id	sid	tid	token	lemma	pos
ejpam-4671	1	1	european	european	PROPN
ejpam-4671	1	2	journal	journal	PROPN
ejpam-4671	1	3	of	of	ADP
ejpam-4671	1	4	pure	pure	ADJ
ejpam-4671	1	5	and	and	CCONJ
ejpam-4671	1	6	applied	apply	VERB
ejpam-4671	1	7	mathematics	mathematic	NOUN
ejpam-4671	1	8	vol	vol	NOUN
ejpam-4671	1	9	.	.	PUNCT
ejpam-4671	2	1	16	16	NUM
ejpam-4671	2	2	,	,	PUNCT
ejpam-4671	2	3	no	no	INTJ
ejpam-4671	2	4	.	.	NOUN
ejpam-4671	2	5	1	1	NUM
ejpam-4671	2	6	,	,	PUNCT
ejpam-4671	2	7	2023	2023	NUM
ejpam-4671	2	8	,	,	PUNCT
ejpam-4671	2	9	418	418	NUM
ejpam-4671	2	10	-	-	SYM
ejpam-4671	2	11	429	429	NUM
ejpam-4671	2	12	issn	issn	PROPN
ejpam-4671	2	13	1307	1307	NUM
ejpam-4671	2	14	-	-	SYM
ejpam-4671	2	15	5543	5543	NUM
ejpam-4671	2	16	–	–	PUNCT
ejpam-4671	2	17	ejpam.com	ejpam.com	X
ejpam-4671	2	18	published	publish	VERB
ejpam-4671	2	19	by	by	ADP
ejpam-4671	2	20	new	new	PROPN
ejpam-4671	2	21	york	york	PROPN
ejpam-4671	2	22	business	business	PROPN
ejpam-4671	2	23	global	global	ADJ
ejpam-4671	2	24	1	1	NUM
ejpam-4671	2	25	-	-	PUNCT
ejpam-4671	2	26	movable	movable	ADJ
ejpam-4671	2	27	resolving	resolve	VERB
ejpam-4671	2	28	hop	hop	NOUN
ejpam-4671	2	29	domination	domination	NOUN
ejpam-4671	2	30	in	in	ADP
ejpam-4671	2	31	graphs	graphs	PROPN
ejpam-4671	2	32	jerson	jerson	PROPN
ejpam-4671	2	33	s.	s.	PROPN
ejpam-4671	2	34	mohamad1,∗	mohamad1,∗	PROPN
ejpam-4671	2	35	,	,	PUNCT
ejpam-4671	2	36	helen	helen	PROPN
ejpam-4671	2	37	m.	m.	PROPN
ejpam-4671	2	38	rara2	rara2	PROPN
ejpam-4671	3	1	1	1	NUM
ejpam-4671	3	2	department	department	NOUN
ejpam-4671	3	3	of	of	ADP
ejpam-4671	3	4	mathematics	mathematic	NOUN
ejpam-4671	3	5	and	and	CCONJ
ejpam-4671	3	6	statistics	statistic	NOUN
ejpam-4671	3	7	,	,	PUNCT
ejpam-4671	3	8	college	college	NOUN
ejpam-4671	3	9	of	of	ADP
ejpam-4671	3	10	science	science	NOUN
ejpam-4671	3	11	and	and	CCONJ
ejpam-4671	3	12	mathematics	mathematic	NOUN
ejpam-4671	3	13	,	,	PUNCT
ejpam-4671	3	14	western	western	ADJ
ejpam-4671	3	15	mindanao	mindanao	PROPN
ejpam-4671	3	16	state	state	PROPN
ejpam-4671	3	17	university	university	PROPN
ejpam-4671	3	18	,	,	PUNCT
ejpam-4671	3	19	7000	7000	NUM
ejpam-4671	3	20	zamboanga	zamboanga	PROPN
ejpam-4671	3	21	city	city	PROPN
ejpam-4671	3	22	,	,	PUNCT
ejpam-4671	3	23	philippines	philippines	PROPN
ejpam-4671	3	24	2	2	NUM
ejpam-4671	3	25	department	department	NOUN
ejpam-4671	3	26	of	of	ADP
ejpam-4671	3	27	mathematics	mathematic	NOUN
ejpam-4671	3	28	and	and	CCONJ
ejpam-4671	3	29	statistics	statistic	NOUN
ejpam-4671	3	30	,	,	PUNCT
ejpam-4671	3	31	college	college	NOUN
ejpam-4671	3	32	of	of	ADP
ejpam-4671	3	33	science	science	NOUN
ejpam-4671	3	34	and	and	CCONJ
ejpam-4671	3	35	mathematics	mathematic	NOUN
ejpam-4671	3	36	,	,	PUNCT
ejpam-4671	3	37	center	center	NOUN
ejpam-4671	3	38	of	of	ADP
ejpam-4671	3	39	graph	graph	NOUN
ejpam-4671	3	40	theory	theory	NOUN
ejpam-4671	3	41	,	,	PUNCT
ejpam-4671	3	42	algebra	algebra	NOUN
ejpam-4671	3	43	,	,	PUNCT
ejpam-4671	3	44	and	and	CCONJ
ejpam-4671	3	45	analysis	analysis	NOUN
ejpam-4671	3	46	-	-	PUNCT
ejpam-4671	3	47	premier	premier	NOUN
ejpam-4671	3	48	research	research	NOUN
ejpam-4671	3	49	institute	institute	PROPN
ejpam-4671	3	50	of	of	ADP
ejpam-4671	3	51	science	science	NOUN
ejpam-4671	3	52	and	and	CCONJ
ejpam-4671	3	53	mathematics	mathematic	NOUN
ejpam-4671	3	54	,	,	PUNCT
ejpam-4671	3	55	mindanao	mindanao	PROPN
ejpam-4671	3	56	state	state	PROPN
ejpam-4671	3	57	university	university	PROPN
ejpam-4671	3	58	-	-	PUNCT
ejpam-4671	3	59	iligan	iligan	PROPN
ejpam-4671	3	60	institute	institute	PROPN
ejpam-4671	3	61	of	of	ADP
ejpam-4671	3	62	technology	technology	PROPN
ejpam-4671	3	63	,	,	PUNCT
ejpam-4671	3	64	9200	9200	NUM
ejpam-4671	3	65	iligan	iligan	ADJ
ejpam-4671	3	66	city	city	NOUN
ejpam-4671	3	67	,	,	PUNCT
ejpam-4671	3	68	philippines	philippine	NOUN
ejpam-4671	3	69	abstract	abstract	ADJ
ejpam-4671	3	70	.	.	PUNCT
ejpam-4671	4	1	let	let	VERB
ejpam-4671	4	2	g	g	PRON
ejpam-4671	4	3	be	be	AUX
ejpam-4671	4	4	a	a	DET
ejpam-4671	4	5	connected	connected	ADJ
ejpam-4671	4	6	graph	graph	NOUN
ejpam-4671	4	7	.	.	PUNCT
ejpam-4671	5	1	a	a	DET
ejpam-4671	5	2	set	set	NOUN
ejpam-4671	5	3	w	w	PROPN
ejpam-4671	5	4	⊆	⊆	NUM
ejpam-4671	5	5	v	v	NOUN
ejpam-4671	5	6	(	(	PUNCT
ejpam-4671	5	7	g	g	NOUN
ejpam-4671	5	8	)	)	PUNCT
ejpam-4671	5	9	is	be	AUX
ejpam-4671	5	10	a	a	DET
ejpam-4671	5	11	resolving	resolve	VERB
ejpam-4671	5	12	hop	hop	NOUN
ejpam-4671	5	13	dominating	dominating	NOUN
ejpam-4671	5	14	set	set	NOUN
ejpam-4671	5	15	of	of	ADP
ejpam-4671	5	16	g	g	PROPN
ejpam-4671	5	17	if	if	SCONJ
ejpam-4671	5	18	w	w	NOUN
ejpam-4671	5	19	is	be	AUX
ejpam-4671	5	20	a	a	DET
ejpam-4671	5	21	resolving	resolving	NOUN
ejpam-4671	5	22	set	set	VERB
ejpam-4671	5	23	in	in	ADP
ejpam-4671	5	24	g	g	PROPN
ejpam-4671	5	25	and	and	CCONJ
ejpam-4671	5	26	for	for	ADP
ejpam-4671	5	27	every	every	DET
ejpam-4671	5	28	vertex	vertex	NOUN
ejpam-4671	5	29	v	v	ADP
ejpam-4671	5	30	∈	∈	NOUN
ejpam-4671	5	31	v	v	NOUN
ejpam-4671	5	32	(	(	PUNCT
ejpam-4671	5	33	g	g	NOUN
ejpam-4671	5	34	)	)	PUNCT
ejpam-4671	5	35	\	\	PUNCT
ejpam-4671	6	1	w	w	NOUN
ejpam-4671	6	2	there	there	PRON
ejpam-4671	6	3	exists	exist	VERB
ejpam-4671	6	4	u	u	PROPN
ejpam-4671	6	5	∈	∈	PROPN
ejpam-4671	6	6	w	w	ADP
ejpam-4671	6	7	such	such	ADJ
ejpam-4671	6	8	that	that	DET
ejpam-4671	6	9	dg(u	dg(u	ADJ
ejpam-4671	6	10	,	,	PUNCT
ejpam-4671	6	11	v	v	NOUN
ejpam-4671	6	12	)	)	PUNCT
ejpam-4671	6	13	=	=	SYM
ejpam-4671	6	14	2	2	X
ejpam-4671	6	15	.	.	X
ejpam-4671	6	16	a	a	DET
ejpam-4671	6	17	set	set	NOUN
ejpam-4671	6	18	s	s	NOUN
ejpam-4671	6	19	⊆	⊆	NUM
ejpam-4671	6	20	v	v	NOUN
ejpam-4671	6	21	(	(	PUNCT
ejpam-4671	6	22	g	g	NOUN
ejpam-4671	6	23	)	)	PUNCT
ejpam-4671	6	24	is	be	AUX
ejpam-4671	6	25	a	a	DET
ejpam-4671	6	26	1	1	NUM
ejpam-4671	6	27	-	-	PUNCT
ejpam-4671	6	28	movable	movable	ADJ
ejpam-4671	6	29	resolving	resolve	VERB
ejpam-4671	6	30	hop	hop	NOUN
ejpam-4671	6	31	dominating	dominating	NOUN
ejpam-4671	6	32	set	set	NOUN
ejpam-4671	6	33	of	of	ADP
ejpam-4671	6	34	g	g	PROPN
ejpam-4671	6	35	if	if	SCONJ
ejpam-4671	6	36	s	s	VERB
ejpam-4671	6	37	is	be	AUX
ejpam-4671	6	38	a	a	DET
ejpam-4671	6	39	resolving	resolve	VERB
ejpam-4671	6	40	hop	hop	NOUN
ejpam-4671	6	41	dominating	dominating	NOUN
ejpam-4671	6	42	set	set	NOUN
ejpam-4671	6	43	of	of	ADP
ejpam-4671	6	44	g	g	PROPN
ejpam-4671	6	45	and	and	CCONJ
ejpam-4671	6	46	for	for	ADP
ejpam-4671	6	47	every	every	DET
ejpam-4671	6	48	v	v	NUM
ejpam-4671	6	49	∈	∈	PROPN
ejpam-4671	6	50	s	s	NOUN
ejpam-4671	6	51	,	,	PUNCT
ejpam-4671	6	52	either	either	CCONJ
ejpam-4671	6	53	s	s	VERB
ejpam-4671	6	54	\	\	PROPN
ejpam-4671	6	55	{	{	PUNCT
ejpam-4671	6	56	v	v	NOUN
ejpam-4671	6	57	}	}	PUNCT
ejpam-4671	6	58	is	be	AUX
ejpam-4671	6	59	a	a	DET
ejpam-4671	6	60	resolving	resolve	VERB
ejpam-4671	6	61	hop	hop	NOUN
ejpam-4671	6	62	dominating	dominating	NOUN
ejpam-4671	6	63	set	set	NOUN
ejpam-4671	6	64	of	of	ADP
ejpam-4671	6	65	g	g	NOUN
ejpam-4671	6	66	or	or	CCONJ
ejpam-4671	6	67	there	there	ADV
ejpam-4671	6	68	exists	exist	VERB
ejpam-4671	6	69	a	a	DET
ejpam-4671	6	70	vertex	vertex	NOUN
ejpam-4671	6	71	u	u	NOUN
ejpam-4671	6	72	∈	∈	PROPN
ejpam-4671	6	73	(	(	PUNCT
ejpam-4671	6	74	(	(	PUNCT
ejpam-4671	6	75	v	v	NOUN
ejpam-4671	6	76	(	(	PUNCT
ejpam-4671	6	77	g	g	NOUN
ejpam-4671	6	78	)	)	PUNCT
ejpam-4671	6	79	\	\	PROPN
ejpam-4671	6	80	s	s	X
ejpam-4671	6	81	)	)	PUNCT
ejpam-4671	6	82	∩ng(v	∩ng(v	PROPN
ejpam-4671	6	83	)	)	PUNCT
ejpam-4671	6	84	)	)	PUNCT
ejpam-4671	6	85	such	such	ADJ
ejpam-4671	6	86	that	that	SCONJ
ejpam-4671	6	87	(	(	PUNCT
ejpam-4671	6	88	s	s	NOUN
ejpam-4671	6	89	\	\	X
ejpam-4671	6	90	{	{	PUNCT
ejpam-4671	6	91	v	v	NOUN
ejpam-4671	6	92	}	}	PUNCT
ejpam-4671	6	93	)	)	PUNCT
ejpam-4671	6	94	∪	∪	ADP
ejpam-4671	6	95	{	{	PUNCT
ejpam-4671	6	96	u	u	NOUN
ejpam-4671	6	97	}	}	PUNCT
ejpam-4671	6	98	is	be	AUX
ejpam-4671	6	99	a	a	DET
ejpam-4671	6	100	resolving	resolve	VERB
ejpam-4671	6	101	hop	hop	NOUN
ejpam-4671	6	102	dominating	dominating	NOUN
ejpam-4671	6	103	set	set	NOUN
ejpam-4671	6	104	of	of	ADP
ejpam-4671	6	105	g.	g.	PROPN
ejpam-4671	6	106	the	the	DET
ejpam-4671	6	107	1	1	NUM
ejpam-4671	6	108	-	-	PUNCT
ejpam-4671	6	109	movable	movable	ADJ
ejpam-4671	6	110	resolving	resolve	VERB
ejpam-4671	6	111	hop	hop	NOUN
ejpam-4671	6	112	domination	domination	NOUN
ejpam-4671	6	113	number	number	NOUN
ejpam-4671	6	114	of	of	ADP
ejpam-4671	6	115	g	g	NOUN
ejpam-4671	6	116	,	,	PUNCT
ejpam-4671	6	117	denoted	denote	VERB
ejpam-4671	6	118	by	by	ADP
ejpam-4671	6	119	γ1	γ1	PROPN
ejpam-4671	6	120	mrh(g	mrh(g	NOUN
ejpam-4671	6	121	)	)	PUNCT
ejpam-4671	6	122	is	be	AUX
ejpam-4671	6	123	the	the	DET
ejpam-4671	6	124	smallest	small	ADJ
ejpam-4671	6	125	cardinality	cardinality	NOUN
ejpam-4671	6	126	of	of	ADP
ejpam-4671	6	127	a	a	DET
ejpam-4671	6	128	1	1	NUM
ejpam-4671	6	129	-	-	PUNCT
ejpam-4671	6	130	movable	movable	ADJ
ejpam-4671	6	131	resolving	resolve	VERB
ejpam-4671	6	132	hop	hop	NOUN
ejpam-4671	6	133	dominating	dominating	NOUN
ejpam-4671	6	134	set	set	NOUN
ejpam-4671	6	135	of	of	ADP
ejpam-4671	6	136	g.	g.	PROPN
ejpam-4671	6	137	this	this	DET
ejpam-4671	6	138	paper	paper	NOUN
ejpam-4671	6	139	presents	present	VERB
ejpam-4671	6	140	the	the	DET
ejpam-4671	6	141	characterization	characterization	NOUN
ejpam-4671	6	142	of	of	ADP
ejpam-4671	6	143	the	the	DET
ejpam-4671	6	144	1	1	NUM
ejpam-4671	6	145	-	-	PUNCT
ejpam-4671	6	146	movable	movable	ADJ
ejpam-4671	6	147	resolving	resolve	VERB
ejpam-4671	6	148	hop	hop	NOUN
ejpam-4671	6	149	dominating	dominating	NOUN
ejpam-4671	6	150	sets	set	NOUN
ejpam-4671	6	151	in	in	ADP
ejpam-4671	6	152	the	the	DET
ejpam-4671	6	153	join	join	NOUN
ejpam-4671	6	154	,	,	PUNCT
ejpam-4671	6	155	corona	corona	NOUN
ejpam-4671	6	156	and	and	CCONJ
ejpam-4671	6	157	lexicographic	lexicographic	ADJ
ejpam-4671	6	158	product	product	NOUN
ejpam-4671	6	159	of	of	ADP
ejpam-4671	6	160	graphs	graph	NOUN
ejpam-4671	6	161	.	.	PUNCT
ejpam-4671	7	1	furthermore	furthermore	ADV
ejpam-4671	7	2	,	,	PUNCT
ejpam-4671	7	3	this	this	DET
ejpam-4671	7	4	paper	paper	NOUN
ejpam-4671	7	5	determines	determine	VERB
ejpam-4671	7	6	the	the	DET
ejpam-4671	7	7	exact	exact	ADJ
ejpam-4671	7	8	value	value	NOUN
ejpam-4671	7	9	or	or	CCONJ
ejpam-4671	7	10	bounds	bound	NOUN
ejpam-4671	7	11	of	of	ADP
ejpam-4671	7	12	their	their	PRON
ejpam-4671	7	13	corresponding	corresponding	ADJ
ejpam-4671	7	14	1	1	NUM
ejpam-4671	7	15	-	-	PUNCT
ejpam-4671	7	16	movable	movable	ADJ
ejpam-4671	7	17	resolving	resolve	VERB
ejpam-4671	7	18	hop	hop	NOUN
ejpam-4671	7	19	domination	domination	NOUN
ejpam-4671	7	20	number	number	NOUN
ejpam-4671	7	21	.	.	PUNCT
ejpam-4671	8	1	2020	2020	NUM
ejpam-4671	8	2	mathematics	mathematic	NOUN
ejpam-4671	8	3	subject	subject	NOUN
ejpam-4671	8	4	classifications	classification	NOUN
ejpam-4671	8	5	:	:	PUNCT
ejpam-4671	8	6	05c69	05c69	X
ejpam-4671	8	7	key	key	ADJ
ejpam-4671	8	8	words	word	NOUN
ejpam-4671	8	9	and	and	CCONJ
ejpam-4671	8	10	phrases	phrase	NOUN
ejpam-4671	8	11	:	:	PUNCT
ejpam-4671	8	12	1	1	NUM
ejpam-4671	8	13	-	-	PUNCT
ejpam-4671	8	14	movable	movable	ADJ
ejpam-4671	8	15	resolving	resolve	VERB
ejpam-4671	8	16	hop	hop	NOUN
ejpam-4671	8	17	dominating	dominating	NOUN
ejpam-4671	8	18	set	set	NOUN
ejpam-4671	8	19	,	,	PUNCT
ejpam-4671	8	20	1	1	NUM
ejpam-4671	8	21	-	-	PUNCT
ejpam-4671	8	22	movable	movable	ADJ
ejpam-4671	8	23	resolving	resolve	VERB
ejpam-4671	8	24	hop	hop	NOUN
ejpam-4671	8	25	domination	domination	NOUN
ejpam-4671	8	26	number	number	NOUN
ejpam-4671	8	27	,	,	PUNCT
ejpam-4671	8	28	hop	hop	NOUN
ejpam-4671	8	29	dominated	dominate	VERB
ejpam-4671	8	30	superclique	superclique	NOUN
ejpam-4671	8	31	,	,	PUNCT
ejpam-4671	8	32	join	join	NOUN
ejpam-4671	8	33	,	,	PUNCT
ejpam-4671	8	34	corona	corona	PROPN
ejpam-4671	8	35	,	,	PUNCT
ejpam-4671	8	36	lexicographic	lexicographic	ADJ
ejpam-4671	8	37	product	product	NOUN
ejpam-4671	8	38	1	1	NUM
ejpam-4671	8	39	.	.	PUNCT
ejpam-4671	9	1	introduction	introduction	NOUN
ejpam-4671	9	2	dominating	dominating	NOUN
ejpam-4671	9	3	sets	set	NOUN
ejpam-4671	9	4	in	in	ADP
ejpam-4671	9	5	graphs	graph	NOUN
ejpam-4671	9	6	have	have	AUX
ejpam-4671	9	7	been	be	AUX
ejpam-4671	9	8	studied	study	VERB
ejpam-4671	9	9	extensively	extensively	ADV
ejpam-4671	9	10	and	and	CCONJ
ejpam-4671	9	11	there	there	PRON
ejpam-4671	9	12	have	have	AUX
ejpam-4671	9	13	been	be	AUX
ejpam-4671	9	14	many	many	ADJ
ejpam-4671	9	15	published	publish	VERB
ejpam-4671	9	16	studies	study	NOUN
ejpam-4671	9	17	that	that	PRON
ejpam-4671	9	18	have	have	AUX
ejpam-4671	9	19	introduced	introduce	VERB
ejpam-4671	9	20	different	different	ADJ
ejpam-4671	9	21	variants	variant	NOUN
ejpam-4671	9	22	of	of	ADP
ejpam-4671	9	23	domination	domination	NOUN
ejpam-4671	9	24	in	in	ADP
ejpam-4671	9	25	graphs	graph	NOUN
ejpam-4671	9	26	[	[	X
ejpam-4671	9	27	7	7	NUM
ejpam-4671	9	28	,	,	PUNCT
ejpam-4671	9	29	13	13	NUM
ejpam-4671	9	30	]	]	PUNCT
ejpam-4671	9	31	.	.	PUNCT
ejpam-4671	10	1	in	in	ADP
ejpam-4671	10	2	2015	2015	NUM
ejpam-4671	10	3	,	,	PUNCT
ejpam-4671	10	4	natarajan	natarajan	PROPN
ejpam-4671	10	5	and	and	CCONJ
ejpam-4671	10	6	ayyaswamy	ayyaswamy	PROPN
ejpam-4671	10	7	[	[	X
ejpam-4671	10	8	12	12	NUM
ejpam-4671	10	9	]	]	PUNCT
ejpam-4671	10	10	studied	study	VERB
ejpam-4671	10	11	the	the	DET
ejpam-4671	10	12	concept	concept	NOUN
ejpam-4671	10	13	of	of	ADP
ejpam-4671	10	14	hop	hop	NOUN
ejpam-4671	10	15	domination	domination	NOUN
ejpam-4671	10	16	in	in	ADP
ejpam-4671	10	17	graphs	graph	NOUN
ejpam-4671	10	18	and	and	CCONJ
ejpam-4671	10	19	the	the	DET
ejpam-4671	10	20	hop	hop	NOUN
ejpam-4671	10	21	domination	domination	NOUN
ejpam-4671	10	22	number	number	NOUN
ejpam-4671	10	23	.	.	PUNCT
ejpam-4671	11	1	movable	movable	ADJ
ejpam-4671	11	2	resolving	resolving	NOUN
ejpam-4671	11	3	domination	domination	NOUN
ejpam-4671	11	4	in	in	ADP
ejpam-4671	11	5	graphs	graph	NOUN
ejpam-4671	11	6	was	be	AUX
ejpam-4671	11	7	studied	study	VERB
ejpam-4671	11	8	in	in	ADP
ejpam-4671	11	9	[	[	X
ejpam-4671	11	10	11	11	NUM
ejpam-4671	11	11	]	]	PUNCT
ejpam-4671	11	12	and	and	CCONJ
ejpam-4671	11	13	the	the	DET
ejpam-4671	11	14	resolving	resolve	VERB
ejpam-4671	11	15	hop	hop	NOUN
ejpam-4671	11	16	domination	domination	NOUN
ejpam-4671	11	17	sets	set	NOUN
ejpam-4671	11	18	in	in	ADP
ejpam-4671	11	19	graphs	graph	NOUN
ejpam-4671	11	20	was	be	AUX
ejpam-4671	11	21	introduced	introduce	VERB
ejpam-4671	11	22	in	in	ADP
ejpam-4671	11	23	[	[	X
ejpam-4671	11	24	10	10	NUM
ejpam-4671	11	25	]	]	PUNCT
ejpam-4671	11	26	.	.	PUNCT
ejpam-4671	12	1	other	other	ADJ
ejpam-4671	12	2	variations	variation	NOUN
ejpam-4671	12	3	of	of	ADP
ejpam-4671	12	4	resolving	resolve	VERB
ejpam-4671	12	5	sets	set	NOUN
ejpam-4671	12	6	can	can	AUX
ejpam-4671	12	7	be	be	AUX
ejpam-4671	12	8	found	find	VERB
ejpam-4671	12	9	in	in	ADP
ejpam-4671	12	10	[	[	X
ejpam-4671	12	11	2	2	NUM
ejpam-4671	12	12	,	,	PUNCT
ejpam-4671	12	13	3	3	NUM
ejpam-4671	12	14	,	,	PUNCT
ejpam-4671	12	15	6	6	NUM
ejpam-4671	12	16	]	]	PUNCT
ejpam-4671	12	17	and	and	CCONJ
ejpam-4671	12	18	resolving	resolve	VERB
ejpam-4671	12	19	dominating	dominating	NOUN
ejpam-4671	12	20	sets	set	NOUN
ejpam-4671	12	21	in	in	ADP
ejpam-4671	12	22	[	[	X
ejpam-4671	12	23	1	1	NUM
ejpam-4671	12	24	,	,	PUNCT
ejpam-4671	12	25	4	4	NUM
ejpam-4671	12	26	,	,	PUNCT
ejpam-4671	12	27	5	5	NUM
ejpam-4671	12	28	,	,	PUNCT
ejpam-4671	12	29	9	9	NUM
ejpam-4671	12	30	,	,	PUNCT
ejpam-4671	12	31	14	14	NUM
ejpam-4671	12	32	]	]	PUNCT
ejpam-4671	12	33	.	.	PUNCT
ejpam-4671	13	1	this	this	DET
ejpam-4671	13	2	paper	paper	NOUN
ejpam-4671	13	3	introduces	introduce	NOUN
ejpam-4671	13	4	and	and	CCONJ
ejpam-4671	13	5	characterizes	characterize	VERB
ejpam-4671	13	6	the	the	DET
ejpam-4671	13	7	concept	concept	NOUN
ejpam-4671	13	8	of	of	ADP
ejpam-4671	13	9	1	1	NUM
ejpam-4671	13	10	-	-	PUNCT
ejpam-4671	13	11	movable	movable	ADJ
ejpam-4671	13	12	resolving	resolve	VERB
ejpam-4671	13	13	hop	hop	NOUN
ejpam-4671	13	14	domination	domination	NOUN
ejpam-4671	13	15	in	in	ADP
ejpam-4671	13	16	graphs	graph	NOUN
ejpam-4671	13	17	.	.	PUNCT
ejpam-4671	14	1	∗corresponding	∗corresponde	VERB
ejpam-4671	14	2	author	author	NOUN
ejpam-4671	14	3	.	.	PUNCT
ejpam-4671	15	1	doi	doi	NOUN
ejpam-4671	15	2	:	:	PUNCT
ejpam-4671	15	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4671	https://doi.org/10.29020/nybg.ejpam.v16i1.4671	NOUN
ejpam-4671	15	4	email	email	NOUN
ejpam-4671	15	5	addresses	address	NOUN
ejpam-4671	15	6	:	:	PUNCT
ejpam-4671	15	7	mohamad.jerson@wmsu.edu.ph	mohamad.jerson@wmsu.edu.ph	PROPN
ejpam-4671	15	8	(	(	PUNCT
ejpam-4671	15	9	j.	j.	PROPN
ejpam-4671	15	10	mohamad	mohamad	PROPN
ejpam-4671	15	11	)	)	PUNCT
ejpam-4671	15	12	,	,	PUNCT
ejpam-4671	15	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4671	15	14	(	(	PUNCT
ejpam-4671	15	15	h.	h.	PROPN
ejpam-4671	15	16	rara	rara	PROPN
ejpam-4671	15	17	)	)	PUNCT
ejpam-4671	15	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4671	15	19	418	418	NUM
ejpam-4671	15	20	©	©	ADP
ejpam-4671	15	21	2023	2023	NUM
ejpam-4671	15	22	ejpam	ejpam	NOUN
ejpam-4671	15	23	all	all	DET
ejpam-4671	15	24	rights	right	NOUN
ejpam-4671	15	25	reserved	reserve	VERB
ejpam-4671	15	26	.	.	PUNCT
ejpam-4671	16	1	j.	j.	PROPN
ejpam-4671	16	2	mohamad	mohamad	PROPN
ejpam-4671	16	3	,	,	PUNCT
ejpam-4671	16	4	h.	h.	PROPN
ejpam-4671	16	5	rara	rara	PROPN
ejpam-4671	16	6	/	/	SYM
ejpam-4671	16	7	eur	eur	PROPN
ejpam-4671	16	8	.	.	PUNCT
ejpam-4671	17	1	j.	j.	PROPN
ejpam-4671	17	2	pure	pure	PROPN
ejpam-4671	17	3	appl	appl	PROPN
ejpam-4671	17	4	.	.	PROPN
ejpam-4671	17	5	math	math	PROPN
ejpam-4671	17	6	,	,	PUNCT
ejpam-4671	17	7	16	16	NUM
ejpam-4671	17	8	(	(	PUNCT
ejpam-4671	17	9	1	1	NUM
ejpam-4671	17	10	)	)	PUNCT
ejpam-4671	17	11	(	(	PUNCT
ejpam-4671	17	12	2023	2023	NUM
ejpam-4671	17	13	)	)	PUNCT
ejpam-4671	17	14	,	,	PUNCT
ejpam-4671	17	15	418	418	NUM
ejpam-4671	17	16	-	-	SYM
ejpam-4671	17	17	429	429	NUM
ejpam-4671	17	18	419	419	NUM
ejpam-4671	17	19	we	we	PRON
ejpam-4671	17	20	consider	consider	VERB
ejpam-4671	17	21	connected	connected	ADJ
ejpam-4671	17	22	graphs	graph	NOUN
ejpam-4671	17	23	that	that	PRON
ejpam-4671	17	24	are	be	AUX
ejpam-4671	17	25	finite	finite	ADJ
ejpam-4671	17	26	,	,	PUNCT
ejpam-4671	17	27	simple	simple	ADJ
ejpam-4671	17	28	,	,	PUNCT
ejpam-4671	17	29	and	and	CCONJ
ejpam-4671	17	30	undirected	undirected	ADJ
ejpam-4671	17	31	.	.	PUNCT
ejpam-4671	18	1	for	for	ADP
ejpam-4671	18	2	elementary	elementary	ADJ
ejpam-4671	18	3	graph	graph	NOUN
ejpam-4671	18	4	theory	theory	NOUN
ejpam-4671	18	5	concepts	concept	NOUN
ejpam-4671	18	6	,	,	PUNCT
ejpam-4671	18	7	it	it	PRON
ejpam-4671	18	8	is	be	AUX
ejpam-4671	18	9	recommended	recommend	VERB
ejpam-4671	18	10	that	that	SCONJ
ejpam-4671	18	11	readers	reader	NOUN
ejpam-4671	18	12	refer	refer	VERB
ejpam-4671	18	13	to	to	ADP
ejpam-4671	18	14	[	[	X
ejpam-4671	18	15	8	8	NUM
ejpam-4671	18	16	]	]	PUNCT
ejpam-4671	18	17	.	.	PUNCT
ejpam-4671	19	1	let	let	VERB
ejpam-4671	19	2	g	g	NOUN
ejpam-4671	19	3	=	=	PUNCT
ejpam-4671	19	4	(	(	PUNCT
ejpam-4671	19	5	v	v	NOUN
ejpam-4671	19	6	(	(	PUNCT
ejpam-4671	19	7	g	g	NOUN
ejpam-4671	19	8	)	)	PUNCT
ejpam-4671	19	9	,	,	PUNCT
ejpam-4671	19	10	e(g	e(g	PROPN
ejpam-4671	19	11	)	)	PUNCT
ejpam-4671	19	12	)	)	PUNCT
ejpam-4671	20	1	be	be	AUX
ejpam-4671	20	2	a	a	DET
ejpam-4671	20	3	graph	graph	NOUN
ejpam-4671	20	4	.	.	PUNCT
ejpam-4671	20	5	ng(v	ng(v	PUNCT
ejpam-4671	20	6	)	)	PUNCT
ejpam-4671	21	1	=	=	PRON
ejpam-4671	21	2	{	{	PUNCT
ejpam-4671	21	3	u	u	NOUN
ejpam-4671	21	4	∈	∈	PROPN
ejpam-4671	21	5	v	v	NOUN
ejpam-4671	21	6	(	(	PUNCT
ejpam-4671	21	7	g	g	NOUN
ejpam-4671	21	8	)	)	PUNCT
ejpam-4671	21	9	:	:	PUNCT
ejpam-4671	21	10	uv	uv	PROPN
ejpam-4671	21	11	∈	∈	PROPN
ejpam-4671	21	12	e(g	e(g	PROPN
ejpam-4671	21	13	)	)	PUNCT
ejpam-4671	21	14	}	}	PUNCT
ejpam-4671	21	15	is	be	AUX
ejpam-4671	21	16	a	a	DET
ejpam-4671	21	17	neighborhood	neighborhood	NOUN
ejpam-4671	21	18	of	of	ADP
ejpam-4671	21	19	v.	v.	ADP
ejpam-4671	21	20	an	an	DET
ejpam-4671	21	21	element	element	NOUN
ejpam-4671	21	22	u	u	NOUN
ejpam-4671	21	23	∈	∈	PROPN
ejpam-4671	21	24	ng(v	ng(v	PUNCT
ejpam-4671	21	25	)	)	PUNCT
ejpam-4671	21	26	is	be	AUX
ejpam-4671	21	27	called	call	VERB
ejpam-4671	21	28	a	a	DET
ejpam-4671	21	29	neighbor	neighbor	NOUN
ejpam-4671	21	30	of	of	ADP
ejpam-4671	21	31	v.	v.	CCONJ
ejpam-4671	21	32	ng[v	ng[v	X
ejpam-4671	21	33	]	]	X
ejpam-4671	21	34	=	=	SYM
ejpam-4671	21	35	ng(v	ng(v	X
ejpam-4671	21	36	)	)	PUNCT
ejpam-4671	21	37	∪	∪	ADP
ejpam-4671	21	38	{	{	PUNCT
ejpam-4671	21	39	v	v	NOUN
ejpam-4671	21	40	}	}	PUNCT
ejpam-4671	21	41	is	be	AUX
ejpam-4671	21	42	a	a	DET
ejpam-4671	21	43	closed	closed	ADJ
ejpam-4671	21	44	neighborhood	neighborhood	NOUN
ejpam-4671	21	45	of	of	ADP
ejpam-4671	21	46	v.	v.	ADP
ejpam-4671	21	47	the	the	DET
ejpam-4671	21	48	degree	degree	NOUN
ejpam-4671	21	49	of	of	ADP
ejpam-4671	21	50	v	v	NOUN
ejpam-4671	21	51	,	,	PUNCT
ejpam-4671	21	52	denoted	denote	VERB
ejpam-4671	21	53	by	by	ADP
ejpam-4671	21	54	degg(v	degg(v	PROPN
ejpam-4671	21	55	)	)	PUNCT
ejpam-4671	21	56	,	,	PUNCT
ejpam-4671	21	57	is	be	AUX
ejpam-4671	21	58	equal	equal	ADJ
ejpam-4671	21	59	to	to	ADP
ejpam-4671	21	60	|ng(v)|	|ng(v)|	NOUN
ejpam-4671	21	61	.	.	PUNCT
ejpam-4671	22	1	for	for	ADP
ejpam-4671	22	2	s	s	PROPN
ejpam-4671	22	3	⊆	⊆	NUM
ejpam-4671	22	4	v	v	NOUN
ejpam-4671	22	5	(	(	PUNCT
ejpam-4671	22	6	g	g	NOUN
ejpam-4671	22	7	)	)	PUNCT
ejpam-4671	22	8	,	,	PUNCT
ejpam-4671	22	9	ng(s	ng(s	NUM
ejpam-4671	22	10	)	)	PUNCT
ejpam-4671	22	11	=	=	SYM
ejpam-4671	22	12	⋃	⋃	ADP
ejpam-4671	22	13	v∈s	v∈s	NOUN
ejpam-4671	22	14	ng(v	ng(v	NOUN
ejpam-4671	22	15	)	)	PUNCT
ejpam-4671	22	16	and	and	CCONJ
ejpam-4671	22	17	ng[s	ng[	NOUN
ejpam-4671	22	18	]	]	PUNCT
ejpam-4671	22	19	=	=	PUNCT
ejpam-4671	22	20	⋃	⋃	VERB
ejpam-4671	22	21	v∈s	v∈s	ADJ
ejpam-4671	22	22	ng[v	ng[v	NOUN
ejpam-4671	22	23	]	]	PUNCT
ejpam-4671	22	24	.	.	PUNCT
ejpam-4671	23	1	the	the	DET
ejpam-4671	23	2	distance	distance	NOUN
ejpam-4671	23	3	dg(u	dg(u	NOUN
ejpam-4671	23	4	,	,	PUNCT
ejpam-4671	23	5	v	v	NOUN
ejpam-4671	23	6	)	)	PUNCT
ejpam-4671	23	7	of	of	ADP
ejpam-4671	23	8	two	two	NUM
ejpam-4671	23	9	vertices	vertex	NOUN
ejpam-4671	23	10	u	u	NOUN
ejpam-4671	23	11	,	,	PUNCT
ejpam-4671	23	12	v	v	NOUN
ejpam-4671	23	13	in	in	ADP
ejpam-4671	23	14	g	g	PROPN
ejpam-4671	23	15	is	be	AUX
ejpam-4671	23	16	the	the	DET
ejpam-4671	23	17	length	length	NOUN
ejpam-4671	23	18	of	of	ADP
ejpam-4671	23	19	a	a	DET
ejpam-4671	23	20	shortest	short	ADJ
ejpam-4671	23	21	u	u	NOUN
ejpam-4671	23	22	-	-	NOUN
ejpam-4671	23	23	v	v	ADJ
ejpam-4671	23	24	path	path	NOUN
ejpam-4671	23	25	in	in	ADP
ejpam-4671	23	26	g.	g.	PROPN
ejpam-4671	23	27	the	the	DET
ejpam-4671	23	28	greatest	great	ADJ
ejpam-4671	23	29	distance	distance	NOUN
ejpam-4671	23	30	between	between	ADP
ejpam-4671	23	31	any	any	DET
ejpam-4671	23	32	two	two	NUM
ejpam-4671	23	33	vertices	vertex	NOUN
ejpam-4671	23	34	in	in	ADP
ejpam-4671	23	35	g	g	NOUN
ejpam-4671	23	36	,	,	PUNCT
ejpam-4671	23	37	denoted	denote	VERB
ejpam-4671	23	38	by	by	ADP
ejpam-4671	23	39	diam(g	diam(g	PROPN
ejpam-4671	23	40	)	)	PUNCT
ejpam-4671	23	41	,	,	PUNCT
ejpam-4671	23	42	is	be	AUX
ejpam-4671	23	43	called	call	VERB
ejpam-4671	23	44	the	the	DET
ejpam-4671	23	45	diameter	diameter	NOUN
ejpam-4671	23	46	of	of	ADP
ejpam-4671	23	47	g.	g.	PROPN
ejpam-4671	23	48	a	a	DET
ejpam-4671	23	49	set	set	NOUN
ejpam-4671	23	50	s	s	PROPN
ejpam-4671	23	51	⊆	⊆	NUM
ejpam-4671	23	52	v	v	NOUN
ejpam-4671	23	53	(	(	PUNCT
ejpam-4671	23	54	g	g	NOUN
ejpam-4671	23	55	)	)	PUNCT
ejpam-4671	23	56	is	be	AUX
ejpam-4671	23	57	a	a	DET
ejpam-4671	23	58	dominating	dominating	NOUN
ejpam-4671	23	59	set	set	NOUN
ejpam-4671	23	60	if	if	SCONJ
ejpam-4671	23	61	every	every	DET
ejpam-4671	23	62	u	u	PROPN
ejpam-4671	23	63	∈	∈	PROPN
ejpam-4671	23	64	v	v	NOUN
ejpam-4671	23	65	(	(	PUNCT
ejpam-4671	23	66	g	g	NOUN
ejpam-4671	23	67	)	)	PUNCT
ejpam-4671	23	68	\	\	PROPN
ejpam-4671	24	1	s	s	PART
ejpam-4671	24	2	is	be	AUX
ejpam-4671	24	3	adjacent	adjacent	ADJ
ejpam-4671	24	4	to	to	ADP
ejpam-4671	24	5	at	at	ADV
ejpam-4671	24	6	least	least	ADV
ejpam-4671	24	7	one	one	NUM
ejpam-4671	24	8	vertex	vertex	NOUN
ejpam-4671	24	9	v	v	ADP
ejpam-4671	24	10	∈	∈	NOUN
ejpam-4671	24	11	s.	s.	PROPN
ejpam-4671	25	1	the	the	DET
ejpam-4671	25	2	domination	domination	NOUN
ejpam-4671	25	3	number	number	NOUN
ejpam-4671	25	4	of	of	ADP
ejpam-4671	25	5	a	a	DET
ejpam-4671	25	6	graph	graph	NOUN
ejpam-4671	25	7	g	g	NOUN
ejpam-4671	25	8	,	,	PUNCT
ejpam-4671	25	9	denoted	denote	VERB
ejpam-4671	25	10	by	by	ADP
ejpam-4671	25	11	γ(g	γ(g	PROPN
ejpam-4671	25	12	)	)	PUNCT
ejpam-4671	25	13	,	,	PUNCT
ejpam-4671	25	14	is	be	AUX
ejpam-4671	25	15	given	give	VERB
ejpam-4671	25	16	by	by	ADP
ejpam-4671	25	17	γ(g	γ(g	PROPN
ejpam-4671	25	18	)	)	PUNCT
ejpam-4671	26	1	=	=	NOUN
ejpam-4671	26	2	min{|s|	min{|s|	NOUN
ejpam-4671	26	3	:	:	PUNCT
ejpam-4671	26	4	s	s	VERB
ejpam-4671	26	5	is	be	AUX
ejpam-4671	26	6	a	a	DET
ejpam-4671	26	7	dominating	dominating	NOUN
ejpam-4671	26	8	set	set	NOUN
ejpam-4671	26	9	of	of	ADP
ejpam-4671	26	10	g	g	NOUN
ejpam-4671	26	11	}	}	PUNCT
ejpam-4671	26	12	.	.	PUNCT
ejpam-4671	27	1	a	a	DET
ejpam-4671	27	2	set	set	NOUN
ejpam-4671	27	3	s	s	NOUN
ejpam-4671	27	4	⊆	⊆	NUM
ejpam-4671	27	5	v	v	NOUN
ejpam-4671	27	6	(	(	PUNCT
ejpam-4671	27	7	g	g	NOUN
ejpam-4671	27	8	)	)	PUNCT
ejpam-4671	27	9	is	be	AUX
ejpam-4671	27	10	a	a	DET
ejpam-4671	27	11	total	total	ADJ
ejpam-4671	27	12	dominating	dominating	NOUN
ejpam-4671	27	13	set	set	NOUN
ejpam-4671	27	14	if	if	SCONJ
ejpam-4671	27	15	every	every	DET
ejpam-4671	27	16	vertex	vertex	NOUN
ejpam-4671	27	17	in	in	ADP
ejpam-4671	27	18	graph	graph	NOUN
ejpam-4671	27	19	g	g	PROPN
ejpam-4671	27	20	is	be	AUX
ejpam-4671	27	21	adjacent	adjacent	ADJ
ejpam-4671	27	22	to	to	ADP
ejpam-4671	27	23	some	some	DET
ejpam-4671	27	24	vertex	vertex	NOUN
ejpam-4671	27	25	of	of	ADP
ejpam-4671	27	26	s.	s.	PROPN
ejpam-4671	27	27	the	the	DET
ejpam-4671	27	28	minimum	minimum	ADJ
ejpam-4671	27	29	cardinality	cardinality	NOUN
ejpam-4671	27	30	of	of	ADP
ejpam-4671	27	31	a	a	DET
ejpam-4671	27	32	total	total	ADJ
ejpam-4671	27	33	dominating	dominating	NOUN
ejpam-4671	27	34	set	set	NOUN
ejpam-4671	27	35	in	in	ADP
ejpam-4671	27	36	g	g	PROPN
ejpam-4671	27	37	is	be	AUX
ejpam-4671	27	38	the	the	DET
ejpam-4671	27	39	total	total	ADJ
ejpam-4671	27	40	domination	domination	NOUN
ejpam-4671	27	41	number	number	NOUN
ejpam-4671	27	42	of	of	ADP
ejpam-4671	27	43	g	g	NOUN
ejpam-4671	27	44	,	,	PUNCT
ejpam-4671	27	45	denoted	denote	VERB
ejpam-4671	27	46	by	by	ADP
ejpam-4671	27	47	γt(g	γt(g	NOUN
ejpam-4671	27	48	)	)	PUNCT
ejpam-4671	27	49	,	,	PUNCT
ejpam-4671	27	50	and	and	CCONJ
ejpam-4671	27	51	we	we	PRON
ejpam-4671	27	52	refer	refer	VERB
ejpam-4671	27	53	to	to	ADP
ejpam-4671	27	54	such	such	DET
ejpam-4671	27	55	a	a	DET
ejpam-4671	27	56	set	set	NOUN
ejpam-4671	27	57	as	as	ADP
ejpam-4671	27	58	γt	γt	NOUN
ejpam-4671	27	59	-	-	ADJ
ejpam-4671	27	60	set	set	NOUN
ejpam-4671	27	61	of	of	ADP
ejpam-4671	27	62	g.	g.	PROPN
ejpam-4671	27	63	a	a	DET
ejpam-4671	27	64	set	set	NOUN
ejpam-4671	27	65	s	s	PROPN
ejpam-4671	27	66	⊆	⊆	NUM
ejpam-4671	27	67	v	v	NOUN
ejpam-4671	27	68	(	(	PUNCT
ejpam-4671	27	69	g	g	NOUN
ejpam-4671	27	70	)	)	PUNCT
ejpam-4671	27	71	is	be	AUX
ejpam-4671	27	72	a	a	DET
ejpam-4671	27	73	hop	hop	NOUN
ejpam-4671	27	74	dominating	dominating	NOUN
ejpam-4671	27	75	set	set	NOUN
ejpam-4671	27	76	of	of	ADP
ejpam-4671	27	77	g	g	PROPN
ejpam-4671	27	78	if	if	SCONJ
ejpam-4671	27	79	for	for	ADP
ejpam-4671	27	80	every	every	DET
ejpam-4671	27	81	v	v	NUM
ejpam-4671	27	82	∈	∈	NOUN
ejpam-4671	27	83	v	v	NOUN
ejpam-4671	27	84	(	(	PUNCT
ejpam-4671	27	85	g)\s	g)\s	NOUN
ejpam-4671	27	86	,	,	PUNCT
ejpam-4671	27	87	there	there	PRON
ejpam-4671	27	88	exists	exist	VERB
ejpam-4671	27	89	u	u	PROPN
ejpam-4671	27	90	∈	∈	PROPN
ejpam-4671	27	91	s	s	VERB
ejpam-4671	27	92	such	such	ADJ
ejpam-4671	27	93	that	that	DET
ejpam-4671	27	94	dg(u	dg(u	ADJ
ejpam-4671	27	95	,	,	PUNCT
ejpam-4671	27	96	v	v	NOUN
ejpam-4671	27	97	)	)	PUNCT
ejpam-4671	28	1	=	=	SYM
ejpam-4671	28	2	2	2	X
ejpam-4671	28	3	.	.	PUNCT
ejpam-4671	29	1	the	the	DET
ejpam-4671	29	2	minimum	minimum	ADJ
ejpam-4671	29	3	cardinality	cardinality	NOUN
ejpam-4671	29	4	of	of	ADP
ejpam-4671	29	5	a	a	DET
ejpam-4671	29	6	hop	hop	NOUN
ejpam-4671	29	7	dominating	dominating	NOUN
ejpam-4671	29	8	set	set	NOUN
ejpam-4671	29	9	of	of	ADP
ejpam-4671	29	10	g	g	NOUN
ejpam-4671	29	11	,	,	PUNCT
ejpam-4671	29	12	denoted	denote	VERB
ejpam-4671	29	13	by	by	ADP
ejpam-4671	29	14	γh(g	γh(g	NOUN
ejpam-4671	29	15	)	)	PUNCT
ejpam-4671	29	16	,	,	PUNCT
ejpam-4671	29	17	is	be	AUX
ejpam-4671	29	18	called	call	VERB
ejpam-4671	29	19	the	the	DET
ejpam-4671	29	20	hop	hop	NOUN
ejpam-4671	29	21	domination	domination	NOUN
ejpam-4671	29	22	number	number	NOUN
ejpam-4671	29	23	of	of	ADP
ejpam-4671	29	24	g.	g.	PROPN
ejpam-4671	29	25	any	any	DET
ejpam-4671	29	26	hop	hop	NOUN
ejpam-4671	29	27	dominating	dominating	NOUN
ejpam-4671	29	28	set	set	VERB
ejpam-4671	29	29	with	with	ADP
ejpam-4671	29	30	cardinality	cardinality	NOUN
ejpam-4671	29	31	equal	equal	ADJ
ejpam-4671	29	32	to	to	ADP
ejpam-4671	29	33	γh(g	γh(g	NOUN
ejpam-4671	29	34	)	)	PUNCT
ejpam-4671	29	35	is	be	AUX
ejpam-4671	29	36	called	call	VERB
ejpam-4671	29	37	a	a	DET
ejpam-4671	29	38	γh	γh	ADV
ejpam-4671	29	39	-	-	PUNCT
ejpam-4671	29	40	set	set	NOUN
ejpam-4671	29	41	.	.	PUNCT
ejpam-4671	30	1	a	a	DET
ejpam-4671	30	2	vertex	vertex	NOUN
ejpam-4671	30	3	v	v	NOUN
ejpam-4671	30	4	in	in	ADP
ejpam-4671	30	5	g	g	PROPN
ejpam-4671	30	6	is	be	AUX
ejpam-4671	30	7	a	a	DET
ejpam-4671	30	8	hop	hop	NOUN
ejpam-4671	30	9	neighbor	neighbor	NOUN
ejpam-4671	30	10	of	of	ADP
ejpam-4671	30	11	vertex	vertex	NOUN
ejpam-4671	30	12	u	u	NOUN
ejpam-4671	30	13	in	in	ADP
ejpam-4671	30	14	g	g	PROPN
ejpam-4671	30	15	if	if	SCONJ
