id	sid	tid	token	lemma	pos
ejpam-4590	1	1	european	european	PROPN
ejpam-4590	1	2	journal	journal	PROPN
ejpam-4590	1	3	of	of	ADP
ejpam-4590	1	4	pure	pure	ADJ
ejpam-4590	1	5	and	and	CCONJ
ejpam-4590	1	6	applied	apply	VERB
ejpam-4590	1	7	mathematics	mathematic	NOUN
ejpam-4590	1	8	vol	vol	NOUN
ejpam-4590	1	9	.	.	PROPN
ejpam-4590	2	1	15	15	NUM
ejpam-4590	2	2	,	,	PUNCT
ejpam-4590	2	3	no	no	INTJ
ejpam-4590	2	4	.	.	NOUN
ejpam-4590	2	5	4	4	NUM
ejpam-4590	2	6	,	,	PUNCT
ejpam-4590	2	7	2022	2022	NUM
ejpam-4590	2	8	,	,	PUNCT
ejpam-4590	2	9	1966	1966	NUM
ejpam-4590	2	10	-	-	SYM
ejpam-4590	2	11	1981	1981	NUM
ejpam-4590	2	12	issn	issn	PROPN
ejpam-4590	2	13	1307	1307	NUM
ejpam-4590	2	14	-	-	SYM
ejpam-4590	2	15	5543	5543	NUM
ejpam-4590	2	16	–	–	PUNCT
ejpam-4590	2	17	ejpam.com	ejpam.com	X
ejpam-4590	2	18	published	publish	VERB
ejpam-4590	2	19	by	by	ADP
ejpam-4590	2	20	new	new	PROPN
ejpam-4590	2	21	york	york	PROPN
ejpam-4590	2	22	business	business	PROPN
ejpam-4590	2	23	global	global	ADJ
ejpam-4590	2	24	outer	outer	ADV
ejpam-4590	2	25	-	-	PUNCT
ejpam-4590	2	26	connected	connect	VERB
ejpam-4590	2	27	hop	hop	NOUN
ejpam-4590	2	28	dominating	dominating	NOUN
ejpam-4590	2	29	sets	set	NOUN
ejpam-4590	2	30	in	in	ADP
ejpam-4590	2	31	graphs	graph	NOUN
ejpam-4590	2	32	chrisley	chrisley	PROPN
ejpam-4590	2	33	jade	jade	PROPN
ejpam-4590	2	34	c.	c.	PROPN
ejpam-4590	2	35	saromines1,∗	saromines1,∗	PROPN
ejpam-4590	2	36	,	,	PUNCT
ejpam-4590	2	37	sergio	sergio	PROPN
ejpam-4590	2	38	r.	r.	PROPN
ejpam-4590	2	39	canoy	canoy	PROPN
ejpam-4590	2	40	,	,	PUNCT
ejpam-4590	2	41	jr.1	jr.1	PROPN
ejpam-4590	2	42	1	1	NUM
ejpam-4590	2	43	department	department	NOUN
ejpam-4590	2	44	of	of	ADP
ejpam-4590	2	45	mathematics	mathematic	NOUN
ejpam-4590	2	46	and	and	CCONJ
ejpam-4590	2	47	statistics	statistic	NOUN
ejpam-4590	2	48	,	,	PUNCT
ejpam-4590	2	49	college	college	NOUN
ejpam-4590	2	50	of	of	ADP
ejpam-4590	2	51	science	science	NOUN
ejpam-4590	2	52	and	and	CCONJ
ejpam-4590	2	53	mathematics	mathematic	NOUN
ejpam-4590	2	54	,	,	PUNCT
ejpam-4590	2	55	center	center	NOUN
ejpam-4590	2	56	for	for	ADP
ejpam-4590	2	57	graph	graph	NOUN
ejpam-4590	2	58	theory	theory	NOUN
ejpam-4590	2	59	,	,	PUNCT
ejpam-4590	2	60	algebra	algebra	NOUN
ejpam-4590	2	61	and	and	CCONJ
ejpam-4590	2	62	analysis	analysis	NOUN
ejpam-4590	2	63	-	-	PUNCT
ejpam-4590	2	64	prism	prism	NOUN
ejpam-4590	2	65	,	,	PUNCT
ejpam-4590	2	66	msu	msu	PROPN
ejpam-4590	2	67	-	-	PUNCT
ejpam-4590	2	68	iligan	iligan	PROPN
ejpam-4590	2	69	institute	institute	PROPN
ejpam-4590	2	70	of	of	ADP
ejpam-4590	2	71	technology	technology	PROPN
ejpam-4590	2	72	,	,	PUNCT
ejpam-4590	2	73	9200	9200	NUM
ejpam-4590	2	74	iligan	iligan	ADJ
ejpam-4590	2	75	city	city	NOUN
ejpam-4590	2	76	,	,	PUNCT
ejpam-4590	2	77	philippines	philippine	NOUN
ejpam-4590	2	78	abstract	abstract	ADJ
ejpam-4590	2	79	.	.	PUNCT
ejpam-4590	3	1	let	let	VERB
ejpam-4590	3	2	g	g	PRON
ejpam-4590	3	3	be	be	AUX
ejpam-4590	3	4	an	an	DET
ejpam-4590	3	5	undirected	undirected	ADJ
ejpam-4590	3	6	graph	graph	NOUN
ejpam-4590	3	7	with	with	ADP
ejpam-4590	3	8	vertex	vertex	NOUN
ejpam-4590	3	9	and	and	CCONJ
ejpam-4590	3	10	edge	edge	NOUN
ejpam-4590	3	11	sets	set	NOUN
ejpam-4590	3	12	v	v	ADP
ejpam-4590	3	13	(	(	PUNCT
ejpam-4590	3	14	g	g	NOUN
ejpam-4590	3	15	)	)	PUNCT
ejpam-4590	3	16	and	and	CCONJ
ejpam-4590	3	17	e(g	e(g	PROPN
ejpam-4590	3	18	)	)	PUNCT
ejpam-4590	3	19	,	,	PUNCT
ejpam-4590	3	20	respectively	respectively	ADV
ejpam-4590	3	21	.	.	PUNCT
ejpam-4590	4	1	a	a	DET
ejpam-4590	4	2	hop	hop	NOUN
ejpam-4590	4	3	dominating	dominating	NOUN
ejpam-4590	4	4	set	set	NOUN
ejpam-4590	4	5	s	s	PROPN
ejpam-4590	4	6	⊆	⊆	NUM
ejpam-4590	4	7	v	v	NOUN
ejpam-4590	4	8	(	(	PUNCT
ejpam-4590	4	9	g	g	NOUN
ejpam-4590	4	10	)	)	PUNCT
ejpam-4590	4	11	is	be	AUX
ejpam-4590	4	12	called	call	VERB
ejpam-4590	4	13	an	an	DET
ejpam-4590	4	14	outer	outer	ADV
ejpam-4590	4	15	-	-	PUNCT
ejpam-4590	4	16	connected	connect	VERB
ejpam-4590	4	17	hop	hop	NOUN
ejpam-4590	4	18	dominating	dominating	NOUN
ejpam-4590	4	19	set	set	NOUN
ejpam-4590	4	20	if	if	SCONJ
ejpam-4590	4	21	s	s	VERB
ejpam-4590	4	22	=	=	SYM
ejpam-4590	4	23	v	v	X
ejpam-4590	4	24	(	(	PUNCT
ejpam-4590	4	25	g	g	NOUN
ejpam-4590	4	26	)	)	PUNCT
ejpam-4590	4	27	or	or	CCONJ
ejpam-4590	4	28	the	the	DET
ejpam-4590	4	29	subgraph	subgraph	NOUN
ejpam-4590	4	30	⟨v	⟨v	NOUN
ejpam-4590	4	31	(	(	PUNCT
ejpam-4590	4	32	g	g	NOUN
ejpam-4590	4	33	)	)	PUNCT
ejpam-4590	4	34	\	\	PROPN
ejpam-4590	4	35	s⟩	s⟩	NOUN
ejpam-4590	4	36	induced	induce	VERB
ejpam-4590	4	37	by	by	ADP
ejpam-4590	4	38	v	v	NOUN
ejpam-4590	4	39	(	(	PUNCT
ejpam-4590	4	40	g	g	NOUN
ejpam-4590	4	41	)	)	PUNCT
ejpam-4590	4	42	\	\	PROPN
ejpam-4590	5	1	s	s	PART
ejpam-4590	5	2	is	be	AUX
ejpam-4590	5	3	connected	connect	VERB
ejpam-4590	5	4	.	.	PUNCT
ejpam-4590	6	1	the	the	DET
ejpam-4590	6	2	minimum	minimum	ADJ
ejpam-4590	6	3	size	size	NOUN
ejpam-4590	6	4	of	of	ADP
ejpam-4590	6	5	an	an	DET
ejpam-4590	6	6	outer	outer	ADV
ejpam-4590	6	7	-	-	PUNCT
ejpam-4590	6	8	connected	connect	VERB
ejpam-4590	6	9	hop	hop	NOUN
ejpam-4590	6	10	dominating	dominating	NOUN
ejpam-4590	6	11	set	set	NOUN
ejpam-4590	6	12	is	be	AUX
ejpam-4590	6	13	the	the	DET
ejpam-4590	6	14	outer	outer	ADV
ejpam-4590	6	15	-	-	PUNCT
ejpam-4590	6	16	connected	connect	VERB
ejpam-4590	6	17	hop	hop	NOUN
ejpam-4590	6	18	domination	domination	NOUN
ejpam-4590	6	19	number	number	NOUN
ejpam-4590	6	20	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	6	21	)	)	PUNCT
ejpam-4590	6	22	.	.	PUNCT
ejpam-4590	7	1	a	a	DET
ejpam-4590	7	2	dominating	dominating	NOUN
ejpam-4590	7	3	set	set	NOUN
ejpam-4590	7	4	of	of	ADP
ejpam-4590	7	5	size	size	NOUN
ejpam-4590	7	6	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	7	7	)	)	PUNCT
ejpam-4590	7	8	of	of	ADP
ejpam-4590	7	9	g	g	PROPN
ejpam-4590	7	10	is	be	AUX
ejpam-4590	7	11	called	call	VERB
ejpam-4590	7	12	a	a	DET
ejpam-4590	7	13	γ̃ch	γ̃ch	PROPN
ejpam-4590	7	14	-	-	PUNCT
ejpam-4590	7	15	set	set	NOUN
ejpam-4590	7	16	.	.	PUNCT
ejpam-4590	8	1	in	in	ADP
ejpam-4590	8	2	this	this	DET
ejpam-4590	8	3	paper	paper	NOUN
ejpam-4590	8	4	,	,	PUNCT
ejpam-4590	8	5	we	we	PRON
ejpam-4590	8	6	investigate	investigate	VERB
ejpam-4590	8	7	the	the	DET
ejpam-4590	8	8	concept	concept	NOUN
ejpam-4590	8	9	and	and	CCONJ
ejpam-4590	8	10	study	study	VERB
ejpam-4590	8	11	it	it	PRON
ejpam-4590	8	12	for	for	ADP
ejpam-4590	8	13	graphs	graph	NOUN
ejpam-4590	8	14	resulting	result	VERB
ejpam-4590	8	15	from	from	ADP
ejpam-4590	8	16	some	some	DET
ejpam-4590	8	17	binary	binary	ADJ
ejpam-4590	8	18	operations	operation	NOUN
ejpam-4590	8	19	.	.	PUNCT
ejpam-4590	9	1	specifically	specifically	ADV
ejpam-4590	9	2	,	,	PUNCT
ejpam-4590	9	3	we	we	PRON
ejpam-4590	9	4	characterize	characterize	VERB
ejpam-4590	9	5	the	the	DET
ejpam-4590	9	6	outer	outer	ADV
ejpam-4590	9	7	-	-	PUNCT
ejpam-4590	9	8	connected	connect	VERB
ejpam-4590	9	9	hop	hop	NOUN
ejpam-4590	9	10	dominating	dominating	NOUN
ejpam-4590	9	11	sets	set	NOUN
ejpam-4590	9	12	in	in	ADP
ejpam-4590	9	13	the	the	DET
ejpam-4590	9	14	join	join	NOUN
ejpam-4590	9	15	,	,	PUNCT
ejpam-4590	9	16	corona	corona	NOUN
ejpam-4590	9	17	and	and	CCONJ
ejpam-4590	9	18	lexicographic	lexicographic	ADJ
ejpam-4590	9	19	products	product	NOUN
ejpam-4590	9	20	of	of	ADP
ejpam-4590	9	21	graphs	graph	NOUN
ejpam-4590	9	22	,	,	PUNCT
ejpam-4590	9	23	and	and	CCONJ
ejpam-4590	9	24	determine	determine	VERB
ejpam-4590	9	25	bounds	bound	NOUN
ejpam-4590	9	26	of	of	ADP
ejpam-4590	9	27	the	the	DET
ejpam-4590	9	28	outer	outer	ADV
ejpam-4590	9	29	-	-	PUNCT
ejpam-4590	9	30	connected	connect	VERB
ejpam-4590	9	31	hop	hop	NOUN
ejpam-4590	9	32	domination	domination	NOUN
ejpam-4590	9	33	number	number	NOUN
ejpam-4590	9	34	of	of	ADP
ejpam-4590	9	35	each	each	PRON
ejpam-4590	9	36	of	of	ADP
ejpam-4590	9	37	these	these	DET
ejpam-4590	9	38	graphs	graph	NOUN
ejpam-4590	9	39	.	.	PUNCT
ejpam-4590	10	1	2020	2020	NUM
ejpam-4590	10	2	mathematics	mathematic	NOUN
ejpam-4590	10	3	subject	subject	NOUN
ejpam-4590	10	4	classifications	classification	NOUN
ejpam-4590	10	5	:	:	PUNCT
ejpam-4590	10	6	05c69	05c69	X
ejpam-4590	10	7	key	key	ADJ
ejpam-4590	10	8	words	word	NOUN
ejpam-4590	10	9	and	and	CCONJ
ejpam-4590	10	10	phrases	phrase	NOUN
ejpam-4590	10	11	:	:	PUNCT
ejpam-4590	10	12	hop	hop	NOUN
ejpam-4590	10	13	domination	domination	NOUN
ejpam-4590	10	14	,	,	PUNCT
ejpam-4590	10	15	outer	outer	ADV
ejpam-4590	10	16	-	-	PUNCT
ejpam-4590	10	17	connected	connect	VERB
ejpam-4590	10	18	,	,	PUNCT
ejpam-4590	10	19	join	join	NOUN
ejpam-4590	10	20	,	,	PUNCT
ejpam-4590	10	21	corona	corona	PROPN
ejpam-4590	10	22	,	,	PUNCT
ejpam-4590	10	23	lexicographic	lexicographic	ADJ
ejpam-4590	10	24	1	1	NUM
ejpam-4590	10	25	.	.	PUNCT
ejpam-4590	11	1	introduction	introduction	NOUN
ejpam-4590	11	2	as	as	SCONJ
ejpam-4590	11	3	pointed	point	VERB
ejpam-4590	11	4	out	out	ADP
ejpam-4590	11	5	in	in	ADP
ejpam-4590	11	6	[	[	X
ejpam-4590	11	7	1	1	NUM
ejpam-4590	11	8	]	]	PUNCT
ejpam-4590	11	9	and	and	CCONJ
ejpam-4590	11	10	[	[	X
ejpam-4590	11	11	9	9	NUM
ejpam-4590	11	12	]	]	PUNCT
ejpam-4590	11	13	,	,	PUNCT
ejpam-4590	11	14	the	the	DET
ejpam-4590	11	15	domination	domination	NOUN
ejpam-4590	11	16	concept	concept	NOUN
ejpam-4590	11	17	has	have	AUX
ejpam-4590	11	18	been	be	AUX
ejpam-4590	11	19	one	one	NUM
ejpam-4590	11	20	of	of	ADP
ejpam-4590	11	21	the	the	DET
ejpam-4590	11	22	mainstreams	mainstreams	NOUN
ejpam-4590	11	23	of	of	ADP
ejpam-4590	11	24	research	research	NOUN
ejpam-4590	11	25	in	in	ADP
ejpam-4590	11	26	graph	graph	NOUN
ejpam-4590	11	27	theory	theory	NOUN
ejpam-4590	11	28	and	and	CCONJ
ejpam-4590	11	29	it	it	PRON
ejpam-4590	11	30	has	have	VERB
ejpam-4590	11	31	numerous	numerous	ADJ
ejpam-4590	11	32	applications	application	NOUN
ejpam-4590	11	33	,	,	PUNCT
ejpam-4590	11	34	interesting	interesting	ADJ
ejpam-4590	11	35	questions	question	NOUN
ejpam-4590	11	36	and	and	CCONJ
ejpam-4590	11	37	results	result	NOUN
ejpam-4590	11	38	,	,	PUNCT
ejpam-4590	11	39	and	and	CCONJ
ejpam-4590	11	40	unsolved	unsolved	ADJ
ejpam-4590	11	41	research	research	NOUN
ejpam-4590	11	42	questions	question	NOUN
ejpam-4590	11	43	.	.	PUNCT
ejpam-4590	12	1	moreover	moreover	ADV
ejpam-4590	12	2	,	,	PUNCT
ejpam-4590	12	3	the	the	DET
ejpam-4590	12	4	concept	concept	NOUN
ejpam-4590	12	5	has	have	VERB
ejpam-4590	12	6	already	already	ADV
ejpam-4590	12	7	plenty	plenty	NOUN
ejpam-4590	12	8	of	of	ADP
ejpam-4590	12	9	variations	variation	NOUN
ejpam-4590	12	10	(	(	PUNCT
ejpam-4590	12	11	see	see	VERB
ejpam-4590	12	12	[	[	X
ejpam-4590	12	13	3	3	NUM
ejpam-4590	12	14	]	]	PUNCT
ejpam-4590	12	15	,	,	PUNCT
ejpam-4590	12	16	[	[	X
ejpam-4590	12	17	8	8	NUM
ejpam-4590	12	18	]	]	PUNCT
ejpam-4590	12	19	,	,	PUNCT
ejpam-4590	12	20	[	[	X
ejpam-4590	12	21	13	13	NUM
ejpam-4590	12	22	]	]	PUNCT
ejpam-4590	12	23	,	,	PUNCT
ejpam-4590	12	24	[	[	X
ejpam-4590	12	25	15	15	NUM
ejpam-4590	12	26	]	]	PUNCT
ejpam-4590	12	27	,	,	PUNCT
ejpam-4590	12	28	[	[	X
ejpam-4590	12	29	17	17	NUM
ejpam-4590	12	30	]	]	PUNCT
ejpam-4590	12	31	,	,	PUNCT
ejpam-4590	12	32	[	[	X
ejpam-4590	12	33	18	18	NUM
ejpam-4590	12	34	]	]	NUM
ejpam-4590	12	35	)	)	PUNCT
ejpam-4590	12	36	.	.	PUNCT
ejpam-4590	13	1	outer	outer	ADJ
ejpam-4590	13	2	-	-	PUNCT
ejpam-4590	13	3	connected	connect	VERB
ejpam-4590	13	4	domination	domination	NOUN
ejpam-4590	13	5	,	,	PUNCT
ejpam-4590	13	6	a	a	DET
ejpam-4590	13	7	variation	variation	NOUN
ejpam-4590	13	8	of	of	ADP
ejpam-4590	13	9	domination	domination	NOUN
ejpam-4590	13	10	,	,	PUNCT
ejpam-4590	13	11	was	be	AUX
ejpam-4590	13	12	first	first	ADV
ejpam-4590	13	13	introduced	introduce	VERB
ejpam-4590	13	14	by	by	ADP
ejpam-4590	13	15	cyman	cyman	NOUN
ejpam-4590	13	16	in	in	ADP
ejpam-4590	13	17	2007	2007	NUM
ejpam-4590	13	18	[	[	X
ejpam-4590	13	19	5	5	NUM
ejpam-4590	13	20	]	]	PUNCT
ejpam-4590	13	21	.	.	PUNCT
ejpam-4590	14	1	a	a	DET
ejpam-4590	14	2	set	set	NOUN
ejpam-4590	14	3	d	d	NOUN
ejpam-4590	14	4	⊆	⊆	NUM
ejpam-4590	14	5	v	v	ADP
ejpam-4590	14	6	(	(	PUNCT
ejpam-4590	14	7	g	g	NOUN
ejpam-4590	14	8	)	)	PUNCT
ejpam-4590	14	9	is	be	AUX
ejpam-4590	14	10	said	say	VERB
ejpam-4590	14	11	to	to	PART
ejpam-4590	14	12	be	be	AUX
ejpam-4590	14	13	an	an	DET
ejpam-4590	14	14	outer	outer	ADV
ejpam-4590	14	15	-	-	PUNCT
ejpam-4590	14	16	connected	connect	VERB
ejpam-4590	14	17	dominating	dominating	NOUN
ejpam-4590	14	18	set	set	NOUN
ejpam-4590	14	19	of	of	ADP
ejpam-4590	14	20	g	g	PROPN
ejpam-4590	14	21	if	if	SCONJ
ejpam-4590	14	22	d	d	PROPN
ejpam-4590	14	23	is	be	AUX
ejpam-4590	14	24	dominating	dominate	VERB
ejpam-4590	14	25	and	and	CCONJ
ejpam-4590	14	26	either	either	CCONJ
ejpam-4590	14	27	d	d	PROPN
ejpam-4590	14	28	=	=	SYM
ejpam-4590	14	29	v	v	PROPN
ejpam-4590	14	30	(	(	PUNCT
ejpam-4590	14	31	g	g	NOUN
ejpam-4590	14	32	)	)	PUNCT
ejpam-4590	14	33	or	or	CCONJ
ejpam-4590	14	34	⟨v	⟨v	NUM
ejpam-4590	14	35	(	(	PUNCT
ejpam-4590	14	36	g	g	NOUN
ejpam-4590	14	37	)	)	PUNCT
ejpam-4590	14	38	\d⟩	\d⟩	PROPN
ejpam-4590	14	39	is	be	AUX
ejpam-4590	14	40	connected	connect	VERB
ejpam-4590	14	41	.	.	PUNCT
ejpam-4590	15	1	this	this	DET
ejpam-4590	15	2	concept	concept	NOUN
ejpam-4590	15	3	has	have	AUX
ejpam-4590	15	4	been	be	AUX
ejpam-4590	15	5	studied	study	VERB
ejpam-4590	15	6	by	by	ADP
ejpam-4590	15	7	several	several	ADJ
ejpam-4590	15	8	authors	author	NOUN
ejpam-4590	15	9	like	like	ADP
ejpam-4590	15	10	jiang	jiang	PROPN
ejpam-4590	15	11	and	and	CCONJ
ejpam-4590	15	12	shang	shang	PROPN
ejpam-4590	16	1	[	[	X
ejpam-4590	16	2	11	11	NUM
ejpam-4590	16	3	]	]	PUNCT
ejpam-4590	16	4	and	and	CCONJ
ejpam-4590	16	5	ahkbari	ahkbari	PROPN
ejpam-4590	16	6	et	et	PROPN
ejpam-4590	16	7	al	al	PROPN
ejpam-4590	16	8	.	.	PUNCT
ejpam-4590	17	1	[	[	X
ejpam-4590	17	2	2	2	NUM
ejpam-4590	17	3	]	]	PUNCT
ejpam-4590	17	4	,	,	PUNCT
ejpam-4590	17	5	and	and	CCONJ
ejpam-4590	17	6	an	an	DET
ejpam-4590	17	7	outerconnected	outerconnecte	VERB
ejpam-4590	17	8	domination	domination	NOUN
ejpam-4590	17	9	variant	variant	NOUN
ejpam-4590	17	10	was	be	AUX
ejpam-4590	17	11	introduced	introduce	VERB
ejpam-4590	17	12	in	in	ADP
ejpam-4590	17	13	[	[	X
ejpam-4590	17	14	12	12	NUM
ejpam-4590	17	15	]	]	PUNCT
ejpam-4590	17	16	.	.	PUNCT
ejpam-4590	18	1	in	in	ADP
ejpam-4590	18	2	2015	2015	NUM
ejpam-4590	18	3	,	,	PUNCT
ejpam-4590	18	4	natarajan	natarajan	PROPN
ejpam-4590	18	5	and	and	CCONJ
ejpam-4590	18	6	s.	s.	PROPN
ejpam-4590	18	7	k.	k.	PROPN
ejpam-4590	18	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4590	19	1	[	[	X
ejpam-4590	19	2	16	16	NUM
ejpam-4590	19	3	]	]	PUNCT
ejpam-4590	19	4	introduced	introduce	VERB
ejpam-4590	19	5	a	a	DET
ejpam-4590	19	6	new	new	ADJ
ejpam-4590	19	7	distance	distance	NOUN
ejpam-4590	19	8	related	relate	VERB
ejpam-4590	19	9	domination	domination	NOUN
ejpam-4590	19	10	parameter	parameter	NOUN
ejpam-4590	19	11	and	and	CCONJ
ejpam-4590	19	12	called	call	VERB
ejpam-4590	19	13	it	it	PRON
ejpam-4590	19	14	the	the	DET
ejpam-4590	19	15	hop	hop	NOUN
ejpam-4590	19	16	domination	domination	NOUN
ejpam-4590	19	17	number	number	NOUN
ejpam-4590	19	18	of	of	ADP
ejpam-4590	19	19	a	a	DET
ejpam-4590	19	20	graph	graph	NOUN
ejpam-4590	19	21	.	.	PUNCT
ejpam-4590	20	1	as	as	SCONJ
ejpam-4590	20	2	defined	define	VERB
ejpam-4590	20	3	in	in	ADP
ejpam-4590	20	4	[	[	X
ejpam-4590	20	5	16	16	NUM
ejpam-4590	20	6	]	]	PUNCT
ejpam-4590	20	7	,	,	PUNCT
ejpam-4590	20	8	a	a	DET
ejpam-4590	20	9	subset	subset	NOUN
ejpam-4590	20	10	s	s	X
ejpam-4590	20	11	of	of	ADP
ejpam-4590	20	12	v	v	NOUN
ejpam-4590	20	13	(	(	PUNCT
ejpam-4590	20	14	g	g	NOUN
ejpam-4590	20	15	)	)	PUNCT
ejpam-4590	20	16	is	be	AUX
ejpam-4590	20	17	a	a	DET
ejpam-4590	20	18	hop	hop	NOUN
ejpam-4590	20	19	dominating	dominating	NOUN
ejpam-4590	20	20	set	set	NOUN
ejpam-4590	20	21	of	of	ADP
ejpam-4590	20	22	g	g	PROPN
ejpam-4590	20	23	if	if	SCONJ
ejpam-4590	20	24	for	for	ADP
ejpam-4590	20	25	every	every	PRON
ejpam-4590	20	26	v	v	NUM
ejpam-4590	20	27	∈	∈	NOUN
ejpam-4590	20	28	v	v	NOUN
ejpam-4590	20	29	(	(	PUNCT
ejpam-4590	20	30	g	g	NOUN
ejpam-4590	20	31	)	)	PUNCT
ejpam-4590	20	32	\	\	PROPN
ejpam-4590	21	1	s	s	X
ejpam-4590	21	2	,	,	PUNCT
ejpam-4590	21	3	there	there	PRON
ejpam-4590	21	4	exists	exist	VERB
ejpam-4590	21	5	∗corresponding	∗corresponde	VERB
ejpam-4590	21	6	author	author	NOUN
ejpam-4590	21	7	.	.	PUNCT
ejpam-4590	22	1	doi	doi	NOUN
ejpam-4590	22	2	:	:	PUNCT
ejpam-4590	22	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4590	https://doi.org/10.29020/nybg.ejpam.v15i4.4590	ADJ
ejpam-4590	22	4	email	email	NOUN
ejpam-4590	22	5	addresses	address	NOUN
ejpam-4590	22	6	:	:	PUNCT
ejpam-4590	22	7	chrisleyjade.saromines@g.msuiit.edu.ph	chrisleyjade.saromines@g.msuiit.edu.ph	PROPN
ejpam-4590	22	8	(	(	PUNCT
ejpam-4590	22	9	c.j	c.j	NOUN
ejpam-4590	22	10	.	.	PROPN
ejpam-4590	22	11	saromines	saromine	NOUN
ejpam-4590	22	12	)	)	PUNCT
ejpam-4590	22	13	,	,	PUNCT
ejpam-4590	22	14	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4590	22	15	(	(	PUNCT
ejpam-4590	22	16	s.	s.	PROPN
ejpam-4590	22	17	canoy	canoy	PROPN
ejpam-4590	22	18	,	,	PUNCT
ejpam-4590	22	19	jr	jr	PROPN
ejpam-4590	22	20	.	.	PUNCT
ejpam-4590	22	21	)	)	PUNCT
ejpam-4590	22	22	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4590	22	23	1966	1966	NUM
ejpam-4590	23	1	©	©	NOUN
ejpam-4590	23	2	2022	2022	NUM
ejpam-4590	23	3	ejpam	ejpam	VERB
ejpam-4590	23	4	all	all	DET
ejpam-4590	23	5	rights	right	NOUN
ejpam-4590	23	6	reserved	reserve	VERB
ejpam-4590	23	7	.	.	PUNCT
ejpam-4590	24	1	c.j	c.j	PROPN
ejpam-4590	24	2	.	.	PROPN
ejpam-4590	24	3	saromines	saromines	PROPN
ejpam-4590	24	4	,	,	PUNCT
ejpam-4590	24	5	s.	s.	PROPN
ejpam-4590	24	6	canoy	canoy	PROPN
ejpam-4590	24	7	,	,	PUNCT
ejpam-4590	24	8	jr	jr	PROPN
ejpam-4590	24	9	.	.	PROPN
ejpam-4590	24	10	/	/	SYM
ejpam-4590	24	11	eur	eur	PROPN
ejpam-4590	24	12	.	.	PUNCT
ejpam-4590	25	1	j.	j.	PROPN
ejpam-4590	25	2	pure	pure	PROPN
ejpam-4590	25	3	appl	appl	PROPN
ejpam-4590	25	4	.	.	PROPN
ejpam-4590	25	5	math	math	PROPN
ejpam-4590	25	6	,	,	PUNCT
ejpam-4590	25	7	15	15	NUM
ejpam-4590	25	8	(	(	PUNCT
ejpam-4590	25	9	4	4	NUM
ejpam-4590	25	10	)	)	PUNCT
ejpam-4590	25	11	(	(	PUNCT
ejpam-4590	25	12	2022	2022	NUM
ejpam-4590	25	13	)	)	PUNCT
ejpam-4590	25	14	,	,	PUNCT
ejpam-4590	25	15	1966	1966	NUM
ejpam-4590	25	16	-	-	SYM
ejpam-4590	25	17	1981	1981	NUM
ejpam-4590	25	18	1967	1967	NUM
ejpam-4590	25	19	u	u	NOUN
ejpam-4590	25	20	∈	∈	NOUN
ejpam-4590	25	21	s	s	VERB
ejpam-4590	25	22	such	such	ADJ
ejpam-4590	25	23	that	that	DET
ejpam-4590	25	24	dg(u	dg(u	ADJ
ejpam-4590	25	25	,	,	PUNCT
ejpam-4590	25	26	v	v	NOUN
ejpam-4590	25	27	)	)	PUNCT
ejpam-4590	25	28	=	=	SYM
ejpam-4590	25	29	2.the	2.the	PRON
ejpam-4590	25	30	concept	concept	NOUN
ejpam-4590	25	31	and	and	CCONJ
ejpam-4590	25	32	some	some	PRON
ejpam-4590	25	33	of	of	ADP
ejpam-4590	25	34	its	its	PRON
ejpam-4590	25	35	variants	variant	NOUN
ejpam-4590	25	36	are	be	AUX
ejpam-4590	25	37	also	also	ADV
ejpam-4590	25	38	studied	study	VERB
ejpam-4590	25	39	in	in	ADP
ejpam-4590	25	40	[	[	X
ejpam-4590	25	41	4	4	NUM
ejpam-4590	25	42	]	]	PUNCT
ejpam-4590	25	43	,	,	PUNCT
ejpam-4590	25	44	[	[	X
ejpam-4590	25	45	10	10	NUM
ejpam-4590	25	46	]	]	PUNCT
ejpam-4590	25	47	,	,	PUNCT
ejpam-4590	25	48	[	[	X
ejpam-4590	25	49	14	14	NUM
ejpam-4590	25	50	]	]	PUNCT
ejpam-4590	25	51	,	,	PUNCT
ejpam-4590	25	52	[	[	X
ejpam-4590	25	53	19	19	NUM
ejpam-4590	25	54	]	]	PUNCT
ejpam-4590	25	55	,	,	PUNCT
ejpam-4590	25	56	and	and	CCONJ
ejpam-4590	25	57	[	[	X
ejpam-4590	25	58	20	20	NUM
ejpam-4590	25	59	]	]	PUNCT
ejpam-4590	25	60	.	.	PUNCT
ejpam-4590	26	1	motivated	motivate	VERB
ejpam-4590	26	2	by	by	ADP
ejpam-4590	26	3	the	the	DET
ejpam-4590	26	4	hop	hop	PROPN
ejpam-4590	26	5	domination	domination	NOUN
ejpam-4590	26	6	concept	concept	NOUN
ejpam-4590	26	7	and	and	CCONJ
ejpam-4590	26	8	the	the	DET
ejpam-4590	26	9	introduction	introduction	NOUN
ejpam-4590	26	10	of	of	ADP
ejpam-4590	26	11	the	the	DET
ejpam-4590	26	12	outer	outer	ADV
ejpam-4590	26	13	-	-	PUNCT
ejpam-4590	26	14	connected	connect	VERB
ejpam-4590	26	15	domination	domination	NOUN
ejpam-4590	26	16	concept	concept	NOUN
ejpam-4590	26	17	by	by	ADP
ejpam-4590	26	18	cyman	cyman	NOUN
ejpam-4590	26	19	,	,	PUNCT
ejpam-4590	26	20	the	the	DET
ejpam-4590	26	21	authors	author	NOUN
ejpam-4590	26	22	will	will	AUX
ejpam-4590	26	23	try	try	VERB
ejpam-4590	26	24	to	to	PART
ejpam-4590	26	25	introduce	introduce	VERB
ejpam-4590	26	26	and	and	CCONJ
ejpam-4590	26	27	make	make	VERB
ejpam-4590	26	28	an	an	DET
ejpam-4590	26	29	initial	initial	ADJ
ejpam-4590	26	30	study	study	NOUN
ejpam-4590	26	31	of	of	ADP
ejpam-4590	26	32	the	the	DET
ejpam-4590	26	33	concept	concept	NOUN
ejpam-4590	26	34	of	of	ADP
ejpam-4590	26	35	outer	outer	ADV
ejpam-4590	26	36	-	-	PUNCT
ejpam-4590	26	37	connected	connect	VERB
ejpam-4590	26	38	hop	hop	NOUN
ejpam-4590	26	39	domination	domination	NOUN
ejpam-4590	26	40	.	.	PUNCT
ejpam-4590	27	1	since	since	SCONJ
ejpam-4590	27	2	domination	domination	NOUN
ejpam-4590	27	3	and	and	CCONJ
ejpam-4590	27	4	hop	hop	NOUN
ejpam-4590	27	5	domination	domination	NOUN
ejpam-4590	27	6	(	(	PUNCT
ejpam-4590	27	7	including	include	VERB
ejpam-4590	27	8	their	their	PRON
ejpam-4590	27	9	respective	respective	ADJ
ejpam-4590	27	10	variations	variation	NOUN
ejpam-4590	27	11	)	)	PUNCT
ejpam-4590	27	12	have	have	VERB
ejpam-4590	27	13	similar	similar	ADJ
ejpam-4590	27	14	applications	application	NOUN
ejpam-4590	27	15	(	(	PUNCT
ejpam-4590	27	16	e.g.	e.g.	ADV
ejpam-4590	27	17	in	in	ADP
ejpam-4590	27	18	modeling	model	VERB
ejpam-4590	27	19	facility	facility	NOUN
ejpam-4590	27	20	location	location	NOUN
ejpam-4590	27	21	and	and	CCONJ
ejpam-4590	27	22	protection	protection	NOUN
ejpam-4590	27	23	strategy	strategy	NOUN
ejpam-4590	27	24	problems	problem	NOUN
ejpam-4590	27	25	)	)	PUNCT
ejpam-4590	27	26	,	,	PUNCT
ejpam-4590	27	27	these	these	DET
ejpam-4590	27	28	two	two	NUM
ejpam-4590	27	29	variants	variant	NOUN
ejpam-4590	27	30	can	can	AUX
ejpam-4590	27	31	have	have	VERB
ejpam-4590	27	32	similar	similar	ADJ
ejpam-4590	27	33	applications	application	NOUN
ejpam-4590	27	34	as	as	ADV
ejpam-4590	27	35	well	well	ADV
ejpam-4590	27	36	.	.	PUNCT
ejpam-4590	28	1	2	2	X
ejpam-4590	28	2	.	.	X
ejpam-4590	28	3	terminology	terminology	NOUN
ejpam-4590	28	4	and	and	CCONJ
ejpam-4590	28	5	notation	notation	NOUN
ejpam-4590	28	6	for	for	ADP
ejpam-4590	28	7	any	any	DET
ejpam-4590	28	8	two	two	NUM
ejpam-4590	28	9	vertices	vertex	NOUN
ejpam-4590	28	10	u	u	NOUN
ejpam-4590	28	11	and	and	CCONJ
ejpam-4590	28	12	v	v	NOUN
ejpam-4590	28	13	in	in	ADP
ejpam-4590	28	14	an	an	DET
ejpam-4590	28	15	undirected	undirected	ADJ
ejpam-4590	28	16	connected	connected	ADJ
ejpam-4590	28	17	graph	graph	NOUN
ejpam-4590	28	18	g	g	PROPN
ejpam-4590	28	19	,	,	PUNCT
ejpam-4590	28	20	the	the	DET
ejpam-4590	28	21	distance	distance	NOUN
ejpam-4590	28	22	dg(u	dg(u	X
ejpam-4590	28	23	,	,	PUNCT
ejpam-4590	28	24	v	v	NOUN
ejpam-4590	28	25	)	)	PUNCT
ejpam-4590	28	26	is	be	AUX
ejpam-4590	28	27	the	the	DET
ejpam-4590	28	28	length	length	NOUN
ejpam-4590	28	29	of	of	ADP
ejpam-4590	28	30	a	a	DET
ejpam-4590	28	31	shortest	short	ADJ
ejpam-4590	28	32	path	path	NOUN
ejpam-4590	28	33	joining	join	VERB
ejpam-4590	28	34	u	u	NOUN
ejpam-4590	28	35	and	and	CCONJ
ejpam-4590	28	36	v.	v.	ADP
ejpam-4590	28	37	any	any	DET
ejpam-4590	28	38	u	u	NOUN
ejpam-4590	28	39	-	-	NOUN
ejpam-4590	28	40	v	v	ADJ
ejpam-4590	28	41	path	path	NOUN
ejpam-4590	28	42	of	of	ADP
ejpam-4590	28	43	length	length	NOUN
ejpam-4590	28	44	dg(u	dg(u	PROPN
ejpam-4590	28	45	,	,	PUNCT
ejpam-4590	28	46	v	v	NOUN
ejpam-4590	28	47	)	)	PUNCT
ejpam-4590	28	48	is	be	AUX
ejpam-4590	28	49	called	call	VERB
ejpam-4590	28	50	a	a	DET
ejpam-4590	28	51	u	u	NOUN
ejpam-4590	28	52	-	-	NOUN
ejpam-4590	28	53	v	v	ADJ
ejpam-4590	28	54	geodesic	geodesic	NOUN
ejpam-4590	28	55	.	.	PUNCT
ejpam-4590	29	1	the	the	DET
ejpam-4590	29	2	open	open	ADJ
ejpam-4590	29	3	neighborhood	neighborhood	NOUN
ejpam-4590	29	4	of	of	ADP
ejpam-4590	29	5	a	a	DET
ejpam-4590	29	6	point	point	NOUN
ejpam-4590	29	7	u	u	NOUN
ejpam-4590	29	8	is	be	AUX
ejpam-4590	29	9	the	the	DET
ejpam-4590	29	10	set	set	NOUN
ejpam-4590	29	11	ng(u	ng(u	NOUN
ejpam-4590	29	12	)	)	PUNCT
ejpam-4590	29	13	consisting	consist	VERB
ejpam-4590	29	14	of	of	ADP
ejpam-4590	29	15	all	all	DET
ejpam-4590	29	16	points	point	NOUN
ejpam-4590	29	17	v	v	NUM
ejpam-4590	29	18	which	which	PRON
ejpam-4590	29	19	are	be	AUX
ejpam-4590	29	20	adjacent	adjacent	ADJ
ejpam-4590	29	21	to	to	PART
ejpam-4590	29	22	u.	u.	VERB
ejpam-4590	29	23	the	the	DET
ejpam-4590	29	24	closed	closed	ADJ
ejpam-4590	29	25	interval	interval	NOUN
ejpam-4590	30	1	i	i	PRON
ejpam-4590	30	2	[	[	X
ejpam-4590	30	3	x	x	X
ejpam-4590	30	4	,	,	PUNCT
ejpam-4590	30	5	y	y	PROPN
ejpam-4590	30	6	]	]	PUNCT
ejpam-4590	30	7	consists	consist	VERB
ejpam-4590	30	8	of	of	ADP
ejpam-4590	30	9	x	x	X
ejpam-4590	30	10	,	,	PUNCT
ejpam-4590	30	11	y	y	PROPN
ejpam-4590	30	12	and	and	CCONJ
ejpam-4590	30	13	all	all	DET
ejpam-4590	30	14	vertices	vertex	NOUN
ejpam-4590	30	15	lying	lie	VERB
ejpam-4590	30	16	on	on	ADP
ejpam-4590	30	17	some	some	DET
ejpam-4590	30	18	x	x	NOUN
ejpam-4590	30	19	-	-	NOUN
ejpam-4590	30	20	y	y	ADJ
ejpam-4590	30	21	geodesic	geodesic	NOUN
ejpam-4590	30	22	of	of	ADP
ejpam-4590	30	23	g	g	PROPN
ejpam-4590	30	24	and	and	CCONJ
ejpam-4590	30	25	,	,	PUNCT
ejpam-4590	30	26	for	for	ADP
ejpam-4590	30	27	s	s	PROPN
ejpam-4590	30	28	⊆	⊆	NUM
ejpam-4590	30	29	v	v	NOUN
ejpam-4590	30	30	(	(	PUNCT
ejpam-4590	30	31	g	g	NOUN
ejpam-4590	30	32	)	)	PUNCT
ejpam-4590	30	33	,	,	PUNCT
ejpam-4590	30	34	i	i	PRON
ejpam-4590	31	1	[	[	X
ejpam-4590	31	2	s	s	X
ejpam-4590	31	3	]	]	X
ejpam-4590	31	4	=	=	SYM
ejpam-4590	31	5	⋃	⋃	NOUN
ejpam-4590	31	6	x	x	NOUN
ejpam-4590	31	7	,	,	PUNCT
ejpam-4590	31	8	y∈s	y∈	VERB
ejpam-4590	31	9	i	i	PRON
ejpam-4590	32	1	[	[	X
ejpam-4590	32	2	x	x	X
ejpam-4590	32	3	,	,	PUNCT
ejpam-4590	32	4	y	y	PROPN
ejpam-4590	32	5	]	]	PUNCT
ejpam-4590	32	6	.	.	PUNCT
ejpam-4590	33	1	the	the	DET
ejpam-4590	33	2	closed	closed	ADJ
ejpam-4590	33	3	neighborhood	neighborhood	NOUN
ejpam-4590	33	4	of	of	ADP
ejpam-4590	33	5	u	u	NOUN
ejpam-4590	33	6	is	be	AUX
ejpam-4590	33	7	ng[u	ng[u	PROPN
ejpam-4590	33	8	]	]	X
ejpam-4590	33	9	=	=	SYM
ejpam-4590	33	10	ng(u	ng(u	PROPN
ejpam-4590	33	11	)	)	PUNCT
ejpam-4590	33	12	∪	∪	NOUN
ejpam-4590	33	13	{	{	PUNCT
ejpam-4590	33	14	u	u	NOUN
ejpam-4590	33	15	}	}	PUNCT
ejpam-4590	33	16	.	.	PUNCT
ejpam-4590	34	1	for	for	ADP
ejpam-4590	34	2	any	any	DET
ejpam-4590	34	3	a	a	DET
ejpam-4590	34	4	⊆	⊆	NUM
ejpam-4590	34	5	v	v	NOUN
ejpam-4590	34	6	(	(	PUNCT
ejpam-4590	34	7	g	g	NOUN
ejpam-4590	34	8	)	)	PUNCT
ejpam-4590	34	9	,	,	PUNCT
ejpam-4590	34	10	ng(a	ng(a	X
ejpam-4590	34	11	)	)	PUNCT
ejpam-4590	34	12	=	=	PUNCT
ejpam-4590	34	13	⋃	⋃	NOUN
ejpam-4590	34	14	v∈a	v∈a	NOUN
ejpam-4590	34	15	ng(v	ng(v	PUNCT
ejpam-4590	34	16	)	)	PUNCT
ejpam-4590	34	17	is	be	AUX
ejpam-4590	34	18	called	call	VERB
ejpam-4590	34	19	the	the	DET
ejpam-4590	34	20	open	open	ADJ
ejpam-4590	34	21	neighborhood	neighborhood	NOUN
ejpam-4590	34	22	of	of	ADP
ejpam-4590	34	23	a	a	DET
ejpam-4590	34	24	andng[a	andng[a	NOUN
ejpam-4590	34	25	]	]	X
ejpam-4590	34	26	=	=	SYM
ejpam-4590	34	27	ng(a)∪a	ng(a)∪a	PROPN
ejpam-4590	34	28	is	be	AUX
ejpam-4590	34	29	called	call	VERB
ejpam-4590	34	30	the	the	DET
ejpam-4590	34	31	closed	closed	ADJ
ejpam-4590	34	32	neighborhood	neighborhood	NOUN
ejpam-4590	34	33	of	of	ADP
ejpam-4590	34	34	a.	a.	NOUN
ejpam-4590	34	35	the	the	DET
ejpam-4590	34	36	open	open	ADJ
ejpam-4590	34	37	hop	hop	NOUN
ejpam-4590	34	38	neighborhood	neighborhood	NOUN
ejpam-4590	34	39	of	of	ADP
ejpam-4590	34	40	a	a	DET
ejpam-4590	34	41	point	point	NOUN
ejpam-4590	34	42	u	u	NOUN
ejpam-4590	34	43	is	be	AUX
ejpam-4590	34	44	the	the	DET
ejpam-4590	34	45	set	set	ADJ
ejpam-4590	34	46	n2	n2	ADJ
ejpam-4590	34	47	g(u	g(u	PROPN
ejpam-4590	34	48	)	)	PUNCT
ejpam-4590	34	49	=	=	PRON
ejpam-4590	34	50	{	{	PUNCT
ejpam-4590	34	51	v	v	NUM
ejpam-4590	34	52	∈	∈	NOUN
ejpam-4590	34	53	v	v	NOUN
ejpam-4590	34	54	(	(	PUNCT
ejpam-4590	34	55	g	g	NOUN
ejpam-4590	34	56	)	)	PUNCT
ejpam-4590	34	57	:	:	PUNCT
ejpam-4590	34	58	dg(v	dg(v	X
ejpam-4590	34	59	,	,	PUNCT
ejpam-4590	34	60	u	u	NOUN
ejpam-4590	34	61	)	)	PUNCT
ejpam-4590	34	62	=	=	SYM
ejpam-4590	34	63	2	2	NUM
ejpam-4590	34	64	}	}	PUNCT
ejpam-4590	34	65	.	.	PUNCT
ejpam-4590	35	1	the	the	DET
ejpam-4590	35	2	closed	closed	ADJ
ejpam-4590	35	3	hop	hop	NOUN
ejpam-4590	35	4	neighborhood	neighborhood	NOUN
ejpam-4590	35	5	of	of	ADP
ejpam-4590	35	6	u	u	NOUN
ejpam-4590	35	7	is	be	AUX
ejpam-4590	35	8	n2	n2	ADJ
ejpam-4590	35	9	g[u	g[u	X
ejpam-4590	35	10	]	]	X
ejpam-4590	35	11	=	=	SYM
ejpam-4590	35	12	n2	n2	ADJ
ejpam-4590	35	13	g(u	g(u	PROPN
ejpam-4590	35	14	)	)	PUNCT
ejpam-4590	35	15	∪	∪	NOUN
ejpam-4590	35	16	{	{	PUNCT
ejpam-4590	35	17	u	u	NOUN
ejpam-4590	35	18	}	}	PUNCT
ejpam-4590	35	19	.	.	PUNCT
ejpam-4590	36	1	for	for	ADP
ejpam-4590	36	2	any	any	DET
ejpam-4590	36	3	a	a	DET
ejpam-4590	36	4	⊆	⊆	NUM
ejpam-4590	36	5	v	v	NOUN
ejpam-4590	36	6	(	(	PUNCT
ejpam-4590	36	7	g	g	NOUN
ejpam-4590	36	8	)	)	PUNCT
ejpam-4590	36	9	,	,	PUNCT
ejpam-4590	36	10	n2	n2	PROPN
ejpam-4590	36	11	g(a	g(a	PROPN
ejpam-4590	36	12	)	)	PUNCT
ejpam-4590	36	13	=	=	SYM
ejpam-4590	36	14	⋃	⋃	NOUN
ejpam-4590	36	15	v∈a	v∈a	NOUN
ejpam-4590	36	16	n2	n2	ADJ
ejpam-4590	36	17	g(v	g(v	PROPN
ejpam-4590	36	18	)	)	PUNCT
ejpam-4590	36	19	is	be	AUX
ejpam-4590	36	20	called	call	VERB
ejpam-4590	36	21	the	the	DET
ejpam-4590	36	22	open	open	ADJ
ejpam-4590	36	23	hop	hop	NOUN
ejpam-4590	36	24	neighborhood	neighborhood	NOUN
ejpam-4590	36	25	of	of	ADP
ejpam-4590	36	26	a	a	DET
ejpam-4590	36	27	and	and	CCONJ
ejpam-4590	36	28	n2	n2	ADJ
ejpam-4590	36	29	g[a	g[a	NOUN
ejpam-4590	36	30	]	]	X
ejpam-4590	36	31	=	=	SYM
ejpam-4590	36	32	n2	n2	PROPN
ejpam-4590	36	33	g(a)∪a	g(a)∪a	PROPN
ejpam-4590	36	34	is	be	AUX
ejpam-4590	36	35	called	call	VERB
ejpam-4590	36	36	the	the	DET
ejpam-4590	36	37	closed	closed	ADJ
ejpam-4590	36	38	hop	hop	NOUN
ejpam-4590	36	39	neighborhood	neighborhood	NOUN
ejpam-4590	36	40	of	of	ADP
ejpam-4590	36	41	a.	a.	NOUN
ejpam-4590	36	42	a	a	DET
ejpam-4590	36	43	set	set	NOUN
ejpam-4590	36	44	s	s	NOUN
ejpam-4590	36	45	⊆	⊆	NUM
ejpam-4590	36	46	v	v	NOUN
ejpam-4590	36	47	(	(	PUNCT
ejpam-4590	36	48	g	g	NOUN
ejpam-4590	36	49	)	)	PUNCT
ejpam-4590	36	50	is	be	AUX
ejpam-4590	36	51	a	a	DET
ejpam-4590	36	52	dominating	dominating	NOUN
ejpam-4590	36	53	set	set	NOUN
ejpam-4590	36	54	of	of	ADP
ejpam-4590	36	55	g	g	PROPN
ejpam-4590	36	56	if	if	SCONJ
ejpam-4590	36	57	for	for	ADP
ejpam-4590	36	58	every	every	PRON
ejpam-4590	36	59	v	v	NUM
ejpam-4590	36	60	∈	∈	NOUN
ejpam-4590	36	61	v	v	NOUN
ejpam-4590	36	62	(	(	PUNCT
ejpam-4590	36	63	g	g	NOUN
ejpam-4590	36	64	)	)	PUNCT
ejpam-4590	36	65	\	\	PROPN
ejpam-4590	37	1	s	s	X
ejpam-4590	37	2	,	,	PUNCT
ejpam-4590	37	3	there	there	PRON
ejpam-4590	37	4	exists	exist	VERB
ejpam-4590	37	5	u	u	PROPN
ejpam-4590	37	6	∈	∈	PROPN
ejpam-4590	37	7	s	s	VERB
ejpam-4590	37	8	such	such	ADJ
ejpam-4590	37	9	that	that	DET
ejpam-4590	37	10	uv	uv	PROPN
ejpam-4590	37	11	∈	∈	PROPN
ejpam-4590	37	12	e(g	e(g	PROPN
ejpam-4590	37	13	)	)	PUNCT
ejpam-4590	37	14	,	,	PUNCT
ejpam-4590	37	15	that	that	ADV
ejpam-4590	37	16	is	is	ADV
ejpam-4590	37	17	,	,	PUNCT
ejpam-4590	37	18	ng	ng	PROPN
ejpam-4590	38	1	[	[	X
ejpam-4590	38	2	s	s	X
ejpam-4590	38	3	]	]	X
ejpam-4590	38	4	=	=	SYM
ejpam-4590	38	5	v	v	NOUN
ejpam-4590	38	6	(	(	PUNCT
ejpam-4590	38	7	g	g	NOUN
ejpam-4590	38	8	)	)	PUNCT
ejpam-4590	38	9	.	.	PUNCT
ejpam-4590	39	1	the	the	DET
ejpam-4590	39	2	minimum	minimum	ADJ
ejpam-4590	39	3	cardinality	cardinality	NOUN
ejpam-4590	39	4	of	of	ADP
ejpam-4590	39	5	a	a	DET
ejpam-4590	39	6	dominating	dominating	NOUN
ejpam-4590	39	7	set	set	NOUN
ejpam-4590	39	8	of	of	ADP
ejpam-4590	39	9	a	a	DET
ejpam-4590	39	10	graph	graph	NOUN
ejpam-4590	39	11	g	g	NOUN
ejpam-4590	39	12	,	,	PUNCT
ejpam-4590	39	13	denoted	denote	VERB
ejpam-4590	39	14	by	by	ADP
ejpam-4590	39	15	γ(g	γ(g	PROPN
ejpam-4590	39	16	)	)	PUNCT
ejpam-4590	39	17	,	,	PUNCT
ejpam-4590	39	18	is	be	AUX
ejpam-4590	39	19	called	call	VERB
ejpam-4590	39	20	the	the	DET
ejpam-4590	39	21	domination	domination	NOUN
ejpam-4590	39	22	number	number	NOUN
ejpam-4590	39	23	of	of	ADP
ejpam-4590	39	24	g.	g.	PROPN
ejpam-4590	39	25	a	a	DET
ejpam-4590	39	26	set	set	NOUN
ejpam-4590	39	27	s	s	PROPN
ejpam-4590	39	28	⊆	⊆	NUM
ejpam-4590	39	29	v	v	NOUN
ejpam-4590	39	30	(	(	PUNCT
ejpam-4590	39	31	g	g	NOUN
ejpam-4590	39	32	)	)	PUNCT
ejpam-4590	39	33	is	be	AUX
ejpam-4590	39	34	an	an	DET
ejpam-4590	39	35	outer	outer	ADV
ejpam-4590	39	36	-	-	PUNCT
ejpam-4590	39	37	connected	connect	VERB
ejpam-4590	39	38	dominating	dominating	NOUN
ejpam-4590	39	39	set	set	NOUN
ejpam-4590	39	40	of	of	ADP
ejpam-4590	39	41	g	g	PROPN
ejpam-4590	39	42	if	if	SCONJ
ejpam-4590	39	43	s	s	NOUN
ejpam-4590	39	44	is	be	AUX
ejpam-4590	39	45	dominating	dominate	VERB
ejpam-4590	39	46	and	and	CCONJ
ejpam-4590	39	47	either	either	DET
ejpam-4590	39	48	s	s	PART
ejpam-4590	39	49	=	=	SYM
ejpam-4590	39	50	v	v	X
ejpam-4590	39	51	(	(	PUNCT
ejpam-4590	39	52	g	g	NOUN
ejpam-4590	39	53	)	)	PUNCT
ejpam-4590	39	54	or	or	CCONJ
ejpam-4590	39	55	the	the	DET
ejpam-4590	39	56	subgraph	subgraph	NOUN
ejpam-4590	39	57	⟨v	⟨v	NOUN
ejpam-4590	39	58	(	(	PUNCT
ejpam-4590	39	59	g	g	NOUN
ejpam-4590	39	60	)	)	PUNCT
ejpam-4590	39	61	\	\	PROPN
ejpam-4590	39	62	s⟩	s⟩	NOUN
ejpam-4590	39	63	induced	induce	VERB
ejpam-4590	39	64	by	by	ADP
ejpam-4590	39	65	v	v	NOUN
ejpam-4590	39	66	(	(	PUNCT
ejpam-4590	39	67	g	g	NOUN
ejpam-4590	39	68	)	)	PUNCT
ejpam-4590	39	69	\	\	PROPN
ejpam-4590	40	1	s	s	PART
ejpam-4590	40	2	is	be	AUX
ejpam-4590	40	3	connected	connect	VERB
ejpam-4590	40	4	.	.	PUNCT
ejpam-4590	41	1	the	the	DET
ejpam-4590	41	2	minimum	minimum	ADJ
ejpam-4590	41	3	cardinality	cardinality	NOUN
ejpam-4590	41	4	of	of	ADP
ejpam-4590	41	5	an	an	DET
ejpam-4590	41	6	outer	outer	ADV
ejpam-4590	41	7	-	-	PUNCT
ejpam-4590	41	8	connected	connect	VERB
ejpam-4590	41	9	dominating	dominating	NOUN
ejpam-4590	41	10	set	set	NOUN
ejpam-4590	41	11	of	of	ADP
ejpam-4590	41	12	a	a	DET
ejpam-4590	41	13	graph	graph	NOUN
ejpam-4590	41	14	g	g	NOUN
ejpam-4590	41	15	,	,	PUNCT
ejpam-4590	41	16	denoted	denote	VERB
ejpam-4590	41	17	by	by	ADP
ejpam-4590	41	18	γ̃c(g	γ̃c(g	NOUN
ejpam-4590	41	19	)	)	PUNCT
ejpam-4590	41	20	,	,	PUNCT
ejpam-4590	41	21	is	be	AUX
ejpam-4590	41	22	called	call	VERB
ejpam-4590	41	23	the	the	DET
ejpam-4590	41	24	outerconnected	outerconnecte	VERB
ejpam-4590	41	25	domination	domination	NOUN
ejpam-4590	41	26	number	number	NOUN
ejpam-4590	41	27	of	of	ADP
ejpam-4590	41	28	g.	g.	PROPN
ejpam-4590	41	29	a	a	DET
ejpam-4590	41	30	dominating	dominating	NOUN
ejpam-4590	41	31	set	set	NOUN
ejpam-4590	41	32	(	(	PUNCT
ejpam-4590	41	33	resp	resp	NOUN
ejpam-4590	41	34	.	.	PUNCT
ejpam-4590	42	1	outer	outer	ADJ
ejpam-4590	42	2	-	-	PUNCT
ejpam-4590	42	3	connected	connect	VERB
ejpam-4590	42	4	dominating	dominating	NOUN
ejpam-4590	42	5	set	set	NOUN
ejpam-4590	42	6	)	)	PUNCT
ejpam-4590	43	1	s	s	PROPN
ejpam-4590	43	2	of	of	ADP
ejpam-4590	43	3	g	g	NOUN
ejpam-4590	43	4	with	with	ADP
ejpam-4590	43	5	|s|	|s|	PROPN
ejpam-4590	43	6	=	=	SYM
ejpam-4590	43	7	γ(g	γ(g	PROPN
ejpam-4590	43	8	)	)	PUNCT
ejpam-4590	43	9	(	(	PUNCT
ejpam-4590	43	10	resp	resp	NOUN
ejpam-4590	43	11	.	.	PUNCT
ejpam-4590	44	1	|s|	|s|	PROPN
ejpam-4590	44	2	=	=	SYM
ejpam-4590	44	3	γ̃c(g	γ̃c(g	NUM
ejpam-4590	44	4	)	)	PUNCT
ejpam-4590	44	5	)	)	PUNCT
ejpam-4590	44	6	is	be	AUX
ejpam-4590	44	7	referred	refer	VERB
ejpam-4590	44	8	to	to	ADP
ejpam-4590	44	9	as	as	ADP
ejpam-4590	44	10	a	a	DET
ejpam-4590	44	11	γ	γ	X
ejpam-4590	44	12	-	-	PUNCT
ejpam-4590	44	13	set	set	ADJ
ejpam-4590	44	14	(	(	PUNCT
ejpam-4590	44	15	resp	resp	NOUN
ejpam-4590	44	16	.	.	PUNCT
ejpam-4590	45	1	γ̃c	γ̃c	NUM
ejpam-4590	45	2	-	-	PUNCT
ejpam-4590	45	3	set	set	NOUN
ejpam-4590	45	4	)	)	PUNCT
ejpam-4590	45	5	of	of	ADP
ejpam-4590	45	6	g.	g.	PROPN
ejpam-4590	45	7	a	a	DET
ejpam-4590	45	8	set	set	NOUN
ejpam-4590	45	9	s	s	PROPN
ejpam-4590	45	10	⊆	⊆	NUM
ejpam-4590	45	11	v	v	NOUN
ejpam-4590	45	12	(	(	PUNCT
ejpam-4590	45	13	g	g	NOUN
ejpam-4590	45	14	)	)	PUNCT
ejpam-4590	45	15	is	be	AUX
ejpam-4590	45	16	a	a	DET
ejpam-4590	45	17	hop	hop	NOUN
ejpam-4590	45	18	dominating	dominating	NOUN
ejpam-4590	45	19	set	set	NOUN
ejpam-4590	45	20	(	(	PUNCT
ejpam-4590	45	21	resp	resp	NOUN
ejpam-4590	45	22	.	.	PUNCT
ejpam-4590	46	1	total	total	ADJ
ejpam-4590	46	2	hop	hop	NOUN
ejpam-4590	46	3	dominating	dominating	NOUN
ejpam-4590	46	4	set	set	NOUN
ejpam-4590	46	5	)	)	PUNCT
ejpam-4590	46	6	if	if	SCONJ
ejpam-4590	46	7	n2	n2	ADJ
ejpam-4590	46	8	g[s	g[s	PROPN
ejpam-4590	46	9	]	]	X
ejpam-4590	46	10	=	=	SYM
ejpam-4590	46	11	v	v	X
ejpam-4590	46	12	(	(	PUNCT
ejpam-4590	46	13	g	g	NOUN
ejpam-4590	46	14	)	)	PUNCT
ejpam-4590	46	15	(	(	PUNCT
ejpam-4590	46	16	resp	resp	NOUN
ejpam-4590	46	17	.	.	PUNCT
ejpam-4590	47	1	n2	n2	ADJ
ejpam-4590	47	2	g(s	g(s	PROPN
ejpam-4590	47	3	)	)	PUNCT
ejpam-4590	47	4	=	=	SYM
ejpam-4590	47	5	v	v	X
ejpam-4590	47	6	(	(	PUNCT
ejpam-4590	47	7	g	g	NOUN
ejpam-4590	47	8	)	)	PUNCT
ejpam-4590	47	9	)	)	PUNCT
ejpam-4590	47	10	.	.	PUNCT
ejpam-4590	48	1	the	the	DET
ejpam-4590	48	2	minimum	minimum	ADJ
ejpam-4590	48	3	cardinality	cardinality	NOUN
ejpam-4590	48	4	of	of	ADP
ejpam-4590	48	5	a	a	DET
ejpam-4590	48	6	hop	hop	NOUN
ejpam-4590	48	7	dominating	dominating	NOUN
ejpam-4590	48	8	set	set	NOUN
ejpam-4590	48	9	(	(	PUNCT
ejpam-4590	48	10	resp	resp	NOUN
ejpam-4590	48	11	.	.	PUNCT
ejpam-4590	49	1	total	total	ADJ
ejpam-4590	49	2	hop	hop	NOUN
ejpam-4590	49	3	dominating	dominating	NOUN
ejpam-4590	49	4	set	set	NOUN
ejpam-4590	49	5	)	)	PUNCT
ejpam-4590	49	6	of	of	ADP
ejpam-4590	49	7	a	a	DET
ejpam-4590	49	8	graph	graph	NOUN
ejpam-4590	49	9	g	g	NOUN
ejpam-4590	49	10	,	,	PUNCT
ejpam-4590	49	11	denoted	denote	VERB
ejpam-4590	49	12	by	by	ADP
ejpam-4590	49	13	γh(g	γh(g	NOUN
ejpam-4590	49	14	)	)	PUNCT
ejpam-4590	49	15	(	(	PUNCT
ejpam-4590	49	16	resp	resp	NOUN
ejpam-4590	49	17	.	.	PUNCT
ejpam-4590	50	1	γth(g	γth(g	NOUN
ejpam-4590	50	2	)	)	PUNCT
ejpam-4590	50	3	)	)	PUNCT
ejpam-4590	50	4	is	be	AUX
ejpam-4590	50	5	called	call	VERB
ejpam-4590	50	6	the	the	DET
ejpam-4590	50	7	hop	hop	NOUN
ejpam-4590	50	8	domination	domination	NOUN
ejpam-4590	50	9	number	number	NOUN
ejpam-4590	50	10	(	(	PUNCT
ejpam-4590	50	11	resp	resp	NOUN
ejpam-4590	50	12	.	.	PUNCT
ejpam-4590	51	1	total	total	ADJ
ejpam-4590	51	2	hop	hop	PROPN
ejpam-4590	51	3	domination	domination	NOUN
ejpam-4590	51	4	number	number	NOUN
ejpam-4590	51	5	)	)	PUNCT
ejpam-4590	51	6	of	of	ADP
ejpam-4590	51	7	g.	g.	PROPN
ejpam-4590	51	8	a	a	DET
ejpam-4590	51	9	hop	hop	NOUN
ejpam-4590	51	10	dominating	dominating	NOUN
ejpam-4590	51	11	set	set	NOUN
ejpam-4590	51	12	(	(	PUNCT
ejpam-4590	51	13	resp	resp	NOUN
ejpam-4590	51	14	.	.	PUNCT
ejpam-4590	52	1	total	total	ADJ
ejpam-4590	52	2	hop	hop	NOUN
ejpam-4590	52	3	dominating	dominating	NOUN
ejpam-4590	52	4	set	set	NOUN
ejpam-4590	52	5	)	)	PUNCT
ejpam-4590	52	6	of	of	ADP
ejpam-4590	52	7	g	g	PROPN
ejpam-4590	52	8	with	with	ADP
ejpam-4590	52	9	cardinality	cardinality	NOUN
ejpam-4590	52	10	equal	equal	ADJ
ejpam-4590	52	11	to	to	ADP
ejpam-4590	52	12	γh(g	γh(g	NOUN
ejpam-4590	52	13	)	)	PUNCT
ejpam-4590	52	14	(	(	PUNCT
ejpam-4590	52	15	resp	resp	NOUN
ejpam-4590	52	16	.	.	PUNCT
ejpam-4590	52	17	γth(g	γth(g	NOUN
ejpam-4590	52	18	)	)	PUNCT
ejpam-4590	52	19	)	)	PUNCT
ejpam-4590	52	20	is	be	AUX
ejpam-4590	52	21	referred	refer	VERB
ejpam-4590	52	22	to	to	ADP
ejpam-4590	52	23	as	as	ADP
ejpam-4590	52	24	a	a	DET
ejpam-4590	52	25	γh	γh	ADV
ejpam-4590	52	26	-	-	PUNCT
ejpam-4590	52	27	set	set	VERB
ejpam-4590	52	28	(	(	PUNCT
ejpam-4590	52	29	resp	resp	NOUN
ejpam-4590	52	30	.	.	PUNCT
ejpam-4590	53	1	γth	γth	ADJ
ejpam-4590	53	2	-	-	PUNCT
ejpam-4590	53	3	set	set	NOUN
ejpam-4590	53	4	)	)	PUNCT
ejpam-4590	53	5	of	of	ADP
ejpam-4590	53	6	g.	g.	PROPN
ejpam-4590	53	7	a	a	DET
ejpam-4590	53	8	hop	hop	NOUN
ejpam-4590	53	9	dominating	dominating	NOUN
ejpam-4590	53	10	set	set	NOUN
ejpam-4590	53	11	s	s	PROPN
ejpam-4590	53	12	⊆	⊆	NUM
ejpam-4590	53	13	v	v	NOUN
ejpam-4590	53	14	(	(	PUNCT
ejpam-4590	53	15	g	g	NOUN
ejpam-4590	53	16	)	)	PUNCT
ejpam-4590	53	17	is	be	AUX
ejpam-4590	53	18	called	call	VERB
ejpam-4590	53	19	an	an	DET
ejpam-4590	53	20	outer	outer	ADV
ejpam-4590	53	21	-	-	PUNCT
ejpam-4590	53	22	connected	connect	VERB
ejpam-4590	53	23	hop	hop	NOUN
ejpam-4590	53	24	dominating	dominating	NOUN
ejpam-4590	53	25	set	set	NOUN
ejpam-4590	53	26	if	if	SCONJ
ejpam-4590	53	27	s	s	VERB
ejpam-4590	53	28	=	=	SYM
ejpam-4590	53	29	v	v	X
ejpam-4590	53	30	(	(	PUNCT
ejpam-4590	53	31	g	g	NOUN
ejpam-4590	53	32	)	)	PUNCT
ejpam-4590	53	33	or	or	CCONJ
ejpam-4590	53	34	⟨v	⟨v	NUM
ejpam-4590	53	35	(	(	PUNCT
ejpam-4590	53	36	g	g	NOUN
ejpam-4590	53	37	)	)	PUNCT
ejpam-4590	53	38	\	\	PROPN
ejpam-4590	53	39	s⟩	s⟩	PROPN
ejpam-4590	53	40	is	be	AUX
ejpam-4590	53	41	connected	connect	VERB
ejpam-4590	53	42	.	.	PUNCT
ejpam-4590	54	1	the	the	DET
ejpam-4590	54	2	minimum	minimum	ADJ
ejpam-4590	54	3	cardinality	cardinality	NOUN
ejpam-4590	54	4	of	of	ADP
ejpam-4590	54	5	an	an	DET
ejpam-4590	54	6	outer	outer	ADV
ejpam-4590	54	7	-	-	PUNCT
ejpam-4590	54	8	connected	connect	VERB
ejpam-4590	54	9	hop	hop	NOUN
ejpam-4590	54	10	dominating	dominating	NOUN
ejpam-4590	54	11	set	set	NOUN
ejpam-4590	54	12	of	of	ADP
ejpam-4590	54	13	a	a	DET
ejpam-4590	54	14	graph	graph	NOUN
ejpam-4590	54	15	g	g	NOUN
ejpam-4590	54	16	,	,	PUNCT
ejpam-4590	54	17	denoted	denote	VERB
ejpam-4590	54	18	by	by	ADP
ejpam-4590	54	19	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	54	20	)	)	PUNCT
ejpam-4590	54	21	,	,	PUNCT
ejpam-4590	54	22	is	be	AUX
ejpam-4590	54	23	called	call	VERB
ejpam-4590	54	24	the	the	DET
ejpam-4590	54	25	outer	outer	ADV
ejpam-4590	54	26	-	-	PUNCT
ejpam-4590	54	27	connected	connect	VERB
ejpam-4590	54	28	hop	hop	NOUN
ejpam-4590	54	29	domination	domination	NOUN
ejpam-4590	54	30	number	number	NOUN
ejpam-4590	54	31	of	of	ADP
ejpam-4590	54	32	g.	g.	PROPN
ejpam-4590	54	33	an	an	DET
ejpam-4590	54	34	outer	outer	ADV
ejpam-4590	54	35	-	-	PUNCT
ejpam-4590	54	36	connected	connect	VERB
ejpam-4590	54	37	hop	hop	NOUN
ejpam-4590	54	38	dominating	dominating	NOUN
ejpam-4590	54	39	set	set	NOUN
ejpam-4590	54	40	of	of	ADP
ejpam-4590	54	41	size	size	NOUN
ejpam-4590	54	42	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	54	43	)	)	PUNCT
ejpam-4590	54	44	of	of	ADP
ejpam-4590	54	45	g	g	PROPN
ejpam-4590	54	46	is	be	AUX
ejpam-4590	54	47	c.j	c.j	PROPN
ejpam-4590	54	48	.	.	PROPN
ejpam-4590	54	49	saromines	saromine	NOUN
ejpam-4590	54	50	,	,	PUNCT
ejpam-4590	54	51	s.	s.	PROPN
ejpam-4590	54	52	canoy	canoy	PROPN
ejpam-4590	54	53	,	,	PUNCT
ejpam-4590	54	54	jr	jr	PROPN
ejpam-4590	54	55	.	.	PROPN
ejpam-4590	54	56	/	/	SYM
ejpam-4590	54	57	eur	eur	PROPN
ejpam-4590	54	58	.	.	PUNCT
ejpam-4590	55	1	j.	j.	PROPN
ejpam-4590	55	2	pure	pure	PROPN
ejpam-4590	55	3	appl	appl	PROPN
ejpam-4590	55	4	.	.	PROPN
ejpam-4590	55	5	math	math	PROPN
ejpam-4590	55	6	,	,	PUNCT
ejpam-4590	55	7	15	15	NUM
ejpam-4590	55	8	(	(	PUNCT
ejpam-4590	55	9	4	4	NUM
ejpam-4590	55	10	)	)	PUNCT
ejpam-4590	55	11	(	(	PUNCT
ejpam-4590	55	12	2022	2022	NUM
ejpam-4590	55	13	)	)	PUNCT
ejpam-4590	55	14	,	,	PUNCT
ejpam-4590	55	15	1966	1966	NUM
ejpam-4590	55	16	-	-	SYM
ejpam-4590	55	17	1981	1981	NUM
ejpam-4590	55	18	1968	1968	NUM
ejpam-4590	55	19	called	call	VERB
ejpam-4590	55	20	a	a	DET
ejpam-4590	55	21	γ̃ch	γ̃ch	PROPN
ejpam-4590	55	22	-	-	PUNCT
