id	sid	tid	token	lemma	pos
ejpam-3550	1	1	european	european	PROPN
ejpam-3550	1	2	journal	journal	PROPN
ejpam-3550	1	3	of	of	ADP
ejpam-3550	1	4	pure	pure	ADJ
ejpam-3550	1	5	and	and	CCONJ
ejpam-3550	1	6	applied	apply	VERB
ejpam-3550	1	7	mathematics	mathematic	NOUN
ejpam-3550	1	8	vol	vol	NOUN
ejpam-3550	1	9	.	.	PROPN
ejpam-3550	2	1	12	12	NUM
ejpam-3550	2	2	,	,	PUNCT
ejpam-3550	2	3	no	no	INTJ
ejpam-3550	2	4	.	.	NOUN
ejpam-3550	2	5	4	4	NUM
ejpam-3550	2	6	,	,	PUNCT
ejpam-3550	2	7	2019	2019	NUM
ejpam-3550	2	8	,	,	PUNCT
ejpam-3550	2	9	1455	1455	NUM
ejpam-3550	2	10	-	-	SYM
ejpam-3550	2	11	1463	1463	NUM
ejpam-3550	2	12	issn	issn	PROPN
ejpam-3550	2	13	1307	1307	NUM
ejpam-3550	2	14	-	-	SYM
ejpam-3550	2	15	5543	5543	NUM
ejpam-3550	2	16	–	–	PUNCT
ejpam-3550	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3550	2	18	published	publish	VERB
ejpam-3550	2	19	by	by	ADP
ejpam-3550	2	20	new	new	PROPN
ejpam-3550	2	21	york	york	PROPN
ejpam-3550	2	22	business	business	PROPN
ejpam-3550	2	23	global	global	PROPN
ejpam-3550	2	24	hop	hop	NOUN
ejpam-3550	2	25	dominating	dominating	NOUN
ejpam-3550	2	26	sets	set	NOUN
ejpam-3550	2	27	in	in	ADP
ejpam-3550	2	28	graphs	graph	NOUN
ejpam-3550	2	29	under	under	ADP
ejpam-3550	2	30	binary	binary	ADJ
ejpam-3550	2	31	operations	operation	NOUN
ejpam-3550	2	32	sergio	sergio	PROPN
ejpam-3550	2	33	r.	r.	PROPN
ejpam-3550	2	34	canoy	canoy	PROPN
ejpam-3550	2	35	jr.1	jr.1	PROPN
ejpam-3550	2	36	,	,	PUNCT
ejpam-3550	2	37	reynaldo	reynaldo	PROPN
ejpam-3550	2	38	v.	v.	ADP
ejpam-3550	2	39	mollejon2	mollejon2	PROPN
ejpam-3550	2	40	,	,	PUNCT
ejpam-3550	2	41	john	john	PROPN
ejpam-3550	2	42	gabriel	gabriel	PROPN
ejpam-3550	2	43	e.	e.	PROPN
ejpam-3550	2	44	canoy∗	canoy∗	PROPN
ejpam-3550	2	45	1	1	PROPN
ejpam-3550	2	46	department	department	NOUN
ejpam-3550	2	47	of	of	ADP
ejpam-3550	2	48	mathematics	mathematic	NOUN
ejpam-3550	2	49	and	and	CCONJ
ejpam-3550	2	50	statistics	statistic	NOUN
ejpam-3550	2	51	,	,	PUNCT
ejpam-3550	2	52	college	college	NOUN
ejpam-3550	2	53	of	of	ADP
ejpam-3550	2	54	science	science	NOUN
ejpam-3550	2	55	and	and	CCONJ
ejpam-3550	2	56	mathematics	mathematic	NOUN
ejpam-3550	2	57	,	,	PUNCT
ejpam-3550	2	58	center	center	NOUN
ejpam-3550	2	59	for	for	ADP
ejpam-3550	2	60	graph	graph	NOUN
ejpam-3550	2	61	theory	theory	NOUN
ejpam-3550	2	62	,	,	PUNCT
ejpam-3550	2	63	algebra	algebra	NOUN
ejpam-3550	2	64	,	,	PUNCT
ejpam-3550	2	65	and	and	CCONJ
ejpam-3550	2	66	analysis	analysis	NOUN
ejpam-3550	2	67	,	,	PUNCT
ejpam-3550	2	68	premier	premier	PROPN
ejpam-3550	2	69	research	research	PROPN
ejpam-3550	2	70	institute	institute	PROPN
ejpam-3550	2	71	in	in	ADP
ejpam-3550	2	72	science	science	NOUN
ejpam-3550	2	73	and	and	CCONJ
ejpam-3550	2	74	mathematics	mathematic	NOUN
ejpam-3550	2	75	,	,	PUNCT
ejpam-3550	2	76	msu	msu	PROPN
ejpam-3550	2	77	-	-	PUNCT
ejpam-3550	2	78	iligan	iligan	PROPN
ejpam-3550	2	79	institute	institute	PROPN
ejpam-3550	2	80	of	of	ADP
ejpam-3550	2	81	technology	technology	PROPN
ejpam-3550	2	82	,	,	PUNCT
ejpam-3550	2	83	tibanga	tibanga	PROPN
ejpam-3550	2	84	,	,	PUNCT
ejpam-3550	2	85	iligan	iligan	ADJ
ejpam-3550	2	86	city	city	PROPN
ejpam-3550	2	87	,	,	PUNCT
ejpam-3550	2	88	philippines	philippines	PROPN
ejpam-3550	2	89	2	2	NUM
ejpam-3550	2	90	department	department	NOUN
ejpam-3550	2	91	of	of	ADP
ejpam-3550	2	92	teacher	teacher	NOUN
ejpam-3550	2	93	education	education	NOUN
ejpam-3550	2	94	,	,	PUNCT
ejpam-3550	2	95	visayas	visayas	PROPN
ejpam-3550	2	96	state	state	PROPN
ejpam-3550	2	97	university	university	PROPN
ejpam-3550	2	98	-	-	PUNCT
ejpam-3550	2	99	villaba	villaba	PROPN
ejpam-3550	2	100	,	,	PUNCT
ejpam-3550	2	101	villaba	villaba	PROPN
ejpam-3550	2	102	,	,	PUNCT
ejpam-3550	2	103	leyte	leyte	PROPN
ejpam-3550	2	104	,	,	PUNCT
ejpam-3550	2	105	philippines	philippine	NOUN
ejpam-3550	2	106	abstract	abstract	ADJ
ejpam-3550	2	107	.	.	PUNCT
ejpam-3550	3	1	let	let	VERB
ejpam-3550	3	2	g	g	PRON
ejpam-3550	3	3	be	be	AUX
ejpam-3550	3	4	a	a	DET
ejpam-3550	3	5	(	(	PUNCT
ejpam-3550	3	6	simple	simple	ADJ
ejpam-3550	3	7	)	)	PUNCT
ejpam-3550	3	8	connected	connected	ADJ
ejpam-3550	3	9	graph	graph	NOUN
ejpam-3550	3	10	with	with	ADP
ejpam-3550	3	11	vertex	vertex	NOUN
ejpam-3550	3	12	and	and	CCONJ
ejpam-3550	3	13	edge	edge	NOUN
ejpam-3550	3	14	sets	set	NOUN
ejpam-3550	3	15	v	v	ADP
ejpam-3550	3	16	(	(	PUNCT
ejpam-3550	3	17	g	g	NOUN
ejpam-3550	3	18	)	)	PUNCT
ejpam-3550	3	19	and	and	CCONJ
ejpam-3550	3	20	e(g	e(g	PROPN
ejpam-3550	3	21	)	)	PUNCT
ejpam-3550	3	22	,	,	PUNCT
ejpam-3550	3	23	respectively	respectively	ADV
ejpam-3550	3	24	.	.	PUNCT
ejpam-3550	4	1	a	a	DET
ejpam-3550	4	2	set	set	NOUN
ejpam-3550	4	3	s	s	NOUN
ejpam-3550	4	4	⊆	⊆	NUM
ejpam-3550	4	5	v	v	NOUN
ejpam-3550	4	6	(	(	PUNCT
ejpam-3550	4	7	g	g	NOUN
ejpam-3550	4	8	)	)	PUNCT
ejpam-3550	4	9	is	be	AUX
ejpam-3550	4	10	a	a	DET
ejpam-3550	4	11	hop	hop	NOUN
ejpam-3550	4	12	dominating	dominating	NOUN
ejpam-3550	4	13	set	set	NOUN
ejpam-3550	4	14	of	of	ADP
ejpam-3550	4	15	g	g	PROPN
ejpam-3550	4	16	if	if	SCONJ
ejpam-3550	4	17	for	for	ADP
ejpam-3550	4	18	each	each	PRON
ejpam-3550	4	19	v	v	NUM
ejpam-3550	4	20	∈	∈	PROPN
ejpam-3550	4	21	v	v	NOUN
ejpam-3550	4	22	(	(	PUNCT
ejpam-3550	4	23	g	g	NOUN
ejpam-3550	4	24	)	)	PUNCT
ejpam-3550	4	25	\	\	PROPN
ejpam-3550	5	1	s	s	X
ejpam-3550	5	2	,	,	PUNCT
ejpam-3550	5	3	there	there	PRON
ejpam-3550	5	4	exists	exist	VERB
ejpam-3550	5	5	w	w	PROPN
ejpam-3550	5	6	∈	∈	PROPN
ejpam-3550	5	7	s	s	VERB
ejpam-3550	5	8	such	such	ADJ
ejpam-3550	5	9	that	that	PRON
ejpam-3550	5	10	dg(v	dg(v	ADJ
ejpam-3550	5	11	,	,	PUNCT
ejpam-3550	5	12	w	w	NOUN
ejpam-3550	5	13	)	)	PUNCT
ejpam-3550	5	14	=	=	SYM
ejpam-3550	5	15	2	2	X
ejpam-3550	5	16	.	.	PUNCT
ejpam-3550	5	17	the	the	DET
ejpam-3550	5	18	minimum	minimum	ADJ
ejpam-3550	5	19	cardinality	cardinality	NOUN
ejpam-3550	5	20	of	of	ADP
ejpam-3550	5	21	a	a	DET
ejpam-3550	5	22	hop	hop	NOUN
ejpam-3550	5	23	dominating	dominating	NOUN
ejpam-3550	5	24	set	set	NOUN
ejpam-3550	5	25	of	of	ADP
ejpam-3550	5	26	g	g	NOUN
ejpam-3550	5	27	,	,	PUNCT
ejpam-3550	5	28	denoted	denote	VERB
ejpam-3550	5	29	by	by	ADP
ejpam-3550	5	30	γh(g	γh(g	NOUN
ejpam-3550	5	31	)	)	PUNCT
ejpam-3550	5	32	,	,	PUNCT
ejpam-3550	5	33	is	be	AUX
ejpam-3550	5	34	called	call	VERB
ejpam-3550	5	35	the	the	DET
ejpam-3550	5	36	hop	hop	NOUN
ejpam-3550	5	37	domination	domination	NOUN
ejpam-3550	5	38	number	number	NOUN
ejpam-3550	5	39	of	of	ADP
ejpam-3550	5	40	g.	g.	PROPN
ejpam-3550	5	41	in	in	ADP
ejpam-3550	5	42	this	this	DET
ejpam-3550	5	43	paper	paper	NOUN
ejpam-3550	5	44	we	we	PRON
ejpam-3550	5	45	revisit	revisit	VERB
ejpam-3550	5	46	the	the	DET
ejpam-3550	5	47	concept	concept	NOUN
ejpam-3550	5	48	of	of	ADP
ejpam-3550	5	49	hop	hop	NOUN
ejpam-3550	5	50	domination	domination	NOUN
ejpam-3550	5	51	,	,	PUNCT
ejpam-3550	5	52	relate	relate	VERB
ejpam-3550	5	53	it	it	PRON
ejpam-3550	5	54	with	with	ADP
ejpam-3550	5	55	other	other	ADJ
ejpam-3550	5	56	domination	domination	NOUN
ejpam-3550	5	57	concepts	concept	NOUN
ejpam-3550	5	58	,	,	PUNCT
ejpam-3550	5	59	and	and	CCONJ
ejpam-3550	5	60	investigate	investigate	VERB
ejpam-3550	5	61	it	it	PRON
ejpam-3550	5	62	in	in	ADP
ejpam-3550	5	63	graphs	graph	NOUN
ejpam-3550	5	64	resulting	result	VERB
ejpam-3550	5	65	from	from	ADP
ejpam-3550	5	66	some	some	DET
ejpam-3550	5	67	binary	binary	ADJ
ejpam-3550	5	68	operations	operation	NOUN
ejpam-3550	5	69	.	.	PUNCT
ejpam-3550	6	1	2010	2010	NUM
ejpam-3550	6	2	mathematics	mathematic	NOUN
ejpam-3550	6	3	subject	subject	NOUN
ejpam-3550	6	4	classifications	classification	NOUN
ejpam-3550	6	5	:	:	PUNCT
ejpam-3550	6	6	05c69	05c69	X
ejpam-3550	6	7	key	key	ADJ
ejpam-3550	6	8	words	word	NOUN
ejpam-3550	6	9	and	and	CCONJ
ejpam-3550	6	10	phrases	phrase	NOUN
ejpam-3550	6	11	:	:	PUNCT
ejpam-3550	6	12	domination	domination	NOUN
ejpam-3550	6	13	,	,	PUNCT
ejpam-3550	6	14	hop	hop	NOUN
ejpam-3550	6	15	domination	domination	NOUN
ejpam-3550	6	16	,	,	PUNCT
ejpam-3550	6	17	join	join	NOUN
ejpam-3550	6	18	,	,	PUNCT
ejpam-3550	6	19	corona	corona	PROPN
ejpam-3550	6	20	,	,	PUNCT
ejpam-3550	6	21	and	and	CCONJ
ejpam-3550	6	22	lexicographic	lexicographic	ADJ
ejpam-3550	6	23	product	product	NOUN
ejpam-3550	6	24	1	1	NUM
ejpam-3550	6	25	.	.	PUNCT
ejpam-3550	7	1	introduction	introduction	NOUN
ejpam-3550	7	2	domination	domination	NOUN
ejpam-3550	7	3	in	in	ADP
ejpam-3550	7	4	graph	graph	NOUN
ejpam-3550	7	5	and	and	CCONJ
ejpam-3550	7	6	several	several	ADJ
ejpam-3550	7	7	variations	variation	NOUN
ejpam-3550	7	8	of	of	ADP
ejpam-3550	7	9	the	the	DET
ejpam-3550	7	10	concept	concept	NOUN
ejpam-3550	7	11	have	have	AUX
ejpam-3550	7	12	been	be	AUX
ejpam-3550	7	13	widely	widely	ADV
ejpam-3550	7	14	studied	study	VERB
ejpam-3550	7	15	by	by	ADP
ejpam-3550	7	16	many	many	ADJ
ejpam-3550	7	17	researchers	researcher	NOUN
ejpam-3550	7	18	.	.	PUNCT
ejpam-3550	8	1	the	the	DET
ejpam-3550	8	2	two	two	NUM
ejpam-3550	8	3	books	book	NOUN
ejpam-3550	8	4	by	by	ADP
ejpam-3550	8	5	haynes	hayne	NOUN
ejpam-3550	8	6	et	et	PROPN
ejpam-3550	8	7	al	al	PROPN
ejpam-3550	8	8	.	.	PUNCT
ejpam-3550	9	1	[	[	X
ejpam-3550	9	2	3	3	NUM
ejpam-3550	9	3	,	,	PUNCT
ejpam-3550	9	4	4	4	NUM
ejpam-3550	9	5	]	]	PUNCT
ejpam-3550	9	6	give	give	VERB
ejpam-3550	9	7	an	an	DET
ejpam-3550	9	8	excellent	excellent	ADJ
ejpam-3550	9	9	treatment	treatment	NOUN
ejpam-3550	9	10	of	of	ADP
ejpam-3550	9	11	the	the	DET
ejpam-3550	9	12	standard	standard	ADJ
ejpam-3550	9	13	domination	domination	NOUN
ejpam-3550	9	14	concept	concept	NOUN
ejpam-3550	9	15	and	and	CCONJ
ejpam-3550	9	16	some	some	PRON
ejpam-3550	9	17	of	of	ADP
ejpam-3550	9	18	its	its	PRON
ejpam-3550	9	19	variants	variant	NOUN
ejpam-3550	9	20	.	.	PUNCT
ejpam-3550	10	1	recently	recently	ADV
ejpam-3550	10	2	,	,	PUNCT
ejpam-3550	10	3	natarajan	natarajan	PROPN
ejpam-3550	10	4	and	and	CCONJ
ejpam-3550	10	5	ayyaswamy	ayyaswamy	PROPN
ejpam-3550	11	1	[	[	X
ejpam-3550	11	2	6	6	NUM
ejpam-3550	11	3	]	]	PUNCT
ejpam-3550	11	4	introduced	introduce	VERB
ejpam-3550	11	5	and	and	CCONJ
ejpam-3550	11	6	studied	study	VERB
ejpam-3550	11	7	the	the	DET
ejpam-3550	11	8	concept	concept	NOUN
ejpam-3550	11	9	of	of	ADP
ejpam-3550	11	10	hop	hop	NOUN
ejpam-3550	11	11	domination	domination	NOUN
ejpam-3550	11	12	in	in	ADP
ejpam-3550	11	13	a	a	DET
ejpam-3550	11	14	graph	graph	NOUN
ejpam-3550	11	15	.	.	PUNCT
ejpam-3550	12	1	in	in	ADP
ejpam-3550	12	2	another	another	DET
ejpam-3550	12	3	study	study	NOUN
ejpam-3550	12	4	,	,	PUNCT
ejpam-3550	12	5	ayyaswamy	ayyaswamy	PROPN
ejpam-3550	12	6	et	et	PROPN
ejpam-3550	12	7	al	al	PROPN
ejpam-3550	12	8	.	.	PUNCT
ejpam-3550	13	1	[	[	X
ejpam-3550	13	2	2	2	NUM
ejpam-3550	13	3	]	]	PUNCT
ejpam-3550	13	4	investigated	investigate	VERB
ejpam-3550	13	5	the	the	DET
ejpam-3550	13	6	same	same	ADJ
ejpam-3550	13	7	concept	concept	NOUN
ejpam-3550	13	8	and	and	CCONJ
ejpam-3550	13	9	gave	give	VERB
ejpam-3550	13	10	bounds	bound	NOUN
ejpam-3550	13	11	of	of	ADP
ejpam-3550	13	12	the	the	DET
ejpam-3550	13	13	hop	hop	NOUN
ejpam-3550	13	14	domination	domination	NOUN
ejpam-3550	13	15	number	number	NOUN
ejpam-3550	13	16	of	of	ADP
ejpam-3550	13	17	some	some	DET
ejpam-3550	13	18	graphs	graph	NOUN
ejpam-3550	13	19	.	.	PUNCT
ejpam-3550	14	1	henning	henning	NOUN
ejpam-3550	14	2	and	and	CCONJ
ejpam-3550	14	3	rad	rad	NOUN
ejpam-3550	15	1	[	[	X
ejpam-3550	15	2	5	5	NUM
ejpam-3550	15	3	]	]	PUNCT
ejpam-3550	15	4	also	also	ADV
ejpam-3550	15	5	studied	study	VERB
ejpam-3550	15	6	the	the	DET
ejpam-3550	15	7	concept	concept	NOUN
ejpam-3550	15	8	and	and	CCONJ
ejpam-3550	15	9	answered	answer	VERB
ejpam-3550	15	10	a	a	DET
ejpam-3550	15	11	question	question	NOUN
ejpam-3550	15	12	posed	pose	VERB
ejpam-3550	15	13	by	by	ADP
ejpam-3550	15	14	ayyaswamy	ayyaswamy	ADJ
ejpam-3550	15	15	and	and	CCONJ
ejpam-3550	15	16	natarajan	natarajan	PROPN
ejpam-3550	15	17	in	in	ADP
ejpam-3550	15	18	[	[	X
ejpam-3550	15	19	6	6	NUM
ejpam-3550	15	20	]	]	PUNCT
ejpam-3550	15	21	.	.	PUNCT
ejpam-3550	16	1	they	they	PRON
ejpam-3550	16	2	presented	present	VERB
ejpam-3550	16	3	probabilistic	probabilistic	ADJ
ejpam-3550	16	4	upper	upper	ADJ
ejpam-3550	16	5	bounds	bound	NOUN
ejpam-3550	16	6	for	for	ADP
ejpam-3550	16	7	the	the	DET
ejpam-3550	16	8	hop	hop	NOUN
ejpam-3550	16	9	domination	domination	NOUN
ejpam-3550	16	10	number	number	NOUN
ejpam-3550	16	11	and	and	CCONJ
ejpam-3550	16	12	showed	show	VERB
ejpam-3550	16	13	that	that	SCONJ
ejpam-3550	16	14	the	the	DET
ejpam-3550	16	15	decision	decision	NOUN
ejpam-3550	16	16	problems	problem	NOUN
ejpam-3550	16	17	for	for	ADP
ejpam-3550	16	18	the	the	DET
ejpam-3550	16	19	2	2	NUM
ejpam-3550	16	20	-	-	PUNCT
ejpam-3550	16	21	step	step	NOUN
ejpam-3550	16	22	dominating	dominating	NOUN
ejpam-3550	16	23	set	set	NOUN
ejpam-3550	16	24	and	and	CCONJ
ejpam-3550	16	25	hop	hop	NOUN
ejpam-3550	16	26	dominating	dominating	NOUN
ejpam-3550	16	27	set	set	NOUN
ejpam-3550	16	28	problems	problem	NOUN
ejpam-3550	16	29	are	be	AUX
ejpam-3550	16	30	np	np	INTJ
ejpam-3550	16	31	-	-	NOUN
ejpam-3550	16	32	complete	complete	ADJ
ejpam-3550	16	33	for	for	ADP
ejpam-3550	16	34	planar	planar	ADJ
ejpam-3550	16	35	bipartite	bipartite	ADJ
ejpam-3550	16	36	graphs	graph	NOUN
ejpam-3550	16	37	and	and	CCONJ
ejpam-3550	16	38	planar	planar	ADJ
ejpam-3550	16	39	chordal	chordal	ADJ
ejpam-3550	16	40	graphs	graph	NOUN
ejpam-3550	16	41	.	.	PUNCT
ejpam-3550	17	1	pabilona	pabilona	NOUN
ejpam-3550	17	2	and	and	CCONJ
ejpam-3550	17	3	rara	rara	NOUN
ejpam-3550	17	4	[	[	X
ejpam-3550	17	5	7	7	NUM
ejpam-3550	17	6	]	]	PUNCT
ejpam-3550	17	7	considered	consider	VERB
ejpam-3550	17	8	the	the	DET
ejpam-3550	17	9	variant	variant	NOUN
ejpam-3550	17	10	called	call	VERB
ejpam-3550	17	11	connected	connected	ADJ
ejpam-3550	17	12	hop	hop	NOUN
ejpam-3550	17	13	domination	domination	NOUN
ejpam-3550	17	14	and	and	CCONJ
ejpam-3550	17	15	studied	study	VERB
ejpam-3550	17	16	it	it	PRON
ejpam-3550	17	17	in	in	ADP
ejpam-3550	17	18	graphs	graph	NOUN
ejpam-3550	17	19	under	under	ADP
ejpam-3550	17	20	some	some	DET
ejpam-3550	17	21	binary	binary	ADJ
ejpam-3550	17	22	operations	operation	NOUN
ejpam-3550	17	23	.	.	PUNCT
ejpam-3550	18	1	∗corresponding	∗corresponde	VERB
ejpam-3550	18	2	author	author	NOUN
ejpam-3550	18	3	.	.	PUNCT
ejpam-3550	19	1	doi	doi	NOUN
ejpam-3550	19	2	:	:	PUNCT
ejpam-3550	19	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3550	https://doi.org/10.29020/nybg.ejpam.v12i4.3550	PROPN
ejpam-3550	19	4	email	email	NOUN
ejpam-3550	19	5	addresses	address	NOUN
ejpam-3550	19	6	:	:	PUNCT
ejpam-3550	19	7	serge	serge	PROPN
ejpam-3550	19	8	canoy@yahoo.com	canoy@yahoo.com	X
ejpam-3550	20	1	(	(	PUNCT
ejpam-3550	20	2	s.	s.	PROPN
ejpam-3550	20	3	canoy	canoy	PROPN
ejpam-3550	20	4	jr	jr	PROPN
ejpam-3550	20	5	.	.	PROPN
ejpam-3550	20	6	)	)	PUNCT
ejpam-3550	20	7	,	,	PUNCT
ejpam-3550	20	8	reynaldo.mollejon@g.msuiit.edu.ph	reynaldo.mollejon@g.msuiit.edu.ph	PROPN
ejpam-3550	20	9	(	(	PUNCT
ejpam-3550	20	10	r.	r.	PROPN
ejpam-3550	20	11	mollejon),jgcanoy@mail.com	mollejon),jgcanoy@mail.com	PROPN
ejpam-3550	20	12	(	(	PUNCT
ejpam-3550	20	13	jg	jg	PROPN
ejpam-3550	20	14	.	.	PROPN
ejpam-3550	20	15	canoy	canoy	PROPN
ejpam-3550	20	16	)	)	PUNCT
ejpam-3550	20	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3550	21	1	1455	1455	NUM
ejpam-3550	21	2	c	c	X
ejpam-3550	21	3	©	©	PROPN
ejpam-3550	21	4	2019	2019	NUM
ejpam-3550	21	5	ejpam	ejpam	NOUN
ejpam-3550	21	6	all	all	DET
ejpam-3550	21	7	rights	right	NOUN
ejpam-3550	21	8	reserved	reserve	VERB
ejpam-3550	21	9	.	.	PUNCT
ejpam-3550	22	1	s.	s.	PROPN
ejpam-3550	22	2	canoy	canoy	PROPN
ejpam-3550	22	3	jr	jr	PROPN
ejpam-3550	22	4	.	.	PROPN
ejpam-3550	22	5	,	,	PUNCT
ejpam-3550	22	6	r.	r.	PROPN
ejpam-3550	22	7	mollejon	mollejon	NOUN
ejpam-3550	22	8	,	,	PUNCT
ejpam-3550	22	9	jg	jg	PROPN
ejpam-3550	22	10	.	.	PROPN
ejpam-3550	22	11	canoy	canoy	PROPN
ejpam-3550	22	12	/	/	SYM
ejpam-3550	22	13	eur	eur	PROPN
ejpam-3550	22	14	.	.	PUNCT
ejpam-3550	23	1	j.	j.	PROPN
ejpam-3550	23	2	pure	pure	PROPN
ejpam-3550	23	3	appl	appl	PROPN
ejpam-3550	23	4	.	.	PROPN
ejpam-3550	23	5	math	math	PROPN
ejpam-3550	23	6	,	,	PUNCT
ejpam-3550	23	7	12	12	NUM
ejpam-3550	23	8	(	(	PUNCT
ejpam-3550	23	9	4	4	NUM
ejpam-3550	23	10	)	)	PUNCT
ejpam-3550	23	11	(	(	PUNCT
ejpam-3550	23	12	2019	2019	NUM
ejpam-3550	23	13	)	)	PUNCT
ejpam-3550	23	14	,	,	PUNCT
ejpam-3550	23	15	1455	1455	NUM
ejpam-3550	23	16	-	-	SYM
ejpam-3550	23	17	1463	1463	NUM
ejpam-3550	23	18	1456	1456	NUM
ejpam-3550	23	19	let	let	VERB
ejpam-3550	23	20	g	g	NOUN
ejpam-3550	23	21	=	=	SYM
ejpam-3550	23	22	(	(	PUNCT
ejpam-3550	23	23	v	v	NOUN
ejpam-3550	23	24	(	(	PUNCT
ejpam-3550	23	25	g	g	NOUN
ejpam-3550	23	26	)	)	PUNCT
ejpam-3550	23	27	,	,	PUNCT
ejpam-3550	23	28	e(g	e(g	PROPN
ejpam-3550	23	29	)	)	PUNCT
ejpam-3550	23	30	)	)	PUNCT
ejpam-3550	23	31	be	be	AUX
ejpam-3550	23	32	a	a	DET
ejpam-3550	23	33	simple	simple	ADJ
ejpam-3550	23	34	graph	graph	NOUN
ejpam-3550	23	35	.	.	PUNCT
ejpam-3550	24	1	the	the	DET
ejpam-3550	24	2	open	open	ADJ
ejpam-3550	24	3	neighbourhood	neighbourhood	NOUN
ejpam-3550	24	4	of	of	ADP
ejpam-3550	24	5	a	a	DET
ejpam-3550	24	6	vertex	vertex	NOUN
ejpam-3550	24	7	v	v	NOUN
ejpam-3550	24	8	of	of	ADP
ejpam-3550	24	9	g	g	PROPN
ejpam-3550	24	10	is	be	AUX
ejpam-3550	24	11	the	the	DET
ejpam-3550	24	12	set	set	NOUN
ejpam-3550	24	13	ng(v	ng(v	PUNCT
ejpam-3550	24	14	)	)	PUNCT
ejpam-3550	24	15	=	=	SYM
ejpam-3550	25	1	{	{	PUNCT
ejpam-3550	25	2	u	u	NOUN
ejpam-3550	25	3	∈	∈	PROPN
ejpam-3550	25	4	v	v	NOUN
ejpam-3550	25	5	(	(	PUNCT
ejpam-3550	25	6	g	g	NOUN
ejpam-3550	25	7	)	)	PUNCT
ejpam-3550	25	8	:	:	PUNCT
ejpam-3550	25	9	uv	uv	PROPN
ejpam-3550	25	10	∈	∈	PROPN
ejpam-3550	25	11	e(g	e(g	PROPN
ejpam-3550	25	12	)	)	PUNCT
ejpam-3550	25	13	}	}	PUNCT
ejpam-3550	25	14	and	and	CCONJ
ejpam-3550	25	15	its	its	PRON
ejpam-3550	25	16	closed	closed	ADJ
ejpam-3550	25	17	neighbourhood	neighbourhood	NOUN
ejpam-3550	25	18	is	be	AUX
ejpam-3550	25	19	the	the	DET
ejpam-3550	25	20	set	set	NOUN
ejpam-3550	25	21	ng[v	ng[v	NOUN
ejpam-3550	25	22	]	]	X
ejpam-3550	25	23	=	=	SYM
ejpam-3550	25	24	ng(v	ng(v	X
ejpam-3550	25	25	)	)	PUNCT
ejpam-3550	25	26	∪	∪	ADP
ejpam-3550	25	27	{	{	PUNCT
ejpam-3550	25	28	v	v	NOUN
ejpam-3550	25	29	}	}	PUNCT
ejpam-3550	25	30	.	.	PUNCT
ejpam-3550	26	1	the	the	DET
ejpam-3550	26	2	degree	degree	NOUN
ejpam-3550	26	3	of	of	ADP
ejpam-3550	26	4	v	v	NOUN
ejpam-3550	26	5	,	,	PUNCT
ejpam-3550	26	6	denoted	denote	VERB
ejpam-3550	26	7	by	by	ADP
ejpam-3550	26	8	degg(v	degg(v	PROPN
ejpam-3550	26	9	)	)	PUNCT
ejpam-3550	26	10	,	,	PUNCT
ejpam-3550	26	11	is	be	AUX
ejpam-3550	26	12	equal	equal	ADJ
ejpam-3550	26	13	to	to	ADP
ejpam-3550	26	14	|ng(v)|	|ng(v)|	NOUN
ejpam-3550	26	15	and	and	CCONJ
ejpam-3550	26	16	the	the	DET
ejpam-3550	26	17	maximum	maximum	ADJ
ejpam-3550	26	18	degree	degree	NOUN
ejpam-3550	26	19	of	of	ADP
ejpam-3550	26	20	g	g	NOUN
ejpam-3550	26	21	,	,	PUNCT
ejpam-3550	26	22	denoted	denote	VERB
ejpam-3550	26	23	by	by	ADP
ejpam-3550	26	24	∆(g	∆(g	PROPN
ejpam-3550	26	25	)	)	PUNCT
ejpam-3550	26	26	,	,	PUNCT
ejpam-3550	26	27	is	be	AUX
ejpam-3550	26	28	equal	equal	ADJ
ejpam-3550	26	29	to	to	ADP
ejpam-3550	26	30	max{degg(v	max{degg(v	NOUN
ejpam-3550	26	31	)	)	PUNCT
ejpam-3550	26	32	:	:	PUNCT
ejpam-3550	26	33	v	v	X
ejpam-3550	26	34	∈	∈	PROPN
ejpam-3550	26	35	v	v	NOUN
ejpam-3550	26	36	(	(	PUNCT
ejpam-3550	26	37	g	g	NOUN
ejpam-3550	26	38	)	)	PUNCT
ejpam-3550	26	39	}	}	PUNCT
ejpam-3550	26	40	.	.	PUNCT
ejpam-3550	27	1	the	the	DET
ejpam-3550	27	2	open	open	ADJ
ejpam-3550	27	3	hop	hop	NOUN
ejpam-3550	27	4	neighbourhood	neighbourhood	NOUN
ejpam-3550	27	5	of	of	ADP
ejpam-3550	27	6	vertex	vertex	NOUN
ejpam-3550	27	7	v	v	NOUN
ejpam-3550	27	8	is	be	AUX
ejpam-3550	27	9	the	the	DET
ejpam-3550	27	10	set	set	NOUN
ejpam-3550	27	11	ng(v	ng(v	PUNCT
ejpam-3550	27	12	,	,	PUNCT
ejpam-3550	27	13	2	2	X
ejpam-3550	27	14	)	)	PUNCT
ejpam-3550	27	15	=	=	PRON
ejpam-3550	27	16	{	{	PUNCT
ejpam-3550	27	17	w	w	NOUN
ejpam-3550	27	18	∈	∈	PROPN
ejpam-3550	27	19	v	v	ADP
ejpam-3550	27	20	(	(	PUNCT
ejpam-3550	27	21	g	g	NOUN
ejpam-3550	27	22	)	)	PUNCT
ejpam-3550	27	23	:	:	PUNCT
ejpam-3550	27	24	dg(v	dg(v	X
ejpam-3550	27	25	,	,	PUNCT
ejpam-3550	27	26	w	w	NOUN
ejpam-3550	27	27	)	)	PUNCT
ejpam-3550	27	28	=	=	SYM
ejpam-3550	27	29	2	2	NUM
ejpam-3550	27	30	}	}	PUNCT
ejpam-3550	27	31	,	,	PUNCT
ejpam-3550	27	32	where	where	SCONJ
ejpam-3550	27	33	dg(v	dg(v	X
ejpam-3550	27	34	,	,	PUNCT
ejpam-3550	27	35	w	w	NOUN
ejpam-3550	27	36	)	)	PUNCT
ejpam-3550	27	37	denotes	denote	VERB
ejpam-3550	27	38	the	the	DET
ejpam-3550	27	39	distance	distance	NOUN
ejpam-3550	27	40	between	between	ADP
ejpam-3550	27	41	v	v	NOUN
ejpam-3550	27	42	and	and	CCONJ
ejpam-3550	27	43	w	w	PROPN
ejpam-3550	27	44	(	(	PUNCT
ejpam-3550	27	45	the	the	DET
ejpam-3550	27	46	length	length	NOUN
ejpam-3550	27	47	of	of	ADP
ejpam-3550	27	48	a	a	DET
ejpam-3550	27	49	shortest	short	ADJ
ejpam-3550	27	50	path	path	NOUN
ejpam-3550	27	51	joining	join	VERB
ejpam-3550	27	52	v	v	ADP
ejpam-3550	27	53	and	and	CCONJ
ejpam-3550	27	54	w	w	NOUN
ejpam-3550	27	55	)	)	PUNCT
ejpam-3550	27	56	.	.	PUNCT
ejpam-3550	28	1	the	the	DET
ejpam-3550	28	2	open	open	ADJ
ejpam-3550	28	3	neighbourhood	neighbourhood	NOUN
ejpam-3550	28	4	of	of	ADP
ejpam-3550	28	5	a	a	DET
ejpam-3550	28	6	subset	subset	NOUN
ejpam-3550	28	7	s	s	NOUN
ejpam-3550	28	8	of	of	ADP
ejpam-3550	28	9	v	v	NOUN
ejpam-3550	28	10	(	(	PUNCT
ejpam-3550	28	11	g	g	NOUN
ejpam-3550	28	12	)	)	PUNCT
ejpam-3550	28	13	is	be	AUX
ejpam-3550	28	14	the	the	DET
ejpam-3550	28	15	set	set	NOUN
ejpam-3550	28	16	ng(s	ng(s	NOUN
ejpam-3550	28	17	)	)	PUNCT
ejpam-3550	28	18	=	=	SYM
ejpam-3550	28	19	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-3550	28	20	)	)	PUNCT
ejpam-3550	28	21	and	and	CCONJ
ejpam-3550	28	22	its	its	PRON
ejpam-3550	28	23	closed	closed	ADJ
ejpam-3550	28	24	neighbourhood	neighbourhood	NOUN
ejpam-3550	28	25	is	be	AUX
ejpam-3550	28	26	the	the	DET
ejpam-3550	28	27	set	set	VERB
ejpam-3550	28	28	ng[s	ng[	NOUN
ejpam-3550	28	29	]	]	PUNCT
ejpam-3550	28	30	=	=	SYM
ejpam-3550	28	31	ng(s	ng(s	X
ejpam-3550	28	32	)	)	PUNCT
ejpam-3550	28	33	∪	∪	ADP
ejpam-3550	28	34	s.	s.	PROPN
ejpam-3550	28	35	a	a	DET
ejpam-3550	28	36	set	set	NOUN
ejpam-3550	28	37	s	s	PROPN
ejpam-3550	28	38	⊆	⊆	NUM
ejpam-3550	28	39	v	v	NOUN
ejpam-3550	28	40	(	(	PUNCT
ejpam-3550	28	41	g	g	NOUN
ejpam-3550	28	42	)	)	PUNCT
ejpam-3550	28	43	is	be	AUX
ejpam-3550	28	44	a	a	DET
ejpam-3550	28	45	dominating	dominating	NOUN
ejpam-3550	28	46	set	set	NOUN
ejpam-3550	28	47	(	(	PUNCT
ejpam-3550	28	48	resp	resp	NOUN
ejpam-3550	28	49	.	.	PUNCT
ejpam-3550	29	1	total	total	ADJ
ejpam-3550	29	2	dominating	dominating	NOUN
ejpam-3550	29	3	set	set	NOUN
ejpam-3550	29	4	)	)	PUNCT
ejpam-3550	29	5	of	of	ADP
ejpam-3550	29	6	g	g	PROPN
ejpam-3550	29	7	if	if	SCONJ
ejpam-3550	29	8	ng[s	ng[	NOUN
ejpam-3550	29	9	]	]	PUNCT
ejpam-3550	29	10	=	=	SYM
ejpam-3550	29	11	v	v	X
ejpam-3550	29	12	(	(	PUNCT
ejpam-3550	29	13	g	g	NOUN
ejpam-3550	29	14	)	)	PUNCT
ejpam-3550	29	15	(	(	PUNCT
ejpam-3550	29	16	resp	resp	NOUN
ejpam-3550	29	17	.	.	PUNCT
ejpam-3550	29	18	ng(s	ng(s	NUM
ejpam-3550	29	19	)	)	PUNCT
ejpam-3550	30	1	=	=	SYM
ejpam-3550	30	2	v	v	X
ejpam-3550	30	3	(	(	PUNCT
ejpam-3550	30	4	g	g	NOUN
ejpam-3550	30	5	)	)	PUNCT
ejpam-3550	30	6	)	)	PUNCT
ejpam-3550	30	7	.	.	PUNCT
ejpam-3550	31	1	the	the	DET
ejpam-3550	31	2	smallest	small	ADJ
ejpam-3550	31	3	cardinality	cardinality	NOUN
ejpam-3550	31	4	of	of	ADP
ejpam-3550	31	5	a	a	DET
ejpam-3550	31	6	dominating	dominating	NOUN
ejpam-3550	31	7	(	(	PUNCT
ejpam-3550	31	8	resp	resp	NOUN
ejpam-3550	31	9	.	.	PUNCT
ejpam-3550	32	1	total	total	ADJ
ejpam-3550	32	2	dominating	dominating	NOUN
ejpam-3550	32	3	)	)	PUNCT
ejpam-3550	32	4	set	set	NOUN
ejpam-3550	32	5	of	of	ADP
ejpam-3550	32	6	g	g	NOUN
ejpam-3550	32	7	,	,	PUNCT
ejpam-3550	32	8	denoted	denote	VERB
ejpam-3550	32	9	by	by	ADP
ejpam-3550	32	10	γ(g	γ(g	PROPN
ejpam-3550	32	11	)	)	PUNCT
ejpam-3550	32	12	(	(	PUNCT
ejpam-3550	32	13	resp	resp	NOUN
ejpam-3550	32	14	.	.	PUNCT
ejpam-3550	32	15	γt(g	γt(g	PUNCT
ejpam-3550	32	16	)	)	PUNCT
ejpam-3550	32	17	)	)	PUNCT
ejpam-3550	32	18	,	,	PUNCT
ejpam-3550	32	19	is	be	AUX
ejpam-3550	32	20	called	call	VERB
ejpam-3550	32	21	the	the	DET
ejpam-3550	32	22	domination	domination	NOUN
ejpam-3550	32	23	number	number	NOUN
ejpam-3550	32	24	(	(	PUNCT
ejpam-3550	32	25	resp	resp	NOUN
ejpam-3550	32	26	.	.	PUNCT
ejpam-3550	33	1	total	total	ADJ
ejpam-3550	33	2	domination	domination	NOUN
ejpam-3550	33	3	number	number	NOUN
ejpam-3550	33	4	)	)	PUNCT
ejpam-3550	33	5	of	of	ADP
ejpam-3550	33	6	g.	g.	PROPN
ejpam-3550	33	7	a	a	DET
ejpam-3550	33	8	dominating	dominating	NOUN
ejpam-3550	33	9	(	(	PUNCT
ejpam-3550	33	10	resp	resp	NOUN
ejpam-3550	33	11	.	.	PUNCT
ejpam-3550	34	1	total	total	ADJ
ejpam-3550	34	2	dominating	dominating	NOUN
ejpam-3550	34	3	)	)	PUNCT