ejpam-4671	30	16	dg(u	dg(u	NOUN
ejpam-4671	30	17	,	,	PUNCT
ejpam-4671	30	18	v	v	NOUN
ejpam-4671	30	19	)	)	PUNCT
ejpam-4671	30	20	=	=	SYM
ejpam-4671	30	21	2	2	X
ejpam-4671	30	22	.	.	X
ejpam-4671	31	1	the	the	DET
ejpam-4671	31	2	set	set	NOUN
ejpam-4671	31	3	ng(u	ng(u	NOUN
ejpam-4671	31	4	,	,	PUNCT
ejpam-4671	31	5	2	2	NUM
ejpam-4671	31	6	)	)	PUNCT
ejpam-4671	31	7	=	=	PRON
ejpam-4671	31	8	{	{	PUNCT
ejpam-4671	31	9	v	v	NUM
ejpam-4671	31	10	∈	∈	NOUN
ejpam-4671	31	11	v	v	NOUN
ejpam-4671	31	12	(	(	PUNCT
ejpam-4671	31	13	g	g	NOUN
ejpam-4671	31	14	)	)	PUNCT
ejpam-4671	31	15	:	:	PUNCT
ejpam-4671	31	16	dg(v	dg(v	X
ejpam-4671	31	17	,	,	PUNCT
ejpam-4671	31	18	u	u	NOUN
ejpam-4671	31	19	)	)	PUNCT
ejpam-4671	31	20	=	=	SYM
ejpam-4671	31	21	2	2	X
ejpam-4671	31	22	}	}	PUNCT
ejpam-4671	31	23	is	be	AUX
ejpam-4671	31	24	called	call	VERB
ejpam-4671	31	25	the	the	DET
ejpam-4671	31	26	open	open	ADJ
ejpam-4671	31	27	hop	hop	NOUN
ejpam-4671	31	28	neighborhood	neighborhood	NOUN
ejpam-4671	31	29	of	of	ADP
ejpam-4671	31	30	u.	u.	PROPN
ejpam-4671	31	31	the	the	DET
ejpam-4671	31	32	closed	closed	ADJ
ejpam-4671	31	33	hop	hop	NOUN
ejpam-4671	31	34	neighborhood	neighborhood	NOUN
ejpam-4671	31	35	of	of	ADP
ejpam-4671	31	36	u	u	PROPN
ejpam-4671	31	37	in	in	ADP
ejpam-4671	31	38	g	g	PROPN
ejpam-4671	31	39	is	be	AUX
ejpam-4671	31	40	given	give	VERB
ejpam-4671	31	41	by	by	ADP
ejpam-4671	31	42	ng[u	ng[u	PROPN
ejpam-4671	31	43	,	,	PUNCT
ejpam-4671	31	44	2	2	NUM
ejpam-4671	31	45	]	]	PUNCT
ejpam-4671	31	46	=	=	PUNCT
ejpam-4671	31	47	ng(u	ng(u	NOUN
ejpam-4671	31	48	,	,	PUNCT
ejpam-4671	31	49	2	2	X
ejpam-4671	31	50	)	)	PUNCT
ejpam-4671	31	51	∪	∪	NOUN
ejpam-4671	31	52	{	{	PUNCT
ejpam-4671	31	53	u	u	NOUN
ejpam-4671	31	54	}	}	PUNCT
ejpam-4671	31	55	.	.	PUNCT
ejpam-4671	32	1	the	the	DET
ejpam-4671	32	2	open	open	ADJ
ejpam-4671	32	3	hop	hop	NOUN
ejpam-4671	32	4	neighborhood	neighborhood	NOUN
ejpam-4671	32	5	of	of	ADP
ejpam-4671	32	6	x	x	PROPN
ejpam-4671	32	7	⊆	⊆	NUM
ejpam-4671	32	8	v	v	ADP
ejpam-4671	32	9	(	(	PUNCT
ejpam-4671	32	10	g	g	NOUN
ejpam-4671	32	11	)	)	PUNCT
ejpam-4671	32	12	is	be	AUX
ejpam-4671	32	13	the	the	DET
ejpam-4671	32	14	set	set	NOUN
ejpam-4671	32	15	ng(x	ng(x	NUM
ejpam-4671	32	16	,	,	PUNCT
ejpam-4671	32	17	2	2	X
ejpam-4671	32	18	)	)	PUNCT
ejpam-4671	32	19	=	=	NOUN
ejpam-4671	32	20	⋃	⋃	NOUN
ejpam-4671	32	21	u∈x	u∈x	ADJ
ejpam-4671	32	22	ng(u	ng(u	NOUN
ejpam-4671	32	23	,	,	PUNCT
ejpam-4671	32	24	2	2	NUM
ejpam-4671	32	25	)	)	PUNCT
ejpam-4671	32	26	.	.	PUNCT
ejpam-4671	33	1	the	the	DET
ejpam-4671	33	2	closed	closed	ADJ
ejpam-4671	33	3	hop	hop	NOUN
ejpam-4671	33	4	neighborhood	neighborhood	NOUN
ejpam-4671	33	5	of	of	ADP
ejpam-4671	33	6	x	x	PUNCT
ejpam-4671	33	7	in	in	ADP
ejpam-4671	33	8	g	g	PROPN
ejpam-4671	33	9	is	be	AUX
ejpam-4671	33	10	the	the	DET
ejpam-4671	33	11	set	set	PROPN
ejpam-4671	33	12	ng[x	ng[x	PROPN
ejpam-4671	33	13	,	,	PUNCT
ejpam-4671	33	14	2	2	NUM
ejpam-4671	33	15	]	]	PUNCT
ejpam-4671	33	16	=	=	SYM
ejpam-4671	33	17	ng(x	ng(x	X
ejpam-4671	33	18	,	,	PUNCT
ejpam-4671	33	19	2	2	NUM
ejpam-4671	33	20	)	)	PUNCT
ejpam-4671	33	21	∪x	∪x	NUM
ejpam-4671	33	22	.	.	PUNCT
ejpam-4671	34	1	a	a	DET
ejpam-4671	34	2	set	set	NOUN
ejpam-4671	34	3	s	s	NOUN
ejpam-4671	34	4	⊆	⊆	NUM
ejpam-4671	34	5	v	v	NOUN
ejpam-4671	34	6	(	(	PUNCT
ejpam-4671	34	7	g	g	NOUN
ejpam-4671	34	8	)	)	PUNCT
ejpam-4671	34	9	is	be	AUX
ejpam-4671	34	10	a	a	DET
ejpam-4671	34	11	total	total	ADJ
ejpam-4671	34	12	hop	hop	NOUN
ejpam-4671	34	13	dominating	dominating	NOUN
ejpam-4671	34	14	set	set	NOUN
ejpam-4671	34	15	of	of	ADP
ejpam-4671	34	16	g	g	PROPN
ejpam-4671	34	17	if	if	SCONJ
ejpam-4671	34	18	for	for	ADP
ejpam-4671	34	19	every	every	DET
ejpam-4671	34	20	v	v	NUM
ejpam-4671	34	21	∈	∈	NOUN
ejpam-4671	34	22	v	v	NOUN
ejpam-4671	34	23	(	(	PUNCT
ejpam-4671	34	24	g	g	NOUN
ejpam-4671	34	25	)	)	PUNCT
ejpam-4671	34	26	,	,	PUNCT
ejpam-4671	34	27	there	there	PRON
ejpam-4671	34	28	exists	exist	VERB
ejpam-4671	34	29	u	u	PROPN
ejpam-4671	34	30	∈	∈	PROPN
ejpam-4671	34	31	s	s	VERB
ejpam-4671	34	32	such	such	ADJ
ejpam-4671	34	33	that	that	DET
ejpam-4671	34	34	dg(u	dg(u	ADJ
ejpam-4671	34	35	,	,	PUNCT
ejpam-4671	34	36	v	v	NOUN
ejpam-4671	34	37	)	)	PUNCT
ejpam-4671	35	1	=	=	SYM
ejpam-4671	35	2	2	2	X
ejpam-4671	35	3	.	.	X
ejpam-4671	35	4	that	that	PRON
ejpam-4671	35	5	is	be	AUX
ejpam-4671	35	6	,	,	PUNCT
ejpam-4671	35	7	s	s	VERB
ejpam-4671	35	8	is	be	AUX
ejpam-4671	35	9	a	a	DET
ejpam-4671	35	10	hop	hop	NOUN
ejpam-4671	35	11	dominating	dominating	NOUN
ejpam-4671	35	12	set	set	NOUN
ejpam-4671	35	13	of	of	ADP
ejpam-4671	35	14	g	g	PROPN
ejpam-4671	35	15	and	and	CCONJ
ejpam-4671	35	16	for	for	ADP
ejpam-4671	35	17	all	all	DET
ejpam-4671	35	18	z	z	NOUN
ejpam-4671	35	19	∈	∈	PROPN
ejpam-4671	35	20	s	s	NOUN
ejpam-4671	35	21	,	,	PUNCT
ejpam-4671	35	22	ng(z	ng(z	NUM
ejpam-4671	35	23	,	,	PUNCT
ejpam-4671	35	24	2	2	NUM
ejpam-4671	35	25	)	)	PUNCT
ejpam-4671	35	26	∩	∩	NOUN
ejpam-4671	35	27	s	s	PART
ejpam-4671	35	28	̸=	̸=	PROPN
ejpam-4671	35	29	∅.	∅.	ADP
ejpam-4671	35	30	the	the	DET
ejpam-4671	35	31	smallest	small	ADJ
ejpam-4671	35	32	cardinality	cardinality	NOUN
ejpam-4671	35	33	of	of	ADP
ejpam-4671	35	34	a	a	DET
ejpam-4671	35	35	total	total	ADJ
ejpam-4671	35	36	hop	hop	NOUN
ejpam-4671	35	37	dominating	dominating	NOUN
ejpam-4671	35	38	set	set	NOUN
ejpam-4671	35	39	of	of	ADP
ejpam-4671	35	40	g	g	NOUN
ejpam-4671	35	41	,	,	PUNCT
ejpam-4671	35	42	denoted	denote	VERB
ejpam-4671	35	43	by	by	ADP
ejpam-4671	35	44	γth(g	γth(g	NOUN
ejpam-4671	35	45	)	)	PUNCT
ejpam-4671	35	46	,	,	PUNCT
ejpam-4671	35	47	is	be	AUX
ejpam-4671	35	48	called	call	VERB
ejpam-4671	35	49	the	the	DET
ejpam-4671	35	50	total	total	ADJ
ejpam-4671	35	51	hop	hop	NOUN
ejpam-4671	35	52	domination	domination	NOUN
ejpam-4671	35	53	number	number	NOUN
ejpam-4671	35	54	of	of	ADP
ejpam-4671	35	55	g.	g.	PROPN
ejpam-4671	35	56	any	any	DET
ejpam-4671	35	57	total	total	ADJ
ejpam-4671	35	58	hop	hop	NOUN
ejpam-4671	35	59	dominating	dominating	NOUN
ejpam-4671	35	60	set	set	VERB
ejpam-4671	35	61	with	with	ADP
ejpam-4671	35	62	cardinality	cardinality	NOUN
ejpam-4671	35	63	equal	equal	ADJ
ejpam-4671	35	64	to	to	ADP
ejpam-4671	35	65	γth(g	γth(g	NOUN
ejpam-4671	35	66	)	)	PUNCT
ejpam-4671	35	67	is	be	AUX
ejpam-4671	35	68	called	call	VERB
ejpam-4671	35	69	a	a	DET
ejpam-4671	35	70	γth	γth	NOUN
ejpam-4671	35	71	-	-	PUNCT
ejpam-4671	35	72	set	set	NOUN
ejpam-4671	35	73	.	.	PUNCT
ejpam-4671	36	1	a	a	DET
ejpam-4671	36	2	set	set	NOUN
ejpam-4671	36	3	s	s	NOUN
ejpam-4671	36	4	⊆	⊆	NUM
ejpam-4671	36	5	v	v	NOUN
ejpam-4671	36	6	(	(	PUNCT
ejpam-4671	36	7	g	g	NOUN
ejpam-4671	36	8	)	)	PUNCT
ejpam-4671	36	9	is	be	AUX
ejpam-4671	36	10	a	a	DET
ejpam-4671	36	11	locating	locating	NOUN
ejpam-4671	36	12	set	set	NOUN
ejpam-4671	36	13	of	of	ADP
ejpam-4671	36	14	g	g	PROPN
ejpam-4671	36	15	if	if	SCONJ
ejpam-4671	36	16	for	for	SCONJ
ejpam-4671	36	17	every	every	DET
ejpam-4671	36	18	two	two	NUM
ejpam-4671	36	19	distinct	distinct	ADJ
ejpam-4671	36	20	vertices	vertex	NOUN
ejpam-4671	36	21	u	u	NOUN
ejpam-4671	36	22	and	and	CCONJ
ejpam-4671	36	23	v	v	NOUN
ejpam-4671	36	24	of	of	ADP
ejpam-4671	36	25	v	v	NOUN
ejpam-4671	36	26	(	(	PUNCT
ejpam-4671	36	27	g)\s	g)\s	NOUN
ejpam-4671	36	28	,	,	PUNCT
ejpam-4671	36	29	ng(u	ng(u	NOUN
ejpam-4671	36	30	)	)	PUNCT
ejpam-4671	36	31	∩	∩	NOUN
ejpam-4671	36	32	s	s	PART
ejpam-4671	36	33	̸=	̸=	PROPN
ejpam-4671	36	34	ng(v	ng(v	NUM
ejpam-4671	36	35	)	)	PUNCT
ejpam-4671	36	36	∩	∩	PROPN
ejpam-4671	36	37	s.	s.	PROPN
ejpam-4671	37	1	the	the	DET
ejpam-4671	37	2	locating	locate	VERB
ejpam-4671	37	3	number	number	NOUN
ejpam-4671	37	4	of	of	ADP
ejpam-4671	37	5	g	g	NOUN
ejpam-4671	37	6	,	,	PUNCT
ejpam-4671	37	7	denoted	denote	VERB
ejpam-4671	37	8	by	by	ADP
ejpam-4671	37	9	ln(g	ln(g	NOUN
ejpam-4671	37	10	)	)	PUNCT
ejpam-4671	37	11	,	,	PUNCT
ejpam-4671	37	12	is	be	AUX
ejpam-4671	37	13	the	the	DET
ejpam-4671	37	14	smallest	small	ADJ
ejpam-4671	37	15	cardinality	cardinality	NOUN
ejpam-4671	37	16	of	of	ADP
ejpam-4671	37	17	a	a	DET
ejpam-4671	37	18	locating	locating	NOUN
ejpam-4671	37	19	set	set	NOUN
ejpam-4671	37	20	of	of	ADP
ejpam-4671	37	21	g.	g.	PROPN
ejpam-4671	37	22	a	a	DET
ejpam-4671	37	23	locating	locate	VERB
ejpam-4671	37	24	set	set	NOUN
ejpam-4671	37	25	of	of	ADP
ejpam-4671	37	26	g	g	PROPN
ejpam-4671	37	27	of	of	ADP
ejpam-4671	37	28	cardinality	cardinality	PROPN
ejpam-4671	37	29	ln(g	ln(g	PUNCT
ejpam-4671	37	30	)	)	PUNCT
ejpam-4671	37	31	is	be	AUX
ejpam-4671	37	32	referred	refer	VERB
ejpam-4671	37	33	to	to	ADP
ejpam-4671	37	34	as	as	SCONJ
ejpam-4671	37	35	ln	ln	ADV
ejpam-4671	37	36	-	-	PUNCT
ejpam-4671	37	37	set	set	NOUN
ejpam-4671	37	38	of	of	ADP
ejpam-4671	37	39	g.	g.	PROPN
ejpam-4671	37	40	a	a	DET
ejpam-4671	37	41	set	set	NOUN
ejpam-4671	37	42	s	s	PROPN
ejpam-4671	37	43	⊆	⊆	NUM
ejpam-4671	37	44	v	v	NOUN
ejpam-4671	37	45	(	(	PUNCT
ejpam-4671	37	46	g	g	NOUN
ejpam-4671	37	47	)	)	PUNCT
ejpam-4671	37	48	is	be	AUX
ejpam-4671	37	49	a	a	DET
ejpam-4671	37	50	strictly	strictly	ADV
ejpam-4671	37	51	locating	locate	VERB
ejpam-4671	37	52	set	set	NOUN
ejpam-4671	37	53	of	of	ADP
ejpam-4671	37	54	g	g	NOUN
ejpam-4671	37	55	if	if	SCONJ
ejpam-4671	37	56	it	it	PRON
ejpam-4671	37	57	is	be	AUX
ejpam-4671	37	58	a	a	DET
ejpam-4671	37	59	locating	locating	NOUN
ejpam-4671	37	60	set	set	NOUN
ejpam-4671	37	61	of	of	ADP
ejpam-4671	37	62	g	g	PROPN
ejpam-4671	37	63	and	and	CCONJ
ejpam-4671	37	64	ng(u)∩s	ng(u)∩s	PROPN
ejpam-4671	37	65	̸=	̸=	PROPN
ejpam-4671	37	66	s	s	PART
ejpam-4671	37	67	for	for	ADP
ejpam-4671	37	68	all	all	DET
ejpam-4671	37	69	u	u	NOUN
ejpam-4671	37	70	∈	∈	PROPN
ejpam-4671	37	71	v	v	NOUN
ejpam-4671	37	72	(	(	PUNCT
ejpam-4671	37	73	g)\s	g)\s	NOUN
ejpam-4671	37	74	.	.	PUNCT
ejpam-4671	38	1	the	the	DET
ejpam-4671	38	2	strictly	strictly	ADV
ejpam-4671	38	3	locating	locate	VERB
ejpam-4671	38	4	number	number	NOUN
ejpam-4671	38	5	of	of	ADP
ejpam-4671	38	6	g	g	NOUN
ejpam-4671	38	7	,	,	PUNCT
ejpam-4671	38	8	denoted	denote	VERB
ejpam-4671	38	9	by	by	ADP
ejpam-4671	38	10	sln(g	sln(g	PROPN
ejpam-4671	38	11	)	)	PUNCT
ejpam-4671	38	12	,	,	PUNCT
ejpam-4671	38	13	is	be	AUX
ejpam-4671	38	14	the	the	DET
ejpam-4671	38	15	smallest	small	ADJ
ejpam-4671	38	16	cardinality	cardinality	NOUN
ejpam-4671	38	17	of	of	ADP
ejpam-4671	38	18	a	a	DET
ejpam-4671	38	19	strictly	strictly	ADV
ejpam-4671	38	20	locating	locate	VERB
ejpam-4671	38	21	set	set	NOUN
ejpam-4671	38	22	of	of	ADP
ejpam-4671	38	23	g.	g.	PROPN
ejpam-4671	38	24	a	a	DET
ejpam-4671	38	25	strictly	strictly	ADV
ejpam-4671	38	26	locating	locate	VERB
ejpam-4671	38	27	set	set	NOUN
ejpam-4671	38	28	of	of	ADP
ejpam-4671	38	29	g	g	PROPN
ejpam-4671	38	30	of	of	ADP
ejpam-4671	38	31	cardinality	cardinality	PROPN
ejpam-4671	38	32	sln(g	sln(g	PROPN
ejpam-4671	38	33	)	)	PUNCT
ejpam-4671	38	34	is	be	AUX
ejpam-4671	38	35	referred	refer	VERB
ejpam-4671	38	36	to	to	ADP
ejpam-4671	38	37	as	as	ADP
ejpam-4671	38	38	a	a	DET
ejpam-4671	38	39	sln	sln	NOUN
ejpam-4671	38	40	-	-	PUNCT
ejpam-4671	38	41	set	set	NOUN
ejpam-4671	38	42	of	of	ADP
ejpam-4671	38	43	g.	g.	PROPN
ejpam-4671	38	44	a	a	DET
ejpam-4671	38	45	locating	locating	NOUN
ejpam-4671	38	46	(	(	PUNCT
ejpam-4671	38	47	resp	resp	NOUN
ejpam-4671	38	48	.	.	PUNCT
ejpam-4671	39	1	strictly	strictly	ADV
ejpam-4671	39	2	locating	locate	VERB
ejpam-4671	39	3	)	)	PUNCT
ejpam-4671	39	4	subset	subset	NOUN
ejpam-4671	39	5	s	s	PROPN
ejpam-4671	39	6	of	of	ADP
ejpam-4671	39	7	v	v	NOUN
ejpam-4671	39	8	(	(	PUNCT
ejpam-4671	39	9	g	g	NOUN
ejpam-4671	39	10	)	)	PUNCT
ejpam-4671	39	11	is	be	AUX
ejpam-4671	39	12	a	a	DET
ejpam-4671	39	13	1	1	NUM
ejpam-4671	39	14	-	-	PUNCT
ejpam-4671	39	15	movable	movable	ADJ
ejpam-4671	39	16	locating	locating	NOUN
ejpam-4671	39	17	(	(	PUNCT
ejpam-4671	39	18	resp	resp	NOUN
ejpam-4671	39	19	.	.	PUNCT
ejpam-4671	40	1	1	1	NUM
ejpam-4671	40	2	-	-	NUM
ejpam-4671	40	3	movable	movable	ADJ
ejpam-4671	40	4	strictly	strictly	ADV
ejpam-4671	40	5	locating	locate	VERB
ejpam-4671	40	6	)	)	PUNCT
ejpam-4671	40	7	set	set	NOUN
ejpam-4671	40	8	of	of	ADP
ejpam-4671	40	9	g	g	PROPN
ejpam-4671	40	10	if	if	SCONJ
ejpam-4671	40	11	for	for	ADP
ejpam-4671	40	12	every	every	DET
ejpam-4671	40	13	v	v	NUM
ejpam-4671	40	14	∈	∈	PROPN
ejpam-4671	40	15	s	s	NOUN
ejpam-4671	40	16	,	,	PUNCT
ejpam-4671	40	17	either	either	CCONJ
ejpam-4671	40	18	s	s	VERB
ejpam-4671	40	19	\	\	PROPN
ejpam-4671	40	20	{	{	PUNCT
ejpam-4671	40	21	v	v	NOUN
ejpam-4671	40	22	}	}	PUNCT
ejpam-4671	40	23	is	be	AUX
ejpam-4671	40	24	a	a	DET
ejpam-4671	40	25	locating	locating	NOUN
ejpam-4671	40	26	(	(	PUNCT
ejpam-4671	40	27	resp	resp	NOUN
ejpam-4671	40	28	.	.	PUNCT
ejpam-4671	41	1	strictly	strictly	ADV
ejpam-4671	41	2	locating	locate	VERB
ejpam-4671	41	3	)	)	PUNCT
ejpam-4671	41	4	set	set	NOUN
ejpam-4671	41	5	of	of	ADP
ejpam-4671	41	6	g	g	NOUN
ejpam-4671	41	7	or	or	CCONJ
ejpam-4671	41	8	there	there	ADV
ejpam-4671	41	9	exists	exist	VERB
ejpam-4671	41	10	a	a	DET
ejpam-4671	41	11	vertex	vertex	NOUN
ejpam-4671	41	12	u	u	NOUN
ejpam-4671	41	13	∈	∈	PROPN
ejpam-4671	41	14	(	(	PUNCT
ejpam-4671	41	15	(	(	PUNCT
ejpam-4671	41	16	v	v	NOUN
ejpam-4671	41	17	(	(	PUNCT
ejpam-4671	41	18	g	g	NOUN
ejpam-4671	41	19	)	)	PUNCT
ejpam-4671	41	20	\	\	PROPN
ejpam-4671	41	21	s	s	X
ejpam-4671	41	22	)	)	PUNCT
ejpam-4671	41	23	∩ng(v	∩ng(v	PROPN
ejpam-4671	41	24	)	)	PUNCT
ejpam-4671	41	25	)	)	PUNCT
ejpam-4671	41	26	such	such	ADJ
ejpam-4671	41	27	that	that	SCONJ
ejpam-4671	41	28	(	(	PUNCT
ejpam-4671	41	29	s	s	AUX
ejpam-4671	41	30	\	\	X
ejpam-4671	41	31	{	{	PUNCT
ejpam-4671	41	32	v})∪{u	v})∪{u	VERB
ejpam-4671	41	33	}	}	PUNCT
ejpam-4671	41	34	is	be	AUX
ejpam-4671	41	35	a	a	DET
ejpam-4671	41	36	locating	locating	NOUN
ejpam-4671	41	37	(	(	PUNCT
ejpam-4671	41	38	resp	resp	NOUN
ejpam-4671	41	39	.	.	PUNCT
ejpam-4671	42	1	strictly	strictly	ADV
ejpam-4671	42	2	locating	locate	VERB
ejpam-4671	42	3	)	)	PUNCT
ejpam-4671	42	4	set	set	NOUN
ejpam-4671	42	5	of	of	ADP
ejpam-4671	42	6	g.	g.	PROPN
ejpam-4671	42	7	the	the	DET
ejpam-4671	42	8	minimum	minimum	ADJ
ejpam-4671	42	9	cardinality	cardinality	NOUN
ejpam-4671	42	10	of	of	ADP
ejpam-4671	42	11	a	a	DET
ejpam-4671	42	12	1	1	NUM
ejpam-4671	42	13	-	-	PUNCT
ejpam-4671	42	14	movable	movable	ADJ
ejpam-4671	42	15	locating	locating	NOUN
ejpam-4671	42	16	(	(	PUNCT
ejpam-4671	42	17	resp	resp	NOUN
ejpam-4671	42	18	.	.	PUNCT
ejpam-4671	43	1	1	1	NUM
ejpam-4671	43	2	-	-	NUM
ejpam-4671	43	3	movable	movable	ADJ
ejpam-4671	43	4	strictly	strictly	ADV
ejpam-4671	43	5	locating	locate	VERB
ejpam-4671	43	6	)	)	PUNCT
ejpam-4671	43	7	set	set	NOUN
ejpam-4671	43	8	of	of	ADP
ejpam-4671	43	9	g	g	NOUN
ejpam-4671	43	10	,	,	PUNCT
ejpam-4671	43	11	denoted	denote	VERB
ejpam-4671	43	12	by	by	ADP
ejpam-4671	43	13	mln(g)(resp	mln(g)(resp	PROPN
ejpam-4671	43	14	.	.	PUNCT
ejpam-4671	44	1	j.	j.	PROPN
ejpam-4671	44	2	mohamad	mohamad	PROPN
ejpam-4671	44	3	,	,	PUNCT
ejpam-4671	44	4	h.	h.	PROPN
ejpam-4671	44	5	rara	rara	PROPN
ejpam-4671	44	6	/	/	SYM
ejpam-4671	44	7	eur	eur	PROPN
ejpam-4671	44	8	.	.	PUNCT
ejpam-4671	45	1	j.	j.	PROPN
ejpam-4671	45	2	pure	pure	PROPN
ejpam-4671	45	3	appl	appl	PROPN
ejpam-4671	45	4	.	.	PROPN
ejpam-4671	45	5	math	math	PROPN
ejpam-4671	45	6	,	,	PUNCT
ejpam-4671	45	7	16	16	NUM
ejpam-4671	45	8	(	(	PUNCT
ejpam-4671	45	9	1	1	NUM
ejpam-4671	45	10	)	)	PUNCT
ejpam-4671	45	11	(	(	PUNCT
ejpam-4671	45	12	2023	2023	NUM
ejpam-4671	45	13	)	)	PUNCT
ejpam-4671	45	14	,	,	PUNCT
ejpam-4671	45	15	418	418	NUM
ejpam-4671	45	16	-	-	SYM
ejpam-4671	45	17	429	429	NUM
ejpam-4671	45	18	420	420	NUM
ejpam-4671	45	19	msln(g	msln(g	NOUN
ejpam-4671	45	20	)	)	PUNCT
ejpam-4671	45	21	)	)	PUNCT
ejpam-4671	45	22	is	be	AUX
ejpam-4671	45	23	the	the	DET
ejpam-4671	45	24	1	1	NUM
ejpam-4671	45	25	-	-	PUNCT
ejpam-4671	45	26	movable	movable	ADJ
ejpam-4671	45	27	location	location	NOUN
ejpam-4671	45	28	number	number	NOUN
ejpam-4671	45	29	(	(	PUNCT
ejpam-4671	45	30	resp	resp	NOUN
ejpam-4671	45	31	.	.	PUNCT
ejpam-4671	46	1	1	1	NUM
ejpam-4671	46	2	-	-	NUM
ejpam-4671	46	3	movable	movable	ADJ
ejpam-4671	46	4	strictly	strictly	ADV
ejpam-4671	46	5	location	location	NOUN
ejpam-4671	46	6	number	number	NOUN
ejpam-4671	46	7	)	)	PUNCT
ejpam-4671	46	8	of	of	ADP
ejpam-4671	46	9	g.	g.	PROPN
ejpam-4671	46	10	any	any	DET
ejpam-4671	46	11	1	1	NUM
ejpam-4671	46	12	-	-	PUNCT
ejpam-4671	46	13	movable	movable	ADJ
ejpam-4671	46	14	locating	locating	NOUN
ejpam-4671	46	15	(	(	PUNCT
ejpam-4671	46	16	resp	resp	NOUN
ejpam-4671	46	17	.	.	PUNCT
ejpam-4671	47	1	1	1	NUM
ejpam-4671	47	2	-	-	NUM
ejpam-4671	47	3	movable	movable	ADJ
ejpam-4671	47	4	strictly	strictly	ADV
ejpam-4671	47	5	locating	locate	VERB
ejpam-4671	47	6	)	)	PUNCT
ejpam-4671	47	7	set	set	NOUN
ejpam-4671	47	8	of	of	ADP
ejpam-4671	47	9	cardinality	cardinality	PROPN
ejpam-4671	47	10	mln(g	mln(g	PROPN
ejpam-4671	47	11	)	)	PUNCT
ejpam-4671	47	12	(	(	PUNCT
ejpam-4671	47	13	resp	resp	NOUN
ejpam-4671	47	14	.	.	PUNCT
ejpam-4671	48	1	msln(g	msln(g	NOUN
ejpam-4671	48	2	)	)	PUNCT
ejpam-4671	48	3	)	)	PUNCT
ejpam-4671	48	4	is	be	AUX
ejpam-4671	48	5	referred	refer	VERB
ejpam-4671	48	6	to	to	ADP
ejpam-4671	48	7	as	as	ADP
ejpam-4671	48	8	mln	mln	NOUN
ejpam-4671	48	9	-	-	PUNCT
ejpam-4671	48	10	set	set	VERB
ejpam-4671	48	11	(	(	PUNCT
ejpam-4671	48	12	resp	resp	NOUN
ejpam-4671	48	13	.	.	PUNCT
ejpam-4671	49	1	msln	msln	NOUN
ejpam-4671	49	2	-	-	PUNCT
ejpam-4671	49	3	set	set	NOUN
ejpam-4671	49	4	)	)	PUNCT
ejpam-4671	49	5	of	of	ADP
ejpam-4671	49	6	g.	g.	PROPN
ejpam-4671	49	7	a	a	DET
ejpam-4671	49	8	vertex	vertex	NOUN
ejpam-4671	49	9	x	x	X
ejpam-4671	49	10	of	of	ADP
ejpam-4671	49	11	a	a	DET
ejpam-4671	49	12	graph	graph	NOUN
ejpam-4671	49	13	g	g	NOUN
ejpam-4671	49	14	is	be	AUX
ejpam-4671	49	15	said	say	VERB
ejpam-4671	49	16	to	to	PART
ejpam-4671	49	17	resolve	resolve	VERB
ejpam-4671	49	18	two	two	NUM
ejpam-4671	49	19	vertices	vertex	NOUN
ejpam-4671	49	20	u	u	NOUN
ejpam-4671	49	21	and	and	CCONJ
ejpam-4671	49	22	v	v	NOUN
ejpam-4671	49	23	of	of	ADP
ejpam-4671	49	24	g	g	PROPN
ejpam-4671	49	25	if	if	SCONJ
ejpam-4671	49	26	dg(x	dg(x	NUM
ejpam-4671	49	27	,	,	PUNCT
ejpam-4671	49	28	u	u	NOUN
ejpam-4671	49	29	)	)	PUNCT
ejpam-4671	49	30	̸=	̸=	PROPN
ejpam-4671	49	31	dg(x	dg(x	NUM
ejpam-4671	49	32	,	,	PUNCT
ejpam-4671	49	33	v	v	NOUN
ejpam-4671	49	34	)	)	PUNCT
ejpam-4671	49	35	.	.	PUNCT
ejpam-4671	50	1	for	for	ADP
ejpam-4671	50	2	an	an	DET
ejpam-4671	50	3	ordered	order	VERB
ejpam-4671	50	4	set	set	NOUN
ejpam-4671	50	5	w	w	NOUN
ejpam-4671	50	6	=	=	PUNCT
ejpam-4671	50	7	{	{	PUNCT
ejpam-4671	50	8	x1	x1	PROPN
ejpam-4671	50	9	,	,	PUNCT
ejpam-4671	50	10	...	...	PUNCT
ejpam-4671	50	11	,	,	PUNCT
ejpam-4671	50	12	xk	xk	ADJ
ejpam-4671	50	13	}	}	PUNCT
ejpam-4671	50	14	⊆	⊆	NUM
ejpam-4671	50	15	v	v	NOUN
ejpam-4671	50	16	(	(	PUNCT
ejpam-4671	50	17	g	g	NOUN
ejpam-4671	50	18	)	)	PUNCT
ejpam-4671	50	19	and	and	CCONJ
ejpam-4671	50	20	a	a	DET
ejpam-4671	50	21	vertex	vertex	NOUN
ejpam-4671	50	22	v	v	NOUN
ejpam-4671	50	23	in	in	ADP
ejpam-4671	50	24	g	g	PROPN
ejpam-4671	50	25	,	,	PUNCT
ejpam-4671	50	26	the	the	DET
ejpam-4671	50	27	k	k	PROPN
ejpam-4671	50	28	−	−	PROPN
ejpam-4671	50	29	vector	vector	NOUN
ejpam-4671	50	30	rg(v	rg(v	NOUN
ejpam-4671	50	31	/	/	SYM
ejpam-4671	50	32	w	w	NOUN
ejpam-4671	50	33	)	)	PUNCT
ejpam-4671	50	34	=	=	SYM
ejpam-4671	50	35	(	(	PUNCT
ejpam-4671	50	36	dg(v	dg(v	X
ejpam-4671	50	37	,	,	PUNCT
ejpam-4671	50	38	x1	x1	PROPN
ejpam-4671	50	39	)	)	PUNCT
ejpam-4671	50	40	,	,	PUNCT
ejpam-4671	50	41	dg(v	dg(v	X
ejpam-4671	50	42	,	,	PUNCT
ejpam-4671	50	43	x2	x2	PROPN
ejpam-4671	50	44	)	)	PUNCT
ejpam-4671	50	45	,	,	PUNCT
ejpam-4671	50	46	·	·	PUNCT
ejpam-4671	50	47	·	·	PUNCT
ejpam-4671	50	48	·	·	PUNCT
ejpam-4671	50	49	,	,	PUNCT
ejpam-4671	50	50	dg(v	dg(v	X
ejpam-4671	50	51	,	,	PUNCT
ejpam-4671	50	52	xk	xk	NOUN
ejpam-4671	50	53	)	)	PUNCT
ejpam-4671	50	54	)	)	PUNCT
ejpam-4671	50	55	is	be	AUX
ejpam-4671	50	56	called	call	VERB
ejpam-4671	50	57	the	the	DET
ejpam-4671	50	58	representation	representation	NOUN
ejpam-4671	50	59	of	of	ADP
ejpam-4671	50	60	v	v	NOUN
ejpam-4671	50	61	with	with	ADP
ejpam-4671	50	62	respect	respect	NOUN
ejpam-4671	50	63	to	to	ADP
ejpam-4671	50	64	w	w	PROPN
ejpam-4671	50	65	.	.	PUNCT
ejpam-4671	51	1	the	the	DET
ejpam-4671	51	2	set	set	NOUN
ejpam-4671	51	3	w	w	NOUN
ejpam-4671	51	4	is	be	AUX
ejpam-4671	51	5	a	a	DET
ejpam-4671	51	6	resolving	resolving	NOUN
ejpam-4671	51	7	set	set	VERB
ejpam-4671	51	8	for	for	ADP
ejpam-4671	51	9	g	g	PROPN
ejpam-4671	51	10	if	if	SCONJ
ejpam-4671	52	1	and	and	CCONJ
ejpam-4671	52	2	only	only	ADV
ejpam-4671	52	3	if	if	SCONJ
ejpam-4671	52	4	no	no	DET
ejpam-4671	52	5	two	two	NUM
ejpam-4671	52	6	vertices	vertex	NOUN
ejpam-4671	52	7	of	of	ADP
ejpam-4671	52	8	g	g	NOUN
ejpam-4671	52	9	have	have	VERB
ejpam-4671	52	10	the	the	DET
ejpam-4671	52	11	same	same	ADJ
ejpam-4671	52	12	representation	representation	NOUN
ejpam-4671	52	13	with	with	ADP
ejpam-4671	52	14	respect	respect	NOUN
ejpam-4671	52	15	to	to	ADP
ejpam-4671	52	16	w	w	PROPN
ejpam-4671	52	17	.	.	PUNCT
ejpam-4671	53	1	the	the	DET
ejpam-4671	53	2	metric	metric	ADJ
ejpam-4671	53	3	dimension	dimension	NOUN
ejpam-4671	53	4	of	of	ADP
ejpam-4671	53	5	g	g	NOUN
ejpam-4671	53	6	,	,	PUNCT
ejpam-4671	53	7	denoted	denote	VERB
ejpam-4671	53	8	by	by	ADP
ejpam-4671	53	9	,	,	PUNCT
ejpam-4671	53	10	dim(g	dim(g	PROPN
ejpam-4671	53	11	)	)	PUNCT
ejpam-4671	53	12	,	,	PUNCT
ejpam-4671	53	13	is	be	AUX
ejpam-4671	53	14	the	the	DET
ejpam-4671	53	15	minimum	minimum	ADJ
ejpam-4671	53	16	cardinality	cardinality	NOUN
ejpam-4671	53	17	over	over	ADP
ejpam-4671	53	18	all	all	DET
ejpam-4671	53	19	resolving	resolve	VERB
ejpam-4671	53	20	sets	set	NOUN
ejpam-4671	53	21	of	of	ADP
ejpam-4671	53	22	g.	g.	PROPN
ejpam-4671	53	23	a	a	DET
ejpam-4671	53	24	resolving	resolve	VERB
ejpam-4671	53	25	set	set	NOUN
ejpam-4671	53	26	of	of	ADP
ejpam-4671	53	27	cardinality	cardinality	PROPN
ejpam-4671	53	28	dim(g	dim(g	PROPN
ejpam-4671	53	29	)	)	PUNCT
ejpam-4671	53	30	is	be	AUX
ejpam-4671	53	31	called	call	VERB
ejpam-4671	53	32	basis	basis	NOUN
ejpam-4671	53	33	.	.	PUNCT
ejpam-4671	54	1	a	a	DET
ejpam-4671	54	2	set	set	NOUN
ejpam-4671	54	3	s	s	NOUN
ejpam-4671	54	4	⊆	⊆	NUM
ejpam-4671	54	5	v	v	NOUN
ejpam-4671	54	6	(	(	PUNCT
ejpam-4671	54	7	g	g	NOUN
ejpam-4671	54	8	)	)	PUNCT
ejpam-4671	54	9	is	be	AUX
ejpam-4671	54	10	a	a	DET
ejpam-4671	54	11	resolving	resolve	VERB
ejpam-4671	54	12	hop	hop	NOUN
ejpam-4671	54	13	dominating	dominating	NOUN
ejpam-4671	54	14	set	set	NOUN
ejpam-4671	54	15	of	of	ADP
ejpam-4671	54	16	g	g	PROPN
ejpam-4671	54	17	if	if	SCONJ
ejpam-4671	54	18	s	s	VERB
ejpam-4671	54	19	is	be	AUX
ejpam-4671	54	20	both	both	PRON
ejpam-4671	54	21	a	a	DET
ejpam-4671	54	22	resolving	resolving	NOUN
ejpam-4671	54	23	set	set	VERB
ejpam-4671	54	24	and	and	CCONJ
ejpam-4671	54	25	a	a	DET
ejpam-4671	54	26	hop	hop	NOUN
ejpam-4671	54	27	dominating	dominating	NOUN
ejpam-4671	54	28	set	set	NOUN
ejpam-4671	54	29	.	.	PUNCT
ejpam-4671	55	1	the	the	DET
ejpam-4671	55	2	minimum	minimum	ADJ
ejpam-4671	55	3	cardinality	cardinality	NOUN
ejpam-4671	55	4	of	of	ADP
ejpam-4671	55	5	a	a	DET
ejpam-4671	55	6	resolving	resolve	VERB
ejpam-4671	55	7	hop	hop	NOUN
ejpam-4671	55	8	dominating	dominating	NOUN
ejpam-4671	55	9	set	set	NOUN
ejpam-4671	55	10	of	of	ADP
ejpam-4671	55	11	g	g	NOUN
ejpam-4671	55	12	,	,	PUNCT
ejpam-4671	55	13	denoted	denote	VERB
ejpam-4671	55	14	by	by	ADP
ejpam-4671	55	15	γrh(g	γrh(g	NOUN
ejpam-4671	55	16	)	)	PUNCT
ejpam-4671	55	17	,	,	PUNCT
ejpam-4671	55	18	is	be	AUX
ejpam-4671	55	19	called	call	VERB
ejpam-4671	55	20	the	the	DET
ejpam-4671	55	21	resolving	resolve	VERB
ejpam-4671	55	22	hop	hop	NOUN
ejpam-4671	55	23	domination	domination	NOUN
ejpam-4671	55	24	number	number	NOUN
ejpam-4671	55	25	of	of	ADP
ejpam-4671	55	26	g.	g.	PROPN
ejpam-4671	55	27	any	any	PRON
ejpam-4671	55	28	resolving	resolve	VERB
ejpam-4671	55	29	hop	hop	NOUN
ejpam-4671	55	30	dominating	dominating	NOUN
ejpam-4671	55	31	set	set	VERB
ejpam-4671	55	32	with	with	ADP
ejpam-4671	55	33	cardinality	cardinality	NOUN
ejpam-4671	55	34	equal	equal	ADJ
ejpam-4671	55	35	to	to	ADP
ejpam-4671	55	36	γrh(g	γrh(g	NOUN
ejpam-4671	55	37	)	)	PUNCT
ejpam-4671	55	38	is	be	AUX
ejpam-4671	55	39	called	call	VERB
ejpam-4671	55	40	a	a	DET
ejpam-4671	55	41	γrh	γrh	NOUN
ejpam-4671	55	42	-	-	PUNCT
ejpam-4671	55	43	set	set	NOUN
ejpam-4671	55	44	.	.	PUNCT
ejpam-4671	56	1	a	a	DET
ejpam-4671	56	2	set	set	NOUN
ejpam-4671	56	3	s	s	NOUN
ejpam-4671	56	4	⊆	⊆	NUM
ejpam-4671	56	5	v	v	NOUN
ejpam-4671	56	6	(	(	PUNCT
ejpam-4671	56	7	g	g	NOUN
ejpam-4671	56	8	)	)	PUNCT
ejpam-4671	56	9	is	be	AUX
ejpam-4671	56	10	a	a	DET
ejpam-4671	56	11	1	1	NUM
ejpam-4671	56	12	-	-	PUNCT
ejpam-4671	56	13	movable	movable	ADJ
ejpam-4671	56	14	resolving	resolve	VERB
ejpam-4671	56	15	hop	hop	NOUN
ejpam-4671	56	16	dominating	dominating	NOUN
ejpam-4671	56	17	set	set	NOUN
ejpam-4671	56	18	of	of	ADP
ejpam-4671	56	19	g	g	PROPN
ejpam-4671	56	20	if	if	SCONJ
ejpam-4671	56	21	s	s	VERB
ejpam-4671	56	22	is	be	AUX
ejpam-4671	56	23	a	a	DET
ejpam-4671	56	24	resolving	resolve	VERB
ejpam-4671	56	25	hop	hop	NOUN
ejpam-4671	56	26	dominating	dominating	NOUN
ejpam-4671	56	27	set	set	NOUN
ejpam-4671	56	28	of	of	ADP
ejpam-4671	56	29	g	g	PROPN
ejpam-4671	56	30	and	and	CCONJ
ejpam-4671	56	31	for	for	ADP
ejpam-4671	56	32	every	every	DET
ejpam-4671	56	33	v	v	NUM
ejpam-4671	56	34	∈	∈	PROPN
ejpam-4671	56	35	s	s	NOUN
ejpam-4671	56	36	,	,	PUNCT
ejpam-4671	56	37	either	either	CCONJ
ejpam-4671	56	38	s	s	VERB
ejpam-4671	56	39	\	\	PROPN
ejpam-4671	56	40	{	{	PUNCT
ejpam-4671	56	41	v	v	NOUN
ejpam-4671	56	42	}	}	PUNCT
ejpam-4671	56	43	is	be	AUX
ejpam-4671	56	44	a	a	DET
ejpam-4671	56	45	resolving	resolve	VERB
ejpam-4671	56	46	hop	hop	NOUN
ejpam-4671	56	47	dominating	dominating	NOUN
ejpam-4671	56	48	set	set	NOUN
ejpam-4671	56	49	of	of	ADP
ejpam-4671	56	50	g	g	NOUN
ejpam-4671	56	51	or	or	CCONJ
ejpam-4671	56	52	there	there	ADV
ejpam-4671	56	53	exists	exist	VERB
ejpam-4671	56	54	a	a	DET
ejpam-4671	56	55	vertex	vertex	NOUN
ejpam-4671	56	56	u	u	NOUN
ejpam-4671	56	57	∈	∈	PROPN
ejpam-4671	56	58	(	(	PUNCT
ejpam-4671	56	59	(	(	PUNCT
ejpam-4671	56	60	v	v	NOUN
ejpam-4671	56	61	(	(	PUNCT
ejpam-4671	56	62	g	g	NOUN
ejpam-4671	56	63	)	)	PUNCT
ejpam-4671	56	64	\	\	PROPN
ejpam-4671	56	65	s	s	X
ejpam-4671	56	66	)	)	PUNCT
ejpam-4671	56	67	∩ng(v	∩ng(v	PROPN
ejpam-4671	56	68	)	)	PUNCT
ejpam-4671	56	69	)	)	PUNCT
ejpam-4671	56	70	such	such	ADJ
ejpam-4671	56	71	that	that	SCONJ
ejpam-4671	56	72	(	(	PUNCT
ejpam-4671	56	73	s	s	NOUN
ejpam-4671	56	74	\	\	X
ejpam-4671	56	75	{	{	PUNCT
ejpam-4671	56	76	v	v	NOUN
ejpam-4671	56	77	}	}	PUNCT
ejpam-4671	56	78	)	)	PUNCT
ejpam-4671	56	79	∪	∪	ADP
ejpam-4671	56	80	{	{	PUNCT
ejpam-4671	56	81	u	u	NOUN
ejpam-4671	56	82	}	}	PUNCT
ejpam-4671	56	83	is	be	AUX
ejpam-4671	56	84	a	a	DET
ejpam-4671	56	85	resolving	resolve	VERB
ejpam-4671	56	86	hop	hop	NOUN
ejpam-4671	56	87	dominating	dominating	NOUN
ejpam-4671	56	88	set	set	NOUN
ejpam-4671	56	89	of	of	ADP
ejpam-4671	56	90	g.	g.	PROPN
ejpam-4671	56	91	the	the	DET
ejpam-4671	56	92	1	1	NUM
ejpam-4671	56	93	-	-	PUNCT
ejpam-4671	56	94	movable	movable	ADJ
ejpam-4671	56	95	resolving	resolve	VERB
ejpam-4671	56	96	hop	hop	NOUN
ejpam-4671	56	97	domination	domination	NOUN
ejpam-4671	56	98	number	number	NOUN
ejpam-4671	56	99	of	of	ADP
ejpam-4671	56	100	g	g	NOUN
ejpam-4671	56	101	,	,	PUNCT
ejpam-4671	56	102	denoted	denote	VERB
ejpam-4671	56	103	by	by	ADP
ejpam-4671	56	104	γ1mrh(g	γ1mrh(g	NOUN
ejpam-4671	56	105	)	)	PUNCT
ejpam-4671	56	106	is	be	AUX
ejpam-4671	56	107	the	the	DET
ejpam-4671	56	108	smallest	small	ADJ
ejpam-4671	56	109	cardinality	cardinality	NOUN
ejpam-4671	56	110	of	of	ADP
ejpam-4671	56	111	a	a	DET
ejpam-4671	56	112	1	1	NUM
ejpam-4671	56	113	-	-	PUNCT
ejpam-4671	56	114	movable	movable	ADJ
ejpam-4671	56	115	resolving	resolve	VERB
ejpam-4671	56	116	hop	hop	NOUN
ejpam-4671	56	117	dominating	dominating	NOUN
ejpam-4671	56	118	set	set	NOUN
ejpam-4671	56	119	of	of	ADP
ejpam-4671	56	120	g.	g.	PROPN
ejpam-4671	56	121	any	any	DET
ejpam-4671	56	122	1	1	NUM
ejpam-4671	56	123	-	-	PUNCT
ejpam-4671	56	124	movable	movable	ADJ
ejpam-4671	56	125	resolving	resolve	VERB
ejpam-4671	56	126	hop	hop	NOUN
ejpam-4671	56	127	dominating	dominating	NOUN
ejpam-4671	56	128	set	set	NOUN
ejpam-4671	56	129	of	of	ADP
ejpam-4671	56	130	cardinality	cardinality	PROPN
ejpam-4671	56	131	γ1mrh(g	γ1mrh(g	NOUN
ejpam-4671	56	132	)	)	PUNCT
ejpam-4671	56	133	is	be	AUX
ejpam-4671	56	134	referred	refer	VERB
ejpam-4671	56	135	to	to	ADP
ejpam-4671	56	136	as	as	ADP
ejpam-4671	56	137	a	a	DET
ejpam-4671	56	138	γ1mrh	γ1mrh	NOUN
ejpam-4671	56	139	-	-	PUNCT
ejpam-4671	56	140	set	set	NOUN
ejpam-4671	56	141	of	of	ADP
ejpam-4671	56	142	g.	g.	PROPN
ejpam-4671	56	143	2	2	NUM
ejpam-4671	56	144	.	.	PUNCT
ejpam-4671	57	1	preliminary	preliminary	ADJ
ejpam-4671	57	2	results	result	NOUN
ejpam-4671	57	3	remark	remark	VERB
ejpam-4671	57	4	1	1	NUM
ejpam-4671	57	5	.	.	PUNCT
ejpam-4671	58	1	every	every	DET
ejpam-4671	58	2	1	1	NUM
ejpam-4671	58	3	-	-	PUNCT
ejpam-4671	58	4	movable	movable	ADJ
ejpam-4671	58	5	resolving	resolve	VERB
ejpam-4671	58	6	hop	hop	NOUN
ejpam-4671	58	7	dominating	dominating	NOUN
ejpam-4671	58	8	set	set	NOUN
ejpam-4671	58	9	of	of	ADP
ejpam-4671	58	10	g	g	PROPN
ejpam-4671	58	11	is	be	AUX
ejpam-4671	58	12	a	a	DET
ejpam-4671	58	13	resolving	resolve	VERB
ejpam-4671	58	14	hop	hop	NOUN
ejpam-4671	58	15	dominating	dominating	NOUN
ejpam-4671	58	16	set	set	NOUN
ejpam-4671	58	17	.	.	PUNCT
ejpam-4671	59	1	thus	thus	ADV
ejpam-4671	59	2	,	,	PUNCT
ejpam-4671	59	3	2	2	NUM
ejpam-4671	59	4	≤	≤	NUM
ejpam-4671	59	5	γrh(g	γrh(g	NOUN
ejpam-4671	59	6	)	)	PUNCT
ejpam-4671	59	7	≤	≤	NOUN
ejpam-4671	59	8	γ1mrh(g	γ1mrh(g	NOUN
ejpam-4671	59	9	)	)	PUNCT
