id	sid	tid	token	lemma	pos
ejpam-4810	1	1	european	european	PROPN
ejpam-4810	1	2	journal	journal	PROPN
ejpam-4810	1	3	of	of	ADP
ejpam-4810	1	4	pure	pure	ADJ
ejpam-4810	1	5	and	and	CCONJ
ejpam-4810	1	6	applied	apply	VERB
ejpam-4810	1	7	mathematics	mathematic	NOUN
ejpam-4810	1	8	vol	vol	NOUN
ejpam-4810	1	9	.	.	PUNCT
ejpam-4810	2	1	16	16	NUM
ejpam-4810	2	2	,	,	PUNCT
ejpam-4810	2	3	no	no	INTJ
ejpam-4810	2	4	.	.	NOUN
ejpam-4810	2	5	3	3	NUM
ejpam-4810	2	6	,	,	PUNCT
ejpam-4810	2	7	2023	2023	NUM
ejpam-4810	2	8	,	,	PUNCT
ejpam-4810	2	9	1568	1568	NUM
ejpam-4810	2	10	-	-	SYM
ejpam-4810	2	11	1579	1579	NUM
ejpam-4810	2	12	issn	issn	PROPN
ejpam-4810	2	13	1307	1307	NUM
ejpam-4810	2	14	-	-	SYM
ejpam-4810	2	15	5543	5543	NUM
ejpam-4810	2	16	–	–	PUNCT
ejpam-4810	2	17	ejpam.com	ejpam.com	X
ejpam-4810	2	18	published	publish	VERB
ejpam-4810	2	19	by	by	ADP
ejpam-4810	2	20	new	new	PROPN
ejpam-4810	2	21	york	york	PROPN
ejpam-4810	2	22	business	business	PROPN
ejpam-4810	2	23	global	global	PROPN
ejpam-4810	2	24	another	another	DET
ejpam-4810	2	25	look	look	NOUN
ejpam-4810	2	26	at	at	ADP
ejpam-4810	2	27	geodetic	geodetic	ADJ
ejpam-4810	2	28	hop	hop	NOUN
ejpam-4810	2	29	domination	domination	NOUN
ejpam-4810	2	30	in	in	ADP
ejpam-4810	2	31	a	a	DET
ejpam-4810	2	32	graph	graph	NOUN
ejpam-4810	2	33	chrisley	chrisley	NOUN
ejpam-4810	2	34	jade	jade	PROPN
ejpam-4810	2	35	c.	c.	PROPN
ejpam-4810	2	36	saromines1,∗	saromines1,∗	PROPN
ejpam-4810	2	37	,	,	PUNCT
ejpam-4810	2	38	sergio	sergio	PROPN
ejpam-4810	2	39	r.	r.	PROPN
ejpam-4810	2	40	canoy	canoy	PROPN
ejpam-4810	2	41	,	,	PUNCT
ejpam-4810	2	42	jr.1,2	jr.1,2	ADJ
ejpam-4810	2	43	1	1	NUM
ejpam-4810	2	44	department	department	NOUN
ejpam-4810	2	45	of	of	ADP
ejpam-4810	2	46	mathematics	mathematic	NOUN
ejpam-4810	2	47	and	and	CCONJ
ejpam-4810	2	48	statistics	statistic	NOUN
ejpam-4810	2	49	,	,	PUNCT
ejpam-4810	2	50	college	college	NOUN
ejpam-4810	2	51	of	of	ADP
ejpam-4810	2	52	science	science	NOUN
ejpam-4810	2	53	and	and	CCONJ
ejpam-4810	2	54	mathematics	mathematic	NOUN
ejpam-4810	2	55	,	,	PUNCT
ejpam-4810	2	56	msuiligan	msuiligan	PROPN
ejpam-4810	2	57	institute	institute	PROPN
ejpam-4810	2	58	of	of	ADP
ejpam-4810	2	59	technology	technology	PROPN
ejpam-4810	2	60	,	,	PUNCT
ejpam-4810	2	61	philippines	philippine	NOUN
ejpam-4810	2	62	2	2	NUM
ejpam-4810	2	63	center	center	NOUN
ejpam-4810	2	64	for	for	ADP
ejpam-4810	2	65	mathematical	mathematical	ADJ
ejpam-4810	2	66	and	and	CCONJ
ejpam-4810	2	67	theoretical	theoretical	ADJ
ejpam-4810	2	68	physical	physical	ADJ
ejpam-4810	2	69	sciences	science	NOUN
ejpam-4810	2	70	-	-	PUNCT
ejpam-4810	2	71	prism	prism	NOUN
ejpam-4810	2	72	,	,	PUNCT
ejpam-4810	2	73	msu	msu	PROPN
ejpam-4810	2	74	-	-	PUNCT
ejpam-4810	2	75	iligan	iligan	PROPN
ejpam-4810	2	76	institute	institute	PROPN
ejpam-4810	2	77	of	of	ADP
ejpam-4810	2	78	technology	technology	PROPN
ejpam-4810	2	79	,	,	PUNCT
ejpam-4810	3	1	philippines	philippine	NOUN
ejpam-4810	3	2	abstract	abstract	ADJ
ejpam-4810	3	3	.	.	PUNCT
ejpam-4810	4	1	let	let	VERB
ejpam-4810	4	2	g	g	PRON
ejpam-4810	4	3	be	be	AUX
ejpam-4810	4	4	an	an	DET
ejpam-4810	4	5	undirected	undirected	ADJ
ejpam-4810	4	6	graph	graph	NOUN
ejpam-4810	4	7	with	with	ADP
ejpam-4810	4	8	vertex	vertex	NOUN
ejpam-4810	4	9	and	and	CCONJ
ejpam-4810	4	10	edge	edge	NOUN
ejpam-4810	4	11	sets	set	NOUN
ejpam-4810	4	12	v	v	ADP
ejpam-4810	4	13	(	(	PUNCT
ejpam-4810	4	14	g	g	NOUN
ejpam-4810	4	15	)	)	PUNCT
ejpam-4810	4	16	and	and	CCONJ
ejpam-4810	4	17	e(g	e(g	PROPN
ejpam-4810	4	18	)	)	PUNCT
ejpam-4810	4	19	,	,	PUNCT
ejpam-4810	4	20	respectively	respectively	ADV
ejpam-4810	4	21	.	.	PUNCT
ejpam-4810	5	1	a	a	DET
ejpam-4810	5	2	subset	subset	NOUN
ejpam-4810	5	3	s	s	NOUN
ejpam-4810	5	4	of	of	ADP
ejpam-4810	5	5	vertices	vertex	NOUN
ejpam-4810	5	6	of	of	ADP
ejpam-4810	5	7	g	g	PROPN
ejpam-4810	5	8	is	be	AUX
ejpam-4810	5	9	a	a	DET
ejpam-4810	5	10	geodetic	geodetic	ADJ
ejpam-4810	5	11	hop	hop	NOUN
ejpam-4810	5	12	dominating	dominating	NOUN
ejpam-4810	5	13	set	set	NOUN
ejpam-4810	5	14	if	if	SCONJ
ejpam-4810	5	15	it	it	PRON
ejpam-4810	5	16	is	be	AUX
ejpam-4810	5	17	both	both	CCONJ
ejpam-4810	5	18	a	a	DET
ejpam-4810	5	19	geodetic	geodetic	ADJ
ejpam-4810	5	20	set	set	NOUN
ejpam-4810	5	21	and	and	CCONJ
ejpam-4810	5	22	a	a	DET
ejpam-4810	5	23	hop	hop	NOUN
ejpam-4810	5	24	dominating	dominating	NOUN
ejpam-4810	5	25	set	set	NOUN
ejpam-4810	5	26	.	.	PUNCT
ejpam-4810	6	1	the	the	DET
ejpam-4810	6	2	geodetic	geodetic	ADJ
ejpam-4810	6	3	hop	hop	NOUN
ejpam-4810	6	4	domination	domination	NOUN
ejpam-4810	6	5	number	number	NOUN
ejpam-4810	6	6	of	of	ADP
ejpam-4810	6	7	g	g	PROPN
ejpam-4810	6	8	is	be	AUX
ejpam-4810	6	9	the	the	DET
ejpam-4810	6	10	minimum	minimum	ADJ
ejpam-4810	6	11	cardinality	cardinality	NOUN
ejpam-4810	6	12	among	among	ADP
ejpam-4810	6	13	all	all	DET
ejpam-4810	6	14	geodetic	geodetic	ADJ
ejpam-4810	6	15	hop	hop	NOUN
ejpam-4810	6	16	dominating	dominating	NOUN
ejpam-4810	6	17	sets	set	NOUN
ejpam-4810	6	18	in	in	ADP
ejpam-4810	6	19	g.	g.	PROPN
ejpam-4810	6	20	in	in	ADP
ejpam-4810	6	21	this	this	DET
ejpam-4810	6	22	paper	paper	NOUN
ejpam-4810	6	23	,	,	PUNCT
ejpam-4810	6	24	we	we	PRON
ejpam-4810	6	25	characterize	characterize	VERB
ejpam-4810	6	26	the	the	DET
ejpam-4810	6	27	geodetic	geodetic	ADJ
ejpam-4810	6	28	hop	hop	NOUN
ejpam-4810	6	29	dominating	dominating	NOUN
ejpam-4810	6	30	sets	set	NOUN
ejpam-4810	6	31	in	in	ADP
ejpam-4810	6	32	the	the	DET
ejpam-4810	6	33	join	join	NOUN
ejpam-4810	6	34	of	of	ADP
ejpam-4810	6	35	two	two	NUM
ejpam-4810	6	36	graphs	graph	NOUN
ejpam-4810	6	37	.	.	PUNCT
ejpam-4810	7	1	these	these	DET
ejpam-4810	7	2	characterizations	characterization	NOUN
ejpam-4810	7	3	which	which	PRON
ejpam-4810	7	4	use	use	VERB
ejpam-4810	7	5	the	the	DET
ejpam-4810	7	6	concept	concept	NOUN
ejpam-4810	7	7	of	of	ADP
ejpam-4810	7	8	pointwise	pointwise	PROPN
ejpam-4810	7	9	non	non	ADJ
ejpam-4810	7	10	-	-	ADJ
ejpam-4810	7	11	dominating	dominating	ADJ
ejpam-4810	7	12	2	2	NUM
ejpam-4810	7	13	-	-	PUNCT
ejpam-4810	7	14	path	path	NOUN
ejpam-4810	7	15	closure	closure	NOUN
ejpam-4810	7	16	absorbing	absorb	VERB
ejpam-4810	7	17	set	set	NOUN
ejpam-4810	7	18	are	be	AUX
ejpam-4810	7	19	,	,	PUNCT
ejpam-4810	7	20	in	in	ADP
ejpam-4810	7	21	turn	turn	NOUN
ejpam-4810	7	22	,	,	PUNCT
ejpam-4810	7	23	used	use	VERB
ejpam-4810	7	24	to	to	PART
ejpam-4810	7	25	determine	determine	VERB
ejpam-4810	7	26	the	the	DET
ejpam-4810	7	27	geodetic	geodetic	ADJ
ejpam-4810	7	28	hop	hop	NOUN
ejpam-4810	7	29	domination	domination	NOUN
ejpam-4810	7	30	number	number	NOUN
ejpam-4810	7	31	of	of	ADP
ejpam-4810	7	32	the	the	DET
ejpam-4810	7	33	join	join	NOUN
ejpam-4810	7	34	of	of	ADP
ejpam-4810	7	35	graphs	graph	NOUN
ejpam-4810	7	36	.	.	PUNCT
ejpam-4810	8	1	moreover	moreover	ADV
ejpam-4810	8	2	,	,	PUNCT
ejpam-4810	8	3	a	a	DET
ejpam-4810	8	4	realization	realization	NOUN
ejpam-4810	8	5	result	result	NOUN
ejpam-4810	8	6	involving	involve	VERB
ejpam-4810	8	7	the	the	DET
ejpam-4810	8	8	hop	hop	NOUN
ejpam-4810	8	9	domination	domination	NOUN
ejpam-4810	8	10	number	number	NOUN
ejpam-4810	8	11	and	and	CCONJ
ejpam-4810	8	12	geodetic	geodetic	ADJ
ejpam-4810	8	13	hop	hop	NOUN
ejpam-4810	8	14	domination	domination	NOUN
ejpam-4810	8	15	number	number	NOUN
ejpam-4810	8	16	is	be	AUX
ejpam-4810	8	17	also	also	ADV
ejpam-4810	8	18	obtained	obtain	VERB
ejpam-4810	8	19	.	.	PUNCT
ejpam-4810	9	1	2020	2020	NUM
ejpam-4810	9	2	mathematics	mathematic	NOUN
ejpam-4810	9	3	subject	subject	NOUN
ejpam-4810	9	4	classifications	classification	NOUN
ejpam-4810	9	5	:	:	PUNCT
ejpam-4810	9	6	05c69	05c69	X
ejpam-4810	9	7	key	key	ADJ
ejpam-4810	9	8	words	word	NOUN
ejpam-4810	9	9	and	and	CCONJ
ejpam-4810	9	10	phrases	phrase	NOUN
ejpam-4810	9	11	:	:	PUNCT
ejpam-4810	9	12	geodetic	geodetic	ADJ
ejpam-4810	9	13	hop	hop	NOUN
ejpam-4810	9	14	domination	domination	NOUN
ejpam-4810	9	15	,	,	PUNCT
ejpam-4810	9	16	join	join	VERB
ejpam-4810	9	17	1	1	NUM
ejpam-4810	9	18	.	.	PUNCT
ejpam-4810	10	1	introduction	introduction	NOUN
ejpam-4810	10	2	over	over	ADP
ejpam-4810	10	3	the	the	DET
ejpam-4810	10	4	years	year	NOUN
ejpam-4810	10	5	,	,	PUNCT
ejpam-4810	10	6	a	a	DET
ejpam-4810	10	7	number	number	NOUN
ejpam-4810	10	8	of	of	ADP
ejpam-4810	10	9	studies	study	NOUN
ejpam-4810	10	10	dealing	deal	VERB
ejpam-4810	10	11	with	with	ADP
ejpam-4810	10	12	the	the	DET
ejpam-4810	10	13	topic	topic	NOUN
ejpam-4810	10	14	on	on	ADP
ejpam-4810	10	15	hop	hop	PROPN
ejpam-4810	10	16	domination	domination	NOUN
ejpam-4810	10	17	,	,	PUNCT
ejpam-4810	10	18	a	a	DET
ejpam-4810	10	19	concept	concept	NOUN
ejpam-4810	10	20	introduced	introduce	VERB
ejpam-4810	10	21	and	and	CCONJ
ejpam-4810	10	22	initially	initially	ADV
ejpam-4810	10	23	studied	study	VERB
ejpam-4810	10	24	by	by	ADP
ejpam-4810	10	25	natarajan	natarajan	PROPN
ejpam-4810	10	26	and	and	CCONJ
ejpam-4810	10	27	s.	s.	PROPN
ejpam-4810	10	28	k.	k.	PROPN
ejpam-4810	10	29	ayyaswamy	ayyaswamy	PROPN
ejpam-4810	11	1	[	[	X
ejpam-4810	11	2	13	13	NUM
ejpam-4810	11	3	]	]	PUNCT
ejpam-4810	11	4	,	,	PUNCT
ejpam-4810	11	5	had	have	AUX
ejpam-4810	11	6	been	be	AUX
ejpam-4810	11	7	done	do	VERB
ejpam-4810	11	8	.	.	PUNCT
ejpam-4810	12	1	in	in	ADP
ejpam-4810	12	2	particular	particular	ADJ
ejpam-4810	12	3	,	,	PUNCT
ejpam-4810	12	4	some	some	DET
ejpam-4810	12	5	variations	variation	NOUN
ejpam-4810	12	6	of	of	ADP
ejpam-4810	12	7	hop	hop	NOUN
ejpam-4810	12	8	domination	domination	NOUN
ejpam-4810	12	9	had	have	AUX
ejpam-4810	12	10	been	be	AUX
ejpam-4810	12	11	introduced	introduce	VERB
ejpam-4810	12	12	and	and	CCONJ
ejpam-4810	12	13	considered	consider	VERB
ejpam-4810	12	14	in	in	ADP
ejpam-4810	12	15	many	many	ADJ
ejpam-4810	12	16	studies	study	NOUN
ejpam-4810	12	17	(	(	PUNCT
ejpam-4810	12	18	see	see	VERB
ejpam-4810	12	19	[	[	X
ejpam-4810	12	20	2	2	NUM
ejpam-4810	12	21	]	]	PUNCT
ejpam-4810	12	22	,	,	PUNCT
ejpam-4810	12	23	[	[	X
ejpam-4810	12	24	3	3	NUM
ejpam-4810	12	25	]	]	PUNCT
ejpam-4810	12	26	,	,	PUNCT
ejpam-4810	12	27	[	[	X
ejpam-4810	12	28	4	4	NUM
ejpam-4810	12	29	]	]	PUNCT
ejpam-4810	12	30	,	,	PUNCT
ejpam-4810	12	31	[	[	X
ejpam-4810	12	32	5	5	NUM
ejpam-4810	12	33	]	]	PUNCT
ejpam-4810	12	34	,	,	PUNCT
ejpam-4810	12	35	[	[	X
ejpam-4810	12	36	6	6	NUM
ejpam-4810	12	37	]	]	PUNCT
ejpam-4810	12	38	,	,	PUNCT
ejpam-4810	12	39	[	[	X
ejpam-4810	12	40	7	7	NUM
ejpam-4810	12	41	]	]	PUNCT
ejpam-4810	12	42	,	,	PUNCT
ejpam-4810	12	43	[	[	X
ejpam-4810	12	44	10	10	NUM
ejpam-4810	12	45	]	]	PUNCT
ejpam-4810	12	46	,	,	PUNCT
ejpam-4810	12	47	[	[	X
ejpam-4810	12	48	11	11	NUM
ejpam-4810	12	49	]	]	PUNCT
ejpam-4810	12	50	,	,	PUNCT
ejpam-4810	13	1	[	[	X
ejpam-4810	13	2	12	12	NUM
ejpam-4810	13	3	]	]	PUNCT
ejpam-4810	13	4	,	,	PUNCT
ejpam-4810	13	5	[	[	X
ejpam-4810	13	6	14	14	NUM
ejpam-4810	13	7	]	]	PUNCT
ejpam-4810	13	8	,	,	PUNCT
ejpam-4810	14	1	[	[	X
ejpam-4810	14	2	15	15	NUM
ejpam-4810	14	3	]	]	PUNCT
ejpam-4810	14	4	,	,	PUNCT
ejpam-4810	14	5	and	and	CCONJ
ejpam-4810	14	6	[	[	X
ejpam-4810	14	7	16	16	NUM
ejpam-4810	14	8	]	]	PUNCT
ejpam-4810	14	9	)	)	PUNCT
ejpam-4810	14	10	.	.	PUNCT
ejpam-4810	15	1	henning	henning	NOUN
ejpam-4810	15	2	and	and	CCONJ
ejpam-4810	15	3	rad	rad	NOUN
ejpam-4810	16	1	[	[	X
ejpam-4810	16	2	9	9	NUM
ejpam-4810	16	3	]	]	PUNCT
ejpam-4810	16	4	gave	give	VERB
ejpam-4810	16	5	a	a	DET
ejpam-4810	16	6	probabilitics	probabilitic	NOUN
ejpam-4810	16	7	upper	upper	ADJ
ejpam-4810	16	8	bound	bind	VERB
ejpam-4810	16	9	of	of	ADP
ejpam-4810	16	10	the	the	DET
ejpam-4810	16	11	hop	hop	NOUN
ejpam-4810	16	12	domination	domination	NOUN
ejpam-4810	16	13	number	number	NOUN
ejpam-4810	16	14	of	of	ADP
ejpam-4810	16	15	a	a	DET
ejpam-4810	16	16	graph	graph	NOUN
ejpam-4810	16	17	and	and	CCONJ
ejpam-4810	16	18	showed	show	VERB
ejpam-4810	16	19	that	that	SCONJ
ejpam-4810	16	20	the	the	DET
ejpam-4810	16	21	hop	hop	NOUN
ejpam-4810	16	22	dominating	dominating	NOUN
ejpam-4810	16	23	set	set	NOUN
ejpam-4810	16	24	problem	problem	NOUN
ejpam-4810	16	25	is	be	AUX
ejpam-4810	16	26	np	np	INTJ
ejpam-4810	16	27	-	-	NOUN
ejpam-4810	16	28	complete	complete	ADJ
ejpam-4810	16	29	for	for	ADP
ejpam-4810	16	30	planar	planar	ADJ
ejpam-4810	16	31	bipartite	bipartite	ADJ
ejpam-4810	16	32	graphs	graph	NOUN
ejpam-4810	16	33	and	and	CCONJ
ejpam-4810	16	34	planar	planar	ADJ
ejpam-4810	16	35	chordal	chordal	ADJ
ejpam-4810	16	36	graphs	graph	NOUN
ejpam-4810	16	37	.	.	PUNCT
ejpam-4810	17	1	in	in	ADP
ejpam-4810	17	2	a	a	DET
ejpam-4810	17	3	recent	recent	ADJ
ejpam-4810	17	4	study	study	NOUN
ejpam-4810	17	5	,	,	PUNCT
ejpam-4810	17	6	henning	henning	PROPN
ejpam-4810	17	7	et	et	PROPN
ejpam-4810	17	8	al	al	PROPN
ejpam-4810	17	9	.	.	PUNCT
ejpam-4810	18	1	[	[	X
ejpam-4810	18	2	8	8	NUM
ejpam-4810	18	3	]	]	PUNCT
ejpam-4810	18	4	presented	present	VERB
ejpam-4810	18	5	a	a	DET
ejpam-4810	18	6	linear	linear	ADJ
ejpam-4810	18	7	time	time	NOUN
ejpam-4810	18	8	algorithm	algorithm	NOUN
ejpam-4810	18	9	for	for	ADP
ejpam-4810	18	10	computing	compute	VERB
ejpam-4810	18	11	a	a	DET
ejpam-4810	18	12	minimum	minimum	ADJ
ejpam-4810	18	13	hop	hop	NOUN
ejpam-4810	18	14	dominating	dominating	NOUN
ejpam-4810	18	15	set	set	VERB
ejpam-4810	18	16	in	in	ADP
ejpam-4810	18	17	bipartite	bipartite	ADJ
ejpam-4810	18	18	permutation	permutation	NOUN
ejpam-4810	18	19	graphs	graph	NOUN
ejpam-4810	18	20	.	.	PUNCT
ejpam-4810	19	1	the	the	DET
ejpam-4810	19	2	idea	idea	NOUN
ejpam-4810	19	3	of	of	ADP
ejpam-4810	19	4	combining	combine	VERB
ejpam-4810	19	5	the	the	DET
ejpam-4810	19	6	concepts	concept	NOUN
ejpam-4810	19	7	of	of	ADP
ejpam-4810	19	8	hop	hop	NOUN
ejpam-4810	19	9	domination	domination	NOUN
ejpam-4810	19	10	and	and	CCONJ
ejpam-4810	19	11	geodetic	geodetic	ADJ
ejpam-4810	19	12	has	have	AUX
ejpam-4810	19	13	led	lead	VERB
ejpam-4810	19	14	to	to	ADP
ejpam-4810	19	15	the	the	DET
ejpam-4810	19	16	introduction	introduction	NOUN
ejpam-4810	19	17	of	of	ADP
ejpam-4810	19	18	the	the	DET
ejpam-4810	19	19	notion	notion	NOUN
ejpam-4810	19	20	of	of	ADP
ejpam-4810	19	21	geodetic	geodetic	ADJ
ejpam-4810	19	22	hop	hop	NOUN
ejpam-4810	19	23	domination	domination	NOUN
ejpam-4810	19	24	.	.	PUNCT
ejpam-4810	20	1	this	this	DET
ejpam-4810	20	2	hop	hop	PROPN
ejpam-4810	20	3	domination	domination	NOUN
ejpam-4810	20	4	variant	variant	NOUN
ejpam-4810	20	5	was	be	AUX
ejpam-4810	20	6	first	first	ADV
ejpam-4810	20	7	defined	define	VERB
ejpam-4810	20	8	and	and	CCONJ
ejpam-4810	20	9	examined	examine	VERB
ejpam-4810	20	10	by	by	ADP
ejpam-4810	20	11	anusha	anusha	NOUN
ejpam-4810	20	12	and	and	CCONJ
ejpam-4810	20	13	robin	robin	PROPN
ejpam-4810	21	1	[	[	X
ejpam-4810	21	2	1	1	NUM
ejpam-4810	21	3	]	]	PUNCT
ejpam-4810	21	4	.	.	PUNCT
ejpam-4810	22	1	motivated	motivate	VERB
ejpam-4810	22	2	by	by	ADP
ejpam-4810	22	3	the	the	DET
ejpam-4810	22	4	new	new	ADJ
ejpam-4810	22	5	concept	concept	NOUN
ejpam-4810	22	6	,	,	PUNCT
ejpam-4810	22	7	saromines	saromine	NOUN
ejpam-4810	22	8	and	and	CCONJ
ejpam-4810	22	9	canoy	canoy	ADJ
ejpam-4810	23	1	[	[	X
ejpam-4810	23	2	16	16	NUM
ejpam-4810	23	3	]	]	PUNCT
ejpam-4810	23	4	gave	give	VERB
ejpam-4810	23	5	characterizations	characterization	NOUN
ejpam-4810	23	6	of	of	ADP
ejpam-4810	23	7	the	the	DET
ejpam-4810	23	8	geodetic	geodetic	ADJ
ejpam-4810	23	9	hop	hop	NOUN
ejpam-4810	23	10	dominating	dominating	NOUN
ejpam-4810	23	11	sets	set	NOUN
ejpam-4810	23	12	in	in	ADP
ejpam-4810	23	13	the	the	DET
ejpam-4810	23	14	corona	corona	NOUN
ejpam-4810	23	15	and	and	CCONJ
ejpam-4810	23	16	lexicographic	lexicographic	ADJ
ejpam-4810	23	17	product	product	NOUN
ejpam-4810	23	18	of	of	ADP
ejpam-4810	23	19	two	two	NUM
ejpam-4810	23	20	graphs	graph	NOUN
ejpam-4810	23	21	.	.	PUNCT
ejpam-4810	24	1	in	in	ADP
ejpam-4810	24	2	this	this	DET
ejpam-4810	24	3	present	present	ADJ
ejpam-4810	24	4	paper	paper	NOUN
ejpam-4810	24	5	,	,	PUNCT
ejpam-4810	24	6	we	we	PRON
ejpam-4810	24	7	revisit	revisit	VERB
ejpam-4810	24	8	the	the	DET
ejpam-4810	24	9	concept	concept	NOUN
ejpam-4810	24	10	of	of	ADP
ejpam-4810	24	11	geodetic	geodetic	ADJ
ejpam-4810	24	12	hop	hop	NOUN
ejpam-4810	24	13	domination	domination	NOUN
ejpam-4810	24	14	and	and	CCONJ
ejpam-4810	24	15	give	give	VERB
ejpam-4810	24	16	further	further	ADJ
ejpam-4810	24	17	results	result	NOUN
ejpam-4810	24	18	of	of	ADP
ejpam-4810	24	19	this	this	DET
ejpam-4810	24	20	new	new	ADJ
ejpam-4810	24	21	parameter	parameter	NOUN
ejpam-4810	24	22	.	.	PUNCT
ejpam-4810	25	1	∗corresponding	∗corresponde	VERB
ejpam-4810	25	2	author	author	NOUN
ejpam-4810	25	3	.	.	PUNCT
ejpam-4810	26	1	doi	doi	NOUN
ejpam-4810	26	2	:	:	PUNCT
ejpam-4810	26	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4810	https://doi.org/10.29020/nybg.ejpam.v16i3.4810	NUM
ejpam-4810	26	4	email	email	NOUN
ejpam-4810	26	5	addresses	address	VERB
ejpam-4810	26	6	:	:	PUNCT
ejpam-4810	26	7	chrisleyjade.saromines@g.msuiit.edu.ph	chrisleyjade.saromines@g.msuiit.edu.ph	PROPN
ejpam-4810	26	8	(	(	PUNCT
ejpam-4810	26	9	c.j	c.j	NOUN
ejpam-4810	26	10	.	.	PROPN
ejpam-4810	26	11	saromines	saromine	NOUN
ejpam-4810	26	12	)	)	PUNCT
ejpam-4810	26	13	,	,	PUNCT
ejpam-4810	26	14	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4810	26	15	(	(	PUNCT
ejpam-4810	26	16	s.	s.	PROPN
ejpam-4810	26	17	canoy	canoy	PROPN
ejpam-4810	26	18	,	,	PUNCT
ejpam-4810	26	19	jr	jr	PROPN
ejpam-4810	26	20	.	.	PUNCT
ejpam-4810	26	21	)	)	PUNCT
ejpam-4810	26	22	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4810	27	1	1568	1568	NUM
ejpam-4810	28	1	©	©	ADP
ejpam-4810	28	2	2023	2023	NUM
ejpam-4810	28	3	ejpam	ejpam	NOUN
ejpam-4810	28	4	all	all	DET
ejpam-4810	28	5	rights	right	NOUN
ejpam-4810	28	6	reserved	reserve	VERB
ejpam-4810	28	7	.	.	PUNCT
ejpam-4810	29	1	c.j	c.j	PROPN
ejpam-4810	29	2	.	.	PROPN
ejpam-4810	29	3	saromines	saromines	PROPN
ejpam-4810	29	4	,	,	PUNCT
ejpam-4810	29	5	s.	s.	PROPN
ejpam-4810	29	6	canoy	canoy	PROPN
ejpam-4810	29	7	,	,	PUNCT
ejpam-4810	29	8	jr	jr	PROPN
ejpam-4810	29	9	.	.	PROPN
ejpam-4810	29	10	,	,	PUNCT
ejpam-4810	29	11	/	/	SYM
ejpam-4810	29	12	eur	eur	NOUN
ejpam-4810	29	13	.	.	PUNCT
ejpam-4810	30	1	j.	j.	PROPN
ejpam-4810	30	2	pure	pure	PROPN
ejpam-4810	30	3	appl	appl	PROPN
ejpam-4810	30	4	.	.	PROPN
ejpam-4810	30	5	math	math	PROPN
ejpam-4810	30	6	,	,	PUNCT
ejpam-4810	30	7	16	16	NUM
ejpam-4810	30	8	(	(	PUNCT
ejpam-4810	30	9	3	3	NUM
ejpam-4810	30	10	)	)	PUNCT
ejpam-4810	30	11	(	(	PUNCT
ejpam-4810	30	12	2023	2023	NUM
ejpam-4810	30	13	)	)	PUNCT
ejpam-4810	30	14	,	,	PUNCT
ejpam-4810	30	15	1568	1568	NUM
ejpam-4810	30	16	-	-	SYM
ejpam-4810	30	17	1579	1579	NUM
ejpam-4810	30	18	1569	1569	NUM
ejpam-4810	30	19	2	2	NUM
ejpam-4810	30	20	.	.	PUNCT
ejpam-4810	30	21	terminology	terminology	NOUN
ejpam-4810	30	22	and	and	CCONJ
ejpam-4810	30	23	notation	notation	NOUN
ejpam-4810	30	24	for	for	ADP
ejpam-4810	30	25	any	any	DET
ejpam-4810	30	26	two	two	NUM
ejpam-4810	30	27	vertices	vertex	NOUN
ejpam-4810	30	28	u	u	NOUN
ejpam-4810	30	29	and	and	CCONJ
ejpam-4810	30	30	v	v	NOUN
ejpam-4810	30	31	in	in	ADP
ejpam-4810	30	32	an	an	DET
ejpam-4810	30	33	undirected	undirected	ADJ
ejpam-4810	30	34	connected	connected	ADJ
ejpam-4810	30	35	graph	graph	NOUN
ejpam-4810	30	36	g	g	PROPN
ejpam-4810	30	37	,	,	PUNCT
ejpam-4810	30	38	the	the	DET
ejpam-4810	30	39	distance	distance	NOUN
ejpam-4810	30	40	dg(u	dg(u	X
ejpam-4810	30	41	,	,	PUNCT
ejpam-4810	30	42	v	v	NOUN
ejpam-4810	30	43	)	)	PUNCT
ejpam-4810	30	44	is	be	AUX
ejpam-4810	30	45	the	the	DET
ejpam-4810	30	46	length	length	NOUN
ejpam-4810	30	47	of	of	ADP
ejpam-4810	30	48	a	a	DET
ejpam-4810	30	49	shortest	short	ADJ
ejpam-4810	30	50	path	path	NOUN
ejpam-4810	30	51	joining	join	VERB
ejpam-4810	30	52	u	u	NOUN
ejpam-4810	30	53	and	and	CCONJ
ejpam-4810	30	54	v.	v.	ADP
ejpam-4810	30	55	any	any	DET
ejpam-4810	30	56	u	u	NOUN
ejpam-4810	30	57	-	-	NOUN
ejpam-4810	30	58	v	v	ADJ
ejpam-4810	30	59	path	path	NOUN
ejpam-4810	30	60	of	of	ADP
ejpam-4810	30	61	length	length	NOUN
ejpam-4810	30	62	dg(u	dg(u	PROPN
ejpam-4810	30	63	,	,	PUNCT
ejpam-4810	30	64	v	v	NOUN
ejpam-4810	30	65	)	)	PUNCT
ejpam-4810	30	66	is	be	AUX
ejpam-4810	30	67	called	call	VERB
ejpam-4810	30	68	a	a	DET
ejpam-4810	30	69	u	u	NOUN
ejpam-4810	30	70	-	-	NOUN
ejpam-4810	30	71	v	v	ADJ
ejpam-4810	30	72	geodesic	geodesic	NOUN
ejpam-4810	30	73	.	.	PUNCT
ejpam-4810	31	1	the	the	DET
ejpam-4810	31	2	interval	interval	NOUN
ejpam-4810	31	3	ig	ig	PROPN
ejpam-4810	32	1	[	[	X
ejpam-4810	32	2	u	u	NOUN
ejpam-4810	32	3	,	,	PUNCT
ejpam-4810	32	4	v	v	NOUN
ejpam-4810	32	5	]	]	PUNCT
ejpam-4810	32	6	consists	consist	VERB
ejpam-4810	32	7	u	u	NOUN
ejpam-4810	32	8	,	,	PUNCT
ejpam-4810	32	9	v	v	NOUN
ejpam-4810	32	10	and	and	CCONJ
ejpam-4810	32	11	all	all	DET
ejpam-4810	32	12	vertices	vertex	NOUN
ejpam-4810	32	13	lying	lie	VERB
ejpam-4810	32	14	on	on	ADP
ejpam-4810	32	15	a	a	DET
ejpam-4810	32	16	u	u	NOUN
ejpam-4810	32	17	-	-	NOUN
ejpam-4810	32	18	v	v	ADJ
ejpam-4810	32	19	geodesic	geodesic	NOUN
ejpam-4810	32	20	.	.	PUNCT
ejpam-4810	33	1	the	the	DET
ejpam-4810	33	2	interval	interval	NOUN
ejpam-4810	33	3	ig(u	ig(u	NOUN
ejpam-4810	33	4	,	,	PUNCT
ejpam-4810	33	5	v	v	NOUN
ejpam-4810	33	6	)	)	PUNCT
ejpam-4810	33	7	=	=	PUNCT
ejpam-4810	34	1	ig	ig	PROPN
ejpam-4810	35	1	[	[	X
ejpam-4810	35	2	u	u	NOUN
ejpam-4810	35	3	,	,	PUNCT
ejpam-4810	35	4	v	v	ADP
ejpam-4810	35	5	]	]	PUNCT
ejpam-4810	35	6	\	\	NOUN
ejpam-4810	35	7	{	{	PUNCT
ejpam-4810	35	8	u	u	NOUN
ejpam-4810	35	9	,	,	PUNCT
ejpam-4810	35	10	v	v	NOUN
ejpam-4810	35	11	}	}	PUNCT
ejpam-4810	35	12	.	.	PUNCT
ejpam-4810	36	1	the	the	DET
ejpam-4810	36	2	open	open	ADJ
ejpam-4810	36	3	neighborhood	neighborhood	NOUN
ejpam-4810	36	4	of	of	ADP
ejpam-4810	36	5	a	a	DET
ejpam-4810	36	6	vertex	vertex	NOUN
ejpam-4810	36	7	u	u	NOUN
ejpam-4810	36	8	is	be	AUX
ejpam-4810	36	9	the	the	DET
ejpam-4810	36	10	set	set	NOUN
ejpam-4810	36	11	ng(u	ng(u	NOUN
ejpam-4810	36	12	)	)	PUNCT
ejpam-4810	36	13	consisting	consist	VERB
ejpam-4810	36	14	of	of	ADP
ejpam-4810	36	15	all	all	DET
ejpam-4810	36	16	vertices	vertex	NOUN
ejpam-4810	36	17	v	v	NUM
ejpam-4810	36	18	which	which	PRON
ejpam-4810	36	19	are	be	AUX
ejpam-4810	36	20	adjacent	adjacent	ADJ
ejpam-4810	36	21	to	to	PART
ejpam-4810	36	22	u.	u.	VERB
ejpam-4810	36	23	the	the	DET
ejpam-4810	36	24	closed	closed	ADJ
ejpam-4810	36	25	neighborhood	neighborhood	NOUN
ejpam-4810	36	26	of	of	ADP
ejpam-4810	36	27	u	u	NOUN
ejpam-4810	36	28	is	be	AUX
ejpam-4810	36	29	ng[u	ng[u	PROPN
ejpam-4810	36	30	]	]	X
ejpam-4810	36	31	=	=	SYM
ejpam-4810	36	32	ng(u	ng(u	PROPN
ejpam-4810	36	33	)	)	PUNCT
ejpam-4810	36	34	∪	∪	NOUN
ejpam-4810	36	35	{	{	PUNCT
ejpam-4810	36	36	u	u	NOUN
ejpam-4810	36	37	}	}	PUNCT
ejpam-4810	36	38	.	.	PUNCT
ejpam-4810	37	1	for	for	ADP
ejpam-4810	37	2	any	any	DET
ejpam-4810	37	3	a	a	DET
ejpam-4810	37	4	⊆	⊆	NUM
ejpam-4810	37	5	v	v	NOUN
ejpam-4810	37	6	(	(	PUNCT
ejpam-4810	37	7	g	g	NOUN
ejpam-4810	37	8	)	)	PUNCT
ejpam-4810	37	9	,	,	PUNCT
ejpam-4810	37	10	ng(a	ng(a	X
ejpam-4810	37	11	)	)	PUNCT
ejpam-4810	37	12	=	=	PUNCT
ejpam-4810	37	13	⋃	⋃	NOUN
ejpam-4810	37	14	v∈a	v∈a	NOUN
ejpam-4810	37	15	ng(v	ng(v	PUNCT
ejpam-4810	37	16	)	)	PUNCT
ejpam-4810	37	17	is	be	AUX
ejpam-4810	37	18	called	call	VERB
ejpam-4810	37	19	the	the	DET
ejpam-4810	37	20	open	open	ADJ
ejpam-4810	37	21	neighborhood	neighborhood	NOUN
ejpam-4810	37	22	of	of	ADP
ejpam-4810	37	23	a	a	DET
ejpam-4810	37	24	andng[a	andng[a	NOUN
ejpam-4810	37	25	]	]	X
ejpam-4810	37	26	=	=	SYM
ejpam-4810	37	27	ng(a)∪a	ng(a)∪a	PROPN
ejpam-4810	37	28	is	be	AUX
ejpam-4810	37	29	called	call	VERB
ejpam-4810	37	30	the	the	DET
ejpam-4810	37	31	closed	closed	ADJ
ejpam-4810	37	32	neighborhood	neighborhood	NOUN
ejpam-4810	37	33	of	of	ADP
ejpam-4810	37	34	a.	a.	NOUN
ejpam-4810	37	35	the	the	DET
ejpam-4810	37	36	open	open	ADJ
ejpam-4810	37	37	hop	hop	NOUN
ejpam-4810	37	38	neighborhood	neighborhood	NOUN
ejpam-4810	37	39	of	of	ADP
ejpam-4810	37	40	a	a	DET
ejpam-4810	37	41	vertex	vertex	NOUN
ejpam-4810	37	42	u	u	NOUN
ejpam-4810	37	43	is	be	AUX
ejpam-4810	37	44	the	the	DET
ejpam-4810	37	45	set	set	ADJ
ejpam-4810	37	46	n2	n2	ADJ
ejpam-4810	37	47	g(u	g(u	PROPN
ejpam-4810	37	48	)	)	PUNCT
ejpam-4810	37	49	=	=	PRON
ejpam-4810	37	50	{	{	PUNCT
ejpam-4810	37	51	v	v	NUM
ejpam-4810	37	52	∈	∈	NOUN
ejpam-4810	37	53	v	v	NOUN
ejpam-4810	37	54	(	(	PUNCT
ejpam-4810	37	55	g	g	NOUN
ejpam-4810	37	56	)	)	PUNCT
ejpam-4810	37	57	:	:	PUNCT
ejpam-4810	37	58	dg(v	dg(v	X
ejpam-4810	37	59	,	,	PUNCT
ejpam-4810	37	60	u	u	NOUN
ejpam-4810	37	61	)	)	PUNCT
ejpam-4810	37	62	=	=	SYM
ejpam-4810	37	63	2	2	NUM
ejpam-4810	37	64	}	}	PUNCT
ejpam-4810	37	65	.	.	PUNCT
ejpam-4810	38	1	the	the	DET
ejpam-4810	38	2	closed	closed	ADJ
ejpam-4810	38	3	hop	hop	NOUN
ejpam-4810	38	4	neighborhood	neighborhood	NOUN
ejpam-4810	38	5	of	of	ADP
ejpam-4810	38	6	u	u	NOUN
ejpam-4810	38	7	is	be	AUX
ejpam-4810	38	8	n2	n2	ADJ
ejpam-4810	38	9	g[u	g[u	X
ejpam-4810	38	10	]	]	X
ejpam-4810	38	11	=	=	SYM
ejpam-4810	38	12	n2	n2	ADJ
ejpam-4810	38	13	g(u	g(u	PROPN
ejpam-4810	38	14	)	)	PUNCT
ejpam-4810	38	15	∪	∪	NOUN
ejpam-4810	38	16	{	{	PUNCT
ejpam-4810	38	17	u	u	NOUN
ejpam-4810	38	18	}	}	PUNCT
ejpam-4810	38	19	.	.	PUNCT
ejpam-4810	39	1	for	for	ADP
ejpam-4810	39	2	any	any	DET
ejpam-4810	39	3	a	a	DET
ejpam-4810	39	4	⊆	⊆	NUM
ejpam-4810	39	5	v	v	NOUN
ejpam-4810	39	6	(	(	PUNCT
ejpam-4810	39	7	g	g	NOUN
ejpam-4810	39	8	)	)	PUNCT
ejpam-4810	39	9	,	,	PUNCT
ejpam-4810	39	10	n2	n2	PROPN
ejpam-4810	39	11	g(a	g(a	PROPN
ejpam-4810	39	12	)	)	PUNCT
ejpam-4810	39	13	=	=	SYM
ejpam-4810	39	14	⋃	⋃	NOUN
ejpam-4810	39	15	v∈a	v∈a	NOUN
ejpam-4810	39	16	n2	n2	ADJ
ejpam-4810	39	17	g(v	g(v	PROPN
ejpam-4810	39	18	)	)	PUNCT
ejpam-4810	39	19	is	be	AUX
ejpam-4810	39	20	called	call	VERB
ejpam-4810	39	21	the	the	DET
ejpam-4810	39	22	open	open	ADJ
ejpam-4810	39	23	hop	hop	NOUN
ejpam-4810	39	24	neighborhood	neighborhood	NOUN
ejpam-4810	39	25	of	of	ADP
ejpam-4810	39	26	a	a	DET
ejpam-4810	39	27	and	and	CCONJ
ejpam-4810	39	28	n2	n2	ADJ
ejpam-4810	39	29	g[a	g[a	NOUN
ejpam-4810	39	30	]	]	X
ejpam-4810	39	31	=	=	SYM
ejpam-4810	39	32	n2	n2	PROPN
ejpam-4810	39	33	g(a)∪a	g(a)∪a	PROPN
ejpam-4810	39	34	is	be	AUX
ejpam-4810	39	35	called	call	VERB
ejpam-4810	39	36	the	the	DET
ejpam-4810	39	37	closed	closed	ADJ
ejpam-4810	39	38	hop	hop	NOUN
ejpam-4810	39	39	neighborhood	neighborhood	NOUN
ejpam-4810	39	40	of	of	ADP
ejpam-4810	39	41	a.	a.	NOUN
ejpam-4810	39	42	a	a	DET
ejpam-4810	39	43	set	set	NOUN
ejpam-4810	39	44	s	s	NOUN
ejpam-4810	39	45	⊆	⊆	NUM
ejpam-4810	39	46	v	v	NOUN
ejpam-4810	39	47	(	(	PUNCT
ejpam-4810	39	48	g	g	NOUN
ejpam-4810	39	49	)	)	PUNCT
ejpam-4810	39	50	is	be	AUX
ejpam-4810	39	51	a	a	DET
ejpam-4810	39	52	dominating	dominating	NOUN
ejpam-4810	39	53	set	set	VERB
ejpam-4810	39	54	in	in	ADP
ejpam-4810	39	55	g	g	PROPN
ejpam-4810	39	56	if	if	SCONJ
ejpam-4810	39	57	ng[s	ng[	NOUN
ejpam-4810	39	58	]	]	PUNCT
ejpam-4810	39	59	=	=	SYM
ejpam-4810	39	60	v	v	NOUN
ejpam-4810	39	61	(	(	PUNCT
ejpam-4810	39	62	g	g	NOUN
ejpam-4810	39	63	)	)	PUNCT
ejpam-4810	39	64	.	.	PUNCT
ejpam-4810	40	1	the	the	DET
ejpam-4810	40	2	smallest	small	ADJ
ejpam-4810	40	3	cardinality	cardinality	NOUN
ejpam-4810	40	4	of	of	ADP
ejpam-4810	40	5	a	a	DET
ejpam-4810	40	6	dominating	dominating	NOUN
ejpam-4810	40	7	set	set	NOUN
ejpam-4810	40	8	in	in	ADP
ejpam-4810	40	9	g	g	NOUN
ejpam-4810	40	10	,	,	PUNCT
ejpam-4810	40	11	denoted	denote	VERB
ejpam-4810	40	12	by	by	ADP
ejpam-4810	40	13	γ(g	γ(g	PROPN
ejpam-4810	40	14	)	)	PUNCT
ejpam-4810	40	15	is	be	AUX
ejpam-4810	40	16	called	call	VERB
ejpam-4810	40	17	the	the	DET
ejpam-4810	40	18	domination	domination	NOUN
ejpam-4810	40	19	number	number	NOUN
ejpam-4810	40	20	of	of	ADP
ejpam-4810	40	21	g.	g.	PROPN
ejpam-4810	40	22	the	the	DET
ejpam-4810	40	23	geodetic	geodetic	ADJ
ejpam-4810	40	24	closure	closure	NOUN
ejpam-4810	40	25	of	of	ADP
ejpam-4810	40	26	a	a	DET
ejpam-4810	40	27	set	set	NOUN
ejpam-4810	40	28	s	s	NOUN
ejpam-4810	40	29	⊆	⊆	NUM
ejpam-4810	40	30	v	v	NOUN
ejpam-4810	40	31	(	(	PUNCT
ejpam-4810	40	32	g	g	NOUN
ejpam-4810	40	33	)	)	PUNCT
ejpam-4810	40	34	,	,	PUNCT
ejpam-4810	40	35	denoted	denote	VERB
ejpam-4810	40	36	by	by	ADP
ejpam-4810	40	37	ig	ig	PROPN
ejpam-4810	41	1	[	[	X
ejpam-4810	41	2	s	s	X
ejpam-4810	41	3	]	]	X
ejpam-4810	41	4	,	,	PUNCT
ejpam-4810	41	5	is	be	AUX
ejpam-4810	41	6	the	the	DET
ejpam-4810	41	7	union	union	NOUN
ejpam-4810	41	8	of	of	ADP
ejpam-4810	41	9	the	the	DET
ejpam-4810	41	10	intervals	interval	NOUN
ejpam-4810	41	11	ig[u	ig[u	VERB
ejpam-4810	41	12	,	,	PUNCT
ejpam-4810	41	13	v	v	NOUN
ejpam-4810	41	14	]	]	X
ejpam-4810	41	15	,	,	PUNCT
ejpam-4810	41	16	where	where	SCONJ
ejpam-4810	41	17	u	u	NOUN
ejpam-4810	41	18	,	,	PUNCT
ejpam-4810	41	19	v	v	PROPN
ejpam-4810	41	20	∈	∈	PROPN
ejpam-4810	41	21	s.	s.	PROPN
ejpam-4810	41	22	set	set	VERB
ejpam-4810	41	23	s	s	VERB
ejpam-4810	41	24	is	be	AUX
ejpam-4810	41	25	geodetic	geodetic	ADJ
ejpam-4810	41	26	set	set	NOUN
ejpam-4810	41	27	in	in	ADP
ejpam-4810	41	28	g	g	PROPN
ejpam-4810	41	29	if	if	SCONJ
ejpam-4810	41	30	ig[s	ig[	NOUN
ejpam-4810	41	31	]	]	X
ejpam-4810	41	32	=	=	SYM
ejpam-4810	41	33	v	v	X
ejpam-4810	41	34	(	(	PUNCT
ejpam-4810	41	35	g	g	NOUN
ejpam-4810	41	36	)	)	PUNCT
ejpam-4810	41	37	.	.	PUNCT
ejpam-4810	42	1	the	the	DET
ejpam-4810	42	2	smallest	small	ADJ
ejpam-4810	42	3	cardinality	cardinality	NOUN
ejpam-4810	42	4	among	among	ADP
ejpam-4810	42	5	all	all	DET
ejpam-4810	42	6	geodetic	geodetic	ADJ
ejpam-4810	42	7	sets	set	NOUN
ejpam-4810	42	8	in	in	ADP
ejpam-4810	42	9	g	g	NOUN
ejpam-4810	42	10	,	,	PUNCT
ejpam-4810	42	11	denoted	denote	VERB
ejpam-4810	42	12	by	by	ADP
ejpam-4810	42	13	g(g	g(g	PROPN
ejpam-4810	42	14	)	)	PUNCT
ejpam-4810	42	15	,	,	PUNCT
ejpam-4810	42	16	is	be	AUX
ejpam-4810	42	17	called	call	VERB
ejpam-4810	42	18	the	the	DET
ejpam-4810	42	19	geodetic	geodetic	ADJ
ejpam-4810	42	20	number	number	NOUN
ejpam-4810	42	21	of	of	ADP
ejpam-4810	42	22	g.	g.	PROPN
ejpam-4810	42	23	a	a	DET
ejpam-4810	42	24	geodetic	geodetic	ADJ
ejpam-4810	42	25	set	set	NOUN
ejpam-4810	42	26	of	of	ADP
ejpam-4810	42	27	cardinality	cardinality	PROPN
ejpam-4810	42	28	g(g	g(g	PROPN
ejpam-4810	42	29	)	)	PUNCT
ejpam-4810	42	30	is	be	AUX
ejpam-4810	42	31	called	call	VERB
ejpam-4810	42	32	a	a	DET
ejpam-4810	42	33	g	g	NOUN
ejpam-4810	42	34	-	-	PUNCT
ejpam-4810	42	35	set	set	NOUN
ejpam-4810	42	36	of	of	ADP
ejpam-4810	42	37	g.	g.	PROPN
ejpam-4810	42	38	a	a	DET
ejpam-4810	42	39	set	set	NOUN
ejpam-4810	42	40	s	s	PROPN
ejpam-4810	42	41	⊆	⊆	NUM
ejpam-4810	42	42	v	v	NOUN
ejpam-4810	42	43	(	(	PUNCT
ejpam-4810	42	44	g	g	NOUN
ejpam-4810	42	45	)	)	PUNCT
ejpam-4810	42	46	is	be	AUX
ejpam-4810	42	47	a	a	DET
ejpam-4810	42	48	geodetic	geodetic	ADJ
ejpam-4810	42	49	dominating	dominating	NOUN
ejpam-4810	42	50	set	set	VERB
ejpam-4810	42	51	in	in	ADP
ejpam-4810	42	52	g	g	PROPN
ejpam-4810	42	53	if	if	SCONJ
ejpam-4810	42	54	it	it	PRON
ejpam-4810	42	55	is	be	AUX
ejpam-4810	42	56	both	both	CCONJ
ejpam-4810	42	57	a	a	DET
ejpam-4810	42	58	dominating	dominating	NOUN
ejpam-4810	42	59	and	and	CCONJ
ejpam-4810	42	60	a	a	DET
ejpam-4810	42	61	geodetic	geodetic	ADJ
ejpam-4810	42	62	set	set	NOUN
ejpam-4810	42	63	.	.	PUNCT
ejpam-4810	43	1	a	a	DET
ejpam-4810	43	2	set	set	NOUN
ejpam-4810	43	3	s	s	NOUN
ejpam-4810	43	4	⊆	⊆	NUM
ejpam-4810	43	5	v	v	NOUN
ejpam-4810	43	6	(	(	PUNCT
ejpam-4810	43	7	g	g	NOUN
ejpam-4810	43	8	)	)	PUNCT
ejpam-4810	43	9	is	be	AUX
ejpam-4810	43	10	a	a	DET
ejpam-4810	43	11	hop	hop	NOUN
ejpam-4810	43	12	dominating	dominating	NOUN
ejpam-4810	43	13	set	set	NOUN
ejpam-4810	43	14	if	if	SCONJ
ejpam-4810	43	15	n2	n2	ADJ
ejpam-4810	43	16	g[s	g[s	PROPN
ejpam-4810	43	17	]	]	X
ejpam-4810	43	18	=	=	SYM
ejpam-4810	43	19	v	v	NOUN
ejpam-4810	43	20	(	(	PUNCT
ejpam-4810	43	21	g	g	NOUN
ejpam-4810	43	22	)	)	PUNCT
ejpam-4810	43	23	.	.	PUNCT
ejpam-4810	44	1	the	the	DET
ejpam-4810	44	2	minimum	minimum	ADJ