ejpam-3550	34	4	set	set	NOUN
ejpam-3550	34	5	s	s	PRON
ejpam-3550	34	6	of	of	ADP
ejpam-3550	34	7	g	g	NOUN
ejpam-3550	34	8	with	with	ADP
ejpam-3550	34	9	|s|	|s|	PROPN
ejpam-3550	34	10	=	=	SYM
ejpam-3550	34	11	γ(g	γ(g	PROPN
ejpam-3550	34	12	)	)	PUNCT
ejpam-3550	34	13	(	(	PUNCT
ejpam-3550	34	14	resp	resp	NOUN
ejpam-3550	34	15	.	.	PUNCT
ejpam-3550	35	1	|s|	|s|	PROPN
ejpam-3550	35	2	=	=	SYM
ejpam-3550	35	3	γt(g	γt(g	NUM
ejpam-3550	35	4	)	)	PUNCT
ejpam-3550	35	5	)	)	PUNCT
ejpam-3550	35	6	,	,	PUNCT
ejpam-3550	35	7	is	be	AUX
ejpam-3550	35	8	called	call	VERB
ejpam-3550	35	9	a	a	DET
ejpam-3550	35	10	γ	γ	NOUN
ejpam-3550	35	11	-	-	PUNCT
ejpam-3550	35	12	set	set	ADJ
ejpam-3550	35	13	(	(	PUNCT
ejpam-3550	35	14	resp	resp	NOUN
ejpam-3550	35	15	.	.	PUNCT
ejpam-3550	36	1	γt	γt	NOUN
ejpam-3550	36	2	-	-	PUNCT
ejpam-3550	36	3	set	set	NOUN
ejpam-3550	36	4	)	)	PUNCT
ejpam-3550	36	5	of	of	ADP
ejpam-3550	36	6	g.	g.	PROPN
ejpam-3550	37	1	it	it	PRON
ejpam-3550	37	2	should	should	AUX
ejpam-3550	37	3	be	be	AUX
ejpam-3550	37	4	noted	note	VERB
ejpam-3550	37	5	that	that	SCONJ
ejpam-3550	37	6	only	only	ADJ
ejpam-3550	37	7	graphs	graph	NOUN
ejpam-3550	37	8	without	without	ADP
ejpam-3550	37	9	isolated	isolated	ADJ
ejpam-3550	37	10	vertices	vertex	NOUN
ejpam-3550	37	11	admit	admit	VERB
ejpam-3550	37	12	total	total	ADJ
ejpam-3550	37	13	dominating	dominating	NOUN
ejpam-3550	37	14	sets	set	NOUN
ejpam-3550	37	15	.	.	PUNCT
ejpam-3550	38	1	a	a	DET
ejpam-3550	38	2	set	set	NOUN
ejpam-3550	38	3	s	s	NOUN
ejpam-3550	38	4	⊆	⊆	NUM
ejpam-3550	38	5	v	v	NOUN
ejpam-3550	38	6	(	(	PUNCT
ejpam-3550	38	7	g	g	NOUN
ejpam-3550	38	8	)	)	PUNCT
ejpam-3550	38	9	is	be	AUX
ejpam-3550	38	10	a	a	DET
ejpam-3550	38	11	hop	hop	NOUN
ejpam-3550	38	12	dominating	dominating	NOUN
ejpam-3550	38	13	set	set	NOUN
ejpam-3550	38	14	(	(	PUNCT
ejpam-3550	38	15	total	total	ADJ
ejpam-3550	38	16	hop	hop	NOUN
ejpam-3550	38	17	dominating	dominating	NOUN
ejpam-3550	38	18	set	set	NOUN
ejpam-3550	38	19	)	)	PUNCT
ejpam-3550	38	20	of	of	ADP
ejpam-3550	38	21	g	g	PROPN
ejpam-3550	38	22	if	if	SCONJ
ejpam-3550	38	23	for	for	ADP
ejpam-3550	38	24	each	each	DET
ejpam-3550	38	25	x	x	SYM
ejpam-3550	38	26	∈	∈	PROPN
ejpam-3550	38	27	v	v	ADP
ejpam-3550	38	28	(	(	PUNCT
ejpam-3550	38	29	g	g	NOUN
ejpam-3550	38	30	)	)	PUNCT
ejpam-3550	38	31	\	\	PROPN
ejpam-3550	39	1	s	s	PART
ejpam-3550	39	2	(	(	PUNCT
ejpam-3550	39	3	resp	resp	NOUN
ejpam-3550	39	4	.	.	PUNCT
ejpam-3550	40	1	x	x	PUNCT
ejpam-3550	40	2	∈	∈	NOUN
ejpam-3550	40	3	v	v	ADP
ejpam-3550	40	4	(	(	PUNCT
ejpam-3550	40	5	g	g	NOUN
ejpam-3550	40	6	)	)	PUNCT
ejpam-3550	40	7	)	)	PUNCT
ejpam-3550	40	8	,	,	PUNCT
ejpam-3550	40	9	there	there	PRON
ejpam-3550	40	10	exists	exist	VERB
ejpam-3550	40	11	z	z	PROPN
ejpam-3550	40	12	∈	∈	PROPN
ejpam-3550	40	13	s	s	VERB
ejpam-3550	41	1	such	such	ADJ
ejpam-3550	41	2	that	that	PRON
ejpam-3550	41	3	dg(x	dg(x	NOUN
ejpam-3550	41	4	,	,	PUNCT
ejpam-3550	41	5	z	z	NOUN
ejpam-3550	41	6	)	)	PUNCT
ejpam-3550	41	7	=	=	SYM
ejpam-3550	41	8	2	2	X
ejpam-3550	41	9	.	.	X
ejpam-3550	41	10	the	the	DET
ejpam-3550	41	11	smallest	small	ADJ
ejpam-3550	41	12	cardinality	cardinality	NOUN
ejpam-3550	41	13	of	of	ADP
ejpam-3550	41	14	a	a	DET
ejpam-3550	41	15	hop	hop	NOUN
ejpam-3550	41	16	dominating	dominating	NOUN
ejpam-3550	41	17	(	(	PUNCT
ejpam-3550	41	18	total	total	ADJ
ejpam-3550	41	19	hop	hop	NOUN
ejpam-3550	41	20	dominating	dominating	NOUN
ejpam-3550	41	21	)	)	PUNCT
ejpam-3550	41	22	set	set	NOUN
ejpam-3550	41	23	of	of	ADP
ejpam-3550	41	24	g	g	NOUN
ejpam-3550	41	25	,	,	PUNCT
ejpam-3550	41	26	denoted	denote	VERB
ejpam-3550	41	27	by	by	ADP
ejpam-3550	41	28	γh(g	γh(g	NOUN
ejpam-3550	41	29	)	)	PUNCT
ejpam-3550	41	30	(	(	PUNCT
ejpam-3550	41	31	resp	resp	NOUN
ejpam-3550	41	32	.	.	PUNCT
ejpam-3550	41	33	γth(g	γth(g	NOUN
ejpam-3550	41	34	)	)	PUNCT
ejpam-3550	41	35	)	)	PUNCT
ejpam-3550	41	36	,	,	PUNCT
ejpam-3550	41	37	is	be	AUX
ejpam-3550	41	38	called	call	VERB
ejpam-3550	41	39	the	the	DET
ejpam-3550	41	40	hop	hop	NOUN
ejpam-3550	41	41	domination	domination	NOUN
ejpam-3550	41	42	number	number	NOUN
ejpam-3550	41	43	(	(	PUNCT
ejpam-3550	41	44	total	total	ADJ
ejpam-3550	41	45	hop	hop	NOUN
ejpam-3550	41	46	domination	domination	NOUN
ejpam-3550	41	47	number	number	NOUN
ejpam-3550	41	48	)	)	PUNCT
ejpam-3550	41	49	of	of	ADP
ejpam-3550	41	50	g.	g.	PROPN
ejpam-3550	41	51	a	a	DET
ejpam-3550	41	52	hop	hop	NOUN
ejpam-3550	41	53	dominating	dominating	NOUN
ejpam-3550	41	54	(	(	PUNCT
ejpam-3550	41	55	total	total	ADJ
ejpam-3550	41	56	hop	hop	NOUN
ejpam-3550	41	57	dominating	dominating	NOUN
ejpam-3550	41	58	)	)	PUNCT
ejpam-3550	41	59	set	set	NOUN
ejpam-3550	41	60	s	s	PRON
ejpam-3550	41	61	of	of	ADP
ejpam-3550	41	62	g	g	NOUN
ejpam-3550	41	63	with	with	ADP
ejpam-3550	41	64	|s|	|s|	NOUN
ejpam-3550	41	65	=	=	NOUN
ejpam-3550	41	66	γh(g	γh(g	NOUN
ejpam-3550	41	67	)	)	PUNCT
ejpam-3550	41	68	(	(	PUNCT
ejpam-3550	41	69	resp	resp	NOUN
ejpam-3550	41	70	.	.	PUNCT
ejpam-3550	41	71	|s|	|s|	PROPN
ejpam-3550	41	72	=	=	PUNCT
ejpam-3550	41	73	γth(g	γth(g	NOUN
ejpam-3550	41	74	)	)	PUNCT
ejpam-3550	41	75	)	)	PUNCT
ejpam-3550	41	76	is	be	AUX
ejpam-3550	41	77	called	call	VERB
ejpam-3550	41	78	a	a	DET
ejpam-3550	41	79	γh	γh	ADV
ejpam-3550	41	80	-	-	PUNCT
ejpam-3550	41	81	set	set	VERB
ejpam-3550	41	82	(	(	PUNCT
ejpam-3550	41	83	resp	resp	NOUN
ejpam-3550	41	84	.	.	PUNCT
ejpam-3550	42	1	γth	γth	ADJ
ejpam-3550	42	2	-	-	PUNCT
ejpam-3550	42	3	set	set	NOUN
ejpam-3550	42	4	)	)	PUNCT
ejpam-3550	42	5	of	of	ADP
ejpam-3550	42	6	g.	g.	PROPN
ejpam-3550	42	7	a	a	DET
ejpam-3550	42	8	set	set	NOUN
ejpam-3550	42	9	s	s	PROPN
ejpam-3550	42	10	⊆	⊆	NUM
ejpam-3550	42	11	v	v	NOUN
ejpam-3550	42	12	(	(	PUNCT
ejpam-3550	42	13	g	g	NOUN
ejpam-3550	42	14	)	)	PUNCT
ejpam-3550	42	15	is	be	AUX
ejpam-3550	42	16	a	a	DET
ejpam-3550	42	17	(	(	PUNCT
ejpam-3550	42	18	1	1	NUM
ejpam-3550	42	19	,	,	PUNCT
ejpam-3550	42	20	2)∗-dominating	2)∗-dominate	VERB
ejpam-3550	42	21	set	set	NOUN
ejpam-3550	42	22	(	(	PUNCT
ejpam-3550	42	23	resp	resp	NOUN
ejpam-3550	42	24	.	.	PUNCT
ejpam-3550	43	1	(	(	PUNCT
ejpam-3550	43	2	1	1	NUM
ejpam-3550	43	3	,	,	PUNCT
ejpam-3550	43	4	2)∗-total	2)∗-total	ADJ
ejpam-3550	43	5	dominating	dominating	NOUN
ejpam-3550	43	6	set	set	NOUN
ejpam-3550	43	7	)	)	PUNCT
ejpam-3550	43	8	of	of	ADP
ejpam-3550	43	9	g	g	PROPN
ejpam-3550	43	10	if	if	SCONJ
ejpam-3550	43	11	it	it	PRON
ejpam-3550	43	12	is	be	AUX
ejpam-3550	43	13	a	a	DET
ejpam-3550	43	14	dominating	dominating	NOUN
ejpam-3550	43	15	(	(	PUNCT
ejpam-3550	43	16	resp	resp	NOUN
ejpam-3550	43	17	.	.	PUNCT
ejpam-3550	44	1	total	total	ADJ
ejpam-3550	44	2	dominating	dominating	NOUN
ejpam-3550	44	3	)	)	PUNCT
ejpam-3550	44	4	set	set	NOUN
ejpam-3550	44	5	of	of	ADP
ejpam-3550	44	6	g	g	PROPN
ejpam-3550	44	7	and	and	CCONJ
ejpam-3550	44	8	for	for	ADP
ejpam-3550	44	9	each	each	DET
ejpam-3550	44	10	x	x	SYM
ejpam-3550	44	11	∈	∈	PROPN
ejpam-3550	44	12	v	v	ADP
ejpam-3550	44	13	(	(	PUNCT
ejpam-3550	44	14	g	g	NOUN
ejpam-3550	44	15	)	)	PUNCT
ejpam-3550	44	16	\	\	PROPN
ejpam-3550	45	1	s	s	X
ejpam-3550	45	2	,	,	PUNCT
ejpam-3550	45	3	there	there	PRON
ejpam-3550	45	4	exists	exist	VERB
ejpam-3550	45	5	z	z	PROPN
ejpam-3550	45	6	∈	∈	PROPN
ejpam-3550	45	7	s	s	VERB
ejpam-3550	46	1	such	such	ADJ
ejpam-3550	46	2	that	that	PRON
ejpam-3550	46	3	dg(x	dg(x	NOUN
ejpam-3550	46	4	,	,	PUNCT
ejpam-3550	46	5	z	z	NOUN
ejpam-3550	46	6	)	)	PUNCT
ejpam-3550	46	7	=	=	SYM
ejpam-3550	46	8	2	2	X
ejpam-3550	46	9	.	.	X
ejpam-3550	46	10	the	the	DET
ejpam-3550	46	11	smallest	small	ADJ
ejpam-3550	46	12	cardinality	cardinality	NOUN
ejpam-3550	46	13	of	of	ADP
ejpam-3550	46	14	a	a	DET
ejpam-3550	46	15	(	(	PUNCT
ejpam-3550	46	16	1	1	NUM
ejpam-3550	46	17	,	,	PUNCT
ejpam-3550	46	18	2)∗-dominating	2)∗-dominating	NUM
ejpam-3550	46	19	(	(	PUNCT
ejpam-3550	46	20	resp	resp	NOUN
ejpam-3550	46	21	.	.	PUNCT
ejpam-3550	47	1	(	(	PUNCT
ejpam-3550	47	2	1	1	NUM
ejpam-3550	47	3	,	,	PUNCT
ejpam-3550	47	4	2)∗-total	2)∗-total	ADJ
ejpam-3550	47	5	dominating	dominating	NOUN
ejpam-3550	47	6	)	)	PUNCT
ejpam-3550	47	7	set	set	NOUN
ejpam-3550	47	8	of	of	ADP
ejpam-3550	47	9	g	g	NOUN
ejpam-3550	47	10	,	,	PUNCT
ejpam-3550	47	11	denoted	denote	VERB
ejpam-3550	47	12	by	by	ADP
ejpam-3550	47	13	γ∗1,2(g	γ∗1,2(g	NOUN
ejpam-3550	47	14	)	)	PUNCT
ejpam-3550	47	15	(	(	PUNCT
ejpam-3550	47	16	resp	resp	NOUN
ejpam-3550	47	17	.	.	PUNCT
ejpam-3550	48	1	γ∗t1,2(g	γ∗t1,2(g	NUM
ejpam-3550	48	2	)	)	PUNCT
ejpam-3550	48	3	)	)	PUNCT
ejpam-3550	48	4	,	,	PUNCT
ejpam-3550	48	5	is	be	AUX
ejpam-3550	48	6	called	call	VERB
ejpam-3550	48	7	the	the	DET
ejpam-3550	48	8	(	(	PUNCT
ejpam-3550	48	9	1	1	NUM
ejpam-3550	48	10	,	,	PUNCT
ejpam-3550	48	11	2)∗domination	2)∗domination	NUM
ejpam-3550	48	12	number	number	NOUN
ejpam-3550	48	13	(	(	PUNCT
ejpam-3550	48	14	resp	resp	NOUN
ejpam-3550	48	15	.	.	PUNCT
ejpam-3550	49	1	(	(	PUNCT
ejpam-3550	49	2	1	1	NUM
ejpam-3550	49	3	,	,	PUNCT
ejpam-3550	49	4	2)∗-total	2)∗-total	ADJ
ejpam-3550	49	5	domination	domination	NOUN
ejpam-3550	49	6	number	number	NOUN
ejpam-3550	49	7	)	)	PUNCT
ejpam-3550	49	8	of	of	ADP
ejpam-3550	49	9	g.	g.	PROPN
ejpam-3550	49	10	a	a	DET
ejpam-3550	49	11	(	(	PUNCT
ejpam-3550	49	12	1	1	NUM
ejpam-3550	49	13	,	,	PUNCT
ejpam-3550	49	14	2)∗-dominating	2)∗-dominating	NUM
ejpam-3550	49	15	(	(	PUNCT
ejpam-3550	49	16	resp	resp	NOUN
ejpam-3550	49	17	.	.	PUNCT
ejpam-3550	50	1	(	(	PUNCT
ejpam-3550	50	2	1	1	NUM
ejpam-3550	50	3	,	,	PUNCT
ejpam-3550	50	4	2)∗total	2)∗total	NUM
ejpam-3550	50	5	dominating	dominating	NOUN
ejpam-3550	50	6	)	)	PUNCT
ejpam-3550	50	7	set	set	VERB
ejpam-3550	50	8	s	s	PRON
ejpam-3550	50	9	with	with	ADP
ejpam-3550	50	10	|s|	|s|	PROPN
ejpam-3550	50	11	=	=	PUNCT
ejpam-3550	50	12	γ∗1,2(g	γ∗1,2(g	NOUN
ejpam-3550	50	13	)	)	PUNCT
ejpam-3550	50	14	(	(	PUNCT
ejpam-3550	50	15	resp	resp	NOUN
ejpam-3550	50	16	.	.	PUNCT
ejpam-3550	51	1	|s|	|s|	PROPN
ejpam-3550	51	2	=	=	SYM
ejpam-3550	51	3	γ∗t1,2(g	γ∗t1,2(g	PROPN
ejpam-3550	51	4	)	)	PUNCT
ejpam-3550	51	5	)	)	PUNCT
ejpam-3550	51	6	is	be	AUX
ejpam-3550	51	7	called	call	VERB
ejpam-3550	51	8	a	a	DET
ejpam-3550	51	9	γ∗1,2	γ∗1,2	NOUN
ejpam-3550	51	10	-	-	PUNCT
ejpam-3550	51	11	set	set	VERB
ejpam-3550	51	12	(	(	PUNCT
ejpam-3550	51	13	resp	resp	NOUN
ejpam-3550	51	14	.	.	PUNCT
ejpam-3550	52	1	γ∗t1,2	γ∗t1,2	ADJ
ejpam-3550	52	2	-	-	PUNCT
ejpam-3550	52	3	set	set	NOUN
ejpam-3550	52	4	)	)	PUNCT
ejpam-3550	52	5	of	of	ADP
ejpam-3550	52	6	g.	g.	PROPN
ejpam-3550	52	7	clearly	clearly	ADV
ejpam-3550	52	8	,	,	PUNCT
ejpam-3550	52	9	s	s	VERB
ejpam-3550	52	10	⊆	⊆	NUM
ejpam-3550	52	11	v	v	NOUN
ejpam-3550	52	12	(	(	PUNCT
ejpam-3550	52	13	g	g	NOUN
ejpam-3550	52	14	)	)	PUNCT
ejpam-3550	52	15	is	be	AUX
ejpam-3550	52	16	a	a	DET
ejpam-3550	52	17	(	(	PUNCT
ejpam-3550	52	18	1	1	NUM
ejpam-3550	52	19	,	,	PUNCT
ejpam-3550	52	20	2)∗-dominating	2)∗-dominating	NUM
ejpam-3550	52	21	(	(	PUNCT
ejpam-3550	52	22	resp	resp	NOUN
ejpam-3550	52	23	.	.	PUNCT
ejpam-3550	53	1	(	(	PUNCT
ejpam-3550	53	2	1	1	NUM
ejpam-3550	53	3	,	,	PUNCT
ejpam-3550	53	4	2)∗-total	2)∗-total	ADJ
ejpam-3550	53	5	dominating	dominating	NOUN
ejpam-3550	53	6	)	)	PUNCT
ejpam-3550	53	7	set	set	VERB
ejpam-3550	53	8	if	if	SCONJ
ejpam-3550	53	9	and	and	CCONJ
ejpam-3550	53	10	only	only	ADV
ejpam-3550	53	11	if	if	SCONJ
ejpam-3550	53	12	it	it	PRON
ejpam-3550	53	13	is	be	AUX
ejpam-3550	53	14	both	both	CCONJ
ejpam-3550	53	15	a	a	DET
ejpam-3550	53	16	dominating	dominating	NOUN
ejpam-3550	53	17	(	(	PUNCT
ejpam-3550	53	18	resp	resp	NOUN
ejpam-3550	53	19	.	.	PUNCT
ejpam-3550	54	1	total	total	ADJ
ejpam-3550	54	2	dominating	dominating	NOUN
ejpam-3550	54	3	)	)	PUNCT
ejpam-3550	54	4	and	and	CCONJ
ejpam-3550	54	5	a	a	DET
ejpam-3550	54	6	hop	hop	NOUN
ejpam-3550	54	7	dominating	dominating	NOUN
ejpam-3550	54	8	set	set	NOUN
ejpam-3550	54	9	.	.	PUNCT
ejpam-3550	55	1	the	the	DET
ejpam-3550	55	2	concept	concept	NOUN
ejpam-3550	55	3	of	of	ADP
ejpam-3550	55	4	(	(	PUNCT
ejpam-3550	55	5	1	1	NUM
ejpam-3550	55	6	,	,	PUNCT
ejpam-3550	55	7	2)∗-domination	2)∗-domination	NOUN
ejpam-3550	55	8	(	(	PUNCT
ejpam-3550	55	9	a	a	DET
ejpam-3550	55	10	variation	variation	NOUN
ejpam-3550	55	11	of	of	ADP
ejpam-3550	55	12	(	(	PUNCT
ejpam-3550	55	13	1	1	NUM
ejpam-3550	55	14	,	,	PUNCT
ejpam-3550	55	15	2)-domination	2)-domination	NUM
ejpam-3550	55	16	)	)	PUNCT
ejpam-3550	55	17	is	be	AUX
ejpam-3550	55	18	introduced	introduce	VERB
ejpam-3550	55	19	and	and	CCONJ
ejpam-3550	55	20	investigated	investigate	VERB
ejpam-3550	55	21	in	in	ADP
ejpam-3550	55	22	[	[	X
ejpam-3550	55	23	1	1	NUM
ejpam-3550	55	24	]	]	PUNCT
ejpam-3550	55	25	.	.	PUNCT
ejpam-3550	56	1	a	a	DET
ejpam-3550	56	2	set	set	NOUN
ejpam-3550	56	3	d	d	NOUN
ejpam-3550	56	4	⊆	⊆	NUM
ejpam-3550	56	5	v	v	ADP
ejpam-3550	56	6	(	(	PUNCT
ejpam-3550	56	7	g	g	NOUN
ejpam-3550	56	8	)	)	PUNCT
ejpam-3550	56	9	is	be	AUX
ejpam-3550	56	10	a	a	DET
ejpam-3550	56	11	point	point	NOUN
ejpam-3550	56	12	-	-	PUNCT
ejpam-3550	56	13	wise	wise	ADJ
ejpam-3550	56	14	non	non	ADJ
ejpam-3550	56	15	-	-	ADJ
ejpam-3550	56	16	dominating	dominating	ADJ
ejpam-3550	56	17	set	set	NOUN
ejpam-3550	56	18	of	of	ADP
ejpam-3550	56	19	g	g	PROPN
ejpam-3550	56	20	if	if	SCONJ
ejpam-3550	56	21	for	for	ADP
ejpam-3550	56	22	each	each	PRON
ejpam-3550	56	23	v	v	NUM
ejpam-3550	56	24	∈	∈	PROPN
ejpam-3550	56	25	v	v	NOUN
ejpam-3550	56	26	(	(	PUNCT
ejpam-3550	56	27	g	g	NOUN
ejpam-3550	56	28	)	)	PUNCT
ejpam-3550	56	29	\	\	PROPN
ejpam-3550	57	1	s	s	X
ejpam-3550	57	2	,	,	PUNCT
ejpam-3550	57	3	there	there	PRON
ejpam-3550	57	4	exists	exist	VERB
ejpam-3550	57	5	u	u	PROPN
ejpam-3550	57	6	∈	∈	PROPN
ejpam-3550	57	7	s	s	VERB
ejpam-3550	57	8	such	such	ADJ
ejpam-3550	57	9	that	that	DET
ejpam-3550	57	10	v	v	NOUN
ejpam-3550	57	11	/∈	/∈	PUNCT
ejpam-3550	57	12	ng(u	ng(u	NOUN
ejpam-3550	57	13	)	)	PUNCT
ejpam-3550	57	14	.	.	PUNCT
ejpam-3550	58	1	the	the	DET
ejpam-3550	58	2	smallest	small	ADJ
ejpam-3550	58	3	cardinality	cardinality	NOUN
ejpam-3550	58	4	of	of	ADP
ejpam-3550	58	5	a	a	DET
ejpam-3550	58	6	point	point	NOUN
ejpam-3550	58	7	-	-	PUNCT
ejpam-3550	58	8	wise	wise	ADJ
ejpam-3550	58	9	nondominating	nondominate	VERB
ejpam-3550	58	10	set	set	NOUN
ejpam-3550	58	11	of	of	ADP
ejpam-3550	58	12	g	g	NOUN
ejpam-3550	58	13	,	,	PUNCT
ejpam-3550	58	14	denoted	denote	VERB
ejpam-3550	58	15	by	by	ADP
ejpam-3550	58	16	pnd(g	pnd(g	PROPN
ejpam-3550	58	17	)	)	PUNCT
ejpam-3550	58	18	,	,	PUNCT
ejpam-3550	58	19	is	be	AUX
ejpam-3550	58	20	called	call	VERB
ejpam-3550	58	21	the	the	DET
ejpam-3550	58	22	point	point	NOUN
ejpam-3550	58	23	-	-	PUNCT
ejpam-3550	58	24	wise	wise	ADJ
ejpam-3550	58	25	non	non	ADJ
ejpam-3550	58	26	-	-	ADJ
ejpam-3550	58	27	domination	domination	ADJ
ejpam-3550	58	28	number	number	NOUN
ejpam-3550	58	29	of	of	ADP
ejpam-3550	58	30	g.	g.	PROPN
ejpam-3550	58	31	a	a	DET
ejpam-3550	58	32	dominating	dominating	NOUN
ejpam-3550	58	33	set	set	NOUN
ejpam-3550	58	34	s	s	PRON
ejpam-3550	58	35	which	which	PRON
ejpam-3550	58	36	is	be	AUX
ejpam-3550	58	37	also	also	ADV
ejpam-3550	58	38	a	a	DET
ejpam-3550	58	39	point	point	NOUN
ejpam-3550	58	40	-	-	PUNCT
ejpam-3550	58	41	wise	wise	ADJ
ejpam-3550	58	42	non	non	ADJ
ejpam-3550	58	43	-	-	ADJ
ejpam-3550	58	44	dominating	dominating	ADJ
ejpam-3550	58	45	set	set	NOUN
ejpam-3550	58	46	of	of	ADP
ejpam-3550	58	47	g	g	PROPN
ejpam-3550	58	48	is	be	AUX
ejpam-3550	58	49	called	call	VERB
ejpam-3550	58	50	a	a	DET
ejpam-3550	58	51	dominating	dominating	NOUN
ejpam-3550	58	52	point	point	NOUN
ejpam-3550	58	53	-	-	PUNCT
ejpam-3550	58	54	wise	wise	ADJ
ejpam-3550	58	55	non	non	ADJ
ejpam-3550	58	56	-	-	ADJ
ejpam-3550	58	57	dominating	dominating	ADJ
ejpam-3550	58	58	set	set	NOUN
ejpam-3550	58	59	of	of	ADP
ejpam-3550	58	60	g.	g.	PROPN
ejpam-3550	58	61	the	the	DET
ejpam-3550	58	62	smallest	small	ADJ
ejpam-3550	58	63	cardinality	cardinality	NOUN
ejpam-3550	58	64	of	of	ADP
ejpam-3550	58	65	a	a	DET
ejpam-3550	58	66	dominating	dominating	NOUN
ejpam-3550	58	67	point	point	NOUN
ejpam-3550	58	68	-	-	PUNCT
ejpam-3550	58	69	wise	wise	ADJ
ejpam-3550	58	70	non	non	ADJ
ejpam-3550	58	71	-	-	ADJ
ejpam-3550	58	72	dominating	dominating	ADJ
ejpam-3550	58	73	set	set	NOUN
ejpam-3550	58	74	of	of	ADP
ejpam-3550	58	75	g	g	NOUN
ejpam-3550	58	76	will	will	AUX
ejpam-3550	58	77	be	be	AUX
ejpam-3550	58	78	denoted	denote	VERB
ejpam-3550	58	79	by	by	ADP
ejpam-3550	58	80	γpnd(g	γpnd(g	PROPN
ejpam-3550	58	81	)	)	PUNCT
ejpam-3550	58	82	.	.	PUNCT
ejpam-3550	59	1	any	any	DET
ejpam-3550	59	2	point	point	NOUN
ejpam-3550	59	3	-	-	PUNCT
ejpam-3550	59	4	wise	wise	ADV
ejpam-3550	59	5	nondominating	nondominate	VERB
ejpam-3550	59	6	(	(	PUNCT
ejpam-3550	59	7	resp	resp	NOUN
ejpam-3550	59	8	.	.	PUNCT
ejpam-3550	60	1	dominating	dominating	NOUN
ejpam-3550	60	2	point	point	NOUN
ejpam-3550	60	3	-	-	PUNCT
ejpam-3550	60	4	wise	wise	ADJ
ejpam-3550	60	5	non	non	ADJ
ejpam-3550	60	6	-	-	ADJ
ejpam-3550	60	7	dominating	dominating	ADJ
ejpam-3550	60	8	)	)	PUNCT
ejpam-3550	60	9	set	set	NOUN
ejpam-3550	60	10	s	s	PRON
ejpam-3550	60	11	of	of	ADP
ejpam-3550	60	12	g	g	NOUN
ejpam-3550	60	13	with	with	ADP
ejpam-3550	60	14	|s|	|s|	NOUN
ejpam-3550	60	15	=	=	SYM
ejpam-3550	60	16	pnd(g	pnd(g	PROPN
ejpam-3550	60	17	)	)	PUNCT
ejpam-3550	60	18	(	(	PUNCT
ejpam-3550	60	19	resp	resp	NOUN
ejpam-3550	60	20	.	.	PUNCT
ejpam-3550	61	1	|s|	|s|	PROPN
ejpam-3550	61	2	=	=	SYM
ejpam-3550	61	3	γpnd(g	γpnd(g	PROPN
ejpam-3550	61	4	)	)	PUNCT
ejpam-3550	61	5	)	)	PUNCT
ejpam-3550	62	1	,	,	PUNCT
ejpam-3550	62	2	is	be	AUX
ejpam-3550	62	3	called	call	VERB
ejpam-3550	62	4	a	a	DET
ejpam-3550	62	5	pnd	pnd	NOUN
ejpam-3550	62	6	-	-	PUNCT
ejpam-3550	62	7	set	set	VERB
ejpam-3550	62	8	(	(	PUNCT
ejpam-3550	62	9	resp	resp	NOUN
ejpam-3550	62	10	.	.	PUNCT
ejpam-3550	63	1	γpnd	γpnd	NOUN
ejpam-3550	63	2	-	-	PUNCT
ejpam-3550	63	3	set	set	NOUN
ejpam-3550	63	4	)	)	PUNCT
ejpam-3550	63	5	of	of	ADP
ejpam-3550	63	6	g.	g.	PROPN
ejpam-3550	63	7	2	2	NUM
ejpam-3550	63	8	.	.	PUNCT
ejpam-3550	63	9	results	result	VERB
ejpam-3550	63	10	the	the	DET
ejpam-3550	63	11	first	first	ADJ
ejpam-3550	63	12	result	result	NOUN
ejpam-3550	63	13	,	,	PUNCT
ejpam-3550	63	14	which	which	PRON
ejpam-3550	63	15	will	will	AUX
ejpam-3550	63	16	be	be	AUX
ejpam-3550	63	17	needed	need	VERB
ejpam-3550	63	18	later	later	ADV
ejpam-3550	63	19	,	,	PUNCT
ejpam-3550	63	20	is	be	AUX
ejpam-3550	63	21	found	find	VERB
ejpam-3550	63	22	in	in	ADP
ejpam-3550	63	23	[	[	X
ejpam-3550	63	24	1	1	NUM
ejpam-3550	63	25	]	]	PUNCT
ejpam-3550	63	26	.	.	PUNCT
ejpam-3550	64	1	s.	s.	PROPN
ejpam-3550	64	2	canoy	canoy	PROPN
ejpam-3550	64	3	jr	jr	PROPN
ejpam-3550	64	4	.	.	PROPN
ejpam-3550	64	5	,	,	PUNCT
ejpam-3550	64	6	r.	r.	PROPN
ejpam-3550	64	7	mollejon	mollejon	NOUN
ejpam-3550	64	8	,	,	PUNCT
ejpam-3550	64	9	jg	jg	PROPN
ejpam-3550	64	10	.	.	PROPN
ejpam-3550	64	11	canoy	canoy	PROPN
ejpam-3550	64	12	/	/	SYM
ejpam-3550	64	13	eur	eur	PROPN
ejpam-3550	64	14	.	.	PUNCT
ejpam-3550	65	1	j.	j.	PROPN
ejpam-3550	65	2	pure	pure	PROPN
ejpam-3550	65	3	appl	appl	PROPN
ejpam-3550	65	4	.	.	PROPN
ejpam-3550	65	5	math	math	PROPN
ejpam-3550	65	6	,	,	PUNCT
ejpam-3550	65	7	12	12	NUM
ejpam-3550	65	8	(	(	PUNCT
ejpam-3550	65	9	4	4	NUM
ejpam-3550	65	10	)	)	PUNCT
ejpam-3550	65	11	(	(	PUNCT
ejpam-3550	65	12	2019	2019	NUM
ejpam-3550	65	13	)	)	PUNCT
ejpam-3550	65	14	,	,	PUNCT
ejpam-3550	65	15	1455	1455	NUM
ejpam-3550	65	16	-	-	SYM
ejpam-3550	65	17	1463	1463	NUM
ejpam-3550	65	18	1457	1457	NUM
ejpam-3550	65	19	proposition	proposition	NOUN
ejpam-3550	65	20	1	1	NUM
ejpam-3550	65	21	.	.	PUNCT
ejpam-3550	66	1	[	[	X
ejpam-3550	66	2	1	1	X
ejpam-3550	66	3	]	]	PUNCT
ejpam-3550	66	4	let	let	VERB
ejpam-3550	66	5	g	g	PRON
ejpam-3550	66	6	be	be	AUX
ejpam-3550	66	7	a	a	DET
ejpam-3550	66	8	graph	graph	NOUN
ejpam-3550	66	9	.	.	PUNCT
ejpam-3550	67	1	then	then	ADV
ejpam-3550	67	2	1	1	NUM
ejpam-3550	67	3	≤	≤	NUM
ejpam-3550	67	4	pnd(g	pnd(g	ADP
ejpam-3550	67	5	)	)	PUNCT
ejpam-3550	67	6	≤	≤	NOUN
ejpam-3550	67	7	|v	|v	X
ejpam-3550	67	8	(	(	PUNCT
ejpam-3550	67	9	g)|	g)|	PROPN
ejpam-3550	67	10	.	.	PUNCT
ejpam-3550	68	1	moreover	moreover	ADV
ejpam-3550	68	2	,	,	PUNCT
ejpam-3550	68	3	(	(	PUNCT
ejpam-3550	68	4	i	i	NOUN
ejpam-3550	68	5	)	)	PUNCT
ejpam-3550	68	6	pnd(g	pnd(g	PROPN
ejpam-3550	68	7	)	)	PUNCT
ejpam-3550	68	8	=	=	SYM
ejpam-3550	68	9	|v	|v	PROPN
ejpam-3550	68	10	(	(	PUNCT
ejpam-3550	68	11	g)|	g)|	VERB
ejpam-3550	68	12	if	if	SCONJ
ejpam-3550	68	13	and	and	CCONJ
ejpam-3550	68	14	only	only	ADV
ejpam-3550	68	15	if	if	SCONJ
ejpam-3550	68	16	g	g	PROPN
ejpam-3550	68	17	is	be	AUX
ejpam-3550	68	18	a	a	DET
ejpam-3550	68	19	complete	complete	ADJ
ejpam-3550	68	20	graph	graph	NOUN
ejpam-3550	68	21	;	;	PUNCT
ejpam-3550	68	22	(	(	PUNCT
ejpam-3550	68	23	ii	ii	NOUN
ejpam-3550	68	24	)	)	PUNCT
ejpam-3550	68	25	pnd(g	pnd(g	PROPN
ejpam-3550	68	26	)	)	PUNCT
ejpam-3550	68	27	=	=	SYM
ejpam-3550	68	28	1	1	NUM
ejpam-3550	68	29	if	if	SCONJ
ejpam-3550	68	30	and	and	CCONJ
ejpam-3550	68	31	only	only	ADV
ejpam-3550	68	32	if	if	SCONJ
ejpam-3550	68	33	g	g	PROPN
ejpam-3550	68	34	has	have	VERB
ejpam-3550	68	35	an	an	DET
ejpam-3550	68	36	isolated	isolated	ADJ
ejpam-3550	68	37	vertex	vertex	NOUN
ejpam-3550	68	38	;	;	PUNCT
ejpam-3550	68	39	and	and	CCONJ
ejpam-3550	68	40	(	(	PUNCT
ejpam-3550	68	41	iii	iii	NOUN
ejpam-3550	68	42	)	)	PUNCT
ejpam-3550	68	43	pnd(g	pnd(g	PROPN
ejpam-3550	68	44	)	)	PUNCT
ejpam-3550	68	45	=	=	SYM
ejpam-3550	68	46	2	2	NUM
ejpam-3550	68	47	if	if	SCONJ
ejpam-3550	68	48	and	and	CCONJ
ejpam-3550	68	49	only	only	ADV
ejpam-3550	68	50	if	if	SCONJ
ejpam-3550	68	51	g	g	PROPN
ejpam-3550	68	52	has	have	VERB
ejpam-3550	68	53	no	no	DET
ejpam-3550	68	54	isolated	isolated	ADJ
ejpam-3550	68	55	vertex	vertex	NOUN
ejpam-3550	68	56	and	and	CCONJ
ejpam-3550	68	57	there	there	PRON
ejpam-3550	68	58	exist	exist	VERB
ejpam-3550	68	59	distinct	distinct	ADJ
ejpam-3550	68	60	vertices	vertex	NOUN
ejpam-3550	68	61	a	a	PRON
ejpam-3550	68	62	and	and	CCONJ
ejpam-3550	68	63	b	b	NOUN
ejpam-3550	68	64	of	of	ADP
ejpam-3550	68	65	g	g	NOUN
ejpam-3550	68	66	such	such	ADJ
ejpam-3550	68	67	that	that	PRON
ejpam-3550	68	68	ng(a	ng(a	NOUN
ejpam-3550	68	69	)	)	PUNCT
ejpam-3550	68	70	∩ng(b	∩ng(b	NOUN
ejpam-3550	68	71	)	)	PUNCT
ejpam-3550	68	72	=	=	PUNCT
ejpam-3550	68	73	∅.	∅.	PRON
ejpam-3550	68	74	the	the	DET
ejpam-3550	68	75	join	join	NOUN
ejpam-3550	68	76	of	of	ADP
ejpam-3550	68	77	graphs	graph	NOUN
ejpam-3550	68	78	g	g	NOUN
ejpam-3550	68	79	and	and	CCONJ
ejpam-3550	68	80	h	h	NOUN
ejpam-3550	68	81	is	be	AUX
ejpam-3550	68	82	the	the	DET
ejpam-3550	68	83	graph	graph	NOUN
ejpam-3550	68	84	g+h	g+h	PROPN
ejpam-3550	68	85	with	with	ADP
ejpam-3550	68	86	vertex	vertex	NOUN
ejpam-3550	68	87	set	set	VERB
ejpam-3550	68	88	v	v	NOUN
ejpam-3550	68	89	(	(	PUNCT
ejpam-3550	68	90	g+h	g+h	NOUN
ejpam-3550	68	91	)	)	PUNCT
ejpam-3550	69	1	=	=	SYM
ejpam-3550	69	2	v	v	X
ejpam-3550	69	3	(	(	PUNCT
ejpam-3550	69	4	g	g	NOUN
ejpam-3550	69	5	)	)	PUNCT
ejpam-3550	69	6	∪	∪	NOUN
ejpam-3550	69	7	v	v	NOUN
ejpam-3550	69	8	(	(	PUNCT
ejpam-3550	69	9	h	h	NOUN
ejpam-3550	69	10	)	)	PUNCT
ejpam-3550	69	11	and	and	CCONJ
ejpam-3550	69	12	edge	edge	NOUN
ejpam-3550	69	13	set	set	VERB
ejpam-3550	69	14	e(g+h	e(g+h	NUM
ejpam-3550	69	15	)	)	PUNCT
ejpam-3550	69	16	=	=	SYM
ejpam-3550	69	17	e(g	e(g	NOUN
ejpam-3550	69	18	)	)	PUNCT
ejpam-3550	69	19	∪	∪	ADP
ejpam-3550	69	20	e(h	e(h	PROPN
ejpam-3550	69	21	)	)	PUNCT
ejpam-3550	69	22	∪	∪	NOUN
ejpam-3550	69	23	{	{	PUNCT
ejpam-3550	69	24	uv	uv	NOUN
ejpam-3550	69	25	:	:	PUNCT
ejpam-3550	69	26	u	u	PROPN
ejpam-3550	69	27	∈	∈	PROPN
ejpam-3550	69	28	v	v	ADP
ejpam-3550	69	29	(	(	PUNCT
ejpam-3550	69	30	g	g	NOUN
ejpam-3550	69	31	)	)	PUNCT
ejpam-3550	69	32	and	and	CCONJ
ejpam-3550	69	33	v	v	ADP
ejpam-3550	69	34	∈	∈	PROPN
ejpam-3550	69	35	v	v	NOUN
ejpam-3550	69	36	(	(	PUNCT
ejpam-3550	69	37	h	h	NOUN
ejpam-3550	69	38	)	)	PUNCT
ejpam-3550	69	39	}	}	PUNCT
ejpam-3550	69	40	.	.	PUNCT
ejpam-3550	70	1	theorem	theorem	NOUN
ejpam-3550	70	2	1	1	NUM
ejpam-3550	70	3	.	.	PUNCT
ejpam-3550	71	1	let	let	VERB
ejpam-3550	71	2	g	g	NOUN
ejpam-3550	72	1	and	and	CCONJ
ejpam-3550	72	2	h	h	NOUN
ejpam-3550	72	3	be	be	VERB
ejpam-3550	72	4	any	any	DET
ejpam-3550	72	5	two	two	NUM
ejpam-3550	72	6	graphs	graph	NOUN
ejpam-3550	72	7	.	.	PUNCT
ejpam-3550	73	1	a	a	DET
ejpam-3550	73	2	set	set	NOUN
ejpam-3550	73	3	s	s	NOUN
ejpam-3550	73	4	⊆	⊆	NUM
ejpam-3550	73	5	v	v	NOUN
ejpam-3550	73	6	(	(	PUNCT
ejpam-3550	73	7	g	g	PROPN
ejpam-3550	73	8	+	+	NOUN
ejpam-3550	73	9	h	h	NOUN
ejpam-3550	73	10	)	)	PUNCT
ejpam-3550	73	11	is	be	AUX
ejpam-3550	73	12	hop	hop	NOUN
ejpam-3550	73	13	dominating	dominate	VERB
ejpam-3550	73	14	set	set	NOUN
ejpam-3550	73	15	of	of	ADP
ejpam-3550	73	16	g+h	g+h	PROPN
ejpam-3550	74	1	if	if	SCONJ
ejpam-3550	74	2	and	and	CCONJ
ejpam-3550	74	3	only	only	ADV
ejpam-3550	74	4	if	if	SCONJ
ejpam-3550	74	5	s	s	X
ejpam-3550	74	6	=	=	PUNCT
