	inc	PROPN
ejpam-5241	706	8	.	.	PROPN
ejpam-5241	706	9	,	,	PUNCT
ejpam-5241	706	10	redwood	redwood	NOUN
ejpam-5241	706	11	city	city	NOUN
ejpam-5241	706	12	,	,	PUNCT
ejpam-5241	706	13	ca	ca	NOUN
ejpam-5241	706	14	,	,	PUNCT
ejpam-5241	706	15	1990	1990	NUM
ejpam-5241	706	16	.	.	PUNCT
ejpam-5241	707	1	[	[	X
ejpam-5241	707	2	7	7	X
ejpam-5241	707	3	]	]	X
ejpam-5241	707	4	g.	g.	PROPN
ejpam-5241	707	5	cagaanan	cagaanan	PROPN
ejpam-5241	707	6	.	.	PUNCT
ejpam-5241	708	1	on	on	ADP
ejpam-5241	708	2	geodesic	geodesic	ADJ
ejpam-5241	708	3	convexity	convexity	NOUN
ejpam-5241	708	4	in	in	ADP
ejpam-5241	708	5	graphs	graph	NOUN
ejpam-5241	708	6	.	.	PUNCT
ejpam-5241	709	1	phd	phd	NOUN
ejpam-5241	709	2	thesis	thesis	NOUN
ejpam-5241	709	3	,	,	PUNCT
ejpam-5241	709	4	msu	msu	PROPN
ejpam-5241	709	5	-	-	PUNCT
ejpam-5241	709	6	iligan	iligan	PROPN
ejpam-5241	709	7	institute	institute	PROPN
ejpam-5241	709	8	of	of	ADP
ejpam-5241	709	9	technology	technology	PROPN
ejpam-5241	709	10	,	,	PUNCT
ejpam-5241	709	11	2004	2004	NUM
ejpam-5241	709	12	.	.	PUNCT
ejpam-5241	710	1	[	[	X
ejpam-5241	710	2	8	8	NUM
ejpam-5241	710	3	]	]	X
ejpam-5241	710	4	g.	g.	PROPN
ejpam-5241	710	5	chartrand	chartrand	PROPN
ejpam-5241	710	6	,	,	PUNCT
ejpam-5241	710	7	f.	f.	PROPN
ejpam-5241	710	8	harary	harary	PROPN
ejpam-5241	710	9	,	,	PUNCT
ejpam-5241	710	10	and	and	CCONJ
ejpam-5241	710	11	p.	p.	PROPN
ejpam-5241	710	12	zhang	zhang	PROPN
ejpam-5241	710	13	.	.	PUNCT
ejpam-5241	711	1	geodetic	geodetic	ADJ
ejpam-5241	711	2	sets	set	NOUN
ejpam-5241	711	3	in	in	ADP
ejpam-5241	711	4	graphs	graph	NOUN
ejpam-5241	711	5	.	.	PUNCT
ejpam-5241	712	1	discussiones	discussione	NOUN
ejpam-5241	712	2	mathematicae	mathematicae	PROPN
ejpam-5241	712	3	graph	graph	NOUN
ejpam-5241	712	4	theory	theory	NOUN
ejpam-5241	712	5	,	,	PUNCT
ejpam-5241	712	6	20:129–138	20:129–138	PROPN
ejpam-5241	712	7	,	,	PUNCT
ejpam-5241	712	8	2000	2000	NUM
ejpam-5241	712	9	.	.	PUNCT
ejpam-5241	713	1	[	[	X
ejpam-5241	713	2	9	9	NUM
ejpam-5241	713	3	]	]	PUNCT
ejpam-5241	713	4	f.	f.	PROPN
ejpam-5241	713	5	harary	harary	PROPN
ejpam-5241	713	6	.	.	PUNCT
ejpam-5241	714	1	convexity	convexity	NOUN
ejpam-5241	714	2	in	in	ADP
ejpam-5241	714	3	graphs	graph	NOUN
ejpam-5241	714	4	:	:	PUNCT
ejpam-5241	714	5	achievement	achievement	NOUN
ejpam-5241	714	6	and	and	CCONJ
ejpam-5241	714	7	avoidance	avoidance	NOUN
ejpam-5241	714	8	games	game	NOUN
ejpam-5241	714	9	.	.	PUNCT
ejpam-5241	715	1	ann	ann	PROPN
ejpam-5241	715	2	.	.	PROPN