ejpam-4810	44	3	cardinality	cardinality	NOUN
ejpam-4810	44	4	of	of	ADP
ejpam-4810	44	5	a	a	DET
ejpam-4810	44	6	hop	hop	NOUN
ejpam-4810	44	7	dominating	dominating	NOUN
ejpam-4810	44	8	set	set	NOUN
ejpam-4810	44	9	of	of	ADP
ejpam-4810	44	10	a	a	DET
ejpam-4810	44	11	graph	graph	NOUN
ejpam-4810	44	12	g	g	NOUN
ejpam-4810	44	13	,	,	PUNCT
ejpam-4810	44	14	denoted	denote	VERB
ejpam-4810	44	15	by	by	ADP
ejpam-4810	44	16	γh(g	γh(g	NOUN
ejpam-4810	44	17	)	)	PUNCT
ejpam-4810	44	18	,	,	PUNCT
ejpam-4810	44	19	is	be	AUX
ejpam-4810	44	20	called	call	VERB
ejpam-4810	44	21	the	the	DET
ejpam-4810	44	22	hop	hop	NOUN
ejpam-4810	44	23	domination	domination	NOUN
ejpam-4810	44	24	number	number	NOUN
ejpam-4810	44	25	of	of	ADP
ejpam-4810	44	26	g.	g.	PROPN
ejpam-4810	44	27	a	a	DET
ejpam-4810	44	28	subset	subset	NOUN
ejpam-4810	44	29	s	s	NOUN
ejpam-4810	44	30	of	of	ADP
ejpam-4810	44	31	v	v	NOUN
ejpam-4810	44	32	(	(	PUNCT
ejpam-4810	44	33	g	g	NOUN
ejpam-4810	44	34	)	)	PUNCT
ejpam-4810	44	35	is	be	AUX
ejpam-4810	44	36	a	a	DET
ejpam-4810	44	37	total	total	ADJ
ejpam-4810	44	38	hop	hop	NOUN
ejpam-4810	44	39	dominating	dominating	NOUN
ejpam-4810	44	40	set	set	NOUN
ejpam-4810	44	41	of	of	ADP
ejpam-4810	44	42	g	g	PROPN
ejpam-4810	44	43	if	if	SCONJ
ejpam-4810	44	44	for	for	ADP
ejpam-4810	44	45	every	every	DET
ejpam-4810	44	46	v	v	NUM
ejpam-4810	44	47	∈	∈	NOUN
ejpam-4810	44	48	v	v	NOUN
ejpam-4810	44	49	(	(	PUNCT
ejpam-4810	44	50	g	g	NOUN
ejpam-4810	44	51	)	)	PUNCT
ejpam-4810	44	52	,	,	PUNCT
ejpam-4810	44	53	there	there	PRON
ejpam-4810	44	54	exists	exist	VERB
ejpam-4810	44	55	u	u	PROPN
ejpam-4810	44	56	∈	∈	PROPN
ejpam-4810	44	57	s	s	VERB
ejpam-4810	44	58	such	such	ADJ
ejpam-4810	44	59	that	that	DET
ejpam-4810	44	60	dg(u	dg(u	ADJ
ejpam-4810	44	61	,	,	PUNCT
ejpam-4810	44	62	v	v	NOUN
ejpam-4810	44	63	)	)	PUNCT
ejpam-4810	45	1	=	=	SYM
ejpam-4810	45	2	2	2	X
ejpam-4810	45	3	.	.	X
ejpam-4810	45	4	the	the	DET
ejpam-4810	45	5	smallest	small	ADJ
ejpam-4810	45	6	cardinality	cardinality	NOUN
ejpam-4810	45	7	of	of	ADP
ejpam-4810	45	8	a	a	DET
ejpam-4810	45	9	total	total	ADJ
ejpam-4810	45	10	hop	hop	NOUN
ejpam-4810	45	11	dominating	dominating	NOUN
ejpam-4810	45	12	set	set	NOUN
ejpam-4810	45	13	of	of	ADP
ejpam-4810	45	14	g	g	NOUN
ejpam-4810	45	15	,	,	PUNCT
ejpam-4810	45	16	denoted	denote	VERB
ejpam-4810	45	17	by	by	ADP
ejpam-4810	45	18	γth(g	γth(g	NOUN
ejpam-4810	45	19	)	)	PUNCT
ejpam-4810	45	20	is	be	AUX
ejpam-4810	45	21	called	call	VERB
ejpam-4810	45	22	the	the	DET
ejpam-4810	45	23	total	total	ADJ
ejpam-4810	45	24	hop	hop	NOUN
ejpam-4810	45	25	domination	domination	NOUN
ejpam-4810	45	26	number	number	NOUN
ejpam-4810	45	27	of	of	ADP
ejpam-4810	45	28	g.	g.	PROPN
ejpam-4810	45	29	any	any	DET
ejpam-4810	45	30	total	total	ADJ
ejpam-4810	45	31	hop	hop	NOUN
ejpam-4810	45	32	dominating	dominating	NOUN
ejpam-4810	45	33	set	set	NOUN
ejpam-4810	45	34	of	of	ADP
ejpam-4810	45	35	g	g	PROPN
ejpam-4810	45	36	with	with	ADP
ejpam-4810	45	37	cardinality	cardinality	PROPN
ejpam-4810	45	38	γth(g	γth(g	NOUN
ejpam-4810	45	39	)	)	PUNCT
ejpam-4810	45	40	is	be	AUX
ejpam-4810	45	41	called	call	VERB
ejpam-4810	45	42	a	a	DET
ejpam-4810	45	43	γth	γth	NOUN
ejpam-4810	45	44	-	-	PUNCT
ejpam-4810	45	45	set	set	NOUN
ejpam-4810	45	46	.	.	PUNCT
ejpam-4810	46	1	a	a	DET
ejpam-4810	46	2	subset	subset	NOUN
ejpam-4810	46	3	s	s	NOUN
ejpam-4810	46	4	of	of	ADP
ejpam-4810	46	5	vertices	vertex	NOUN
ejpam-4810	46	6	of	of	ADP
ejpam-4810	46	7	g	g	PROPN
ejpam-4810	46	8	is	be	AUX
ejpam-4810	46	9	a	a	DET
ejpam-4810	46	10	geodetic	geodetic	ADJ
ejpam-4810	46	11	hop	hop	NOUN
ejpam-4810	46	12	dominating	dominating	NOUN
ejpam-4810	46	13	set	set	NOUN
ejpam-4810	46	14	if	if	SCONJ
ejpam-4810	46	15	it	it	PRON
ejpam-4810	46	16	is	be	AUX
ejpam-4810	46	17	both	both	CCONJ
ejpam-4810	46	18	a	a	DET
ejpam-4810	46	19	geodetic	geodetic	ADJ
ejpam-4810	46	20	and	and	CCONJ
ejpam-4810	46	21	a	a	DET
ejpam-4810	46	22	hop	hop	NOUN
ejpam-4810	46	23	dominating	dominating	NOUN
ejpam-4810	46	24	set	set	NOUN
ejpam-4810	46	25	.	.	PUNCT
ejpam-4810	47	1	the	the	DET
ejpam-4810	47	2	geodetic	geodetic	ADJ
ejpam-4810	47	3	hop	hop	NOUN
ejpam-4810	47	4	domination	domination	NOUN
ejpam-4810	47	5	number	number	NOUN
ejpam-4810	47	6	γhg(g	γhg(g	PROPN
ejpam-4810	47	7	)	)	PUNCT
ejpam-4810	47	8	of	of	ADP
ejpam-4810	47	9	g	g	PROPN
ejpam-4810	47	10	is	be	AUX
ejpam-4810	47	11	the	the	DET
ejpam-4810	47	12	minimum	minimum	ADJ
ejpam-4810	47	13	cardinality	cardinality	NOUN
ejpam-4810	47	14	among	among	ADP
ejpam-4810	47	15	all	all	DET
ejpam-4810	47	16	geodetic	geodetic	ADJ
ejpam-4810	47	17	hop	hop	NOUN
ejpam-4810	47	18	dominating	dominating	NOUN
ejpam-4810	47	19	sets	set	NOUN
ejpam-4810	47	20	in	in	ADP
ejpam-4810	47	21	g.	g.	PROPN
ejpam-4810	47	22	any	any	DET
ejpam-4810	47	23	geodetic	geodetic	ADJ
ejpam-4810	47	24	hop	hop	NOUN
ejpam-4810	47	25	dominating	dominating	NOUN
ejpam-4810	47	26	set	set	NOUN
ejpam-4810	47	27	of	of	ADP
ejpam-4810	47	28	g	g	PROPN
ejpam-4810	47	29	with	with	ADP
ejpam-4810	47	30	cardinality	cardinality	PROPN
ejpam-4810	47	31	γhg(g	γhg(g	PROPN
ejpam-4810	47	32	)	)	PUNCT
ejpam-4810	47	33	is	be	AUX
ejpam-4810	47	34	called	call	VERB
ejpam-4810	47	35	a	a	DET
ejpam-4810	47	36	γhg	γhg	NOUN
ejpam-4810	47	37	-	-	PUNCT
ejpam-4810	47	38	set	set	NOUN
ejpam-4810	47	39	.	.	PUNCT
ejpam-4810	48	1	a	a	DET
ejpam-4810	48	2	set	set	NOUN
ejpam-4810	48	3	s	s	NOUN
ejpam-4810	48	4	⊆	⊆	NUM
ejpam-4810	48	5	v	v	NOUN
ejpam-4810	48	6	(	(	PUNCT
ejpam-4810	48	7	g	g	NOUN
ejpam-4810	48	8	)	)	PUNCT
ejpam-4810	48	9	of	of	ADP
ejpam-4810	48	10	a	a	DET
ejpam-4810	48	11	graph	graph	NOUN
ejpam-4810	48	12	g	g	NOUN
ejpam-4810	48	13	is	be	AUX
ejpam-4810	48	14	called	call	VERB
ejpam-4810	48	15	a	a	DET
ejpam-4810	48	16	2	2	NUM
ejpam-4810	48	17	-	-	PUNCT
ejpam-4810	48	18	path	path	NOUN
ejpam-4810	48	19	closure	closure	NOUN
ejpam-4810	48	20	absorbing	absorb	VERB
ejpam-4810	48	21	if	if	SCONJ
ejpam-4810	48	22	for	for	ADP
ejpam-4810	48	23	each	each	DET
ejpam-4810	48	24	x	x	SYM
ejpam-4810	48	25	∈	∈	PROPN
ejpam-4810	48	26	v	v	X
ejpam-4810	48	27	(	(	PUNCT
ejpam-4810	48	28	g)\s	g)\s	VERB
ejpam-4810	48	29	there	there	ADV
ejpam-4810	48	30	exist	exist	VERB
ejpam-4810	48	31	u	u	NOUN
ejpam-4810	48	32	,	,	PUNCT
ejpam-4810	48	33	v	v	PROPN
ejpam-4810	48	34	∈	∈	NOUN
ejpam-4810	48	35	s	s	VERB
ejpam-4810	48	36	such	such	ADJ
ejpam-4810	48	37	that	that	DET
ejpam-4810	48	38	dg(u	dg(u	ADJ
ejpam-4810	48	39	,	,	PUNCT
ejpam-4810	48	40	v	v	NOUN
ejpam-4810	48	41	)	)	PUNCT
ejpam-4810	48	42	=	=	SYM
ejpam-4810	48	43	2	2	NUM
ejpam-4810	48	44	and	and	CCONJ
ejpam-4810	48	45	x	x	PROPN
ejpam-4810	48	46	∈	∈	PROPN
ejpam-4810	48	47	ig(u	ig(u	NOUN
ejpam-4810	48	48	,	,	PUNCT
ejpam-4810	48	49	v	v	NOUN
ejpam-4810	48	50	)	)	PUNCT
ejpam-4810	48	51	.	.	PUNCT
ejpam-4810	49	1	the	the	DET
ejpam-4810	49	2	minimum	minimum	ADJ
ejpam-4810	49	3	cardinality	cardinality	NOUN
ejpam-4810	49	4	of	of	ADP
ejpam-4810	49	5	a	a	DET
ejpam-4810	49	6	2	2	NUM
ejpam-4810	49	7	-	-	PUNCT
ejpam-4810	49	8	path	path	NOUN
ejpam-4810	49	9	closure	closure	NOUN
ejpam-4810	49	10	absorbing	absorb	VERB
ejpam-4810	49	11	set	set	NOUN
ejpam-4810	49	12	in	in	ADP
ejpam-4810	49	13	g	g	PROPN
ejpam-4810	49	14	is	be	AUX
ejpam-4810	49	15	denoted	denote	VERB
ejpam-4810	49	16	by	by	ADP
ejpam-4810	49	17	ρ2(g	ρ2(g	NOUN
ejpam-4810	49	18	)	)	PUNCT
ejpam-4810	49	19	.	.	PUNCT
ejpam-4810	50	1	any	any	DET
ejpam-4810	50	2	2	2	NUM
ejpam-4810	50	3	-	-	PUNCT
ejpam-4810	50	4	path	path	NOUN
ejpam-4810	50	5	closure	closure	NOUN
ejpam-4810	50	6	absorbing	absorb	VERB
ejpam-4810	50	7	set	set	NOUN
ejpam-4810	50	8	of	of	ADP
ejpam-4810	50	9	g	g	NOUN
ejpam-4810	50	10	with	with	ADP
ejpam-4810	50	11	cardinality	cardinality	PROPN
ejpam-4810	50	12	ρ2(g	ρ2(g	NUM
ejpam-4810	50	13	)	)	PUNCT
ejpam-4810	50	14	is	be	AUX
ejpam-4810	50	15	called	call	VERB
ejpam-4810	50	16	a	a	DET
ejpam-4810	50	17	ρ2	ρ2	NOUN
ejpam-4810	50	18	-	-	PUNCT
ejpam-4810	50	19	set	set	NOUN
ejpam-4810	50	20	.	.	PUNCT
ejpam-4810	51	1	a	a	DET
ejpam-4810	51	2	set	set	NOUN
ejpam-4810	51	3	d	d	NOUN
ejpam-4810	51	4	⊆	⊆	NUM
ejpam-4810	51	5	v	v	ADP
ejpam-4810	51	6	(	(	PUNCT
ejpam-4810	51	7	g	g	NOUN
ejpam-4810	51	8	)	)	PUNCT
ejpam-4810	51	9	is	be	AUX
ejpam-4810	51	10	a	a	DET
ejpam-4810	51	11	pointwise	pointwise	ADJ
ejpam-4810	51	12	non	non	ADJ
ejpam-4810	51	13	-	-	ADJ
ejpam-4810	51	14	dominating	dominating	ADJ
ejpam-4810	51	15	set	set	NOUN
ejpam-4810	51	16	of	of	ADP
ejpam-4810	51	17	g	g	PROPN
ejpam-4810	51	18	if	if	SCONJ
ejpam-4810	51	19	for	for	ADP
ejpam-4810	51	20	each	each	PRON
ejpam-4810	51	21	v	v	NUM
ejpam-4810	51	22	∈	∈	PROPN
ejpam-4810	51	23	v	v	NOUN
ejpam-4810	51	24	(	(	PUNCT
ejpam-4810	51	25	g	g	NOUN
ejpam-4810	51	26	)	)	PUNCT
ejpam-4810	51	27	\	\	PROPN
ejpam-4810	52	1	s	s	X
ejpam-4810	52	2	,	,	PUNCT
ejpam-4810	52	3	there	there	PRON
ejpam-4810	52	4	exists	exist	VERB
ejpam-4810	52	5	u	u	PROPN
ejpam-4810	52	6	∈	∈	PROPN
ejpam-4810	52	7	s	s	VERB
ejpam-4810	52	8	such	such	ADJ
ejpam-4810	52	9	that	that	DET
ejpam-4810	52	10	v	v	NOUN
ejpam-4810	52	11	/∈	/∈	PUNCT
ejpam-4810	52	12	ng(u	ng(u	NOUN
ejpam-4810	52	13	)	)	PUNCT
ejpam-4810	52	14	.	.	PUNCT
ejpam-4810	53	1	the	the	DET
ejpam-4810	53	2	smallest	small	ADJ
ejpam-4810	53	3	cardinality	cardinality	NOUN
ejpam-4810	53	4	of	of	ADP
ejpam-4810	53	5	a	a	DET
ejpam-4810	53	6	pointwise	pointwise	ADJ
ejpam-4810	53	7	non	non	ADJ
ejpam-4810	53	8	-	-	ADJ
ejpam-4810	53	9	dominating	dominating	ADJ
ejpam-4810	53	10	set	set	NOUN
ejpam-4810	53	11	of	of	ADP
ejpam-4810	53	12	g	g	NOUN
ejpam-4810	53	13	,	,	PUNCT
ejpam-4810	53	14	denoted	denote	VERB
ejpam-4810	53	15	by	by	ADP
ejpam-4810	53	16	pnd(g	pnd(g	PROPN
ejpam-4810	53	17	)	)	PUNCT
ejpam-4810	53	18	,	,	PUNCT
ejpam-4810	53	19	is	be	AUX
ejpam-4810	53	20	called	call	VERB
ejpam-4810	53	21	the	the	DET
ejpam-4810	53	22	pointwise	pointwise	ADJ
ejpam-4810	53	23	non	non	ADJ
ejpam-4810	53	24	-	-	ADJ
ejpam-4810	53	25	domination	domination	ADJ
ejpam-4810	53	26	number	number	NOUN
ejpam-4810	53	27	of	of	ADP
ejpam-4810	53	28	g.	g.	PROPN
ejpam-4810	53	29	a	a	DET
ejpam-4810	53	30	pointwise	pointwise	ADJ
ejpam-4810	53	31	non	non	ADJ
ejpam-4810	53	32	-	-	ADJ
ejpam-4810	53	33	dominating	dominating	ADJ
ejpam-4810	53	34	set	set	NOUN
ejpam-4810	53	35	s	s	PROPN
ejpam-4810	53	36	⊆	⊆	NUM
ejpam-4810	53	37	v	v	NOUN
ejpam-4810	53	38	(	(	PUNCT
ejpam-4810	53	39	g	g	NOUN
ejpam-4810	53	40	)	)	PUNCT
ejpam-4810	53	41	of	of	ADP
ejpam-4810	53	42	a	a	DET
ejpam-4810	53	43	graph	graph	NOUN
ejpam-4810	53	44	g	g	NOUN
ejpam-4810	53	45	is	be	AUX
ejpam-4810	53	46	called	call	VERB
ejpam-4810	53	47	a	a	DET
ejpam-4810	53	48	2	2	NUM
ejpam-4810	53	49	-	-	PUNCT
ejpam-4810	53	50	path	path	NOUN
ejpam-4810	53	51	closure	closure	NOUN
ejpam-4810	53	52	absorbing	absorb	VERB
ejpam-4810	53	53	pointwise	pointwise	PROPN
ejpam-4810	53	54	non	non	ADJ
ejpam-4810	53	55	-	-	ADJ
ejpam-4810	53	56	dominating	dominating	ADJ
ejpam-4810	53	57	set	set	NOUN
ejpam-4810	53	58	if	if	SCONJ
ejpam-4810	53	59	it	it	PRON
ejpam-4810	53	60	is	be	AUX
ejpam-4810	53	61	a	a	DET
ejpam-4810	53	62	2	2	NUM
ejpam-4810	53	63	-	-	PUNCT
ejpam-4810	53	64	path	path	NOUN
ejpam-4810	53	65	closure	closure	NOUN
ejpam-4810	53	66	absorbing	absorb	VERB
ejpam-4810	53	67	set	set	NOUN
ejpam-4810	53	68	.	.	PUNCT
ejpam-4810	54	1	the	the	DET
ejpam-4810	54	2	minimum	minimum	ADJ
ejpam-4810	54	3	cardinality	cardinality	NOUN
ejpam-4810	54	4	of	of	ADP
ejpam-4810	54	5	a	a	DET
ejpam-4810	54	6	2	2	NUM
ejpam-4810	54	7	-	-	PUNCT
ejpam-4810	54	8	path	path	NOUN
ejpam-4810	54	9	closure	closure	NOUN
ejpam-4810	54	10	absorbing	absorb	VERB
ejpam-4810	54	11	pointwise	pointwise	PROPN
ejpam-4810	54	12	non	non	ADJ
ejpam-4810	54	13	-	-	ADJ
ejpam-4810	54	14	dominating	dominating	ADJ
ejpam-4810	54	15	set	set	NOUN
ejpam-4810	54	16	in	in	ADP
ejpam-4810	54	17	g	g	PROPN
ejpam-4810	54	18	is	be	AUX
ejpam-4810	54	19	denoted	denote	VERB
ejpam-4810	54	20	by	by	ADP
ejpam-4810	54	21	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	54	22	)	)	PUNCT
ejpam-4810	54	23	.	.	PUNCT
ejpam-4810	55	1	any	any	DET
ejpam-4810	55	2	2	2	NUM
ejpam-4810	55	3	-	-	PUNCT
ejpam-4810	55	4	path	path	NOUN
ejpam-4810	55	5	closure	closure	NOUN
ejpam-4810	55	6	absorbing	absorb	VERB
ejpam-4810	55	7	pointwise	pointwise	PROPN
ejpam-4810	55	8	non	non	ADJ
ejpam-4810	55	9	-	-	ADJ
ejpam-4810	55	10	dominating	dominating	ADJ
ejpam-4810	55	11	set	set	NOUN
ejpam-4810	55	12	of	of	ADP
ejpam-4810	55	13	g	g	PROPN
ejpam-4810	55	14	c.j	c.j	PROPN
ejpam-4810	55	15	.	.	PROPN
ejpam-4810	55	16	saromines	saromines	PROPN
ejpam-4810	55	17	,	,	PUNCT
ejpam-4810	55	18	s.	s.	PROPN
ejpam-4810	55	19	canoy	canoy	PROPN
ejpam-4810	55	20	,	,	PUNCT
ejpam-4810	55	21	jr	jr	PROPN
ejpam-4810	55	22	.	.	PROPN
ejpam-4810	55	23	,	,	PUNCT
ejpam-4810	55	24	/	/	SYM
ejpam-4810	55	25	eur	eur	NOUN
ejpam-4810	55	26	.	.	PUNCT
ejpam-4810	56	1	j.	j.	PROPN
ejpam-4810	56	2	pure	pure	PROPN
ejpam-4810	56	3	appl	appl	PROPN
ejpam-4810	56	4	.	.	PROPN
ejpam-4810	56	5	math	math	PROPN
ejpam-4810	56	6	,	,	PUNCT
ejpam-4810	56	7	16	16	NUM
ejpam-4810	56	8	(	(	PUNCT
ejpam-4810	56	9	3	3	NUM
ejpam-4810	56	10	)	)	PUNCT
ejpam-4810	56	11	(	(	PUNCT
ejpam-4810	56	12	2023	2023	NUM
ejpam-4810	56	13	)	)	PUNCT
ejpam-4810	56	14	,	,	PUNCT
ejpam-4810	56	15	1568	1568	NUM
ejpam-4810	56	16	-	-	SYM
ejpam-4810	56	17	1579	1579	NUM
ejpam-4810	56	18	1570	1570	NUM
ejpam-4810	56	19	with	with	ADP
ejpam-4810	56	20	cardinality	cardinality	PROPN
ejpam-4810	56	21	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	56	22	)	)	PUNCT
ejpam-4810	56	23	is	be	AUX
ejpam-4810	56	24	called	call	VERB
ejpam-4810	56	25	a	a	DET
ejpam-4810	56	26	ρ2pnd	ρ2pnd	ADV
ejpam-4810	56	27	-	-	PUNCT
ejpam-4810	56	28	set	set	NOUN
ejpam-4810	56	29	.	.	PUNCT
ejpam-4810	57	1	let	let	VERB
ejpam-4810	57	2	g	g	NOUN
ejpam-4810	57	3	and	and	CCONJ
ejpam-4810	57	4	h	h	NOUN
ejpam-4810	57	5	be	be	VERB
ejpam-4810	57	6	two	two	NUM
ejpam-4810	57	7	graphs	graph	NOUN
ejpam-4810	57	8	.	.	PUNCT
ejpam-4810	58	1	the	the	DET
ejpam-4810	58	2	join	join	NOUN
ejpam-4810	58	3	g+h	g+h	PROPN
ejpam-4810	58	4	is	be	AUX
ejpam-4810	58	5	the	the	DET
ejpam-4810	58	6	graph	graph	NOUN
ejpam-4810	58	7	with	with	ADP
ejpam-4810	58	8	vertex	vertex	NOUN
ejpam-4810	58	9	set	set	VERB
ejpam-4810	58	10	v	v	NOUN
ejpam-4810	58	11	(	(	PUNCT
ejpam-4810	58	12	g+h	g+h	NOUN
ejpam-4810	58	13	)	)	PUNCT
ejpam-4810	58	14	=	=	SYM
ejpam-4810	58	15	v	v	X
ejpam-4810	58	16	(	(	PUNCT
ejpam-4810	58	17	g	g	NOUN
ejpam-4810	58	18	)	)	PUNCT
ejpam-4810	58	19	∪	∪	NOUN
ejpam-4810	58	20	v	v	NOUN
ejpam-4810	58	21	(	(	PUNCT
ejpam-4810	58	22	h	h	NOUN
ejpam-4810	58	23	)	)	PUNCT
ejpam-4810	58	24	and	and	CCONJ
ejpam-4810	58	25	edge	edge	NOUN
ejpam-4810	58	26	set	set	VERB
ejpam-4810	58	27	e(g+h	e(g+h	NUM
ejpam-4810	58	28	)	)	PUNCT
ejpam-4810	58	29	=	=	SYM
ejpam-4810	58	30	e(g	e(g	NOUN
ejpam-4810	58	31	)	)	PUNCT
ejpam-4810	58	32	∪	∪	ADP
ejpam-4810	58	33	e(h	e(h	PROPN
ejpam-4810	58	34	)	)	PUNCT
ejpam-4810	58	35	∪	∪	NOUN
ejpam-4810	58	36	{	{	PUNCT
ejpam-4810	58	37	uv	uv	NOUN
ejpam-4810	58	38	:	:	PUNCT
ejpam-4810	58	39	u	u	PROPN
ejpam-4810	58	40	∈	∈	PROPN
ejpam-4810	58	41	v	v	ADP
ejpam-4810	58	42	(	(	PUNCT
ejpam-4810	58	43	g	g	NOUN
ejpam-4810	58	44	)	)	PUNCT
ejpam-4810	58	45	,	,	PUNCT
ejpam-4810	58	46	v	v	X
ejpam-4810	58	47	∈	∈	PROPN
ejpam-4810	58	48	v	v	NOUN
ejpam-4810	58	49	(	(	PUNCT
ejpam-4810	58	50	h	h	NOUN
ejpam-4810	58	51	)	)	PUNCT
ejpam-4810	58	52	}	}	PUNCT
ejpam-4810	58	53	.	.	PUNCT
ejpam-4810	59	1	3	3	X
ejpam-4810	59	2	.	.	X
ejpam-4810	59	3	results	result	NOUN
ejpam-4810	59	4	since	since	SCONJ
ejpam-4810	59	5	every	every	DET
ejpam-4810	59	6	geodetic	geodetic	ADJ
ejpam-4810	59	7	hop	hop	NOUN
ejpam-4810	59	8	dominating	dominating	NOUN
ejpam-4810	59	9	set	set	NOUN
ejpam-4810	59	10	is	be	AUX
ejpam-4810	59	11	a	a	DET
ejpam-4810	59	12	hop	hop	NOUN
ejpam-4810	59	13	dominating	dominating	NOUN
ejpam-4810	59	14	set	set	NOUN
ejpam-4810	59	15	,	,	PUNCT
ejpam-4810	59	16	we	we	PRON
ejpam-4810	59	17	have	have	VERB
ejpam-4810	59	18	the	the	DET
ejpam-4810	59	19	following	follow	VERB
ejpam-4810	59	20	remark	remark	NOUN
ejpam-4810	59	21	.	.	PUNCT
ejpam-4810	60	1	remark	remark	PROPN
ejpam-4810	60	2	1	1	NUM
ejpam-4810	60	3	.	.	PUNCT
ejpam-4810	61	1	let	let	VERB
ejpam-4810	61	2	g	g	NOUN
ejpam-4810	61	3	be	be	AUX
ejpam-4810	61	4	any	any	DET
ejpam-4810	61	5	connected	connected	ADJ
ejpam-4810	61	6	graph	graph	NOUN
ejpam-4810	61	7	on	on	ADP
ejpam-4810	61	8	n	n	DET
ejpam-4810	61	9	vertices	vertex	NOUN
ejpam-4810	61	10	.	.	PUNCT
ejpam-4810	62	1	then	then	ADV
ejpam-4810	62	2	γh(g	γh(g	PUNCT
ejpam-4810	62	3	)	)	PUNCT
ejpam-4810	62	4	≤	≤	NUM
ejpam-4810	62	5	γhg(g	γhg(g	PROPN
ejpam-4810	62	6	)	)	PUNCT
ejpam-4810	62	7	.	.	PUNCT
ejpam-4810	63	1	remark	remark	NOUN
ejpam-4810	63	2	2	2	NUM
ejpam-4810	63	3	.	.	PUNCT
ejpam-4810	64	1	the	the	DET
ejpam-4810	64	2	bound	bind	VERB
ejpam-4810	64	3	given	give	VERB
ejpam-4810	64	4	in	in	ADP
ejpam-4810	64	5	remark	remark	NOUN
ejpam-4810	64	6	1	1	NUM
ejpam-4810	64	7	is	be	AUX
ejpam-4810	64	8	tight	tight	ADJ
ejpam-4810	64	9	.	.	PUNCT
ejpam-4810	65	1	moreover	moreover	ADV
ejpam-4810	65	2	,	,	PUNCT
ejpam-4810	65	3	strict	strict	ADJ
ejpam-4810	65	4	inequality	inequality	NOUN
ejpam-4810	65	5	can	can	AUX
ejpam-4810	65	6	also	also	ADV
ejpam-4810	65	7	be	be	AUX
ejpam-4810	65	8	attained	attain	VERB
ejpam-4810	65	9	.	.	PUNCT
ejpam-4810	66	1	to	to	PART
ejpam-4810	66	2	see	see	VERB
ejpam-4810	66	3	this	this	PRON
ejpam-4810	66	4	,	,	PUNCT
ejpam-4810	66	5	consider	consider	VERB
ejpam-4810	66	6	g	g	NOUN
ejpam-4810	66	7	=	=	NOUN
ejpam-4810	66	8	k4	k4	NOUN
ejpam-4810	66	9	and	and	CCONJ
ejpam-4810	66	10	h	h	NOUN
ejpam-4810	66	11	=	=	SYM
ejpam-4810	66	12	k1,3	k1,3	PROPN
ejpam-4810	66	13	.	.	PUNCT
ejpam-4810	67	1	it	it	PRON
ejpam-4810	67	2	can	can	AUX
ejpam-4810	67	3	easily	easily	ADV
ejpam-4810	67	4	be	be	AUX
ejpam-4810	67	5	verified	verify	VERB
ejpam-4810	67	6	that	that	SCONJ
ejpam-4810	67	7	γh(g	γh(g	NOUN
ejpam-4810	67	8	)	)	PUNCT
ejpam-4810	67	9	=	=	SYM
ejpam-4810	67	10	γhg(g	γhg(g	PROPN
ejpam-4810	67	11	)	)	PUNCT
ejpam-4810	67	12	=	=	SYM
ejpam-4810	67	13	4	4	NUM
ejpam-4810	67	14	and	and	CCONJ
ejpam-4810	67	15	γh(h	γh(h	NUM
ejpam-4810	67	16	)	)	PUNCT
ejpam-4810	67	17	=	=	SYM
ejpam-4810	67	18	2	2	NUM
ejpam-4810	67	19	<	<	SYM
ejpam-4810	67	20	4	4	NUM
ejpam-4810	67	21	=	=	SYM
ejpam-4810	67	22	γhg(h	γhg(h	PROPN
ejpam-4810	67	23	)	)	PUNCT
ejpam-4810	67	24	.	.	PUNCT
ejpam-4810	68	1	theorem	theorem	NOUN
ejpam-4810	68	2	1	1	NUM
ejpam-4810	68	3	.	.	PUNCT
ejpam-4810	69	1	let	let	VERB
ejpam-4810	69	2	a	a	PRON
ejpam-4810	69	3	and	and	CCONJ
ejpam-4810	69	4	b	b	NOUN
ejpam-4810	69	5	be	be	AUX
ejpam-4810	69	6	positive	positive	ADJ
ejpam-4810	69	7	integers	integer	NOUN
ejpam-4810	69	8	such	such	ADJ
ejpam-4810	69	9	that	that	SCONJ
ejpam-4810	69	10	2	2	NUM
ejpam-4810	69	11	≤	≤	NUM
ejpam-4810	69	12	a	a	DET
ejpam-4810	69	13	≤	≤	PROPN
ejpam-4810	69	14	b.	b.	NOUN
ejpam-4810	70	1	then	then	ADV
ejpam-4810	70	2	there	there	PRON
ejpam-4810	70	3	exists	exist	VERB
ejpam-4810	70	4	a	a	DET
ejpam-4810	70	5	connected	connected	ADJ
ejpam-4810	70	6	graph	graph	NOUN
ejpam-4810	70	7	g	g	ADP
ejpam-4810	70	8	such	such	ADJ
ejpam-4810	70	9	that	that	PRON
ejpam-4810	70	10	γh(g	γh(g	NOUN
ejpam-4810	70	11	)	)	PUNCT
ejpam-4810	70	12	=	=	PUNCT
ejpam-4810	70	13	a	a	PROPN
ejpam-4810	70	14	and	and	CCONJ
ejpam-4810	70	15	γhg(g	γhg(g	NUM
ejpam-4810	70	16	)	)	PUNCT
ejpam-4810	70	17	=	=	SYM
ejpam-4810	70	18	b.	b.	PROPN
ejpam-4810	70	19	proof	proof	NOUN
ejpam-4810	70	20	.	.	PUNCT
ejpam-4810	71	1	consider	consider	VERB
ejpam-4810	71	2	the	the	DET
ejpam-4810	71	3	following	follow	VERB
ejpam-4810	71	4	cases	case	NOUN
ejpam-4810	71	5	:	:	PUNCT
ejpam-4810	71	6	case	case	NOUN
ejpam-4810	71	7	1	1	NUM
ejpam-4810	71	8	.	.	PUNCT
ejpam-4810	72	1	a	a	DET
ejpam-4810	72	2	=	=	X
ejpam-4810	72	3	b.	b.	PROPN
ejpam-4810	72	4	let	let	VERB
ejpam-4810	72	5	g	g	PROPN
ejpam-4810	72	6	=	=	SYM
ejpam-4810	72	7	ka	ka	PROPN
ejpam-4810	72	8	.	.	PROPN
ejpam-4810	72	9	then	then	ADV
ejpam-4810	72	10	γh(g	γh(g	NOUN
ejpam-4810	72	11	)	)	PUNCT
ejpam-4810	72	12	=	=	SYM
ejpam-4810	72	13	a	a	DET
ejpam-4810	72	14	=	=	SYM
ejpam-4810	72	15	γhg(g	γhg(g	PROPN
ejpam-4810	72	16	)	)	PUNCT
ejpam-4810	72	17	.	.	PUNCT
ejpam-4810	73	1	case	case	NOUN
ejpam-4810	73	2	2	2	NUM
ejpam-4810	73	3	.	.	PUNCT
ejpam-4810	74	1	a	a	DET
ejpam-4810	74	2	<	<	X
ejpam-4810	74	3	b.	b.	PROPN
ejpam-4810	74	4	consider	consider	VERB
ejpam-4810	74	5	the	the	DET
ejpam-4810	74	6	following	follow	VERB
ejpam-4810	74	7	subcases	subcase	NOUN
ejpam-4810	74	8	:	:	PUNCT
ejpam-4810	74	9	subcase	subcase	NOUN
ejpam-4810	74	10	2.1	2.1	NUM
ejpam-4810	74	11	.	.	PUNCT
ejpam-4810	75	1	a	a	PRON
ejpam-4810	75	2	is	be	AUX
ejpam-4810	75	3	even	even	ADV
ejpam-4810	75	4	.	.	PUNCT
ejpam-4810	76	1	suppose	suppose	VERB
ejpam-4810	76	2	a	a	DET
ejpam-4810	76	3	=	=	SYM
ejpam-4810	76	4	2	2	NUM
ejpam-4810	76	5	and	and	CCONJ
ejpam-4810	76	6	let	let	VERB
ejpam-4810	76	7	m	m	PROPN
ejpam-4810	76	8	=	=	NOUN
ejpam-4810	76	9	b−a	b−a	NOUN
ejpam-4810	76	10	.	.	PUNCT
ejpam-4810	77	1	consider	consider	VERB
ejpam-4810	77	2	the	the	DET
ejpam-4810	77	3	graph	graph	NOUN
ejpam-4810	77	4	g	g	NOUN
ejpam-4810	77	5	in	in	ADP
ejpam-4810	77	6	figure	figure	NOUN
ejpam-4810	77	7	1	1	NUM
ejpam-4810	77	8	.	.	PUNCT
ejpam-4810	78	1	let	let	VERB
ejpam-4810	78	2	s1	s1	PROPN
ejpam-4810	78	3	=	=	PUNCT
ejpam-4810	78	4	{	{	PUNCT
ejpam-4810	78	5	x1	x1	PROPN
ejpam-4810	78	6	,	,	PUNCT
ejpam-4810	78	7	x2	x2	PROPN
ejpam-4810	78	8	}	}	PUNCT
ejpam-4810	78	9	and	and	CCONJ
ejpam-4810	78	10	s2	s2	VERB
ejpam-4810	78	11	=	=	SYM
ejpam-4810	78	12	{	{	PUNCT
ejpam-4810	78	13	y1	y1	PROPN
ejpam-4810	78	14	,	,	PUNCT
ejpam-4810	78	15	y2	y2	PROPN
ejpam-4810	78	16	,	,	PUNCT
ejpam-4810	78	17	z1	z1	PROPN
ejpam-4810	78	18	,	,	PUNCT
ejpam-4810	78	19	z2	z2	PROPN
ejpam-4810	78	20	,	,	PUNCT
ejpam-4810	78	21	...	...	PUNCT
ejpam-4810	78	22	,	,	PUNCT
ejpam-4810	78	23	zm	zm	PROPN
ejpam-4810	78	24	}	}	PUNCT
ejpam-4810	78	25	.	.	PUNCT
ejpam-4810	79	1	then	then	ADV
ejpam-4810	79	2	s1	s1	PROPN
ejpam-4810	79	3	and	and	CCONJ
ejpam-4810	79	4	s2	s2	PROPN
ejpam-4810	79	5	are	be	AUX
ejpam-4810	79	6	,	,	PUNCT
ejpam-4810	79	7	respectively	respectively	ADV
ejpam-4810	79	8	,	,	PUNCT
ejpam-4810	79	9	γh	γh	ADV
ejpam-4810	79	10	-	-	PUNCT
ejpam-4810	79	11	set	set	VERB
ejpam-4810	79	12	and	and	CCONJ
ejpam-4810	79	13	γhg	γhg	VERB
ejpam-4810	79	14	-	-	PUNCT
ejpam-4810	79	15	set	set	NOUN
ejpam-4810	79	16	of	of	ADP
ejpam-4810	79	17	g.	g.	PROPN
ejpam-4810	79	18	hence	hence	ADV
ejpam-4810	79	19	,	,	PUNCT
ejpam-4810	79	20	γh(g	γh(g	NOUN
ejpam-4810	79	21	)	)	PUNCT
ejpam-4810	79	22	=	=	SYM
ejpam-4810	79	23	a	a	PROPN
ejpam-4810	79	24	and	and	CCONJ
ejpam-4810	79	25	γhg(g	γhg(g	NUM
ejpam-4810	79	26	)	)	PUNCT
ejpam-4810	79	27	=	=	PUNCT
ejpam-4810	80	1	a+m	a+m	NUM
ejpam-4810	80	2	=	=	SYM
ejpam-4810	80	3	b.	b.	PROPN
ejpam-4810	80	4	....................................	....................................	PUNCT
ejpam-4810	80	5	....................................	....................................	PUNCT
ejpam-4810	80	6	....................................	....................................	PUNCT
ejpam-4810	80	7	....................................	....................................	PUNCT
ejpam-4810	80	8	....................................	....................................	PUNCT
ejpam-4810	80	9	....................................	....................................	PUNCT
ejpam-4810	80	10	....................................	....................................	PUNCT
ejpam-4810	80	11	....................................	....................................	PUNCT
ejpam-4810	80	12	.........	.........	PUNCT
ejpam-4810	80	13	........	........	PUNCT
ejpam-4810	80	14	........	........	PUNCT
ejpam-4810	80	15	........	........	PUNCT
ejpam-4810	80	16	........	........	PUNCT
ejpam-4810	80	17	........	........	PUNCT
ejpam-4810	80	18	........	........	PUNCT
ejpam-4810	80	19	........	........	PUNCT
ejpam-4810	80	20	........	........	PUNCT
ejpam-4810	80	21	........	........	PUNCT
ejpam-4810	80	22	........	........	PUNCT
ejpam-4810	80	23	........	........	PUNCT
ejpam-4810	80	24	........	........	PUNCT
ejpam-4810	80	25	........	........	PUNCT
ejpam-4810	80	26	........	........	PUNCT
ejpam-4810	80	27	........	........	PUNCT
ejpam-4810	80	28	........	........	PUNCT
ejpam-4810	80	29	........	........	PUNCT
ejpam-4810	80	30	........	........	PUNCT
ejpam-4810	80	31	........	........	PUNCT
ejpam-4810	80	32	.	.	PUNCT
ejpam-4810	80	33	....................................	....................................	PUNCT
ejpam-4810	81	1	....................................	....................................	PUNCT
ejpam-4810	81	2	.........	.........	PUNCT
ejpam-4810	82	1	........	........	PUNCT
ejpam-4810	82	2	........	........	PUNCT
ejpam-4810	82	3	........	........	PUNCT
ejpam-4810	82	4	........	........	PUNCT
ejpam-4810	82	5	........	........	PUNCT
ejpam-4810	82	6	........	........	PUNCT
ejpam-4810	82	7	........	........	PUNCT
ejpam-4810	82	8	........	........	PUNCT
ejpam-4810	82	9	........	........	PUNCT
ejpam-4810	82	10	........	........	PUNCT
ejpam-4810	82	11	........	........	PUNCT
ejpam-4810	82	12	........	........	PUNCT
ejpam-4810	82	13	........	........	PUNCT
ejpam-4810	82	14	........	........	PUNCT
ejpam-4810	82	15	........	........	PUNCT
ejpam-4810	82	16	........	........	PUNCT
ejpam-4810	82	17	........	........	PUNCT
ejpam-4810	82	18	........	........	PUNCT
ejpam-4810	82	19	........	........	PUNCT
ejpam-4810	82	20	.	.	PUNCT
ejpam-4810	83	1	....................................	....................................	PUNCT
ejpam-4810	83	2	....................................	....................................	PUNCT
ejpam-4810	83	3	...................................................................................	...................................................................................	PUNCT
ejpam-4810	83	4	...................................................................................	...................................................................................	PUNCT
ejpam-4810	84	1	....................................	....................................	PUNCT
ejpam-4810	84	2	...........	...........	PUNCT
ejpam-4810	85	1	..........	..........	PUNCT
ejpam-4810	85	2	..........	..........	PUNCT
ejpam-4810	86	1	..........	..........	PUNCT
ejpam-4810	86	2	..........	..........	PUNCT
ejpam-4810	87	1	..........	..........	PUNCT
ejpam-4810	87	2	..........	..........	PUNCT
ejpam-4810	88	1	..........	..........	PUNCT
ejpam-4810	88	2	..........	..........	PUNCT
ejpam-4810	89	1	..........	..........	PUNCT
ejpam-4810	89	2	..........	..........	PUNCT
ejpam-4810	90	1	..........	..........	PUNCT
ejpam-4810	90	2	..........	..........	PUNCT
ejpam-4810	91	1	..........	..........	PUNCT
ejpam-4810	91	2	..........	..........	PUNCT
ejpam-4810	92	1	......	......	PUNCT
ejpam-4810	92	2	....................................	....................................	PUNCT
ejpam-4810	93	1	...........	...........	PUNCT
ejpam-4810	93	2	..........	..........	PUNCT
ejpam-4810	94	1	..........	..........	PUNCT
ejpam-4810	94	2	..........	..........	PUNCT
ejpam-4810	95	1	..........	..........	PUNCT
ejpam-4810	95	2	..........	..........	PUNCT
ejpam-4810	96	1	..........	..........	PUNCT
ejpam-4810	96	2	..........	..........	PUNCT
ejpam-4810	97	1	..........	..........	PUNCT
ejpam-4810	97	2	..........	..........	PUNCT
ejpam-4810	98	1	..........	..........	PUNCT
ejpam-4810	98	2	..........	..........	PUNCT
ejpam-4810	99	1	..........	..........	PUNCT
ejpam-4810	99	2	..........	..........	PUNCT
ejpam-4810	100	1	..........	..........	PUNCT
ejpam-4810	100	2	......	......	PUNCT
ejpam-4810	101	1	....................................	....................................	PUNCT
ejpam-4810	101	2	............	............	PUNCT
ejpam-4810	101	3	...........	...........	PUNCT
ejpam-4810	101	4	...........	...........	PUNCT
ejpam-4810	101	5	...........	...........	PUNCT
ejpam-4810	101	6	...........	...........	PUNCT
ejpam-4810	101	7	...........	...........	PUNCT
ejpam-4810	101	8	...........	...........	PUNCT
ejpam-4810	101	9	...........	...........	PUNCT
ejpam-4810	101	10	...........	...........	PUNCT
ejpam-4810	101	11	...........	...........	PUNCT
ejpam-4810	101	12	....................................	....................................	PUNCT
ejpam-4810	101	13	............	............	PUNCT
ejpam-4810	101	14	...........	...........	PUNCT
ejpam-4810	101	15	...........	...........	PUNCT
ejpam-4810	101	16	...........	...........	PUNCT
ejpam-4810	101	17	...........	...........	PUNCT
ejpam-4810	101	18	...........	...........	PUNCT
ejpam-4810	101	19	...........	...........	PUNCT
ejpam-4810	101	20	...........	...........	PUNCT
ejpam-4810	101	21	...........	...........	PUNCT
ejpam-4810	101	22	...........	...........	PUNCT
ejpam-4810	101	23	....................................	....................................	PUNCT
ejpam-4810	101	24	................................................................................	................................................................................	PUNCT
ejpam-4810	102	1	....................................	....................................	PUNCT
ejpam-4810	102	2	....................................	....................................	PUNCT
ejpam-4810	103	1	...	...	PUNCT
ejpam-4810	104	1	y1	y1	INTJ
ejpam-4810	105	1	y2	y2	NOUN
ejpam-4810	105	2	x1	x1	NOUN
ejpam-4810	105	3	x2	x2	PROPN
ejpam-4810	105	4	z1	z1	PROPN
ejpam-4810	105	5	z2	z2	PROPN
ejpam-4810	105	6	zm	zm	PROPN
ejpam-4810	105	7	g	g	PROPN
ejpam-4810	105	8	:	:	PUNCT
ejpam-4810	105	9	figure	figure	NOUN
ejpam-4810	105	10	1	1	NUM
ejpam-4810	105	11	suppose	suppose	VERB
ejpam-4810	105	12	a	a	DET
ejpam-4810	105	13	≥	≥	NOUN
ejpam-4810	105	14	4	4	NUM
ejpam-4810	105	15	.	.	PUNCT
ejpam-4810	105	16	consider	consider	VERB
ejpam-4810	105	17	the	the	DET
ejpam-4810	105	18	graph	graph	NOUN
ejpam-4810	105	19	g′	g′	NOUN
ejpam-4810	105	20	in	in	ADP
ejpam-4810	105	21	figure	figure	NOUN
ejpam-4810	105	22	2	2	NUM
ejpam-4810	105	23	.	.	PUNCT
ejpam-4810	105	24	let	let	VERB
ejpam-4810	105	25	s3	s3	PROPN
ejpam-4810	105	26	=	=	SYM
ejpam-4810	105	27	{	{	PUNCT
ejpam-4810	105	28	x1	x1	PROPN
ejpam-4810	105	29	,	,	PUNCT
ejpam-4810	105	30	x2	x2	PROPN
ejpam-4810	105	31	,	,	PUNCT
ejpam-4810	105	32	...	...	PUNCT
ejpam-4810	105	33	,	,	PUNCT
ejpam-4810	105	34	xa−1	xa−1	PROPN
ejpam-4810	105	35	,	,	PUNCT
ejpam-4810	105	36	xa	xa	PROPN
ejpam-4810	105	37	}	}	PUNCT
ejpam-4810	105	38	and	and	CCONJ
ejpam-4810	105	39	s4	s4	PROPN
ejpam-4810	105	40	=	=	SYM
ejpam-4810	105	41	{	{	PUNCT
ejpam-4810	105	42	y1	y1	PROPN
ejpam-4810	105	43	,	,	PUNCT
ejpam-4810	105	44	y2	y2	PROPN
ejpam-4810	105	45	,	,	PUNCT
ejpam-4810	105	46	...	...	PUNCT
ejpam-4810	105	47	,	,	PUNCT
ejpam-4810	105	48	ya−1	ya−1	PROPN
ejpam-4810	105	49	,	,	PUNCT
ejpam-4810	105	50	ya	ya	PROPN
ejpam-4810	105	51	,	,	PUNCT
ejpam-4810	105	52	z1	z1	PROPN
ejpam-4810	105	53	,	,	PUNCT
ejpam-4810	105	54	z2	z2	PROPN
ejpam-4810	105	55	,	,	PUNCT
ejpam-4810	105	56	...	...	PUNCT
ejpam-4810	105	57	,	,	PUNCT
ejpam-4810	105	58	zm	zm	PROPN
ejpam-4810	105	59	}	}	PUNCT
ejpam-4810	105	60	.	.	PUNCT
ejpam-4810	106	1	then	then	ADV
ejpam-4810	106	2	s3	s3	PROPN
ejpam-4810	106	3	and	and	CCONJ
ejpam-4810	106	4	s4	s4	PROPN
ejpam-4810	106	5	are	be	AUX
ejpam-4810	106	6	,	,	PUNCT
ejpam-4810	106	7	respectively	respectively	ADV
ejpam-4810	106	8	,	,	PUNCT
ejpam-4810	106	9	γh	γh	ADV
ejpam-4810	106	10	-	-	PUNCT
ejpam-4810	106	11	set	set	VERB
ejpam-4810	106	12	and	and	CCONJ
ejpam-4810	106	13	γhg	γhg	VERB
ejpam-4810	106	14	-	-	PUNCT