ejpam-4671	59	10	.	.	PUNCT
ejpam-4671	60	1	remark	remark	NOUN
ejpam-4671	60	2	2	2	NUM
ejpam-4671	60	3	.	.	PUNCT
ejpam-4671	61	1	every	every	DET
ejpam-4671	61	2	1	1	NUM
ejpam-4671	61	3	-	-	PUNCT
ejpam-4671	61	4	movable	movable	ADJ
ejpam-4671	61	5	resolving	resolve	VERB
ejpam-4671	61	6	hop	hop	NOUN
ejpam-4671	61	7	dominating	dominating	NOUN
ejpam-4671	61	8	set	set	NOUN
ejpam-4671	61	9	of	of	ADP
ejpam-4671	61	10	g	g	PROPN
ejpam-4671	61	11	is	be	AUX
ejpam-4671	61	12	a	a	DET
ejpam-4671	61	13	hop	hop	NOUN
ejpam-4671	61	14	dominating	dominating	NOUN
ejpam-4671	61	15	set	set	NOUN
ejpam-4671	61	16	.	.	PUNCT
ejpam-4671	62	1	thus	thus	ADV
ejpam-4671	62	2	,	,	PUNCT
ejpam-4671	62	3	2	2	NUM
ejpam-4671	62	4	≤	≤	NOUN
ejpam-4671	62	5	γh(g	γh(g	NOUN
ejpam-4671	62	6	)	)	PUNCT
ejpam-4671	62	7	≤	≤	NUM
ejpam-4671	62	8	γ1mrh(g	γ1mrh(g	NOUN
ejpam-4671	62	9	)	)	PUNCT
ejpam-4671	62	10	.	.	PUNCT
ejpam-4671	63	1	remark	remark	PROPN
ejpam-4671	63	2	3	3	NUM
ejpam-4671	63	3	.	.	PUNCT
ejpam-4671	64	1	every	every	DET
ejpam-4671	64	2	1	1	NUM
ejpam-4671	64	3	-	-	PUNCT
ejpam-4671	64	4	movable	movable	ADJ
ejpam-4671	64	5	resolving	resolve	VERB
ejpam-4671	64	6	hop	hop	NOUN
ejpam-4671	64	7	dominating	dominating	NOUN
ejpam-4671	64	8	set	set	NOUN
ejpam-4671	64	9	of	of	ADP
ejpam-4671	64	10	g	g	PROPN
ejpam-4671	64	11	is	be	AUX
ejpam-4671	64	12	a	a	DET
ejpam-4671	64	13	resolving	resolving	NOUN
ejpam-4671	64	14	set	set	NOUN
ejpam-4671	64	15	.	.	PUNCT
ejpam-4671	65	1	thus	thus	ADV
ejpam-4671	65	2	,	,	PUNCT
ejpam-4671	65	3	1	1	NUM
ejpam-4671	65	4	≤	≤	NUM
ejpam-4671	65	5	dim(g	dim(g	PROPN
ejpam-4671	65	6	)	)	PUNCT
ejpam-4671	65	7	≤	≤	NOUN
ejpam-4671	65	8	γ1mrh(g	γ1mrh(g	NOUN
ejpam-4671	65	9	)	)	PUNCT
ejpam-4671	65	10	.	.	PUNCT
ejpam-4671	66	1	consider	consider	VERB
ejpam-4671	66	2	g	g	NOUN
ejpam-4671	66	3	=	=	SYM
ejpam-4671	66	4	p5	p5	ADJ
ejpam-4671	67	1	where	where	SCONJ
ejpam-4671	67	2	v	v	NOUN
ejpam-4671	67	3	(	(	PUNCT
ejpam-4671	67	4	g	g	NOUN
ejpam-4671	67	5	)	)	PUNCT
ejpam-4671	67	6	=	=	SYM
ejpam-4671	67	7	{	{	PUNCT
ejpam-4671	67	8	v1	v1	PROPN
ejpam-4671	67	9	,	,	PUNCT
ejpam-4671	67	10	v2	v2	PROPN
ejpam-4671	67	11	,	,	PUNCT
ejpam-4671	67	12	v3	v3	PROPN
ejpam-4671	67	13	,	,	PUNCT
ejpam-4671	67	14	v4	v4	PROPN
ejpam-4671	67	15	,	,	PUNCT
ejpam-4671	67	16	v5	v5	PROPN
ejpam-4671	67	17	}	}	PUNCT
ejpam-4671	67	18	with	with	ADP
ejpam-4671	67	19	deg(v1	deg(v1	NOUN
ejpam-4671	67	20	)	)	PUNCT
ejpam-4671	67	21	=	=	SYM
ejpam-4671	67	22	deg(v5	deg(v5	NOUN
ejpam-4671	67	23	)	)	PUNCT
ejpam-4671	67	24	=	=	SYM
ejpam-4671	67	25	1	1	NUM
ejpam-4671	67	26	and	and	CCONJ
ejpam-4671	67	27	ng(v3	ng(v3	NUM
ejpam-4671	67	28	)	)	PUNCT
ejpam-4671	67	29	=	=	PRON
ejpam-4671	67	30	{	{	PUNCT
ejpam-4671	67	31	v2	v2	PROPN
ejpam-4671	67	32	,	,	PUNCT
ejpam-4671	67	33	v4	v4	PROPN
ejpam-4671	67	34	}	}	PUNCT
ejpam-4671	67	35	.	.	PUNCT
ejpam-4671	68	1	let	let	VERB
ejpam-4671	68	2	s1	s1	PROPN
ejpam-4671	68	3	=	=	SYM
ejpam-4671	68	4	{	{	PUNCT
ejpam-4671	68	5	v1	v1	NOUN
ejpam-4671	68	6	}	}	PUNCT
ejpam-4671	68	7	,	,	PUNCT
ejpam-4671	68	8	s2	s2	NOUN
ejpam-4671	68	9	=	=	SYM
ejpam-4671	68	10	{	{	PUNCT
ejpam-4671	68	11	v2	v2	PROPN
ejpam-4671	68	12	,	,	PUNCT
ejpam-4671	68	13	v3	v3	PROPN
ejpam-4671	68	14	}	}	PUNCT
ejpam-4671	68	15	and	and	CCONJ
ejpam-4671	68	16	s3	s3	PROPN
ejpam-4671	68	17	=	=	SYM
ejpam-4671	68	18	v	v	PROPN
ejpam-4671	68	19	(	(	PUNCT
ejpam-4671	68	20	g	g	NOUN
ejpam-4671	68	21	)	)	PUNCT
ejpam-4671	68	22	.	.	PUNCT
ejpam-4671	69	1	then	then	ADV
ejpam-4671	69	2	,	,	PUNCT
ejpam-4671	69	3	s1	s1	PROPN
ejpam-4671	69	4	is	be	AUX
ejpam-4671	69	5	a	a	DET
ejpam-4671	69	6	resolving	resolving	NOUN
ejpam-4671	69	7	set	set	NOUN
ejpam-4671	69	8	of	of	ADP
ejpam-4671	69	9	g	g	PROPN
ejpam-4671	69	10	,	,	PUNCT
ejpam-4671	69	11	s2	s2	PROPN
ejpam-4671	69	12	is	be	AUX
ejpam-4671	69	13	a	a	DET
ejpam-4671	69	14	hop	hop	NOUN
ejpam-4671	69	15	dominating	dominating	NOUN
ejpam-4671	69	16	set	set	NOUN
ejpam-4671	69	17	and	and	CCONJ
ejpam-4671	69	18	a	a	DET
ejpam-4671	69	19	resolving	resolving	NOUN
ejpam-4671	69	20	set	set	NOUN
ejpam-4671	69	21	of	of	ADP
ejpam-4671	69	22	g	g	PROPN
ejpam-4671	69	23	and	and	CCONJ
ejpam-4671	69	24	s3	s3	PROPN
ejpam-4671	69	25	is	be	AUX
ejpam-4671	69	26	a	a	DET
ejpam-4671	69	27	1	1	NUM
ejpam-4671	69	28	-	-	PUNCT
ejpam-4671	69	29	movable	movable	ADJ
ejpam-4671	69	30	resolving	resolve	VERB
ejpam-4671	69	31	hop	hop	NOUN
ejpam-4671	69	32	dominating	dominating	NOUN
ejpam-4671	69	33	set	set	NOUN
ejpam-4671	69	34	of	of	ADP
ejpam-4671	69	35	g.	g.	PROPN
ejpam-4671	70	1	it	it	PRON
ejpam-4671	70	2	can	can	AUX
ejpam-4671	70	3	be	be	AUX
ejpam-4671	70	4	verified	verify	VERB
ejpam-4671	70	5	that	that	SCONJ
ejpam-4671	70	6	dim(g	dim(g	PROPN
ejpam-4671	70	7	)	)	PUNCT
ejpam-4671	70	8	=	=	SYM
ejpam-4671	70	9	1	1	NUM
ejpam-4671	70	10	,	,	PUNCT
ejpam-4671	70	11	γh(g	γh(g	NOUN
ejpam-4671	70	12	)	)	PUNCT
ejpam-4671	70	13	=	=	SYM
ejpam-4671	70	14	2	2	NUM
ejpam-4671	70	15	,	,	PUNCT
ejpam-4671	70	16	γrh(g	γrh(g	NOUN
ejpam-4671	70	17	)	)	PUNCT
ejpam-4671	70	18	=	=	SYM
ejpam-4671	70	19	2	2	NUM
ejpam-4671	70	20	and	and	CCONJ
ejpam-4671	70	21	γ1mrh(g	γ1mrh(g	NUM
ejpam-4671	70	22	)	)	PUNCT
ejpam-4671	70	23	=	=	SYM
ejpam-4671	71	1	5	5	X
ejpam-4671	71	2	.	.	X
ejpam-4671	71	3	hence	hence	ADV
ejpam-4671	71	4	for	for	ADP
ejpam-4671	71	5	g	g	NOUN
ejpam-4671	71	6	=	=	SYM
ejpam-4671	71	7	p5	p5	PROPN
ejpam-4671	71	8	,	,	PUNCT
ejpam-4671	71	9	remarks	remark	VERB
ejpam-4671	71	10	1	1	NUM
ejpam-4671	71	11	,	,	PUNCT
ejpam-4671	71	12	2	2	NUM
ejpam-4671	71	13	and	and	CCONJ
ejpam-4671	71	14	3	3	NUM
ejpam-4671	71	15	holds	hold	NOUN
ejpam-4671	71	16	.	.	PUNCT
ejpam-4671	72	1	j.	j.	PROPN
ejpam-4671	72	2	mohamad	mohamad	PROPN
ejpam-4671	72	3	,	,	PUNCT
ejpam-4671	72	4	h.	h.	PROPN
ejpam-4671	72	5	rara	rara	PROPN
ejpam-4671	72	6	/	/	SYM
ejpam-4671	72	7	eur	eur	PROPN
ejpam-4671	72	8	.	.	PUNCT
ejpam-4671	73	1	j.	j.	PROPN
ejpam-4671	73	2	pure	pure	PROPN
ejpam-4671	73	3	appl	appl	PROPN
ejpam-4671	73	4	.	.	PROPN
ejpam-4671	73	5	math	math	PROPN
ejpam-4671	73	6	,	,	PUNCT
ejpam-4671	73	7	16	16	NUM
ejpam-4671	73	8	(	(	PUNCT
ejpam-4671	73	9	1	1	NUM
ejpam-4671	73	10	)	)	PUNCT
ejpam-4671	73	11	(	(	PUNCT
ejpam-4671	73	12	2023	2023	NUM
ejpam-4671	73	13	)	)	PUNCT
ejpam-4671	73	14	,	,	PUNCT
ejpam-4671	73	15	418	418	NUM
ejpam-4671	73	16	-	-	SYM
ejpam-4671	73	17	429	429	NUM
ejpam-4671	73	18	421	421	NUM
ejpam-4671	73	19	proposition	proposition	NOUN
ejpam-4671	73	20	1	1	NUM
ejpam-4671	73	21	.	.	PUNCT
ejpam-4671	74	1	let	let	VERB
ejpam-4671	74	2	g	g	PRON
ejpam-4671	74	3	be	be	AUX
ejpam-4671	74	4	a	a	DET
ejpam-4671	74	5	nontrivial	nontrivial	ADJ
ejpam-4671	74	6	connected	connect	VERB
ejpam-4671	74	7	graph	graph	NOUN
ejpam-4671	74	8	.	.	PUNCT
ejpam-4671	75	1	then	then	ADV
ejpam-4671	75	2	g	g	PROPN
ejpam-4671	75	3	admits	admit	VERB
ejpam-4671	75	4	a	a	DET
ejpam-4671	75	5	1	1	NUM
ejpam-4671	75	6	-	-	PUNCT
ejpam-4671	75	7	movable	movable	ADJ
ejpam-4671	75	8	resolving	resolve	VERB
ejpam-4671	75	9	hop	hop	NOUN
ejpam-4671	75	10	dominating	dominating	NOUN
ejpam-4671	75	11	set	set	VERB
ejpam-4671	75	12	if	if	SCONJ
ejpam-4671	75	13	and	and	CCONJ
ejpam-4671	75	14	only	only	ADV
ejpam-4671	75	15	if	if	SCONJ
ejpam-4671	75	16	γ(g	γ(g	NOUN
ejpam-4671	75	17	)	)	PUNCT
ejpam-4671	75	18	̸=	̸=	PROPN
ejpam-4671	75	19	1	1	NUM
ejpam-4671	75	20	.	.	PUNCT
ejpam-4671	76	1	proof	proof	NOUN
ejpam-4671	76	2	:	:	PUNCT
ejpam-4671	76	3	suppose	suppose	VERB
ejpam-4671	76	4	g	g	PROPN
ejpam-4671	76	5	has	have	VERB
ejpam-4671	76	6	a	a	DET
ejpam-4671	76	7	1	1	NUM
ejpam-4671	76	8	-	-	PUNCT
ejpam-4671	76	9	movable	movable	ADJ
ejpam-4671	76	10	resolving	resolve	VERB
ejpam-4671	76	11	hop	hop	NOUN
ejpam-4671	76	12	dominating	dominating	NOUN
ejpam-4671	76	13	set	set	NOUN
ejpam-4671	76	14	s.	s.	PROPN
ejpam-4671	76	15	suppose	suppose	VERB
ejpam-4671	76	16	further	far	ADV
ejpam-4671	76	17	that	that	PRON
ejpam-4671	76	18	γ(g	γ(g	PROPN
ejpam-4671	76	19	)	)	PUNCT
ejpam-4671	76	20	=	=	SYM
ejpam-4671	77	1	1	1	X
ejpam-4671	77	2	.	.	PUNCT
ejpam-4671	77	3	let	let	VERB
ejpam-4671	77	4	a	a	PRON
ejpam-4671	77	5	=	=	SYM
ejpam-4671	77	6	{	{	PUNCT
ejpam-4671	77	7	x	x	PROPN
ejpam-4671	77	8	∈	∈	PROPN
ejpam-4671	77	9	v	v	NOUN
ejpam-4671	77	10	(	(	PUNCT
ejpam-4671	77	11	g	g	NOUN
ejpam-4671	77	12	)	)	PUNCT
ejpam-4671	77	13	:	:	PUNCT
ejpam-4671	77	14	{	{	PUNCT
ejpam-4671	77	15	x	x	X
ejpam-4671	77	16	}	}	PUNCT
ejpam-4671	77	17	is	be	AUX
ejpam-4671	77	18	a	a	DET
ejpam-4671	77	19	dominating	dominating	NOUN
ejpam-4671	77	20	set	set	NOUN
ejpam-4671	77	21	of	of	ADP
ejpam-4671	77	22	g	g	NOUN
ejpam-4671	77	23	}	}	PUNCT
ejpam-4671	77	24	.	.	PUNCT
ejpam-4671	78	1	then	then	ADV
ejpam-4671	78	2	a	a	DET
ejpam-4671	78	3	̸=	̸=	PROPN
ejpam-4671	78	4	∅	∅	NOUN
ejpam-4671	78	5	since	since	SCONJ
ejpam-4671	78	6	γ(g	γ(g	PROPN
ejpam-4671	78	7	)	)	PUNCT
ejpam-4671	78	8	=	=	PUNCT
ejpam-4671	79	1	1	1	X
ejpam-4671	79	2	.	.	PUNCT
ejpam-4671	79	3	since	since	SCONJ
ejpam-4671	79	4	s	s	PROPN
ejpam-4671	79	5	is	be	AUX
ejpam-4671	79	6	a	a	DET
ejpam-4671	79	7	hop	hop	NOUN
ejpam-4671	79	8	dominating	dominating	NOUN
ejpam-4671	79	9	set	set	NOUN
ejpam-4671	79	10	,	,	PUNCT
ejpam-4671	79	11	a	a	DET
ejpam-4671	79	12	⊆	⊆	NUM
ejpam-4671	79	13	s.	s.	PROPN
ejpam-4671	79	14	let	let	VERB
ejpam-4671	79	15	x	x	X
ejpam-4671	79	16	∈	∈	VERB
ejpam-4671	79	17	a.	a.	NOUN
ejpam-4671	79	18	then	then	ADV
ejpam-4671	79	19	s	s	VERB
ejpam-4671	79	20	\	\	X
ejpam-4671	79	21	{	{	PUNCT
ejpam-4671	79	22	x	x	NOUN
ejpam-4671	79	23	}	}	PUNCT
ejpam-4671	79	24	and	and	CCONJ
ejpam-4671	79	25	(	(	PUNCT
ejpam-4671	79	26	s	s	NOUN
ejpam-4671	79	27	\	\	X
ejpam-4671	79	28	{	{	PUNCT
ejpam-4671	79	29	x	x	NOUN
ejpam-4671	79	30	}	}	PUNCT
ejpam-4671	79	31	)	)	PUNCT
ejpam-4671	79	32	∪	∪	ADP
ejpam-4671	79	33	{	{	PUNCT
ejpam-4671	79	34	y	y	NOUN
ejpam-4671	79	35	}	}	PUNCT
ejpam-4671	79	36	for	for	ADP
ejpam-4671	79	37	each	each	DET
ejpam-4671	79	38	y	y	PROPN
ejpam-4671	79	39	∈	∈	PROPN
ejpam-4671	79	40	v	v	ADP
ejpam-4671	79	41	(	(	PUNCT
ejpam-4671	79	42	g	g	NOUN
ejpam-4671	79	43	)	)	PUNCT
ejpam-4671	79	44	\	\	PROPN
ejpam-4671	80	1	s	s	VERB
ejpam-4671	80	2	are	be	AUX
ejpam-4671	80	3	not	not	PART
ejpam-4671	80	4	hop	hop	ADJ
ejpam-4671	80	5	dominating	dominating	NOUN
ejpam-4671	80	6	sets	set	NOUN
ejpam-4671	80	7	of	of	ADP
ejpam-4671	80	8	g.	g.	PROPN
ejpam-4671	80	9	thus	thus	ADV
ejpam-4671	80	10	,	,	PUNCT
ejpam-4671	80	11	s	s	VERB
ejpam-4671	80	12	is	be	AUX
ejpam-4671	80	13	not	not	PART
ejpam-4671	80	14	a	a	DET
ejpam-4671	80	15	1	1	NUM
ejpam-4671	80	16	-	-	PUNCT
ejpam-4671	80	17	movable	movable	ADJ
ejpam-4671	80	18	resolving	resolve	VERB
ejpam-4671	80	19	hop	hop	NOUN
ejpam-4671	80	20	dominating	dominating	NOUN
ejpam-4671	80	21	set	set	NOUN
ejpam-4671	80	22	,	,	PUNCT
ejpam-4671	80	23	a	a	DET
ejpam-4671	80	24	contradiction	contradiction	NOUN
ejpam-4671	80	25	.	.	PUNCT
ejpam-4671	81	1	conversely	conversely	ADV
ejpam-4671	81	2	,	,	PUNCT
ejpam-4671	81	3	suppose	suppose	VERB
ejpam-4671	81	4	that	that	SCONJ
ejpam-4671	81	5	γ(g	γ(g	PROPN
ejpam-4671	81	6	)	)	PUNCT
ejpam-4671	81	7	̸=	̸=	PROPN
ejpam-4671	81	8	1	1	NUM
ejpam-4671	81	9	.	.	PUNCT
ejpam-4671	82	1	let	let	VERB
ejpam-4671	82	2	s	s	NOUN
ejpam-4671	82	3	=	=	X
ejpam-4671	82	4	v	v	ADJ
ejpam-4671	82	5	(	(	PUNCT
ejpam-4671	82	6	g	g	NOUN
ejpam-4671	82	7	)	)	PUNCT
ejpam-4671	82	8	.	.	PUNCT
ejpam-4671	83	1	then	then	ADV
ejpam-4671	83	2	s	s	VERB
ejpam-4671	83	3	is	be	AUX
ejpam-4671	83	4	a	a	DET
ejpam-4671	83	5	resolving	resolve	VERB
ejpam-4671	83	6	hop	hop	NOUN
ejpam-4671	83	7	dominating	dominating	NOUN
ejpam-4671	83	8	set	set	NOUN
ejpam-4671	83	9	of	of	ADP
ejpam-4671	83	10	g.	g.	PROPN
ejpam-4671	83	11	for	for	ADP
ejpam-4671	83	12	each	each	DET
ejpam-4671	83	13	x	x	SYM
ejpam-4671	83	14	∈	∈	PROPN
ejpam-4671	83	15	s	s	PROPN
ejpam-4671	83	16	,	,	PUNCT
ejpam-4671	83	17	s	s	NOUN
ejpam-4671	83	18	\	\	X
ejpam-4671	83	19	{	{	PUNCT
ejpam-4671	83	20	x	x	NOUN
ejpam-4671	83	21	}	}	PUNCT
ejpam-4671	83	22	is	be	AUX
ejpam-4671	83	23	a	a	DET
ejpam-4671	83	24	resolving	resolving	NOUN
ejpam-4671	83	25	set	set	NOUN
ejpam-4671	83	26	of	of	ADP
ejpam-4671	83	27	g.	g.	PROPN
ejpam-4671	83	28	also	also	ADV
ejpam-4671	83	29	,	,	PUNCT
ejpam-4671	83	30	since	since	SCONJ
ejpam-4671	83	31	{	{	PUNCT
ejpam-4671	83	32	x	x	X
ejpam-4671	83	33	}	}	PUNCT
ejpam-4671	83	34	is	be	AUX
ejpam-4671	83	35	not	not	PART
ejpam-4671	83	36	a	a	DET
ejpam-4671	83	37	dominating	dominating	NOUN
ejpam-4671	83	38	set	set	NOUN
ejpam-4671	83	39	,	,	PUNCT
ejpam-4671	83	40	there	there	PRON
ejpam-4671	83	41	exists	exist	VERB
ejpam-4671	83	42	y	y	PROPN
ejpam-4671	83	43	∈	∈	PROPN
ejpam-4671	83	44	(	(	PUNCT
ejpam-4671	83	45	s	s	NOUN
ejpam-4671	83	46	\	\	X
ejpam-4671	83	47	{	{	PUNCT
ejpam-4671	83	48	x	x	NOUN
ejpam-4671	83	49	}	}	PUNCT
ejpam-4671	83	50	)	)	PUNCT
ejpam-4671	83	51	∩	∩	NOUN
ejpam-4671	83	52	ng(x	ng(x	NUM
ejpam-4671	83	53	,	,	PUNCT
ejpam-4671	83	54	2	2	NUM
ejpam-4671	83	55	)	)	PUNCT
ejpam-4671	83	56	.	.	PUNCT
ejpam-4671	84	1	hence	hence	ADV
ejpam-4671	84	2	,	,	PUNCT
ejpam-4671	84	3	s	s	NOUN
ejpam-4671	84	4	\	\	X
ejpam-4671	84	5	{	{	PUNCT
ejpam-4671	84	6	x	x	NOUN
ejpam-4671	84	7	}	}	PUNCT
ejpam-4671	84	8	is	be	AUX
ejpam-4671	84	9	a	a	DET
ejpam-4671	84	10	hop	hop	NOUN
ejpam-4671	84	11	dominating	dominating	NOUN
ejpam-4671	84	12	set	set	NOUN
ejpam-4671	84	13	of	of	ADP
ejpam-4671	84	14	g.	g.	PROPN
ejpam-4671	84	15	therefore	therefore	ADV
ejpam-4671	84	16	,	,	PUNCT
ejpam-4671	84	17	s	s	VERB
ejpam-4671	84	18	\	\	X
ejpam-4671	84	19	{	{	PUNCT
ejpam-4671	84	20	x	x	NOUN
ejpam-4671	84	21	}	}	PUNCT
ejpam-4671	84	22	is	be	AUX
ejpam-4671	84	23	a	a	DET
ejpam-4671	84	24	resolving	resolve	VERB
ejpam-4671	84	25	hop	hop	NOUN
ejpam-4671	84	26	dominating	dominating	NOUN
ejpam-4671	84	27	set	set	NOUN
ejpam-4671	84	28	of	of	ADP
ejpam-4671	84	29	g	g	PROPN
ejpam-4671	84	30	for	for	ADP
ejpam-4671	84	31	each	each	DET
ejpam-4671	84	32	x	x	PROPN
ejpam-4671	84	33	∈	∈	PROPN
ejpam-4671	84	34	s.	s.	PROPN
ejpam-4671	84	35	accordingly	accordingly	ADV
ejpam-4671	84	36	,	,	PUNCT
ejpam-4671	84	37	s	s	VERB
ejpam-4671	84	38	is	be	AUX
ejpam-4671	84	39	a	a	DET
ejpam-4671	84	40	1	1	NUM
ejpam-4671	84	41	-	-	PUNCT
ejpam-4671	84	42	movable	movable	ADJ
ejpam-4671	84	43	resolving	resolve	VERB
ejpam-4671	84	44	hop	hop	NOUN
ejpam-4671	84	45	dominating	dominating	NOUN
ejpam-4671	84	46	set	set	NOUN
ejpam-4671	84	47	of	of	ADP
ejpam-4671	84	48	g.	g.	PROPN
ejpam-4671	84	49	as	as	ADP
ejpam-4671	84	50	a	a	DET
ejpam-4671	84	51	consequence	consequence	NOUN
ejpam-4671	84	52	of	of	ADP
ejpam-4671	84	53	proposition	proposition	NOUN
ejpam-4671	84	54	1	1	NUM
ejpam-4671	84	55	the	the	DET
ejpam-4671	84	56	next	next	ADJ
ejpam-4671	84	57	result	result	NOUN
ejpam-4671	84	58	follows	follow	VERB
ejpam-4671	84	59	.	.	PUNCT
ejpam-4671	85	1	corollary	corollary	ADJ
ejpam-4671	85	2	1	1	NUM
ejpam-4671	85	3	.	.	PUNCT
ejpam-4671	86	1	a	a	DET
ejpam-4671	86	2	graph	graph	NOUN
ejpam-4671	86	3	g	g	NOUN
ejpam-4671	86	4	does	do	AUX
ejpam-4671	86	5	not	not	PART
ejpam-4671	86	6	admit	admit	VERB
ejpam-4671	86	7	a	a	DET
ejpam-4671	86	8	1	1	NUM
ejpam-4671	86	9	-	-	PUNCT
ejpam-4671	86	10	movable	movable	ADJ
ejpam-4671	86	11	resolving	resolve	VERB
ejpam-4671	86	12	hop	hop	NOUN
ejpam-4671	86	13	dominating	dominating	NOUN
ejpam-4671	86	14	set	set	VERB
ejpam-4671	86	15	if	if	SCONJ
ejpam-4671	86	16	and	and	CCONJ
ejpam-4671	86	17	only	only	ADV
ejpam-4671	86	18	if	if	SCONJ
ejpam-4671	86	19	g	g	NOUN
ejpam-4671	86	20	=	=	PROPN
ejpam-4671	86	21	k1	k1	PROPN
ejpam-4671	87	1	+	+	NOUN
ejpam-4671	87	2	h	h	NOUN
ejpam-4671	87	3	for	for	ADP
ejpam-4671	87	4	any	any	DET
ejpam-4671	87	5	graph	graph	NOUN
ejpam-4671	87	6	h.	h.	NOUN
ejpam-4671	87	7	proposition	proposition	NOUN
ejpam-4671	87	8	2	2	X
ejpam-4671	87	9	.	.	PUNCT
ejpam-4671	88	1	let	let	VERB
ejpam-4671	88	2	g	g	PRON
ejpam-4671	88	3	be	be	AUX
ejpam-4671	88	4	a	a	DET
ejpam-4671	88	5	connected	connected	ADJ
ejpam-4671	88	6	graph	graph	NOUN
ejpam-4671	88	7	and	and	CCONJ
ejpam-4671	88	8	s	s	VERB
ejpam-4671	88	9	a	a	DET
ejpam-4671	88	10	1	1	NUM
ejpam-4671	88	11	-	-	PUNCT
ejpam-4671	88	12	movable	movable	ADJ
ejpam-4671	88	13	resolving	resolve	VERB
ejpam-4671	88	14	hop	hop	NOUN
ejpam-4671	88	15	dominating	dominating	NOUN
ejpam-4671	88	16	set	set	NOUN
ejpam-4671	88	17	of	of	ADP
ejpam-4671	88	18	g.	g.	PROPN
ejpam-4671	88	19	then	then	ADV
ejpam-4671	88	20	for	for	ADP
ejpam-4671	88	21	all	all	DET
ejpam-4671	88	22	z	z	NOUN
ejpam-4671	88	23	∈	∈	PROPN
ejpam-4671	88	24	s	s	PROPN
ejpam-4671	88	25	,	,	PUNCT
ejpam-4671	88	26	ng(z	ng(z	PROPN
ejpam-4671	88	27	,	,	PUNCT
ejpam-4671	88	28	2)∩s	2)∩s	PROPN
ejpam-4671	88	29	̸=	̸=	PROPN
ejpam-4671	88	30	∅	∅	NOUN
ejpam-4671	88	31	and	and	CCONJ
ejpam-4671	88	32	for	for	ADP
ejpam-4671	88	33	each	each	DET
ejpam-4671	88	34	x	x	SYM
ejpam-4671	88	35	∈	∈	PROPN
ejpam-4671	88	36	v	v	NOUN
ejpam-4671	88	37	(	(	PUNCT
ejpam-4671	88	38	g)\s	g)\s	NOUN
ejpam-4671	88	39	,	,	PUNCT
ejpam-4671	88	40	|ng(x	|ng(x	PRON
ejpam-4671	88	41	,	,	PUNCT
ejpam-4671	88	42	2)∩s|	2)∩s|	NUM
ejpam-4671	88	43	≥	≥	NUM
ejpam-4671	88	44	1	1	NUM
ejpam-4671	88	45	and	and	CCONJ
ejpam-4671	88	46	there	there	PRON
ejpam-4671	88	47	exists	exist	VERB
ejpam-4671	88	48	w	w	PROPN
ejpam-4671	88	49	∈	∈	PROPN
ejpam-4671	88	50	(	(	PUNCT
ejpam-4671	88	51	v	v	NOUN
ejpam-4671	88	52	(	(	PUNCT
ejpam-4671	88	53	g	g	NOUN
ejpam-4671	88	54	)	)	PUNCT
ejpam-4671	88	55	\	\	PROPN
ejpam-4671	89	1	s	s	X
ejpam-4671	89	2	)	)	PUNCT
ejpam-4671	89	3	∩ng(x	∩ng(x	NOUN
ejpam-4671	89	4	,	,	PUNCT
ejpam-4671	89	5	2	2	X
ejpam-4671	89	6	)	)	PUNCT
ejpam-4671	89	7	∩ng(v	∩ng(v	PROPN
ejpam-4671	89	8	)	)	PUNCT
ejpam-4671	89	9	whenever	whenever	SCONJ
ejpam-4671	89	10	ng(x	ng(x	NUM
ejpam-4671	89	11	,	,	PUNCT
ejpam-4671	89	12	2	2	X
ejpam-4671	89	13	)	)	PUNCT
ejpam-4671	89	14	∩	∩	NOUN
ejpam-4671	89	15	s	s	PART
ejpam-4671	89	16	=	=	PUNCT
ejpam-4671	89	17	{	{	PUNCT
ejpam-4671	89	18	v	v	NOUN
ejpam-4671	89	19	}	}	PUNCT
ejpam-4671	89	20	.	.	PUNCT
ejpam-4671	90	1	proof	proof	NOUN
ejpam-4671	90	2	:	:	PUNCT
ejpam-4671	90	3	let	let	VERB
ejpam-4671	90	4	s	s	PRON
ejpam-4671	90	5	be	be	AUX
ejpam-4671	90	6	a	a	DET
ejpam-4671	90	7	1	1	NUM
ejpam-4671	90	8	-	-	PUNCT
ejpam-4671	90	9	movable	movable	ADJ
ejpam-4671	90	10	resolving	resolve	VERB
ejpam-4671	90	11	hop	hop	NOUN
ejpam-4671	90	12	dominating	dominating	NOUN
ejpam-4671	90	13	set	set	NOUN
ejpam-4671	90	14	of	of	ADP
ejpam-4671	90	15	g	g	PROPN
ejpam-4671	90	16	and	and	CCONJ
ejpam-4671	90	17	z	z	PROPN
ejpam-4671	90	18	∈	∈	PROPN
ejpam-4671	90	19	s.	s.	PROPN
ejpam-4671	90	20	suppose	suppose	VERB
ejpam-4671	90	21	ng(z	ng(z	PROPN
ejpam-4671	90	22	,	,	PUNCT
ejpam-4671	90	23	2	2	NUM
ejpam-4671	90	24	)	)	PUNCT
ejpam-4671	90	25	∩	∩	NOUN
ejpam-4671	90	26	s	s	PART
ejpam-4671	90	27	=	=	X
ejpam-4671	90	28	∅.	∅.	X
ejpam-4671	90	29	then	then	ADV
ejpam-4671	90	30	s	s	VERB
ejpam-4671	90	31	\	\	X
ejpam-4671	90	32	{	{	PUNCT
ejpam-4671	90	33	z	z	NOUN
ejpam-4671	90	34	}	}	PUNCT
ejpam-4671	90	35	and	and	CCONJ
ejpam-4671	90	36	(	(	PUNCT
ejpam-4671	90	37	s	s	NOUN
ejpam-4671	90	38	\	\	X
ejpam-4671	90	39	{	{	PUNCT
ejpam-4671	90	40	z	z	NOUN
ejpam-4671	90	41	}	}	PUNCT
ejpam-4671	90	42	)	)	PUNCT
ejpam-4671	90	43	∪	∪	ADP
ejpam-4671	90	44	{	{	PUNCT
ejpam-4671	90	45	u	u	NOUN
ejpam-4671	90	46	}	}	PUNCT
ejpam-4671	90	47	where	where	SCONJ
ejpam-4671	90	48	u	u	PROPN
ejpam-4671	90	49	∈	∈	PROPN
ejpam-4671	90	50	(	(	PUNCT
ejpam-4671	90	51	v	v	NOUN
ejpam-4671	90	52	(	(	PUNCT
ejpam-4671	90	53	g	g	NOUN
ejpam-4671	90	54	)	)	PUNCT
ejpam-4671	90	55	\	\	PROPN
ejpam-4671	90	56	s	s	X
ejpam-4671	90	57	)	)	PUNCT
ejpam-4671	90	58	∩	∩	NOUN
ejpam-4671	90	59	ng(z	ng(z	NUM
ejpam-4671	90	60	)	)	PUNCT
ejpam-4671	90	61	are	be	AUX
ejpam-4671	90	62	not	not	PART
ejpam-4671	90	63	hop	hop	ADJ
ejpam-4671	90	64	dominating	dominating	NOUN
ejpam-4671	90	65	sets	set	NOUN
ejpam-4671	90	66	of	of	ADP
ejpam-4671	90	67	g	g	PROPN
ejpam-4671	90	68	since	since	SCONJ
ejpam-4671	90	69	z	z	PROPN
ejpam-4671	90	70	has	have	VERB
ejpam-4671	90	71	no	no	DET
ejpam-4671	90	72	hop	hop	NOUN
ejpam-4671	90	73	neighbor	neighbor	NOUN
ejpam-4671	90	74	in	in	ADP
ejpam-4671	90	75	both	both	DET
ejpam-4671	90	76	sets	set	NOUN
ejpam-4671	90	77	,	,	PUNCT
ejpam-4671	90	78	a	a	DET
ejpam-4671	90	79	contradiction	contradiction	NOUN
ejpam-4671	90	80	.	.	PUNCT
ejpam-4671	91	1	thus	thus	ADV
ejpam-4671	91	2	,	,	PUNCT
ejpam-4671	91	3	ng(z	ng(z	NUM
ejpam-4671	91	4	,	,	PUNCT
ejpam-4671	91	5	2	2	NUM
ejpam-4671	91	6	)	)	PUNCT
ejpam-4671	91	7	∩	∩	NOUN
ejpam-4671	91	8	s	s	PART
ejpam-4671	91	9	̸=	̸=	PROPN
ejpam-4671	91	10	∅.	∅.	ADV
ejpam-4671	91	11	now	now	ADV
ejpam-4671	91	12	,	,	PUNCT
ejpam-4671	91	13	let	let	VERB
ejpam-4671	91	14	x	x	PUNCT
ejpam-4671	91	15	∈	∈	PROPN
ejpam-4671	91	16	v	v	X
ejpam-4671	91	17	(	(	PUNCT
ejpam-4671	91	18	g	g	NOUN
ejpam-4671	91	19	)	)	PUNCT
ejpam-4671	91	20	\	\	PUNCT
ejpam-4671	92	1	s.	s.	PROPN
ejpam-4671	92	2	since	since	SCONJ
ejpam-4671	92	3	s	s	PROPN
ejpam-4671	92	4	is	be	AUX
ejpam-4671	92	5	hop	hop	NOUN
ejpam-4671	92	6	dominating	dominating	NOUN
ejpam-4671	92	7	,	,	PUNCT
ejpam-4671	92	8	ng(x	ng(x	NUM
ejpam-4671	92	9	,	,	PUNCT
ejpam-4671	92	10	2)∩s	2)∩s	PROPN
ejpam-4671	92	11	̸=	̸=	PROPN
ejpam-4671	92	12	∅.	∅.	ADV
ejpam-4671	92	13	suppose	suppose	VERB
ejpam-4671	92	14	|ng(x	|ng(x	NOUN
ejpam-4671	92	15	,	,	PUNCT
ejpam-4671	92	16	2)∩s|	2)∩s|	NUM
ejpam-4671	92	17	=	=	SYM
ejpam-4671	92	18	1	1	X
ejpam-4671	92	19	.	.	PUNCT
ejpam-4671	93	1	let	let	VERB
ejpam-4671	93	2	v	v	ADP
ejpam-4671	93	3	∈	∈	PROPN
ejpam-4671	93	4	ng(x	ng(x	NUM
ejpam-4671	93	5	,	,	PUNCT
ejpam-4671	93	6	2)∩s	2)∩s	PROPN
ejpam-4671	93	7	.	.	PUNCT
ejpam-4671	94	1	then	then	ADV
ejpam-4671	94	2	s\{v	s\{v	VERB
ejpam-4671	94	3	}	}	PUNCT
ejpam-4671	94	4	is	be	AUX
ejpam-4671	94	5	not	not	PART
ejpam-4671	94	6	hop	hop	NOUN
ejpam-4671	94	7	dominating	dominating	NOUN
ejpam-4671	94	8	,	,	PUNCT
ejpam-4671	94	9	since	since	SCONJ
ejpam-4671	94	10	x	x	PRON
ejpam-4671	94	11	has	have	VERB
ejpam-4671	94	12	no	no	DET
ejpam-4671	94	13	hop	hop	NOUN
ejpam-4671	94	14	neighbor	neighbor	NOUN
ejpam-4671	94	15	in	in	ADP
ejpam-4671	94	16	s	s	NOUN
ejpam-4671	94	17	\{v	\{v	PROPN
ejpam-4671	94	18	}	}	PUNCT
ejpam-4671	94	19	.	.	PUNCT
ejpam-4671	95	1	it	it	PRON
ejpam-4671	95	2	follows	follow	VERB
ejpam-4671	95	3	that	that	SCONJ
ejpam-4671	95	4	(	(	PUNCT
ejpam-4671	95	5	s	s	VERB
ejpam-4671	95	6	\{v})∪{w	\{v})∪{w	NOUN
ejpam-4671	95	7	}	}	PUNCT
ejpam-4671	95	8	for	for	ADP
ejpam-4671	95	9	some	some	DET
ejpam-4671	95	10	w	w	PROPN
ejpam-4671	95	11	∈	∈	PROPN
ejpam-4671	95	12	(	(	PUNCT
ejpam-4671	95	13	v	v	NOUN
ejpam-4671	95	14	(	(	PUNCT
ejpam-4671	95	15	g	g	NOUN
ejpam-4671	95	16	)	)	PUNCT
ejpam-4671	95	17	\	\	PROPN
ejpam-4671	95	18	s	s	X
ejpam-4671	95	19	)	)	PUNCT
ejpam-4671	95	20	∩ng(v	∩ng(v	PROPN
ejpam-4671	95	21	)	)	PUNCT
ejpam-4671	95	22	is	be	AUX
ejpam-4671	95	23	a	a	DET
ejpam-4671	95	24	resolving	resolve	VERB
ejpam-4671	95	25	hop	hop	NOUN
ejpam-4671	95	26	dominating	dominating	NOUN
ejpam-4671	95	27	set	set	NOUN
ejpam-4671	95	28	of	of	ADP
ejpam-4671	95	29	g.	g.	PROPN
ejpam-4671	95	30	hence	hence	ADV
ejpam-4671	95	31	,	,	PUNCT
ejpam-4671	95	32	x	x	PRON
ejpam-4671	95	33	must	must	AUX
ejpam-4671	95	34	be	be	AUX
ejpam-4671	95	35	a	a	DET
ejpam-4671	95	36	hop	hop	NOUN
ejpam-4671	95	37	neighbor	neighbor	NOUN
ejpam-4671	95	38	of	of	ADP
ejpam-4671	95	39	w	w	PROPN
ejpam-4671	95	40	and	and	CCONJ
ejpam-4671	95	41	so	so	ADV
ejpam-4671	95	42	w	w	PROPN
ejpam-4671	95	43	∈	∈	PROPN
ejpam-4671	95	44	(	(	PUNCT
ejpam-4671	95	45	v	v	NOUN
ejpam-4671	95	46	(	(	PUNCT
ejpam-4671	95	47	g	g	NOUN
ejpam-4671	95	48	)	)	PUNCT
ejpam-4671	95	49	\	\	PROPN
ejpam-4671	96	1	s	s	X
ejpam-4671	96	2	)	)	PUNCT
ejpam-4671	96	3	∩ng(x	∩ng(x	NOUN
ejpam-4671	96	4	,	,	PUNCT
ejpam-4671	96	5	2	2	X
ejpam-4671	96	6	)	)	PUNCT
ejpam-4671	96	7	∩ng(v	∩ng(v	PROPN
ejpam-4671	96	8	)	)	PUNCT
ejpam-4671	96	9	.	.	PUNCT
ejpam-4671	97	1	as	as	ADP
ejpam-4671	97	2	a	a	DET
ejpam-4671	97	3	consequence	consequence	NOUN
ejpam-4671	97	4	of	of	ADP
ejpam-4671	97	5	proposition	proposition	NOUN
ejpam-4671	97	6	2	2	NUM
ejpam-4671	97	7	,	,	PUNCT
ejpam-4671	97	8	the	the	DET
ejpam-4671	97	9	next	next	ADJ
ejpam-4671	97	10	corollary	corollary	NOUN
ejpam-4671	97	11	follows	follow	VERB
ejpam-4671	97	12	.	.	PUNCT
ejpam-4671	98	1	corollary	corollary	ADJ
ejpam-4671	98	2	2	2	NUM
ejpam-4671	98	3	.	.	PUNCT
ejpam-4671	99	1	every	every	DET
ejpam-4671	99	2	1	1	NUM
ejpam-4671	99	3	-	-	PUNCT
ejpam-4671	99	4	movable	movable	ADJ
ejpam-4671	99	5	resolving	resolve	VERB
ejpam-4671	99	6	hop	hop	NOUN
ejpam-4671	99	7	dominating	dominating	NOUN
ejpam-4671	99	8	set	set	NOUN
ejpam-4671	99	9	is	be	AUX
ejpam-4671	99	10	a	a	DET
ejpam-4671	99	11	total	total	ADJ
ejpam-4671	99	12	hop	hop	NOUN
ejpam-4671	99	13	dominating	dominating	NOUN
ejpam-4671	99	14	set	set	NOUN
ejpam-4671	99	15	.	.	PUNCT
ejpam-4671	100	1	moreover	moreover	ADV
ejpam-4671	100	2	,	,	PUNCT
ejpam-4671	100	3	γth(g	γth(g	NOUN
ejpam-4671	100	4	)	)	PUNCT
ejpam-4671	100	5	≤	≤	NOUN
ejpam-4671	100	6	γ1mrh(g	γ1mrh(g	NOUN
ejpam-4671	100	7	)	)	PUNCT
ejpam-4671	100	8	.	.	PUNCT
ejpam-4671	101	1	3	3	X
ejpam-4671	101	2	.	.	X
ejpam-4671	102	1	on	on	ADP
ejpam-4671	102	2	1	1	NUM
ejpam-4671	102	3	-	-	PUNCT
ejpam-4671	102	4	movable	movable	ADJ
ejpam-4671	102	5	resolving	resolve	VERB
ejpam-4671	102	6	hop	hop	NOUN
ejpam-4671	102	7	domination	domination	NOUN
ejpam-4671	102	8	in	in	ADP
ejpam-4671	102	9	the	the	DET
ejpam-4671	102	10	join	join	NOUN
ejpam-4671	102	11	of	of	ADP
ejpam-4671	102	12	graphs	graph	NOUN
ejpam-4671	102	13	let	let	VERB
ejpam-4671	102	14	a	a	PRON
ejpam-4671	102	15	and	and	CCONJ
ejpam-4671	102	16	b	b	NOUN
ejpam-4671	102	17	be	be	NOUN
ejpam-4671	102	18	sets	set	NOUN
ejpam-4671	102	19	which	which	PRON
ejpam-4671	102	20	are	be	AUX
ejpam-4671	102	21	not	not	PART
ejpam-4671	102	22	necessarily	necessarily	ADV
ejpam-4671	102	23	disjoint	disjoint	VERB
ejpam-4671	102	24	.	.	PUNCT
ejpam-4671	103	1	the	the	DET
ejpam-4671	103	2	disjoint	disjoint	PROPN
ejpam-4671	103	3	union	union	NOUN
ejpam-4671	103	4	of	of	ADP
ejpam-4671	103	5	a	a	PRON
ejpam-4671	103	6	and	and	CCONJ
ejpam-4671	103	7	b	b	NOUN
ejpam-4671	103	8	,	,	PUNCT
ejpam-4671	103	9	denoted	denote	VERB
ejpam-4671	103	10	by	by	ADP
ejpam-4671	103	11	a	a	DET
ejpam-4671	103	12	•	•	NOUN
ejpam-4671	103	13	∪	∪	NOUN
ejpam-4671	103	14	b	b	NOUN
ejpam-4671	103	15	,	,	PUNCT
ejpam-4671	103	16	is	be	AUX
ejpam-4671	103	17	the	the	DET
ejpam-4671	103	18	set	set	NOUN
ejpam-4671	103	19	obtained	obtain	VERB
ejpam-4671	103	20	by	by	ADP
ejpam-4671	103	21	taking	take	VERB
ejpam-4671	103	22	the	the	DET
ejpam-4671	103	23	union	union	NOUN
ejpam-4671	103	24	of	of	ADP
ejpam-4671	103	25	a	a	PRON
ejpam-4671	103	26	and	and	CCONJ
ejpam-4671	103	27	b	b	NOUN
ejpam-4671	103	28	treating	treat	VERB
ejpam-4671	103	29	each	each	DET
ejpam-4671	103	30	element	element	NOUN
ejpam-4671	103	31	in	in	ADP
ejpam-4671	103	32	a	a	DET
ejpam-4671	103	33	as	as	ADV
ejpam-4671	103	34	distinct	distinct	ADJ
ejpam-4671	103	35	from	from	ADP
ejpam-4671	103	36	each	each	DET
ejpam-4671	103	37	element	element	NOUN
ejpam-4671	103	38	in	in	ADP
ejpam-4671	103	39	b.	b.	PROPN
ejpam-4671	104	1	the	the	DET
ejpam-4671	104	2	union	union	PROPN
ejpam-4671	104	3	g1	g1	PROPN
ejpam-4671	104	4	∪	∪	ADP
ejpam-4671	104	5	g2	g2	PROPN
ejpam-4671	104	6	of	of	ADP
ejpam-4671	104	7	graphs	graph	NOUN
ejpam-4671	104	8	g1	g1	PROPN
ejpam-4671	104	9	and	and	CCONJ
ejpam-4671	104	10	g2	g2	PROPN
ejpam-4671	104	11	with	with	ADP
ejpam-4671	104	12	disjoint	disjoint	PROPN
ejpam-4671	104	13	vertex	vertex	NOUN
ejpam-4671	104	14	-	-	PUNCT
ejpam-4671	104	15	sets	set	NOUN
ejpam-4671	104	16	v	v	NOUN
ejpam-4671	104	17	(	(	PUNCT
ejpam-4671	104	18	g1	g1	PROPN
ejpam-4671	104	19	)	)	PUNCT
ejpam-4671	104	20	and	and	CCONJ
ejpam-4671	104	21	v	v	NOUN
ejpam-4671	104	22	(	(	PUNCT
ejpam-4671	104	23	g2	g2	PROPN
ejpam-4671	104	24	)	)	PUNCT
ejpam-4671	104	25	,	,	PUNCT
ejpam-4671	104	26	respectively	respectively	ADV
ejpam-4671	104	27	,	,	PUNCT
ejpam-4671	104	28	is	be	AUX
ejpam-4671	104	29	the	the	DET
ejpam-4671	104	30	graph	graph	NOUN
ejpam-4671	104	31	g	g	NOUN
ejpam-4671	104	32	with	with	ADP
ejpam-4671	104	33	v	v	NOUN
ejpam-4671	104	34	(	(	PUNCT
ejpam-4671	104	35	g	g	NOUN
ejpam-4671	104	36	)	)	PUNCT
ejpam-4671	105	1	=	=	NOUN
ejpam-4671	105	2	v	v	X
ejpam-4671	105	3	(	(	PUNCT
ejpam-4671	105	4	g1	g1	PROPN
ejpam-4671	105	5	)	)	PUNCT
ejpam-4671	105	6	•	•	ADP
ejpam-4671	105	7	∪	∪	X
ejpam-4671	105	8	v	v	NOUN
ejpam-4671	105	9	(	(	PUNCT
ejpam-4671	105	10	g2	g2	PROPN
ejpam-4671	105	11	)	)	PUNCT
ejpam-4671	105	12	and	and	CCONJ
ejpam-4671	105	13	e(g	e(g	PROPN
ejpam-4671	105	14	)	)	PUNCT
ejpam-4671	105	15	=	=	SYM
ejpam-4671	105	16	e(g1	e(g1	ADJ
ejpam-4671	105	17	)	)	PUNCT
ejpam-4671	105	18	•	•	ADP
ejpam-4671	105	19	∪	∪	ADP
ejpam-4671	105	20	e(g2	e(g2	ADV
ejpam-4671	105	21	)	)	PUNCT
ejpam-4671	105	22	.	.	PUNCT
ejpam-4671	106	1	the	the	DET
ejpam-4671	106	2	join	join	NOUN
ejpam-4671	106	3	of	of	ADP
ejpam-4671	106	4	two	two	NUM
ejpam-4671	106	5	graphs	graph	NOUN
ejpam-4671	106	6	g	g	NOUN
ejpam-4671	106	7	and	and	CCONJ
ejpam-4671	106	8	h	h	NOUN
ejpam-4671	106	9	,	,	PUNCT
ejpam-4671	106	10	denoted	denote	VERB
ejpam-4671	106	11	by	by	ADP
ejpam-4671	106	12	g+h	g+h	PROPN
ejpam-4671	106	13	,	,	PUNCT
ejpam-4671	106	14	is	be	AUX
ejpam-4671	106	15	the	the	DET
ejpam-4671	106	16	graph	graph	NOUN
ejpam-4671	106	17	with	with	ADP
ejpam-4671	106	18	vertex	vertex	NOUN
ejpam-4671	106	19	-	-	PUNCT
ejpam-4671	106	20	set	set	VERB
ejpam-4671	106	21	v	v	NOUN
ejpam-4671	106	22	(	(	PUNCT
ejpam-4671	106	23	g+h	g+h	NOUN
ejpam-4671	106	24	)	)	PUNCT
ejpam-4671	106	25	=	=	SYM
ejpam-4671	106	26	v	v	X
ejpam-4671	106	27	(	(	PUNCT
ejpam-4671	106	28	g	g	NOUN
ejpam-4671	106	29	)	)	PUNCT
ejpam-4671	106	30	•	•	ADP
