id	sid	tid	token	lemma	pos
ejpam-4587	1	1	european	european	PROPN
ejpam-4587	1	2	journal	journal	PROPN
ejpam-4587	1	3	of	of	ADP
ejpam-4587	1	4	pure	pure	ADJ
ejpam-4587	1	5	and	and	CCONJ
ejpam-4587	1	6	applied	apply	VERB
ejpam-4587	1	7	mathematics	mathematic	NOUN
ejpam-4587	1	8	vol	vol	NOUN
ejpam-4587	1	9	.	.	PUNCT
ejpam-4587	2	1	16	16	NUM
ejpam-4587	2	2	,	,	PUNCT
ejpam-4587	2	3	no	no	INTJ
ejpam-4587	2	4	.	.	NOUN
ejpam-4587	2	5	1	1	NUM
ejpam-4587	2	6	,	,	PUNCT
ejpam-4587	2	7	2023	2023	NUM
ejpam-4587	2	8	,	,	PUNCT
ejpam-4587	2	9	454	454	NUM
ejpam-4587	2	10	-	-	SYM
ejpam-4587	2	11	464	464	NUM
ejpam-4587	2	12	issn	issn	PROPN
ejpam-4587	2	13	1307	1307	NUM
ejpam-4587	2	14	-	-	SYM
ejpam-4587	2	15	5543	5543	NUM
ejpam-4587	2	16	–	–	PUNCT
ejpam-4587	2	17	ejpam.com	ejpam.com	X
ejpam-4587	2	18	published	publish	VERB
ejpam-4587	2	19	by	by	ADP
ejpam-4587	2	20	new	new	PROPN
ejpam-4587	2	21	york	york	PROPN
ejpam-4587	2	22	business	business	PROPN
ejpam-4587	2	23	global	global	ADJ
ejpam-4587	2	24	weakly	weakly	ADJ
ejpam-4587	2	25	connected	connect	VERB
ejpam-4587	2	26	hop	hop	NOUN
ejpam-4587	2	27	domination	domination	NOUN
ejpam-4587	2	28	in	in	ADP
ejpam-4587	2	29	graphs	graph	NOUN
ejpam-4587	2	30	resulting	result	VERB
ejpam-4587	2	31	from	from	ADP
ejpam-4587	2	32	some	some	DET
ejpam-4587	2	33	binary	binary	ADJ
ejpam-4587	2	34	operations	operation	NOUN
ejpam-4587	2	35	jamil	jamil	PROPN
ejpam-4587	2	36	j.	j.	PROPN
ejpam-4587	2	37	hamja1,∗	hamja1,∗	PROPN
ejpam-4587	2	38	,	,	PUNCT
ejpam-4587	2	39	imelda	imelda	PROPN
ejpam-4587	2	40	s.	s.	PROPN
ejpam-4587	2	41	aniversario2	aniversario2	PROPN
ejpam-4587	2	42	,	,	PUNCT
ejpam-4587	2	43	catherine	catherine	PROPN
ejpam-4587	2	44	i.	i.	PROPN
ejpam-4587	2	45	merca2	merca2	PROPN
ejpam-4587	2	46	1	1	NUM
ejpam-4587	2	47	office	office	NOUN
ejpam-4587	2	48	of	of	ADP
ejpam-4587	2	49	the	the	DET
ejpam-4587	2	50	vice	vice	NOUN
ejpam-4587	2	51	chancellor	chancellor	NOUN
ejpam-4587	2	52	for	for	ADP
ejpam-4587	2	53	academic	academic	ADJ
ejpam-4587	2	54	affairs	affair	NOUN
ejpam-4587	2	55	,	,	PUNCT
ejpam-4587	2	56	msu	msu	PROPN
ejpam-4587	2	57	-	-	PUNCT
ejpam-4587	2	58	tawi	tawi	NOUN
ejpam-4587	2	59	-	-	PUNCT
ejpam-4587	2	60	tawi	tawi	NOUN
ejpam-4587	2	61	college	college	PROPN
ejpam-4587	2	62	of	of	ADP
ejpam-4587	2	63	technology	technology	NOUN
ejpam-4587	2	64	and	and	CCONJ
ejpam-4587	2	65	oceanography	oceanography	NOUN
ejpam-4587	2	66	,	,	PUNCT
ejpam-4587	2	67	7500	7500	NUM
ejpam-4587	2	68	tawi	tawi	NOUN
ejpam-4587	2	69	-	-	PUNCT
ejpam-4587	2	70	tawi	tawi	NOUN
ejpam-4587	2	71	,	,	PUNCT
ejpam-4587	2	72	philippines	philippines	PROPN
ejpam-4587	2	73	2	2	NUM
ejpam-4587	2	74	department	department	NOUN
ejpam-4587	2	75	of	of	ADP
ejpam-4587	2	76	mathematics	mathematic	NOUN
ejpam-4587	2	77	and	and	CCONJ
ejpam-4587	2	78	statistics	statistic	NOUN
ejpam-4587	2	79	,	,	PUNCT
ejpam-4587	2	80	college	college	NOUN
ejpam-4587	2	81	of	of	ADP
ejpam-4587	2	82	science	science	NOUN
ejpam-4587	2	83	in	in	ADP
ejpam-4587	2	84	mathematics	mathematic	NOUN
ejpam-4587	2	85	,	,	PUNCT
ejpam-4587	2	86	msu	msu	PROPN
ejpam-4587	2	87	-	-	PUNCT
ejpam-4587	2	88	iligan	iligan	PROPN
ejpam-4587	2	89	institute	institute	PROPN
ejpam-4587	2	90	of	of	ADP
ejpam-4587	2	91	technology	technology	PROPN
ejpam-4587	2	92	,	,	PUNCT
ejpam-4587	2	93	9200	9200	NUM
ejpam-4587	2	94	iligan	iligan	ADJ
ejpam-4587	2	95	city	city	NOUN
ejpam-4587	2	96	,	,	PUNCT
ejpam-4587	2	97	philippines	philippine	NOUN
ejpam-4587	2	98	abstract	abstract	ADJ
ejpam-4587	2	99	.	.	PUNCT
ejpam-4587	3	1	let	let	VERB
ejpam-4587	3	2	g	g	PROPN
ejpam-4587	3	3	=	=	SYM
ejpam-4587	3	4	(	(	PUNCT
ejpam-4587	3	5	v	v	NOUN
ejpam-4587	3	6	(	(	PUNCT
ejpam-4587	3	7	g	g	NOUN
ejpam-4587	3	8	)	)	PUNCT
ejpam-4587	3	9	,	,	PUNCT
ejpam-4587	3	10	e(g	e(g	PROPN
ejpam-4587	3	11	)	)	PUNCT
ejpam-4587	3	12	)	)	PUNCT
ejpam-4587	4	1	be	be	AUX
ejpam-4587	4	2	a	a	DET
ejpam-4587	4	3	simple	simple	ADJ
ejpam-4587	4	4	connected	connected	ADJ
ejpam-4587	4	5	graph	graph	NOUN
ejpam-4587	4	6	.	.	PUNCT
ejpam-4587	5	1	a	a	DET
ejpam-4587	5	2	set	set	NOUN
ejpam-4587	5	3	s	s	NOUN
ejpam-4587	5	4	⊆	⊆	NUM
ejpam-4587	5	5	v	v	NOUN
ejpam-4587	5	6	(	(	PUNCT
ejpam-4587	5	7	g	g	NOUN
ejpam-4587	5	8	)	)	PUNCT
ejpam-4587	5	9	is	be	AUX
ejpam-4587	5	10	a	a	DET
ejpam-4587	5	11	weakly	weakly	ADV
ejpam-4587	5	12	connected	connected	ADJ
ejpam-4587	5	13	hop	hop	NOUN
ejpam-4587	5	14	dominating	dominating	NOUN
ejpam-4587	5	15	set	set	NOUN
ejpam-4587	5	16	of	of	ADP
ejpam-4587	5	17	g	g	PROPN
ejpam-4587	5	18	if	if	SCONJ
ejpam-4587	5	19	for	for	ADP
ejpam-4587	5	20	every	every	DET
ejpam-4587	5	21	q	q	PROPN
ejpam-4587	5	22	∈	∈	PROPN
ejpam-4587	5	23	v	v	ADP
ejpam-4587	5	24	\s	\s	NOUN
ejpam-4587	5	25	,	,	PUNCT
ejpam-4587	5	26	there	there	PRON
ejpam-4587	5	27	exists	exist	VERB
ejpam-4587	5	28	r	r	NOUN
ejpam-4587	5	29	∈	∈	PROPN
ejpam-4587	5	30	s	s	VERB
ejpam-4587	5	31	such	such	ADJ
ejpam-4587	5	32	that	that	PRON
ejpam-4587	5	33	dg(q	dg(q	NOUN
ejpam-4587	5	34	,	,	PUNCT
ejpam-4587	5	35	r	r	NOUN
ejpam-4587	5	36	)	)	PUNCT
ejpam-4587	5	37	=	=	SYM
ejpam-4587	5	38	2	2	NUM
ejpam-4587	5	39	,	,	PUNCT
ejpam-4587	5	40	the	the	DET
ejpam-4587	5	41	subgraph	subgraph	NOUN
ejpam-4587	5	42	weakly	weakly	ADV
ejpam-4587	5	43	induced	induce	VERB
ejpam-4587	5	44	by	by	ADP
ejpam-4587	5	45	s	s	PROPN
ejpam-4587	5	46	,	,	PUNCT
ejpam-4587	5	47	denoted	denote	VERB
ejpam-4587	5	48	by	by	ADP
ejpam-4587	5	49	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4587	5	50	=	=	PUNCT
ejpam-4587	5	51	⟨ng[s	⟨ng[	NOUN
ejpam-4587	5	52	]	]	PUNCT
ejpam-4587	5	53	,	,	PUNCT
ejpam-4587	5	54	ew⟩	ew⟩	ADP
ejpam-4587	5	55	where	where	SCONJ
ejpam-4587	5	56	ew	ew	AUX
ejpam-4587	5	57	=	=	PRON
ejpam-4587	5	58	{	{	PUNCT
ejpam-4587	5	59	qr	qr	PROPN
ejpam-4587	5	60	∈	∈	PROPN
ejpam-4587	5	61	e(g	e(g	PROPN
ejpam-4587	5	62	)	)	PUNCT
ejpam-4587	5	63	:	:	PUNCT
ejpam-4587	6	1	q	q	PUNCT
ejpam-4587	6	2	∈	∈	PROPN
ejpam-4587	6	3	s	s	PART
ejpam-4587	6	4	or	or	CCONJ
ejpam-4587	6	5	r	r	NOUN
ejpam-4587	6	6	∈	∈	NOUN
ejpam-4587	6	7	s	s	AUX
ejpam-4587	6	8	}	}	PUNCT
ejpam-4587	6	9	is	be	AUX
ejpam-4587	6	10	connected	connect	VERB
ejpam-4587	6	11	and	and	CCONJ
ejpam-4587	6	12	s	s	VERB
ejpam-4587	6	13	is	be	AUX
ejpam-4587	6	14	a	a	DET
ejpam-4587	6	15	dominating	dominating	NOUN
ejpam-4587	6	16	set	set	NOUN
ejpam-4587	6	17	of	of	ADP
ejpam-4587	6	18	g.	g.	PROPN
ejpam-4587	6	19	the	the	DET
ejpam-4587	6	20	minimum	minimum	ADJ
ejpam-4587	6	21	cardinality	cardinality	NOUN
ejpam-4587	6	22	of	of	ADP
ejpam-4587	6	23	a	a	DET
ejpam-4587	6	24	weakly	weakly	ADV
ejpam-4587	6	25	connected	connected	ADJ
ejpam-4587	6	26	hop	hop	NOUN
ejpam-4587	6	27	dominating	dominating	NOUN
ejpam-4587	6	28	set	set	NOUN
ejpam-4587	6	29	of	of	ADP
ejpam-4587	6	30	g	g	PROPN
ejpam-4587	6	31	is	be	AUX
ejpam-4587	6	32	called	call	VERB
ejpam-4587	6	33	weakly	weakly	ADV
ejpam-4587	6	34	connected	connect	VERB
ejpam-4587	6	35	hop	hop	NOUN
ejpam-4587	6	36	domination	domination	NOUN
ejpam-4587	6	37	number	number	NOUN
ejpam-4587	6	38	and	and	CCONJ
ejpam-4587	6	39	is	be	AUX
ejpam-4587	6	40	denoted	denote	VERB
ejpam-4587	6	41	by	by	ADP
ejpam-4587	6	42	γwh(g	γwh(g	NOUN
ejpam-4587	6	43	)	)	PUNCT
ejpam-4587	6	44	.	.	PUNCT
ejpam-4587	7	1	in	in	ADP
ejpam-4587	7	2	this	this	DET
ejpam-4587	7	3	paper	paper	NOUN
ejpam-4587	7	4	,	,	PUNCT
ejpam-4587	7	5	the	the	DET
ejpam-4587	7	6	authors	author	NOUN
ejpam-4587	7	7	show	show	VERB
ejpam-4587	7	8	and	and	CCONJ
ejpam-4587	7	9	explore	explore	VERB
ejpam-4587	7	10	the	the	DET
ejpam-4587	7	11	concept	concept	NOUN
ejpam-4587	7	12	of	of	ADP
ejpam-4587	7	13	weakly	weakly	ADJ
ejpam-4587	7	14	connected	connected	ADJ
ejpam-4587	7	15	hop	hop	NOUN
ejpam-4587	7	16	dominating	dominating	NOUN
ejpam-4587	7	17	set	set	NOUN
ejpam-4587	7	18	.	.	PUNCT
ejpam-4587	8	1	the	the	DET
ejpam-4587	8	2	weakly	weakly	ADV
ejpam-4587	8	3	connected	connected	ADJ
ejpam-4587	8	4	hop	hop	NOUN
ejpam-4587	8	5	dominating	dominating	NOUN
ejpam-4587	8	6	set	set	NOUN
ejpam-4587	8	7	of	of	ADP
ejpam-4587	8	8	some	some	DET
ejpam-4587	8	9	special	special	ADJ
ejpam-4587	8	10	graphs	graph	NOUN
ejpam-4587	8	11	,	,	PUNCT
ejpam-4587	8	12	shadow	shadow	NOUN
ejpam-4587	8	13	of	of	ADP
ejpam-4587	8	14	graphs	graph	NOUN
ejpam-4587	8	15	,	,	PUNCT
ejpam-4587	8	16	join	join	NOUN
ejpam-4587	8	17	,	,	PUNCT
ejpam-4587	8	18	corona	corona	NOUN
ejpam-4587	8	19	and	and	CCONJ
ejpam-4587	8	20	lexicographic	lexicographic	ADJ
ejpam-4587	8	21	product	product	NOUN
ejpam-4587	8	22	of	of	ADP
ejpam-4587	8	23	two	two	NUM
ejpam-4587	8	24	graphs	graph	NOUN
ejpam-4587	8	25	are	be	AUX
ejpam-4587	8	26	characterized	characterize	VERB
ejpam-4587	8	27	.	.	PUNCT
ejpam-4587	9	1	also	also	ADV
ejpam-4587	9	2	,	,	PUNCT
ejpam-4587	9	3	the	the	DET
ejpam-4587	9	4	weakly	weakly	ADJ
ejpam-4587	9	5	connected	connected	ADJ
ejpam-4587	9	6	domination	domination	NOUN
ejpam-4587	9	7	number	number	NOUN
ejpam-4587	9	8	of	of	ADP
ejpam-4587	9	9	the	the	DET
ejpam-4587	9	10	aforementioned	aforementione	VERB
ejpam-4587	9	11	graphs	graph	NOUN
ejpam-4587	9	12	are	be	AUX
ejpam-4587	9	13	determined	determine	VERB
ejpam-4587	9	14	.	.	PUNCT
ejpam-4587	10	1	2020	2020	NUM
ejpam-4587	10	2	mathematics	mathematic	NOUN
ejpam-4587	10	3	subject	subject	NOUN
ejpam-4587	10	4	classifications	classification	NOUN
ejpam-4587	10	5	:	:	PUNCT
ejpam-4587	10	6	05c69	05c69	NUM
ejpam-4587	10	7	and	and	CCONJ
ejpam-4587	10	8	0576	0576	NUM
ejpam-4587	10	9	key	key	ADJ
ejpam-4587	10	10	words	word	NOUN
ejpam-4587	10	11	and	and	CCONJ
ejpam-4587	10	12	phrases	phrase	NOUN
ejpam-4587	10	13	:	:	PUNCT
ejpam-4587	10	14	weakly	weakly	ADV
ejpam-4587	10	15	connected	connected	ADJ
ejpam-4587	10	16	set	set	NOUN
ejpam-4587	10	17	,	,	PUNCT
ejpam-4587	10	18	hop	hop	NOUN
ejpam-4587	10	19	dominating	dominating	NOUN
ejpam-4587	10	20	set	set	NOUN
ejpam-4587	10	21	,	,	PUNCT
ejpam-4587	10	22	hop	hop	NOUN
ejpam-4587	10	23	domination	domination	NOUN
ejpam-4587	10	24	number	number	NOUN
ejpam-4587	10	25	,	,	PUNCT
ejpam-4587	10	26	weakly	weakly	ADV
ejpam-4587	10	27	connected	connected	ADJ
ejpam-4587	10	28	hop	hop	NOUN
ejpam-4587	10	29	dominating	dominating	NOUN
ejpam-4587	10	30	set	set	NOUN
ejpam-4587	10	31	,	,	PUNCT
ejpam-4587	10	32	and	and	CCONJ
ejpam-4587	10	33	weakly	weakly	ADV
ejpam-4587	10	34	connected	connect	VERB
ejpam-4587	10	35	hop	hop	NOUN
ejpam-4587	10	36	domination	domination	NOUN
ejpam-4587	10	37	number	number	NOUN
ejpam-4587	10	38	1	1	NUM
ejpam-4587	10	39	.	.	PUNCT
ejpam-4587	11	1	introduction	introduction	NOUN
ejpam-4587	11	2	the	the	DET
ejpam-4587	11	3	weakly	weakly	ADV
ejpam-4587	11	4	connected	connected	ADJ
ejpam-4587	11	5	domination	domination	NOUN
ejpam-4587	11	6	in	in	ADP
ejpam-4587	11	7	graph	graph	NOUN
ejpam-4587	11	8	was	be	AUX
ejpam-4587	11	9	studied	study	VERB
ejpam-4587	11	10	by	by	ADP
ejpam-4587	11	11	dunbar	dunbar	PROPN
ejpam-4587	11	12	,	,	PUNCT
ejpam-4587	11	13	et.al	et.al	PROPN
ejpam-4587	11	14	.	.	PUNCT
ejpam-4587	12	1	in	in	ADP
ejpam-4587	12	2	[	[	X
ejpam-4587	12	3	3	3	NUM
ejpam-4587	12	4	]	]	PUNCT
ejpam-4587	12	5	.	.	PUNCT
ejpam-4587	13	1	they	they	PRON
ejpam-4587	13	2	considered	consider	VERB
ejpam-4587	13	3	the	the	DET
ejpam-4587	13	4	weakly	weakly	ADJ
ejpam-4587	13	5	connected	connected	ADJ
ejpam-4587	13	6	domination	domination	NOUN
ejpam-4587	13	7	number	number	NOUN
ejpam-4587	13	8	γw(g	γw(g	PUNCT
ejpam-4587	13	9	)	)	PUNCT
ejpam-4587	13	10	of	of	ADP
ejpam-4587	13	11	a	a	DET
ejpam-4587	13	12	graph	graph	NOUN
ejpam-4587	13	13	g	g	NOUN
ejpam-4587	13	14	and	and	CCONJ
ejpam-4587	13	15	some	some	DET
ejpam-4587	13	16	related	relate	VERB
ejpam-4587	13	17	domination	domination	NOUN
ejpam-4587	13	18	parameters	parameter	NOUN
ejpam-4587	13	19	.	.	PUNCT
ejpam-4587	14	1	they	they	PRON
ejpam-4587	14	2	have	have	AUX
ejpam-4587	14	3	shown	show	VERB
ejpam-4587	14	4	that	that	SCONJ
ejpam-4587	14	5	the	the	DET
ejpam-4587	14	6	problem	problem	NOUN
ejpam-4587	14	7	of	of	ADP
ejpam-4587	14	8	computing	compute	VERB
ejpam-4587	14	9	γw(g	γw(g	PUNCT
ejpam-4587	14	10	)	)	PUNCT
ejpam-4587	14	11	is	be	AUX
ejpam-4587	14	12	np	np	INTJ
ejpam-4587	14	13	-	-	PUNCT
ejpam-4587	14	14	hard	hard	ADJ
ejpam-4587	14	15	in	in	ADP
ejpam-4587	14	16	general	general	ADJ
ejpam-4587	14	17	but	but	CCONJ
ejpam-4587	14	18	linear	linear	ADJ
ejpam-4587	14	19	for	for	ADP
ejpam-4587	14	20	trees	tree	NOUN
ejpam-4587	14	21	.	.	PUNCT
ejpam-4587	15	1	in	in	ADP
ejpam-4587	15	2	addition	addition	NOUN
ejpam-4587	15	3	,	,	PUNCT
ejpam-4587	15	4	several	several	ADJ
ejpam-4587	15	5	sharp	sharp	ADJ
ejpam-4587	15	6	upper	upper	ADJ
ejpam-4587	15	7	and	and	CCONJ
ejpam-4587	15	8	lower	low	ADJ
ejpam-4587	15	9	bounds	bound	NOUN
ejpam-4587	15	10	for	for	ADP
ejpam-4587	15	11	γw(g	γw(g	NOUN
ejpam-4587	15	12	)	)	PUNCT
ejpam-4587	15	13	are	be	AUX
ejpam-4587	15	14	obtained	obtain	VERB
ejpam-4587	15	15	,	,	PUNCT
ejpam-4587	15	16	and	and	CCONJ
ejpam-4587	15	17	it	it	PRON
ejpam-4587	15	18	was	be	AUX
ejpam-4587	15	19	further	far	ADV
ejpam-4587	15	20	investigated	investigate	VERB
ejpam-4587	15	21	by	by	ADP
ejpam-4587	15	22	domke	domke	PROPN
ejpam-4587	15	23	,	,	PUNCT
ejpam-4587	15	24	et	et	PROPN
ejpam-4587	15	25	.	.	PUNCT
ejpam-4587	16	1	al	al	PROPN
ejpam-4587	16	2	.	.	PUNCT
ejpam-4587	17	1	in	in	ADP
ejpam-4587	17	2	[	[	X
ejpam-4587	17	3	2	2	NUM
ejpam-4587	17	4	]	]	PUNCT
ejpam-4587	17	5	.	.	PUNCT
ejpam-4587	18	1	they	they	PRON
ejpam-4587	18	2	provided	provide	VERB
ejpam-4587	18	3	a	a	DET
ejpam-4587	18	4	constructive	constructive	ADJ
ejpam-4587	18	5	characterization	characterization	NOUN
ejpam-4587	18	6	for	for	ADP
ejpam-4587	18	7	trees	tree	NOUN
ejpam-4587	18	8	t	t	PROPN
ejpam-4587	18	9	for	for	ADP
ejpam-4587	18	10	which	which	PRON
ejpam-4587	18	11	γ(t	γ(t	NOUN
ejpam-4587	18	12	)	)	PUNCT
ejpam-4587	19	1	=	=	SYM
ejpam-4587	19	2	γwc(t	γwc(t	PROPN
ejpam-4587	19	3	)	)	PUNCT
ejpam-4587	19	4	.	.	PUNCT
ejpam-4587	20	1	moreover	moreover	ADV
ejpam-4587	20	2	,	,	PUNCT
ejpam-4587	20	3	some	some	DET
ejpam-4587	20	4	related	related	ADJ
ejpam-4587	20	5	variations	variation	NOUN
ejpam-4587	20	6	and	and	CCONJ
ejpam-4587	20	7	parameters	parameter	NOUN
ejpam-4587	20	8	are	be	AUX
ejpam-4587	20	9	studied	study	VERB
ejpam-4587	20	10	in	in	ADP
ejpam-4587	20	11	many	many	ADJ
ejpam-4587	20	12	classes	class	NOUN
ejpam-4587	20	13	of	of	ADP
ejpam-4587	20	14	graphs	graph	NOUN
ejpam-4587	20	15	including	include	VERB
ejpam-4587	20	16	those	those	DET
ejpam-4587	20	17	results	result	NOUN
ejpam-4587	20	18	under	under	ADP
ejpam-4587	20	19	some	some	DET
ejpam-4587	20	20	binary	binary	ADJ
ejpam-4587	20	21	operations	operation	NOUN
ejpam-4587	20	22	(	(	PUNCT
ejpam-4587	20	23	see	see	VERB
ejpam-4587	20	24	[	[	X
ejpam-4587	20	25	4	4	NUM
ejpam-4587	20	26	]	]	PUNCT
ejpam-4587	20	27	,	,	PUNCT
ejpam-4587	21	1	[	[	X
ejpam-4587	21	2	9	9	NUM
ejpam-4587	21	3	]	]	PUNCT
ejpam-4587	21	4	,	,	PUNCT
ejpam-4587	21	5	[	[	X
ejpam-4587	21	6	10	10	NUM
ejpam-4587	21	7	]	]	PUNCT
ejpam-4587	21	8	and	and	CCONJ
ejpam-4587	21	9	[	[	X
ejpam-4587	21	10	11	11	NUM
ejpam-4587	21	11	]	]	NUM
ejpam-4587	21	12	)	)	PUNCT
ejpam-4587	21	13	.	.	PUNCT
ejpam-4587	22	1	∗corresponding	∗corresponde	VERB
ejpam-4587	22	2	author	author	NOUN
ejpam-4587	22	3	.	.	PUNCT
ejpam-4587	23	1	doi	doi	NOUN
ejpam-4587	23	2	:	:	PUNCT
ejpam-4587	23	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4587	https://doi.org/10.29020/nybg.ejpam.v16i1.4587	ADJ
ejpam-4587	23	4	email	email	NOUN
ejpam-4587	23	5	addresses	address	NOUN
ejpam-4587	23	6	:	:	PUNCT
ejpam-4587	23	7	jamilhamja@msutawi-tawi.edu.ph	jamilhamja@msutawi-tawi.edu.ph	PROPN
ejpam-4587	23	8	(	(	PUNCT
ejpam-4587	23	9	j.	j.	PROPN
ejpam-4587	23	10	hamja	hamja	PROPN
ejpam-4587	23	11	)	)	PUNCT
ejpam-4587	23	12	,	,	PUNCT
ejpam-4587	23	13	imelda.aniversario@g.msuiit.edu.ph	imelda.aniversario@g.msuiit.edu.ph	PROPN
ejpam-4587	23	14	(	(	PUNCT
ejpam-4587	23	15	i.	i.	PROPN
ejpam-4587	23	16	aniversario	aniversario	PROPN
ejpam-4587	23	17	)	)	PUNCT
ejpam-4587	23	18	,	,	PUNCT
ejpam-4587	23	19	catherine.merca@g.msuiit.edu.ph	catherine.merca@g.msuiit.edu.ph	PROPN
ejpam-4587	23	20	(	(	PUNCT
ejpam-4587	23	21	c.	c.	PROPN
ejpam-4587	23	22	merca	merca	PROPN
ejpam-4587	23	23	)	)	PUNCT
ejpam-4587	23	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4587	24	1	454	454	NUM
ejpam-4587	25	1	©	©	PROPN
ejpam-4587	25	2	2023	2023	NUM
ejpam-4587	25	3	ejpam	ejpam	NOUN
ejpam-4587	25	4	all	all	DET
ejpam-4587	25	5	rights	right	NOUN
ejpam-4587	25	6	reserved	reserve	VERB
ejpam-4587	25	7	.	.	PUNCT
ejpam-4587	26	1	j.	j.	PROPN
ejpam-4587	26	2	hamja	hamja	PROPN
ejpam-4587	26	3	,	,	PUNCT
ejpam-4587	26	4	i.	i.	PROPN
ejpam-4587	26	5	aniversario	aniversario	PROPN
ejpam-4587	26	6	,	,	PUNCT
ejpam-4587	26	7	c.	c.	PROPN
ejpam-4587	26	8	merca	merca	PROPN
ejpam-4587	26	9	/	/	SYM
ejpam-4587	26	10	eur	eur	PROPN
ejpam-4587	26	11	.	.	PUNCT
ejpam-4587	27	1	j.	j.	PROPN
ejpam-4587	27	2	pure	pure	PROPN
ejpam-4587	27	3	appl	appl	PROPN
ejpam-4587	27	4	.	.	PROPN
ejpam-4587	27	5	math	math	PROPN
ejpam-4587	27	6	,	,	PUNCT
ejpam-4587	27	7	16	16	NUM
ejpam-4587	27	8	(	(	PUNCT
ejpam-4587	27	9	1	1	NUM
ejpam-4587	27	10	)	)	PUNCT
ejpam-4587	27	11	(	(	PUNCT
ejpam-4587	27	12	2023	2023	NUM
ejpam-4587	27	13	)	)	PUNCT
ejpam-4587	27	14	,	,	PUNCT
ejpam-4587	27	15	454	454	NUM
ejpam-4587	27	16	-	-	SYM
ejpam-4587	27	17	464	464	NUM
ejpam-4587	27	18	455	455	NUM
ejpam-4587	27	19	the	the	DET
ejpam-4587	27	20	concept	concept	NOUN
ejpam-4587	27	21	of	of	ADP
ejpam-4587	27	22	hop	hop	NOUN
ejpam-4587	27	23	dominating	dominating	NOUN
ejpam-4587	27	24	set	set	NOUN
ejpam-4587	27	25	of	of	ADP
ejpam-4587	27	26	a	a	DET
ejpam-4587	27	27	graph	graph	NOUN
ejpam-4587	27	28	g	g	NOUN
ejpam-4587	27	29	was	be	AUX
ejpam-4587	27	30	investigated	investigate	VERB
ejpam-4587	27	31	and	and	CCONJ
ejpam-4587	27	32	introduced	introduce	VERB
ejpam-4587	27	33	by	by	ADP
ejpam-4587	27	34	ayyaswamy	ayyaswamy	ADJ
ejpam-4587	27	35	,	,	PUNCT
ejpam-4587	27	36	et	et	PROPN
ejpam-4587	27	37	.	.	PUNCT
ejpam-4587	28	1	al	al	PROPN
ejpam-4587	28	2	.	.	PUNCT
ejpam-4587	29	1	in	in	ADP
ejpam-4587	29	2	[	[	X
ejpam-4587	29	3	1	1	NUM
ejpam-4587	29	4	]	]	PUNCT
ejpam-4587	29	5	.	.	PUNCT
ejpam-4587	30	1	later	later	ADV
ejpam-4587	30	2	on	on	ADV
ejpam-4587	30	3	,	,	PUNCT
ejpam-4587	30	4	they	they	PRON
ejpam-4587	30	5	presented	present	VERB
ejpam-4587	30	6	the	the	DET
ejpam-4587	30	7	strong	strong	ADJ
ejpam-4587	30	8	equality	equality	NOUN
ejpam-4587	30	9	of	of	ADP
ejpam-4587	30	10	hop	hop	NOUN
ejpam-4587	30	11	domination	domination	NOUN
ejpam-4587	30	12	and	and	CCONJ
ejpam-4587	30	13	hop	hop	NOUN
ejpam-4587	30	14	independent	independent	ADJ
ejpam-4587	30	15	domination	domination	NOUN
ejpam-4587	30	16	numbers	number	NOUN
ejpam-4587	30	17	for	for	ADP
ejpam-4587	30	18	trees	tree	NOUN
ejpam-4587	30	19	.	.	PUNCT
ejpam-4587	31	1	hop	hop	PROPN
ejpam-4587	31	2	domination	domination	NOUN
ejpam-4587	31	3	numbers	number	NOUN
ejpam-4587	31	4	of	of	ADP
ejpam-4587	31	5	shadow	shadow	NOUN
ejpam-4587	31	6	graph	graph	NOUN
ejpam-4587	31	7	and	and	CCONJ
ejpam-4587	31	8	mycielskian	mycielskian	ADJ
ejpam-4587	31	9	graph	graph	NOUN
ejpam-4587	31	10	are	be	AUX
ejpam-4587	31	11	also	also	ADV
ejpam-4587	31	12	discussed	discuss	VERB
ejpam-4587	31	13	in	in	ADP
ejpam-4587	31	14	[	[	X
ejpam-4587	31	15	8	8	NUM
ejpam-4587	31	16	]	]	PUNCT
ejpam-4587	31	17	.	.	PUNCT
ejpam-4587	32	1	canoy	canoy	PROPN
ejpam-4587	32	2	,	,	PUNCT
ejpam-4587	32	3	et.al	et.al	PROPN
ejpam-4587	32	4	.	.	PUNCT
ejpam-4587	33	1	in	in	ADP
ejpam-4587	33	2	[	[	X
ejpam-4587	33	3	7	7	NUM
ejpam-4587	33	4	]	]	PUNCT
ejpam-4587	33	5	,	,	PUNCT
ejpam-4587	33	6	revisited	revisit	VERB
ejpam-4587	33	7	the	the	DET
ejpam-4587	33	8	concept	concept	NOUN
ejpam-4587	33	9	of	of	ADP
ejpam-4587	33	10	hop	hop	NOUN
ejpam-4587	33	11	domination	domination	NOUN
ejpam-4587	33	12	,	,	PUNCT
ejpam-4587	33	13	related	relate	VERB
ejpam-4587	33	14	it	it	PRON
ejpam-4587	33	15	with	with	ADP
ejpam-4587	33	16	other	other	ADJ
ejpam-4587	33	17	domination	domination	NOUN
ejpam-4587	33	18	concepts	concept	NOUN
ejpam-4587	33	19	,	,	PUNCT
ejpam-4587	33	20	and	and	CCONJ
ejpam-4587	33	21	investigated	investigate	VERB
ejpam-4587	33	22	it	it	PRON
ejpam-4587	33	23	in	in	ADP
ejpam-4587	33	24	graphs	graph	NOUN
ejpam-4587	33	25	resulting	result	VERB
ejpam-4587	33	26	from	from	ADP
ejpam-4587	33	27	some	some	DET
ejpam-4587	33	28	binary	binary	ADJ
ejpam-4587	33	29	operations	operation	NOUN
ejpam-4587	33	30	.	.	PUNCT
ejpam-4587	34	1	in	in	ADP
ejpam-4587	34	2	this	this	DET
ejpam-4587	34	3	paper	paper	NOUN
ejpam-4587	34	4	,	,	PUNCT
ejpam-4587	34	5	we	we	PRON
ejpam-4587	34	6	introduce	introduce	VERB
ejpam-4587	34	7	the	the	DET
ejpam-4587	34	8	concept	concept	NOUN
ejpam-4587	34	9	of	of	ADP
ejpam-4587	34	10	weakly	weakly	ADJ
ejpam-4587	34	11	connected	connected	ADJ
ejpam-4587	34	12	hop	hop	NOUN
ejpam-4587	34	13	dominating	dominating	NOUN
ejpam-4587	34	14	set	set	NOUN
ejpam-4587	34	15	of	of	ADP
ejpam-4587	34	16	a	a	DET
ejpam-4587	34	17	graph	graph	NOUN
ejpam-4587	34	18	g.	g.	NOUN
ejpam-4587	34	19	we	we	PRON
ejpam-4587	34	20	show	show	VERB
ejpam-4587	34	21	and	and	CCONJ
ejpam-4587	34	22	investigate	investigate	VERB
ejpam-4587	34	23	a	a	DET
ejpam-4587	34	24	parameter	parameter	NOUN
ejpam-4587	34	25	that	that	PRON
ejpam-4587	34	26	is	be	AUX
ejpam-4587	34	27	,	,	PUNCT
ejpam-4587	34	28	defined	define	VERB
ejpam-4587	34	29	in	in	ADP
ejpam-4587	34	30	a	a	DET
ejpam-4587	34	31	manner	manner	NOUN
ejpam-4587	34	32	that	that	SCONJ
ejpam-4587	34	33	a	a	DET
ejpam-4587	34	34	wellknown	wellknown	ADJ
ejpam-4587	34	35	weakly	weakly	ADV
ejpam-4587	34	36	connected	connected	ADJ
ejpam-4587	34	37	set	set	NOUN
ejpam-4587	34	38	and	and	CCONJ
ejpam-4587	34	39	hop	hop	NOUN
ejpam-4587	34	40	dominating	dominating	NOUN
ejpam-4587	34	41	set	set	NOUN
ejpam-4587	34	42	are	be	AUX
ejpam-4587	34	43	put	put	VERB
ejpam-4587	34	44	into	into	ADP
ejpam-4587	34	45	one	one	NUM
ejpam-4587	34	46	.	.	PUNCT
ejpam-4587	35	1	indeed	indeed	ADV
ejpam-4587	35	2	,	,	PUNCT
ejpam-4587	35	3	notwithstanding	notwithstanding	ADP
ejpam-4587	35	4	hop	hop	NOUN
ejpam-4587	35	5	dominating	dominating	NOUN
ejpam-4587	35	6	set	set	NOUN
ejpam-4587	35	7	of	of	ADP
ejpam-4587	35	8	a	a	DET
ejpam-4587	35	9	graph	graph	NOUN
ejpam-4587	35	10	g	g	NOUN
ejpam-4587	35	11	requires	require	VERB
ejpam-4587	35	12	the	the	DET
ejpam-4587	35	13	subgraph	subgraph	NOUN
ejpam-4587	35	14	weakly	weakly	ADV
ejpam-4587	35	15	induced	induce	VERB
ejpam-4587	35	16	by	by	ADP
ejpam-4587	35	17	s	s	PROPN
ejpam-4587	35	18	,	,	PUNCT
ejpam-4587	35	19	denoted	denote	VERB
ejpam-4587	35	20	by	by	ADP
ejpam-4587	35	21	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4587	35	22	=	=	PUNCT
ejpam-4587	35	23	⟨ng[s	⟨ng[	NOUN
ejpam-4587	35	24	]	]	PUNCT
ejpam-4587	35	25	,	,	PUNCT
ejpam-4587	35	26	ew⟩	ew⟩	ADP
ejpam-4587	35	27	where	where	SCONJ
ejpam-4587	35	28	ew	ew	AUX
ejpam-4587	35	29	=	=	PRON
ejpam-4587	35	30	{	{	PUNCT
ejpam-4587	35	31	qr	qr	PROPN
ejpam-4587	35	32	∈	∈	PROPN
ejpam-4587	35	33	e(g	e(g	PROPN
ejpam-4587	35	34	)	)	PUNCT
ejpam-4587	35	35	:	:	PUNCT
ejpam-4587	35	36	q	q	PUNCT
ejpam-4587	35	37	∈	∈	PROPN
ejpam-4587	35	38	s	s	PART
ejpam-4587	35	39	or	or	CCONJ
ejpam-4587	35	40	r	r	NOUN
ejpam-4587	35	41	∈	∈	NOUN
ejpam-4587	35	42	s	s	VERB
ejpam-4587	35	43	}	}	PUNCT
ejpam-4587	35	44	is	be	AUX
ejpam-4587	35	45	connected	connect	VERB
ejpam-4587	35	46	.	.	PUNCT
ejpam-4587	36	1	the	the	DET
ejpam-4587	36	2	motivation	motivation	NOUN
ejpam-4587	36	3	of	of	ADP
ejpam-4587	36	4	introducing	introduce	VERB
ejpam-4587	36	5	the	the	DET
ejpam-4587	36	6	concept	concept	NOUN
ejpam-4587	36	7	is	be	AUX
ejpam-4587	36	8	to	to	PART
ejpam-4587	36	9	give	give	VERB
ejpam-4587	36	10	further	further	ADJ
ejpam-4587	36	11	investigation	investigation	NOUN
ejpam-4587	36	12	on	on	ADP
ejpam-4587	36	13	weakly	weakly	ADV
ejpam-4587	36	14	connected	connect	VERB
ejpam-4587	36	15	,	,	PUNCT
ejpam-4587	36	16	hop	hop	NOUN
ejpam-4587	36	17	domination	domination	NOUN
ejpam-4587	36	18	and	and	CCONJ
ejpam-4587	36	19	some	some	PRON
ejpam-4587	36	20	of	of	ADP
ejpam-4587	36	21	its	its	PRON
ejpam-4587	36	22	variations	variation	NOUN
ejpam-4587	36	23	.	.	PUNCT
ejpam-4587	37	1	in	in	ADP
ejpam-4587	37	2	fact	fact	NOUN
ejpam-4587	37	3	,	,	PUNCT
ejpam-4587	37	4	it	it	PRON
ejpam-4587	37	5	can	can	AUX
ejpam-4587	37	6	be	be	AUX
ejpam-4587	37	7	shown	show	VERB
ejpam-4587	37	8	that	that	SCONJ
ejpam-4587	37	9	every	every	DET
ejpam-4587	37	10	weakly	weakly	ADV
ejpam-4587	37	11	connected	connected	ADJ
ejpam-4587	37	12	hop	hop	NOUN
ejpam-4587	37	13	dominating	dominating	NOUN
ejpam-4587	37	14	set	set	NOUN
ejpam-4587	37	15	is	be	AUX
ejpam-4587	37	16	a	a	DET
ejpam-4587	37	17	hop	hop	NOUN
ejpam-4587	37	18	dominating	dominating	NOUN
ejpam-4587	37	19	set	set	NOUN
ejpam-4587	37	20	of	of	ADP
ejpam-4587	37	21	a	a	DET
ejpam-4587	37	22	graph	graph	NOUN
ejpam-4587	37	23	g.	g.	NOUN
ejpam-4587	37	24	therefore	therefore	ADV
ejpam-4587	37	25	,	,	PUNCT
ejpam-4587	37	26	the	the	DET
ejpam-4587	37	27	hop	hop	NOUN
ejpam-4587	37	28	domination	domination	NOUN
ejpam-4587	37	29	number	number	NOUN
ejpam-4587	37	30	a	a	DET
ejpam-4587	37	31	graph	graph	NOUN
ejpam-4587	37	32	g	g	NOUN
ejpam-4587	37	33	is	be	AUX
ejpam-4587	37	34	at	at	ADP
ejpam-4587	37	35	most	most	ADV
ejpam-4587	37	36	equal	equal	ADJ
ejpam-4587	37	37	to	to	ADP
ejpam-4587	37	38	the	the	DET
ejpam-4587	37	39	weakly	weakly	ADV
ejpam-4587	37	40	connected	connect	VERB
ejpam-4587	37	41	hop	hop	NOUN
ejpam-4587	37	42	domination	domination	NOUN
ejpam-4587	37	43	number	number	NOUN
ejpam-4587	37	44	of	of	ADP
ejpam-4587	37	45	a	a	DET
ejpam-4587	37	46	graph	graph	NOUN
ejpam-4587	37	47	g.	g.	NOUN
ejpam-4587	37	48	2	2	NUM
ejpam-4587	37	49	.	.	PUNCT
ejpam-4587	37	50	terminology	terminology	NOUN
ejpam-4587	37	51	and	and	CCONJ
ejpam-4587	37	52	notation	notation	NOUN
ejpam-4587	37	53	a	a	DET
ejpam-4587	37	54	simple	simple	ADJ
ejpam-4587	37	55	connected	connected	ADJ
ejpam-4587	37	56	graph	graph	NOUN
ejpam-4587	37	57	g	g	PROPN
ejpam-4587	37	58	=	=	PUNCT
ejpam-4587	37	59	(	(	PUNCT
ejpam-4587	37	60	v	v	NOUN
ejpam-4587	37	61	(	(	PUNCT
ejpam-4587	37	62	g	g	NOUN
ejpam-4587	37	63	)	)	PUNCT
ejpam-4587	37	64	,	,	PUNCT
ejpam-4587	37	65	e(g	e(g	PROPN
ejpam-4587	37	66	)	)	PUNCT
ejpam-4587	37	67	)	)	PUNCT
ejpam-4587	37	68	,	,	PUNCT
ejpam-4587	37	69	where	where	SCONJ
ejpam-4587	37	70	v	v	X
ejpam-4587	37	71	(	(	PUNCT
ejpam-4587	37	72	g	g	NOUN
ejpam-4587	37	73	)	)	PUNCT
ejpam-4587	37	74	is	be	AUX
ejpam-4587	37	75	a	a	DET
ejpam-4587	37	76	vertex	vertex	NOUN
ejpam-4587	37	77	-	-	PUNCT
ejpam-4587	37	78	set	set	NOUN
ejpam-4587	37	79	of	of	ADP
ejpam-4587	37	80	g	g	PROPN
ejpam-4587	37	81	and	and	CCONJ
ejpam-4587	37	82	e(g	e(g	PROPN
ejpam-4587	37	83	)	)	PUNCT
ejpam-4587	37	84	is	be	AUX
ejpam-4587	37	85	an	an	DET
ejpam-4587	37	86	edge	edge	NOUN
ejpam-4587	37	87	-	-	PUNCT
ejpam-4587	37	88	set	set	NOUN
ejpam-4587	37	89	of	of	ADP
ejpam-4587	37	90	g.	g.	PROPN
ejpam-4587	37	91	the	the	DET
ejpam-4587	37	92	elements	element	NOUN
ejpam-4587	37	93	of	of	ADP
ejpam-4587	37	94	v	v	NOUN
ejpam-4587	37	95	(	(	PUNCT
ejpam-4587	37	96	g	g	NOUN
ejpam-4587	37	97	)	)	PUNCT
ejpam-4587	37	98	are	be	AUX
ejpam-4587	37	99	called	call	VERB
