id	sid	tid	token	lemma	pos
ejpam-4766	1	1	european	european	PROPN
ejpam-4766	1	2	journal	journal	PROPN
ejpam-4766	1	3	of	of	ADP
ejpam-4766	1	4	pure	pure	ADJ
ejpam-4766	1	5	and	and	CCONJ
ejpam-4766	1	6	applied	apply	VERB
ejpam-4766	1	7	mathematics	mathematic	NOUN
ejpam-4766	1	8	vol	vol	NOUN
ejpam-4766	1	9	.	.	PUNCT
ejpam-4766	2	1	16	16	NUM
ejpam-4766	2	2	,	,	PUNCT
ejpam-4766	2	3	no	no	INTJ
ejpam-4766	2	4	.	.	NOUN
ejpam-4766	2	5	3	3	NUM
ejpam-4766	2	6	,	,	PUNCT
ejpam-4766	2	7	2023	2023	NUM
ejpam-4766	2	8	,	,	PUNCT
ejpam-4766	2	9	1817	1817	NUM
ejpam-4766	2	10	-	-	SYM
ejpam-4766	2	11	1829	1829	NUM
ejpam-4766	2	12	issn	issn	PROPN
ejpam-4766	2	13	1307	1307	NUM
ejpam-4766	2	14	-	-	SYM
ejpam-4766	2	15	5543	5543	NUM
ejpam-4766	2	16	–	–	PUNCT
ejpam-4766	2	17	ejpam.com	ejpam.com	X
ejpam-4766	2	18	published	publish	VERB
ejpam-4766	2	19	by	by	ADP
ejpam-4766	2	20	new	new	PROPN
ejpam-4766	2	21	york	york	PROPN
ejpam-4766	2	22	business	business	PROPN
ejpam-4766	2	23	global	global	ADJ
ejpam-4766	2	24	connected	connect	VERB
ejpam-4766	2	25	outer	outer	ADJ
ejpam-4766	2	26	-	-	PUNCT
ejpam-4766	2	27	hop	hop	NOUN
ejpam-4766	2	28	independent	independent	ADJ
ejpam-4766	2	29	dominating	dominating	NOUN
ejpam-4766	2	30	sets	set	NOUN
ejpam-4766	2	31	in	in	ADP
ejpam-4766	2	32	graphs	graph	NOUN
ejpam-4766	2	33	under	under	ADP
ejpam-4766	2	34	some	some	DET
ejpam-4766	2	35	binary	binary	ADJ
ejpam-4766	2	36	operations	operation	NOUN
ejpam-4766	2	37	jahiri	jahiri	NOUN
ejpam-4766	2	38	u.	u.	PROPN
ejpam-4766	2	39	manditong1	manditong1	PROPN
ejpam-4766	2	40	,	,	PUNCT
ejpam-4766	2	41	javier	javier	PROPN
ejpam-4766	2	42	a.	a.	PROPN
ejpam-4766	2	43	hassan1,∗	hassan1,∗	PROPN
ejpam-4766	2	44	,	,	PUNCT
ejpam-4766	2	45	ladznar	ladznar	ADJ
ejpam-4766	2	46	s.	s.	PROPN
ejpam-4766	2	47	laja1	laja1	PROPN
ejpam-4766	2	48	,	,	PUNCT
ejpam-4766	2	49	amy	amy	PROPN
ejpam-4766	2	50	a.	a.	PROPN
ejpam-4766	2	51	laja1	laja1	PROPN
ejpam-4766	2	52	,	,	PUNCT
ejpam-4766	2	53	nurijam	nurijam	PROPN
ejpam-4766	2	54	hanna	hanna	PROPN
ejpam-4766	2	55	m.	m.	PROPN
ejpam-4766	2	56	mohammad1	mohammad1	PROPN
ejpam-4766	2	57	,	,	PUNCT
ejpam-4766	2	58	sisteta	sisteta	PROPN
ejpam-4766	2	59	u.	u.	PROPN
ejpam-4766	2	60	kamdon1	kamdon1	PROPN
ejpam-4766	2	61	1	1	NUM
ejpam-4766	2	62	mathematics	mathematic	NOUN
ejpam-4766	2	63	and	and	CCONJ
ejpam-4766	2	64	sciences	sciences	PROPN
ejpam-4766	2	65	department	department	PROPN
ejpam-4766	2	66	,	,	PUNCT
ejpam-4766	2	67	college	college	NOUN
ejpam-4766	2	68	of	of	ADP
ejpam-4766	2	69	arts	art	NOUN
ejpam-4766	2	70	and	and	CCONJ
ejpam-4766	2	71	sciences	science	NOUN
ejpam-4766	2	72	,	,	PUNCT
ejpam-4766	2	73	msu	msu	PROPN
ejpam-4766	2	74	tawi	tawi	PROPN
ejpam-4766	2	75	-	-	PUNCT
ejpam-4766	2	76	tawi	tawi	PROPN
ejpam-4766	2	77	college	college	PROPN
ejpam-4766	2	78	of	of	ADP
ejpam-4766	2	79	technology	technology	NOUN
ejpam-4766	2	80	and	and	CCONJ
ejpam-4766	2	81	oceanography	oceanography	NOUN
ejpam-4766	2	82	,	,	PUNCT
ejpam-4766	2	83	bongao	bongao	NOUN
ejpam-4766	2	84	,	,	PUNCT
ejpam-4766	2	85	tawi	tawi	NOUN
ejpam-4766	2	86	-	-	PUNCT
ejpam-4766	2	87	tawi	tawi	NOUN
ejpam-4766	2	88	,	,	PUNCT
ejpam-4766	2	89	philippines	philippine	NOUN
ejpam-4766	2	90	abstract	abstract	ADJ
ejpam-4766	2	91	.	.	PUNCT
ejpam-4766	3	1	let	let	VERB
ejpam-4766	3	2	g	g	PRON
ejpam-4766	3	3	be	be	AUX
ejpam-4766	3	4	a	a	DET
ejpam-4766	3	5	connected	connected	ADJ
ejpam-4766	3	6	graph	graph	NOUN
ejpam-4766	3	7	.	.	PUNCT
ejpam-4766	4	1	a	a	DET
ejpam-4766	4	2	set	set	NOUN
ejpam-4766	4	3	d	d	NOUN
ejpam-4766	4	4	⊆	⊆	NUM
ejpam-4766	4	5	v	v	ADP
ejpam-4766	4	6	(	(	PUNCT
ejpam-4766	4	7	g	g	NOUN
ejpam-4766	4	8	)	)	PUNCT
ejpam-4766	4	9	is	be	AUX
ejpam-4766	4	10	called	call	VERB
ejpam-4766	4	11	a	a	DET
ejpam-4766	4	12	connected	connected	ADJ
ejpam-4766	4	13	outer	outer	ADJ
ejpam-4766	4	14	-	-	PUNCT
ejpam-4766	4	15	hop	hop	NOUN
ejpam-4766	4	16	independent	independent	ADJ
ejpam-4766	4	17	dominating	dominating	NOUN
ejpam-4766	4	18	if	if	SCONJ
ejpam-4766	4	19	d	d	NOUN
ejpam-4766	4	20	is	be	AUX
ejpam-4766	4	21	a	a	DET
ejpam-4766	4	22	connected	connect	VERB
ejpam-4766	4	23	dominating	dominating	NOUN
ejpam-4766	4	24	set	set	NOUN
ejpam-4766	4	25	and	and	CCONJ
ejpam-4766	4	26	v	v	NOUN
ejpam-4766	4	27	(	(	PUNCT
ejpam-4766	4	28	g	g	NOUN
ejpam-4766	4	29	)	)	PUNCT
ejpam-4766	4	30	\d	\d	NOUN
ejpam-4766	4	31	is	be	AUX
ejpam-4766	4	32	a	a	DET
ejpam-4766	4	33	hop	hop	NOUN
ejpam-4766	4	34	independent	independent	ADJ
ejpam-4766	4	35	set	set	NOUN
ejpam-4766	4	36	in	in	ADP
ejpam-4766	4	37	g.	g.	PROPN
ejpam-4766	4	38	the	the	DET
ejpam-4766	4	39	minimum	minimum	ADJ
ejpam-4766	4	40	cardinality	cardinality	NOUN
ejpam-4766	4	41	among	among	ADP
ejpam-4766	4	42	all	all	DET
ejpam-4766	4	43	connected	connected	ADJ
ejpam-4766	4	44	outer	outer	ADJ
ejpam-4766	4	45	-	-	PUNCT
ejpam-4766	4	46	hop	hop	NOUN
ejpam-4766	4	47	independent	independent	ADJ
ejpam-4766	4	48	dominating	dominating	NOUN
ejpam-4766	4	49	sets	set	NOUN
ejpam-4766	4	50	in	in	ADP
ejpam-4766	4	51	g	g	NOUN
ejpam-4766	4	52	,	,	PUNCT
ejpam-4766	4	53	denoted	denote	VERB
ejpam-4766	4	54	by	by	ADP
ejpam-4766	4	55	γohi	γohi	PROPN
ejpam-4766	4	56	c	c	PROPN
ejpam-4766	4	57	(	(	PUNCT
ejpam-4766	4	58	g	g	NOUN
ejpam-4766	4	59	)	)	PUNCT
ejpam-4766	4	60	,	,	PUNCT
ejpam-4766	4	61	is	be	AUX
ejpam-4766	4	62	called	call	VERB
ejpam-4766	4	63	the	the	DET
ejpam-4766	4	64	connected	connected	ADJ
ejpam-4766	4	65	outer	outer	ADJ
ejpam-4766	4	66	-	-	PUNCT
ejpam-4766	4	67	hop	hop	NOUN
ejpam-4766	4	68	independent	independent	ADJ
ejpam-4766	4	69	domination	domination	NOUN
ejpam-4766	4	70	number	number	NOUN
ejpam-4766	4	71	of	of	ADP
ejpam-4766	4	72	g.	g.	PROPN
ejpam-4766	4	73	in	in	ADP
ejpam-4766	4	74	this	this	DET
ejpam-4766	4	75	paper	paper	NOUN
ejpam-4766	4	76	,	,	PUNCT
ejpam-4766	4	77	we	we	PRON
ejpam-4766	4	78	initiate	initiate	VERB
ejpam-4766	4	79	the	the	DET
ejpam-4766	4	80	study	study	NOUN
ejpam-4766	4	81	and	and	CCONJ
ejpam-4766	4	82	investigation	investigation	NOUN
ejpam-4766	4	83	of	of	ADP
ejpam-4766	4	84	connected	connected	ADJ
ejpam-4766	4	85	outer	outer	ADJ
ejpam-4766	4	86	-	-	PUNCT
ejpam-4766	4	87	hop	hop	NOUN
ejpam-4766	4	88	independent	independent	ADJ
ejpam-4766	4	89	domination	domination	NOUN
ejpam-4766	4	90	in	in	ADP
ejpam-4766	4	91	some	some	DET
ejpam-4766	4	92	families	family	NOUN
ejpam-4766	4	93	of	of	ADP
ejpam-4766	4	94	graphs	graph	NOUN
ejpam-4766	4	95	and	and	CCONJ
ejpam-4766	4	96	graphs	graph	NOUN
ejpam-4766	4	97	under	under	ADP
ejpam-4766	4	98	some	some	DET
ejpam-4766	4	99	binary	binary	ADJ
ejpam-4766	4	100	operations	operation	NOUN
ejpam-4766	4	101	.	.	PUNCT
ejpam-4766	5	1	we	we	PRON
ejpam-4766	5	2	construct	construct	VERB
ejpam-4766	5	3	properties	property	NOUN
ejpam-4766	5	4	and	and	CCONJ
ejpam-4766	5	5	determine	determine	VERB
ejpam-4766	5	6	its	its	PRON
ejpam-4766	5	7	connections	connection	NOUN
ejpam-4766	5	8	with	with	ADP
ejpam-4766	5	9	other	other	ADJ
ejpam-4766	5	10	known	know	VERB
ejpam-4766	5	11	concepts	concept	NOUN
ejpam-4766	5	12	and	and	CCONJ
ejpam-4766	5	13	parameters	parameter	NOUN
ejpam-4766	5	14	in	in	ADP
ejpam-4766	5	15	graph	graph	NOUN
ejpam-4766	5	16	theory	theory	NOUN
ejpam-4766	5	17	.	.	PUNCT
ejpam-4766	6	1	moreover	moreover	ADV
ejpam-4766	6	2	,	,	PUNCT
ejpam-4766	6	3	we	we	PRON
ejpam-4766	6	4	characterize	characterize	VERB
ejpam-4766	6	5	this	this	DET
ejpam-4766	6	6	type	type	NOUN
ejpam-4766	6	7	of	of	ADP
ejpam-4766	6	8	sets	set	NOUN
ejpam-4766	6	9	in	in	ADP
ejpam-4766	6	10	the	the	DET
ejpam-4766	6	11	join	join	NOUN
ejpam-4766	6	12	and	and	CCONJ
ejpam-4766	6	13	corona	corona	NOUN
ejpam-4766	6	14	of	of	ADP
ejpam-4766	6	15	two	two	NUM
ejpam-4766	6	16	graphs	graph	NOUN
ejpam-4766	6	17	,	,	PUNCT
ejpam-4766	6	18	and	and	CCONJ
ejpam-4766	6	19	we	we	PRON
ejpam-4766	6	20	use	use	VERB
ejpam-4766	6	21	these	these	DET
ejpam-4766	6	22	results	result	NOUN
ejpam-4766	6	23	to	to	PART
ejpam-4766	6	24	determine	determine	VERB
ejpam-4766	6	25	the	the	DET
ejpam-4766	6	26	exact	exact	ADJ
ejpam-4766	6	27	values	value	NOUN
ejpam-4766	6	28	or	or	CCONJ
ejpam-4766	6	29	bounds	bound	NOUN
ejpam-4766	6	30	of	of	ADP
ejpam-4766	6	31	the	the	DET
ejpam-4766	6	32	parameters	parameter	NOUN
ejpam-4766	6	33	of	of	ADP
ejpam-4766	6	34	these	these	DET
ejpam-4766	6	35	graphs	graph	NOUN
ejpam-4766	6	36	.	.	PUNCT
ejpam-4766	7	1	2020	2020	NUM
ejpam-4766	7	2	mathematics	mathematic	NOUN
ejpam-4766	7	3	subject	subject	NOUN
ejpam-4766	7	4	classifications	classification	NOUN
ejpam-4766	7	5	:	:	PUNCT
ejpam-4766	7	6	05c69	05c69	X
ejpam-4766	7	7	key	key	ADJ
ejpam-4766	7	8	words	word	NOUN
ejpam-4766	7	9	and	and	CCONJ
ejpam-4766	7	10	phrases	phrase	NOUN
ejpam-4766	7	11	:	:	PUNCT
ejpam-4766	7	12	outer	outer	ADJ
ejpam-4766	7	13	-	-	PUNCT
ejpam-4766	7	14	hop	hop	NOUN
ejpam-4766	7	15	independent	independent	ADJ
ejpam-4766	7	16	,	,	PUNCT
ejpam-4766	7	17	connected	connected	ADJ
ejpam-4766	7	18	outer	outer	ADJ
ejpam-4766	7	19	-	-	PUNCT
ejpam-4766	7	20	hop	hop	NOUN
ejpam-4766	7	21	independent	independent	ADJ
ejpam-4766	7	22	dominating	dominating	NOUN
ejpam-4766	7	23	set	set	NOUN
ejpam-4766	7	24	,	,	PUNCT
ejpam-4766	7	25	connected	connected	ADJ
ejpam-4766	7	26	outer	outer	ADJ
ejpam-4766	7	27	-	-	PUNCT
ejpam-4766	7	28	hop	hop	NOUN
ejpam-4766	7	29	independent	independent	ADJ
ejpam-4766	7	30	domination	domination	NOUN
ejpam-4766	7	31	number	number	NOUN
ejpam-4766	7	32	1	1	NUM
ejpam-4766	7	33	.	.	PUNCT
ejpam-4766	7	34	introduction	introduction	NOUN
ejpam-4766	7	35	the	the	DET
ejpam-4766	7	36	concept	concept	NOUN
ejpam-4766	7	37	of	of	ADP
ejpam-4766	7	38	domination	domination	NOUN
ejpam-4766	7	39	in	in	ADP
ejpam-4766	7	40	a	a	DET
ejpam-4766	7	41	graph	graph	NOUN
ejpam-4766	7	42	has	have	AUX
ejpam-4766	7	43	been	be	AUX
ejpam-4766	7	44	one	one	NUM
ejpam-4766	7	45	of	of	ADP
ejpam-4766	7	46	the	the	DET
ejpam-4766	7	47	interesting	interesting	ADJ
ejpam-4766	7	48	topics	topic	NOUN
ejpam-4766	7	49	of	of	ADP
ejpam-4766	7	50	research	research	NOUN
ejpam-4766	7	51	in	in	ADP
ejpam-4766	7	52	graph	graph	NOUN
ejpam-4766	7	53	theory	theory	NOUN
ejpam-4766	7	54	.	.	PUNCT
ejpam-4766	8	1	let	let	VERB
ejpam-4766	8	2	g	g	PRON
ejpam-4766	8	3	be	be	AUX
ejpam-4766	8	4	a	a	DET
ejpam-4766	8	5	graph	graph	NOUN
ejpam-4766	8	6	.	.	PUNCT
ejpam-4766	9	1	a	a	DET
ejpam-4766	9	2	subset	subset	NOUN
ejpam-4766	9	3	d	d	NOUN
ejpam-4766	9	4	of	of	ADP
ejpam-4766	9	5	v	v	NOUN
ejpam-4766	9	6	(	(	PUNCT
ejpam-4766	9	7	g	g	NOUN
ejpam-4766	9	8	)	)	PUNCT
ejpam-4766	9	9	is	be	AUX
ejpam-4766	9	10	called	call	VERB
ejpam-4766	9	11	a	a	DET
ejpam-4766	9	12	dominating	dominating	NOUN
ejpam-4766	9	13	of	of	ADP
ejpam-4766	9	14	g	g	PROPN
ejpam-4766	9	15	if	if	SCONJ
ejpam-4766	9	16	for	for	ADP
ejpam-4766	9	17	every	every	DET
ejpam-4766	9	18	v	v	NUM
ejpam-4766	9	19	∈	∈	NOUN
ejpam-4766	9	20	v	v	NOUN
ejpam-4766	9	21	(	(	PUNCT
ejpam-4766	9	22	g	g	NOUN
ejpam-4766	9	23	)	)	PUNCT
ejpam-4766	9	24	\d	\d	NOUN
ejpam-4766	9	25	,	,	PUNCT
ejpam-4766	9	26	there	there	PRON
ejpam-4766	9	27	exists	exist	VERB
ejpam-4766	9	28	u	u	NOUN
ejpam-4766	9	29	∈	∈	PROPN
ejpam-4766	9	30	d	d	ADP
ejpam-4766	9	31	such	such	ADJ
ejpam-4766	9	32	that	that	DET
ejpam-4766	9	33	uv	uv	PROPN
ejpam-4766	9	34	∈	∈	PROPN
ejpam-4766	9	35	e(g	e(g	PROPN
ejpam-4766	9	36	)	)	PUNCT
ejpam-4766	9	37	,	,	PUNCT
ejpam-4766	9	38	that	that	ADV
ejpam-4766	9	39	is	is	ADV
ejpam-4766	9	40	,	,	PUNCT
ejpam-4766	9	41	a	a	DET
ejpam-4766	9	42	set	set	NOUN
ejpam-4766	9	43	d	d	NOUN
ejpam-4766	9	44	is	be	AUX
ejpam-4766	9	45	called	call	VERB
ejpam-4766	9	46	a	a	DET
ejpam-4766	9	47	dominating	dominating	NOUN
ejpam-4766	9	48	set	set	NOUN
ejpam-4766	9	49	of	of	ADP
ejpam-4766	9	50	g	g	PROPN
ejpam-4766	9	51	if	if	SCONJ
ejpam-4766	9	52	ng[d	ng[d	PROPN
ejpam-4766	9	53	]	]	PUNCT
ejpam-4766	9	54	=	=	SYM
ejpam-4766	9	55	v	v	X
ejpam-4766	9	56	(	(	PUNCT
ejpam-4766	9	57	g	g	NOUN
ejpam-4766	9	58	)	)	PUNCT
ejpam-4766	9	59	.	.	PUNCT
ejpam-4766	10	1	the	the	DET
ejpam-4766	10	2	domination	domination	NOUN
ejpam-4766	10	3	number	number	NOUN
ejpam-4766	10	4	of	of	ADP
ejpam-4766	10	5	g	g	NOUN
ejpam-4766	10	6	,	,	PUNCT
ejpam-4766	10	7	denoted	denote	VERB
ejpam-4766	10	8	by	by	ADP
ejpam-4766	10	9	γ(g	γ(g	PROPN
ejpam-4766	10	10	)	)	PUNCT
ejpam-4766	10	11	,	,	PUNCT
ejpam-4766	10	12	is	be	AUX
ejpam-4766	10	13	the	the	DET
ejpam-4766	10	14	minimum	minimum	ADJ
ejpam-4766	10	15	cardinality	cardinality	NOUN
ejpam-4766	10	16	among	among	ADP
ejpam-4766	10	17	all	all	DET
ejpam-4766	10	18	dominating	dominating	NOUN
ejpam-4766	10	19	sets	set	NOUN
ejpam-4766	10	20	in	in	ADP
ejpam-4766	10	21	g.	g.	NOUN
ejpam-4766	10	22	researchers	researcher	NOUN
ejpam-4766	10	23	have	have	AUX
ejpam-4766	10	24	been	be	AUX
ejpam-4766	10	25	studied	study	VERB
ejpam-4766	10	26	this	this	DET
ejpam-4766	10	27	concept	concept	NOUN
ejpam-4766	10	28	and	and	CCONJ
ejpam-4766	10	29	introduced	introduce	VERB
ejpam-4766	10	30	new	new	ADJ
ejpam-4766	10	31	variants	variant	NOUN
ejpam-4766	10	32	by	by	ADP
ejpam-4766	10	33	imposing	impose	VERB
ejpam-4766	10	34	additional	additional	ADJ
ejpam-4766	10	35	conditions	condition	NOUN
ejpam-4766	10	36	to	to	ADP
ejpam-4766	10	37	the	the	DET
ejpam-4766	10	38	usual	usual	ADJ
ejpam-4766	10	39	concept	concept	NOUN
ejpam-4766	10	40	of	of	ADP
ejpam-4766	10	41	domination	domination	NOUN
ejpam-4766	10	42	.	.	PUNCT
ejpam-4766	11	1	some	some	DET
ejpam-4766	11	2	studies	study	NOUN
ejpam-4766	11	3	on	on	ADP
ejpam-4766	11	4	domination	domination	NOUN
ejpam-4766	11	5	and	and	CCONJ
ejpam-4766	11	6	its	its	PRON
ejpam-4766	11	7	variants	variant	NOUN
ejpam-4766	11	8	can	can	AUX
ejpam-4766	11	9	be	be	AUX
ejpam-4766	11	10	found	find	VERB
ejpam-4766	11	11	in	in	ADP
ejpam-4766	11	12	these	these	DET
ejpam-4766	11	13	references	reference	NOUN
ejpam-4766	11	14	[	[	X
ejpam-4766	11	15	1–6	1–6	NUM
ejpam-4766	11	16	,	,	PUNCT
ejpam-4766	11	17	8–14	8–14	PROPN
ejpam-4766	11	18	]	]	PUNCT
ejpam-4766	11	19	.	.	PUNCT
ejpam-4766	12	1	∗corresponding	∗corresponde	VERB
ejpam-4766	12	2	author	author	NOUN
ejpam-4766	12	3	.	.	PUNCT
ejpam-4766	13	1	doi	doi	NOUN
ejpam-4766	13	2	:	:	PUNCT
ejpam-4766	13	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4766	https://doi.org/10.29020/nybg.ejpam.v16i3.4766	NOUN
ejpam-4766	13	4	email	email	NOUN
ejpam-4766	13	5	addresses	address	VERB
ejpam-4766	13	6	:	:	PUNCT
ejpam-4766	13	7	jahirimanditong@msutawi-tawi.edu.ph	jahirimanditong@msutawi-tawi.edu.ph	PROPN
ejpam-4766	13	8	(	(	PUNCT
ejpam-4766	13	9	j.	j.	PROPN
ejpam-4766	13	10	manditong	manditong	PROPN
ejpam-4766	13	11	)	)	PUNCT
ejpam-4766	13	12	,	,	PUNCT
ejpam-4766	13	13	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-4766	13	14	(	(	PUNCT
ejpam-4766	13	15	j.	j.	PROPN
ejpam-4766	13	16	hassan	hassan	PROPN
ejpam-4766	13	17	)	)	PUNCT
ejpam-4766	13	18	,	,	PUNCT
ejpam-4766	13	19	ladznarlaja@msutawi-tawi.edu.ph	ladznarlaja@msutawi-tawi.edu.ph	PROPN
ejpam-4766	13	20	(	(	PUNCT
ejpam-4766	13	21	l.	l.	PROPN
ejpam-4766	13	22	laja	laja	PROPN
ejpam-4766	13	23	)	)	PUNCT
ejpam-4766	13	24	,	,	PUNCT
ejpam-4766	13	25	amylaja@msutawi-tawi.edu.ph	amylaja@msutawi-tawi.edu.ph	PROPN
ejpam-4766	13	26	(	(	PUNCT
ejpam-4766	13	27	a.	a.	NOUN
ejpam-4766	13	28	laja	laja	PROPN
ejpam-4766	13	29	)	)	PUNCT
ejpam-4766	13	30	,	,	PUNCT
ejpam-4766	13	31	hannamohammad@msutawi-tawi.edu.ph	hannamohammad@msutawi-tawi.edu.ph	PROPN
ejpam-4766	13	32	(	(	PUNCT
ejpam-4766	13	33	n.h	n.h	PROPN
ejpam-4766	13	34	.	.	PUNCT
ejpam-4766	13	35	mohammad	mohammad	PROPN
ejpam-4766	13	36	)	)	PUNCT
ejpam-4766	13	37	sistetakamdon@msutawi-tawi.edu.ph	sistetakamdon@msutawi-tawi.edu.ph	PROPN
ejpam-4766	13	38	(	(	PUNCT
ejpam-4766	13	39	s.	s.	PROPN
ejpam-4766	13	40	kamdon	kamdon	PROPN
ejpam-4766	13	41	)	)	PUNCT
ejpam-4766	13	42	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4766	13	43	1817	1817	NUM
ejpam-4766	13	44	©	©	ADP
ejpam-4766	13	45	2023	2023	NUM
ejpam-4766	13	46	ejpam	ejpam	NOUN
ejpam-4766	13	47	all	all	DET
ejpam-4766	13	48	rights	right	NOUN
ejpam-4766	13	49	reserved	reserve	VERB
ejpam-4766	13	50	.	.	PUNCT
ejpam-4766	14	1	j.	j.	PROPN
ejpam-4766	14	2	hassan	hassan	PROPN
ejpam-4766	14	3	et	et	PROPN
ejpam-4766	14	4	al	al	PROPN
ejpam-4766	14	5	.	.	PUNCT
ejpam-4766	14	6	/	/	SYM
ejpam-4766	14	7	eur	eur	PROPN
ejpam-4766	14	8	.	.	PUNCT
ejpam-4766	15	1	j.	j.	PROPN
ejpam-4766	15	2	pure	pure	PROPN
ejpam-4766	15	3	appl	appl	PROPN
ejpam-4766	15	4	.	.	PROPN
ejpam-4766	15	5	math	math	PROPN
ejpam-4766	15	6	,	,	PUNCT
ejpam-4766	15	7	16	16	NUM
ejpam-4766	15	8	(	(	PUNCT
ejpam-4766	15	9	3	3	NUM
ejpam-4766	15	10	)	)	PUNCT
ejpam-4766	15	11	(	(	PUNCT
ejpam-4766	15	12	2023	2023	NUM
ejpam-4766	15	13	)	)	PUNCT
ejpam-4766	15	14	,	,	PUNCT
ejpam-4766	15	15	1817	1817	NUM
ejpam-4766	15	16	-	-	SYM
ejpam-4766	15	17	1829	1829	NUM
ejpam-4766	15	18	1818	1818	NUM
ejpam-4766	15	19	recently	recently	ADV
ejpam-4766	15	20	,	,	PUNCT
ejpam-4766	15	21	hassan	hassan	PROPN
ejpam-4766	15	22	et	et	PROPN
ejpam-4766	15	23	al	al	PROPN
ejpam-4766	15	24	.	.	PUNCT
ejpam-4766	16	1	[	[	X
ejpam-4766	16	2	7	7	X
ejpam-4766	16	3	]	]	PUNCT
ejpam-4766	16	4	introduced	introduce	VERB
ejpam-4766	16	5	the	the	DET
ejpam-4766	16	6	concept	concept	NOUN
ejpam-4766	16	7	of	of	ADP
ejpam-4766	16	8	hop	hop	NOUN
ejpam-4766	16	9	independent	independent	ADJ
ejpam-4766	16	10	sets	set	NOUN
ejpam-4766	16	11	in	in	ADP
ejpam-4766	16	12	a	a	DET
ejpam-4766	16	13	graph	graph	NOUN
ejpam-4766	16	14	.	.	PUNCT
ejpam-4766	17	1	let	let	VERB
ejpam-4766	17	2	g	g	PRON
ejpam-4766	17	3	be	be	AUX
ejpam-4766	17	4	a	a	DET
ejpam-4766	17	5	graph	graph	NOUN
ejpam-4766	17	6	.	.	PUNCT
ejpam-4766	18	1	a	a	DET
ejpam-4766	18	2	subset	subset	NOUN
ejpam-4766	18	3	s	s	NOUN
ejpam-4766	18	4	of	of	ADP
ejpam-4766	18	5	v	v	NOUN
ejpam-4766	18	6	(	(	PUNCT
ejpam-4766	18	7	g	g	NOUN
ejpam-4766	18	8	)	)	PUNCT
ejpam-4766	18	9	is	be	AUX
ejpam-4766	18	10	called	call	VERB
ejpam-4766	18	11	a	a	DET
ejpam-4766	18	12	hop	hop	NOUN
ejpam-4766	18	13	independent	independent	ADJ
ejpam-4766	18	14	if	if	SCONJ
ejpam-4766	18	15	for	for	ADP
ejpam-4766	18	16	every	every	DET
ejpam-4766	18	17	pair	pair	NOUN
ejpam-4766	18	18	of	of	ADP
ejpam-4766	18	19	distinct	distinct	ADJ
ejpam-4766	18	20	vertices	vertex	NOUN
ejpam-4766	18	21	v	v	ADP
ejpam-4766	18	22	,	,	PUNCT
ejpam-4766	18	23	w	w	PROPN
ejpam-4766	18	24	∈	∈	PROPN
ejpam-4766	18	25	s	s	NOUN
ejpam-4766	18	26	,	,	PUNCT
ejpam-4766	18	27	dg(v	dg(v	X
ejpam-4766	18	28	,	,	PUNCT
ejpam-4766	18	29	w	w	NOUN
ejpam-4766	18	30	)	)	PUNCT
ejpam-4766	18	31	̸=	̸=	PROPN
ejpam-4766	18	32	2	2	NUM
ejpam-4766	18	33	.	.	PUNCT
ejpam-4766	19	1	the	the	DET
ejpam-4766	19	2	maximum	maximum	ADJ
ejpam-4766	19	3	cardinality	cardinality	NOUN
ejpam-4766	19	4	of	of	ADP
ejpam-4766	19	5	a	a	DET
ejpam-4766	19	6	hop	hop	NOUN
ejpam-4766	19	7	independent	independent	ADJ
ejpam-4766	19	8	set	set	NOUN
ejpam-4766	19	9	in	in	ADP
ejpam-4766	19	10	g	g	NOUN
ejpam-4766	19	11	,	,	PUNCT
ejpam-4766	19	12	denoted	denote	VERB
ejpam-4766	19	13	by	by	ADP
ejpam-4766	19	14	αh(g	αh(g	NOUN
ejpam-4766	19	15	)	)	PUNCT
ejpam-4766	19	16	,	,	PUNCT
ejpam-4766	19	17	is	be	AUX
ejpam-4766	19	18	called	call	VERB
ejpam-4766	19	19	the	the	DET
ejpam-4766	19	20	hop	hop	NOUN
ejpam-4766	19	21	independence	independence	NOUN
ejpam-4766	19	22	number	number	NOUN
ejpam-4766	19	23	of	of	ADP
ejpam-4766	19	24	g.	g.	PROPN
ejpam-4766	19	25	they	they	PRON
ejpam-4766	19	26	have	have	AUX
ejpam-4766	19	27	shown	show	VERB
ejpam-4766	19	28	that	that	SCONJ
ejpam-4766	19	29	the	the	DET
ejpam-4766	19	30	maximum	maximum	ADJ
ejpam-4766	19	31	hop	hop	NOUN
ejpam-4766	19	32	independent	independent	ADJ
ejpam-4766	19	33	set	set	NOUN
ejpam-4766	19	34	in	in	ADP
ejpam-4766	19	35	a	a	DET
ejpam-4766	19	36	graph	graph	NOUN
ejpam-4766	19	37	is	be	AUX
ejpam-4766	19	38	a	a	DET
ejpam-4766	19	39	hop	hop	NOUN
ejpam-4766	19	40	dominating	dominating	NOUN
ejpam-4766	19	41	set	set	NOUN
ejpam-4766	19	42	,	,	PUNCT
ejpam-4766	19	43	that	that	ADV
ejpam-4766	19	44	is	is	ADV
ejpam-4766	19	45	,	,	PUNCT
ejpam-4766	19	46	the	the	DET
ejpam-4766	19	47	hop	hop	NOUN
ejpam-4766	19	48	independence	independence	NOUN
ejpam-4766	19	49	number	number	NOUN
ejpam-4766	19	50	is	be	AUX
ejpam-4766	19	51	at	at	ADP
ejpam-4766	19	52	least	least	ADJ
ejpam-4766	19	53	equal	equal	ADJ
ejpam-4766	19	54	to	to	ADP
ejpam-4766	19	55	the	the	DET
ejpam-4766	19	56	hop	hop	NOUN
ejpam-4766	19	57	domination	domination	NOUN
ejpam-4766	19	58	number	number	NOUN
ejpam-4766	19	59	.	.	PUNCT
ejpam-4766	20	1	moreover	moreover	ADV
ejpam-4766	20	2	,	,	PUNCT
ejpam-4766	20	3	they	they	PRON
ejpam-4766	20	4	have	have	AUX
ejpam-4766	20	5	found	find	VERB
ejpam-4766	20	6	that	that	SCONJ
ejpam-4766	20	7	that	that	DET
ejpam-4766	20	8	hop	hop	ADJ
ejpam-4766	20	9	independence	independence	NOUN
ejpam-4766	20	10	number	number	NOUN
ejpam-4766	20	11	is	be	AUX
ejpam-4766	20	12	incomparable	incomparable	ADJ
ejpam-4766	20	13	to	to	ADP
ejpam-4766	20	14	the	the	DET
ejpam-4766	20	15	independence	independence	NOUN
ejpam-4766	20	16	number	number	NOUN
ejpam-4766	20	17	of	of	ADP
ejpam-4766	20	18	a	a	DET
ejpam-4766	20	19	graph	graph	NOUN
ejpam-4766	20	20	.	.	PUNCT
ejpam-4766	21	1	in	in	ADP
ejpam-4766	21	2	fact	fact	NOUN
ejpam-4766	21	3	,	,	PUNCT
ejpam-4766	21	4	they	they	PRON
ejpam-4766	21	5	have	have	AUX
ejpam-4766	21	6	shown	show	VERB
ejpam-4766	21	7	that	that	SCONJ
ejpam-4766	21	8	the	the	DET
ejpam-4766	21	9	absolute	absolute	ADJ
ejpam-4766	21	10	difference	difference	NOUN
ejpam-4766	21	11	between	between	ADP
ejpam-4766	21	12	the	the	DET
