id	sid	tid	token	lemma	pos
ejpam-4055	1	1	european	european	PROPN
ejpam-4055	1	2	journal	journal	PROPN
ejpam-4055	1	3	of	of	ADP
ejpam-4055	1	4	pure	pure	ADJ
ejpam-4055	1	5	and	and	CCONJ
ejpam-4055	1	6	applied	apply	VERB
ejpam-4055	1	7	mathematics	mathematic	NOUN
ejpam-4055	1	8	vol	vol	NOUN
ejpam-4055	1	9	.	.	PUNCT
ejpam-4055	2	1	14	14	NUM
ejpam-4055	2	2	,	,	PUNCT
ejpam-4055	2	3	no	no	INTJ
ejpam-4055	2	4	.	.	NOUN
ejpam-4055	2	5	3	3	NUM
ejpam-4055	2	6	,	,	PUNCT
ejpam-4055	2	7	2021	2021	NUM
ejpam-4055	2	8	,	,	PUNCT
ejpam-4055	2	9	1015	1015	NUM
ejpam-4055	2	10	-	-	SYM
ejpam-4055	2	11	1023	1023	NUM
ejpam-4055	2	12	issn	issn	PROPN
ejpam-4055	2	13	1307	1307	NUM
ejpam-4055	2	14	-	-	SYM
ejpam-4055	2	15	5543	5543	NUM
ejpam-4055	2	16	–	–	PUNCT
ejpam-4055	2	17	ejpam.com	ejpam.com	X
ejpam-4055	2	18	published	publish	VERB
ejpam-4055	2	19	by	by	ADP
ejpam-4055	2	20	new	new	PROPN
ejpam-4055	2	21	york	york	PROPN
ejpam-4055	2	22	business	business	PROPN
ejpam-4055	2	23	global	global	ADJ
ejpam-4055	2	24	on	on	ADP
ejpam-4055	2	25	resolving	resolve	VERB
ejpam-4055	2	26	hop	hop	NOUN
ejpam-4055	2	27	domination	domination	NOUN
ejpam-4055	2	28	in	in	ADP
ejpam-4055	2	29	graphs	graphs	PROPN
ejpam-4055	2	30	jerson	jerson	PROPN
ejpam-4055	2	31	s.	s.	PROPN
ejpam-4055	2	32	mohamad1,∗	mohamad1,∗	PROPN
ejpam-4055	2	33	,	,	PUNCT
ejpam-4055	3	1	helen	helen	PROPN
ejpam-4055	3	2	m.	m.	PROPN
ejpam-4055	3	3	rara2	rara2	PROPN
ejpam-4055	4	1	1	1	NUM
ejpam-4055	4	2	department	department	NOUN
ejpam-4055	4	3	of	of	ADP
ejpam-4055	4	4	mathematics	mathematic	NOUN
ejpam-4055	4	5	and	and	CCONJ
ejpam-4055	4	6	statistics	statistic	NOUN
ejpam-4055	4	7	,	,	PUNCT
ejpam-4055	4	8	college	college	NOUN
ejpam-4055	4	9	of	of	ADP
ejpam-4055	4	10	science	science	NOUN
ejpam-4055	4	11	and	and	CCONJ
ejpam-4055	4	12	mathematics	mathematic	NOUN
ejpam-4055	4	13	,	,	PUNCT
ejpam-4055	4	14	western	western	ADJ
ejpam-4055	4	15	mindanao	mindanao	PROPN
ejpam-4055	4	16	state	state	PROPN
ejpam-4055	4	17	university	university	PROPN
ejpam-4055	4	18	,	,	PUNCT
ejpam-4055	4	19	7000	7000	NUM
ejpam-4055	4	20	zamboanga	zamboanga	PROPN
ejpam-4055	4	21	city	city	PROPN
ejpam-4055	4	22	,	,	PUNCT
ejpam-4055	4	23	philippines	philippines	PROPN
ejpam-4055	4	24	2	2	NUM
ejpam-4055	4	25	department	department	NOUN
ejpam-4055	4	26	of	of	ADP
ejpam-4055	4	27	mathematics	mathematic	NOUN
ejpam-4055	4	28	and	and	CCONJ
ejpam-4055	4	29	statistics	statistic	NOUN
ejpam-4055	4	30	,	,	PUNCT
ejpam-4055	4	31	college	college	NOUN
ejpam-4055	4	32	of	of	ADP
ejpam-4055	4	33	science	science	NOUN
ejpam-4055	4	34	and	and	CCONJ
ejpam-4055	4	35	mathematics	mathematic	NOUN
ejpam-4055	4	36	,	,	PUNCT
ejpam-4055	4	37	center	center	NOUN
ejpam-4055	4	38	of	of	ADP
ejpam-4055	4	39	graph	graph	NOUN
ejpam-4055	4	40	theory	theory	NOUN
ejpam-4055	4	41	,	,	PUNCT
ejpam-4055	4	42	algebra	algebra	NOUN
ejpam-4055	4	43	,	,	PUNCT
ejpam-4055	4	44	and	and	CCONJ
ejpam-4055	4	45	analysis	analysis	NOUN
ejpam-4055	4	46	-	-	PUNCT
ejpam-4055	4	47	premier	premier	NOUN
ejpam-4055	4	48	research	research	NOUN
ejpam-4055	4	49	institute	institute	PROPN
ejpam-4055	4	50	of	of	ADP
ejpam-4055	4	51	science	science	NOUN
ejpam-4055	4	52	and	and	CCONJ
ejpam-4055	4	53	mathematics	mathematic	NOUN
ejpam-4055	4	54	,	,	PUNCT
ejpam-4055	4	55	mindanao	mindanao	PROPN
ejpam-4055	4	56	state	state	PROPN
ejpam-4055	4	57	university	university	PROPN
ejpam-4055	4	58	-	-	PUNCT
ejpam-4055	4	59	iligan	iligan	PROPN
ejpam-4055	4	60	institute	institute	PROPN
ejpam-4055	4	61	of	of	ADP
ejpam-4055	4	62	technology	technology	PROPN
ejpam-4055	4	63	,	,	PUNCT
ejpam-4055	4	64	9200	9200	NUM
ejpam-4055	4	65	iligan	iligan	ADJ
ejpam-4055	4	66	city	city	NOUN
ejpam-4055	4	67	,	,	PUNCT
ejpam-4055	4	68	philippines	philippine	NOUN
ejpam-4055	4	69	abstract	abstract	ADJ
ejpam-4055	4	70	.	.	PUNCT
ejpam-4055	5	1	a	a	DET
ejpam-4055	5	2	set	set	NOUN
ejpam-4055	5	3	s	s	NOUN
ejpam-4055	5	4	of	of	ADP
ejpam-4055	5	5	vertices	vertex	NOUN
ejpam-4055	5	6	in	in	ADP
ejpam-4055	5	7	a	a	DET
ejpam-4055	5	8	connected	connected	ADJ
ejpam-4055	5	9	graph	graph	NOUN
ejpam-4055	5	10	g	g	PROPN
ejpam-4055	5	11	is	be	AUX
ejpam-4055	5	12	a	a	DET
ejpam-4055	5	13	resolving	resolve	VERB
ejpam-4055	5	14	hop	hop	NOUN
ejpam-4055	5	15	dominating	dominating	NOUN
ejpam-4055	5	16	set	set	NOUN
ejpam-4055	5	17	of	of	ADP
ejpam-4055	5	18	g	g	PROPN
ejpam-4055	5	19	if	if	SCONJ
ejpam-4055	5	20	s	s	VERB
ejpam-4055	5	21	is	be	AUX
ejpam-4055	5	22	a	a	DET
ejpam-4055	5	23	resolving	resolving	NOUN
ejpam-4055	5	24	set	set	VERB
ejpam-4055	5	25	in	in	ADP
ejpam-4055	5	26	g	g	PROPN
ejpam-4055	5	27	and	and	CCONJ
ejpam-4055	5	28	for	for	ADP
ejpam-4055	5	29	every	every	DET
ejpam-4055	5	30	vertex	vertex	NOUN
ejpam-4055	5	31	v	v	ADP
ejpam-4055	5	32	∈	∈	NOUN
ejpam-4055	5	33	v	v	NOUN
ejpam-4055	5	34	(	(	PUNCT
ejpam-4055	5	35	g	g	NOUN
ejpam-4055	5	36	)	)	PUNCT
ejpam-4055	5	37	\s	\s	NOUN
ejpam-4055	5	38	there	there	PRON
ejpam-4055	5	39	exists	exist	VERB
ejpam-4055	5	40	u	u	PROPN
ejpam-4055	5	41	∈	∈	PROPN
ejpam-4055	5	42	s	s	VERB
ejpam-4055	5	43	such	such	ADJ
ejpam-4055	5	44	that	that	DET
ejpam-4055	5	45	dg(u	dg(u	ADJ
ejpam-4055	5	46	,	,	PUNCT
ejpam-4055	5	47	v	v	NOUN
ejpam-4055	5	48	)	)	PUNCT
ejpam-4055	5	49	=	=	SYM
ejpam-4055	5	50	2	2	X
ejpam-4055	5	51	.	.	X
ejpam-4055	5	52	the	the	DET
ejpam-4055	5	53	smallest	small	ADJ
ejpam-4055	5	54	cardinality	cardinality	NOUN
ejpam-4055	5	55	of	of	ADP
ejpam-4055	5	56	such	such	DET
ejpam-4055	5	57	a	a	DET
ejpam-4055	5	58	set	set	NOUN
ejpam-4055	5	59	s	s	PART
ejpam-4055	5	60	is	be	AUX
ejpam-4055	5	61	called	call	VERB
ejpam-4055	5	62	the	the	DET
ejpam-4055	5	63	resolving	resolve	VERB
ejpam-4055	5	64	hop	hop	NOUN
ejpam-4055	5	65	domination	domination	NOUN
ejpam-4055	5	66	number	number	NOUN
ejpam-4055	5	67	of	of	ADP
ejpam-4055	5	68	g.	g.	PROPN
ejpam-4055	5	69	this	this	DET
ejpam-4055	5	70	paper	paper	NOUN
ejpam-4055	5	71	presents	present	VERB
ejpam-4055	5	72	the	the	DET
ejpam-4055	5	73	characterizations	characterization	NOUN
ejpam-4055	5	74	of	of	ADP
ejpam-4055	5	75	the	the	DET
ejpam-4055	5	76	resolving	resolve	VERB
ejpam-4055	5	77	hop	hop	NOUN
ejpam-4055	5	78	dominating	dominating	NOUN
ejpam-4055	5	79	sets	set	NOUN
ejpam-4055	5	80	in	in	ADP
ejpam-4055	5	81	the	the	DET
ejpam-4055	5	82	join	join	NOUN
ejpam-4055	5	83	,	,	PUNCT
ejpam-4055	5	84	corona	corona	NOUN
ejpam-4055	5	85	and	and	CCONJ
ejpam-4055	5	86	lexicographic	lexicographic	ADJ
ejpam-4055	5	87	product	product	NOUN
ejpam-4055	5	88	of	of	ADP
ejpam-4055	5	89	two	two	NUM
ejpam-4055	5	90	graphs	graph	NOUN
ejpam-4055	5	91	and	and	CCONJ
ejpam-4055	5	92	determines	determine	VERB
ejpam-4055	5	93	the	the	DET
ejpam-4055	5	94	exact	exact	ADJ
ejpam-4055	5	95	values	value	NOUN
ejpam-4055	5	96	of	of	ADP
ejpam-4055	5	97	their	their	PRON
ejpam-4055	5	98	corresponding	correspond	VERB
ejpam-4055	5	99	resolving	resolve	VERB
ejpam-4055	5	100	hop	hop	NOUN
ejpam-4055	5	101	domination	domination	NOUN
ejpam-4055	5	102	number	number	NOUN
ejpam-4055	5	103	.	.	PUNCT
ejpam-4055	6	1	2020	2020	NUM
ejpam-4055	6	2	mathematics	mathematic	NOUN
ejpam-4055	6	3	subject	subject	NOUN
ejpam-4055	6	4	classifications	classification	NOUN
ejpam-4055	6	5	:	:	PUNCT
ejpam-4055	6	6	05c69	05c69	X
ejpam-4055	6	7	key	key	ADJ
ejpam-4055	6	8	words	word	NOUN
ejpam-4055	6	9	and	and	CCONJ
ejpam-4055	6	10	phrases	phrase	NOUN
ejpam-4055	6	11	:	:	PUNCT
ejpam-4055	6	12	resolving	resolve	VERB
ejpam-4055	6	13	hop	hop	NOUN
ejpam-4055	6	14	dominating	dominating	NOUN
ejpam-4055	6	15	set	set	NOUN
ejpam-4055	6	16	,	,	PUNCT
ejpam-4055	6	17	resolving	resolve	VERB
ejpam-4055	6	18	hop	hop	NOUN
ejpam-4055	6	19	domination	domination	NOUN
ejpam-4055	6	20	number	number	NOUN
ejpam-4055	6	21	,	,	PUNCT
ejpam-4055	6	22	join	join	NOUN
ejpam-4055	6	23	,	,	PUNCT
ejpam-4055	6	24	corona	corona	PROPN
ejpam-4055	6	25	,	,	PUNCT
ejpam-4055	6	26	lexicographic	lexicographic	ADJ
ejpam-4055	6	27	product	product	NOUN
ejpam-4055	6	28	1	1	NUM
ejpam-4055	6	29	.	.	PUNCT
ejpam-4055	7	1	introduction	introduction	NOUN
ejpam-4055	7	2	domination	domination	NOUN
ejpam-4055	7	3	in	in	ADP
ejpam-4055	7	4	graphs	graph	NOUN
ejpam-4055	7	5	was	be	AUX
ejpam-4055	7	6	first	first	ADV
ejpam-4055	7	7	introduced	introduce	VERB
ejpam-4055	7	8	by	by	ADP
ejpam-4055	7	9	c.	c.	PROPN
ejpam-4055	7	10	berge	berge	PROPN
ejpam-4055	7	11	in	in	ADP
ejpam-4055	7	12	1958	1958	NUM
ejpam-4055	7	13	[	[	X
ejpam-4055	7	14	3	3	NUM
ejpam-4055	7	15	]	]	PUNCT
ejpam-4055	7	16	.	.	PUNCT
ejpam-4055	8	1	there	there	PRON
ejpam-4055	8	2	are	be	VERB
ejpam-4055	8	3	now	now	ADV
ejpam-4055	8	4	many	many	ADJ
ejpam-4055	8	5	studies	study	NOUN
ejpam-4055	8	6	involving	involve	VERB
ejpam-4055	8	7	domination	domination	NOUN
ejpam-4055	8	8	and	and	CCONJ
ejpam-4055	8	9	its	its	PRON
ejpam-4055	8	10	variations	variation	NOUN
ejpam-4055	8	11	.	.	PUNCT
ejpam-4055	9	1	natarajan	natarajan	PROPN
ejpam-4055	9	2	and	and	CCONJ
ejpam-4055	9	3	ayyaswamy	ayyaswamy	PROPN
ejpam-4055	9	4	[	[	X
ejpam-4055	9	5	9	9	NUM
ejpam-4055	9	6	]	]	PUNCT
ejpam-4055	9	7	introduced	introduce	VERB
ejpam-4055	9	8	and	and	CCONJ
ejpam-4055	9	9	studied	study	VERB
ejpam-4055	9	10	the	the	DET
ejpam-4055	9	11	concept	concept	NOUN
ejpam-4055	9	12	of	of	ADP
ejpam-4055	9	13	hop	hop	NOUN
ejpam-4055	9	14	domination	domination	NOUN
ejpam-4055	9	15	in	in	ADP
ejpam-4055	9	16	graphs	graph	NOUN
ejpam-4055	9	17	.	.	PUNCT
ejpam-4055	10	1	hop	hop	PROPN
ejpam-4055	10	2	domination	domination	NOUN
ejpam-4055	10	3	in	in	ADP
ejpam-4055	10	4	graphs	graph	NOUN
ejpam-4055	10	5	were	be	AUX
ejpam-4055	10	6	also	also	ADV
ejpam-4055	10	7	studied	study	VERB
ejpam-4055	10	8	in	in	ADP
ejpam-4055	10	9	[	[	X
ejpam-4055	10	10	6	6	NUM
ejpam-4055	10	11	,	,	PUNCT
ejpam-4055	10	12	10	10	NUM
ejpam-4055	10	13	,	,	PUNCT
ejpam-4055	10	14	11	11	NUM
ejpam-4055	10	15	]	]	PUNCT
ejpam-4055	10	16	.	.	PUNCT
ejpam-4055	11	1	slater	slater	NOUN
ejpam-4055	12	1	[	[	X
ejpam-4055	12	2	12	12	NUM
ejpam-4055	12	3	]	]	PUNCT
ejpam-4055	12	4	introduced	introduce	VERB
ejpam-4055	12	5	and	and	CCONJ
ejpam-4055	12	6	studied	study	VERB
ejpam-4055	12	7	the	the	DET
ejpam-4055	12	8	concept	concept	NOUN
ejpam-4055	12	9	of	of	ADP
ejpam-4055	12	10	resolving	resolve	VERB
ejpam-4055	12	11	set	set	NOUN
ejpam-4055	12	12	.	.	PUNCT
ejpam-4055	13	1	resolving	resolve	VERB
ejpam-4055	13	2	sets	set	NOUN
ejpam-4055	13	3	and	and	CCONJ
ejpam-4055	13	4	resolving	resolve	VERB
ejpam-4055	13	5	dominating	dominating	NOUN
ejpam-4055	13	6	sets	set	NOUN
ejpam-4055	13	7	were	be	AUX
ejpam-4055	13	8	studied	study	VERB
ejpam-4055	13	9	in	in	ADP
ejpam-4055	13	10	[	[	X
ejpam-4055	13	11	1	1	NUM
ejpam-4055	13	12	,	,	PUNCT
ejpam-4055	13	13	2	2	NUM
ejpam-4055	13	14	,	,	PUNCT
ejpam-4055	13	15	4	4	NUM
ejpam-4055	13	16	,	,	PUNCT
ejpam-4055	13	17	7	7	NUM
ejpam-4055	13	18	,	,	PUNCT
ejpam-4055	13	19	8	8	NUM
ejpam-4055	13	20	]	]	PUNCT
ejpam-4055	13	21	.	.	PUNCT
ejpam-4055	14	1	this	this	DET
ejpam-4055	14	2	paper	paper	NOUN
ejpam-4055	14	3	combines	combine	VERB
ejpam-4055	14	4	the	the	DET
ejpam-4055	14	5	idea	idea	NOUN
ejpam-4055	14	6	of	of	ADP
ejpam-4055	14	7	resolving	resolving	NOUN
ejpam-4055	14	8	and	and	CCONJ
ejpam-4055	14	9	hop	hop	NOUN
ejpam-4055	14	10	domination	domination	NOUN
ejpam-4055	14	11	sets	set	NOUN
ejpam-4055	14	12	by	by	ADP
ejpam-4055	14	13	introducing	introduce	VERB
ejpam-4055	14	14	the	the	DET
ejpam-4055	14	15	concept	concept	NOUN
ejpam-4055	14	16	of	of	ADP
ejpam-4055	14	17	resolving	resolve	VERB
ejpam-4055	14	18	hop	hop	NOUN
ejpam-4055	14	19	domination	domination	NOUN
ejpam-4055	14	20	in	in	ADP
ejpam-4055	14	21	graphs	graph	NOUN
ejpam-4055	14	22	.	.	PUNCT
ejpam-4055	15	1	resolving	resolve	VERB
ejpam-4055	15	2	hop	hop	NOUN
ejpam-4055	15	3	dominating	dominating	NOUN
ejpam-4055	15	4	sets	set	NOUN
ejpam-4055	15	5	in	in	ADP
ejpam-4055	15	6	graphs	graph	NOUN
ejpam-4055	15	7	can	can	AUX
ejpam-4055	15	8	have	have	VERB
ejpam-4055	15	9	real	real	ADJ
ejpam-4055	15	10	world	world	NOUN
ejpam-4055	15	11	applications	application	NOUN
ejpam-4055	15	12	.	.	PUNCT
ejpam-4055	16	1	one	one	NUM
ejpam-4055	16	2	possible	possible	ADJ
ejpam-4055	16	3	application	application	NOUN
ejpam-4055	16	4	is	be	AUX
ejpam-4055	16	5	in	in	ADP
ejpam-4055	16	6	the	the	DET
ejpam-4055	16	7	minimization	minimization	NOUN
ejpam-4055	16	8	problem	problem	NOUN
ejpam-4055	16	9	with	with	ADP
ejpam-4055	16	10	specific	specific	ADJ
ejpam-4055	16	11	conditions	condition	NOUN
ejpam-4055	16	12	.	.	PUNCT
ejpam-4055	17	1	for	for	ADP
ejpam-4055	17	2	example	example	NOUN
ejpam-4055	17	3	,	,	PUNCT
ejpam-4055	17	4	a	a	DET
ejpam-4055	17	5	company	company	NOUN
ejpam-4055	17	6	that	that	PRON
ejpam-4055	17	7	makes	make	VERB
ejpam-4055	17	8	electric	electric	ADJ
ejpam-4055	17	9	cars	car	NOUN
ejpam-4055	17	10	with	with	ADP
ejpam-4055	17	11	a	a	DET
ejpam-4055	17	12	smart	smart	ADJ
ejpam-4055	17	13	navigation	navigation	NOUN
ejpam-4055	17	14	feature	feature	NOUN
ejpam-4055	17	15	,	,	PUNCT
ejpam-4055	17	16	wants	want	VERB
ejpam-4055	17	17	to	to	PART
ejpam-4055	17	18	build	build	VERB
ejpam-4055	17	19	the	the	DET
ejpam-4055	17	20	least	least	ADJ
ejpam-4055	17	21	number	number	NOUN
ejpam-4055	17	22	of	of	ADP
ejpam-4055	17	23	charging	charge	VERB
ejpam-4055	17	24	stations	station	NOUN
ejpam-4055	17	25	in	in	ADP
ejpam-4055	17	26	a	a	DET
ejpam-4055	17	27	given	give	VERB
ejpam-4055	17	28	city	city	NOUN
ejpam-4055	17	29	,	,	PUNCT
ejpam-4055	17	30	such	such	ADJ
ejpam-4055	17	31	that	that	SCONJ
ejpam-4055	17	32	any	any	DET
ejpam-4055	17	33	car	car	NOUN
ejpam-4055	17	34	with	with	ADP
ejpam-4055	17	35	a	a	DET
ejpam-4055	17	36	low	low	ADJ
ejpam-4055	17	37	charge	charge	NOUN
ejpam-4055	17	38	,	,	PUNCT
ejpam-4055	17	39	from	from	ADP
ejpam-4055	17	40	any	any	DET
ejpam-4055	17	41	area	area	NOUN
ejpam-4055	17	42	,	,	PUNCT
ejpam-4055	17	43	can	can	AUX
ejpam-4055	17	44	reach	reach	VERB
ejpam-4055	17	45	a	a	DET
ejpam-4055	17	46	charging	charge	VERB
ejpam-4055	17	47	station	station	NOUN
ejpam-4055	17	48	before	before	ADP
ejpam-4055	17	49	∗corresponding	∗corresponde	VERB
ejpam-4055	17	50	author	author	NOUN
ejpam-4055	17	51	.	.	PUNCT
ejpam-4055	18	1	doi	doi	NOUN
ejpam-4055	18	2	:	:	PUNCT
ejpam-4055	18	3	https://doi.org/10.29020/nybg.ejpam.v14i3.4055	https://doi.org/10.29020/nybg.ejpam.v14i3.4055	NOUN
ejpam-4055	18	4	email	email	NOUN
ejpam-4055	18	5	addresses	address	NOUN
ejpam-4055	18	6	:	:	PUNCT
ejpam-4055	19	1	mohamadjerson@gmail.com	mohamadjerson@gmail.com	X
ejpam-4055	19	2	(	(	PUNCT
ejpam-4055	19	3	j.	j.	PROPN
ejpam-4055	19	4	mohamad	mohamad	PROPN
ejpam-4055	19	5	)	)	PUNCT
ejpam-4055	19	6	,	,	PUNCT
ejpam-4055	19	7	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4055	19	8	(	(	PUNCT
ejpam-4055	19	9	h.	h.	PROPN
ejpam-4055	19	10	rara	rara	PROPN
ejpam-4055	19	11	)	)	PUNCT
ejpam-4055	19	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4055	19	13	1015	1015	NUM
ejpam-4055	19	14	c	c	NOUN
ejpam-4055	19	15	©	©	PROPN
ejpam-4055	19	16	2021	2021	NUM
ejpam-4055	19	17	ejpam	ejpam	VERB
ejpam-4055	19	18	all	all	DET
ejpam-4055	19	19	rights	right	NOUN
ejpam-4055	19	20	reserved	reserve	VERB
ejpam-4055	19	21	.	.	PUNCT
ejpam-4055	20	1	j.	j.	PROPN
ejpam-4055	20	2	mohamad	mohamad	PROPN
ejpam-4055	20	3	,	,	PUNCT
ejpam-4055	20	4	h.	h.	PROPN
ejpam-4055	20	5	rara	rara	PROPN
ejpam-4055	20	6	/	/	SYM
ejpam-4055	20	7	eur	eur	PROPN
ejpam-4055	20	8	.	.	PUNCT
ejpam-4055	21	1	j.	j.	PROPN
ejpam-4055	21	2	pure	pure	PROPN
ejpam-4055	21	3	appl	appl	PROPN
ejpam-4055	21	4	.	.	PROPN
ejpam-4055	21	5	math	math	PROPN
ejpam-4055	21	6	,	,	PUNCT
ejpam-4055	21	7	14	14	NUM
ejpam-4055	21	8	(	(	PUNCT
ejpam-4055	21	9	3	3	NUM
ejpam-4055	21	10	)	)	PUNCT
ejpam-4055	21	11	(	(	PUNCT
ejpam-4055	21	12	2021	2021	NUM
ejpam-4055	21	13	)	)	PUNCT
ejpam-4055	21	14	,	,	PUNCT
ejpam-4055	21	15	1015	1015	NUM
ejpam-4055	21	16	-	-	SYM
ejpam-4055	21	17	1023	1023	NUM
ejpam-4055	21	18	1016	1016	NUM
ejpam-4055	21	19	running	run	VERB
ejpam-4055	21	20	out	out	ADP
ejpam-4055	21	21	of	of	ADP
ejpam-4055	21	22	either	either	PRON
ejpam-4055	21	23	or	or	CCONJ
ejpam-4055	21	24	both	both	PRON
ejpam-4055	21	25	its	its	PRON
ejpam-4055	21	26	remaining	remain	VERB
ejpam-4055	21	27	charge	charge	NOUN
ejpam-4055	21	28	and	and	CCONJ
ejpam-4055	21	29	auxiliary	auxiliary	ADJ
ejpam-4055	21	30	power	power	NOUN
ejpam-4055	21	31	.	.	PUNCT
ejpam-4055	22	1	however	however	ADV
ejpam-4055	22	2	,	,	PUNCT
ejpam-4055	22	3	fully	fully	ADV
ejpam-4055	22	4	charging	charge	VERB
ejpam-4055	22	5	a	a	DET
ejpam-4055	22	6	car	car	NOUN
ejpam-4055	22	7	takes	take	VERB
ejpam-4055	22	8	time	time	NOUN
ejpam-4055	22	9	,	,	PUNCT
ejpam-4055	22	10	which	which	PRON
ejpam-4055	22	11	at	at	ADP
ejpam-4055	22	12	some	some	DET
ejpam-4055	22	13	point	point	NOUN
ejpam-4055	22	14	can	can	AUX
ejpam-4055	22	15	overwhelm	overwhelm	VERB
ejpam-4055	22	16	a	a	DET
ejpam-4055	22	17	station	station	NOUN
ejpam-4055	22	18	’s	’s	PART
ejpam-4055	22	19	capacity	capacity	NOUN
ejpam-4055	22	20	.	.	PUNCT
ejpam-4055	23	1	to	to	PART
ejpam-4055	23	2	reduce	reduce	VERB
ejpam-4055	23	3	the	the	DET
ejpam-4055	23	4	chance	chance	NOUN
ejpam-4055	23	5	of	of	ADP
ejpam-4055	23	6	this	this	PRON
ejpam-4055	23	7	from	from	ADP
ejpam-4055	23	8	happening	happen	VERB
ejpam-4055	23	9	,	,	PUNCT
ejpam-4055	23	10	the	the	DET
ejpam-4055	23	11	company	company	NOUN
ejpam-4055	23	12	may	may	AUX
ejpam-4055	23	13	require	require	VERB
ejpam-4055	23	14	,	,	PUNCT
ejpam-4055	23	15	as	as	ADV
ejpam-4055	23	16	much	much	ADV
ejpam-4055	23	17	as	as	ADP
ejpam-4055	23	18	possible	possible	ADJ
ejpam-4055	23	19	,	,	PUNCT
ejpam-4055	23	20	that	that	SCONJ
ejpam-4055	23	21	no	no	DET
ejpam-4055	23	22	such	such	ADJ
ejpam-4055	23	23	two	two	NUM
ejpam-4055	23	24	cars	car	NOUN
ejpam-4055	23	25	from	from	ADP
ejpam-4055	23	26	different	different	ADJ
ejpam-4055	23	27	areas	area	NOUN
ejpam-4055	23	28	arrive	arrive	VERB
ejpam-4055	23	29	at	at	ADP
ejpam-4055	23	30	the	the	DET
ejpam-4055	23	31	same	same	ADJ
ejpam-4055	23	32	station	station	NOUN
ejpam-4055	23	33	at	at	ADP
ejpam-4055	23	34	about	about	ADV
ejpam-4055	23	35	the	the	DET
ejpam-4055	23	36	same	same	ADJ
ejpam-4055	23	37	time	time	NOUN
ejpam-4055	23	38	.	.	PUNCT
ejpam-4055	24	1	assuming	assume	VERB
ejpam-4055	24	2	that	that	SCONJ
ejpam-4055	24	3	both	both	CCONJ
ejpam-4055	24	4	the	the	DET
ejpam-4055	24	5	remaining	remain	VERB
ejpam-4055	24	6	low	low	ADJ
ejpam-4055	24	7	charge	charge	NOUN
ejpam-4055	24	8	and	and	CCONJ
ejpam-4055	24	9	auxiliary	auxiliary	ADJ
ejpam-4055	24	10	power	power	NOUN
ejpam-4055	24	11	can	can	AUX
ejpam-4055	24	12	each	each	PRON
ejpam-4055	24	13	cover	cover	VERB
ejpam-4055	24	14	the	the	DET
ejpam-4055	24	15	same	same	ADJ
ejpam-4055	24	16	travel	travel	NOUN
ejpam-4055	24	17	distance	distance	NOUN
ejpam-4055	24	18	d	d	NOUN
ejpam-4055	24	19	,	,	PUNCT
ejpam-4055	24	20	the	the	DET
ejpam-4055	24	21	graph	graph	NOUN
ejpam-4055	24	22	-	-	PUNCT
ejpam-4055	24	23	theoretic	theoretic	NOUN
ejpam-4055	24	24	model	model	NOUN
ejpam-4055	24	25	for	for	ADP
ejpam-4055	24	26	this	this	DET
ejpam-4055	24	27	scenario	scenario	NOUN
ejpam-4055	24	28	could	could	AUX
ejpam-4055	24	29	be	be	AUX
ejpam-4055	24	30	that	that	DET
ejpam-4055	24	31	vertices	vertex	NOUN
ejpam-4055	24	32	represents	represent	VERB
ejpam-4055	24	33	the	the	DET
ejpam-4055	24	34	areas	area	NOUN
ejpam-4055	24	35	,	,	PUNCT
ejpam-4055	24	36	and	and	CCONJ
ejpam-4055	24	37	adjacency	adjacency	NOUN
ejpam-4055	24	38	of	of	ADP
ejpam-4055	24	39	vertices	vertex	NOUN
ejpam-4055	24	40	represent	represent	VERB
ejpam-4055	24	41	a	a	DET
ejpam-4055	24	42	connected	connected	ADJ
ejpam-4055	24	43	route	route	NOUN
ejpam-4055	24	44	of	of	ADP
ejpam-4055	24	45	distance	distance	NOUN
ejpam-4055	24	46	d.	d.	PROPN
ejpam-4055	24	47	resolving	resolve	VERB
ejpam-4055	24	48	hop	hop	NOUN
ejpam-4055	24	49	domination	domination	NOUN
ejpam-4055	24	50	in	in	ADP
ejpam-4055	24	51	graphs	graph	NOUN
ejpam-4055	24	52	can	can	AUX
ejpam-4055	24	53	be	be	AUX
ejpam-4055	24	54	used	use	VERB
ejpam-4055	24	55	to	to	PART
ejpam-4055	24	56	determine	determine	VERB
ejpam-4055	24	57	the	the	DET
ejpam-4055	24	58	minimum	minimum	ADJ
ejpam-4055	24	59	number	number	NOUN
ejpam-4055	24	60	of	of	ADP
ejpam-4055	24	61	charging	charge	VERB
ejpam-4055	24	62	stations	station	NOUN
ejpam-4055	24	63	and	and	CCONJ
ejpam-4055	24	64	where	where	SCONJ
ejpam-4055	24	65	to	to	PART
ejpam-4055	24	66	build	build	VERB
ejpam-4055	24	67	them	they	PRON
ejpam-4055	24	68	in	in	ADP
ejpam-4055	24	69	such	such	DET
ejpam-4055	24	70	a	a	DET
ejpam-4055	24	71	manner	manner	NOUN
ejpam-4055	24	72	that	that	SCONJ
ejpam-4055	24	73	cars	car	NOUN
ejpam-4055	24	74	from	from	ADP
ejpam-4055	24	75	different	different	ADJ
ejpam-4055	24	76	areas	area	NOUN
ejpam-4055	24	77	have	have	VERB
ejpam-4055	24	78	relatively	relatively	ADV
ejpam-4055	24	79	distinct	distinct	ADJ
ejpam-4055	24	80	distances	distance	NOUN
ejpam-4055	24	81	from	from	ADP
ejpam-4055	24	82	these	these	DET
ejpam-4055	24	83	stations	station	NOUN
ejpam-4055	24	84	.	.	PUNCT
ejpam-4055	25	1	in	in	ADP
ejpam-4055	25	2	this	this	DET
ejpam-4055	25	3	study	study	NOUN
ejpam-4055	25	4	,	,	PUNCT
ejpam-4055	25	5	we	we	PRON
ejpam-4055	25	6	only	only	ADV
ejpam-4055	25	7	consider	consider	VERB
ejpam-4055	25	8	graphs	graph	NOUN
ejpam-4055	25	9	that	that	PRON
ejpam-4055	25	10	are	be	AUX
ejpam-4055	25	11	finite	finite	ADJ
ejpam-4055	25	12	,	,	PUNCT
ejpam-4055	25	13	simple	simple	ADJ
ejpam-4055	25	14	,	,	PUNCT
ejpam-4055	25	15	undirected	undirected	ADJ
ejpam-4055	25	16	and	and	CCONJ
ejpam-4055	25	17	connected	connected	ADJ
ejpam-4055	25	18	.	.	PUNCT
ejpam-4055	26	1	readers	reader	NOUN
ejpam-4055	26	2	are	be	AUX
ejpam-4055	26	3	referred	refer	VERB
ejpam-4055	26	4	to	to	ADP
ejpam-4055	26	5	[	[	X
ejpam-4055	26	6	5	5	NUM
ejpam-4055	26	7	]	]	PUNCT
ejpam-4055	26	8	for	for	ADP
ejpam-4055	26	9	elementary	elementary	ADJ
ejpam-4055	26	10	graph	graph	NOUN
ejpam-4055	26	11	theory	theory	NOUN
ejpam-4055	26	12	concepts	concept	NOUN
ejpam-4055	26	13	.	.	PUNCT