ejpam-5241	716	1	discrete	discrete	ADJ
ejpam-5241	716	2	math	math	NOUN
ejpam-5241	716	3	,	,	PUNCT
ejpam-5241	716	4	20:323	20:323	NUM
ejpam-5241	716	5	,	,	PUNCT
ejpam-5241	716	6	1983	1983	NUM
ejpam-5241	716	7	.	.	PUNCT
ejpam-5241	717	1	[	[	X
ejpam-5241	717	2	10	10	NUM
ejpam-5241	717	3	]	]	X
ejpam-5241	717	4	f.	f.	PROPN
ejpam-5241	717	5	harary	harary	PROPN
ejpam-5241	717	6	,	,	PUNCT
ejpam-5241	717	7	e.	e.	PROPN
ejpam-5241	717	8	loukakis	loukakis	PROPN
ejpam-5241	717	9	,	,	PUNCT
ejpam-5241	717	10	and	and	CCONJ
ejpam-5241	717	11	c.	c.	PROPN
ejpam-5241	717	12	tsouros	tsouros	PROPN
ejpam-5241	717	13	.	.	PUNCT
ejpam-5241	718	1	the	the	DET
ejpam-5241	718	2	geodetic	geodetic	ADJ
ejpam-5241	718	3	number	number	NOUN
ejpam-5241	718	4	of	of	ADP
ejpam-5241	718	5	a	a	DET
ejpam-5241	718	6	graph	graph	NOUN
ejpam-5241	718	7	.	.	PUNCT
ejpam-5241	719	1	mathl	mathl	NOUN
ejpam-5241	719	2	.	.	PUNCT
ejpam-5241	720	1	comput	comput	NOUN
ejpam-5241	720	2	.	.	PUNCT
ejpam-5241	721	1	modelling	modelling	NOUN
ejpam-5241	721	2	,	,	PUNCT
ejpam-5241	721	3	17(11):89–95	17(11):89–95	NUM
ejpam-5241	721	4	,	,	PUNCT
ejpam-5241	721	5	1993	1993	NUM
ejpam-5241	721	6	.	.	PUNCT
ejpam-5241	722	1	[	[	X
ejpam-5241	722	2	11	11	NUM
ejpam-5241	722	3	]	]	X
ejpam-5241	722	4	f.	f.	PROPN
ejpam-5241	722	5	jamil	jamil	PROPN
ejpam-5241	722	6	and	and	CCONJ
ejpam-5241	722	7	i	i	PROPN
ejpam-5241	722	8	aniversario	aniversario	PROPN
ejpam-5241	722	9	s.	s.	PROPN
ejpam-5241	722	10	canoy	canoy	PROPN
ejpam-5241	722	11	jr	jr	PROPN
ejpam-5241	722	12	.	.	PROPN
ejpam-5241	722	13	on	on	ADP
ejpam-5241	722	14	closed	closed	ADJ
ejpam-5241	722	15	and	and	CCONJ
ejpam-5241	722	16	upper	upper	ADJ
ejpam-5241	722	17	closed	closed	ADJ
ejpam-5241	722	18	geodetic	geodetic	ADJ
ejpam-5241	722	19	numbers	number	NOUN
ejpam-5241	722	20	of	of	ADP
ejpam-5241	722	21	graphs	graph	NOUN
ejpam-5241	722	22	.	.	PUNCT
ejpam-5241	723	1	ars	ar	NOUN
ejpam-5241	723	2	combinatoria	combinatoria	NOUN
ejpam-5241	723	3	,	,	PUNCT
ejpam-5241	723	4	84:191–203	84:191–203	NUM
ejpam-5241	723	5	,	,	PUNCT
ejpam-5241	723	6	2007	2007	NUM
ejpam-5241	723	7	.	.	PUNCT
ejpam-5241	724	1	references	reference	NOUN
ejpam-5241	724	2	1636	1636	NUM
ejpam-5241	724	3	[	[	X
ejpam-5241	724	4	12	12	NUM
ejpam-5241	724	5	]	]	X
ejpam-5241	724	6	s.	s.	PROPN
ejpam-5241	724	7	canoy	canoy	PROPN
ejpam-5241	724	8	jr	jr	PROPN
ejpam-5241	724	9	.	.	PROPN
ejpam-5241	724	10	,	,	PUNCT
ejpam-5241	724	11	r.	r.	PROPN
ejpam-5241	724	12	mollejon	mollejon	NOUN