ejpam-4587	37	100	vertices	vertex	NOUN
ejpam-4587	37	101	and	and	CCONJ
ejpam-4587	37	102	the	the	DET
ejpam-4587	37	103	cardinality	cardinality	NOUN
ejpam-4587	37	104	|v	|v	PROPN
ejpam-4587	37	105	(	(	PUNCT
ejpam-4587	37	106	g)|	g)|	NOUN
ejpam-4587	37	107	of	of	ADP
ejpam-4587	37	108	v	v	NOUN
ejpam-4587	37	109	(	(	PUNCT
ejpam-4587	37	110	g	g	NOUN
ejpam-4587	37	111	)	)	PUNCT
ejpam-4587	37	112	is	be	AUX
ejpam-4587	37	113	the	the	DET
ejpam-4587	37	114	order	order	NOUN
ejpam-4587	37	115	of	of	ADP
ejpam-4587	37	116	g.	g.	PROPN
ejpam-4587	37	117	the	the	DET
ejpam-4587	37	118	elements	element	NOUN
ejpam-4587	37	119	of	of	ADP
ejpam-4587	37	120	e(g	e(g	PROPN
ejpam-4587	37	121	)	)	PUNCT
ejpam-4587	37	122	are	be	AUX
ejpam-4587	37	123	called	call	VERB
ejpam-4587	37	124	edges	edge	NOUN
ejpam-4587	37	125	and	and	CCONJ
ejpam-4587	37	126	the	the	DET
ejpam-4587	37	127	cardinality	cardinality	NOUN
ejpam-4587	37	128	|e(g)|	|e(g)|	PROPN
ejpam-4587	37	129	of	of	ADP
ejpam-4587	37	130	e(g	e(g	PROPN
ejpam-4587	37	131	)	)	PUNCT
ejpam-4587	37	132	is	be	AUX
ejpam-4587	37	133	the	the	DET
ejpam-4587	37	134	size	size	NOUN
ejpam-4587	37	135	of	of	ADP
ejpam-4587	37	136	g.	g.	PROPN
ejpam-4587	37	137	two	two	NUM
ejpam-4587	37	138	vertices	vertice	VERB
ejpam-4587	37	139	u	u	NOUN
ejpam-4587	37	140	,	,	PUNCT
ejpam-4587	37	141	v	v	NOUN
ejpam-4587	37	142	of	of	ADP
ejpam-4587	37	143	a	a	DET
ejpam-4587	37	144	graph	graph	NOUN
ejpam-4587	37	145	g	g	NOUN
ejpam-4587	37	146	are	be	AUX
ejpam-4587	37	147	adjacent	adjacent	ADJ
ejpam-4587	37	148	,	,	PUNCT
ejpam-4587	37	149	or	or	CCONJ
ejpam-4587	37	150	neighbors	neighbor	NOUN
ejpam-4587	37	151	,	,	PUNCT
ejpam-4587	37	152	if	if	SCONJ
ejpam-4587	37	153	uv	uv	NOUN
ejpam-4587	37	154	is	be	AUX
ejpam-4587	37	155	an	an	DET
ejpam-4587	37	156	edge	edge	NOUN
ejpam-4587	37	157	of	of	ADP
ejpam-4587	37	158	g.	g.	PROPN
ejpam-4587	37	159	the	the	DET
ejpam-4587	37	160	set	set	NOUN
ejpam-4587	37	161	of	of	ADP
ejpam-4587	37	162	neighbors	neighbor	NOUN
ejpam-4587	37	163	of	of	ADP
ejpam-4587	37	164	a	a	DET
ejpam-4587	37	165	vertex	vertex	NOUN
ejpam-4587	37	166	u	u	NOUN
ejpam-4587	37	167	in	in	ADP
ejpam-4587	37	168	g	g	PROPN
ejpam-4587	37	169	is	be	AUX
ejpam-4587	37	170	called	call	VERB
ejpam-4587	37	171	the	the	DET
ejpam-4587	37	172	open	open	ADJ
ejpam-4587	37	173	neighborhood	neighborhood	NOUN
ejpam-4587	37	174	of	of	ADP
ejpam-4587	37	175	u	u	NOUN
ejpam-4587	37	176	in	in	ADP
ejpam-4587	37	177	g	g	PROPN
ejpam-4587	37	178	and	and	CCONJ
ejpam-4587	37	179	is	be	AUX
ejpam-4587	37	180	denoted	denote	VERB
ejpam-4587	37	181	by	by	ADP
ejpam-4587	37	182	ng(u	ng(u	NOUN
ejpam-4587	37	183	)	)	PUNCT
ejpam-4587	37	184	.	.	PUNCT
ejpam-4587	38	1	the	the	DET
ejpam-4587	38	2	closed	closed	ADJ
ejpam-4587	38	3	neighborhood	neighborhood	NOUN
ejpam-4587	38	4	of	of	ADP
ejpam-4587	38	5	u	u	NOUN
ejpam-4587	38	6	in	in	ADP
ejpam-4587	38	7	g	g	PROPN
ejpam-4587	38	8	is	be	AUX
ejpam-4587	38	9	the	the	DET
ejpam-4587	38	10	set	set	NOUN
ejpam-4587	38	11	ng[u	ng[u	PROPN
ejpam-4587	38	12	]	]	X
ejpam-4587	38	13	=	=	PUNCT
ejpam-4587	38	14	ng(u)∪{u	ng(u)∪{u	VERB
ejpam-4587	38	15	}	}	PUNCT
ejpam-4587	38	16	,	,	PUNCT
ejpam-4587	38	17	defined	define	VERB
ejpam-4587	38	18	by	by	ADP
ejpam-4587	38	19	harary	harary	NOUN
ejpam-4587	38	20	in	in	ADP
ejpam-4587	38	21	[	[	X
ejpam-4587	38	22	5	5	NUM
ejpam-4587	38	23	]	]	PUNCT
ejpam-4587	38	24	.	.	PUNCT
ejpam-4587	39	1	a	a	DET
ejpam-4587	39	2	set	set	NOUN
ejpam-4587	39	3	s	s	NOUN
ejpam-4587	39	4	⊆	⊆	NUM
ejpam-4587	39	5	v	v	NOUN
ejpam-4587	39	6	(	(	PUNCT
ejpam-4587	39	7	g	g	NOUN
ejpam-4587	39	8	)	)	PUNCT
ejpam-4587	39	9	is	be	AUX
ejpam-4587	39	10	a	a	DET
ejpam-4587	39	11	dominating	dominating	NOUN
ejpam-4587	39	12	set	set	NOUN
ejpam-4587	39	13	of	of	ADP
ejpam-4587	39	14	g	g	PROPN
ejpam-4587	39	15	if	if	SCONJ
ejpam-4587	39	16	ng[s	ng[	NOUN
ejpam-4587	39	17	]	]	PUNCT
ejpam-4587	39	18	=	=	SYM
ejpam-4587	39	19	v	v	NOUN
ejpam-4587	39	20	(	(	PUNCT
ejpam-4587	39	21	g	g	NOUN
ejpam-4587	39	22	)	)	PUNCT
ejpam-4587	39	23	.	.	PUNCT
ejpam-4587	40	1	the	the	DET
ejpam-4587	40	2	domination	domination	NOUN
ejpam-4587	40	3	number	number	NOUN
ejpam-4587	40	4	of	of	ADP
ejpam-4587	40	5	g	g	NOUN
ejpam-4587	40	6	,	,	PUNCT
ejpam-4587	40	7	denoted	denote	VERB
ejpam-4587	40	8	by	by	ADP
ejpam-4587	40	9	γ(g	γ(g	PROPN
ejpam-4587	40	10	)	)	PUNCT
ejpam-4587	40	11	,	,	PUNCT
ejpam-4587	40	12	is	be	AUX
ejpam-4587	40	13	the	the	DET
ejpam-4587	40	14	minimum	minimum	ADJ
ejpam-4587	40	15	cardinality	cardinality	NOUN
ejpam-4587	40	16	among	among	ADP
ejpam-4587	40	17	the	the	DET
ejpam-4587	40	18	dominating	dominating	NOUN
ejpam-4587	40	19	sets	set	NOUN
ejpam-4587	40	20	of	of	ADP
ejpam-4587	40	21	g.	g.	PROPN
ejpam-4587	40	22	a	a	DET
ejpam-4587	40	23	dominating	dominating	NOUN
ejpam-4587	40	24	set	set	NOUN
ejpam-4587	40	25	s	s	NOUN
ejpam-4587	40	26	with	with	ADP
ejpam-4587	40	27	|s|	|s|	PROPN
ejpam-4587	40	28	=	=	SYM
ejpam-4587	40	29	γ(g	γ(g	PROPN
ejpam-4587	40	30	)	)	PUNCT
ejpam-4587	40	31	is	be	AUX
ejpam-4587	40	32	said	say	VERB
ejpam-4587	40	33	to	to	PART
ejpam-4587	40	34	be	be	AUX
ejpam-4587	40	35	γ	γ	X
ejpam-4587	40	36	-	-	PUNCT
ejpam-4587	40	37	set	set	NOUN
ejpam-4587	40	38	of	of	ADP
ejpam-4587	40	39	g	g	NOUN
ejpam-4587	40	40	,	,	PUNCT
ejpam-4587	40	41	defined	define	VERB
ejpam-4587	40	42	by	by	ADP
ejpam-4587	40	43	j.	j.	PROPN
ejpam-4587	40	44	tarr	tarr	PROPN
ejpam-4587	40	45	,	,	PUNCT
ejpam-4587	40	46	et.al	et.al	VERB
ejpam-4587	40	47	in	in	ADP
ejpam-4587	40	48	[	[	X
ejpam-4587	40	49	12	12	NUM
ejpam-4587	40	50	]	]	PUNCT
ejpam-4587	40	51	.	.	PUNCT
ejpam-4587	41	1	let	let	VERB
ejpam-4587	41	2	s	s	PRON
ejpam-4587	41	3	⊆	⊆	NUM
ejpam-4587	41	4	v	v	NOUN
ejpam-4587	41	5	(	(	PUNCT
ejpam-4587	41	6	g	g	NOUN
ejpam-4587	41	7	)	)	PUNCT
ejpam-4587	41	8	.	.	PUNCT
ejpam-4587	42	1	the	the	DET
ejpam-4587	42	2	subgraph	subgraph	NOUN
ejpam-4587	42	3	weakly	weakly	ADV
ejpam-4587	42	4	induced	induce	VERB
ejpam-4587	42	5	by	by	ADP
ejpam-4587	42	6	s	s	PROPN
ejpam-4587	42	7	is	be	AUX
ejpam-4587	42	8	the	the	DET
ejpam-4587	42	9	graph	graph	NOUN
ejpam-4587	42	10	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4587	42	11	=	=	PUNCT
ejpam-4587	42	12	⟨ng[s	⟨ng[	NOUN
ejpam-4587	42	13	]	]	X
ejpam-4587	42	14	,	,	PUNCT
ejpam-4587	42	15	ew⟩	ew⟩	PROPN
ejpam-4587	42	16	,	,	PUNCT
ejpam-4587	42	17	where	where	SCONJ
ejpam-4587	42	18	ew	ew	AUX
ejpam-4587	42	19	=	=	PUNCT
ejpam-4587	42	20	{	{	PUNCT
ejpam-4587	42	21	qr	qr	PROPN
ejpam-4587	42	22	∈	∈	PROPN
ejpam-4587	42	23	e(g	e(g	PROPN
ejpam-4587	42	24	)	)	PUNCT
ejpam-4587	42	25	:	:	PUNCT
ejpam-4587	42	26	q	q	PUNCT
ejpam-4587	42	27	∈	∈	PROPN
ejpam-4587	42	28	s	s	PART
ejpam-4587	42	29	or	or	CCONJ
ejpam-4587	42	30	r	r	NOUN
ejpam-4587	42	31	∈	∈	NOUN
ejpam-4587	42	32	s	s	PART
ejpam-4587	42	33	}	}	PUNCT
ejpam-4587	42	34	,	,	PUNCT
ejpam-4587	42	35	patangan	patangan	NOUN
ejpam-4587	42	36	,	,	PUNCT
ejpam-4587	42	37	et.al	et.al	VERB
ejpam-4587	42	38	[	[	X
ejpam-4587	42	39	9	9	NUM
ejpam-4587	42	40	]	]	PUNCT
ejpam-4587	42	41	.	.	PUNCT
ejpam-4587	43	1	a	a	DET
ejpam-4587	43	2	dominating	dominating	NOUN
ejpam-4587	43	3	set	set	NOUN
ejpam-4587	43	4	s	s	PROPN
ejpam-4587	43	5	⊆	⊆	NUM
ejpam-4587	43	6	v	v	NOUN
ejpam-4587	43	7	(	(	PUNCT
ejpam-4587	43	8	g	g	NOUN
ejpam-4587	43	9	)	)	PUNCT
ejpam-4587	43	10	is	be	AUX
ejpam-4587	43	11	a	a	DET
ejpam-4587	43	12	weakly	weakly	ADV
ejpam-4587	43	13	connected	connected	ADJ
ejpam-4587	43	14	dominating	dominating	NOUN
ejpam-4587	43	15	set	set	VERB
ejpam-4587	43	16	in	in	ADP
ejpam-4587	43	17	g	g	PROPN
ejpam-4587	43	18	if	if	SCONJ
ejpam-4587	43	19	the	the	DET
ejpam-4587	43	20	subgraph	subgraph	PROPN
ejpam-4587	43	21	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4587	43	22	weakly	weakly	ADV
ejpam-4587	43	23	induced	induce	VERB
ejpam-4587	43	24	by	by	ADP
ejpam-4587	43	25	s	s	PRON
ejpam-4587	43	26	is	be	AUX
ejpam-4587	43	27	connected	connect	VERB
ejpam-4587	43	28	.	.	PUNCT
ejpam-4587	44	1	the	the	DET
ejpam-4587	44	2	weakly	weakly	ADJ
ejpam-4587	44	3	connected	connected	ADJ
ejpam-4587	44	4	domination	domination	NOUN
ejpam-4587	44	5	number	number	NOUN
ejpam-4587	44	6	γw(g	γw(g	PUNCT
ejpam-4587	44	7	)	)	PUNCT
ejpam-4587	44	8	of	of	ADP
ejpam-4587	44	9	g	g	PROPN
ejpam-4587	44	10	is	be	AUX
ejpam-4587	44	11	the	the	DET
ejpam-4587	44	12	minimum	minimum	ADJ
ejpam-4587	44	13	cardinality	cardinality	NOUN
ejpam-4587	44	14	among	among	ADP
ejpam-4587	44	15	all	all	DET
ejpam-4587	44	16	weakly	weakly	ADV
ejpam-4587	44	17	connected	connected	ADJ
ejpam-4587	44	18	dominating	dominating	NOUN
ejpam-4587	44	19	sets	set	NOUN
ejpam-4587	44	20	of	of	ADP
ejpam-4587	44	21	g.	g.	PROPN
ejpam-4587	44	22	a	a	DET
ejpam-4587	44	23	weakly	weakly	ADV
ejpam-4587	44	24	connected	connected	ADJ
ejpam-4587	44	25	dominating	dominating	NOUN
ejpam-4587	44	26	set	set	NOUN
ejpam-4587	44	27	s	s	NOUN
ejpam-4587	44	28	with	with	ADP
ejpam-4587	44	29	|s|	|s|	NOUN
ejpam-4587	44	30	=	=	NOUN
ejpam-4587	44	31	γw(g	γw(g	X
ejpam-4587	44	32	)	)	PUNCT
ejpam-4587	44	33	is	be	AUX
ejpam-4587	44	34	said	say	VERB
ejpam-4587	44	35	to	to	PART
ejpam-4587	44	36	be	be	AUX
ejpam-4587	44	37	γw	γw	NOUN
ejpam-4587	44	38	-	-	PUNCT
ejpam-4587	44	39	set	set	NOUN
ejpam-4587	44	40	of	of	ADP
ejpam-4587	44	41	g	g	PROPN
ejpam-4587	44	42	,	,	PUNCT
ejpam-4587	44	43	sandueta	sandueta	ADJ
ejpam-4587	44	44	,	,	PUNCT
ejpam-4587	44	45	et.al	et.al	VERB
ejpam-4587	44	46	in	in	ADP
ejpam-4587	44	47	[	[	X
ejpam-4587	44	48	10	10	NUM
ejpam-4587	44	49	]	]	PUNCT
ejpam-4587	44	50	.	.	PUNCT
ejpam-4587	45	1	a	a	DET
ejpam-4587	45	2	set	set	NOUN
ejpam-4587	45	3	s	s	NOUN
ejpam-4587	45	4	⊆	⊆	NUM
ejpam-4587	45	5	v	v	NOUN
ejpam-4587	45	6	(	(	PUNCT
ejpam-4587	45	7	g	g	NOUN
ejpam-4587	45	8	)	)	PUNCT
ejpam-4587	45	9	is	be	AUX
ejpam-4587	45	10	a	a	DET
ejpam-4587	45	11	hop	hop	NOUN
ejpam-4587	45	12	dominating	dominating	NOUN
ejpam-4587	45	13	set	set	NOUN
ejpam-4587	45	14	of	of	ADP
ejpam-4587	45	15	g	g	PROPN
ejpam-4587	45	16	if	if	SCONJ
ejpam-4587	45	17	for	for	ADP
ejpam-4587	45	18	every	every	DET
ejpam-4587	45	19	q	q	PROPN
ejpam-4587	45	20	∈	∈	PROPN
ejpam-4587	45	21	v	v	NOUN
ejpam-4587	45	22	(	(	PUNCT
ejpam-4587	45	23	g	g	NOUN
ejpam-4587	45	24	)	)	PUNCT
ejpam-4587	45	25	\	\	PROPN
ejpam-4587	46	1	s	s	X
ejpam-4587	46	2	,	,	PUNCT
ejpam-4587	46	3	there	there	PRON
ejpam-4587	46	4	exists	exist	VERB
ejpam-4587	46	5	r	r	NOUN
ejpam-4587	46	6	∈	∈	PROPN
ejpam-4587	46	7	s	s	VERB
ejpam-4587	46	8	such	such	ADJ
ejpam-4587	46	9	that	that	PRON
ejpam-4587	46	10	dg(q	dg(q	NOUN
ejpam-4587	46	11	,	,	PUNCT
ejpam-4587	46	12	r	r	NOUN
ejpam-4587	46	13	)	)	PUNCT
ejpam-4587	47	1	=	=	SYM
ejpam-4587	47	2	2	2	X
ejpam-4587	47	3	.	.	X
ejpam-4587	48	1	the	the	DET
ejpam-4587	48	2	hop	hop	NOUN
ejpam-4587	48	3	domination	domination	NOUN
ejpam-4587	48	4	number	number	NOUN
ejpam-4587	48	5	of	of	ADP
ejpam-4587	48	6	g	g	NOUN
ejpam-4587	48	7	,	,	PUNCT
ejpam-4587	48	8	denoted	denote	VERB
ejpam-4587	48	9	by	by	ADP
ejpam-4587	48	10	γh(g	γh(g	NOUN
ejpam-4587	48	11	)	)	PUNCT
ejpam-4587	48	12	,	,	PUNCT
ejpam-4587	48	13	is	be	AUX
ejpam-4587	48	14	the	the	DET
ejpam-4587	48	15	minimum	minimum	ADJ
ejpam-4587	48	16	cardinality	cardinality	NOUN
ejpam-4587	48	17	among	among	ADP
ejpam-4587	48	18	the	the	DET
ejpam-4587	48	19	hop	hop	NOUN
ejpam-4587	48	20	dominating	dominating	NOUN
ejpam-4587	48	21	sets	set	NOUN
ejpam-4587	48	22	of	of	ADP
ejpam-4587	48	23	g.	g.	PROPN
ejpam-4587	48	24	any	any	DET
ejpam-4587	48	25	hop	hop	NOUN
ejpam-4587	48	26	dominating	dominating	NOUN
ejpam-4587	48	27	set	set	NOUN
ejpam-4587	48	28	s	s	NOUN
ejpam-4587	48	29	of	of	ADP
ejpam-4587	48	30	g	g	NOUN
ejpam-4587	48	31	with	with	ADP
ejpam-4587	48	32	|s|=	|s|=	NOUN
ejpam-4587	48	33	γh(g	γh(g	NOUN
ejpam-4587	48	34	)	)	PUNCT
ejpam-4587	48	35	is	be	AUX
ejpam-4587	48	36	refered	refer	VERB
ejpam-4587	48	37	to	to	ADP
ejpam-4587	48	38	as	as	ADP
ejpam-4587	48	39	γh	γh	ADP
ejpam-4587	48	40	−	−	PROPN
ejpam-4587	48	41	set	set	NOUN
ejpam-4587	48	42	of	of	ADP
ejpam-4587	48	43	g	g	NOUN
ejpam-4587	48	44	,	,	PUNCT
ejpam-4587	48	45	ayyaswamy	ayyaswamy	ADJ
ejpam-4587	48	46	,	,	PUNCT
ejpam-4587	48	47	et.al	et.al	PROPN
ejpam-4587	48	48	.	.	PUNCT
ejpam-4587	49	1	in	in	ADP
ejpam-4587	49	2	[	[	X
ejpam-4587	49	3	1	1	NUM
ejpam-4587	49	4	]	]	PUNCT
ejpam-4587	49	5	.	.	PUNCT
ejpam-4587	50	1	j.	j.	PROPN
ejpam-4587	50	2	hamja	hamja	PROPN
ejpam-4587	50	3	,	,	PUNCT
ejpam-4587	50	4	i.	i.	PROPN
ejpam-4587	50	5	aniversario	aniversario	PROPN
ejpam-4587	50	6	,	,	PUNCT
ejpam-4587	50	7	c.	c.	PROPN
ejpam-4587	50	8	merca	merca	PROPN
ejpam-4587	50	9	/	/	SYM
ejpam-4587	50	10	eur	eur	PROPN
ejpam-4587	50	11	.	.	PUNCT
ejpam-4587	51	1	j.	j.	PROPN
ejpam-4587	51	2	pure	pure	PROPN
ejpam-4587	51	3	appl	appl	PROPN
ejpam-4587	51	4	.	.	PROPN
ejpam-4587	51	5	math	math	PROPN
ejpam-4587	51	6	,	,	PUNCT
ejpam-4587	51	7	16	16	NUM
ejpam-4587	51	8	(	(	PUNCT
ejpam-4587	51	9	1	1	NUM
ejpam-4587	51	10	)	)	PUNCT
ejpam-4587	51	11	(	(	PUNCT
ejpam-4587	51	12	2023	2023	NUM
ejpam-4587	51	13	)	)	PUNCT
ejpam-4587	51	14	,	,	PUNCT
ejpam-4587	51	15	454	454	NUM
ejpam-4587	51	16	-	-	SYM
ejpam-4587	51	17	464	464	NUM
ejpam-4587	51	18	456	456	NUM
ejpam-4587	51	19	3	3	NUM
ejpam-4587	51	20	.	.	PUNCT
ejpam-4587	51	21	results	result	NOUN
ejpam-4587	51	22	definition	definition	NOUN
ejpam-4587	51	23	1	1	NUM
ejpam-4587	51	24	.	.	PUNCT
ejpam-4587	52	1	a	a	DET
ejpam-4587	52	2	set	set	NOUN
ejpam-4587	52	3	s	s	NOUN
ejpam-4587	52	4	⊆	⊆	NUM
ejpam-4587	52	5	v	v	NOUN
ejpam-4587	52	6	(	(	PUNCT
ejpam-4587	52	7	g	g	NOUN
ejpam-4587	52	8	)	)	PUNCT
ejpam-4587	52	9	is	be	AUX
ejpam-4587	52	10	a	a	DET
ejpam-4587	52	11	weakly	weakly	ADJ
ejpam-4587	52	12	connecetd	connecetd	NOUN
ejpam-4587	52	13	hop	hop	NOUN
ejpam-4587	52	14	dominating	dominating	NOUN
ejpam-4587	52	15	set	set	NOUN
ejpam-4587	52	16	of	of	ADP
ejpam-4587	52	17	g	g	PROPN
ejpam-4587	52	18	if	if	SCONJ
ejpam-4587	52	19	s	s	VERB
ejpam-4587	52	20	is	be	AUX
ejpam-4587	52	21	both	both	PRON
ejpam-4587	52	22	a	a	DET
ejpam-4587	52	23	weakly	weakly	ADV
ejpam-4587	52	24	connected	connected	ADJ
ejpam-4587	52	25	set	set	NOUN
ejpam-4587	52	26	and	and	CCONJ
ejpam-4587	52	27	hop	hop	NOUN
ejpam-4587	52	28	dominating	dominating	NOUN
ejpam-4587	52	29	set	set	NOUN
ejpam-4587	52	30	of	of	ADP
ejpam-4587	52	31	g.	g.	PROPN
ejpam-4587	52	32	the	the	DET
ejpam-4587	52	33	minimum	minimum	ADJ
ejpam-4587	52	34	cardinality	cardinality	NOUN
ejpam-4587	52	35	of	of	ADP
ejpam-4587	52	36	a	a	DET
ejpam-4587	52	37	weakly	weakly	ADV
ejpam-4587	52	38	connected	connected	ADJ
ejpam-4587	52	39	hop	hop	NOUN
ejpam-4587	52	40	dominating	dominating	NOUN
ejpam-4587	52	41	set	set	NOUN
ejpam-4587	52	42	of	of	ADP
ejpam-4587	52	43	g	g	PROPN
ejpam-4587	52	44	is	be	AUX
ejpam-4587	52	45	called	call	VERB
ejpam-4587	52	46	weakly	weakly	ADV
ejpam-4587	52	47	connected	connect	VERB
ejpam-4587	52	48	hop	hop	NOUN
ejpam-4587	52	49	domination	domination	NOUN
ejpam-4587	52	50	number	number	NOUN
ejpam-4587	52	51	and	and	CCONJ
ejpam-4587	52	52	is	be	AUX
ejpam-4587	52	53	denoted	denote	VERB
ejpam-4587	52	54	by	by	ADP
ejpam-4587	52	55	γwh(g	γwh(g	NOUN
ejpam-4587	52	56	)	)	PUNCT
ejpam-4587	52	57	.	.	PUNCT
ejpam-4587	53	1	a	a	DET
ejpam-4587	53	2	weakly	weakly	ADV
ejpam-4587	53	3	connected	connected	ADJ
ejpam-4587	53	4	hop	hop	NOUN
ejpam-4587	53	5	dominating	dominating	NOUN
ejpam-4587	53	6	set	set	NOUN
ejpam-4587	53	7	s	s	NOUN
ejpam-4587	53	8	with	with	ADP
ejpam-4587	53	9	|s|	|s|	NOUN
ejpam-4587	53	10	=	=	PUNCT
ejpam-4587	53	11	γwh(g	γwh(g	PROPN
ejpam-4587	53	12	)	)	PUNCT
ejpam-4587	53	13	is	be	AUX
ejpam-4587	53	14	said	say	VERB
ejpam-4587	53	15	to	to	PART
ejpam-4587	53	16	be	be	AUX
ejpam-4587	53	17	γwh	γwh	NOUN
ejpam-4587	53	18	-	-	PUNCT
ejpam-4587	53	19	set	set	NOUN
ejpam-4587	53	20	of	of	ADP
ejpam-4587	53	21	g.	g.	PROPN
ejpam-4587	53	22	example	example	NOUN
ejpam-4587	54	1	1	1	X
ejpam-4587	54	2	.	.	PUNCT
ejpam-4587	55	1	let	let	VERB
ejpam-4587	55	2	g	g	NOUN
ejpam-4587	55	3	be	be	AUX
ejpam-4587	55	4	the	the	DET
ejpam-4587	55	5	graph	graph	NOUN
ejpam-4587	55	6	in	in	ADP
ejpam-4587	55	7	figure	figure	NOUN
ejpam-4587	55	8	1	1	NUM
ejpam-4587	55	9	and	and	CCONJ
ejpam-4587	55	10	s	s	NOUN
ejpam-4587	55	11	=	=	SYM
ejpam-4587	55	12	{	{	PUNCT
ejpam-4587	55	13	b	b	PROPN
ejpam-4587	55	14	,	,	PUNCT
ejpam-4587	55	15	d	d	PROPN
ejpam-4587	55	16	,	,	PUNCT
ejpam-4587	55	17	h	h	NOUN
ejpam-4587	55	18	}	}	PUNCT
ejpam-4587	55	19	⊆	⊆	NUM
ejpam-4587	55	20	v	v	NOUN
ejpam-4587	55	21	(	(	PUNCT
ejpam-4587	55	22	g	g	NOUN
ejpam-4587	55	23	)	)	PUNCT
ejpam-4587	55	24	.	.	PUNCT
ejpam-4587	56	1	observe	observe	VERB
ejpam-4587	56	2	that	that	SCONJ
ejpam-4587	56	3	for	for	ADP
ejpam-4587	56	4	all	all	DET
ejpam-4587	56	5	vertices	vertex	NOUN
ejpam-4587	56	6	a	a	DET
ejpam-4587	56	7	,	,	PUNCT
ejpam-4587	56	8	c	c	NOUN
ejpam-4587	56	9	,	,	PUNCT
ejpam-4587	56	10	e	e	NOUN
ejpam-4587	56	11	,	,	PUNCT
ejpam-4587	56	12	f	f	X
ejpam-4587	56	13	,	,	PUNCT
ejpam-4587	56	14	g	g	PROPN
ejpam-4587	56	15	∈	∈	PROPN
ejpam-4587	56	16	v	v	ADP
ejpam-4587	56	17	(	(	PUNCT
ejpam-4587	56	18	g	g	NOUN
ejpam-4587	56	19	)	)	PUNCT
ejpam-4587	56	20	\	\	PROPN
ejpam-4587	57	1	s	s	X
ejpam-4587	57	2	,	,	PUNCT
ejpam-4587	57	3	there	there	PRON
ejpam-4587	57	4	are	be	VERB
ejpam-4587	57	5	b	b	NOUN
ejpam-4587	57	6	,	,	PUNCT
ejpam-4587	57	7	d	d	PROPN
ejpam-4587	57	8	,	,	PUNCT
ejpam-4587	57	9	h	h	PROPN
ejpam-4587	57	10	∈	∈	PROPN
ejpam-4587	57	11	s	s	VERB
ejpam-4587	57	12	such	such	ADJ
ejpam-4587	57	13	that	that	PRON
ejpam-4587	57	14	dg(b	dg(b	NOUN
ejpam-4587	57	15	,	,	PUNCT
ejpam-4587	57	16	g	g	NOUN
ejpam-4587	57	17	)	)	PUNCT
ejpam-4587	57	18	=	=	SYM
ejpam-4587	57	19	2	2	NUM
ejpam-4587	57	20	,	,	PUNCT
ejpam-4587	57	21	dg(d	dg(d	NOUN
ejpam-4587	57	22	,	,	PUNCT
ejpam-4587	57	23	f	f	X
ejpam-4587	57	24	)	)	PUNCT
ejpam-4587	57	25	=	=	SYM
ejpam-4587	57	26	2	2	NUM
ejpam-4587	57	27	,	,	PUNCT
ejpam-4587	57	28	dg(h	dg(h	NUM
ejpam-4587	57	29	,	,	PUNCT
ejpam-4587	57	30	a	a	X
ejpam-4587	57	31	)	)	PUNCT
ejpam-4587	57	32	=	=	SYM
ejpam-4587	57	33	2	2	NUM
ejpam-4587	57	34	,	,	PUNCT
ejpam-4587	57	35	dg(h	dg(h	NUM
ejpam-4587	57	36	,	,	PUNCT
ejpam-4587	57	37	e	e	X
ejpam-4587	57	38	)	)	PUNCT
ejpam-4587	57	39	=	=	SYM
ejpam-4587	57	40	2	2	NUM
ejpam-4587	57	41	,	,	PUNCT
ejpam-4587	57	42	and	and	CCONJ
ejpam-4587	57	43	dg(h	dg(h	NUM
ejpam-4587	57	44	,	,	PUNCT
ejpam-4587	57	45	c	c	X
ejpam-4587	57	46	)	)	PUNCT
ejpam-4587	57	47	=	=	SYM
ejpam-4587	57	48	2	2	NUM
ejpam-4587	57	49	,	,	PUNCT
ejpam-4587	57	50	and	and	CCONJ
ejpam-4587	57	51	ng[s	ng[s	PROPN
ejpam-4587	57	52	]	]	PUNCT
ejpam-4587	57	53	=	=	SYM
ejpam-4587	57	54	v	v	X
ejpam-4587	57	55	(	(	PUNCT
ejpam-4587	57	56	g	g	NOUN
ejpam-4587	57	57	)	)	PUNCT
ejpam-4587	57	58	.	.	PUNCT
ejpam-4587	58	1	thus	thus	ADV
ejpam-4587	58	2	,	,	PUNCT
ejpam-4587	58	3	s	s	VERB
ejpam-4587	58	4	is	be	AUX
ejpam-4587	58	5	a	a	DET
ejpam-4587	58	6	hop	hop	NOUN
ejpam-4587	58	7	dominating	dominating	NOUN
ejpam-4587	58	8	set	set	NOUN
ejpam-4587	58	9	.	.	PUNCT
ejpam-4587	59	1	moreover	moreover	ADV
ejpam-4587	59	2	,	,	PUNCT
ejpam-4587	59	3	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4587	59	4	=	=	PUNCT
ejpam-4587	59	5	⟨ng(s	⟨ng(s	NUM
ejpam-4587	59	6	)	)	PUNCT
ejpam-4587	59	7	,	,	PUNCT
ejpam-4587	59	8	{	{	PUNCT
ejpam-4587	59	9	ba	ba	PROPN
ejpam-4587	59	10	,	,	PUNCT
ejpam-4587	59	11	bc	bc	PROPN
ejpam-4587	59	12	,	,	PUNCT
ejpam-4587	59	13	bh	bh	PROPN
ejpam-4587	59	14	,	,	PUNCT
ejpam-4587	59	15	dc	dc	PROPN
ejpam-4587	59	16	,	,	PUNCT
ejpam-4587	59	17	de	de	X
ejpam-4587	59	18	,	,	PUNCT
ejpam-4587	59	19	dh	dh	NOUN
ejpam-4587	59	20	,	,	PUNCT
ejpam-4587	59	21	hg	hg	PROPN
ejpam-4587	59	22	,	,	PUNCT
ejpam-4587	59	23	hf}⟩	hf}⟩	X
ejpam-4587	59	24	is	be	AUX
ejpam-4587	59	25	connected	connect	VERB
ejpam-4587	59	26	.	.	PUNCT
ejpam-4587	60	1	therefore	therefore	ADV
ejpam-4587	60	2	,	,	PUNCT
ejpam-4587	60	3	s	s	VERB
ejpam-4587	60	4	is	be	AUX
ejpam-4587	60	5	a	a	DET
ejpam-4587	60	6	weakly	weakly	ADV
ejpam-4587	60	7	connected	connected	ADJ
ejpam-4587	60	8	hop	hop	NOUN
ejpam-4587	60	9	dominating	dominating	NOUN
ejpam-4587	60	10	set	set	NOUN
ejpam-4587	60	11	of	of	ADP
ejpam-4587	60	12	g.	g.	PROPN
ejpam-4587	60	13	a	a	DET
ejpam-4587	60	14	b	b	PROPN
ejpam-4587	61	1	d	d	X
ejpam-4587	61	2	e	e	PROPN
ejpam-4587	61	3	h	h	NOUN
ejpam-4587	61	4	g	g	PROPN
ejpam-4587	62	1	f	f	PROPN
ejpam-4587	62	2	c	c	PROPN
ejpam-4587	62	3	g	g	PROPN
ejpam-4587	62	4	:	:	PUNCT
ejpam-4587	62	5	a	a	DET
ejpam-4587	62	6	b	b	X
ejpam-4587	62	7	d	d	X
ejpam-4587	62	8	e	e	PROPN
ejpam-4587	62	9	h	h	NOUN
ejpam-4587	62	10	g	g	PROPN
ejpam-4587	62	11	f	f	PROPN
ejpam-4587	62	12	c	c	PROPN
ejpam-4587	62	13	⟨s⟩w	⟨s⟩w	PROPN
ejpam-4587	62	14	:	:	PUNCT
ejpam-4587	62	15	figure	figure	VERB
ejpam-4587	62	16	1	1	NUM
ejpam-4587	62	17	:	:	PUNCT
ejpam-4587	62	18	graph	graph	VERB
ejpam-4587	62	19	g	g	NOUN
ejpam-4587	62	20	with	with	ADP
ejpam-4587	62	21	γwh(g	γwh(g	NOUN
ejpam-4587	62	22	)	)	PUNCT
ejpam-4587	62	23	=	=	SYM
ejpam-4587	62	24	3	3	NUM
ejpam-4587	62	25	and	and	CCONJ
ejpam-4587	62	26	its	its	PRON
ejpam-4587	62	27	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4587	62	28	remark	remark	NOUN
ejpam-4587	62	29	1	1	NUM
ejpam-4587	62	30	.	.	PUNCT
ejpam-4587	63	1	every	every	DET
ejpam-4587	63	2	weakly	weakly	ADV
ejpam-4587	63	3	connected	connected	ADJ
ejpam-4587	63	4	hop	hop	NOUN
ejpam-4587	63	5	dominating	dominating	NOUN
ejpam-4587	63	6	set	set	NOUN
ejpam-4587	63	7	of	of	ADP
ejpam-4587	63	8	a	a	DET
ejpam-4587	63	9	connected	connected	ADJ
ejpam-4587	63	10	graph	graph	NOUN
ejpam-4587	63	11	g	g	PROPN
ejpam-4587	63	12	is	be	AUX
ejpam-4587	63	13	a	a	DET
ejpam-4587	63	14	weakly	weakly	ADV
ejpam-4587	63	15	connected	connected	ADJ
ejpam-4587	63	16	dominating	dominating	NOUN
ejpam-4587	63	17	set	set	NOUN
ejpam-4587	63	18	of	of	ADP
ejpam-4587	63	19	g.	g.	PROPN
ejpam-4587	63	20	proposition	proposition	PROPN
ejpam-4587	63	21	1	1	NUM
ejpam-4587	63	22	.	.	PUNCT
ejpam-4587	64	1	every	every	DET
ejpam-4587	64	2	weakly	weakly	ADV
ejpam-4587	64	3	connected	connected	ADJ
ejpam-4587	64	4	hop	hop	NOUN
ejpam-4587	64	5	dominating	dominating	NOUN
ejpam-4587	64	6	set	set	NOUN
ejpam-4587	64	7	of	of	ADP
ejpam-4587	64	8	a	a	DET
ejpam-4587	64	9	connected	connected	ADJ
ejpam-4587	64	10	graph	graph	NOUN
ejpam-4587	64	11	g	g	PROPN
ejpam-4587	64	12	is	be	AUX
ejpam-4587	64	13	a	a	DET
ejpam-4587	64	14	hop	hop	NOUN
ejpam-4587	64	15	dominating	dominating	NOUN
ejpam-4587	64	16	set	set	NOUN
ejpam-4587	64	17	of	of	ADP
ejpam-4587	64	18	g.	g.	PROPN
ejpam-4587	64	19	thus	thus	ADV
ejpam-4587	64	20	,	,	PUNCT
ejpam-4587	64	21	γh(g	γh(g	NOUN
ejpam-4587	64	22	)	)	PUNCT
ejpam-4587	64	23	≤	≤	NUM
ejpam-4587	64	24	γwh(g	γwh(g	NOUN
ejpam-4587	64	25	)	)	PUNCT
ejpam-4587	64	26	.	.	PUNCT
ejpam-4587	65	1	proof	proof	NOUN
ejpam-4587	65	2	.	.	PUNCT
ejpam-4587	66	1	let	let	VERB
ejpam-4587	66	2	s	s	PRON
ejpam-4587	66	3	⊆	⊆	NUM
ejpam-4587	66	4	v	v	NOUN
ejpam-4587	66	5	(	(	PUNCT
ejpam-4587	66	6	g	g	NOUN
ejpam-4587	66	7	)	)	PUNCT
ejpam-4587	66	8	be	be	AUX
ejpam-4587	66	9	a	a	DET
ejpam-4587	66	10	weakly	weakly	ADV
ejpam-4587	66	11	connected	connected	ADJ
ejpam-4587	66	12	hop	hop	NOUN
ejpam-4587	66	13	dominating	dominating	NOUN
ejpam-4587	66	14	set	set	NOUN
ejpam-4587	66	15	of	of	ADP
ejpam-4587	66	16	g.	g.	PROPN
ejpam-4587	67	1	then	then	ADV
ejpam-4587	67	2	s	s	VERB
ejpam-4587	67	3	is	be	AUX
ejpam-4587	67	4	a	a	DET
ejpam-4587	67	5	weakly	weakly	ADV
ejpam-4587	67	6	connected	connect	VERB
ejpam-4587	67	7	and	and	CCONJ
ejpam-4587	67	8	a	a	DET
ejpam-4587	67	9	hop	hop	NOUN
ejpam-4587	67	10	dominating	dominating	NOUN
ejpam-4587	67	11	set	set	NOUN
ejpam-4587	67	12	of	of	ADP
ejpam-4587	67	13	g.	g.	PROPN
ejpam-4587	67	14	thus	thus	ADV
ejpam-4587	67	15	,	,	PUNCT
ejpam-4587	67	16	the	the	DET
ejpam-4587	67	17	inequality	inequality	NOUN
ejpam-4587	67	18	holds	hold	VERB
ejpam-4587	67	19	.	.	PUNCT
ejpam-4587	68	1	proposition	proposition	NOUN
ejpam-4587	68	2	2	2	NUM
ejpam-4587	68	3	.	.	PUNCT
ejpam-4587	69	1	let	let	VERB
ejpam-4587	69	2	g	g	NOUN
ejpam-4587	69	3	be	be	AUX
ejpam-4587	69	4	any	any	DET
ejpam-4587	69	5	connected	connected	ADJ
ejpam-4587	69	6	graph	graph	NOUN
ejpam-4587	69	7	.	.	PUNCT
ejpam-4587	70	1	then	then	ADV
ejpam-4587	70	2	s	s	VERB
ejpam-4587	70	3	⊆	⊆	NUM
ejpam-4587	70	4	v	v	NOUN
ejpam-4587	70	5	(	(	PUNCT
ejpam-4587	70	6	g	g	NOUN
ejpam-4587	70	7	)	)	PUNCT
ejpam-4587	70	8	is	be	AUX
ejpam-4587	70	9	weakly	weakly	ADV
ejpam-4587	70	10	connected	connected	ADJ
ejpam-4587	70	11	hop	hop	NOUN
ejpam-4587	70	12	dominating	dominating	NOUN
ejpam-4587	70	13	set	set	NOUN
ejpam-4587	70	14	of	of	ADP
ejpam-4587	70	15	g	g	PROPN
ejpam-4587	70	16	if	if	SCONJ
ejpam-4587	70	17	and	and	CCONJ
ejpam-4587	70	18	only	only	ADV
ejpam-4587	70	19	if	if	SCONJ
ejpam-4587	70	20	s	s	NOUN
ejpam-4587	70	21	is	be	AUX
ejpam-4587	70	22	hop	hop	NOUN
ejpam-4587	70	23	dominating	dominate	VERB
ejpam-4587	70	24	set	set	NOUN
ejpam-4587	70	25	of	of	ADP
ejpam-4587	70	26	g.	g.	PROPN
ejpam-4587	70	27	proof	proof	NOUN
ejpam-4587	70	28	.	.	PUNCT
ejpam-4587	71	1	by	by	ADP
ejpam-4587	71	2	proposition	proposition	NOUN
ejpam-4587	71	3	1	1	NUM
ejpam-4587	71	4	,	,	PUNCT
ejpam-4587	71	5	we	we	PRON
ejpam-4587	71	6	only	only	ADV
ejpam-4587	71	7	need	need	VERB
ejpam-4587	71	8	to	to	PART
ejpam-4587	71	9	show	show	VERB
ejpam-4587	71	10	that	that	SCONJ
ejpam-4587	71	11	a	a	DET
ejpam-4587	71	12	hop	hop	NOUN
ejpam-4587	71	13	dominating	dominating	NOUN
ejpam-4587	71	14	set	set	NOUN
ejpam-4587	71	15	s	s	PROPN
ejpam-4587	71	16	of	of	ADP
ejpam-4587	71	17	g	g	PROPN
ejpam-4587	71	18	is	be	AUX
ejpam-4587	71	19	a	a	DET
ejpam-4587	71	20	weakly	weakly	ADV
ejpam-4587	71	21	connected	connected	ADJ
ejpam-4587	71	22	hop	hop	NOUN
ejpam-4587	71	23	dominating	dominating	NOUN
ejpam-4587	71	24	set	set	NOUN
ejpam-4587	71	25	of	of	ADP
ejpam-4587	71	26	g.	g.	PROPN
ejpam-4587	71	27	suppose	suppose	VERB
ejpam-4587	71	28	there	there	PRON
ejpam-4587	71	29	exists	exist	VERB
ejpam-4587	71	30	a	a	DET
ejpam-4587	71	31	set	set	NOUN
ejpam-4587	71	32	s	s	NOUN
ejpam-4587	71	33	⊆	⊆	NUM
ejpam-4587	71	34	v	v	NOUN
ejpam-4587	71	35	(	(	PUNCT
ejpam-4587	71	36	g	g	NOUN
ejpam-4587	71	37	)	)	PUNCT
ejpam-4587	71	38	such	such	ADJ
ejpam-4587	71	39	that	that	SCONJ
ejpam-4587	71	40	s	s	VERB
ejpam-4587	71	41	is	be	AUX
ejpam-4587	71	42	not	not	PART
ejpam-4587	71	43	a	a	DET
ejpam-4587	71	44	weakly	weakly	ADV
ejpam-4587	71	45	connected	connected	ADJ
ejpam-4587	71	46	hop	hop	NOUN
ejpam-4587	71	47	dominating	dominating	NOUN
ejpam-4587	71	48	set	set	NOUN
ejpam-4587	71	49	.	.	PUNCT
ejpam-4587	72	1	since	since	SCONJ
ejpam-4587	72	2	by	by	ADP
ejpam-4587	72	3	assumption	assumption	NOUN
ejpam-4587	72	4	,	,	PUNCT
ejpam-4587	72	5	s	s	PART
ejpam-4587	72	6	is	be	AUX
ejpam-4587	72	7	hop	hop	NOUN
ejpam-4587	72	8	dominating	dominate	VERB
ejpam-4587	72	9	set	set	NOUN
ejpam-4587	72	10	of	of	ADP
ejpam-4587	72	11	g.	g.	PROPN
ejpam-4587	72	12	it	it	PRON
ejpam-4587	72	13	follows	follow	VERB
ejpam-4587	72	14	that	that	SCONJ
ejpam-4587	72	15	for	for	ADP
ejpam-4587	72	16	all	all	DET
ejpam-4587	72	17	q	q	PROPN
ejpam-4587	72	18	∈	∈	PROPN
ejpam-4587	72	19	v	v	NOUN
ejpam-4587	72	20	(	(	PUNCT
ejpam-4587	72	21	g	g	NOUN
ejpam-4587	72	22	)	)	PUNCT
ejpam-4587	72	23	\	\	PROPN
ejpam-4587	73	1	s	s	X