ejpam-4055	27	1	let	let	VERB
ejpam-4055	27	2	g	g	PROPN
ejpam-4055	27	3	=	=	PUNCT
ejpam-4055	27	4	(	(	PUNCT
ejpam-4055	27	5	v	v	NOUN
ejpam-4055	27	6	(	(	PUNCT
ejpam-4055	27	7	g	g	NOUN
ejpam-4055	27	8	)	)	PUNCT
ejpam-4055	27	9	,	,	PUNCT
ejpam-4055	27	10	e(g	e(g	PROPN
ejpam-4055	27	11	)	)	PUNCT
ejpam-4055	27	12	)	)	PUNCT
ejpam-4055	28	1	be	be	AUX
ejpam-4055	28	2	a	a	DET
ejpam-4055	28	3	graph	graph	NOUN
ejpam-4055	28	4	.	.	PUNCT
ejpam-4055	28	5	ng(v	ng(v	PUNCT
ejpam-4055	28	6	)	)	PUNCT
ejpam-4055	29	1	=	=	PRON
ejpam-4055	29	2	{	{	PUNCT
ejpam-4055	29	3	u	u	NOUN
ejpam-4055	29	4	∈	∈	PROPN
ejpam-4055	29	5	v	v	NOUN
ejpam-4055	29	6	(	(	PUNCT
ejpam-4055	29	7	g	g	NOUN
ejpam-4055	29	8	)	)	PUNCT
ejpam-4055	29	9	:	:	PUNCT
ejpam-4055	29	10	uv	uv	PROPN
ejpam-4055	29	11	∈	∈	PROPN
ejpam-4055	29	12	e(g	e(g	PROPN
ejpam-4055	29	13	)	)	PUNCT
ejpam-4055	29	14	}	}	PUNCT
ejpam-4055	29	15	is	be	AUX
ejpam-4055	29	16	a	a	DET
ejpam-4055	29	17	neighborhood	neighborhood	NOUN
ejpam-4055	29	18	of	of	ADP
ejpam-4055	29	19	v.	v.	ADP
ejpam-4055	29	20	an	an	DET
ejpam-4055	29	21	element	element	NOUN
ejpam-4055	29	22	u	u	NOUN
ejpam-4055	29	23	∈	∈	PROPN
ejpam-4055	29	24	ng(v	ng(v	PUNCT
ejpam-4055	29	25	)	)	PUNCT
ejpam-4055	29	26	is	be	AUX
ejpam-4055	29	27	called	call	VERB
ejpam-4055	29	28	a	a	DET
ejpam-4055	29	29	neighbor	neighbor	NOUN
ejpam-4055	29	30	of	of	ADP
ejpam-4055	29	31	v.	v.	CCONJ
ejpam-4055	29	32	ng[v	ng[v	X
ejpam-4055	29	33	]	]	X
ejpam-4055	29	34	=	=	SYM
ejpam-4055	29	35	ng(v	ng(v	X
ejpam-4055	29	36	)	)	PUNCT
ejpam-4055	29	37	∪	∪	ADP
ejpam-4055	29	38	{	{	PUNCT
ejpam-4055	29	39	v	v	NOUN
ejpam-4055	29	40	}	}	PUNCT
ejpam-4055	29	41	is	be	AUX
ejpam-4055	29	42	a	a	DET
ejpam-4055	29	43	closed	closed	ADJ
ejpam-4055	29	44	neighborhood	neighborhood	NOUN
ejpam-4055	29	45	of	of	ADP
ejpam-4055	29	46	v.	v.	ADP
ejpam-4055	29	47	the	the	DET
ejpam-4055	29	48	degree	degree	NOUN
ejpam-4055	29	49	of	of	ADP
ejpam-4055	29	50	v	v	NOUN
ejpam-4055	29	51	,	,	PUNCT
ejpam-4055	29	52	denoted	denote	VERB
ejpam-4055	29	53	by	by	ADP
ejpam-4055	29	54	degg(v	degg(v	PROPN
ejpam-4055	29	55	)	)	PUNCT
ejpam-4055	29	56	,	,	PUNCT
ejpam-4055	29	57	is	be	AUX
ejpam-4055	29	58	equal	equal	ADJ
ejpam-4055	29	59	to	to	ADP
ejpam-4055	29	60	|ng(v)|	|ng(v)|	NOUN
ejpam-4055	29	61	.	.	PUNCT
ejpam-4055	30	1	for	for	ADP
ejpam-4055	30	2	s	s	PROPN
ejpam-4055	30	3	⊆	⊆	NUM
ejpam-4055	30	4	v	v	NOUN
ejpam-4055	30	5	(	(	PUNCT
ejpam-4055	30	6	g	g	NOUN
ejpam-4055	30	7	)	)	PUNCT
ejpam-4055	30	8	,	,	PUNCT
ejpam-4055	30	9	ng(s	ng(s	NUM
ejpam-4055	30	10	)	)	PUNCT
ejpam-4055	30	11	=	=	SYM
ejpam-4055	30	12	⋃	⋃	ADP
ejpam-4055	30	13	v∈s	v∈s	NOUN
ejpam-4055	30	14	ng(v	ng(v	NOUN
ejpam-4055	30	15	)	)	PUNCT
ejpam-4055	30	16	and	and	CCONJ
ejpam-4055	30	17	ng[s	ng[	NOUN
ejpam-4055	30	18	]	]	PUNCT
ejpam-4055	30	19	=	=	PUNCT
ejpam-4055	30	20	⋃	⋃	VERB
ejpam-4055	30	21	v∈s	v∈s	ADJ
ejpam-4055	30	22	ng[v	ng[v	NOUN
ejpam-4055	30	23	]	]	PUNCT
ejpam-4055	30	24	.	.	PUNCT
ejpam-4055	31	1	a	a	DET
ejpam-4055	31	2	connected	connected	ADJ
ejpam-4055	31	3	graph	graph	NOUN
ejpam-4055	31	4	g	g	NOUN
ejpam-4055	31	5	is	be	AUX
ejpam-4055	31	6	said	say	VERB
ejpam-4055	31	7	to	to	PART
ejpam-4055	31	8	be	be	AUX
ejpam-4055	31	9	point	point	NOUN
ejpam-4055	31	10	determining	determine	VERB
ejpam-4055	31	11	if	if	SCONJ
ejpam-4055	31	12	distinct	distinct	ADJ
ejpam-4055	31	13	vertices	vertex	NOUN
ejpam-4055	31	14	have	have	VERB
ejpam-4055	31	15	distinct	distinct	ADJ
ejpam-4055	31	16	neighborhoods	neighborhood	NOUN
ejpam-4055	31	17	,	,	PUNCT
ejpam-4055	31	18	that	that	ADV
ejpam-4055	31	19	is	is	ADV
ejpam-4055	31	20	,	,	PUNCT
ejpam-4055	31	21	ng(a	ng(a	X
ejpam-4055	31	22	)	)	PUNCT
ejpam-4055	31	23	6=	6=	NUM
ejpam-4055	32	1	ng(b	ng(b	NOUN
ejpam-4055	32	2	)	)	PUNCT
ejpam-4055	33	1	whenever	whenever	SCONJ
ejpam-4055	33	2	a	a	DET
ejpam-4055	33	3	,	,	PUNCT
ejpam-4055	33	4	b	b	PROPN
ejpam-4055	33	5	∈	∈	PROPN
ejpam-4055	33	6	v	v	NOUN
ejpam-4055	33	7	(	(	PUNCT
ejpam-4055	33	8	g	g	NOUN
ejpam-4055	33	9	)	)	PUNCT
ejpam-4055	33	10	and	and	CCONJ
ejpam-4055	33	11	a	a	DET
ejpam-4055	33	12	6=	6=	NUM
ejpam-4055	33	13	b.	b.	PROPN
ejpam-4055	33	14	a	a	DET
ejpam-4055	33	15	connected	connected	ADJ
ejpam-4055	33	16	graph	graph	NOUN
ejpam-4055	33	17	g	g	NOUN
ejpam-4055	33	18	of	of	ADP
ejpam-4055	33	19	order	order	NOUN
ejpam-4055	33	20	n	n	PRON
ejpam-4055	33	21	≥	≥	NOUN
ejpam-4055	33	22	3	3	NUM
ejpam-4055	33	23	is	be	AUX
ejpam-4055	33	24	totally	totally	ADV
ejpam-4055	33	25	point	point	NOUN
ejpam-4055	33	26	determining	determine	VERB
ejpam-4055	33	27	if	if	SCONJ
ejpam-4055	33	28	for	for	ADP
ejpam-4055	33	29	any	any	DET
ejpam-4055	33	30	two	two	NUM
ejpam-4055	33	31	distinct	distinct	ADJ
ejpam-4055	33	32	vertices	vertex	NOUN
ejpam-4055	33	33	u	u	NOUN
ejpam-4055	33	34	and	and	CCONJ
ejpam-4055	33	35	v	v	NOUN
ejpam-4055	33	36	of	of	ADP
ejpam-4055	33	37	g	g	NOUN
ejpam-4055	33	38	,	,	PUNCT
ejpam-4055	33	39	ng(u	ng(u	NOUN
ejpam-4055	33	40	)	)	PUNCT
ejpam-4055	33	41	6=	6=	NUM
ejpam-4055	34	1	ng(v	ng(v	NUM
ejpam-4055	34	2	)	)	PUNCT
ejpam-4055	34	3	and	and	CCONJ
ejpam-4055	34	4	ng[u	ng[u	PROPN
ejpam-4055	34	5	]	]	PUNCT
ejpam-4055	35	1	6=	6=	PUNCT
ejpam-4055	36	1	ng[v	ng[v	PROPN
ejpam-4055	36	2	]	]	PUNCT
ejpam-4055	36	3	.	.	PUNCT
ejpam-4055	37	1	a	a	DET
ejpam-4055	37	2	vertex	vertex	NOUN
ejpam-4055	37	3	x	x	X
ejpam-4055	37	4	of	of	ADP
ejpam-4055	37	5	a	a	DET
ejpam-4055	37	6	graph	graph	NOUN
ejpam-4055	37	7	g	g	NOUN
ejpam-4055	37	8	is	be	AUX
ejpam-4055	37	9	said	say	VERB
ejpam-4055	37	10	to	to	PART
ejpam-4055	37	11	resolve	resolve	VERB
ejpam-4055	37	12	two	two	NUM
ejpam-4055	37	13	vertices	vertex	NOUN
ejpam-4055	37	14	u	u	NOUN
ejpam-4055	37	15	and	and	CCONJ
ejpam-4055	37	16	v	v	NOUN
ejpam-4055	37	17	of	of	ADP
ejpam-4055	37	18	g	g	PROPN
ejpam-4055	37	19	if	if	SCONJ
ejpam-4055	37	20	dg(x	dg(x	NUM
ejpam-4055	37	21	,	,	PUNCT
ejpam-4055	37	22	u	u	NOUN
ejpam-4055	37	23	)	)	PUNCT
ejpam-4055	37	24	6=	6=	ADP
ejpam-4055	37	25	dg(x	dg(x	SYM
ejpam-4055	37	26	,	,	PUNCT
ejpam-4055	37	27	v	v	NOUN
ejpam-4055	37	28	)	)	PUNCT
ejpam-4055	37	29	.	.	PUNCT
ejpam-4055	38	1	for	for	ADP
ejpam-4055	38	2	an	an	DET
ejpam-4055	38	3	ordered	order	VERB
ejpam-4055	38	4	set	set	NOUN
ejpam-4055	38	5	w	w	NOUN
ejpam-4055	38	6	=	=	PUNCT
ejpam-4055	38	7	{	{	PUNCT
ejpam-4055	38	8	x1	x1	PROPN
ejpam-4055	38	9	,	,	PUNCT
ejpam-4055	38	10	...	...	PUNCT
ejpam-4055	38	11	,	,	PUNCT
ejpam-4055	38	12	xk	xk	ADJ
ejpam-4055	38	13	}	}	PUNCT
ejpam-4055	38	14	⊆	⊆	NUM
ejpam-4055	38	15	v	v	NOUN
ejpam-4055	38	16	(	(	PUNCT
ejpam-4055	38	17	g	g	NOUN
ejpam-4055	38	18	)	)	PUNCT
ejpam-4055	38	19	and	and	CCONJ
ejpam-4055	38	20	a	a	DET
ejpam-4055	38	21	vertex	vertex	NOUN
ejpam-4055	38	22	v	v	NOUN
ejpam-4055	38	23	in	in	ADP
ejpam-4055	38	24	g	g	PROPN
ejpam-4055	38	25	,	,	PUNCT
ejpam-4055	38	26	the	the	DET
ejpam-4055	38	27	k	k	NOUN
ejpam-4055	38	28	-	-	NOUN
ejpam-4055	38	29	vector	vector	NOUN
ejpam-4055	38	30	rg(v	rg(v	NOUN
ejpam-4055	38	31	/	/	SYM
ejpam-4055	38	32	w	w	NOUN
ejpam-4055	38	33	)	)	PUNCT
ejpam-4055	38	34	=	=	SYM
ejpam-4055	38	35	(	(	PUNCT
ejpam-4055	38	36	dg(v	dg(v	X
ejpam-4055	38	37	,	,	PUNCT
ejpam-4055	38	38	x1	x1	PROPN
ejpam-4055	38	39	)	)	PUNCT
ejpam-4055	38	40	,	,	PUNCT
ejpam-4055	38	41	dg(v	dg(v	X
ejpam-4055	38	42	,	,	PUNCT
ejpam-4055	38	43	x2	x2	PROPN
ejpam-4055	38	44	)	)	PUNCT
ejpam-4055	38	45	,	,	PUNCT
ejpam-4055	38	46	...	...	PUNCT
ejpam-4055	38	47	,	,	PUNCT
ejpam-4055	38	48	dg(v	dg(v	X
ejpam-4055	38	49	,	,	PUNCT
ejpam-4055	38	50	xk	xk	NOUN
ejpam-4055	38	51	)	)	PUNCT
ejpam-4055	38	52	)	)	PUNCT
ejpam-4055	38	53	is	be	AUX
ejpam-4055	38	54	called	call	VERB
ejpam-4055	38	55	the	the	DET
ejpam-4055	38	56	representation	representation	NOUN
ejpam-4055	38	57	of	of	ADP
ejpam-4055	38	58	v	v	NOUN
ejpam-4055	38	59	with	with	ADP
ejpam-4055	38	60	respect	respect	NOUN
ejpam-4055	38	61	to	to	ADP
ejpam-4055	38	62	w	w	PROPN
ejpam-4055	38	63	.	.	PUNCT
ejpam-4055	39	1	the	the	DET
ejpam-4055	39	2	set	set	NOUN
ejpam-4055	39	3	w	w	NOUN
ejpam-4055	39	4	is	be	AUX
ejpam-4055	39	5	a	a	DET
ejpam-4055	39	6	resolving	resolving	NOUN
ejpam-4055	39	7	set	set	VERB
ejpam-4055	39	8	for	for	ADP
ejpam-4055	39	9	g	g	PROPN
ejpam-4055	39	10	if	if	SCONJ
ejpam-4055	40	1	and	and	CCONJ
ejpam-4055	40	2	only	only	ADV
ejpam-4055	40	3	if	if	SCONJ
ejpam-4055	40	4	no	no	DET
ejpam-4055	40	5	two	two	NUM
ejpam-4055	40	6	vertices	vertex	NOUN
ejpam-4055	40	7	of	of	ADP
ejpam-4055	40	8	g	g	NOUN
ejpam-4055	40	9	have	have	VERB
ejpam-4055	40	10	the	the	DET
ejpam-4055	40	11	same	same	ADJ
ejpam-4055	40	12	representation	representation	NOUN
ejpam-4055	40	13	with	with	ADP
ejpam-4055	40	14	respect	respect	NOUN
ejpam-4055	40	15	to	to	ADP
ejpam-4055	40	16	w	w	PROPN
ejpam-4055	40	17	.	.	PUNCT
ejpam-4055	41	1	the	the	DET
ejpam-4055	41	2	metric	metric	ADJ
ejpam-4055	41	3	dimension	dimension	NOUN
ejpam-4055	41	4	of	of	ADP
ejpam-4055	41	5	g	g	NOUN
ejpam-4055	41	6	,	,	PUNCT
ejpam-4055	41	7	denoted	denote	VERB
ejpam-4055	41	8	by	by	ADP
ejpam-4055	41	9	dim(g	dim(g	PROPN
ejpam-4055	41	10	)	)	PUNCT
ejpam-4055	41	11	,	,	PUNCT
ejpam-4055	41	12	is	be	AUX
ejpam-4055	41	13	the	the	DET
ejpam-4055	41	14	minimum	minimum	ADJ
ejpam-4055	41	15	cardinality	cardinality	NOUN
ejpam-4055	41	16	over	over	ADP
ejpam-4055	41	17	all	all	DET
ejpam-4055	41	18	resolving	resolve	VERB
ejpam-4055	41	19	sets	set	NOUN
ejpam-4055	41	20	of	of	ADP
ejpam-4055	41	21	g.	g.	PROPN
ejpam-4055	41	22	a	a	DET
ejpam-4055	41	23	resolving	resolve	VERB
ejpam-4055	41	24	set	set	NOUN
ejpam-4055	41	25	of	of	ADP
ejpam-4055	41	26	cardinality	cardinality	PROPN
ejpam-4055	41	27	dim(g	dim(g	PROPN
ejpam-4055	41	28	)	)	PUNCT
ejpam-4055	41	29	is	be	AUX
ejpam-4055	41	30	called	call	VERB
ejpam-4055	41	31	basis	basis	NOUN
ejpam-4055	41	32	.	.	PUNCT
ejpam-4055	42	1	a	a	DET
ejpam-4055	42	2	set	set	NOUN
ejpam-4055	42	3	s	s	NOUN
ejpam-4055	42	4	⊆	⊆	NUM
ejpam-4055	42	5	v	v	NOUN
ejpam-4055	42	6	(	(	PUNCT
ejpam-4055	42	7	g	g	NOUN
ejpam-4055	42	8	)	)	PUNCT
ejpam-4055	42	9	of	of	ADP
ejpam-4055	42	10	vertices	vertex	NOUN
ejpam-4055	42	11	of	of	ADP
ejpam-4055	42	12	g	g	PROPN
ejpam-4055	42	13	is	be	AUX
ejpam-4055	42	14	a	a	DET
ejpam-4055	42	15	dominating	dominating	NOUN
ejpam-4055	42	16	set	set	NOUN
ejpam-4055	42	17	if	if	SCONJ
ejpam-4055	42	18	every	every	DET
ejpam-4055	42	19	u	u	PROPN
ejpam-4055	42	20	∈	∈	PROPN
ejpam-4055	42	21	v	v	NOUN
ejpam-4055	42	22	(	(	PUNCT
ejpam-4055	42	23	g	g	NOUN
ejpam-4055	42	24	)	)	PUNCT
ejpam-4055	42	25	\	\	PROPN
ejpam-4055	43	1	s	s	PART
ejpam-4055	43	2	is	be	AUX
ejpam-4055	43	3	adjacent	adjacent	ADJ
ejpam-4055	43	4	to	to	ADP
ejpam-4055	43	5	at	at	ADV
ejpam-4055	43	6	least	least	ADV
ejpam-4055	43	7	one	one	NUM
ejpam-4055	43	8	vertex	vertex	NOUN
ejpam-4055	43	9	v	v	ADP
ejpam-4055	43	10	∈	∈	NOUN
ejpam-4055	43	11	s.	s.	PROPN
ejpam-4055	44	1	the	the	DET
ejpam-4055	44	2	domination	domination	NOUN
ejpam-4055	44	3	number	number	NOUN
ejpam-4055	44	4	of	of	ADP
ejpam-4055	44	5	a	a	DET
ejpam-4055	44	6	graph	graph	NOUN
ejpam-4055	44	7	g	g	NOUN
ejpam-4055	44	8	,	,	PUNCT
ejpam-4055	44	9	denoted	denote	VERB
ejpam-4055	44	10	by	by	ADP
ejpam-4055	44	11	γ(g	γ(g	PROPN
ejpam-4055	44	12	)	)	PUNCT
ejpam-4055	44	13	,	,	PUNCT
ejpam-4055	44	14	is	be	AUX
ejpam-4055	44	15	given	give	VERB
ejpam-4055	44	16	by	by	ADP
ejpam-4055	44	17	γ(g	γ(g	PROPN
ejpam-4055	44	18	)	)	PUNCT
ejpam-4055	45	1	=	=	NOUN
ejpam-4055	45	2	min{|s|	min{|s|	NOUN
ejpam-4055	45	3	:	:	PUNCT
ejpam-4055	45	4	s	s	VERB
ejpam-4055	45	5	is	be	AUX
ejpam-4055	45	6	a	a	DET
ejpam-4055	45	7	dominating	dominating	NOUN
ejpam-4055	45	8	set	set	NOUN
ejpam-4055	45	9	of	of	ADP
ejpam-4055	45	10	g	g	NOUN
ejpam-4055	45	11	}	}	PUNCT
ejpam-4055	45	12	.	.	PUNCT
ejpam-4055	46	1	a	a	DET
ejpam-4055	46	2	set	set	NOUN
ejpam-4055	46	3	s	s	NOUN
ejpam-4055	46	4	⊆	⊆	NUM
ejpam-4055	46	5	v	v	NOUN
ejpam-4055	46	6	(	(	PUNCT
ejpam-4055	46	7	g	g	NOUN
ejpam-4055	46	8	)	)	PUNCT
ejpam-4055	46	9	is	be	AUX
ejpam-4055	46	10	a	a	DET
ejpam-4055	46	11	hop	hop	NOUN
ejpam-4055	46	12	dominating	dominating	NOUN
ejpam-4055	46	13	set	set	NOUN
ejpam-4055	46	14	of	of	ADP
ejpam-4055	46	15	g	g	PROPN
ejpam-4055	46	16	if	if	SCONJ
ejpam-4055	46	17	for	for	ADP
ejpam-4055	46	18	every	every	DET
ejpam-4055	46	19	v	v	NUM
ejpam-4055	46	20	∈	∈	NOUN
ejpam-4055	46	21	v	v	NOUN
ejpam-4055	46	22	(	(	PUNCT
ejpam-4055	46	23	g)\s	g)\s	NOUN
ejpam-4055	46	24	,	,	PUNCT
ejpam-4055	46	25	there	there	PRON
ejpam-4055	46	26	exists	exist	VERB
ejpam-4055	46	27	u	u	PROPN
ejpam-4055	46	28	∈	∈	PROPN
ejpam-4055	46	29	s	s	VERB
ejpam-4055	46	30	such	such	ADJ
ejpam-4055	46	31	that	that	DET
ejpam-4055	46	32	dg(u	dg(u	ADJ
ejpam-4055	46	33	,	,	PUNCT
ejpam-4055	46	34	v	v	NOUN
ejpam-4055	46	35	)	)	PUNCT
ejpam-4055	47	1	=	=	SYM
ejpam-4055	47	2	2	2	X
ejpam-4055	47	3	.	.	PUNCT
ejpam-4055	48	1	the	the	DET
ejpam-4055	48	2	minimum	minimum	ADJ
ejpam-4055	48	3	cardinality	cardinality	NOUN
ejpam-4055	48	4	of	of	ADP
ejpam-4055	48	5	a	a	DET
ejpam-4055	48	6	hop	hop	NOUN
ejpam-4055	48	7	dominating	dominating	NOUN
ejpam-4055	48	8	set	set	NOUN
ejpam-4055	48	9	of	of	ADP
ejpam-4055	48	10	g	g	NOUN
ejpam-4055	48	11	,	,	PUNCT
ejpam-4055	48	12	denoted	denote	VERB
ejpam-4055	48	13	by	by	ADP
ejpam-4055	48	14	γh(g	γh(g	NOUN
ejpam-4055	48	15	)	)	PUNCT
ejpam-4055	48	16	,	,	PUNCT
ejpam-4055	48	17	is	be	AUX
ejpam-4055	48	18	called	call	VERB
ejpam-4055	48	19	the	the	DET
ejpam-4055	48	20	hop	hop	NOUN
ejpam-4055	48	21	domination	domination	NOUN
ejpam-4055	48	22	number	number	NOUN
ejpam-4055	48	23	of	of	ADP
ejpam-4055	48	24	g.	g.	PROPN
ejpam-4055	48	25	any	any	DET
ejpam-4055	48	26	hop	hop	NOUN
ejpam-4055	48	27	dominating	dominating	NOUN
ejpam-4055	48	28	set	set	VERB
ejpam-4055	48	29	with	with	ADP
ejpam-4055	48	30	cardinality	cardinality	NOUN
ejpam-4055	48	31	equal	equal	ADJ
ejpam-4055	48	32	to	to	ADP
ejpam-4055	48	33	γh(g	γh(g	NOUN
ejpam-4055	48	34	)	)	PUNCT
ejpam-4055	48	35	is	be	AUX
ejpam-4055	48	36	called	call	VERB
ejpam-4055	48	37	a	a	DET
ejpam-4055	48	38	γh	γh	ADV
ejpam-4055	48	39	-	-	PUNCT
ejpam-4055	48	40	set	set	NOUN
ejpam-4055	48	41	.	.	PUNCT
ejpam-4055	49	1	a	a	DET
ejpam-4055	49	2	vertex	vertex	NOUN
ejpam-4055	49	3	v	v	NOUN
ejpam-4055	49	4	in	in	ADP
ejpam-4055	49	5	g	g	PROPN
ejpam-4055	49	6	is	be	AUX
ejpam-4055	49	7	a	a	DET
ejpam-4055	49	8	hop	hop	NOUN
ejpam-4055	49	9	neighbor	neighbor	NOUN
ejpam-4055	49	10	of	of	ADP
ejpam-4055	49	11	vertex	vertex	NOUN
ejpam-4055	49	12	u	u	NOUN
ejpam-4055	49	13	in	in	ADP
ejpam-4055	49	14	g	g	PROPN
ejpam-4055	49	15	if	if	SCONJ
ejpam-4055	49	16	dg(u	dg(u	NOUN
ejpam-4055	49	17	,	,	PUNCT
ejpam-4055	49	18	v	v	NOUN
ejpam-4055	49	19	)	)	PUNCT
ejpam-4055	49	20	=	=	SYM
ejpam-4055	49	21	2	2	X
ejpam-4055	49	22	.	.	X
ejpam-4055	50	1	the	the	DET
ejpam-4055	50	2	set	set	NOUN
ejpam-4055	50	3	ng(u	ng(u	NOUN
ejpam-4055	50	4	,	,	PUNCT
ejpam-4055	50	5	2	2	NUM
ejpam-4055	50	6	)	)	PUNCT
ejpam-4055	50	7	=	=	PRON
ejpam-4055	50	8	{	{	PUNCT
ejpam-4055	50	9	v	v	NUM
ejpam-4055	50	10	∈	∈	NOUN
ejpam-4055	50	11	v	v	NOUN
ejpam-4055	50	12	(	(	PUNCT
ejpam-4055	50	13	g	g	NOUN
ejpam-4055	50	14	)	)	PUNCT
ejpam-4055	50	15	:	:	PUNCT
ejpam-4055	50	16	dg(v	dg(v	X
ejpam-4055	50	17	,	,	PUNCT
ejpam-4055	50	18	u	u	NOUN
ejpam-4055	50	19	)	)	PUNCT
ejpam-4055	50	20	=	=	SYM
ejpam-4055	50	21	2	2	X
ejpam-4055	50	22	}	}	PUNCT
ejpam-4055	50	23	is	be	AUX
ejpam-4055	50	24	called	call	VERB
ejpam-4055	50	25	the	the	DET
ejpam-4055	50	26	open	open	ADJ
ejpam-4055	50	27	hop	hop	NOUN
ejpam-4055	50	28	neighborhood	neighborhood	NOUN
ejpam-4055	50	29	of	of	ADP
ejpam-4055	50	30	u.	u.	PROPN
ejpam-4055	50	31	the	the	DET
ejpam-4055	50	32	closed	closed	ADJ
ejpam-4055	50	33	hop	hop	NOUN
ejpam-4055	50	34	neighborhood	neighborhood	NOUN
ejpam-4055	50	35	of	of	ADP
ejpam-4055	50	36	u	u	PROPN
ejpam-4055	50	37	in	in	ADP
ejpam-4055	50	38	g	g	PROPN
ejpam-4055	50	39	is	be	AUX
ejpam-4055	50	40	given	give	VERB
ejpam-4055	50	41	by	by	ADP
ejpam-4055	50	42	ng[u	ng[u	PROPN
ejpam-4055	50	43	,	,	PUNCT
ejpam-4055	50	44	2	2	NUM
ejpam-4055	50	45	]	]	PUNCT
ejpam-4055	51	1	=	=	SYM
ejpam-4055	51	2	ng(u	ng(u	PROPN
ejpam-4055	51	3	,	,	PUNCT
ejpam-4055	51	4	2)∪	2)∪	NUM
ejpam-4055	51	5	{	{	PUNCT
ejpam-4055	51	6	u	u	NOUN
ejpam-4055	51	7	}	}	PUNCT
ejpam-4055	51	8	.	.	PUNCT
ejpam-4055	52	1	the	the	DET
ejpam-4055	52	2	open	open	ADJ
ejpam-4055	52	3	hop	hop	NOUN
ejpam-4055	52	4	neighborhood	neighborhood	NOUN
ejpam-4055	52	5	of	of	ADP
ejpam-4055	52	6	x	x	PROPN
ejpam-4055	52	7	⊆	⊆	NUM
ejpam-4055	52	8	v	v	ADP
ejpam-4055	52	9	(	(	PUNCT
ejpam-4055	52	10	g	g	NOUN
ejpam-4055	52	11	)	)	PUNCT
ejpam-4055	52	12	is	be	AUX
ejpam-4055	52	13	the	the	DET
ejpam-4055	52	14	set	set	NOUN
ejpam-4055	52	15	ng(x	ng(x	NUM
ejpam-4055	52	16	,	,	PUNCT
ejpam-4055	52	17	2	2	X
ejpam-4055	52	18	)	)	PUNCT
ejpam-4055	52	19	=	=	NOUN
ejpam-4055	52	20	⋃	⋃	NOUN
ejpam-4055	52	21	u∈x	u∈x	ADJ
ejpam-4055	52	22	ng(u	ng(u	NOUN
ejpam-4055	52	23	,	,	PUNCT
ejpam-4055	52	24	2	2	NUM
ejpam-4055	52	25	)	)	PUNCT
ejpam-4055	52	26	.	.	PUNCT
ejpam-4055	53	1	the	the	DET
ejpam-4055	53	2	closed	closed	ADJ
ejpam-4055	53	3	hop	hop	NOUN
ejpam-4055	53	4	neighborhood	neighborhood	NOUN
ejpam-4055	53	5	of	of	ADP
ejpam-4055	53	6	x	x	PUNCT
ejpam-4055	53	7	in	in	ADP
ejpam-4055	53	8	g	g	PROPN
ejpam-4055	53	9	is	be	AUX
ejpam-4055	53	10	the	the	DET
ejpam-4055	53	11	set	set	PROPN
ejpam-4055	53	12	ng[x	ng[x	PROPN
ejpam-4055	53	13	,	,	PUNCT
ejpam-4055	53	14	2	2	NUM
ejpam-4055	53	15	]	]	PUNCT
ejpam-4055	53	16	=	=	SYM
ejpam-4055	53	17	ng(x	ng(x	X
ejpam-4055	53	18	,	,	PUNCT
ejpam-4055	53	19	2	2	NUM
ejpam-4055	53	20	)	)	PUNCT
ejpam-4055	53	21	∪x	∪x	PROPN
ejpam-4055	53	22	.	.	PUNCT
ejpam-4055	53	23	j.	j.	PROPN
ejpam-4055	53	24	mohamad	mohamad	PROPN
ejpam-4055	53	25	,	,	PUNCT
ejpam-4055	53	26	h.	h.	PROPN
ejpam-4055	53	27	rara	rara	PROPN
ejpam-4055	53	28	/	/	SYM
ejpam-4055	53	29	eur	eur	PROPN
ejpam-4055	53	30	.	.	PUNCT
ejpam-4055	54	1	j.	j.	PROPN
ejpam-4055	54	2	pure	pure	PROPN
ejpam-4055	54	3	appl	appl	PROPN
ejpam-4055	54	4	.	.	PROPN
ejpam-4055	54	5	math	math	PROPN
ejpam-4055	54	6	,	,	PUNCT
ejpam-4055	54	7	14	14	NUM
ejpam-4055	54	8	(	(	PUNCT
ejpam-4055	54	9	3	3	NUM
ejpam-4055	54	10	)	)	PUNCT
ejpam-4055	54	11	(	(	PUNCT
ejpam-4055	54	12	2021	2021	NUM
ejpam-4055	54	13	)	)	PUNCT
ejpam-4055	54	14	,	,	PUNCT
ejpam-4055	54	15	1015	1015	NUM
ejpam-4055	54	16	-	-	SYM
ejpam-4055	54	17	1023	1023	NUM
ejpam-4055	54	18	1017	1017	NUM
ejpam-4055	54	19	a	a	DET
ejpam-4055	54	20	set	set	NOUN
ejpam-4055	54	21	s	s	NOUN
ejpam-4055	54	22	⊆	⊆	NUM
ejpam-4055	54	23	v	v	NOUN
ejpam-4055	54	24	(	(	PUNCT
ejpam-4055	54	25	g	g	NOUN
ejpam-4055	54	26	)	)	PUNCT
ejpam-4055	54	27	is	be	AUX
ejpam-4055	54	28	a	a	DET
ejpam-4055	54	29	locating	locating	NOUN
ejpam-4055	54	30	set	set	NOUN
ejpam-4055	54	31	of	of	ADP
ejpam-4055	54	32	g	g	PROPN
ejpam-4055	54	33	if	if	SCONJ
ejpam-4055	54	34	for	for	ADP
ejpam-4055	54	35	every	every	DET
ejpam-4055	54	36	two	two	NUM
ejpam-4055	54	37	distinct	distinct	ADJ
ejpam-4055	54	38	vertices	vertex	NOUN
ejpam-4055	54	39	u	u	NOUN
ejpam-4055	54	40	and	and	CCONJ
ejpam-4055	54	41	v	v	NOUN
ejpam-4055	54	42	of	of	ADP
ejpam-4055	54	43	v	v	NOUN
ejpam-4055	54	44	(	(	PUNCT
ejpam-4055	54	45	g)\s	g)\s	NOUN
ejpam-4055	54	46	,	,	PUNCT
ejpam-4055	54	47	ng(u	ng(u	NOUN
ejpam-4055	54	48	)	)	PUNCT
ejpam-4055	54	49	∩	∩	X
ejpam-4055	54	50	s	s	PART
ejpam-4055	54	51	6=	6=	NUM
ejpam-4055	54	52	ng(v	ng(v	NUM
ejpam-4055	54	53	)	)	PUNCT
ejpam-4055	54	54	∩	∩	PROPN
ejpam-4055	54	55	s.	s.	PROPN
ejpam-4055	55	1	the	the	DET
ejpam-4055	55	2	locating	locate	VERB
ejpam-4055	55	3	number	number	NOUN
ejpam-4055	55	4	of	of	ADP
ejpam-4055	55	5	g	g	NOUN
ejpam-4055	55	6	,	,	PUNCT
ejpam-4055	55	7	denoted	denote	VERB
ejpam-4055	55	8	by	by	ADP
ejpam-4055	55	9	ln(g	ln(g	NOUN
ejpam-4055	55	10	)	)	PUNCT
ejpam-4055	55	11	,	,	PUNCT
ejpam-4055	55	12	is	be	AUX
ejpam-4055	55	13	the	the	DET
ejpam-4055	55	14	smallest	small	ADJ
ejpam-4055	55	15	cardinality	cardinality	NOUN
ejpam-4055	55	16	of	of	ADP
ejpam-4055	55	17	a	a	DET
ejpam-4055	55	18	locating	locating	NOUN
ejpam-4055	55	19	set	set	NOUN
ejpam-4055	55	20	of	of	ADP
ejpam-4055	55	21	g.	g.	PROPN
ejpam-4055	55	22	a	a	DET
ejpam-4055	55	23	locating	locate	VERB
ejpam-4055	55	24	set	set	NOUN
ejpam-4055	55	25	of	of	ADP
ejpam-4055	55	26	g	g	PROPN
ejpam-4055	55	27	of	of	ADP
ejpam-4055	55	28	cardinality	cardinality	PROPN
ejpam-4055	55	29	ln(g	ln(g	PUNCT
ejpam-4055	55	30	)	)	PUNCT
ejpam-4055	55	31	is	be	AUX
ejpam-4055	55	32	referred	refer	VERB
ejpam-4055	55	33	to	to	ADP
ejpam-4055	55	34	as	as	ADP
ejpam-4055	55	35	a	a	DET
ejpam-4055	55	36	ln	ln	ADV
ejpam-4055	55	37	-	-	PUNCT
ejpam-4055	55	38	set	set	NOUN
ejpam-4055	55	39	of	of	ADP
ejpam-4055	55	40	g.	g.	PROPN
ejpam-4055	55	41	a	a	DET
ejpam-4055	55	42	set	set	NOUN
ejpam-4055	55	43	s	s	PROPN
ejpam-4055	55	44	⊆	⊆	NUM
ejpam-4055	55	45	v	v	NOUN
ejpam-4055	55	46	(	(	PUNCT
ejpam-4055	55	47	g	g	NOUN
ejpam-4055	55	48	)	)	PUNCT
ejpam-4055	55	49	is	be	AUX
ejpam-4055	55	50	a	a	DET
ejpam-4055	55	51	strictly	strictly	ADV
ejpam-4055	55	52	locating	locate	VERB
ejpam-4055	55	53	set	set	NOUN
ejpam-4055	55	54	of	of	ADP
ejpam-4055	55	55	g	g	NOUN
ejpam-4055	55	56	if	if	SCONJ
ejpam-4055	55	57	it	it	PRON
ejpam-4055	55	58	is	be	AUX
ejpam-4055	55	59	a	a	DET
ejpam-4055	55	60	locating	locating	NOUN
ejpam-4055	55	61	set	set	NOUN
ejpam-4055	55	62	of	of	ADP
ejpam-4055	55	63	g	g	PROPN
ejpam-4055	55	64	and	and	CCONJ
ejpam-4055	55	65	ng(u)∩s	ng(u)∩s	PROPN
ejpam-4055	55	66	6=	6=	PROPN
ejpam-4055	55	67	s	s	X
ejpam-4055	55	68	for	for	ADP
ejpam-4055	55	69	all	all	DET
ejpam-4055	55	70	u	u	PROPN
ejpam-4055	55	71	∈	∈	PROPN
ejpam-4055	55	72	v	v	NOUN
ejpam-4055	55	73	(	(	PUNCT
ejpam-4055	55	74	g)\s	g)\s	NOUN
ejpam-4055	55	75	.	.	PUNCT
ejpam-4055	56	1	the	the	DET
ejpam-4055	56	2	strictly	strictly	ADV
ejpam-4055	56	3	locating	locate	VERB
ejpam-4055	56	4	number	number	NOUN
ejpam-4055	56	5	of	of	ADP
ejpam-4055	56	6	g	g	NOUN
ejpam-4055	56	7	,	,	PUNCT
ejpam-4055	56	8	denoted	denote	VERB
ejpam-4055	56	9	by	by	ADP
ejpam-4055	56	10	sln(g	sln(g	PROPN
ejpam-4055	56	11	)	)	PUNCT