ejpam-4766	21	13	independence	independence	NOUN
ejpam-4766	21	14	number	number	NOUN
ejpam-4766	21	15	and	and	CCONJ
ejpam-4766	21	16	hop	hop	NOUN
ejpam-4766	21	17	independence	independence	NOUN
ejpam-4766	21	18	number	number	NOUN
ejpam-4766	21	19	of	of	ADP
ejpam-4766	21	20	a	a	DET
ejpam-4766	21	21	graph	graph	NOUN
ejpam-4766	21	22	can	can	AUX
ejpam-4766	21	23	be	be	AUX
ejpam-4766	21	24	made	make	VERB
ejpam-4766	21	25	arbitrarily	arbitrarily	ADV
ejpam-4766	21	26	large	large	ADJ
ejpam-4766	21	27	.	.	PUNCT
ejpam-4766	22	1	in	in	ADP
ejpam-4766	22	2	this	this	DET
ejpam-4766	22	3	study	study	NOUN
ejpam-4766	22	4	,	,	PUNCT
ejpam-4766	22	5	the	the	DET
ejpam-4766	22	6	concept	concept	NOUN
ejpam-4766	22	7	of	of	ADP
ejpam-4766	22	8	connected	connected	ADJ
ejpam-4766	22	9	outer	outer	ADJ
ejpam-4766	22	10	-	-	PUNCT
ejpam-4766	22	11	hop	hop	NOUN
ejpam-4766	22	12	independent	independent	ADJ
ejpam-4766	22	13	domination	domination	NOUN
ejpam-4766	22	14	in	in	ADP
ejpam-4766	22	15	a	a	DET
ejpam-4766	22	16	graph	graph	NOUN
ejpam-4766	22	17	will	will	AUX
ejpam-4766	22	18	be	be	AUX
ejpam-4766	22	19	introduced	introduce	VERB
ejpam-4766	22	20	and	and	CCONJ
ejpam-4766	22	21	investigated	investigate	VERB
ejpam-4766	22	22	.	.	PUNCT
ejpam-4766	23	1	this	this	PRON
ejpam-4766	23	2	will	will	AUX
ejpam-4766	23	3	be	be	AUX
ejpam-4766	23	4	investigated	investigate	VERB
ejpam-4766	23	5	for	for	ADP
ejpam-4766	23	6	some	some	DET
ejpam-4766	23	7	special	special	ADJ
ejpam-4766	23	8	graphs	graph	NOUN
ejpam-4766	23	9	including	include	VERB
ejpam-4766	23	10	those	those	DET
ejpam-4766	23	11	graphs	graph	NOUN
ejpam-4766	23	12	obtained	obtain	VERB
ejpam-4766	23	13	from	from	ADP
ejpam-4766	23	14	some	some	DET
ejpam-4766	23	15	binary	binary	ADJ
ejpam-4766	23	16	operations	operation	NOUN
ejpam-4766	23	17	.	.	PUNCT
ejpam-4766	24	1	moreover	moreover	ADV
ejpam-4766	24	2	,	,	PUNCT
ejpam-4766	24	3	exact	exact	ADJ
ejpam-4766	24	4	values	value	NOUN
ejpam-4766	24	5	or	or	CCONJ
ejpam-4766	24	6	bounds	bound	NOUN
ejpam-4766	24	7	for	for	ADP
ejpam-4766	24	8	the	the	DET
ejpam-4766	24	9	parameter	parameter	NOUN
ejpam-4766	24	10	will	will	AUX
ejpam-4766	24	11	be	be	AUX
ejpam-4766	24	12	given	give	VERB
ejpam-4766	24	13	for	for	ADP
ejpam-4766	24	14	some	some	DET
ejpam-4766	24	15	families	family	NOUN
ejpam-4766	24	16	of	of	ADP
ejpam-4766	24	17	graphs	graph	NOUN
ejpam-4766	24	18	and	and	CCONJ
ejpam-4766	24	19	graphs	graph	NOUN
ejpam-4766	24	20	under	under	ADP
ejpam-4766	24	21	some	some	DET
ejpam-4766	24	22	binary	binary	ADJ
ejpam-4766	24	23	operations	operation	NOUN
ejpam-4766	24	24	.	.	PUNCT
ejpam-4766	25	1	2	2	X
ejpam-4766	25	2	.	.	X
ejpam-4766	25	3	terminology	terminology	NOUN
ejpam-4766	25	4	and	and	CCONJ
ejpam-4766	25	5	notation	notation	NOUN
ejpam-4766	25	6	let	let	VERB
ejpam-4766	25	7	g	g	PRON
ejpam-4766	25	8	be	be	AUX
ejpam-4766	25	9	a	a	DET
ejpam-4766	25	10	simple	simple	ADJ
ejpam-4766	25	11	graph	graph	NOUN
ejpam-4766	25	12	.	.	PUNCT
ejpam-4766	26	1	two	two	NUM
ejpam-4766	26	2	vertices	vertex	NOUN
ejpam-4766	26	3	u	u	NOUN
ejpam-4766	26	4	,	,	PUNCT
ejpam-4766	26	5	v	v	NOUN
ejpam-4766	26	6	of	of	ADP
ejpam-4766	26	7	a	a	DET
ejpam-4766	26	8	graph	graph	NOUN
ejpam-4766	26	9	g	g	NOUN
ejpam-4766	26	10	are	be	AUX
ejpam-4766	26	11	adjacent	adjacent	ADJ
ejpam-4766	26	12	,	,	PUNCT
ejpam-4766	26	13	or	or	CCONJ
ejpam-4766	26	14	neighbors	neighbor	NOUN
ejpam-4766	26	15	,	,	PUNCT
ejpam-4766	26	16	if	if	SCONJ
ejpam-4766	26	17	uv	uv	NOUN
ejpam-4766	26	18	is	be	AUX
ejpam-4766	26	19	an	an	DET
ejpam-4766	26	20	edge	edge	NOUN
ejpam-4766	26	21	of	of	ADP
ejpam-4766	26	22	g.	g.	PROPN
ejpam-4766	26	23	the	the	DET
ejpam-4766	26	24	set	set	NOUN
ejpam-4766	26	25	of	of	ADP
ejpam-4766	26	26	neighbors	neighbor	NOUN
ejpam-4766	26	27	of	of	ADP
ejpam-4766	26	28	a	a	DET
ejpam-4766	26	29	vertex	vertex	NOUN
ejpam-4766	26	30	u	u	NOUN
ejpam-4766	26	31	in	in	ADP
ejpam-4766	26	32	g	g	NOUN
ejpam-4766	26	33	,	,	PUNCT
ejpam-4766	26	34	denoted	denote	VERB
ejpam-4766	26	35	by	by	ADP
ejpam-4766	26	36	ng(u	ng(u	NOUN
ejpam-4766	26	37	)	)	PUNCT
ejpam-4766	26	38	,	,	PUNCT
ejpam-4766	26	39	is	be	AUX
ejpam-4766	26	40	called	call	VERB
ejpam-4766	26	41	the	the	DET
ejpam-4766	26	42	open	open	ADJ
ejpam-4766	26	43	neighborhood	neighborhood	NOUN
ejpam-4766	26	44	of	of	ADP
ejpam-4766	26	45	u	u	PROPN
ejpam-4766	26	46	in	in	ADP
ejpam-4766	26	47	g.	g.	PROPN
ejpam-4766	26	48	the	the	DET
ejpam-4766	26	49	closed	close	VERB
ejpam-4766	26	50	neighborhood	neighborhood	NOUN
ejpam-4766	26	51	of	of	ADP
ejpam-4766	26	52	u	u	NOUN
ejpam-4766	26	53	in	in	ADP
ejpam-4766	26	54	g	g	PROPN
ejpam-4766	26	55	is	be	AUX
ejpam-4766	26	56	the	the	DET
ejpam-4766	26	57	set	set	NOUN
ejpam-4766	26	58	ng[u	ng[u	PROPN
ejpam-4766	26	59	]	]	X
ejpam-4766	26	60	=	=	SYM
ejpam-4766	26	61	ng(u	ng(u	PROPN
ejpam-4766	26	62	)	)	PUNCT
ejpam-4766	26	63	∪	∪	NOUN
ejpam-4766	26	64	{	{	PUNCT
ejpam-4766	26	65	u	u	NOUN
ejpam-4766	26	66	}	}	PUNCT
ejpam-4766	26	67	.	.	PUNCT
ejpam-4766	27	1	if	if	SCONJ
ejpam-4766	27	2	x	x	PROPN
ejpam-4766	27	3	⊆	⊆	NUM
ejpam-4766	27	4	v	v	X
ejpam-4766	27	5	(	(	PUNCT
ejpam-4766	27	6	g	g	NOUN
ejpam-4766	27	7	)	)	PUNCT
ejpam-4766	27	8	,	,	PUNCT
ejpam-4766	27	9	the	the	DET
ejpam-4766	27	10	open	open	ADJ
ejpam-4766	27	11	neighborhood	neighborhood	NOUN
ejpam-4766	27	12	of	of	ADP
ejpam-4766	27	13	x	x	PUNCT
ejpam-4766	27	14	in	in	ADP
ejpam-4766	27	15	g	g	PROPN
ejpam-4766	27	16	is	be	AUX
ejpam-4766	27	17	the	the	DET
ejpam-4766	27	18	set	set	NOUN
ejpam-4766	27	19	ng(x	ng(x	NUM
ejpam-4766	27	20	)	)	PUNCT
ejpam-4766	28	1	=	=	SYM
ejpam-4766	28	2	⋃	⋃	NOUN
ejpam-4766	28	3	u∈x	u∈x	NOUN
ejpam-4766	28	4	ng(u	ng(u	NOUN
ejpam-4766	28	5	)	)	PUNCT
ejpam-4766	28	6	.	.	PUNCT
ejpam-4766	29	1	the	the	DET
ejpam-4766	29	2	closed	closed	ADJ
ejpam-4766	29	3	neighborhood	neighborhood	NOUN
ejpam-4766	29	4	of	of	ADP
ejpam-4766	29	5	x	x	PUNCT
ejpam-4766	29	6	in	in	ADP
ejpam-4766	29	7	g	g	PROPN
ejpam-4766	29	8	is	be	AUX
ejpam-4766	29	9	the	the	DET
ejpam-4766	29	10	set	set	NOUN
ejpam-4766	29	11	ng[x	ng[x	PROPN
ejpam-4766	29	12	]	]	X
ejpam-4766	29	13	=	=	SYM
ejpam-4766	29	14	ng(x)∪x	ng(x)∪x	PROPN
ejpam-4766	29	15	.	.	PUNCT
ejpam-4766	30	1	a	a	DET
ejpam-4766	30	2	subset	subset	NOUN
ejpam-4766	30	3	d	d	NOUN
ejpam-4766	30	4	of	of	ADP
ejpam-4766	30	5	v	v	NOUN
ejpam-4766	30	6	(	(	PUNCT
ejpam-4766	30	7	g	g	NOUN
ejpam-4766	30	8	)	)	PUNCT
ejpam-4766	30	9	is	be	AUX
ejpam-4766	30	10	called	call	VERB
ejpam-4766	30	11	a	a	DET
ejpam-4766	30	12	dominating	dominating	NOUN
ejpam-4766	30	13	of	of	ADP
ejpam-4766	30	14	g	g	PROPN
ejpam-4766	30	15	if	if	SCONJ
ejpam-4766	30	16	for	for	ADP
ejpam-4766	30	17	every	every	PRON
ejpam-4766	30	18	v	v	NUM
ejpam-4766	30	19	∈	∈	NOUN
ejpam-4766	30	20	v	v	NOUN
ejpam-4766	30	21	(	(	PUNCT
ejpam-4766	30	22	g	g	NOUN
ejpam-4766	30	23	)	)	PUNCT
ejpam-4766	30	24	\	\	PUNCT
ejpam-4766	31	1	d	d	X
ejpam-4766	31	2	,	,	PUNCT
ejpam-4766	31	3	there	there	PRON
ejpam-4766	31	4	exists	exist	VERB
ejpam-4766	31	5	u	u	NOUN
ejpam-4766	31	6	∈	∈	PROPN
ejpam-4766	31	7	d	d	ADP
ejpam-4766	31	8	such	such	ADJ
ejpam-4766	31	9	that	that	DET
ejpam-4766	31	10	uv	uv	PROPN
ejpam-4766	31	11	∈	∈	PROPN
ejpam-4766	31	12	e(g	e(g	PROPN
ejpam-4766	31	13	)	)	PUNCT
ejpam-4766	31	14	,	,	PUNCT
ejpam-4766	31	15	that	that	ADV
ejpam-4766	31	16	is	is	ADV
ejpam-4766	31	17	,	,	PUNCT
ejpam-4766	31	18	ng[d	ng[d	PROPN
ejpam-4766	31	19	]	]	PUNCT
ejpam-4766	31	20	=	=	SYM
ejpam-4766	31	21	v	v	X
ejpam-4766	31	22	(	(	PUNCT
ejpam-4766	31	23	g	g	NOUN
ejpam-4766	31	24	)	)	PUNCT
ejpam-4766	31	25	.	.	PUNCT
ejpam-4766	32	1	the	the	DET
ejpam-4766	32	2	domination	domination	NOUN
ejpam-4766	32	3	number	number	NOUN
ejpam-4766	32	4	of	of	ADP
ejpam-4766	32	5	g	g	NOUN
ejpam-4766	32	6	,	,	PUNCT
ejpam-4766	32	7	denoted	denote	VERB
ejpam-4766	32	8	by	by	ADP
ejpam-4766	32	9	γ(g	γ(g	PROPN
ejpam-4766	32	10	)	)	PUNCT
ejpam-4766	32	11	,	,	PUNCT
ejpam-4766	32	12	is	be	AUX
ejpam-4766	32	13	the	the	DET
ejpam-4766	32	14	minimum	minimum	ADJ
ejpam-4766	32	15	cardinality	cardinality	NOUN
ejpam-4766	32	16	among	among	ADP
ejpam-4766	32	17	all	all	DET
ejpam-4766	32	18	dominating	dominating	NOUN
ejpam-4766	32	19	sets	set	NOUN
ejpam-4766	32	20	in	in	ADP
ejpam-4766	32	21	g.	g.	PROPN
ejpam-4766	32	22	any	any	DET
ejpam-4766	32	23	dominating	dominating	NOUN
ejpam-4766	32	24	set	set	NOUN
ejpam-4766	32	25	d	d	NOUN
ejpam-4766	32	26	with	with	ADP
ejpam-4766	32	27	cardinality	cardinality	NOUN
ejpam-4766	32	28	equal	equal	ADJ
ejpam-4766	32	29	to	to	ADP
ejpam-4766	32	30	γ(g	γ(g	PROPN
ejpam-4766	32	31	)	)	PUNCT
ejpam-4766	32	32	is	be	AUX
ejpam-4766	32	33	called	call	VERB
ejpam-4766	32	34	a	a	DET
ejpam-4766	32	35	γ	γ	NOUN
ejpam-4766	32	36	-	-	PUNCT
ejpam-4766	32	37	set	set	NOUN
ejpam-4766	32	38	of	of	ADP
ejpam-4766	32	39	g.	g.	PROPN
ejpam-4766	32	40	a	a	DET
ejpam-4766	32	41	dominating	dominating	NOUN
ejpam-4766	32	42	set	set	NOUN
ejpam-4766	32	43	d	d	NOUN
ejpam-4766	32	44	of	of	ADP
ejpam-4766	32	45	g	g	PROPN
ejpam-4766	32	46	is	be	AUX
ejpam-4766	32	47	called	call	VERB
ejpam-4766	32	48	a	a	DET
ejpam-4766	32	49	connected	connect	VERB
ejpam-4766	32	50	dominating	dominating	NOUN
ejpam-4766	32	51	set	set	NOUN
ejpam-4766	32	52	if	if	SCONJ
ejpam-4766	32	53	the	the	DET
ejpam-4766	32	54	induced	induced	ADJ
ejpam-4766	32	55	subgraph	subgraph	NOUN
ejpam-4766	32	56	⟨d⟩	⟨d⟩	PROPN
ejpam-4766	32	57	of	of	ADP
ejpam-4766	32	58	d	d	PROPN
ejpam-4766	32	59	is	be	AUX
ejpam-4766	32	60	connected	connect	VERB
ejpam-4766	32	61	.	.	PUNCT
ejpam-4766	33	1	the	the	DET
ejpam-4766	33	2	connected	connected	ADJ
ejpam-4766	33	3	domination	domination	NOUN
ejpam-4766	33	4	number	number	NOUN
ejpam-4766	33	5	of	of	ADP
ejpam-4766	33	6	g	g	NOUN
ejpam-4766	33	7	,	,	PUNCT
ejpam-4766	33	8	denoted	denote	VERB
ejpam-4766	33	9	by	by	ADP
ejpam-4766	33	10	γc(g	γc(g	NOUN
ejpam-4766	33	11	)	)	PUNCT
ejpam-4766	33	12	,	,	PUNCT
ejpam-4766	33	13	is	be	AUX
ejpam-4766	33	14	the	the	DET
ejpam-4766	33	15	minimum	minimum	ADJ
ejpam-4766	33	16	cardinality	cardinality	NOUN
ejpam-4766	33	17	of	of	ADP
ejpam-4766	33	18	a	a	DET
ejpam-4766	33	19	connected	connect	VERB
ejpam-4766	33	20	dominating	dominating	NOUN
ejpam-4766	33	21	set	set	NOUN
ejpam-4766	33	22	of	of	ADP
ejpam-4766	33	23	g.	g.	PROPN
ejpam-4766	33	24	any	any	DET
ejpam-4766	33	25	connected	connect	VERB
ejpam-4766	33	26	dominating	dominating	NOUN
ejpam-4766	33	27	set	set	VERB
ejpam-4766	33	28	d	d	NOUN
ejpam-4766	33	29	with	with	ADP
ejpam-4766	33	30	cardinality	cardinality	NOUN
ejpam-4766	33	31	equal	equal	ADJ
ejpam-4766	33	32	to	to	ADP
ejpam-4766	33	33	γc(g	γc(g	NUM
ejpam-4766	33	34	)	)	PUNCT
ejpam-4766	33	35	is	be	AUX
ejpam-4766	33	36	called	call	VERB
ejpam-4766	33	37	a	a	DET
ejpam-4766	33	38	γc	γc	NOUN
ejpam-4766	33	39	-	-	PUNCT
ejpam-4766	33	40	set	set	NOUN
ejpam-4766	33	41	of	of	ADP
ejpam-4766	33	42	g.	g.	PROPN
ejpam-4766	33	43	a	a	DET
ejpam-4766	33	44	subset	subset	NOUN
ejpam-4766	33	45	b	b	NOUN
ejpam-4766	33	46	of	of	ADP
ejpam-4766	33	47	v	v	NOUN
ejpam-4766	33	48	(	(	PUNCT
ejpam-4766	33	49	g	g	NOUN
ejpam-4766	33	50	)	)	PUNCT
ejpam-4766	33	51	is	be	AUX
ejpam-4766	33	52	an	an	DET
ejpam-4766	33	53	independent	independent	ADJ
ejpam-4766	33	54	if	if	SCONJ
ejpam-4766	33	55	for	for	ADP
ejpam-4766	33	56	every	every	DET
ejpam-4766	33	57	pair	pair	NOUN
ejpam-4766	33	58	of	of	ADP
ejpam-4766	33	59	distinct	distinct	ADJ
ejpam-4766	33	60	vertices	vertex	NOUN
ejpam-4766	33	61	v	v	ADP
ejpam-4766	33	62	,	,	PUNCT
ejpam-4766	33	63	w	w	PROPN
ejpam-4766	33	64	∈	∈	PROPN
ejpam-4766	33	65	b	b	PROPN
ejpam-4766	33	66	,	,	PUNCT
ejpam-4766	33	67	dg(v	dg(v	X
ejpam-4766	33	68	,	,	PUNCT
ejpam-4766	33	69	w	w	NOUN
ejpam-4766	33	70	)	)	PUNCT
ejpam-4766	33	71	̸=	̸=	PROPN
ejpam-4766	33	72	1	1	NUM
ejpam-4766	33	73	.	.	PUNCT
ejpam-4766	34	1	the	the	DET
ejpam-4766	34	2	maximum	maximum	ADJ
ejpam-4766	34	3	cardinality	cardinality	NOUN
ejpam-4766	34	4	of	of	ADP
ejpam-4766	34	5	an	an	DET
ejpam-4766	34	6	independent	independent	ADJ
ejpam-4766	34	7	set	set	NOUN
ejpam-4766	34	8	in	in	ADP
ejpam-4766	34	9	g	g	NOUN
ejpam-4766	34	10	,	,	PUNCT
ejpam-4766	34	11	denoted	denote	VERB
ejpam-4766	34	12	by	by	ADP
ejpam-4766	34	13	α(g	α(g	NOUN
ejpam-4766	34	14	)	)	PUNCT
ejpam-4766	34	15	,	,	PUNCT
ejpam-4766	34	16	is	be	AUX
ejpam-4766	34	17	called	call	VERB
ejpam-4766	34	18	the	the	DET
ejpam-4766	34	19	independence	independence	NOUN
ejpam-4766	34	20	number	number	NOUN
ejpam-4766	34	21	of	of	ADP
ejpam-4766	34	22	g.	g.	PROPN
ejpam-4766	34	23	any	any	DET
ejpam-4766	34	24	independent	independent	ADJ
ejpam-4766	34	25	set	set	NOUN
ejpam-4766	34	26	b	b	PROPN
ejpam-4766	34	27	with	with	ADP
ejpam-4766	34	28	cardinality	cardinality	NOUN
ejpam-4766	34	29	equal	equal	ADJ
ejpam-4766	34	30	to	to	ADP
ejpam-4766	34	31	α(g	α(g	NUM
ejpam-4766	34	32	)	)	PUNCT
ejpam-4766	34	33	is	be	AUX
ejpam-4766	34	34	called	call	VERB
ejpam-4766	34	35	an	an	DET
ejpam-4766	34	36	α	α	NOUN
ejpam-4766	34	37	-	-	PUNCT
ejpam-4766	34	38	set	set	NOUN
ejpam-4766	34	39	of	of	ADP
ejpam-4766	34	40	g.	g.	PROPN
ejpam-4766	34	41	let	let	VERB
ejpam-4766	34	42	g	g	NOUN
ejpam-4766	34	43	be	be	AUX
ejpam-4766	34	44	a	a	DET
ejpam-4766	34	45	connected	connected	ADJ
ejpam-4766	34	46	graph	graph	NOUN
ejpam-4766	34	47	.	.	PUNCT
ejpam-4766	35	1	then	then	ADV
ejpam-4766	35	2	d	d	PROPN
ejpam-4766	35	3	⊆	⊆	NUM
ejpam-4766	35	4	v	v	ADP
ejpam-4766	35	5	(	(	PUNCT
ejpam-4766	35	6	g	g	NOUN
ejpam-4766	35	7	)	)	PUNCT
ejpam-4766	35	8	is	be	AUX
ejpam-4766	35	9	called	call	VERB
ejpam-4766	35	10	a	a	DET
ejpam-4766	35	11	connected	connected	ADJ
ejpam-4766	35	12	outer	outer	ADJ
ejpam-4766	35	13	-	-	PUNCT
ejpam-4766	35	14	independent	independent	ADJ
ejpam-4766	35	15	dominating	dominating	NOUN
ejpam-4766	35	16	set	set	NOUN
ejpam-4766	35	17	if	if	SCONJ
ejpam-4766	35	18	d	d	PROPN
ejpam-4766	35	19	is	be	AUX
ejpam-4766	35	20	connected	connect	VERB
ejpam-4766	35	21	dominating	dominating	NOUN
ejpam-4766	35	22	set	set	NOUN
ejpam-4766	35	23	and	and	CCONJ
ejpam-4766	35	24	v	v	NOUN
ejpam-4766	35	25	(	(	PUNCT
ejpam-4766	35	26	g	g	NOUN
ejpam-4766	35	27	)	)	PUNCT
ejpam-4766	35	28	\	\	PUNCT
ejpam-4766	36	1	d	d	NOUN
ejpam-4766	36	2	is	be	AUX
ejpam-4766	36	3	an	an	DET
ejpam-4766	36	4	independent	independent	ADJ
ejpam-4766	36	5	set	set	NOUN
ejpam-4766	36	6	in	in	ADP
ejpam-4766	36	7	g.	g.	PROPN
ejpam-4766	36	8	the	the	DET
ejpam-4766	36	9	minimum	minimum	ADJ
ejpam-4766	36	10	cardinality	cardinality	NOUN
ejpam-4766	36	11	of	of	ADP
ejpam-4766	36	12	a	a	DET
ejpam-4766	36	13	connected	connected	ADJ
ejpam-4766	36	14	outer	outer	ADJ
ejpam-4766	36	15	-	-	PUNCT
ejpam-4766	36	16	independent	independent	ADJ
ejpam-4766	36	17	dominating	dominating	NOUN
ejpam-4766	36	18	set	set	NOUN
ejpam-4766	36	19	in	in	ADP
ejpam-4766	36	20	g	g	NOUN
ejpam-4766	36	21	,	,	PUNCT
ejpam-4766	36	22	denoted	denote	VERB
ejpam-4766	36	23	by	by	ADP
ejpam-4766	36	24	,	,	PUNCT
ejpam-4766	36	25	γoic	γoic	ADJ
ejpam-4766	36	26	(	(	PUNCT
ejpam-4766	36	27	g	g	NOUN
ejpam-4766	36	28	)	)	PUNCT
ejpam-4766	36	29	is	be	AUX
ejpam-4766	36	30	called	call	VERB
ejpam-4766	36	31	the	the	DET
ejpam-4766	36	32	connected	connected	ADJ
ejpam-4766	36	33	outer	outer	ADJ
ejpam-4766	36	34	-	-	PUNCT
ejpam-4766	36	35	independent	independent	ADJ
ejpam-4766	36	36	domination	domination	NOUN
ejpam-4766	36	37	number	number	NOUN
ejpam-4766	36	38	of	of	ADP
ejpam-4766	36	39	g.	g.	PROPN
ejpam-4766	36	40	any	any	DET
ejpam-4766	36	41	connected	connected	ADJ
ejpam-4766	36	42	outer	outer	ADJ
ejpam-4766	36	43	-	-	PUNCT
ejpam-4766	36	44	independent	independent	ADJ
ejpam-4766	36	45	dominating	dominating	NOUN
ejpam-4766	36	46	set	set	VERB
ejpam-4766	36	47	with	with	ADP
ejpam-4766	36	48	cardinality	cardinality	NOUN
ejpam-4766	36	49	equal	equal	ADJ
ejpam-4766	36	50	to	to	ADP
ejpam-4766	36	51	γoic	γoic	ADJ
ejpam-4766	36	52	(	(	PUNCT
ejpam-4766	36	53	g	g	NOUN
ejpam-4766	36	54	)	)	PUNCT
ejpam-4766	36	55	is	be	AUX
ejpam-4766	36	56	called	call	VERB
ejpam-4766	36	57	a	a	DET
ejpam-4766	36	58	γoic	γoic	ADJ
ejpam-4766	36	59	-set	-set	ADJ
ejpam-4766	36	60	of	of	ADP
ejpam-4766	36	61	g.	g.	PROPN
ejpam-4766	36	62	a	a	DET
ejpam-4766	36	63	subset	subset	NOUN
ejpam-4766	36	64	s	s	NOUN
ejpam-4766	36	65	of	of	ADP
ejpam-4766	36	66	v	v	NOUN
ejpam-4766	36	67	(	(	PUNCT
ejpam-4766	36	68	g	g	NOUN
ejpam-4766	36	69	)	)	PUNCT
ejpam-4766	36	70	is	be	AUX
ejpam-4766	36	71	called	call	VERB
ejpam-4766	36	72	a	a	DET
ejpam-4766	36	73	hop	hop	NOUN
ejpam-4766	36	74	independent	independent	ADJ
ejpam-4766	36	75	if	if	SCONJ
ejpam-4766	36	76	for	for	ADP
ejpam-4766	36	77	every	every	DET
ejpam-4766	36	78	pair	pair	NOUN
ejpam-4766	36	79	of	of	ADP
ejpam-4766	36	80	distinct	distinct	ADJ
ejpam-4766	36	81	vertices	vertex	NOUN
ejpam-4766	36	82	j.	j.	PROPN
ejpam-4766	36	83	hassan	hassan	PROPN
ejpam-4766	36	84	et	et	PROPN
ejpam-4766	36	85	al	al	PROPN
ejpam-4766	36	86	.	.	PUNCT
ejpam-4766	36	87	/	/	SYM
ejpam-4766	36	88	eur	eur	PROPN
ejpam-4766	36	89	.	.	PUNCT
ejpam-4766	37	1	j.	j.	PROPN
ejpam-4766	37	2	pure	pure	PROPN
ejpam-4766	37	3	appl	appl	PROPN
ejpam-4766	37	4	.	.	PROPN
ejpam-4766	37	5	math	math	PROPN
ejpam-4766	37	6	,	,	PUNCT
ejpam-4766	37	7	16	16	NUM
ejpam-4766	37	8	(	(	PUNCT
ejpam-4766	37	9	3	3	NUM
ejpam-4766	37	10	)	)	PUNCT
ejpam-4766	37	11	(	(	PUNCT
ejpam-4766	37	12	2023	2023	NUM
ejpam-4766	37	13	)	)	PUNCT
ejpam-4766	37	14	,	,	PUNCT
ejpam-4766	37	15	1817	1817	NUM
ejpam-4766	37	16	-	-	SYM
ejpam-4766	37	17	1829	1829	NUM
ejpam-4766	37	18	1819	1819	NUM
ejpam-4766	37	19	v	v	NOUN
ejpam-4766	37	20	,	,	PUNCT
ejpam-4766	37	21	w	w	PROPN
ejpam-4766	37	22	∈	∈	PROPN
ejpam-4766	37	23	s	s	NOUN
ejpam-4766	37	24	,	,	PUNCT
ejpam-4766	37	25	dg(v	dg(v	X
ejpam-4766	37	26	,	,	PUNCT
ejpam-4766	37	27	w	w	NOUN
ejpam-4766	37	28	)	)	PUNCT
ejpam-4766	37	29	̸=	̸=	PROPN
ejpam-4766	37	30	2	2	NUM
ejpam-4766	37	31	.	.	PUNCT
ejpam-4766	38	1	the	the	DET
ejpam-4766	38	2	maximum	maximum	ADJ
ejpam-4766	38	3	cardinality	cardinality	NOUN
ejpam-4766	38	4	of	of	ADP
ejpam-4766	38	5	a	a	DET
ejpam-4766	38	6	hop	hop	NOUN
ejpam-4766	38	7	independent	independent	ADJ
ejpam-4766	38	8	set	set	NOUN
ejpam-4766	38	9	in	in	ADP
ejpam-4766	38	10	g	g	NOUN
ejpam-4766	38	11	,	,	PUNCT
ejpam-4766	38	12	denoted	denote	VERB
ejpam-4766	38	13	by	by	ADP
ejpam-4766	38	14	αh(g	αh(g	NOUN
ejpam-4766	38	15	)	)	PUNCT
ejpam-4766	38	16	,	,	PUNCT
ejpam-4766	38	17	is	be	AUX
ejpam-4766	38	18	called	call	VERB
ejpam-4766	38	19	the	the	DET
ejpam-4766	38	20	hop	hop	NOUN
ejpam-4766	38	21	independence	independence	NOUN
ejpam-4766	38	22	number	number	NOUN
ejpam-4766	38	23	of	of	ADP
ejpam-4766	38	24	g.	g.	PROPN
ejpam-4766	38	25	any	any	DET
ejpam-4766	38	26	hop	hop	NOUN
ejpam-4766	38	27	independent	independent	ADJ
ejpam-4766	38	28	set	set	NOUN
ejpam-4766	38	29	s	s	PROPN
ejpam-4766	38	30	with	with	ADP
ejpam-4766	38	31	cardinality	cardinality	NOUN
ejpam-4766	38	32	equal	equal	ADJ
ejpam-4766	38	33	to	to	ADP
ejpam-4766	38	34	αh(g	αh(g	NOUN
ejpam-4766	38	35	)	)	PUNCT
ejpam-4766	38	36	is	be	AUX
ejpam-4766	38	37	called	call	VERB
ejpam-4766	38	38	a	a	DET
ejpam-4766	38	39	αh	αh	NOUN
ejpam-4766	38	40	-	-	PUNCT
ejpam-4766	38	41	set	set	NOUN
ejpam-4766	38	42	of	of	ADP
ejpam-4766	38	43	g.	g.	PROPN
ejpam-4766	38	44	let	let	VERB
ejpam-4766	38	45	g	g	NOUN
ejpam-4766	38	46	and	and	CCONJ
ejpam-4766	38	47	h	h	NOUN
ejpam-4766	38	48	be	be	VERB
ejpam-4766	38	49	two	two	NUM
ejpam-4766	38	50	graphs	graph	NOUN
ejpam-4766	38	51	.	.	PUNCT
ejpam-4766	39	1	the	the	DET
ejpam-4766	39	2	join	join	NOUN
ejpam-4766	39	3	of	of	ADP
ejpam-4766	39	4	g	g	PROPN
ejpam-4766	39	5	and	and	CCONJ
ejpam-4766	39	6	h	h	NOUN
ejpam-4766	39	7	,	,	PUNCT
ejpam-4766	39	8	denoted	denote	VERB
ejpam-4766	39	9	by	by	ADP
ejpam-4766	39	10	g	g	PROPN
ejpam-4766	39	11	+	+	PROPN
ejpam-4766	39	12	h	h	NOUN
ejpam-4766	39	13	,	,	PUNCT
ejpam-4766	39	14	is	be	AUX
ejpam-4766	39	15	the	the	DET
ejpam-4766	39	16	graph	graph	NOUN
ejpam-4766	39	17	with	with	ADP
ejpam-4766	39	18	vertex	vertex	NOUN
ejpam-4766	39	19	set	set	VERB
ejpam-4766	39	20	v	v	NOUN
ejpam-4766	39	21	(	(	PUNCT
ejpam-4766	39	22	g+h	g+h	NOUN
ejpam-4766	39	23	)	)	PUNCT
ejpam-4766	39	24	=	=	SYM
ejpam-4766	39	25	v	v	X
ejpam-4766	39	26	(	(	PUNCT
ejpam-4766	39	27	g)∪v	g)∪v	NOUN
ejpam-4766	39	28	(	(	PUNCT
ejpam-4766	39	29	h	h	NOUN
ejpam-4766	39	30	)	)	PUNCT
ejpam-4766	39	31	and	and	CCONJ
ejpam-4766	39	32	edge	edge	NOUN
ejpam-4766	39	33	set	set	VERB
ejpam-4766	39	34	e(g+h	e(g+h	NUM
ejpam-4766	39	35	)	)	PUNCT
ejpam-4766	40	1	=	=	SYM
ejpam-4766	40	2	e(g)∪e(h)∪{uv	e(g)∪e(h)∪{uv	X
ejpam-4766	40	3	:	:	PUNCT
ejpam-4766	40	4	u	u	PROPN
ejpam-4766	40	5	∈	∈	PROPN
ejpam-4766	40	6	v	v	NOUN
ejpam-4766	40	7	(	(	PUNCT
ejpam-4766	40	8	g	g	NOUN
ejpam-4766	40	9	)	)	PUNCT
ejpam-4766	40	10	,	,	PUNCT
ejpam-4766	40	11	v	v	X
ejpam-4766	40	12	∈	∈	PROPN
ejpam-4766	40	13	v	v	NOUN
ejpam-4766	40	14	(	(	PUNCT
ejpam-4766	40	15	h	h	NOUN
ejpam-4766	40	16	)	)	PUNCT
ejpam-4766	40	17	}	}	PUNCT
ejpam-4766	40	18	.	.	PUNCT
ejpam-4766	41	1	the	the	DET
ejpam-4766	41	2	corona	corona	NOUN
ejpam-4766	41	3	g	g	PROPN
ejpam-4766	41	4	and	and	CCONJ
ejpam-4766	41	5	h	h	NOUN
ejpam-4766	41	6	,	,	PUNCT
ejpam-4766	41	7	denoted	denote	VERB
ejpam-4766	41	8	by	by	ADP
ejpam-4766	41	9	g	g	PROPN
ejpam-4766	41	10	◦	◦	NOUN
ejpam-4766	41	11	h	h	NOUN
ejpam-4766	41	12	,	,	PUNCT
ejpam-4766	41	13	is	be	AUX
ejpam-4766	41	14	the	the	DET
ejpam-4766	41	15	graph	graph	NOUN
ejpam-4766	41	16	obtained	obtain	VERB
ejpam-4766	41	17	by	by	ADP
ejpam-4766	41	18	taking	take	VERB
ejpam-4766	41	19	one	one	NUM
ejpam-4766	41	20	copy	copy	NOUN