ejpam-5241	724	13	,	,	PUNCT
ejpam-5241	724	14	and	and	CCONJ
ejpam-5241	724	15	j.g	j.g	PROPN
ejpam-5241	724	16	.	.	PROPN
ejpam-5241	724	17	canoya	canoya	PROPN
ejpam-5241	724	18	.	.	PUNCT
ejpam-5241	725	1	hop	hop	PROPN
ejpam-5241	725	2	dominating	dominating	NOUN
ejpam-5241	725	3	sets	set	NOUN
ejpam-5241	725	4	in	in	ADP
ejpam-5241	725	5	graphs	graph	NOUN
ejpam-5241	725	6	under	under	ADP
ejpam-5241	725	7	binary	binary	ADJ
ejpam-5241	725	8	operations	operation	NOUN
ejpam-5241	725	9	.	.	PUNCT
ejpam-5241	726	1	european	european	ADJ
ejpam-5241	726	2	journal	journal	PROPN
ejpam-5241	726	3	of	of	ADP
ejpam-5241	726	4	pure	pure	ADJ
ejpam-5241	726	5	and	and	CCONJ
ejpam-5241	726	6	applied	applied	ADJ
ejpam-5241	726	7	mathematics	mathematic	NOUN
ejpam-5241	726	8	,	,	PUNCT
ejpam-5241	726	9	12(4):1455	12(4):1455	NUM
ejpam-5241	726	10	–	–	PUNCT
ejpam-5241	726	11	1463	1463	NUM
ejpam-5241	726	12	,	,	PUNCT
ejpam-5241	726	13	2019	2019	NUM
ejpam-5241	726	14	.	.	PUNCT
ejpam-5241	727	1	[	[	X
ejpam-5241	727	2	13	13	NUM
ejpam-5241	727	3	]	]	PUNCT
ejpam-5241	727	4	s.	s.	PROPN
ejpam-5241	727	5	canoy	canoy	PROPN
ejpam-5241	727	6	jr	jr	PROPN
ejpam-5241	727	7	.	.	PROPN
ejpam-5241	727	8	and	and	CCONJ
ejpam-5241	727	9	g.	g.	PROPN
ejpam-5241	727	10	salasalan	salasalan	NOUN
ejpam-5241	727	11	.	.	PUNCT
ejpam-5241	728	1	locating	locate	VERB
ejpam-5241	728	2	-	-	PUNCT
ejpam-5241	728	3	hop	hop	NOUN
ejpam-5241	728	4	domination	domination	NOUN
ejpam-5241	728	5	in	in	ADP
ejpam-5241	728	6	graphs	graph	NOUN
ejpam-5241	728	7	.	.	PUNCT
ejpam-5241	729	1	kyungpook	kyungpook	PROPN
ejpam-5241	729	2	mathematical	mathematical	PROPN
ejpam-5241	729	3	journal	journal	PROPN
ejpam-5241	729	4	,	,	PUNCT
ejpam-5241	729	5	62:193–204	62:193–204	PROPN
ejpam-5241	729	6	,	,	PUNCT
ejpam-5241	729	7	2022	2022	NUM
ejpam-5241	729	8	.	.	PUNCT
ejpam-5241	730	1	[	[	X
ejpam-5241	730	2	14	14	NUM
ejpam-5241	730	3	]	]	X
ejpam-5241	730	4	c.	c.	PROPN
ejpam-5241	730	5	natarajan	natarajan	PROPN
ejpam-5241	730	6	and	and	CCONJ
ejpam-5241	730	7	s.	s.	PROPN
ejpam-5241	730	8	ayyaswamy	ayyaswamy	PROPN
ejpam-5241	730	9	.	.	PUNCT
ejpam-5241	731	1	hop	hop	PROPN
ejpam-5241	731	2	domination	domination	NOUN
ejpam-5241	731	3	in	in	ADP
ejpam-5241	731	4	graphs	graphs	PROPN
ejpam-5241	731	5	ii	ii	PROPN
ejpam-5241	731	6	.	.	PUNCT
ejpam-5241	731	7	versita	versita	PROPN
ejpam-5241	731	8	,	,	PUNCT
ejpam-5241	731	9	23:187–199	23:187–199	PROPN
ejpam-5241	731	10	,	,	PUNCT