ejpam-4055	56	12	,	,	PUNCT
ejpam-4055	56	13	is	be	AUX
ejpam-4055	56	14	the	the	DET
ejpam-4055	56	15	smallest	small	ADJ
ejpam-4055	56	16	cardinality	cardinality	NOUN
ejpam-4055	56	17	of	of	ADP
ejpam-4055	56	18	a	a	DET
ejpam-4055	56	19	strictly	strictly	ADV
ejpam-4055	56	20	locating	locate	VERB
ejpam-4055	56	21	set	set	NOUN
ejpam-4055	56	22	of	of	ADP
ejpam-4055	56	23	g.	g.	PROPN
ejpam-4055	56	24	a	a	DET
ejpam-4055	56	25	strictly	strictly	ADV
ejpam-4055	56	26	locating	locate	VERB
ejpam-4055	56	27	set	set	NOUN
ejpam-4055	56	28	of	of	ADP
ejpam-4055	56	29	g	g	PROPN
ejpam-4055	56	30	of	of	ADP
ejpam-4055	56	31	cardinality	cardinality	PROPN
ejpam-4055	56	32	sln(g	sln(g	PROPN
ejpam-4055	56	33	)	)	PUNCT
ejpam-4055	56	34	is	be	AUX
ejpam-4055	56	35	referred	refer	VERB
ejpam-4055	56	36	to	to	ADP
ejpam-4055	56	37	as	as	ADP
ejpam-4055	56	38	a	a	DET
ejpam-4055	56	39	sln	sln	NOUN
ejpam-4055	56	40	-	-	PUNCT
ejpam-4055	56	41	set	set	NOUN
ejpam-4055	56	42	of	of	ADP
ejpam-4055	56	43	g.	g.	PROPN
ejpam-4055	56	44	a	a	DET
ejpam-4055	56	45	set	set	NOUN
ejpam-4055	56	46	s	s	PROPN
ejpam-4055	56	47	⊆	⊆	NUM
ejpam-4055	56	48	v	v	NOUN
ejpam-4055	56	49	(	(	PUNCT
ejpam-4055	56	50	g	g	NOUN
ejpam-4055	56	51	)	)	PUNCT
ejpam-4055	56	52	is	be	AUX
ejpam-4055	56	53	a	a	DET
ejpam-4055	56	54	resolving	resolve	VERB
ejpam-4055	56	55	hop	hop	NOUN
ejpam-4055	56	56	dominating	dominating	NOUN
ejpam-4055	56	57	set	set	NOUN
ejpam-4055	56	58	of	of	ADP
ejpam-4055	56	59	g	g	PROPN
ejpam-4055	56	60	if	if	SCONJ
ejpam-4055	56	61	s	s	VERB
ejpam-4055	56	62	is	be	AUX
ejpam-4055	56	63	both	both	PRON
ejpam-4055	56	64	a	a	DET
ejpam-4055	56	65	resolving	resolving	NOUN
ejpam-4055	56	66	set	set	VERB
ejpam-4055	56	67	and	and	CCONJ
ejpam-4055	56	68	a	a	DET
ejpam-4055	56	69	hop	hop	NOUN
ejpam-4055	56	70	dominating	dominating	NOUN
ejpam-4055	56	71	set	set	NOUN
ejpam-4055	56	72	.	.	PUNCT
ejpam-4055	57	1	the	the	DET
ejpam-4055	57	2	minimum	minimum	ADJ
ejpam-4055	57	3	cardinality	cardinality	NOUN
ejpam-4055	57	4	of	of	ADP
ejpam-4055	57	5	a	a	DET
ejpam-4055	57	6	resolving	resolve	VERB
ejpam-4055	57	7	hop	hop	NOUN
ejpam-4055	57	8	dominating	dominating	NOUN
ejpam-4055	57	9	set	set	NOUN
ejpam-4055	57	10	of	of	ADP
ejpam-4055	57	11	g	g	NOUN
ejpam-4055	57	12	,	,	PUNCT
ejpam-4055	57	13	denoted	denote	VERB
ejpam-4055	57	14	by	by	ADP
ejpam-4055	57	15	γrh(g	γrh(g	NOUN
ejpam-4055	57	16	)	)	PUNCT
ejpam-4055	57	17	,	,	PUNCT
ejpam-4055	57	18	is	be	AUX
ejpam-4055	57	19	called	call	VERB
ejpam-4055	57	20	the	the	DET
ejpam-4055	57	21	resolving	resolve	VERB
ejpam-4055	57	22	hop	hop	NOUN
ejpam-4055	57	23	domination	domination	NOUN
ejpam-4055	57	24	number	number	NOUN
ejpam-4055	57	25	of	of	ADP
ejpam-4055	57	26	g.	g.	PROPN
ejpam-4055	57	27	any	any	PRON
ejpam-4055	57	28	resolving	resolve	VERB
ejpam-4055	57	29	hop	hop	NOUN
ejpam-4055	57	30	dominating	dominating	NOUN
ejpam-4055	57	31	set	set	VERB
ejpam-4055	57	32	with	with	ADP
ejpam-4055	57	33	cardinality	cardinality	NOUN
ejpam-4055	57	34	equal	equal	ADJ
ejpam-4055	57	35	to	to	ADP
ejpam-4055	57	36	γrh(g	γrh(g	NOUN
ejpam-4055	57	37	)	)	PUNCT
ejpam-4055	57	38	is	be	AUX
ejpam-4055	57	39	called	call	VERB
ejpam-4055	57	40	a	a	DET
ejpam-4055	57	41	γrh	γrh	NOUN
ejpam-4055	57	42	-	-	PUNCT
ejpam-4055	57	43	set	set	NOUN
ejpam-4055	57	44	.	.	PUNCT
ejpam-4055	58	1	2	2	X
ejpam-4055	58	2	.	.	X
ejpam-4055	58	3	preliminary	preliminary	ADJ
ejpam-4055	58	4	results	result	NOUN
ejpam-4055	58	5	remark	remark	VERB
ejpam-4055	58	6	1	1	NUM
ejpam-4055	58	7	.	.	PUNCT
ejpam-4055	59	1	for	for	ADP
ejpam-4055	59	2	any	any	DET
ejpam-4055	59	3	connected	connected	ADJ
ejpam-4055	59	4	graph	graph	NOUN
ejpam-4055	59	5	g	g	NOUN
ejpam-4055	59	6	of	of	ADP
ejpam-4055	59	7	order	order	NOUN
ejpam-4055	59	8	n	n	PRON
ejpam-4055	59	9	≥	≥	NOUN
ejpam-4055	59	10	2	2	NUM
ejpam-4055	59	11	,	,	PUNCT
ejpam-4055	59	12	2	2	NUM
ejpam-4055	59	13	≤	≤	NUM
ejpam-4055	59	14	γrh(g	γrh(g	NOUN
ejpam-4055	59	15	)	)	PUNCT
ejpam-4055	59	16	≤	≤	NOUN
ejpam-4055	59	17	n.	n.	NOUN
ejpam-4055	59	18	moreover	moreover	ADV
ejpam-4055	59	19	,	,	PUNCT
ejpam-4055	59	20	γrh(p2	γrh(p2	PROPN
ejpam-4055	59	21	)	)	PUNCT
ejpam-4055	59	22	=	=	SYM
ejpam-4055	59	23	2	2	NUM
ejpam-4055	59	24	and	and	CCONJ
ejpam-4055	59	25	γrh(kn	γrh(kn	NUM
ejpam-4055	59	26	)	)	PUNCT
ejpam-4055	60	1	=	=	PUNCT
ejpam-4055	60	2	n.	n.	NOUN
ejpam-4055	60	3	proposition	proposition	NOUN
ejpam-4055	60	4	1	1	NUM
ejpam-4055	60	5	.	.	PUNCT
ejpam-4055	61	1	for	for	ADP
ejpam-4055	61	2	any	any	DET
ejpam-4055	61	3	connected	connected	ADJ
ejpam-4055	61	4	graph	graph	NOUN
ejpam-4055	61	5	g	g	NOUN
ejpam-4055	61	6	of	of	ADP
ejpam-4055	61	7	order	order	NOUN
ejpam-4055	61	8	n	n	PRON
ejpam-4055	61	9	≥	≥	NOUN
ejpam-4055	61	10	2	2	NUM
ejpam-4055	61	11	.	.	PUNCT
ejpam-4055	61	12	then	then	ADV
ejpam-4055	61	13	,	,	PUNCT
ejpam-4055	61	14	γrh(g	γrh(g	PROPN
ejpam-4055	61	15	)	)	PUNCT
ejpam-4055	61	16	=	=	SYM
ejpam-4055	61	17	n	n	NOUN
ejpam-4055	61	18	if	if	SCONJ
ejpam-4055	61	19	and	and	CCONJ
ejpam-4055	61	20	only	only	ADV
ejpam-4055	61	21	if	if	SCONJ
ejpam-4055	61	22	g	g	PROPN
ejpam-4055	61	23	=	=	PROPN
ejpam-4055	61	24	kn	kn	PROPN
ejpam-4055	61	25	.	.	PUNCT
ejpam-4055	62	1	proof	proof	NOUN
ejpam-4055	62	2	:	:	PUNCT
ejpam-4055	62	3	if	if	SCONJ
ejpam-4055	62	4	g	g	PROPN
ejpam-4055	62	5	=	=	SYM
ejpam-4055	62	6	kn	kn	PROPN
ejpam-4055	62	7	,	,	PUNCT
ejpam-4055	62	8	then	then	ADV
ejpam-4055	62	9	γrh(g	γrh(g	PROPN
ejpam-4055	62	10	)	)	PUNCT
ejpam-4055	62	11	=	=	SYM
ejpam-4055	63	1	n.	n.	NOUN
ejpam-4055	63	2	suppose	suppose	VERB
ejpam-4055	63	3	γrh(g	γrh(g	NOUN
ejpam-4055	63	4	)	)	PUNCT
ejpam-4055	63	5	=	=	SYM
ejpam-4055	63	6	n	n	NOUN
ejpam-4055	63	7	and	and	CCONJ
ejpam-4055	63	8	g	g	PROPN
ejpam-4055	63	9	6=	6=	PROPN
ejpam-4055	64	1	kn	kn	PROPN
ejpam-4055	64	2	.	.	PUNCT
ejpam-4055	65	1	then	then	ADV
ejpam-4055	65	2	there	there	PRON
ejpam-4055	65	3	exists	exist	VERB
ejpam-4055	65	4	x	x	X
ejpam-4055	65	5	,	,	PUNCT
ejpam-4055	65	6	y	y	PROPN
ejpam-4055	65	7	∈	∈	PROPN
ejpam-4055	65	8	v	v	ADP
ejpam-4055	65	9	(	(	PUNCT
ejpam-4055	65	10	g	g	NOUN
ejpam-4055	65	11	)	)	PUNCT
ejpam-4055	65	12	such	such	ADJ
ejpam-4055	65	13	that	that	SCONJ
ejpam-4055	65	14	d(x	d(x	PROPN
ejpam-4055	65	15	,	,	PUNCT
ejpam-4055	65	16	y	y	NOUN
ejpam-4055	65	17	)	)	PUNCT
ejpam-4055	65	18	=	=	SYM
ejpam-4055	66	1	2	2	X
ejpam-4055	66	2	.	.	X
ejpam-4055	66	3	let	let	VERB
ejpam-4055	66	4	s	s	NOUN
ejpam-4055	66	5	=	=	X
ejpam-4055	66	6	v	v	ADJ
ejpam-4055	66	7	(	(	PUNCT
ejpam-4055	66	8	g	g	NOUN
ejpam-4055	66	9	)	)	PUNCT
ejpam-4055	66	10	\	\	NOUN
ejpam-4055	66	11	{	{	PUNCT
ejpam-4055	66	12	y	y	NOUN
ejpam-4055	66	13	}	}	PUNCT
ejpam-4055	66	14	)	)	PUNCT
ejpam-4055	66	15	.	.	PUNCT
ejpam-4055	67	1	then	then	ADV
ejpam-4055	67	2	s	s	VERB
ejpam-4055	67	3	is	be	AUX
ejpam-4055	67	4	a	a	DET
ejpam-4055	67	5	resolving	resolve	VERB
ejpam-4055	67	6	hop	hop	NOUN
ejpam-4055	67	7	dominating	dominating	NOUN
ejpam-4055	67	8	set	set	NOUN
ejpam-4055	67	9	of	of	ADP
ejpam-4055	67	10	g.	g.	PROPN
ejpam-4055	67	11	hence	hence	ADV
ejpam-4055	67	12	,	,	PUNCT
ejpam-4055	67	13	γrh(g	γrh(g	PROPN
ejpam-4055	67	14	)	)	PUNCT
ejpam-4055	67	15	≤	≤	NUM
ejpam-4055	67	16	|s|	|s|	PROPN
ejpam-4055	67	17	=	=	SYM
ejpam-4055	67	18	n−	n−	NOUN
ejpam-4055	67	19	1	1	NUM
ejpam-4055	67	20	,	,	PUNCT
ejpam-4055	67	21	a	a	DET
ejpam-4055	67	22	contradiction	contradiction	NOUN
ejpam-4055	67	23	.	.	PUNCT
ejpam-4055	68	1	remark	remark	NOUN
ejpam-4055	68	2	2	2	NUM
ejpam-4055	68	3	.	.	PUNCT
ejpam-4055	69	1	let	let	VERB
ejpam-4055	69	2	g	g	PRON
ejpam-4055	69	3	be	be	AUX
ejpam-4055	69	4	a	a	DET
ejpam-4055	69	5	connected	connected	ADJ
ejpam-4055	69	6	graph	graph	NOUN
ejpam-4055	69	7	and	and	CCONJ
ejpam-4055	69	8	s	s	VERB
ejpam-4055	69	9	⊆	⊆	NUM
ejpam-4055	69	10	v	v	NOUN
ejpam-4055	69	11	(	(	PUNCT
ejpam-4055	69	12	g	g	NOUN
ejpam-4055	69	13	)	)	PUNCT
ejpam-4055	69	14	.	.	PUNCT
ejpam-4055	70	1	then	then	ADV
ejpam-4055	70	2	for	for	ADP
ejpam-4055	70	3	any	any	DET
ejpam-4055	70	4	two	two	NUM
ejpam-4055	70	5	distinct	distinct	ADJ
ejpam-4055	70	6	vertices	vertex	NOUN
ejpam-4055	70	7	x	x	X
ejpam-4055	70	8	,	,	PUNCT
ejpam-4055	70	9	y	y	PROPN
ejpam-4055	70	10	∈	∈	PROPN
ejpam-4055	70	11	v	v	ADP
ejpam-4055	70	12	(	(	PUNCT
ejpam-4055	70	13	g	g	NOUN
ejpam-4055	70	14	)	)	PUNCT
ejpam-4055	70	15	\	\	PROPN
ejpam-4055	70	16	s	s	PART
ejpam-4055	70	17	with	with	ADP
ejpam-4055	70	18	ng(x	ng(x	NUM
ejpam-4055	70	19	,	,	PUNCT
ejpam-4055	70	20	2	2	X
ejpam-4055	70	21	)	)	PUNCT
ejpam-4055	70	22	∩	∩	X
ejpam-4055	70	23	s	s	PART
ejpam-4055	70	24	6=	6=	PROPN
ejpam-4055	70	25	ng(y	ng(y	NOUN
ejpam-4055	70	26	,	,	PUNCT
ejpam-4055	70	27	2	2	X
ejpam-4055	70	28	)	)	PUNCT
ejpam-4055	70	29	∩	∩	NOUN
ejpam-4055	70	30	s	s	X
ejpam-4055	70	31	,	,	PUNCT
ejpam-4055	70	32	we	we	PRON
ejpam-4055	70	33	have	have	AUX
ejpam-4055	70	34	rg(x	rg(x	X
ejpam-4055	70	35	/	/	SYM
ejpam-4055	70	36	s	s	NOUN
ejpam-4055	70	37	)	)	PUNCT
ejpam-4055	70	38	6=	6=	ADP
ejpam-4055	70	39	rg(y	rg(y	NOUN
ejpam-4055	70	40	/	/	SYM
ejpam-4055	70	41	s	s	NOUN
ejpam-4055	70	42	)	)	PUNCT
ejpam-4055	70	43	.	.	PUNCT
ejpam-4055	71	1	remark	remark	PROPN
ejpam-4055	71	2	3	3	NUM
ejpam-4055	71	3	.	.	PUNCT
ejpam-4055	72	1	every	every	DET
ejpam-4055	72	2	resolving	resolve	VERB
ejpam-4055	72	3	hop	hop	NOUN
ejpam-4055	72	4	dominating	dominating	NOUN
ejpam-4055	72	5	set	set	NOUN
ejpam-4055	72	6	of	of	ADP
ejpam-4055	72	7	a	a	DET
ejpam-4055	72	8	connected	connected	ADJ
ejpam-4055	72	9	graph	graph	NOUN
ejpam-4055	72	10	g	g	PROPN
ejpam-4055	72	11	is	be	AUX
ejpam-4055	72	12	a	a	DET
ejpam-4055	72	13	resolving	resolving	NOUN
ejpam-4055	72	14	set	set	NOUN
ejpam-4055	72	15	of	of	ADP
ejpam-4055	72	16	g.	g.	PROPN
ejpam-4055	72	17	thus	thus	ADV
ejpam-4055	72	18	,	,	PUNCT
ejpam-4055	72	19	dim(g	dim(g	PROPN
ejpam-4055	72	20	)	)	PUNCT
ejpam-4055	72	21	≤	≤	NUM
ejpam-4055	72	22	γrh(g	γrh(g	NOUN
ejpam-4055	72	23	)	)	PUNCT
ejpam-4055	72	24	.	.	PUNCT
ejpam-4055	73	1	proposition	proposition	NOUN
ejpam-4055	73	2	2	2	NUM
ejpam-4055	73	3	.	.	PUNCT
ejpam-4055	74	1	let	let	VERB
ejpam-4055	74	2	g	g	PRON
ejpam-4055	74	3	be	be	AUX
ejpam-4055	74	4	a	a	DET
ejpam-4055	74	5	connected	connected	ADJ
ejpam-4055	74	6	graph	graph	NOUN
ejpam-4055	74	7	of	of	ADP
ejpam-4055	74	8	order	order	NOUN
ejpam-4055	74	9	4	4	NUM
ejpam-4055	74	10	.	.	PUNCT
ejpam-4055	74	11	then	then	ADV
ejpam-4055	74	12	γrh(g	γrh(g	NOUN
ejpam-4055	74	13	)	)	PUNCT
ejpam-4055	74	14	=	=	SYM
ejpam-4055	74	15	2	2	NUM
ejpam-4055	74	16	if	if	SCONJ
ejpam-4055	74	17	and	and	CCONJ
ejpam-4055	74	18	only	only	ADV
ejpam-4055	74	19	if	if	SCONJ
ejpam-4055	74	20	g	g	PROPN
ejpam-4055	74	21	=	=	SYM
ejpam-4055	74	22	c4	c4	NOUN
ejpam-4055	74	23	or	or	CCONJ
ejpam-4055	74	24	g	g	NOUN
ejpam-4055	74	25	=	=	PUNCT
ejpam-4055	74	26	p4	p4	ADJ
ejpam-4055	74	27	.	.	PUNCT
ejpam-4055	75	1	proof	proof	NOUN
ejpam-4055	75	2	:	:	PUNCT
ejpam-4055	75	3	if	if	SCONJ
ejpam-4055	75	4	g	g	PROPN
ejpam-4055	75	5	=	=	SYM
ejpam-4055	75	6	c4	c4	NOUN
ejpam-4055	75	7	or	or	CCONJ
ejpam-4055	75	8	p4	p4	ADJ
ejpam-4055	75	9	,	,	PUNCT
ejpam-4055	75	10	then	then	ADV
ejpam-4055	75	11	γrh(g	γrh(g	PROPN
ejpam-4055	75	12	)	)	PUNCT
ejpam-4055	75	13	=	=	SYM
ejpam-4055	75	14	2	2	X
ejpam-4055	75	15	.	.	PUNCT
ejpam-4055	75	16	suppose	suppose	VERB
ejpam-4055	75	17	that	that	SCONJ
ejpam-4055	75	18	γrh(g	γrh(g	NOUN
ejpam-4055	75	19	)	)	PUNCT
ejpam-4055	75	20	=	=	SYM
ejpam-4055	75	21	2	2	X
ejpam-4055	75	22	.	.	X
ejpam-4055	75	23	let	let	VERB
ejpam-4055	75	24	w	w	VERB
ejpam-4055	75	25	=	=	PUNCT
ejpam-4055	75	26	{	{	PUNCT
ejpam-4055	75	27	x1	x1	PROPN
ejpam-4055	75	28	,	,	PUNCT
ejpam-4055	75	29	x2	x2	PROPN
ejpam-4055	75	30	}	}	PUNCT
ejpam-4055	75	31	be	be	VERB
ejpam-4055	75	32	a	a	DET
ejpam-4055	75	33	γrh	γrh	NOUN
ejpam-4055	75	34	-	-	PUNCT
ejpam-4055	75	35	set	set	NOUN
ejpam-4055	75	36	of	of	ADP
ejpam-4055	75	37	g.	g.	PROPN
ejpam-4055	75	38	since	since	SCONJ
ejpam-4055	75	39	w	w	PROPN
ejpam-4055	75	40	is	be	AUX
ejpam-4055	75	41	a	a	DET
ejpam-4055	75	42	hop	hop	NOUN
ejpam-4055	75	43	dominating	dominating	NOUN
ejpam-4055	75	44	set	set	NOUN
ejpam-4055	75	45	,	,	PUNCT
ejpam-4055	75	46	possible	possible	ADJ
ejpam-4055	75	47	representations	representation	NOUN
ejpam-4055	75	48	of	of	ADP
ejpam-4055	75	49	distinct	distinct	ADJ
ejpam-4055	75	50	vertices	vertex	NOUN
ejpam-4055	75	51	u	u	NOUN
ejpam-4055	75	52	,	,	PUNCT
ejpam-4055	75	53	v	v	NOUN
ejpam-4055	75	54	∈	∈	PROPN
ejpam-4055	75	55	v	v	NOUN
ejpam-4055	75	56	(	(	PUNCT
ejpam-4055	75	57	g	g	NOUN
ejpam-4055	75	58	)	)	PUNCT
ejpam-4055	76	1	\w	\w	ADJ
ejpam-4055	76	2	are	be	AUX
ejpam-4055	76	3	(	(	PUNCT
ejpam-4055	76	4	1,2	1,2	NUM
ejpam-4055	76	5	)	)	PUNCT
ejpam-4055	76	6	,	,	PUNCT
ejpam-4055	76	7	(	(	PUNCT
ejpam-4055	76	8	2,1	2,1	NUM
ejpam-4055	76	9	)	)	PUNCT
ejpam-4055	76	10	or	or	CCONJ
ejpam-4055	76	11	(	(	PUNCT
ejpam-4055	76	12	2,2	2,2	NUM
ejpam-4055	76	13	)	)	PUNCT
ejpam-4055	76	14	.	.	PUNCT
ejpam-4055	77	1	clearly	clearly	ADV
ejpam-4055	77	2	(	(	PUNCT
ejpam-4055	77	3	2,2	2,2	NUM
ejpam-4055	77	4	)	)	PUNCT
ejpam-4055	77	5	can	can	AUX
ejpam-4055	77	6	not	not	PART
ejpam-4055	77	7	be	be	AUX
ejpam-4055	77	8	a	a	DET
ejpam-4055	77	9	representation	representation	NOUN
ejpam-4055	77	10	of	of	ADP
ejpam-4055	77	11	vertex	vertex	NOUN
ejpam-4055	77	12	u	u	NOUN
ejpam-4055	77	13	or	or	CCONJ
ejpam-4055	77	14	v	v	NOUN
ejpam-4055	77	15	since	since	SCONJ
ejpam-4055	77	16	g	g	PROPN
ejpam-4055	77	17	is	be	AUX
ejpam-4055	77	18	of	of	ADP
ejpam-4055	77	19	order	order	NOUN
ejpam-4055	77	20	4	4	NUM
ejpam-4055	77	21	.	.	PUNCT
ejpam-4055	78	1	thus	thus	ADV
ejpam-4055	78	2	we	we	PRON
ejpam-4055	78	3	consider	consider	VERB
ejpam-4055	78	4	the	the	DET
ejpam-4055	78	5	following	follow	VERB
ejpam-4055	78	6	cases	case	NOUN
ejpam-4055	78	7	:	:	PUNCT
ejpam-4055	78	8	case	case	NOUN
ejpam-4055	78	9	1	1	NUM
ejpam-4055	78	10	.	.	PUNCT
ejpam-4055	78	11	rg(u	rg(u	PROPN
ejpam-4055	78	12	/	/	SYM
ejpam-4055	78	13	w	w	NOUN
ejpam-4055	78	14	)	)	PUNCT
ejpam-4055	78	15	=	=	SYM
ejpam-4055	78	16	(	(	PUNCT
ejpam-4055	78	17	1	1	NUM
ejpam-4055	78	18	,	,	PUNCT
ejpam-4055	78	19	2	2	NUM
ejpam-4055	78	20	)	)	PUNCT
ejpam-4055	78	21	and	and	CCONJ
ejpam-4055	78	22	rg(v	rg(v	PROPN
ejpam-4055	78	23	/	/	SYM
ejpam-4055	78	24	w	w	NOUN
ejpam-4055	78	25	)	)	PUNCT
ejpam-4055	79	1	=	=	SYM
ejpam-4055	79	2	(	(	PUNCT
ejpam-4055	79	3	2	2	NUM
ejpam-4055	79	4	,	,	PUNCT
ejpam-4055	79	5	1	1	NUM
ejpam-4055	79	6	)	)	PUNCT
ejpam-4055	79	7	case	case	NOUN
ejpam-4055	79	8	2	2	NUM
ejpam-4055	79	9	.	.	NUM
ejpam-4055	79	10	rg(u	rg(u	X
ejpam-4055	79	11	/	/	SYM
ejpam-4055	79	12	w	w	NOUN
ejpam-4055	79	13	)	)	PUNCT
ejpam-4055	79	14	=	=	SYM
ejpam-4055	79	15	(	(	PUNCT
ejpam-4055	79	16	2	2	NUM
ejpam-4055	79	17	,	,	PUNCT
ejpam-4055	79	18	1	1	NUM
ejpam-4055	79	19	)	)	PUNCT
ejpam-4055	79	20	and	and	CCONJ
ejpam-4055	79	21	rg(v	rg(v	PROPN
ejpam-4055	79	22	/	/	SYM
ejpam-4055	79	23	w	w	NOUN
ejpam-4055	79	24	)	)	PUNCT
ejpam-4055	80	1	=	=	SYM
ejpam-4055	80	2	(	(	PUNCT
ejpam-4055	80	3	1	1	NUM
ejpam-4055	80	4	,	,	PUNCT
ejpam-4055	80	5	2	2	NUM
ejpam-4055	80	6	)	)	PUNCT
ejpam-4055	80	7	for	for	ADP
ejpam-4055	80	8	case	case	NOUN
ejpam-4055	80	9	1	1	NUM
ejpam-4055	80	10	,	,	PUNCT
ejpam-4055	80	11	ux1	ux1	NOUN
ejpam-4055	80	12	,	,	PUNCT
ejpam-4055	80	13	vx2	vx2	X
ejpam-4055	80	14	∈	∈	PROPN
ejpam-4055	80	15	e(g	e(g	PROPN
ejpam-4055	80	16	)	)	PUNCT
ejpam-4055	80	17	and	and	CCONJ
ejpam-4055	80	18	either	either	ADV
ejpam-4055	80	19	x1x2	x1x2	PUNCT
ejpam-4055	80	20	∈	∈	PROPN
ejpam-4055	80	21	e(g	e(g	PROPN
ejpam-4055	80	22	)	)	PUNCT
ejpam-4055	80	23	or	or	CCONJ
ejpam-4055	80	24	uv	uv	NOUN
ejpam-4055	80	25	∈	∈	PROPN
ejpam-4055	80	26	e(g	e(g	PROPN
ejpam-4055	80	27	)	)	PUNCT
ejpam-4055	80	28	or	or	CCONJ
ejpam-4055	80	29	both	both	PRON
ejpam-4055	80	30	x1x2	x1x2	PUNCT
ejpam-4055	80	31	,	,	PUNCT
ejpam-4055	80	32	uv	uv	PROPN
ejpam-4055	80	33	∈	∈	PROPN
ejpam-4055	80	34	e(g	e(g	PROPN
ejpam-4055	80	35	)	)	PUNCT
ejpam-4055	80	36	.	.	PUNCT
ejpam-4055	81	1	hence	hence	ADV
ejpam-4055	81	2	,	,	PUNCT
ejpam-4055	81	3	g	g	PROPN
ejpam-4055	81	4	=	=	PUNCT
ejpam-4055	82	1	[	[	X
ejpam-4055	82	2	u	u	NOUN
ejpam-4055	82	3	,	,	PUNCT
ejpam-4055	82	4	x1	x1	PROPN
ejpam-4055	82	5	,	,	PUNCT
ejpam-4055	82	6	x2	x2	PROPN
ejpam-4055	82	7	,	,	PUNCT
ejpam-4055	82	8	v	v	NOUN
ejpam-4055	82	9	]	]	PUNCT
ejpam-4055	82	10	or	or	CCONJ
ejpam-4055	82	11	g	g	NOUN
ejpam-4055	82	12	=	=	SYM
ejpam-4055	83	1	[	[	X
ejpam-4055	83	2	x1	x1	PROPN
ejpam-4055	83	3	,	,	PUNCT
ejpam-4055	83	4	u	u	NOUN
ejpam-4055	83	5	,	,	PUNCT
ejpam-4055	83	6	v	v	NOUN
ejpam-4055	83	7	,	,	PUNCT
ejpam-4055	83	8	x2	x2	PROPN
ejpam-4055	83	9	]	]	PUNCT
ejpam-4055	83	10	or	or	CCONJ
ejpam-4055	83	11	g	g	NOUN
ejpam-4055	83	12	=	=	SYM
ejpam-4055	84	1	[	[	X
ejpam-4055	84	2	u	u	NOUN
ejpam-4055	84	3	,	,	PUNCT
ejpam-4055	84	4	x1	x1	PROPN
ejpam-4055	84	5	,	,	PUNCT
ejpam-4055	84	6	x2	x2	PROPN
ejpam-4055	84	7	,	,	PUNCT
ejpam-4055	84	8	v	v	NOUN
ejpam-4055	84	9	,	,	PUNCT
ejpam-4055	84	10	u	u	NOUN
ejpam-4055	84	11	]	]	X
ejpam-4055	84	12	.	.	PUNCT
ejpam-4055	85	1	thus	thus	ADV
ejpam-4055	85	2	,	,	PUNCT
ejpam-4055	85	3	g	g	PROPN
ejpam-4055	85	4	is	be	AUX
ejpam-4055	85	5	either	either	CCONJ
ejpam-4055	85	6	a	a	DET
ejpam-4055	85	7	path	path	NOUN
ejpam-4055	85	8	p4	p4	NOUN
ejpam-4055	85	9	or	or	CCONJ
ejpam-4055	85	10	a	a	DET
ejpam-4055	85	11	cycle	cycle	NOUN
ejpam-4055	85	12	c4	c4	NOUN
ejpam-4055	85	13	.	.	PUNCT
ejpam-4055	86	1	similarly	similarly	ADV
ejpam-4055	86	2	,	,	PUNCT
ejpam-4055	86	3	if	if	SCONJ
ejpam-4055	86	4	case	case	NOUN
ejpam-4055	86	5	2	2	NUM
ejpam-4055	86	6	holds	hold	VERB
ejpam-4055	86	7	,	,	PUNCT
ejpam-4055	86	8	then	then	ADV
ejpam-4055	86	9	g	g	PROPN
ejpam-4055	86	10	=	=	PUNCT
ejpam-4055	86	11	p4	p4	ADJ
ejpam-4055	86	12	or	or	CCONJ
ejpam-4055	86	13	g	g	NOUN
ejpam-4055	86	14	=	=	NOUN
ejpam-4055	86	15	c4	c4	NOUN
ejpam-4055	86	16	.	.	PUNCT
ejpam-4055	87	1	proposition	proposition	NOUN
ejpam-4055	87	2	3	3	NUM
ejpam-4055	87	3	.	.	PUNCT
ejpam-4055	88	1	let	let	VERB
ejpam-4055	88	2	n	n	PRON
ejpam-4055	88	3	be	be	AUX
ejpam-4055	88	4	a	a	DET
ejpam-4055	88	5	positive	positive	ADJ
ejpam-4055	88	6	number	number	NOUN
ejpam-4055	88	7	.	.	PUNCT
ejpam-4055	89	1	(	(	PUNCT
ejpam-4055	89	2	i	i	NOUN
ejpam-4055	89	3	)	)	PUNCT
ejpam-4055	89	4	for	for	ADP
ejpam-4055	89	5	a	a	DET
ejpam-4055	89	6	path	path	NOUN
ejpam-4055	89	7	pn	pn	NOUN
ejpam-4055	89	8	on	on	ADP
ejpam-4055	89	9	n	n	PRON
ejpam-4055	89	10	vertices	vertex	NOUN
ejpam-4055	89	11	,	,	PUNCT
ejpam-4055	89	12	n	n	CCONJ
ejpam-4055	89	13	>	>	X
ejpam-4055	89	14	1	1	NUM
ejpam-4055	89	15	j.	j.	PROPN
ejpam-4055	89	16	mohamad	mohamad	PROPN
ejpam-4055	89	17	,	,	PUNCT
ejpam-4055	89	18	h.	h.	PROPN
ejpam-4055	89	19	rara	rara	PROPN
ejpam-4055	89	20	/	/	SYM
ejpam-4055	89	21	eur	eur	PROPN
ejpam-4055	89	22	.	.	PUNCT
ejpam-4055	90	1	j.	j.	PROPN
ejpam-4055	90	2	pure	pure	PROPN
ejpam-4055	90	3	appl	appl	PROPN
ejpam-4055	90	4	.	.	PROPN
ejpam-4055	90	5	math	math	PROPN
ejpam-4055	90	6	,	,	PUNCT
ejpam-4055	90	7	14	14	NUM
ejpam-4055	90	8	(	(	PUNCT
ejpam-4055	90	9	3	3	NUM
ejpam-4055	90	10	)	)	PUNCT
ejpam-4055	90	11	(	(	PUNCT
ejpam-4055	90	12	2021	2021	NUM
ejpam-4055	90	13	)	)	PUNCT
ejpam-4055	90	14	,	,	PUNCT
ejpam-4055	90	15	1015	1015	NUM
ejpam-4055	90	16	-	-	SYM
ejpam-4055	90	17	1023	1023	NUM
ejpam-4055	90	18	1018	1018	NUM
ejpam-4055	90	19	γrh(pn	γrh(pn	NOUN
ejpam-4055	90	20	)	)	PUNCT
ejpam-4055	90	21	=	=	SYM
ejpam-4055	90	22			NUM
ejpam-4055	90	23	2	2	NUM
ejpam-4055	90	24	if	if	SCONJ
ejpam-4055	90	25	n	n	NOUN
ejpam-4055	90	26	=	=	SYM
ejpam-4055	90	27	2	2	NUM
ejpam-4055	90	28	,	,	PUNCT
ejpam-4055	90	29	3	3	NUM
ejpam-4055	90	30	,	,	PUNCT
ejpam-4055	90	31	4	4	NUM
ejpam-4055	90	32	,	,	PUNCT
ejpam-4055	90	33	5	5	NUM
ejpam-4055	90	34	2r	2r	NUM
ejpam-4055	90	35	if	if	SCONJ
ejpam-4055	90	36	n	n	NOUN
ejpam-4055	90	37	=	=	SYM
ejpam-4055	90	38	6r	6r	NUM
ejpam-4055	90	39	2r	2r	NUM
ejpam-4055	91	1	+	+	CCONJ
ejpam-4055	91	2	1	1	NUM
ejpam-4055	91	3	if	if	SCONJ
ejpam-4055	91	4	n	n	ADV
ejpam-4055	91	5	=	=	SYM
ejpam-4055	92	1	6r	6r	NUM
ejpam-4055	92	2	+	+	CCONJ
ejpam-4055	92	3	1	1	NUM
ejpam-4055	92	4	2r	2r	NUM
ejpam-4055	92	5	+	+	CCONJ
ejpam-4055	92	6	2	2	NUM
ejpam-4055	92	7	if	if	SCONJ
ejpam-4055	92	8	n	n	NOUN
ejpam-4055	92	9	=	=	SYM
ejpam-4055	92	10	6r	6r	NUM
ejpam-4055	93	1	+	+	SYM
ejpam-4055	93	2	s	s	X
ejpam-4055	93	3	;	;	PUNCT
ejpam-4055	93	4	2	2	NUM
ejpam-4055	93	5	≤	≤	NOUN
ejpam-4055	93	6	s	s	PART
ejpam-4055	93	7	≤	≤	NUM
ejpam-4055	93	8	5	5	NUM
ejpam-4055	93	9	.	.	PUNCT
ejpam-4055	94	1	(	(	PUNCT
ejpam-4055	94	2	ii	ii	NOUN
ejpam-4055	94	3	)	)	PUNCT
ejpam-4055	94	4	for	for	ADP
ejpam-4055	94	5	a	a	DET
ejpam-4055	94	6	cycle	cycle	NOUN
ejpam-4055	94	7	cn	cn	NOUN
ejpam-4055	94	8	of	of	ADP
ejpam-4055	94	9	length	length	NOUN
ejpam-4055	94	10	n	n	CCONJ
ejpam-4055	94	11	,	,	PUNCT
ejpam-4055	94	12	γrh(cn	γrh(cn	NOUN
ejpam-4055	94	13	)	)	PUNCT
ejpam-4055	94	14	=	=	PUNCT
ejpam-4055	94	15			NUM
ejpam-4055	94	16	2	2	NUM
ejpam-4055	94	17	if	if	SCONJ
ejpam-4055	94	18	n	n	X
ejpam-4055	94	19	=	=	SYM
ejpam-4055	94	20	4	4	NUM
ejpam-4055	94	21	,	,	PUNCT
ejpam-4055	94	22	5	5	NUM
ejpam-4055	94	23	2r	2r	NUM
ejpam-4055	94	24	if	if	SCONJ
ejpam-4055	94	25	n	n	NOUN
ejpam-4055	94	26	=	=	SYM
ejpam-4055	94	27	6r	6r	NUM
ejpam-4055	94	28	2r	2r	NUM
ejpam-4055	95	1	+	+	CCONJ
ejpam-4055	95	2	1	1	NUM
ejpam-4055	95	3	if	if	SCONJ
ejpam-4055	95	4	n	n	ADV
ejpam-4055	95	5	=	=	SYM
ejpam-4055	96	1	6r	6r	NUM
ejpam-4055	96	2	+	+	CCONJ
ejpam-4055	96	3	1	1	NUM
ejpam-4055	96	4	2r	2r	NUM
ejpam-4055	96	5	+	+	CCONJ
ejpam-4055	96	6	2	2	NUM
ejpam-4055	96	7	if	if	SCONJ
ejpam-4055	96	8	n	n	NOUN
ejpam-4055	96	9	=	=	SYM
ejpam-4055	96	10	6r	6r	NUM
ejpam-4055	97	1	+	+	SYM
ejpam-4055	97	2	s	s	X
ejpam-4055	97	3	;	;	PUNCT
ejpam-4055	97	4	2	2	NUM
ejpam-4055	97	5	≤	≤	NOUN
ejpam-4055	97	6	s	s	PART
ejpam-4055	97	7	≤	≤	NOUN
ejpam-4055	97	8	5	5	NUM
ejpam-4055	97	9	.	.	NOUN
ejpam-4055	97	10	3	3	X
ejpam-4055	97	11	.	.	X
ejpam-4055	97	12	on	on	ADP
ejpam-4055	97	13	resolving	resolve	VERB
ejpam-4055	97	14	hop	hop	NOUN