ejpam-4766	41	21	of	of	ADP
ejpam-4766	41	22	g	g	PROPN
ejpam-4766	41	23	and	and	CCONJ
ejpam-4766	41	24	|v	|v	PROPN
ejpam-4766	41	25	(	(	PUNCT
ejpam-4766	41	26	g)|	g)|	NOUN
ejpam-4766	41	27	copies	copy	NOUN
ejpam-4766	41	28	of	of	ADP
ejpam-4766	41	29	h	h	NOUN
ejpam-4766	41	30	,	,	PUNCT
ejpam-4766	41	31	and	and	CCONJ
ejpam-4766	41	32	then	then	ADV
ejpam-4766	41	33	joining	join	VERB
ejpam-4766	41	34	the	the	DET
ejpam-4766	41	35	ith	ith	PROPN
ejpam-4766	41	36	vertex	vertex	NOUN
ejpam-4766	41	37	of	of	ADP
ejpam-4766	41	38	g	g	NOUN
ejpam-4766	41	39	to	to	ADP
ejpam-4766	41	40	every	every	DET
ejpam-4766	41	41	vertex	vertex	NOUN
ejpam-4766	41	42	of	of	ADP
ejpam-4766	41	43	the	the	DET
ejpam-4766	41	44	ith	ith	PROPN
ejpam-4766	41	45	copy	copy	NOUN
ejpam-4766	41	46	of	of	ADP
ejpam-4766	41	47	h.	h.	PROPN
ejpam-4766	41	48	we	we	PRON
ejpam-4766	41	49	denote	denote	VERB
ejpam-4766	41	50	by	by	ADP
ejpam-4766	41	51	hv	hv	PROPN
ejpam-4766	41	52	the	the	DET
ejpam-4766	41	53	copy	copy	NOUN
ejpam-4766	41	54	of	of	ADP
ejpam-4766	41	55	h	h	NOUN
ejpam-4766	41	56	in	in	ADP
ejpam-4766	41	57	g	g	ADP
ejpam-4766	41	58	◦	◦	NOUN
ejpam-4766	41	59	h	h	NOUN
ejpam-4766	41	60	corresponding	correspond	VERB
ejpam-4766	41	61	to	to	ADP
ejpam-4766	41	62	the	the	DET
ejpam-4766	41	63	vertex	vertex	NOUN
ejpam-4766	41	64	v	v	ADP
ejpam-4766	41	65	∈	∈	PROPN
ejpam-4766	41	66	g	g	NOUN
ejpam-4766	41	67	and	and	CCONJ
ejpam-4766	41	68	write	write	VERB
ejpam-4766	41	69	v	v	ADP
ejpam-4766	41	70	+	+	PROPN
ejpam-4766	41	71	hv	hv	NOUN
ejpam-4766	41	72	for	for	ADP
ejpam-4766	41	73	⟨{v}+hv⟩.	⟨{v}+hv⟩.	X
ejpam-4766	41	74	3	3	X
ejpam-4766	41	75	.	.	X
ejpam-4766	41	76	results	result	NOUN
ejpam-4766	41	77	we	we	PRON
ejpam-4766	41	78	begin	begin	VERB
ejpam-4766	41	79	this	this	DET
ejpam-4766	41	80	section	section	NOUN
ejpam-4766	41	81	by	by	ADP
ejpam-4766	41	82	introducing	introduce	VERB
ejpam-4766	41	83	the	the	DET
ejpam-4766	41	84	concept	concept	NOUN
ejpam-4766	41	85	of	of	ADP
ejpam-4766	41	86	connected	connected	ADJ
ejpam-4766	41	87	outer	outer	ADJ
ejpam-4766	41	88	-	-	PUNCT
ejpam-4766	41	89	hop	hop	NOUN
ejpam-4766	41	90	independent	independent	ADJ
ejpam-4766	41	91	domination	domination	NOUN
ejpam-4766	41	92	in	in	ADP
ejpam-4766	41	93	a	a	DET
ejpam-4766	41	94	graph	graph	NOUN
ejpam-4766	41	95	.	.	PUNCT
ejpam-4766	42	1	definition	definition	NOUN
ejpam-4766	42	2	1	1	NUM
ejpam-4766	42	3	.	.	PUNCT
ejpam-4766	43	1	let	let	VERB
ejpam-4766	43	2	g	g	PRON
ejpam-4766	43	3	be	be	AUX
ejpam-4766	43	4	a	a	DET
ejpam-4766	43	5	connected	connected	ADJ
ejpam-4766	43	6	graph	graph	NOUN
ejpam-4766	43	7	.	.	PUNCT
ejpam-4766	44	1	then	then	ADV
ejpam-4766	44	2	d	d	PROPN
ejpam-4766	44	3	⊆	⊆	NUM
ejpam-4766	44	4	v	v	ADP
ejpam-4766	44	5	(	(	PUNCT
ejpam-4766	44	6	g	g	NOUN
ejpam-4766	44	7	)	)	PUNCT
ejpam-4766	44	8	is	be	AUX
ejpam-4766	44	9	called	call	VERB
ejpam-4766	44	10	a	a	DET
ejpam-4766	44	11	connected	connected	ADJ
ejpam-4766	44	12	outerhop	outerhop	ADJ
ejpam-4766	44	13	independent	independent	ADJ
ejpam-4766	44	14	dominating	dominating	NOUN
ejpam-4766	44	15	set	set	NOUN
ejpam-4766	44	16	if	if	SCONJ
ejpam-4766	44	17	d	d	PROPN
ejpam-4766	44	18	is	be	AUX
ejpam-4766	44	19	connected	connect	VERB
ejpam-4766	44	20	dominating	dominating	NOUN
ejpam-4766	44	21	set	set	NOUN
ejpam-4766	44	22	and	and	CCONJ
ejpam-4766	44	23	v	v	NOUN
ejpam-4766	44	24	(	(	PUNCT
ejpam-4766	44	25	g	g	NOUN
ejpam-4766	44	26	)	)	PUNCT
ejpam-4766	44	27	\d	\d	NOUN
ejpam-4766	44	28	is	be	AUX
ejpam-4766	44	29	a	a	DET
ejpam-4766	44	30	hop	hop	NOUN
ejpam-4766	44	31	independent	independent	ADJ
ejpam-4766	44	32	set	set	NOUN
ejpam-4766	44	33	in	in	ADP
ejpam-4766	44	34	g.	g.	PROPN
ejpam-4766	44	35	the	the	DET
ejpam-4766	44	36	minimum	minimum	ADJ
ejpam-4766	44	37	cardinality	cardinality	NOUN
ejpam-4766	44	38	of	of	ADP
ejpam-4766	44	39	a	a	DET
ejpam-4766	44	40	connected	connected	ADJ
ejpam-4766	44	41	outer	outer	ADJ
ejpam-4766	44	42	-	-	PUNCT
ejpam-4766	44	43	hop	hop	NOUN
ejpam-4766	44	44	independent	independent	ADJ
ejpam-4766	44	45	dominating	dominating	NOUN
ejpam-4766	44	46	set	set	VERB
ejpam-4766	44	47	in	in	ADP
ejpam-4766	44	48	g	g	NOUN
ejpam-4766	44	49	,	,	PUNCT
ejpam-4766	44	50	denoted	denote	VERB
ejpam-4766	44	51	by	by	ADP
ejpam-4766	44	52	,	,	PUNCT
ejpam-4766	44	53	γohic	γohic	ADJ
ejpam-4766	44	54	(	(	PUNCT
ejpam-4766	44	55	g	g	NOUN
ejpam-4766	44	56	)	)	PUNCT
ejpam-4766	44	57	is	be	AUX
ejpam-4766	44	58	called	call	VERB
ejpam-4766	44	59	the	the	DET
ejpam-4766	44	60	connected	connected	ADJ
ejpam-4766	44	61	outer	outer	ADJ
ejpam-4766	44	62	-	-	PUNCT
ejpam-4766	44	63	hop	hop	NOUN
ejpam-4766	44	64	independent	independent	ADJ
ejpam-4766	44	65	domination	domination	NOUN
ejpam-4766	44	66	number	number	NOUN
ejpam-4766	44	67	of	of	ADP
ejpam-4766	44	68	g.	g.	PROPN
ejpam-4766	44	69	any	any	DET
ejpam-4766	44	70	connected	connected	ADJ
ejpam-4766	44	71	outer	outer	ADJ
ejpam-4766	44	72	-	-	PUNCT
ejpam-4766	44	73	hop	hop	NOUN
ejpam-4766	44	74	independent	independent	ADJ
ejpam-4766	44	75	dominating	dominating	NOUN
ejpam-4766	44	76	set	set	VERB
ejpam-4766	44	77	d	d	NOUN
ejpam-4766	44	78	with	with	ADP
ejpam-4766	44	79	cardinality	cardinality	NOUN
ejpam-4766	44	80	equal	equal	ADJ
ejpam-4766	44	81	to	to	ADP
ejpam-4766	44	82	γohic	γohic	ADJ
ejpam-4766	44	83	(	(	PUNCT
ejpam-4766	44	84	g	g	NOUN
ejpam-4766	44	85	)	)	PUNCT
ejpam-4766	44	86	is	be	AUX
ejpam-4766	44	87	called	call	VERB
ejpam-4766	44	88	a	a	DET
ejpam-4766	44	89	γohic	γohic	ADJ
ejpam-4766	44	90	-set	-set	NUM
ejpam-4766	44	91	of	of	ADP
ejpam-4766	44	92	g.	g.	PROPN
ejpam-4766	44	93	it	it	PRON
ejpam-4766	44	94	is	be	AUX
ejpam-4766	44	95	worth	worth	ADJ
ejpam-4766	44	96	mentioning	mention	VERB
ejpam-4766	44	97	that	that	SCONJ
ejpam-4766	44	98	every	every	DET
ejpam-4766	44	99	connected	connected	ADJ
ejpam-4766	44	100	graph	graph	NOUN
ejpam-4766	44	101	g	g	PROPN
ejpam-4766	44	102	admits	admit	VERB
ejpam-4766	44	103	a	a	DET
ejpam-4766	44	104	connected	connected	ADJ
ejpam-4766	44	105	outer	outer	ADJ
ejpam-4766	44	106	-	-	PUNCT
ejpam-4766	44	107	hop	hop	NOUN
ejpam-4766	44	108	independent	independent	ADJ
ejpam-4766	44	109	domination	domination	NOUN
ejpam-4766	44	110	.	.	PUNCT
ejpam-4766	45	1	the	the	DET
ejpam-4766	45	2	following	follow	VERB
ejpam-4766	45	3	first	first	ADJ
ejpam-4766	45	4	remark	remark	NOUN
ejpam-4766	45	5	is	be	AUX
ejpam-4766	45	6	the	the	DET
ejpam-4766	45	7	result	result	NOUN
ejpam-4766	45	8	concerning	concern	VERB
ejpam-4766	45	9	the	the	DET
ejpam-4766	45	10	relationship	relationship	NOUN
ejpam-4766	45	11	between	between	ADP
ejpam-4766	45	12	connected	connected	ADJ
ejpam-4766	45	13	domination	domination	NOUN
ejpam-4766	45	14	number	number	NOUN
ejpam-4766	45	15	and	and	CCONJ
ejpam-4766	45	16	connected	connected	ADJ
ejpam-4766	45	17	outer	outer	ADJ
ejpam-4766	45	18	-	-	PUNCT
ejpam-4766	45	19	hop	hop	NOUN
ejpam-4766	45	20	independent	independent	ADJ
ejpam-4766	45	21	domination	domination	NOUN
ejpam-4766	45	22	number	number	NOUN
ejpam-4766	45	23	of	of	ADP
ejpam-4766	45	24	a	a	DET
ejpam-4766	45	25	graph	graph	NOUN
ejpam-4766	45	26	g.	g.	NOUN
ejpam-4766	45	27	remark	remark	NOUN
ejpam-4766	45	28	1	1	NUM
ejpam-4766	45	29	.	.	PUNCT
ejpam-4766	46	1	let	let	VERB
ejpam-4766	46	2	g	g	PRON
ejpam-4766	46	3	be	be	AUX
ejpam-4766	46	4	a	a	DET
ejpam-4766	46	5	connected	connected	ADJ
ejpam-4766	46	6	graph	graph	NOUN
ejpam-4766	46	7	.	.	PUNCT
ejpam-4766	47	1	then	then	ADV
ejpam-4766	47	2	γc(g	γc(g	PUNCT
ejpam-4766	47	3	)	)	PUNCT
ejpam-4766	47	4	≤	≤	NUM
ejpam-4766	47	5	γohic	γohic	ADJ
ejpam-4766	47	6	(	(	PUNCT
ejpam-4766	47	7	g	g	NOUN
ejpam-4766	47	8	)	)	PUNCT
ejpam-4766	47	9	.	.	PUNCT
ejpam-4766	48	1	it	it	PRON
ejpam-4766	48	2	is	be	AUX
ejpam-4766	48	3	clear	clear	ADJ
ejpam-4766	48	4	since	since	SCONJ
ejpam-4766	48	5	every	every	DET
ejpam-4766	48	6	connected	connected	ADJ
ejpam-4766	48	7	outer	outer	ADJ
ejpam-4766	48	8	-	-	PUNCT
ejpam-4766	48	9	hop	hop	NOUN
ejpam-4766	48	10	independent	independent	ADJ
ejpam-4766	48	11	dominating	dominating	NOUN
ejpam-4766	48	12	set	set	NOUN
ejpam-4766	48	13	is	be	AUX
ejpam-4766	48	14	connected	connect	VERB
ejpam-4766	48	15	dominating	dominating	NOUN
ejpam-4766	48	16	.	.	PUNCT
ejpam-4766	49	1	remark	remark	NOUN
ejpam-4766	49	2	2	2	NUM
ejpam-4766	49	3	.	.	PUNCT
ejpam-4766	50	1	the	the	DET
ejpam-4766	50	2	bound	bind	VERB
ejpam-4766	50	3	given	give	VERB
ejpam-4766	50	4	in	in	ADP
ejpam-4766	50	5	remark	remark	NOUN
ejpam-4766	50	6	1	1	NUM
ejpam-4766	50	7	is	be	AUX
ejpam-4766	50	8	tight	tight	ADJ
ejpam-4766	50	9	.	.	PUNCT
ejpam-4766	51	1	moreover	moreover	ADV
ejpam-4766	51	2	,	,	PUNCT
ejpam-4766	51	3	strict	strict	ADJ
ejpam-4766	51	4	inequality	inequality	NOUN
ejpam-4766	51	5	can	can	AUX
ejpam-4766	51	6	be	be	AUX
ejpam-4766	51	7	attained	attain	VERB
ejpam-4766	51	8	.	.	PUNCT
ejpam-4766	52	1	for	for	ADP
ejpam-4766	52	2	the	the	DET
ejpam-4766	52	3	equality	equality	NOUN
ejpam-4766	52	4	,	,	PUNCT
ejpam-4766	52	5	consider	consider	VERB
ejpam-4766	52	6	the	the	DET
ejpam-4766	52	7	graph	graph	NOUN
ejpam-4766	52	8	h	h	NOUN
ejpam-4766	52	9	given	give	VERB
ejpam-4766	52	10	in	in	ADP
ejpam-4766	52	11	figure	figure	NOUN
ejpam-4766	52	12	1	1	NUM
ejpam-4766	52	13	.	.	PUNCT
ejpam-4766	53	1	let	let	VERB
ejpam-4766	53	2	d	d	NOUN
ejpam-4766	53	3	=	=	PUNCT
ejpam-4766	53	4	{	{	PUNCT
ejpam-4766	53	5	d	d	NOUN
ejpam-4766	53	6	,	,	PUNCT
ejpam-4766	53	7	g	g	PROPN
ejpam-4766	53	8	,	,	PUNCT
ejpam-4766	53	9	h	h	NOUN
ejpam-4766	53	10	,	,	PUNCT
ejpam-4766	53	11	k	k	NOUN
ejpam-4766	53	12	}	}	PUNCT
ejpam-4766	53	13	.	.	PUNCT
ejpam-4766	54	1	then	then	ADV
ejpam-4766	54	2	d	d	PROPN
ejpam-4766	54	3	is	be	AUX
ejpam-4766	54	4	both	both	PRON
ejpam-4766	54	5	γc	γc	NOUN
ejpam-4766	54	6	-	-	PUNCT
ejpam-4766	54	7	set	set	ADJ
ejpam-4766	54	8	and	and	CCONJ
ejpam-4766	54	9	γohic	γohic	ADJ
ejpam-4766	54	10	-set	-set	NUM
ejpam-4766	54	11	of	of	ADP
ejpam-4766	54	12	h.	h.	PROPN
ejpam-4766	54	13	thus	thus	ADV
ejpam-4766	54	14	,	,	PUNCT
ejpam-4766	54	15	γc(h	γc(h	PUNCT
ejpam-4766	54	16	)	)	PUNCT
ejpam-4766	54	17	=	=	SYM
ejpam-4766	54	18	4	4	NUM
ejpam-4766	54	19	=	=	SYM
ejpam-4766	54	20	γohic	γohic	ADJ
ejpam-4766	54	21	(	(	PUNCT
ejpam-4766	54	22	h	h	NOUN
ejpam-4766	54	23	)	)	PUNCT
ejpam-4766	54	24	.	.	PUNCT
ejpam-4766	55	1	j.	j.	PROPN
ejpam-4766	55	2	hassan	hassan	PROPN
ejpam-4766	55	3	et	et	PROPN
ejpam-4766	55	4	al	al	PROPN
ejpam-4766	55	5	.	.	PUNCT
ejpam-4766	55	6	/	/	SYM
ejpam-4766	55	7	eur	eur	PROPN
ejpam-4766	55	8	.	.	PUNCT
ejpam-4766	56	1	j.	j.	PROPN
ejpam-4766	56	2	pure	pure	PROPN
ejpam-4766	56	3	appl	appl	PROPN
ejpam-4766	56	4	.	.	PROPN
ejpam-4766	56	5	math	math	PROPN
ejpam-4766	56	6	,	,	PUNCT
ejpam-4766	56	7	16	16	NUM
ejpam-4766	56	8	(	(	PUNCT
ejpam-4766	56	9	3	3	NUM
ejpam-4766	56	10	)	)	PUNCT
ejpam-4766	56	11	(	(	PUNCT
ejpam-4766	56	12	2023	2023	NUM
ejpam-4766	56	13	)	)	PUNCT
ejpam-4766	56	14	,	,	PUNCT
ejpam-4766	56	15	1817	1817	NUM
ejpam-4766	56	16	-	-	SYM
ejpam-4766	56	17	1829	1829	NUM
ejpam-4766	56	18	1820	1820	NUM
ejpam-4766	57	1	a	a	DET
ejpam-4766	57	2	b	b	NOUN
ejpam-4766	57	3	c	c	NOUN
ejpam-4766	57	4	d	d	PROPN
ejpam-4766	57	5	e	e	X
ejpam-4766	57	6	f	f	PROPN
ejpam-4766	57	7	g	g	PROPN
ejpam-4766	57	8	h	h	NOUN
ejpam-4766	58	1	i	i	PRON
ejpam-4766	58	2	j	j	PROPN
ejpam-4766	59	1	k	k	PROPN
ejpam-4766	59	2	l	l	PROPN
ejpam-4766	59	3	h	h	NOUN
ejpam-4766	59	4	:	:	PUNCT
ejpam-4766	59	5	figure	figure	VERB
ejpam-4766	59	6	1	1	NUM
ejpam-4766	59	7	:	:	PUNCT
ejpam-4766	59	8	a	a	DET
ejpam-4766	59	9	graph	graph	NOUN
ejpam-4766	59	10	g	g	NOUN
ejpam-4766	59	11	with	with	ADP
ejpam-4766	59	12	γc(h	γc(h	NUM
ejpam-4766	59	13	)	)	PUNCT
ejpam-4766	59	14	=	=	SYM
ejpam-4766	60	1	γohi	γohi	NOUN
ejpam-4766	60	2	c	c	PROPN
ejpam-4766	60	3	(	(	PUNCT
ejpam-4766	60	4	h	h	NOUN
ejpam-4766	60	5	)	)	PUNCT
ejpam-4766	60	6	for	for	ADP
ejpam-4766	60	7	strict	strict	ADJ
ejpam-4766	60	8	inequality	inequality	NOUN
ejpam-4766	60	9	,	,	PUNCT
ejpam-4766	60	10	consider	consider	VERB
ejpam-4766	60	11	the	the	DET
ejpam-4766	60	12	graph	graph	NOUN
ejpam-4766	60	13	g	g	NOUN
ejpam-4766	60	14	given	give	VERB
ejpam-4766	60	15	in	in	ADP
ejpam-4766	60	16	figure	figure	NOUN
ejpam-4766	60	17	2	2	NUM
ejpam-4766	60	18	.	.	PUNCT
ejpam-4766	61	1	let	let	VERB
ejpam-4766	61	2	c	c	NOUN
ejpam-4766	61	3	=	=	PUNCT
ejpam-4766	61	4	{	{	PUNCT
ejpam-4766	61	5	b	b	PROPN
ejpam-4766	61	6	,	,	PUNCT
ejpam-4766	61	7	c	c	X
ejpam-4766	61	8	,	,	PUNCT
ejpam-4766	61	9	f	f	NOUN
ejpam-4766	61	10	}	}	PUNCT
ejpam-4766	61	11	and	and	CCONJ
ejpam-4766	61	12	c	c	NOUN
ejpam-4766	61	13	′	′	NUM
ejpam-4766	62	1	=	=	PUNCT
ejpam-4766	62	2	{	{	PUNCT
ejpam-4766	62	3	b	b	NOUN
ejpam-4766	62	4	,	,	PUNCT
ejpam-4766	62	5	c	c	X
ejpam-4766	62	6	,	,	PUNCT
ejpam-4766	62	7	f	f	PROPN
ejpam-4766	62	8	,	,	PUNCT
ejpam-4766	62	9	g	g	PROPN
ejpam-4766	62	10	,	,	PUNCT
ejpam-4766	62	11	h	h	NOUN
ejpam-4766	62	12	}	}	PUNCT
ejpam-4766	62	13	.	.	PUNCT
ejpam-4766	63	1	then	then	ADV
ejpam-4766	63	2	c	c	PROPN
ejpam-4766	63	3	and	and	CCONJ
ejpam-4766	63	4	c	c	PROPN
ejpam-4766	63	5	′	′	NOUN
ejpam-4766	63	6	are	be	AUX
ejpam-4766	63	7	γc	γc	NOUN
ejpam-4766	63	8	-	-	PUNCT
ejpam-4766	63	9	set	set	ADJ
ejpam-4766	63	10	and	and	CCONJ
ejpam-4766	63	11	γohic	γohic	ADJ
ejpam-4766	63	12	-set	-set	ADJ
ejpam-4766	63	13	of	of	ADP
ejpam-4766	63	14	g	g	NOUN
ejpam-4766	63	15	,	,	PUNCT
ejpam-4766	63	16	respectively	respectively	ADV
ejpam-4766	63	17	.	.	PUNCT
ejpam-4766	64	1	hence	hence	ADV
ejpam-4766	64	2	,	,	PUNCT
ejpam-4766	64	3	γc(g	γc(g	ADV
ejpam-4766	64	4	)	)	PUNCT
ejpam-4766	64	5	=	=	SYM
ejpam-4766	65	1	3	3	NUM
ejpam-4766	65	2	<	<	SYM
ejpam-4766	65	3	5	5	NUM
ejpam-4766	65	4	=	=	SYM
ejpam-4766	65	5	γohic	γohic	ADJ
ejpam-4766	65	6	(	(	PUNCT
ejpam-4766	65	7	g	g	NOUN
ejpam-4766	65	8	)	)	PUNCT
ejpam-4766	65	9	.	.	PUNCT
ejpam-4766	66	1	a	a	DET
ejpam-4766	66	2	b	b	X
ejpam-4766	66	3	c	c	NOUN
ejpam-4766	66	4	d	d	X
ejpam-4766	66	5	e	e	X
ejpam-4766	66	6	f	f	X
ejpam-4766	66	7	g	g	PROPN
ejpam-4766	66	8	h	h	NOUN
ejpam-4766	66	9	g	g	NOUN
ejpam-4766	66	10	:	:	PUNCT
ejpam-4766	66	11	figure	figure	NOUN
ejpam-4766	66	12	2	2	NUM
ejpam-4766	66	13	:	:	PUNCT
ejpam-4766	66	14	a	a	DET
ejpam-4766	66	15	graph	graph	NOUN
ejpam-4766	66	16	g	g	NOUN
ejpam-4766	66	17	with	with	ADP
ejpam-4766	66	18	γc(g	γc(g	NOUN
ejpam-4766	66	19	)	)	PUNCT
ejpam-4766	66	20	<	<	X
ejpam-4766	67	1	γohi	γohi	PROPN
ejpam-4766	67	2	c	c	PROPN
ejpam-4766	67	3	(	(	PUNCT
ejpam-4766	67	4	g	g	NOUN
ejpam-4766	67	5	)	)	PUNCT
ejpam-4766	67	6	theorem	theorem	NOUN
ejpam-4766	67	7	1	1	NUM
ejpam-4766	67	8	.	.	PUNCT
ejpam-4766	68	1	let	let	VERB
ejpam-4766	68	2	g	g	PRON
ejpam-4766	68	3	be	be	AUX
ejpam-4766	68	4	a	a	DET
ejpam-4766	68	5	connected	connected	ADJ
ejpam-4766	68	6	graph	graph	NOUN
ejpam-4766	68	7	on	on	ADP
ejpam-4766	68	8	n	n	DET
ejpam-4766	68	9	vertices	vertex	NOUN
ejpam-4766	68	10	.	.	PUNCT
ejpam-4766	69	1	then	then	ADV
ejpam-4766	69	2	1	1	NUM
ejpam-4766	69	3	≤	≤	ADV
ejpam-4766	69	4	γohic	γohic	ADJ
ejpam-4766	69	5	(	(	PUNCT
ejpam-4766	69	6	g	g	NOUN
ejpam-4766	69	7	)	)	PUNCT
ejpam-4766	69	8	≤	≤	NOUN
ejpam-4766	69	9	n	n	CCONJ
ejpam-4766	69	10	−	−	PROPN
ejpam-4766	69	11	1	1	NUM
ejpam-4766	69	12	.	.	PUNCT
ejpam-4766	70	1	moreover	moreover	ADV
ejpam-4766	70	2	,	,	PUNCT
ejpam-4766	70	3	each	each	PRON
ejpam-4766	70	4	of	of	ADP
ejpam-4766	70	5	the	the	DET
ejpam-4766	70	6	following	following	ADJ
ejpam-4766	70	7	statements	statement	NOUN
ejpam-4766	70	8	holds	hold	VERB
ejpam-4766	70	9	.	.	PUNCT
ejpam-4766	71	1	(	(	PUNCT
ejpam-4766	71	2	i	i	NOUN
ejpam-4766	71	3	)	)	PUNCT
ejpam-4766	71	4	γohic	γohic	ADJ
ejpam-4766	71	5	(	(	PUNCT
ejpam-4766	71	6	g	g	NOUN
ejpam-4766	71	7	)	)	PUNCT
ejpam-4766	71	8	=	=	SYM
ejpam-4766	71	9	1	1	NUM
ejpam-4766	71	10	if	if	SCONJ
ejpam-4766	71	11	and	and	CCONJ
ejpam-4766	71	12	only	only	ADV
ejpam-4766	71	13	if	if	SCONJ
ejpam-4766	71	14	g	g	PROPN
ejpam-4766	71	15	is	be	AUX
ejpam-4766	71	16	complete	complete	ADJ
ejpam-4766	71	17	.	.	PUNCT
ejpam-4766	72	1	(	(	PUNCT
ejpam-4766	72	2	ii	ii	NOUN
ejpam-4766	72	3	)	)	PUNCT
ejpam-4766	72	4	γohic	γohic	ADJ
ejpam-4766	72	5	(	(	PUNCT
ejpam-4766	72	6	g	g	NOUN
ejpam-4766	72	7	)	)	PUNCT
ejpam-4766	72	8	=	=	SYM
ejpam-4766	72	9	2	2	NUM
ejpam-4766	72	10	if	if	SCONJ
ejpam-4766	72	11	and	and	CCONJ
ejpam-4766	72	12	only	only	ADV
ejpam-4766	72	13	if	if	SCONJ
ejpam-4766	72	14	for	for	ADP
ejpam-4766	72	15	each	each	DET
ejpam-4766	72	16	pair	pair	NOUN
ejpam-4766	72	17	of	of	ADP
ejpam-4766	72	18	adjacent	adjacent	ADJ
ejpam-4766	72	19	vertices	vertex	NOUN
ejpam-4766	72	20	a	a	PRON
ejpam-4766	72	21	,	,	PUNCT
ejpam-4766	72	22	b	b	PROPN
ejpam-4766	72	23	∈	∈	PROPN
ejpam-4766	72	24	v	v	NOUN
ejpam-4766	72	25	(	(	PUNCT
ejpam-4766	72	26	g	g	NOUN
ejpam-4766	72	27	)	)	PUNCT
ejpam-4766	72	28	such	such	ADJ
ejpam-4766	72	29	that	that	DET
ejpam-4766	72	30	ng[a	ng[a	NOUN
ejpam-4766	72	31	]	]	PUNCT
ejpam-4766	72	32	̸=	̸=	PROPN
ejpam-4766	72	33	ng[b	ng[b	VERB
ejpam-4766	72	34	]	]	PUNCT
ejpam-4766	72	35	,	,	PUNCT
ejpam-4766	72	36	d	d	NOUN
ejpam-4766	72	37	=	=	PRON
ejpam-4766	72	38	{	{	PUNCT
ejpam-4766	72	39	x	x	NOUN
ejpam-4766	72	40	,	,	PUNCT
ejpam-4766	72	41	y	y	PRON
ejpam-4766	72	42	}	}	PUNCT
ejpam-4766	72	43	is	be	AUX
ejpam-4766	72	44	a	a	DET
ejpam-4766	72	45	dominating	dominating	NOUN
ejpam-4766	72	46	set	set	NOUN
ejpam-4766	72	47	of	of	ADP
ejpam-4766	72	48	g	g	PROPN
ejpam-4766	72	49	and	and	CCONJ
ejpam-4766	72	50	v	v	NOUN
ejpam-4766	72	51	(	(	PUNCT
ejpam-4766	72	52	g)\d	g)\d	NOUN
ejpam-4766	72	53	is	be	AUX
ejpam-4766	72	54	hop	hop	ADV
ejpam-4766	72	55	independent	independent	ADJ
ejpam-4766	72	56	set	set	NOUN
ejpam-4766	72	57	in	in	ADP
ejpam-4766	72	58	g.	g.	PROPN
ejpam-4766	72	59	proof	proof	PROPN
ejpam-4766	72	60	.	.	PUNCT
ejpam-4766	73	1	let	let	VERB
ejpam-4766	73	2	g	g	NOUN
ejpam-4766	73	3	be	be	AUX
ejpam-4766	73	4	any	any	DET
ejpam-4766	73	5	connected	connected	ADJ
ejpam-4766	73	6	graph	graph	NOUN
ejpam-4766	73	7	.	.	PUNCT
ejpam-4766	74	1	since	since	SCONJ
ejpam-4766	74	2	∅	∅	NOUN
ejpam-4766	74	3	is	be	AUX
ejpam-4766	74	4	not	not	PART
ejpam-4766	74	5	a	a	DET
ejpam-4766	74	6	connected	connected	ADJ
ejpam-4766	74	7	outer	outer	ADJ
ejpam-4766	74	8	-	-	PUNCT
ejpam-4766	74	9	hop	hop	NOUN
ejpam-4766	74	10	independent	independent	ADJ
ejpam-4766	74	11	dominating	dominating	NOUN
ejpam-4766	74	12	set	set	VERB
ejpam-4766	74	13	in	in	ADP
ejpam-4766	74	14	g	g	PROPN
ejpam-4766	74	15	,	,	PUNCT
ejpam-4766	74	16	it	it	PRON
ejpam-4766	74	17	follows	follow	VERB
ejpam-4766	74	18	that	that	SCONJ
ejpam-4766	74	19	γohic	γohic	ADJ
ejpam-4766	74	20	(	(	PUNCT
ejpam-4766	74	21	g	g	NOUN
ejpam-4766	74	22	)	)	PUNCT
ejpam-4766	74	23	≥	≥	NOUN
ejpam-4766	74	24	1	1	NUM
ejpam-4766	74	25	.	.	PUNCT
ejpam-4766	75	1	let	let	VERB
ejpam-4766	75	2	a	a	PRON
ejpam-4766	75	3	be	be	AUX
ejpam-4766	75	4	a	a	DET
ejpam-4766	75	5	non	non	ADJ
ejpam-4766	75	6	-	-	ADJ
ejpam-4766	75	7	cutting	cutting	ADJ
ejpam-4766	75	8	vertex	vertex	NOUN
ejpam-4766	75	9	of	of	ADP
ejpam-4766	75	10	g.	g.	PROPN
ejpam-4766	76	1	then	then	ADV
ejpam-4766	76	2	v	v	X
ejpam-4766	76	3	(	(	PUNCT
ejpam-4766	76	4	g	g	NOUN
ejpam-4766	76	5	)	)	PUNCT
ejpam-4766	76	6	\	\	NOUN
ejpam-4766	76	7	{	{	PUNCT
ejpam-4766	76	8	a	a	PRON
ejpam-4766	76	9	}	}	PUNCT
ejpam-4766	76	10	is	be	AUX
ejpam-4766	76	11	a	a	DET
ejpam-4766	76	12	connected	connected	ADJ
ejpam-4766	76	13	outer	outer	ADJ
ejpam-4766	76	14	-	-	PUNCT
ejpam-4766	76	15	hop	hop	NOUN
ejpam-4766	76	16	independent	independent	ADJ
ejpam-4766	76	17	dominating	dominating	NOUN
ejpam-4766	76	18	set	set	VERB
ejpam-4766	76	19	in	in	ADP
ejpam-4766	76	20	g.	g.	PROPN
ejpam-4766	76	21	thus	thus	ADV
ejpam-4766	76	22	,	,	PUNCT
ejpam-4766	76	23	γohoc	γohoc	PROPN
ejpam-4766	76	24	(	(	PUNCT
ejpam-4766	76	25	g	g	NOUN
ejpam-4766	76	26	)	)	PUNCT
ejpam-4766	76	27	≤	≤	NUM
ejpam-4766	76	28	n−	n−	NOUN
ejpam-4766	76	29	1	1	NUM
ejpam-4766	76	30	.	.	PUNCT
ejpam-4766	77	1	consequently	consequently	ADV
ejpam-4766	77	2	,	,	PUNCT
ejpam-4766	77	3	1	1	NUM
ejpam-4766	77	4	≤	≤	NUM
ejpam-4766	77	5	γohic	γohic	ADJ
ejpam-4766	77	6	(	(	PUNCT
ejpam-4766	77	7	g	g	NOUN
ejpam-4766	77	8	)	)	PUNCT
ejpam-4766	77	9	≤	≤	NUM
ejpam-4766	77	10	n−	n−	NOUN
ejpam-4766	77	11	1	1	NUM
ejpam-4766	77	12	.	.	PUNCT
ejpam-4766	78	1	(	(	PUNCT
ejpam-4766	78	2	i	i	NOUN
ejpam-4766	78	3	)	)	PUNCT
ejpam-4766	78	4	assume	assume	VERB
ejpam-4766	78	5	that	that	SCONJ
ejpam-4766	78	6	γohic	γohic	ADJ
ejpam-4766	78	7	(	(	PUNCT
ejpam-4766	78	8	g	g	NOUN
ejpam-4766	78	9	)	)	PUNCT
ejpam-4766	78	10	=	=	SYM
ejpam-4766	79	1	1	1	X
ejpam-4766	79	2	.	.	PUNCT
ejpam-4766	79	3	suppose	suppose	VERB
ejpam-4766	79	4	g	g	PROPN
ejpam-4766	79	5	is	be	AUX
ejpam-4766	79	6	not	not	PART
ejpam-4766	79	7	a	a	DET
ejpam-4766	79	8	complete	complete	ADJ
ejpam-4766	79	9	graph	graph	NOUN
ejpam-4766	79	10	.	.	PUNCT
ejpam-4766	80	1	then	then	ADV
ejpam-4766	80	2	there	there	PRON
ejpam-4766	80	3	exists	exist	VERB
ejpam-4766	80	4	a	a	DET
ejpam-4766	80	5	,	,	PUNCT
ejpam-4766	80	6	b	b	PROPN
ejpam-4766	80	7	∈	∈	PROPN
ejpam-4766	80	8	v	v	NOUN
ejpam-4766	80	9	(	(	PUNCT
ejpam-4766	80	10	g	g	NOUN
ejpam-4766	80	11	)	)	PUNCT
ejpam-4766	80	12	such	such	ADJ
ejpam-4766	80	13	that	that	SCONJ
ejpam-4766	80	14	dg(a	dg(a	PROPN
ejpam-4766	80	15	,	,	PUNCT
ejpam-4766	80	16	b	b	X
ejpam-4766	80	17	)	)	PUNCT
ejpam-4766	80	18	=	=	SYM
ejpam-4766	80	19	2	2	X
ejpam-4766	80	20	.	.	PUNCT
ejpam-4766	80	21	let	let	VERB
ejpam-4766	80	22	c	c	NOUN
ejpam-4766	80	23	∈	∈	PROPN
ejpam-4766	80	24	ng(a	ng(a	NOUN
ejpam-4766	80	25	)	)	PUNCT
ejpam-4766	80	26	∩	∩	NOUN