ejpam-4590	55	23	set	set	NOUN
ejpam-4590	55	24	.	.	PUNCT
ejpam-4590	56	1	a	a	DET
ejpam-4590	56	2	set	set	NOUN
ejpam-4590	56	3	d	d	NOUN
ejpam-4590	56	4	⊆	⊆	NUM
ejpam-4590	56	5	v	v	ADP
ejpam-4590	56	6	(	(	PUNCT
ejpam-4590	56	7	g	g	NOUN
ejpam-4590	56	8	)	)	PUNCT
ejpam-4590	56	9	is	be	AUX
ejpam-4590	56	10	pointwise	pointwise	VERB
ejpam-4590	56	11	non	non	ADJ
ejpam-4590	56	12	-	-	ADJ
ejpam-4590	56	13	dominating	dominating	ADJ
ejpam-4590	56	14	if	if	SCONJ
ejpam-4590	56	15	for	for	ADP
ejpam-4590	56	16	each	each	PRON
ejpam-4590	56	17	v	v	NUM
ejpam-4590	56	18	∈	∈	PROPN
ejpam-4590	56	19	v	v	NOUN
ejpam-4590	56	20	(	(	PUNCT
ejpam-4590	56	21	g	g	NOUN
ejpam-4590	56	22	)	)	PUNCT
ejpam-4590	56	23	\	\	PUNCT
ejpam-4590	57	1	d	d	X
ejpam-4590	57	2	,	,	PUNCT
ejpam-4590	57	3	there	there	PRON
ejpam-4590	57	4	exists	exist	VERB
ejpam-4590	57	5	u	u	NOUN
ejpam-4590	57	6	∈	∈	PROPN
ejpam-4590	57	7	d	d	ADP
ejpam-4590	57	8	such	such	ADJ
ejpam-4590	57	9	that	that	DET
ejpam-4590	57	10	v	v	NOUN
ejpam-4590	57	11	/∈	/∈	PUNCT
ejpam-4590	57	12	ng(u	ng(u	NOUN
ejpam-4590	57	13	)	)	PUNCT
ejpam-4590	57	14	.	.	PUNCT
ejpam-4590	58	1	the	the	DET
ejpam-4590	58	2	minimum	minimum	ADJ
ejpam-4590	58	3	cardinality	cardinality	NOUN
ejpam-4590	58	4	of	of	ADP
ejpam-4590	58	5	a	a	DET
ejpam-4590	58	6	pointwise	pointwise	ADJ
ejpam-4590	58	7	non	non	ADJ
ejpam-4590	58	8	-	-	ADJ
ejpam-4590	58	9	dominating	dominating	ADJ
ejpam-4590	58	10	set	set	NOUN
ejpam-4590	58	11	of	of	ADP
ejpam-4590	58	12	a	a	DET
ejpam-4590	58	13	graph	graph	NOUN
ejpam-4590	58	14	g	g	NOUN
ejpam-4590	58	15	,	,	PUNCT
ejpam-4590	58	16	denoted	denote	VERB
ejpam-4590	58	17	by	by	ADP
ejpam-4590	58	18	pnd(g	pnd(g	PROPN
ejpam-4590	58	19	)	)	PUNCT
ejpam-4590	58	20	,	,	PUNCT
ejpam-4590	58	21	is	be	AUX
ejpam-4590	58	22	called	call	VERB
ejpam-4590	58	23	the	the	DET
ejpam-4590	58	24	pointwise	pointwise	ADJ
ejpam-4590	58	25	non	non	ADJ
ejpam-4590	58	26	-	-	ADJ
ejpam-4590	58	27	domination	domination	ADJ
ejpam-4590	58	28	number	number	NOUN
ejpam-4590	58	29	of	of	ADP
ejpam-4590	58	30	g.	g.	PROPN
ejpam-4590	58	31	a	a	DET
ejpam-4590	58	32	pointwise	pointwise	ADJ
ejpam-4590	58	33	non	non	ADJ
ejpam-4590	58	34	-	-	ADJ
ejpam-4590	58	35	dominating	dominating	ADJ
ejpam-4590	58	36	set	set	NOUN
ejpam-4590	58	37	d	d	PROPN
ejpam-4590	58	38	of	of	ADP
ejpam-4590	58	39	v	v	NOUN
ejpam-4590	58	40	(	(	PUNCT
ejpam-4590	58	41	g	g	NOUN
ejpam-4590	58	42	)	)	PUNCT
ejpam-4590	58	43	is	be	AUX
ejpam-4590	58	44	an	an	DET
ejpam-4590	58	45	outer	outer	ADV
ejpam-4590	58	46	-	-	PUNCT
ejpam-4590	58	47	connected	connect	VERB
ejpam-4590	58	48	pointwise	pointwise	PROPN
ejpam-4590	58	49	non	non	ADJ
ejpam-4590	58	50	-	-	ADJ
ejpam-4590	58	51	dominating	dominating	ADJ
ejpam-4590	58	52	set	set	NOUN
ejpam-4590	58	53	if	if	SCONJ
ejpam-4590	58	54	d	d	PROPN
ejpam-4590	58	55	=	=	SYM
ejpam-4590	58	56	v	v	X
ejpam-4590	58	57	(	(	PUNCT
ejpam-4590	58	58	g	g	NOUN
ejpam-4590	58	59	)	)	PUNCT
ejpam-4590	58	60	or	or	CCONJ
ejpam-4590	58	61	⟨v	⟨v	NUM
ejpam-4590	58	62	(	(	PUNCT
ejpam-4590	58	63	g	g	NOUN
ejpam-4590	58	64	)	)	PUNCT
ejpam-4590	58	65	\d⟩	\d⟩	PROPN
ejpam-4590	58	66	is	be	AUX
ejpam-4590	58	67	connected	connect	VERB
ejpam-4590	58	68	.	.	PUNCT
ejpam-4590	59	1	the	the	DET
ejpam-4590	59	2	minimum	minimum	ADJ
ejpam-4590	59	3	cardinality	cardinality	NOUN
ejpam-4590	59	4	of	of	ADP
ejpam-4590	59	5	an	an	DET
ejpam-4590	59	6	outerconnected	outerconnecte	VERB
ejpam-4590	59	7	pointwise	pointwise	PROPN
ejpam-4590	59	8	non	non	ADJ
ejpam-4590	59	9	-	-	ADJ
ejpam-4590	59	10	dominating	dominating	ADJ
ejpam-4590	59	11	set	set	NOUN
ejpam-4590	59	12	of	of	ADP
ejpam-4590	59	13	a	a	DET
ejpam-4590	59	14	graph	graph	NOUN
ejpam-4590	59	15	g	g	NOUN
ejpam-4590	59	16	,	,	PUNCT
ejpam-4590	59	17	denoted	denote	VERB
ejpam-4590	59	18	by	by	ADP
ejpam-4590	59	19	p̃nd(g	p̃nd(g	NOUN
ejpam-4590	59	20	)	)	PUNCT
ejpam-4590	59	21	,	,	PUNCT
ejpam-4590	59	22	is	be	AUX
ejpam-4590	59	23	called	call	VERB
ejpam-4590	59	24	the	the	DET
ejpam-4590	59	25	outer	outer	ADV
ejpam-4590	59	26	-	-	PUNCT
ejpam-4590	59	27	connected	connect	VERB
ejpam-4590	59	28	pointwise	pointwise	PROPN
ejpam-4590	59	29	non	non	ADJ
ejpam-4590	59	30	-	-	ADJ
ejpam-4590	59	31	domination	domination	ADJ
ejpam-4590	59	32	number	number	NOUN
ejpam-4590	59	33	of	of	ADP
ejpam-4590	59	34	g.	g.	PROPN
ejpam-4590	59	35	let	let	VERB
ejpam-4590	59	36	g	g	NOUN
ejpam-4590	59	37	and	and	CCONJ
ejpam-4590	59	38	h	h	NOUN
ejpam-4590	59	39	be	be	VERB
ejpam-4590	59	40	any	any	DET
ejpam-4590	59	41	two	two	NUM
ejpam-4590	59	42	graphs	graph	NOUN
ejpam-4590	59	43	.	.	PUNCT
ejpam-4590	60	1	the	the	DET
ejpam-4590	60	2	join	join	NOUN
ejpam-4590	60	3	g	g	PROPN
ejpam-4590	60	4	+	+	CCONJ
ejpam-4590	60	5	h	h	NOUN
ejpam-4590	60	6	is	be	AUX
ejpam-4590	60	7	the	the	DET
ejpam-4590	60	8	graph	graph	NOUN
ejpam-4590	60	9	with	with	ADP
ejpam-4590	60	10	vertex	vertex	NOUN
ejpam-4590	60	11	set	set	VERB
ejpam-4590	60	12	v	v	NOUN
ejpam-4590	60	13	(	(	PUNCT
ejpam-4590	60	14	g+h	g+h	NOUN
ejpam-4590	60	15	)	)	PUNCT
ejpam-4590	60	16	=	=	SYM
ejpam-4590	60	17	v	v	NOUN
ejpam-4590	60	18	(	(	PUNCT
ejpam-4590	60	19	g)∪	g)∪	VERB
ejpam-4590	60	20	v	v	NUM
ejpam-4590	60	21	(	(	PUNCT
ejpam-4590	60	22	h	h	NOUN
ejpam-4590	60	23	)	)	PUNCT
ejpam-4590	60	24	and	and	CCONJ
ejpam-4590	60	25	edge	edge	NOUN
ejpam-4590	60	26	set	set	VERB
ejpam-4590	60	27	e(g+h	e(g+h	NUM
ejpam-4590	60	28	)	)	PUNCT
ejpam-4590	61	1	=	=	SYM
ejpam-4590	61	2	e(g)∪e(h)∪	e(g)∪e(h)∪	NOUN
ejpam-4590	61	3	{	{	PUNCT
ejpam-4590	61	4	uv	uv	NOUN
ejpam-4590	61	5	:	:	PUNCT
ejpam-4590	61	6	u	u	PROPN
ejpam-4590	61	7	∈	∈	PROPN
ejpam-4590	61	8	v	v	ADP
ejpam-4590	61	9	(	(	PUNCT
ejpam-4590	61	10	g	g	NOUN
ejpam-4590	61	11	)	)	PUNCT
ejpam-4590	61	12	,	,	PUNCT
ejpam-4590	61	13	v	v	X
ejpam-4590	61	14	∈	∈	PROPN
ejpam-4590	61	15	v	v	NOUN
ejpam-4590	61	16	(	(	PUNCT
ejpam-4590	61	17	h	h	NOUN
ejpam-4590	61	18	)	)	PUNCT
ejpam-4590	61	19	}	}	PUNCT
ejpam-4590	61	20	.	.	PUNCT
ejpam-4590	62	1	the	the	DET
ejpam-4590	62	2	corona	corona	NOUN
ejpam-4590	62	3	g	g	PROPN
ejpam-4590	62	4	◦	◦	NOUN
ejpam-4590	62	5	h	h	NOUN
ejpam-4590	62	6	is	be	AUX
ejpam-4590	62	7	the	the	DET
ejpam-4590	62	8	graph	graph	NOUN
ejpam-4590	62	9	obtained	obtain	VERB
ejpam-4590	62	10	by	by	ADP
ejpam-4590	62	11	taking	take	VERB
ejpam-4590	62	12	one	one	NUM
ejpam-4590	62	13	copy	copy	NOUN
ejpam-4590	62	14	of	of	ADP
ejpam-4590	62	15	g	g	PROPN
ejpam-4590	62	16	and	and	CCONJ
ejpam-4590	62	17	|v	|v	PROPN
ejpam-4590	62	18	(	(	PUNCT
ejpam-4590	62	19	g)|	g)|	NOUN
ejpam-4590	62	20	copies	copy	NOUN
ejpam-4590	62	21	of	of	ADP
ejpam-4590	62	22	h	h	NOUN
ejpam-4590	62	23	,	,	PUNCT
ejpam-4590	62	24	and	and	CCONJ
ejpam-4590	62	25	then	then	ADV
ejpam-4590	62	26	joining	join	VERB
ejpam-4590	62	27	the	the	DET
ejpam-4590	62	28	ith	ith	PROPN
ejpam-4590	62	29	vertex	vertex	NOUN
ejpam-4590	62	30	of	of	ADP
ejpam-4590	62	31	g	g	NOUN
ejpam-4590	62	32	to	to	ADP
ejpam-4590	62	33	every	every	DET
ejpam-4590	62	34	vertex	vertex	NOUN
ejpam-4590	62	35	of	of	ADP
ejpam-4590	62	36	the	the	DET
ejpam-4590	62	37	ith	ith	PROPN
ejpam-4590	62	38	copy	copy	NOUN
ejpam-4590	62	39	of	of	ADP
ejpam-4590	62	40	h.	h.	PROPN
ejpam-4590	62	41	we	we	PRON
ejpam-4590	62	42	denote	denote	VERB
ejpam-4590	62	43	by	by	ADP
ejpam-4590	62	44	hv	hv	PROPN
ejpam-4590	63	1	the	the	DET
ejpam-4590	63	2	copy	copy	NOUN
ejpam-4590	63	3	of	of	ADP
ejpam-4590	63	4	h	h	NOUN
ejpam-4590	63	5	in	in	ADP
ejpam-4590	63	6	g	g	PROPN
ejpam-4590	63	7	◦	◦	NOUN
ejpam-4590	63	8	h	h	NOUN
ejpam-4590	63	9	corresponding	correspond	VERB
ejpam-4590	63	10	to	to	ADP
ejpam-4590	63	11	the	the	DET
ejpam-4590	63	12	vertex	vertex	NOUN
ejpam-4590	63	13	v	v	ADP
ejpam-4590	63	14	∈	∈	PROPN
ejpam-4590	63	15	g	g	NOUN
ejpam-4590	63	16	and	and	CCONJ
ejpam-4590	63	17	write	write	VERB
ejpam-4590	63	18	v	v	ADP
ejpam-4590	63	19	+	+	CCONJ
ejpam-4590	63	20	hv	hv	NOUN
ejpam-4590	63	21	for	for	ADP
ejpam-4590	63	22	⟨{v}⟩	⟨{v}⟩	NOUN
ejpam-4590	63	23	+	+	X
ejpam-4590	63	24	hv	hv	X
ejpam-4590	63	25	.	.	PUNCT
ejpam-4590	64	1	the	the	DET
ejpam-4590	64	2	lexicographic	lexicographic	ADJ
ejpam-4590	64	3	product	product	NOUN
ejpam-4590	64	4	g[h	g[h	PROPN
ejpam-4590	64	5	]	]	PUNCT
ejpam-4590	64	6	is	be	AUX
ejpam-4590	64	7	the	the	DET
ejpam-4590	64	8	graph	graph	NOUN
ejpam-4590	64	9	with	with	ADP
ejpam-4590	64	10	vertex	vertex	NOUN
ejpam-4590	64	11	set	set	VERB
ejpam-4590	64	12	v	v	NOUN
ejpam-4590	64	13	(	(	PUNCT
ejpam-4590	64	14	g[h	g[h	PROPN
ejpam-4590	64	15	]	]	PUNCT
ejpam-4590	64	16	)	)	PUNCT
ejpam-4590	64	17	=	=	SYM
ejpam-4590	64	18	v	v	X
ejpam-4590	64	19	(	(	PUNCT
ejpam-4590	64	20	g	g	NOUN
ejpam-4590	64	21	)	)	PUNCT
ejpam-4590	64	22	×	×	NOUN
ejpam-4590	64	23	v	v	NOUN
ejpam-4590	64	24	(	(	PUNCT
ejpam-4590	64	25	h	h	NOUN
ejpam-4590	64	26	)	)	PUNCT
ejpam-4590	64	27	and	and	CCONJ
ejpam-4590	64	28	(	(	PUNCT
ejpam-4590	64	29	v	v	NOUN
ejpam-4590	64	30	,	,	PUNCT
ejpam-4590	64	31	a)(u	a)(u	ADJ
ejpam-4590	64	32	,	,	PUNCT
ejpam-4590	64	33	b	b	X
ejpam-4590	64	34	)	)	PUNCT
ejpam-4590	64	35	∈	∈	NOUN
ejpam-4590	64	36	e(g[h	e(g[h	NOUN
ejpam-4590	64	37	]	]	PUNCT
ejpam-4590	64	38	)	)	PUNCT
ejpam-4590	64	39	if	if	SCONJ
ejpam-4590	64	40	and	and	CCONJ
ejpam-4590	64	41	only	only	ADV
ejpam-4590	64	42	if	if	SCONJ
ejpam-4590	64	43	either	either	DET
ejpam-4590	64	44	uv	uv	PROPN
ejpam-4590	64	45	∈	∈	PROPN
ejpam-4590	64	46	e(g	e(g	PROPN
ejpam-4590	64	47	)	)	PUNCT
ejpam-4590	64	48	or	or	CCONJ
ejpam-4590	64	49	u	u	X
ejpam-4590	64	50	=	=	PROPN
ejpam-4590	64	51	v	v	PROPN
ejpam-4590	64	52	and	and	CCONJ
ejpam-4590	64	53	ab	ab	PROPN
ejpam-4590	64	54	∈	∈	PROPN
ejpam-4590	64	55	e(h	e(h	PROPN
ejpam-4590	64	56	)	)	PUNCT
ejpam-4590	64	57	.	.	PUNCT
ejpam-4590	65	1	any	any	DET
ejpam-4590	65	2	non	non	ADJ
ejpam-4590	65	3	-	-	ADJ
ejpam-4590	65	4	empty	empty	ADJ
ejpam-4590	65	5	set	set	NOUN
ejpam-4590	65	6	c	c	NOUN
ejpam-4590	65	7	⊆	⊆	NUM
ejpam-4590	65	8	v	v	NOUN
ejpam-4590	65	9	(	(	PUNCT
ejpam-4590	65	10	g	g	NOUN
ejpam-4590	65	11	)	)	PUNCT
ejpam-4590	65	12	×	×	NOUN
ejpam-4590	65	13	v	v	NOUN
ejpam-4590	65	14	(	(	PUNCT
ejpam-4590	65	15	h	h	NOUN
ejpam-4590	65	16	)	)	PUNCT
ejpam-4590	65	17	can	can	AUX
ejpam-4590	65	18	be	be	AUX
ejpam-4590	65	19	written	write	VERB
ejpam-4590	65	20	as	as	ADP
ejpam-4590	65	21	c	c	NOUN
ejpam-4590	65	22	=	=	PUNCT
ejpam-4590	65	23	⋃	⋃	PROPN
ejpam-4590	66	1	x∈s	x∈s	NOUN
ejpam-4590	67	1	[	[	X
ejpam-4590	67	2	{	{	PUNCT
ejpam-4590	67	3	x	x	NOUN
ejpam-4590	67	4	}	}	PUNCT
ejpam-4590	67	5	×	×	PROPN
ejpam-4590	67	6	tx	tx	PROPN
ejpam-4590	67	7	]	]	X
ejpam-4590	67	8	,	,	PUNCT
ejpam-4590	67	9	where	where	SCONJ
ejpam-4590	67	10	s	s	VERB
ejpam-4590	67	11	⊆	⊆	NUM
ejpam-4590	67	12	v	v	NOUN
ejpam-4590	67	13	(	(	PUNCT
ejpam-4590	67	14	g	g	NOUN
ejpam-4590	67	15	)	)	PUNCT
ejpam-4590	67	16	and	and	CCONJ
ejpam-4590	67	17	tx	tx	VERB
ejpam-4590	67	18	⊆	⊆	NUM
ejpam-4590	67	19	v	v	NOUN
ejpam-4590	67	20	(	(	PUNCT
ejpam-4590	67	21	h	h	NOUN
ejpam-4590	67	22	)	)	PUNCT
ejpam-4590	67	23	for	for	ADP
ejpam-4590	67	24	each	each	DET
ejpam-4590	67	25	x	x	PROPN
ejpam-4590	67	26	∈	∈	PROPN
ejpam-4590	67	27	s.	s.	PROPN
ejpam-4590	67	28	specifically	specifically	ADV
ejpam-4590	67	29	,	,	PUNCT
ejpam-4590	67	30	tx	tx	PROPN
ejpam-4590	67	31	=	=	PUNCT
ejpam-4590	67	32	{	{	PUNCT
ejpam-4590	67	33	a	a	DET
ejpam-4590	67	34	∈	∈	PROPN
ejpam-4590	67	35	v	v	ADP
ejpam-4590	67	36	(	(	PUNCT
ejpam-4590	67	37	h	h	NOUN
ejpam-4590	67	38	)	)	PUNCT
ejpam-4590	67	39	:	:	PUNCT
ejpam-4590	67	40	(	(	PUNCT
ejpam-4590	67	41	x	x	X
ejpam-4590	67	42	,	,	PUNCT
ejpam-4590	67	43	a	a	PRON
ejpam-4590	67	44	)	)	PUNCT
ejpam-4590	67	45	∈	∈	PROPN
ejpam-4590	67	46	c	c	NOUN
ejpam-4590	67	47	}	}	PUNCT
ejpam-4590	67	48	for	for	ADP
ejpam-4590	67	49	each	each	DET
ejpam-4590	67	50	x	x	SYM
ejpam-4590	67	51	∈	∈	PROPN
ejpam-4590	67	52	s.	s.	PROPN
ejpam-4590	67	53	some	some	DET
ejpam-4590	67	54	parameters	parameter	NOUN
ejpam-4590	67	55	studied	study	VERB
ejpam-4590	67	56	on	on	ADP
ejpam-4590	67	57	these	these	DET
ejpam-4590	67	58	types	type	NOUN
ejpam-4590	67	59	of	of	ADP
ejpam-4590	67	60	graphs	graph	NOUN
ejpam-4590	67	61	can	can	AUX
ejpam-4590	67	62	be	be	AUX
ejpam-4590	67	63	found	find	VERB
ejpam-4590	67	64	in	in	ADP
ejpam-4590	67	65	[	[	X
ejpam-4590	67	66	6	6	NUM
ejpam-4590	67	67	]	]	PUNCT
ejpam-4590	67	68	and	and	CCONJ
ejpam-4590	67	69	[	[	X
ejpam-4590	67	70	7	7	NUM
ejpam-4590	67	71	]	]	PUNCT
ejpam-4590	67	72	.	.	PUNCT
ejpam-4590	68	1	3	3	X
ejpam-4590	68	2	.	.	X
ejpam-4590	68	3	known	know	VERB
ejpam-4590	68	4	results	result	NOUN
ejpam-4590	68	5	proposition	proposition	NOUN
ejpam-4590	68	6	1	1	NUM
ejpam-4590	68	7	.	.	PUNCT
ejpam-4590	69	1	[	[	X
ejpam-4590	69	2	13	13	NUM
ejpam-4590	69	3	]	]	PUNCT
ejpam-4590	69	4	let	let	VERB
ejpam-4590	69	5	g	g	PRON
ejpam-4590	69	6	be	be	AUX
ejpam-4590	69	7	a	a	DET
ejpam-4590	69	8	graph	graph	NOUN
ejpam-4590	69	9	.	.	PUNCT
ejpam-4590	70	1	then	then	ADV
ejpam-4590	70	2	1	1	NUM
ejpam-4590	70	3	≤	≤	NUM
ejpam-4590	70	4	pnd(g	pnd(g	ADP
ejpam-4590	70	5	)	)	PUNCT
ejpam-4590	70	6	≤	≤	NOUN
ejpam-4590	70	7	|v	|v	X
ejpam-4590	70	8	(	(	PUNCT
ejpam-4590	70	9	g)|	g)|	PROPN
ejpam-4590	70	10	.	.	PUNCT
ejpam-4590	71	1	moreover	moreover	ADV
ejpam-4590	71	2	,	,	PUNCT
ejpam-4590	71	3	(	(	PUNCT
ejpam-4590	71	4	i	i	NOUN
ejpam-4590	71	5	)	)	PUNCT
ejpam-4590	71	6	pnd(g	pnd(g	PROPN
ejpam-4590	71	7	)	)	PUNCT
ejpam-4590	71	8	=	=	SYM
ejpam-4590	71	9	|v	|v	PROPN
ejpam-4590	71	10	(	(	PUNCT
ejpam-4590	71	11	g)|	g)|	VERB
ejpam-4590	71	12	if	if	SCONJ
ejpam-4590	71	13	and	and	CCONJ
ejpam-4590	71	14	only	only	ADV
ejpam-4590	71	15	if	if	SCONJ
ejpam-4590	71	16	g	g	PROPN
ejpam-4590	71	17	is	be	AUX
ejpam-4590	71	18	a	a	DET
ejpam-4590	71	19	complete	complete	ADJ
ejpam-4590	71	20	graph	graph	NOUN
ejpam-4590	71	21	,	,	PUNCT
ejpam-4590	71	22	(	(	PUNCT
ejpam-4590	71	23	ii	ii	NOUN
ejpam-4590	71	24	)	)	PUNCT
ejpam-4590	71	25	pnd(g	pnd(g	PROPN
ejpam-4590	71	26	)	)	PUNCT
ejpam-4590	71	27	=	=	SYM
ejpam-4590	71	28	1	1	NUM
ejpam-4590	71	29	if	if	SCONJ
ejpam-4590	71	30	and	and	CCONJ
ejpam-4590	71	31	only	only	ADV
ejpam-4590	71	32	if	if	SCONJ
ejpam-4590	71	33	g	g	PROPN
ejpam-4590	71	34	has	have	VERB
ejpam-4590	71	35	an	an	DET
ejpam-4590	71	36	isolated	isolated	ADJ
ejpam-4590	71	37	vetex	vetex	NOUN
ejpam-4590	71	38	,	,	PUNCT
ejpam-4590	71	39	and	and	CCONJ
ejpam-4590	71	40	(	(	PUNCT
ejpam-4590	71	41	iii	iii	NOUN
ejpam-4590	71	42	)	)	PUNCT
ejpam-4590	71	43	pnd(g	pnd(g	PROPN
ejpam-4590	71	44	)	)	PUNCT
ejpam-4590	71	45	=	=	SYM
ejpam-4590	71	46	2	2	NUM
ejpam-4590	71	47	if	if	SCONJ
ejpam-4590	71	48	and	and	CCONJ
ejpam-4590	71	49	only	only	ADV
ejpam-4590	71	50	of	of	ADP
ejpam-4590	71	51	g	g	PROPN
ejpam-4590	71	52	has	have	VERB
ejpam-4590	71	53	no	no	DET
ejpam-4590	71	54	isolated	isolated	ADJ
ejpam-4590	71	55	vertex	vertex	NOUN
ejpam-4590	71	56	and	and	CCONJ
ejpam-4590	71	57	there	there	PRON
ejpam-4590	71	58	exist	exist	VERB
ejpam-4590	71	59	distinct	distinct	ADJ
ejpam-4590	71	60	vertices	vertex	NOUN
ejpam-4590	71	61	a	a	PRON
ejpam-4590	71	62	and	and	CCONJ
ejpam-4590	71	63	b	b	NOUN
ejpam-4590	71	64	such	such	ADJ
ejpam-4590	71	65	that	that	DET
ejpam-4590	71	66	ng(a	ng(a	NOUN
ejpam-4590	71	67	)	)	PUNCT
ejpam-4590	71	68	∩ng(b	∩ng(b	NOUN
ejpam-4590	71	69	)	)	PUNCT
ejpam-4590	71	70	=	=	PUNCT
ejpam-4590	71	71	∅.	∅.	NOUN
ejpam-4590	71	72	theorem	theorem	VERB
ejpam-4590	71	73	1	1	NUM
ejpam-4590	71	74	.	.	PUNCT
ejpam-4590	72	1	[	[	X
ejpam-4590	72	2	14	14	NUM
ejpam-4590	72	3	]	]	PUNCT
ejpam-4590	72	4	let	let	VERB
ejpam-4590	72	5	g	g	NOUN
ejpam-4590	72	6	and	and	CCONJ
ejpam-4590	72	7	h	h	NOUN
ejpam-4590	72	8	be	be	VERB
ejpam-4590	72	9	any	any	DET
ejpam-4590	72	10	two	two	NUM
ejpam-4590	72	11	graphs	graph	NOUN
ejpam-4590	72	12	.	.	PUNCT
ejpam-4590	73	1	a	a	DET
ejpam-4590	73	2	set	set	NOUN
ejpam-4590	73	3	s	s	NOUN
ejpam-4590	73	4	⊆	⊆	NUM
ejpam-4590	73	5	v	v	NOUN
ejpam-4590	73	6	(	(	PUNCT
ejpam-4590	73	7	g+h	g+h	PROPN
ejpam-4590	73	8	)	)	PUNCT
ejpam-4590	73	9	is	be	AUX
ejpam-4590	73	10	hop	hop	NOUN
ejpam-4590	73	11	dominating	dominate	VERB
ejpam-4590	73	12	set	set	NOUN
ejpam-4590	73	13	of	of	ADP
ejpam-4590	73	14	g+h	g+h	PROPN
ejpam-4590	73	15	if	if	SCONJ
ejpam-4590	74	1	and	and	CCONJ
ejpam-4590	74	2	only	only	ADV
ejpam-4590	74	3	if	if	SCONJ
ejpam-4590	74	4	s	s	NOUN
ejpam-4590	74	5	=	=	PUNCT
ejpam-4590	74	6	sg	sg	PROPN
ejpam-4590	74	7	∪sh	∪sh	NOUN
ejpam-4590	74	8	,	,	PUNCT
ejpam-4590	74	9	where	where	SCONJ
ejpam-4590	74	10	sg	sg	PROPN
ejpam-4590	74	11	and	and	CCONJ
ejpam-4590	74	12	sh	sh	PROPN
ejpam-4590	74	13	are	be	AUX
ejpam-4590	74	14	pointwise	pointwise	PROPN
ejpam-4590	74	15	non	non	ADJ
ejpam-4590	74	16	-	-	ADJ
ejpam-4590	74	17	dominating	dominating	ADJ
ejpam-4590	74	18	sets	set	NOUN
ejpam-4590	74	19	of	of	ADP
ejpam-4590	74	20	g	g	PROPN
ejpam-4590	74	21	and	and	CCONJ
ejpam-4590	74	22	h	h	NOUN
ejpam-4590	74	23	,	,	PUNCT
ejpam-4590	74	24	respectively	respectively	ADV
ejpam-4590	74	25	.	.	PUNCT
ejpam-4590	74	26	theorem	theorem	NOUN
ejpam-4590	74	27	2	2	NUM
ejpam-4590	74	28	.	.	PUNCT
ejpam-4590	75	1	[	[	X
ejpam-4590	75	2	14	14	NUM
ejpam-4590	75	3	]	]	PUNCT
ejpam-4590	75	4	let	let	VERB
ejpam-4590	75	5	g	g	PROPN
ejpam-4590	75	6	and	and	CCONJ
ejpam-4590	75	7	h	h	NOUN
ejpam-4590	75	8	be	be	AUX
ejpam-4590	75	9	connected	connect	VERB
ejpam-4590	75	10	non	non	ADJ
ejpam-4590	75	11	-	-	ADJ
ejpam-4590	75	12	trivial	trivial	ADJ
ejpam-4590	75	13	graphs	graph	NOUN
ejpam-4590	75	14	.	.	PUNCT
ejpam-4590	76	1	a	a	DET
ejpam-4590	76	2	subset	subset	NOUN
ejpam-4590	76	3	c	c	NOUN
ejpam-4590	76	4	=	=	PUNCT
ejpam-4590	76	5	⋃	⋃	PROPN
ejpam-4590	76	6	x∈s	x∈s	NOUN
ejpam-4590	77	1	[	[	X
ejpam-4590	77	2	x×	x×	PROPN
ejpam-4590	77	3	tx	tx	PROPN
ejpam-4590	77	4	]	]	PUNCT
ejpam-4590	77	5	of	of	ADP
ejpam-4590	77	6	v	v	NOUN
ejpam-4590	77	7	(	(	PUNCT
ejpam-4590	77	8	g[h	g[h	PROPN
ejpam-4590	77	9	]	]	PUNCT
ejpam-4590	77	10	)	)	PUNCT
ejpam-4590	77	11	is	be	AUX
ejpam-4590	77	12	a	a	DET
ejpam-4590	77	13	hop	hop	NOUN
ejpam-4590	77	14	dominating	dominating	NOUN
ejpam-4590	77	15	set	set	NOUN
ejpam-4590	77	16	of	of	ADP
ejpam-4590	77	17	g[h	g[h	PROPN
ejpam-4590	77	18	]	]	PUNCT
ejpam-4590	77	19	if	if	SCONJ
ejpam-4590	77	20	and	and	CCONJ
ejpam-4590	77	21	only	only	ADV
ejpam-4590	77	22	if	if	SCONJ
ejpam-4590	77	23	the	the	DET
ejpam-4590	77	24	following	follow	VERB
ejpam-4590	77	25	conditions	condition	NOUN
ejpam-4590	77	26	hold	hold	VERB
ejpam-4590	77	27	:	:	PUNCT
ejpam-4590	77	28	(	(	PUNCT
ejpam-4590	77	29	i	i	NOUN
ejpam-4590	77	30	)	)	PUNCT
ejpam-4590	77	31	s	s	AUX
ejpam-4590	77	32	is	be	AUX
ejpam-4590	77	33	a	a	DET
ejpam-4590	77	34	hop	hop	NOUN
ejpam-4590	77	35	dominating	dominating	NOUN
ejpam-4590	77	36	set	set	NOUN
ejpam-4590	77	37	of	of	ADP
ejpam-4590	77	38	g	g	NOUN
ejpam-4590	77	39	;	;	PUNCT
ejpam-4590	77	40	(	(	PUNCT
ejpam-4590	77	41	ii	ii	NOUN
ejpam-4590	77	42	)	)	PUNCT
ejpam-4590	77	43	tx	tx	PROPN
ejpam-4590	77	44	is	be	AUX
ejpam-4590	77	45	a	a	DET
ejpam-4590	77	46	pointwise	pointwise	ADJ
ejpam-4590	77	47	non	non	ADJ
ejpam-4590	77	48	-	-	ADJ
ejpam-4590	77	49	dominating	dominating	ADJ
ejpam-4590	77	50	set	set	NOUN
ejpam-4590	77	51	of	of	ADP
ejpam-4590	77	52	h	h	NOUN
ejpam-4590	77	53	for	for	ADP
ejpam-4590	77	54	each	each	DET
ejpam-4590	77	55	x	x	SYM
ejpam-4590	77	56	∈	∈	PROPN
ejpam-4590	77	57	s	s	VERB
ejpam-4590	77	58	with	with	ADP
ejpam-4590	77	59	|n2	|n2	PROPN
ejpam-4590	77	60	g(x	g(x	NOUN
ejpam-4590	77	61	)	)	PUNCT
ejpam-4590	77	62	∩	∩	NOUN
ejpam-4590	77	63	s|	s|	VERB
ejpam-4590	77	64	=	=	SYM
ejpam-4590	78	1	0	0	X
ejpam-4590	78	2	.	.	PUNCT
ejpam-4590	78	3	theorem	theorem	NOUN
ejpam-4590	78	4	3	3	NUM
ejpam-4590	78	5	.	.	PUNCT
ejpam-4590	79	1	[	[	X
ejpam-4590	79	2	14	14	NUM
ejpam-4590	79	3	]	]	PUNCT
ejpam-4590	79	4	let	let	VERB
ejpam-4590	79	5	g	g	PRON
ejpam-4590	79	6	be	be	AUX
ejpam-4590	79	7	a	a	DET
ejpam-4590	79	8	connected	connected	ADJ
ejpam-4590	79	9	graph	graph	NOUN
ejpam-4590	79	10	with	with	ADP
ejpam-4590	79	11	γ(g	γ(g	PROPN
ejpam-4590	79	12	)	)	PUNCT
ejpam-4590	79	13	̸=	̸=	PROPN
ejpam-4590	79	14	1	1	NUM
ejpam-4590	79	15	.	.	PUNCT
ejpam-4590	80	1	if	if	SCONJ
ejpam-4590	80	2	s	s	PROPN
ejpam-4590	80	3	is	be	AUX
ejpam-4590	80	4	a	a	DET
ejpam-4590	80	5	hop	hop	NOUN
ejpam-4590	80	6	dominating	dominating	NOUN
ejpam-4590	80	7	set	set	NOUN
ejpam-4590	80	8	of	of	ADP
ejpam-4590	80	9	g	g	PROPN
ejpam-4590	80	10	,	,	PUNCT
ejpam-4590	80	11	then	then	ADV
ejpam-4590	80	12	γth(g	γth(g	NOUN
ejpam-4590	80	13	)	)	PUNCT
ejpam-4590	80	14	≤	≤	NUM
ejpam-4590	81	1	|s	|s	PROPN
ejpam-4590	81	2	∩n2	∩n2	PROPN
ejpam-4590	81	3	g(s)|+	g(s)|+	PROPN
ejpam-4590	81	4	2|s	2|s	PROPN
ejpam-4590	81	5	\n2	\n2	PROPN
ejpam-4590	81	6	g(s)|	g(s)|	PROPN
ejpam-4590	81	7	.	.	PUNCT
ejpam-4590	82	1	moreover	moreover	ADV
ejpam-4590	82	2	,	,	PUNCT
ejpam-4590	82	3	γth(g	γth(g	NOUN
ejpam-4590	82	4	)	)	PUNCT
ejpam-4590	82	5	≤	≤	NOUN
ejpam-4590	82	6	2γh(g	2γh(g	NOUN
ejpam-4590	82	7	)	)	PUNCT
ejpam-4590	82	8	.	.	PUNCT
ejpam-4590	83	1	c.j	c.j	PROPN
ejpam-4590	83	2	.	.	PROPN
ejpam-4590	83	3	saromines	saromines	PROPN
ejpam-4590	83	4	,	,	PUNCT
ejpam-4590	83	5	s.	s.	PROPN
ejpam-4590	83	6	canoy	canoy	PROPN
ejpam-4590	83	7	,	,	PUNCT
ejpam-4590	83	8	jr	jr	PROPN
ejpam-4590	83	9	.	.	PROPN
ejpam-4590	83	10	/	/	SYM
ejpam-4590	83	11	eur	eur	PROPN
ejpam-4590	83	12	.	.	PUNCT
ejpam-4590	84	1	j.	j.	PROPN
ejpam-4590	84	2	pure	pure	PROPN
ejpam-4590	84	3	appl	appl	PROPN
ejpam-4590	84	4	.	.	PROPN
ejpam-4590	84	5	math	math	PROPN
ejpam-4590	84	6	,	,	PUNCT
ejpam-4590	84	7	15	15	NUM
ejpam-4590	84	8	(	(	PUNCT
ejpam-4590	84	9	4	4	NUM
ejpam-4590	84	10	)	)	PUNCT
ejpam-4590	84	11	(	(	PUNCT
ejpam-4590	84	12	2022	2022	NUM
ejpam-4590	84	13	)	)	PUNCT
ejpam-4590	84	14	,	,	PUNCT
ejpam-4590	84	15	1966	1966	NUM
ejpam-4590	84	16	-	-	SYM
ejpam-4590	84	17	1981	1981	NUM
ejpam-4590	84	18	1969	1969	NUM
ejpam-4590	84	19	4	4	NUM
ejpam-4590	84	20	.	.	PUNCT
ejpam-4590	85	1	results	result	NOUN
ejpam-4590	85	2	theorem	theorem	VERB
ejpam-4590	85	3	4	4	NUM
ejpam-4590	85	4	.	.	PUNCT
ejpam-4590	86	1	let	let	VERB
ejpam-4590	86	2	g	g	NOUN
ejpam-4590	86	3	be	be	AUX
ejpam-4590	86	4	any	any	DET
ejpam-4590	86	5	graph	graph	NOUN
ejpam-4590	86	6	on	on	ADP
ejpam-4590	86	7	n	n	PRON
ejpam-4590	86	8	≥	≥	NUM
ejpam-4590	86	9	2	2	NUM
ejpam-4590	86	10	vertices	vertex	NOUN
ejpam-4590	86	11	.	.	PUNCT
ejpam-4590	87	1	then	then	ADV
ejpam-4590	87	2	2	2	NUM
ejpam-4590	87	3	≤	≤	NOUN
ejpam-4590	87	4	γh(g	γh(g	NOUN
ejpam-4590	87	5	)	)	PUNCT
ejpam-4590	87	6	≤	≤	NUM
ejpam-4590	87	7	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	87	8	)	)	PUNCT
ejpam-4590	87	9	≤	≤	NOUN
ejpam-4590	87	10	n.	n.	NOUN
ejpam-4590	87	11	moreover	moreover	ADV
ejpam-4590	87	12	,	,	PUNCT
ejpam-4590	87	13	(	(	PUNCT
ejpam-4590	87	14	i	i	NOUN
ejpam-4590	87	15	)	)	PUNCT
ejpam-4590	87	16	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	87	17	)	)	PUNCT
ejpam-4590	87	18	=	=	SYM
ejpam-4590	87	19	2	2	NUM
ejpam-4590	87	20	if	if	SCONJ
ejpam-4590	87	21	and	and	CCONJ
ejpam-4590	87	22	only	only	ADV
ejpam-4590	87	23	if	if	SCONJ
ejpam-4590	87	24	there	there	PRON
ejpam-4590	87	25	exist	exist	VERB
ejpam-4590	87	26	distinct	distinct	ADJ
ejpam-4590	87	27	vertices	vertex	NOUN
ejpam-4590	87	28	x	x	X
ejpam-4590	87	29	,	,	PUNCT
ejpam-4590	87	30	y	y	PROPN
ejpam-4590	87	31	∈	∈	PROPN
ejpam-4590	87	32	v	v	ADP
ejpam-4590	87	33	(	(	PUNCT
ejpam-4590	87	34	g	g	NOUN
ejpam-4590	87	35	)	)	PUNCT
ejpam-4590	87	36	such	such	ADJ
ejpam-4590	87	37	that	that	PRON
ejpam-4590	87	38	⟨v	⟨v	NOUN
ejpam-4590	87	39	(	(	PUNCT
ejpam-4590	87	40	g	g	NOUN
ejpam-4590	87	41	)	)	PUNCT
ejpam-4590	87	42	\	\	NOUN
ejpam-4590	88	1	{	{	PUNCT
ejpam-4590	88	2	x	x	X
ejpam-4590	88	3	,	,	PUNCT
ejpam-4590	88	4	y}⟩	y}⟩	PROPN
ejpam-4590	88	5	is	be	AUX
ejpam-4590	88	6	connected	connect	VERB
ejpam-4590	88	7	and	and	CCONJ
ejpam-4590	88	8	the	the	DET
ejpam-4590	88	9	following	follow	VERB
ejpam-4590	88	10	hold	hold	NOUN
ejpam-4590	88	11	:	:	PUNCT
ejpam-4590	88	12	(	(	PUNCT
ejpam-4590	88	13	a	a	X
ejpam-4590	88	14	)	)	PUNCT
ejpam-4590	88	15	|ng(v	|ng(v	PROPN
ejpam-4590	88	16	)	)	PUNCT
ejpam-4590	88	17	\	\	NOUN
ejpam-4590	88	18	{	{	PUNCT
ejpam-4590	88	19	x	x	NOUN
ejpam-4590	88	20	,	,	PUNCT
ejpam-4590	88	21	y	y	NOUN
ejpam-4590	88	22	}	}	PUNCT
ejpam-4590	88	23	∩	∩	NOUN
ejpam-4590	88	24	{	{	PUNCT
ejpam-4590	88	25	x	x	NOUN
ejpam-4590	88	26	,	,	PUNCT
ejpam-4590	88	27	y}|	y}|	NOUN
ejpam-4590	88	28	≤	≤	NOUN
ejpam-4590	88	29	1	1	NUM
ejpam-4590	88	30	for	for	ADP
ejpam-4590	88	31	all	all	PRON
ejpam-4590	88	32	v	v	ADP
ejpam-4590	88	33	∈	∈	NUM
ejpam-4590	88	34	v	v	NOUN
ejpam-4590	88	35	(	(	PUNCT
ejpam-4590	88	36	g	g	NOUN
ejpam-4590	88	37	)	)	PUNCT
ejpam-4590	88	38	\	\	NOUN
ejpam-4590	89	1	{	{	PUNCT
ejpam-4590	89	2	x	x	NOUN
ejpam-4590	89	3	,	,	PUNCT
ejpam-4590	89	4	y	y	PROPN
ejpam-4590	89	5	}	}	PUNCT
ejpam-4590	89	6	.	.	PUNCT
ejpam-4590	90	1	(	(	PUNCT
ejpam-4590	90	2	b	b	X
ejpam-4590	90	3	)	)	PUNCT
ejpam-4590	90	4	ng(v)∩ng	ng(v)∩ng	PROPN
ejpam-4590	90	5	(	(	PUNCT
ejpam-4590	90	6	{	{	PUNCT
ejpam-4590	90	7	x	x	NOUN
ejpam-4590	90	8	,	,	PUNCT
ejpam-4590	90	9	y	y	NOUN
ejpam-4590	90	10	}	}	PUNCT
ejpam-4590	90	11	)	)	PUNCT
ejpam-4590	90	12	̸=	̸=	NOUN
ejpam-4590	90	13	∅	∅	NOUN
ejpam-4590	90	14	for	for	ADP
ejpam-4590	90	15	all	all	PRON
ejpam-4590	90	16	v	v	ADP
ejpam-4590	90	17	∈	∈	NUM
ejpam-4590	90	18	v	v	NOUN
ejpam-4590	90	19	(	(	PUNCT
ejpam-4590	90	20	g)\{x	g)\{x	PROPN
ejpam-4590	90	21	,	,	PUNCT
ejpam-4590	90	22	y	y	NOUN
ejpam-4590	90	23	}	}	PUNCT
ejpam-4590	90	24	such	such	ADJ
ejpam-4590	90	25	that	that	SCONJ
ejpam-4590	90	26	ng(v)∩{x	ng(v)∩{x	PROPN
ejpam-4590	90	27	,	,	PUNCT
ejpam-4590	90	28	y	y	NOUN
ejpam-4590	90	29	}	}	PUNCT
ejpam-4590	90	30	=	=	X
ejpam-4590	90	31	∅.	∅.	X
ejpam-4590	90	32	(	(	PUNCT
ejpam-4590	90	33	c	c	NOUN
ejpam-4590	90	34	)	)	PUNCT
ejpam-4590	90	35	for	for	ADP
ejpam-4590	90	36	all	all	PRON
ejpam-4590	90	37	v	v	ADP
ejpam-4590	90	38	∈	∈	NOUN
ejpam-4590	90	39	v	v	NOUN
ejpam-4590	90	40	(	(	PUNCT
ejpam-4590	90	41	g)\{x	g)\{x	PROPN
ejpam-4590	90	42	,	,	PUNCT
ejpam-4590	90	43	y	y	NOUN
ejpam-4590	90	44	}	}	PUNCT
ejpam-4590	90	45	,	,	PUNCT
ejpam-4590	90	46	ng(v)∩ng(x	ng(v)∩ng(x	ADJ
ejpam-4590	90	47	)	)	PUNCT
ejpam-4590	90	48	̸=	̸=	PROPN
ejpam-4590	90	49	∅	∅	NOUN
ejpam-4590	90	50	if	if	SCONJ
ejpam-4590	90	51	v	v	NUM
ejpam-4590	90	52	∈	∈	PROPN
ejpam-4590	90	53	ng(y	ng(y	NOUN
ejpam-4590	90	54	)	)	PUNCT
ejpam-4590	90	55	and	and	CCONJ
ejpam-4590	90	56	ng(v)∩ng(y	ng(v)∩ng(y	PROPN
ejpam-4590	90	57	)	)	PUNCT
ejpam-4590	90	58	̸=	̸=	PROPN
ejpam-4590	90	59	∅	∅	NOUN
ejpam-4590	90	60	if	if	SCONJ
ejpam-4590	90	61	v	v	PRON
ejpam-4590	90	62	∈	∈	PROPN
ejpam-4590	90	63	ng(x	ng(x	NUM
ejpam-4590	90	64	)	)	PUNCT
ejpam-4590	90	65	.	.	PUNCT
ejpam-4590	91	1	(	(	PUNCT
ejpam-4590	91	2	ii	ii	NOUN
ejpam-4590	91	3	)	)	PUNCT
ejpam-4590	91	4	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	91	5	)	)	PUNCT
ejpam-4590	92	1	=	=	SYM
ejpam-4590	92	2	n	n	NOUN
ejpam-4590	92	3	if	if	SCONJ
ejpam-4590	92	4	and	and	CCONJ
ejpam-4590	92	5	only	only	ADV
ejpam-4590	92	6	if	if	SCONJ
ejpam-4590	92	7	every	every	DET
ejpam-4590	92	8	component	component	NOUN
ejpam-4590	92	9	of	of	ADP
ejpam-4590	92	10	g	g	PROPN
ejpam-4590	92	11	is	be	AUX
ejpam-4590	92	12	complete	complete	ADJ
ejpam-4590	92	13	.	.	PUNCT
ejpam-4590	93	1	proof	proof	NOUN
ejpam-4590	93	2	.	.	PUNCT
ejpam-4590	94	1	since	since	SCONJ
ejpam-4590	94	2	every	every	DET
ejpam-4590	94	3	outer	outer	ADV
ejpam-4590	94	4	-	-	PUNCT
ejpam-4590	94	5	connected	connect	VERB
ejpam-4590	94	6	hop	hop	NOUN
ejpam-4590	94	7	dominating	dominating	NOUN
ejpam-4590	94	8	set	set	NOUN
ejpam-4590	94	9	of	of	ADP
ejpam-4590	94	10	g	g	PROPN
ejpam-4590	94	11	is	be	AUX
ejpam-4590	94	12	a	a	DET
ejpam-4590	94	13	hop	hop	NOUN
ejpam-4590	94	14	dominating	dominating	NOUN
ejpam-4590	94	15	set	set	NOUN
ejpam-4590	94	16	,	,	PUNCT
ejpam-4590	94	17	γh(g	γh(g	NOUN
ejpam-4590	94	18	)	)	PUNCT
ejpam-4590	94	19	≤	≤	NUM
ejpam-4590	94	20	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	94	21	)	)	PUNCT
ejpam-4590	94	22	.	.	PUNCT
ejpam-4590	95	1	also	also	ADV
ejpam-4590	95	2	,	,	PUNCT
ejpam-4590	95	3	since	since	SCONJ
ejpam-4590	95	4	v	v	NOUN
ejpam-4590	95	5	(	(	PUNCT
ejpam-4590	95	6	g	g	NOUN
ejpam-4590	95	7	)	)	PUNCT
ejpam-4590	95	8	is	be	AUX
ejpam-4590	95	9	an	an	DET
ejpam-4590	95	10	outer	outer	ADV
ejpam-4590	95	11	-	-	PUNCT
ejpam-4590	95	12	connected	connect	VERB
ejpam-4590	95	13	hop	hop	NOUN
ejpam-4590	95	14	dominating	dominating	NOUN
ejpam-4590	95	15	set	set	NOUN
ejpam-4590	95	16	of	of	ADP
ejpam-4590	95	17	g	g	PROPN
ejpam-4590	95	18	and	and	CCONJ
ejpam-4590	95	19	any	any	DET
ejpam-4590	95	20	connected	connected	ADJ
ejpam-4590	95	21	graph	graph	NOUN
ejpam-4590	95	22	g	g	NOUN
ejpam-4590	95	23	with	with	ADP
ejpam-4590	95	24	at	at	ADV
ejpam-4590	95	25	least	least	ADV
ejpam-4590	95	26	two	two	NUM
ejpam-4590	95	27	vertices	vertex	NOUN
ejpam-4590	95	28	satisfies	satisfy	VERB
ejpam-4590	95	29	2	2	NUM
ejpam-4590	95	30	≤	≤	NOUN
ejpam-4590	95	31	γh(g	γh(g	NOUN
ejpam-4590	95	32	)	)	PUNCT
ejpam-4590	95	33	,	,	PUNCT
ejpam-4590	95	34	it	it	PRON
ejpam-4590	95	35	follows	follow	VERB
ejpam-4590	95	36	that	that	SCONJ
ejpam-4590	95	37	2	2	NUM
ejpam-4590	95	38	≤	≤	NOUN
ejpam-4590	95	39	γh(g	γh(g	NOUN
ejpam-4590	95	40	)	)	PUNCT
ejpam-4590	95	41	≤	≤	NUM
ejpam-4590	95	42	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	95	43	)	)	PUNCT
ejpam-4590	95	44	≤	≤	NUM
ejpam-4590	95	45	n.	n.	NOUN
ejpam-4590	95	46	for	for	ADP
ejpam-4590	95	47	(	(	PUNCT
ejpam-4590	95	48	i	i	NOUN
ejpam-4590	95	49	)	)	PUNCT
ejpam-4590	95	50	,	,	PUNCT
ejpam-4590	95	51	suppose	suppose	VERB
ejpam-4590	95	52	that	that	SCONJ
ejpam-4590	95	53	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	95	54	)	)	PUNCT
ejpam-4590	95	55	=	=	SYM
ejpam-4590	95	56	2	2	X
ejpam-4590	95	57	.	.	X
ejpam-4590	95	58	let	let	VERB
ejpam-4590	95	59	s	s	VERB
ejpam-4590	95	60	=	=	PUNCT
ejpam-4590	95	61	{	{	PUNCT
ejpam-4590	95	62	x	x	PROPN
ejpam-4590	95	63	,	,	PUNCT
ejpam-4590	95	64	y	y	PROPN
ejpam-4590	95	65	}	}	PUNCT
ejpam-4590	95	66	be	be	AUX
ejpam-4590	95	67	a	a	DET
ejpam-4590	95	68	γ̃ch	γ̃ch	NOUN
ejpam-4590	95	69	-	-	PUNCT
ejpam-4590	95	70	set	set	NOUN
ejpam-4590	95	71	of	of	ADP
ejpam-4590	95	72	g.	g.	PROPN
ejpam-4590	95	73	since	since	SCONJ
ejpam-4590	95	74	s	s	PROPN
ejpam-4590	95	75	is	be	AUX
ejpam-4590	95	76	an	an	DET
ejpam-4590	95	77	outerconnected	outerconnected	ADJ
ejpam-4590	95	78	hop	hop	NOUN
ejpam-4590	95	79	dominating	dominating	NOUN
ejpam-4590	95	80	set	set	NOUN
ejpam-4590	95	81	,	,	PUNCT
ejpam-4590	95	82	⟨v	⟨v	PROPN
ejpam-4590	95	83	(	(	PUNCT
ejpam-4590	95	84	g	g	NOUN
ejpam-4590	95	85	)	)	PUNCT
ejpam-4590	95	86	\	\	NOUN
ejpam-4590	96	1	{	{	PUNCT
ejpam-4590	96	2	x	x	X
ejpam-4590	96	3	,	,	PUNCT
ejpam-4590	96	4	y}⟩	y}⟩	PROPN
ejpam-4590	96	5	is	be	AUX
ejpam-4590	96	6	connected	connect	VERB
ejpam-4590	96	7	.	.	PUNCT
ejpam-4590	97	1	let	let	VERB
ejpam-4590	97	2	v	v	NUM
ejpam-4590	97	3	∈	∈	PROPN
ejpam-4590	97	4	v	v	NOUN
ejpam-4590	97	5	(	(	PUNCT
ejpam-4590	97	6	g)\{x	g)\{x	PROPN
ejpam-4590	97	7	,	,	PUNCT
ejpam-4590	97	8	y	y	NOUN
ejpam-4590	97	9	}	}	PUNCT
ejpam-4590	97	10	.	.	PUNCT
ejpam-4590	98	1	since	since	SCONJ
ejpam-4590	98	2	s	s	PROPN
ejpam-4590	98	3	is	be	AUX
ejpam-4590	98	4	a	a	DET
ejpam-4590	98	5	hop	hop	NOUN
ejpam-4590	98	6	dominating	dominating	NOUN
ejpam-4590	98	7	set	set	NOUN
ejpam-4590	98	8	,	,	PUNCT
ejpam-4590	98	9	dg(x	dg(x	NUM
ejpam-4590	98	10	,	,	PUNCT
ejpam-4590	98	11	v	v	NOUN
ejpam-4590	98	12	)	)	PUNCT
ejpam-4590	98	13	=	=	SYM
ejpam-4590	98	14	2	2	NUM
ejpam-4590	98	15	or	or	CCONJ
ejpam-4590	98	16	dg(y	dg(y	ADJ
ejpam-4590	98	17	,	,	PUNCT
ejpam-4590	98	18	v	v	NOUN
ejpam-4590	98	19	)	)	PUNCT
ejpam-4590	98	20	=	=	SYM
ejpam-4590	98	21	2	2	X
ejpam-4590	98	22	.	.	X
ejpam-4590	99	1	hence	hence	ADV
ejpam-4590	99	2	,	,	PUNCT
ejpam-4590	99	3	|ng(v	|ng(v	ADJ
ejpam-4590	99	4	)	)	PUNCT
ejpam-4590	99	5	∩	∩	NOUN
ejpam-4590	99	6	{	{	PUNCT
ejpam-4590	99	7	x	x	NOUN
ejpam-4590	99	8	,	,	PUNCT
ejpam-4590	99	9	y}|	y}|	NOUN
ejpam-4590	99	10	≤	≤	NOUN
ejpam-4590	99	11	1	1	NUM
ejpam-4590	99	12	,	,	PUNCT
ejpam-4590	99	13	showing	show	VERB
ejpam-4590	99	14	that	that	SCONJ
ejpam-4590	99	15	(	(	PUNCT
ejpam-4590	99	16	a	a	X
ejpam-4590	99	17	)	)	PUNCT
ejpam-4590	99	18	holds	hold	NOUN
ejpam-4590	99	19	.	.	PUNCT
ejpam-4590	100	1	if	if	SCONJ
ejpam-4590	100	2	dg(x	dg(x	NUM
ejpam-4590	100	3	,	,	PUNCT
ejpam-4590	100	4	v	v	NOUN
ejpam-4590	100	5	)	)	PUNCT
ejpam-4590	100	6	=	=	SYM
ejpam-4590	100	7	2	2	NUM
ejpam-4590	100	8	(	(	PUNCT
ejpam-4590	100	9	or	or	CCONJ
ejpam-4590	100	10	dg(y	dg(y	ADJ
ejpam-4590	100	11	,	,	PUNCT
ejpam-4590	100	12	v	v	NOUN
ejpam-4590	100	13	)	)	PUNCT
ejpam-4590	100	14	=	=	SYM
ejpam-4590	100	15	2	2	NUM
ejpam-4590	100	16	)	)	PUNCT
ejpam-4590	101	1	,	,	PUNCT
ejpam-4590	101	2	then	then	ADV
ejpam-4590	101	3	there	there	PRON
ejpam-4590	101	4	exists	exist	VERB
ejpam-4590	101	5	z	z	PROPN
ejpam-4590	101	6	∈	∈	PROPN
ejpam-4590	101	7	ng(x	ng(x	NUM
ejpam-4590	101	8	)	)	PUNCT
ejpam-4590	101	9	∩	∩	NOUN
ejpam-4590	101	10	ng(v	ng(v	NUM
ejpam-4590	101	11	)	)	PUNCT
ejpam-4590	101	12	(	(	PUNCT
ejpam-4590	101	13	resp	resp	NOUN
ejpam-4590	101	14	.	.	PUNCT
ejpam-4590	102	1	there	there	PRON
ejpam-4590	102	2	exists	exist	VERB
ejpam-4590	102	3	w	w	PROPN
ejpam-4590	102	4	∈	∈	PROPN
ejpam-4590	102	5	ng(y)∩ng(v	ng(y)∩ng(v	PROPN
ejpam-4590	102	6	)	)	PUNCT
ejpam-4590	102	7	)	)	PUNCT
ejpam-4590	102	8	.	.	PUNCT
ejpam-4590	103	1	hence	hence	ADV
ejpam-4590	103	2	,	,	PUNCT
ejpam-4590	103	3	ng(v)∩ng({x	ng(v)∩ng({x	PROPN
ejpam-4590	103	4	,	,	PUNCT
ejpam-4590	103	5	y	y	NOUN
ejpam-4590	103	6	}	}	PUNCT
ejpam-4590	103	7	)	)	PUNCT
ejpam-4590	103	8	̸=	̸=	NOUN
ejpam-4590	103	9	∅	∅	NOUN
ejpam-4590	103	10	whenever	whenever	SCONJ
ejpam-4590	103	11	ng(v)∩	ng(v)∩	ADJ
ejpam-4590	103	12	{	{	PUNCT
ejpam-4590	103	13	x	x	NOUN
ejpam-4590	103	14	,	,	PUNCT
ejpam-4590	103	15	y	y	NOUN
ejpam-4590	103	16	}	}	PUNCT
ejpam-4590	103	17	=	=	NOUN
ejpam-4590	103	18	∅	∅	NOUN
ejpam-4590	103	19	,	,	PUNCT
ejpam-4590	103	20	showing	show	VERB
ejpam-4590	103	21	(	(	PUNCT
ejpam-4590	103	22	b	b	NOUN
ejpam-4590	103	23	)	)	PUNCT
ejpam-4590	103	24	holds	hold	VERB
ejpam-4590	103	25	.	.	PUNCT
ejpam-4590	104	1	finally	finally	ADV
ejpam-4590	104	2	,	,	PUNCT
ejpam-4590	104	3	suppose	suppose	VERB
ejpam-4590	104	4	that	that	SCONJ
ejpam-4590	104	5	|ng(v	|ng(v	ADP
ejpam-4590	104	6	)	)	PUNCT
ejpam-4590	104	7	∩	∩	NOUN
ejpam-4590	104	8	{	{	PUNCT
ejpam-4590	104	9	x	x	NOUN
ejpam-4590	104	10	,	,	PUNCT
ejpam-4590	104	11	y}|	y}|	NOUN
ejpam-4590	104	12	=	=	SYM
ejpam-4590	105	1	1	1	X
ejpam-4590	105	2	.	.	X
ejpam-4590	106	1	if	if	SCONJ
ejpam-4590	106	2	v	v	NUM
ejpam-4590	106	3	∈	∈	PROPN
ejpam-4590	106	4	ng(y	ng(y	NOUN
ejpam-4590	106	5	)	)	PUNCT
ejpam-4590	106	6	,	,	PUNCT
ejpam-4590	106	7	then	then	ADV
ejpam-4590	106	8	dg(x	dg(x	NUM
ejpam-4590	106	9	,	,	PUNCT
ejpam-4590	106	10	v	v	NOUN
ejpam-4590	106	11	)	)	PUNCT
ejpam-4590	106	12	=	=	SYM
ejpam-4590	107	1	2	2	X
ejpam-4590	107	2	.	.	X
ejpam-4590	108	1	hence	hence	ADV
ejpam-4590	108	2	,	,	PUNCT
ejpam-4590	108	3	there	there	PRON
ejpam-4590	108	4	exist	exist	VERB
ejpam-4590	108	5	p	p	PRON
ejpam-4590	108	6	∈	∈	PROPN
ejpam-4590	108	7	ng(v	ng(v	NOUN
ejpam-4590	108	8	)	)	PUNCT
ejpam-4590	108	9	∩	∩	NOUN
ejpam-4590	108	10	ng(x	ng(x	NUM
ejpam-4590	108	11	)	)	PUNCT
ejpam-4590	108	12	,	,	PUNCT
ejpam-4590	108	13	that	that	ADV
ejpam-4590	108	14	is	is	ADV
ejpam-4590	108	15	,	,	PUNCT
ejpam-4590	108	16	ng(v	ng(v	NOUN
ejpam-4590	108	17	)	)	PUNCT
ejpam-4590	108	18	∩	∩	NOUN
ejpam-4590	108	19	ng(x	ng(x	NUM
ejpam-4590	108	20	)	)	PUNCT
ejpam-4590	108	21	̸=	̸=	PROPN
ejpam-4590	108	22	∅.	∅.	PRON
ejpam-4590	108	23	similarly	similarly	ADV
ejpam-4590	108	24	,	,	PUNCT
ejpam-4590	108	25	ng(v	ng(v	PUNCT
ejpam-4590	108	26	)	)	PUNCT
ejpam-4590	108	27	∩ng(y	∩ng(y	PROPN
ejpam-4590	108	28	)	)	PUNCT
ejpam-4590	108	29	̸=	̸=	PROPN
ejpam-4590	108	30	∅	∅	NOUN
ejpam-4590	108	31	if	if	SCONJ
ejpam-4590	108	32	v	v	PRON
ejpam-4590	108	33	∈	∈	PROPN
ejpam-4590	108	34	ng(x	ng(x	NUM
ejpam-4590	108	35	)	)	PUNCT
ejpam-4590	108	36	.	.	PUNCT
ejpam-4590	109	1	this	this	PRON
ejpam-4590	109	2	shows	show	VERB
ejpam-4590	109	3	that	that	SCONJ
ejpam-4590	109	4	(	(	PUNCT
ejpam-4590	109	5	c	c	X
ejpam-4590	109	6	)	)	PUNCT
ejpam-4590	109	7	holds	hold	NOUN
ejpam-4590	109	8	.	.	PUNCT
ejpam-4590	110	1	conversely	conversely	ADV
ejpam-4590	110	2	,	,	PUNCT
ejpam-4590	110	3	suppose	suppose	VERB
ejpam-4590	110	4	there	there	PRON
ejpam-4590	110	5	exist	exist	VERB
ejpam-4590	110	6	distinct	distinct	ADJ
ejpam-4590	110	7	vertices	vertex	NOUN
ejpam-4590	110	8	x	x	X
ejpam-4590	110	9	,	,	PUNCT
ejpam-4590	110	10	y	y	PROPN
ejpam-4590	110	11	∈	∈	PROPN
ejpam-4590	110	12	v	v	ADP
ejpam-4590	110	13	(	(	PUNCT
ejpam-4590	110	14	g	g	NOUN
ejpam-4590	110	15	)	)	PUNCT
ejpam-4590	110	16	such	such	ADJ
ejpam-4590	110	17	that	that	PRON
ejpam-4590	110	18	⟨v	⟨v	NOUN
ejpam-4590	110	19	(	(	PUNCT
ejpam-4590	110	20	g	g	NOUN
ejpam-4590	110	21	)	)	PUNCT
ejpam-4590	110	22	\	\	NOUN
ejpam-4590	110	23	{	{	PUNCT
ejpam-4590	110	24	x	x	X
ejpam-4590	110	25	,	,	PUNCT
ejpam-4590	110	26	y}⟩	y}⟩	PROPN
ejpam-4590	110	27	is	be	AUX
ejpam-4590	110	28	connected	connect	VERB
ejpam-4590	110	29	and	and	CCONJ
ejpam-4590	110	30	satisfy	satisfy	VERB
ejpam-4590	110	31	(	(	PUNCT
ejpam-4590	110	32	a	a	X
ejpam-4590	110	33	)	)	PUNCT
ejpam-4590	110	34	,	,	PUNCT
ejpam-4590	110	35	(	(	PUNCT
ejpam-4590	110	36	b	b	X
ejpam-4590	110	37	)	)	PUNCT
ejpam-4590	110	38	and	and	CCONJ
ejpam-4590	110	39	(	(	PUNCT
ejpam-4590	110	40	c	c	NOUN
ejpam-4590	110	41	)	)	PUNCT
ejpam-4590	110	42	.	.	PUNCT
ejpam-4590	111	1	let	let	VERB
ejpam-4590	111	2	v	v	X
ejpam-4590	111	3	∈	∈	NOUN
ejpam-4590	111	4	⟨v	⟨v	NOUN
ejpam-4590	111	5	(	(	PUNCT
ejpam-4590	111	6	g	g	NOUN
ejpam-4590	111	7	)	)	PUNCT
ejpam-4590	111	8	\	\	NOUN
ejpam-4590	112	1	{	{	PUNCT
ejpam-4590	112	2	x	x	NOUN
ejpam-4590	112	3	,	,	PUNCT
ejpam-4590	112	4	y}⟩.	y}⟩.	ADJ
ejpam-4590	112	5	by	by	ADP
ejpam-4590	112	6	(	(	PUNCT
ejpam-4590	112	7	a	a	NOUN
ejpam-4590	112	8	)	)	PUNCT
ejpam-4590	112	9	,	,	PUNCT
ejpam-4590	112	10	|ng(v	|ng(v	PROPN
ejpam-4590	112	11	)	)	PUNCT
ejpam-4590	112	12	∩	∩	NOUN
ejpam-4590	112	13	{	{	PUNCT
ejpam-4590	112	14	x	x	NOUN
ejpam-4590	112	15	,	,	PUNCT
ejpam-4590	112	16	y}|	y}|	NOUN
ejpam-4590	112	17	≤	≤	NOUN
ejpam-4590	112	18	1	1	NUM
ejpam-4590	112	19	.	.	PUNCT
ejpam-4590	113	1	if	if	SCONJ
ejpam-4590	113	2	|ng(v	|ng(v	NOUN
ejpam-4590	113	3	)	)	PUNCT
ejpam-4590	113	4	∩	∩	NOUN
ejpam-4590	113	5	{	{	PUNCT
ejpam-4590	113	6	x	x	NOUN
ejpam-4590	113	7	,	,	PUNCT
ejpam-4590	113	8	y}|	y}|	NOUN
ejpam-4590	113	9	=	=	SYM
ejpam-4590	113	10	0	0	NUM
ejpam-4590	113	11	,	,	PUNCT
ejpam-4590	113	12	then	then	ADV
ejpam-4590	113	13	dg(v	dg(v	NOUN
ejpam-4590	113	14	,	,	PUNCT
ejpam-4590	113	15	x	x	X
ejpam-4590	113	16	)	)	PUNCT
ejpam-4590	113	17	=	=	SYM
ejpam-4590	113	18	2	2	NUM
ejpam-4590	113	19	or	or	CCONJ
ejpam-4590	113	20	dg(v	dg(v	PROPN
ejpam-4590	113	21	,	,	PUNCT
ejpam-4590	113	22	y	y	NOUN
ejpam-4590	113	23	)	)	PUNCT
ejpam-4590	113	24	=	=	SYM
ejpam-4590	113	25	2	2	NUM
ejpam-4590	113	26	by	by	ADP
ejpam-4590	113	27	(	(	PUNCT
ejpam-4590	113	28	b	b	NOUN
ejpam-4590	113	29	)	)	PUNCT
ejpam-4590	113	30	.	.	PUNCT
ejpam-4590	114	1	suppose	suppose	VERB
ejpam-4590	114	2	|ng(v	|ng(v	NOUN
ejpam-4590	114	3	)	)	PUNCT
ejpam-4590	114	4	∩	∩	NOUN
ejpam-4590	114	5	{	{	PUNCT
ejpam-4590	114	6	x	x	NOUN
ejpam-4590	114	7	,	,	PUNCT
ejpam-4590	114	8	y}|	y}|	NOUN
ejpam-4590	114	9	=	=	SYM
ejpam-4590	114	10	1	1	NUM
ejpam-4590	114	11	,	,	PUNCT
ejpam-4590	114	12	say	say	VERB
ejpam-4590	114	13	v	v	ADP
ejpam-4590	114	14	∈	∈	NOUN
ejpam-4590	114	15	ng(y	ng(y	PUNCT
ejpam-4590	114	16	)	)	PUNCT
ejpam-4590	114	17	.	.	PUNCT
ejpam-4590	115	1	by	by	ADP
ejpam-4590	115	2	(	(	PUNCT
ejpam-4590	115	3	c	c	NOUN
ejpam-4590	115	4	)	)	PUNCT
ejpam-4590	115	5	,	,	PUNCT
ejpam-4590	115	6	ng(v	ng(v	X
ejpam-4590	115	7	)	)	PUNCT
ejpam-4590	115	8	∩ng(x	∩ng(x	NOUN
ejpam-4590	115	9	)	)	PUNCT
ejpam-4590	115	10	̸=	̸=	PROPN
ejpam-4590	115	11	∅.	∅.	ADP
ejpam-4590	115	12	this	this	PRON
ejpam-4590	115	13	implies	imply	VERB
ejpam-4590	115	14	that	that	PRON
ejpam-4590	115	15	dg(v	dg(v	NOUN
ejpam-4590	115	16	,	,	PUNCT
ejpam-4590	115	17	x	x	X
ejpam-4590	115	18	)	)	PUNCT
ejpam-4590	115	19	=	=	SYM
ejpam-4590	115	20	2	2	X
ejpam-4590	115	21	.	.	X
ejpam-4590	116	1	therefore	therefore	ADV
ejpam-4590	116	2	s	s	X
ejpam-4590	116	3	is	be	AUX
ejpam-4590	116	4	an	an	DET
ejpam-4590	116	5	outer	outer	ADV
ejpam-4590	116	6	-	-	PUNCT
ejpam-4590	116	7	connected	connect	VERB
ejpam-4590	116	8	hop	hop	NOUN
ejpam-4590	116	9	dominating	dominating	NOUN
ejpam-4590	116	10	set	set	NOUN
ejpam-4590	116	11	of	of	ADP
ejpam-4590	116	12	g.	g.	PROPN
ejpam-4590	116	13	since	since	SCONJ
ejpam-4590	116	14	g	g	PROPN
ejpam-4590	116	15	is	be	AUX
ejpam-4590	116	16	non	non	ADJ
ejpam-4590	116	17	-	-	ADJ
ejpam-4590	116	18	trivial	trivial	ADJ
ejpam-4590	116	19	,	,	PUNCT
ejpam-4590	116	20	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	116	21	)	)	PUNCT
ejpam-4590	116	22	=	=	SYM
ejpam-4590	116	23	2	2	X
ejpam-4590	116	24	.	.	X
ejpam-4590	116	25	for	for	ADP
ejpam-4590	116	26	(	(	PUNCT
ejpam-4590	116	27	ii	ii	NOUN
ejpam-4590	116	28	)	)	PUNCT
ejpam-4590	116	29	,	,	PUNCT
ejpam-4590	116	30	suppose	suppose	VERB
ejpam-4590	116	31	that	that	SCONJ
ejpam-4590	116	32	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	116	33	)	)	PUNCT
ejpam-4590	116	34	=	=	SYM
ejpam-4590	116	35	|v	|v	PROPN
ejpam-4590	116	36	(	(	PUNCT
ejpam-4590	116	37	g)|	g)|	VERB
ejpam-4590	116	38	and	and	CCONJ
ejpam-4590	116	39	suppose	suppose	VERB
ejpam-4590	116	40	that	that	SCONJ
ejpam-4590	116	41	one	one	NUM
ejpam-4590	116	42	component	component	NOUN
ejpam-4590	116	43	of	of	ADP
ejpam-4590	116	44	g	g	NOUN
ejpam-4590	116	45	,	,	PUNCT
ejpam-4590	116	46	say	say	VERB
ejpam-4590	116	47	g1	g1	NOUN
ejpam-4590	116	48	,	,	PUNCT
ejpam-4590	116	49	is	be	AUX
ejpam-4590	116	50	not	not	PART
ejpam-4590	116	51	complete	complete	ADJ
ejpam-4590	116	52	.	.	PUNCT
ejpam-4590	117	1	then	then	ADV
ejpam-4590	117	2	there	there	PRON
ejpam-4590	117	3	exist	exist	VERB
ejpam-4590	117	4	distinct	distinct	ADJ
ejpam-4590	117	5	vertices	vertex	NOUN
ejpam-4590	117	6	x1	x1	PROPN
ejpam-4590	117	7	,	,	PUNCT
ejpam-4590	117	8	y1	y1	PROPN
ejpam-4590	117	9	∈	∈	PROPN
ejpam-4590	117	10	v	v	NOUN
ejpam-4590	117	11	(	(	PUNCT
ejpam-4590	117	12	g1	g1	PROPN
ejpam-4590	117	13	)	)	PUNCT
ejpam-4590	117	14	such	such	ADJ
ejpam-4590	117	15	that	that	DET
ejpam-4590	117	16	dg(x1	dg(x1	NOUN
ejpam-4590	117	17	,	,	PUNCT
ejpam-4590	117	18	y1	y1	NOUN
ejpam-4590	117	19	)	)	PUNCT
ejpam-4590	117	20	=	=	SYM
ejpam-4590	117	21	2	2	X
ejpam-4590	117	22	.	.	PUNCT
ejpam-4590	117	23	consequently	consequently	ADV
ejpam-4590	117	24	,	,	PUNCT
ejpam-4590	117	25	s	s	NOUN
ejpam-4590	117	26	=	=	SYM
ejpam-4590	117	27	v	v	X
ejpam-4590	117	28	(	(	PUNCT
ejpam-4590	117	29	g	g	NOUN
ejpam-4590	117	30	)	)	PUNCT
ejpam-4590	117	31	\	\	NOUN
ejpam-4590	117	32	{	{	PUNCT
ejpam-4590	117	33	y1	y1	NOUN
ejpam-4590	117	34	}	}	PUNCT
ejpam-4590	117	35	is	be	AUX
ejpam-4590	117	36	an	an	DET
ejpam-4590	117	37	outer	outer	ADV
ejpam-4590	117	38	-	-	PUNCT
ejpam-4590	117	39	connected	connect	VERB
ejpam-4590	117	40	hop	hop	NOUN
ejpam-4590	117	41	dominating	dominating	NOUN
ejpam-4590	117	42	set	set	NOUN
ejpam-4590	117	43	of	of	ADP
ejpam-4590	117	44	g	g	PROPN
ejpam-4590	117	45	,	,	PUNCT
ejpam-4590	117	46	contrary	contrary	ADJ
ejpam-4590	117	47	to	to	ADP
ejpam-4590	117	48	our	our	PRON
ejpam-4590	117	49	assumption	assumption	NOUN