ejpam-4810	106	15	set	set	NOUN
ejpam-4810	106	16	of	of	ADP
ejpam-4810	106	17	g	g	PROPN
ejpam-4810	106	18	′.	′.	NOUN
ejpam-4810	106	19	hence	hence	ADV
ejpam-4810	106	20	,	,	PUNCT
ejpam-4810	106	21	γh(g	γh(g	PUNCT
ejpam-4810	106	22	′	′	NUM
ejpam-4810	106	23	)	)	PUNCT
ejpam-4810	106	24	=	=	PUNCT
ejpam-4810	106	25	a	a	PRON
ejpam-4810	106	26	and	and	CCONJ
ejpam-4810	106	27	γhg(g	γhg(g	PROPN
ejpam-4810	106	28	′	′	NUM
ejpam-4810	106	29	)	)	PUNCT
ejpam-4810	107	1	=	=	PUNCT
ejpam-4810	107	2	a+m	a+m	NUM
ejpam-4810	107	3	=	=	PUNCT
ejpam-4810	107	4	b.	b.	PROPN
ejpam-4810	107	5	c.j	c.j	PROPN
ejpam-4810	107	6	.	.	PROPN
ejpam-4810	107	7	saromines	saromines	PROPN
ejpam-4810	107	8	,	,	PUNCT
ejpam-4810	107	9	s.	s.	PROPN
ejpam-4810	107	10	canoy	canoy	PROPN
ejpam-4810	107	11	,	,	PUNCT
ejpam-4810	107	12	jr	jr	PROPN
ejpam-4810	107	13	.	.	PROPN
ejpam-4810	107	14	,	,	PUNCT
ejpam-4810	107	15	/	/	SYM
ejpam-4810	107	16	eur	eur	NOUN
ejpam-4810	107	17	.	.	PUNCT
ejpam-4810	108	1	j.	j.	PROPN
ejpam-4810	108	2	pure	pure	PROPN
ejpam-4810	108	3	appl	appl	PROPN
ejpam-4810	108	4	.	.	PROPN
ejpam-4810	108	5	math	math	PROPN
ejpam-4810	108	6	,	,	PUNCT
ejpam-4810	108	7	16	16	NUM
ejpam-4810	108	8	(	(	PUNCT
ejpam-4810	108	9	3	3	NUM
ejpam-4810	108	10	)	)	PUNCT
ejpam-4810	108	11	(	(	PUNCT
ejpam-4810	108	12	2023	2023	NUM
ejpam-4810	108	13	)	)	PUNCT
ejpam-4810	108	14	,	,	PUNCT
ejpam-4810	108	15	1568	1568	NUM
ejpam-4810	108	16	-	-	SYM
ejpam-4810	108	17	1579	1579	NUM
ejpam-4810	108	18	1571	1571	NUM
ejpam-4810	108	19	....................................	....................................	PUNCT
ejpam-4810	108	20	....................................	....................................	PUNCT
ejpam-4810	109	1	....................................	....................................	PUNCT
ejpam-4810	109	2	....................................	....................................	PUNCT
ejpam-4810	110	1	....................................	....................................	PUNCT
ejpam-4810	110	2	....................................	....................................	PUNCT
ejpam-4810	111	1	....................................	....................................	PUNCT
ejpam-4810	111	2	....................................	....................................	PUNCT
ejpam-4810	112	1	....................................	....................................	PUNCT
ejpam-4810	112	2	....................................	....................................	PUNCT
ejpam-4810	113	1	....................................	....................................	PUNCT
ejpam-4810	113	2	....................................	....................................	PUNCT
ejpam-4810	114	1	....................................	....................................	PUNCT
ejpam-4810	114	2	....................................	....................................	PUNCT
ejpam-4810	115	1	....................................	....................................	PUNCT
ejpam-4810	115	2	....................................	....................................	PUNCT
ejpam-4810	116	1	....................................	....................................	PUNCT
ejpam-4810	116	2	....................................	....................................	PUNCT
ejpam-4810	117	1	....................................	....................................	PUNCT
ejpam-4810	117	2	....................................	....................................	PUNCT
ejpam-4810	118	1	....................................	....................................	PUNCT
ejpam-4810	118	2	....................................	....................................	PUNCT
ejpam-4810	119	1	.........	.........	PUNCT
ejpam-4810	119	2	........	........	PUNCT
ejpam-4810	119	3	........	........	PUNCT
ejpam-4810	119	4	........	........	PUNCT
ejpam-4810	119	5	........	........	PUNCT
ejpam-4810	119	6	........	........	PUNCT
ejpam-4810	119	7	........	........	PUNCT
ejpam-4810	119	8	........	........	PUNCT
ejpam-4810	119	9	........	........	PUNCT
ejpam-4810	119	10	........	........	PUNCT
ejpam-4810	119	11	........	........	PUNCT
ejpam-4810	119	12	........	........	PUNCT
ejpam-4810	119	13	........	........	PUNCT
ejpam-4810	119	14	........	........	PUNCT
ejpam-4810	119	15	........	........	PUNCT
ejpam-4810	119	16	........	........	PUNCT
ejpam-4810	119	17	........	........	PUNCT
ejpam-4810	119	18	........	........	PUNCT
ejpam-4810	119	19	........	........	PUNCT
ejpam-4810	119	20	........	........	PUNCT
ejpam-4810	119	21	.	.	PUNCT
ejpam-4810	120	1	..	..	PUNCT
ejpam-4810	120	2	..................................	..................................	PUNCT
ejpam-4810	120	3	.......................................................................................................................	.......................................................................................................................	PUNCT
ejpam-4810	121	1	....................................	....................................	PUNCT
ejpam-4810	121	2	.........	.........	PUNCT
ejpam-4810	121	3	........	........	PUNCT
ejpam-4810	121	4	........	........	PUNCT
ejpam-4810	121	5	........	........	PUNCT
ejpam-4810	121	6	........	........	PUNCT
ejpam-4810	121	7	........	........	PUNCT
ejpam-4810	121	8	........	........	PUNCT
ejpam-4810	121	9	........	........	PUNCT
ejpam-4810	121	10	........	........	PUNCT
ejpam-4810	121	11	........	........	PUNCT
ejpam-4810	121	12	........	........	PUNCT
ejpam-4810	121	13	........	........	PUNCT
ejpam-4810	121	14	........	........	PUNCT
ejpam-4810	121	15	........	........	PUNCT
ejpam-4810	121	16	........	........	PUNCT
ejpam-4810	121	17	........	........	PUNCT
ejpam-4810	121	18	........	........	PUNCT
ejpam-4810	121	19	........	........	PUNCT
ejpam-4810	121	20	........	........	PUNCT
ejpam-4810	121	21	........	........	PUNCT
ejpam-4810	121	22	.	.	PUNCT
ejpam-4810	122	1	....................................	....................................	PUNCT
ejpam-4810	122	2	....................................	....................................	PUNCT
ejpam-4810	123	1	.........	.........	PUNCT
ejpam-4810	123	2	........	........	PUNCT
ejpam-4810	123	3	........	........	PUNCT
ejpam-4810	123	4	........	........	PUNCT
ejpam-4810	123	5	........	........	PUNCT
ejpam-4810	123	6	........	........	PUNCT
ejpam-4810	123	7	........	........	PUNCT
ejpam-4810	123	8	........	........	PUNCT
ejpam-4810	123	9	........	........	PUNCT
ejpam-4810	123	10	........	........	PUNCT
ejpam-4810	123	11	........	........	PUNCT
ejpam-4810	123	12	........	........	PUNCT
ejpam-4810	123	13	........	........	PUNCT
ejpam-4810	123	14	........	........	PUNCT
ejpam-4810	123	15	........	........	PUNCT
ejpam-4810	123	16	........	........	PUNCT
ejpam-4810	123	17	........	........	PUNCT
ejpam-4810	123	18	........	........	PUNCT
ejpam-4810	123	19	........	........	PUNCT
ejpam-4810	123	20	........	........	PUNCT
ejpam-4810	123	21	.	.	PUNCT
ejpam-4810	124	1	....................................	....................................	PUNCT
ejpam-4810	124	2	....................................	....................................	PUNCT
ejpam-4810	125	1	.........	.........	PUNCT
ejpam-4810	125	2	........	........	PUNCT
ejpam-4810	125	3	........	........	PUNCT
ejpam-4810	125	4	........	........	PUNCT
ejpam-4810	125	5	........	........	PUNCT
ejpam-4810	125	6	........	........	PUNCT
ejpam-4810	125	7	........	........	PUNCT
ejpam-4810	125	8	........	........	PUNCT
ejpam-4810	125	9	........	........	PUNCT
ejpam-4810	125	10	........	........	PUNCT
ejpam-4810	125	11	........	........	PUNCT
ejpam-4810	125	12	........	........	PUNCT
ejpam-4810	125	13	........	........	PUNCT
ejpam-4810	125	14	........	........	PUNCT
ejpam-4810	125	15	........	........	PUNCT
ejpam-4810	125	16	........	........	PUNCT
ejpam-4810	125	17	........	........	PUNCT
ejpam-4810	125	18	........	........	PUNCT
ejpam-4810	125	19	........	........	PUNCT
ejpam-4810	125	20	........	........	PUNCT
ejpam-4810	125	21	.	.	PUNCT
ejpam-4810	126	1	....................................	....................................	PUNCT
ejpam-4810	126	2	....................................	....................................	PUNCT
ejpam-4810	127	1	.........	.........	PUNCT
ejpam-4810	127	2	........	........	PUNCT
ejpam-4810	127	3	........	........	PUNCT
ejpam-4810	127	4	........	........	PUNCT
ejpam-4810	127	5	........	........	PUNCT
ejpam-4810	127	6	........	........	PUNCT
ejpam-4810	127	7	........	........	PUNCT
ejpam-4810	127	8	........	........	PUNCT
ejpam-4810	127	9	........	........	PUNCT
ejpam-4810	127	10	........	........	PUNCT
ejpam-4810	127	11	........	........	PUNCT
ejpam-4810	127	12	........	........	PUNCT
ejpam-4810	127	13	........	........	PUNCT
ejpam-4810	127	14	........	........	PUNCT
ejpam-4810	127	15	........	........	PUNCT
ejpam-4810	127	16	........	........	PUNCT
ejpam-4810	127	17	........	........	PUNCT
ejpam-4810	127	18	........	........	PUNCT
ejpam-4810	127	19	........	........	PUNCT
ejpam-4810	127	20	........	........	PUNCT
ejpam-4810	127	21	.	.	PUNCT
ejpam-4810	128	1	....................................	....................................	PUNCT
ejpam-4810	128	2	....................................	....................................	PUNCT
ejpam-4810	129	1	...................................................................................	...................................................................................	PUNCT
ejpam-4810	129	2	....................................	....................................	PUNCT
ejpam-4810	130	1	.........	.........	PUNCT
ejpam-4810	130	2	........	........	PUNCT
ejpam-4810	130	3	........	........	PUNCT
ejpam-4810	130	4	........	........	PUNCT
ejpam-4810	130	5	........	........	PUNCT
ejpam-4810	130	6	........	........	PUNCT
ejpam-4810	130	7	........	........	PUNCT
ejpam-4810	130	8	........	........	PUNCT
ejpam-4810	130	9	........	........	PUNCT
ejpam-4810	130	10	........	........	PUNCT
ejpam-4810	130	11	........	........	PUNCT
ejpam-4810	130	12	........	........	PUNCT
ejpam-4810	130	13	........	........	PUNCT
ejpam-4810	130	14	........	........	PUNCT
ejpam-4810	130	15	........	........	PUNCT
ejpam-4810	130	16	........	........	PUNCT
ejpam-4810	130	17	........	........	PUNCT
ejpam-4810	130	18	........	........	PUNCT
ejpam-4810	130	19	........	........	PUNCT
ejpam-4810	130	20	........	........	PUNCT
ejpam-4810	130	21	.	.	PUNCT
ejpam-4810	131	1	....................................	....................................	PUNCT
ejpam-4810	131	2	....................................	....................................	PUNCT
ejpam-4810	131	3	...................................................................................	...................................................................................	PUNCT
ejpam-4810	131	4	...................................................................................	...................................................................................	PUNCT
ejpam-4810	131	5	...................................................................................	...................................................................................	PUNCT
ejpam-4810	131	6	...................................................................................	...................................................................................	PUNCT
ejpam-4810	131	7	...................................................................................	...................................................................................	PUNCT
ejpam-4810	131	8	...................................................................................	...................................................................................	PUNCT
ejpam-4810	132	1	....................................	....................................	PUNCT
ejpam-4810	132	2	...................................................................................	...................................................................................	PUNCT
ejpam-4810	132	3	...................................................................................	...................................................................................	PUNCT
ejpam-4810	132	4	...................................................................................	...................................................................................	PUNCT
ejpam-4810	133	1	....................................	....................................	PUNCT
ejpam-4810	133	2	...........	...........	PUNCT
ejpam-4810	134	1	..........	..........	PUNCT
ejpam-4810	134	2	..........	..........	PUNCT
ejpam-4810	135	1	..........	..........	PUNCT
ejpam-4810	135	2	..........	..........	PUNCT
ejpam-4810	136	1	..........	..........	PUNCT
ejpam-4810	136	2	..........	..........	PUNCT
ejpam-4810	137	1	..........	..........	PUNCT
ejpam-4810	137	2	..........	..........	PUNCT
ejpam-4810	138	1	..........	..........	PUNCT
ejpam-4810	138	2	..........	..........	PUNCT
ejpam-4810	139	1	..........	..........	PUNCT
ejpam-4810	139	2	..........	..........	PUNCT
ejpam-4810	140	1	..........	..........	PUNCT
ejpam-4810	140	2	..........	..........	PUNCT
ejpam-4810	141	1	......	......	PUNCT
ejpam-4810	141	2	....................................	....................................	PUNCT
ejpam-4810	142	1	...........	...........	PUNCT
ejpam-4810	142	2	..........	..........	PUNCT
ejpam-4810	143	1	..........	..........	PUNCT
ejpam-4810	143	2	..........	..........	PUNCT
ejpam-4810	144	1	..........	..........	PUNCT
ejpam-4810	144	2	..........	..........	PUNCT
ejpam-4810	145	1	..........	..........	PUNCT
ejpam-4810	145	2	..........	..........	PUNCT
ejpam-4810	146	1	..........	..........	PUNCT
ejpam-4810	146	2	..........	..........	PUNCT
ejpam-4810	147	1	..........	..........	PUNCT
ejpam-4810	147	2	..........	..........	PUNCT
ejpam-4810	148	1	..........	..........	PUNCT
ejpam-4810	148	2	..........	..........	PUNCT
ejpam-4810	149	1	..........	..........	PUNCT
ejpam-4810	149	2	......	......	PUNCT
ejpam-4810	150	1	....................................	....................................	PUNCT
ejpam-4810	150	2	............	............	PUNCT
ejpam-4810	150	3	...........	...........	PUNCT
ejpam-4810	150	4	...........	...........	PUNCT
ejpam-4810	150	5	...........	...........	PUNCT
ejpam-4810	150	6	...........	...........	PUNCT
ejpam-4810	150	7	...........	...........	PUNCT
ejpam-4810	150	8	...........	...........	PUNCT
ejpam-4810	150	9	...........	...........	PUNCT
ejpam-4810	150	10	...........	...........	PUNCT
ejpam-4810	150	11	...........	...........	PUNCT
ejpam-4810	150	12	....................................	....................................	PUNCT
ejpam-4810	150	13	............	............	PUNCT
ejpam-4810	150	14	...........	...........	PUNCT
ejpam-4810	150	15	...........	...........	PUNCT
ejpam-4810	150	16	...........	...........	PUNCT
ejpam-4810	150	17	...........	...........	PUNCT
ejpam-4810	150	18	...........	...........	PUNCT
ejpam-4810	150	19	...........	...........	PUNCT
ejpam-4810	150	20	...........	...........	PUNCT
ejpam-4810	150	21	...........	...........	PUNCT
ejpam-4810	150	22	...........	...........	PUNCT
ejpam-4810	150	23	....................................	....................................	PUNCT
ejpam-4810	150	24	................................................................................	................................................................................	PUNCT
ejpam-4810	151	1	....................................	....................................	PUNCT
ejpam-4810	151	2	....................................	....................................	PUNCT
ejpam-4810	151	3	.	.	PUNCT
ejpam-4810	151	4	.	.	PUNCT
ejpam-4810	151	5	.	.	PUNCT
ejpam-4810	151	6	.	.	PUNCT
ejpam-4810	151	7	.	.	PUNCT
ejpam-4810	152	1	.	.	PUNCT
ejpam-4810	153	1	...	...	PUNCT
ejpam-4810	154	1	y1	y1	INTJ
ejpam-4810	155	1	y2	y2	NOUN
ejpam-4810	155	2	x1	x1	NOUN
ejpam-4810	156	1	x2	x2	PROPN
ejpam-4810	156	2	y3	y3	PROPN
ejpam-4810	156	3	y4	y4	PROPN
ejpam-4810	156	4	x3	x3	PROPN
ejpam-4810	157	1	x4	x4	PROPN
ejpam-4810	157	2	ya−1	ya−1	PROPN
ejpam-4810	157	3	ya	ya	PROPN
ejpam-4810	157	4	xa−1	xa−1	PROPN
ejpam-4810	157	5	xa	xa	PROPN
ejpam-4810	157	6	z1	z1	PROPN
ejpam-4810	157	7	z2	z2	PROPN
ejpam-4810	157	8	zm	zm	PROPN
ejpam-4810	157	9	g′	g′	PROPN
ejpam-4810	157	10	:	:	PUNCT
ejpam-4810	157	11	figure	figure	NOUN
ejpam-4810	157	12	2	2	NUM
ejpam-4810	157	13	subcase	subcase	NOUN
ejpam-4810	157	14	2.2	2.2	NUM
ejpam-4810	157	15	.	.	PUNCT
ejpam-4810	158	1	a	a	PRON
ejpam-4810	158	2	is	be	AUX
ejpam-4810	158	3	odd	odd	ADJ
ejpam-4810	158	4	.	.	PUNCT
ejpam-4810	159	1	suppose	suppose	VERB
ejpam-4810	159	2	a	a	DET
ejpam-4810	159	3	=	=	SYM
ejpam-4810	159	4	3	3	NUM
ejpam-4810	159	5	and	and	CCONJ
ejpam-4810	159	6	let	let	VERB
ejpam-4810	159	7	m	m	NOUN
ejpam-4810	159	8	=	=	VERB
ejpam-4810	159	9	b	b	X
ejpam-4810	159	10	−	−	PROPN
ejpam-4810	159	11	a	a	DET
ejpam-4810	159	12	+	+	NOUN
ejpam-4810	159	13	1	1	NUM
ejpam-4810	159	14	.	.	X
ejpam-4810	159	15	consider	consider	VERB
ejpam-4810	159	16	the	the	DET
ejpam-4810	159	17	graph	graph	NOUN
ejpam-4810	159	18	h	h	NOUN
ejpam-4810	159	19	in	in	ADP
ejpam-4810	159	20	figure	figure	NOUN
ejpam-4810	159	21	3	3	NUM
ejpam-4810	159	22	.	.	PUNCT
ejpam-4810	160	1	let	let	VERB
ejpam-4810	160	2	s5	s5	PROPN
ejpam-4810	160	3	=	=	PUNCT
ejpam-4810	160	4	{	{	PUNCT
ejpam-4810	160	5	x1	x1	PROPN
ejpam-4810	160	6	,	,	PUNCT
ejpam-4810	160	7	x2	x2	PROPN
ejpam-4810	160	8	,	,	PUNCT
ejpam-4810	160	9	x3	x3	ADJ
ejpam-4810	160	10	}	}	PUNCT
ejpam-4810	160	11	and	and	CCONJ
ejpam-4810	160	12	s6	s6	PROPN
ejpam-4810	160	13	=	=	SYM
ejpam-4810	160	14	{	{	PUNCT
ejpam-4810	160	15	y1	y1	PROPN
ejpam-4810	160	16	,	,	PUNCT
ejpam-4810	160	17	y2	y2	PROPN
ejpam-4810	160	18	,	,	PUNCT
ejpam-4810	160	19	z1	z1	PROPN
ejpam-4810	160	20	,	,	PUNCT
ejpam-4810	160	21	z2	z2	PROPN
ejpam-4810	160	22	,	,	PUNCT
ejpam-4810	160	23	...	...	PUNCT
ejpam-4810	160	24	,	,	PUNCT
ejpam-4810	160	25	zm	zm	PROPN
ejpam-4810	160	26	}	}	PUNCT
ejpam-4810	160	27	.	.	PUNCT
ejpam-4810	161	1	then	then	ADV
ejpam-4810	161	2	s5	s5	PROPN
ejpam-4810	161	3	and	and	CCONJ
ejpam-4810	161	4	s6	s6	PROPN
ejpam-4810	161	5	are	be	AUX
ejpam-4810	161	6	,	,	PUNCT
ejpam-4810	161	7	respectively	respectively	ADV
ejpam-4810	161	8	,	,	PUNCT
ejpam-4810	161	9	γh	γh	ADV
ejpam-4810	161	10	-	-	PUNCT
ejpam-4810	161	11	set	set	VERB
ejpam-4810	161	12	and	and	CCONJ
ejpam-4810	161	13	γhg	γhg	VERB
ejpam-4810	161	14	-	-	PUNCT
ejpam-4810	161	15	set	set	NOUN
ejpam-4810	161	16	of	of	ADP
ejpam-4810	161	17	h.	h.	PROPN
ejpam-4810	161	18	hence	hence	ADV
ejpam-4810	161	19	,	,	PUNCT
ejpam-4810	161	20	γh(h	γh(h	PUNCT
ejpam-4810	161	21	)	)	PUNCT
ejpam-4810	161	22	=	=	SYM
ejpam-4810	161	23	a	a	PROPN
ejpam-4810	161	24	and	and	CCONJ
ejpam-4810	161	25	γhg(h	γhg(h	PROPN
ejpam-4810	161	26	)	)	PUNCT
ejpam-4810	162	1	=	=	SYM
ejpam-4810	162	2	m+	m+	VERB
ejpam-4810	162	3	a−	a−	PROPN
ejpam-4810	162	4	1	1	NUM
ejpam-4810	162	5	=	=	SYM
ejpam-4810	162	6	b.	b.	PROPN
ejpam-4810	162	7	....................................	....................................	PUNCT
ejpam-4810	162	8	....................................	....................................	PUNCT
ejpam-4810	163	1	....................................	....................................	PUNCT
ejpam-4810	163	2	....................................	....................................	PUNCT
ejpam-4810	164	1	....................................	....................................	PUNCT
ejpam-4810	164	2	....................................	....................................	PUNCT
ejpam-4810	165	1	....................................	....................................	PUNCT
ejpam-4810	165	2	....................................	....................................	PUNCT
ejpam-4810	166	1	....................................	....................................	PUNCT
ejpam-4810	166	2	....................................	....................................	PUNCT
ejpam-4810	167	1	....................................	....................................	PUNCT
ejpam-4810	167	2	.........	.........	PUNCT
ejpam-4810	167	3	........	........	PUNCT
ejpam-4810	167	4	........	........	PUNCT
ejpam-4810	167	5	........	........	PUNCT
ejpam-4810	167	6	........	........	PUNCT
ejpam-4810	167	7	........	........	PUNCT
ejpam-4810	167	8	........	........	PUNCT
ejpam-4810	167	9	........	........	PUNCT
ejpam-4810	167	10	........	........	PUNCT
ejpam-4810	167	11	........	........	PUNCT
ejpam-4810	167	12	........	........	PUNCT
ejpam-4810	167	13	........	........	PUNCT
ejpam-4810	167	14	........	........	PUNCT
ejpam-4810	167	15	........	........	PUNCT
ejpam-4810	167	16	........	........	PUNCT
ejpam-4810	167	17	........	........	PUNCT
ejpam-4810	167	18	........	........	PUNCT
ejpam-4810	167	19	........	........	PUNCT
ejpam-4810	167	20	........	........	PUNCT
ejpam-4810	167	21	........	........	PUNCT
ejpam-4810	167	22	.	.	PUNCT
ejpam-4810	168	1	....................................	....................................	PUNCT
ejpam-4810	168	2	....................................	....................................	PUNCT
ejpam-4810	169	1	.........	.........	PUNCT
ejpam-4810	169	2	........	........	PUNCT
ejpam-4810	169	3	........	........	PUNCT
ejpam-4810	169	4	........	........	PUNCT
ejpam-4810	169	5	........	........	PUNCT
ejpam-4810	169	6	........	........	PUNCT
ejpam-4810	169	7	........	........	PUNCT
ejpam-4810	169	8	........	........	PUNCT
ejpam-4810	169	9	........	........	PUNCT
ejpam-4810	169	10	........	........	PUNCT
ejpam-4810	169	11	........	........	PUNCT
ejpam-4810	169	12	........	........	PUNCT
ejpam-4810	169	13	........	........	PUNCT
ejpam-4810	169	14	........	........	PUNCT
ejpam-4810	169	15	........	........	PUNCT
ejpam-4810	169	16	........	........	PUNCT
ejpam-4810	169	17	........	........	PUNCT
ejpam-4810	169	18	........	........	PUNCT
ejpam-4810	169	19	........	........	PUNCT
ejpam-4810	169	20	........	........	PUNCT
ejpam-4810	169	21	.	.	PUNCT
ejpam-4810	170	1	....................................	....................................	PUNCT
ejpam-4810	170	2	....................................	....................................	PUNCT
ejpam-4810	170	3	...................................................................................	...................................................................................	PUNCT
ejpam-4810	170	4	...................................................................................	...................................................................................	PUNCT
ejpam-4810	171	1	....................................	....................................	PUNCT
ejpam-4810	171	2	............	............	PUNCT
ejpam-4810	171	3	...........	...........	PUNCT
ejpam-4810	171	4	...........	...........	PUNCT
ejpam-4810	171	5	...........	...........	PUNCT
ejpam-4810	171	6	...........	...........	PUNCT
ejpam-4810	171	7	...........	...........	PUNCT
ejpam-4810	171	8	...........	...........	PUNCT
ejpam-4810	171	9	...........	...........	PUNCT
ejpam-4810	171	10	...........	...........	PUNCT
ejpam-4810	171	11	...........	...........	PUNCT
ejpam-4810	171	12	....................................	....................................	PUNCT
ejpam-4810	171	13	....................................	....................................	PUNCT
ejpam-4810	171	14	............	............	PUNCT
ejpam-4810	171	15	...........	...........	PUNCT
ejpam-4810	171	16	...........	...........	PUNCT
ejpam-4810	171	17	...........	...........	PUNCT
ejpam-4810	171	18	...........	...........	PUNCT
ejpam-4810	171	19	...........	...........	PUNCT
ejpam-4810	171	20	...........	...........	PUNCT
ejpam-4810	171	21	...........	...........	PUNCT
ejpam-4810	171	22	...........	...........	PUNCT
ejpam-4810	171	23	...........	...........	PUNCT
ejpam-4810	171	24	....................................	....................................	PUNCT
ejpam-4810	171	25	............	............	PUNCT
ejpam-4810	171	26	...........	...........	PUNCT
ejpam-4810	171	27	...........	...........	PUNCT
ejpam-4810	171	28	...........	...........	PUNCT
ejpam-4810	171	29	...........	...........	PUNCT
ejpam-4810	171	30	...........	...........	PUNCT
ejpam-4810	171	31	...........	...........	PUNCT
ejpam-4810	171	32	...........	...........	PUNCT
ejpam-4810	171	33	...........	...........	PUNCT
ejpam-4810	171	34	...........	...........	PUNCT
ejpam-4810	171	35	....................................	....................................	PUNCT
ejpam-4810	171	36	.................................	.................................	PUNCT
ejpam-4810	171	37	................................	................................	PUNCT
ejpam-4810	171	38	................................	................................	PUNCT
ejpam-4810	171	39	...........	...........	PUNCT
ejpam-4810	171	40	........................................	........................................	PUNCT
ejpam-4810	171	41	................................	................................	PUNCT
ejpam-4810	171	42	................................	................................	PUNCT
ejpam-4810	171	43	................................	................................	PUNCT
ejpam-4810	171	44	........	........	PUNCT
ejpam-4810	172	1	....................................	....................................	PUNCT
ejpam-4810	172	2	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-4810	173	1	..........................................................................................................................................................	..........................................................................................................................................................	PUNCT
ejpam-4810	173	2	....................................	....................................	PUNCT
ejpam-4810	174	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4810	174	2	....................................	....................................	PUNCT
ejpam-4810	175	1	...........................................................................................................	...........................................................................................................	PUNCT
ejpam-4810	175	2	....................................	....................................	PUNCT
ejpam-4810	176	1	....................................	....................................	PUNCT
ejpam-4810	176	2	...	...	PUNCT
ejpam-4810	177	1	y1	y1	INTJ
ejpam-4810	178	1	y2	y2	NOUN
ejpam-4810	178	2	x1	x1	NOUN
ejpam-4810	179	1	x2	x2	PROPN
ejpam-4810	179	2	x3	x3	ADJ
ejpam-4810	179	3	z1	z1	PROPN
ejpam-4810	179	4	z2	z2	PROPN
ejpam-4810	179	5	zm−1	zm−1	PROPN
ejpam-4810	179	6	zm	zm	PROPN
ejpam-4810	179	7	h	h	NOUN
ejpam-4810	179	8	:	:	PUNCT
ejpam-4810	179	9	figure	figure	NOUN
ejpam-4810	179	10	3	3	NUM
ejpam-4810	179	11	suppose	suppose	VERB
ejpam-4810	179	12	a	a	DET
ejpam-4810	179	13	≥	≥	NOUN
ejpam-4810	179	14	5	5	NUM
ejpam-4810	179	15	and	and	CCONJ
ejpam-4810	179	16	let	let	VERB
ejpam-4810	179	17	m	m	NOUN
ejpam-4810	179	18	=	=	VERB
ejpam-4810	180	1	b	b	X
ejpam-4810	180	2	−	−	PROPN
ejpam-4810	180	3	a	a	DET
ejpam-4810	180	4	+	+	NOUN
ejpam-4810	180	5	1	1	NUM
ejpam-4810	180	6	.	.	X
ejpam-4810	180	7	consider	consider	VERB
ejpam-4810	180	8	the	the	DET
ejpam-4810	180	9	graph	graph	NOUN
ejpam-4810	180	10	h	h	NOUN
ejpam-4810	180	11	′	′	NUM
ejpam-4810	181	1	in	in	ADP
ejpam-4810	181	2	figure	figure	NOUN
ejpam-4810	181	3	4	4	NUM
ejpam-4810	181	4	.	.	PUNCT
ejpam-4810	182	1	let	let	VERB
ejpam-4810	182	2	s7	s7	VERB
ejpam-4810	182	3	=	=	PUNCT
ejpam-4810	182	4	{	{	PUNCT
ejpam-4810	182	5	x1	x1	PROPN
ejpam-4810	182	6	,	,	PUNCT
ejpam-4810	182	7	x2	x2	PROPN
ejpam-4810	182	8	,	,	PUNCT
ejpam-4810	182	9	...	...	PUNCT
ejpam-4810	182	10	,	,	PUNCT
ejpam-4810	182	11	xa−1	xa−1	PROPN
ejpam-4810	182	12	,	,	PUNCT
ejpam-4810	182	13	xa	xa	PROPN
ejpam-4810	182	14	}	}	PUNCT
ejpam-4810	182	15	and	and	CCONJ
ejpam-4810	182	16	s8	s8	PROPN
ejpam-4810	182	17	=	=	SYM
ejpam-4810	182	18	{	{	PUNCT
ejpam-4810	182	19	y1	y1	PROPN
ejpam-4810	182	20	,	,	PUNCT
ejpam-4810	182	21	y2	y2	PROPN
ejpam-4810	182	22	,	,	PUNCT
ejpam-4810	182	23	...	...	PUNCT
ejpam-4810	182	24	,	,	PUNCT
ejpam-4810	182	25	ya−1	ya−1	PROPN
ejpam-4810	182	26	,	,	PUNCT
ejpam-4810	182	27	z1	z1	PROPN
ejpam-4810	182	28	,	,	PUNCT
ejpam-4810	182	29	z2	z2	PROPN
ejpam-4810	182	30	,	,	PUNCT
ejpam-4810	182	31	...	...	PUNCT
ejpam-4810	182	32	,	,	PUNCT
ejpam-4810	182	33	zm	zm	PROPN
ejpam-4810	182	34	}	}	PUNCT
ejpam-4810	182	35	.	.	PUNCT
ejpam-4810	183	1	then	then	ADV
ejpam-4810	183	2	s7	s7	VERB
ejpam-4810	183	3	and	and	CCONJ
ejpam-4810	183	4	s8	s8	PROPN
ejpam-4810	183	5	are	be	AUX
ejpam-4810	183	6	,	,	PUNCT
ejpam-4810	183	7	respectively	respectively	ADV
ejpam-4810	183	8	,	,	PUNCT
ejpam-4810	183	9	γh	γh	ADV
ejpam-4810	183	10	-	-	PUNCT
ejpam-4810	183	11	set	set	VERB
ejpam-4810	183	12	and	and	CCONJ
ejpam-4810	183	13	γhg	γhg	VERB
ejpam-4810	183	14	-	-	PUNCT
ejpam-4810	183	15	set	set	NOUN
ejpam-4810	183	16	of	of	ADP
ejpam-4810	183	17	h	h	NOUN
ejpam-4810	183	18	′.	′.	NOUN
ejpam-4810	183	19	hence	hence	ADV
ejpam-4810	183	20	,	,	PUNCT
ejpam-4810	183	21	γh(h	γh(h	PUNCT
ejpam-4810	183	22	′	′	NUM
ejpam-4810	183	23	)	)	PUNCT
ejpam-4810	183	24	=	=	PUNCT
ejpam-4810	183	25	a	a	PROPN
ejpam-4810	183	26	and	and	CCONJ
ejpam-4810	183	27	γhg(h	γhg(h	PROPN
ejpam-4810	183	28	′	′	NUM
ejpam-4810	183	29	)	)	PUNCT
ejpam-4810	184	1	=	=	VERB
ejpam-4810	184	2	m+	m+	NUM
ejpam-4810	184	3	a−	a−	PROPN
ejpam-4810	184	4	1	1	NUM
ejpam-4810	184	5	=	=	SYM
ejpam-4810	184	6	b.	b.	PROPN
ejpam-4810	184	7	....................................	....................................	PUNCT
ejpam-4810	184	8	....................................	....................................	PUNCT
ejpam-4810	185	1	....................................	....................................	PUNCT
ejpam-4810	185	2	....................................	....................................	PUNCT
ejpam-4810	186	1	....................................	....................................	PUNCT
ejpam-4810	186	2	....................................	....................................	PUNCT
ejpam-4810	187	1	....................................	....................................	PUNCT
ejpam-4810	187	2	....................................	....................................	PUNCT
ejpam-4810	188	1	....................................	....................................	PUNCT
ejpam-4810	188	2	....................................	....................................	PUNCT
ejpam-4810	189	1	....................................	....................................	PUNCT
ejpam-4810	189	2	....................................	....................................	PUNCT
ejpam-4810	190	1	....................................	....................................	PUNCT
ejpam-4810	190	2	....................................	....................................	PUNCT
ejpam-4810	191	1	....................................	....................................	PUNCT
ejpam-4810	191	2	....................................	....................................	PUNCT
ejpam-4810	192	1	....................................	....................................	PUNCT
ejpam-4810	192	2	....................................	....................................	PUNCT