ejpam-4055	97	15	domination	domination	NOUN
ejpam-4055	97	16	in	in	ADP
ejpam-4055	97	17	the	the	DET
ejpam-4055	97	18	join	join	NOUN
ejpam-4055	97	19	of	of	ADP
ejpam-4055	97	20	graphs	graph	NOUN
ejpam-4055	97	21	the	the	DET
ejpam-4055	97	22	join	join	NOUN
ejpam-4055	97	23	of	of	ADP
ejpam-4055	97	24	two	two	NUM
ejpam-4055	97	25	graphs	graph	NOUN
ejpam-4055	97	26	g	g	NOUN
ejpam-4055	98	1	and	and	CCONJ
ejpam-4055	98	2	h	h	NOUN
ejpam-4055	98	3	is	be	AUX
ejpam-4055	98	4	the	the	DET
ejpam-4055	98	5	graph	graph	NOUN
ejpam-4055	98	6	g	g	NOUN
ejpam-4055	98	7	+	+	CCONJ
ejpam-4055	98	8	h	h	NOUN
ejpam-4055	98	9	with	with	ADP
ejpam-4055	98	10	vertex	vertex	NOUN
ejpam-4055	98	11	set	set	VERB
ejpam-4055	98	12	v	v	NOUN
ejpam-4055	98	13	(	(	PUNCT
ejpam-4055	98	14	g	g	PROPN
ejpam-4055	98	15	+	+	NOUN
ejpam-4055	98	16	h	h	NOUN
ejpam-4055	98	17	)	)	PUNCT
ejpam-4055	99	1	=	=	NOUN
ejpam-4055	99	2	v	v	X
ejpam-4055	99	3	(	(	PUNCT
ejpam-4055	99	4	g	g	NOUN
ejpam-4055	99	5	)	)	PUNCT
ejpam-4055	99	6	•	•	ADP
ejpam-4055	99	7	∪	∪	X
ejpam-4055	99	8	v	v	NOUN
ejpam-4055	99	9	(	(	PUNCT
ejpam-4055	99	10	h	h	NOUN
ejpam-4055	99	11	)	)	PUNCT
ejpam-4055	99	12	and	and	CCONJ
ejpam-4055	99	13	edge	edge	NOUN
ejpam-4055	99	14	set	set	VERB
ejpam-4055	99	15	e(g	e(g	PROPN
ejpam-4055	100	1	+	+	CCONJ
ejpam-4055	100	2	h	h	NOUN
ejpam-4055	100	3	)	)	PUNCT
ejpam-4055	100	4	=	=	SYM
ejpam-4055	100	5	e(g	e(g	PROPN
ejpam-4055	100	6	)	)	PUNCT
ejpam-4055	101	1	•	•	ADP
ejpam-4055	101	2	∪	∪	ADP
ejpam-4055	101	3	e(h	e(h	PROPN
ejpam-4055	101	4	)	)	PUNCT
ejpam-4055	101	5	∪	∪	NOUN
ejpam-4055	101	6	{	{	PUNCT
ejpam-4055	101	7	uv	uv	NOUN
ejpam-4055	101	8	:	:	PUNCT
ejpam-4055	101	9	u	u	PROPN
ejpam-4055	101	10	∈	∈	PROPN
ejpam-4055	101	11	v	v	ADP
ejpam-4055	101	12	(	(	PUNCT
ejpam-4055	101	13	g	g	NOUN
ejpam-4055	101	14	)	)	PUNCT
ejpam-4055	101	15	,	,	PUNCT
ejpam-4055	101	16	v	v	X
ejpam-4055	101	17	∈	∈	PROPN
ejpam-4055	101	18	v	v	NOUN
ejpam-4055	101	19	(	(	PUNCT
ejpam-4055	101	20	h	h	NOUN
ejpam-4055	101	21	)	)	PUNCT
ejpam-4055	101	22	}	}	PUNCT
ejpam-4055	101	23	.	.	PUNCT
ejpam-4055	102	1	theorem	theorem	NOUN
ejpam-4055	102	2	1	1	NUM
ejpam-4055	102	3	.	.	PUNCT
ejpam-4055	103	1	[	[	X
ejpam-4055	103	2	7	7	NUM
ejpam-4055	103	3	,	,	PUNCT
ejpam-4055	103	4	8	8	NUM
ejpam-4055	103	5	]	]	PUNCT
ejpam-4055	103	6	let	let	VERB
ejpam-4055	103	7	g	g	NOUN
ejpam-4055	103	8	and	and	CCONJ
ejpam-4055	103	9	h	h	PROPN
ejpam-4055	103	10	be	be	VERB
ejpam-4055	103	11	non	non	ADJ
ejpam-4055	103	12	-	-	ADJ
ejpam-4055	103	13	trivial	trivial	ADJ
ejpam-4055	103	14	connected	connected	ADJ
ejpam-4055	103	15	graphs	graph	NOUN
ejpam-4055	103	16	.	.	PUNCT
ejpam-4055	104	1	a	a	DET
ejpam-4055	104	2	set	set	NOUN
ejpam-4055	104	3	w	w	PROPN
ejpam-4055	104	4	⊆	⊆	NUM
ejpam-4055	104	5	v	v	NOUN
ejpam-4055	104	6	(	(	PUNCT
ejpam-4055	104	7	g+h	g+h	NOUN
ejpam-4055	104	8	)	)	PUNCT
ejpam-4055	104	9	is	be	AUX
ejpam-4055	104	10	a	a	DET
ejpam-4055	104	11	resolving	resolving	NOUN
ejpam-4055	104	12	set	set	NOUN
ejpam-4055	104	13	of	of	ADP
ejpam-4055	104	14	g+h	g+h	PROPN
ejpam-4055	104	15	if	if	SCONJ
ejpam-4055	104	16	and	and	CCONJ
ejpam-4055	104	17	only	only	ADV
ejpam-4055	104	18	if	if	SCONJ
ejpam-4055	104	19	w	w	PROPN
ejpam-4055	104	20	=	=	PROPN
ejpam-4055	104	21	wg∪wh	wg∪wh	PROPN
ejpam-4055	104	22	where	where	SCONJ
ejpam-4055	104	23	wg	wg	VERB
ejpam-4055	104	24	⊆	⊆	NUM
ejpam-4055	104	25	v	v	NOUN
ejpam-4055	104	26	(	(	PUNCT
ejpam-4055	104	27	g	g	NOUN
ejpam-4055	104	28	)	)	PUNCT
ejpam-4055	104	29	and	and	CCONJ
ejpam-4055	104	30	wh	wh	VERB
ejpam-4055	104	31	⊆	⊆	NUM
ejpam-4055	104	32	v	v	NOUN
ejpam-4055	104	33	(	(	PUNCT
ejpam-4055	104	34	h	h	NOUN
ejpam-4055	104	35	)	)	PUNCT
ejpam-4055	104	36	are	be	AUX
ejpam-4055	104	37	locating	locate	VERB
ejpam-4055	104	38	sets	set	NOUN
ejpam-4055	104	39	of	of	ADP
ejpam-4055	104	40	g	g	PROPN
ejpam-4055	104	41	and	and	CCONJ
ejpam-4055	104	42	h	h	NOUN
ejpam-4055	104	43	,	,	PUNCT
ejpam-4055	104	44	respectively	respectively	ADV
ejpam-4055	104	45	,	,	PUNCT
ejpam-4055	104	46	where	where	SCONJ
ejpam-4055	104	47	wg	wg	NOUN
ejpam-4055	104	48	or	or	CCONJ
ejpam-4055	104	49	wh	wh	PROPN
ejpam-4055	104	50	is	be	AUX
ejpam-4055	104	51	a	a	DET
ejpam-4055	104	52	strictly	strictly	ADV
ejpam-4055	104	53	locating	locate	VERB
ejpam-4055	104	54	set	set	NOUN
ejpam-4055	104	55	.	.	PUNCT
ejpam-4055	105	1	theorem	theorem	NOUN
ejpam-4055	105	2	2	2	NUM
ejpam-4055	105	3	.	.	PUNCT
ejpam-4055	106	1	let	let	VERB
ejpam-4055	106	2	g	g	NOUN
ejpam-4055	106	3	and	and	CCONJ
ejpam-4055	106	4	h	h	PROPN
ejpam-4055	106	5	be	be	VERB
ejpam-4055	106	6	non	non	ADJ
ejpam-4055	106	7	-	-	ADJ
ejpam-4055	106	8	trivial	trivial	ADJ
ejpam-4055	106	9	connected	connected	ADJ
ejpam-4055	106	10	graphs	graph	NOUN
ejpam-4055	106	11	.	.	PUNCT
ejpam-4055	107	1	a	a	DET
ejpam-4055	107	2	set	set	NOUN
ejpam-4055	107	3	w	w	PROPN
ejpam-4055	107	4	⊆	⊆	NUM
ejpam-4055	107	5	v	v	NOUN
ejpam-4055	107	6	(	(	PUNCT
ejpam-4055	107	7	g	g	PROPN
ejpam-4055	107	8	+	+	NOUN
ejpam-4055	107	9	h	h	NOUN
ejpam-4055	107	10	)	)	PUNCT
ejpam-4055	107	11	is	be	AUX
ejpam-4055	107	12	a	a	DET
ejpam-4055	107	13	resolving	resolve	VERB
ejpam-4055	107	14	hop	hop	NOUN
ejpam-4055	107	15	dominating	dominating	NOUN
ejpam-4055	107	16	set	set	NOUN
ejpam-4055	107	17	of	of	ADP
ejpam-4055	107	18	g+h	g+h	PROPN
ejpam-4055	108	1	if	if	SCONJ
ejpam-4055	108	2	and	and	CCONJ
ejpam-4055	108	3	only	only	ADV
ejpam-4055	108	4	if	if	SCONJ
ejpam-4055	108	5	w	w	PROPN
ejpam-4055	108	6	=	=	VERB
ejpam-4055	108	7	wg	wg	PROPN
ejpam-4055	108	8	∪wh	∪wh	NOUN
ejpam-4055	108	9	where	where	SCONJ
ejpam-4055	108	10	wg	wg	PROPN
ejpam-4055	108	11	and	and	CCONJ
ejpam-4055	108	12	wh	wh	PROPN
ejpam-4055	108	13	are	be	AUX
ejpam-4055	108	14	strictly	strictly	ADV
ejpam-4055	108	15	locating	locate	VERB
ejpam-4055	108	16	sets	set	NOUN
ejpam-4055	108	17	of	of	ADP
ejpam-4055	108	18	g	g	PROPN
ejpam-4055	108	19	and	and	CCONJ
ejpam-4055	108	20	h	h	NOUN
ejpam-4055	108	21	,	,	PUNCT
ejpam-4055	108	22	respectively	respectively	ADV
ejpam-4055	108	23	.	.	PUNCT
ejpam-4055	109	1	proof	proof	NOUN
ejpam-4055	109	2	:	:	PUNCT
ejpam-4055	109	3	suppose	suppose	VERB
ejpam-4055	109	4	that	that	SCONJ
ejpam-4055	109	5	w	w	NOUN
ejpam-4055	109	6	is	be	AUX
ejpam-4055	109	7	a	a	DET
ejpam-4055	109	8	resolving	resolve	VERB
ejpam-4055	109	9	hop	hop	NOUN
ejpam-4055	109	10	dominating	dominating	NOUN
ejpam-4055	109	11	set	set	NOUN
ejpam-4055	109	12	of	of	ADP
ejpam-4055	109	13	g	g	PROPN
ejpam-4055	109	14	+	+	CCONJ
ejpam-4055	109	15	h.	h.	PROPN
ejpam-4055	109	16	then	then	ADV
ejpam-4055	109	17	w	w	PROPN
ejpam-4055	109	18	is	be	AUX
ejpam-4055	109	19	a	a	DET
ejpam-4055	109	20	resolving	resolving	NOUN
ejpam-4055	109	21	set	set	NOUN
ejpam-4055	109	22	of	of	ADP
ejpam-4055	109	23	g	g	PROPN
ejpam-4055	109	24	+	+	CCONJ
ejpam-4055	109	25	h.	h.	PROPN
ejpam-4055	109	26	by	by	ADP
ejpam-4055	109	27	theorem	theorem	NOUN
ejpam-4055	109	28	1	1	NUM
ejpam-4055	109	29	,	,	PUNCT
ejpam-4055	109	30	w	w	NOUN
ejpam-4055	109	31	=	=	PUNCT
ejpam-4055	109	32	wg	wg	PROPN
ejpam-4055	109	33	∪	∪	ADJ
ejpam-4055	109	34	wh	wh	VERB
ejpam-4055	109	35	where	where	SCONJ
ejpam-4055	109	36	wg	wg	VERB
ejpam-4055	109	37	⊆	⊆	NUM
ejpam-4055	109	38	v	v	NOUN
ejpam-4055	109	39	(	(	PUNCT
ejpam-4055	109	40	g	g	NOUN
ejpam-4055	109	41	)	)	PUNCT
ejpam-4055	109	42	and	and	CCONJ
ejpam-4055	109	43	wh	wh	VERB
ejpam-4055	109	44	⊆	⊆	NUM
ejpam-4055	109	45	v	v	NOUN
ejpam-4055	109	46	(	(	PUNCT
ejpam-4055	109	47	h	h	NOUN
ejpam-4055	109	48	)	)	PUNCT
ejpam-4055	109	49	are	be	AUX
ejpam-4055	109	50	locating	locate	VERB
ejpam-4055	109	51	sets	set	NOUN
ejpam-4055	109	52	of	of	ADP
ejpam-4055	109	53	g	g	PROPN
ejpam-4055	109	54	and	and	CCONJ
ejpam-4055	109	55	h	h	NOUN
ejpam-4055	109	56	,	,	PUNCT
ejpam-4055	109	57	respectively	respectively	ADV
ejpam-4055	109	58	.	.	PUNCT
ejpam-4055	110	1	suppose	suppose	VERB
ejpam-4055	110	2	wg	wg	VERB
ejpam-4055	110	3	or	or	CCONJ
ejpam-4055	110	4	wh	wh	PROPN
ejpam-4055	110	5	is	be	AUX
ejpam-4055	110	6	not	not	PART
ejpam-4055	110	7	strictly	strictly	ADV
ejpam-4055	110	8	locating	locate	VERB
ejpam-4055	110	9	set	set	NOUN
ejpam-4055	110	10	,	,	PUNCT
ejpam-4055	110	11	say	say	VERB
ejpam-4055	110	12	wg	wg	PROPN
ejpam-4055	110	13	is	be	AUX
ejpam-4055	110	14	not	not	PART
ejpam-4055	110	15	strictly	strictly	ADV
ejpam-4055	110	16	locating	locate	VERB
ejpam-4055	110	17	.	.	PUNCT
ejpam-4055	111	1	then	then	ADV
ejpam-4055	111	2	there	there	PRON
ejpam-4055	111	3	exists	exist	VERB
ejpam-4055	111	4	v	v	ADP
ejpam-4055	111	5	∈	∈	PROPN
ejpam-4055	111	6	v	v	NOUN
ejpam-4055	111	7	(	(	PUNCT
ejpam-4055	111	8	g	g	NOUN
ejpam-4055	111	9	)	)	PUNCT
ejpam-4055	111	10	\wg	\wg	PROPN
ejpam-4055	111	11	such	such	ADJ
ejpam-4055	111	12	that	that	SCONJ
ejpam-4055	111	13	ng(v	ng(v	PUNCT
ejpam-4055	111	14	)	)	PUNCT
ejpam-4055	111	15	∩wg	∩wg	NOUN
ejpam-4055	111	16	=	=	PUNCT
ejpam-4055	111	17	wg	wg	PROPN
ejpam-4055	111	18	.	.	PUNCT
ejpam-4055	112	1	hence	hence	ADV
ejpam-4055	112	2	,	,	PUNCT
ejpam-4055	112	3	v	v	PROPN
ejpam-4055	112	4	∈	∈	PROPN
ejpam-4055	112	5	v	v	NOUN
ejpam-4055	112	6	(	(	PUNCT
ejpam-4055	112	7	g+h	g+h	NOUN
ejpam-4055	112	8	)	)	PUNCT
ejpam-4055	112	9	\w	\w	ADJ
ejpam-4055	112	10	and	and	CCONJ
ejpam-4055	112	11	dg+h(v	dg+h(v	NOUN
ejpam-4055	112	12	,	,	PUNCT
ejpam-4055	112	13	w	w	NOUN
ejpam-4055	112	14	)	)	PUNCT
ejpam-4055	112	15	=	=	SYM
ejpam-4055	112	16	1	1	NUM
ejpam-4055	112	17	for	for	ADP
ejpam-4055	112	18	all	all	DET
ejpam-4055	112	19	w	w	PROPN
ejpam-4055	112	20	∈	∈	PROPN
ejpam-4055	112	21	w	w	NOUN
ejpam-4055	112	22	.	.	PUNCT
ejpam-4055	113	1	this	this	PRON
ejpam-4055	113	2	contradicts	contradict	VERB
ejpam-4055	113	3	the	the	DET
ejpam-4055	113	4	assumption	assumption	NOUN
ejpam-4055	113	5	that	that	SCONJ
ejpam-4055	113	6	w	w	NOUN
ejpam-4055	113	7	is	be	AUX
ejpam-4055	113	8	a	a	DET
ejpam-4055	113	9	hop	hop	NOUN
ejpam-4055	113	10	dominating	dominating	NOUN
ejpam-4055	113	11	set	set	NOUN
ejpam-4055	113	12	of	of	ADP
ejpam-4055	113	13	g+h	g+h	PROPN
ejpam-4055	113	14	.	.	PUNCT
ejpam-4055	114	1	similarly	similarly	ADV
ejpam-4055	114	2	,	,	PUNCT
ejpam-4055	114	3	if	if	SCONJ
ejpam-4055	114	4	wh	wh	NOUN
ejpam-4055	114	5	is	be	AUX
ejpam-4055	114	6	not	not	PART
ejpam-4055	114	7	strictly	strictly	ADV
ejpam-4055	114	8	locating	locate	VERB
ejpam-4055	114	9	,	,	PUNCT
ejpam-4055	114	10	then	then	ADV
ejpam-4055	114	11	a	a	DET
ejpam-4055	114	12	contradiction	contradiction	NOUN
ejpam-4055	114	13	follows	follow	VERB
ejpam-4055	114	14	.	.	PUNCT
ejpam-4055	115	1	hence	hence	ADV
ejpam-4055	115	2	,	,	PUNCT
ejpam-4055	115	3	wg	wg	VERB
ejpam-4055	115	4	and	and	CCONJ
ejpam-4055	115	5	wh	wh	PROPN
ejpam-4055	115	6	are	be	AUX
ejpam-4055	115	7	both	both	PRON
ejpam-4055	115	8	strictly	strictly	ADV
ejpam-4055	115	9	locating	locate	VERB
ejpam-4055	115	10	.	.	PUNCT
ejpam-4055	116	1	for	for	ADP
ejpam-4055	116	2	the	the	DET
ejpam-4055	116	3	converse	converse	NOUN
ejpam-4055	116	4	,	,	PUNCT
ejpam-4055	116	5	suppose	suppose	VERB
ejpam-4055	116	6	that	that	SCONJ
ejpam-4055	116	7	w	w	PROPN
ejpam-4055	116	8	=	=	PUNCT
ejpam-4055	116	9	wg	wg	PROPN
ejpam-4055	116	10	∪wh	∪wh	NOUN
ejpam-4055	116	11	where	where	SCONJ
ejpam-4055	116	12	wg	wg	PROPN
ejpam-4055	116	13	⊆	⊆	NUM
ejpam-4055	116	14	v	v	NOUN
ejpam-4055	116	15	(	(	PUNCT
ejpam-4055	116	16	g	g	NOUN
ejpam-4055	116	17	)	)	PUNCT
ejpam-4055	116	18	,	,	PUNCT
ejpam-4055	116	19	wh	wh	VERB
ejpam-4055	116	20	⊆	⊆	NUM
ejpam-4055	116	21	v	v	NOUN
ejpam-4055	116	22	(	(	PUNCT
ejpam-4055	116	23	h	h	NOUN
ejpam-4055	116	24	)	)	PUNCT
ejpam-4055	116	25	and	and	CCONJ
ejpam-4055	116	26	both	both	PRON
ejpam-4055	116	27	wg	wg	VERB
ejpam-4055	116	28	and	and	CCONJ
ejpam-4055	116	29	wh	wh	PROPN
ejpam-4055	116	30	are	be	AUX
ejpam-4055	116	31	strictly	strictly	ADV
ejpam-4055	116	32	locating	locate	VERB
ejpam-4055	116	33	sets	set	NOUN
ejpam-4055	116	34	of	of	ADP
ejpam-4055	116	35	g	g	PROPN
ejpam-4055	116	36	and	and	CCONJ
ejpam-4055	116	37	h	h	NOUN
ejpam-4055	116	38	,	,	PUNCT
ejpam-4055	116	39	respectively	respectively	ADV
ejpam-4055	116	40	.	.	PUNCT
ejpam-4055	117	1	since	since	SCONJ
ejpam-4055	117	2	wg	wg	PROPN
ejpam-4055	117	3	and	and	CCONJ
ejpam-4055	117	4	wh	wh	PROPN
ejpam-4055	117	5	are	be	AUX
ejpam-4055	117	6	locating	locate	VERB
ejpam-4055	117	7	sets	set	NOUN
ejpam-4055	117	8	by	by	ADP
ejpam-4055	117	9	theorem	theorem	NOUN
ejpam-4055	117	10	1	1	NUM
ejpam-4055	117	11	,	,	PUNCT
ejpam-4055	117	12	w	w	NOUN
ejpam-4055	117	13	is	be	AUX
ejpam-4055	117	14	a	a	DET
ejpam-4055	117	15	resolving	resolving	NOUN
ejpam-4055	117	16	set	set	NOUN
ejpam-4055	117	17	of	of	ADP
ejpam-4055	117	18	g+h	g+h	PROPN
ejpam-4055	117	19	.	.	PUNCT
ejpam-4055	118	1	let	let	VERB
ejpam-4055	118	2	v	v	NUM
ejpam-4055	118	3	∈	∈	PROPN
ejpam-4055	118	4	v	v	NOUN
ejpam-4055	118	5	(	(	PUNCT
ejpam-4055	118	6	g+h	g+h	NOUN
ejpam-4055	118	7	)	)	PUNCT
ejpam-4055	118	8	\w	\w	ADJ
ejpam-4055	118	9	.	.	PUNCT
ejpam-4055	119	1	if	if	SCONJ
ejpam-4055	119	2	v	v	NUM
ejpam-4055	119	3	∈	∈	PROPN
ejpam-4055	119	4	v	v	NOUN
ejpam-4055	119	5	(	(	PUNCT
ejpam-4055	119	6	g	g	NOUN
ejpam-4055	119	7	)	)	PUNCT
ejpam-4055	119	8	,	,	PUNCT
ejpam-4055	119	9	then	then	ADV
ejpam-4055	119	10	v	v	ADP
ejpam-4055	119	11	/∈wg	/∈wg	PUNCT
ejpam-4055	119	12	.	.	PUNCT
ejpam-4055	120	1	since	since	SCONJ
ejpam-4055	120	2	wg	wg	PROPN
ejpam-4055	120	3	is	be	AUX
ejpam-4055	120	4	strictly	strictly	ADV
ejpam-4055	120	5	locating	locate	VERB
ejpam-4055	120	6	there	there	ADV
ejpam-4055	120	7	exists	exist	VERB
ejpam-4055	120	8	u	u	NOUN
ejpam-4055	120	9	∈wg	∈wg	NOUN
ejpam-4055	120	10	\ng(v	\ng(v	NOUN
ejpam-4055	120	11	)	)	PUNCT
ejpam-4055	120	12	.	.	PUNCT
ejpam-4055	121	1	hence	hence	ADV
ejpam-4055	121	2	,	,	PUNCT
ejpam-4055	121	3	dg+h(v	dg+h(v	PROPN
ejpam-4055	121	4	,	,	PUNCT
ejpam-4055	121	5	u	u	NOUN
ejpam-4055	121	6	)	)	PUNCT
ejpam-4055	121	7	=	=	SYM
ejpam-4055	121	8	2	2	X
ejpam-4055	121	9	.	.	X
ejpam-4055	121	10	similarly	similarly	ADV
ejpam-4055	121	11	,	,	PUNCT
ejpam-4055	121	12	if	if	SCONJ
ejpam-4055	121	13	v	v	NUM
ejpam-4055	121	14	∈	∈	PROPN
ejpam-4055	121	15	v	v	NOUN
ejpam-4055	121	16	(	(	PUNCT
ejpam-4055	121	17	h	h	NOUN
ejpam-4055	121	18	)	)	PUNCT
ejpam-4055	121	19	,	,	PUNCT
ejpam-4055	121	20	then	then	ADV
ejpam-4055	121	21	v	v	X
ejpam-4055	121	22	/∈	/∈	INTJ
ejpam-4055	122	1	wh	wh	NOUN
ejpam-4055	122	2	and	and	CCONJ
ejpam-4055	122	3	there	there	PRON
ejpam-4055	122	4	exists	exist	VERB
ejpam-4055	122	5	w	w	PROPN
ejpam-4055	122	6	∈	∈	PROPN
ejpam-4055	122	7	wg	wg	NOUN
ejpam-4055	122	8	\ng(v	\ng(v	NOUN
ejpam-4055	122	9	)	)	PUNCT
ejpam-4055	122	10	.	.	PUNCT
ejpam-4055	123	1	thus	thus	ADV
ejpam-4055	123	2	,	,	PUNCT
ejpam-4055	123	3	dg(v	dg(v	X
ejpam-4055	123	4	,	,	PUNCT
ejpam-4055	123	5	w	w	NOUN
ejpam-4055	123	6	)	)	PUNCT
ejpam-4055	123	7	=	=	SYM
ejpam-4055	123	8	2	2	X
ejpam-4055	123	9	.	.	X
ejpam-4055	123	10	therefore	therefore	ADV
ejpam-4055	123	11	w	w	PROPN
ejpam-4055	123	12	is	be	AUX
ejpam-4055	123	13	a	a	DET
ejpam-4055	123	14	hop	hop	NOUN
ejpam-4055	123	15	dominating	dominating	NOUN
ejpam-4055	123	16	set	set	NOUN
ejpam-4055	123	17	of	of	ADP
ejpam-4055	123	18	g+h	g+h	PROPN
ejpam-4055	123	19	.	.	PUNCT
ejpam-4055	124	1	accordingly	accordingly	ADV
ejpam-4055	124	2	,	,	PUNCT
ejpam-4055	124	3	w	w	PROPN
ejpam-4055	124	4	is	be	AUX
ejpam-4055	124	5	a	a	DET
ejpam-4055	124	6	resolving	resolve	VERB
ejpam-4055	124	7	hop	hop	NOUN
ejpam-4055	124	8	dominating	dominating	NOUN
ejpam-4055	124	9	set	set	NOUN
ejpam-4055	124	10	of	of	ADP
ejpam-4055	124	11	g+h	g+h	PROPN
ejpam-4055	124	12	.	.	PUNCT
ejpam-4055	125	1	the	the	DET
ejpam-4055	125	2	next	next	ADJ
ejpam-4055	125	3	result	result	NOUN
ejpam-4055	125	4	follows	follow	VERB
ejpam-4055	125	5	immediately	immediately	ADV
ejpam-4055	125	6	from	from	ADP
ejpam-4055	125	7	theorem	theorem	ADJ
ejpam-4055	125	8	2	2	NUM
ejpam-4055	125	9	.	.	PUNCT
ejpam-4055	125	10	corollary	corollary	ADJ
ejpam-4055	125	11	1	1	NUM
ejpam-4055	125	12	.	.	PUNCT
ejpam-4055	126	1	let	let	VERB
ejpam-4055	126	2	g	g	NOUN
ejpam-4055	126	3	and	and	CCONJ
ejpam-4055	126	4	h	h	PROPN
ejpam-4055	126	5	be	be	VERB
ejpam-4055	126	6	non	non	ADJ
ejpam-4055	126	7	-	-	ADJ
ejpam-4055	126	8	trivial	trivial	ADJ
ejpam-4055	126	9	connected	connected	ADJ
ejpam-4055	126	10	graphs	graph	NOUN
ejpam-4055	126	11	.	.	PUNCT
ejpam-4055	127	1	then	then	ADV
ejpam-4055	127	2	γrh(g+h	γrh(g+h	NOUN
ejpam-4055	127	3	)	)	PUNCT
ejpam-4055	127	4	=	=	PUNCT
ejpam-4055	127	5	sln(g	sln(g	NOUN
ejpam-4055	127	6	)	)	PUNCT
ejpam-4055	128	1	+	+	X
ejpam-4055	128	2	sln(h	sln(h	ADJ
ejpam-4055	128	3	)	)	PUNCT
ejpam-4055	128	4	.	.	PUNCT
ejpam-4055	129	1	j.	j.	PROPN
ejpam-4055	129	2	mohamad	mohamad	PROPN
ejpam-4055	129	3	,	,	PUNCT
ejpam-4055	129	4	h.	h.	PROPN
ejpam-4055	129	5	rara	rara	PROPN
ejpam-4055	129	6	/	/	SYM
ejpam-4055	129	7	eur	eur	PROPN
ejpam-4055	129	8	.	.	PUNCT
ejpam-4055	130	1	j.	j.	PROPN
ejpam-4055	130	2	pure	pure	PROPN
ejpam-4055	130	3	appl	appl	PROPN
ejpam-4055	130	4	.	.	PROPN
ejpam-4055	130	5	math	math	PROPN
ejpam-4055	130	6	,	,	PUNCT
ejpam-4055	130	7	14	14	NUM
ejpam-4055	130	8	(	(	PUNCT
ejpam-4055	130	9	3	3	NUM
ejpam-4055	130	10	)	)	PUNCT
ejpam-4055	130	11	(	(	PUNCT
ejpam-4055	130	12	2021	2021	NUM
ejpam-4055	130	13	)	)	PUNCT
ejpam-4055	130	14	,	,	PUNCT
ejpam-4055	130	15	1015	1015	NUM
ejpam-4055	130	16	-	-	SYM
ejpam-4055	130	17	1023	1023	NUM
ejpam-4055	130	18	1019	1019	NUM
ejpam-4055	130	19	4	4	NUM
ejpam-4055	130	20	.	.	PUNCT
ejpam-4055	130	21	on	on	ADP
ejpam-4055	130	22	resolving	resolve	VERB
ejpam-4055	130	23	hop	hop	NOUN
ejpam-4055	130	24	domination	domination	NOUN
ejpam-4055	130	25	in	in	ADP
ejpam-4055	130	26	the	the	DET
ejpam-4055	130	27	corona	corona	NOUN
ejpam-4055	130	28	of	of	ADP
ejpam-4055	130	29	graphs	graph	NOUN
ejpam-4055	130	30	the	the	DET
ejpam-4055	130	31	corona	corona	NOUN
ejpam-4055	130	32	of	of	ADP
ejpam-4055	130	33	two	two	NUM
ejpam-4055	130	34	graphs	graph	NOUN
ejpam-4055	130	35	g	g	NOUN
ejpam-4055	130	36	and	and	CCONJ
ejpam-4055	130	37	h	h	NOUN
ejpam-4055	130	38	,	,	PUNCT
ejpam-4055	130	39	denoted	denote	VERB
ejpam-4055	130	40	by	by	ADP
ejpam-4055	130	41	g	g	PROPN
ejpam-4055	130	42	◦	◦	NOUN
ejpam-4055	130	43	h	h	NOUN
ejpam-4055	130	44	,	,	PUNCT
ejpam-4055	130	45	is	be	AUX
ejpam-4055	130	46	the	the	DET
ejpam-4055	130	47	graph	graph	NOUN
ejpam-4055	130	48	obtained	obtain	VERB
ejpam-4055	130	49	by	by	ADP
ejpam-4055	130	50	taking	take	VERB
ejpam-4055	130	51	one	one	NUM
ejpam-4055	130	52	copy	copy	NOUN
ejpam-4055	130	53	of	of	ADP
ejpam-4055	130	54	g	g	NOUN
ejpam-4055	130	55	of	of	ADP
ejpam-4055	130	56	order	order	NOUN
ejpam-4055	130	57	n	n	NOUN
ejpam-4055	130	58	and	and	CCONJ
ejpam-4055	130	59	n	n	PRON
ejpam-4055	130	60	copies	copy	NOUN
ejpam-4055	130	61	of	of	ADP
ejpam-4055	130	62	h	h	NOUN
ejpam-4055	130	63	,	,	PUNCT
ejpam-4055	130	64	and	and	CCONJ
ejpam-4055	130	65	then	then	ADV
ejpam-4055	130	66	joining	join	VERB
ejpam-4055	130	67	every	every	DET
ejpam-4055	130	68	vertex	vertex	NOUN
ejpam-4055	130	69	of	of	ADP
ejpam-4055	130	70	the	the	DET
ejpam-4055	130	71	ith	ith	PROPN
ejpam-4055	130	72	copy	copy	NOUN
ejpam-4055	130	73	of	of	ADP
ejpam-4055	130	74	h	h	NOUN
ejpam-4055	130	75	to	to	ADP
ejpam-4055	130	76	the	the	DET
ejpam-4055	130	77	ith	ith	PROPN
ejpam-4055	130	78	vertex	vertex	NOUN
ejpam-4055	130	79	of	of	ADP
ejpam-4055	130	80	g.	g.	PROPN
ejpam-4055	130	81	for	for	ADP
ejpam-4055	130	82	v	v	NOUN
ejpam-4055	130	83	∈	∈	PROPN
ejpam-4055	130	84	v	v	NOUN
ejpam-4055	130	85	(	(	PUNCT
ejpam-4055	130	86	g	g	NOUN
ejpam-4055	130	87	)	)	PUNCT
ejpam-4055	130	88	,	,	PUNCT
ejpam-4055	130	89	denote	denote	VERB
ejpam-4055	130	90	by	by	ADP
ejpam-4055	130	91	hv	hv	PROPN
ejpam-4055	130	92	the	the	DET
ejpam-4055	130	93	copy	copy	NOUN
ejpam-4055	130	94	of	of	ADP
ejpam-4055	130	95	h	h	NOUN
ejpam-4055	130	96	whose	whose	DET
ejpam-4055	130	97	vertices	vertex	NOUN
ejpam-4055	130	98	are	be	AUX
ejpam-4055	130	99	attached	attach	VERB
ejpam-4055	130	100	one	one	NUM
ejpam-4055	130	101	by	by	ADP
ejpam-4055	130	102	one	one	NUM
ejpam-4055	130	103	to	to	ADP
ejpam-4055	130	104	the	the	DET
ejpam-4055	130	105	vertex	vertex	NOUN
ejpam-4055	130	106	v.	v.	ADP
ejpam-4055	130	107	subsequently	subsequently	ADV
ejpam-4055	130	108	,	,	PUNCT
ejpam-4055	130	109	denote	denote	VERB
ejpam-4055	130	110	by	by	ADP
ejpam-4055	130	111	v+hv	v+hv	NOUN
ejpam-4055	130	112	the	the	DET
ejpam-4055	130	113	subgraph	subgraph	NOUN
ejpam-4055	130	114	of	of	ADP
ejpam-4055	130	115	the	the	DET
ejpam-4055	130	116	corona	corona	NOUN
ejpam-4055	130	117	g	g	PROPN
ejpam-4055	130	118	◦	◦	NOUN
ejpam-4055	130	119	h	h	NOUN
ejpam-4055	130	120	corresponding	correspond	VERB
ejpam-4055	130	121	to	to	ADP
ejpam-4055	130	122	the	the	DET
ejpam-4055	130	123	join	join	NOUN
ejpam-4055	130	124	〈	〈	PROPN
ejpam-4055	130	125	{	{	PUNCT
ejpam-4055	130	126	v}〉+hv	v}〉+hv	PROPN
ejpam-4055	130	127	,	,	PUNCT
ejpam-4055	130	128	v	v	NOUN
ejpam-4055	130	129	∈	∈	PROPN
ejpam-4055	130	130	v	v	NOUN
ejpam-4055	130	131	(	(	PUNCT
ejpam-4055	130	132	g	g	NOUN
ejpam-4055	130	133	)	)	PUNCT
ejpam-4055	130	134	.	.	PUNCT
ejpam-4055	131	1	theorem	theorem	NOUN
ejpam-4055	131	2	3	3	NUM
ejpam-4055	131	3	.	.	PUNCT
ejpam-4055	132	1	[	[	X
ejpam-4055	132	2	7	7	NUM
ejpam-4055	132	3	,	,	PUNCT
ejpam-4055	132	4	8	8	NUM
ejpam-4055	132	5	]	]	PUNCT
ejpam-4055	132	6	let	let	VERB
ejpam-4055	132	7	g	g	NOUN
ejpam-4055	132	8	and	and	CCONJ
ejpam-4055	132	9	h	h	PROPN
ejpam-4055	132	10	be	be	VERB
ejpam-4055	132	11	non	non	ADJ
ejpam-4055	132	12	-	-	ADJ
ejpam-4055	132	13	trivial	trivial	ADJ
ejpam-4055	132	14	connected	connected	ADJ
ejpam-4055	132	15	graphs	graph	NOUN
ejpam-4055	132	16	.	.	PUNCT
ejpam-4055	133	1	then	then	ADV
ejpam-4055	133	2	w	w	PROPN
ejpam-4055	133	3	⊆	⊆	NUM
ejpam-4055	133	4	v	v	NOUN
ejpam-4055	133	5	(	(	PUNCT
ejpam-4055	133	6	g	g	PROPN
ejpam-4055	133	7	◦	◦	NOUN
ejpam-4055	133	8	h	h	NOUN
ejpam-4055	133	9	)	)	PUNCT
ejpam-4055	133	10	is	be	AUX
ejpam-4055	133	11	a	a	DET
ejpam-4055	133	12	resolving	resolving	NOUN
ejpam-4055	133	13	set	set	NOUN
ejpam-4055	133	14	of	of	ADP