ejpam-4590	117	50	that	that	SCONJ
ejpam-4590	117	51	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	117	52	)	)	PUNCT
ejpam-4590	117	53	=	=	SYM
ejpam-4590	117	54	|v	|v	PROPN
ejpam-4590	117	55	(	(	PUNCT
ejpam-4590	117	56	g)|	g)|	NOUN
ejpam-4590	117	57	.	.	PUNCT
ejpam-4590	118	1	thus	thus	ADV
ejpam-4590	118	2	,	,	PUNCT
ejpam-4590	118	3	every	every	DET
ejpam-4590	118	4	component	component	NOUN
ejpam-4590	118	5	of	of	ADP
ejpam-4590	118	6	g	g	PROPN
ejpam-4590	118	7	is	be	AUX
ejpam-4590	118	8	complete	complete	ADJ
ejpam-4590	118	9	.	.	PUNCT
ejpam-4590	119	1	suppose	suppose	VERB
ejpam-4590	119	2	every	every	DET
ejpam-4590	119	3	component	component	NOUN
ejpam-4590	119	4	of	of	ADP
ejpam-4590	119	5	g	g	PROPN
ejpam-4590	119	6	is	be	AUX
ejpam-4590	119	7	complete	complete	ADJ
ejpam-4590	119	8	.	.	PUNCT
ejpam-4590	120	1	suppose	suppose	VERB
ejpam-4590	120	2	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	120	3	)	)	PUNCT
ejpam-4590	121	1	=	=	SYM
ejpam-4590	121	2	r	r	NOUN
ejpam-4590	121	3	<	<	X
ejpam-4590	121	4	|v	|v	X
ejpam-4590	121	5	(	(	PUNCT
ejpam-4590	121	6	g)|	g)|	PROPN
ejpam-4590	121	7	,	,	PUNCT
ejpam-4590	121	8	say	say	VERB
ejpam-4590	121	9	s	s	PRON
ejpam-4590	121	10	is	be	AUX
ejpam-4590	121	11	a	a	DET
ejpam-4590	121	12	γ̃ch	γ̃ch	NOUN
ejpam-4590	121	13	-	-	PUNCT
ejpam-4590	121	14	set	set	NOUN
ejpam-4590	121	15	of	of	ADP
ejpam-4590	121	16	g.	g.	PROPN
ejpam-4590	121	17	suppose	suppose	VERB
ejpam-4590	121	18	{	{	PUNCT
ejpam-4590	121	19	g1	g1	PROPN
ejpam-4590	121	20	,	,	PUNCT
ejpam-4590	121	21	g2	g2	PROPN
ejpam-4590	121	22	,	,	PUNCT
ejpam-4590	121	23	...	...	PUNCT
ejpam-4590	121	24	,	,	PUNCT
ejpam-4590	121	25	gk	gk	PROPN
ejpam-4590	121	26	}	}	PUNCT
ejpam-4590	121	27	contains	contain	VERB
ejpam-4590	121	28	all	all	DET
ejpam-4590	121	29	the	the	DET
ejpam-4590	121	30	components	component	NOUN
ejpam-4590	121	31	of	of	ADP
ejpam-4590	121	32	g.	g.	PROPN
ejpam-4590	121	33	since	since	SCONJ
ejpam-4590	121	34	⟨v	⟨v	PROPN
ejpam-4590	121	35	(	(	PUNCT
ejpam-4590	121	36	g	g	NOUN
ejpam-4590	121	37	)	)	PUNCT
ejpam-4590	121	38	\	\	PROPN
ejpam-4590	121	39	s⟩	s⟩	PROPN
ejpam-4590	121	40	is	be	AUX
ejpam-4590	121	41	connected	connect	VERB
ejpam-4590	121	42	,	,	PUNCT
ejpam-4590	121	43	there	there	PRON
ejpam-4590	121	44	exists	exist	VERB
ejpam-4590	121	45	m	m	VERB
ejpam-4590	121	46	∈	∈	NOUN
ejpam-4590	121	47	{	{	PUNCT
ejpam-4590	121	48	1	1	NUM
ejpam-4590	121	49	,	,	PUNCT
ejpam-4590	121	50	2	2	NUM
ejpam-4590	121	51	,	,	PUNCT
ejpam-4590	121	52	...	...	PUNCT
ejpam-4590	121	53	,	,	PUNCT
ejpam-4590	121	54	k	k	X
ejpam-4590	121	55	}	}	PUNCT
ejpam-4590	121	56	such	such	ADJ
ejpam-4590	121	57	that	that	DET
ejpam-4590	121	58	v	v	NOUN
ejpam-4590	121	59	(	(	PUNCT
ejpam-4590	121	60	g	g	NOUN
ejpam-4590	121	61	)	)	PUNCT
ejpam-4590	121	62	\	\	PUNCT
ejpam-4590	122	1	s	s	PART
ejpam-4590	122	2	⊆	⊆	NUM
ejpam-4590	122	3	v	v	NOUN
ejpam-4590	122	4	(	(	PUNCT
ejpam-4590	122	5	gm	gm	PROPN
ejpam-4590	122	6	)	)	PUNCT
ejpam-4590	122	7	.	.	PUNCT
ejpam-4590	123	1	hence	hence	ADV
ejpam-4590	123	2	,	,	PUNCT
ejpam-4590	123	3	s	s	PART
ejpam-4590	123	4	=	=	PUNCT
ejpam-4590	123	5	(	(	PUNCT
ejpam-4590	123	6	v	v	PROPN
ejpam-4590	123	7	(	(	PUNCT
ejpam-4590	123	8	gm	gm	PROPN
ejpam-4590	123	9	)	)	PUNCT
ejpam-4590	123	10	∩	∩	PROPN
ejpam-4590	123	11	s	s	PART
ejpam-4590	123	12	)	)	PUNCT
ejpam-4590	123	13	∪	∪	ADP
ejpam-4590	123	14	[	[	PUNCT
ejpam-4590	123	15	∪j	∪j	X
ejpam-4590	123	16	̸=mv	̸=mv	NOUN
ejpam-4590	123	17	(	(	PUNCT
ejpam-4590	123	18	gj	gj	PROPN
ejpam-4590	123	19	)	)	PUNCT
ejpam-4590	123	20	]	]	PUNCT
ejpam-4590	123	21	.	.	PUNCT
ejpam-4590	124	1	let	let	VERB
ejpam-4590	124	2	v	v	NUM
ejpam-4590	124	3	∈	∈	PROPN
ejpam-4590	124	4	v	v	NOUN
ejpam-4590	124	5	(	(	PUNCT
ejpam-4590	124	6	gm	gm	PROPN
ejpam-4590	124	7	)	)	PUNCT
ejpam-4590	124	8	\	\	PROPN
ejpam-4590	124	9	s	s	PART
ejpam-4590	125	1	(	(	PUNCT
ejpam-4590	125	2	this	this	DET
ejpam-4590	125	3	v	v	NOUN
ejpam-4590	125	4	exists	exist	VERB
ejpam-4590	125	5	because	because	SCONJ
ejpam-4590	125	6	r	r	NOUN
ejpam-4590	125	7	<	<	X
ejpam-4590	125	8	|v	|v	X
ejpam-4590	125	9	(	(	PUNCT
ejpam-4590	125	10	g)|	g)|	PROPN
ejpam-4590	125	11	)	)	PUNCT
ejpam-4590	125	12	.	.	PUNCT
ejpam-4590	126	1	since	since	SCONJ
ejpam-4590	126	2	gm	gm	PROPN
ejpam-4590	126	3	is	be	AUX
ejpam-4590	126	4	complete	complete	ADJ
ejpam-4590	126	5	,	,	PUNCT
ejpam-4590	126	6	dg(v	dg(v	X
ejpam-4590	126	7	,	,	PUNCT
ejpam-4590	126	8	s	s	X
ejpam-4590	126	9	)	)	PUNCT
ejpam-4590	126	10	=	=	SYM
ejpam-4590	126	11	1	1	NUM
ejpam-4590	126	12	for	for	ADP
ejpam-4590	126	13	all	all	DET
ejpam-4590	126	14	s	s	PART
ejpam-4590	126	15	∈	∈	NOUN
ejpam-4590	126	16	v	v	NOUN
ejpam-4590	126	17	(	(	PUNCT
ejpam-4590	126	18	gm	gm	PROPN
ejpam-4590	126	19	)	)	PUNCT
ejpam-4590	126	20	∩	∩	PROPN
ejpam-4590	126	21	s	s	SYM
ejpam-4590	126	22	,	,	PUNCT
ejpam-4590	126	23	contrary	contrary	ADJ
ejpam-4590	126	24	to	to	ADP
ejpam-4590	126	25	the	the	DET
ejpam-4590	126	26	assumption	assumption	NOUN
ejpam-4590	126	27	that	that	SCONJ
ejpam-4590	126	28	s	s	VERB
ejpam-4590	126	29	is	be	AUX
ejpam-4590	126	30	a	a	DET
ejpam-4590	126	31	hop	hop	NOUN
ejpam-4590	126	32	dominating	dominating	NOUN
ejpam-4590	126	33	set	set	NOUN
ejpam-4590	126	34	of	of	ADP
ejpam-4590	126	35	g.	g.	PROPN
ejpam-4590	126	36	therefore	therefore	ADV
ejpam-4590	126	37	,	,	PUNCT
ejpam-4590	126	38	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	126	39	)	)	PUNCT
ejpam-4590	127	1	=	=	SYM
ejpam-4590	127	2	|v	|v	PROPN
ejpam-4590	127	3	(	(	PUNCT
ejpam-4590	127	4	g)|	g)|	PROPN
ejpam-4590	127	5	.	.	PUNCT
ejpam-4590	127	6	corollary	corollary	ADJ
ejpam-4590	128	1	1	1	NUM
ejpam-4590	128	2	.	.	PUNCT
ejpam-4590	129	1	let	let	VERB
ejpam-4590	129	2	g	g	PRON
ejpam-4590	129	3	be	be	AUX
ejpam-4590	129	4	a	a	DET
ejpam-4590	129	5	graph	graph	NOUN
ejpam-4590	129	6	with	with	ADP
ejpam-4590	129	7	n	n	ADP
ejpam-4590	129	8	vertices	vertex	NOUN
ejpam-4590	129	9	.	.	PUNCT
ejpam-4590	130	1	then	then	ADV
ejpam-4590	130	2	γ̃ch(kn	γ̃ch(kn	NOUN
ejpam-4590	130	3	)	)	PUNCT
ejpam-4590	130	4	=	=	SYM
ejpam-4590	130	5	γ̃ch(kn	γ̃ch(kn	NOUN
ejpam-4590	130	6	)	)	PUNCT
ejpam-4590	130	7	=	=	PUNCT
ejpam-4590	131	1	n.	n.	PROPN
ejpam-4590	131	2	c.j	c.j	PROPN
ejpam-4590	131	3	.	.	PROPN
ejpam-4590	131	4	saromines	saromines	PROPN
ejpam-4590	131	5	,	,	PUNCT
ejpam-4590	131	6	s.	s.	PROPN
ejpam-4590	131	7	canoy	canoy	PROPN
ejpam-4590	131	8	,	,	PUNCT
ejpam-4590	131	9	jr	jr	PROPN
ejpam-4590	131	10	.	.	PROPN
ejpam-4590	131	11	/	/	SYM
ejpam-4590	131	12	eur	eur	PROPN
ejpam-4590	131	13	.	.	PUNCT
ejpam-4590	132	1	j.	j.	PROPN
ejpam-4590	132	2	pure	pure	PROPN
ejpam-4590	132	3	appl	appl	PROPN
ejpam-4590	132	4	.	.	PROPN
ejpam-4590	132	5	math	math	PROPN
ejpam-4590	132	6	,	,	PUNCT
ejpam-4590	132	7	15	15	NUM
ejpam-4590	132	8	(	(	PUNCT
ejpam-4590	132	9	4	4	NUM
ejpam-4590	132	10	)	)	PUNCT
ejpam-4590	132	11	(	(	PUNCT
ejpam-4590	132	12	2022	2022	NUM
ejpam-4590	132	13	)	)	PUNCT
ejpam-4590	132	14	,	,	PUNCT
ejpam-4590	132	15	1966	1966	NUM
ejpam-4590	132	16	-	-	SYM
ejpam-4590	132	17	1981	1981	NUM
ejpam-4590	132	18	1970	1970	NUM
ejpam-4590	132	19	proposition	proposition	NOUN
ejpam-4590	132	20	2	2	NUM
ejpam-4590	132	21	.	.	PUNCT
ejpam-4590	133	1	let	let	VERB
ejpam-4590	133	2	n	n	PRON
ejpam-4590	133	3	be	be	AUX
ejpam-4590	133	4	a	a	DET
ejpam-4590	133	5	positive	positive	ADJ
ejpam-4590	133	6	integer	integer	NOUN
ejpam-4590	133	7	.	.	PUNCT
ejpam-4590	134	1	(	(	PUNCT
ejpam-4590	134	2	i	i	NOUN
ejpam-4590	134	3	)	)	PUNCT
ejpam-4590	134	4	for	for	ADP
ejpam-4590	134	5	path	path	NOUN
ejpam-4590	134	6	pn	pn	PROPN
ejpam-4590	134	7	on	on	ADP
ejpam-4590	134	8	n	n	PRON
ejpam-4590	134	9	vertices	vertex	NOUN
ejpam-4590	134	10	,	,	PUNCT
ejpam-4590	134	11	γ̃ch(pn	γ̃ch(pn	NOUN
ejpam-4590	134	12	)	)	PUNCT
ejpam-4590	134	13	=	=	PUNCT
ejpam-4590	135	1			NOUN
ejpam-4590	135	2	2	2	NUM
ejpam-4590	135	3	,	,	PUNCT
ejpam-4590	135	4	if	if	SCONJ
ejpam-4590	135	5	n	n	NOUN
ejpam-4590	135	6	=	=	SYM
ejpam-4590	135	7	3	3	NUM
ejpam-4590	135	8	n−	n−	NOUN
ejpam-4590	135	9	2	2	NUM
ejpam-4590	135	10	,	,	PUNCT
ejpam-4590	135	11	if	if	SCONJ
ejpam-4590	135	12	n	n	NOUN
ejpam-4590	135	13	=	=	SYM
ejpam-4590	135	14	4	4	NUM
ejpam-4590	135	15	,	,	PUNCT
ejpam-4590	135	16	5	5	NUM
ejpam-4590	135	17	,	,	PUNCT
ejpam-4590	135	18	6	6	NUM
ejpam-4590	135	19	n−	n−	NOUN
ejpam-4590	135	20	3	3	NUM
ejpam-4590	135	21	,	,	PUNCT
ejpam-4590	135	22	if	if	SCONJ
ejpam-4590	135	23	n	n	NOUN
ejpam-4590	135	24	=	=	SYM
ejpam-4590	135	25	7	7	NUM
ejpam-4590	135	26	n−	n−	NOUN
ejpam-4590	135	27	4	4	NUM
ejpam-4590	135	28	,	,	PUNCT
ejpam-4590	135	29	if	if	SCONJ
ejpam-4590	135	30	n	n	PRON
ejpam-4590	135	31	≥	≥	NOUN
ejpam-4590	135	32	8	8	NUM
ejpam-4590	135	33	.	.	PUNCT
ejpam-4590	135	34	(	(	PUNCT
ejpam-4590	135	35	ii	ii	NOUN
ejpam-4590	135	36	)	)	PUNCT
ejpam-4590	135	37	for	for	ADP
ejpam-4590	135	38	cycle	cycle	NOUN
ejpam-4590	135	39	cn	cn	PROPN
ejpam-4590	135	40	on	on	ADP
ejpam-4590	135	41	n	n	PRON
ejpam-4590	135	42	vertices	vertex	NOUN
ejpam-4590	135	43	,	,	PUNCT
ejpam-4590	135	44	γ̃ch(cn	γ̃ch(cn	NOUN
ejpam-4590	135	45	)	)	PUNCT
ejpam-4590	135	46	=	=	PUNCT
ejpam-4590	136	1			NOUN
ejpam-4590	136	2	3	3	NUM
ejpam-4590	136	3	,	,	PUNCT
ejpam-4590	136	4	if	if	SCONJ
ejpam-4590	136	5	n	n	NOUN
ejpam-4590	136	6	=	=	SYM
ejpam-4590	136	7	3	3	NUM
ejpam-4590	136	8	2	2	NUM
ejpam-4590	136	9	,	,	PUNCT
ejpam-4590	136	10	if	if	SCONJ
ejpam-4590	136	11	n	n	NOUN
ejpam-4590	136	12	=	=	SYM
ejpam-4590	136	13	4	4	NUM
ejpam-4590	136	14	,	,	PUNCT
ejpam-4590	136	15	5	5	NUM
ejpam-4590	136	16	n−	n−	NOUN
ejpam-4590	136	17	4	4	NUM
ejpam-4590	136	18	,	,	PUNCT
ejpam-4590	136	19	if	if	SCONJ
ejpam-4590	136	20	n	n	PRON
ejpam-4590	136	21	≥	≥	NOUN
ejpam-4590	136	22	6	6	NUM
ejpam-4590	136	23	.	.	PUNCT
ejpam-4590	137	1	proof	proof	NOUN
ejpam-4590	137	2	.	.	PUNCT
ejpam-4590	138	1	(	(	PUNCT
ejpam-4590	138	2	i	i	NOUN
ejpam-4590	138	3	)	)	PUNCT
ejpam-4590	138	4	let	let	VERB
ejpam-4590	138	5	pn	pn	NOUN
ejpam-4590	138	6	=	=	PUNCT
ejpam-4590	139	1	[	[	X
ejpam-4590	139	2	v1	v1	NOUN
ejpam-4590	139	3	,	,	PUNCT
ejpam-4590	139	4	v2	v2	PROPN
ejpam-4590	139	5	,	,	PUNCT
ejpam-4590	139	6	...	...	PUNCT
ejpam-4590	139	7	,	,	PUNCT
ejpam-4590	139	8	vn	vn	X
ejpam-4590	139	9	]	]	PUNCT
ejpam-4590	139	10	.	.	PUNCT
ejpam-4590	140	1	clearly	clearly	ADV
ejpam-4590	140	2	,	,	PUNCT
ejpam-4590	140	3	γ̃ch(pn	γ̃ch(pn	NOUN
ejpam-4590	140	4	)	)	PUNCT
ejpam-4590	140	5	=	=	SYM
ejpam-4590	140	6	2	2	NUM
ejpam-4590	140	7	for	for	ADP
ejpam-4590	140	8	n	n	NOUN
ejpam-4590	140	9	=	=	SYM
ejpam-4590	140	10	3	3	NUM
ejpam-4590	140	11	,	,	PUNCT
ejpam-4590	140	12	4	4	NUM
ejpam-4590	140	13	.	.	PUNCT
ejpam-4590	141	1	let	let	VERB
ejpam-4590	141	2	n	n	PRON
ejpam-4590	141	3	≥	≥	X
ejpam-4590	141	4	5	5	NUM
ejpam-4590	141	5	and	and	CCONJ
ejpam-4590	141	6	let	let	VERB
ejpam-4590	141	7	s	s	PRON
ejpam-4590	141	8	be	be	AUX
ejpam-4590	141	9	a	a	DET
ejpam-4590	141	10	γ̃ch	γ̃ch	NOUN
ejpam-4590	141	11	-	-	PUNCT
ejpam-4590	141	12	set	set	NOUN
ejpam-4590	141	13	of	of	ADP
ejpam-4590	141	14	pn	pn	PROPN
ejpam-4590	141	15	.	.	PUNCT
ejpam-4590	142	1	since	since	SCONJ
ejpam-4590	142	2	⟨v	⟨v	PROPN
ejpam-4590	142	3	(	(	PUNCT
ejpam-4590	142	4	pn	pn	NOUN
ejpam-4590	142	5	)	)	PUNCT
ejpam-4590	142	6	\	\	PROPN
ejpam-4590	142	7	s⟩	s⟩	PROPN
ejpam-4590	142	8	is	be	AUX
ejpam-4590	142	9	connected	connect	VERB
ejpam-4590	142	10	and	and	CCONJ
ejpam-4590	142	11	s	s	VERB
ejpam-4590	142	12	is	be	AUX
ejpam-4590	142	13	a	a	DET
ejpam-4590	142	14	hop	hop	NOUN
ejpam-4590	142	15	dominating	dominating	NOUN
ejpam-4590	142	16	set	set	NOUN
ejpam-4590	142	17	,	,	PUNCT
ejpam-4590	143	1	2	2	NUM
ejpam-4590	143	2	≤	≤	NOUN
ejpam-4590	143	3	|v	|v	X
ejpam-4590	143	4	(	(	PUNCT
ejpam-4590	143	5	pn	pn	NOUN
ejpam-4590	143	6	)	)	PUNCT
ejpam-4590	143	7	\	\	PROPN
ejpam-4590	143	8	s|	s|	VERB
ejpam-4590	143	9	≤	≤	NUM
ejpam-4590	143	10	4	4	NUM
ejpam-4590	143	11	.	.	PUNCT
ejpam-4590	143	12	clearly	clearly	ADV
ejpam-4590	143	13	,	,	PUNCT
ejpam-4590	143	14	at	at	ADV
ejpam-4590	143	15	least	least	ADJ
ejpam-4590	143	16	one	one	NUM
ejpam-4590	143	17	of	of	ADP
ejpam-4590	143	18	v1	v1	NOUN
ejpam-4590	143	19	and	and	CCONJ
ejpam-4590	143	20	vn	vn	PROPN
ejpam-4590	143	21	is	be	AUX
ejpam-4590	143	22	in	in	ADP
ejpam-4590	143	23	s.	s.	PROPN
ejpam-4590	143	24	suppose	suppose	VERB
ejpam-4590	143	25	that	that	SCONJ
ejpam-4590	143	26	v1	v1	PROPN
ejpam-4590	143	27	∈	∈	PROPN
ejpam-4590	143	28	s.	s.	PROPN
ejpam-4590	143	29	suppose	suppose	VERB
ejpam-4590	143	30	further	far	ADV
ejpam-4590	143	31	that	that	SCONJ
ejpam-4590	143	32	|v	|v	PROPN
ejpam-4590	143	33	(	(	PUNCT
ejpam-4590	143	34	pn	pn	NOUN
ejpam-4590	143	35	)	)	PUNCT
ejpam-4590	143	36	\	\	PROPN
ejpam-4590	143	37	s|	s|	NOUN
ejpam-4590	143	38	=	=	SYM
ejpam-4590	144	1	2	2	X
ejpam-4590	144	2	.	.	PUNCT
ejpam-4590	144	3	then	then	ADV
ejpam-4590	144	4	n	n	CCONJ
ejpam-4590	144	5	=	=	SYM
ejpam-4590	144	6	5	5	NUM
ejpam-4590	144	7	or	or	CCONJ
ejpam-4590	144	8	n	n	NOUN
ejpam-4590	144	9	=	=	SYM
ejpam-4590	144	10	6	6	NUM
ejpam-4590	144	11	.	.	PUNCT
ejpam-4590	145	1	hence	hence	ADV
ejpam-4590	145	2	,	,	PUNCT
ejpam-4590	145	3	γ̃ch(p5	γ̃ch(p5	NOUN
ejpam-4590	145	4	)	)	PUNCT
ejpam-4590	145	5	=	=	SYM
ejpam-4590	146	1	5	5	NUM
ejpam-4590	146	2	−	−	NUM
ejpam-4590	146	3	2	2	NUM
ejpam-4590	146	4	=	=	SYM
ejpam-4590	146	5	3	3	NUM
ejpam-4590	146	6	and	and	CCONJ
ejpam-4590	146	7	γ̃ch(p6	γ̃ch(p6	NOUN
ejpam-4590	146	8	)	)	PUNCT
ejpam-4590	146	9	=	=	SYM
ejpam-4590	147	1	6	6	NUM
ejpam-4590	147	2	−	−	NUM
ejpam-4590	147	3	2	2	NUM
ejpam-4590	147	4	=	=	SYM
ejpam-4590	147	5	4	4	NUM
ejpam-4590	147	6	.	.	PUNCT
ejpam-4590	148	1	next	next	ADV
ejpam-4590	148	2	,	,	PUNCT
ejpam-4590	148	3	suppose	suppose	VERB
ejpam-4590	148	4	that	that	SCONJ
ejpam-4590	148	5	|v	|v	PROPN
ejpam-4590	148	6	(	(	PUNCT
ejpam-4590	148	7	pn	pn	NOUN
ejpam-4590	148	8	)	)	PUNCT
ejpam-4590	148	9	\	\	NOUN
ejpam-4590	148	10	s|	s|	NOUN
ejpam-4590	148	11	=	=	SYM
ejpam-4590	149	1	3	3	X
ejpam-4590	149	2	.	.	X
ejpam-4590	150	1	if	if	SCONJ
ejpam-4590	150	2	p	p	NOUN
ejpam-4590	150	3	is	be	AUX
ejpam-4590	150	4	the	the	DET
ejpam-4590	150	5	smallest	small	ADJ
ejpam-4590	150	6	positive	positive	ADJ
ejpam-4590	150	7	integer	integer	NOUN
ejpam-4590	150	8	such	such	ADJ
ejpam-4590	150	9	that	that	DET
ejpam-4590	150	10	vp	vp	PROPN
ejpam-4590	150	11	/∈	/∈	PUNCT
ejpam-4590	151	1	s	s	X
ejpam-4590	151	2	,	,	PUNCT
ejpam-4590	151	3	then	then	ADV
ejpam-4590	151	4	p	p	X
ejpam-4590	151	5	/∈	/∈	PUNCT
ejpam-4590	151	6	{	{	PUNCT
ejpam-4590	151	7	1	1	NUM
ejpam-4590	151	8	,	,	PUNCT
ejpam-4590	151	9	2	2	NUM
ejpam-4590	151	10	,	,	PUNCT
ejpam-4590	151	11	n−	n−	NOUN
ejpam-4590	151	12	3	3	NUM
ejpam-4590	151	13	,	,	PUNCT
ejpam-4590	151	14	n−	n−	NOUN
ejpam-4590	151	15	2	2	NUM
ejpam-4590	151	16	}	}	PUNCT
ejpam-4590	151	17	.	.	PUNCT
ejpam-4590	152	1	it	it	PRON
ejpam-4590	152	2	follows	follow	VERB
ejpam-4590	152	3	that	that	SCONJ
ejpam-4590	152	4	v1	v1	NOUN
ejpam-4590	152	5	,	,	PUNCT
ejpam-4590	152	6	v2	v2	PROPN
ejpam-4590	152	7	,	,	PUNCT
ejpam-4590	152	8	vn−1	vn−1	PROPN
ejpam-4590	152	9	,	,	PUNCT
ejpam-4590	152	10	vn	vn	PROPN
ejpam-4590	152	11	∈	∈	PROPN
ejpam-4590	152	12	s.	s.	PROPN
ejpam-4590	152	13	in	in	ADP
ejpam-4590	152	14	this	this	DET
ejpam-4590	152	15	case	case	NOUN
ejpam-4590	152	16	,	,	PUNCT
ejpam-4590	152	17	it	it	PRON
ejpam-4590	152	18	can	can	AUX
ejpam-4590	152	19	easily	easily	ADV
ejpam-4590	152	20	be	be	AUX
ejpam-4590	152	21	verified	verify	VERB
ejpam-4590	152	22	that	that	SCONJ
ejpam-4590	152	23	n	n	NOUN
ejpam-4590	152	24	=	=	SYM
ejpam-4590	152	25	7	7	NUM
ejpam-4590	152	26	,	,	PUNCT
ejpam-4590	152	27	and	and	CCONJ
ejpam-4590	152	28	so	so	ADV
ejpam-4590	152	29	γ̃ch(p7	γ̃ch(p7	NUM
ejpam-4590	152	30	)	)	PUNCT
ejpam-4590	153	1	=	=	PUNCT
ejpam-4590	154	1	7−	7−	NUM
ejpam-4590	154	2	3	3	NUM
ejpam-4590	154	3	=	=	SYM
ejpam-4590	154	4	4	4	NUM
ejpam-4590	154	5	.	.	NOUN
ejpam-4590	154	6	for	for	ADP
ejpam-4590	154	7	n	n	NUM
ejpam-4590	154	8	≥	≥	NUM
ejpam-4590	154	9	8	8	NUM
ejpam-4590	154	10	,	,	PUNCT
ejpam-4590	154	11	the	the	DET
ejpam-4590	154	12	set	set	NOUN
ejpam-4590	154	13	s	s	PART
ejpam-4590	154	14	′	′	NOUN
ejpam-4590	154	15	=	=	SYM
ejpam-4590	154	16	v	v	NOUN
ejpam-4590	154	17	(	(	PUNCT
ejpam-4590	154	18	pn	pn	NOUN
ejpam-4590	154	19	)	)	PUNCT
ejpam-4590	154	20	\	\	PROPN
ejpam-4590	154	21	{	{	PUNCT
ejpam-4590	154	22	v3	v3	PROPN
ejpam-4590	154	23	,	,	PUNCT
ejpam-4590	154	24	v4	v4	PROPN
ejpam-4590	154	25	,	,	PUNCT
ejpam-4590	154	26	v5	v5	PROPN
ejpam-4590	154	27	,	,	PUNCT
ejpam-4590	154	28	v6	v6	NOUN
ejpam-4590	154	29	}	}	PUNCT
ejpam-4590	154	30	is	be	AUX
ejpam-4590	154	31	clearly	clearly	ADV
ejpam-4590	154	32	an	an	DET
ejpam-4590	154	33	outer	outer	ADV
ejpam-4590	154	34	-	-	PUNCT
ejpam-4590	154	35	connected	connect	VERB
ejpam-4590	154	36	hop	hop	NOUN
ejpam-4590	154	37	dominating	dominating	NOUN
ejpam-4590	154	38	set	set	NOUN
ejpam-4590	154	39	.	.	PUNCT
ejpam-4590	155	1	thus	thus	ADV
ejpam-4590	155	2	,	,	PUNCT
ejpam-4590	155	3	γ̃ch(pn	γ̃ch(pn	NOUN
ejpam-4590	155	4	)	)	PUNCT
ejpam-4590	155	5	=	=	PUNCT
ejpam-4590	156	1	n−	n−	NOUN
ejpam-4590	156	2	4	4	NUM
ejpam-4590	156	3	for	for	ADP
ejpam-4590	156	4	all	all	DET
ejpam-4590	156	5	.n	.n	PROPN
ejpam-4590	156	6	≥	≥	NUM
ejpam-4590	156	7	8	8	NUM
ejpam-4590	156	8	.	.	PUNCT
ejpam-4590	157	1	(	(	PUNCT
ejpam-4590	157	2	ii	ii	NOUN
ejpam-4590	157	3	)	)	PUNCT
ejpam-4590	157	4	let	let	VERB
ejpam-4590	157	5	cn	cn	PROPN
ejpam-4590	157	6	=	=	PUNCT
ejpam-4590	158	1	[	[	X
ejpam-4590	158	2	v1	v1	NOUN
ejpam-4590	158	3	,	,	PUNCT
ejpam-4590	158	4	v2	v2	PROPN
ejpam-4590	158	5	,	,	PUNCT
ejpam-4590	158	6	...	...	PUNCT
ejpam-4590	158	7	,	,	PUNCT
ejpam-4590	158	8	vn	vn	X
ejpam-4590	158	9	,	,	PUNCT
ejpam-4590	158	10	v1	v1	PROPN
ejpam-4590	158	11	]	]	PUNCT
ejpam-4590	158	12	.	.	PUNCT
ejpam-4590	159	1	clearly	clearly	ADV
ejpam-4590	159	2	,	,	PUNCT
ejpam-4590	159	3	γ̃ch(c3	γ̃ch(c3	NOUN
ejpam-4590	159	4	)	)	PUNCT
ejpam-4590	159	5	=	=	SYM
ejpam-4590	159	6	γ̃ch(k3	γ̃ch(k3	PROPN
ejpam-4590	159	7	)	)	PUNCT
ejpam-4590	159	8	=	=	SYM
ejpam-4590	160	1	3	3	X
ejpam-4590	160	2	.	.	X
ejpam-4590	160	3	let	let	VERB
ejpam-4590	160	4	n	n	PRON
ejpam-4590	160	5	≥	≥	X
ejpam-4590	160	6	4	4	NUM
ejpam-4590	160	7	and	and	CCONJ
ejpam-4590	160	8	let	let	VERB
ejpam-4590	160	9	s	s	PRON
ejpam-4590	160	10	be	be	AUX
ejpam-4590	160	11	a	a	DET
ejpam-4590	160	12	γ̃ch	γ̃ch	NOUN
ejpam-4590	160	13	-	-	PUNCT
ejpam-4590	160	14	set	set	NOUN
ejpam-4590	160	15	of	of	ADP
ejpam-4590	160	16	cn	cn	PROPN
ejpam-4590	160	17	.	.	PUNCT
ejpam-4590	161	1	since	since	SCONJ
ejpam-4590	161	2	⟨v	⟨v	PROPN
ejpam-4590	161	3	(	(	PUNCT
ejpam-4590	161	4	cn	cn	PROPN
ejpam-4590	161	5	)	)	PUNCT
ejpam-4590	161	6	\	\	PROPN
ejpam-4590	161	7	s⟩	s⟩	PROPN
ejpam-4590	161	8	is	be	AUX
ejpam-4590	161	9	connected	connect	VERB
ejpam-4590	161	10	and	and	CCONJ
ejpam-4590	161	11	s	s	VERB
ejpam-4590	161	12	is	be	AUX
ejpam-4590	161	13	a	a	DET
ejpam-4590	161	14	hop	hop	NOUN
ejpam-4590	161	15	dominating	dominating	NOUN
ejpam-4590	161	16	set	set	NOUN
ejpam-4590	161	17	,	,	PUNCT
ejpam-4590	162	1	2	2	NUM
ejpam-4590	162	2	≤	≤	NOUN
ejpam-4590	162	3	|v	|v	X
ejpam-4590	162	4	(	(	PUNCT
ejpam-4590	162	5	cn	cn	PROPN
ejpam-4590	162	6	)	)	PUNCT
ejpam-4590	162	7	\	\	PROPN
ejpam-4590	162	8	s|	s|	VERB
ejpam-4590	162	9	≤	≤	NUM
ejpam-4590	162	10	4	4	NUM
ejpam-4590	162	11	.	.	PUNCT
ejpam-4590	163	1	if	if	SCONJ
ejpam-4590	163	2	|v	|v	PROPN
ejpam-4590	163	3	(	(	PUNCT
ejpam-4590	163	4	cn	cn	PROPN
ejpam-4590	163	5	)	)	PUNCT
ejpam-4590	163	6	\	\	PROPN
ejpam-4590	163	7	s|	s|	NOUN
ejpam-4590	163	8	=	=	SYM
ejpam-4590	163	9	2	2	NUM
ejpam-4590	163	10	,	,	PUNCT
ejpam-4590	163	11	then	then	ADV
ejpam-4590	163	12	n	n	NOUN
ejpam-4590	163	13	=	=	SYM
ejpam-4590	163	14	4	4	NUM
ejpam-4590	163	15	.	.	PUNCT
ejpam-4590	164	1	thus	thus	ADV
ejpam-4590	164	2	,	,	PUNCT
ejpam-4590	164	3	γ̃ch(c4	γ̃ch(c4	NOUN
ejpam-4590	164	4	)	)	PUNCT
ejpam-4590	165	1	=	=	SYM
ejpam-4590	165	2	2	2	X
ejpam-4590	165	3	.	.	X
ejpam-4590	166	1	if	if	SCONJ
ejpam-4590	166	2	|v	|v	PROPN
ejpam-4590	166	3	(	(	PUNCT
ejpam-4590	166	4	cn	cn	PROPN
ejpam-4590	166	5	)	)	PUNCT
ejpam-4590	166	6	\	\	PROPN
ejpam-4590	166	7	s|	s|	NOUN
ejpam-4590	166	8	=	=	SYM
ejpam-4590	166	9	3	3	NUM
ejpam-4590	166	10	,	,	PUNCT
ejpam-4590	166	11	then	then	ADV
ejpam-4590	166	12	n	n	NOUN
ejpam-4590	166	13	=	=	SYM
ejpam-4590	166	14	5	5	NUM
ejpam-4590	166	15	.	.	PUNCT
ejpam-4590	167	1	hence	hence	ADV
ejpam-4590	167	2	,	,	PUNCT
ejpam-4590	167	3	γ̃ch(c5	γ̃ch(c5	PROPN
ejpam-4590	167	4	)	)	PUNCT
ejpam-4590	167	5	=	=	SYM
ejpam-4590	168	1	2	2	X
ejpam-4590	168	2	.	.	X
ejpam-4590	168	3	suppose	suppose	VERB
ejpam-4590	168	4	n	n	PRON
ejpam-4590	168	5	≥	≥	NUM
ejpam-4590	168	6	6	6	NUM
ejpam-4590	168	7	.	.	PUNCT
ejpam-4590	169	1	then	then	ADV
ejpam-4590	169	2	v	v	INTJ
ejpam-4590	169	3	(	(	PUNCT
ejpam-4590	169	4	cn	cn	PROPN
ejpam-4590	169	5	)	)	PUNCT
ejpam-4590	169	6	\	\	NOUN
ejpam-4590	169	7	{	{	PUNCT
ejpam-4590	169	8	v2	v2	PROPN
ejpam-4590	169	9	,	,	PUNCT
ejpam-4590	169	10	v3	v3	PROPN
ejpam-4590	169	11	,	,	PUNCT
ejpam-4590	169	12	v4	v4	PROPN
ejpam-4590	169	13	,	,	PUNCT
ejpam-4590	169	14	v5	v5	PROPN
ejpam-4590	169	15	}	}	PUNCT
ejpam-4590	169	16	is	be	AUX
ejpam-4590	169	17	an	an	DET
ejpam-4590	169	18	outer	outer	ADV
ejpam-4590	169	19	-	-	PUNCT
ejpam-4590	169	20	connected	connect	VERB
ejpam-4590	169	21	hop	hop	NOUN
ejpam-4590	169	22	dominating	dominating	NOUN
ejpam-4590	169	23	set	set	NOUN
ejpam-4590	169	24	of	of	ADP
ejpam-4590	169	25	cn	cn	PROPN
ejpam-4590	169	26	.	.	PUNCT
ejpam-4590	170	1	therefore	therefore	ADV
ejpam-4590	170	2	,	,	PUNCT
ejpam-4590	170	3	γ̃ch(cn	γ̃ch(cn	NOUN
ejpam-4590	170	4	)	)	PUNCT
ejpam-4590	171	1	=	=	PUNCT
ejpam-4590	171	2	n−	n−	NOUN
ejpam-4590	171	3	4	4	NUM
ejpam-4590	171	4	.	.	PUNCT
ejpam-4590	171	5	theorem	theorem	NOUN
ejpam-4590	171	6	5	5	NUM
ejpam-4590	171	7	.	.	PUNCT
ejpam-4590	172	1	let	let	VERB
ejpam-4590	172	2	a	a	PRON
ejpam-4590	172	3	and	and	CCONJ
ejpam-4590	172	4	b	b	NOUN
ejpam-4590	172	5	be	be	AUX
ejpam-4590	172	6	positive	positive	ADJ
ejpam-4590	172	7	integers	integer	NOUN
ejpam-4590	172	8	such	such	ADJ
ejpam-4590	172	9	that	that	SCONJ
ejpam-4590	172	10	2	2	NUM
ejpam-4590	172	11	≤	≤	NOUN
ejpam-4590	172	12	a	a	DET
ejpam-4590	172	13	≤	≤	NUM
ejpam-4590	172	14	b	b	NOUN
ejpam-4590	172	15	≤	≤	ADJ
ejpam-4590	172	16	n.	n.	NOUN
ejpam-4590	172	17	then	then	ADV
ejpam-4590	172	18	there	there	PRON
ejpam-4590	172	19	exists	exist	VERB
ejpam-4590	172	20	a	a	DET
ejpam-4590	172	21	connected	connected	ADJ
ejpam-4590	172	22	graph	graph	NOUN
ejpam-4590	172	23	g	g	ADP
ejpam-4590	172	24	such	such	ADJ
ejpam-4590	172	25	that	that	PRON
ejpam-4590	172	26	γh(g	γh(g	NOUN
ejpam-4590	172	27	)	)	PUNCT
ejpam-4590	172	28	=	=	PUNCT
ejpam-4590	172	29	a	a	PRON
ejpam-4590	172	30	and	and	CCONJ
ejpam-4590	172	31	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	172	32	)	)	PUNCT
ejpam-4590	172	33	=	=	SYM
ejpam-4590	172	34	b.	b.	NOUN
ejpam-4590	172	35	proof	proof	NOUN
ejpam-4590	172	36	.	.	PUNCT
ejpam-4590	173	1	suppose	suppose	VERB
ejpam-4590	173	2	that	that	SCONJ
ejpam-4590	173	3	a	a	DET
ejpam-4590	173	4	=	=	X
ejpam-4590	173	5	b.	b.	NOUN
ejpam-4590	173	6	consider	consider	VERB
ejpam-4590	173	7	the	the	DET
ejpam-4590	173	8	graph	graph	NOUN
ejpam-4590	173	9	g	g	PROPN
ejpam-4590	173	10	=	=	SYM
ejpam-4590	173	11	ka	ka	PROPN
ejpam-4590	173	12	.	.	PROPN
ejpam-4590	173	13	then	then	ADV
ejpam-4590	173	14	γh(g	γh(g	NOUN
ejpam-4590	173	15	)	)	PUNCT
ejpam-4590	173	16	=	=	SYM
ejpam-4590	173	17	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	173	18	)	)	PUNCT
ejpam-4590	173	19	=	=	PUNCT
ejpam-4590	173	20	a.	a.	NOUN
ejpam-4590	173	21	next	next	ADV
ejpam-4590	173	22	,	,	PUNCT
ejpam-4590	173	23	suppose	suppose	VERB
ejpam-4590	173	24	that	that	SCONJ
ejpam-4590	173	25	a	a	DET
ejpam-4590	173	26	<	<	X
ejpam-4590	173	27	b.	b.	NOUN
ejpam-4590	173	28	consider	consider	VERB
ejpam-4590	173	29	the	the	DET
ejpam-4590	173	30	following	follow	VERB
ejpam-4590	173	31	cases	case	NOUN
ejpam-4590	173	32	:	:	PUNCT
ejpam-4590	173	33	case	case	NOUN
ejpam-4590	173	34	1	1	NUM
ejpam-4590	173	35	.	.	PUNCT
ejpam-4590	174	1	a	a	DET
ejpam-4590	174	2	=	=	ADJ
ejpam-4590	174	3	2	2	X
ejpam-4590	174	4	.	.	PUNCT
ejpam-4590	174	5	let	let	VERB
ejpam-4590	174	6	m	m	VERB
ejpam-4590	174	7	=	=	VERB
ejpam-4590	175	1	b	b	X
ejpam-4590	175	2	−	−	PROPN
ejpam-4590	175	3	a	a	PRON
ejpam-4590	176	1	and	and	CCONJ
ejpam-4590	176	2	consider	consider	VERB
ejpam-4590	176	3	the	the	DET
ejpam-4590	176	4	graph	graph	NOUN
ejpam-4590	176	5	g	g	NOUN
ejpam-4590	176	6	in	in	ADP
ejpam-4590	176	7	figure	figure	NOUN
ejpam-4590	176	8	1	1	NUM
ejpam-4590	176	9	.	.	PUNCT
ejpam-4590	177	1	let	let	VERB
ejpam-4590	177	2	s1	s1	PROPN
ejpam-4590	177	3	=	=	PUNCT
ejpam-4590	177	4	{	{	PUNCT
ejpam-4590	177	5	y1	y1	PROPN
ejpam-4590	177	6	,	,	PUNCT
ejpam-4590	177	7	y2	y2	NOUN
ejpam-4590	177	8	}	}	PUNCT
ejpam-4590	177	9	and	and	CCONJ
ejpam-4590	177	10	s2	s2	VERB
ejpam-4590	177	11	=	=	SYM
ejpam-4590	177	12	{	{	PUNCT
ejpam-4590	177	13	x1	x1	PROPN
ejpam-4590	177	14	,	,	PUNCT
ejpam-4590	177	15	x2	x2	PROPN
ejpam-4590	177	16	,	,	PUNCT
ejpam-4590	177	17	z1	z1	PROPN
ejpam-4590	177	18	,	,	PUNCT
ejpam-4590	177	19	...	...	PUNCT
ejpam-4590	177	20	,	,	PUNCT
ejpam-4590	177	21	zm	zm	PROPN
ejpam-4590	177	22	}	}	PUNCT
ejpam-4590	177	23	.	.	PUNCT
ejpam-4590	178	1	then	then	ADV
ejpam-4590	178	2	s1	s1	PROPN
ejpam-4590	178	3	and	and	CCONJ
ejpam-4590	178	4	s2	s2	PROPN
ejpam-4590	178	5	are	be	AUX
ejpam-4590	178	6	γh	γh	ADV
ejpam-4590	178	7	-	-	PUNCT
ejpam-4590	178	8	set	set	VERB
ejpam-4590	178	9	and	and	CCONJ
ejpam-4590	178	10	γ̃ch	γ̃ch	PROPN
ejpam-4590	178	11	-	-	PUNCT
ejpam-4590	178	12	set	set	NOUN
ejpam-4590	178	13	,	,	PUNCT
ejpam-4590	178	14	respectively	respectively	ADV
ejpam-4590	178	15	,	,	PUNCT
ejpam-4590	178	16	of	of	ADP
ejpam-4590	178	17	g.	g.	PROPN
ejpam-4590	178	18	hence	hence	ADV
ejpam-4590	178	19	,	,	PUNCT
ejpam-4590	178	20	γh(g	γh(g	NOUN
ejpam-4590	178	21	)	)	PUNCT
ejpam-4590	178	22	=	=	SYM
ejpam-4590	178	23	a	a	PRON
ejpam-4590	178	24	and	and	CCONJ
ejpam-4590	178	25	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	178	26	)	)	PUNCT
ejpam-4590	178	27	=	=	PUNCT
ejpam-4590	179	1	a+m	a+m	NUM
ejpam-4590	179	2	=	=	PUNCT
ejpam-4590	179	3	b.	b.	PROPN
ejpam-4590	179	4	c.j	c.j	PROPN
ejpam-4590	179	5	.	.	PROPN
ejpam-4590	179	6	saromines	saromines	PROPN
ejpam-4590	179	7	,	,	PUNCT
ejpam-4590	179	8	s.	s.	PROPN
ejpam-4590	179	9	canoy	canoy	PROPN
ejpam-4590	179	10	,	,	PUNCT
ejpam-4590	179	11	jr	jr	PROPN
ejpam-4590	179	12	.	.	PROPN
ejpam-4590	179	13	/	/	SYM
ejpam-4590	179	14	eur	eur	PROPN
ejpam-4590	179	15	.	.	PUNCT
ejpam-4590	180	1	j.	j.	PROPN
ejpam-4590	180	2	pure	pure	PROPN
ejpam-4590	180	3	appl	appl	PROPN
ejpam-4590	180	4	.	.	PROPN
ejpam-4590	180	5	math	math	PROPN
ejpam-4590	180	6	,	,	PUNCT
ejpam-4590	180	7	15	15	NUM
ejpam-4590	180	8	(	(	PUNCT
ejpam-4590	180	9	4	4	NUM
ejpam-4590	180	10	)	)	PUNCT
ejpam-4590	180	11	(	(	PUNCT
ejpam-4590	180	12	2022	2022	NUM
ejpam-4590	180	13	)	)	PUNCT
ejpam-4590	180	14	,	,	PUNCT
ejpam-4590	180	15	1966	1966	NUM
ejpam-4590	180	16	-	-	SYM
ejpam-4590	180	17	1981	1981	NUM
ejpam-4590	180	18	1971	1971	NUM
ejpam-4590	180	19	....................................	....................................	PUNCT
ejpam-4590	180	20	....................................	....................................	PUNCT
ejpam-4590	181	1	....................................	....................................	PUNCT
ejpam-4590	181	2	....................................	....................................	PUNCT
ejpam-4590	182	1	....................................	....................................	PUNCT
ejpam-4590	182	2	....................................	....................................	PUNCT
ejpam-4590	182	3	............................................................................	............................................................................	PUNCT
ejpam-4590	182	4	.........	.........	PUNCT
ejpam-4590	182	5	........	........	PUNCT
ejpam-4590	182	6	........	........	PUNCT
ejpam-4590	182	7	........	........	PUNCT
ejpam-4590	182	8	........	........	PUNCT
ejpam-4590	182	9	........	........	PUNCT
ejpam-4590	182	10	........	........	PUNCT
ejpam-4590	182	11	........	........	PUNCT
ejpam-4590	182	12	........	........	PUNCT
ejpam-4590	182	13	........	........	PUNCT
ejpam-4590	182	14	........	........	PUNCT
ejpam-4590	182	15	........	........	PUNCT
ejpam-4590	182	16	........	........	PUNCT
ejpam-4590	182	17	........	........	PUNCT
ejpam-4590	182	18	........	........	PUNCT
ejpam-4590	182	19	........	........	PUNCT
ejpam-4590	182	20	........	........	PUNCT
ejpam-4590	182	21	........	........	PUNCT
ejpam-4590	182	22	........	........	PUNCT
ejpam-4590	182	23	........	........	PUNCT
ejpam-4590	182	24	.	.	PUNCT
ejpam-4590	183	1	..	..	PUNCT
ejpam-4590	183	2	..................................	..................................	PUNCT
ejpam-4590	184	1	....................................	....................................	PUNCT
ejpam-4590	184	2	.........	.........	PUNCT
ejpam-4590	184	3	........	........	PUNCT
ejpam-4590	184	4	........	........	PUNCT
ejpam-4590	184	5	........	........	PUNCT
ejpam-4590	184	6	........	........	PUNCT
ejpam-4590	184	7	........	........	PUNCT
ejpam-4590	184	8	........	........	PUNCT
ejpam-4590	184	9	........	........	PUNCT
ejpam-4590	184	10	........	........	PUNCT
ejpam-4590	184	11	........	........	PUNCT
ejpam-4590	184	12	........	........	PUNCT
ejpam-4590	184	13	........	........	PUNCT
ejpam-4590	184	14	........	........	PUNCT
ejpam-4590	184	15	........	........	PUNCT
ejpam-4590	184	16	........	........	PUNCT
ejpam-4590	184	17	........	........	PUNCT
ejpam-4590	184	18	........	........	PUNCT
ejpam-4590	184	19	........	........	PUNCT
ejpam-4590	184	20	........	........	PUNCT
ejpam-4590	184	21	........	........	PUNCT
ejpam-4590	184	22	.	.	PUNCT
ejpam-4590	185	1	..	..	PUNCT
ejpam-4590	185	2	..................................	..................................	PUNCT
ejpam-4590	186	1	....................................	....................................	PUNCT
ejpam-4590	186	2	....................................	....................................	PUNCT
ejpam-4590	187	1	....................................	....................................	PUNCT
ejpam-4590	187	2	....................................	....................................	PUNCT
ejpam-4590	188	1	z1	z1	ADJ
ejpam-4590	188	2	z2	z2	PROPN
ejpam-4590	188	3	zm	zm	PROPN
ejpam-4590	188	4	y1	y1	PROPN
ejpam-4590	188	5	y2	y2	PROPN
ejpam-4590	189	1	x1	x1	NOUN
ejpam-4590	189	2	x2	x2	PROPN
ejpam-4590	189	3	............	............	PUNCT
ejpam-4590	189	4	...........	...........	PUNCT
ejpam-4590	189	5	...........	...........	PUNCT
ejpam-4590	189	6	...........	...........	PUNCT
ejpam-4590	189	7	...........	...........	PUNCT
ejpam-4590	189	8	...........	...........	PUNCT
ejpam-4590	189	9	...........	...........	PUNCT
ejpam-4590	189	10	...........	...........	PUNCT
ejpam-4590	189	11	...........	...........	PUNCT
ejpam-4590	189	12	...........	...........	PUNCT
ejpam-4590	189	13	.....................	.....................	PUNCT
ejpam-4590	189	14	....................	....................	PUNCT
ejpam-4590	189	15	....................	....................	PUNCT
ejpam-4590	189	16	....................	....................	PUNCT
ejpam-4590	189	17	..................	..................	PUNCT
ejpam-4590	190	1	.........................................................................................................	.........................................................................................................	PROPN
ejpam-4590	190	2	...	...	PUNCT
ejpam-4590	191	1	figure	figure	NOUN
ejpam-4590	191	2	1	1	NUM
ejpam-4590	191	3	g	g	NOUN
ejpam-4590	191	4	:	:	PUNCT
ejpam-4590	191	5	case	case	NOUN
ejpam-4590	191	6	2	2	NUM
ejpam-4590	191	7	.	.	PUNCT
ejpam-4590	192	1	a	a	DET
ejpam-4590	192	2	≥	≥	NOUN
ejpam-4590	192	3	3	3	NUM
ejpam-4590	192	4	.	.	PUNCT
ejpam-4590	193	1	let	let	VERB
ejpam-4590	193	2	r	r	NOUN
ejpam-4590	193	3	=	=	PUNCT
ejpam-4590	193	4	b−	b−	NOUN
ejpam-4590	193	5	a+	a+	PUNCT
ejpam-4590	193	6	1	1	NUM
ejpam-4590	193	7	and	and	CCONJ
ejpam-4590	193	8	consider	consider	VERB
ejpam-4590	193	9	the	the	DET
ejpam-4590	193	10	graph	graph	NOUN
ejpam-4590	193	11	g	g	VERB
ejpam-4590	193	12	′	′	NUM
ejpam-4590	193	13	in	in	ADP
ejpam-4590	193	14	figure	figure	NOUN
ejpam-4590	193	15	2	2	NUM
ejpam-4590	193	16	.	.	PUNCT
ejpam-4590	194	1	let	let	VERB
ejpam-4590	194	2	d1	d1	PROPN
ejpam-4590	194	3	=	=	PUNCT
ejpam-4590	194	4	{	{	PUNCT
ejpam-4590	194	5	x1	x1	PROPN
ejpam-4590	194	6	,	,	PUNCT
ejpam-4590	194	7	x2	x2	PROPN
ejpam-4590	194	8	,	,	PUNCT
ejpam-4590	194	9	...	...	PUNCT
ejpam-4590	194	10	,	,	PUNCT
ejpam-4590	194	11	xa	xa	PROPN
ejpam-4590	194	12	}	}	PUNCT
ejpam-4590	194	13	and	and	CCONJ
ejpam-4590	194	14	d2	d2	PROPN
ejpam-4590	194	15	=	=	SYM
ejpam-4590	194	16	{	{	PUNCT
ejpam-4590	194	17	x1	x1	PROPN
ejpam-4590	194	18	,	,	PUNCT
ejpam-4590	194	19	x2	x2	PROPN
ejpam-4590	194	20	,	,	PUNCT
ejpam-4590	194	21	...	...	PUNCT
ejpam-4590	194	22	,	,	PUNCT
ejpam-4590	194	23	xa−1	xa−1	PROPN
ejpam-4590	194	24	,	,	PUNCT
ejpam-4590	194	25	z1	z1	PROPN
ejpam-4590	194	26	,	,	PUNCT
ejpam-4590	194	27	...	...	PUNCT
ejpam-4590	194	28	,	,	PUNCT
ejpam-4590	194	29	zr	zr	PROPN
ejpam-4590	194	30	}	}	PUNCT
ejpam-4590	194	31	.	.	PUNCT
ejpam-4590	195	1	then	then	ADV
ejpam-4590	195	2	d1	d1	PROPN
ejpam-4590	195	3	and	and	CCONJ
ejpam-4590	195	4	d2	d2	PROPN
ejpam-4590	195	5	are	be	AUX
ejpam-4590	195	6	γh	γh	ADV
ejpam-4590	195	7	-	-	PUNCT
ejpam-4590	195	8	set	set	VERB
ejpam-4590	195	9	and	and	CCONJ
ejpam-4590	195	10	γ̃ch	γ̃ch	PROPN
ejpam-4590	195	11	-	-	PUNCT
ejpam-4590	195	12	set	set	NOUN
ejpam-4590	195	13	,	,	PUNCT
ejpam-4590	195	14	respectively	respectively	ADV
ejpam-4590	195	15	,	,	PUNCT
ejpam-4590	195	16	of	of	ADP
ejpam-4590	195	17	g′.	g′.	NOUN
ejpam-4590	195	18	hence	hence	ADV
ejpam-4590	195	19	,	,	PUNCT
ejpam-4590	195	20	γh(g	γh(g	PUNCT
ejpam-4590	195	21	′	′	NUM
ejpam-4590	195	22	)	)	PUNCT
ejpam-4590	196	1	=	=	PUNCT
ejpam-4590	196	2	a	a	PRON
ejpam-4590	196	3	and	and	CCONJ
ejpam-4590	196	4	γ̃ch(g	γ̃ch(g	NOUN
ejpam-4590	196	5	′	′	NUM
ejpam-4590	196	6	)	)	PUNCT
ejpam-4590	197	1	=	=	PUNCT
ejpam-4590	197	2	r	r	NOUN
ejpam-4590	197	3	+	+	SYM
ejpam-4590	197	4	a−	a−	PROPN
ejpam-4590	197	5	1	1	NUM
ejpam-4590	197	6	=	=	SYM
ejpam-4590	197	7	b.	b.	PROPN
ejpam-4590	197	8	....................................	....................................	PUNCT
ejpam-4590	197	9	....................................	....................................	PUNCT
ejpam-4590	198	1	....................................	....................................	PUNCT
ejpam-4590	198	2	....................................	....................................	PUNCT
ejpam-4590	199	1	....................................	....................................	PUNCT
ejpam-4590	199	2	....................................	....................................	PUNCT
ejpam-4590	200	1	....................................	....................................	PUNCT
ejpam-4590	200	2	....................................	....................................	PUNCT
ejpam-4590	201	1	....................................	....................................	PUNCT
ejpam-4590	201	2	....................................	....................................	PUNCT
ejpam-4590	202	1	....................................	....................................	PUNCT
ejpam-4590	202	2	....................................	....................................	PUNCT
ejpam-4590	203	1	....................................	....................................	PUNCT
ejpam-4590	204	1	x1	x1	NUM
ejpam-4590	204	2	x2	x2	PROPN
ejpam-4590	204	3	xa−1	xa−1	PROPN
ejpam-4590	204	4	xa	xa	PROPN
ejpam-4590	204	5	.........	.........	PUNCT
ejpam-4590	204	6	........	........	PUNCT
ejpam-4590	204	7	........	........	PUNCT
ejpam-4590	204	8	........	........	PUNCT
ejpam-4590	204	9	........	........	PUNCT
ejpam-4590	204	10	........	........	PUNCT
ejpam-4590	204	11	........	........	PUNCT
ejpam-4590	204	12	........	........	PUNCT
ejpam-4590	204	13	........	........	PUNCT
ejpam-4590	204	14	........	........	PUNCT
ejpam-4590	204	15	........	........	PUNCT
ejpam-4590	204	16	........	........	PUNCT
ejpam-4590	204	17	........	........	PUNCT
ejpam-4590	204	18	........	........	PUNCT
ejpam-4590	204	19	........	........	PUNCT
ejpam-4590	204	20	........	........	PUNCT
ejpam-4590	204	21	........	........	PUNCT
ejpam-4590	204	22	........	........	PUNCT
ejpam-4590	204	23	........	........	PUNCT
ejpam-4590	204	24	........	........	PUNCT
ejpam-4590	204	25	.	.	PUNCT
ejpam-4590	204	26	..	..	PUNCT
ejpam-4590	204	27	..................................	..................................	PUNCT
ejpam-4590	204	28	....................................	....................................	PUNCT
ejpam-4590	204	29	.........	.........	PUNCT
ejpam-4590	204	30	........	........	PUNCT
ejpam-4590	204	31	........	........	PUNCT
ejpam-4590	204	32	........	........	PUNCT
ejpam-4590	204	33	........	........	PUNCT
ejpam-4590	204	34	........	........	PUNCT
ejpam-4590	204	35	........	........	PUNCT
ejpam-4590	204	36	........	........	PUNCT
ejpam-4590	204	37	........	........	PUNCT
ejpam-4590	204	38	........	........	PUNCT
ejpam-4590	204	39	........	........	PUNCT
ejpam-4590	204	40	........	........	PUNCT
ejpam-4590	204	41	........	........	PUNCT
ejpam-4590	204	42	........	........	PUNCT
ejpam-4590	204	43	........	........	PUNCT
ejpam-4590	204	44	........	........	PUNCT
ejpam-4590	204	45	........	........	PUNCT
ejpam-4590	204	46	........	........	PUNCT
ejpam-4590	204	47	........	........	PUNCT
ejpam-4590	204	48	........	........	PUNCT
ejpam-4590	204	49	.	.	PUNCT
ejpam-4590	204	50	..	..	PUNCT
ejpam-4590	204	51	..................................	..................................	PUNCT
ejpam-4590	204	52	....................................	....................................	PUNCT
ejpam-4590	204	53	............................................................................	............................................................................	PUNCT
ejpam-4590	204	54	............	............	PUNCT
ejpam-4590	204	55	...........	...........	PUNCT
ejpam-4590	204	56	...........	...........	PUNCT
ejpam-4590	204	57	...........	...........	PUNCT
ejpam-4590	204	58	...........	...........	PUNCT
ejpam-4590	204	59	...........	...........	PUNCT
ejpam-4590	204	60	...........	...........	PUNCT
ejpam-4590	204	61	...........	...........	PUNCT
ejpam-4590	204	62	...........	...........	PUNCT
ejpam-4590	204	63	...........	...........	PUNCT
ejpam-4590	205	1	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4590	205	2	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4590	205	3	............	............	PUNCT
ejpam-4590	205	4	...........	...........	PUNCT
ejpam-4590	205	5	...........	...........	PUNCT
ejpam-4590	205	6	...........	...........	PUNCT
ejpam-4590	205	7	...........	...........	PUNCT
ejpam-4590	205	8	...........	...........	PUNCT
ejpam-4590	205	9	...........	...........	PUNCT
ejpam-4590	205	10	...........	...........	PUNCT
ejpam-4590	205	11	...........	...........	PUNCT
ejpam-4590	205	12	...........	...........	PUNCT
ejpam-4590	205	13	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4590	206	1	............................................................................	............................................................................	PUNCT
ejpam-4590	206	2	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4590	206	3	............................................................................	............................................................................	PUNCT
ejpam-4590	206	4	............	............	PUNCT
ejpam-4590	206	5	...........	...........	PUNCT
ejpam-4590	206	6	...........	...........	PUNCT
ejpam-4590	206	7	...........	...........	PUNCT
ejpam-4590	206	8	...........	...........	PUNCT
ejpam-4590	206	9	...........	...........	PUNCT
ejpam-4590	206	10	...........	...........	PUNCT
ejpam-4590	206	11	...........	...........	PUNCT
ejpam-4590	206	12	...........	...........	PUNCT
ejpam-4590	206	13	...........	...........	PUNCT
ejpam-4590	206	14	.........	.........	PUNCT
ejpam-4590	206	15	........	........	PUNCT
ejpam-4590	206	16	........	........	PUNCT
ejpam-4590	206	17	........	........	PUNCT
ejpam-4590	206	18	........	........	PUNCT
ejpam-4590	206	19	........	........	PUNCT
ejpam-4590	206	20	........	........	PUNCT
ejpam-4590	206	21	........	........	PUNCT
ejpam-4590	206	22	........	........	PUNCT
ejpam-4590	206	23	........	........	PUNCT
ejpam-4590	206	24	........	........	PUNCT
ejpam-4590	206	25	........	........	PUNCT
ejpam-4590	206	26	........	........	PUNCT
ejpam-4590	206	27	........	........	PUNCT
ejpam-4590	206	28	........	........	PUNCT
ejpam-4590	206	29	........	........	PUNCT
ejpam-4590	206	30	........	........	PUNCT
ejpam-4590	206	31	........	........	PUNCT
ejpam-4590	207	1	........	........	PUNCT
ejpam-4590	207	2	........	........	PUNCT
ejpam-4590	207	3	.	.	PUNCT
ejpam-4590	208	1	....................................	....................................	PUNCT
ejpam-4590	208	2	....................................	....................................	PUNCT
ejpam-4590	209	1	....................................	....................................	PUNCT
ejpam-4590	209	2	....................................	....................................	PUNCT
ejpam-4590	210	1	....................................	....................................	PUNCT
ejpam-4590	210	2	....................................	....................................	PUNCT
ejpam-4590	211	1	z1	z1	PROPN
ejpam-4590	211	2	z2	z2	PROPN
ejpam-4590	211	3	zr	zr	PROPN
ejpam-4590	211	4	............	............	PUNCT
ejpam-4590	211	5	...........	...........	PUNCT
ejpam-4590	211	6	...........	...........	PUNCT
ejpam-4590	211	7	...........	...........	PUNCT
ejpam-4590	211	8	...........	...........	PUNCT
ejpam-4590	211	9	...........	...........	PUNCT
ejpam-4590	211	10	...........	...........	PUNCT
ejpam-4590	211	11	...........	...........	PUNCT
ejpam-4590	211	12	...........	...........	PUNCT
ejpam-4590	211	13	...........	...........	PUNCT
ejpam-4590	211	14	.....................	.....................	PUNCT
ejpam-4590	211	15	....................	....................	PUNCT
ejpam-4590	211	16	....................	....................	PUNCT
ejpam-4590	211	17	....................	....................	PUNCT
ejpam-4590	211	18	..................	..................	PUNCT
ejpam-4590	212	1	.........................................................................................................	.........................................................................................................	PROPN
ejpam-4590	212	2	............	............	PUNCT
ejpam-4590	212	3	...........	...........	PUNCT
ejpam-4590	212	4	...........	...........	PUNCT
ejpam-4590	212	5	...........	...........	PUNCT
ejpam-4590	212	6	...........	...........	PUNCT
ejpam-4590	212	7	...........	...........	PUNCT
ejpam-4590	212	8	....	....	PUNCT
ejpam-4590	212	9	.....................	.....................	PUNCT