ejpam-4587	73	2	,	,	PUNCT
ejpam-4587	73	3	there	there	PRON
ejpam-4587	73	4	exists	exist	VERB
ejpam-4587	73	5	r	r	NOUN
ejpam-4587	73	6	∈	∈	PROPN
ejpam-4587	73	7	s	s	VERB
ejpam-4587	73	8	such	such	ADJ
ejpam-4587	73	9	that	that	PRON
ejpam-4587	73	10	dg(q	dg(q	NOUN
ejpam-4587	73	11	,	,	PUNCT
ejpam-4587	73	12	r	r	NOUN
ejpam-4587	73	13	)	)	PUNCT
ejpam-4587	73	14	=	=	SYM
ejpam-4587	73	15	2	2	X
ejpam-4587	73	16	.	.	PUNCT
ejpam-4587	74	1	thus	thus	ADV
ejpam-4587	74	2	,	,	PUNCT
ejpam-4587	74	3	rq	rq	VERB
ejpam-4587	74	4	∈	∈	PROPN
ejpam-4587	74	5	e(⟨s⟩w	e(⟨s⟩w	PROPN
ejpam-4587	74	6	)	)	PUNCT
ejpam-4587	74	7	where	where	SCONJ
ejpam-4587	74	8	q	q	PROPN
ejpam-4587	74	9	∈	∈	PROPN
ejpam-4587	74	10	v	v	ADP
ejpam-4587	74	11	(	(	PUNCT
ejpam-4587	74	12	g	g	NOUN
ejpam-4587	74	13	)	)	PUNCT
ejpam-4587	74	14	\	\	PROPN
ejpam-4587	74	15	s	s	PART
ejpam-4587	74	16	and	and	CCONJ
ejpam-4587	74	17	r	r	PROPN
ejpam-4587	74	18	∈	∈	PROPN
ejpam-4587	74	19	s.	s.	PROPN
ejpam-4587	74	20	hence	hence	ADV
ejpam-4587	74	21	,	,	PUNCT
ejpam-4587	74	22	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4587	74	23	=	=	PUNCT
ejpam-4587	74	24	⟨ng[s	⟨ng[	NOUN
ejpam-4587	74	25	]	]	PUNCT
ejpam-4587	74	26	,	,	PUNCT
ejpam-4587	74	27	ew⟩	ew⟩	PUNCT
ejpam-4587	74	28	with	with	ADP
ejpam-4587	74	29	j.	j.	PROPN
ejpam-4587	74	30	hamja	hamja	PROPN
ejpam-4587	74	31	,	,	PUNCT
ejpam-4587	74	32	i.	i.	PROPN
ejpam-4587	74	33	aniversario	aniversario	PROPN
ejpam-4587	74	34	,	,	PUNCT
ejpam-4587	74	35	c.	c.	PROPN
ejpam-4587	74	36	merca	merca	PROPN
ejpam-4587	74	37	/	/	SYM
ejpam-4587	74	38	eur	eur	PROPN
ejpam-4587	74	39	.	.	PUNCT
ejpam-4587	75	1	j.	j.	PROPN
ejpam-4587	75	2	pure	pure	PROPN
ejpam-4587	75	3	appl	appl	PROPN
ejpam-4587	75	4	.	.	PROPN
ejpam-4587	75	5	math	math	PROPN
ejpam-4587	75	6	,	,	PUNCT
ejpam-4587	75	7	16	16	NUM
ejpam-4587	75	8	(	(	PUNCT
ejpam-4587	75	9	1	1	NUM
ejpam-4587	75	10	)	)	PUNCT
ejpam-4587	75	11	(	(	PUNCT
ejpam-4587	75	12	2023	2023	NUM
ejpam-4587	75	13	)	)	PUNCT
ejpam-4587	75	14	,	,	PUNCT
ejpam-4587	75	15	454	454	NUM
ejpam-4587	75	16	-	-	SYM
ejpam-4587	75	17	464	464	NUM
ejpam-4587	75	18	457	457	NUM
ejpam-4587	75	19	ew	ew	NOUN
ejpam-4587	75	20	=	=	PUNCT
ejpam-4587	75	21	{	{	PUNCT
ejpam-4587	75	22	rq	rq	NOUN
ejpam-4587	75	23	∈	∈	PROPN
ejpam-4587	75	24	e(g	e(g	PROPN
ejpam-4587	75	25	)	)	PUNCT
ejpam-4587	75	26	:	:	PUNCT
ejpam-4587	76	1	r	r	X
ejpam-4587	76	2	∈	∈	PROPN
ejpam-4587	76	3	s	s	NOUN
ejpam-4587	76	4	or	or	CCONJ
ejpam-4587	76	5	q	q	ADJ
ejpam-4587	76	6	∈	∈	PROPN
ejpam-4587	76	7	s	s	PART
ejpam-4587	76	8	}	}	PUNCT
ejpam-4587	76	9	.	.	PUNCT
ejpam-4587	77	1	finally	finally	ADV
ejpam-4587	77	2	,	,	PUNCT
ejpam-4587	77	3	since	since	SCONJ
ejpam-4587	77	4	for	for	ADP
ejpam-4587	77	5	all	all	PRON
ejpam-4587	77	6	q	q	PROPN
ejpam-4587	77	7	∈	∈	PROPN
ejpam-4587	77	8	v	v	NOUN
ejpam-4587	77	9	(	(	PUNCT
ejpam-4587	77	10	g	g	NOUN
ejpam-4587	77	11	)	)	PUNCT
ejpam-4587	77	12	\	\	PROPN
ejpam-4587	78	1	s	s	X
ejpam-4587	78	2	,	,	PUNCT
ejpam-4587	78	3	there	there	PRON
ejpam-4587	78	4	exists	exist	VERB
ejpam-4587	78	5	r	r	NOUN
ejpam-4587	78	6	∈	∈	PROPN
ejpam-4587	78	7	s	s	VERB
ejpam-4587	78	8	such	such	ADJ
ejpam-4587	78	9	that	that	PRON
ejpam-4587	78	10	dg(q	dg(q	NOUN
ejpam-4587	78	11	,	,	PUNCT
ejpam-4587	78	12	r	r	NOUN
ejpam-4587	78	13	)	)	PUNCT
ejpam-4587	78	14	=	=	SYM
ejpam-4587	78	15	2	2	NUM
ejpam-4587	78	16	which	which	PRON
ejpam-4587	78	17	implies	imply	VERB
ejpam-4587	78	18	that	that	SCONJ
ejpam-4587	78	19	there	there	PRON
ejpam-4587	78	20	exists	exist	VERB
ejpam-4587	78	21	w	w	PROPN
ejpam-4587	78	22	∈	∈	PROPN
ejpam-4587	78	23	v	v	ADP
ejpam-4587	78	24	(	(	PUNCT
ejpam-4587	78	25	g	g	NOUN
ejpam-4587	78	26	)	)	PUNCT
ejpam-4587	78	27	with	with	ADP
ejpam-4587	78	28	qw	qw	NOUN
ejpam-4587	78	29	,	,	PUNCT
ejpam-4587	78	30	wr	wr	PROPN
ejpam-4587	78	31	∈	∈	PROPN
ejpam-4587	78	32	e(⟨s⟩w	e(⟨s⟩w	PROPN
ejpam-4587	78	33	)	)	PUNCT
ejpam-4587	78	34	.	.	PUNCT
ejpam-4587	79	1	thus	thus	ADV
ejpam-4587	79	2	,	,	PUNCT
ejpam-4587	79	3	⟨s⟩w	⟨s⟩w	PROPN
ejpam-4587	79	4	is	be	AUX
ejpam-4587	79	5	connected	connect	VERB
ejpam-4587	79	6	.	.	PUNCT
ejpam-4587	80	1	consequently	consequently	ADV
ejpam-4587	80	2	,	,	PUNCT
ejpam-4587	80	3	s	s	VERB
ejpam-4587	80	4	is	be	AUX
ejpam-4587	80	5	a	a	DET
ejpam-4587	80	6	weakly	weakly	ADV
ejpam-4587	80	7	connected	connected	ADJ
ejpam-4587	80	8	hop	hop	NOUN
ejpam-4587	80	9	dominating	dominating	NOUN
ejpam-4587	80	10	set	set	NOUN
ejpam-4587	80	11	of	of	ADP
ejpam-4587	80	12	g.	g.	PROPN
ejpam-4587	80	13	remark	remark	PROPN
ejpam-4587	80	14	2	2	NUM
ejpam-4587	80	15	.	.	X
ejpam-4587	81	1	for	for	ADP
ejpam-4587	81	2	any	any	DET
ejpam-4587	81	3	connected	connected	ADJ
ejpam-4587	81	4	graph	graph	NOUN
ejpam-4587	81	5	g	g	NOUN
ejpam-4587	81	6	of	of	ADP
ejpam-4587	81	7	order	order	NOUN
ejpam-4587	81	8	n	n	PRON
ejpam-4587	81	9	≥	≥	NOUN
ejpam-4587	81	10	3	3	NUM
ejpam-4587	81	11	,	,	PUNCT
ejpam-4587	81	12	then	then	ADV
ejpam-4587	81	13	2	2	NUM
ejpam-4587	81	14	≤	≤	NOUN
ejpam-4587	81	15	γh(g	γh(g	NOUN
ejpam-4587	81	16	)	)	PUNCT
ejpam-4587	81	17	≤	≤	NUM
ejpam-4587	81	18	γwh(g	γwh(g	PROPN
ejpam-4587	81	19	)	)	PUNCT
ejpam-4587	81	20	≤	≤	NUM
ejpam-4587	81	21	n.	n.	NOUN
ejpam-4587	81	22	theorem	theorem	NOUN
ejpam-4587	81	23	1	1	X
ejpam-4587	81	24	.	.	PUNCT
ejpam-4587	82	1	let	let	VERB
ejpam-4587	82	2	g	g	NOUN
ejpam-4587	82	3	be	be	AUX
ejpam-4587	82	4	any	any	DET
ejpam-4587	82	5	connected	connected	ADJ
ejpam-4587	82	6	graph	graph	NOUN
ejpam-4587	82	7	of	of	ADP
ejpam-4587	82	8	order	order	NOUN
ejpam-4587	82	9	n	n	PRON
ejpam-4587	82	10	≥	≥	NOUN
ejpam-4587	82	11	3	3	NUM
ejpam-4587	82	12	.	.	PUNCT
ejpam-4587	83	1	then	then	ADV
ejpam-4587	83	2	γwh(g	γwh(g	NOUN
ejpam-4587	83	3	)	)	PUNCT
ejpam-4587	83	4	=	=	SYM
ejpam-4587	83	5	2	2	NUM
ejpam-4587	83	6	if	if	SCONJ
ejpam-4587	83	7	and	and	CCONJ
ejpam-4587	83	8	only	only	ADV
ejpam-4587	83	9	if	if	SCONJ
ejpam-4587	83	10	γh(g	γh(g	NOUN
ejpam-4587	83	11	)	)	PUNCT
ejpam-4587	83	12	=	=	SYM
ejpam-4587	83	13	2	2	X
ejpam-4587	83	14	.	.	PUNCT
ejpam-4587	83	15	proof	proof	NOUN
ejpam-4587	83	16	.	.	PUNCT
ejpam-4587	84	1	if	if	SCONJ
ejpam-4587	84	2	γh(g	γh(g	NOUN
ejpam-4587	84	3	)	)	PUNCT
ejpam-4587	84	4	=	=	SYM
ejpam-4587	84	5	2	2	X
ejpam-4587	84	6	.	.	PUNCT
ejpam-4587	84	7	by	by	ADP
ejpam-4587	84	8	remark	remark	NOUN
ejpam-4587	84	9	2	2	NUM
ejpam-4587	84	10	,	,	PUNCT
ejpam-4587	84	11	γwh(g	γwh(g	PROPN
ejpam-4587	84	12	)	)	PUNCT
ejpam-4587	84	13	=	=	SYM
ejpam-4587	84	14	2	2	X
ejpam-4587	84	15	.	.	X
ejpam-4587	84	16	let	let	VERB
ejpam-4587	84	17	s	s	VERB
ejpam-4587	84	18	=	=	NOUN
ejpam-4587	84	19	{	{	PUNCT
ejpam-4587	84	20	v1	v1	PROPN
ejpam-4587	84	21	,	,	PUNCT
ejpam-4587	84	22	v2	v2	PROPN
ejpam-4587	84	23	}	}	PUNCT
ejpam-4587	84	24	be	be	AUX
ejpam-4587	84	25	a	a	DET
ejpam-4587	84	26	weakly	weakly	ADV
ejpam-4587	84	27	connected	connected	ADJ
ejpam-4587	84	28	hop	hop	NOUN
ejpam-4587	84	29	dominating	dominating	NOUN
ejpam-4587	84	30	set	set	NOUN
ejpam-4587	84	31	of	of	ADP
ejpam-4587	84	32	g.	g.	PROPN
ejpam-4587	84	33	then	then	ADV
ejpam-4587	84	34	by	by	ADP
ejpam-4587	84	35	remark	remark	NOUN
ejpam-4587	84	36	1	1	NUM
ejpam-4587	84	37	,	,	PUNCT
ejpam-4587	84	38	s	s	VERB
ejpam-4587	84	39	is	be	AUX
ejpam-4587	84	40	a	a	DET
ejpam-4587	84	41	hop	hop	NOUN
ejpam-4587	84	42	dominating	dominating	NOUN
ejpam-4587	84	43	set	set	NOUN
ejpam-4587	84	44	of	of	ADP
ejpam-4587	84	45	g.	g.	PROPN
ejpam-4587	84	46	therefore	therefore	ADV
ejpam-4587	84	47	,	,	PUNCT
ejpam-4587	84	48	γh(g	γh(g	NOUN
ejpam-4587	84	49	)	)	PUNCT
ejpam-4587	84	50	=	=	SYM
ejpam-4587	84	51	2	2	X
ejpam-4587	84	52	.	.	X
ejpam-4587	84	53	theorem	theorem	NOUN
ejpam-4587	84	54	2	2	NUM
ejpam-4587	84	55	.	.	PUNCT
ejpam-4587	85	1	let	let	VERB
ejpam-4587	85	2	g	g	NOUN
ejpam-4587	85	3	be	be	AUX
ejpam-4587	85	4	any	any	DET
ejpam-4587	85	5	connected	connected	ADJ
ejpam-4587	85	6	graph	graph	NOUN
ejpam-4587	85	7	of	of	ADP
ejpam-4587	85	8	order	order	NOUN
ejpam-4587	85	9	n	n	PRON
ejpam-4587	85	10	≥	≥	NOUN
ejpam-4587	85	11	3	3	NUM
ejpam-4587	85	12	.	.	PUNCT
ejpam-4587	86	1	then	then	ADV
ejpam-4587	86	2	,	,	PUNCT
ejpam-4587	86	3	γwh(g	γwh(g	PROPN
ejpam-4587	86	4	)	)	PUNCT
ejpam-4587	86	5	=	=	SYM
ejpam-4587	87	1	n	n	NOUN
ejpam-4587	87	2	if	if	SCONJ
ejpam-4587	88	1	and	and	CCONJ
ejpam-4587	88	2	only	only	ADV
ejpam-4587	88	3	if	if	SCONJ
ejpam-4587	88	4	g	g	PROPN
ejpam-4587	88	5	=	=	PROPN
ejpam-4587	88	6	kn	kn	PROPN
ejpam-4587	88	7	.	.	PUNCT
ejpam-4587	88	8	proof	proof	NOUN
ejpam-4587	88	9	.	.	PUNCT
ejpam-4587	89	1	let	let	VERB
ejpam-4587	89	2	g	g	NOUN
ejpam-4587	89	3	be	be	AUX
ejpam-4587	89	4	any	any	DET
ejpam-4587	89	5	connected	connected	ADJ
ejpam-4587	89	6	graph	graph	NOUN
ejpam-4587	89	7	of	of	ADP
ejpam-4587	89	8	order	order	NOUN
ejpam-4587	89	9	n	n	PRON
ejpam-4587	89	10	≥	≥	NOUN
ejpam-4587	89	11	3	3	NUM
ejpam-4587	89	12	.	.	PUNCT
ejpam-4587	90	1	if	if	SCONJ
ejpam-4587	90	2	g	g	PROPN
ejpam-4587	90	3	=	=	SYM
ejpam-4587	90	4	kn	kn	PROPN
ejpam-4587	90	5	,	,	PUNCT
ejpam-4587	90	6	then	then	ADV
ejpam-4587	90	7	γwh(g	γwh(g	PROPN
ejpam-4587	90	8	)	)	PUNCT
ejpam-4587	90	9	=	=	VERB
ejpam-4587	90	10	n.	n.	NOUN
ejpam-4587	90	11	suppose	suppose	VERB
ejpam-4587	90	12	γwh(g	γwh(g	NOUN
ejpam-4587	90	13	)	)	PUNCT
ejpam-4587	90	14	=	=	SYM
ejpam-4587	90	15	n	n	NOUN
ejpam-4587	90	16	and	and	CCONJ
ejpam-4587	90	17	g	g	PROPN
ejpam-4587	90	18	̸=	̸=	PROPN
ejpam-4587	90	19	kn	kn	PROPN
ejpam-4587	90	20	.	.	PUNCT
ejpam-4587	91	1	let	let	VERB
ejpam-4587	91	2	s	s	PRON
ejpam-4587	91	3	⊆	⊆	NUM
ejpam-4587	91	4	v	v	NOUN
ejpam-4587	91	5	(	(	PUNCT
ejpam-4587	91	6	g	g	NOUN
ejpam-4587	91	7	)	)	PUNCT
ejpam-4587	91	8	be	be	AUX
ejpam-4587	91	9	a	a	DET
ejpam-4587	91	10	weakly	weakly	ADV
ejpam-4587	91	11	connected	connected	ADJ
ejpam-4587	91	12	hop	hop	NOUN
ejpam-4587	91	13	dominating	dominating	NOUN
ejpam-4587	91	14	set	set	NOUN
ejpam-4587	91	15	of	of	ADP
ejpam-4587	91	16	g.	g.	PROPN
ejpam-4587	91	17	then	then	ADV
ejpam-4587	91	18	for	for	ADP
ejpam-4587	91	19	all	all	DET
ejpam-4587	91	20	q	q	PROPN
ejpam-4587	91	21	∈	∈	PROPN
ejpam-4587	91	22	v	v	NOUN
ejpam-4587	91	23	(	(	PUNCT
ejpam-4587	91	24	g	g	NOUN
ejpam-4587	91	25	)	)	PUNCT
ejpam-4587	91	26	\	\	PROPN
ejpam-4587	92	1	s	s	PART
ejpam-4587	92	2	there	there	PRON
ejpam-4587	92	3	exists	exist	VERB
ejpam-4587	92	4	r	r	NOUN
ejpam-4587	92	5	∈	∈	PROPN
ejpam-4587	92	6	s	s	VERB
ejpam-4587	92	7	such	such	ADJ
ejpam-4587	92	8	that	that	PRON
ejpam-4587	92	9	dg(q	dg(q	NOUN
ejpam-4587	92	10	,	,	PUNCT
ejpam-4587	92	11	r	r	NOUN
ejpam-4587	92	12	)	)	PUNCT
ejpam-4587	92	13	=	=	SYM
ejpam-4587	92	14	2	2	X
ejpam-4587	92	15	.	.	PUNCT
ejpam-4587	92	16	thus	thus	ADV
ejpam-4587	92	17	,	,	PUNCT
ejpam-4587	92	18	s	s	VERB
ejpam-4587	92	19	=	=	SYM
ejpam-4587	92	20	v	v	X
ejpam-4587	92	21	(	(	PUNCT
ejpam-4587	92	22	g	g	NOUN
ejpam-4587	92	23	)	)	PUNCT
ejpam-4587	92	24	\	\	NOUN
ejpam-4587	92	25	{	{	PUNCT
ejpam-4587	92	26	q	q	NOUN
ejpam-4587	92	27	}	}	PUNCT
ejpam-4587	92	28	.	.	PUNCT
ejpam-4587	93	1	consequently	consequently	ADV
ejpam-4587	93	2	,	,	PUNCT
ejpam-4587	93	3	γwh(g	γwh(g	PROPN
ejpam-4587	93	4	)	)	PUNCT
ejpam-4587	93	5	≤	≤	NUM
ejpam-4587	93	6	|s|	|s|	PROPN
ejpam-4587	93	7	=	=	SYM
ejpam-4587	93	8	n−	n−	NOUN
ejpam-4587	93	9	1	1	NUM
ejpam-4587	93	10	,	,	PUNCT
ejpam-4587	93	11	this	this	PRON
ejpam-4587	93	12	contradicts	contradict	VERB
ejpam-4587	93	13	to	to	ADP
ejpam-4587	93	14	the	the	DET
ejpam-4587	93	15	assumption	assumption	NOUN
ejpam-4587	93	16	.	.	PUNCT
ejpam-4587	94	1	theorem	theorem	NOUN
ejpam-4587	94	2	3	3	NUM
ejpam-4587	94	3	.	.	X
ejpam-4587	94	4	for	for	ADP
ejpam-4587	94	5	a	a	DET
ejpam-4587	94	6	complete	complete	ADJ
ejpam-4587	94	7	bipartite	bipartite	PROPN
ejpam-4587	94	8	km	km	PROPN
ejpam-4587	94	9	,	,	PUNCT
ejpam-4587	94	10	n	n	NOUN
ejpam-4587	94	11	of	of	ADP
ejpam-4587	94	12	order	order	NOUN
ejpam-4587	94	13	m	m	NOUN
ejpam-4587	94	14	,	,	PUNCT
ejpam-4587	94	15	n	n	PRON
ejpam-4587	94	16	≥	≥	NOUN
ejpam-4587	94	17	2	2	NUM
ejpam-4587	94	18	,	,	PUNCT
ejpam-4587	94	19	γwh(km	γwh(km	NOUN
ejpam-4587	94	20	,	,	PUNCT
ejpam-4587	94	21	n	n	CCONJ
ejpam-4587	94	22	)	)	PUNCT
ejpam-4587	94	23	=	=	SYM
ejpam-4587	94	24	2	2	X
ejpam-4587	94	25	.	.	PUNCT
ejpam-4587	94	26	proof	proof	NOUN
ejpam-4587	94	27	.	.	PUNCT
ejpam-4587	95	1	write	write	VERB
ejpam-4587	95	2	km	km	PROPN
ejpam-4587	95	3	,	,	PUNCT
ejpam-4587	95	4	n	n	NOUN
ejpam-4587	95	5	=	=	SYM
ejpam-4587	95	6	km	km	PROPN
ejpam-4587	95	7	+	+	CCONJ
ejpam-4587	95	8	kn	kn	PROPN
ejpam-4587	95	9	.	.	PUNCT
ejpam-4587	96	1	let	let	VERB
ejpam-4587	96	2	x	x	PRON
ejpam-4587	96	3	and	and	CCONJ
ejpam-4587	96	4	y	y	PROPN
ejpam-4587	96	5	be	be	AUX
ejpam-4587	96	6	the	the	DET
ejpam-4587	96	7	partite	partite	ADJ
ejpam-4587	96	8	sets	set	NOUN
ejpam-4587	96	9	of	of	ADP
ejpam-4587	96	10	v	v	NOUN
ejpam-4587	96	11	(	(	PUNCT
ejpam-4587	96	12	km	km	PROPN
ejpam-4587	96	13	,	,	PUNCT
ejpam-4587	96	14	n	n	CCONJ
ejpam-4587	96	15	)	)	PUNCT
ejpam-4587	96	16	where	where	SCONJ
ejpam-4587	96	17	v	v	NOUN
ejpam-4587	96	18	(	(	PUNCT
ejpam-4587	96	19	km	km	NOUN
ejpam-4587	96	20	)	)	PUNCT
ejpam-4587	96	21	=	=	PUNCT
ejpam-4587	97	1	x	x	PROPN
ejpam-4587	97	2	and	and	CCONJ
ejpam-4587	97	3	v	v	X
ejpam-4587	97	4	(	(	PUNCT
ejpam-4587	97	5	kn	kn	PROPN
ejpam-4587	97	6	)	)	PUNCT
ejpam-4587	97	7	=	=	SYM
ejpam-4587	97	8	y	y	PROPN
ejpam-4587	97	9	and	and	CCONJ
ejpam-4587	97	10	let	let	VERB
ejpam-4587	97	11	s	s	PRON
ejpam-4587	97	12	=	=	PUNCT
ejpam-4587	97	13	{	{	PUNCT
ejpam-4587	97	14	x1	x1	PROPN
ejpam-4587	97	15	,	,	PUNCT
ejpam-4587	97	16	y1	y1	NOUN
ejpam-4587	97	17	}	}	PUNCT
ejpam-4587	97	18	where	where	SCONJ
ejpam-4587	97	19	x1	x1	PROPN
ejpam-4587	97	20	∈	∈	PROPN
ejpam-4587	97	21	x	x	X
ejpam-4587	97	22	and	and	CCONJ
ejpam-4587	97	23	y1	y1	PROPN
ejpam-4587	97	24	∈	∈	PROPN
ejpam-4587	97	25	y	y	NOUN
ejpam-4587	97	26	be	be	AUX
ejpam-4587	97	27	a	a	DET
ejpam-4587	97	28	weakly	weakly	ADV
ejpam-4587	97	29	connected	connect	VERB
ejpam-4587	97	30	and	and	CCONJ
ejpam-4587	97	31	dominating	dominating	NOUN
ejpam-4587	97	32	set	set	NOUN
ejpam-4587	97	33	of	of	ADP
ejpam-4587	97	34	km	km	PROPN
ejpam-4587	97	35	,	,	PUNCT
ejpam-4587	97	36	n.	n.	NOUN
ejpam-4587	97	37	since	since	SCONJ
ejpam-4587	97	38	for	for	ADP
ejpam-4587	97	39	every	every	DET
ejpam-4587	97	40	vertex	vertex	NOUN
ejpam-4587	97	41	x	x	SYM
ejpam-4587	97	42	∈	∈	NOUN
ejpam-4587	97	43	x	x	PUNCT
ejpam-4587	97	44	\	\	PROPN
ejpam-4587	97	45	s	s	PART
ejpam-4587	97	46	there	there	PRON
ejpam-4587	97	47	exists	exist	VERB
ejpam-4587	97	48	yi	yi	PROPN
ejpam-4587	97	49	∈	∈	PROPN
ejpam-4587	97	50	s	s	PROPN
ejpam-4587	97	51	,	,	PUNCT
ejpam-4587	97	52	1	1	NUM
ejpam-4587	97	53	≤	≤	NUM
ejpam-4587	97	54	i	i	X
ejpam-4587	97	55	≤	≤	NOUN
ejpam-4587	97	56	m	m	VERB
ejpam-4587	97	57	,	,	PUNCT
ejpam-4587	97	58	such	such	ADJ
ejpam-4587	97	59	that	that	DET
ejpam-4587	97	60	dg(x	dg(x	NOUN
ejpam-4587	97	61	,	,	PUNCT
ejpam-4587	97	62	yi	yi	NOUN
ejpam-4587	97	63	)	)	PUNCT
ejpam-4587	97	64	=	=	SYM
ejpam-4587	97	65	2	2	NUM
ejpam-4587	97	66	,	,	PUNCT
ejpam-4587	97	67	and	and	CCONJ
ejpam-4587	97	68	for	for	ADP
ejpam-4587	97	69	every	every	DET
ejpam-4587	97	70	vertex	vertex	NOUN
ejpam-4587	97	71	y	y	PROPN
ejpam-4587	97	72	∈	∈	PROPN
ejpam-4587	97	73	y	y	PROPN
ejpam-4587	97	74	\	\	PROPN
ejpam-4587	97	75	s	s	PART
ejpam-4587	97	76	there	there	PRON
ejpam-4587	97	77	exists	exist	VERB
ejpam-4587	97	78	xj	xj	PROPN
ejpam-4587	97	79	∈	∈	PROPN
ejpam-4587	97	80	s	s	PROPN
ejpam-4587	97	81	,	,	PUNCT
ejpam-4587	97	82	1	1	NUM
ejpam-4587	97	83	<	<	X
ejpam-4587	97	84	j	j	X
ejpam-4587	97	85	<	<	X
ejpam-4587	97	86	n	n	CCONJ
ejpam-4587	97	87	such	such	ADJ
ejpam-4587	97	88	that	that	PRON
ejpam-4587	97	89	dg(xj	dg(xj	PROPN
ejpam-4587	97	90	,	,	PUNCT
ejpam-4587	97	91	y	y	PROPN
ejpam-4587	97	92	)	)	PUNCT
ejpam-4587	97	93	=	=	SYM
ejpam-4587	98	1	2	2	X
ejpam-4587	98	2	.	.	PUNCT
ejpam-4587	98	3	it	it	PRON
ejpam-4587	98	4	follows	follow	VERB
ejpam-4587	98	5	that	that	SCONJ
ejpam-4587	98	6	,	,	PUNCT
ejpam-4587	98	7	s	s	VERB
ejpam-4587	98	8	is	be	AUX
ejpam-4587	98	9	a	a	DET
ejpam-4587	98	10	hop	hop	NOUN
ejpam-4587	98	11	dominating	dominating	NOUN
ejpam-4587	98	12	set	set	NOUN
ejpam-4587	98	13	of	of	ADP
ejpam-4587	98	14	km	km	PROPN
ejpam-4587	98	15	,	,	PUNCT
ejpam-4587	98	16	n.	n.	PROPN
ejpam-4587	98	17	thus	thus	ADV
ejpam-4587	98	18	,	,	PUNCT
ejpam-4587	98	19	s	s	VERB
ejpam-4587	98	20	is	be	AUX
ejpam-4587	98	21	a	a	DET
ejpam-4587	98	22	weakly	weakly	ADV
ejpam-4587	98	23	connected	connected	ADJ
ejpam-4587	98	24	hop	hop	NOUN
ejpam-4587	98	25	dominating	dominating	NOUN
ejpam-4587	98	26	set	set	NOUN
ejpam-4587	98	27	of	of	ADP
ejpam-4587	98	28	km	km	PROPN
ejpam-4587	98	29	,	,	PUNCT
ejpam-4587	98	30	n.	n.	PROPN
ejpam-4587	98	31	consquently	consquently	ADV
ejpam-4587	98	32	,	,	PUNCT
ejpam-4587	98	33	γwh(km	γwh(km	NOUN
ejpam-4587	98	34	,	,	PUNCT
ejpam-4587	98	35	n	n	CCONJ
ejpam-4587	98	36	)	)	PUNCT
ejpam-4587	99	1	=	=	NOUN
ejpam-4587	99	2	|s|	|s|	NOUN
ejpam-4587	99	3	=	=	SYM
ejpam-4587	99	4	2	2	NUM
ejpam-4587	99	5	.	.	PUNCT
ejpam-4587	99	6	corollary	corollary	ADJ
ejpam-4587	99	7	1	1	NUM
ejpam-4587	99	8	.	.	PUNCT
ejpam-4587	100	1	let	let	VERB
ejpam-4587	100	2	g	g	NOUN
ejpam-4587	100	3	beany	beany	NOUN
ejpam-4587	100	4	connected	connect	VERB
ejpam-4587	100	5	grap	grap	ADV
ejpam-4587	100	6	with	with	ADP
ejpam-4587	100	7	γ(g	γ(g	PROPN
ejpam-4587	100	8	)	)	PUNCT
ejpam-4587	100	9	=	=	SYM
ejpam-4587	101	1	1	1	X
ejpam-4587	101	2	.	.	PUNCT
ejpam-4587	101	3	then	then	ADV
ejpam-4587	101	4	γwh(g	γwh(g	NOUN
ejpam-4587	101	5	)	)	PUNCT
ejpam-4587	101	6	=	=	SYM
ejpam-4587	101	7	2	2	NUM
ejpam-4587	101	8	if	if	SCONJ
ejpam-4587	101	9	and	and	CCONJ
ejpam-4587	101	10	only	only	ADV
ejpam-4587	101	11	if	if	SCONJ
ejpam-4587	101	12	g	g	PROPN
ejpam-4587	101	13	=	=	SYM
ejpam-4587	101	14	km	km	PROPN
ejpam-4587	101	15	,	,	PUNCT
ejpam-4587	101	16	n	n	NOUN
ejpam-4587	101	17	for	for	ADP
ejpam-4587	101	18	m	m	PROPN
ejpam-4587	101	19	=	=	SYM
ejpam-4587	101	20	1	1	NUM
ejpam-4587	101	21	and	and	CCONJ
ejpam-4587	101	22	n	n	PRON
ejpam-4587	101	23	≥	≥	NOUN
ejpam-4587	101	24	2	2	NUM
ejpam-4587	101	25	.	.	PUNCT
ejpam-4587	101	26	corollary	corollary	ADJ
ejpam-4587	101	27	2	2	NUM
ejpam-4587	101	28	.	.	PUNCT
ejpam-4587	102	1	for	for	ADP
ejpam-4587	102	2	a	a	DET
ejpam-4587	102	3	star	star	NOUN
ejpam-4587	102	4	sn	sn	NOUN
ejpam-4587	102	5	of	of	ADP
ejpam-4587	102	6	order	order	NOUN
ejpam-4587	102	7	n	n	PRON
ejpam-4587	102	8	≥	≥	NOUN
ejpam-4587	102	9	2	2	NUM
ejpam-4587	102	10	,	,	PUNCT
ejpam-4587	102	11	γwh(sn	γwh(sn	NOUN
ejpam-4587	102	12	)	)	PUNCT
ejpam-4587	102	13	=	=	SYM
ejpam-4587	102	14	2	2	X
ejpam-4587	102	15	.	.	X
ejpam-4587	102	16	theorem	theorem	NOUN
ejpam-4587	102	17	4	4	NUM
ejpam-4587	102	18	.	.	PUNCT
ejpam-4587	103	1	let	let	VERB
ejpam-4587	103	2	g	g	PRON
ejpam-4587	103	3	be	be	AUX
ejpam-4587	103	4	a	a	DET
ejpam-4587	103	5	connected	connected	ADJ
ejpam-4587	103	6	graph	graph	NOUN
ejpam-4587	103	7	of	of	ADP
ejpam-4587	103	8	order	order	NOUN
ejpam-4587	103	9	n	n	NOUN
ejpam-4587	103	10	=	=	SYM
ejpam-4587	103	11	4	4	X
ejpam-4587	103	12	.	.	PUNCT
ejpam-4587	103	13	then	then	ADV
ejpam-4587	103	14	γwh(g	γwh(g	NOUN
ejpam-4587	103	15	)	)	PUNCT
ejpam-4587	103	16	=	=	SYM
ejpam-4587	103	17	2	2	NUM
ejpam-4587	103	18	if	if	SCONJ
ejpam-4587	103	19	and	and	CCONJ
ejpam-4587	103	20	only	only	ADV
ejpam-4587	103	21	if	if	SCONJ
ejpam-4587	103	22	g	g	PROPN
ejpam-4587	103	23	is	be	AUX
ejpam-4587	103	24	either	either	CCONJ
ejpam-4587	103	25	p4	p4	ADJ
ejpam-4587	103	26	,	,	PUNCT
ejpam-4587	103	27	c4	c4	NOUN
ejpam-4587	103	28	,	,	PUNCT
ejpam-4587	103	29	or	or	CCONJ
ejpam-4587	103	30	s4	s4	NOUN
ejpam-4587	103	31	.	.	PUNCT
ejpam-4587	104	1	proof	proof	NOUN
ejpam-4587	104	2	.	.	PUNCT
ejpam-4587	105	1	if	if	SCONJ
ejpam-4587	105	2	g	g	NOUN
ejpam-4587	105	3	=	=	SYM
ejpam-4587	105	4	p4	p4	ADJ
ejpam-4587	105	5	,	,	PUNCT
ejpam-4587	105	6	g	g	NOUN
ejpam-4587	105	7	=	=	SYM
ejpam-4587	105	8	c4	c4	NOUN
ejpam-4587	105	9	or	or	CCONJ
ejpam-4587	105	10	g	g	NOUN
ejpam-4587	105	11	=	=	PROPN
ejpam-4587	105	12	s4	s4	PROPN
ejpam-4587	105	13	,	,	PUNCT
ejpam-4587	105	14	then	then	ADV
ejpam-4587	105	15	γwh(g	γwh(g	PROPN
ejpam-4587	105	16	)	)	PUNCT
ejpam-4587	105	17	=	=	SYM
ejpam-4587	106	1	2	2	X
ejpam-4587	106	2	.	.	X
ejpam-4587	106	3	let	let	VERB
ejpam-4587	106	4	s	s	VERB
ejpam-4587	106	5	=	=	NOUN
ejpam-4587	106	6	{	{	PUNCT
ejpam-4587	106	7	v1	v1	PROPN
ejpam-4587	106	8	,	,	PUNCT
ejpam-4587	106	9	v2	v2	PROPN
ejpam-4587	106	10	}	}	PUNCT
ejpam-4587	106	11	be	be	AUX
ejpam-4587	106	12	a	a	DET
ejpam-4587	106	13	weakly	weakly	ADV
ejpam-4587	106	14	connected	connected	ADJ
ejpam-4587	106	15	hop	hop	NOUN
ejpam-4587	106	16	dominating	dominating	NOUN
ejpam-4587	106	17	set	set	NOUN
ejpam-4587	106	18	of	of	ADP
ejpam-4587	106	19	g.	g.	PROPN
ejpam-4587	106	20	since	since	SCONJ
ejpam-4587	106	21	s	s	PROPN
ejpam-4587	106	22	is	be	AUX
ejpam-4587	106	23	a	a	DET
ejpam-4587	106	24	hop	hop	NOUN
ejpam-4587	106	25	dominating	dominating	NOUN
ejpam-4587	106	26	set	set	NOUN
ejpam-4587	106	27	there	there	ADV
ejpam-4587	106	28	exist	exist	VERB
ejpam-4587	106	29	q	q	NOUN
ejpam-4587	106	30	,	,	PUNCT
ejpam-4587	106	31	r	r	NOUN
ejpam-4587	106	32	∈	∈	PROPN
ejpam-4587	106	33	v	v	NOUN
ejpam-4587	106	34	(	(	PUNCT
ejpam-4587	106	35	g	g	NOUN
ejpam-4587	106	36	)	)	PUNCT
ejpam-4587	106	37	\	\	PUNCT
ejpam-4587	107	1	s	s	VERB
ejpam-4587	107	2	such	such	ADJ
ejpam-4587	107	3	that	that	PRON
ejpam-4587	107	4	dg(q	dg(q	NOUN
ejpam-4587	107	5	,	,	PUNCT
ejpam-4587	107	6	v1	v1	NOUN
ejpam-4587	107	7	)	)	PUNCT
ejpam-4587	107	8	=	=	SYM
ejpam-4587	107	9	2	2	NUM
ejpam-4587	107	10	and	and	CCONJ
ejpam-4587	107	11	dg(r	dg(r	NOUN
ejpam-4587	107	12	,	,	PUNCT
ejpam-4587	107	13	v2	v2	PROPN
ejpam-4587	107	14	)	)	PUNCT
ejpam-4587	107	15	=	=	SYM
ejpam-4587	108	1	2	2	X
ejpam-4587	108	2	.	.	PUNCT
ejpam-4587	108	3	now	now	ADV
ejpam-4587	108	4	,	,	PUNCT
ejpam-4587	108	5	observe	observe	VERB
ejpam-4587	108	6	that	that	SCONJ
ejpam-4587	108	7	j.	j.	PROPN
ejpam-4587	108	8	hamja	hamja	PROPN
ejpam-4587	108	9	,	,	PUNCT
ejpam-4587	108	10	i.	i.	PROPN
ejpam-4587	108	11	aniversario	aniversario	PROPN
ejpam-4587	108	12	,	,	PUNCT
ejpam-4587	108	13	c.	c.	PROPN
ejpam-4587	108	14	merca	merca	PROPN
ejpam-4587	108	15	/	/	SYM
ejpam-4587	108	16	eur	eur	PROPN
ejpam-4587	108	17	.	.	PUNCT
ejpam-4587	109	1	j.	j.	PROPN
ejpam-4587	109	2	pure	pure	PROPN
ejpam-4587	109	3	appl	appl	PROPN
ejpam-4587	109	4	.	.	PROPN
ejpam-4587	109	5	math	math	PROPN
ejpam-4587	109	6	,	,	PUNCT
ejpam-4587	109	7	16	16	NUM
ejpam-4587	109	8	(	(	PUNCT
ejpam-4587	109	9	1	1	NUM
ejpam-4587	109	10	)	)	PUNCT
ejpam-4587	109	11	(	(	PUNCT
ejpam-4587	109	12	2023	2023	NUM
ejpam-4587	109	13	)	)	PUNCT
ejpam-4587	109	14	,	,	PUNCT
ejpam-4587	109	15	454	454	NUM
ejpam-4587	109	16	-	-	SYM
ejpam-4587	109	17	464	464	NUM
ejpam-4587	109	18	458	458	NUM
ejpam-4587	109	19	ng[v1	ng[v1	NOUN
ejpam-4587	109	20	]	]	X
ejpam-4587	109	21	=	=	SYM
ejpam-4587	109	22	{	{	PUNCT
ejpam-4587	109	23	v1	v1	PROPN
ejpam-4587	109	24	,	,	PUNCT
ejpam-4587	109	25	q	q	NOUN
ejpam-4587	109	26	,	,	PUNCT
ejpam-4587	109	27	v2	v2	NOUN
ejpam-4587	109	28	}	}	PUNCT
ejpam-4587	109	29	and	and	CCONJ
ejpam-4587	109	30	ng(v2	ng(v2	NOUN
ejpam-4587	109	31	)	)	PUNCT
ejpam-4587	109	32	=	=	PRON
ejpam-4587	109	33	{	{	PUNCT
ejpam-4587	109	34	v2	v2	PROPN
ejpam-4587	109	35	,	,	PUNCT
ejpam-4587	109	36	v1	v1	NOUN
ejpam-4587	109	37	,	,	PUNCT
ejpam-4587	109	38	r	r	NOUN
ejpam-4587	109	39	}	}	PUNCT
ejpam-4587	109	40	.	.	PUNCT
ejpam-4587	110	1	thus	thus	ADV
ejpam-4587	110	2	,	,	PUNCT
ejpam-4587	110	3	ng[s	ng[s	PROPN
ejpam-4587	110	4	]	]	X
ejpam-4587	110	5	=	=	PUNCT
ejpam-4587	110	6	{	{	PUNCT
ejpam-4587	110	7	q	q	NOUN
ejpam-4587	110	8	,	,	PUNCT
ejpam-4587	110	9	r	r	NOUN
ejpam-4587	110	10	,	,	PUNCT
ejpam-4587	110	11	v1	v1	NOUN
ejpam-4587	110	12	,	,	PUNCT
ejpam-4587	110	13	v2	v2	NOUN
ejpam-4587	110	14	}	}	PUNCT
ejpam-4587	110	15	=	=	SYM
ejpam-4587	110	16	v	v	NOUN
ejpam-4587	110	17	(	(	PUNCT
ejpam-4587	110	18	g	g	NOUN
ejpam-4587	110	19	)	)	PUNCT
ejpam-4587	110	20	and	and	CCONJ
ejpam-4587	110	21	e(⟨s⟩w	e(⟨s⟩w	NOUN
ejpam-4587	110	22	)	)	PUNCT
ejpam-4587	110	23	=	=	PRON
ejpam-4587	110	24	{	{	PUNCT
ejpam-4587	110	25	qv1	qv1	ADV
ejpam-4587	110	26	,	,	PUNCT
ejpam-4587	110	27	v1v2	v1v2	NOUN
ejpam-4587	110	28	,	,	PUNCT
ejpam-4587	110	29	v1r	v1r	NOUN
ejpam-4587	110	30	}	}	PUNCT
ejpam-4587	110	31	=	=	SYM
ejpam-4587	110	32	ew	ew	INTJ
ejpam-4587	110	33	which	which	PRON
ejpam-4587	110	34	implies	imply	VERB
ejpam-4587	110	35	that	that	SCONJ
ejpam-4587	110	36	⟨sw⟩	⟨sw⟩	PROPN
ejpam-4587	110	37	is	be	AUX
ejpam-4587	110	38	connected	connect	VERB
ejpam-4587	110	39	for	for	ADP
ejpam-4587	110	40	e(g	e(g	NOUN
ejpam-4587	110	41	)	)	PUNCT
ejpam-4587	111	1	=	=	PRON
ejpam-4587	111	2	{	{	PUNCT
ejpam-4587	111	3	qv1	qv1	ADV
ejpam-4587	111	4	,	,	PUNCT
ejpam-4587	111	5	v1v2	v1v2	NOUN
ejpam-4587	111	6	,	,	PUNCT
ejpam-4587	111	7	v2r	v2r	NOUN
ejpam-4587	111	8	}	}	PUNCT
ejpam-4587	111	9	or	or	CCONJ
ejpam-4587	111	10	e(g	e(g	NOUN
ejpam-4587	111	11	)	)	PUNCT
ejpam-4587	112	1	=	=	PRON
ejpam-4587	112	2	{	{	PUNCT
ejpam-4587	112	3	qv1	qv1	ADV
ejpam-4587	112	4	,	,	PUNCT
ejpam-4587	112	5	v1v2	v1v2	NOUN
ejpam-4587	112	6	,	,	PUNCT
ejpam-4587	112	7	v2r	v2r	PROPN
ejpam-4587	112	8	,	,	PUNCT
ejpam-4587	112	9	rq	rq	X
ejpam-4587	112	10	}	}	PUNCT
ejpam-4587	112	11	.	.	PUNCT
ejpam-4587	113	1	therefore	therefore	ADV
ejpam-4587	113	2	,	,	PUNCT
ejpam-4587	113	3	g	g	PROPN
ejpam-4587	113	4	is	be	AUX
ejpam-4587	113	5	either	either	DET
ejpam-4587	113	6	path	path	NOUN
ejpam-4587	113	7	p4	p4	ADJ
ejpam-4587	113	8	,	,	PUNCT
ejpam-4587	113	9	cycle	cycle	NOUN
ejpam-4587	113	10	c4	c4	NOUN
ejpam-4587	113	11	or	or	CCONJ
ejpam-4587	113	12	star	star	NOUN
ejpam-4587	113	13	s4	s4	PROPN
ejpam-4587	113	14	.	.	PUNCT
ejpam-4587	114	1	proposition	proposition	NOUN
ejpam-4587	114	2	3	3	NUM
ejpam-4587	114	3	.	.	PUNCT
ejpam-4587	115	1	let	let	VERB
ejpam-4587	115	2	n	n	PRON
ejpam-4587	115	3	be	be	AUX
ejpam-4587	115	4	a	a	DET
ejpam-4587	115	5	positive	positive	ADJ
ejpam-4587	115	6	integer	integer	NOUN
ejpam-4587	115	7	,	,	PUNCT
ejpam-4587	115	8	then	then	ADV
ejpam-4587	115	9	(	(	PUNCT
ejpam-4587	115	10	i	i	NOUN
ejpam-4587	115	11	)	)	PUNCT
ejpam-4587	115	12	for	for	ADP
ejpam-4587	115	13	a	a	DET
ejpam-4587	115	14	path	path	NOUN
ejpam-4587	115	15	pn	pn	PROPN
ejpam-4587	115	16	,	,	PUNCT
ejpam-4587	115	17	γwh(pn	γwh(pn	NOUN
ejpam-4587	115	18	)	)	PUNCT
ejpam-4587	115	19	=	=	PUNCT
ejpam-4587	115	20			PUNCT
ejpam-4587	115	21	⌊n+1	⌊n+1	NOUN
ejpam-4587	115	22	2	2	NUM
ejpam-4587	115	23	⌋	⌋	NOUN
ejpam-4587	115	24	,	,	PUNCT
ejpam-4587	115	25	if	if	SCONJ
ejpam-4587	115	26	n	n	NOUN
ejpam-4587	115	27	=	=	SYM
ejpam-4587	115	28	3	3	NUM
ejpam-4587	115	29	,	,	PUNCT
ejpam-4587	115	30	4	4	NUM
ejpam-4587	115	31	,	,	PUNCT
ejpam-4587	115	32	5	5	NUM
ejpam-4587	115	33	;	;	PUNCT
ejpam-4587	115	34	3r	3r	NUM
ejpam-4587	115	35	+	+	SYM
ejpam-4587	115	36	1	1	NUM
ejpam-4587	115	37	,	,	PUNCT
ejpam-4587	115	38	if	if	SCONJ
ejpam-4587	115	39	n	n	NOUN
ejpam-4587	115	40	=	=	SYM
ejpam-4587	115	41	6r	6r	NUM
ejpam-4587	115	42	;	;	PUNCT
ejpam-4587	115	43	3r	3r	NUM
ejpam-4587	115	44	+	+	CCONJ
ejpam-4587	115	45	⌊	⌊	VERB
ejpam-4587	115	46	s+1	s+1	NUM
ejpam-4587	115	47	2	2	NUM