ejpam-4766	80	27	ng(b	ng(b	NOUN
ejpam-4766	80	28	)	)	PUNCT
ejpam-4766	80	29	.	.	PUNCT
ejpam-4766	81	1	clearly	clearly	ADV
ejpam-4766	81	2	,	,	PUNCT
ejpam-4766	81	3	γohic	γohic	ADJ
ejpam-4766	81	4	(	(	PUNCT
ejpam-4766	81	5	g	g	NOUN
ejpam-4766	81	6	)	)	PUNCT
ejpam-4766	81	7	≥	≥	NOUN
ejpam-4766	81	8	2	2	NUM
ejpam-4766	81	9	,	,	PUNCT
ejpam-4766	81	10	a	a	DET
ejpam-4766	81	11	contradiction	contradiction	NOUN
ejpam-4766	81	12	.	.	PUNCT
ejpam-4766	82	1	hence	hence	ADV
ejpam-4766	82	2	,	,	PUNCT
ejpam-4766	82	3	g	g	PROPN
ejpam-4766	82	4	is	be	AUX
ejpam-4766	82	5	complete	complete	ADJ
ejpam-4766	82	6	.	.	PUNCT
ejpam-4766	83	1	j.	j.	PROPN
ejpam-4766	83	2	hassan	hassan	PROPN
ejpam-4766	83	3	et	et	PROPN
ejpam-4766	83	4	al	al	PROPN
ejpam-4766	83	5	.	.	PUNCT
ejpam-4766	83	6	/	/	SYM
ejpam-4766	83	7	eur	eur	PROPN
ejpam-4766	83	8	.	.	PUNCT
ejpam-4766	84	1	j.	j.	PROPN
ejpam-4766	84	2	pure	pure	PROPN
ejpam-4766	84	3	appl	appl	PROPN
ejpam-4766	84	4	.	.	PROPN
ejpam-4766	84	5	math	math	PROPN
ejpam-4766	84	6	,	,	PUNCT
ejpam-4766	84	7	16	16	NUM
ejpam-4766	84	8	(	(	PUNCT
ejpam-4766	84	9	3	3	NUM
ejpam-4766	84	10	)	)	PUNCT
ejpam-4766	84	11	(	(	PUNCT
ejpam-4766	84	12	2023	2023	NUM
ejpam-4766	84	13	)	)	PUNCT
ejpam-4766	84	14	,	,	PUNCT
ejpam-4766	84	15	1817	1817	NUM
ejpam-4766	84	16	-	-	SYM
ejpam-4766	84	17	1829	1829	NUM
ejpam-4766	84	18	1821	1821	NUM
ejpam-4766	84	19	conversely	conversely	ADV
ejpam-4766	84	20	,	,	PUNCT
ejpam-4766	84	21	suppose	suppose	VERB
ejpam-4766	84	22	g	g	PROPN
ejpam-4766	84	23	is	be	AUX
ejpam-4766	84	24	complete	complete	ADJ
ejpam-4766	84	25	.	.	PUNCT
ejpam-4766	85	1	then	then	ADV
ejpam-4766	85	2	every	every	DET
ejpam-4766	85	3	v	v	NOUN
ejpam-4766	85	4	∈	∈	NOUN
ejpam-4766	85	5	v	v	NOUN
ejpam-4766	85	6	(	(	PUNCT
ejpam-4766	85	7	g	g	NOUN
ejpam-4766	85	8	)	)	PUNCT
ejpam-4766	85	9	is	be	AUX
ejpam-4766	85	10	a	a	DET
ejpam-4766	85	11	connected	connected	ADJ
ejpam-4766	85	12	outer	outer	ADJ
ejpam-4766	85	13	-	-	PUNCT
ejpam-4766	85	14	hop	hop	NOUN
ejpam-4766	85	15	independent	independent	ADJ
ejpam-4766	85	16	dominating	dominating	NOUN
ejpam-4766	85	17	vertex	vertex	NOUN
ejpam-4766	85	18	of	of	ADP
ejpam-4766	85	19	g.	g.	PROPN
ejpam-4766	85	20	thus	thus	ADV
ejpam-4766	85	21	,	,	PUNCT
ejpam-4766	85	22	γohic	γohic	ADJ
ejpam-4766	85	23	(	(	PUNCT
ejpam-4766	85	24	g	g	NOUN
ejpam-4766	85	25	)	)	PUNCT
ejpam-4766	85	26	≤	≤	NUM
ejpam-4766	85	27	1	1	NUM
ejpam-4766	85	28	.	.	PUNCT
ejpam-4766	86	1	consequently	consequently	ADV
ejpam-4766	86	2	,	,	PUNCT
ejpam-4766	86	3	γohic	γohic	ADJ
ejpam-4766	86	4	(	(	PUNCT
ejpam-4766	86	5	g	g	NOUN
ejpam-4766	86	6	)	)	PUNCT
ejpam-4766	86	7	=	=	SYM
ejpam-4766	87	1	1	1	X
ejpam-4766	87	2	.	.	PUNCT
ejpam-4766	87	3	(	(	PUNCT
ejpam-4766	87	4	ii	ii	NOUN
ejpam-4766	87	5	)	)	PUNCT
ejpam-4766	87	6	assume	assume	VERB
ejpam-4766	87	7	that	that	SCONJ
ejpam-4766	87	8	γohic	γohic	ADJ
ejpam-4766	87	9	(	(	PUNCT
ejpam-4766	87	10	g	g	NOUN
ejpam-4766	87	11	)	)	PUNCT
ejpam-4766	87	12	=	=	SYM
ejpam-4766	87	13	2	2	X
ejpam-4766	87	14	.	.	X
ejpam-4766	87	15	let	let	VERB
ejpam-4766	87	16	a	a	PRON
ejpam-4766	87	17	and	and	CCONJ
ejpam-4766	87	18	b	b	NOUN
ejpam-4766	87	19	be	be	AUX
ejpam-4766	87	20	two	two	NUM
ejpam-4766	87	21	distinct	distinct	ADJ
ejpam-4766	87	22	adjacent	adjacent	ADJ
ejpam-4766	87	23	vertices	vertex	NOUN
ejpam-4766	87	24	of	of	ADP
ejpam-4766	87	25	g	g	NOUN
ejpam-4766	87	26	such	such	ADJ
ejpam-4766	87	27	that	that	DET
ejpam-4766	87	28	ng[a	ng[a	NOUN
ejpam-4766	87	29	]	]	PUNCT
ejpam-4766	87	30	̸=	̸=	PROPN
ejpam-4766	87	31	ng[b	ng[b	NOUN
ejpam-4766	87	32	]	]	PUNCT
ejpam-4766	87	33	.	.	PUNCT
ejpam-4766	88	1	suppose	suppose	VERB
ejpam-4766	88	2	there	there	PRON
ejpam-4766	88	3	exists	exist	VERB
ejpam-4766	88	4	x	x	X
ejpam-4766	88	5	∈	∈	PROPN
ejpam-4766	88	6	v	v	X
ejpam-4766	88	7	(	(	PUNCT
ejpam-4766	88	8	g	g	NOUN
ejpam-4766	88	9	)	)	PUNCT
ejpam-4766	88	10	\	\	PUNCT
ejpam-4766	88	11	(	(	PUNCT
ejpam-4766	88	12	ng[a	ng[a	PROPN
ejpam-4766	88	13	]	]	X
ejpam-4766	88	14	∪ng[b	∪ng[b	NOUN
ejpam-4766	88	15	]	]	PUNCT
ejpam-4766	88	16	)	)	PUNCT
ejpam-4766	88	17	.	.	PUNCT
ejpam-4766	89	1	since	since	SCONJ
ejpam-4766	89	2	a	a	PRON
ejpam-4766	89	3	and	and	CCONJ
ejpam-4766	89	4	b	b	NOUN
ejpam-4766	89	5	are	be	AUX
ejpam-4766	89	6	arbitrary	arbitrary	ADJ
ejpam-4766	89	7	,	,	PUNCT
ejpam-4766	89	8	it	it	PRON
ejpam-4766	89	9	follows	follow	VERB
ejpam-4766	89	10	that	that	SCONJ
ejpam-4766	89	11	γohic	γohic	ADJ
ejpam-4766	89	12	(	(	PUNCT
ejpam-4766	89	13	g	g	NOUN
ejpam-4766	89	14	)	)	PUNCT
ejpam-4766	89	15	≥	≥	NOUN
ejpam-4766	89	16	3	3	NUM
ejpam-4766	89	17	,	,	PUNCT
ejpam-4766	89	18	a	a	DET
ejpam-4766	89	19	contradiction	contradiction	NOUN
ejpam-4766	89	20	.	.	PUNCT
ejpam-4766	90	1	therefore	therefore	ADV
ejpam-4766	90	2	,	,	PUNCT
ejpam-4766	90	3	{	{	PUNCT
ejpam-4766	90	4	a	a	DET
ejpam-4766	90	5	,	,	PUNCT
ejpam-4766	90	6	b	b	NOUN
ejpam-4766	90	7	}	}	PUNCT
ejpam-4766	90	8	is	be	AUX
ejpam-4766	90	9	a	a	DET
ejpam-4766	90	10	dominating	dominating	NOUN
ejpam-4766	90	11	set	set	NOUN
ejpam-4766	90	12	of	of	ADP
ejpam-4766	90	13	g.	g.	PROPN
ejpam-4766	90	14	by	by	ADP
ejpam-4766	90	15	letting	let	VERB
ejpam-4766	90	16	d	d	X
ejpam-4766	90	17	=	=	PRON
ejpam-4766	90	18	{	{	PUNCT
ejpam-4766	90	19	a	a	DET
ejpam-4766	90	20	,	,	PUNCT
ejpam-4766	90	21	b	b	NOUN
ejpam-4766	90	22	}	}	PUNCT
ejpam-4766	90	23	to	to	PART
ejpam-4766	90	24	be	be	AUX
ejpam-4766	90	25	the	the	DET
ejpam-4766	90	26	γohic	γohic	ADJ
ejpam-4766	90	27	-set	-set	ADJ
ejpam-4766	90	28	of	of	ADP
ejpam-4766	90	29	g	g	PROPN
ejpam-4766	90	30	,	,	PUNCT
ejpam-4766	90	31	it	it	PRON
ejpam-4766	90	32	would	would	AUX
ejpam-4766	90	33	imply	imply	VERB
ejpam-4766	90	34	that	that	PRON
ejpam-4766	90	35	v	v	NOUN
ejpam-4766	90	36	(	(	PUNCT
ejpam-4766	90	37	g	g	NOUN
ejpam-4766	90	38	)	)	PUNCT
ejpam-4766	90	39	\d	\d	NOUN
ejpam-4766	90	40	is	be	AUX
ejpam-4766	90	41	a	a	DET
ejpam-4766	90	42	hop	hop	NOUN
ejpam-4766	90	43	independent	independent	ADJ
ejpam-4766	90	44	set	set	NOUN
ejpam-4766	90	45	in	in	ADP
ejpam-4766	90	46	g.	g.	NOUN
ejpam-4766	90	47	conversely	conversely	ADV
ejpam-4766	90	48	,	,	PUNCT
ejpam-4766	90	49	suppose	suppose	VERB
ejpam-4766	90	50	that	that	SCONJ
ejpam-4766	90	51	for	for	ADP
ejpam-4766	90	52	each	each	DET
ejpam-4766	90	53	pair	pair	NOUN
ejpam-4766	90	54	of	of	ADP
ejpam-4766	90	55	distinct	distinct	ADJ
ejpam-4766	90	56	adjacent	adjacent	ADJ
ejpam-4766	90	57	vertices	vertex	NOUN
ejpam-4766	90	58	a	a	PRON
ejpam-4766	90	59	,	,	PUNCT
ejpam-4766	90	60	b	b	PROPN
ejpam-4766	90	61	∈	∈	PROPN
ejpam-4766	90	62	v	v	NOUN
ejpam-4766	90	63	(	(	PUNCT
ejpam-4766	90	64	g	g	NOUN
ejpam-4766	90	65	)	)	PUNCT
ejpam-4766	90	66	such	such	ADJ
ejpam-4766	90	67	that	that	DET
ejpam-4766	90	68	ng[a	ng[a	NOUN
ejpam-4766	90	69	]	]	PUNCT
ejpam-4766	90	70	̸=	̸=	PROPN
ejpam-4766	90	71	ng[b	ng[b	NOUN
ejpam-4766	90	72	]	]	PUNCT
ejpam-4766	90	73	,	,	PUNCT
ejpam-4766	90	74	{	{	PUNCT
ejpam-4766	90	75	a	a	DET
ejpam-4766	90	76	,	,	PUNCT
ejpam-4766	90	77	b	b	NOUN
ejpam-4766	90	78	}	}	PUNCT
ejpam-4766	90	79	is	be	AUX
ejpam-4766	90	80	a	a	DET
ejpam-4766	90	81	dominating	dominating	NOUN
ejpam-4766	90	82	set	set	NOUN
ejpam-4766	90	83	of	of	ADP
ejpam-4766	90	84	g	g	PROPN
ejpam-4766	90	85	and	and	CCONJ
ejpam-4766	90	86	d	d	NOUN
ejpam-4766	90	87	=	=	X
ejpam-4766	90	88	{	{	PUNCT
ejpam-4766	90	89	a	a	PRON
ejpam-4766	90	90	,	,	PUNCT
ejpam-4766	90	91	b	b	NOUN
ejpam-4766	90	92	}	}	PUNCT
ejpam-4766	90	93	is	be	AUX
ejpam-4766	90	94	a	a	DET
ejpam-4766	90	95	hop	hop	NOUN
ejpam-4766	90	96	independent	independent	ADJ
ejpam-4766	90	97	set	set	NOUN
ejpam-4766	90	98	in	in	ADP
ejpam-4766	90	99	g.	g.	PROPN
ejpam-4766	90	100	then	then	ADV
ejpam-4766	90	101	g	g	PROPN
ejpam-4766	90	102	is	be	AUX
ejpam-4766	90	103	non	non	ADJ
ejpam-4766	90	104	-	-	ADJ
ejpam-4766	90	105	complete	complete	ADJ
ejpam-4766	90	106	and	and	CCONJ
ejpam-4766	90	107	d	d	NOUN
ejpam-4766	90	108	is	be	AUX
ejpam-4766	90	109	a	a	DET
ejpam-4766	90	110	connected	connected	ADJ
ejpam-4766	90	111	outer	outer	ADJ
ejpam-4766	90	112	-	-	PUNCT
ejpam-4766	90	113	hop	hop	NOUN
ejpam-4766	90	114	independent	independent	ADJ
ejpam-4766	90	115	dominating	dominating	NOUN
ejpam-4766	90	116	set	set	NOUN
ejpam-4766	90	117	of	of	ADP
ejpam-4766	90	118	g.	g.	PROPN
ejpam-4766	90	119	hence	hence	ADV
ejpam-4766	90	120	,	,	PUNCT
ejpam-4766	90	121	by	by	ADP
ejpam-4766	90	122	(	(	PUNCT
ejpam-4766	90	123	i	i	NOUN
ejpam-4766	90	124	)	)	PUNCT
ejpam-4766	90	125	,	,	PUNCT
ejpam-4766	90	126	γohic	γohic	ADJ
ejpam-4766	90	127	(	(	PUNCT
ejpam-4766	90	128	g	g	NOUN
ejpam-4766	90	129	)	)	PUNCT
ejpam-4766	90	130	=	=	SYM
ejpam-4766	91	1	2	2	X
ejpam-4766	91	2	.	.	PUNCT
ejpam-4766	91	3	the	the	DET
ejpam-4766	91	4	next	next	ADJ
ejpam-4766	91	5	result	result	NOUN
ejpam-4766	91	6	follows	follow	VERB
ejpam-4766	91	7	from	from	ADP
ejpam-4766	91	8	theorem	theorem	ADJ
ejpam-4766	91	9	1	1	NUM
ejpam-4766	91	10	.	.	PUNCT
ejpam-4766	91	11	corollary	corollary	ADJ
ejpam-4766	91	12	1	1	NUM
ejpam-4766	91	13	.	.	PUNCT
ejpam-4766	92	1	let	let	VERB
ejpam-4766	92	2	g	g	PRON
ejpam-4766	92	3	be	be	AUX
ejpam-4766	92	4	a	a	DET
ejpam-4766	92	5	non	non	ADJ
ejpam-4766	92	6	-	-	ADJ
ejpam-4766	92	7	trivial	trivial	ADJ
ejpam-4766	92	8	connected	connected	ADJ
ejpam-4766	92	9	graph	graph	NOUN
ejpam-4766	92	10	on	on	ADP
ejpam-4766	92	11	n	n	PRON
ejpam-4766	92	12	vertices	vertex	NOUN
ejpam-4766	92	13	such	such	ADJ
ejpam-4766	92	14	that	that	SCONJ
ejpam-4766	92	15	g	g	PROPN
ejpam-4766	92	16	is	be	AUX
ejpam-4766	92	17	connected	connect	VERB
ejpam-4766	92	18	.	.	PUNCT
ejpam-4766	93	1	then	then	ADV
ejpam-4766	93	2	each	each	PRON
ejpam-4766	93	3	of	of	ADP
ejpam-4766	93	4	the	the	DET
ejpam-4766	93	5	following	following	ADJ
ejpam-4766	93	6	statements	statement	NOUN
ejpam-4766	93	7	holds	hold	VERB
ejpam-4766	93	8	.	.	PUNCT
ejpam-4766	94	1	(	(	PUNCT
ejpam-4766	94	2	i	i	NOUN
ejpam-4766	94	3	)	)	PUNCT
ejpam-4766	94	4	γohic	γohic	ADJ
ejpam-4766	94	5	(	(	PUNCT
ejpam-4766	94	6	g	g	NOUN
ejpam-4766	94	7	)	)	PUNCT
ejpam-4766	94	8	≥	≥	NOUN
ejpam-4766	94	9	2	2	NUM
ejpam-4766	94	10	if	if	SCONJ
ejpam-4766	94	11	and	and	CCONJ
ejpam-4766	94	12	only	only	ADV
ejpam-4766	94	13	if	if	SCONJ
ejpam-4766	94	14	g	g	PROPN
ejpam-4766	94	15	is	be	AUX
ejpam-4766	94	16	non	non	ADJ
ejpam-4766	94	17	-	-	ADJ
ejpam-4766	94	18	complete	complete	ADJ
ejpam-4766	94	19	.	.	PUNCT
ejpam-4766	95	1	(	(	PUNCT
ejpam-4766	95	2	ii	ii	NOUN
ejpam-4766	95	3	)	)	PUNCT
ejpam-4766	95	4	if	if	SCONJ
ejpam-4766	95	5	g	g	PROPN
ejpam-4766	95	6	is	be	AUX
ejpam-4766	95	7	non	non	ADJ
ejpam-4766	95	8	-	-	ADJ
ejpam-4766	95	9	complete	complete	ADJ
ejpam-4766	95	10	,	,	PUNCT
ejpam-4766	95	11	then	then	ADV
ejpam-4766	95	12	(	(	PUNCT
ejpam-4766	95	13	a	a	X
ejpam-4766	95	14	)	)	PUNCT
ejpam-4766	95	15	4	4	NUM
ejpam-4766	95	16	≤	≤	NOUN
ejpam-4766	95	17	γohic	γohic	ADJ
ejpam-4766	95	18	(	(	PUNCT
ejpam-4766	95	19	g	g	NOUN
ejpam-4766	95	20	)	)	PUNCT
ejpam-4766	95	21	+	+	CCONJ
ejpam-4766	95	22	γohic	γohic	ADJ
ejpam-4766	95	23	(	(	PUNCT
ejpam-4766	95	24	g	g	NOUN
ejpam-4766	95	25	)	)	PUNCT
ejpam-4766	95	26	≤	≤	NOUN
ejpam-4766	96	1	2n−	2n−	NUM
ejpam-4766	96	2	2	2	NUM
ejpam-4766	96	3	,	,	PUNCT
ejpam-4766	96	4	and	and	CCONJ
ejpam-4766	96	5	(	(	PUNCT
ejpam-4766	96	6	b	b	NOUN
ejpam-4766	96	7	)	)	PUNCT
ejpam-4766	96	8	4	4	NUM
ejpam-4766	96	9	≤	≤	NOUN
ejpam-4766	96	10	γohic	γohic	ADJ
ejpam-4766	96	11	(	(	PUNCT
ejpam-4766	96	12	g	g	NOUN
ejpam-4766	96	13	)	)	PUNCT
ejpam-4766	96	14	·	·	PUNCT
ejpam-4766	96	15	γohic	γohic	ADJ
ejpam-4766	96	16	(	(	PUNCT
ejpam-4766	96	17	g	g	NOUN
ejpam-4766	96	18	)	)	PUNCT
ejpam-4766	96	19	≤	≤	NOUN
ejpam-4766	96	20	n2	n2	NOUN
ejpam-4766	96	21	−	−	PROPN
ejpam-4766	96	22	2n+	2n+	NUM
ejpam-4766	96	23	1	1	NUM
ejpam-4766	96	24	.	.	PUNCT
ejpam-4766	97	1	proposition	proposition	NOUN
ejpam-4766	97	2	1	1	NUM
ejpam-4766	97	3	.	.	PUNCT
ejpam-4766	98	1	for	for	ADP
ejpam-4766	98	2	any	any	DET
ejpam-4766	98	3	positive	positive	ADJ
ejpam-4766	98	4	integer	integer	NOUN
ejpam-4766	98	5	n	n	PRON
ejpam-4766	98	6	≥	≥	NOUN
ejpam-4766	98	7	1	1	NUM
ejpam-4766	98	8	,	,	PUNCT
ejpam-4766	98	9	γohi	γohi	PROPN
ejpam-4766	98	10	c	c	PROPN
ejpam-4766	98	11	(	(	PUNCT
ejpam-4766	98	12	pn	pn	NOUN
ejpam-4766	98	13	)	)	PUNCT
ejpam-4766	98	14	=	=	PUNCT
ejpam-4766	99	1			NOUN
ejpam-4766	99	2	1	1	NUM
ejpam-4766	99	3	if	if	SCONJ
ejpam-4766	99	4	n	n	NOUN
ejpam-4766	99	5	=	=	SYM
ejpam-4766	99	6	1	1	NUM
ejpam-4766	99	7	,	,	PUNCT
ejpam-4766	99	8	2	2	NUM
ejpam-4766	99	9	2	2	NUM
ejpam-4766	99	10	if	if	SCONJ
ejpam-4766	99	11	n	n	NOUN
ejpam-4766	99	12	=	=	SYM
ejpam-4766	99	13	3	3	NUM
ejpam-4766	99	14	n−	n−	NOUN
ejpam-4766	99	15	2	2	NUM
ejpam-4766	99	16	if	if	SCONJ
ejpam-4766	99	17	n	n	PRON
ejpam-4766	99	18	≥	≥	VERB
ejpam-4766	99	19	4	4	NUM
ejpam-4766	99	20	proof	proof	NOUN
ejpam-4766	99	21	.	.	PUNCT
ejpam-4766	100	1	clearly	clearly	ADV
ejpam-4766	100	2	,	,	PUNCT
ejpam-4766	100	3	γohic	γohic	ADJ
ejpam-4766	100	4	(	(	PUNCT
ejpam-4766	100	5	pn	pn	NOUN
ejpam-4766	100	6	)	)	PUNCT
ejpam-4766	100	7	=	=	SYM
ejpam-4766	100	8	1	1	NUM
ejpam-4766	100	9	for	for	ADP
ejpam-4766	100	10	n	n	NOUN
ejpam-4766	100	11	=	=	SYM
ejpam-4766	100	12	1	1	NUM
ejpam-4766	100	13	,	,	PUNCT
ejpam-4766	100	14	2	2	NUM
ejpam-4766	100	15	and	and	CCONJ
ejpam-4766	100	16	γohic	γohic	ADJ
ejpam-4766	100	17	(	(	PUNCT
ejpam-4766	100	18	p3	p3	NOUN
ejpam-4766	100	19	)	)	PUNCT
ejpam-4766	100	20	=	=	SYM
ejpam-4766	101	1	2	2	X
ejpam-4766	101	2	.	.	X
ejpam-4766	101	3	suppose	suppose	VERB
ejpam-4766	101	4	n	n	PRON
ejpam-4766	101	5	≥	≥	NUM
ejpam-4766	101	6	4	4	NUM
ejpam-4766	101	7	.	.	PUNCT
ejpam-4766	102	1	let	let	VERB
ejpam-4766	102	2	pn	pn	VERB
ejpam-4766	102	3	=	=	PUNCT
ejpam-4766	103	1	[	[	X
ejpam-4766	103	2	v1	v1	NOUN
ejpam-4766	103	3	,	,	PUNCT
ejpam-4766	103	4	v2	v2	NOUN
ejpam-4766	103	5	,	,	PUNCT
ejpam-4766	103	6	.	.	PUNCT
ejpam-4766	103	7	.	.	PUNCT
ejpam-4766	103	8	.	.	PUNCT
ejpam-4766	104	1	,	,	PUNCT
ejpam-4766	104	2	vn	vn	X
ejpam-4766	104	3	]	]	PUNCT
ejpam-4766	104	4	and	and	CCONJ
ejpam-4766	104	5	let	let	VERB
ejpam-4766	104	6	d	d	NOUN
ejpam-4766	104	7	=	=	PUNCT
ejpam-4766	104	8	{	{	PUNCT
ejpam-4766	104	9	v2	v2	PROPN
ejpam-4766	104	10	,	,	PUNCT
ejpam-4766	104	11	·	·	PUNCT
ejpam-4766	104	12	·	·	PUNCT
ejpam-4766	104	13	·	·	PUNCT
ejpam-4766	104	14	,	,	PUNCT
ejpam-4766	104	15	vn−1	vn−1	ADJ
ejpam-4766	104	16	}	}	PUNCT
ejpam-4766	104	17	.	.	PUNCT
ejpam-4766	105	1	clearly	clearly	ADV
ejpam-4766	105	2	,	,	PUNCT
ejpam-4766	105	3	d	d	PRON
ejpam-4766	105	4	is	be	AUX
ejpam-4766	105	5	a	a	DET
ejpam-4766	105	6	connected	connected	ADJ
ejpam-4766	105	7	dominating	dominating	NOUN
ejpam-4766	105	8	set	set	NOUN
ejpam-4766	105	9	of	of	ADP
ejpam-4766	105	10	pn	pn	PROPN
ejpam-4766	105	11	.	.	PUNCT
ejpam-4766	106	1	since	since	SCONJ
ejpam-4766	106	2	n	n	PROPN
ejpam-4766	106	3	≥	≥	NOUN
ejpam-4766	106	4	4	4	NUM
ejpam-4766	106	5	,	,	PUNCT
ejpam-4766	106	6	it	it	PRON
ejpam-4766	106	7	follows	follow	VERB
ejpam-4766	106	8	that	that	SCONJ
ejpam-4766	106	9	dpn(v1	dpn(v1	NOUN
ejpam-4766	106	10	,	,	PUNCT
ejpam-4766	106	11	vn	vn	PROPN
ejpam-4766	106	12	)	)	PUNCT
ejpam-4766	106	13	≥	≥	NOUN
ejpam-4766	106	14	3	3	NUM
ejpam-4766	106	15	.	.	PUNCT
ejpam-4766	107	1	thus	thus	ADV
ejpam-4766	107	2	,	,	PUNCT
ejpam-4766	107	3	v	v	INTJ
ejpam-4766	107	4	(	(	PUNCT
ejpam-4766	107	5	pn	pn	NOUN
ejpam-4766	107	6	)	)	PUNCT
ejpam-4766	107	7	\d	\d	NOUN
ejpam-4766	107	8	=	=	PROPN
ejpam-4766	107	9	{	{	PUNCT
ejpam-4766	107	10	v1	v1	PROPN
ejpam-4766	107	11	,	,	PUNCT
ejpam-4766	107	12	vn	vn	PROPN
ejpam-4766	107	13	}	}	PUNCT
ejpam-4766	107	14	is	be	AUX
ejpam-4766	107	15	a	a	DET
ejpam-4766	107	16	hop	hop	NOUN
ejpam-4766	107	17	independent	independent	ADJ
ejpam-4766	107	18	set	set	NOUN
ejpam-4766	107	19	of	of	ADP
ejpam-4766	107	20	pn	pn	PROPN
ejpam-4766	107	21	.	.	PUNCT
ejpam-4766	108	1	thus	thus	ADV
ejpam-4766	108	2	,	,	PUNCT
ejpam-4766	108	3	d	d	PRON
ejpam-4766	108	4	is	be	AUX
ejpam-4766	108	5	a	a	DET
ejpam-4766	108	6	connected	connected	ADJ
ejpam-4766	108	7	outer	outer	ADJ
ejpam-4766	108	8	-	-	PUNCT
ejpam-4766	108	9	hop	hop	NOUN
ejpam-4766	108	10	independent	independent	ADJ
ejpam-4766	108	11	dominating	dominating	NOUN
ejpam-4766	108	12	set	set	VERB
ejpam-4766	108	13	in	in	ADP
ejpam-4766	108	14	pn	pn	PROPN
ejpam-4766	108	15	,	,	PUNCT
ejpam-4766	108	16	and	and	CCONJ
ejpam-4766	108	17	so	so	ADV
ejpam-4766	108	18	γohic	γohic	ADJ
ejpam-4766	108	19	(	(	PUNCT
ejpam-4766	108	20	pn	pn	NOUN
ejpam-4766	108	21	)	)	PUNCT
ejpam-4766	108	22	≤	≤	NOUN
ejpam-4766	108	23	n−	n−	NOUN
ejpam-4766	108	24	2	2	NUM
ejpam-4766	108	25	.	.	X
ejpam-4766	109	1	observe	observe	VERB
ejpam-4766	109	2	that	that	SCONJ
ejpam-4766	109	3	every	every	DET
ejpam-4766	109	4	connected	connected	ADJ
ejpam-4766	109	5	dominating	dominating	NOUN
ejpam-4766	109	6	set	set	NOUN
ejpam-4766	109	7	of	of	ADP
ejpam-4766	109	8	pn	pn	PROPN
ejpam-4766	109	9	contains	contain	VERB
ejpam-4766	109	10	d.	d.	PROPN
ejpam-4766	109	11	therefore	therefore	ADV
ejpam-4766	109	12	,	,	PUNCT
ejpam-4766	109	13	γohic	γohic	ADJ
ejpam-4766	109	14	(	(	PUNCT
ejpam-4766	109	15	pn	pn	NOUN
ejpam-4766	109	16	)	)	PUNCT
ejpam-4766	109	17	=	=	PUNCT
ejpam-4766	109	18	n−	n−	NOUN
ejpam-4766	109	19	2	2	NUM
ejpam-4766	109	20	by	by	ADP
ejpam-4766	109	21	remark	remark	NOUN
ejpam-4766	109	22	1	1	NUM
ejpam-4766	109	23	.	.	PUNCT
ejpam-4766	109	24	proposition	proposition	NOUN
ejpam-4766	109	25	2	2	NUM
ejpam-4766	109	26	.	.	X
ejpam-4766	110	1	for	for	ADP
ejpam-4766	110	2	any	any	DET
ejpam-4766	110	3	positive	positive	ADJ
ejpam-4766	110	4	integer	integer	NOUN
ejpam-4766	110	5	n	n	PRON
ejpam-4766	110	6	≥	≥	NOUN
ejpam-4766	110	7	3	3	NUM
ejpam-4766	110	8	,	,	PUNCT
ejpam-4766	110	9	γohi	γohi	PROPN
ejpam-4766	110	10	c	c	PROPN
ejpam-4766	110	11	(	(	PUNCT
ejpam-4766	110	12	cn	cn	PROPN
ejpam-4766	110	13	)	)	PUNCT
ejpam-4766	110	14	=	=	PRON
ejpam-4766	110	15	{	{	PUNCT
ejpam-4766	110	16	1	1	NUM
ejpam-4766	110	17	if	if	SCONJ
ejpam-4766	110	18	n	n	NOUN
ejpam-4766	110	19	=	=	SYM
ejpam-4766	110	20	3	3	NUM
ejpam-4766	110	21	n−	n−	NOUN
ejpam-4766	110	22	2	2	NUM
ejpam-4766	110	23	if	if	SCONJ
ejpam-4766	110	24	n	n	PRON
ejpam-4766	110	25	≥	≥	VERB
ejpam-4766	110	26	4	4	NUM
ejpam-4766	110	27	proof	proof	NOUN
ejpam-4766	110	28	.	.	PUNCT
ejpam-4766	111	1	clearly	clearly	ADV
ejpam-4766	111	2	,	,	PUNCT
ejpam-4766	111	3	γohic	γohic	ADJ
ejpam-4766	111	4	(	(	PUNCT
ejpam-4766	111	5	c3	c3	NOUN
ejpam-4766	111	6	)	)	PUNCT
ejpam-4766	111	7	=	=	SYM
ejpam-4766	112	1	1	1	X
ejpam-4766	112	2	.	.	PUNCT
ejpam-4766	112	3	suppose	suppose	VERB
ejpam-4766	112	4	that	that	SCONJ
ejpam-4766	112	5	n	n	PROPN
ejpam-4766	112	6	≥	≥	NUM
ejpam-4766	112	7	4	4	NUM
ejpam-4766	112	8	.	.	PUNCT
ejpam-4766	113	1	let	let	VERB
ejpam-4766	113	2	cn	cn	PROPN
ejpam-4766	113	3	=	=	PUNCT
ejpam-4766	114	1	[	[	X
ejpam-4766	114	2	v1	v1	NOUN
ejpam-4766	114	3	,	,	PUNCT
ejpam-4766	114	4	v2	v2	NOUN
ejpam-4766	114	5	,	,	PUNCT
ejpam-4766	114	6	.	.	PUNCT
ejpam-4766	114	7	.	.	PUNCT
ejpam-4766	114	8	.	.	PUNCT
ejpam-4766	115	1	,	,	PUNCT
ejpam-4766	115	2	vn	vn	X
ejpam-4766	115	3	,	,	PUNCT
ejpam-4766	115	4	v1	v1	PROPN
ejpam-4766	115	5	]	]	PUNCT
ejpam-4766	115	6	and	and	CCONJ
ejpam-4766	115	7	consider	consider	VERB
ejpam-4766	115	8	d′	d′	X
ejpam-4766	115	9	=	=	SYM
ejpam-4766	115	10	{	{	PUNCT
ejpam-4766	115	11	v1	v1	PROPN
ejpam-4766	115	12	,	,	PUNCT
ejpam-4766	115	13	v2	v2	PROPN
ejpam-4766	115	14	,	,	PUNCT
ejpam-4766	115	15	·	·	PUNCT
ejpam-4766	115	16	·	·	PUNCT
ejpam-4766	115	17	·	·	PUNCT
ejpam-4766	115	18	,	,	PUNCT
ejpam-4766	115	19	vn−2	vn−2	PROPN
ejpam-4766	115	20	}	}	PUNCT
ejpam-4766	115	21	.	.	PUNCT
ejpam-4766	116	1	then	then	ADV
ejpam-4766	116	2	d′	d′	PRON
ejpam-4766	116	3	is	be	AUX
ejpam-4766	116	4	a	a	DET
ejpam-4766	116	5	connected	connected	ADJ
ejpam-4766	116	6	dominating	dominating	NOUN
ejpam-4766	116	7	set	set	NOUN
ejpam-4766	116	8	of	of	ADP
ejpam-4766	116	9	cn	cn	PROPN
ejpam-4766	116	10	.	.	PUNCT
ejpam-4766	117	1	since	since	SCONJ
ejpam-4766	117	2	dcn(vn−1	dcn(vn−1	PROPN
ejpam-4766	117	3	,	,	PUNCT
ejpam-4766	117	4	vn	vn	NOUN
ejpam-4766	117	5	)	)	PUNCT
ejpam-4766	118	1	=	=	SYM
ejpam-4766	118	2	1	1	NUM
ejpam-4766	118	3	,	,	PUNCT
ejpam-4766	118	4	it	it	PRON
ejpam-4766	118	5	follows	follow	VERB
ejpam-4766	118	6	that	that	SCONJ
ejpam-4766	118	7	v	v	X
ejpam-4766	118	8	(	(	PUNCT
ejpam-4766	118	9	cn	cn	PROPN
ejpam-4766	118	10	)	)	PUNCT
ejpam-4766	118	11	\	\	NOUN
ejpam-4766	118	12	d′	d′	X
ejpam-4766	118	13	=	=	PUNCT
ejpam-4766	118	14	{	{	PUNCT
ejpam-4766	118	15	vn−1	vn−1	PROPN
ejpam-4766	118	16	,	,	PUNCT
ejpam-4766	118	17	vn	vn	VERB
ejpam-4766	118	18	}	}	PUNCT
ejpam-4766	118	19	is	be	AUX
ejpam-4766	118	20	a	a	DET
ejpam-4766	118	21	hop	hop	NOUN
ejpam-4766	118	22	independent	independent	ADJ
ejpam-4766	118	23	set	set	NOUN
ejpam-4766	118	24	in	in	ADP
ejpam-4766	118	25	cn	cn	PROPN
ejpam-4766	118	26	.	.	PUNCT
ejpam-4766	119	1	thus	thus	ADV
ejpam-4766	119	2	,	,	PUNCT
ejpam-4766	119	3	d′	d′	PRON
ejpam-4766	119	4	is	be	AUX
ejpam-4766	119	5	a	a	DET
ejpam-4766	119	6	connected	connected	ADJ
ejpam-4766	119	7	outer	outer	ADJ
ejpam-4766	119	8	-	-	PUNCT
ejpam-4766	119	9	hop	hop	NOUN
ejpam-4766	119	10	independent	independent	ADJ
ejpam-4766	119	11	dominating	dominating	NOUN
ejpam-4766	119	12	set	set	NOUN
ejpam-4766	119	13	in	in	ADP
ejpam-4766	119	14	cn	cn	PROPN
ejpam-4766	119	15	,	,	PUNCT
ejpam-4766	119	16	and	and	CCONJ
ejpam-4766	119	17	so	so	ADV
ejpam-4766	119	18	j.	j.	PROPN
ejpam-4766	119	19	hassan	hassan	PROPN
ejpam-4766	119	20	et	et	PROPN
ejpam-4766	119	21	al	al	PROPN