ejpam-4590	212	10	....................	....................	PUNCT
ejpam-4590	212	11	....................	....................	PUNCT
ejpam-4590	212	12	.......	.......	PUNCT
ejpam-4590	212	13	........................................................................	........................................................................	PUNCT
ejpam-4590	212	14	...	...	PUNCT
ejpam-4590	212	15	.	.	PUNCT
ejpam-4590	212	16	.	.	PUNCT
ejpam-4590	212	17	.	.	PUNCT
ejpam-4590	212	18	.	.	PUNCT
ejpam-4590	212	19	.	.	PUNCT
ejpam-4590	212	20	.	.	PUNCT
ejpam-4590	212	21	.	.	PUNCT
ejpam-4590	212	22	.	.	PUNCT
ejpam-4590	213	1	.	.	PUNCT
ejpam-4590	214	1	figure	figure	NOUN
ejpam-4590	214	2	2	2	NUM
ejpam-4590	214	3	g	g	NOUN
ejpam-4590	214	4	′	′	NUM
ejpam-4590	214	5	:	:	PUNCT
ejpam-4590	215	1	corollary	corollary	ADJ
ejpam-4590	215	2	2	2	NUM
ejpam-4590	215	3	.	.	PUNCT
ejpam-4590	216	1	for	for	ADP
ejpam-4590	216	2	each	each	DET
ejpam-4590	216	3	positive	positive	ADJ
ejpam-4590	216	4	integer	integer	NOUN
ejpam-4590	216	5	n	n	CCONJ
ejpam-4590	216	6	,	,	PUNCT
ejpam-4590	216	7	there	there	PRON
ejpam-4590	216	8	exists	exist	VERB
ejpam-4590	216	9	a	a	DET
ejpam-4590	216	10	connected	connected	ADJ
ejpam-4590	216	11	graph	graph	NOUN
ejpam-4590	216	12	g	g	ADP
ejpam-4590	216	13	such	such	ADJ
ejpam-4590	216	14	that	that	DET
ejpam-4590	216	15	γ̃ch(g)−	γ̃ch(g)−	PROPN
ejpam-4590	216	16	γh(g	γh(g	NOUN
ejpam-4590	216	17	)	)	PUNCT
ejpam-4590	216	18	=	=	SYM
ejpam-4590	217	1	n	n	CCONJ
ejpam-4590	217	2	,	,	PUNCT
ejpam-4590	217	3	that	that	ADV
ejpam-4590	217	4	is	is	ADV
ejpam-4590	217	5	,	,	PUNCT
ejpam-4590	217	6	γ̃chγh	γ̃chγh	PROPN
ejpam-4590	217	7	can	can	AUX
ejpam-4590	217	8	be	be	AUX
ejpam-4590	217	9	made	make	VERB
ejpam-4590	217	10	arbitrarily	arbitrarily	ADV
ejpam-4590	217	11	large	large	ADJ
ejpam-4590	217	12	.	.	PUNCT
ejpam-4590	218	1	the	the	DET
ejpam-4590	218	2	next	next	ADJ
ejpam-4590	218	3	few	few	ADJ
ejpam-4590	218	4	results	result	NOUN
ejpam-4590	218	5	deal	deal	VERB
ejpam-4590	218	6	with	with	ADP
ejpam-4590	218	7	the	the	DET
ejpam-4590	218	8	concept	concept	NOUN
ejpam-4590	218	9	of	of	ADP
ejpam-4590	218	10	outer	outer	ADV
ejpam-4590	218	11	-	-	PUNCT
ejpam-4590	218	12	connected	connect	VERB
ejpam-4590	218	13	pointwise	pointwise	PROPN
ejpam-4590	218	14	non	non	ADJ
ejpam-4590	218	15	-	-	ADJ
ejpam-4590	218	16	dominating	dominating	ADJ
ejpam-4590	218	17	sets	set	NOUN
ejpam-4590	218	18	.	.	PUNCT
ejpam-4590	219	1	theorem	theorem	NOUN
ejpam-4590	219	2	6	6	NUM
ejpam-4590	219	3	.	.	PUNCT
ejpam-4590	220	1	let	let	VERB
ejpam-4590	220	2	g	g	PRON
ejpam-4590	220	3	be	be	AUX
ejpam-4590	220	4	a	a	DET
ejpam-4590	220	5	graph	graph	NOUN
ejpam-4590	220	6	.	.	PUNCT
ejpam-4590	221	1	then	then	ADV
ejpam-4590	221	2	1	1	NUM
ejpam-4590	221	3	≤	≤	NUM
ejpam-4590	221	4	pnd(g	pnd(g	ADP
ejpam-4590	221	5	)	)	PUNCT
ejpam-4590	221	6	≤	≤	NOUN
ejpam-4590	221	7	p̃nd(g	p̃nd(g	NOUN
ejpam-4590	221	8	)	)	PUNCT
ejpam-4590	221	9	≤	≤	NUM
ejpam-4590	221	10	|v	|v	X
ejpam-4590	221	11	(	(	PUNCT
ejpam-4590	221	12	g)|	g)|	PROPN
ejpam-4590	221	13	.	.	PUNCT
ejpam-4590	222	1	moreover	moreover	ADV
ejpam-4590	222	2	,	,	PUNCT
ejpam-4590	222	3	(	(	PUNCT
ejpam-4590	222	4	i	i	NOUN
ejpam-4590	222	5	)	)	PUNCT
ejpam-4590	222	6	p̃nd(g	p̃nd(g	ADV
ejpam-4590	222	7	)	)	PUNCT
ejpam-4590	222	8	=	=	SYM
ejpam-4590	222	9	|v	|v	PROPN
ejpam-4590	222	10	(	(	PUNCT
ejpam-4590	222	11	g)|	g)|	VERB
ejpam-4590	222	12	if	if	SCONJ
ejpam-4590	222	13	and	and	CCONJ
ejpam-4590	222	14	only	only	ADV
ejpam-4590	222	15	if	if	SCONJ
ejpam-4590	222	16	g	g	PROPN
ejpam-4590	222	17	is	be	AUX
ejpam-4590	222	18	a	a	DET
ejpam-4590	222	19	complete	complete	ADJ
ejpam-4590	222	20	graph	graph	NOUN
ejpam-4590	222	21	,	,	PUNCT
ejpam-4590	222	22	(	(	PUNCT
ejpam-4590	222	23	ii	ii	NOUN
ejpam-4590	222	24	)	)	PUNCT
ejpam-4590	222	25	p̃nd(g	p̃nd(g	NOUN
ejpam-4590	222	26	)	)	PUNCT
ejpam-4590	222	27	=	=	SYM
ejpam-4590	222	28	1	1	NUM
ejpam-4590	222	29	if	if	SCONJ
ejpam-4590	222	30	and	and	CCONJ
ejpam-4590	222	31	only	only	ADV
ejpam-4590	222	32	if	if	SCONJ
ejpam-4590	222	33	g	g	PROPN
ejpam-4590	222	34	has	have	VERB
ejpam-4590	222	35	at	at	ADP
ejpam-4590	222	36	most	most	ADV
ejpam-4590	222	37	two	two	NUM
ejpam-4590	222	38	components	component	NOUN
ejpam-4590	222	39	such	such	ADJ
ejpam-4590	222	40	that	that	SCONJ
ejpam-4590	222	41	one	one	NUM
ejpam-4590	222	42	of	of	ADP
ejpam-4590	222	43	them	they	PRON
ejpam-4590	222	44	is	be	AUX
ejpam-4590	222	45	the	the	DET
ejpam-4590	222	46	trivial	trivial	ADJ
ejpam-4590	222	47	graph	graph	NOUN
ejpam-4590	222	48	,	,	PUNCT
ejpam-4590	222	49	and	and	CCONJ
ejpam-4590	222	50	(	(	PUNCT
ejpam-4590	222	51	iii	iii	NOUN
ejpam-4590	222	52	)	)	PUNCT
ejpam-4590	222	53	p̃nd(g	p̃nd(g	NOUN
ejpam-4590	222	54	)	)	PUNCT
ejpam-4590	222	55	=	=	SYM
ejpam-4590	222	56	2	2	NUM
ejpam-4590	222	57	if	if	SCONJ
ejpam-4590	222	58	and	and	CCONJ
ejpam-4590	222	59	only	only	ADV
ejpam-4590	222	60	if	if	SCONJ
ejpam-4590	222	61	g	g	NOUN
ejpam-4590	222	62	satisfies	satisfy	VERB
ejpam-4590	222	63	one	one	NUM
ejpam-4590	222	64	of	of	ADP
ejpam-4590	222	65	the	the	DET
ejpam-4590	222	66	following	following	ADJ
ejpam-4590	222	67	conditions	condition	NOUN
ejpam-4590	222	68	:	:	PUNCT
ejpam-4590	222	69	(	(	PUNCT
ejpam-4590	222	70	a	a	X
ejpam-4590	222	71	)	)	PUNCT
ejpam-4590	222	72	g	g	NOUN
ejpam-4590	222	73	has	have	VERB
ejpam-4590	222	74	at	at	ADP
ejpam-4590	222	75	most	most	ADJ
ejpam-4590	222	76	two	two	NUM
ejpam-4590	222	77	non	non	ADJ
ejpam-4590	222	78	-	-	ADJ
ejpam-4590	222	79	trivial	trivial	ADJ
ejpam-4590	222	80	components	component	NOUN
ejpam-4590	222	81	such	such	ADJ
ejpam-4590	222	82	that	that	SCONJ
ejpam-4590	222	83	one	one	NUM
ejpam-4590	222	84	of	of	ADP
ejpam-4590	222	85	them	they	PRON
ejpam-4590	222	86	is	be	AUX
ejpam-4590	222	87	k2	k2	ADJ
ejpam-4590	222	88	.	.	PUNCT
ejpam-4590	223	1	(	(	PUNCT
ejpam-4590	223	2	b	b	X
ejpam-4590	223	3	)	)	PUNCT
ejpam-4590	223	4	g	g	NOUN
ejpam-4590	223	5	has	have	VERB
ejpam-4590	223	6	exactly	exactly	ADV
ejpam-4590	223	7	three	three	NUM
ejpam-4590	223	8	components	component	NOUN
ejpam-4590	223	9	such	such	ADJ
ejpam-4590	223	10	that	that	SCONJ
ejpam-4590	223	11	at	at	ADV
ejpam-4590	223	12	least	least	ADV
ejpam-4590	223	13	two	two	NUM
ejpam-4590	223	14	of	of	ADP
ejpam-4590	223	15	them	they	PRON
ejpam-4590	223	16	are	be	AUX
ejpam-4590	223	17	trivial	trivial	ADJ
ejpam-4590	223	18	graphs	graph	NOUN
ejpam-4590	223	19	.	.	PUNCT
ejpam-4590	224	1	(	(	PUNCT
ejpam-4590	224	2	c	c	X
ejpam-4590	224	3	)	)	PUNCT
ejpam-4590	224	4	g	g	NOUN
ejpam-4590	224	5	is	be	AUX
ejpam-4590	224	6	connected	connect	VERB
ejpam-4590	224	7	non	non	ADJ
ejpam-4590	224	8	-	-	ADJ
ejpam-4590	224	9	complete	complete	ADJ
ejpam-4590	224	10	graph	graph	NOUN
ejpam-4590	224	11	and	and	CCONJ
ejpam-4590	224	12	there	there	PRON
ejpam-4590	224	13	exist	exist	VERB
ejpam-4590	224	14	a	a	DET
ejpam-4590	224	15	,	,	PUNCT
ejpam-4590	224	16	b	b	PROPN
ejpam-4590	224	17	∈	∈	PROPN
ejpam-4590	224	18	v	v	NOUN
ejpam-4590	224	19	(	(	PUNCT
ejpam-4590	224	20	g)(a	g)(a	VERB
ejpam-4590	224	21	̸=	̸=	PROPN
ejpam-4590	224	22	b	b	NUM
ejpam-4590	224	23	)	)	PUNCT
ejpam-4590	224	24	such	such	ADJ
ejpam-4590	224	25	that	that	PRON
ejpam-4590	224	26	ng(a	ng(a	NOUN
ejpam-4590	224	27	)	)	PUNCT
ejpam-4590	224	28	∩ng(b	∩ng(b	NOUN
ejpam-4590	224	29	)	)	PUNCT
ejpam-4590	224	30	=	=	SYM
ejpam-4590	224	31	∅	∅	NOUN
ejpam-4590	224	32	and	and	CCONJ
ejpam-4590	224	33	⟨v	⟨v	NUM
ejpam-4590	224	34	(	(	PUNCT
ejpam-4590	224	35	g	g	NOUN
ejpam-4590	224	36	)	)	PUNCT
ejpam-4590	224	37	\	\	NOUN
ejpam-4590	224	38	{	{	PUNCT
ejpam-4590	224	39	a	a	X
ejpam-4590	224	40	,	,	PUNCT
ejpam-4590	224	41	b}⟩	b}⟩	PROPN
ejpam-4590	224	42	is	be	AUX
ejpam-4590	224	43	connected	connect	VERB
ejpam-4590	224	44	.	.	PUNCT
ejpam-4590	225	1	c.j	c.j	PROPN
ejpam-4590	225	2	.	.	PROPN
ejpam-4590	225	3	saromines	saromines	PROPN
ejpam-4590	225	4	,	,	PUNCT
ejpam-4590	225	5	s.	s.	PROPN
ejpam-4590	225	6	canoy	canoy	PROPN
ejpam-4590	225	7	,	,	PUNCT
ejpam-4590	225	8	jr	jr	PROPN
ejpam-4590	225	9	.	.	PROPN
ejpam-4590	225	10	/	/	SYM
ejpam-4590	225	11	eur	eur	PROPN
ejpam-4590	225	12	.	.	PUNCT
ejpam-4590	226	1	j.	j.	PROPN
ejpam-4590	226	2	pure	pure	PROPN
ejpam-4590	226	3	appl	appl	PROPN
ejpam-4590	226	4	.	.	PROPN
ejpam-4590	226	5	math	math	PROPN
ejpam-4590	226	6	,	,	PUNCT
ejpam-4590	226	7	15	15	NUM
ejpam-4590	226	8	(	(	PUNCT
ejpam-4590	226	9	4	4	NUM
ejpam-4590	226	10	)	)	PUNCT
ejpam-4590	226	11	(	(	PUNCT
ejpam-4590	226	12	2022	2022	NUM
ejpam-4590	226	13	)	)	PUNCT
ejpam-4590	226	14	,	,	PUNCT
ejpam-4590	226	15	1966	1966	NUM
ejpam-4590	226	16	-	-	SYM
ejpam-4590	226	17	1981	1981	NUM
ejpam-4590	226	18	1972	1972	NUM
ejpam-4590	226	19	proof	proof	NOUN
ejpam-4590	226	20	.	.	PUNCT
ejpam-4590	227	1	since	since	SCONJ
ejpam-4590	227	2	an	an	DET
ejpam-4590	227	3	empty	empty	ADJ
ejpam-4590	227	4	set	set	NOUN
ejpam-4590	227	5	can	can	AUX
ejpam-4590	227	6	not	not	PART
ejpam-4590	227	7	be	be	AUX
ejpam-4590	227	8	an	an	DET
ejpam-4590	227	9	outer	outer	ADV
ejpam-4590	227	10	-	-	PUNCT
ejpam-4590	227	11	connected	connect	VERB
ejpam-4590	227	12	pointwise	pointwise	PROPN
ejpam-4590	227	13	non	non	ADJ
ejpam-4590	227	14	-	-	ADJ
ejpam-4590	227	15	dominating	dominating	ADJ
ejpam-4590	227	16	set	set	NOUN
ejpam-4590	227	17	of	of	ADP
ejpam-4590	227	18	g	g	PROPN
ejpam-4590	227	19	and	and	CCONJ
ejpam-4590	227	20	v	v	NOUN
ejpam-4590	227	21	(	(	PUNCT
ejpam-4590	227	22	g	g	NOUN
ejpam-4590	227	23	)	)	PUNCT
ejpam-4590	227	24	is	be	AUX
ejpam-4590	227	25	an	an	DET
ejpam-4590	227	26	outer	outer	ADJ
ejpam-4590	227	27	connected	connect	VERB
ejpam-4590	227	28	pointwise	pointwise	PROPN
ejpam-4590	227	29	non	non	ADJ
ejpam-4590	227	30	-	-	ADJ
ejpam-4590	227	31	dominating	dominating	ADJ
ejpam-4590	227	32	set	set	NOUN
ejpam-4590	227	33	of	of	ADP
ejpam-4590	227	34	g	g	PROPN
ejpam-4590	227	35	,	,	PUNCT
ejpam-4590	227	36	it	it	PRON
ejpam-4590	227	37	follows	follow	VERB
ejpam-4590	227	38	that	that	SCONJ
ejpam-4590	227	39	1	1	NUM
ejpam-4590	227	40	≤	≤	NUM
ejpam-4590	227	41	p̃nd(g	p̃nd(g	NOUN
ejpam-4590	227	42	)	)	PUNCT
ejpam-4590	227	43	≤	≤	NUM
ejpam-4590	227	44	|v	|v	X
ejpam-4590	227	45	(	(	PUNCT
ejpam-4590	227	46	g)|	g)|	NOUN
ejpam-4590	227	47	.	.	PUNCT
ejpam-4590	228	1	for	for	ADP
ejpam-4590	228	2	(	(	PUNCT
ejpam-4590	228	3	i	i	NOUN
ejpam-4590	228	4	)	)	PUNCT
ejpam-4590	228	5	,	,	PUNCT
ejpam-4590	228	6	suppose	suppose	VERB
ejpam-4590	228	7	first	first	ADV
ejpam-4590	228	8	that	that	SCONJ
ejpam-4590	228	9	p̃nd(g	p̃nd(g	ADV
ejpam-4590	228	10	)	)	PUNCT
ejpam-4590	229	1	=	=	SYM
ejpam-4590	229	2	|v	|v	PROPN
ejpam-4590	229	3	(	(	PUNCT
ejpam-4590	229	4	g)|	g)|	NOUN
ejpam-4590	229	5	and	and	CCONJ
ejpam-4590	229	6	suppose	suppose	VERB
ejpam-4590	229	7	thatg	thatg	PROPN
ejpam-4590	229	8	is	be	AUX
ejpam-4590	229	9	not	not	PART
ejpam-4590	229	10	a	a	DET
ejpam-4590	229	11	complete	complete	ADJ
ejpam-4590	229	12	graph	graph	NOUN
ejpam-4590	229	13	.	.	PUNCT
ejpam-4590	230	1	then	then	ADV
ejpam-4590	230	2	there	there	PRON
ejpam-4590	230	3	exist	exist	VERB
ejpam-4590	230	4	non	non	ADJ
ejpam-4590	230	5	-	-	ADJ
ejpam-4590	230	6	adjacent	adjacent	ADJ
ejpam-4590	230	7	vertices	vertex	NOUN
ejpam-4590	230	8	x	x	PUNCT
ejpam-4590	230	9	and	and	CCONJ
ejpam-4590	230	10	y	y	PROPN
ejpam-4590	230	11	of	of	ADP
ejpam-4590	230	12	g.	g.	PROPN
ejpam-4590	230	13	consequently	consequently	ADV
ejpam-4590	230	14	,	,	PUNCT
ejpam-4590	230	15	s	s	NOUN
ejpam-4590	230	16	=	=	SYM
ejpam-4590	230	17	v	v	X
ejpam-4590	230	18	(	(	PUNCT
ejpam-4590	230	19	g	g	NOUN
ejpam-4590	230	20	)	)	PUNCT
ejpam-4590	230	21	\	\	NOUN
ejpam-4590	231	1	{	{	PUNCT
ejpam-4590	231	2	y	y	NOUN
ejpam-4590	231	3	}	}	PUNCT
ejpam-4590	231	4	is	be	AUX
ejpam-4590	231	5	an	an	DET
ejpam-4590	231	6	outer	outer	ADV
ejpam-4590	231	7	-	-	PUNCT
ejpam-4590	231	8	connected	connect	VERB
ejpam-4590	231	9	pointwise	pointwise	PROPN
ejpam-4590	231	10	non	non	ADJ
ejpam-4590	231	11	-	-	ADJ
ejpam-4590	231	12	dominating	dominating	ADJ
ejpam-4590	231	13	set	set	NOUN
ejpam-4590	231	14	of	of	ADP
ejpam-4590	231	15	g	g	PROPN
ejpam-4590	231	16	,	,	PUNCT
ejpam-4590	231	17	contrary	contrary	ADJ
ejpam-4590	231	18	to	to	ADP
ejpam-4590	231	19	our	our	PRON
ejpam-4590	231	20	assumption	assumption	NOUN
ejpam-4590	231	21	that	that	SCONJ
ejpam-4590	231	22	p̃nd(g	p̃nd(g	ADV
ejpam-4590	231	23	)	)	PUNCT
ejpam-4590	232	1	=	=	SYM
ejpam-4590	232	2	|v	|v	X
ejpam-4590	232	3	(	(	PUNCT
ejpam-4590	232	4	g)|.thus	g)|.thus	X
ejpam-4590	232	5	,	,	PUNCT
ejpam-4590	232	6	g	g	PROPN
ejpam-4590	232	7	must	must	AUX
ejpam-4590	232	8	be	be	AUX
ejpam-4590	232	9	a	a	DET
ejpam-4590	232	10	complete	complete	ADJ
ejpam-4590	232	11	graph	graph	NOUN
ejpam-4590	232	12	.	.	PUNCT
ejpam-4590	233	1	conversely	conversely	ADV
ejpam-4590	233	2	,	,	PUNCT
ejpam-4590	233	3	suppose	suppose	VERB
ejpam-4590	233	4	g	g	PROPN
ejpam-4590	233	5	is	be	AUX
ejpam-4590	233	6	a	a	DET
ejpam-4590	233	7	complete	complete	ADJ
ejpam-4590	233	8	graph	graph	NOUN
ejpam-4590	233	9	.	.	PUNCT
ejpam-4590	233	10	suppose	suppose	VERB
ejpam-4590	233	11	that	that	SCONJ
ejpam-4590	233	12	p̃nd(g	p̃nd(g	ADV
ejpam-4590	233	13	)	)	PUNCT
ejpam-4590	233	14	=	=	SYM
ejpam-4590	234	1	k	k	X
ejpam-4590	234	2	<	<	X
ejpam-4590	234	3	|v	|v	X
ejpam-4590	234	4	(	(	PUNCT
ejpam-4590	234	5	g)|	g)|	PROPN
ejpam-4590	234	6	,	,	PUNCT
ejpam-4590	234	7	say	say	VERB
ejpam-4590	234	8	s	s	PRON
ejpam-4590	234	9	is	be	AUX
ejpam-4590	234	10	an	an	DET
ejpam-4590	234	11	p̃nd	p̃nd	NOUN
ejpam-4590	234	12	-	-	PUNCT
ejpam-4590	234	13	set	set	NOUN
ejpam-4590	234	14	.	.	PUNCT
ejpam-4590	235	1	choose	choose	VERB
ejpam-4590	235	2	any	any	DET
ejpam-4590	235	3	w	w	PROPN
ejpam-4590	235	4	∈	∈	PROPN
ejpam-4590	235	5	v	v	ADP
ejpam-4590	235	6	(	(	PUNCT
ejpam-4590	235	7	g	g	NOUN
ejpam-4590	235	8	)	)	PUNCT
ejpam-4590	235	9	\	\	PUNCT
ejpam-4590	236	1	s.	s.	PROPN
ejpam-4590	236	2	since	since	SCONJ
ejpam-4590	236	3	s	s	PROPN
ejpam-4590	236	4	is	be	AUX
ejpam-4590	236	5	a	a	DET
ejpam-4590	236	6	pointwise	pointwise	ADJ
ejpam-4590	236	7	non	non	ADJ
ejpam-4590	236	8	-	-	ADJ
ejpam-4590	236	9	dominating	dominating	ADJ
ejpam-4590	236	10	set	set	NOUN
ejpam-4590	236	11	,	,	PUNCT
ejpam-4590	236	12	there	there	PRON
ejpam-4590	236	13	exists	exist	VERB
ejpam-4590	236	14	u	u	PROPN
ejpam-4590	236	15	∈	∈	PROPN
ejpam-4590	236	16	s	s	VERB
ejpam-4590	236	17	such	such	ADJ
ejpam-4590	236	18	that	that	SCONJ
ejpam-4590	236	19	uw	uw	PROPN
ejpam-4590	236	20	/∈	/∈	PUNCT
ejpam-4590	236	21	e(g	e(g	PROPN
ejpam-4590	236	22	)	)	PUNCT
ejpam-4590	236	23	,	,	PUNCT
ejpam-4590	236	24	a	a	DET
ejpam-4590	236	25	contradiction	contradiction	NOUN
ejpam-4590	236	26	.	.	PUNCT
ejpam-4590	237	1	therefore	therefore	ADV
ejpam-4590	237	2	,	,	PUNCT
ejpam-4590	237	3	p̃nd(g	p̃nd(g	ADV
ejpam-4590	237	4	)	)	PUNCT
ejpam-4590	237	5	=	=	SYM
ejpam-4590	237	6	|v	|v	PROPN
ejpam-4590	237	7	(	(	PUNCT
ejpam-4590	237	8	g)|	g)|	PROPN
ejpam-4590	237	9	.	.	PUNCT
ejpam-4590	238	1	next	next	ADV
ejpam-4590	238	2	,	,	PUNCT
ejpam-4590	238	3	suppose	suppose	VERB
ejpam-4590	238	4	that	that	SCONJ
ejpam-4590	238	5	p̃nd(g	p̃nd(g	ADV
ejpam-4590	238	6	)	)	PUNCT
ejpam-4590	238	7	=	=	SYM
ejpam-4590	238	8	1	1	X
ejpam-4590	238	9	,	,	PUNCT
ejpam-4590	238	10	say	say	VERB
ejpam-4590	238	11	s	s	X
ejpam-4590	238	12	=	=	VERB
ejpam-4590	238	13	{	{	PUNCT
ejpam-4590	238	14	v	v	NOUN
ejpam-4590	238	15	}	}	PUNCT
ejpam-4590	238	16	is	be	AUX
ejpam-4590	238	17	an	an	DET
ejpam-4590	238	18	outer	outer	ADV
ejpam-4590	238	19	-	-	PUNCT
ejpam-4590	238	20	connected	connect	VERB
ejpam-4590	238	21	pointwise	pointwise	NOUN
ejpam-4590	238	22	nondominating	nondominate	VERB
ejpam-4590	238	23	set	set	NOUN
ejpam-4590	238	24	of	of	ADP
ejpam-4590	238	25	g.	g.	PROPN
ejpam-4590	238	26	since	since	SCONJ
ejpam-4590	238	27	⟨v	⟨v	PROPN
ejpam-4590	238	28	(	(	PUNCT
ejpam-4590	238	29	g	g	NOUN
ejpam-4590	238	30	)	)	PUNCT
ejpam-4590	238	31	\	\	PROPN
ejpam-4590	238	32	s⟩	s⟩	PROPN
ejpam-4590	238	33	is	be	AUX
ejpam-4590	238	34	connected	connect	VERB
ejpam-4590	238	35	,	,	PUNCT
ejpam-4590	238	36	v	v	INTJ
ejpam-4590	238	37	(	(	PUNCT
ejpam-4590	238	38	g	g	NOUN
ejpam-4590	238	39	)	)	PUNCT
ejpam-4590	238	40	\s	\s	NOUN
ejpam-4590	238	41	is	be	AUX
ejpam-4590	238	42	contained	contain	VERB
ejpam-4590	238	43	in	in	ADP
ejpam-4590	238	44	a	a	DET
ejpam-4590	238	45	component	component	NOUN
ejpam-4590	238	46	of	of	ADP
ejpam-4590	238	47	g.	g.	PROPN
ejpam-4590	238	48	thus	thus	ADV
ejpam-4590	238	49	,	,	PUNCT
ejpam-4590	238	50	g	g	PROPN
ejpam-4590	238	51	has	have	AUX
ejpam-4590	238	52	at	at	ADP
ejpam-4590	238	53	most	most	ADJ
ejpam-4590	238	54	two	two	NUM
ejpam-4590	238	55	components	component	NOUN
ejpam-4590	238	56	and	and	CCONJ
ejpam-4590	238	57	one	one	NUM
ejpam-4590	238	58	of	of	ADP
ejpam-4590	238	59	them	they	PRON
ejpam-4590	238	60	is	be	AUX
ejpam-4590	238	61	a	a	DET
ejpam-4590	238	62	trivial	trivial	ADJ
ejpam-4590	238	63	graph	graph	NOUN
ejpam-4590	238	64	.	.	PUNCT
ejpam-4590	239	1	conversely	conversely	ADV
ejpam-4590	239	2	,	,	PUNCT
ejpam-4590	239	3	if	if	SCONJ
ejpam-4590	239	4	g	g	PROPN
ejpam-4590	239	5	has	have	VERB
ejpam-4590	239	6	at	at	ADP
ejpam-4590	239	7	most	most	ADV
ejpam-4590	239	8	two	two	NUM
ejpam-4590	239	9	components	component	NOUN
ejpam-4590	239	10	g1	g1	NOUN
ejpam-4590	239	11	and	and	CCONJ
ejpam-4590	239	12	g2	g2	PROPN
ejpam-4590	239	13	where	where	SCONJ
ejpam-4590	239	14	g1	g1	PROPN
ejpam-4590	239	15	is	be	AUX
ejpam-4590	239	16	a	a	DET
ejpam-4590	239	17	trivial	trivial	ADJ
ejpam-4590	239	18	graph	graph	NOUN
ejpam-4590	239	19	,	,	PUNCT
ejpam-4590	239	20	then	then	ADV
ejpam-4590	239	21	s	s	VERB
ejpam-4590	239	22	=	=	SYM
ejpam-4590	239	23	v	v	PROPN
ejpam-4590	239	24	(	(	PUNCT
ejpam-4590	239	25	g1	g1	PROPN
ejpam-4590	239	26	)	)	PUNCT
ejpam-4590	239	27	is	be	AUX
ejpam-4590	239	28	an	an	DET
ejpam-4590	239	29	outer	outer	ADV
ejpam-4590	239	30	-	-	PUNCT
ejpam-4590	239	31	connected	connect	VERB
ejpam-4590	239	32	point	point	NOUN
ejpam-4590	239	33	-	-	PUNCT
ejpam-4590	239	34	wise	wise	ADJ
ejpam-4590	239	35	non	non	ADJ
ejpam-4590	239	36	-	-	ADJ
ejpam-4590	239	37	dominating	dominating	ADJ
ejpam-4590	239	38	set	set	NOUN
ejpam-4590	239	39	of	of	ADP
ejpam-4590	239	40	g.	g.	PROPN
ejpam-4590	239	41	this	this	PRON
ejpam-4590	239	42	shows	show	VERB
ejpam-4590	239	43	that	that	SCONJ
ejpam-4590	239	44	(	(	PUNCT
ejpam-4590	239	45	ii	ii	NOUN
ejpam-4590	239	46	)	)	PUNCT
ejpam-4590	239	47	holds	hold	VERB
ejpam-4590	239	48	.	.	PUNCT
ejpam-4590	240	1	finally	finally	ADV
ejpam-4590	240	2	,	,	PUNCT
ejpam-4590	240	3	suppose	suppose	VERB
ejpam-4590	240	4	that	that	SCONJ
ejpam-4590	240	5	p̃nd(g	p̃nd(g	ADV
ejpam-4590	240	6	)	)	PUNCT
ejpam-4590	240	7	=	=	SYM
ejpam-4590	240	8	2	2	X
ejpam-4590	240	9	.	.	X
ejpam-4590	240	10	let	let	VERB
ejpam-4590	240	11	s1	s1	PROPN
ejpam-4590	240	12	=	=	PUNCT
ejpam-4590	240	13	{	{	PUNCT
ejpam-4590	240	14	a	a	PRON
ejpam-4590	240	15	,	,	PUNCT
ejpam-4590	240	16	b	b	AUX
ejpam-4590	240	17	}	}	PUNCT
ejpam-4590	240	18	be	be	AUX
ejpam-4590	240	19	an	an	DET
ejpam-4590	240	20	p̃nd	p̃nd	NOUN
ejpam-4590	240	21	-	-	PUNCT
ejpam-4590	240	22	set	set	NOUN
ejpam-4590	240	23	of	of	ADP
ejpam-4590	240	24	g.	g.	PROPN
ejpam-4590	240	25	case	case	PROPN
ejpam-4590	240	26	1	1	X
ejpam-4590	240	27	.	.	PUNCT
ejpam-4590	240	28	suppose	suppose	VERB
ejpam-4590	240	29	a	a	DET
ejpam-4590	240	30	,	,	PUNCT
ejpam-4590	240	31	b	b	PROPN
ejpam-4590	240	32	∈	∈	PROPN
ejpam-4590	240	33	v	v	NOUN
ejpam-4590	240	34	(	(	PUNCT
ejpam-4590	240	35	g1	g1	PROPN
ejpam-4590	240	36	)	)	PUNCT
ejpam-4590	240	37	,	,	PUNCT
ejpam-4590	240	38	where	where	SCONJ
ejpam-4590	240	39	g1	g1	PROPN
ejpam-4590	240	40	is	be	AUX
ejpam-4590	240	41	a	a	DET
ejpam-4590	240	42	component	component	NOUN
ejpam-4590	240	43	of	of	ADP
ejpam-4590	240	44	g.	g.	PROPN
ejpam-4590	240	45	if	if	SCONJ
ejpam-4590	240	46	g	g	PROPN
ejpam-4590	240	47	is	be	AUX
ejpam-4590	240	48	connected	connect	VERB
ejpam-4590	240	49	,	,	PUNCT
ejpam-4590	240	50	then	then	ADV
ejpam-4590	240	51	g	g	PROPN
ejpam-4590	240	52	=	=	PUNCT
ejpam-4590	240	53	g1	g1	PROPN
ejpam-4590	240	54	.	.	PUNCT
ejpam-4590	241	1	if	if	SCONJ
ejpam-4590	241	2	s1	s1	PROPN
ejpam-4590	241	3	=	=	SYM
ejpam-4590	241	4	v	v	PROPN
ejpam-4590	241	5	(	(	PUNCT
ejpam-4590	241	6	g	g	NOUN
ejpam-4590	241	7	)	)	PUNCT
ejpam-4590	241	8	,	,	PUNCT
ejpam-4590	241	9	then	then	ADV
ejpam-4590	241	10	g	g	PROPN
ejpam-4590	241	11	=	=	PROPN
ejpam-4590	241	12	k2	k2	PROPN
ejpam-4590	241	13	.	.	PUNCT
ejpam-4590	241	14	suppose	suppose	VERB
ejpam-4590	241	15	s1	s1	PROPN
ejpam-4590	241	16	̸=	̸=	PROPN
ejpam-4590	241	17	v	v	NOUN
ejpam-4590	241	18	(	(	PUNCT
ejpam-4590	241	19	g	g	NOUN
ejpam-4590	241	20	)	)	PUNCT
ejpam-4590	241	21	.	.	PUNCT
ejpam-4590	242	1	then	then	ADV
ejpam-4590	242	2	by	by	ADP
ejpam-4590	242	3	(	(	PUNCT
ejpam-4590	242	4	i	i	NOUN
ejpam-4590	242	5	)	)	PUNCT
ejpam-4590	242	6	,	,	PUNCT
ejpam-4590	242	7	g	g	PROPN
ejpam-4590	242	8	is	be	AUX
ejpam-4590	242	9	a	a	DET
ejpam-4590	242	10	non	non	ADJ
ejpam-4590	242	11	-	-	ADJ
ejpam-4590	242	12	complete	complete	ADJ
ejpam-4590	242	13	graph	graph	NOUN
ejpam-4590	242	14	.	.	PUNCT
ejpam-4590	243	1	since	since	SCONJ
ejpam-4590	243	2	s1	s1	PROPN
ejpam-4590	243	3	is	be	AUX
ejpam-4590	243	4	an	an	DET
ejpam-4590	243	5	outer	outer	ADV
ejpam-4590	243	6	-	-	PUNCT
ejpam-4590	243	7	connected	connect	VERB
ejpam-4590	243	8	pointwise	pointwise	PROPN
ejpam-4590	243	9	non	non	ADJ
ejpam-4590	243	10	-	-	ADJ
ejpam-4590	243	11	dominating	dominating	ADJ
ejpam-4590	243	12	set	set	NOUN
ejpam-4590	243	13	,	,	PUNCT
ejpam-4590	243	14	ng(a	ng(a	NOUN
ejpam-4590	243	15	)	)	PUNCT
ejpam-4590	243	16	∩	∩	NOUN
ejpam-4590	243	17	ng(b	ng(b	CCONJ
ejpam-4590	243	18	)	)	PUNCT
ejpam-4590	243	19	=	=	SYM
ejpam-4590	243	20	∅	∅	NOUN
ejpam-4590	243	21	and	and	CCONJ
ejpam-4590	243	22	⟨v	⟨v	NUM
ejpam-4590	243	23	(	(	PUNCT
ejpam-4590	243	24	g	g	NOUN
ejpam-4590	243	25	)	)	PUNCT
ejpam-4590	243	26	\	\	NOUN
ejpam-4590	243	27	s1⟩	s1⟩	NOUN
ejpam-4590	243	28	is	be	AUX
ejpam-4590	243	29	connected	connect	VERB
ejpam-4590	243	30	.	.	PUNCT
ejpam-4590	244	1	suppose	suppose	VERB
ejpam-4590	244	2	g	g	PROPN
ejpam-4590	244	3	is	be	AUX
ejpam-4590	244	4	disconnected	disconnect	VERB
ejpam-4590	244	5	.	.	PUNCT
ejpam-4590	245	1	since	since	SCONJ
ejpam-4590	245	2	⟨v	⟨v	PROPN
ejpam-4590	245	3	(	(	PUNCT
ejpam-4590	245	4	g	g	NOUN
ejpam-4590	245	5	)	)	PUNCT
ejpam-4590	245	6	\	\	NOUN
ejpam-4590	245	7	s1⟩	s1⟩	PRON
ejpam-4590	245	8	is	be	AUX
ejpam-4590	245	9	connected	connect	VERB
ejpam-4590	245	10	,	,	PUNCT
ejpam-4590	245	11	g1	g1	PROPN
ejpam-4590	245	12	=	=	SYM
ejpam-4590	245	13	k2	k2	PROPN
ejpam-4590	245	14	and	and	CCONJ
ejpam-4590	245	15	g	g	PROPN
ejpam-4590	245	16	has	have	VERB
ejpam-4590	245	17	exactly	exactly	ADV
ejpam-4590	245	18	2	2	NUM
ejpam-4590	245	19	components	component	NOUN
ejpam-4590	245	20	g1	g1	NOUN
ejpam-4590	245	21	and	and	CCONJ
ejpam-4590	245	22	g2	g2	PROPN
ejpam-4590	245	23	.	.	PUNCT
ejpam-4590	246	1	hence	hence	ADV
ejpam-4590	246	2	,	,	PUNCT
ejpam-4590	246	3	(	(	PUNCT
ejpam-4590	246	4	a	a	X
ejpam-4590	246	5	)	)	PUNCT
ejpam-4590	246	6	or	or	CCONJ
ejpam-4590	246	7	(	(	PUNCT
ejpam-4590	246	8	c	c	NOUN
ejpam-4590	246	9	)	)	PUNCT
ejpam-4590	246	10	holds	hold	NOUN
ejpam-4590	246	11	.	.	PUNCT
ejpam-4590	247	1	case	case	NOUN
ejpam-4590	247	2	2	2	NUM
ejpam-4590	247	3	.	.	PUNCT
ejpam-4590	247	4	suppose	suppose	VERB
ejpam-4590	247	5	a	a	DET
ejpam-4590	247	6	∈	∈	PROPN
ejpam-4590	247	7	v	v	NOUN
ejpam-4590	247	8	(	(	PUNCT
ejpam-4590	247	9	g1	g1	PROPN
ejpam-4590	247	10	)	)	PUNCT
ejpam-4590	247	11	and	and	CCONJ
ejpam-4590	247	12	b	b	X
ejpam-4590	247	13	∈	∈	PROPN
ejpam-4590	247	14	v	v	NOUN
ejpam-4590	247	15	(	(	PUNCT
ejpam-4590	247	16	g2	g2	PROPN
ejpam-4590	247	17	)	)	PUNCT
ejpam-4590	247	18	,	,	PUNCT
ejpam-4590	247	19	where	where	SCONJ
ejpam-4590	247	20	g1	g1	PROPN
ejpam-4590	247	21	and	and	CCONJ
ejpam-4590	247	22	g2	g2	PROPN
ejpam-4590	247	23	are	be	AUX
ejpam-4590	247	24	distinct	distinct	ADJ
ejpam-4590	247	25	components	component	NOUN
ejpam-4590	247	26	of	of	ADP
ejpam-4590	247	27	g.	g.	PROPN
ejpam-4590	247	28	suppose	suppose	VERB
ejpam-4590	247	29	g	g	PROPN
ejpam-4590	247	30	=	=	PROPN
ejpam-4590	247	31	g1	g1	PROPN
ejpam-4590	247	32	∪	∪	ADP
ejpam-4590	247	33	g2	g2	PROPN
ejpam-4590	247	34	.	.	PUNCT
ejpam-4590	248	1	then	then	ADV
ejpam-4590	248	2	g1	g1	PROPN
ejpam-4590	248	3	and	and	CCONJ
ejpam-4590	248	4	g2	g2	PROPN
ejpam-4590	248	5	are	be	AUX
ejpam-4590	248	6	non	non	ADJ
ejpam-4590	248	7	-	-	ADJ
ejpam-4590	248	8	trivial	trivial	ADJ
ejpam-4590	248	9	graphs	graph	NOUN
ejpam-4590	248	10	by	by	ADP
ejpam-4590	248	11	(	(	PUNCT
ejpam-4590	248	12	ii	ii	NOUN
ejpam-4590	248	13	)	)	PUNCT
ejpam-4590	248	14	and	and	CCONJ
ejpam-4590	248	15	the	the	DET
ejpam-4590	248	16	assumption	assumption	NOUN
ejpam-4590	248	17	that	that	SCONJ
ejpam-4590	248	18	p̃nd(g	p̃nd(g	ADV
ejpam-4590	248	19	)	)	PUNCT
ejpam-4590	248	20	=	=	SYM
ejpam-4590	249	1	2	2	X
ejpam-4590	249	2	.	.	X
ejpam-4590	249	3	hence	hence	ADV
ejpam-4590	249	4	,	,	PUNCT
ejpam-4590	249	5	⟨v	⟨v	X
ejpam-4590	249	6	(	(	PUNCT
ejpam-4590	249	7	g	g	NOUN
ejpam-4590	249	8	)	)	PUNCT
ejpam-4590	249	9	\	\	NOUN
ejpam-4590	250	1	s1⟩	s1⟩	NOUN
ejpam-4590	250	2	is	be	AUX
ejpam-4590	250	3	disconnected	disconnect	VERB
ejpam-4590	250	4	,	,	PUNCT
ejpam-4590	250	5	a	a	DET
ejpam-4590	250	6	contradiction	contradiction	NOUN
ejpam-4590	250	7	.	.	PUNCT
ejpam-4590	251	1	therefore	therefore	ADV
ejpam-4590	251	2	,	,	PUNCT
ejpam-4590	251	3	g	g	PROPN
ejpam-4590	251	4	has	have	VERB
ejpam-4590	251	5	more	more	ADJ
ejpam-4590	251	6	than	than	ADP
ejpam-4590	251	7	2	2	NUM
ejpam-4590	251	8	components	component	NOUN
ejpam-4590	251	9	.	.	PUNCT
ejpam-4590	252	1	this	this	PRON
ejpam-4590	252	2	would	would	AUX
ejpam-4590	252	3	imply	imply	VERB
ejpam-4590	252	4	that	that	SCONJ
ejpam-4590	252	5	g1	g1	PROPN
ejpam-4590	252	6	=	=	SYM
ejpam-4590	252	7	g2	g2	PROPN
ejpam-4590	252	8	=	=	PUNCT
ejpam-4590	252	9	k1	k1	PROPN
ejpam-4590	252	10	.	.	PUNCT
ejpam-4590	253	1	since	since	SCONJ
ejpam-4590	253	2	⟨v	⟨v	PROPN
ejpam-4590	253	3	(	(	PUNCT
ejpam-4590	253	4	g	g	NOUN
ejpam-4590	253	5	)	)	PUNCT
ejpam-4590	253	6	\	\	NOUN
ejpam-4590	253	7	s1⟩	s1⟩	PRON
ejpam-4590	253	8	is	be	AUX
ejpam-4590	253	9	connected	connect	VERB
ejpam-4590	253	10	,	,	PUNCT
ejpam-4590	253	11	it	it	PRON
ejpam-4590	253	12	follows	follow	VERB
ejpam-4590	253	13	that	that	SCONJ
ejpam-4590	253	14	g	g	PROPN
ejpam-4590	253	15	has	have	VERB
ejpam-4590	253	16	exactly	exactly	ADV
ejpam-4590	253	17	3	3	NUM
ejpam-4590	253	18	components	component	NOUN
ejpam-4590	253	19	.	.	PUNCT
ejpam-4590	254	1	in	in	ADP
ejpam-4590	254	2	particular	particular	ADJ
ejpam-4590	254	3	,	,	PUNCT
ejpam-4590	254	4	the	the	DET
ejpam-4590	254	5	g1	g1	NOUN
ejpam-4590	254	6	,	,	PUNCT
ejpam-4590	254	7	g2	g2	PROPN
ejpam-4590	254	8	and	and	CCONJ
ejpam-4590	254	9	⟨v	⟨v	NUM
ejpam-4590	254	10	(	(	PUNCT
ejpam-4590	254	11	g	g	NOUN
ejpam-4590	254	12	)	)	PUNCT
ejpam-4590	254	13	\	\	NOUN
ejpam-4590	255	1	s1⟩	s1⟩	NOUN
ejpam-4590	255	2	are	be	AUX
ejpam-4590	255	3	the	the	DET
ejpam-4590	255	4	components	component	NOUN
ejpam-4590	255	5	of	of	ADP
ejpam-4590	255	6	g.	g.	PROPN
ejpam-4590	255	7	thus	thus	ADV
ejpam-4590	255	8	,	,	PUNCT
ejpam-4590	255	9	(	(	PUNCT
ejpam-4590	255	10	b	b	X
ejpam-4590	255	11	)	)	PUNCT
ejpam-4590	255	12	holds	hold	VERB
ejpam-4590	255	13	.	.	PUNCT
ejpam-4590	256	1	conversely	conversely	ADV
ejpam-4590	256	2	,	,	PUNCT
ejpam-4590	256	3	suppose	suppose	VERB
ejpam-4590	256	4	that	that	SCONJ
ejpam-4590	256	5	(	(	PUNCT
ejpam-4590	256	6	a	a	PRON
ejpam-4590	256	7	)	)	PUNCT
ejpam-4590	256	8	holds	hold	NOUN
ejpam-4590	256	9	.	.	PUNCT
ejpam-4590	257	1	if	if	SCONJ
ejpam-4590	257	2	g	g	PROPN
ejpam-4590	257	3	has	have	VERB
ejpam-4590	257	4	only	only	ADV
ejpam-4590	257	5	one	one	NUM
ejpam-4590	257	6	component	component	NOUN
ejpam-4590	257	7	,	,	PUNCT
ejpam-4590	257	8	then	then	ADV
ejpam-4590	257	9	g	g	PROPN
ejpam-4590	257	10	=	=	SYM
ejpam-4590	257	11	k2	k2	PROPN
ejpam-4590	257	12	.	.	PUNCT
ejpam-4590	258	1	hence	hence	ADV
ejpam-4590	258	2	,	,	PUNCT
ejpam-4590	258	3	p̃nd(g	p̃nd(g	ADV
ejpam-4590	258	4	)	)	PUNCT
ejpam-4590	258	5	=	=	SYM
ejpam-4590	259	1	2	2	X
ejpam-4590	259	2	.	.	X
ejpam-4590	259	3	suppose	suppose	VERB
ejpam-4590	259	4	g	g	PROPN
ejpam-4590	259	5	has	have	VERB
ejpam-4590	259	6	two	two	NUM
ejpam-4590	259	7	non	non	ADJ
ejpam-4590	259	8	-	-	ADJ
ejpam-4590	259	9	trivial	trivial	ADJ
ejpam-4590	259	10	components	component	NOUN
ejpam-4590	259	11	,	,	PUNCT
ejpam-4590	259	12	say	say	VERB
ejpam-4590	259	13	g1	g1	PROPN
ejpam-4590	259	14	and	and	CCONJ
ejpam-4590	259	15	g2	g2	PROPN
ejpam-4590	259	16	,	,	PUNCT
ejpam-4590	259	17	where	where	SCONJ
ejpam-4590	259	18	g1	g1	PROPN
ejpam-4590	259	19	=	=	SYM
ejpam-4590	259	20	k2	k2	PROPN
ejpam-4590	259	21	.	.	PUNCT
ejpam-4590	260	1	let	let	VERB
ejpam-4590	260	2	s	s	PRON
ejpam-4590	260	3	=	=	X
ejpam-4590	260	4	v	v	PROPN
ejpam-4590	260	5	(	(	PUNCT
ejpam-4590	260	6	g1	g1	PROPN
ejpam-4590	260	7	)	)	PUNCT
ejpam-4590	260	8	.	.	PUNCT
ejpam-4590	261	1	clearly	clearly	ADV
ejpam-4590	261	2	,	,	PUNCT
ejpam-4590	261	3	s	s	VERB
ejpam-4590	261	4	is	be	AUX
ejpam-4590	261	5	a	a	DET
ejpam-4590	261	6	pointwise	pointwise	ADJ
ejpam-4590	261	7	non	non	ADJ
ejpam-4590	261	8	-	-	ADJ
ejpam-4590	261	9	dominating	dominating	ADJ
ejpam-4590	261	10	set	set	NOUN
ejpam-4590	261	11	and	and	CCONJ
ejpam-4590	261	12	⟨v	⟨v	NUM
ejpam-4590	261	13	(	(	PUNCT
ejpam-4590	261	14	g	g	NOUN
ejpam-4590	261	15	)	)	PUNCT
ejpam-4590	261	16	\	\	NOUN
ejpam-4590	261	17	s⟩	s⟩	PUNCT
ejpam-4590	262	1	=	=	PUNCT
ejpam-4590	262	2	g2	g2	PROPN
ejpam-4590	262	3	is	be	AUX
ejpam-4590	262	4	connected	connect	VERB
ejpam-4590	262	5	.	.	PUNCT
ejpam-4590	263	1	hence	hence	ADV
ejpam-4590	263	2	,	,	PUNCT
ejpam-4590	263	3	p̃nd(g	p̃nd(g	ADV
ejpam-4590	263	4	)	)	PUNCT
ejpam-4590	263	5	=	=	SYM
ejpam-4590	264	1	2	2	X
ejpam-4590	264	2	.	.	X
ejpam-4590	264	3	suppose	suppose	VERB
ejpam-4590	264	4	(	(	PUNCT
ejpam-4590	264	5	b	b	NOUN
ejpam-4590	264	6	)	)	PUNCT
ejpam-4590	264	7	holds	hold	VERB
ejpam-4590	264	8	.	.	PUNCT
ejpam-4590	265	1	let	let	VERB
ejpam-4590	265	2	g1	g1	PROPN
ejpam-4590	265	3	,	,	PUNCT
ejpam-4590	265	4	g2	g2	PROPN
ejpam-4590	265	5	and	and	CCONJ
ejpam-4590	265	6	g3	g3	PROPN
ejpam-4590	265	7	be	be	AUX
ejpam-4590	265	8	the	the	DET
ejpam-4590	265	9	components	component	NOUN
ejpam-4590	265	10	of	of	ADP
ejpam-4590	265	11	g	g	PROPN
ejpam-4590	265	12	such	such	ADJ
ejpam-4590	265	13	that	that	SCONJ
ejpam-4590	265	14	g1	g1	PROPN
ejpam-4590	265	15	and	and	CCONJ
ejpam-4590	265	16	g2	g2	PROPN
ejpam-4590	265	17	are	be	AUX
ejpam-4590	265	18	trivial	trivial	ADJ
ejpam-4590	265	19	graphs	graph	NOUN
ejpam-4590	265	20	.	.	PUNCT
ejpam-4590	266	1	let	let	VERB
ejpam-4590	266	2	s	s	PRON
ejpam-4590	266	3	′	′	NOUN
ejpam-4590	266	4	=	=	SYM
ejpam-4590	266	5	v	v	X
ejpam-4590	266	6	(	(	PUNCT
ejpam-4590	266	7	g1	g1	PROPN
ejpam-4590	266	8	)	)	PUNCT
ejpam-4590	266	9	∪	∪	NOUN
ejpam-4590	266	10	v	v	PROPN
ejpam-4590	266	11	(	(	PUNCT
ejpam-4590	266	12	g2	g2	PROPN
ejpam-4590	266	13	)	)	PUNCT
ejpam-4590	266	14	.	.	PUNCT
ejpam-4590	267	1	clearly	clearly	ADV
ejpam-4590	267	2	,	,	PUNCT
ejpam-4590	267	3	s	s	VERB
ejpam-4590	267	4	′	′	NOUN
ejpam-4590	267	5	is	be	AUX
ejpam-4590	267	6	a	a	DET
ejpam-4590	267	7	pointwise	pointwise	ADJ
ejpam-4590	267	8	non	non	ADJ
ejpam-4590	267	9	-	-	ADJ
ejpam-4590	267	10	dominating	dominating	ADJ
ejpam-4590	267	11	set	set	NOUN
ejpam-4590	267	12	and	and	CCONJ
ejpam-4590	267	13	〈	〈	PROPN
ejpam-4590	267	14	v	v	NOUN
ejpam-4590	267	15	(	(	PUNCT
ejpam-4590	267	16	g	g	NOUN
ejpam-4590	267	17	)	)	PUNCT
ejpam-4590	267	18	\	\	NOUN
ejpam-4590	267	19	s′	s′	VERB
ejpam-4590	267	20	〉	〉	NOUN
ejpam-4590	267	21	=	=	SYM
ejpam-4590	267	22	g3	g3	NOUN
ejpam-4590	267	23	is	be	AUX
ejpam-4590	267	24	connected	connect	VERB
ejpam-4590	267	25	.	.	PUNCT
ejpam-4590	268	1	hence	hence	ADV
ejpam-4590	268	2	,	,	PUNCT
ejpam-4590	268	3	p̃nd(g	p̃nd(g	ADV
ejpam-4590	268	4	)	)	PUNCT
ejpam-4590	268	5	=	=	SYM
ejpam-4590	269	1	2	2	X
ejpam-4590	269	2	.	.	X
ejpam-4590	269	3	suppose	suppose	VERB
ejpam-4590	269	4	(	(	PUNCT
ejpam-4590	269	5	c	c	NOUN
ejpam-4590	269	6	)	)	PUNCT
ejpam-4590	269	7	holds	hold	NOUN
ejpam-4590	269	8	.	.	PUNCT
ejpam-4590	270	1	set	set	NOUN
ejpam-4590	270	2	s	s	PART
ejpam-4590	270	3	′′	′′	NOUN
ejpam-4590	270	4	=	=	PRON
ejpam-4590	270	5	{	{	PUNCT
ejpam-4590	270	6	a	a	DET
ejpam-4590	270	7	,	,	PUNCT
ejpam-4590	270	8	b	b	NOUN
ejpam-4590	270	9	}	}	PUNCT
ejpam-4590	270	10	and	and	CCONJ
ejpam-4590	270	11	let	let	VERB
ejpam-4590	270	12	w	w	PROPN
ejpam-4590	270	13	∈	∈	PROPN
ejpam-4590	270	14	v	v	ADP
ejpam-4590	270	15	(	(	PUNCT
ejpam-4590	270	16	g	g	NOUN
ejpam-4590	270	17	)	)	PUNCT
ejpam-4590	270	18	\	\	PROPN
ejpam-4590	270	19	s′′	s′′	PROPN
ejpam-4590	270	20	.	.	PUNCT
ejpam-4590	271	1	then	then	ADV
ejpam-4590	271	2	by	by	ADP
ejpam-4590	271	3	assumption	assumption	NOUN
ejpam-4590	271	4	,	,	PUNCT
ejpam-4590	271	5	w	w	NOUN
ejpam-4590	271	6	is	be	AUX
ejpam-4590	271	7	not	not	PART
ejpam-4590	271	8	adjacent	adjacent	ADJ
ejpam-4590	271	9	to	to	ADP
ejpam-4590	271	10	a	a	PRON
ejpam-4590	271	11	or	or	CCONJ
ejpam-4590	271	12	b.	b.	NOUN
ejpam-4590	271	13	this	this	PRON
ejpam-4590	271	14	implies	imply	VERB
ejpam-4590	271	15	that	that	SCONJ
ejpam-4590	271	16	s	s	VERB
ejpam-4590	271	17	′′	′′	PROPN
ejpam-4590	271	18	is	be	AUX
ejpam-4590	271	19	a	a	DET
ejpam-4590	271	20	pointwise	pointwise	ADJ
ejpam-4590	271	21	non	non	ADJ
ejpam-4590	271	22	-	-	ADJ
ejpam-4590	271	23	dominating	dominating	ADJ
ejpam-4590	271	24	set	set	NOUN
ejpam-4590	271	25	of	of	ADP
ejpam-4590	271	26	g.	g.	PROPN
ejpam-4590	271	27	since	since	SCONJ
ejpam-4590	271	28	g	g	PROPN
ejpam-4590	271	29	is	be	AUX
ejpam-4590	271	30	connected	connect	VERB
ejpam-4590	271	31	and	and	CCONJ
ejpam-4590	271	32	non	non	ADJ
ejpam-4590	271	33	-	-	ADJ
ejpam-4590	271	34	complete	complete	ADJ
ejpam-4590	271	35	,	,	PUNCT
ejpam-4590	271	36	p̃nd(g	p̃nd(g	ADJ
ejpam-4590	271	37	)	)	PUNCT
ejpam-4590	271	38	̸=	̸=	PROPN
ejpam-4590	271	39	1	1	NUM
ejpam-4590	271	40	by	by	ADP
ejpam-4590	271	41	(	(	PUNCT
ejpam-4590	271	42	ii	ii	NOUN
ejpam-4590	271	43	)	)	PUNCT
ejpam-4590	271	44	.	.	PUNCT
ejpam-4590	272	1	hence	hence	ADV
ejpam-4590	272	2	,	,	PUNCT
ejpam-4590	272	3	p̃nd(g	p̃nd(g	ADV
ejpam-4590	272	4	)	)	PUNCT
ejpam-4590	272	5	=	=	SYM
ejpam-4590	273	1	2	2	X
ejpam-4590	273	2	.	.	PUNCT
ejpam-4590	273	3	the	the	DET
ejpam-4590	273	4	next	next	ADJ
ejpam-4590	273	5	result	result	NOUN
ejpam-4590	273	6	is	be	AUX
ejpam-4590	273	7	a	a	DET
ejpam-4590	273	8	consequence	consequence	NOUN
ejpam-4590	273	9	of	of	ADP
ejpam-4590	273	10	theorem	theorem	ADJ
ejpam-4590	273	11	6	6	NUM
ejpam-4590	273	12	(	(	PUNCT
ejpam-4590	273	13	iii)(c	iii)(c	PROPN
ejpam-4590	273	14	)	)	PUNCT
ejpam-4590	273	15	.	.	PUNCT
ejpam-4590	274	1	corollary	corollary	ADJ
ejpam-4590	274	2	3	3	X
ejpam-4590	274	3	.	.	PUNCT
ejpam-4590	275	1	let	let	VERB
ejpam-4590	275	2	g	g	PRON
ejpam-4590	275	3	be	be	AUX
ejpam-4590	275	4	a	a	DET
ejpam-4590	275	5	graph	graph	NOUN
ejpam-4590	275	6	on	on	ADP
ejpam-4590	275	7	n	n	DET
ejpam-4590	275	8	vertices	vertex	NOUN
ejpam-4590	275	9	.	.	PUNCT
ejpam-4590	276	1	then	then	ADV
ejpam-4590	276	2	p̃nd(pn	p̃nd(pn	NOUN
ejpam-4590	276	3	)	)	PUNCT
ejpam-4590	276	4	=	=	SYM
ejpam-4590	276	5	2	2	NUM
ejpam-4590	276	6	for	for	ADP
ejpam-4590	276	7	all	all	DET
ejpam-4590	276	8	n	n	PRON
ejpam-4590	276	9	≥	≥	NOUN
ejpam-4590	276	10	3	3	NUM
ejpam-4590	276	11	and	and	CCONJ
ejpam-4590	276	12	p̃nd(cn	p̃nd(cn	NOUN
ejpam-4590	276	13	)	)	PUNCT
ejpam-4590	276	14	=	=	SYM
ejpam-4590	276	15	2	2	NUM
ejpam-4590	276	16	for	for	ADP
ejpam-4590	276	17	all	all	DET
ejpam-4590	276	18	n	n	PRON
ejpam-4590	276	19	≥	≥	NOUN
ejpam-4590	276	20	4	4	NUM
ejpam-4590	276	21	.	.	PUNCT
ejpam-4590	277	1	c.j	c.j	PROPN
ejpam-4590	277	2	.	.	PROPN
ejpam-4590	277	3	saromines	saromines	PROPN
ejpam-4590	277	4	,	,	PUNCT
ejpam-4590	277	5	s.	s.	PROPN
ejpam-4590	277	6	canoy	canoy	PROPN
ejpam-4590	277	7	,	,	PUNCT
ejpam-4590	277	8	jr	jr	PROPN
ejpam-4590	277	9	.	.	PROPN
ejpam-4590	277	10	/	/	SYM
ejpam-4590	277	11	eur	eur	PROPN
ejpam-4590	277	12	.	.	PUNCT
ejpam-4590	278	1	j.	j.	PROPN
ejpam-4590	278	2	pure	pure	PROPN
ejpam-4590	278	3	appl	appl	PROPN
ejpam-4590	278	4	.	.	PROPN
ejpam-4590	278	5	math	math	PROPN
ejpam-4590	278	6	,	,	PUNCT
ejpam-4590	278	7	15	15	NUM
ejpam-4590	278	8	(	(	PUNCT
ejpam-4590	278	9	4	4	NUM
ejpam-4590	278	10	)	)	PUNCT
ejpam-4590	278	11	(	(	PUNCT
ejpam-4590	278	12	2022	2022	NUM
ejpam-4590	278	13	)	)	PUNCT
ejpam-4590	278	14	,	,	PUNCT
ejpam-4590	278	15	1966	1966	NUM
ejpam-4590	278	16	-	-	SYM
ejpam-4590	278	17	1981	1981	NUM
ejpam-4590	278	18	1973	1973	NUM
ejpam-4590	278	19	proposition	proposition	NOUN
ejpam-4590	278	20	3	3	X
ejpam-4590	278	21	.	.	PUNCT
ejpam-4590	279	1	let	let	VERB
ejpam-4590	279	2	g	g	PRON
ejpam-4590	279	3	be	be	AUX
ejpam-4590	279	4	a	a	DET
ejpam-4590	279	5	graph	graph	NOUN
ejpam-4590	279	6	with	with	ADP
ejpam-4590	279	7	components	component	NOUN
ejpam-4590	279	8	g1	g1	PROPN
ejpam-4590	279	9	,	,	PUNCT
ejpam-4590	279	10	g2	g2	PROPN
ejpam-4590	279	11	,	,	PUNCT
ejpam-4590	279	12	...	...	PUNCT
ejpam-4590	279	13	,	,	PUNCT
ejpam-4590	279	14	gk	gk	INTJ
ejpam-4590	279	15	where	where	SCONJ
ejpam-4590	279	16	k	k	PROPN
ejpam-4590	279	17	≥	≥	NUM
ejpam-4590	280	1	2	2	NUM
ejpam-4590	280	2	.	.	PUNCT
ejpam-4590	280	3	then	then	ADV
ejpam-4590	280	4	p̃nd(g	p̃nd(g	ADV
ejpam-4590	280	5	)	)	PUNCT
ejpam-4590	281	1	=	=	SYM
ejpam-4590	281	2	|v	|v	PROPN
ejpam-4590	281	3	(	(	PUNCT
ejpam-4590	281	4	g)|	g)|	PROPN
ejpam-4590	281	5	max	max	PROPN
ejpam-4590	281	6	{	{	PUNCT
ejpam-4590	281	7	|v	|v	PROPN
ejpam-4590	281	8	(	(	PUNCT
ejpam-4590	281	9	gj)|	gj)|	NOUN
ejpam-4590	281	10	:	:	PUNCT
ejpam-4590	281	11	j	j	PROPN
ejpam-4590	281	12	∈	∈	PROPN
ejpam-4590	281	13	{	{	PUNCT
ejpam-4590	281	14	1	1	NUM
ejpam-4590	281	15	,	,	PUNCT
ejpam-4590	281	16	...	...	PUNCT
ejpam-4590	281	17	,	,	PUNCT
ejpam-4590	281	18	k	k	NOUN
ejpam-4590	281	19	}	}	PUNCT
ejpam-4590	281	20	}	}	PUNCT
ejpam-4590	281	21	.	.	PUNCT
ejpam-4590	282	1	proof	proof	NOUN
ejpam-4590	282	2	.	.	PUNCT
ejpam-4590	283	1	let	let	VERB
ejpam-4590	283	2	s	s	PRON
ejpam-4590	283	3	be	be	AUX
ejpam-4590	283	4	a	a	DET
ejpam-4590	283	5	p̃nd	p̃nd	NOUN
ejpam-4590	283	6	-	-	PUNCT
ejpam-4590	283	7	set	set	NOUN
ejpam-4590	283	8	of	of	ADP
ejpam-4590	283	9	g.	g.	PROPN
ejpam-4590	283	10	since	since	SCONJ
ejpam-4590	283	11	s	s	PROPN
ejpam-4590	283	12	is	be	AUX
ejpam-4590	283	13	outer	outer	ADV
ejpam-4590	283	14	-	-	PUNCT
ejpam-4590	283	15	connected	connect	VERB
ejpam-4590	283	16	,	,	PUNCT
ejpam-4590	283	17	⟨v	⟨v	PROPN
ejpam-4590	283	18	(	(	PUNCT
ejpam-4590	283	19	g	g	NOUN
ejpam-4590	283	20	)	)	PUNCT
ejpam-4590	283	21	\	\	PROPN
ejpam-4590	283	22	s⟩	s⟩	PROPN
ejpam-4590	283	23	is	be	AUX
ejpam-4590	283	24	connected	connect	VERB
ejpam-4590	283	25	.	.	PUNCT
ejpam-4590	284	1	this	this	PRON
ejpam-4590	284	2	implies	imply	VERB
ejpam-4590	284	3	that	that	PRON
ejpam-4590	284	4	⟨v	⟨v	NOUN
ejpam-4590	284	5	(	(	PUNCT
ejpam-4590	284	6	g	g	NOUN
ejpam-4590	284	7	)	)	PUNCT
ejpam-4590	284	8	\	\	NOUN
ejpam-4590	284	9	s⟩	s⟩	PUNCT
ejpam-4590	285	1	=	=	NOUN
ejpam-4590	285	2	gj	gj	NOUN
ejpam-4590	285	3	for	for	ADP
ejpam-4590	285	4	some	some	DET
ejpam-4590	285	5	j	j	PROPN
ejpam-4590	285	6	∈	∈	PROPN
ejpam-4590	285	7	{	{	PUNCT
ejpam-4590	285	8	1	1	NUM
ejpam-4590	285	9	,	,	PUNCT
ejpam-4590	285	10	2	2	NUM
ejpam-4590	285	11	,	,	PUNCT
ejpam-4590	285	12	...	...	PUNCT
ejpam-4590	285	13	,	,	PUNCT
ejpam-4590	285	14	k	k	NOUN
ejpam-4590	285	15	}	}	PUNCT
ejpam-4590	285	16	.	.	PUNCT
ejpam-4590	286	1	since	since	SCONJ
ejpam-4590	286	2	s	s	PROPN
ejpam-4590	286	3	is	be	AUX
ejpam-4590	286	4	a	a	DET
ejpam-4590	286	5	p̃nd	p̃nd	NOUN
ejpam-4590	286	6	-	-	PUNCT
ejpam-4590	286	7	set	set	NOUN
ejpam-4590	286	8	,	,	PUNCT
ejpam-4590	286	9	it	it	PRON
ejpam-4590	286	10	follows	follow	VERB
ejpam-4590	286	11	that	that	SCONJ
ejpam-4590	286	12	|v	|v	PROPN
ejpam-4590	286	13	(	(	PUNCT
ejpam-4590	286	14	gj)|	gj)|	X
ejpam-4590	286	15	≥	≥	NOUN
ejpam-4590	286	16	|v	|v	NOUN
ejpam-4590	286	17	(	(	PUNCT
ejpam-4590	286	18	gi|	gi|	PROPN
ejpam-4590	286	19	for	for	ADP
ejpam-4590	286	20	all	all	PRON
ejpam-4590	286	21	i	i	PRON
ejpam-4590	286	22	∈	∈	PROPN
ejpam-4590	286	23	{	{	PUNCT
ejpam-4590	286	24	1	1	NUM
ejpam-4590	286	25	,	,	PUNCT
ejpam-4590	286	26	2	2	NUM
ejpam-4590	286	27	,	,	PUNCT
ejpam-4590	286	28	...	...	PUNCT
ejpam-4590	286	29	,	,	PUNCT
ejpam-4590	286	30	k	k	NOUN
ejpam-4590	286	31	}	}	PUNCT
ejpam-4590	286	32	.	.	PUNCT
ejpam-4590	287	1	therefore	therefore	ADV
ejpam-4590	287	2	,	,	PUNCT
ejpam-4590	287	3	p̃nd(g	p̃nd(g	ADJ
ejpam-4590	287	4	)	)	PUNCT
ejpam-4590	287	5	=	=	PUNCT
ejpam-4590	287	6	|s|	|s|	NOUN
ejpam-4590	287	7	=	=	NOUN
ejpam-4590	287	8	|∪i	|∪i	NOUN
ejpam-4590	287	9	̸=jv	̸=jv	NOUN
ejpam-4590	287	10	(	(	PUNCT
ejpam-4590	287	11	gi)|	gi)|	X
ejpam-4590	287	12	=	=	SYM
ejpam-4590	287	13	|v	|v	PROPN
ejpam-4590	287	14	(	(	PUNCT
ejpam-4590	287	15	g)|	g)|	PROPN
ejpam-4590	287	16	−	−	PROPN
ejpam-4590	287	17	|v	|v	NOUN
ejpam-4590	287	18	(	(	PUNCT
ejpam-4590	287	19	gj	gj	NOUN
ejpam-4590	287	20	|	|	ADV
ejpam-4590	287	21	=	=	SYM
ejpam-4590	287	22	|v	|v	PROPN
ejpam-4590	287	23	(	(	PUNCT
ejpam-4590	287	24	g)|	g)|	NOUN
ejpam-4590	287	25	−max	−max	PRON
ejpam-4590	287	26	{	{	PUNCT
ejpam-4590	287	27	|v	|v	PROPN
ejpam-4590	287	28	(	(	PUNCT
ejpam-4590	288	1	gi)|	gi)|	INTJ
ejpam-4590	288	2	:	:	PUNCT
ejpam-4590	288	3	i	i	PRON
ejpam-4590	288	4	∈	∈	PROPN
ejpam-4590	288	5	{	{	PUNCT
ejpam-4590	288	6	1	1	NUM
ejpam-4590	288	7	,	,	PUNCT
ejpam-4590	288	8	2	2	NUM
ejpam-4590	288	9	,	,	PUNCT
ejpam-4590	288	10	...	...	PUNCT
ejpam-4590	288	11	,	,	PUNCT
ejpam-4590	288	12	k	k	NOUN
ejpam-4590	288	13	}	}	PUNCT
ejpam-4590	288	14	}	}	PUNCT
ejpam-4590	288	15	.	.	PUNCT
ejpam-4590	289	1	this	this	PRON
ejpam-4590	289	2	proves	prove	VERB
ejpam-4590	289	3	the	the	DET
ejpam-4590	289	4	assertion	assertion	NOUN
ejpam-4590	289	5	.	.	PUNCT
ejpam-4590	290	1	corollary	corollary	ADJ
ejpam-4590	290	2	4	4	NUM
ejpam-4590	290	3	.	.	PUNCT
ejpam-4590	291	1	let	let	VERB
ejpam-4590	291	2	g	g	PRON
ejpam-4590	291	3	be	be	AUX
ejpam-4590	291	4	a	a	DET
ejpam-4590	291	5	disconnected	disconnected	ADJ
ejpam-4590	291	6	graph	graph	NOUN
ejpam-4590	291	7	of	of	ADP
ejpam-4590	291	8	order	order	NOUN
ejpam-4590	291	9	n	n	PRON
ejpam-4590	291	10	≥	≥	NOUN
ejpam-4590	291	11	2	2	NUM
ejpam-4590	291	12	.	.	PUNCT
ejpam-4590	292	1	then	then	ADV
ejpam-4590	292	2	p̃nd(g	p̃nd(g	ADV
ejpam-4590	292	3	)	)	PUNCT
ejpam-4590	293	1	=	=	PUNCT
ejpam-4590	293	2	n−	n−	NOUN
ejpam-4590	293	3	1	1	NUM
ejpam-4590	293	4	if	if	SCONJ
ejpam-4590	293	5	and	and	CCONJ
ejpam-4590	293	6	only	only	ADV
ejpam-4590	293	7	if	if	SCONJ
ejpam-4590	293	8	g	g	PROPN
ejpam-4590	293	9	=	=	PROPN
ejpam-4590	293	10	kn	kn	PROPN
ejpam-4590	293	11	.	.	PUNCT
ejpam-4590	293	12	proof	proof	NOUN
ejpam-4590	293	13	.	.	PUNCT
ejpam-4590	294	1	let	let	VERB
ejpam-4590	294	2	g1	g1	PROPN
ejpam-4590	294	3	,	,	PUNCT
ejpam-4590	294	4	g2	g2	PROPN
ejpam-4590	294	5	,	,	PUNCT
ejpam-4590	294	6	...	...	PUNCT
ejpam-4590	294	7	,	,	PUNCT
ejpam-4590	294	8	gk	gk	PROPN
ejpam-4590	294	9	be	be	AUX
ejpam-4590	294	10	components	component	NOUN
ejpam-4590	294	11	of	of	ADP
ejpam-4590	294	12	g	g	NOUN
ejpam-4590	294	13	and	and	CCONJ
ejpam-4590	294	14	suppose	suppose	VERB
ejpam-4590	294	15	that	that	SCONJ
ejpam-4590	294	16	p̃nd(g	p̃nd(g	ADV
ejpam-4590	294	17	)	)	PUNCT
ejpam-4590	295	1	=	=	SYM