ejpam-5241	731	11	2015	2015	NUM
ejpam-5241	731	12	.	.	PUNCT
ejpam-5241	732	1	[	[	X
ejpam-5241	732	2	15	15	NUM
ejpam-5241	732	3	]	]	X
ejpam-5241	732	4	y.	y.	PROPN
ejpam-5241	732	5	pabilona	pabilona	PROPN
ejpam-5241	732	6	and	and	CCONJ
ejpam-5241	732	7	h.	h.	PROPN
ejpam-5241	732	8	rara	rara	PROPN
ejpam-5241	732	9	.	.	PUNCT
ejpam-5241	733	1	connected	connect	VERB
ejpam-5241	733	2	hop	hop	NOUN
ejpam-5241	733	3	domination	domination	NOUN
ejpam-5241	733	4	in	in	ADP
ejpam-5241	733	5	graphs	graph	NOUN
ejpam-5241	733	6	under	under	ADP
ejpam-5241	733	7	some	some	DET
ejpam-5241	733	8	binary	binary	ADJ
ejpam-5241	733	9	operations	operation	NOUN
ejpam-5241	733	10	.	.	PUNCT
ejpam-5241	734	1	asian	asian	ADJ
ejpam-5241	734	2	-	-	PUNCT
ejpam-5241	734	3	european	european	ADJ
ejpam-5241	734	4	journal	journal	NOUN
ejpam-5241	734	5	of	of	ADP
ejpam-5241	734	6	mathematics	mathematic	NOUN
ejpam-5241	734	7	,	,	PUNCT
ejpam-5241	734	8	11	11	NUM
ejpam-5241	734	9	,	,	PUNCT
ejpam-5241	734	10	2018	2018	NUM
ejpam-5241	734	11	.	.	PUNCT
ejpam-5241	735	1	[	[	X
ejpam-5241	735	2	16	16	NUM
ejpam-5241	735	3	]	]	X
ejpam-5241	735	4	g.	g.	PROPN
ejpam-5241	735	5	salasalan	salasalan	NOUN
ejpam-5241	735	6	and	and	CCONJ
ejpam-5241	735	7	s.	s.	PROPN
ejpam-5241	735	8	canoy	canoy	PROPN
ejpam-5241	735	9	jr	jr	PROPN
ejpam-5241	735	10	.	.	PUNCT
ejpam-5241	736	1	some	some	DET
ejpam-5241	736	2	related	relate	VERB
ejpam-5241	736	3	concepts	concept	NOUN
ejpam-5241	736	4	of	of	ADP
ejpam-5241	736	5	hop	hop	NOUN
ejpam-5241	736	6	domination	domination	NOUN
ejpam-5241	736	7	in	in	ADP
ejpam-5241	736	8	a	a	DET
ejpam-5241	736	9	graph	graph	NOUN
ejpam-5241	736	10	.	.	PUNCT
ejpam-5241	737	1	phd	phd	NOUN
ejpam-5241	737	2	thesis	thesis	NOUN
ejpam-5241	737	3	,	,	PUNCT
ejpam-5241	737	4	2021	2021	NUM
ejpam-5241	737	5	.	.	PUNCT
ejpam-5241	738	1	[	[	X
ejpam-5241	738	2	17	17	NUM
ejpam-5241	738	3	]	]	X
ejpam-5241	738	4	c.j	c.j	PROPN
ejpam-5241	738	5	.	.	PROPN
ejpam-5241	738	6	saromines	saromine	NOUN
ejpam-5241	738	7	and	and	CCONJ
ejpam-5241	738	8	s.	s.	PROPN
ejpam-5241	738	9	canoy	canoy	PROPN
ejpam-5241	738	10	jr	jr	PROPN
ejpam-5241	738	11	.	.	PUNCT
ejpam-5241	738	12	outer	outer	ADV
ejpam-5241	738	13	-	-	PUNCT
ejpam-5241	738	14	connected	connect	VERB
ejpam-5241	738	15	hop	hop	NOUN
ejpam-5241	738	16	dominating	dominating	NOUN
ejpam-5241	738	17	sets	set	NOUN
ejpam-5241	738	18	in	in	ADP
ejpam-5241	738	19	graphs	graph	NOUN
ejpam-5241	738	20	.	.	PUNCT
ejpam-5241	739	1	european	european	ADJ