ejpam-4766	119	22	.	.	PUNCT
ejpam-4766	119	23	/	/	SYM
ejpam-4766	119	24	eur	eur	PROPN
ejpam-4766	119	25	.	.	PUNCT
ejpam-4766	120	1	j.	j.	PROPN
ejpam-4766	120	2	pure	pure	PROPN
ejpam-4766	120	3	appl	appl	PROPN
ejpam-4766	120	4	.	.	PROPN
ejpam-4766	120	5	math	math	PROPN
ejpam-4766	120	6	,	,	PUNCT
ejpam-4766	120	7	16	16	NUM
ejpam-4766	120	8	(	(	PUNCT
ejpam-4766	120	9	3	3	NUM
ejpam-4766	120	10	)	)	PUNCT
ejpam-4766	120	11	(	(	PUNCT
ejpam-4766	120	12	2023	2023	NUM
ejpam-4766	120	13	)	)	PUNCT
ejpam-4766	120	14	,	,	PUNCT
ejpam-4766	120	15	1817	1817	NUM
ejpam-4766	120	16	-	-	SYM
ejpam-4766	120	17	1829	1829	NUM
ejpam-4766	120	18	1822	1822	NUM
ejpam-4766	120	19	γohic	γohic	ADJ
ejpam-4766	120	20	(	(	PUNCT
ejpam-4766	120	21	cn	cn	NOUN
ejpam-4766	120	22	)	)	PUNCT
ejpam-4766	120	23	≤	≤	NUM
ejpam-4766	120	24	n−	n−	NOUN
ejpam-4766	120	25	2	2	NUM
ejpam-4766	120	26	.	.	PUNCT
ejpam-4766	120	27	since	since	SCONJ
ejpam-4766	120	28	γc(cn	γc(cn	PROPN
ejpam-4766	120	29	)	)	PUNCT
ejpam-4766	121	1	=	=	PUNCT
ejpam-4766	121	2	n−	n−	NOUN
ejpam-4766	121	3	2	2	NUM
ejpam-4766	121	4	for	for	ADP
ejpam-4766	121	5	all	all	DET
ejpam-4766	121	6	n	n	PRON
ejpam-4766	121	7	≥	≥	NOUN
ejpam-4766	121	8	4	4	NUM
ejpam-4766	121	9	,	,	PUNCT
ejpam-4766	121	10	it	it	PRON
ejpam-4766	121	11	follows	follow	VERB
ejpam-4766	121	12	that	that	SCONJ
ejpam-4766	121	13	γohic	γohic	ADJ
ejpam-4766	121	14	(	(	PUNCT
ejpam-4766	121	15	cn	cn	NOUN
ejpam-4766	121	16	)	)	PUNCT
ejpam-4766	121	17	=	=	PUNCT
ejpam-4766	121	18	n−	n−	NOUN
ejpam-4766	121	19	2	2	NUM
ejpam-4766	121	20	for	for	ADP
ejpam-4766	121	21	all	all	DET
ejpam-4766	121	22	n	n	PRON
ejpam-4766	121	23	≥	≥	NOUN
ejpam-4766	121	24	4	4	NUM
ejpam-4766	121	25	by	by	ADP
ejpam-4766	121	26	remark	remark	NOUN
ejpam-4766	121	27	1	1	NUM
ejpam-4766	121	28	.	.	PUNCT
ejpam-4766	122	1	the	the	DET
ejpam-4766	122	2	next	next	ADJ
ejpam-4766	122	3	theorem	theorem	NOUN
ejpam-4766	122	4	is	be	AUX
ejpam-4766	122	5	a	a	DET
ejpam-4766	122	6	realization	realization	NOUN
ejpam-4766	122	7	result	result	NOUN
ejpam-4766	122	8	involving	involve	VERB
ejpam-4766	122	9	connected	connect	VERB
ejpam-4766	122	10	domination	domination	NOUN
ejpam-4766	122	11	number	number	NOUN
ejpam-4766	122	12	and	and	CCONJ
ejpam-4766	122	13	connected	connected	ADJ
ejpam-4766	122	14	outer	outer	ADJ
ejpam-4766	122	15	-	-	PUNCT
ejpam-4766	122	16	hop	hop	NOUN
ejpam-4766	122	17	independent	independent	ADJ
ejpam-4766	122	18	domination	domination	NOUN
ejpam-4766	122	19	number	number	NOUN
ejpam-4766	122	20	of	of	ADP
ejpam-4766	122	21	a	a	DET
ejpam-4766	122	22	graph	graph	NOUN
ejpam-4766	122	23	.	.	PUNCT
ejpam-4766	123	1	theorem	theorem	NOUN
ejpam-4766	123	2	2	2	NUM
ejpam-4766	123	3	.	.	PUNCT
ejpam-4766	123	4	let	let	VERB
ejpam-4766	123	5	a	a	PRON
ejpam-4766	123	6	and	and	CCONJ
ejpam-4766	123	7	b	b	NOUN
ejpam-4766	123	8	be	be	AUX
ejpam-4766	123	9	positive	positive	ADJ
ejpam-4766	123	10	integers	integer	NOUN
ejpam-4766	123	11	such	such	ADJ
ejpam-4766	123	12	that	that	SCONJ
ejpam-4766	123	13	2	2	NUM
ejpam-4766	123	14	≤	≤	NUM
ejpam-4766	123	15	a	a	DET
ejpam-4766	123	16	≤	≤	PROPN
ejpam-4766	123	17	b.	b.	NOUN
ejpam-4766	124	1	then	then	ADV
ejpam-4766	124	2	there	there	PRON
ejpam-4766	124	3	exists	exist	VERB
ejpam-4766	124	4	a	a	DET
ejpam-4766	124	5	connected	connected	ADJ
ejpam-4766	124	6	graph	graph	NOUN
ejpam-4766	124	7	g	g	ADP
ejpam-4766	124	8	such	such	ADJ
ejpam-4766	124	9	that	that	PRON
ejpam-4766	124	10	γc(g	γc(g	PUNCT
ejpam-4766	124	11	)	)	PUNCT
ejpam-4766	124	12	=	=	SYM
ejpam-4766	124	13	a	a	PRON
ejpam-4766	124	14	and	and	CCONJ
ejpam-4766	124	15	γohic	γohic	ADJ
ejpam-4766	124	16	(	(	PUNCT
ejpam-4766	124	17	g	g	NOUN
ejpam-4766	124	18	)	)	PUNCT
ejpam-4766	124	19	=	=	SYM
ejpam-4766	124	20	b.	b.	PROPN
ejpam-4766	125	1	in	in	ADP
ejpam-4766	125	2	other	other	ADJ
ejpam-4766	125	3	words	word	NOUN
ejpam-4766	125	4	,	,	PUNCT
ejpam-4766	125	5	γohic	γohic	ADJ
ejpam-4766	125	6	(	(	PUNCT
ejpam-4766	125	7	g)−	g)−	PROPN
ejpam-4766	125	8	γc(g	γc(g	PUNCT
ejpam-4766	125	9	)	)	PUNCT
ejpam-4766	125	10	can	can	AUX
ejpam-4766	125	11	be	be	AUX
ejpam-4766	125	12	made	make	VERB
ejpam-4766	125	13	arbitrarily	arbitrarily	ADV
ejpam-4766	125	14	large	large	ADJ
ejpam-4766	125	15	.	.	PUNCT
ejpam-4766	126	1	proof	proof	NOUN
ejpam-4766	126	2	.	.	PUNCT
ejpam-4766	127	1	for	for	ADP
ejpam-4766	127	2	a	a	DET
ejpam-4766	127	3	=	=	SYM
ejpam-4766	127	4	b	b	NOUN
ejpam-4766	127	5	,	,	PUNCT
ejpam-4766	127	6	consider	consider	VERB
ejpam-4766	127	7	a	a	DET
ejpam-4766	127	8	path	path	NOUN
ejpam-4766	127	9	graph	graph	NOUN
ejpam-4766	127	10	pa+2	pa+2	NOUN
ejpam-4766	127	11	.	.	PUNCT
ejpam-4766	127	12	then	then	ADV
ejpam-4766	127	13	γc(pa+2	γc(pa+2	PROPN
ejpam-4766	127	14	)	)	PUNCT
ejpam-4766	127	15	=	=	SYM
ejpam-4766	128	1	a	a	DET
ejpam-4766	128	2	=	=	X
ejpam-4766	128	3	γohic	γohic	ADJ
ejpam-4766	128	4	(	(	PUNCT
ejpam-4766	128	5	pa+2	pa+2	NOUN
ejpam-4766	128	6	)	)	PUNCT
ejpam-4766	128	7	by	by	ADP
ejpam-4766	128	8	proposition	proposition	NOUN
ejpam-4766	128	9	1	1	NUM
ejpam-4766	128	10	.	.	PUNCT
ejpam-4766	128	11	suppose	suppose	VERB
ejpam-4766	128	12	a	a	DET
ejpam-4766	128	13	<	<	X
ejpam-4766	128	14	b.	b.	NOUN
ejpam-4766	128	15	consider	consider	VERB
ejpam-4766	128	16	the	the	DET
ejpam-4766	128	17	following	follow	VERB
ejpam-4766	128	18	two	two	NUM
ejpam-4766	128	19	cases	case	NOUN
ejpam-4766	128	20	:	:	PUNCT
ejpam-4766	128	21	case	case	NOUN
ejpam-4766	128	22	1	1	NUM
ejpam-4766	128	23	:	:	PUNCT
ejpam-4766	128	24	a	a	PRON
ejpam-4766	128	25	is	be	AUX
ejpam-4766	128	26	odd	odd	ADJ
ejpam-4766	128	27	.	.	PUNCT
ejpam-4766	129	1	let	let	VERB
ejpam-4766	129	2	m	m	VERB
ejpam-4766	129	3	=	=	VERB
ejpam-4766	130	1	b	b	X
ejpam-4766	130	2	−	−	PROPN
ejpam-4766	130	3	a	a	PRON
ejpam-4766	131	1	and	and	CCONJ
ejpam-4766	131	2	consider	consider	VERB
ejpam-4766	131	3	the	the	DET
ejpam-4766	131	4	graph	graph	NOUN
ejpam-4766	131	5	g1	g1	NOUN
ejpam-4766	131	6	given	give	VERB
ejpam-4766	131	7	in	in	ADP
ejpam-4766	131	8	figure	figure	NOUN
ejpam-4766	131	9	3	3	NUM
ejpam-4766	131	10	.	.	PUNCT
ejpam-4766	132	1	let	let	VERB
ejpam-4766	132	2	d1	d1	PROPN
ejpam-4766	132	3	=	=	SYM
ejpam-4766	132	4	{	{	PUNCT
ejpam-4766	132	5	d1	d1	PROPN
ejpam-4766	132	6	,	,	PUNCT
ejpam-4766	132	7	d2	d2	PROPN
ejpam-4766	132	8	,	,	PUNCT
ejpam-4766	132	9	.	.	PUNCT
ejpam-4766	132	10	.	.	PUNCT
ejpam-4766	133	1	.	.	PUNCT
ejpam-4766	134	1	,	,	PUNCT
ejpam-4766	134	2	da	da	ADJ
ejpam-4766	134	3	}	}	PUNCT
ejpam-4766	134	4	and	and	CCONJ
ejpam-4766	134	5	d2	d2	PROPN
ejpam-4766	134	6	=	=	SYM
ejpam-4766	134	7	{	{	PUNCT
ejpam-4766	134	8	d1	d1	PROPN
ejpam-4766	134	9	,	,	PUNCT
ejpam-4766	134	10	d2	d2	PROPN
ejpam-4766	134	11	,	,	PUNCT
ejpam-4766	134	12	.	.	PUNCT
ejpam-4766	134	13	.	.	PUNCT
ejpam-4766	135	1	.	.	PUNCT
ejpam-4766	136	1	,	,	PUNCT
ejpam-4766	136	2	da	da	NOUN
ejpam-4766	136	3	,	,	PUNCT
ejpam-4766	136	4	v1	v1	NOUN
ejpam-4766	136	5	,	,	PUNCT
ejpam-4766	136	6	v2	v2	NOUN
ejpam-4766	136	7	,	,	PUNCT
ejpam-4766	136	8	.	.	PUNCT
ejpam-4766	136	9	.	.	PUNCT
ejpam-4766	137	1	.	.	PUNCT
ejpam-4766	138	1	,	,	PUNCT
ejpam-4766	139	1	vm	vm	NOUN
ejpam-4766	139	2	}	}	PUNCT
ejpam-4766	139	3	.	.	PUNCT
ejpam-4766	140	1	then	then	ADV
ejpam-4766	140	2	d1	d1	PROPN
ejpam-4766	140	3	and	and	CCONJ
ejpam-4766	140	4	d2	d2	PROPN
ejpam-4766	140	5	are	be	AUX
ejpam-4766	140	6	γc	γc	NOUN
ejpam-4766	140	7	-	-	PUNCT
ejpam-4766	140	8	set	set	ADJ
ejpam-4766	140	9	and	and	CCONJ
ejpam-4766	140	10	γohic	γohic	ADJ
ejpam-4766	140	11	-set	-set	ADJ
ejpam-4766	140	12	of	of	ADP
ejpam-4766	140	13	g1	g1	PROPN
ejpam-4766	140	14	,	,	PUNCT
ejpam-4766	140	15	respectively	respectively	ADV
ejpam-4766	140	16	.	.	PUNCT
ejpam-4766	141	1	hence	hence	ADV
ejpam-4766	141	2	,	,	PUNCT
ejpam-4766	141	3	γc(g1	γc(g1	ADV
ejpam-4766	141	4	)	)	PUNCT
ejpam-4766	141	5	=	=	SYM
ejpam-4766	141	6	a	a	PRON
ejpam-4766	141	7	and	and	CCONJ
ejpam-4766	141	8	γohic	γohic	ADJ
ejpam-4766	141	9	(	(	PUNCT
ejpam-4766	141	10	g1	g1	PROPN
ejpam-4766	141	11	)	)	PUNCT
ejpam-4766	142	1	=	=	PUNCT
ejpam-4766	142	2	m+	m+	NUM
ejpam-4766	142	3	a	a	DET
ejpam-4766	142	4	=	=	X
ejpam-4766	142	5	b.	b.	PROPN
ejpam-4766	142	6	.	.	PUNCT
ejpam-4766	142	7	.	.	PUNCT
ejpam-4766	142	8	.	.	PUNCT
ejpam-4766	142	9	.	.	PUNCT
ejpam-4766	142	10	.	.	PUNCT
ejpam-4766	143	1	.	.	PUNCT
ejpam-4766	144	1	d1	d1	PROPN
ejpam-4766	144	2	d2	d2	PROPN
ejpam-4766	144	3	d3	d3	PROPN
ejpam-4766	144	4	dada−1	dada−1	PROPN
ejpam-4766	144	5	v1	v1	PROPN
ejpam-4766	144	6	v2	v2	PROPN
ejpam-4766	144	7	vm	vm	PROPN
ejpam-4766	144	8	g1	g1	PROPN
ejpam-4766	144	9	:	:	PUNCT
ejpam-4766	144	10	figure	figure	VERB
ejpam-4766	144	11	3	3	NUM
ejpam-4766	144	12	:	:	PUNCT
ejpam-4766	144	13	a	a	DET
ejpam-4766	144	14	graph	graph	NOUN
ejpam-4766	144	15	g1	g1	NOUN
ejpam-4766	144	16	with	with	ADP
ejpam-4766	144	17	γc(g1	γc(g1	NOUN
ejpam-4766	144	18	)	)	PUNCT
ejpam-4766	144	19	<	<	X
ejpam-4766	144	20	γohi	γohi	PROPN
ejpam-4766	144	21	c	c	PROPN
ejpam-4766	144	22	(	(	PUNCT
ejpam-4766	144	23	g1	g1	PROPN
ejpam-4766	144	24	)	)	PUNCT
ejpam-4766	144	25	case	case	NOUN
ejpam-4766	144	26	2	2	NUM
ejpam-4766	144	27	:	:	PUNCT
ejpam-4766	144	28	a	a	PRON
ejpam-4766	144	29	is	be	AUX
ejpam-4766	144	30	even	even	ADV
ejpam-4766	144	31	.	.	PUNCT
ejpam-4766	145	1	let	let	VERB
ejpam-4766	145	2	m	m	VERB
ejpam-4766	145	3	=	=	VERB
ejpam-4766	146	1	b	b	X
ejpam-4766	146	2	−	−	PROPN
ejpam-4766	146	3	a	a	PRON
ejpam-4766	147	1	and	and	CCONJ
ejpam-4766	147	2	consider	consider	VERB
ejpam-4766	147	3	the	the	DET
ejpam-4766	147	4	graph	graph	NOUN
ejpam-4766	147	5	g2	g2	PROPN
ejpam-4766	147	6	given	give	VERB
ejpam-4766	147	7	in	in	ADP
ejpam-4766	147	8	figure	figure	NOUN
ejpam-4766	147	9	4	4	NUM
ejpam-4766	147	10	.	.	PUNCT
ejpam-4766	148	1	let	let	VERB
ejpam-4766	148	2	d	d	NOUN
ejpam-4766	148	3	=	=	PUNCT
ejpam-4766	148	4	{	{	PUNCT
ejpam-4766	148	5	u1	u1	NOUN
ejpam-4766	148	6	,	,	PUNCT
ejpam-4766	148	7	u2	u2	NOUN
ejpam-4766	148	8	,	,	PUNCT
ejpam-4766	148	9	.	.	PUNCT
ejpam-4766	148	10	.	.	PUNCT
ejpam-4766	149	1	.	.	PUNCT
ejpam-4766	150	1	,	,	PUNCT
ejpam-4766	150	2	ua	ua	PROPN
ejpam-4766	150	3	}	}	PUNCT
ejpam-4766	150	4	and	and	CCONJ
ejpam-4766	150	5	d∗	d∗	PROPN
ejpam-4766	150	6	=	=	SYM
ejpam-4766	150	7	{	{	PUNCT
ejpam-4766	150	8	u1	u1	NOUN
ejpam-4766	150	9	,	,	PUNCT
ejpam-4766	150	10	u2	u2	NOUN
ejpam-4766	150	11	,	,	PUNCT
ejpam-4766	150	12	.	.	PUNCT
ejpam-4766	150	13	.	.	PUNCT
ejpam-4766	151	1	.	.	PUNCT
ejpam-4766	152	1	,	,	PUNCT
ejpam-4766	152	2	ua	ua	PROPN
ejpam-4766	152	3	,	,	PUNCT
ejpam-4766	152	4	w1	w1	NOUN
ejpam-4766	152	5	,	,	PUNCT
ejpam-4766	152	6	w2	w2	NOUN
ejpam-4766	152	7	,	,	PUNCT
ejpam-4766	152	8	.	.	PUNCT
ejpam-4766	152	9	.	.	PUNCT
ejpam-4766	152	10	.	.	PUNCT
ejpam-4766	153	1	,	,	PUNCT
ejpam-4766	153	2	wm	wm	PROPN
ejpam-4766	153	3	}	}	PUNCT
ejpam-4766	153	4	.	.	PUNCT
ejpam-4766	154	1	then	then	ADV
ejpam-4766	154	2	d	d	NOUN
ejpam-4766	154	3	and	and	CCONJ
ejpam-4766	154	4	d∗	d∗	PROPN
ejpam-4766	154	5	are	be	AUX
ejpam-4766	154	6	γc	γc	NOUN
ejpam-4766	154	7	-	-	PUNCT
ejpam-4766	154	8	set	set	ADJ
ejpam-4766	154	9	and	and	CCONJ
ejpam-4766	154	10	γohic	γohic	ADJ
ejpam-4766	154	11	-set	-set	ADJ
ejpam-4766	154	12	of	of	ADP
ejpam-4766	154	13	g2	g2	PROPN
ejpam-4766	154	14	,	,	PUNCT
ejpam-4766	154	15	respectively	respectively	ADV
ejpam-4766	154	16	.	.	PUNCT
ejpam-4766	155	1	therefore	therefore	ADV
ejpam-4766	155	2	,	,	PUNCT
ejpam-4766	155	3	γc(g2	γc(g2	NUM
ejpam-4766	155	4	)	)	PUNCT
ejpam-4766	155	5	=	=	SYM
ejpam-4766	155	6	a	a	PRON
ejpam-4766	155	7	and	and	CCONJ
ejpam-4766	155	8	γohic	γohic	ADJ
ejpam-4766	155	9	(	(	PUNCT
ejpam-4766	155	10	g2	g2	PROPN
ejpam-4766	155	11	)	)	PUNCT
ejpam-4766	156	1	=	=	PUNCT
ejpam-4766	157	1	m+	m+	NUM
ejpam-4766	157	2	a	a	DET
ejpam-4766	157	3	=	=	PROPN
ejpam-4766	157	4	b.	b.	PROPN
ejpam-4766	157	5	j.	j.	PROPN
ejpam-4766	157	6	hassan	hassan	PROPN
ejpam-4766	157	7	et	et	PROPN
ejpam-4766	157	8	al	al	PROPN
ejpam-4766	157	9	.	.	PUNCT
ejpam-4766	157	10	/	/	SYM
ejpam-4766	157	11	eur	eur	PROPN
ejpam-4766	157	12	.	.	PUNCT
ejpam-4766	158	1	j.	j.	PROPN
ejpam-4766	158	2	pure	pure	PROPN
ejpam-4766	158	3	appl	appl	PROPN
ejpam-4766	158	4	.	.	PROPN
ejpam-4766	158	5	math	math	PROPN
ejpam-4766	158	6	,	,	PUNCT
ejpam-4766	158	7	16	16	NUM
ejpam-4766	158	8	(	(	PUNCT
ejpam-4766	158	9	3	3	NUM
ejpam-4766	158	10	)	)	PUNCT
ejpam-4766	158	11	(	(	PUNCT
ejpam-4766	158	12	2023	2023	NUM
ejpam-4766	158	13	)	)	PUNCT
ejpam-4766	158	14	,	,	PUNCT
ejpam-4766	158	15	1817	1817	NUM
ejpam-4766	158	16	-	-	SYM
ejpam-4766	158	17	1829	1829	NUM
ejpam-4766	158	18	1823	1823	NUM
ejpam-4766	158	19	.	.	PUNCT
ejpam-4766	158	20	.	.	PUNCT
ejpam-4766	158	21	.	.	PUNCT
ejpam-4766	158	22	.	.	PUNCT
ejpam-4766	158	23	.	.	PUNCT
ejpam-4766	158	24	.	.	PUNCT
ejpam-4766	159	1	u1	u1	PROPN
ejpam-4766	159	2	u2	u2	PROPN
ejpam-4766	159	3	u3	u3	PROPN
ejpam-4766	159	4	uaua−1	uaua−1	PROPN
ejpam-4766	159	5	w1	w1	NOUN
ejpam-4766	159	6	w2	w2	PROPN
ejpam-4766	159	7	wm	wm	PROPN
ejpam-4766	159	8	g2	g2	PROPN
ejpam-4766	159	9	:	:	PUNCT
ejpam-4766	159	10	u4	u4	PROPN
ejpam-4766	159	11	figure	figure	NOUN
ejpam-4766	159	12	4	4	NUM
ejpam-4766	159	13	:	:	PUNCT
ejpam-4766	159	14	a	a	DET
ejpam-4766	159	15	graph	graph	NOUN
ejpam-4766	159	16	g2	g2	PROPN
ejpam-4766	159	17	with	with	ADP
ejpam-4766	159	18	γc(g2	γc(g2	NOUN
ejpam-4766	159	19	)	)	PUNCT
ejpam-4766	159	20	<	<	X
ejpam-4766	160	1	γohi	γohi	PROPN
ejpam-4766	160	2	c	c	PROPN
ejpam-4766	160	3	(	(	PUNCT
ejpam-4766	160	4	g2	g2	PROPN
ejpam-4766	160	5	)	)	PUNCT
ejpam-4766	160	6	the	the	DET
ejpam-4766	160	7	next	next	ADJ
ejpam-4766	160	8	theorem	theorem	NOUN
ejpam-4766	160	9	is	be	AUX
ejpam-4766	160	10	a	a	DET
ejpam-4766	160	11	realization	realization	NOUN
ejpam-4766	160	12	result	result	NOUN
ejpam-4766	160	13	involving	involve	VERB
ejpam-4766	160	14	connected	connected	ADJ
ejpam-4766	160	15	outer	outer	ADJ
ejpam-4766	160	16	-	-	PUNCT
ejpam-4766	160	17	independent	independent	ADJ
ejpam-4766	160	18	domination	domination	NOUN
ejpam-4766	160	19	number	number	NOUN
ejpam-4766	160	20	and	and	CCONJ
ejpam-4766	160	21	connected	connected	ADJ
ejpam-4766	160	22	outer	outer	ADJ
ejpam-4766	160	23	-	-	PUNCT
ejpam-4766	160	24	hop	hop	NOUN
ejpam-4766	160	25	independent	independent	ADJ
ejpam-4766	160	26	domination	domination	NOUN
ejpam-4766	160	27	number	number	NOUN
ejpam-4766	160	28	of	of	ADP
ejpam-4766	160	29	a	a	DET
ejpam-4766	160	30	graph	graph	NOUN
ejpam-4766	160	31	.	.	PUNCT
ejpam-4766	161	1	theorem	theorem	NOUN
ejpam-4766	161	2	3	3	X
ejpam-4766	161	3	.	.	PUNCT
ejpam-4766	162	1	let	let	VERB
ejpam-4766	162	2	a	a	PRON
ejpam-4766	162	3	and	and	CCONJ
ejpam-4766	162	4	b	b	NOUN
ejpam-4766	162	5	be	be	AUX
ejpam-4766	162	6	positive	positive	ADJ
ejpam-4766	162	7	integers	integer	NOUN
ejpam-4766	162	8	such	such	ADJ
ejpam-4766	162	9	that	that	SCONJ
ejpam-4766	162	10	2	2	NUM
ejpam-4766	162	11	≤	≤	NUM
ejpam-4766	162	12	a	a	DET
ejpam-4766	162	13	≤	≤	PROPN
ejpam-4766	162	14	b.	b.	NOUN
ejpam-4766	163	1	then	then	ADV
ejpam-4766	163	2	(	(	PUNCT
ejpam-4766	163	3	i	i	NOUN
ejpam-4766	163	4	)	)	PUNCT
ejpam-4766	163	5	there	there	PRON
ejpam-4766	163	6	exists	exist	VERB
ejpam-4766	163	7	a	a	DET
ejpam-4766	163	8	connected	connected	ADJ
ejpam-4766	163	9	graph	graph	NOUN
ejpam-4766	163	10	g	g	ADP
ejpam-4766	163	11	such	such	DET
ejpam-4766	163	12	that	that	DET
ejpam-4766	163	13	γohic	γohic	ADJ
ejpam-4766	163	14	(	(	PUNCT
ejpam-4766	163	15	g	g	NOUN
ejpam-4766	163	16	)	)	PUNCT
ejpam-4766	163	17	=	=	PUNCT
ejpam-4766	163	18	a	a	PRON
ejpam-4766	163	19	and	and	CCONJ
ejpam-4766	163	20	γoic	γoic	ADJ
ejpam-4766	163	21	(	(	PUNCT
ejpam-4766	163	22	g	g	NOUN
ejpam-4766	163	23	)	)	PUNCT
ejpam-4766	163	24	=	=	SYM
ejpam-4766	163	25	b.	b.	PROPN
ejpam-4766	163	26	(	(	PUNCT
ejpam-4766	163	27	ii	ii	PROPN
ejpam-4766	163	28	)	)	PUNCT
ejpam-4766	163	29	there	there	PRON
ejpam-4766	163	30	exists	exist	VERB
ejpam-4766	163	31	a	a	DET
ejpam-4766	163	32	connected	connected	ADJ
ejpam-4766	163	33	graph	graph	NOUN
ejpam-4766	163	34	g	g	ADP
ejpam-4766	163	35	such	such	DET
ejpam-4766	163	36	that	that	DET
ejpam-4766	163	37	γoic	γoic	ADJ
ejpam-4766	163	38	(	(	PUNCT
ejpam-4766	163	39	g	g	NOUN
ejpam-4766	163	40	)	)	PUNCT
ejpam-4766	163	41	=	=	SYM
ejpam-4766	163	42	a	a	PRON
ejpam-4766	163	43	and	and	CCONJ
ejpam-4766	163	44	γohic	γohic	ADJ
ejpam-4766	163	45	(	(	PUNCT
ejpam-4766	163	46	g	g	NOUN
ejpam-4766	163	47	)	)	PUNCT
ejpam-4766	163	48	=	=	SYM
ejpam-4766	163	49	b.	b.	PROPN
ejpam-4766	164	1	in	in	ADP
ejpam-4766	164	2	other	other	ADJ
ejpam-4766	164	3	words	word	NOUN
ejpam-4766	164	4	,	,	PUNCT
ejpam-4766	164	5	|γoic	|γoic	NOUN
ejpam-4766	164	6	(	(	PUNCT
ejpam-4766	164	7	g)−	g)−	PROPN
ejpam-4766	164	8	γohic	γohic	ADJ
ejpam-4766	164	9	(	(	PUNCT
ejpam-4766	164	10	g)|	g)|	NOUN
ejpam-4766	164	11	can	can	AUX
ejpam-4766	164	12	be	be	AUX
ejpam-4766	164	13	made	make	VERB
ejpam-4766	164	14	arbitrarily	arbitrarily	ADV
ejpam-4766	164	15	large	large	ADJ
ejpam-4766	164	16	.	.	PUNCT
ejpam-4766	165	1	proof	proof	NOUN
ejpam-4766	165	2	.	.	PUNCT
ejpam-4766	166	1	(	(	PUNCT
ejpam-4766	166	2	i	i	NOUN
ejpam-4766	166	3	)	)	PUNCT
ejpam-4766	166	4	suppose	suppose	VERB
ejpam-4766	166	5	a	a	DET
ejpam-4766	166	6	<	<	X
ejpam-4766	166	7	b.	b.	NOUN
ejpam-4766	166	8	let	let	VERB
ejpam-4766	166	9	m	m	VERB
ejpam-4766	166	10	=	=	VERB
ejpam-4766	167	1	b	b	X
ejpam-4766	167	2	−	−	PROPN
ejpam-4766	167	3	a	a	PRON
ejpam-4766	168	1	and	and	CCONJ
ejpam-4766	168	2	consider	consider	VERB
ejpam-4766	168	3	the	the	DET
ejpam-4766	168	4	graph	graph	NOUN
ejpam-4766	168	5	g	g	NOUN
ejpam-4766	168	6	in	in	ADP
ejpam-4766	168	7	figure	figure	NOUN
ejpam-4766	168	8	5	5	NUM
ejpam-4766	168	9	.	.	PUNCT
ejpam-4766	169	1	let	let	VERB
ejpam-4766	169	2	d1	d1	PROPN
ejpam-4766	169	3	=	=	PUNCT
ejpam-4766	169	4	{	{	PUNCT
ejpam-4766	169	5	x1	x1	PROPN
ejpam-4766	169	6	,	,	PUNCT
ejpam-4766	169	7	x2	x2	PROPN
ejpam-4766	169	8	,	,	PUNCT
ejpam-4766	169	9	.	.	PUNCT
ejpam-4766	169	10	.	.	PUNCT
ejpam-4766	170	1	.	.	PUNCT
ejpam-4766	171	1	,	,	PUNCT
ejpam-4766	171	2	xa	xa	PROPN
ejpam-4766	171	3	}	}	PUNCT
ejpam-4766	171	4	and	and	CCONJ
ejpam-4766	171	5	d2	d2	PROPN
ejpam-4766	171	6	=	=	SYM
ejpam-4766	171	7	{	{	PUNCT
ejpam-4766	171	8	x1	x1	PROPN
ejpam-4766	171	9	,	,	PUNCT
ejpam-4766	171	10	x2	x2	PROPN
ejpam-4766	171	11	,	,	PUNCT
ejpam-4766	171	12	.	.	PUNCT
ejpam-4766	171	13	.	.	PUNCT
ejpam-4766	172	1	.	.	PUNCT
ejpam-4766	173	1	,	,	PUNCT
ejpam-4766	173	2	xa	xa	PROPN
ejpam-4766	173	3	,	,	PUNCT
ejpam-4766	173	4	y1	y1	PROPN
ejpam-4766	173	5	,	,	PUNCT
ejpam-4766	173	6	y2	y2	PROPN
ejpam-4766	173	7	,	,	PUNCT
ejpam-4766	173	8	.	.	PUNCT
ejpam-4766	173	9	.	.	PUNCT
ejpam-4766	173	10	.	.	PUNCT
ejpam-4766	174	1	,	,	PUNCT
ejpam-4766	174	2	ym	ym	PROPN
ejpam-4766	174	3	}	}	PUNCT
ejpam-4766	174	4	.	.	PUNCT
ejpam-4766	175	1	then	then	ADV
ejpam-4766	175	2	d1	d1	PROPN
ejpam-4766	175	3	and	and	CCONJ
ejpam-4766	175	4	d2	d2	PROPN
ejpam-4766	175	5	are	be	AUX
ejpam-4766	175	6	γohic	γohic	ADJ
ejpam-4766	175	7	-set	-set	PUNCT
ejpam-4766	175	8	and	and	CCONJ
ejpam-4766	175	9	γoic	γoic	ADJ
ejpam-4766	175	10	-set	-set	ADJ
ejpam-4766	175	11	of	of	ADP
ejpam-4766	175	12	g	g	NOUN
ejpam-4766	175	13	,	,	PUNCT
ejpam-4766	175	14	respectively	respectively	ADV
ejpam-4766	175	15	.	.	PUNCT
ejpam-4766	176	1	hence	hence	ADV
ejpam-4766	176	2	,	,	PUNCT
ejpam-4766	176	3	γohic	γohic	ADJ
ejpam-4766	176	4	(	(	PUNCT
ejpam-4766	176	5	g	g	NOUN
ejpam-4766	176	6	)	)	PUNCT
ejpam-4766	176	7	=	=	PUNCT
ejpam-4766	177	1	a	a	PRON
ejpam-4766	177	2	and	and	CCONJ
ejpam-4766	177	3	γoic	γoic	ADJ
ejpam-4766	177	4	(	(	PUNCT
ejpam-4766	177	5	g	g	NOUN
ejpam-4766	177	6	)	)	PUNCT
ejpam-4766	177	7	=	=	VERB
ejpam-4766	178	1	m+	m+	NUM
ejpam-4766	178	2	a	a	DET
ejpam-4766	178	3	=	=	X
ejpam-4766	178	4	b.	b.	PROPN
ejpam-4766	178	5	g	g	NOUN
ejpam-4766	178	6	:	:	PUNCT
ejpam-4766	178	7	x2	x2	PROPN
ejpam-4766	178	8	y1	y1	INTJ
ejpam-4766	178	9	.	.	PUNCT
ejpam-4766	178	10	.	.	PUNCT
ejpam-4766	178	11	.	.	PUNCT
ejpam-4766	179	1	xaxa−1x3	xaxa−1x3	NOUN
ejpam-4766	179	2	y2	y2	NOUN
ejpam-4766	179	3	ym+1	ym+1	PROPN
ejpam-4766	179	4	x1	x1	PROPN
ejpam-4766	179	5	.	.	PUNCT
ejpam-4766	179	6	.	.	PUNCT
ejpam-4766	179	7	.	.	PUNCT
ejpam-4766	180	1	figure	figure	VERB
ejpam-4766	180	2	5	5	NUM
ejpam-4766	180	3	:	:	PUNCT
ejpam-4766	180	4	a	a	DET
ejpam-4766	180	5	graph	graph	NOUN
ejpam-4766	180	6	g	g	NOUN
ejpam-4766	180	7	with	with	ADP
ejpam-4766	180	8	γohi	γohi	PROPN
ejpam-4766	180	9	c	c	PROPN
ejpam-4766	180	10	(	(	PUNCT
ejpam-4766	180	11	g	g	NOUN
ejpam-4766	180	12	)	)	PUNCT
ejpam-4766	180	13	<	<	X
ejpam-4766	180	14	γoi	γoi	X
ejpam-4766	180	15	c	c	NOUN
ejpam-4766	180	16	(	(	PUNCT
ejpam-4766	180	17	g	g	NOUN
ejpam-4766	180	18	)	)	PUNCT
ejpam-4766	180	19	(	(	PUNCT
ejpam-4766	180	20	ii	ii	NOUN
ejpam-4766	180	21	)	)	PUNCT
ejpam-4766	180	22	suppose	suppose	VERB
ejpam-4766	180	23	a	a	DET
ejpam-4766	180	24	<	<	X
ejpam-4766	180	25	b.	b.	NOUN
ejpam-4766	180	26	let	let	VERB
ejpam-4766	180	27	m	m	VERB
ejpam-4766	180	28	=	=	VERB
ejpam-4766	181	1	b	b	X
ejpam-4766	181	2	−	−	PROPN
ejpam-4766	181	3	a	a	PRON
ejpam-4766	182	1	and	and	CCONJ
ejpam-4766	182	2	consider	consider	VERB
ejpam-4766	182	3	the	the	DET
ejpam-4766	182	4	graph	graph	NOUN
ejpam-4766	182	5	g∗	g∗	NOUN
ejpam-4766	182	6	in	in	ADP
ejpam-4766	182	7	figure	figure	NOUN
ejpam-4766	182	8	6	6	NUM
ejpam-4766	182	9	.	.	PUNCT
ejpam-4766	183	1	let	let	VERB
ejpam-4766	183	2	d′	d′	X
ejpam-4766	183	3	=	=	PUNCT
ejpam-4766	183	4	{	{	PUNCT
ejpam-4766	183	5	x1	x1	PROPN
ejpam-4766	183	6	,	,	PUNCT
ejpam-4766	183	7	x2	x2	PROPN