ejpam-4590	295	2	n−1	n−1	PROPN
ejpam-4590	295	3	.	.	PUNCT
ejpam-4590	296	1	then	then	ADV
ejpam-4590	296	2	,	,	PUNCT
ejpam-4590	296	3	by	by	ADP
ejpam-4590	296	4	proposition	proposition	NOUN
ejpam-4590	296	5	3	3	NUM
ejpam-4590	296	6	,	,	PUNCT
ejpam-4590	296	7	max	max	PROPN
ejpam-4590	296	8	{	{	PUNCT
ejpam-4590	296	9	|v	|v	PROPN
ejpam-4590	296	10	(	(	PUNCT
ejpam-4590	296	11	gj)|	gj)|	NOUN
ejpam-4590	296	12	:	:	PUNCT
ejpam-4590	296	13	j	j	PROPN
ejpam-4590	296	14	∈	∈	PROPN
ejpam-4590	296	15	{	{	PUNCT
ejpam-4590	296	16	1	1	NUM
ejpam-4590	296	17	,	,	PUNCT
ejpam-4590	296	18	2	2	NUM
ejpam-4590	296	19	,	,	PUNCT
ejpam-4590	296	20	...	...	PUNCT
ejpam-4590	296	21	,	,	PUNCT
ejpam-4590	296	22	k	k	NOUN
ejpam-4590	296	23	}	}	PUNCT
ejpam-4590	296	24	}	}	PUNCT
ejpam-4590	296	25	=	=	SYM
ejpam-4590	296	26	1	1	X
ejpam-4590	296	27	.	.	PUNCT
ejpam-4590	297	1	this	this	PRON
ejpam-4590	297	2	implies	imply	VERB
ejpam-4590	297	3	that	that	SCONJ
ejpam-4590	297	4	gj	gj	NOUN
ejpam-4590	297	5	=	=	SYM
ejpam-4590	297	6	k1	k1	PROPN
ejpam-4590	297	7	for	for	ADP
ejpam-4590	297	8	every	every	DET
ejpam-4590	297	9	j	j	PROPN
ejpam-4590	297	10	∈	∈	PROPN
ejpam-4590	297	11	{	{	PUNCT
ejpam-4590	297	12	1	1	NUM
ejpam-4590	297	13	,	,	PUNCT
ejpam-4590	297	14	2	2	NUM
ejpam-4590	297	15	,	,	PUNCT
ejpam-4590	297	16	...	...	PUNCT
ejpam-4590	297	17	,	,	PUNCT
ejpam-4590	297	18	k	k	NOUN
ejpam-4590	297	19	}	}	PUNCT
ejpam-4590	297	20	.	.	PUNCT
ejpam-4590	298	1	therefore	therefore	ADV
ejpam-4590	298	2	,	,	PUNCT
ejpam-4590	298	3	g	g	PROPN
ejpam-4590	298	4	=	=	SYM
ejpam-4590	298	5	kn	kn	PROPN
ejpam-4590	298	6	.	.	PUNCT
ejpam-4590	299	1	the	the	DET
ejpam-4590	299	2	converse	converse	NOUN
ejpam-4590	299	3	also	also	ADV
ejpam-4590	299	4	follows	follow	VERB
ejpam-4590	299	5	from	from	ADP
ejpam-4590	299	6	proposition	proposition	NOUN
ejpam-4590	299	7	3	3	NUM
ejpam-4590	299	8	.	.	PUNCT
ejpam-4590	300	1	given	give	VERB
ejpam-4590	300	2	a	a	DET
ejpam-4590	300	3	complete	complete	ADJ
ejpam-4590	300	4	graph	graph	NOUN
ejpam-4590	300	5	kn	kn	PROPN
ejpam-4590	300	6	on	on	ADP
ejpam-4590	300	7	n	n	PRON
ejpam-4590	300	8	≥	≥	NUM
ejpam-4590	300	9	2	2	NUM
ejpam-4590	300	10	vertices	vertex	NOUN
ejpam-4590	300	11	and	and	CCONJ
ejpam-4590	300	12	e	e	NOUN
ejpam-4590	300	13	⊆	⊆	NUM
ejpam-4590	300	14	e(kn	e(kn	NUM
ejpam-4590	300	15	)	)	PUNCT
ejpam-4590	300	16	,	,	PUNCT
ejpam-4590	300	17	we	we	PRON
ejpam-4590	300	18	denote	denote	VERB
ejpam-4590	300	19	by	by	ADP
ejpam-4590	300	20	kn	kn	PROPN
ejpam-4590	300	21	\	\	PROPN
ejpam-4590	300	22	e	e	NOUN
ejpam-4590	300	23	the	the	DET
ejpam-4590	300	24	graph	graph	NOUN
ejpam-4590	300	25	obtained	obtain	VERB
ejpam-4590	300	26	from	from	ADP
ejpam-4590	300	27	kn	kn	PROPN
ejpam-4590	300	28	by	by	ADP
ejpam-4590	300	29	deleting	delete	VERB
ejpam-4590	300	30	the	the	DET
ejpam-4590	300	31	edges	edge	NOUN
ejpam-4590	300	32	in	in	ADP
ejpam-4590	300	33	set	set	PROPN
ejpam-4590	300	34	e.	e.	PROPN
ejpam-4590	300	35	theorem	theorem	PROPN
ejpam-4590	300	36	7	7	PROPN
ejpam-4590	300	37	.	.	PUNCT
ejpam-4590	301	1	let	let	VERB
ejpam-4590	301	2	g	g	PRON
ejpam-4590	301	3	be	be	AUX
ejpam-4590	301	4	a	a	DET
ejpam-4590	301	5	connected	connected	ADJ
ejpam-4590	301	6	graph	graph	NOUN
ejpam-4590	301	7	on	on	ADP
ejpam-4590	301	8	n	n	PRON
ejpam-4590	301	9	≥	≥	NUM
ejpam-4590	301	10	3	3	NUM
ejpam-4590	301	11	vertices	vertex	NOUN
ejpam-4590	301	12	.	.	PUNCT
ejpam-4590	302	1	then	then	ADV
ejpam-4590	302	2	p̃nd(g	p̃nd(g	ADV
ejpam-4590	302	3	)	)	PUNCT
ejpam-4590	303	1	=	=	SYM
ejpam-4590	303	2	n	n	CCONJ
ejpam-4590	303	3	−	−	PROPN
ejpam-4590	303	4	1	1	NUM
ejpam-4590	304	1	if	if	SCONJ
ejpam-4590	304	2	and	and	CCONJ
ejpam-4590	304	3	only	only	ADV
ejpam-4590	304	4	if	if	SCONJ
ejpam-4590	304	5	g	g	PROPN
ejpam-4590	304	6	=	=	SYM
ejpam-4590	304	7	kn	kn	PROPN
ejpam-4590	304	8	\	\	PROPN
ejpam-4590	304	9	eg	eg	PROPN
ejpam-4590	304	10	,	,	PUNCT
ejpam-4590	304	11	where	where	SCONJ
ejpam-4590	304	12	eg	eg	ADP
ejpam-4590	304	13	⊆	⊆	NUM
ejpam-4590	304	14	e(kn	e(kn	NUM
ejpam-4590	304	15	)	)	PUNCT
ejpam-4590	304	16	and	and	CCONJ
ejpam-4590	304	17	for	for	ADP
ejpam-4590	304	18	some	some	DET
ejpam-4590	304	19	2	2	NUM
ejpam-4590	304	20	≤	≤	NOUN
ejpam-4590	304	21	r	r	NOUN
ejpam-4590	304	22	≤	≤	NOUN
ejpam-4590	304	23	n	n	CCONJ
ejpam-4590	304	24	−	−	PROPN
ejpam-4590	304	25	1	1	NUM
ejpam-4590	304	26	,	,	PUNCT
ejpam-4590	304	27	⟨{x	⟨{x	PUNCT
ejpam-4590	304	28	:	:	PUNCT
ejpam-4590	304	29	xy	xy	PROPN
ejpam-4590	304	30	∈	∈	PROPN
ejpam-4590	304	31	eg	eg	NOUN
ejpam-4590	304	32	for	for	ADP
ejpam-4590	304	33	some	some	DET
ejpam-4590	304	34	y	y	PROPN
ejpam-4590	304	35	∈	∈	PROPN
ejpam-4590	304	36	v	v	PROPN
ejpam-4590	304	37	(	(	PUNCT
ejpam-4590	304	38	g)}⟩	g)}⟩	X
ejpam-4590	304	39	=	=	SYM
ejpam-4590	304	40	kr	kr	PROPN
ejpam-4590	304	41	in	in	ADP
ejpam-4590	304	42	g.	g.	PROPN
ejpam-4590	304	43	proof	proof	PROPN
ejpam-4590	304	44	.	.	PUNCT
ejpam-4590	305	1	construct	construct	VERB
ejpam-4590	305	2	a	a	DET
ejpam-4590	305	3	complete	complete	ADJ
ejpam-4590	305	4	graph	graph	NOUN
ejpam-4590	305	5	kn	kn	PROPN
ejpam-4590	305	6	with	with	ADP
ejpam-4590	305	7	v	v	PROPN
ejpam-4590	305	8	(	(	PUNCT
ejpam-4590	305	9	kn	kn	PROPN
ejpam-4590	305	10	)	)	PUNCT
ejpam-4590	305	11	=	=	SYM
ejpam-4590	305	12	v	v	X
ejpam-4590	305	13	(	(	PUNCT
ejpam-4590	305	14	g	g	NOUN
ejpam-4590	305	15	)	)	PUNCT
ejpam-4590	305	16	.	.	PUNCT
ejpam-4590	306	1	then	then	ADV
ejpam-4590	306	2	g	g	PROPN
ejpam-4590	306	3	=	=	SYM
ejpam-4590	306	4	kn\eg	kn\eg	PROPN
ejpam-4590	306	5	where	where	SCONJ
ejpam-4590	306	6	eg	eg	NOUN
ejpam-4590	306	7	⊆	⊆	NUM
ejpam-4590	306	8	e(kn	e(kn	NUM
ejpam-4590	306	9	)	)	PUNCT
ejpam-4590	306	10	.	.	PUNCT
ejpam-4590	307	1	let	let	VERB
ejpam-4590	307	2	vg	vg	NOUN
ejpam-4590	307	3	=	=	PUNCT
ejpam-4590	307	4	{	{	PUNCT
ejpam-4590	307	5	x	x	X
ejpam-4590	307	6	:	:	PUNCT
ejpam-4590	307	7	xy	xy	PROPN
ejpam-4590	307	8	∈	∈	PROPN
ejpam-4590	307	9	eg	eg	NOUN
ejpam-4590	307	10	for	for	ADP
ejpam-4590	307	11	some	some	DET
ejpam-4590	307	12	y	y	PROPN
ejpam-4590	307	13	∈	∈	PROPN
ejpam-4590	307	14	v	v	ADP
ejpam-4590	307	15	(	(	PUNCT
ejpam-4590	307	16	g	g	NOUN
ejpam-4590	307	17	)	)	PUNCT
ejpam-4590	307	18	}	}	PUNCT
ejpam-4590	307	19	.	.	PUNCT
ejpam-4590	308	1	suppose	suppose	VERB
ejpam-4590	308	2	p̃nd(g	p̃nd(g	NOUN
ejpam-4590	308	3	)	)	PUNCT
ejpam-4590	309	1	=	=	PUNCT
ejpam-4590	309	2	n−	n−	NOUN
ejpam-4590	309	3	1	1	NUM
ejpam-4590	309	4	,	,	PUNCT
ejpam-4590	309	5	say	say	VERB
ejpam-4590	309	6	s	s	VERB
ejpam-4590	309	7	=	=	SYM
ejpam-4590	309	8	v	v	PROPN
ejpam-4590	309	9	(	(	PUNCT
ejpam-4590	309	10	g)\{v	g)\{v	PROPN
ejpam-4590	309	11	}	}	PUNCT
ejpam-4590	309	12	is	be	AUX
ejpam-4590	309	13	a	a	DET
ejpam-4590	309	14	p̃nd	p̃nd	NOUN
ejpam-4590	309	15	-	-	PUNCT
ejpam-4590	309	16	set	set	NOUN
ejpam-4590	309	17	of	of	ADP
ejpam-4590	309	18	g.	g.	PROPN
ejpam-4590	309	19	since	since	SCONJ
ejpam-4590	309	20	g	g	PROPN
ejpam-4590	309	21	is	be	AUX
ejpam-4590	309	22	connected	connect	VERB
ejpam-4590	309	23	and	and	CCONJ
ejpam-4590	309	24	s	s	X
ejpam-4590	309	25	is	be	AUX
ejpam-4590	309	26	pointwise	pointwise	ADJ
ejpam-4590	309	27	non	non	ADJ
ejpam-4590	309	28	-	-	ADJ
ejpam-4590	309	29	dominating	dominating	ADJ
ejpam-4590	309	30	,	,	PUNCT
ejpam-4590	309	31	there	there	PRON
ejpam-4590	309	32	exists	exist	VERB
ejpam-4590	309	33	w	w	PROPN
ejpam-4590	309	34	∈	∈	PROPN
ejpam-4590	309	35	v	v	ADP
ejpam-4590	309	36	(	(	PUNCT
ejpam-4590	309	37	g	g	NOUN
ejpam-4590	309	38	)	)	PUNCT
ejpam-4590	309	39	such	such	ADJ
ejpam-4590	309	40	that	that	PRON
ejpam-4590	309	41	dg(v	dg(v	NOUN
ejpam-4590	309	42	,	,	PUNCT
ejpam-4590	309	43	w	w	NOUN
ejpam-4590	309	44	)	)	PUNCT
ejpam-4590	309	45	=	=	SYM
ejpam-4590	309	46	2	2	X
ejpam-4590	309	47	.	.	X
ejpam-4590	310	1	hence	hence	ADV
ejpam-4590	310	2	,	,	PUNCT
ejpam-4590	310	3	vw	vw	PROPN
ejpam-4590	310	4	∈	∈	PROPN
ejpam-4590	310	5	eg	eg	NOUN
ejpam-4590	310	6	.	.	PUNCT
ejpam-4590	311	1	let	let	VERB
ejpam-4590	311	2	r	r	NOUN
ejpam-4590	311	3	be	be	AUX
ejpam-4590	311	4	the	the	DET
ejpam-4590	311	5	largest	large	ADJ
ejpam-4590	311	6	index	index	NOUN
ejpam-4590	311	7	such	such	ADJ
ejpam-4590	311	8	that	that	DET
ejpam-4590	311	9	v	v	NOUN
ejpam-4590	311	10	,	,	PUNCT
ejpam-4590	311	11	w	w	PROPN
ejpam-4590	311	12	∈	∈	PROPN
ejpam-4590	311	13	v	v	NOUN
ejpam-4590	311	14	(	(	PUNCT
ejpam-4590	311	15	kr	kr	PROPN
ejpam-4590	311	16	)	)	PUNCT
ejpam-4590	311	17	and	and	CCONJ
ejpam-4590	311	18	v	v	NOUN
ejpam-4590	311	19	(	(	PUNCT
ejpam-4590	311	20	kr	kr	PROPN
ejpam-4590	311	21	)	)	PUNCT
ejpam-4590	311	22	⊆	⊆	NUM
ejpam-4590	311	23	vg	vg	NOUN
ejpam-4590	311	24	.	.	PUNCT
ejpam-4590	312	1	since	since	SCONJ
ejpam-4590	312	2	g	g	PROPN
ejpam-4590	312	3	is	be	AUX
ejpam-4590	312	4	connected	connect	VERB
ejpam-4590	312	5	,	,	PUNCT
ejpam-4590	312	6	2	2	NUM
ejpam-4590	312	7	≤	≤	NOUN
ejpam-4590	312	8	r	r	NOUN
ejpam-4590	312	9	≤	≤	NOUN
ejpam-4590	312	10	n	n	CCONJ
ejpam-4590	312	11	−	−	PROPN
ejpam-4590	312	12	1	1	NUM
ejpam-4590	312	13	.	.	PUNCT
ejpam-4590	313	1	let	let	VERB
ejpam-4590	313	2	z	z	PROPN
ejpam-4590	313	3	∈	∈	PROPN
ejpam-4590	313	4	ng(v	ng(v	NOUN
ejpam-4590	313	5	)	)	PUNCT
ejpam-4590	313	6	∩	∩	NOUN
ejpam-4590	313	7	ng(w	ng(w	NOUN
ejpam-4590	313	8	)	)	PUNCT
ejpam-4590	313	9	.	.	PUNCT
ejpam-4590	314	1	suppose	suppose	VERB
ejpam-4590	314	2	that	that	SCONJ
ejpam-4590	314	3	there	there	PRON
ejpam-4590	314	4	exists	exist	VERB
ejpam-4590	314	5	u	u	PROPN
ejpam-4590	314	6	∈	∈	PROPN
ejpam-4590	314	7	v	v	ADP
ejpam-4590	314	8	(	(	PUNCT
ejpam-4590	314	9	g	g	NOUN
ejpam-4590	314	10	)	)	PUNCT
ejpam-4590	314	11	such	such	ADJ
ejpam-4590	314	12	that	that	SCONJ
ejpam-4590	314	13	uz	uz	PROPN
ejpam-4590	314	14	/∈	/∈	PROPN
ejpam-4590	314	15	e(g	e(g	PROPN
ejpam-4590	314	16	)	)	PUNCT
ejpam-4590	314	17	.	.	PUNCT
ejpam-4590	315	1	then	then	ADV
ejpam-4590	315	2	v	v	X
ejpam-4590	315	3	(	(	PUNCT
ejpam-4590	315	4	g	g	NOUN
ejpam-4590	315	5	)	)	PUNCT
ejpam-4590	315	6	\	\	NOUN
ejpam-4590	316	1	{	{	PUNCT
ejpam-4590	316	2	v	v	NOUN
ejpam-4590	316	3	,	,	PUNCT
ejpam-4590	316	4	z	z	NOUN
ejpam-4590	316	5	}	}	PUNCT
ejpam-4590	316	6	is	be	AUX
ejpam-4590	316	7	an	an	DET
ejpam-4590	316	8	outer	outer	ADV
ejpam-4590	316	9	-	-	PUNCT
ejpam-4590	316	10	connected	connect	VERB
ejpam-4590	316	11	pointwise	pointwise	PROPN
ejpam-4590	316	12	non	non	ADJ
ejpam-4590	316	13	-	-	ADJ
ejpam-4590	316	14	dominating	dominating	ADJ
ejpam-4590	316	15	set	set	NOUN
ejpam-4590	316	16	,	,	PUNCT
ejpam-4590	316	17	contrary	contrary	ADV
ejpam-4590	316	18	to	to	ADP
ejpam-4590	316	19	our	our	PRON
ejpam-4590	316	20	assumption	assumption	NOUN
ejpam-4590	316	21	that	that	SCONJ
ejpam-4590	316	22	p̃nd(g	p̃nd(g	ADV
ejpam-4590	316	23	)	)	PUNCT
ejpam-4590	317	1	=	=	PUNCT
ejpam-4590	317	2	n−	n−	NOUN
ejpam-4590	317	3	1	1	NUM
ejpam-4590	317	4	.	.	PUNCT
ejpam-4590	318	1	hence	hence	ADV
ejpam-4590	318	2	,	,	PUNCT
ejpam-4590	318	3	zy	zy	PROPN
ejpam-4590	318	4	∈	∈	PROPN
ejpam-4590	318	5	e(g	e(g	PROPN
ejpam-4590	318	6	)	)	PUNCT
ejpam-4590	319	1	for	for	ADP
ejpam-4590	319	2	all	all	DET
ejpam-4590	319	3	y	y	PROPN
ejpam-4590	319	4	∈	∈	PROPN
ejpam-4590	319	5	v	v	ADP
ejpam-4590	319	6	(	(	PUNCT
ejpam-4590	319	7	g	g	NOUN
ejpam-4590	319	8	)	)	PUNCT
ejpam-4590	319	9	\	\	NOUN
ejpam-4590	319	10	{	{	PUNCT
ejpam-4590	319	11	z	z	NOUN
ejpam-4590	319	12	}	}	PUNCT
ejpam-4590	319	13	.	.	PUNCT
ejpam-4590	320	1	suppose	suppose	VERB
ejpam-4590	320	2	now	now	ADV
ejpam-4590	320	3	that	that	SCONJ
ejpam-4590	320	4	vg	vg	VERB
ejpam-4590	320	5	̸=	̸=	PROPN
ejpam-4590	320	6	v	v	NOUN
ejpam-4590	320	7	(	(	PUNCT
ejpam-4590	320	8	kr	kr	PROPN
ejpam-4590	320	9	)	)	PUNCT
ejpam-4590	320	10	,	,	PUNCT
ejpam-4590	320	11	say	say	VERB
ejpam-4590	320	12	q	q	NOUN
ejpam-4590	320	13	∈	∈	PROPN
ejpam-4590	320	14	vg	vg	ADP
ejpam-4590	320	15	\	\	PROPN
ejpam-4590	320	16	v	v	NOUN
ejpam-4590	320	17	(	(	PUNCT
ejpam-4590	320	18	kr	kr	PROPN
ejpam-4590	320	19	)	)	PUNCT
ejpam-4590	320	20	.	.	PUNCT
ejpam-4590	321	1	by	by	ADP
ejpam-4590	321	2	our	our	PRON
ejpam-4590	321	3	assumption	assumption	NOUN
ejpam-4590	321	4	of	of	ADP
ejpam-4590	321	5	r	r	NOUN
ejpam-4590	321	6	,	,	PUNCT
ejpam-4590	321	7	there	there	PRON
ejpam-4590	321	8	exists	exist	VERB
ejpam-4590	321	9	t	t	PROPN
ejpam-4590	321	10	∈	∈	PROPN
ejpam-4590	321	11	v	v	PROPN
ejpam-4590	321	12	(	(	PUNCT
ejpam-4590	321	13	kr	kr	PROPN
ejpam-4590	321	14	)	)	PUNCT
ejpam-4590	321	15	such	such	ADJ
ejpam-4590	321	16	that	that	SCONJ
ejpam-4590	321	17	qt	qt	PROPN
ejpam-4590	321	18	∈	∈	PROPN
ejpam-4590	321	19	e(g	e(g	PROPN
ejpam-4590	321	20	)	)	PUNCT
ejpam-4590	321	21	.	.	PUNCT
ejpam-4590	322	1	note	note	VERB
ejpam-4590	322	2	that	that	SCONJ
ejpam-4590	322	3	tv	tv	NOUN
ejpam-4590	322	4	,	,	PUNCT
ejpam-4590	322	5	tw	tw	INTJ
ejpam-4590	322	6	/∈	/∈	PUNCT
ejpam-4590	322	7	e(g	e(g	PROPN
ejpam-4590	322	8	)	)	PUNCT
ejpam-4590	323	1	because	because	SCONJ
ejpam-4590	323	2	t	t	PROPN
ejpam-4590	323	3	,	,	PUNCT
ejpam-4590	323	4	v	v	NOUN
ejpam-4590	323	5	,	,	PUNCT
ejpam-4590	323	6	w	w	PROPN
ejpam-4590	323	7	∈	∈	PROPN
ejpam-4590	323	8	v	v	X
ejpam-4590	323	9	(	(	PUNCT
ejpam-4590	323	10	kr	kr	PROPN
ejpam-4590	323	11	)	)	PUNCT
ejpam-4590	323	12	.	.	PUNCT
ejpam-4590	324	1	also	also	ADV
ejpam-4590	324	2	,	,	PUNCT
ejpam-4590	324	3	since	since	SCONJ
ejpam-4590	324	4	q	q	PROPN
ejpam-4590	324	5	∈	∈	PROPN
ejpam-4590	324	6	vg	vg	NOUN
ejpam-4590	324	7	,	,	PUNCT
ejpam-4590	324	8	there	there	PRON
ejpam-4590	324	9	exists	exist	VERB
ejpam-4590	324	10	x	x	X
ejpam-4590	324	11	∈	∈	NOUN
ejpam-4590	324	12	vg	vg	ADP
ejpam-4590	324	13	such	such	ADJ
ejpam-4590	324	14	that	that	SCONJ
ejpam-4590	324	15	xq	xq	PROPN
ejpam-4590	324	16	∈	∈	PROPN
ejpam-4590	324	17	eg	eg	NOUN
ejpam-4590	324	18	,	,	PUNCT
ejpam-4590	324	19	that	that	ADV
ejpam-4590	324	20	is	is	ADV
ejpam-4590	324	21	,	,	PUNCT
ejpam-4590	324	22	xq	xq	PROPN
ejpam-4590	324	23	/∈	/∈	PROPN
ejpam-4590	324	24	e(g	e(g	PROPN
ejpam-4590	324	25	)	)	PUNCT
ejpam-4590	324	26	.	.	PUNCT
ejpam-4590	325	1	hence	hence	ADV
ejpam-4590	325	2	,	,	PUNCT
ejpam-4590	325	3	v	v	PROPN
ejpam-4590	325	4	(	(	PUNCT
ejpam-4590	325	5	g)\{q	g)\{q	PROPN
ejpam-4590	325	6	,	,	PUNCT
ejpam-4590	325	7	t	t	PROPN
ejpam-4590	325	8	}	}	PUNCT
ejpam-4590	325	9	is	be	AUX
ejpam-4590	325	10	an	an	DET
ejpam-4590	325	11	outer	outer	ADV
ejpam-4590	325	12	-	-	PUNCT
ejpam-4590	325	13	connected	connect	VERB
ejpam-4590	325	14	pointwise	pointwise	PROPN
ejpam-4590	325	15	non	non	ADJ
ejpam-4590	325	16	-	-	ADJ
ejpam-4590	325	17	dominating	dominating	ADJ
ejpam-4590	325	18	set	set	NOUN
ejpam-4590	325	19	of	of	ADP
ejpam-4590	325	20	g	g	PROPN
ejpam-4590	325	21	,	,	PUNCT
ejpam-4590	325	22	a	a	DET
ejpam-4590	325	23	contradiction	contradiction	NOUN
ejpam-4590	325	24	.	.	PUNCT
ejpam-4590	326	1	thus	thus	ADV
ejpam-4590	326	2	,	,	PUNCT
ejpam-4590	326	3	⟨vg⟩	⟨vg⟩	PROPN
ejpam-4590	326	4	=	=	SYM
ejpam-4590	326	5	kr	kr	PROPN
ejpam-4590	326	6	.	.	PROPN
ejpam-4590	326	7	for	for	ADP
ejpam-4590	326	8	the	the	DET
ejpam-4590	326	9	converse	converse	NOUN
ejpam-4590	326	10	,	,	PUNCT
ejpam-4590	326	11	suppose	suppose	VERB
ejpam-4590	326	12	that	that	SCONJ
ejpam-4590	326	13	g	g	PROPN
ejpam-4590	326	14	is	be	AUX
ejpam-4590	326	15	obtained	obtain	VERB
ejpam-4590	326	16	from	from	ADP
ejpam-4590	326	17	kn	kn	PROPN
ejpam-4590	326	18	as	as	SCONJ
ejpam-4590	326	19	described	describe	VERB
ejpam-4590	326	20	.	.	PUNCT
ejpam-4590	327	1	let	let	VERB
ejpam-4590	327	2	s	s	PRON
ejpam-4590	327	3	be	be	AUX
ejpam-4590	327	4	a	a	DET
ejpam-4590	327	5	p̃nd	p̃nd	NOUN
ejpam-4590	327	6	-	-	PUNCT
ejpam-4590	327	7	set	set	NOUN
ejpam-4590	327	8	of	of	ADP
ejpam-4590	327	9	g.	g.	PROPN
ejpam-4590	327	10	then	then	ADV
ejpam-4590	327	11	v	v	X
ejpam-4590	327	12	(	(	PUNCT
ejpam-4590	327	13	g	g	NOUN
ejpam-4590	327	14	)	)	PUNCT
ejpam-4590	327	15	\	\	NOUN
ejpam-4590	328	1	vg	vg	NOUN
ejpam-4590	328	2	contains	contain	VERB
ejpam-4590	328	3	all	all	DET
ejpam-4590	328	4	the	the	DET
ejpam-4590	328	5	dominating	dominating	NOUN
ejpam-4590	328	6	vertices	vertex	NOUN
ejpam-4590	328	7	of	of	ADP
ejpam-4590	328	8	g.	g.	PROPN
ejpam-4590	328	9	consequently	consequently	ADV
ejpam-4590	328	10	,	,	PUNCT
ejpam-4590	328	11	c.j	c.j	PROPN
ejpam-4590	328	12	.	.	PROPN
ejpam-4590	328	13	saromines	saromines	PROPN
ejpam-4590	328	14	,	,	PUNCT
ejpam-4590	328	15	s.	s.	PROPN
ejpam-4590	328	16	canoy	canoy	PROPN
ejpam-4590	328	17	,	,	PUNCT
ejpam-4590	328	18	jr	jr	PROPN
ejpam-4590	328	19	.	.	PROPN
ejpam-4590	328	20	/	/	SYM
ejpam-4590	328	21	eur	eur	PROPN
ejpam-4590	328	22	.	.	PUNCT
ejpam-4590	329	1	j.	j.	PROPN
ejpam-4590	329	2	pure	pure	PROPN
ejpam-4590	329	3	appl	appl	PROPN
ejpam-4590	329	4	.	.	PROPN
ejpam-4590	329	5	math	math	PROPN
ejpam-4590	329	6	,	,	PUNCT
ejpam-4590	329	7	15	15	NUM
ejpam-4590	329	8	(	(	PUNCT
ejpam-4590	329	9	4	4	NUM
ejpam-4590	329	10	)	)	PUNCT
ejpam-4590	329	11	(	(	PUNCT
ejpam-4590	329	12	2022	2022	NUM
ejpam-4590	329	13	)	)	PUNCT
ejpam-4590	329	14	,	,	PUNCT
ejpam-4590	329	15	1966	1966	NUM
ejpam-4590	329	16	-	-	SYM
ejpam-4590	329	17	1981	1981	NUM
ejpam-4590	329	18	1974	1974	NUM
ejpam-4590	329	19	v	v	NOUN
ejpam-4590	329	20	(	(	PUNCT
ejpam-4590	329	21	g	g	NOUN
ejpam-4590	329	22	)	)	PUNCT
ejpam-4590	329	23	\	\	NOUN
ejpam-4590	329	24	vg	vg	ADP
ejpam-4590	329	25	⊆	⊆	NUM
ejpam-4590	329	26	s.	s.	PROPN
ejpam-4590	329	27	since	since	SCONJ
ejpam-4590	329	28	⟨v	⟨v	PROPN
ejpam-4590	329	29	(	(	PUNCT
ejpam-4590	329	30	g	g	NOUN
ejpam-4590	329	31	)	)	PUNCT
ejpam-4590	329	32	\	\	PROPN
ejpam-4590	329	33	s⟩	s⟩	NOUN
ejpam-4590	329	34	is	be	AUX
ejpam-4590	329	35	connected	connect	VERB
ejpam-4590	329	36	and	and	CCONJ
ejpam-4590	329	37	⟨vg⟩	⟨vg⟩	NUM
ejpam-4590	329	38	=	=	SYM
ejpam-4590	329	39	kr	kr	PROPN
ejpam-4590	329	40	,	,	PUNCT
ejpam-4590	329	41	s	s	PART
ejpam-4590	329	42	contains	contain	VERB
ejpam-4590	329	43	all	all	PRON
ejpam-4590	329	44	but	but	SCONJ
ejpam-4590	329	45	a	a	DET
ejpam-4590	329	46	single	single	ADJ
ejpam-4590	329	47	vertex	vertex	NOUN
ejpam-4590	329	48	of	of	ADP
ejpam-4590	329	49	vg	vg	PROPN
ejpam-4590	329	50	.	.	PUNCT
ejpam-4590	330	1	thus	thus	ADV
ejpam-4590	330	2	,	,	PUNCT
ejpam-4590	330	3	p̃nd(g	p̃nd(g	ADJ
ejpam-4590	330	4	)	)	PUNCT
ejpam-4590	330	5	=	=	SYM
ejpam-4590	331	1	|s|	|s|	NOUN
ejpam-4590	331	2	=	=	SYM
ejpam-4590	331	3	n−	n−	NOUN
ejpam-4590	331	4	1	1	NUM
ejpam-4590	331	5	.	.	PUNCT
ejpam-4590	331	6	corollary	corollary	ADJ
ejpam-4590	331	7	5	5	NUM
ejpam-4590	331	8	.	.	PUNCT
ejpam-4590	331	9	for	for	ADP
ejpam-4590	331	10	n	n	PRON
ejpam-4590	331	11	≥	≥	NUM
ejpam-4590	331	12	3	3	NUM
ejpam-4590	331	13	,	,	PUNCT
ejpam-4590	331	14	p̃nd(k1,n−1	p̃nd(k1,n−1	PROPN
ejpam-4590	331	15	)	)	PUNCT
ejpam-4590	331	16	=	=	SYM
ejpam-4590	331	17	p̃nd(kn	p̃nd(kn	NOUN
ejpam-4590	331	18	\	\	PUNCT
ejpam-4590	331	19	e	e	X
ejpam-4590	331	20	)	)	PUNCT
ejpam-4590	331	21	=	=	SYM
ejpam-4590	331	22	n−	n−	NOUN
ejpam-4590	331	23	1	1	NUM
ejpam-4590	331	24	,	,	PUNCT
ejpam-4590	331	25	where	where	SCONJ
ejpam-4590	331	26	e	e	PROPN
ejpam-4590	331	27	∈	∈	PROPN
ejpam-4590	331	28	e(kn	e(kn	NUM
ejpam-4590	331	29	)	)	PUNCT
ejpam-4590	331	30	.	.	PUNCT
ejpam-4590	332	1	we	we	PRON
ejpam-4590	332	2	now	now	ADV
ejpam-4590	332	3	characterize	characterize	VERB
ejpam-4590	332	4	the	the	DET
ejpam-4590	332	5	outer	outer	ADV
ejpam-4590	332	6	-	-	PUNCT
ejpam-4590	332	7	connected	connect	VERB
ejpam-4590	332	8	hop	hop	NOUN
ejpam-4590	332	9	dominating	dominating	NOUN
ejpam-4590	332	10	sets	set	NOUN
ejpam-4590	332	11	in	in	ADP
ejpam-4590	332	12	some	some	DET
ejpam-4590	332	13	graphs	graph	NOUN
ejpam-4590	332	14	under	under	ADP
ejpam-4590	332	15	some	some	DET
ejpam-4590	332	16	binary	binary	ADJ
ejpam-4590	332	17	operations	operation	NOUN
ejpam-4590	332	18	.	.	PUNCT
ejpam-4590	333	1	theorem	theorem	ADJ
ejpam-4590	333	2	8	8	NUM
ejpam-4590	333	3	.	.	PUNCT
ejpam-4590	334	1	let	let	VERB
ejpam-4590	334	2	g	g	NOUN
ejpam-4590	334	3	and	and	CCONJ
ejpam-4590	334	4	h	h	NOUN
ejpam-4590	334	5	be	be	VERB
ejpam-4590	334	6	any	any	DET
ejpam-4590	334	7	two	two	NUM
ejpam-4590	334	8	graphs	graph	NOUN
ejpam-4590	334	9	.	.	PUNCT
ejpam-4590	335	1	a	a	DET
ejpam-4590	335	2	set	set	NOUN
ejpam-4590	335	3	s	s	NOUN
ejpam-4590	335	4	⊆	⊆	NUM
ejpam-4590	335	5	v	v	NOUN
ejpam-4590	335	6	(	(	PUNCT
ejpam-4590	335	7	g+h	g+h	PROPN
ejpam-4590	335	8	)	)	PUNCT
ejpam-4590	335	9	is	be	AUX
ejpam-4590	335	10	an	an	DET
ejpam-4590	335	11	outer	outer	ADV
ejpam-4590	335	12	-	-	PUNCT
ejpam-4590	335	13	connected	connect	VERB
ejpam-4590	335	14	hop	hop	NOUN
ejpam-4590	335	15	dominating	dominating	NOUN
ejpam-4590	335	16	set	set	NOUN
ejpam-4590	335	17	of	of	ADP
ejpam-4590	335	18	g+h	g+h	PROPN
ejpam-4590	335	19	if	if	SCONJ
ejpam-4590	335	20	and	and	CCONJ
ejpam-4590	335	21	only	only	ADV
ejpam-4590	335	22	if	if	SCONJ
ejpam-4590	335	23	s	s	NOUN
ejpam-4590	335	24	=	=	PUNCT
ejpam-4590	335	25	sg	sg	PROPN
ejpam-4590	335	26	∪sh	∪sh	NOUN
ejpam-4590	335	27	,	,	PUNCT
ejpam-4590	335	28	where	where	SCONJ
ejpam-4590	335	29	sg	sg	PROPN
ejpam-4590	335	30	and	and	CCONJ
ejpam-4590	335	31	sh	sh	PROPN
ejpam-4590	335	32	are	be	AUX
ejpam-4590	335	33	pointwise	pointwise	PROPN
ejpam-4590	335	34	non	non	ADJ
ejpam-4590	335	35	-	-	ADJ
ejpam-4590	335	36	dominating	dominating	ADJ
ejpam-4590	335	37	subsets	subset	NOUN
ejpam-4590	335	38	of	of	ADP
ejpam-4590	335	39	g	g	PROPN
ejpam-4590	335	40	and	and	CCONJ
ejpam-4590	335	41	h	h	NOUN
ejpam-4590	335	42	,	,	PUNCT
ejpam-4590	335	43	respectively	respectively	ADV
ejpam-4590	335	44	,	,	PUNCT
ejpam-4590	335	45	such	such	ADJ
ejpam-4590	335	46	that	that	SCONJ
ejpam-4590	335	47	(	(	PUNCT
ejpam-4590	335	48	i	i	NOUN
ejpam-4590	335	49	)	)	PUNCT
ejpam-4590	335	50	⟨v	⟨v	NOUN
ejpam-4590	335	51	(	(	PUNCT
ejpam-4590	335	52	h	h	NOUN
ejpam-4590	335	53	)	)	PUNCT
ejpam-4590	335	54	\	\	PROPN
ejpam-4590	335	55	sh⟩	sh⟩	NOUN
ejpam-4590	335	56	is	be	AUX
ejpam-4590	335	57	connected	connect	VERB
ejpam-4590	336	1	whenever	whenever	SCONJ
ejpam-4590	336	2	sh	sh	PROPN
ejpam-4590	336	3	̸=	̸=	PROPN
ejpam-4590	336	4	v	v	ADP
ejpam-4590	336	5	(	(	PUNCT
ejpam-4590	336	6	h	h	NOUN
ejpam-4590	336	7	)	)	PUNCT
ejpam-4590	336	8	and	and	CCONJ
ejpam-4590	336	9	sg	sg	X
ejpam-4590	336	10	=	=	SYM
ejpam-4590	336	11	v	v	PROPN
ejpam-4590	336	12	(	(	PUNCT
ejpam-4590	336	13	g	g	NOUN
ejpam-4590	336	14	)	)	PUNCT
ejpam-4590	336	15	and	and	CCONJ
ejpam-4590	336	16	(	(	PUNCT
ejpam-4590	336	17	ii	ii	NOUN
ejpam-4590	336	18	)	)	PUNCT
ejpam-4590	336	19	⟨v	⟨v	NOUN
ejpam-4590	336	20	(	(	PUNCT
ejpam-4590	336	21	g	g	NOUN
ejpam-4590	336	22	)	)	PUNCT
ejpam-4590	336	23	\	\	NOUN
ejpam-4590	336	24	sg⟩	sg⟩	NOUN
ejpam-4590	336	25	is	be	AUX
ejpam-4590	336	26	connected	connect	VERB
ejpam-4590	336	27	whenever	whenever	SCONJ
ejpam-4590	336	28	sg	sg	ADP
ejpam-4590	336	29	̸=	̸=	PROPN
ejpam-4590	336	30	v	v	NOUN
ejpam-4590	336	31	(	(	PUNCT
ejpam-4590	336	32	g	g	NOUN
ejpam-4590	336	33	)	)	PUNCT
ejpam-4590	336	34	and	and	CCONJ
ejpam-4590	336	35	sh	sh	INTJ
ejpam-4590	336	36	=	=	SYM
ejpam-4590	336	37	v	v	PROPN
ejpam-4590	336	38	(	(	PUNCT
ejpam-4590	336	39	h	h	NOUN
ejpam-4590	336	40	)	)	PUNCT
ejpam-4590	336	41	.	.	PUNCT
ejpam-4590	337	1	proof	proof	NOUN
ejpam-4590	337	2	.	.	PUNCT
ejpam-4590	338	1	suppose	suppose	VERB
ejpam-4590	338	2	s	s	NOUN
ejpam-4590	338	3	is	be	AUX
ejpam-4590	338	4	an	an	DET
ejpam-4590	338	5	outer	outer	ADV
ejpam-4590	338	6	-	-	PUNCT
ejpam-4590	338	7	connected	connect	VERB
ejpam-4590	338	8	hop	hop	NOUN
ejpam-4590	338	9	dominating	dominating	NOUN
ejpam-4590	338	10	set	set	NOUN
ejpam-4590	338	11	of	of	ADP
ejpam-4590	338	12	g+h	g+h	PROPN
ejpam-4590	338	13	.	.	PUNCT
ejpam-4590	339	1	since	since	SCONJ
ejpam-4590	339	2	s	s	PROPN
ejpam-4590	339	3	is	be	AUX
ejpam-4590	339	4	hop	hop	NOUN
ejpam-4590	339	5	dominating	dominating	NOUN
ejpam-4590	339	6	,	,	PUNCT
ejpam-4590	339	7	by	by	ADP
ejpam-4590	339	8	theorem	theorem	NOUN
ejpam-4590	339	9	1	1	NUM
ejpam-4590	339	10	,	,	PUNCT
ejpam-4590	339	11	s	s	PART
ejpam-4590	339	12	=	=	PUNCT
ejpam-4590	339	13	sg	sg	ADP
ejpam-4590	339	14	∪sh	∪sh	NOUN
ejpam-4590	339	15	where	where	SCONJ
ejpam-4590	339	16	sg	sg	PROPN
ejpam-4590	339	17	and	and	CCONJ
ejpam-4590	339	18	sh	sh	PROPN
ejpam-4590	339	19	are	be	AUX
ejpam-4590	339	20	pointwise	pointwise	PROPN
ejpam-4590	339	21	non	non	ADJ
ejpam-4590	339	22	-	-	ADJ
ejpam-4590	339	23	dominating	dominating	ADJ
ejpam-4590	339	24	sets	set	NOUN
ejpam-4590	339	25	of	of	ADP
ejpam-4590	339	26	g	g	PROPN
ejpam-4590	339	27	and	and	CCONJ
ejpam-4590	339	28	h	h	NOUN
ejpam-4590	339	29	,	,	PUNCT
ejpam-4590	339	30	respectively	respectively	ADV
ejpam-4590	339	31	.	.	PUNCT
ejpam-4590	340	1	suppose	suppose	VERB
ejpam-4590	340	2	sg	sg	PROPN
ejpam-4590	340	3	=	=	SYM
ejpam-4590	340	4	v	v	PROPN
ejpam-4590	340	5	(	(	PUNCT
ejpam-4590	340	6	g	g	NOUN
ejpam-4590	340	7	)	)	PUNCT
ejpam-4590	340	8	and	and	CCONJ
ejpam-4590	340	9	sh	sh	INTJ
ejpam-4590	340	10	̸=	̸=	PROPN
ejpam-4590	340	11	v	v	NOUN
ejpam-4590	340	12	(	(	PUNCT
ejpam-4590	340	13	h	h	NOUN
ejpam-4590	340	14	)	)	PUNCT
ejpam-4590	340	15	.	.	PUNCT
ejpam-4590	341	1	since	since	SCONJ
ejpam-4590	341	2	s	s	PROPN
ejpam-4590	341	3	is	be	AUX
ejpam-4590	341	4	outerconnected	outerconnecte	VERB
ejpam-4590	341	5	,	,	PUNCT
ejpam-4590	341	6	⟨v	⟨v	X
ejpam-4590	341	7	(	(	PUNCT
ejpam-4590	341	8	g+h	g+h	NOUN
ejpam-4590	341	9	)	)	PUNCT
ejpam-4590	341	10	\	\	NOUN
ejpam-4590	342	1	s⟩	s⟩	NOUN
ejpam-4590	343	1	=	=	SYM
ejpam-4590	343	2	⟨v	⟨v	NUM
ejpam-4590	343	3	(	(	PUNCT
ejpam-4590	343	4	h	h	NOUN
ejpam-4590	343	5	)	)	PUNCT
ejpam-4590	343	6	\	\	PROPN
ejpam-4590	343	7	sh⟩	sh⟩	NOUN
ejpam-4590	343	8	is	be	AUX
ejpam-4590	343	9	connected	connect	VERB
ejpam-4590	343	10	.	.	PUNCT
ejpam-4590	344	1	therefore	therefore	ADV
ejpam-4590	344	2	(	(	PUNCT
ejpam-4590	344	3	i	i	NOUN
ejpam-4590	344	4	)	)	PUNCT
ejpam-4590	344	5	holds	hold	VERB
ejpam-4590	344	6	.	.	PUNCT
ejpam-4590	345	1	similarly	similarly	ADV
ejpam-4590	345	2	,	,	PUNCT
ejpam-4590	345	3	(	(	PUNCT
ejpam-4590	345	4	ii	ii	NOUN
ejpam-4590	345	5	)	)	PUNCT
ejpam-4590	345	6	holds	hold	VERB
ejpam-4590	345	7	.	.	PUNCT
ejpam-4590	346	1	for	for	ADP
ejpam-4590	346	2	the	the	DET
ejpam-4590	346	3	converse	converse	NOUN
ejpam-4590	346	4	,	,	PUNCT
ejpam-4590	346	5	let	let	VERB
ejpam-4590	346	6	s	s	PRON
ejpam-4590	346	7	=	=	VERB
ejpam-4590	346	8	sg	sg	X
ejpam-4590	346	9	∪	∪	ADJ
ejpam-4590	346	10	sh	sh	PROPN
ejpam-4590	346	11	,	,	PUNCT
ejpam-4590	346	12	where	where	SCONJ
ejpam-4590	346	13	sg	sg	PROPN
ejpam-4590	346	14	and	and	CCONJ
ejpam-4590	346	15	sh	sh	PROPN
ejpam-4590	346	16	are	be	AUX
ejpam-4590	346	17	pointwise	pointwise	PROPN
ejpam-4590	346	18	non	non	ADJ
ejpam-4590	346	19	-	-	ADJ
ejpam-4590	346	20	dominating	dominating	ADJ
ejpam-4590	346	21	subsets	subset	NOUN
ejpam-4590	346	22	of	of	ADP
ejpam-4590	346	23	g	g	PROPN
ejpam-4590	346	24	and	and	CCONJ
ejpam-4590	346	25	h	h	NOUN
ejpam-4590	346	26	,	,	PUNCT
ejpam-4590	346	27	respectively	respectively	ADV
ejpam-4590	346	28	.	.	PUNCT
ejpam-4590	347	1	then	then	ADV
ejpam-4590	347	2	s	s	VERB
ejpam-4590	347	3	is	be	AUX
ejpam-4590	347	4	a	a	DET
ejpam-4590	347	5	hop	hop	NOUN
ejpam-4590	347	6	dominating	dominating	NOUN
ejpam-4590	347	7	set	set	VERB
ejpam-4590	347	8	by	by	ADP
ejpam-4590	347	9	theorem	theorem	NOUN
ejpam-4590	347	10	1	1	NUM
ejpam-4590	347	11	.	.	PUNCT
ejpam-4590	348	1	if	if	SCONJ
ejpam-4590	348	2	s	s	NOUN
ejpam-4590	348	3	=	=	SYM
ejpam-4590	348	4	v	v	PROPN
ejpam-4590	348	5	(	(	PUNCT
ejpam-4590	348	6	g+h	g+h	PROPN
ejpam-4590	348	7	)	)	PUNCT
ejpam-4590	348	8	,	,	PUNCT
ejpam-4590	348	9	then	then	ADV
ejpam-4590	348	10	it	it	PRON
ejpam-4590	348	11	is	be	AUX
ejpam-4590	348	12	an	an	DET
ejpam-4590	348	13	outer	outer	ADV
ejpam-4590	348	14	-	-	PUNCT
ejpam-4590	348	15	connected	connect	VERB
ejpam-4590	348	16	hop	hop	NOUN
ejpam-4590	348	17	dominating	dominating	NOUN
ejpam-4590	348	18	set	set	NOUN
ejpam-4590	348	19	.	.	PUNCT
ejpam-4590	349	1	suppose	suppose	VERB
ejpam-4590	349	2	s	s	VERB
ejpam-4590	349	3	̸=	̸=	PROPN
ejpam-4590	349	4	v	v	NOUN
ejpam-4590	349	5	(	(	PUNCT
ejpam-4590	349	6	g+h	g+h	PROPN
ejpam-4590	349	7	)	)	PUNCT
ejpam-4590	349	8	.	.	PUNCT
ejpam-4590	350	1	consider	consider	VERB
ejpam-4590	350	2	the	the	DET
ejpam-4590	350	3	following	follow	VERB
ejpam-4590	350	4	cases	case	NOUN
ejpam-4590	350	5	:	:	PUNCT
ejpam-4590	350	6	case	case	NOUN
ejpam-4590	350	7	1	1	NUM
ejpam-4590	350	8	.	.	PUNCT
ejpam-4590	351	1	sg	sg	ADP
ejpam-4590	351	2	̸=	̸=	PROPN
ejpam-4590	351	3	v	v	PROPN
ejpam-4590	351	4	(	(	PUNCT
ejpam-4590	351	5	g	g	NOUN
ejpam-4590	351	6	)	)	PUNCT
ejpam-4590	351	7	and	and	CCONJ
ejpam-4590	351	8	sh	sh	INTJ
ejpam-4590	351	9	̸=	̸=	PROPN
ejpam-4590	351	10	v	v	NOUN
ejpam-4590	351	11	(	(	PUNCT
ejpam-4590	351	12	h	h	NOUN
ejpam-4590	351	13	)	)	PUNCT
ejpam-4590	351	14	.	.	PUNCT
ejpam-4590	352	1	then	then	ADV
ejpam-4590	352	2	⟨v	⟨v	CCONJ
ejpam-4590	352	3	(	(	PUNCT
ejpam-4590	352	4	g+h	g+h	NOUN
ejpam-4590	352	5	)	)	PUNCT
ejpam-4590	352	6	\	\	NOUN
ejpam-4590	352	7	s⟩	s⟩	NOUN
ejpam-4590	352	8	=	=	SYM
ejpam-4590	352	9	⟨v	⟨v	NUM
ejpam-4590	352	10	(	(	PUNCT
ejpam-4590	352	11	g	g	NOUN
ejpam-4590	352	12	)	)	PUNCT
ejpam-4590	352	13	\	\	NOUN
ejpam-4590	352	14	sg⟩+	sg⟩+	PROPN
ejpam-4590	352	15	⟨v	⟨v	NUM
ejpam-4590	352	16	(	(	PUNCT
ejpam-4590	352	17	h	h	NOUN
ejpam-4590	352	18	)	)	PUNCT
ejpam-4590	352	19	\	\	PROPN
ejpam-4590	352	20	sh⟩	sh⟩	NOUN
ejpam-4590	352	21	is	be	AUX
ejpam-4590	352	22	connected	connect	VERB
ejpam-4590	352	23	.	.	PUNCT
ejpam-4590	353	1	case	case	NOUN
ejpam-4590	353	2	2	2	NUM
ejpam-4590	353	3	.	.	X
ejpam-4590	353	4	sg	sg	PROPN
ejpam-4590	353	5	=	=	SYM
ejpam-4590	353	6	v	v	PROPN
ejpam-4590	353	7	(	(	PUNCT
ejpam-4590	353	8	g	g	NOUN
ejpam-4590	353	9	)	)	PUNCT
ejpam-4590	353	10	and	and	CCONJ
ejpam-4590	353	11	sh	sh	INTJ
ejpam-4590	353	12	̸=	̸=	PROPN
ejpam-4590	353	13	v	v	NOUN
ejpam-4590	353	14	(	(	PUNCT
ejpam-4590	353	15	h	h	NOUN
ejpam-4590	353	16	)	)	PUNCT
ejpam-4590	353	17	.	.	PUNCT
ejpam-4590	354	1	then	then	ADV
ejpam-4590	354	2	⟨v	⟨v	CCONJ
ejpam-4590	354	3	(	(	PUNCT
ejpam-4590	354	4	g+h	g+h	NOUN
ejpam-4590	354	5	)	)	PUNCT
ejpam-4590	354	6	\	\	NOUN
ejpam-4590	354	7	s⟩	s⟩	NOUN
ejpam-4590	354	8	=	=	SYM
ejpam-4590	354	9	⟨v	⟨v	NUM
ejpam-4590	354	10	(	(	PUNCT
ejpam-4590	354	11	h	h	NOUN
ejpam-4590	354	12	)	)	PUNCT
ejpam-4590	354	13	\	\	PROPN
ejpam-4590	354	14	sh⟩	sh⟩	NOUN
ejpam-4590	354	15	is	be	AUX
ejpam-4590	354	16	connected	connect	VERB
ejpam-4590	354	17	by	by	ADP
ejpam-4590	354	18	(	(	PUNCT
ejpam-4590	354	19	i	i	NOUN
ejpam-4590	354	20	)	)	PUNCT
ejpam-4590	354	21	.	.	PUNCT
ejpam-4590	355	1	case	case	NOUN
ejpam-4590	355	2	3	3	X
ejpam-4590	355	3	.	.	PUNCT
ejpam-4590	356	1	sh	sh	PROPN
ejpam-4590	356	2	=	=	SYM
ejpam-4590	356	3	v	v	PROPN
ejpam-4590	356	4	(	(	PUNCT
ejpam-4590	356	5	h	h	NOUN
ejpam-4590	356	6	)	)	PUNCT
ejpam-4590	356	7	and	and	CCONJ
ejpam-4590	356	8	sg	sg	ADP
ejpam-4590	356	9	̸=	̸=	PROPN
ejpam-4590	356	10	v	v	NOUN
ejpam-4590	356	11	(	(	PUNCT
ejpam-4590	356	12	g	g	NOUN
ejpam-4590	356	13	)	)	PUNCT
ejpam-4590	356	14	.	.	PUNCT
ejpam-4590	357	1	then	then	ADV
ejpam-4590	357	2	⟨v	⟨v	CCONJ
ejpam-4590	357	3	(	(	PUNCT
ejpam-4590	357	4	g+h	g+h	NOUN
ejpam-4590	357	5	)	)	PUNCT
ejpam-4590	357	6	\	\	NOUN
ejpam-4590	357	7	s⟩	s⟩	NOUN
ejpam-4590	357	8	=	=	SYM
ejpam-4590	357	9	⟨v	⟨v	NUM
ejpam-4590	357	10	(	(	PUNCT
ejpam-4590	357	11	g	g	NOUN
ejpam-4590	357	12	)	)	PUNCT
ejpam-4590	357	13	\	\	NOUN
ejpam-4590	357	14	sg⟩	sg⟩	NOUN
ejpam-4590	357	15	is	be	AUX
ejpam-4590	357	16	connected	connect	VERB
ejpam-4590	357	17	by	by	ADP
ejpam-4590	357	18	(	(	PUNCT
ejpam-4590	357	19	ii	ii	NOUN
ejpam-4590	357	20	)	)	PUNCT
ejpam-4590	357	21	.	.	PUNCT
ejpam-4590	358	1	therefore	therefore	ADV
ejpam-4590	358	2	s	s	VERB
ejpam-4590	358	3	is	be	AUX
ejpam-4590	358	4	an	an	DET
ejpam-4590	358	5	outer	outer	ADV
ejpam-4590	358	6	-	-	PUNCT
ejpam-4590	358	7	connected	connect	VERB
ejpam-4590	358	8	hop	hop	NOUN
ejpam-4590	358	9	dominating	dominating	NOUN
ejpam-4590	358	10	set	set	NOUN
ejpam-4590	358	11	of	of	ADP
ejpam-4590	358	12	g+h	g+h	PROPN
ejpam-4590	358	13	.	.	PUNCT
ejpam-4590	359	1	the	the	DET
ejpam-4590	359	2	next	next	ADJ
ejpam-4590	359	3	result	result	NOUN
ejpam-4590	359	4	is	be	AUX
ejpam-4590	359	5	based	base	VERB
ejpam-4590	359	6	from	from	ADP
ejpam-4590	359	7	proposition	proposition	NOUN
ejpam-4590	359	8	1	1	NUM
ejpam-4590	359	9	(	(	PUNCT
ejpam-4590	359	10	i	i	NOUN
ejpam-4590	359	11	)	)	PUNCT
ejpam-4590	359	12	,	,	PUNCT
ejpam-4590	359	13	theorem	theorem	VERB
ejpam-4590	359	14	6	6	NUM
ejpam-4590	359	15	,	,	PUNCT
ejpam-4590	359	16	corollary	corollary	ADJ
ejpam-4590	359	17	3	3	NUM
ejpam-4590	359	18	,	,	PUNCT
ejpam-4590	359	19	corollary	corollary	ADJ
ejpam-4590	359	20	4	4	NUM
ejpam-4590	359	21	and	and	CCONJ
ejpam-4590	359	22	theorem	theorem	VERB
ejpam-4590	359	23	8	8	NUM
ejpam-4590	359	24	.	.	PUNCT
ejpam-4590	359	25	corollary	corollary	ADJ
ejpam-4590	359	26	6	6	NUM
ejpam-4590	359	27	.	.	PUNCT
ejpam-4590	360	1	let	let	VERB
ejpam-4590	360	2	g	g	NOUN
ejpam-4590	360	3	and	and	CCONJ
ejpam-4590	360	4	h	h	NOUN
ejpam-4590	360	5	be	be	VERB
ejpam-4590	360	6	any	any	DET
ejpam-4590	360	7	two	two	NUM
ejpam-4590	360	8	graphs	graph	NOUN
ejpam-4590	360	9	of	of	ADP
ejpam-4590	360	10	orders	order	NOUN
ejpam-4590	360	11	m	m	VERB
ejpam-4590	360	12	and	and	CCONJ
ejpam-4590	360	13	n	n	CCONJ
ejpam-4590	360	14	,	,	PUNCT
ejpam-4590	360	15	respectively	respectively	ADV
ejpam-4590	360	16	.	.	PUNCT
ejpam-4590	361	1	then	then	ADV
ejpam-4590	361	2	γ̃ch(g+h	γ̃ch(g+h	NOUN
ejpam-4590	361	3	)	)	PUNCT
ejpam-4590	361	4	=	=	SYM
ejpam-4590	362	1			PRON
ejpam-4590	362	2	pnd(g	pnd(g	ADP
ejpam-4590	362	3	)	)	PUNCT
ejpam-4590	362	4	+	+	NUM
ejpam-4590	362	5	pnd(h	pnd(h	PROPN
ejpam-4590	362	6	)	)	PUNCT
ejpam-4590	362	7	,	,	PUNCT
ejpam-4590	362	8	g	g	PROPN
ejpam-4590	362	9	and	and	CCONJ
ejpam-4590	362	10	hare	hare	NOUN
ejpam-4590	362	11	non	non	ADJ
ejpam-4590	362	12	-	-	ADJ
ejpam-4590	362	13	complete	complete	ADJ
ejpam-4590	362	14	,	,	PUNCT
ejpam-4590	362	15	|v	|v	PROPN
ejpam-4590	362	16	(	(	PUNCT
ejpam-4590	362	17	g)|+	g)|+	PROPN
ejpam-4590	362	18	p̃nd(h	p̃nd(h	PROPN
ejpam-4590	362	19	)	)	PUNCT
ejpam-4590	362	20	,	,	PUNCT
ejpam-4590	362	21	g	g	PROPN
ejpam-4590	362	22	is	be	AUX
ejpam-4590	362	23	complete	complete	ADJ
ejpam-4590	362	24	and	and	CCONJ
ejpam-4590	362	25	his	his	PRON
ejpam-4590	362	26	non	non	ADJ
ejpam-4590	362	27	-	-	ADJ
ejpam-4590	362	28	complete	complete	ADJ
ejpam-4590	362	29	and	and	CCONJ
ejpam-4590	362	30	|v	|v	PROPN
ejpam-4590	362	31	(	(	PUNCT
ejpam-4590	362	32	h)|+	h)|+	ADJ
ejpam-4590	362	33	p̃nd(g	p̃nd(g	NOUN
ejpam-4590	362	34	)	)	PUNCT
ejpam-4590	362	35	,	,	PUNCT
ejpam-4590	362	36	h	h	NOUN
ejpam-4590	362	37	is	be	AUX
ejpam-4590	362	38	complete	complete	ADJ
ejpam-4590	362	39	and	and	CCONJ
ejpam-4590	362	40	gis	gis	VERB
ejpam-4590	362	41	non	non	ADJ
ejpam-4590	362	42	-	-	ADJ
ejpam-4590	362	43	complete	complete	ADJ
ejpam-4590	362	44	in	in	ADP
ejpam-4590	362	45	particular	particular	ADJ
ejpam-4590	362	46	,	,	PUNCT
ejpam-4590	362	47	(	(	PUNCT
ejpam-4590	362	48	i	i	NOUN
ejpam-4590	362	49	)	)	PUNCT
ejpam-4590	363	1	γ̃ch(g+h	γ̃ch(g+h	NOUN
ejpam-4590	363	2	)	)	PUNCT
ejpam-4590	363	3	=	=	SYM
ejpam-4590	364	1	m+	m+	NUM
ejpam-4590	364	2	n	n	CCONJ
ejpam-4590	364	3	,	,	PUNCT
ejpam-4590	364	4	if	if	SCONJ
ejpam-4590	364	5	g	g	PROPN
ejpam-4590	364	6	and	and	CCONJ
ejpam-4590	364	7	h	h	NOUN
ejpam-4590	364	8	are	be	AUX
ejpam-4590	364	9	complete	complete	ADJ
ejpam-4590	364	10	;	;	PUNCT
ejpam-4590	364	11	c.j	c.j	PROPN
ejpam-4590	364	12	.	.	PROPN
ejpam-4590	364	13	saromines	saromines	PROPN
ejpam-4590	364	14	,	,	PUNCT
ejpam-4590	364	15	s.	s.	PROPN
ejpam-4590	364	16	canoy	canoy	PROPN
ejpam-4590	364	17	,	,	PUNCT
ejpam-4590	364	18	jr	jr	PROPN
ejpam-4590	364	19	.	.	PROPN
ejpam-4590	364	20	/	/	SYM
ejpam-4590	364	21	eur	eur	PROPN
ejpam-4590	364	22	.	.	PUNCT
ejpam-4590	365	1	j.	j.	PROPN
ejpam-4590	365	2	pure	pure	PROPN
ejpam-4590	365	3	appl	appl	PROPN
ejpam-4590	365	4	.	.	PROPN
ejpam-4590	365	5	math	math	PROPN
ejpam-4590	365	6	,	,	PUNCT
ejpam-4590	365	7	15	15	NUM
ejpam-4590	365	8	(	(	PUNCT
ejpam-4590	365	9	4	4	NUM
ejpam-4590	365	10	)	)	PUNCT
ejpam-4590	365	11	(	(	PUNCT
ejpam-4590	365	12	2022	2022	NUM
ejpam-4590	365	13	)	)	PUNCT
ejpam-4590	365	14	,	,	PUNCT
ejpam-4590	365	15	1966	1966	NUM
ejpam-4590	365	16	-	-	SYM
ejpam-4590	365	17	1981	1981	NUM
ejpam-4590	365	18	1975	1975	NUM
ejpam-4590	365	19	(	(	PUNCT
ejpam-4590	365	20	ii	ii	NOUN
ejpam-4590	365	21	)	)	PUNCT
ejpam-4590	365	22	γ̃ch(k1,n	γ̃ch(k1,n	NOUN
ejpam-4590	365	23	)	)	PUNCT
ejpam-4590	365	24	=	=	SYM
ejpam-4590	365	25	γ̃ch(k1	γ̃ch(k1	PROPN
ejpam-4590	365	26	+	+	PROPN
ejpam-4590	365	27	kn	kn	PROPN
ejpam-4590	365	28	)	)	PUNCT
ejpam-4590	365	29	=	=	SYM
ejpam-4590	366	1	1	1	NUM
ejpam-4590	366	2	+	+	NUM
ejpam-4590	366	3	p̃nd(kn	p̃nd(kn	NOUN
ejpam-4590	366	4	)	)	PUNCT
ejpam-4590	366	5	=	=	SYM
ejpam-4590	366	6	n	n	PROPN
ejpam-4590	366	7	for	for	ADP
ejpam-4590	366	8	n	n	PRON
ejpam-4590	366	9	≥	≥	NUM
ejpam-4590	366	10	2	2	NUM
ejpam-4590	366	11	.	.	PUNCT
ejpam-4590	366	12	(	(	PUNCT
ejpam-4590	366	13	iii	iii	NOUN
ejpam-4590	366	14	)	)	PUNCT
ejpam-4590	366	15	γ̃ch(fn	γ̃ch(fn	PROPN
ejpam-4590	366	16	)	)	PUNCT
ejpam-4590	366	17	=	=	SYM
ejpam-4590	366	18	1	1	NUM
ejpam-4590	366	19	+	+	NUM
ejpam-4590	366	20	p̃nd(pn	p̃nd(pn	NOUN
ejpam-4590	366	21	)	)	PUNCT
ejpam-4590	366	22	=	=	SYM
ejpam-4590	366	23	3	3	NUM
ejpam-4590	366	24	for	for	ADP
ejpam-4590	366	25	n	n	X
ejpam-4590	366	26	≥	≥	NOUN
ejpam-4590	366	27	2	2	NUM
ejpam-4590	366	28	.	.	PUNCT
ejpam-4590	366	29	(	(	PUNCT
ejpam-4590	366	30	iv	iv	NOUN
ejpam-4590	366	31	)	)	PUNCT
ejpam-4590	366	32	γ̃ch(wn	γ̃ch(wn	NOUN
ejpam-4590	366	33	)	)	PUNCT
ejpam-4590	366	34	=	=	SYM
ejpam-4590	366	35	1	1	NUM
ejpam-4590	366	36	+	+	NUM
ejpam-4590	366	37	p̃nd(cn	p̃nd(cn	NOUN
ejpam-4590	366	38	)	)	PUNCT
ejpam-4590	366	39	=	=	SYM
ejpam-4590	366	40	3	3	NUM
ejpam-4590	366	41	for	for	ADP
ejpam-4590	366	42	n	n	X
ejpam-4590	366	43	≥	≥	NOUN
ejpam-4590	366	44	4	4	NUM
ejpam-4590	366	45	.	.	PUNCT
ejpam-4590	367	1	(	(	PUNCT
ejpam-4590	367	2	v	v	NOUN
ejpam-4590	367	3	)	)	PUNCT
ejpam-4590	367	4	γ̃ch(km	γ̃ch(km	PROPN
ejpam-4590	367	5	,	,	PUNCT
ejpam-4590	367	6	n	n	CCONJ
ejpam-4590	367	7	)	)	PUNCT
ejpam-4590	367	8	=	=	SYM
ejpam-4590	367	9	pnd(km	pnd(km	NOUN
ejpam-4590	367	10	)	)	PUNCT
ejpam-4590	368	1	+	+	NUM
ejpam-4590	368	2	pnd(kn	pnd(kn	NOUN
ejpam-4590	368	3	)	)	PUNCT
ejpam-4590	368	4	=	=	SYM
ejpam-4590	368	5	2	2	NUM
ejpam-4590	368	6	for	for	ADP
ejpam-4590	368	7	m	m	PROPN
ejpam-4590	368	8	,	,	PUNCT
ejpam-4590	368	9	n	n	PRON
ejpam-4590	368	10	≥	≥	NOUN
ejpam-4590	368	11	2	2	NUM
ejpam-4590	368	12	.	.	PUNCT
ejpam-4590	368	13	theorem	theorem	NOUN
ejpam-4590	368	14	9	9	NUM
ejpam-4590	368	15	.	.	PUNCT
ejpam-4590	369	1	let	let	VERB
ejpam-4590	369	2	g	g	PRON
ejpam-4590	369	3	be	be	AUX
ejpam-4590	369	4	a	a	DET
ejpam-4590	369	5	connected	connected	ADJ
ejpam-4590	369	6	graph	graph	NOUN
ejpam-4590	369	7	and	and	CCONJ
ejpam-4590	369	8	let	let	VERB
ejpam-4590	369	9	h	h	NOUN
ejpam-4590	369	10	be	be	AUX
ejpam-4590	369	11	any	any	DET
ejpam-4590	369	12	graph	graph	NOUN
ejpam-4590	369	13	.	.	PUNCT
ejpam-4590	370	1	then	then	ADV
ejpam-4590	370	2	a	a	DET
ejpam-4590	370	3	subset	subset	NOUN
ejpam-4590	370	4	c	c	NOUN
ejpam-4590	370	5	of	of	ADP
ejpam-4590	370	6	v	v	PROPN
ejpam-4590	370	7	(	(	PUNCT
ejpam-4590	370	8	g	g	PROPN
ejpam-4590	370	9	◦	◦	NOUN
ejpam-4590	370	10	h	h	NOUN
ejpam-4590	370	11	)	)	PUNCT
ejpam-4590	370	12	is	be	AUX
ejpam-4590	370	13	an	an	DET
ejpam-4590	370	14	outer	outer	ADJ
ejpam-4590	370	15	connected	connect	VERB
ejpam-4590	370	16	hop	hop	NOUN
ejpam-4590	370	17	dominating	dominating	NOUN
ejpam-4590	370	18	set	set	NOUN
ejpam-4590	370	19	of	of	ADP
ejpam-4590	370	20	g	g	PROPN
ejpam-4590	370	21	◦	◦	NOUN
ejpam-4590	370	22	h	h	NOUN
ejpam-4590	370	23	if	if	SCONJ
ejpam-4590	371	1	and	and	CCONJ
ejpam-4590	371	2	only	only	ADV
ejpam-4590	371	3	if	if	SCONJ
ejpam-4590	371	4	c	c	X
ejpam-4590	371	5	=	=	PUNCT
ejpam-4590	371	6	a	a	PRON
ejpam-4590	371	7	∪	∪	ADJ
ejpam-4590	371	8			PROPN
ejpam-4590	371	9	⋃	⋃	ADJ
ejpam-4590	371	10	v∈v	v∈v	NOUN
ejpam-4590	371	11	(	(	PUNCT
ejpam-4590	371	12	g	g	NOUN
ejpam-4590	371	13	)	)	PUNCT
ejpam-4590	371	14	sv	sv	INTJ
ejpam-4590	372	1			PROPN
ejpam-4590	372	2	where	where	SCONJ
ejpam-4590	372	3	sv	sv	PROPN
ejpam-4590	372	4	⊆	⊆	NUM
ejpam-4590	372	5	v	v	PROPN
ejpam-4590	372	6	(	(	PUNCT
ejpam-4590	372	7	hv	hv	PROPN
ejpam-4590	372	8	)	)	PUNCT
ejpam-4590	372	9	for	for	ADP
ejpam-4590	372	10	each	each	DET
ejpam-4590	372	11	v	v	NUM
ejpam-4590	372	12	∈	∈	PROPN
ejpam-4590	372	13	v	v	NOUN
ejpam-4590	372	14	(	(	PUNCT
ejpam-4590	372	15	g	g	NOUN
ejpam-4590	372	16	)	)	PUNCT
ejpam-4590	372	17	and	and	CCONJ
ejpam-4590	372	18	satisfies	satisfy	VERB
ejpam-4590	372	19	each	each	PRON
ejpam-4590	372	20	of	of	ADP
ejpam-4590	372	21	the	the	DET
ejpam-4590	372	22	following	following	ADJ
ejpam-4590	372	23	statements	statement	NOUN
ejpam-4590	372	24	:	:	PUNCT
ejpam-4590	372	25	(	(	PUNCT
ejpam-4590	372	26	i	i	NOUN
ejpam-4590	372	27	)	)	PUNCT
ejpam-4590	373	1	a	a	DET
ejpam-4590	373	2	=	=	SYM
ejpam-4590	373	3	v	v	NOUN
ejpam-4590	373	4	(	(	PUNCT
ejpam-4590	373	5	g	g	NOUN
ejpam-4590	373	6	)	)	PUNCT
ejpam-4590	373	7	or	or	CCONJ
ejpam-4590	373	8	⟨v	⟨v	NUM
ejpam-4590	373	9	(	(	PUNCT
ejpam-4590	373	10	g	g	NOUN
ejpam-4590	373	11	)	)	PUNCT
ejpam-4590	373	12	\a⟩	\a⟩	PROPN
ejpam-4590	373	13	is	be	AUX
ejpam-4590	373	14	connected	connect	VERB
ejpam-4590	373	15	.	.	PUNCT
ejpam-4590	374	1	(	(	PUNCT
ejpam-4590	374	2	ii	ii	NOUN
ejpam-4590	374	3	)	)	PUNCT
ejpam-4590	374	4	if	if	SCONJ
ejpam-4590	374	5	a	a	DET
ejpam-4590	374	6	=	=	X
ejpam-4590	374	7	v	v	NOUN
ejpam-4590	374	8	(	(	PUNCT
ejpam-4590	374	9	g	g	NOUN
ejpam-4590	374	10	)	)	PUNCT
ejpam-4590	374	11	,	,	PUNCT
ejpam-4590	374	12	then	then	ADV
ejpam-4590	374	13	⟨v	⟨v	NUM
ejpam-4590	374	14	(	(	PUNCT
ejpam-4590	374	15	hv	hv	NOUN
ejpam-4590	374	16	)	)	PUNCT
ejpam-4590	374	17	\	\	PROPN
ejpam-4590	375	1	sv⟩	sv⟩	PROPN
ejpam-4590	375	2	is	be	AUX
ejpam-4590	375	3	a	a	DET
ejpam-4590	375	4	connected	connected	ADJ
ejpam-4590	375	5	proper	proper	ADJ
ejpam-4590	375	6	subgraph	subgraph	NOUN
ejpam-4590	375	7	of	of	ADP
ejpam-4590	375	8	hv	hv	PROPN
ejpam-4590	375	9	for	for	ADP
ejpam-4590	375	10	at	at	ADP
ejpam-4590	375	11	most	most	ADV
ejpam-4590	375	12	one	one	NUM
ejpam-4590	375	13	vertex	vertex	NOUN
ejpam-4590	375	14	v	v	ADP
ejpam-4590	375	15	∈	∈	PROPN
ejpam-4590	375	16	a.	a.	NOUN
ejpam-4590	375	17	otherwise	otherwise	ADV
ejpam-4590	375	18	,	,	PUNCT
ejpam-4590	375	19	sv	sv	PROPN
ejpam-4590	375	20	=	=	SYM
ejpam-4590	375	21	v	v	PROPN
ejpam-4590	375	22	(	(	PUNCT
ejpam-4590	375	23	hv	hv	PROPN
ejpam-4590	375	24	)	)	PUNCT
ejpam-4590	375	25	for	for	ADP
ejpam-4590	375	26	all	all	DET
ejpam-4590	375	27	v	v	NOUN
ejpam-4590	375	28	∈	∈	NOUN
ejpam-4590	375	29	a.	a.	NOUN
ejpam-4590	375	30	(	(	PUNCT
ejpam-4590	375	31	iii	iii	NOUN
ejpam-4590	375	32	)	)	PUNCT
ejpam-4590	375	33	for	for	ADP
ejpam-4590	375	34	all	all	PRON
ejpam-4590	375	35	v	v	NOUN
ejpam-4590	375	36	∈	∈	NOUN
ejpam-4590	375	37	(	(	PUNCT
ejpam-4590	375	38	v	v	NOUN
ejpam-4590	375	39	(	(	PUNCT
ejpam-4590	375	40	g	g	NOUN
ejpam-4590	375	41	)	)	PUNCT
ejpam-4590	375	42	\n2	\n2	VERB
ejpam-4590	375	43	g	g	PROPN
ejpam-4590	376	1	[	[	X
ejpam-4590	376	2	a	a	X
ejpam-4590	376	3	]	]	X
ejpam-4590	376	4	)	)	PUNCT
ejpam-4590	376	5	,	,	PUNCT
ejpam-4590	376	6	there	there	PRON
ejpam-4590	376	7	exists	exist	VERB
ejpam-4590	376	8	w	w	PROPN
ejpam-4590	376	9	∈	∈	PROPN
ejpam-4590	376	10	ng(v	ng(v	PUNCT