ejpam-5241	739	2	journal	journal	PROPN
ejpam-5241	739	3	of	of	ADP
ejpam-5241	739	4	pure	pure	ADJ
ejpam-5241	739	5	and	and	CCONJ
ejpam-5241	739	6	applied	applied	ADJ
ejpam-5241	739	7	mathematics	mathematic	NOUN
ejpam-5241	739	8	,	,	PUNCT
ejpam-5241	739	9	15(4):1966–1981	15(4):1966–1981	NUM
ejpam-5241	739	10	,	,	PUNCT
ejpam-5241	739	11	2022	2022	NUM
ejpam-5241	739	12	.	.	PUNCT
ejpam-5241	740	1	[	[	X
ejpam-5241	740	2	18	18	NUM
ejpam-5241	740	3	]	]	X
ejpam-5241	740	4	c.j	c.j	PROPN
ejpam-5241	740	5	.	.	PROPN
ejpam-5241	740	6	saromines	saromine	NOUN
ejpam-5241	740	7	and	and	CCONJ
ejpam-5241	740	8	s.	s.	PROPN
ejpam-5241	740	9	canoy	canoy	PROPN
ejpam-5241	740	10	jr	jr	PROPN
ejpam-5241	740	11	.	.	PUNCT
ejpam-5241	741	1	another	another	DET
ejpam-5241	741	2	look	look	NOUN
ejpam-5241	741	3	at	at	ADP
ejpam-5241	741	4	geodetic	geodetic	ADJ
ejpam-5241	741	5	hop	hop	NOUN
ejpam-5241	741	6	domination	domination	NOUN
ejpam-5241	741	7	in	in	ADP
ejpam-5241	741	8	a	a	DET
ejpam-5241	741	9	graph	graph	NOUN
ejpam-5241	741	10	.	.	PUNCT
ejpam-5241	742	1	european	european	ADJ
ejpam-5241	742	2	journal	journal	PROPN
ejpam-5241	742	3	of	of	ADP
ejpam-5241	742	4	pure	pure	ADJ
ejpam-5241	742	5	and	and	CCONJ
ejpam-5241	742	6	applied	applied	ADJ
ejpam-5241	742	7	mathematics	mathematic	NOUN
ejpam-5241	742	8	,	,	PUNCT
ejpam-5241	742	9	16(3):1568–1579	16(3):1568–1579	NUM
ejpam-5241	742	10	,	,	PUNCT
ejpam-5241	742	11	2023	2023	NUM
ejpam-5241	742	12	.	.	PUNCT
ejpam-5241	743	1	[	[	X
ejpam-5241	743	2	19	19	NUM
ejpam-5241	743	3	]	]	X
ejpam-5241	743	4	c.j	c.j	PROPN
ejpam-5241	743	5	.	.	PROPN
ejpam-5241	743	6	saromines	saromine	NOUN
ejpam-5241	743	7	and	and	CCONJ
ejpam-5241	743	8	s.	s.	PROPN
ejpam-5241	743	9	canoy	canoy	PROPN
ejpam-5241	743	10	jr	jr	PROPN
ejpam-5241	743	11	.	.	PROPN
ejpam-5241	743	12	geodetic	geodetic	ADJ
ejpam-5241	743	13	hop	hop	NOUN
ejpam-5241	743	14	dominating	dominating	NOUN
ejpam-5241	743	15	sets	set	NOUN
ejpam-5241	743	16	in	in	ADP
ejpam-5241	743	17	a	a	DET
ejpam-5241	743	18	graph	graph	NOUN
ejpam-5241	743	19	.	.	PUNCT
ejpam-5241	744	1	european	european	ADJ
ejpam-5241	744	2	journal	journal	PROPN
ejpam-5241	744	3	of	of	ADP
ejpam-5241	744	4	pure	pure	ADJ
ejpam-5241	744	5	and	and	CCONJ
ejpam-5241	744	6	applied	applied	ADJ
ejpam-5241	744	7	mathematics	mathematic	NOUN
ejpam-5241	744	8	,	,	PUNCT
ejpam-5241	744	9	16(1):5–17	16(1):5–17	NUM
ejpam-5241	744	10	,	,	PUNCT
ejpam-5241	744	11	2023	2023	NUM
ejpam-5241	744	12	.	.	PUNCT