ejpam-4055	133	15	g	g	PROPN
ejpam-4055	133	16	◦	◦	NOUN
ejpam-4055	133	17	h	h	NOUN
ejpam-4055	133	18	if	if	SCONJ
ejpam-4055	134	1	and	and	CCONJ
ejpam-4055	134	2	only	only	ADV
ejpam-4055	134	3	if	if	SCONJ
ejpam-4055	134	4	w	w	PROPN
ejpam-4055	134	5	∩	∩	ADJ
ejpam-4055	134	6	v	v	X
ejpam-4055	134	7	(	(	PUNCT
ejpam-4055	134	8	hv	hv	PROPN
ejpam-4055	134	9	)	)	PUNCT
ejpam-4055	134	10	6=	6=	NOUN
ejpam-4055	134	11	∅	∅	NOUN
ejpam-4055	134	12	for	for	ADP
ejpam-4055	134	13	all	all	PRON
ejpam-4055	134	14	v	v	ADP
ejpam-4055	134	15	∈	∈	NUM
ejpam-4055	134	16	v	v	NOUN
ejpam-4055	134	17	(	(	PUNCT
ejpam-4055	134	18	g	g	NOUN
ejpam-4055	134	19	)	)	PUNCT
ejpam-4055	134	20	and	and	CCONJ
ejpam-4055	134	21	w	w	X
ejpam-4055	134	22	=	=	PUNCT
ejpam-4055	134	23	a	a	DET
ejpam-4055	134	24	∪b	∪b	NOUN
ejpam-4055	134	25	,	,	PUNCT
ejpam-4055	134	26	where	where	SCONJ
ejpam-4055	134	27	a	a	DET
ejpam-4055	134	28	⊆	⊆	NUM
ejpam-4055	134	29	v	v	NOUN
ejpam-4055	134	30	(	(	PUNCT
ejpam-4055	134	31	g	g	NOUN
ejpam-4055	134	32	)	)	PUNCT
ejpam-4055	134	33	,	,	PUNCT
ejpam-4055	134	34	and	and	CCONJ
ejpam-4055	134	35	b	b	X
ejpam-4055	134	36	=	=	SYM
ejpam-4055	134	37	∪{bv	∪{bv	NOUN
ejpam-4055	134	38	:	:	PUNCT
ejpam-4055	134	39	v	v	NUM
ejpam-4055	134	40	∈	∈	PROPN
ejpam-4055	134	41	v	v	NOUN
ejpam-4055	134	42	(	(	PUNCT
ejpam-4055	134	43	g	g	NOUN
ejpam-4055	134	44	)	)	PUNCT
ejpam-4055	134	45	and	and	CCONJ
ejpam-4055	134	46	bv	bv	PROPN
ejpam-4055	134	47	is	be	AUX
ejpam-4055	134	48	a	a	DET
ejpam-4055	134	49	locating	locate	VERB
ejpam-4055	134	50	set	set	NOUN
ejpam-4055	134	51	of	of	ADP
ejpam-4055	134	52	hv	hv	PROPN
ejpam-4055	134	53	}	}	PUNCT
ejpam-4055	134	54	.	.	PUNCT
ejpam-4055	135	1	theorem	theorem	ADJ
ejpam-4055	135	2	4	4	NUM
ejpam-4055	135	3	.	.	PUNCT
ejpam-4055	136	1	let	let	VERB
ejpam-4055	136	2	g	g	NOUN
ejpam-4055	136	3	and	and	CCONJ
ejpam-4055	136	4	h	h	PROPN
ejpam-4055	136	5	be	be	VERB
ejpam-4055	136	6	non	non	ADJ
ejpam-4055	136	7	-	-	ADJ
ejpam-4055	136	8	trivial	trivial	ADJ
ejpam-4055	136	9	connected	connected	ADJ
ejpam-4055	136	10	graphs	graph	NOUN
ejpam-4055	136	11	.	.	PUNCT
ejpam-4055	137	1	then	then	ADV
ejpam-4055	137	2	w	w	PROPN
ejpam-4055	137	3	⊆	⊆	NUM
ejpam-4055	137	4	v	v	NOUN
ejpam-4055	137	5	(	(	PUNCT
ejpam-4055	137	6	g	g	PROPN
ejpam-4055	137	7	◦	◦	NOUN
ejpam-4055	137	8	h	h	NOUN
ejpam-4055	137	9	)	)	PUNCT
ejpam-4055	137	10	is	be	AUX
ejpam-4055	137	11	a	a	DET
ejpam-4055	137	12	resolving	resolve	VERB
ejpam-4055	137	13	hop	hop	NOUN
ejpam-4055	137	14	dominating	dominating	NOUN
ejpam-4055	137	15	set	set	NOUN
ejpam-4055	137	16	of	of	ADP
ejpam-4055	137	17	g	g	PROPN
ejpam-4055	137	18	◦	◦	NOUN
ejpam-4055	137	19	h	h	NOUN
ejpam-4055	137	20	if	if	SCONJ
ejpam-4055	138	1	and	and	CCONJ
ejpam-4055	138	2	only	only	ADV
ejpam-4055	138	3	if	if	SCONJ
ejpam-4055	138	4	w	w	PROPN
ejpam-4055	138	5	∩	∩	ADJ
ejpam-4055	138	6	v	v	X
ejpam-4055	138	7	(	(	PUNCT
ejpam-4055	138	8	hv	hv	PROPN
ejpam-4055	138	9	)	)	PUNCT
ejpam-4055	138	10	6=	6=	NOUN
ejpam-4055	138	11	∅	∅	NOUN
ejpam-4055	138	12	for	for	ADP
ejpam-4055	138	13	every	every	DET
ejpam-4055	138	14	v	v	NUM
ejpam-4055	138	15	∈	∈	PROPN
ejpam-4055	138	16	v	v	NOUN
ejpam-4055	138	17	(	(	PUNCT
ejpam-4055	138	18	g	g	NOUN
ejpam-4055	138	19	)	)	PUNCT
ejpam-4055	138	20	and	and	CCONJ
ejpam-4055	138	21	w	w	X
ejpam-4055	138	22	=	=	PUNCT
ejpam-4055	138	23	a	a	PRON
ejpam-4055	138	24	∪b	∪b	X
ejpam-4055	138	25	∪d	∪d	PUNCT
ejpam-4055	138	26	where	where	SCONJ
ejpam-4055	138	27	a	a	DET
ejpam-4055	138	28	⊆	⊆	NUM
ejpam-4055	138	29	v	v	NOUN
ejpam-4055	138	30	(	(	PUNCT
ejpam-4055	138	31	g	g	NOUN
ejpam-4055	138	32	)	)	PUNCT
ejpam-4055	138	33	,	,	PUNCT
ejpam-4055	138	34	b	b	X
ejpam-4055	138	35	=	=	SYM
ejpam-4055	138	36	∪	∪	X
ejpam-4055	138	37	{	{	PUNCT
ejpam-4055	138	38	bv	bv	NOUN
ejpam-4055	138	39	:	:	PUNCT
ejpam-4055	138	40	v	v	NUM
ejpam-4055	138	41	∈	∈	PROPN
ejpam-4055	138	42	v	v	NOUN
ejpam-4055	138	43	(	(	PUNCT
ejpam-4055	138	44	g	g	NOUN
ejpam-4055	138	45	)	)	PUNCT
ejpam-4055	138	46	∩ng(a	∩ng(a	NOUN
ejpam-4055	138	47	)	)	PUNCT
ejpam-4055	138	48	and	and	CCONJ
ejpam-4055	138	49	bv	bv	PROPN
ejpam-4055	138	50	is	be	AUX
ejpam-4055	138	51	a	a	DET
ejpam-4055	138	52	locating	locate	VERB
ejpam-4055	138	53	set	set	NOUN
ejpam-4055	138	54	of	of	ADP
ejpam-4055	138	55	hv	hv	PROPN
ejpam-4055	138	56	}	}	PUNCT
ejpam-4055	138	57	and	and	CCONJ
ejpam-4055	138	58	d	d	NOUN
ejpam-4055	138	59	=	=	SYM
ejpam-4055	138	60	∪	∪	X
ejpam-4055	138	61	{	{	PUNCT
ejpam-4055	138	62	du	du	NOUN
ejpam-4055	138	63	:	:	PUNCT
ejpam-4055	138	64	u	u	PROPN
ejpam-4055	138	65	∈	∈	PROPN
ejpam-4055	138	66	v	v	ADP
ejpam-4055	138	67	(	(	PUNCT
ejpam-4055	138	68	g	g	NOUN
ejpam-4055	138	69	)	)	PUNCT
ejpam-4055	138	70	\ng(a	\ng(a	PROPN
ejpam-4055	138	71	)	)	PUNCT
ejpam-4055	138	72	and	and	CCONJ
ejpam-4055	138	73	du	du	PROPN
ejpam-4055	138	74	is	be	AUX
ejpam-4055	138	75	a	a	DET
ejpam-4055	138	76	strictly	strictly	ADV
ejpam-4055	138	77	locating	locate	VERB
ejpam-4055	138	78	set	set	NOUN
ejpam-4055	138	79	of	of	ADP
ejpam-4055	138	80	hu	hu	PROPN
ejpam-4055	138	81	}	}	PUNCT
ejpam-4055	138	82	.	.	PUNCT
ejpam-4055	139	1	proof	proof	NOUN
ejpam-4055	139	2	:	:	PUNCT
ejpam-4055	139	3	suppose	suppose	VERB
ejpam-4055	139	4	w	w	NOUN
ejpam-4055	139	5	is	be	AUX
ejpam-4055	139	6	a	a	DET
ejpam-4055	139	7	resolving	resolve	VERB
ejpam-4055	139	8	hop	hop	NOUN
ejpam-4055	139	9	dominating	dominating	NOUN
ejpam-4055	139	10	set	set	NOUN
ejpam-4055	139	11	of	of	ADP
ejpam-4055	139	12	g	g	PROPN
ejpam-4055	139	13	◦	◦	NOUN
ejpam-4055	139	14	h.	h.	NOUN
ejpam-4055	139	15	then	then	ADV
ejpam-4055	139	16	by	by	ADP
ejpam-4055	139	17	theorem	theorem	NOUN
ejpam-4055	139	18	3	3	NUM
ejpam-4055	139	19	,	,	PUNCT
ejpam-4055	140	1	w	w	PROPN
ejpam-4055	140	2	∩	∩	ADJ
ejpam-4055	140	3	v	v	X
ejpam-4055	140	4	(	(	PUNCT
ejpam-4055	140	5	hv	hv	PROPN
ejpam-4055	140	6	)	)	PUNCT
ejpam-4055	140	7	6=	6=	NOUN
ejpam-4055	140	8	∅	∅	NOUN
ejpam-4055	140	9	for	for	ADP
ejpam-4055	140	10	every	every	DET
ejpam-4055	140	11	v	v	NUM
ejpam-4055	140	12	∈	∈	NOUN
ejpam-4055	140	13	v	v	NOUN
ejpam-4055	140	14	(	(	PUNCT
ejpam-4055	140	15	g	g	NOUN
ejpam-4055	140	16	)	)	PUNCT
ejpam-4055	140	17	.	.	PUNCT
ejpam-4055	141	1	let	let	VERB
ejpam-4055	141	2	a	a	DET
ejpam-4055	141	3	=	=	SYM
ejpam-4055	141	4	w	w	PROPN
ejpam-4055	141	5	∩	∩	ADJ
ejpam-4055	141	6	v	v	ADJ
ejpam-4055	141	7	(	(	PUNCT
ejpam-4055	141	8	g	g	NOUN
ejpam-4055	141	9	)	)	PUNCT
ejpam-4055	141	10	,	,	PUNCT
ejpam-4055	141	11	bv	bv	PROPN
ejpam-4055	141	12	=	=	PROPN
ejpam-4055	141	13	w	w	PROPN
ejpam-4055	141	14	∩	∩	ADJ
ejpam-4055	141	15	v	v	X
ejpam-4055	141	16	(	(	PUNCT
ejpam-4055	141	17	hv	hv	PROPN
ejpam-4055	141	18	)	)	PUNCT
ejpam-4055	141	19	for	for	ADP
ejpam-4055	141	20	each	each	DET
ejpam-4055	141	21	v	v	NUM
ejpam-4055	141	22	∈	∈	PROPN
ejpam-4055	141	23	v	v	NOUN
ejpam-4055	141	24	(	(	PUNCT
ejpam-4055	141	25	g	g	NOUN
ejpam-4055	141	26	)	)	PUNCT
ejpam-4055	141	27	∩ng(a	∩ng(a	NOUN
ejpam-4055	141	28	)	)	PUNCT
ejpam-4055	141	29	and	and	CCONJ
ejpam-4055	141	30	du	du	PROPN
ejpam-4055	141	31	=	=	NOUN
ejpam-4055	141	32	w	w	PROPN
ejpam-4055	141	33	∩	∩	ADJ
ejpam-4055	141	34	v	v	X
ejpam-4055	141	35	(	(	PUNCT
ejpam-4055	141	36	hu	hu	PROPN
ejpam-4055	141	37	)	)	PUNCT
ejpam-4055	141	38	for	for	ADP
ejpam-4055	141	39	each	each	DET
ejpam-4055	141	40	u	u	PROPN
ejpam-4055	141	41	∈	∈	PROPN
ejpam-4055	141	42	v	v	NOUN
ejpam-4055	141	43	(	(	PUNCT
ejpam-4055	141	44	g	g	NOUN
ejpam-4055	141	45	)	)	PUNCT
ejpam-4055	141	46	\ng(a	\ng(a	PROPN
ejpam-4055	141	47	)	)	PUNCT
ejpam-4055	141	48	.	.	PUNCT
ejpam-4055	142	1	set	set	PROPN
ejpam-4055	142	2	b	b	NOUN
ejpam-4055	142	3	=	=	PUNCT
ejpam-4055	142	4	⋃	⋃	PROPN
ejpam-4055	142	5	bv	bv	NOUN
ejpam-4055	142	6	and	and	CCONJ
ejpam-4055	143	1	d	d	PROPN
ejpam-4055	143	2	=	=	PUNCT
ejpam-4055	143	3	⋃	⋃	NOUN
ejpam-4055	143	4	du	du	X
ejpam-4055	143	5	.	.	PUNCT
ejpam-4055	144	1	then	then	ADV
ejpam-4055	144	2	w	w	X
ejpam-4055	144	3	=	=	PUNCT
ejpam-4055	144	4	a	a	DET
ejpam-4055	144	5	∪	∪	NOUN
ejpam-4055	144	6	b	b	NOUN
ejpam-4055	144	7	∪	∪	NOUN
ejpam-4055	144	8	d	d	NOUN
ejpam-4055	144	9	where	where	SCONJ
ejpam-4055	144	10	a	a	DET
ejpam-4055	144	11	⊆	⊆	NUM
ejpam-4055	144	12	v	v	NOUN
ejpam-4055	144	13	(	(	PUNCT
ejpam-4055	144	14	g	g	NOUN
ejpam-4055	144	15	)	)	PUNCT
ejpam-4055	144	16	.	.	PUNCT
ejpam-4055	145	1	by	by	ADP
ejpam-4055	145	2	theorem	theorem	NOUN
ejpam-4055	145	3	3	3	NUM
ejpam-4055	145	4	,	,	PUNCT
ejpam-4055	145	5	bv	bv	PROPN
ejpam-4055	145	6	and	and	CCONJ
ejpam-4055	145	7	du	du	PROPN
ejpam-4055	145	8	are	be	AUX
ejpam-4055	145	9	locating	locate	VERB
ejpam-4055	145	10	sets	set	NOUN
ejpam-4055	145	11	of	of	ADP
ejpam-4055	145	12	hv	hv	PROPN
ejpam-4055	145	13	and	and	CCONJ
ejpam-4055	145	14	hu	hu	PROPN
ejpam-4055	145	15	,	,	PUNCT
ejpam-4055	145	16	respectively	respectively	ADV
ejpam-4055	145	17	.	.	PUNCT
ejpam-4055	146	1	let	let	VERB
ejpam-4055	146	2	x	x	SYM
ejpam-4055	146	3	∈	∈	PROPN
ejpam-4055	146	4	v	v	ADP
ejpam-4055	146	5	(	(	PUNCT
ejpam-4055	146	6	hu	hu	PROPN
ejpam-4055	146	7	)	)	PUNCT
ejpam-4055	146	8	\du	\du	PROPN
ejpam-4055	146	9	.	.	PUNCT
ejpam-4055	147	1	then	then	ADV
ejpam-4055	147	2	x	x	SYM
ejpam-4055	147	3	∈	∈	PROPN
ejpam-4055	147	4	v	v	NOUN
ejpam-4055	147	5	(	(	PUNCT
ejpam-4055	147	6	g	g	PROPN
ejpam-4055	147	7	◦	◦	NOUN
ejpam-4055	147	8	h	h	NOUN
ejpam-4055	147	9	)	)	PUNCT
ejpam-4055	147	10	\w	\w	ADJ
ejpam-4055	147	11	.	.	PUNCT
ejpam-4055	148	1	since	since	SCONJ
ejpam-4055	148	2	w	w	PROPN
ejpam-4055	148	3	is	be	AUX
ejpam-4055	148	4	a	a	DET
ejpam-4055	148	5	hop	hop	NOUN
ejpam-4055	148	6	dominating	dominating	NOUN
ejpam-4055	148	7	set	set	NOUN
ejpam-4055	148	8	of	of	ADP
ejpam-4055	148	9	g	g	PROPN
ejpam-4055	148	10	◦	◦	NOUN
ejpam-4055	148	11	h	h	NOUN
ejpam-4055	148	12	,	,	PUNCT
ejpam-4055	148	13	there	there	PRON
ejpam-4055	148	14	exists	exist	VERB
ejpam-4055	148	15	y	y	PROPN
ejpam-4055	148	16	∈	∈	PROPN
ejpam-4055	148	17	w	w	ADP
ejpam-4055	148	18	such	such	ADJ
ejpam-4055	148	19	that	that	SCONJ
ejpam-4055	148	20	dg	dg	AUX
ejpam-4055	148	21	◦	◦	NOUN
ejpam-4055	148	22	h(x	h(x	PROPN
ejpam-4055	148	23	,	,	PUNCT
ejpam-4055	148	24	y	y	PROPN
ejpam-4055	148	25	)	)	PUNCT
ejpam-4055	149	1	=	=	SYM
ejpam-4055	149	2	2	2	X
ejpam-4055	149	3	.	.	PUNCT
ejpam-4055	150	1	since	since	SCONJ
ejpam-4055	150	2	u	u	PROPN
ejpam-4055	150	3	∈	∈	PROPN
ejpam-4055	150	4	v	v	ADP
ejpam-4055	150	5	(	(	PUNCT
ejpam-4055	150	6	g	g	NOUN
ejpam-4055	150	7	)	)	PUNCT
ejpam-4055	150	8	\ng(a	\ng(a	PROPN
ejpam-4055	150	9	)	)	PUNCT
ejpam-4055	150	10	,	,	PUNCT
ejpam-4055	150	11	y	y	PROPN
ejpam-4055	150	12	∈	∈	PROPN
ejpam-4055	150	13	v	v	NOUN
ejpam-4055	150	14	(	(	PUNCT
ejpam-4055	150	15	hu)∩du	hu)∩du	NOUN
ejpam-4055	150	16	.	.	PUNCT
ejpam-4055	151	1	hence	hence	ADV
ejpam-4055	151	2	,	,	PUNCT
ejpam-4055	151	3	y	y	PROPN
ejpam-4055	151	4	∈	∈	PROPN
ejpam-4055	151	5	du	du	NOUN
ejpam-4055	151	6	\nhu(x	\nhu(x	NOUN
ejpam-4055	151	7	)	)	PUNCT
ejpam-4055	151	8	.	.	PUNCT
ejpam-4055	152	1	thus	thus	ADV
ejpam-4055	152	2	,	,	PUNCT
ejpam-4055	152	3	nhu(x	nhu(x	NOUN
ejpam-4055	152	4	)	)	PUNCT
ejpam-4055	152	5	∩du	∩du	NOUN
ejpam-4055	152	6	6=	6=	ADP
ejpam-4055	152	7	du	du	PROPN
ejpam-4055	152	8	,	,	PUNCT
ejpam-4055	152	9	showing	show	VERB
ejpam-4055	152	10	that	that	SCONJ
ejpam-4055	152	11	du	du	PROPN
ejpam-4055	152	12	is	be	AUX
ejpam-4055	152	13	strictly	strictly	ADV
ejpam-4055	152	14	locating	locate	VERB
ejpam-4055	152	15	.	.	PUNCT
ejpam-4055	153	1	for	for	ADP
ejpam-4055	153	2	the	the	DET
ejpam-4055	153	3	converse	converse	NOUN
ejpam-4055	153	4	,	,	PUNCT
ejpam-4055	153	5	suppose	suppose	VERB
ejpam-4055	153	6	that	that	SCONJ
ejpam-4055	153	7	w	w	PROPN
ejpam-4055	153	8	∩v	∩v	PROPN
ejpam-4055	153	9	(	(	PUNCT
ejpam-4055	153	10	hv	hv	PROPN
ejpam-4055	153	11	)	)	PUNCT
ejpam-4055	153	12	6=	6=	ADP
ejpam-4055	153	13	∅	∅	NOUN
ejpam-4055	153	14	for	for	ADP
ejpam-4055	153	15	every	every	DET
ejpam-4055	153	16	v	v	NUM
ejpam-4055	153	17	∈	∈	PROPN
ejpam-4055	153	18	v	v	NOUN
ejpam-4055	153	19	(	(	PUNCT
ejpam-4055	153	20	g	g	NOUN
ejpam-4055	153	21	)	)	PUNCT
ejpam-4055	153	22	and	and	CCONJ
ejpam-4055	153	23	w	w	NOUN
ejpam-4055	153	24	=	=	PUNCT
ejpam-4055	153	25	a∪b∪d	a∪b∪d	NOUN
ejpam-4055	153	26	where	where	SCONJ
ejpam-4055	153	27	a	a	DET
ejpam-4055	153	28	,	,	PUNCT
ejpam-4055	153	29	b	b	NOUN
ejpam-4055	153	30	and	and	CCONJ
ejpam-4055	153	31	d	d	AUX
ejpam-4055	153	32	satisfy	satisfy	VERB
ejpam-4055	153	33	the	the	DET
ejpam-4055	153	34	given	give	VERB
ejpam-4055	153	35	conditions	condition	NOUN
ejpam-4055	153	36	.	.	PUNCT
ejpam-4055	154	1	let	let	VERB
ejpam-4055	154	2	x	x	SYM
ejpam-4055	154	3	∈	∈	PROPN
ejpam-4055	154	4	v	v	X
ejpam-4055	154	5	(	(	PUNCT
ejpam-4055	154	6	g	g	PROPN
ejpam-4055	154	7	◦	◦	NOUN
ejpam-4055	154	8	h	h	NOUN
ejpam-4055	154	9	)	)	PUNCT
ejpam-4055	154	10	\w	\w	PUNCT
ejpam-4055	154	11	and	and	CCONJ
ejpam-4055	154	12	let	let	VERB
ejpam-4055	154	13	v	v	NUM
ejpam-4055	154	14	∈	∈	PROPN
ejpam-4055	154	15	v	v	NOUN
ejpam-4055	154	16	(	(	PUNCT
ejpam-4055	154	17	g	g	NOUN
ejpam-4055	154	18	)	)	PUNCT
ejpam-4055	154	19	such	such	ADJ
ejpam-4055	154	20	that	that	SCONJ
ejpam-4055	154	21	x	x	SYM
ejpam-4055	154	22	∈	∈	NOUN
ejpam-4055	154	23	v	v	NOUN
ejpam-4055	154	24	(	(	PUNCT
ejpam-4055	154	25	v	v	NOUN
ejpam-4055	154	26	+	+	CCONJ
ejpam-4055	154	27	hv	hv	NOUN
ejpam-4055	154	28	)	)	PUNCT
ejpam-4055	154	29	.	.	PUNCT
ejpam-4055	155	1	suppose	suppose	VERB
ejpam-4055	155	2	x	x	PUNCT
ejpam-4055	156	1	=	=	PUNCT
ejpam-4055	156	2	v.	v.	ADP
ejpam-4055	156	3	then	then	ADV
ejpam-4055	156	4	v	v	X
ejpam-4055	156	5	/∈	/∈	PUNCT
ejpam-4055	156	6	a.	a.	NOUN
ejpam-4055	156	7	let	let	VERB
ejpam-4055	156	8	u	u	PROPN
ejpam-4055	156	9	∈	∈	PROPN
ejpam-4055	156	10	v	v	ADP
ejpam-4055	156	11	(	(	PUNCT
ejpam-4055	156	12	g	g	NOUN
ejpam-4055	156	13	)	)	PUNCT
ejpam-4055	156	14	∩	∩	NOUN
ejpam-4055	156	15	ng(v	ng(v	NUM
ejpam-4055	156	16	)	)	PUNCT
ejpam-4055	156	17	.	.	PUNCT
ejpam-4055	157	1	since	since	SCONJ
ejpam-4055	157	2	w	w	PROPN
ejpam-4055	157	3	∩	∩	PROPN
ejpam-4055	157	4	v	v	X
ejpam-4055	157	5	(	(	PUNCT
ejpam-4055	157	6	hu	hu	PROPN
ejpam-4055	157	7	)	)	PUNCT
ejpam-4055	157	8	6=	6=	ADP
ejpam-4055	157	9	∅	∅	NOUN
ejpam-4055	157	10	,	,	PUNCT
ejpam-4055	157	11	there	there	PRON
ejpam-4055	157	12	exists	exist	VERB
ejpam-4055	157	13	y	y	PROPN
ejpam-4055	157	14	∈	∈	PROPN
ejpam-4055	157	15	w	w	PROPN
ejpam-4055	157	16	∩	∩	ADJ
ejpam-4055	157	17	v	v	X
ejpam-4055	157	18	(	(	PUNCT
ejpam-4055	157	19	hu	hu	PROPN
ejpam-4055	157	20	)	)	PUNCT
ejpam-4055	157	21	and	and	CCONJ
ejpam-4055	157	22	dg	dg	PROPN
ejpam-4055	157	23	◦	◦	NOUN
ejpam-4055	157	24	h(x	h(x	PROPN
ejpam-4055	157	25	,	,	PUNCT
ejpam-4055	157	26	y	y	PROPN
ejpam-4055	157	27	)	)	PUNCT
ejpam-4055	157	28	=	=	SYM
ejpam-4055	157	29	2	2	X
ejpam-4055	157	30	.	.	PUNCT
ejpam-4055	157	31	suppose	suppose	VERB
ejpam-4055	157	32	x	x	PUNCT
ejpam-4055	157	33	6=	6=	ADP
ejpam-4055	157	34	v.	v.	ADP
ejpam-4055	157	35	if	if	SCONJ
ejpam-4055	157	36	v	v	NOUN
ejpam-4055	157	37	∈	∈	PROPN
ejpam-4055	157	38	ng(a	ng(a	NOUN
ejpam-4055	157	39	)	)	PUNCT
ejpam-4055	157	40	,	,	PUNCT
ejpam-4055	157	41	then	then	ADV
ejpam-4055	157	42	there	there	PRON
ejpam-4055	157	43	exists	exist	VERB
ejpam-4055	157	44	z	z	PROPN
ejpam-4055	157	45	∈	∈	PROPN
ejpam-4055	157	46	a	a	DET
ejpam-4055	157	47	∩	∩	NOUN
ejpam-4055	157	48	ng(v	ng(v	NUM
ejpam-4055	157	49	)	)	PUNCT
ejpam-4055	157	50	.	.	PUNCT
ejpam-4055	158	1	hence	hence	ADV
ejpam-4055	158	2	,	,	PUNCT
ejpam-4055	158	3	z	z	PROPN
ejpam-4055	158	4	∈	∈	PROPN
ejpam-4055	158	5	w	w	PROPN
ejpam-4055	158	6	and	and	CCONJ
ejpam-4055	158	7	dg	dg	PROPN
ejpam-4055	158	8	◦	◦	NOUN
ejpam-4055	158	9	h(x	h(x	PROPN
ejpam-4055	158	10	,	,	PUNCT
ejpam-4055	158	11	z	z	NOUN
ejpam-4055	158	12	)	)	PUNCT
ejpam-4055	158	13	=	=	SYM
ejpam-4055	158	14	2	2	X
ejpam-4055	158	15	.	.	PUNCT
ejpam-4055	158	16	suppose	suppose	VERB
ejpam-4055	158	17	v	v	X
ejpam-4055	158	18	/∈	/∈	PUNCT
ejpam-4055	158	19	ng(a	ng(a	NUM
ejpam-4055	158	20	)	)	PUNCT
ejpam-4055	158	21	.	.	PUNCT
ejpam-4055	159	1	then	then	ADV
ejpam-4055	159	2	x	x	SYM
ejpam-4055	159	3	∈	∈	PROPN
ejpam-4055	159	4	v	v	ADP
ejpam-4055	159	5	(	(	PUNCT
ejpam-4055	159	6	hv	hv	PROPN
ejpam-4055	159	7	)	)	PUNCT
ejpam-4055	159	8	\	\	PROPN
ejpam-4055	159	9	dv	dv	PROPN
ejpam-4055	159	10	.	.	PROPN
ejpam-4055	160	1	since	since	SCONJ
ejpam-4055	160	2	dv	dv	PROPN
ejpam-4055	160	3	is	be	AUX
ejpam-4055	160	4	strictly	strictly	ADV
ejpam-4055	160	5	locating	locate	VERB
ejpam-4055	160	6	there	there	ADV
ejpam-4055	160	7	exists	exist	VERB
ejpam-4055	160	8	y	y	PROPN
ejpam-4055	160	9	∈	∈	PROPN
ejpam-4055	160	10	dv	dv	PROPN
ejpam-4055	160	11	\	\	PROPN
ejpam-4055	160	12	nhv(x	nhv(x	PROPN
ejpam-4055	160	13	)	)	PUNCT
ejpam-4055	160	14	.	.	PUNCT
ejpam-4055	161	1	thus	thus	ADV
ejpam-4055	161	2	,	,	PUNCT
ejpam-4055	161	3	y	y	PROPN
ejpam-4055	161	4	∈	∈	PROPN
ejpam-4055	161	5	w	w	PROPN
ejpam-4055	161	6	and	and	CCONJ
ejpam-4055	161	7	dg	dg	PROPN
ejpam-4055	161	8	◦	◦	NOUN
ejpam-4055	161	9	h(x	h(x	PROPN
ejpam-4055	161	10	,	,	PUNCT
ejpam-4055	161	11	y	y	PROPN
ejpam-4055	161	12	)	)	PUNCT
ejpam-4055	161	13	=	=	SYM
ejpam-4055	162	1	2	2	X
ejpam-4055	162	2	.	.	PUNCT
ejpam-4055	162	3	this	this	PRON
ejpam-4055	162	4	shows	show	VERB
ejpam-4055	162	5	that	that	SCONJ
ejpam-4055	162	6	w	w	NOUN
ejpam-4055	162	7	is	be	AUX
ejpam-4055	162	8	a	a	DET
ejpam-4055	162	9	hop	hop	NOUN
ejpam-4055	162	10	dominating	dominating	NOUN
ejpam-4055	162	11	set	set	NOUN
ejpam-4055	162	12	of	of	ADP
ejpam-4055	162	13	g	g	PROPN
ejpam-4055	162	14	◦	◦	NOUN
ejpam-4055	162	15	h.	h.	PROPN
ejpam-4055	162	16	since	since	SCONJ
ejpam-4055	162	17	bv	bv	PROPN
ejpam-4055	162	18	or	or	CCONJ
ejpam-4055	162	19	dv	dv	PROPN
ejpam-4055	162	20	is	be	AUX
ejpam-4055	162	21	a	a	DET
ejpam-4055	162	22	locating	locating	NOUN
ejpam-4055	162	23	set	set	NOUN
ejpam-4055	162	24	for	for	ADP
ejpam-4055	162	25	each	each	DET
ejpam-4055	162	26	v	v	NUM
ejpam-4055	162	27	∈	∈	PROPN
ejpam-4055	162	28	v	v	NOUN
ejpam-4055	162	29	(	(	PUNCT
ejpam-4055	162	30	g	g	NOUN
ejpam-4055	162	31	)	)	PUNCT
ejpam-4055	162	32	,	,	PUNCT
ejpam-4055	162	33	by	by	ADP
ejpam-4055	162	34	theorem	theorem	NOUN
ejpam-4055	162	35	3	3	NUM
ejpam-4055	162	36	,	,	PUNCT
ejpam-4055	162	37	w	w	PROPN
ejpam-4055	162	38	is	be	AUX
ejpam-4055	162	39	a	a	DET
ejpam-4055	162	40	resolving	resolving	NOUN
ejpam-4055	162	41	set	set	NOUN
ejpam-4055	162	42	of	of	ADP
ejpam-4055	162	43	g	g	PROPN
ejpam-4055	162	44	◦	◦	NOUN
ejpam-4055	162	45	h.	h.	NOUN
ejpam-4055	162	46	accordingly	accordingly	ADV
ejpam-4055	162	47	,	,	PUNCT
ejpam-4055	162	48	w	w	PROPN
ejpam-4055	162	49	is	be	AUX
ejpam-4055	162	50	a	a	DET
ejpam-4055	162	51	resolving	resolve	VERB
ejpam-4055	162	52	hop	hop	NOUN
ejpam-4055	162	53	dominating	dominating	NOUN
ejpam-4055	162	54	set	set	NOUN
ejpam-4055	162	55	of	of	ADP
ejpam-4055	162	56	g	g	PROPN
ejpam-4055	162	57	◦	◦	NOUN
ejpam-4055	162	58	h.	h.	NOUN
ejpam-4055	162	59	corollary	corollary	ADJ
ejpam-4055	162	60	2	2	PROPN
ejpam-4055	162	61	.	.	PUNCT
ejpam-4055	163	1	let	let	VERB
ejpam-4055	163	2	g	g	PRON
ejpam-4055	163	3	be	be	AUX
ejpam-4055	163	4	a	a	DET
ejpam-4055	163	5	non	non	ADJ
ejpam-4055	163	6	-	-	ADJ
ejpam-4055	163	7	trivial	trivial	ADJ
ejpam-4055	163	8	graph	graph	NOUN
ejpam-4055	163	9	of	of	ADP
ejpam-4055	163	10	order	order	NOUN
ejpam-4055	163	11	m	m	VERB
ejpam-4055	163	12	and	and	CCONJ
ejpam-4055	163	13	h	h	NOUN
ejpam-4055	163	14	be	be	VERB
ejpam-4055	163	15	any	any	DET
ejpam-4055	163	16	graph	graph	NOUN
ejpam-4055	163	17	.	.	PUNCT
ejpam-4055	164	1	then	then	ADV
ejpam-4055	164	2	the	the	DET
ejpam-4055	164	3	following	follow	VERB
ejpam-4055	164	4	statements	statement	NOUN
ejpam-4055	164	5	hold	hold	VERB
ejpam-4055	164	6	.	.	PUNCT
ejpam-4055	165	1	(	(	PUNCT
ejpam-4055	165	2	i	i	NOUN
ejpam-4055	165	3	)	)	PUNCT
ejpam-4055	165	4	γrh(g	γrh(g	PROPN
ejpam-4055	165	5	◦	◦	NOUN
ejpam-4055	165	6	h	h	NOUN
ejpam-4055	165	7	)	)	PUNCT
ejpam-4055	165	8	≤	≤	NOUN
ejpam-4055	165	9	m(1	m(1	NOUN
ejpam-4055	165	10	+	+	CCONJ
ejpam-4055	165	11	ln(h	ln(h	NUM
ejpam-4055	165	12	)	)	PUNCT
ejpam-4055	165	13	)	)	PUNCT
ejpam-4055	165	14	.	.	PUNCT
ejpam-4055	166	1	j.	j.	PROPN
ejpam-4055	166	2	mohamad	mohamad	PROPN
ejpam-4055	166	3	,	,	PUNCT
ejpam-4055	166	4	h.	h.	PROPN
ejpam-4055	166	5	rara	rara	PROPN
ejpam-4055	166	6	/	/	SYM
ejpam-4055	166	7	eur	eur	PROPN
ejpam-4055	166	8	.	.	PUNCT
ejpam-4055	167	1	j.	j.	PROPN
ejpam-4055	167	2	pure	pure	PROPN
ejpam-4055	167	3	appl	appl	PROPN
ejpam-4055	167	4	.	.	PROPN
ejpam-4055	167	5	math	math	PROPN
ejpam-4055	167	6	,	,	PUNCT
ejpam-4055	167	7	14	14	NUM
ejpam-4055	167	8	(	(	PUNCT
ejpam-4055	167	9	3	3	NUM
ejpam-4055	167	10	)	)	PUNCT
ejpam-4055	167	11	(	(	PUNCT
ejpam-4055	167	12	2021	2021	NUM
ejpam-4055	167	13	)	)	PUNCT
ejpam-4055	167	14	,	,	PUNCT
ejpam-4055	167	15	1015	1015	NUM
ejpam-4055	167	16	-	-	SYM
ejpam-4055	167	17	1023	1023	NUM
ejpam-4055	167	18	1020	1020	NUM
ejpam-4055	167	19	(	(	PUNCT
ejpam-4055	167	20	ii	ii	NOUN
ejpam-4055	167	21	)	)	PUNCT
ejpam-4055	167	22	if	if	SCONJ
ejpam-4055	167	23	sln(h	sln(h	ADJ
ejpam-4055	167	24	)	)	PUNCT
ejpam-4055	167	25	=	=	SYM
ejpam-4055	167	26	ln(h	ln(h	NUM
ejpam-4055	167	27	)	)	PUNCT
ejpam-4055	167	28	,	,	PUNCT
ejpam-4055	167	29	then	then	ADV
ejpam-4055	167	30	γrh(g	γrh(g	PROPN
ejpam-4055	167	31	◦	◦	NOUN
ejpam-4055	167	32	h	h	NOUN
ejpam-4055	167	33	)	)	PUNCT
ejpam-4055	167	34	=	=	SYM
ejpam-4055	167	35	m(sln(h	m(sln(h	PROPN
ejpam-4055	167	36	)	)	PUNCT
ejpam-4055	167	37	)	)	PUNCT
ejpam-4055	167	38	.	.	PUNCT
ejpam-4055	168	1	proof	proof	NOUN
ejpam-4055	168	2	:	:	PUNCT
ejpam-4055	168	3	(	(	PUNCT
ejpam-4055	168	4	i	i	NOUN
ejpam-4055	168	5	)	)	PUNCT
ejpam-4055	168	6	set	set	VERB
ejpam-4055	168	7	a1	a1	NOUN
ejpam-4055	168	8	=	=	SYM
ejpam-4055	168	9	v	v	NOUN
ejpam-4055	168	10	(	(	PUNCT
ejpam-4055	168	11	g	g	NOUN
ejpam-4055	168	12	)	)	PUNCT
ejpam-4055	168	13	and	and	CCONJ
ejpam-4055	168	14	let	let	VERB
ejpam-4055	168	15	bv	bv	PRON
ejpam-4055	168	16	be	be	AUX
ejpam-4055	168	17	an	an	DET
ejpam-4055	168	18	ln	ln	ADV
ejpam-4055	168	19	-	-	PUNCT