ejpam-3550	74	7	sg∪sh	sg∪sh	PROPN
ejpam-3550	74	8	,	,	PUNCT
ejpam-3550	74	9	where	where	SCONJ
ejpam-3550	74	10	sg	sg	PROPN
ejpam-3550	74	11	and	and	CCONJ
ejpam-3550	74	12	sh	sh	PROPN
ejpam-3550	74	13	are	be	AUX
ejpam-3550	74	14	point	point	ADV
ejpam-3550	74	15	-	-	PUNCT
ejpam-3550	74	16	wise	wise	ADJ
ejpam-3550	74	17	non	non	ADJ
ejpam-3550	74	18	-	-	ADJ
ejpam-3550	74	19	dominating	dominating	ADJ
ejpam-3550	74	20	sets	set	NOUN
ejpam-3550	74	21	of	of	ADP
ejpam-3550	74	22	g	g	PROPN
ejpam-3550	74	23	and	and	CCONJ
ejpam-3550	74	24	h	h	NOUN
ejpam-3550	74	25	,	,	PUNCT
ejpam-3550	74	26	respectively	respectively	ADV
ejpam-3550	74	27	.	.	PUNCT
ejpam-3550	75	1	proof	proof	NOUN
ejpam-3550	75	2	.	.	PUNCT
ejpam-3550	76	1	suppose	suppose	VERB
ejpam-3550	76	2	that	that	SCONJ
ejpam-3550	76	3	s	s	VERB
ejpam-3550	76	4	is	be	AUX
ejpam-3550	76	5	a	a	DET
ejpam-3550	76	6	hop	hop	NOUN
ejpam-3550	76	7	dominating	dominating	NOUN
ejpam-3550	76	8	set	set	NOUN
ejpam-3550	76	9	of	of	ADP
ejpam-3550	76	10	g	g	PROPN
ejpam-3550	76	11	+	+	CCONJ
ejpam-3550	76	12	h.	h.	PROPN
ejpam-3550	76	13	let	let	VERB
ejpam-3550	76	14	sg	sg	VERB
ejpam-3550	76	15	=	=	SYM
ejpam-3550	76	16	s	s	PART
ejpam-3550	76	17	∩	∩	ADJ
ejpam-3550	76	18	v	v	X
ejpam-3550	76	19	(	(	PUNCT
ejpam-3550	76	20	g	g	NOUN
ejpam-3550	76	21	)	)	PUNCT
ejpam-3550	76	22	and	and	CCONJ
ejpam-3550	76	23	sh	sh	INTJ
ejpam-3550	76	24	=	=	SYM
ejpam-3550	76	25	s	s	PROPN
ejpam-3550	76	26	∩	∩	ADJ
ejpam-3550	76	27	v	v	ADJ
ejpam-3550	76	28	(	(	PUNCT
ejpam-3550	76	29	h	h	NOUN
ejpam-3550	76	30	)	)	PUNCT
ejpam-3550	76	31	.	.	PUNCT
ejpam-3550	77	1	if	if	SCONJ
ejpam-3550	77	2	sg	sg	PROPN
ejpam-3550	77	3	were	be	AUX
ejpam-3550	77	4	empty	empty	ADJ
ejpam-3550	77	5	,	,	PUNCT
ejpam-3550	77	6	then	then	ADV
ejpam-3550	77	7	s	s	VERB
ejpam-3550	77	8	=	=	ADJ
ejpam-3550	77	9	sh	sh	INTJ
ejpam-3550	77	10	.	.	PUNCT
ejpam-3550	78	1	since	since	SCONJ
ejpam-3550	78	2	v	v	NOUN
ejpam-3550	78	3	(	(	PUNCT
ejpam-3550	78	4	g	g	NOUN
ejpam-3550	78	5	)	)	PUNCT
ejpam-3550	78	6	⊆	⊆	NUM
ejpam-3550	78	7	ng(s	ng(s	NUM
ejpam-3550	78	8	)	)	PUNCT
ejpam-3550	78	9	,	,	PUNCT
ejpam-3550	78	10	it	it	PRON
ejpam-3550	78	11	follows	follow	VERB
ejpam-3550	78	12	that	that	SCONJ
ejpam-3550	78	13	s	s	VERB
ejpam-3550	78	14	is	be	AUX
ejpam-3550	78	15	not	not	PART
ejpam-3550	78	16	a	a	DET
ejpam-3550	78	17	hop	hop	NOUN
ejpam-3550	78	18	dominating	dominating	NOUN
ejpam-3550	78	19	set	set	NOUN
ejpam-3550	78	20	,	,	PUNCT
ejpam-3550	78	21	a	a	DET
ejpam-3550	78	22	contradiction	contradiction	NOUN
ejpam-3550	78	23	.	.	PUNCT
ejpam-3550	79	1	thus	thus	ADV
ejpam-3550	79	2	,	,	PUNCT
ejpam-3550	79	3	sg	sg	PROPN
ejpam-3550	79	4	6=	6=	X
ejpam-3550	79	5	∅.	∅.	ADP
ejpam-3550	79	6	similarly	similarly	ADV
ejpam-3550	79	7	,	,	PUNCT
ejpam-3550	79	8	sh	sh	PROPN
ejpam-3550	79	9	6=	6=	ADP
ejpam-3550	79	10	∅.	∅.	NOUN
ejpam-3550	79	11	now	now	ADV
ejpam-3550	79	12	let	let	VERB
ejpam-3550	79	13	v	v	ADP
ejpam-3550	79	14	∈	∈	PROPN
ejpam-3550	79	15	v	v	NOUN
ejpam-3550	79	16	(	(	PUNCT
ejpam-3550	79	17	g)\sg	g)\sg	PROPN
ejpam-3550	79	18	.	.	PUNCT
ejpam-3550	80	1	since	since	SCONJ
ejpam-3550	80	2	s	s	PROPN
ejpam-3550	80	3	is	be	AUX
ejpam-3550	80	4	hop	hop	NOUN
ejpam-3550	80	5	dominating	dominating	NOUN
ejpam-3550	80	6	set	set	NOUN
ejpam-3550	80	7	,	,	PUNCT
ejpam-3550	80	8	there	there	PRON
ejpam-3550	80	9	exists	exist	VERB
ejpam-3550	80	10	z	z	PROPN
ejpam-3550	80	11	∈	∈	PROPN
ejpam-3550	80	12	s	s	VERB
ejpam-3550	80	13	such	such	ADJ
ejpam-3550	80	14	that	that	SCONJ
ejpam-3550	80	15	dg+h(v	dg+h(v	PROPN
ejpam-3550	80	16	,	,	PUNCT
ejpam-3550	80	17	z	z	NOUN
ejpam-3550	80	18	)	)	PUNCT
ejpam-3550	80	19	=	=	SYM
ejpam-3550	80	20	2	2	X
ejpam-3550	80	21	.	.	X
ejpam-3550	81	1	hence	hence	ADV
ejpam-3550	81	2	,	,	PUNCT
ejpam-3550	81	3	z	z	PROPN
ejpam-3550	81	4	∈	∈	PROPN
ejpam-3550	81	5	sg	sg	NOUN
ejpam-3550	81	6	and	and	CCONJ
ejpam-3550	81	7	v	v	NOUN
ejpam-3550	81	8	/∈	/∈	PUNCT
ejpam-3550	81	9	ng(z	ng(z	NUM
ejpam-3550	81	10	)	)	PUNCT
ejpam-3550	81	11	.	.	PUNCT
ejpam-3550	82	1	this	this	PRON
ejpam-3550	82	2	shows	show	VERB
ejpam-3550	82	3	that	that	SCONJ
ejpam-3550	82	4	sg	sg	PROPN
ejpam-3550	82	5	is	be	AUX
ejpam-3550	82	6	a	a	DET
ejpam-3550	82	7	point	point	NOUN
ejpam-3550	82	8	-	-	PUNCT
ejpam-3550	82	9	wise	wise	ADJ
ejpam-3550	82	10	non	non	ADJ
ejpam-3550	82	11	-	-	ADJ
ejpam-3550	82	12	dominating	dominating	ADJ
ejpam-3550	82	13	set	set	NOUN
ejpam-3550	82	14	of	of	ADP
ejpam-3550	82	15	g.	g.	PROPN
ejpam-3550	82	16	similarly	similarly	ADV
ejpam-3550	82	17	,	,	PUNCT
ejpam-3550	82	18	sh	sh	PROPN
ejpam-3550	82	19	is	be	AUX
ejpam-3550	82	20	a	a	DET
ejpam-3550	82	21	point	point	NOUN
ejpam-3550	82	22	-	-	PUNCT
ejpam-3550	82	23	wise	wise	ADJ
ejpam-3550	82	24	non	non	ADJ
ejpam-3550	82	25	-	-	ADJ
ejpam-3550	82	26	dominating	dominating	ADJ
ejpam-3550	82	27	set	set	NOUN
ejpam-3550	82	28	of	of	ADP
ejpam-3550	82	29	h.	h.	PROPN
ejpam-3550	82	30	for	for	ADP
ejpam-3550	82	31	the	the	DET
ejpam-3550	82	32	converse	converse	NOUN
ejpam-3550	82	33	,	,	PUNCT
ejpam-3550	82	34	suppose	suppose	VERB
ejpam-3550	82	35	that	that	SCONJ
ejpam-3550	82	36	s	s	VERB
ejpam-3550	82	37	=	=	PUNCT
ejpam-3550	82	38	sg	sg	X
ejpam-3550	82	39	∪	∪	ADJ
ejpam-3550	82	40	sh	sh	PROPN
ejpam-3550	82	41	,	,	PUNCT
ejpam-3550	82	42	where	where	SCONJ
ejpam-3550	82	43	sg	sg	PROPN
ejpam-3550	82	44	and	and	CCONJ
ejpam-3550	82	45	sh	sh	PROPN
ejpam-3550	82	46	are	be	AUX
ejpam-3550	82	47	point	point	ADV
ejpam-3550	82	48	-	-	PUNCT
ejpam-3550	82	49	wise	wise	ADJ
ejpam-3550	82	50	nondominating	nondominate	VERB
ejpam-3550	82	51	sets	set	NOUN
ejpam-3550	82	52	of	of	ADP
ejpam-3550	82	53	g	g	PROPN
ejpam-3550	82	54	and	and	CCONJ
ejpam-3550	82	55	h	h	NOUN
ejpam-3550	82	56	,	,	PUNCT
ejpam-3550	82	57	respectively	respectively	ADV
ejpam-3550	82	58	.	.	PUNCT
ejpam-3550	83	1	let	let	VERB
ejpam-3550	83	2	v	v	NUM
ejpam-3550	83	3	∈	∈	PROPN
ejpam-3550	83	4	v	v	NOUN
ejpam-3550	83	5	(	(	PUNCT
ejpam-3550	83	6	g	g	PROPN
ejpam-3550	83	7	+	+	NOUN
ejpam-3550	83	8	h	h	NOUN
ejpam-3550	83	9	)	)	PUNCT
ejpam-3550	83	10	\	\	PUNCT
ejpam-3550	84	1	s.	s.	PROPN
ejpam-3550	84	2	if	if	SCONJ
ejpam-3550	84	3	v	v	NUM
ejpam-3550	84	4	∈	∈	PROPN
ejpam-3550	84	5	v	v	NOUN
ejpam-3550	84	6	(	(	PUNCT
ejpam-3550	84	7	g	g	NOUN
ejpam-3550	84	8	)	)	PUNCT
ejpam-3550	84	9	,	,	PUNCT
ejpam-3550	84	10	then	then	ADV
ejpam-3550	84	11	v	v	X
ejpam-3550	84	12	∈	∈	PROPN
ejpam-3550	84	13	ng+h(sh	ng+h(sh	PROPN
ejpam-3550	84	14	)	)	PUNCT
ejpam-3550	84	15	.	.	PUNCT
ejpam-3550	85	1	since	since	SCONJ
ejpam-3550	85	2	sg	sg	PROPN
ejpam-3550	85	3	is	be	AUX
ejpam-3550	85	4	a	a	DET
ejpam-3550	85	5	point	point	NOUN
ejpam-3550	85	6	-	-	PUNCT
ejpam-3550	85	7	wise	wise	ADJ
ejpam-3550	85	8	non	non	ADJ
ejpam-3550	85	9	-	-	ADJ
ejpam-3550	85	10	dominating	dominating	ADJ
ejpam-3550	85	11	set	set	NOUN
ejpam-3550	85	12	of	of	ADP
ejpam-3550	85	13	g	g	NOUN
ejpam-3550	85	14	,	,	PUNCT
ejpam-3550	85	15	there	there	PRON
ejpam-3550	85	16	is	be	VERB
ejpam-3550	85	17	a	a	DET
ejpam-3550	85	18	vertex	vertex	NOUN
ejpam-3550	85	19	y	y	PROPN
ejpam-3550	85	20	∈	∈	PROPN
ejpam-3550	85	21	sg	sg	ADP
ejpam-3550	85	22	\	\	PROPN
ejpam-3550	85	23	ng(v	ng(v	PUNCT
ejpam-3550	85	24	)	)	PUNCT
ejpam-3550	85	25	.	.	PUNCT
ejpam-3550	86	1	it	it	PRON
ejpam-3550	86	2	follows	follow	VERB
ejpam-3550	86	3	that	that	SCONJ
ejpam-3550	86	4	dg+h(v	dg+h(v	PROPN
ejpam-3550	86	5	,	,	PUNCT
ejpam-3550	86	6	y	y	NOUN
ejpam-3550	86	7	)	)	PUNCT
ejpam-3550	86	8	=	=	SYM
ejpam-3550	87	1	2	2	X
ejpam-3550	87	2	.	.	PUNCT
ejpam-3550	87	3	the	the	DET
ejpam-3550	87	4	same	same	ADJ
ejpam-3550	87	5	argument	argument	NOUN
ejpam-3550	87	6	can	can	AUX
ejpam-3550	87	7	be	be	AUX
ejpam-3550	87	8	used	use	VERB
ejpam-3550	87	9	if	if	SCONJ
ejpam-3550	87	10	v	v	NUM
ejpam-3550	87	11	∈	∈	PROPN
ejpam-3550	87	12	v	v	NOUN
ejpam-3550	87	13	(	(	PUNCT
ejpam-3550	87	14	h	h	NOUN
ejpam-3550	87	15	)	)	PUNCT
ejpam-3550	87	16	.	.	PUNCT
ejpam-3550	88	1	therefore	therefore	ADV
ejpam-3550	88	2	s	s	VERB
ejpam-3550	88	3	is	be	AUX
ejpam-3550	88	4	a	a	DET
ejpam-3550	88	5	hop	hop	NOUN
ejpam-3550	88	6	dominating	dominating	NOUN
ejpam-3550	88	7	set	set	NOUN
ejpam-3550	88	8	of	of	ADP
ejpam-3550	88	9	g+h	g+h	PROPN
ejpam-3550	88	10	.	.	PUNCT
ejpam-3550	89	1	the	the	DET
ejpam-3550	89	2	next	next	ADJ
ejpam-3550	89	3	result	result	NOUN
ejpam-3550	89	4	is	be	AUX
ejpam-3550	89	5	a	a	DET
ejpam-3550	89	6	consequence	consequence	NOUN
ejpam-3550	89	7	of	of	ADP
ejpam-3550	89	8	theorem	theorem	ADJ
ejpam-3550	89	9	1	1	NUM
ejpam-3550	89	10	and	and	CCONJ
ejpam-3550	89	11	proposition	proposition	NOUN
ejpam-3550	89	12	1	1	NUM
ejpam-3550	89	13	corollary	corollary	NOUN
ejpam-3550	89	14	1	1	NUM
ejpam-3550	89	15	.	.	PUNCT
ejpam-3550	90	1	let	let	VERB
ejpam-3550	90	2	g	g	NOUN
ejpam-3550	90	3	and	and	CCONJ
ejpam-3550	90	4	h	h	NOUN
ejpam-3550	90	5	be	be	VERB
ejpam-3550	90	6	any	any	DET
ejpam-3550	90	7	two	two	NUM
ejpam-3550	90	8	graphs	graph	NOUN
ejpam-3550	90	9	of	of	ADP
ejpam-3550	90	10	orders	order	NOUN
ejpam-3550	90	11	m	m	VERB
ejpam-3550	90	12	and	and	CCONJ
ejpam-3550	90	13	n	n	CCONJ
ejpam-3550	90	14	,	,	PUNCT
ejpam-3550	90	15	respectively	respectively	ADV
ejpam-3550	90	16	.	.	PUNCT
ejpam-3550	91	1	then	then	ADV
ejpam-3550	91	2	γh(g+h	γh(g+h	NUM
ejpam-3550	91	3	)	)	PUNCT
ejpam-3550	91	4	=	=	SYM
ejpam-3550	91	5	pnd(g	pnd(g	PROPN
ejpam-3550	91	6	)	)	PUNCT
ejpam-3550	91	7	+	+	NUM
ejpam-3550	91	8	pnd(h	pnd(h	PROPN
ejpam-3550	91	9	)	)	PUNCT
ejpam-3550	91	10	.	.	PUNCT
ejpam-3550	92	1	in	in	ADP
ejpam-3550	92	2	particular	particular	ADJ
ejpam-3550	92	3	,	,	PUNCT
ejpam-3550	92	4	(	(	PUNCT
ejpam-3550	92	5	i	i	NOUN
ejpam-3550	92	6	)	)	PUNCT
ejpam-3550	92	7	γh(g+h	γh(g+h	PROPN
ejpam-3550	92	8	)	)	PUNCT
ejpam-3550	92	9	=	=	PUNCT
ejpam-3550	93	1	m+	m+	NUM
ejpam-3550	93	2	n	n	NOUN
ejpam-3550	93	3	if	if	SCONJ
ejpam-3550	93	4	g	g	PROPN
ejpam-3550	93	5	and	and	CCONJ
ejpam-3550	93	6	h	h	NOUN
ejpam-3550	93	7	are	be	AUX
ejpam-3550	93	8	complete	complete	ADJ
ejpam-3550	93	9	;	;	PUNCT
ejpam-3550	93	10	(	(	PUNCT
ejpam-3550	93	11	ii	ii	NOUN
ejpam-3550	93	12	)	)	PUNCT
ejpam-3550	93	13	γh(g+h	γh(g+h	PROPN
ejpam-3550	93	14	)	)	PUNCT
ejpam-3550	93	15	=	=	SYM
ejpam-3550	93	16	2	2	NUM
ejpam-3550	93	17	if	if	SCONJ
ejpam-3550	93	18	g	g	PROPN
ejpam-3550	93	19	and	and	CCONJ
ejpam-3550	93	20	h	h	NOUN
ejpam-3550	93	21	have	have	VERB
ejpam-3550	93	22	isolated	isolate	VERB
ejpam-3550	93	23	vertices	vertex	NOUN
ejpam-3550	93	24	;	;	PUNCT
ejpam-3550	93	25	(	(	PUNCT
ejpam-3550	93	26	iii	iii	X
ejpam-3550	93	27	)	)	PUNCT
ejpam-3550	93	28	γh(g+h	γh(g+h	PROPN
ejpam-3550	93	29	)	)	PUNCT
ejpam-3550	93	30	=	=	SYM
ejpam-3550	94	1	1	1	NUM
ejpam-3550	94	2	+	+	NUM
ejpam-3550	94	3	pnd(h	pnd(h	NUM
ejpam-3550	94	4	)	)	PUNCT
ejpam-3550	94	5	if	if	SCONJ
ejpam-3550	94	6	g	g	PROPN
ejpam-3550	94	7	=	=	SYM
ejpam-3550	94	8	k1	k1	PROPN
ejpam-3550	94	9	;	;	PUNCT
ejpam-3550	94	10	(	(	PUNCT
ejpam-3550	94	11	iv	iv	X
ejpam-3550	94	12	)	)	PUNCT
ejpam-3550	94	13	γh(g+h	γh(g+h	PROPN
ejpam-3550	94	14	)	)	PUNCT
ejpam-3550	94	15	=	=	SYM
ejpam-3550	94	16	4	4	NUM
ejpam-3550	94	17	if	if	SCONJ
ejpam-3550	94	18	g	g	NOUN
ejpam-3550	94	19	=	=	VERB
ejpam-3550	94	20	pm	pm	NOUN
ejpam-3550	94	21	and	and	CCONJ
ejpam-3550	94	22	h	h	NOUN
ejpam-3550	95	1	=	=	NOUN
ejpam-3550	95	2	pn	pn	PROPN
ejpam-3550	95	3	(	(	PUNCT
ejpam-3550	95	4	m	m	PROPN
ejpam-3550	95	5	,	,	PUNCT
ejpam-3550	95	6	n	n	PRON
ejpam-3550	95	7	≥	≥	NOUN
ejpam-3550	95	8	2	2	NUM
ejpam-3550	95	9	)	)	PUNCT
ejpam-3550	95	10	;	;	PUNCT
ejpam-3550	95	11	and	and	CCONJ
ejpam-3550	95	12	(	(	PUNCT
ejpam-3550	95	13	v	v	NOUN
ejpam-3550	95	14	)	)	PUNCT
ejpam-3550	95	15	γh(g+h	γh(g+h	PROPN
ejpam-3550	95	16	)	)	PUNCT
ejpam-3550	95	17	=	=	SYM
ejpam-3550	95	18	4	4	NUM
ejpam-3550	95	19	if	if	SCONJ
ejpam-3550	95	20	g	g	NOUN
ejpam-3550	95	21	=	=	NOUN
ejpam-3550	95	22	cm	cm	NOUN
ejpam-3550	96	1	and	and	CCONJ
ejpam-3550	96	2	h	h	NOUN
ejpam-3550	96	3	=	=	SYM
ejpam-3550	96	4	cn	cn	PROPN
ejpam-3550	96	5	(	(	PUNCT
ejpam-3550	96	6	m	m	PROPN
ejpam-3550	96	7	,	,	PUNCT
ejpam-3550	96	8	n	n	PRON
ejpam-3550	96	9	≥	≥	NOUN
ejpam-3550	96	10	4	4	NUM
ejpam-3550	96	11	)	)	PUNCT
ejpam-3550	96	12	.	.	PUNCT
ejpam-3550	97	1	the	the	DET
ejpam-3550	97	2	corona	corona	NOUN
ejpam-3550	97	3	of	of	ADP
ejpam-3550	97	4	graphs	graph	NOUN
ejpam-3550	97	5	g	g	PROPN
ejpam-3550	97	6	and	and	CCONJ
ejpam-3550	97	7	h	h	NOUN
ejpam-3550	97	8	,	,	PUNCT
ejpam-3550	97	9	denoted	denote	VERB
ejpam-3550	97	10	by	by	ADP
ejpam-3550	97	11	g	g	PROPN
ejpam-3550	97	12	◦	◦	NOUN
ejpam-3550	97	13	h	h	NOUN
ejpam-3550	97	14	,	,	PUNCT
ejpam-3550	97	15	is	be	AUX
ejpam-3550	97	16	the	the	DET
ejpam-3550	97	17	graph	graph	NOUN
ejpam-3550	97	18	obtained	obtain	VERB
ejpam-3550	97	19	from	from	ADP
ejpam-3550	97	20	g	g	NOUN
ejpam-3550	97	21	by	by	ADP
ejpam-3550	97	22	taking	take	VERB
ejpam-3550	97	23	a	a	DET
ejpam-3550	97	24	copy	copy	NOUN
ejpam-3550	97	25	hv	hv	PROPN
ejpam-3550	97	26	of	of	ADP
ejpam-3550	97	27	h	h	PROPN
ejpam-3550	97	28	and	and	CCONJ
ejpam-3550	97	29	forming	form	VERB
ejpam-3550	97	30	the	the	DET
ejpam-3550	97	31	join	join	NOUN
ejpam-3550	97	32	〈	〈	PROPN
ejpam-3550	97	33	v〉+hv	v〉+hv	NOUN
ejpam-3550	97	34	=	=	SYM
ejpam-3550	97	35	v	v	ADP
ejpam-3550	97	36	+	+	NOUN
ejpam-3550	97	37	hv	hv	NOUN
ejpam-3550	97	38	for	for	ADP
ejpam-3550	97	39	each	each	DET
ejpam-3550	97	40	v	v	NUM
ejpam-3550	97	41	∈	∈	PROPN
ejpam-3550	97	42	v	v	NOUN
ejpam-3550	97	43	(	(	PUNCT
ejpam-3550	97	44	g	g	NOUN
ejpam-3550	97	45	)	)	PUNCT
ejpam-3550	97	46	.	.	PUNCT
ejpam-3550	98	1	s.	s.	PROPN
ejpam-3550	98	2	canoy	canoy	PROPN
ejpam-3550	98	3	jr	jr	PROPN
ejpam-3550	98	4	.	.	PROPN
ejpam-3550	98	5	,	,	PUNCT
ejpam-3550	98	6	r.	r.	PROPN
ejpam-3550	98	7	mollejon	mollejon	NOUN
ejpam-3550	98	8	,	,	PUNCT
ejpam-3550	98	9	jg	jg	PROPN
ejpam-3550	98	10	.	.	PROPN
ejpam-3550	98	11	canoy	canoy	PROPN
ejpam-3550	98	12	/	/	SYM
ejpam-3550	98	13	eur	eur	PROPN
ejpam-3550	98	14	.	.	PUNCT
ejpam-3550	99	1	j.	j.	PROPN
ejpam-3550	99	2	pure	pure	PROPN
ejpam-3550	99	3	appl	appl	PROPN
ejpam-3550	99	4	.	.	PROPN
ejpam-3550	99	5	math	math	PROPN
ejpam-3550	99	6	,	,	PUNCT
ejpam-3550	99	7	12	12	NUM
ejpam-3550	99	8	(	(	PUNCT
ejpam-3550	99	9	4	4	NUM
ejpam-3550	99	10	)	)	PUNCT
ejpam-3550	99	11	(	(	PUNCT
ejpam-3550	99	12	2019	2019	NUM
ejpam-3550	99	13	)	)	PUNCT
ejpam-3550	99	14	,	,	PUNCT
ejpam-3550	99	15	1455	1455	NUM
ejpam-3550	99	16	-	-	SYM
ejpam-3550	99	17	1463	1463	NUM
ejpam-3550	99	18	1458	1458	NUM
ejpam-3550	99	19	theorem	theorem	NOUN
ejpam-3550	99	20	2	2	NUM
ejpam-3550	99	21	.	.	PUNCT
ejpam-3550	100	1	let	let	VERB
ejpam-3550	100	2	g	g	NOUN
ejpam-3550	101	1	and	and	CCONJ
ejpam-3550	101	2	h	h	NOUN
ejpam-3550	101	3	be	be	VERB
ejpam-3550	101	4	any	any	DET
ejpam-3550	101	5	two	two	NUM
ejpam-3550	101	6	graphs	graph	NOUN
ejpam-3550	101	7	.	.	PUNCT
ejpam-3550	102	1	a	a	DET
ejpam-3550	102	2	set	set	NOUN
ejpam-3550	102	3	c	c	NOUN
ejpam-3550	102	4	⊆	⊆	NUM
ejpam-3550	102	5	v	v	NOUN
ejpam-3550	102	6	(	(	PUNCT
ejpam-3550	102	7	g	g	PROPN
ejpam-3550	102	8	◦	◦	NOUN
ejpam-3550	102	9	h	h	NOUN
ejpam-3550	102	10	)	)	PUNCT
ejpam-3550	102	11	is	be	AUX
ejpam-3550	102	12	a	a	DET
ejpam-3550	102	13	hop	hop	NOUN
ejpam-3550	102	14	dominating	dominating	NOUN
ejpam-3550	102	15	set	set	NOUN
ejpam-3550	102	16	of	of	ADP
ejpam-3550	102	17	g	g	PROPN
ejpam-3550	102	18	◦	◦	NOUN
ejpam-3550	102	19	h	h	NOUN
ejpam-3550	102	20	if	if	SCONJ
ejpam-3550	103	1	and	and	CCONJ
ejpam-3550	103	2	only	only	ADV
ejpam-3550	103	3	if	if	SCONJ
ejpam-3550	103	4	c	c	X
ejpam-3550	103	5	=	=	PUNCT
ejpam-3550	103	6	a	a	DET
ejpam-3550	103	7	∪	∪	X
ejpam-3550	103	8	(	(	PUNCT
ejpam-3550	103	9	∪v∈v	∪v∈v	X
ejpam-3550	103	10	(	(	PUNCT
ejpam-3550	103	11	g)∩ng(a)sv	g)∩ng(a)sv	PROPN
ejpam-3550	103	12	)	)	PUNCT
ejpam-3550	103	13	∪	∪	NOUN
ejpam-3550	103	14	(	(	PUNCT
ejpam-3550	103	15	∪w∈v	∪w∈v	PROPN
ejpam-3550	103	16	(	(	PUNCT
ejpam-3550	103	17	g)\ng(a)ew	g)\ng(a)ew	PROPN
ejpam-3550	103	18	)	)	PUNCT
ejpam-3550	103	19	,	,	PUNCT
ejpam-3550	103	20	where	where	SCONJ
ejpam-3550	103	21	(	(	PUNCT
ejpam-3550	103	22	i	i	NOUN
ejpam-3550	103	23	)	)	PUNCT
ejpam-3550	103	24	a	a	DET
ejpam-3550	103	25	⊆	⊆	NUM
ejpam-3550	103	26	v	v	NOUN
ejpam-3550	103	27	(	(	PUNCT
ejpam-3550	103	28	g	g	NOUN
ejpam-3550	103	29	)	)	PUNCT
ejpam-3550	103	30	such	such	ADJ
ejpam-3550	103	31	that	that	PRON
ejpam-3550	103	32	for	for	ADP
ejpam-3550	103	33	each	each	DET
ejpam-3550	103	34	w	w	PROPN
ejpam-3550	103	35	∈	∈	PROPN
ejpam-3550	103	36	v	v	ADP
ejpam-3550	103	37	(	(	PUNCT
ejpam-3550	103	38	g	g	NOUN
ejpam-3550	103	39	)	)	PUNCT
ejpam-3550	103	40	\a	\a	ADJ
ejpam-3550	103	41	,	,	PUNCT
ejpam-3550	103	42	there	there	PRON
ejpam-3550	103	43	exists	exist	VERB
ejpam-3550	103	44	x	x	X
ejpam-3550	103	45	∈	∈	PROPN
ejpam-3550	103	46	a	a	PRON
ejpam-3550	103	47	with	with	ADP
ejpam-3550	103	48	dg(w	dg(w	NOUN
ejpam-3550	103	49	,	,	PUNCT
ejpam-3550	103	50	x	x	X
ejpam-3550	103	51	)	)	PUNCT
ejpam-3550	103	52	=	=	SYM
ejpam-3550	103	53	2	2	NUM
ejpam-3550	103	54	or	or	CCONJ
ejpam-3550	103	55	there	there	PRON
ejpam-3550	103	56	exists	exist	VERB
ejpam-3550	103	57	y	y	PROPN
ejpam-3550	103	58	∈	∈	PROPN
ejpam-3550	103	59	v	v	ADP
ejpam-3550	103	60	(	(	PUNCT
ejpam-3550	103	61	g	g	NOUN
ejpam-3550	103	62	)	)	PUNCT
ejpam-3550	103	63	∩ng(w	∩ng(w	PROPN
ejpam-3550	103	64	)	)	PUNCT
ejpam-3550	103	65	with	with	ADP
ejpam-3550	103	66	v	v	NUM
ejpam-3550	103	67	(	(	PUNCT
ejpam-3550	103	68	hy	hy	NOUN
ejpam-3550	103	69	)	)	PUNCT
ejpam-3550	103	70	∩	∩	PROPN
ejpam-3550	103	71	c	c	PROPN
ejpam-3550	103	72	6=	6=	PROPN
ejpam-3550	103	73	∅	∅	NOUN
ejpam-3550	103	74	,	,	PUNCT
ejpam-3550	103	75	(	(	PUNCT
ejpam-3550	103	76	ii	ii	NOUN
ejpam-3550	103	77	)	)	PUNCT
ejpam-3550	103	78	sv	sv	VERB
ejpam-3550	104	1	⊆	⊆	NUM
ejpam-3550	104	2	v	v	X
ejpam-3550	104	3	(	(	PUNCT
ejpam-3550	104	4	hv	hv	PROPN
ejpam-3550	104	5	)	)	PUNCT
ejpam-3550	104	6	for	for	ADP
ejpam-3550	104	7	each	each	DET
ejpam-3550	104	8	v	v	NUM
ejpam-3550	104	9	∈	∈	PROPN
ejpam-3550	104	10	v	v	NOUN
ejpam-3550	104	11	(	(	PUNCT
ejpam-3550	104	12	g	g	NOUN
ejpam-3550	104	13	)	)	PUNCT
ejpam-3550	104	14	∩ng(a	∩ng(a	NOUN
ejpam-3550	104	15	)	)	PUNCT
ejpam-3550	104	16	,	,	PUNCT
ejpam-3550	104	17	and	and	CCONJ
ejpam-3550	104	18	(	(	PUNCT
ejpam-3550	104	19	iii	iii	NOUN
ejpam-3550	104	20	)	)	PUNCT
ejpam-3550	104	21	ew	ew	NOUN
ejpam-3550	104	22	⊆	⊆	NUM
ejpam-3550	104	23	v	v	NOUN
ejpam-3550	104	24	(	(	PUNCT
ejpam-3550	104	25	hw	hw	NOUN
ejpam-3550	104	26	)	)	PUNCT
ejpam-3550	104	27	is	be	AUX
ejpam-3550	104	28	a	a	DET
ejpam-3550	104	29	point	point	NOUN
ejpam-3550	104	30	-	-	PUNCT
ejpam-3550	104	31	wise	wise	ADJ
ejpam-3550	104	32	non	non	ADJ
ejpam-3550	104	33	-	-	ADJ
ejpam-3550	104	34	dominating	dominating	ADJ
ejpam-3550	104	35	set	set	NOUN
ejpam-3550	104	36	of	of	ADP
ejpam-3550	104	37	hw	hw	PRON
ejpam-3550	104	38	for	for	ADP
ejpam-3550	104	39	each	each	DET
ejpam-3550	104	40	w	w	PROPN
ejpam-3550	104	41	∈	∈	PROPN
ejpam-3550	104	42	v	v	NOUN
ejpam-3550	104	43	(	(	PUNCT
ejpam-3550	104	44	g)\ng(a	g)\ng(a	NOUN
ejpam-3550	104	45	)	)	PUNCT
ejpam-3550	104	46	.	.	PUNCT
ejpam-3550	105	1	proof	proof	NOUN
ejpam-3550	105	2	.	.	PUNCT
ejpam-3550	106	1	suppose	suppose	VERB
ejpam-3550	106	2	c	c	NOUN
ejpam-3550	106	3	is	be	AUX
ejpam-3550	106	4	a	a	DET
ejpam-3550	106	5	hop	hop	NOUN
ejpam-3550	106	6	dominating	dominating	NOUN
ejpam-3550	106	7	set	set	NOUN
ejpam-3550	106	8	of	of	ADP
ejpam-3550	106	9	g	g	PROPN
ejpam-3550	106	10	◦	◦	NOUN
ejpam-3550	106	11	h	h	NOUN
ejpam-3550	106	12	and	and	CCONJ
ejpam-3550	106	13	set	set	VERB
ejpam-3550	106	14	a	a	DET
ejpam-3550	106	15	=	=	SYM
ejpam-3550	106	16	c	c	NOUN
ejpam-3550	106	17	∩	∩	X
ejpam-3550	106	18	v	v	X
ejpam-3550	106	19	(	(	PUNCT
ejpam-3550	106	20	g	g	NOUN
ejpam-3550	106	21	)	)	PUNCT
ejpam-3550	106	22	.	.	PUNCT
ejpam-3550	107	1	let	let	VERB
ejpam-3550	107	2	w	w	NOUN
ejpam-3550	107	3	∈	∈	PROPN
ejpam-3550	107	4	v	v	ADP
ejpam-3550	107	5	(	(	PUNCT
ejpam-3550	107	6	g	g	NOUN
ejpam-3550	107	7	)	)	PUNCT
ejpam-3550	107	8	\	\	NOUN
ejpam-3550	108	1	a.	a.	NOUN
ejpam-3550	108	2	then	then	ADV
ejpam-3550	108	3	there	there	PRON
ejpam-3550	108	4	exists	exist	VERB
ejpam-3550	108	5	x	x	X
ejpam-3550	108	6	∈	∈	PROPN
ejpam-3550	108	7	c	c	NOUN
ejpam-3550	108	8	such	such	ADJ
ejpam-3550	108	9	that	that	SCONJ
ejpam-3550	108	10	dg	dg	PROPN
ejpam-3550	108	11	◦	◦	NOUN
ejpam-3550	108	12	h(w	h(w	PROPN
ejpam-3550	108	13	,	,	PUNCT
ejpam-3550	108	14	x	x	X
ejpam-3550	108	15	)	)	PUNCT
ejpam-3550	109	1	=	=	SYM
ejpam-3550	109	2	2	2	X
ejpam-3550	109	3	.	.	PUNCT
ejpam-3550	110	1	if	if	SCONJ
ejpam-3550	110	2	x	x	SYM
ejpam-3550	110	3	∈	∈	PROPN
ejpam-3550	110	4	a	a	PRON
ejpam-3550	110	5	,	,	PUNCT
ejpam-3550	110	6	then	then	ADV
ejpam-3550	110	7	dg(w	dg(w	NOUN
ejpam-3550	110	8	,	,	PUNCT
ejpam-3550	110	9	x	x	X
ejpam-3550	110	10	)	)	PUNCT
ejpam-3550	110	11	=	=	SYM
ejpam-3550	110	12	2	2	X
ejpam-3550	110	13	.	.	PUNCT
ejpam-3550	110	14	suppose	suppose	VERB
ejpam-3550	110	15	that	that	SCONJ
ejpam-3550	110	16	x	x	SYM
ejpam-3550	110	17	/∈	/∈	PUNCT
ejpam-3550	110	18	a.	a.	NOUN
ejpam-3550	110	19	then	then	ADV
ejpam-3550	110	20	there	there	PRON
ejpam-3550	110	21	exists	exist	VERB
ejpam-3550	110	22	y	y	PROPN
ejpam-3550	110	23	∈	∈	PROPN
ejpam-3550	110	24	v	v	ADP
ejpam-3550	110	25	(	(	PUNCT
ejpam-3550	110	26	g	g	NOUN
ejpam-3550	110	27	)	)	PUNCT
ejpam-3550	110	28	such	such	ADJ
ejpam-3550	110	29	that	that	SCONJ
ejpam-3550	110	30	x	x	SYM
ejpam-3550	110	31	∈	∈	NOUN
ejpam-3550	110	32	v	v	ADP
ejpam-3550	110	33	(	(	PUNCT
ejpam-3550	110	34	hy	hy	NOUN
ejpam-3550	110	35	)	)	PUNCT
ejpam-3550	110	36	.	.	PUNCT
ejpam-3550	111	1	since	since	SCONJ
ejpam-3550	111	2	dg	dg	PROPN
ejpam-3550	111	3	◦	◦	PROPN
ejpam-3550	111	4	h(w	h(w	PROPN
ejpam-3550	111	5	,	,	PUNCT
ejpam-3550	111	6	x	x	X
ejpam-3550	111	7	)	)	PUNCT
ejpam-3550	111	8	=	=	SYM
ejpam-3550	111	9	2	2	NUM
ejpam-3550	111	10	,	,	PUNCT
ejpam-3550	111	11	it	it	PRON
ejpam-3550	111	12	follows	follow	VERB
ejpam-3550	111	13	that	that	SCONJ
ejpam-3550	111	14	y	y	PROPN
ejpam-3550	111	15	∈	∈	PROPN
ejpam-3550	111	16	ng(w	ng(w	NOUN
ejpam-3550	111	17	)	)	PUNCT
ejpam-3550	111	18	.	.	PUNCT
ejpam-3550	112	1	thus	thus	ADV
ejpam-3550	112	2	,	,	PUNCT
ejpam-3550	112	3	(	(	PUNCT
ejpam-3550	112	4	i	i	NOUN
ejpam-3550	112	5	)	)	PUNCT
ejpam-3550	112	6	holds	hold	VERB
ejpam-3550	112	7	.	.	PUNCT
ejpam-3550	113	1	let	let	VERB
ejpam-3550	113	2	v	v	NUM
ejpam-3550	113	3	∈	∈	PROPN
ejpam-3550	113	4	v	v	NOUN
ejpam-3550	113	5	(	(	PUNCT
ejpam-3550	113	6	g	g	NOUN
ejpam-3550	113	7	)	)	PUNCT
ejpam-3550	113	8	.	.	PUNCT
ejpam-3550	114	1	set	set	VERB
ejpam-3550	114	2	sv	sv	X
ejpam-3550	115	1	=	=	SYM
ejpam-3550	115	2	c	c	PROPN
ejpam-3550	115	3	∩	∩	X
ejpam-3550	115	4	v	v	X
ejpam-3550	115	5	(	(	PUNCT
ejpam-3550	115	6	hv	hv	PROPN
ejpam-3550	115	7	)	)	PUNCT
ejpam-3550	115	8	if	if	SCONJ
ejpam-3550	115	9	v	v	NUM
ejpam-3550	115	10	∈	∈	PROPN
ejpam-3550	115	11	v	v	NOUN
ejpam-3550	115	12	(	(	PUNCT
ejpam-3550	115	13	g	g	NOUN
ejpam-3550	115	14	)	)	PUNCT
ejpam-3550	115	15	∩	∩	NOUN
ejpam-3550	115	16	ng(a	ng(a	NOUN
ejpam-3550	115	17	)	)	PUNCT
ejpam-3550	115	18	and	and	CCONJ
ejpam-3550	115	19	ew	ew	INTJ
ejpam-3550	115	20	=	=	SYM
ejpam-3550	115	21	c	c	PROPN
ejpam-3550	115	22	∩	∩	X
ejpam-3550	115	23	v	v	X
ejpam-3550	115	24	(	(	PUNCT
ejpam-3550	115	25	hw	hw	NOUN
ejpam-3550	115	26	)	)	PUNCT
ejpam-3550	115	27	if	if	SCONJ
ejpam-3550	115	28	v	v	NUM
ejpam-3550	115	29	∈	∈	PROPN
ejpam-3550	115	30	v	v	NOUN
ejpam-3550	115	31	(	(	PUNCT
ejpam-3550	115	32	g	g	NOUN
ejpam-3550	115	33	)	)	PUNCT
ejpam-3550	115	34	\	\	NOUN
ejpam-3550	115	35	ng(a	ng(a	NOUN
ejpam-3550	115	36	)	)	PUNCT
ejpam-3550	115	37	.	.	PUNCT
ejpam-3550	116	1	then	then	ADV
ejpam-3550	116	2	,	,	PUNCT
ejpam-3550	116	3	clearly	clearly	ADV
ejpam-3550	116	4	,	,	PUNCT
ejpam-3550	116	5	sv	sv	PROPN
ejpam-3550	116	6	⊆	⊆	NUM
ejpam-3550	116	7	v	v	X
ejpam-3550	116	8	(	(	PUNCT
ejpam-3550	116	9	hv	hv	NOUN
ejpam-3550	116	10	)	)	PUNCT
ejpam-3550	116	11	and	and	CCONJ
ejpam-3550	116	12	ew	ew	VERB
ejpam-3550	116	13	⊆	⊆	NUM
ejpam-3550	116	14	v	v	NOUN
ejpam-3550	116	15	(	(	PUNCT
ejpam-3550	116	16	hw	hw	NOUN
ejpam-3550	116	17	)	)	PUNCT
ejpam-3550	116	18	.	.	PUNCT
ejpam-3550	117	1	suppose	suppose	VERB
ejpam-3550	117	2	that	that	SCONJ
ejpam-3550	117	3	w	w	PROPN
ejpam-3550	117	4	∈	∈	PROPN
ejpam-3550	117	5	v	v	ADP
ejpam-3550	117	6	(	(	PUNCT
ejpam-3550	117	7	g	g	NOUN
ejpam-3550	117	8	)	)	PUNCT
ejpam-3550	117	9	\	\	NOUN
ejpam-3550	117	10	ng(a	ng(a	NOUN
ejpam-3550	117	11	)	)	PUNCT
ejpam-3550	117	12	and	and	CCONJ
ejpam-3550	117	13	let	let	VERB
ejpam-3550	117	14	q	q	PROPN
ejpam-3550	117	15	∈	∈	PROPN
ejpam-3550	117	16	v	v	NOUN
ejpam-3550	117	17	(	(	PUNCT
ejpam-3550	117	18	hw	hw	NOUN
ejpam-3550	117	19	)	)	PUNCT
ejpam-3550	117	20	\	\	NOUN
ejpam-3550	118	1	ew	ew	PROPN
ejpam-3550	118	2	.	.	PUNCT
ejpam-3550	119	1	since	since	SCONJ