ejpam-4671	106	31	∪	∪	X
ejpam-4671	106	32	v	v	NOUN
ejpam-4671	106	33	(	(	PUNCT
ejpam-4671	106	34	h	h	NOUN
ejpam-4671	106	35	)	)	PUNCT
ejpam-4671	106	36	and	and	CCONJ
ejpam-4671	106	37	edge	edge	NOUN
ejpam-4671	106	38	-	-	PUNCT
ejpam-4671	106	39	set	set	VERB
ejpam-4671	106	40	e(g+h	e(g+h	NUM
ejpam-4671	106	41	)	)	PUNCT
ejpam-4671	106	42	=	=	SYM
ejpam-4671	106	43	e(g	e(g	PROPN
ejpam-4671	106	44	)	)	PUNCT
ejpam-4671	106	45	•	•	ADP
ejpam-4671	106	46	∪	∪	ADP
ejpam-4671	106	47	e(h	e(h	PROPN
ejpam-4671	106	48	)	)	PUNCT
ejpam-4671	106	49	∪	∪	NOUN
ejpam-4671	106	50	{	{	PUNCT
ejpam-4671	106	51	uv	uv	NOUN
ejpam-4671	106	52	:	:	PUNCT
ejpam-4671	106	53	u	u	PROPN
ejpam-4671	106	54	∈	∈	PROPN
ejpam-4671	106	55	v	v	ADP
ejpam-4671	106	56	(	(	PUNCT
ejpam-4671	106	57	g	g	NOUN
ejpam-4671	106	58	)	)	PUNCT
ejpam-4671	106	59	,	,	PUNCT
ejpam-4671	106	60	v	v	X
ejpam-4671	106	61	∈	∈	PROPN
ejpam-4671	106	62	v	v	NOUN
ejpam-4671	106	63	(	(	PUNCT
ejpam-4671	106	64	h	h	NOUN
ejpam-4671	106	65	)	)	PUNCT
ejpam-4671	106	66	}	}	PUNCT
ejpam-4671	106	67	.	.	PUNCT
ejpam-4671	107	1	j.	j.	PROPN
ejpam-4671	107	2	mohamad	mohamad	PROPN
ejpam-4671	107	3	,	,	PUNCT
ejpam-4671	107	4	h.	h.	PROPN
ejpam-4671	107	5	rara	rara	PROPN
ejpam-4671	107	6	/	/	SYM
ejpam-4671	107	7	eur	eur	PROPN
ejpam-4671	107	8	.	.	PUNCT
ejpam-4671	108	1	j.	j.	PROPN
ejpam-4671	108	2	pure	pure	PROPN
ejpam-4671	108	3	appl	appl	PROPN
ejpam-4671	108	4	.	.	PROPN
ejpam-4671	108	5	math	math	PROPN
ejpam-4671	108	6	,	,	PUNCT
ejpam-4671	108	7	16	16	NUM
ejpam-4671	108	8	(	(	PUNCT
ejpam-4671	108	9	1	1	NUM
ejpam-4671	108	10	)	)	PUNCT
ejpam-4671	108	11	(	(	PUNCT
ejpam-4671	108	12	2023	2023	NUM
ejpam-4671	108	13	)	)	PUNCT
ejpam-4671	108	14	,	,	PUNCT
ejpam-4671	108	15	418	418	NUM
ejpam-4671	108	16	-	-	SYM
ejpam-4671	108	17	429	429	NUM
ejpam-4671	108	18	422	422	NUM
ejpam-4671	108	19	theorem	theorem	NOUN
ejpam-4671	108	20	1	1	NUM
ejpam-4671	108	21	.	.	PUNCT
ejpam-4671	109	1	[	[	X
ejpam-4671	109	2	10	10	NUM
ejpam-4671	109	3	]	]	PUNCT
ejpam-4671	109	4	let	let	VERB
ejpam-4671	109	5	g	g	NOUN
ejpam-4671	109	6	and	and	CCONJ
ejpam-4671	109	7	h	h	NOUN
ejpam-4671	109	8	be	be	AUX
ejpam-4671	109	9	nontrivial	nontrivial	ADJ
ejpam-4671	109	10	connected	connected	ADJ
ejpam-4671	109	11	graphs	graph	NOUN
ejpam-4671	109	12	.	.	PUNCT
ejpam-4671	110	1	a	a	DET
ejpam-4671	110	2	set	set	NOUN
ejpam-4671	110	3	w	w	PROPN
ejpam-4671	110	4	⊆	⊆	NUM
ejpam-4671	110	5	v	v	NOUN
ejpam-4671	110	6	(	(	PUNCT
ejpam-4671	110	7	g+h	g+h	NOUN
ejpam-4671	110	8	)	)	PUNCT
ejpam-4671	110	9	is	be	AUX
ejpam-4671	110	10	a	a	DET
ejpam-4671	110	11	resolving	resolve	VERB
ejpam-4671	110	12	hop	hop	NOUN
ejpam-4671	110	13	dominating	dominating	NOUN
ejpam-4671	110	14	set	set	NOUN
ejpam-4671	110	15	of	of	ADP
ejpam-4671	110	16	g+h	g+h	PROPN
ejpam-4671	111	1	if	if	SCONJ
ejpam-4671	111	2	and	and	CCONJ
ejpam-4671	111	3	only	only	ADV
ejpam-4671	111	4	if	if	SCONJ
ejpam-4671	111	5	w	w	PROPN
ejpam-4671	111	6	=	=	VERB
ejpam-4671	111	7	wg	wg	PROPN
ejpam-4671	111	8	∪wh	∪wh	NOUN
ejpam-4671	111	9	where	where	SCONJ
ejpam-4671	111	10	wg	wg	PROPN
ejpam-4671	111	11	and	and	CCONJ
ejpam-4671	111	12	wh	wh	PROPN
ejpam-4671	111	13	are	be	AUX
ejpam-4671	111	14	strictly	strictly	ADV
ejpam-4671	111	15	locating	locate	VERB
ejpam-4671	111	16	sets	set	NOUN
ejpam-4671	111	17	of	of	ADP
ejpam-4671	111	18	g	g	PROPN
ejpam-4671	111	19	and	and	CCONJ
ejpam-4671	111	20	h	h	NOUN
ejpam-4671	111	21	,	,	PUNCT
ejpam-4671	111	22	respectively	respectively	ADV
ejpam-4671	111	23	.	.	PUNCT
ejpam-4671	112	1	as	as	ADP
ejpam-4671	112	2	an	an	DET
ejpam-4671	112	3	illustration	illustration	NOUN
ejpam-4671	112	4	,	,	PUNCT
ejpam-4671	112	5	consider	consider	VERB
ejpam-4671	112	6	the	the	DET
ejpam-4671	112	7	graph	graph	NOUN
ejpam-4671	112	8	p3	p3	NOUN
ejpam-4671	112	9	+	+	CCONJ
ejpam-4671	112	10	p3	p3	PROPN
ejpam-4671	112	11	in	in	ADP
ejpam-4671	112	12	figure	figure	NOUN
ejpam-4671	112	13	1	1	NUM
ejpam-4671	112	14	.	.	PUNCT
ejpam-4671	113	1	it	it	PRON
ejpam-4671	113	2	is	be	AUX
ejpam-4671	113	3	easy	easy	ADJ
ejpam-4671	113	4	to	to	PART
ejpam-4671	113	5	verify	verify	VERB
ejpam-4671	113	6	that	that	SCONJ
ejpam-4671	113	7	sln(p3	sln(p3	NOUN
ejpam-4671	113	8	)	)	PUNCT
ejpam-4671	113	9	=	=	SYM
ejpam-4671	113	10	2	2	NUM
ejpam-4671	113	11	,	,	PUNCT
ejpam-4671	113	12	and	and	CCONJ
ejpam-4671	113	13	by	by	ADP
ejpam-4671	113	14	theorem	theorem	NOUN
ejpam-4671	113	15	1	1	NUM
ejpam-4671	113	16	,	,	PUNCT
ejpam-4671	113	17	the	the	DET
ejpam-4671	113	18	set	set	NOUN
ejpam-4671	113	19	of	of	ADP
ejpam-4671	113	20	shaded	shade	VERB
ejpam-4671	113	21	vertices	vertex	NOUN
ejpam-4671	113	22	is	be	AUX
ejpam-4671	113	23	a	a	DET
ejpam-4671	113	24	resolving	resolve	VERB
ejpam-4671	113	25	hop	hop	NOUN
ejpam-4671	113	26	dominating	dominating	NOUN
ejpam-4671	113	27	set	set	NOUN
ejpam-4671	113	28	of	of	ADP
ejpam-4671	113	29	p3	p3	PROPN
ejpam-4671	113	30	+	+	CCONJ
ejpam-4671	113	31	p3	p3	PROPN
ejpam-4671	113	32	.	.	PUNCT
ejpam-4671	114	1	it	it	PRON
ejpam-4671	114	2	follows	follow	VERB
ejpam-4671	114	3	that	that	SCONJ
ejpam-4671	114	4	γrh(p3	γrh(p3	PROPN
ejpam-4671	114	5	+	+	CCONJ
ejpam-4671	114	6	p3	p3	PROPN
ejpam-4671	114	7	)	)	PUNCT
ejpam-4671	114	8	=	=	SYM
ejpam-4671	115	1	4	4	X
ejpam-4671	115	2	.	.	X
ejpam-4671	115	3	p3	p3	PROPN
ejpam-4671	115	4	+	+	CCONJ
ejpam-4671	115	5	p3	p3	PROPN
ejpam-4671	115	6	:	:	PUNCT
ejpam-4671	115	7	figure	figure	NOUN
ejpam-4671	115	8	1	1	NUM
ejpam-4671	115	9	:	:	PUNCT
ejpam-4671	115	10	graph	graph	NOUN
ejpam-4671	115	11	p3	p3	PROPN
ejpam-4671	115	12	+	+	CCONJ
ejpam-4671	115	13	p3	p3	PROPN
ejpam-4671	115	14	with	with	ADP
ejpam-4671	115	15	γrh(p3	γrh(p3	PROPN
ejpam-4671	115	16	+	+	CCONJ
ejpam-4671	115	17	p3	p3	PROPN
ejpam-4671	115	18	)	)	PUNCT
ejpam-4671	115	19	=	=	SYM
ejpam-4671	115	20	4	4	NUM
ejpam-4671	115	21	theorem	theorem	NOUN
ejpam-4671	115	22	2	2	NUM
ejpam-4671	115	23	.	.	PUNCT
ejpam-4671	115	24	let	let	VERB
ejpam-4671	115	25	g	g	NOUN
ejpam-4671	115	26	and	and	CCONJ
ejpam-4671	115	27	h	h	NOUN
ejpam-4671	115	28	be	be	AUX
ejpam-4671	115	29	connected	connect	VERB
ejpam-4671	115	30	graphs	graph	NOUN
ejpam-4671	115	31	with	with	ADP
ejpam-4671	115	32	γ(g	γ(g	NOUN
ejpam-4671	115	33	)	)	PUNCT
ejpam-4671	115	34	̸=	̸=	PROPN
ejpam-4671	115	35	1	1	NUM
ejpam-4671	115	36	and	and	CCONJ
ejpam-4671	115	37	γ(h	γ(h	NOUN
ejpam-4671	115	38	)	)	PUNCT
ejpam-4671	115	39	̸=	̸=	PROPN
ejpam-4671	115	40	1	1	NUM
ejpam-4671	115	41	.	.	PUNCT
ejpam-4671	116	1	a	a	DET
ejpam-4671	116	2	set	set	NOUN
ejpam-4671	116	3	w	w	PROPN
ejpam-4671	116	4	⊆	⊆	NUM
ejpam-4671	116	5	v	v	NOUN
ejpam-4671	116	6	(	(	PUNCT
ejpam-4671	116	7	g	g	PROPN
ejpam-4671	116	8	+	+	NOUN
ejpam-4671	116	9	h	h	NOUN
ejpam-4671	116	10	)	)	PUNCT
ejpam-4671	116	11	is	be	AUX
ejpam-4671	116	12	a	a	DET
ejpam-4671	116	13	1	1	NUM
ejpam-4671	116	14	-	-	PUNCT
ejpam-4671	116	15	movable	movable	ADJ
ejpam-4671	116	16	resolving	resolve	VERB
ejpam-4671	116	17	hop	hop	NOUN
ejpam-4671	116	18	dominating	dominating	NOUN
ejpam-4671	116	19	set	set	NOUN
ejpam-4671	116	20	of	of	ADP
ejpam-4671	116	21	g	g	PROPN
ejpam-4671	116	22	+	+	PROPN
ejpam-4671	116	23	h	h	NOUN
ejpam-4671	116	24	if	if	SCONJ
ejpam-4671	117	1	and	and	CCONJ
ejpam-4671	117	2	only	only	ADV
ejpam-4671	117	3	if	if	SCONJ
ejpam-4671	117	4	w	w	PROPN
ejpam-4671	117	5	=	=	VERB
ejpam-4671	117	6	wg	wg	PROPN
ejpam-4671	117	7	∪wh	∪wh	NOUN
ejpam-4671	117	8	where	where	SCONJ
ejpam-4671	117	9	wg	wg	PROPN
ejpam-4671	117	10	⊆	⊆	NUM
ejpam-4671	117	11	v	v	NOUN
ejpam-4671	117	12	(	(	PUNCT
ejpam-4671	117	13	g	g	NOUN
ejpam-4671	117	14	)	)	PUNCT
ejpam-4671	117	15	and	and	CCONJ
ejpam-4671	117	16	wh	wh	VERB
ejpam-4671	117	17	⊆	⊆	NUM
ejpam-4671	117	18	v	v	NOUN
ejpam-4671	117	19	(	(	PUNCT
ejpam-4671	117	20	h	h	NOUN
ejpam-4671	117	21	)	)	PUNCT
ejpam-4671	117	22	are	be	AUX
ejpam-4671	117	23	1	1	NUM
ejpam-4671	117	24	-	-	PUNCT
ejpam-4671	117	25	movable	movable	ADJ
ejpam-4671	117	26	strictly	strictly	ADV
ejpam-4671	117	27	locating	locate	VERB
ejpam-4671	117	28	sets	set	NOUN
ejpam-4671	117	29	of	of	ADP
ejpam-4671	117	30	g	g	PROPN
ejpam-4671	117	31	and	and	CCONJ
ejpam-4671	117	32	h	h	NOUN
ejpam-4671	117	33	,	,	PUNCT
ejpam-4671	117	34	respectively	respectively	ADV
ejpam-4671	117	35	,	,	PUNCT
ejpam-4671	117	36	and	and	CCONJ
ejpam-4671	117	37	one	one	NUM
ejpam-4671	117	38	of	of	ADP
ejpam-4671	117	39	the	the	DET
ejpam-4671	117	40	following	following	ADJ
ejpam-4671	117	41	statements	statement	NOUN
ejpam-4671	117	42	holds	hold	VERB
ejpam-4671	117	43	:	:	PUNCT
ejpam-4671	117	44	(	(	PUNCT
ejpam-4671	117	45	i	i	NOUN
ejpam-4671	117	46	)	)	PUNCT
ejpam-4671	117	47	for	for	ADP
ejpam-4671	117	48	each	each	DET
ejpam-4671	117	49	u	u	PROPN
ejpam-4671	117	50	∈	∈	PROPN
ejpam-4671	117	51	wg	wg	PROPN
ejpam-4671	117	52	,	,	PUNCT
ejpam-4671	117	53	wg	wg	PROPN
ejpam-4671	117	54	\	\	PROPN
ejpam-4671	117	55	{	{	PUNCT
ejpam-4671	117	56	u	u	NOUN
ejpam-4671	117	57	}	}	PUNCT
ejpam-4671	117	58	and	and	CCONJ
ejpam-4671	117	59	wh	wh	VERB
ejpam-4671	117	60	∪	∪	NOUN
ejpam-4671	117	61	{	{	PUNCT
ejpam-4671	117	62	v	v	NOUN
ejpam-4671	117	63	}	}	PUNCT
ejpam-4671	117	64	are	be	AUX
ejpam-4671	117	65	strictly	strictly	ADV
ejpam-4671	117	66	locating	locate	VERB
ejpam-4671	117	67	sets	set	NOUN
ejpam-4671	117	68	of	of	ADP
ejpam-4671	117	69	g	g	PROPN
ejpam-4671	117	70	and	and	CCONJ
ejpam-4671	117	71	h	h	NOUN
ejpam-4671	117	72	,	,	PUNCT
ejpam-4671	117	73	respectively	respectively	ADV
ejpam-4671	117	74	,	,	PUNCT
ejpam-4671	117	75	for	for	ADP
ejpam-4671	117	76	some	some	DET
ejpam-4671	117	77	v	v	ADP
ejpam-4671	117	78	∈	∈	PROPN
ejpam-4671	117	79	v	v	NOUN
ejpam-4671	117	80	(	(	PUNCT
ejpam-4671	117	81	h	h	NOUN
ejpam-4671	117	82	)	)	PUNCT
ejpam-4671	117	83	\wh	\wh	PROPN
ejpam-4671	117	84	;	;	PUNCT
ejpam-4671	117	85	(	(	PUNCT
ejpam-4671	117	86	ii	ii	NOUN
ejpam-4671	117	87	)	)	PUNCT
ejpam-4671	117	88	for	for	ADP
ejpam-4671	117	89	each	each	DET
ejpam-4671	117	90	q	q	PROPN
ejpam-4671	117	91	∈	∈	PROPN
ejpam-4671	117	92	wh	wh	NOUN
ejpam-4671	117	93	,	,	PUNCT
ejpam-4671	117	94	wh	wh	VERB
ejpam-4671	117	95	\	\	PROPN
ejpam-4671	117	96	{	{	PUNCT
ejpam-4671	117	97	q	q	NOUN
ejpam-4671	117	98	}	}	PUNCT
ejpam-4671	117	99	and	and	CCONJ
ejpam-4671	117	100	wg	wg	VERB
ejpam-4671	117	101	∪	∪	ADJ
ejpam-4671	117	102	{	{	PUNCT
ejpam-4671	117	103	b	b	NOUN
ejpam-4671	117	104	}	}	PUNCT
ejpam-4671	117	105	are	be	AUX
ejpam-4671	117	106	strictly	strictly	ADV
ejpam-4671	117	107	locating	locate	VERB
ejpam-4671	117	108	sets	set	NOUN
ejpam-4671	117	109	of	of	ADP
ejpam-4671	117	110	h	h	NOUN
ejpam-4671	117	111	and	and	CCONJ
ejpam-4671	117	112	g	g	NOUN
ejpam-4671	117	113	,	,	PUNCT
ejpam-4671	117	114	respectively	respectively	ADV
ejpam-4671	117	115	,	,	PUNCT
ejpam-4671	117	116	for	for	ADP
ejpam-4671	117	117	some	some	DET
ejpam-4671	117	118	b	b	PROPN
ejpam-4671	117	119	∈	∈	PROPN
ejpam-4671	117	120	v	v	NOUN
ejpam-4671	117	121	(	(	PUNCT
ejpam-4671	117	122	g	g	NOUN
ejpam-4671	117	123	)	)	PUNCT
ejpam-4671	117	124	\wg	\wg	PROPN
ejpam-4671	117	125	.	.	PUNCT
ejpam-4671	118	1	proof	proof	NOUN
ejpam-4671	118	2	:	:	PUNCT
ejpam-4671	118	3	suppose	suppose	VERB
ejpam-4671	118	4	that	that	SCONJ
ejpam-4671	118	5	w	w	PROPN
ejpam-4671	118	6	⊆	⊆	NUM
ejpam-4671	118	7	v	v	NOUN
ejpam-4671	118	8	(	(	PUNCT
ejpam-4671	118	9	g	g	PROPN
ejpam-4671	118	10	+	+	NOUN
ejpam-4671	118	11	h	h	NOUN
ejpam-4671	118	12	)	)	PUNCT
ejpam-4671	118	13	is	be	AUX
ejpam-4671	118	14	a	a	DET
ejpam-4671	118	15	1	1	NUM
ejpam-4671	118	16	-	-	PUNCT
ejpam-4671	118	17	movable	movable	ADJ
ejpam-4671	118	18	resolving	resolve	VERB
ejpam-4671	118	19	hop	hop	NOUN
ejpam-4671	118	20	dominating	dominating	NOUN
ejpam-4671	118	21	set	set	NOUN
ejpam-4671	118	22	of	of	ADP
ejpam-4671	118	23	g	g	PROPN
ejpam-4671	118	24	+	+	PROPN
ejpam-4671	118	25	h.	h.	PROPN
ejpam-4671	118	26	then	then	ADV
ejpam-4671	118	27	w	w	PROPN
ejpam-4671	118	28	is	be	AUX
ejpam-4671	118	29	resolving	resolve	VERB
ejpam-4671	118	30	hop	hop	NOUN
ejpam-4671	118	31	dominating	dominating	NOUN
ejpam-4671	118	32	.	.	PUNCT
ejpam-4671	119	1	by	by	ADP
ejpam-4671	119	2	theorem	theorem	NOUN
ejpam-4671	119	3	1	1	NUM
ejpam-4671	119	4	,	,	PUNCT
ejpam-4671	119	5	w	w	NOUN
ejpam-4671	119	6	=	=	PUNCT
ejpam-4671	119	7	wg	wg	PROPN
ejpam-4671	119	8	∪wh	∪wh	NOUN
ejpam-4671	119	9	where	where	SCONJ
ejpam-4671	119	10	wg	wg	PROPN
ejpam-4671	119	11	⊆	⊆	NUM
ejpam-4671	119	12	v	v	NOUN
ejpam-4671	119	13	(	(	PUNCT
ejpam-4671	119	14	g	g	NOUN
ejpam-4671	119	15	)	)	PUNCT
ejpam-4671	119	16	andwh	andwh	NOUN
ejpam-4671	119	17	⊆	⊆	NUM
ejpam-4671	119	18	v	v	NOUN
ejpam-4671	119	19	(	(	PUNCT
ejpam-4671	119	20	h	h	NOUN
ejpam-4671	119	21	)	)	PUNCT
ejpam-4671	119	22	are	be	AUX
ejpam-4671	119	23	strictly	strictly	ADV
ejpam-4671	119	24	locating	locate	VERB
ejpam-4671	119	25	sets	set	NOUN
ejpam-4671	119	26	ofg	ofg	PROPN
ejpam-4671	119	27	andh	andh	NOUN
ejpam-4671	119	28	,	,	PUNCT
ejpam-4671	119	29	respectively	respectively	ADV
ejpam-4671	119	30	.	.	PUNCT
ejpam-4671	120	1	moreover	moreover	ADV
ejpam-4671	120	2	,	,	PUNCT
ejpam-4671	120	3	since	since	SCONJ
ejpam-4671	120	4	g	g	PROPN
ejpam-4671	120	5	and	and	CCONJ
ejpam-4671	120	6	h	h	NOUN
ejpam-4671	120	7	are	be	AUX
ejpam-4671	120	8	connected	connect	VERB
ejpam-4671	120	9	graphs	graph	NOUN
ejpam-4671	120	10	with	with	ADP
ejpam-4671	120	11	γ(g	γ(g	NOUN
ejpam-4671	120	12	)	)	PUNCT
ejpam-4671	120	13	̸=	̸=	PROPN
ejpam-4671	120	14	1	1	NUM
ejpam-4671	120	15	and	and	CCONJ
ejpam-4671	120	16	γ(h	γ(h	NOUN
ejpam-4671	120	17	)	)	PUNCT
ejpam-4671	120	18	̸=	̸=	PROPN
ejpam-4671	120	19	1	1	NUM
ejpam-4671	120	20	,	,	PUNCT
ejpam-4671	120	21	wg	wg	PROPN
ejpam-4671	120	22	̸=	̸=	PROPN
ejpam-4671	120	23	∅	∅	NOUN
ejpam-4671	120	24	and	and	CCONJ
ejpam-4671	120	25	wh	wh	VERB
ejpam-4671	120	26	̸=	̸=	PROPN
ejpam-4671	120	27	∅.	∅.	ADV
ejpam-4671	120	28	let	let	VERB
ejpam-4671	120	29	x	x	SYM
ejpam-4671	120	30	∈	∈	PROPN
ejpam-4671	120	31	wg	wg	PROPN
ejpam-4671	120	32	.	.	PUNCT
ejpam-4671	121	1	by	by	ADP
ejpam-4671	121	2	assumption	assumption	NOUN
ejpam-4671	121	3	,	,	PUNCT
ejpam-4671	121	4	w	w	PROPN
ejpam-4671	121	5	\	\	X
ejpam-4671	121	6	{	{	PUNCT
ejpam-4671	121	7	x	x	NOUN
ejpam-4671	121	8	}	}	PUNCT
ejpam-4671	121	9	=	=	SYM
ejpam-4671	121	10	(	(	PUNCT
ejpam-4671	121	11	wg	wg	PROPN
ejpam-4671	121	12	\	\	PROPN
ejpam-4671	121	13	{	{	PUNCT
ejpam-4671	121	14	x	x	NOUN
ejpam-4671	121	15	}	}	PUNCT
ejpam-4671	121	16	)	)	PUNCT
ejpam-4671	121	17	∪	∪	ADP
ejpam-4671	121	18	wh	wh	PROPN
ejpam-4671	121	19	or	or	CCONJ
ejpam-4671	121	20	(	(	PUNCT
ejpam-4671	121	21	w	w	PROPN
ejpam-4671	121	22	\	\	NOUN
ejpam-4671	121	23	{	{	PUNCT
ejpam-4671	121	24	x	x	NOUN
ejpam-4671	121	25	}	}	PUNCT
ejpam-4671	121	26	)	)	PUNCT
ejpam-4671	121	27	∪	∪	ADP
ejpam-4671	121	28	{	{	PUNCT
ejpam-4671	121	29	w	w	NOUN
ejpam-4671	121	30	}	}	PUNCT
ejpam-4671	121	31	=	=	SYM
ejpam-4671	122	1	[	[	X
ejpam-4671	122	2	(	(	PUNCT
ejpam-4671	122	3	wg	wg	PROPN
ejpam-4671	122	4	\	\	PROPN
ejpam-4671	122	5	{	{	PUNCT
ejpam-4671	122	6	x	x	X
ejpam-4671	122	7	}	}	PUNCT
ejpam-4671	122	8	∪	∪	ADJ
ejpam-4671	122	9	{	{	PUNCT
ejpam-4671	122	10	w	w	NOUN
ejpam-4671	122	11	}	}	PUNCT
ejpam-4671	122	12	)	)	PUNCT
ejpam-4671	122	13	]	]	PUNCT
ejpam-4671	122	14	∪	∪	X
ejpam-4671	122	15	wh	wh	NOUN
ejpam-4671	122	16	for	for	ADP
ejpam-4671	122	17	some	some	DET
ejpam-4671	122	18	w	w	PROPN
ejpam-4671	122	19	∈	∈	PROPN
ejpam-4671	122	20	ng(x	ng(x	NUM
ejpam-4671	122	21	)	)	PUNCT
ejpam-4671	122	22	∩	∩	NOUN
ejpam-4671	122	23	(	(	PUNCT
ejpam-4671	122	24	v	v	NOUN
ejpam-4671	122	25	(	(	PUNCT
ejpam-4671	122	26	g	g	NOUN
ejpam-4671	122	27	)	)	PUNCT
ejpam-4671	122	28	\	\	PROPN
ejpam-4671	122	29	wg	wg	PROPN
ejpam-4671	122	30	)	)	PUNCT
ejpam-4671	122	31	or	or	CCONJ
ejpam-4671	122	32	(	(	PUNCT
ejpam-4671	122	33	w	w	PROPN
ejpam-4671	122	34	\	\	NOUN
ejpam-4671	122	35	{	{	PUNCT
ejpam-4671	122	36	x	x	NOUN
ejpam-4671	122	37	}	}	PUNCT
ejpam-4671	122	38	)	)	PUNCT
ejpam-4671	122	39	∪	∪	ADP
ejpam-4671	122	40	{	{	PUNCT
ejpam-4671	122	41	z	z	NOUN
ejpam-4671	122	42	}	}	PUNCT
ejpam-4671	122	43	=	=	SYM
ejpam-4671	122	44	(	(	PUNCT
ejpam-4671	122	45	wg	wg	PROPN
ejpam-4671	122	46	\	\	PROPN
ejpam-4671	122	47	{	{	PUNCT
ejpam-4671	122	48	x	x	NOUN
ejpam-4671	122	49	}	}	PUNCT
ejpam-4671	122	50	)	)	PUNCT
ejpam-4671	122	51	∪	∪	NOUN
ejpam-4671	122	52	(	(	PUNCT
ejpam-4671	122	53	wh	wh	NOUN
ejpam-4671	122	54	∪	∪	NOUN
ejpam-4671	122	55	{	{	PUNCT
ejpam-4671	122	56	z	z	NOUN
ejpam-4671	122	57	}	}	PUNCT
ejpam-4671	122	58	)	)	PUNCT
ejpam-4671	122	59	for	for	ADP
ejpam-4671	122	60	some	some	DET
ejpam-4671	122	61	z	z	NOUN
ejpam-4671	122	62	∈	∈	PROPN
ejpam-4671	122	63	v	v	ADP
ejpam-4671	122	64	(	(	PUNCT
ejpam-4671	122	65	h	h	NOUN
ejpam-4671	122	66	)	)	PUNCT
ejpam-4671	122	67	\wh	\wh	PROPN
ejpam-4671	122	68	is	be	AUX
ejpam-4671	122	69	a	a	DET
ejpam-4671	122	70	resolving	resolve	VERB
ejpam-4671	122	71	hop	hop	NOUN
ejpam-4671	122	72	dominating	dominating	NOUN
ejpam-4671	122	73	set	set	NOUN
ejpam-4671	122	74	of	of	ADP
ejpam-4671	122	75	g+h	g+h	PROPN
ejpam-4671	122	76	.	.	PUNCT
ejpam-4671	123	1	thus	thus	ADV
ejpam-4671	123	2	,	,	PUNCT
ejpam-4671	123	3	by	by	ADP
ejpam-4671	123	4	theorem	theorem	NOUN
ejpam-4671	123	5	1	1	NUM
ejpam-4671	123	6	,	,	PUNCT
ejpam-4671	123	7	wg	wg	PROPN
ejpam-4671	123	8	\	\	PROPN
ejpam-4671	123	9	{	{	PUNCT
ejpam-4671	123	10	x	x	NOUN
ejpam-4671	123	11	}	}	PUNCT
ejpam-4671	123	12	or	or	CCONJ
ejpam-4671	123	13	(	(	PUNCT
ejpam-4671	123	14	wg	wg	PROPN
ejpam-4671	123	15	\	\	PROPN
ejpam-4671	123	16	{	{	PUNCT
ejpam-4671	123	17	x})∪{w	x})∪{w	PROPN
ejpam-4671	123	18	}	}	PUNCT
ejpam-4671	123	19	is	be	AUX
ejpam-4671	123	20	a	a	DET
ejpam-4671	123	21	strictly	strictly	ADV
ejpam-4671	123	22	locating	locate	VERB
ejpam-4671	123	23	set	set	NOUN
ejpam-4671	123	24	of	of	ADP
ejpam-4671	123	25	g.	g.	PROPN
ejpam-4671	123	26	this	this	PRON
ejpam-4671	123	27	implies	imply	VERB
ejpam-4671	123	28	that	that	SCONJ
ejpam-4671	123	29	wg	wg	PROPN
ejpam-4671	123	30	is	be	AUX
ejpam-4671	123	31	a	a	DET
ejpam-4671	123	32	1	1	NUM
ejpam-4671	123	33	-	-	PUNCT
ejpam-4671	123	34	movable	movable	ADJ
ejpam-4671	123	35	-	-	PUNCT
ejpam-4671	123	36	strictly	strictly	ADV
ejpam-4671	123	37	locating	locate	VERB
ejpam-4671	123	38	set	set	NOUN
ejpam-4671	123	39	of	of	ADP
ejpam-4671	123	40	g.	g.	PROPN
ejpam-4671	123	41	similarly	similarly	ADV
ejpam-4671	123	42	,	,	PUNCT
ejpam-4671	123	43	wh	wh	PROPN
ejpam-4671	123	44	is	be	AUX
ejpam-4671	123	45	a	a	DET
ejpam-4671	123	46	1	1	NUM
ejpam-4671	123	47	-	-	PUNCT
ejpam-4671	123	48	movable	movable	NOUN
ejpam-4671	123	49	strictly	strictly	ADV
ejpam-4671	123	50	locating	locate	VERB
ejpam-4671	123	51	set	set	NOUN
ejpam-4671	123	52	of	of	ADP
ejpam-4671	123	53	h.	h.	PROPN
ejpam-4671	123	54	now	now	ADV
ejpam-4671	123	55	,	,	PUNCT
ejpam-4671	123	56	let	let	VERB
ejpam-4671	123	57	u	u	PRON
ejpam-4671	123	58	∈	∈	PROPN
ejpam-4671	123	59	wg	wg	PROPN
ejpam-4671	123	60	.	.	PUNCT
ejpam-4671	124	1	since	since	SCONJ
ejpam-4671	124	2	w	w	PROPN
ejpam-4671	124	3	is	be	AUX
ejpam-4671	124	4	a	a	DET
ejpam-4671	124	5	1	1	NUM
ejpam-4671	124	6	-	-	PUNCT
ejpam-4671	124	7	movable	movable	ADJ
ejpam-4671	124	8	resolving	resolve	VERB
ejpam-4671	124	9	hop	hop	NOUN
ejpam-4671	124	10	dominating	dominating	NOUN
ejpam-4671	124	11	set	set	NOUN
ejpam-4671	124	12	,	,	PUNCT
ejpam-4671	124	13	w	w	PROPN
ejpam-4671	124	14	\	\	PROPN
ejpam-4671	124	15	{	{	PUNCT
ejpam-4671	124	16	u	u	NOUN
ejpam-4671	124	17	}	}	PUNCT
ejpam-4671	124	18	=	=	SYM
ejpam-4671	124	19	(	(	PUNCT
ejpam-4671	124	20	wg	wg	PROPN
ejpam-4671	124	21	\	\	PROPN
ejpam-4671	124	22	{	{	PUNCT
ejpam-4671	124	23	u	u	NOUN
ejpam-4671	124	24	}	}	PUNCT
ejpam-4671	124	25	)	)	PUNCT
ejpam-4671	124	26	∪	∪	ADP
ejpam-4671	124	27	wh	wh	PROPN
ejpam-4671	124	28	or	or	CCONJ
ejpam-4671	124	29	(	(	PUNCT
ejpam-4671	124	30	w	w	PROPN
ejpam-4671	124	31	\	\	NOUN
ejpam-4671	124	32	{	{	PUNCT
ejpam-4671	124	33	u	u	NOUN
ejpam-4671	124	34	}	}	PUNCT
ejpam-4671	124	35	)	)	PUNCT
ejpam-4671	124	36	∪	∪	ADP
ejpam-4671	124	37	{	{	PUNCT
ejpam-4671	124	38	r	r	NOUN
ejpam-4671	124	39	}	}	PUNCT
ejpam-4671	124	40	=	=	SYM
ejpam-4671	125	1	[	[	X
ejpam-4671	125	2	(	(	PUNCT
ejpam-4671	125	3	wg	wg	PROPN
ejpam-4671	125	4	\	\	PROPN
ejpam-4671	125	5	{	{	PUNCT
ejpam-4671	125	6	u	u	NOUN
ejpam-4671	125	7	}	}	PUNCT
ejpam-4671	125	8	)	)	PUNCT
ejpam-4671	125	9	∪	∪	ADP
ejpam-4671	125	10	{	{	PUNCT
ejpam-4671	125	11	r	r	NOUN
ejpam-4671	125	12	}	}	PUNCT
ejpam-4671	125	13	]	]	PUNCT
ejpam-4671	125	14	∪	∪	X
ejpam-4671	125	15	wh	wh	NOUN
ejpam-4671	125	16	for	for	ADP
ejpam-4671	125	17	some	some	DET
ejpam-4671	125	18	r	r	NOUN
ejpam-4671	125	19	∈	∈	PROPN
ejpam-4671	125	20	ng(u	ng(u	NOUN
ejpam-4671	125	21	)	)	PUNCT
ejpam-4671	125	22	∩	∩	NOUN
ejpam-4671	125	23	(	(	PUNCT
ejpam-4671	125	24	v	v	NOUN
ejpam-4671	125	25	(	(	PUNCT
ejpam-4671	125	26	g	g	NOUN
ejpam-4671	125	27	)	)	PUNCT
ejpam-4671	125	28	\	\	PROPN
ejpam-4671	125	29	wg	wg	PROPN
ejpam-4671	125	30	)	)	PUNCT
ejpam-4671	125	31	or	or	CCONJ
ejpam-4671	125	32	(	(	PUNCT
ejpam-4671	125	33	w	w	PROPN
ejpam-4671	125	34	\	\	NOUN
ejpam-4671	125	35	{	{	PUNCT
ejpam-4671	125	36	u	u	NOUN
ejpam-4671	125	37	}	}	PUNCT
ejpam-4671	125	38	)	)	PUNCT
ejpam-4671	125	39	∪	∪	ADP
ejpam-4671	125	40	{	{	PUNCT
ejpam-4671	125	41	v	v	NOUN
ejpam-4671	125	42	}	}	PUNCT
ejpam-4671	125	43	=	=	PUNCT
ejpam-4671	125	44	(	(	PUNCT
ejpam-4671	125	45	wg	wg	PROPN
ejpam-4671	125	46	\	\	PROPN
ejpam-4671	125	47	{	{	PUNCT
ejpam-4671	125	48	u	u	NOUN
ejpam-4671	125	49	}	}	PUNCT
ejpam-4671	125	50	)	)	PUNCT
ejpam-4671	125	51	∪	∪	NOUN
ejpam-4671	125	52	(	(	PUNCT
ejpam-4671	125	53	wh	wh	NOUN
ejpam-4671	125	54	∪	∪	NOUN
ejpam-4671	125	55	{	{	PUNCT
ejpam-4671	125	56	v	v	NOUN
ejpam-4671	125	57	}	}	PUNCT
ejpam-4671	125	58	)	)	PUNCT
ejpam-4671	125	59	for	for	ADP
ejpam-4671	125	60	some	some	DET
ejpam-4671	125	61	v	v	ADP
ejpam-4671	125	62	∈	∈	PROPN
ejpam-4671	125	63	v	v	NOUN
ejpam-4671	125	64	(	(	PUNCT
ejpam-4671	125	65	h	h	NOUN
ejpam-4671	125	66	)	)	PUNCT
ejpam-4671	125	67	\wh	\wh	PROPN
ejpam-4671	125	68	is	be	AUX
ejpam-4671	125	69	a	a	DET
ejpam-4671	125	70	resolving	resolve	VERB
ejpam-4671	125	71	hop	hop	NOUN
ejpam-4671	125	72	dominating	dominating	NOUN
ejpam-4671	125	73	set	set	NOUN
ejpam-4671	125	74	of	of	ADP
ejpam-4671	125	75	g	g	PROPN
ejpam-4671	125	76	+	+	PROPN
ejpam-4671	125	77	h.	h.	PROPN
ejpam-4671	125	78	it	it	PRON
ejpam-4671	125	79	follows	follow	VERB
ejpam-4671	125	80	from	from	ADP
ejpam-4671	125	81	theorem	theorem	ADJ
ejpam-4671	125	82	1	1	NUM
ejpam-4671	125	83	that	that	PRON
ejpam-4671	125	84	wg	wg	VERB
ejpam-4671	125	85	\	\	NOUN
ejpam-4671	125	86	{	{	PUNCT
ejpam-4671	125	87	u	u	NOUN
ejpam-4671	125	88	}	}	PUNCT
ejpam-4671	125	89	and	and	CCONJ
ejpam-4671	125	90	wh	wh	VERB
ejpam-4671	125	91	∪{v	∪{v	NOUN
ejpam-4671	125	92	}	}	PUNCT
ejpam-4671	125	93	are	be	AUX
ejpam-4671	125	94	strictly	strictly	ADV
ejpam-4671	125	95	locating	locate	VERB
ejpam-4671	125	96	sets	set	NOUN
ejpam-4671	125	97	of	of	ADP
ejpam-4671	125	98	g	g	PROPN
ejpam-4671	125	99	and	and	CCONJ
ejpam-4671	125	100	h	h	NOUN
ejpam-4671	125	101	,	,	PUNCT
ejpam-4671	125	102	respectively	respectively	ADV
ejpam-4671	125	103	.	.	PUNCT
ejpam-4671	126	1	thus	thus	ADV
ejpam-4671	126	2	,	,	PUNCT
ejpam-4671	126	3	(	(	PUNCT
ejpam-4671	126	4	i	i	NOUN
ejpam-4671	126	5	)	)	PUNCT
ejpam-4671	126	6	holds	hold	VERB
ejpam-4671	126	7	.	.	PUNCT
ejpam-4671	127	1	similarly	similarly	ADV
ejpam-4671	127	2	,	,	PUNCT
ejpam-4671	127	3	(	(	PUNCT
ejpam-4671	127	4	ii	ii	NOUN
ejpam-4671	127	5	)	)	PUNCT
ejpam-4671	127	6	holds	hold	VERB
ejpam-4671	127	7	.	.	PUNCT
ejpam-4671	128	1	for	for	ADP
ejpam-4671	128	2	the	the	DET
ejpam-4671	128	3	converse	converse	NOUN
ejpam-4671	128	4	,	,	PUNCT
ejpam-4671	128	5	suppose	suppose	VERB
ejpam-4671	128	6	that	that	SCONJ
ejpam-4671	128	7	wg	wg	PROPN
ejpam-4671	128	8	and	and	CCONJ
ejpam-4671	128	9	wh	wh	PROPN
ejpam-4671	128	10	are	be	AUX
ejpam-4671	128	11	1	1	NUM
ejpam-4671	128	12	-	-	PUNCT
ejpam-4671	128	13	movable	movable	ADJ
ejpam-4671	128	14	strictly	strictly	ADV
ejpam-4671	128	15	locating	locate	VERB
ejpam-4671	128	16	sets	set	NOUN
ejpam-4671	128	17	of	of	ADP
ejpam-4671	128	18	g	g	PROPN
ejpam-4671	128	19	and	and	CCONJ
ejpam-4671	128	20	h	h	NOUN
ejpam-4671	128	21	,	,	PUNCT
ejpam-4671	128	22	respectively	respectively	ADV
ejpam-4671	128	23	.	.	PUNCT
ejpam-4671	129	1	suppose	suppose	VERB
ejpam-4671	129	2	(	(	PUNCT
ejpam-4671	129	3	i	i	NOUN
ejpam-4671	129	4	)	)	PUNCT
ejpam-4671	129	5	holds	hold	VERB
ejpam-4671	129	6	.	.	PUNCT
ejpam-4671	130	1	then	then	ADV
ejpam-4671	130	2	w	w	X
ejpam-4671	130	3	=	=	PUNCT
ejpam-4671	130	4	wg	wg	PROPN
ejpam-4671	130	5	∪	∪	ADJ
ejpam-4671	130	6	wh	wh	NOUN
ejpam-4671	130	7	is	be	AUX
ejpam-4671	130	8	a	a	DET
ejpam-4671	130	9	resolving	resolve	VERB
ejpam-4671	130	10	hop	hop	PROPN
ejpam-4671	130	11	j.	j.	PROPN
ejpam-4671	130	12	mohamad	mohamad	PROPN
ejpam-4671	130	13	,	,	PUNCT
ejpam-4671	130	14	h.	h.	PROPN
ejpam-4671	130	15	rara	rara	PROPN
ejpam-4671	130	16	/	/	SYM
ejpam-4671	130	17	eur	eur	PROPN
ejpam-4671	130	18	.	.	PUNCT
ejpam-4671	131	1	j.	j.	PROPN
ejpam-4671	131	2	pure	pure	PROPN
ejpam-4671	131	3	appl	appl	PROPN
ejpam-4671	131	4	.	.	PROPN
ejpam-4671	131	5	math	math	PROPN
ejpam-4671	131	6	,	,	PUNCT
ejpam-4671	131	7	16	16	NUM
ejpam-4671	131	8	(	(	PUNCT
ejpam-4671	131	9	1	1	NUM
ejpam-4671	131	10	)	)	PUNCT
ejpam-4671	131	11	(	(	PUNCT
ejpam-4671	131	12	2023	2023	NUM
ejpam-4671	131	13	)	)	PUNCT
ejpam-4671	131	14	,	,	PUNCT
ejpam-4671	131	15	418	418	NUM
ejpam-4671	131	16	-	-	SYM
ejpam-4671	131	17	429	429	NUM
ejpam-4671	131	18	423	423	NUM
ejpam-4671	131	19	dominating	dominating	NOUN
ejpam-4671	131	20	set	set	NOUN
ejpam-4671	131	21	of	of	ADP
ejpam-4671	131	22	g+h	g+h	PROPN
ejpam-4671	131	23	by	by	ADP
ejpam-4671	131	24	theorem	theorem	NOUN
ejpam-4671	131	25	1	1	NUM
ejpam-4671	131	26	.	.	PUNCT
ejpam-4671	132	1	let	let	VERB
ejpam-4671	132	2	u	u	PRON
ejpam-4671	132	3	∈	∈	PROPN
ejpam-4671	132	4	w	w	NOUN
ejpam-4671	132	5	.	.	PUNCT
ejpam-4671	133	1	if	if	SCONJ
ejpam-4671	133	2	u	u	PROPN
ejpam-4671	133	3	∈	∈	PROPN
ejpam-4671	133	4	wg	wg	PROPN
ejpam-4671	133	5	,	,	PUNCT
ejpam-4671	133	6	then	then	ADV
ejpam-4671	133	7	by	by	ADP
ejpam-4671	133	8	assumption	assumption	NOUN
ejpam-4671	133	9	and	and	CCONJ
ejpam-4671	133	10	theorem	theorem	VERB
ejpam-4671	133	11	1	1	NUM
ejpam-4671	133	12	,	,	PUNCT
ejpam-4671	133	13	w	w	PROPN
ejpam-4671	133	14	\	\	NOUN
ejpam-4671	133	15	{	{	PUNCT
ejpam-4671	133	16	u	u	NOUN
ejpam-4671	133	17	}	}	PUNCT
ejpam-4671	133	18	=	=	SYM
ejpam-4671	133	19	(	(	PUNCT
ejpam-4671	133	20	wg	wg	PROPN
ejpam-4671	133	21	\	\	PROPN
ejpam-4671	133	22	{	{	PUNCT
ejpam-4671	133	23	u	u	NOUN
ejpam-4671	133	24	}	}	PUNCT
ejpam-4671	133	25	)	)	PUNCT
ejpam-4671	133	26	∪wh	∪wh	NOUN
ejpam-4671	133	27	or	or	CCONJ
ejpam-4671	133	28	(	(	PUNCT
ejpam-4671	133	29	w	w	PROPN
ejpam-4671	133	30	\	\	NOUN
ejpam-4671	133	31	{	{	PUNCT
ejpam-4671	133	32	u	u	NOUN
ejpam-4671	133	33	}	}	PUNCT
ejpam-4671	133	34	)	)	PUNCT
ejpam-4671	133	35	∪	∪	ADP
ejpam-4671	133	36	{	{	PUNCT
ejpam-4671	133	37	w	w	NOUN
ejpam-4671	133	38	}	}	PUNCT
ejpam-4671	133	39	=	=	SYM
ejpam-4671	134	1	[	[	X
ejpam-4671	134	2	(	(	PUNCT
ejpam-4671	134	3	wg	wg	PROPN
ejpam-4671	134	4	\	\	PROPN
ejpam-4671	134	5	{	{	PUNCT
ejpam-4671	134	6	u	u	NOUN
ejpam-4671	134	7	}	}	PUNCT
ejpam-4671	134	8	)	)	PUNCT
ejpam-4671	134	9	∪	∪	ADP
ejpam-4671	134	10	{	{	PUNCT
ejpam-4671	134	11	w	w	NOUN
ejpam-4671	134	12	}	}	PUNCT
ejpam-4671	134	13	]	]	PUNCT
ejpam-4671	134	14	∪wh	∪wh	NOUN
ejpam-4671	134	15	for	for	ADP
ejpam-4671	134	16	some	some	DET
ejpam-4671	134	17	w	w	NOUN
ejpam-4671	134	18	∈	∈	PROPN
ejpam-4671	134	19	ng(u)∩	ng(u)∩	X
ejpam-4671	134	20	(	(	PUNCT
ejpam-4671	134	21	v	v	NOUN
ejpam-4671	134	22	(	(	PUNCT
ejpam-4671	134	23	g	g	NOUN
ejpam-4671	134	24	)	)	PUNCT
ejpam-4671	134	25	\wg	\wg	PROPN
ejpam-4671	134	26	)	)	PUNCT
ejpam-4671	134	27	or	or	CCONJ
ejpam-4671	134	28	w	w	PROPN
ejpam-4671	134	29	\	\	PROPN
ejpam-4671	134	30	{	{	PUNCT
ejpam-4671	134	31	u}∪	u}∪	PRON
ejpam-4671	134	32	{	{	PUNCT
ejpam-4671	134	33	z	z	NOUN
ejpam-4671	134	34	}	}	PUNCT
ejpam-4671	134	35	=	=	SYM
ejpam-4671	134	36	(	(	PUNCT
ejpam-4671	134	37	wg	wg	PROPN
ejpam-4671	134	38	\	\	PROPN
ejpam-4671	134	39	{	{	PUNCT
ejpam-4671	134	40	u})∪	u})∪	PROPN
ejpam-4671	134	41	(	(	PUNCT
ejpam-4671	134	42	wh	wh	NOUN
ejpam-4671	134	43	∪{z	∪{z	PROPN
ejpam-4671	134	44	}	}	PUNCT
ejpam-4671	134	45	)	)	PUNCT
ejpam-4671	134	46	for	for	ADP
ejpam-4671	134	47	some	some	DET
ejpam-4671	134	48	z	z	NOUN
ejpam-4671	134	49	∈	∈	PROPN
ejpam-4671	134	50	v	v	NOUN
ejpam-4671	134	51	(	(	PUNCT
ejpam-4671	134	52	h	h	NOUN
ejpam-4671	134	53	\wh	\wh	PROPN
ejpam-4671	134	54	)	)	PUNCT
ejpam-4671	134	55	is	be	AUX
ejpam-4671	134	56	a	a	DET
ejpam-4671	134	57	resolving	resolve	VERB
ejpam-4671	134	58	hop	hop	NOUN
ejpam-4671	134	59	dominating	dominating	NOUN
ejpam-4671	134	60	set	set	NOUN
ejpam-4671	134	61	of	of	ADP
ejpam-4671	134	62	g+h	g+h	PROPN
ejpam-4671	134	63	.	.	PUNCT
ejpam-4671	135	1	now	now	ADV
ejpam-4671	135	2	,	,	PUNCT
ejpam-4671	135	3	suppose	suppose	VERB
ejpam-4671	135	4	that	that	SCONJ
ejpam-4671	135	5	u	u	PROPN
ejpam-4671	135	6	∈	∈	PROPN
ejpam-4671	135	7	wh	wh	VERB
ejpam-4671	135	8	.	.	PUNCT
ejpam-4671	136	1	since	since	SCONJ
ejpam-4671	136	2	wg	wg	PROPN
ejpam-4671	136	3	and	and	CCONJ
ejpam-4671	136	4	wh	wh	PROPN
ejpam-4671	136	5	are	be	AUX
ejpam-4671	136	6	1	1	NUM
ejpam-4671	136	7	-	-	PUNCT
ejpam-4671	136	8	movable	movable	ADJ
ejpam-4671	136	9	strictly	strictly	ADV
ejpam-4671	136	10	locating	locate	VERB
ejpam-4671	136	11	sets	set	NOUN
ejpam-4671	136	12	of	of	ADP
ejpam-4671	136	13	g	g	PROPN
ejpam-4671	136	14	and	and	CCONJ
ejpam-4671	136	15	h	h	NOUN
ejpam-4671	136	16	,	,	PUNCT
ejpam-4671	136	17	respectively	respectively	ADV
ejpam-4671	136	18	,	,	PUNCT
ejpam-4671	136	19	it	it	PRON