ejpam-4766	183	8	,	,	PUNCT
ejpam-4766	183	9	.	.	PUNCT
ejpam-4766	183	10	.	.	PUNCT
ejpam-4766	184	1	.	.	PUNCT
ejpam-4766	185	1	,	,	PUNCT
ejpam-4766	185	2	xa	xa	PROPN
ejpam-4766	185	3	}	}	PUNCT
ejpam-4766	185	4	and	and	CCONJ
ejpam-4766	185	5	d′′	d′′	NOUN
ejpam-4766	185	6	=	=	PUNCT
ejpam-4766	185	7	{	{	PUNCT
ejpam-4766	185	8	x1	x1	PROPN
ejpam-4766	185	9	,	,	PUNCT
ejpam-4766	185	10	x2	x2	PROPN
ejpam-4766	185	11	,	,	PUNCT
ejpam-4766	185	12	.	.	PUNCT
ejpam-4766	185	13	.	.	PUNCT
ejpam-4766	186	1	.	.	PUNCT
ejpam-4766	187	1	,	,	PUNCT
ejpam-4766	187	2	xa	xa	PROPN
ejpam-4766	187	3	,	,	PUNCT
ejpam-4766	187	4	z1	z1	PROPN
ejpam-4766	187	5	,	,	PUNCT
ejpam-4766	187	6	z2	z2	PROPN
ejpam-4766	187	7	,	,	PUNCT
ejpam-4766	187	8	.	.	PUNCT
ejpam-4766	187	9	.	.	PUNCT
ejpam-4766	187	10	.	.	PUNCT
ejpam-4766	188	1	,	,	PUNCT
ejpam-4766	188	2	zm	zm	PROPN
ejpam-4766	188	3	}	}	PUNCT
ejpam-4766	188	4	.	.	PUNCT
ejpam-4766	189	1	then	then	ADV
ejpam-4766	189	2	d′	d′	PROPN
ejpam-4766	189	3	and	and	CCONJ
ejpam-4766	189	4	d′′	d′′	PROPN
ejpam-4766	189	5	are	be	AUX
ejpam-4766	189	6	γoic	γoic	ADJ
ejpam-4766	189	7	-set	-set	ADJ
ejpam-4766	189	8	and	and	CCONJ
ejpam-4766	189	9	γohic	γohic	ADJ
ejpam-4766	189	10	-set	-set	ADJ
ejpam-4766	189	11	of	of	ADP
ejpam-4766	189	12	g∗	g∗	PROPN
ejpam-4766	189	13	,	,	PUNCT
ejpam-4766	189	14	respectively	respectively	ADV
ejpam-4766	189	15	.	.	PUNCT
ejpam-4766	190	1	therefore	therefore	ADV
ejpam-4766	190	2	,	,	PUNCT
ejpam-4766	190	3	γoic	γoic	ADJ
ejpam-4766	190	4	(	(	PUNCT
ejpam-4766	190	5	g∗	g∗	PROPN
ejpam-4766	190	6	)	)	PUNCT
ejpam-4766	190	7	=	=	SYM
ejpam-4766	190	8	a	a	PRON
ejpam-4766	190	9	and	and	CCONJ
ejpam-4766	190	10	γohic	γohic	ADJ
ejpam-4766	190	11	(	(	PUNCT
ejpam-4766	190	12	g∗	g∗	PROPN
ejpam-4766	190	13	)	)	PUNCT
ejpam-4766	190	14	=	=	VERB
ejpam-4766	191	1	m+	m+	NUM
ejpam-4766	191	2	a	a	DET
ejpam-4766	191	3	=	=	PROPN
ejpam-4766	191	4	b.	b.	PROPN
ejpam-4766	191	5	j.	j.	PROPN
ejpam-4766	191	6	hassan	hassan	PROPN
ejpam-4766	191	7	et	et	PROPN
ejpam-4766	191	8	al	al	PROPN
ejpam-4766	191	9	.	.	PUNCT
ejpam-4766	191	10	/	/	SYM
ejpam-4766	191	11	eur	eur	PROPN
ejpam-4766	191	12	.	.	PUNCT
ejpam-4766	192	1	j.	j.	PROPN
ejpam-4766	192	2	pure	pure	PROPN
ejpam-4766	192	3	appl	appl	PROPN
ejpam-4766	192	4	.	.	PROPN
ejpam-4766	192	5	math	math	PROPN
ejpam-4766	192	6	,	,	PUNCT
ejpam-4766	192	7	16	16	NUM
ejpam-4766	192	8	(	(	PUNCT
ejpam-4766	192	9	3	3	NUM
ejpam-4766	192	10	)	)	PUNCT
ejpam-4766	192	11	(	(	PUNCT
ejpam-4766	192	12	2023	2023	NUM
ejpam-4766	192	13	)	)	PUNCT
ejpam-4766	192	14	,	,	PUNCT
ejpam-4766	192	15	1817	1817	NUM
ejpam-4766	192	16	-	-	SYM
ejpam-4766	192	17	1829	1829	NUM
ejpam-4766	192	18	1824	1824	NUM
ejpam-4766	192	19	xa−1	xa−1	PROPN
ejpam-4766	192	20	g∗	g∗	PROPN
ejpam-4766	192	21	:	:	PUNCT
ejpam-4766	193	1	x2x1	x2x1	INTJ
ejpam-4766	193	2	xa	xa	PROPN
ejpam-4766	193	3	.	.	PUNCT
ejpam-4766	193	4	.	.	PUNCT
ejpam-4766	193	5	.	.	PUNCT
ejpam-4766	194	1	z1	z1	PROPN
ejpam-4766	194	2	z2	z2	PROPN
ejpam-4766	194	3	zm	zm	PROPN
ejpam-4766	194	4	.	.	PUNCT
ejpam-4766	194	5	.	.	PUNCT
ejpam-4766	195	1	.	.	PUNCT
ejpam-4766	196	1	figure	figure	VERB
ejpam-4766	196	2	6	6	NUM
ejpam-4766	196	3	:	:	PUNCT
ejpam-4766	196	4	a	a	DET
ejpam-4766	196	5	graph	graph	NOUN
ejpam-4766	196	6	g∗	g∗	VERB
ejpam-4766	196	7	with	with	ADP
ejpam-4766	196	8	γoi	γoi	NOUN
ejpam-4766	196	9	c	c	PROPN
ejpam-4766	196	10	(	(	PUNCT
ejpam-4766	196	11	g∗	g∗	PROPN
ejpam-4766	196	12	)	)	PUNCT
ejpam-4766	196	13	<	<	X
ejpam-4766	197	1	γohi	γohi	PROPN
ejpam-4766	197	2	c	c	PROPN
ejpam-4766	197	3	(	(	PUNCT
ejpam-4766	197	4	g∗	g∗	PROPN
ejpam-4766	197	5	)	)	PUNCT
ejpam-4766	197	6	the	the	DET
ejpam-4766	197	7	following	follow	VERB
ejpam-4766	197	8	concept	concept	NOUN
ejpam-4766	197	9	will	will	AUX
ejpam-4766	197	10	be	be	AUX
ejpam-4766	197	11	used	use	VERB
ejpam-4766	197	12	in	in	ADP
ejpam-4766	197	13	characterizing	characterize	VERB
ejpam-4766	197	14	the	the	DET
ejpam-4766	197	15	connected	connected	ADJ
ejpam-4766	197	16	outer	outer	ADJ
ejpam-4766	197	17	-	-	PUNCT
ejpam-4766	197	18	hop	hop	NOUN
ejpam-4766	197	19	independent	independent	ADJ
ejpam-4766	197	20	dominating	dominating	NOUN
ejpam-4766	197	21	sets	set	NOUN
ejpam-4766	197	22	in	in	ADP
ejpam-4766	197	23	the	the	DET
ejpam-4766	197	24	join	join	NOUN
ejpam-4766	197	25	and	and	CCONJ
ejpam-4766	197	26	corona	corona	NOUN
ejpam-4766	197	27	of	of	ADP
ejpam-4766	197	28	two	two	NUM
ejpam-4766	197	29	graphs	graph	NOUN
ejpam-4766	197	30	.	.	PUNCT
ejpam-4766	198	1	definition	definition	NOUN
ejpam-4766	198	2	2	2	NUM
ejpam-4766	198	3	.	.	PUNCT
ejpam-4766	199	1	let	let	VERB
ejpam-4766	199	2	g	g	PRON
ejpam-4766	199	3	be	be	AUX
ejpam-4766	199	4	a	a	DET
ejpam-4766	199	5	non	non	ADJ
ejpam-4766	199	6	-	-	ADJ
ejpam-4766	199	7	complete	complete	ADJ
ejpam-4766	199	8	graph	graph	NOUN
ejpam-4766	199	9	.	.	PUNCT
ejpam-4766	200	1	a	a	DET
ejpam-4766	200	2	non	non	ADJ
ejpam-4766	200	3	-	-	ADJ
ejpam-4766	200	4	empty	empty	ADJ
ejpam-4766	200	5	subset	subset	NOUN
ejpam-4766	200	6	o	o	NOUN
ejpam-4766	200	7	⊆	⊆	NUM
ejpam-4766	200	8	v	v	NOUN
ejpam-4766	200	9	(	(	PUNCT
ejpam-4766	200	10	g	g	NOUN
ejpam-4766	200	11	)	)	PUNCT
ejpam-4766	200	12	is	be	AUX
ejpam-4766	200	13	called	call	VERB
ejpam-4766	200	14	an	an	DET
ejpam-4766	200	15	outer	outer	ADJ
ejpam-4766	200	16	-	-	PUNCT
ejpam-4766	200	17	clique	clique	NOUN
ejpam-4766	200	18	set	set	NOUN
ejpam-4766	200	19	if	if	SCONJ
ejpam-4766	200	20	v	v	NOUN
ejpam-4766	200	21	(	(	PUNCT
ejpam-4766	200	22	g	g	NOUN
ejpam-4766	200	23	)	)	PUNCT
ejpam-4766	200	24	\o	\o	PROPN
ejpam-4766	200	25	is	be	AUX
ejpam-4766	200	26	clique	clique	NOUN
ejpam-4766	200	27	in	in	ADP
ejpam-4766	200	28	g.	g.	PROPN
ejpam-4766	200	29	the	the	DET
ejpam-4766	200	30	smallest	small	ADJ
ejpam-4766	200	31	cardinality	cardinality	NOUN
ejpam-4766	200	32	of	of	ADP
ejpam-4766	200	33	an	an	DET
ejpam-4766	200	34	outer	outer	ADJ
ejpam-4766	200	35	-	-	PUNCT
ejpam-4766	200	36	clique	clique	NOUN
ejpam-4766	200	37	set	set	NOUN
ejpam-4766	200	38	of	of	ADP
ejpam-4766	200	39	g	g	NOUN
ejpam-4766	200	40	,	,	PUNCT
ejpam-4766	200	41	denoted	denote	VERB
ejpam-4766	200	42	by	by	ADP
ejpam-4766	200	43	ω̃(g	ω̃(g	NOUN
ejpam-4766	200	44	)	)	PUNCT
ejpam-4766	200	45	,	,	PUNCT
ejpam-4766	200	46	is	be	AUX
ejpam-4766	200	47	called	call	VERB
ejpam-4766	200	48	the	the	DET
ejpam-4766	200	49	outer	outer	ADJ
ejpam-4766	200	50	-	-	PUNCT
ejpam-4766	200	51	clique	clique	NOUN
ejpam-4766	200	52	number	number	NOUN
ejpam-4766	200	53	of	of	ADP
ejpam-4766	200	54	g.	g.	PROPN
ejpam-4766	200	55	any	any	DET
ejpam-4766	200	56	outer	outer	ADJ
ejpam-4766	200	57	-	-	PUNCT
ejpam-4766	200	58	clique	clique	NOUN
ejpam-4766	200	59	set	set	NOUN
ejpam-4766	200	60	o	o	NOUN
ejpam-4766	200	61	of	of	ADP
ejpam-4766	200	62	g	g	PROPN
ejpam-4766	200	63	with	with	ADP
ejpam-4766	200	64	cardinality	cardinality	NOUN
ejpam-4766	200	65	equal	equal	ADJ
ejpam-4766	200	66	to	to	ADP
ejpam-4766	200	67	ω̃(g	ω̃(g	NOUN
ejpam-4766	200	68	)	)	PUNCT
ejpam-4766	200	69	,	,	PUNCT
ejpam-4766	200	70	is	be	AUX
ejpam-4766	200	71	called	call	VERB
ejpam-4766	200	72	an	an	DET
ejpam-4766	200	73	ω̃-set	ω̃-set	NOUN
ejpam-4766	200	74	of	of	ADP
ejpam-4766	200	75	g.	g.	PROPN
ejpam-4766	200	76	remark	remark	PROPN
ejpam-4766	200	77	3	3	NUM
ejpam-4766	200	78	.	.	PUNCT
ejpam-4766	201	1	let	let	VERB
ejpam-4766	201	2	n	n	PRON
ejpam-4766	201	3	≥	≥	X
ejpam-4766	201	4	2	2	NUM
ejpam-4766	201	5	be	be	AUX
ejpam-4766	201	6	any	any	DET
ejpam-4766	201	7	positive	positive	ADJ
ejpam-4766	201	8	integer	integer	NOUN
ejpam-4766	201	9	.	.	PUNCT
ejpam-4766	202	1	then	then	ADV
ejpam-4766	202	2	each	each	PRON
ejpam-4766	202	3	of	of	ADP
ejpam-4766	202	4	the	the	DET
ejpam-4766	202	5	following	follow	VERB
ejpam-4766	202	6	holds	hold	NOUN
ejpam-4766	202	7	.	.	PUNCT
ejpam-4766	203	1	(	(	PUNCT
ejpam-4766	203	2	i	i	NOUN
ejpam-4766	203	3	)	)	PUNCT
ejpam-4766	203	4	ω̃(g	ω̃(g	NOUN
ejpam-4766	203	5	)	)	PUNCT
ejpam-4766	203	6	=	=	PUNCT
ejpam-4766	203	7	n−	n−	NOUN
ejpam-4766	203	8	1	1	NUM
ejpam-4766	203	9	if	if	SCONJ
ejpam-4766	203	10	g	g	PROPN
ejpam-4766	203	11	=	=	PROPN
ejpam-4766	203	12	kn	kn	PROPN
ejpam-4766	203	13	(	(	PUNCT
ejpam-4766	203	14	ii	ii	NOUN
ejpam-4766	203	15	)	)	PUNCT
ejpam-4766	203	16	ω̃(pn	ω̃(pn	NOUN
ejpam-4766	203	17	)	)	PUNCT
ejpam-4766	204	1	=	=	SYM
ejpam-4766	204	2	{	{	PUNCT
ejpam-4766	204	3	1	1	NUM
ejpam-4766	204	4	if	if	SCONJ
ejpam-4766	204	5	n	n	NOUN
ejpam-4766	204	6	=	=	SYM
ejpam-4766	204	7	3	3	NUM
ejpam-4766	204	8	n−	n−	NOUN
ejpam-4766	204	9	2	2	NUM
ejpam-4766	204	10	if	if	SCONJ
ejpam-4766	204	11	n	n	PRON
ejpam-4766	204	12	≥	≥	NOUN
ejpam-4766	204	13	4	4	NUM
ejpam-4766	204	14	;	;	PUNCT
ejpam-4766	204	15	and	and	CCONJ
ejpam-4766	204	16	(	(	PUNCT
ejpam-4766	204	17	iii	iii	NOUN
ejpam-4766	204	18	)	)	PUNCT
ejpam-4766	204	19	ω̃(cn	ω̃(cn	NOUN
ejpam-4766	204	20	)	)	PUNCT
ejpam-4766	205	1	=	=	PUNCT
ejpam-4766	205	2	n−	n−	NOUN
ejpam-4766	205	3	2	2	NUM
ejpam-4766	205	4	for	for	ADP
ejpam-4766	205	5	all	all	DET
ejpam-4766	205	6	n	n	PRON
ejpam-4766	205	7	≥	≥	NUM
ejpam-4766	205	8	4	4	NUM
ejpam-4766	205	9	.	.	PUNCT
ejpam-4766	205	10	theorem	theorem	NOUN
ejpam-4766	205	11	4	4	NUM
ejpam-4766	205	12	.	.	PUNCT
ejpam-4766	206	1	let	let	VERB
ejpam-4766	206	2	g	g	NOUN
ejpam-4766	206	3	and	and	CCONJ
ejpam-4766	206	4	h	h	NOUN
ejpam-4766	206	5	be	be	VERB
ejpam-4766	206	6	two	two	NUM
ejpam-4766	206	7	non	non	ADJ
ejpam-4766	206	8	-	-	ADJ
ejpam-4766	206	9	complete	complete	ADJ
ejpam-4766	206	10	graphs	graph	NOUN
ejpam-4766	206	11	.	.	PUNCT
ejpam-4766	207	1	then	then	ADV
ejpam-4766	207	2	d	d	PROPN
ejpam-4766	207	3	⊆	⊆	NUM
ejpam-4766	207	4	v	v	X
ejpam-4766	207	5	(	(	PUNCT
ejpam-4766	207	6	g	g	PROPN
ejpam-4766	207	7	+	+	NOUN
ejpam-4766	207	8	h	h	NOUN
ejpam-4766	207	9	)	)	PUNCT
ejpam-4766	207	10	is	be	AUX
ejpam-4766	207	11	a	a	DET
ejpam-4766	207	12	connected	connected	ADJ
ejpam-4766	207	13	outer	outer	ADJ
ejpam-4766	207	14	-	-	PUNCT
ejpam-4766	207	15	hop	hop	NOUN
ejpam-4766	207	16	independent	independent	ADJ
ejpam-4766	207	17	dominating	dominating	NOUN
ejpam-4766	207	18	in	in	ADP
ejpam-4766	207	19	g+h	g+h	PROPN
ejpam-4766	208	1	if	if	SCONJ
ejpam-4766	208	2	and	and	CCONJ
ejpam-4766	208	3	only	only	ADV
ejpam-4766	208	4	if	if	SCONJ
ejpam-4766	208	5	d	d	PROPN
ejpam-4766	208	6	=	=	PUNCT
ejpam-4766	208	7	dg∪dh	dg∪dh	PROPN
ejpam-4766	208	8	,	,	PUNCT
ejpam-4766	208	9	where	where	SCONJ
ejpam-4766	208	10	dg	dg	NOUN
ejpam-4766	208	11	and	and	CCONJ
ejpam-4766	208	12	dh	dh	NOUN
ejpam-4766	208	13	are	be	AUX
ejpam-4766	208	14	outer	outer	ADJ
ejpam-4766	208	15	-	-	PUNCT
ejpam-4766	208	16	clique	clique	NOUN
ejpam-4766	208	17	sets	set	NOUN
ejpam-4766	208	18	in	in	ADP
ejpam-4766	208	19	g	g	PROPN
ejpam-4766	208	20	and	and	CCONJ
ejpam-4766	208	21	h	h	NOUN
ejpam-4766	208	22	,	,	PUNCT
ejpam-4766	208	23	respectively	respectively	ADV
ejpam-4766	208	24	.	.	PUNCT
ejpam-4766	209	1	proof	proof	NOUN
ejpam-4766	209	2	.	.	PUNCT
ejpam-4766	210	1	suppose	suppose	VERB
ejpam-4766	210	2	d	d	SYM
ejpam-4766	210	3	⊆	⊆	NUM
ejpam-4766	210	4	v	v	NOUN
ejpam-4766	210	5	(	(	PUNCT
ejpam-4766	210	6	g	g	PROPN
ejpam-4766	210	7	+	+	NOUN
ejpam-4766	210	8	h	h	NOUN
ejpam-4766	210	9	)	)	PUNCT
ejpam-4766	210	10	is	be	AUX
ejpam-4766	210	11	a	a	DET
ejpam-4766	210	12	connected	connected	ADJ
ejpam-4766	210	13	outer	outer	ADJ
ejpam-4766	210	14	-	-	PUNCT
ejpam-4766	210	15	hop	hop	NOUN
ejpam-4766	210	16	independent	independent	ADJ
ejpam-4766	210	17	dominating	dominating	NOUN
ejpam-4766	210	18	set	set	VERB
ejpam-4766	210	19	in	in	ADP
ejpam-4766	210	20	g	g	PROPN
ejpam-4766	210	21	+	+	CCONJ
ejpam-4766	210	22	h.	h.	PROPN
ejpam-4766	210	23	let	let	VERB
ejpam-4766	210	24	dg	dg	NOUN
ejpam-4766	210	25	=	=	SYM
ejpam-4766	210	26	v	v	PROPN
ejpam-4766	210	27	(	(	PUNCT
ejpam-4766	210	28	g	g	NOUN
ejpam-4766	210	29	)	)	PUNCT
ejpam-4766	210	30	∩	∩	ADJ
ejpam-4766	211	1	d	d	NOUN
ejpam-4766	211	2	and	and	CCONJ
ejpam-4766	211	3	dh	dh	NOUN
ejpam-4766	211	4	=	=	SYM
ejpam-4766	211	5	v	v	PROPN
ejpam-4766	211	6	(	(	PUNCT
ejpam-4766	211	7	h	h	NOUN
ejpam-4766	211	8	)	)	PUNCT
ejpam-4766	211	9	∩	∩	PROPN
ejpam-4766	211	10	d.	d.	PROPN
ejpam-4766	211	11	since	since	SCONJ
ejpam-4766	211	12	g	g	PROPN
ejpam-4766	211	13	and	and	CCONJ
ejpam-4766	211	14	h	h	NOUN
ejpam-4766	211	15	are	be	AUX
ejpam-4766	211	16	noncomplete	noncomplete	ADJ
ejpam-4766	211	17	,	,	PUNCT
ejpam-4766	211	18	it	it	PRON
ejpam-4766	211	19	follows	follow	VERB
ejpam-4766	211	20	that	that	SCONJ
ejpam-4766	211	21	dg	dg	VERB
ejpam-4766	211	22	̸=	̸=	PROPN
ejpam-4766	211	23	∅	∅	NOUN
ejpam-4766	211	24	and	and	CCONJ
ejpam-4766	211	25	dh	dh	NOUN
ejpam-4766	211	26	̸=	̸=	PROPN
ejpam-4766	211	27	∅.	∅.	ADV
ejpam-4766	211	28	suppose	suppose	VERB
ejpam-4766	211	29	v	v	ADP
ejpam-4766	211	30	(	(	PUNCT
ejpam-4766	211	31	g	g	NOUN
ejpam-4766	211	32	)	)	PUNCT
ejpam-4766	211	33	\	\	NOUN
ejpam-4766	211	34	dg	dg	PROPN
ejpam-4766	211	35	is	be	AUX
ejpam-4766	211	36	not	not	PART
ejpam-4766	211	37	a	a	DET
ejpam-4766	211	38	clique	clique	NOUN
ejpam-4766	211	39	in	in	ADP
ejpam-4766	211	40	g.	g.	PROPN
ejpam-4766	211	41	then	then	ADV
ejpam-4766	211	42	there	there	PRON
ejpam-4766	211	43	exist	exist	VERB
ejpam-4766	211	44	a	a	DET
ejpam-4766	211	45	,	,	PUNCT
ejpam-4766	211	46	b	b	PROPN
ejpam-4766	211	47	∈	∈	PROPN
ejpam-4766	211	48	v	v	NOUN
ejpam-4766	211	49	(	(	PUNCT
ejpam-4766	211	50	g	g	NOUN
ejpam-4766	211	51	)	)	PUNCT
ejpam-4766	211	52	\	\	PUNCT
ejpam-4766	212	1	dg	dg	VERB
ejpam-4766	212	2	such	such	ADJ
ejpam-4766	212	3	that	that	SCONJ
ejpam-4766	212	4	dg(a	dg(a	PROPN
ejpam-4766	212	5	,	,	PUNCT
ejpam-4766	212	6	b	b	X
ejpam-4766	212	7	)	)	PUNCT
ejpam-4766	212	8	=	=	SYM
ejpam-4766	212	9	2	2	NUM
ejpam-4766	212	10	=	=	SYM
ejpam-4766	212	11	dg+h(a	dg+h(a	PROPN
ejpam-4766	212	12	,	,	PUNCT
ejpam-4766	212	13	b	b	NOUN
ejpam-4766	212	14	)	)	PUNCT
ejpam-4766	212	15	.	.	PUNCT
ejpam-4766	213	1	since	since	SCONJ
ejpam-4766	213	2	v	v	NOUN
ejpam-4766	213	3	(	(	PUNCT
ejpam-4766	213	4	g	g	NOUN
ejpam-4766	213	5	)	)	PUNCT
ejpam-4766	213	6	\dg	\dg	PROPN
ejpam-4766	213	7	⊆	⊆	NUM
ejpam-4766	213	8	v	v	NOUN
ejpam-4766	213	9	(	(	PUNCT
ejpam-4766	213	10	g+h	g+h	NOUN
ejpam-4766	213	11	)	)	PUNCT
ejpam-4766	213	12	\d	\d	NOUN
ejpam-4766	213	13	,	,	PUNCT
ejpam-4766	213	14	it	it	PRON
ejpam-4766	213	15	follows	follow	VERB
ejpam-4766	213	16	that	that	SCONJ
ejpam-4766	213	17	v	v	X
ejpam-4766	213	18	(	(	PUNCT
ejpam-4766	213	19	g+h	g+h	NOUN
ejpam-4766	213	20	)	)	PUNCT
ejpam-4766	213	21	\d	\d	NOUN
ejpam-4766	213	22	is	be	AUX
ejpam-4766	213	23	not	not	PART
ejpam-4766	213	24	a	a	DET
ejpam-4766	213	25	hop	hop	NOUN
ejpam-4766	213	26	independent	independent	ADJ
ejpam-4766	213	27	set	set	NOUN
ejpam-4766	213	28	,	,	PUNCT
ejpam-4766	213	29	a	a	DET
ejpam-4766	213	30	contradiction	contradiction	NOUN
ejpam-4766	213	31	to	to	ADP
ejpam-4766	213	32	the	the	DET
ejpam-4766	213	33	fact	fact	NOUN
ejpam-4766	213	34	that	that	SCONJ
ejpam-4766	213	35	d	d	NOUN
ejpam-4766	213	36	is	be	AUX
ejpam-4766	213	37	a	a	DET
ejpam-4766	213	38	connected	connected	ADJ
ejpam-4766	213	39	outer	outer	ADJ
ejpam-4766	213	40	-	-	PUNCT
ejpam-4766	213	41	hop	hop	NOUN
ejpam-4766	213	42	independent	independent	ADJ
ejpam-4766	213	43	dominating	dominating	NOUN
ejpam-4766	213	44	set	set	VERB
ejpam-4766	213	45	in	in	ADP
ejpam-4766	213	46	g+h	g+h	PROPN
ejpam-4766	213	47	.	.	PUNCT
ejpam-4766	214	1	therefore	therefore	ADV
ejpam-4766	214	2	,	,	PUNCT
ejpam-4766	214	3	v	v	X
ejpam-4766	214	4	(	(	PUNCT
ejpam-4766	214	5	g	g	NOUN
ejpam-4766	214	6	)	)	PUNCT
ejpam-4766	214	7	\dg	\dg	PROPN
ejpam-4766	214	8	is	be	AUX
ejpam-4766	214	9	clique	clique	NOUN
ejpam-4766	214	10	in	in	ADP
ejpam-4766	214	11	g.	g.	PROPN
ejpam-4766	214	12	similarly	similarly	ADV
ejpam-4766	214	13	,	,	PUNCT
ejpam-4766	214	14	v	v	X
ejpam-4766	214	15	(	(	PUNCT
ejpam-4766	214	16	h	h	NOUN
ejpam-4766	214	17	)	)	PUNCT
ejpam-4766	214	18	\dh	\dh	NOUN
ejpam-4766	214	19	is	be	AUX
ejpam-4766	214	20	clique	clique	NOUN
ejpam-4766	214	21	in	in	ADP
ejpam-4766	214	22	h.	h.	PROPN
ejpam-4766	214	23	conversely	conversely	ADV
ejpam-4766	214	24	,	,	PUNCT
ejpam-4766	214	25	suppose	suppose	VERB
ejpam-4766	214	26	d	d	X
ejpam-4766	214	27	=	=	X
ejpam-4766	214	28	dg	dg	PROPN
ejpam-4766	214	29	∪dh	∪dh	NOUN
ejpam-4766	214	30	,	,	PUNCT
ejpam-4766	214	31	where	where	SCONJ
ejpam-4766	214	32	dg	dg	NOUN
ejpam-4766	214	33	and	and	CCONJ
ejpam-4766	214	34	dh	dh	NOUN
ejpam-4766	214	35	are	be	AUX
ejpam-4766	214	36	outer	outer	ADJ
ejpam-4766	214	37	-	-	PUNCT
ejpam-4766	214	38	cliques	clique	NOUN
ejpam-4766	214	39	in	in	ADP
ejpam-4766	214	40	g	g	PROPN
ejpam-4766	214	41	and	and	CCONJ
ejpam-4766	214	42	h	h	NOUN
ejpam-4766	214	43	,	,	PUNCT
ejpam-4766	214	44	respectively	respectively	ADV
ejpam-4766	214	45	.	.	PUNCT
ejpam-4766	215	1	clearly	clearly	ADV
ejpam-4766	215	2	,	,	PUNCT
ejpam-4766	215	3	d	d	PRON
ejpam-4766	215	4	is	be	AUX
ejpam-4766	215	5	a	a	DET
ejpam-4766	215	6	connected	connected	ADJ
ejpam-4766	215	7	dominating	dominating	NOUN
ejpam-4766	215	8	set	set	NOUN
ejpam-4766	215	9	of	of	ADP
ejpam-4766	215	10	g+h	g+h	PROPN
ejpam-4766	215	11	.	.	PUNCT
ejpam-4766	216	1	suppose	suppose	VERB
ejpam-4766	216	2	that	that	SCONJ
ejpam-4766	216	3	v	v	X
ejpam-4766	216	4	(	(	PUNCT
ejpam-4766	216	5	g+h)\d	g+h)\d	PROPN
ejpam-4766	216	6	j.	j.	PROPN
ejpam-4766	216	7	hassan	hassan	PROPN
ejpam-4766	216	8	et	et	PROPN
ejpam-4766	216	9	al	al	PROPN
ejpam-4766	216	10	.	.	PUNCT
ejpam-4766	216	11	/	/	SYM
ejpam-4766	216	12	eur	eur	PROPN
ejpam-4766	216	13	.	.	PUNCT
ejpam-4766	217	1	j.	j.	PROPN
ejpam-4766	217	2	pure	pure	PROPN
ejpam-4766	217	3	appl	appl	PROPN
ejpam-4766	217	4	.	.	PROPN
ejpam-4766	217	5	math	math	PROPN
ejpam-4766	217	6	,	,	PUNCT
ejpam-4766	217	7	16	16	NUM
ejpam-4766	217	8	(	(	PUNCT
ejpam-4766	217	9	3	3	NUM
ejpam-4766	217	10	)	)	PUNCT
ejpam-4766	217	11	(	(	PUNCT
ejpam-4766	217	12	2023	2023	NUM
ejpam-4766	217	13	)	)	PUNCT
ejpam-4766	217	14	,	,	PUNCT
ejpam-4766	217	15	1817	1817	NUM
ejpam-4766	217	16	-	-	SYM
ejpam-4766	217	17	1829	1829	NUM
ejpam-4766	217	18	1825	1825	NUM
ejpam-4766	217	19	is	be	AUX
ejpam-4766	217	20	not	not	PART
ejpam-4766	217	21	a	a	DET
ejpam-4766	217	22	hop	hop	NOUN
ejpam-4766	217	23	independent	independent	ADJ
ejpam-4766	217	24	set	set	NOUN
ejpam-4766	217	25	in	in	ADP
ejpam-4766	217	26	g+h	g+h	PROPN
ejpam-4766	217	27	.	.	PUNCT
ejpam-4766	218	1	then	then	ADV
ejpam-4766	218	2	there	there	PRON
ejpam-4766	218	3	exist	exist	VERB
ejpam-4766	218	4	x	x	NOUN
ejpam-4766	218	5	,	,	PUNCT
ejpam-4766	218	6	y	y	PROPN
ejpam-4766	218	7	∈	∈	PROPN
ejpam-4766	218	8	v	v	PROPN
ejpam-4766	218	9	(	(	PUNCT
ejpam-4766	218	10	g+h	g+h	NOUN
ejpam-4766	218	11	)	)	PUNCT
ejpam-4766	218	12	\d	\d	NOUN
ejpam-4766	218	13	such	such	ADJ
ejpam-4766	218	14	that	that	SCONJ
ejpam-4766	218	15	dg+h(x	dg+h(x	PROPN
ejpam-4766	218	16	,	,	PUNCT
ejpam-4766	218	17	y	y	NOUN
ejpam-4766	218	18	)	)	PUNCT
ejpam-4766	218	19	=	=	SYM
ejpam-4766	219	1	2	2	X
ejpam-4766	219	2	.	.	PUNCT
ejpam-4766	219	3	this	this	PRON
ejpam-4766	219	4	means	mean	VERB
ejpam-4766	219	5	that	that	SCONJ
ejpam-4766	219	6	either	either	CCONJ
ejpam-4766	219	7	x	x	X
ejpam-4766	219	8	,	,	PUNCT
ejpam-4766	219	9	y	y	PROPN
ejpam-4766	219	10	∈	∈	PROPN
ejpam-4766	219	11	v	v	ADP
ejpam-4766	219	12	(	(	PUNCT
ejpam-4766	219	13	g	g	NOUN
ejpam-4766	219	14	)	)	PUNCT
ejpam-4766	219	15	\	\	NOUN
ejpam-4766	219	16	dg	dg	PROPN
ejpam-4766	219	17	or	or	CCONJ
ejpam-4766	219	18	x	x	X
ejpam-4766	219	19	,	,	PUNCT
ejpam-4766	219	20	y	y	PROPN
ejpam-4766	219	21	∈	∈	PROPN
ejpam-4766	219	22	v	v	ADP
ejpam-4766	219	23	(	(	PUNCT
ejpam-4766	219	24	h	h	NOUN
ejpam-4766	219	25	)	)	PUNCT
ejpam-4766	219	26	\	\	PROPN
ejpam-4766	219	27	dh	dh	NOUN
ejpam-4766	219	28	,	,	PUNCT
ejpam-4766	219	29	and	and	CCONJ
ejpam-4766	219	30	this	this	PRON
ejpam-4766	219	31	is	be	AUX
ejpam-4766	219	32	a	a	DET
ejpam-4766	219	33	contradiction	contradiction	NOUN
ejpam-4766	219	34	to	to	ADP
ejpam-4766	219	35	our	our	PRON
ejpam-4766	219	36	assumption	assumption	NOUN
ejpam-4766	219	37	that	that	SCONJ
ejpam-4766	219	38	dg	dg	PROPN
ejpam-4766	219	39	and	and	CCONJ
ejpam-4766	219	40	dh	dh	NOUN
ejpam-4766	219	41	are	be	AUX
ejpam-4766	219	42	outer	outer	ADJ
ejpam-4766	219	43	-	-	PUNCT
ejpam-4766	219	44	cliques	clique	NOUN
ejpam-4766	219	45	in	in	ADP
ejpam-4766	219	46	g	g	PROPN
ejpam-4766	219	47	and	and	CCONJ
ejpam-4766	219	48	h	h	NOUN
ejpam-4766	219	49	,	,	PUNCT
ejpam-4766	219	50	respectively	respectively	ADV
ejpam-4766	219	51	.	.	PUNCT
ejpam-4766	220	1	therefore	therefore	ADV
ejpam-4766	220	2	,	,	PUNCT
ejpam-4766	220	3	v	v	X
ejpam-4766	220	4	(	(	PUNCT
ejpam-4766	220	5	g+h	g+h	NOUN
ejpam-4766	220	6	)	)	PUNCT
ejpam-4766	220	7	\d	\d	NOUN
ejpam-4766	220	8	is	be	AUX
ejpam-4766	220	9	a	a	DET
ejpam-4766	220	10	hop	hop	NOUN
ejpam-4766	220	11	independent	independent	ADJ
ejpam-4766	220	12	set	set	NOUN
ejpam-4766	220	13	in	in	ADP
ejpam-4766	220	14	g+h	g+h	PROPN
ejpam-4766	220	15	.	.	PUNCT
ejpam-4766	221	1	consequently	consequently	ADV
ejpam-4766	221	2	,	,	PUNCT
ejpam-4766	221	3	d	d	PROPN
ejpam-4766	221	4	is	be	AUX
ejpam-4766	221	5	a	a	DET
ejpam-4766	221	6	connected	connected	ADJ
ejpam-4766	221	7	outer	outer	ADJ
ejpam-4766	221	8	-	-	PUNCT
ejpam-4766	221	9	hop	hop	NOUN
ejpam-4766	221	10	independent	independent	ADJ
ejpam-4766	221	11	dominating	dominating	NOUN
ejpam-4766	221	12	in	in	ADP
ejpam-4766	221	13	g+h	g+h	PROPN
ejpam-4766	221	14	.	.	PUNCT
ejpam-4766	222	1	the	the	DET
ejpam-4766	222	2	next	next	ADJ
ejpam-4766	222	3	result	result	NOUN
ejpam-4766	222	4	follows	follow	VERB