ejpam-4810	193	1	....................................	....................................	PUNCT
ejpam-4810	193	2	....................................	....................................	PUNCT
ejpam-4810	194	1	....................................	....................................	PUNCT
ejpam-4810	194	2	....................................	....................................	PUNCT
ejpam-4810	195	1	....................................	....................................	PUNCT
ejpam-4810	195	2	....................................	....................................	PUNCT
ejpam-4810	196	1	....................................	....................................	PUNCT
ejpam-4810	196	2	.........	.........	PUNCT
ejpam-4810	196	3	........	........	PUNCT
ejpam-4810	196	4	........	........	PUNCT
ejpam-4810	196	5	........	........	PUNCT
ejpam-4810	196	6	........	........	PUNCT
ejpam-4810	196	7	........	........	PUNCT
ejpam-4810	196	8	........	........	PUNCT
ejpam-4810	196	9	........	........	PUNCT
ejpam-4810	196	10	........	........	PUNCT
ejpam-4810	196	11	........	........	PUNCT
ejpam-4810	196	12	........	........	PUNCT
ejpam-4810	196	13	........	........	PUNCT
ejpam-4810	196	14	........	........	PUNCT
ejpam-4810	196	15	........	........	PUNCT
ejpam-4810	196	16	........	........	PUNCT
ejpam-4810	196	17	........	........	PUNCT
ejpam-4810	196	18	........	........	PUNCT
ejpam-4810	196	19	........	........	PUNCT
ejpam-4810	196	20	........	........	PUNCT
ejpam-4810	196	21	........	........	PUNCT
ejpam-4810	196	22	.	.	PUNCT
ejpam-4810	197	1	..	..	PUNCT
ejpam-4810	197	2	..................................	..................................	PUNCT
ejpam-4810	197	3	.......................................................................................................................	.......................................................................................................................	PUNCT
ejpam-4810	198	1	....................................	....................................	PUNCT
ejpam-4810	198	2	.........	.........	PUNCT
ejpam-4810	198	3	........	........	PUNCT
ejpam-4810	198	4	........	........	PUNCT
ejpam-4810	198	5	........	........	PUNCT
ejpam-4810	198	6	........	........	PUNCT
ejpam-4810	198	7	........	........	PUNCT
ejpam-4810	198	8	........	........	PUNCT
ejpam-4810	198	9	........	........	PUNCT
ejpam-4810	198	10	........	........	PUNCT
ejpam-4810	198	11	........	........	PUNCT
ejpam-4810	198	12	........	........	PUNCT
ejpam-4810	198	13	........	........	PUNCT
ejpam-4810	198	14	........	........	PUNCT
ejpam-4810	198	15	........	........	PUNCT
ejpam-4810	198	16	........	........	PUNCT
ejpam-4810	198	17	........	........	PUNCT
ejpam-4810	198	18	........	........	PUNCT
ejpam-4810	198	19	........	........	PUNCT
ejpam-4810	198	20	........	........	PUNCT
ejpam-4810	198	21	........	........	PUNCT
ejpam-4810	198	22	.	.	PUNCT
ejpam-4810	199	1	....................................	....................................	PUNCT
ejpam-4810	199	2	....................................	....................................	PUNCT
ejpam-4810	200	1	.........	.........	PUNCT
ejpam-4810	200	2	........	........	PUNCT
ejpam-4810	200	3	........	........	PUNCT
ejpam-4810	200	4	........	........	PUNCT
ejpam-4810	200	5	........	........	PUNCT
ejpam-4810	200	6	........	........	PUNCT
ejpam-4810	200	7	........	........	PUNCT
ejpam-4810	200	8	........	........	PUNCT
ejpam-4810	200	9	........	........	PUNCT
ejpam-4810	200	10	........	........	PUNCT
ejpam-4810	200	11	........	........	PUNCT
ejpam-4810	200	12	........	........	PUNCT
ejpam-4810	200	13	........	........	PUNCT
ejpam-4810	200	14	........	........	PUNCT
ejpam-4810	200	15	........	........	PUNCT
ejpam-4810	200	16	........	........	PUNCT
ejpam-4810	200	17	........	........	PUNCT
ejpam-4810	200	18	........	........	PUNCT
ejpam-4810	200	19	........	........	PUNCT
ejpam-4810	200	20	........	........	PUNCT
ejpam-4810	200	21	.	.	PUNCT
ejpam-4810	201	1	....................................	....................................	PUNCT
ejpam-4810	201	2	....................................	....................................	PUNCT
ejpam-4810	202	1	.........	.........	PUNCT
ejpam-4810	202	2	........	........	PUNCT
ejpam-4810	202	3	........	........	PUNCT
ejpam-4810	202	4	........	........	PUNCT
ejpam-4810	202	5	........	........	PUNCT
ejpam-4810	202	6	........	........	PUNCT
ejpam-4810	202	7	........	........	PUNCT
ejpam-4810	202	8	........	........	PUNCT
ejpam-4810	202	9	........	........	PUNCT
ejpam-4810	202	10	........	........	PUNCT
ejpam-4810	202	11	........	........	PUNCT
ejpam-4810	202	12	........	........	PUNCT
ejpam-4810	202	13	........	........	PUNCT
ejpam-4810	202	14	........	........	PUNCT
ejpam-4810	202	15	........	........	PUNCT
ejpam-4810	202	16	........	........	PUNCT
ejpam-4810	202	17	........	........	PUNCT
ejpam-4810	202	18	........	........	PUNCT
ejpam-4810	202	19	........	........	PUNCT
ejpam-4810	202	20	........	........	PUNCT
ejpam-4810	202	21	.	.	PUNCT
ejpam-4810	203	1	....................................	....................................	PUNCT
ejpam-4810	203	2	....................................	....................................	PUNCT
ejpam-4810	204	1	.........	.........	PUNCT
ejpam-4810	204	2	........	........	PUNCT
ejpam-4810	204	3	........	........	PUNCT
ejpam-4810	204	4	........	........	PUNCT
ejpam-4810	204	5	........	........	PUNCT
ejpam-4810	204	6	........	........	PUNCT
ejpam-4810	204	7	........	........	PUNCT
ejpam-4810	204	8	........	........	PUNCT
ejpam-4810	204	9	........	........	PUNCT
ejpam-4810	204	10	........	........	PUNCT
ejpam-4810	204	11	........	........	PUNCT
ejpam-4810	204	12	........	........	PUNCT
ejpam-4810	204	13	........	........	PUNCT
ejpam-4810	204	14	........	........	PUNCT
ejpam-4810	204	15	........	........	PUNCT
ejpam-4810	204	16	........	........	PUNCT
ejpam-4810	204	17	........	........	PUNCT
ejpam-4810	204	18	........	........	PUNCT
ejpam-4810	204	19	........	........	PUNCT
ejpam-4810	204	20	........	........	PUNCT
ejpam-4810	204	21	.	.	PUNCT
ejpam-4810	205	1	....................................	....................................	PUNCT
ejpam-4810	205	2	....................................	....................................	PUNCT
ejpam-4810	206	1	...................................................................................	...................................................................................	PUNCT
ejpam-4810	206	2	....................................	....................................	PUNCT
ejpam-4810	207	1	.........	.........	PUNCT
ejpam-4810	207	2	........	........	PUNCT
ejpam-4810	207	3	........	........	PUNCT
ejpam-4810	207	4	........	........	PUNCT
ejpam-4810	207	5	........	........	PUNCT
ejpam-4810	207	6	........	........	PUNCT
ejpam-4810	207	7	........	........	PUNCT
ejpam-4810	207	8	........	........	PUNCT
ejpam-4810	207	9	........	........	PUNCT
ejpam-4810	207	10	........	........	PUNCT
ejpam-4810	207	11	........	........	PUNCT
ejpam-4810	207	12	........	........	PUNCT
ejpam-4810	207	13	........	........	PUNCT
ejpam-4810	207	14	........	........	PUNCT
ejpam-4810	207	15	........	........	PUNCT
ejpam-4810	207	16	........	........	PUNCT
ejpam-4810	207	17	........	........	PUNCT
ejpam-4810	207	18	........	........	PUNCT
ejpam-4810	207	19	........	........	PUNCT
ejpam-4810	207	20	........	........	PUNCT
ejpam-4810	207	21	.	.	PUNCT
ejpam-4810	208	1	....................................	....................................	PUNCT
ejpam-4810	208	2	....................................	....................................	PUNCT
ejpam-4810	208	3	...................................................................................	...................................................................................	PUNCT
ejpam-4810	208	4	...................................................................................	...................................................................................	PUNCT
ejpam-4810	208	5	...................................................................................	...................................................................................	PUNCT
ejpam-4810	208	6	...................................................................................	...................................................................................	PUNCT
ejpam-4810	208	7	...................................................................................	...................................................................................	PUNCT
ejpam-4810	208	8	...................................................................................	...................................................................................	PUNCT
ejpam-4810	209	1	....................................	....................................	PUNCT
ejpam-4810	209	2	...................................................................................	...................................................................................	PUNCT
ejpam-4810	209	3	...................................................................................	...................................................................................	PUNCT
ejpam-4810	209	4	...................................................................................	...................................................................................	PUNCT
ejpam-4810	210	1	....................................	....................................	PUNCT
ejpam-4810	210	2	.........	.........	PUNCT
ejpam-4810	210	3	........	........	PUNCT
ejpam-4810	210	4	........	........	PUNCT
ejpam-4810	210	5	........	........	PUNCT
ejpam-4810	210	6	........	........	PUNCT
ejpam-4810	210	7	........	........	PUNCT
ejpam-4810	210	8	........	........	PUNCT
ejpam-4810	210	9	........	........	PUNCT
ejpam-4810	210	10	........	........	PUNCT
ejpam-4810	210	11	........	........	PUNCT
ejpam-4810	210	12	........	........	PUNCT
ejpam-4810	210	13	........	........	PUNCT
ejpam-4810	210	14	........	........	PUNCT
ejpam-4810	210	15	........	........	PUNCT
ejpam-4810	210	16	........	........	PUNCT
ejpam-4810	210	17	........	........	PUNCT
ejpam-4810	210	18	........	........	PUNCT
ejpam-4810	210	19	........	........	PUNCT
ejpam-4810	210	20	........	........	PUNCT
ejpam-4810	210	21	........	........	PUNCT
ejpam-4810	210	22	.	.	PUNCT
ejpam-4810	211	1	....................................	....................................	PUNCT
ejpam-4810	211	2	....................................	....................................	PUNCT
ejpam-4810	212	1	.........	.........	PUNCT
ejpam-4810	212	2	........	........	PUNCT
ejpam-4810	212	3	........	........	PUNCT
ejpam-4810	212	4	........	........	PUNCT
ejpam-4810	212	5	........	........	PUNCT
ejpam-4810	212	6	........	........	PUNCT
ejpam-4810	212	7	........	........	PUNCT
ejpam-4810	212	8	........	........	PUNCT
ejpam-4810	212	9	........	........	PUNCT
ejpam-4810	212	10	........	........	PUNCT
ejpam-4810	212	11	........	........	PUNCT
ejpam-4810	212	12	........	........	PUNCT
ejpam-4810	212	13	........	........	PUNCT
ejpam-4810	212	14	........	........	PUNCT
ejpam-4810	212	15	........	........	PUNCT
ejpam-4810	212	16	........	........	PUNCT
ejpam-4810	212	17	........	........	PUNCT
ejpam-4810	212	18	........	........	PUNCT
ejpam-4810	212	19	........	........	PUNCT
ejpam-4810	212	20	........	........	PUNCT
ejpam-4810	212	21	.	.	PUNCT
ejpam-4810	213	1	....................................	....................................	PUNCT
ejpam-4810	213	2	....................................	....................................	PUNCT
ejpam-4810	213	3	...................................................................................	...................................................................................	PUNCT
ejpam-4810	213	4	...................................................................................	...................................................................................	PUNCT
ejpam-4810	214	1	....................................	....................................	PUNCT
ejpam-4810	214	2	............	............	PUNCT
ejpam-4810	214	3	...........	...........	PUNCT
ejpam-4810	214	4	...........	...........	PUNCT
ejpam-4810	214	5	...........	...........	PUNCT
ejpam-4810	214	6	...........	...........	PUNCT
ejpam-4810	214	7	...........	...........	PUNCT
ejpam-4810	214	8	...........	...........	PUNCT
ejpam-4810	214	9	...........	...........	PUNCT
ejpam-4810	214	10	...........	...........	PUNCT
ejpam-4810	214	11	...........	...........	PUNCT
ejpam-4810	214	12	....................................	....................................	PUNCT
ejpam-4810	214	13	....................................	....................................	PUNCT
ejpam-4810	214	14	............	............	PUNCT
ejpam-4810	214	15	...........	...........	PUNCT
ejpam-4810	214	16	...........	...........	PUNCT
ejpam-4810	214	17	...........	...........	PUNCT
ejpam-4810	214	18	...........	...........	PUNCT
ejpam-4810	214	19	...........	...........	PUNCT
ejpam-4810	214	20	...........	...........	PUNCT
ejpam-4810	214	21	...........	...........	PUNCT
ejpam-4810	214	22	...........	...........	PUNCT
ejpam-4810	214	23	...........	...........	PUNCT
ejpam-4810	214	24	....................................	....................................	PUNCT
ejpam-4810	214	25	............	............	PUNCT
ejpam-4810	214	26	...........	...........	PUNCT
ejpam-4810	214	27	...........	...........	PUNCT
ejpam-4810	214	28	...........	...........	PUNCT
ejpam-4810	214	29	...........	...........	PUNCT
ejpam-4810	214	30	...........	...........	PUNCT
ejpam-4810	214	31	...........	...........	PUNCT
ejpam-4810	214	32	...........	...........	PUNCT
ejpam-4810	214	33	...........	...........	PUNCT
ejpam-4810	214	34	...........	...........	PUNCT
ejpam-4810	214	35	....................................	....................................	PUNCT
ejpam-4810	214	36	.................................	.................................	PUNCT
ejpam-4810	214	37	................................	................................	PUNCT
ejpam-4810	214	38	................................	................................	PUNCT
ejpam-4810	214	39	...........	...........	PUNCT
ejpam-4810	214	40	........................................	........................................	PUNCT
ejpam-4810	214	41	................................	................................	PUNCT
ejpam-4810	214	42	................................	................................	PUNCT
ejpam-4810	214	43	................................	................................	PUNCT
ejpam-4810	214	44	........	........	PUNCT
ejpam-4810	215	1	....................................	....................................	PUNCT
ejpam-4810	215	2	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-4810	216	1	..........................................................................................................................................................	..........................................................................................................................................................	PUNCT
ejpam-4810	216	2	....................................	....................................	PUNCT
ejpam-4810	217	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4810	217	2	....................................	....................................	PUNCT
ejpam-4810	218	1	...........................................................................................................	...........................................................................................................	PUNCT
ejpam-4810	218	2	....................................	....................................	PUNCT
ejpam-4810	219	1	....................................	....................................	PUNCT
ejpam-4810	219	2	...	...	PUNCT
ejpam-4810	219	3	.	.	PUNCT
ejpam-4810	219	4	.	.	PUNCT
ejpam-4810	219	5	.	.	PUNCT
ejpam-4810	219	6	.	.	PUNCT
ejpam-4810	219	7	.	.	PUNCT
ejpam-4810	219	8	.	.	PUNCT
ejpam-4810	220	1	y1	y1	INTJ
ejpam-4810	221	1	y2	y2	INTJ
ejpam-4810	221	2	x1	x1	NOUN
ejpam-4810	222	1	x2	x2	PROPN
ejpam-4810	222	2	y3	y3	PROPN
ejpam-4810	222	3	y4	y4	PROPN
ejpam-4810	222	4	x3	x3	PROPN
ejpam-4810	222	5	x4	x4	PROPN
ejpam-4810	222	6	ya−2	ya−2	PROPN
ejpam-4810	222	7	ya−1	ya−1	PROPN
ejpam-4810	222	8	xa−2	xa−2	PROPN
ejpam-4810	222	9	xa−1	xa−1	PROPN
ejpam-4810	222	10	xa	xa	PROPN
ejpam-4810	223	1	z1	z1	PROPN
ejpam-4810	223	2	z2	z2	PROPN
ejpam-4810	223	3	zm−1	zm−1	PROPN
ejpam-4810	223	4	zm	zm	PROPN
ejpam-4810	223	5	h	h	PROPN
ejpam-4810	223	6	′	′	NUM
ejpam-4810	223	7	:	:	PUNCT
ejpam-4810	223	8	figure	figure	VERB
ejpam-4810	223	9	4	4	NUM
ejpam-4810	223	10	this	this	PRON
ejpam-4810	223	11	proves	prove	VERB
ejpam-4810	223	12	the	the	DET
ejpam-4810	223	13	assertion	assertion	NOUN
ejpam-4810	223	14	.	.	PUNCT
ejpam-4810	224	1	corollary	corollary	ADJ
ejpam-4810	224	2	1	1	NUM
ejpam-4810	224	3	.	.	PUNCT
ejpam-4810	225	1	let	let	VERB
ejpam-4810	225	2	n	n	PRON
ejpam-4810	225	3	be	be	AUX
ejpam-4810	225	4	a	a	DET
ejpam-4810	225	5	positive	positive	ADJ
ejpam-4810	225	6	integer	integer	NOUN
ejpam-4810	225	7	.	.	PUNCT
ejpam-4810	226	1	then	then	ADV
ejpam-4810	226	2	there	there	PRON
ejpam-4810	226	3	exists	exist	VERB
ejpam-4810	226	4	a	a	DET
ejpam-4810	226	5	connected	connected	ADJ
ejpam-4810	226	6	graph	graph	NOUN
ejpam-4810	226	7	such	such	ADJ
ejpam-4810	226	8	that	that	SCONJ
ejpam-4810	226	9	γhg(g)−γh(g	γhg(g)−γh(g	NOUN
ejpam-4810	226	10	)	)	PUNCT
ejpam-4810	226	11	=	=	VERB
ejpam-4810	227	1	n.	n.	NOUN
ejpam-4810	227	2	in	in	ADP
ejpam-4810	227	3	other	other	ADJ
ejpam-4810	227	4	words	word	NOUN
ejpam-4810	227	5	,	,	PUNCT
ejpam-4810	227	6	the	the	DET
ejpam-4810	227	7	difference	difference	NOUN
ejpam-4810	227	8	γhg(g)−γh(g	γhg(g)−γh(g	NOUN
ejpam-4810	227	9	)	)	PUNCT
ejpam-4810	227	10	can	can	AUX
ejpam-4810	227	11	be	be	AUX
ejpam-4810	227	12	made	make	VERB
ejpam-4810	227	13	arbitrarily	arbitrarily	ADV
ejpam-4810	227	14	large	large	ADJ
ejpam-4810	227	15	.	.	PUNCT
ejpam-4810	228	1	c.j	c.j	PROPN
ejpam-4810	228	2	.	.	PROPN
ejpam-4810	228	3	saromines	saromines	PROPN
ejpam-4810	228	4	,	,	PUNCT
ejpam-4810	228	5	s.	s.	PROPN
ejpam-4810	228	6	canoy	canoy	PROPN
ejpam-4810	228	7	,	,	PUNCT
ejpam-4810	228	8	jr	jr	PROPN
ejpam-4810	228	9	.	.	PROPN
ejpam-4810	228	10	,	,	PUNCT
ejpam-4810	228	11	/	/	SYM
ejpam-4810	228	12	eur	eur	NOUN
ejpam-4810	228	13	.	.	PUNCT
ejpam-4810	229	1	j.	j.	PROPN
ejpam-4810	229	2	pure	pure	PROPN
ejpam-4810	229	3	appl	appl	PROPN
ejpam-4810	229	4	.	.	PROPN
ejpam-4810	229	5	math	math	PROPN
ejpam-4810	229	6	,	,	PUNCT
ejpam-4810	229	7	16	16	NUM
ejpam-4810	229	8	(	(	PUNCT
ejpam-4810	229	9	3	3	NUM
ejpam-4810	229	10	)	)	PUNCT
ejpam-4810	229	11	(	(	PUNCT
ejpam-4810	229	12	2023	2023	NUM
ejpam-4810	229	13	)	)	PUNCT
ejpam-4810	229	14	,	,	PUNCT
ejpam-4810	229	15	1568	1568	NUM
ejpam-4810	229	16	-	-	SYM
ejpam-4810	229	17	1579	1579	NUM
ejpam-4810	229	18	1572	1572	NUM
ejpam-4810	229	19	the	the	DET
ejpam-4810	229	20	next	next	ADJ
ejpam-4810	229	21	few	few	ADJ
ejpam-4810	229	22	results	result	NOUN
ejpam-4810	229	23	deal	deal	VERB
ejpam-4810	229	24	with	with	ADP
ejpam-4810	229	25	the	the	DET
ejpam-4810	229	26	concept	concept	NOUN
ejpam-4810	229	27	of	of	ADP
ejpam-4810	229	28	pointwise	pointwise	PROPN
ejpam-4810	229	29	non	non	ADJ
ejpam-4810	229	30	-	-	ADJ
ejpam-4810	229	31	dominating	dominating	ADJ
ejpam-4810	229	32	2	2	NUM
ejpam-4810	229	33	-	-	PUNCT
ejpam-4810	229	34	path	path	NOUN
ejpam-4810	229	35	closure	closure	NOUN
ejpam-4810	229	36	absorbing	absorbing	NOUN
ejpam-4810	229	37	sets	set	NOUN
ejpam-4810	229	38	.	.	PUNCT
ejpam-4810	230	1	remark	remark	NOUN
ejpam-4810	230	2	3	3	NUM
ejpam-4810	230	3	.	.	PUNCT
ejpam-4810	231	1	every	every	DET
ejpam-4810	231	2	pointwise	pointwise	ADJ
ejpam-4810	231	3	non	non	ADJ
ejpam-4810	231	4	-	-	ADJ
ejpam-4810	231	5	dominating	dominating	ADJ
ejpam-4810	231	6	2	2	NUM
ejpam-4810	231	7	-	-	PUNCT
ejpam-4810	231	8	path	path	NOUN
ejpam-4810	231	9	closure	closure	NOUN
ejpam-4810	231	10	absorbing	absorb	VERB
ejpam-4810	231	11	is	be	AUX
ejpam-4810	231	12	both	both	PRON
ejpam-4810	231	13	a	a	DET
ejpam-4810	231	14	pointwise	pointwise	ADJ
ejpam-4810	231	15	non	non	ADJ
ejpam-4810	231	16	-	-	ADJ
ejpam-4810	231	17	dominating	dominating	ADJ
ejpam-4810	231	18	set	set	NOUN
ejpam-4810	231	19	and	and	CCONJ
ejpam-4810	231	20	a	a	DET
ejpam-4810	231	21	2	2	NUM
ejpam-4810	231	22	-	-	PUNCT
ejpam-4810	231	23	path	path	NOUN
ejpam-4810	231	24	closure	closure	NOUN
ejpam-4810	231	25	absorbing	absorb	VERB
ejpam-4810	231	26	set	set	VERB
ejpam-4810	231	27	in	in	ADP
ejpam-4810	231	28	g.	g.	PROPN
ejpam-4810	231	29	hence	hence	ADV
ejpam-4810	231	30	,	,	PUNCT
ejpam-4810	231	31	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	231	32	)	)	PUNCT
ejpam-4810	231	33	≥	≥	PROPN
ejpam-4810	231	34	max	max	PROPN
ejpam-4810	231	35	{	{	PUNCT
ejpam-4810	231	36	pnd(g	pnd(g	PROPN
ejpam-4810	231	37	)	)	PUNCT
ejpam-4810	231	38	,	,	PUNCT
ejpam-4810	231	39	ρ2(g	ρ2(g	X
ejpam-4810	231	40	)	)	PUNCT
ejpam-4810	231	41	}	}	PUNCT
ejpam-4810	231	42	.	.	PUNCT
ejpam-4810	232	1	theorem	theorem	NOUN
ejpam-4810	232	2	2	2	NUM
ejpam-4810	232	3	.	.	PUNCT
ejpam-4810	233	1	let	let	VERB
ejpam-4810	233	2	g	g	PRON
ejpam-4810	233	3	be	be	AUX
ejpam-4810	233	4	a	a	DET
ejpam-4810	233	5	graph	graph	NOUN
ejpam-4810	233	6	on	on	ADP
ejpam-4810	233	7	n	n	PRON
ejpam-4810	233	8	≥	≥	NUM
ejpam-4810	233	9	3	3	NUM
ejpam-4810	233	10	vertices	vertex	NOUN
ejpam-4810	233	11	.	.	PUNCT
ejpam-4810	234	1	then	then	ADV
ejpam-4810	234	2	3	3	NUM
ejpam-4810	234	3	≤	≤	NUM
ejpam-4810	234	4	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	234	5	)	)	PUNCT
ejpam-4810	234	6	≤	≤	PROPN
ejpam-4810	234	7	n.	n.	NOUN
ejpam-4810	234	8	moreover	moreover	ADV
ejpam-4810	234	9	,	,	PUNCT
ejpam-4810	234	10	(	(	PUNCT
ejpam-4810	234	11	i	i	NOUN
ejpam-4810	234	12	)	)	PUNCT
ejpam-4810	234	13	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	234	14	)	)	PUNCT
ejpam-4810	234	15	=	=	SYM
ejpam-4810	234	16	3	3	NUM
ejpam-4810	235	1	if	if	SCONJ
ejpam-4810	235	2	and	and	CCONJ
ejpam-4810	235	3	only	only	ADV
ejpam-4810	235	4	if	if	SCONJ
ejpam-4810	235	5	n	n	PROPN
ejpam-4810	235	6	=	=	SYM
ejpam-4810	235	7	3	3	NUM
ejpam-4810	235	8	or	or	CCONJ
ejpam-4810	235	9	n	n	ADJ
ejpam-4810	235	10	>	>	ADP
ejpam-4810	235	11	3	3	NUM
ejpam-4810	235	12	and	and	CCONJ
ejpam-4810	235	13	there	there	PRON
ejpam-4810	235	14	exists	exist	VERB
ejpam-4810	235	15	s	s	PROPN
ejpam-4810	236	1	⊆	⊆	NUM
ejpam-4810	236	2	v	v	NOUN
ejpam-4810	236	3	(	(	PUNCT
ejpam-4810	236	4	g	g	NOUN
ejpam-4810	236	5	)	)	PUNCT
ejpam-4810	236	6	with	with	ADP
ejpam-4810	236	7	|s|	|s|	PROPN
ejpam-4810	236	8	=	=	SYM
ejpam-4810	236	9	3	3	NUM
ejpam-4810	236	10	such	such	ADJ
ejpam-4810	236	11	that	that	PRON
ejpam-4810	236	12	for	for	ADP
ejpam-4810	236	13	each	each	PRON
ejpam-4810	236	14	v	v	NUM
ejpam-4810	236	15	∈	∈	PROPN
ejpam-4810	236	16	v	v	NOUN
ejpam-4810	236	17	(	(	PUNCT
ejpam-4810	236	18	g	g	NOUN
ejpam-4810	236	19	)	)	PUNCT
ejpam-4810	236	20	\	\	PROPN
ejpam-4810	236	21	s	s	X
ejpam-4810	236	22	,	,	PUNCT
ejpam-4810	236	23	|ng(v	|ng(v	ADJ
ejpam-4810	236	24	)	)	PUNCT
ejpam-4810	236	25	∩	∩	NOUN
ejpam-4810	236	26	s|	s|	NOUN
ejpam-4810	236	27	=	=	SYM
ejpam-4810	236	28	2	2	NUM
ejpam-4810	236	29	and	and	CCONJ
ejpam-4810	236	30	dg(a	dg(a	NUM
ejpam-4810	236	31	,	,	PUNCT
ejpam-4810	236	32	b	b	X
ejpam-4810	236	33	)	)	PUNCT
ejpam-4810	236	34	=	=	SYM
ejpam-4810	236	35	2	2	NUM
ejpam-4810	236	36	for	for	ADP
ejpam-4810	236	37	a	a	DET
ejpam-4810	236	38	,	,	PUNCT
ejpam-4810	236	39	b	b	PROPN
ejpam-4810	236	40	∈	∈	PROPN
ejpam-4810	236	41	ng(v	ng(v	PUNCT
ejpam-4810	236	42	)	)	PUNCT
ejpam-4810	236	43	∩	∩	PROPN
ejpam-4810	236	44	s.	s.	PROPN
ejpam-4810	236	45	(	(	PUNCT
ejpam-4810	236	46	ii	ii	PROPN
ejpam-4810	236	47	)	)	PUNCT
ejpam-4810	236	48	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	236	49	)	)	PUNCT
ejpam-4810	236	50	=	=	SYM
ejpam-4810	237	1	n	n	NOUN
ejpam-4810	237	2	if	if	SCONJ
ejpam-4810	237	3	and	and	CCONJ
ejpam-4810	237	4	only	only	ADV
ejpam-4810	237	5	if	if	SCONJ
ejpam-4810	237	6	one	one	NUM
ejpam-4810	237	7	of	of	ADP
ejpam-4810	237	8	the	the	DET
ejpam-4810	237	9	following	following	NOUN
ejpam-4810	237	10	holds	hold	VERB
ejpam-4810	237	11	:	:	PUNCT
ejpam-4810	237	12	(	(	PUNCT
ejpam-4810	237	13	a	a	X
ejpam-4810	237	14	)	)	PUNCT
ejpam-4810	237	15	g	g	NOUN
ejpam-4810	237	16	is	be	AUX
ejpam-4810	237	17	connected	connect	VERB
ejpam-4810	237	18	and	and	CCONJ
ejpam-4810	237	19	for	for	ADP
ejpam-4810	237	20	every	every	DET
ejpam-4810	237	21	pair	pair	NOUN
ejpam-4810	237	22	of	of	ADP
ejpam-4810	237	23	vertices	vertex	NOUN
ejpam-4810	237	24	x	x	X
ejpam-4810	237	25	,	,	PUNCT
ejpam-4810	237	26	y	y	PROPN
ejpam-4810	237	27	with	with	ADP
ejpam-4810	237	28	dg(x	dg(x	PROPN
ejpam-4810	237	29	,	,	PUNCT
ejpam-4810	237	30	y	y	NOUN
ejpam-4810	237	31	)	)	PUNCT
ejpam-4810	237	32	=	=	SYM
ejpam-4810	237	33	2	2	NUM
ejpam-4810	237	34	,	,	PUNCT
ejpam-4810	237	35	the	the	DET
ejpam-4810	237	36	set	set	NOUN
ejpam-4810	237	37	ng(x	ng(x	NUM
ejpam-4810	237	38	)	)	PUNCT
ejpam-4810	237	39	∩ng(y	∩ng(y	PROPN
ejpam-4810	237	40	)	)	PUNCT
ejpam-4810	237	41	contains	contain	VERB
ejpam-4810	237	42	dominating	dominating	NOUN
ejpam-4810	237	43	vertices	vertex	NOUN
ejpam-4810	237	44	of	of	ADP
ejpam-4810	237	45	g	g	NOUN
ejpam-4810	237	46	only	only	ADV
ejpam-4810	237	47	or	or	CCONJ
ejpam-4810	237	48	(	(	PUNCT
ejpam-4810	237	49	b	b	NOUN
ejpam-4810	237	50	)	)	PUNCT
ejpam-4810	237	51	g	g	NOUN
ejpam-4810	237	52	is	be	AUX
ejpam-4810	237	53	disconnected	disconnect	VERB
ejpam-4810	237	54	such	such	ADJ
ejpam-4810	237	55	that	that	SCONJ
ejpam-4810	237	56	every	every	DET
ejpam-4810	237	57	component	component	NOUN
ejpam-4810	237	58	h	h	NOUN
ejpam-4810	237	59	of	of	ADP
ejpam-4810	237	60	g	g	PROPN
ejpam-4810	237	61	is	be	AUX
ejpam-4810	237	62	complete	complete	ADJ
ejpam-4810	237	63	.	.	PUNCT
ejpam-4810	238	1	proof	proof	NOUN
ejpam-4810	238	2	.	.	PUNCT
ejpam-4810	239	1	let	let	VERB
ejpam-4810	239	2	s	s	PRON
ejpam-4810	239	3	be	be	AUX
ejpam-4810	239	4	a	a	DET
ejpam-4810	239	5	ρ2pnd	ρ2pnd	ADV
ejpam-4810	239	6	-	-	PUNCT
ejpam-4810	239	7	set	set	NOUN
ejpam-4810	239	8	of	of	ADP
ejpam-4810	239	9	g.	g.	PROPN
ejpam-4810	239	10	suppose	suppose	VERB
ejpam-4810	239	11	|s|	|s|	NOUN
ejpam-4810	239	12	≤	≤	ADV
ejpam-4810	239	13	2	2	NUM
ejpam-4810	239	14	and	and	CCONJ
ejpam-4810	239	15	let	let	VERB
ejpam-4810	239	16	v	v	NUM
ejpam-4810	239	17	∈	∈	PROPN
ejpam-4810	239	18	v	v	NOUN
ejpam-4810	239	19	(	(	PUNCT
ejpam-4810	239	20	g	g	NOUN
ejpam-4810	239	21	)	)	PUNCT
ejpam-4810	239	22	\	\	PUNCT
ejpam-4810	240	1	s.	s.	PROPN
ejpam-4810	240	2	since	since	SCONJ
ejpam-4810	240	3	s	s	PROPN
ejpam-4810	240	4	is	be	AUX
ejpam-4810	240	5	a	a	DET
ejpam-4810	240	6	2	2	NUM
ejpam-4810	240	7	-	-	PUNCT
ejpam-4810	240	8	path	path	NOUN
ejpam-4810	240	9	closure	closure	NOUN
ejpam-4810	240	10	absorbing	absorb	VERB
ejpam-4810	240	11	set	set	NOUN
ejpam-4810	240	12	,	,	PUNCT
ejpam-4810	240	13	there	there	PRON
ejpam-4810	240	14	exist	exist	VERB
ejpam-4810	240	15	p	p	PRON
ejpam-4810	240	16	,	,	PUNCT
ejpam-4810	240	17	q	q	PROPN
ejpam-4810	240	18	∈	∈	PROPN
ejpam-4810	240	19	s	s	VERB
ejpam-4810	240	20	such	such	ADJ
ejpam-4810	240	21	that	that	SCONJ
ejpam-4810	240	22	dg(p	dg(p	NOUN
ejpam-4810	240	23	,	,	PUNCT
ejpam-4810	240	24	q	q	X
ejpam-4810	240	25	)	)	PUNCT
ejpam-4810	240	26	=	=	SYM
ejpam-4810	240	27	2	2	NUM
ejpam-4810	240	28	and	and	CCONJ
ejpam-4810	240	29	v	v	ADP
ejpam-4810	240	30	∈	∈	NOUN
ejpam-4810	240	31	ig(p	ig(p	NOUN
ejpam-4810	240	32	,	,	PUNCT
ejpam-4810	240	33	q	q	NOUN
ejpam-4810	240	34	)	)	PUNCT
ejpam-4810	240	35	.	.	PUNCT
ejpam-4810	241	1	hence	hence	ADV
ejpam-4810	241	2	,	,	PUNCT
ejpam-4810	241	3	s	s	VERB
ejpam-4810	241	4	can	can	AUX
ejpam-4810	241	5	not	not	PART
ejpam-4810	241	6	be	be	AUX
ejpam-4810	241	7	a	a	DET
ejpam-4810	241	8	pointwise	pointwise	ADJ
ejpam-4810	241	9	non	non	ADJ
ejpam-4810	241	10	-	-	ADJ
ejpam-4810	241	11	dominating	dominating	ADJ
ejpam-4810	241	12	set	set	NOUN
ejpam-4810	241	13	,	,	PUNCT
ejpam-4810	241	14	contradicting	contradict	VERB
ejpam-4810	241	15	our	our	PRON
ejpam-4810	241	16	assumption	assumption	NOUN
ejpam-4810	241	17	that	that	SCONJ
ejpam-4810	241	18	s	s	VERB
ejpam-4810	241	19	is	be	AUX
ejpam-4810	241	20	a	a	DET
ejpam-4810	241	21	ρ2pnd	ρ2pnd	ADV
ejpam-4810	241	22	-	-	PUNCT
ejpam-4810	241	23	set	set	NOUN
ejpam-4810	241	24	of	of	ADP
ejpam-4810	241	25	g.	g.	PROPN
ejpam-4810	241	26	therefore	therefore	ADV
ejpam-4810	241	27	,	,	PUNCT
ejpam-4810	241	28	3	3	NUM
ejpam-4810	241	29	≤	≤	NUM
ejpam-4810	241	30	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	241	31	)	)	PUNCT
ejpam-4810	241	32	.	.	PUNCT
ejpam-4810	242	1	(	(	PUNCT
ejpam-4810	242	2	i	i	NOUN
ejpam-4810	242	3	)	)	PUNCT
ejpam-4810	242	4	suppose	suppose	VERB
ejpam-4810	242	5	ρ2pnd(g	ρ2pnd(g	X
ejpam-4810	242	6	)	)	PUNCT
ejpam-4810	242	7	=	=	SYM
ejpam-4810	243	1	3	3	X
ejpam-4810	243	2	.	.	PUNCT
ejpam-4810	243	3	suppose	suppose	VERB
ejpam-4810	243	4	further	far	ADV
ejpam-4810	243	5	that	that	SCONJ
ejpam-4810	243	6	n	n	CCONJ
ejpam-4810	243	7	>	>	X
ejpam-4810	243	8	3	3	NUM
ejpam-4810	243	9	and	and	CCONJ
ejpam-4810	243	10	let	let	VERB
ejpam-4810	243	11	s	s	PRON
ejpam-4810	243	12	be	be	AUX
ejpam-4810	243	13	a	a	DET
ejpam-4810	243	14	ρ2pnd	ρ2pnd	ADV
ejpam-4810	243	15	-	-	PUNCT
ejpam-4810	243	16	set	set	NOUN
ejpam-4810	243	17	of	of	ADP
ejpam-4810	243	18	g.	g.	PROPN
ejpam-4810	243	19	then	then	ADV
ejpam-4810	243	20	|s|	|s|	PROPN
ejpam-4810	243	21	=	=	SYM
ejpam-4810	243	22	3	3	X
ejpam-4810	243	23	.	.	PUNCT
ejpam-4810	243	24	let	let	VERB
ejpam-4810	243	25	v	v	NUM
ejpam-4810	243	26	∈	∈	PROPN
ejpam-4810	243	27	v	v	NOUN
ejpam-4810	243	28	(	(	PUNCT
ejpam-4810	243	29	g	g	NOUN
ejpam-4810	243	30	)	)	PUNCT
ejpam-4810	243	31	\	\	PUNCT
ejpam-4810	244	1	s.	s.	PROPN
ejpam-4810	244	2	then	then	ADV
ejpam-4810	244	3	there	there	PRON
ejpam-4810	244	4	exist	exist	VERB
ejpam-4810	244	5	vertices	vertex	NOUN
ejpam-4810	244	6	a	a	DET
ejpam-4810	244	7	,	,	PUNCT
ejpam-4810	244	8	b	b	X
ejpam-4810	244	9	∈	∈	NOUN
ejpam-4810	244	10	s	s	VERB
ejpam-4810	244	11	such	such	ADJ
ejpam-4810	244	12	that	that	SCONJ
ejpam-4810	244	13	dg(a	dg(a	PROPN
ejpam-4810	244	14	,	,	PUNCT
ejpam-4810	244	15	b	b	X
ejpam-4810	244	16	)	)	PUNCT
ejpam-4810	244	17	=	=	SYM
ejpam-4810	244	18	2	2	NUM
ejpam-4810	244	19	and	and	CCONJ
ejpam-4810	244	20	v	v	ADP
ejpam-4810	244	21	∈	∈	PROPN
ejpam-4810	244	22	ig(a	ig(a	NOUN
ejpam-4810	244	23	,	,	PUNCT
ejpam-4810	244	24	b	b	NOUN
ejpam-4810	244	25	)	)	PUNCT
ejpam-4810	244	26	because	because	SCONJ
ejpam-4810	244	27	s	s	NOUN
ejpam-4810	244	28	is	be	AUX
ejpam-4810	244	29	a	a	DET
ejpam-4810	244	30	2	2	NUM
ejpam-4810	244	31	-	-	PUNCT
ejpam-4810	244	32	path	path	NOUN
ejpam-4810	244	33	closure	closure	NOUN
ejpam-4810	244	34	absorbing	absorb	VERB
ejpam-4810	244	35	set	set	NOUN
ejpam-4810	244	36	.	.	PUNCT
ejpam-4810	245	1	also	also	ADV
ejpam-4810	245	2	,	,	PUNCT
ejpam-4810	245	3	since	since	SCONJ
ejpam-4810	245	4	s	s	NOUN
ejpam-4810	245	5	is	be	AUX
ejpam-4810	245	6	a	a	DET
ejpam-4810	245	7	pointwise	pointwise	ADJ
ejpam-4810	245	8	non	non	ADJ
ejpam-4810	245	9	-	-	ADJ
ejpam-4810	245	10	dominating	dominating	ADJ
ejpam-4810	245	11	set	set	NOUN
ejpam-4810	245	12	,	,	PUNCT
ejpam-4810	245	13	there	there	PRON
ejpam-4810	245	14	exists	exist	VERB
ejpam-4810	245	15	z	z	PROPN
ejpam-4810	245	16	∈	∈	PROPN