ejpam-4590	376	11	)	)	PUNCT
ejpam-4590	376	12	such	such	ADJ
ejpam-4590	376	13	that	that	SCONJ
ejpam-4590	376	14	sw	sw	PROPN
ejpam-4590	376	15	̸=	̸=	PROPN
ejpam-4590	376	16	∅.	∅.	ADP
ejpam-4590	376	17	(	(	PUNCT
ejpam-4590	376	18	iv	iv	NOUN
ejpam-4590	376	19	)	)	PUNCT
ejpam-4590	376	20	for	for	ADP
ejpam-4590	376	21	all	all	DET
ejpam-4590	376	22	v	v	ADP
ejpam-4590	376	23	∈	∈	NOUN
ejpam-4590	376	24	(	(	PUNCT
ejpam-4590	376	25	v	v	NOUN
ejpam-4590	376	26	(	(	PUNCT
ejpam-4590	376	27	g	g	NOUN
ejpam-4590	376	28	)	)	PUNCT
ejpam-4590	376	29	\ng	\ng	PROPN
ejpam-4590	377	1	[	[	X
ejpam-4590	377	2	a	a	X
ejpam-4590	377	3	]	]	X
ejpam-4590	377	4	)	)	PUNCT
ejpam-4590	377	5	,	,	PUNCT
ejpam-4590	377	6	sv	sv	PROPN
ejpam-4590	377	7	is	be	AUX
ejpam-4590	377	8	a	a	DET
ejpam-4590	377	9	pointwise	pointwise	ADJ
ejpam-4590	377	10	non	non	ADJ
ejpam-4590	377	11	-	-	ADJ
ejpam-4590	377	12	dominating	dominating	ADJ
ejpam-4590	377	13	set	set	NOUN
ejpam-4590	377	14	of	of	ADP
ejpam-4590	377	15	hv	hv	PROPN
ejpam-4590	377	16	.	.	PUNCT
ejpam-4590	378	1	proof	proof	NOUN
ejpam-4590	378	2	.	.	PUNCT
ejpam-4590	379	1	let	let	VERB
ejpam-4590	379	2	c	c	PRON
ejpam-4590	379	3	be	be	AUX
ejpam-4590	379	4	an	an	DET
ejpam-4590	379	5	outer	outer	ADV
ejpam-4590	379	6	-	-	PUNCT
ejpam-4590	379	7	connected	connect	VERB
ejpam-4590	379	8	hop	hop	NOUN
ejpam-4590	379	9	dominating	dominating	NOUN
ejpam-4590	379	10	set	set	NOUN
ejpam-4590	379	11	of	of	ADP
ejpam-4590	379	12	g	g	PROPN
ejpam-4590	379	13	◦	◦	NOUN
ejpam-4590	379	14	h	h	NOUN
ejpam-4590	379	15	,	,	PUNCT
ejpam-4590	379	16	sv	sv	PROPN
ejpam-4590	379	17	=	=	SYM
ejpam-4590	379	18	v	v	PROPN
ejpam-4590	379	19	(	(	PUNCT
ejpam-4590	379	20	hv)∩c	hv)∩c	ADJ
ejpam-4590	379	21	for	for	ADP
ejpam-4590	379	22	each	each	DET
ejpam-4590	379	23	v	v	NUM
ejpam-4590	379	24	∈	∈	PROPN
ejpam-4590	379	25	v	v	NOUN
ejpam-4590	379	26	(	(	PUNCT
ejpam-4590	379	27	g	g	NOUN
ejpam-4590	379	28	)	)	PUNCT
ejpam-4590	379	29	and	and	CCONJ
ejpam-4590	379	30	set	set	VERB
ejpam-4590	379	31	a	a	DET
ejpam-4590	379	32	=	=	SYM
ejpam-4590	379	33	v	v	NOUN
ejpam-4590	379	34	(	(	PUNCT
ejpam-4590	379	35	g)∩c	g)∩c	PROPN
ejpam-4590	379	36	.	.	PUNCT
ejpam-4590	380	1	suppose	suppose	VERB
ejpam-4590	380	2	a	a	DET
ejpam-4590	380	3	̸=	̸=	PROPN
ejpam-4590	380	4	v	v	NOUN
ejpam-4590	380	5	(	(	PUNCT
ejpam-4590	380	6	g	g	NOUN
ejpam-4590	380	7	)	)	PUNCT
ejpam-4590	380	8	.	.	PUNCT
ejpam-4590	381	1	if	if	SCONJ
ejpam-4590	381	2	|v	|v	PROPN
ejpam-4590	381	3	(	(	PUNCT
ejpam-4590	381	4	g	g	NOUN
ejpam-4590	381	5	)	)	PUNCT
ejpam-4590	381	6	\a|	\a|	NOUN
ejpam-4590	381	7	=	=	SYM
ejpam-4590	381	8	1	1	NUM
ejpam-4590	381	9	,	,	PUNCT
ejpam-4590	381	10	then	then	ADV
ejpam-4590	381	11	we	we	PRON
ejpam-4590	381	12	are	be	AUX
ejpam-4590	381	13	done	do	VERB
ejpam-4590	381	14	.	.	PUNCT
ejpam-4590	382	1	suppose	suppose	VERB
ejpam-4590	382	2	|v	|v	PROPN
ejpam-4590	382	3	(	(	PUNCT
ejpam-4590	382	4	g	g	NOUN
ejpam-4590	382	5	)	)	PUNCT
ejpam-4590	382	6	\a|	\a|	NOUN
ejpam-4590	382	7	≥	≥	NOUN
ejpam-4590	382	8	2	2	X
ejpam-4590	382	9	.	.	PUNCT
ejpam-4590	383	1	let	let	VERB
ejpam-4590	383	2	u	u	NOUN
ejpam-4590	383	3	,	,	PUNCT
ejpam-4590	383	4	v	v	PROPN
ejpam-4590	383	5	∈	∈	PROPN
ejpam-4590	383	6	v	v	NOUN
ejpam-4590	383	7	(	(	PUNCT
ejpam-4590	383	8	g)\a	g)\a	NOUN
ejpam-4590	383	9	where	where	SCONJ
ejpam-4590	383	10	u	u	NOUN
ejpam-4590	383	11	̸=	̸=	PROPN
ejpam-4590	383	12	v.	v.	CCONJ
ejpam-4590	383	13	then	then	ADV
ejpam-4590	383	14	u	u	PROPN
ejpam-4590	383	15	,	,	PUNCT
ejpam-4590	383	16	v	v	PROPN
ejpam-4590	383	17	∈	∈	PROPN
ejpam-4590	383	18	v	v	NOUN
ejpam-4590	383	19	(	(	PUNCT
ejpam-4590	383	20	g	g	NOUN
ejpam-4590	383	21	◦	◦	NOUN
ejpam-4590	383	22	h)\c	h)\c	NOUN
ejpam-4590	383	23	.	.	PUNCT
ejpam-4590	384	1	since	since	SCONJ
ejpam-4590	384	2	⟨v	⟨v	PROPN
ejpam-4590	384	3	(	(	PUNCT
ejpam-4590	384	4	g	g	PROPN
ejpam-4590	384	5	◦	◦	NOUN
ejpam-4590	384	6	h	h	NOUN
ejpam-4590	384	7	)	)	PUNCT
ejpam-4590	384	8	\	\	NOUN
ejpam-4590	384	9	c⟩	c⟩	PUNCT
ejpam-4590	384	10	is	be	AUX
ejpam-4590	384	11	connected	connect	VERB
ejpam-4590	384	12	,	,	PUNCT
ejpam-4590	384	13	there	there	PRON
ejpam-4590	384	14	is	be	VERB
ejpam-4590	384	15	a	a	DET
ejpam-4590	384	16	u	u	NOUN
ejpam-4590	384	17	-	-	NOUN
ejpam-4590	384	18	v	v	ADJ
ejpam-4590	384	19	geodesic	geodesic	NOUN
ejpam-4590	384	20	p	p	NOUN
ejpam-4590	384	21	in	in	ADP
ejpam-4590	384	22	⟨v	⟨v	PROPN
ejpam-4590	384	23	(	(	PUNCT
ejpam-4590	384	24	g	g	PROPN
ejpam-4590	384	25	◦	◦	NOUN
ejpam-4590	384	26	h	h	NOUN
ejpam-4590	384	27	)	)	PUNCT
ejpam-4590	384	28	\	\	PROPN
ejpam-4590	384	29	c⟩.	c⟩.	PROPN
ejpam-4590	384	30	hence	hence	ADV
ejpam-4590	384	31	,	,	PUNCT
ejpam-4590	384	32	p	p	PROPN
ejpam-4590	384	33	is	be	AUX
ejpam-4590	384	34	a	a	DET
ejpam-4590	384	35	u	u	NOUN
ejpam-4590	384	36	-	-	NOUN
ejpam-4590	384	37	v	v	ADJ
ejpam-4590	384	38	geodesic	geodesic	NOUN
ejpam-4590	384	39	in	in	ADP
ejpam-4590	384	40	⟨v	⟨v	PROPN
ejpam-4590	384	41	(	(	PUNCT
ejpam-4590	384	42	g	g	NOUN
ejpam-4590	384	43	)	)	PUNCT
ejpam-4590	384	44	\a⟩.	\a⟩.	PROPN
ejpam-4590	384	45	thus	thus	ADV
ejpam-4590	384	46	,	,	PUNCT
ejpam-4590	384	47	⟨v	⟨v	NOUN
ejpam-4590	384	48	(	(	PUNCT
ejpam-4590	384	49	g	g	NOUN
ejpam-4590	384	50	)	)	PUNCT
ejpam-4590	384	51	\a⟩	\a⟩	PROPN
ejpam-4590	384	52	is	be	AUX
ejpam-4590	384	53	connected	connect	VERB
ejpam-4590	384	54	,	,	PUNCT
ejpam-4590	384	55	showing	show	VERB
ejpam-4590	384	56	that	that	SCONJ
ejpam-4590	384	57	(	(	PUNCT
ejpam-4590	384	58	i	i	NOUN
ejpam-4590	384	59	)	)	PUNCT
ejpam-4590	384	60	holds	hold	VERB
ejpam-4590	384	61	.	.	PUNCT
ejpam-4590	385	1	suppose	suppose	VERB
ejpam-4590	385	2	a	a	DET
ejpam-4590	385	3	=	=	SYM
ejpam-4590	385	4	v	v	NOUN
ejpam-4590	385	5	(	(	PUNCT
ejpam-4590	385	6	g	g	NOUN
ejpam-4590	385	7	)	)	PUNCT
ejpam-4590	385	8	.	.	PUNCT
ejpam-4590	386	1	if	if	SCONJ
ejpam-4590	386	2	sv	sv	PROPN
ejpam-4590	386	3	=	=	SYM
ejpam-4590	386	4	v	v	PROPN
ejpam-4590	386	5	(	(	PUNCT
ejpam-4590	386	6	hv	hv	PROPN
ejpam-4590	386	7	)	)	PUNCT
ejpam-4590	386	8	for	for	ADP
ejpam-4590	386	9	all	all	PRON
ejpam-4590	386	10	v	v	ADP
ejpam-4590	386	11	∈	∈	PRON
ejpam-4590	386	12	a	a	PRON
ejpam-4590	386	13	,	,	PUNCT
ejpam-4590	386	14	then	then	ADV
ejpam-4590	386	15	we	we	PRON
ejpam-4590	386	16	are	be	AUX
ejpam-4590	386	17	done	do	VERB
ejpam-4590	386	18	.	.	PUNCT
ejpam-4590	387	1	suppose	suppose	VERB
ejpam-4590	387	2	there	there	PRON
ejpam-4590	387	3	exists	exist	VERB
ejpam-4590	387	4	v	v	ADP
ejpam-4590	387	5	∈	∈	PROPN
ejpam-4590	387	6	a	a	DET
ejpam-4590	387	7	such	such	ADJ
ejpam-4590	387	8	that	that	DET
ejpam-4590	387	9	sv	sv	PROPN
ejpam-4590	387	10	̸=	̸=	PROPN
ejpam-4590	387	11	v	v	PROPN
ejpam-4590	387	12	(	(	PUNCT
ejpam-4590	387	13	hv	hv	PROPN
ejpam-4590	387	14	)	)	PUNCT
ejpam-4590	387	15	.	.	PUNCT
ejpam-4590	388	1	suppose	suppose	VERB
ejpam-4590	388	2	further	far	ADV
ejpam-4590	388	3	there	there	PRON
ejpam-4590	388	4	exists	exist	VERB
ejpam-4590	388	5	w	w	PROPN
ejpam-4590	388	6	∈	∈	PROPN
ejpam-4590	388	7	a	a	DET
ejpam-4590	388	8	\	\	PROPN
ejpam-4590	388	9	{	{	PUNCT
ejpam-4590	388	10	v	v	NOUN
ejpam-4590	388	11	}	}	PUNCT
ejpam-4590	388	12	such	such	ADJ
ejpam-4590	388	13	that	that	SCONJ
ejpam-4590	388	14	sw	sw	PROPN
ejpam-4590	388	15	̸=	̸=	PROPN
ejpam-4590	388	16	v	v	PROPN
ejpam-4590	388	17	(	(	PUNCT
ejpam-4590	388	18	hw	hw	NOUN
ejpam-4590	388	19	)	)	PUNCT
ejpam-4590	388	20	.	.	PUNCT
ejpam-4590	389	1	let	let	VERB
ejpam-4590	389	2	p	p	PRON
ejpam-4590	389	3	∈	∈	PROPN
ejpam-4590	389	4	v	v	X
ejpam-4590	389	5	(	(	PUNCT
ejpam-4590	389	6	hv	hv	PROPN
ejpam-4590	389	7	)	)	PUNCT
ejpam-4590	389	8	\	\	PROPN
ejpam-4590	389	9	sv	sv	PROPN
ejpam-4590	389	10	and	and	CCONJ
ejpam-4590	389	11	q	q	PROPN
ejpam-4590	389	12	∈	∈	PROPN
ejpam-4590	389	13	v	v	ADP
ejpam-4590	389	14	(	(	PUNCT
ejpam-4590	389	15	hw	hw	NOUN
ejpam-4590	389	16	)	)	PUNCT
ejpam-4590	389	17	\	\	PROPN
ejpam-4590	389	18	sw	sw	PROPN
ejpam-4590	389	19	.	.	PUNCT
ejpam-4590	390	1	since	since	SCONJ
ejpam-4590	390	2	every	every	DET
ejpam-4590	390	3	p	p	NOUN
ejpam-4590	390	4	-	-	PUNCT
ejpam-4590	390	5	q	q	NOUN
ejpam-4590	390	6	path	path	NOUN
ejpam-4590	390	7	contains	contain	VERB
ejpam-4590	390	8	vertices	vertex	NOUN
ejpam-4590	390	9	v	v	ADP
ejpam-4590	390	10	and	and	CCONJ
ejpam-4590	390	11	w	w	NOUN
ejpam-4590	390	12	,	,	PUNCT
ejpam-4590	390	13	it	it	PRON
ejpam-4590	390	14	follows	follow	VERB
ejpam-4590	390	15	that	that	SCONJ
ejpam-4590	390	16	there	there	PRON
ejpam-4590	390	17	is	be	VERB
ejpam-4590	390	18	no	no	DET
ejpam-4590	390	19	p	p	NOUN
ejpam-4590	390	20	-	-	PUNCT
ejpam-4590	390	21	q	q	NOUN
ejpam-4590	390	22	path	path	NOUN
ejpam-4590	390	23	in	in	ADP
ejpam-4590	390	24	⟨v	⟨v	PROPN
ejpam-4590	390	25	(	(	PUNCT
ejpam-4590	390	26	g	g	PROPN
ejpam-4590	390	27	◦	◦	NOUN
ejpam-4590	390	28	h	h	NOUN
ejpam-4590	390	29	)	)	PUNCT
ejpam-4590	390	30	\	\	NOUN
ejpam-4590	391	1	c⟩	c⟩	ADV
ejpam-4590	391	2	,	,	PUNCT
ejpam-4590	391	3	contrary	contrary	ADV
ejpam-4590	391	4	to	to	ADP
ejpam-4590	391	5	the	the	DET
ejpam-4590	391	6	assumption	assumption	NOUN
ejpam-4590	391	7	that	that	SCONJ
ejpam-4590	391	8	⟨v	⟨v	NOUN
ejpam-4590	391	9	(	(	PUNCT
ejpam-4590	391	10	g	g	PROPN
ejpam-4590	391	11	◦	◦	NOUN
ejpam-4590	391	12	h	h	NOUN
ejpam-4590	391	13	)	)	PUNCT
ejpam-4590	391	14	\	\	NOUN
ejpam-4590	391	15	c⟩	c⟩	PUNCT
ejpam-4590	391	16	is	be	AUX
ejpam-4590	391	17	connected	connect	VERB
ejpam-4590	391	18	.	.	PUNCT
ejpam-4590	392	1	hence	hence	ADV
ejpam-4590	392	2	,	,	PUNCT
ejpam-4590	392	3	there	there	PRON
ejpam-4590	392	4	is	be	VERB
ejpam-4590	392	5	at	at	ADP
ejpam-4590	392	6	most	most	ADJ
ejpam-4590	392	7	a	a	DET
ejpam-4590	392	8	single	single	ADJ
ejpam-4590	392	9	vertex	vertex	NOUN
ejpam-4590	392	10	v	v	ADP
ejpam-4590	392	11	∈	∈	PROPN
ejpam-4590	392	12	a	a	DET
ejpam-4590	392	13	such	such	ADJ
ejpam-4590	392	14	that	that	DET
ejpam-4590	392	15	sv	sv	PROPN
ejpam-4590	392	16	̸=	̸=	PROPN
ejpam-4590	392	17	v	v	PROPN
ejpam-4590	392	18	(	(	PUNCT
ejpam-4590	392	19	hv	hv	PROPN
ejpam-4590	392	20	)	)	PUNCT
ejpam-4590	392	21	.	.	PUNCT
ejpam-4590	393	1	suppose	suppose	VERB
ejpam-4590	393	2	a	a	DET
ejpam-4590	393	3	̸=	̸=	PROPN
ejpam-4590	393	4	v	v	NOUN
ejpam-4590	393	5	(	(	PUNCT
ejpam-4590	393	6	g	g	NOUN
ejpam-4590	393	7	)	)	PUNCT
ejpam-4590	393	8	.	.	PUNCT
ejpam-4590	394	1	suppose	suppose	VERB
ejpam-4590	394	2	further	far	ADV
ejpam-4590	394	3	that	that	SCONJ
ejpam-4590	394	4	there	there	PRON
ejpam-4590	394	5	exists	exist	VERB
ejpam-4590	394	6	v	v	ADP
ejpam-4590	394	7	∈	∈	PROPN
ejpam-4590	394	8	a	a	DET
ejpam-4590	394	9	such	such	ADJ
ejpam-4590	394	10	that	that	DET
ejpam-4590	394	11	sv	sv	PROPN
ejpam-4590	394	12	̸=	̸=	PROPN
ejpam-4590	394	13	v	v	PROPN
ejpam-4590	394	14	(	(	PUNCT
ejpam-4590	394	15	hv	hv	PROPN
ejpam-4590	394	16	)	)	PUNCT
ejpam-4590	394	17	.	.	PUNCT
ejpam-4590	395	1	choose	choose	VERB
ejpam-4590	395	2	any	any	DET
ejpam-4590	395	3	z	z	NOUN
ejpam-4590	395	4	∈	∈	PROPN
ejpam-4590	395	5	v	v	ADP
ejpam-4590	395	6	(	(	PUNCT
ejpam-4590	395	7	g	g	NOUN
ejpam-4590	395	8	)	)	PUNCT
ejpam-4590	395	9	\	\	PROPN
ejpam-4590	396	1	a	a	PRON
ejpam-4590	396	2	and	and	CCONJ
ejpam-4590	396	3	y	y	PROPN
ejpam-4590	396	4	∈	∈	PROPN
ejpam-4590	396	5	v	v	PROPN
ejpam-4590	396	6	(	(	PUNCT
ejpam-4590	396	7	hv	hv	PROPN
ejpam-4590	396	8	)	)	PUNCT
ejpam-4590	396	9	\	\	PROPN
ejpam-4590	397	1	sv	sv	PROPN
ejpam-4590	397	2	.	.	PUNCT
ejpam-4590	398	1	since	since	SCONJ
ejpam-4590	398	2	any	any	DET
ejpam-4590	398	3	y	y	PROPN
ejpam-4590	398	4	-	-	PUNCT
ejpam-4590	398	5	z	z	NOUN
ejpam-4590	398	6	path	path	NOUN
ejpam-4590	398	7	contains	contain	VERB
ejpam-4590	398	8	v	v	NOUN
ejpam-4590	398	9	as	as	ADP
ejpam-4590	398	10	a	a	DET
ejpam-4590	398	11	vertex	vertex	NOUN
ejpam-4590	398	12	it	it	PRON
ejpam-4590	398	13	follows	follow	VERB
ejpam-4590	398	14	that	that	SCONJ
ejpam-4590	398	15	there	there	PRON
ejpam-4590	398	16	is	be	VERB
ejpam-4590	398	17	no	no	DET
ejpam-4590	398	18	y	y	PROPN
ejpam-4590	398	19	-	-	PUNCT
ejpam-4590	398	20	z	z	NOUN
ejpam-4590	398	21	path	path	NOUN
ejpam-4590	398	22	in	in	ADP
ejpam-4590	398	23	⟨v	⟨v	PROPN
ejpam-4590	398	24	(	(	PUNCT
ejpam-4590	398	25	g	g	PROPN
ejpam-4590	398	26	◦	◦	NOUN
ejpam-4590	398	27	h	h	NOUN
ejpam-4590	398	28	)	)	PUNCT
ejpam-4590	398	29	\	\	NOUN
ejpam-4590	398	30	c⟩	c⟩	ADV
ejpam-4590	398	31	,	,	PUNCT
ejpam-4590	398	32	a	a	DET
ejpam-4590	398	33	contradiction	contradiction	NOUN
ejpam-4590	398	34	.	.	PUNCT
ejpam-4590	399	1	therefore	therefore	ADV
ejpam-4590	399	2	sv	sv	PROPN
ejpam-4590	399	3	=	=	SYM
ejpam-4590	399	4	v	v	PROPN
ejpam-4590	399	5	(	(	PUNCT
ejpam-4590	399	6	hv	hv	PROPN
ejpam-4590	399	7	)	)	PUNCT
ejpam-4590	399	8	for	for	ADP
ejpam-4590	399	9	all	all	PRON
ejpam-4590	399	10	v	v	NOUN
ejpam-4590	399	11	∈	∈	NOUN
ejpam-4590	399	12	a.	a.	NOUN
ejpam-4590	399	13	hence	hence	ADV
ejpam-4590	399	14	,	,	PUNCT
ejpam-4590	399	15	(	(	PUNCT
ejpam-4590	399	16	ii	ii	NOUN
ejpam-4590	399	17	)	)	PUNCT
ejpam-4590	399	18	holds	hold	VERB
ejpam-4590	399	19	.	.	PUNCT
ejpam-4590	400	1	next	next	ADV
ejpam-4590	400	2	,	,	PUNCT
ejpam-4590	400	3	let	let	VERB
ejpam-4590	400	4	v	v	X
ejpam-4590	400	5	∈	∈	NOUN
ejpam-4590	400	6	(	(	PUNCT
ejpam-4590	400	7	v	v	NOUN
ejpam-4590	400	8	(	(	PUNCT
ejpam-4590	400	9	g	g	NOUN
ejpam-4590	400	10	)	)	PUNCT
ejpam-4590	400	11	\n2	\n2	VERB
ejpam-4590	400	12	g	g	PROPN
ejpam-4590	401	1	[	[	X
ejpam-4590	401	2	a	a	X
ejpam-4590	401	3	]	]	X
ejpam-4590	401	4	)	)	PUNCT
ejpam-4590	401	5	.	.	PUNCT
ejpam-4590	402	1	then	then	ADV
ejpam-4590	402	2	v	v	X
ejpam-4590	402	3	/∈	/∈	PUNCT
ejpam-4590	402	4	c	c	PROPN
ejpam-4590	402	5	∪n2	∪n2	PROPN
ejpam-4590	402	6	g(a	g(a	PROPN
ejpam-4590	402	7	)	)	PUNCT
ejpam-4590	402	8	.	.	PUNCT
ejpam-4590	403	1	since	since	SCONJ
ejpam-4590	403	2	c	c	PROPN
ejpam-4590	403	3	is	be	AUX
ejpam-4590	403	4	a	a	DET
ejpam-4590	403	5	hop	hop	NOUN
ejpam-4590	403	6	dominating	dominating	NOUN
ejpam-4590	403	7	set	set	NOUN
ejpam-4590	403	8	,	,	PUNCT
ejpam-4590	403	9	there	there	PRON
ejpam-4590	403	10	exists	exist	VERB
ejpam-4590	403	11	y	y	PROPN
ejpam-4590	403	12	∈	∈	PROPN
ejpam-4590	404	1	c	c	PROPN
ejpam-4590	404	2	∩n2	∩n2	NOUN
ejpam-4590	404	3	g	g	PROPN
ejpam-4590	404	4	◦	◦	NOUN
ejpam-4590	404	5	h(v	h(v	NOUN
ejpam-4590	404	6	)	)	PUNCT
ejpam-4590	404	7	.	.	PUNCT
ejpam-4590	405	1	since	since	SCONJ
ejpam-4590	405	2	v	v	NUM
ejpam-4590	405	3	/∈	/∈	PROPN
ejpam-4590	405	4	n2	n2	PROPN
ejpam-4590	405	5	g(a	g(a	PROPN
ejpam-4590	405	6	)	)	PUNCT
ejpam-4590	405	7	and	and	CCONJ
ejpam-4590	405	8	dg	dg	NOUN
ejpam-4590	405	9	◦	◦	NOUN
ejpam-4590	405	10	h(y	h(y	ADV
ejpam-4590	405	11	,	,	PUNCT
ejpam-4590	405	12	v	v	NOUN
ejpam-4590	405	13	)	)	PUNCT
ejpam-4590	405	14	=	=	SYM
ejpam-4590	405	15	2	2	NUM
ejpam-4590	405	16	,	,	PUNCT
ejpam-4590	405	17	it	it	PRON
ejpam-4590	405	18	follows	follow	VERB
ejpam-4590	405	19	that	that	SCONJ
ejpam-4590	405	20	there	there	PRON
ejpam-4590	405	21	exists	exist	VERB
ejpam-4590	405	22	w	w	PROPN
ejpam-4590	405	23	∈	∈	PROPN
ejpam-4590	405	24	ng(v	ng(v	PUNCT
ejpam-4590	405	25	)	)	PUNCT
ejpam-4590	406	1	such	such	ADJ
ejpam-4590	406	2	that	that	SCONJ
ejpam-4590	406	3	y	y	PROPN
ejpam-4590	406	4	∈	∈	PROPN
ejpam-4590	406	5	sw	sw	PROPN
ejpam-4590	406	6	.	.	PUNCT
ejpam-4590	407	1	hence	hence	ADV
ejpam-4590	407	2	,	,	PUNCT
ejpam-4590	407	3	(	(	PUNCT
ejpam-4590	407	4	iii	iii	NOUN
ejpam-4590	407	5	)	)	PUNCT
ejpam-4590	407	6	holds	hold	VERB
ejpam-4590	407	7	.	.	PUNCT
ejpam-4590	408	1	finally	finally	ADV
ejpam-4590	408	2	,	,	PUNCT
ejpam-4590	408	3	let	let	VERB
ejpam-4590	408	4	v	v	NUM
ejpam-4590	408	5	∈	∈	PROPN
ejpam-4590	408	6	v	v	NOUN
ejpam-4590	408	7	(	(	PUNCT
ejpam-4590	408	8	g	g	NOUN
ejpam-4590	408	9	)	)	PUNCT
ejpam-4590	408	10	\	\	PROPN
ejpam-4590	409	1	ng	ng	PROPN
ejpam-4590	410	1	[	[	X
ejpam-4590	410	2	a	a	X
ejpam-4590	410	3	]	]	X
ejpam-4590	410	4	and	and	CCONJ
ejpam-4590	410	5	let	let	VERB
ejpam-4590	410	6	z	z	NOUN
ejpam-4590	410	7	∈	∈	PROPN
ejpam-4590	410	8	v	v	ADP
ejpam-4590	410	9	(	(	PUNCT
ejpam-4590	410	10	hv	hv	PROPN
ejpam-4590	410	11	)	)	PUNCT
ejpam-4590	410	12	\	\	PROPN
ejpam-4590	411	1	sv	sv	PROPN
ejpam-4590	411	2	.	.	PUNCT
ejpam-4590	412	1	then	then	ADV
ejpam-4590	412	2	z	z	PROPN
ejpam-4590	412	3	/∈	/∈	PUNCT
ejpam-4590	412	4	c.	c.	NOUN
ejpam-4590	412	5	since	since	SCONJ
ejpam-4590	412	6	c	c	PROPN
ejpam-4590	412	7	is	be	AUX
ejpam-4590	412	8	hop	hop	NOUN
ejpam-4590	412	9	dominating	dominating	NOUN
ejpam-4590	412	10	,	,	PUNCT
ejpam-4590	412	11	there	there	PRON
ejpam-4590	412	12	exists	exist	VERB
ejpam-4590	412	13	x	x	X
ejpam-4590	412	14	∈	∈	PROPN
ejpam-4590	412	15	c∩n2	c∩n2	PROPN
ejpam-4590	412	16	g	g	PROPN
ejpam-4590	412	17	◦	◦	NOUN
ejpam-4590	412	18	h(z	h(z	NOUN
ejpam-4590	412	19	)	)	PUNCT
ejpam-4590	412	20	.	.	PUNCT
ejpam-4590	413	1	hence	hence	ADV
ejpam-4590	413	2	,	,	PUNCT
ejpam-4590	413	3	x	x	PUNCT
ejpam-4590	413	4	∈	∈	PROPN
ejpam-4590	413	5	sv	sv	NOUN
ejpam-4590	413	6	and	and	CCONJ
ejpam-4590	413	7	dg	dg	PROPN
ejpam-4590	413	8	◦	◦	NOUN
ejpam-4590	413	9	h(z	h(z	NOUN
ejpam-4590	413	10	,	,	PUNCT
ejpam-4590	413	11	x	x	NOUN
ejpam-4590	413	12	)	)	PUNCT
ejpam-4590	413	13	=	=	SYM
ejpam-4590	413	14	dhv(z	dhv(z	PROPN
ejpam-4590	413	15	,	,	PUNCT
ejpam-4590	413	16	x	x	NOUN
ejpam-4590	413	17	)	)	PUNCT
ejpam-4590	413	18	=	=	SYM
ejpam-4590	413	19	2	2	X
ejpam-4590	413	20	.	.	X
ejpam-4590	413	21	therefore	therefore	ADV
ejpam-4590	413	22	,	,	PUNCT
ejpam-4590	413	23	sv	sv	PROPN
ejpam-4590	413	24	is	be	AUX
ejpam-4590	413	25	a	a	DET
ejpam-4590	413	26	pointwise	pointwise	ADJ
ejpam-4590	413	27	non	non	ADJ
ejpam-4590	413	28	-	-	ADJ
ejpam-4590	413	29	dominating	dominating	ADJ
ejpam-4590	413	30	set	set	NOUN
ejpam-4590	413	31	of	of	ADP
ejpam-4590	413	32	hv	hv	PROPN
ejpam-4590	413	33	,	,	PUNCT
ejpam-4590	413	34	showing	show	VERB
ejpam-4590	413	35	that	that	SCONJ
ejpam-4590	413	36	(	(	PUNCT
ejpam-4590	413	37	iv	iv	X
ejpam-4590	413	38	)	)	PUNCT
ejpam-4590	413	39	holds	hold	NOUN
ejpam-4590	413	40	.	.	PUNCT
ejpam-4590	414	1	c.j	c.j	PROPN
ejpam-4590	414	2	.	.	PROPN
ejpam-4590	414	3	saromines	saromines	PROPN
ejpam-4590	414	4	,	,	PUNCT
ejpam-4590	414	5	s.	s.	PROPN
ejpam-4590	414	6	canoy	canoy	PROPN
ejpam-4590	414	7	,	,	PUNCT
ejpam-4590	414	8	jr	jr	PROPN
ejpam-4590	414	9	.	.	PROPN
ejpam-4590	414	10	/	/	SYM
ejpam-4590	414	11	eur	eur	PROPN
ejpam-4590	414	12	.	.	PUNCT
ejpam-4590	415	1	j.	j.	PROPN
ejpam-4590	415	2	pure	pure	PROPN
ejpam-4590	415	3	appl	appl	PROPN
ejpam-4590	415	4	.	.	PROPN
ejpam-4590	415	5	math	math	PROPN
ejpam-4590	415	6	,	,	PUNCT
ejpam-4590	415	7	15	15	NUM
ejpam-4590	415	8	(	(	PUNCT
ejpam-4590	415	9	4	4	NUM
ejpam-4590	415	10	)	)	PUNCT
ejpam-4590	415	11	(	(	PUNCT
ejpam-4590	415	12	2022	2022	NUM
ejpam-4590	415	13	)	)	PUNCT
ejpam-4590	415	14	,	,	PUNCT
ejpam-4590	415	15	1966	1966	NUM
ejpam-4590	415	16	-	-	SYM
ejpam-4590	415	17	1981	1981	NUM
ejpam-4590	415	18	1976	1976	NUM
ejpam-4590	415	19	conversely	conversely	ADV
ejpam-4590	415	20	,	,	PUNCT
ejpam-4590	415	21	suppose	suppose	VERB
ejpam-4590	415	22	that	that	SCONJ
ejpam-4590	415	23	c	c	PROPN
ejpam-4590	415	24	has	have	VERB
ejpam-4590	415	25	the	the	DET
ejpam-4590	415	26	given	give	VERB
ejpam-4590	415	27	form	form	NOUN
ejpam-4590	415	28	and	and	CCONJ
ejpam-4590	415	29	satisfies	satisfie	NOUN
ejpam-4590	415	30	properties	property	NOUN
ejpam-4590	415	31	(	(	PUNCT
ejpam-4590	415	32	i	i	NOUN
ejpam-4590	415	33	)	)	PUNCT
ejpam-4590	415	34	,	,	PUNCT
ejpam-4590	415	35	(	(	PUNCT
ejpam-4590	415	36	ii	ii	NOUN
ejpam-4590	415	37	)	)	PUNCT
ejpam-4590	415	38	,	,	PUNCT
ejpam-4590	415	39	(	(	PUNCT
ejpam-4590	415	40	iii	iii	NOUN
ejpam-4590	415	41	)	)	PUNCT
ejpam-4590	415	42	and	and	CCONJ
ejpam-4590	415	43	(	(	PUNCT
ejpam-4590	415	44	iv	iv	X
ejpam-4590	415	45	)	)	PUNCT
ejpam-4590	415	46	.	.	PUNCT
ejpam-4590	416	1	let	let	VERB
ejpam-4590	416	2	x	x	SYM
ejpam-4590	416	3	∈	∈	PROPN
ejpam-4590	416	4	v	v	X
ejpam-4590	416	5	(	(	PUNCT
ejpam-4590	416	6	g	g	PROPN
ejpam-4590	416	7	+	+	NOUN
ejpam-4590	416	8	h	h	NOUN
ejpam-4590	416	9	)	)	PUNCT
ejpam-4590	416	10	\	\	NOUN
ejpam-4590	416	11	c	c	NOUN
ejpam-4590	416	12	and	and	CCONJ
ejpam-4590	416	13	let	let	VERB
ejpam-4590	416	14	v	v	NUM
ejpam-4590	416	15	∈	∈	PROPN
ejpam-4590	416	16	v	v	NOUN
ejpam-4590	416	17	(	(	PUNCT
ejpam-4590	416	18	g	g	NOUN
ejpam-4590	416	19	)	)	PUNCT
ejpam-4590	416	20	such	such	ADJ
ejpam-4590	416	21	that	that	SCONJ
ejpam-4590	416	22	x	x	SYM
ejpam-4590	416	23	∈	∈	NOUN
ejpam-4590	416	24	v	v	NOUN
ejpam-4590	416	25	(	(	PUNCT
ejpam-4590	416	26	v	v	NOUN
ejpam-4590	416	27	+	+	CCONJ
ejpam-4590	416	28	hv	hv	NOUN
ejpam-4590	416	29	)	)	PUNCT
ejpam-4590	416	30	.	.	PUNCT
ejpam-4590	417	1	suppose	suppose	VERB
ejpam-4590	417	2	x	x	PUNCT
ejpam-4590	418	1	=	=	PUNCT
ejpam-4590	418	2	v.	v.	INTJ
ejpam-4590	418	3	if	if	SCONJ
ejpam-4590	418	4	v	v	PROPN
ejpam-4590	418	5	∈	∈	PROPN
ejpam-4590	418	6	n2	n2	NOUN
ejpam-4590	418	7	g(a	g(a	PROPN
ejpam-4590	418	8	)	)	PUNCT
ejpam-4590	418	9	,	,	PUNCT
ejpam-4590	418	10	then	then	ADV
ejpam-4590	418	11	we	we	PRON
ejpam-4590	418	12	are	be	AUX
ejpam-4590	418	13	done	do	VERB
ejpam-4590	418	14	.	.	PUNCT
ejpam-4590	419	1	suppose	suppose	VERB
ejpam-4590	419	2	v	v	ADP
ejpam-4590	419	3	∈	∈	PROPN
ejpam-4590	419	4	(	(	PUNCT
ejpam-4590	419	5	v	v	NOUN
ejpam-4590	419	6	(	(	PUNCT
ejpam-4590	419	7	g)\n2	g)\n2	NOUN
ejpam-4590	419	8	g	g	NOUN
ejpam-4590	419	9	[	[	X
ejpam-4590	419	10	a	a	X
ejpam-4590	419	11	]	]	X
ejpam-4590	419	12	.	.	PUNCT
ejpam-4590	420	1	by	by	ADP
ejpam-4590	420	2	(	(	PUNCT
ejpam-4590	420	3	iii	iii	NOUN
ejpam-4590	420	4	)	)	PUNCT
ejpam-4590	420	5	,	,	PUNCT
ejpam-4590	420	6	there	there	PRON
ejpam-4590	420	7	exists	exist	VERB
ejpam-4590	420	8	w	w	PROPN
ejpam-4590	420	9	∈	∈	PROPN
ejpam-4590	420	10	ng(v	ng(v	PUNCT
ejpam-4590	420	11	)	)	PUNCT
ejpam-4590	420	12	such	such	ADJ
ejpam-4590	420	13	that	that	SCONJ
ejpam-4590	420	14	sw	sw	PROPN
ejpam-4590	420	15	̸=	̸=	PROPN
ejpam-4590	420	16	∅.	∅.	ADV
ejpam-4590	420	17	choose	choose	VERB
ejpam-4590	420	18	any	any	DET
ejpam-4590	420	19	p	p	PROPN
ejpam-4590	420	20	∈	∈	PROPN
ejpam-4590	420	21	sw	sw	NOUN
ejpam-4590	421	1	then	then	ADV
ejpam-4590	421	2	p	p	PROPN
ejpam-4590	421	3	∈	∈	PROPN
ejpam-4590	421	4	c	c	PROPN
ejpam-4590	421	5	and	and	CCONJ
ejpam-4590	421	6	dg	dg	PROPN
ejpam-4590	421	7	◦	◦	NOUN
ejpam-4590	421	8	h	h	NOUN
ejpam-4590	421	9	=	=	ADJ
ejpam-4590	421	10	2	2	X
ejpam-4590	421	11	.	.	X
ejpam-4590	421	12	therefore	therefore	ADV
ejpam-4590	421	13	c	c	PROPN
ejpam-4590	421	14	is	be	AUX
ejpam-4590	421	15	a	a	DET
ejpam-4590	421	16	hop	hop	NOUN
ejpam-4590	421	17	dominating	dominating	NOUN
ejpam-4590	421	18	set	set	NOUN
ejpam-4590	421	19	.	.	PUNCT
ejpam-4590	422	1	let	let	VERB
ejpam-4590	422	2	a	a	DET
ejpam-4590	422	3	,	,	PUNCT
ejpam-4590	422	4	b	b	PROPN
ejpam-4590	422	5	∈	∈	PROPN
ejpam-4590	422	6	v	v	NOUN
ejpam-4590	422	7	(	(	PUNCT
ejpam-4590	422	8	g	g	PROPN
ejpam-4590	422	9	◦	◦	NOUN
ejpam-4590	422	10	h	h	NOUN
ejpam-4590	422	11	)	)	PUNCT
ejpam-4590	422	12	\	\	PROPN
ejpam-4590	423	1	c	c	NOUN
ejpam-4590	423	2	with	with	ADP
ejpam-4590	423	3	a	a	DET
ejpam-4590	423	4	̸=	̸=	PROPN
ejpam-4590	423	5	b	b	PROPN
ejpam-4590	423	6	and	and	CCONJ
ejpam-4590	423	7	let	let	VERB
ejpam-4590	423	8	v	v	NOUN
ejpam-4590	423	9	,	,	PUNCT
ejpam-4590	423	10	w	w	PROPN
ejpam-4590	423	11	∈	∈	PROPN
ejpam-4590	423	12	v	v	ADP
ejpam-4590	423	13	(	(	PUNCT
ejpam-4590	423	14	g	g	NOUN
ejpam-4590	423	15	)	)	PUNCT
ejpam-4590	423	16	such	such	ADJ
ejpam-4590	423	17	that	that	SCONJ
ejpam-4590	423	18	a	a	DET
ejpam-4590	423	19	∈	∈	PROPN
ejpam-4590	423	20	v	v	NOUN
ejpam-4590	423	21	(	(	PUNCT
ejpam-4590	423	22	v	v	PROPN
ejpam-4590	423	23	+	+	NOUN
ejpam-4590	423	24	hv	hv	NOUN
ejpam-4590	423	25	)	)	PUNCT
ejpam-4590	423	26	and	and	CCONJ
ejpam-4590	423	27	b	b	X
ejpam-4590	423	28	∈	∈	PROPN
ejpam-4590	423	29	v	v	NOUN
ejpam-4590	423	30	(	(	PUNCT
ejpam-4590	423	31	w	w	NOUN
ejpam-4590	423	32	+	+	NOUN
ejpam-4590	423	33	hw	hw	NOUN
ejpam-4590	423	34	)	)	PUNCT
ejpam-4590	423	35	.	.	PUNCT
ejpam-4590	424	1	consider	consider	VERB
ejpam-4590	424	2	the	the	DET
ejpam-4590	424	3	following	follow	VERB
ejpam-4590	424	4	cases	case	NOUN
ejpam-4590	424	5	:	:	PUNCT
ejpam-4590	424	6	case	case	NOUN
ejpam-4590	424	7	1	1	NUM
ejpam-4590	424	8	.	.	PUNCT
ejpam-4590	425	1	v	v	X
ejpam-4590	425	2	=	=	PUNCT
ejpam-4590	425	3	w.	w.	NOUN
ejpam-4590	425	4	if	if	SCONJ
ejpam-4590	425	5	a	a	DET
ejpam-4590	425	6	=	=	SYM
ejpam-4590	425	7	v	v	NOUN
ejpam-4590	425	8	and	and	CCONJ
ejpam-4590	425	9	b	b	NOUN
ejpam-4590	425	10	∈	∈	PROPN
ejpam-4590	425	11	v	v	NOUN
ejpam-4590	425	12	(	(	PUNCT
ejpam-4590	425	13	hv)\sv	hv)\sv	PROPN
ejpam-4590	425	14	,	,	PUNCT
ejpam-4590	425	15	then	then	ADV
ejpam-4590	425	16	ab	ab	PROPN
ejpam-4590	425	17	∈	∈	PROPN
ejpam-4590	425	18	e(g	e(g	PROPN
ejpam-4590	425	19	◦	◦	NOUN
ejpam-4590	425	20	h	h	NOUN
ejpam-4590	425	21	)	)	PUNCT
ejpam-4590	425	22	and	and	CCONJ
ejpam-4590	425	23	we	we	PRON
ejpam-4590	425	24	are	be	AUX
ejpam-4590	425	25	done	do	VERB
ejpam-4590	425	26	.	.	PUNCT
ejpam-4590	426	1	let	let	VERB
ejpam-4590	426	2	a	a	DET
ejpam-4590	426	3	,	,	PUNCT
ejpam-4590	426	4	b	b	PROPN
ejpam-4590	426	5	∈	∈	PROPN
ejpam-4590	426	6	v	v	NOUN
ejpam-4590	426	7	(	(	PUNCT
ejpam-4590	426	8	hv)\sv	hv)\sv	PROPN
ejpam-4590	426	9	.	.	PUNCT
ejpam-4590	427	1	if	if	SCONJ
ejpam-4590	427	2	a	a	DET
ejpam-4590	427	3	=	=	X
ejpam-4590	427	4	v	v	NOUN
ejpam-4590	427	5	(	(	PUNCT
ejpam-4590	427	6	g	g	NOUN
ejpam-4590	427	7	)	)	PUNCT
ejpam-4590	427	8	,	,	PUNCT
ejpam-4590	427	9	then	then	ADV
ejpam-4590	427	10	v	v	X
ejpam-4590	427	11	∈	∈	NOUN
ejpam-4590	427	12	a.	a.	NOUN
ejpam-4590	427	13	by	by	ADP
ejpam-4590	427	14	(	(	PUNCT
ejpam-4590	427	15	ii	ii	NOUN
ejpam-4590	427	16	)	)	PUNCT
ejpam-4590	427	17	,	,	PUNCT
ejpam-4590	427	18	⟨v	⟨v	PROPN
ejpam-4590	427	19	(	(	PUNCT
ejpam-4590	427	20	hv	hv	NOUN
ejpam-4590	427	21	)	)	PUNCT
ejpam-4590	427	22	\	\	PROPN
ejpam-4590	427	23	sv⟩	sv⟩	PROPN
ejpam-4590	427	24	is	be	AUX
ejpam-4590	427	25	connected	connect	VERB
ejpam-4590	427	26	,	,	PUNCT
ejpam-4590	427	27	hence	hence	ADV
ejpam-4590	427	28	,	,	PUNCT
ejpam-4590	427	29	there	there	PRON
ejpam-4590	427	30	exists	exist	VERB
ejpam-4590	427	31	an	an	DET
ejpam-4590	427	32	a	a	PRON
ejpam-4590	427	33	-	-	PUNCT
ejpam-4590	427	34	b	b	NOUN
ejpam-4590	427	35	path	path	NOUN
ejpam-4590	427	36	in	in	ADP
ejpam-4590	427	37	⟨v	⟨v	PROPN
ejpam-4590	427	38	(	(	PUNCT
ejpam-4590	427	39	hv	hv	NOUN
ejpam-4590	427	40	)	)	PUNCT
ejpam-4590	427	41	\	\	PUNCT
ejpam-4590	428	1	sv⟩.	sv⟩.	SCONJ
ejpam-4590	428	2	this	this	DET
ejpam-4590	428	3	a	a	PROPN
ejpam-4590	428	4	-	-	PUNCT
ejpam-4590	428	5	b	b	NOUN
ejpam-4590	428	6	path	path	NOUN
ejpam-4590	428	7	is	be	AUX
ejpam-4590	428	8	also	also	ADV
ejpam-4590	428	9	an	an	DET
ejpam-4590	428	10	a	a	PRON
ejpam-4590	428	11	-	-	PUNCT
ejpam-4590	428	12	b	b	NOUN
ejpam-4590	428	13	path	path	NOUN
ejpam-4590	428	14	in	in	ADP
ejpam-4590	428	15	⟨v	⟨v	PROPN
ejpam-4590	428	16	(	(	PUNCT
ejpam-4590	428	17	g	g	PROPN
ejpam-4590	428	18	◦	◦	NOUN
ejpam-4590	428	19	h	h	NOUN
ejpam-4590	428	20	)	)	PUNCT
ejpam-4590	428	21	\	\	PROPN
ejpam-4590	428	22	c⟩.	c⟩.	PROPN
ejpam-4590	428	23	if	if	SCONJ
ejpam-4590	428	24	a	a	DET
ejpam-4590	428	25	̸=	̸=	PROPN
ejpam-4590	428	26	v	v	NOUN
ejpam-4590	428	27	(	(	PUNCT
ejpam-4590	428	28	g	g	NOUN
ejpam-4590	428	29	)	)	PUNCT
ejpam-4590	428	30	,	,	PUNCT
ejpam-4590	428	31	then	then	ADV
ejpam-4590	428	32	v	v	X
ejpam-4590	428	33	/∈	/∈	PUNCT
ejpam-4590	428	34	a	a	PRON
ejpam-4590	428	35	by	by	ADP
ejpam-4590	428	36	the	the	DET
ejpam-4590	428	37	second	second	ADJ
ejpam-4590	428	38	part	part	NOUN
ejpam-4590	428	39	of	of	ADP
ejpam-4590	428	40	(	(	PUNCT
ejpam-4590	428	41	ii	ii	NOUN
ejpam-4590	428	42	)	)	PUNCT
ejpam-4590	428	43	.	.	PUNCT
ejpam-4590	429	1	therefore	therefore	ADV
ejpam-4590	429	2	,	,	PUNCT
ejpam-4590	429	3	[	[	X
ejpam-4590	429	4	a	a	X
ejpam-4590	429	5	,	,	PUNCT
ejpam-4590	429	6	v	v	NOUN
ejpam-4590	429	7	,	,	PUNCT
ejpam-4590	429	8	b	b	AUX
ejpam-4590	429	9	]	]	X
ejpam-4590	429	10	is	be	AUX
ejpam-4590	429	11	an	an	DET
ejpam-4590	429	12	a	a	PRON
ejpam-4590	429	13	-	-	PUNCT
ejpam-4590	429	14	b	b	NOUN
ejpam-4590	429	15	path	path	NOUN
ejpam-4590	429	16	in	in	ADP
ejpam-4590	429	17	⟨v	⟨v	PROPN
ejpam-4590	429	18	(	(	PUNCT
ejpam-4590	429	19	g	g	PROPN
ejpam-4590	429	20	◦	◦	NOUN
ejpam-4590	429	21	h	h	NOUN
ejpam-4590	429	22	)	)	PUNCT
ejpam-4590	429	23	\	\	NOUN
ejpam-4590	429	24	c⟩.	c⟩.	ADJ
ejpam-4590	429	25	case	case	NOUN
ejpam-4590	429	26	2	2	NUM
ejpam-4590	429	27	.	.	NOUN
ejpam-4590	429	28	v	v	ADP
ejpam-4590	429	29	̸=	̸=	PROPN
ejpam-4590	429	30	w.	w.	NOUN
ejpam-4590	429	31	if	if	SCONJ
ejpam-4590	429	32	a	a	DET
ejpam-4590	429	33	=	=	SYM
ejpam-4590	429	34	v	v	NOUN
ejpam-4590	429	35	and	and	CCONJ
ejpam-4590	429	36	b	b	NOUN
ejpam-4590	429	37	=	=	SYM
ejpam-4590	429	38	w	w	PROPN
ejpam-4590	429	39	,	,	PUNCT
ejpam-4590	429	40	then	then	ADV
ejpam-4590	429	41	v	v	NOUN
ejpam-4590	429	42	,	,	PUNCT
ejpam-4590	429	43	w	w	PROPN
ejpam-4590	429	44	∈	∈	PROPN
ejpam-4590	429	45	v	v	ADP
ejpam-4590	429	46	(	(	PUNCT
ejpam-4590	429	47	g	g	NOUN
ejpam-4590	429	48	)	)	PUNCT
ejpam-4590	429	49	\	\	NOUN
ejpam-4590	429	50	a.	a.	NOUN
ejpam-4590	429	51	by	by	ADP
ejpam-4590	429	52	(	(	PUNCT
ejpam-4590	429	53	i	i	NOUN
ejpam-4590	429	54	)	)	PUNCT
ejpam-4590	429	55	,	,	PUNCT
ejpam-4590	429	56	there	there	PRON
ejpam-4590	429	57	exists	exist	VERB
ejpam-4590	429	58	an	an	DET
ejpam-4590	429	59	a	a	PRON
ejpam-4590	429	60	-	-	PUNCT
ejpam-4590	429	61	b	b	NOUN
ejpam-4590	429	62	path	path	NOUN
ejpam-4590	429	63	p	p	NOUN
ejpam-4590	429	64	in	in	ADP
ejpam-4590	429	65	⟨v	⟨v	PROPN
ejpam-4590	429	66	(	(	PUNCT
ejpam-4590	429	67	g	g	NOUN
ejpam-4590	429	68	)	)	PUNCT
ejpam-4590	429	69	\a⟩.	\a⟩.	PROPN
ejpam-4590	429	70	hence	hence	ADV
ejpam-4590	429	71	,	,	PUNCT
ejpam-4590	429	72	p	p	PROPN
ejpam-4590	429	73	is	be	AUX
ejpam-4590	429	74	a	a	DET
ejpam-4590	429	75	path	path	NOUN
ejpam-4590	429	76	in	in	ADP
ejpam-4590	429	77	⟨v	⟨v	PROPN
ejpam-4590	429	78	(	(	PUNCT
ejpam-4590	429	79	g	g	PROPN
ejpam-4590	429	80	◦	◦	NOUN
ejpam-4590	429	81	h	h	NOUN
ejpam-4590	429	82	)	)	PUNCT
ejpam-4590	429	83	\	\	PROPN
ejpam-4590	429	84	c⟩.	c⟩.	PROPN
ejpam-4590	429	85	suppose	suppose	VERB
ejpam-4590	429	86	a	a	DET
ejpam-4590	429	87	∈	∈	PROPN
ejpam-4590	429	88	v	v	ADP
ejpam-4590	429	89	(	(	PUNCT
ejpam-4590	429	90	hv	hv	PROPN
ejpam-4590	429	91	)	)	PUNCT
ejpam-4590	429	92	\	\	PROPN
ejpam-4590	429	93	sv	sv	PROPN
ejpam-4590	429	94	and	and	CCONJ
ejpam-4590	429	95	b	b	PROPN
ejpam-4590	429	96	∈	∈	PROPN
ejpam-4590	429	97	v	v	ADP
ejpam-4590	429	98	(	(	PUNCT
ejpam-4590	429	99	hw	hw	NOUN
ejpam-4590	429	100	)	)	PUNCT
ejpam-4590	429	101	\	\	PROPN
ejpam-4590	429	102	sw	sw	PROPN
ejpam-4590	429	103	.	.	PUNCT
ejpam-4590	430	1	by	by	ADP
ejpam-4590	430	2	(	(	PUNCT
ejpam-4590	430	3	ii	ii	NOUN
ejpam-4590	430	4	)	)	PUNCT
ejpam-4590	430	5	,	,	PUNCT
ejpam-4590	430	6	v	v	NOUN
ejpam-4590	430	7	,	,	PUNCT
ejpam-4590	430	8	w	w	PROPN
ejpam-4590	430	9	/∈	/∈	NOUN
ejpam-4590	430	10	a.	a.	NOUN
ejpam-4590	430	11	by	by	ADP
ejpam-4590	430	12	(	(	PUNCT
ejpam-4590	430	13	i	i	NOUN
ejpam-4590	430	14	)	)	PUNCT
ejpam-4590	430	15	,	,	PUNCT
ejpam-4590	430	16	there	there	PRON
ejpam-4590	430	17	exists	exist	VERB
ejpam-4590	430	18	a	a	DET
ejpam-4590	430	19	v	v	NOUN
ejpam-4590	430	20	-	-	PUNCT
ejpam-4590	430	21	w	w	NOUN
ejpam-4590	430	22	path	path	NOUN
ejpam-4590	430	23	p	p	NOUN
ejpam-4590	430	24	=	=	PUNCT
ejpam-4590	431	1	[	[	X
ejpam-4590	431	2	v1	v1	NOUN
ejpam-4590	431	3	,	,	PUNCT
ejpam-4590	431	4	v2	v2	PROPN
ejpam-4590	431	5	,	,	PUNCT
ejpam-4590	431	6	...	...	PUNCT
ejpam-4590	431	7	,	,	PUNCT
ejpam-4590	431	8	vk	vk	ADP
ejpam-4590	431	9	]	]	PUNCT
ejpam-4590	431	10	where	where	SCONJ
ejpam-4590	431	11	v1	v1	NOUN
ejpam-4590	431	12	=	=	SYM
ejpam-4590	431	13	v	v	NOUN
ejpam-4590	431	14	,	,	PUNCT
ejpam-4590	431	15	vk	vk	ADP
ejpam-4590	431	16	=	=	SYM
ejpam-4590	431	17	w	w	NOUN
ejpam-4590	431	18	in	in	ADP
ejpam-4590	431	19	⟨v	⟨v	PROPN
ejpam-4590	431	20	(	(	PUNCT
ejpam-4590	431	21	g	g	NOUN
ejpam-4590	431	22	)	)	PUNCT
ejpam-4590	431	23	\a⟩.	\a⟩.	PROPN
ejpam-4590	431	24	hence	hence	ADV
ejpam-4590	431	25	,	,	PUNCT
ejpam-4590	431	26	p	p	NOUN
ejpam-4590	431	27	′	′	NOUN
ejpam-4590	432	1	=	=	PUNCT
ejpam-4590	433	1	[	[	X
ejpam-4590	433	2	a	a	DET
ejpam-4590	433	3	,	,	PUNCT
ejpam-4590	433	4	v1	v1	NOUN
ejpam-4590	433	5	,	,	PUNCT
ejpam-4590	433	6	v2	v2	PROPN
ejpam-4590	433	7	,	,	PUNCT
ejpam-4590	433	8	...	...	PUNCT
ejpam-4590	433	9	,	,	PUNCT
ejpam-4590	433	10	vk	vk	X
ejpam-4590	433	11	,	,	PUNCT
ejpam-4590	433	12	b	b	AUX
ejpam-4590	433	13	]	]	X
ejpam-4590	433	14	is	be	AUX
ejpam-4590	433	15	an	an	DET
ejpam-4590	433	16	a	a	PRON
ejpam-4590	433	17	-	-	PUNCT
ejpam-4590	433	18	b	b	NOUN
ejpam-4590	433	19	path	path	NOUN
ejpam-4590	433	20	in	in	ADP
ejpam-4590	433	21	⟨v	⟨v	PROPN
ejpam-4590	433	22	(	(	PUNCT
ejpam-4590	433	23	g	g	PROPN
ejpam-4590	433	24	◦	◦	NOUN
ejpam-4590	433	25	h	h	NOUN
ejpam-4590	433	26	)	)	PUNCT
ejpam-4590	433	27	\	\	PROPN
ejpam-4590	433	28	c⟩.	c⟩.	PROPN
ejpam-4590	433	29	suppose	suppose	VERB
ejpam-4590	433	30	a	a	DET
ejpam-4590	433	31	=	=	X
ejpam-4590	433	32	v	v	NOUN
ejpam-4590	433	33	and	and	CCONJ
ejpam-4590	433	34	b	b	NOUN
ejpam-4590	433	35	∈	∈	PROPN
ejpam-4590	433	36	(	(	PUNCT
ejpam-4590	433	37	v	v	NOUN
ejpam-4590	433	38	(	(	PUNCT
ejpam-4590	433	39	hw	hw	NOUN
ejpam-4590	433	40	)	)	PUNCT
ejpam-4590	433	41	\	\	PROPN
ejpam-4590	433	42	sw	sw	PROPN
ejpam-4590	433	43	)	)	PUNCT
ejpam-4590	433	44	.	.	PUNCT
ejpam-4590	434	1	since	since	SCONJ
ejpam-4590	434	2	v	v	NUM
ejpam-4590	434	3	/∈	/∈	PUNCT
ejpam-4590	434	4	a	a	PRON
ejpam-4590	434	5	,	,	PUNCT
ejpam-4590	434	6	a	a	DET
ejpam-4590	434	7	̸=	̸=	PROPN
ejpam-4590	434	8	v	v	NOUN
ejpam-4590	434	9	(	(	PUNCT
ejpam-4590	434	10	g	g	NOUN
ejpam-4590	434	11	)	)	PUNCT
ejpam-4590	434	12	.	.	PUNCT
ejpam-4590	435	1	hence	hence	ADV
ejpam-4590	435	2	,	,	PUNCT
ejpam-4590	435	3	by	by	ADP
ejpam-4590	435	4	the	the	DET
ejpam-4590	435	5	second	second	ADJ
ejpam-4590	435	6	part	part	NOUN
ejpam-4590	435	7	of	of	ADP
ejpam-4590	435	8	(	(	PUNCT
ejpam-4590	435	9	ii	ii	NOUN
ejpam-4590	435	10	)	)	PUNCT
ejpam-4590	435	11	,	,	PUNCT
ejpam-4590	435	12	w	w	PROPN
ejpam-4590	435	13	/∈	/∈	NOUN
ejpam-4590	435	14	a.	a.	NOUN
ejpam-4590	436	1	it	it	PRON
ejpam-4590	436	2	follows	follow	VERB
ejpam-4590	436	3	from	from	ADP
ejpam-4590	436	4	(	(	PUNCT
ejpam-4590	436	5	i	i	NOUN
ejpam-4590	436	6	)	)	PUNCT
ejpam-4590	436	7	that	that	SCONJ
ejpam-4590	436	8	there	there	PRON
ejpam-4590	436	9	exists	exist	VERB
ejpam-4590	436	10	a	a	DET
ejpam-4590	436	11	v	v	NOUN
ejpam-4590	436	12	-	-	PUNCT
ejpam-4590	436	13	w	w	NOUN
ejpam-4590	436	14	path	path	NOUN
ejpam-4590	436	15	p	p	NOUN
ejpam-4590	436	16	=	=	PUNCT
ejpam-4590	437	1	[	[	X
ejpam-4590	437	2	v1	v1	NOUN
ejpam-4590	437	3	,	,	PUNCT
ejpam-4590	437	4	v2	v2	PROPN
ejpam-4590	437	5	,	,	PUNCT
ejpam-4590	437	6	...	...	PUNCT
ejpam-4590	437	7	,	,	PUNCT
ejpam-4590	437	8	vk	vk	ADP
ejpam-4590	437	9	]	]	PUNCT
ejpam-4590	437	10	where	where	SCONJ
ejpam-4590	437	11	v1	v1	NOUN
ejpam-4590	437	12	=	=	SYM
ejpam-4590	437	13	a	a	NOUN
ejpam-4590	437	14	,	,	PUNCT
ejpam-4590	437	15	vk	vk	X
ejpam-4590	437	16	=	=	SYM
ejpam-4590	437	17	w	w	NOUN
ejpam-4590	437	18	in	in	ADP
ejpam-4590	437	19	⟨v	⟨v	PROPN
ejpam-4590	437	20	(	(	PUNCT
ejpam-4590	437	21	g	g	NOUN
ejpam-4590	437	22	)	)	PUNCT
ejpam-4590	437	23	\a⟩.	\a⟩.	PROPN
ejpam-4590	437	24	consequently	consequently	ADV
ejpam-4590	437	25	,	,	PUNCT
ejpam-4590	437	26	p	p	NOUN
ejpam-4590	437	27	∗	∗	NOUN
ejpam-4590	437	28	=	=	PUNCT
ejpam-4590	438	1	[	[	X
ejpam-4590	438	2	v1	v1	NOUN
ejpam-4590	438	3	,	,	PUNCT
ejpam-4590	438	4	v2	v2	PROPN
ejpam-4590	438	5	,	,	PUNCT
ejpam-4590	438	6	...	...	PUNCT
ejpam-4590	438	7	,	,	PUNCT
ejpam-4590	438	8	vk	vk	X
ejpam-4590	438	9	,	,	PUNCT
ejpam-4590	438	10	b	b	AUX
ejpam-4590	438	11	]	]	X
ejpam-4590	438	12	is	be	AUX
ejpam-4590	438	13	an	an	DET
ejpam-4590	438	14	a	a	PRON
ejpam-4590	438	15	-	-	PUNCT
ejpam-4590	438	16	b	b	NOUN
ejpam-4590	438	17	path	path	NOUN
ejpam-4590	438	18	in	in	ADP
ejpam-4590	438	19	⟨v	⟨v	PROPN
ejpam-4590	438	20	(	(	PUNCT
ejpam-4590	438	21	g	g	PROPN
ejpam-4590	438	22	◦	◦	NOUN
ejpam-4590	438	23	h	h	NOUN
ejpam-4590	438	24	)	)	PUNCT
ejpam-4590	438	25	\	\	PROPN
ejpam-4590	438	26	c⟩.	c⟩.	PROPN
ejpam-4590	438	27	therefore	therefore	ADV
ejpam-4590	438	28	,	,	PUNCT
ejpam-4590	438	29	⟨v	⟨v	X
ejpam-4590	438	30	(	(	PUNCT
ejpam-4590	438	31	g	g	NOUN
ejpam-4590	438	32	)	)	PUNCT
ejpam-4590	438	33	\	\	NOUN
ejpam-4590	439	1	c⟩	c⟩	PUNCT
ejpam-4590	439	2	is	be	AUX
ejpam-4590	439	3	connected	connect	VERB
ejpam-4590	439	4	.	.	PUNCT
ejpam-4590	440	1	accordingly	accordingly	ADV
ejpam-4590	440	2	,	,	PUNCT
ejpam-4590	440	3	c	c	PROPN
ejpam-4590	440	4	is	be	AUX
ejpam-4590	440	5	an	an	DET
ejpam-4590	440	6	outer	outer	ADV
ejpam-4590	440	7	-	-	PUNCT
ejpam-4590	440	8	connected	connect	VERB
ejpam-4590	440	9	hop	hop	NOUN
ejpam-4590	440	10	dominating	dominating	NOUN
ejpam-4590	440	11	set	set	NOUN
ejpam-4590	440	12	of	of	ADP
ejpam-4590	440	13	g	g	PROPN
ejpam-4590	440	14	◦	◦	NOUN
ejpam-4590	440	15	h.	h.	NOUN
ejpam-4590	440	16	corollary	corollary	ADJ
ejpam-4590	440	17	7	7	PROPN
ejpam-4590	440	18	.	.	PUNCT
ejpam-4590	441	1	let	let	VERB
ejpam-4590	441	2	g	g	PRON
ejpam-4590	441	3	be	be	AUX
ejpam-4590	441	4	a	a	DET
ejpam-4590	441	5	connected	connected	ADJ
ejpam-4590	441	6	graph	graph	NOUN
ejpam-4590	441	7	and	and	CCONJ
ejpam-4590	441	8	let	let	VERB
ejpam-4590	441	9	h	h	NOUN
ejpam-4590	441	10	be	be	AUX
ejpam-4590	441	11	any	any	DET
ejpam-4590	441	12	graph	graph	NOUN
ejpam-4590	441	13	of	of	ADP
ejpam-4590	441	14	orders	order	NOUN
ejpam-4590	441	15	m	m	PROPN
ejpam-4590	441	16	and	and	CCONJ
ejpam-4590	441	17	n	n	CCONJ
ejpam-4590	441	18	,	,	PUNCT
ejpam-4590	441	19	respectively	respectively	ADV
ejpam-4590	441	20	.	.	PUNCT
ejpam-4590	442	1	then	then	ADV
ejpam-4590	442	2	γ̃ch(g	γ̃ch(g	VERB
ejpam-4590	442	3	◦	◦	NOUN
ejpam-4590	442	4	h	h	NOUN
ejpam-4590	442	5	)	)	PUNCT
ejpam-4590	442	6	≤	≤	NUM
ejpam-4590	442	7	min	min	NOUN
ejpam-4590	442	8	{	{	PUNCT
ejpam-4590	442	9	(	(	PUNCT
ejpam-4590	442	10	n+	n+	NUM
ejpam-4590	442	11	1)γ̃c(g),m(pnd(h	1)γ̃c(g),m(pnd(h	NUM
ejpam-4590	442	12	)	)	PUNCT
ejpam-4590	442	13	)	)	PUNCT
ejpam-4590	442	14	}	}	PUNCT
ejpam-4590	442	15	.	.	PUNCT
ejpam-4590	443	1	proof	proof	NOUN
ejpam-4590	443	2	.	.	PUNCT
ejpam-4590	444	1	let	let	VERB
ejpam-4590	444	2	a	a	PRON
ejpam-4590	444	3	be	be	AUX
ejpam-4590	444	4	a	a	DET
ejpam-4590	444	5	γ̃c	γ̃c	ADV
ejpam-4590	444	6	-	-	PUNCT
ejpam-4590	444	7	set	set	VERB
ejpam-4590	444	8	in	in	ADP
ejpam-4590	444	9	g.	g.	PROPN
ejpam-4590	444	10	by	by	ADP
ejpam-4590	444	11	theorem	theorem	NOUN
ejpam-4590	444	12	9	9	NUM
ejpam-4590	444	13	,	,	PUNCT
ejpam-4590	444	14	c	c	NOUN
ejpam-4590	444	15	=	=	PUNCT
ejpam-4590	444	16	a	a	DET
ejpam-4590	444	17	∪	∪	ADJ
ejpam-4590	444	18	(	(	PUNCT
ejpam-4590	444	19	⋃	⋃	PROPN
ejpam-4590	444	20	v∈a	v∈a	NOUN
ejpam-4590	444	21	v	v	NOUN
ejpam-4590	444	22	(	(	PUNCT
ejpam-4590	444	23	hv	hv	PROPN
ejpam-4590	444	24	)	)	PUNCT
ejpam-4590	444	25	)	)	PUNCT
ejpam-4590	444	26	is	be	AUX
ejpam-4590	444	27	an	an	DET
ejpam-4590	444	28	outer	outer	ADV
ejpam-4590	444	29	-	-	PUNCT
ejpam-4590	444	30	connected	connect	VERB
ejpam-4590	444	31	hop	hop	NOUN
ejpam-4590	444	32	dominating	dominating	NOUN
ejpam-4590	444	33	set	set	VERB
ejpam-4590	444	34	in	in	ADP
ejpam-4590	444	35	g	g	PROPN
ejpam-4590	444	36	◦	◦	NOUN
ejpam-4590	444	37	h.	h.	PROPN
ejpam-4590	444	38	thus	thus	ADV
ejpam-4590	444	39	,	,	PUNCT
ejpam-4590	444	40	γ̃ch	γ̃ch	PROPN
ejpam-4590	444	41	(	(	PUNCT
ejpam-4590	444	42	g	g	PROPN
ejpam-4590	444	43	◦	◦	NOUN
ejpam-4590	444	44	h	h	NOUN
ejpam-4590	444	45	)	)	PUNCT
ejpam-4590	444	46	≤	≤	NOUN
ejpam-4590	444	47	|c|	|c|	PROPN
ejpam-4590	444	48	=	=	PRON
ejpam-4590	445	1	|a|+	|a|+	VERB
ejpam-4590	445	2	∑	∑	PUNCT
ejpam-4590	445	3	v∈a	v∈a	NOUN
ejpam-4590	445	4	|v	|v	PROPN
ejpam-4590	445	5	(	(	PUNCT
ejpam-4590	445	6	hv)|	hv)|	PROPN
ejpam-4590	445	7	=	=	SYM
ejpam-4590	445	8	(	(	PUNCT
ejpam-4590	445	9	n+	n+	NUM
ejpam-4590	445	10	1)γ̃c(g	1)γ̃c(g	NUM
ejpam-4590	445	11	)	)	PUNCT
ejpam-4590	445	12	.	.	PUNCT
ejpam-4590	446	1	next	next	ADJ
ejpam-4590	446	2	.	.	PUNCT
ejpam-4590	447	1	let	let	VERB
ejpam-4590	447	2	a	a	DET
ejpam-4590	447	3	=	=	NOUN
ejpam-4590	447	4	∅	∅	NOUN
ejpam-4590	447	5	and	and	CCONJ
ejpam-4590	447	6	sv	sv	AUX
ejpam-4590	447	7	be	be	AUX
ejpam-4590	447	8	a	a	DET
ejpam-4590	447	9	pnd	pnd	NOUN
ejpam-4590	447	10	-	-	PUNCT
ejpam-4590	447	11	set	set	NOUN
ejpam-4590	447	12	of	of	ADP
ejpam-4590	447	13	h	h	NOUN
ejpam-4590	447	14	for	for	ADP
ejpam-4590	447	15	each	each	DET
ejpam-4590	447	16	v	v	NUM
ejpam-4590	447	17	∈	∈	PROPN
ejpam-4590	447	18	v	v	NOUN
ejpam-4590	447	19	(	(	PUNCT
ejpam-4590	447	20	g	g	NOUN
ejpam-4590	447	21	)	)	PUNCT
ejpam-4590	447	22	.	.	PUNCT
ejpam-4590	448	1	by	by	ADP
ejpam-4590	448	2	theorem	theorem	NOUN
ejpam-4590	448	3	9	9	NUM
ejpam-4590	448	4	,	,	PUNCT
ejpam-4590	448	5	c∗	c∗	NOUN
ejpam-4590	448	6	=	=	SYM
ejpam-4590	448	7	⋃	⋃	NOUN
ejpam-4590	448	8	v∈v	v∈v	NOUN
ejpam-4590	448	9	(	(	PUNCT
ejpam-4590	448	10	g	g	NOUN
ejpam-4590	448	11	)	)	PUNCT
ejpam-4590	448	12	sv	sv	PROPN
ejpam-4590	449	1	c.j	c.j	PROPN
ejpam-4590	449	2	.	.	PROPN
ejpam-4590	449	3	saromines	saromines	PROPN
ejpam-4590	449	4	,	,	PUNCT
ejpam-4590	449	5	s.	s.	PROPN
ejpam-4590	449	6	canoy	canoy	PROPN
ejpam-4590	449	7	,	,	PUNCT
ejpam-4590	449	8	jr	jr	PROPN
ejpam-4590	449	9	.	.	PROPN
ejpam-4590	449	10	/	/	SYM
ejpam-4590	449	11	eur	eur	PROPN
ejpam-4590	449	12	.	.	PUNCT
ejpam-4590	450	1	j.	j.	PROPN
ejpam-4590	450	2	pure	pure	PROPN
ejpam-4590	450	3	appl	appl	PROPN
ejpam-4590	450	4	.	.	PROPN
ejpam-4590	450	5	math	math	PROPN
ejpam-4590	450	6	,	,	PUNCT
ejpam-4590	450	7	15	15	NUM
ejpam-4590	450	8	(	(	PUNCT
ejpam-4590	450	9	4	4	NUM
ejpam-4590	450	10	)	)	PUNCT
ejpam-4590	450	11	(	(	PUNCT
ejpam-4590	450	12	2022	2022	NUM
ejpam-4590	450	13	)	)	PUNCT
ejpam-4590	450	14	,	,	PUNCT
ejpam-4590	450	15	1966	1966	NUM
ejpam-4590	450	16	-	-	SYM
ejpam-4590	450	17	1981	1981	NUM
ejpam-4590	450	18	1977	1977	NUM
ejpam-4590	450	19	is	be	AUX
ejpam-4590	450	20	an	an	DET
ejpam-4590	450	21	outer	outer	ADV
ejpam-4590	450	22	-	-	PUNCT
ejpam-4590	450	23	connected	connect	VERB
ejpam-4590	450	24	hop	hop	NOUN
ejpam-4590	450	25	dominating	dominating	NOUN
ejpam-4590	450	26	set	set	VERB
ejpam-4590	450	27	in	in	ADP
ejpam-4590	450	28	g	g	PROPN
ejpam-4590	450	29	◦	◦	NOUN
ejpam-4590	450	30	h.	h.	NOUN
ejpam-4590	450	31	hence	hence	ADV
ejpam-4590	450	32	,	,	PUNCT
ejpam-4590	450	33	γ̃ch	γ̃ch	PROPN
ejpam-4590	450	34	(	(	PUNCT
ejpam-4590	450	35	g	g	PROPN
ejpam-4590	450	36	◦	◦	NOUN
ejpam-4590	450	37	h	h	NOUN
ejpam-4590	450	38	)	)	PUNCT
ejpam-4590	450	39	≤	≤	NOUN
ejpam-4590	450	40	|c∗|	|c∗|	VERB
ejpam-4590	450	41	=	=	X
ejpam-4590	450	42	∑	∑	PUNCT
ejpam-4590	450	43	v∈v	v∈v	PROPN
ejpam-4590	450	44	(	(	PUNCT
ejpam-4590	450	45	g	g	NOUN
ejpam-4590	450	46	)	)	PUNCT
ejpam-4590	450	47	|sv|	|sv|	PROPN
ejpam-4590	450	48	=	=	SYM
ejpam-4590	450	49	m(pnd(h	m(pnd(h	NOUN
ejpam-4590	450	50	)	)	PUNCT
ejpam-4590	450	51	)	)	PUNCT
ejpam-4590	450	52	.	.	PUNCT
ejpam-4590	451	1	therefore	therefore	ADV
ejpam-4590	451	2	,	,	PUNCT
ejpam-4590	451	3	γ̃ch(g	γ̃ch(g	VERB
ejpam-4590	451	4	◦	◦	NOUN
ejpam-4590	451	5	h	h	NOUN
ejpam-4590	451	6	)	)	PUNCT
ejpam-4590	451	7	≤	≤	NUM
ejpam-4590	451	8	min	min	NOUN
ejpam-4590	451	9	{	{	PUNCT
ejpam-4590	451	10	(	(	PUNCT
ejpam-4590	451	11	n+	n+	NUM
ejpam-4590	451	12	1)γ̃c(g),m(pnd(h	1)γ̃c(g),m(pnd(h	NUM
ejpam-4590	451	13	)	)	PUNCT
ejpam-4590	451	14	)	)	PUNCT
ejpam-4590	451	15	}	}	PUNCT