ejpam-3550	119	2	c	c	PROPN
ejpam-3550	119	3	is	be	AUX
ejpam-3550	119	4	a	a	DET
ejpam-3550	119	5	hop	hop	NOUN
ejpam-3550	119	6	dominating	dominating	NOUN
ejpam-3550	119	7	set	set	NOUN
ejpam-3550	119	8	of	of	ADP
ejpam-3550	119	9	g	g	PROPN
ejpam-3550	119	10	◦	◦	NOUN
ejpam-3550	119	11	h	h	NOUN
ejpam-3550	119	12	,	,	PUNCT
ejpam-3550	119	13	there	there	PRON
ejpam-3550	119	14	exists	exist	VERB
ejpam-3550	119	15	u	u	PROPN
ejpam-3550	119	16	∈	∈	PROPN
ejpam-3550	119	17	c	c	NOUN
ejpam-3550	119	18	such	such	ADJ
ejpam-3550	119	19	that	that	SCONJ
ejpam-3550	119	20	dg	dg	VERB
ejpam-3550	119	21	◦	◦	NOUN
ejpam-3550	119	22	h(q	h(q	ADJ
ejpam-3550	119	23	,	,	PUNCT
ejpam-3550	119	24	u	u	NOUN
ejpam-3550	119	25	)	)	PUNCT
ejpam-3550	119	26	=	=	SYM
ejpam-3550	119	27	2	2	X
ejpam-3550	119	28	.	.	PUNCT
ejpam-3550	119	29	by	by	ADP
ejpam-3550	119	30	assumption	assumption	NOUN
ejpam-3550	119	31	,	,	PUNCT
ejpam-3550	119	32	u	u	NOUN
ejpam-3550	119	33	/∈	/∈	NOUN
ejpam-3550	119	34	a.	a.	PROPN
ejpam-3550	119	35	thus	thus	ADV
ejpam-3550	119	36	,	,	PUNCT
ejpam-3550	119	37	u	u	PROPN
ejpam-3550	119	38	∈	∈	PROPN
ejpam-3550	119	39	ew	ew	X
ejpam-3550	119	40	and	and	CCONJ
ejpam-3550	119	41	qu	qu	PROPN
ejpam-3550	119	42	/∈	/∈	PUNCT
ejpam-3550	119	43	e(hw	e(hw	PROPN
ejpam-3550	119	44	)	)	PUNCT
ejpam-3550	119	45	.	.	PUNCT
ejpam-3550	120	1	therefore	therefore	ADV
ejpam-3550	120	2	ew	ew	INTJ
ejpam-3550	120	3	is	be	VERB
ejpam-3550	120	4	a	a	DET
ejpam-3550	120	5	point	point	NOUN
ejpam-3550	120	6	-	-	PUNCT
ejpam-3550	120	7	wise	wise	ADJ
ejpam-3550	120	8	non	non	ADJ
ejpam-3550	120	9	-	-	ADJ
ejpam-3550	120	10	dominating	dominating	ADJ
ejpam-3550	120	11	set	set	NOUN
ejpam-3550	120	12	of	of	ADP
ejpam-3550	120	13	hw	hw	PRON
ejpam-3550	120	14	,	,	PUNCT
ejpam-3550	120	15	showing	show	VERB
ejpam-3550	120	16	that	that	SCONJ
ejpam-3550	120	17	(	(	PUNCT
ejpam-3550	120	18	iii	iii	NOUN
ejpam-3550	120	19	)	)	PUNCT
ejpam-3550	120	20	holds	hold	VERB
ejpam-3550	120	21	.	.	PUNCT
ejpam-3550	121	1	for	for	ADP
ejpam-3550	121	2	the	the	DET
ejpam-3550	121	3	converse	converse	NOUN
ejpam-3550	121	4	,	,	PUNCT
ejpam-3550	121	5	suppose	suppose	VERB
ejpam-3550	121	6	that	that	SCONJ
ejpam-3550	121	7	c	c	PROPN
ejpam-3550	121	8	has	have	VERB
ejpam-3550	121	9	the	the	DET
ejpam-3550	121	10	given	give	VERB
ejpam-3550	121	11	form	form	NOUN
ejpam-3550	121	12	and	and	CCONJ
ejpam-3550	121	13	satisfies	satisfie	NOUN
ejpam-3550	121	14	properties	property	NOUN
ejpam-3550	121	15	(	(	PUNCT
ejpam-3550	121	16	i	i	NOUN
ejpam-3550	121	17	)	)	PUNCT
ejpam-3550	121	18	,	,	PUNCT
ejpam-3550	121	19	(	(	PUNCT
ejpam-3550	121	20	ii	ii	NOUN
ejpam-3550	121	21	)	)	PUNCT
ejpam-3550	121	22	,	,	PUNCT
ejpam-3550	121	23	and	and	CCONJ
ejpam-3550	121	24	(	(	PUNCT
ejpam-3550	121	25	iii	iii	NOUN
ejpam-3550	121	26	)	)	PUNCT
ejpam-3550	121	27	.	.	PUNCT
ejpam-3550	122	1	let	let	VERB
ejpam-3550	122	2	z	z	NOUN
ejpam-3550	122	3	∈	∈	PROPN
ejpam-3550	122	4	v	v	NOUN
ejpam-3550	122	5	(	(	PUNCT
ejpam-3550	122	6	g	g	PROPN
ejpam-3550	122	7	◦	◦	NOUN
ejpam-3550	122	8	h	h	NOUN
ejpam-3550	122	9	)	)	PUNCT
ejpam-3550	122	10	\c	\c	NOUN
ejpam-3550	122	11	and	and	CCONJ
ejpam-3550	122	12	let	let	VERB
ejpam-3550	122	13	v	v	NUM
ejpam-3550	122	14	∈	∈	PROPN
ejpam-3550	122	15	v	v	NOUN
ejpam-3550	122	16	(	(	PUNCT
ejpam-3550	122	17	g	g	NOUN
ejpam-3550	122	18	)	)	PUNCT
ejpam-3550	122	19	such	such	ADJ
ejpam-3550	122	20	that	that	SCONJ
ejpam-3550	122	21	z	z	PROPN
ejpam-3550	122	22	∈	∈	PROPN
ejpam-3550	122	23	v	v	NOUN
ejpam-3550	122	24	(	(	PUNCT
ejpam-3550	122	25	v	v	PROPN
ejpam-3550	122	26	+	+	PROPN
ejpam-3550	122	27	hv	hv	NOUN
ejpam-3550	122	28	)	)	PUNCT
ejpam-3550	122	29	.	.	PUNCT
ejpam-3550	123	1	consider	consider	VERB
ejpam-3550	123	2	the	the	DET
ejpam-3550	123	3	following	follow	VERB
ejpam-3550	123	4	cases	case	NOUN
ejpam-3550	123	5	:	:	PUNCT
ejpam-3550	123	6	case	case	NOUN
ejpam-3550	123	7	1	1	NUM
ejpam-3550	123	8	.	.	PUNCT
ejpam-3550	124	1	z	z	NOUN
ejpam-3550	124	2	=	=	NOUN
ejpam-3550	124	3	v	v	NOUN
ejpam-3550	124	4	then	then	ADV
ejpam-3550	124	5	z	z	PROPN
ejpam-3550	124	6	/∈	/∈	PUNCT
ejpam-3550	124	7	a.	a.	NOUN
ejpam-3550	124	8	from	from	ADP
ejpam-3550	124	9	the	the	DET
ejpam-3550	124	10	assumption	assumption	NOUN
ejpam-3550	124	11	that	that	SCONJ
ejpam-3550	124	12	(	(	PUNCT
ejpam-3550	124	13	i	i	NOUN
ejpam-3550	124	14	)	)	PUNCT
ejpam-3550	124	15	holds	hold	VERB
ejpam-3550	124	16	,	,	PUNCT
ejpam-3550	124	17	it	it	PRON
ejpam-3550	124	18	follows	follow	VERB
ejpam-3550	124	19	that	that	SCONJ
ejpam-3550	124	20	there	there	PRON
ejpam-3550	124	21	exists	exist	VERB
ejpam-3550	124	22	y	y	PROPN
ejpam-3550	124	23	∈	∈	PROPN
ejpam-3550	124	24	c	c	PROPN
ejpam-3550	124	25	such	such	ADJ
ejpam-3550	124	26	that	that	SCONJ
ejpam-3550	124	27	dg	dg	AUX
ejpam-3550	124	28	◦	◦	NOUN
ejpam-3550	124	29	h(z	h(z	NOUN
ejpam-3550	124	30	,	,	PUNCT
ejpam-3550	124	31	y	y	NOUN
ejpam-3550	124	32	)	)	PUNCT
ejpam-3550	124	33	=	=	SYM
ejpam-3550	124	34	2	2	X
ejpam-3550	124	35	.	.	X
ejpam-3550	124	36	case	case	NOUN
ejpam-3550	124	37	2	2	NUM
ejpam-3550	124	38	.	.	PUNCT
ejpam-3550	124	39	z	z	NOUN
ejpam-3550	125	1	6=	6=	ADP
ejpam-3550	125	2	v	v	ADP
ejpam-3550	125	3	then	then	ADV
ejpam-3550	125	4	z	z	PROPN
ejpam-3550	125	5	∈	∈	PROPN
ejpam-3550	125	6	v	v	ADP
ejpam-3550	125	7	(	(	PUNCT
ejpam-3550	125	8	hv	hv	PROPN
ejpam-3550	125	9	)	)	PUNCT
ejpam-3550	125	10	.	.	PUNCT
ejpam-3550	126	1	if	if	SCONJ
ejpam-3550	126	2	v	v	NUM
ejpam-3550	126	3	∈	∈	PROPN
ejpam-3550	126	4	ng(a	ng(a	NOUN
ejpam-3550	126	5	)	)	PUNCT
ejpam-3550	127	1	,	,	PUNCT
ejpam-3550	127	2	say	say	VERB
ejpam-3550	127	3	vw	vw	PROPN
ejpam-3550	127	4	∈	∈	PROPN
ejpam-3550	127	5	e(g	e(g	PROPN
ejpam-3550	127	6	)	)	PUNCT
ejpam-3550	127	7	for	for	ADP
ejpam-3550	127	8	some	some	DET
ejpam-3550	127	9	w	w	PROPN
ejpam-3550	127	10	∈	∈	PROPN
ejpam-3550	127	11	a	a	PRON
ejpam-3550	127	12	,	,	PUNCT
ejpam-3550	127	13	then	then	ADV
ejpam-3550	127	14	dg	dg	VERB
ejpam-3550	127	15	◦	◦	NOUN
ejpam-3550	127	16	h(z	h(z	NOUN
ejpam-3550	127	17	,	,	PUNCT
ejpam-3550	127	18	w	w	NOUN
ejpam-3550	127	19	)	)	PUNCT
ejpam-3550	127	20	=	=	SYM
ejpam-3550	127	21	2	2	X
ejpam-3550	127	22	.	.	PUNCT
ejpam-3550	127	23	suppose	suppose	VERB
ejpam-3550	127	24	that	that	SCONJ
ejpam-3550	127	25	v	v	NOUN
ejpam-3550	127	26	/∈	/∈	PUNCT
ejpam-3550	127	27	ng(a	ng(a	NUM
ejpam-3550	127	28	)	)	PUNCT
ejpam-3550	127	29	.	.	PUNCT
ejpam-3550	128	1	then	then	ADV
ejpam-3550	128	2	z	z	PROPN
ejpam-3550	128	3	∈	∈	PROPN
ejpam-3550	128	4	v	v	ADP
ejpam-3550	128	5	(	(	PUNCT
ejpam-3550	128	6	hv	hv	PROPN
ejpam-3550	128	7	)	)	PUNCT
ejpam-3550	128	8	\ev	\ev	PROPN
ejpam-3550	128	9	where	where	SCONJ
ejpam-3550	128	10	ev	ev	PROPN
ejpam-3550	128	11	is	be	AUX
ejpam-3550	128	12	a	a	DET
ejpam-3550	128	13	point	point	NOUN
ejpam-3550	128	14	-	-	PUNCT
ejpam-3550	128	15	wise	wise	ADJ
ejpam-3550	128	16	non	non	ADJ
ejpam-3550	128	17	-	-	ADJ
ejpam-3550	128	18	dominating	dominating	ADJ
ejpam-3550	128	19	set	set	NOUN
ejpam-3550	128	20	of	of	ADP
ejpam-3550	128	21	hv	hv	PROPN
ejpam-3550	128	22	by	by	ADP
ejpam-3550	128	23	property	property	NOUN
ejpam-3550	128	24	(	(	PUNCT
ejpam-3550	128	25	iii	iii	NOUN
ejpam-3550	128	26	)	)	PUNCT
ejpam-3550	128	27	.	.	PUNCT
ejpam-3550	129	1	thus	thus	ADV
ejpam-3550	129	2	,	,	PUNCT
ejpam-3550	129	3	there	there	PRON
ejpam-3550	129	4	exists	exist	VERB
ejpam-3550	129	5	p	p	PROPN
ejpam-3550	129	6	∈	∈	PROPN
ejpam-3550	129	7	ev	ev	ADP
ejpam-3550	129	8	⊂	⊂	PROPN
ejpam-3550	129	9	c	c	PROPN
ejpam-3550	129	10	such	such	ADJ
ejpam-3550	129	11	that	that	SCONJ
ejpam-3550	129	12	dg	dg	AUX
ejpam-3550	129	13	◦	◦	NOUN
ejpam-3550	129	14	h(x	h(x	PROPN
ejpam-3550	129	15	,	,	PUNCT
ejpam-3550	129	16	p	p	NOUN
ejpam-3550	129	17	)	)	PUNCT
ejpam-3550	129	18	=	=	SYM
ejpam-3550	129	19	2	2	X
ejpam-3550	129	20	.	.	PUNCT
ejpam-3550	129	21	accordingly	accordingly	ADV
ejpam-3550	129	22	,	,	PUNCT
ejpam-3550	129	23	c	c	PROPN
ejpam-3550	129	24	is	be	AUX
ejpam-3550	129	25	a	a	DET
ejpam-3550	129	26	hop	hop	NOUN
ejpam-3550	129	27	dominating	dominating	NOUN
ejpam-3550	129	28	set	set	NOUN
ejpam-3550	129	29	of	of	ADP
ejpam-3550	129	30	g	g	PROPN
ejpam-3550	129	31	◦	◦	NOUN
ejpam-3550	129	32	h.	h.	NOUN
ejpam-3550	129	33	corollary	corollary	ADJ
ejpam-3550	129	34	2	2	PROPN
ejpam-3550	129	35	.	.	PUNCT
ejpam-3550	130	1	let	let	VERB
ejpam-3550	130	2	g	g	PRON
ejpam-3550	130	3	be	be	AUX
ejpam-3550	130	4	a	a	DET
ejpam-3550	130	5	connected	connected	ADJ
ejpam-3550	130	6	non	non	ADJ
ejpam-3550	130	7	-	-	ADJ
ejpam-3550	130	8	trivial	trivial	ADJ
ejpam-3550	130	9	graph	graph	NOUN
ejpam-3550	130	10	and	and	CCONJ
ejpam-3550	130	11	let	let	VERB
ejpam-3550	130	12	h	h	NOUN
ejpam-3550	130	13	be	be	AUX
ejpam-3550	130	14	any	any	DET
ejpam-3550	130	15	graph	graph	NOUN
ejpam-3550	130	16	.	.	PUNCT
ejpam-3550	131	1	then	then	ADV
ejpam-3550	131	2	:	:	PUNCT
ejpam-3550	131	3	(	(	PUNCT
ejpam-3550	131	4	i	i	NOUN
ejpam-3550	131	5	)	)	PUNCT
ejpam-3550	131	6	γh(g	γh(g	PUNCT
ejpam-3550	131	7	◦	◦	NOUN
ejpam-3550	131	8	h	h	NOUN
ejpam-3550	131	9	)	)	PUNCT
ejpam-3550	131	10	≤	≤	NOUN
ejpam-3550	131	11	min{γ∗t1,2(g	min{γ∗t1,2(g	NOUN
ejpam-3550	131	12	)	)	PUNCT
ejpam-3550	131	13	,	,	PUNCT
ejpam-3550	131	14	[	[	X
ejpam-3550	131	15	1	1	NUM
ejpam-3550	131	16	+	+	NUM
ejpam-3550	131	17	pnd(h)]γ(g	pnd(h)]γ(g	NOUN
ejpam-3550	131	18	)	)	PUNCT
ejpam-3550	131	19	}	}	PUNCT
ejpam-3550	131	20	.	.	PUNCT
ejpam-3550	132	1	(	(	PUNCT
ejpam-3550	132	2	ii	ii	NOUN
ejpam-3550	132	3	)	)	PUNCT
ejpam-3550	132	4	γh(g	γh(g	PUNCT
ejpam-3550	132	5	◦	◦	NOUN
ejpam-3550	132	6	h	h	NOUN
ejpam-3550	132	7	)	)	PUNCT
ejpam-3550	132	8	=	=	SYM
ejpam-3550	132	9	2	2	NUM
ejpam-3550	132	10	if	if	SCONJ
ejpam-3550	132	11	γ∗t1,2(g	γ∗t1,2(g	PROPN
ejpam-3550	132	12	)	)	PUNCT
ejpam-3550	132	13	=	=	SYM
ejpam-3550	132	14	2	2	X
ejpam-3550	132	15	.	.	PUNCT
ejpam-3550	132	16	(	(	PUNCT
ejpam-3550	132	17	iii	iii	NOUN
ejpam-3550	132	18	)	)	PUNCT
ejpam-3550	132	19	γh(g	γh(g	PUNCT
ejpam-3550	132	20	◦	◦	NOUN
ejpam-3550	132	21	h	h	NOUN
ejpam-3550	132	22	)	)	PUNCT
ejpam-3550	132	23	=	=	SYM
ejpam-3550	132	24	2	2	NUM
ejpam-3550	132	25	if	if	SCONJ
ejpam-3550	132	26	γ(g	γ(g	NOUN
ejpam-3550	132	27	)	)	PUNCT
ejpam-3550	132	28	=	=	SYM
ejpam-3550	133	1	1	1	NUM
ejpam-3550	133	2	and	and	CCONJ
ejpam-3550	133	3	h	h	NOUN
ejpam-3550	133	4	has	have	VERB
ejpam-3550	133	5	an	an	DET
ejpam-3550	133	6	isolated	isolated	ADJ
ejpam-3550	133	7	vertex	vertex	NOUN
ejpam-3550	133	8	.	.	PUNCT
ejpam-3550	134	1	let	let	VERB
ejpam-3550	134	2	a	a	PRON
ejpam-3550	134	3	be	be	AUX
ejpam-3550	134	4	a	a	DET
ejpam-3550	134	5	γ∗t1,2	γ∗t1,2	NOUN
ejpam-3550	134	6	-	-	PUNCT
ejpam-3550	134	7	set	set	NOUN
ejpam-3550	134	8	of	of	ADP
ejpam-3550	134	9	g.	g.	PROPN
ejpam-3550	134	10	since	since	SCONJ
ejpam-3550	134	11	a	a	PRON
ejpam-3550	134	12	is	be	AUX
ejpam-3550	134	13	a	a	DET
ejpam-3550	134	14	total	total	ADJ
ejpam-3550	134	15	dominating	dominating	NOUN
ejpam-3550	134	16	set	set	NOUN
ejpam-3550	134	17	of	of	ADP
ejpam-3550	134	18	g	g	PROPN
ejpam-3550	134	19	,	,	PUNCT
ejpam-3550	134	20	v	v	NOUN
ejpam-3550	134	21	(	(	PUNCT
ejpam-3550	134	22	g	g	NOUN
ejpam-3550	134	23	)	)	PUNCT
ejpam-3550	134	24	\ng(a	\ng(a	PROPN
ejpam-3550	134	25	)	)	PUNCT
ejpam-3550	134	26	=	=	VERB
ejpam-3550	134	27	∅.	∅.	AUX
ejpam-3550	134	28	let	let	VERB
ejpam-3550	134	29	w	w	PROPN
ejpam-3550	134	30	∈	∈	PROPN
ejpam-3550	134	31	v	v	ADP
ejpam-3550	134	32	(	(	PUNCT
ejpam-3550	134	33	g	g	NOUN
ejpam-3550	134	34	)	)	PUNCT
ejpam-3550	134	35	\	\	PROPN
ejpam-3550	134	36	a.	a.	NOUN
ejpam-3550	134	37	since	since	SCONJ
ejpam-3550	134	38	a	a	PRON
ejpam-3550	134	39	is	be	AUX
ejpam-3550	134	40	a	a	DET
ejpam-3550	134	41	hop	hop	NOUN
ejpam-3550	134	42	dominating	dominating	NOUN
ejpam-3550	134	43	set	set	NOUN
ejpam-3550	134	44	of	of	ADP
ejpam-3550	134	45	g	g	NOUN
ejpam-3550	134	46	,	,	PUNCT
ejpam-3550	134	47	there	there	PRON
ejpam-3550	134	48	exists	exist	VERB
ejpam-3550	134	49	x	x	X
ejpam-3550	134	50	∈	∈	PROPN
ejpam-3550	135	1	a	a	DET
ejpam-3550	135	2	such	such	ADJ
ejpam-3550	135	3	that	that	PRON
ejpam-3550	135	4	dg(x	dg(x	ADJ
ejpam-3550	135	5	,	,	PUNCT
ejpam-3550	135	6	w	w	NOUN
ejpam-3550	135	7	)	)	PUNCT
ejpam-3550	135	8	=	=	SYM
ejpam-3550	135	9	2	2	X
ejpam-3550	135	10	.	.	X
ejpam-3550	135	11	setting	set	VERB
ejpam-3550	135	12	sv	sv	X
ejpam-3550	135	13	=	=	NOUN
ejpam-3550	135	14	∅	∅	NOUN
ejpam-3550	135	15	for	for	ADP
ejpam-3550	135	16	each	each	DET
ejpam-3550	135	17	v	v	ADP
ejpam-3550	135	18	∈	∈	PROPN
ejpam-3550	135	19	a	a	DET
ejpam-3550	135	20	∩ng(a	∩ng(a	NOUN
ejpam-3550	135	21	)	)	PUNCT
ejpam-3550	135	22	=	=	SYM
ejpam-3550	135	23	a	a	X
ejpam-3550	135	24	,	,	PUNCT
ejpam-3550	135	25	we	we	PRON
ejpam-3550	135	26	find	find	VERB
ejpam-3550	135	27	that	that	SCONJ
ejpam-3550	135	28	c	c	NOUN
ejpam-3550	135	29	=	=	PUNCT
ejpam-3550	135	30	a	a	DET
ejpam-3550	135	31	satisfies	satisfie	NOUN
ejpam-3550	135	32	s.	s.	PROPN
ejpam-3550	135	33	canoy	canoy	PROPN
ejpam-3550	135	34	jr	jr	PROPN
ejpam-3550	135	35	.	.	PROPN
ejpam-3550	135	36	,	,	PUNCT
ejpam-3550	135	37	r.	r.	PROPN
ejpam-3550	135	38	mollejon	mollejon	NOUN
ejpam-3550	135	39	,	,	PUNCT
ejpam-3550	135	40	jg	jg	PROPN
ejpam-3550	135	41	.	.	PROPN
ejpam-3550	135	42	canoy	canoy	PROPN
ejpam-3550	135	43	/	/	SYM
ejpam-3550	135	44	eur	eur	PROPN
ejpam-3550	135	45	.	.	PUNCT
ejpam-3550	136	1	j.	j.	PROPN
ejpam-3550	136	2	pure	pure	PROPN
ejpam-3550	136	3	appl	appl	PROPN
ejpam-3550	136	4	.	.	PROPN
ejpam-3550	136	5	math	math	PROPN
ejpam-3550	136	6	,	,	PUNCT
ejpam-3550	136	7	12	12	NUM
ejpam-3550	136	8	(	(	PUNCT
ejpam-3550	136	9	4	4	NUM
ejpam-3550	136	10	)	)	PUNCT
ejpam-3550	136	11	(	(	PUNCT
ejpam-3550	136	12	2019	2019	NUM
ejpam-3550	136	13	)	)	PUNCT
ejpam-3550	136	14	,	,	PUNCT
ejpam-3550	136	15	1455	1455	NUM
ejpam-3550	136	16	-	-	SYM
ejpam-3550	136	17	1463	1463	NUM
ejpam-3550	136	18	1459	1459	NUM
ejpam-3550	136	19	conditions	condition	NOUN
ejpam-3550	136	20	(	(	PUNCT
ejpam-3550	136	21	i	i	NOUN
ejpam-3550	136	22	)	)	PUNCT
ejpam-3550	136	23	,	,	PUNCT
ejpam-3550	136	24	(	(	PUNCT
ejpam-3550	136	25	ii	ii	NOUN
ejpam-3550	136	26	)	)	PUNCT
ejpam-3550	136	27	,	,	PUNCT
ejpam-3550	136	28	and	and	CCONJ
ejpam-3550	136	29	(	(	PUNCT
ejpam-3550	136	30	iii	iii	NOUN
ejpam-3550	136	31	)	)	PUNCT
ejpam-3550	136	32	of	of	ADP
ejpam-3550	136	33	theorem	theorem	NOUN
ejpam-3550	136	34	2	2	NUM
ejpam-3550	136	35	.	.	PUNCT
ejpam-3550	137	1	thus	thus	ADV
ejpam-3550	137	2	,	,	PUNCT
ejpam-3550	137	3	c	c	X
ejpam-3550	137	4	=	=	PUNCT
ejpam-3550	137	5	a	a	PRON
ejpam-3550	137	6	is	be	AUX
ejpam-3550	137	7	a	a	DET
ejpam-3550	137	8	hop	hop	NOUN
ejpam-3550	137	9	dominating	dominating	NOUN
ejpam-3550	137	10	set	set	NOUN
ejpam-3550	137	11	of	of	ADP
ejpam-3550	137	12	g	g	NOUN
ejpam-3550	137	13	◦	◦	NOUN
ejpam-3550	137	14	h	h	NOUN
ejpam-3550	137	15	and	and	CCONJ
ejpam-3550	137	16	γh(g	γh(g	ADP
ejpam-3550	137	17	◦	◦	NOUN
ejpam-3550	137	18	h	h	NOUN
ejpam-3550	137	19	)	)	PUNCT
ejpam-3550	137	20	≤	≤	NOUN
ejpam-3550	137	21	|c|	|c|	PROPN
ejpam-3550	137	22	=	=	SYM
ejpam-3550	137	23	|a|	|a|	PROPN
ejpam-3550	137	24	=	=	PROPN
ejpam-3550	137	25	γ∗t1,2(g	γ∗t1,2(g	PROPN
ejpam-3550	137	26	)	)	PUNCT
ejpam-3550	137	27	.	.	PUNCT
ejpam-3550	138	1	next	next	ADV
ejpam-3550	138	2	,	,	PUNCT
ejpam-3550	138	3	let	let	VERB
ejpam-3550	138	4	a0	a0	PROPN
ejpam-3550	138	5	be	be	AUX
ejpam-3550	138	6	a	a	DET
ejpam-3550	138	7	γ	γ	NOUN
ejpam-3550	138	8	-	-	PUNCT
ejpam-3550	138	9	set	set	NOUN
ejpam-3550	138	10	of	of	ADP
ejpam-3550	138	11	g	g	NOUN
ejpam-3550	138	12	and	and	CCONJ
ejpam-3550	138	13	let	let	VERB
ejpam-3550	138	14	d0	d0	NOUN
ejpam-3550	138	15	be	be	AUX
ejpam-3550	138	16	a	a	DET
ejpam-3550	138	17	pnd	pnd	NOUN
ejpam-3550	138	18	-	-	PUNCT
ejpam-3550	138	19	set	set	NOUN
ejpam-3550	138	20	of	of	ADP
ejpam-3550	138	21	h.	h.	PROPN
ejpam-3550	138	22	set	set	PROPN
ejpam-3550	138	23	sv	sv	PROPN
ejpam-3550	138	24	=	=	SYM
ejpam-3550	138	25	dv	dv	PROPN
ejpam-3550	138	26	,	,	PUNCT
ejpam-3550	138	27	where	where	SCONJ
ejpam-3550	138	28	dv	dv	PROPN
ejpam-3550	138	29	⊆	⊆	NUM
ejpam-3550	138	30	v	v	PROPN
ejpam-3550	138	31	(	(	PUNCT
ejpam-3550	138	32	hv	hv	PROPN
ejpam-3550	138	33	)	)	PUNCT
ejpam-3550	138	34	and	and	CCONJ
ejpam-3550	138	35	〈	〈	PROPN
ejpam-3550	138	36	dv	dv	PROPN
ejpam-3550	138	37	〉	〉	PROPN
ejpam-3550	138	38	∼=	∼=	PROPN
ejpam-3550	138	39	〈	〈	PROPN
ejpam-3550	138	40	d	d	PROPN
ejpam-3550	138	41	〉	〉	PROPN
ejpam-3550	138	42	,	,	PUNCT
ejpam-3550	138	43	for	for	ADP
ejpam-3550	138	44	each	each	DET
ejpam-3550	138	45	v	v	PROPN
ejpam-3550	138	46	∈	∈	PROPN
ejpam-3550	138	47	a0	a0	NOUN
ejpam-3550	138	48	.	.	PUNCT
ejpam-3550	139	1	since	since	SCONJ
ejpam-3550	139	2	a0	a0	PROPN
ejpam-3550	139	3	is	be	AUX
ejpam-3550	139	4	a	a	DET
ejpam-3550	139	5	dominating	dominating	NOUN
ejpam-3550	139	6	set	set	NOUN
ejpam-3550	139	7	of	of	ADP
ejpam-3550	139	8	g	g	PROPN
ejpam-3550	139	9	,	,	PUNCT
ejpam-3550	139	10	w	w	PROPN
ejpam-3550	139	11	∈	∈	PROPN
ejpam-3550	139	12	ng(a0	ng(a0	NOUN
ejpam-3550	139	13	)	)	PUNCT
ejpam-3550	139	14	for	for	ADP
ejpam-3550	139	15	each	each	DET
ejpam-3550	139	16	w	w	PROPN
ejpam-3550	139	17	∈	∈	PROPN
ejpam-3550	139	18	v	v	ADP
ejpam-3550	139	19	(	(	PUNCT
ejpam-3550	139	20	g	g	NOUN
ejpam-3550	139	21	)	)	PUNCT
ejpam-3550	139	22	\	\	PROPN
ejpam-3550	139	23	a0	a0	NOUN
ejpam-3550	139	24	(	(	PUNCT
ejpam-3550	139	25	hence	hence	ADV
ejpam-3550	139	26	,	,	PUNCT
ejpam-3550	139	27	[	[	X
ejpam-3550	139	28	v	v	X
ejpam-3550	139	29	(	(	PUNCT
ejpam-3550	139	30	g	g	NOUN
ejpam-3550	139	31	)	)	PUNCT
ejpam-3550	139	32	\	\	PROPN
ejpam-3550	139	33	a0	a0	PROPN
ejpam-3550	139	34	]	]	PUNCT
ejpam-3550	139	35	\	\	X
ejpam-3550	139	36	ng(a0	ng(a0	X
ejpam-3550	139	37	)	)	PUNCT
ejpam-3550	139	38	=	=	SYM
ejpam-3550	139	39	∅	∅	NOUN
ejpam-3550	139	40	)	)	PUNCT
ejpam-3550	139	41	.	.	PUNCT
ejpam-3550	140	1	thus	thus	ADV
ejpam-3550	140	2	,	,	PUNCT
ejpam-3550	140	3	by	by	ADP
ejpam-3550	140	4	theorem	theorem	NOUN
ejpam-3550	140	5	2	2	NUM
ejpam-3550	140	6	,	,	PUNCT
ejpam-3550	140	7	c0	c0	PROPN
ejpam-3550	140	8	=	=	SYM
ejpam-3550	140	9	a0	a0	PROPN
ejpam-3550	140	10	∪	∪	X
ejpam-3550	140	11	(	(	PUNCT
ejpam-3550	140	12	∪u∈a0sv	∪u∈a0sv	NOUN
ejpam-3550	140	13	)	)	PUNCT
ejpam-3550	140	14	is	be	AUX
ejpam-3550	140	15	a	a	DET
ejpam-3550	140	16	hop	hop	NOUN
ejpam-3550	140	17	dominating	dominating	NOUN
ejpam-3550	140	18	set	set	NOUN
ejpam-3550	140	19	of	of	ADP
ejpam-3550	140	20	g	g	PROPN
ejpam-3550	140	21	◦	◦	NOUN
ejpam-3550	140	22	h	h	NOUN
ejpam-3550	140	23	,	,	PUNCT
ejpam-3550	140	24	and	and	CCONJ
ejpam-3550	140	25	γh(g	γh(g	PUNCT
ejpam-3550	140	26	◦	◦	NOUN
ejpam-3550	140	27	h	h	NOUN
ejpam-3550	140	28	)	)	PUNCT
ejpam-3550	140	29	≤	≤	NOUN
ejpam-3550	140	30	|c0|	|c0|	NOUN
ejpam-3550	140	31	=	=	SYM
ejpam-3550	140	32	|a0|+	|a0|+	X
ejpam-3550	140	33	|a0|.pnd(h	|a0|.pnd(h	NOUN
ejpam-3550	140	34	)	)	PUNCT
ejpam-3550	140	35	=	=	PUNCT
ejpam-3550	141	1	[	[	X
ejpam-3550	141	2	1	1	NUM
ejpam-3550	141	3	+	+	NUM
ejpam-3550	141	4	pnd(h)]γ(g	pnd(h)]γ(g	NOUN
ejpam-3550	141	5	)	)	PUNCT
ejpam-3550	141	6	.	.	PUNCT
ejpam-3550	142	1	therefore	therefore	ADV
ejpam-3550	142	2	,	,	PUNCT
ejpam-3550	142	3	γh(g	γh(g	PUNCT
ejpam-3550	142	4	◦	◦	NOUN
ejpam-3550	142	5	h	h	NOUN
ejpam-3550	142	6	)	)	PUNCT
ejpam-3550	142	7	≤	≤	NOUN
ejpam-3550	142	8	min{γ∗t1,2(g	min{γ∗t1,2(g	NOUN
ejpam-3550	142	9	)	)	PUNCT
ejpam-3550	142	10	,	,	PUNCT
ejpam-3550	142	11	[	[	X
ejpam-3550	142	12	1	1	NUM
ejpam-3550	142	13	+	+	NUM
ejpam-3550	142	14	pnd(h)]γ(g	pnd(h)]γ(g	NOUN
ejpam-3550	142	15	)	)	PUNCT
ejpam-3550	142	16	}	}	PUNCT
ejpam-3550	142	17	,	,	PUNCT
ejpam-3550	142	18	showing	show	VERB
ejpam-3550	142	19	that	that	SCONJ
ejpam-3550	142	20	(	(	PUNCT
ejpam-3550	142	21	i	i	NOUN
ejpam-3550	142	22	)	)	PUNCT
ejpam-3550	142	23	holds	hold	VERB
ejpam-3550	142	24	.	.	PUNCT
ejpam-3550	143	1	statements	statement	NOUN
ejpam-3550	143	2	(	(	PUNCT
ejpam-3550	143	3	ii	ii	NOUN
ejpam-3550	143	4	)	)	PUNCT
ejpam-3550	143	5	and	and	CCONJ
ejpam-3550	143	6	(	(	PUNCT
ejpam-3550	143	7	iii	iii	X
ejpam-3550	143	8	)	)	PUNCT
ejpam-3550	143	9	are	be	AUX
ejpam-3550	143	10	immediate	immediate	ADJ
ejpam-3550	143	11	from	from	ADP
ejpam-3550	143	12	(	(	PUNCT
ejpam-3550	143	13	i	i	NOUN
ejpam-3550	143	14	)	)	PUNCT
ejpam-3550	143	15	and	and	CCONJ
ejpam-3550	143	16	the	the	DET
ejpam-3550	143	17	fact	fact	NOUN
ejpam-3550	143	18	that	that	SCONJ
ejpam-3550	143	19	γh(g	γh(g	ADP
ejpam-3550	143	20	◦	◦	NOUN
ejpam-3550	143	21	h	h	NOUN
ejpam-3550	143	22	)	)	PUNCT
ejpam-3550	143	23	≥	≥	NOUN
ejpam-3550	143	24	2	2	NUM
ejpam-3550	143	25	.	.	PUNCT
ejpam-3550	144	1	observation	observation	NOUN
ejpam-3550	144	2	:	:	PUNCT
ejpam-3550	144	3	the	the	DET
ejpam-3550	144	4	bound	bind	VERB
ejpam-3550	144	5	given	give	VERB
ejpam-3550	144	6	in	in	ADP
ejpam-3550	144	7	corollary	corollary	ADJ
ejpam-3550	144	8	2(i	2(i	NUM
ejpam-3550	144	9	)	)	PUNCT
ejpam-3550	144	10	is	be	AUX
ejpam-3550	144	11	attainable	attainable	ADJ
ejpam-3550	144	12	(	(	PUNCT
ejpam-3550	144	13	as	as	SCONJ
ejpam-3550	144	14	given	give	VERB
ejpam-3550	144	15	in	in	ADP
ejpam-3550	144	16	(	(	PUNCT
ejpam-3550	144	17	ii	ii	NOUN
ejpam-3550	144	18	)	)	PUNCT
ejpam-3550	144	19	and	and	CCONJ
ejpam-3550	144	20	(	(	PUNCT
ejpam-3550	144	21	iii	iii	NOUN
ejpam-3550	144	22	)	)	PUNCT
ejpam-3550	144	23	)	)	PUNCT
ejpam-3550	144	24	.	.	PUNCT
ejpam-3550	145	1	it	it	PRON
ejpam-3550	145	2	can	can	AUX
ejpam-3550	145	3	also	also	ADV
ejpam-3550	145	4	be	be	AUX
ejpam-3550	145	5	verified	verify	VERB
ejpam-3550	145	6	easily	easily	ADV
ejpam-3550	145	7	that	that	PRON
ejpam-3550	145	8	γh(c5	γh(c5	NOUN
ejpam-3550	145	9	◦	◦	NOUN
ejpam-3550	145	10	p3	p3	PROPN
ejpam-3550	145	11	)	)	PUNCT
ejpam-3550	146	1	=	=	SYM
ejpam-3550	146	2	γ∗t1,2(c5	γ∗t1,2(c5	ADJ
ejpam-3550	146	3	)	)	PUNCT
ejpam-3550	146	4	=	=	SYM
ejpam-3550	146	5	3	3	NUM
ejpam-3550	146	6	<	<	SYM
ejpam-3550	146	7	6	6	NUM
ejpam-3550	146	8	=	=	SYM
ejpam-3550	147	1	[	[	PUNCT
ejpam-3550	147	2	1	1	NUM
ejpam-3550	147	3	+	+	NUM
ejpam-3550	147	4	pnd(p3)]γ(c5	pnd(p3)]γ(c5	NOUN
ejpam-3550	147	5	)	)	PUNCT
ejpam-3550	147	6	and	and	CCONJ
ejpam-3550	147	7	γh(k4	γh(k4	ADP
ejpam-3550	147	8	◦	◦	NOUN
ejpam-3550	147	9	p3	p3	PROPN
ejpam-3550	147	10	)	)	PUNCT
ejpam-3550	148	1	=	=	PUNCT
ejpam-3550	149	1	[	[	X
ejpam-3550	149	2	1	1	NUM
ejpam-3550	149	3	+	+	NUM
ejpam-3550	149	4	pnd(p3)]γ(k4	pnd(p3)]γ(k4	NOUN
ejpam-3550	149	5	)	)	PUNCT
ejpam-3550	149	6	=	=	SYM
ejpam-3550	149	7	3	3	NUM
ejpam-3550	149	8	<	<	SYM
ejpam-3550	149	9	4	4	NUM
ejpam-3550	149	10	=	=	SYM
ejpam-3550	149	11	γ∗t1,2(k4	γ∗t1,2(k4	PROPN
ejpam-3550	149	12	)	)	PUNCT
ejpam-3550	149	13	.	.	PUNCT
ejpam-3550	150	1	it	it	PRON
ejpam-3550	150	2	is	be	AUX
ejpam-3550	150	3	worth	worth	ADJ
ejpam-3550	150	4	noting	note	VERB
ejpam-3550	150	5	that	that	SCONJ
ejpam-3550	150	6	the	the	DET
ejpam-3550	150	7	inequality	inequality	NOUN
ejpam-3550	150	8	is	be	AUX
ejpam-3550	150	9	also	also	ADV
ejpam-3550	150	10	attainable	attainable	ADJ
ejpam-3550	150	11	.	.	PUNCT
ejpam-3550	151	1	as	as	ADP
ejpam-3550	151	2	a	a	DET
ejpam-3550	151	3	matter	matter	NOUN
ejpam-3550	151	4	of	of	ADP
ejpam-3550	151	5	fact	fact	NOUN
ejpam-3550	151	6	,	,	PUNCT
ejpam-3550	151	7	it	it	PRON
ejpam-3550	151	8	can	can	AUX
ejpam-3550	151	9	be	be	AUX
ejpam-3550	151	10	shown	show	VERB
ejpam-3550	151	11	that	that	SCONJ
ejpam-3550	151	12	γh(k5	γh(k5	PROPN
ejpam-3550	151	13	◦	◦	NOUN
ejpam-3550	151	14	k4	k4	NOUN
ejpam-3550	151	15	)	)	PUNCT
ejpam-3550	151	16	=	=	SYM
ejpam-3550	151	17	3	3	NUM
ejpam-3550	151	18	<	<	SYM
ejpam-3550	151	19	5	5	NUM
ejpam-3550	151	20	=	=	NOUN
ejpam-3550	151	21	min{[1	min{[1	NOUN
ejpam-3550	151	22	+	+	CCONJ
ejpam-3550	151	23	pnd(k4)]γ(k5	pnd(k4)]γ(k5	ADJ
ejpam-3550	151	24	)	)	PUNCT
ejpam-3550	151	25	,	,	PUNCT
ejpam-3550	151	26	γ	γ	PROPN
ejpam-3550	151	27	∗t	∗t	PROPN
ejpam-3550	151	28	1,2(k5	1,2(k5	NUM
ejpam-3550	151	29	)	)	PUNCT
ejpam-3550	151	30	}	}	PUNCT
ejpam-3550	151	31	.	.	PUNCT
ejpam-3550	152	1	the	the	DET
ejpam-3550	152	2	lexicographic	lexicographic	ADJ
ejpam-3550	152	3	product	product	NOUN
ejpam-3550	152	4	of	of	ADP
ejpam-3550	152	5	graphs	graph	NOUN
ejpam-3550	152	6	g	g	PROPN
ejpam-3550	152	7	and	and	CCONJ
ejpam-3550	152	8	h	h	NOUN
ejpam-3550	152	9	,	,	PUNCT
ejpam-3550	152	10	denoted	denote	VERB
ejpam-3550	152	11	by	by	ADP
ejpam-3550	152	12	g[h	g[h	NOUN
ejpam-3550	152	13	]	]	PUNCT
ejpam-3550	152	14	,	,	PUNCT
ejpam-3550	152	15	is	be	AUX
ejpam-3550	152	16	the	the	DET
ejpam-3550	152	17	graph	graph	NOUN
ejpam-3550	152	18	with	with	ADP
ejpam-3550	152	19	vertex	vertex	NOUN
ejpam-3550	152	20	set	set	VERB
ejpam-3550	152	21	v	v	NOUN
ejpam-3550	152	22	(	(	PUNCT
ejpam-3550	152	23	g[h	g[h	PROPN
ejpam-3550	152	24	]	]	PUNCT
ejpam-3550	152	25	)	)	PUNCT
ejpam-3550	152	26	=	=	SYM
ejpam-3550	152	27	v	v	X
ejpam-3550	152	28	(	(	PUNCT
ejpam-3550	152	29	g)×	g)×	NOUN
ejpam-3550	152	30	v	v	NOUN
ejpam-3550	152	31	(	(	PUNCT