ejpam-4766	222	5	from	from	ADP
ejpam-4766	222	6	theorem	theorem	ADJ
ejpam-4766	222	7	4	4	NUM
ejpam-4766	222	8	corollary	corollary	ADJ
ejpam-4766	222	9	2	2	NUM
ejpam-4766	222	10	.	.	PUNCT
ejpam-4766	223	1	let	let	VERB
ejpam-4766	223	2	g	g	NOUN
ejpam-4766	223	3	and	and	CCONJ
ejpam-4766	223	4	h	h	NOUN
ejpam-4766	223	5	be	be	VERB
ejpam-4766	223	6	two	two	NUM
ejpam-4766	223	7	non	non	ADJ
ejpam-4766	223	8	-	-	ADJ
ejpam-4766	223	9	complete	complete	ADJ
ejpam-4766	223	10	graphs	graph	NOUN
ejpam-4766	223	11	.	.	PUNCT
ejpam-4766	224	1	then	then	ADV
ejpam-4766	224	2	γohic	γohic	ADJ
ejpam-4766	224	3	(	(	PUNCT
ejpam-4766	224	4	g+h	g+h	NOUN
ejpam-4766	224	5	)	)	PUNCT
ejpam-4766	224	6	=	=	SYM
ejpam-4766	224	7	ω̃(g	ω̃(g	NOUN
ejpam-4766	224	8	)	)	PUNCT
ejpam-4766	224	9	+	+	NUM
ejpam-4766	224	10	ω̃(h	ω̃(h	NOUN
ejpam-4766	224	11	)	)	PUNCT
ejpam-4766	224	12	.	.	PUNCT
ejpam-4766	225	1	in	in	ADP
ejpam-4766	225	2	particular	particular	ADJ
ejpam-4766	225	3	,	,	PUNCT
ejpam-4766	225	4	we	we	PRON
ejpam-4766	225	5	have	have	VERB
ejpam-4766	225	6	(	(	PUNCT
ejpam-4766	225	7	i	i	NOUN
ejpam-4766	225	8	)	)	PUNCT
ejpam-4766	225	9	γohic	γohic	ADJ
ejpam-4766	225	10	(	(	PUNCT
ejpam-4766	225	11	pn	pn	NOUN
ejpam-4766	225	12	+	+	CCONJ
ejpam-4766	225	13	pm	pm	NOUN
ejpam-4766	225	14	)	)	PUNCT
ejpam-4766	225	15	=	=	SYM
ejpam-4766	225	16	n+m−	n+m−	NOUN
ejpam-4766	225	17	4	4	NUM
ejpam-4766	225	18	for	for	ADP
ejpam-4766	225	19	all	all	DET
ejpam-4766	225	20	n	n	CCONJ
ejpam-4766	225	21	,	,	PUNCT
ejpam-4766	225	22	m	m	VERB
ejpam-4766	225	23	≥	≥	NOUN
ejpam-4766	225	24	3	3	NUM
ejpam-4766	225	25	;	;	PUNCT
ejpam-4766	225	26	(	(	PUNCT
ejpam-4766	225	27	ii	ii	NOUN
ejpam-4766	225	28	)	)	PUNCT
ejpam-4766	225	29	γohic	γohic	ADJ
ejpam-4766	225	30	(	(	PUNCT
ejpam-4766	225	31	cn	cn	PROPN
ejpam-4766	225	32	+	+	NOUN
ejpam-4766	225	33	cm	cm	NOUN
ejpam-4766	225	34	)	)	PUNCT
ejpam-4766	225	35	=	=	PRON
ejpam-4766	225	36	n+m−	n+m−	NOUN
ejpam-4766	225	37	4	4	NUM
ejpam-4766	225	38	for	for	ADP
ejpam-4766	225	39	all	all	DET
ejpam-4766	225	40	n	n	CCONJ
ejpam-4766	225	41	,	,	PUNCT
ejpam-4766	225	42	m	m	VERB
ejpam-4766	225	43	≥	≥	NOUN
ejpam-4766	225	44	4	4	NUM
ejpam-4766	225	45	;	;	PUNCT
ejpam-4766	225	46	and	and	CCONJ
ejpam-4766	225	47	(	(	PUNCT
ejpam-4766	225	48	iii	iii	NOUN
ejpam-4766	225	49	)	)	PUNCT
ejpam-4766	225	50	γohic	γohic	ADJ
ejpam-4766	225	51	(	(	PUNCT
ejpam-4766	225	52	pn	pn	NOUN
ejpam-4766	225	53	+	+	CCONJ
ejpam-4766	225	54	cm	cm	NOUN
ejpam-4766	225	55	)	)	PUNCT
ejpam-4766	226	1	=	=	PRON
ejpam-4766	226	2	n+m−	n+m−	NOUN
ejpam-4766	226	3	4	4	NUM
ejpam-4766	226	4	for	for	ADP
ejpam-4766	226	5	all	all	DET
ejpam-4766	226	6	n	n	CCONJ
ejpam-4766	226	7	,	,	PUNCT
ejpam-4766	226	8	m	m	VERB
ejpam-4766	226	9	≥	≥	NOUN
ejpam-4766	226	10	4	4	NUM
ejpam-4766	226	11	.	.	PUNCT
ejpam-4766	227	1	the	the	DET
ejpam-4766	227	2	following	follow	VERB
ejpam-4766	227	3	concept	concept	NOUN
ejpam-4766	227	4	will	will	AUX
ejpam-4766	227	5	be	be	AUX
ejpam-4766	227	6	used	use	VERB
ejpam-4766	227	7	in	in	ADP
ejpam-4766	227	8	characterizing	characterize	VERB
ejpam-4766	227	9	connected	connected	ADJ
ejpam-4766	227	10	outer	outer	ADJ
ejpam-4766	227	11	-	-	PUNCT
ejpam-4766	227	12	hop	hop	NOUN
ejpam-4766	227	13	independent	independent	ADJ
ejpam-4766	227	14	dominating	dominating	NOUN
ejpam-4766	227	15	sets	set	NOUN
ejpam-4766	227	16	in	in	ADP
ejpam-4766	227	17	the	the	DET
ejpam-4766	227	18	join	join	NOUN
ejpam-4766	227	19	of	of	ADP
ejpam-4766	227	20	complete	complete	ADJ
ejpam-4766	227	21	and	and	CCONJ
ejpam-4766	227	22	non	non	ADJ
ejpam-4766	227	23	-	-	ADJ
ejpam-4766	227	24	complete	complete	ADJ
ejpam-4766	227	25	graphs	graph	NOUN
ejpam-4766	227	26	.	.	PUNCT
ejpam-4766	228	1	definition	definition	NOUN
ejpam-4766	228	2	3	3	NUM
ejpam-4766	228	3	.	.	PUNCT
ejpam-4766	229	1	let	let	VERB
ejpam-4766	229	2	g	g	PRON
ejpam-4766	229	3	be	be	AUX
ejpam-4766	229	4	a	a	DET
ejpam-4766	229	5	connected	connected	ADJ
ejpam-4766	229	6	graph	graph	NOUN
ejpam-4766	229	7	.	.	PUNCT
ejpam-4766	230	1	a	a	DET
ejpam-4766	230	2	connected	connect	VERB
ejpam-4766	230	3	dominating	dominating	NOUN
ejpam-4766	230	4	set	set	NOUN
ejpam-4766	230	5	c	c	PROPN
ejpam-4766	230	6	⊆	⊆	NUM
ejpam-4766	230	7	v	v	NOUN
ejpam-4766	230	8	(	(	PUNCT
ejpam-4766	230	9	g	g	NOUN
ejpam-4766	230	10	)	)	PUNCT
ejpam-4766	230	11	is	be	AUX
ejpam-4766	230	12	called	call	VERB
ejpam-4766	230	13	a	a	DET
ejpam-4766	230	14	connected	connected	ADJ
ejpam-4766	230	15	outer	outer	ADJ
ejpam-4766	230	16	-	-	PUNCT
ejpam-4766	230	17	clique	clique	NOUN
ejpam-4766	230	18	dominating	dominating	NOUN
ejpam-4766	230	19	if	if	SCONJ
ejpam-4766	230	20	v	v	NOUN
ejpam-4766	230	21	(	(	PUNCT
ejpam-4766	230	22	g	g	NOUN
ejpam-4766	230	23	)	)	PUNCT
ejpam-4766	230	24	\c	\c	NOUN
ejpam-4766	230	25	is	be	AUX
ejpam-4766	230	26	a	a	DET
ejpam-4766	230	27	clique	clique	NOUN
ejpam-4766	230	28	set	set	VERB
ejpam-4766	230	29	in	in	ADP
ejpam-4766	230	30	g.	g.	PROPN
ejpam-4766	230	31	the	the	DET
ejpam-4766	230	32	connected	connected	ADJ
ejpam-4766	230	33	outer	outer	ADJ
ejpam-4766	230	34	-	-	PUNCT
ejpam-4766	230	35	clique	clique	NOUN
ejpam-4766	230	36	domination	domination	NOUN
ejpam-4766	230	37	number	number	NOUN
ejpam-4766	230	38	of	of	ADP
ejpam-4766	230	39	g	g	NOUN
ejpam-4766	230	40	,	,	PUNCT
ejpam-4766	230	41	denoted	denote	VERB
ejpam-4766	230	42	by	by	ADP
ejpam-4766	230	43	γocc	γocc	NOUN
ejpam-4766	230	44	(	(	PUNCT
ejpam-4766	230	45	g	g	NOUN
ejpam-4766	230	46	)	)	PUNCT
ejpam-4766	230	47	,	,	PUNCT
ejpam-4766	230	48	is	be	AUX
ejpam-4766	230	49	the	the	DET
ejpam-4766	230	50	minimum	minimum	ADJ
ejpam-4766	230	51	cardinality	cardinality	NOUN
ejpam-4766	230	52	of	of	ADP
ejpam-4766	230	53	a	a	DET
ejpam-4766	230	54	connected	connected	ADJ
ejpam-4766	230	55	outer	outer	ADJ
ejpam-4766	230	56	-	-	PUNCT
ejpam-4766	230	57	clique	clique	NOUN
ejpam-4766	230	58	dominating	dominating	NOUN
ejpam-4766	230	59	set	set	NOUN
ejpam-4766	230	60	of	of	ADP
ejpam-4766	230	61	g.	g.	PROPN
ejpam-4766	230	62	any	any	DET
ejpam-4766	230	63	connected	connected	ADJ
ejpam-4766	230	64	outer	outer	ADJ
ejpam-4766	230	65	-	-	PUNCT
ejpam-4766	230	66	clique	clique	NOUN
ejpam-4766	230	67	dominating	dominating	NOUN
ejpam-4766	230	68	set	set	NOUN
ejpam-4766	230	69	c	c	PROPN
ejpam-4766	230	70	with	with	ADP
ejpam-4766	230	71	cardinality	cardinality	NOUN
ejpam-4766	230	72	equal	equal	ADJ
ejpam-4766	230	73	to	to	ADP
ejpam-4766	230	74	γocc	γocc	NOUN
ejpam-4766	230	75	(	(	PUNCT
ejpam-4766	230	76	g	g	NOUN
ejpam-4766	230	77	)	)	PUNCT
ejpam-4766	230	78	,	,	PUNCT
ejpam-4766	230	79	is	be	AUX
ejpam-4766	230	80	called	call	VERB
ejpam-4766	230	81	a	a	DET
ejpam-4766	230	82	γocc	γocc	NOUN
ejpam-4766	230	83	-set	-set	PUNCT
ejpam-4766	230	84	of	of	ADP
ejpam-4766	230	85	g.	g.	PROPN
ejpam-4766	230	86	theorem	theorem	VERB
ejpam-4766	230	87	5	5	NUM
ejpam-4766	230	88	.	.	PUNCT
ejpam-4766	231	1	let	let	VERB
ejpam-4766	231	2	g	g	PRON
ejpam-4766	231	3	be	be	AUX
ejpam-4766	231	4	a	a	DET
ejpam-4766	231	5	complete	complete	ADJ
ejpam-4766	231	6	graph	graph	NOUN
ejpam-4766	231	7	and	and	CCONJ
ejpam-4766	231	8	h	h	NOUN
ejpam-4766	231	9	be	be	AUX
ejpam-4766	231	10	any	any	DET
ejpam-4766	231	11	non	non	ADJ
ejpam-4766	231	12	-	-	ADJ
ejpam-4766	231	13	complete	complete	ADJ
ejpam-4766	231	14	connected	connected	ADJ
ejpam-4766	231	15	graph	graph	NOUN
ejpam-4766	231	16	.	.	PUNCT
ejpam-4766	232	1	then	then	ADV
ejpam-4766	232	2	d	d	PROPN
ejpam-4766	232	3	⊆	⊆	NUM
ejpam-4766	232	4	v	v	X
ejpam-4766	232	5	(	(	PUNCT
ejpam-4766	232	6	g	g	PROPN
ejpam-4766	232	7	+	+	NOUN
ejpam-4766	232	8	h	h	NOUN
ejpam-4766	232	9	)	)	PUNCT
ejpam-4766	232	10	is	be	AUX
ejpam-4766	232	11	a	a	DET
ejpam-4766	232	12	connected	connected	ADJ
ejpam-4766	232	13	outer	outer	ADJ
ejpam-4766	232	14	-	-	PUNCT
ejpam-4766	232	15	hop	hop	NOUN
ejpam-4766	232	16	independent	independent	ADJ
ejpam-4766	232	17	dominating	dominating	NOUN
ejpam-4766	232	18	set	set	VERB
ejpam-4766	232	19	in	in	ADP
ejpam-4766	232	20	g	g	PROPN
ejpam-4766	233	1	+	+	NOUN
ejpam-4766	233	2	h	h	NOUN
ejpam-4766	233	3	if	if	SCONJ
ejpam-4766	233	4	and	and	CCONJ
ejpam-4766	233	5	only	only	ADV
ejpam-4766	233	6	if	if	SCONJ
ejpam-4766	233	7	d	d	PROPN
ejpam-4766	233	8	=	=	X
ejpam-4766	233	9	dg	dg	X
ejpam-4766	233	10	∪dh	∪dh	NOUN
ejpam-4766	233	11	and	and	CCONJ
ejpam-4766	233	12	satisfies	satisfy	VERB
ejpam-4766	233	13	one	one	NUM
ejpam-4766	233	14	of	of	ADP
ejpam-4766	233	15	the	the	DET
ejpam-4766	233	16	following	following	ADJ
ejpam-4766	233	17	conditions	condition	NOUN
ejpam-4766	233	18	:	:	PUNCT
ejpam-4766	233	19	(	(	PUNCT
ejpam-4766	233	20	i	i	NOUN
ejpam-4766	233	21	)	)	PUNCT
ejpam-4766	233	22	if	if	SCONJ
ejpam-4766	233	23	dg	dg	NOUN
ejpam-4766	233	24	=	=	SYM
ejpam-4766	233	25	∅	∅	NOUN
ejpam-4766	233	26	,	,	PUNCT
ejpam-4766	233	27	then	then	ADV
ejpam-4766	233	28	dh	dh	PROPN
ejpam-4766	233	29	is	be	AUX
ejpam-4766	233	30	a	a	DET
ejpam-4766	233	31	connected	connected	ADJ
ejpam-4766	233	32	outer	outer	ADJ
ejpam-4766	233	33	-	-	PUNCT
ejpam-4766	233	34	clique	clique	NOUN
ejpam-4766	233	35	dominating	dominating	NOUN
ejpam-4766	233	36	set	set	NOUN
ejpam-4766	233	37	in	in	ADP
ejpam-4766	233	38	h.	h.	PROPN
ejpam-4766	233	39	(	(	PUNCT
ejpam-4766	233	40	ii	ii	PROPN
ejpam-4766	233	41	)	)	PUNCT
ejpam-4766	233	42	if	if	SCONJ
ejpam-4766	233	43	dg	dg	PROPN
ejpam-4766	233	44	̸=	̸=	PROPN
ejpam-4766	233	45	∅	∅	NOUN
ejpam-4766	233	46	,	,	PUNCT
ejpam-4766	233	47	then	then	ADV
ejpam-4766	233	48	dh	dh	NOUN
ejpam-4766	233	49	is	be	AUX
ejpam-4766	233	50	an	an	DET
ejpam-4766	233	51	outer	outer	ADJ
ejpam-4766	233	52	-	-	PUNCT
ejpam-4766	233	53	clique	clique	NOUN
ejpam-4766	233	54	set	set	NOUN
ejpam-4766	233	55	in	in	ADP
ejpam-4766	233	56	h.	h.	PROPN
ejpam-4766	233	57	proof	proof	NOUN
ejpam-4766	233	58	.	.	PUNCT
ejpam-4766	234	1	suppose	suppose	VERB
ejpam-4766	234	2	s	s	VERB
ejpam-4766	234	3	⊆	⊆	NUM
ejpam-4766	234	4	v	v	NOUN
ejpam-4766	234	5	(	(	PUNCT
ejpam-4766	234	6	g	g	PROPN
ejpam-4766	234	7	+	+	NOUN
ejpam-4766	234	8	h	h	NOUN
ejpam-4766	234	9	)	)	PUNCT
ejpam-4766	234	10	is	be	AUX
ejpam-4766	234	11	a	a	DET
ejpam-4766	234	12	connected	connected	ADJ
ejpam-4766	234	13	outer	outer	ADJ
ejpam-4766	234	14	-	-	PUNCT
ejpam-4766	234	15	hop	hop	NOUN
ejpam-4766	234	16	independent	independent	ADJ
ejpam-4766	234	17	dominating	dominating	NOUN
ejpam-4766	234	18	in	in	ADP
ejpam-4766	234	19	g	g	PROPN
ejpam-4766	234	20	+	+	PROPN
ejpam-4766	234	21	h.	h.	PROPN
ejpam-4766	234	22	then	then	ADV
ejpam-4766	234	23	v	v	VERB
ejpam-4766	234	24	(	(	PUNCT
ejpam-4766	234	25	g	g	PROPN
ejpam-4766	234	26	+	+	NOUN
ejpam-4766	234	27	h	h	NOUN
ejpam-4766	234	28	)	)	PUNCT
ejpam-4766	234	29	\	\	PROPN
ejpam-4766	235	1	s	s	PART
ejpam-4766	235	2	is	be	AUX
ejpam-4766	235	3	a	a	DET
ejpam-4766	235	4	hop	hop	NOUN
ejpam-4766	235	5	independent	independent	ADJ
ejpam-4766	235	6	set	set	NOUN
ejpam-4766	235	7	in	in	ADP
ejpam-4766	235	8	g	g	PROPN
ejpam-4766	235	9	+	+	PROPN
ejpam-4766	235	10	h.	h.	PROPN
ejpam-4766	235	11	let	let	VERB
ejpam-4766	235	12	dg	dg	NOUN
ejpam-4766	235	13	=	=	PRON
ejpam-4766	235	14	∅.	∅.	VERB
ejpam-4766	235	15	suppose	suppose	VERB
ejpam-4766	235	16	on	on	ADP
ejpam-4766	235	17	the	the	DET
ejpam-4766	235	18	contrary	contrary	NOUN
ejpam-4766	235	19	that	that	SCONJ
ejpam-4766	235	20	dh	dh	PROPN
ejpam-4766	235	21	is	be	AUX
ejpam-4766	235	22	not	not	PART
ejpam-4766	235	23	a	a	DET
ejpam-4766	235	24	connected	connected	ADJ
ejpam-4766	235	25	outer	outer	ADJ
ejpam-4766	235	26	-	-	PUNCT
ejpam-4766	235	27	clique	clique	NOUN
ejpam-4766	235	28	dominating	dominating	NOUN
ejpam-4766	235	29	set	set	NOUN
ejpam-4766	235	30	in	in	ADP
ejpam-4766	235	31	h.	h.	PROPN
ejpam-4766	235	32	then	then	ADV
ejpam-4766	235	33	dh	dh	PROPN
ejpam-4766	235	34	is	be	AUX
ejpam-4766	235	35	either	either	CCONJ
ejpam-4766	235	36	not	not	PART
ejpam-4766	235	37	a	a	DET
ejpam-4766	235	38	connected	connect	VERB
ejpam-4766	235	39	,	,	PUNCT
ejpam-4766	235	40	not	not	PART
ejpam-4766	235	41	a	a	DET
ejpam-4766	235	42	dominating	dominating	NOUN
ejpam-4766	235	43	or	or	CCONJ
ejpam-4766	235	44	v	v	NOUN
ejpam-4766	235	45	(	(	PUNCT
ejpam-4766	235	46	h	h	NOUN
ejpam-4766	235	47	)	)	PUNCT
ejpam-4766	235	48	\	\	NOUN
ejpam-4766	235	49	dh	dh	NOUN
ejpam-4766	235	50	not	not	PART
ejpam-4766	235	51	a	a	DET
ejpam-4766	235	52	clique	clique	NOUN
ejpam-4766	235	53	sets	set	NOUN
ejpam-4766	235	54	in	in	ADP
ejpam-4766	235	55	h	h	NOUN
ejpam-4766	235	56	,	,	PUNCT
ejpam-4766	235	57	respectively	respectively	ADV
ejpam-4766	235	58	.	.	PUNCT
ejpam-4766	236	1	assume	assume	VERB
ejpam-4766	236	2	first	first	ADV
ejpam-4766	236	3	that	that	SCONJ
ejpam-4766	236	4	dh	dh	PROPN
ejpam-4766	236	5	is	be	AUX
ejpam-4766	236	6	not	not	PART
ejpam-4766	236	7	a	a	DET
ejpam-4766	236	8	dominating	dominating	NOUN
ejpam-4766	236	9	set	set	NOUN
ejpam-4766	236	10	in	in	ADP
ejpam-4766	236	11	h.	h.	PROPN
ejpam-4766	236	12	then	then	ADV
ejpam-4766	236	13	there	there	PRON
ejpam-4766	236	14	exists	exist	VERB
ejpam-4766	236	15	a	a	DET
ejpam-4766	236	16	∈	∈	PROPN
ejpam-4766	236	17	v	v	NOUN
ejpam-4766	236	18	(	(	PUNCT
ejpam-4766	236	19	h	h	NOUN
ejpam-4766	236	20	)	)	PUNCT
ejpam-4766	236	21	\dh	\dh	NOUN
ejpam-4766	236	22	such	such	ADJ
ejpam-4766	236	23	that	that	SCONJ
ejpam-4766	236	24	a	a	PRON
ejpam-4766	236	25	/∈	/∈	NOUN
ejpam-4766	236	26	nh	nh	PROPN
ejpam-4766	237	1	[	[	X
ejpam-4766	237	2	dh	dh	X
ejpam-4766	237	3	]	]	X
ejpam-4766	237	4	.	.	PUNCT
ejpam-4766	238	1	since	since	SCONJ
ejpam-4766	238	2	dg	dg	NOUN
ejpam-4766	238	3	=	=	SYM
ejpam-4766	238	4	∅	∅	NOUN
ejpam-4766	238	5	,	,	PUNCT
ejpam-4766	238	6	it	it	PRON
ejpam-4766	238	7	follows	follow	VERB
ejpam-4766	238	8	that	that	SCONJ
ejpam-4766	238	9	a	a	PRON
ejpam-4766	238	10	/∈	/∈	INTJ
ejpam-4766	239	1	ng+h	ng+h	PROPN
ejpam-4766	240	1	[	[	X
ejpam-4766	240	2	d	d	X
ejpam-4766	240	3	]	]	X
ejpam-4766	240	4	,	,	PUNCT
ejpam-4766	240	5	a	a	DET
ejpam-4766	240	6	contradiction	contradiction	NOUN
ejpam-4766	240	7	.	.	PUNCT
ejpam-4766	241	1	therefore	therefore	ADV
ejpam-4766	241	2	,	,	PUNCT
ejpam-4766	241	3	dh	dh	NOUN
ejpam-4766	241	4	is	be	AUX
ejpam-4766	241	5	a	a	DET
ejpam-4766	241	6	dominating	dominating	NOUN
ejpam-4766	241	7	set	set	NOUN
ejpam-4766	241	8	in	in	ADP
ejpam-4766	241	9	h.	h.	PROPN
ejpam-4766	241	10	similarly	similarly	ADV
ejpam-4766	241	11	,	,	PUNCT
ejpam-4766	241	12	a	a	DET
ejpam-4766	241	13	contradiction	contradiction	NOUN
ejpam-4766	241	14	follows	follow	VERB
ejpam-4766	241	15	if	if	SCONJ
ejpam-4766	241	16	dh	dh	NOUN
ejpam-4766	241	17	is	be	AUX
ejpam-4766	241	18	not	not	PART
ejpam-4766	241	19	a	a	DET
ejpam-4766	241	20	connected	connected	ADJ
ejpam-4766	241	21	or	or	CCONJ
ejpam-4766	241	22	v	v	NOUN
ejpam-4766	241	23	(	(	PUNCT
ejpam-4766	241	24	h)\dh	h)\dh	PROPN
ejpam-4766	241	25	is	be	AUX
ejpam-4766	241	26	not	not	PART
ejpam-4766	241	27	a	a	DET
ejpam-4766	241	28	clique	clique	NOUN
ejpam-4766	241	29	in	in	ADP
ejpam-4766	241	30	h.	h.	PROPN
ejpam-4766	241	31	hence	hence	ADV
ejpam-4766	241	32	,	,	PUNCT
ejpam-4766	241	33	(	(	PUNCT
ejpam-4766	241	34	i	i	NOUN
ejpam-4766	241	35	)	)	PUNCT
ejpam-4766	241	36	holds	hold	VERB
ejpam-4766	241	37	.	.	PUNCT
ejpam-4766	242	1	next	next	ADV
ejpam-4766	242	2	,	,	PUNCT
ejpam-4766	242	3	suppose	suppose	VERB
ejpam-4766	242	4	that	that	SCONJ
ejpam-4766	242	5	dg	dg	VERB
ejpam-4766	242	6	̸=	̸=	PROPN
ejpam-4766	242	7	∅	∅	NOUN
ejpam-4766	242	8	and	and	CCONJ
ejpam-4766	242	9	suppose	suppose	VERB
ejpam-4766	242	10	that	that	SCONJ
ejpam-4766	242	11	dh	dh	PROPN
ejpam-4766	242	12	is	be	AUX
ejpam-4766	242	13	not	not	PART
ejpam-4766	242	14	an	an	DET
ejpam-4766	242	15	outer	outer	ADJ
ejpam-4766	242	16	-	-	PUNCT
ejpam-4766	242	17	clique	clique	NOUN
ejpam-4766	242	18	set	set	NOUN
ejpam-4766	242	19	in	in	ADP
ejpam-4766	242	20	h.	h.	PROPN
ejpam-4766	242	21	then	then	ADV
ejpam-4766	242	22	there	there	PRON
ejpam-4766	242	23	exist	exist	VERB
ejpam-4766	242	24	j.	j.	PROPN
ejpam-4766	242	25	hassan	hassan	PROPN
ejpam-4766	242	26	et	et	PROPN
ejpam-4766	242	27	al	al	PROPN
ejpam-4766	242	28	.	.	PUNCT
ejpam-4766	242	29	/	/	SYM
ejpam-4766	242	30	eur	eur	PROPN
ejpam-4766	242	31	.	.	PUNCT
ejpam-4766	243	1	j.	j.	PROPN
ejpam-4766	243	2	pure	pure	PROPN
ejpam-4766	243	3	appl	appl	PROPN
ejpam-4766	243	4	.	.	PROPN
ejpam-4766	243	5	math	math	PROPN
ejpam-4766	243	6	,	,	PUNCT
ejpam-4766	243	7	16	16	NUM
ejpam-4766	243	8	(	(	PUNCT
ejpam-4766	243	9	3	3	NUM
ejpam-4766	243	10	)	)	PUNCT
ejpam-4766	243	11	(	(	PUNCT
ejpam-4766	243	12	2023	2023	NUM
ejpam-4766	243	13	)	)	PUNCT
ejpam-4766	243	14	,	,	PUNCT
ejpam-4766	243	15	1817	1817	NUM
ejpam-4766	243	16	-	-	SYM
ejpam-4766	243	17	1829	1829	NUM
ejpam-4766	243	18	1826	1826	NUM
ejpam-4766	243	19	x	x	NOUN
ejpam-4766	243	20	,	,	PUNCT
ejpam-4766	243	21	y	y	PROPN
ejpam-4766	243	22	∈	∈	PROPN
ejpam-4766	243	23	v	v	ADP
ejpam-4766	243	24	(	(	PUNCT
ejpam-4766	243	25	h	h	NOUN
ejpam-4766	243	26	)	)	PUNCT
ejpam-4766	243	27	\dh	\dh	NOUN
ejpam-4766	243	28	⊆	⊆	NUM
ejpam-4766	243	29	v	v	NOUN
ejpam-4766	243	30	(	(	PUNCT
ejpam-4766	243	31	g+h	g+h	NOUN
ejpam-4766	243	32	)	)	PUNCT
ejpam-4766	243	33	\d	\d	NOUN
ejpam-4766	244	1	such	such	ADJ
ejpam-4766	244	2	that	that	SCONJ
ejpam-4766	244	3	dh(x	dh(x	NOUN
ejpam-4766	244	4	,	,	PUNCT
ejpam-4766	244	5	y	y	NOUN
ejpam-4766	244	6	)	)	PUNCT
ejpam-4766	244	7	=	=	SYM
ejpam-4766	244	8	dg+h(x	dg+h(x	PROPN
ejpam-4766	244	9	,	,	PUNCT
ejpam-4766	244	10	y	y	NOUN
ejpam-4766	244	11	)	)	PUNCT
ejpam-4766	244	12	=	=	SYM
ejpam-4766	244	13	2	2	NUM
ejpam-4766	244	14	,	,	PUNCT
ejpam-4766	244	15	a	a	DET
ejpam-4766	244	16	contradiction	contradiction	NOUN
ejpam-4766	244	17	.	.	PUNCT
ejpam-4766	245	1	hence	hence	ADV
ejpam-4766	245	2	,	,	PUNCT
ejpam-4766	245	3	dh	dh	PROPN
ejpam-4766	245	4	must	must	AUX
ejpam-4766	245	5	be	be	AUX
ejpam-4766	245	6	an	an	DET
ejpam-4766	245	7	outer	outer	ADJ
ejpam-4766	245	8	-	-	PUNCT
ejpam-4766	245	9	clique	clique	NOUN
ejpam-4766	245	10	set	set	NOUN
ejpam-4766	245	11	in	in	ADP
ejpam-4766	245	12	h	h	NOUN
ejpam-4766	245	13	showing	show	VERB
ejpam-4766	245	14	that	that	SCONJ
ejpam-4766	245	15	(	(	PUNCT
ejpam-4766	245	16	ii	ii	NOUN
ejpam-4766	245	17	)	)	PUNCT
ejpam-4766	245	18	holds	hold	VERB
ejpam-4766	245	19	.	.	PUNCT
ejpam-4766	246	1	for	for	ADP
ejpam-4766	246	2	the	the	DET
ejpam-4766	246	3	converse	converse	NOUN
ejpam-4766	246	4	,	,	PUNCT
ejpam-4766	246	5	suppose	suppose	VERB
ejpam-4766	246	6	(	(	PUNCT
ejpam-4766	246	7	i	i	NOUN
ejpam-4766	246	8	)	)	PUNCT
ejpam-4766	246	9	holds	hold	VERB
ejpam-4766	246	10	.	.	PUNCT
ejpam-4766	247	1	since	since	SCONJ
ejpam-4766	247	2	g	g	PROPN
ejpam-4766	247	3	is	be	AUX
ejpam-4766	247	4	complete	complete	ADJ
ejpam-4766	247	5	,	,	PUNCT
ejpam-4766	247	6	it	it	PRON
ejpam-4766	247	7	follows	follow	VERB
ejpam-4766	247	8	that	that	SCONJ
ejpam-4766	247	9	d	d	NOUN
ejpam-4766	247	10	is	be	AUX
ejpam-4766	247	11	an	an	DET
ejpam-4766	247	12	outerhop	outerhop	ADJ
ejpam-4766	247	13	independent	independent	ADJ
ejpam-4766	247	14	set	set	NOUN
ejpam-4766	247	15	in	in	ADP
ejpam-4766	247	16	g+h	g+h	PROPN
ejpam-4766	247	17	.	.	PUNCT
ejpam-4766	248	1	clearly	clearly	ADV
ejpam-4766	248	2	,	,	PUNCT
ejpam-4766	248	3	d	d	PRON
ejpam-4766	248	4	is	be	AUX
ejpam-4766	248	5	a	a	DET
ejpam-4766	248	6	connected	connect	VERB
ejpam-4766	248	7	dominating	dominating	NOUN
ejpam-4766	248	8	set	set	VERB
ejpam-4766	248	9	in	in	ADP
ejpam-4766	248	10	g+h	g+h	PROPN
ejpam-4766	248	11	.	.	PUNCT
ejpam-4766	249	1	hence	hence	ADV
ejpam-4766	249	2	,	,	PUNCT
ejpam-4766	249	3	d	d	PROPN
ejpam-4766	249	4	is	be	AUX
ejpam-4766	249	5	a	a	DET
ejpam-4766	249	6	connected	connected	ADJ
ejpam-4766	249	7	outer	outer	ADJ
ejpam-4766	249	8	-	-	PUNCT
ejpam-4766	249	9	hop	hop	NOUN
ejpam-4766	249	10	independent	independent	ADJ
ejpam-4766	249	11	dominating	dominating	NOUN
ejpam-4766	249	12	set	set	VERB
ejpam-4766	249	13	in	in	ADP
ejpam-4766	249	14	g+h	g+h	PROPN
ejpam-4766	249	15	.	.	PUNCT
ejpam-4766	250	1	similarly	similarly	ADV
ejpam-4766	250	2	,	,	PUNCT
ejpam-4766	250	3	if	if	SCONJ
ejpam-4766	250	4	(	(	PUNCT
ejpam-4766	250	5	ii	ii	NOUN
ejpam-4766	250	6	)	)	PUNCT
ejpam-4766	250	7	holds	hold	VERB
ejpam-4766	250	8	,	,	PUNCT
ejpam-4766	250	9	then	then	ADV
ejpam-4766	250	10	d	d	PROPN
ejpam-4766	250	11	is	be	AUX
ejpam-4766	250	12	a	a	DET
ejpam-4766	250	13	connected	connected	ADJ
ejpam-4766	250	14	outer	outer	ADJ
ejpam-4766	250	15	-	-	PUNCT
ejpam-4766	250	16	hop	hop	NOUN
ejpam-4766	250	17	independent	independent	ADJ
ejpam-4766	250	18	dominating	dominating	NOUN
ejpam-4766	250	19	set	set	VERB
ejpam-4766	250	20	in	in	ADP
ejpam-4766	250	21	g+h	g+h	PROPN
ejpam-4766	250	22	.	.	PUNCT
ejpam-4766	251	1	the	the	DET
ejpam-4766	251	2	next	next	ADJ
ejpam-4766	251	3	result	result	NOUN
ejpam-4766	251	4	follows	follow	VERB
ejpam-4766	251	5	from	from	ADP
ejpam-4766	251	6	theorem	theorem	ADJ
ejpam-4766	251	7	5	5	NUM
ejpam-4766	251	8	.	.	PUNCT
ejpam-4766	251	9	corollary	corollary	ADJ
ejpam-4766	251	10	3	3	X
ejpam-4766	251	11	.	.	PUNCT
ejpam-4766	252	1	let	let	VERB
ejpam-4766	252	2	g	g	PRON
ejpam-4766	252	3	be	be	AUX
ejpam-4766	252	4	a	a	DET
ejpam-4766	252	5	complete	complete	ADJ
ejpam-4766	252	6	graph	graph	NOUN
ejpam-4766	252	7	and	and	CCONJ
ejpam-4766	252	8	h	h	NOUN
ejpam-4766	252	9	be	be	AUX
ejpam-4766	252	10	any	any	DET
ejpam-4766	252	11	non	non	ADJ
ejpam-4766	252	12	-	-	ADJ
ejpam-4766	252	13	complete	complete	ADJ
ejpam-4766	252	14	connected	connected	ADJ
ejpam-4766	252	15	graph	graph	NOUN
ejpam-4766	252	16	.	.	PUNCT
ejpam-4766	253	1	then	then	ADV
ejpam-4766	253	2	γohic	γohic	ADJ