ejpam-4810	245	17	s	s	PART
ejpam-4810	245	18	\	\	X
ejpam-4810	245	19	{	{	PUNCT
ejpam-4810	245	20	a	a	PROPN
ejpam-4810	245	21	,	,	PUNCT
ejpam-4810	245	22	b	b	NOUN
ejpam-4810	245	23	}	}	PUNCT
ejpam-4810	245	24	such	such	ADJ
ejpam-4810	245	25	that	that	DET
ejpam-4810	245	26	v	v	NOUN
ejpam-4810	245	27	/∈	/∈	PUNCT
ejpam-4810	245	28	ng(z	ng(z	NUM
ejpam-4810	245	29	)	)	PUNCT
ejpam-4810	245	30	.	.	PUNCT
ejpam-4810	246	1	therefore	therefore	ADV
ejpam-4810	246	2	,	,	PUNCT
ejpam-4810	246	3	|ng(v	|ng(v	ADJ
ejpam-4810	246	4	)	)	PUNCT
ejpam-4810	246	5	∩	∩	NOUN
ejpam-4810	246	6	s|	s|	NOUN
ejpam-4810	246	7	=	=	SYM
ejpam-4810	246	8	2	2	X
ejpam-4810	246	9	.	.	X
ejpam-4810	246	10	for	for	ADP
ejpam-4810	246	11	the	the	DET
ejpam-4810	246	12	converse	converse	NOUN
ejpam-4810	246	13	,	,	PUNCT
ejpam-4810	246	14	suppose	suppose	VERB
ejpam-4810	246	15	that	that	SCONJ
ejpam-4810	246	16	n	n	PROPN
ejpam-4810	246	17	>	>	X
ejpam-4810	246	18	3	3	NUM
ejpam-4810	246	19	and	and	CCONJ
ejpam-4810	246	20	there	there	PRON
ejpam-4810	246	21	exists	exist	VERB
ejpam-4810	246	22	s	s	PROPN
ejpam-4810	246	23	⊆	⊆	NUM
ejpam-4810	246	24	v	v	NOUN
ejpam-4810	246	25	(	(	PUNCT
ejpam-4810	246	26	g	g	NOUN
ejpam-4810	246	27	)	)	PUNCT
ejpam-4810	246	28	with	with	ADP
ejpam-4810	246	29	|s|	|s|	NOUN
ejpam-4810	246	30	=	=	SYM
ejpam-4810	246	31	3	3	NUM
ejpam-4810	246	32	that	that	PRON
ejpam-4810	246	33	satisfies	satisfy	VERB
ejpam-4810	246	34	the	the	DET
ejpam-4810	246	35	given	give	VERB
ejpam-4810	246	36	conditions	condition	NOUN
ejpam-4810	246	37	.	.	PUNCT
ejpam-4810	247	1	let	let	VERB
ejpam-4810	247	2	v	v	NUM
ejpam-4810	247	3	∈	∈	PROPN
ejpam-4810	247	4	v	v	NOUN
ejpam-4810	247	5	(	(	PUNCT
ejpam-4810	247	6	g	g	NOUN
ejpam-4810	247	7	)	)	PUNCT
ejpam-4810	247	8	\	\	PUNCT
ejpam-4810	248	1	s.	s.	PROPN
ejpam-4810	248	2	then	then	ADV
ejpam-4810	248	3	,	,	PUNCT
ejpam-4810	248	4	by	by	ADP
ejpam-4810	248	5	assumption	assumption	NOUN
ejpam-4810	248	6	,	,	PUNCT
ejpam-4810	248	7	there	there	PRON
ejpam-4810	248	8	exist	exist	VERB
ejpam-4810	248	9	a	a	DET
ejpam-4810	248	10	,	,	PUNCT
ejpam-4810	248	11	b	b	PROPN
ejpam-4810	248	12	∈	∈	NOUN
ejpam-4810	248	13	s	s	VERB
ejpam-4810	248	14	with	with	ADP
ejpam-4810	248	15	dg(a	dg(a	PROPN
ejpam-4810	248	16	,	,	PUNCT
ejpam-4810	248	17	b	b	NOUN
ejpam-4810	248	18	)	)	PUNCT
ejpam-4810	248	19	=	=	SYM
ejpam-4810	248	20	2	2	NUM
ejpam-4810	248	21	and	and	CCONJ
ejpam-4810	248	22	v	v	ADP
ejpam-4810	248	23	∈	∈	PROPN
ejpam-4810	248	24	ig(a	ig(a	NOUN
ejpam-4810	248	25	,	,	PUNCT
ejpam-4810	248	26	b	b	NOUN
ejpam-4810	248	27	)	)	PUNCT
ejpam-4810	248	28	.	.	PUNCT
ejpam-4810	249	1	this	this	PRON
ejpam-4810	249	2	implies	imply	VERB
ejpam-4810	249	3	that	that	SCONJ
ejpam-4810	249	4	s	s	VERB
ejpam-4810	249	5	is	be	AUX
ejpam-4810	249	6	a	a	DET
ejpam-4810	249	7	2	2	NUM
ejpam-4810	249	8	-	-	PUNCT
ejpam-4810	249	9	path	path	NOUN
ejpam-4810	249	10	closure	closure	NOUN
ejpam-4810	249	11	absorbing	absorb	VERB
ejpam-4810	249	12	set	set	NOUN
ejpam-4810	249	13	of	of	ADP
ejpam-4810	249	14	g.	g.	PROPN
ejpam-4810	249	15	since	since	SCONJ
ejpam-4810	249	16	|ng(v	|ng(v	NOUN
ejpam-4810	249	17	)	)	PUNCT
ejpam-4810	249	18	∩	∩	NOUN
ejpam-4810	249	19	s|	s|	NOUN
ejpam-4810	249	20	=	=	SYM
ejpam-4810	249	21	2	2	NUM
ejpam-4810	249	22	,	,	PUNCT
ejpam-4810	249	23	s	s	VERB
ejpam-4810	249	24	is	be	AUX
ejpam-4810	249	25	also	also	ADV
ejpam-4810	249	26	a	a	DET
ejpam-4810	249	27	pointwise	pointwise	ADJ
ejpam-4810	249	28	non	non	ADJ
ejpam-4810	249	29	-	-	ADJ
ejpam-4810	249	30	dominating	dominating	ADJ
ejpam-4810	249	31	set	set	NOUN
ejpam-4810	249	32	of	of	ADP
ejpam-4810	249	33	g.	g.	PROPN
ejpam-4810	249	34	finally	finally	ADV
ejpam-4810	249	35	,	,	PUNCT
ejpam-4810	249	36	suppose	suppose	VERB
ejpam-4810	249	37	that	that	SCONJ
ejpam-4810	249	38	n	n	PROPN
ejpam-4810	249	39	=	=	SYM
ejpam-4810	249	40	3	3	X
ejpam-4810	249	41	.	.	PUNCT
ejpam-4810	249	42	then	then	ADV
ejpam-4810	249	43	s	s	VERB
ejpam-4810	249	44	=	=	SYM
ejpam-4810	249	45	v	v	PROPN
ejpam-4810	249	46	(	(	PUNCT
ejpam-4810	249	47	g	g	NOUN
ejpam-4810	249	48	)	)	PUNCT
ejpam-4810	249	49	is	be	AUX
ejpam-4810	249	50	both	both	PRON
ejpam-4810	249	51	a	a	DET
ejpam-4810	249	52	pointwise	pointwise	ADJ
ejpam-4810	249	53	non	non	ADJ
ejpam-4810	249	54	-	-	ADJ
ejpam-4810	249	55	dominating	dominating	ADJ
ejpam-4810	249	56	and	and	CCONJ
ejpam-4810	249	57	2	2	NUM
ejpam-4810	249	58	-	-	PUNCT
ejpam-4810	249	59	path	path	NOUN
ejpam-4810	249	60	closure	closure	NOUN
ejpam-4810	249	61	absorbing	absorb	VERB
ejpam-4810	249	62	set	set	NOUN
ejpam-4810	249	63	.	.	PUNCT
ejpam-4810	250	1	since	since	SCONJ
ejpam-4810	250	2	3	3	NUM
ejpam-4810	250	3	≤	≤	NUM
ejpam-4810	250	4	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	250	5	)	)	PUNCT
ejpam-4810	250	6	,	,	PUNCT
ejpam-4810	250	7	it	it	PRON
ejpam-4810	250	8	follows	follow	VERB
ejpam-4810	250	9	that	that	PRON
ejpam-4810	250	10	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	250	11	)	)	PUNCT
ejpam-4810	250	12	=	=	SYM
ejpam-4810	250	13	3	3	X
ejpam-4810	250	14	.	.	PUNCT
ejpam-4810	250	15	(	(	PUNCT
ejpam-4810	250	16	ii	ii	NOUN
ejpam-4810	250	17	)	)	PUNCT
ejpam-4810	250	18	suppose	suppose	VERB
ejpam-4810	250	19	ρ2pnd(g	ρ2pnd(g	X
ejpam-4810	250	20	)	)	PUNCT
ejpam-4810	250	21	=	=	VERB
ejpam-4810	250	22	n.	n.	NOUN
ejpam-4810	250	23	consider	consider	VERB
ejpam-4810	250	24	the	the	DET
ejpam-4810	250	25	following	follow	VERB
ejpam-4810	250	26	cases	case	NOUN
ejpam-4810	250	27	:	:	PUNCT
ejpam-4810	250	28	case	case	NOUN
ejpam-4810	250	29	1	1	NUM
ejpam-4810	250	30	.	.	PUNCT
ejpam-4810	251	1	g	g	PROPN
ejpam-4810	251	2	is	be	AUX
ejpam-4810	251	3	connected	connect	VERB
ejpam-4810	251	4	.	.	PUNCT
ejpam-4810	252	1	c.j	c.j	PROPN
ejpam-4810	252	2	.	.	PROPN
ejpam-4810	252	3	saromines	saromines	PROPN
ejpam-4810	252	4	,	,	PUNCT
ejpam-4810	252	5	s.	s.	PROPN
ejpam-4810	252	6	canoy	canoy	PROPN
ejpam-4810	252	7	,	,	PUNCT
ejpam-4810	252	8	jr	jr	PROPN
ejpam-4810	252	9	.	.	PROPN
ejpam-4810	252	10	,	,	PUNCT
ejpam-4810	252	11	/	/	SYM
ejpam-4810	252	12	eur	eur	NOUN
ejpam-4810	252	13	.	.	PUNCT
ejpam-4810	253	1	j.	j.	PROPN
ejpam-4810	253	2	pure	pure	PROPN
ejpam-4810	253	3	appl	appl	PROPN
ejpam-4810	253	4	.	.	PROPN
ejpam-4810	253	5	math	math	PROPN
ejpam-4810	253	6	,	,	PUNCT
ejpam-4810	253	7	16	16	NUM
ejpam-4810	253	8	(	(	PUNCT
ejpam-4810	253	9	3	3	NUM
ejpam-4810	253	10	)	)	PUNCT
ejpam-4810	253	11	(	(	PUNCT
ejpam-4810	253	12	2023	2023	NUM
ejpam-4810	253	13	)	)	PUNCT
ejpam-4810	253	14	,	,	PUNCT
ejpam-4810	253	15	1568	1568	NUM
ejpam-4810	253	16	-	-	SYM
ejpam-4810	253	17	1579	1579	NUM
ejpam-4810	253	18	1573	1573	NUM
ejpam-4810	253	19	suppose	suppose	VERB
ejpam-4810	253	20	there	there	PRON
ejpam-4810	253	21	exist	exist	VERB
ejpam-4810	253	22	p	p	PRON
ejpam-4810	253	23	,	,	PUNCT
ejpam-4810	253	24	q	q	PROPN
ejpam-4810	253	25	∈	∈	PROPN
ejpam-4810	253	26	v	v	NOUN
ejpam-4810	253	27	(	(	PUNCT
ejpam-4810	253	28	g	g	NOUN
ejpam-4810	253	29	)	)	PUNCT
ejpam-4810	253	30	with	with	ADP
ejpam-4810	253	31	dg(p	dg(p	NOUN
ejpam-4810	253	32	,	,	PUNCT
ejpam-4810	253	33	q	q	X
ejpam-4810	253	34	)	)	PUNCT
ejpam-4810	253	35	=	=	SYM
ejpam-4810	253	36	2	2	NUM
ejpam-4810	253	37	such	such	ADJ
ejpam-4810	253	38	that	that	DET
ejpam-4810	253	39	ng(p)∩ng(q	ng(p)∩ng(q	NOUN
ejpam-4810	253	40	)	)	PUNCT
ejpam-4810	253	41	contains	contain	VERB
ejpam-4810	253	42	a	a	DET
ejpam-4810	253	43	non	non	ADJ
ejpam-4810	253	44	-	-	ADJ
ejpam-4810	253	45	dominating	dominating	ADJ
ejpam-4810	253	46	vertex	vertex	NOUN
ejpam-4810	253	47	,	,	PUNCT
ejpam-4810	253	48	say	say	VERB
ejpam-4810	253	49	z.	z.	PROPN
ejpam-4810	253	50	then	then	ADV
ejpam-4810	253	51	there	there	PRON
ejpam-4810	253	52	is	be	VERB
ejpam-4810	253	53	a	a	DET
ejpam-4810	253	54	vertex	vertex	NOUN
ejpam-4810	253	55	w	w	NOUN
ejpam-4810	253	56	∈	∈	PROPN
ejpam-4810	253	57	v	v	ADP
ejpam-4810	253	58	(	(	PUNCT
ejpam-4810	253	59	g)\ng(z	g)\ng(z	NOUN
ejpam-4810	253	60	)	)	PUNCT
ejpam-4810	253	61	.	.	PUNCT
ejpam-4810	254	1	this	this	PRON
ejpam-4810	254	2	implies	imply	VERB
ejpam-4810	254	3	that	that	SCONJ
ejpam-4810	254	4	v	v	X
ejpam-4810	254	5	(	(	PUNCT
ejpam-4810	254	6	g	g	NOUN
ejpam-4810	254	7	)	)	PUNCT
ejpam-4810	254	8	\	\	NOUN
ejpam-4810	254	9	{	{	PUNCT
ejpam-4810	254	10	z	z	NOUN
ejpam-4810	254	11	}	}	PUNCT
ejpam-4810	254	12	is	be	AUX
ejpam-4810	254	13	a	a	DET
ejpam-4810	254	14	pointwise	pointwise	ADJ
ejpam-4810	254	15	non	non	ADJ
ejpam-4810	254	16	-	-	ADJ
ejpam-4810	254	17	dominating	dominating	ADJ
ejpam-4810	254	18	and	and	CCONJ
ejpam-4810	254	19	2	2	NUM
ejpam-4810	254	20	-	-	PUNCT
ejpam-4810	254	21	path	path	NOUN
ejpam-4810	254	22	closure	closure	NOUN
ejpam-4810	254	23	absorbing	absorb	VERB
ejpam-4810	254	24	set	set	NOUN
ejpam-4810	254	25	of	of	ADP
ejpam-4810	254	26	g	g	NOUN
ejpam-4810	254	27	,	,	PUNCT
ejpam-4810	254	28	contrary	contrary	ADV
ejpam-4810	254	29	to	to	ADP
ejpam-4810	254	30	the	the	DET
ejpam-4810	254	31	assumption	assumption	NOUN
ejpam-4810	254	32	that	that	SCONJ
ejpam-4810	254	33	ρ2pnd(g	ρ2pnd(g	X
ejpam-4810	254	34	)	)	PUNCT
ejpam-4810	254	35	=	=	VERB
ejpam-4810	254	36	n.	n.	PROPN
ejpam-4810	254	37	thus	thus	ADV
ejpam-4810	254	38	,	,	PUNCT
ejpam-4810	254	39	ng(x	ng(x	NUM
ejpam-4810	254	40	)	)	PUNCT
ejpam-4810	254	41	∩	∩	NOUN
ejpam-4810	254	42	ng(y	ng(y	NOUN
ejpam-4810	254	43	)	)	PUNCT
ejpam-4810	254	44	contains	contain	VERB
ejpam-4810	254	45	dominating	dominating	NOUN
ejpam-4810	254	46	vertices	vertex	NOUN
ejpam-4810	254	47	of	of	ADP
ejpam-4810	254	48	g	g	NOUN
ejpam-4810	254	49	only	only	ADV
ejpam-4810	254	50	for	for	ADP
ejpam-4810	254	51	every	every	DET
ejpam-4810	254	52	pair	pair	NOUN
ejpam-4810	254	53	of	of	ADP
ejpam-4810	254	54	vertices	vertex	NOUN
ejpam-4810	254	55	x	x	X
ejpam-4810	254	56	,	,	PUNCT
ejpam-4810	254	57	y	y	PROPN
ejpam-4810	254	58	with	with	ADP
ejpam-4810	254	59	dg(x	dg(x	PROPN
ejpam-4810	254	60	,	,	PUNCT
ejpam-4810	254	61	y	y	NOUN
ejpam-4810	254	62	)	)	PUNCT
ejpam-4810	254	63	=	=	SYM
ejpam-4810	254	64	2	2	NUM
ejpam-4810	254	65	,	,	PUNCT
ejpam-4810	254	66	showing	show	VERB
ejpam-4810	254	67	that	that	SCONJ
ejpam-4810	254	68	(	(	PUNCT
ejpam-4810	254	69	a	a	X
ejpam-4810	254	70	)	)	PUNCT
ejpam-4810	254	71	holds	hold	NOUN
ejpam-4810	254	72	.	.	PUNCT
ejpam-4810	255	1	case	case	NOUN
ejpam-4810	255	2	2	2	NUM
ejpam-4810	255	3	.	.	X
ejpam-4810	256	1	g	g	PROPN
ejpam-4810	256	2	is	be	AUX
ejpam-4810	256	3	disconnected	disconnect	VERB
ejpam-4810	256	4	.	.	PUNCT
ejpam-4810	257	1	suppose	suppose	VERB
ejpam-4810	257	2	there	there	PRON
ejpam-4810	257	3	exists	exist	VERB
ejpam-4810	257	4	a	a	DET
ejpam-4810	257	5	component	component	NOUN
ejpam-4810	257	6	h	h	NOUN
ejpam-4810	257	7	of	of	ADP
ejpam-4810	257	8	g	g	PROPN
ejpam-4810	257	9	that	that	PRON
ejpam-4810	257	10	is	be	AUX
ejpam-4810	257	11	not	not	PART
ejpam-4810	257	12	complete	complete	ADJ
ejpam-4810	257	13	.	.	PUNCT
ejpam-4810	258	1	then	then	ADV
ejpam-4810	258	2	there	there	PRON
ejpam-4810	258	3	exist	exist	VERB
ejpam-4810	258	4	v	v	ADP
ejpam-4810	258	5	,	,	PUNCT
ejpam-4810	258	6	w	w	PROPN
ejpam-4810	258	7	∈	∈	PROPN
ejpam-4810	258	8	v	v	ADP
ejpam-4810	258	9	(	(	PUNCT
ejpam-4810	258	10	h	h	NOUN
ejpam-4810	258	11	)	)	PUNCT
ejpam-4810	258	12	such	such	ADJ
ejpam-4810	258	13	that	that	PRON
ejpam-4810	258	14	dg(v	dg(v	NOUN
ejpam-4810	258	15	,	,	PUNCT
ejpam-4810	258	16	w	w	NOUN
ejpam-4810	258	17	)	)	PUNCT
ejpam-4810	258	18	=	=	SYM
ejpam-4810	258	19	2	2	X
ejpam-4810	258	20	.	.	X
ejpam-4810	258	21	let	let	VERB
ejpam-4810	258	22	u	u	PRON
ejpam-4810	258	23	∈	∈	PROPN
ejpam-4810	258	24	ng(v	ng(v	NOUN
ejpam-4810	258	25	)	)	PUNCT
ejpam-4810	258	26	∩	∩	NOUN
ejpam-4810	258	27	ng(w	ng(w	NOUN
ejpam-4810	258	28	)	)	PUNCT
ejpam-4810	258	29	.	.	PUNCT
ejpam-4810	259	1	then	then	ADV
ejpam-4810	259	2	v	v	X
ejpam-4810	259	3	(	(	PUNCT
ejpam-4810	259	4	g	g	NOUN
ejpam-4810	259	5	)	)	PUNCT
ejpam-4810	259	6	\	\	NOUN
ejpam-4810	259	7	{	{	PUNCT
ejpam-4810	259	8	u	u	NOUN
ejpam-4810	259	9	}	}	PUNCT
ejpam-4810	259	10	is	be	AUX
ejpam-4810	259	11	a	a	DET
ejpam-4810	259	12	2	2	NUM
ejpam-4810	259	13	-	-	PUNCT
ejpam-4810	259	14	path	path	NOUN
ejpam-4810	259	15	closure	closure	NOUN
ejpam-4810	259	16	absorbing	absorb	VERB
ejpam-4810	259	17	set	set	NOUN
ejpam-4810	259	18	of	of	ADP
ejpam-4810	259	19	g.	g.	PROPN
ejpam-4810	259	20	let	let	VERB
ejpam-4810	259	21	h	h	PRON
ejpam-4810	259	22	′	′	PROPN
ejpam-4810	259	23	be	be	AUX
ejpam-4810	259	24	a	a	DET
ejpam-4810	259	25	component	component	NOUN
ejpam-4810	259	26	of	of	ADP
ejpam-4810	259	27	g	g	NOUN
ejpam-4810	259	28	with	with	ADP
ejpam-4810	259	29	h	h	NOUN
ejpam-4810	259	30	′	′	NUM
ejpam-4810	260	1	̸=	̸=	PROPN
ejpam-4810	260	2	h	h	NOUN
ejpam-4810	261	1	and	and	CCONJ
ejpam-4810	261	2	pick	pick	VERB
ejpam-4810	261	3	u	u	NOUN
ejpam-4810	261	4	′	′	NOUN
ejpam-4810	261	5	∈	∈	PROPN
ejpam-4810	261	6	v	v	NOUN
ejpam-4810	261	7	(	(	PUNCT
ejpam-4810	261	8	h	h	NOUN
ejpam-4810	261	9	)	)	PUNCT
ejpam-4810	261	10	.	.	PUNCT
ejpam-4810	262	1	then	then	ADV
ejpam-4810	262	2	u	u	NOUN
ejpam-4810	262	3	′	′	NOUN
ejpam-4810	262	4	∈	∈	PROPN
ejpam-4810	262	5	v	v	NOUN
ejpam-4810	262	6	(	(	PUNCT
ejpam-4810	262	7	g	g	NOUN
ejpam-4810	262	8	)	)	PUNCT
ejpam-4810	262	9	\	\	NOUN
ejpam-4810	263	1	{	{	PUNCT
ejpam-4810	263	2	u	u	NOUN
ejpam-4810	263	3	}	}	PUNCT
ejpam-4810	263	4	and	and	CCONJ
ejpam-4810	263	5	uu	uu	INTJ
ejpam-4810	263	6	′	′	NUM
ejpam-4810	263	7	∈	∈	PROPN
ejpam-4810	263	8	e(g	e(g	PROPN
ejpam-4810	263	9	)	)	PUNCT
ejpam-4810	263	10	.	.	PUNCT
ejpam-4810	264	1	hence	hence	ADV
ejpam-4810	264	2	,	,	PUNCT
ejpam-4810	264	3	v	v	X
ejpam-4810	264	4	(	(	PUNCT
ejpam-4810	264	5	g	g	NOUN
ejpam-4810	264	6	)	)	PUNCT
ejpam-4810	264	7	\	\	NOUN
ejpam-4810	264	8	{	{	PUNCT
ejpam-4810	264	9	u	u	NOUN
ejpam-4810	264	10	}	}	PUNCT
ejpam-4810	264	11	is	be	AUX
ejpam-4810	264	12	also	also	ADV
ejpam-4810	264	13	a	a	DET
ejpam-4810	264	14	pointwise	pointwise	ADJ
ejpam-4810	264	15	non	non	ADJ
ejpam-4810	264	16	-	-	ADJ
ejpam-4810	264	17	dominating	dominating	ADJ
ejpam-4810	264	18	set	set	NOUN
ejpam-4810	264	19	of	of	ADP
ejpam-4810	264	20	g.	g.	PROPN
ejpam-4810	264	21	this	this	PRON
ejpam-4810	264	22	gives	give	VERB
ejpam-4810	264	23	a	a	DET
ejpam-4810	264	24	contradiction	contradiction	NOUN
ejpam-4810	264	25	.	.	PUNCT
ejpam-4810	265	1	thus	thus	ADV
ejpam-4810	265	2	,	,	PUNCT
ejpam-4810	265	3	every	every	DET
ejpam-4810	265	4	component	component	NOUN
ejpam-4810	265	5	of	of	ADP
ejpam-4810	265	6	g	g	PROPN
ejpam-4810	265	7	is	be	AUX
ejpam-4810	265	8	complete	complete	ADJ
ejpam-4810	265	9	.	.	PUNCT
ejpam-4810	266	1	for	for	ADP
ejpam-4810	266	2	the	the	DET
ejpam-4810	266	3	converse	converse	NOUN
ejpam-4810	266	4	,	,	PUNCT
ejpam-4810	266	5	suppose	suppose	VERB
ejpam-4810	266	6	first	first	ADV
ejpam-4810	266	7	that	that	SCONJ
ejpam-4810	266	8	(	(	PUNCT
ejpam-4810	266	9	a	a	PRON
ejpam-4810	266	10	)	)	PUNCT
ejpam-4810	266	11	holds	hold	VERB
ejpam-4810	266	12	.	.	PUNCT
ejpam-4810	267	1	let	let	VERB
ejpam-4810	267	2	s	s	PRON
ejpam-4810	267	3	be	be	AUX
ejpam-4810	267	4	a	a	DET
ejpam-4810	267	5	ρ2pnd	ρ2pnd	ADV
ejpam-4810	267	6	-	-	PUNCT
ejpam-4810	267	7	set	set	NOUN
ejpam-4810	267	8	of	of	ADP
ejpam-4810	267	9	g.	g.	PROPN
ejpam-4810	267	10	suppose	suppose	VERB
ejpam-4810	267	11	s	s	VERB
ejpam-4810	267	12	̸=	̸=	PROPN
ejpam-4810	267	13	v	v	NOUN
ejpam-4810	267	14	(	(	PUNCT
ejpam-4810	267	15	g	g	NOUN
ejpam-4810	267	16	)	)	PUNCT
ejpam-4810	267	17	,	,	PUNCT
ejpam-4810	267	18	say	say	VERB
ejpam-4810	267	19	v	v	NUM
ejpam-4810	267	20	∈	∈	PROPN
ejpam-4810	267	21	v	v	NOUN
ejpam-4810	267	22	(	(	PUNCT
ejpam-4810	267	23	g	g	NOUN
ejpam-4810	267	24	)	)	PUNCT
ejpam-4810	267	25	\	\	PUNCT
ejpam-4810	268	1	s.	s.	PROPN
ejpam-4810	268	2	since	since	SCONJ
ejpam-4810	268	3	s	s	PROPN
ejpam-4810	268	4	is	be	AUX
ejpam-4810	268	5	a	a	DET
ejpam-4810	268	6	2	2	NUM
ejpam-4810	268	7	-	-	PUNCT
ejpam-4810	268	8	path	path	NOUN
ejpam-4810	268	9	closure	closure	NOUN
ejpam-4810	268	10	absorbing	absorb	VERB
ejpam-4810	268	11	set	set	NOUN
ejpam-4810	268	12	of	of	ADP
ejpam-4810	268	13	g	g	NOUN
ejpam-4810	268	14	,	,	PUNCT
ejpam-4810	268	15	there	there	PRON
ejpam-4810	268	16	exist	exist	VERB
ejpam-4810	268	17	x	x	NOUN
ejpam-4810	268	18	,	,	PUNCT
ejpam-4810	268	19	y	y	PROPN
ejpam-4810	268	20	∈	∈	PROPN
ejpam-4810	268	21	s	s	VERB
ejpam-4810	268	22	such	such	ADJ
ejpam-4810	268	23	that	that	DET
ejpam-4810	268	24	dg(x	dg(x	NOUN
ejpam-4810	268	25	,	,	PUNCT
ejpam-4810	268	26	y	y	NOUN
ejpam-4810	268	27	)	)	PUNCT
ejpam-4810	268	28	=	=	SYM
ejpam-4810	268	29	2	2	NUM
ejpam-4810	268	30	and	and	CCONJ
ejpam-4810	268	31	v	v	ADP
ejpam-4810	268	32	∈	∈	NOUN
ejpam-4810	268	33	ig(x	ig(x	X
ejpam-4810	268	34	,	,	PUNCT
ejpam-4810	268	35	y	y	NOUN
ejpam-4810	268	36	)	)	PUNCT
ejpam-4810	268	37	.	.	PUNCT
ejpam-4810	269	1	by	by	ADP
ejpam-4810	269	2	assumption	assumption	NOUN
ejpam-4810	269	3	,	,	PUNCT
ejpam-4810	269	4	v	v	NOUN
ejpam-4810	269	5	is	be	AUX
ejpam-4810	269	6	a	a	DET
ejpam-4810	269	7	dominating	dominating	NOUN
ejpam-4810	269	8	vertex	vertex	NOUN
ejpam-4810	269	9	of	of	ADP
ejpam-4810	269	10	g.	g.	PROPN
ejpam-4810	269	11	therefore	therefore	ADV
ejpam-4810	269	12	,	,	PUNCT
ejpam-4810	269	13	s	s	VERB
ejpam-4810	269	14	is	be	AUX
ejpam-4810	269	15	not	not	PART
ejpam-4810	269	16	a	a	DET
ejpam-4810	269	17	pointwise	pointwise	ADJ
ejpam-4810	269	18	non	non	ADJ
ejpam-4810	269	19	-	-	ADJ
ejpam-4810	269	20	dominating	dominating	ADJ
ejpam-4810	269	21	set	set	NOUN
ejpam-4810	269	22	,	,	PUNCT
ejpam-4810	269	23	a	a	DET
ejpam-4810	269	24	contradiction	contradiction	NOUN
ejpam-4810	269	25	.	.	PUNCT
ejpam-4810	270	1	hence	hence	ADV
ejpam-4810	270	2	,	,	PUNCT
ejpam-4810	270	3	s	s	NOUN
ejpam-4810	270	4	=	=	SYM
ejpam-4810	270	5	v	v	X
ejpam-4810	270	6	(	(	PUNCT
ejpam-4810	270	7	g	g	NOUN
ejpam-4810	270	8	)	)	PUNCT
ejpam-4810	270	9	and	and	CCONJ
ejpam-4810	270	10	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	270	11	)	)	PUNCT
ejpam-4810	270	12	=	=	VERB
ejpam-4810	271	1	n.	n.	PROPN
ejpam-4810	271	2	next	next	ADV
ejpam-4810	271	3	,	,	PUNCT
ejpam-4810	271	4	suppose	suppose	VERB
ejpam-4810	271	5	that	that	SCONJ
ejpam-4810	271	6	(	(	PUNCT
ejpam-4810	271	7	b	b	X
ejpam-4810	271	8	)	)	PUNCT
ejpam-4810	271	9	holds	hold	NOUN
ejpam-4810	271	10	.	.	PUNCT
ejpam-4810	272	1	then	then	ADV
ejpam-4810	272	2	the	the	DET
ejpam-4810	272	3	only	only	ADJ
ejpam-4810	272	4	2	2	NUM
ejpam-4810	272	5	-	-	PUNCT
ejpam-4810	272	6	path	path	NOUN
ejpam-4810	272	7	closure	closure	NOUN
ejpam-4810	272	8	absorbing	absorb	VERB
ejpam-4810	272	9	set	set	NOUN
ejpam-4810	272	10	of	of	ADP
ejpam-4810	272	11	g	g	PROPN
ejpam-4810	272	12	is	be	AUX
ejpam-4810	272	13	v	v	NOUN
ejpam-4810	272	14	(	(	PUNCT
ejpam-4810	272	15	g	g	NOUN
ejpam-4810	272	16	)	)	PUNCT
ejpam-4810	272	17	.	.	PUNCT
ejpam-4810	273	1	therefore	therefore	ADV
ejpam-4810	273	2	,	,	PUNCT
ejpam-4810	273	3	v	v	X
ejpam-4810	273	4	(	(	PUNCT
ejpam-4810	273	5	g	g	NOUN
ejpam-4810	273	6	)	)	PUNCT
ejpam-4810	273	7	is	be	AUX
ejpam-4810	273	8	the	the	DET
ejpam-4810	273	9	only	only	ADJ
ejpam-4810	273	10	pointwise	pointwise	PROPN
ejpam-4810	273	11	non	non	ADJ
ejpam-4810	273	12	-	-	ADJ
ejpam-4810	273	13	dominating	dominating	ADJ
ejpam-4810	273	14	and	and	CCONJ
ejpam-4810	273	15	2	2	NUM
ejpam-4810	273	16	-	-	PUNCT
ejpam-4810	273	17	path	path	NOUN
ejpam-4810	273	18	closure	closure	NOUN
ejpam-4810	273	19	absorbing	absorb	VERB
ejpam-4810	273	20	set	set	NOUN
ejpam-4810	273	21	of	of	ADP
ejpam-4810	273	22	g.	g.	PROPN
ejpam-4810	273	23	accordingly	accordingly	ADV
ejpam-4810	273	24	,	,	PUNCT
ejpam-4810	273	25	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	273	26	)	)	PUNCT
ejpam-4810	274	1	=	=	VERB
ejpam-4810	274	2	n.	n.	NOUN
ejpam-4810	274	3	the	the	DET
ejpam-4810	274	4	next	next	ADJ
ejpam-4810	274	5	result	result	NOUN
ejpam-4810	274	6	follows	follow	VERB
ejpam-4810	274	7	from	from	ADP
ejpam-4810	274	8	theorem	theorem	ADJ
ejpam-4810	274	9	2	2	NUM
ejpam-4810	274	10	.	.	PUNCT
ejpam-4810	274	11	corollary	corollary	ADJ
ejpam-4810	274	12	2	2	NUM
ejpam-4810	274	13	.	.	PUNCT
ejpam-4810	275	1	let	let	VERB
ejpam-4810	275	2	n	n	PRON
ejpam-4810	275	3	be	be	AUX
ejpam-4810	275	4	a	a	DET
ejpam-4810	275	5	positive	positive	ADJ
ejpam-4810	275	6	integer	integer	NOUN
ejpam-4810	275	7	and	and	CCONJ
ejpam-4810	275	8	n	n	PRON
ejpam-4810	275	9	≥	≥	NOUN
ejpam-4810	275	10	2	2	NUM
ejpam-4810	275	11	.	.	PUNCT
ejpam-4810	275	12	then	then	ADV
ejpam-4810	275	13	ρ2pnd(kn	ρ2pnd(kn	NUM
ejpam-4810	275	14	)	)	PUNCT
ejpam-4810	276	1	=	=	SYM
ejpam-4810	276	2	ρ2pnd(kn	ρ2pnd(kn	NUM
ejpam-4810	276	3	)	)	PUNCT
ejpam-4810	276	4	=	=	SYM
ejpam-4810	276	5	ρ2pnd(k1,n−1	ρ2pnd(k1,n−1	PROPN
ejpam-4810	276	6	)	)	PUNCT
ejpam-4810	276	7	=	=	SYM
ejpam-4810	277	1	n.	n.	NOUN
ejpam-4810	277	2	proposition	proposition	NOUN
ejpam-4810	277	3	1	1	X
ejpam-4810	277	4	.	.	PUNCT
ejpam-4810	278	1	let	let	VERB
ejpam-4810	278	2	m	m	PRON
ejpam-4810	278	3	and	and	CCONJ
ejpam-4810	278	4	n	n	ADV
ejpam-4810	278	5	be	be	AUX
ejpam-4810	278	6	positive	positive	ADJ
ejpam-4810	278	7	integers	integer	NOUN
ejpam-4810	278	8	with	with	ADP
ejpam-4810	278	9	m	m	PROPN
ejpam-4810	278	10	,	,	PUNCT
ejpam-4810	278	11	n	n	PRON
ejpam-4810	278	12	≥	≥	NOUN
ejpam-4810	278	13	2	2	NUM
ejpam-4810	278	14	.	.	PUNCT
ejpam-4810	279	1	then	then	ADV
ejpam-4810	279	2	ρ2pnd(km	ρ2pnd(km	NOUN
ejpam-4810	279	3	,	,	PUNCT
ejpam-4810	279	4	n	n	CCONJ
ejpam-4810	279	5	)	)	PUNCT
ejpam-4810	280	1	=	=	PRON
ejpam-4810	280	2	{	{	PUNCT
ejpam-4810	280	3	3	3	NUM
ejpam-4810	280	4	if	if	SCONJ
ejpam-4810	280	5	m	m	VERB
ejpam-4810	280	6	=	=	SYM
ejpam-4810	280	7	2	2	NUM
ejpam-4810	280	8	or	or	CCONJ
ejpam-4810	280	9	n	n	NOUN
ejpam-4810	280	10	=	=	SYM
ejpam-4810	280	11	2	2	NUM
ejpam-4810	280	12	4	4	NUM
ejpam-4810	280	13	if	if	SCONJ
ejpam-4810	280	14	m	m	PROPN
ejpam-4810	280	15	≥	≥	NOUN
ejpam-4810	280	16	3	3	NUM
ejpam-4810	280	17	and	and	CCONJ
ejpam-4810	280	18	n	n	PRON
ejpam-4810	280	19	≥	≥	NOUN
ejpam-4810	280	20	2	2	NUM
ejpam-4810	280	21	.	.	PUNCT
ejpam-4810	281	1	proof	proof	NOUN
ejpam-4810	281	2	.	.	PUNCT
ejpam-4810	282	1	suppose	suppose	VERB
ejpam-4810	282	2	m	m	VERB
ejpam-4810	282	3	=	=	SYM
ejpam-4810	282	4	2	2	NUM
ejpam-4810	282	5	or	or	CCONJ
ejpam-4810	282	6	n	n	NOUN
ejpam-4810	282	7	=	=	SYM
ejpam-4810	282	8	2	2	NUM
ejpam-4810	282	9	,	,	PUNCT
ejpam-4810	282	10	say	say	VERB
ejpam-4810	282	11	m	m	VERB
ejpam-4810	282	12	=	=	ADJ
ejpam-4810	282	13	2	2	X
ejpam-4810	282	14	.	.	X
ejpam-4810	282	15	choose	choose	VERB
ejpam-4810	282	16	any	any	DET
ejpam-4810	282	17	w	w	PROPN
ejpam-4810	282	18	∈	∈	PROPN
ejpam-4810	282	19	v	v	NOUN
ejpam-4810	282	20	(	(	PUNCT
ejpam-4810	282	21	kn	kn	PROPN
ejpam-4810	282	22	)	)	PUNCT
ejpam-4810	282	23	.	.	PUNCT
ejpam-4810	283	1	then	then	ADV
ejpam-4810	283	2	s	s	VERB
ejpam-4810	283	3	=	=	SYM
ejpam-4810	283	4	v	v	PROPN
ejpam-4810	283	5	(	(	PUNCT
ejpam-4810	283	6	km	km	NOUN
ejpam-4810	283	7	)	)	PUNCT
ejpam-4810	283	8	∪	∪	NOUN
ejpam-4810	283	9	{	{	PUNCT
ejpam-4810	283	10	w	w	NOUN
ejpam-4810	283	11	}	}	PUNCT
ejpam-4810	283	12	is	be	AUX
ejpam-4810	283	13	a	a	DET
ejpam-4810	283	14	pointwise	pointwise	ADJ
ejpam-4810	283	15	non	non	ADJ
ejpam-4810	283	16	-	-	ADJ
ejpam-4810	283	17	dominating	dominating	ADJ
ejpam-4810	283	18	and	and	CCONJ
ejpam-4810	283	19	2	2	NUM
ejpam-4810	283	20	-	-	PUNCT
ejpam-4810	283	21	path	path	NOUN
ejpam-4810	283	22	closure	closure	NOUN
ejpam-4810	283	23	absorbing	absorb	VERB
ejpam-4810	283	24	set	set	NOUN
ejpam-4810	283	25	of	of	ADP
ejpam-4810	283	26	km	km	PROPN
ejpam-4810	283	27	,	,	PUNCT
ejpam-4810	283	28	n.	n.	NOUN
ejpam-4810	283	29	by	by	ADP
ejpam-4810	283	30	theorem	theorem	NOUN
ejpam-4810	283	31	2	2	NUM
ejpam-4810	283	32	,	,	PUNCT
ejpam-4810	283	33	ρ2pnd(km	ρ2pnd(km	ADJ
ejpam-4810	283	34	,	,	PUNCT
ejpam-4810	283	35	n	n	CCONJ
ejpam-4810	283	36	)	)	PUNCT
ejpam-4810	283	37	=	=	SYM
ejpam-4810	283	38	|s|	|s|	NOUN
ejpam-4810	283	39	=	=	SYM
ejpam-4810	283	40	3	3	NUM
ejpam-4810	283	41	.	.	PUNCT
ejpam-4810	284	1	next	next	ADV
ejpam-4810	284	2	,	,	PUNCT
ejpam-4810	284	3	suppose	suppose	VERB
ejpam-4810	284	4	that	that	SCONJ
ejpam-4810	284	5	m	m	PROPN
ejpam-4810	284	6	≥	≥	NUM
ejpam-4810	284	7	3	3	NUM
ejpam-4810	284	8	and	and	CCONJ
ejpam-4810	284	9	n	n	PRON
ejpam-4810	284	10	≥	≥	NOUN
ejpam-4810	284	11	3	3	NUM
ejpam-4810	284	12	.	.	PUNCT
ejpam-4810	284	13	pick	pick	VERB
ejpam-4810	284	14	any	any	DET
ejpam-4810	284	15	x	x	NOUN
ejpam-4810	284	16	,	,	PUNCT
ejpam-4810	284	17	y	y	PROPN
ejpam-4810	284	18	∈	∈	PROPN
ejpam-4810	284	19	v	v	PROPN
ejpam-4810	284	20	(	(	PUNCT
ejpam-4810	284	21	km	km	PROPN
ejpam-4810	284	22	)	)	PUNCT
ejpam-4810	284	23	and	and	CCONJ
ejpam-4810	284	24	p	p	X
ejpam-4810	284	25	,	,	PUNCT
ejpam-4810	284	26	q	q	PROPN
ejpam-4810	284	27	∈	∈	PROPN
ejpam-4810	284	28	v	v	NOUN
ejpam-4810	284	29	(	(	PUNCT
ejpam-4810	284	30	kn	kn	PROPN
ejpam-4810	284	31	)	)	PUNCT
ejpam-4810	284	32	.	.	PUNCT
ejpam-4810	285	1	then	then	ADV
ejpam-4810	285	2	{	{	PUNCT
ejpam-4810	285	3	x	x	X
ejpam-4810	285	4	,	,	PUNCT
ejpam-4810	285	5	y	y	PROPN
ejpam-4810	285	6	,	,	PUNCT
ejpam-4810	285	7	p	p	X
ejpam-4810	285	8	,	,	PUNCT
ejpam-4810	285	9	q	q	X
ejpam-4810	285	10	}	}	PUNCT
ejpam-4810	285	11	is	be	AUX
ejpam-4810	285	12	a	a	DET
ejpam-4810	285	13	pointwise	pointwise	ADJ
ejpam-4810	285	14	non	non	ADJ
ejpam-4810	285	15	-	-	ADJ
ejpam-4810	285	16	dominating	dominating	ADJ
ejpam-4810	285	17	and	and	CCONJ
ejpam-4810	285	18	2	2	NUM
ejpam-4810	285	19	-	-	PUNCT
ejpam-4810	285	20	path	path	NOUN
ejpam-4810	285	21	closure	closure	NOUN
ejpam-4810	285	22	absorbing	absorb	VERB
ejpam-4810	285	23	set	set	NOUN
ejpam-4810	285	24	of	of	ADP
ejpam-4810	285	25	km	km	PROPN
ejpam-4810	285	26	,	,	PUNCT
ejpam-4810	285	27	n.	n.	NOUN
ejpam-4810	285	28	this	this	PRON
ejpam-4810	285	29	implies	imply	VERB
ejpam-4810	285	30	that	that	SCONJ
ejpam-4810	285	31	ρ2pnd(km	ρ2pnd(km	ADJ
ejpam-4810	285	32	,	,	PUNCT
ejpam-4810	285	33	n	n	CCONJ
ejpam-4810	285	34	)	)	PUNCT
ejpam-4810	285	35	≤	≤	NUM
ejpam-4810	285	36	4	4	NUM
ejpam-4810	285	37	.	.	PUNCT
ejpam-4810	286	1	let	let	VERB
ejpam-4810	286	2	s	s	PRON
ejpam-4810	286	3	◦	◦	VERB
ejpam-4810	286	4	be	be	AUX
ejpam-4810	286	5	a	a	DET
ejpam-4810	286	6	ρ2pnd	ρ2pnd	ADV
ejpam-4810	286	7	-	-	PUNCT
ejpam-4810	286	8	set	set	NOUN
ejpam-4810	286	9	of	of	ADP
ejpam-4810	286	10	km	km	PROPN
ejpam-4810	286	11	,	,	PUNCT
ejpam-4810	286	12	n.	n.	PROPN
ejpam-4810	286	13	suppose	suppose	VERB
ejpam-4810	286	14	further	far	ADV
ejpam-4810	286	15	that	that	SCONJ
ejpam-4810	286	16	|s	|s	NOUN
ejpam-4810	286	17	◦	◦	NOUN
ejpam-4810	286	18	|	|	NOUN
ejpam-4810	286	19	=	=	NOUN
ejpam-4810	286	20	3	3	X
ejpam-4810	286	21	.	.	PUNCT
ejpam-4810	286	22	since	since	SCONJ
ejpam-4810	286	23	s	s	NOUN
ejpam-4810	286	24	◦	◦	NOUN
ejpam-4810	286	25	is	be	AUX
ejpam-4810	286	26	a	a	DET
ejpam-4810	286	27	pointwise	pointwise	ADJ
ejpam-4810	286	28	non	non	ADJ
ejpam-4810	286	29	-	-	ADJ
ejpam-4810	286	30	dominating	dominating	ADJ
ejpam-4810	286	31	set	set	NOUN
ejpam-4810	286	32	,	,	PUNCT
ejpam-4810	286	33	s1	s1	PROPN
ejpam-4810	286	34	=	=	SYM
ejpam-4810	286	35	s	s	PROPN
ejpam-4810	286	36	◦	◦	NOUN
ejpam-4810	286	37	∩	∩	ADJ
ejpam-4810	286	38	v	v	X
ejpam-4810	286	39	(	(	PUNCT
ejpam-4810	286	40	km	km	NOUN
ejpam-4810	286	41	)	)	PUNCT
ejpam-4810	286	42	̸=	̸=	PROPN
ejpam-4810	286	43	∅	∅	NOUN
ejpam-4810	286	44	and	and	CCONJ
ejpam-4810	286	45	s2	s2	VERB
ejpam-4810	286	46	=	=	SYM
ejpam-4810	286	47	s	s	PROPN
ejpam-4810	286	48	◦	◦	NOUN
ejpam-4810	286	49	∩v	∩v	NOUN
ejpam-4810	286	50	(	(	PUNCT
ejpam-4810	286	51	kn	kn	PROPN
ejpam-4810	286	52	)	)	PUNCT
ejpam-4810	286	53	̸=	̸=	PROPN
ejpam-4810	286	54	∅.	∅.	NOUN
ejpam-4810	286	55	we	we	PRON
ejpam-4810	286	56	may	may	AUX
ejpam-4810	286	57	assume	assume	VERB
ejpam-4810	286	58	that	that	SCONJ
ejpam-4810	286	59	|s1|	|s1|	NOUN
ejpam-4810	286	60	=	=	SYM
ejpam-4810	287	1	1	1	X
ejpam-4810	287	2	.	.	PUNCT
ejpam-4810	287	3	then	then	ADV
ejpam-4810	287	4	|s2|	|s2|	NOUN
ejpam-4810	287	5	=	=	NOUN
ejpam-4810	287	6	2	2	X
ejpam-4810	287	7	.	.	PUNCT
ejpam-4810	287	8	let	let	VERB
ejpam-4810	287	9	z	z	NOUN
ejpam-4810	287	10	∈	∈	PROPN
ejpam-4810	287	11	v	v	NOUN
ejpam-4810	287	12	(	(	PUNCT
ejpam-4810	287	13	kn)\s	kn)\s	NOUN
ejpam-4810	287	14	◦	◦	NOUN
ejpam-4810	287	15	.	.	PUNCT
ejpam-4810	288	1	then	then	ADV
ejpam-4810	288	2	z	z	PROPN
ejpam-4810	288	3	/∈	/∈	PUNCT
ejpam-4810	288	4	ikm	ikm	PROPN
ejpam-4810	288	5	,	,	PUNCT
ejpam-4810	288	6	n(u	n(u	PROPN
ejpam-4810	288	7	,	,	PUNCT
ejpam-4810	288	8	v	v	NOUN
ejpam-4810	288	9	)	)	PUNCT
ejpam-4810	288	10	for	for	ADP
ejpam-4810	288	11	all	all	DET
ejpam-4810	288	12	u	u	NOUN
ejpam-4810	288	13	,	,	PUNCT
ejpam-4810	288	14	v	v	NOUN
ejpam-4810	288	15	∈	∈	PROPN
ejpam-4810	288	16	s	s	NOUN
ejpam-4810	288	17	◦	◦	NOUN
ejpam-4810	288	18	,	,	PUNCT
ejpam-4810	288	19	a	a	DET
ejpam-4810	288	20	contradiction	contradiction	NOUN
ejpam-4810	288	21	.	.	PUNCT
ejpam-4810	289	1	therefore	therefore	ADV
ejpam-4810	289	2	,	,	PUNCT
ejpam-4810	289	3	|s	|s	PROPN
ejpam-4810	289	4	◦	◦	NOUN
ejpam-4810	289	5	|	|	CCONJ
ejpam-4810	289	6	≥	≥	NOUN
ejpam-4810	289	7	4	4	NUM
ejpam-4810	289	8	.	.	PUNCT
ejpam-4810	289	9	accordingly	accordingly	ADV
ejpam-4810	289	10	,	,	PUNCT
ejpam-4810	289	11	ρ2pnd(km	ρ2pnd(km	ADJ
ejpam-4810	289	12	,	,	PUNCT
ejpam-4810	289	13	n	n	CCONJ
ejpam-4810	289	14	)	)	PUNCT
ejpam-4810	289	15	=	=	SYM
ejpam-4810	290	1	4	4	X
ejpam-4810	290	2	.	.	PUNCT
ejpam-4810	290	3	c.j	c.j	PROPN
ejpam-4810	290	4	.	.	PROPN
ejpam-4810	290	5	saromines	saromines	PROPN
ejpam-4810	290	6	,	,	PUNCT
ejpam-4810	290	7	s.	s.	PROPN
ejpam-4810	290	8	canoy	canoy	PROPN
ejpam-4810	290	9	,	,	PUNCT
ejpam-4810	290	10	jr	jr	PROPN
ejpam-4810	290	11	.	.	PROPN
ejpam-4810	290	12	,	,	PUNCT
ejpam-4810	290	13	/	/	SYM
ejpam-4810	290	14	eur	eur	NOUN
ejpam-4810	290	15	.	.	PUNCT
ejpam-4810	291	1	j.	j.	PROPN
ejpam-4810	291	2	pure	pure	PROPN
ejpam-4810	291	3	appl	appl	PROPN
ejpam-4810	291	4	.	.	PROPN
ejpam-4810	291	5	math	math	PROPN
ejpam-4810	291	6	,	,	PUNCT
ejpam-4810	291	7	16	16	NUM
ejpam-4810	291	8	(	(	PUNCT
ejpam-4810	291	9	3	3	NUM
ejpam-4810	291	10	)	)	PUNCT
ejpam-4810	291	11	(	(	PUNCT
ejpam-4810	291	12	2023	2023	NUM
ejpam-4810	291	13	)	)	PUNCT
ejpam-4810	291	14	,	,	PUNCT
ejpam-4810	291	15	1568	1568	NUM
ejpam-4810	291	16	-	-	SYM
ejpam-4810	291	17	1579	1579	NUM
ejpam-4810	291	18	1574	1574	NUM
ejpam-4810	291	19	proposition	proposition	NOUN
ejpam-4810	291	20	2	2	NUM
ejpam-4810	291	21	.	.	X
ejpam-4810	292	1	for	for	ADP
ejpam-4810	292	2	each	each	DET
ejpam-4810	292	3	positive	positive	ADJ
ejpam-4810	292	4	integer	integer	NOUN
ejpam-4810	292	5	n	n	PRON
ejpam-4810	292	6	≥	≥	NOUN
ejpam-4810	292	7	2	2	NUM
ejpam-4810	292	8	,	,	PUNCT
ejpam-4810	292	9	(	(	PUNCT
ejpam-4810	292	10	i	i	NOUN
ejpam-4810	292	11	)	)	PUNCT
ejpam-4810	292	12	ρ2pnd(pn	ρ2pnd(pn	NUM
ejpam-4810	292	13	)	)	PUNCT
ejpam-4810	292	14	=	=	SYM
ejpam-4810	293	1			NOUN
ejpam-4810	293	2	2	2	NUM
ejpam-4810	293	3	if	if	SCONJ
ejpam-4810	293	4	n	n	NOUN
ejpam-4810	293	5	=	=	SYM
ejpam-4810	293	6	2	2	NUM
ejpam-4810	293	7	3	3	NUM
ejpam-4810	293	8	if	if	SCONJ
ejpam-4810	293	9	n	n	NOUN
ejpam-4810	293	10	=	=	SYM
ejpam-4810	293	11	3	3	NUM
ejpam-4810	293	12	,	,	PUNCT
ejpam-4810	293	13	4	4	NUM
ejpam-4810	293	14	⌈n+1	⌈n+1	NOUN
ejpam-4810	293	15	2	2	NUM
ejpam-4810	293	16	⌉	⌉	NOUN
ejpam-4810	293	17	if	if	SCONJ
ejpam-4810	293	18	n	n	PRON
ejpam-4810	293	19	≥	≥	NOUN
ejpam-4810	293	20	5	5	NUM
ejpam-4810	293	21	(	(	PUNCT
ejpam-4810	293	22	ii	ii	NOUN
ejpam-4810	293	23	)	)	PUNCT
ejpam-4810	293	24	ρ2pnd(cn	ρ2pnd(cn	NOUN
ejpam-4810	293	25	)	)	PUNCT
ejpam-4810	294	1	=	=	PRON
ejpam-4810	294	2	{	{	PUNCT
ejpam-4810	294	3	3	3	NUM
ejpam-4810	294	4	if	if	SCONJ
ejpam-4810	294	5	n	n	X
ejpam-4810	294	6	=	=	SYM
ejpam-4810	294	7	3	3	NUM
ejpam-4810	294	8	,	,	PUNCT
ejpam-4810	294	9	4	4	NUM
ejpam-4810	294	10	⌈n2	⌈n2	NOUN