ejpam-3550	152	32	h	h	NOUN
ejpam-3550	152	33	)	)	PUNCT
ejpam-3550	152	34	such	such	ADJ
ejpam-3550	152	35	that	that	SCONJ
ejpam-3550	152	36	(	(	PUNCT
ejpam-3550	152	37	v	v	NOUN
ejpam-3550	152	38	,	,	PUNCT
ejpam-3550	152	39	a)(u	a)(u	ADJ
ejpam-3550	152	40	,	,	PUNCT
ejpam-3550	152	41	b	b	X
ejpam-3550	152	42	)	)	PUNCT
ejpam-3550	152	43	∈	∈	NOUN
ejpam-3550	152	44	e(g[h	e(g[h	NOUN
ejpam-3550	152	45	]	]	PUNCT
ejpam-3550	152	46	)	)	PUNCT
ejpam-3550	152	47	if	if	SCONJ
ejpam-3550	152	48	and	and	CCONJ
ejpam-3550	152	49	only	only	ADV
ejpam-3550	152	50	if	if	SCONJ
ejpam-3550	152	51	either	either	DET
ejpam-3550	152	52	uv	uv	PROPN
ejpam-3550	152	53	∈	∈	PROPN
ejpam-3550	152	54	e(g	e(g	PROPN
ejpam-3550	152	55	)	)	PUNCT
ejpam-3550	152	56	or	or	CCONJ
ejpam-3550	152	57	u	u	X
ejpam-3550	152	58	=	=	PROPN
ejpam-3550	152	59	v	v	PROPN
ejpam-3550	152	60	and	and	CCONJ
ejpam-3550	152	61	ab	ab	PROPN
ejpam-3550	152	62	∈	∈	PROPN
ejpam-3550	152	63	e(h	e(h	PROPN
ejpam-3550	152	64	)	)	PUNCT
ejpam-3550	152	65	.	.	PUNCT
ejpam-3550	153	1	note	note	VERB
ejpam-3550	153	2	that	that	SCONJ
ejpam-3550	153	3	every	every	DET
ejpam-3550	153	4	non	non	ADJ
ejpam-3550	153	5	-	-	ADJ
ejpam-3550	153	6	empty	empty	ADJ
ejpam-3550	153	7	subset	subset	NOUN
ejpam-3550	153	8	c	c	NOUN
ejpam-3550	153	9	of	of	ADP
ejpam-3550	153	10	v	v	PROPN
ejpam-3550	153	11	(	(	PUNCT
ejpam-3550	153	12	g)×v	g)×v	PROPN
ejpam-3550	153	13	(	(	PUNCT
ejpam-3550	153	14	h	h	NOUN
ejpam-3550	153	15	)	)	PUNCT
ejpam-3550	153	16	can	can	AUX
ejpam-3550	153	17	be	be	AUX
ejpam-3550	153	18	expressed	express	VERB
ejpam-3550	153	19	as	as	ADP
ejpam-3550	153	20	c	c	X
ejpam-3550	153	21	=	=	SYM
ejpam-3550	153	22	∪x∈s	∪x∈s	PROPN
ejpam-3550	153	23	[	[	X
ejpam-3550	153	24	{	{	PUNCT
ejpam-3550	153	25	x}×tx	x}×tx	X
ejpam-3550	153	26	]	]	X
ejpam-3550	153	27	,	,	PUNCT
ejpam-3550	153	28	where	where	SCONJ
ejpam-3550	153	29	s	s	VERB
ejpam-3550	153	30	⊆	⊆	NUM
ejpam-3550	153	31	v	v	NOUN
ejpam-3550	153	32	(	(	PUNCT
ejpam-3550	153	33	g	g	NOUN
ejpam-3550	153	34	)	)	PUNCT
ejpam-3550	153	35	and	and	CCONJ
ejpam-3550	153	36	tx	tx	VERB
ejpam-3550	153	37	⊆	⊆	NUM
ejpam-3550	153	38	v	v	NOUN
ejpam-3550	153	39	(	(	PUNCT
ejpam-3550	153	40	h	h	NOUN
ejpam-3550	153	41	)	)	PUNCT
ejpam-3550	153	42	for	for	ADP
ejpam-3550	153	43	each	each	DET
ejpam-3550	153	44	x	x	PROPN
ejpam-3550	153	45	∈	∈	PROPN
ejpam-3550	153	46	s.	s.	PROPN
ejpam-3550	153	47	theorem	theorem	VERB
ejpam-3550	153	48	3	3	X
ejpam-3550	153	49	.	.	PUNCT
ejpam-3550	154	1	let	let	VERB
ejpam-3550	154	2	g	g	NOUN
ejpam-3550	155	1	and	and	CCONJ
ejpam-3550	155	2	h	h	NOUN
ejpam-3550	155	3	be	be	AUX
ejpam-3550	155	4	connected	connect	VERB
ejpam-3550	155	5	non	non	ADJ
ejpam-3550	155	6	-	-	ADJ
ejpam-3550	155	7	trivial	trivial	ADJ
ejpam-3550	155	8	graphs	graph	NOUN
ejpam-3550	155	9	.	.	PUNCT
ejpam-3550	156	1	a	a	DET
ejpam-3550	156	2	subset	subset	NOUN
ejpam-3550	156	3	c	c	NOUN
ejpam-3550	156	4	=	=	SYM
ejpam-3550	156	5	∪x∈s	∪x∈s	PROPN
ejpam-3550	156	6	[	[	X
ejpam-3550	156	7	{	{	PUNCT
ejpam-3550	156	8	x}×tx	x}×tx	X
ejpam-3550	156	9	]	]	X
ejpam-3550	156	10	of	of	ADP
ejpam-3550	156	11	v	v	NOUN
ejpam-3550	156	12	(	(	PUNCT
ejpam-3550	156	13	g[h	g[h	PROPN
ejpam-3550	156	14	]	]	PUNCT
ejpam-3550	156	15	)	)	PUNCT
ejpam-3550	156	16	is	be	AUX
ejpam-3550	156	17	a	a	DET
ejpam-3550	156	18	hop	hop	NOUN
ejpam-3550	156	19	dominating	dominating	NOUN
ejpam-3550	156	20	set	set	NOUN
ejpam-3550	156	21	of	of	ADP
ejpam-3550	156	22	g[h	g[h	PROPN
ejpam-3550	156	23	]	]	PUNCT
ejpam-3550	157	1	if	if	SCONJ
ejpam-3550	157	2	and	and	CCONJ
ejpam-3550	157	3	only	only	ADV
ejpam-3550	157	4	if	if	SCONJ
ejpam-3550	157	5	the	the	DET
ejpam-3550	157	6	following	follow	VERB
ejpam-3550	157	7	conditions	condition	NOUN
ejpam-3550	157	8	hold	hold	VERB
ejpam-3550	157	9	:	:	PUNCT
ejpam-3550	157	10	(	(	PUNCT
ejpam-3550	157	11	i	i	NOUN
ejpam-3550	157	12	)	)	PUNCT
ejpam-3550	157	13	s	s	AUX
ejpam-3550	157	14	is	be	AUX
ejpam-3550	157	15	a	a	DET
ejpam-3550	157	16	hop	hop	NOUN
ejpam-3550	157	17	dominating	dominating	NOUN
ejpam-3550	157	18	set	set	NOUN
ejpam-3550	157	19	of	of	ADP
ejpam-3550	157	20	g	g	NOUN
ejpam-3550	157	21	;	;	PUNCT
ejpam-3550	157	22	(	(	PUNCT
ejpam-3550	157	23	ii	ii	NOUN
ejpam-3550	157	24	)	)	PUNCT
ejpam-3550	157	25	tx	tx	PROPN
ejpam-3550	157	26	is	be	AUX
ejpam-3550	157	27	a	a	DET
ejpam-3550	157	28	point	point	NOUN
ejpam-3550	157	29	-	-	PUNCT
ejpam-3550	157	30	wise	wise	ADJ
ejpam-3550	157	31	non	non	ADJ
ejpam-3550	157	32	-	-	ADJ
ejpam-3550	157	33	dominating	dominating	ADJ
ejpam-3550	157	34	set	set	NOUN
ejpam-3550	157	35	of	of	ADP
ejpam-3550	157	36	h	h	NOUN
ejpam-3550	157	37	for	for	ADP
ejpam-3550	157	38	each	each	DET
ejpam-3550	157	39	x	x	SYM
ejpam-3550	157	40	∈	∈	PROPN
ejpam-3550	157	41	s	s	VERB
ejpam-3550	157	42	with	with	ADP
ejpam-3550	157	43	|ng(x	|ng(x	ADP
ejpam-3550	157	44	,	,	PUNCT
ejpam-3550	157	45	2	2	X
ejpam-3550	157	46	)	)	PUNCT
ejpam-3550	157	47	∩	∩	NOUN
ejpam-3550	157	48	s|	s|	VERB
ejpam-3550	157	49	=	=	SYM
ejpam-3550	158	1	0	0	X
ejpam-3550	158	2	.	.	PUNCT
ejpam-3550	158	3	proof	proof	NOUN
ejpam-3550	158	4	.	.	PUNCT
ejpam-3550	159	1	suppose	suppose	VERB
ejpam-3550	159	2	c	c	NOUN
ejpam-3550	159	3	is	be	AUX
ejpam-3550	159	4	a	a	DET
ejpam-3550	159	5	hop	hop	NOUN
ejpam-3550	159	6	dominating	dominating	NOUN
ejpam-3550	159	7	set	set	NOUN
ejpam-3550	159	8	of	of	ADP
ejpam-3550	159	9	g[h	g[h	PROPN
ejpam-3550	159	10	]	]	PUNCT
ejpam-3550	159	11	.	.	PUNCT
ejpam-3550	160	1	let	let	VERB
ejpam-3550	160	2	u	u	PRON
ejpam-3550	160	3	∈	∈	PROPN
ejpam-3550	160	4	v	v	ADP
ejpam-3550	160	5	(	(	PUNCT
ejpam-3550	160	6	g	g	NOUN
ejpam-3550	160	7	)	)	PUNCT
ejpam-3550	160	8	\	\	PROPN
ejpam-3550	160	9	s	s	PART
ejpam-3550	160	10	and	and	CCONJ
ejpam-3550	160	11	pick	pick	VERB
ejpam-3550	160	12	any	any	PRON
ejpam-3550	160	13	a	a	DET
ejpam-3550	160	14	∈	∈	PROPN
ejpam-3550	160	15	v	v	NOUN
ejpam-3550	160	16	(	(	PUNCT
ejpam-3550	160	17	h	h	NOUN
ejpam-3550	160	18	)	)	PUNCT
ejpam-3550	160	19	.	.	PUNCT
ejpam-3550	161	1	since	since	SCONJ
ejpam-3550	161	2	c	c	PROPN
ejpam-3550	161	3	is	be	AUX
ejpam-3550	161	4	a	a	DET
ejpam-3550	161	5	hop	hop	NOUN
ejpam-3550	161	6	dominating	dominating	NOUN
ejpam-3550	161	7	set	set	NOUN
ejpam-3550	161	8	and	and	CCONJ
ejpam-3550	161	9	(	(	PUNCT
ejpam-3550	161	10	u	u	NOUN
ejpam-3550	161	11	,	,	PUNCT
ejpam-3550	161	12	a	a	PRON
ejpam-3550	161	13	)	)	PUNCT
ejpam-3550	161	14	/∈	/∈	PUNCT
ejpam-3550	162	1	c	c	X
ejpam-3550	162	2	,	,	PUNCT
ejpam-3550	162	3	there	there	PRON
ejpam-3550	162	4	exists	exist	VERB
ejpam-3550	162	5	(	(	PUNCT
ejpam-3550	162	6	y	y	PROPN
ejpam-3550	162	7	,	,	PUNCT
ejpam-3550	162	8	b	b	NOUN
ejpam-3550	162	9	)	)	PUNCT
ejpam-3550	162	10	∈	∈	PROPN
ejpam-3550	162	11	c	c	NOUN
ejpam-3550	162	12	such	such	ADJ
ejpam-3550	162	13	that	that	SCONJ
ejpam-3550	162	14	dg[h]((u	dg[h]((u	NOUN
ejpam-3550	162	15	,	,	PUNCT
ejpam-3550	162	16	a)(y	a)(y	PROPN
ejpam-3550	162	17	,	,	PUNCT
ejpam-3550	162	18	b	b	NOUN
ejpam-3550	162	19	)	)	PUNCT
ejpam-3550	162	20	)	)	PUNCT
ejpam-3550	163	1	=	=	SYM
ejpam-3550	163	2	2	2	X
ejpam-3550	163	3	.	.	PUNCT
ejpam-3550	164	1	this	this	PRON
ejpam-3550	164	2	implies	imply	VERB
ejpam-3550	164	3	that	that	SCONJ
ejpam-3550	164	4	y	y	PROPN
ejpam-3550	164	5	∈	∈	PROPN
ejpam-3550	164	6	s	s	X
ejpam-3550	164	7	and	and	CCONJ
ejpam-3550	164	8	dg(u	dg(u	X
ejpam-3550	164	9	,	,	PUNCT
ejpam-3550	164	10	y	y	NOUN
ejpam-3550	164	11	)	)	PUNCT
ejpam-3550	164	12	=	=	SYM
ejpam-3550	164	13	2	2	X
ejpam-3550	164	14	.	.	PUNCT
ejpam-3550	164	15	since	since	SCONJ
ejpam-3550	164	16	u	u	PRON
ejpam-3550	164	17	was	be	AUX
ejpam-3550	164	18	arbitrarily	arbitrarily	ADV
ejpam-3550	164	19	chosen	choose	VERB
ejpam-3550	164	20	,	,	PUNCT
ejpam-3550	164	21	it	it	PRON
ejpam-3550	164	22	follows	follow	VERB
ejpam-3550	164	23	that	that	SCONJ
ejpam-3550	164	24	s	s	VERB
ejpam-3550	164	25	is	be	AUX
ejpam-3550	164	26	a	a	DET
ejpam-3550	164	27	hop	hop	NOUN
ejpam-3550	164	28	dominating	dominating	NOUN
ejpam-3550	164	29	set	set	NOUN
ejpam-3550	164	30	of	of	ADP
ejpam-3550	164	31	g.	g.	PROPN
ejpam-3550	164	32	thus	thus	ADV
ejpam-3550	164	33	,	,	PUNCT
ejpam-3550	164	34	(	(	PUNCT
ejpam-3550	164	35	i	i	NOUN
ejpam-3550	164	36	)	)	PUNCT
ejpam-3550	164	37	holds	hold	VERB
ejpam-3550	164	38	.	.	PUNCT
ejpam-3550	165	1	now	now	ADV
ejpam-3550	165	2	let	let	VERB
ejpam-3550	165	3	x	x	X
ejpam-3550	165	4	∈	∈	PROPN
ejpam-3550	165	5	s∗	s∗	NOUN
ejpam-3550	165	6	and	and	CCONJ
ejpam-3550	165	7	let	let	VERB
ejpam-3550	165	8	p	p	PRON
ejpam-3550	165	9	∈	∈	PROPN
ejpam-3550	165	10	v	v	ADP
ejpam-3550	165	11	(	(	PUNCT
ejpam-3550	165	12	h	h	NOUN
ejpam-3550	165	13	)	)	PUNCT
ejpam-3550	165	14	\	\	PROPN
ejpam-3550	165	15	tx	tx	PROPN
ejpam-3550	165	16	.	.	PUNCT
ejpam-3550	166	1	then	then	ADV
ejpam-3550	166	2	(	(	PUNCT
ejpam-3550	166	3	x	x	X
ejpam-3550	166	4	,	,	PUNCT
ejpam-3550	166	5	p	p	NOUN
ejpam-3550	166	6	)	)	PUNCT
ejpam-3550	166	7	/∈	/∈	PUNCT
ejpam-3550	166	8	c.	c.	NOUN
ejpam-3550	166	9	again	again	ADV
ejpam-3550	166	10	,	,	PUNCT
ejpam-3550	166	11	noting	note	VERB
ejpam-3550	166	12	that	that	SCONJ
ejpam-3550	166	13	c	c	PROPN
ejpam-3550	166	14	is	be	AUX
ejpam-3550	166	15	a	a	DET
ejpam-3550	166	16	hop	hop	NOUN
ejpam-3550	166	17	dominating	dominating	NOUN
ejpam-3550	166	18	set	set	NOUN
ejpam-3550	166	19	of	of	ADP
ejpam-3550	166	20	g[h	g[h	PROPN
ejpam-3550	166	21	]	]	PUNCT
ejpam-3550	166	22	,	,	PUNCT
ejpam-3550	166	23	there	there	PRON
ejpam-3550	166	24	exists	exist	VERB
ejpam-3550	166	25	(	(	PUNCT
ejpam-3550	166	26	z	z	NOUN
ejpam-3550	166	27	,	,	PUNCT
ejpam-3550	166	28	q	q	X
ejpam-3550	166	29	)	)	PUNCT
ejpam-3550	166	30	∈	∈	PROPN
ejpam-3550	166	31	c	c	NOUN
ejpam-3550	166	32	such	such	ADJ
ejpam-3550	166	33	that	that	DET
ejpam-3550	166	34	dg[h]((x	dg[h]((x	NOUN
ejpam-3550	166	35	,	,	PUNCT
ejpam-3550	166	36	p)(z	p)(z	PROPN
ejpam-3550	166	37	,	,	PUNCT
ejpam-3550	166	38	q	q	NOUN
ejpam-3550	166	39	)	)	PUNCT
ejpam-3550	166	40	)	)	PUNCT
ejpam-3550	167	1	=	=	SYM
ejpam-3550	167	2	2	2	X
ejpam-3550	167	3	.	.	PUNCT
ejpam-3550	167	4	by	by	ADP
ejpam-3550	167	5	the	the	DET
ejpam-3550	167	6	assumption	assumption	NOUN
ejpam-3550	167	7	that	that	SCONJ
ejpam-3550	167	8	x	x	PROPN
ejpam-3550	167	9	∈	∈	PROPN
ejpam-3550	167	10	s∗	s∗	PROPN
ejpam-3550	167	11	,	,	PUNCT
ejpam-3550	167	12	we	we	PRON
ejpam-3550	167	13	find	find	VERB
ejpam-3550	167	14	that	that	SCONJ
ejpam-3550	167	15	x	x	PROPN
ejpam-3550	167	16	=	=	PUNCT
ejpam-3550	167	17	z.	z.	PROPN
ejpam-3550	167	18	hence	hence	ADV
ejpam-3550	167	19	,	,	PUNCT
ejpam-3550	167	20	q	q	PROPN
ejpam-3550	167	21	∈	∈	PROPN
ejpam-3550	167	22	tx	tx	PROPN
ejpam-3550	167	23	and	and	CCONJ
ejpam-3550	167	24	q	q	PROPN
ejpam-3550	167	25	/∈	/∈	PUNCT
ejpam-3550	167	26	nh(p	nh(p	NUM
ejpam-3550	167	27	)	)	PUNCT
ejpam-3550	167	28	.	.	PUNCT
ejpam-3550	168	1	thus	thus	ADV
ejpam-3550	168	2	,	,	PUNCT
ejpam-3550	168	3	tx	tx	PROPN
ejpam-3550	168	4	is	be	AUX
ejpam-3550	168	5	a	a	DET
ejpam-3550	168	6	point	point	NOUN
ejpam-3550	168	7	-	-	PUNCT
ejpam-3550	168	8	wise	wise	ADJ
ejpam-3550	168	9	non	non	ADJ
ejpam-3550	168	10	-	-	ADJ
ejpam-3550	168	11	dominating	dominating	ADJ
ejpam-3550	168	12	set	set	NOUN
ejpam-3550	168	13	of	of	ADP
ejpam-3550	168	14	h	h	NOUN
ejpam-3550	168	15	,	,	PUNCT
ejpam-3550	168	16	showing	show	VERB
ejpam-3550	168	17	that	that	SCONJ
ejpam-3550	168	18	(	(	PUNCT
ejpam-3550	168	19	ii	ii	NOUN
ejpam-3550	168	20	)	)	PUNCT
ejpam-3550	168	21	holds	hold	VERB
ejpam-3550	168	22	.	.	PUNCT
ejpam-3550	169	1	for	for	ADP
ejpam-3550	169	2	the	the	DET
ejpam-3550	169	3	converse	converse	NOUN
ejpam-3550	169	4	,	,	PUNCT
ejpam-3550	169	5	suppose	suppose	VERB
ejpam-3550	169	6	that	that	SCONJ
ejpam-3550	169	7	c	c	PROPN
ejpam-3550	169	8	satisfies	satisfy	VERB
ejpam-3550	169	9	properties	property	NOUN
ejpam-3550	169	10	(	(	PUNCT
ejpam-3550	169	11	i	i	NOUN
ejpam-3550	169	12	)	)	PUNCT
ejpam-3550	169	13	and	and	CCONJ
ejpam-3550	169	14	(	(	PUNCT
ejpam-3550	169	15	ii	ii	NOUN
ejpam-3550	169	16	)	)	PUNCT
ejpam-3550	169	17	.	.	PUNCT
ejpam-3550	170	1	let	let	VERB
ejpam-3550	170	2	(	(	PUNCT
ejpam-3550	170	3	v	v	NOUN
ejpam-3550	170	4	,	,	PUNCT
ejpam-3550	170	5	t	t	PROPN
ejpam-3550	170	6	)	)	PUNCT
ejpam-3550	170	7	∈	∈	PROPN
ejpam-3550	170	8	v	v	NOUN
ejpam-3550	170	9	(	(	PUNCT
ejpam-3550	170	10	g[h])\	g[h])\	NOUN
ejpam-3550	170	11	c	c	NOUN
ejpam-3550	170	12	and	and	CCONJ
ejpam-3550	170	13	consider	consider	VERB
ejpam-3550	170	14	the	the	DET
ejpam-3550	170	15	following	follow	VERB
ejpam-3550	170	16	cases	case	NOUN
ejpam-3550	170	17	:	:	PUNCT
ejpam-3550	170	18	case	case	NOUN
ejpam-3550	170	19	1	1	NUM
ejpam-3550	170	20	.	.	X
ejpam-3550	171	1	v	v	NUM
ejpam-3550	171	2	/∈	/∈	PUNCT
ejpam-3550	171	3	s	s	PART
ejpam-3550	171	4	since	since	SCONJ
ejpam-3550	171	5	s	s	NOUN
ejpam-3550	171	6	is	be	AUX
ejpam-3550	171	7	a	a	DET
ejpam-3550	171	8	hop	hop	NOUN
ejpam-3550	171	9	dominating	dominating	NOUN
ejpam-3550	171	10	set	set	NOUN
ejpam-3550	171	11	of	of	ADP
ejpam-3550	171	12	g	g	NOUN
ejpam-3550	171	13	,	,	PUNCT
ejpam-3550	171	14	there	there	PRON
ejpam-3550	171	15	exists	exist	VERB
ejpam-3550	171	16	w	w	PROPN
ejpam-3550	171	17	∈	∈	PROPN
ejpam-3550	171	18	s	s	VERB
ejpam-3550	171	19	such	such	ADJ
ejpam-3550	171	20	that	that	PRON
ejpam-3550	171	21	dg(v	dg(v	ADJ
ejpam-3550	171	22	,	,	PUNCT
ejpam-3550	171	23	w	w	NOUN
ejpam-3550	171	24	)	)	PUNCT
ejpam-3550	171	25	=	=	SYM
ejpam-3550	171	26	2	2	X
ejpam-3550	171	27	.	.	X
ejpam-3550	171	28	pick	pick	VERB
ejpam-3550	171	29	any	any	DET
ejpam-3550	171	30	d	d	PROPN
ejpam-3550	171	31	∈	∈	PROPN
ejpam-3550	171	32	tw	tw	PROPN
ejpam-3550	171	33	.	.	PUNCT
ejpam-3550	172	1	then	then	ADV
ejpam-3550	172	2	(	(	PUNCT
ejpam-3550	172	3	w	w	PROPN
ejpam-3550	172	4	,	,	PUNCT
ejpam-3550	172	5	d	d	NOUN
ejpam-3550	172	6	)	)	PUNCT
ejpam-3550	172	7	∈	∈	PROPN
ejpam-3550	172	8	c	c	NOUN
ejpam-3550	172	9	and	and	CCONJ
ejpam-3550	172	10	dg[h]((v	dg[h]((v	NOUN
ejpam-3550	172	11	,	,	PUNCT
ejpam-3550	172	12	t)(w	t)(w	NOUN
ejpam-3550	172	13	,	,	PUNCT
ejpam-3550	172	14	d	d	NOUN
ejpam-3550	172	15	)	)	PUNCT
ejpam-3550	172	16	)	)	PUNCT
ejpam-3550	173	1	=	=	SYM
ejpam-3550	173	2	2	2	X
ejpam-3550	173	3	.	.	X
ejpam-3550	173	4	case	case	NOUN
ejpam-3550	173	5	2	2	NUM
ejpam-3550	173	6	.	.	NOUN
ejpam-3550	174	1	v	v	NUM
ejpam-3550	174	2	∈	∈	PROPN
ejpam-3550	174	3	s	s	PART
ejpam-3550	174	4	s.	s.	PROPN
ejpam-3550	174	5	canoy	canoy	PROPN
ejpam-3550	174	6	jr	jr	PROPN
ejpam-3550	174	7	.	.	PROPN
ejpam-3550	174	8	,	,	PUNCT
ejpam-3550	174	9	r.	r.	PROPN
ejpam-3550	174	10	mollejon	mollejon	NOUN
ejpam-3550	174	11	,	,	PUNCT
ejpam-3550	174	12	jg	jg	PROPN
ejpam-3550	174	13	.	.	PROPN
ejpam-3550	174	14	canoy	canoy	PROPN
ejpam-3550	174	15	/	/	SYM
ejpam-3550	174	16	eur	eur	PROPN
ejpam-3550	174	17	.	.	PUNCT
ejpam-3550	175	1	j.	j.	PROPN
ejpam-3550	175	2	pure	pure	PROPN
ejpam-3550	175	3	appl	appl	PROPN
ejpam-3550	175	4	.	.	PROPN
ejpam-3550	175	5	math	math	PROPN
ejpam-3550	175	6	,	,	PUNCT
ejpam-3550	175	7	12	12	NUM
ejpam-3550	175	8	(	(	PUNCT
ejpam-3550	175	9	4	4	NUM
ejpam-3550	175	10	)	)	PUNCT
ejpam-3550	175	11	(	(	PUNCT
ejpam-3550	175	12	2019	2019	NUM
ejpam-3550	175	13	)	)	PUNCT
ejpam-3550	175	14	,	,	PUNCT
ejpam-3550	175	15	1455	1455	NUM
ejpam-3550	175	16	-	-	SYM
ejpam-3550	175	17	1463	1463	NUM
ejpam-3550	175	18	1460	1460	NUM
ejpam-3550	175	19	if	if	SCONJ
ejpam-3550	175	20	v	v	X
ejpam-3550	175	21	/∈	/∈	PUNCT
ejpam-3550	175	22	s∗	s∗	PROPN
ejpam-3550	175	23	,	,	PUNCT
ejpam-3550	175	24	then	then	ADV
ejpam-3550	175	25	there	there	PRON
ejpam-3550	175	26	exists	exist	VERB
ejpam-3550	175	27	z	z	PROPN
ejpam-3550	175	28	∈	∈	PROPN
ejpam-3550	175	29	s	s	VERB
ejpam-3550	175	30	such	such	ADJ
ejpam-3550	175	31	that	that	PRON
ejpam-3550	175	32	dg(v	dg(v	ADJ
ejpam-3550	175	33	,	,	PUNCT
ejpam-3550	175	34	z	z	NOUN
ejpam-3550	175	35	)	)	PUNCT
ejpam-3550	175	36	=	=	SYM
ejpam-3550	175	37	2	2	X
ejpam-3550	175	38	.	.	PUNCT
ejpam-3550	176	1	it	it	PRON
ejpam-3550	176	2	follows	follow	VERB
ejpam-3550	176	3	that	that	DET
ejpam-3550	176	4	dg[h]((v	dg[h]((v	NOUN
ejpam-3550	176	5	,	,	PUNCT
ejpam-3550	176	6	t)(z	t)(z	ADP
ejpam-3550	176	7	,	,	PUNCT
ejpam-3550	176	8	a	a	DET
ejpam-3550	176	9	)	)	PUNCT
ejpam-3550	176	10	)	)	PUNCT
ejpam-3550	177	1	=	=	SYM
ejpam-3550	177	2	2	2	NUM
ejpam-3550	177	3	for	for	ADP
ejpam-3550	177	4	any	any	DET
ejpam-3550	177	5	a	a	DET
ejpam-3550	177	6	∈	∈	PROPN
ejpam-3550	177	7	tz	tz	NOUN
ejpam-3550	177	8	.	.	PUNCT
ejpam-3550	177	9	suppose	suppose	VERB
ejpam-3550	177	10	that	that	SCONJ
ejpam-3550	177	11	v	v	PROPN
ejpam-3550	177	12	∈	∈	PROPN
ejpam-3550	177	13	s∗.	s∗.	ADJ
ejpam-3550	177	14	then	then	ADV
ejpam-3550	177	15	,	,	PUNCT
ejpam-3550	177	16	by	by	ADP
ejpam-3550	177	17	property	property	NOUN
ejpam-3550	177	18	(	(	PUNCT
ejpam-3550	177	19	ii	ii	NOUN
ejpam-3550	177	20	)	)	PUNCT
ejpam-3550	177	21	,	,	PUNCT
ejpam-3550	177	22	there	there	PRON
ejpam-3550	177	23	exists	exist	VERB
ejpam-3550	177	24	c	c	NOUN
ejpam-3550	177	25	∈	∈	PROPN
ejpam-3550	177	26	tv	tv	NOUN
ejpam-3550	178	1	such	such	ADJ
ejpam-3550	178	2	that	that	PRON
ejpam-3550	178	3	tc	tc	NOUN
ejpam-3550	178	4	/∈	/∈	PUNCT
ejpam-3550	178	5	e(h	e(h	PROPN
ejpam-3550	178	6	)	)	PUNCT
ejpam-3550	178	7	.	.	PUNCT
ejpam-3550	179	1	since	since	SCONJ
ejpam-3550	179	2	g	g	PROPN
ejpam-3550	179	3	is	be	AUX
ejpam-3550	179	4	non	non	ADJ
ejpam-3550	179	5	-	-	ADJ
ejpam-3550	179	6	trivial	trivial	ADJ
ejpam-3550	179	7	and	and	CCONJ
ejpam-3550	179	8	connected	connected	ADJ
ejpam-3550	179	9	,	,	PUNCT
ejpam-3550	179	10	dg[h]((v	dg[h]((v	NOUN
ejpam-3550	179	11	,	,	PUNCT
ejpam-3550	179	12	t)(v	t)(v	PROPN
ejpam-3550	179	13	,	,	PUNCT
ejpam-3550	179	14	c	c	NOUN
ejpam-3550	179	15	)	)	PUNCT
ejpam-3550	179	16	)	)	PUNCT
ejpam-3550	180	1	=	=	SYM
ejpam-3550	180	2	2	2	X
ejpam-3550	180	3	.	.	PUNCT
ejpam-3550	180	4	accordingly	accordingly	ADV
ejpam-3550	180	5	,	,	PUNCT
ejpam-3550	180	6	c	c	PROPN
ejpam-3550	180	7	is	be	AUX
ejpam-3550	180	8	a	a	DET
ejpam-3550	180	9	hop	hop	NOUN
ejpam-3550	180	10	dominating	dominating	NOUN
ejpam-3550	180	11	set	set	NOUN
ejpam-3550	180	12	of	of	ADP
ejpam-3550	180	13	g[h	g[h	PROPN
ejpam-3550	180	14	]	]	PUNCT
ejpam-3550	180	15	.	.	PUNCT
ejpam-3550	181	1	lemma	lemma	PROPN
ejpam-3550	181	2	1	1	NUM
ejpam-3550	181	3	.	.	PUNCT
ejpam-3550	182	1	a	a	DET
ejpam-3550	182	2	non	non	ADJ
ejpam-3550	182	3	-	-	ADJ
ejpam-3550	182	4	trivial	trivial	ADJ
ejpam-3550	182	5	graph	graph	NOUN
ejpam-3550	182	6	g	g	PROPN
ejpam-3550	182	7	admits	admit	VERB
ejpam-3550	182	8	a	a	DET
ejpam-3550	182	9	total	total	ADJ
ejpam-3550	182	10	hop	hop	NOUN
ejpam-3550	182	11	dominating	dominating	NOUN
ejpam-3550	182	12	set	set	VERB
ejpam-3550	182	13	if	if	SCONJ
ejpam-3550	182	14	and	and	CCONJ
ejpam-3550	182	15	only	only	ADV
ejpam-3550	182	16	if	if	SCONJ
ejpam-3550	182	17	γ(c	γ(c	NUM
ejpam-3550	182	18	)	)	PUNCT
ejpam-3550	182	19	6=	6=	ADP
ejpam-3550	182	20	1	1	NUM
ejpam-3550	182	21	for	for	ADP
ejpam-3550	182	22	every	every	DET
ejpam-3550	182	23	component	component	NOUN
ejpam-3550	182	24	c	c	PROPN
ejpam-3550	182	25	of	of	ADP
ejpam-3550	182	26	g.	g.	PROPN
ejpam-3550	182	27	proof	proof	PROPN
ejpam-3550	182	28	.	.	PUNCT
ejpam-3550	183	1	suppose	suppose	VERB
ejpam-3550	183	2	g	g	PROPN
ejpam-3550	183	3	admits	admit	VERB
ejpam-3550	183	4	a	a	DET
ejpam-3550	183	5	total	total	ADJ
ejpam-3550	183	6	hop	hop	NOUN
ejpam-3550	183	7	dominating	dominating	NOUN
ejpam-3550	183	8	set	set	NOUN
ejpam-3550	183	9	,	,	PUNCT
ejpam-3550	183	10	say	say	VERB
ejpam-3550	183	11	s.	s.	PROPN
ejpam-3550	183	12	suppose	suppose	VERB
ejpam-3550	183	13	further	far	ADV
ejpam-3550	183	14	that	that	SCONJ
ejpam-3550	183	15	there	there	PRON
ejpam-3550	183	16	exists	exist	VERB
ejpam-3550	183	17	a	a	DET
ejpam-3550	183	18	component	component	NOUN
ejpam-3550	183	19	c	c	NOUN
ejpam-3550	183	20	of	of	ADP
ejpam-3550	183	21	g	g	PROPN
ejpam-3550	183	22	such	such	ADJ
ejpam-3550	183	23	that	that	DET
ejpam-3550	183	24	γ(c	γ(c	PROPN
ejpam-3550	183	25	)	)	PUNCT
ejpam-3550	183	26	=	=	SYM
ejpam-3550	184	1	1	1	X
ejpam-3550	184	2	.	.	PUNCT
ejpam-3550	184	3	let	let	VERB
ejpam-3550	184	4	v	v	NUM
ejpam-3550	184	5	∈	∈	PROPN
ejpam-3550	184	6	v	v	NOUN
ejpam-3550	184	7	(	(	PUNCT
ejpam-3550	184	8	c	c	NOUN
ejpam-3550	184	9	)	)	PUNCT
ejpam-3550	184	10	be	be	AUX
ejpam-3550	184	11	such	such	ADJ
ejpam-3550	184	12	that	that	SCONJ
ejpam-3550	184	13	{	{	PUNCT
ejpam-3550	184	14	v	v	NOUN
ejpam-3550	184	15	}	}	PUNCT
ejpam-3550	184	16	is	be	AUX
ejpam-3550	184	17	a	a	DET
ejpam-3550	184	18	dominating	dominating	NOUN
ejpam-3550	184	19	set	set	NOUN
ejpam-3550	184	20	of	of	ADP
ejpam-3550	184	21	c.	c.	NOUN
ejpam-3550	184	22	since	since	SCONJ
ejpam-3550	184	23	s	s	PROPN
ejpam-3550	184	24	is	be	AUX
ejpam-3550	184	25	a	a	DET
ejpam-3550	184	26	hop	hop	NOUN
ejpam-3550	184	27	dominating	dominating	NOUN
ejpam-3550	184	28	set	set	NOUN
ejpam-3550	184	29	of	of	ADP
ejpam-3550	184	30	g	g	PROPN
ejpam-3550	184	31	,	,	PUNCT
ejpam-3550	184	32	v	v	ADP
ejpam-3550	184	33	∈	∈	PROPN
ejpam-3550	184	34	s.	s.	PROPN
ejpam-3550	184	35	this	this	PRON
ejpam-3550	184	36	,	,	PUNCT
ejpam-3550	184	37	however	however	ADV
ejpam-3550	184	38	,	,	PUNCT
ejpam-3550	184	39	contradicts	contradict	VERB
ejpam-3550	184	40	the	the	DET
ejpam-3550	184	41	fact	fact	NOUN
ejpam-3550	184	42	that	that	SCONJ
ejpam-3550	184	43	s	s	VERB
ejpam-3550	184	44	is	be	AUX
ejpam-3550	184	45	a	a	DET
ejpam-3550	184	46	total	total	ADJ
ejpam-3550	184	47	hop	hop	NOUN
ejpam-3550	184	48	dominating	dominating	NOUN
ejpam-3550	184	49	set	set	NOUN
ejpam-3550	184	50	.	.	PUNCT
ejpam-3550	185	1	thus	thus	ADV
ejpam-3550	185	2	,	,	PUNCT
ejpam-3550	185	3	γ(c	γ(c	PROPN
ejpam-3550	185	4	)	)	PUNCT
ejpam-3550	185	5	6=	6=	ADP
ejpam-3550	185	6	1	1	NUM
ejpam-3550	185	7	for	for	ADP
ejpam-3550	185	8	every	every	DET
ejpam-3550	185	9	component	component	NOUN
ejpam-3550	185	10	c	c	PROPN
ejpam-3550	185	11	of	of	ADP
ejpam-3550	185	12	g.	g.	PROPN
ejpam-3550	185	13	for	for	ADP
ejpam-3550	185	14	the	the	DET
ejpam-3550	185	15	converse	converse	NOUN
ejpam-3550	185	16	,	,	PUNCT
ejpam-3550	185	17	suppose	suppose	VERB
ejpam-3550	185	18	that	that	SCONJ
ejpam-3550	185	19	γ(c	γ(c	PROPN
ejpam-3550	185	20	)	)	PUNCT
ejpam-3550	185	21	6=	6=	ADP
ejpam-3550	185	22	1	1	NUM
ejpam-3550	185	23	for	for	ADP
ejpam-3550	185	24	every	every	DET
ejpam-3550	185	25	component	component	NOUN
ejpam-3550	185	26	c	c	PROPN
ejpam-3550	185	27	of	of	ADP
ejpam-3550	185	28	g.	g.	PROPN
ejpam-3550	185	29	clearly	clearly	ADV
ejpam-3550	185	30	,	,	PUNCT
ejpam-3550	185	31	s	s	VERB
ejpam-3550	185	32	=	=	SYM
ejpam-3550	185	33	v	v	X
ejpam-3550	185	34	(	(	PUNCT
ejpam-3550	185	35	g	g	NOUN
ejpam-3550	185	36	)	)	PUNCT
ejpam-3550	185	37	is	be	AUX
ejpam-3550	185	38	a	a	DET
ejpam-3550	185	39	hop	hop	NOUN
ejpam-3550	185	40	dominating	dominating	NOUN
ejpam-3550	185	41	set	set	NOUN
ejpam-3550	185	42	of	of	ADP
ejpam-3550	185	43	g.	g.	PROPN
ejpam-3550	185	44	let	let	VERB
ejpam-3550	185	45	w	w	PROPN
ejpam-3550	185	46	∈	∈	PROPN
ejpam-3550	185	47	v	v	ADP
ejpam-3550	185	48	(	(	PUNCT
ejpam-3550	185	49	g	g	NOUN
ejpam-3550	185	50	)	)	PUNCT
ejpam-3550	185	51	and	and	CCONJ
ejpam-3550	185	52	cw	cw	NOUN
ejpam-3550	185	53	be	be	AUX
ejpam-3550	185	54	the	the	DET
ejpam-3550	185	55	component	component	NOUN
ejpam-3550	185	56	of	of	ADP
ejpam-3550	185	57	g	g	NOUN
ejpam-3550	185	58	with	with	ADP
ejpam-3550	185	59	w	w	PROPN
ejpam-3550	185	60	∈	∈	PROPN
ejpam-3550	185	61	v	v	NOUN
ejpam-3550	185	62	(	(	PUNCT
ejpam-3550	185	63	cw	cw	NOUN
ejpam-3550	185	64	)	)	PUNCT
ejpam-3550	185	65	.	.	PUNCT
ejpam-3550	186	1	since	since	SCONJ
ejpam-3550	186	2	{	{	PUNCT
ejpam-3550	186	3	w	w	NOUN
ejpam-3550	186	4	}	}	PUNCT
ejpam-3550	186	5	is	be	AUX
ejpam-3550	186	6	not	not	PART
ejpam-3550	186	7	a	a	DET
ejpam-3550	186	8	dominating	dominating	NOUN
ejpam-3550	186	9	set	set	NOUN
ejpam-3550	186	10	of	of	ADP
ejpam-3550	186	11	cw	cw	NOUN
ejpam-3550	186	12	,	,	PUNCT
ejpam-3550	186	13	there	there	PRON
ejpam-3550	186	14	exists	exist	VERB
ejpam-3550	186	15	u	u	PROPN
ejpam-3550	186	16	∈	∈	PROPN
ejpam-3550	186	17	v	v	NOUN
ejpam-3550	186	18	(	(	PUNCT
ejpam-3550	186	19	c	c	NOUN
ejpam-3550	186	20	)	)	PUNCT
ejpam-3550	186	21	\	\	NOUN
ejpam-3550	186	22	{	{	PUNCT
ejpam-3550	186	23	w	w	NOUN
ejpam-3550	186	24	}	}	PUNCT
ejpam-3550	186	25	such	such	ADJ
ejpam-3550	186	26	that	that	DET
ejpam-3550	186	27	dc(u	dc(u	PROPN
ejpam-3550	186	28	,	,	PUNCT
ejpam-3550	186	29	w	w	NOUN
ejpam-3550	186	30	)	)	PUNCT
ejpam-3550	186	31	=	=	SYM
ejpam-3550	186	32	dg(u	dg(u	X
ejpam-3550	186	33	,	,	PUNCT
ejpam-3550	186	34	w	w	NOUN
ejpam-3550	186	35	)	)	PUNCT
ejpam-3550	187	1	=	=	SYM
ejpam-3550	187	2	2	2	X
ejpam-3550	187	3	.	.	PUNCT
ejpam-3550	188	1	this	this	PRON
ejpam-3550	188	2	shows	show	VERB
ejpam-3550	188	3	that	that	SCONJ
ejpam-3550	188	4	s	s	VERB
ejpam-3550	188	5	=	=	SYM
ejpam-3550	188	6	v	v	X
ejpam-3550	188	7	(	(	PUNCT