ejpam-4055	168	20	set	set	NOUN
ejpam-4055	168	21	of	of	ADP
ejpam-4055	168	22	h	h	NOUN
ejpam-4055	168	23	for	for	ADP
ejpam-4055	168	24	each	each	DET
ejpam-4055	168	25	v	v	NUM
ejpam-4055	168	26	∈	∈	PROPN
ejpam-4055	168	27	v	v	NOUN
ejpam-4055	168	28	(	(	PUNCT
ejpam-4055	168	29	g	g	NOUN
ejpam-4055	168	30	)	)	PUNCT
ejpam-4055	168	31	.	.	PUNCT
ejpam-4055	169	1	then	then	ADV
ejpam-4055	169	2	w1	w1	NOUN
ejpam-4055	169	3	=	=	SYM
ejpam-4055	169	4	a1	a1	NOUN
ejpam-4055	169	5	∪	∪	X
ejpam-4055	169	6	(	(	PUNCT
ejpam-4055	169	7	⋃	⋃	NOUN
ejpam-4055	169	8	v∈v	v∈v	NOUN
ejpam-4055	169	9	(	(	PUNCT
ejpam-4055	169	10	g)bv	g)bv	PROPN
ejpam-4055	169	11	)	)	PUNCT
ejpam-4055	169	12	is	be	AUX
ejpam-4055	169	13	a	a	DET
ejpam-4055	169	14	resolving	resolve	VERB
ejpam-4055	169	15	hop	hop	NOUN
ejpam-4055	169	16	dominating	dominating	NOUN
ejpam-4055	169	17	set	set	NOUN
ejpam-4055	169	18	of	of	ADP
ejpam-4055	169	19	g	g	PROPN
ejpam-4055	169	20	◦	◦	NOUN
ejpam-4055	169	21	h	h	NOUN
ejpam-4055	169	22	by	by	ADP
ejpam-4055	169	23	theorem	theorem	NOUN
ejpam-4055	169	24	4	4	NUM
ejpam-4055	169	25	,	,	PUNCT
ejpam-4055	169	26	hence	hence	ADV
ejpam-4055	169	27	,	,	PUNCT
ejpam-4055	169	28	γrh(g	γrh(g	PROPN
ejpam-4055	169	29	◦	◦	NOUN
ejpam-4055	169	30	h	h	NOUN
ejpam-4055	169	31	)	)	PUNCT
ejpam-4055	169	32	≤	≤	ADJ
ejpam-4055	169	33	|w1|	|w1|	NOUN
ejpam-4055	169	34	=	=	SYM
ejpam-4055	169	35	|v	|v	X
ejpam-4055	169	36	(	(	PUNCT
ejpam-4055	169	37	g)|+	g)|+	PROPN
ejpam-4055	169	38	|v	|v	PROPN
ejpam-4055	169	39	(	(	PUNCT
ejpam-4055	169	40	g)||bv|	g)||bv|	PROPN
ejpam-4055	169	41	=	=	SYM
ejpam-4055	169	42	m(1	m(1	PROPN
ejpam-4055	169	43	+	+	NUM
ejpam-4055	169	44	ln(h	ln(h	NUM
ejpam-4055	169	45	)	)	PUNCT
ejpam-4055	169	46	)	)	PUNCT
ejpam-4055	169	47	.	.	PUNCT
ejpam-4055	170	1	(	(	PUNCT
ejpam-4055	170	2	ii	ii	NOUN
ejpam-4055	170	3	)	)	PUNCT
ejpam-4055	170	4	suppose	suppose	VERB
ejpam-4055	170	5	that	that	SCONJ
ejpam-4055	170	6	sln(h	sln(h	ADJ
ejpam-4055	170	7	)	)	PUNCT
ejpam-4055	170	8	=	=	PUNCT
ejpam-4055	170	9	ln(h	ln(h	NUM
ejpam-4055	170	10	)	)	PUNCT
ejpam-4055	170	11	.	.	PUNCT
ejpam-4055	171	1	set	set	VERB
ejpam-4055	171	2	a2	a2	PROPN
ejpam-4055	171	3	=	=	SYM
ejpam-4055	171	4	∅	∅	NOUN
ejpam-4055	172	1	and	and	CCONJ
ejpam-4055	172	2	let	let	VERB
ejpam-4055	172	3	du	du	NOUN
ejpam-4055	172	4	be	be	AUX
ejpam-4055	172	5	an	an	DET
ejpam-4055	172	6	sln	sln	NOUN
ejpam-4055	172	7	-	-	PUNCT
ejpam-4055	172	8	set	set	NOUN
ejpam-4055	172	9	of	of	ADP
ejpam-4055	172	10	h	h	NOUN
ejpam-4055	172	11	for	for	ADP
ejpam-4055	172	12	each	each	DET
ejpam-4055	172	13	u	u	PROPN
ejpam-4055	172	14	∈	∈	PROPN
ejpam-4055	172	15	v	v	NOUN
ejpam-4055	172	16	(	(	PUNCT
ejpam-4055	172	17	g	g	NOUN
ejpam-4055	172	18	)	)	PUNCT
ejpam-4055	172	19	.	.	PUNCT
ejpam-4055	173	1	then	then	ADV
ejpam-4055	173	2	w2	w2	NOUN
ejpam-4055	173	3	=	=	PROPN
ejpam-4055	173	4	a2	a2	PROPN
ejpam-4055	173	5	∪	∪	ADV
ejpam-4055	173	6	(	(	PUNCT
ejpam-4055	173	7	⋃	⋃	NOUN
ejpam-4055	173	8	u∈v	u∈v	NOUN
ejpam-4055	173	9	(	(	PUNCT
ejpam-4055	173	10	g)du	g)du	PROPN
ejpam-4055	173	11	)	)	PUNCT
ejpam-4055	173	12	is	be	AUX
ejpam-4055	173	13	a	a	DET
ejpam-4055	173	14	resolving	resolve	VERB
ejpam-4055	173	15	hop	hop	NOUN
ejpam-4055	173	16	dominating	dominating	NOUN
ejpam-4055	173	17	set	set	NOUN
ejpam-4055	173	18	of	of	ADP
ejpam-4055	173	19	g	g	PROPN
ejpam-4055	173	20	◦	◦	NOUN
ejpam-4055	173	21	h	h	NOUN
ejpam-4055	173	22	by	by	ADP
ejpam-4055	173	23	theorem	theorem	NOUN
ejpam-4055	173	24	4	4	NUM
ejpam-4055	173	25	.	.	PUNCT
ejpam-4055	174	1	thus	thus	ADV
ejpam-4055	174	2	,	,	PUNCT
ejpam-4055	174	3	γrh(g	γrh(g	PROPN
ejpam-4055	174	4	◦	◦	NOUN
ejpam-4055	174	5	h	h	NOUN
ejpam-4055	174	6	)	)	PUNCT
ejpam-4055	174	7	≤	≤	NOUN
ejpam-4055	174	8	|w2|	|w2|	NOUN
ejpam-4055	174	9	=	=	SYM
ejpam-4055	174	10	|a2|+	|a2|+	X
ejpam-4055	174	11	|v	|v	X
ejpam-4055	174	12	(	(	PUNCT
ejpam-4055	174	13	g)||du|	g)||du|	NOUN
ejpam-4055	174	14	=	=	PUNCT
ejpam-4055	174	15	m(sln(h	m(sln(h	PROPN
ejpam-4055	174	16	)	)	PUNCT
ejpam-4055	174	17	)	)	PUNCT
ejpam-4055	174	18	.	.	PUNCT
ejpam-4055	175	1	now	now	ADV
ejpam-4055	175	2	,	,	PUNCT
ejpam-4055	175	3	let	let	VERB
ejpam-4055	175	4	w0	w0	PROPN
ejpam-4055	175	5	=	=	PROPN
ejpam-4055	175	6	a0	a0	PROPN
ejpam-4055	175	7	∪	∪	X
ejpam-4055	175	8	(	(	PUNCT
ejpam-4055	175	9	⋃	⋃	NOUN
ejpam-4055	175	10	u∈v	u∈v	NOUN
ejpam-4055	175	11	(	(	PUNCT
ejpam-4055	175	12	g)\s0	g)\s0	NOUN
ejpam-4055	175	13	bv	bv	NOUN
ejpam-4055	175	14	)	)	PUNCT
ejpam-4055	175	15	∪	∪	NOUN
ejpam-4055	175	16	(	(	PUNCT
ejpam-4055	175	17	⋃	⋃	PROPN
ejpam-4055	175	18	u∈s0	u∈s0	ADJ
ejpam-4055	175	19	du	du	X
ejpam-4055	175	20	)	)	PUNCT
ejpam-4055	175	21	be	be	AUX
ejpam-4055	175	22	a	a	DET
ejpam-4055	175	23	γrh	γrh	NOUN
ejpam-4055	175	24	-	-	PUNCT
ejpam-4055	175	25	set	set	NOUN
ejpam-4055	175	26	of	of	ADP
ejpam-4055	175	27	g	g	PROPN
ejpam-4055	175	28	◦	◦	NOUN
ejpam-4055	175	29	h.	h.	NOUN
ejpam-4055	175	30	by	by	ADP
ejpam-4055	175	31	theorem	theorem	NOUN
ejpam-4055	175	32	4	4	NUM
ejpam-4055	175	33	,	,	PUNCT
ejpam-4055	175	34	a0	a0	NOUN
ejpam-4055	175	35	⊆	⊆	NUM
ejpam-4055	175	36	v	v	NOUN
ejpam-4055	175	37	(	(	PUNCT
ejpam-4055	175	38	g	g	NOUN
ejpam-4055	175	39	)	)	PUNCT
ejpam-4055	175	40	,	,	PUNCT
ejpam-4055	175	41	s0	s0	PROPN
ejpam-4055	175	42	=	=	PUNCT
ejpam-4055	175	43	{	{	PUNCT
ejpam-4055	175	44	x	x	PROPN
ejpam-4055	175	45	∈	∈	PROPN
ejpam-4055	175	46	v	v	NOUN
ejpam-4055	175	47	(	(	PUNCT
ejpam-4055	175	48	g	g	NOUN
ejpam-4055	175	49	)	)	PUNCT
ejpam-4055	175	50	:	:	PUNCT
ejpam-4055	175	51	x	x	X
ejpam-4055	175	52	/∈	/∈	PUNCT
ejpam-4055	175	53	ng(a0	ng(a0	NOUN
ejpam-4055	175	54	)	)	PUNCT
ejpam-4055	175	55	}	}	PUNCT
ejpam-4055	175	56	,	,	PUNCT
ejpam-4055	175	57	bv	bv	PROPN
ejpam-4055	175	58	is	be	AUX
ejpam-4055	175	59	a	a	DET
ejpam-4055	175	60	locating	locating	NOUN
ejpam-4055	175	61	set	set	NOUN
ejpam-4055	175	62	of	of	ADP
ejpam-4055	175	63	hv	hv	PROPN
ejpam-4055	175	64	for	for	ADP
ejpam-4055	175	65	each	each	DET
ejpam-4055	175	66	v	v	NUM
ejpam-4055	175	67	∈	∈	PROPN
ejpam-4055	175	68	v	v	NOUN
ejpam-4055	175	69	(	(	PUNCT
ejpam-4055	175	70	g	g	NOUN
ejpam-4055	175	71	)	)	PUNCT
ejpam-4055	175	72	\	\	NOUN
ejpam-4055	175	73	s0	s0	PROPN
ejpam-4055	175	74	and	and	CCONJ
ejpam-4055	175	75	du	du	PROPN
ejpam-4055	175	76	is	be	AUX
ejpam-4055	175	77	a	a	DET
ejpam-4055	175	78	strict	strict	ADJ
ejpam-4055	175	79	locating	locating	NOUN
ejpam-4055	175	80	set	set	NOUN
ejpam-4055	175	81	of	of	ADP
ejpam-4055	175	82	hu	hu	PROPN
ejpam-4055	175	83	for	for	ADP
ejpam-4055	175	84	each	each	DET
ejpam-4055	175	85	u	u	PROPN
ejpam-4055	175	86	∈	∈	PROPN
ejpam-4055	175	87	s0	s0	NOUN
ejpam-4055	175	88	.	.	PUNCT
ejpam-4055	176	1	thus	thus	ADV
ejpam-4055	176	2	,	,	PUNCT
ejpam-4055	176	3	γrh(g	γrh(g	PROPN
ejpam-4055	176	4	◦	◦	NOUN
ejpam-4055	176	5	h	h	NOUN
ejpam-4055	176	6	)	)	PUNCT
ejpam-4055	176	7	=	=	NOUN
ejpam-4055	176	8	|w0|	|w0|	X
ejpam-4055	176	9	=	=	SYM
ejpam-4055	176	10	|a0|+	|a0|+	X
ejpam-4055	176	11	|v	|v	X
ejpam-4055	176	12	(	(	PUNCT
ejpam-4055	176	13	g	g	NOUN
ejpam-4055	176	14	)	)	PUNCT
ejpam-4055	176	15	\	\	PUNCT
ejpam-4055	177	1	s0|	s0|	PROPN
ejpam-4055	177	2	|bv|+	|bv|+	PROPN
ejpam-4055	177	3	|s0|	|s0|	NOUN
ejpam-4055	177	4	|du|	|du|	PROPN
ejpam-4055	177	5	≥	≥	PROPN
ejpam-4055	177	6	|v	|v	PROPN
ejpam-4055	177	7	(	(	PUNCT
ejpam-4055	177	8	g	g	NOUN
ejpam-4055	177	9	)	)	PUNCT
ejpam-4055	177	10	\	\	PROPN
ejpam-4055	178	1	s0|	s0|	PROPN
ejpam-4055	178	2	ln(h	ln(h	PUNCT
ejpam-4055	178	3	)	)	PUNCT
ejpam-4055	179	1	+	+	CCONJ
ejpam-4055	179	2	|s0|	|s0|	NOUN
ejpam-4055	179	3	sln(h	sln(h	PROPN
ejpam-4055	179	4	)	)	PUNCT
ejpam-4055	179	5	=	=	PRON
ejpam-4055	179	6	(	(	PUNCT
ejpam-4055	179	7	|v	|v	X
ejpam-4055	179	8	(	(	PUNCT
ejpam-4055	179	9	g)|	g)|	PROPN
ejpam-4055	179	10	−	−	PROPN
ejpam-4055	179	11	|s0|	|s0|	NOUN
ejpam-4055	179	12	)	)	PUNCT
ejpam-4055	179	13	sln(h	sln(h	PROPN
ejpam-4055	179	14	)	)	PUNCT
ejpam-4055	179	15	+	+	NUM
ejpam-4055	179	16	|s0|	|s0|	NOUN
ejpam-4055	179	17	sln(h	sln(h	PROPN
ejpam-4055	179	18	)	)	PUNCT
ejpam-4055	179	19	=	=	SYM
ejpam-4055	179	20	m(sln(h	m(sln(h	PROPN
ejpam-4055	179	21	)	)	PUNCT
ejpam-4055	179	22	)	)	PUNCT
ejpam-4055	179	23	.	.	PUNCT
ejpam-4055	180	1	therefore	therefore	ADV
ejpam-4055	180	2	,	,	PUNCT
ejpam-4055	180	3	γrh(g	γrh(g	PROPN
ejpam-4055	180	4	◦	◦	NOUN
ejpam-4055	180	5	h	h	NOUN
ejpam-4055	180	6	)	)	PUNCT
ejpam-4055	180	7	=	=	SYM
ejpam-4055	180	8	m(sln(h	m(sln(h	PROPN
ejpam-4055	180	9	)	)	PUNCT
ejpam-4055	180	10	)	)	PUNCT
ejpam-4055	180	11	.	.	PUNCT
ejpam-4055	181	1	5	5	X
ejpam-4055	181	2	.	.	X
ejpam-4055	181	3	on	on	ADP
ejpam-4055	181	4	resolving	resolve	VERB
ejpam-4055	181	5	hop	hop	NOUN
ejpam-4055	181	6	domination	domination	NOUN
ejpam-4055	181	7	in	in	ADP
ejpam-4055	181	8	the	the	DET
ejpam-4055	181	9	lexicographic	lexicographic	ADJ
ejpam-4055	181	10	product	product	NOUN
ejpam-4055	181	11	of	of	ADP
ejpam-4055	181	12	graphs	graph	NOUN
ejpam-4055	181	13	the	the	DET
ejpam-4055	181	14	lexicographic	lexicographic	ADJ
ejpam-4055	181	15	product	product	NOUN
ejpam-4055	181	16	of	of	ADP
ejpam-4055	181	17	two	two	NUM
ejpam-4055	181	18	graphs	graph	NOUN
ejpam-4055	181	19	g	g	NOUN
ejpam-4055	181	20	and	and	CCONJ
ejpam-4055	181	21	h	h	NOUN
ejpam-4055	181	22	,	,	PUNCT
ejpam-4055	181	23	denoted	denote	VERB
ejpam-4055	181	24	by	by	ADP
ejpam-4055	181	25	g[h	g[h	NOUN
ejpam-4055	181	26	]	]	PUNCT
ejpam-4055	181	27	,	,	PUNCT
ejpam-4055	181	28	is	be	AUX
ejpam-4055	181	29	the	the	DET
ejpam-4055	181	30	graph	graph	NOUN
ejpam-4055	181	31	with	with	ADP
ejpam-4055	181	32	vertex	vertex	NOUN
ejpam-4055	181	33	-	-	PUNCT
ejpam-4055	181	34	set	set	VERB
ejpam-4055	181	35	v	v	NOUN
ejpam-4055	181	36	(	(	PUNCT
ejpam-4055	181	37	g[h	g[h	PROPN
ejpam-4055	181	38	]	]	PUNCT
ejpam-4055	181	39	)	)	PUNCT
ejpam-4055	181	40	=	=	SYM
ejpam-4055	181	41	v	v	X
ejpam-4055	181	42	(	(	PUNCT
ejpam-4055	181	43	g	g	NOUN
ejpam-4055	181	44	)	)	PUNCT
ejpam-4055	181	45	×	×	NOUN
ejpam-4055	181	46	v	v	NOUN
ejpam-4055	181	47	(	(	PUNCT
ejpam-4055	181	48	h	h	NOUN
ejpam-4055	181	49	)	)	PUNCT
ejpam-4055	181	50	such	such	ADJ
ejpam-4055	181	51	that	that	SCONJ
ejpam-4055	181	52	(	(	PUNCT
ejpam-4055	181	53	u1	u1	NOUN
ejpam-4055	181	54	,	,	PUNCT
ejpam-4055	181	55	u2)(v1	u2)(v1	NOUN
ejpam-4055	181	56	,	,	PUNCT
ejpam-4055	181	57	v2	v2	NOUN
ejpam-4055	181	58	)	)	PUNCT
ejpam-4055	181	59	∈	∈	NOUN
ejpam-4055	181	60	e(g[h	e(g[h	NOUN
ejpam-4055	181	61	]	]	PUNCT
ejpam-4055	181	62	)	)	PUNCT
ejpam-4055	181	63	if	if	SCONJ
ejpam-4055	181	64	either	either	CCONJ
ejpam-4055	181	65	u1v1	u1v1	PROPN
ejpam-4055	181	66	∈	∈	PROPN
ejpam-4055	181	67	e(g	e(g	PROPN
ejpam-4055	181	68	)	)	PUNCT
ejpam-4055	181	69	or	or	CCONJ
ejpam-4055	181	70	u1	u1	NOUN
ejpam-4055	181	71	=	=	SYM
ejpam-4055	181	72	v1	v1	NOUN
ejpam-4055	181	73	and	and	CCONJ
ejpam-4055	181	74	u2v2	u2v2	ADJ
ejpam-4055	181	75	∈	∈	PROPN
ejpam-4055	181	76	e(h	e(h	PROPN
ejpam-4055	181	77	)	)	PUNCT
ejpam-4055	181	78	.	.	PUNCT
ejpam-4055	182	1	theorem	theorem	ADJ
ejpam-4055	182	2	5	5	NUM
ejpam-4055	182	3	.	.	PUNCT
ejpam-4055	183	1	[	[	X
ejpam-4055	183	2	7	7	NUM
ejpam-4055	183	3	,	,	PUNCT
ejpam-4055	183	4	8	8	NUM
ejpam-4055	183	5	]	]	PUNCT
ejpam-4055	183	6	let	let	VERB
ejpam-4055	183	7	g	g	NOUN
ejpam-4055	183	8	and	and	CCONJ
ejpam-4055	183	9	h	h	PROPN
ejpam-4055	183	10	be	be	VERB
ejpam-4055	183	11	non	non	ADJ
ejpam-4055	183	12	-	-	ADJ
ejpam-4055	183	13	trivial	trivial	ADJ
ejpam-4055	183	14	connected	connected	ADJ
ejpam-4055	183	15	graphs	graph	NOUN
ejpam-4055	183	16	with4(h	with4(h	NOUN
ejpam-4055	183	17	)	)	PUNCT
ejpam-4055	183	18	≤	≤	NOUN
ejpam-4055	183	19	|v	|v	X
ejpam-4055	183	20	(	(	PUNCT
ejpam-4055	183	21	h)|−2	h)|−2	PROPN
ejpam-4055	183	22	.	.	PUNCT
ejpam-4055	184	1	then	then	ADV
ejpam-4055	184	2	w	w	PROPN
ejpam-4055	184	3	=	=	PUNCT
ejpam-4055	184	4	⋃	⋃	PROPN
ejpam-4055	184	5	x∈s	x∈s	NOUN
ejpam-4055	185	1	[	[	X
ejpam-4055	185	2	{	{	PUNCT
ejpam-4055	185	3	x}×tx	x}×tx	X
ejpam-4055	185	4	]	]	X
ejpam-4055	185	5	,	,	PUNCT
ejpam-4055	185	6	where	where	SCONJ
ejpam-4055	185	7	s	s	VERB
ejpam-4055	185	8	⊆	⊆	NUM
ejpam-4055	185	9	v	v	NOUN
ejpam-4055	185	10	(	(	PUNCT
ejpam-4055	185	11	g	g	NOUN
ejpam-4055	185	12	)	)	PUNCT
ejpam-4055	185	13	and	and	CCONJ
ejpam-4055	185	14	tx	tx	VERB
ejpam-4055	185	15	⊆	⊆	NUM
ejpam-4055	185	16	v	v	NOUN
ejpam-4055	185	17	(	(	PUNCT
ejpam-4055	185	18	h	h	NOUN
ejpam-4055	185	19	)	)	PUNCT
ejpam-4055	185	20	for	for	ADP
ejpam-4055	185	21	each	each	DET
ejpam-4055	185	22	x	x	SYM
ejpam-4055	185	23	∈	∈	PROPN
ejpam-4055	185	24	s	s	NOUN
ejpam-4055	185	25	,	,	PUNCT
ejpam-4055	185	26	is	be	AUX
ejpam-4055	185	27	a	a	DET
ejpam-4055	185	28	resolving	resolving	NOUN
ejpam-4055	185	29	set	set	NOUN
ejpam-4055	185	30	of	of	ADP
ejpam-4055	185	31	g[h	g[h	NOUN
ejpam-4055	185	32	]	]	PUNCT
ejpam-4055	185	33	if	if	SCONJ
ejpam-4055	185	34	and	and	CCONJ
ejpam-4055	185	35	only	only	ADV
ejpam-4055	185	36	if	if	SCONJ
ejpam-4055	185	37	(	(	PUNCT
ejpam-4055	185	38	i	i	NOUN
ejpam-4055	185	39	)	)	PUNCT
ejpam-4055	185	40	s	s	PART
ejpam-4055	185	41	=	=	SYM
ejpam-4055	185	42	v	v	NOUN
ejpam-4055	185	43	(	(	PUNCT
ejpam-4055	185	44	g	g	NOUN
ejpam-4055	185	45	)	)	PUNCT
ejpam-4055	185	46	;	;	PUNCT
ejpam-4055	185	47	(	(	PUNCT
ejpam-4055	185	48	ii	ii	NOUN
ejpam-4055	185	49	)	)	PUNCT
ejpam-4055	185	50	tx	tx	PROPN
ejpam-4055	185	51	is	be	AUX
ejpam-4055	185	52	a	a	DET
ejpam-4055	185	53	locating	locating	NOUN
ejpam-4055	185	54	set	set	NOUN
ejpam-4055	185	55	for	for	ADP
ejpam-4055	185	56	every	every	DET
ejpam-4055	185	57	x	x	SYM
ejpam-4055	185	58	∈	∈	PROPN
ejpam-4055	185	59	v	v	NOUN
ejpam-4055	185	60	(	(	PUNCT
ejpam-4055	185	61	g	g	NOUN
ejpam-4055	185	62	)	)	PUNCT
ejpam-4055	185	63	;	;	PUNCT
ejpam-4055	185	64	(	(	PUNCT
ejpam-4055	185	65	iii	iii	X
ejpam-4055	185	66	)	)	PUNCT
ejpam-4055	185	67	tx	tx	NOUN
ejpam-4055	186	1	or	or	CCONJ
ejpam-4055	186	2	ty	ty	INTJ
ejpam-4055	186	3	is	be	AUX
ejpam-4055	186	4	a	a	DET
ejpam-4055	186	5	strictly	strictly	ADV
ejpam-4055	186	6	locating	locate	VERB
ejpam-4055	186	7	set	set	NOUN
ejpam-4055	186	8	of	of	ADP
ejpam-4055	186	9	h	h	NOUN
ejpam-4055	186	10	whenever	whenever	SCONJ
ejpam-4055	186	11	x	x	PRON
ejpam-4055	186	12	and	and	CCONJ
ejpam-4055	186	13	y	y	PROPN
ejpam-4055	186	14	are	be	AUX
ejpam-4055	186	15	adjacent	adjacent	ADJ
ejpam-4055	186	16	vertices	vertex	NOUN
ejpam-4055	186	17	of	of	ADP
ejpam-4055	186	18	g	g	NOUN
ejpam-4055	186	19	with	with	ADP
ejpam-4055	186	20	ng[x	ng[x	PROPN
ejpam-4055	186	21	]	]	X
ejpam-4055	186	22	=	=	PUNCT
ejpam-4055	186	23	ng[y	ng[y	PROPN
ejpam-4055	186	24	]	]	X
ejpam-4055	186	25	;	;	PUNCT
ejpam-4055	186	26	and	and	CCONJ
ejpam-4055	186	27	(	(	PUNCT
ejpam-4055	186	28	iv	iv	X
ejpam-4055	186	29	)	)	PUNCT
ejpam-4055	186	30	tx	tx	NOUN
ejpam-4055	187	1	or	or	CCONJ
ejpam-4055	187	2	ty	ty	INTJ
ejpam-4055	187	3	is	be	AUX
ejpam-4055	187	4	a	a	DET
ejpam-4055	187	5	(	(	PUNCT
ejpam-4055	187	6	locating	locating	NOUN
ejpam-4055	187	7	)	)	PUNCT
ejpam-4055	187	8	dominating	dominating	NOUN
ejpam-4055	187	9	set	set	NOUN
ejpam-4055	187	10	of	of	ADP
ejpam-4055	187	11	h	h	NOUN
ejpam-4055	187	12	whenever	whenever	SCONJ
ejpam-4055	187	13	x	x	PRON
ejpam-4055	187	14	and	and	CCONJ
ejpam-4055	187	15	y	y	PROPN
ejpam-4055	187	16	are	be	AUX
ejpam-4055	187	17	nonadjacent	nonadjacent	ADJ
ejpam-4055	187	18	vertices	vertex	NOUN
ejpam-4055	187	19	of	of	ADP
ejpam-4055	187	20	g	g	NOUN
ejpam-4055	187	21	with	with	ADP
ejpam-4055	187	22	ng(x	ng(x	NUM
ejpam-4055	187	23	)	)	PUNCT
ejpam-4055	187	24	=	=	PUNCT
ejpam-4055	187	25	ng(y	ng(y	NOUN
ejpam-4055	187	26	)	)	PUNCT
ejpam-4055	187	27	.	.	PUNCT
ejpam-4055	188	1	j.	j.	PROPN
ejpam-4055	188	2	mohamad	mohamad	PROPN
ejpam-4055	188	3	,	,	PUNCT
ejpam-4055	188	4	h.	h.	PROPN
ejpam-4055	188	5	rara	rara	PROPN
ejpam-4055	188	6	/	/	SYM
ejpam-4055	188	7	eur	eur	PROPN
ejpam-4055	188	8	.	.	PUNCT
ejpam-4055	189	1	j.	j.	PROPN
ejpam-4055	189	2	pure	pure	PROPN
ejpam-4055	189	3	appl	appl	PROPN
ejpam-4055	189	4	.	.	PROPN
ejpam-4055	189	5	math	math	PROPN
ejpam-4055	189	6	,	,	PUNCT
ejpam-4055	189	7	14	14	NUM
ejpam-4055	189	8	(	(	PUNCT
ejpam-4055	189	9	3	3	NUM
ejpam-4055	189	10	)	)	PUNCT
ejpam-4055	189	11	(	(	PUNCT
ejpam-4055	189	12	2021	2021	NUM
ejpam-4055	189	13	)	)	PUNCT
ejpam-4055	189	14	,	,	PUNCT
ejpam-4055	189	15	1015	1015	NUM
ejpam-4055	189	16	-	-	SYM
ejpam-4055	189	17	1023	1023	NUM
ejpam-4055	189	18	1021	1021	NUM
ejpam-4055	189	19	theorem	theorem	VERB
ejpam-4055	189	20	6	6	NUM
ejpam-4055	189	21	.	.	PUNCT
ejpam-4055	190	1	let	let	VERB
ejpam-4055	190	2	g	g	NOUN
ejpam-4055	190	3	and	and	CCONJ
ejpam-4055	190	4	h	h	PROPN
ejpam-4055	190	5	be	be	VERB
ejpam-4055	190	6	non	non	ADJ
ejpam-4055	190	7	-	-	ADJ
ejpam-4055	190	8	trivial	trivial	ADJ
ejpam-4055	190	9	connected	connected	ADJ
ejpam-4055	190	10	graphs	graph	NOUN
ejpam-4055	190	11	with	with	ADP
ejpam-4055	190	12	4(h	4(h	NUM
ejpam-4055	190	13	)	)	PUNCT
ejpam-4055	191	1	≤	≤	NOUN
ejpam-4055	191	2	|v	|v	X
ejpam-4055	191	3	(	(	PUNCT
ejpam-4055	191	4	h)|	h)|	NOUN
ejpam-4055	191	5	−	−	PROPN
ejpam-4055	191	6	2	2	NUM
ejpam-4055	191	7	.	.	PUNCT
ejpam-4055	191	8	then	then	ADV
ejpam-4055	191	9	w	w	PROPN
ejpam-4055	191	10	=	=	PUNCT
ejpam-4055	191	11	⋃	⋃	PROPN
ejpam-4055	191	12	x∈s	x∈s	NOUN
ejpam-4055	192	1	[	[	X
ejpam-4055	192	2	{	{	PUNCT
ejpam-4055	192	3	x}×tx	x}×tx	X
ejpam-4055	192	4	]	]	X
ejpam-4055	192	5	,	,	PUNCT
ejpam-4055	192	6	where	where	SCONJ
ejpam-4055	192	7	s	s	VERB
ejpam-4055	192	8	⊆	⊆	NUM
ejpam-4055	192	9	v	v	NOUN
ejpam-4055	192	10	(	(	PUNCT
ejpam-4055	192	11	g	g	NOUN
ejpam-4055	192	12	)	)	PUNCT
ejpam-4055	192	13	and	and	CCONJ
ejpam-4055	192	14	tx	tx	VERB
ejpam-4055	192	15	⊆	⊆	NUM
ejpam-4055	192	16	v	v	NOUN
ejpam-4055	192	17	(	(	PUNCT
ejpam-4055	192	18	h	h	NOUN
ejpam-4055	192	19	)	)	PUNCT
ejpam-4055	192	20	for	for	ADP
ejpam-4055	192	21	each	each	DET
ejpam-4055	192	22	x	x	SYM
ejpam-4055	192	23	∈	∈	PROPN
ejpam-4055	192	24	s	s	NOUN
ejpam-4055	192	25	,	,	PUNCT
ejpam-4055	192	26	is	be	AUX
ejpam-4055	192	27	a	a	DET
ejpam-4055	192	28	resolving	resolve	VERB
ejpam-4055	192	29	hop	hop	NOUN
ejpam-4055	192	30	dominating	dominating	NOUN
ejpam-4055	192	31	set	set	NOUN
ejpam-4055	192	32	of	of	ADP
ejpam-4055	192	33	g[h	g[h	PROPN
ejpam-4055	192	34	]	]	PUNCT
ejpam-4055	192	35	if	if	SCONJ
ejpam-4055	192	36	and	and	CCONJ
ejpam-4055	192	37	only	only	ADV
ejpam-4055	192	38	if	if	SCONJ
ejpam-4055	192	39	(	(	PUNCT
ejpam-4055	192	40	i	i	NOUN
ejpam-4055	192	41	)	)	PUNCT
ejpam-4055	192	42	s	s	PART
ejpam-4055	192	43	=	=	SYM
ejpam-4055	192	44	v	v	NOUN
ejpam-4055	192	45	(	(	PUNCT
ejpam-4055	192	46	g	g	NOUN
ejpam-4055	192	47	)	)	PUNCT
ejpam-4055	192	48	;	;	PUNCT
ejpam-4055	192	49	(	(	PUNCT
ejpam-4055	192	50	ii	ii	NOUN
ejpam-4055	192	51	)	)	PUNCT
ejpam-4055	192	52	tx	tx	PROPN
ejpam-4055	192	53	is	be	AUX
ejpam-4055	192	54	a	a	DET
ejpam-4055	192	55	locating	locating	NOUN
ejpam-4055	192	56	set	set	NOUN
ejpam-4055	192	57	for	for	ADP
ejpam-4055	192	58	every	every	DET
ejpam-4055	192	59	x	x	SYM
ejpam-4055	192	60	∈	∈	PROPN
ejpam-4055	192	61	v	v	NOUN
ejpam-4055	192	62	(	(	PUNCT
ejpam-4055	192	63	g	g	NOUN
ejpam-4055	192	64	)	)	PUNCT
ejpam-4055	192	65	;	;	PUNCT
ejpam-4055	192	66	(	(	PUNCT
ejpam-4055	192	67	iii	iii	X
ejpam-4055	192	68	)	)	PUNCT
ejpam-4055	192	69	tx	tx	NOUN
ejpam-4055	193	1	or	or	CCONJ
ejpam-4055	193	2	ty	ty	INTJ
ejpam-4055	193	3	is	be	AUX
ejpam-4055	193	4	a	a	DET
ejpam-4055	193	5	strictly	strictly	ADV
ejpam-4055	193	6	locating	locate	VERB
ejpam-4055	193	7	set	set	NOUN
ejpam-4055	193	8	of	of	ADP
ejpam-4055	193	9	h	h	NOUN
ejpam-4055	193	10	whenever	whenever	SCONJ
ejpam-4055	193	11	x	x	PRON
ejpam-4055	193	12	and	and	CCONJ
ejpam-4055	193	13	y	y	PROPN
ejpam-4055	193	14	are	be	AUX
ejpam-4055	193	15	adjacent	adjacent	ADJ
ejpam-4055	193	16	vertices	vertex	NOUN
ejpam-4055	193	17	of	of	ADP
ejpam-4055	193	18	g	g	NOUN
ejpam-4055	193	19	with	with	ADP
ejpam-4055	193	20	ng[x	ng[x	PROPN
ejpam-4055	193	21	]	]	X
ejpam-4055	193	22	=	=	PUNCT
ejpam-4055	193	23	ng[y	ng[y	PROPN
ejpam-4055	193	24	]	]	PUNCT
ejpam-4055	193	25	;	;	PUNCT
ejpam-4055	193	26	(	(	PUNCT
ejpam-4055	193	27	iv	iv	X
ejpam-4055	193	28	)	)	PUNCT
ejpam-4055	193	29	tx	tx	NOUN
ejpam-4055	193	30	or	or	CCONJ
ejpam-4055	193	31	ty	ty	INTJ
ejpam-4055	193	32	is	be	AUX
ejpam-4055	193	33	a	a	DET
ejpam-4055	193	34	(	(	PUNCT
ejpam-4055	193	35	locating	locating	NOUN
ejpam-4055	193	36	)	)	PUNCT
ejpam-4055	193	37	dominating	dominating	NOUN
ejpam-4055	193	38	set	set	NOUN
ejpam-4055	193	39	of	of	ADP
ejpam-4055	193	40	h	h	NOUN
ejpam-4055	193	41	whenever	whenever	SCONJ
ejpam-4055	193	42	x	x	PRON
ejpam-4055	193	43	and	and	CCONJ
ejpam-4055	193	44	y	y	PROPN
ejpam-4055	193	45	are	be	AUX
ejpam-4055	193	46	nonadjacent	nonadjacent	ADJ
ejpam-4055	193	47	vertices	vertex	NOUN
ejpam-4055	193	48	of	of	ADP
ejpam-4055	193	49	g	g	NOUN
ejpam-4055	193	50	with	with	ADP
ejpam-4055	193	51	ng(x	ng(x	NUM
ejpam-4055	193	52	)	)	PUNCT
ejpam-4055	193	53	=	=	PUNCT
ejpam-4055	193	54	ng(y	ng(y	NOUN
ejpam-4055	193	55	)	)	PUNCT
ejpam-4055	193	56	;	;	PUNCT
ejpam-4055	193	57	and	and	CCONJ
ejpam-4055	193	58	(	(	PUNCT
ejpam-4055	193	59	v	v	NOUN
ejpam-4055	193	60	)	)	PUNCT
ejpam-4055	193	61	tx	tx	PROPN
ejpam-4055	193	62	is	be	AUX
ejpam-4055	193	63	a	a	DET
ejpam-4055	193	64	strictly	strictly	ADV
ejpam-4055	193	65	locating	locate	VERB
ejpam-4055	193	66	set	set	NOUN
ejpam-4055	193	67	of	of	ADP
ejpam-4055	193	68	h	h	NOUN
ejpam-4055	193	69	for	for	ADP
ejpam-4055	193	70	each	each	DET
ejpam-4055	193	71	x	x	SYM
ejpam-4055	193	72	∈	∈	PROPN
ejpam-4055	193	73	s	s	PART
ejpam-4055	193	74	\ng(s	\ng(s	NOUN
ejpam-4055	193	75	,	,	PUNCT
ejpam-4055	193	76	2	2	NUM
ejpam-4055	193	77	)	)	PUNCT
ejpam-4055	193	78	.	.	PUNCT
ejpam-4055	194	1	proof	proof	NOUN
ejpam-4055	194	2	:	:	PUNCT
ejpam-4055	194	3	suppose	suppose	VERB
ejpam-4055	194	4	w	w	NOUN
ejpam-4055	194	5	is	be	AUX
ejpam-4055	194	6	a	a	DET
ejpam-4055	194	7	resolving	resolve	VERB
ejpam-4055	194	8	hop	hop	NOUN
ejpam-4055	194	9	dominating	dominating	NOUN
ejpam-4055	194	10	set	set	NOUN
ejpam-4055	194	11	of	of	ADP