ejpam-4671	136	20	follows	follow	VERB
ejpam-4671	136	21	from	from	ADP
ejpam-4671	136	22	theorem	theorem	ADJ
ejpam-4671	136	23	1	1	NUM
ejpam-4671	136	24	thatw\{u	thatw\{u	NOUN
ejpam-4671	136	25	}	}	PUNCT
ejpam-4671	136	26	=	=	SYM
ejpam-4671	136	27	(	(	PUNCT
ejpam-4671	136	28	wh\{u})∪wg	wh\{u})∪wg	PROPN
ejpam-4671	136	29	or	or	CCONJ
ejpam-4671	136	30	(	(	PUNCT
ejpam-4671	136	31	w\{u})∪{y	w\{u})∪{y	NOUN
ejpam-4671	136	32	}	}	PUNCT
ejpam-4671	136	33	=	=	SYM
ejpam-4671	137	1	[	[	X
ejpam-4671	137	2	(	(	PUNCT
ejpam-4671	137	3	wh\{u})∪{y}]∪wg	wh\{u})∪{y}]∪wg	NOUN
ejpam-4671	137	4	for	for	ADP
ejpam-4671	137	5	some	some	DET
ejpam-4671	137	6	y	y	PROPN
ejpam-4671	137	7	∈	∈	PROPN
ejpam-4671	137	8	nh(u)∩	nh(u)∩	X
ejpam-4671	137	9	(	(	PUNCT
ejpam-4671	137	10	v	v	X
ejpam-4671	137	11	(	(	PUNCT
ejpam-4671	137	12	h)\wh	h)\wh	PROPN
ejpam-4671	137	13	)	)	PUNCT
ejpam-4671	137	14	is	be	AUX
ejpam-4671	137	15	a	a	DET
ejpam-4671	137	16	resolving	resolve	VERB
ejpam-4671	137	17	hop	hop	NOUN
ejpam-4671	137	18	dominating	dominating	NOUN
ejpam-4671	137	19	set	set	NOUN
ejpam-4671	137	20	of	of	ADP
ejpam-4671	137	21	g+h	g+h	PROPN
ejpam-4671	137	22	.	.	PUNCT
ejpam-4671	138	1	therefore	therefore	ADV
ejpam-4671	138	2	,	,	PUNCT
ejpam-4671	138	3	w	w	PROPN
ejpam-4671	138	4	is	be	AUX
ejpam-4671	138	5	a	a	DET
ejpam-4671	138	6	1	1	NUM
ejpam-4671	138	7	-	-	PUNCT
ejpam-4671	138	8	movable	movable	ADJ
ejpam-4671	138	9	resolving	resolve	VERB
ejpam-4671	138	10	hop	hop	NOUN
ejpam-4671	138	11	dominating	dominating	NOUN
ejpam-4671	138	12	set	set	NOUN
ejpam-4671	138	13	of	of	ADP
ejpam-4671	138	14	g	g	PROPN
ejpam-4671	138	15	+	+	CCONJ
ejpam-4671	138	16	h.	h.	PROPN
ejpam-4671	138	17	similarly	similarly	ADV
ejpam-4671	138	18	,	,	PUNCT
ejpam-4671	138	19	w	w	PROPN
ejpam-4671	138	20	is	be	AUX
ejpam-4671	138	21	a	a	PRON
ejpam-4671	138	22	1	1	NUM
ejpam-4671	138	23	-	-	PUNCT
ejpam-4671	138	24	movable	movable	ADJ
ejpam-4671	138	25	resolving	resolve	VERB
ejpam-4671	138	26	hop	hop	NOUN
ejpam-4671	138	27	dominating	dominating	NOUN
ejpam-4671	138	28	set	set	NOUN
ejpam-4671	138	29	of	of	ADP
ejpam-4671	138	30	g+h	g+h	PROPN
ejpam-4671	138	31	if	if	SCONJ
ejpam-4671	138	32	(	(	PUNCT
ejpam-4671	138	33	ii	ii	NOUN
ejpam-4671	138	34	)	)	PUNCT
ejpam-4671	138	35	holds	hold	VERB
ejpam-4671	138	36	.	.	PUNCT
ejpam-4671	139	1	corollary	corollary	ADJ
ejpam-4671	139	2	3	3	X
ejpam-4671	139	3	.	.	PUNCT
ejpam-4671	140	1	let	let	VERB
ejpam-4671	140	2	g	g	NOUN
ejpam-4671	140	3	and	and	CCONJ
ejpam-4671	140	4	h	h	NOUN
ejpam-4671	140	5	be	be	AUX
ejpam-4671	140	6	nontrivial	nontrivial	ADJ
ejpam-4671	140	7	connected	connect	VERB
ejpam-4671	140	8	graphs	graph	NOUN
ejpam-4671	140	9	with	with	ADP
ejpam-4671	140	10	γ(g	γ(g	NOUN
ejpam-4671	140	11	)	)	PUNCT
ejpam-4671	140	12	̸=	̸=	PROPN
ejpam-4671	140	13	1	1	NUM
ejpam-4671	140	14	and	and	CCONJ
ejpam-4671	140	15	γ(h	γ(h	NOUN
ejpam-4671	140	16	)	)	PUNCT
ejpam-4671	140	17	̸=	̸=	PROPN
ejpam-4671	140	18	1	1	NUM
ejpam-4671	140	19	.	.	PUNCT
ejpam-4671	141	1	if	if	SCONJ
ejpam-4671	141	2	g	g	PROPN
ejpam-4671	141	3	and	and	CCONJ
ejpam-4671	141	4	h	h	NOUN
ejpam-4671	141	5	have	have	VERB
ejpam-4671	141	6	1	1	NUM
ejpam-4671	141	7	-	-	PUNCT
ejpam-4671	141	8	movable	movable	ADJ
ejpam-4671	141	9	strictly	strictly	ADV
ejpam-4671	141	10	locating	locate	VERB
ejpam-4671	141	11	sets	set	NOUN
ejpam-4671	141	12	,	,	PUNCT
ejpam-4671	141	13	then	then	ADV
ejpam-4671	141	14	γ1mrh(g+h	γ1mrh(g+h	PROPN
ejpam-4671	141	15	)	)	PUNCT
ejpam-4671	141	16	≤	≤	NUM
ejpam-4671	141	17	msln(g	msln(g	NOUN
ejpam-4671	141	18	)	)	PUNCT
ejpam-4671	141	19	+	+	NOUN
ejpam-4671	141	20	msln(h	msln(h	NOUN
ejpam-4671	141	21	)	)	PUNCT
ejpam-4671	141	22	.	.	PUNCT
ejpam-4671	142	1	proof	proof	NOUN
ejpam-4671	142	2	:	:	PUNCT
ejpam-4671	142	3	suppose	suppose	VERB
ejpam-4671	142	4	g	g	PROPN
ejpam-4671	142	5	and	and	CCONJ
ejpam-4671	142	6	h	h	NOUN
ejpam-4671	142	7	have	have	VERB
ejpam-4671	142	8	1	1	NUM
ejpam-4671	142	9	-	-	PUNCT
ejpam-4671	142	10	movable	movable	ADJ
ejpam-4671	142	11	strictly	strictly	ADV
ejpam-4671	142	12	locating	locate	VERB
ejpam-4671	142	13	sets	set	NOUN
ejpam-4671	142	14	.	.	PUNCT
ejpam-4671	143	1	let	let	VERB
ejpam-4671	143	2	wg	wg	VERB
ejpam-4671	143	3	and	and	CCONJ
ejpam-4671	143	4	wh	wh	VERB
ejpam-4671	143	5	be	be	AUX
ejpam-4671	143	6	msln	msln	NOUN
ejpam-4671	143	7	-	-	PUNCT
ejpam-4671	143	8	sets	set	NOUN
ejpam-4671	143	9	of	of	ADP
ejpam-4671	143	10	g	g	PROPN
ejpam-4671	143	11	and	and	CCONJ
ejpam-4671	143	12	h	h	NOUN
ejpam-4671	143	13	,	,	PUNCT
ejpam-4671	143	14	respectively	respectively	ADV
ejpam-4671	143	15	.	.	PUNCT
ejpam-4671	144	1	then	then	ADV
ejpam-4671	144	2	w	w	X
ejpam-4671	144	3	=	=	PUNCT
ejpam-4671	144	4	wg	wg	PROPN
ejpam-4671	144	5	∪	∪	ADJ
ejpam-4671	144	6	wh	wh	NOUN
ejpam-4671	144	7	is	be	AUX
ejpam-4671	144	8	a	a	DET
ejpam-4671	144	9	1	1	NUM
ejpam-4671	144	10	-	-	PUNCT
ejpam-4671	144	11	movable	movable	ADJ
ejpam-4671	144	12	resolving	resolve	VERB
ejpam-4671	144	13	hop	hop	NOUN
ejpam-4671	144	14	dominating	dominating	NOUN
ejpam-4671	144	15	set	set	NOUN
ejpam-4671	144	16	of	of	ADP
ejpam-4671	144	17	g+h	g+h	PROPN
ejpam-4671	144	18	by	by	ADP
ejpam-4671	144	19	theorem	theorem	NOUN
ejpam-4671	144	20	2	2	NUM
ejpam-4671	144	21	.	.	PUNCT
ejpam-4671	144	22	thus	thus	ADV
ejpam-4671	144	23	,	,	PUNCT
ejpam-4671	144	24	γ1mrh(g+h	γ1mrh(g+h	PROPN
ejpam-4671	144	25	)	)	PUNCT
ejpam-4671	144	26	≤	≤	NOUN
ejpam-4671	144	27	|w	|w	NOUN
ejpam-4671	145	1	|	|	NOUN
ejpam-4671	145	2	=	=	PUNCT
ejpam-4671	145	3	|wg|+	|wg|+	NOUN
ejpam-4671	145	4	|wh	|wh	X
ejpam-4671	145	5	|	|	NOUN
ejpam-4671	145	6	=	=	SYM
ejpam-4671	145	7	msln(g	msln(g	NOUN
ejpam-4671	145	8	)	)	PUNCT
ejpam-4671	145	9	+	+	NOUN
ejpam-4671	145	10	msln(h	msln(h	NOUN
ejpam-4671	145	11	)	)	PUNCT
ejpam-4671	145	12	.	.	PUNCT
ejpam-4671	146	1	4	4	X
ejpam-4671	146	2	.	.	X
ejpam-4671	146	3	on	on	ADP
ejpam-4671	146	4	1	1	NUM
ejpam-4671	146	5	-	-	PUNCT
ejpam-4671	146	6	movable	movable	ADJ
ejpam-4671	146	7	resolving	resolve	VERB
ejpam-4671	146	8	hop	hop	NOUN
ejpam-4671	146	9	domination	domination	NOUN
ejpam-4671	146	10	in	in	ADP
ejpam-4671	146	11	the	the	DET
ejpam-4671	146	12	corona	corona	NOUN
ejpam-4671	146	13	of	of	ADP
ejpam-4671	146	14	graphs	graph	NOUN
ejpam-4671	146	15	the	the	DET
ejpam-4671	146	16	corona	corona	NOUN
ejpam-4671	146	17	of	of	ADP
ejpam-4671	146	18	two	two	NUM
ejpam-4671	146	19	graphs	graph	NOUN
ejpam-4671	146	20	g	g	NOUN
ejpam-4671	146	21	and	and	CCONJ
ejpam-4671	146	22	h	h	NOUN
ejpam-4671	146	23	,	,	PUNCT
ejpam-4671	146	24	denoted	denote	VERB
ejpam-4671	146	25	by	by	ADP
ejpam-4671	146	26	g	g	PROPN
ejpam-4671	146	27	◦	◦	NOUN
ejpam-4671	146	28	h	h	NOUN
ejpam-4671	146	29	,	,	PUNCT
ejpam-4671	146	30	is	be	AUX
ejpam-4671	146	31	the	the	DET
ejpam-4671	146	32	graph	graph	NOUN
ejpam-4671	146	33	obtained	obtain	VERB
ejpam-4671	146	34	by	by	ADP
ejpam-4671	146	35	taking	take	VERB
ejpam-4671	146	36	one	one	NUM
ejpam-4671	146	37	copy	copy	NOUN
ejpam-4671	146	38	of	of	ADP
ejpam-4671	146	39	g	g	NOUN
ejpam-4671	146	40	of	of	ADP
ejpam-4671	146	41	order	order	NOUN
ejpam-4671	146	42	n	n	NOUN
ejpam-4671	146	43	and	and	CCONJ
ejpam-4671	146	44	n	n	PRON
ejpam-4671	146	45	copies	copy	NOUN
ejpam-4671	146	46	of	of	ADP
ejpam-4671	146	47	h	h	NOUN
ejpam-4671	146	48	,	,	PUNCT
ejpam-4671	146	49	and	and	CCONJ
ejpam-4671	146	50	then	then	ADV
ejpam-4671	146	51	joining	join	VERB
ejpam-4671	146	52	every	every	DET
ejpam-4671	146	53	vertex	vertex	NOUN
ejpam-4671	146	54	of	of	ADP
ejpam-4671	146	55	the	the	DET
ejpam-4671	146	56	ith	ith	PROPN
ejpam-4671	146	57	copy	copy	NOUN
ejpam-4671	146	58	of	of	ADP
ejpam-4671	146	59	h	h	NOUN
ejpam-4671	146	60	to	to	ADP
ejpam-4671	146	61	the	the	DET
ejpam-4671	146	62	ith	ith	PROPN
ejpam-4671	146	63	vertex	vertex	NOUN
ejpam-4671	146	64	of	of	ADP
ejpam-4671	146	65	g.	g.	PROPN
ejpam-4671	146	66	for	for	ADP
ejpam-4671	146	67	v	v	NOUN
ejpam-4671	146	68	∈	∈	PROPN
ejpam-4671	146	69	v	v	NOUN
ejpam-4671	146	70	(	(	PUNCT
ejpam-4671	146	71	g	g	NOUN
ejpam-4671	146	72	)	)	PUNCT
ejpam-4671	146	73	,	,	PUNCT
ejpam-4671	146	74	denote	denote	VERB
ejpam-4671	146	75	by	by	ADP
ejpam-4671	146	76	hv	hv	PROPN
ejpam-4671	146	77	the	the	DET
ejpam-4671	146	78	copy	copy	NOUN
ejpam-4671	146	79	of	of	ADP
ejpam-4671	146	80	h	h	NOUN
ejpam-4671	146	81	whose	whose	DET
ejpam-4671	146	82	vertices	vertex	NOUN
ejpam-4671	146	83	are	be	AUX
ejpam-4671	146	84	attached	attach	VERB
ejpam-4671	146	85	one	one	NUM
ejpam-4671	146	86	by	by	ADP
ejpam-4671	146	87	one	one	NUM
ejpam-4671	146	88	to	to	ADP
ejpam-4671	146	89	the	the	DET
ejpam-4671	146	90	vertex	vertex	NOUN
ejpam-4671	146	91	v.	v.	ADP
ejpam-4671	146	92	subsequently	subsequently	ADV
ejpam-4671	146	93	,	,	PUNCT
ejpam-4671	146	94	denote	denote	VERB
ejpam-4671	146	95	by	by	ADP
ejpam-4671	146	96	v+hv	v+hv	NOUN
ejpam-4671	146	97	the	the	DET
ejpam-4671	146	98	subgraph	subgraph	NOUN
ejpam-4671	146	99	of	of	ADP
ejpam-4671	146	100	the	the	DET
ejpam-4671	146	101	corona	corona	NOUN
ejpam-4671	146	102	g	g	PROPN
ejpam-4671	146	103	◦	◦	NOUN
ejpam-4671	146	104	h	h	NOUN
ejpam-4671	146	105	corresponding	correspond	VERB
ejpam-4671	146	106	to	to	ADP
ejpam-4671	146	107	the	the	DET
ejpam-4671	146	108	join	join	NOUN
ejpam-4671	146	109	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4671	146	110	,	,	PUNCT
ejpam-4671	146	111	v	v	PROPN
ejpam-4671	146	112	∈	∈	PROPN
ejpam-4671	146	113	v	v	NOUN
ejpam-4671	146	114	(	(	PUNCT
ejpam-4671	146	115	g	g	NOUN
ejpam-4671	146	116	)	)	PUNCT
ejpam-4671	146	117	.	.	PUNCT
ejpam-4671	147	1	theorem	theorem	NOUN
ejpam-4671	147	2	3	3	NUM
ejpam-4671	147	3	.	.	PUNCT
ejpam-4671	148	1	[	[	X
ejpam-4671	148	2	10	10	NUM
ejpam-4671	148	3	]	]	PUNCT
ejpam-4671	148	4	let	let	VERB
ejpam-4671	148	5	g	g	NOUN
ejpam-4671	148	6	and	and	CCONJ
ejpam-4671	148	7	h	h	NOUN
ejpam-4671	148	8	be	be	AUX
ejpam-4671	148	9	nontrivial	nontrivial	ADJ
ejpam-4671	148	10	connected	connected	ADJ
ejpam-4671	148	11	graphs	graph	NOUN
ejpam-4671	148	12	.	.	PUNCT
ejpam-4671	149	1	then	then	ADV
ejpam-4671	149	2	w	w	PROPN
ejpam-4671	149	3	⊆	⊆	NUM
ejpam-4671	149	4	v	v	NOUN
ejpam-4671	149	5	(	(	PUNCT
ejpam-4671	149	6	g	g	PROPN
ejpam-4671	149	7	◦	◦	NOUN
ejpam-4671	149	8	h	h	NOUN
ejpam-4671	149	9	)	)	PUNCT
ejpam-4671	149	10	is	be	AUX
ejpam-4671	149	11	a	a	DET
ejpam-4671	149	12	resolving	resolve	VERB
ejpam-4671	149	13	hop	hop	NOUN
ejpam-4671	149	14	dominating	dominating	NOUN
ejpam-4671	149	15	set	set	NOUN
ejpam-4671	149	16	of	of	ADP
ejpam-4671	149	17	g	g	PROPN
ejpam-4671	149	18	◦	◦	NOUN
ejpam-4671	149	19	h	h	NOUN
ejpam-4671	150	1	if	if	SCONJ
ejpam-4671	151	1	and	and	CCONJ
ejpam-4671	151	2	only	only	ADV
ejpam-4671	151	3	if	if	SCONJ
ejpam-4671	151	4	w	w	PROPN
ejpam-4671	151	5	∩	∩	ADJ
ejpam-4671	151	6	v	v	X
ejpam-4671	151	7	(	(	PUNCT
ejpam-4671	151	8	hv	hv	NOUN
ejpam-4671	151	9	)	)	PUNCT
ejpam-4671	151	10	̸=	̸=	PROPN
ejpam-4671	151	11	∅	∅	NOUN
ejpam-4671	151	12	for	for	ADP
ejpam-4671	151	13	every	every	DET
ejpam-4671	151	14	v	v	NUM
ejpam-4671	151	15	∈	∈	PROPN
ejpam-4671	151	16	v	v	NOUN
ejpam-4671	151	17	(	(	PUNCT
ejpam-4671	151	18	g	g	NOUN
ejpam-4671	151	19	)	)	PUNCT
ejpam-4671	151	20	and	and	CCONJ
ejpam-4671	151	21	w	w	X
ejpam-4671	151	22	=	=	PUNCT
ejpam-4671	151	23	a	a	PRON
ejpam-4671	151	24	∪b	∪b	X
ejpam-4671	151	25	∪d	∪d	PUNCT
ejpam-4671	151	26	where	where	SCONJ
ejpam-4671	151	27	a	a	DET
ejpam-4671	151	28	⊆	⊆	NUM
ejpam-4671	151	29	v	v	NOUN
ejpam-4671	151	30	(	(	PUNCT
ejpam-4671	151	31	g	g	NOUN
ejpam-4671	151	32	)	)	PUNCT
ejpam-4671	151	33	,	,	PUNCT
ejpam-4671	151	34	b	b	X
ejpam-4671	151	35	=	=	SYM
ejpam-4671	151	36	∪	∪	X
ejpam-4671	151	37	{	{	PUNCT
ejpam-4671	151	38	bv	bv	NOUN
ejpam-4671	151	39	:	:	PUNCT
ejpam-4671	151	40	v	v	NUM
ejpam-4671	151	41	∈	∈	PROPN
ejpam-4671	151	42	v	v	NOUN
ejpam-4671	151	43	(	(	PUNCT
ejpam-4671	151	44	g	g	NOUN
ejpam-4671	151	45	)	)	PUNCT
ejpam-4671	151	46	∩ng(a	∩ng(a	NOUN
ejpam-4671	151	47	)	)	PUNCT
ejpam-4671	151	48	and	and	CCONJ
ejpam-4671	151	49	bv	bv	PROPN
ejpam-4671	151	50	is	be	AUX
ejpam-4671	151	51	a	a	DET
ejpam-4671	151	52	locating	locate	VERB
ejpam-4671	151	53	set	set	NOUN
ejpam-4671	151	54	of	of	ADP
ejpam-4671	151	55	hv	hv	PROPN
ejpam-4671	151	56	}	}	PUNCT
ejpam-4671	151	57	and	and	CCONJ
ejpam-4671	151	58	d	d	NOUN
ejpam-4671	151	59	=	=	SYM
ejpam-4671	151	60	∪	∪	X
ejpam-4671	151	61	{	{	PUNCT
ejpam-4671	151	62	du	du	NOUN
ejpam-4671	151	63	:	:	PUNCT
ejpam-4671	151	64	u	u	PROPN
ejpam-4671	151	65	∈	∈	PROPN
ejpam-4671	151	66	v	v	ADP
ejpam-4671	151	67	(	(	PUNCT
ejpam-4671	151	68	g	g	NOUN
ejpam-4671	151	69	)	)	PUNCT
ejpam-4671	151	70	\ng(a	\ng(a	PROPN
ejpam-4671	151	71	)	)	PUNCT
ejpam-4671	151	72	and	and	CCONJ
ejpam-4671	151	73	du	du	PROPN
ejpam-4671	151	74	is	be	AUX
ejpam-4671	151	75	a	a	DET
ejpam-4671	151	76	strictly	strictly	ADV
ejpam-4671	151	77	locating	locate	VERB
ejpam-4671	151	78	set	set	NOUN
ejpam-4671	151	79	of	of	ADP
ejpam-4671	151	80	hu	hu	PROPN
ejpam-4671	151	81	}	}	PUNCT
ejpam-4671	151	82	.	.	PUNCT
ejpam-4671	152	1	as	as	ADP
ejpam-4671	152	2	an	an	DET
ejpam-4671	152	3	illustration	illustration	NOUN
ejpam-4671	152	4	,	,	PUNCT
ejpam-4671	152	5	consider	consider	VERB
ejpam-4671	152	6	the	the	DET
ejpam-4671	152	7	graph	graph	NOUN
ejpam-4671	152	8	p3	p3	PROPN
ejpam-4671	152	9	◦	◦	NOUN
ejpam-4671	152	10	p4	p4	ADJ
ejpam-4671	152	11	in	in	ADP
ejpam-4671	152	12	figure	figure	NOUN
ejpam-4671	152	13	2	2	NUM
ejpam-4671	152	14	and	and	CCONJ
ejpam-4671	152	15	let	let	VERB
ejpam-4671	152	16	g	g	PROPN
ejpam-4671	152	17	=	=	PROPN
ejpam-4671	152	18	p3	p3	PROPN
ejpam-4671	152	19	and	and	CCONJ
ejpam-4671	152	20	h	h	NOUN
ejpam-4671	152	21	=	=	NOUN
ejpam-4671	152	22	p4	p4	ADJ
ejpam-4671	152	23	.	.	PUNCT
ejpam-4671	153	1	it	it	PRON
ejpam-4671	153	2	can	can	AUX
ejpam-4671	153	3	be	be	AUX
ejpam-4671	153	4	easily	easily	ADV
ejpam-4671	153	5	verified	verify	VERB
ejpam-4671	153	6	that	that	SCONJ
ejpam-4671	153	7	ln(p4	ln(p4	NOUN
ejpam-4671	153	8	)	)	PUNCT
ejpam-4671	153	9	=	=	SYM
ejpam-4671	153	10	sln(p4	sln(p4	PROPN
ejpam-4671	153	11	)	)	PUNCT
ejpam-4671	153	12	=	=	SYM
ejpam-4671	153	13	2	2	NUM
ejpam-4671	153	14	and	and	CCONJ
ejpam-4671	153	15	by	by	ADP
ejpam-4671	153	16	theorem	theorem	NOUN
ejpam-4671	153	17	3	3	NUM
ejpam-4671	153	18	,	,	PUNCT
ejpam-4671	153	19	the	the	DET
ejpam-4671	153	20	set	set	NOUN
ejpam-4671	153	21	of	of	ADP
ejpam-4671	153	22	shaded	shade	VERB
ejpam-4671	153	23	vertices	vertex	NOUN
ejpam-4671	153	24	is	be	AUX
ejpam-4671	153	25	a	a	DET
ejpam-4671	153	26	resolving	resolve	VERB
ejpam-4671	153	27	hop	hop	NOUN
ejpam-4671	153	28	dominating	dominating	NOUN
ejpam-4671	153	29	set	set	NOUN
ejpam-4671	153	30	of	of	ADP
ejpam-4671	153	31	p3	p3	PROPN
ejpam-4671	153	32	◦	◦	NOUN
ejpam-4671	153	33	p4	p4	ADJ
ejpam-4671	153	34	.	.	PUNCT
ejpam-4671	154	1	it	it	PRON
ejpam-4671	154	2	can	can	AUX
ejpam-4671	154	3	be	be	AUX
ejpam-4671	154	4	verified	verify	VERB
ejpam-4671	154	5	that	that	SCONJ
ejpam-4671	154	6	γrh(p3	γrh(p3	PROPN
ejpam-4671	154	7	◦	◦	NOUN
ejpam-4671	154	8	p4	p4	ADJ
ejpam-4671	154	9	)	)	PUNCT
ejpam-4671	154	10	=	=	SYM
ejpam-4671	154	11	6	6	X
ejpam-4671	154	12	.	.	PUNCT
ejpam-4671	154	13	j.	j.	PROPN
ejpam-4671	154	14	mohamad	mohamad	PROPN
ejpam-4671	154	15	,	,	PUNCT
ejpam-4671	154	16	h.	h.	PROPN
ejpam-4671	154	17	rara	rara	PROPN
ejpam-4671	154	18	/	/	SYM
ejpam-4671	154	19	eur	eur	PROPN
ejpam-4671	154	20	.	.	PUNCT
ejpam-4671	155	1	j.	j.	PROPN
ejpam-4671	155	2	pure	pure	PROPN
ejpam-4671	155	3	appl	appl	PROPN
ejpam-4671	155	4	.	.	PROPN
ejpam-4671	155	5	math	math	PROPN
ejpam-4671	155	6	,	,	PUNCT
ejpam-4671	155	7	16	16	NUM
ejpam-4671	155	8	(	(	PUNCT
ejpam-4671	155	9	1	1	NUM
ejpam-4671	155	10	)	)	PUNCT
ejpam-4671	155	11	(	(	PUNCT
ejpam-4671	155	12	2023	2023	NUM
ejpam-4671	155	13	)	)	PUNCT
ejpam-4671	155	14	,	,	PUNCT
ejpam-4671	155	15	418	418	NUM
ejpam-4671	155	16	-	-	SYM
ejpam-4671	155	17	429	429	NUM
ejpam-4671	155	18	424	424	NUM
ejpam-4671	155	19	figure	figure	NOUN
ejpam-4671	155	20	2	2	NUM
ejpam-4671	155	21	:	:	PUNCT
ejpam-4671	155	22	graph	graph	NOUN
ejpam-4671	155	23	p3	p3	PROPN
ejpam-4671	155	24	◦	◦	NOUN
ejpam-4671	155	25	p4	p4	ADJ
ejpam-4671	155	26	with	with	ADP
ejpam-4671	155	27	γrh(p3	γrh(p3	PROPN
ejpam-4671	155	28	◦	◦	NOUN
ejpam-4671	155	29	p4	p4	ADJ
ejpam-4671	155	30	)	)	PUNCT
ejpam-4671	155	31	=	=	SYM
ejpam-4671	155	32	6	6	NUM
ejpam-4671	155	33	theorem	theorem	NOUN
ejpam-4671	155	34	4	4	NUM
ejpam-4671	155	35	.	.	PUNCT
ejpam-4671	156	1	let	let	VERB
ejpam-4671	156	2	g	g	NOUN
ejpam-4671	156	3	and	and	CCONJ
ejpam-4671	156	4	h	h	NOUN
ejpam-4671	156	5	be	be	AUX
ejpam-4671	156	6	nontrivial	nontrivial	ADJ
ejpam-4671	156	7	connected	connected	ADJ
ejpam-4671	156	8	graphs	graph	NOUN
ejpam-4671	156	9	.	.	PUNCT
ejpam-4671	157	1	then	then	ADV
ejpam-4671	157	2	w	w	PROPN
ejpam-4671	157	3	⊆	⊆	NUM
ejpam-4671	157	4	v	v	NOUN
ejpam-4671	157	5	(	(	PUNCT
ejpam-4671	157	6	g	g	PROPN
ejpam-4671	157	7	◦	◦	NOUN
ejpam-4671	157	8	h	h	NOUN
ejpam-4671	157	9	)	)	PUNCT
ejpam-4671	157	10	is	be	AUX
ejpam-4671	157	11	a	a	DET
ejpam-4671	157	12	1	1	NUM
ejpam-4671	157	13	-	-	PUNCT
ejpam-4671	157	14	movable	movable	ADJ
ejpam-4671	157	15	resolving	resolve	VERB
ejpam-4671	157	16	hop	hop	NOUN
ejpam-4671	157	17	dominating	dominating	NOUN
ejpam-4671	157	18	set	set	NOUN
ejpam-4671	157	19	of	of	ADP
ejpam-4671	157	20	g	g	PROPN
ejpam-4671	157	21	◦	◦	NOUN
ejpam-4671	157	22	h	h	NOUN
ejpam-4671	157	23	if	if	SCONJ
ejpam-4671	158	1	and	and	CCONJ
ejpam-4671	158	2	only	only	ADV
ejpam-4671	158	3	if	if	SCONJ
ejpam-4671	158	4	w	w	PROPN
ejpam-4671	158	5	∩	∩	ADJ
ejpam-4671	158	6	v	v	X
ejpam-4671	158	7	(	(	PUNCT
ejpam-4671	158	8	hv	hv	NOUN
ejpam-4671	158	9	)	)	PUNCT
ejpam-4671	158	10	̸=	̸=	PROPN
ejpam-4671	158	11	∅	∅	NOUN
ejpam-4671	158	12	for	for	ADP
ejpam-4671	158	13	every	every	DET
ejpam-4671	158	14	v	v	NUM
ejpam-4671	158	15	∈	∈	PROPN
ejpam-4671	158	16	v	v	NOUN
ejpam-4671	158	17	(	(	PUNCT
ejpam-4671	158	18	g	g	NOUN
ejpam-4671	158	19	)	)	PUNCT
ejpam-4671	158	20	and	and	CCONJ
ejpam-4671	158	21	w	w	NOUN
ejpam-4671	158	22	=	=	NOUN
ejpam-4671	158	23	a	a	PRON
ejpam-4671	158	24	∪	∪	ADJ
ejpam-4671	158	25			PROPN
ejpam-4671	158	26	⋃	⋃	PROPN
ejpam-4671	158	27	v∈ng(a	v∈ng(a	PROPN
ejpam-4671	158	28	)	)	PUNCT
ejpam-4671	158	29	bv	bv	PROPN
ejpam-4671	158	30			PROPN
ejpam-4671	158	31	∪	∪	VERB
ejpam-4671	158	32			PROPN
ejpam-4671	158	33	⋃	⋃	ADJ
ejpam-4671	158	34	u∈v	u∈v	NOUN
ejpam-4671	158	35	(	(	PUNCT
ejpam-4671	158	36	g)\ng(a	g)\ng(a	NOUN
ejpam-4671	158	37	)	)	PUNCT
ejpam-4671	158	38	du	du	NOUN
ejpam-4671	158	39			PROPN
ejpam-4671	158	40	where	where	SCONJ
ejpam-4671	158	41	a	a	DET
ejpam-4671	158	42	⊆	⊆	NUM
ejpam-4671	158	43	v	v	NOUN
ejpam-4671	158	44	(	(	PUNCT
ejpam-4671	158	45	g	g	NOUN
ejpam-4671	158	46	)	)	PUNCT
ejpam-4671	158	47	,	,	PUNCT
ejpam-4671	158	48	bv	bv	PROPN
ejpam-4671	158	49	⊆	⊆	NUM
ejpam-4671	158	50	v	v	PROPN
ejpam-4671	158	51	(	(	PUNCT
ejpam-4671	158	52	hv	hv	NOUN
ejpam-4671	158	53	)	)	PUNCT
ejpam-4671	158	54	for	for	ADP
ejpam-4671	158	55	all	all	DET
ejpam-4671	158	56	v	v	ADP
ejpam-4671	158	57	∈	∈	NOUN
ejpam-4671	158	58	v	v	NOUN
ejpam-4671	158	59	(	(	PUNCT
ejpam-4671	158	60	g	g	NOUN
ejpam-4671	158	61	)	)	PUNCT
ejpam-4671	158	62	∩	∩	NOUN
ejpam-4671	158	63	ng(a	ng(a	NOUN
ejpam-4671	158	64	)	)	PUNCT
ejpam-4671	158	65	and	and	CCONJ
ejpam-4671	158	66	du	du	VERB
ejpam-4671	158	67	⊆	⊆	NUM
ejpam-4671	158	68	v	v	NOUN
ejpam-4671	158	69	(	(	PUNCT
ejpam-4671	158	70	hu	hu	PROPN
ejpam-4671	158	71	)	)	PUNCT
ejpam-4671	158	72	for	for	ADP
ejpam-4671	158	73	all	all	PRON
ejpam-4671	158	74	u	u	PROPN
ejpam-4671	158	75	∈	∈	PROPN
ejpam-4671	158	76	v	v	NOUN
ejpam-4671	158	77	(	(	PUNCT
ejpam-4671	158	78	g	g	NOUN
ejpam-4671	158	79	)	)	PUNCT
ejpam-4671	158	80	\ng(a	\ng(a	PROPN
ejpam-4671	158	81	)	)	PUNCT
ejpam-4671	158	82	are	be	AUX
ejpam-4671	158	83	1	1	NUM
ejpam-4671	158	84	-	-	PUNCT
ejpam-4671	158	85	movable	movable	ADJ
ejpam-4671	158	86	locating	locating	NOUN
ejpam-4671	158	87	and	and	CCONJ
ejpam-4671	158	88	1	1	NUM
ejpam-4671	158	89	-	-	NUM
ejpam-4671	158	90	movable	movable	NOUN
ejpam-4671	158	91	strictly	strictly	ADV
ejpam-4671	158	92	locating	locate	VERB
ejpam-4671	158	93	sets	set	NOUN
ejpam-4671	158	94	of	of	ADP
ejpam-4671	158	95	hv	hv	PROPN
ejpam-4671	158	96	and	and	CCONJ
ejpam-4671	158	97	hu	hu	PROPN
ejpam-4671	158	98	,	,	PUNCT
ejpam-4671	158	99	respectively	respectively	ADV
ejpam-4671	158	100	.	.	PUNCT
ejpam-4671	159	1	proof	proof	NOUN
ejpam-4671	159	2	:	:	PUNCT
ejpam-4671	159	3	suppose	suppose	VERB
ejpam-4671	159	4	that	that	SCONJ
ejpam-4671	159	5	w	w	PROPN
ejpam-4671	159	6	⊆	⊆	NUM
ejpam-4671	159	7	v	v	NOUN
ejpam-4671	159	8	(	(	PUNCT
ejpam-4671	159	9	g	g	PROPN
ejpam-4671	159	10	◦	◦	NOUN
ejpam-4671	159	11	h	h	NOUN
ejpam-4671	159	12	)	)	PUNCT
ejpam-4671	159	13	is	be	AUX
ejpam-4671	159	14	a	a	DET
ejpam-4671	159	15	1	1	NUM
ejpam-4671	159	16	-	-	PUNCT
ejpam-4671	159	17	movable	movable	ADJ
ejpam-4671	159	18	resolving	resolve	VERB
ejpam-4671	159	19	hop	hop	NOUN
ejpam-4671	159	20	dominating	dominating	NOUN
ejpam-4671	159	21	set	set	NOUN
ejpam-4671	159	22	of	of	ADP
ejpam-4671	159	23	g	g	PROPN
ejpam-4671	159	24	◦	◦	NOUN
ejpam-4671	159	25	h.	h.	PROPN
ejpam-4671	159	26	then	then	ADV
ejpam-4671	159	27	w	w	PROPN
ejpam-4671	159	28	is	be	AUX
ejpam-4671	159	29	a	a	DET
ejpam-4671	159	30	resolving	resolve	VERB
ejpam-4671	159	31	hop	hop	NOUN
ejpam-4671	159	32	dominating	dominating	NOUN
ejpam-4671	159	33	set	set	NOUN
ejpam-4671	159	34	.	.	PUNCT
ejpam-4671	160	1	by	by	ADP
ejpam-4671	160	2	theorem	theorem	NOUN
ejpam-4671	160	3	3	3	NUM
ejpam-4671	160	4	,	,	PUNCT
ejpam-4671	160	5	w	w	PROPN
ejpam-4671	160	6	∩	∩	ADJ
ejpam-4671	160	7	v	v	X
ejpam-4671	160	8	(	(	PUNCT
ejpam-4671	160	9	hv	hv	NOUN
ejpam-4671	160	10	)	)	PUNCT
ejpam-4671	160	11	̸=	̸=	PROPN
ejpam-4671	160	12	∅	∅	NOUN
ejpam-4671	160	13	and	and	CCONJ
ejpam-4671	160	14	w	w	NOUN
ejpam-4671	160	15	∩v	∩v	NOUN
ejpam-4671	160	16	(	(	PUNCT
ejpam-4671	160	17	hv	hv	X
ejpam-4671	160	18	)	)	PUNCT
ejpam-4671	160	19	is	be	AUX
ejpam-4671	160	20	a	a	DET
ejpam-4671	160	21	locating	locating	NOUN
ejpam-4671	160	22	set	set	NOUN
ejpam-4671	160	23	of	of	ADP
ejpam-4671	160	24	hv	hv	NOUN
ejpam-4671	160	25	for	for	ADP
ejpam-4671	160	26	all	all	PRON
ejpam-4671	160	27	v	v	ADP
ejpam-4671	160	28	∈	∈	NUM
ejpam-4671	160	29	v	v	NOUN
ejpam-4671	160	30	(	(	PUNCT
ejpam-4671	160	31	g	g	NOUN
ejpam-4671	160	32	)	)	PUNCT
ejpam-4671	160	33	.	.	PUNCT
ejpam-4671	161	1	let	let	VERB
ejpam-4671	161	2	a	a	DET
ejpam-4671	161	3	=	=	PROPN
ejpam-4671	161	4	w	w	PROPN
ejpam-4671	161	5	∩v	∩v	NOUN
ejpam-4671	161	6	(	(	PUNCT
ejpam-4671	161	7	g	g	NOUN
ejpam-4671	161	8	)	)	PUNCT
ejpam-4671	161	9	,	,	PUNCT
ejpam-4671	161	10	bv	bv	PROPN
ejpam-4671	161	11	=	=	PROPN
ejpam-4671	161	12	w	w	PROPN
ejpam-4671	161	13	∩v	∩v	PROPN
ejpam-4671	161	14	(	(	PUNCT
ejpam-4671	161	15	hv	hv	X
ejpam-4671	161	16	)	)	PUNCT
ejpam-4671	161	17	for	for	ADP
ejpam-4671	161	18	all	all	DET
ejpam-4671	161	19	v	v	ADP
ejpam-4671	161	20	∈	∈	NOUN
ejpam-4671	161	21	v	v	NOUN
ejpam-4671	161	22	(	(	PUNCT
ejpam-4671	161	23	g	g	NOUN
ejpam-4671	161	24	)	)	PUNCT
ejpam-4671	161	25	∩ng(a	∩ng(a	NOUN
ejpam-4671	161	26	)	)	PUNCT
ejpam-4671	161	27	and	and	CCONJ
ejpam-4671	161	28	du	du	PROPN
ejpam-4671	161	29	=	=	SYM
ejpam-4671	161	30	w	w	PROPN
ejpam-4671	161	31	∩	∩	PROPN
ejpam-4671	161	32	v	v	X
ejpam-4671	161	33	(	(	PUNCT
ejpam-4671	161	34	hu	hu	PROPN
ejpam-4671	161	35	)	)	PUNCT
ejpam-4671	161	36	for	for	ADP
ejpam-4671	161	37	all	all	DET
ejpam-4671	161	38	u	u	PROPN
ejpam-4671	161	39	∈	∈	PROPN
ejpam-4671	161	40	v	v	NOUN
ejpam-4671	161	41	(	(	PUNCT
ejpam-4671	161	42	g	g	NOUN
ejpam-4671	161	43	)	)	PUNCT
ejpam-4671	161	44	\ng(a	\ng(a	PROPN
ejpam-4671	161	45	)	)	PUNCT
ejpam-4671	161	46	.	.	PUNCT
ejpam-4671	162	1	by	by	ADP
ejpam-4671	162	2	theorem	theorem	NOUN
ejpam-4671	162	3	3	3	NUM
ejpam-4671	162	4	,	,	PUNCT
ejpam-4671	162	5	bv	bv	PROPN
ejpam-4671	162	6	is	be	AUX
ejpam-4671	162	7	a	a	DET
ejpam-4671	162	8	locating	locating	NOUN
ejpam-4671	162	9	set	set	NOUN
ejpam-4671	162	10	of	of	ADP
ejpam-4671	162	11	hv	hv	PROPN
ejpam-4671	162	12	and	and	CCONJ
ejpam-4671	162	13	du	du	PROPN
ejpam-4671	162	14	is	be	AUX
ejpam-4671	162	15	a	a	DET
ejpam-4671	162	16	strictly	strictly	ADV
ejpam-4671	162	17	locating	locate	VERB
ejpam-4671	162	18	set	set	NOUN
ejpam-4671	162	19	of	of	ADP
ejpam-4671	162	20	hu	hu	PROPN
ejpam-4671	162	21	.	.	PUNCT
ejpam-4671	163	1	let	let	VERB
ejpam-4671	163	2	x	x	SYM
ejpam-4671	163	3	∈	∈	PROPN
ejpam-4671	163	4	bv	bv	PROPN
ejpam-4671	163	5	.	.	PROPN
ejpam-4671	164	1	since	since	SCONJ
ejpam-4671	164	2	w	w	PROPN
ejpam-4671	164	3	is	be	AUX
ejpam-4671	164	4	a	a	DET
ejpam-4671	164	5	1	1	NUM
ejpam-4671	164	6	-	-	PUNCT
ejpam-4671	164	7	movable	movable	ADJ
ejpam-4671	164	8	resolving	resolve	VERB
ejpam-4671	164	9	hop	hop	NOUN
ejpam-4671	164	10	dominating	dominating	NOUN
ejpam-4671	164	11	set	set	NOUN
ejpam-4671	164	12	and	and	CCONJ
ejpam-4671	164	13	x	x	SYM
ejpam-4671	164	14	∈	∈	PROPN
ejpam-4671	164	15	w	w	NOUN
ejpam-4671	164	16	,	,	PUNCT
ejpam-4671	164	17	either	either	CCONJ
ejpam-4671	164	18	w	w	ADP
ejpam-4671	164	19	\	\	NOUN
ejpam-4671	164	20	{	{	PUNCT
ejpam-4671	164	21	x	x	NOUN
ejpam-4671	164	22	}	}	PUNCT
ejpam-4671	164	23	is	be	AUX
ejpam-4671	164	24	a	a	DET
ejpam-4671	164	25	resolving	resolve	VERB
ejpam-4671	164	26	hop	hop	NOUN
ejpam-4671	164	27	dominating	dominating	NOUN
ejpam-4671	164	28	set	set	NOUN
ejpam-4671	164	29	of	of	ADP
ejpam-4671	164	30	g	g	PROPN
ejpam-4671	164	31	◦	◦	NOUN
ejpam-4671	164	32	h	h	NOUN
ejpam-4671	164	33	or	or	CCONJ
ejpam-4671	164	34	there	there	PRON
ejpam-4671	164	35	exists	exist	VERB
ejpam-4671	164	36	y	y	PROPN
ejpam-4671	164	37	∈	∈	PROPN
ejpam-4671	164	38	(	(	PUNCT
ejpam-4671	164	39	v	v	NOUN
ejpam-4671	164	40	(	(	PUNCT
ejpam-4671	164	41	g	g	PROPN
ejpam-4671	164	42	◦	◦	NOUN
ejpam-4671	164	43	h	h	NOUN
ejpam-4671	164	44	)	)	PUNCT
ejpam-4671	164	45	\	\	PROPN
ejpam-4671	164	46	w	w	PROPN
ejpam-4671	164	47	)	)	PUNCT
ejpam-4671	164	48	∩	∩	PROPN
ejpam-4671	164	49	ng	ng	PROPN
ejpam-4671	164	50	◦	◦	PROPN
ejpam-4671	164	51	h(x	h(x	PROPN
ejpam-4671	164	52	)	)	PUNCT
ejpam-4671	164	53	such	such	ADJ
ejpam-4671	164	54	that	that	SCONJ
ejpam-4671	164	55	(	(	PUNCT
ejpam-4671	164	56	w	w	PROPN
ejpam-4671	164	57	\	\	PUNCT
ejpam-4671	164	58	{	{	PUNCT
ejpam-4671	164	59	x	x	NOUN
ejpam-4671	164	60	}	}	PUNCT
ejpam-4671	164	61	)	)	PUNCT
ejpam-4671	164	62	∪	∪	ADP
ejpam-4671	164	63	{	{	PUNCT
ejpam-4671	164	64	y	y	NOUN
ejpam-4671	164	65	}	}	PUNCT
ejpam-4671	164	66	is	be	AUX
ejpam-4671	164	67	a	a	DET
ejpam-4671	164	68	resolving	resolve	VERB
ejpam-4671	164	69	hop	hop	NOUN
ejpam-4671	164	70	dominating	dominating	NOUN
ejpam-4671	164	71	set	set	NOUN
ejpam-4671	164	72	of	of	ADP
ejpam-4671	164	73	g	g	PROPN
ejpam-4671	164	74	◦	◦	PROPN
ejpam-4671	164	75	h.	h.	NOUN
ejpam-4671	164	76	note	note	NOUN
ejpam-4671	164	77	that	that	SCONJ
ejpam-4671	164	78	w	w	ADP
ejpam-4671	164	79	\	\	NOUN
ejpam-4671	164	80	{	{	PUNCT
ejpam-4671	164	81	x	x	NOUN
ejpam-4671	164	82	}	}	PUNCT
ejpam-4671	164	83	=	=	SYM
ejpam-4671	164	84	(	(	PUNCT
ejpam-4671	164	85	bv	bv	PROPN
ejpam-4671	164	86	\	\	PROPN
ejpam-4671	164	87	{	{	PUNCT
ejpam-4671	164	88	x	x	NOUN
ejpam-4671	164	89	}	}	PUNCT
ejpam-4671	164	90	)	)	PUNCT
ejpam-4671	164	91	∪	∪	ADP
ejpam-4671	164	92			PROPN
ejpam-4671	164	93	⋃	⋃	ADJ
ejpam-4671	164	94	u∈v	u∈v	NOUN
ejpam-4671	164	95	(	(	PUNCT
ejpam-4671	164	96	g)\{v	g)\{v	PROPN
ejpam-4671	164	97	}	}	PUNCT
ejpam-4671	164	98	d∗	d∗	PROPN
ejpam-4671	164	99	u	u	NOUN
ejpam-4671	164	100			PROPN
ejpam-4671	164	101	∪a	∪a	X
ejpam-4671	164	102	and	and	CCONJ
ejpam-4671	164	103	(	(	PUNCT
ejpam-4671	164	104	w\{x})∪{y	w\{x})∪{y	NOUN
ejpam-4671	164	105	}	}	PUNCT
ejpam-4671	164	106	is	be	AUX
ejpam-4671	164	107	equal	equal	ADJ
ejpam-4671	164	108	to	to	ADP
ejpam-4671	164	109	(	(	PUNCT
ejpam-4671	164	110	(	(	PUNCT
ejpam-4671	164	111	bv	bv	PROPN
ejpam-4671	164	112	\	\	PROPN
ejpam-4671	164	113	{	{	PUNCT
ejpam-4671	164	114	x	x	NOUN
ejpam-4671	164	115	}	}	PUNCT
ejpam-4671	164	116	)	)	PUNCT
ejpam-4671	164	117	∪	∪	ADP
ejpam-4671	164	118	{	{	PUNCT
ejpam-4671	164	119	y})∪	y})∪	PROPN
ejpam-4671	164	120			PROPN
ejpam-4671	164	121	⋃	⋃	ADJ
ejpam-4671	164	122	u∈v	u∈v	NOUN
ejpam-4671	164	123	(	(	PUNCT
ejpam-4671	164	124	g)\{v	g)\{v	PROPN
ejpam-4671	164	125	}	}	PUNCT
ejpam-4671	164	126	d∗	d∗	VERB
ejpam-4671	164	127	u	u	NOUN
ejpam-4671	164	128	∪a	∪a	PRON
ejpam-4671	164	129	if	if	SCONJ
ejpam-4671	164	130	y	y	PROPN
ejpam-4671	164	131	∈	∈	PROPN
ejpam-4671	164	132	v	v	ADP
ejpam-4671	164	133	(	(	PUNCT
ejpam-4671	164	134	hv)\bv	hv)\bv	NOUN
ejpam-4671	164	135	or	or	CCONJ
ejpam-4671	164	136	equal	equal	ADJ
ejpam-4671	164	137	to	to	ADP
ejpam-4671	164	138	(	(	PUNCT
ejpam-4671	164	139	bv	bv	PROPN
ejpam-4671	164	140	\	\	PROPN
ejpam-4671	164	141	{	{	PUNCT
ejpam-4671	164	142	x	x	NOUN
ejpam-4671	164	143	}	}	PUNCT
ejpam-4671	164	144	)	)	PUNCT
ejpam-4671	164	145	∪	∪	ADP
ejpam-4671	164	146			PROPN
ejpam-4671	164	147	⋃	⋃	ADJ
ejpam-4671	164	148	u∈v	u∈v	NOUN
ejpam-4671	164	149	(	(	PUNCT
ejpam-4671	164	150	g)\{v	g)\{v	PROPN
ejpam-4671	164	151	}	}	PUNCT
ejpam-4671	164	152	d∗	d∗	PROPN
ejpam-4671	164	153	u	u	NOUN
ejpam-4671	164	154			PROPN
ejpam-4671	164	155	∪	∪	ADV
ejpam-4671	164	156	(	(	PUNCT
ejpam-4671	164	157	a	a	DET
ejpam-4671	164	158	∪	∪	ADJ
ejpam-4671	164	159	{	{	PUNCT
ejpam-4671	164	160	y	y	NOUN
ejpam-4671	164	161	}	}	PUNCT
ejpam-4671	164	162	)	)	PUNCT
ejpam-4671	164	163	if	if	SCONJ
ejpam-4671	164	164	y	y	PROPN
ejpam-4671	164	165	=	=	SYM
ejpam-4671	164	166	v	v	PROPN
ejpam-4671	164	167	∈	∈	PROPN
ejpam-4671	164	168	v	v	NOUN
ejpam-4671	164	169	(	(	PUNCT
ejpam-4671	164	170	g	g	NOUN
ejpam-4671	164	171	)	)	PUNCT
ejpam-4671	165	1	\	\	NOUN
ejpam-4671	165	2	a.	a.	NOUN
ejpam-4671	165	3	hence	hence	ADV