ejpam-3550	188	8	g	g	NOUN
ejpam-3550	188	9	)	)	PUNCT
ejpam-3550	188	10	is	be	AUX
ejpam-3550	188	11	a	a	DET
ejpam-3550	188	12	total	total	ADJ
ejpam-3550	188	13	hop	hop	NOUN
ejpam-3550	188	14	dominating	dominating	NOUN
ejpam-3550	188	15	set	set	NOUN
ejpam-3550	188	16	of	of	ADP
ejpam-3550	188	17	g.	g.	PROPN
ejpam-3550	188	18	theorem	theorem	VERB
ejpam-3550	188	19	4	4	X
ejpam-3550	188	20	.	.	PUNCT
ejpam-3550	189	1	let	let	VERB
ejpam-3550	189	2	g	g	PRON
ejpam-3550	189	3	be	be	AUX
ejpam-3550	189	4	a	a	DET
ejpam-3550	189	5	connected	connected	ADJ
ejpam-3550	189	6	graph	graph	NOUN
ejpam-3550	189	7	with	with	ADP
ejpam-3550	189	8	γ(g	γ(g	PROPN
ejpam-3550	189	9	)	)	PUNCT
ejpam-3550	189	10	6=	6=	ADP
ejpam-3550	190	1	1	1	X
ejpam-3550	190	2	.	.	PUNCT
ejpam-3550	191	1	if	if	SCONJ
ejpam-3550	191	2	s	s	PROPN
ejpam-3550	191	3	is	be	AUX
ejpam-3550	191	4	a	a	DET
ejpam-3550	191	5	hop	hop	NOUN
ejpam-3550	191	6	dominating	dominating	NOUN
ejpam-3550	191	7	set	set	NOUN
ejpam-3550	191	8	of	of	ADP
ejpam-3550	191	9	g	g	PROPN
ejpam-3550	191	10	,	,	PUNCT
ejpam-3550	191	11	then	then	ADV
ejpam-3550	191	12	γth(g	γth(g	NOUN
ejpam-3550	191	13	)	)	PUNCT
ejpam-3550	191	14	≤	≤	NOUN
ejpam-3550	191	15	|s	|s	PROPN
ejpam-3550	191	16	∩ng(s	∩ng(s	PROPN
ejpam-3550	191	17	,	,	PUNCT
ejpam-3550	191	18	2)|+	2)|+	NUM
ejpam-3550	191	19	2|s	2|s	NUM
ejpam-3550	191	20	\ng(s	\ng(s	NUM
ejpam-3550	191	21	,	,	PUNCT
ejpam-3550	191	22	2)|	2)|	NUM
ejpam-3550	191	23	.	.	PUNCT
ejpam-3550	192	1	moreover	moreover	ADV
ejpam-3550	192	2	,	,	PUNCT
ejpam-3550	192	3	γth(g	γth(g	NOUN
ejpam-3550	192	4	)	)	PUNCT
ejpam-3550	192	5	≤	≤	NOUN
ejpam-3550	192	6	2γh(g	2γh(g	NOUN
ejpam-3550	192	7	)	)	PUNCT
ejpam-3550	192	8	.	.	PUNCT
ejpam-3550	193	1	proof	proof	NOUN
ejpam-3550	193	2	.	.	PUNCT
ejpam-3550	194	1	let	let	VERB
ejpam-3550	194	2	s	s	PRON
ejpam-3550	194	3	be	be	AUX
ejpam-3550	194	4	a	a	DET
ejpam-3550	194	5	hop	hop	NOUN
ejpam-3550	194	6	dominating	dominating	NOUN
ejpam-3550	194	7	set	set	NOUN
ejpam-3550	194	8	of	of	ADP
ejpam-3550	194	9	g.	g.	PROPN
ejpam-3550	194	10	if	if	SCONJ
ejpam-3550	194	11	s	s	VERB
ejpam-3550	194	12	is	be	AUX
ejpam-3550	194	13	a	a	DET
ejpam-3550	194	14	total	total	ADJ
ejpam-3550	194	15	hop	hop	NOUN
ejpam-3550	194	16	dominating	dominating	NOUN
ejpam-3550	194	17	set	set	NOUN
ejpam-3550	194	18	of	of	ADP
ejpam-3550	194	19	g	g	PROPN
ejpam-3550	194	20	(	(	PUNCT
ejpam-3550	194	21	possible	possible	ADJ
ejpam-3550	194	22	by	by	ADP
ejpam-3550	194	23	lemma	lemma	PROPN
ejpam-3550	194	24	1	1	NUM
ejpam-3550	194	25	)	)	PUNCT
ejpam-3550	194	26	,	,	PUNCT
ejpam-3550	194	27	then	then	ADV
ejpam-3550	194	28	s∩ng(s	s∩ng(s	NOUN
ejpam-3550	194	29	,	,	PUNCT
ejpam-3550	194	30	2	2	NUM
ejpam-3550	194	31	)	)	PUNCT
ejpam-3550	194	32	=	=	SYM
ejpam-3550	194	33	s	s	PROPN
ejpam-3550	194	34	and	and	CCONJ
ejpam-3550	194	35	s\ng(s	s\ng(s	ADJ
ejpam-3550	194	36	,	,	PUNCT
ejpam-3550	194	37	2	2	X
ejpam-3550	194	38	)	)	PUNCT
ejpam-3550	194	39	=	=	NOUN
ejpam-3550	194	40	∅.	∅.	VERB
ejpam-3550	194	41	hence	hence	ADV
ejpam-3550	194	42	,	,	PUNCT
ejpam-3550	194	43	the	the	DET
ejpam-3550	194	44	inequality	inequality	NOUN
ejpam-3550	194	45	holds	hold	VERB
ejpam-3550	194	46	.	.	PUNCT
ejpam-3550	195	1	suppose	suppose	VERB
ejpam-3550	195	2	now	now	ADV
ejpam-3550	195	3	that	that	PRON
ejpam-3550	195	4	s	s	VERB
ejpam-3550	195	5	is	be	AUX
ejpam-3550	195	6	not	not	PART
ejpam-3550	195	7	a	a	DET
ejpam-3550	195	8	total	total	ADJ
ejpam-3550	195	9	hop	hop	NOUN
ejpam-3550	195	10	dominating	dominating	NOUN
ejpam-3550	195	11	set	set	NOUN
ejpam-3550	195	12	.	.	PUNCT
ejpam-3550	196	1	then	then	ADV
ejpam-3550	196	2	s	s	VERB
ejpam-3550	196	3	\ng(s	\ng(s	NOUN
ejpam-3550	196	4	,	,	PUNCT
ejpam-3550	196	5	2	2	NUM
ejpam-3550	196	6	)	)	PUNCT
ejpam-3550	196	7	6=	6=	ADP
ejpam-3550	196	8	∅.	∅.	AUX
ejpam-3550	196	9	let	let	VERB
ejpam-3550	196	10	x	x	X
ejpam-3550	196	11	∈	∈	PROPN
ejpam-3550	196	12	s\ng(s	s\ng(s	NOUN
ejpam-3550	196	13	,	,	PUNCT
ejpam-3550	196	14	2	2	NUM
ejpam-3550	196	15	)	)	PUNCT
ejpam-3550	196	16	.	.	PUNCT
ejpam-3550	197	1	then	then	ADV
ejpam-3550	197	2	,	,	PUNCT
ejpam-3550	197	3	since	since	SCONJ
ejpam-3550	197	4	γ(g	γ(g	PROPN
ejpam-3550	197	5	)	)	PUNCT
ejpam-3550	197	6	6=	6=	ADP
ejpam-3550	197	7	1	1	NUM
ejpam-3550	197	8	,	,	PUNCT
ejpam-3550	197	9	there	there	PRON
ejpam-3550	197	10	exists	exist	VERB
ejpam-3550	197	11	vx	vx	PROPN
ejpam-3550	197	12	∈	∈	PROPN
ejpam-3550	197	13	v	v	X
ejpam-3550	197	14	(	(	PUNCT
ejpam-3550	197	15	g)\s	g)\s	VERB
ejpam-3550	197	16	such	such	ADJ
ejpam-3550	197	17	that	that	PRON
ejpam-3550	197	18	dg(x	dg(x	NOUN
ejpam-3550	197	19	,	,	PUNCT
ejpam-3550	197	20	vx	vx	NOUN
ejpam-3550	197	21	)	)	PUNCT
ejpam-3550	197	22	=	=	SYM
ejpam-3550	197	23	2	2	X
ejpam-3550	197	24	.	.	X
ejpam-3550	197	25	let	let	VERB
ejpam-3550	197	26	ds	ds	VERB
ejpam-3550	197	27	=	=	SYM
ejpam-3550	197	28	{	{	PUNCT
ejpam-3550	197	29	vx	vx	X
ejpam-3550	197	30	:	:	PUNCT
ejpam-3550	197	31	x	x	PUNCT
ejpam-3550	197	32	∈	∈	NOUN
ejpam-3550	197	33	s	s	PART
ejpam-3550	197	34	\ng(s	\ng(s	NOUN
ejpam-3550	197	35	,	,	PUNCT
ejpam-3550	197	36	2	2	NUM
ejpam-3550	197	37	)	)	PUNCT
ejpam-3550	197	38	}	}	PUNCT
ejpam-3550	197	39	.	.	PUNCT
ejpam-3550	198	1	then	then	ADV
ejpam-3550	198	2	,	,	PUNCT
ejpam-3550	198	3	clearly	clearly	ADV
ejpam-3550	198	4	,	,	PUNCT
ejpam-3550	198	5	|ds	|ds	PRON
ejpam-3550	198	6	|	|	ADV
ejpam-3550	198	7	≤	≤	NUM
ejpam-3550	198	8	|s	|s	X
ejpam-3550	198	9	\ng(s	\ng(s	NUM
ejpam-3550	198	10	,	,	PUNCT
ejpam-3550	198	11	2)|	2)|	NUM
ejpam-3550	198	12	and	and	CCONJ
ejpam-3550	198	13	s∗	s∗	PROPN
ejpam-3550	198	14	=	=	SYM
ejpam-3550	198	15	s	s	PART
ejpam-3550	198	16	∪ds	∪ds	PROPN
ejpam-3550	198	17	is	be	AUX
ejpam-3550	198	18	a	a	DET
ejpam-3550	198	19	total	total	ADJ
ejpam-3550	198	20	hop	hop	NOUN
ejpam-3550	198	21	dominating	dominating	NOUN
ejpam-3550	198	22	set	set	NOUN
ejpam-3550	198	23	of	of	ADP
ejpam-3550	198	24	g.	g.	PROPN
ejpam-3550	198	25	thus	thus	ADV
ejpam-3550	198	26	,	,	PUNCT
ejpam-3550	198	27	γth(g	γth(g	NOUN
ejpam-3550	198	28	)	)	PUNCT
ejpam-3550	198	29	≤	≤	NOUN
ejpam-3550	198	30	|s∗|	|s∗|	NUM
ejpam-3550	198	31	≤	≤	NUM
ejpam-3550	198	32	|s	|s	PROPN
ejpam-3550	198	33	∩ng(s	∩ng(s	PROPN
ejpam-3550	198	34	,	,	PUNCT
ejpam-3550	198	35	2)|+	2)|+	NUM
ejpam-3550	198	36	2|s	2|s	NUM
ejpam-3550	198	37	\ng(s	\ng(s	NUM
ejpam-3550	198	38	,	,	PUNCT
ejpam-3550	198	39	2)|	2)|	NUM
ejpam-3550	198	40	.	.	PUNCT
ejpam-3550	199	1	in	in	ADP
ejpam-3550	199	2	particular	particular	ADJ
ejpam-3550	199	3	,	,	PUNCT
ejpam-3550	199	4	γth(g	γth(g	NOUN
ejpam-3550	199	5	)	)	PUNCT
ejpam-3550	199	6	≤	≤	NOUN
ejpam-3550	199	7	2γh(g	2γh(g	NOUN
ejpam-3550	199	8	)	)	PUNCT
ejpam-3550	199	9	.	.	PUNCT
ejpam-3550	200	1	in	in	ADP
ejpam-3550	200	2	what	what	PRON
ejpam-3550	200	3	follows	follow	VERB
ejpam-3550	200	4	,	,	PUNCT
ejpam-3550	200	5	ρh(g	ρh(g	NOUN
ejpam-3550	200	6	)	)	PUNCT
ejpam-3550	200	7	=	=	SYM
ejpam-3550	200	8	min{|s∩ng(s	min{|s∩ng(s	NOUN
ejpam-3550	200	9	,	,	PUNCT
ejpam-3550	200	10	2)|+pnd(h)|s\ng(s	2)|+pnd(h)|s\ng(s	NUM
ejpam-3550	200	11	,	,	PUNCT
ejpam-3550	200	12	2)|	2)|	NUM
ejpam-3550	200	13	:	:	PUNCT
ejpam-3550	200	14	s	s	X
ejpam-3550	200	15	is	be	AUX
ejpam-3550	200	16	a	a	DET
ejpam-3550	200	17	hop	hop	NOUN
ejpam-3550	200	18	dominating	dominating	NOUN
ejpam-3550	200	19	set	set	VERB
ejpam-3550	200	20	ofg	ofg	PROPN
ejpam-3550	200	21	}	}	PUNCT
ejpam-3550	200	22	.	.	PUNCT
ejpam-3550	201	1	corollary	corollary	ADJ
ejpam-3550	201	2	3	3	X
ejpam-3550	201	3	.	.	PUNCT
ejpam-3550	202	1	let	let	VERB
ejpam-3550	202	2	g	g	NOUN
ejpam-3550	202	3	and	and	CCONJ
ejpam-3550	202	4	h	h	PROPN
ejpam-3550	202	5	be	be	VERB
ejpam-3550	202	6	non	non	ADJ
ejpam-3550	202	7	-	-	ADJ
ejpam-3550	202	8	trivial	trivial	ADJ
ejpam-3550	202	9	connected	connected	ADJ
ejpam-3550	202	10	graphs	graph	NOUN
ejpam-3550	202	11	of	of	ADP
ejpam-3550	202	12	orders	order	NOUN
ejpam-3550	202	13	m	m	VERB
ejpam-3550	202	14	and	and	CCONJ
ejpam-3550	202	15	n	n	CCONJ
ejpam-3550	202	16	,	,	PUNCT
ejpam-3550	202	17	respectively	respectively	ADV
ejpam-3550	202	18	.	.	PUNCT
ejpam-3550	203	1	then	then	ADV
ejpam-3550	203	2	(	(	PUNCT
ejpam-3550	203	3	i	i	NOUN
ejpam-3550	203	4	)	)	PUNCT
ejpam-3550	203	5	γh(g[h	γh(g[h	NOUN
ejpam-3550	203	6	]	]	X
ejpam-3550	203	7	)	)	PUNCT
ejpam-3550	203	8	=	=	SYM
ejpam-3550	203	9	ρh(g	ρh(g	NOUN
ejpam-3550	203	10	)	)	PUNCT
ejpam-3550	203	11	if	if	SCONJ
ejpam-3550	203	12	γ(g	γ(g	PROPN
ejpam-3550	203	13	)	)	PUNCT
ejpam-3550	203	14	=	=	SYM
ejpam-3550	204	1	1	1	NUM
ejpam-3550	204	2	;	;	PUNCT
ejpam-3550	204	3	(	(	PUNCT
ejpam-3550	204	4	ii	ii	NOUN
ejpam-3550	204	5	)	)	PUNCT
ejpam-3550	204	6	γh(g[h	γh(g[h	NOUN
ejpam-3550	204	7	]	]	X
ejpam-3550	204	8	)	)	PUNCT
ejpam-3550	204	9	=	=	SYM
ejpam-3550	204	10	γth(g	γth(g	NOUN
ejpam-3550	204	11	)	)	PUNCT
ejpam-3550	204	12	if	if	SCONJ
ejpam-3550	204	13	γ(g	γ(g	PROPN
ejpam-3550	204	14	)	)	PUNCT
ejpam-3550	204	15	6=	6=	ADP
ejpam-3550	204	16	1	1	NUM
ejpam-3550	204	17	;	;	PUNCT
ejpam-3550	204	18	and	and	CCONJ
ejpam-3550	204	19	(	(	PUNCT
ejpam-3550	204	20	iii	iii	NOUN
ejpam-3550	204	21	)	)	PUNCT
ejpam-3550	204	22	γh(g[h	γh(g[h	NOUN
ejpam-3550	204	23	]	]	X
ejpam-3550	204	24	)	)	PUNCT
ejpam-3550	204	25	=	=	SYM
ejpam-3550	204	26	m[pnd(h	m[pnd(h	NOUN
ejpam-3550	204	27	)	)	PUNCT
ejpam-3550	204	28	]	]	PUNCT
ejpam-3550	205	1	if	if	SCONJ
ejpam-3550	205	2	g	g	PROPN
ejpam-3550	205	3	=	=	SYM
ejpam-3550	205	4	km	km	PROPN
ejpam-3550	205	5	.	.	PUNCT
ejpam-3550	206	1	proof	proof	NOUN
ejpam-3550	206	2	.	.	PUNCT
ejpam-3550	207	1	(	(	PUNCT
ejpam-3550	207	2	i	i	NOUN
ejpam-3550	207	3	)	)	PUNCT
ejpam-3550	207	4	suppose	suppose	VERB
ejpam-3550	207	5	first	first	ADV
ejpam-3550	207	6	that	that	PRON
ejpam-3550	207	7	γ(g	γ(g	PROPN
ejpam-3550	207	8	)	)	PUNCT
ejpam-3550	207	9	=	=	PUNCT
ejpam-3550	208	1	1	1	X
ejpam-3550	208	2	.	.	PUNCT
ejpam-3550	208	3	then	then	ADV
ejpam-3550	208	4	,	,	PUNCT
ejpam-3550	208	5	by	by	ADP
ejpam-3550	208	6	lemma	lemma	PROPN
ejpam-3550	208	7	1	1	NUM
ejpam-3550	208	8	,	,	PUNCT
ejpam-3550	208	9	g	g	PROPN
ejpam-3550	208	10	does	do	AUX
ejpam-3550	208	11	not	not	PART
ejpam-3550	208	12	admit	admit	VERB
ejpam-3550	208	13	a	a	DET
ejpam-3550	208	14	total	total	ADJ
ejpam-3550	208	15	hop	hop	NOUN
ejpam-3550	208	16	dominating	dominating	NOUN
ejpam-3550	208	17	set	set	NOUN
ejpam-3550	208	18	(	(	PUNCT
ejpam-3550	208	19	hence	hence	ADV
ejpam-3550	208	20	,	,	PUNCT
ejpam-3550	208	21	γh(g[h	γh(g[h	NOUN
ejpam-3550	208	22	]	]	X
ejpam-3550	208	23	)	)	PUNCT
ejpam-3550	208	24	6=	6=	ADP
ejpam-3550	208	25	γth(g	γth(g	NOUN
ejpam-3550	208	26	)	)	PUNCT
ejpam-3550	208	27	)	)	PUNCT
ejpam-3550	208	28	.	.	PUNCT
ejpam-3550	209	1	now	now	ADV
ejpam-3550	209	2	let	let	VERB
ejpam-3550	209	3	s′	s′	NOUN
ejpam-3550	209	4	be	be	AUX
ejpam-3550	209	5	a	a	DET
ejpam-3550	209	6	hop	hop	NOUN
ejpam-3550	209	7	dominating	dominating	NOUN
ejpam-3550	209	8	set	set	NOUN
ejpam-3550	209	9	of	of	ADP
ejpam-3550	209	10	g	g	NOUN
ejpam-3550	209	11	such	such	ADJ
ejpam-3550	209	12	that	that	SCONJ
ejpam-3550	209	13	ρh(g	ρh(g	NOUN
ejpam-3550	209	14	)	)	PUNCT
ejpam-3550	209	15	=	=	SYM
ejpam-3550	209	16	|s′	|s′	NOUN
ejpam-3550	209	17	∩	∩	X
ejpam-3550	209	18	ng(s′	ng(s′	PROPN
ejpam-3550	209	19	,	,	PUNCT
ejpam-3550	209	20	2)|	2)|	NUM
ejpam-3550	209	21	+	+	CCONJ
ejpam-3550	209	22	pnd(h)|s′	pnd(h)|s′	ADJ
ejpam-3550	209	23	\	\	NOUN
ejpam-3550	209	24	ng(s′	ng(s′	PROPN
ejpam-3550	209	25	,	,	PUNCT
ejpam-3550	209	26	2)|	2)|	NUM
ejpam-3550	209	27	,	,	PUNCT
ejpam-3550	209	28	and	and	CCONJ
ejpam-3550	209	29	let	let	VERB
ejpam-3550	209	30	d′	d′	PRON
ejpam-3550	209	31	be	be	AUX
ejpam-3550	209	32	a	a	DET
ejpam-3550	209	33	s.	s.	PROPN
ejpam-3550	209	34	canoy	canoy	PROPN
ejpam-3550	209	35	jr	jr	PROPN
ejpam-3550	209	36	.	.	PROPN
ejpam-3550	209	37	,	,	PUNCT
ejpam-3550	209	38	r.	r.	PROPN
ejpam-3550	209	39	mollejon	mollejon	NOUN
ejpam-3550	209	40	,	,	PUNCT
ejpam-3550	209	41	jg	jg	PROPN
ejpam-3550	209	42	.	.	PROPN
ejpam-3550	209	43	canoy	canoy	PROPN
ejpam-3550	209	44	/	/	SYM
ejpam-3550	209	45	eur	eur	PROPN
ejpam-3550	209	46	.	.	PUNCT
ejpam-3550	210	1	j.	j.	PROPN
ejpam-3550	210	2	pure	pure	PROPN
ejpam-3550	210	3	appl	appl	PROPN
ejpam-3550	210	4	.	.	PROPN
ejpam-3550	210	5	math	math	PROPN
ejpam-3550	210	6	,	,	PUNCT
ejpam-3550	210	7	12	12	NUM
ejpam-3550	210	8	(	(	PUNCT
ejpam-3550	210	9	4	4	NUM
ejpam-3550	210	10	)	)	PUNCT
ejpam-3550	210	11	(	(	PUNCT
ejpam-3550	210	12	2019	2019	NUM
ejpam-3550	210	13	)	)	PUNCT
ejpam-3550	210	14	,	,	PUNCT
ejpam-3550	210	15	1455	1455	NUM
ejpam-3550	210	16	-	-	SYM
ejpam-3550	210	17	1463	1463	NUM
ejpam-3550	210	18	1461	1461	NUM
ejpam-3550	210	19	pnd	pnd	NOUN
ejpam-3550	210	20	-	-	PUNCT
ejpam-3550	210	21	set	set	NOUN
ejpam-3550	210	22	of	of	ADP
ejpam-3550	210	23	h.	h.	PROPN
ejpam-3550	210	24	set	set	VERB
ejpam-3550	210	25	qx	qx	PROPN
ejpam-3550	210	26	=	=	PROPN
ejpam-3550	210	27	d′	d′	PROPN
ejpam-3550	210	28	for	for	ADP
ejpam-3550	210	29	each	each	DET
ejpam-3550	210	30	x	x	PROPN
ejpam-3550	210	31	∈	∈	PROPN
ejpam-3550	210	32	s′	s′	PUNCT
ejpam-3550	210	33	\	\	PROPN
ejpam-3550	210	34	ng(s′	ng(s′	PROPN
ejpam-3550	210	35	,	,	PUNCT
ejpam-3550	210	36	2	2	NUM
ejpam-3550	210	37	)	)	PUNCT
ejpam-3550	210	38	and	and	CCONJ
ejpam-3550	210	39	qy	qy	NOUN
ejpam-3550	210	40	=	=	SYM
ejpam-3550	210	41	{	{	PUNCT
ejpam-3550	210	42	q	q	X
ejpam-3550	210	43	}	}	PUNCT
ejpam-3550	210	44	,	,	PUNCT
ejpam-3550	210	45	where	where	SCONJ
ejpam-3550	210	46	q	q	PROPN
ejpam-3550	210	47	∈	∈	PROPN
ejpam-3550	210	48	v	v	ADP
ejpam-3550	210	49	(	(	PUNCT
ejpam-3550	210	50	h	h	NOUN
ejpam-3550	210	51	)	)	PUNCT
ejpam-3550	210	52	,	,	PUNCT
ejpam-3550	210	53	for	for	ADP
ejpam-3550	210	54	each	each	DET
ejpam-3550	210	55	y	y	PROPN
ejpam-3550	210	56	∈	∈	PROPN
ejpam-3550	210	57	s′	s′	NUM
ejpam-3550	210	58	∩ng(s′	∩ng(s′	NOUN
ejpam-3550	210	59	,	,	PUNCT
ejpam-3550	210	60	2	2	NUM
ejpam-3550	210	61	)	)	PUNCT
ejpam-3550	210	62	.	.	PUNCT
ejpam-3550	211	1	then	then	ADV
ejpam-3550	211	2	c	c	NOUN
ejpam-3550	211	3	′	′	NOUN
ejpam-3550	212	1	=	=	PUNCT
ejpam-3550	212	2	∪x∈s′	∪x∈s′	X
ejpam-3550	212	3	[	[	X
ejpam-3550	212	4	{	{	PUNCT
ejpam-3550	212	5	x	x	ADJ
ejpam-3550	212	6	}	}	PUNCT
ejpam-3550	212	7	×qx	×qx	NOUN
ejpam-3550	212	8	]	]	PUNCT
ejpam-3550	212	9	is	be	AUX
ejpam-3550	212	10	a	a	DET
ejpam-3550	212	11	hop	hop	NOUN
ejpam-3550	212	12	dominating	dominating	NOUN
ejpam-3550	212	13	set	set	NOUN
ejpam-3550	212	14	of	of	ADP
ejpam-3550	212	15	g[h	g[h	PROPN
ejpam-3550	212	16	]	]	PUNCT
ejpam-3550	212	17	by	by	ADP
ejpam-3550	212	18	theorem	theorem	NOUN
ejpam-3550	212	19	3	3	NUM
ejpam-3550	212	20	.	.	PUNCT
ejpam-3550	212	21	hence	hence	ADV
ejpam-3550	212	22	,	,	PUNCT
ejpam-3550	212	23	γh(g[h	γh(g[h	NOUN
ejpam-3550	212	24	]	]	X
ejpam-3550	212	25	)	)	PUNCT
ejpam-3550	212	26	≤	≤	NOUN
ejpam-3550	212	27	|c	|c	VERB
ejpam-3550	212	28	′|	′|	NUM
ejpam-3550	212	29	=	=	SYM
ejpam-3550	212	30	∑	∑	PUNCT
ejpam-3550	212	31	x∈s′∩ng(s′,2	x∈s′∩ng(s′,2	PROPN
ejpam-3550	212	32	)	)	PUNCT
ejpam-3550	212	33	|qx|+	|qx|+	ADP
ejpam-3550	212	34	∑	∑	PROPN
ejpam-3550	212	35	x∈s′\ng(s′,2	x∈s′\ng(s′,2	PROPN
ejpam-3550	212	36	)	)	PUNCT
ejpam-3550	212	37	|qx|	|qx|	PROPN
ejpam-3550	213	1	=	=	SYM
ejpam-3550	213	2	ρh(g	ρh(g	NOUN
ejpam-3550	213	3	)	)	PUNCT
ejpam-3550	213	4	.	.	PUNCT
ejpam-3550	214	1	next	next	ADV
ejpam-3550	214	2	,	,	PUNCT
ejpam-3550	214	3	suppose	suppose	VERB
ejpam-3550	214	4	that	that	SCONJ
ejpam-3550	214	5	c0	c0	PROPN
ejpam-3550	214	6	=	=	PROPN
ejpam-3550	214	7	∪x∈s0	∪x∈s0	PROPN
ejpam-3550	215	1	[	[	X
ejpam-3550	215	2	{	{	PUNCT
ejpam-3550	215	3	x	x	NOUN
ejpam-3550	215	4	}	}	PUNCT
ejpam-3550	215	5	×	×	PROPN
ejpam-3550	215	6	tx	tx	PROPN
ejpam-3550	215	7	]	]	PUNCT
ejpam-3550	215	8	is	be	AUX
ejpam-3550	215	9	a	a	DET
ejpam-3550	215	10	γh	γh	ADV
ejpam-3550	215	11	-	-	PUNCT
ejpam-3550	215	12	set	set	NOUN
ejpam-3550	215	13	of	of	ADP
ejpam-3550	215	14	g[h	g[h	NOUN
ejpam-3550	215	15	]	]	PUNCT
ejpam-3550	215	16	.	.	PUNCT
ejpam-3550	216	1	by	by	ADP
ejpam-3550	216	2	theorem	theorem	NOUN
ejpam-3550	216	3	3	3	NUM
ejpam-3550	216	4	,	,	PUNCT
ejpam-3550	216	5	s0	s0	PROPN
ejpam-3550	216	6	is	be	AUX
ejpam-3550	216	7	a	a	DET
ejpam-3550	216	8	hop	hop	NOUN
ejpam-3550	216	9	dominating	dominating	NOUN
ejpam-3550	216	10	set	set	NOUN
ejpam-3550	216	11	of	of	ADP
ejpam-3550	216	12	g	g	PROPN
ejpam-3550	216	13	and	and	CCONJ
ejpam-3550	216	14	tx	tx	PROPN
ejpam-3550	216	15	is	be	AUX
ejpam-3550	216	16	a	a	DET
ejpam-3550	216	17	pnd	pnd	NOUN
ejpam-3550	216	18	-	-	PUNCT
ejpam-3550	216	19	set	set	NOUN
ejpam-3550	216	20	of	of	ADP
ejpam-3550	216	21	h	h	NOUN
ejpam-3550	216	22	for	for	ADP
ejpam-3550	216	23	each	each	DET
ejpam-3550	216	24	x	x	SYM
ejpam-3550	216	25	∈	∈	PROPN
ejpam-3550	216	26	s0	s0	PROPN
ejpam-3550	216	27	\	\	PROPN
ejpam-3550	216	28	ng(s0	ng(s0	NOUN
ejpam-3550	216	29	,	,	PUNCT
ejpam-3550	216	30	2	2	NUM
ejpam-3550	216	31	)	)	PUNCT
ejpam-3550	216	32	.	.	PUNCT
ejpam-3550	217	1	clearly	clearly	ADV
ejpam-3550	217	2	,	,	PUNCT
ejpam-3550	217	3	|tx|	|tx|	X
ejpam-3550	217	4	=	=	SYM
ejpam-3550	217	5	1	1	NUM
ejpam-3550	217	6	for	for	ADP
ejpam-3550	217	7	all	all	DET
ejpam-3550	217	8	x	x	SYM
ejpam-3550	217	9	∈	∈	PROPN
ejpam-3550	217	10	s0	s0	PROPN
ejpam-3550	217	11	∩ng(s0	∩ng(s0	PROPN
ejpam-3550	217	12	,	,	PUNCT
ejpam-3550	217	13	2	2	NUM
ejpam-3550	217	14	)	)	PUNCT
ejpam-3550	217	15	.	.	PUNCT
ejpam-3550	218	1	hence	hence	ADV
ejpam-3550	218	2	,	,	PUNCT
ejpam-3550	218	3	γh(g[h	γh(g[h	NOUN
ejpam-3550	218	4	]	]	X
ejpam-3550	218	5	)	)	PUNCT
ejpam-3550	218	6	=	=	SYM
ejpam-3550	218	7	|c0|	|c0|	NOUN
ejpam-3550	218	8	=	=	SYM
ejpam-3550	218	9	|s0	|s0	ADJ
ejpam-3550	218	10	∩ng(s0	∩ng(s0	PROPN
ejpam-3550	218	11	,	,	PUNCT
ejpam-3550	218	12	2)|+	2)|+	NUM
ejpam-3550	218	13	pnd(h)|s0	pnd(h)|s0	ADJ
ejpam-3550	218	14	\ng(s0	\ng(s0	PROPN
ejpam-3550	218	15	,	,	PUNCT
ejpam-3550	218	16	2)|	2)|	NUM
ejpam-3550	218	17	≥	≥	NUM
ejpam-3550	218	18	ρh(g	ρh(g	NOUN
ejpam-3550	218	19	)	)	PUNCT
ejpam-3550	218	20	,	,	PUNCT
ejpam-3550	218	21	showing	show	VERB
ejpam-3550	218	22	that	that	DET
ejpam-3550	218	23	equality	equality	NOUN
ejpam-3550	218	24	in	in	ADP
ejpam-3550	218	25	(	(	PUNCT
ejpam-3550	218	26	i	i	NOUN
ejpam-3550	218	27	)	)	PUNCT
ejpam-3550	218	28	holds	hold	VERB
ejpam-3550	218	29	.	.	PUNCT
ejpam-3550	219	1	(	(	PUNCT
ejpam-3550	219	2	ii	ii	NOUN
ejpam-3550	219	3	)	)	PUNCT
ejpam-3550	219	4	suppose	suppose	VERB
ejpam-3550	219	5	that	that	SCONJ
ejpam-3550	219	6	γ(g	γ(g	PROPN
ejpam-3550	219	7	)	)	PUNCT
ejpam-3550	219	8	6=	6=	ADP
ejpam-3550	220	1	1	1	X
ejpam-3550	220	2	.	.	PUNCT
ejpam-3550	220	3	then	then	ADV
ejpam-3550	220	4	g	g	PROPN
ejpam-3550	220	5	admits	admit	VERB
ejpam-3550	220	6	a	a	DET
ejpam-3550	220	7	total	total	ADJ
ejpam-3550	220	8	hop	hop	NOUN
ejpam-3550	220	9	dominating	dominating	NOUN
ejpam-3550	220	10	set	set	VERB
ejpam-3550	220	11	by	by	ADP
ejpam-3550	220	12	lemma	lemma	PROPN
ejpam-3550	220	13	1	1	NUM
ejpam-3550	220	14	.	.	PUNCT
ejpam-3550	221	1	let	let	VERB
ejpam-3550	221	2	s	s	PRON
ejpam-3550	221	3	be	be	AUX
ejpam-3550	221	4	a	a	DET
ejpam-3550	221	5	γth	γth	NOUN
ejpam-3550	221	6	-	-	PUNCT
ejpam-3550	221	7	set	set	NOUN
ejpam-3550	221	8	of	of	ADP
ejpam-3550	221	9	g	g	NOUN
ejpam-3550	221	10	and	and	CCONJ
ejpam-3550	221	11	let	let	VERB
ejpam-3550	221	12	d	d	NOUN
ejpam-3550	221	13	=	=	PRON
ejpam-3550	221	14	{	{	PUNCT
ejpam-3550	221	15	a	a	NOUN
ejpam-3550	221	16	}	}	PUNCT
ejpam-3550	221	17	,	,	PUNCT
ejpam-3550	221	18	where	where	SCONJ
ejpam-3550	221	19	a	a	DET
ejpam-3550	221	20	∈	∈	PROPN
ejpam-3550	221	21	v	v	NOUN
ejpam-3550	221	22	(	(	PUNCT
ejpam-3550	221	23	h	h	NOUN
ejpam-3550	221	24	)	)	PUNCT
ejpam-3550	221	25	.	.	PUNCT
ejpam-3550	222	1	set	set	VERB
ejpam-3550	222	2	tx	tx	PROPN
ejpam-3550	223	1	=	=	SYM
ejpam-3550	224	1	d	d	PROPN
ejpam-3550	224	2	for	for	ADP
ejpam-3550	224	3	each	each	DET
ejpam-3550	224	4	x	x	SYM
ejpam-3550	224	5	∈	∈	PROPN
ejpam-3550	224	6	s.	s.	PROPN
ejpam-3550	224	7	then	then	ADV
ejpam-3550	224	8	c	c	X
ejpam-3550	224	9	=	=	SYM
ejpam-3550	224	10	∪x∈s	∪x∈s	PROPN
ejpam-3550	224	11	[	[	X
ejpam-3550	224	12	{	{	PUNCT
ejpam-3550	224	13	x}×tx	x}×tx	X
ejpam-3550	224	14	]	]	X
ejpam-3550	224	15	=	=	PUNCT
ejpam-3550	224	16	s×d	s×d	PROPN
ejpam-3550	224	17	is	be	AUX
ejpam-3550	224	18	a	a	DET
ejpam-3550	224	19	hop	hop	NOUN
ejpam-3550	224	20	dominating	dominating	NOUN
ejpam-3550	224	21	set	set	NOUN
ejpam-3550	224	22	of	of	ADP
ejpam-3550	224	23	g[h	g[h	PROPN
ejpam-3550	224	24	]	]	PUNCT
ejpam-3550	224	25	by	by	ADP
ejpam-3550	224	26	theorem	theorem	NOUN
ejpam-3550	224	27	3	3	NUM
ejpam-3550	224	28	.	.	PUNCT
ejpam-3550	224	29	hence	hence	ADV
ejpam-3550	224	30	,	,	PUNCT
ejpam-3550	224	31	γh(g[h	γh(g[h	NOUN
ejpam-3550	224	32	]	]	X
ejpam-3550	224	33	)	)	PUNCT
ejpam-3550	224	34	≤	≤	PROPN
ejpam-3550	224	35	|s||d|	|s||d|	PROPN
ejpam-3550	224	36	=	=	PUNCT
ejpam-3550	224	37	γth(g	γth(g	PROPN
ejpam-3550	224	38	)	)	PUNCT
ejpam-3550	224	39	.	.	PUNCT
ejpam-3550	225	1	next	next	ADV
ejpam-3550	225	2	,	,	PUNCT
ejpam-3550	225	3	suppose	suppose	VERB
ejpam-3550	225	4	that	that	SCONJ
ejpam-3550	225	5	c∗	c∗	PROPN
ejpam-3550	225	6	=	=	PUNCT
ejpam-3550	225	7	∪x∈s∗	∪x∈s∗	PROPN
ejpam-3550	225	8	[	[	X
ejpam-3550	225	9	{	{	PUNCT
ejpam-3550	225	10	x	x	ADJ
ejpam-3550	225	11	}	}	PUNCT
ejpam-3550	225	12	×rx	×rx	PROPN
ejpam-3550	225	13	]	]	PUNCT
ejpam-3550	225	14	is	be	AUX
ejpam-3550	225	15	a	a	DET
ejpam-3550	225	16	γh	γh	ADV
ejpam-3550	225	17	-	-	PUNCT
ejpam-3550	225	18	set	set	NOUN
ejpam-3550	225	19	of	of	ADP
ejpam-3550	225	20	g[h	g[h	NOUN
ejpam-3550	225	21	]	]	PUNCT
ejpam-3550	225	22	.	.	PUNCT
ejpam-3550	226	1	by	by	ADP
ejpam-3550	226	2	theorem	theorem	NOUN
ejpam-3550	226	3	3	3	NUM
ejpam-3550	226	4	,	,	PUNCT
ejpam-3550	226	5	s∗	s∗	PROPN
ejpam-3550	226	6	is	be	AUX
ejpam-3550	226	7	a	a	DET
ejpam-3550	226	8	hop	hop	NOUN
ejpam-3550	226	9	dominating	dominating	NOUN
ejpam-3550	226	10	set	set	NOUN
ejpam-3550	226	11	of	of	ADP
ejpam-3550	226	12	g	g	PROPN
ejpam-3550	226	13	and	and	CCONJ
ejpam-3550	226	14	rx	rx	VERB
ejpam-3550	226	15	is	be	AUX
ejpam-3550	226	16	a	a	DET
ejpam-3550	226	17	pnd	pnd	NOUN
ejpam-3550	226	18	-	-	PUNCT
ejpam-3550	226	19	set	set	NOUN
ejpam-3550	226	20	of	of	ADP
ejpam-3550	226	21	h	h	NOUN
ejpam-3550	226	22	for	for	ADP
ejpam-3550	226	23	each	each	DET
ejpam-3550	226	24	x	x	PROPN
ejpam-3550	226	25	∈	∈	PROPN
ejpam-3550	226	26	s∗	s∗	PROPN
ejpam-3550	226	27	\ng(s∗	\ng(s∗	PROPN
ejpam-3550	226	28	,	,	PUNCT
ejpam-3550	226	29	2	2	NUM
ejpam-3550	226	30	)	)	PUNCT
ejpam-3550	226	31	.	.	PUNCT
ejpam-3550	227	1	since	since	SCONJ
ejpam-3550	227	2	c∗	c∗	PROPN
ejpam-3550	227	3	is	be	AUX
ejpam-3550	227	4	a	a	DET
ejpam-3550	227	5	γh	γh	ADV
ejpam-3550	227	6	-	-	PUNCT
ejpam-3550	227	7	set	set	NOUN
ejpam-3550	227	8	,	,	PUNCT
ejpam-3550	227	9	|rx|	|rx|	NOUN
ejpam-3550	227	10	=	=	NOUN
ejpam-3550	227	11	1	1	NUM
ejpam-3550	227	12	for	for	ADP
ejpam-3550	227	13	all	all	DET
ejpam-3550	227	14	x	x	PROPN
ejpam-3550	227	15	∈	∈	PROPN
ejpam-3550	227	16	s∗	s∗	PROPN
ejpam-3550	227	17	∩ng(s∗	∩ng(s∗	PROPN
ejpam-3550	227	18	,	,	PUNCT
ejpam-3550	227	19	2	2	NUM
ejpam-3550	227	20	)	)	PUNCT
ejpam-3550	227	21	.	.	PUNCT
ejpam-3550	228	1	moreover	moreover	ADV
ejpam-3550	228	2	,	,	PUNCT
ejpam-3550	228	3	since	since	SCONJ
ejpam-3550	228	4	h	h	NOUN
ejpam-3550	228	5	is	be	AUX
ejpam-3550	228	6	a	a	DET
ejpam-3550	228	7	non	non	ADJ
ejpam-3550	228	8	-	-	ADJ
ejpam-3550	228	9	trivial	trivial	ADJ
ejpam-3550	228	10	connected	connected	ADJ
ejpam-3550	228	11	graph	graph	NOUN
ejpam-3550	228	12	,	,	PUNCT
ejpam-3550	228	13	|rx|	|rx|	NOUN
ejpam-3550	228	14	=	=	SYM
ejpam-3550	228	15	pnd(h	pnd(h	PROPN
ejpam-3550	228	16	)	)	PUNCT
ejpam-3550	228	17	≥	≥	NOUN
ejpam-3550	228	18	2	2	NUM
ejpam-3550	228	19	for	for	ADP
ejpam-3550	228	20	each	each	DET
ejpam-3550	228	21	x	x	PROPN
ejpam-3550	228	22	∈	∈	PROPN
ejpam-3550	228	23	s∗	s∗	PROPN
ejpam-3550	228	24	\	\	PROPN
ejpam-3550	228	25	ng(s∗	ng(s∗	PROPN
ejpam-3550	228	26	,	,	PUNCT
ejpam-3550	228	27	2	2	NUM
ejpam-3550	228	28	)	)	PUNCT
ejpam-3550	228	29	by	by	ADP
ejpam-3550	228	30	proposition	proposition	NOUN
ejpam-3550	228	31	1(ii	1(ii	NUM
ejpam-3550	228	32	)	)	PUNCT
ejpam-3550	228	33	.	.	PUNCT
ejpam-3550	229	1	thus	thus	ADV
ejpam-3550	229	2	,	,	PUNCT
ejpam-3550	229	3	by	by	ADP
ejpam-3550	229	4	theorem	theorem	NOUN
ejpam-3550	229	5	4	4	NUM
ejpam-3550	229	6	,	,	PUNCT
ejpam-3550	229	7	γh(g[h	γh(g[h	NOUN
ejpam-3550	229	8	]	]	X
ejpam-3550	229	9	)	)	PUNCT
ejpam-3550	229	10	=	=	SYM
ejpam-3550	229	11	|c∗|	|c∗|	X
ejpam-3550	229	12	≥	≥	NOUN
ejpam-3550	229	13	|s∗	|s∗	PROPN
ejpam-3550	229	14	∩ng(s∗	∩ng(s∗	PROPN
ejpam-3550	229	15	,	,	PUNCT
ejpam-3550	229	16	2)|+	2)|+	NUM
ejpam-3550	229	17	2|s∗	2|s∗	NOUN
ejpam-3550	229	18	\ng(s∗	\ng(s∗	PROPN
ejpam-3550	229	19	,	,	PUNCT
ejpam-3550	229	20	2)|	2)|	NUM
ejpam-3550	229	21	≥	≥	NUM
ejpam-3550	229	22	γth(g	γth(g	NOUN