ejpam-4055	194	12	g[h	g[h	PROPN
ejpam-4055	194	13	]	]	PUNCT
ejpam-4055	194	14	.	.	PUNCT
ejpam-4055	195	1	then	then	ADV
ejpam-4055	195	2	w	w	PROPN
ejpam-4055	195	3	is	be	AUX
ejpam-4055	195	4	a	a	DET
ejpam-4055	195	5	resolving	resolving	NOUN
ejpam-4055	195	6	set	set	NOUN
ejpam-4055	195	7	.	.	PUNCT
ejpam-4055	196	1	by	by	ADP
ejpam-4055	196	2	theorem	theorem	NOUN
ejpam-4055	196	3	5	5	NUM
ejpam-4055	196	4	,	,	PUNCT
ejpam-4055	196	5	(	(	PUNCT
ejpam-4055	196	6	i	i	NOUN
ejpam-4055	196	7	)	)	PUNCT
ejpam-4055	196	8	to	to	PART
ejpam-4055	196	9	(	(	PUNCT
ejpam-4055	196	10	iv	iv	X
ejpam-4055	196	11	)	)	PUNCT
ejpam-4055	196	12	hold	hold	NOUN
ejpam-4055	196	13	.	.	PUNCT
ejpam-4055	197	1	let	let	VERB
ejpam-4055	197	2	x	x	PUNCT
ejpam-4055	197	3	∈	∈	PROPN
ejpam-4055	197	4	s	s	PART
ejpam-4055	197	5	\	\	NOUN
ejpam-4055	197	6	ng(s	ng(s	PUNCT
ejpam-4055	197	7	,	,	PUNCT
ejpam-4055	197	8	2	2	NUM
ejpam-4055	197	9	)	)	PUNCT
ejpam-4055	197	10	.	.	PUNCT
ejpam-4055	198	1	if	if	SCONJ
ejpam-4055	198	2	tx	tx	PROPN
ejpam-4055	198	3	=	=	SYM
ejpam-4055	198	4	v	v	PROPN
ejpam-4055	198	5	(	(	PUNCT
ejpam-4055	198	6	h	h	NOUN
ejpam-4055	198	7	)	)	PUNCT
ejpam-4055	198	8	,	,	PUNCT
ejpam-4055	198	9	then	then	ADV
ejpam-4055	198	10	tx	tx	PROPN
ejpam-4055	198	11	is	be	AUX
ejpam-4055	198	12	a	a	DET
ejpam-4055	198	13	strictly	strictly	ADV
ejpam-4055	198	14	locating	locate	VERB
ejpam-4055	198	15	set	set	NOUN
ejpam-4055	198	16	of	of	ADP
ejpam-4055	198	17	h.	h.	PROPN
ejpam-4055	198	18	so	so	ADV
ejpam-4055	198	19	suppose	suppose	VERB
ejpam-4055	198	20	that	that	SCONJ
ejpam-4055	198	21	tx	tx	PROPN
ejpam-4055	198	22	6=	6=	ADP
ejpam-4055	198	23	v	v	ADP
ejpam-4055	198	24	(	(	PUNCT
ejpam-4055	198	25	h	h	NOUN
ejpam-4055	198	26	)	)	PUNCT
ejpam-4055	198	27	and	and	CCONJ
ejpam-4055	198	28	let	let	VERB
ejpam-4055	198	29	a	a	DET
ejpam-4055	198	30	∈	∈	PROPN
ejpam-4055	198	31	v	v	NOUN
ejpam-4055	198	32	(	(	PUNCT
ejpam-4055	198	33	h	h	NOUN
ejpam-4055	198	34	)	)	PUNCT
ejpam-4055	198	35	\	\	PROPN
ejpam-4055	198	36	tx	tx	PROPN
ejpam-4055	198	37	.	.	PUNCT
ejpam-4055	199	1	since	since	SCONJ
ejpam-4055	199	2	w	w	PROPN
ejpam-4055	199	3	is	be	AUX
ejpam-4055	199	4	hop	hop	NOUN
ejpam-4055	199	5	dominating	dominating	NOUN
ejpam-4055	199	6	and	and	CCONJ
ejpam-4055	199	7	(	(	PUNCT
ejpam-4055	199	8	x	x	X
ejpam-4055	199	9	,	,	PUNCT
ejpam-4055	199	10	a	a	PRON
ejpam-4055	199	11	)	)	PUNCT
ejpam-4055	199	12	/∈w	/∈w	PUNCT
ejpam-4055	199	13	,	,	PUNCT
ejpam-4055	199	14	there	there	PRON
ejpam-4055	199	15	exists	exist	VERB
ejpam-4055	199	16	(	(	PUNCT
ejpam-4055	199	17	y	y	PROPN
ejpam-4055	199	18	,	,	PUNCT
ejpam-4055	199	19	b	b	NOUN
ejpam-4055	199	20	)	)	PUNCT
ejpam-4055	199	21	∈w	∈w	NOUN
ejpam-4055	199	22	such	such	ADJ
ejpam-4055	199	23	that	that	DET
ejpam-4055	199	24	dg[h]((x	dg[h]((x	NOUN
ejpam-4055	199	25	,	,	PUNCT
ejpam-4055	199	26	a	a	PRON
ejpam-4055	199	27	)	)	PUNCT
ejpam-4055	199	28	,	,	PUNCT
ejpam-4055	199	29	(	(	PUNCT
ejpam-4055	199	30	y	y	PROPN
ejpam-4055	199	31	,	,	PUNCT
ejpam-4055	199	32	b	b	NOUN
ejpam-4055	199	33	)	)	PUNCT
ejpam-4055	199	34	)	)	PUNCT
ejpam-4055	200	1	=	=	SYM
ejpam-4055	200	2	2	2	X
ejpam-4055	200	3	.	.	PUNCT
ejpam-4055	201	1	the	the	DET
ejpam-4055	201	2	condition	condition	NOUN
ejpam-4055	201	3	x	x	X
ejpam-4055	201	4	∈	∈	PROPN
ejpam-4055	201	5	s	s	PART
ejpam-4055	201	6	\	\	PROPN
ejpam-4055	201	7	n(s	n(s	PROPN
ejpam-4055	201	8	,	,	PUNCT
ejpam-4055	201	9	2	2	NUM
ejpam-4055	201	10	)	)	PUNCT
ejpam-4055	201	11	would	would	AUX
ejpam-4055	201	12	imply	imply	VERB
ejpam-4055	201	13	that	that	SCONJ
ejpam-4055	201	14	y	y	PROPN
ejpam-4055	201	15	=	=	PUNCT
ejpam-4055	201	16	x	x	PROPN
ejpam-4055	201	17	and	and	CCONJ
ejpam-4055	201	18	b	b	X
ejpam-4055	201	19	∈	∈	PROPN
ejpam-4055	201	20	(	(	PUNCT
ejpam-4055	201	21	v	v	NOUN
ejpam-4055	201	22	(	(	PUNCT
ejpam-4055	201	23	h	h	NOUN
ejpam-4055	201	24	)	)	PUNCT
ejpam-4055	201	25	\	\	NOUN
ejpam-4055	201	26	nh(a	nh(a	PROPN
ejpam-4055	201	27	)	)	PUNCT
ejpam-4055	201	28	)	)	PUNCT
ejpam-4055	202	1	∩	∩	PROPN
ejpam-4055	202	2	tx	tx	PROPN
ejpam-4055	202	3	.	.	PUNCT
ejpam-4055	203	1	hence	hence	ADV
ejpam-4055	203	2	,	,	PUNCT
ejpam-4055	203	3	tx	tx	PROPN
ejpam-4055	203	4	is	be	AUX
ejpam-4055	203	5	a	a	DET
ejpam-4055	203	6	strictly	strictly	ADV
ejpam-4055	203	7	locating	locate	VERB
ejpam-4055	203	8	set	set	NOUN
ejpam-4055	203	9	of	of	ADP
ejpam-4055	203	10	h.	h.	NOUN
ejpam-4055	203	11	conversely	conversely	ADV
ejpam-4055	203	12	,	,	PUNCT
ejpam-4055	203	13	supose	supose	VERB
ejpam-4055	203	14	that	that	SCONJ
ejpam-4055	203	15	w	w	NOUN
ejpam-4055	203	16	satisfies	satisfie	NOUN
ejpam-4055	203	17	(	(	PUNCT
ejpam-4055	203	18	i	i	NOUN
ejpam-4055	203	19	)	)	PUNCT
ejpam-4055	203	20	to	to	ADP
ejpam-4055	203	21	(	(	PUNCT
ejpam-4055	203	22	v	v	NOUN
ejpam-4055	203	23	)	)	PUNCT
ejpam-4055	203	24	.	.	PUNCT
ejpam-4055	204	1	by	by	ADP
ejpam-4055	204	2	theorem	theorem	NOUN
ejpam-4055	204	3	5	5	NUM
ejpam-4055	204	4	,	,	PUNCT
ejpam-4055	204	5	w	w	PROPN
ejpam-4055	204	6	is	be	AUX
ejpam-4055	204	7	a	a	DET
ejpam-4055	204	8	resolving	resolving	NOUN
ejpam-4055	204	9	set	set	NOUN
ejpam-4055	204	10	.	.	PUNCT
ejpam-4055	205	1	let	let	VERB
ejpam-4055	205	2	(	(	PUNCT
ejpam-4055	205	3	x	x	NOUN
ejpam-4055	205	4	,	,	PUNCT
ejpam-4055	205	5	a	a	DET
ejpam-4055	205	6	)	)	PUNCT
ejpam-4055	205	7	∈	∈	NOUN
ejpam-4055	205	8	v	v	NOUN
ejpam-4055	205	9	(	(	PUNCT
ejpam-4055	205	10	g[h	g[h	PROPN
ejpam-4055	205	11	]	]	PUNCT
ejpam-4055	205	12	)	)	PUNCT
ejpam-4055	205	13	\w	\w	ADJ
ejpam-4055	205	14	.	.	PUNCT
ejpam-4055	206	1	since	since	SCONJ
ejpam-4055	206	2	s	s	PART
ejpam-4055	206	3	=	=	SYM
ejpam-4055	206	4	v	v	PROPN
ejpam-4055	206	5	(	(	PUNCT
ejpam-4055	206	6	g	g	NOUN
ejpam-4055	206	7	)	)	PUNCT
ejpam-4055	206	8	,	,	PUNCT
ejpam-4055	206	9	a	a	DET
ejpam-4055	206	10	∈	∈	PROPN
ejpam-4055	206	11	v	v	ADP
ejpam-4055	206	12	(	(	PUNCT
ejpam-4055	206	13	h	h	NOUN
ejpam-4055	206	14	)	)	PUNCT
ejpam-4055	206	15	\	\	PROPN
ejpam-4055	206	16	tx	tx	PROPN
ejpam-4055	206	17	.	.	PUNCT
ejpam-4055	207	1	if	if	SCONJ
ejpam-4055	207	2	x	x	SYM
ejpam-4055	207	3	∈	∈	PROPN
ejpam-4055	207	4	ng(s	ng(s	NOUN
ejpam-4055	207	5	,	,	PUNCT
ejpam-4055	207	6	2	2	NUM
ejpam-4055	207	7	)	)	PUNCT
ejpam-4055	207	8	,	,	PUNCT
ejpam-4055	207	9	then	then	ADV
ejpam-4055	207	10	there	there	PRON
ejpam-4055	207	11	exists	exist	VERB
ejpam-4055	207	12	z	z	PROPN
ejpam-4055	207	13	∈	∈	PROPN
ejpam-4055	207	14	ng(x	ng(x	NUM
ejpam-4055	207	15	,	,	PUNCT
ejpam-4055	207	16	2	2	NUM
ejpam-4055	207	17	)	)	PUNCT
ejpam-4055	207	18	.	.	PUNCT
ejpam-4055	208	1	let	let	VERB
ejpam-4055	208	2	b	b	X
ejpam-4055	208	3	∈	∈	PROPN
ejpam-4055	208	4	tz	tz	PROPN
ejpam-4055	208	5	.	.	PUNCT
ejpam-4055	209	1	then	then	ADV
ejpam-4055	209	2	(	(	PUNCT
ejpam-4055	209	3	z	z	NOUN
ejpam-4055	209	4	,	,	PUNCT
ejpam-4055	209	5	b	b	NOUN
ejpam-4055	209	6	)	)	PUNCT
ejpam-4055	209	7	∈	∈	PROPN
ejpam-4055	209	8	w	w	PROPN
ejpam-4055	209	9	∩ng[h]((x	∩ng[h]((x	NOUN
ejpam-4055	209	10	,	,	PUNCT
ejpam-4055	209	11	a	a	PRON
ejpam-4055	209	12	)	)	PUNCT
ejpam-4055	209	13	,	,	PUNCT
ejpam-4055	209	14	2	2	NUM
ejpam-4055	209	15	)	)	PUNCT
ejpam-4055	209	16	.	.	PUNCT
ejpam-4055	210	1	suppose	suppose	VERB
ejpam-4055	210	2	x	x	X
ejpam-4055	210	3	∈	∈	PROPN
ejpam-4055	210	4	s	s	PART
ejpam-4055	210	5	\ng(s	\ng(s	NOUN
ejpam-4055	210	6	,	,	PUNCT
ejpam-4055	210	7	2	2	NUM
ejpam-4055	210	8	)	)	PUNCT
ejpam-4055	210	9	.	.	PUNCT
ejpam-4055	211	1	by	by	ADP
ejpam-4055	211	2	(	(	PUNCT
ejpam-4055	211	3	v	v	NOUN
ejpam-4055	211	4	)	)	PUNCT
ejpam-4055	211	5	,	,	PUNCT
ejpam-4055	211	6	tx	tx	PROPN
ejpam-4055	211	7	is	be	AUX
ejpam-4055	211	8	a	a	DET
ejpam-4055	211	9	strictly	strictly	ADV
ejpam-4055	211	10	locating	locate	VERB
ejpam-4055	211	11	set	set	NOUN
ejpam-4055	211	12	of	of	ADP
ejpam-4055	211	13	h.	h.	PROPN
ejpam-4055	211	14	hence	hence	ADV
ejpam-4055	211	15	,	,	PUNCT
ejpam-4055	211	16	there	there	PRON
ejpam-4055	211	17	exists	exist	VERB
ejpam-4055	211	18	p	p	PROPN
ejpam-4055	211	19	∈	∈	PROPN
ejpam-4055	212	1	[	[	X
ejpam-4055	212	2	v	v	X
ejpam-4055	212	3	(	(	PUNCT
ejpam-4055	212	4	h	h	NOUN
ejpam-4055	212	5	)	)	PUNCT
ejpam-4055	212	6	\	\	NOUN
ejpam-4055	212	7	nh(a	nh(a	PROPN
ejpam-4055	212	8	)	)	PUNCT
ejpam-4055	212	9	]	]	PUNCT
ejpam-4055	213	1	∩	∩	PROPN
ejpam-4055	213	2	tx	tx	PROPN
ejpam-4055	213	3	.	.	PUNCT
ejpam-4055	214	1	this	this	PRON
ejpam-4055	214	2	implies	imply	VERB
ejpam-4055	214	3	that	that	SCONJ
ejpam-4055	214	4	(	(	PUNCT
ejpam-4055	214	5	x	x	X
ejpam-4055	214	6	,	,	PUNCT
ejpam-4055	214	7	p	p	NOUN
ejpam-4055	214	8	)	)	PUNCT
ejpam-4055	214	9	∈	∈	PROPN
ejpam-4055	214	10	w	w	PROPN
ejpam-4055	214	11	∩ng[h]((x	∩ng[h]((x	NOUN
ejpam-4055	214	12	,	,	PUNCT
ejpam-4055	214	13	a	a	PRON
ejpam-4055	214	14	)	)	PUNCT
ejpam-4055	214	15	,	,	PUNCT
ejpam-4055	214	16	2	2	NUM
ejpam-4055	214	17	)	)	PUNCT
ejpam-4055	214	18	.	.	PUNCT
ejpam-4055	215	1	therefore	therefore	ADV
ejpam-4055	215	2	,	,	PUNCT
ejpam-4055	215	3	w	w	PROPN
ejpam-4055	215	4	is	be	AUX
ejpam-4055	215	5	a	a	DET
ejpam-4055	215	6	hop	hop	NOUN
ejpam-4055	215	7	dominating	dominating	NOUN
ejpam-4055	215	8	set	set	NOUN
ejpam-4055	215	9	of	of	ADP
ejpam-4055	215	10	g[h	g[h	PROPN
ejpam-4055	215	11	]	]	PUNCT
ejpam-4055	215	12	.	.	PUNCT
ejpam-4055	216	1	accordingly	accordingly	ADV
ejpam-4055	216	2	,	,	PUNCT
ejpam-4055	216	3	w	w	PROPN
ejpam-4055	216	4	is	be	AUX
ejpam-4055	216	5	a	a	DET
ejpam-4055	216	6	resolving	resolve	VERB
ejpam-4055	216	7	hop	hop	NOUN
ejpam-4055	216	8	dominating	dominating	NOUN
ejpam-4055	216	9	set	set	NOUN
ejpam-4055	216	10	of	of	ADP
ejpam-4055	216	11	g[h	g[h	PROPN
ejpam-4055	216	12	]	]	PUNCT
ejpam-4055	216	13	.	.	PUNCT
ejpam-4055	217	1	corollary	corollary	ADJ
ejpam-4055	217	2	3	3	X
ejpam-4055	217	3	.	.	PUNCT
ejpam-4055	218	1	let	let	VERB
ejpam-4055	218	2	g	g	NOUN
ejpam-4055	218	3	and	and	CCONJ
ejpam-4055	218	4	h	h	PROPN
ejpam-4055	218	5	be	be	VERB
ejpam-4055	218	6	non	non	ADJ
ejpam-4055	218	7	-	-	ADJ
ejpam-4055	218	8	trivial	trivial	ADJ
ejpam-4055	218	9	connected	connected	ADJ
ejpam-4055	218	10	graphs	graph	NOUN
ejpam-4055	218	11	.	.	PUNCT
ejpam-4055	219	1	then	then	ADV
ejpam-4055	219	2	γrh(g[h	γrh(g[h	NUM
ejpam-4055	219	3	]	]	X
ejpam-4055	219	4	)	)	PUNCT
ejpam-4055	219	5	≤	≤	NUM
ejpam-4055	219	6	|v	|v	PROPN
ejpam-4055	219	7	(	(	PUNCT
ejpam-4055	219	8	g)|sln(h	g)|sln(h	NOUN
ejpam-4055	219	9	)	)	PUNCT
ejpam-4055	219	10	.	.	PUNCT
ejpam-4055	220	1	if	if	SCONJ
ejpam-4055	220	2	g	g	PROPN
ejpam-4055	220	3	is	be	AUX
ejpam-4055	220	4	totally	totally	ADV
ejpam-4055	220	5	point	point	NOUN
ejpam-4055	220	6	determining	determine	VERB
ejpam-4055	220	7	graph	graph	NOUN
ejpam-4055	220	8	and	and	CCONJ
ejpam-4055	220	9	γ(g	γ(g	PROPN
ejpam-4055	220	10	)	)	PUNCT
ejpam-4055	220	11	6=	6=	ADP
ejpam-4055	220	12	1	1	NUM
ejpam-4055	220	13	,	,	PUNCT
ejpam-4055	220	14	then	then	ADV
ejpam-4055	220	15	γrh(g[h	γrh(g[h	NUM
ejpam-4055	220	16	]	]	PUNCT
ejpam-4055	220	17	)	)	PUNCT
ejpam-4055	220	18	=	=	SYM
ejpam-4055	220	19	|v	|v	X
ejpam-4055	220	20	(	(	PUNCT
ejpam-4055	220	21	g)|ln(h	g)|ln(h	PROPN
ejpam-4055	220	22	)	)	PUNCT
ejpam-4055	220	23	.	.	PUNCT
ejpam-4055	221	1	proof	proof	NOUN
ejpam-4055	221	2	:	:	PUNCT
ejpam-4055	221	3	let	let	VERB
ejpam-4055	221	4	s	s	PRON
ejpam-4055	221	5	=	=	X
ejpam-4055	221	6	v	v	ADJ
ejpam-4055	221	7	(	(	PUNCT
ejpam-4055	221	8	g	g	NOUN
ejpam-4055	221	9	)	)	PUNCT
ejpam-4055	221	10	and	and	CCONJ
ejpam-4055	221	11	let	let	VERB
ejpam-4055	221	12	tx	tx	PART
ejpam-4055	221	13	be	be	AUX
ejpam-4055	221	14	an	an	DET
ejpam-4055	221	15	sln	sln	NOUN
ejpam-4055	221	16	-	-	PUNCT
ejpam-4055	221	17	set	set	NOUN
ejpam-4055	221	18	of	of	ADP
ejpam-4055	221	19	h.	h.	PROPN
ejpam-4055	221	20	by	by	ADP
ejpam-4055	221	21	theorem	theorem	NOUN
ejpam-4055	221	22	6	6	NUM
ejpam-4055	221	23	,	,	PUNCT
ejpam-4055	221	24	w	w	NOUN
ejpam-4055	221	25	=	=	PUNCT
ejpam-4055	221	26	⋃	⋃	PROPN
ejpam-4055	221	27	x∈s	x∈s	NOUN
ejpam-4055	222	1	[	[	X
ejpam-4055	222	2	{	{	PUNCT
ejpam-4055	222	3	x	x	NOUN
ejpam-4055	222	4	}	}	PUNCT
ejpam-4055	222	5	×	×	PROPN
ejpam-4055	222	6	tx	tx	PROPN
ejpam-4055	222	7	]	]	PUNCT
ejpam-4055	222	8	is	be	AUX
ejpam-4055	222	9	a	a	DET
ejpam-4055	222	10	resolving	resolve	VERB
ejpam-4055	222	11	hop	hop	NOUN
ejpam-4055	222	12	dominating	dominating	NOUN
ejpam-4055	222	13	set	set	NOUN
ejpam-4055	222	14	of	of	ADP
ejpam-4055	222	15	g[h	g[h	NOUN
ejpam-4055	222	16	]	]	PUNCT
ejpam-4055	222	17	.	.	PUNCT
ejpam-4055	223	1	it	it	PRON
ejpam-4055	223	2	follows	follow	VERB
ejpam-4055	223	3	that	that	SCONJ
ejpam-4055	223	4	γrh(g[h	γrh(g[h	NUM
ejpam-4055	223	5	]	]	NOUN
ejpam-4055	223	6	)	)	PUNCT
ejpam-4055	223	7	≤	≤	NOUN
ejpam-4055	223	8	|w	|w	NOUN
ejpam-4055	223	9	|	|	NOUN
ejpam-4055	223	10	=	=	SYM
ejpam-4055	223	11	|v	|v	PROPN
ejpam-4055	223	12	(	(	PUNCT
ejpam-4055	223	13	g)||tx|	g)||tx|	PROPN
ejpam-4055	223	14	=	=	PRON
ejpam-4055	223	15	|v	|v	PROPN
ejpam-4055	223	16	(	(	PUNCT
ejpam-4055	223	17	g)|sln(h	g)|sln(h	NOUN
ejpam-4055	223	18	)	)	PUNCT
ejpam-4055	223	19	.	.	PUNCT
ejpam-4055	224	1	next	next	ADV
ejpam-4055	224	2	,	,	PUNCT
ejpam-4055	224	3	supppose	supppose	VERB
ejpam-4055	224	4	that	that	SCONJ
ejpam-4055	224	5	g	g	PROPN
ejpam-4055	224	6	is	be	AUX
ejpam-4055	224	7	totally	totally	ADV
ejpam-4055	224	8	point	point	NOUN
ejpam-4055	224	9	determining	determine	VERB
ejpam-4055	224	10	graph	graph	NOUN
ejpam-4055	224	11	and	and	CCONJ
ejpam-4055	224	12	γ(g	γ(g	PROPN
ejpam-4055	224	13	)	)	PUNCT
ejpam-4055	224	14	6=	6=	ADP
ejpam-4055	225	1	1	1	X
ejpam-4055	225	2	.	.	PUNCT
ejpam-4055	225	3	let	let	VERB
ejpam-4055	225	4	s	s	NOUN
ejpam-4055	225	5	=	=	X
ejpam-4055	225	6	v	v	ADJ
ejpam-4055	225	7	(	(	PUNCT
ejpam-4055	225	8	g	g	NOUN
ejpam-4055	225	9	)	)	PUNCT
ejpam-4055	225	10	and	and	CCONJ
ejpam-4055	225	11	let	let	VERB
ejpam-4055	225	12	rx	rx	AUX
ejpam-4055	225	13	be	be	AUX
ejpam-4055	225	14	an	an	DET
ejpam-4055	225	15	ln	ln	ADV
ejpam-4055	225	16	-	-	PUNCT
ejpam-4055	225	17	set	set	NOUN
ejpam-4055	225	18	of	of	ADP
ejpam-4055	225	19	h	h	NOUN
ejpam-4055	225	20	for	for	ADP
ejpam-4055	225	21	each	each	DET
ejpam-4055	225	22	x	x	PROPN
ejpam-4055	225	23	∈	∈	PROPN
ejpam-4055	225	24	s.	s.	PROPN
ejpam-4055	225	25	since	since	SCONJ
ejpam-4055	225	26	γ(g	γ(g	PROPN
ejpam-4055	225	27	)	)	PUNCT
ejpam-4055	225	28	6=	6=	ADP
ejpam-4055	225	29	1	1	NUM
ejpam-4055	225	30	,	,	PUNCT
ejpam-4055	225	31	x	x	SYM
ejpam-4055	225	32	∈	∈	NOUN
ejpam-4055	225	33	ng(s	ng(s	NOUN
ejpam-4055	225	34	,	,	PUNCT
ejpam-4055	225	35	2	2	NUM
ejpam-4055	225	36	)	)	PUNCT
ejpam-4055	225	37	for	for	ADP
ejpam-4055	225	38	each	each	DET
ejpam-4055	225	39	x	x	PROPN
ejpam-4055	225	40	∈	∈	PROPN
ejpam-4055	225	41	s.	s.	PROPN
ejpam-4055	225	42	by	by	ADP
ejpam-4055	225	43	theorem	theorem	NOUN
ejpam-4055	225	44	6	6	NUM
ejpam-4055	225	45	,	,	PUNCT
ejpam-4055	225	46	w	w	NOUN
ejpam-4055	225	47	=	=	PUNCT
ejpam-4055	225	48	⋃	⋃	PROPN
ejpam-4055	225	49	x∈s	x∈s	NOUN
ejpam-4055	226	1	[	[	X
ejpam-4055	226	2	{	{	PUNCT
ejpam-4055	226	3	x}×rx	x}×rx	X
ejpam-4055	226	4	]	]	X
ejpam-4055	226	5	is	be	AUX
ejpam-4055	226	6	a	a	DET
ejpam-4055	226	7	resolving	resolve	VERB
ejpam-4055	226	8	hop	hop	NOUN
ejpam-4055	226	9	dominating	dominating	NOUN
ejpam-4055	226	10	set	set	NOUN
ejpam-4055	226	11	of	of	ADP
ejpam-4055	226	12	g[h	g[h	NOUN
ejpam-4055	226	13	]	]	PUNCT
ejpam-4055	226	14	.	.	PUNCT
ejpam-4055	227	1	it	it	PRON
ejpam-4055	227	2	follows	follow	VERB
ejpam-4055	227	3	that	that	SCONJ
ejpam-4055	227	4	γrh(g[h	γrh(g[h	NUM
ejpam-4055	227	5	]	]	NOUN
ejpam-4055	227	6	)	)	PUNCT
ejpam-4055	227	7	≤	≤	NOUN
ejpam-4055	227	8	|w	|w	NOUN
ejpam-4055	227	9	|	|	NOUN
ejpam-4055	227	10	=	=	SYM
ejpam-4055	227	11	|v	|v	PROPN
ejpam-4055	227	12	(	(	PUNCT
ejpam-4055	227	13	g)||rx|	g)||rx|	PROPN
ejpam-4055	227	14	=	=	SYM
ejpam-4055	227	15	|v	|v	X
ejpam-4055	227	16	(	(	PUNCT
ejpam-4055	227	17	g)|ln(h	g)|ln(h	PROPN
ejpam-4055	227	18	)	)	PUNCT
ejpam-4055	227	19	.	.	PUNCT
ejpam-4055	228	1	j.	j.	PROPN
ejpam-4055	228	2	mohamad	mohamad	PROPN
ejpam-4055	228	3	,	,	PUNCT
ejpam-4055	228	4	h.	h.	PROPN
ejpam-4055	228	5	rara	rara	PROPN
ejpam-4055	228	6	/	/	SYM
ejpam-4055	228	7	eur	eur	PROPN
ejpam-4055	228	8	.	.	PUNCT
ejpam-4055	229	1	j.	j.	PROPN
ejpam-4055	229	2	pure	pure	PROPN
ejpam-4055	229	3	appl	appl	PROPN
ejpam-4055	229	4	.	.	PROPN
ejpam-4055	229	5	math	math	PROPN
ejpam-4055	229	6	,	,	PUNCT
ejpam-4055	229	7	14	14	NUM
ejpam-4055	229	8	(	(	PUNCT
ejpam-4055	229	9	3	3	NUM
ejpam-4055	229	10	)	)	PUNCT
ejpam-4055	229	11	(	(	PUNCT
ejpam-4055	229	12	2021	2021	NUM
ejpam-4055	229	13	)	)	PUNCT
ejpam-4055	229	14	,	,	PUNCT
ejpam-4055	229	15	1015	1015	NUM
ejpam-4055	229	16	-	-	SYM
ejpam-4055	229	17	1023	1023	NUM
ejpam-4055	229	18	1022	1022	NUM
ejpam-4055	229	19	now	now	ADV
ejpam-4055	229	20	,	,	PUNCT
ejpam-4055	229	21	if	if	SCONJ
ejpam-4055	229	22	w0	w0	PROPN
ejpam-4055	229	23	=	=	PUNCT
ejpam-4055	229	24	⋃	⋃	PROPN
ejpam-4055	229	25	x∈s0	x∈s0	NOUN
ejpam-4055	230	1	[	[	X
ejpam-4055	230	2	{	{	PUNCT
ejpam-4055	230	3	x	x	NOUN
ejpam-4055	230	4	}	}	PUNCT
ejpam-4055	230	5	×	×	PROPN
ejpam-4055	230	6	tx	tx	PROPN
ejpam-4055	230	7	]	]	PUNCT
ejpam-4055	230	8	is	be	AUX
ejpam-4055	230	9	a	a	DET
ejpam-4055	230	10	γrh	γrh	NOUN
ejpam-4055	230	11	-	-	PUNCT
ejpam-4055	230	12	set	set	NOUN
ejpam-4055	230	13	of	of	ADP
ejpam-4055	230	14	g[h	g[h	PROPN
ejpam-4055	230	15	]	]	PUNCT
ejpam-4055	230	16	,	,	PUNCT
ejpam-4055	230	17	then	then	ADV
ejpam-4055	230	18	s0	s0	PROPN
ejpam-4055	230	19	=	=	SYM
ejpam-4055	230	20	v	v	PROPN
ejpam-4055	230	21	(	(	PUNCT
ejpam-4055	230	22	g	g	NOUN
ejpam-4055	230	23	)	)	PUNCT
ejpam-4055	230	24	and	and	CCONJ
ejpam-4055	230	25	tx	tx	PROPN
ejpam-4055	230	26	is	be	AUX
ejpam-4055	230	27	a	a	DET
ejpam-4055	230	28	locating	locating	NOUN
ejpam-4055	230	29	set	set	NOUN
ejpam-4055	230	30	of	of	ADP
ejpam-4055	230	31	h	h	NOUN
ejpam-4055	230	32	for	for	ADP
ejpam-4055	230	33	each	each	DET
ejpam-4055	230	34	x	x	SYM
ejpam-4055	230	35	∈	∈	PROPN
ejpam-4055	230	36	v	v	ADP
ejpam-4055	230	37	(	(	PUNCT
ejpam-4055	230	38	g	g	NOUN
ejpam-4055	230	39	)	)	PUNCT
ejpam-4055	230	40	by	by	ADP
ejpam-4055	230	41	theorem	theorem	NOUN
ejpam-4055	230	42	6	6	NUM
ejpam-4055	230	43	.	.	PUNCT
ejpam-4055	231	1	hence	hence	ADV
ejpam-4055	231	2	,	,	PUNCT
ejpam-4055	231	3	γrh(g[h	γrh(g[h	NUM
ejpam-4055	231	4	]	]	X
ejpam-4055	231	5	)	)	PUNCT
ejpam-4055	232	1	=	=	NOUN
ejpam-4055	232	2	|w0|	|w0|	X
ejpam-4055	232	3	=	=	SYM
ejpam-4055	232	4	|v	|v	X
ejpam-4055	232	5	(	(	PUNCT
ejpam-4055	232	6	g)||tx|	g)||tx|	PROPN
ejpam-4055	232	7	≥	≥	NUM
ejpam-4055	232	8	|v	|v	PROPN
ejpam-4055	232	9	(	(	PUNCT
ejpam-4055	232	10	g)|ln(h	g)|ln(h	PROPN
ejpam-4055	232	11	)	)	PUNCT
ejpam-4055	232	12	.	.	PUNCT
ejpam-4055	233	1	therefore	therefore	ADV
ejpam-4055	233	2	,	,	PUNCT
ejpam-4055	233	3	γrh(g[h	γrh(g[h	NUM
ejpam-4055	233	4	]	]	X
ejpam-4055	233	5	)	)	PUNCT
ejpam-4055	233	6	=	=	SYM
ejpam-4055	233	7	|v	|v	X
ejpam-4055	233	8	(	(	PUNCT
ejpam-4055	233	9	g)|ln(h	g)|ln(h	PROPN
ejpam-4055	233	10	)	)	PUNCT
ejpam-4055	233	11	.	.	PUNCT
ejpam-4055	234	1	corollary	corollary	ADJ
ejpam-4055	234	2	4	4	NUM
ejpam-4055	234	3	.	.	PUNCT
ejpam-4055	235	1	let	let	VERB
ejpam-4055	235	2	g	g	NOUN
ejpam-4055	235	3	and	and	CCONJ
ejpam-4055	235	4	h	h	PROPN
ejpam-4055	235	5	be	be	VERB
ejpam-4055	235	6	non	non	ADJ
ejpam-4055	235	7	-	-	ADJ
ejpam-4055	235	8	trivial	trivial	ADJ
ejpam-4055	235	9	connected	connected	ADJ
ejpam-4055	235	10	graphs	graph	NOUN
ejpam-4055	235	11	.	.	PUNCT
ejpam-4055	236	1	if	if	SCONJ
ejpam-4055	236	2	g	g	PROPN
ejpam-4055	236	3	is	be	AUX
ejpam-4055	236	4	totally	totally	ADV
ejpam-4055	236	5	point	point	NOUN
ejpam-4055	236	6	determining	determining	NOUN
ejpam-4055	236	7	and	and	CCONJ
ejpam-4055	236	8	γ(g	γ(g	PROPN
ejpam-4055	236	9	)	)	PUNCT
ejpam-4055	236	10	=	=	SYM
ejpam-4055	237	1	1	1	NUM
ejpam-4055	237	2	,	,	PUNCT
ejpam-4055	237	3	then	then	ADV
ejpam-4055	237	4	γrh(g[h	γrh(g[h	NUM
ejpam-4055	237	5	]	]	PUNCT
ejpam-4055	237	6	)	)	PUNCT
ejpam-4055	237	7	=	=	PUNCT
ejpam-4055	237	8	sln(h	sln(h	VERB
ejpam-4055	237	9	)	)	PUNCT
ejpam-4055	238	1	+	+	CCONJ
ejpam-4055	238	2	(	(	PUNCT
ejpam-4055	238	3	|v	|v	X
ejpam-4055	238	4	(	(	PUNCT
ejpam-4055	238	5	g)|	g)|	NOUN
ejpam-4055	238	6	−	−	NOUN
ejpam-4055	238	7	1)ln(h	1)ln(h	NUM
ejpam-4055	238	8	)	)	PUNCT
ejpam-4055	238	9	.	.	PUNCT
ejpam-4055	239	1	proof	proof	NOUN
ejpam-4055	239	2	:	:	PUNCT
ejpam-4055	239	3	let	let	VERB
ejpam-4055	239	4	dg	dg	X
ejpam-4055	239	5	=	=	PUNCT
ejpam-4055	239	6	{	{	PUNCT
ejpam-4055	239	7	v	v	NUM
ejpam-4055	239	8	∈	∈	NOUN
ejpam-4055	239	9	v	v	NOUN
ejpam-4055	239	10	(	(	PUNCT
ejpam-4055	239	11	g	g	NOUN
ejpam-4055	239	12	)	)	PUNCT
ejpam-4055	239	13	:	:	PUNCT
ejpam-4055	239	14	{	{	PUNCT
ejpam-4055	239	15	v	v	NOUN
ejpam-4055	239	16	}	}	PUNCT
ejpam-4055	239	17	is	be	AUX
ejpam-4055	239	18	a	a	DET
ejpam-4055	239	19	dominating	dominating	NOUN
ejpam-4055	239	20	set	set	NOUN
ejpam-4055	239	21	of	of	ADP
ejpam-4055	239	22	g	g	NOUN
ejpam-4055	239	23	}	}	PUNCT
ejpam-4055	239	24	.	.	PUNCT
ejpam-4055	240	1	since	since	SCONJ
ejpam-4055	240	2	g	g	PROPN
ejpam-4055	240	3	is	be	AUX
ejpam-4055	240	4	totally	totally	ADV
ejpam-4055	240	5	point	point	NOUN
ejpam-4055	240	6	determining	determine	VERB
ejpam-4055	240	7	,	,	PUNCT
ejpam-4055	240	8	it	it	PRON
ejpam-4055	240	9	follows	follow	VERB
ejpam-4055	240	10	that	that	SCONJ
ejpam-4055	240	11	|dg|	|dg|	PROPN
ejpam-4055	240	12	=	=	SYM
ejpam-4055	240	13	1	1	X
ejpam-4055	240	14	.	.	X
ejpam-4055	241	1	set	set	VERB
ejpam-4055	241	2	s	s	PART
ejpam-4055	241	3	=	=	X
ejpam-4055	241	4	v	v	ADJ
ejpam-4055	241	5	(	(	PUNCT
ejpam-4055	241	6	g	g	NOUN
ejpam-4055	241	7	)	)	PUNCT
ejpam-4055	241	8	.	.	PUNCT
ejpam-4055	242	1	let	let	VERB
ejpam-4055	242	2	tv	tv	NOUN
ejpam-4055	242	3	be	be	AUX
ejpam-4055	242	4	an	an	DET
ejpam-4055	242	5	sln	sln	NOUN
ejpam-4055	242	6	-	-	PUNCT
ejpam-4055	242	7	set	set	NOUN
ejpam-4055	242	8	of	of	ADP
ejpam-4055	242	9	h	h	NOUN
ejpam-4055	242	10	for	for	ADP
ejpam-4055	242	11	v	v	NOUN
ejpam-4055	242	12	∈	∈	NOUN
ejpam-4055	242	13	dg	dg	NOUN
ejpam-4055	242	14	and	and	CCONJ
ejpam-4055	242	15	let	let	VERB
ejpam-4055	242	16	tx	tx	PART