ejpam-4671	165	4	,	,	PUNCT
ejpam-4671	165	5	either	either	CCONJ
ejpam-4671	165	6	bv	bv	PROPN
ejpam-4671	165	7	\	\	PROPN
ejpam-4671	165	8	{	{	PUNCT
ejpam-4671	165	9	x	x	X
ejpam-4671	165	10	}	}	PUNCT
ejpam-4671	165	11	is	be	AUX
ejpam-4671	165	12	a	a	DET
ejpam-4671	165	13	locating	locating	NOUN
ejpam-4671	165	14	set	set	NOUN
ejpam-4671	165	15	of	of	ADP
ejpam-4671	165	16	hv	hv	PROPN
ejpam-4671	165	17	or	or	CCONJ
ejpam-4671	165	18	(	(	PUNCT
ejpam-4671	165	19	bv	bv	PROPN
ejpam-4671	165	20	\	\	PROPN
ejpam-4671	165	21	{	{	PUNCT
ejpam-4671	165	22	x	x	NOUN
ejpam-4671	165	23	}	}	PUNCT
ejpam-4671	165	24	)	)	PUNCT
ejpam-4671	165	25	∪	∪	ADP
ejpam-4671	165	26	{	{	PUNCT
ejpam-4671	165	27	y	y	NOUN
ejpam-4671	165	28	}	}	PUNCT
ejpam-4671	165	29	for	for	ADP
ejpam-4671	165	30	some	some	DET
ejpam-4671	165	31	y	y	PROPN
ejpam-4671	165	32	∈	∈	PROPN
ejpam-4671	165	33	(	(	PUNCT
ejpam-4671	165	34	v	v	NOUN
ejpam-4671	165	35	(	(	PUNCT
ejpam-4671	165	36	hv	hv	PROPN
ejpam-4671	165	37	)	)	PUNCT
ejpam-4671	165	38	\	\	PROPN
ejpam-4671	165	39	bv	bv	PROPN
ejpam-4671	165	40	)	)	PUNCT
ejpam-4671	165	41	∩	∩	NOUN
ejpam-4671	165	42	nhv(x	nhv(x	X
ejpam-4671	165	43	)	)	PUNCT
ejpam-4671	165	44	is	be	AUX
ejpam-4671	165	45	a	a	DET
ejpam-4671	165	46	locating	locate	VERB
ejpam-4671	165	47	set	set	NOUN
ejpam-4671	165	48	of	of	ADP
ejpam-4671	165	49	hv	hv	PROPN
ejpam-4671	165	50	.	.	PUNCT
ejpam-4671	166	1	thus	thus	ADV
ejpam-4671	166	2	,	,	PUNCT
ejpam-4671	166	3	bv	bv	PROPN
ejpam-4671	166	4	is	be	AUX
ejpam-4671	166	5	a	a	DET
ejpam-4671	166	6	movable	movable	ADJ
ejpam-4671	166	7	locating	locating	NOUN
ejpam-4671	166	8	set	set	NOUN
ejpam-4671	166	9	of	of	ADP
ejpam-4671	166	10	hv	hv	PROPN
ejpam-4671	166	11	.	.	PUNCT
ejpam-4671	167	1	the	the	DET
ejpam-4671	167	2	proof	proof	NOUN
ejpam-4671	167	3	that	that	SCONJ
ejpam-4671	167	4	du	du	PROPN
ejpam-4671	167	5	is	be	AUX
ejpam-4671	167	6	a	a	DET
ejpam-4671	167	7	1	1	NUM
ejpam-4671	167	8	-	-	PUNCT
ejpam-4671	167	9	movable	movable	NOUN
ejpam-4671	167	10	strictly	strictly	ADV
ejpam-4671	167	11	locating	locate	VERB
ejpam-4671	167	12	set	set	NOUN
ejpam-4671	167	13	of	of	ADP
ejpam-4671	167	14	hu	hu	PROPN
ejpam-4671	167	15	is	be	AUX
ejpam-4671	167	16	similar	similar	ADJ
ejpam-4671	167	17	.	.	PUNCT
ejpam-4671	168	1	for	for	ADP
ejpam-4671	168	2	the	the	DET
ejpam-4671	168	3	converse	converse	NOUN
ejpam-4671	168	4	,	,	PUNCT
ejpam-4671	168	5	suppose	suppose	VERB
ejpam-4671	168	6	that	that	SCONJ
ejpam-4671	168	7	w	w	NOUN
ejpam-4671	168	8	is	be	AUX
ejpam-4671	168	9	a	a	DET
ejpam-4671	168	10	set	set	NOUN
ejpam-4671	168	11	described	describe	VERB
ejpam-4671	168	12	above	above	ADV
ejpam-4671	168	13	.	.	PUNCT
ejpam-4671	169	1	then	then	ADV
ejpam-4671	169	2	by	by	ADP
ejpam-4671	169	3	theorem	theorem	NOUN
ejpam-4671	169	4	3	3	NUM
ejpam-4671	169	5	,	,	PUNCT
ejpam-4671	169	6	w	w	PROPN
ejpam-4671	169	7	is	be	AUX
ejpam-4671	169	8	a	a	DET
ejpam-4671	169	9	resolving	resolve	VERB
ejpam-4671	169	10	hop	hop	NOUN
ejpam-4671	169	11	dominating	dominating	NOUN
ejpam-4671	169	12	set	set	NOUN
ejpam-4671	169	13	.	.	PUNCT
ejpam-4671	170	1	let	let	VERB
ejpam-4671	170	2	x	x	SYM
ejpam-4671	170	3	∈	∈	PROPN
ejpam-4671	170	4	w	w	NOUN
ejpam-4671	170	5	and	and	CCONJ
ejpam-4671	170	6	let	let	VERB
ejpam-4671	170	7	v	v	NUM
ejpam-4671	170	8	∈	∈	PROPN
ejpam-4671	170	9	v	v	NOUN
ejpam-4671	170	10	(	(	PUNCT
ejpam-4671	170	11	g	g	NOUN
ejpam-4671	170	12	)	)	PUNCT
ejpam-4671	170	13	such	such	ADJ
ejpam-4671	170	14	that	that	SCONJ
ejpam-4671	170	15	x	x	SYM
ejpam-4671	170	16	∈	∈	PROPN
ejpam-4671	170	17	v	v	X
ejpam-4671	170	18	(	(	PUNCT
ejpam-4671	170	19	⟨v⟩+hv	⟨v⟩+hv	NOUN
ejpam-4671	170	20	)	)	PUNCT
ejpam-4671	170	21	.	.	PUNCT
ejpam-4671	171	1	suppose	suppose	VERB
ejpam-4671	171	2	that	that	SCONJ
ejpam-4671	171	3	x	x	X
ejpam-4671	171	4	̸=	̸=	PROPN
ejpam-4671	171	5	v.	v.	CCONJ
ejpam-4671	171	6	consider	consider	VERB
ejpam-4671	171	7	the	the	DET
ejpam-4671	171	8	following	follow	VERB
ejpam-4671	171	9	cases	case	NOUN
ejpam-4671	171	10	.	.	PUNCT
ejpam-4671	172	1	j.	j.	PROPN
ejpam-4671	172	2	mohamad	mohamad	PROPN
ejpam-4671	172	3	,	,	PUNCT
ejpam-4671	172	4	h.	h.	PROPN
ejpam-4671	172	5	rara	rara	PROPN
ejpam-4671	172	6	/	/	SYM
ejpam-4671	172	7	eur	eur	PROPN
ejpam-4671	172	8	.	.	PUNCT
ejpam-4671	173	1	j.	j.	PROPN
ejpam-4671	173	2	pure	pure	PROPN
ejpam-4671	173	3	appl	appl	PROPN
ejpam-4671	173	4	.	.	PROPN
ejpam-4671	173	5	math	math	PROPN
ejpam-4671	173	6	,	,	PUNCT
ejpam-4671	173	7	16	16	NUM
ejpam-4671	173	8	(	(	PUNCT
ejpam-4671	173	9	1	1	NUM
ejpam-4671	173	10	)	)	PUNCT
ejpam-4671	173	11	(	(	PUNCT
ejpam-4671	173	12	2023	2023	NUM
ejpam-4671	173	13	)	)	PUNCT
ejpam-4671	173	14	,	,	PUNCT
ejpam-4671	173	15	418	418	NUM
ejpam-4671	173	16	-	-	SYM
ejpam-4671	173	17	429	429	NUM
ejpam-4671	173	18	425	425	NUM
ejpam-4671	173	19	case	case	NOUN
ejpam-4671	173	20	1	1	NUM
ejpam-4671	173	21	.	.	PUNCT
ejpam-4671	173	22	v	v	NUM
ejpam-4671	173	23	∈	∈	PROPN
ejpam-4671	173	24	v	v	NOUN
ejpam-4671	173	25	(	(	PUNCT
ejpam-4671	173	26	g	g	NOUN
ejpam-4671	173	27	)	)	PUNCT
ejpam-4671	173	28	∩ng(a	∩ng(a	NOUN
ejpam-4671	173	29	)	)	PUNCT
ejpam-4671	173	30	then	then	ADV
ejpam-4671	173	31	x	x	SYM
ejpam-4671	173	32	∈	∈	PROPN
ejpam-4671	173	33	bv	bv	PROPN
ejpam-4671	173	34	and	and	CCONJ
ejpam-4671	173	35	w	w	PROPN
ejpam-4671	173	36	\	\	PROPN
ejpam-4671	173	37	{	{	PUNCT
ejpam-4671	173	38	x	x	NOUN
ejpam-4671	173	39	}	}	PUNCT
ejpam-4671	173	40	=	=	SYM
ejpam-4671	173	41	(	(	PUNCT
ejpam-4671	173	42	bv	bv	PROPN
ejpam-4671	173	43	\	\	PROPN
ejpam-4671	173	44	{	{	PUNCT
ejpam-4671	173	45	x	x	NOUN
ejpam-4671	173	46	}	}	PUNCT
ejpam-4671	173	47	)	)	PUNCT
ejpam-4671	173	48	∪	∪	ADP
ejpam-4671	173	49			PROPN
ejpam-4671	173	50	⋃	⋃	ADJ
ejpam-4671	173	51	u∈v	u∈v	NOUN
ejpam-4671	173	52	(	(	PUNCT
ejpam-4671	173	53	g)\{v	g)\{v	PROPN
ejpam-4671	173	54	}	}	PUNCT
ejpam-4671	173	55	du	du	NOUN
ejpam-4671	173	56			PROPN
ejpam-4671	173	57	∪	∪	VERB
ejpam-4671	173	58	a	a	PRON
ejpam-4671	173	59	or	or	CCONJ
ejpam-4671	173	60	(	(	PUNCT
ejpam-4671	173	61	w	w	PROPN
ejpam-4671	173	62	\	\	NOUN
ejpam-4671	173	63	{	{	PUNCT
ejpam-4671	173	64	x	x	NOUN
ejpam-4671	173	65	}	}	PUNCT
ejpam-4671	173	66	)	)	PUNCT
ejpam-4671	173	67	∪	∪	ADP
ejpam-4671	173	68	{	{	PUNCT
ejpam-4671	173	69	y	y	NOUN
ejpam-4671	173	70	}	}	PUNCT
ejpam-4671	173	71	for	for	ADP
ejpam-4671	173	72	some	some	DET
ejpam-4671	173	73	y	y	PROPN
ejpam-4671	173	74	∈	∈	PROPN
ejpam-4671	173	75	(	(	PUNCT
ejpam-4671	173	76	v	v	NOUN
ejpam-4671	173	77	(	(	PUNCT
ejpam-4671	173	78	g	g	PROPN
ejpam-4671	173	79	◦	◦	NOUN
ejpam-4671	173	80	h	h	NOUN
ejpam-4671	173	81	)	)	PUNCT
ejpam-4671	173	82	\	\	PROPN
ejpam-4671	173	83	w	w	PROPN
ejpam-4671	173	84	)	)	PUNCT
ejpam-4671	173	85	∩	∩	PROPN
ejpam-4671	173	86	ng	ng	PROPN
ejpam-4671	173	87	◦	◦	PROPN
ejpam-4671	173	88	h(x	h(x	PROPN
ejpam-4671	173	89	)	)	PUNCT
ejpam-4671	173	90	is	be	AUX
ejpam-4671	173	91	a	a	DET
ejpam-4671	173	92	resolving	resolve	VERB
ejpam-4671	173	93	hop	hop	NOUN
ejpam-4671	173	94	dominating	dominating	NOUN
ejpam-4671	173	95	set	set	VERB
ejpam-4671	173	96	by	by	ADP
ejpam-4671	173	97	theorem	theorem	ADJ
ejpam-4671	173	98	3	3	NUM
ejpam-4671	173	99	.	.	NOUN
ejpam-4671	173	100	case	case	NOUN
ejpam-4671	173	101	2	2	NUM
ejpam-4671	173	102	.	.	NOUN
ejpam-4671	173	103	v	v	NUM
ejpam-4671	173	104	∈	∈	PROPN
ejpam-4671	173	105	v	v	NOUN
ejpam-4671	173	106	(	(	PUNCT
ejpam-4671	173	107	g	g	NOUN
ejpam-4671	173	108	)	)	PUNCT
ejpam-4671	173	109	\ng(a	\ng(a	PROPN
ejpam-4671	173	110	)	)	PUNCT
ejpam-4671	173	111	then	then	ADV
ejpam-4671	173	112	x	x	SYM
ejpam-4671	173	113	∈	∈	PROPN
ejpam-4671	173	114	dv	dv	PROPN
ejpam-4671	173	115	and	and	CCONJ
ejpam-4671	173	116	w	w	PROPN
ejpam-4671	173	117	\	\	PROPN
ejpam-4671	173	118	{	{	PUNCT
ejpam-4671	173	119	x	x	NOUN
ejpam-4671	173	120	}	}	PUNCT
ejpam-4671	173	121	=	=	SYM
ejpam-4671	173	122	(	(	PUNCT
ejpam-4671	173	123	dv	dv	PROPN
ejpam-4671	173	124	\	\	PROPN
ejpam-4671	173	125	{	{	PUNCT
ejpam-4671	173	126	x	x	NOUN
ejpam-4671	173	127	}	}	PUNCT
ejpam-4671	173	128	)	)	PUNCT
ejpam-4671	173	129	∪	∪	ADP
ejpam-4671	173	130			PROPN
ejpam-4671	173	131	⋃	⋃	ADJ
ejpam-4671	173	132	u∈v	u∈v	NOUN
ejpam-4671	173	133	(	(	PUNCT
ejpam-4671	173	134	g)\{v	g)\{v	PROPN
ejpam-4671	173	135	}	}	PUNCT
ejpam-4671	173	136	bu	bu	ADP
ejpam-4671	173	137			PROPN
ejpam-4671	173	138	∪	∪	VERB
ejpam-4671	173	139	a	a	PRON
ejpam-4671	173	140	or	or	CCONJ
ejpam-4671	173	141	(	(	PUNCT
ejpam-4671	173	142	w	w	PROPN
ejpam-4671	173	143	\	\	NOUN
ejpam-4671	173	144	{	{	PUNCT
ejpam-4671	173	145	x	x	NOUN
ejpam-4671	173	146	}	}	PUNCT
ejpam-4671	173	147	)	)	PUNCT
ejpam-4671	173	148	∪	∪	ADP
ejpam-4671	173	149	{	{	PUNCT
ejpam-4671	173	150	y	y	NOUN
ejpam-4671	173	151	}	}	PUNCT
ejpam-4671	173	152	is	be	AUX
ejpam-4671	173	153	a	a	DET
ejpam-4671	173	154	resolving	resolve	VERB
ejpam-4671	173	155	hop	hop	NOUN
ejpam-4671	173	156	dominating	dominating	NOUN
ejpam-4671	173	157	set	set	VERB
ejpam-4671	173	158	by	by	ADP
ejpam-4671	173	159	theorem	theorem	NOUN
ejpam-4671	173	160	3	3	NUM
ejpam-4671	173	161	.	.	X
ejpam-4671	174	1	therefore	therefore	ADV
ejpam-4671	174	2	w	w	PROPN
ejpam-4671	174	3	is	be	AUX
ejpam-4671	174	4	a	a	DET
ejpam-4671	174	5	1	1	NUM
ejpam-4671	174	6	-	-	PUNCT
ejpam-4671	174	7	movable	movable	ADJ
ejpam-4671	174	8	resolving	resolve	VERB
ejpam-4671	174	9	hop	hop	NOUN
ejpam-4671	174	10	dominating	dominating	NOUN
ejpam-4671	174	11	set	set	NOUN
ejpam-4671	174	12	of	of	ADP
ejpam-4671	174	13	g	g	PROPN
ejpam-4671	174	14	◦	◦	NOUN
ejpam-4671	174	15	h.	h.	NOUN
ejpam-4671	174	16	corollary	corollary	ADJ
ejpam-4671	174	17	4	4	NUM
ejpam-4671	174	18	.	.	PUNCT
ejpam-4671	175	1	let	let	VERB
ejpam-4671	175	2	g	g	NOUN
ejpam-4671	175	3	and	and	CCONJ
ejpam-4671	175	4	h	h	NOUN
ejpam-4671	175	5	be	be	AUX
ejpam-4671	175	6	nontrivial	nontrivial	ADJ
ejpam-4671	175	7	connected	connect	VERB
ejpam-4671	175	8	graphs	graph	NOUN
ejpam-4671	175	9	where	where	SCONJ
ejpam-4671	175	10	|v	|v	PROPN
ejpam-4671	175	11	(	(	PUNCT
ejpam-4671	175	12	g)|	g)|	PROPN
ejpam-4671	175	13	=	=	SYM
ejpam-4671	175	14	p.	p.	NOUN
ejpam-4671	175	15	then	then	ADV
ejpam-4671	175	16	γ1mrrh(g	γ1mrrh(g	VERB
ejpam-4671	175	17	◦	◦	NOUN
ejpam-4671	175	18	h	h	NOUN
ejpam-4671	175	19	)	)	PUNCT
ejpam-4671	175	20	≤	≤	NUM
ejpam-4671	175	21	min	min	NOUN
ejpam-4671	175	22	{	{	PUNCT
ejpam-4671	175	23	p(msln(h	p(msln(h	PROPN
ejpam-4671	175	24	)	)	PUNCT
ejpam-4671	175	25	)	)	PUNCT
ejpam-4671	175	26	,	,	PUNCT
ejpam-4671	175	27	γt(g	γt(g	PUNCT
ejpam-4671	175	28	)	)	PUNCT
ejpam-4671	176	1	+	+	CCONJ
ejpam-4671	176	2	p(mln(h	p(mln(h	NOUN
ejpam-4671	176	3	)	)	PUNCT
ejpam-4671	176	4	)	)	PUNCT
ejpam-4671	176	5	}	}	PUNCT
ejpam-4671	176	6	.	.	PUNCT
ejpam-4671	177	1	proof	proof	NOUN
ejpam-4671	177	2	:	:	PUNCT
ejpam-4671	177	3	let	let	VERB
ejpam-4671	177	4	w	w	ADP
ejpam-4671	177	5	⊆	⊆	NUM
ejpam-4671	177	6	v	v	NOUN
ejpam-4671	177	7	(	(	PUNCT
ejpam-4671	177	8	g	g	PROPN
ejpam-4671	177	9	◦	◦	NOUN
ejpam-4671	177	10	h	h	NOUN
ejpam-4671	177	11	)	)	PUNCT
ejpam-4671	177	12	be	be	VERB
ejpam-4671	177	13	a	a	DET
ejpam-4671	177	14	1	1	NUM
ejpam-4671	177	15	-	-	PUNCT
ejpam-4671	177	16	movable	movable	ADJ
ejpam-4671	177	17	resolving	resolve	VERB
ejpam-4671	177	18	hop	hop	NOUN
ejpam-4671	177	19	dominating	dominating	NOUN
ejpam-4671	177	20	set	set	NOUN
ejpam-4671	177	21	of	of	ADP
ejpam-4671	177	22	g	g	PROPN
ejpam-4671	177	23	◦	◦	PROPN
ejpam-4671	177	24	h.	h.	PROPN
ejpam-4671	177	25	then	then	ADV
ejpam-4671	177	26	w	w	PROPN
ejpam-4671	177	27	∩	∩	PROPN
ejpam-4671	177	28	v	v	X
ejpam-4671	177	29	(	(	PUNCT
ejpam-4671	177	30	hv	hv	NOUN
ejpam-4671	177	31	)	)	PUNCT
ejpam-4671	177	32	̸=	̸=	PROPN
ejpam-4671	177	33	∅	∅	NOUN
ejpam-4671	177	34	and	and	CCONJ
ejpam-4671	177	35	w	w	PROPN
ejpam-4671	177	36	∩	∩	ADJ
ejpam-4671	177	37	v	v	X
ejpam-4671	177	38	(	(	PUNCT
ejpam-4671	177	39	hv	hv	X
ejpam-4671	177	40	)	)	PUNCT
ejpam-4671	177	41	is	be	AUX
ejpam-4671	177	42	a	a	DET
ejpam-4671	177	43	1	1	NUM
ejpam-4671	177	44	-	-	PUNCT
ejpam-4671	177	45	movable	movable	ADJ
ejpam-4671	177	46	locating	locating	NOUN
ejpam-4671	177	47	set	set	VERB
ejpam-4671	177	48	for	for	ADP
ejpam-4671	177	49	each	each	DET
ejpam-4671	177	50	v	v	NUM
ejpam-4671	177	51	∈	∈	PROPN
ejpam-4671	177	52	v	v	NOUN
ejpam-4671	177	53	(	(	PUNCT
ejpam-4671	177	54	g	g	NOUN
ejpam-4671	177	55	)	)	PUNCT
ejpam-4671	177	56	and	and	CCONJ
ejpam-4671	178	1	w	w	NOUN
ejpam-4671	178	2	=	=	NOUN
ejpam-4671	178	3	a	a	PRON
ejpam-4671	178	4	∪	∪	ADJ
ejpam-4671	178	5			PROPN
ejpam-4671	178	6	⋃	⋃	PROPN
ejpam-4671	178	7	v∈ng(a	v∈ng(a	PROPN
ejpam-4671	178	8	)	)	PUNCT
ejpam-4671	178	9	bv	bv	PROPN
ejpam-4671	178	10			PROPN
ejpam-4671	178	11	∪	∪	VERB
ejpam-4671	178	12			PROPN
ejpam-4671	178	13	⋃	⋃	ADJ
ejpam-4671	178	14	u∈v	u∈v	NOUN
ejpam-4671	178	15	(	(	PUNCT
ejpam-4671	178	16	g)\ng(a	g)\ng(a	NOUN
ejpam-4671	178	17	)	)	PUNCT
ejpam-4671	178	18	du	du	NOUN
ejpam-4671	178	19			PROPN
ejpam-4671	178	20	where	where	SCONJ
ejpam-4671	178	21	a	a	DET
ejpam-4671	178	22	⊆	⊆	NUM
ejpam-4671	178	23	v	v	NOUN
ejpam-4671	178	24	(	(	PUNCT
ejpam-4671	178	25	g	g	NOUN
ejpam-4671	178	26	)	)	PUNCT
ejpam-4671	178	27	and	and	CCONJ
ejpam-4671	178	28	bv	bv	PROPN
ejpam-4671	178	29	and	and	CCONJ
ejpam-4671	178	30	du	du	AUX
ejpam-4671	178	31	satisfy	satisfy	VERB
ejpam-4671	178	32	the	the	DET
ejpam-4671	178	33	given	give	VERB
ejpam-4671	178	34	properties	property	NOUN
ejpam-4671	178	35	in	in	ADP
ejpam-4671	178	36	theorem	theorem	NOUN
ejpam-4671	178	37	4	4	NUM
ejpam-4671	178	38	.	.	PUNCT
ejpam-4671	179	1	consider	consider	VERB
ejpam-4671	179	2	the	the	DET
ejpam-4671	179	3	following	follow	VERB
ejpam-4671	179	4	cases	case	NOUN
ejpam-4671	179	5	for	for	ADP
ejpam-4671	179	6	set	set	ADJ
ejpam-4671	179	7	a.	a.	NOUN
ejpam-4671	179	8	case	case	NOUN
ejpam-4671	179	9	1	1	NUM
ejpam-4671	179	10	.	.	PUNCT
ejpam-4671	180	1	a	a	DET
ejpam-4671	180	2	=	=	ADJ
ejpam-4671	180	3	∅	∅	NOUN
ejpam-4671	180	4	then	then	ADV
ejpam-4671	180	5	ng(a	ng(a	PRON
ejpam-4671	180	6	)	)	PUNCT
ejpam-4671	181	1	=	=	PUNCT
ejpam-4671	181	2	∅.	∅.	NOUN
ejpam-4671	181	3	let	let	VERB
ejpam-4671	181	4	du	du	PROPN
ejpam-4671	181	5	=	=	SYM
ejpam-4671	181	6	w	w	PROPN
ejpam-4671	181	7	∩	∩	PROPN
ejpam-4671	181	8	v	v	X
ejpam-4671	181	9	(	(	PUNCT
ejpam-4671	181	10	hu	hu	PROPN
ejpam-4671	181	11	)	)	PUNCT
ejpam-4671	181	12	be	be	VERB
ejpam-4671	181	13	an	an	DET
ejpam-4671	181	14	msln	msln	NOUN
ejpam-4671	181	15	-	-	PUNCT
ejpam-4671	181	16	set	set	NOUN
ejpam-4671	181	17	of	of	ADP
ejpam-4671	181	18	hu	hu	PROPN
ejpam-4671	181	19	for	for	ADP
ejpam-4671	181	20	each	each	DET
ejpam-4671	181	21	u	u	PROPN
ejpam-4671	181	22	∈	∈	PROPN
ejpam-4671	181	23	v	v	NOUN
ejpam-4671	181	24	(	(	PUNCT
ejpam-4671	181	25	g	g	NOUN
ejpam-4671	181	26	)	)	PUNCT
ejpam-4671	181	27	.	.	PUNCT
ejpam-4671	182	1	thus	thus	ADV
ejpam-4671	182	2	,	,	PUNCT
ejpam-4671	182	3	w	w	PROPN
ejpam-4671	182	4	=	=	SYM
ejpam-4671	182	5			PROPN
ejpam-4671	182	6	⋃	⋃	ADJ
ejpam-4671	182	7	u∈v	u∈v	NOUN
ejpam-4671	182	8	(	(	PUNCT
ejpam-4671	182	9	g	g	NOUN
ejpam-4671	182	10	)	)	PUNCT
ejpam-4671	182	11	du	du	PROPN
ejpam-4671	182	12			PROPN
ejpam-4671	182	13	is	be	AUX
ejpam-4671	182	14	a	a	DET
ejpam-4671	182	15	1	1	NUM
ejpam-4671	182	16	-	-	PUNCT
ejpam-4671	182	17	movable	movable	ADJ
ejpam-4671	182	18	resolving	resolve	VERB
ejpam-4671	182	19	hop	hop	NOUN
ejpam-4671	182	20	dominating	dominating	NOUN
ejpam-4671	182	21	set	set	VERB
ejpam-4671	182	22	ofg	ofg	PROPN
ejpam-4671	182	23	◦	◦	NOUN
ejpam-4671	182	24	h	h	NOUN
ejpam-4671	182	25	by	by	ADP
ejpam-4671	182	26	theorem	theorem	NOUN
ejpam-4671	182	27	4	4	NUM
ejpam-4671	182	28	.	.	PUNCT
ejpam-4671	182	29	implying	imply	VERB
ejpam-4671	182	30	that	that	SCONJ
ejpam-4671	182	31	,	,	PUNCT
ejpam-4671	182	32	γ1mrh(g	γ1mrh(g	PRON
ejpam-4671	182	33	◦	◦	NOUN
ejpam-4671	182	34	h	h	NOUN
ejpam-4671	182	35	)	)	PUNCT
ejpam-4671	182	36	≤	≤	NOUN
ejpam-4671	182	37	|w	|w	NOUN
ejpam-4671	182	38	|	|	NOUN
ejpam-4671	182	39	=	=	SYM
ejpam-4671	182	40	|v	|v	PROPN
ejpam-4671	182	41	(	(	PUNCT
ejpam-4671	182	42	g)||du|	g)||du|	PROPN
ejpam-4671	182	43	≤	≤	NOUN
ejpam-4671	182	44	p(msln(h	p(msln(h	VERB
ejpam-4671	182	45	)	)	PUNCT
ejpam-4671	182	46	)	)	PUNCT
ejpam-4671	182	47	.	.	PUNCT
ejpam-4671	183	1	case	case	NOUN
ejpam-4671	183	2	2	2	NUM
ejpam-4671	183	3	.	.	X
ejpam-4671	184	1	a	a	PRON
ejpam-4671	184	2	is	be	AUX
ejpam-4671	184	3	a	a	DET
ejpam-4671	184	4	γt	γt	NOUN
ejpam-4671	184	5	-	-	NOUN
ejpam-4671	184	6	set	set	NOUN
ejpam-4671	184	7	of	of	ADP
ejpam-4671	184	8	g	g	PROPN
ejpam-4671	184	9	then	then	ADV
ejpam-4671	184	10	ng(a	ng(a	PRON
ejpam-4671	184	11	)	)	PUNCT
ejpam-4671	184	12	=	=	SYM
ejpam-4671	184	13	v	v	X
ejpam-4671	184	14	(	(	PUNCT
ejpam-4671	184	15	g	g	NOUN
ejpam-4671	184	16	)	)	PUNCT
ejpam-4671	184	17	.	.	PUNCT
ejpam-4671	185	1	let	let	VERB
ejpam-4671	185	2	bv	bv	PROPN
ejpam-4671	185	3	=	=	PROPN
ejpam-4671	185	4	w	w	PROPN
ejpam-4671	185	5	∩	∩	PROPN
ejpam-4671	185	6	v	v	X
ejpam-4671	185	7	(	(	PUNCT
ejpam-4671	185	8	hv	hv	NOUN
ejpam-4671	185	9	)	)	PUNCT
ejpam-4671	185	10	be	be	VERB
ejpam-4671	185	11	an	an	DET
ejpam-4671	185	12	mln	mln	NOUN
ejpam-4671	185	13	-	-	PUNCT
ejpam-4671	185	14	set	set	NOUN
ejpam-4671	185	15	of	of	ADP
ejpam-4671	185	16	hv	hv	PROPN
ejpam-4671	185	17	for	for	ADP
ejpam-4671	185	18	each	each	DET
ejpam-4671	185	19	v	v	NUM
ejpam-4671	185	20	∈	∈	PROPN
ejpam-4671	185	21	v	v	NOUN
ejpam-4671	185	22	(	(	PUNCT
ejpam-4671	185	23	g	g	NOUN
ejpam-4671	185	24	)	)	PUNCT
ejpam-4671	185	25	.	.	PUNCT
ejpam-4671	186	1	hence	hence	ADV
ejpam-4671	186	2	,	,	PUNCT
ejpam-4671	186	3	w	w	NOUN
ejpam-4671	186	4	=	=	PUNCT
ejpam-4671	186	5	a	a	PRON
ejpam-4671	186	6	∪	∪	ADJ
ejpam-4671	186	7			PROPN
ejpam-4671	186	8	⋃	⋃	ADJ
ejpam-4671	186	9	v∈v	v∈v	NOUN
ejpam-4671	186	10	(	(	PUNCT
ejpam-4671	186	11	g	g	NOUN
ejpam-4671	186	12	)	)	PUNCT
ejpam-4671	186	13	bv	bv	PROPN
ejpam-4671	186	14			PROPN
ejpam-4671	186	15	is	be	AUX
ejpam-4671	186	16	a	a	DET
ejpam-4671	186	17	1	1	NUM
ejpam-4671	186	18	-	-	PUNCT
ejpam-4671	186	19	movable	movable	ADJ
ejpam-4671	186	20	resolving	resolve	VERB
ejpam-4671	186	21	hop	hop	NOUN
ejpam-4671	186	22	dominating	dominating	NOUN
ejpam-4671	186	23	set	set	NOUN
ejpam-4671	186	24	of	of	ADP
ejpam-4671	186	25	g	g	PROPN
ejpam-4671	186	26	◦	◦	NOUN
ejpam-4671	186	27	h	h	NOUN
ejpam-4671	186	28	by	by	ADP
ejpam-4671	186	29	theorem	theorem	NOUN
ejpam-4671	186	30	4	4	NUM
ejpam-4671	186	31	.	.	PUNCT
ejpam-4671	187	1	it	it	PRON
ejpam-4671	187	2	follows	follow	VERB
ejpam-4671	187	3	that	that	SCONJ
ejpam-4671	187	4	γ1mrh(g	γ1mrh(g	ADP
ejpam-4671	187	5	◦	◦	NOUN
ejpam-4671	187	6	h	h	NOUN
ejpam-4671	187	7	)	)	PUNCT
ejpam-4671	187	8	≤	≤	NOUN
ejpam-4671	187	9	|w	|w	NOUN
ejpam-4671	188	1	|	|	NOUN
ejpam-4671	188	2	=	=	PUNCT
ejpam-4671	189	1	|a|+	|a|+	NOUN
ejpam-4671	189	2	|v	|v	X
ejpam-4671	189	3	(	(	PUNCT
ejpam-4671	189	4	g)||bv|	g)||bv|	PROPN
ejpam-4671	189	5	=	=	PUNCT
ejpam-4671	189	6	γt(g	γt(g	NUM
ejpam-4671	189	7	)	)	PUNCT
ejpam-4671	189	8	+	+	CCONJ
ejpam-4671	189	9	p(mln(h	p(mln(h	NOUN
ejpam-4671	189	10	)	)	PUNCT
ejpam-4671	189	11	)	)	PUNCT
ejpam-4671	189	12	.	.	PUNCT
ejpam-4671	190	1	therefore	therefore	ADV
ejpam-4671	190	2	,	,	PUNCT
ejpam-4671	190	3	γ1mrrh(g	γ1mrrh(g	ADP
ejpam-4671	190	4	◦	◦	NOUN
ejpam-4671	190	5	h	h	NOUN
ejpam-4671	190	6	)	)	PUNCT
ejpam-4671	190	7	≤	≤	NUM
ejpam-4671	190	8	min	min	NOUN
ejpam-4671	190	9	{	{	PUNCT
ejpam-4671	190	10	p(msln(h	p(msln(h	PROPN
ejpam-4671	190	11	)	)	PUNCT
ejpam-4671	190	12	)	)	PUNCT
ejpam-4671	190	13	,	,	PUNCT
ejpam-4671	190	14	γt(g	γt(g	PUNCT
ejpam-4671	190	15	)	)	PUNCT
ejpam-4671	190	16	+	+	CCONJ
ejpam-4671	190	17	p(mln(h	p(mln(h	NOUN
ejpam-4671	190	18	)	)	PUNCT
ejpam-4671	190	19	)	)	PUNCT
ejpam-4671	190	20	}	}	PUNCT
ejpam-4671	190	21	.	.	PUNCT
ejpam-4671	191	1	j.	j.	PROPN
ejpam-4671	191	2	mohamad	mohamad	PROPN
ejpam-4671	191	3	,	,	PUNCT
ejpam-4671	191	4	h.	h.	PROPN
ejpam-4671	191	5	rara	rara	PROPN
ejpam-4671	191	6	/	/	SYM
ejpam-4671	191	7	eur	eur	PROPN
ejpam-4671	191	8	.	.	PUNCT
ejpam-4671	192	1	j.	j.	PROPN
ejpam-4671	192	2	pure	pure	PROPN
ejpam-4671	192	3	appl	appl	PROPN
ejpam-4671	192	4	.	.	PROPN
ejpam-4671	192	5	math	math	PROPN
ejpam-4671	192	6	,	,	PUNCT
ejpam-4671	192	7	16	16	NUM
ejpam-4671	192	8	(	(	PUNCT
ejpam-4671	192	9	1	1	NUM
ejpam-4671	192	10	)	)	PUNCT
ejpam-4671	192	11	(	(	PUNCT
ejpam-4671	192	12	2023	2023	NUM
ejpam-4671	192	13	)	)	PUNCT
ejpam-4671	192	14	,	,	PUNCT
ejpam-4671	192	15	418	418	NUM
ejpam-4671	192	16	-	-	SYM
ejpam-4671	192	17	429	429	NUM
ejpam-4671	192	18	426	426	NUM
ejpam-4671	192	19	5	5	NUM
ejpam-4671	192	20	.	.	PUNCT
ejpam-4671	193	1	on	on	ADP
ejpam-4671	193	2	1	1	NUM
ejpam-4671	193	3	-	-	PUNCT
ejpam-4671	193	4	movable	movable	ADJ
ejpam-4671	193	5	resolving	resolve	VERB
ejpam-4671	193	6	hop	hop	NOUN
ejpam-4671	193	7	domination	domination	NOUN
ejpam-4671	193	8	in	in	ADP
ejpam-4671	193	9	the	the	DET
ejpam-4671	193	10	lexicographic	lexicographic	ADJ
ejpam-4671	193	11	product	product	NOUN
ejpam-4671	193	12	of	of	ADP
ejpam-4671	193	13	graphs	graph	NOUN
ejpam-4671	193	14	the	the	DET
ejpam-4671	193	15	lexicographic	lexicographic	ADJ
ejpam-4671	193	16	product	product	NOUN
ejpam-4671	193	17	of	of	ADP
ejpam-4671	193	18	two	two	NUM
ejpam-4671	193	19	graphs	graph	NOUN
ejpam-4671	193	20	g	g	NOUN
ejpam-4671	193	21	and	and	CCONJ
ejpam-4671	193	22	h	h	NOUN
ejpam-4671	193	23	,	,	PUNCT
ejpam-4671	193	24	denoted	denote	VERB
ejpam-4671	193	25	by	by	ADP
ejpam-4671	193	26	g[h	g[h	NOUN
ejpam-4671	193	27	]	]	PUNCT
ejpam-4671	193	28	,	,	PUNCT
ejpam-4671	193	29	is	be	AUX
ejpam-4671	193	30	the	the	DET
ejpam-4671	193	31	graph	graph	NOUN
ejpam-4671	193	32	with	with	ADP
ejpam-4671	193	33	vertex	vertex	NOUN
ejpam-4671	193	34	-	-	PUNCT
ejpam-4671	193	35	set	set	VERB
ejpam-4671	193	36	v	v	NOUN
ejpam-4671	193	37	(	(	PUNCT
ejpam-4671	193	38	g[h	g[h	PROPN
ejpam-4671	193	39	]	]	PUNCT
ejpam-4671	193	40	)	)	PUNCT
ejpam-4671	193	41	=	=	SYM
ejpam-4671	193	42	v	v	X
ejpam-4671	193	43	(	(	PUNCT
ejpam-4671	193	44	g	g	NOUN
ejpam-4671	193	45	)	)	PUNCT
ejpam-4671	193	46	×	×	NOUN
ejpam-4671	193	47	v	v	NOUN
ejpam-4671	193	48	(	(	PUNCT
ejpam-4671	193	49	h	h	NOUN
ejpam-4671	193	50	)	)	PUNCT
ejpam-4671	193	51	such	such	ADJ
ejpam-4671	193	52	that	that	SCONJ
ejpam-4671	193	53	(	(	PUNCT
ejpam-4671	193	54	u1	u1	NOUN
ejpam-4671	193	55	,	,	PUNCT
ejpam-4671	193	56	u2)(v1	u2)(v1	NOUN
ejpam-4671	193	57	,	,	PUNCT
ejpam-4671	193	58	v2	v2	NOUN
ejpam-4671	193	59	)	)	PUNCT
ejpam-4671	193	60	∈	∈	NOUN
ejpam-4671	193	61	e(g[h	e(g[h	NOUN
ejpam-4671	193	62	]	]	PUNCT
ejpam-4671	193	63	)	)	PUNCT
ejpam-4671	193	64	if	if	SCONJ
ejpam-4671	193	65	either	either	CCONJ
ejpam-4671	193	66	u1v1	u1v1	PROPN
ejpam-4671	193	67	∈	∈	PROPN
ejpam-4671	193	68	e(g	e(g	PROPN
ejpam-4671	193	69	)	)	PUNCT
ejpam-4671	193	70	or	or	CCONJ
ejpam-4671	193	71	u1	u1	NOUN
ejpam-4671	193	72	=	=	SYM
ejpam-4671	193	73	v1	v1	NOUN
ejpam-4671	193	74	and	and	CCONJ
ejpam-4671	193	75	u2v2	u2v2	ADJ
ejpam-4671	193	76	∈	∈	PROPN
ejpam-4671	193	77	e(h	e(h	PROPN
ejpam-4671	193	78	)	)	PUNCT
ejpam-4671	193	79	.	.	PUNCT
ejpam-4671	194	1	theorem	theorem	ADJ
ejpam-4671	194	2	5	5	NUM
ejpam-4671	194	3	.	.	PUNCT
ejpam-4671	195	1	[	[	X
ejpam-4671	195	2	10	10	NUM
ejpam-4671	195	3	]	]	PUNCT
ejpam-4671	195	4	let	let	VERB
ejpam-4671	195	5	g	g	NOUN
ejpam-4671	195	6	and	and	CCONJ
ejpam-4671	195	7	h	h	NOUN
ejpam-4671	195	8	be	be	AUX
ejpam-4671	195	9	nontrivial	nontrivial	ADJ
ejpam-4671	195	10	connected	connect	VERB
ejpam-4671	195	11	graphs	graph	NOUN
ejpam-4671	195	12	with	with	ADP
ejpam-4671	195	13	△	△	X
ejpam-4671	195	14	(	(	PUNCT
ejpam-4671	195	15	h	h	NOUN
ejpam-4671	195	16	)	)	PUNCT
ejpam-4671	195	17	≤	≤	NOUN
ejpam-4671	195	18	|v	|v	X
ejpam-4671	195	19	(	(	PUNCT
ejpam-4671	195	20	h)|	h)|	NOUN
ejpam-4671	195	21	−	−	PROPN
ejpam-4671	195	22	2	2	NUM
ejpam-4671	195	23	.	.	PUNCT
ejpam-4671	196	1	then	then	ADV
ejpam-4671	196	2	w	w	PROPN
ejpam-4671	196	3	=	=	PUNCT
ejpam-4671	196	4	⋃	⋃	PROPN
ejpam-4671	196	5	x∈s	x∈s	NOUN
ejpam-4671	197	1	[	[	X
ejpam-4671	197	2	{	{	PUNCT
ejpam-4671	197	3	x	x	NOUN
ejpam-4671	197	4	}	}	PUNCT
ejpam-4671	197	5	×	×	PROPN
ejpam-4671	197	6	tx	tx	PROPN
ejpam-4671	197	7	]	]	X
ejpam-4671	197	8	,	,	PUNCT
ejpam-4671	197	9	where	where	SCONJ
ejpam-4671	197	10	s	s	VERB
ejpam-4671	197	11	⊆	⊆	NUM
ejpam-4671	197	12	v	v	NOUN
ejpam-4671	197	13	(	(	PUNCT
ejpam-4671	197	14	g	g	NOUN
ejpam-4671	197	15	)	)	PUNCT
ejpam-4671	197	16	and	and	CCONJ
ejpam-4671	197	17	tx	tx	VERB
ejpam-4671	197	18	⊆	⊆	NUM
ejpam-4671	197	19	v	v	NOUN
ejpam-4671	197	20	(	(	PUNCT
ejpam-4671	197	21	h	h	NOUN
ejpam-4671	197	22	)	)	PUNCT
ejpam-4671	197	23	for	for	ADP
ejpam-4671	197	24	each	each	DET
ejpam-4671	197	25	x	x	SYM
ejpam-4671	197	26	∈	∈	PROPN
ejpam-4671	197	27	s	s	NOUN
ejpam-4671	197	28	,	,	PUNCT
ejpam-4671	197	29	is	be	AUX
ejpam-4671	197	30	a	a	DET
ejpam-4671	197	31	resolving	resolve	VERB
ejpam-4671	197	32	hop	hop	NOUN
ejpam-4671	197	33	dominating	dominating	NOUN
ejpam-4671	197	34	set	set	NOUN
ejpam-4671	197	35	of	of	ADP
ejpam-4671	197	36	g[h	g[h	PROPN
ejpam-4671	197	37	]	]	PUNCT
ejpam-4671	197	38	if	if	SCONJ
ejpam-4671	197	39	and	and	CCONJ
ejpam-4671	197	40	only	only	ADV
ejpam-4671	197	41	if	if	SCONJ
ejpam-4671	197	42	(	(	PUNCT
ejpam-4671	197	43	i	i	NOUN
ejpam-4671	197	44	)	)	PUNCT
ejpam-4671	197	45	s	s	PART
ejpam-4671	197	46	=	=	SYM
ejpam-4671	197	47	v	v	NOUN
ejpam-4671	197	48	(	(	PUNCT
ejpam-4671	197	49	g	g	NOUN
ejpam-4671	197	50	)	)	PUNCT
ejpam-4671	197	51	;	;	PUNCT
ejpam-4671	197	52	(	(	PUNCT
ejpam-4671	197	53	ii	ii	NOUN
ejpam-4671	197	54	)	)	PUNCT
ejpam-4671	197	55	tx	tx	PROPN
ejpam-4671	197	56	is	be	AUX
ejpam-4671	197	57	a	a	DET
ejpam-4671	197	58	locating	locating	NOUN
ejpam-4671	197	59	set	set	NOUN
ejpam-4671	197	60	for	for	ADP
ejpam-4671	197	61	every	every	DET
ejpam-4671	197	62	x	x	SYM
ejpam-4671	197	63	∈	∈	PROPN
ejpam-4671	197	64	v	v	NOUN
ejpam-4671	197	65	(	(	PUNCT
ejpam-4671	197	66	g	g	NOUN
ejpam-4671	197	67	)	)	PUNCT
ejpam-4671	197	68	;	;	PUNCT
ejpam-4671	197	69	(	(	PUNCT
ejpam-4671	197	70	iii	iii	X
ejpam-4671	197	71	)	)	PUNCT
ejpam-4671	197	72	tx	tx	NOUN
ejpam-4671	198	1	or	or	CCONJ
ejpam-4671	198	2	ty	ty	INTJ
ejpam-4671	198	3	is	be	AUX
ejpam-4671	198	4	a	a	DET
ejpam-4671	198	5	strictly	strictly	ADV
ejpam-4671	198	6	locating	locate	VERB
ejpam-4671	198	7	set	set	NOUN
ejpam-4671	198	8	of	of	ADP
ejpam-4671	198	9	h	h	NOUN
ejpam-4671	198	10	whenever	whenever	SCONJ
ejpam-4671	198	11	x	x	PRON
ejpam-4671	198	12	and	and	CCONJ
ejpam-4671	198	13	y	y	PROPN
ejpam-4671	198	14	are	be	AUX
ejpam-4671	198	15	adjacent	adjacent	ADJ
ejpam-4671	198	16	vertices	vertex	NOUN
ejpam-4671	198	17	of	of	ADP
ejpam-4671	198	18	g	g	NOUN
ejpam-4671	198	19	with	with	ADP
ejpam-4671	198	20	ng[x	ng[x	PROPN
ejpam-4671	198	21	]	]	X
ejpam-4671	198	22	=	=	PUNCT
ejpam-4671	198	23	ng[y	ng[y	PROPN
ejpam-4671	198	24	]	]	PUNCT
ejpam-4671	198	25	;	;	PUNCT
ejpam-4671	198	26	(	(	PUNCT
ejpam-4671	198	27	iv	iv	X
ejpam-4671	198	28	)	)	PUNCT
ejpam-4671	198	29	tx	tx	NOUN
ejpam-4671	198	30	or	or	CCONJ
ejpam-4671	198	31	ty	ty	INTJ
ejpam-4671	198	32	is	be	AUX
ejpam-4671	198	33	a	a	DET
ejpam-4671	198	34	(	(	PUNCT
ejpam-4671	198	35	locating	locating	NOUN
ejpam-4671	198	36	)	)	PUNCT
ejpam-4671	198	37	dominating	dominating	NOUN
ejpam-4671	198	38	set	set	NOUN
ejpam-4671	198	39	of	of	ADP
ejpam-4671	198	40	h	h	NOUN
ejpam-4671	198	41	whenever	whenever	SCONJ
ejpam-4671	198	42	x	x	PRON
ejpam-4671	198	43	and	and	CCONJ
ejpam-4671	198	44	y	y	PROPN
ejpam-4671	198	45	are	be	AUX
ejpam-4671	198	46	nonadjacent	nonadjacent	ADJ
ejpam-4671	198	47	vertices	vertex	NOUN
ejpam-4671	198	48	of	of	ADP
ejpam-4671	198	49	g	g	NOUN
ejpam-4671	198	50	with	with	ADP
ejpam-4671	198	51	ng(x	ng(x	NUM
ejpam-4671	198	52	)	)	PUNCT
ejpam-4671	198	53	=	=	PUNCT
ejpam-4671	198	54	ng(y	ng(y	NOUN
ejpam-4671	198	55	)	)	PUNCT
ejpam-4671	198	56	;	;	PUNCT
ejpam-4671	198	57	and	and	CCONJ
ejpam-4671	198	58	(	(	PUNCT
ejpam-4671	198	59	v	v	NOUN
ejpam-4671	198	60	)	)	PUNCT
ejpam-4671	198	61	tx	tx	PROPN
ejpam-4671	198	62	is	be	AUX
ejpam-4671	198	63	a	a	DET
ejpam-4671	198	64	strictly	strictly	ADV
ejpam-4671	198	65	locating	locate	VERB
ejpam-4671	198	66	set	set	NOUN
ejpam-4671	198	67	of	of	ADP
ejpam-4671	198	68	h	h	NOUN
ejpam-4671	198	69	for	for	ADP
ejpam-4671	198	70	each	each	DET
ejpam-4671	198	71	x	x	SYM
ejpam-4671	198	72	∈	∈	PROPN
ejpam-4671	198	73	s	s	PART
ejpam-4671	198	74	\ng(s	\ng(s	NOUN
ejpam-4671	198	75	,	,	PUNCT
ejpam-4671	198	76	2	2	NUM
ejpam-4671	198	77	)	)	PUNCT
ejpam-4671	198	78	.	.	PUNCT
ejpam-4671	199	1	the	the	DET
ejpam-4671	199	2	set	set	NOUN
ejpam-4671	199	3	of	of	ADP
ejpam-4671	199	4	shaded	shade	VERB
ejpam-4671	199	5	vertices	vertex	NOUN
ejpam-4671	199	6	in	in	ADP
ejpam-4671	199	7	the	the	DET
ejpam-4671	199	8	lexicographic	lexicographic	ADJ
ejpam-4671	199	9	product	product	NOUN
ejpam-4671	199	10	p3[p4	p3[p4	NOUN
ejpam-4671	199	11	]	]	X
ejpam-4671	199	12	in	in	ADP
ejpam-4671	199	13	figure	figure	NOUN
ejpam-4671	199	14	3	3	NUM
ejpam-4671	199	15	where	where	SCONJ
ejpam-4671	199	16	g	g	PROPN
ejpam-4671	199	17	=	=	SYM
ejpam-4671	199	18	p3	p3	PROPN
ejpam-4671	199	19	and	and	CCONJ
ejpam-4671	199	20	h	h	NOUN
ejpam-4671	199	21	=	=	SYM
ejpam-4671	199	22	p4	p4	ADJ
ejpam-4671	199	23	satisfies	satisfy	VERB
ejpam-4671	199	24	the	the	DET
ejpam-4671	199	25	conditions	condition	NOUN
ejpam-4671	199	26	in	in	ADP
ejpam-4671	199	27	theorem	theorem	NOUN
ejpam-4671	199	28	5	5	NUM
ejpam-4671	199	29	and	and	CCONJ
ejpam-4671	199	30	thus	thus	ADV
ejpam-4671	199	31	it	it	PRON
ejpam-4671	199	32	is	be	AUX
ejpam-4671	199	33	a	a	DET
ejpam-4671	199	34	resolving	resolve	VERB
ejpam-4671	199	35	hop	hop	NOUN
ejpam-4671	199	36	dominating	dominating	NOUN
ejpam-4671	199	37	set	set	NOUN
ejpam-4671	199	38	of	of	ADP
ejpam-4671	199	39	g[h	g[h	NOUN
ejpam-4671	199	40	]	]	PUNCT