ejpam-4810	294	11	⌉	⌉	PUNCT
ejpam-4810	294	12	if	if	SCONJ
ejpam-4810	294	13	n	n	PRON
ejpam-4810	294	14	≥	≥	NOUN
ejpam-4810	294	15	5	5	NUM
ejpam-4810	294	16	proof	proof	NOUN
ejpam-4810	294	17	.	.	PUNCT
ejpam-4810	295	1	(	(	PUNCT
ejpam-4810	295	2	i	i	NOUN
ejpam-4810	295	3	)	)	PUNCT
ejpam-4810	295	4	clearly	clearly	ADV
ejpam-4810	295	5	,	,	PUNCT
ejpam-4810	295	6	ρ2pnd(p2	ρ2pnd(p2	PROPN
ejpam-4810	295	7	)	)	PUNCT
ejpam-4810	295	8	=	=	SYM
ejpam-4810	295	9	2	2	NUM
ejpam-4810	295	10	and	and	CCONJ
ejpam-4810	295	11	ρ2pnd(p3	ρ2pnd(p3	PROPN
ejpam-4810	295	12	)	)	PUNCT
ejpam-4810	295	13	=	=	SYM
ejpam-4810	295	14	ρ2pnd(p4	ρ2pnd(p4	NOUN
ejpam-4810	295	15	)	)	PUNCT
ejpam-4810	295	16	=	=	SYM
ejpam-4810	295	17	3	3	X
ejpam-4810	295	18	.	.	X
ejpam-4810	295	19	let	let	VERB
ejpam-4810	295	20	n	n	PRON
ejpam-4810	295	21	≥	≥	NOUN
ejpam-4810	295	22	5	5	NUM
ejpam-4810	295	23	.	.	PUNCT
ejpam-4810	296	1	if	if	SCONJ
ejpam-4810	296	2	n	n	NOUN
ejpam-4810	296	3	is	be	AUX
ejpam-4810	296	4	odd	odd	ADJ
ejpam-4810	296	5	,	,	PUNCT
ejpam-4810	296	6	then	then	ADV
ejpam-4810	296	7	s1	s1	PROPN
ejpam-4810	296	8	=	=	SYM
ejpam-4810	296	9	{	{	PUNCT
ejpam-4810	296	10	v1	v1	PROPN
ejpam-4810	296	11	,	,	PUNCT
ejpam-4810	296	12	v3	v3	PROPN
ejpam-4810	296	13	,	,	PUNCT
ejpam-4810	296	14	...	...	PUNCT
ejpam-4810	296	15	,	,	PUNCT
ejpam-4810	296	16	vn−2	vn−2	PROPN
ejpam-4810	296	17	,	,	PUNCT
ejpam-4810	296	18	vn	vn	PROPN
ejpam-4810	296	19	}	}	PUNCT
ejpam-4810	296	20	is	be	AUX
ejpam-4810	296	21	the	the	DET
ejpam-4810	296	22	only	only	ADJ
ejpam-4810	296	23	ρ2pnd	ρ2pnd	ADV
ejpam-4810	296	24	-	-	PUNCT
ejpam-4810	296	25	set	set	NOUN
ejpam-4810	296	26	of	of	ADP
ejpam-4810	296	27	pn	pn	PROPN
ejpam-4810	296	28	.	.	PROPN
ejpam-4810	296	29	hence	hence	ADV
ejpam-4810	296	30	,	,	PUNCT
ejpam-4810	296	31	ρ2pnd(pn	ρ2pnd(pn	PUNCT
ejpam-4810	296	32	)	)	PUNCT
ejpam-4810	296	33	=	=	SYM
ejpam-4810	296	34	n+1	n+1	PROPN
ejpam-4810	296	35	2	2	NUM
ejpam-4810	296	36	.	.	PUNCT
ejpam-4810	297	1	if	if	SCONJ
ejpam-4810	297	2	n	n	PRON
ejpam-4810	297	3	is	be	AUX
ejpam-4810	297	4	even	even	ADV
ejpam-4810	297	5	,	,	PUNCT
ejpam-4810	297	6	then	then	ADV
ejpam-4810	297	7	s2	s2	VERB
ejpam-4810	297	8	=	=	SYM
ejpam-4810	297	9	{	{	PUNCT
ejpam-4810	297	10	v1	v1	PROPN
ejpam-4810	297	11	,	,	PUNCT
ejpam-4810	297	12	v3	v3	PROPN
ejpam-4810	297	13	,	,	PUNCT
ejpam-4810	297	14	...	...	PUNCT
ejpam-4810	297	15	,	,	PUNCT
ejpam-4810	297	16	vn−3	vn−3	PROPN
ejpam-4810	297	17	,	,	PUNCT
ejpam-4810	297	18	vn−1	vn−1	ADJ
ejpam-4810	297	19	,	,	PUNCT
ejpam-4810	297	20	vn	vn	NOUN
ejpam-4810	297	21	}	}	PUNCT
ejpam-4810	297	22	and	and	CCONJ
ejpam-4810	297	23	s3	s3	PROPN
ejpam-4810	297	24	=	=	SYM
ejpam-4810	297	25	{	{	PUNCT
ejpam-4810	297	26	v1	v1	PROPN
ejpam-4810	297	27	,	,	PUNCT
ejpam-4810	297	28	v3	v3	PROPN
ejpam-4810	297	29	,	,	PUNCT
ejpam-4810	297	30	v4	v4	PROPN
ejpam-4810	297	31	...	...	PUNCT
ejpam-4810	297	32	,	,	PUNCT
ejpam-4810	297	33	vn−2	vn−2	PROPN
ejpam-4810	297	34	,	,	PUNCT
ejpam-4810	297	35	vn	vn	PROPN
ejpam-4810	297	36	}	}	PUNCT
ejpam-4810	297	37	are	be	AUX
ejpam-4810	297	38	the	the	DET
ejpam-4810	297	39	only	only	ADJ
ejpam-4810	297	40	ρ2pnd	ρ2pnd	NUM
ejpam-4810	297	41	-	-	PUNCT
ejpam-4810	297	42	sets	set	NOUN
ejpam-4810	297	43	of	of	ADP
ejpam-4810	297	44	pn	pn	PROPN
ejpam-4810	297	45	.	.	PUNCT
ejpam-4810	298	1	it	it	PRON
ejpam-4810	298	2	follows	follow	VERB
ejpam-4810	298	3	that	that	PRON
ejpam-4810	298	4	ρ2pnd(pn	ρ2pnd(pn	PUNCT
ejpam-4810	298	5	)	)	PUNCT
ejpam-4810	298	6	=	=	SYM
ejpam-4810	298	7	n+2	n+2	NUM
ejpam-4810	298	8	2	2	NUM
ejpam-4810	298	9	.	.	PUNCT
ejpam-4810	298	10	(	(	PUNCT
ejpam-4810	298	11	ii	ii	NOUN
ejpam-4810	298	12	)	)	PUNCT
ejpam-4810	298	13	by	by	ADP
ejpam-4810	298	14	theorem	theorem	NOUN
ejpam-4810	298	15	2(i	2(i	NUM
ejpam-4810	298	16	)	)	PUNCT
ejpam-4810	298	17	,	,	PUNCT
ejpam-4810	298	18	ρ2pnd(c3	ρ2pnd(c3	NUM
ejpam-4810	298	19	)	)	PUNCT
ejpam-4810	298	20	=	=	PUNCT
ejpam-4810	299	1	ρ2pnd(c4	ρ2pnd(c4	NOUN
ejpam-4810	299	2	)	)	PUNCT
ejpam-4810	299	3	=	=	SYM
ejpam-4810	300	1	3	3	X
ejpam-4810	300	2	.	.	X
ejpam-4810	300	3	let	let	VERB
ejpam-4810	300	4	n	n	PRON
ejpam-4810	300	5	≥	≥	NOUN
ejpam-4810	300	6	5	5	NUM
ejpam-4810	300	7	.	.	PUNCT
ejpam-4810	301	1	if	if	SCONJ
ejpam-4810	301	2	n	n	NOUN
ejpam-4810	301	3	is	be	AUX
ejpam-4810	301	4	odd	odd	ADJ
ejpam-4810	301	5	,	,	PUNCT
ejpam-4810	301	6	then	then	ADV
ejpam-4810	301	7	{	{	PUNCT
ejpam-4810	301	8	v1	v1	PROPN
ejpam-4810	301	9	,	,	PUNCT
ejpam-4810	301	10	v3	v3	PROPN
ejpam-4810	301	11	,	,	PUNCT
ejpam-4810	301	12	v5	v5	PROPN
ejpam-4810	301	13	,	,	PUNCT
ejpam-4810	301	14	...	...	PUNCT
ejpam-4810	301	15	,	,	PUNCT
ejpam-4810	301	16	vn−2	vn−2	PROPN
ejpam-4810	301	17	,	,	PUNCT
ejpam-4810	301	18	vn	vn	PROPN
ejpam-4810	301	19	}	}	PUNCT
ejpam-4810	301	20	is	be	AUX
ejpam-4810	301	21	a	a	DET
ejpam-4810	301	22	ρ2pnd	ρ2pnd	ADV
ejpam-4810	301	23	-	-	PUNCT
ejpam-4810	301	24	set	set	NOUN
ejpam-4810	301	25	of	of	ADP
ejpam-4810	301	26	cn	cn	PROPN
ejpam-4810	301	27	.	.	PUNCT
ejpam-4810	302	1	if	if	SCONJ
ejpam-4810	302	2	n	n	PRON
ejpam-4810	302	3	is	be	AUX
ejpam-4810	302	4	even	even	ADV
ejpam-4810	302	5	,	,	PUNCT
ejpam-4810	302	6	then	then	ADV
ejpam-4810	302	7	{	{	PUNCT
ejpam-4810	302	8	v1	v1	PROPN
ejpam-4810	302	9	,	,	PUNCT
ejpam-4810	302	10	v3	v3	PROPN
ejpam-4810	302	11	,	,	PUNCT
ejpam-4810	302	12	v5	v5	PROPN
ejpam-4810	302	13	,	,	PUNCT
ejpam-4810	302	14	...	...	PUNCT
ejpam-4810	302	15	,	,	PUNCT
ejpam-4810	302	16	vn−1	vn−1	PROPN
ejpam-4810	302	17	}	}	PUNCT
ejpam-4810	302	18	is	be	AUX
ejpam-4810	302	19	a	a	DET
ejpam-4810	302	20	ρ2pnd	ρ2pnd	ADV
ejpam-4810	302	21	-	-	PUNCT
ejpam-4810	302	22	set	set	NOUN
ejpam-4810	302	23	of	of	ADP
ejpam-4810	302	24	cn	cn	PROPN
ejpam-4810	302	25	.	.	PUNCT
ejpam-4810	302	26	therefore	therefore	ADV
ejpam-4810	302	27	,	,	PUNCT
ejpam-4810	302	28	ρ2pnd(cn	ρ2pnd(cn	NOUN
ejpam-4810	302	29	)	)	PUNCT
ejpam-4810	303	1	=	=	NOUN
ejpam-4810	303	2	⌈n2	⌈n2	VERB
ejpam-4810	303	3	⌉.	⌉.	ADV
ejpam-4810	303	4	from	from	ADP
ejpam-4810	303	5	the	the	DET
ejpam-4810	303	6	proof	proof	NOUN
ejpam-4810	303	7	of	of	ADP
ejpam-4810	303	8	proposition	proposition	NOUN
ejpam-4810	303	9	2	2	NUM
ejpam-4810	303	10	,	,	PUNCT
ejpam-4810	303	11	the	the	DET
ejpam-4810	303	12	next	next	ADJ
ejpam-4810	303	13	result	result	NOUN
ejpam-4810	303	14	follows	follow	VERB
ejpam-4810	303	15	.	.	PUNCT
ejpam-4810	304	1	corollary	corollary	ADJ
ejpam-4810	304	2	3	3	X
ejpam-4810	304	3	.	.	PUNCT
ejpam-4810	305	1	let	let	VERB
ejpam-4810	305	2	n	n	PRON
ejpam-4810	305	3	be	be	AUX
ejpam-4810	305	4	a	a	DET
ejpam-4810	305	5	positive	positive	ADJ
ejpam-4810	305	6	integer	integer	NOUN
ejpam-4810	305	7	.	.	PUNCT
ejpam-4810	306	1	then	then	ADV
ejpam-4810	306	2	(	(	PUNCT
ejpam-4810	306	3	i	i	NOUN
ejpam-4810	306	4	)	)	PUNCT
ejpam-4810	306	5	ρ2pnd(pn	ρ2pnd(pn	NUM
ejpam-4810	306	6	)	)	PUNCT
ejpam-4810	306	7	=	=	SYM
ejpam-4810	306	8	ρ2(pn	ρ2(pn	PROPN
ejpam-4810	306	9	)	)	PUNCT
ejpam-4810	306	10	for	for	ADP
ejpam-4810	306	11	all	all	DET
ejpam-4810	306	12	n	n	PRON
ejpam-4810	306	13	̸=	̸=	PROPN
ejpam-4810	306	14	3	3	NUM
ejpam-4810	306	15	and	and	CCONJ
ejpam-4810	306	16	(	(	PUNCT
ejpam-4810	306	17	ii	ii	NOUN
ejpam-4810	306	18	)	)	PUNCT
ejpam-4810	306	19	ρ2pnd(cn	ρ2pnd(cn	NOUN
ejpam-4810	306	20	)	)	PUNCT
ejpam-4810	306	21	=	=	SYM
ejpam-4810	307	1	ρ2(cn	ρ2(cn	NUM
ejpam-4810	307	2	)	)	PUNCT
ejpam-4810	307	3	for	for	ADP
ejpam-4810	307	4	all	all	DET
ejpam-4810	307	5	n	n	PRON
ejpam-4810	307	6	≥	≥	NOUN
ejpam-4810	307	7	3	3	NUM
ejpam-4810	307	8	.	.	PUNCT
ejpam-4810	308	1	the	the	DET
ejpam-4810	308	2	next	next	ADJ
ejpam-4810	308	3	result	result	NOUN
ejpam-4810	308	4	is	be	AUX
ejpam-4810	308	5	found	find	VERB
ejpam-4810	308	6	in	in	ADP
ejpam-4810	308	7	[	[	X
ejpam-4810	308	8	11	11	NUM
ejpam-4810	308	9	]	]	PUNCT
ejpam-4810	308	10	.	.	PUNCT
ejpam-4810	309	1	theorem	theorem	NOUN
ejpam-4810	309	2	3	3	X
ejpam-4810	309	3	.	.	PUNCT
ejpam-4810	310	1	let	let	VERB
ejpam-4810	310	2	g	g	NOUN
ejpam-4810	311	1	and	and	CCONJ
ejpam-4810	311	2	h	h	NOUN
ejpam-4810	311	3	be	be	VERB
ejpam-4810	311	4	any	any	DET
ejpam-4810	311	5	two	two	NUM
ejpam-4810	311	6	graphs	graph	NOUN
ejpam-4810	311	7	.	.	PUNCT
ejpam-4810	312	1	a	a	DET
ejpam-4810	312	2	set	set	NOUN
ejpam-4810	312	3	s	s	NOUN
ejpam-4810	312	4	⊆	⊆	NUM
ejpam-4810	312	5	v	v	NOUN
ejpam-4810	312	6	(	(	PUNCT
ejpam-4810	312	7	g	g	PROPN
ejpam-4810	312	8	+	+	NOUN
ejpam-4810	312	9	h	h	NOUN
ejpam-4810	312	10	)	)	PUNCT
ejpam-4810	312	11	is	be	AUX
ejpam-4810	312	12	hop	hop	NOUN
ejpam-4810	312	13	dominating	dominate	VERB
ejpam-4810	312	14	set	set	NOUN
ejpam-4810	312	15	of	of	ADP
ejpam-4810	312	16	g+h	g+h	PROPN
ejpam-4810	312	17	if	if	SCONJ
ejpam-4810	313	1	and	and	CCONJ
ejpam-4810	313	2	only	only	ADV
ejpam-4810	313	3	if	if	SCONJ
ejpam-4810	313	4	s	s	NOUN
ejpam-4810	313	5	=	=	PUNCT
ejpam-4810	313	6	sg	sg	PROPN
ejpam-4810	313	7	∪sh	∪sh	NOUN
ejpam-4810	313	8	,	,	PUNCT
ejpam-4810	313	9	where	where	SCONJ
ejpam-4810	313	10	sg	sg	PROPN
ejpam-4810	313	11	and	and	CCONJ
ejpam-4810	313	12	sh	sh	PROPN
ejpam-4810	313	13	are	be	AUX
ejpam-4810	313	14	pointwise	pointwise	PROPN
ejpam-4810	313	15	non	non	ADJ
ejpam-4810	313	16	-	-	ADJ
ejpam-4810	313	17	dominating	dominating	ADJ
ejpam-4810	313	18	sets	set	NOUN
ejpam-4810	313	19	of	of	ADP
ejpam-4810	313	20	g	g	PROPN
ejpam-4810	313	21	and	and	CCONJ
ejpam-4810	313	22	h	h	NOUN
ejpam-4810	313	23	,	,	PUNCT
ejpam-4810	313	24	respectively	respectively	ADV
ejpam-4810	313	25	.	.	PUNCT
ejpam-4810	314	1	theorem	theorem	ADJ
ejpam-4810	314	2	4	4	NUM
ejpam-4810	314	3	.	.	PUNCT
ejpam-4810	315	1	let	let	VERB
ejpam-4810	315	2	g	g	NOUN
ejpam-4810	315	3	and	and	CCONJ
ejpam-4810	315	4	h	h	NOUN
ejpam-4810	315	5	be	be	VERB
ejpam-4810	315	6	any	any	DET
ejpam-4810	315	7	two	two	NUM
ejpam-4810	315	8	graphs	graph	NOUN
ejpam-4810	315	9	.	.	PUNCT
ejpam-4810	316	1	a	a	DET
ejpam-4810	316	2	set	set	NOUN
ejpam-4810	316	3	s	s	NOUN
ejpam-4810	316	4	⊆	⊆	NUM
ejpam-4810	316	5	v	v	NOUN
ejpam-4810	316	6	(	(	PUNCT
ejpam-4810	316	7	g	g	PROPN
ejpam-4810	316	8	+	+	NOUN
ejpam-4810	316	9	h	h	NOUN
ejpam-4810	316	10	)	)	PUNCT
ejpam-4810	316	11	is	be	AUX
ejpam-4810	316	12	geodetic	geodetic	ADJ
ejpam-4810	316	13	hop	hop	NOUN
ejpam-4810	316	14	dominating	dominating	NOUN
ejpam-4810	316	15	set	set	NOUN
ejpam-4810	316	16	of	of	ADP
ejpam-4810	316	17	g	g	PROPN
ejpam-4810	317	1	+	+	CCONJ
ejpam-4810	317	2	h	h	NOUN
ejpam-4810	317	3	if	if	SCONJ
ejpam-4810	317	4	and	and	CCONJ
ejpam-4810	317	5	only	only	ADV
ejpam-4810	317	6	if	if	SCONJ
ejpam-4810	317	7	s	s	VERB
ejpam-4810	317	8	=	=	PUNCT
ejpam-4810	317	9	sg	sg	X
ejpam-4810	317	10	∪	∪	ADJ
ejpam-4810	317	11	sh	sh	PROPN
ejpam-4810	317	12	,	,	PUNCT
ejpam-4810	317	13	where	where	SCONJ
ejpam-4810	317	14	sg	sg	PROPN
ejpam-4810	317	15	and	and	CCONJ
ejpam-4810	317	16	sh	sh	PROPN
ejpam-4810	317	17	are	be	AUX
ejpam-4810	317	18	pointwise	pointwise	PROPN
ejpam-4810	317	19	non	non	ADJ
ejpam-4810	317	20	-	-	ADJ
ejpam-4810	317	21	dominating	dominating	ADJ
ejpam-4810	317	22	sets	set	NOUN
ejpam-4810	317	23	of	of	ADP
ejpam-4810	317	24	g	g	PROPN
ejpam-4810	317	25	and	and	CCONJ
ejpam-4810	317	26	h	h	NOUN
ejpam-4810	317	27	,	,	PUNCT
ejpam-4810	317	28	respectively	respectively	ADV
ejpam-4810	317	29	,	,	PUNCT
ejpam-4810	317	30	such	such	ADJ
ejpam-4810	317	31	that	that	SCONJ
ejpam-4810	317	32	(	(	PUNCT
ejpam-4810	317	33	i	i	NOUN
ejpam-4810	317	34	)	)	PUNCT
ejpam-4810	317	35	sg	sg	PROPN
ejpam-4810	317	36	is	be	AUX
ejpam-4810	317	37	a	a	DET
ejpam-4810	317	38	2	2	NUM
ejpam-4810	317	39	-	-	PUNCT
ejpam-4810	317	40	path	path	NOUN
ejpam-4810	317	41	closure	closure	NOUN
ejpam-4810	317	42	absorbing	absorb	VERB
ejpam-4810	317	43	set	set	NOUN
ejpam-4810	317	44	in	in	ADP
ejpam-4810	317	45	g	g	NOUN
ejpam-4810	317	46	whenever	whenever	SCONJ
ejpam-4810	317	47	⟨sh⟩	⟨sh⟩	PRON
ejpam-4810	317	48	is	be	AUX
ejpam-4810	317	49	a	a	DET
ejpam-4810	317	50	complete	complete	ADJ
ejpam-4810	317	51	subgraph	subgraph	NOUN
ejpam-4810	317	52	of	of	ADP
ejpam-4810	317	53	h	h	PROPN
ejpam-4810	317	54	and	and	CCONJ
ejpam-4810	317	55	(	(	PUNCT
ejpam-4810	317	56	ii	ii	NOUN
ejpam-4810	317	57	)	)	PUNCT
ejpam-4810	317	58	sh	sh	PROPN
ejpam-4810	317	59	is	be	AUX
ejpam-4810	317	60	a	a	DET
ejpam-4810	317	61	2	2	NUM
ejpam-4810	317	62	-	-	PUNCT
ejpam-4810	317	63	path	path	NOUN
ejpam-4810	317	64	closure	closure	NOUN
ejpam-4810	317	65	absorbing	absorb	VERB
ejpam-4810	317	66	set	set	NOUN
ejpam-4810	317	67	in	in	ADP
ejpam-4810	317	68	h	h	NOUN
ejpam-4810	317	69	whenever	whenever	SCONJ
ejpam-4810	317	70	⟨sg⟩	⟨sg⟩	PRON
ejpam-4810	317	71	is	be	AUX
ejpam-4810	317	72	a	a	DET
ejpam-4810	317	73	complete	complete	ADJ
ejpam-4810	317	74	subgraph	subgraph	NOUN
ejpam-4810	317	75	of	of	ADP
ejpam-4810	317	76	g.	g.	PROPN
ejpam-4810	317	77	proof	proof	PROPN
ejpam-4810	317	78	.	.	PUNCT
ejpam-4810	318	1	suppose	suppose	VERB
ejpam-4810	318	2	that	that	SCONJ
ejpam-4810	318	3	s	s	VERB
ejpam-4810	318	4	is	be	AUX
ejpam-4810	318	5	a	a	DET
ejpam-4810	318	6	geodetic	geodetic	ADJ
ejpam-4810	318	7	hop	hop	NOUN
ejpam-4810	318	8	dominating	dominating	NOUN
ejpam-4810	318	9	set	set	NOUN
ejpam-4810	318	10	of	of	ADP
ejpam-4810	318	11	g+h	g+h	PROPN
ejpam-4810	318	12	.	.	PUNCT
ejpam-4810	319	1	let	let	VERB
ejpam-4810	319	2	sg	sg	VERB
ejpam-4810	319	3	=	=	VERB
ejpam-4810	319	4	s	s	PART
ejpam-4810	319	5	∩v	∩v	NOUN
ejpam-4810	319	6	(	(	PUNCT
ejpam-4810	319	7	g	g	NOUN
ejpam-4810	319	8	)	)	PUNCT
ejpam-4810	319	9	and	and	CCONJ
ejpam-4810	319	10	sh	sh	INTJ
ejpam-4810	319	11	=	=	SYM
ejpam-4810	319	12	s	s	PROPN
ejpam-4810	319	13	∩	∩	ADJ
ejpam-4810	319	14	v	v	ADJ
ejpam-4810	319	15	(	(	PUNCT
ejpam-4810	319	16	h	h	NOUN
ejpam-4810	319	17	)	)	PUNCT
ejpam-4810	319	18	.	.	PUNCT
ejpam-4810	320	1	since	since	SCONJ
ejpam-4810	320	2	s	s	PROPN
ejpam-4810	320	3	is	be	AUX
ejpam-4810	320	4	a	a	DET
ejpam-4810	320	5	hop	hop	NOUN
ejpam-4810	320	6	dominating	dominating	NOUN
ejpam-4810	320	7	set	set	NOUN
ejpam-4810	320	8	,	,	PUNCT
ejpam-4810	320	9	by	by	ADP
ejpam-4810	320	10	theorem	theorem	NOUN
ejpam-4810	320	11	3	3	NUM
ejpam-4810	320	12	,	,	PUNCT
ejpam-4810	320	13	sg	sg	PROPN
ejpam-4810	320	14	and	and	CCONJ
ejpam-4810	320	15	sh	sh	PROPN
ejpam-4810	320	16	are	be	AUX
ejpam-4810	320	17	pointwise	pointwise	PROPN
ejpam-4810	320	18	non	non	ADJ
ejpam-4810	320	19	-	-	ADJ
ejpam-4810	320	20	dominating	dominating	ADJ
ejpam-4810	320	21	sets	set	NOUN
ejpam-4810	320	22	of	of	ADP
ejpam-4810	320	23	g	g	PROPN
ejpam-4810	320	24	and	and	CCONJ
ejpam-4810	320	25	h	h	NOUN
ejpam-4810	320	26	,	,	PUNCT
ejpam-4810	320	27	respectively	respectively	ADV
ejpam-4810	320	28	.	.	PUNCT
ejpam-4810	321	1	next	next	ADV
ejpam-4810	321	2	,	,	PUNCT
ejpam-4810	321	3	suppose	suppose	VERB
ejpam-4810	321	4	that	that	SCONJ
ejpam-4810	321	5	⟨sh⟩	⟨sh⟩	NOUN
ejpam-4810	321	6	is	be	AUX
ejpam-4810	321	7	a	a	DET
ejpam-4810	321	8	c.j	c.j	PROPN
ejpam-4810	321	9	.	.	PROPN
ejpam-4810	321	10	saromines	saromine	NOUN
ejpam-4810	321	11	,	,	PUNCT
ejpam-4810	321	12	s.	s.	PROPN
ejpam-4810	321	13	canoy	canoy	PROPN
ejpam-4810	321	14	,	,	PUNCT
ejpam-4810	321	15	jr	jr	PROPN
ejpam-4810	321	16	.	.	PROPN
ejpam-4810	321	17	,	,	PUNCT
ejpam-4810	321	18	/	/	SYM
ejpam-4810	321	19	eur	eur	NOUN
ejpam-4810	321	20	.	.	PUNCT
ejpam-4810	322	1	j.	j.	PROPN
ejpam-4810	322	2	pure	pure	PROPN
ejpam-4810	322	3	appl	appl	PROPN
ejpam-4810	322	4	.	.	PROPN
ejpam-4810	322	5	math	math	PROPN
ejpam-4810	322	6	,	,	PUNCT
ejpam-4810	322	7	16	16	NUM
ejpam-4810	322	8	(	(	PUNCT
ejpam-4810	322	9	3	3	NUM
ejpam-4810	322	10	)	)	PUNCT
ejpam-4810	322	11	(	(	PUNCT
ejpam-4810	322	12	2023	2023	NUM
ejpam-4810	322	13	)	)	PUNCT
ejpam-4810	322	14	,	,	PUNCT
ejpam-4810	322	15	1568	1568	NUM
ejpam-4810	322	16	-	-	SYM
ejpam-4810	322	17	1579	1579	NUM
ejpam-4810	322	18	1575	1575	NUM
ejpam-4810	322	19	complete	complete	ADJ
ejpam-4810	322	20	subgraph	subgraph	NOUN
ejpam-4810	322	21	of	of	ADP
ejpam-4810	322	22	h.	h.	PROPN
ejpam-4810	322	23	if	if	SCONJ
ejpam-4810	322	24	sg	sg	PROPN
ejpam-4810	322	25	=	=	SYM
ejpam-4810	322	26	v	v	NOUN
ejpam-4810	322	27	(	(	PUNCT
ejpam-4810	322	28	g	g	NOUN
ejpam-4810	322	29	)	)	PUNCT
ejpam-4810	322	30	,	,	PUNCT
ejpam-4810	322	31	then	then	ADV
ejpam-4810	322	32	we	we	PRON
ejpam-4810	322	33	are	be	AUX
ejpam-4810	322	34	done	do	VERB
ejpam-4810	322	35	.	.	PUNCT
ejpam-4810	323	1	suppose	suppose	VERB
ejpam-4810	323	2	sg	sg	ADP
ejpam-4810	323	3	̸=	̸=	PROPN
ejpam-4810	323	4	v	v	NOUN
ejpam-4810	323	5	(	(	PUNCT
ejpam-4810	323	6	g	g	NOUN
ejpam-4810	323	7	)	)	PUNCT
ejpam-4810	323	8	.	.	PUNCT
ejpam-4810	324	1	let	let	VERB
ejpam-4810	324	2	x	x	SYM
ejpam-4810	324	3	∈	∈	PROPN
ejpam-4810	324	4	v	v	X
ejpam-4810	324	5	(	(	PUNCT
ejpam-4810	324	6	g	g	NOUN
ejpam-4810	324	7	)	)	PUNCT
ejpam-4810	324	8	\	\	PROPN
ejpam-4810	324	9	sg	sg	PROPN
ejpam-4810	324	10	.	.	PUNCT
ejpam-4810	325	1	since	since	SCONJ
ejpam-4810	325	2	s	s	PROPN
ejpam-4810	325	3	is	be	AUX
ejpam-4810	325	4	a	a	DET
ejpam-4810	325	5	geodetic	geodetic	ADJ
ejpam-4810	325	6	set	set	NOUN
ejpam-4810	325	7	of	of	ADP
ejpam-4810	325	8	g	g	PROPN
ejpam-4810	325	9	+	+	CCONJ
ejpam-4810	325	10	h	h	NOUN
ejpam-4810	325	11	,	,	PUNCT
ejpam-4810	325	12	there	there	PRON
ejpam-4810	325	13	exist	exist	VERB
ejpam-4810	325	14	y	y	PROPN
ejpam-4810	325	15	,	,	PUNCT
ejpam-4810	325	16	z	z	PROPN
ejpam-4810	325	17	∈	∈	PROPN
ejpam-4810	325	18	s	s	VERB
ejpam-4810	325	19	such	such	ADJ
ejpam-4810	325	20	that	that	SCONJ
ejpam-4810	325	21	x	x	SYM
ejpam-4810	325	22	∈	∈	PROPN
ejpam-4810	325	23	ig+h(y	ig+h(y	PROPN
ejpam-4810	325	24	,	,	PUNCT
ejpam-4810	325	25	z	z	NOUN
ejpam-4810	325	26	)	)	PUNCT
ejpam-4810	325	27	.	.	PUNCT
ejpam-4810	326	1	since	since	SCONJ
ejpam-4810	326	2	⟨sh⟩	⟨sh⟩	NOUN
ejpam-4810	326	3	is	be	AUX
ejpam-4810	326	4	complete	complete	ADJ
ejpam-4810	326	5	,	,	PUNCT
ejpam-4810	326	6	y	y	PROPN
ejpam-4810	326	7	,	,	PUNCT
ejpam-4810	326	8	z	z	PROPN
ejpam-4810	326	9	∈	∈	PROPN
ejpam-4810	326	10	sg	sg	PROPN
ejpam-4810	326	11	.	.	PUNCT
ejpam-4810	327	1	thus	thus	ADV
ejpam-4810	327	2	,	,	PUNCT
ejpam-4810	327	3	dg(y	dg(y	ADJ
ejpam-4810	327	4	,	,	PUNCT
ejpam-4810	327	5	z	z	NOUN
ejpam-4810	327	6	)	)	PUNCT
ejpam-4810	327	7	=	=	SYM
ejpam-4810	327	8	2	2	X
ejpam-4810	327	9	.	.	X
ejpam-4810	328	1	hence	hence	ADV
ejpam-4810	328	2	,	,	PUNCT
ejpam-4810	328	3	sg	sg	PROPN
ejpam-4810	328	4	is	be	AUX
ejpam-4810	328	5	2	2	NUM
ejpam-4810	328	6	-	-	PUNCT
ejpam-4810	328	7	path	path	NOUN
ejpam-4810	328	8	closure	closure	NOUN
ejpam-4810	328	9	absorbing	absorb	VERB
ejpam-4810	328	10	set	set	VERB
ejpam-4810	328	11	in	in	ADP
ejpam-4810	328	12	g.	g.	PROPN
ejpam-4810	328	13	similarly	similarly	ADV
ejpam-4810	328	14	,	,	PUNCT
ejpam-4810	328	15	(	(	PUNCT
ejpam-4810	328	16	ii	ii	NOUN
ejpam-4810	328	17	)	)	PUNCT
ejpam-4810	328	18	holds	hold	VERB
ejpam-4810	328	19	.	.	PUNCT
ejpam-4810	329	1	conversely	conversely	ADV
ejpam-4810	329	2	,	,	PUNCT
ejpam-4810	329	3	suppose	suppose	VERB
ejpam-4810	329	4	s	s	PRON
ejpam-4810	329	5	satisfies	satisfie	NOUN
ejpam-4810	329	6	the	the	DET
ejpam-4810	329	7	given	give	VERB
ejpam-4810	329	8	conditions	condition	NOUN
ejpam-4810	329	9	.	.	PUNCT
ejpam-4810	330	1	by	by	ADP
ejpam-4810	330	2	theorem	theorem	NOUN
ejpam-4810	330	3	3	3	NUM
ejpam-4810	330	4	,	,	PUNCT
ejpam-4810	330	5	s	s	VERB
ejpam-4810	330	6	is	be	AUX
ejpam-4810	330	7	a	a	DET
ejpam-4810	330	8	hop	hop	NOUN
ejpam-4810	330	9	dominating	dominating	NOUN
ejpam-4810	330	10	set	set	NOUN
ejpam-4810	330	11	of	of	ADP
ejpam-4810	330	12	g	g	PROPN
ejpam-4810	330	13	+	+	CCONJ
ejpam-4810	330	14	h.	h.	PROPN
ejpam-4810	330	15	let	let	VERB
ejpam-4810	330	16	u	u	PRON
ejpam-4810	330	17	∈	∈	PROPN
ejpam-4810	330	18	v	v	NOUN
ejpam-4810	330	19	(	(	PUNCT
ejpam-4810	330	20	g	g	PROPN
ejpam-4810	330	21	+	+	NOUN
ejpam-4810	330	22	h	h	NOUN
ejpam-4810	330	23	)	)	PUNCT
ejpam-4810	330	24	\	\	PUNCT
ejpam-4810	331	1	s.	s.	PROPN
ejpam-4810	331	2	suppose	suppose	VERB
ejpam-4810	331	3	u	u	PROPN
ejpam-4810	331	4	∈	∈	PROPN
ejpam-4810	331	5	v	v	ADP
ejpam-4810	331	6	(	(	PUNCT
ejpam-4810	331	7	h	h	NOUN
ejpam-4810	331	8	)	)	PUNCT
ejpam-4810	331	9	\	\	PUNCT
ejpam-4810	332	1	sh	sh	INTJ
ejpam-4810	332	2	.	.	PUNCT
ejpam-4810	333	1	if	if	SCONJ
ejpam-4810	333	2	⟨sg⟩	⟨sg⟩	PRON
ejpam-4810	333	3	is	be	AUX
ejpam-4810	333	4	non	non	ADJ
ejpam-4810	333	5	-	-	ADJ
ejpam-4810	333	6	complete	complete	ADJ
ejpam-4810	333	7	,	,	PUNCT
ejpam-4810	333	8	then	then	ADV
ejpam-4810	333	9	there	there	PRON
ejpam-4810	333	10	exist	exist	VERB
ejpam-4810	333	11	v	v	ADP
ejpam-4810	333	12	,	,	PUNCT
ejpam-4810	333	13	w	w	PROPN
ejpam-4810	333	14	∈	∈	PROPN
ejpam-4810	333	15	sg	sg	ADP
ejpam-4810	333	16	⊆	⊆	NUM
ejpam-4810	333	17	s	s	NOUN
ejpam-4810	333	18	such	such	ADJ
ejpam-4810	333	19	that	that	SCONJ
ejpam-4810	333	20	dg+h(v	dg+h(v	PROPN
ejpam-4810	333	21	,	,	PUNCT
ejpam-4810	333	22	w	w	NOUN
ejpam-4810	333	23	)	)	PUNCT
ejpam-4810	333	24	=	=	SYM
ejpam-4810	333	25	2	2	X
ejpam-4810	333	26	.	.	X
ejpam-4810	334	1	hence	hence	ADV
ejpam-4810	334	2	,	,	PUNCT
ejpam-4810	334	3	u	u	PROPN
ejpam-4810	334	4	∈	∈	PROPN
ejpam-4810	334	5	ig+h(v	ig+h(v	PROPN
ejpam-4810	334	6	,	,	PUNCT
ejpam-4810	334	7	w	w	NOUN
ejpam-4810	334	8	)	)	PUNCT
ejpam-4810	334	9	.	.	PUNCT
ejpam-4810	335	1	if	if	SCONJ
ejpam-4810	335	2	⟨sg⟩	⟨sg⟩	PRON
ejpam-4810	335	3	is	be	AUX
ejpam-4810	335	4	complete	complete	ADJ
ejpam-4810	335	5	,	,	PUNCT
ejpam-4810	335	6	then	then	ADV
ejpam-4810	335	7	there	there	PRON
ejpam-4810	335	8	exist	exist	VERB
ejpam-4810	335	9	s	s	PROPN
ejpam-4810	335	10	,	,	PUNCT
ejpam-4810	335	11	t	t	PROPN
ejpam-4810	335	12	∈	∈	PROPN
ejpam-4810	335	13	sh	sh	ADP
ejpam-4810	336	1	⊆	⊆	NUM
ejpam-4810	336	2	s	s	VERB
ejpam-4810	336	3	such	such	ADJ
ejpam-4810	336	4	that	that	DET
ejpam-4810	336	5	dh(s	dh(s	PROPN
ejpam-4810	336	6	,	,	PUNCT
ejpam-4810	336	7	t	t	PROPN
ejpam-4810	336	8	)	)	PUNCT
ejpam-4810	336	9	=	=	SYM
ejpam-4810	336	10	2	2	NUM
ejpam-4810	336	11	and	and	CCONJ
ejpam-4810	336	12	u	u	PROPN
ejpam-4810	336	13	∈	∈	PROPN
ejpam-4810	336	14	ig(s	ig(s	NUM
ejpam-4810	336	15	,	,	PUNCT
ejpam-4810	336	16	t	t	PROPN
ejpam-4810	336	17	)	)	PUNCT
ejpam-4810	336	18	=	=	SYM
ejpam-4810	336	19	ig+h(s	ig+h(s	PROPN
ejpam-4810	336	20	,	,	PUNCT
ejpam-4810	336	21	t	t	PROPN
ejpam-4810	336	22	)	)	PUNCT
ejpam-4810	336	23	by	by	ADP
ejpam-4810	336	24	(	(	PUNCT
ejpam-4810	336	25	ii	ii	NOUN
ejpam-4810	336	26	)	)	PUNCT
ejpam-4810	336	27	.	.	PUNCT
ejpam-4810	337	1	similarly	similarly	ADV
ejpam-4810	337	2	,	,	PUNCT
ejpam-4810	337	3	there	there	PRON
ejpam-4810	337	4	exist	exist	VERB
ejpam-4810	337	5	p	p	PRON
ejpam-4810	337	6	,	,	PUNCT
ejpam-4810	337	7	q	q	PROPN
ejpam-4810	337	8	∈	∈	PROPN
ejpam-4810	337	9	s	s	VERB
ejpam-4810	337	10	such	such	ADJ
ejpam-4810	337	11	that	that	SCONJ
ejpam-4810	337	12	[	[	X
ejpam-4810	337	13	p	p	X
ejpam-4810	337	14	,	,	PUNCT
ejpam-4810	337	15	u	u	NOUN
ejpam-4810	337	16	,	,	PUNCT
ejpam-4810	337	17	q	q	X
ejpam-4810	337	18	]	]	X
ejpam-4810	337	19	is	be	AUX
ejpam-4810	337	20	a	a	DET
ejpam-4810	337	21	geodesic	geodesic	NOUN
ejpam-4810	337	22	in	in	ADP
ejpam-4810	337	23	g	g	PROPN
ejpam-4810	337	24	+	+	NOUN
ejpam-4810	337	25	h	h	NOUN
ejpam-4810	337	26	if	if	SCONJ
ejpam-4810	337	27	u	u	PROPN
ejpam-4810	337	28	∈	∈	PROPN
ejpam-4810	337	29	v	v	ADP
ejpam-4810	337	30	(	(	PUNCT
ejpam-4810	337	31	g	g	NOUN
ejpam-4810	337	32	)	)	PUNCT
ejpam-4810	337	33	\	\	PROPN
ejpam-4810	337	34	sg	sg	PROPN
ejpam-4810	337	35	.	.	PUNCT
ejpam-4810	338	1	therefore	therefore	ADV
ejpam-4810	338	2	,	,	PUNCT
ejpam-4810	338	3	s	s	VERB
ejpam-4810	338	4	is	be	AUX
ejpam-4810	338	5	a	a	DET
ejpam-4810	338	6	geodetic	geodetic	ADJ
ejpam-4810	338	7	hop	hop	NOUN
ejpam-4810	338	8	dominating	dominating	NOUN
ejpam-4810	338	9	set	set	NOUN
ejpam-4810	338	10	of	of	ADP
ejpam-4810	338	11	g+h	g+h	PROPN
ejpam-4810	338	12	.	.	PUNCT
ejpam-4810	339	1	lemma	lemma	PROPN
ejpam-4810	339	2	1	1	X
ejpam-4810	339	3	.	.	PUNCT
ejpam-4810	340	1	let	let	VERB
ejpam-4810	340	2	g	g	PRON
ejpam-4810	340	3	be	be	AUX
ejpam-4810	340	4	a	a	DET
ejpam-4810	340	5	non	non	ADJ
ejpam-4810	340	6	-	-	ADJ
ejpam-4810	340	7	complete	complete	ADJ
ejpam-4810	340	8	graph	graph	NOUN
ejpam-4810	340	9	.	.	PUNCT
ejpam-4810	341	1	then	then	ADV
ejpam-4810	341	2	the	the	DET
ejpam-4810	341	3	following	follow	VERB
ejpam-4810	341	4	hold	hold	NOUN
ejpam-4810	341	5	:	:	PUNCT
ejpam-4810	341	6	(	(	PUNCT
ejpam-4810	341	7	i	i	NOUN
ejpam-4810	341	8	)	)	PUNCT
ejpam-4810	341	9	if	if	SCONJ
ejpam-4810	341	10	d	d	PROPN
ejpam-4810	341	11	is	be	AUX
ejpam-4810	341	12	a	a	DET
ejpam-4810	341	13	pnd	pnd	NOUN
ejpam-4810	341	14	-	-	PUNCT
ejpam-4810	341	15	set	set	NOUN
ejpam-4810	341	16	of	of	ADP
ejpam-4810	341	17	g	g	NOUN
ejpam-4810	341	18	such	such	ADJ
ejpam-4810	341	19	that	that	SCONJ
ejpam-4810	341	20	⟨d⟩	⟨d⟩	PROPN
ejpam-4810	341	21	is	be	AUX
ejpam-4810	341	22	complete	complete	ADJ
ejpam-4810	341	23	,	,	PUNCT
ejpam-4810	341	24	then	then	ADV
ejpam-4810	341	25	d	d	X
ejpam-4810	341	26	∪	∪	X
ejpam-4810	341	27	{	{	PUNCT
ejpam-4810	341	28	v	v	NOUN
ejpam-4810	341	29	}	}	PUNCT
ejpam-4810	341	30	is	be	AUX
ejpam-4810	341	31	a	a	DET
ejpam-4810	341	32	pointwise	pointwise	ADJ
ejpam-4810	341	33	nondominating	nondominate	VERB
ejpam-4810	341	34	set	set	NOUN
ejpam-4810	341	35	and	and	CCONJ
ejpam-4810	341	36	⟨d	⟨d	PROPN
ejpam-4810	341	37	∪	∪	X
ejpam-4810	341	38	{	{	PUNCT
ejpam-4810	341	39	v}⟩	v}⟩	PROPN
ejpam-4810	341	40	is	be	AUX
ejpam-4810	341	41	non	non	ADJ
ejpam-4810	341	42	-	-	ADJ
ejpam-4810	341	43	complete	complete	ADJ
ejpam-4810	341	44	for	for	ADP
ejpam-4810	341	45	every	every	DET
ejpam-4810	341	46	v	v	NUM
ejpam-4810	341	47	∈	∈	NOUN
ejpam-4810	341	48	v	v	NOUN
ejpam-4810	341	49	(	(	PUNCT
ejpam-4810	341	50	g	g	NOUN
ejpam-4810	341	51	)	)	PUNCT
ejpam-4810	341	52	\d	\d	NOUN
ejpam-4810	341	53	.	.	PUNCT
ejpam-4810	342	1	(	(	PUNCT
ejpam-4810	342	2	ii	ii	NOUN
ejpam-4810	342	3	)	)	PUNCT
ejpam-4810	342	4	if	if	SCONJ
ejpam-4810	342	5	e	e	PRON
ejpam-4810	342	6	is	be	AUX
ejpam-4810	342	7	a	a	DET
ejpam-4810	342	8	ρ2pnd	ρ2pnd	ADV
ejpam-4810	342	9	-	-	PUNCT
ejpam-4810	342	10	set	set	NOUN
ejpam-4810	342	11	of	of	ADP
ejpam-4810	342	12	g	g	NOUN
ejpam-4810	342	13	,	,	PUNCT
ejpam-4810	342	14	then	then	ADV
ejpam-4810	342	15	⟨e⟩	⟨e⟩	PROPN
ejpam-4810	342	16	is	be	AUX
ejpam-4810	342	17	non	non	ADJ
ejpam-4810	342	18	-	-	ADJ
ejpam-4810	342	19	complete	complete	ADJ
ejpam-4810	342	20	.	.	PUNCT
ejpam-4810	343	1	proof	proof	NOUN
ejpam-4810	343	2	.	.	PUNCT
ejpam-4810	344	1	(	(	PUNCT
ejpam-4810	344	2	i	i	NOUN
ejpam-4810	344	3	)	)	PUNCT
ejpam-4810	344	4	let	let	VERB
ejpam-4810	344	5	v	v	NUM
ejpam-4810	344	6	∈	∈	PROPN
ejpam-4810	344	7	v	v	NOUN
ejpam-4810	344	8	(	(	PUNCT
ejpam-4810	344	9	g)\d	g)\d	NOUN
ejpam-4810	344	10	.	.	PUNCT
ejpam-4810	345	1	since	since	SCONJ
ejpam-4810	345	2	d	d	PROPN
ejpam-4810	345	3	is	be	AUX
ejpam-4810	345	4	a	a	DET
ejpam-4810	345	5	pointwise	pointwise	ADJ
ejpam-4810	345	6	non	non	ADJ
ejpam-4810	345	7	-	-	ADJ
ejpam-4810	345	8	dominating	dominating	ADJ
ejpam-4810	345	9	set	set	NOUN
ejpam-4810	345	10	,	,	PUNCT
ejpam-4810	345	11	d∪{v	d∪{v	PRON
ejpam-4810	345	12	}	}	PUNCT
ejpam-4810	345	13	is	be	AUX
ejpam-4810	345	14	a	a	DET
ejpam-4810	345	15	pointwise	pointwise	ADJ
ejpam-4810	345	16	non	non	ADJ
ejpam-4810	345	17	-	-	ADJ
ejpam-4810	345	18	dominating	dominating	ADJ
ejpam-4810	345	19	set	set	NOUN
ejpam-4810	345	20	and	and	CCONJ
ejpam-4810	345	21	there	there	PRON
ejpam-4810	345	22	exists	exist	VERB
ejpam-4810	345	23	w	w	PROPN
ejpam-4810	345	24	∈	∈	PROPN
ejpam-4810	345	25	d	d	SYM
ejpam-4810	345	26	\	\	PROPN
ejpam-4810	345	27	ng(v	ng(v	PUNCT
ejpam-4810	345	28	)	)	PUNCT
ejpam-4810	345	29	.	.	PUNCT
ejpam-4810	346	1	therefore	therefore	ADV
ejpam-4810	346	2	,	,	PUNCT
ejpam-4810	346	3	⟨d	⟨d	PROPN
ejpam-4810	346	4	∪	∪	X
ejpam-4810	346	5	{	{	PUNCT
ejpam-4810	346	6	v}⟩	v}⟩	NOUN
ejpam-4810	346	7	is	be	AUX
ejpam-4810	346	8	noncomplete	noncomplete	ADJ
ejpam-4810	346	9	.	.	PUNCT
ejpam-4810	347	1	(	(	PUNCT
ejpam-4810	347	2	ii	ii	NOUN
ejpam-4810	347	3	)	)	PUNCT
ejpam-4810	347	4	if	if	SCONJ
ejpam-4810	347	5	e	e	PROPN
ejpam-4810	347	6	=	=	SYM
ejpam-4810	347	7	v	v	X
ejpam-4810	347	8	(	(	PUNCT
ejpam-4810	347	9	g	g	NOUN
ejpam-4810	347	10	)	)	PUNCT
ejpam-4810	347	11	,	,	PUNCT
ejpam-4810	347	12	then	then	ADV
ejpam-4810	347	13	we	we	PRON
ejpam-4810	347	14	are	be	AUX
ejpam-4810	347	15	done	do	VERB
ejpam-4810	347	16	.	.	PUNCT
ejpam-4810	348	1	suppose	suppose	VERB
ejpam-4810	349	1	e	e	X
ejpam-4810	349	2	̸=	̸=	PROPN
ejpam-4810	349	3	v	v	ADP
ejpam-4810	349	4	(	(	PUNCT
ejpam-4810	349	5	g	g	NOUN
ejpam-4810	349	6	)	)	PUNCT
ejpam-4810	349	7	.	.	PUNCT
ejpam-4810	350	1	let	let	VERB
ejpam-4810	350	2	x	x	SYM
ejpam-4810	350	3	∈	∈	PROPN
ejpam-4810	350	4	v	v	X
ejpam-4810	350	5	(	(	PUNCT
ejpam-4810	350	6	g	g	NOUN
ejpam-4810	350	7	)	)	PUNCT
ejpam-4810	350	8	\	\	PROPN
ejpam-4810	350	9	e.	e.	PROPN
ejpam-4810	350	10	since	since	SCONJ
ejpam-4810	350	11	e	e	PROPN
ejpam-4810	350	12	is	be	AUX
ejpam-4810	350	13	a	a	DET
ejpam-4810	350	14	2	2	NUM
ejpam-4810	350	15	-	-	PUNCT
ejpam-4810	350	16	path	path	NOUN
ejpam-4810	350	17	closure	closure	NOUN
ejpam-4810	350	18	absorbing	absorbing	NOUN
ejpam-4810	350	19	,	,	PUNCT
ejpam-4810	350	20	there	there	PRON
ejpam-4810	350	21	exist	exist	VERB
ejpam-4810	350	22	p	p	PRON
ejpam-4810	350	23	,	,	PUNCT
ejpam-4810	350	24	q	q	SYM
ejpam-4810	350	25	∈	∈	NOUN
ejpam-4810	350	26	e	e	NOUN
ejpam-4810	350	27	such	such	ADJ
ejpam-4810	350	28	that	that	SCONJ
ejpam-4810	350	29	dg(p	dg(p	NOUN
ejpam-4810	350	30	,	,	PUNCT
ejpam-4810	350	31	q	q	X
ejpam-4810	350	32	)	)	PUNCT
ejpam-4810	350	33	=	=	SYM
ejpam-4810	350	34	2	2	NUM
ejpam-4810	350	35	and	and	CCONJ
ejpam-4810	350	36	x	x	PUNCT
ejpam-4810	350	37	∈	∈	NOUN
ejpam-4810	350	38	ig(p	ig(p	NOUN
ejpam-4810	350	39	,	,	PUNCT
ejpam-4810	350	40	q	q	NOUN
ejpam-4810	350	41	)	)	PUNCT
ejpam-4810	350	42	.	.	PUNCT
ejpam-4810	351	1	therefore	therefore	ADV
ejpam-4810	351	2	,	,	PUNCT
ejpam-4810	351	3	⟨e⟩	⟨e⟩	PROPN
ejpam-4810	351	4	is	be	AUX
ejpam-4810	351	5	non	non	ADJ
ejpam-4810	351	6	-	-	ADJ
ejpam-4810	351	7	complete	complete	ADJ
ejpam-4810	351	8	.	.	PUNCT
ejpam-4810	352	1	before	before	ADP
ejpam-4810	352	2	proceeding	proceed	VERB
ejpam-4810	352	3	to	to	ADP
ejpam-4810	352	4	the	the	DET
ejpam-4810	352	5	next	next	ADJ
ejpam-4810	352	6	result	result	NOUN
ejpam-4810	352	7	,	,	PUNCT
ejpam-4810	352	8	we	we	PRON
ejpam-4810	352	9	denote	denote	VERB
ejpam-4810	352	10	the	the	DET
ejpam-4810	352	11	family	family	NOUN
ejpam-4810	352	12	c	c	NOUN
ejpam-4810	352	13	of	of	ADP
ejpam-4810	352	14	graphs	graph	NOUN
ejpam-4810	352	15	by	by	ADP
ejpam-4810	352	16	c	c	NOUN
ejpam-4810	352	17	=	=	SYM
ejpam-4810	352	18	{	{	PUNCT
ejpam-4810	352	19	g	g	NOUN
ejpam-4810	352	20	:	:	PUNCT
ejpam-4810	352	21	g	g	PROPN
ejpam-4810	352	22	has	have	VERB
ejpam-4810	352	23	a	a	DET
ejpam-4810	352	24	pnd	pnd	NOUN
ejpam-4810	352	25	-	-	PUNCT
ejpam-4810	352	26	set	set	NOUN
ejpam-4810	352	27	which	which	PRON
ejpam-4810	352	28	induces	induce	VERB
ejpam-4810	352	29	a	a	DET
ejpam-4810	352	30	non	non	ADJ
ejpam-4810	352	31	-	-	ADJ
ejpam-4810	352	32	complete	complete	ADJ
ejpam-4810	352	33	graph	graph	NOUN
ejpam-4810	352	34	}	}	PUNCT
ejpam-4810	352	35	.	.	PUNCT
ejpam-4810	353	1	lemma	lemma	PROPN
ejpam-4810	353	2	2	2	X
ejpam-4810	353	3	.	.	PUNCT
ejpam-4810	354	1	let	let	VERB
ejpam-4810	354	2	g	g	PRON
ejpam-4810	354	3	be	be	AUX
ejpam-4810	354	4	a	a	DET
ejpam-4810	354	5	non	non	ADJ
ejpam-4810	354	6	-	-	ADJ
ejpam-4810	354	7	complete	complete	ADJ
ejpam-4810	354	8	graph	graph	NOUN
ejpam-4810	354	9	.	.	PUNCT
ejpam-4810	355	1	if	if	SCONJ
ejpam-4810	355	2	g	g	PROPN
ejpam-4810	355	3	/∈	/∈	PUNCT
ejpam-4810	356	1	c	c	X
ejpam-4810	356	2	,	,	PUNCT
ejpam-4810	356	3	then	then	ADV
ejpam-4810	356	4	pnd(g	pnd(g	ADP
ejpam-4810	356	5	)	)	PUNCT
ejpam-4810	356	6	<	<	X
ejpam-4810	356	7	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	356	8	)	)	PUNCT