ejpam-4590	451	16	.	.	PUNCT
ejpam-4590	452	1	example	example	NOUN
ejpam-4590	453	1	1	1	NUM
ejpam-4590	453	2	.	.	X
ejpam-4590	453	3	consider	consider	VERB
ejpam-4590	453	4	the	the	DET
ejpam-4590	453	5	corona	corona	NOUN
ejpam-4590	453	6	c4	c4	NOUN
ejpam-4590	453	7	◦	◦	PROPN
ejpam-4590	453	8	p3	p3	PROPN
ejpam-4590	453	9	in	in	ADP
ejpam-4590	453	10	figure	figure	NOUN
ejpam-4590	453	11	1	1	NUM
ejpam-4590	453	12	.	.	PUNCT
ejpam-4590	454	1	it	it	PRON
ejpam-4590	454	2	can	can	AUX
ejpam-4590	454	3	be	be	AUX
ejpam-4590	454	4	verified	verify	VERB
ejpam-4590	454	5	that	that	SCONJ
ejpam-4590	454	6	γ̃ch	γ̃ch	NOUN
ejpam-4590	454	7	(	(	PUNCT
ejpam-4590	454	8	c4	c4	NOUN
ejpam-4590	454	9	◦	◦	PROPN
ejpam-4590	454	10	p3	p3	PROPN
ejpam-4590	454	11	)	)	PUNCT
ejpam-4590	454	12	=	=	PUNCT
ejpam-4590	454	13	6	6	NUM
ejpam-4590	454	14	<	<	SYM
ejpam-4590	454	15	8	8	NUM
ejpam-4590	454	16	=	=	SYM
ejpam-4590	454	17	|v	|v	X
ejpam-4590	454	18	(	(	PUNCT
ejpam-4590	454	19	c4)|	c4)|	PROPN
ejpam-4590	454	20	pnd(p3	pnd(p3	PROPN
ejpam-4590	454	21	)	)	PUNCT
ejpam-4590	454	22	and	and	CCONJ
ejpam-4590	454	23	γ̃ch	γ̃ch	PROPN
ejpam-4590	454	24	(	(	PUNCT
ejpam-4590	454	25	c4	c4	NOUN
ejpam-4590	454	26	◦	◦	PROPN
ejpam-4590	454	27	p3	p3	PROPN
ejpam-4590	454	28	)	)	PUNCT
ejpam-4590	454	29	=	=	PUNCT
ejpam-4590	454	30	6	6	NUM
ejpam-4590	454	31	<	<	SYM
ejpam-4590	454	32	8	8	NUM
ejpam-4590	454	33	=	=	SYM
ejpam-4590	454	34	γ̃c(c4	γ̃c(c4	NOUN
ejpam-4590	454	35	)	)	PUNCT
ejpam-4590	454	36	(	(	PUNCT
ejpam-4590	454	37	|v	|v	X
ejpam-4590	454	38	(	(	PUNCT
ejpam-4590	454	39	p3)|+	p3)|+	NOUN
ejpam-4590	454	40	1	1	NUM
ejpam-4590	454	41	)	)	PUNCT
ejpam-4590	454	42	.	.	PUNCT
ejpam-4590	455	1	....................................	....................................	PUNCT
ejpam-4590	455	2	....................................	....................................	PUNCT
ejpam-4590	456	1	....................................	....................................	PUNCT
ejpam-4590	456	2	....................................	....................................	PUNCT
ejpam-4590	457	1	.........	.........	PUNCT
ejpam-4590	457	2	........	........	PUNCT
ejpam-4590	457	3	........	........	PUNCT
ejpam-4590	457	4	........	........	PUNCT
ejpam-4590	457	5	........	........	PUNCT
ejpam-4590	457	6	........	........	PUNCT
ejpam-4590	457	7	........	........	PUNCT
ejpam-4590	457	8	........	........	PUNCT
ejpam-4590	457	9	........	........	PUNCT
ejpam-4590	457	10	........	........	PUNCT
ejpam-4590	458	1	........	........	PUNCT
ejpam-4590	458	2	....	....	PUNCT
ejpam-4590	459	1	.................................................................................................................	.................................................................................................................	PUNCT
ejpam-4590	459	2	....	....	PUNCT
ejpam-4590	460	1	........	........	PUNCT
ejpam-4590	460	2	........	........	PUNCT
ejpam-4590	460	3	........	........	PUNCT
ejpam-4590	460	4	........	........	PUNCT
ejpam-4590	460	5	........	........	PUNCT
ejpam-4590	460	6	........	........	PUNCT
ejpam-4590	460	7	........	........	PUNCT
ejpam-4590	460	8	........	........	PUNCT
ejpam-4590	460	9	........	........	PUNCT
ejpam-4590	460	10	........	........	PUNCT
ejpam-4590	460	11	........	........	PUNCT
ejpam-4590	460	12	..................................................................................................................	..................................................................................................................	X
ejpam-4590	460	13	............	............	PUNCT
ejpam-4590	460	14	...........	...........	PUNCT
ejpam-4590	460	15	.......	.......	PUNCT
ejpam-4590	460	16	....................................	....................................	PUNCT
ejpam-4590	460	17	............	............	PUNCT
ejpam-4590	461	1	...........	...........	PUNCT
ejpam-4590	461	2	.......	.......	PUNCT
ejpam-4590	461	3	....................................	....................................	PUNCT
ejpam-4590	461	4	....................................	....................................	PUNCT
ejpam-4590	462	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4590	462	2	..............................................................................................	..............................................................................................	PUNCT
ejpam-4590	462	3	..........................................................................................	..........................................................................................	PUNCT
ejpam-4590	462	4	..............................	..............................	PUNCT
ejpam-4590	463	1	....................................	....................................	PUNCT
ejpam-4590	463	2	..............................	..............................	PUNCT
ejpam-4590	464	1	....................................	....................................	PUNCT
ejpam-4590	464	2	....................................	....................................	PUNCT
ejpam-4590	465	1	.................................................	.................................................	PUNCT
ejpam-4590	465	2	................................................	................................................	PUNCT
ejpam-4590	465	3	...............	...............	PUNCT
ejpam-4590	465	4	..................	..................	PUNCT
ejpam-4590	466	1	.................	.................	PUNCT
ejpam-4590	466	2	.................	.................	PUNCT
ejpam-4590	467	1	.................	.................	PUNCT
ejpam-4590	467	2	.................	.................	PUNCT
ejpam-4590	467	3	........	........	PUNCT
ejpam-4590	467	4	...........	...........	PUNCT
ejpam-4590	468	1	..........	..........	PUNCT
ejpam-4590	468	2	..........	..........	PUNCT
ejpam-4590	469	1	..........	..........	PUNCT
ejpam-4590	469	2	..........	..........	PUNCT
ejpam-4590	470	1	..........	..........	PUNCT
ejpam-4590	470	2	..........	..........	PUNCT
ejpam-4590	471	1	..........	..........	PUNCT
ejpam-4590	471	2	.........	.........	PUNCT
ejpam-4590	471	3	..............................	..............................	PUNCT
ejpam-4590	471	4	....................................	....................................	PUNCT
ejpam-4590	471	5	..............................	..............................	PUNCT
ejpam-4590	472	1	....................................	....................................	PUNCT
ejpam-4590	472	2	....................................	....................................	PUNCT
ejpam-4590	472	3	..............................................	..............................................	PUNCT
ejpam-4590	472	4	.............................................	.............................................	PUNCT
ejpam-4590	472	5	...............	...............	PUNCT
ejpam-4590	473	1	.................	.................	PUNCT
ejpam-4590	473	2	................	................	PUNCT
ejpam-4590	474	1	................	................	PUNCT
ejpam-4590	474	2	................	................	PUNCT
ejpam-4590	474	3	................	................	PUNCT
ejpam-4590	474	4	........	........	PUNCT
ejpam-4590	474	5	...........	...........	PUNCT
ejpam-4590	474	6	..........	..........	PUNCT
ejpam-4590	475	1	..........	..........	PUNCT
ejpam-4590	475	2	..........	..........	PUNCT
ejpam-4590	476	1	..........	..........	PUNCT
ejpam-4590	476	2	..........	..........	PUNCT
ejpam-4590	477	1	..........	..........	PUNCT
ejpam-4590	477	2	..........	..........	PUNCT
ejpam-4590	478	1	.....	.....	PUNCT
ejpam-4590	478	2	............	............	PUNCT
ejpam-4590	478	3	...........	...........	PUNCT
ejpam-4590	478	4	.......	.......	PUNCT
ejpam-4590	478	5	....................................	....................................	PUNCT
ejpam-4590	478	6	............	............	PUNCT
ejpam-4590	478	7	...........	...........	PUNCT
ejpam-4590	478	8	.......	.......	PUNCT
ejpam-4590	478	9	....................................	....................................	PUNCT
ejpam-4590	478	10	....................................	....................................	PUNCT
ejpam-4590	479	1	..........................................................................................................	..........................................................................................................	PUNCT
ejpam-4590	479	2	.........................................................................................	.........................................................................................	PUNCT
ejpam-4590	480	1	......................................................................................	......................................................................................	PUNCT
ejpam-4590	481	1	•	•	NUM
ejpam-4590	481	2	•	•	NUM
ejpam-4590	481	3	•	•	NUM
ejpam-4590	481	4	•	•	NUM
ejpam-4590	481	5	•	•	NOUN
ejpam-4590	481	6	•	•	NUM
ejpam-4590	481	7	figure	figure	NOUN
ejpam-4590	481	8	1	1	NUM
ejpam-4590	481	9	:	:	PUNCT
ejpam-4590	481	10	the	the	DET
ejpam-4590	481	11	corona	corona	PROPN
ejpam-4590	481	12	c4	c4	NOUN
ejpam-4590	481	13	◦	◦	PROPN
ejpam-4590	481	14	p3	p3	PROPN
ejpam-4590	481	15	example	example	NOUN
ejpam-4590	481	16	2	2	X
ejpam-4590	481	17	.	.	X
ejpam-4590	481	18	consider	consider	VERB
ejpam-4590	481	19	the	the	DET
ejpam-4590	481	20	corona	corona	NOUN
ejpam-4590	481	21	of	of	ADP
ejpam-4590	481	22	k2	k2	PROPN
ejpam-4590	481	23	◦	◦	PROPN
ejpam-4590	481	24	p3	p3	PROPN
ejpam-4590	481	25	.	.	PUNCT
ejpam-4590	482	1	then	then	ADV
ejpam-4590	482	2	γ̃ch(k2	γ̃ch(k2	PROPN
ejpam-4590	482	3	◦	◦	PROPN
ejpam-4590	482	4	p3	p3	PROPN
ejpam-4590	482	5	)	)	PUNCT
ejpam-4590	482	6	=	=	SYM
ejpam-4590	482	7	4	4	NUM
ejpam-4590	482	8	=	=	SYM
ejpam-4590	482	9	γ̃c(k2)(|v	γ̃c(k2)(|v	PROPN
ejpam-4590	482	10	(	(	PUNCT
ejpam-4590	482	11	p3)|+	p3)|+	NOUN
ejpam-4590	482	12	1	1	NUM
ejpam-4590	482	13	)	)	PUNCT
ejpam-4590	482	14	=	=	SYM
ejpam-4590	482	15	|v	|v	X
ejpam-4590	482	16	(	(	PUNCT
ejpam-4590	482	17	k2)|	k2)|	PROPN
ejpam-4590	482	18	(	(	PUNCT
ejpam-4590	482	19	pnd(p3	pnd(p3	PROPN
ejpam-4590	482	20	)	)	PUNCT
ejpam-4590	482	21	)	)	PUNCT
ejpam-4590	483	1	c.j	c.j	PROPN
ejpam-4590	483	2	.	.	PROPN
ejpam-4590	483	3	saromines	saromines	PROPN
ejpam-4590	483	4	,	,	PUNCT
ejpam-4590	483	5	s.	s.	PROPN
ejpam-4590	483	6	canoy	canoy	PROPN
ejpam-4590	483	7	,	,	PUNCT
ejpam-4590	483	8	jr	jr	PROPN
ejpam-4590	483	9	.	.	PROPN
ejpam-4590	483	10	/	/	SYM
ejpam-4590	483	11	eur	eur	PROPN
ejpam-4590	483	12	.	.	PUNCT
ejpam-4590	484	1	j.	j.	PROPN
ejpam-4590	484	2	pure	pure	PROPN
ejpam-4590	484	3	appl	appl	PROPN
ejpam-4590	484	4	.	.	PROPN
ejpam-4590	484	5	math	math	PROPN
ejpam-4590	484	6	,	,	PUNCT
ejpam-4590	484	7	15	15	NUM
ejpam-4590	484	8	(	(	PUNCT
ejpam-4590	484	9	4	4	NUM
ejpam-4590	484	10	)	)	PUNCT
ejpam-4590	484	11	(	(	PUNCT
ejpam-4590	484	12	2022	2022	NUM
ejpam-4590	484	13	)	)	PUNCT
ejpam-4590	484	14	,	,	PUNCT
ejpam-4590	484	15	1966	1966	NUM
ejpam-4590	484	16	-	-	SYM
ejpam-4590	484	17	1981	1981	NUM
ejpam-4590	484	18	1978	1978	NUM
ejpam-4590	484	19	....................................	....................................	PUNCT
ejpam-4590	484	20	....................................	....................................	PUNCT
ejpam-4590	485	1	....................................	....................................	PUNCT
ejpam-4590	485	2	.........................................................................................................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4590	486	1	.....................................................................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4590	486	2	....................................	....................................	PUNCT
ejpam-4590	487	1	....................................	....................................	PUNCT
ejpam-4590	487	2	....................................	....................................	PUNCT
ejpam-4590	488	1	...............................................................................................................................................................................................	...............................................................................................................................................................................................	PUNCT
ejpam-4590	488	2	...................................................................................	...................................................................................	PUNCT
ejpam-4590	488	3	....................................	....................................	PUNCT
ejpam-4590	488	4	...............................................	...............................................	PUNCT
ejpam-4590	488	5	...................................................................................	...................................................................................	PUNCT
ejpam-4590	489	1	...............................................................................................................................................	...............................................................................................................................................	PUNCT
ejpam-4590	489	2	............	............	PUNCT
ejpam-4590	489	3	...........	...........	PUNCT
ejpam-4590	489	4	...........	...........	PUNCT
ejpam-4590	489	5	...........	...........	PUNCT
ejpam-4590	489	6	...........	...........	PUNCT
ejpam-4590	489	7	...........	...........	PUNCT
ejpam-4590	489	8	....	....	PUNCT
ejpam-4590	489	9	............	............	PUNCT
ejpam-4590	489	10	...........	...........	PUNCT
ejpam-4590	489	11	...........	...........	PUNCT
ejpam-4590	489	12	...........	...........	PUNCT
ejpam-4590	489	13	...........	...........	PUNCT
ejpam-4590	489	14	...........	...........	PUNCT
ejpam-4590	489	15	...........................................................................	...........................................................................	PUNCT
ejpam-4590	489	16	............................................................................................................	............................................................................................................	PUNCT
ejpam-4590	489	17	....................................	....................................	PUNCT
ejpam-4590	489	18	....................................	....................................	PUNCT
ejpam-4590	489	19	...................................................................................	...................................................................................	PUNCT
ejpam-4590	489	20	...................................................................................	...................................................................................	PUNCT
ejpam-4590	489	21	........................................................................	........................................................................	PUNCT
ejpam-4590	489	22	...................................................................................	...................................................................................	PUNCT
ejpam-4590	489	23	...................................................................................	...................................................................................	PUNCT
ejpam-4590	489	24	....................................	....................................	PUNCT
ejpam-4590	489	25	............	............	PUNCT
ejpam-4590	489	26	...........	...........	PUNCT
ejpam-4590	489	27	...........	...........	PUNCT
ejpam-4590	489	28	...........	...........	PUNCT
ejpam-4590	489	29	...........	...........	PUNCT
ejpam-4590	489	30	...........	...........	PUNCT
ejpam-4590	489	31	...........................................................................	...........................................................................	PUNCT
ejpam-4590	489	32	.......................................................................	.......................................................................	PUNCT
ejpam-4590	489	33	............	............	PUNCT
ejpam-4590	489	34	...........	...........	PUNCT
ejpam-4590	489	35	...........	...........	PUNCT
ejpam-4590	489	36	...........	...........	PUNCT
ejpam-4590	489	37	...........	...........	PUNCT
ejpam-4590	489	38	...........	...........	PUNCT
ejpam-4590	490	1	....	....	PUNCT
ejpam-4590	490	2	•	•	NUM
ejpam-4590	490	3	••	••	NOUN
ejpam-4590	490	4	•	•	NUM
ejpam-4590	490	5	•	•	NOUN
ejpam-4590	490	6	•••	•••	ADV
ejpam-4590	490	7	figure	figure	NOUN
ejpam-4590	490	8	2	2	NUM
ejpam-4590	490	9	:	:	PUNCT
ejpam-4590	490	10	the	the	DET
ejpam-4590	490	11	corona	corona	PROPN
ejpam-4590	490	12	k2	k2	PROPN
ejpam-4590	490	13	◦	◦	PROPN
ejpam-4590	490	14	p3	p3	PROPN
ejpam-4590	490	15	note	note	VERB
ejpam-4590	490	16	that	that	DET
ejpam-4590	490	17	example	example	NOUN
ejpam-4590	490	18	2	2	NUM
ejpam-4590	490	19	shows	show	VERB
ejpam-4590	490	20	that	that	SCONJ
ejpam-4590	490	21	the	the	DET
ejpam-4590	490	22	given	give	VERB
ejpam-4590	490	23	bound	bind	VERB
ejpam-4590	490	24	in	in	ADP
ejpam-4590	490	25	corollary	corollary	ADJ
ejpam-4590	490	26	7	7	NUM
ejpam-4590	490	27	can	can	AUX
ejpam-4590	490	28	not	not	PART
ejpam-4590	490	29	be	be	AUX
ejpam-4590	490	30	improved	improve	VERB
ejpam-4590	490	31	.	.	PUNCT
ejpam-4590	491	1	on	on	ADP
ejpam-4590	491	2	the	the	DET
ejpam-4590	491	3	other	other	ADJ
ejpam-4590	491	4	hand	hand	NOUN
ejpam-4590	491	5	,	,	PUNCT
ejpam-4590	491	6	example	example	NOUN
ejpam-4590	491	7	1	1	NUM
ejpam-4590	491	8	shows	show	VERB
ejpam-4590	491	9	that	that	SCONJ
ejpam-4590	491	10	strict	strict	ADJ
ejpam-4590	491	11	inequality	inequality	NOUN
ejpam-4590	491	12	given	give	VERB
ejpam-4590	491	13	in	in	ADP
ejpam-4590	491	14	corollary	corollary	ADJ
ejpam-4590	491	15	7	7	NUM
ejpam-4590	491	16	is	be	AUX
ejpam-4590	491	17	attainable	attainable	ADJ
ejpam-4590	491	18	.	.	PUNCT
ejpam-4590	492	1	theorem	theorem	NOUN
ejpam-4590	492	2	10	10	NUM
ejpam-4590	492	3	.	.	PUNCT
ejpam-4590	493	1	let	let	VERB
ejpam-4590	493	2	g	g	NOUN
ejpam-4590	493	3	and	and	CCONJ
ejpam-4590	493	4	h	h	NOUN
ejpam-4590	493	5	be	be	AUX
ejpam-4590	493	6	connected	connect	VERB
ejpam-4590	493	7	non	non	ADJ
ejpam-4590	493	8	-	-	ADJ
ejpam-4590	493	9	trivial	trivial	ADJ
ejpam-4590	493	10	graphs	graph	NOUN
ejpam-4590	493	11	.	.	PUNCT
ejpam-4590	494	1	a	a	DET
ejpam-4590	494	2	subset	subset	NOUN
ejpam-4590	494	3	c	c	NOUN
ejpam-4590	494	4	=	=	PUNCT
ejpam-4590	494	5	⋃	⋃	PROPN
ejpam-4590	494	6	x∈s	x∈s	NOUN
ejpam-4590	495	1	[	[	X
ejpam-4590	495	2	{	{	PUNCT
ejpam-4590	495	3	x	x	NOUN
ejpam-4590	495	4	}	}	PUNCT
ejpam-4590	495	5	×	×	PROPN
ejpam-4590	495	6	tx	tx	PROPN
ejpam-4590	495	7	]	]	PUNCT
ejpam-4590	495	8	of	of	ADP
ejpam-4590	495	9	v	v	NOUN
ejpam-4590	495	10	(	(	PUNCT
ejpam-4590	495	11	g	g	PROPN
ejpam-4590	495	12	[	[	X
ejpam-4590	495	13	h	h	X
ejpam-4590	495	14	]	]	X
ejpam-4590	495	15	)	)	PUNCT
ejpam-4590	495	16	is	be	AUX
ejpam-4590	495	17	an	an	DET
ejpam-4590	495	18	outer	outer	ADV
ejpam-4590	495	19	-	-	PUNCT
ejpam-4590	495	20	connected	connect	VERB
ejpam-4590	495	21	hop	hop	NOUN
ejpam-4590	495	22	dominating	dominating	NOUN
ejpam-4590	495	23	set	set	NOUN
ejpam-4590	495	24	of	of	ADP
ejpam-4590	495	25	g	g	PROPN
ejpam-4590	496	1	[	[	X
ejpam-4590	496	2	h	h	X
ejpam-4590	496	3	]	]	X
ejpam-4590	496	4	if	if	SCONJ
ejpam-4590	496	5	and	and	CCONJ
ejpam-4590	496	6	only	only	ADV
ejpam-4590	496	7	if	if	SCONJ
ejpam-4590	496	8	the	the	DET
ejpam-4590	496	9	following	follow	VERB
ejpam-4590	496	10	conditions	condition	NOUN
ejpam-4590	496	11	hold	hold	VERB
ejpam-4590	496	12	:	:	PUNCT
ejpam-4590	496	13	(	(	PUNCT
ejpam-4590	496	14	i	i	NOUN
ejpam-4590	496	15	)	)	PUNCT
ejpam-4590	496	16	s	s	AUX
ejpam-4590	496	17	is	be	AUX
ejpam-4590	496	18	a	a	DET
ejpam-4590	496	19	hop	hop	NOUN
ejpam-4590	496	20	dominating	dominating	NOUN
ejpam-4590	496	21	set	set	NOUN
ejpam-4590	496	22	of	of	ADP
ejpam-4590	496	23	g	g	NOUN
ejpam-4590	496	24	;	;	PUNCT
ejpam-4590	496	25	and	and	CCONJ
ejpam-4590	496	26	(	(	PUNCT
ejpam-4590	496	27	ii	ii	NOUN
ejpam-4590	496	28	)	)	PUNCT
ejpam-4590	496	29	tx	tx	PROPN
ejpam-4590	496	30	is	be	AUX
ejpam-4590	496	31	a	a	DET
ejpam-4590	496	32	pointwise	pointwise	ADJ
ejpam-4590	496	33	non	non	ADJ
ejpam-4590	496	34	-	-	ADJ
ejpam-4590	496	35	dominating	dominating	ADJ
ejpam-4590	496	36	set	set	NOUN
ejpam-4590	496	37	of	of	ADP
ejpam-4590	496	38	h	h	NOUN
ejpam-4590	496	39	for	for	ADP
ejpam-4590	496	40	each	each	DET
ejpam-4590	496	41	x	x	SYM
ejpam-4590	496	42	∈	∈	PROPN
ejpam-4590	496	43	s	s	X
ejpam-4590	496	44	with	with	ADP
ejpam-4590	496	45	∣∣n2	∣∣n2	ADJ
ejpam-4590	496	46	g(x	g(x	NOUN
ejpam-4590	496	47	)	)	PUNCT
ejpam-4590	496	48	∩	∩	NOUN
ejpam-4590	496	49	s	s	PART
ejpam-4590	496	50	∣∣	∣∣	X
ejpam-4590	496	51	=	=	SYM
ejpam-4590	496	52	0	0	X
ejpam-4590	496	53	.	.	PUNCT
ejpam-4590	497	1	(	(	PUNCT
ejpam-4590	497	2	iii	iii	X
ejpam-4590	497	3	)	)	PUNCT
ejpam-4590	497	4	⟨(v	⟨(v	NOUN
ejpam-4590	497	5	(	(	PUNCT
ejpam-4590	497	6	g	g	NOUN
ejpam-4590	497	7	)	)	PUNCT
ejpam-4590	497	8	\	\	PROPN
ejpam-4590	498	1	s	s	X
ejpam-4590	498	2	)	)	PUNCT
ejpam-4590	498	3	∪	∪	NOUN
ejpam-4590	498	4	{	{	PUNCT
ejpam-4590	498	5	v	v	NOUN
ejpam-4590	498	6	∈	∈	NOUN
ejpam-4590	498	7	s	s	PART
ejpam-4590	498	8	:	:	PUNCT
ejpam-4590	498	9	tv	tv	NOUN
ejpam-4590	498	10	̸=	̸=	PROPN
ejpam-4590	498	11	v	v	NOUN
ejpam-4590	498	12	(	(	PUNCT
ejpam-4590	498	13	h)}⟩	h)}⟩	NUM
ejpam-4590	498	14	is	be	AUX
ejpam-4590	498	15	a	a	DET
ejpam-4590	498	16	connected	connected	ADJ
ejpam-4590	498	17	graph	graph	NOUN
ejpam-4590	498	18	in	in	ADP
ejpam-4590	498	19	g.	g.	PROPN
ejpam-4590	498	20	proof	proof	PROPN
ejpam-4590	498	21	.	.	PUNCT
ejpam-4590	499	1	suppose	suppose	VERB
ejpam-4590	499	2	c	c	NOUN
ejpam-4590	499	3	is	be	AUX
ejpam-4590	499	4	an	an	DET
ejpam-4590	499	5	outer	outer	ADV
ejpam-4590	499	6	-	-	PUNCT
ejpam-4590	499	7	connected	connect	VERB
ejpam-4590	499	8	hop	hop	NOUN
ejpam-4590	499	9	dominating	dominating	NOUN
ejpam-4590	499	10	set	set	NOUN
ejpam-4590	499	11	of	of	ADP
ejpam-4590	499	12	g	g	PROPN
ejpam-4590	500	1	[	[	X
ejpam-4590	500	2	h	h	X
ejpam-4590	500	3	]	]	X
ejpam-4590	500	4	and	and	CCONJ
ejpam-4590	500	5	let	let	VERB
ejpam-4590	500	6	w	w	NOUN
ejpam-4590	500	7	=	=	SYM
ejpam-4590	500	8	(	(	PUNCT
ejpam-4590	500	9	v	v	NOUN
ejpam-4590	500	10	(	(	PUNCT
ejpam-4590	500	11	g	g	NOUN
ejpam-4590	500	12	)	)	PUNCT
ejpam-4590	500	13	\	\	PROPN
ejpam-4590	501	1	s	s	X
ejpam-4590	501	2	)	)	PUNCT
ejpam-4590	501	3	∪	∪	NOUN
ejpam-4590	501	4	{	{	PUNCT
ejpam-4590	501	5	v	v	NOUN
ejpam-4590	501	6	∈	∈	NOUN
ejpam-4590	501	7	s	s	PART
ejpam-4590	501	8	:	:	PUNCT
ejpam-4590	501	9	tv	tv	NOUN
ejpam-4590	501	10	̸=	̸=	PROPN
ejpam-4590	501	11	v	v	NOUN
ejpam-4590	501	12	(	(	PUNCT
ejpam-4590	501	13	h	h	NOUN
ejpam-4590	501	14	)	)	PUNCT
ejpam-4590	501	15	}	}	PUNCT
ejpam-4590	501	16	.	.	PUNCT
ejpam-4590	502	1	since	since	SCONJ
ejpam-4590	502	2	every	every	DET
ejpam-4590	502	3	outer	outer	ADV
ejpam-4590	502	4	-	-	PUNCT
ejpam-4590	502	5	connected	connect	VERB
ejpam-4590	502	6	hop	hop	NOUN
ejpam-4590	502	7	dominating	dominating	NOUN
ejpam-4590	502	8	set	set	NOUN
ejpam-4590	502	9	is	be	AUX
ejpam-4590	502	10	a	a	DET
ejpam-4590	502	11	hop	hop	NOUN
ejpam-4590	502	12	dominating	dominating	NOUN
ejpam-4590	502	13	set	set	NOUN
ejpam-4590	502	14	,	,	PUNCT
ejpam-4590	502	15	(	(	PUNCT
ejpam-4590	502	16	i	i	NOUN
ejpam-4590	502	17	)	)	PUNCT
ejpam-4590	502	18	and	and	CCONJ
ejpam-4590	502	19	(	(	PUNCT
ejpam-4590	502	20	ii	ii	NOUN
ejpam-4590	502	21	)	)	PUNCT
ejpam-4590	502	22	hold	hold	VERB
ejpam-4590	502	23	by	by	ADP
ejpam-4590	502	24	theorem	theorem	NOUN
ejpam-4590	502	25	2	2	NUM
ejpam-4590	502	26	.	.	PUNCT
ejpam-4590	503	1	let	let	VERB
ejpam-4590	503	2	u	u	NOUN
ejpam-4590	503	3	,	,	PUNCT
ejpam-4590	503	4	v	v	ADP
ejpam-4590	503	5	∈	∈	PROPN
ejpam-4590	503	6	w	w	ADP
ejpam-4590	503	7	where	where	SCONJ
ejpam-4590	503	8	u	u	NOUN
ejpam-4590	503	9	̸=	̸=	PROPN
ejpam-4590	503	10	v.	v.	CCONJ
ejpam-4590	503	11	suppose	suppose	VERB
ejpam-4590	503	12	u	u	NOUN
ejpam-4590	503	13	,	,	PUNCT
ejpam-4590	503	14	v	v	PROPN
ejpam-4590	503	15	∈	∈	NOUN
ejpam-4590	503	16	v	v	NOUN
ejpam-4590	503	17	(	(	PUNCT
ejpam-4590	503	18	g)\s	g)\s	NOUN
ejpam-4590	503	19	.	.	PUNCT
ejpam-4590	504	1	let	let	VERB
ejpam-4590	504	2	a	a	DET
ejpam-4590	504	3	∈	∈	PROPN
ejpam-4590	504	4	v	v	NOUN
ejpam-4590	504	5	(	(	PUNCT
ejpam-4590	504	6	h	h	NOUN
ejpam-4590	504	7	)	)	PUNCT
ejpam-4590	504	8	.	.	PUNCT
ejpam-4590	505	1	then	then	ADV
ejpam-4590	505	2	(	(	PUNCT
ejpam-4590	505	3	u	u	NOUN
ejpam-4590	505	4	,	,	PUNCT
ejpam-4590	505	5	a	a	PRON
ejpam-4590	505	6	)	)	PUNCT
ejpam-4590	505	7	,	,	PUNCT
ejpam-4590	505	8	(	(	PUNCT
ejpam-4590	505	9	v	v	NOUN
ejpam-4590	505	10	,	,	PUNCT
ejpam-4590	505	11	a	a	PRON
ejpam-4590	505	12	)	)	PUNCT
ejpam-4590	505	13	∈	∈	NOUN
ejpam-4590	505	14	v	v	NOUN
ejpam-4590	505	15	(	(	PUNCT
ejpam-4590	505	16	g	g	PROPN
ejpam-4590	505	17	[	[	X
ejpam-4590	505	18	h])\c	h])\c	NOUN
ejpam-4590	505	19	.	.	PUNCT
ejpam-4590	506	1	since	since	SCONJ
ejpam-4590	506	2	⟨v	⟨v	PROPN
ejpam-4590	506	3	(	(	PUNCT
ejpam-4590	506	4	g	g	PROPN
ejpam-4590	506	5	[	[	X
ejpam-4590	506	6	h	h	X
ejpam-4590	506	7	]	]	X
ejpam-4590	506	8	)	)	PUNCT
ejpam-4590	506	9	\	\	NOUN
ejpam-4590	507	1	c⟩	c⟩	PUNCT
ejpam-4590	507	2	is	be	AUX
ejpam-4590	507	3	connected	connect	VERB
ejpam-4590	507	4	,	,	PUNCT
ejpam-4590	507	5	there	there	PRON
ejpam-4590	507	6	exists	exist	VERB
ejpam-4590	507	7	(	(	PUNCT
ejpam-4590	507	8	u	u	NOUN
ejpam-4590	507	9	,	,	PUNCT
ejpam-4590	507	10	a)-(v	a)-(v	PROPN
ejpam-4590	507	11	,	,	PUNCT
ejpam-4590	507	12	a	a	PRON
ejpam-4590	507	13	)	)	PUNCT
ejpam-4590	507	14	geodesic	geodesic	NOUN
ejpam-4590	507	15	[	[	X
ejpam-4590	507	16	(	(	PUNCT
ejpam-4590	507	17	u1	u1	NOUN
ejpam-4590	507	18	,	,	PUNCT
ejpam-4590	507	19	a1	a1	PROPN
ejpam-4590	507	20	)	)	PUNCT
ejpam-4590	507	21	,	,	PUNCT
ejpam-4590	507	22	(	(	PUNCT
ejpam-4590	507	23	u2	u2	PROPN
ejpam-4590	507	24	,	,	PUNCT
ejpam-4590	507	25	a2	a2	PROPN
ejpam-4590	507	26	)	)	PUNCT
ejpam-4590	507	27	,	,	PUNCT
ejpam-4590	507	28	...	...	PUNCT
ejpam-4590	507	29	,	,	PUNCT
ejpam-4590	507	30	(	(	PUNCT
ejpam-4590	507	31	uk	uk	PROPN
ejpam-4590	507	32	,	,	PUNCT
ejpam-4590	507	33	ak	ak	PROPN
ejpam-4590	507	34	)	)	PUNCT
ejpam-4590	507	35	]	]	PUNCT
ejpam-4590	507	36	,	,	PUNCT
ejpam-4590	507	37	where	where	SCONJ
ejpam-4590	507	38	(	(	PUNCT
ejpam-4590	507	39	u1	u1	NOUN
ejpam-4590	507	40	,	,	PUNCT
ejpam-4590	507	41	a1	a1	NOUN
ejpam-4590	507	42	)	)	PUNCT
ejpam-4590	507	43	=	=	SYM
ejpam-4590	507	44	(	(	PUNCT
ejpam-4590	507	45	u	u	NOUN
ejpam-4590	507	46	,	,	PUNCT
ejpam-4590	507	47	a	a	PRON
ejpam-4590	507	48	)	)	PUNCT
ejpam-4590	507	49	and	and	CCONJ
ejpam-4590	507	50	(	(	PUNCT
ejpam-4590	507	51	uk	uk	PROPN
ejpam-4590	507	52	,	,	PUNCT
ejpam-4590	507	53	ak	ak	PROPN
ejpam-4590	507	54	)	)	PUNCT
ejpam-4590	507	55	=	=	SYM
ejpam-4590	507	56	(	(	PUNCT
ejpam-4590	507	57	v	v	NOUN
ejpam-4590	507	58	,	,	PUNCT
ejpam-4590	507	59	a	a	PRON
ejpam-4590	507	60	)	)	PUNCT
ejpam-4590	507	61	,	,	PUNCT
ejpam-4590	507	62	in	in	ADP
ejpam-4590	507	63	⟨v	⟨v	NOUN
ejpam-4590	507	64	(	(	PUNCT
ejpam-4590	507	65	g	g	PROPN
ejpam-4590	507	66	[	[	X
ejpam-4590	507	67	h	h	X
ejpam-4590	507	68	]	]	X
ejpam-4590	507	69	)	)	PUNCT
ejpam-4590	507	70	\	\	PROPN
ejpam-4590	508	1	c⟩.	c⟩.	PRON
ejpam-4590	508	2	then	then	ADV
ejpam-4590	508	3	ui	ui	PROPN
ejpam-4590	508	4	∈	∈	PROPN
ejpam-4590	508	5	w	w	PROPN
ejpam-4590	508	6	for	for	ADP
ejpam-4590	508	7	all	all	PRON
ejpam-4590	508	8	i	i	PRON
ejpam-4590	508	9	∈	∈	PROPN
ejpam-4590	508	10	{	{	PUNCT
ejpam-4590	508	11	1	1	NUM
ejpam-4590	508	12	,	,	PUNCT
ejpam-4590	508	13	2	2	NUM
ejpam-4590	508	14	,	,	PUNCT
ejpam-4590	508	15	...	...	PUNCT
ejpam-4590	508	16	,	,	PUNCT
ejpam-4590	508	17	k	k	NOUN
ejpam-4590	508	18	}	}	PUNCT
ejpam-4590	508	19	.	.	PUNCT
ejpam-4590	509	1	thus	thus	ADV
ejpam-4590	509	2	,	,	PUNCT
ejpam-4590	509	3	[	[	X
ejpam-4590	509	4	u1	u1	NOUN
ejpam-4590	509	5	,	,	PUNCT
ejpam-4590	509	6	...	...	PUNCT
ejpam-4590	509	7	,	,	PUNCT
ejpam-4590	509	8	uk	uk	PROPN
ejpam-4590	509	9	]	]	PUNCT
ejpam-4590	509	10	is	be	AUX
ejpam-4590	509	11	a	a	DET
ejpam-4590	509	12	u	u	NOUN
ejpam-4590	509	13	-	-	NOUN
ejpam-4590	509	14	v	v	ADJ
ejpam-4590	509	15	path	path	NOUN
ejpam-4590	509	16	in	in	ADP
ejpam-4590	509	17	⟨w	⟨w	X
ejpam-4590	509	18	⟩.	⟩.	PROPN
ejpam-4590	509	19	suppose	suppose	VERB
ejpam-4590	509	20	u	u	NOUN
ejpam-4590	509	21	,	,	PUNCT
ejpam-4590	509	22	v	v	PROPN
ejpam-4590	509	23	∈	∈	NOUN
ejpam-4590	509	24	s	s	VERB
ejpam-4590	509	25	where	where	SCONJ
ejpam-4590	509	26	tu	tu	PROPN
ejpam-4590	509	27	̸=	̸=	PROPN
ejpam-4590	509	28	v	v	PROPN
ejpam-4590	509	29	(	(	PUNCT
ejpam-4590	509	30	h	h	NOUN
ejpam-4590	509	31	)	)	PUNCT
ejpam-4590	509	32	and	and	CCONJ
ejpam-4590	509	33	tv	tv	NOUN
ejpam-4590	509	34	̸=	̸=	PROPN
ejpam-4590	509	35	v	v	NOUN
ejpam-4590	509	36	(	(	PUNCT
ejpam-4590	509	37	h	h	NOUN
ejpam-4590	509	38	)	)	PUNCT
ejpam-4590	509	39	.	.	PUNCT
ejpam-4590	510	1	let	let	VERB
ejpam-4590	510	2	a	a	DET
ejpam-4590	510	3	∈	∈	PROPN
ejpam-4590	510	4	v	v	NOUN
ejpam-4590	510	5	(	(	PUNCT
ejpam-4590	510	6	h	h	NOUN
ejpam-4590	510	7	)	)	PUNCT
ejpam-4590	510	8	\	\	NOUN
ejpam-4590	510	9	tu	tu	PROPN
ejpam-4590	510	10	and	and	CCONJ
ejpam-4590	510	11	b	b	PROPN
ejpam-4590	510	12	∈	∈	PROPN
ejpam-4590	510	13	v	v	NOUN
ejpam-4590	510	14	(	(	PUNCT
ejpam-4590	510	15	h)\tv	h)\tv	PROPN
ejpam-4590	510	16	.	.	PUNCT
ejpam-4590	511	1	then	then	ADV
ejpam-4590	511	2	(	(	PUNCT
ejpam-4590	511	3	u	u	NOUN
ejpam-4590	511	4	,	,	PUNCT
ejpam-4590	511	5	a	a	PRON
ejpam-4590	511	6	)	)	PUNCT
ejpam-4590	511	7	,	,	PUNCT
ejpam-4590	511	8	(	(	PUNCT
ejpam-4590	511	9	v	v	NOUN
ejpam-4590	511	10	,	,	PUNCT
ejpam-4590	511	11	b	b	NOUN
ejpam-4590	511	12	)	)	PUNCT
ejpam-4590	511	13	∈	∈	NOUN
ejpam-4590	511	14	v	v	NOUN
ejpam-4590	511	15	(	(	PUNCT
ejpam-4590	511	16	g	g	PROPN
ejpam-4590	511	17	[	[	X
ejpam-4590	511	18	h])\c	h])\c	NOUN
ejpam-4590	511	19	.	.	PUNCT
ejpam-4590	512	1	since	since	SCONJ
ejpam-4590	512	2	⟨v	⟨v	PROPN
ejpam-4590	512	3	(	(	PUNCT
ejpam-4590	512	4	g	g	PROPN
ejpam-4590	512	5	[	[	X
ejpam-4590	512	6	h	h	X
ejpam-4590	512	7	]	]	X
ejpam-4590	512	8	)	)	PUNCT
ejpam-4590	512	9	\	\	NOUN
ejpam-4590	513	1	c⟩	c⟩	PUNCT
ejpam-4590	513	2	is	be	AUX
ejpam-4590	513	3	connected	connect	VERB
ejpam-4590	513	4	,	,	PUNCT
ejpam-4590	513	5	there	there	PRON
ejpam-4590	513	6	exists	exist	VERB
ejpam-4590	513	7	(	(	PUNCT
ejpam-4590	513	8	u	u	NOUN
ejpam-4590	513	9	,	,	PUNCT
ejpam-4590	513	10	a)-(v	a)-(v	PROPN
ejpam-4590	513	11	,	,	PUNCT
ejpam-4590	513	12	b	b	NOUN
ejpam-4590	513	13	)	)	PUNCT
ejpam-4590	513	14	geodesic	geodesic	NOUN
ejpam-4590	513	15	[	[	X
ejpam-4590	513	16	(	(	PUNCT
ejpam-4590	513	17	u1	u1	NOUN
ejpam-4590	513	18	,	,	PUNCT
ejpam-4590	513	19	a1	a1	NOUN
ejpam-4590	513	20	)	)	PUNCT
ejpam-4590	513	21	,	,	PUNCT
ejpam-4590	513	22	...	...	PUNCT
ejpam-4590	513	23	,	,	PUNCT
ejpam-4590	513	24	(	(	PUNCT
ejpam-4590	513	25	um	um	INTJ
ejpam-4590	513	26	,	,	PUNCT
ejpam-4590	513	27	am	be	AUX
ejpam-4590	513	28	)	)	PUNCT
ejpam-4590	513	29	]	]	PUNCT
ejpam-4590	513	30	,	,	PUNCT
ejpam-4590	513	31	where	where	SCONJ
ejpam-4590	513	32	(	(	PUNCT
ejpam-4590	513	33	u	u	NOUN
ejpam-4590	513	34	,	,	PUNCT
ejpam-4590	513	35	a	a	PRON
ejpam-4590	513	36	)	)	PUNCT
ejpam-4590	513	37	=	=	SYM
ejpam-4590	513	38	(	(	PUNCT
ejpam-4590	513	39	u1	u1	PROPN
ejpam-4590	513	40	,	,	PUNCT
ejpam-4590	513	41	a1	a1	NOUN
ejpam-4590	513	42	)	)	PUNCT
ejpam-4590	513	43	and	and	CCONJ
ejpam-4590	513	44	(	(	PUNCT
ejpam-4590	513	45	um	um	INTJ
ejpam-4590	513	46	,	,	PUNCT
ejpam-4590	513	47	am	be	AUX
ejpam-4590	513	48	)	)	PUNCT
ejpam-4590	513	49	=	=	SYM
ejpam-4590	513	50	(	(	PUNCT
ejpam-4590	513	51	v	v	NOUN
ejpam-4590	513	52	,	,	PUNCT
ejpam-4590	513	53	b	b	NOUN
ejpam-4590	513	54	)	)	PUNCT
ejpam-4590	513	55	,	,	PUNCT
ejpam-4590	513	56	in	in	ADP
ejpam-4590	513	57	⟨v	⟨v	NOUN
ejpam-4590	513	58	(	(	PUNCT
ejpam-4590	513	59	g	g	PROPN
ejpam-4590	513	60	[	[	X
ejpam-4590	513	61	h	h	X
ejpam-4590	513	62	]	]	X
ejpam-4590	513	63	)	)	PUNCT
ejpam-4590	513	64	\	\	PROPN
ejpam-4590	514	1	c⟩.	c⟩.	NUM
ejpam-4590	514	2	again	again	ADV
ejpam-4590	514	3	,	,	PUNCT
ejpam-4590	514	4	ui	ui	PROPN
ejpam-4590	514	5	∈	∈	PROPN
ejpam-4590	514	6	w	w	NOUN
ejpam-4590	514	7	for	for	ADP
ejpam-4590	514	8	all	all	PRON
ejpam-4590	514	9	i	i	PRON
ejpam-4590	514	10	∈	∈	PROPN
ejpam-4590	514	11	{	{	PUNCT
ejpam-4590	514	12	1	1	NUM
ejpam-4590	514	13	,	,	PUNCT
ejpam-4590	514	14	2	2	NUM
ejpam-4590	514	15	,	,	PUNCT
ejpam-4590	514	16	...	...	PUNCT
ejpam-4590	514	17	,	,	PUNCT
ejpam-4590	514	18	k	k	NOUN
ejpam-4590	514	19	}	}	PUNCT
ejpam-4590	514	20	.	.	PUNCT
ejpam-4590	515	1	thus	thus	ADV
ejpam-4590	515	2	,	,	PUNCT
ejpam-4590	515	3	[	[	X
ejpam-4590	515	4	u1	u1	NOUN
ejpam-4590	515	5	,	,	PUNCT
ejpam-4590	515	6	...	...	PUNCT
ejpam-4590	515	7	,	,	PUNCT
ejpam-4590	515	8	uk	uk	PROPN
ejpam-4590	515	9	]	]	PUNCT
ejpam-4590	515	10	is	be	AUX
ejpam-4590	515	11	a	a	DET
ejpam-4590	515	12	u	u	NOUN
ejpam-4590	515	13	-	-	NOUN
ejpam-4590	515	14	v	v	ADJ
ejpam-4590	515	15	path	path	NOUN
ejpam-4590	515	16	in	in	ADP
ejpam-4590	515	17	⟨w	⟨w	X
ejpam-4590	515	18	⟩.	⟩.	PROPN
ejpam-4590	515	19	similarly	similarly	ADV
ejpam-4590	515	20	if	if	SCONJ
ejpam-4590	515	21	u	u	PROPN
ejpam-4590	515	22	∈	∈	PROPN
ejpam-4590	515	23	v	v	ADP
ejpam-4590	515	24	(	(	PUNCT
ejpam-4590	515	25	g	g	NOUN
ejpam-4590	515	26	)	)	PUNCT
ejpam-4590	515	27	\	\	PROPN
ejpam-4590	516	1	s	s	PART
ejpam-4590	516	2	and	and	CCONJ
ejpam-4590	516	3	v	v	ADP
ejpam-4590	516	4	∈	∈	NOUN
ejpam-4590	516	5	s	s	PART
ejpam-4590	516	6	and	and	CCONJ
ejpam-4590	516	7	tv	tv	NOUN
ejpam-4590	516	8	̸=	̸=	PROPN
ejpam-4590	516	9	v	v	NOUN
ejpam-4590	516	10	(	(	PUNCT
ejpam-4590	516	11	h	h	NOUN
ejpam-4590	516	12	)	)	PUNCT
ejpam-4590	516	13	,	,	PUNCT
ejpam-4590	516	14	then	then	ADV
ejpam-4590	516	15	it	it	PRON
ejpam-4590	516	16	can	can	AUX
ejpam-4590	516	17	be	be	AUX
ejpam-4590	516	18	shown	show	VERB
ejpam-4590	516	19	that	that	SCONJ
ejpam-4590	516	20	a	a	DET
ejpam-4590	516	21	u	u	NOUN
ejpam-4590	516	22	-	-	NOUN
ejpam-4590	516	23	v	v	ADJ
ejpam-4590	516	24	path	path	NOUN
ejpam-4590	516	25	in	in	ADP
ejpam-4590	516	26	⟨w	⟨w	X
ejpam-4590	516	27	⟩	⟩	NOUN
ejpam-4590	516	28	exists	exist	VERB
ejpam-4590	516	29	.	.	PUNCT
ejpam-4590	517	1	therefore	therefore	ADV
ejpam-4590	517	2	,	,	PUNCT
ejpam-4590	517	3	⟨w	⟨w	X
ejpam-4590	517	4	⟩	⟩	NOUN
ejpam-4590	517	5	is	be	AUX
ejpam-4590	517	6	connected	connect	VERB
ejpam-4590	517	7	.	.	PUNCT
ejpam-4590	518	1	conversely	conversely	ADV
ejpam-4590	518	2	,	,	PUNCT
ejpam-4590	518	3	suppose	suppose	VERB
ejpam-4590	518	4	that	that	SCONJ
ejpam-4590	518	5	c	c	PROPN
ejpam-4590	518	6	has	have	VERB
ejpam-4590	518	7	the	the	DET
ejpam-4590	518	8	given	give	VERB
ejpam-4590	518	9	form	form	NOUN
ejpam-4590	518	10	and	and	CCONJ
ejpam-4590	518	11	satisfies	satisfie	NOUN
ejpam-4590	518	12	properties	property	NOUN
ejpam-4590	518	13	(	(	PUNCT
ejpam-4590	518	14	i	i	NOUN
ejpam-4590	518	15	)	)	PUNCT
ejpam-4590	518	16	,	,	PUNCT
ejpam-4590	518	17	(	(	PUNCT
ejpam-4590	518	18	ii	ii	NOUN
ejpam-4590	518	19	)	)	PUNCT
ejpam-4590	518	20	and	and	CCONJ
ejpam-4590	518	21	(	(	PUNCT
ejpam-4590	518	22	iii	iii	NOUN
ejpam-4590	518	23	)	)	PUNCT
ejpam-4590	518	24	.	.	PUNCT
ejpam-4590	519	1	by	by	ADP
ejpam-4590	519	2	(	(	PUNCT
ejpam-4590	519	3	i	i	NOUN
ejpam-4590	519	4	)	)	PUNCT
ejpam-4590	519	5	,	,	PUNCT
ejpam-4590	519	6	(	(	PUNCT
ejpam-4590	519	7	ii	ii	NOUN
ejpam-4590	519	8	)	)	PUNCT
ejpam-4590	519	9	and	and	CCONJ
ejpam-4590	519	10	theorem	theorem	VERB
ejpam-4590	519	11	2	2	NUM
ejpam-4590	519	12	,	,	PUNCT
ejpam-4590	519	13	c	c	PROPN
ejpam-4590	519	14	is	be	AUX
ejpam-4590	519	15	a	a	DET
ejpam-4590	519	16	hop	hop	NOUN
ejpam-4590	519	17	dominating	dominating	NOUN
ejpam-4590	519	18	set	set	NOUN
ejpam-4590	519	19	.	.	PUNCT
ejpam-4590	520	1	let	let	VERB
ejpam-4590	520	2	(	(	PUNCT
ejpam-4590	520	3	u	u	NOUN
ejpam-4590	520	4	,	,	PUNCT
ejpam-4590	520	5	a	a	PRON
ejpam-4590	520	6	)	)	PUNCT
ejpam-4590	520	7	,	,	PUNCT
ejpam-4590	520	8	(	(	PUNCT
ejpam-4590	520	9	v	v	NOUN
ejpam-4590	520	10	,	,	PUNCT
ejpam-4590	520	11	b	b	NOUN
ejpam-4590	520	12	)	)	PUNCT
ejpam-4590	520	13	∈	∈	NOUN
ejpam-4590	520	14	v	v	NOUN
ejpam-4590	520	15	(	(	PUNCT
ejpam-4590	520	16	g	g	PROPN
ejpam-4590	520	17	[	[	X
ejpam-4590	520	18	h	h	X
ejpam-4590	520	19	]	]	X
ejpam-4590	520	20	)	)	PUNCT
ejpam-4590	520	21	\	\	PROPN
ejpam-4590	521	1	c	c	NOUN
ejpam-4590	521	2	with	with	ADP
ejpam-4590	521	3	(	(	PUNCT
ejpam-4590	521	4	u	u	NOUN
ejpam-4590	521	5	,	,	PUNCT
ejpam-4590	521	6	a	a	PRON
ejpam-4590	521	7	)	)	PUNCT
ejpam-4590	521	8	̸=	̸=	PROPN
ejpam-4590	521	9	(	(	PUNCT
ejpam-4590	521	10	v	v	NOUN
ejpam-4590	521	11	,	,	PUNCT
ejpam-4590	521	12	b	b	NOUN
ejpam-4590	521	13	)	)	PUNCT
ejpam-4590	521	14	.	.	PUNCT
ejpam-4590	522	1	consider	consider	VERB
ejpam-4590	522	2	the	the	DET
ejpam-4590	522	3	following	follow	VERB
ejpam-4590	522	4	cases	case	NOUN
ejpam-4590	522	5	.	.	PUNCT
ejpam-4590	523	1	case	case	NOUN
ejpam-4590	523	2	1	1	NUM
ejpam-4590	523	3	.	.	X
ejpam-4590	523	4	u	u	NOUN
ejpam-4590	523	5	,	,	PUNCT
ejpam-4590	523	6	v	v	PROPN
ejpam-4590	523	7	∈	∈	PROPN
ejpam-4590	523	8	v	v	NOUN
ejpam-4590	523	9	(	(	PUNCT
ejpam-4590	523	10	g	g	NOUN
ejpam-4590	523	11	)	)	PUNCT
ejpam-4590	523	12	\	\	PUNCT
ejpam-4590	524	1	s.	s.	PROPN
ejpam-4590	524	2	subcase	subcase	VERB
ejpam-4590	524	3	1.1	1.1	NUM
ejpam-4590	524	4	u	u	NOUN
ejpam-4590	524	5	=	=	PROPN
ejpam-4590	524	6	v.	v.	ADP
ejpam-4590	524	7	then	then	ADV
ejpam-4590	524	8	a	a	DET
ejpam-4590	524	9	̸=	̸=	PROPN
ejpam-4590	524	10	b.	b.	NOUN
ejpam-4590	524	11	since	since	SCONJ
ejpam-4590	524	12	h	h	NOUN
ejpam-4590	524	13	is	be	AUX
ejpam-4590	524	14	connected	connect	VERB
ejpam-4590	524	15	,	,	PUNCT
ejpam-4590	524	16	there	there	PRON
ejpam-4590	524	17	exists	exist	VERB
ejpam-4590	524	18	an	an	DET
ejpam-4590	524	19	a	a	PRON
ejpam-4590	524	20	-	-	PUNCT
ejpam-4590	524	21	b	b	NOUN
ejpam-4590	524	22	path	path	NOUN
ejpam-4590	524	23	[	[	X
ejpam-4590	524	24	a1	a1	NOUN
ejpam-4590	524	25	,	,	PUNCT
ejpam-4590	524	26	a2	a2	PROPN
ejpam-4590	524	27	,	,	PUNCT
ejpam-4590	524	28	...	...	PUNCT
ejpam-4590	524	29	,	,	PUNCT
ejpam-4590	524	30	ak	ak	PROPN
ejpam-4590	524	31	]	]	PUNCT
ejpam-4590	524	32	with	with	ADP
ejpam-4590	524	33	a1	a1	NOUN
ejpam-4590	524	34	=	=	PUNCT
ejpam-4590	524	35	a	a	NOUN
ejpam-4590	524	36	and	and	CCONJ
ejpam-4590	524	37	ak	ak	PROPN
ejpam-4590	524	38	=	=	PROPN
ejpam-4590	524	39	b	b	PROPN
ejpam-4590	524	40	in	in	ADP
ejpam-4590	524	41	h.	h.	PROPN
ejpam-4590	524	42	hence	hence	ADV
ejpam-4590	524	43	,	,	PUNCT
ejpam-4590	524	44	the	the	DET
ejpam-4590	524	45	path	path	NOUN
ejpam-4590	524	46	[	[	X
ejpam-4590	524	47	(	(	PUNCT
ejpam-4590	524	48	u	u	NOUN
ejpam-4590	524	49	,	,	PUNCT
ejpam-4590	524	50	a1	a1	PROPN
ejpam-4590	524	51	)	)	PUNCT
ejpam-4590	524	52	,	,	PUNCT
ejpam-4590	524	53	(	(	PUNCT
ejpam-4590	524	54	u	u	NOUN
ejpam-4590	524	55	,	,	PUNCT
ejpam-4590	524	56	a2	a2	PROPN
ejpam-4590	524	57	)	)	PUNCT
ejpam-4590	524	58	,	,	PUNCT
ejpam-4590	524	59	...	...	PUNCT
ejpam-4590	524	60	,	,	PUNCT
ejpam-4590	524	61	(	(	PUNCT
ejpam-4590	524	62	u	u	NOUN
ejpam-4590	524	63	,	,	PUNCT
ejpam-4590	524	64	ak	ak	PROPN
ejpam-4590	524	65	)	)	PUNCT
ejpam-4590	524	66	]	]	PUNCT
ejpam-4590	524	67	is	be	AUX
ejpam-4590	524	68	a	a	DET
ejpam-4590	524	69	(	(	PUNCT
ejpam-4590	524	70	u	u	NOUN
ejpam-4590	524	71	,	,	PUNCT
ejpam-4590	524	72	a)-(v	a)-(v	PROPN
ejpam-4590	524	73	,	,	PUNCT
ejpam-4590	524	74	b	b	NOUN
ejpam-4590	524	75	)	)	PUNCT
ejpam-4590	524	76	path	path	NOUN
ejpam-4590	524	77	in	in	ADP
ejpam-4590	524	78	⟨v	⟨v	PROPN
ejpam-4590	524	79	(	(	PUNCT
ejpam-4590	524	80	g	g	PROPN
ejpam-4590	524	81	[	[	X
ejpam-4590	524	82	h	h	X
ejpam-4590	524	83	]	]	X
ejpam-4590	524	84	)	)	PUNCT
ejpam-4590	524	85	\	\	PROPN
ejpam-4590	524	86	c⟩.	c⟩.	PROPN
ejpam-4590	524	87	subcase	subcase	NOUN
ejpam-4590	524	88	1.2	1.2	NUM
ejpam-4590	524	89	u	u	NOUN
ejpam-4590	524	90	̸=	̸=	PROPN
ejpam-4590	524	91	v.	v.	CCONJ
ejpam-4590	524	92	since	since	SCONJ
ejpam-4590	524	93	u	u	PROPN
ejpam-4590	524	94	,	,	PUNCT
ejpam-4590	524	95	v	v	PROPN
ejpam-4590	524	96	∈	∈	PROPN
ejpam-4590	524	97	v	v	NOUN
ejpam-4590	524	98	(	(	PUNCT
ejpam-4590	524	99	g	g	NOUN
ejpam-4590	524	100	)	)	PUNCT
ejpam-4590	524	101	\	\	PROPN
ejpam-4590	525	1	s	s	X
ejpam-4590	525	2	,	,	PUNCT
ejpam-4590	525	3	there	there	PRON
ejpam-4590	525	4	exists	exist	VERB
ejpam-4590	525	5	a	a	DET
ejpam-4590	525	6	u	u	NOUN
ejpam-4590	525	7	-	-	NOUN
ejpam-4590	525	8	v	v	ADJ
ejpam-4590	525	9	path	path	NOUN
ejpam-4590	525	10	[	[	X
ejpam-4590	525	11	u1	u1	NOUN
ejpam-4590	525	12	,	,	PUNCT
ejpam-4590	525	13	u2	u2	NOUN
ejpam-4590	525	14	,	,	PUNCT
ejpam-4590	525	15	...	...	PUNCT
ejpam-4590	525	16	,	,	PUNCT
ejpam-4590	525	17	uk	uk	PROPN
ejpam-4590	525	18	]	]	X
ejpam-4590	525	19	where	where	SCONJ
ejpam-4590	525	20	u1	u1	NOUN
ejpam-4590	525	21	=	=	SYM
ejpam-4590	525	22	u	u	PROPN
ejpam-4590	525	23	and	and	CCONJ
ejpam-4590	525	24	uk	uk	PROPN
ejpam-4590	525	25	=	=	SYM
ejpam-4590	525	26	v	v	PROPN
ejpam-4590	525	27	,	,	PUNCT
ejpam-4590	525	28	in	in	ADP
ejpam-4590	525	29	⟨w	⟨w	X
ejpam-4590	525	30	⟩	⟩	NOUN
ejpam-4590	525	31	by	by	ADP
ejpam-4590	525	32	(	(	PUNCT
ejpam-4590	525	33	iii	iii	NOUN
ejpam-4590	525	34	)	)	PUNCT
ejpam-4590	525	35	.	.	PUNCT
ejpam-4590	526	1	for	for	ADP
ejpam-4590	526	2	each	each	DET
ejpam-4590	526	3	i	i	PRON
ejpam-4590	526	4	∈	∈	PROPN
ejpam-4590	526	5	{	{	PUNCT
ejpam-4590	526	6	2	2	NUM
ejpam-4590	526	7	,	,	PUNCT
ejpam-4590	526	8	3	3	NUM
ejpam-4590	526	9	,	,	PUNCT
ejpam-4590	526	10	...	...	PUNCT
ejpam-4590	526	11	,	,	PUNCT
ejpam-4590	526	12	k	k	PROPN
ejpam-4590	526	13	−	−	PROPN
ejpam-4590	526	14	1	1	NUM
ejpam-4590	526	15	}	}	PUNCT
ejpam-4590	526	16	,	,	PUNCT
ejpam-4590	526	17	choose	choose	VERB
ejpam-4590	526	18	any	any	DET
ejpam-4590	526	19	ai	ai	PROPN
ejpam-4590	526	20	∈	∈	PROPN
ejpam-4590	526	21	v	v	NOUN
ejpam-4590	526	22	(	(	PUNCT
ejpam-4590	526	23	h	h	NOUN
ejpam-4590	526	24	)	)	PUNCT
ejpam-4590	526	25	if	if	SCONJ
ejpam-4590	526	26	ui	ui	PROPN
ejpam-4590	526	27	∈	∈	PROPN
ejpam-4590	526	28	v	v	X
ejpam-4590	526	29	(	(	PUNCT
ejpam-4590	526	30	g)\s	g)\s	NOUN
ejpam-4590	526	31	.	.	PUNCT
ejpam-4590	527	1	otherwise	otherwise	ADV
ejpam-4590	527	2	let	let	VERB
ejpam-4590	527	3	ai	ai	VERB
ejpam-4590	527	4	∈	∈	PROPN
ejpam-4590	527	5	v	v	ADP
ejpam-4590	527	6	(	(	PUNCT
ejpam-4590	527	7	h	h	NOUN
ejpam-4590	527	8	)	)	PUNCT
ejpam-4590	527	9	\	\	PROPN
ejpam-4590	527	10	tuj	tuj	PROPN
ejpam-4590	527	11	if	if	SCONJ
ejpam-4590	527	12	uj	uj	PROPN
ejpam-4590	527	13	∈	∈	PROPN
ejpam-4590	527	14	s.	s.	PROPN
ejpam-4590	528	1	then	then	ADV
ejpam-4590	528	2	[	[	X
ejpam-4590	528	3	(	(	PUNCT
ejpam-4590	528	4	u1	u1	NOUN
ejpam-4590	528	5	,	,	PUNCT
ejpam-4590	528	6	a1	a1	PROPN
ejpam-4590	528	7	)	)	PUNCT
ejpam-4590	528	8	,	,	PUNCT
ejpam-4590	528	9	(	(	PUNCT
ejpam-4590	528	10	u2	u2	PROPN
ejpam-4590	528	11	,	,	PUNCT
ejpam-4590	528	12	a2	a2	PROPN
ejpam-4590	528	13	)	)	PUNCT
ejpam-4590	528	14	,	,	PUNCT
ejpam-4590	528	15	...	...	PUNCT
ejpam-4590	528	16	,	,	PUNCT
ejpam-4590	528	17	(	(	PUNCT