ejpam-4671	199	41	.	.	PUNCT
ejpam-4671	200	1	in	in	ADP
ejpam-4671	200	2	fact	fact	NOUN
ejpam-4671	200	3	,	,	PUNCT
ejpam-4671	200	4	the	the	DET
ejpam-4671	200	5	set	set	NOUN
ejpam-4671	200	6	of	of	ADP
ejpam-4671	200	7	vertices	vertex	NOUN
ejpam-4671	200	8	that	that	PRON
ejpam-4671	200	9	are	be	AUX
ejpam-4671	200	10	not	not	PART
ejpam-4671	200	11	shaded	shade	VERB
ejpam-4671	200	12	is	be	AUX
ejpam-4671	200	13	also	also	ADV
ejpam-4671	200	14	a	a	DET
ejpam-4671	200	15	resolving	resolve	VERB
ejpam-4671	200	16	hop	hop	NOUN
ejpam-4671	200	17	dominating	dominating	NOUN
ejpam-4671	200	18	set	set	NOUN
ejpam-4671	200	19	of	of	ADP
ejpam-4671	200	20	g[h	g[h	PROPN
ejpam-4671	200	21	]	]	PUNCT
ejpam-4671	200	22	.	.	PUNCT
ejpam-4671	201	1	figure	figure	VERB
ejpam-4671	201	2	3	3	NUM
ejpam-4671	201	3	:	:	PUNCT
ejpam-4671	201	4	resolving	resolve	VERB
ejpam-4671	201	5	hop	hop	NOUN
ejpam-4671	201	6	dominating	dominating	NOUN
ejpam-4671	201	7	sets	set	NOUN
ejpam-4671	201	8	of	of	ADP
ejpam-4671	201	9	p3[p4	p3[p4	NOUN
ejpam-4671	201	10	]	]	X
ejpam-4671	201	11	theorem	theorem	NOUN
ejpam-4671	201	12	6	6	NUM
ejpam-4671	201	13	.	.	PUNCT
ejpam-4671	202	1	let	let	VERB
ejpam-4671	202	2	g	g	NOUN
ejpam-4671	202	3	and	and	CCONJ
ejpam-4671	202	4	h	h	NOUN
ejpam-4671	202	5	be	be	AUX
ejpam-4671	202	6	nontrivial	nontrivial	ADJ
ejpam-4671	202	7	connected	connect	VERB
ejpam-4671	202	8	graphs	graph	NOUN
ejpam-4671	202	9	with	with	ADP
ejpam-4671	202	10	△	△	X
ejpam-4671	202	11	(	(	PUNCT
ejpam-4671	202	12	h	h	NOUN
ejpam-4671	202	13	)	)	PUNCT
ejpam-4671	202	14	≤	≤	NOUN
ejpam-4671	202	15	|v	|v	X
ejpam-4671	202	16	(	(	PUNCT
ejpam-4671	202	17	h)|	h)|	NOUN
ejpam-4671	202	18	−	−	PROPN
ejpam-4671	202	19	2	2	NUM
ejpam-4671	202	20	.	.	PUNCT
ejpam-4671	203	1	then	then	ADV
ejpam-4671	203	2	w	w	PROPN
ejpam-4671	203	3	=	=	PUNCT
ejpam-4671	203	4	⋃	⋃	PROPN
ejpam-4671	203	5	x∈s	x∈s	NOUN
ejpam-4671	203	6	(	(	PUNCT
ejpam-4671	203	7	{	{	PUNCT
ejpam-4671	203	8	x	x	NOUN
ejpam-4671	203	9	}	}	PUNCT
ejpam-4671	203	10	×	×	PROPN
ejpam-4671	203	11	tx	tx	PROPN
ejpam-4671	203	12	)	)	PUNCT
ejpam-4671	203	13	where	where	SCONJ
ejpam-4671	203	14	s	s	VERB
ejpam-4671	203	15	⊆	⊆	NUM
ejpam-4671	203	16	v	v	NOUN
ejpam-4671	203	17	(	(	PUNCT
ejpam-4671	203	18	g	g	NOUN
ejpam-4671	203	19	)	)	PUNCT
ejpam-4671	203	20	and	and	CCONJ
ejpam-4671	203	21	tx	tx	VERB
ejpam-4671	203	22	⊆	⊆	NUM
ejpam-4671	203	23	v	v	NOUN
ejpam-4671	203	24	(	(	PUNCT
ejpam-4671	203	25	h	h	NOUN
ejpam-4671	203	26	)	)	PUNCT
ejpam-4671	203	27	for	for	ADP
ejpam-4671	203	28	each	each	DET
ejpam-4671	203	29	x	x	SYM
ejpam-4671	203	30	∈	∈	PROPN
ejpam-4671	203	31	s	s	NOUN
ejpam-4671	203	32	,	,	PUNCT
ejpam-4671	203	33	is	be	AUX
ejpam-4671	203	34	a	a	DET
ejpam-4671	203	35	1	1	NUM
ejpam-4671	203	36	-	-	PUNCT
ejpam-4671	203	37	movable	movable	ADJ
ejpam-4671	203	38	resolving	resolve	VERB
ejpam-4671	203	39	hop	hop	NOUN
ejpam-4671	203	40	dominating	dominating	NOUN
ejpam-4671	203	41	set	set	NOUN
ejpam-4671	203	42	of	of	ADP
ejpam-4671	203	43	g[h	g[h	PROPN
ejpam-4671	203	44	]	]	PUNCT
ejpam-4671	203	45	if	if	SCONJ
ejpam-4671	203	46	and	and	CCONJ
ejpam-4671	203	47	only	only	ADV
ejpam-4671	203	48	if	if	SCONJ
ejpam-4671	203	49	the	the	DET
ejpam-4671	203	50	following	follow	VERB
ejpam-4671	203	51	conditions	condition	NOUN
ejpam-4671	203	52	hold	hold	VERB
ejpam-4671	203	53	:	:	PUNCT
ejpam-4671	203	54	(	(	PUNCT
ejpam-4671	203	55	i	i	NOUN
ejpam-4671	203	56	)	)	PUNCT
ejpam-4671	203	57	s	s	PART
ejpam-4671	203	58	=	=	SYM
ejpam-4671	203	59	v	v	NOUN
ejpam-4671	203	60	(	(	PUNCT
ejpam-4671	203	61	g	g	NOUN
ejpam-4671	203	62	)	)	PUNCT
ejpam-4671	203	63	.	.	PUNCT
ejpam-4671	204	1	(	(	PUNCT
ejpam-4671	204	2	ii	ii	NOUN
ejpam-4671	204	3	)	)	PUNCT
ejpam-4671	204	4	tx	tx	PROPN
ejpam-4671	204	5	is	be	AUX
ejpam-4671	204	6	a	a	DET
ejpam-4671	204	7	1	1	NUM
ejpam-4671	204	8	-	-	PUNCT
ejpam-4671	204	9	movable	movable	ADJ
ejpam-4671	204	10	locating	locating	NOUN
ejpam-4671	204	11	set	set	VERB
ejpam-4671	204	12	for	for	ADP
ejpam-4671	204	13	each	each	DET
ejpam-4671	204	14	x	x	PROPN
ejpam-4671	204	15	∈	∈	PROPN
ejpam-4671	204	16	s.	s.	PROPN
ejpam-4671	204	17	j.	j.	PROPN
ejpam-4671	204	18	mohamad	mohamad	PROPN
ejpam-4671	204	19	,	,	PUNCT
ejpam-4671	204	20	h.	h.	PROPN
ejpam-4671	204	21	rara	rara	PROPN
ejpam-4671	204	22	/	/	SYM
ejpam-4671	204	23	eur	eur	PROPN
ejpam-4671	204	24	.	.	PUNCT
ejpam-4671	205	1	j.	j.	PROPN
ejpam-4671	205	2	pure	pure	PROPN
ejpam-4671	205	3	appl	appl	PROPN
ejpam-4671	205	4	.	.	PROPN
ejpam-4671	205	5	math	math	PROPN
ejpam-4671	205	6	,	,	PUNCT
ejpam-4671	205	7	16	16	NUM
ejpam-4671	205	8	(	(	PUNCT
ejpam-4671	205	9	1	1	NUM
ejpam-4671	205	10	)	)	PUNCT
ejpam-4671	205	11	(	(	PUNCT
ejpam-4671	205	12	2023	2023	NUM
ejpam-4671	205	13	)	)	PUNCT
ejpam-4671	205	14	,	,	PUNCT
ejpam-4671	205	15	418	418	NUM
ejpam-4671	205	16	-	-	SYM
ejpam-4671	205	17	429	429	NUM
ejpam-4671	205	18	427	427	NUM
ejpam-4671	205	19	(	(	PUNCT
ejpam-4671	205	20	iii	iii	NOUN
ejpam-4671	205	21	)	)	PUNCT
ejpam-4671	205	22	tx	tx	PROPN
ejpam-4671	205	23	\	\	PROPN
ejpam-4671	205	24	{	{	PUNCT
ejpam-4671	205	25	a	a	NOUN
ejpam-4671	205	26	}	}	PUNCT
ejpam-4671	205	27	or	or	CCONJ
ejpam-4671	205	28	ty	ty	INTJ
ejpam-4671	205	29	is	be	AUX
ejpam-4671	205	30	a	a	DET
ejpam-4671	205	31	strictly	strictly	ADV
ejpam-4671	205	32	locating	locate	VERB
ejpam-4671	205	33	set	set	NOUN
ejpam-4671	205	34	of	of	ADP
ejpam-4671	205	35	h	h	NOUN
ejpam-4671	205	36	whenever	whenever	SCONJ
ejpam-4671	205	37	x	x	PRON
ejpam-4671	205	38	and	and	CCONJ
ejpam-4671	205	39	y	y	PROPN
ejpam-4671	205	40	are	be	AUX
ejpam-4671	205	41	adjacent	adjacent	ADJ
ejpam-4671	205	42	vertices	vertex	NOUN
ejpam-4671	205	43	of	of	ADP
ejpam-4671	205	44	g	g	NOUN
ejpam-4671	205	45	with	with	ADP
ejpam-4671	205	46	ng[x	ng[x	PROPN
ejpam-4671	205	47	]	]	X
ejpam-4671	205	48	=	=	PUNCT
ejpam-4671	205	49	ng[y	ng[y	PROPN
ejpam-4671	205	50	]	]	PUNCT
ejpam-4671	205	51	and	and	CCONJ
ejpam-4671	205	52	for	for	ADP
ejpam-4671	205	53	each	each	PRON
ejpam-4671	205	54	a	a	DET
ejpam-4671	205	55	∈	∈	PROPN
ejpam-4671	205	56	tx	tx	PROPN
ejpam-4671	205	57	.	.	PUNCT
ejpam-4671	206	1	(	(	PUNCT
ejpam-4671	206	2	iv	iv	X
ejpam-4671	206	3	)	)	PUNCT
ejpam-4671	206	4	tx	tx	PROPN
ejpam-4671	206	5	\	\	PROPN
ejpam-4671	206	6	{	{	PUNCT
ejpam-4671	206	7	a	a	NOUN
ejpam-4671	206	8	}	}	PUNCT
ejpam-4671	206	9	or	or	CCONJ
ejpam-4671	206	10	tx	tx	ADP
ejpam-4671	206	11	\	\	PROPN
ejpam-4671	206	12	{	{	PUNCT
ejpam-4671	206	13	a	a	DET
ejpam-4671	206	14	}	}	PUNCT
ejpam-4671	206	15	∪	∪	ADJ
ejpam-4671	206	16	{	{	PUNCT
ejpam-4671	206	17	b	b	NOUN
ejpam-4671	206	18	}	}	PUNCT
ejpam-4671	206	19	or	or	CCONJ
ejpam-4671	206	20	ty	ty	INTJ
ejpam-4671	206	21	is	be	AUX
ejpam-4671	206	22	a	a	DET
ejpam-4671	206	23	(	(	PUNCT
ejpam-4671	206	24	locating	locating	NOUN
ejpam-4671	206	25	)	)	PUNCT
ejpam-4671	206	26	dominating	dominating	NOUN
ejpam-4671	206	27	set	set	NOUN
ejpam-4671	206	28	of	of	ADP
ejpam-4671	206	29	h	h	NOUN
ejpam-4671	206	30	whenever	whenever	SCONJ
ejpam-4671	206	31	x	x	PRON
ejpam-4671	206	32	and	and	CCONJ
ejpam-4671	206	33	y	y	PROPN
ejpam-4671	206	34	are	be	AUX
ejpam-4671	206	35	nonadjacent	nonadjacent	ADJ
ejpam-4671	206	36	vertices	vertex	NOUN
ejpam-4671	206	37	of	of	ADP
ejpam-4671	206	38	g	g	NOUN
ejpam-4671	206	39	with	with	ADP
ejpam-4671	206	40	ng(x	ng(x	NUM
ejpam-4671	206	41	)	)	PUNCT
ejpam-4671	206	42	=	=	SYM
ejpam-4671	207	1	ng(y	ng(y	NOUN
ejpam-4671	207	2	)	)	PUNCT
ejpam-4671	207	3	and	and	CCONJ
ejpam-4671	207	4	for	for	ADP
ejpam-4671	207	5	each	each	DET
ejpam-4671	207	6	a	a	DET
ejpam-4671	207	7	∈	∈	PROPN
ejpam-4671	207	8	tx	tx	NOUN
ejpam-4671	207	9	and	and	CCONJ
ejpam-4671	207	10	for	for	ADP
ejpam-4671	207	11	some	some	DET
ejpam-4671	207	12	b	b	PROPN
ejpam-4671	207	13	∈	∈	PROPN
ejpam-4671	207	14	nh(a	nh(a	NUM
ejpam-4671	207	15	)	)	PUNCT
ejpam-4671	207	16	.	.	PUNCT
ejpam-4671	208	1	(	(	PUNCT
ejpam-4671	208	2	v	v	NOUN
ejpam-4671	208	3	)	)	PUNCT
ejpam-4671	208	4	tx	tx	PROPN
ejpam-4671	208	5	\	\	PROPN
ejpam-4671	208	6	{	{	PUNCT
ejpam-4671	208	7	a	a	NOUN
ejpam-4671	208	8	}	}	PUNCT
ejpam-4671	208	9	or	or	CCONJ
ejpam-4671	208	10	tx	tx	ADP
ejpam-4671	208	11	\	\	PROPN
ejpam-4671	208	12	{	{	PUNCT
ejpam-4671	208	13	a	a	DET
ejpam-4671	208	14	}	}	PUNCT
ejpam-4671	208	15	∪	∪	NOUN
ejpam-4671	208	16	{	{	PUNCT
ejpam-4671	208	17	b	b	NOUN
ejpam-4671	208	18	}	}	PUNCT
ejpam-4671	208	19	is	be	AUX
ejpam-4671	208	20	a	a	DET
ejpam-4671	208	21	strictly	strictly	ADV
ejpam-4671	208	22	locating	locate	VERB
ejpam-4671	208	23	set	set	NOUN
ejpam-4671	208	24	of	of	ADP
ejpam-4671	208	25	h	h	NOUN
ejpam-4671	208	26	for	for	ADP
ejpam-4671	208	27	each	each	DET
ejpam-4671	208	28	x	x	SYM
ejpam-4671	208	29	∈	∈	PROPN
ejpam-4671	208	30	s	s	PART
ejpam-4671	208	31	\ng(s	\ng(s	NOUN
ejpam-4671	208	32	,	,	PUNCT
ejpam-4671	208	33	2	2	NUM
ejpam-4671	208	34	)	)	PUNCT
ejpam-4671	208	35	and	and	CCONJ
ejpam-4671	208	36	for	for	ADP
ejpam-4671	208	37	each	each	PRON
ejpam-4671	208	38	a	a	DET
ejpam-4671	208	39	∈	∈	PROPN
ejpam-4671	208	40	tx	tx	NOUN
ejpam-4671	208	41	and	and	CCONJ
ejpam-4671	208	42	for	for	ADP
ejpam-4671	208	43	some	some	DET
ejpam-4671	208	44	b	b	PROPN
ejpam-4671	208	45	∈	∈	PROPN
ejpam-4671	208	46	nh(a	nh(a	NUM
ejpam-4671	208	47	)	)	PUNCT
ejpam-4671	208	48	.	.	PUNCT
ejpam-4671	209	1	proof	proof	NOUN
ejpam-4671	209	2	:	:	PUNCT
ejpam-4671	209	3	suppose	suppose	VERB
ejpam-4671	209	4	w	w	NOUN
ejpam-4671	209	5	is	be	AUX
ejpam-4671	209	6	a	a	DET
ejpam-4671	209	7	1	1	NUM
ejpam-4671	209	8	-	-	PUNCT
ejpam-4671	209	9	movable	movable	ADJ
ejpam-4671	209	10	resolving	resolve	VERB
ejpam-4671	209	11	hop	hop	NOUN
ejpam-4671	209	12	dominating	dominating	NOUN
ejpam-4671	209	13	set	set	NOUN
ejpam-4671	209	14	of	of	ADP
ejpam-4671	209	15	g[h	g[h	PROPN
ejpam-4671	209	16	]	]	PUNCT
ejpam-4671	209	17	.	.	PUNCT
ejpam-4671	210	1	then	then	ADV
ejpam-4671	210	2	by	by	ADP
ejpam-4671	210	3	theorem	theorem	NOUN
ejpam-4671	210	4	5	5	NUM
ejpam-4671	210	5	,	,	PUNCT
ejpam-4671	210	6	s	s	PART
ejpam-4671	210	7	=	=	SYM
ejpam-4671	210	8	v	v	X
ejpam-4671	210	9	(	(	PUNCT
ejpam-4671	210	10	g	g	NOUN
ejpam-4671	210	11	)	)	PUNCT
ejpam-4671	210	12	and	and	CCONJ
ejpam-4671	210	13	tx	tx	PROPN
ejpam-4671	210	14	is	be	AUX
ejpam-4671	210	15	a	a	DET
ejpam-4671	210	16	locating	locating	NOUN
ejpam-4671	210	17	set	set	NOUN
ejpam-4671	210	18	of	of	ADP
ejpam-4671	210	19	h	h	NOUN
ejpam-4671	210	20	for	for	ADP
ejpam-4671	210	21	each	each	DET
ejpam-4671	210	22	x	x	SYM
ejpam-4671	210	23	∈	∈	PROPN
ejpam-4671	210	24	v	v	NOUN
ejpam-4671	210	25	(	(	PUNCT
ejpam-4671	210	26	g	g	NOUN
ejpam-4671	210	27	)	)	PUNCT
ejpam-4671	210	28	.	.	PUNCT
ejpam-4671	211	1	let	let	VERB
ejpam-4671	211	2	a	a	DET
ejpam-4671	211	3	∈	∈	PROPN
ejpam-4671	211	4	tx	tx	PROPN
ejpam-4671	211	5	.	.	PUNCT
ejpam-4671	212	1	then	then	ADV
ejpam-4671	212	2	(	(	PUNCT
ejpam-4671	212	3	x	x	X
ejpam-4671	212	4	,	,	PUNCT
ejpam-4671	212	5	a	a	DET
ejpam-4671	212	6	)	)	PUNCT
ejpam-4671	212	7	∈	∈	PROPN
ejpam-4671	212	8	w	w	NOUN
ejpam-4671	212	9	.	.	PUNCT
ejpam-4671	213	1	since	since	SCONJ
ejpam-4671	213	2	w	w	PROPN
ejpam-4671	213	3	is	be	AUX
ejpam-4671	213	4	a	a	DET
ejpam-4671	213	5	1	1	NUM
ejpam-4671	213	6	-	-	PUNCT
ejpam-4671	213	7	movable	movable	ADJ
ejpam-4671	213	8	resolving	resolve	VERB
ejpam-4671	213	9	hop	hop	NOUN
ejpam-4671	213	10	dominating	dominating	NOUN
ejpam-4671	213	11	set	set	NOUN
ejpam-4671	213	12	,	,	PUNCT
ejpam-4671	213	13	either	either	CCONJ
ejpam-4671	213	14	w	w	ADP
ejpam-4671	213	15	\	\	NOUN
ejpam-4671	213	16	{	{	PUNCT
ejpam-4671	213	17	(	(	PUNCT
ejpam-4671	213	18	x	x	X
ejpam-4671	213	19	,	,	PUNCT
ejpam-4671	213	20	a	a	NOUN
ejpam-4671	213	21	)	)	PUNCT
ejpam-4671	213	22	}	}	PUNCT
ejpam-4671	213	23	=	=	SYM
ejpam-4671	213	24			PROPN
ejpam-4671	213	25	⋃	⋃	NOUN
ejpam-4671	213	26	v∈s\{x	v∈s\{x	NOUN
ejpam-4671	213	27	}	}	PUNCT
ejpam-4671	213	28	(	(	PUNCT
ejpam-4671	213	29	{	{	PUNCT
ejpam-4671	213	30	v	v	NOUN
ejpam-4671	213	31	}	}	PUNCT
ejpam-4671	213	32	×	×	NOUN
ejpam-4671	213	33	tv	tv	NOUN
ejpam-4671	213	34	)	)	PUNCT
ejpam-4671	213	35			NOUN
ejpam-4671	213	36	∪	∪	ADP
ejpam-4671	213	37	[	[	PUNCT
ejpam-4671	213	38	{	{	PUNCT
ejpam-4671	213	39	x	x	NOUN
ejpam-4671	213	40	}	}	PUNCT
ejpam-4671	213	41	×	×	NOUN
ejpam-4671	213	42	(	(	PUNCT
ejpam-4671	213	43	tx	tx	PROPN
ejpam-4671	213	44	\	\	PROPN
ejpam-4671	213	45	{	{	PUNCT
ejpam-4671	213	46	a	a	NOUN
ejpam-4671	213	47	}	}	PUNCT
ejpam-4671	213	48	)	)	PUNCT
ejpam-4671	213	49	]	]	PUNCT
ejpam-4671	213	50	or	or	CCONJ
ejpam-4671	213	51	(	(	PUNCT
ejpam-4671	213	52	w	w	PROPN
ejpam-4671	213	53	\	\	NOUN
ejpam-4671	213	54	{	{	PUNCT
ejpam-4671	213	55	(	(	PUNCT
ejpam-4671	213	56	x	x	X
ejpam-4671	213	57	,	,	PUNCT
ejpam-4671	213	58	a	a	NOUN
ejpam-4671	213	59	)	)	PUNCT
ejpam-4671	213	60	}	}	PUNCT
ejpam-4671	213	61	)	)	PUNCT
ejpam-4671	213	62	∪	∪	X
ejpam-4671	213	63	{	{	PUNCT
ejpam-4671	213	64	(	(	PUNCT
ejpam-4671	213	65	x	x	NOUN
ejpam-4671	213	66	,	,	PUNCT
ejpam-4671	213	67	b	b	NOUN
ejpam-4671	213	68	)	)	PUNCT
ejpam-4671	213	69	}	}	PUNCT
ejpam-4671	214	1	=	=	SYM
ejpam-4671	214	2			PROPN
ejpam-4671	214	3	⋃	⋃	VERB
ejpam-4671	214	4	z∈s\{x	z∈s\{x	PROPN
ejpam-4671	214	5	}	}	PUNCT
ejpam-4671	214	6	(	(	PUNCT
ejpam-4671	214	7	{	{	PUNCT
ejpam-4671	214	8	z	z	NOUN
ejpam-4671	214	9	}	}	PUNCT
ejpam-4671	214	10	×	×	PROPN
ejpam-4671	214	11	tz	tz	NOUN
ejpam-4671	214	12	)	)	PUNCT
ejpam-4671	214	13			NOUN
ejpam-4671	214	14	∪	∪	ADP
ejpam-4671	214	15	[	[	PUNCT
ejpam-4671	214	16	{	{	PUNCT
ejpam-4671	214	17	x	x	NOUN
ejpam-4671	214	18	}	}	PUNCT
ejpam-4671	214	19	×	×	NOUN
ejpam-4671	214	20	(	(	PUNCT
ejpam-4671	214	21	tx	tx	PROPN
ejpam-4671	214	22	\	\	PROPN
ejpam-4671	214	23	{	{	PUNCT
ejpam-4671	214	24	a	a	DET
ejpam-4671	214	25	}	}	PUNCT
ejpam-4671	214	26	∪	∪	NOUN
ejpam-4671	214	27	{	{	PUNCT
ejpam-4671	214	28	b	b	NOUN
ejpam-4671	214	29	}	}	PUNCT
ejpam-4671	214	30	)	)	PUNCT
ejpam-4671	214	31	]	]	PUNCT
ejpam-4671	214	32	for	for	ADP
ejpam-4671	214	33	some	some	DET
ejpam-4671	214	34	b	b	PROPN
ejpam-4671	214	35	∈	∈	PROPN
ejpam-4671	214	36	nh(a	nh(a	NUM
ejpam-4671	214	37	)	)	PUNCT
ejpam-4671	214	38	∩	∩	NOUN
ejpam-4671	214	39	(	(	PUNCT
ejpam-4671	214	40	v	v	NOUN
ejpam-4671	214	41	(	(	PUNCT
ejpam-4671	214	42	h	h	NOUN
ejpam-4671	214	43	)	)	PUNCT
ejpam-4671	214	44	\	\	PUNCT
ejpam-4671	214	45	tx	tx	PROPN
ejpam-4671	214	46	)	)	PUNCT
ejpam-4671	214	47	or	or	CCONJ
ejpam-4671	214	48	(	(	PUNCT
ejpam-4671	214	49	w	w	PROPN
ejpam-4671	214	50	\	\	NOUN
ejpam-4671	214	51	{	{	PUNCT
ejpam-4671	214	52	(	(	PUNCT
ejpam-4671	214	53	x	x	X
ejpam-4671	214	54	,	,	PUNCT
ejpam-4671	214	55	a	a	NOUN
ejpam-4671	214	56	)	)	PUNCT
ejpam-4671	214	57	}	}	PUNCT
ejpam-4671	214	58	)	)	PUNCT
ejpam-4671	214	59	∪	∪	X
ejpam-4671	214	60	{	{	PUNCT
ejpam-4671	214	61	(	(	PUNCT
ejpam-4671	214	62	y	y	PROPN
ejpam-4671	214	63	,	,	PUNCT
ejpam-4671	214	64	u	u	NOUN
ejpam-4671	214	65	)	)	PUNCT
ejpam-4671	214	66	}	}	PUNCT
ejpam-4671	214	67	=	=	SYM
ejpam-4671	214	68			NOUN
ejpam-4671	214	69	⋃	⋃	NOUN
ejpam-4671	214	70	p∈s\{(x	p∈s\{(x	NOUN
ejpam-4671	214	71	,	,	PUNCT
ejpam-4671	214	72	y	y	NOUN
ejpam-4671	214	73	)	)	PUNCT
ejpam-4671	214	74	}	}	PUNCT
ejpam-4671	214	75	(	(	PUNCT
ejpam-4671	214	76	{	{	PUNCT
ejpam-4671	214	77	p	p	NOUN
ejpam-4671	214	78	}	}	PUNCT
ejpam-4671	214	79	×	×	PROPN
ejpam-4671	214	80	tp	tp	NOUN
ejpam-4671	214	81	)	)	PUNCT
ejpam-4671	214	82			NOUN
ejpam-4671	214	83	∪	∪	ADP
ejpam-4671	214	84	[	[	PUNCT
ejpam-4671	214	85	{	{	PUNCT
ejpam-4671	214	86	x	x	NOUN
ejpam-4671	214	87	}	}	PUNCT
ejpam-4671	214	88	×	×	NOUN
ejpam-4671	214	89	(	(	PUNCT
ejpam-4671	214	90	tx	tx	PROPN
ejpam-4671	214	91	\	\	PROPN
ejpam-4671	214	92	{	{	PUNCT
ejpam-4671	214	93	a	a	NOUN
ejpam-4671	214	94	}	}	PUNCT
ejpam-4671	214	95	)	)	PUNCT
ejpam-4671	214	96	]	]	PUNCT
ejpam-4671	214	97	∪	∪	ADP
ejpam-4671	214	98	[	[	X
ejpam-4671	214	99	{	{	PUNCT
ejpam-4671	214	100	y	y	NOUN
ejpam-4671	214	101	}	}	PUNCT
ejpam-4671	214	102	×	×	NOUN
ejpam-4671	214	103	(	(	PUNCT
ejpam-4671	214	104	ty	ty	NOUN
ejpam-4671	214	105	∪	∪	X
ejpam-4671	214	106	{	{	PUNCT
ejpam-4671	214	107	u	u	NOUN
ejpam-4671	214	108	}	}	PUNCT
ejpam-4671	214	109	)	)	PUNCT
ejpam-4671	214	110	]	]	PUNCT
ejpam-4671	214	111	for	for	ADP
ejpam-4671	214	112	some	some	DET
ejpam-4671	214	113	y	y	PROPN
ejpam-4671	214	114	∈	∈	PROPN
ejpam-4671	214	115	v	v	ADP
ejpam-4671	214	116	(	(	PUNCT
ejpam-4671	214	117	g	g	NOUN
ejpam-4671	214	118	)	)	PUNCT
ejpam-4671	214	119	∩	∩	NOUN
ejpam-4671	214	120	ng(x	ng(x	NUM
ejpam-4671	214	121	)	)	PUNCT
ejpam-4671	214	122	and	and	CCONJ
ejpam-4671	214	123	u	u	PROPN
ejpam-4671	214	124	∈	∈	PROPN
ejpam-4671	214	125	v	v	ADP
ejpam-4671	214	126	(	(	PUNCT
ejpam-4671	214	127	h	h	NOUN
ejpam-4671	214	128	)	)	PUNCT
ejpam-4671	214	129	\	\	NOUN
ejpam-4671	215	1	ty	ty	PRON
ejpam-4671	215	2	is	be	AUX
ejpam-4671	215	3	a	a	DET
ejpam-4671	215	4	resolving	resolve	VERB
ejpam-4671	215	5	hop	hop	NOUN
ejpam-4671	215	6	dominating	dominating	NOUN
ejpam-4671	215	7	set	set	NOUN
ejpam-4671	215	8	of	of	ADP
ejpam-4671	215	9	g[h	g[h	NOUN
ejpam-4671	215	10	]	]	PUNCT
ejpam-4671	215	11	.	.	PUNCT
ejpam-4671	216	1	by	by	ADP
ejpam-4671	216	2	theorem	theorem	NOUN
ejpam-4671	216	3	5	5	NUM
ejpam-4671	216	4	,	,	PUNCT
ejpam-4671	216	5	tx	tx	ADP
ejpam-4671	216	6	\	\	PROPN
ejpam-4671	216	7	{	{	PUNCT
ejpam-4671	216	8	a	a	NOUN
ejpam-4671	216	9	}	}	PUNCT
ejpam-4671	216	10	or	or	CCONJ
ejpam-4671	216	11	(	(	PUNCT
ejpam-4671	216	12	tx	tx	PROPN
ejpam-4671	216	13	\	\	PROPN
ejpam-4671	216	14	{	{	PUNCT
ejpam-4671	216	15	a	a	NOUN
ejpam-4671	216	16	}	}	PUNCT
ejpam-4671	216	17	)	)	PUNCT
ejpam-4671	216	18	∪	∪	ADP
ejpam-4671	216	19	{	{	PUNCT
ejpam-4671	216	20	b	b	NOUN
ejpam-4671	216	21	}	}	PUNCT
ejpam-4671	216	22	is	be	AUX
ejpam-4671	216	23	a	a	DET
ejpam-4671	216	24	locating	locating	NOUN
ejpam-4671	216	25	set	set	NOUN
ejpam-4671	216	26	of	of	ADP
ejpam-4671	216	27	h	h	NOUN
ejpam-4671	216	28	for	for	ADP
ejpam-4671	216	29	each	each	PRON
ejpam-4671	216	30	a	a	DET
ejpam-4671	216	31	∈	∈	PROPN
ejpam-4671	216	32	tx	tx	NOUN
ejpam-4671	216	33	and	and	CCONJ
ejpam-4671	216	34	for	for	ADP
ejpam-4671	216	35	some	some	DET
ejpam-4671	216	36	b	b	PROPN
ejpam-4671	216	37	∈	∈	PROPN
ejpam-4671	216	38	nh(a	nh(a	NUM
ejpam-4671	216	39	)	)	PUNCT
ejpam-4671	216	40	∩	∩	NOUN
ejpam-4671	216	41	(	(	PUNCT
ejpam-4671	216	42	v	v	NOUN
ejpam-4671	216	43	(	(	PUNCT
ejpam-4671	216	44	h	h	NOUN
ejpam-4671	216	45	)	)	PUNCT
ejpam-4671	216	46	\	\	PUNCT
ejpam-4671	216	47	tx	tx	PROPN
ejpam-4671	216	48	)	)	PUNCT
ejpam-4671	216	49	.	.	PUNCT
ejpam-4671	217	1	hence	hence	ADV
ejpam-4671	217	2	,	,	PUNCT
ejpam-4671	217	3	tx	tx	PROPN
ejpam-4671	217	4	is	be	AUX
ejpam-4671	217	5	a	a	DET
ejpam-4671	217	6	1	1	NUM
ejpam-4671	217	7	-	-	PUNCT
ejpam-4671	217	8	movable	movable	ADJ
ejpam-4671	217	9	locating	locating	NOUN
ejpam-4671	217	10	set	set	NOUN
ejpam-4671	217	11	of	of	ADP
ejpam-4671	217	12	h	h	NOUN
ejpam-4671	217	13	for	for	ADP
ejpam-4671	217	14	each	each	DET
ejpam-4671	217	15	x	x	SYM
ejpam-4671	217	16	∈	∈	PROPN
ejpam-4671	217	17	v	v	ADP
ejpam-4671	217	18	(	(	PUNCT
ejpam-4671	217	19	g	g	NOUN
ejpam-4671	217	20	)	)	PUNCT
ejpam-4671	217	21	or	or	CCONJ
ejpam-4671	217	22	tx	tx	ADP
ejpam-4671	217	23	\	\	PROPN
ejpam-4671	217	24	{	{	PUNCT
ejpam-4671	217	25	a	a	PRON
ejpam-4671	217	26	}	}	PUNCT
ejpam-4671	217	27	is	be	AUX
ejpam-4671	217	28	locating	locate	VERB
ejpam-4671	217	29	and	and	CCONJ
ejpam-4671	217	30	(	(	PUNCT
ejpam-4671	217	31	ii	ii	NOUN
ejpam-4671	217	32	)	)	PUNCT
ejpam-4671	217	33	holds	hold	VERB
ejpam-4671	217	34	.	.	PUNCT
ejpam-4671	218	1	suppose	suppose	VERB
ejpam-4671	218	2	(	(	PUNCT
ejpam-4671	218	3	iii	iii	X
ejpam-4671	218	4	)	)	PUNCT
ejpam-4671	218	5	does	do	AUX
ejpam-4671	218	6	not	not	PART
ejpam-4671	218	7	hold	hold	VERB
ejpam-4671	218	8	.	.	PUNCT
ejpam-4671	219	1	then	then	ADV
ejpam-4671	219	2	there	there	PRON
ejpam-4671	219	3	exist	exist	VERB
ejpam-4671	219	4	p	p	PROPN
ejpam-4671	219	5	∈	∈	PROPN
ejpam-4671	219	6	v	v	ADP
ejpam-4671	219	7	(	(	PUNCT
ejpam-4671	219	8	h	h	NOUN
ejpam-4671	219	9	)	)	PUNCT
ejpam-4671	219	10	\	\	PUNCT
ejpam-4671	220	1	(	(	PUNCT
ejpam-4671	220	2	tx	tx	PROPN
ejpam-4671	220	3	\	\	PROPN
ejpam-4671	220	4	{	{	PUNCT
ejpam-4671	220	5	a	a	NOUN
ejpam-4671	220	6	}	}	PUNCT
ejpam-4671	220	7	)	)	PUNCT
ejpam-4671	220	8	and	and	CCONJ
ejpam-4671	220	9	q	q	PROPN
ejpam-4671	220	10	∈	∈	PROPN
ejpam-4671	220	11	v	v	ADP
ejpam-4671	220	12	(	(	PUNCT
ejpam-4671	220	13	h	h	NOUN
ejpam-4671	220	14	)	)	PUNCT
ejpam-4671	220	15	\	\	NOUN
ejpam-4671	221	1	ty	ty	INTJ
ejpam-4671	221	2	such	such	ADJ
ejpam-4671	221	3	that	that	PRON
ejpam-4671	221	4	nh(p	nh(p	NUM
ejpam-4671	221	5	)	)	PUNCT
ejpam-4671	221	6	∩	∩	NOUN
ejpam-4671	221	7	(	(	PUNCT
ejpam-4671	221	8	tx	tx	PROPN
ejpam-4671	221	9	\	\	PROPN
ejpam-4671	221	10	{	{	PUNCT
ejpam-4671	221	11	a	a	NOUN
ejpam-4671	221	12	}	}	PUNCT
ejpam-4671	221	13	)	)	PUNCT
ejpam-4671	221	14	=	=	SYM
ejpam-4671	221	15	tx	tx	PROPN
ejpam-4671	221	16	\	\	PROPN
ejpam-4671	221	17	{	{	PUNCT
ejpam-4671	221	18	a	a	NOUN
ejpam-4671	221	19	}	}	PUNCT
ejpam-4671	221	20	and	and	CCONJ
ejpam-4671	221	21	nh(q)∩ty	nh(q)∩ty	PROPN
ejpam-4671	221	22	=	=	PUNCT
ejpam-4671	222	1	ty	ty	INTJ
ejpam-4671	222	2	for	for	ADP
ejpam-4671	222	3	some	some	DET
ejpam-4671	222	4	adjacent	adjacent	ADJ
ejpam-4671	222	5	vertices	vertex	NOUN
ejpam-4671	222	6	x	x	PUNCT
ejpam-4671	222	7	and	and	CCONJ
ejpam-4671	222	8	y	y	PROPN
ejpam-4671	222	9	of	of	ADP
ejpam-4671	222	10	g	g	PROPN
ejpam-4671	222	11	with	with	ADP
ejpam-4671	222	12	ng[x	ng[x	PROPN
ejpam-4671	222	13	]	]	X
ejpam-4671	222	14	=	=	PUNCT
ejpam-4671	222	15	ng[y	ng[y	PROPN
ejpam-4671	222	16	]	]	PUNCT
ejpam-4671	222	17	and	and	CCONJ
ejpam-4671	222	18	for	for	ADP
ejpam-4671	222	19	some	some	PRON
ejpam-4671	222	20	a	a	DET
ejpam-4671	222	21	∈	∈	PROPN
ejpam-4671	222	22	tx	tx	PROPN
ejpam-4671	222	23	.	.	PUNCT
ejpam-4671	223	1	hence	hence	ADV
ejpam-4671	223	2	,	,	PUNCT
ejpam-4671	223	3	both	both	PRON
ejpam-4671	223	4	w	w	ADP
ejpam-4671	223	5	\	\	NOUN
ejpam-4671	223	6	{	{	PUNCT
ejpam-4671	223	7	(	(	PUNCT
ejpam-4671	223	8	x	x	X
ejpam-4671	223	9	,	,	PUNCT
ejpam-4671	223	10	a	a	NOUN
ejpam-4671	223	11	)	)	PUNCT
ejpam-4671	223	12	}	}	PUNCT
ejpam-4671	223	13	and	and	CCONJ
ejpam-4671	223	14	(	(	PUNCT
ejpam-4671	223	15	w	w	PROPN
ejpam-4671	223	16	\	\	NOUN
ejpam-4671	223	17	{	{	PUNCT
ejpam-4671	223	18	(	(	PUNCT
ejpam-4671	223	19	x	x	X
ejpam-4671	223	20	,	,	PUNCT
ejpam-4671	223	21	a)})∪{(y	a)})∪{(y	ADJ
ejpam-4671	223	22	,	,	PUNCT
ejpam-4671	223	23	b	b	NOUN
ejpam-4671	223	24	)	)	PUNCT
ejpam-4671	223	25	}	}	PUNCT
ejpam-4671	223	26	are	be	AUX
ejpam-4671	223	27	not	not	PART
ejpam-4671	223	28	resolving	resolve	VERB
ejpam-4671	223	29	sets	set	NOUN
ejpam-4671	223	30	,	,	PUNCT
ejpam-4671	223	31	a	a	DET
ejpam-4671	223	32	contradiction	contradiction	NOUN
ejpam-4671	223	33	.	.	PUNCT
ejpam-4671	224	1	thus	thus	ADV
ejpam-4671	224	2	,	,	PUNCT
ejpam-4671	224	3	(	(	PUNCT
ejpam-4671	224	4	iii	iii	NOUN
ejpam-4671	224	5	)	)	PUNCT
ejpam-4671	224	6	holds	hold	VERB
ejpam-4671	224	7	.	.	PUNCT
ejpam-4671	225	1	statement	statement	NOUN
ejpam-4671	225	2	(	(	PUNCT
ejpam-4671	225	3	iv	iv	X
ejpam-4671	225	4	)	)	PUNCT
ejpam-4671	225	5	is	be	AUX
ejpam-4671	225	6	proved	prove	VERB
ejpam-4671	225	7	similarly	similarly	ADV
ejpam-4671	225	8	.	.	PUNCT
ejpam-4671	226	1	if	if	SCONJ
ejpam-4671	226	2	(	(	PUNCT
ejpam-4671	226	3	v	v	NOUN
ejpam-4671	226	4	)	)	PUNCT
ejpam-4671	226	5	does	do	AUX
ejpam-4671	226	6	not	not	PART
ejpam-4671	226	7	hold	hold	VERB
ejpam-4671	226	8	,	,	PUNCT
ejpam-4671	226	9	then	then	ADV
ejpam-4671	226	10	w	w	PROPN
ejpam-4671	226	11	\	\	PROPN
ejpam-4671	226	12	{	{	PUNCT
ejpam-4671	226	13	(	(	PUNCT
ejpam-4671	226	14	x	x	X
ejpam-4671	226	15	,	,	PUNCT
ejpam-4671	226	16	a	a	NOUN
ejpam-4671	226	17	)	)	PUNCT
ejpam-4671	226	18	}	}	PUNCT
ejpam-4671	226	19	and	and	CCONJ
ejpam-4671	226	20	(	(	PUNCT
ejpam-4671	226	21	w	w	PROPN
ejpam-4671	226	22	\	\	NOUN
ejpam-4671	226	23	{	{	PUNCT
ejpam-4671	226	24	(	(	PUNCT
ejpam-4671	226	25	x	x	X
ejpam-4671	226	26	,	,	PUNCT
ejpam-4671	226	27	a	a	PRON
ejpam-4671	226	28	)	)	PUNCT
ejpam-4671	226	29	}	}	PUNCT
ejpam-4671	226	30	∪	∪	X
ejpam-4671	226	31	{	{	PUNCT
ejpam-4671	226	32	(	(	PUNCT
ejpam-4671	226	33	y	y	PROPN
ejpam-4671	226	34	,	,	PUNCT
ejpam-4671	226	35	b	b	NOUN
ejpam-4671	226	36	)	)	PUNCT
ejpam-4671	226	37	}	}	PUNCT
ejpam-4671	226	38	)	)	PUNCT
ejpam-4671	226	39	are	be	AUX
ejpam-4671	226	40	not	not	PART
ejpam-4671	226	41	hop	hop	ADJ
ejpam-4671	226	42	dominating	dominating	NOUN
ejpam-4671	226	43	sets	set	NOUN
ejpam-4671	226	44	of	of	ADP
ejpam-4671	226	45	g[h	g[h	NOUN
ejpam-4671	226	46	]	]	PUNCT
ejpam-4671	226	47	for	for	ADP
ejpam-4671	226	48	all	all	DET
ejpam-4671	226	49	y	y	PROPN
ejpam-4671	226	50	∈	∈	PROPN
ejpam-4671	226	51	ng(x	ng(x	NUM
ejpam-4671	226	52	)	)	PUNCT
ejpam-4671	226	53	and	and	CCONJ
ejpam-4671	226	54	b	b	X
ejpam-4671	226	55	∈	∈	PROPN
ejpam-4671	226	56	v	v	ADP
ejpam-4671	226	57	(	(	PUNCT
ejpam-4671	226	58	h	h	NOUN
ejpam-4671	226	59	)	)	PUNCT
ejpam-4671	226	60	\	\	NOUN
ejpam-4671	226	61	tx	tx	PROPN
ejpam-4671	226	62	or	or	CCONJ
ejpam-4671	226	63	x	x	X
ejpam-4671	226	64	=	=	SYM
ejpam-4671	226	65	y	y	PROPN
ejpam-4671	226	66	and	and	CCONJ
ejpam-4671	226	67	b	b	PROPN
ejpam-4671	226	68	∈	∈	PROPN
ejpam-4671	226	69	nh(a	nh(a	NUM
ejpam-4671	226	70	)	)	PUNCT
ejpam-4671	226	71	.	.	PUNCT
ejpam-4671	227	1	this	this	PRON
ejpam-4671	227	2	is	be	AUX
ejpam-4671	227	3	a	a	DET
ejpam-4671	227	4	contradiction	contradiction	NOUN
ejpam-4671	227	5	to	to	ADP
ejpam-4671	227	6	w	w	NOUN
ejpam-4671	227	7	being	be	AUX
ejpam-4671	227	8	a	a	DET
ejpam-4671	227	9	1	1	NUM
ejpam-4671	227	10	-	-	PUNCT
ejpam-4671	227	11	movable	movable	ADJ
ejpam-4671	227	12	resolving	resolve	VERB
ejpam-4671	227	13	hop	hop	NOUN
ejpam-4671	227	14	dominating	dominating	NOUN
ejpam-4671	227	15	set	set	NOUN
ejpam-4671	227	16	of	of	ADP
ejpam-4671	227	17	g[h	g[h	NOUN
ejpam-4671	227	18	]	]	PUNCT
ejpam-4671	227	19	.	.	PUNCT
ejpam-4671	228	1	hence	hence	ADV
ejpam-4671	228	2	,	,	PUNCT
ejpam-4671	228	3	(	(	PUNCT
ejpam-4671	228	4	v	v	NOUN
ejpam-4671	228	5	)	)	PUNCT
ejpam-4671	228	6	holds	hold	NOUN
ejpam-4671	228	7	.	.	PUNCT
ejpam-4671	229	1	for	for	ADP
ejpam-4671	229	2	the	the	DET
ejpam-4671	229	3	converse	converse	NOUN
ejpam-4671	229	4	,	,	PUNCT
ejpam-4671	229	5	suppose	suppose	VERB
ejpam-4671	229	6	that	that	SCONJ
ejpam-4671	229	7	w	w	NOUN
ejpam-4671	229	8	satisfies	satisfie	NOUN
ejpam-4671	229	9	properties	property	NOUN
ejpam-4671	229	10	(	(	PUNCT
ejpam-4671	229	11	i	i	NOUN
ejpam-4671	229	12	)	)	PUNCT
ejpam-4671	229	13	to	to	ADP
ejpam-4671	229	14	(	(	PUNCT
ejpam-4671	229	15	v	v	NOUN
ejpam-4671	229	16	)	)	PUNCT
ejpam-4671	229	17	.	.	PUNCT
ejpam-4671	230	1	by	by	ADP
ejpam-4671	230	2	theorem	theorem	NOUN
ejpam-4671	230	3	5	5	NUM
ejpam-4671	230	4	,	,	PUNCT
ejpam-4671	230	5	w	w	PROPN
ejpam-4671	230	6	is	be	AUX
ejpam-4671	230	7	a	a	DET
ejpam-4671	230	8	resolving	resolve	VERB
ejpam-4671	230	9	hop	hop	NOUN
ejpam-4671	230	10	dominating	dominating	NOUN
ejpam-4671	230	11	set	set	NOUN
ejpam-4671	230	12	of	of	ADP
ejpam-4671	230	13	g[h	g[h	PROPN
ejpam-4671	230	14	]	]	PUNCT
ejpam-4671	230	15	.	.	PUNCT
ejpam-4671	231	1	let	let	VERB
ejpam-4671	231	2	x	x	SYM
ejpam-4671	231	3	∈	∈	PROPN
ejpam-4671	231	4	v	v	X
ejpam-4671	231	5	(	(	PUNCT
ejpam-4671	231	6	g	g	NOUN
ejpam-4671	231	7	)	)	PUNCT
ejpam-4671	231	8	and	and	CCONJ
ejpam-4671	231	9	a	a	DET
ejpam-4671	231	10	∈	∈	PROPN
ejpam-4671	231	11	tx	tx	PROPN
ejpam-4671	231	12	.	.	PUNCT
ejpam-4671	232	1	then	then	ADV
ejpam-4671	232	2	(	(	PUNCT
ejpam-4671	232	3	x	x	X
ejpam-4671	232	4	,	,	PUNCT
ejpam-4671	232	5	a	a	PRON
ejpam-4671	232	6	)	)	PUNCT
ejpam-4671	232	7	∈	∈	PROPN
ejpam-4671	232	8	w	w	NOUN
ejpam-4671	232	9	and	and	CCONJ
ejpam-4671	232	10	w	w	PROPN
ejpam-4671	232	11	\	\	PROPN
ejpam-4671	232	12	{	{	PUNCT
ejpam-4671	232	13	(	(	PUNCT
ejpam-4671	232	14	x	x	X
ejpam-4671	232	15	,	,	PUNCT
ejpam-4671	232	16	a	a	NOUN
ejpam-4671	232	17	)	)	PUNCT
ejpam-4671	232	18	}	}	PUNCT
ejpam-4671	232	19	=	=	SYM
ejpam-4671	232	20			PROPN
ejpam-4671	232	21	⋃	⋃	NOUN
ejpam-4671	232	22	v∈s\{x	v∈s\{x	NOUN
ejpam-4671	232	23	}	}	PUNCT
ejpam-4671	232	24	(	(	PUNCT
ejpam-4671	232	25	{	{	PUNCT
ejpam-4671	232	26	v	v	NOUN
ejpam-4671	232	27	}	}	PUNCT
ejpam-4671	232	28	×	×	NOUN
ejpam-4671	232	29	tv	tv	NOUN
ejpam-4671	232	30	)	)	PUNCT
ejpam-4671	232	31			NOUN
ejpam-4671	232	32	∪	∪	ADP
ejpam-4671	232	33	[	[	PUNCT
ejpam-4671	232	34	{	{	PUNCT
ejpam-4671	232	35	x	x	NOUN
ejpam-4671	232	36	}	}	PUNCT
ejpam-4671	232	37	×	×	NOUN
ejpam-4671	232	38	(	(	PUNCT
ejpam-4671	232	39	tx	tx	PROPN
ejpam-4671	232	40	\	\	PROPN
ejpam-4671	232	41	{	{	PUNCT
ejpam-4671	232	42	a	a	NOUN
ejpam-4671	232	43	}	}	PUNCT
ejpam-4671	232	44	)	)	PUNCT
ejpam-4671	232	45	]	]	PUNCT
ejpam-4671	233	1	j.	j.	PROPN
ejpam-4671	233	2	mohamad	mohamad	PROPN
ejpam-4671	233	3	,	,	PUNCT
ejpam-4671	233	4	h.	h.	PROPN
ejpam-4671	233	5	rara	rara	PROPN
ejpam-4671	233	6	/	/	SYM
ejpam-4671	233	7	eur	eur	PROPN
ejpam-4671	233	8	.	.	PUNCT
ejpam-4671	234	1	j.	j.	PROPN
ejpam-4671	234	2	pure	pure	PROPN
ejpam-4671	234	3	appl	appl	PROPN
ejpam-4671	234	4	.	.	PROPN
ejpam-4671	234	5	math	math	PROPN
ejpam-4671	234	6	,	,	PUNCT
ejpam-4671	234	7	16	16	NUM
ejpam-4671	234	8	(	(	PUNCT
ejpam-4671	234	9	1	1	NUM
ejpam-4671	234	10	)	)	PUNCT
ejpam-4671	234	11	(	(	PUNCT
ejpam-4671	234	12	2023	2023	NUM
ejpam-4671	234	13	)	)	PUNCT
ejpam-4671	234	14	,	,	PUNCT
ejpam-4671	234	15	418	418	NUM
ejpam-4671	234	16	-	-	SYM
ejpam-4671	234	17	429	429	NUM
ejpam-4671	234	18	428	428	NUM
ejpam-4671	234	19	and	and	CCONJ
ejpam-4671	234	20	for	for	ADP
ejpam-4671	234	21	some	some	DET
ejpam-4671	234	22	b	b	PROPN
ejpam-4671	234	23	∈	∈	PROPN
ejpam-4671	234	24	nh(a	nh(a	NUM
ejpam-4671	234	25	)	)	PUNCT
ejpam-4671	234	26	∩	∩	NOUN
ejpam-4671	234	27	(	(	PUNCT