ejpam-4810	356	9	,	,	PUNCT
ejpam-4810	356	10	that	that	ADV
ejpam-4810	356	11	is	is	ADV
ejpam-4810	356	12	,	,	PUNCT
ejpam-4810	356	13	pnd(g	pnd(g	ADP
ejpam-4810	356	14	)	)	PUNCT
ejpam-4810	356	15	+	+	CCONJ
ejpam-4810	356	16	1	1	NUM
ejpam-4810	356	17	≤	≤	NUM
ejpam-4810	356	18	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	356	19	)	)	PUNCT
ejpam-4810	356	20	.	.	PUNCT
ejpam-4810	357	1	proof	proof	NOUN
ejpam-4810	357	2	.	.	PUNCT
ejpam-4810	358	1	let	let	VERB
ejpam-4810	358	2	s	s	PRON
ejpam-4810	358	3	be	be	AUX
ejpam-4810	358	4	a	a	DET
ejpam-4810	358	5	pnd	pnd	NOUN
ejpam-4810	358	6	-	-	PUNCT
ejpam-4810	358	7	set	set	NOUN
ejpam-4810	358	8	of	of	ADP
ejpam-4810	358	9	g.	g.	PROPN
ejpam-4810	358	10	then	then	ADV
ejpam-4810	358	11	⟨s⟩	⟨s⟩	PROPN
ejpam-4810	358	12	is	be	AUX
ejpam-4810	358	13	complete	complete	ADJ
ejpam-4810	358	14	because	because	SCONJ
ejpam-4810	358	15	g	g	PROPN
ejpam-4810	358	16	/∈	/∈	PROPN
ejpam-4810	358	17	c.	c.	PROPN
ejpam-4810	358	18	therefore	therefore	ADV
ejpam-4810	358	19	,	,	PUNCT
ejpam-4810	358	20	pnd(g	pnd(g	ADP
ejpam-4810	358	21	)	)	PUNCT
ejpam-4810	358	22	<	<	X
ejpam-4810	358	23	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	358	24	)	)	PUNCT
ejpam-4810	358	25	by	by	ADP
ejpam-4810	358	26	remark	remark	NOUN
ejpam-4810	358	27	3	3	NUM
ejpam-4810	358	28	and	and	CCONJ
ejpam-4810	358	29	lemma	lemma	PROPN
ejpam-4810	358	30	1(ii	1(ii	NUM
ejpam-4810	358	31	)	)	PUNCT
ejpam-4810	358	32	.	.	PUNCT
ejpam-4810	359	1	corollary	corollary	ADJ
ejpam-4810	359	2	4	4	NUM
ejpam-4810	359	3	.	.	PUNCT
ejpam-4810	360	1	let	let	VERB
ejpam-4810	360	2	g	g	NOUN
ejpam-4810	360	3	and	and	CCONJ
ejpam-4810	360	4	h	h	NOUN
ejpam-4810	360	5	be	be	VERB
ejpam-4810	360	6	any	any	DET
ejpam-4810	360	7	two	two	NUM
ejpam-4810	360	8	non	non	ADJ
ejpam-4810	360	9	-	-	ADJ
ejpam-4810	360	10	complete	complete	ADJ
ejpam-4810	360	11	graphs	graph	NOUN
ejpam-4810	360	12	of	of	ADP
ejpam-4810	360	13	orders	order	NOUN
ejpam-4810	360	14	m	m	VERB
ejpam-4810	360	15	and	and	CCONJ
ejpam-4810	360	16	n	n	CCONJ
ejpam-4810	360	17	,	,	PUNCT
ejpam-4810	360	18	respectively	respectively	ADV
ejpam-4810	360	19	.	.	PUNCT
ejpam-4810	361	1	then	then	ADV
ejpam-4810	361	2	γhg(g	γhg(g	PROPN
ejpam-4810	361	3	)	)	PUNCT
ejpam-4810	361	4	=	=	PUNCT
ejpam-4810	362	1			NUM
ejpam-4810	362	2	pnd(g	pnd(g	ADP
ejpam-4810	362	3	)	)	PUNCT
ejpam-4810	362	4	+	+	NUM
ejpam-4810	363	1	pnd(h	pnd(h	NUM
ejpam-4810	363	2	)	)	PUNCT
ejpam-4810	363	3	,	,	PUNCT
ejpam-4810	363	4	if	if	SCONJ
ejpam-4810	363	5	g	g	PROPN
ejpam-4810	363	6	,	,	PUNCT
ejpam-4810	363	7	h	h	NOUN
ejpam-4810	363	8	∈	∈	PROPN
ejpam-4810	364	1	c	c	PROPN
ejpam-4810	364	2	min	min	X
ejpam-4810	364	3	{	{	PUNCT
ejpam-4810	364	4	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	364	5	)	)	PUNCT
ejpam-4810	364	6	+	+	NUM
ejpam-4810	364	7	pnd(h	pnd(h	NUM
ejpam-4810	364	8	)	)	PUNCT
ejpam-4810	364	9	,	,	PUNCT
ejpam-4810	364	10	pnd(g	pnd(g	ADP
ejpam-4810	364	11	)	)	PUNCT
ejpam-4810	364	12	+	+	NUM
ejpam-4810	364	13	pnd(h	pnd(h	NUM
ejpam-4810	364	14	)	)	PUNCT
ejpam-4810	365	1	+	+	CCONJ
ejpam-4810	365	2	1	1	X
ejpam-4810	365	3	}	}	PUNCT
ejpam-4810	365	4	if	if	SCONJ
ejpam-4810	365	5	g	g	PROPN
ejpam-4810	365	6	∈	∈	PROPN
ejpam-4810	365	7	c	c	PROPN
ejpam-4810	365	8	and	and	CCONJ
ejpam-4810	365	9	h	h	NOUN
ejpam-4810	365	10	/∈	/∈	PUNCT
ejpam-4810	365	11	c	c	PROPN
ejpam-4810	365	12	min	min	NOUN
ejpam-4810	365	13	{	{	PUNCT
ejpam-4810	365	14	pnd(g	pnd(g	PROPN
ejpam-4810	365	15	)	)	PUNCT
ejpam-4810	365	16	+	+	NUM
ejpam-4810	365	17	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4810	365	18	)	)	PUNCT
ejpam-4810	365	19	,	,	PUNCT
ejpam-4810	365	20	pnd(g	pnd(g	ADP
ejpam-4810	365	21	)	)	PUNCT
ejpam-4810	365	22	+	+	NUM
ejpam-4810	365	23	pnd(h	pnd(h	NUM
ejpam-4810	365	24	)	)	PUNCT
ejpam-4810	366	1	+	+	CCONJ
ejpam-4810	366	2	1	1	X
ejpam-4810	366	3	}	}	PUNCT
ejpam-4810	366	4	if	if	SCONJ
ejpam-4810	366	5	g	g	PROPN
ejpam-4810	366	6	/∈	/∈	PUNCT
ejpam-4810	367	1	c	c	X
ejpam-4810	367	2	,	,	PUNCT
ejpam-4810	367	3	h	h	NOUN
ejpam-4810	367	4	∈	∈	PROPN
ejpam-4810	367	5	c	c	PROPN
ejpam-4810	367	6	min{ρ2pnd(g	min{ρ2pnd(g	PROPN
ejpam-4810	367	7	)	)	PUNCT
ejpam-4810	368	1	+	+	CCONJ
ejpam-4810	368	2	pnd(h	pnd(h	NUM
ejpam-4810	368	3	)	)	PUNCT
ejpam-4810	368	4	,	,	PUNCT
ejpam-4810	368	5	pnd(g	pnd(g	ADP
ejpam-4810	368	6	)	)	PUNCT
ejpam-4810	368	7	+	+	NUM
ejpam-4810	368	8	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4810	368	9	)	)	PUNCT
ejpam-4810	368	10	pnd(g	pnd(g	ADP
ejpam-4810	368	11	)	)	PUNCT
ejpam-4810	368	12	+	+	NUM
ejpam-4810	369	1	pnd(h	pnd(h	NUM
ejpam-4810	369	2	)	)	PUNCT
ejpam-4810	370	1	+	+	CCONJ
ejpam-4810	370	2	2	2	X
ejpam-4810	370	3	}	}	PUNCT
ejpam-4810	370	4	if	if	SCONJ
ejpam-4810	370	5	g	g	PROPN
ejpam-4810	370	6	,	,	PUNCT
ejpam-4810	370	7	h	h	NOUN
ejpam-4810	370	8	/∈	/∈	PUNCT
ejpam-4810	371	1	c.	c.	PROPN
ejpam-4810	371	2	c.j	c.j	PROPN
ejpam-4810	371	3	.	.	PROPN
ejpam-4810	371	4	saromines	saromines	PROPN
ejpam-4810	371	5	,	,	PUNCT
ejpam-4810	371	6	s.	s.	PROPN
ejpam-4810	371	7	canoy	canoy	PROPN
ejpam-4810	371	8	,	,	PUNCT
ejpam-4810	371	9	jr	jr	PROPN
ejpam-4810	371	10	.	.	PROPN
ejpam-4810	371	11	,	,	PUNCT
ejpam-4810	371	12	/	/	SYM
ejpam-4810	371	13	eur	eur	NOUN
ejpam-4810	371	14	.	.	PUNCT
ejpam-4810	372	1	j.	j.	PROPN
ejpam-4810	372	2	pure	pure	PROPN
ejpam-4810	372	3	appl	appl	PROPN
ejpam-4810	372	4	.	.	PROPN
ejpam-4810	372	5	math	math	PROPN
ejpam-4810	372	6	,	,	PUNCT
ejpam-4810	372	7	16	16	NUM
ejpam-4810	372	8	(	(	PUNCT
ejpam-4810	372	9	3	3	NUM
ejpam-4810	372	10	)	)	PUNCT
ejpam-4810	372	11	(	(	PUNCT
ejpam-4810	372	12	2023	2023	NUM
ejpam-4810	372	13	)	)	PUNCT
ejpam-4810	372	14	,	,	PUNCT
ejpam-4810	372	15	1568	1568	NUM
ejpam-4810	372	16	-	-	SYM
ejpam-4810	372	17	1579	1579	NUM
ejpam-4810	372	18	1576	1576	NUM
ejpam-4810	372	19	proof	proof	NOUN
ejpam-4810	372	20	.	.	PUNCT
ejpam-4810	373	1	let	let	VERB
ejpam-4810	373	2	s	s	PRON
ejpam-4810	373	3	be	be	AUX
ejpam-4810	373	4	a	a	DET
ejpam-4810	373	5	γhg	γhg	NOUN
ejpam-4810	373	6	-	-	PUNCT
ejpam-4810	373	7	set	set	NOUN
ejpam-4810	373	8	of	of	ADP
ejpam-4810	373	9	g	g	PROPN
ejpam-4810	373	10	+	+	CCONJ
ejpam-4810	373	11	h.	h.	PROPN
ejpam-4810	373	12	then	then	ADV
ejpam-4810	373	13	sg	sg	VERB
ejpam-4810	373	14	=	=	SYM
ejpam-4810	373	15	s	s	PROPN
ejpam-4810	373	16	∩	∩	ADJ
ejpam-4810	373	17	v	v	X
ejpam-4810	373	18	(	(	PUNCT
ejpam-4810	373	19	g	g	NOUN
ejpam-4810	373	20	)	)	PUNCT
ejpam-4810	373	21	and	and	CCONJ
ejpam-4810	373	22	sh	sh	INTJ
ejpam-4810	373	23	=	=	SYM
ejpam-4810	373	24	s	s	PROPN
ejpam-4810	373	25	∩	∩	ADJ
ejpam-4810	373	26	v	v	ADJ
ejpam-4810	373	27	(	(	PUNCT
ejpam-4810	373	28	h	h	NOUN
ejpam-4810	373	29	)	)	PUNCT
ejpam-4810	373	30	are	be	AUX
ejpam-4810	373	31	pointwise	pointwise	PROPN
ejpam-4810	373	32	non	non	ADJ
ejpam-4810	373	33	-	-	ADJ
ejpam-4810	373	34	dominating	dominating	ADJ
ejpam-4810	373	35	sets	set	NOUN
ejpam-4810	373	36	of	of	ADP
ejpam-4810	373	37	g	g	PROPN
ejpam-4810	373	38	and	and	CCONJ
ejpam-4810	373	39	h	h	NOUN
ejpam-4810	373	40	,	,	PUNCT
ejpam-4810	373	41	respectively	respectively	ADV
ejpam-4810	373	42	,	,	PUNCT
ejpam-4810	373	43	by	by	ADP
ejpam-4810	373	44	theorem	theorem	NOUN
ejpam-4810	373	45	4	4	NUM
ejpam-4810	373	46	.	.	PUNCT
ejpam-4810	374	1	hence	hence	ADV
ejpam-4810	374	2	,	,	PUNCT
ejpam-4810	374	3	if	if	SCONJ
ejpam-4810	374	4	g	g	PROPN
ejpam-4810	374	5	and	and	CCONJ
ejpam-4810	374	6	h	h	NOUN
ejpam-4810	374	7	are	be	AUX
ejpam-4810	374	8	in	in	ADP
ejpam-4810	374	9	c	c	NOUN
ejpam-4810	374	10	,	,	PUNCT
ejpam-4810	374	11	then	then	ADV
ejpam-4810	374	12	sg	sg	PROPN
ejpam-4810	374	13	and	and	CCONJ
ejpam-4810	374	14	sh	sh	PROPN
ejpam-4810	374	15	are	be	AUX
ejpam-4810	374	16	pnd	pnd	NOUN
ejpam-4810	374	17	-	-	PUNCT
ejpam-4810	374	18	sets	set	NOUN
ejpam-4810	374	19	of	of	ADP
ejpam-4810	374	20	g	g	PROPN
ejpam-4810	374	21	and	and	CCONJ
ejpam-4810	374	22	h	h	NOUN
ejpam-4810	374	23	,	,	PUNCT
ejpam-4810	374	24	respectively	respectively	ADV
ejpam-4810	374	25	.	.	PUNCT
ejpam-4810	375	1	therefore	therefore	ADV
ejpam-4810	375	2	,	,	PUNCT
ejpam-4810	375	3	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	375	4	)	)	PUNCT
ejpam-4810	376	1	=	=	SYM
ejpam-4810	376	2	pnd(g	pnd(g	PROPN
ejpam-4810	376	3	)	)	PUNCT
ejpam-4810	376	4	+	+	NUM
ejpam-4810	377	1	pnd(h	pnd(h	X
ejpam-4810	377	2	)	)	PUNCT
ejpam-4810	377	3	if	if	SCONJ
ejpam-4810	377	4	g	g	PROPN
ejpam-4810	377	5	,	,	PUNCT
ejpam-4810	377	6	h	h	PROPN
ejpam-4810	377	7	∈	∈	PROPN
ejpam-4810	377	8	c.	c.	PROPN
ejpam-4810	377	9	next	next	ADV
ejpam-4810	377	10	,	,	PUNCT
ejpam-4810	377	11	suppose	suppose	VERB
ejpam-4810	377	12	that	that	SCONJ
ejpam-4810	377	13	g	g	PROPN
ejpam-4810	377	14	∈	∈	PROPN
ejpam-4810	377	15	c	c	PROPN
ejpam-4810	377	16	and	and	CCONJ
ejpam-4810	377	17	h	h	NOUN
ejpam-4810	377	18	/∈	/∈	PROPN
ejpam-4810	378	1	c.	c.	PROPN
ejpam-4810	378	2	let	let	VERB
ejpam-4810	378	3	dg	dg	NOUN
ejpam-4810	378	4	be	be	AUX
ejpam-4810	378	5	a	a	DET
ejpam-4810	378	6	ρ2pnd	ρ2pnd	ADV
ejpam-4810	378	7	-	-	PUNCT
ejpam-4810	378	8	set	set	NOUN
ejpam-4810	378	9	of	of	ADP
ejpam-4810	378	10	g	g	NOUN
ejpam-4810	378	11	and	and	CCONJ
ejpam-4810	378	12	let	let	VERB
ejpam-4810	378	13	dh	dh	NOUN
ejpam-4810	378	14	be	be	AUX
ejpam-4810	378	15	a	a	DET
ejpam-4810	378	16	pndset	pndset	NOUN
ejpam-4810	378	17	of	of	ADP
ejpam-4810	378	18	h.	h.	PROPN
ejpam-4810	378	19	then	then	ADV
ejpam-4810	378	20	⟨dg⟩	⟨dg⟩	PROPN
ejpam-4810	378	21	is	be	AUX
ejpam-4810	378	22	non	non	ADJ
ejpam-4810	378	23	-	-	ADJ
ejpam-4810	378	24	complete	complete	ADJ
ejpam-4810	378	25	by	by	ADP
ejpam-4810	378	26	lemma	lemma	PROPN
ejpam-4810	378	27	1(ii	1(ii	NUM
ejpam-4810	378	28	)	)	PUNCT
ejpam-4810	378	29	.	.	PUNCT
ejpam-4810	379	1	since	since	SCONJ
ejpam-4810	379	2	h	h	PROPN
ejpam-4810	379	3	/∈	/∈	PUNCT
ejpam-4810	379	4	c	c	X
ejpam-4810	379	5	,	,	PUNCT
ejpam-4810	379	6	⟨dh⟩	⟨dh⟩	PROPN
ejpam-4810	379	7	is	be	AUX
ejpam-4810	379	8	complete	complete	ADJ
ejpam-4810	379	9	.	.	PUNCT
ejpam-4810	380	1	hence	hence	ADV
ejpam-4810	380	2	,	,	PUNCT
ejpam-4810	380	3	dh	dh	PROPN
ejpam-4810	380	4	̸=	̸=	PROPN
ejpam-4810	380	5	v	v	NOUN
ejpam-4810	380	6	(	(	PUNCT
ejpam-4810	380	7	h	h	NOUN
ejpam-4810	380	8	)	)	PUNCT
ejpam-4810	380	9	because	because	SCONJ
ejpam-4810	380	10	h	h	NOUN
ejpam-4810	380	11	is	be	AUX
ejpam-4810	380	12	non	non	ADJ
ejpam-4810	380	13	-	-	ADJ
ejpam-4810	380	14	complete	complete	ADJ
ejpam-4810	380	15	.	.	PUNCT
ejpam-4810	381	1	let	let	VERB
ejpam-4810	381	2	w	w	NOUN
ejpam-4810	381	3	∈	∈	PROPN
ejpam-4810	381	4	v	v	ADP
ejpam-4810	381	5	(	(	PUNCT
ejpam-4810	381	6	h	h	NOUN
ejpam-4810	381	7	)	)	PUNCT
ejpam-4810	381	8	\	\	PROPN
ejpam-4810	381	9	dh	dh	NOUN
ejpam-4810	381	10	.	.	PUNCT
ejpam-4810	382	1	by	by	ADP
ejpam-4810	382	2	lemma	lemma	PROPN
ejpam-4810	382	3	1(i	1(i	NUM
ejpam-4810	382	4	)	)	PUNCT
ejpam-4810	382	5	,	,	PUNCT
ejpam-4810	383	1	d	d	NOUN
ejpam-4810	383	2	′	′	NUM
ejpam-4810	384	1	h	h	NOUN
ejpam-4810	384	2	=	=	NOUN
ejpam-4810	385	1	dh	dh	NOUN
ejpam-4810	385	2	∪	∪	X
ejpam-4810	385	3	{	{	PUNCT
ejpam-4810	385	4	w	w	NOUN
ejpam-4810	385	5	}	}	PUNCT
ejpam-4810	385	6	is	be	AUX
ejpam-4810	385	7	a	a	DET
ejpam-4810	385	8	pointwise	pointwise	ADJ
ejpam-4810	385	9	non	non	ADJ
ejpam-4810	385	10	-	-	ADJ
ejpam-4810	385	11	dominating	dominating	ADJ
ejpam-4810	385	12	set	set	NOUN
ejpam-4810	385	13	of	of	ADP
ejpam-4810	385	14	h	h	NOUN
ejpam-4810	385	15	and	and	CCONJ
ejpam-4810	385	16	〈	〈	PROPN
ejpam-4810	385	17	d	d	NOUN
ejpam-4810	385	18	′	′	NUM
ejpam-4810	385	19	h	h	NOUN
ejpam-4810	385	20	〉	〉	NOUN
ejpam-4810	385	21	is	be	AUX
ejpam-4810	385	22	non	non	ADJ
ejpam-4810	385	23	-	-	ADJ
ejpam-4810	385	24	complete	complete	ADJ
ejpam-4810	385	25	.	.	PUNCT
ejpam-4810	386	1	let	let	VERB
ejpam-4810	386	2	d	d	NOUN
ejpam-4810	386	3	′	′	NOUN
ejpam-4810	386	4	g	g	NOUN
ejpam-4810	386	5	be	be	AUX
ejpam-4810	386	6	a	a	DET
ejpam-4810	386	7	pnd	pnd	NOUN
ejpam-4810	386	8	-	-	PUNCT
ejpam-4810	386	9	set	set	NOUN
ejpam-4810	386	10	of	of	ADP
ejpam-4810	386	11	g	g	NOUN
ejpam-4810	386	12	such	such	ADJ
ejpam-4810	386	13	that	that	PRON
ejpam-4810	386	14	〈	〈	PROPN
ejpam-4810	386	15	d	d	NOUN
ejpam-4810	386	16	′	′	NOUN
ejpam-4810	386	17	g	g	NOUN
ejpam-4810	386	18	〉	〉	NOUN
ejpam-4810	386	19	is	be	AUX
ejpam-4810	386	20	non	non	ADJ
ejpam-4810	386	21	-	-	ADJ
ejpam-4810	386	22	complete	complete	ADJ
ejpam-4810	386	23	.	.	PUNCT
ejpam-4810	387	1	then	then	ADV
ejpam-4810	387	2	s1	s1	PROPN
ejpam-4810	387	3	=	=	PUNCT
ejpam-4810	387	4	dg	dg	PROPN
ejpam-4810	387	5	∪	∪	NOUN
ejpam-4810	387	6	dh	dh	NOUN
ejpam-4810	387	7	and	and	CCONJ
ejpam-4810	387	8	s2	s2	PROPN
ejpam-4810	387	9	=	=	PUNCT
ejpam-4810	388	1	d	d	NOUN
ejpam-4810	388	2	′	′	NUM
ejpam-4810	388	3	g	g	NOUN
ejpam-4810	388	4	∪	∪	ADJ
ejpam-4810	388	5	d	d	NOUN
ejpam-4810	388	6	′	′	NUM
ejpam-4810	388	7	h	h	NOUN
ejpam-4810	388	8	are	be	AUX
ejpam-4810	388	9	geodetic	geodetic	ADJ
ejpam-4810	388	10	hop	hop	NOUN
ejpam-4810	388	11	dominating	dominating	NOUN
ejpam-4810	388	12	sets	set	NOUN
ejpam-4810	388	13	of	of	ADP
ejpam-4810	388	14	g	g	PROPN
ejpam-4810	388	15	+	+	CCONJ
ejpam-4810	388	16	h	h	NOUN
ejpam-4810	388	17	by	by	ADP
ejpam-4810	388	18	theorem	theorem	NOUN
ejpam-4810	388	19	4	4	NUM
ejpam-4810	388	20	.	.	PUNCT
ejpam-4810	389	1	thus	thus	ADV
ejpam-4810	389	2	,	,	PUNCT
ejpam-4810	389	3	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	389	4	)	)	PUNCT
ejpam-4810	389	5	≤	≤	NOUN
ejpam-4810	389	6	|s1|	|s1|	NOUN
ejpam-4810	389	7	=	=	SYM
ejpam-4810	389	8	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	389	9	)	)	PUNCT
ejpam-4810	389	10	+	+	NUM
ejpam-4810	389	11	pnd(h	pnd(h	NUM
ejpam-4810	389	12	)	)	PUNCT
ejpam-4810	389	13	and	and	CCONJ
ejpam-4810	389	14	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	389	15	)	)	PUNCT
ejpam-4810	389	16	≤	≤	NUM
ejpam-4810	389	17	|s2|	|s2|	NOUN
ejpam-4810	389	18	=	=	SYM
ejpam-4810	389	19	pnd(g	pnd(g	PROPN
ejpam-4810	389	20	)	)	PUNCT
ejpam-4810	389	21	+	+	NUM
ejpam-4810	389	22	pnd(h	pnd(h	NUM
ejpam-4810	389	23	)	)	PUNCT
ejpam-4810	390	1	+	+	CCONJ
ejpam-4810	390	2	1	1	X
ejpam-4810	390	3	.	.	PUNCT
ejpam-4810	390	4	consequently	consequently	ADV
ejpam-4810	390	5	,	,	PUNCT
ejpam-4810	390	6	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	390	7	)	)	PUNCT
ejpam-4810	390	8	≤	≤	NUM
ejpam-4810	390	9	min	min	NOUN
ejpam-4810	390	10	{	{	PUNCT
ejpam-4810	390	11	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	390	12	)	)	PUNCT
ejpam-4810	390	13	+	+	NUM
ejpam-4810	390	14	pnd(h	pnd(h	NUM
ejpam-4810	390	15	)	)	PUNCT
ejpam-4810	390	16	,	,	PUNCT
ejpam-4810	390	17	pnd(g	pnd(g	ADP
ejpam-4810	390	18	)	)	PUNCT
ejpam-4810	390	19	+	+	NUM
ejpam-4810	390	20	pnd(h	pnd(h	NUM
ejpam-4810	390	21	)	)	PUNCT
ejpam-4810	391	1	+	+	CCONJ
ejpam-4810	391	2	1	1	NUM
ejpam-4810	391	3	}	}	PUNCT
ejpam-4810	391	4	.	.	PUNCT
ejpam-4810	392	1	now	now	ADV
ejpam-4810	392	2	,	,	PUNCT
ejpam-4810	392	3	suppose	suppose	VERB
ejpam-4810	392	4	that	that	SCONJ
ejpam-4810	392	5	s∗	s∗	PROPN
ejpam-4810	392	6	=	=	PRON
ejpam-4810	392	7	s∗	s∗	PROPN
ejpam-4810	392	8	g	g	PROPN
ejpam-4810	392	9	∪	∪	ADJ
ejpam-4810	392	10	s∗	s∗	PROPN
ejpam-4810	392	11	h	h	NOUN
ejpam-4810	392	12	is	be	AUX
ejpam-4810	392	13	a	a	DET
ejpam-4810	392	14	γhg	γhg	NOUN
ejpam-4810	392	15	-	-	PUNCT
ejpam-4810	392	16	set	set	NOUN
ejpam-4810	392	17	of	of	ADP
ejpam-4810	392	18	g	g	PROPN
ejpam-4810	392	19	+	+	CCONJ
ejpam-4810	392	20	h.	h.	PROPN
ejpam-4810	392	21	then	then	ADV
ejpam-4810	392	22	s∗	s∗	VERB
ejpam-4810	392	23	g	g	PROPN
ejpam-4810	392	24	and	and	CCONJ
ejpam-4810	392	25	s∗	s∗	PROPN
ejpam-4810	392	26	h	h	PROPN
ejpam-4810	392	27	satisfy	satisfy	VERB
ejpam-4810	392	28	the	the	DET
ejpam-4810	392	29	conditions	condition	NOUN
ejpam-4810	392	30	in	in	ADP
ejpam-4810	392	31	theorem	theorem	NOUN
ejpam-4810	392	32	4	4	NUM
ejpam-4810	392	33	.	.	PUNCT
ejpam-4810	392	34	suppose	suppose	VERB
ejpam-4810	392	35	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	392	36	)	)	PUNCT
ejpam-4810	392	37	+	+	NUM
ejpam-4810	393	1	pnd(h	pnd(h	NUM
ejpam-4810	393	2	)	)	PUNCT
ejpam-4810	393	3	≤	≤	NUM
ejpam-4810	393	4	pnd(g	pnd(g	ADP
ejpam-4810	393	5	)	)	PUNCT
ejpam-4810	393	6	+	+	NUM
ejpam-4810	393	7	pnd(h	pnd(h	NUM
ejpam-4810	393	8	)	)	PUNCT
ejpam-4810	394	1	+	+	CCONJ
ejpam-4810	394	2	1	1	X
ejpam-4810	394	3	.	.	X
ejpam-4810	394	4	if	if	SCONJ
ejpam-4810	394	5	⟨s∗	⟨s∗	PROPN
ejpam-4810	394	6	h⟩	h⟩	PROPN
ejpam-4810	394	7	is	be	AUX
ejpam-4810	394	8	complete	complete	ADJ
ejpam-4810	394	9	,	,	PUNCT
ejpam-4810	394	10	then	then	ADV
ejpam-4810	394	11	s∗	s∗	PROPN
ejpam-4810	394	12	g	g	PROPN
ejpam-4810	394	13	is	be	AUX
ejpam-4810	394	14	pointwise	pointwise	PROPN
ejpam-4810	394	15	non	non	ADJ
ejpam-4810	394	16	-	-	ADJ
ejpam-4810	394	17	dominating	dominating	ADJ
ejpam-4810	394	18	2	2	NUM
ejpam-4810	394	19	-	-	PUNCT
ejpam-4810	394	20	path	path	NOUN
ejpam-4810	394	21	closure	closure	NOUN
ejpam-4810	394	22	absorbing	absorb	VERB
ejpam-4810	394	23	set	set	NOUN
ejpam-4810	394	24	of	of	ADP
ejpam-4810	394	25	g	g	NOUN
ejpam-4810	394	26	by	by	ADP
ejpam-4810	394	27	theorem	theorem	NOUN
ejpam-4810	394	28	4	4	NUM
ejpam-4810	394	29	.	.	PUNCT
ejpam-4810	395	1	it	it	PRON
ejpam-4810	395	2	follows	follow	VERB
ejpam-4810	395	3	that	that	SCONJ
ejpam-4810	395	4	γhg(g	γhg(g	PROPN
ejpam-4810	396	1	+	+	NUM
ejpam-4810	396	2	h	h	NOUN
ejpam-4810	396	3	)	)	PUNCT
ejpam-4810	396	4	=	=	SYM
ejpam-4810	397	1	|s∗	|s∗	PROPN
ejpam-4810	397	2	g|	g|	PROPN
ejpam-4810	397	3	+	+	CCONJ
ejpam-4810	397	4	|s∗	|s∗	PROPN
ejpam-4810	397	5	h	h	NOUN
ejpam-4810	397	6	|	|	ADV
ejpam-4810	397	7	≥	≥	NOUN
ejpam-4810	397	8	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	397	9	)	)	PUNCT
ejpam-4810	397	10	+	+	NUM
ejpam-4810	397	11	pnd(h	pnd(h	NUM
ejpam-4810	397	12	)	)	PUNCT
ejpam-4810	397	13	.	.	PUNCT
ejpam-4810	398	1	suppose	suppose	VERB
ejpam-4810	398	2	⟨s∗	⟨s∗	NOUN
ejpam-4810	398	3	h⟩	h⟩	PROPN
ejpam-4810	398	4	is	be	AUX
ejpam-4810	398	5	non	non	ADJ
ejpam-4810	398	6	-	-	ADJ
ejpam-4810	398	7	complete	complete	ADJ
ejpam-4810	398	8	.	.	PUNCT
ejpam-4810	399	1	since	since	SCONJ
ejpam-4810	399	2	h	h	PROPN
ejpam-4810	399	3	/∈	/∈	PUNCT
ejpam-4810	399	4	c	c	X
ejpam-4810	399	5	,	,	PUNCT
ejpam-4810	399	6	h	h	PROPN
ejpam-4810	399	7	is	be	AUX
ejpam-4810	399	8	non	non	ADJ
ejpam-4810	399	9	-	-	ADJ
ejpam-4810	399	10	complete	complete	ADJ
ejpam-4810	399	11	,	,	PUNCT
ejpam-4810	399	12	and	and	CCONJ
ejpam-4810	399	13	s∗	s∗	PROPN
ejpam-4810	399	14	is	be	AUX
ejpam-4810	399	15	γhg	γhg	ADV
ejpam-4810	399	16	-	-	PUNCT
ejpam-4810	399	17	set	set	NOUN
ejpam-4810	399	18	of	of	ADP
ejpam-4810	399	19	g	g	PROPN
ejpam-4810	400	1	+	+	CCONJ
ejpam-4810	400	2	h	h	NOUN
ejpam-4810	400	3	,	,	PUNCT
ejpam-4810	400	4	|s∗	|s∗	PROPN
ejpam-4810	400	5	h	h	NOUN
ejpam-4810	400	6	|	|	ADV
ejpam-4810	400	7	≥	≥	X
ejpam-4810	400	8	pnd(h	pnd(h	NUM
ejpam-4810	400	9	)	)	PUNCT
ejpam-4810	401	1	+	+	CCONJ
ejpam-4810	401	2	1	1	NUM
ejpam-4810	401	3	(	(	PUNCT
ejpam-4810	401	4	see	see	VERB
ejpam-4810	401	5	lemma	lemma	PROPN
ejpam-4810	401	6	1(i	1(i	NUM
ejpam-4810	401	7	)	)	PUNCT
ejpam-4810	401	8	)	)	PUNCT
ejpam-4810	401	9	.	.	PUNCT
ejpam-4810	402	1	it	it	PRON
ejpam-4810	402	2	follows	follow	VERB
ejpam-4810	402	3	that	that	SCONJ
ejpam-4810	402	4	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	402	5	)	)	PUNCT
ejpam-4810	402	6	=	=	NOUN
ejpam-4810	402	7	|s∗|	|s∗|	NOUN
ejpam-4810	403	1	=	=	PUNCT
ejpam-4810	403	2	|s∗	|s∗	PROPN
ejpam-4810	403	3	g|+	g|+	PROPN
ejpam-4810	403	4	|s∗	|s∗	PROPN
ejpam-4810	403	5	h	h	NOUN
ejpam-4810	404	1	|	|	ADV
ejpam-4810	404	2	≥	≥	NOUN
ejpam-4810	404	3	pnd(g	pnd(g	ADP
ejpam-4810	404	4	)	)	PUNCT
ejpam-4810	405	1	+	+	NUM
ejpam-4810	406	1	pnd(h	pnd(h	NUM
ejpam-4810	406	2	)	)	PUNCT
ejpam-4810	407	1	+	+	CCONJ
ejpam-4810	407	2	1	1	NUM
ejpam-4810	407	3	≥	≥	NOUN
ejpam-4810	407	4	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	407	5	)	)	PUNCT
ejpam-4810	407	6	+	+	NUM
ejpam-4810	408	1	pnd(h	pnd(h	NUM
ejpam-4810	408	2	)	)	PUNCT
ejpam-4810	408	3	.	.	PUNCT
ejpam-4810	409	1	similar	similar	ADJ
ejpam-4810	409	2	arguments	argument	NOUN
ejpam-4810	409	3	may	may	AUX
ejpam-4810	409	4	be	be	AUX
ejpam-4810	409	5	used	use	VERB
ejpam-4810	409	6	to	to	PART
ejpam-4810	409	7	show	show	VERB
ejpam-4810	409	8	that	that	PRON
ejpam-4810	409	9	γhg(g	γhg(g	PROPN
ejpam-4810	410	1	+	+	NUM
ejpam-4810	410	2	h	h	NOUN
ejpam-4810	410	3	)	)	PUNCT
ejpam-4810	410	4	≥	≥	NOUN
ejpam-4810	410	5	pnd(g	pnd(g	ADP
ejpam-4810	410	6	)	)	PUNCT
ejpam-4810	411	1	+	+	NUM
ejpam-4810	412	1	pnd(h	pnd(h	NUM
ejpam-4810	412	2	)	)	PUNCT
ejpam-4810	413	1	+	+	CCONJ
ejpam-4810	413	2	1	1	NUM
ejpam-4810	413	3	if	if	SCONJ
ejpam-4810	413	4	pnd(g	pnd(g	ADP
ejpam-4810	413	5	)	)	PUNCT
ejpam-4810	413	6	+	+	NUM
ejpam-4810	413	7	pnd(h	pnd(h	NUM
ejpam-4810	413	8	)	)	PUNCT
ejpam-4810	414	1	+	+	CCONJ
ejpam-4810	414	2	1	1	NUM
ejpam-4810	414	3	≤	≤	NUM
ejpam-4810	414	4	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	414	5	)	)	PUNCT
ejpam-4810	415	1	+	+	NUM
ejpam-4810	415	2	pnd(h	pnd(h	NUM
ejpam-4810	415	3	)	)	PUNCT
ejpam-4810	415	4	.	.	PUNCT
ejpam-4810	416	1	therefore	therefore	ADV
ejpam-4810	416	2	,	,	PUNCT
ejpam-4810	416	3	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	416	4	)	)	PUNCT
ejpam-4810	417	1	=	=	SYM
ejpam-4810	417	2	min	min	PROPN
ejpam-4810	417	3	{	{	PUNCT
ejpam-4810	417	4	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	417	5	)	)	PUNCT
ejpam-4810	417	6	+	+	NUM
ejpam-4810	417	7	pnd(h	pnd(h	NUM
ejpam-4810	417	8	)	)	PUNCT
ejpam-4810	417	9	,	,	PUNCT
ejpam-4810	417	10	pnd(g	pnd(g	ADP
ejpam-4810	417	11	)	)	PUNCT
ejpam-4810	417	12	+	+	NUM
ejpam-4810	417	13	pnd(h	pnd(h	NUM
ejpam-4810	417	14	)	)	PUNCT
ejpam-4810	418	1	+	+	CCONJ
ejpam-4810	418	2	1	1	X
ejpam-4810	418	3	}	}	PUNCT
ejpam-4810	418	4	if	if	SCONJ
ejpam-4810	418	5	g	g	PROPN
ejpam-4810	418	6	∈	∈	PROPN
ejpam-4810	418	7	c	c	PROPN
ejpam-4810	418	8	and	and	CCONJ
ejpam-4810	418	9	h	h	NOUN
ejpam-4810	418	10	/∈	/∈	PROPN
ejpam-4810	418	11	c.	c.	PROPN
ejpam-4810	418	12	similarly	similarly	ADV
ejpam-4810	418	13	,	,	PUNCT
ejpam-4810	418	14	γhg(g	γhg(g	PROPN
ejpam-4810	419	1	+	+	CCONJ
ejpam-4810	419	2	h	h	NOUN
ejpam-4810	419	3	)	)	PUNCT
ejpam-4810	419	4	=	=	SYM
ejpam-4810	419	5	min	min	NOUN
ejpam-4810	419	6	{	{	PUNCT
ejpam-4810	419	7	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4810	419	8	)	)	PUNCT
ejpam-4810	420	1	+	+	CCONJ
ejpam-4810	420	2	pnd(g	pnd(g	ADP
ejpam-4810	420	3	)	)	PUNCT
ejpam-4810	420	4	,	,	PUNCT
ejpam-4810	420	5	pnd(g	pnd(g	ADP
ejpam-4810	420	6	)	)	PUNCT
ejpam-4810	420	7	+	+	NUM
ejpam-4810	420	8	pnd(h	pnd(h	NUM
ejpam-4810	420	9	)	)	PUNCT
ejpam-4810	421	1	+	+	CCONJ
ejpam-4810	421	2	1	1	X
ejpam-4810	421	3	}	}	PUNCT
ejpam-4810	421	4	if	if	SCONJ
ejpam-4810	421	5	g	g	PROPN
ejpam-4810	421	6	/∈	/∈	PUNCT
ejpam-4810	421	7	c	c	PROPN
ejpam-4810	421	8	and	and	CCONJ
ejpam-4810	421	9	h	h	PROPN
ejpam-4810	421	10	∈	∈	PROPN
ejpam-4810	421	11	c.	c.	PROPN
ejpam-4810	421	12	suppose	suppose	VERB
ejpam-4810	421	13	g	g	PROPN
ejpam-4810	421	14	,	,	PUNCT
ejpam-4810	421	15	h	h	NOUN
ejpam-4810	421	16	/∈	/∈	PUNCT
ejpam-4810	421	17	c.	c.	PROPN
ejpam-4810	421	18	let	let	VERB
ejpam-4810	421	19	r	r	NOUN
ejpam-4810	421	20	=	=	SYM
ejpam-4810	421	21	min{ρ2pnd(g	min{ρ2pnd(g	PROPN
ejpam-4810	421	22	)	)	PUNCT
ejpam-4810	422	1	+	+	NUM
ejpam-4810	422	2	pnd(h	pnd(h	NUM
ejpam-4810	422	3	)	)	PUNCT
ejpam-4810	422	4	,	,	PUNCT
ejpam-4810	422	5	pnd(g	pnd(g	ADP
ejpam-4810	422	6	)	)	PUNCT
ejpam-4810	422	7	+	+	NUM
ejpam-4810	422	8	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4810	422	9	)	)	PUNCT
ejpam-4810	422	10	,	,	PUNCT
ejpam-4810	422	11	pnd(g	pnd(g	ADP
ejpam-4810	422	12	)	)	PUNCT
ejpam-4810	422	13	+	+	NUM
ejpam-4810	422	14	pnd(h	pnd(h	NUM
ejpam-4810	422	15	)	)	PUNCT
ejpam-4810	423	1	+	+	CCONJ
ejpam-4810	423	2	2	2	NUM
ejpam-4810	423	3	}	}	PUNCT
ejpam-4810	423	4	.	.	PUNCT
ejpam-4810	424	1	clearly	clearly	ADV
ejpam-4810	424	2	,	,	PUNCT
ejpam-4810	424	3	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	424	4	)	)	PUNCT
ejpam-4810	424	5	≤	≤	NUM
ejpam-4810	424	6	min	min	NOUN
ejpam-4810	424	7	{	{	PUNCT
ejpam-4810	424	8	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	424	9	)	)	PUNCT
ejpam-4810	424	10	+	+	NUM
ejpam-4810	424	11	pnd(h	pnd(h	NUM
ejpam-4810	424	12	)	)	PUNCT
ejpam-4810	424	13	,	,	PUNCT
ejpam-4810	424	14	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4810	424	15	)	)	PUNCT
ejpam-4810	425	1	+	+	CCONJ
ejpam-4810	425	2	pnd(g	pnd(g	PROPN
ejpam-4810	425	3	)	)	PUNCT
ejpam-4810	425	4	)	)	PUNCT
ejpam-4810	425	5	}	}	PUNCT
ejpam-4810	425	6	.	.	PUNCT
ejpam-4810	426	1	let	let	VERB
ejpam-4810	426	2	s1	s1	NOUN
ejpam-4810	426	3	and	and	CCONJ
ejpam-4810	426	4	s2	s2	PROPN
ejpam-4810	426	5	be	be	VERB
ejpam-4810	426	6	pnd	pnd	NOUN
ejpam-4810	426	7	-	-	PUNCT
ejpam-4810	426	8	sets	set	NOUN
ejpam-4810	426	9	of	of	ADP
ejpam-4810	426	10	g	g	PROPN
ejpam-4810	426	11	and	and	CCONJ
ejpam-4810	426	12	h	h	NOUN
ejpam-4810	426	13	,	,	PUNCT
ejpam-4810	426	14	respectively	respectively	ADV
ejpam-4810	426	15	.	.	PUNCT
ejpam-4810	427	1	let	let	VERB
ejpam-4810	427	2	s	s	PRON
ejpam-4810	427	3	′	′	ADJ
ejpam-4810	427	4	1	1	NUM
ejpam-4810	427	5	=	=	SYM
ejpam-4810	427	6	s1	s1	PROPN
ejpam-4810	427	7	∪{p	∪{p	PROPN
ejpam-4810	427	8	}	}	PUNCT
ejpam-4810	427	9	and	and	CCONJ
ejpam-4810	427	10	s	s	VERB
ejpam-4810	427	11	′	′	ADJ
ejpam-4810	427	12	2	2	NUM
ejpam-4810	427	13	=	=	NOUN
ejpam-4810	427	14	s2	s2	NOUN
ejpam-4810	427	15	∪{q	∪{q	NOUN
ejpam-4810	427	16	}	}	PUNCT
ejpam-4810	427	17	,	,	PUNCT
ejpam-4810	427	18	where	where	SCONJ
ejpam-4810	427	19	p	p	PROPN
ejpam-4810	427	20	∈	∈	PROPN
ejpam-4810	427	21	v	v	ADP
ejpam-4810	427	22	(	(	PUNCT
ejpam-4810	427	23	g)\s1	g)\s1	NOUN
ejpam-4810	427	24	and	and	CCONJ
ejpam-4810	427	25	q	q	NOUN
ejpam-4810	427	26	∈	∈	PROPN
ejpam-4810	427	27	v	v	NOUN
ejpam-4810	427	28	(	(	PUNCT
ejpam-4810	427	29	h)\s2	h)\s2	PROPN
ejpam-4810	427	30	.	.	PUNCT
ejpam-4810	428	1	then	then	ADV
ejpam-4810	428	2	s	s	VERB
ejpam-4810	428	3	′	′	NOUN
ejpam-4810	428	4	1	1	NUM
ejpam-4810	428	5	and	and	CCONJ
ejpam-4810	428	6	s	s	VERB
ejpam-4810	428	7	′	′	ADJ
ejpam-4810	428	8	2	2	NUM
ejpam-4810	428	9	are	be	AUX
ejpam-4810	428	10	pointwise	pointwise	ADJ
ejpam-4810	428	11	non	non	ADJ
ejpam-4810	428	12	-	-	ADJ
ejpam-4810	428	13	dominating	dominating	ADJ
ejpam-4810	428	14	sets	set	NOUN
ejpam-4810	428	15	of	of	ADP
ejpam-4810	428	16	g	g	PROPN
ejpam-4810	428	17	and	and	CCONJ
ejpam-4810	428	18	h	h	NOUN
ejpam-4810	428	19	,	,	PUNCT
ejpam-4810	428	20	respectively	respectively	ADV
ejpam-4810	428	21	,	,	PUNCT
ejpam-4810	428	22	and	and	CCONJ
ejpam-4810	428	23	〈	〈	PROPN
ejpam-4810	428	24	s	s	PART
ejpam-4810	428	25	′	′	NUM
ejpam-4810	428	26	1	1	NUM
ejpam-4810	428	27	〉	〉	NOUN
ejpam-4810	428	28	and	and	CCONJ
ejpam-4810	428	29	〈	〈	PROPN
ejpam-4810	428	30	s	s	PART
ejpam-4810	428	31	′	′	ADJ
ejpam-4810	428	32	2	2	NUM
ejpam-4810	428	33	〉	〉	NOUN
ejpam-4810	428	34	are	be	AUX
ejpam-4810	428	35	non	non	ADJ
ejpam-4810	428	36	-	-	ADJ
ejpam-4810	428	37	complete	complete	ADJ
ejpam-4810	428	38	by	by	ADP
ejpam-4810	428	39	lemma	lemma	PROPN
ejpam-4810	428	40	1(i	1(i	NUM
ejpam-4810	428	41	)	)	PUNCT
ejpam-4810	428	42	.	.	PUNCT
ejpam-4810	429	1	hence	hence	ADV
ejpam-4810	429	2	,	,	PUNCT
ejpam-4810	429	3	c.j	c.j	PROPN
ejpam-4810	429	4	.	.	PROPN
ejpam-4810	429	5	saromines	saromines	PROPN
ejpam-4810	429	6	,	,	PUNCT
ejpam-4810	429	7	s.	s.	PROPN
ejpam-4810	429	8	canoy	canoy	PROPN
ejpam-4810	429	9	,	,	PUNCT
ejpam-4810	429	10	jr	jr	PROPN
ejpam-4810	429	11	.	.	PROPN
ejpam-4810	429	12	,	,	PUNCT
ejpam-4810	429	13	/	/	SYM
ejpam-4810	429	14	eur	eur	NOUN
ejpam-4810	429	15	.	.	PUNCT
ejpam-4810	430	1	j.	j.	PROPN
ejpam-4810	430	2	pure	pure	PROPN
ejpam-4810	430	3	appl	appl	PROPN
ejpam-4810	430	4	.	.	PROPN
ejpam-4810	430	5	math	math	PROPN
ejpam-4810	430	6	,	,	PUNCT
ejpam-4810	430	7	16	16	NUM
ejpam-4810	430	8	(	(	PUNCT
ejpam-4810	430	9	3	3	NUM
ejpam-4810	430	10	)	)	PUNCT
ejpam-4810	430	11	(	(	PUNCT
ejpam-4810	430	12	2023	2023	NUM
ejpam-4810	430	13	)	)	PUNCT
ejpam-4810	430	14	,	,	PUNCT
ejpam-4810	430	15	1568	1568	NUM
ejpam-4810	430	16	-	-	SYM
ejpam-4810	430	17	1579	1579	NUM
ejpam-4810	430	18	1577	1577	NUM
ejpam-4810	430	19	s	s	NOUN
ejpam-4810	430	20	′	′	NOUN
ejpam-4810	431	1	=	=	PUNCT
ejpam-4810	431	2	s	s	VERB
ejpam-4810	431	3	′	′	NUM
ejpam-4810	431	4	1	1	NUM
ejpam-4810	431	5	∪	∪	NOUN
ejpam-4810	431	6	s	s	VERB
ejpam-4810	431	7	′	′	NUM
ejpam-4810	431	8	2	2	NUM
ejpam-4810	431	9	is	be	AUX
ejpam-4810	431	10	a	a	DET
ejpam-4810	431	11	geodetic	geodetic	ADJ
ejpam-4810	431	12	hop	hop	NOUN
ejpam-4810	431	13	dominating	dominating	NOUN
ejpam-4810	431	14	set	set	NOUN
ejpam-4810	431	15	of	of	ADP
ejpam-4810	431	16	g+h	g+h	PROPN
ejpam-4810	431	17	by	by	ADP
ejpam-4810	431	18	theorem	theorem	NOUN
ejpam-4810	431	19	5	5	NUM
ejpam-4810	431	20	.	.	PUNCT
ejpam-4810	432	1	it	it	PRON
ejpam-4810	432	2	follows	follow	VERB
ejpam-4810	432	3	that	that	SCONJ
ejpam-4810	432	4	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	432	5	)	)	PUNCT
ejpam-4810	432	6	≤	≤	NOUN
ejpam-4810	432	7	∣∣∣s′	∣∣∣s′	PROPN
ejpam-4810	432	8	∣∣∣	∣∣∣	NOUN
ejpam-4810	432	9	=	=	SYM
ejpam-4810	432	10	pnd(g	pnd(g	NOUN
ejpam-4810	432	11	)	)	PUNCT
ejpam-4810	432	12	+	+	NUM
ejpam-4810	433	1	pnd(h	pnd(h	NUM
ejpam-4810	433	2	)	)	PUNCT
ejpam-4810	434	1	+	+	CCONJ
ejpam-4810	434	2	2	2	X
ejpam-4810	434	3	.	.	X
ejpam-4810	434	4	therefore	therefore	ADV
ejpam-4810	434	5	,	,	PUNCT
ejpam-4810	434	6	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	434	7	)	)	PUNCT
ejpam-4810	434	8	≤	≤	PROPN
ejpam-4810	434	9	r.	r.	PROPN
ejpam-4810	434	10	let	let	VERB
ejpam-4810	435	1	s	s	PRON
ejpam-4810	435	2	◦	◦	VERB
ejpam-4810	435	3	=	=	SYM
ejpam-4810	435	4	s	s	X
ejpam-4810	435	5	◦	◦	NOUN
ejpam-4810	435	6	g	g	NOUN
ejpam-4810	435	7	∪	∪	NOUN
ejpam-4810	435	8	s	s	NOUN
ejpam-4810	435	9	◦	◦	NOUN
ejpam-4810	435	10	h	h	NOUN
ejpam-4810	435	11	be	be	VERB
ejpam-4810	435	12	a	a	DET
ejpam-4810	435	13	γhg	γhg	NOUN
ejpam-4810	435	14	-	-	PUNCT
ejpam-4810	435	15	set	set	NOUN
ejpam-4810	435	16	of	of	ADP
ejpam-4810	435	17	g	g	PROPN
ejpam-4810	435	18	+	+	PROPN
ejpam-4810	435	19	h.	h.	PROPN
ejpam-4810	435	20	then	then	ADV
ejpam-4810	435	21	s	s	AUX
ejpam-4810	435	22	◦	◦	NOUN
ejpam-4810	435	23	h	h	NOUN
ejpam-4810	435	24	and	and	CCONJ
ejpam-4810	435	25	s	s	NOUN
ejpam-4810	435	26	◦	◦	NOUN
ejpam-4810	435	27	h	h	NOUN
ejpam-4810	435	28	satisfy	satisfy	VERB
ejpam-4810	435	29	the	the	DET
ejpam-4810	435	30	conditions	condition	NOUN
ejpam-4810	435	31	in	in	ADP
ejpam-4810	435	32	theorem	theorem	NOUN
ejpam-4810	435	33	5	5	NUM
ejpam-4810	435	34	.	.	PUNCT
ejpam-4810	436	1	consider	consider	VERB
ejpam-4810	436	2	the	the	DET
ejpam-4810	436	3	following	follow	VERB
ejpam-4810	436	4	cases	case	NOUN
ejpam-4810	436	5	:	:	PUNCT
ejpam-4810	436	6	case	case	NOUN
ejpam-4810	436	7	1	1	NUM
ejpam-4810	436	8	.	.	X
ejpam-4810	436	9	⟨s	⟨s	NOUN
ejpam-4810	436	10	◦	◦	NOUN
ejpam-4810	436	11	h⟩	h⟩	NOUN
ejpam-4810	436	12	is	be	AUX
ejpam-4810	436	13	complete	complete	ADJ
ejpam-4810	436	14	.	.	PUNCT
ejpam-4810	437	1	by	by	ADP
ejpam-4810	437	2	theorem	theorem	NOUN
ejpam-4810	437	3	4	4	NUM
ejpam-4810	437	4	,	,	PUNCT
ejpam-4810	437	5	s	s	X
ejpam-4810	437	6	◦	◦	NOUN
ejpam-4810	437	7	g	g	NOUN
ejpam-4810	437	8	is	be	AUX
ejpam-4810	437	9	a	a	DET
ejpam-4810	437	10	pointwise	pointwise	ADJ
ejpam-4810	437	11	non	non	ADJ
ejpam-4810	437	12	-	-	ADJ
ejpam-4810	437	13	dominating	dominating	ADJ
ejpam-4810	437	14	2	2	NUM
ejpam-4810	437	15	-	-	PUNCT
ejpam-4810	437	16	path	path	NOUN
ejpam-4810	437	17	closure	closure	NOUN
ejpam-4810	437	18	absorbing	absorb	VERB
ejpam-4810	437	19	set	set	NOUN
ejpam-4810	437	20	of	of	ADP
ejpam-4810	437	21	g	g	PROPN
ejpam-4810	437	22	and	and	CCONJ
ejpam-4810	437	23	|s	|s	PROPN
ejpam-4810	437	24	◦	◦	PROPN
ejpam-4810	437	25	g|	g|	PROPN
ejpam-4810	437	26	≥	≥	NOUN