ejpam-4587	115	48	⌋	⌋	NOUN
ejpam-4587	115	49	,	,	PUNCT
ejpam-4587	115	50	if	if	SCONJ
ejpam-4587	115	51	n	n	NOUN
ejpam-4587	115	52	=	=	SYM
ejpam-4587	116	1	6r	6r	NUM
ejpam-4587	116	2	+	+	CCONJ
ejpam-4587	116	3	s	s	X
ejpam-4587	116	4	;	;	PUNCT
ejpam-4587	116	5	1	1	NUM
ejpam-4587	116	6	≤	≤	NUM
ejpam-4587	116	7	s	s	PART
ejpam-4587	116	8	≤	≤	NUM
ejpam-4587	116	9	5	5	NUM
ejpam-4587	116	10	.	.	PUNCT
ejpam-4587	116	11	(	(	PUNCT
ejpam-4587	116	12	ii	ii	NOUN
ejpam-4587	116	13	)	)	PUNCT
ejpam-4587	116	14	for	for	ADP
ejpam-4587	116	15	a	a	DET
ejpam-4587	116	16	cycle	cycle	NOUN
ejpam-4587	116	17	cn	cn	PROPN
ejpam-4587	116	18	,	,	PUNCT
ejpam-4587	116	19	γwh(cn	γwh(cn	NOUN
ejpam-4587	116	20	)	)	PUNCT
ejpam-4587	116	21	=	=	PUNCT
ejpam-4587	116	22			PUNCT
ejpam-4587	116	23	⌊n+1	⌊n+1	NOUN
ejpam-4587	116	24	2	2	NUM
ejpam-4587	116	25	⌋	⌋	NOUN
ejpam-4587	116	26	,	,	PUNCT
ejpam-4587	116	27	if	if	SCONJ
ejpam-4587	116	28	n	n	NOUN
ejpam-4587	116	29	=	=	SYM
ejpam-4587	116	30	4	4	NUM
ejpam-4587	116	31	,	,	PUNCT
ejpam-4587	116	32	5	5	NUM
ejpam-4587	116	33	;	;	PUNCT
ejpam-4587	116	34	3r	3r	NUM
ejpam-4587	116	35	+	+	SYM
ejpam-4587	116	36	1	1	NUM
ejpam-4587	116	37	,	,	PUNCT
ejpam-4587	116	38	if	if	SCONJ
ejpam-4587	116	39	n	n	NOUN
ejpam-4587	116	40	=	=	SYM
ejpam-4587	116	41	6r	6r	NUM
ejpam-4587	116	42	;	;	PUNCT
ejpam-4587	116	43	3r	3r	NUM
ejpam-4587	116	44	+	+	CCONJ
ejpam-4587	116	45	⌊	⌊	VERB
ejpam-4587	116	46	s+1	s+1	NUM
ejpam-4587	116	47	2	2	NUM
ejpam-4587	116	48	⌋	⌋	NOUN
ejpam-4587	116	49	,	,	PUNCT
ejpam-4587	116	50	if	if	SCONJ
ejpam-4587	116	51	n	n	NOUN
ejpam-4587	116	52	=	=	SYM
ejpam-4587	117	1	6r	6r	NUM
ejpam-4587	117	2	+	+	CCONJ
ejpam-4587	117	3	s	s	X
ejpam-4587	117	4	;	;	PUNCT
ejpam-4587	117	5	1	1	NUM
ejpam-4587	117	6	≤	≤	NUM
ejpam-4587	117	7	s	s	PART
ejpam-4587	117	8	≤	≤	NUM
ejpam-4587	117	9	5	5	NUM
ejpam-4587	117	10	.	.	PUNCT
ejpam-4587	118	1	(	(	PUNCT
ejpam-4587	118	2	iii	iii	NOUN
ejpam-4587	118	3	)	)	PUNCT
ejpam-4587	118	4	for	for	ADP
ejpam-4587	118	5	a	a	DET
ejpam-4587	118	6	wheel	wheel	NOUN
ejpam-4587	118	7	wn	wn	NOUN
ejpam-4587	118	8	of	of	ADP
ejpam-4587	118	9	order	order	NOUN
ejpam-4587	118	10	n	n	PRON
ejpam-4587	118	11	with	with	ADP
ejpam-4587	118	12	n−	n−	NOUN
ejpam-4587	118	13	1	1	NUM
ejpam-4587	118	14	spokes	spoke	NOUN
ejpam-4587	118	15	,	,	PUNCT
ejpam-4587	118	16	γwh(wn	γwh(wn	NOUN
ejpam-4587	118	17	)	)	PUNCT
ejpam-4587	118	18	=	=	SYM
ejpam-4587	119	1	3	3	X
ejpam-4587	119	2	.	.	PUNCT
ejpam-4587	119	3	(	(	PUNCT
ejpam-4587	119	4	iv	iv	X
ejpam-4587	119	5	)	)	PUNCT
ejpam-4587	119	6	for	for	ADP
ejpam-4587	119	7	a	a	DET
ejpam-4587	119	8	fan	fan	NOUN
ejpam-4587	119	9	fn	fn	NOUN
ejpam-4587	119	10	of	of	ADP
ejpam-4587	119	11	order	order	NOUN
ejpam-4587	119	12	n	n	CCONJ
ejpam-4587	119	13	,	,	PUNCT
ejpam-4587	119	14	γwh(fn	γwh(fn	X
ejpam-4587	119	15	)	)	PUNCT
ejpam-4587	119	16	=	=	SYM
ejpam-4587	120	1	3	3	X
ejpam-4587	120	2	.	.	PUNCT
ejpam-4587	120	3	(	(	PUNCT
ejpam-4587	120	4	v	v	NOUN
ejpam-4587	120	5	)	)	PUNCT
ejpam-4587	120	6	for	for	ADP
ejpam-4587	120	7	a	a	DET
ejpam-4587	120	8	petersen	petersen	NOUN
ejpam-4587	120	9	graph	graph	NOUN
ejpam-4587	120	10	p	p	PROPN
ejpam-4587	120	11	,	,	PUNCT
ejpam-4587	120	12	γwh(p	γwh(p	PROPN
ejpam-4587	120	13	)	)	PUNCT
ejpam-4587	120	14	=	=	SYM
ejpam-4587	121	1	4	4	X
ejpam-4587	121	2	.	.	X
ejpam-4587	122	1	the	the	DET
ejpam-4587	122	2	shadow	shadow	NOUN
ejpam-4587	122	3	graph	graph	NOUN
ejpam-4587	122	4	sh(g	sh(g	NOUN
ejpam-4587	122	5	)	)	PUNCT
ejpam-4587	122	6	of	of	ADP
ejpam-4587	122	7	a	a	DET
ejpam-4587	122	8	graph	graph	NOUN
ejpam-4587	122	9	g	g	NOUN
ejpam-4587	122	10	is	be	AUX
ejpam-4587	122	11	constructed	construct	VERB
ejpam-4587	122	12	by	by	ADP
ejpam-4587	122	13	taking	take	VERB
ejpam-4587	122	14	two	two	NUM
ejpam-4587	122	15	copies	copy	NOUN
ejpam-4587	122	16	of	of	ADP
ejpam-4587	122	17	g	g	NOUN
ejpam-4587	122	18	,	,	PUNCT
ejpam-4587	122	19	say	say	VERB
ejpam-4587	122	20	g1	g1	PROPN
ejpam-4587	122	21	and	and	CCONJ
ejpam-4587	122	22	g2	g2	PROPN
ejpam-4587	122	23	.	.	PUNCT
ejpam-4587	123	1	join	join	VERB
ejpam-4587	123	2	each	each	DET
ejpam-4587	123	3	vertex	vertex	NOUN
ejpam-4587	123	4	u	u	PROPN
ejpam-4587	123	5	∈	∈	PROPN
ejpam-4587	123	6	v	v	NOUN
ejpam-4587	123	7	(	(	PUNCT
ejpam-4587	123	8	g1	g1	PROPN
ejpam-4587	123	9	)	)	PUNCT
ejpam-4587	123	10	to	to	ADP
ejpam-4587	123	11	the	the	DET
ejpam-4587	123	12	neighbors	neighbor	NOUN
ejpam-4587	123	13	of	of	ADP
ejpam-4587	123	14	the	the	DET
ejpam-4587	123	15	corresponding	corresponding	ADJ
ejpam-4587	123	16	vertex	vertex	NOUN
ejpam-4587	123	17	u	u	NOUN
ejpam-4587	123	18	′	′	NOUN
ejpam-4587	123	19	∈	∈	PROPN
ejpam-4587	123	20	v	v	X
ejpam-4587	123	21	(	(	PUNCT
ejpam-4587	123	22	g2	g2	PROPN
ejpam-4587	123	23	)	)	PUNCT
ejpam-4587	123	24	,	,	PUNCT
ejpam-4587	123	25	defined	define	VERB
ejpam-4587	123	26	by	by	ADP
ejpam-4587	123	27	jayagopal	jayagopal	ADJ
ejpam-4587	123	28	,	,	PUNCT
ejpam-4587	123	29	et.al	et.al	PROPN
ejpam-4587	123	30	.	.	PUNCT
ejpam-4587	124	1	[	[	X
ejpam-4587	124	2	6	6	NUM
ejpam-4587	124	3	]	]	PUNCT
ejpam-4587	124	4	.	.	PUNCT
ejpam-4587	125	1	theorem	theorem	NOUN
ejpam-4587	125	2	5	5	NUM
ejpam-4587	125	3	.	.	PUNCT
ejpam-4587	125	4	(	(	PUNCT
ejpam-4587	125	5	natarajan	natarajan	PROPN
ejpam-4587	125	6	,	,	PUNCT
ejpam-4587	125	7	et	et	PROPN
ejpam-4587	125	8	.	.	PUNCT
ejpam-4587	126	1	al	al	PROPN
ejpam-4587	126	2	.	.	PROPN
ejpam-4587	126	3	,	,	PUNCT
ejpam-4587	126	4	in	in	ADP
ejpam-4587	126	5	[	[	X
ejpam-4587	126	6	8	8	NUM
ejpam-4587	126	7	]	]	PUNCT
ejpam-4587	126	8	)	)	PUNCT
ejpam-4587	126	9	for	for	ADP
ejpam-4587	126	10	any	any	DET
ejpam-4587	126	11	connected	connected	ADJ
ejpam-4587	126	12	graph	graph	NOUN
ejpam-4587	126	13	g	g	NOUN
ejpam-4587	126	14	,	,	PUNCT
ejpam-4587	126	15	γh(sh(g	γh(sh(g	NOUN
ejpam-4587	126	16	)	)	PUNCT
ejpam-4587	126	17	)	)	PUNCT
ejpam-4587	127	1	=	=	NOUN
ejpam-4587	127	2	γh(g	γh(g	NOUN
ejpam-4587	127	3	)	)	PUNCT
ejpam-4587	127	4	.	.	PUNCT
ejpam-4587	128	1	theorem	theorem	NOUN
ejpam-4587	128	2	6	6	NUM
ejpam-4587	128	3	.	.	PUNCT
ejpam-4587	129	1	let	let	VERB
ejpam-4587	129	2	g	g	NOUN
ejpam-4587	129	3	be	be	AUX
ejpam-4587	129	4	any	any	DET
ejpam-4587	129	5	graph	graph	NOUN
ejpam-4587	129	6	of	of	ADP
ejpam-4587	129	7	order	order	NOUN
ejpam-4587	129	8	n	n	PRON
ejpam-4587	129	9	≥	≥	NOUN
ejpam-4587	129	10	3	3	NUM
ejpam-4587	129	11	,	,	PUNCT
ejpam-4587	129	12	then	then	ADV
ejpam-4587	129	13	γwh(sh(g	γwh(sh(g	NOUN
ejpam-4587	129	14	)	)	PUNCT
ejpam-4587	129	15	)	)	PUNCT
ejpam-4587	130	1	=	=	PUNCT
ejpam-4587	130	2	γwh(g	γwh(g	PROPN
ejpam-4587	130	3	)	)	PUNCT
ejpam-4587	130	4	.	.	PUNCT
ejpam-4587	131	1	proof	proof	NOUN
ejpam-4587	131	2	.	.	PUNCT
ejpam-4587	132	1	let	let	VERB
ejpam-4587	132	2	s	s	PRON
ejpam-4587	132	3	be	be	AUX
ejpam-4587	132	4	a	a	DET
ejpam-4587	132	5	weakly	weakly	ADV
ejpam-4587	132	6	connected	connected	ADJ
ejpam-4587	132	7	hop	hop	NOUN
ejpam-4587	132	8	dominating	dominating	NOUN
ejpam-4587	132	9	set	set	NOUN
ejpam-4587	132	10	of	of	ADP
ejpam-4587	132	11	g.	g.	PROPN
ejpam-4587	132	12	by	by	ADP
ejpam-4587	132	13	remark	remark	NOUN
ejpam-4587	132	14	1	1	NUM
ejpam-4587	132	15	,	,	PUNCT
ejpam-4587	132	16	s	s	VERB
ejpam-4587	132	17	is	be	AUX
ejpam-4587	132	18	a	a	DET
ejpam-4587	132	19	hop	hop	NOUN
ejpam-4587	132	20	dominating	dominating	NOUN
ejpam-4587	132	21	set	set	NOUN
ejpam-4587	132	22	of	of	ADP
ejpam-4587	132	23	g	g	PROPN
ejpam-4587	132	24	and	and	CCONJ
ejpam-4587	132	25	by	by	ADP
ejpam-4587	132	26	theorem	theorem	NOUN
ejpam-4587	132	27	5	5	NUM
ejpam-4587	132	28	,	,	PUNCT
ejpam-4587	132	29	γh(sh(g	γh(sh(g	NOUN
ejpam-4587	132	30	)	)	PUNCT
ejpam-4587	132	31	)	)	PUNCT
ejpam-4587	133	1	=	=	NOUN
ejpam-4587	133	2	γh(g	γh(g	NOUN
ejpam-4587	133	3	)	)	PUNCT
ejpam-4587	133	4	.	.	PUNCT
ejpam-4587	134	1	so	so	ADV
ejpam-4587	134	2	we	we	PRON
ejpam-4587	134	3	are	be	AUX
ejpam-4587	134	4	left	leave	VERB
ejpam-4587	134	5	to	to	PART
ejpam-4587	134	6	show	show	VERB
ejpam-4587	134	7	that	that	DET
ejpam-4587	134	8	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4587	134	9	=	=	PUNCT
ejpam-4587	134	10	⟨ng[s	⟨ng[	NOUN
ejpam-4587	134	11	]	]	PUNCT
ejpam-4587	134	12	,	,	PUNCT
ejpam-4587	134	13	ew⟩	ew⟩	PROPN
ejpam-4587	134	14	is	be	AUX
ejpam-4587	134	15	connected	connect	VERB
ejpam-4587	134	16	,	,	PUNCT
ejpam-4587	134	17	where	where	SCONJ
ejpam-4587	134	18	ew	ew	AUX
ejpam-4587	134	19	=	=	PRON
ejpam-4587	134	20	{	{	PUNCT
ejpam-4587	134	21	uv′	uv′	PROPN
ejpam-4587	134	22	∈	∈	PROPN
ejpam-4587	134	23	e(sh(g	e(sh(g	NOUN
ejpam-4587	134	24	)	)	PUNCT
ejpam-4587	134	25	)	)	PUNCT
ejpam-4587	134	26	:	:	PUNCT
ejpam-4587	135	1	u	u	PROPN
ejpam-4587	135	2	∈	∈	PROPN
ejpam-4587	135	3	s	s	X
ejpam-4587	135	4	or	or	CCONJ
ejpam-4587	135	5	v	v	ADP
ejpam-4587	135	6	′	′	NUM
ejpam-4587	136	1	∈	∈	PROPN
ejpam-4587	137	1	s	s	PART
ejpam-4587	137	2	}	}	PUNCT
ejpam-4587	137	3	.	.	PUNCT
ejpam-4587	138	1	let	let	VERB
ejpam-4587	138	2	u	u	PRON
ejpam-4587	138	3	′	′	NOUN
ejpam-4587	138	4	∈	∈	PROPN
ejpam-4587	138	5	v	v	NOUN
ejpam-4587	138	6	(	(	PUNCT
ejpam-4587	138	7	sh(g	sh(g	NOUN
ejpam-4587	138	8	)	)	PUNCT
ejpam-4587	138	9	)	)	PUNCT
ejpam-4587	138	10	be	be	AUX
ejpam-4587	138	11	a	a	DET
ejpam-4587	138	12	twin	twin	ADJ
ejpam-4587	138	13	vertex	vertex	NOUN
ejpam-4587	138	14	of	of	ADP
ejpam-4587	138	15	u	u	NOUN
ejpam-4587	138	16	∈	∈	PROPN
ejpam-4587	138	17	v	v	NOUN
ejpam-4587	138	18	(	(	PUNCT
ejpam-4587	138	19	g	g	NOUN
ejpam-4587	138	20	)	)	PUNCT
ejpam-4587	138	21	.	.	PUNCT
ejpam-4587	139	1	for	for	ADP
ejpam-4587	139	2	every	every	DET
ejpam-4587	139	3	vertex	vertex	NOUN
ejpam-4587	139	4	u	u	NOUN
ejpam-4587	139	5	′	′	NOUN
ejpam-4587	139	6	∈	∈	PROPN
ejpam-4587	139	7	v	v	NOUN
ejpam-4587	139	8	(	(	PUNCT
ejpam-4587	139	9	sh(g	sh(g	NOUN
ejpam-4587	139	10	)	)	PUNCT
ejpam-4587	139	11	)	)	PUNCT
ejpam-4587	139	12	,	,	PUNCT
ejpam-4587	139	13	there	there	PRON
ejpam-4587	139	14	exists	exist	VERB
ejpam-4587	139	15	v	v	ADP
ejpam-4587	139	16	∈	∈	PROPN
ejpam-4587	139	17	s	s	PART
ejpam-4587	139	18	\	\	X
ejpam-4587	139	19	{	{	PUNCT
ejpam-4587	139	20	u	u	NOUN
ejpam-4587	139	21	}	}	PUNCT
ejpam-4587	139	22	such	such	ADJ
ejpam-4587	139	23	that	that	SCONJ
ejpam-4587	139	24	v	v	NUM
ejpam-4587	139	25	∈	∈	PROPN
ejpam-4587	139	26	nsh(g)[v	nsh(g)[v	PROPN
ejpam-4587	139	27	]	]	PUNCT
ejpam-4587	139	28	∪nsh(g)[u	∪nsh(g)[u	NOUN
ejpam-4587	139	29	]	]	PUNCT
ejpam-4587	139	30	.	.	PUNCT
ejpam-4587	140	1	now	now	ADV
ejpam-4587	140	2	,	,	PUNCT
ejpam-4587	140	3	u′	u′	PROPN
ejpam-4587	140	4	∈	∈	PROPN
ejpam-4587	140	5	nsh(g)(v	nsh(g)(v	NOUN
ejpam-4587	140	6	)	)	PUNCT
ejpam-4587	140	7	implies	imply	VERB
ejpam-4587	140	8	that	that	SCONJ
ejpam-4587	140	9	u	u	PROPN
ejpam-4587	140	10	′	′	NOUN
ejpam-4587	140	11	v	v	ADP
ejpam-4587	140	12	∈	∈	PROPN
ejpam-4587	140	13	e(sh(g	e(sh(g	NOUN
ejpam-4587	140	14	)	)	PUNCT
ejpam-4587	140	15	)	)	PUNCT
ejpam-4587	140	16	.	.	PUNCT
ejpam-4587	141	1	hence	hence	ADV
ejpam-4587	141	2	,	,	PUNCT
ejpam-4587	141	3	⟨s⟩w	⟨s⟩w	PROPN
ejpam-4587	141	4	is	be	AUX
ejpam-4587	141	5	connected	connect	VERB
ejpam-4587	141	6	.	.	PUNCT
ejpam-4587	142	1	since	since	SCONJ
ejpam-4587	142	2	dsh(g)(u	dsh(g)(u	NUM
ejpam-4587	142	3	′	′	NUM
ejpam-4587	142	4	,	,	PUNCT
ejpam-4587	142	5	v	v	NOUN
ejpam-4587	142	6	)	)	PUNCT
ejpam-4587	142	7	=	=	SYM
ejpam-4587	142	8	1	1	X
ejpam-4587	142	9	.	.	PUNCT
ejpam-4587	143	1	this	this	PRON
ejpam-4587	143	2	implies	imply	VERB
ejpam-4587	143	3	that	that	SCONJ
ejpam-4587	143	4	dsh(g)(u	dsh(g)(u	VERB
ejpam-4587	143	5	′	′	NUM
ejpam-4587	143	6	,	,	PUNCT
ejpam-4587	143	7	u	u	NOUN
ejpam-4587	143	8	)	)	PUNCT
ejpam-4587	143	9	=	=	SYM
ejpam-4587	143	10	2	2	X
ejpam-4587	143	11	.	.	PUNCT
ejpam-4587	143	12	thus	thus	ADV
ejpam-4587	143	13	,	,	PUNCT
ejpam-4587	143	14	s	s	VERB
ejpam-4587	143	15	is	be	AUX
ejpam-4587	143	16	a	a	DET
ejpam-4587	143	17	weakly	weakly	ADV
ejpam-4587	143	18	connected	connected	ADJ
ejpam-4587	143	19	hop	hop	NOUN
ejpam-4587	143	20	dominating	dominating	NOUN
ejpam-4587	143	21	set	set	NOUN
ejpam-4587	143	22	of	of	ADP
ejpam-4587	143	23	sh(g	sh(g	NOUN
ejpam-4587	143	24	)	)	PUNCT
ejpam-4587	143	25	.	.	PUNCT
ejpam-4587	144	1	this	this	PRON
ejpam-4587	144	2	concludes	conclude	VERB
ejpam-4587	144	3	that	that	SCONJ
ejpam-4587	144	4	γwh(sh(g	γwh(sh(g	NOUN
ejpam-4587	144	5	)	)	PUNCT
ejpam-4587	144	6	)	)	PUNCT
ejpam-4587	145	1	=	=	PUNCT
ejpam-4587	145	2	γwh(g	γwh(g	PROPN
ejpam-4587	145	3	)	)	PUNCT
ejpam-4587	145	4	.	.	PUNCT
ejpam-4587	146	1	the	the	DET
ejpam-4587	146	2	next	next	ADJ
ejpam-4587	146	3	results	result	NOUN
ejpam-4587	146	4	show	show	VERB
ejpam-4587	146	5	the	the	DET
ejpam-4587	146	6	equality	equality	NOUN
ejpam-4587	146	7	of	of	ADP
ejpam-4587	146	8	γwh(sh(g	γwh(sh(g	NOUN
ejpam-4587	146	9	)	)	PUNCT
ejpam-4587	146	10	)	)	PUNCT
ejpam-4587	147	1	=	=	PUNCT
ejpam-4587	147	2	γwh(g	γwh(g	PROPN
ejpam-4587	147	3	)	)	PUNCT
ejpam-4587	147	4	.	.	PUNCT
ejpam-4587	148	1	corollary	corollary	ADJ
ejpam-4587	148	2	3	3	NUM
ejpam-4587	148	3	.	.	PUNCT
ejpam-4587	149	1	for	for	ADP
ejpam-4587	149	2	a	a	DET
ejpam-4587	149	3	shadow	shadow	NOUN
ejpam-4587	149	4	graph	graph	NOUN
ejpam-4587	149	5	of	of	ADP
ejpam-4587	149	6	pn	pn	PROPN
ejpam-4587	149	7	,	,	PUNCT
ejpam-4587	149	8	cn	cn	PROPN
ejpam-4587	149	9	,	,	PUNCT
ejpam-4587	149	10	kn	kn	PROPN
ejpam-4587	149	11	,	,	PUNCT
ejpam-4587	149	12	and	and	CCONJ
ejpam-4587	149	13	km	km	PROPN
ejpam-4587	149	14	,	,	PUNCT
ejpam-4587	149	15	n	n	CCONJ
ejpam-4587	149	16	with	with	ADP
ejpam-4587	149	17	m	m	PROPN
ejpam-4587	149	18	,	,	PUNCT
ejpam-4587	149	19	n	n	PRON
ejpam-4587	149	20	vertices	vertex	NOUN
ejpam-4587	149	21	.	.	PUNCT
ejpam-4587	150	1	(	(	PUNCT
ejpam-4587	150	2	i	i	NOUN
ejpam-4587	150	3	)	)	PUNCT
ejpam-4587	150	4	for	for	ADP
ejpam-4587	150	5	a	a	DET
ejpam-4587	150	6	path	path	NOUN
ejpam-4587	150	7	pn	pn	NOUN
ejpam-4587	150	8	of	of	ADP
ejpam-4587	150	9	order	order	NOUN
ejpam-4587	150	10	n	n	CCONJ
ejpam-4587	150	11	,	,	PUNCT
ejpam-4587	150	12	γwh(sh(pn	γwh(sh(pn	NOUN
ejpam-4587	150	13	)	)	PUNCT
ejpam-4587	150	14	)	)	PUNCT
ejpam-4587	151	1	=	=	PUNCT
ejpam-4587	151	2			PUNCT
ejpam-4587	151	3	⌊n+1	⌊n+1	NOUN
ejpam-4587	151	4	2	2	NUM
ejpam-4587	151	5	⌋	⌋	NOUN
ejpam-4587	151	6	,	,	PUNCT
ejpam-4587	151	7	if	if	SCONJ
ejpam-4587	151	8	n	n	NOUN
ejpam-4587	151	9	=	=	SYM
ejpam-4587	151	10	3	3	NUM
ejpam-4587	151	11	,	,	PUNCT
ejpam-4587	151	12	4	4	NUM
ejpam-4587	151	13	,	,	PUNCT
ejpam-4587	151	14	5	5	NUM
ejpam-4587	151	15	;	;	PUNCT
ejpam-4587	151	16	3r	3r	NUM
ejpam-4587	151	17	+	+	SYM
ejpam-4587	151	18	1	1	NUM
ejpam-4587	151	19	,	,	PUNCT
ejpam-4587	151	20	if	if	SCONJ
ejpam-4587	151	21	n	n	NOUN
ejpam-4587	151	22	=	=	SYM
ejpam-4587	151	23	6r	6r	NUM
ejpam-4587	151	24	;	;	PUNCT
ejpam-4587	151	25	3r	3r	NUM
ejpam-4587	151	26	+	+	CCONJ
ejpam-4587	151	27	⌊	⌊	VERB
ejpam-4587	151	28	s+1	s+1	NUM
ejpam-4587	151	29	2	2	NUM
ejpam-4587	151	30	⌋	⌋	NOUN
ejpam-4587	151	31	,	,	PUNCT
ejpam-4587	151	32	if	if	SCONJ
ejpam-4587	151	33	n	n	NOUN
ejpam-4587	151	34	=	=	SYM
ejpam-4587	151	35	6r	6r	NUM
ejpam-4587	151	36	+	+	CCONJ
ejpam-4587	151	37	s	s	X
ejpam-4587	151	38	;	;	PUNCT
ejpam-4587	151	39	1	1	NUM
ejpam-4587	151	40	≤	≤	NUM
ejpam-4587	151	41	s	s	PART
ejpam-4587	151	42	≤	≤	NUM
ejpam-4587	151	43	5	5	NUM
ejpam-4587	151	44	.	.	PUNCT
ejpam-4587	152	1	=	=	SYM
ejpam-4587	152	2	γwh(pn	γwh(pn	NOUN
ejpam-4587	152	3	)	)	PUNCT
ejpam-4587	152	4	j.	j.	PROPN
ejpam-4587	152	5	hamja	hamja	PROPN
ejpam-4587	152	6	,	,	PUNCT
ejpam-4587	152	7	i.	i.	PROPN
ejpam-4587	152	8	aniversario	aniversario	PROPN
ejpam-4587	152	9	,	,	PUNCT
ejpam-4587	152	10	c.	c.	PROPN
ejpam-4587	152	11	merca	merca	PROPN
ejpam-4587	152	12	/	/	SYM
ejpam-4587	152	13	eur	eur	PROPN
ejpam-4587	152	14	.	.	PUNCT
ejpam-4587	153	1	j.	j.	PROPN
ejpam-4587	153	2	pure	pure	PROPN
ejpam-4587	153	3	appl	appl	PROPN
ejpam-4587	153	4	.	.	PROPN
ejpam-4587	153	5	math	math	PROPN
ejpam-4587	153	6	,	,	PUNCT
ejpam-4587	153	7	16	16	NUM
ejpam-4587	153	8	(	(	PUNCT
ejpam-4587	153	9	1	1	NUM
ejpam-4587	153	10	)	)	PUNCT
ejpam-4587	153	11	(	(	PUNCT
ejpam-4587	153	12	2023	2023	NUM
ejpam-4587	153	13	)	)	PUNCT
ejpam-4587	153	14	,	,	PUNCT
ejpam-4587	153	15	454	454	NUM
ejpam-4587	153	16	-	-	SYM
ejpam-4587	153	17	464	464	NUM
ejpam-4587	153	18	459	459	NUM
ejpam-4587	153	19	(	(	PUNCT
ejpam-4587	153	20	ii	ii	NOUN
ejpam-4587	153	21	)	)	PUNCT
ejpam-4587	153	22	for	for	ADP
ejpam-4587	153	23	a	a	DET
ejpam-4587	153	24	cycle	cycle	NOUN
ejpam-4587	153	25	cn	cn	NOUN
ejpam-4587	153	26	of	of	ADP
ejpam-4587	153	27	order	order	NOUN
ejpam-4587	153	28	n	n	CCONJ
ejpam-4587	153	29	,	,	PUNCT
ejpam-4587	153	30	γwh(sh(cn	γwh(sh(cn	PROPN
ejpam-4587	153	31	)	)	PUNCT
ejpam-4587	153	32	)	)	PUNCT
ejpam-4587	154	1	=	=	PUNCT
ejpam-4587	154	2			PUNCT
ejpam-4587	154	3	⌊n+1	⌊n+1	NOUN
ejpam-4587	154	4	2	2	NUM
ejpam-4587	154	5	⌋	⌋	NOUN
ejpam-4587	154	6	,	,	PUNCT
ejpam-4587	154	7	if	if	SCONJ
ejpam-4587	154	8	n	n	NOUN
ejpam-4587	154	9	=	=	SYM
ejpam-4587	154	10	4	4	NUM
ejpam-4587	154	11	,	,	PUNCT
ejpam-4587	154	12	5	5	NUM
ejpam-4587	154	13	;	;	PUNCT
ejpam-4587	154	14	3r	3r	NUM
ejpam-4587	154	15	+	+	SYM
ejpam-4587	154	16	1	1	NUM
ejpam-4587	154	17	,	,	PUNCT
ejpam-4587	154	18	if	if	SCONJ
ejpam-4587	154	19	n	n	NOUN
ejpam-4587	154	20	=	=	SYM
ejpam-4587	154	21	6r	6r	NUM
ejpam-4587	154	22	;	;	PUNCT
ejpam-4587	154	23	3r	3r	NUM
ejpam-4587	154	24	+	+	CCONJ
ejpam-4587	154	25	⌊	⌊	VERB
ejpam-4587	154	26	s+1	s+1	NUM
ejpam-4587	154	27	2	2	NUM
ejpam-4587	154	28	⌋	⌋	NOUN
ejpam-4587	154	29	,	,	PUNCT
ejpam-4587	154	30	if	if	SCONJ
ejpam-4587	154	31	n	n	NOUN
ejpam-4587	154	32	=	=	SYM
ejpam-4587	154	33	6r	6r	NUM
ejpam-4587	154	34	+	+	CCONJ
ejpam-4587	154	35	s	s	X
ejpam-4587	154	36	;	;	PUNCT
ejpam-4587	154	37	1	1	NUM
ejpam-4587	154	38	≤	≤	NUM
ejpam-4587	154	39	s	s	PART
ejpam-4587	154	40	≤	≤	NUM
ejpam-4587	154	41	5	5	NUM
ejpam-4587	154	42	.	.	PUNCT
ejpam-4587	155	1	=	=	SYM
ejpam-4587	156	1	γwh(cn	γwh(cn	NOUN
ejpam-4587	156	2	)	)	PUNCT
ejpam-4587	156	3	(	(	PUNCT
ejpam-4587	156	4	iii	iii	NOUN
ejpam-4587	156	5	)	)	PUNCT
ejpam-4587	156	6	for	for	ADP
ejpam-4587	156	7	a	a	DET
ejpam-4587	156	8	complete	complete	ADJ
ejpam-4587	156	9	graph	graph	NOUN
ejpam-4587	156	10	kn	kn	NOUN
ejpam-4587	156	11	of	of	ADP
ejpam-4587	156	12	order	order	NOUN
ejpam-4587	156	13	n	n	CCONJ
ejpam-4587	156	14	,	,	PUNCT
ejpam-4587	156	15	γwh(sh(kn	γwh(sh(kn	PROPN
ejpam-4587	156	16	)	)	PUNCT
ejpam-4587	156	17	)	)	PUNCT
ejpam-4587	157	1	=	=	PUNCT
ejpam-4587	157	2	n	n	NOUN
ejpam-4587	157	3	=	=	PUNCT
ejpam-4587	157	4	γwh(kn	γwh(kn	NUM
ejpam-4587	157	5	)	)	PUNCT
ejpam-4587	157	6	.	.	PUNCT
ejpam-4587	158	1	(	(	PUNCT
ejpam-4587	158	2	iv	iv	X
ejpam-4587	158	3	)	)	PUNCT
ejpam-4587	158	4	for	for	ADP
ejpam-4587	158	5	a	a	DET
ejpam-4587	158	6	complete	complete	ADJ
ejpam-4587	158	7	bipartite	bipartite	PROPN
ejpam-4587	158	8	km	km	PROPN
ejpam-4587	158	9	,	,	PUNCT
ejpam-4587	158	10	n	n	NOUN
ejpam-4587	158	11	of	of	ADP
ejpam-4587	158	12	order	order	NOUN
ejpam-4587	158	13	m	m	NOUN
ejpam-4587	158	14	,	,	PUNCT
ejpam-4587	158	15	n	n	PRON
ejpam-4587	158	16	≥	≥	NOUN
ejpam-4587	158	17	2	2	NUM
ejpam-4587	158	18	,	,	PUNCT
ejpam-4587	158	19	γwh(sh(km	γwh(sh(km	NOUN
ejpam-4587	158	20	,	,	PUNCT
ejpam-4587	158	21	n	n	CCONJ
ejpam-4587	158	22	)	)	PUNCT
ejpam-4587	158	23	)	)	PUNCT
ejpam-4587	159	1	=	=	SYM
ejpam-4587	159	2	2	2	NUM
ejpam-4587	159	3	=	=	SYM
ejpam-4587	159	4	γwh(km	γwh(km	NOUN
ejpam-4587	159	5	,	,	PUNCT
ejpam-4587	159	6	n	n	CCONJ
ejpam-4587	159	7	)	)	PUNCT
ejpam-4587	159	8	.	.	PUNCT
ejpam-4587	160	1	the	the	DET
ejpam-4587	160	2	join	join	NOUN
ejpam-4587	160	3	of	of	ADP
ejpam-4587	160	4	two	two	NUM
ejpam-4587	160	5	graphs	graph	NOUN
ejpam-4587	160	6	g	g	NOUN
ejpam-4587	160	7	and	and	CCONJ
ejpam-4587	160	8	h	h	NOUN
ejpam-4587	160	9	,	,	PUNCT
ejpam-4587	160	10	denoted	denote	VERB
ejpam-4587	160	11	by	by	ADP
ejpam-4587	160	12	g	g	PROPN
ejpam-4587	160	13	+	+	PROPN
ejpam-4587	160	14	h	h	NOUN
ejpam-4587	160	15	,	,	PUNCT
ejpam-4587	160	16	is	be	AUX
ejpam-4587	160	17	the	the	DET
ejpam-4587	160	18	graph	graph	NOUN
ejpam-4587	160	19	with	with	ADP
ejpam-4587	160	20	vertex	vertex	NOUN
ejpam-4587	160	21	-	-	PUNCT
ejpam-4587	160	22	set	set	VERB
ejpam-4587	160	23	v	v	NOUN
ejpam-4587	160	24	(	(	PUNCT
ejpam-4587	160	25	g+h	g+h	NOUN
ejpam-4587	160	26	)	)	PUNCT
ejpam-4587	160	27	=	=	SYM
ejpam-4587	160	28	v	v	X
ejpam-4587	160	29	(	(	PUNCT
ejpam-4587	160	30	g	g	NOUN
ejpam-4587	160	31	)	)	PUNCT
ejpam-4587	160	32	•	•	ADP
ejpam-4587	160	33	∪	∪	X
ejpam-4587	160	34	v	v	NOUN
ejpam-4587	160	35	(	(	PUNCT
ejpam-4587	160	36	h	h	NOUN
ejpam-4587	160	37	)	)	PUNCT
ejpam-4587	160	38	and	and	CCONJ
ejpam-4587	160	39	edge	edge	NOUN
ejpam-4587	160	40	-	-	PUNCT
ejpam-4587	160	41	set	set	VERB
ejpam-4587	160	42	e(g+h	e(g+h	NUM
ejpam-4587	160	43	)	)	PUNCT
ejpam-4587	160	44	=	=	SYM
ejpam-4587	160	45	e(g	e(g	PROPN
ejpam-4587	160	46	)	)	PUNCT
ejpam-4587	160	47	•	•	NOUN
ejpam-4587	160	48	∪e(h	∪e(h	NOUN
ejpam-4587	160	49	)	)	PUNCT
ejpam-4587	160	50	•	•	NOUN
ejpam-4587	160	51	∪	∪	X
ejpam-4587	160	52	{	{	PUNCT
ejpam-4587	160	53	uv	uv	NOUN
ejpam-4587	160	54	:	:	PUNCT
ejpam-4587	160	55	u	u	PROPN
ejpam-4587	160	56	∈	∈	PROPN
ejpam-4587	160	57	v	v	ADP
ejpam-4587	160	58	(	(	PUNCT
ejpam-4587	160	59	g	g	NOUN
ejpam-4587	160	60	)	)	PUNCT
ejpam-4587	160	61	,	,	PUNCT
ejpam-4587	160	62	v	v	X
ejpam-4587	160	63	∈	∈	PROPN
ejpam-4587	160	64	v	v	NOUN
ejpam-4587	160	65	(	(	PUNCT
ejpam-4587	160	66	h	h	NOUN
ejpam-4587	160	67	)	)	PUNCT
ejpam-4587	160	68	}	}	PUNCT
ejpam-4587	160	69	,	,	PUNCT
ejpam-4587	160	70	harary	harary	NOUN
ejpam-4587	161	1	[	[	X
ejpam-4587	161	2	5	5	NUM
ejpam-4587	161	3	]	]	PUNCT
ejpam-4587	161	4	.	.	PUNCT
ejpam-4587	162	1	lemma	lemma	PROPN
ejpam-4587	162	2	1	1	X
ejpam-4587	162	3	.	.	PUNCT
ejpam-4587	163	1	let	let	AUX
ejpam-4587	163	2	g+h	g+h	PROPN
ejpam-4587	163	3	be	be	AUX
ejpam-4587	163	4	the	the	DET
ejpam-4587	163	5	join	join	NOUN
ejpam-4587	163	6	of	of	ADP
ejpam-4587	163	7	g	g	PROPN
ejpam-4587	163	8	and	and	CCONJ
ejpam-4587	163	9	h.	h.	PROPN
ejpam-4587	163	10	then	then	ADV
ejpam-4587	163	11	s	s	VERB
ejpam-4587	163	12	⊆	⊆	NUM
ejpam-4587	163	13	v	v	NOUN
ejpam-4587	163	14	(	(	PUNCT
ejpam-4587	163	15	g+h	g+h	PROPN
ejpam-4587	163	16	)	)	PUNCT
ejpam-4587	163	17	is	be	AUX
ejpam-4587	163	18	a	a	DET
ejpam-4587	163	19	weakly	weakly	ADV
ejpam-4587	163	20	connected	connected	ADJ
ejpam-4587	163	21	hop	hop	NOUN
ejpam-4587	163	22	dominating	dominating	NOUN
ejpam-4587	163	23	set	set	NOUN
ejpam-4587	163	24	of	of	ADP
ejpam-4587	163	25	g+h	g+h	PROPN
ejpam-4587	163	26	if	if	SCONJ
ejpam-4587	163	27	and	and	CCONJ
ejpam-4587	163	28	only	only	ADV
ejpam-4587	163	29	if	if	SCONJ
ejpam-4587	163	30	either	either	PRON
ejpam-4587	163	31	s	s	VERB
ejpam-4587	163	32	is	be	AUX
ejpam-4587	163	33	a	a	DET
ejpam-4587	163	34	hop	hop	NOUN
ejpam-4587	163	35	dominating	dominating	NOUN
ejpam-4587	163	36	set	set	NOUN
ejpam-4587	163	37	of	of	ADP
ejpam-4587	163	38	g	g	PROPN
ejpam-4587	163	39	or	or	CCONJ
ejpam-4587	163	40	s	s	NOUN
ejpam-4587	163	41	is	be	AUX
ejpam-4587	163	42	a	a	DET
ejpam-4587	163	43	hop	hop	NOUN
ejpam-4587	163	44	dominating	dominating	NOUN
ejpam-4587	163	45	set	set	NOUN
ejpam-4587	163	46	of	of	ADP
ejpam-4587	163	47	h.	h.	PROPN
ejpam-4587	163	48	proof	proof	NOUN
ejpam-4587	163	49	.	.	PUNCT
ejpam-4587	164	1	suppose	suppose	VERB
ejpam-4587	164	2	s	s	PRON
ejpam-4587	164	3	is	be	AUX
ejpam-4587	164	4	a	a	DET
ejpam-4587	164	5	weakly	weakly	ADV
ejpam-4587	164	6	connected	connected	ADJ
ejpam-4587	164	7	hop	hop	NOUN
ejpam-4587	164	8	dominating	dominating	NOUN
ejpam-4587	164	9	set	set	NOUN
ejpam-4587	164	10	of	of	ADP
ejpam-4587	164	11	g	g	PROPN
ejpam-4587	164	12	+	+	CCONJ
ejpam-4587	165	1	h.	h.	PROPN
ejpam-4587	165	2	suppose	suppose	PUNCT
ejpam-4587	165	3	s	s	VERB
ejpam-4587	165	4	∩	∩	ADJ
ejpam-4587	165	5	v	v	X
ejpam-4587	165	6	(	(	PUNCT
ejpam-4587	165	7	g	g	NOUN
ejpam-4587	165	8	)	)	PUNCT
ejpam-4587	165	9	̸=	̸=	PROPN
ejpam-4587	165	10	∅	∅	NOUN
ejpam-4587	165	11	and	and	CCONJ
ejpam-4587	165	12	s	s	VERB
ejpam-4587	165	13	∩	∩	ADJ
ejpam-4587	165	14	v	v	ADJ
ejpam-4587	165	15	(	(	PUNCT
ejpam-4587	165	16	h	h	NOUN
ejpam-4587	165	17	)	)	PUNCT
ejpam-4587	165	18	̸=	̸=	PROPN
ejpam-4587	165	19	∅.	∅.	ADV
ejpam-4587	165	20	let	let	VERB
ejpam-4587	165	21	u	u	NOUN
ejpam-4587	165	22	,	,	PUNCT
ejpam-4587	165	23	v	v	ADP
ejpam-4587	165	24	∈	∈	NOUN
ejpam-4587	165	25	s	s	PART
ejpam-4587	165	26	and	and	CCONJ
ejpam-4587	165	27	let	let	VERB
ejpam-4587	165	28	u	u	NOUN
ejpam-4587	165	29	,	,	PUNCT
ejpam-4587	165	30	v	v	PROPN
ejpam-4587	165	31	∈	∈	PROPN
ejpam-4587	165	32	v	v	NOUN
ejpam-4587	165	33	(	(	PUNCT
ejpam-4587	165	34	g	g	NOUN
ejpam-4587	165	35	)	)	PUNCT
ejpam-4587	165	36	or	or	CCONJ
ejpam-4587	165	37	u	u	NOUN
ejpam-4587	165	38	,	,	PUNCT
ejpam-4587	165	39	v	v	PROPN
ejpam-4587	165	40	∈	∈	PROPN
ejpam-4587	165	41	v	v	NOUN
ejpam-4587	165	42	(	(	PUNCT
ejpam-4587	165	43	h	h	NOUN
ejpam-4587	165	44	)	)	PUNCT
ejpam-4587	165	45	.	.	PUNCT
ejpam-4587	166	1	pick	pick	VERB
ejpam-4587	166	2	u	u	PRON
ejpam-4587	166	3	∈	∈	PROPN
ejpam-4587	166	4	s	s	PART
ejpam-4587	166	5	∩	∩	ADJ
ejpam-4587	166	6	v	v	X
ejpam-4587	166	7	(	(	PUNCT
ejpam-4587	166	8	g	g	NOUN
ejpam-4587	166	9	)	)	PUNCT
ejpam-4587	166	10	and	and	CCONJ
ejpam-4587	166	11	v	v	ADP
ejpam-4587	166	12	∈	∈	NOUN
ejpam-4587	166	13	s	s	PART
ejpam-4587	166	14	∩	∩	ADJ
ejpam-4587	166	15	v	v	ADJ
ejpam-4587	166	16	(	(	PUNCT
ejpam-4587	166	17	h	h	NOUN
ejpam-4587	166	18	)	)	PUNCT
ejpam-4587	166	19	.	.	PUNCT
ejpam-4587	167	1	then	then	ADV
ejpam-4587	167	2	for	for	ADP
ejpam-4587	167	3	every	every	DET
ejpam-4587	167	4	x	x	SYM
ejpam-4587	167	5	∈	∈	PROPN
ejpam-4587	167	6	v	v	ADP
ejpam-4587	167	7	(	(	PUNCT
ejpam-4587	167	8	g	g	NOUN
ejpam-4587	167	9	)	)	PUNCT
ejpam-4587	167	10	\	\	PROPN
ejpam-4587	167	11	s	s	VERB
ejpam-4587	167	12	there	there	PRON
ejpam-4587	167	13	exists	exist	VERB
ejpam-4587	167	14	u	u	PROPN
ejpam-4587	167	15	∈	∈	PROPN
ejpam-4587	167	16	s	s	PART
ejpam-4587	167	17	∩	∩	ADJ
ejpam-4587	167	18	v	v	X
ejpam-4587	167	19	(	(	PUNCT
ejpam-4587	167	20	g	g	NOUN
ejpam-4587	167	21	)	)	PUNCT
ejpam-4587	167	22	such	such	ADJ
ejpam-4587	167	23	that	that	DET
ejpam-4587	167	24	dg(x	dg(x	NOUN
ejpam-4587	167	25	,	,	PUNCT
ejpam-4587	167	26	u	u	NOUN
ejpam-4587	167	27	)	)	PUNCT
ejpam-4587	167	28	=	=	SYM
ejpam-4587	167	29	2	2	NUM
ejpam-4587	167	30	or	or	CCONJ
ejpam-4587	167	31	for	for	ADP
ejpam-4587	167	32	every	every	DET
ejpam-4587	167	33	x	x	SYM
ejpam-4587	167	34	∈	∈	PROPN
ejpam-4587	167	35	v	v	ADP
ejpam-4587	167	36	(	(	PUNCT
ejpam-4587	167	37	h	h	NOUN
ejpam-4587	167	38	)	)	PUNCT
ejpam-4587	167	39	\	\	PROPN
ejpam-4587	168	1	s	s	X
ejpam-4587	168	2	,	,	PUNCT
ejpam-4587	168	3	there	there	PRON
ejpam-4587	168	4	exists	exist	VERB
ejpam-4587	168	5	v	v	ADP
ejpam-4587	168	6	∈	∈	PROPN
ejpam-4587	168	7	s	s	PART
ejpam-4587	168	8	∩	∩	ADJ
ejpam-4587	168	9	v	v	ADJ
ejpam-4587	168	10	(	(	PUNCT
ejpam-4587	168	11	h	h	NOUN
ejpam-4587	168	12	)	)	PUNCT
ejpam-4587	168	13	such	such	ADJ
ejpam-4587	168	14	that	that	DET
ejpam-4587	168	15	dg(x	dg(x	ADJ
ejpam-4587	168	16	,	,	PUNCT
ejpam-4587	168	17	v	v	NOUN
ejpam-4587	168	18	)	)	PUNCT
ejpam-4587	168	19	=	=	SYM
ejpam-4587	168	20	2	2	X
ejpam-4587	168	21	.	.	PUNCT
ejpam-4587	168	22	thus	thus	ADV
ejpam-4587	168	23	,	,	PUNCT
ejpam-4587	168	24	s	s	VERB