ejpam-4671	234	28	v	v	NOUN
ejpam-4671	234	29	(	(	PUNCT
ejpam-4671	234	30	h	h	NOUN
ejpam-4671	234	31	)	)	PUNCT
ejpam-4671	234	32	\	\	PUNCT
ejpam-4671	234	33	tx	tx	PROPN
ejpam-4671	234	34	)	)	PUNCT
ejpam-4671	234	35	,	,	PUNCT
ejpam-4671	234	36	(	(	PUNCT
ejpam-4671	234	37	w	w	NOUN
ejpam-4671	234	38	\	\	NOUN
ejpam-4671	234	39	{	{	PUNCT
ejpam-4671	234	40	(	(	PUNCT
ejpam-4671	234	41	x	x	X
ejpam-4671	234	42	,	,	PUNCT
ejpam-4671	234	43	a	a	NOUN
ejpam-4671	234	44	)	)	PUNCT
ejpam-4671	234	45	}	}	PUNCT
ejpam-4671	234	46	)	)	PUNCT
ejpam-4671	234	47	∪	∪	X
ejpam-4671	234	48	{	{	PUNCT
ejpam-4671	234	49	(	(	PUNCT
ejpam-4671	234	50	x	x	NOUN
ejpam-4671	234	51	,	,	PUNCT
ejpam-4671	234	52	b	b	NOUN
ejpam-4671	234	53	)	)	PUNCT
ejpam-4671	234	54	}	}	PUNCT
ejpam-4671	234	55	=	=	SYM
ejpam-4671	234	56			PROPN
ejpam-4671	234	57	⋃	⋃	VERB
ejpam-4671	234	58	z∈s\{x	z∈s\{x	PROPN
ejpam-4671	234	59	}	}	PUNCT
ejpam-4671	234	60	(	(	PUNCT
ejpam-4671	234	61	{	{	PUNCT
ejpam-4671	234	62	z	z	NOUN
ejpam-4671	234	63	}	}	PUNCT
ejpam-4671	234	64	×	×	PROPN
ejpam-4671	234	65	tz	tz	NOUN
ejpam-4671	234	66	)	)	PUNCT
ejpam-4671	234	67			NOUN
ejpam-4671	234	68	∪	∪	ADP
ejpam-4671	234	69	[	[	PUNCT
ejpam-4671	234	70	{	{	PUNCT
ejpam-4671	234	71	x	x	NOUN
ejpam-4671	234	72	}	}	PUNCT
ejpam-4671	234	73	×	×	NOUN
ejpam-4671	234	74	(	(	PUNCT
ejpam-4671	234	75	(	(	PUNCT
ejpam-4671	234	76	tx	tx	PROPN
ejpam-4671	234	77	\	\	PROPN
ejpam-4671	234	78	{	{	PUNCT
ejpam-4671	234	79	a	a	NOUN
ejpam-4671	234	80	}	}	PUNCT
ejpam-4671	234	81	)	)	PUNCT
ejpam-4671	234	82	∪	∪	ADP
ejpam-4671	234	83	{	{	PUNCT
ejpam-4671	234	84	b	b	NOUN
ejpam-4671	234	85	}	}	PUNCT
ejpam-4671	234	86	)	)	PUNCT
ejpam-4671	234	87	]	]	PUNCT
ejpam-4671	234	88	and	and	CCONJ
ejpam-4671	234	89	(	(	PUNCT
ejpam-4671	234	90	w	w	PROPN
ejpam-4671	234	91	\	\	NOUN
ejpam-4671	234	92	{	{	PUNCT
ejpam-4671	234	93	(	(	PUNCT
ejpam-4671	234	94	x	x	X
ejpam-4671	234	95	,	,	PUNCT
ejpam-4671	234	96	a	a	NOUN
ejpam-4671	234	97	)	)	PUNCT
ejpam-4671	234	98	}	}	PUNCT
ejpam-4671	234	99	)	)	PUNCT
ejpam-4671	234	100	∪	∪	X
ejpam-4671	234	101	{	{	PUNCT
ejpam-4671	234	102	(	(	PUNCT
ejpam-4671	234	103	y	y	PROPN
ejpam-4671	234	104	,	,	PUNCT
ejpam-4671	234	105	q	q	NOUN
ejpam-4671	234	106	)	)	PUNCT
ejpam-4671	234	107	}	}	PUNCT
ejpam-4671	234	108	=	=	SYM
ejpam-4671	234	109			NOUN
ejpam-4671	234	110	⋃	⋃	NOUN
ejpam-4671	234	111	p∈s\{(x	p∈s\{(x	NOUN
ejpam-4671	234	112	,	,	PUNCT
ejpam-4671	234	113	y	y	NOUN
ejpam-4671	234	114	)	)	PUNCT
ejpam-4671	234	115	}	}	PUNCT
ejpam-4671	234	116	(	(	PUNCT
ejpam-4671	234	117	{	{	PUNCT
ejpam-4671	234	118	p	p	NOUN
ejpam-4671	234	119	}	}	PUNCT
ejpam-4671	234	120	×	×	PROPN
ejpam-4671	234	121	tp	tp	NOUN
ejpam-4671	234	122	)	)	PUNCT
ejpam-4671	234	123			NOUN
ejpam-4671	234	124	∪	∪	ADP
ejpam-4671	234	125	[	[	PUNCT
ejpam-4671	234	126	{	{	PUNCT
ejpam-4671	234	127	x	x	NOUN
ejpam-4671	234	128	}	}	PUNCT
ejpam-4671	234	129	×	×	NOUN
ejpam-4671	234	130	(	(	PUNCT
ejpam-4671	234	131	tx	tx	PROPN
ejpam-4671	234	132	\	\	PROPN
ejpam-4671	234	133	{	{	PUNCT
ejpam-4671	234	134	a	a	NOUN
ejpam-4671	234	135	}	}	PUNCT
ejpam-4671	234	136	)	)	PUNCT
ejpam-4671	234	137	]	]	PUNCT
ejpam-4671	234	138	∪	∪	ADP
ejpam-4671	234	139	[	[	X
ejpam-4671	234	140	{	{	PUNCT
ejpam-4671	234	141	y	y	NOUN
ejpam-4671	234	142	}	}	PUNCT
ejpam-4671	234	143	×	×	NOUN
ejpam-4671	234	144	(	(	PUNCT
ejpam-4671	234	145	ty	ty	NOUN
ejpam-4671	234	146	∪	∪	X
ejpam-4671	234	147	{	{	PUNCT
ejpam-4671	234	148	q	q	NOUN
ejpam-4671	234	149	}	}	PUNCT
ejpam-4671	234	150	)	)	PUNCT
ejpam-4671	234	151	]	]	PUNCT
ejpam-4671	234	152	for	for	ADP
ejpam-4671	234	153	some	some	DET
ejpam-4671	234	154	y	y	PROPN
ejpam-4671	234	155	∈	∈	PROPN
ejpam-4671	234	156	v	v	ADP
ejpam-4671	234	157	(	(	PUNCT
ejpam-4671	234	158	g	g	NOUN
ejpam-4671	234	159	)	)	PUNCT
ejpam-4671	234	160	∩ng(x	∩ng(x	NOUN
ejpam-4671	234	161	)	)	PUNCT
ejpam-4671	234	162	and	and	CCONJ
ejpam-4671	234	163	q	q	PROPN
ejpam-4671	234	164	∈	∈	PROPN
ejpam-4671	234	165	v	v	ADP
ejpam-4671	234	166	(	(	PUNCT
ejpam-4671	234	167	h	h	NOUN
ejpam-4671	234	168	)	)	PUNCT
ejpam-4671	234	169	\	\	PROPN
ejpam-4671	235	1	ty	ty	X
ejpam-4671	235	2	.	.	PUNCT
ejpam-4671	236	1	by	by	ADP
ejpam-4671	236	2	(	(	PUNCT
ejpam-4671	236	3	i	i	NOUN
ejpam-4671	236	4	)	)	PUNCT
ejpam-4671	236	5	to	to	ADP
ejpam-4671	236	6	(	(	PUNCT
ejpam-4671	236	7	v	v	NOUN
ejpam-4671	236	8	)	)	PUNCT
ejpam-4671	236	9	and	and	CCONJ
ejpam-4671	236	10	theorem	theorem	VERB
ejpam-4671	236	11	5	5	NUM
ejpam-4671	236	12	,	,	PUNCT
ejpam-4671	236	13	for	for	ADP
ejpam-4671	236	14	every	every	DET
ejpam-4671	236	15	(	(	PUNCT
ejpam-4671	236	16	x	x	NOUN
ejpam-4671	236	17	,	,	PUNCT
ejpam-4671	236	18	a	a	PRON
ejpam-4671	236	19	)	)	PUNCT
ejpam-4671	236	20	∈	∈	NOUN
ejpam-4671	236	21	w	w	NOUN
ejpam-4671	236	22	either	either	CCONJ
ejpam-4671	236	23	w	w	ADJ
ejpam-4671	236	24	\{(x	\{(x	PROPN
ejpam-4671	236	25	,	,	PUNCT
ejpam-4671	236	26	a	a	PRON
ejpam-4671	236	27	)	)	PUNCT
ejpam-4671	236	28	}	}	PUNCT
ejpam-4671	236	29	is	be	AUX
ejpam-4671	236	30	a	a	DET
ejpam-4671	236	31	resolving	resolve	VERB
ejpam-4671	236	32	hop	hop	NOUN
ejpam-4671	236	33	dominating	dominating	NOUN
ejpam-4671	236	34	set	set	NOUN
ejpam-4671	236	35	of	of	ADP
ejpam-4671	236	36	g[h	g[h	PROPN
ejpam-4671	236	37	]	]	PUNCT
ejpam-4671	236	38	or	or	CCONJ
ejpam-4671	236	39	there	there	PRON
ejpam-4671	236	40	exists	exist	VERB
ejpam-4671	236	41	(	(	PUNCT
ejpam-4671	236	42	y	y	PROPN
ejpam-4671	236	43	,	,	PUNCT
ejpam-4671	236	44	b	b	NOUN
ejpam-4671	236	45	)	)	PUNCT
ejpam-4671	236	46	∈	∈	PROPN
ejpam-4671	236	47	ng[h]((x	ng[h]((x	NOUN
ejpam-4671	236	48	,	,	PUNCT
ejpam-4671	236	49	a	a	PRON
ejpam-4671	236	50	)	)	PUNCT
ejpam-4671	236	51	)	)	PUNCT
ejpam-4671	236	52	∩	∩	NOUN
ejpam-4671	236	53	(	(	PUNCT
ejpam-4671	236	54	v	v	NOUN
ejpam-4671	236	55	(	(	PUNCT
ejpam-4671	236	56	g[h	g[h	PROPN
ejpam-4671	236	57	]	]	PUNCT
ejpam-4671	236	58	)	)	PUNCT
ejpam-4671	236	59	\	\	PROPN
ejpam-4671	237	1	w	w	X
ejpam-4671	237	2	)	)	PUNCT
ejpam-4671	237	3	such	such	ADJ
ejpam-4671	237	4	that	that	SCONJ
ejpam-4671	237	5	(	(	PUNCT
ejpam-4671	237	6	w	w	PROPN
ejpam-4671	237	7	\	\	NOUN
ejpam-4671	237	8	{	{	PUNCT
ejpam-4671	237	9	(	(	PUNCT
ejpam-4671	237	10	x	x	X
ejpam-4671	237	11	,	,	PUNCT
ejpam-4671	237	12	a	a	NOUN
ejpam-4671	237	13	)	)	PUNCT
ejpam-4671	237	14	}	}	PUNCT
ejpam-4671	237	15	)	)	PUNCT
ejpam-4671	237	16	∪	∪	X
ejpam-4671	237	17	{	{	PUNCT
ejpam-4671	237	18	(	(	PUNCT
ejpam-4671	237	19	y	y	PROPN
ejpam-4671	237	20	,	,	PUNCT
ejpam-4671	237	21	b	b	NOUN
ejpam-4671	237	22	)	)	PUNCT
ejpam-4671	237	23	}	}	PUNCT
ejpam-4671	237	24	is	be	AUX
ejpam-4671	237	25	a	a	DET
ejpam-4671	237	26	resolving	resolve	VERB
ejpam-4671	237	27	hop	hop	NOUN
ejpam-4671	237	28	dominating	dominating	NOUN
ejpam-4671	237	29	set	set	NOUN
ejpam-4671	237	30	of	of	ADP
ejpam-4671	237	31	g[h	g[h	PROPN
ejpam-4671	237	32	]	]	PUNCT
ejpam-4671	237	33	.	.	PUNCT
ejpam-4671	238	1	therefore	therefore	ADV
ejpam-4671	238	2	,	,	PUNCT
ejpam-4671	238	3	w	w	PROPN
ejpam-4671	238	4	is	be	AUX
ejpam-4671	238	5	a	a	DET
ejpam-4671	238	6	1	1	NUM
ejpam-4671	238	7	-	-	PUNCT
ejpam-4671	238	8	movable	movable	ADJ
ejpam-4671	238	9	resolving	resolve	VERB
ejpam-4671	238	10	hop	hop	NOUN
ejpam-4671	238	11	dominating	dominating	NOUN
ejpam-4671	238	12	set	set	NOUN
ejpam-4671	238	13	of	of	ADP
ejpam-4671	238	14	g[h	g[h	PROPN
ejpam-4671	238	15	]	]	PUNCT
ejpam-4671	238	16	.	.	PUNCT
ejpam-4671	239	1	corollary	corollary	ADJ
ejpam-4671	239	2	5	5	NUM
ejpam-4671	239	3	.	.	PUNCT
ejpam-4671	240	1	let	let	VERB
ejpam-4671	240	2	g	g	PRON
ejpam-4671	240	3	be	be	AUX
ejpam-4671	240	4	a	a	DET
ejpam-4671	240	5	nontrivial	nontrivial	NOUN
ejpam-4671	240	6	connected	connect	VERB
ejpam-4671	240	7	totally	totally	ADV
ejpam-4671	240	8	point	point	VERB
ejpam-4671	240	9	determining	determine	VERB
ejpam-4671	240	10	graph	graph	NOUN
ejpam-4671	240	11	with	with	ADP
ejpam-4671	240	12	γ(g	γ(g	PROPN
ejpam-4671	240	13	)	)	PUNCT
ejpam-4671	240	14	̸=	̸=	PROPN
ejpam-4671	240	15	1	1	NUM
ejpam-4671	240	16	and	and	CCONJ
ejpam-4671	240	17	h	h	NOUN
ejpam-4671	240	18	be	be	VERB
ejpam-4671	240	19	a	a	DET
ejpam-4671	240	20	nontrivial	nontrivial	ADJ
ejpam-4671	240	21	connected	connect	VERB
ejpam-4671	240	22	graph	graph	NOUN
ejpam-4671	240	23	with	with	ADP
ejpam-4671	240	24	△	△	PROPN
ejpam-4671	240	25	(	(	PUNCT
ejpam-4671	240	26	h	h	NOUN
ejpam-4671	240	27	)	)	PUNCT
ejpam-4671	240	28	≤	≤	NOUN
ejpam-4671	240	29	|v	|v	X
ejpam-4671	240	30	(	(	PUNCT
ejpam-4671	240	31	h)|	h)|	NOUN
ejpam-4671	240	32	−	−	PROPN
ejpam-4671	240	33	2	2	NUM
ejpam-4671	240	34	.	.	PUNCT
ejpam-4671	241	1	then	then	ADV
ejpam-4671	241	2	γ1mrh(g[h	γ1mrh(g[h	NUM
ejpam-4671	241	3	]	]	PUNCT
ejpam-4671	241	4	)	)	PUNCT
ejpam-4671	242	1	=	=	SYM
ejpam-4671	242	2	|v	|v	PROPN
ejpam-4671	242	3	(	(	PUNCT
ejpam-4671	242	4	g)|mln(h	g)|mln(h	PROPN
ejpam-4671	242	5	)	)	PUNCT
ejpam-4671	242	6	.	.	PUNCT
ejpam-4671	243	1	proof	proof	NOUN
ejpam-4671	243	2	:	:	PUNCT
ejpam-4671	243	3	let	let	VERB
ejpam-4671	243	4	s	s	PRON
ejpam-4671	243	5	=	=	X
ejpam-4671	243	6	v	v	ADJ
ejpam-4671	243	7	(	(	PUNCT
ejpam-4671	243	8	g	g	NOUN
ejpam-4671	243	9	)	)	PUNCT
ejpam-4671	243	10	and	and	CCONJ
ejpam-4671	243	11	let	let	VERB
ejpam-4671	243	12	rx	rx	AUX
ejpam-4671	243	13	be	be	AUX
ejpam-4671	243	14	an	an	DET
ejpam-4671	243	15	mln	mln	NOUN
ejpam-4671	243	16	-	-	PUNCT
ejpam-4671	243	17	set	set	NOUN
ejpam-4671	243	18	of	of	ADP
ejpam-4671	243	19	h	h	NOUN
ejpam-4671	243	20	for	for	ADP
ejpam-4671	243	21	each	each	DET
ejpam-4671	243	22	x	x	PROPN
ejpam-4671	243	23	∈	∈	PROPN
ejpam-4671	243	24	s.	s.	PROPN
ejpam-4671	243	25	since	since	SCONJ
ejpam-4671	243	26	γg	γg	PROPN
ejpam-4671	243	27	̸=	̸=	PROPN
ejpam-4671	243	28	1	1	NUM
ejpam-4671	243	29	,	,	PUNCT
ejpam-4671	243	30	x	x	SYM
ejpam-4671	243	31	∈	∈	NOUN
ejpam-4671	243	32	ng(s	ng(s	NOUN
ejpam-4671	243	33	,	,	PUNCT
ejpam-4671	243	34	2	2	NUM
ejpam-4671	243	35	)	)	PUNCT
ejpam-4671	243	36	for	for	ADP
ejpam-4671	243	37	each	each	DET
ejpam-4671	243	38	x	x	PROPN
ejpam-4671	243	39	∈	∈	PROPN
ejpam-4671	243	40	s.	s.	PROPN
ejpam-4671	243	41	by	by	ADP
ejpam-4671	243	42	theorem	theorem	NOUN
ejpam-4671	243	43	6	6	NUM
ejpam-4671	243	44	,	,	PUNCT
ejpam-4671	243	45	w	w	NOUN
ejpam-4671	243	46	=	=	PUNCT
ejpam-4671	243	47	⋃	⋃	PROPN
ejpam-4671	243	48	x∈s	x∈s	NOUN
ejpam-4671	244	1	[	[	X
ejpam-4671	244	2	{	{	PUNCT
ejpam-4671	244	3	x	x	ADJ
ejpam-4671	244	4	}	}	PUNCT
ejpam-4671	244	5	×rx	×rx	PROPN
ejpam-4671	244	6	]	]	PUNCT
ejpam-4671	244	7	is	be	AUX
ejpam-4671	244	8	a	a	DET
ejpam-4671	244	9	1	1	NUM
ejpam-4671	244	10	-	-	PUNCT
ejpam-4671	244	11	movable	movable	ADJ
ejpam-4671	244	12	resolving	resolve	VERB
ejpam-4671	244	13	hop	hop	NOUN
ejpam-4671	244	14	dominating	dominating	NOUN
ejpam-4671	244	15	set	set	NOUN
ejpam-4671	244	16	of	of	ADP
ejpam-4671	244	17	g[h	g[h	PROPN
ejpam-4671	244	18	]	]	PUNCT
ejpam-4671	244	19	.	.	PUNCT
ejpam-4671	245	1	thus	thus	ADV
ejpam-4671	245	2	,	,	PUNCT
ejpam-4671	245	3	γ1mrh(g[h	γ1mrh(g[h	ADV
ejpam-4671	245	4	]	]	PUNCT
ejpam-4671	245	5	)	)	PUNCT
ejpam-4671	245	6	≤	≤	NOUN
ejpam-4671	245	7	|w	|w	NOUN
ejpam-4671	245	8	|	|	NOUN
ejpam-4671	245	9	=	=	SYM
ejpam-4671	245	10	|v	|v	PROPN
ejpam-4671	245	11	(	(	PUNCT
ejpam-4671	245	12	g)||rx|	g)||rx|	PROPN
ejpam-4671	245	13	=	=	SYM
ejpam-4671	245	14	|v	|v	PROPN
ejpam-4671	245	15	(	(	PUNCT
ejpam-4671	245	16	g)|mln(h	g)|mln(h	PROPN
ejpam-4671	245	17	)	)	PUNCT
ejpam-4671	245	18	.	.	PUNCT
ejpam-4671	246	1	now	now	ADV
ejpam-4671	246	2	,	,	PUNCT
ejpam-4671	246	3	if	if	SCONJ
ejpam-4671	246	4	w0	w0	PROPN
ejpam-4671	246	5	=	=	PUNCT
ejpam-4671	246	6	⋃	⋃	PROPN
ejpam-4671	246	7	x∈s0	x∈s0	NOUN
ejpam-4671	246	8	(	(	PUNCT
ejpam-4671	246	9	{	{	PUNCT
ejpam-4671	246	10	x	x	NOUN
ejpam-4671	246	11	}	}	PUNCT
ejpam-4671	246	12	×	×	PROPN
ejpam-4671	246	13	tx	tx	PROPN
ejpam-4671	246	14	)	)	PUNCT
ejpam-4671	246	15	is	be	AUX
ejpam-4671	246	16	a	a	DET
ejpam-4671	246	17	γ1mrh	γ1mrh	NOUN
ejpam-4671	246	18	-	-	PUNCT
ejpam-4671	246	19	set	set	NOUN
ejpam-4671	246	20	of	of	ADP
ejpam-4671	246	21	g[h	g[h	NOUN
ejpam-4671	246	22	]	]	PUNCT
ejpam-4671	246	23	then	then	ADV
ejpam-4671	246	24	s0	s0	PROPN
ejpam-4671	246	25	=	=	SYM
ejpam-4671	246	26	v	v	PROPN
ejpam-4671	246	27	(	(	PUNCT
ejpam-4671	246	28	g	g	NOUN
ejpam-4671	246	29	)	)	PUNCT
ejpam-4671	246	30	and	and	CCONJ
ejpam-4671	246	31	tx	tx	PROPN
ejpam-4671	246	32	is	be	AUX
ejpam-4671	246	33	a	a	DET
ejpam-4671	246	34	1	1	NUM
ejpam-4671	246	35	-	-	PUNCT
ejpam-4671	246	36	movable	movable	ADJ
ejpam-4671	246	37	locating	locating	NOUN
ejpam-4671	246	38	set	set	NOUN
ejpam-4671	246	39	of	of	ADP
ejpam-4671	246	40	h	h	NOUN
ejpam-4671	246	41	for	for	ADP
ejpam-4671	246	42	each	each	DET
ejpam-4671	246	43	x	x	SYM
ejpam-4671	246	44	∈	∈	PROPN
ejpam-4671	246	45	v	v	ADP
ejpam-4671	246	46	(	(	PUNCT
ejpam-4671	246	47	g	g	NOUN
ejpam-4671	246	48	)	)	PUNCT
ejpam-4671	246	49	by	by	ADP
ejpam-4671	246	50	theorem	theorem	NOUN
ejpam-4671	246	51	6	6	NUM
ejpam-4671	246	52	.	.	PUNCT
ejpam-4671	246	53	hence	hence	ADV
ejpam-4671	246	54	,	,	PUNCT
ejpam-4671	246	55	γ1mrh(g[h	γ1mrh(g[h	ADV
ejpam-4671	246	56	]	]	PUNCT
ejpam-4671	246	57	)	)	PUNCT
ejpam-4671	247	1	=	=	VERB
ejpam-4671	247	2	|w0|	|w0|	X
ejpam-4671	247	3	=	=	SYM
ejpam-4671	247	4	|v	|v	X
ejpam-4671	247	5	(	(	PUNCT
ejpam-4671	247	6	g)||tx|	g)||tx|	PROPN
ejpam-4671	247	7	≥	≥	NUM
ejpam-4671	247	8	|v	|v	PROPN
ejpam-4671	247	9	(	(	PUNCT
ejpam-4671	247	10	g)|mln(h	g)|mln(h	PROPN
ejpam-4671	247	11	)	)	PUNCT
ejpam-4671	247	12	.	.	PUNCT
ejpam-4671	248	1	therefore	therefore	ADV
ejpam-4671	248	2	,	,	PUNCT
ejpam-4671	248	3	γ1mrh(g[h	γ1mrh(g[h	ADV
ejpam-4671	248	4	]	]	PUNCT
ejpam-4671	248	5	)	)	PUNCT
ejpam-4671	248	6	=	=	SYM
ejpam-4671	248	7	|v	|v	PROPN
ejpam-4671	248	8	(	(	PUNCT
ejpam-4671	248	9	g)|mln(h	g)|mln(h	PROPN
ejpam-4671	248	10	)	)	PUNCT
ejpam-4671	248	11	.	.	PUNCT
ejpam-4671	249	1	acknowledgements	acknowledgement	NOUN
ejpam-4671	249	2	this	this	DET
ejpam-4671	249	3	research	research	NOUN
ejpam-4671	249	4	is	be	AUX
ejpam-4671	249	5	funded	fund	VERB
ejpam-4671	249	6	by	by	ADP
ejpam-4671	249	7	the	the	DET
ejpam-4671	249	8	department	department	PROPN
ejpam-4671	249	9	of	of	ADP
ejpam-4671	249	10	science	science	NOUN
ejpam-4671	249	11	and	and	CCONJ
ejpam-4671	249	12	technology	technology	NOUN
ejpam-4671	249	13	accelerated	accelerate	VERB
ejpam-4671	249	14	science	science	NOUN
ejpam-4671	249	15	and	and	CCONJ
ejpam-4671	249	16	technology	technology	NOUN
ejpam-4671	249	17	human	human	ADJ
ejpam-4671	249	18	resource	resource	NOUN
ejpam-4671	249	19	development	development	NOUN
ejpam-4671	249	20	program	program	NOUN
ejpam-4671	249	21	(	(	PUNCT
ejpam-4671	249	22	dost	dost	NOUN
ejpam-4671	249	23	-	-	PUNCT
ejpam-4671	249	24	asthrdp	asthrdp	NOUN
ejpam-4671	249	25	)	)	PUNCT
ejpam-4671	249	26	,	,	PUNCT
ejpam-4671	249	27	mindanao	mindanao	PROPN
ejpam-4671	249	28	state	state	PROPN
ejpam-4671	249	29	university	university	PROPN
ejpam-4671	249	30	iligan	iligan	PROPN
ejpam-4671	249	31	institute	institute	PROPN
ejpam-4671	249	32	of	of	ADP
ejpam-4671	249	33	technology	technology	NOUN
ejpam-4671	249	34	,	,	PUNCT
ejpam-4671	249	35	and	and	CCONJ
ejpam-4671	249	36	western	western	ADJ
ejpam-4671	249	37	mindanao	mindanao	PROPN
ejpam-4671	249	38	state	state	PROPN
ejpam-4671	249	39	university	university	PROPN
ejpam-4671	249	40	,	,	PUNCT
ejpam-4671	249	41	philippines	philippine	NOUN
ejpam-4671	249	42	.	.	PUNCT
ejpam-4671	250	1	references	reference	NOUN
ejpam-4671	250	2	429	429	NUM
ejpam-4671	250	3	references	reference	NOUN
ejpam-4671	250	4	[	[	X
ejpam-4671	250	5	1	1	NUM
ejpam-4671	250	6	]	]	PUNCT
ejpam-4671	250	7	a.	a.	NOUN
ejpam-4671	250	8	abragan	abragan	NOUN
ejpam-4671	250	9	and	and	CCONJ
ejpam-4671	250	10	h.	h.	PROPN
ejpam-4671	250	11	rara	rara	PROPN
ejpam-4671	250	12	.	.	PUNCT
ejpam-4671	251	1	restrained	restrain	VERB
ejpam-4671	251	2	strong	strong	ADJ
ejpam-4671	251	3	resolving	resolve	VERB
ejpam-4671	251	4	hop	hop	NOUN
ejpam-4671	251	5	domination	domination	NOUN
ejpam-4671	251	6	in	in	ADP
ejpam-4671	251	7	graphs	graph	NOUN
ejpam-4671	251	8	.	.	PUNCT
ejpam-4671	252	1	european	european	ADJ
ejpam-4671	252	2	journal	journal	PROPN
ejpam-4671	252	3	of	of	ADP
ejpam-4671	252	4	pure	pure	ADJ
ejpam-4671	252	5	and	and	CCONJ
ejpam-4671	252	6	applied	applied	ADJ
ejpam-4671	252	7	mathematics	mathematic	NOUN
ejpam-4671	252	8	,	,	PUNCT
ejpam-4671	252	9	15(4):1472–1481	15(4):1472–1481	NUM
ejpam-4671	252	10	,	,	PUNCT
ejpam-4671	252	11	2022	2022	NUM
ejpam-4671	252	12	.	.	PUNCT
ejpam-4671	253	1	[	[	X
ejpam-4671	253	2	2	2	X
ejpam-4671	253	3	]	]	PUNCT
ejpam-4671	253	4	p.	p.	NOUN
ejpam-4671	253	5	acal	acal	ADJ
ejpam-4671	253	6	and	and	CCONJ
ejpam-4671	253	7	h.	h.	PROPN
ejpam-4671	253	8	rara	rara	PROPN
ejpam-4671	253	9	.	.	PUNCT
ejpam-4671	254	1	the	the	DET
ejpam-4671	254	2	strong	strong	ADJ
ejpam-4671	254	3	connected	connected	ADJ
ejpam-4671	254	4	metric	metric	ADJ
ejpam-4671	254	5	dimension	dimension	NOUN
ejpam-4671	254	6	in	in	ADP
ejpam-4671	254	7	the	the	DET
ejpam-4671	254	8	join	join	NOUN
ejpam-4671	254	9	and	and	CCONJ
ejpam-4671	254	10	corona	corona	NOUN
ejpam-4671	254	11	of	of	ADP
ejpam-4671	254	12	graphs	graph	NOUN
ejpam-4671	254	13	.	.	PUNCT
ejpam-4671	255	1	advances	advance	NOUN
ejpam-4671	255	2	and	and	CCONJ
ejpam-4671	255	3	applications	application	NOUN
ejpam-4671	255	4	in	in	ADP
ejpam-4671	255	5	discrete	discrete	ADJ
ejpam-4671	255	6	mathematics	mathematic	NOUN
ejpam-4671	255	7	,	,	PUNCT
ejpam-4671	255	8	21(1):91–101	21(1):91–101	NUM
ejpam-4671	255	9	,	,	PUNCT
ejpam-4671	255	10	2019	2019	NUM
ejpam-4671	255	11	.	.	PUNCT
ejpam-4671	256	1	[	[	X
ejpam-4671	256	2	3	3	X
ejpam-4671	256	3	]	]	X
ejpam-4671	256	4	j.	j.	PROPN
ejpam-4671	256	5	cabaro	cabaro	PROPN
ejpam-4671	256	6	and	and	CCONJ
ejpam-4671	256	7	h.	h.	PROPN
ejpam-4671	256	8	rara	rara	PROPN
ejpam-4671	256	9	.	.	PUNCT
ejpam-4671	257	1	on	on	ADP
ejpam-4671	257	2	2	2	NUM
ejpam-4671	257	3	-	-	PUNCT
ejpam-4671	257	4	resolving	resolve	VERB
ejpam-4671	257	5	sets	set	NOUN
ejpam-4671	257	6	in	in	ADP
ejpam-4671	257	7	the	the	DET
ejpam-4671	257	8	join	join	NOUN
ejpam-4671	257	9	and	and	CCONJ
ejpam-4671	257	10	corona	corona	NOUN
ejpam-4671	257	11	of	of	ADP
ejpam-4671	257	12	graphs	graph	NOUN
ejpam-4671	257	13	.	.	PUNCT
ejpam-4671	258	1	european	european	ADJ
ejpam-4671	258	2	journal	journal	PROPN
ejpam-4671	258	3	of	of	ADP
ejpam-4671	258	4	pure	pure	ADJ
ejpam-4671	258	5	and	and	CCONJ
ejpam-4671	258	6	applied	applied	ADJ
ejpam-4671	258	7	mathematics	mathematic	NOUN
ejpam-4671	258	8	,	,	PUNCT
ejpam-4671	258	9	14(3):773–782	14(3):773–782	PROPN
ejpam-4671	258	10	,	,	PUNCT
ejpam-4671	258	11	2021	2021	NUM
ejpam-4671	258	12	.	.	PUNCT
ejpam-4671	259	1	[	[	X
ejpam-4671	259	2	4	4	X
ejpam-4671	259	3	]	]	X
ejpam-4671	259	4	j.	j.	PROPN
ejpam-4671	259	5	cabaro	cabaro	PROPN
ejpam-4671	259	6	and	and	CCONJ
ejpam-4671	259	7	h.	h.	PROPN
ejpam-4671	259	8	rara	rara	PROPN
ejpam-4671	259	9	.	.	PUNCT
ejpam-4671	260	1	on	on	ADP
ejpam-4671	260	2	2	2	NUM
ejpam-4671	260	3	-	-	PUNCT
ejpam-4671	260	4	resolving	resolve	VERB
ejpam-4671	260	5	dominating	dominating	NOUN
ejpam-4671	260	6	sets	set	NOUN
ejpam-4671	260	7	in	in	ADP
ejpam-4671	260	8	the	the	DET
ejpam-4671	260	9	join	join	NOUN
ejpam-4671	260	10	,	,	PUNCT
ejpam-4671	260	11	corona	corona	NOUN
ejpam-4671	260	12	and	and	CCONJ
ejpam-4671	260	13	lexicographic	lexicographic	ADJ
ejpam-4671	260	14	product	product	NOUN
ejpam-4671	260	15	of	of	ADP
ejpam-4671	260	16	two	two	NUM
ejpam-4671	260	17	graphs	graph	NOUN
ejpam-4671	260	18	.	.	PUNCT
ejpam-4671	261	1	european	european	ADJ
ejpam-4671	261	2	journal	journal	PROPN
ejpam-4671	261	3	of	of	ADP
ejpam-4671	261	4	pure	pure	ADJ
ejpam-4671	261	5	and	and	CCONJ
ejpam-4671	261	6	applied	applied	ADJ
ejpam-4671	261	7	mathematics	mathematic	NOUN
ejpam-4671	261	8	,	,	PUNCT
ejpam-4671	261	9	15(3):1417–1425	15(3):1417–1425	NUM
ejpam-4671	261	10	,	,	PUNCT
ejpam-4671	261	11	2022	2022	NUM
ejpam-4671	261	12	.	.	PUNCT
ejpam-4671	262	1	[	[	X
ejpam-4671	262	2	5	5	X
ejpam-4671	262	3	]	]	PUNCT
ejpam-4671	262	4	j.	j.	PROPN
ejpam-4671	262	5	cabaro	cabaro	PROPN
ejpam-4671	262	6	and	and	CCONJ
ejpam-4671	262	7	h.	h.	PROPN
ejpam-4671	262	8	rara	rara	PROPN
ejpam-4671	262	9	.	.	PUNCT
ejpam-4671	263	1	restrained	restrain	VERB
ejpam-4671	263	2	2	2	NUM
ejpam-4671	263	3	-	-	PUNCT
ejpam-4671	263	4	resolving	resolve	VERB
ejpam-4671	263	5	dominating	dominating	NOUN
ejpam-4671	263	6	sets	set	NOUN
ejpam-4671	263	7	in	in	ADP
ejpam-4671	263	8	the	the	DET
ejpam-4671	263	9	join	join	NOUN
ejpam-4671	263	10	,	,	PUNCT
ejpam-4671	263	11	corona	corona	NOUN
ejpam-4671	263	12	and	and	CCONJ
ejpam-4671	263	13	lexicographic	lexicographic	ADJ
ejpam-4671	263	14	product	product	NOUN
ejpam-4671	263	15	of	of	ADP
ejpam-4671	263	16	two	two	NUM
ejpam-4671	263	17	graphs	graph	NOUN
ejpam-4671	263	18	.	.	PUNCT
ejpam-4671	264	1	european	european	ADJ
ejpam-4671	264	2	journal	journal	PROPN
ejpam-4671	264	3	of	of	ADP
ejpam-4671	264	4	pure	pure	ADJ
ejpam-4671	264	5	and	and	CCONJ
ejpam-4671	264	6	applied	applied	ADJ
ejpam-4671	264	7	mathematics	mathematic	NOUN
ejpam-4671	264	8	,	,	PUNCT
ejpam-4671	264	9	15(3):1047–1053	15(3):1047–1053	NUM
ejpam-4671	264	10	,	,	PUNCT
ejpam-4671	264	11	2022	2022	NUM
ejpam-4671	264	12	.	.	PUNCT
ejpam-4671	265	1	[	[	X
ejpam-4671	265	2	6	6	NUM
ejpam-4671	265	3	]	]	PUNCT
ejpam-4671	265	4	j.	j.	PROPN
ejpam-4671	265	5	cabaro	cabaro	PROPN
ejpam-4671	265	6	and	and	CCONJ
ejpam-4671	265	7	h.	h.	PROPN
ejpam-4671	265	8	rara	rara	PROPN
ejpam-4671	265	9	.	.	PUNCT
ejpam-4671	266	1	restrained	restrain	VERB
ejpam-4671	266	2	2	2	NUM
ejpam-4671	266	3	-	-	PUNCT
ejpam-4671	266	4	resolving	resolve	VERB
ejpam-4671	266	5	sets	set	NOUN
ejpam-4671	266	6	in	in	ADP
ejpam-4671	266	7	the	the	DET
ejpam-4671	266	8	join	join	NOUN
ejpam-4671	266	9	,	,	PUNCT
ejpam-4671	266	10	corona	corona	NOUN
ejpam-4671	266	11	and	and	CCONJ
ejpam-4671	266	12	lexicographic	lexicographic	ADJ
ejpam-4671	266	13	product	product	NOUN
ejpam-4671	266	14	of	of	ADP
ejpam-4671	266	15	two	two	NUM
ejpam-4671	266	16	graphs	graph	NOUN
ejpam-4671	266	17	.	.	PUNCT
ejpam-4671	267	1	european	european	ADJ
ejpam-4671	267	2	journal	journal	PROPN
ejpam-4671	267	3	of	of	ADP
ejpam-4671	267	4	pure	pure	ADJ
ejpam-4671	267	5	and	and	CCONJ
ejpam-4671	267	6	applied	applied	ADJ
ejpam-4671	267	7	mathematics	mathematic	NOUN
ejpam-4671	267	8	,	,	PUNCT
ejpam-4671	267	9	15(3):1229–1236	15(3):1229–1236	NUM
ejpam-4671	267	10	,	,	PUNCT
ejpam-4671	267	11	2022	2022	NUM
ejpam-4671	267	12	.	.	PUNCT
ejpam-4671	268	1	[	[	X
ejpam-4671	268	2	7	7	NUM
ejpam-4671	268	3	]	]	PUNCT
ejpam-4671	268	4	a.	a.	NOUN
ejpam-4671	268	5	gamorez	gamorez	NOUN
ejpam-4671	268	6	and	and	CCONJ
ejpam-4671	268	7	s.	s.	PROPN
ejpam-4671	268	8	canoy	canoy	PROPN
ejpam-4671	268	9	jr	jr	PROPN
ejpam-4671	268	10	.	.	PROPN
ejpam-4671	268	11	monophonic	monophonic	ADJ
ejpam-4671	268	12	eccentric	eccentric	ADJ
ejpam-4671	268	13	domination	domination	NOUN
ejpam-4671	268	14	numbers	number	NOUN
ejpam-4671	268	15	of	of	ADP
ejpam-4671	268	16	graphs	graph	NOUN
ejpam-4671	268	17	.	.	PUNCT
ejpam-4671	269	1	european	european	ADJ
ejpam-4671	269	2	journal	journal	PROPN
ejpam-4671	269	3	of	of	ADP
ejpam-4671	269	4	pure	pure	ADJ
ejpam-4671	269	5	and	and	CCONJ
ejpam-4671	269	6	applied	applied	ADJ
ejpam-4671	269	7	mathematics	mathematic	NOUN
ejpam-4671	269	8	,	,	PUNCT
ejpam-4671	269	9	15(2):635–645	15(2):635–645	PROPN
ejpam-4671	269	10	,	,	PUNCT
ejpam-4671	269	11	2022	2022	NUM
ejpam-4671	269	12	.	.	PUNCT
ejpam-4671	270	1	[	[	X
ejpam-4671	270	2	8	8	NUM
ejpam-4671	270	3	]	]	X
ejpam-4671	270	4	f.	f.	PROPN
ejpam-4671	270	5	harary	harary	PROPN
ejpam-4671	270	6	.	.	PUNCT
ejpam-4671	271	1	graph	graph	NOUN
ejpam-4671	271	2	theory	theory	NOUN
ejpam-4671	271	3	.	.	PUNCT
ejpam-4671	272	1	addison	addison	PROPN
ejpam-4671	272	2	-	-	PUNCT
ejpam-4671	272	3	wesley	wesley	PROPN
ejpam-4671	272	4	publishing	publishing	PROPN
ejpam-4671	272	5	company	company	NOUN
ejpam-4671	272	6	,	,	PUNCT
ejpam-4671	272	7	usa	usa	PROPN
ejpam-4671	272	8	,	,	PUNCT
ejpam-4671	272	9	1969	1969	NUM
ejpam-4671	272	10	.	.	PUNCT
ejpam-4671	273	1	[	[	X
ejpam-4671	273	2	9	9	NUM
ejpam-4671	273	3	]	]	PUNCT
ejpam-4671	273	4	a.	a.	NOUN
ejpam-4671	273	5	mahistrado	mahistrado	NOUN
ejpam-4671	273	6	and	and	CCONJ
ejpam-4671	273	7	h.	h.	PROPN
ejpam-4671	273	8	rara	rara	PROPN
ejpam-4671	273	9	.	.	PUNCT
ejpam-4671	274	1	on	on	ADP
ejpam-4671	274	2	2	2	NUM
ejpam-4671	274	3	-	-	PUNCT
ejpam-4671	274	4	resolving	resolve	VERB
ejpam-4671	274	5	hop	hop	NOUN
ejpam-4671	274	6	dominating	dominating	NOUN
ejpam-4671	274	7	sets	set	NOUN
ejpam-4671	274	8	in	in	ADP
ejpam-4671	274	9	the	the	DET
ejpam-4671	274	10	join	join	NOUN
ejpam-4671	274	11	,	,	PUNCT
ejpam-4671	274	12	corona	corona	NOUN
ejpam-4671	274	13	and	and	CCONJ
ejpam-4671	274	14	lexicographic	lexicographic	ADJ
ejpam-4671	274	15	product	product	NOUN
ejpam-4671	274	16	of	of	ADP
ejpam-4671	274	17	graphs	graph	NOUN
ejpam-4671	274	18	.	.	PUNCT
ejpam-4671	275	1	european	european	ADJ
ejpam-4671	275	2	journal	journal	PROPN
ejpam-4671	275	3	of	of	ADP
ejpam-4671	275	4	pure	pure	ADJ
ejpam-4671	275	5	and	and	CCONJ
ejpam-4671	275	6	applied	applied	ADJ
ejpam-4671	275	7	mathematics	mathematic	NOUN
ejpam-4671	275	8	,	,	PUNCT
ejpam-4671	275	9	15(4):1982–1997	15(4):1982–1997	NUM
ejpam-4671	275	10	,	,	PUNCT
ejpam-4671	275	11	2022	2022	NUM
ejpam-4671	275	12	.	.	PUNCT
ejpam-4671	276	1	[	[	X
ejpam-4671	276	2	10	10	NUM
ejpam-4671	276	3	]	]	X
ejpam-4671	276	4	j.	j.	PROPN
ejpam-4671	276	5	mohamad	mohamad	PROPN
ejpam-4671	276	6	and	and	CCONJ
ejpam-4671	276	7	h.	h.	PROPN
ejpam-4671	276	8	rara	rara	PROPN
ejpam-4671	276	9	.	.	PUNCT
ejpam-4671	277	1	on	on	ADP
ejpam-4671	277	2	resolving	resolve	VERB
ejpam-4671	277	3	hop	hop	NOUN
ejpam-4671	277	4	domination	domination	NOUN
ejpam-4671	277	5	in	in	ADP
ejpam-4671	277	6	graphs	graph	NOUN
ejpam-4671	277	7	.	.	PUNCT
ejpam-4671	278	1	european	european	ADJ
ejpam-4671	278	2	journal	journal	PROPN
ejpam-4671	278	3	of	of	ADP
ejpam-4671	278	4	pure	pure	ADJ
ejpam-4671	278	5	and	and	CCONJ
ejpam-4671	278	6	applied	applied	ADJ
ejpam-4671	278	7	mathematics	mathematic	NOUN
ejpam-4671	278	8	,	,	PUNCT
ejpam-4671	278	9	14(3):1015–1023	14(3):1015–1023	NUM
ejpam-4671	278	10	,	,	PUNCT
ejpam-4671	278	11	2021	2021	NUM
ejpam-4671	278	12	.	.	PUNCT
ejpam-4671	279	1	[	[	X
ejpam-4671	279	2	11	11	NUM
ejpam-4671	279	3	]	]	X
ejpam-4671	279	4	g.	g.	PROPN
ejpam-4671	279	5	monsanto	monsanto	PROPN
ejpam-4671	279	6	and	and	CCONJ
ejpam-4671	279	7	h.	h.	PROPN
ejpam-4671	279	8	rara	rara	PROPN
ejpam-4671	279	9	.	.	PUNCT
ejpam-4671	280	1	movable	movable	ADJ
ejpam-4671	280	2	resolving	resolve	VERB
ejpam-4671	280	3	domination	domination	NOUN
ejpam-4671	280	4	in	in	ADP
ejpam-4671	280	5	graphs	graph	NOUN
ejpam-4671	280	6	.	.	PUNCT
ejpam-4671	281	1	discrete	discrete	ADJ
ejpam-4671	281	2	mathematics	mathematic	NOUN
ejpam-4671	281	3	,	,	PUNCT
ejpam-4671	281	4	algorithms	algorithm	NOUN
ejpam-4671	281	5	and	and	CCONJ
ejpam-4671	281	6	applications	application	NOUN
ejpam-4671	281	7	,	,	PUNCT
ejpam-4671	281	8	14(06):2250016	14(06):2250016	NUM
ejpam-4671	281	9	,	,	PUNCT
ejpam-4671	281	10	2022	2022	NUM
ejpam-4671	281	11	.	.	PUNCT
ejpam-4671	282	1	[	[	X
ejpam-4671	282	2	12	12	NUM
ejpam-4671	282	3	]	]	X
ejpam-4671	282	4	c.	c.	PROPN
ejpam-4671	282	5	natarajan	natarajan	PROPN
ejpam-4671	282	6	and	and	CCONJ
ejpam-4671	282	7	s.	s.	PROPN
ejpam-4671	282	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4671	282	9	.	.	PUNCT
ejpam-4671	283	1	hop	hop	PROPN
ejpam-4671	283	2	domination	domination	NOUN
ejpam-4671	283	3	in	in	ADP
ejpam-4671	283	4	graphs	graph	NOUN
ejpam-4671	283	5	-	-	PUNCT
ejpam-4671	283	6	ii	ii	NOUN
ejpam-4671	283	7	.	.	PUNCT
ejpam-4671	283	8	versita	versita	PROPN
ejpam-4671	283	9	,	,	PUNCT
ejpam-4671	283	10	23(2):187	23(2):187	NUM
ejpam-4671	283	11	–	–	PUNCT
ejpam-4671	283	12	199	199	NUM
ejpam-4671	283	13	,	,	PUNCT
ejpam-4671	283	14	2015	2015	NUM
ejpam-4671	283	15	.	.	PUNCT
ejpam-4671	284	1	[	[	X
ejpam-4671	284	2	13	13	NUM
ejpam-4671	284	3	]	]	PUNCT
ejpam-4671	284	4	m.	m.	NOUN
ejpam-4671	284	5	n.	n.	PROPN
ejpam-4671	284	6	paspasan	paspasan	PROPN
ejpam-4671	284	7	.	.	PUNCT
ejpam-4671	285	1	perfect	perfect	ADJ
ejpam-4671	285	2	edge	edge	NOUN
ejpam-4671	285	3	domination	domination	NOUN
ejpam-4671	285	4	in	in	ADP
ejpam-4671	285	5	graphs	graph	NOUN
ejpam-4671	285	6	.	.	PUNCT
ejpam-4671	286	1	advances	advance	NOUN
ejpam-4671	286	2	and	and	CCONJ
ejpam-4671	286	3	applications	application	NOUN
ejpam-4671	286	4	in	in	ADP
ejpam-4671	286	5	discrete	discrete	ADJ
ejpam-4671	286	6	mathematics	mathematic	NOUN
ejpam-4671	286	7	,	,	PUNCT
ejpam-4671	286	8	27(2):173–181	27(2):173–181	PROPN
ejpam-4671	286	9	,	,	PUNCT
ejpam-4671	286	10	2021	2021	NUM
ejpam-4671	286	11	.	.	PUNCT
ejpam-4671	287	1	[	[	X
ejpam-4671	287	2	14	14	NUM
ejpam-4671	287	3	]	]	X
ejpam-4671	287	4	h.	h.	NOUN
ejpam-4671	287	5	sumaoy	sumaoy	NOUN
ejpam-4671	287	6	and	and	CCONJ
ejpam-4671	287	7	h.	h.	PROPN
ejpam-4671	287	8	rara	rara	PROPN
ejpam-4671	287	9	.	.	PUNCT
ejpam-4671	288	1	on	on	ADP
ejpam-4671	288	2	restrained	restrained	ADJ
ejpam-4671	288	3	strong	strong	ADJ
ejpam-4671	288	4	resolving	resolving	NOUN
ejpam-4671	288	5	domination	domination	NOUN
ejpam-4671	288	6	in	in	ADP
ejpam-4671	288	7	graphs	graph	NOUN
ejpam-4671	288	8	.	.	PUNCT
ejpam-4671	289	1	european	european	ADJ
ejpam-4671	289	2	journal	journal	PROPN
ejpam-4671	289	3	of	of	ADP
ejpam-4671	289	4	pure	pure	ADJ
ejpam-4671	289	5	and	and	CCONJ
ejpam-4671	289	6	applied	applied	ADJ
ejpam-4671	289	7	mathematics	mathematic	NOUN
ejpam-4671	289	8	,	,	PUNCT
ejpam-4671	289	9	14(3):1367–1378	14(3):1367–1378	NUM
ejpam-4671	289	10	,	,	PUNCT
ejpam-4671	289	11	2021	2021	NUM
ejpam-4671	289	12	.	.	PUNCT