ejpam-4810	437	27	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	437	28	)	)	PUNCT
ejpam-4810	437	29	.	.	PUNCT
ejpam-4810	438	1	hence	hence	ADV
ejpam-4810	438	2	,	,	PUNCT
ejpam-4810	438	3	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	438	4	)	)	PUNCT
ejpam-4810	438	5	=	=	SYM
ejpam-4810	439	1	|s	|s	NUM
ejpam-4810	439	2	◦	◦	NOUN
ejpam-4810	439	3	|	|	NOUN
ejpam-4810	439	4	=	=	SYM
ejpam-4810	439	5	|s	|s	PROPN
ejpam-4810	439	6	◦	◦	NOUN
ejpam-4810	439	7	g|+	g|+	PROPN
ejpam-4810	439	8	|s	|s	PROPN
ejpam-4810	439	9	◦	◦	NOUN
ejpam-4810	439	10	h	h	NOUN
ejpam-4810	439	11	|	|	ADV
ejpam-4810	439	12	≥	≥	NOUN
ejpam-4810	439	13	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	439	14	)	)	PUNCT
ejpam-4810	440	1	+	+	NUM
ejpam-4810	440	2	pnd(h	pnd(h	PROPN
ejpam-4810	440	3	)	)	PUNCT
ejpam-4810	440	4	≥	≥	PROPN
ejpam-4810	440	5	r.	r.	PROPN
ejpam-4810	440	6	case	case	NOUN
ejpam-4810	440	7	2	2	NUM
ejpam-4810	440	8	.	.	X
ejpam-4810	440	9	⟨s	⟨s	NOUN
ejpam-4810	440	10	◦	◦	NOUN
ejpam-4810	440	11	g⟩	g⟩	AUX
ejpam-4810	440	12	is	be	AUX
ejpam-4810	440	13	complete	complete	ADJ
ejpam-4810	440	14	.	.	PUNCT
ejpam-4810	441	1	then	then	ADV
ejpam-4810	441	2	s	s	X
ejpam-4810	441	3	◦	◦	NOUN
ejpam-4810	441	4	h	h	NOUN
ejpam-4810	441	5	is	be	AUX
ejpam-4810	441	6	a	a	DET
ejpam-4810	441	7	pointwise	pointwise	ADJ
ejpam-4810	441	8	non	non	ADJ
ejpam-4810	441	9	-	-	ADJ
ejpam-4810	441	10	dominating	dominating	ADJ
ejpam-4810	441	11	and	and	CCONJ
ejpam-4810	441	12	2	2	NUM
ejpam-4810	441	13	-	-	PUNCT
ejpam-4810	441	14	path	path	NOUN
ejpam-4810	441	15	closure	closure	NOUN
ejpam-4810	441	16	absorbing	absorb	VERB
ejpam-4810	441	17	set	set	NOUN
ejpam-4810	441	18	of	of	ADP
ejpam-4810	441	19	h.	h.	PROPN
ejpam-4810	441	20	hence	hence	PROPN
ejpam-4810	441	21	,	,	PUNCT
ejpam-4810	441	22	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	441	23	)	)	PUNCT
ejpam-4810	442	1	=	=	SYM
ejpam-4810	443	1	|s	|s	NUM
ejpam-4810	443	2	◦	◦	NOUN
ejpam-4810	443	3	|	|	NOUN
ejpam-4810	443	4	=	=	SYM
ejpam-4810	443	5	|s	|s	PROPN
ejpam-4810	443	6	◦	◦	NOUN
ejpam-4810	443	7	g|+	g|+	PROPN
ejpam-4810	443	8	|s	|s	PROPN
ejpam-4810	443	9	◦	◦	NOUN
ejpam-4810	443	10	h	h	NOUN
ejpam-4810	443	11	|	|	ADV
ejpam-4810	443	12	≥	≥	NOUN
ejpam-4810	443	13	ρ2pnd(h	ρ2pnd(h	NUM
ejpam-4810	443	14	)	)	PUNCT
ejpam-4810	444	1	+	+	CCONJ
ejpam-4810	444	2	pnd(g	pnd(g	ADJ
ejpam-4810	444	3	)	)	PUNCT
ejpam-4810	444	4	≥	≥	PROPN
ejpam-4810	444	5	r.	r.	PROPN
ejpam-4810	444	6	case	case	NOUN
ejpam-4810	444	7	3	3	NUM
ejpam-4810	444	8	.	.	X
ejpam-4810	444	9	⟨s	⟨s	NOUN
ejpam-4810	444	10	◦	◦	NOUN
ejpam-4810	444	11	g⟩	g⟩	NOUN
ejpam-4810	444	12	and	and	CCONJ
ejpam-4810	444	13	⟨s	⟨s	VERB
ejpam-4810	444	14	◦	◦	NOUN
ejpam-4810	444	15	h⟩	h⟩	NOUN
ejpam-4810	444	16	are	be	AUX
ejpam-4810	444	17	non	non	ADJ
ejpam-4810	444	18	-	-	ADJ
ejpam-4810	444	19	complete	complete	ADJ
ejpam-4810	444	20	.	.	PUNCT
ejpam-4810	445	1	then	then	ADV
ejpam-4810	445	2	|s	|s	PROPN
ejpam-4810	445	3	◦	◦	PROPN
ejpam-4810	445	4	g|	g|	PROPN
ejpam-4810	445	5	≥	≥	NOUN
ejpam-4810	445	6	pnd(g	pnd(g	ADP
ejpam-4810	445	7	)	)	PUNCT
ejpam-4810	446	1	+	+	CCONJ
ejpam-4810	446	2	1	1	NUM
ejpam-4810	446	3	and	and	CCONJ
ejpam-4810	446	4	|s	|s	NUM
ejpam-4810	446	5	◦	◦	NOUN
ejpam-4810	446	6	h	h	NOUN
ejpam-4810	446	7	|	|	ADV
ejpam-4810	446	8	≥	≥	NOUN
ejpam-4810	446	9	pnd(h	pnd(h	NUM
ejpam-4810	446	10	)	)	PUNCT
ejpam-4810	447	1	+	+	CCONJ
ejpam-4810	447	2	1	1	NUM
ejpam-4810	447	3	by	by	ADP
ejpam-4810	447	4	lemma	lemma	PROPN
ejpam-4810	447	5	1(i	1(i	NUM
ejpam-4810	447	6	)	)	PUNCT
ejpam-4810	447	7	.	.	PUNCT
ejpam-4810	448	1	hence	hence	ADV
ejpam-4810	448	2	,	,	PUNCT
ejpam-4810	448	3	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	448	4	)	)	PUNCT
ejpam-4810	448	5	=	=	SYM
ejpam-4810	449	1	|s	|s	NUM
ejpam-4810	449	2	◦	◦	NOUN
ejpam-4810	449	3	|	|	NOUN
ejpam-4810	449	4	=	=	SYM
ejpam-4810	449	5	|s	|s	PROPN
ejpam-4810	449	6	◦	◦	NOUN
ejpam-4810	449	7	g|+	g|+	PROPN
ejpam-4810	449	8	|s	|s	PROPN
ejpam-4810	449	9	◦	◦	NOUN
ejpam-4810	449	10	h	h	NOUN
ejpam-4810	450	1	|	|	ADV
ejpam-4810	450	2	≥	≥	NOUN
ejpam-4810	450	3	pnd(g	pnd(g	ADP
ejpam-4810	450	4	)	)	PUNCT
ejpam-4810	450	5	+	+	NUM
ejpam-4810	451	1	pnd(h	pnd(h	NUM
ejpam-4810	451	2	)	)	PUNCT
ejpam-4810	452	1	+	+	CCONJ
ejpam-4810	452	2	2	2	NUM
ejpam-4810	452	3	≥	≥	NOUN
ejpam-4810	452	4	r.	r.	PROPN
ejpam-4810	452	5	accordingly	accordingly	ADV
ejpam-4810	452	6	,	,	PUNCT
ejpam-4810	452	7	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	452	8	)	)	PUNCT
ejpam-4810	452	9	=	=	PUNCT
ejpam-4810	453	1	r.	r.	PROPN
ejpam-4810	453	2	corollary	corollary	NOUN
ejpam-4810	453	3	5	5	NUM
ejpam-4810	453	4	.	.	PUNCT
ejpam-4810	454	1	let	let	VERB
ejpam-4810	454	2	g	g	PRON
ejpam-4810	454	3	be	be	AUX
ejpam-4810	454	4	a	a	DET
ejpam-4810	454	5	non	non	ADJ
ejpam-4810	454	6	-	-	ADJ
ejpam-4810	454	7	complete	complete	ADJ
ejpam-4810	454	8	graph	graph	NOUN
ejpam-4810	454	9	and	and	CCONJ
ejpam-4810	454	10	n	n	DET
ejpam-4810	454	11	a	a	DET
ejpam-4810	454	12	positive	positive	ADJ
ejpam-4810	454	13	integer	integer	NOUN
ejpam-4810	454	14	.	.	PUNCT
ejpam-4810	455	1	then	then	ADV
ejpam-4810	455	2	s	s	VERB
ejpam-4810	455	3	⊆	⊆	NUM
ejpam-4810	455	4	v	v	NOUN
ejpam-4810	455	5	(	(	PUNCT
ejpam-4810	455	6	kn+	kn+	VERB
ejpam-4810	455	7	g	g	NOUN
ejpam-4810	455	8	)	)	PUNCT
ejpam-4810	455	9	is	be	AUX
ejpam-4810	455	10	a	a	DET
ejpam-4810	455	11	geodetic	geodetic	ADJ
ejpam-4810	455	12	hop	hop	NOUN
ejpam-4810	455	13	dominating	dominating	NOUN
ejpam-4810	455	14	set	set	NOUN
ejpam-4810	455	15	of	of	ADP
ejpam-4810	455	16	kn	kn	PROPN
ejpam-4810	455	17	+	+	CCONJ
ejpam-4810	455	18	g	g	PROPN
ejpam-4810	455	19	if	if	SCONJ
ejpam-4810	456	1	and	and	CCONJ
ejpam-4810	456	2	only	only	ADV
ejpam-4810	456	3	if	if	SCONJ
ejpam-4810	456	4	s	s	VERB
ejpam-4810	456	5	=	=	SYM
ejpam-4810	456	6	v	v	PROPN
ejpam-4810	456	7	(	(	PUNCT
ejpam-4810	456	8	kn	kn	PROPN
ejpam-4810	456	9	)	)	PUNCT
ejpam-4810	456	10	∪	∪	ADP
ejpam-4810	456	11	sg	sg	PROPN
ejpam-4810	456	12	,	,	PUNCT
ejpam-4810	456	13	where	where	SCONJ
ejpam-4810	456	14	sg	sg	PROPN
ejpam-4810	456	15	is	be	AUX
ejpam-4810	456	16	a	a	DET
ejpam-4810	456	17	pointwise	pointwise	ADJ
ejpam-4810	456	18	non	non	ADJ
ejpam-4810	456	19	-	-	ADJ
ejpam-4810	456	20	dominating	dominating	ADJ
ejpam-4810	456	21	and	and	CCONJ
ejpam-4810	456	22	2	2	NUM
ejpam-4810	456	23	-	-	PUNCT
ejpam-4810	456	24	path	path	NOUN
ejpam-4810	456	25	closure	closure	NOUN
ejpam-4810	456	26	absorbing	absorb	VERB
ejpam-4810	456	27	set	set	VERB
ejpam-4810	456	28	in	in	ADP
ejpam-4810	456	29	g.	g.	PROPN
ejpam-4810	456	30	in	in	ADP
ejpam-4810	456	31	particular	particular	ADJ
ejpam-4810	456	32	,	,	PUNCT
ejpam-4810	456	33	γhg(kn	γhg(kn	ADP
ejpam-4810	456	34	+	+	SYM
ejpam-4810	456	35	g	g	NOUN
ejpam-4810	456	36	)	)	PUNCT
ejpam-4810	456	37	=	=	SYM
ejpam-4810	456	38	n+	n+	X
ejpam-4810	456	39	ρ2pnd(g	ρ2pnd(g	NUM
ejpam-4810	456	40	)	)	PUNCT
ejpam-4810	456	41	.	.	PUNCT
ejpam-4810	457	1	corollary	corollary	ADJ
ejpam-4810	457	2	6	6	NUM
ejpam-4810	457	3	.	.	PUNCT
ejpam-4810	458	1	let	let	VERB
ejpam-4810	458	2	g	g	NOUN
ejpam-4810	458	3	and	and	CCONJ
ejpam-4810	458	4	h	h	NOUN
ejpam-4810	458	5	be	be	VERB
ejpam-4810	458	6	any	any	DET
ejpam-4810	458	7	two	two	NUM
ejpam-4810	458	8	graphs	graph	NOUN
ejpam-4810	458	9	of	of	ADP
ejpam-4810	458	10	orders	order	NOUN
ejpam-4810	458	11	m	m	VERB
ejpam-4810	458	12	and	and	CCONJ
ejpam-4810	458	13	n	n	PRON
ejpam-4810	458	14	respectively	respectively	ADV
ejpam-4810	458	15	.	.	PUNCT
ejpam-4810	459	1	then	then	ADV
ejpam-4810	459	2	(	(	PUNCT
ejpam-4810	459	3	i	i	NOUN
ejpam-4810	459	4	)	)	PUNCT
ejpam-4810	459	5	γhg(g+h	γhg(g+h	NOUN
ejpam-4810	459	6	)	)	PUNCT
ejpam-4810	460	1	=	=	PUNCT
ejpam-4810	461	1	m+	m+	NUM
ejpam-4810	461	2	n	n	NOUN
ejpam-4810	461	3	if	if	SCONJ
ejpam-4810	461	4	g	g	PROPN
ejpam-4810	461	5	and	and	CCONJ
ejpam-4810	461	6	h	h	NOUN
ejpam-4810	461	7	are	be	AUX
ejpam-4810	461	8	complete	complete	ADJ
ejpam-4810	461	9	;	;	PUNCT
ejpam-4810	461	10	(	(	PUNCT
ejpam-4810	461	11	ii	ii	NOUN
ejpam-4810	461	12	)	)	PUNCT
ejpam-4810	461	13	γhg(k1,n−1	γhg(k1,n−1	NUM
ejpam-4810	461	14	)	)	PUNCT
ejpam-4810	462	1	=	=	PUNCT
ejpam-4810	463	1	γhg(k1	γhg(k1	PROPN
ejpam-4810	463	2	+	+	SYM
ejpam-4810	463	3	kn−1	kn−1	PROPN
ejpam-4810	463	4	)	)	PUNCT
ejpam-4810	463	5	=	=	SYM
ejpam-4810	464	1	n	n	PROPN
ejpam-4810	464	2	for	for	ADP
ejpam-4810	464	3	n	n	PRON
ejpam-4810	464	4	≥	≥	NOUN
ejpam-4810	464	5	2	2	NUM
ejpam-4810	464	6	;	;	PUNCT
ejpam-4810	464	7	(	(	PUNCT
ejpam-4810	464	8	iii	iii	NOUN
ejpam-4810	464	9	)	)	PUNCT
ejpam-4810	464	10	γhg(fn	γhg(fn	NOUN
ejpam-4810	464	11	)	)	PUNCT
ejpam-4810	464	12	=	=	SYM
ejpam-4810	464	13	1	1	NUM
ejpam-4810	464	14	+	+	NUM
ejpam-4810	464	15	ρ2pnd(pn	ρ2pnd(pn	NUM
ejpam-4810	464	16	)	)	PUNCT
ejpam-4810	464	17	;	;	PUNCT
ejpam-4810	464	18	(	(	PUNCT
ejpam-4810	464	19	iv	iv	X
ejpam-4810	464	20	)	)	PUNCT
ejpam-4810	464	21	γhg(wn	γhg(wn	NOUN
ejpam-4810	464	22	)	)	PUNCT
ejpam-4810	464	23	=	=	SYM
ejpam-4810	464	24	1	1	NUM
ejpam-4810	464	25	+	+	NUM
ejpam-4810	464	26	ρ2pnd(cn	ρ2pnd(cn	NOUN
ejpam-4810	464	27	)	)	PUNCT
ejpam-4810	464	28	;	;	PUNCT
ejpam-4810	464	29	and	and	CCONJ
ejpam-4810	464	30	(	(	PUNCT
ejpam-4810	464	31	v	v	NOUN
ejpam-4810	464	32	)	)	PUNCT
ejpam-4810	464	33	γhg(km	γhg(km	PROPN
ejpam-4810	464	34	,	,	PUNCT
ejpam-4810	464	35	n)=	n)=	NOUN
ejpam-4810	464	36	{	{	PUNCT
ejpam-4810	464	37	3	3	NUM
ejpam-4810	464	38	if	if	SCONJ
ejpam-4810	464	39	m	m	VERB
ejpam-4810	464	40	=	=	SYM
ejpam-4810	464	41	2	2	NUM
ejpam-4810	464	42	or	or	CCONJ
ejpam-4810	464	43	n	n	NOUN
ejpam-4810	464	44	=	=	SYM
ejpam-4810	464	45	2	2	NUM
ejpam-4810	464	46	.	.	NOUN
ejpam-4810	464	47	4	4	NUM
ejpam-4810	464	48	otherwise	otherwise	ADV
ejpam-4810	464	49	.	.	PUNCT
ejpam-4810	465	1	references	reference	NOUN
ejpam-4810	465	2	1578	1578	NUM
ejpam-4810	465	3	4	4	NUM
ejpam-4810	465	4	.	.	PUNCT
ejpam-4810	465	5	conclusion	conclusion	NOUN
ejpam-4810	465	6	a	a	DET
ejpam-4810	465	7	realization	realization	NOUN
ejpam-4810	465	8	result	result	NOUN
ejpam-4810	465	9	involving	involve	VERB
ejpam-4810	465	10	the	the	DET
ejpam-4810	465	11	hop	hop	NOUN
ejpam-4810	465	12	domination	domination	NOUN
ejpam-4810	465	13	number	number	NOUN
ejpam-4810	465	14	and	and	CCONJ
ejpam-4810	465	15	the	the	DET
ejpam-4810	465	16	geodetic	geodetic	ADJ
ejpam-4810	465	17	hop	hop	NOUN
ejpam-4810	465	18	domination	domination	NOUN
ejpam-4810	465	19	number	number	NOUN
ejpam-4810	465	20	was	be	AUX
ejpam-4810	465	21	obtained	obtain	VERB
ejpam-4810	465	22	.	.	PUNCT
ejpam-4810	466	1	this	this	DET
ejpam-4810	466	2	result	result	NOUN
ejpam-4810	466	3	shows	show	VERB
ejpam-4810	466	4	that	that	SCONJ
ejpam-4810	466	5	the	the	DET
ejpam-4810	466	6	difference	difference	NOUN
ejpam-4810	466	7	of	of	ADP
ejpam-4810	466	8	these	these	DET
ejpam-4810	466	9	two	two	NUM
ejpam-4810	466	10	parameters	parameter	NOUN
ejpam-4810	466	11	can	can	AUX
ejpam-4810	466	12	be	be	AUX
ejpam-4810	466	13	made	make	VERB
ejpam-4810	466	14	arbitrarily	arbitrarily	ADV
ejpam-4810	466	15	large	large	ADJ
ejpam-4810	466	16	.	.	PUNCT
ejpam-4810	467	1	the	the	DET
ejpam-4810	467	2	concept	concept	NOUN
ejpam-4810	467	3	of	of	ADP
ejpam-4810	467	4	pointwise	pointwise	PROPN
ejpam-4810	467	5	non	non	ADJ
ejpam-4810	467	6	-	-	ADJ
ejpam-4810	467	7	dominating	dominating	ADJ
ejpam-4810	467	8	2	2	NUM
ejpam-4810	467	9	-	-	PUNCT
ejpam-4810	467	10	path	path	NOUN
ejpam-4810	467	11	closure	closure	NOUN
ejpam-4810	467	12	absorbing	absorb	VERB
ejpam-4810	467	13	set	set	NOUN
ejpam-4810	467	14	was	be	AUX
ejpam-4810	467	15	defined	define	VERB
ejpam-4810	467	16	and	and	CCONJ
ejpam-4810	467	17	studied	study	VERB
ejpam-4810	467	18	for	for	ADP
ejpam-4810	467	19	some	some	DET
ejpam-4810	467	20	graphs	graph	NOUN
ejpam-4810	467	21	.	.	PUNCT
ejpam-4810	468	1	the	the	DET
ejpam-4810	468	2	geodetic	geodetic	ADJ
ejpam-4810	468	3	hop	hop	NOUN
ejpam-4810	468	4	dominating	dominating	NOUN
ejpam-4810	468	5	sets	set	NOUN
ejpam-4810	468	6	in	in	ADP
ejpam-4810	468	7	the	the	DET
ejpam-4810	468	8	join	join	NOUN
ejpam-4810	468	9	of	of	ADP
ejpam-4810	468	10	two	two	NUM
ejpam-4810	468	11	graphs	graph	NOUN
ejpam-4810	468	12	were	be	AUX
ejpam-4810	468	13	characterized	characterize	VERB
ejpam-4810	468	14	using	use	VERB
ejpam-4810	468	15	the	the	DET
ejpam-4810	468	16	concept	concept	NOUN
ejpam-4810	468	17	of	of	ADP
ejpam-4810	468	18	2	2	NUM
ejpam-4810	468	19	-	-	PUNCT
ejpam-4810	468	20	path	path	NOUN
ejpam-4810	468	21	closure	closure	NOUN
ejpam-4810	468	22	absorbing	absorb	VERB
ejpam-4810	468	23	pointwise	pointwise	PROPN
ejpam-4810	468	24	non	non	ADJ
ejpam-4810	468	25	-	-	ADJ
ejpam-4810	468	26	dominating	dominating	ADJ
ejpam-4810	468	27	set	set	NOUN
ejpam-4810	468	28	.	.	PUNCT
ejpam-4810	469	1	complexity	complexity	NOUN
ejpam-4810	469	2	of	of	ADP
ejpam-4810	469	3	the	the	DET
ejpam-4810	469	4	geodetic	geodetic	ADJ
ejpam-4810	469	5	hop	hop	NOUN
ejpam-4810	469	6	domination	domination	NOUN
ejpam-4810	469	7	problem	problem	NOUN
ejpam-4810	469	8	may	may	AUX
ejpam-4810	469	9	be	be	AUX
ejpam-4810	469	10	investigated	investigate	VERB
ejpam-4810	469	11	and	and	CCONJ
ejpam-4810	469	12	the	the	DET
ejpam-4810	469	13	parameter	parameter	NOUN
ejpam-4810	469	14	may	may	AUX
ejpam-4810	469	15	studied	study	VERB
ejpam-4810	469	16	for	for	ADP
ejpam-4810	469	17	other	other	ADJ
ejpam-4810	469	18	graphs	graph	NOUN
ejpam-4810	469	19	.	.	PUNCT
ejpam-4810	470	1	acknowledgements	acknowledgement	NOUN
ejpam-4810	470	2	the	the	DET
ejpam-4810	470	3	authors	author	NOUN
ejpam-4810	470	4	are	be	AUX
ejpam-4810	470	5	very	very	ADV
ejpam-4810	470	6	much	much	ADV
ejpam-4810	470	7	grateful	grateful	ADJ
ejpam-4810	470	8	to	to	ADP
ejpam-4810	470	9	the	the	DET
ejpam-4810	470	10	referees	referee	NOUN
ejpam-4810	470	11	for	for	ADP
ejpam-4810	470	12	the	the	DET
ejpam-4810	470	13	corrections	correction	NOUN
ejpam-4810	470	14	and	and	CCONJ
ejpam-4810	470	15	suggestions	suggestion	NOUN
ejpam-4810	470	16	they	they	PRON
ejpam-4810	470	17	made	make	VERB
ejpam-4810	470	18	in	in	ADP
ejpam-4810	470	19	the	the	DET
ejpam-4810	470	20	initial	initial	ADJ
ejpam-4810	470	21	manuscript	manuscript	NOUN
ejpam-4810	470	22	.	.	PUNCT
ejpam-4810	471	1	also	also	ADV
ejpam-4810	471	2	,	,	PUNCT
ejpam-4810	471	3	the	the	DET
ejpam-4810	471	4	authors	author	NOUN
ejpam-4810	471	5	would	would	AUX
ejpam-4810	471	6	like	like	VERB
ejpam-4810	471	7	to	to	PART
ejpam-4810	471	8	thank	thank	VERB
ejpam-4810	471	9	the	the	DET
ejpam-4810	471	10	department	department	NOUN
ejpam-4810	471	11	of	of	ADP
ejpam-4810	471	12	science	science	NOUN
ejpam-4810	471	13	and	and	CCONJ
ejpam-4810	471	14	technology	technology	NOUN
ejpam-4810	471	15	accelerated	accelerate	VERB
ejpam-4810	471	16	science	science	NOUN
ejpam-4810	471	17	and	and	CCONJ
ejpam-4810	471	18	technology	technology	NOUN
ejpam-4810	471	19	human	human	ADJ
ejpam-4810	471	20	resource	resource	NOUN
ejpam-4810	471	21	development	development	NOUN
ejpam-4810	471	22	program	program	NOUN
ejpam-4810	471	23	(	(	PUNCT
ejpam-4810	471	24	dost	dost	NOUN
ejpam-4810	471	25	-	-	PUNCT
ejpam-4810	471	26	asthrdp)-philippines	asthrdp)-philippine	NOUN
ejpam-4810	471	27	,	,	PUNCT
ejpam-4810	471	28	and	and	CCONJ
ejpam-4810	471	29	msu	msu	PROPN
ejpam-4810	471	30	-	-	PUNCT
ejpam-4810	471	31	iligan	iligan	PROPN
ejpam-4810	471	32	institute	institute	PROPN
ejpam-4810	471	33	of	of	ADP
ejpam-4810	471	34	technology	technology	NOUN
ejpam-4810	471	35	for	for	ADP
ejpam-4810	471	36	funding	fund	VERB
ejpam-4810	471	37	this	this	DET
ejpam-4810	471	38	research	research	NOUN
ejpam-4810	471	39	.	.	PUNCT
ejpam-4810	472	1	references	reference	NOUN
ejpam-4810	472	2	[	[	X
ejpam-4810	472	3	1	1	X
ejpam-4810	472	4	]	]	X
ejpam-4810	472	5	d.	d.	NOUN
ejpam-4810	472	6	anusha	anusha	PROPN
ejpam-4810	472	7	and	and	CCONJ
ejpam-4810	472	8	s.	s.	PROPN
ejpam-4810	472	9	joseph	joseph	PROPN
ejpam-4810	472	10	robin	robin	PROPN
ejpam-4810	472	11	.	.	PUNCT
ejpam-4810	473	1	geodetic	geodetic	ADJ
ejpam-4810	473	2	hop	hop	NOUN
ejpam-4810	473	3	domination	domination	NOUN
ejpam-4810	473	4	in	in	ADP
ejpam-4810	473	5	join	join	NOUN
ejpam-4810	473	6	and	and	CCONJ
ejpam-4810	473	7	corona	corona	NOUN
ejpam-4810	473	8	of	of	ADP
ejpam-4810	473	9	graphs	graph	NOUN
ejpam-4810	473	10	.	.	PUNCT
ejpam-4810	474	1	journal	journal	NOUN
ejpam-4810	474	2	of	of	ADP
ejpam-4810	474	3	combinatorial	combinatorial	ADJ
ejpam-4810	474	4	mathematics	mathematic	NOUN
ejpam-4810	474	5	and	and	CCONJ
ejpam-4810	474	6	combinatorial	combinatorial	ADJ
ejpam-4810	474	7	computing	computing	NOUN
ejpam-4810	474	8	,	,	PUNCT
ejpam-4810	474	9	21(3):1117–1127	21(3):1117–1127	NUM
ejpam-4810	474	10	,	,	PUNCT
ejpam-4810	474	11	2011	2011	NUM
ejpam-4810	474	12	.	.	PUNCT
ejpam-4810	475	1	[	[	X
ejpam-4810	475	2	2	2	NUM
ejpam-4810	475	3	]	]	PUNCT
ejpam-4810	475	4	s.	s.	PROPN
ejpam-4810	475	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4810	475	6	,	,	PUNCT
ejpam-4810	475	7	b.	b.	PROPN
ejpam-4810	475	8	krishnakumari	krishnakumari	PROPN
ejpam-4810	475	9	,	,	PUNCT
ejpam-4810	475	10	b.	b.	PROPN
ejpam-4810	475	11	natarjan	natarjan	PROPN
ejpam-4810	475	12	,	,	PUNCT
ejpam-4810	475	13	and	and	CCONJ
ejpam-4810	475	14	y.	y.	PROPN
ejpam-4810	475	15	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4810	475	16	.	.	PUNCT
ejpam-4810	476	1	bounds	bound	NOUN
ejpam-4810	476	2	on	on	ADP
ejpam-4810	476	3	the	the	DET
ejpam-4810	476	4	hop	hop	NOUN
ejpam-4810	476	5	domination	domination	NOUN
ejpam-4810	476	6	number	number	NOUN
ejpam-4810	476	7	of	of	ADP
ejpam-4810	476	8	a	a	DET
ejpam-4810	476	9	tree	tree	NOUN
ejpam-4810	476	10	.	.	PUNCT
ejpam-4810	477	1	proceedings	proceeding	NOUN
ejpam-4810	477	2	-	-	PUNCT
ejpam-4810	477	3	mathematical	mathematical	ADJ
ejpam-4810	477	4	sciences	science	NOUN
ejpam-4810	477	5	,	,	PUNCT
ejpam-4810	477	6	125(4):449	125(4):449	NUM
ejpam-4810	477	7	–	–	PUNCT
ejpam-4810	477	8	455	455	NUM
ejpam-4810	477	9	,	,	PUNCT
ejpam-4810	477	10	2015	2015	NUM
ejpam-4810	477	11	.	.	PUNCT
ejpam-4810	478	1	[	[	X
ejpam-4810	478	2	3	3	X
ejpam-4810	478	3	]	]	X
ejpam-4810	478	4	s.	s.	PROPN
ejpam-4810	478	5	canoy	canoy	PROPN
ejpam-4810	478	6	and	and	CCONJ
ejpam-4810	478	7	g.	g.	PROPN
ejpam-4810	478	8	salasalan	salasalan	NOUN
ejpam-4810	478	9	.	.	PUNCT
ejpam-4810	479	1	revisiting	revisit	VERB
ejpam-4810	479	2	domination	domination	NOUN
ejpam-4810	479	3	,	,	PUNCT
ejpam-4810	479	4	hop	hop	NOUN
ejpam-4810	479	5	domination	domination	NOUN
ejpam-4810	479	6	,	,	PUNCT
ejpam-4810	479	7	and	and	CCONJ
ejpam-4810	479	8	global	global	ADJ
ejpam-4810	479	9	hop	hop	NOUN
ejpam-4810	479	10	domination	domination	NOUN
ejpam-4810	479	11	in	in	ADP
ejpam-4810	479	12	graphs	graph	NOUN
ejpam-4810	479	13	.	.	PUNCT
ejpam-4810	480	1	european	european	ADJ
ejpam-4810	480	2	journal	journal	PROPN
ejpam-4810	480	3	of	of	ADP
ejpam-4810	480	4	pure	pure	ADJ
ejpam-4810	480	5	and	and	CCONJ
ejpam-4810	480	6	applied	applied	ADJ
ejpam-4810	480	7	mathematics	mathematic	NOUN
ejpam-4810	480	8	,	,	PUNCT
ejpam-4810	480	9	14:1415	14:1415	NUM
ejpam-4810	480	10	–	–	PUNCT
ejpam-4810	480	11	1428	1428	NUM
ejpam-4810	480	12	,	,	PUNCT
ejpam-4810	480	13	2021	2021	NUM
ejpam-4810	480	14	.	.	PUNCT
ejpam-4810	481	1	[	[	X
ejpam-4810	481	2	4	4	X
ejpam-4810	481	3	]	]	X
ejpam-4810	481	4	s.	s.	PROPN
ejpam-4810	481	5	canoy	canoy	PROPN
ejpam-4810	481	6	and	and	CCONJ
ejpam-4810	481	7	g.	g.	PROPN
ejpam-4810	481	8	salasalan	salasalan	NOUN
ejpam-4810	481	9	.	.	PUNCT
ejpam-4810	482	1	a	a	DET
ejpam-4810	482	2	variant	variant	NOUN
ejpam-4810	482	3	of	of	ADP
ejpam-4810	482	4	hop	hop	NOUN
ejpam-4810	482	5	domination	domination	NOUN
ejpam-4810	482	6	in	in	ADP
ejpam-4810	482	7	a	a	DET
ejpam-4810	482	8	graph	graph	NOUN
ejpam-4810	482	9	.	.	PUNCT
ejpam-4810	483	1	european	european	ADJ
ejpam-4810	483	2	journal	journal	PROPN
ejpam-4810	483	3	of	of	ADP
ejpam-4810	483	4	pure	pure	ADJ
ejpam-4810	483	5	and	and	CCONJ
ejpam-4810	483	6	applied	applied	ADJ
ejpam-4810	483	7	mathematics	mathematic	NOUN
ejpam-4810	483	8	,	,	PUNCT
ejpam-4810	483	9	15(2):342–353	15(2):342–353	NUM
ejpam-4810	483	10	,	,	PUNCT
ejpam-4810	483	11	2022	2022	NUM
ejpam-4810	483	12	.	.	PUNCT
ejpam-4810	484	1	[	[	X
ejpam-4810	484	2	5	5	X
ejpam-4810	484	3	]	]	PUNCT
ejpam-4810	484	4	j.	j.	PROPN
ejpam-4810	484	5	hassan	hassan	PROPN
ejpam-4810	484	6	and	and	CCONJ
ejpam-4810	484	7	s.	s.	PROPN
ejpam-4810	484	8	canoy	canoy	PROPN
ejpam-4810	484	9	jr	jr	PROPN
ejpam-4810	484	10	.	.	PUNCT
ejpam-4810	485	1	grundy	grundy	PROPN
ejpam-4810	485	2	hop	hop	PROPN
ejpam-4810	485	3	domination	domination	PROPN
ejpam-4810	485	4	in	in	ADP
ejpam-4810	485	5	graphs	graph	NOUN
ejpam-4810	485	6	.	.	PUNCT
ejpam-4810	486	1	european	european	ADJ
ejpam-4810	486	2	journal	journal	PROPN
ejpam-4810	486	3	of	of	ADP
ejpam-4810	486	4	pure	pure	ADJ
ejpam-4810	486	5	and	and	CCONJ
ejpam-4810	486	6	applied	applied	ADJ
ejpam-4810	486	7	mathematics	mathematic	NOUN
ejpam-4810	486	8	,	,	PUNCT
ejpam-4810	486	9	15(4):1623–1636	15(4):1623–1636	NUM
ejpam-4810	486	10	,	,	PUNCT
ejpam-4810	486	11	2022	2022	NUM
ejpam-4810	486	12	.	.	PUNCT
ejpam-4810	487	1	[	[	X
ejpam-4810	487	2	6	6	NUM
ejpam-4810	487	3	]	]	PUNCT
ejpam-4810	487	4	j.	j.	PROPN
ejpam-4810	487	5	hassan	hassan	PROPN
ejpam-4810	487	6	and	and	CCONJ
ejpam-4810	487	7	s.	s.	PROPN
ejpam-4810	487	8	canoy	canoy	PROPN
ejpam-4810	487	9	jr	jr	PROPN
ejpam-4810	487	10	.	.	PROPN
ejpam-4810	487	11	hop	hop	PROPN
ejpam-4810	487	12	independent	independent	ADJ
ejpam-4810	487	13	domination	domination	NOUN
ejpam-4810	487	14	in	in	ADP
ejpam-4810	487	15	graphs	graph	NOUN
ejpam-4810	487	16	.	.	PUNCT
ejpam-4810	488	1	european	european	ADJ
ejpam-4810	488	2	journal	journal	PROPN
ejpam-4810	488	3	of	of	ADP
ejpam-4810	488	4	pure	pure	ADJ
ejpam-4810	488	5	and	and	CCONJ
ejpam-4810	488	6	applied	applied	ADJ
ejpam-4810	488	7	mathematics	mathematic	NOUN
ejpam-4810	488	8	,	,	PUNCT
ejpam-4810	488	9	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-4810	488	10	,	,	PUNCT
ejpam-4810	488	11	2022	2022	NUM
ejpam-4810	488	12	.	.	PUNCT
ejpam-4810	489	1	[	[	X
ejpam-4810	489	2	7	7	X
ejpam-4810	489	3	]	]	X
ejpam-4810	489	4	m.	m.	NOUN
ejpam-4810	489	5	henning	henning	PROPN
ejpam-4810	489	6	and	and	CCONJ
ejpam-4810	489	7	n.rad	n.rad	PROPN
ejpam-4810	489	8	.	.	PUNCT
ejpam-4810	490	1	on	on	ADP
ejpam-4810	490	2	2	2	NUM
ejpam-4810	490	3	-	-	PUNCT
ejpam-4810	490	4	step	step	NOUN
ejpam-4810	490	5	and	and	CCONJ
ejpam-4810	490	6	hop	hop	NOUN
ejpam-4810	490	7	dominating	dominating	NOUN
ejpam-4810	490	8	sets	set	NOUN
ejpam-4810	490	9	in	in	ADP
ejpam-4810	490	10	graphs	graph	NOUN
ejpam-4810	490	11	.	.	PUNCT
ejpam-4810	491	1	graphs	graph	NOUN
ejpam-4810	491	2	and	and	CCONJ
ejpam-4810	491	3	combinatorics	combinatoric	NOUN
ejpam-4810	491	4	,	,	PUNCT
ejpam-4810	491	5	33(4):913–927	33(4):913–927	PROPN
ejpam-4810	491	6	,	,	PUNCT
ejpam-4810	491	7	2017	2017	NUM
ejpam-4810	491	8	.	.	PUNCT
ejpam-4810	492	1	[	[	X
ejpam-4810	492	2	8	8	NUM
ejpam-4810	492	3	]	]	X
ejpam-4810	492	4	m.	m.	NOUN
ejpam-4810	492	5	henning	henning	PROPN
ejpam-4810	492	6	,	,	PUNCT
ejpam-4810	492	7	a.	a.	NOUN
ejpam-4810	492	8	pal	pal	NOUN
ejpam-4810	492	9	,	,	PUNCT
ejpam-4810	492	10	and	and	CCONJ
ejpam-4810	492	11	d.	d.	PROPN
ejpam-4810	492	12	pradhan	pradhan	PROPN
ejpam-4810	492	13	.	.	PUNCT
ejpam-4810	493	1	algorithm	algorithm	PROPN
ejpam-4810	493	2	and	and	CCONJ
ejpam-4810	493	3	hardness	hardness	NOUN
ejpam-4810	493	4	results	result	NOUN
ejpam-4810	493	5	on	on	ADP
ejpam-4810	493	6	hop	hop	NOUN
ejpam-4810	493	7	domination	domination	NOUN
ejpam-4810	493	8	in	in	ADP
ejpam-4810	493	9	graphs	graph	NOUN
ejpam-4810	493	10	.	.	PUNCT
ejpam-4810	494	1	information	information	NOUN
ejpam-4810	494	2	processing	processing	NOUN
ejpam-4810	494	3	letters	letter	NOUN
ejpam-4810	494	4	,	,	PUNCT
ejpam-4810	494	5	153:105872	153:105872	NUM
ejpam-4810	494	6	,	,	PUNCT
ejpam-4810	494	7	2020	2020	NUM
ejpam-4810	494	8	.	.	PUNCT
ejpam-4810	495	1	references	reference	NOUN
ejpam-4810	495	2	1579	1579	NUM
ejpam-4810	495	3	[	[	X
ejpam-4810	495	4	9	9	NUM
ejpam-4810	495	5	]	]	PUNCT
ejpam-4810	495	6	m.	m.	NOUN
ejpam-4810	495	7	henning	henning	PROPN
ejpam-4810	495	8	and	and	CCONJ
ejpam-4810	495	9	j.	j.	PROPN
ejpam-4810	495	10	rad	rad	PROPN
ejpam-4810	495	11	.	.	PROPN
ejpam-4810	496	1	on	on	ADP
ejpam-4810	496	2	2	2	NUM
ejpam-4810	496	3	-	-	PUNCT
ejpam-4810	496	4	step	step	NOUN
ejpam-4810	496	5	and	and	CCONJ
ejpam-4810	496	6	hop	hop	NOUN
ejpam-4810	496	7	dominating	dominating	NOUN
ejpam-4810	496	8	sets	set	NOUN
ejpam-4810	496	9	in	in	ADP
ejpam-4810	496	10	graphs	graph	NOUN
ejpam-4810	496	11	.	.	PUNCT
ejpam-4810	497	1	graphs	graph	NOUN
ejpam-4810	497	2	and	and	CCONJ
ejpam-4810	497	3	combinatorics	combinatoric	NOUN
ejpam-4810	497	4	,	,	PUNCT
ejpam-4810	497	5	33(2):1–15	33(2):1–15	NUM
ejpam-4810	497	6	,	,	PUNCT
ejpam-4810	497	7	2017	2017	NUM
ejpam-4810	497	8	.	.	PUNCT
ejpam-4810	498	1	[	[	X
ejpam-4810	498	2	10	10	NUM
ejpam-4810	498	3	]	]	X
ejpam-4810	498	4	s.	s.	PROPN
ejpam-4810	498	5	canoy	canoy	PROPN
ejpam-4810	498	6	jr	jr	PROPN
ejpam-4810	498	7	.	.	PROPN
ejpam-4810	498	8	and	and	CCONJ
ejpam-4810	498	9	s.	s.	PROPN
ejpam-4810	498	10	arriola	arriola	PROPN
ejpam-4810	498	11	.	.	PUNCT
ejpam-4810	499	1	(	(	PUNCT
ejpam-4810	499	2	1	1	NUM
ejpam-4810	499	3	,	,	PUNCT
ejpam-4810	499	4	2)∗-domination	2)∗-domination	NOUN
ejpam-4810	499	5	in	in	ADP
ejpam-4810	499	6	graphs	graph	NOUN
ejpam-4810	499	7	.	.	PUNCT
ejpam-4810	500	1	advances	advance	NOUN
ejpam-4810	500	2	and	and	CCONJ
ejpam-4810	500	3	applications	application	NOUN
ejpam-4810	500	4	in	in	ADP
ejpam-4810	500	5	discrete	discrete	ADJ
ejpam-4810	500	6	mathematics	mathematic	NOUN
ejpam-4810	500	7	.	.	PUNCT
ejpam-4810	500	8	,	,	PUNCT
ejpam-4810	500	9	18(2):179–190	18(2):179–190	NUM
ejpam-4810	500	10	,	,	PUNCT
ejpam-4810	500	11	2017	2017	NUM
ejpam-4810	500	12	.	.	PUNCT
ejpam-4810	501	1	[	[	X
ejpam-4810	501	2	11	11	NUM
ejpam-4810	501	3	]	]	X
ejpam-4810	501	4	s.	s.	PROPN
ejpam-4810	501	5	canoy	canoy	PROPN
ejpam-4810	501	6	jr	jr	PROPN
ejpam-4810	501	7	.	.	PROPN
ejpam-4810	501	8	,	,	PUNCT
ejpam-4810	501	9	r.	r.	PROPN
ejpam-4810	501	10	mollejon	mollejon	NOUN
ejpam-4810	501	11	,	,	PUNCT
ejpam-4810	501	12	and	and	CCONJ
ejpam-4810	501	13	j.	j.	PROPN
ejpam-4810	501	14	g.	g.	PROPN
ejpam-4810	501	15	canoy	canoy	PROPN
ejpam-4810	501	16	.	.	PUNCT
ejpam-4810	502	1	hop	hop	PROPN
ejpam-4810	502	2	dominating	dominating	NOUN
ejpam-4810	502	3	sets	set	NOUN
ejpam-4810	502	4	in	in	ADP
ejpam-4810	502	5	graphs	graph	NOUN
ejpam-4810	502	6	under	under	ADP
ejpam-4810	502	7	binary	binary	ADJ
ejpam-4810	502	8	operations	operation	NOUN
ejpam-4810	502	9	.	.	PUNCT
ejpam-4810	503	1	eur	eur	PROPN
ejpam-4810	503	2	.	.	PUNCT
ejpam-4810	504	1	j.	j.	PROPN
ejpam-4810	504	2	pure	pure	PROPN
ejpam-4810	504	3	appl	appl	PROPN
ejpam-4810	504	4	.	.	PUNCT
ejpam-4810	504	5	math	math	PROPN
ejpam-4810	504	6	.	.	PUNCT
ejpam-4810	504	7	,	,	PUNCT
ejpam-4810	505	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4810	505	2	,	,	PUNCT
ejpam-4810	505	3	2019	2019	NUM
ejpam-4810	505	4	.	.	PUNCT
ejpam-4810	506	1	[	[	X
ejpam-4810	506	2	12	12	NUM
ejpam-4810	506	3	]	]	X
ejpam-4810	506	4	s.	s.	PROPN
ejpam-4810	506	5	canoy	canoy	PROPN
ejpam-4810	506	6	jr	jr	PROPN
ejpam-4810	506	7	.	.	PROPN
ejpam-4810	506	8	and	and	CCONJ
ejpam-4810	506	9	g.	g.	PROPN
ejpam-4810	506	10	salasalan	salasalan	NOUN
ejpam-4810	506	11	.	.	PUNCT
ejpam-4810	507	1	global	global	ADJ
ejpam-4810	507	2	hop	hop	PROPN
ejpam-4810	507	3	domination	domination	NOUN
ejpam-4810	507	4	number	number	NOUN
ejpam-4810	507	5	of	of	ADP
ejpam-4810	507	6	graphs	graph	NOUN
ejpam-4810	507	7	.	.	PUNCT
ejpam-4810	508	1	european	european	ADJ
ejpam-4810	508	2	journal	journal	PROPN
ejpam-4810	508	3	of	of	ADP
ejpam-4810	508	4	pure	pure	ADJ
ejpam-4810	508	5	and	and	CCONJ
ejpam-4810	508	6	applied	applied	ADJ
ejpam-4810	508	7	mathematics	mathematic	NOUN
ejpam-4810	508	8	,	,	PUNCT
ejpam-4810	508	9	14(1):112	14(1):112	NUM
ejpam-4810	508	10	–	–	PUNCT
ejpam-4810	508	11	125	125	NUM
ejpam-4810	508	12	,	,	PUNCT
ejpam-4810	508	13	2021	2021	NUM
ejpam-4810	508	14	.	.	PUNCT
ejpam-4810	509	1	[	[	X
ejpam-4810	509	2	13	13	NUM
ejpam-4810	509	3	]	]	X
ejpam-4810	509	4	c.	c.	PROPN
ejpam-4810	509	5	natarajan	natarajan	PROPN
ejpam-4810	509	6	and	and	CCONJ
ejpam-4810	509	7	s.	s.	PROPN
ejpam-4810	509	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4810	509	9	.	.	PUNCT
ejpam-4810	510	1	hop	hop	PROPN
ejpam-4810	510	2	domination	domination	NOUN
ejpam-4810	510	3	in	in	ADP
ejpam-4810	510	4	graphs	graphs	PROPN
ejpam-4810	510	5	ii	ii	PROPN
ejpam-4810	510	6	.	.	PUNCT
ejpam-4810	510	7	versita	versita	PROPN
ejpam-4810	510	8	,	,	PUNCT
ejpam-4810	510	9	23(2):187	23(2):187	NUM
ejpam-4810	510	10	–	–	PUNCT
ejpam-4810	510	11	199	199	NUM
ejpam-4810	510	12	,	,	PUNCT
ejpam-4810	510	13	2015	2015	NUM
ejpam-4810	510	14	.	.	PUNCT
ejpam-4810	511	1	[	[	X
ejpam-4810	511	2	14	14	NUM
ejpam-4810	511	3	]	]	X
ejpam-4810	511	4	r.	r.	PROPN
ejpam-4810	511	5	rakim	rakim	PROPN
ejpam-4810	511	6	and	and	CCONJ
ejpam-4810	511	7	h.	h.	PROPN
ejpam-4810	511	8	rara	rara	PROPN
ejpam-4810	511	9	.	.	PUNCT
ejpam-4810	512	1	perfect	perfect	ADJ
ejpam-4810	512	2	hop	hop	NOUN
ejpam-4810	512	3	domination	domination	NOUN
ejpam-4810	512	4	in	in	ADP
ejpam-4810	512	5	graphs	graph	NOUN
ejpam-4810	512	6	.	.	PUNCT
ejpam-4810	513	1	applied	apply	VERB
ejpam-4810	513	2	mathematical	mathematical	ADJ
ejpam-4810	513	3	sciences	sciences	PROPN
ejpam-4810	513	4	,	,	PUNCT
ejpam-4810	513	5	12(13):635–649	12(13):635–649	NUM
ejpam-4810	513	6	,	,	PUNCT
ejpam-4810	513	7	2018	2018	NUM
ejpam-4810	513	8	.	.	PUNCT
ejpam-4810	514	1	[	[	X
ejpam-4810	514	2	15	15	NUM
ejpam-4810	514	3	]	]	X
ejpam-4810	514	4	r.	r.	PROPN
ejpam-4810	514	5	rakim	rakim	PROPN
ejpam-4810	514	6	and	and	CCONJ
ejpam-4810	514	7	h.	h.	PROPN
ejpam-4810	514	8	rara	rara	PROPN
ejpam-4810	514	9	.	.	PUNCT
ejpam-4810	515	1	total	total	ADJ
ejpam-4810	515	2	perfect	perfect	ADJ
ejpam-4810	515	3	hop	hop	NOUN
ejpam-4810	515	4	domination	domination	NOUN
ejpam-4810	515	5	in	in	ADP
ejpam-4810	515	6	graphs	graph	NOUN
ejpam-4810	515	7	under	under	ADP
ejpam-4810	515	8	some	some	DET
ejpam-4810	515	9	binary	binary	ADJ
ejpam-4810	515	10	operations	operation	NOUN
ejpam-4810	515	11	.	.	PUNCT
ejpam-4810	516	1	european	european	ADJ
ejpam-4810	516	2	journal	journal	PROPN
ejpam-4810	516	3	of	of	ADP
ejpam-4810	516	4	pure	pure	ADJ
ejpam-4810	516	5	and	and	CCONJ
ejpam-4810	516	6	applied	applied	ADJ
ejpam-4810	516	7	mathematics	mathematic	NOUN
ejpam-4810	516	8	,	,	PUNCT
ejpam-4810	516	9	14(3):803–815	14(3):803–815	PROPN
ejpam-4810	516	10	,	,	PUNCT
ejpam-4810	516	11	2021	2021	NUM
ejpam-4810	516	12	.	.	PUNCT
ejpam-4810	517	1	[	[	X
ejpam-4810	517	2	16	16	NUM
ejpam-4810	517	3	]	]	X
ejpam-4810	517	4	c.j	c.j	PROPN
ejpam-4810	517	5	.	.	PROPN
ejpam-4810	517	6	saromines	saromine	NOUN
ejpam-4810	517	7	and	and	CCONJ
ejpam-4810	517	8	s.	s.	PROPN
ejpam-4810	517	9	canoy	canoy	PROPN
ejpam-4810	517	10	jr	jr	PROPN
ejpam-4810	517	11	.	.	PUNCT
ejpam-4810	517	12	outer	outer	ADV
ejpam-4810	517	13	-	-	PUNCT
ejpam-4810	517	14	connected	connect	VERB
ejpam-4810	517	15	hop	hop	NOUN
ejpam-4810	517	16	dominating	dominating	NOUN
ejpam-4810	517	17	sets	set	NOUN
ejpam-4810	517	18	in	in	ADP
ejpam-4810	517	19	graphs	graph	NOUN
ejpam-4810	517	20	.	.	PUNCT
ejpam-4810	518	1	european	european	ADJ
ejpam-4810	518	2	journal	journal	PROPN
ejpam-4810	518	3	of	of	ADP
ejpam-4810	518	4	pure	pure	ADJ
ejpam-4810	518	5	and	and	CCONJ
ejpam-4810	518	6	applied	applied	ADJ
ejpam-4810	518	7	mathematics	mathematic	NOUN
ejpam-4810	518	8	,	,	PUNCT
ejpam-4810	518	9	15(4):1996–1981	15(4):1996–1981	NUM
ejpam-4810	518	10	,	,	PUNCT
ejpam-4810	518	11	2022	2022	NUM
ejpam-4810	518	12	.	.	PUNCT