ejpam-4587	168	25	is	be	AUX
ejpam-4587	168	26	a	a	DET
ejpam-4587	168	27	hop	hop	NOUN
ejpam-4587	168	28	dominating	dominating	NOUN
ejpam-4587	168	29	set	set	NOUN
ejpam-4587	168	30	of	of	ADP
ejpam-4587	168	31	g	g	PROPN
ejpam-4587	168	32	or	or	CCONJ
ejpam-4587	168	33	s	s	NOUN
ejpam-4587	168	34	is	be	AUX
ejpam-4587	168	35	a	a	DET
ejpam-4587	168	36	hop	hop	NOUN
ejpam-4587	168	37	dominating	dominating	NOUN
ejpam-4587	168	38	set	set	NOUN
ejpam-4587	168	39	of	of	ADP
ejpam-4587	168	40	h.	h.	NOUN
ejpam-4587	168	41	conversely	conversely	ADV
ejpam-4587	168	42	,	,	PUNCT
ejpam-4587	168	43	suppose	suppose	VERB
ejpam-4587	168	44	without	without	ADP
ejpam-4587	168	45	loss	loss	NOUN
ejpam-4587	168	46	of	of	ADP
ejpam-4587	168	47	generality	generality	NOUN
ejpam-4587	168	48	,	,	PUNCT
ejpam-4587	168	49	s	s	PART
ejpam-4587	168	50	is	be	AUX
ejpam-4587	168	51	a	a	DET
ejpam-4587	168	52	hop	hop	NOUN
ejpam-4587	168	53	dominating	dominating	NOUN
ejpam-4587	168	54	set	set	NOUN
ejpam-4587	168	55	of	of	ADP
ejpam-4587	168	56	g	g	PROPN
ejpam-4587	168	57	or	or	CCONJ
ejpam-4587	168	58	s	s	NOUN
ejpam-4587	168	59	is	be	AUX
ejpam-4587	168	60	a	a	DET
ejpam-4587	168	61	hop	hop	NOUN
ejpam-4587	168	62	dominating	dominating	NOUN
ejpam-4587	168	63	set	set	NOUN
ejpam-4587	168	64	of	of	ADP
ejpam-4587	168	65	h.	h.	PROPN
ejpam-4587	168	66	it	it	PRON
ejpam-4587	168	67	follows	follow	VERB
ejpam-4587	168	68	that	that	SCONJ
ejpam-4587	168	69	s	s	VERB
ejpam-4587	168	70	is	be	AUX
ejpam-4587	168	71	a	a	DET
ejpam-4587	168	72	hop	hop	NOUN
ejpam-4587	168	73	dominating	dominating	NOUN
ejpam-4587	168	74	set	set	NOUN
ejpam-4587	168	75	of	of	ADP
ejpam-4587	168	76	g+h	g+h	PROPN
ejpam-4587	168	77	.	.	PUNCT
ejpam-4587	169	1	consider	consider	VERB
ejpam-4587	169	2	the	the	DET
ejpam-4587	169	3	following	follow	VERB
ejpam-4587	169	4	cases	case	NOUN
ejpam-4587	169	5	:	:	PUNCT
ejpam-4587	169	6	case	case	NOUN
ejpam-4587	169	7	i.	i.	NOUN
ejpam-4587	169	8	let	let	VERB
ejpam-4587	169	9	u	u	NOUN
ejpam-4587	169	10	,	,	PUNCT
ejpam-4587	169	11	v	v	PROPN
ejpam-4587	169	12	∈	∈	PROPN
ejpam-4587	169	13	s.	s.	PROPN
ejpam-4587	169	14	pick	pick	VERB
ejpam-4587	169	15	x	x	PUNCT
ejpam-4587	169	16	∈	∈	PROPN
ejpam-4587	169	17	v	v	NOUN
ejpam-4587	169	18	(	(	PUNCT
ejpam-4587	169	19	g	g	NOUN
ejpam-4587	169	20	)	)	PUNCT
ejpam-4587	169	21	.	.	PUNCT
ejpam-4587	170	1	then	then	ADV
ejpam-4587	170	2	there	there	PRON
ejpam-4587	170	3	exists	exist	VERB
ejpam-4587	170	4	xu	xu	PROPN
ejpam-4587	170	5	,	,	PUNCT
ejpam-4587	170	6	xv	xv	PROPN
ejpam-4587	170	7	∈	∈	PROPN
ejpam-4587	170	8	e(g	e(g	PROPN
ejpam-4587	171	1	+	+	CCONJ
ejpam-4587	171	2	h	h	X
ejpam-4587	171	3	)	)	PUNCT
ejpam-4587	171	4	such	such	ADJ
ejpam-4587	171	5	that	that	SCONJ
ejpam-4587	171	6	u	u	NOUN
ejpam-4587	171	7	,	,	PUNCT
ejpam-4587	171	8	v	v	PROPN
ejpam-4587	171	9	∈	∈	PROPN
ejpam-4587	171	10	s.	s.	PROPN
ejpam-4587	171	11	hence	hence	ADV
ejpam-4587	171	12	,	,	PUNCT
ejpam-4587	171	13	x	x	X
ejpam-4587	171	14	∈	∈	PROPN
ejpam-4587	171	15	ng+h(s	ng+h(s	PROPN
ejpam-4587	171	16	)	)	PUNCT
ejpam-4587	171	17	.	.	PUNCT
ejpam-4587	172	1	it	it	PRON
ejpam-4587	172	2	follows	follow	VERB
ejpam-4587	172	3	that	that	SCONJ
ejpam-4587	172	4	,	,	PUNCT
ejpam-4587	172	5	ng+h	ng+h	PROPN
ejpam-4587	173	1	[	[	X
ejpam-4587	173	2	s	s	X
ejpam-4587	173	3	]	]	X
ejpam-4587	173	4	=	=	SYM
ejpam-4587	173	5	v	v	NOUN
ejpam-4587	173	6	(	(	PUNCT
ejpam-4587	173	7	g	g	NOUN
ejpam-4587	173	8	)	)	PUNCT
ejpam-4587	173	9	.	.	PUNCT
ejpam-4587	174	1	hence	hence	ADV
ejpam-4587	174	2	,	,	PUNCT
ejpam-4587	174	3	⟨s⟩w	⟨s⟩w	PROPN
ejpam-4587	174	4	is	be	AUX
ejpam-4587	174	5	connected	connect	VERB
ejpam-4587	174	6	.	.	PUNCT
ejpam-4587	175	1	case	case	NOUN
ejpam-4587	175	2	ii	ii	X
ejpam-4587	175	3	.	.	PUNCT
ejpam-4587	176	1	let	let	VERB
ejpam-4587	176	2	u	u	NOUN
ejpam-4587	176	3	,	,	PUNCT
ejpam-4587	176	4	v	v	PROPN
ejpam-4587	176	5	∈	∈	PROPN
ejpam-4587	176	6	s.	s.	PROPN
ejpam-4587	176	7	pick	pick	VERB
ejpam-4587	176	8	x	x	PUNCT
ejpam-4587	176	9	∈	∈	PROPN
ejpam-4587	176	10	v	v	ADP
ejpam-4587	176	11	(	(	PUNCT
ejpam-4587	176	12	h	h	NOUN
ejpam-4587	176	13	)	)	PUNCT
ejpam-4587	176	14	.	.	PUNCT
ejpam-4587	177	1	similar	similar	ADJ
ejpam-4587	177	2	process	process	NOUN
ejpam-4587	177	3	to	to	PART
ejpam-4587	177	4	case	case	VERB
ejpam-4587	177	5	i	i	PRON
ejpam-4587	177	6	,	,	PUNCT
ejpam-4587	177	7	⟨s⟩w	⟨s⟩w	PROPN
ejpam-4587	177	8	is	be	AUX
ejpam-4587	177	9	connected	connect	VERB
ejpam-4587	177	10	.	.	PUNCT
ejpam-4587	178	1	therefore	therefore	ADV
ejpam-4587	178	2	,	,	PUNCT
ejpam-4587	178	3	we	we	PRON
ejpam-4587	178	4	conclude	conclude	VERB
ejpam-4587	178	5	the	the	DET
ejpam-4587	178	6	fact	fact	NOUN
ejpam-4587	178	7	that	that	SCONJ
ejpam-4587	178	8	s	s	VERB
ejpam-4587	178	9	is	be	AUX
ejpam-4587	178	10	a	a	DET
ejpam-4587	178	11	weakly	weakly	ADV
ejpam-4587	178	12	connected	connected	ADJ
ejpam-4587	178	13	hop	hop	NOUN
ejpam-4587	178	14	dominating	dominating	NOUN
ejpam-4587	178	15	set	set	NOUN
ejpam-4587	178	16	of	of	ADP
ejpam-4587	178	17	g+h	g+h	PROPN
ejpam-4587	178	18	.	.	PUNCT
ejpam-4587	179	1	proposition	proposition	NOUN
ejpam-4587	179	2	4	4	NUM
ejpam-4587	179	3	.	.	PUNCT
ejpam-4587	180	1	let	let	VERB
ejpam-4587	180	2	g	g	NOUN
ejpam-4587	180	3	+	+	CCONJ
ejpam-4587	180	4	h	h	NOUN
ejpam-4587	180	5	be	be	VERB
ejpam-4587	180	6	the	the	DET
ejpam-4587	180	7	join	join	NOUN
ejpam-4587	180	8	of	of	ADP
ejpam-4587	180	9	g	g	PROPN
ejpam-4587	180	10	and	and	CCONJ
ejpam-4587	180	11	h	h	NOUN
ejpam-4587	180	12	,	,	PUNCT
ejpam-4587	180	13	a	a	DET
ejpam-4587	180	14	set	set	NOUN
ejpam-4587	180	15	s	s	NOUN
ejpam-4587	180	16	⊆	⊆	NUM
ejpam-4587	180	17	v	v	NOUN
ejpam-4587	180	18	(	(	PUNCT
ejpam-4587	180	19	g	g	PROPN
ejpam-4587	180	20	+	+	NOUN
ejpam-4587	180	21	h	h	NOUN
ejpam-4587	180	22	)	)	PUNCT
ejpam-4587	180	23	is	be	AUX
ejpam-4587	180	24	a	a	DET
ejpam-4587	180	25	weakly	weakly	ADV
ejpam-4587	180	26	connected	connected	ADJ
ejpam-4587	180	27	hop	hop	NOUN
ejpam-4587	180	28	dominating	dominating	NOUN
ejpam-4587	180	29	set	set	NOUN
ejpam-4587	180	30	if	if	SCONJ
ejpam-4587	180	31	and	and	CCONJ
ejpam-4587	180	32	only	only	ADV
ejpam-4587	180	33	if	if	SCONJ
ejpam-4587	180	34	one	one	NUM
ejpam-4587	180	35	of	of	ADP
ejpam-4587	180	36	the	the	DET
ejpam-4587	180	37	following	follow	VERB
ejpam-4587	180	38	is	be	AUX
ejpam-4587	180	39	satisfied	satisfied	ADJ
ejpam-4587	180	40	:	:	PUNCT
ejpam-4587	180	41	(	(	PUNCT
ejpam-4587	180	42	i	i	NOUN
ejpam-4587	180	43	)	)	PUNCT
ejpam-4587	180	44	s	s	VERB
ejpam-4587	180	45	⊆	⊆	NUM
ejpam-4587	180	46	v	v	NOUN
ejpam-4587	180	47	(	(	PUNCT
ejpam-4587	180	48	g	g	NOUN
ejpam-4587	180	49	)	)	PUNCT
ejpam-4587	180	50	and	and	CCONJ
ejpam-4587	180	51	s	s	VERB
ejpam-4587	180	52	is	be	AUX
ejpam-4587	180	53	a	a	DET
ejpam-4587	180	54	weakly	weakly	ADV
ejpam-4587	180	55	connected	connected	ADJ
ejpam-4587	180	56	hop	hop	NOUN
ejpam-4587	180	57	dominating	dominating	NOUN
ejpam-4587	180	58	set	set	VERB
ejpam-4587	180	59	in	in	ADP
ejpam-4587	180	60	g.	g.	PROPN
ejpam-4587	180	61	(	(	PUNCT
ejpam-4587	180	62	ii	ii	PROPN
ejpam-4587	180	63	)	)	PUNCT
ejpam-4587	180	64	s	s	PART
ejpam-4587	180	65	⊆	⊆	NUM
ejpam-4587	180	66	v	v	NOUN
ejpam-4587	180	67	(	(	PUNCT
ejpam-4587	180	68	h	h	NOUN
ejpam-4587	180	69	)	)	PUNCT
ejpam-4587	180	70	and	and	CCONJ
ejpam-4587	180	71	s	s	VERB
ejpam-4587	180	72	is	be	AUX
ejpam-4587	180	73	a	a	DET
ejpam-4587	180	74	weakly	weakly	ADV
ejpam-4587	180	75	connected	connected	ADJ
ejpam-4587	180	76	hop	hop	NOUN
ejpam-4587	180	77	dominating	dominating	NOUN
ejpam-4587	180	78	set	set	VERB
ejpam-4587	180	79	in	in	ADP
ejpam-4587	180	80	h.	h.	PROPN
ejpam-4587	180	81	(	(	PUNCT
ejpam-4587	180	82	iii	iii	NOUN
ejpam-4587	180	83	)	)	PUNCT
ejpam-4587	180	84	s	s	PART
ejpam-4587	180	85	∩	∩	ADJ
ejpam-4587	180	86	v	v	ADJ
ejpam-4587	180	87	(	(	PUNCT
ejpam-4587	180	88	g	g	NOUN
ejpam-4587	180	89	)	)	PUNCT
ejpam-4587	180	90	̸=	̸=	PROPN
ejpam-4587	180	91	∅	∅	NOUN
ejpam-4587	180	92	and	and	CCONJ
ejpam-4587	180	93	s	s	VERB
ejpam-4587	180	94	∩	∩	ADJ
ejpam-4587	180	95	v	v	ADJ
ejpam-4587	180	96	(	(	PUNCT
ejpam-4587	180	97	h	h	NOUN
ejpam-4587	180	98	)	)	PUNCT
ejpam-4587	180	99	̸=	̸=	PROPN
ejpam-4587	180	100	∅.	∅.	ADV
ejpam-4587	180	101	theorem	theorem	VERB
ejpam-4587	180	102	7	7	NUM
ejpam-4587	180	103	.	.	PUNCT
ejpam-4587	181	1	let	let	VERB
ejpam-4587	181	2	g+h	g+h	PROPN
ejpam-4587	181	3	be	be	AUX
ejpam-4587	181	4	the	the	DET
ejpam-4587	181	5	join	join	NOUN
ejpam-4587	181	6	of	of	ADP
ejpam-4587	181	7	g	g	NOUN
ejpam-4587	181	8	of	of	ADP
ejpam-4587	181	9	order	order	NOUN
ejpam-4587	181	10	m	m	VERB
ejpam-4587	181	11	and	and	CCONJ
ejpam-4587	181	12	h	h	NOUN
ejpam-4587	181	13	of	of	ADP
ejpam-4587	181	14	order	order	NOUN
ejpam-4587	181	15	n	n	PRON
ejpam-4587	181	16	with	with	ADP
ejpam-4587	181	17	γh(g	γh(g	NOUN
ejpam-4587	181	18	)	)	PUNCT
ejpam-4587	181	19	=	=	SYM
ejpam-4587	181	20	2	2	NUM
ejpam-4587	181	21	or	or	CCONJ
ejpam-4587	181	22	γh(h	γh(h	NUM
ejpam-4587	181	23	)	)	PUNCT
ejpam-4587	181	24	=	=	SYM
ejpam-4587	182	1	2	2	X
ejpam-4587	182	2	.	.	NUM
ejpam-4587	182	3	then	then	ADV
ejpam-4587	182	4	γwh(g+h	γwh(g+h	ADV
ejpam-4587	182	5	)	)	PUNCT
ejpam-4587	182	6	=	=	SYM
ejpam-4587	182	7	4	4	X
ejpam-4587	182	8	.	.	PUNCT
ejpam-4587	182	9	j.	j.	PROPN
ejpam-4587	182	10	hamja	hamja	PROPN
ejpam-4587	182	11	,	,	PUNCT
ejpam-4587	182	12	i.	i.	PROPN
ejpam-4587	182	13	aniversario	aniversario	PROPN
ejpam-4587	182	14	,	,	PUNCT
ejpam-4587	182	15	c.	c.	PROPN
ejpam-4587	182	16	merca	merca	PROPN
ejpam-4587	182	17	/	/	SYM
ejpam-4587	182	18	eur	eur	PROPN
ejpam-4587	182	19	.	.	PUNCT
ejpam-4587	183	1	j.	j.	PROPN
ejpam-4587	183	2	pure	pure	PROPN
ejpam-4587	183	3	appl	appl	PROPN
ejpam-4587	183	4	.	.	PROPN
ejpam-4587	183	5	math	math	PROPN
ejpam-4587	183	6	,	,	PUNCT
ejpam-4587	183	7	16	16	NUM
ejpam-4587	183	8	(	(	PUNCT
ejpam-4587	183	9	1	1	NUM
ejpam-4587	183	10	)	)	PUNCT
ejpam-4587	183	11	(	(	PUNCT
ejpam-4587	183	12	2023	2023	NUM
ejpam-4587	183	13	)	)	PUNCT
ejpam-4587	183	14	,	,	PUNCT
ejpam-4587	183	15	454	454	NUM
ejpam-4587	183	16	-	-	SYM
ejpam-4587	183	17	464	464	NUM
ejpam-4587	183	18	460	460	NUM
ejpam-4587	183	19	proof	proof	NOUN
ejpam-4587	183	20	.	.	PUNCT
ejpam-4587	184	1	let	let	VERB
ejpam-4587	184	2	s	s	PRON
ejpam-4587	184	3	=	=	NOUN
ejpam-4587	184	4	{	{	PUNCT
ejpam-4587	184	5	u1	u1	NOUN
ejpam-4587	184	6	,	,	PUNCT
ejpam-4587	184	7	u2	u2	PROPN
ejpam-4587	184	8	,	,	PUNCT
ejpam-4587	184	9	v1	v1	NOUN
ejpam-4587	184	10	,	,	PUNCT
ejpam-4587	184	11	v2	v2	NOUN
ejpam-4587	184	12	}	}	PUNCT
ejpam-4587	184	13	where	where	SCONJ
ejpam-4587	184	14	u1	u1	NOUN
ejpam-4587	184	15	,	,	PUNCT
ejpam-4587	184	16	u2	u2	PROPN
ejpam-4587	184	17	∈	∈	PROPN
ejpam-4587	184	18	v	v	ADP
ejpam-4587	184	19	(	(	PUNCT
ejpam-4587	184	20	g	g	NOUN
ejpam-4587	184	21	)	)	PUNCT
ejpam-4587	184	22	and	and	CCONJ
ejpam-4587	184	23	v1	v1	NOUN
ejpam-4587	184	24	,	,	PUNCT
ejpam-4587	184	25	v2	v2	PROPN
ejpam-4587	184	26	∈	∈	PROPN
ejpam-4587	184	27	v	v	NOUN
ejpam-4587	184	28	(	(	PUNCT
ejpam-4587	184	29	h	h	NOUN
ejpam-4587	184	30	)	)	PUNCT
ejpam-4587	184	31	.	.	PUNCT
ejpam-4587	185	1	observe	observe	VERB
ejpam-4587	185	2	that	that	PRON
ejpam-4587	185	3	u1	u1	NOUN
ejpam-4587	185	4	,	,	PUNCT
ejpam-4587	185	5	u2	u2	NOUN
ejpam-4587	185	6	,	,	PUNCT
ejpam-4587	185	7	v1	v1	NOUN
ejpam-4587	185	8	,	,	PUNCT
ejpam-4587	185	9	v2	v2	PROPN
ejpam-4587	185	10	∈	∈	PROPN
ejpam-4587	185	11	v	v	NOUN
ejpam-4587	185	12	(	(	PUNCT
ejpam-4587	185	13	g+h	g+h	NOUN
ejpam-4587	185	14	)	)	PUNCT
ejpam-4587	185	15	will	will	AUX
ejpam-4587	185	16	compromise	compromise	VERB
ejpam-4587	185	17	a	a	DET
ejpam-4587	185	18	set	set	NOUN
ejpam-4587	185	19	that	that	PRON
ejpam-4587	185	20	will	will	AUX
ejpam-4587	185	21	induce	induce	VERB
ejpam-4587	185	22	a	a	DET
ejpam-4587	185	23	complete	complete	ADJ
ejpam-4587	185	24	graph	graph	NOUN
ejpam-4587	185	25	of	of	ADP
ejpam-4587	185	26	order	order	NOUN
ejpam-4587	185	27	4	4	NUM
ejpam-4587	185	28	in	in	ADP
ejpam-4587	185	29	g+h	g+h	PROPN
ejpam-4587	185	30	.	.	PUNCT
ejpam-4587	186	1	by	by	ADP
ejpam-4587	186	2	theorem	theorem	NOUN
ejpam-4587	186	3	2	2	NUM
ejpam-4587	186	4	,	,	PUNCT
ejpam-4587	186	5	γwh(k4	γwh(k4	NOUN
ejpam-4587	186	6	)	)	PUNCT
ejpam-4587	186	7	=	=	PUNCT
ejpam-4587	186	8	4	4	X
ejpam-4587	186	9	.	.	PUNCT
ejpam-4587	186	10	also	also	ADV
ejpam-4587	186	11	,	,	PUNCT
ejpam-4587	186	12	for	for	ADP
ejpam-4587	186	13	every	every	DET
ejpam-4587	186	14	vertex	vertex	NOUN
ejpam-4587	186	15	q	q	X
ejpam-4587	186	16	∈	∈	PROPN
ejpam-4587	186	17	v	v	NOUN
ejpam-4587	186	18	(	(	PUNCT
ejpam-4587	186	19	g+h	g+h	NOUN
ejpam-4587	186	20	)	)	PUNCT
ejpam-4587	186	21	\	\	PROPN
ejpam-4587	187	1	s	s	X
ejpam-4587	187	2	,	,	PUNCT
ejpam-4587	187	3	there	there	PRON
ejpam-4587	187	4	exists	exist	VERB
ejpam-4587	187	5	an	an	DET
ejpam-4587	187	6	element	element	NOUN
ejpam-4587	187	7	in	in	ADP
ejpam-4587	187	8	s	s	PRON
ejpam-4587	187	9	say	say	VERB
ejpam-4587	187	10	u2	u2	NOUN
ejpam-4587	187	11	or	or	CCONJ
ejpam-4587	187	12	v2	v2	NOUN
ejpam-4587	187	13	such	such	DET
ejpam-4587	187	14	that	that	PRON
ejpam-4587	187	15	dg(q	dg(q	NOUN
ejpam-4587	187	16	,	,	PUNCT
ejpam-4587	187	17	u2	u2	NOUN
ejpam-4587	187	18	)	)	PUNCT
ejpam-4587	187	19	=	=	SYM
ejpam-4587	187	20	2	2	NUM
ejpam-4587	187	21	or	or	CCONJ
ejpam-4587	187	22	dg(q	dg(q	NOUN
ejpam-4587	187	23	,	,	PUNCT
ejpam-4587	187	24	v2	v2	NOUN
ejpam-4587	187	25	)	)	PUNCT
ejpam-4587	187	26	=	=	SYM
ejpam-4587	187	27	2	2	X
ejpam-4587	187	28	.	.	PUNCT
ejpam-4587	187	29	moreover	moreover	ADV
ejpam-4587	187	30	,	,	PUNCT
ejpam-4587	187	31	⟨s⟩w	⟨s⟩w	PROPN
ejpam-4587	187	32	is	be	AUX
ejpam-4587	187	33	connected	connect	VERB
ejpam-4587	187	34	since	since	SCONJ
ejpam-4587	187	35	for	for	ADP
ejpam-4587	187	36	every	every	DET
ejpam-4587	187	37	vertex	vertex	NOUN
ejpam-4587	187	38	q	q	NOUN
ejpam-4587	187	39	in	in	ADP
ejpam-4587	187	40	v	v	NOUN
ejpam-4587	187	41	(	(	PUNCT
ejpam-4587	187	42	g+h	g+h	NOUN
ejpam-4587	187	43	)	)	PUNCT
ejpam-4587	187	44	\s	\s	NOUN
ejpam-4587	187	45	is	be	AUX
ejpam-4587	187	46	adjacent	adjacent	ADJ
ejpam-4587	187	47	to	to	PART
ejpam-4587	187	48	u1	u1	VERB
ejpam-4587	187	49	,	,	PUNCT
ejpam-4587	187	50	u2	u2	PROPN
ejpam-4587	187	51	∈	∈	PROPN
ejpam-4587	187	52	v	v	ADP
ejpam-4587	187	53	(	(	PUNCT
ejpam-4587	187	54	g	g	NOUN
ejpam-4587	187	55	)	)	PUNCT
ejpam-4587	187	56	or	or	CCONJ
ejpam-4587	187	57	v1	v1	NOUN
ejpam-4587	187	58	,	,	PUNCT
ejpam-4587	187	59	v2	v2	PROPN
ejpam-4587	187	60	∈	∈	PROPN
ejpam-4587	187	61	v	v	NOUN
ejpam-4587	187	62	(	(	PUNCT
ejpam-4587	187	63	h	h	NOUN
ejpam-4587	187	64	)	)	PUNCT
ejpam-4587	187	65	and	and	CCONJ
ejpam-4587	187	66	s	s	VERB
ejpam-4587	187	67	is	be	AUX
ejpam-4587	187	68	dominating	dominate	VERB
ejpam-4587	187	69	.	.	PUNCT
ejpam-4587	188	1	hence	hence	ADV
ejpam-4587	188	2	,	,	PUNCT
ejpam-4587	188	3	s	s	VERB
ejpam-4587	188	4	is	be	AUX
ejpam-4587	188	5	a	a	DET
ejpam-4587	188	6	weakly	weakly	ADV
ejpam-4587	188	7	connected	connected	ADJ
ejpam-4587	188	8	hop	hop	NOUN
ejpam-4587	188	9	dominating	dominating	NOUN
ejpam-4587	188	10	set	set	VERB
ejpam-4587	188	11	in	in	ADP
ejpam-4587	188	12	g+h	g+h	PROPN
ejpam-4587	188	13	.	.	PUNCT
ejpam-4587	189	1	thus	thus	ADV
ejpam-4587	189	2	γwh(g+h	γwh(g+h	PRON
ejpam-4587	189	3	)	)	PUNCT
ejpam-4587	190	1	=	=	NOUN
ejpam-4587	190	2	|s|=	|s|=	NOUN
ejpam-4587	190	3	4	4	NUM
ejpam-4587	190	4	.	.	PUNCT
ejpam-4587	190	5	corollary	corollary	ADJ
ejpam-4587	190	6	4	4	NUM
ejpam-4587	190	7	.	.	PUNCT
ejpam-4587	190	8	the	the	DET
ejpam-4587	190	9	weakly	weakly	ADV
ejpam-4587	190	10	connected	connect	VERB
ejpam-4587	190	11	hop	hop	NOUN
ejpam-4587	190	12	domination	domination	NOUN
ejpam-4587	190	13	number	number	NOUN
ejpam-4587	190	14	of	of	ADP
ejpam-4587	190	15	the	the	DET
ejpam-4587	190	16	join	join	NOUN
ejpam-4587	190	17	of	of	ADP
ejpam-4587	190	18	path	path	NOUN
ejpam-4587	190	19	and	and	CCONJ
ejpam-4587	190	20	cycle	cycle	NOUN
ejpam-4587	190	21	graphs	graph	NOUN
ejpam-4587	190	22	of	of	ADP
ejpam-4587	190	23	order	order	NOUN
ejpam-4587	190	24	m	m	PRON
ejpam-4587	190	25	,	,	PUNCT
ejpam-4587	190	26	n	n	PRON
ejpam-4587	190	27	≥	≥	NOUN
ejpam-4587	190	28	2	2	NUM
ejpam-4587	190	29	are	be	AUX
ejpam-4587	190	30	given	give	VERB
ejpam-4587	190	31	as	as	SCONJ
ejpam-4587	190	32	follows	follow	VERB
ejpam-4587	190	33	:	:	PUNCT
ejpam-4587	190	34	(	(	PUNCT
ejpam-4587	190	35	i	i	NOUN
ejpam-4587	190	36	)	)	PUNCT
ejpam-4587	190	37	γwh(pm	γwh(pm	PROPN
ejpam-4587	191	1	+	+	CCONJ
ejpam-4587	191	2	pn	pn	NOUN
ejpam-4587	191	3	)	)	PUNCT
ejpam-4587	191	4	=	=	PUNCT
ejpam-4587	192	1	4	4	X
ejpam-4587	192	2	.	.	PUNCT
ejpam-4587	192	3	(	(	PUNCT
ejpam-4587	192	4	ii	ii	NOUN
ejpam-4587	192	5	)	)	PUNCT
ejpam-4587	192	6	γwh(cm	γwh(cm	X
ejpam-4587	193	1	+	+	CCONJ
ejpam-4587	193	2	cn	cn	ADJ
ejpam-4587	193	3	)	)	PUNCT
ejpam-4587	193	4	=	=	SYM
ejpam-4587	193	5	4	4	X
ejpam-4587	193	6	.	.	PUNCT
ejpam-4587	193	7	(	(	PUNCT
ejpam-4587	193	8	iii	iii	NOUN
ejpam-4587	193	9	)	)	PUNCT
ejpam-4587	193	10	γwh(pm	γwh(pm	NOUN
ejpam-4587	194	1	+	+	CCONJ
ejpam-4587	194	2	cn	cn	ADJ
ejpam-4587	194	3	)	)	PUNCT
ejpam-4587	194	4	=	=	SYM
ejpam-4587	194	5	4	4	X
ejpam-4587	194	6	.	.	X
ejpam-4587	194	7	proposition	proposition	NOUN
ejpam-4587	194	8	5	5	NUM
ejpam-4587	194	9	.	.	PUNCT
ejpam-4587	195	1	let	let	VERB
ejpam-4587	195	2	g	g	PROPN
ejpam-4587	195	3	+	+	NOUN
ejpam-4587	195	4	h	h	NOUN
ejpam-4587	195	5	be	be	VERB
ejpam-4587	195	6	the	the	DET
ejpam-4587	195	7	join	join	NOUN
ejpam-4587	195	8	of	of	ADP
ejpam-4587	195	9	g	g	NOUN
ejpam-4587	195	10	of	of	ADP
ejpam-4587	195	11	order	order	NOUN
ejpam-4587	195	12	m	m	VERB
ejpam-4587	195	13	≥	≥	NOUN
ejpam-4587	195	14	2	2	NUM
ejpam-4587	195	15	and	and	CCONJ
ejpam-4587	195	16	h	h	NOUN
ejpam-4587	195	17	of	of	ADP
ejpam-4587	195	18	order	order	NOUN
ejpam-4587	195	19	n	n	PRON
ejpam-4587	195	20	≥	≥	NOUN
ejpam-4587	195	21	2	2	NUM
ejpam-4587	195	22	,	,	PUNCT
ejpam-4587	195	23	then	then	ADV
ejpam-4587	195	24	γwh(g+h	γwh(g+h	ADJ
ejpam-4587	195	25	)	)	PUNCT
ejpam-4587	196	1	=	=	SYM
ejpam-4587	196	2	4	4	X
ejpam-4587	196	3	.	.	PUNCT
ejpam-4587	197	1	the	the	DET
ejpam-4587	197	2	corona	corona	NOUN
ejpam-4587	197	3	g	g	PROPN
ejpam-4587	197	4	◦	◦	NOUN
ejpam-4587	197	5	h	h	NOUN
ejpam-4587	197	6	of	of	ADP
ejpam-4587	197	7	graphs	graph	NOUN
ejpam-4587	197	8	g	g	PROPN
ejpam-4587	197	9	and	and	CCONJ
ejpam-4587	197	10	h	h	NOUN
ejpam-4587	197	11	,	,	PUNCT
ejpam-4587	197	12	is	be	AUX
ejpam-4587	197	13	the	the	DET
ejpam-4587	197	14	graph	graph	NOUN
ejpam-4587	197	15	obtained	obtain	VERB
ejpam-4587	197	16	by	by	ADP
ejpam-4587	197	17	taking	take	VERB
ejpam-4587	197	18	one	one	NUM
ejpam-4587	197	19	copy	copy	NOUN
ejpam-4587	197	20	of	of	ADP
ejpam-4587	197	21	g	g	PROPN
ejpam-4587	197	22	and	and	CCONJ
ejpam-4587	197	23	|v	|v	PROPN
ejpam-4587	197	24	(	(	PUNCT
ejpam-4587	197	25	g)|	g)|	NOUN
ejpam-4587	197	26	copies	copy	NOUN
ejpam-4587	197	27	of	of	ADP
ejpam-4587	197	28	h	h	NOUN
ejpam-4587	197	29	,	,	PUNCT
ejpam-4587	197	30	and	and	CCONJ
ejpam-4587	197	31	then	then	ADV
ejpam-4587	197	32	joining	join	VERB
ejpam-4587	197	33	the	the	DET
ejpam-4587	197	34	ith	ith	PROPN
ejpam-4587	197	35	vertex	vertex	NOUN
ejpam-4587	197	36	of	of	ADP
ejpam-4587	197	37	g	g	NOUN
ejpam-4587	197	38	to	to	ADP
ejpam-4587	197	39	every	every	DET
ejpam-4587	197	40	vertex	vertex	NOUN
ejpam-4587	197	41	of	of	ADP
ejpam-4587	197	42	the	the	DET
ejpam-4587	197	43	ith	ith	PROPN
ejpam-4587	197	44	copy	copy	NOUN
ejpam-4587	197	45	of	of	ADP
ejpam-4587	197	46	h.	h.	PROPN
ejpam-4587	197	47	for	for	ADP
ejpam-4587	197	48	every	every	DET
ejpam-4587	197	49	v	v	NUM
ejpam-4587	197	50	∈	∈	PROPN
ejpam-4587	197	51	v	v	NOUN
ejpam-4587	197	52	(	(	PUNCT
ejpam-4587	197	53	g	g	NOUN
ejpam-4587	197	54	)	)	PUNCT
ejpam-4587	197	55	,	,	PUNCT
ejpam-4587	197	56	denote	denote	VERB
ejpam-4587	197	57	by	by	ADP
ejpam-4587	197	58	hv	hv	PROPN
ejpam-4587	197	59	the	the	DET
ejpam-4587	197	60	copy	copy	NOUN
ejpam-4587	197	61	of	of	ADP
ejpam-4587	197	62	h	h	NOUN
ejpam-4587	197	63	whose	whose	DET
ejpam-4587	197	64	vertices	vertex	NOUN
ejpam-4587	197	65	are	be	AUX
ejpam-4587	197	66	attached	attach	VERB
ejpam-4587	197	67	one	one	NUM
ejpam-4587	197	68	by	by	ADP
ejpam-4587	197	69	one	one	NUM
ejpam-4587	197	70	to	to	ADP
ejpam-4587	197	71	the	the	DET
ejpam-4587	197	72	vertex	vertex	NOUN
ejpam-4587	197	73	v.	v.	ADP
ejpam-4587	197	74	subsequently	subsequently	ADV
ejpam-4587	197	75	,	,	PUNCT
ejpam-4587	197	76	denote	denote	VERB
ejpam-4587	197	77	by	by	ADP
ejpam-4587	197	78	v+hv	v+hv	NOUN
ejpam-4587	197	79	the	the	DET
ejpam-4587	197	80	subgraph	subgraph	NOUN
ejpam-4587	197	81	of	of	ADP
ejpam-4587	197	82	the	the	DET
ejpam-4587	197	83	corona	corona	NOUN
ejpam-4587	197	84	g	g	PROPN
ejpam-4587	197	85	◦	◦	NOUN
ejpam-4587	197	86	h	h	NOUN
ejpam-4587	197	87	corresponding	correspond	VERB
ejpam-4587	197	88	to	to	ADP
ejpam-4587	197	89	the	the	DET
ejpam-4587	197	90	join	join	NOUN
ejpam-4587	197	91	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4587	197	92	,	,	PUNCT
ejpam-4587	197	93	v	v	PROPN
ejpam-4587	197	94	∈	∈	PROPN
ejpam-4587	197	95	v	v	NOUN
ejpam-4587	197	96	(	(	PUNCT
ejpam-4587	197	97	g	g	NOUN
ejpam-4587	197	98	)	)	PUNCT
ejpam-4587	197	99	,	,	PUNCT
ejpam-4587	197	100	harary	harary	NOUN
ejpam-4587	198	1	[	[	X
ejpam-4587	198	2	5	5	NUM
ejpam-4587	198	3	]	]	PUNCT
ejpam-4587	198	4	.	.	PUNCT
ejpam-4587	199	1	theorem	theorem	ADJ
ejpam-4587	199	2	8	8	NUM
ejpam-4587	199	3	.	.	PUNCT
ejpam-4587	200	1	let	let	VERB
ejpam-4587	200	2	g	g	NOUN
ejpam-4587	200	3	and	and	CCONJ
ejpam-4587	200	4	h	h	NOUN
ejpam-4587	200	5	be	be	AUX
ejpam-4587	200	6	connected	connect	VERB
ejpam-4587	200	7	graph	graph	NOUN
ejpam-4587	200	8	of	of	ADP
ejpam-4587	200	9	orders	order	NOUN
ejpam-4587	200	10	m	m	PROPN
ejpam-4587	200	11	and	and	CCONJ
ejpam-4587	200	12	n	n	CCONJ
ejpam-4587	200	13	,	,	PUNCT
ejpam-4587	200	14	respectively	respectively	ADV
ejpam-4587	200	15	.	.	PUNCT
ejpam-4587	201	1	let	let	VERB
ejpam-4587	201	2	s	s	PRON
ejpam-4587	201	3	⊆	⊆	NUM
ejpam-4587	201	4	v	v	NOUN
ejpam-4587	201	5	(	(	PUNCT
ejpam-4587	201	6	g	g	PROPN
ejpam-4587	201	7	◦	◦	NOUN
ejpam-4587	201	8	h	h	NOUN
ejpam-4587	201	9	)	)	PUNCT
ejpam-4587	201	10	be	be	VERB
ejpam-4587	201	11	a	a	DET
ejpam-4587	201	12	weakly	weakly	ADV
ejpam-4587	201	13	connected	connected	ADJ
ejpam-4587	201	14	hop	hop	NOUN
ejpam-4587	201	15	dominating	dominating	NOUN
ejpam-4587	201	16	set	set	NOUN
ejpam-4587	201	17	of	of	ADP
ejpam-4587	201	18	g	g	PROPN
ejpam-4587	201	19	◦	◦	NOUN
ejpam-4587	201	20	h	h	NOUN
ejpam-4587	201	21	and	and	CCONJ
ejpam-4587	201	22	h1	h1	PROPN
ejpam-4587	201	23	,	,	PUNCT
ejpam-4587	201	24	h2	h2	PROPN
ejpam-4587	201	25	,	,	PUNCT
ejpam-4587	201	26	...	...	PUNCT
ejpam-4587	201	27	,	,	PUNCT
ejpam-4587	201	28	hn	hn	PROPN
ejpam-4587	201	29	be	be	VERB
ejpam-4587	201	30	the	the	DET
ejpam-4587	201	31	copies	copy	NOUN
ejpam-4587	201	32	of	of	ADP
ejpam-4587	201	33	h.	h.	PROPN
ejpam-4587	201	34	then	then	ADV
ejpam-4587	201	35	(	(	PUNCT
ejpam-4587	201	36	i	i	NOUN
ejpam-4587	201	37	)	)	PUNCT
ejpam-4587	201	38	s	s	PART
ejpam-4587	201	39	∩	∩	ADJ
ejpam-4587	201	40	v	v	X
ejpam-4587	201	41	(	(	PUNCT
ejpam-4587	201	42	h	h	NOUN
ejpam-4587	201	43	i	i	NOUN
ejpam-4587	201	44	)	)	PUNCT
ejpam-4587	202	1	=	=	NOUN
ejpam-4587	202	2	∅	∅	NOUN
ejpam-4587	202	3	for	for	ADP
ejpam-4587	202	4	all	all	DET
ejpam-4587	202	5	1	1	NUM
ejpam-4587	202	6	≤	≤	NUM
ejpam-4587	202	7	i	i	PRON
ejpam-4587	202	8	≤	≤	PROPN
ejpam-4587	203	1	n.	n.	NOUN
ejpam-4587	203	2	(	(	PUNCT
ejpam-4587	203	3	ii	ii	PROPN
ejpam-4587	203	4	)	)	PUNCT
ejpam-4587	203	5	s	s	PART
ejpam-4587	203	6	∩	∩	ADJ
ejpam-4587	203	7	v	v	ADJ
ejpam-4587	203	8	(	(	PUNCT
ejpam-4587	203	9	g	g	NOUN
ejpam-4587	203	10	)	)	PUNCT
ejpam-4587	203	11	̸=	̸=	PROPN
ejpam-4587	203	12	∅.	∅.	ADP
ejpam-4587	203	13	proof	proof	NOUN
ejpam-4587	203	14	.	.	PUNCT
ejpam-4587	204	1	let	let	VERB
ejpam-4587	204	2	s	s	PRON
ejpam-4587	204	3	⊆	⊆	NUM
ejpam-4587	204	4	v	v	NOUN
ejpam-4587	204	5	(	(	PUNCT
ejpam-4587	204	6	g	g	PROPN
ejpam-4587	204	7	◦	◦	NOUN
ejpam-4587	204	8	h	h	NOUN
ejpam-4587	204	9	)	)	PUNCT
ejpam-4587	204	10	be	be	VERB
ejpam-4587	204	11	γwh	γwh	NOUN
ejpam-4587	204	12	-	-	PUNCT
ejpam-4587	204	13	set	set	NOUN
ejpam-4587	204	14	of	of	ADP
ejpam-4587	204	15	g	g	PROPN
ejpam-4587	204	16	◦	◦	NOUN
ejpam-4587	204	17	h.	h.	PROPN
ejpam-4587	204	18	(	(	PUNCT
ejpam-4587	204	19	i	i	NOUN
ejpam-4587	204	20	)	)	PUNCT
ejpam-4587	204	21	suppose	suppose	VERB
ejpam-4587	204	22	that	that	SCONJ
ejpam-4587	204	23	s	s	VERB
ejpam-4587	204	24	∩	∩	ADJ
ejpam-4587	204	25	v	v	NOUN
ejpam-4587	204	26	(	(	PUNCT
ejpam-4587	204	27	h	h	NOUN
ejpam-4587	204	28	i	i	NOUN
ejpam-4587	204	29	)	)	PUNCT
ejpam-4587	204	30	=	=	NOUN
ejpam-4587	204	31	∅	∅	NOUN
ejpam-4587	204	32	for	for	ADP
ejpam-4587	204	33	some	some	DET
ejpam-4587	204	34	i	i	PRON
ejpam-4587	204	35	,	,	PUNCT
ejpam-4587	204	36	1	1	NUM
ejpam-4587	204	37	≤	≤	NUM
ejpam-4587	204	38	i	i	PRON
ejpam-4587	204	39	≤	≤	PROPN
ejpam-4587	204	40	n.	n.	NOUN
ejpam-4587	204	41	since	since	SCONJ
ejpam-4587	204	42	every	every	DET
ejpam-4587	204	43	vertex	vertex	NOUN
ejpam-4587	204	44	of	of	ADP
ejpam-4587	204	45	h	h	NOUN
ejpam-4587	204	46	i	i	PROPN
ejpam-4587	204	47	for	for	ADP
ejpam-4587	204	48	all	all	DET
ejpam-4587	204	49	i	i	PRON
ejpam-4587	204	50	,	,	PUNCT
ejpam-4587	204	51	1	1	NUM
ejpam-4587	204	52	≤	≤	NUM
ejpam-4587	204	53	i	i	X
ejpam-4587	204	54	≤	≤	NOUN
ejpam-4587	204	55	n	n	PRON
ejpam-4587	204	56	is	be	AUX
ejpam-4587	204	57	adjacent	adjacent	ADJ
ejpam-4587	204	58	to	to	ADP
ejpam-4587	204	59	exactly	exactly	ADV
ejpam-4587	204	60	one	one	NUM
ejpam-4587	204	61	vertex	vertex	NOUN
ejpam-4587	204	62	of	of	ADP
ejpam-4587	204	63	g.	g.	PROPN
ejpam-4587	204	64	it	it	PRON
ejpam-4587	204	65	follows	follow	VERB
ejpam-4587	204	66	that	that	SCONJ
ejpam-4587	204	67	s	s	VERB
ejpam-4587	204	68	is	be	AUX
ejpam-4587	204	69	a	a	DET
ejpam-4587	204	70	γwh	γwh	NOUN
ejpam-4587	204	71	-	-	PUNCT
ejpam-4587	204	72	set	set	NOUN
ejpam-4587	204	73	of	of	ADP
ejpam-4587	204	74	g	g	PROPN
ejpam-4587	204	75	◦	◦	PROPN
ejpam-4587	204	76	h.	h.	PROPN
ejpam-4587	204	77	(	(	PUNCT
ejpam-4587	204	78	ii	ii	NOUN
ejpam-4587	204	79	)	)	PUNCT
ejpam-4587	204	80	suppose	suppose	VERB
ejpam-4587	204	81	that	that	SCONJ
ejpam-4587	204	82	s	s	VERB
ejpam-4587	204	83	∩	∩	ADJ
ejpam-4587	204	84	v	v	ADJ
ejpam-4587	204	85	(	(	PUNCT
ejpam-4587	204	86	g	g	NOUN
ejpam-4587	204	87	)	)	PUNCT
ejpam-4587	204	88	̸=	̸=	PROPN
ejpam-4587	204	89	∅.	∅.	ADV
ejpam-4587	204	90	let	let	VERB
ejpam-4587	204	91	u	u	PRON
ejpam-4587	204	92	be	be	AUX
ejpam-4587	204	93	a	a	DET
ejpam-4587	204	94	vertex	vertex	NOUN
ejpam-4587	204	95	of	of	ADP
ejpam-4587	204	96	s	s	NOUN
ejpam-4587	204	97	∩	∩	ADJ
ejpam-4587	204	98	v	v	ADJ
ejpam-4587	204	99	(	(	PUNCT
ejpam-4587	204	100	g	g	NOUN
ejpam-4587	204	101	)	)	PUNCT
ejpam-4587	204	102	.	.	PUNCT
ejpam-4587	205	1	hence	hence	ADV
ejpam-4587	205	2	u	u	X
ejpam-4587	205	3	∈	∈	PROPN
ejpam-4587	205	4	s	s	PART
ejpam-4587	205	5	and	and	CCONJ
ejpam-4587	205	6	u	u	PROPN
ejpam-4587	205	7	∈	∈	PROPN
ejpam-4587	205	8	v	v	NOUN
ejpam-4587	205	9	(	(	PUNCT
ejpam-4587	205	10	g	g	NOUN
ejpam-4587	205	11	)	)	PUNCT
ejpam-4587	205	12	.	.	PUNCT
ejpam-4587	206	1	since	since	SCONJ
ejpam-4587	206	2	|s|	|s|	PROPN