ejpam-3550	229	23	)	)	PUNCT
ejpam-3550	229	24	.	.	PUNCT
ejpam-3550	230	1	this	this	PRON
ejpam-3550	230	2	establishes	establish	VERB
ejpam-3550	230	3	the	the	DET
ejpam-3550	230	4	desired	desire	VERB
ejpam-3550	230	5	equality	equality	NOUN
ejpam-3550	230	6	in	in	ADP
ejpam-3550	230	7	(	(	PUNCT
ejpam-3550	230	8	ii	ii	NOUN
ejpam-3550	230	9	)	)	PUNCT
ejpam-3550	230	10	.	.	PUNCT
ejpam-3550	231	1	(	(	PUNCT
ejpam-3550	231	2	iii	iii	X
ejpam-3550	231	3	)	)	PUNCT
ejpam-3550	231	4	suppose	suppose	VERB
ejpam-3550	231	5	that	that	SCONJ
ejpam-3550	231	6	g	g	PROPN
ejpam-3550	231	7	=	=	SYM
ejpam-3550	231	8	km	km	PROPN
ejpam-3550	231	9	.	.	PUNCT
ejpam-3550	232	1	since	since	SCONJ
ejpam-3550	232	2	γ(g	γ(g	PROPN
ejpam-3550	232	3	)	)	PUNCT
ejpam-3550	232	4	=	=	SYM
ejpam-3550	232	5	1	1	NUM
ejpam-3550	232	6	,	,	PUNCT
ejpam-3550	232	7	γh(g[h	γh(g[h	NOUN
ejpam-3550	232	8	]	]	X
ejpam-3550	232	9	)	)	PUNCT
ejpam-3550	232	10	=	=	SYM
ejpam-3550	232	11	ρh(g	ρh(g	NOUN
ejpam-3550	232	12	)	)	PUNCT
ejpam-3550	232	13	.	.	PUNCT
ejpam-3550	233	1	now	now	ADV
ejpam-3550	233	2	,	,	PUNCT
ejpam-3550	233	3	since	since	SCONJ
ejpam-3550	233	4	s	s	PART
ejpam-3550	233	5	=	=	SYM
ejpam-3550	233	6	v	v	PROPN
ejpam-3550	233	7	(	(	PUNCT
ejpam-3550	233	8	km	km	PROPN
ejpam-3550	233	9	)	)	PUNCT
ejpam-3550	233	10	is	be	AUX
ejpam-3550	233	11	the	the	DET
ejpam-3550	233	12	only	only	ADJ
ejpam-3550	233	13	hop	hop	NOUN
ejpam-3550	233	14	dominating	dominating	NOUN
ejpam-3550	233	15	set	set	NOUN
ejpam-3550	233	16	of	of	ADP
ejpam-3550	233	17	g	g	PROPN
ejpam-3550	233	18	,	,	PUNCT
ejpam-3550	233	19	it	it	PRON
ejpam-3550	233	20	follows	follow	VERB
ejpam-3550	233	21	that	that	PRON
ejpam-3550	233	22	γh(g[h	γh(g[h	NOUN
ejpam-3550	233	23	]	]	X
ejpam-3550	233	24	)	)	PUNCT
ejpam-3550	233	25	=	=	SYM
ejpam-3550	233	26	ρh(g	ρh(g	NOUN
ejpam-3550	233	27	)	)	PUNCT
ejpam-3550	233	28	=	=	SYM
ejpam-3550	233	29	m[pnd(h	m[pnd(h	NOUN
ejpam-3550	233	30	)	)	PUNCT
ejpam-3550	233	31	]	]	PUNCT
ejpam-3550	233	32	.	.	PUNCT
ejpam-3550	234	1	this	this	PRON
ejpam-3550	234	2	proves	prove	VERB
ejpam-3550	234	3	the	the	DET
ejpam-3550	234	4	assertion	assertion	NOUN
ejpam-3550	234	5	in	in	ADP
ejpam-3550	234	6	(	(	PUNCT
ejpam-3550	234	7	iii	iii	NOUN
ejpam-3550	234	8	)	)	PUNCT
ejpam-3550	234	9	.	.	PUNCT
ejpam-3550	235	1	corollary	corollary	ADJ
ejpam-3550	235	2	4	4	NUM
ejpam-3550	235	3	.	.	PUNCT
ejpam-3550	236	1	let	let	VERB
ejpam-3550	236	2	g	g	PRON
ejpam-3550	236	3	be	be	AUX
ejpam-3550	236	4	a	a	DET
ejpam-3550	236	5	non	non	ADJ
ejpam-3550	236	6	-	-	ADJ
ejpam-3550	236	7	trivial	trivial	ADJ
ejpam-3550	236	8	connected	connected	ADJ
ejpam-3550	236	9	graph	graph	NOUN
ejpam-3550	236	10	and	and	CCONJ
ejpam-3550	236	11	let	let	VERB
ejpam-3550	236	12	h	h	NOUN
ejpam-3550	236	13	be	be	AUX
ejpam-3550	236	14	any	any	DET
ejpam-3550	236	15	non	non	ADJ
ejpam-3550	236	16	-	-	ADJ
ejpam-3550	236	17	trivial	trivial	ADJ
ejpam-3550	236	18	graph	graph	NOUN
ejpam-3550	236	19	.	.	PUNCT
ejpam-3550	237	1	if	if	SCONJ
ejpam-3550	237	2	h	h	NOUN
ejpam-3550	237	3	has	have	VERB
ejpam-3550	237	4	an	an	DET
ejpam-3550	237	5	isolated	isolated	ADJ
ejpam-3550	237	6	vertex	vertex	NOUN
ejpam-3550	237	7	,	,	PUNCT
ejpam-3550	237	8	then	then	ADV
ejpam-3550	237	9	γh(g[h	γh(g[h	NOUN
ejpam-3550	237	10	]	]	X
ejpam-3550	237	11	)	)	PUNCT
ejpam-3550	237	12	=	=	NOUN
ejpam-3550	237	13	γh(g	γh(g	NOUN
ejpam-3550	237	14	)	)	PUNCT
ejpam-3550	237	15	.	.	PUNCT
ejpam-3550	238	1	proof	proof	NOUN
ejpam-3550	238	2	.	.	PUNCT
ejpam-3550	239	1	since	since	SCONJ
ejpam-3550	239	2	h	h	NOUN
ejpam-3550	239	3	has	have	VERB
ejpam-3550	239	4	an	an	DET
ejpam-3550	239	5	isolated	isolated	ADJ
ejpam-3550	239	6	vertex	vertex	NOUN
ejpam-3550	239	7	,	,	PUNCT
ejpam-3550	239	8	pnd(h	pnd(h	PROPN
ejpam-3550	239	9	)	)	PUNCT
ejpam-3550	239	10	=	=	SYM
ejpam-3550	239	11	1	1	NUM
ejpam-3550	239	12	by	by	ADP
ejpam-3550	239	13	proposition	proposition	NOUN
ejpam-3550	239	14	1(ii	1(ii	NUM
ejpam-3550	239	15	)	)	PUNCT
ejpam-3550	239	16	.	.	PUNCT
ejpam-3550	240	1	let	let	VERB
ejpam-3550	240	2	c	c	NOUN
ejpam-3550	240	3	=	=	PUNCT
ejpam-3550	240	4	∪x∈s	∪x∈s	PROPN
ejpam-3550	240	5	[	[	X
ejpam-3550	240	6	{	{	PUNCT
ejpam-3550	240	7	x	x	NOUN
ejpam-3550	240	8	}	}	PUNCT
ejpam-3550	240	9	×	×	PROPN
ejpam-3550	240	10	tx	tx	PROPN
ejpam-3550	240	11	]	]	PUNCT
ejpam-3550	240	12	be	be	AUX
ejpam-3550	240	13	a	a	DET
ejpam-3550	240	14	γh	γh	ADV
ejpam-3550	240	15	-	-	PUNCT
ejpam-3550	240	16	set	set	NOUN
ejpam-3550	240	17	of	of	ADP
ejpam-3550	240	18	g[h	g[h	NOUN
ejpam-3550	240	19	]	]	PUNCT
ejpam-3550	240	20	.	.	PUNCT
ejpam-3550	241	1	by	by	ADP
ejpam-3550	241	2	theorem	theorem	NOUN
ejpam-3550	241	3	3	3	NUM
ejpam-3550	241	4	,	,	PUNCT
ejpam-3550	241	5	s	s	VERB
ejpam-3550	241	6	is	be	AUX
ejpam-3550	241	7	a	a	DET
ejpam-3550	241	8	hop	hop	NOUN
ejpam-3550	241	9	dominating	dominating	NOUN
ejpam-3550	241	10	set	set	NOUN
ejpam-3550	241	11	of	of	ADP
ejpam-3550	241	12	g	g	PROPN
ejpam-3550	241	13	and	and	CCONJ
ejpam-3550	241	14	tx	tx	PROPN
ejpam-3550	241	15	is	be	AUX
ejpam-3550	241	16	a	a	DET
ejpam-3550	241	17	pnd	pnd	NOUN
ejpam-3550	241	18	-	-	PUNCT
ejpam-3550	241	19	set	set	NOUN
ejpam-3550	241	20	of	of	ADP
ejpam-3550	241	21	h	h	NOUN
ejpam-3550	241	22	for	for	ADP
ejpam-3550	241	23	each	each	DET
ejpam-3550	241	24	x	x	SYM
ejpam-3550	241	25	∈	∈	PROPN
ejpam-3550	241	26	s	s	PART
ejpam-3550	241	27	\ng(s	\ng(s	NOUN
ejpam-3550	241	28	,	,	PUNCT
ejpam-3550	241	29	2	2	NUM
ejpam-3550	241	30	)	)	PUNCT
ejpam-3550	241	31	.	.	PUNCT
ejpam-3550	242	1	further	far	ADV
ejpam-3550	242	2	,	,	PUNCT
ejpam-3550	242	3	since	since	SCONJ
ejpam-3550	242	4	c	c	PROPN
ejpam-3550	242	5	is	be	AUX
ejpam-3550	242	6	γh	γh	ADV
ejpam-3550	242	7	-	-	PUNCT
ejpam-3550	242	8	set	set	NOUN
ejpam-3550	242	9	,	,	PUNCT
ejpam-3550	242	10	|tx|	|tx|	X
ejpam-3550	242	11	=	=	SYM
ejpam-3550	242	12	1	1	NUM
ejpam-3550	242	13	for	for	SCONJ
ejpam-3550	242	14	all	all	DET
ejpam-3550	242	15	x	x	SYM
ejpam-3550	242	16	∈	∈	NOUN
ejpam-3550	242	17	s	s	VERB
ejpam-3550	242	18	∩ng(s	∩ng(s	ADJ
ejpam-3550	242	19	,	,	PUNCT
ejpam-3550	242	20	2	2	NUM
ejpam-3550	242	21	)	)	PUNCT
ejpam-3550	242	22	.	.	PUNCT
ejpam-3550	243	1	hence	hence	ADV
ejpam-3550	243	2	,	,	PUNCT
ejpam-3550	243	3	γh(g[h	γh(g[h	NOUN
ejpam-3550	243	4	]	]	X
ejpam-3550	243	5	)	)	PUNCT
ejpam-3550	243	6	=	=	SYM
ejpam-3550	243	7	|c|	|c|	PROPN
ejpam-3550	243	8	=	=	SYM
ejpam-3550	243	9	|s	|s	PROPN
ejpam-3550	243	10	∩ng(s	∩ng(s	PROPN
ejpam-3550	243	11	,	,	PUNCT
ejpam-3550	243	12	2)|+	2)|+	NUM
ejpam-3550	243	13	|s	|s	PROPN
ejpam-3550	243	14	\ng(s	\ng(s	ADP
ejpam-3550	243	15	,	,	PUNCT
ejpam-3550	243	16	2)|	2)|	NUM
ejpam-3550	243	17	=	=	SYM
ejpam-3550	243	18	|s|	|s|	PROPN
ejpam-3550	243	19	≥	≥	NOUN
ejpam-3550	243	20	γh(g	γh(g	NOUN
ejpam-3550	243	21	)	)	PUNCT
ejpam-3550	243	22	.	.	PUNCT
ejpam-3550	244	1	s.	s.	PROPN
ejpam-3550	244	2	canoy	canoy	PROPN
ejpam-3550	244	3	jr	jr	PROPN
ejpam-3550	244	4	.	.	PROPN
ejpam-3550	244	5	,	,	PUNCT
ejpam-3550	244	6	r.	r.	PROPN
ejpam-3550	244	7	mollejon	mollejon	NOUN
ejpam-3550	244	8	,	,	PUNCT
ejpam-3550	244	9	jg	jg	PROPN
ejpam-3550	244	10	.	.	PROPN
ejpam-3550	244	11	canoy	canoy	PROPN
ejpam-3550	244	12	/	/	SYM
ejpam-3550	244	13	eur	eur	PROPN
ejpam-3550	244	14	.	.	PUNCT
ejpam-3550	245	1	j.	j.	PROPN
ejpam-3550	245	2	pure	pure	PROPN
ejpam-3550	245	3	appl	appl	PROPN
ejpam-3550	245	4	.	.	PROPN
ejpam-3550	245	5	math	math	PROPN
ejpam-3550	245	6	,	,	PUNCT
ejpam-3550	245	7	12	12	NUM
ejpam-3550	245	8	(	(	PUNCT
ejpam-3550	245	9	4	4	NUM
ejpam-3550	245	10	)	)	PUNCT
ejpam-3550	245	11	(	(	PUNCT
ejpam-3550	245	12	2019	2019	NUM
ejpam-3550	245	13	)	)	PUNCT
ejpam-3550	245	14	,	,	PUNCT
ejpam-3550	245	15	1455	1455	NUM
ejpam-3550	245	16	-	-	SYM
ejpam-3550	245	17	1463	1463	NUM
ejpam-3550	245	18	1462	1462	NUM
ejpam-3550	245	19	now	now	ADV
ejpam-3550	245	20	if	if	SCONJ
ejpam-3550	245	21	s0	s0	PROPN
ejpam-3550	245	22	is	be	AUX
ejpam-3550	245	23	a	a	DET
ejpam-3550	245	24	γh	γh	ADV
ejpam-3550	245	25	-	-	PUNCT
ejpam-3550	245	26	set	set	NOUN
ejpam-3550	245	27	of	of	ADP
ejpam-3550	245	28	g	g	NOUN
ejpam-3550	245	29	and	and	CCONJ
ejpam-3550	245	30	d0	d0	NOUN
ejpam-3550	245	31	is	be	AUX
ejpam-3550	245	32	a	a	DET
ejpam-3550	245	33	pnd	pnd	NOUN
ejpam-3550	245	34	-	-	PUNCT
ejpam-3550	245	35	set	set	NOUN
ejpam-3550	245	36	of	of	ADP
ejpam-3550	245	37	h	h	NOUN
ejpam-3550	245	38	,	,	PUNCT
ejpam-3550	245	39	then	then	ADV
ejpam-3550	245	40	c0	c0	PROPN
ejpam-3550	245	41	=	=	PROPN
ejpam-3550	245	42	s0	s0	PROPN
ejpam-3550	245	43	×d0	×d0	PROPN
ejpam-3550	245	44	is	be	AUX
ejpam-3550	245	45	a	a	DET
ejpam-3550	245	46	γh	γh	ADV
ejpam-3550	245	47	-	-	PUNCT
ejpam-3550	245	48	set	set	NOUN
ejpam-3550	245	49	of	of	ADP
ejpam-3550	245	50	g[h	g[h	NOUN
ejpam-3550	245	51	]	]	PUNCT
ejpam-3550	245	52	by	by	ADP
ejpam-3550	245	53	theorem	theorem	NOUN
ejpam-3550	245	54	3	3	NUM
ejpam-3550	245	55	.	.	PUNCT
ejpam-3550	245	56	thus	thus	ADV
ejpam-3550	245	57	,	,	PUNCT
ejpam-3550	245	58	γh(g[h	γh(g[h	NOUN
ejpam-3550	245	59	]	]	X
ejpam-3550	245	60	)	)	PUNCT
ejpam-3550	245	61	≤	≤	NUM
ejpam-3550	245	62	|c0|	|c0|	NOUN
ejpam-3550	245	63	=	=	SYM
ejpam-3550	245	64	|s0||d0|	|s0||d0|	NUM
ejpam-3550	245	65	=	=	SYM
ejpam-3550	245	66	|s0|	|s0|	NOUN
ejpam-3550	245	67	=	=	PRON
ejpam-3550	245	68	γh(g	γh(g	NOUN
ejpam-3550	245	69	)	)	PUNCT
ejpam-3550	245	70	.	.	PUNCT
ejpam-3550	246	1	this	this	PRON
ejpam-3550	246	2	establishes	establish	VERB
ejpam-3550	246	3	the	the	DET
ejpam-3550	246	4	desired	desire	VERB
ejpam-3550	246	5	equality	equality	NOUN
ejpam-3550	246	6	.	.	PUNCT
ejpam-3550	247	1	the	the	DET
ejpam-3550	247	2	cartesian	cartesian	ADJ
ejpam-3550	247	3	product	product	NOUN
ejpam-3550	247	4	of	of	ADP
ejpam-3550	247	5	graphs	graph	NOUN
ejpam-3550	247	6	g	g	PROPN
ejpam-3550	247	7	and	and	CCONJ
ejpam-3550	247	8	h	h	NOUN
ejpam-3550	247	9	,	,	PUNCT
ejpam-3550	247	10	denoted	denote	VERB
ejpam-3550	247	11	by	by	ADP
ejpam-3550	247	12	g	g	PROPN
ejpam-3550	247	13	�	�	PROPN
ejpam-3550	247	14	h	h	NOUN
ejpam-3550	247	15	,	,	PUNCT
ejpam-3550	247	16	is	be	AUX
ejpam-3550	247	17	the	the	DET
ejpam-3550	247	18	graph	graph	NOUN
ejpam-3550	247	19	with	with	ADP
ejpam-3550	247	20	vertex	vertex	NOUN
ejpam-3550	247	21	set	set	VERB
ejpam-3550	247	22	v	v	NOUN
ejpam-3550	247	23	(	(	PUNCT
ejpam-3550	247	24	g	g	PROPN
ejpam-3550	247	25	�	�	NOUN
ejpam-3550	247	26	h	h	NOUN
ejpam-3550	247	27	)	)	PUNCT
ejpam-3550	247	28	=	=	NOUN
ejpam-3550	247	29	v	v	X
ejpam-3550	247	30	(	(	PUNCT
ejpam-3550	247	31	g	g	NOUN
ejpam-3550	247	32	)	)	PUNCT
ejpam-3550	247	33	×	×	NOUN
ejpam-3550	247	34	v	v	NOUN
ejpam-3550	247	35	(	(	PUNCT
ejpam-3550	247	36	h	h	NOUN
ejpam-3550	247	37	)	)	PUNCT
ejpam-3550	247	38	such	such	ADJ
ejpam-3550	247	39	that	that	SCONJ
ejpam-3550	247	40	(	(	PUNCT
ejpam-3550	247	41	v	v	NOUN
ejpam-3550	247	42	,	,	PUNCT
ejpam-3550	247	43	p)(u	p)(u	ADJ
ejpam-3550	247	44	,	,	PUNCT
ejpam-3550	247	45	q	q	ADJ
ejpam-3550	247	46	)	)	PUNCT
ejpam-3550	247	47	∈	∈	PROPN
ejpam-3550	247	48	e(g	e(g	PROPN
ejpam-3550	247	49	�	�	PROPN
ejpam-3550	247	50	h	h	PROPN
ejpam-3550	247	51	)	)	PUNCT
ejpam-3550	247	52	if	if	SCONJ
ejpam-3550	247	53	and	and	CCONJ
ejpam-3550	247	54	only	only	ADV
ejpam-3550	247	55	if	if	SCONJ
ejpam-3550	247	56	uv	uv	PROPN
ejpam-3550	247	57	∈	∈	PROPN
ejpam-3550	247	58	e(g	e(g	PROPN
ejpam-3550	247	59	)	)	PUNCT
ejpam-3550	247	60	and	and	CCONJ
ejpam-3550	247	61	p	p	NOUN
ejpam-3550	247	62	=	=	X
ejpam-3550	247	63	q	q	PUNCT
ejpam-3550	247	64	∈	∈	PROPN
ejpam-3550	247	65	e(h	e(h	PROPN
ejpam-3550	247	66	)	)	PUNCT
ejpam-3550	247	67	]	]	PUNCT
ejpam-3550	247	68	or	or	CCONJ
ejpam-3550	247	69	u	u	X
ejpam-3550	247	70	=	=	PROPN
ejpam-3550	247	71	v	v	PROPN
ejpam-3550	247	72	and	and	CCONJ
ejpam-3550	247	73	pq	pq	NOUN
ejpam-3550	247	74	∈	∈	PROPN
ejpam-3550	247	75	e(h	e(h	PROPN
ejpam-3550	247	76	)	)	PUNCT
ejpam-3550	247	77	.	.	PUNCT
ejpam-3550	248	1	theorem	theorem	NOUN
ejpam-3550	248	2	5	5	NUM
ejpam-3550	248	3	.	.	PUNCT
ejpam-3550	249	1	let	let	VERB
ejpam-3550	249	2	g	g	NOUN
ejpam-3550	249	3	and	and	CCONJ
ejpam-3550	249	4	h	h	NOUN
ejpam-3550	249	5	be	be	AUX
ejpam-3550	249	6	connected	connect	VERB
ejpam-3550	249	7	non	non	ADJ
ejpam-3550	249	8	-	-	ADJ
ejpam-3550	249	9	trivial	trivial	ADJ
ejpam-3550	249	10	graphs	graph	NOUN
ejpam-3550	249	11	.	.	PUNCT
ejpam-3550	250	1	a	a	DET
ejpam-3550	250	2	subset	subset	NOUN
ejpam-3550	250	3	c	c	NOUN
ejpam-3550	250	4	=	=	SYM
ejpam-3550	250	5	∪x∈s	∪x∈s	PROPN
ejpam-3550	250	6	[	[	X
ejpam-3550	250	7	{	{	PUNCT
ejpam-3550	250	8	x}×tx	x}×tx	X
ejpam-3550	250	9	]	]	X
ejpam-3550	250	10	of	of	ADP
ejpam-3550	250	11	v	v	NOUN
ejpam-3550	250	12	(	(	PUNCT
ejpam-3550	250	13	g	g	PROPN
ejpam-3550	250	14	�	�	NOUN
ejpam-3550	250	15	h	h	NOUN
ejpam-3550	250	16	)	)	PUNCT
ejpam-3550	250	17	is	be	AUX
ejpam-3550	250	18	a	a	DET
ejpam-3550	250	19	hop	hop	NOUN
ejpam-3550	250	20	dominating	dominating	NOUN
ejpam-3550	250	21	set	set	NOUN
ejpam-3550	250	22	of	of	ADP
ejpam-3550	250	23	g	g	PROPN
ejpam-3550	250	24	�	�	PROPN
ejpam-3550	250	25	h	h	NOUN
ejpam-3550	250	26	if	if	SCONJ
ejpam-3550	251	1	and	and	CCONJ
ejpam-3550	251	2	only	only	ADV
ejpam-3550	251	3	if	if	SCONJ
ejpam-3550	251	4	the	the	DET
ejpam-3550	251	5	following	follow	VERB
ejpam-3550	251	6	conditions	condition	NOUN
ejpam-3550	251	7	hold	hold	VERB
ejpam-3550	251	8	:	:	PUNCT
ejpam-3550	251	9	(	(	PUNCT
ejpam-3550	251	10	i	i	NOUN
ejpam-3550	251	11	)	)	PUNCT
ejpam-3550	251	12	for	for	ADP
ejpam-3550	251	13	each	each	DET
ejpam-3550	251	14	x	x	SYM
ejpam-3550	251	15	∈	∈	PROPN
ejpam-3550	251	16	v	v	NOUN
ejpam-3550	251	17	(	(	PUNCT
ejpam-3550	251	18	g)\s	g)\s	NOUN
ejpam-3550	251	19	and	and	CCONJ
ejpam-3550	251	20	for	for	ADP
ejpam-3550	251	21	each	each	DET
ejpam-3550	251	22	p	p	PROPN
ejpam-3550	251	23	∈	∈	PROPN
ejpam-3550	251	24	v	v	ADP
ejpam-3550	251	25	(	(	PUNCT
ejpam-3550	251	26	h	h	NOUN
ejpam-3550	251	27	)	)	PUNCT
ejpam-3550	251	28	,	,	PUNCT
ejpam-3550	251	29	at	at	ADP
ejpam-3550	251	30	least	least	ADJ
ejpam-3550	251	31	one	one	NUM
ejpam-3550	251	32	of	of	ADP
ejpam-3550	251	33	the	the	DET
ejpam-3550	251	34	following	following	ADJ
ejpam-3550	251	35	statements	statement	NOUN
ejpam-3550	251	36	is	be	AUX
ejpam-3550	251	37	satisfied	satisfied	ADJ
ejpam-3550	251	38	:	:	PUNCT
ejpam-3550	251	39	(	(	PUNCT
ejpam-3550	251	40	a	a	X
ejpam-3550	251	41	)	)	PUNCT
ejpam-3550	251	42	there	there	PRON
ejpam-3550	251	43	exists	exist	VERB
ejpam-3550	251	44	y	y	PROPN
ejpam-3550	251	45	∈	∈	PROPN
ejpam-3550	251	46	s	s	PART
ejpam-3550	251	47	∩ng(x	∩ng(x	NOUN
ejpam-3550	251	48	)	)	PUNCT
ejpam-3550	251	49	such	such	ADJ
ejpam-3550	251	50	that	that	SCONJ
ejpam-3550	251	51	ty	ty	NUM
ejpam-3550	251	52	∩nh(p	∩nh(p	NOUN
ejpam-3550	251	53	)	)	PUNCT
ejpam-3550	251	54	6=	6=	ADP
ejpam-3550	251	55	∅.	∅.	PROPN
ejpam-3550	251	56	(	(	PUNCT
ejpam-3550	251	57	b	b	NOUN
ejpam-3550	251	58	)	)	PUNCT
ejpam-3550	251	59	there	there	PRON
ejpam-3550	251	60	exists	exist	VERB
ejpam-3550	251	61	z	z	PROPN
ejpam-3550	251	62	∈	∈	PROPN
ejpam-3550	251	63	s	s	PART
ejpam-3550	251	64	∩ng(x	∩ng(x	NOUN
ejpam-3550	251	65	,	,	PUNCT
ejpam-3550	251	66	2	2	NUM
ejpam-3550	251	67	)	)	PUNCT
ejpam-3550	251	68	such	such	ADJ
ejpam-3550	251	69	that	that	SCONJ
ejpam-3550	251	70	p	p	PROPN
ejpam-3550	251	71	∈	∈	PROPN
ejpam-3550	251	72	tz	tz	X
ejpam-3550	251	73	.	.	PUNCT
ejpam-3550	251	74	(	(	PUNCT
ejpam-3550	251	75	ii	ii	NOUN
ejpam-3550	251	76	)	)	PUNCT
ejpam-3550	251	77	for	for	ADP
ejpam-3550	251	78	each	each	DET
ejpam-3550	251	79	v	v	NOUN
ejpam-3550	251	80	∈	∈	PROPN
ejpam-3550	251	81	s	s	NOUN
ejpam-3550	251	82	and	and	CCONJ
ejpam-3550	251	83	for	for	ADP
ejpam-3550	251	84	each	each	DET
ejpam-3550	251	85	p	p	PROPN
ejpam-3550	251	86	∈	∈	PROPN
ejpam-3550	251	87	v	v	ADP
ejpam-3550	251	88	(	(	PUNCT
ejpam-3550	251	89	h	h	NOUN
ejpam-3550	251	90	)	)	PUNCT
ejpam-3550	251	91	\	\	NOUN
ejpam-3550	251	92	tv	tv	NOUN
ejpam-3550	251	93	,	,	PUNCT
ejpam-3550	251	94	at	at	ADV
ejpam-3550	251	95	least	least	ADJ
ejpam-3550	251	96	one	one	NUM
ejpam-3550	251	97	of	of	ADP
ejpam-3550	251	98	the	the	DET
ejpam-3550	251	99	following	following	ADJ
ejpam-3550	251	100	statements	statement	NOUN
ejpam-3550	251	101	is	be	AUX
ejpam-3550	251	102	satisfied	satisfied	ADJ
ejpam-3550	251	103	:	:	PUNCT
ejpam-3550	251	104	(	(	PUNCT
ejpam-3550	251	105	c	c	X
ejpam-3550	251	106	)	)	PUNCT
ejpam-3550	251	107	nh(p	nh(p	NOUN
ejpam-3550	251	108	,	,	PUNCT
ejpam-3550	251	109	2	2	X
ejpam-3550	251	110	)	)	PUNCT
ejpam-3550	251	111	∩	∩	ADJ
ejpam-3550	251	112	tv	tv	NOUN
ejpam-3550	251	113	6=	6=	ADP
ejpam-3550	251	114	∅.	∅.	PROPN
ejpam-3550	251	115	(	(	PUNCT
ejpam-3550	251	116	d	d	X
ejpam-3550	251	117	)	)	PUNCT
ejpam-3550	251	118	there	there	PRON
ejpam-3550	251	119	exists	exist	VERB
ejpam-3550	251	120	y	y	PROPN
ejpam-3550	251	121	∈	∈	PROPN
ejpam-3550	251	122	s	s	PART
ejpam-3550	251	123	∩ng(v	∩ng(v	PROPN
ejpam-3550	251	124	)	)	PUNCT
ejpam-3550	251	125	such	such	ADJ
ejpam-3550	251	126	that	that	SCONJ
ejpam-3550	251	127	ty	ty	NUM
ejpam-3550	251	128	∩nh(p	∩nh(p	NOUN
ejpam-3550	251	129	)	)	PUNCT
ejpam-3550	251	130	6=	6=	ADP
ejpam-3550	251	131	∅.	∅.	PROPN
ejpam-3550	251	132	(	(	PUNCT
ejpam-3550	251	133	e	e	NOUN
ejpam-3550	251	134	)	)	PUNCT
ejpam-3550	251	135	there	there	PRON
ejpam-3550	251	136	exists	exist	VERB
ejpam-3550	251	137	z	z	PROPN
ejpam-3550	251	138	∈	∈	PROPN
ejpam-3550	251	139	s	s	PART
ejpam-3550	251	140	∩ng(v	∩ng(v	PROPN
ejpam-3550	251	141	,	,	PUNCT
ejpam-3550	251	142	2	2	NUM
ejpam-3550	251	143	)	)	PUNCT
ejpam-3550	251	144	such	such	ADJ
ejpam-3550	251	145	that	that	SCONJ
ejpam-3550	251	146	p	p	PROPN
ejpam-3550	251	147	∈	∈	PROPN
ejpam-3550	251	148	tz	tz	NOUN
ejpam-3550	251	149	.	.	PUNCT
ejpam-3550	251	150	proof	proof	NOUN
ejpam-3550	251	151	.	.	PUNCT
ejpam-3550	252	1	suppose	suppose	VERB
ejpam-3550	252	2	c	c	NOUN
ejpam-3550	252	3	is	be	AUX
ejpam-3550	252	4	a	a	DET
ejpam-3550	252	5	hop	hop	NOUN
ejpam-3550	252	6	dominating	dominating	NOUN
ejpam-3550	252	7	set	set	NOUN
ejpam-3550	252	8	of	of	ADP
ejpam-3550	252	9	g	g	PROPN
ejpam-3550	252	10	�	�	PROPN
ejpam-3550	252	11	h.	h.	PROPN
ejpam-3550	252	12	let	let	VERB
ejpam-3550	252	13	x	x	SYM
ejpam-3550	252	14	∈	∈	PROPN
ejpam-3550	252	15	v	v	X
ejpam-3550	252	16	(	(	PUNCT
ejpam-3550	252	17	g	g	NOUN
ejpam-3550	252	18	)	)	PUNCT
ejpam-3550	252	19	\	\	PROPN
ejpam-3550	252	20	s	s	PART
ejpam-3550	252	21	and	and	CCONJ
ejpam-3550	252	22	let	let	VERB
ejpam-3550	252	23	p	p	PRON
ejpam-3550	252	24	∈	∈	PROPN
ejpam-3550	252	25	v	v	ADP
ejpam-3550	252	26	(	(	PUNCT
ejpam-3550	252	27	h	h	NOUN
ejpam-3550	252	28	)	)	PUNCT
ejpam-3550	252	29	.	.	PUNCT
ejpam-3550	253	1	since	since	SCONJ
ejpam-3550	253	2	c	c	PROPN
ejpam-3550	253	3	is	be	AUX
ejpam-3550	253	4	a	a	DET
ejpam-3550	253	5	hop	hop	NOUN
ejpam-3550	253	6	dominating	dominating	NOUN
ejpam-3550	253	7	set	set	NOUN
ejpam-3550	253	8	and	and	CCONJ
ejpam-3550	253	9	(	(	PUNCT
ejpam-3550	253	10	x	x	X
ejpam-3550	253	11	,	,	PUNCT
ejpam-3550	253	12	p	p	NOUN
ejpam-3550	253	13	)	)	PUNCT
ejpam-3550	253	14	/∈	/∈	PUNCT
ejpam-3550	254	1	c	c	X
ejpam-3550	254	2	,	,	PUNCT
ejpam-3550	254	3	there	there	PRON
ejpam-3550	254	4	exists	exist	VERB
ejpam-3550	254	5	(	(	PUNCT
ejpam-3550	254	6	y	y	NOUN
ejpam-3550	254	7	,	,	PUNCT
ejpam-3550	254	8	q	q	X
ejpam-3550	254	9	)	)	PUNCT
ejpam-3550	254	10	∈	∈	PROPN
ejpam-3550	254	11	c	c	NOUN
ejpam-3550	254	12	such	such	ADJ
ejpam-3550	254	13	that	that	SCONJ
ejpam-3550	254	14	dg	dg	PROPN
ejpam-3550	254	15	�	�	PROPN
ejpam-3550	254	16	h((x	h((x	NOUN
ejpam-3550	254	17	,	,	PUNCT
ejpam-3550	254	18	p)(y	p)(y	PROPN
ejpam-3550	254	19	,	,	PUNCT
ejpam-3550	254	20	q	q	NOUN
ejpam-3550	254	21	)	)	PUNCT
ejpam-3550	254	22	)	)	PUNCT
ejpam-3550	255	1	=	=	SYM
ejpam-3550	255	2	2	2	X
ejpam-3550	255	3	.	.	PUNCT
ejpam-3550	255	4	since	since	SCONJ
ejpam-3550	255	5	y	y	PROPN
ejpam-3550	255	6	∈	∈	PROPN
ejpam-3550	255	7	s	s	PROPN
ejpam-3550	255	8	,	,	PUNCT
ejpam-3550	255	9	x	x	SYM
ejpam-3550	255	10	6=	6=	ADP
ejpam-3550	255	11	y.	y.	NOUN
ejpam-3550	255	12	if	if	SCONJ
ejpam-3550	255	13	xy	xy	PROPN
ejpam-3550	255	14	∈	∈	PROPN
ejpam-3550	255	15	e(g	e(g	PROPN
ejpam-3550	255	16	)	)	PUNCT
ejpam-3550	255	17	,	,	PUNCT
ejpam-3550	255	18	then	then	ADV
ejpam-3550	255	19	pq	pq	PROPN
ejpam-3550	255	20	∈	∈	PROPN
ejpam-3550	255	21	e(h	e(h	PROPN
ejpam-3550	255	22	)	)	PUNCT
ejpam-3550	255	23	.	.	PUNCT
ejpam-3550	256	1	hence	hence	ADV
ejpam-3550	256	2	,	,	PUNCT
ejpam-3550	256	3	q	q	PROPN
ejpam-3550	256	4	∈	∈	NOUN
ejpam-3550	256	5	ty	ty	PRON
ejpam-3550	256	6	∩	∩	NOUN
ejpam-3550	256	7	nh(p	nh(p	NUM
ejpam-3550	256	8	)	)	PUNCT
ejpam-3550	256	9	,	,	PUNCT
ejpam-3550	256	10	showing	show	VERB
ejpam-3550	256	11	that	that	SCONJ
ejpam-3550	256	12	(	(	PUNCT
ejpam-3550	256	13	a	a	X
ejpam-3550	256	14	)	)	PUNCT
ejpam-3550	256	15	holds	hold	NOUN
ejpam-3550	256	16	.	.	PUNCT
ejpam-3550	257	1	so	so	ADV
ejpam-3550	257	2	suppose	suppose	VERB
ejpam-3550	257	3	that	that	SCONJ
ejpam-3550	257	4	y	y	PROPN
ejpam-3550	257	5	/∈	/∈	PUNCT
ejpam-3550	257	6	ng(x	ng(x	NUM
ejpam-3550	257	7	)	)	PUNCT
ejpam-3550	257	8	.	.	PUNCT
ejpam-3550	258	1	since	since	SCONJ
ejpam-3550	258	2	dg	dg	PROPN
ejpam-3550	258	3	�	�	PROPN
ejpam-3550	258	4	h((x	h((x	NOUN
ejpam-3550	258	5	,	,	PUNCT
ejpam-3550	258	6	p)(y	p)(y	PROPN
ejpam-3550	258	7	,	,	PUNCT
ejpam-3550	258	8	q	q	NOUN
ejpam-3550	258	9	)	)	PUNCT
ejpam-3550	258	10	)	)	PUNCT
ejpam-3550	258	11	=	=	SYM
ejpam-3550	258	12	2	2	X
ejpam-3550	258	13	,	,	PUNCT
ejpam-3550	258	14	it	it	PRON
ejpam-3550	258	15	follows	follow	VERB
ejpam-3550	258	16	that	that	SCONJ
ejpam-3550	258	17	y	y	PROPN
ejpam-3550	258	18	∈	∈	PROPN
ejpam-3550	258	19	ng(x	ng(x	NUM
ejpam-3550	258	20	,	,	PUNCT
ejpam-3550	258	21	2	2	NUM
ejpam-3550	258	22	)	)	PUNCT
ejpam-3550	258	23	and	and	CCONJ
ejpam-3550	258	24	p	p	X
ejpam-3550	258	25	=	=	NOUN
ejpam-3550	258	26	q.	q.	NOUN
ejpam-3550	258	27	hence	hence	ADV
ejpam-3550	258	28	,	,	PUNCT
ejpam-3550	258	29	p	p	PROPN
ejpam-3550	258	30	∈	∈	PROPN
ejpam-3550	258	31	ty	ty	NOUN
ejpam-3550	258	32	,	,	PUNCT
ejpam-3550	258	33	showing	show	VERB
ejpam-3550	258	34	that	that	SCONJ
ejpam-3550	258	35	(	(	PUNCT
ejpam-3550	258	36	b	b	X
ejpam-3550	258	37	)	)	PUNCT
ejpam-3550	258	38	holds	hold	VERB
ejpam-3550	258	39	.	.	PUNCT
ejpam-3550	259	1	next	next	ADV
ejpam-3550	259	2	,	,	PUNCT
ejpam-3550	259	3	let	let	VERB
ejpam-3550	259	4	v	v	NUM
ejpam-3550	259	5	∈	∈	NOUN
ejpam-3550	259	6	s	s	PART
ejpam-3550	259	7	and	and	CCONJ
ejpam-3550	259	8	let	let	VERB
ejpam-3550	259	9	p	p	PRON
ejpam-3550	259	10	∈	∈	PROPN
ejpam-3550	259	11	v	v	NOUN
ejpam-3550	259	12	(	(	PUNCT
ejpam-3550	259	13	h)\tv	h)\tv	PROPN
ejpam-3550	259	14	.	.	PUNCT
ejpam-3550	260	1	since	since	SCONJ
ejpam-3550	260	2	c	c	PROPN
ejpam-3550	260	3	is	be	AUX
ejpam-3550	260	4	a	a	DET
ejpam-3550	260	5	hop	hop	NOUN
ejpam-3550	260	6	dominating	dominating	NOUN
ejpam-3550	260	7	set	set	NOUN
ejpam-3550	260	8	and	and	CCONJ
ejpam-3550	260	9	(	(	PUNCT
ejpam-3550	260	10	v	v	NOUN
ejpam-3550	260	11	,	,	PUNCT
ejpam-3550	260	12	p	p	NOUN
ejpam-3550	260	13	)	)	PUNCT
ejpam-3550	260	14	/∈	/∈	PUNCT
ejpam-3550	261	1	c	c	X
ejpam-3550	261	2	,	,	PUNCT
ejpam-3550	261	3	there	there	PRON
ejpam-3550	261	4	exists	exist	VERB
ejpam-3550	261	5	(	(	PUNCT
ejpam-3550	261	6	w	w	NOUN
ejpam-3550	261	7	,	,	PUNCT
ejpam-3550	261	8	q	q	NOUN
ejpam-3550	261	9	)	)	PUNCT
ejpam-3550	261	10	∈	∈	PROPN
ejpam-3550	261	11	c	c	NOUN
ejpam-3550	261	12	such	such	ADJ
ejpam-3550	261	13	that	that	SCONJ
ejpam-3550	261	14	dg	dg	PROPN
ejpam-3550	261	15	�	�	PROPN
ejpam-3550	261	16	h((v	h((v	NOUN
ejpam-3550	261	17	,	,	PUNCT
ejpam-3550	261	18	p)(w	p)(w	PROPN
ejpam-3550	261	19	,	,	PUNCT
ejpam-3550	261	20	q	q	NOUN
ejpam-3550	261	21	)	)	PUNCT
ejpam-3550	261	22	)	)	PUNCT
ejpam-3550	262	1	=	=	SYM
ejpam-3550	262	2	2	2	X
ejpam-3550	262	3	.	.	PUNCT
ejpam-3550	262	4	suppose	suppose	VERB
ejpam-3550	262	5	that	that	SCONJ
ejpam-3550	262	6	(	(	PUNCT
ejpam-3550	262	7	d	d	X
ejpam-3550	262	8	)	)	PUNCT
ejpam-3550	262	9	and	and	CCONJ
ejpam-3550	262	10	(	(	PUNCT
ejpam-3550	262	11	e	e	X
ejpam-3550	262	12	)	)	PUNCT
ejpam-3550	262	13	do	do	AUX
ejpam-3550	262	14	not	not	PART
ejpam-3550	262	15	hold	hold	VERB
ejpam-3550	262	16	.	.	PUNCT
ejpam-3550	263	1	then	then	ADV
ejpam-3550	263	2	,	,	PUNCT
ejpam-3550	263	3	since	since	SCONJ
ejpam-3550	263	4	dg	dg	PROPN
ejpam-3550	263	5	�	�	PROPN
ejpam-3550	263	6	h((v	h((v	NOUN
ejpam-3550	263	7	,	,	PUNCT
ejpam-3550	263	8	p)(w	p)(w	PROPN
ejpam-3550	263	9	,	,	PUNCT
ejpam-3550	263	10	q	q	NOUN
ejpam-3550	263	11	)	)	PUNCT
ejpam-3550	263	12	)	)	PUNCT
ejpam-3550	264	1	=	=	SYM
ejpam-3550	264	2	2	2	NUM
ejpam-3550	264	3	,	,	PUNCT
ejpam-3550	264	4	v	v	NOUN
ejpam-3550	264	5	=	=	SYM
ejpam-3550	264	6	w	w	PROPN
ejpam-3550	264	7	and	and	CCONJ
ejpam-3550	264	8	dh(p	dh(p	PROPN
ejpam-3550	264	9	,	,	PUNCT
ejpam-3550	264	10	q	q	X
ejpam-3550	264	11	)	)	PUNCT
ejpam-3550	264	12	=	=	SYM
ejpam-3550	264	13	2	2	X