ejpam-4590	528	18	uk	uk	PROPN
ejpam-4590	528	19	,	,	PUNCT
ejpam-4590	528	20	ak	ak	PROPN
ejpam-4590	528	21	)	)	PUNCT
ejpam-4590	528	22	]	]	PUNCT
ejpam-4590	528	23	where	where	SCONJ
ejpam-4590	528	24	a1	a1	NOUN
ejpam-4590	528	25	=	=	PUNCT
ejpam-4590	528	26	a	a	NOUN
ejpam-4590	528	27	and	and	CCONJ
ejpam-4590	528	28	ak	ak	PROPN
ejpam-4590	528	29	=	=	SYM
ejpam-4590	528	30	b	b	PROPN
ejpam-4590	528	31	is	be	AUX
ejpam-4590	528	32	a	a	DET
ejpam-4590	528	33	(	(	PUNCT
ejpam-4590	528	34	u	u	NOUN
ejpam-4590	528	35	,	,	PUNCT
ejpam-4590	528	36	a)-(v	a)-(v	PROPN
ejpam-4590	528	37	,	,	PUNCT
ejpam-4590	528	38	b	b	NOUN
ejpam-4590	528	39	)	)	PUNCT
ejpam-4590	528	40	path	path	NOUN
ejpam-4590	528	41	in	in	ADP
ejpam-4590	528	42	⟨v	⟨v	PROPN
ejpam-4590	528	43	(	(	PUNCT
ejpam-4590	528	44	g	g	PROPN
ejpam-4590	529	1	[	[	X
ejpam-4590	529	2	h	h	X
ejpam-4590	529	3	]	]	X
ejpam-4590	529	4	)	)	PUNCT
ejpam-4590	529	5	\	\	PROPN
ejpam-4590	530	1	c⟩.	c⟩.	PROPN
ejpam-4590	530	2	hence	hence	ADV
ejpam-4590	530	3	,	,	PUNCT
ejpam-4590	530	4	the	the	DET
ejpam-4590	530	5	path	path	NOUN
ejpam-4590	530	6	[	[	X
ejpam-4590	530	7	(	(	PUNCT
ejpam-4590	530	8	u	u	NOUN
ejpam-4590	530	9	,	,	PUNCT
ejpam-4590	530	10	a1	a1	PROPN
ejpam-4590	530	11	)	)	PUNCT
ejpam-4590	530	12	,	,	PUNCT
ejpam-4590	530	13	(	(	PUNCT
ejpam-4590	530	14	u	u	NOUN
ejpam-4590	530	15	,	,	PUNCT
ejpam-4590	530	16	a2	a2	PROPN
ejpam-4590	530	17	)	)	PUNCT
ejpam-4590	530	18	,	,	PUNCT
ejpam-4590	530	19	...	...	PUNCT
ejpam-4590	530	20	,	,	PUNCT
ejpam-4590	530	21	(	(	PUNCT
ejpam-4590	530	22	u	u	NOUN
ejpam-4590	530	23	,	,	PUNCT
ejpam-4590	530	24	ak	ak	PROPN
ejpam-4590	530	25	)	)	PUNCT
ejpam-4590	530	26	]	]	PUNCT
ejpam-4590	530	27	is	be	AUX
ejpam-4590	530	28	a	a	DET
ejpam-4590	530	29	(	(	PUNCT
ejpam-4590	530	30	u	u	NOUN
ejpam-4590	530	31	,	,	PUNCT
ejpam-4590	530	32	a)-(v	a)-(v	PROPN
ejpam-4590	530	33	,	,	PUNCT
ejpam-4590	530	34	b	b	NOUN
ejpam-4590	530	35	)	)	PUNCT
ejpam-4590	530	36	path	path	NOUN
ejpam-4590	530	37	in	in	ADP
ejpam-4590	530	38	⟨v	⟨v	PROPN
ejpam-4590	530	39	(	(	PUNCT
ejpam-4590	530	40	g	g	PROPN
ejpam-4590	530	41	[	[	X
ejpam-4590	530	42	h	h	X
ejpam-4590	530	43	]	]	X
ejpam-4590	530	44	)	)	PUNCT
ejpam-4590	530	45	\	\	PROPN
ejpam-4590	530	46	c⟩.	c⟩.	PROPN
ejpam-4590	530	47	c.j	c.j	PROPN
ejpam-4590	530	48	.	.	PROPN
ejpam-4590	530	49	saromines	saromines	PROPN
ejpam-4590	530	50	,	,	PUNCT
ejpam-4590	530	51	s.	s.	PROPN
ejpam-4590	530	52	canoy	canoy	PROPN
ejpam-4590	530	53	,	,	PUNCT
ejpam-4590	530	54	jr	jr	PROPN
ejpam-4590	530	55	.	.	PROPN
ejpam-4590	530	56	/	/	SYM
ejpam-4590	530	57	eur	eur	PROPN
ejpam-4590	530	58	.	.	PUNCT
ejpam-4590	531	1	j.	j.	PROPN
ejpam-4590	531	2	pure	pure	PROPN
ejpam-4590	531	3	appl	appl	PROPN
ejpam-4590	531	4	.	.	PROPN
ejpam-4590	531	5	math	math	PROPN
ejpam-4590	531	6	,	,	PUNCT
ejpam-4590	531	7	15	15	NUM
ejpam-4590	531	8	(	(	PUNCT
ejpam-4590	531	9	4	4	NUM
ejpam-4590	531	10	)	)	PUNCT
ejpam-4590	531	11	(	(	PUNCT
ejpam-4590	531	12	2022	2022	NUM
ejpam-4590	531	13	)	)	PUNCT
ejpam-4590	531	14	,	,	PUNCT
ejpam-4590	531	15	1966	1966	NUM
ejpam-4590	531	16	-	-	SYM
ejpam-4590	531	17	1981	1981	NUM
ejpam-4590	531	18	1979	1979	NUM
ejpam-4590	531	19	case	case	NOUN
ejpam-4590	531	20	2	2	NUM
ejpam-4590	531	21	.	.	X
ejpam-4590	531	22	u	u	PROPN
ejpam-4590	531	23	∈	∈	PROPN
ejpam-4590	531	24	v	v	ADP
ejpam-4590	531	25	(	(	PUNCT
ejpam-4590	531	26	g	g	NOUN
ejpam-4590	531	27	)	)	PUNCT
ejpam-4590	531	28	\	\	PROPN
ejpam-4590	532	1	s	s	PROPN
ejpam-4590	532	2	and	and	CCONJ
ejpam-4590	532	3	v	v	NOUN
ejpam-4590	532	4	∈	∈	PROPN
ejpam-4590	532	5	s.	s.	PROPN
ejpam-4590	533	1	then	then	ADV
ejpam-4590	533	2	b	b	PROPN
ejpam-4590	533	3	∈	∈	PROPN
ejpam-4590	533	4	v	v	ADP
ejpam-4590	533	5	(	(	PUNCT
ejpam-4590	533	6	h	h	NOUN
ejpam-4590	533	7	)	)	PUNCT
ejpam-4590	533	8	\	\	PROPN
ejpam-4590	533	9	tv	tv	NOUN
ejpam-4590	533	10	.	.	PUNCT
ejpam-4590	534	1	by	by	ADP
ejpam-4590	534	2	(	(	PUNCT
ejpam-4590	534	3	iii	iii	NOUN
ejpam-4590	534	4	)	)	PUNCT
ejpam-4590	534	5	,	,	PUNCT
ejpam-4590	534	6	a	a	DET
ejpam-4590	534	7	u	u	NOUN
ejpam-4590	534	8	-	-	NOUN
ejpam-4590	534	9	v	v	ADJ
ejpam-4590	534	10	path	path	NOUN
ejpam-4590	534	11	[	[	X
ejpam-4590	534	12	u1	u1	NOUN
ejpam-4590	534	13	,	,	PUNCT
ejpam-4590	534	14	u2	u2	NOUN
ejpam-4590	534	15	,	,	PUNCT
ejpam-4590	534	16	...	...	PUNCT
ejpam-4590	534	17	,	,	PUNCT
ejpam-4590	534	18	up	up	ADP
ejpam-4590	534	19	]	]	PUNCT
ejpam-4590	534	20	where	where	SCONJ
ejpam-4590	534	21	u1	u1	NOUN
ejpam-4590	534	22	=	=	SYM
ejpam-4590	534	23	u	u	PROPN
ejpam-4590	534	24	,	,	PUNCT
ejpam-4590	534	25	up	up	ADV
ejpam-4590	534	26	=	=	SYM
ejpam-4590	534	27	v	v	NOUN
ejpam-4590	534	28	exists	exist	VERB
ejpam-4590	534	29	in	in	ADP
ejpam-4590	534	30	⟨w	⟨w	X
ejpam-4590	534	31	⟩.	⟩.	PROPN
ejpam-4590	534	32	for	for	ADP
ejpam-4590	534	33	each	each	DET
ejpam-4590	534	34	i	i	PRON
ejpam-4590	534	35	∈	∈	PROPN
ejpam-4590	534	36	{	{	PUNCT
ejpam-4590	534	37	2	2	NUM
ejpam-4590	534	38	,	,	PUNCT
ejpam-4590	534	39	3	3	NUM
ejpam-4590	534	40	,	,	PUNCT
ejpam-4590	534	41	...	...	PUNCT
ejpam-4590	534	42	,	,	PUNCT
ejpam-4590	534	43	p−	p−	NOUN
ejpam-4590	534	44	1	1	NUM
ejpam-4590	534	45	}	}	PUNCT
ejpam-4590	534	46	,	,	PUNCT
ejpam-4590	534	47	choose	choose	VERB
ejpam-4590	534	48	any	any	DET
ejpam-4590	534	49	ai	ai	PROPN
ejpam-4590	534	50	∈	∈	PROPN
ejpam-4590	534	51	v	v	NOUN
ejpam-4590	534	52	(	(	PUNCT
ejpam-4590	534	53	h	h	NOUN
ejpam-4590	534	54	)	)	PUNCT
ejpam-4590	534	55	if	if	SCONJ
ejpam-4590	534	56	ui	ui	PROPN
ejpam-4590	534	57	∈	∈	PROPN
ejpam-4590	534	58	v	v	ADP
ejpam-4590	534	59	(	(	PUNCT
ejpam-4590	534	60	g	g	NOUN
ejpam-4590	534	61	)	)	PUNCT
ejpam-4590	534	62	\	\	PUNCT
ejpam-4590	535	1	s.	s.	PROPN
ejpam-4590	535	2	otherwise	otherwise	ADV
ejpam-4590	535	3	let	let	VERB
ejpam-4590	535	4	ai	ai	VERB
ejpam-4590	535	5	∈	∈	PROPN
ejpam-4590	535	6	v	v	ADP
ejpam-4590	535	7	(	(	PUNCT
ejpam-4590	535	8	h	h	NOUN
ejpam-4590	535	9	)	)	PUNCT
ejpam-4590	535	10	\	\	PROPN
ejpam-4590	535	11	tuj	tuj	PROPN
ejpam-4590	535	12	if	if	SCONJ
ejpam-4590	535	13	uj	uj	PROPN
ejpam-4590	535	14	∈	∈	PROPN
ejpam-4590	535	15	s.	s.	PROPN
ejpam-4590	535	16	hence	hence	ADV
ejpam-4590	535	17	,	,	PUNCT
ejpam-4590	535	18	[	[	X
ejpam-4590	535	19	(	(	PUNCT
ejpam-4590	535	20	u1	u1	NOUN
ejpam-4590	535	21	,	,	PUNCT
ejpam-4590	535	22	a1	a1	PROPN
ejpam-4590	535	23	)	)	PUNCT
ejpam-4590	535	24	,	,	PUNCT
ejpam-4590	535	25	(	(	PUNCT
ejpam-4590	535	26	u2	u2	PROPN
ejpam-4590	535	27	,	,	PUNCT
ejpam-4590	535	28	a2	a2	PROPN
ejpam-4590	535	29	)	)	PUNCT
ejpam-4590	535	30	,	,	PUNCT
ejpam-4590	535	31	...	...	PUNCT
ejpam-4590	535	32	,	,	PUNCT
ejpam-4590	535	33	(	(	PUNCT
ejpam-4590	535	34	up	up	ADP
ejpam-4590	535	35	,	,	PUNCT
ejpam-4590	535	36	ap	ap	PROPN
ejpam-4590	535	37	)	)	PUNCT
ejpam-4590	535	38	]	]	PUNCT
ejpam-4590	535	39	,	,	PUNCT
ejpam-4590	535	40	where	where	SCONJ
ejpam-4590	535	41	a1	a1	NOUN
ejpam-4590	535	42	=	=	SYM
ejpam-4590	535	43	a	a	PROPN
ejpam-4590	535	44	,	,	PUNCT
ejpam-4590	535	45	ap	ap	PROPN
ejpam-4590	535	46	=	=	SYM
ejpam-4590	535	47	b	b	PROPN
ejpam-4590	535	48	,	,	PUNCT
ejpam-4590	535	49	is	be	AUX
ejpam-4590	535	50	a	a	DET
ejpam-4590	535	51	(	(	PUNCT
ejpam-4590	535	52	u	u	NOUN
ejpam-4590	535	53	,	,	PUNCT
ejpam-4590	535	54	a)-(v	a)-(v	PROPN
ejpam-4590	535	55	,	,	PUNCT
ejpam-4590	535	56	b	b	NOUN
ejpam-4590	535	57	)	)	PUNCT
ejpam-4590	535	58	path	path	NOUN
ejpam-4590	535	59	in	in	ADP
ejpam-4590	535	60	⟨v	⟨v	PROPN
ejpam-4590	535	61	(	(	PUNCT
ejpam-4590	535	62	g	g	PROPN
ejpam-4590	536	1	[	[	X
ejpam-4590	536	2	h	h	X
ejpam-4590	536	3	]	]	X
ejpam-4590	536	4	)	)	PUNCT
ejpam-4590	536	5	\	\	PROPN
ejpam-4590	536	6	c⟩.	c⟩.	ADJ
ejpam-4590	536	7	case	case	NOUN
ejpam-4590	536	8	3	3	NUM
ejpam-4590	536	9	.	.	X
ejpam-4590	536	10	u	u	NOUN
ejpam-4590	536	11	,	,	PUNCT
ejpam-4590	536	12	v	v	PROPN
ejpam-4590	536	13	∈	∈	PROPN
ejpam-4590	536	14	s.	s.	PROPN
ejpam-4590	536	15	then	then	ADV
ejpam-4590	536	16	a	a	DET
ejpam-4590	536	17	∈	∈	PROPN
ejpam-4590	536	18	v	v	NOUN
ejpam-4590	536	19	(	(	PUNCT
ejpam-4590	536	20	h)\tu	h)\tu	PROPN
ejpam-4590	536	21	.	.	PROPN
ejpam-4590	536	22	and	and	CCONJ
ejpam-4590	536	23	b	b	X
ejpam-4590	536	24	∈	∈	NOUN
ejpam-4590	536	25	v	v	NOUN
ejpam-4590	536	26	(	(	PUNCT
ejpam-4590	536	27	h)\tv	h)\tv	PROPN
ejpam-4590	536	28	.	.	PUNCT
ejpam-4590	536	29	again	again	ADV
ejpam-4590	536	30	,	,	PUNCT
ejpam-4590	536	31	by	by	ADP
ejpam-4590	536	32	(	(	PUNCT
ejpam-4590	536	33	iii	iii	NOUN
ejpam-4590	536	34	)	)	PUNCT
ejpam-4590	536	35	and	and	CCONJ
ejpam-4590	536	36	by	by	ADP
ejpam-4590	536	37	using	use	VERB
ejpam-4590	536	38	similar	similar	ADJ
ejpam-4590	536	39	arguments	argument	NOUN
ejpam-4590	536	40	used	use	VERB
ejpam-4590	536	41	in	in	ADP
ejpam-4590	536	42	case	case	NOUN
ejpam-4590	536	43	1	1	NUM
ejpam-4590	536	44	and	and	CCONJ
ejpam-4590	536	45	case	case	NOUN
ejpam-4590	536	46	2	2	NUM
ejpam-4590	536	47	,	,	PUNCT
ejpam-4590	536	48	there	there	PRON
ejpam-4590	536	49	exists	exist	VERB
ejpam-4590	536	50	(	(	PUNCT
ejpam-4590	536	51	u	u	NOUN
ejpam-4590	536	52	,	,	PUNCT
ejpam-4590	536	53	a)-(v	a)-(v	PROPN
ejpam-4590	536	54	,	,	PUNCT
ejpam-4590	536	55	b	b	NOUN
ejpam-4590	536	56	)	)	PUNCT
ejpam-4590	536	57	path	path	NOUN
ejpam-4590	536	58	in	in	ADP
ejpam-4590	536	59	⟨v	⟨v	PROPN
ejpam-4590	536	60	(	(	PUNCT
ejpam-4590	536	61	g	g	PROPN
ejpam-4590	536	62	[	[	X
ejpam-4590	536	63	h	h	X
ejpam-4590	536	64	]	]	X
ejpam-4590	536	65	\	\	PROPN
ejpam-4590	536	66	c⟩.	c⟩.	NUM
ejpam-4590	536	67	accordingly	accordingly	ADV
ejpam-4590	536	68	,	,	PUNCT
ejpam-4590	536	69	c	c	PROPN
ejpam-4590	536	70	is	be	AUX
ejpam-4590	536	71	an	an	DET
ejpam-4590	536	72	outer	outer	ADV
ejpam-4590	536	73	-	-	PUNCT
ejpam-4590	536	74	connected	connect	VERB
ejpam-4590	536	75	hop	hop	NOUN
ejpam-4590	536	76	dominating	dominating	NOUN
ejpam-4590	536	77	set	set	NOUN
ejpam-4590	536	78	of	of	ADP
ejpam-4590	536	79	g	g	PROPN
ejpam-4590	537	1	[	[	X
ejpam-4590	537	2	h	h	X
ejpam-4590	537	3	]	]	X
ejpam-4590	537	4	.	.	PUNCT
ejpam-4590	538	1	corollary	corollary	ADJ
ejpam-4590	538	2	8	8	NUM
ejpam-4590	538	3	.	.	PUNCT
ejpam-4590	539	1	let	let	VERB
ejpam-4590	539	2	g	g	NOUN
ejpam-4590	539	3	and	and	CCONJ
ejpam-4590	539	4	h	h	PROPN
ejpam-4590	539	5	be	be	VERB
ejpam-4590	539	6	non	non	ADJ
ejpam-4590	539	7	-	-	ADJ
ejpam-4590	539	8	trivial	trivial	ADJ
ejpam-4590	539	9	connected	connected	ADJ
ejpam-4590	539	10	graphs	graph	NOUN
ejpam-4590	539	11	such	such	ADJ
ejpam-4590	539	12	that	that	PRON
ejpam-4590	539	13	γ(g	γ(g	PROPN
ejpam-4590	539	14	)	)	PUNCT
ejpam-4590	539	15	̸=	̸=	PROPN
ejpam-4590	539	16	1	1	NUM
ejpam-4590	539	17	.	.	PUNCT
ejpam-4590	540	1	then	then	ADV
ejpam-4590	540	2	γ̃ch(g	γ̃ch(g	VERB
ejpam-4590	541	1	[	[	X
ejpam-4590	541	2	h	h	X
ejpam-4590	541	3	]	]	X
ejpam-4590	541	4	)	)	PUNCT
ejpam-4590	541	5	=	=	SYM
ejpam-4590	541	6	γth(g	γth(g	NOUN
ejpam-4590	541	7	)	)	PUNCT
ejpam-4590	541	8	proof	proof	NOUN
ejpam-4590	541	9	.	.	PUNCT
ejpam-4590	542	1	let	let	VERB
ejpam-4590	542	2	s	s	PRON
ejpam-4590	542	3	be	be	AUX
ejpam-4590	542	4	a	a	DET
ejpam-4590	542	5	γth	γth	NOUN
ejpam-4590	542	6	-	-	PUNCT
ejpam-4590	542	7	set	set	NOUN
ejpam-4590	542	8	of	of	ADP
ejpam-4590	542	9	g	g	NOUN
ejpam-4590	542	10	and	and	CCONJ
ejpam-4590	542	11	let	let	VERB
ejpam-4590	542	12	p	p	PRON
ejpam-4590	542	13	∈	∈	PROPN
ejpam-4590	542	14	v	v	ADP
ejpam-4590	542	15	(	(	PUNCT
ejpam-4590	542	16	h	h	NOUN
ejpam-4590	542	17	)	)	PUNCT
ejpam-4590	542	18	.	.	PUNCT
ejpam-4590	543	1	set	set	VERB
ejpam-4590	543	2	tx	tx	PROPN
ejpam-4590	543	3	=	=	PUNCT
ejpam-4590	543	4	{	{	PUNCT
ejpam-4590	543	5	p	p	X
ejpam-4590	543	6	}	}	PUNCT
ejpam-4590	543	7	for	for	ADP
ejpam-4590	543	8	every	every	DET
ejpam-4590	543	9	x	x	PROPN
ejpam-4590	543	10	∈	∈	PROPN
ejpam-4590	543	11	s.	s.	PROPN
ejpam-4590	543	12	then	then	ADV
ejpam-4590	543	13	c	c	PROPN
ejpam-4590	544	1	=	=	PUNCT
ejpam-4590	544	2	⋃	⋃	PROPN
ejpam-4590	544	3	x∈s	x∈s	NOUN
ejpam-4590	544	4	(	(	PUNCT
ejpam-4590	544	5	{	{	PUNCT
ejpam-4590	544	6	x	x	NOUN
ejpam-4590	544	7	}	}	PUNCT
ejpam-4590	544	8	×	×	PROPN
ejpam-4590	544	9	tx	tx	PROPN
ejpam-4590	544	10	)	)	PUNCT
ejpam-4590	545	1	=	=	SYM
ejpam-4590	545	2	s	s	PART
ejpam-4590	545	3	×	×	NOUN
ejpam-4590	545	4	{	{	PUNCT
ejpam-4590	545	5	p	p	NOUN
ejpam-4590	545	6	}	}	PUNCT
ejpam-4590	545	7	is	be	AUX
ejpam-4590	545	8	an	an	DET
ejpam-4590	545	9	outer	outer	ADV
ejpam-4590	545	10	-	-	PUNCT
ejpam-4590	545	11	connected	connect	VERB
ejpam-4590	545	12	hop	hop	NOUN
ejpam-4590	545	13	dominating	dominating	NOUN
ejpam-4590	545	14	set	set	VERB
ejpam-4590	545	15	in	in	ADP
ejpam-4590	545	16	g	g	PROPN
ejpam-4590	546	1	[	[	X
ejpam-4590	546	2	h	h	X
ejpam-4590	546	3	]	]	X
ejpam-4590	546	4	by	by	ADP
ejpam-4590	546	5	theorem	theorem	NOUN
ejpam-4590	546	6	10	10	NUM
ejpam-4590	546	7	.	.	PUNCT
ejpam-4590	547	1	hence	hence	ADV
ejpam-4590	547	2	γ̃ch	γ̃ch	PROPN
ejpam-4590	547	3	(	(	PUNCT
ejpam-4590	547	4	g	g	NOUN
ejpam-4590	547	5	[	[	X
ejpam-4590	547	6	h	h	X
ejpam-4590	547	7	]	]	X
ejpam-4590	547	8	)	)	PUNCT
ejpam-4590	547	9	≤	≤	PROPN
ejpam-4590	547	10	|c|	|c|	PROPN
ejpam-4590	547	11	=	=	SYM
ejpam-4590	547	12	|s	|s	PROPN
ejpam-4590	547	13	×	×	NOUN
ejpam-4590	547	14	{	{	PUNCT
ejpam-4590	547	15	p}|	p}|	NOUN
ejpam-4590	547	16	=	=	PUNCT
ejpam-4590	547	17	γth(g	γth(g	NOUN
ejpam-4590	547	18	)	)	PUNCT
ejpam-4590	547	19	.	.	PUNCT
ejpam-4590	548	1	next	next	ADV
ejpam-4590	548	2	,	,	PUNCT
ejpam-4590	548	3	let	let	VERB
ejpam-4590	548	4	c0	c0	PROPN
ejpam-4590	548	5	=	=	PROPN
ejpam-4590	548	6	∪x∈s0	∪x∈s0	PROPN
ejpam-4590	548	7	(	(	PUNCT
ejpam-4590	548	8	{	{	PUNCT
ejpam-4590	548	9	x	x	NOUN
ejpam-4590	548	10	}	}	PUNCT
ejpam-4590	548	11	×rx	×rx	PROPN
ejpam-4590	548	12	)	)	PUNCT
ejpam-4590	548	13	be	be	VERB
ejpam-4590	548	14	γ̃ch	γ̃ch	NOUN
ejpam-4590	548	15	-	-	PUNCT
ejpam-4590	548	16	set	set	NOUN
ejpam-4590	548	17	of	of	ADP
ejpam-4590	548	18	g	g	PROPN
ejpam-4590	549	1	[	[	X
ejpam-4590	549	2	h	h	X
ejpam-4590	549	3	]	]	X
ejpam-4590	549	4	.	.	PUNCT
ejpam-4590	550	1	then	then	ADV
ejpam-4590	550	2	s0	s0	PROPN
ejpam-4590	550	3	is	be	AUX
ejpam-4590	550	4	a	a	DET
ejpam-4590	550	5	hop	hop	NOUN
ejpam-4590	550	6	dominating	dominating	NOUN
ejpam-4590	550	7	set	set	NOUN
ejpam-4590	550	8	and	and	CCONJ
ejpam-4590	550	9	rx	rx	VERB
ejpam-4590	550	10	is	be	AUX
ejpam-4590	550	11	a	a	DET
ejpam-4590	550	12	pointwise	pointwise	ADJ
ejpam-4590	550	13	non	non	ADJ
ejpam-4590	550	14	-	-	ADJ
ejpam-4590	550	15	dominating	dominating	ADJ
ejpam-4590	550	16	set	set	NOUN
ejpam-4590	550	17	of	of	ADP
ejpam-4590	550	18	h	h	NOUN
ejpam-4590	550	19	for	for	ADP
ejpam-4590	550	20	each	each	DET
ejpam-4590	550	21	x	x	SYM
ejpam-4590	550	22	∈	∈	PROPN
ejpam-4590	550	23	s0	s0	PROPN
ejpam-4590	550	24	\n2	\n2	PROPN
ejpam-4590	550	25	g(s0	g(s0	PROPN
ejpam-4590	550	26	)	)	PUNCT
ejpam-4590	550	27	,	,	PUNCT
ejpam-4590	550	28	by	by	ADP
ejpam-4590	550	29	theorem	theorem	NOUN
ejpam-4590	550	30	10	10	NUM
ejpam-4590	550	31	hence	hence	ADV
ejpam-4590	550	32	,	,	PUNCT
ejpam-4590	550	33	γ̃ch(g	γ̃ch(g	VERB
ejpam-4590	551	1	[	[	X
ejpam-4590	551	2	h	h	X
ejpam-4590	551	3	]	]	X
ejpam-4590	551	4	)	)	PUNCT
ejpam-4590	551	5	=	=	SYM
ejpam-4590	551	6	|c0|	|c0|	NOUN
ejpam-4590	551	7	=	=	SYM
ejpam-4590	551	8	∑	∑	PUNCT
ejpam-4590	551	9	x∈s0	x∈s0	PROPN
ejpam-4590	551	10	|rx|	|rx|	NOUN
ejpam-4590	551	11	=	=	PUNCT
ejpam-4590	551	12	∑	∑	PUNCT
ejpam-4590	551	13	x∈s0∩n2	x∈s0∩n2	PROPN
ejpam-4590	551	14	g(s	g(s	PROPN
ejpam-4590	551	15	)	)	PUNCT
ejpam-4590	551	16	|rx|+	|rx|+	ADV
ejpam-4590	551	17	∑	∑	X
ejpam-4590	551	18	x∈s\n2	x∈s\n2	X
ejpam-4590	551	19	g(s0	g(s0	NOUN
ejpam-4590	551	20	)	)	PUNCT
ejpam-4590	551	21	|rx|	|rx|	PROPN
ejpam-4590	551	22	≥	≥	PROPN
ejpam-4590	551	23	∣∣s0	∣∣s0	NOUN
ejpam-4590	551	24	∩n2	∩n2	PROPN
ejpam-4590	551	25	g(s0	g(s0	PROPN
ejpam-4590	551	26	)	)	PUNCT
ejpam-4590	552	1	∣∣+	∣∣+	PROPN
ejpam-4590	552	2	∣∣s0	∣∣s0	NOUN
ejpam-4590	552	3	\n2	\n2	PROPN
ejpam-4590	552	4	g(s0	g(s0	NOUN
ejpam-4590	552	5	)	)	PUNCT
ejpam-4590	552	6	∣∣	∣∣	X
ejpam-4590	552	7	pnd(h	pnd(h	PROPN
ejpam-4590	552	8	)	)	PUNCT
ejpam-4590	552	9	.	.	PUNCT
ejpam-4590	553	1	since	since	SCONJ
ejpam-4590	553	2	h	h	PROPN
ejpam-4590	553	3	is	be	AUX
ejpam-4590	553	4	a	a	DET
ejpam-4590	553	5	non	non	ADJ
ejpam-4590	553	6	-	-	ADJ
ejpam-4590	553	7	trivial	trivial	ADJ
ejpam-4590	553	8	connected	connected	ADJ
ejpam-4590	553	9	graph	graph	NOUN
ejpam-4590	553	10	,	,	PUNCT
ejpam-4590	553	11	pnd(h	pnd(h	PROPN
ejpam-4590	553	12	)	)	PUNCT
ejpam-4590	553	13	≥	≥	NOUN
ejpam-4590	553	14	2	2	NUM
ejpam-4590	553	15	.	.	PUNCT
ejpam-4590	554	1	thus	thus	ADV
ejpam-4590	554	2	,	,	PUNCT
ejpam-4590	554	3	by	by	ADP
ejpam-4590	554	4	theorem	theorem	NOUN
ejpam-4590	554	5	3	3	NUM
ejpam-4590	554	6	,	,	PUNCT
ejpam-4590	554	7	γ̃ch	γ̃ch	PROPN
ejpam-4590	554	8	(	(	PUNCT
ejpam-4590	554	9	g	g	NOUN
ejpam-4590	554	10	[	[	X
ejpam-4590	554	11	h	h	X
ejpam-4590	554	12	]	]	X
ejpam-4590	554	13	)	)	PUNCT
ejpam-4590	554	14	≥	≥	PROPN
ejpam-4590	554	15	γth(g	γth(g	NOUN
ejpam-4590	554	16	)	)	PUNCT
ejpam-4590	554	17	.	.	PUNCT
ejpam-4590	555	1	this	this	PRON
ejpam-4590	555	2	establishes	establish	VERB
ejpam-4590	555	3	the	the	DET
ejpam-4590	555	4	desired	desire	VERB
ejpam-4590	555	5	equality	equality	NOUN
ejpam-4590	555	6	.	.	PUNCT
ejpam-4590	556	1	5	5	X
ejpam-4590	556	2	.	.	X
ejpam-4590	556	3	conclusion	conclusion	NOUN
ejpam-4590	556	4	outer	outer	ADV
ejpam-4590	556	5	-	-	PUNCT
ejpam-4590	556	6	connected	connect	VERB
ejpam-4590	556	7	hop	hop	NOUN
ejpam-4590	556	8	domination	domination	NOUN
ejpam-4590	556	9	,	,	PUNCT
ejpam-4590	556	10	a	a	DET
ejpam-4590	556	11	variant	variant	NOUN
ejpam-4590	556	12	of	of	ADP
ejpam-4590	556	13	hop	hop	NOUN
ejpam-4590	556	14	domination	domination	NOUN
ejpam-4590	556	15	,	,	PUNCT
ejpam-4590	556	16	has	have	AUX
ejpam-4590	556	17	been	be	AUX
ejpam-4590	556	18	introduced	introduce	VERB
ejpam-4590	556	19	and	and	CCONJ
ejpam-4590	556	20	studied	study	VERB
ejpam-4590	556	21	for	for	ADP
ejpam-4590	556	22	some	some	DET
ejpam-4590	556	23	graphs	graph	NOUN
ejpam-4590	556	24	and	and	CCONJ
ejpam-4590	556	25	graphs	graph	NOUN
ejpam-4590	556	26	resulting	result	VERB
ejpam-4590	556	27	from	from	ADP
ejpam-4590	556	28	the	the	DET
ejpam-4590	556	29	join	join	NOUN
ejpam-4590	556	30	,	,	PUNCT
ejpam-4590	556	31	corona	corona	NOUN
ejpam-4590	556	32	and	and	CCONJ
ejpam-4590	556	33	lexicographic	lexicographic	ADJ
ejpam-4590	556	34	references	reference	NOUN
ejpam-4590	556	35	1980	1980	NUM
ejpam-4590	556	36	product	product	NOUN
ejpam-4590	556	37	of	of	ADP
ejpam-4590	556	38	two	two	NUM
ejpam-4590	556	39	graphs	graph	NOUN
ejpam-4590	556	40	.	.	PUNCT
ejpam-4590	557	1	in	in	ADP
ejpam-4590	557	2	the	the	DET
ejpam-4590	557	3	case	case	NOUN
ejpam-4590	557	4	of	of	ADP
ejpam-4590	557	5	the	the	DET
ejpam-4590	557	6	join	join	NOUN
ejpam-4590	557	7	of	of	ADP
ejpam-4590	557	8	graphs	graph	NOUN
ejpam-4590	557	9	,	,	PUNCT
ejpam-4590	557	10	the	the	DET
ejpam-4590	557	11	concept	concept	NOUN
ejpam-4590	557	12	of	of	ADP
ejpam-4590	557	13	outer	outer	ADV
ejpam-4590	557	14	-	-	PUNCT
ejpam-4590	557	15	connected	connect	VERB
ejpam-4590	557	16	pointwise	pointwise	PROPN
ejpam-4590	557	17	non	non	ADJ
ejpam-4590	557	18	-	-	NOUN
ejpam-4590	557	19	domination	domination	NOUN
ejpam-4590	557	20	plays	play	VERB
ejpam-4590	557	21	a	a	DET
ejpam-4590	557	22	vital	vital	ADJ
ejpam-4590	557	23	role	role	NOUN
ejpam-4590	557	24	.	.	PUNCT
ejpam-4590	558	1	it	it	PRON
ejpam-4590	558	2	is	be	AUX
ejpam-4590	558	3	recommended	recommend	VERB
ejpam-4590	558	4	that	that	SCONJ
ejpam-4590	558	5	some	some	DET
ejpam-4590	558	6	bounds	bound	NOUN
ejpam-4590	558	7	on	on	ADP
ejpam-4590	558	8	the	the	DET
ejpam-4590	558	9	outer	outer	ADV
ejpam-4590	558	10	-	-	PUNCT
ejpam-4590	558	11	connected	connect	VERB
ejpam-4590	558	12	hop	hop	NOUN
ejpam-4590	558	13	domination	domination	NOUN
ejpam-4590	558	14	be	be	AUX
ejpam-4590	558	15	determined	determine	VERB
ejpam-4590	558	16	and	and	CCONJ
ejpam-4590	558	17	that	that	SCONJ
ejpam-4590	558	18	the	the	DET
ejpam-4590	558	19	parameter	parameter	NOUN
ejpam-4590	558	20	be	be	AUX
ejpam-4590	558	21	studied	study	VERB
ejpam-4590	558	22	for	for	ADP
ejpam-4590	558	23	other	other	ADJ
ejpam-4590	558	24	graphs	graph	NOUN
ejpam-4590	558	25	.	.	PUNCT
ejpam-4590	559	1	acknowledgements	acknowledgement	NOUN
ejpam-4590	559	2	the	the	DET
ejpam-4590	559	3	authors	author	NOUN
ejpam-4590	559	4	are	be	AUX
ejpam-4590	559	5	very	very	ADV
ejpam-4590	559	6	much	much	ADV
ejpam-4590	559	7	grateful	grateful	ADJ
ejpam-4590	559	8	to	to	ADP
ejpam-4590	559	9	the	the	DET
ejpam-4590	559	10	referees	referee	NOUN
ejpam-4590	559	11	for	for	ADP
ejpam-4590	559	12	the	the	DET
ejpam-4590	559	13	corrections	correction	NOUN
ejpam-4590	559	14	and	and	CCONJ
ejpam-4590	559	15	suggestions	suggestion	NOUN
ejpam-4590	559	16	they	they	PRON
ejpam-4590	559	17	made	make	VERB
ejpam-4590	559	18	in	in	ADP
ejpam-4590	559	19	the	the	DET
ejpam-4590	559	20	initial	initial	ADJ
ejpam-4590	559	21	manuscript	manuscript	NOUN
ejpam-4590	559	22	.	.	PUNCT
ejpam-4590	560	1	this	this	DET
ejpam-4590	560	2	paper	paper	NOUN
ejpam-4590	560	3	had	have	AUX
ejpam-4590	560	4	been	be	AUX
ejpam-4590	560	5	improved	improve	VERB
ejpam-4590	560	6	due	due	ADJ
ejpam-4590	560	7	to	to	ADP
ejpam-4590	560	8	the	the	DET
ejpam-4590	560	9	additional	additional	ADJ
ejpam-4590	560	10	inputs	input	NOUN
ejpam-4590	560	11	and	and	CCONJ
ejpam-4590	560	12	insights	insight	NOUN
ejpam-4590	560	13	the	the	DET
ejpam-4590	560	14	referees	referee	NOUN
ejpam-4590	560	15	had	have	AUX
ejpam-4590	560	16	given	give	VERB
ejpam-4590	560	17	to	to	ADP
ejpam-4590	560	18	the	the	DET
ejpam-4590	560	19	authors	author	NOUN
ejpam-4590	560	20	.	.	PUNCT
ejpam-4590	561	1	the	the	DET
ejpam-4590	561	2	authors	author	NOUN
ejpam-4590	561	3	would	would	AUX
ejpam-4590	561	4	like	like	VERB
ejpam-4590	561	5	to	to	PART
ejpam-4590	561	6	thank	thank	VERB
ejpam-4590	561	7	the	the	DET
ejpam-4590	561	8	department	department	NOUN
ejpam-4590	561	9	of	of	ADP
ejpam-4590	561	10	science	science	NOUN
ejpam-4590	561	11	and	and	CCONJ
ejpam-4590	561	12	technology	technology	NOUN
ejpam-4590	561	13	accelerated	accelerate	VERB
ejpam-4590	561	14	science	science	NOUN
ejpam-4590	561	15	and	and	CCONJ
ejpam-4590	561	16	technology	technology	NOUN
ejpam-4590	561	17	human	human	ADJ
ejpam-4590	561	18	resource	resource	NOUN
ejpam-4590	561	19	development	development	NOUN
ejpam-4590	561	20	program	program	NOUN
ejpam-4590	561	21	(	(	PUNCT
ejpam-4590	561	22	dost	dost	NOUN
ejpam-4590	561	23	-	-	PUNCT
ejpam-4590	561	24	asthrdp)-philippines	asthrdp)-philippine	NOUN
ejpam-4590	561	25	,	,	PUNCT
ejpam-4590	561	26	and	and	CCONJ
ejpam-4590	561	27	msu	msu	PROPN
ejpam-4590	561	28	-	-	PUNCT
ejpam-4590	561	29	iligan	iligan	PROPN
ejpam-4590	561	30	institute	institute	PROPN
ejpam-4590	561	31	of	of	ADP
ejpam-4590	561	32	technology	technology	NOUN
ejpam-4590	561	33	for	for	ADP
ejpam-4590	561	34	funding	fund	VERB
ejpam-4590	561	35	this	this	DET
ejpam-4590	561	36	research	research	NOUN
ejpam-4590	561	37	.	.	PUNCT
ejpam-4590	562	1	references	reference	NOUN
ejpam-4590	562	2	[	[	X
ejpam-4590	562	3	1	1	NUM
ejpam-4590	562	4	]	]	X
ejpam-4590	562	5	b.d	b.d	PROPN
ejpam-4590	562	6	.	.	PROPN
ejpam-4590	562	7	acharaya	acharaya	PROPN
ejpam-4590	562	8	,	,	PUNCT
ejpam-4590	562	9	s.	s.	PROPN
ejpam-4590	562	10	arumugan	arumugan	PROPN
ejpam-4590	562	11	,	,	PUNCT
ejpam-4590	562	12	and	and	CCONJ
ejpam-4590	562	13	p.j	p.j	PROPN
ejpam-4590	562	14	.	.	PROPN
ejpam-4590	562	15	slater	slater	PROPN
ejpam-4590	562	16	.	.	PUNCT
ejpam-4590	563	1	domination	domination	NOUN
ejpam-4590	563	2	in	in	ADP
ejpam-4590	563	3	discrete	discrete	ADJ
ejpam-4590	563	4	structures	structure	NOUN
ejpam-4590	563	5	new	new	ADJ
ejpam-4590	563	6	directions	direction	NOUN
ejpam-4590	563	7	.	.	PUNCT
ejpam-4590	564	1	akce	akce	PROPN
ejpam-4590	564	2	j.	j.	PROPN
ejpam-4590	564	3	graphs	graphs	PROPN
ejpam-4590	564	4	combin	combin	PROPN
ejpam-4590	564	5	.	.	PUNCT
ejpam-4590	564	6	,	,	PUNCT
ejpam-4590	564	7	pages	page	NOUN
ejpam-4590	564	8	113–115	113–115	NUM
ejpam-4590	564	9	,	,	PUNCT
ejpam-4590	564	10	2007	2007	NUM
ejpam-4590	564	11	.	.	PUNCT
ejpam-4590	565	1	[	[	X
ejpam-4590	565	2	2	2	X
ejpam-4590	565	3	]	]	X
ejpam-4590	565	4	m.h	m.h	PROPN
ejpam-4590	565	5	.	.	PROPN
ejpam-4590	565	6	akhbari	akhbari	PROPN
ejpam-4590	565	7	,	,	PUNCT
ejpam-4590	565	8	r.	r.	PROPN
ejpam-4590	565	9	hasni	hasni	PROPN
ejpam-4590	565	10	,	,	PUNCT
ejpam-4590	565	11	o.	o.	PROPN
ejpam-4590	565	12	favaron	favaron	PROPN
ejpam-4590	565	13	,	,	PUNCT
ejpam-4590	565	14	h.	h.	PROPN
ejpam-4590	565	15	karami	karami	PROPN
ejpam-4590	565	16	,	,	PUNCT
ejpam-4590	565	17	and	and	CCONJ
ejpam-4590	565	18	s.m	s.m	PROPN
ejpam-4590	565	19	.	.	PROPN
ejpam-4590	565	20	sheikholeslami	sheikholeslami	PROPN
ejpam-4590	565	21	.	.	PUNCT
ejpam-4590	566	1	on	on	ADP
ejpam-4590	566	2	the	the	DET
ejpam-4590	566	3	outer	outer	ADV
ejpam-4590	566	4	-	-	PUNCT
ejpam-4590	566	5	conected	conecte	VERB
ejpam-4590	566	6	domination	domination	NOUN
ejpam-4590	566	7	numbers	number	NOUN
ejpam-4590	566	8	of	of	ADP
ejpam-4590	566	9	graphs	graph	NOUN
ejpam-4590	566	10	.	.	PUNCT
ejpam-4590	567	1	journal	journal	NOUN
ejpam-4590	567	2	of	of	ADP
ejpam-4590	567	3	combinatorial	combinatorial	ADJ
ejpam-4590	567	4	optimization	optimization	NOUN
ejpam-4590	567	5	,	,	PUNCT
ejpam-4590	567	6	26(1):10–18	26(1):10–18	NUM
ejpam-4590	567	7	,	,	PUNCT
ejpam-4590	567	8	2013	2013	NUM
ejpam-4590	567	9	.	.	PUNCT
ejpam-4590	568	1	[	[	X
ejpam-4590	568	2	3	3	X
ejpam-4590	568	3	]	]	X
ejpam-4590	568	4	c.	c.	PROPN
ejpam-4590	568	5	armada	armada	PROPN
ejpam-4590	568	6	,	,	PUNCT
ejpam-4590	568	7	s.	s.	PROPN
ejpam-4590	568	8	canoy	canoy	PROPN
ejpam-4590	568	9	jr	jr	PROPN
ejpam-4590	568	10	.	.	PROPN
ejpam-4590	568	11	,	,	PUNCT
ejpam-4590	568	12	and	and	CCONJ
ejpam-4590	568	13	c.	c.	PROPN
ejpam-4590	568	14	go	go	VERB
ejpam-4590	568	15	.	.	PUNCT
ejpam-4590	569	1	forcing	force	VERB
ejpam-4590	569	2	domination	domination	NOUN
ejpam-4590	569	3	numbers	number	NOUN
ejpam-4590	569	4	of	of	ADP
ejpam-4590	569	5	graphs	graph	NOUN
ejpam-4590	569	6	under	under	ADP
ejpam-4590	569	7	some	some	DET
ejpam-4590	569	8	binary	binary	ADJ
ejpam-4590	569	9	operations	operation	NOUN
ejpam-4590	569	10	.	.	PUNCT
ejpam-4590	570	1	advances	advance	NOUN
ejpam-4590	570	2	and	and	CCONJ
ejpam-4590	570	3	applications	application	NOUN
ejpam-4590	570	4	in	in	ADP
ejpam-4590	570	5	discrete	discrete	ADJ
ejpam-4590	570	6	mathematics	mathematic	NOUN
ejpam-4590	570	7	,	,	PUNCT
ejpam-4590	570	8	19(3):213–228	19(3):213–228	NUM
ejpam-4590	570	9	,	,	PUNCT
ejpam-4590	570	10	2018	2018	NUM
ejpam-4590	570	11	.	.	PUNCT
ejpam-4590	571	1	[	[	X
ejpam-4590	571	2	4	4	X
ejpam-4590	571	3	]	]	PUNCT
ejpam-4590	571	4	s.	s.	PROPN
ejpam-4590	571	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4590	571	6	,	,	PUNCT
ejpam-4590	571	7	b.	b.	PROPN
ejpam-4590	571	8	krishnakumari	krishnakumari	PROPN
ejpam-4590	571	9	,	,	PUNCT
ejpam-4590	571	10	b.	b.	PROPN
ejpam-4590	571	11	natarjan	natarjan	PROPN
ejpam-4590	571	12	,	,	PUNCT
ejpam-4590	571	13	and	and	CCONJ
ejpam-4590	571	14	y.	y.	PROPN
ejpam-4590	571	15	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4590	571	16	.	.	PUNCT
ejpam-4590	572	1	bounds	bound	NOUN
ejpam-4590	572	2	on	on	ADP
ejpam-4590	572	3	the	the	DET
ejpam-4590	572	4	hop	hop	NOUN
ejpam-4590	572	5	domination	domination	NOUN
ejpam-4590	572	6	number	number	NOUN
ejpam-4590	572	7	of	of	ADP
ejpam-4590	572	8	a	a	DET
ejpam-4590	572	9	tree	tree	NOUN
ejpam-4590	572	10	.	.	PUNCT
ejpam-4590	573	1	proceedings	proceeding	NOUN
ejpam-4590	573	2	-	-	PUNCT
ejpam-4590	573	3	mathematical	mathematical	ADJ
ejpam-4590	573	4	sciences	science	NOUN
ejpam-4590	573	5	,	,	PUNCT
ejpam-4590	573	6	125(4):449	125(4):449	NUM
ejpam-4590	573	7	–	–	PUNCT
ejpam-4590	573	8	455	455	NUM
ejpam-4590	573	9	,	,	PUNCT
ejpam-4590	573	10	2015	2015	NUM
ejpam-4590	573	11	.	.	PUNCT
ejpam-4590	574	1	[	[	X
ejpam-4590	574	2	5	5	X
ejpam-4590	574	3	]	]	PUNCT
ejpam-4590	574	4	j.	j.	PROPN
ejpam-4590	574	5	cyman	cyman	PROPN
ejpam-4590	574	6	.	.	PUNCT
ejpam-4590	575	1	the	the	DET
ejpam-4590	575	2	outer	outer	ADV
ejpam-4590	575	3	-	-	PUNCT
ejpam-4590	575	4	conected	conecte	VERB
ejpam-4590	575	5	domination	domination	NOUN
ejpam-4590	575	6	numbers	number	NOUN
ejpam-4590	575	7	of	of	ADP
ejpam-4590	575	8	graphs	graph	NOUN
ejpam-4590	575	9	.	.	PUNCT
ejpam-4590	576	1	australasian	australasian	ADJ
ejpam-4590	576	2	journal	journal	NOUN
ejpam-4590	576	3	of	of	ADP
ejpam-4590	576	4	combinatorics	combinatoric	NOUN
ejpam-4590	576	5	,	,	PUNCT
ejpam-4590	576	6	38(1):35–46	38(1):35–46	NUM
ejpam-4590	576	7	,	,	PUNCT
ejpam-4590	576	8	2007	2007	NUM
ejpam-4590	576	9	.	.	PUNCT
ejpam-4590	577	1	[	[	X
ejpam-4590	577	2	6	6	NUM
ejpam-4590	577	3	]	]	PUNCT
ejpam-4590	577	4	t.	t.	PROPN
ejpam-4590	577	5	daniel	daniel	PROPN
ejpam-4590	577	6	and	and	CCONJ
ejpam-4590	577	7	s.	s.	PROPN
ejpam-4590	577	8	canoy	canoy	PROPN
ejpam-4590	577	9	jr	jr	PROPN
ejpam-4590	577	10	.	.	PROPN
ejpam-4590	577	11	clique	clique	PROPN
ejpam-4590	577	12	domination	domination	PROPN
ejpam-4590	577	13	in	in	ADP
ejpam-4590	577	14	graphs	graph	NOUN
ejpam-4590	577	15	.	.	PUNCT
ejpam-4590	578	1	applied	apply	VERB
ejpam-4590	578	2	mathematical	mathematical	ADJ
ejpam-4590	578	3	sciences	science	NOUN
ejpam-4590	578	4	,	,	PUNCT
ejpam-4590	578	5	9(116):5749–5755	9(116):5749–5755	NUM
ejpam-4590	578	6	,	,	PUNCT
ejpam-4590	578	7	2015	2015	NUM
ejpam-4590	578	8	.	.	PUNCT
ejpam-4590	579	1	[	[	X
ejpam-4590	579	2	7	7	X
ejpam-4590	579	3	]	]	X
ejpam-4590	579	4	r.	r.	NOUN
ejpam-4590	579	5	eballe	eballe	PROPN
ejpam-4590	579	6	and	and	CCONJ
ejpam-4590	579	7	s.	s.	PROPN
ejpam-4590	579	8	canoy	canoy	PROPN
ejpam-4590	579	9	jr	jr	PROPN
ejpam-4590	579	10	.	.	PROPN
ejpam-4590	579	11	steiner	steiner	PROPN
ejpam-4590	579	12	sets	set	NOUN
ejpam-4590	579	13	in	in	ADP
ejpam-4590	579	14	the	the	DET
ejpam-4590	579	15	join	join	NOUN
ejpam-4590	579	16	and	and	CCONJ
ejpam-4590	579	17	composition	composition	NOUN
ejpam-4590	579	18	of	of	ADP
ejpam-4590	579	19	graphs	graph	NOUN
ejpam-4590	579	20	.	.	PUNCT
ejpam-4590	580	1	congressus	congressus	PROPN
ejpam-4590	580	2	numerantium	numerantium	PROPN
ejpam-4590	580	3	,	,	PUNCT
ejpam-4590	580	4	170:65–73	170:65–73	NUM
ejpam-4590	580	5	,	,	PUNCT
ejpam-4590	580	6	2004	2004	NUM
ejpam-4590	580	7	.	.	PUNCT
ejpam-4590	581	1	[	[	X
ejpam-4590	581	2	8	8	NUM
ejpam-4590	581	3	]	]	PUNCT
ejpam-4590	581	4	s.	s.	PROPN
ejpam-4590	581	5	omega	omega	NOUN
ejpam-4590	581	6	espinola	espinola	PROPN
ejpam-4590	581	7	and	and	CCONJ
ejpam-4590	581	8	s.	s.	PROPN
ejpam-4590	581	9	canoy	canoy	PROPN
ejpam-4590	581	10	jr	jr	PROPN
ejpam-4590	581	11	.	.	PROPN
ejpam-4590	581	12	restrained	restrained	ADJ
ejpam-4590	581	13	locating	locating	NOUN
ejpam-4590	581	14	-	-	PUNCT
ejpam-4590	581	15	domination	domination	NOUN
ejpam-4590	581	16	and	and	CCONJ
ejpam-4590	581	17	restrained	restrained	ADJ
ejpam-4590	581	18	differentiating	differentiating	NOUN
ejpam-4590	581	19	-	-	PUNCT
ejpam-4590	581	20	domination	domination	NOUN
ejpam-4590	581	21	in	in	ADP
ejpam-4590	581	22	graphs	graph	NOUN
ejpam-4590	581	23	.	.	PUNCT
ejpam-4590	582	1	international	international	ADJ
ejpam-4590	582	2	journal	journal	NOUN
ejpam-4590	582	3	of	of	ADP
ejpam-4590	582	4	mathematics	mathematics	PROPN
ejpam-4590	582	5	analysis	analysis	NOUN
ejpam-4590	582	6	,	,	PUNCT
ejpam-4590	582	7	9(45):2243–2255	9(45):2243–2255	NOUN
ejpam-4590	582	8	,	,	PUNCT
ejpam-4590	582	9	2015	2015	NUM
ejpam-4590	582	10	.	.	PUNCT
ejpam-4590	583	1	[	[	X
ejpam-4590	583	2	9	9	X
ejpam-4590	583	3	]	]	PUNCT
ejpam-4590	583	4	t.	t.	PROPN
ejpam-4590	583	5	w.	w.	PROPN
ejpam-4590	583	6	haynes	haynes	PROPN
ejpam-4590	583	7	,	,	PUNCT
ejpam-4590	583	8	s.t	s.t	PROPN
ejpam-4590	583	9	.	.	PROPN
ejpam-4590	583	10	hedetnieme	hedetnieme	PROPN
ejpam-4590	583	11	,	,	PUNCT
ejpam-4590	583	12	and	and	CCONJ
ejpam-4590	583	13	p.j	p.j	PROPN
ejpam-4590	583	14	.	.	PROPN
ejpam-4590	583	15	slater	slater	PROPN
ejpam-4590	583	16	.	.	PUNCT
ejpam-4590	584	1	fundamentals	fundamental	NOUN
ejpam-4590	584	2	of	of	ADP
ejpam-4590	584	3	domination	domination	NOUN
ejpam-4590	584	4	in	in	ADP
ejpam-4590	584	5	graphs	graph	NOUN
ejpam-4590	584	6	.	.	PUNCT
ejpam-4590	585	1	monographs	monograph	NOUN
ejpam-4590	585	2	and	and	CCONJ
ejpam-4590	585	3	textbooks	textbook	NOUN
ejpam-4590	585	4	in	in	ADP
ejpam-4590	585	5	pure	pure	ADJ
ejpam-4590	585	6	and	and	CCONJ
ejpam-4590	585	7	applied	applied	ADJ
ejpam-4590	585	8	mathematics	mathematic	NOUN
ejpam-4590	585	9	,	,	PUNCT
ejpam-4590	585	10	28	28	NUM
ejpam-4590	585	11	,	,	PUNCT
ejpam-4590	585	12	1998	1998	NUM
ejpam-4590	585	13	.	.	PUNCT
ejpam-4590	586	1	references	reference	NOUN
ejpam-4590	586	2	1981	1981	NUM
ejpam-4590	586	3	[	[	X
ejpam-4590	586	4	10	10	NUM
ejpam-4590	586	5	]	]	PUNCT
ejpam-4590	586	6	m.	m.	NOUN
ejpam-4590	586	7	henning	henning	PROPN
ejpam-4590	586	8	and	and	CCONJ
ejpam-4590	586	9	n.	n.	PROPN
ejpam-4590	586	10	rad	rad	PROPN
ejpam-4590	586	11	.	.	PROPN
ejpam-4590	587	1	on	on	ADP
ejpam-4590	587	2	2	2	NUM
ejpam-4590	587	3	-	-	PUNCT
ejpam-4590	587	4	step	step	NOUN
ejpam-4590	587	5	and	and	CCONJ
ejpam-4590	587	6	hop	hop	NOUN
ejpam-4590	587	7	dominating	dominating	NOUN
ejpam-4590	587	8	sets	set	NOUN
ejpam-4590	587	9	in	in	ADP
ejpam-4590	587	10	graphs	graph	NOUN
ejpam-4590	587	11	.	.	PUNCT
ejpam-4590	588	1	graphs	graph	NOUN
ejpam-4590	588	2	and	and	CCONJ
ejpam-4590	588	3	combinatorics	combinatoric	NOUN
ejpam-4590	588	4	.	.	PUNCT
ejpam-4590	588	5	,	,	PUNCT
ejpam-4590	588	6	33(4):913–927	33(4):913–927	PROPN
ejpam-4590	588	7	,	,	PUNCT
ejpam-4590	588	8	2017	2017	NUM
ejpam-4590	588	9	.	.	PUNCT
ejpam-4590	589	1	[	[	X
ejpam-4590	589	2	11	11	NUM
ejpam-4590	589	3	]	]	X
ejpam-4590	589	4	h.	h.	PROPN
ejpam-4590	589	5	jiang	jiang	PROPN
ejpam-4590	589	6	and	and	CCONJ
ejpam-4590	589	7	e.	e.	PROPN
ejpam-4590	589	8	shan	shan	PROPN
ejpam-4590	589	9	.	.	PUNCT
ejpam-4590	590	1	outer	outer	ADJ
ejpam-4590	590	2	-	-	PUNCT
ejpam-4590	590	3	conected	conecte	VERB
ejpam-4590	590	4	domination	domination	NOUN
ejpam-4590	590	5	numbers	number	NOUN
ejpam-4590	590	6	of	of	ADP
ejpam-4590	590	7	graphs	graph	NOUN
ejpam-4590	590	8	.	.	PUNCT
ejpam-4590	591	1	american	american	PROPN
ejpam-4590	591	2	mathematical	mathematical	PROPN
ejpam-4590	591	3	society	society	NOUN
ejpam-4590	591	4	,	,	PUNCT
ejpam-4590	591	5	81(1):265–274	81(1):265–274	NOUN
ejpam-4590	591	6	,	,	PUNCT
ejpam-4590	591	7	2010	2010	NUM
ejpam-4590	591	8	.	.	PUNCT
ejpam-4590	592	1	[	[	X
ejpam-4590	592	2	12	12	NUM
ejpam-4590	592	3	]	]	X
ejpam-4590	592	4	r.	r.	PROPN
ejpam-4590	592	5	hinampas	hinampas	PROPN
ejpam-4590	592	6	jr	jr	PROPN
ejpam-4590	592	7	,	,	PUNCT
ejpam-4590	592	8	j.	j.	PROPN
ejpam-4590	592	9	hinampas	hinampas	PROPN
ejpam-4590	592	10	,	,	PUNCT
ejpam-4590	592	11	and	and	CCONJ
ejpam-4590	592	12	a.	a.	NOUN
ejpam-4590	592	13	dahuman	dahuman	PROPN
ejpam-4590	592	14	.	.	PUNCT
ejpam-4590	593	1	independent	independent	ADJ
ejpam-4590	593	2	outer	outer	ADV
ejpam-4590	593	3	-	-	PUNCT
ejpam-4590	593	4	connected	connect	VERB
ejpam-4590	593	5	domination	domination	NOUN
ejpam-4590	593	6	in	in	ADP
ejpam-4590	593	7	graphs	graph	NOUN
ejpam-4590	593	8	.	.	PUNCT
ejpam-4590	594	1	global	global	ADJ
ejpam-4590	594	2	journal	journal	PROPN
ejpam-4590	594	3	of	of	ADP
ejpam-4590	594	4	pure	pure	ADJ
ejpam-4590	594	5	and	and	CCONJ
ejpam-4590	594	6	applied	applied	ADJ
ejpam-4590	594	7	mathematics	mathematic	NOUN
ejpam-4590	594	8	,	,	PUNCT
ejpam-4590	594	9	13(1):1–7	13(1):1–7	NUM
ejpam-4590	594	10	,	,	PUNCT
ejpam-4590	594	11	2017	2017	NUM
ejpam-4590	594	12	.	.	PUNCT
ejpam-4590	595	1	[	[	X
ejpam-4590	595	2	13	13	NUM
ejpam-4590	595	3	]	]	PUNCT
ejpam-4590	595	4	s.	s.	PROPN
ejpam-4590	595	5	canoy	canoy	PROPN
ejpam-4590	595	6	jr	jr	PROPN
ejpam-4590	595	7	.	.	PROPN
ejpam-4590	595	8	and	and	CCONJ
ejpam-4590	595	9	s.	s.	PROPN
ejpam-4590	595	10	arriola	arriola	PROPN
ejpam-4590	595	11	.	.	PUNCT
ejpam-4590	596	1	(	(	PUNCT
ejpam-4590	596	2	1	1	NUM
ejpam-4590	596	3	,	,	PUNCT
ejpam-4590	596	4	2)∗-domination	2)∗-domination	NOUN
ejpam-4590	596	5	in	in	ADP
ejpam-4590	596	6	graphs	graph	NOUN
ejpam-4590	596	7	.	.	PUNCT
ejpam-4590	597	1	advances	advance	NOUN
ejpam-4590	597	2	and	and	CCONJ
ejpam-4590	597	3	applications	application	NOUN
ejpam-4590	597	4	in	in	ADP
ejpam-4590	597	5	discrete	discrete	ADJ
ejpam-4590	597	6	mathematics	mathematic	NOUN
ejpam-4590	597	7	.	.	PUNCT
ejpam-4590	597	8	,	,	PUNCT
ejpam-4590	597	9	18(2):179–190	18(2):179–190	NUM
ejpam-4590	597	10	,	,	PUNCT
ejpam-4590	597	11	2017	2017	NUM
ejpam-4590	597	12	.	.	PUNCT
ejpam-4590	598	1	[	[	X
ejpam-4590	598	2	14	14	NUM
ejpam-4590	598	3	]	]	X
ejpam-4590	598	4	s.	s.	PROPN
ejpam-4590	598	5	canoy	canoy	PROPN
ejpam-4590	598	6	jr	jr	PROPN
ejpam-4590	598	7	.	.	PROPN
ejpam-4590	598	8	,	,	PUNCT
ejpam-4590	598	9	r.	r.	PROPN
ejpam-4590	598	10	mollejon	mollejon	NOUN
ejpam-4590	598	11	,	,	PUNCT
ejpam-4590	598	12	and	and	CCONJ
ejpam-4590	598	13	j.	j.	PROPN
ejpam-4590	598	14	g.	g.	PROPN
ejpam-4590	598	15	canoy	canoy	PROPN
ejpam-4590	598	16	.	.	PUNCT
ejpam-4590	599	1	hop	hop	PROPN
ejpam-4590	599	2	dominating	dominating	NOUN
ejpam-4590	599	3	sets	set	NOUN
ejpam-4590	599	4	in	in	ADP
ejpam-4590	599	5	graphs	graph	NOUN
ejpam-4590	599	6	under	under	ADP
ejpam-4590	599	7	binary	binary	ADJ
ejpam-4590	599	8	operations	operation	NOUN
ejpam-4590	599	9	.	.	PUNCT
ejpam-4590	600	1	eur	eur	PROPN
ejpam-4590	600	2	.	.	PUNCT
ejpam-4590	601	1	j.	j.	PROPN
ejpam-4590	601	2	pure	pure	PROPN
ejpam-4590	601	3	appl	appl	PROPN
ejpam-4590	601	4	.	.	PUNCT
ejpam-4590	601	5	math	math	PROPN
ejpam-4590	601	6	.	.	PUNCT
ejpam-4590	601	7	,	,	PUNCT
ejpam-4590	602	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4590	602	2	,	,	PUNCT
ejpam-4590	602	3	2019	2019	NUM
ejpam-4590	602	4	.	.	PUNCT
ejpam-4590	603	1	[	[	X
ejpam-4590	603	2	15	15	NUM
ejpam-4590	603	3	]	]	X
ejpam-4590	603	4	g.	g.	PROPN
ejpam-4590	603	5	monsanto	monsanto	PROPN
ejpam-4590	603	6	and	and	CCONJ
ejpam-4590	603	7	h.	h.	PROPN
ejpam-4590	603	8	rara	rara	PROPN
ejpam-4590	603	9	.	.	PUNCT
ejpam-4590	604	1	resolving	resolve	VERB
ejpam-4590	604	2	restrained	restrained	ADJ
ejpam-4590	604	3	domination	domination	NOUN
ejpam-4590	604	4	domination	domination	NOUN
ejpam-4590	604	5	in	in	ADP
ejpam-4590	604	6	graphs	graph	NOUN
ejpam-4590	604	7	.	.	PUNCT
ejpam-4590	605	1	european	european	ADJ
ejpam-4590	605	2	journal	journal	PROPN
ejpam-4590	605	3	of	of	ADP
ejpam-4590	605	4	pure	pure	ADJ
ejpam-4590	605	5	and	and	CCONJ
ejpam-4590	605	6	applied	applied	ADJ
ejpam-4590	605	7	mathematics	mathematic	NOUN
ejpam-4590	605	8	,	,	PUNCT
ejpam-4590	605	9	14(3):829–841	14(3):829–841	PROPN
ejpam-4590	605	10	,	,	PUNCT
ejpam-4590	605	11	2021	2021	NUM
ejpam-4590	605	12	.	.	PUNCT
ejpam-4590	606	1	[	[	X
ejpam-4590	606	2	16	16	NUM
ejpam-4590	606	3	]	]	X
ejpam-4590	606	4	c.	c.	PROPN
ejpam-4590	606	5	natarajan	natarajan	PROPN
ejpam-4590	606	6	and	and	CCONJ
ejpam-4590	606	7	s.	s.	PROPN
ejpam-4590	606	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4590	606	9	.	.	PUNCT
ejpam-4590	607	1	hop	hop	PROPN
ejpam-4590	607	2	domination	domination	NOUN
ejpam-4590	607	3	in	in	ADP
ejpam-4590	607	4	graphs	graphs	PROPN
ejpam-4590	607	5	ii	ii	PROPN
ejpam-4590	607	6	.	.	PUNCT
ejpam-4590	607	7	versita	versita	PROPN
ejpam-4590	607	8	,	,	PUNCT
ejpam-4590	607	9	23(2):187	23(2):187	NUM
ejpam-4590	607	10	–	–	PUNCT
ejpam-4590	607	11	199	199	NUM
ejpam-4590	607	12	,	,	PUNCT
ejpam-4590	607	13	2015	2015	NUM
ejpam-4590	607	14	.	.	PUNCT
ejpam-4590	608	1	[	[	X
ejpam-4590	608	2	17	17	NUM
ejpam-4590	608	3	]	]	X
ejpam-4590	608	4	y.	y.	PROPN
ejpam-4590	608	5	pabilona	pabilona	PROPN
ejpam-4590	608	6	and	and	CCONJ
ejpam-4590	608	7	h.	h.	PROPN
ejpam-4590	608	8	rara	rara	PROPN
ejpam-4590	608	9	.	.	PUNCT
ejpam-4590	609	1	connected	connect	VERB
ejpam-4590	609	2	hop	hop	NOUN
ejpam-4590	609	3	domination	domination	NOUN
ejpam-4590	609	4	in	in	ADP
ejpam-4590	609	5	graphs	graph	NOUN
ejpam-4590	609	6	under	under	ADP
ejpam-4590	609	7	some	some	DET
ejpam-4590	609	8	binary	binary	ADJ
ejpam-4590	609	9	operations	operation	NOUN
ejpam-4590	609	10	.	.	PUNCT
ejpam-4590	610	1	asian	asian	ADJ
ejpam-4590	610	2	-	-	PUNCT
ejpam-4590	610	3	eur	eur	NOUN
ejpam-4590	610	4	.	.	PUNCT
ejpam-4590	611	1	j.	j.	PROPN
ejpam-4590	611	2	math	math	PROPN
ejpam-4590	611	3	.	.	PROPN
ejpam-4590	611	4	,	,	PUNCT
ejpam-4590	611	5	11(5):1850075–1–1850075–11	11(5):1850075–1–1850075–11	NUM
ejpam-4590	611	6	,	,	PUNCT
ejpam-4590	611	7	2018	2018	NUM
ejpam-4590	611	8	.	.	PUNCT
ejpam-4590	612	1	[	[	X
ejpam-4590	612	2	18	18	NUM
ejpam-4590	612	3	]	]	X
ejpam-4590	612	4	s.	s.	PROPN
ejpam-4590	612	5	pacardo	pacardo	PROPN
ejpam-4590	612	6	and	and	CCONJ
ejpam-4590	612	7	h.	h.	PROPN
ejpam-4590	612	8	rara	rara	PROPN
ejpam-4590	612	9	.	.	PUNCT
ejpam-4590	613	1	interior	interior	ADJ
ejpam-4590	613	2	domination	domination	NOUN
ejpam-4590	613	3	in	in	ADP
ejpam-4590	613	4	graphs	graph	NOUN
ejpam-4590	613	5	under	under	ADP
ejpam-4590	613	6	some	some	DET
ejpam-4590	613	7	binary	binary	ADJ
ejpam-4590	613	8	operations	operation	NOUN
ejpam-4590	613	9	.	.	PUNCT
ejpam-4590	614	1	applied	apply	VERB
ejpam-4590	614	2	mathematical	mathematical	ADJ
ejpam-4590	614	3	sciences	science	NOUN
ejpam-4590	614	4	,	,	PUNCT
ejpam-4590	614	5	12(14):677–690	12(14):677–690	NUM
ejpam-4590	614	6	,	,	PUNCT
ejpam-4590	614	7	2018	2018	NUM
ejpam-4590	614	8	.	.	PUNCT
ejpam-4590	615	1	[	[	X
ejpam-4590	615	2	19	19	NUM
ejpam-4590	615	3	]	]	X
ejpam-4590	615	4	r.	r.	PROPN
ejpam-4590	615	5	rakim	rakim	PROPN
ejpam-4590	615	6	and	and	CCONJ
ejpam-4590	615	7	h.	h.	PROPN
ejpam-4590	615	8	rara	rara	PROPN
ejpam-4590	615	9	.	.	PUNCT
ejpam-4590	616	1	total	total	ADJ
ejpam-4590	616	2	perfect	perfect	ADJ
ejpam-4590	616	3	hop	hop	NOUN
ejpam-4590	616	4	domination	domination	NOUN
ejpam-4590	616	5	in	in	ADP
ejpam-4590	616	6	graphs	graph	NOUN
ejpam-4590	616	7	under	under	ADP
ejpam-4590	616	8	some	some	DET
ejpam-4590	616	9	binary	binary	ADJ
ejpam-4590	616	10	operations	operation	NOUN
ejpam-4590	616	11	.	.	PUNCT
ejpam-4590	617	1	european	european	ADJ
ejpam-4590	617	2	journal	journal	PROPN
ejpam-4590	617	3	of	of	ADP
ejpam-4590	617	4	pure	pure	ADJ
ejpam-4590	617	5	and	and	CCONJ
ejpam-4590	617	6	applied	applied	ADJ
ejpam-4590	617	7	mathematics	mathematic	NOUN
ejpam-4590	617	8	,	,	PUNCT
ejpam-4590	617	9	14(3):803–815	14(3):803–815	PROPN
ejpam-4590	617	10	,	,	PUNCT
ejpam-4590	617	11	2021	2021	NUM
ejpam-4590	617	12	.	.	PUNCT
ejpam-4590	618	1	[	[	X
ejpam-4590	618	2	20	20	NUM
ejpam-4590	618	3	]	]	PUNCT
ejpam-4590	618	4	r.	r.	PROPN
ejpam-4590	618	5	rakim	rakim	PROPN
ejpam-4590	618	6	,	,	PUNCT
ejpam-4590	618	7	h.	h.	PROPN
ejpam-4590	618	8	rara	rara	PROPN
ejpam-4590	618	9	,	,	PUNCT
ejpam-4590	618	10	and	and	CCONJ
ejpam-4590	618	11	c.j	c.j	PROPN
ejpam-4590	618	12	.	.	PROPN
ejpam-4590	618	13	saromines	saromine	NOUN
ejpam-4590	618	14	.	.	PUNCT
ejpam-4590	619	1	perfect	perfect	ADJ
ejpam-4590	619	2	hop	hop	NOUN
ejpam-4590	619	3	domination	domination	NOUN
ejpam-4590	619	4	in	in	ADP
ejpam-4590	619	5	graphs	graph	NOUN
ejpam-4590	619	6	.	.	PUNCT
ejpam-4590	620	1	applied	apply	VERB
ejpam-4590	620	2	mathematical	mathematical	ADJ
ejpam-4590	620	3	sciences	sciences	PROPN
ejpam-4590	620	4	,	,	PUNCT
ejpam-4590	620	5	12(13):635–649	12(13):635–649	NUM
ejpam-4590	620	6	,	,	PUNCT
ejpam-4590	620	7	2018	2018	NUM
ejpam-4590	620	8	.	.	PUNCT