ejpam-4587	206	3	=	=	PROPN
ejpam-4587	206	4	|v	|v	PROPN
ejpam-4587	206	5	(	(	PUNCT
ejpam-4587	206	6	g)|	g)|	PROPN
ejpam-4587	206	7	,	,	PUNCT
ejpam-4587	206	8	dg(u	dg(u	X
ejpam-4587	206	9	,	,	PUNCT
ejpam-4587	206	10	v	v	NOUN
ejpam-4587	206	11	)	)	PUNCT
ejpam-4587	206	12	=	=	SYM
ejpam-4587	206	13	2	2	NUM
ejpam-4587	206	14	for	for	ADP
ejpam-4587	206	15	all	all	DET
ejpam-4587	206	16	v	v	ADP
ejpam-4587	206	17	∈	∈	NOUN
ejpam-4587	206	18	v	v	NOUN
ejpam-4587	206	19	(	(	PUNCT
ejpam-4587	206	20	h	h	NOUN
ejpam-4587	206	21	i	i	NOUN
ejpam-4587	206	22	)	)	PUNCT
ejpam-4587	206	23	for	for	ADP
ejpam-4587	206	24	all	all	DET
ejpam-4587	206	25	i	i	PRON
ejpam-4587	206	26	,	,	PUNCT
ejpam-4587	206	27	1	1	NUM
ejpam-4587	206	28	≤	≤	NUM
ejpam-4587	206	29	i	i	PRON
ejpam-4587	206	30	≤	≤	PROPN
ejpam-4587	206	31	n.	n.	NOUN
ejpam-4587	206	32	therefore	therefore	ADV
ejpam-4587	206	33	,	,	PUNCT
ejpam-4587	206	34	s	s	PART
ejpam-4587	206	35	is	be	AUX
ejpam-4587	206	36	a	a	DET
ejpam-4587	206	37	γwh	γwh	NOUN
ejpam-4587	206	38	-	-	PUNCT
ejpam-4587	206	39	set	set	NOUN
ejpam-4587	206	40	of	of	ADP
ejpam-4587	206	41	g	g	PROPN
ejpam-4587	206	42	◦	◦	PROPN
ejpam-4587	206	43	h.	h.	PROPN
ejpam-4587	206	44	j.	j.	PROPN
ejpam-4587	206	45	hamja	hamja	PROPN
ejpam-4587	206	46	,	,	PUNCT
ejpam-4587	206	47	i.	i.	PROPN
ejpam-4587	206	48	aniversario	aniversario	PROPN
ejpam-4587	206	49	,	,	PUNCT
ejpam-4587	206	50	c.	c.	PROPN
ejpam-4587	206	51	merca	merca	PROPN
ejpam-4587	206	52	/	/	SYM
ejpam-4587	206	53	eur	eur	PROPN
ejpam-4587	206	54	.	.	PUNCT
ejpam-4587	207	1	j.	j.	PROPN
ejpam-4587	207	2	pure	pure	PROPN
ejpam-4587	207	3	appl	appl	PROPN
ejpam-4587	207	4	.	.	PROPN
ejpam-4587	207	5	math	math	PROPN
ejpam-4587	207	6	,	,	PUNCT
ejpam-4587	207	7	16	16	NUM
ejpam-4587	207	8	(	(	PUNCT
ejpam-4587	207	9	1	1	NUM
ejpam-4587	207	10	)	)	PUNCT
ejpam-4587	207	11	(	(	PUNCT
ejpam-4587	207	12	2023	2023	NUM
ejpam-4587	207	13	)	)	PUNCT
ejpam-4587	207	14	,	,	PUNCT
ejpam-4587	207	15	454	454	NUM
ejpam-4587	207	16	-	-	SYM
ejpam-4587	207	17	464	464	NUM
ejpam-4587	207	18	461	461	NUM
ejpam-4587	207	19	theorem	theorem	NOUN
ejpam-4587	207	20	9	9	NUM
ejpam-4587	207	21	.	.	PUNCT
ejpam-4587	208	1	(	(	PUNCT
ejpam-4587	208	2	sandueta	sandueta	PROPN
ejpam-4587	208	3	,	,	PUNCT
ejpam-4587	208	4	et	et	PROPN
ejpam-4587	208	5	.	.	PUNCT
ejpam-4587	209	1	al	al	PROPN
ejpam-4587	209	2	.	.	PROPN
ejpam-4587	209	3	,	,	PUNCT
ejpam-4587	209	4	in	in	ADP
ejpam-4587	209	5	[	[	X
ejpam-4587	209	6	10	10	NUM
ejpam-4587	209	7	]	]	PUNCT
ejpam-4587	209	8	)	)	PUNCT
ejpam-4587	209	9	let	let	VERB
ejpam-4587	209	10	g	g	PRON
ejpam-4587	209	11	be	be	AUX
ejpam-4587	209	12	a	a	DET
ejpam-4587	209	13	connected	connected	ADJ
ejpam-4587	209	14	graph	graph	NOUN
ejpam-4587	209	15	of	of	ADP
ejpam-4587	209	16	order	order	NOUN
ejpam-4587	209	17	m	m	VERB
ejpam-4587	209	18	≥	≥	NOUN
ejpam-4587	209	19	2	2	NUM
ejpam-4587	209	20	and	and	CCONJ
ejpam-4587	209	21	h	h	DET
ejpam-4587	209	22	a	a	DET
ejpam-4587	209	23	graph	graph	NOUN
ejpam-4587	209	24	of	of	ADP
ejpam-4587	209	25	order	order	NOUN
ejpam-4587	209	26	n.	n.	NOUN
ejpam-4587	209	27	then	then	ADV
ejpam-4587	209	28	s	s	VERB
ejpam-4587	209	29	⊆	⊆	NUM
ejpam-4587	209	30	v	v	NOUN
ejpam-4587	209	31	(	(	PUNCT
ejpam-4587	209	32	g	g	PROPN
ejpam-4587	209	33	◦	◦	NOUN
ejpam-4587	209	34	h	h	NOUN
ejpam-4587	209	35	)	)	PUNCT
ejpam-4587	209	36	is	be	AUX
ejpam-4587	209	37	a	a	DET
ejpam-4587	209	38	weakly	weakly	ADV
ejpam-4587	209	39	connected	connected	ADJ
ejpam-4587	209	40	dominating	dominating	NOUN
ejpam-4587	209	41	set	set	NOUN
ejpam-4587	209	42	of	of	ADP
ejpam-4587	209	43	g	g	PROPN
ejpam-4587	209	44	◦	◦	NOUN
ejpam-4587	209	45	h	h	NOUN
ejpam-4587	210	1	if	if	SCONJ
ejpam-4587	210	2	and	and	CCONJ
ejpam-4587	210	3	only	only	ADV
ejpam-4587	210	4	if	if	SCONJ
ejpam-4587	210	5	v	v	X
ejpam-4587	210	6	(	(	PUNCT
ejpam-4587	210	7	v+hv)∩c	v+hv)∩c	PROPN
ejpam-4587	210	8	is	be	AUX
ejpam-4587	210	9	a	a	DET
ejpam-4587	210	10	dominating	dominating	NOUN
ejpam-4587	210	11	set	set	NOUN
ejpam-4587	210	12	of	of	ADP
ejpam-4587	210	13	v+hv	v+hv	NOUN
ejpam-4587	210	14	for	for	ADP
ejpam-4587	210	15	all	all	PRON
ejpam-4587	210	16	v	v	ADP
ejpam-4587	210	17	∈	∈	NOUN
ejpam-4587	210	18	v	v	NOUN
ejpam-4587	210	19	(	(	PUNCT
ejpam-4587	210	20	g	g	NOUN
ejpam-4587	210	21	)	)	PUNCT
ejpam-4587	210	22	and	and	CCONJ
ejpam-4587	210	23	v	v	X
ejpam-4587	210	24	(	(	PUNCT
ejpam-4587	210	25	g)∩c	g)∩c	NOUN
ejpam-4587	210	26	is	be	AUX
ejpam-4587	210	27	a	a	DET
ejpam-4587	210	28	weakly	weakly	ADV
ejpam-4587	210	29	connected	connected	ADJ
ejpam-4587	210	30	dominating	dominating	NOUN
ejpam-4587	210	31	set	set	NOUN
ejpam-4587	210	32	of	of	ADP
ejpam-4587	210	33	g.	g.	PROPN
ejpam-4587	210	34	theorem	theorem	VERB
ejpam-4587	210	35	10	10	NUM
ejpam-4587	210	36	.	.	PUNCT
ejpam-4587	211	1	let	let	VERB
ejpam-4587	211	2	g	g	PRON
ejpam-4587	211	3	be	be	AUX
ejpam-4587	211	4	a	a	DET
ejpam-4587	211	5	connected	connected	ADJ
ejpam-4587	211	6	graph	graph	NOUN
ejpam-4587	211	7	of	of	ADP
ejpam-4587	211	8	order	order	NOUN
ejpam-4587	211	9	m	m	VERB
ejpam-4587	211	10	≥	≥	NOUN
ejpam-4587	211	11	2	2	NUM
ejpam-4587	211	12	and	and	CCONJ
ejpam-4587	211	13	h	h	DET
ejpam-4587	211	14	a	a	DET
ejpam-4587	211	15	graph	graph	NOUN
ejpam-4587	211	16	of	of	ADP
ejpam-4587	211	17	order	order	NOUN
ejpam-4587	211	18	n.	n.	NOUN
ejpam-4587	211	19	then	then	ADV
ejpam-4587	211	20	s	s	VERB
ejpam-4587	211	21	⊆	⊆	NUM
ejpam-4587	211	22	v	v	NOUN
ejpam-4587	211	23	(	(	PUNCT
ejpam-4587	211	24	g	g	PROPN
ejpam-4587	211	25	◦	◦	NOUN
ejpam-4587	211	26	h	h	NOUN
ejpam-4587	211	27	)	)	PUNCT
ejpam-4587	211	28	is	be	AUX
ejpam-4587	211	29	a	a	DET
ejpam-4587	211	30	weakly	weakly	ADV
ejpam-4587	211	31	connected	connected	ADJ
ejpam-4587	211	32	hop	hop	NOUN
ejpam-4587	211	33	dominating	dominating	NOUN
ejpam-4587	211	34	set	set	NOUN
ejpam-4587	211	35	of	of	ADP
ejpam-4587	211	36	g	g	PROPN
ejpam-4587	211	37	◦	◦	NOUN
ejpam-4587	211	38	h	h	NOUN
ejpam-4587	212	1	if	if	SCONJ
ejpam-4587	212	2	and	and	CCONJ
ejpam-4587	212	3	only	only	ADV
ejpam-4587	212	4	if	if	SCONJ
ejpam-4587	212	5	s	s	ADP
ejpam-4587	212	6	∩	∩	ADJ
ejpam-4587	212	7	v	v	ADJ
ejpam-4587	212	8	(	(	PUNCT
ejpam-4587	212	9	v	v	PROPN
ejpam-4587	212	10	+	+	NOUN
ejpam-4587	212	11	hv	hv	NOUN
ejpam-4587	212	12	)	)	PUNCT
ejpam-4587	212	13	is	be	AUX
ejpam-4587	212	14	a	a	DET
ejpam-4587	212	15	dominating	dominating	NOUN
ejpam-4587	212	16	set	set	NOUN
ejpam-4587	212	17	of	of	ADP
ejpam-4587	212	18	v	v	DET
ejpam-4587	212	19	+	+	NOUN
ejpam-4587	212	20	hv	hv	NOUN
ejpam-4587	212	21	for	for	ADP
ejpam-4587	212	22	all	all	DET
ejpam-4587	212	23	v	v	ADP
ejpam-4587	212	24	∈	∈	NUM
ejpam-4587	212	25	v	v	NOUN
ejpam-4587	212	26	(	(	PUNCT
ejpam-4587	212	27	g	g	NOUN
ejpam-4587	212	28	)	)	PUNCT
ejpam-4587	212	29	and	and	CCONJ
ejpam-4587	212	30	s	s	VERB
ejpam-4587	212	31	∩	∩	ADJ
ejpam-4587	212	32	v	v	ADJ
ejpam-4587	212	33	(	(	PUNCT
ejpam-4587	212	34	g	g	NOUN
ejpam-4587	212	35	)	)	PUNCT
ejpam-4587	212	36	is	be	AUX
ejpam-4587	212	37	a	a	DET
ejpam-4587	212	38	weakly	weakly	ADV
ejpam-4587	212	39	connected	connected	ADJ
ejpam-4587	212	40	hop	hop	NOUN
ejpam-4587	212	41	dominating	dominating	NOUN
ejpam-4587	212	42	set	set	NOUN
ejpam-4587	212	43	of	of	ADP
ejpam-4587	212	44	g.	g.	PROPN
ejpam-4587	212	45	proof	proof	PROPN
ejpam-4587	212	46	.	.	PUNCT
ejpam-4587	213	1	suppose	suppose	VERB
ejpam-4587	213	2	s	s	PRON
ejpam-4587	213	3	is	be	AUX
ejpam-4587	213	4	a	a	DET
ejpam-4587	213	5	weakly	weakly	ADV
ejpam-4587	213	6	conncted	conncte	VERB
ejpam-4587	213	7	hop	hop	NOUN
ejpam-4587	213	8	dominating	dominating	NOUN
ejpam-4587	213	9	set	set	NOUN
ejpam-4587	213	10	of	of	ADP
ejpam-4587	213	11	g	g	NOUN
ejpam-4587	213	12	◦	◦	NOUN
ejpam-4587	213	13	h	h	NOUN
ejpam-4587	213	14	and	and	CCONJ
ejpam-4587	213	15	u	u	PROPN
ejpam-4587	213	16	∈	∈	PROPN
ejpam-4587	213	17	v	v	NOUN
ejpam-4587	213	18	(	(	PUNCT
ejpam-4587	213	19	g	g	NOUN
ejpam-4587	213	20	)	)	PUNCT
ejpam-4587	213	21	.	.	PUNCT
ejpam-4587	214	1	by	by	ADP
ejpam-4587	214	2	remark	remark	NOUN
ejpam-4587	214	3	1	1	NUM
ejpam-4587	214	4	,	,	PUNCT
ejpam-4587	214	5	s	s	VERB
ejpam-4587	214	6	is	be	AUX
ejpam-4587	214	7	a	a	DET
ejpam-4587	214	8	hop	hop	NOUN
ejpam-4587	214	9	dominating	dominating	NOUN
ejpam-4587	214	10	set	set	NOUN
ejpam-4587	214	11	of	of	ADP
ejpam-4587	214	12	g	g	PROPN
ejpam-4587	214	13	◦	◦	NOUN
ejpam-4587	214	14	h.	h.	NOUN
ejpam-4587	214	15	by	by	ADP
ejpam-4587	214	16	theorem	theorem	NOUN
ejpam-4587	214	17	9	9	NUM
ejpam-4587	214	18	,	,	PUNCT
ejpam-4587	214	19	if	if	SCONJ
ejpam-4587	214	20	s	s	VERB
ejpam-4587	214	21	is	be	AUX
ejpam-4587	214	22	a	a	DET
ejpam-4587	214	23	weakly	weakly	ADV
ejpam-4587	214	24	connected	connected	ADJ
ejpam-4587	214	25	dominating	dominating	NOUN
ejpam-4587	214	26	set	set	NOUN
ejpam-4587	214	27	of	of	ADP
ejpam-4587	214	28	g	g	NOUN
ejpam-4587	214	29	◦	◦	NOUN
ejpam-4587	214	30	h	h	NOUN
ejpam-4587	214	31	and	and	CCONJ
ejpam-4587	214	32	u	u	PROPN
ejpam-4587	214	33	∈	∈	PROPN
ejpam-4587	214	34	v	v	NOUN
ejpam-4587	214	35	(	(	PUNCT
ejpam-4587	214	36	g	g	NOUN
ejpam-4587	214	37	)	)	PUNCT
ejpam-4587	214	38	,	,	PUNCT
ejpam-4587	214	39	then	then	ADV
ejpam-4587	214	40	s∩v	s∩v	PROPN
ejpam-4587	214	41	(	(	PUNCT
ejpam-4587	214	42	v+hv	v+hv	PROPN
ejpam-4587	214	43	)	)	PUNCT
ejpam-4587	214	44	is	be	AUX
ejpam-4587	214	45	a	a	DET
ejpam-4587	214	46	dominating	dominating	NOUN
ejpam-4587	214	47	set	set	NOUN
ejpam-4587	214	48	of	of	ADP
ejpam-4587	214	49	(	(	PUNCT
ejpam-4587	214	50	v+hv	v+hv	NOUN
ejpam-4587	214	51	)	)	PUNCT
ejpam-4587	214	52	.	.	PUNCT
ejpam-4587	215	1	since	since	SCONJ
ejpam-4587	215	2	s	s	PROPN
ejpam-4587	215	3	is	be	AUX
ejpam-4587	215	4	a	a	DET
ejpam-4587	215	5	weakly	weakly	ADV
ejpam-4587	215	6	connected	connected	ADJ
ejpam-4587	215	7	hop	hop	NOUN
ejpam-4587	215	8	dominating	dominating	NOUN
ejpam-4587	215	9	set	set	NOUN
ejpam-4587	215	10	of	of	ADP
ejpam-4587	215	11	g	g	PROPN
ejpam-4587	215	12	◦	◦	NOUN
ejpam-4587	215	13	h	h	NOUN
ejpam-4587	215	14	,	,	PUNCT
ejpam-4587	215	15	s	s	NOUN
ejpam-4587	215	16	∩	∩	ADJ
ejpam-4587	215	17	v	v	ADJ
ejpam-4587	215	18	(	(	PUNCT
ejpam-4587	215	19	g	g	NOUN
ejpam-4587	215	20	)	)	PUNCT
ejpam-4587	215	21	̸=	̸=	PROPN
ejpam-4587	215	22	∅	∅	NOUN
ejpam-4587	215	23	(	(	PUNCT
ejpam-4587	215	24	unless	unless	SCONJ
ejpam-4587	215	25	,	,	PUNCT
ejpam-4587	215	26	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4587	215	27	is	be	AUX
ejpam-4587	215	28	disconneted	disconnete	VERB
ejpam-4587	215	29	)	)	PUNCT
ejpam-4587	215	30	.	.	PUNCT
ejpam-4587	216	1	by	by	ADP
ejpam-4587	216	2	theorem	theorem	NOUN
ejpam-4587	216	3	9	9	NUM
ejpam-4587	216	4	,	,	PUNCT
ejpam-4587	216	5	s	s	VERB
ejpam-4587	216	6	∩	∩	ADJ
ejpam-4587	216	7	v	v	ADJ
ejpam-4587	216	8	(	(	PUNCT
ejpam-4587	216	9	g	g	NOUN
ejpam-4587	216	10	)	)	PUNCT
ejpam-4587	216	11	is	be	AUX
ejpam-4587	216	12	a	a	DET
ejpam-4587	216	13	weakly	weakly	ADV
ejpam-4587	216	14	connected	connected	ADJ
ejpam-4587	216	15	dominating	dominating	NOUN
ejpam-4587	216	16	set	set	NOUN
ejpam-4587	216	17	of	of	ADP
ejpam-4587	216	18	g.	g.	PROPN
ejpam-4587	217	1	so	so	ADV
ejpam-4587	217	2	we	we	PRON
ejpam-4587	217	3	are	be	AUX
ejpam-4587	217	4	left	leave	VERB
ejpam-4587	217	5	to	to	PART
ejpam-4587	217	6	show	show	VERB
ejpam-4587	217	7	that	that	SCONJ
ejpam-4587	217	8	s	s	VERB
ejpam-4587	217	9	∩	∩	ADJ
ejpam-4587	217	10	v	v	ADJ
ejpam-4587	217	11	(	(	PUNCT
ejpam-4587	217	12	g	g	NOUN
ejpam-4587	217	13	)	)	PUNCT
ejpam-4587	217	14	is	be	AUX
ejpam-4587	217	15	hop	hop	NOUN
ejpam-4587	217	16	dominating	dominate	VERB
ejpam-4587	217	17	set	set	NOUN
ejpam-4587	217	18	of	of	ADP
ejpam-4587	217	19	g.	g.	PROPN
ejpam-4587	217	20	let	let	VERB
ejpam-4587	217	21	u	u	PRON
ejpam-4587	217	22	∈	∈	PROPN
ejpam-4587	217	23	s	s	PART
ejpam-4587	217	24	∩	∩	ADJ
ejpam-4587	217	25	v	v	X
ejpam-4587	217	26	(	(	PUNCT
ejpam-4587	217	27	g	g	NOUN
ejpam-4587	217	28	)	)	PUNCT
ejpam-4587	217	29	for	for	ADP
ejpam-4587	217	30	all	all	DET
ejpam-4587	217	31	u	u	PROPN
ejpam-4587	217	32	∈	∈	PROPN
ejpam-4587	217	33	s	s	X
ejpam-4587	217	34	and	and	CCONJ
ejpam-4587	217	35	u	u	PROPN
ejpam-4587	217	36	∈	∈	PROPN
ejpam-4587	217	37	v	v	NOUN
ejpam-4587	217	38	(	(	PUNCT
ejpam-4587	217	39	g	g	NOUN
ejpam-4587	217	40	)	)	PUNCT
ejpam-4587	217	41	.	.	PUNCT
ejpam-4587	218	1	then	then	ADV
ejpam-4587	218	2	|s|=	|s|=	DET
ejpam-4587	218	3	|v	|v	PROPN
ejpam-4587	218	4	(	(	PUNCT
ejpam-4587	218	5	g)|	g)|	PROPN
ejpam-4587	218	6	.	.	PUNCT
ejpam-4587	219	1	since	since	SCONJ
ejpam-4587	219	2	every	every	DET
ejpam-4587	219	3	vertex	vertex	NOUN
ejpam-4587	219	4	of	of	ADP
ejpam-4587	219	5	hv	hv	PROPN
ejpam-4587	219	6	is	be	AUX
ejpam-4587	219	7	adjacent	adjacent	ADJ
ejpam-4587	219	8	to	to	ADP
ejpam-4587	219	9	exactly	exactly	ADV
ejpam-4587	219	10	one	one	NUM
ejpam-4587	219	11	vertex	vertex	NOUN
ejpam-4587	219	12	of	of	ADP
ejpam-4587	219	13	v	v	NOUN
ejpam-4587	219	14	(	(	PUNCT
ejpam-4587	219	15	g	g	NOUN
ejpam-4587	219	16	)	)	PUNCT
ejpam-4587	219	17	,	,	PUNCT
ejpam-4587	219	18	say	say	VERB
ejpam-4587	219	19	x	x	X
ejpam-4587	219	20	∈	∈	PROPN
ejpam-4587	219	21	v	v	NOUN
ejpam-4587	219	22	(	(	PUNCT
ejpam-4587	219	23	v	v	PROPN
ejpam-4587	219	24	+	+	PROPN
ejpam-4587	219	25	hv	hv	NOUN
ejpam-4587	219	26	)	)	PUNCT
ejpam-4587	219	27	,	,	PUNCT
ejpam-4587	219	28	this	this	PRON
ejpam-4587	219	29	implies	imply	VERB
ejpam-4587	219	30	that	that	SCONJ
ejpam-4587	219	31	for	for	ADP
ejpam-4587	219	32	each	each	DET
ejpam-4587	219	33	x	x	SYM
ejpam-4587	219	34	∈	∈	PROPN
ejpam-4587	219	35	v	v	NOUN
ejpam-4587	219	36	(	(	PUNCT
ejpam-4587	219	37	v	v	PROPN
ejpam-4587	219	38	+	+	PROPN
ejpam-4587	219	39	hv	hv	NOUN
ejpam-4587	219	40	)	)	PUNCT
ejpam-4587	219	41	,	,	PUNCT
ejpam-4587	219	42	there	there	PRON
ejpam-4587	219	43	exists	exist	VERB
ejpam-4587	219	44	u	u	PROPN
ejpam-4587	219	45	∈	∈	PROPN
ejpam-4587	219	46	s	s	PART
ejpam-4587	219	47	∩	∩	ADJ
ejpam-4587	219	48	v	v	X
ejpam-4587	219	49	(	(	PUNCT
ejpam-4587	219	50	g	g	NOUN
ejpam-4587	219	51	)	)	PUNCT
ejpam-4587	219	52	such	such	ADJ
ejpam-4587	219	53	that	that	PRON
ejpam-4587	219	54	dg(u	dg(u	ADJ
ejpam-4587	219	55	,	,	PUNCT
ejpam-4587	219	56	x	x	X
ejpam-4587	219	57	)	)	PUNCT
ejpam-4587	219	58	=	=	SYM
ejpam-4587	220	1	2	2	X
ejpam-4587	220	2	.	.	X
ejpam-4587	220	3	therefore	therefore	ADV
ejpam-4587	220	4	,	,	PUNCT
ejpam-4587	220	5	the	the	DET
ejpam-4587	220	6	conclusion	conclusion	NOUN
ejpam-4587	220	7	follows	follow	VERB
ejpam-4587	220	8	.	.	PUNCT
ejpam-4587	221	1	conversely	conversely	ADV
ejpam-4587	221	2	,	,	PUNCT
ejpam-4587	221	3	assume	assume	VERB
ejpam-4587	221	4	that	that	SCONJ
ejpam-4587	221	5	s	s	VERB
ejpam-4587	221	6	∩	∩	ADJ
ejpam-4587	221	7	v	v	X
ejpam-4587	221	8	(	(	PUNCT
ejpam-4587	221	9	v+hv	v+hv	NOUN
ejpam-4587	221	10	)	)	PUNCT
ejpam-4587	221	11	is	be	AUX
ejpam-4587	221	12	a	a	DET
ejpam-4587	221	13	dominating	dominating	NOUN
ejpam-4587	221	14	set	set	NOUN
ejpam-4587	221	15	of	of	ADP
ejpam-4587	221	16	v+hv	v+hv	NOUN
ejpam-4587	221	17	for	for	ADP
ejpam-4587	221	18	all	all	PRON
ejpam-4587	221	19	v	v	ADP
ejpam-4587	221	20	∈	∈	NOUN
ejpam-4587	221	21	v	v	NOUN
ejpam-4587	221	22	(	(	PUNCT
ejpam-4587	221	23	g	g	NOUN
ejpam-4587	221	24	)	)	PUNCT
ejpam-4587	221	25	and	and	CCONJ
ejpam-4587	221	26	s	s	VERB
ejpam-4587	221	27	∩	∩	ADJ
ejpam-4587	221	28	v	v	ADJ
ejpam-4587	221	29	(	(	PUNCT
ejpam-4587	221	30	g	g	NOUN
ejpam-4587	221	31	)	)	PUNCT
ejpam-4587	221	32	is	be	AUX
ejpam-4587	221	33	a	a	DET
ejpam-4587	221	34	weakly	weakly	ADV
ejpam-4587	221	35	connected	connected	ADJ
ejpam-4587	221	36	hop	hop	NOUN
ejpam-4587	221	37	dominating	dominating	NOUN
ejpam-4587	221	38	set	set	NOUN
ejpam-4587	221	39	of	of	ADP
ejpam-4587	221	40	g.	g.	PROPN
ejpam-4587	221	41	suppose	suppose	VERB
ejpam-4587	221	42	s	s	VERB
ejpam-4587	221	43	⊆	⊆	NUM
ejpam-4587	221	44	v	v	NOUN
ejpam-4587	221	45	(	(	PUNCT
ejpam-4587	221	46	g	g	PROPN
ejpam-4587	221	47	◦	◦	NOUN
ejpam-4587	221	48	h	h	NOUN
ejpam-4587	221	49	)	)	PUNCT
ejpam-4587	221	50	is	be	AUX
ejpam-4587	221	51	not	not	PART
ejpam-4587	221	52	a	a	DET
ejpam-4587	221	53	dominating	dominating	NOUN
ejpam-4587	221	54	set	set	NOUN
ejpam-4587	221	55	of	of	ADP
ejpam-4587	221	56	g	g	PROPN
ejpam-4587	221	57	◦	◦	NOUN
ejpam-4587	221	58	h.	h.	NOUN
ejpam-4587	221	59	let	let	VERB
ejpam-4587	222	1	x	x	SYM
ejpam-4587	222	2	∈	∈	PROPN
ejpam-4587	222	3	v	v	X
ejpam-4587	222	4	(	(	PUNCT
ejpam-4587	222	5	g	g	NOUN
ejpam-4587	222	6	)	)	PUNCT
ejpam-4587	222	7	\	\	PROPN
ejpam-4587	222	8	s	s	PART
ejpam-4587	222	9	or	or	CCONJ
ejpam-4587	222	10	x	x	SYM
ejpam-4587	222	11	∈	∈	PROPN
ejpam-4587	222	12	v	v	ADP
ejpam-4587	222	13	(	(	PUNCT
ejpam-4587	222	14	v+hv	v+hv	NOUN
ejpam-4587	222	15	)	)	PUNCT
ejpam-4587	222	16	\	\	PUNCT
ejpam-4587	223	1	s.	s.	PROPN
ejpam-4587	223	2	then	then	ADV
ejpam-4587	223	3	there	there	PRON
ejpam-4587	223	4	exists	exist	VERB
ejpam-4587	223	5	u	u	PROPN
ejpam-4587	223	6	∈	∈	PROPN
ejpam-4587	223	7	v	v	NOUN
ejpam-4587	223	8	(	(	PUNCT
ejpam-4587	223	9	g	g	PROPN
ejpam-4587	223	10	◦	◦	NOUN
ejpam-4587	223	11	h	h	NOUN
ejpam-4587	223	12	)	)	PUNCT
ejpam-4587	223	13	\	\	PROPN
ejpam-4587	224	1	s	s	VERB
ejpam-4587	224	2	such	such	ADJ
ejpam-4587	224	3	that	that	SCONJ
ejpam-4587	224	4	ux	ux	PROPN
ejpam-4587	224	5	∈	∈	PROPN
ejpam-4587	224	6	e(g	e(g	PROPN
ejpam-4587	224	7	◦	◦	PROPN
ejpam-4587	224	8	h	h	NOUN
ejpam-4587	224	9	)	)	PUNCT
ejpam-4587	224	10	,	,	PUNCT
ejpam-4587	224	11	which	which	PRON
ejpam-4587	224	12	is	be	AUX
ejpam-4587	224	13	a	a	DET
ejpam-4587	224	14	contradiction	contradiction	NOUN
ejpam-4587	224	15	in	in	ADP
ejpam-4587	224	16	both	both	DET
ejpam-4587	224	17	cases	case	NOUN
ejpam-4587	224	18	.	.	PUNCT
ejpam-4587	225	1	suppose	suppose	VERB
ejpam-4587	225	2	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4587	225	3	is	be	AUX
ejpam-4587	225	4	disconnected	disconnect	VERB
ejpam-4587	225	5	.	.	PUNCT
ejpam-4587	226	1	then	then	ADV
ejpam-4587	226	2	⟨s	⟨s	VERB
ejpam-4587	226	3	∩	∩	ADJ
ejpam-4587	226	4	v	v	X
ejpam-4587	226	5	(	(	PUNCT
ejpam-4587	226	6	g)⟩w	g)⟩w	PROPN
ejpam-4587	226	7	must	must	AUX
ejpam-4587	226	8	be	be	AUX
ejpam-4587	226	9	disconnected	disconnect	VERB
ejpam-4587	226	10	.	.	PUNCT
ejpam-4587	227	1	this	this	PRON
ejpam-4587	227	2	implies	imply	VERB
ejpam-4587	227	3	that	that	SCONJ
ejpam-4587	227	4	s	s	VERB
ejpam-4587	227	5	∩	∩	ADJ
ejpam-4587	227	6	v	v	ADJ
ejpam-4587	227	7	(	(	PUNCT
ejpam-4587	227	8	g	g	NOUN
ejpam-4587	227	9	)	)	PUNCT
ejpam-4587	227	10	is	be	AUX
ejpam-4587	227	11	not	not	PART
ejpam-4587	227	12	weakly	weakly	ADV
ejpam-4587	227	13	connected	connected	ADJ
ejpam-4587	227	14	hop	hop	NOUN
ejpam-4587	227	15	dominating	dominating	NOUN
ejpam-4587	227	16	set	set	NOUN
ejpam-4587	227	17	of	of	ADP
ejpam-4587	227	18	g	g	PROPN
ejpam-4587	227	19	,	,	PUNCT
ejpam-4587	227	20	which	which	PRON
ejpam-4587	227	21	is	be	AUX
ejpam-4587	227	22	a	a	DET
ejpam-4587	227	23	contradiction	contradiction	NOUN
ejpam-4587	227	24	to	to	ADP
ejpam-4587	227	25	our	our	PRON
ejpam-4587	227	26	assumption	assumption	NOUN
ejpam-4587	227	27	.	.	PUNCT
ejpam-4587	228	1	therefore	therefore	ADV
ejpam-4587	228	2	,	,	PUNCT
ejpam-4587	228	3	s	s	VERB
ejpam-4587	228	4	⊆	⊆	NUM
ejpam-4587	228	5	v	v	NOUN
ejpam-4587	228	6	(	(	PUNCT
ejpam-4587	228	7	g	g	PROPN
ejpam-4587	228	8	◦	◦	NOUN
ejpam-4587	228	9	h	h	NOUN
ejpam-4587	228	10	)	)	PUNCT
ejpam-4587	228	11	is	be	AUX
ejpam-4587	228	12	a	a	DET
ejpam-4587	228	13	weakly	weakly	ADV
ejpam-4587	228	14	connected	connected	ADJ
ejpam-4587	228	15	hop	hop	NOUN
ejpam-4587	228	16	dominating	dominating	NOUN
ejpam-4587	228	17	set	set	NOUN
ejpam-4587	228	18	of	of	ADP
ejpam-4587	228	19	g	g	PROPN
ejpam-4587	228	20	◦	◦	PROPN
ejpam-4587	228	21	h.	h.	NOUN
ejpam-4587	228	22	theorem	theorem	NOUN
ejpam-4587	228	23	11	11	NUM
ejpam-4587	228	24	.	.	PUNCT
ejpam-4587	229	1	let	let	VERB
ejpam-4587	229	2	g	g	NOUN
ejpam-4587	229	3	be	be	AUX
ejpam-4587	229	4	any	any	DET
ejpam-4587	229	5	connected	connected	ADJ
ejpam-4587	229	6	graph	graph	NOUN
ejpam-4587	229	7	of	of	ADP
ejpam-4587	229	8	order	order	NOUN
ejpam-4587	229	9	m	m	VERB
ejpam-4587	229	10	≥	≥	NOUN
ejpam-4587	229	11	2	2	NUM
ejpam-4587	229	12	and	and	CCONJ
ejpam-4587	229	13	h	h	DET
ejpam-4587	229	14	a	a	DET
ejpam-4587	229	15	graph	graph	NOUN
ejpam-4587	229	16	of	of	ADP
ejpam-4587	229	17	order	order	NOUN
ejpam-4587	229	18	n.	n.	VERB
ejpam-4587	229	19	a	a	DET
ejpam-4587	229	20	set	set	NOUN
ejpam-4587	229	21	s	s	PROPN
ejpam-4587	229	22	⊆	⊆	NUM
ejpam-4587	229	23	v	v	NOUN
ejpam-4587	229	24	(	(	PUNCT
ejpam-4587	229	25	g	g	PROPN
ejpam-4587	229	26	◦	◦	NOUN
ejpam-4587	229	27	h	h	NOUN
ejpam-4587	229	28	)	)	PUNCT
ejpam-4587	229	29	is	be	AUX
ejpam-4587	229	30	a	a	DET
ejpam-4587	229	31	weakly	weakly	ADV
ejpam-4587	229	32	connected	connected	ADJ
ejpam-4587	229	33	hop	hop	NOUN
ejpam-4587	229	34	dominating	dominating	NOUN
ejpam-4587	229	35	set	set	NOUN
ejpam-4587	230	1	if	if	SCONJ
ejpam-4587	230	2	|s|=	|s|=	DET
ejpam-4587	230	3	|v	|v	PROPN
ejpam-4587	230	4	(	(	PUNCT
ejpam-4587	230	5	g)|	g)|	NOUN
ejpam-4587	230	6	.	.	PUNCT
ejpam-4587	230	7	proof	proof	NOUN
ejpam-4587	230	8	.	.	PUNCT
ejpam-4587	231	1	let	let	VERB
ejpam-4587	231	2	s1	s1	PROPN
ejpam-4587	231	3	=	=	SYM
ejpam-4587	231	4	v	v	PROPN
ejpam-4587	231	5	(	(	PUNCT
ejpam-4587	231	6	g	g	NOUN
ejpam-4587	231	7	)	)	PUNCT
ejpam-4587	231	8	.	.	PUNCT
ejpam-4587	232	1	then	then	ADV
ejpam-4587	232	2	by	by	ADP
ejpam-4587	232	3	theorem	theorem	NOUN
ejpam-4587	232	4	10	10	NUM
ejpam-4587	232	5	,	,	PUNCT
ejpam-4587	232	6	s1	s1	NOUN
ejpam-4587	232	7	is	be	AUX
ejpam-4587	232	8	a	a	DET
ejpam-4587	232	9	weakly	weakly	ADV
ejpam-4587	232	10	connected	connected	ADJ
ejpam-4587	232	11	hop	hop	NOUN
ejpam-4587	232	12	dominating	dominating	NOUN
ejpam-4587	232	13	set	set	NOUN
ejpam-4587	232	14	of	of	ADP
ejpam-4587	232	15	g	g	PROPN
ejpam-4587	232	16	◦	◦	PROPN
ejpam-4587	232	17	h.	h.	PROPN
ejpam-4587	232	18	thus	thus	ADV
ejpam-4587	232	19	,	,	PUNCT
ejpam-4587	232	20	γwh(g	γwh(g	PROPN
ejpam-4587	232	21	◦	◦	NOUN
ejpam-4587	232	22	h	h	NOUN
ejpam-4587	232	23	)	)	PUNCT
ejpam-4587	232	24	≤	≤	NOUN
ejpam-4587	232	25	|s1|	|s1|	NOUN
ejpam-4587	232	26	=	=	SYM
ejpam-4587	232	27	|v	|v	X
ejpam-4587	232	28	(	(	PUNCT
ejpam-4587	232	29	g)|	g)|	PROPN
ejpam-4587	232	30	.	.	PUNCT
ejpam-4587	233	1	next	next	ADV
ejpam-4587	233	2	,	,	PUNCT
ejpam-4587	233	3	suppose	suppose	VERB
ejpam-4587	233	4	s2	s2	NOUN
ejpam-4587	233	5	is	be	AUX
ejpam-4587	233	6	a	a	DET
ejpam-4587	233	7	γwh	γwh	NOUN
ejpam-4587	233	8	-	-	PUNCT
ejpam-4587	233	9	set	set	NOUN
ejpam-4587	233	10	of	of	ADP
ejpam-4587	233	11	g	g	PROPN
ejpam-4587	233	12	◦	◦	PROPN
ejpam-4587	233	13	h.	h.	NOUN
ejpam-4587	233	14	then	then	ADV
ejpam-4587	233	15	|s2	|s2	VERB
ejpam-4587	233	16	∩	∩	ADJ
ejpam-4587	233	17	v	v	NOUN
ejpam-4587	233	18	(	(	PUNCT
ejpam-4587	233	19	v	v	NOUN
ejpam-4587	233	20	+	+	CCONJ
ejpam-4587	233	21	hv)|	hv)|	NOUN
ejpam-4587	233	22	=	=	SYM
ejpam-4587	233	23	1	1	NUM
ejpam-4587	233	24	for	for	ADP
ejpam-4587	233	25	all	all	DET
ejpam-4587	233	26	v	v	ADP
ejpam-4587	233	27	∈	∈	NUM
ejpam-4587	233	28	v	v	NOUN
ejpam-4587	233	29	(	(	PUNCT
ejpam-4587	233	30	g	g	NOUN
ejpam-4587	233	31	)	)	PUNCT
ejpam-4587	233	32	since	since	SCONJ
ejpam-4587	233	33	every	every	DET
ejpam-4587	233	34	vertex	vertex	NOUN
ejpam-4587	233	35	of	of	ADP
ejpam-4587	233	36	hv	hv	PROPN
ejpam-4587	233	37	is	be	AUX
ejpam-4587	233	38	adjacent	adjacent	ADJ
ejpam-4587	233	39	to	to	ADP
ejpam-4587	233	40	exactly	exactly	ADV
ejpam-4587	233	41	one	one	NUM
ejpam-4587	233	42	vertex	vertex	NOUN
ejpam-4587	233	43	of	of	ADP
ejpam-4587	233	44	v	v	NOUN
ejpam-4587	233	45	(	(	PUNCT
ejpam-4587	233	46	g	g	NOUN
ejpam-4587	233	47	)	)	PUNCT
ejpam-4587	233	48	.	.	PUNCT
ejpam-4587	234	1	thus	thus	ADV
ejpam-4587	234	2	,	,	PUNCT
ejpam-4587	234	3	γwh(g	γwh(g	PROPN
ejpam-4587	234	4	◦	◦	NOUN
ejpam-4587	234	5	h	h	NOUN
ejpam-4587	234	6	)	)	PUNCT
ejpam-4587	234	7	=	=	SYM
ejpam-4587	234	8	|s2|	|s2|	NOUN
ejpam-4587	234	9	=	=	SYM
ejpam-4587	234	10	|v	|v	PROPN
ejpam-4587	234	11	(	(	PUNCT
ejpam-4587	234	12	g)|	g)|	PROPN
ejpam-4587	234	13	.	.	PUNCT
ejpam-4587	235	1	therefore	therefore	ADV
ejpam-4587	235	2	,	,	PUNCT
ejpam-4587	235	3	γwh(g	γwh(g	PROPN
ejpam-4587	235	4	◦	◦	NOUN
ejpam-4587	235	5	h	h	NOUN
ejpam-4587	235	6	)	)	PUNCT
ejpam-4587	235	7	=	=	SYM
ejpam-4587	235	8	|v	|v	PROPN
ejpam-4587	235	9	(	(	PUNCT
ejpam-4587	235	10	g)|	g)|	NOUN
ejpam-4587	235	11	.	.	PUNCT
ejpam-4587	236	1	proposition	proposition	NOUN
ejpam-4587	236	2	6	6	NUM
ejpam-4587	236	3	.	.	PUNCT
ejpam-4587	237	1	let	let	VERB
ejpam-4587	237	2	g	g	PRON
ejpam-4587	237	3	be	be	AUX
ejpam-4587	237	4	a	a	DET
ejpam-4587	237	5	complete	complete	ADJ
ejpam-4587	237	6	graph	graph	NOUN
ejpam-4587	237	7	of	of	ADP
ejpam-4587	237	8	order	order	NOUN
ejpam-4587	237	9	m	m	VERB
ejpam-4587	237	10	≥	≥	NOUN
ejpam-4587	237	11	2	2	NUM
ejpam-4587	237	12	and	and	CCONJ
ejpam-4587	237	13	h	h	NOUN
ejpam-4587	237	14	be	be	VERB
ejpam-4587	237	15	any	any	DET
ejpam-4587	237	16	noncomplete	noncomplete	ADJ
ejpam-4587	237	17	graph	graph	NOUN
ejpam-4587	237	18	of	of	ADP
ejpam-4587	237	19	order	order	NOUN
ejpam-4587	238	1	n.	n.	NOUN
ejpam-4587	238	2	then	then	ADV
ejpam-4587	238	3	γwh(g	γwh(g	PROPN
ejpam-4587	238	4	◦	◦	NOUN
ejpam-4587	238	5	h	h	NOUN
ejpam-4587	238	6	)	)	PUNCT
ejpam-4587	239	1	=	=	SYM
ejpam-4587	239	2	|v	|v	PROPN
ejpam-4587	239	3	(	(	PUNCT
ejpam-4587	239	4	g)|	g)|	NOUN
ejpam-4587	239	5	.	.	PUNCT
ejpam-4587	240	1	proposition	proposition	NOUN
ejpam-4587	240	2	7	7	NUM
ejpam-4587	240	3	.	.	PUNCT
ejpam-4587	241	1	let	let	VERB
ejpam-4587	241	2	g	g	PRON
ejpam-4587	241	3	be	be	AUX
ejpam-4587	241	4	a	a	DET
ejpam-4587	241	5	path	path	NOUN
ejpam-4587	241	6	of	of	ADP
ejpam-4587	241	7	order	order	NOUN
ejpam-4587	241	8	m	m	VERB
ejpam-4587	241	9	≥	≥	NOUN
ejpam-4587	241	10	2	2	NUM
ejpam-4587	241	11	and	and	CCONJ
ejpam-4587	241	12	h	h	NOUN
ejpam-4587	241	13	be	be	VERB
ejpam-4587	241	14	any	any	DET
ejpam-4587	241	15	noncomplete	noncomplete	ADJ
ejpam-4587	241	16	graph	graph	NOUN
ejpam-4587	241	17	of	of	ADP
ejpam-4587	241	18	order	order	NOUN
ejpam-4587	242	1	n.	n.	NOUN
ejpam-4587	242	2	then	then	ADV
ejpam-4587	242	3	γwh(g	γwh(g	PROPN
ejpam-4587	242	4	◦	◦	NOUN
ejpam-4587	242	5	h	h	NOUN
ejpam-4587	242	6	)	)	PUNCT
ejpam-4587	242	7	=	=	SYM
ejpam-4587	242	8	|v	|v	PROPN
ejpam-4587	242	9	(	(	PUNCT
ejpam-4587	242	10	g)|	g)|	NOUN
ejpam-4587	242	11	.	.	PUNCT
ejpam-4587	242	12	proposition	proposition	NOUN
ejpam-4587	242	13	8	8	NUM
ejpam-4587	242	14	.	.	PUNCT
ejpam-4587	243	1	for	for	ADP
ejpam-4587	243	2	any	any	DET
ejpam-4587	243	3	positive	positive	ADJ
ejpam-4587	243	4	integers	integer	NOUN
ejpam-4587	243	5	m	m	PRON
ejpam-4587	243	6	,	,	PUNCT
ejpam-4587	243	7	n	n	PRON
ejpam-4587	243	8	≥	≥	NOUN
ejpam-4587	243	9	2	2	NUM
ejpam-4587	243	10	,	,	PUNCT
ejpam-4587	243	11	we	we	PRON
ejpam-4587	243	12	have	have	AUX
ejpam-4587	243	13	(	(	PUNCT
ejpam-4587	243	14	i	i	NOUN
ejpam-4587	243	15	)	)	PUNCT
ejpam-4587	243	16	γwh(pm	γwh(pm	PROPN
ejpam-4587	243	17	◦	◦	NOUN
ejpam-4587	243	18	kn	kn	NOUN
ejpam-4587	243	19	)	)	PUNCT
ejpam-4587	243	20	=	=	SYM
ejpam-4587	243	21	|v	|v	PROPN
ejpam-4587	243	22	(	(	PUNCT
ejpam-4587	243	23	pm)|	pm)|	PROPN
ejpam-4587	243	24	.	.	PUNCT
ejpam-4587	244	1	j.	j.	PROPN
ejpam-4587	244	2	hamja	hamja	PROPN
ejpam-4587	244	3	,	,	PUNCT