ejpam-4055	242	17	be	be	AUX
ejpam-4055	242	18	an	an	DET
ejpam-4055	242	19	ln	ln	ADV
ejpam-4055	242	20	-	-	PUNCT
ejpam-4055	242	21	set	set	NOUN
ejpam-4055	242	22	of	of	ADP
ejpam-4055	242	23	h	h	NOUN
ejpam-4055	242	24	for	for	ADP
ejpam-4055	242	25	each	each	DET
ejpam-4055	242	26	x	x	SYM
ejpam-4055	242	27	∈	∈	PROPN
ejpam-4055	242	28	v	v	ADP
ejpam-4055	242	29	(	(	PUNCT
ejpam-4055	242	30	g	g	NOUN
ejpam-4055	242	31	)	)	PUNCT
ejpam-4055	242	32	\	\	NOUN
ejpam-4055	242	33	{	{	PUNCT
ejpam-4055	242	34	v	v	NOUN
ejpam-4055	242	35	}	}	PUNCT
ejpam-4055	242	36	.	.	PUNCT
ejpam-4055	243	1	then	then	ADV
ejpam-4055	243	2	by	by	ADP
ejpam-4055	243	3	theorem	theorem	NOUN
ejpam-4055	243	4	6	6	NUM
ejpam-4055	243	5	,	,	PUNCT
ejpam-4055	243	6	w	w	NOUN
ejpam-4055	243	7	=	=	X
ejpam-4055	243	8	⋃	⋃	PROPN
ejpam-4055	243	9	x∈s\{v}[{x	x∈s\{v}[{x	PROPN
ejpam-4055	243	10	}	}	PUNCT
ejpam-4055	243	11	×	×	PROPN
ejpam-4055	243	12	tx	tx	PROPN
ejpam-4055	243	13	]	]	X
ejpam-4055	243	14	∪	∪	X
ejpam-4055	243	15	(	(	PUNCT
ejpam-4055	243	16	{	{	PUNCT
ejpam-4055	243	17	v	v	NOUN
ejpam-4055	243	18	}	}	PUNCT
ejpam-4055	243	19	×	×	NOUN
ejpam-4055	243	20	tv	tv	NOUN
ejpam-4055	243	21	)	)	PUNCT
ejpam-4055	243	22	is	be	AUX
ejpam-4055	243	23	a	a	DET
ejpam-4055	243	24	resolving	resolve	VERB
ejpam-4055	243	25	hop	hop	NOUN
ejpam-4055	243	26	dominating	dominating	NOUN
ejpam-4055	243	27	set	set	NOUN
ejpam-4055	243	28	of	of	ADP
ejpam-4055	243	29	g[h	g[h	NOUN
ejpam-4055	243	30	]	]	PUNCT
ejpam-4055	243	31	.	.	PUNCT
ejpam-4055	244	1	hence	hence	ADV
ejpam-4055	244	2	,	,	PUNCT
ejpam-4055	244	3	γrh(g[h	γrh(g[h	NUM
ejpam-4055	244	4	]	]	PUNCT
ejpam-4055	244	5	)	)	PUNCT
ejpam-4055	244	6	≤	≤	NOUN
ejpam-4055	244	7	|w	|w	NOUN
ejpam-4055	245	1	|	|	NOUN
ejpam-4055	245	2	=	=	SYM
ejpam-4055	245	3	(	(	PUNCT
ejpam-4055	245	4	|v	|v	X
ejpam-4055	245	5	(	(	PUNCT
ejpam-4055	245	6	g)|	g)|	NOUN
ejpam-4055	245	7	−	−	NOUN
ejpam-4055	245	8	1)ln(h	1)ln(h	NUM
ejpam-4055	245	9	)	)	PUNCT
ejpam-4055	245	10	+	+	NUM
ejpam-4055	245	11	sln(h	sln(h	ADJ
ejpam-4055	245	12	)	)	PUNCT
ejpam-4055	245	13	.	.	PUNCT
ejpam-4055	246	1	supose	supose	VERB
ejpam-4055	246	2	now	now	ADV
ejpam-4055	246	3	that	that	SCONJ
ejpam-4055	246	4	w	w	NOUN
ejpam-4055	246	5	∗	∗	NOUN
ejpam-4055	246	6	=	=	PUNCT
ejpam-4055	246	7	⋃	⋃	PROPN
ejpam-4055	246	8	x∈s∗	x∈s∗	PROPN
ejpam-4055	247	1	[	[	X
ejpam-4055	247	2	{	{	PUNCT
ejpam-4055	247	3	x	x	NOUN
ejpam-4055	247	4	}	}	PUNCT
ejpam-4055	247	5	×	×	NOUN
ejpam-4055	247	6	rx	rx	NOUN
ejpam-4055	247	7	]	]	PUNCT
ejpam-4055	247	8	is	be	AUX
ejpam-4055	247	9	a	a	DET
ejpam-4055	247	10	γrh	γrh	NOUN
ejpam-4055	247	11	-	-	PUNCT
ejpam-4055	247	12	set	set	NOUN
ejpam-4055	247	13	of	of	ADP
ejpam-4055	247	14	g[h	g[h	NOUN
ejpam-4055	247	15	]	]	PUNCT
ejpam-4055	247	16	.	.	PUNCT
ejpam-4055	248	1	then	then	ADV
ejpam-4055	248	2	there	there	PRON
ejpam-4055	248	3	exists	exist	VERB
ejpam-4055	248	4	a	a	DET
ejpam-4055	248	5	unique	unique	ADJ
ejpam-4055	248	6	vertex	vertex	NOUN
ejpam-4055	248	7	v	v	ADP
ejpam-4055	248	8	such	such	ADJ
ejpam-4055	248	9	that	that	SCONJ
ejpam-4055	248	10	{	{	PUNCT
ejpam-4055	248	11	v	v	NOUN
ejpam-4055	248	12	}	}	PUNCT
ejpam-4055	248	13	is	be	AUX
ejpam-4055	248	14	a	a	DET
ejpam-4055	248	15	dominating	dominating	NOUN
ejpam-4055	248	16	set	set	NOUN
ejpam-4055	248	17	of	of	ADP
ejpam-4055	248	18	g.	g.	PROPN
ejpam-4055	248	19	by	by	ADP
ejpam-4055	248	20	theorem	theorem	NOUN
ejpam-4055	248	21	6	6	NUM
ejpam-4055	248	22	,	,	PUNCT
ejpam-4055	248	23	s∗	s∗	PROPN
ejpam-4055	248	24	=	=	SYM
ejpam-4055	248	25	v	v	PROPN
ejpam-4055	248	26	(	(	PUNCT
ejpam-4055	248	27	g	g	NOUN
ejpam-4055	248	28	)	)	PUNCT
ejpam-4055	248	29	,	,	PUNCT
ejpam-4055	248	30	rv	rv	PROPN
ejpam-4055	248	31	is	be	AUX
ejpam-4055	248	32	a	a	DET
ejpam-4055	248	33	strictly	strictly	ADV
ejpam-4055	248	34	locating	locate	VERB
ejpam-4055	248	35	set	set	NOUN
ejpam-4055	248	36	of	of	ADP
ejpam-4055	248	37	h	h	NOUN
ejpam-4055	248	38	and	and	CCONJ
ejpam-4055	248	39	rx	rx	VERB
ejpam-4055	248	40	is	be	AUX
ejpam-4055	248	41	a	a	DET
ejpam-4055	248	42	locating	locating	NOUN
ejpam-4055	248	43	set	set	NOUN
ejpam-4055	248	44	of	of	ADP
ejpam-4055	248	45	h	h	NOUN
ejpam-4055	248	46	for	for	ADP
ejpam-4055	248	47	each	each	DET
ejpam-4055	248	48	x	x	SYM
ejpam-4055	248	49	∈	∈	PROPN
ejpam-4055	248	50	v	v	ADP
ejpam-4055	248	51	(	(	PUNCT
ejpam-4055	248	52	g	g	NOUN
ejpam-4055	248	53	)	)	PUNCT
ejpam-4055	248	54	\	\	NOUN
ejpam-4055	248	55	{	{	PUNCT
ejpam-4055	248	56	v	v	NOUN
ejpam-4055	248	57	}	}	PUNCT
ejpam-4055	248	58	.	.	PUNCT
ejpam-4055	249	1	thus	thus	ADV
ejpam-4055	249	2	,	,	PUNCT
ejpam-4055	249	3	γrh(g[h	γrh(g[h	NUM
ejpam-4055	249	4	]	]	X
ejpam-4055	249	5	)	)	PUNCT
ejpam-4055	250	1	=	=	NOUN
ejpam-4055	250	2	|w	|w	ADJ
ejpam-4055	250	3	∗|	∗|	NOUN
ejpam-4055	250	4	=	=	NOUN
ejpam-4055	250	5	|rv|+	|rv|+	PROPN
ejpam-4055	250	6	∑	∑	ADJ
ejpam-4055	250	7	x∈s∗\{v	x∈s∗\{v	PROPN
ejpam-4055	250	8	}	}	PUNCT
ejpam-4055	250	9	|rx|	|rx|	NOUN
ejpam-4055	250	10	≥sln(h	≥sln(h	PROPN
ejpam-4055	250	11	)	)	PUNCT
ejpam-4055	250	12	+	+	CCONJ
ejpam-4055	250	13	(	(	PUNCT
ejpam-4055	250	14	|v	|v	X
ejpam-4055	250	15	(	(	PUNCT
ejpam-4055	250	16	g)|	g)|	NOUN
ejpam-4055	250	17	−	−	NOUN
ejpam-4055	250	18	1)ln(h	1)ln(h	NUM
ejpam-4055	250	19	)	)	PUNCT
ejpam-4055	250	20	.	.	PUNCT
ejpam-4055	251	1	therefore	therefore	ADV
ejpam-4055	251	2	,	,	PUNCT
ejpam-4055	251	3	γrh(g[h	γrh(g[h	NUM
ejpam-4055	251	4	]	]	PUNCT
ejpam-4055	251	5	)	)	PUNCT
ejpam-4055	251	6	=	=	PUNCT
ejpam-4055	251	7	sln(h	sln(h	VERB
ejpam-4055	251	8	)	)	PUNCT
ejpam-4055	252	1	+	+	CCONJ
ejpam-4055	252	2	(	(	PUNCT
ejpam-4055	252	3	|v	|v	X
ejpam-4055	252	4	(	(	PUNCT
ejpam-4055	252	5	g)|	g)|	NOUN
ejpam-4055	252	6	−	−	NOUN
ejpam-4055	252	7	1)ln(h	1)ln(h	NUM
ejpam-4055	252	8	)	)	PUNCT
ejpam-4055	252	9	.	.	PUNCT
ejpam-4055	253	1	corollary	corollary	ADJ
ejpam-4055	253	2	5	5	NUM
ejpam-4055	253	3	.	.	PUNCT
ejpam-4055	254	1	let	let	VERB
ejpam-4055	254	2	h	h	PRON
ejpam-4055	254	3	be	be	AUX
ejpam-4055	254	4	a	a	DET
ejpam-4055	254	5	non	non	ADJ
ejpam-4055	254	6	-	-	ADJ
ejpam-4055	254	7	trivial	trivial	ADJ
ejpam-4055	254	8	connected	connected	ADJ
ejpam-4055	254	9	graph	graph	NOUN
ejpam-4055	254	10	and	and	CCONJ
ejpam-4055	254	11	let	let	VERB
ejpam-4055	254	12	n	n	PRON
ejpam-4055	254	13	≥	≥	X
ejpam-4055	254	14	2	2	NUM
ejpam-4055	254	15	be	be	AUX
ejpam-4055	254	16	an	an	DET
ejpam-4055	254	17	integer	integer	NOUN
ejpam-4055	254	18	.	.	PUNCT
ejpam-4055	255	1	then	then	ADV
ejpam-4055	255	2	γrh(kn[h	γrh(kn[h	X
ejpam-4055	255	3	]	]	X
ejpam-4055	255	4	)	)	PUNCT
ejpam-4055	255	5	=	=	SYM
ejpam-4055	255	6	n(sln(h	n(sln(h	PROPN
ejpam-4055	255	7	)	)	PUNCT
ejpam-4055	255	8	)	)	PUNCT
ejpam-4055	255	9	.	.	PUNCT
ejpam-4055	256	1	proof	proof	NOUN
ejpam-4055	256	2	:	:	PUNCT
ejpam-4055	256	3	let	let	VERB
ejpam-4055	256	4	g	g	PROPN
ejpam-4055	256	5	=	=	PROPN
ejpam-4055	256	6	kn	kn	PROPN
ejpam-4055	256	7	.	.	PUNCT
ejpam-4055	257	1	then	then	ADV
ejpam-4055	257	2	v	v	NOUN
ejpam-4055	257	3	is	be	AUX
ejpam-4055	257	4	a	a	DET
ejpam-4055	257	5	dominating	dominating	NOUN
ejpam-4055	257	6	vertex	vertex	NOUN
ejpam-4055	257	7	of	of	ADP
ejpam-4055	257	8	g	g	NOUN
ejpam-4055	257	9	for	for	ADP
ejpam-4055	257	10	each	each	DET
ejpam-4055	257	11	v	v	NUM
ejpam-4055	257	12	∈	∈	PROPN
ejpam-4055	257	13	v	v	NOUN
ejpam-4055	257	14	(	(	PUNCT
ejpam-4055	257	15	g	g	NOUN
ejpam-4055	257	16	)	)	PUNCT
ejpam-4055	257	17	.	.	PUNCT
ejpam-4055	258	1	thus	thus	ADV
ejpam-4055	258	2	,	,	PUNCT
ejpam-4055	258	3	if	if	SCONJ
ejpam-4055	258	4	w0	w0	PROPN
ejpam-4055	258	5	=	=	PUNCT
ejpam-4055	258	6	⋃	⋃	PROPN
ejpam-4055	258	7	x∈s0	x∈s0	NOUN
ejpam-4055	258	8	(	(	PUNCT
ejpam-4055	258	9	{	{	PUNCT
ejpam-4055	258	10	x	x	NOUN
ejpam-4055	258	11	}	}	PUNCT
ejpam-4055	258	12	×	×	PROPN
ejpam-4055	258	13	tx	tx	PROPN
ejpam-4055	258	14	)	)	PUNCT
ejpam-4055	258	15	is	be	AUX
ejpam-4055	258	16	a	a	DET
ejpam-4055	258	17	γrh	γrh	NOUN
ejpam-4055	258	18	-	-	PUNCT
ejpam-4055	258	19	set	set	NOUN
ejpam-4055	258	20	of	of	ADP
ejpam-4055	258	21	g[h	g[h	PROPN
ejpam-4055	258	22	]	]	PUNCT
ejpam-4055	258	23	,	,	PUNCT
ejpam-4055	258	24	then	then	ADV
ejpam-4055	258	25	s0	s0	PROPN
ejpam-4055	258	26	=	=	SYM
ejpam-4055	258	27	v	v	PROPN
ejpam-4055	258	28	(	(	PUNCT
ejpam-4055	258	29	g	g	NOUN
ejpam-4055	258	30	)	)	PUNCT
ejpam-4055	258	31	and	and	CCONJ
ejpam-4055	258	32	tx	tx	PROPN
ejpam-4055	258	33	is	be	AUX
ejpam-4055	258	34	an	an	DET
ejpam-4055	258	35	sln	sln	NOUN
ejpam-4055	258	36	-	-	PUNCT
ejpam-4055	258	37	set	set	NOUN
ejpam-4055	258	38	of	of	ADP
ejpam-4055	258	39	h	h	NOUN
ejpam-4055	258	40	for	for	ADP
ejpam-4055	258	41	each	each	DET
ejpam-4055	258	42	x	x	SYM
ejpam-4055	258	43	∈	∈	PROPN
ejpam-4055	258	44	s0	s0	NOUN
ejpam-4055	258	45	,	,	PUNCT
ejpam-4055	258	46	by	by	ADP
ejpam-4055	258	47	theorem	theorem	NOUN
ejpam-4055	258	48	6	6	NUM
ejpam-4055	258	49	.	.	PUNCT
ejpam-4055	259	1	hence	hence	ADV
ejpam-4055	259	2	,	,	PUNCT
ejpam-4055	259	3	γrh(kn[h	γrh(kn[h	PROPN
ejpam-4055	259	4	]	]	X
ejpam-4055	259	5	)	)	PUNCT
ejpam-4055	259	6	=	=	NOUN
ejpam-4055	259	7	|w0|	|w0|	X
ejpam-4055	259	8	=	=	SYM
ejpam-4055	259	9	|v	|v	X
ejpam-4055	259	10	(	(	PUNCT
ejpam-4055	259	11	kn)|sln(h	kn)|sln(h	PROPN
ejpam-4055	259	12	)	)	PUNCT
ejpam-4055	259	13	=	=	SYM
ejpam-4055	259	14	n(sln(h	n(sln(h	PROPN
ejpam-4055	259	15	)	)	PUNCT
ejpam-4055	259	16	)	)	PUNCT
ejpam-4055	259	17	.	.	PUNCT
ejpam-4055	260	1	acknowledgements	acknowledgement	NOUN
ejpam-4055	260	2	this	this	DET
ejpam-4055	260	3	research	research	NOUN
ejpam-4055	260	4	is	be	AUX
ejpam-4055	260	5	funded	fund	VERB
ejpam-4055	260	6	by	by	ADP
ejpam-4055	260	7	the	the	DET
ejpam-4055	260	8	department	department	PROPN
ejpam-4055	260	9	of	of	ADP
ejpam-4055	260	10	science	science	NOUN
ejpam-4055	260	11	and	and	CCONJ
ejpam-4055	260	12	technology	technology	NOUN
ejpam-4055	260	13	accelerated	accelerate	VERB
ejpam-4055	260	14	science	science	NOUN
ejpam-4055	260	15	and	and	CCONJ
ejpam-4055	260	16	technology	technology	NOUN
ejpam-4055	260	17	human	human	ADJ
ejpam-4055	260	18	resource	resource	NOUN
ejpam-4055	260	19	development	development	NOUN
ejpam-4055	260	20	program	program	NOUN
ejpam-4055	260	21	(	(	PUNCT
ejpam-4055	260	22	dost	dost	NOUN
ejpam-4055	260	23	-	-	PUNCT
ejpam-4055	260	24	asthrdp	asthrdp	NOUN
ejpam-4055	260	25	)	)	PUNCT
ejpam-4055	260	26	,	,	PUNCT
ejpam-4055	260	27	philippines	philippine	NOUN
ejpam-4055	260	28	.	.	PUNCT
ejpam-4055	261	1	references	reference	NOUN
ejpam-4055	261	2	1023	1023	NUM
ejpam-4055	261	3	references	reference	NOUN
ejpam-4055	261	4	[	[	X
ejpam-4055	261	5	1	1	NUM
ejpam-4055	261	6	]	]	X
ejpam-4055	261	7	g.	g.	PROPN
ejpam-4055	261	8	monsanto	monsanto	PROPN
ejpam-4055	261	9	,	,	PUNCT
ejpam-4055	261	10	p.	p.	NOUN
ejpam-4055	261	11	acal	acal	ADJ
ejpam-4055	261	12	and	and	CCONJ
ejpam-4055	261	13	h.	h.	PROPN
ejpam-4055	261	14	rara	rara	PROPN
ejpam-4055	261	15	.	.	PUNCT
ejpam-4055	262	1	on	on	ADP
ejpam-4055	262	2	strong	strong	ADJ
ejpam-4055	262	3	resolving	resolving	NOUN
ejpam-4055	262	4	domination	domination	NOUN
ejpam-4055	262	5	in	in	ADP
ejpam-4055	262	6	the	the	DET
ejpam-4055	262	7	join	join	NOUN
ejpam-4055	262	8	and	and	CCONJ
ejpam-4055	262	9	corona	corona	NOUN
ejpam-4055	262	10	of	of	ADP
ejpam-4055	262	11	graphs	graph	NOUN
ejpam-4055	262	12	.	.	PUNCT
ejpam-4055	263	1	european	european	ADJ
ejpam-4055	263	2	journal	journal	PROPN
ejpam-4055	263	3	of	of	ADP
ejpam-4055	263	4	pure	pure	ADJ
ejpam-4055	263	5	and	and	CCONJ
ejpam-4055	263	6	applied	applied	ADJ
ejpam-4055	263	7	mathematics	mathematic	NOUN
ejpam-4055	263	8	,	,	PUNCT
ejpam-4055	263	9	13(1):170	13(1):170	NUM
ejpam-4055	263	10	–	–	PUNCT
ejpam-4055	263	11	179	179	NUM
ejpam-4055	263	12	,	,	PUNCT
ejpam-4055	263	13	2020	2020	NUM
ejpam-4055	263	14	.	.	PUNCT
ejpam-4055	264	1	[	[	X
ejpam-4055	264	2	2	2	X
ejpam-4055	264	3	]	]	PUNCT
ejpam-4055	264	4	p.	p.	NOUN
ejpam-4055	264	5	acal	acal	ADJ
ejpam-4055	264	6	and	and	CCONJ
ejpam-4055	264	7	h.	h.	PROPN
ejpam-4055	264	8	rara	rara	PROPN
ejpam-4055	264	9	.	.	PUNCT
ejpam-4055	265	1	the	the	DET
ejpam-4055	265	2	strong	strong	ADJ
ejpam-4055	265	3	connected	connected	ADJ
ejpam-4055	265	4	metric	metric	ADJ
ejpam-4055	265	5	dimension	dimension	NOUN
ejpam-4055	265	6	in	in	ADP
ejpam-4055	265	7	the	the	DET
ejpam-4055	265	8	join	join	NOUN
ejpam-4055	265	9	and	and	CCONJ
ejpam-4055	265	10	corona	corona	NOUN
ejpam-4055	265	11	of	of	ADP
ejpam-4055	265	12	graphs	graph	NOUN
ejpam-4055	265	13	.	.	PUNCT
ejpam-4055	266	1	advances	advance	NOUN
ejpam-4055	266	2	and	and	CCONJ
ejpam-4055	266	3	applications	application	NOUN
ejpam-4055	266	4	in	in	ADP
ejpam-4055	266	5	discrete	discrete	ADJ
ejpam-4055	266	6	mathematics	mathematic	NOUN
ejpam-4055	266	7	,	,	PUNCT
ejpam-4055	266	8	21(1):91–101	21(1):91–101	NUM
ejpam-4055	266	9	,	,	PUNCT
ejpam-4055	266	10	2019	2019	NUM
ejpam-4055	266	11	.	.	PUNCT
ejpam-4055	267	1	[	[	X
ejpam-4055	267	2	3	3	X
ejpam-4055	267	3	]	]	X
ejpam-4055	267	4	c.	c.	PROPN
ejpam-4055	267	5	berge	berge	PROPN
ejpam-4055	267	6	.	.	PUNCT
ejpam-4055	268	1	theorie	theorie	PROPN
ejpam-4055	268	2	des	des	PROPN
ejpam-4055	268	3	graphes	graphes	PROPN
ejpam-4055	268	4	et	et	PROPN
ejpam-4055	268	5	ses	ses	PROPN
ejpam-4055	268	6	applications	application	NOUN
ejpam-4055	268	7	.	.	PUNCT
ejpam-4055	269	1	metheun	metheun	NOUN
ejpam-4055	269	2	and	and	CCONJ
ejpam-4055	269	3	wiley	wiley	PROPN
ejpam-4055	269	4	,	,	PUNCT
ejpam-4055	269	5	london	london	PROPN
ejpam-4055	269	6	and	and	CCONJ
ejpam-4055	269	7	new	new	PROPN
ejpam-4055	269	8	york	york	PROPN
ejpam-4055	269	9	,	,	PUNCT
ejpam-4055	269	10	1962	1962	NUM
ejpam-4055	269	11	.	.	PUNCT
ejpam-4055	270	1	[	[	X
ejpam-4055	270	2	4	4	X
ejpam-4055	270	3	]	]	X
ejpam-4055	270	4	j.	j.	PROPN
ejpam-4055	270	5	cabaro	cabaro	PROPN
ejpam-4055	270	6	and	and	CCONJ
ejpam-4055	270	7	h.	h.	PROPN
ejpam-4055	270	8	rara	rara	PROPN
ejpam-4055	270	9	.	.	PUNCT
ejpam-4055	271	1	on	on	ADP
ejpam-4055	271	2	2	2	NUM
ejpam-4055	271	3	-	-	PUNCT
ejpam-4055	271	4	resolving	resolve	VERB
ejpam-4055	271	5	sets	set	NOUN
ejpam-4055	271	6	in	in	ADP
ejpam-4055	271	7	the	the	DET
ejpam-4055	271	8	join	join	NOUN
ejpam-4055	271	9	and	and	CCONJ
ejpam-4055	271	10	corona	corona	NOUN
ejpam-4055	271	11	of	of	ADP
ejpam-4055	271	12	graphs	graph	NOUN
ejpam-4055	271	13	.	.	PUNCT
ejpam-4055	272	1	european	european	ADJ
ejpam-4055	272	2	journal	journal	PROPN
ejpam-4055	272	3	of	of	ADP
ejpam-4055	272	4	pure	pure	ADJ
ejpam-4055	272	5	and	and	CCONJ
ejpam-4055	272	6	applied	applied	ADJ
ejpam-4055	272	7	mathematics	mathematic	NOUN
ejpam-4055	272	8	,	,	PUNCT
ejpam-4055	272	9	accepted	accept	VERB
ejpam-4055	272	10	article	article	NOUN
ejpam-4055	272	11	2020	2020	NUM
ejpam-4055	272	12	.	.	PUNCT
ejpam-4055	273	1	[	[	X
ejpam-4055	273	2	5	5	NUM
ejpam-4055	273	3	]	]	PUNCT
ejpam-4055	273	4	f.	f.	PROPN
ejpam-4055	273	5	harary	harary	PROPN
ejpam-4055	273	6	.	.	PUNCT
ejpam-4055	274	1	graph	graph	NOUN
ejpam-4055	274	2	theory	theory	NOUN
ejpam-4055	274	3	.	.	PUNCT
ejpam-4055	275	1	addison	addison	PROPN
ejpam-4055	275	2	-	-	PUNCT
ejpam-4055	275	3	wesley	wesley	PROPN
ejpam-4055	275	4	publishing	publishing	PROPN
ejpam-4055	275	5	company	company	NOUN
ejpam-4055	275	6	,	,	PUNCT
ejpam-4055	275	7	usa	usa	PROPN
ejpam-4055	275	8	,	,	PUNCT
ejpam-4055	275	9	1969	1969	NUM
ejpam-4055	275	10	.	.	PUNCT
ejpam-4055	276	1	[	[	X
ejpam-4055	276	2	6	6	NUM
ejpam-4055	276	3	]	]	PUNCT
ejpam-4055	276	4	s.	s.	PROPN
ejpam-4055	276	5	canoy	canoy	PROPN
ejpam-4055	276	6	,	,	PUNCT
ejpam-4055	276	7	r.	r.	NOUN
ejpam-4055	276	8	mollejon	mollejon	NOUN
ejpam-4055	276	9	and	and	CCONJ
ejpam-4055	276	10	j.	j.	PROPN
ejpam-4055	276	11	canoy	canoy	PROPN
ejpam-4055	276	12	.	.	PUNCT
ejpam-4055	277	1	hop	hop	PROPN
ejpam-4055	277	2	dominating	dominating	NOUN
ejpam-4055	277	3	sets	set	NOUN
ejpam-4055	277	4	in	in	ADP
ejpam-4055	277	5	graphs	graph	NOUN
ejpam-4055	277	6	under	under	ADP
ejpam-4055	277	7	binary	binary	ADJ
ejpam-4055	277	8	operations	operation	NOUN
ejpam-4055	277	9	.	.	PUNCT
ejpam-4055	278	1	european	european	ADJ
ejpam-4055	278	2	journal	journal	PROPN
ejpam-4055	278	3	of	of	ADP
ejpam-4055	278	4	pure	pure	ADJ
ejpam-4055	278	5	and	and	CCONJ
ejpam-4055	278	6	applied	applied	ADJ
ejpam-4055	278	7	mathematics	mathematic	NOUN
ejpam-4055	278	8	,	,	PUNCT
ejpam-4055	278	9	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4055	278	10	,	,	PUNCT
ejpam-4055	278	11	2019	2019	NUM
ejpam-4055	278	12	.	.	PUNCT
ejpam-4055	279	1	[	[	X
ejpam-4055	279	2	7	7	X
ejpam-4055	279	3	]	]	X
ejpam-4055	279	4	g.	g.	PROPN
ejpam-4055	279	5	monsanto	monsanto	PROPN
ejpam-4055	279	6	and	and	CCONJ
ejpam-4055	279	7	h.	h.	PROPN
ejpam-4055	279	8	rara	rara	PROPN
ejpam-4055	279	9	.	.	PUNCT
ejpam-4055	280	1	resolving	resolve	VERB
ejpam-4055	280	2	sets	set	NOUN
ejpam-4055	280	3	in	in	ADP
ejpam-4055	280	4	graphs	graph	NOUN
ejpam-4055	280	5	.	.	PUNCT
ejpam-4055	281	1	international	international	ADJ
ejpam-4055	281	2	journal	journal	NOUN
ejpam-4055	281	3	of	of	ADP
ejpam-4055	281	4	pure	pure	ADJ
ejpam-4055	281	5	and	and	CCONJ
ejpam-4055	281	6	applied	applied	ADJ
ejpam-4055	281	7	mathematics	mathematic	NOUN
ejpam-4055	281	8	,	,	PUNCT
ejpam-4055	281	9	accepted	accept	VERB
ejpam-4055	281	10	article	article	NOUN
ejpam-4055	281	11	2020	2020	NUM
ejpam-4055	281	12	.	.	PUNCT
ejpam-4055	282	1	[	[	X
ejpam-4055	282	2	8	8	NUM
ejpam-4055	282	3	]	]	X
ejpam-4055	282	4	g.	g.	PROPN
ejpam-4055	282	5	monsanto	monsanto	PROPN
ejpam-4055	282	6	and	and	CCONJ
ejpam-4055	282	7	h.	h.	PROPN
ejpam-4055	282	8	rara	rara	PROPN
ejpam-4055	282	9	.	.	PUNCT
ejpam-4055	283	1	resolving	resolve	VERB
ejpam-4055	283	2	restrained	restrained	ADJ
ejpam-4055	283	3	domination	domination	NOUN
ejpam-4055	283	4	in	in	ADP
ejpam-4055	283	5	graphs	graph	NOUN
ejpam-4055	283	6	.	.	PUNCT
ejpam-4055	284	1	european	european	ADJ
ejpam-4055	284	2	journal	journal	PROPN
ejpam-4055	284	3	of	of	ADP
ejpam-4055	284	4	pure	pure	ADJ
ejpam-4055	284	5	and	and	CCONJ
ejpam-4055	284	6	applied	applied	ADJ
ejpam-4055	284	7	mathematics	mathematic	NOUN
ejpam-4055	284	8	,	,	PUNCT
ejpam-4055	284	9	accepted	accept	VERB
ejpam-4055	284	10	article	article	NOUN
ejpam-4055	284	11	2021	2021	NUM
ejpam-4055	284	12	.	.	PUNCT
ejpam-4055	285	1	[	[	X
ejpam-4055	285	2	9	9	NUM
ejpam-4055	285	3	]	]	PUNCT
ejpam-4055	285	4	c.	c.	PROPN
ejpam-4055	285	5	natarajan	natarajan	PROPN
ejpam-4055	285	6	and	and	CCONJ
ejpam-4055	285	7	s.	s.	PROPN
ejpam-4055	285	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4055	285	9	.	.	PUNCT
ejpam-4055	286	1	hop	hop	PROPN
ejpam-4055	286	2	domination	domination	NOUN
ejpam-4055	286	3	in	in	ADP
ejpam-4055	286	4	graphs	graph	NOUN
ejpam-4055	286	5	-	-	PUNCT
ejpam-4055	286	6	ii	ii	NOUN
ejpam-4055	286	7	.	.	PUNCT
ejpam-4055	286	8	versita	versita	PROPN
ejpam-4055	286	9	,	,	PUNCT
ejpam-4055	286	10	23(2):187	23(2):187	NUM
ejpam-4055	286	11	–	–	PUNCT
ejpam-4055	286	12	199	199	NUM
ejpam-4055	286	13	,	,	PUNCT
ejpam-4055	286	14	2015	2015	NUM
ejpam-4055	286	15	.	.	PUNCT
ejpam-4055	287	1	[	[	X
ejpam-4055	287	2	10	10	NUM
ejpam-4055	287	3	]	]	X
ejpam-4055	287	4	s.	s.	PROPN
ejpam-4055	287	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4055	287	6	,	,	PUNCT
ejpam-4055	287	7	c.	c.	PROPN
ejpam-4055	287	8	natarajan	natarajan	PROPN
ejpam-4055	287	9	and	and	CCONJ
ejpam-4055	287	10	g.	g.	PROPN
ejpam-4055	287	11	sathiamoorphy	sathiamoorphy	PROPN
ejpam-4055	287	12	.	.	PUNCT
ejpam-4055	288	1	a	a	DET
ejpam-4055	288	2	note	note	NOUN
ejpam-4055	288	3	on	on	ADP
ejpam-4055	288	4	hop	hop	NOUN
ejpam-4055	288	5	domination	domination	NOUN
ejpam-4055	288	6	number	number	NOUN
ejpam-4055	288	7	of	of	ADP
ejpam-4055	288	8	some	some	DET
ejpam-4055	288	9	special	special	ADJ
ejpam-4055	288	10	families	family	NOUN
ejpam-4055	288	11	of	of	ADP
ejpam-4055	288	12	graphs	graph	NOUN
ejpam-4055	288	13	.	.	PUNCT
ejpam-4055	289	1	international	international	ADJ
ejpam-4055	289	2	journal	journal	NOUN
ejpam-4055	289	3	of	of	ADP
ejpam-4055	289	4	pure	pure	ADJ
ejpam-4055	289	5	and	and	CCONJ
ejpam-4055	289	6	applied	applied	ADJ
ejpam-4055	289	7	mathematics	mathematic	NOUN
ejpam-4055	289	8	,	,	PUNCT
ejpam-4055	289	9	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-4055	289	10	,	,	PUNCT
ejpam-4055	289	11	2018	2018	NUM
ejpam-4055	289	12	.	.	PUNCT
ejpam-4055	290	1	[	[	X
ejpam-4055	290	2	11	11	NUM
ejpam-4055	290	3	]	]	X
ejpam-4055	290	4	g.	g.	NOUN
ejpam-4055	290	5	salasalan	salasalan	NOUN
ejpam-4055	290	6	and	and	CCONJ
ejpam-4055	290	7	s.	s.	PROPN
ejpam-4055	290	8	canoy	canoy	PROPN
ejpam-4055	290	9	.	.	PUNCT
ejpam-4055	291	1	global	global	ADJ
ejpam-4055	291	2	hop	hop	PROPN
ejpam-4055	291	3	domination	domination	NOUN
ejpam-4055	291	4	number	number	NOUN
ejpam-4055	291	5	of	of	ADP
ejpam-4055	291	6	graphs	graph	NOUN
ejpam-4055	291	7	.	.	PUNCT
ejpam-4055	292	1	european	european	ADJ
ejpam-4055	292	2	journal	journal	PROPN
ejpam-4055	292	3	of	of	ADP
ejpam-4055	292	4	pure	pure	ADJ
ejpam-4055	292	5	and	and	CCONJ
ejpam-4055	292	6	applied	applied	ADJ
ejpam-4055	292	7	mathematics	mathematic	NOUN
ejpam-4055	292	8	,	,	PUNCT
ejpam-4055	292	9	14(1):112–125	14(1):112–125	NUM
ejpam-4055	292	10	,	,	PUNCT
ejpam-4055	292	11	2021	2021	NUM
ejpam-4055	292	12	.	.	PUNCT
ejpam-4055	293	1	[	[	X
ejpam-4055	293	2	12	12	NUM
ejpam-4055	293	3	]	]	X
ejpam-4055	293	4	p.	p.	NOUN
ejpam-4055	293	5	slater	slater	PROPN
ejpam-4055	293	6	.	.	PUNCT
ejpam-4055	294	1	dominating	dominating	NOUN
ejpam-4055	294	2	and	and	CCONJ
ejpam-4055	294	3	reference	reference	NOUN
ejpam-4055	294	4	sets	set	NOUN
ejpam-4055	294	5	in	in	ADP
ejpam-4055	294	6	a	a	DET
ejpam-4055	294	7	graph	graph	NOUN
ejpam-4055	294	8	.	.	PUNCT
ejpam-4055	295	1	journal	journal	NOUN
ejpam-4055	295	2	of	of	ADP
ejpam-4055	295	3	mathematics	mathematic	NOUN
ejpam-4055	295	4	and	and	CCONJ
ejpam-4055	295	5	physical	physical	ADJ
ejpam-4055	295	6	science	science	NOUN
ejpam-4055	295	7	,	,	PUNCT
ejpam-4055	295	8	22(4):445–455	22(4):445–455	PROPN
ejpam-4055	295	9	,	,	PUNCT
ejpam-4055	295	10	1988	1988	NUM
ejpam-4055	295	11	.	.	PUNCT