ejpam-3550	264	14	.	.	PUNCT
ejpam-3550	264	15	thus	thus	ADV
ejpam-3550	264	16	,	,	PUNCT
ejpam-3550	264	17	q	q	PROPN
ejpam-3550	264	18	∈	∈	PROPN
ejpam-3550	264	19	tv∩nh(p	tv∩nh(p	NOUN
ejpam-3550	264	20	,	,	PUNCT
ejpam-3550	264	21	2	2	NUM
ejpam-3550	264	22	)	)	PUNCT
ejpam-3550	264	23	,	,	PUNCT
ejpam-3550	264	24	showing	show	VERB
ejpam-3550	264	25	that	that	SCONJ
ejpam-3550	264	26	(	(	PUNCT
ejpam-3550	264	27	c	c	X
ejpam-3550	264	28	)	)	PUNCT
ejpam-3550	264	29	holds	hold	NOUN
ejpam-3550	264	30	.	.	PUNCT
ejpam-3550	265	1	for	for	ADP
ejpam-3550	265	2	the	the	DET
ejpam-3550	265	3	converse	converse	NOUN
ejpam-3550	265	4	,	,	PUNCT
ejpam-3550	265	5	suppose	suppose	VERB
ejpam-3550	265	6	that	that	SCONJ
ejpam-3550	265	7	c	c	PROPN
ejpam-3550	265	8	satisfies	satisfy	VERB
ejpam-3550	265	9	properties	property	NOUN
ejpam-3550	265	10	(	(	PUNCT
ejpam-3550	265	11	i	i	NOUN
ejpam-3550	265	12	)	)	PUNCT
ejpam-3550	265	13	and	and	CCONJ
ejpam-3550	265	14	(	(	PUNCT
ejpam-3550	265	15	ii	ii	NOUN
ejpam-3550	265	16	)	)	PUNCT
ejpam-3550	265	17	.	.	PUNCT
ejpam-3550	266	1	let	let	VERB
ejpam-3550	266	2	(	(	PUNCT
ejpam-3550	266	3	v	v	NOUN
ejpam-3550	266	4	,	,	PUNCT
ejpam-3550	266	5	t	t	PROPN
ejpam-3550	266	6	)	)	PUNCT
ejpam-3550	266	7	∈	∈	PROPN
ejpam-3550	266	8	v	v	NOUN
ejpam-3550	266	9	(	(	PUNCT
ejpam-3550	266	10	g[h])\	g[h])\	NOUN
ejpam-3550	266	11	c	c	NOUN
ejpam-3550	266	12	and	and	CCONJ
ejpam-3550	266	13	consider	consider	VERB
ejpam-3550	266	14	the	the	DET
ejpam-3550	266	15	following	follow	VERB
ejpam-3550	266	16	cases	case	NOUN
ejpam-3550	266	17	:	:	PUNCT
ejpam-3550	266	18	case	case	NOUN
ejpam-3550	266	19	1	1	NUM
ejpam-3550	266	20	.	.	X
ejpam-3550	267	1	v	v	AUX
ejpam-3550	267	2	/∈	/∈	PUNCT
ejpam-3550	267	3	s	s	PART
ejpam-3550	268	1	if	if	SCONJ
ejpam-3550	268	2	(	(	PUNCT
ejpam-3550	268	3	a	a	NOUN
ejpam-3550	268	4	)	)	PUNCT
ejpam-3550	268	5	of	of	ADP
ejpam-3550	268	6	(	(	PUNCT
ejpam-3550	268	7	i	i	NOUN
ejpam-3550	268	8	)	)	PUNCT
ejpam-3550	268	9	holds	hold	VERB
ejpam-3550	268	10	,	,	PUNCT
ejpam-3550	268	11	then	then	ADV
ejpam-3550	268	12	there	there	PRON
ejpam-3550	268	13	exist	exist	VERB
ejpam-3550	268	14	y	y	PROPN
ejpam-3550	268	15	∈	∈	PROPN
ejpam-3550	268	16	s	s	PART
ejpam-3550	268	17	∩	∩	NOUN
ejpam-3550	268	18	ng(v	ng(v	X
ejpam-3550	268	19	)	)	PUNCT
ejpam-3550	268	20	and	and	CCONJ
ejpam-3550	268	21	h	h	NOUN
ejpam-3550	268	22	∈	∈	PROPN
ejpam-3550	268	23	ty	ty	PRON
ejpam-3550	268	24	∩	∩	NOUN
ejpam-3550	268	25	nh(p	nh(p	NUM
ejpam-3550	268	26	)	)	PUNCT
ejpam-3550	268	27	.	.	PUNCT
ejpam-3550	269	1	hence	hence	ADV
ejpam-3550	269	2	,	,	PUNCT
ejpam-3550	269	3	(	(	PUNCT
ejpam-3550	269	4	y	y	NOUN
ejpam-3550	269	5	,	,	PUNCT
ejpam-3550	269	6	h	h	NOUN
ejpam-3550	269	7	)	)	PUNCT
ejpam-3550	269	8	∈	∈	PROPN
ejpam-3550	269	9	c	c	PROPN
ejpam-3550	269	10	∩	∩	PROPN
ejpam-3550	269	11	ng	ng	PROPN
ejpam-3550	269	12	�	�	PROPN
ejpam-3550	269	13	h((v	h((v	PROPN
ejpam-3550	269	14	,	,	PUNCT
ejpam-3550	269	15	t	t	PROPN
ejpam-3550	269	16	)	)	PUNCT
ejpam-3550	269	17	,	,	PUNCT
ejpam-3550	269	18	2	2	NUM
ejpam-3550	269	19	)	)	PUNCT
ejpam-3550	269	20	.	.	PUNCT
ejpam-3550	270	1	if	if	SCONJ
ejpam-3550	270	2	(	(	PUNCT
ejpam-3550	270	3	b	b	NOUN
ejpam-3550	270	4	)	)	PUNCT
ejpam-3550	270	5	of	of	ADP
ejpam-3550	270	6	(	(	PUNCT
ejpam-3550	270	7	i	i	NOUN
ejpam-3550	270	8	)	)	PUNCT
ejpam-3550	270	9	holds	hold	VERB
ejpam-3550	270	10	,	,	PUNCT
ejpam-3550	270	11	then	then	ADV
ejpam-3550	270	12	there	there	PRON
ejpam-3550	270	13	exists	exist	VERB
ejpam-3550	270	14	z	z	PROPN
ejpam-3550	270	15	∈	∈	PROPN
ejpam-3550	270	16	s	s	PART
ejpam-3550	270	17	∩	∩	NOUN
ejpam-3550	270	18	ng(v	ng(v	NOUN
ejpam-3550	270	19	,	,	PUNCT
ejpam-3550	270	20	2	2	X
ejpam-3550	270	21	)	)	PUNCT
ejpam-3550	270	22	such	such	ADJ
ejpam-3550	270	23	that	that	SCONJ
ejpam-3550	270	24	t	t	PROPN
ejpam-3550	270	25	∈	∈	PROPN
ejpam-3550	270	26	tz	tz	NOUN
ejpam-3550	270	27	.	.	PUNCT
ejpam-3550	271	1	it	it	PRON
ejpam-3550	271	2	follows	follow	VERB
ejpam-3550	271	3	that	that	SCONJ
ejpam-3550	271	4	(	(	PUNCT
ejpam-3550	271	5	z	z	X
ejpam-3550	271	6	,	,	PUNCT
ejpam-3550	271	7	t	t	PROPN
ejpam-3550	271	8	)	)	PUNCT
ejpam-3550	271	9	∈	∈	PROPN
ejpam-3550	271	10	c	c	PROPN
ejpam-3550	271	11	∩ng	∩ng	PROPN
ejpam-3550	271	12	�	�	PROPN
ejpam-3550	271	13	h((v	h((v	NOUN
ejpam-3550	271	14	,	,	PUNCT
ejpam-3550	271	15	t	t	PROPN
ejpam-3550	271	16	)	)	PUNCT
ejpam-3550	271	17	,	,	PUNCT
ejpam-3550	271	18	2	2	NUM
ejpam-3550	271	19	)	)	PUNCT
ejpam-3550	271	20	.	.	PUNCT
ejpam-3550	272	1	case	case	NOUN
ejpam-3550	272	2	2	2	NUM
ejpam-3550	272	3	.	.	NOUN
ejpam-3550	272	4	v	v	NUM
ejpam-3550	272	5	∈	∈	PROPN
ejpam-3550	273	1	s	s	VERB
ejpam-3550	273	2	then	then	ADV
ejpam-3550	273	3	t	t	PROPN
ejpam-3550	273	4	/∈	/∈	PUNCT
ejpam-3550	274	1	tv	tv	NOUN
ejpam-3550	274	2	.	.	PUNCT
ejpam-3550	275	1	if	if	SCONJ
ejpam-3550	275	2	(	(	PUNCT
ejpam-3550	275	3	c	c	NOUN
ejpam-3550	275	4	)	)	PUNCT
ejpam-3550	275	5	of	of	ADP
ejpam-3550	275	6	(	(	PUNCT
ejpam-3550	275	7	ii	ii	NOUN
ejpam-3550	275	8	)	)	PUNCT
ejpam-3550	275	9	holds	hold	VERB
ejpam-3550	275	10	,	,	PUNCT
ejpam-3550	275	11	then	then	ADV
ejpam-3550	275	12	we	we	PRON
ejpam-3550	275	13	may	may	AUX
ejpam-3550	275	14	take	take	VERB
ejpam-3550	275	15	any	any	DET
ejpam-3550	275	16	q	q	PROPN
ejpam-3550	275	17	∈	∈	PROPN
ejpam-3550	275	18	nh(t	nh(t	NOUN
ejpam-3550	275	19	,	,	PUNCT
ejpam-3550	275	20	2	2	NUM
ejpam-3550	275	21	)	)	PUNCT
ejpam-3550	275	22	∩	∩	ADJ
ejpam-3550	275	23	tv	tv	NOUN
ejpam-3550	275	24	.	.	PUNCT
ejpam-3550	276	1	clearly	clearly	ADV
ejpam-3550	276	2	,	,	PUNCT
ejpam-3550	276	3	(	(	PUNCT
ejpam-3550	276	4	v	v	NOUN
ejpam-3550	276	5	,	,	PUNCT
ejpam-3550	276	6	q	q	NOUN
ejpam-3550	276	7	)	)	PUNCT
ejpam-3550	276	8	∈	∈	PROPN
ejpam-3550	276	9	c∩ng	c∩ng	PROPN
ejpam-3550	276	10	�	�	PROPN
ejpam-3550	276	11	h((v	h((v	NOUN
ejpam-3550	276	12	,	,	PUNCT
ejpam-3550	276	13	t	t	PROPN
ejpam-3550	276	14	)	)	PUNCT
ejpam-3550	276	15	,	,	PUNCT
ejpam-3550	276	16	2	2	NUM
ejpam-3550	276	17	)	)	PUNCT
ejpam-3550	276	18	.	.	PUNCT
ejpam-3550	277	1	as	as	ADP
ejpam-3550	277	2	in	in	ADP
ejpam-3550	277	3	the	the	DET
ejpam-3550	277	4	first	first	ADJ
ejpam-3550	277	5	case	case	NOUN
ejpam-3550	277	6	,	,	PUNCT
ejpam-3550	277	7	if	if	SCONJ
ejpam-3550	277	8	(	(	PUNCT
ejpam-3550	277	9	d	d	NOUN
ejpam-3550	277	10	)	)	PUNCT
ejpam-3550	277	11	or	or	CCONJ
ejpam-3550	277	12	(	(	PUNCT
ejpam-3550	277	13	e	e	NOUN
ejpam-3550	277	14	)	)	PUNCT
ejpam-3550	277	15	of	of	ADP
ejpam-3550	277	16	(	(	PUNCT
ejpam-3550	277	17	ii	ii	NOUN
ejpam-3550	277	18	)	)	PUNCT
ejpam-3550	277	19	holds	hold	VERB
ejpam-3550	277	20	,	,	PUNCT
ejpam-3550	277	21	then	then	ADV
ejpam-3550	277	22	there	there	PRON
ejpam-3550	277	23	exists	exist	VERB
ejpam-3550	277	24	(	(	PUNCT
ejpam-3550	277	25	w	w	NOUN
ejpam-3550	277	26	,	,	PUNCT
ejpam-3550	277	27	h	h	NOUN
ejpam-3550	277	28	)	)	PUNCT
ejpam-3550	277	29	∈	∈	PROPN
ejpam-3550	277	30	c	c	PROPN
ejpam-3550	277	31	∩ng	∩ng	PROPN
ejpam-3550	277	32	�	�	PROPN
ejpam-3550	277	33	h((v	h((v	NOUN
ejpam-3550	277	34	,	,	PUNCT
ejpam-3550	277	35	t	t	PROPN
ejpam-3550	277	36	)	)	PUNCT
ejpam-3550	277	37	,	,	PUNCT
ejpam-3550	277	38	2	2	NUM
ejpam-3550	277	39	)	)	PUNCT
ejpam-3550	277	40	.	.	PUNCT
ejpam-3550	278	1	accordingly	accordingly	ADV
ejpam-3550	278	2	,	,	PUNCT
ejpam-3550	278	3	c	c	PROPN
ejpam-3550	278	4	is	be	AUX
ejpam-3550	278	5	a	a	DET
ejpam-3550	278	6	hop	hop	NOUN
ejpam-3550	278	7	dominating	dominating	NOUN
ejpam-3550	278	8	set	set	NOUN
ejpam-3550	278	9	of	of	ADP
ejpam-3550	278	10	g	g	PROPN
ejpam-3550	278	11	�	�	PROPN
ejpam-3550	278	12	h.	h.	PROPN
ejpam-3550	278	13	references	reference	VERB
ejpam-3550	278	14	1463	1463	NUM
ejpam-3550	278	15	corollary	corollary	ADJ
ejpam-3550	278	16	5	5	NUM
ejpam-3550	278	17	.	.	PUNCT
ejpam-3550	279	1	let	let	VERB
ejpam-3550	279	2	g	g	NOUN
ejpam-3550	279	3	and	and	CCONJ
ejpam-3550	279	4	h	h	PROPN
ejpam-3550	279	5	be	be	VERB
ejpam-3550	279	6	non	non	ADJ
ejpam-3550	279	7	-	-	ADJ
ejpam-3550	279	8	trivial	trivial	ADJ
ejpam-3550	279	9	connected	connected	ADJ
ejpam-3550	279	10	graphs	graph	NOUN
ejpam-3550	279	11	.	.	PUNCT
ejpam-3550	280	1	then	then	ADV
ejpam-3550	280	2	γh(g	γh(g	PUNCT
ejpam-3550	280	3	�	�	NOUN
ejpam-3550	280	4	h	h	NOUN
ejpam-3550	280	5	)	)	PUNCT
ejpam-3550	280	6	≤	≤	NOUN
ejpam-3550	280	7	min{γ(g)γ∗t1,2(h	min{γ(g)γ∗t1,2(h	PROPN
ejpam-3550	280	8	)	)	PUNCT
ejpam-3550	280	9	,	,	PUNCT
ejpam-3550	280	10	γ(h)γ∗t1,2(g	γ(h)γ∗t1,2(g	NOUN
ejpam-3550	280	11	)	)	PUNCT
ejpam-3550	280	12	}	}	PUNCT
ejpam-3550	280	13	.	.	PUNCT
ejpam-3550	281	1	proof	proof	NOUN
ejpam-3550	281	2	.	.	PUNCT
ejpam-3550	282	1	let	let	VERB
ejpam-3550	282	2	s	s	PRON
ejpam-3550	282	3	be	be	AUX
ejpam-3550	282	4	a	a	DET
ejpam-3550	282	5	γ	γ	NOUN
ejpam-3550	282	6	-	-	PUNCT
ejpam-3550	282	7	set	set	NOUN
ejpam-3550	282	8	of	of	ADP
ejpam-3550	282	9	g	g	NOUN
ejpam-3550	282	10	and	and	CCONJ
ejpam-3550	282	11	let	let	VERB
ejpam-3550	282	12	d	d	PRON
ejpam-3550	282	13	be	be	AUX
ejpam-3550	282	14	a	a	DET
ejpam-3550	282	15	γ∗t1,2	γ∗t1,2	NOUN
ejpam-3550	282	16	-	-	PUNCT
ejpam-3550	282	17	set	set	NOUN
ejpam-3550	282	18	of	of	ADP
ejpam-3550	282	19	h.	h.	PROPN
ejpam-3550	282	20	set	set	VERB
ejpam-3550	282	21	tx	tx	PROPN
ejpam-3550	282	22	=	=	SYM
ejpam-3550	283	1	d	d	PROPN
ejpam-3550	283	2	for	for	ADP
ejpam-3550	283	3	each	each	DET
ejpam-3550	283	4	x	x	SYM
ejpam-3550	283	5	∈	∈	PROPN
ejpam-3550	283	6	s	s	PART
ejpam-3550	283	7	and	and	CCONJ
ejpam-3550	283	8	let	let	VERB
ejpam-3550	283	9	c	c	NOUN
ejpam-3550	283	10	=	=	PUNCT
ejpam-3550	283	11	∪x∈s	∪x∈s	PROPN
ejpam-3550	283	12	[	[	X
ejpam-3550	283	13	{	{	PUNCT
ejpam-3550	283	14	x	x	NOUN
ejpam-3550	283	15	}	}	PUNCT
ejpam-3550	283	16	×	×	NOUN
ejpam-3550	283	17	tx	tx	NOUN
ejpam-3550	283	18	]	]	X
ejpam-3550	283	19	=	=	SYM
ejpam-3550	283	20	s	s	NOUN
ejpam-3550	283	21	×d	×d	NOUN
ejpam-3550	283	22	.	.	PUNCT
ejpam-3550	284	1	let	let	VERB
ejpam-3550	284	2	x	x	SYM
ejpam-3550	284	3	∈	∈	PROPN
ejpam-3550	284	4	v	v	X
ejpam-3550	284	5	(	(	PUNCT
ejpam-3550	284	6	g	g	NOUN
ejpam-3550	284	7	)	)	PUNCT
ejpam-3550	284	8	\	\	PROPN
ejpam-3550	284	9	s	s	PART
ejpam-3550	284	10	and	and	CCONJ
ejpam-3550	284	11	let	let	VERB
ejpam-3550	284	12	p	p	PRON
ejpam-3550	284	13	∈	∈	PROPN
ejpam-3550	284	14	v	v	ADP
ejpam-3550	284	15	(	(	PUNCT
ejpam-3550	284	16	h	h	NOUN
ejpam-3550	284	17	)	)	PUNCT
ejpam-3550	284	18	.	.	PUNCT
ejpam-3550	285	1	since	since	SCONJ
ejpam-3550	285	2	s	s	PROPN
ejpam-3550	285	3	is	be	AUX
ejpam-3550	285	4	a	a	DET
ejpam-3550	285	5	dominating	dominating	NOUN
ejpam-3550	285	6	set	set	NOUN
ejpam-3550	285	7	of	of	ADP
ejpam-3550	285	8	g	g	NOUN
ejpam-3550	285	9	,	,	PUNCT
ejpam-3550	285	10	there	there	PRON
ejpam-3550	285	11	exists	exist	VERB
ejpam-3550	285	12	y	y	PROPN
ejpam-3550	285	13	∈	∈	PROPN
ejpam-3550	285	14	s	s	PART
ejpam-3550	285	15	∩	∩	NOUN
ejpam-3550	285	16	ng(x	ng(x	NUM
ejpam-3550	285	17	)	)	PUNCT
ejpam-3550	285	18	.	.	PUNCT
ejpam-3550	286	1	now	now	ADV
ejpam-3550	286	2	,	,	PUNCT
ejpam-3550	286	3	since	since	SCONJ
ejpam-3550	286	4	ty	ty	NUM
ejpam-3550	286	5	=	=	SYM
ejpam-3550	286	6	d	d	NOUN
ejpam-3550	286	7	is	be	AUX
ejpam-3550	286	8	a	a	DET
ejpam-3550	286	9	total	total	ADJ
ejpam-3550	286	10	dominating	dominating	NOUN
ejpam-3550	286	11	set	set	NOUN
ejpam-3550	286	12	of	of	ADP
ejpam-3550	286	13	h	h	NOUN
ejpam-3550	286	14	,	,	PUNCT
ejpam-3550	286	15	there	there	PRON
ejpam-3550	286	16	exists	exist	VERB
ejpam-3550	286	17	q	q	PROPN
ejpam-3550	286	18	∈	∈	PROPN
ejpam-3550	286	19	ty	ty	PRON
ejpam-3550	286	20	∩	∩	NOUN
ejpam-3550	286	21	nh(p	nh(p	NUM
ejpam-3550	286	22	)	)	PUNCT
ejpam-3550	286	23	.	.	PUNCT
ejpam-3550	287	1	thus	thus	ADV
ejpam-3550	287	2	,	,	PUNCT
ejpam-3550	287	3	(	(	PUNCT
ejpam-3550	287	4	a	a	X
ejpam-3550	287	5	)	)	PUNCT
ejpam-3550	287	6	of	of	ADP
ejpam-3550	287	7	property	property	NOUN
ejpam-3550	287	8	(	(	PUNCT
ejpam-3550	287	9	i	i	NOUN
ejpam-3550	287	10	)	)	PUNCT
ejpam-3550	287	11	of	of	ADP
ejpam-3550	287	12	theorem	theorem	ADJ
ejpam-3550	287	13	5	5	NUM
ejpam-3550	287	14	holds	hold	NOUN
ejpam-3550	287	15	.	.	PUNCT
ejpam-3550	288	1	next	next	ADV
ejpam-3550	288	2	,	,	PUNCT
ejpam-3550	288	3	let	let	VERB
ejpam-3550	288	4	v	v	NUM
ejpam-3550	288	5	∈	∈	NOUN
ejpam-3550	288	6	s	s	PART
ejpam-3550	288	7	and	and	CCONJ
ejpam-3550	288	8	let	let	VERB
ejpam-3550	288	9	t	t	PROPN
ejpam-3550	288	10	∈	∈	PROPN
ejpam-3550	288	11	v	v	ADP
ejpam-3550	288	12	(	(	PUNCT
ejpam-3550	288	13	h	h	NOUN
ejpam-3550	288	14	)	)	PUNCT
ejpam-3550	288	15	\	\	NOUN
ejpam-3550	288	16	tv	tv	NOUN
ejpam-3550	288	17	.	.	PUNCT
ejpam-3550	289	1	since	since	SCONJ
ejpam-3550	289	2	tv	tv	NOUN
ejpam-3550	289	3	=	=	PUNCT
ejpam-3550	289	4	d	d	NOUN
ejpam-3550	289	5	is	be	AUX
ejpam-3550	289	6	a	a	DET
ejpam-3550	289	7	hop	hop	NOUN
ejpam-3550	289	8	dominating	dominating	NOUN
ejpam-3550	289	9	set	set	NOUN
ejpam-3550	289	10	of	of	ADP
ejpam-3550	289	11	h	h	NOUN
ejpam-3550	289	12	,	,	PUNCT
ejpam-3550	289	13	tv	tv	NOUN
ejpam-3550	289	14	∩	∩	NOUN
ejpam-3550	289	15	nh(t	nh(t	NOUN
ejpam-3550	289	16	,	,	PUNCT
ejpam-3550	289	17	2	2	NUM
ejpam-3550	289	18	)	)	PUNCT
ejpam-3550	289	19	6=	6=	ADP
ejpam-3550	289	20	∅.	∅.	ADP
ejpam-3550	289	21	hence	hence	ADV
ejpam-3550	289	22	,	,	PUNCT
ejpam-3550	289	23	(	(	PUNCT
ejpam-3550	289	24	c	c	NOUN
ejpam-3550	289	25	)	)	PUNCT
ejpam-3550	289	26	of	of	ADP
ejpam-3550	289	27	property	property	NOUN
ejpam-3550	289	28	(	(	PUNCT
ejpam-3550	289	29	ii	ii	NOUN
ejpam-3550	289	30	)	)	PUNCT
ejpam-3550	289	31	of	of	ADP
ejpam-3550	289	32	theorem	theorem	ADJ
ejpam-3550	289	33	5	5	NUM
ejpam-3550	289	34	holds	hold	NOUN
ejpam-3550	289	35	.	.	PUNCT
ejpam-3550	290	1	therefore	therefore	ADV
ejpam-3550	290	2	,	,	PUNCT
ejpam-3550	290	3	by	by	ADP
ejpam-3550	290	4	theorem	theorem	NOUN
ejpam-3550	290	5	5	5	NUM
ejpam-3550	290	6	,	,	PUNCT
ejpam-3550	290	7	c	c	PROPN
ejpam-3550	290	8	is	be	AUX
ejpam-3550	290	9	a	a	DET
ejpam-3550	290	10	hop	hop	NOUN
ejpam-3550	290	11	dominating	dominating	NOUN
ejpam-3550	290	12	set	set	NOUN
ejpam-3550	290	13	of	of	ADP
ejpam-3550	290	14	g	g	PROPN
ejpam-3550	290	15	�	�	PROPN
ejpam-3550	290	16	h.	h.	PROPN
ejpam-3550	290	17	thus	thus	ADV
ejpam-3550	290	18	,	,	PUNCT
ejpam-3550	290	19	γh(g	γh(g	NOUN
ejpam-3550	290	20	�	�	NOUN
ejpam-3550	290	21	h	h	NOUN
ejpam-3550	290	22	)	)	PUNCT
ejpam-3550	290	23	≤	≤	NOUN
ejpam-3550	290	24	|c|	|c|	PROPN
ejpam-3550	290	25	=	=	SYM
ejpam-3550	290	26	γ(g)γ∗t1,2(h	γ(g)γ∗t1,2(h	PROPN
ejpam-3550	290	27	)	)	PUNCT
ejpam-3550	290	28	.	.	PUNCT
ejpam-3550	291	1	this	this	PRON
ejpam-3550	291	2	proves	prove	VERB
ejpam-3550	291	3	the	the	DET
ejpam-3550	291	4	assertion	assertion	NOUN
ejpam-3550	291	5	.	.	PUNCT
ejpam-3550	292	1	remark	remark	PROPN
ejpam-3550	292	2	1	1	NUM
ejpam-3550	292	3	.	.	PUNCT
ejpam-3550	293	1	the	the	DET
ejpam-3550	293	2	bound	bind	VERB
ejpam-3550	293	3	given	give	VERB
ejpam-3550	293	4	in	in	ADP
ejpam-3550	293	5	corollary	corollary	ADJ
ejpam-3550	293	6	5	5	NUM
ejpam-3550	293	7	is	be	AUX
ejpam-3550	293	8	tight	tight	ADJ
ejpam-3550	293	9	.	.	PUNCT
ejpam-3550	294	1	moreover	moreover	ADV
ejpam-3550	294	2	,	,	PUNCT
ejpam-3550	294	3	the	the	DET
ejpam-3550	294	4	inequality	inequality	NOUN
ejpam-3550	294	5	is	be	AUX
ejpam-3550	294	6	also	also	ADV
ejpam-3550	294	7	attainable	attainable	ADJ
ejpam-3550	294	8	.	.	PUNCT
ejpam-3550	295	1	to	to	PART
ejpam-3550	295	2	see	see	VERB
ejpam-3550	295	3	this	this	PRON
ejpam-3550	295	4	,	,	PUNCT
ejpam-3550	295	5	consider	consider	VERB
ejpam-3550	295	6	p3	p3	PROPN
ejpam-3550	295	7	�	�	NOUN
ejpam-3550	295	8	p4	p4	ADJ
ejpam-3550	295	9	and	and	CCONJ
ejpam-3550	295	10	p4	p4	ADJ
ejpam-3550	295	11	�	�	PROPN
ejpam-3550	295	12	p4	p4	ADJ
ejpam-3550	295	13	.	.	PUNCT
ejpam-3550	296	1	it	it	PRON
ejpam-3550	296	2	can	can	AUX
ejpam-3550	296	3	easily	easily	ADV
ejpam-3550	296	4	be	be	AUX
ejpam-3550	296	5	verified	verify	VERB
ejpam-3550	296	6	that	that	SCONJ
ejpam-3550	296	7	γh(p3	γh(p3	PROPN
ejpam-3550	296	8	�	�	PROPN
ejpam-3550	296	9	p4	p4	ADJ
ejpam-3550	296	10	)	)	PUNCT
ejpam-3550	296	11	=	=	SYM
ejpam-3550	296	12	2	2	NUM
ejpam-3550	296	13	=	=	SYM
ejpam-3550	296	14	γ(p3)γ	γ(p3)γ	PROPN
ejpam-3550	296	15	∗t	∗t	PROPN
ejpam-3550	296	16	1,2(p4	1,2(p4	NUM
ejpam-3550	296	17	)	)	PUNCT
ejpam-3550	296	18	and	and	CCONJ
ejpam-3550	296	19	γh(p4	γh(p4	NOUN
ejpam-3550	296	20	�	�	NOUN
ejpam-3550	296	21	p4	p4	ADJ
ejpam-3550	296	22	)	)	PUNCT
ejpam-3550	296	23	=	=	SYM
ejpam-3550	296	24	4	4	NUM
ejpam-3550	296	25	=	=	SYM
ejpam-3550	296	26	γ(p4)γ	γ(p4)γ	PROPN
ejpam-3550	296	27	∗t	∗t	PROPN
ejpam-3550	296	28	1,2(p4	1,2(p4	NUM
ejpam-3550	296	29	)	)	PUNCT
ejpam-3550	296	30	.	.	PUNCT
ejpam-3550	297	1	the	the	DET
ejpam-3550	297	2	inequality	inequality	NOUN
ejpam-3550	297	3	is	be	AUX
ejpam-3550	297	4	attainable	attainable	ADJ
ejpam-3550	297	5	since	since	SCONJ
ejpam-3550	297	6	γh(k4	γh(k4	NOUN
ejpam-3550	297	7	�	�	NOUN
ejpam-3550	297	8	k4	k4	NOUN
ejpam-3550	297	9	)	)	PUNCT
ejpam-3550	297	10	=	=	PUNCT
ejpam-3550	297	11	3	3	NUM
ejpam-3550	297	12	<	<	SYM
ejpam-3550	297	13	4	4	NUM
ejpam-3550	297	14	=	=	SYM
ejpam-3550	297	15	γ(k4)γ	γ(k4)γ	PROPN
ejpam-3550	297	16	∗t	∗t	ADJ
ejpam-3550	297	17	1,2(k4	1,2(k4	NUM
ejpam-3550	297	18	)	)	PUNCT
ejpam-3550	297	19	.	.	PUNCT
ejpam-3550	298	1	references	reference	NOUN
ejpam-3550	298	2	[	[	X
ejpam-3550	298	3	1	1	X
ejpam-3550	298	4	]	]	PUNCT
ejpam-3550	298	5	s.	s.	PROPN
ejpam-3550	298	6	arriola	arriola	PROPN
ejpam-3550	298	7	,	,	PUNCT
ejpam-3550	298	8	and	and	CCONJ
ejpam-3550	298	9	s.	s.	PROPN
ejpam-3550	298	10	canoy	canoy	PROPN
ejpam-3550	298	11	,	,	PUNCT
ejpam-3550	298	12	jr	jr	PROPN
ejpam-3550	298	13	.	.	PROPN
ejpam-3550	298	14	,	,	PUNCT
ejpam-3550	298	15	(	(	PUNCT
ejpam-3550	298	16	1	1	NUM
ejpam-3550	298	17	,	,	PUNCT
ejpam-3550	298	18	2)∗-domination	2)∗-domination	NOUN
ejpam-3550	298	19	in	in	ADP
ejpam-3550	298	20	graphs	graph	NOUN
ejpam-3550	298	21	,	,	PUNCT
ejpam-3550	298	22	advances	advance	NOUN
ejpam-3550	298	23	and	and	CCONJ
ejpam-3550	298	24	applications	application	NOUN
ejpam-3550	298	25	in	in	ADP
ejpam-3550	298	26	discrete	discrete	ADJ
ejpam-3550	298	27	mathematics	mathematic	NOUN
ejpam-3550	298	28	,	,	PUNCT
ejpam-3550	298	29	2017,18	2017,18	NUM
ejpam-3550	298	30	,	,	PUNCT
ejpam-3550	298	31	2	2	NUM
ejpam-3550	298	32	,	,	PUNCT
ejpam-3550	298	33	179−	179−	NUM
ejpam-3550	298	34	190	190	NUM
ejpam-3550	298	35	.	.	PUNCT
ejpam-3550	299	1	[	[	X
ejpam-3550	299	2	2	2	X
ejpam-3550	299	3	]	]	PUNCT
ejpam-3550	299	4	s.	s.	PROPN
ejpam-3550	299	5	ayyaswamy	ayyaswamy	PROPN
ejpam-3550	299	6	,	,	PUNCT
ejpam-3550	299	7	b.	b.	PROPN
ejpam-3550	299	8	krishnakumari	krishnakumari	PROPN
ejpam-3550	299	9	,	,	PUNCT
ejpam-3550	299	10	b.	b.	PROPN
ejpam-3550	299	11	natarjan	natarjan	PROPN
ejpam-3550	299	12	,	,	PUNCT
ejpam-3550	299	13	and	and	CCONJ
ejpam-3550	299	14	y.	y.	PROPN
ejpam-3550	299	15	venkatakrishnan	venkatakrishnan	NOUN
ejpam-3550	299	16	,	,	PUNCT
ejpam-3550	299	17	bounds	bound	VERB
ejpam-3550	299	18	on	on	ADP
ejpam-3550	299	19	the	the	DET
ejpam-3550	299	20	hop	hop	NOUN
ejpam-3550	299	21	domination	domination	NOUN
ejpam-3550	299	22	number	number	NOUN
ejpam-3550	299	23	of	of	ADP
ejpam-3550	299	24	a	a	DET
ejpam-3550	299	25	tree	tree	NOUN
ejpam-3550	299	26	,	,	PUNCT
ejpam-3550	299	27	proceedings	proceeding	NOUN
ejpam-3550	299	28	-mathematical	-mathematical	ADJ
ejpam-3550	299	29	sciences	science	NOUN
ejpam-3550	299	30	,	,	PUNCT
ejpam-3550	299	31	2015	2015	NUM
ejpam-3550	299	32	,	,	PUNCT
ejpam-3550	299	33	125	125	NUM
ejpam-3550	299	34	,	,	PUNCT
ejpam-3550	299	35	4	4	NUM
ejpam-3550	299	36	,	,	PUNCT
ejpam-3550	299	37	449	449	NUM
ejpam-3550	299	38	-	-	SYM
ejpam-3550	299	39	455	455	NUM
ejpam-3550	299	40	.	.	PUNCT
ejpam-3550	300	1	[	[	X
ejpam-3550	300	2	3	3	X
ejpam-3550	300	3	]	]	X
ejpam-3550	300	4	t.w	t.w	PROPN
ejpam-3550	300	5	.	.	PROPN
ejpam-3550	300	6	haynes	haynes	PROPN
ejpam-3550	300	7	,	,	PUNCT
ejpam-3550	300	8	s.t	s.t	PROPN
ejpam-3550	300	9	.	.	PROPN
ejpam-3550	300	10	hedetniemi	hedetniemi	PROPN
ejpam-3550	300	11	,	,	PUNCT
ejpam-3550	300	12	and	and	CCONJ
ejpam-3550	300	13	p.j	p.j	PROPN
ejpam-3550	300	14	.	.	PROPN
ejpam-3550	300	15	slater	slater	PROPN
ejpam-3550	300	16	,	,	PUNCT
ejpam-3550	300	17	fundamentals	fundamental	NOUN
ejpam-3550	300	18	of	of	ADP
ejpam-3550	300	19	domination	domination	NOUN
ejpam-3550	300	20	in	in	ADP
ejpam-3550	300	21	graphs	graph	NOUN
ejpam-3550	300	22	,	,	PUNCT
ejpam-3550	300	23	marcell	marcell	PROPN
ejpam-3550	300	24	dekker	dekker	PROPN
ejpam-3550	300	25	,	,	PUNCT
ejpam-3550	300	26	1998	1998	NUM
ejpam-3550	300	27	,	,	PUNCT
ejpam-3550	300	28	new	new	PROPN
ejpam-3550	300	29	york	york	PROPN
ejpam-3550	300	30	.	.	PUNCT
ejpam-3550	301	1	[	[	X
ejpam-3550	301	2	4	4	X
ejpam-3550	301	3	]	]	X
ejpam-3550	301	4	t.w	t.w	PROPN
ejpam-3550	301	5	.	.	PROPN
ejpam-3550	301	6	haynes	haynes	PROPN
ejpam-3550	301	7	,	,	PUNCT
ejpam-3550	301	8	s.t	s.t	PROPN
ejpam-3550	301	9	.	.	PROPN
ejpam-3550	301	10	hedetniemi	hedetniemi	PROPN
ejpam-3550	301	11	,	,	PUNCT
ejpam-3550	301	12	and	and	CCONJ
ejpam-3550	301	13	p.j	p.j	PROPN
ejpam-3550	301	14	.	.	PROPN
ejpam-3550	301	15	slater	slater	PROPN
ejpam-3550	301	16	,	,	PUNCT
ejpam-3550	301	17	domination	domination	NOUN
ejpam-3550	301	18	in	in	ADP
ejpam-3550	301	19	graphs	graph	NOUN
ejpam-3550	301	20	,	,	PUNCT
ejpam-3550	301	21	advanced	advanced	ADJ
ejpam-3550	301	22	topics	topic	NOUN
ejpam-3550	301	23	,	,	PUNCT
ejpam-3550	301	24	marcell	marcell	PROPN
ejpam-3550	301	25	dekker	dekker	PROPN
ejpam-3550	301	26	,	,	PUNCT
ejpam-3550	301	27	1998	1998	NUM
ejpam-3550	301	28	,	,	PUNCT
ejpam-3550	301	29	new	new	PROPN
ejpam-3550	301	30	york	york	PROPN
ejpam-3550	301	31	.	.	PUNCT
ejpam-3550	302	1	[	[	X
ejpam-3550	302	2	5	5	NUM
ejpam-3550	302	3	]	]	PUNCT
ejpam-3550	302	4	m.	m.	NOUN
ejpam-3550	302	5	henning	henning	PROPN
ejpam-3550	302	6	,	,	PUNCT
ejpam-3550	302	7	and	and	CCONJ
ejpam-3550	302	8	n.	n.	PROPN
ejpam-3550	302	9	rad	rad	PROPN
ejpam-3550	302	10	,	,	PUNCT
ejpam-3550	302	11	on	on	ADP
ejpam-3550	302	12	2	2	NUM
ejpam-3550	302	13	-	-	PUNCT
ejpam-3550	302	14	step	step	NOUN
ejpam-3550	302	15	and	and	CCONJ
ejpam-3550	302	16	hop	hop	NOUN
ejpam-3550	302	17	dominating	dominating	NOUN
ejpam-3550	302	18	sets	set	NOUN
ejpam-3550	302	19	in	in	ADP
ejpam-3550	302	20	graphs	graph	NOUN
ejpam-3550	302	21	,	,	PUNCT
ejpam-3550	302	22	graphs	graph	NOUN
ejpam-3550	302	23	and	and	CCONJ
ejpam-3550	302	24	combinatorics	combinatoric	NOUN
ejpam-3550	302	25	,	,	PUNCT
ejpam-3550	302	26	2017	2017	NUM
ejpam-3550	302	27	,	,	PUNCT
ejpam-3550	302	28	33	33	NUM
ejpam-3550	302	29	,	,	PUNCT
ejpam-3550	302	30	4	4	NUM
ejpam-3550	302	31	,	,	PUNCT
ejpam-3550	302	32	913	913	NUM
ejpam-3550	302	33	-	-	SYM
ejpam-3550	302	34	927	927	NUM
ejpam-3550	302	35	.	.	PUNCT
ejpam-3550	303	1	[	[	X
ejpam-3550	303	2	6	6	NUM
ejpam-3550	303	3	]	]	PUNCT
ejpam-3550	303	4	c.	c.	PROPN
ejpam-3550	303	5	natarajan	natarajan	PROPN
ejpam-3550	303	6	and	and	CCONJ
ejpam-3550	303	7	s.	s.	PROPN
ejpam-3550	303	8	ayyaswamy	ayyaswamy	PROPN
ejpam-3550	303	9	,	,	PUNCT
ejpam-3550	303	10	hop	hop	NOUN
ejpam-3550	303	11	domination	domination	NOUN
ejpam-3550	303	12	in	in	ADP
ejpam-3550	303	13	graphs	graphs	PROPN
ejpam-3550	303	14	ii	ii	PROPN
ejpam-3550	303	15	,	,	PUNCT
ejpam-3550	303	16	versita	versita	PROPN
ejpam-3550	303	17	,	,	PUNCT
ejpam-3550	303	18	2015	2015	NUM
ejpam-3550	303	19	,	,	PUNCT
ejpam-3550	303	20	23	23	NUM
ejpam-3550	303	21	,	,	PUNCT
ejpam-3550	303	22	2	2	NUM
ejpam-3550	303	23	,	,	PUNCT
ejpam-3550	303	24	187	187	NUM
ejpam-3550	303	25	-	-	SYM
ejpam-3550	303	26	199	199	NUM
ejpam-3550	303	27	.	.	PUNCT
ejpam-3550	304	1	[	[	X
ejpam-3550	304	2	7	7	X
ejpam-3550	304	3	]	]	X
ejpam-3550	304	4	y.	y.	NOUN
ejpam-3550	304	5	pabilona	pabilona	PROPN
ejpam-3550	304	6	and	and	CCONJ
ejpam-3550	304	7	h.	h.	PROPN
ejpam-3550	304	8	rara	rara	PROPN
ejpam-3550	304	9	,	,	PUNCT
ejpam-3550	304	10	connected	connect	VERB
ejpam-3550	304	11	hop	hop	NOUN
ejpam-3550	304	12	domination	domination	NOUN
ejpam-3550	304	13	in	in	ADP
ejpam-3550	304	14	graphs	graph	NOUN
ejpam-3550	304	15	under	under	ADP
ejpam-3550	304	16	some	some	DET
ejpam-3550	304	17	binary	binary	ADJ
ejpam-3550	304	18	operations	operation	NOUN
ejpam-3550	304	19	,	,	PUNCT
ejpam-3550	304	20	asian	asian	ADJ
ejpam-3550	304	21	-	-	PUNCT
ejpam-3550	304	22	european	european	ADJ
ejpam-3550	304	23	journal	journal	NOUN
ejpam-3550	304	24	of	of	ADP
ejpam-3550	304	25	mathematics	mathematic	NOUN
ejpam-3550	304	26	,	,	PUNCT
ejpam-3550	304	27	11(2018	11(2018	NUM
ejpam-3550	304	28	)	)	PUNCT
ejpam-3550	304	29	,	,	PUNCT
ejpam-3550	304	30	11	11	NUM
ejpam-3550	304	31	,	,	PUNCT
ejpam-3550	304	32	5	5	NUM
ejpam-3550	304	33	,	,	PUNCT
ejpam-3550	304	34	1850075	1850075	NUM
ejpam-3550	304	35	-	-	SYM
ejpam-3550	304	36	11850075	11850075	NUM
ejpam-3550	304	37	-	-	SYM
ejpam-3550	304	38	11	11	NUM
ejpam-3550	304	39	.	.	PUNCT