ejpam-4587	244	4	i.	i.	PROPN
ejpam-4587	244	5	aniversario	aniversario	PROPN
ejpam-4587	244	6	,	,	PUNCT
ejpam-4587	244	7	c.	c.	PROPN
ejpam-4587	244	8	merca	merca	PROPN
ejpam-4587	244	9	/	/	SYM
ejpam-4587	244	10	eur	eur	PROPN
ejpam-4587	244	11	.	.	PUNCT
ejpam-4587	245	1	j.	j.	PROPN
ejpam-4587	245	2	pure	pure	PROPN
ejpam-4587	245	3	appl	appl	PROPN
ejpam-4587	245	4	.	.	PROPN
ejpam-4587	245	5	math	math	PROPN
ejpam-4587	245	6	,	,	PUNCT
ejpam-4587	245	7	16	16	NUM
ejpam-4587	245	8	(	(	PUNCT
ejpam-4587	245	9	1	1	NUM
ejpam-4587	245	10	)	)	PUNCT
ejpam-4587	245	11	(	(	PUNCT
ejpam-4587	245	12	2023	2023	NUM
ejpam-4587	245	13	)	)	PUNCT
ejpam-4587	245	14	,	,	PUNCT
ejpam-4587	245	15	454	454	NUM
ejpam-4587	245	16	-	-	SYM
ejpam-4587	245	17	464	464	NUM
ejpam-4587	245	18	462	462	NUM
ejpam-4587	245	19	(	(	PUNCT
ejpam-4587	245	20	ii	ii	NOUN
ejpam-4587	245	21	)	)	PUNCT
ejpam-4587	245	22	γwh(cm	γwh(cm	PUNCT
ejpam-4587	246	1	◦	◦	PROPN
ejpam-4587	246	2	kn	kn	PROPN
ejpam-4587	246	3	)	)	PUNCT
ejpam-4587	246	4	=	=	SYM
ejpam-4587	246	5	|v	|v	PROPN
ejpam-4587	246	6	(	(	PUNCT
ejpam-4587	246	7	cm)|	cm)|	PROPN
ejpam-4587	246	8	.	.	PUNCT
ejpam-4587	247	1	the	the	DET
ejpam-4587	247	2	lexicographic	lexicographic	ADJ
ejpam-4587	247	3	product	product	NOUN
ejpam-4587	247	4	of	of	ADP
ejpam-4587	247	5	graphs	graph	NOUN
ejpam-4587	247	6	g	g	PROPN
ejpam-4587	247	7	and	and	CCONJ
ejpam-4587	247	8	h	h	NOUN
ejpam-4587	247	9	,	,	PUNCT
ejpam-4587	247	10	denoted	denote	VERB
ejpam-4587	247	11	by	by	ADP
ejpam-4587	247	12	g[h	g[h	NOUN
ejpam-4587	247	13	]	]	PUNCT
ejpam-4587	247	14	,	,	PUNCT
ejpam-4587	247	15	is	be	AUX
ejpam-4587	247	16	the	the	DET
ejpam-4587	247	17	graph	graph	NOUN
ejpam-4587	247	18	with	with	ADP
ejpam-4587	247	19	vertex	vertex	NOUN
ejpam-4587	247	20	set	set	VERB
ejpam-4587	247	21	v	v	NOUN
ejpam-4587	247	22	(	(	PUNCT
ejpam-4587	247	23	g[h	g[h	PROPN
ejpam-4587	247	24	]	]	PUNCT
ejpam-4587	247	25	)	)	PUNCT
ejpam-4587	247	26	=	=	SYM
ejpam-4587	247	27	v	v	X
ejpam-4587	247	28	(	(	PUNCT
ejpam-4587	247	29	g)×v	g)×v	PROPN
ejpam-4587	247	30	(	(	PUNCT
ejpam-4587	247	31	h	h	NOUN
ejpam-4587	247	32	)	)	PUNCT
ejpam-4587	247	33	such	such	ADJ
ejpam-4587	247	34	that	that	SCONJ
ejpam-4587	247	35	(	(	PUNCT
ejpam-4587	247	36	v	v	NOUN
ejpam-4587	247	37	,	,	PUNCT
ejpam-4587	247	38	a)(u	a)(u	ADJ
ejpam-4587	247	39	,	,	PUNCT
ejpam-4587	247	40	b	b	X
ejpam-4587	247	41	)	)	PUNCT
ejpam-4587	247	42	∈	∈	NOUN
ejpam-4587	247	43	e(g[h	e(g[h	NOUN
ejpam-4587	247	44	]	]	PUNCT
ejpam-4587	247	45	)	)	PUNCT
ejpam-4587	248	1	if	if	SCONJ
ejpam-4587	248	2	and	and	CCONJ
ejpam-4587	248	3	only	only	ADV
ejpam-4587	248	4	if	if	SCONJ
ejpam-4587	248	5	either	either	DET
ejpam-4587	248	6	uv	uv	PROPN
ejpam-4587	248	7	∈	∈	PROPN
ejpam-4587	248	8	e(g	e(g	PROPN
ejpam-4587	248	9	)	)	PUNCT
ejpam-4587	248	10	or	or	CCONJ
ejpam-4587	248	11	u	u	X
ejpam-4587	248	12	=	=	PROPN
ejpam-4587	248	13	v	v	PROPN
ejpam-4587	248	14	and	and	CCONJ
ejpam-4587	248	15	ab	ab	PROPN
ejpam-4587	248	16	∈	∈	PROPN
ejpam-4587	248	17	e(h	e(h	PROPN
ejpam-4587	248	18	)	)	PUNCT
ejpam-4587	248	19	.	.	PUNCT
ejpam-4587	249	1	observe	observe	VERB
ejpam-4587	249	2	that	that	SCONJ
ejpam-4587	249	3	every	every	DET
ejpam-4587	249	4	non	non	ADJ
ejpam-4587	249	5	-	-	ADJ
ejpam-4587	249	6	empty	empty	ADJ
ejpam-4587	249	7	set	set	NOUN
ejpam-4587	249	8	f	f	PROPN
ejpam-4587	249	9	⊆	⊆	NUM
ejpam-4587	249	10	v	v	NOUN
ejpam-4587	249	11	(	(	PUNCT
ejpam-4587	249	12	g)×v	g)×v	PROPN
ejpam-4587	249	13	(	(	PUNCT
ejpam-4587	249	14	h	h	NOUN
ejpam-4587	249	15	)	)	PUNCT
ejpam-4587	249	16	can	can	AUX
ejpam-4587	249	17	be	be	AUX
ejpam-4587	249	18	expressed	express	VERB
ejpam-4587	249	19	as	as	ADP
ejpam-4587	249	20	f	f	PROPN
ejpam-4587	249	21	=	=	PUNCT
ejpam-4587	249	22	⋃	⋃	PROPN
ejpam-4587	249	23	x∈s	x∈s	NOUN
ejpam-4587	250	1	[	[	X
ejpam-4587	250	2	{	{	PUNCT
ejpam-4587	250	3	x}×	x}×	PROPN
ejpam-4587	250	4	tx	tx	PROPN
ejpam-4587	250	5	]	]	X
ejpam-4587	250	6	,	,	PUNCT
ejpam-4587	250	7	where	where	SCONJ
ejpam-4587	250	8	s	s	VERB
ejpam-4587	250	9	⊆	⊆	NUM
ejpam-4587	250	10	v	v	NOUN
ejpam-4587	250	11	(	(	PUNCT
ejpam-4587	250	12	g	g	NOUN
ejpam-4587	250	13	)	)	PUNCT
ejpam-4587	250	14	,	,	PUNCT
ejpam-4587	250	15	tx	tx	VERB
ejpam-4587	250	16	⊆	⊆	NUM
ejpam-4587	250	17	v	v	NOUN
ejpam-4587	250	18	(	(	PUNCT
ejpam-4587	250	19	h	h	NOUN
ejpam-4587	250	20	)	)	PUNCT
ejpam-4587	250	21	for	for	ADP
ejpam-4587	250	22	each	each	DET
ejpam-4587	250	23	x	x	SYM
ejpam-4587	250	24	∈	∈	PROPN
ejpam-4587	250	25	s	s	X
ejpam-4587	250	26	and	and	CCONJ
ejpam-4587	250	27	tx	tx	PROPN
ejpam-4587	250	28	=	=	PUNCT
ejpam-4587	250	29	{	{	PUNCT
ejpam-4587	250	30	y	y	PROPN
ejpam-4587	250	31	∈	∈	PROPN
ejpam-4587	250	32	v	v	NOUN
ejpam-4587	250	33	(	(	PUNCT
ejpam-4587	250	34	h)|(x	h)|(x	NOUN
ejpam-4587	250	35	,	,	PUNCT
ejpam-4587	250	36	y	y	NOUN
ejpam-4587	250	37	)	)	PUNCT
ejpam-4587	250	38	∈	∈	PROPN
ejpam-4587	250	39	c	c	X
ejpam-4587	250	40	}	}	PUNCT
ejpam-4587	250	41	,	,	PUNCT
ejpam-4587	250	42	harary	harary	NOUN
ejpam-4587	251	1	[	[	X
ejpam-4587	251	2	5	5	NUM
ejpam-4587	251	3	]	]	PUNCT
ejpam-4587	251	4	.	.	PUNCT
ejpam-4587	252	1	lemma	lemma	PROPN
ejpam-4587	252	2	2	2	NUM
ejpam-4587	252	3	.	.	X
ejpam-4587	253	1	for	for	ADP
ejpam-4587	253	2	any	any	DET
ejpam-4587	253	3	non	non	ADJ
ejpam-4587	253	4	-	-	ADJ
ejpam-4587	253	5	trivial	trivial	ADJ
ejpam-4587	253	6	connected	connected	ADJ
ejpam-4587	253	7	graphs	graph	NOUN
ejpam-4587	253	8	g	g	NOUN
ejpam-4587	253	9	and	and	CCONJ
ejpam-4587	253	10	h	h	NOUN
ejpam-4587	253	11	,	,	PUNCT
ejpam-4587	253	12	a	a	DET
ejpam-4587	253	13	set	set	NOUN
ejpam-4587	253	14	f	f	NOUN
ejpam-4587	253	15	=	=	PUNCT
ejpam-4587	253	16	⋃	⋃	PROPN
ejpam-4587	253	17	x∈s	x∈s	NOUN
ejpam-4587	254	1	[	[	X
ejpam-4587	254	2	{	{	PUNCT
ejpam-4587	254	3	x	x	NOUN
ejpam-4587	254	4	}	}	PUNCT
ejpam-4587	254	5	×	×	PROPN
ejpam-4587	254	6	tx	tx	PROPN
ejpam-4587	254	7	]	]	X
ejpam-4587	254	8	⊆	⊆	NUM
ejpam-4587	254	9	v	v	NOUN
ejpam-4587	254	10	(	(	PUNCT
ejpam-4587	254	11	g[h	g[h	PROPN
ejpam-4587	254	12	]	]	PUNCT
ejpam-4587	254	13	)	)	PUNCT
ejpam-4587	254	14	where	where	SCONJ
ejpam-4587	254	15	s	s	VERB
ejpam-4587	254	16	⊆	⊆	NUM
ejpam-4587	254	17	v	v	NOUN
ejpam-4587	254	18	(	(	PUNCT
ejpam-4587	254	19	g	g	NOUN
ejpam-4587	254	20	)	)	PUNCT
ejpam-4587	254	21	and	and	CCONJ
ejpam-4587	254	22	tx	tx	VERB
ejpam-4587	254	23	⊆	⊆	NUM
ejpam-4587	254	24	v	v	NOUN
ejpam-4587	254	25	(	(	PUNCT
ejpam-4587	254	26	h	h	NOUN
ejpam-4587	254	27	)	)	PUNCT
ejpam-4587	254	28	for	for	ADP
ejpam-4587	254	29	all	all	PRON
ejpam-4587	254	30	x	x	SYM
ejpam-4587	254	31	∈	∈	PROPN
ejpam-4587	254	32	s	s	NOUN
ejpam-4587	254	33	,	,	PUNCT
ejpam-4587	254	34	is	be	AUX
ejpam-4587	254	35	a	a	DET
ejpam-4587	254	36	weakly	weakly	ADV
ejpam-4587	254	37	connected	connected	ADJ
ejpam-4587	254	38	hop	hop	NOUN
ejpam-4587	254	39	dominating	dominating	NOUN
ejpam-4587	254	40	set	set	NOUN
ejpam-4587	254	41	of	of	ADP
ejpam-4587	254	42	g[h	g[h	PROPN
ejpam-4587	254	43	]	]	PUNCT
ejpam-4587	254	44	if	if	SCONJ
ejpam-4587	254	45	and	and	CCONJ
ejpam-4587	254	46	only	only	ADV
ejpam-4587	254	47	if	if	SCONJ
ejpam-4587	254	48	s	s	NOUN
ejpam-4587	254	49	is	be	AUX
ejpam-4587	254	50	a	a	DET
ejpam-4587	254	51	weakly	weakly	ADV
ejpam-4587	254	52	connected	connected	ADJ
ejpam-4587	254	53	hop	hop	NOUN
ejpam-4587	254	54	dominating	dominating	NOUN
ejpam-4587	254	55	set	set	NOUN
ejpam-4587	254	56	of	of	ADP
ejpam-4587	254	57	g.	g.	PROPN
ejpam-4587	254	58	proof	proof	PROPN
ejpam-4587	254	59	.	.	PUNCT
ejpam-4587	255	1	suppose	suppose	VERB
ejpam-4587	255	2	f	f	PROPN
ejpam-4587	255	3	is	be	AUX
ejpam-4587	255	4	a	a	DET
ejpam-4587	255	5	weakly	weakly	ADV
ejpam-4587	255	6	connected	connected	ADJ
ejpam-4587	255	7	hop	hop	NOUN
ejpam-4587	255	8	dominating	dominating	NOUN
ejpam-4587	255	9	set	set	NOUN
ejpam-4587	255	10	of	of	ADP
ejpam-4587	255	11	g[h	g[h	PROPN
ejpam-4587	255	12	]	]	PUNCT
ejpam-4587	255	13	.	.	PUNCT
ejpam-4587	256	1	let	let	VERB
ejpam-4587	256	2	s	s	PRON
ejpam-4587	256	3	⊆	⊆	NUM
ejpam-4587	256	4	v	v	NOUN
ejpam-4587	256	5	(	(	PUNCT
ejpam-4587	256	6	g	g	NOUN
ejpam-4587	256	7	)	)	PUNCT
ejpam-4587	256	8	and	and	CCONJ
ejpam-4587	256	9	y	y	PROPN
ejpam-4587	256	10	/∈	/∈	PUNCT
ejpam-4587	257	1	v	v	INTJ
ejpam-4587	257	2	(	(	PUNCT
ejpam-4587	257	3	g	g	NOUN
ejpam-4587	257	4	)	)	PUNCT
ejpam-4587	257	5	\	\	PUNCT
ejpam-4587	258	1	s.	s.	PROPN
ejpam-4587	258	2	choose	choose	VERB
ejpam-4587	258	3	k	k	PROPN
ejpam-4587	258	4	∈	∈	PROPN
ejpam-4587	258	5	v	v	PROPN
ejpam-4587	258	6	(	(	PUNCT
ejpam-4587	258	7	h	h	NOUN
ejpam-4587	258	8	)	)	PUNCT
ejpam-4587	258	9	.	.	PUNCT
ejpam-4587	259	1	then	then	ADV
ejpam-4587	259	2	(	(	PUNCT
ejpam-4587	259	3	y	y	PROPN
ejpam-4587	259	4	,	,	PUNCT
ejpam-4587	259	5	k	k	NOUN
ejpam-4587	259	6	)	)	PUNCT
ejpam-4587	259	7	/∈	/∈	PUNCT
ejpam-4587	259	8	v	v	X
ejpam-4587	259	9	(	(	PUNCT
ejpam-4587	259	10	g[f	g[f	PROPN
ejpam-4587	259	11	]	]	X
ejpam-4587	259	12	)	)	PUNCT
ejpam-4587	259	13	.	.	PUNCT
ejpam-4587	260	1	observe	observe	VERB
ejpam-4587	260	2	that	that	SCONJ
ejpam-4587	260	3	for	for	ADP
ejpam-4587	260	4	(	(	PUNCT
ejpam-4587	260	5	y	y	PROPN
ejpam-4587	260	6	,	,	PUNCT
ejpam-4587	260	7	k	k	NOUN
ejpam-4587	260	8	)	)	PUNCT
ejpam-4587	260	9	/∈	/∈	PUNCT
ejpam-4587	261	1	v	v	NOUN
ejpam-4587	261	2	(	(	PUNCT
ejpam-4587	261	3	g[h	g[h	PROPN
ejpam-4587	261	4	]	]	PUNCT
ejpam-4587	261	5	)	)	PUNCT
ejpam-4587	261	6	\	\	PROPN
ejpam-4587	262	1	f	f	PROPN
ejpam-4587	262	2	,	,	PUNCT
ejpam-4587	262	3	there	there	PRON
ejpam-4587	262	4	exists	exist	VERB
ejpam-4587	262	5	(	(	PUNCT
ejpam-4587	262	6	x	x	X
ejpam-4587	262	7	,	,	PUNCT
ejpam-4587	262	8	l	l	NOUN
ejpam-4587	262	9	)	)	PUNCT
ejpam-4587	262	10	∈	∈	PROPN
ejpam-4587	262	11	f	f	PROPN
ejpam-4587	262	12	such	such	ADJ
ejpam-4587	262	13	that	that	DET
ejpam-4587	262	14	dg[h]((y	dg[h]((y	NOUN
ejpam-4587	262	15	,	,	PUNCT
ejpam-4587	262	16	k	k	NOUN
ejpam-4587	262	17	)	)	PUNCT
ejpam-4587	262	18	,	,	PUNCT
ejpam-4587	262	19	(	(	PUNCT
ejpam-4587	262	20	x	x	X
ejpam-4587	262	21	,	,	PUNCT
ejpam-4587	262	22	l	l	NOUN
ejpam-4587	262	23	)	)	PUNCT
ejpam-4587	262	24	)	)	PUNCT
ejpam-4587	263	1	=	=	SYM
ejpam-4587	263	2	2	2	X
ejpam-4587	263	3	.	.	X
ejpam-4587	263	4	for	for	ADP
ejpam-4587	263	5	all	all	DET
ejpam-4587	263	6	x	x	SYM
ejpam-4587	263	7	∈	∈	PROPN
ejpam-4587	263	8	s	s	PART
ejpam-4587	263	9	and	and	CCONJ
ejpam-4587	263	10	l	l	NOUN
ejpam-4587	263	11	∈	∈	PROPN
ejpam-4587	263	12	tx	tx	PROPN
ejpam-4587	263	13	.	.	PUNCT
ejpam-4587	264	1	it	it	PRON
ejpam-4587	264	2	follows	follow	VERB
ejpam-4587	264	3	that	that	SCONJ
ejpam-4587	264	4	dg(x	dg(x	ADV
ejpam-4587	264	5	,	,	PUNCT
ejpam-4587	264	6	l	l	NOUN
ejpam-4587	264	7	)	)	PUNCT
ejpam-4587	264	8	=	=	SYM
ejpam-4587	264	9	2	2	X
ejpam-4587	264	10	.	.	PUNCT
ejpam-4587	264	11	thus	thus	ADV
ejpam-4587	264	12	,	,	PUNCT
ejpam-4587	264	13	s	s	VERB
ejpam-4587	264	14	is	be	AUX
ejpam-4587	264	15	a	a	DET
ejpam-4587	264	16	hop	hop	NOUN
ejpam-4587	264	17	dominating	dominating	NOUN
ejpam-4587	264	18	set	set	NOUN
ejpam-4587	264	19	of	of	ADP
ejpam-4587	264	20	g.	g.	PROPN
ejpam-4587	264	21	now	now	ADV
ejpam-4587	264	22	,	,	PUNCT
ejpam-4587	264	23	let	let	VERB
ejpam-4587	264	24	w	w	ADV
ejpam-4587	264	25	,	,	PUNCT
ejpam-4587	264	26	x	x	PUNCT
ejpam-4587	264	27	∈	∈	PROPN
ejpam-4587	264	28	s	s	NOUN
ejpam-4587	264	29	,	,	PUNCT
ejpam-4587	264	30	with	with	ADP
ejpam-4587	264	31	x	x	X
ejpam-4587	264	32	̸=	̸=	PROPN
ejpam-4587	264	33	y	y	PROPN
ejpam-4587	264	34	and	and	CCONJ
ejpam-4587	264	35	xy	xy	PROPN
ejpam-4587	264	36	∈	∈	PROPN
ejpam-4587	264	37	e(g	e(g	PROPN
ejpam-4587	264	38	)	)	PUNCT
ejpam-4587	264	39	.	.	PUNCT
ejpam-4587	265	1	if	if	SCONJ
ejpam-4587	265	2	m	m	PROPN
ejpam-4587	265	3	∈	∈	NOUN
ejpam-4587	265	4	tw	tw	NOUN
ejpam-4587	265	5	and	and	CCONJ
ejpam-4587	265	6	l	l	NOUN
ejpam-4587	265	7	∈	∈	PROPN
ejpam-4587	265	8	tx	tx	PROPN
ejpam-4587	265	9	.	.	PUNCT
ejpam-4587	266	1	then	then	ADV
ejpam-4587	266	2	(	(	PUNCT
ejpam-4587	266	3	m	m	PROPN
ejpam-4587	266	4	,	,	PUNCT
ejpam-4587	266	5	w	w	NOUN
ejpam-4587	266	6	)	)	PUNCT
ejpam-4587	266	7	,	,	PUNCT
ejpam-4587	266	8	(	(	PUNCT
ejpam-4587	266	9	l	l	NOUN
ejpam-4587	266	10	,	,	PUNCT
ejpam-4587	266	11	x	x	X
ejpam-4587	266	12	)	)	PUNCT
ejpam-4587	266	13	∈	∈	PROPN
ejpam-4587	266	14	f	f	PROPN
ejpam-4587	266	15	and	and	CCONJ
ejpam-4587	266	16	dg[h]((m	dg[h]((m	PROPN
ejpam-4587	266	17	,	,	PUNCT
ejpam-4587	266	18	w	w	NOUN
ejpam-4587	266	19	)	)	PUNCT
ejpam-4587	266	20	,	,	PUNCT
ejpam-4587	266	21	(	(	PUNCT
ejpam-4587	266	22	x	x	X
ejpam-4587	266	23	,	,	PUNCT
ejpam-4587	266	24	l	l	NOUN
ejpam-4587	266	25	)	)	PUNCT
ejpam-4587	266	26	)	)	PUNCT
ejpam-4587	267	1	=	=	PUNCT
ejpam-4587	267	2	1	1	X
ejpam-4587	267	3	.	.	PUNCT
ejpam-4587	268	1	this	this	PRON
ejpam-4587	268	2	implies	imply	VERB
ejpam-4587	268	3	that	that	SCONJ
ejpam-4587	268	4	(	(	PUNCT
ejpam-4587	268	5	m	m	PROPN
ejpam-4587	268	6	,	,	PUNCT
ejpam-4587	268	7	w)(x	w)(x	PROPN
ejpam-4587	268	8	,	,	PUNCT
ejpam-4587	268	9	l	l	NOUN
ejpam-4587	268	10	)	)	PUNCT
ejpam-4587	268	11	∈	∈	NOUN
ejpam-4587	268	12	e(g[h	e(g[h	NOUN
ejpam-4587	268	13	]	]	PUNCT
ejpam-4587	268	14	)	)	PUNCT
ejpam-4587	268	15	.	.	PUNCT
ejpam-4587	269	1	since	since	SCONJ
ejpam-4587	269	2	dg[h]((y	dg[h]((y	PROPN
ejpam-4587	269	3	,	,	PUNCT
ejpam-4587	269	4	k	k	NOUN
ejpam-4587	269	5	)	)	PUNCT
ejpam-4587	269	6	,	,	PUNCT
ejpam-4587	269	7	(	(	PUNCT
ejpam-4587	269	8	x	x	X
ejpam-4587	269	9	,	,	PUNCT
ejpam-4587	269	10	l	l	NOUN
ejpam-4587	269	11	)	)	PUNCT
ejpam-4587	269	12	)	)	PUNCT
ejpam-4587	269	13	=	=	SYM
ejpam-4587	269	14	2	2	NUM
ejpam-4587	269	15	for	for	ADP
ejpam-4587	269	16	all	all	DET
ejpam-4587	269	17	(	(	PUNCT
ejpam-4587	269	18	y	y	PROPN
ejpam-4587	269	19	,	,	PUNCT
ejpam-4587	269	20	k	k	NOUN
ejpam-4587	269	21	)	)	PUNCT
ejpam-4587	269	22	∈	∈	NOUN
ejpam-4587	269	23	v	v	NOUN
ejpam-4587	269	24	(	(	PUNCT
ejpam-4587	269	25	g[h	g[h	PROPN
ejpam-4587	269	26	]	]	PUNCT
ejpam-4587	269	27	)	)	PUNCT
ejpam-4587	269	28	\	\	PROPN
ejpam-4587	270	1	f	f	PROPN
ejpam-4587	270	2	,	,	PUNCT
ejpam-4587	270	3	(	(	PUNCT
ejpam-4587	270	4	y	y	NOUN
ejpam-4587	270	5	,	,	PUNCT
ejpam-4587	270	6	k)(m	k)(m	PROPN
ejpam-4587	270	7	,	,	PUNCT
ejpam-4587	270	8	w	w	NOUN
ejpam-4587	270	9	)	)	PUNCT
ejpam-4587	270	10	,	,	PUNCT
ejpam-4587	270	11	(	(	PUNCT
ejpam-4587	270	12	y	y	PROPN
ejpam-4587	270	13	,	,	PUNCT
ejpam-4587	270	14	k)(x	k)(x	PROPN
ejpam-4587	270	15	,	,	PUNCT
ejpam-4587	270	16	l	l	NOUN
ejpam-4587	270	17	)	)	PUNCT
ejpam-4587	270	18	∈	∈	NOUN
ejpam-4587	270	19	e(g[h	e(g[h	NOUN
ejpam-4587	270	20	]	]	PUNCT
ejpam-4587	270	21	)	)	PUNCT
ejpam-4587	270	22	.	.	PUNCT
ejpam-4587	271	1	it	it	PRON
ejpam-4587	271	2	follows	follow	VERB
ejpam-4587	271	3	that	that	SCONJ
ejpam-4587	271	4	xy	xy	PROPN
ejpam-4587	271	5	,	,	PUNCT
ejpam-4587	271	6	kl	kl	PROPN
ejpam-4587	271	7	∈	∈	PROPN
ejpam-4587	271	8	e(g[h	e(g[h	X
ejpam-4587	271	9	]	]	PUNCT
ejpam-4587	271	10	)	)	PUNCT
ejpam-4587	271	11	for	for	ADP
ejpam-4587	271	12	all	all	DET
ejpam-4587	271	13	x	x	NOUN
ejpam-4587	271	14	,	,	PUNCT
ejpam-4587	271	15	y	y	PROPN
ejpam-4587	271	16	∈	∈	PROPN
ejpam-4587	271	17	s.	s.	PROPN
ejpam-4587	271	18	hence	hence	ADV
ejpam-4587	271	19	,	,	PUNCT
ejpam-4587	271	20	ng(s	ng(s	NUM
ejpam-4587	271	21	)	)	PUNCT
ejpam-4587	271	22	=	=	SYM
ejpam-4587	271	23	v	v	X
ejpam-4587	271	24	(	(	PUNCT
ejpam-4587	271	25	g	g	NOUN
ejpam-4587	271	26	)	)	PUNCT
ejpam-4587	271	27	.	.	PUNCT
ejpam-4587	272	1	so	so	ADV
ejpam-4587	272	2	,	,	PUNCT
ejpam-4587	272	3	⟨s⟩w	⟨s⟩w	PROPN
ejpam-4587	272	4	is	be	AUX
ejpam-4587	272	5	connected	connect	VERB
ejpam-4587	272	6	.	.	PUNCT
ejpam-4587	273	1	therefore	therefore	ADV
ejpam-4587	273	2	,	,	PUNCT
ejpam-4587	273	3	s	s	VERB
ejpam-4587	273	4	is	be	AUX
ejpam-4587	273	5	a	a	DET
ejpam-4587	273	6	weakly	weakly	ADV
ejpam-4587	273	7	connected	connected	ADJ
ejpam-4587	273	8	hop	hop	NOUN
ejpam-4587	273	9	dominating	dominating	NOUN
ejpam-4587	273	10	set	set	NOUN
ejpam-4587	273	11	of	of	ADP
ejpam-4587	273	12	g.	g.	PROPN
ejpam-4587	273	13	conversely	conversely	ADV
ejpam-4587	273	14	,	,	PUNCT
ejpam-4587	273	15	suppose	suppose	VERB
ejpam-4587	273	16	that	that	SCONJ
ejpam-4587	273	17	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4587	273	18	is	be	AUX
ejpam-4587	273	19	connected	connect	VERB
ejpam-4587	273	20	and	and	CCONJ
ejpam-4587	273	21	s	s	VERB
ejpam-4587	273	22	is	be	AUX
ejpam-4587	273	23	a	a	DET
ejpam-4587	273	24	weakly	weakly	ADV
ejpam-4587	273	25	connected	connected	ADJ
ejpam-4587	273	26	hop	hop	NOUN
ejpam-4587	273	27	dominating	dominating	NOUN
ejpam-4587	273	28	set	set	NOUN
ejpam-4587	273	29	of	of	ADP
ejpam-4587	273	30	g.	g.	PROPN
ejpam-4587	273	31	observe	observe	VERB
ejpam-4587	273	32	that	that	SCONJ
ejpam-4587	273	33	for	for	ADP
ejpam-4587	273	34	every	every	DET
ejpam-4587	273	35	w	w	PROPN
ejpam-4587	273	36	∈	∈	PROPN
ejpam-4587	273	37	s	s	NOUN
ejpam-4587	273	38	,	,	PUNCT
ejpam-4587	273	39	there	there	PRON
ejpam-4587	273	40	exists	exist	VERB
ejpam-4587	273	41	y	y	PROPN
ejpam-4587	273	42	∈	∈	PROPN
ejpam-4587	273	43	s	s	VERB
ejpam-4587	273	44	such	such	ADJ
ejpam-4587	273	45	that	that	SCONJ
ejpam-4587	273	46	dg(w	dg(w	NUM
ejpam-4587	273	47	,	,	PUNCT
ejpam-4587	273	48	y	y	NOUN
ejpam-4587	273	49	)	)	PUNCT
ejpam-4587	273	50	=	=	SYM
ejpam-4587	273	51	2	2	X
ejpam-4587	273	52	.	.	X
ejpam-4587	273	53	choose	choose	VERB
ejpam-4587	273	54	m	m	PROPN
ejpam-4587	273	55	∈	∈	PROPN
ejpam-4587	273	56	tx	tx	PROPN
ejpam-4587	273	57	.	.	PUNCT
ejpam-4587	274	1	then	then	ADV
ejpam-4587	274	2	(	(	PUNCT
ejpam-4587	274	3	m	m	PROPN
ejpam-4587	274	4	,	,	PUNCT
ejpam-4587	274	5	x	x	NOUN
ejpam-4587	274	6	)	)	PUNCT
ejpam-4587	274	7	∈	∈	PROPN
ejpam-4587	274	8	f	f	PROPN
ejpam-4587	274	9	and	and	CCONJ
ejpam-4587	274	10	dg[h]((y	dg[h]((y	PROPN
ejpam-4587	274	11	,	,	PUNCT
ejpam-4587	274	12	k	k	NOUN
ejpam-4587	274	13	)	)	PUNCT
ejpam-4587	274	14	,	,	PUNCT
ejpam-4587	274	15	(	(	PUNCT
ejpam-4587	274	16	x	x	X
ejpam-4587	274	17	,	,	PUNCT
ejpam-4587	274	18	m	m	NOUN
ejpam-4587	274	19	)	)	PUNCT
ejpam-4587	274	20	)	)	PUNCT
ejpam-4587	275	1	=	=	SYM
ejpam-4587	275	2	2	2	X
ejpam-4587	275	3	.	.	X
ejpam-4587	275	4	hence	hence	ADV
ejpam-4587	275	5	,	,	PUNCT
ejpam-4587	275	6	(	(	PUNCT
ejpam-4587	275	7	y	y	PROPN
ejpam-4587	275	8	,	,	PUNCT
ejpam-4587	275	9	k)(x	k)(x	PROPN
ejpam-4587	275	10	,	,	PUNCT
ejpam-4587	275	11	l	l	NOUN
ejpam-4587	275	12	)	)	PUNCT
ejpam-4587	275	13	∈	∈	NOUN
ejpam-4587	275	14	e(g[h	e(g[h	NOUN
ejpam-4587	275	15	]	]	PUNCT
ejpam-4587	275	16	)	)	PUNCT
ejpam-4587	275	17	for	for	ADP
ejpam-4587	275	18	all	all	PRON
ejpam-4587	275	19	(	(	PUNCT
ejpam-4587	275	20	y	y	PROPN
ejpam-4587	275	21	,	,	PUNCT
ejpam-4587	275	22	k	k	NOUN
ejpam-4587	275	23	)	)	PUNCT
ejpam-4587	275	24	∈	∈	NOUN
ejpam-4587	275	25	v	v	NOUN
ejpam-4587	275	26	(	(	PUNCT
ejpam-4587	275	27	g(h	g(h	NOUN
ejpam-4587	275	28	)	)	PUNCT
ejpam-4587	275	29	)	)	PUNCT
ejpam-4587	275	30	\	\	PROPN
ejpam-4587	276	1	f	f	PROPN
ejpam-4587	276	2	.	.	PUNCT
ejpam-4587	277	1	thus	thus	ADV
ejpam-4587	277	2	,	,	PUNCT
ejpam-4587	277	3	ng[h](f	ng[h](f	NOUN
ejpam-4587	277	4	)	)	PUNCT
ejpam-4587	277	5	=	=	SYM
ejpam-4587	277	6	v	v	X
ejpam-4587	277	7	(	(	PUNCT
ejpam-4587	277	8	g[h	g[h	PROPN
ejpam-4587	277	9	]	]	PUNCT
ejpam-4587	277	10	)	)	PUNCT
ejpam-4587	277	11	.	.	PUNCT
ejpam-4587	278	1	therefore	therefore	ADV
ejpam-4587	278	2	,	,	PUNCT
ejpam-4587	278	3	⟨f	⟨f	NUM
ejpam-4587	278	4	⟩w	⟩w	PROPN
ejpam-4587	278	5	is	be	AUX
ejpam-4587	278	6	connected	connect	VERB
ejpam-4587	278	7	.	.	PUNCT
ejpam-4587	279	1	consequently	consequently	ADV
ejpam-4587	279	2	,	,	PUNCT
ejpam-4587	279	3	f	f	PROPN
ejpam-4587	279	4	is	be	AUX
ejpam-4587	279	5	a	a	DET
ejpam-4587	279	6	weakly	weakly	ADV
ejpam-4587	279	7	connected	connected	ADJ
ejpam-4587	279	8	hop	hop	NOUN
ejpam-4587	279	9	dominating	dominating	NOUN
ejpam-4587	279	10	set	set	NOUN
ejpam-4587	279	11	of	of	ADP
ejpam-4587	279	12	g[h	g[h	PROPN
ejpam-4587	279	13	]	]	PUNCT
ejpam-4587	279	14	.	.	PUNCT
ejpam-4587	280	1	theorem	theorem	NOUN
ejpam-4587	280	2	12	12	NUM
ejpam-4587	280	3	.	.	PUNCT
ejpam-4587	281	1	for	for	ADP
ejpam-4587	281	2	any	any	DET
ejpam-4587	281	3	non	non	ADJ
ejpam-4587	281	4	-	-	ADJ
ejpam-4587	281	5	trivial	trivial	ADJ
ejpam-4587	281	6	connected	connected	ADJ
ejpam-4587	281	7	graphs	graph	NOUN
ejpam-4587	281	8	g	g	PROPN
ejpam-4587	281	9	and	and	CCONJ
ejpam-4587	281	10	h.	h.	PROPN
ejpam-4587	281	11	a	a	DET
ejpam-4587	281	12	set	set	NOUN
ejpam-4587	281	13	f	f	NOUN
ejpam-4587	281	14	=	=	PUNCT
ejpam-4587	281	15	⋃	⋃	PROPN
ejpam-4587	281	16	x∈s	x∈s	NOUN
ejpam-4587	282	1	[	[	X
ejpam-4587	282	2	{	{	PUNCT
ejpam-4587	282	3	x	x	NOUN
ejpam-4587	282	4	}	}	PUNCT
ejpam-4587	282	5	×	×	PROPN
ejpam-4587	282	6	tx	tx	PROPN
ejpam-4587	282	7	]	]	X
ejpam-4587	282	8	⊆	⊆	NUM
ejpam-4587	282	9	v	v	NOUN
ejpam-4587	282	10	(	(	PUNCT
ejpam-4587	282	11	g[h	g[h	PROPN
ejpam-4587	282	12	]	]	PUNCT
ejpam-4587	282	13	)	)	PUNCT
ejpam-4587	282	14	where	where	SCONJ
ejpam-4587	282	15	s	s	VERB
ejpam-4587	282	16	⊆	⊆	NUM
ejpam-4587	282	17	v	v	NOUN
ejpam-4587	282	18	(	(	PUNCT
ejpam-4587	282	19	g	g	NOUN
ejpam-4587	282	20	)	)	PUNCT
ejpam-4587	282	21	and	and	CCONJ
ejpam-4587	282	22	tx	tx	VERB
ejpam-4587	282	23	⊆	⊆	NUM
ejpam-4587	282	24	v	v	NOUN
ejpam-4587	282	25	(	(	PUNCT
ejpam-4587	282	26	h	h	NOUN
ejpam-4587	282	27	)	)	PUNCT
ejpam-4587	282	28	for	for	ADP
ejpam-4587	282	29	all	all	PRON
ejpam-4587	282	30	x	x	SYM
ejpam-4587	282	31	∈	∈	PROPN
ejpam-4587	282	32	s	s	NOUN
ejpam-4587	282	33	,	,	PUNCT
ejpam-4587	282	34	is	be	AUX
ejpam-4587	282	35	a	a	DET
ejpam-4587	282	36	weakly	weakly	ADV
ejpam-4587	282	37	connected	connected	ADJ
ejpam-4587	282	38	hop	hop	NOUN
ejpam-4587	282	39	dominating	dominating	NOUN
ejpam-4587	282	40	set	set	NOUN
ejpam-4587	282	41	of	of	ADP
ejpam-4587	282	42	g[h	g[h	PROPN
ejpam-4587	282	43	]	]	PUNCT
ejpam-4587	282	44	if	if	SCONJ
ejpam-4587	282	45	and	and	CCONJ
ejpam-4587	282	46	only	only	ADV
ejpam-4587	282	47	if	if	SCONJ
ejpam-4587	282	48	s	s	NOUN
ejpam-4587	282	49	is	be	AUX
ejpam-4587	282	50	a	a	DET
ejpam-4587	282	51	weakly	weakly	ADV
ejpam-4587	282	52	connected	connected	ADJ
ejpam-4587	282	53	hop	hop	NOUN
ejpam-4587	282	54	dominating	dominating	NOUN
ejpam-4587	282	55	set	set	NOUN
ejpam-4587	282	56	of	of	ADP
ejpam-4587	282	57	g	g	PROPN
ejpam-4587	282	58	and	and	CCONJ
ejpam-4587	282	59	tx	tx	PROPN
ejpam-4587	282	60	is	be	AUX
ejpam-4587	282	61	a	a	DET
ejpam-4587	282	62	dominating	dominating	NOUN
ejpam-4587	282	63	set	set	VERB
ejpam-4587	282	64	in	in	ADP
ejpam-4587	282	65	h	h	NOUN
ejpam-4587	282	66	for	for	ADP
ejpam-4587	282	67	all	all	DET
ejpam-4587	282	68	x	x	SYM
ejpam-4587	282	69	∈	∈	PROPN
ejpam-4587	282	70	s.	s.	PROPN
ejpam-4587	282	71	proof	proof	PROPN
ejpam-4587	282	72	.	.	PUNCT
ejpam-4587	283	1	suppose	suppose	VERB
ejpam-4587	283	2	f	f	PROPN
ejpam-4587	283	3	is	be	AUX
ejpam-4587	283	4	a	a	DET
ejpam-4587	283	5	weakly	weakly	ADV
ejpam-4587	283	6	connected	connected	ADJ
ejpam-4587	283	7	hop	hop	NOUN
ejpam-4587	283	8	dominating	dominating	NOUN
ejpam-4587	283	9	set	set	NOUN
ejpam-4587	283	10	of	of	ADP
ejpam-4587	283	11	g[h	g[h	PROPN
ejpam-4587	283	12	]	]	PUNCT
ejpam-4587	283	13	.	.	PUNCT
ejpam-4587	284	1	let	let	VERB
ejpam-4587	284	2	y	y	PROPN
ejpam-4587	284	3	∈	∈	PROPN
ejpam-4587	284	4	v	v	NOUN
ejpam-4587	284	5	(	(	PUNCT
ejpam-4587	284	6	g)\s	g)\s	VERB
ejpam-4587	284	7	and	and	CCONJ
ejpam-4587	284	8	choose	choose	VERB
ejpam-4587	284	9	k	k	PROPN
ejpam-4587	284	10	∈	∈	PROPN
ejpam-4587	284	11	v	v	PROPN
ejpam-4587	284	12	(	(	PUNCT
ejpam-4587	284	13	h	h	NOUN
ejpam-4587	284	14	)	)	PUNCT
ejpam-4587	284	15	.	.	PUNCT
ejpam-4587	285	1	then	then	ADV
ejpam-4587	285	2	(	(	PUNCT
ejpam-4587	285	3	y	y	PROPN
ejpam-4587	285	4	,	,	PUNCT
ejpam-4587	285	5	k	k	NOUN
ejpam-4587	285	6	)	)	PUNCT
ejpam-4587	285	7	∈	∈	NOUN
ejpam-4587	285	8	v	v	ADP
ejpam-4587	286	1	[	[	X
ejpam-4587	286	2	g	g	X
ejpam-4587	286	3	]	]	X
ejpam-4587	286	4	.	.	PUNCT
ejpam-4587	287	1	since	since	SCONJ
ejpam-4587	287	2	f	f	PROPN
ejpam-4587	287	3	is	be	AUX
ejpam-4587	287	4	a	a	DET
ejpam-4587	287	5	dominating	dominating	NOUN
ejpam-4587	287	6	set	set	NOUN
ejpam-4587	287	7	of	of	ADP
ejpam-4587	287	8	g[h	g[h	PROPN
ejpam-4587	287	9	]	]	PUNCT
ejpam-4587	287	10	,	,	PUNCT
ejpam-4587	287	11	there	there	PRON
ejpam-4587	287	12	exists	exist	VERB
ejpam-4587	287	13	(	(	PUNCT
ejpam-4587	287	14	x	x	X
ejpam-4587	287	15	,	,	PUNCT
ejpam-4587	287	16	l	l	NOUN
ejpam-4587	287	17	)	)	PUNCT
ejpam-4587	287	18	∈	∈	PROPN
ejpam-4587	288	1	f	f	PROPN
ejpam-4587	288	2	such	such	ADJ
ejpam-4587	288	3	that	that	DET
ejpam-4587	288	4	(	(	PUNCT
ejpam-4587	288	5	y	y	PROPN
ejpam-4587	288	6	,	,	PUNCT
ejpam-4587	288	7	k)(x	k)(x	PROPN
ejpam-4587	288	8	,	,	PUNCT
ejpam-4587	288	9	l	l	NOUN
ejpam-4587	288	10	)	)	PUNCT
ejpam-4587	288	11	∈	∈	NOUN
ejpam-4587	288	12	e(g[h	e(g[h	NOUN
ejpam-4587	288	13	]	]	PUNCT
ejpam-4587	288	14	)	)	PUNCT
ejpam-4587	288	15	.	.	PUNCT
ejpam-4587	289	1	it	it	PRON
ejpam-4587	289	2	follows	follow	VERB
ejpam-4587	289	3	that	that	SCONJ
ejpam-4587	289	4	x	x	PUNCT
ejpam-4587	289	5	∈	∈	NOUN
ejpam-4587	289	6	s	s	X
ejpam-4587	289	7	and	and	CCONJ
ejpam-4587	289	8	y	y	PROPN
ejpam-4587	289	9	∈	∈	PROPN
ejpam-4587	289	10	ng(x	ng(x	NUM
ejpam-4587	289	11	)	)	PUNCT
ejpam-4587	289	12	.	.	PUNCT
ejpam-4587	290	1	this	this	PRON
ejpam-4587	290	2	shows	show	VERB
ejpam-4587	290	3	that	that	SCONJ
ejpam-4587	290	4	s	s	VERB
ejpam-4587	290	5	is	be	AUX
ejpam-4587	290	6	a	a	DET
ejpam-4587	290	7	dominating	dominating	NOUN
ejpam-4587	290	8	set	set	NOUN
ejpam-4587	290	9	of	of	ADP
ejpam-4587	290	10	g.	g.	PROPN
ejpam-4587	290	11	furthermore	furthermore	ADV
ejpam-4587	290	12	,	,	PUNCT
ejpam-4587	290	13	by	by	ADP
ejpam-4587	290	14	lemma	lemma	PROPN
ejpam-4587	290	15	2	2	NUM
ejpam-4587	290	16	,	,	PUNCT
ejpam-4587	290	17	⟨s⟩w	⟨s⟩w	NOUN
ejpam-4587	290	18	is	be	AUX
ejpam-4587	290	19	connected	connect	VERB
ejpam-4587	290	20	.	.	PUNCT
ejpam-4587	291	1	now	now	ADV
ejpam-4587	291	2	,	,	PUNCT
ejpam-4587	291	3	let	let	VERB
ejpam-4587	291	4	v	v	NUM
ejpam-4587	291	5	∈	∈	PROPN
ejpam-4587	291	6	v	v	NOUN
ejpam-4587	291	7	(	(	PUNCT
ejpam-4587	291	8	g	g	NOUN
ejpam-4587	291	9	)	)	PUNCT
ejpam-4587	291	10	\	\	PROPN
ejpam-4587	291	11	s	s	PART
ejpam-4587	291	12	and	and	CCONJ
ejpam-4587	291	13	choose	choose	VERB
ejpam-4587	291	14	k	k	PROPN
ejpam-4587	291	15	∈	∈	PROPN
ejpam-4587	291	16	v	v	PROPN
ejpam-4587	291	17	(	(	PUNCT
ejpam-4587	291	18	h	h	NOUN
ejpam-4587	291	19	)	)	PUNCT
ejpam-4587	291	20	for	for	ADP
ejpam-4587	291	21	all	all	DET
ejpam-4587	291	22	k	k	PROPN
ejpam-4587	291	23	∈	∈	PROPN
ejpam-4587	291	24	tx	tx	PROPN
ejpam-4587	291	25	.	.	PUNCT
ejpam-4587	292	1	then	then	ADV
ejpam-4587	292	2	(	(	PUNCT
ejpam-4587	292	3	x	x	X
ejpam-4587	292	4	,	,	PUNCT
ejpam-4587	292	5	m	m	NOUN
ejpam-4587	292	6	)	)	PUNCT
ejpam-4587	292	7	∈	∈	PROPN
ejpam-4587	292	8	v	v	NOUN
ejpam-4587	292	9	(	(	PUNCT
ejpam-4587	292	10	g[h	g[h	PROPN
ejpam-4587	292	11	]	]	PUNCT
ejpam-4587	292	12	)	)	PUNCT
ejpam-4587	292	13	\	\	PROPN
ejpam-4587	293	1	f	f	PROPN
ejpam-4587	293	2	which	which	PRON
ejpam-4587	293	3	implies	imply	VERB
ejpam-4587	293	4	that	that	SCONJ
ejpam-4587	293	5	km	km	PROPN
ejpam-4587	293	6	∈	∈	PROPN
ejpam-4587	293	7	e(h	e(h	PROPN
ejpam-4587	293	8	)	)	PUNCT
ejpam-4587	293	9	for	for	ADP
ejpam-4587	293	10	all	all	DET
ejpam-4587	293	11	k	k	PROPN
ejpam-4587	293	12	∈	∈	PROPN
ejpam-4587	293	13	tx	tx	PROPN
ejpam-4587	293	14	.	.	PUNCT
ejpam-4587	294	1	therefore	therefore	ADV
ejpam-4587	294	2	,	,	PUNCT
ejpam-4587	294	3	nh	nh	PROPN
ejpam-4587	295	1	[	[	X
ejpam-4587	295	2	tx	tx	X
ejpam-4587	295	3	]	]	X
ejpam-4587	295	4	=	=	SYM
ejpam-4587	295	5	v	v	X
ejpam-4587	295	6	(	(	PUNCT
ejpam-4587	295	7	h	h	NOUN
ejpam-4587	295	8	)	)	PUNCT
ejpam-4587	295	9	.	.	PUNCT
ejpam-4587	296	1	that	that	PRON
ejpam-4587	296	2	is	be	AUX
ejpam-4587	296	3	tx	tx	PROPN
ejpam-4587	296	4	is	be	AUX
ejpam-4587	296	5	a	a	DET
ejpam-4587	296	6	dominating	dominating	NOUN
ejpam-4587	296	7	set	set	VERB
ejpam-4587	296	8	in	in	ADP
ejpam-4587	296	9	h.	h.	NOUN
ejpam-4587	296	10	conversely	conversely	ADV
ejpam-4587	296	11	,	,	PUNCT
ejpam-4587	296	12	suppose	suppose	VERB
ejpam-4587	296	13	that	that	SCONJ
ejpam-4587	296	14	s	s	VERB
ejpam-4587	296	15	is	be	AUX
ejpam-4587	296	16	weakly	weakly	ADV
ejpam-4587	296	17	connected	connected	ADJ
ejpam-4587	296	18	hop	hop	NOUN
ejpam-4587	296	19	dominating	dominating	NOUN
ejpam-4587	296	20	set	set	NOUN
ejpam-4587	296	21	of	of	ADP
ejpam-4587	296	22	g.	g.	PROPN
ejpam-4587	296	23	let	let	VERB
ejpam-4587	296	24	y	y	PROPN
ejpam-4587	296	25	∈	∈	PROPN
ejpam-4587	296	26	v	v	NOUN
ejpam-4587	296	27	(	(	PUNCT
ejpam-4587	296	28	g)\s	g)\s	VERB
ejpam-4587	296	29	and	and	CCONJ
ejpam-4587	296	30	choose	choose	VERB
ejpam-4587	296	31	n	n	PRON
ejpam-4587	296	32	∈	∈	PROPN
ejpam-4587	296	33	v	v	NOUN
ejpam-4587	296	34	(	(	PUNCT
ejpam-4587	296	35	h	h	NOUN
ejpam-4587	296	36	)	)	PUNCT
ejpam-4587	296	37	.	.	PUNCT
ejpam-4587	297	1	then	then	ADV
ejpam-4587	297	2	(	(	PUNCT
ejpam-4587	297	3	y	y	NOUN
ejpam-4587	297	4	,	,	PUNCT
ejpam-4587	297	5	n	n	CCONJ
ejpam-4587	297	6	)	)	PUNCT
ejpam-4587	297	7	∈	∈	NOUN
ejpam-4587	297	8	v	v	NOUN
ejpam-4587	297	9	(	(	PUNCT
ejpam-4587	297	10	g[h	g[h	PROPN
ejpam-4587	297	11	]	]	PUNCT
ejpam-4587	297	12	)	)	PUNCT
ejpam-4587	297	13	\	\	PROPN
ejpam-4587	297	14	f	f	PROPN
ejpam-4587	297	15	and	and	CCONJ
ejpam-4587	297	16	ny	ny	PROPN
ejpam-4587	297	17	∈	∈	PROPN
ejpam-4587	297	18	e(h	e(h	PROPN
ejpam-4587	297	19	)	)	PUNCT
ejpam-4587	297	20	for	for	ADP
ejpam-4587	297	21	all	all	PRON
ejpam-4587	297	22	n	n	PRON
ejpam-4587	297	23	∈	∈	PROPN
ejpam-4587	297	24	tx	tx	PROPN
ejpam-4587	297	25	.	.	PUNCT
ejpam-4587	298	1	hence	hence	ADV
ejpam-4587	298	2	,	,	PUNCT
ejpam-4587	298	3	references	reference	VERB
ejpam-4587	298	4	463	463	NUM
ejpam-4587	298	5	nh	nh	NOUN
ejpam-4587	299	1	[	[	X
ejpam-4587	299	2	tx	tx	X
ejpam-4587	299	3	]	]	X
ejpam-4587	299	4	=	=	SYM
ejpam-4587	299	5	v	v	X
ejpam-4587	299	6	(	(	PUNCT
ejpam-4587	299	7	h	h	NOUN
ejpam-4587	299	8	)	)	PUNCT
ejpam-4587	299	9	.	.	PUNCT
ejpam-4587	300	1	this	this	PRON
ejpam-4587	300	2	shows	show	VERB
ejpam-4587	300	3	that	that	SCONJ
ejpam-4587	300	4	tx	tx	PROPN
ejpam-4587	300	5	is	be	AUX
ejpam-4587	300	6	a	a	DET
ejpam-4587	300	7	dominating	dominating	NOUN
ejpam-4587	300	8	set	set	NOUN
ejpam-4587	300	9	of	of	ADP
ejpam-4587	300	10	g.	g.	PROPN
ejpam-4587	300	11	since	since	SCONJ
ejpam-4587	300	12	(	(	PUNCT
ejpam-4587	300	13	y	y	PROPN
ejpam-4587	300	14	,	,	PUNCT
ejpam-4587	300	15	n	n	CCONJ
ejpam-4587	300	16	)	)	PUNCT
ejpam-4587	300	17	∈	∈	NOUN
ejpam-4587	300	18	v	v	NOUN
ejpam-4587	300	19	(	(	PUNCT
ejpam-4587	300	20	g[h])\s	g[h])\s	VERB
ejpam-4587	300	21	,	,	PUNCT
ejpam-4587	300	22	there	there	PRON
ejpam-4587	300	23	exists	exist	VERB
ejpam-4587	300	24	(	(	PUNCT
ejpam-4587	300	25	x	x	X
ejpam-4587	300	26	,	,	PUNCT
ejpam-4587	300	27	l	l	NOUN
ejpam-4587	300	28	)	)	PUNCT
ejpam-4587	300	29	,	,	PUNCT
ejpam-4587	300	30	(	(	PUNCT
ejpam-4587	301	1	x	x	X
ejpam-4587	301	2	,	,	PUNCT
ejpam-4587	301	3	m	m	NOUN
ejpam-4587	301	4	)	)	PUNCT
ejpam-4587	301	5	∈	∈	PROPN
ejpam-4587	301	6	f	f	PROPN
ejpam-4587	301	7	such	such	ADJ
ejpam-4587	302	1	that	that	PRON
ejpam-4587	302	2	dg[h]((x	dg[h]((x	NOUN
ejpam-4587	302	3	,	,	PUNCT
ejpam-4587	302	4	l	l	NOUN
ejpam-4587	302	5	)	)	PUNCT
ejpam-4587	302	6	,	,	PUNCT
ejpam-4587	302	7	(	(	PUNCT
ejpam-4587	302	8	y	y	NOUN
ejpam-4587	302	9	,	,	PUNCT
ejpam-4587	302	10	n	n	CCONJ
ejpam-4587	302	11	)	)	PUNCT
ejpam-4587	302	12	)	)	PUNCT
ejpam-4587	302	13	=	=	SYM
ejpam-4587	302	14	2	2	NUM
ejpam-4587	302	15	for	for	ADP
ejpam-4587	302	16	all	all	DET
ejpam-4587	302	17	x	x	SYM
ejpam-4587	302	18	∈	∈	PROPN
ejpam-4587	302	19	s	s	NOUN
ejpam-4587	302	20	and	and	CCONJ
ejpam-4587	302	21	l	l	NOUN
ejpam-4587	302	22	,	,	PUNCT
ejpam-4587	302	23	m	m	PROPN
ejpam-4587	302	24	∈	∈	ADJ
ejpam-4587	302	25	v	v	ADP
ejpam-4587	302	26	(	(	PUNCT
ejpam-4587	302	27	h	h	NOUN
ejpam-4587	302	28	)	)	PUNCT
ejpam-4587	302	29	.	.	PUNCT
ejpam-4587	303	1	this	this	PRON
ejpam-4587	303	2	implies	imply	VERB
ejpam-4587	303	3	that	that	SCONJ
ejpam-4587	303	4	(	(	PUNCT
ejpam-4587	303	5	x	x	X
ejpam-4587	303	6	,	,	PUNCT
ejpam-4587	303	7	m)(y	m)(y	NOUN
ejpam-4587	303	8	,	,	PUNCT
ejpam-4587	303	9	n	n	CCONJ
ejpam-4587	303	10	)	)	PUNCT
ejpam-4587	303	11	∈	∈	NOUN
ejpam-4587	303	12	e(g[h	e(g[h	NOUN
ejpam-4587	303	13	]	]	PUNCT
ejpam-4587	303	14	)	)	PUNCT
ejpam-4587	303	15	.	.	PUNCT
ejpam-4587	304	1	hence	hence	ADV
ejpam-4587	304	2	,	,	PUNCT
ejpam-4587	304	3	ng[h][f	ng[h][f	PROPN
ejpam-4587	304	4	]	]	X
ejpam-4587	304	5	=	=	SYM
ejpam-4587	304	6	v	v	X
ejpam-4587	304	7	(	(	PUNCT
ejpam-4587	304	8	g[h	g[h	PROPN
ejpam-4587	304	9	]	]	PUNCT
ejpam-4587	304	10	)	)	PUNCT
ejpam-4587	304	11	and	and	CCONJ
ejpam-4587	304	12	⟨f	⟨f	NUM
ejpam-4587	304	13	⟩w	⟩w	PROPN
ejpam-4587	304	14	is	be	AUX
ejpam-4587	304	15	connected	connect	VERB
ejpam-4587	304	16	.	.	PUNCT
ejpam-4587	305	1	consequently	consequently	ADV
ejpam-4587	305	2	,	,	PUNCT
ejpam-4587	305	3	f	f	PROPN
ejpam-4587	305	4	is	be	AUX
ejpam-4587	305	5	a	a	DET
ejpam-4587	305	6	weakly	weakly	ADV
ejpam-4587	305	7	connected	connected	ADJ
ejpam-4587	305	8	hop	hop	NOUN
ejpam-4587	305	9	dominating	dominating	NOUN
ejpam-4587	305	10	set	set	NOUN
ejpam-4587	305	11	of	of	ADP
ejpam-4587	305	12	g[h	g[h	PROPN
ejpam-4587	305	13	]	]	PUNCT
ejpam-4587	305	14	.	.	PUNCT
ejpam-4587	306	1	proposition	proposition	NOUN
ejpam-4587	306	2	9	9	NUM
ejpam-4587	306	3	.	.	PUNCT
ejpam-4587	307	1	the	the	DET
ejpam-4587	307	2	weakly	weakly	ADJ
ejpam-4587	307	3	connected	connect	VERB
ejpam-4587	307	4	hop	hop	NOUN
ejpam-4587	307	5	domination	domination	NOUN
ejpam-4587	307	6	numbers	number	NOUN
ejpam-4587	307	7	of	of	ADP
ejpam-4587	307	8	pm[pn	pm[pn	NOUN
ejpam-4587	307	9	]	]	PUNCT
ejpam-4587	307	10	,	,	PUNCT
ejpam-4587	307	11	pm[cn	pm[cn	NOUN
ejpam-4587	307	12	]	]	X
ejpam-4587	307	13	,	,	PUNCT
ejpam-4587	307	14	and	and	CCONJ
ejpam-4587	307	15	pm[kn	pm[kn	X
ejpam-4587	307	16	]	]	X
ejpam-4587	307	17	for	for	ADP
ejpam-4587	307	18	positive	positive	ADJ
ejpam-4587	307	19	integers	integer	NOUN
ejpam-4587	307	20	m	m	PRON
ejpam-4587	307	21	,	,	PUNCT
ejpam-4587	307	22	n	n	PRON
ejpam-4587	307	23	are	be	AUX
ejpam-4587	307	24	given	give	VERB
ejpam-4587	307	25	as	as	SCONJ
ejpam-4587	307	26	follows	follow	VERB
ejpam-4587	307	27	:	:	PUNCT
ejpam-4587	307	28	(	(	PUNCT
ejpam-4587	307	29	i	i	NOUN
ejpam-4587	307	30	)	)	PUNCT
ejpam-4587	307	31	γwh(pm[pn	γwh(pm[pn	VERB
ejpam-4587	307	32	]	]	PUNCT
ejpam-4587	307	33	)	)	PUNCT
ejpam-4587	307	34	=	=	SYM
ejpam-4587	307	35	γwh(pm	γwh(pm	NOUN
ejpam-4587	307	36	)	)	PUNCT
ejpam-4587	307	37	·	·	PUNCT
ejpam-4587	307	38	γwh(pn	γwh(pn	NUM
ejpam-4587	307	39	)	)	PUNCT
ejpam-4587	307	40	,	,	PUNCT
ejpam-4587	307	41	m	m	PROPN
ejpam-4587	307	42	,	,	PUNCT
ejpam-4587	307	43	n	n	PRON
ejpam-4587	307	44	≥	≥	NOUN
ejpam-4587	307	45	2	2	NUM
ejpam-4587	307	46	(	(	PUNCT
ejpam-4587	307	47	ii	ii	NOUN
ejpam-4587	307	48	)	)	PUNCT
ejpam-4587	307	49	γwh(pm[cn	γwh(pm[cn	VERB
ejpam-4587	307	50	]	]	NOUN
ejpam-4587	307	51	)	)	PUNCT
ejpam-4587	307	52	=	=	SYM
ejpam-4587	307	53	γwh(pm	γwh(pm	NOUN
ejpam-4587	307	54	)	)	PUNCT
ejpam-4587	307	55	·	·	PUNCT
ejpam-4587	308	1	γwh(cn	γwh(cn	PROPN
ejpam-4587	308	2	)	)	PUNCT
ejpam-4587	308	3	,	,	PUNCT
ejpam-4587	308	4	m	m	VERB
ejpam-4587	308	5	≥	≥	NOUN
ejpam-4587	308	6	2	2	NUM
ejpam-4587	308	7	and	and	CCONJ
ejpam-4587	308	8	n	n	PRON
ejpam-4587	308	9	≥	≥	NOUN
ejpam-4587	308	10	3	3	NUM
ejpam-4587	308	11	(	(	PUNCT
ejpam-4587	308	12	ii	ii	NOUN
ejpam-4587	308	13	)	)	PUNCT
ejpam-4587	308	14	γwh(pm[kn	γwh(pm[kn	NOUN
ejpam-4587	308	15	]	]	X
ejpam-4587	308	16	)	)	PUNCT
ejpam-4587	308	17	=	=	SYM
ejpam-4587	308	18	γwh(pm	γwh(pm	NOUN
ejpam-4587	308	19	)	)	PUNCT
ejpam-4587	308	20	·	·	PUNCT
ejpam-4587	309	1	2	2	NUM
ejpam-4587	309	2	,	,	PUNCT
ejpam-4587	309	3	m	m	PRON
ejpam-4587	309	4	,	,	PUNCT
ejpam-4587	309	5	n	n	PRON
ejpam-4587	309	6	≥	≥	NOUN
ejpam-4587	309	7	2	2	NUM
ejpam-4587	309	8	4	4	NUM
ejpam-4587	309	9	.	.	PUNCT
ejpam-4587	309	10	conclusion	conclusion	NOUN
ejpam-4587	309	11	this	this	DET
ejpam-4587	309	12	paper	paper	NOUN
ejpam-4587	309	13	was	be	AUX
ejpam-4587	309	14	able	able	ADJ
ejpam-4587	309	15	to	to	PART
ejpam-4587	309	16	introduced	introduced	VERB
ejpam-4587	309	17	the	the	DET
ejpam-4587	309	18	concept	concept	NOUN
ejpam-4587	309	19	of	of	ADP
ejpam-4587	309	20	weakly	weakly	ADJ
ejpam-4587	309	21	connected	connected	ADJ
ejpam-4587	309	22	hop	hop	NOUN
ejpam-4587	309	23	dominating	dominating	NOUN
ejpam-4587	309	24	sets	set	NOUN
ejpam-4587	309	25	of	of	ADP
ejpam-4587	309	26	some	some	DET
ejpam-4587	309	27	graphs	graph	NOUN
ejpam-4587	309	28	and	and	CCONJ
ejpam-4587	309	29	discussed	discuss	VERB
ejpam-4587	309	30	its	its	PRON
ejpam-4587	309	31	characterizations	characterization	NOUN
ejpam-4587	309	32	in	in	ADP
ejpam-4587	309	33	the	the	DET
ejpam-4587	309	34	shadow	shadow	NOUN
ejpam-4587	309	35	graph	graph	NOUN
ejpam-4587	309	36	,	,	PUNCT
ejpam-4587	309	37	join	join	NOUN
ejpam-4587	309	38	,	,	PUNCT
ejpam-4587	309	39	corona	corona	NOUN
ejpam-4587	309	40	and	and	CCONJ
ejpam-4587	309	41	lexicographic	lexicographic	ADJ
ejpam-4587	309	42	product	product	NOUN
ejpam-4587	309	43	of	of	ADP
ejpam-4587	309	44	two	two	NUM
ejpam-4587	309	45	graphs	graph	NOUN
ejpam-4587	309	46	.	.	PUNCT
ejpam-4587	310	1	the	the	DET
ejpam-4587	310	2	weakly	weakly	ADV
ejpam-4587	310	3	connected	connect	VERB
ejpam-4587	310	4	hop	hop	NOUN
ejpam-4587	310	5	domination	domination	NOUN
ejpam-4587	310	6	number	number	NOUN
ejpam-4587	310	7	of	of	ADP
ejpam-4587	310	8	these	these	DET
ejpam-4587	310	9	graphs	graph	NOUN
ejpam-4587	310	10	are	be	AUX
ejpam-4587	310	11	determined	determine	VERB
ejpam-4587	310	12	.	.	PUNCT
ejpam-4587	311	1	for	for	ADP
ejpam-4587	311	2	further	further	ADJ
ejpam-4587	311	3	study	study	NOUN
ejpam-4587	311	4	,	,	PUNCT
ejpam-4587	311	5	the	the	DET
ejpam-4587	311	6	authors	author	NOUN
ejpam-4587	311	7	recommend	recommend	VERB
ejpam-4587	311	8	to	to	PART
ejpam-4587	311	9	establish	establish	VERB
ejpam-4587	311	10	other	other	ADJ
ejpam-4587	311	11	variants	variant	NOUN
ejpam-4587	311	12	related	relate	VERB
ejpam-4587	311	13	to	to	ADP
ejpam-4587	311	14	the	the	DET
ejpam-4587	311	15	concept	concept	NOUN
ejpam-4587	311	16	of	of	ADP
ejpam-4587	311	17	the	the	DET
ejpam-4587	311	18	weakly	weakly	ADV
ejpam-4587	311	19	connected	connected	ADJ
ejpam-4587	311	20	hop	hop	NOUN
ejpam-4587	311	21	dominating	dominating	NOUN
ejpam-4587	311	22	sets	set	NOUN
ejpam-4587	311	23	.	.	PUNCT
ejpam-4587	312	1	also	also	ADV
ejpam-4587	312	2	,	,	PUNCT
ejpam-4587	312	3	the	the	DET
ejpam-4587	312	4	characterization	characterization	NOUN
ejpam-4587	312	5	of	of	ADP
ejpam-4587	312	6	the	the	DET
ejpam-4587	312	7	weakly	weakly	ADV
ejpam-4587	312	8	connected	connected	ADJ
ejpam-4587	312	9	hop	hop	NOUN
ejpam-4587	312	10	dominating	dominating	NOUN
ejpam-4587	312	11	sets	set	NOUN
ejpam-4587	312	12	under	under	ADP
ejpam-4587	312	13	some	some	DET
ejpam-4587	312	14	binary	binary	ADJ
ejpam-4587	312	15	operations	operation	NOUN
ejpam-4587	312	16	that	that	PRON
ejpam-4587	312	17	are	be	AUX
ejpam-4587	312	18	not	not	PART
ejpam-4587	312	19	discussed	discuss	VERB
ejpam-4587	312	20	in	in	ADP
ejpam-4587	312	21	the	the	DET
ejpam-4587	312	22	study	study	NOUN
ejpam-4587	312	23	and	and	CCONJ
ejpam-4587	312	24	determine	determine	VERB
ejpam-4587	312	25	the	the	DET
ejpam-4587	312	26	exact	exact	ADJ
ejpam-4587	312	27	values	value	NOUN
ejpam-4587	312	28	of	of	ADP
ejpam-4587	312	29	the	the	DET
ejpam-4587	312	30	parameters	parameter	NOUN
ejpam-4587	312	31	of	of	ADP
ejpam-4587	312	32	the	the	DET
ejpam-4587	312	33	said	say	VERB
ejpam-4587	312	34	graphs	graph	NOUN
ejpam-4587	312	35	are	be	AUX
ejpam-4587	312	36	also	also	ADV
ejpam-4587	312	37	encouraged	encourage	VERB
ejpam-4587	312	38	.	.	PUNCT
ejpam-4587	313	1	acknowledgements	acknowledgement	NOUN
ejpam-4587	313	2	the	the	DET
ejpam-4587	313	3	authors	author	NOUN
ejpam-4587	313	4	would	would	AUX
ejpam-4587	313	5	like	like	VERB
ejpam-4587	313	6	to	to	PART
ejpam-4587	313	7	thank	thank	VERB
ejpam-4587	313	8	the	the	DET
ejpam-4587	313	9	referees	referee	NOUN
ejpam-4587	313	10	for	for	ADP
ejpam-4587	313	11	their	their	PRON
ejpam-4587	313	12	invaluable	invaluable	ADJ
ejpam-4587	313	13	comments	comment	NOUN
ejpam-4587	313	14	and	and	CCONJ
ejpam-4587	313	15	suggestions	suggestion	NOUN
ejpam-4587	313	16	which	which	PRON
ejpam-4587	313	17	led	lead	VERB
ejpam-4587	313	18	to	to	ADP
ejpam-4587	313	19	the	the	DET
ejpam-4587	313	20	enhancement	enhancement	NOUN
ejpam-4587	313	21	of	of	ADP
ejpam-4587	313	22	the	the	DET
ejpam-4587	313	23	paper	paper	NOUN
ejpam-4587	313	24	.	.	PUNCT
ejpam-4587	314	1	this	this	DET
ejpam-4587	314	2	study	study	NOUN
ejpam-4587	314	3	has	have	AUX
ejpam-4587	314	4	been	be	AUX
ejpam-4587	314	5	supported	support	VERB
ejpam-4587	314	6	by	by	ADP
ejpam-4587	314	7	the	the	DET
ejpam-4587	314	8	department	department	PROPN
ejpam-4587	314	9	of	of	ADP
ejpam-4587	314	10	science	science	NOUN
ejpam-4587	314	11	and	and	CCONJ
ejpam-4587	314	12	technology	technology	NOUN
ejpam-4587	314	13	-	-	PUNCT
ejpam-4587	314	14	accelerated	accelerate	VERB
ejpam-4587	314	15	science	science	NOUN
ejpam-4587	314	16	and	and	CCONJ
ejpam-4587	314	17	technology	technology	NOUN
ejpam-4587	314	18	human	human	ADJ
ejpam-4587	314	19	resource	resource	NOUN
ejpam-4587	314	20	development	development	NOUN
ejpam-4587	314	21	program	program	NOUN
ejpam-4587	314	22	(	(	PUNCT
ejpam-4587	314	23	dost	dost	NOUN
ejpam-4587	314	24	-	-	PUNCT
ejpam-4587	314	25	asthrdp	asthrdp	NOUN
ejpam-4587	314	26	)	)	PUNCT
ejpam-4587	314	27	,	,	PUNCT
ejpam-4587	314	28	mindanao	mindanao	PROPN
ejpam-4587	314	29	state	state	PROPN
ejpam-4587	314	30	university	university	PROPN
ejpam-4587	314	31	tawitawi	tawitawi	PROPN
ejpam-4587	314	32	college	college	NOUN
ejpam-4587	314	33	of	of	ADP
ejpam-4587	314	34	technology	technology	NOUN
ejpam-4587	314	35	and	and	CCONJ
ejpam-4587	314	36	oceanography	oceanography	NOUN
ejpam-4587	314	37	and	and	CCONJ
ejpam-4587	314	38	mindanao	mindanao	PROPN
ejpam-4587	314	39	state	state	PROPN
ejpam-4587	314	40	university	university	PROPN
ejpam-4587	314	41	iligan	iligan	PROPN
ejpam-4587	314	42	institute	institute	PROPN
ejpam-4587	314	43	of	of	ADP
ejpam-4587	314	44	technology	technology	PROPN
ejpam-4587	314	45	.	.	PUNCT
ejpam-4587	315	1	references	reference	NOUN
ejpam-4587	315	2	[	[	X
ejpam-4587	315	3	1	1	X
ejpam-4587	315	4	]	]	X
ejpam-4587	315	5	s.k	s.k	PROPN
ejpam-4587	315	6	.	.	PROPN
ejpam-4587	315	7	ayyaswamy	ayyaswamy	PROPN
ejpam-4587	315	8	and	and	CCONJ
ejpam-4587	315	9	c.	c.	PROPN
ejpam-4587	315	10	natarajan	natarajan	PROPN
ejpam-4587	315	11	.	.	PROPN
ejpam-4587	316	1	hop	hop	PROPN
ejpam-4587	316	2	domination	domination	NOUN
ejpam-4587	316	3	in	in	ADP
ejpam-4587	316	4	graphs	graph	NOUN
ejpam-4587	316	5	.	.	PUNCT
ejpam-4587	317	1	discussiones	discussione	NOUN
ejpam-4587	317	2	mathematicae	mathematicae	PROPN
ejpam-4587	317	3	graph	graph	NOUN
ejpam-4587	317	4	theory	theory	NOUN
ejpam-4587	317	5	.	.	PUNCT
ejpam-4587	318	1	[	[	X
ejpam-4587	318	2	2	2	X
ejpam-4587	318	3	]	]	PUNCT
ejpam-4587	318	4	g.	g.	PROPN
ejpam-4587	318	5	domke	domke	PROPN
ejpam-4587	318	6	,	,	PUNCT
ejpam-4587	318	7	j.	j.	PROPN
ejpam-4587	318	8	hattingh	hattingh	PROPN
ejpam-4587	318	9	,	,	PUNCT
ejpam-4587	318	10	and	and	CCONJ
ejpam-4587	318	11	l.	l.	PROPN
ejpam-4587	318	12	markus	markus	PROPN
ejpam-4587	318	13	.	.	PUNCT
ejpam-4587	319	1	on	on	ADP
ejpam-4587	319	2	weakly	weakly	ADJ
ejpam-4587	319	3	connected	connected	ADJ
ejpam-4587	319	4	domination	domination	NOUN
ejpam-4587	319	5	in	in	ADP
ejpam-4587	319	6	graphs	graphs	PROPN
ejpam-4587	319	7	ii	ii	PROPN
ejpam-4587	319	8	.	.	PROPN
ejpam-4587	319	9	discrete	discrete	ADJ
ejpam-4587	319	10	mathematics	mathematic	NOUN
ejpam-4587	319	11	,	,	PUNCT
ejpam-4587	319	12	305:112	305:112	PROPN
ejpam-4587	319	13	–	–	PUNCT
ejpam-4587	319	14	122	122	NUM
ejpam-4587	319	15	,	,	PUNCT
ejpam-4587	319	16	2005	2005	NUM
ejpam-4587	319	17	.	.	PUNCT
ejpam-4587	320	1	[	[	X
ejpam-4587	320	2	3	3	X
ejpam-4587	320	3	]	]	X
ejpam-4587	320	4	j.	j.	PROPN
ejpam-4587	320	5	dunbar	dunbar	PROPN
ejpam-4587	320	6	,	,	PUNCT
ejpam-4587	320	7	j.	j.	PROPN
ejpam-4587	320	8	grossman	grossman	PROPN
ejpam-4587	320	9	,	,	PUNCT
ejpam-4587	320	10	j.	j.	PROPN
ejpam-4587	320	11	hattingh	hattingh	PROPN
ejpam-4587	320	12	,	,	PUNCT
ejpam-4587	320	13	s.	s.	PROPN
ejpam-4587	320	14	hedetniemi	hedetniemi	PROPN
ejpam-4587	320	15	,	,	PUNCT
ejpam-4587	320	16	and	and	CCONJ
ejpam-4587	320	17	a.	a.	NOUN
ejpam-4587	320	18	mcrae	mcrae	PROPN
ejpam-4587	320	19	.	.	PUNCT
ejpam-4587	321	1	on	on	ADP
ejpam-4587	321	2	weakly	weakly	ADJ
ejpam-4587	321	3	connected	connected	ADJ
ejpam-4587	321	4	domination	domination	NOUN
ejpam-4587	321	5	in	in	ADP
ejpam-4587	321	6	graphs	graph	NOUN
ejpam-4587	321	7	.	.	PUNCT
ejpam-4587	322	1	discrete	discrete	ADJ
ejpam-4587	322	2	mathematics	mathematic	NOUN
ejpam-4587	322	3	,	,	PUNCT
ejpam-4587	322	4	pages	page	NOUN
ejpam-4587	322	5	261–269	261–269	NUM
ejpam-4587	322	6	,	,	PUNCT
ejpam-4587	322	7	1997	1997	NUM
ejpam-4587	322	8	.	.	PUNCT
ejpam-4587	323	1	references	reference	NOUN
ejpam-4587	323	2	464	464	NUM
ejpam-4587	324	1	[	[	X
ejpam-4587	324	2	4	4	X
ejpam-4587	324	3	]	]	PUNCT
ejpam-4587	324	4	j.	j.	PROPN
ejpam-4587	324	5	hamja	hamja	PROPN
ejpam-4587	324	6	,	,	PUNCT
ejpam-4587	324	7	i.	i.	PROPN
ejpam-4587	324	8	aniversario	aniversario	PROPN
ejpam-4587	324	9	,	,	PUNCT
ejpam-4587	324	10	and	and	CCONJ
ejpam-4587	324	11	h.	h.	PROPN
ejpam-4587	324	12	rara	rara	PROPN
ejpam-4587	324	13	.	.	PUNCT
ejpam-4587	325	1	on	on	ADP
ejpam-4587	325	2	weakly	weakly	ADJ
ejpam-4587	325	3	connected	connect	VERB
ejpam-4587	325	4	closed	close	VERB
ejpam-4587	325	5	geodetic	geodetic	ADJ
ejpam-4587	325	6	domination	domination	NOUN
ejpam-4587	325	7	in	in	ADP
ejpam-4587	325	8	graphs	graph	NOUN
ejpam-4587	325	9	under	under	ADP
ejpam-4587	325	10	some	some	DET
ejpam-4587	325	11	binary	binary	ADJ
ejpam-4587	325	12	operations	operation	NOUN
ejpam-4587	325	13	.	.	PUNCT
ejpam-4587	326	1	europian	europian	ADJ
ejpam-4587	326	2	journal	journal	PROPN
ejpam-4587	326	3	of	of	ADP
ejpam-4587	326	4	pure	pure	ADJ
ejpam-4587	326	5	and	and	CCONJ
ejpam-4587	326	6	applied	applied	ADJ
ejpam-4587	326	7	mathematics	mathematic	NOUN
ejpam-4587	326	8	,	,	PUNCT
ejpam-4587	326	9	15(2):736–752	15(2):736–752	PROPN
ejpam-4587	326	10	,	,	PUNCT
ejpam-4587	326	11	2022	2022	NUM
ejpam-4587	326	12	.	.	PUNCT
ejpam-4587	327	1	[	[	X
ejpam-4587	327	2	5	5	NUM
ejpam-4587	327	3	]	]	PUNCT
ejpam-4587	327	4	f.	f.	PROPN
ejpam-4587	327	5	harary	harary	PROPN
ejpam-4587	327	6	.	.	PUNCT
ejpam-4587	328	1	graph	graph	NOUN
ejpam-4587	328	2	theory	theory	NOUN
ejpam-4587	328	3	.	.	PUNCT
ejpam-4587	329	1	addison	addison	PROPN
ejpam-4587	329	2	-	-	PUNCT
ejpam-4587	329	3	wesley	wesley	PROPN
ejpam-4587	329	4	publishing	publishing	PROPN
ejpam-4587	329	5	company	company	PROPN
ejpam-4587	329	6	,	,	PUNCT
ejpam-4587	329	7	inc	inc	PROPN
ejpam-4587	329	8	.	.	PROPN
ejpam-4587	329	9	,	,	PUNCT
ejpam-4587	329	10	usa	usa	PROPN
ejpam-4587	329	11	,	,	PUNCT
ejpam-4587	329	12	1969	1969	NUM
ejpam-4587	329	13	.	.	PUNCT
ejpam-4587	330	1	[	[	X
ejpam-4587	330	2	6	6	NUM
ejpam-4587	330	3	]	]	PUNCT
ejpam-4587	330	4	r.	r.	PROPN
ejpam-4587	330	5	jayagopal	jayagopal	PROPN
ejpam-4587	330	6	and	and	CCONJ
ejpam-4587	330	7	v.	v.	ADP
ejpam-4587	330	8	raju	raju	PROPN
ejpam-4587	330	9	.	.	PUNCT
ejpam-4587	331	1	domination	domination	NOUN
ejpam-4587	331	2	parameters	parameter	NOUN
ejpam-4587	331	3	in	in	ADP
ejpam-4587	331	4	shadow	shadow	NOUN
ejpam-4587	331	5	graph	graph	NOUN
ejpam-4587	331	6	and	and	CCONJ
ejpam-4587	331	7	path	path	NOUN
ejpam-4587	331	8	connected	connected	ADJ
ejpam-4587	331	9	graph	graph	NOUN
ejpam-4587	331	10	.	.	PUNCT
ejpam-4587	332	1	international	international	ADJ
ejpam-4587	332	2	journal	journal	NOUN
ejpam-4587	332	3	of	of	ADP
ejpam-4587	332	4	mathematics	mathematic	NOUN
ejpam-4587	332	5	and	and	CCONJ
ejpam-4587	332	6	its	its	PRON
ejpam-4587	332	7	applications	application	NOUN
ejpam-4587	332	8	,	,	PUNCT
ejpam-4587	332	9	6(2	6(2	NUM
ejpam-4587	332	10	-	-	SYM
ejpam-4587	332	11	b):167	b):167	NOUN
ejpam-4587	332	12	–	–	PUNCT
ejpam-4587	332	13	172	172	NUM
ejpam-4587	332	14	,	,	PUNCT
ejpam-4587	332	15	2018	2018	NUM
ejpam-4587	332	16	.	.	PUNCT
ejpam-4587	333	1	[	[	X
ejpam-4587	333	2	7	7	X
ejpam-4587	333	3	]	]	X
ejpam-4587	333	4	s.	s.	PROPN
ejpam-4587	333	5	canoy	canoy	PROPN
ejpam-4587	333	6	jr	jr	PROPN
ejpam-4587	333	7	.	.	PROPN
ejpam-4587	333	8	,	,	PUNCT
ejpam-4587	333	9	r.	r.	PROPN
ejpam-4587	333	10	mollejon	mollejon	NOUN
ejpam-4587	333	11	,	,	PUNCT
ejpam-4587	333	12	and	and	CCONJ
ejpam-4587	333	13	j.g	j.g	PROPN
ejpam-4587	333	14	e.	e.	PROPN
ejpam-4587	333	15	canoy	canoy	PROPN
ejpam-4587	333	16	.	.	PUNCT
ejpam-4587	334	1	hop	hop	PROPN
ejpam-4587	334	2	dominating	dominating	NOUN
ejpam-4587	334	3	sets	set	NOUN
ejpam-4587	334	4	in	in	ADP
ejpam-4587	334	5	graphs	graph	NOUN
ejpam-4587	334	6	under	under	ADP
ejpam-4587	334	7	binary	binary	ADJ
ejpam-4587	334	8	operations	operation	NOUN
ejpam-4587	334	9	.	.	PUNCT
ejpam-4587	335	1	european	european	ADJ
ejpam-4587	335	2	journal	journal	PROPN
ejpam-4587	335	3	of	of	ADP
ejpam-4587	335	4	pure	pure	ADJ
ejpam-4587	335	5	and	and	CCONJ
ejpam-4587	335	6	applied	applied	ADJ
ejpam-4587	335	7	mathematics	mathematic	NOUN
ejpam-4587	335	8	,	,	PUNCT
ejpam-4587	335	9	12(4):1455	12(4):1455	NUM
ejpam-4587	335	10	–	–	PUNCT
ejpam-4587	335	11	1463	1463	NUM
ejpam-4587	335	12	,	,	PUNCT
ejpam-4587	335	13	2019	2019	NUM
ejpam-4587	335	14	.	.	PUNCT
ejpam-4587	336	1	[	[	X
ejpam-4587	336	2	8	8	NUM
ejpam-4587	336	3	]	]	X
ejpam-4587	336	4	c.	c.	PROPN
ejpam-4587	336	5	natarajan	natarajan	PROPN
ejpam-4587	336	6	and	and	CCONJ
ejpam-4587	336	7	s.k	s.k	PROPN
ejpam-4587	336	8	.	.	PROPN
ejpam-4587	336	9	ayyaswamy	ayyaswamy	PROPN
ejpam-4587	336	10	.	.	PUNCT
ejpam-4587	337	1	hop	hop	PROPN
ejpam-4587	337	2	domination	domination	NOUN
ejpam-4587	337	3	in	in	ADP
ejpam-4587	337	4	graphs	graph	NOUN
ejpam-4587	337	5	-	-	PUNCT
ejpam-4587	337	6	ii	ii	NOUN
ejpam-4587	337	7	.	.	PUNCT
ejpam-4587	338	1	versita	versita	PROPN
ejpam-4587	338	2	.	.	PUNCT
ejpam-4587	338	3	,	,	PUNCT
ejpam-4587	338	4	23(2):187–199	23(2):187–199	PROPN
ejpam-4587	338	5	.	.	NOUN
ejpam-4587	338	6	,	,	PUNCT
ejpam-4587	338	7	2015	2015	NUM
ejpam-4587	338	8	.	.	PUNCT
ejpam-4587	339	1	[	[	X
ejpam-4587	339	2	9	9	NUM
ejpam-4587	339	3	]	]	X
ejpam-4587	339	4	r.	r.	PROPN
ejpam-4587	339	5	patangan	patangan	PROPN
ejpam-4587	339	6	,	,	PUNCT
ejpam-4587	339	7	i.	i.	PROPN
ejpam-4587	339	8	aniversario	aniversario	PROPN
ejpam-4587	339	9	,	,	PUNCT
ejpam-4587	339	10	and	and	CCONJ
ejpam-4587	339	11	jr	jr	PROPN
ejpam-4587	339	12	.	.	PUNCT
ejpam-4587	339	13	a.	a.	PROPN
ejpam-4587	339	14	rosalio	rosalio	PROPN
ejpam-4587	339	15	.	.	PUNCT
ejpam-4587	340	1	weakly	weakly	ADV
ejpam-4587	340	2	connected	connected	ADJ
ejpam-4587	340	3	closed	closed	ADJ
ejpam-4587	340	4	geodetic	geodetic	ADJ
ejpam-4587	340	5	numbers	number	NOUN
ejpam-4587	340	6	of	of	ADP
ejpam-4587	340	7	graphs	graph	NOUN
ejpam-4587	340	8	.	.	PUNCT
ejpam-4587	341	1	international	international	ADJ
ejpam-4587	341	2	journal	journal	PROPN
ejpam-4587	341	3	of	of	ADP
ejpam-4587	341	4	mathematical	mathematical	ADJ
ejpam-4587	341	5	analysis	analysis	NOUN
ejpam-4587	341	6	.	.	PUNCT
ejpam-4587	341	7	,	,	PUNCT
ejpam-4587	341	8	10(6):257	10(6):257	PROPN
ejpam-4587	341	9	–	–	PUNCT
ejpam-4587	341	10	270	270	NUM
ejpam-4587	341	11	.	.	NUM
ejpam-4587	341	12	,	,	PUNCT
ejpam-4587	341	13	2016	2016	NUM
ejpam-4587	341	14	.	.	PUNCT
ejpam-4587	342	1	[	[	X
ejpam-4587	342	2	10	10	NUM
ejpam-4587	342	3	]	]	X
ejpam-4587	342	4	e.	e.	PROPN
ejpam-4587	342	5	sandueta	sandueta	PROPN
ejpam-4587	342	6	and	and	CCONJ
ejpam-4587	342	7	jr	jr	PROPN
ejpam-4587	342	8	.	.	PROPN
ejpam-4587	342	9	s.	s.	PROPN
ejpam-4587	342	10	canoy	canoy	PROPN
ejpam-4587	342	11	.	.	PUNCT
ejpam-4587	343	1	weakly	weakly	ADJ
ejpam-4587	343	2	connected	connected	ADJ
ejpam-4587	343	3	domination	domination	NOUN
ejpam-4587	343	4	in	in	ADP
ejpam-4587	343	5	graphs	graph	NOUN
ejpam-4587	343	6	resulting	result	VERB
ejpam-4587	343	7	from	from	ADP
ejpam-4587	343	8	some	some	DET
ejpam-4587	343	9	graph	graph	NOUN
ejpam-4587	343	10	operations	operation	NOUN
ejpam-4587	343	11	.	.	PUNCT
ejpam-4587	344	1	international	international	ADJ
ejpam-4587	344	2	mathematical	mathematical	PROPN
ejpam-4587	344	3	forum	forum	PROPN
ejpam-4587	344	4	.	.	PUNCT
ejpam-4587	344	5	,	,	PUNCT
ejpam-4587	344	6	6(21):1031	6(21):1031	NOUN
ejpam-4587	344	7	–	–	PUNCT
ejpam-4587	344	8	1035	1035	NUM
ejpam-4587	344	9	.	.	PUNCT
ejpam-4587	344	10	,	,	PUNCT
ejpam-4587	344	11	2011	2011	NUM
ejpam-4587	344	12	.	.	PUNCT
ejpam-4587	345	1	[	[	X
ejpam-4587	345	2	11	11	NUM
ejpam-4587	345	3	]	]	X
ejpam-4587	345	4	e.	e.	PROPN
ejpam-4587	345	5	sandueta	sandueta	PROPN
ejpam-4587	345	6	and	and	CCONJ
ejpam-4587	345	7	jr	jr	PROPN
ejpam-4587	345	8	.	.	PROPN
ejpam-4587	345	9	s.	s.	PROPN
ejpam-4587	345	10	canoy	canoy	PROPN
ejpam-4587	345	11	.	.	PUNCT
ejpam-4587	346	1	weakly	weakly	ADJ
ejpam-4587	346	2	connected	connect	VERB
ejpam-4587	346	3	total	total	ADJ
ejpam-4587	346	4	domination	domination	NOUN
ejpam-4587	346	5	in	in	ADP
ejpam-4587	346	6	graphs	graph	NOUN
ejpam-4587	346	7	.	.	PUNCT
ejpam-4587	347	1	international	international	ADJ
ejpam-4587	347	2	mathematical	mathematical	PROPN
ejpam-4587	347	3	forum	forum	PROPN
ejpam-4587	347	4	.	.	PUNCT
ejpam-4587	347	5	,	,	PUNCT
ejpam-4587	347	6	11(11):531	11(11):531	NUM
ejpam-4587	347	7	–	–	PUNCT
ejpam-4587	347	8	537	537	NUM
ejpam-4587	347	9	.	.	NUM
ejpam-4587	347	10	,	,	PUNCT
ejpam-4587	347	11	2016	2016	NUM
ejpam-4587	347	12	.	.	PUNCT
ejpam-4587	348	1	[	[	X
ejpam-4587	348	2	12	12	NUM
ejpam-4587	348	3	]	]	X
ejpam-4587	348	4	j.	j.	PROPN
ejpam-4587	348	5	tarr	tarr	PROPN
ejpam-4587	348	6	and	and	CCONJ
ejpam-4587	348	7	s.	s.	PROPN
ejpam-4587	348	8	suen	suen	PROPN
ejpam-4587	348	9	.	.	PUNCT
ejpam-4587	349	1	domination	domination	NOUN
ejpam-4587	349	2	in	in	ADP
ejpam-4587	349	3	graphs	graph	NOUN
ejpam-4587	349	4	.	.	PUNCT
ejpam-4587	350	1	phd	phd	NOUN
ejpam-4587	350	2	thesis	thesis	PROPN
ejpam-4587	350	3	,	,	PUNCT
ejpam-4587	350	4	university	university	NOUN
ejpam-4587	350	5	of	of	ADP
ejpam-4587	350	6	south	south	PROPN
ejpam-4587	350	7	florida	florida	PROPN
ejpam-4587	350	8	,	,	PUNCT
ejpam-4587	350	9	2010	2010	NUM
ejpam-4587	350	10	.	.	PUNCT