ejpam-4766	253	3	(	(	PUNCT
ejpam-4766	253	4	g+h	g+h	NOUN
ejpam-4766	253	5	)	)	PUNCT
ejpam-4766	253	6	=	=	NOUN
ejpam-4766	253	7	γocc	γocc	NOUN
ejpam-4766	253	8	(	(	PUNCT
ejpam-4766	253	9	h	h	NOUN
ejpam-4766	253	10	)	)	PUNCT
ejpam-4766	253	11	.	.	PUNCT
ejpam-4766	254	1	in	in	ADP
ejpam-4766	254	2	particular	particular	ADJ
ejpam-4766	254	3	,	,	PUNCT
ejpam-4766	254	4	we	we	PRON
ejpam-4766	254	5	have	have	VERB
ejpam-4766	254	6	(	(	PUNCT
ejpam-4766	254	7	i	i	NOUN
ejpam-4766	254	8	)	)	PUNCT
ejpam-4766	254	9	γohic	γohic	ADJ
ejpam-4766	254	10	(	(	PUNCT
ejpam-4766	254	11	wn	wn	PROPN
ejpam-4766	254	12	)	)	PUNCT
ejpam-4766	254	13	=	=	SYM
ejpam-4766	255	1	γohic	γohic	ADJ
ejpam-4766	255	2	(	(	PUNCT
ejpam-4766	255	3	k1	k1	NOUN
ejpam-4766	255	4	+	+	CCONJ
ejpam-4766	255	5	cn	cn	ADJ
ejpam-4766	255	6	)	)	PUNCT
ejpam-4766	255	7	=	=	PUNCT
ejpam-4766	255	8	n−	n−	NOUN
ejpam-4766	255	9	2	2	NUM
ejpam-4766	255	10	for	for	ADP
ejpam-4766	255	11	all	all	DET
ejpam-4766	255	12	n	n	PRON
ejpam-4766	255	13	≥	≥	NOUN
ejpam-4766	255	14	4	4	NUM
ejpam-4766	255	15	;	;	PUNCT
ejpam-4766	255	16	(	(	PUNCT
ejpam-4766	255	17	ii	ii	NOUN
ejpam-4766	255	18	)	)	PUNCT
ejpam-4766	255	19	γohic	γohic	ADJ
ejpam-4766	255	20	(	(	PUNCT
ejpam-4766	255	21	fn	fn	NOUN
ejpam-4766	255	22	)	)	PUNCT
ejpam-4766	255	23	=	=	SYM
ejpam-4766	255	24	γohic	γohic	ADJ
ejpam-4766	255	25	(	(	PUNCT
ejpam-4766	255	26	k1	k1	NOUN
ejpam-4766	255	27	+	+	CCONJ
ejpam-4766	255	28	pn	pn	NOUN
ejpam-4766	255	29	)	)	PUNCT
ejpam-4766	255	30	=	=	PUNCT
ejpam-4766	255	31	n−	n−	NOUN
ejpam-4766	255	32	1	1	NUM
ejpam-4766	255	33	for	for	ADP
ejpam-4766	255	34	all	all	DET
ejpam-4766	255	35	n	n	PRON
ejpam-4766	255	36	≥	≥	NOUN
ejpam-4766	255	37	3	3	NUM
ejpam-4766	255	38	;	;	PUNCT
ejpam-4766	255	39	(	(	PUNCT
ejpam-4766	255	40	iii	iii	X
ejpam-4766	255	41	)	)	PUNCT
ejpam-4766	255	42	γohic	γohic	ADJ
ejpam-4766	255	43	(	(	PUNCT
ejpam-4766	255	44	kn	kn	NOUN
ejpam-4766	255	45	+	+	PROPN
ejpam-4766	255	46	cm	cm	NOUN
ejpam-4766	255	47	)	)	PUNCT
ejpam-4766	255	48	=	=	SYM
ejpam-4766	256	1	m−	m−	PROPN
ejpam-4766	256	2	2	2	NUM
ejpam-4766	256	3	for	for	ADP
ejpam-4766	256	4	all	all	DET
ejpam-4766	256	5	n	n	PRON
ejpam-4766	256	6	≥	≥	NOUN
ejpam-4766	256	7	2,m	2,m	NUM
ejpam-4766	256	8	≥	≥	NOUN
ejpam-4766	256	9	4	4	NUM
ejpam-4766	256	10	;	;	PUNCT
ejpam-4766	256	11	and	and	CCONJ
ejpam-4766	256	12	(	(	PUNCT
ejpam-4766	256	13	iv	iv	X
ejpam-4766	256	14	)	)	PUNCT
ejpam-4766	256	15	γohic	γohic	ADJ
ejpam-4766	256	16	(	(	PUNCT
ejpam-4766	256	17	kn	kn	NOUN
ejpam-4766	256	18	+	+	CCONJ
ejpam-4766	256	19	pm	pm	NOUN
ejpam-4766	256	20	)	)	PUNCT
ejpam-4766	256	21	=	=	SYM
ejpam-4766	256	22	m−	m−	PROPN
ejpam-4766	256	23	1	1	NUM
ejpam-4766	256	24	for	for	ADP
ejpam-4766	256	25	all	all	DET
ejpam-4766	256	26	n	n	PRON
ejpam-4766	256	27	≥	≥	NOUN
ejpam-4766	256	28	2,m	2,m	NUM
ejpam-4766	256	29	≥	≥	NOUN
ejpam-4766	256	30	3	3	NUM
ejpam-4766	256	31	.	.	PUNCT
ejpam-4766	256	32	theorem	theorem	NOUN
ejpam-4766	256	33	6	6	NUM
ejpam-4766	256	34	.	.	PUNCT
ejpam-4766	257	1	let	let	VERB
ejpam-4766	257	2	g	g	PRON
ejpam-4766	257	3	be	be	AUX
ejpam-4766	257	4	a	a	DET
ejpam-4766	257	5	non	non	ADJ
ejpam-4766	257	6	-	-	ADJ
ejpam-4766	257	7	trivial	trivial	ADJ
ejpam-4766	257	8	connected	connected	ADJ
ejpam-4766	257	9	graph	graph	NOUN
ejpam-4766	257	10	and	and	CCONJ
ejpam-4766	257	11	h	h	NOUN
ejpam-4766	257	12	be	be	AUX
ejpam-4766	257	13	any	any	DET
ejpam-4766	257	14	non	non	ADJ
ejpam-4766	257	15	-	-	ADJ
ejpam-4766	257	16	complete	complete	ADJ
ejpam-4766	257	17	graph	graph	NOUN
ejpam-4766	257	18	.	.	PUNCT
ejpam-4766	258	1	a	a	DET
ejpam-4766	258	2	set	set	NOUN
ejpam-4766	258	3	d	d	NOUN
ejpam-4766	258	4	⊆	⊆	NUM
ejpam-4766	258	5	v	v	NOUN
ejpam-4766	258	6	(	(	PUNCT
ejpam-4766	258	7	g	g	PROPN
ejpam-4766	258	8	◦	◦	NOUN
ejpam-4766	258	9	h	h	NOUN
ejpam-4766	258	10	)	)	PUNCT
ejpam-4766	258	11	is	be	AUX
ejpam-4766	258	12	a	a	DET
ejpam-4766	258	13	connected	connected	ADJ
ejpam-4766	258	14	outer	outer	ADJ
ejpam-4766	258	15	-	-	PUNCT
ejpam-4766	258	16	hop	hop	NOUN
ejpam-4766	258	17	independent	independent	ADJ
ejpam-4766	258	18	dominating	dominating	NOUN
ejpam-4766	258	19	set	set	VERB
ejpam-4766	258	20	in	in	ADP
ejpam-4766	258	21	g	g	PROPN
ejpam-4766	258	22	◦	◦	NOUN
ejpam-4766	258	23	h	h	NOUN
ejpam-4766	258	24	if	if	SCONJ
ejpam-4766	259	1	and	and	CCONJ
ejpam-4766	259	2	only	only	ADV
ejpam-4766	259	3	if	if	SCONJ
ejpam-4766	259	4	d	d	PROPN
ejpam-4766	259	5	=	=	SYM
ejpam-4766	259	6	v	v	X
ejpam-4766	259	7	(	(	PUNCT
ejpam-4766	259	8	g	g	NOUN
ejpam-4766	259	9	)	)	PUNCT
ejpam-4766	259	10	∪	∪	NOUN
ejpam-4766	259	11	(	(	PUNCT
ejpam-4766	259	12	⋃	⋃	ADJ
ejpam-4766	259	13	v∈v	v∈v	NOUN
ejpam-4766	259	14	(	(	PUNCT
ejpam-4766	259	15	g)dv	g)dv	PROPN
ejpam-4766	259	16	)	)	PUNCT
ejpam-4766	259	17	,	,	PUNCT
ejpam-4766	259	18	where	where	SCONJ
ejpam-4766	259	19	dv	dv	PROPN
ejpam-4766	259	20	⊆	⊆	NUM
ejpam-4766	259	21	v	v	PROPN
ejpam-4766	259	22	(	(	PUNCT
ejpam-4766	259	23	hv	hv	NOUN
ejpam-4766	259	24	)	)	PUNCT
ejpam-4766	259	25	and	and	CCONJ
ejpam-4766	259	26	v	v	NOUN
ejpam-4766	259	27	(	(	PUNCT
ejpam-4766	259	28	hv	hv	PROPN
ejpam-4766	259	29	)	)	PUNCT
ejpam-4766	259	30	\	\	PROPN
ejpam-4766	260	1	dv	dv	PROPN
ejpam-4766	260	2	is	be	AUX
ejpam-4766	260	3	clique	clique	ADJ
ejpam-4766	260	4	in	in	ADP
ejpam-4766	260	5	hv	hv	PROPN
ejpam-4766	260	6	for	for	ADP
ejpam-4766	260	7	each	each	DET
ejpam-4766	260	8	v	v	NUM
ejpam-4766	260	9	∈	∈	PROPN
ejpam-4766	260	10	v	v	NOUN
ejpam-4766	260	11	(	(	PUNCT
ejpam-4766	260	12	g	g	NOUN
ejpam-4766	260	13	)	)	PUNCT
ejpam-4766	260	14	.	.	PUNCT
ejpam-4766	261	1	proof	proof	NOUN
ejpam-4766	261	2	.	.	PUNCT
ejpam-4766	262	1	assume	assume	VERB
ejpam-4766	262	2	that	that	SCONJ
ejpam-4766	262	3	d	d	NOUN
ejpam-4766	262	4	is	be	AUX
ejpam-4766	262	5	a	a	DET
ejpam-4766	262	6	connected	connected	ADJ
ejpam-4766	262	7	outer	outer	ADJ
ejpam-4766	262	8	-	-	PUNCT
ejpam-4766	262	9	hop	hop	NOUN
ejpam-4766	262	10	independent	independent	ADJ
ejpam-4766	262	11	dominating	dominating	NOUN
ejpam-4766	262	12	set	set	VERB
ejpam-4766	262	13	in	in	ADP
ejpam-4766	262	14	g	g	PROPN
ejpam-4766	262	15	◦	◦	NOUN
ejpam-4766	262	16	h	h	NOUN
ejpam-4766	262	17	and	and	CCONJ
ejpam-4766	262	18	let	let	VERB
ejpam-4766	262	19	dv	dv	PROPN
ejpam-4766	262	20	=	=	PROPN
ejpam-4766	262	21	v	v	PROPN
ejpam-4766	262	22	(	(	PUNCT
ejpam-4766	262	23	hv	hv	NOUN
ejpam-4766	262	24	)	)	PUNCT
ejpam-4766	262	25	∩	∩	PROPN
ejpam-4766	262	26	d	d	NOUN
ejpam-4766	262	27	for	for	ADP
ejpam-4766	262	28	each	each	DET
ejpam-4766	262	29	v	v	NUM
ejpam-4766	262	30	∈	∈	PROPN
ejpam-4766	262	31	v	v	NOUN
ejpam-4766	262	32	(	(	PUNCT
ejpam-4766	262	33	g	g	NOUN
ejpam-4766	262	34	)	)	PUNCT
ejpam-4766	262	35	.	.	PUNCT
ejpam-4766	263	1	since	since	SCONJ
ejpam-4766	263	2	⟨d⟩	⟨d⟩	PROPN
ejpam-4766	263	3	is	be	AUX
ejpam-4766	263	4	connected	connect	VERB
ejpam-4766	263	5	and	and	CCONJ
ejpam-4766	263	6	h	h	NOUN
ejpam-4766	263	7	is	be	AUX
ejpam-4766	263	8	noncomplete	noncomplete	ADJ
ejpam-4766	263	9	,	,	PUNCT
ejpam-4766	263	10	it	it	PRON
ejpam-4766	263	11	follows	follow	VERB
ejpam-4766	263	12	that	that	SCONJ
ejpam-4766	263	13	d	d	PROPN
ejpam-4766	263	14	=	=	SYM
ejpam-4766	263	15	v	v	PROPN
ejpam-4766	263	16	(	(	PUNCT
ejpam-4766	263	17	g	g	NOUN
ejpam-4766	263	18	)	)	PUNCT
ejpam-4766	263	19	∪	∪	NOUN
ejpam-4766	263	20	(	(	PUNCT
ejpam-4766	263	21	⋃	⋃	ADJ
ejpam-4766	263	22	v∈v	v∈v	NOUN
ejpam-4766	263	23	(	(	PUNCT
ejpam-4766	263	24	g)dv	g)dv	PROPN
ejpam-4766	263	25	)	)	PUNCT
ejpam-4766	263	26	.	.	PUNCT
ejpam-4766	264	1	suppose	suppose	VERB
ejpam-4766	264	2	v	v	X
ejpam-4766	264	3	(	(	PUNCT
ejpam-4766	264	4	hv	hv	PROPN
ejpam-4766	264	5	)	)	PUNCT
ejpam-4766	264	6	\dv	\dv	PROPN
ejpam-4766	264	7	is	be	AUX
ejpam-4766	264	8	not	not	PART
ejpam-4766	264	9	a	a	DET
ejpam-4766	264	10	clique	clique	NOUN
ejpam-4766	264	11	in	in	ADP
ejpam-4766	264	12	hv	hv	PROPN
ejpam-4766	264	13	for	for	ADP
ejpam-4766	264	14	some	some	DET
ejpam-4766	264	15	v	v	NUM
ejpam-4766	264	16	∈	∈	PROPN
ejpam-4766	264	17	v	v	NOUN
ejpam-4766	264	18	(	(	PUNCT
ejpam-4766	264	19	g	g	NOUN
ejpam-4766	264	20	)	)	PUNCT
ejpam-4766	264	21	.	.	PUNCT
ejpam-4766	265	1	then	then	ADV
ejpam-4766	265	2	there	there	PRON
ejpam-4766	265	3	exists	exist	VERB
ejpam-4766	265	4	u	u	NOUN
ejpam-4766	265	5	,	,	PUNCT
ejpam-4766	265	6	w	w	PROPN
ejpam-4766	265	7	∈	∈	PROPN
ejpam-4766	265	8	v	v	ADP
ejpam-4766	265	9	(	(	PUNCT
ejpam-4766	265	10	hv	hv	PROPN
ejpam-4766	265	11	)	)	PUNCT
ejpam-4766	265	12	\	\	PROPN
ejpam-4766	266	1	dv	dv	PROPN
ejpam-4766	266	2	⊆	⊆	NUM
ejpam-4766	266	3	v	v	NOUN
ejpam-4766	266	4	(	(	PUNCT
ejpam-4766	266	5	g	g	PROPN
ejpam-4766	266	6	◦	◦	NOUN
ejpam-4766	266	7	h	h	NOUN
ejpam-4766	266	8	)	)	PUNCT
ejpam-4766	266	9	\	\	PUNCT
ejpam-4766	267	1	d	d	ADP
ejpam-4766	267	2	such	such	ADJ
ejpam-4766	267	3	that	that	DET
ejpam-4766	267	4	dhv(u	dhv(u	PROPN
ejpam-4766	267	5	,	,	PUNCT
ejpam-4766	267	6	w	w	NOUN
ejpam-4766	267	7	)	)	PUNCT
ejpam-4766	267	8	=	=	SYM
ejpam-4766	267	9	dg	dg	PROPN
ejpam-4766	267	10	◦	◦	NOUN
ejpam-4766	267	11	h(u	h(u	PROPN
ejpam-4766	267	12	,	,	PUNCT
ejpam-4766	267	13	w	w	NOUN
ejpam-4766	267	14	)	)	PUNCT
ejpam-4766	267	15	=	=	SYM
ejpam-4766	267	16	2	2	NUM
ejpam-4766	267	17	for	for	ADP
ejpam-4766	267	18	some	some	DET
ejpam-4766	267	19	v	v	ADP
ejpam-4766	267	20	∈	∈	NOUN
ejpam-4766	267	21	v	v	NOUN
ejpam-4766	267	22	(	(	PUNCT
ejpam-4766	267	23	g	g	NOUN
ejpam-4766	267	24	)	)	PUNCT
ejpam-4766	267	25	,	,	PUNCT
ejpam-4766	267	26	a	a	DET
ejpam-4766	267	27	contradiction	contradiction	NOUN
ejpam-4766	267	28	to	to	ADP
ejpam-4766	267	29	the	the	DET
ejpam-4766	267	30	fact	fact	NOUN
ejpam-4766	267	31	that	that	SCONJ
ejpam-4766	267	32	d	d	NOUN
ejpam-4766	267	33	is	be	AUX
ejpam-4766	267	34	an	an	DET
ejpam-4766	267	35	outer	outer	ADJ
ejpam-4766	267	36	-	-	PUNCT
ejpam-4766	267	37	hop	hop	NOUN
ejpam-4766	267	38	independent	independent	ADJ
ejpam-4766	267	39	set	set	NOUN
ejpam-4766	267	40	in	in	ADP
ejpam-4766	267	41	g	g	PROPN
ejpam-4766	267	42	◦	◦	NOUN
ejpam-4766	267	43	h.	h.	PROPN
ejpam-4766	267	44	therefore	therefore	ADV
ejpam-4766	267	45	,	,	PUNCT
ejpam-4766	267	46	v	v	PROPN
ejpam-4766	267	47	(	(	PUNCT
ejpam-4766	267	48	hv	hv	PROPN
ejpam-4766	267	49	)	)	PUNCT
ejpam-4766	267	50	\dv	\dv	PROPN
ejpam-4766	267	51	is	be	AUX
ejpam-4766	267	52	clique	clique	NOUN
ejpam-4766	267	53	in	in	ADP
ejpam-4766	267	54	hv	hv	PROPN
ejpam-4766	267	55	for	for	ADP
ejpam-4766	267	56	every	every	DET
ejpam-4766	267	57	v	v	NUM
ejpam-4766	267	58	∈	∈	PROPN
ejpam-4766	267	59	v	v	NOUN
ejpam-4766	267	60	(	(	PUNCT
ejpam-4766	267	61	g	g	NOUN
ejpam-4766	267	62	)	)	PUNCT
ejpam-4766	267	63	.	.	PUNCT
ejpam-4766	268	1	conversely	conversely	ADV
ejpam-4766	268	2	,	,	PUNCT
ejpam-4766	268	3	suppose	suppose	VERB
ejpam-4766	268	4	d	d	X
ejpam-4766	268	5	=	=	SYM
ejpam-4766	268	6	v	v	PROPN
ejpam-4766	268	7	(	(	PUNCT
ejpam-4766	268	8	g	g	NOUN
ejpam-4766	268	9	)	)	PUNCT
ejpam-4766	268	10	∪	∪	NOUN
ejpam-4766	268	11	(	(	PUNCT
ejpam-4766	268	12	⋃	⋃	ADJ
ejpam-4766	268	13	v∈v	v∈v	NOUN
ejpam-4766	268	14	(	(	PUNCT
ejpam-4766	268	15	g)dv	g)dv	PROPN
ejpam-4766	268	16	)	)	PUNCT
ejpam-4766	268	17	,	,	PUNCT
ejpam-4766	268	18	where	where	SCONJ
ejpam-4766	268	19	dv	dv	PROPN
ejpam-4766	268	20	⊆	⊆	NUM
ejpam-4766	268	21	v	v	PROPN
ejpam-4766	268	22	(	(	PUNCT
ejpam-4766	268	23	hv	hv	NOUN
ejpam-4766	268	24	)	)	PUNCT
ejpam-4766	268	25	and	and	CCONJ
ejpam-4766	268	26	v	v	NOUN
ejpam-4766	268	27	(	(	PUNCT
ejpam-4766	268	28	hv	hv	PROPN
ejpam-4766	268	29	)	)	PUNCT
ejpam-4766	268	30	\dv	\dv	PROPN
ejpam-4766	268	31	is	be	AUX
ejpam-4766	268	32	clique	clique	NOUN
ejpam-4766	268	33	of	of	ADP
ejpam-4766	268	34	hv	hv	PROPN
ejpam-4766	268	35	for	for	ADP
ejpam-4766	268	36	each	each	DET
ejpam-4766	268	37	v	v	NUM
ejpam-4766	268	38	∈	∈	PROPN
ejpam-4766	268	39	v	v	NOUN
ejpam-4766	268	40	(	(	PUNCT
ejpam-4766	268	41	g	g	NOUN
ejpam-4766	268	42	)	)	PUNCT
ejpam-4766	268	43	.	.	PUNCT
ejpam-4766	269	1	clearly	clearly	ADV
ejpam-4766	269	2	,	,	PUNCT
ejpam-4766	269	3	d	d	PRON
ejpam-4766	269	4	is	be	AUX
ejpam-4766	269	5	a	a	DET
ejpam-4766	269	6	connected	connected	ADJ
ejpam-4766	269	7	dominating	dominating	NOUN
ejpam-4766	269	8	set	set	NOUN
ejpam-4766	269	9	of	of	ADP
ejpam-4766	269	10	g	g	PROPN
ejpam-4766	269	11	◦	◦	PROPN
ejpam-4766	269	12	h.	h.	PROPN
ejpam-4766	269	13	since	since	SCONJ
ejpam-4766	269	14	v	v	PROPN
ejpam-4766	269	15	(	(	PUNCT
ejpam-4766	269	16	hv	hv	PROPN
ejpam-4766	269	17	)	)	PUNCT
ejpam-4766	269	18	\	\	PROPN
ejpam-4766	270	1	dv	dv	PROPN
ejpam-4766	270	2	is	be	AUX
ejpam-4766	270	3	clique	clique	NOUN
ejpam-4766	270	4	of	of	ADP
ejpam-4766	270	5	hv	hv	PROPN
ejpam-4766	270	6	for	for	ADP
ejpam-4766	270	7	each	each	DET
ejpam-4766	270	8	v	v	NUM
ejpam-4766	270	9	∈	∈	PROPN
ejpam-4766	270	10	v	v	NOUN
ejpam-4766	270	11	(	(	PUNCT
ejpam-4766	270	12	g	g	NOUN
ejpam-4766	270	13	)	)	PUNCT
ejpam-4766	270	14	,	,	PUNCT
ejpam-4766	270	15	it	it	PRON
ejpam-4766	270	16	follows	follow	VERB
ejpam-4766	270	17	that	that	SCONJ
ejpam-4766	270	18	v	v	NOUN
ejpam-4766	270	19	(	(	PUNCT
ejpam-4766	270	20	g	g	PROPN
ejpam-4766	270	21	◦	◦	NOUN
ejpam-4766	270	22	h	h	NOUN
ejpam-4766	270	23	)	)	PUNCT
ejpam-4766	270	24	\	\	PUNCT
ejpam-4766	271	1	d	d	PUNCT
ejpam-4766	271	2	=	=	SYM
ejpam-4766	271	3	⋃	⋃	NOUN
ejpam-4766	271	4	v∈v	v∈v	NOUN
ejpam-4766	271	5	(	(	PUNCT
ejpam-4766	271	6	g)(v	g)(v	X
ejpam-4766	271	7	(	(	PUNCT
ejpam-4766	271	8	hv	hv	X
ejpam-4766	271	9	)	)	PUNCT
ejpam-4766	271	10	\	\	PROPN
ejpam-4766	271	11	dv	dv	PROPN
ejpam-4766	271	12	)	)	PUNCT
ejpam-4766	271	13	is	be	AUX
ejpam-4766	271	14	a	a	DET
ejpam-4766	271	15	hop	hop	NOUN
ejpam-4766	271	16	independent	independent	ADJ
ejpam-4766	271	17	set	set	NOUN
ejpam-4766	271	18	of	of	ADP
ejpam-4766	271	19	g	g	PROPN
ejpam-4766	271	20	◦	◦	PROPN
ejpam-4766	271	21	h.	h.	PROPN
ejpam-4766	271	22	therefore	therefore	ADV
ejpam-4766	271	23	,	,	PUNCT
ejpam-4766	271	24	d	d	PRON
ejpam-4766	271	25	is	be	AUX
ejpam-4766	271	26	a	a	DET
ejpam-4766	271	27	connected	connected	ADJ
ejpam-4766	271	28	outer	outer	ADJ
ejpam-4766	271	29	-	-	PUNCT
ejpam-4766	271	30	hop	hop	NOUN
ejpam-4766	271	31	independent	independent	ADJ
ejpam-4766	271	32	dominating	dominating	NOUN
ejpam-4766	271	33	set	set	VERB
ejpam-4766	271	34	in	in	ADP
ejpam-4766	271	35	g	g	PROPN
ejpam-4766	271	36	◦	◦	NOUN
ejpam-4766	271	37	h.	h.	NOUN
ejpam-4766	271	38	the	the	DET
ejpam-4766	271	39	next	next	ADJ
ejpam-4766	271	40	result	result	NOUN
ejpam-4766	271	41	follows	follow	VERB
ejpam-4766	271	42	from	from	ADP
ejpam-4766	271	43	theorem	theorem	ADJ
ejpam-4766	271	44	6	6	NUM
ejpam-4766	271	45	.	.	PUNCT
ejpam-4766	271	46	corollary	corollary	ADJ
ejpam-4766	271	47	4	4	NUM
ejpam-4766	271	48	.	.	PUNCT
ejpam-4766	272	1	let	let	VERB
ejpam-4766	272	2	g	g	PRON
ejpam-4766	272	3	be	be	AUX
ejpam-4766	272	4	a	a	DET
ejpam-4766	272	5	non	non	ADJ
ejpam-4766	272	6	-	-	ADJ
ejpam-4766	272	7	trivial	trivial	ADJ
ejpam-4766	272	8	connected	connected	ADJ
ejpam-4766	272	9	graph	graph	NOUN
ejpam-4766	272	10	with	with	ADP
ejpam-4766	272	11	|v	|v	PROPN
ejpam-4766	272	12	(	(	PUNCT
ejpam-4766	272	13	g)|	g)|	NOUN
ejpam-4766	272	14	=	=	PUNCT
ejpam-4766	272	15	s	s	PROPN
ejpam-4766	272	16	and	and	CCONJ
ejpam-4766	272	17	h	h	NOUN
ejpam-4766	272	18	be	be	VERB
ejpam-4766	272	19	any	any	DET
ejpam-4766	272	20	non	non	ADJ
ejpam-4766	272	21	-	-	ADJ
ejpam-4766	272	22	complete	complete	ADJ
ejpam-4766	272	23	graph	graph	NOUN
ejpam-4766	272	24	with	with	ADP
ejpam-4766	272	25	|v	|v	PROPN
ejpam-4766	272	26	(	(	PUNCT
ejpam-4766	272	27	h)|	h)|	NOUN
ejpam-4766	272	28	=	=	PUNCT
ejpam-4766	272	29	t.	t.	PROPN
ejpam-4766	272	30	then	then	ADV
ejpam-4766	272	31	γohic	γohic	ADJ
ejpam-4766	272	32	(	(	PUNCT
ejpam-4766	272	33	g	g	PROPN
ejpam-4766	272	34	◦	◦	NOUN
ejpam-4766	272	35	h	h	NOUN
ejpam-4766	272	36	)	)	PUNCT
ejpam-4766	273	1	=	=	PUNCT
ejpam-4766	273	2	s+	s+	NUM
ejpam-4766	273	3	s(ω̃(h	s(ω̃(h	NOUN
ejpam-4766	273	4	)	)	PUNCT
ejpam-4766	273	5	)	)	PUNCT
ejpam-4766	273	6	.	.	PUNCT
ejpam-4766	274	1	in	in	ADP
ejpam-4766	274	2	particular	particular	ADJ
ejpam-4766	274	3	,	,	PUNCT
ejpam-4766	274	4	we	we	PRON
ejpam-4766	274	5	have	have	VERB
ejpam-4766	274	6	j.	j.	PROPN
ejpam-4766	274	7	hassan	hassan	PROPN
ejpam-4766	274	8	et	et	PROPN
ejpam-4766	274	9	al	al	PROPN
ejpam-4766	274	10	.	.	PUNCT
ejpam-4766	274	11	/	/	SYM
ejpam-4766	274	12	eur	eur	PROPN
ejpam-4766	274	13	.	.	PUNCT
ejpam-4766	275	1	j.	j.	PROPN
ejpam-4766	275	2	pure	pure	PROPN
ejpam-4766	275	3	appl	appl	PROPN
ejpam-4766	275	4	.	.	PROPN
ejpam-4766	275	5	math	math	PROPN
ejpam-4766	275	6	,	,	PUNCT
ejpam-4766	275	7	16	16	NUM
ejpam-4766	275	8	(	(	PUNCT
ejpam-4766	275	9	3	3	NUM
ejpam-4766	275	10	)	)	PUNCT
ejpam-4766	275	11	(	(	PUNCT
ejpam-4766	275	12	2023	2023	NUM
ejpam-4766	275	13	)	)	PUNCT
ejpam-4766	275	14	,	,	PUNCT
ejpam-4766	275	15	1817	1817	NUM
ejpam-4766	275	16	-	-	SYM
ejpam-4766	275	17	1829	1829	NUM
ejpam-4766	275	18	1827	1827	NUM
ejpam-4766	275	19	(	(	PUNCT
ejpam-4766	275	20	i	i	NOUN
ejpam-4766	275	21	)	)	PUNCT
ejpam-4766	275	22	γohic	γohic	ADJ
ejpam-4766	275	23	(	(	PUNCT
ejpam-4766	275	24	ps	ps	NOUN
ejpam-4766	275	25	◦	◦	NOUN
ejpam-4766	275	26	pt	pt	NOUN
ejpam-4766	275	27	)	)	PUNCT
ejpam-4766	275	28	=	=	SYM
ejpam-4766	276	1	γohic	γohic	ADJ
ejpam-4766	276	2	(	(	PUNCT
ejpam-4766	276	3	cs	cs	X
ejpam-4766	276	4	◦	◦	NOUN
ejpam-4766	276	5	ct	ct	NUM
ejpam-4766	276	6	)	)	PUNCT
ejpam-4766	276	7	=	=	SYM
ejpam-4766	277	1	γohic	γohic	ADJ
ejpam-4766	277	2	(	(	PUNCT
ejpam-4766	277	3	ps	ps	NOUN
ejpam-4766	277	4	◦	◦	NOUN
ejpam-4766	277	5	ct	ct	NUM
ejpam-4766	277	6	)	)	PUNCT
ejpam-4766	278	1	=	=	PUNCT
ejpam-4766	278	2	s+	s+	PUNCT
ejpam-4766	278	3	s(t−	s(t−	PROPN
ejpam-4766	278	4	2	2	X
ejpam-4766	278	5	)	)	PUNCT
ejpam-4766	278	6	for	for	ADP
ejpam-4766	278	7	all	all	DET
ejpam-4766	278	8	s	s	PART
ejpam-4766	278	9	≥	≥	NUM
ejpam-4766	278	10	2	2	NUM
ejpam-4766	278	11	and	and	CCONJ
ejpam-4766	278	12	t	t	PROPN
ejpam-4766	278	13	≥	≥	NUM
ejpam-4766	278	14	4	4	NUM
ejpam-4766	278	15	;	;	PUNCT
ejpam-4766	278	16	(	(	PUNCT
ejpam-4766	278	17	ii	ii	NOUN
ejpam-4766	278	18	)	)	PUNCT
ejpam-4766	278	19	γohic	γohic	ADJ
ejpam-4766	278	20	(	(	PUNCT
ejpam-4766	278	21	ks	ks	NOUN
ejpam-4766	278	22	◦	◦	NOUN
ejpam-4766	278	23	pt	pt	NOUN
ejpam-4766	278	24	)	)	PUNCT
ejpam-4766	278	25	=	=	SYM
ejpam-4766	278	26	γohic	γohic	ADJ
ejpam-4766	278	27	(	(	PUNCT
ejpam-4766	278	28	ks	ks	NOUN
ejpam-4766	278	29	◦	◦	NOUN
ejpam-4766	278	30	ct	ct	NUM
ejpam-4766	278	31	)	)	PUNCT
ejpam-4766	278	32	=	=	PUNCT
ejpam-4766	279	1	s+	s+	PUNCT
ejpam-4766	279	2	s(t−	s(t−	PROPN
ejpam-4766	279	3	2	2	X
ejpam-4766	279	4	)	)	PUNCT
ejpam-4766	279	5	for	for	ADP
ejpam-4766	279	6	all	all	DET
ejpam-4766	279	7	s	s	PART
ejpam-4766	279	8	≥	≥	NUM
ejpam-4766	279	9	2	2	NUM
ejpam-4766	279	10	and	and	CCONJ
ejpam-4766	279	11	t	t	PROPN
ejpam-4766	279	12	≥	≥	NUM
ejpam-4766	279	13	4	4	NUM
ejpam-4766	279	14	;	;	PUNCT
ejpam-4766	279	15	(	(	PUNCT
ejpam-4766	279	16	iii	iii	X
ejpam-4766	279	17	)	)	PUNCT
ejpam-4766	279	18	γohic	γohic	ADJ
ejpam-4766	279	19	(	(	PUNCT
ejpam-4766	279	20	g	g	PROPN
ejpam-4766	279	21	◦	◦	NOUN
ejpam-4766	279	22	wt	wt	NOUN
ejpam-4766	279	23	)	)	PUNCT
ejpam-4766	279	24	=	=	SYM
ejpam-4766	279	25	|v	|v	PROPN
ejpam-4766	279	26	(	(	PUNCT
ejpam-4766	279	27	g)|+	g)|+	PROPN
ejpam-4766	279	28	|v	|v	PROPN
ejpam-4766	279	29	(	(	PUNCT
ejpam-4766	279	30	g)|(t−	g)|(t−	PROPN
ejpam-4766	279	31	2	2	NUM
ejpam-4766	279	32	)	)	PUNCT
ejpam-4766	279	33	for	for	ADP
ejpam-4766	279	34	all	all	DET
ejpam-4766	279	35	t	t	PROPN
ejpam-4766	279	36	≥	≥	NOUN
ejpam-4766	279	37	4	4	NUM
ejpam-4766	279	38	;	;	PUNCT
ejpam-4766	279	39	and	and	CCONJ
ejpam-4766	279	40	(	(	PUNCT
ejpam-4766	279	41	iv	iv	X
ejpam-4766	279	42	)	)	PUNCT
ejpam-4766	279	43	γohic	γohic	ADJ
ejpam-4766	279	44	(	(	PUNCT
ejpam-4766	279	45	g	g	PROPN
ejpam-4766	279	46	◦	◦	NOUN
ejpam-4766	279	47	ft	ft	NOUN
ejpam-4766	279	48	)	)	PUNCT
ejpam-4766	279	49	=	=	SYM
ejpam-4766	280	1	|v	|v	PROPN
ejpam-4766	280	2	(	(	PUNCT
ejpam-4766	280	3	g)|+	g)|+	PROPN
ejpam-4766	280	4	|v	|v	PROPN
ejpam-4766	280	5	(	(	PUNCT
ejpam-4766	280	6	g)|(t−	g)|(t−	PROPN
ejpam-4766	280	7	2	2	NUM
ejpam-4766	280	8	)	)	PUNCT
ejpam-4766	280	9	for	for	ADP
ejpam-4766	280	10	all	all	DET
ejpam-4766	280	11	t	t	PROPN
ejpam-4766	280	12	≥	≥	NUM
ejpam-4766	280	13	3	3	NUM
ejpam-4766	280	14	.	.	PUNCT
ejpam-4766	280	15	theorem	theorem	VERB
ejpam-4766	280	16	7	7	NUM
ejpam-4766	280	17	.	.	PUNCT
ejpam-4766	281	1	let	let	VERB
ejpam-4766	281	2	g	g	PRON
ejpam-4766	281	3	be	be	AUX
ejpam-4766	281	4	a	a	DET
ejpam-4766	281	5	non	non	ADJ
ejpam-4766	281	6	-	-	ADJ
ejpam-4766	281	7	trivial	trivial	ADJ
ejpam-4766	281	8	connected	connected	ADJ
ejpam-4766	281	9	graph	graph	NOUN
ejpam-4766	281	10	and	and	CCONJ
ejpam-4766	281	11	h	h	NOUN
ejpam-4766	281	12	be	be	AUX
ejpam-4766	281	13	any	any	DET
ejpam-4766	281	14	complete	complete	ADJ
ejpam-4766	281	15	graph	graph	NOUN
ejpam-4766	281	16	.	.	PUNCT
ejpam-4766	282	1	a	a	DET
ejpam-4766	282	2	set	set	NOUN
ejpam-4766	282	3	d	d	NOUN
ejpam-4766	282	4	⊆	⊆	NUM
ejpam-4766	282	5	v	v	NOUN
ejpam-4766	282	6	(	(	PUNCT
ejpam-4766	282	7	g	g	PROPN
ejpam-4766	282	8	◦	◦	NOUN
ejpam-4766	282	9	h	h	NOUN
ejpam-4766	282	10	)	)	PUNCT
ejpam-4766	282	11	is	be	AUX
ejpam-4766	282	12	a	a	DET
ejpam-4766	282	13	connected	connected	ADJ
ejpam-4766	282	14	outer	outer	ADJ
ejpam-4766	282	15	-	-	PUNCT
ejpam-4766	282	16	hop	hop	NOUN
ejpam-4766	282	17	independent	independent	ADJ
ejpam-4766	282	18	dominating	dominating	NOUN
ejpam-4766	282	19	set	set	VERB
ejpam-4766	282	20	in	in	ADP
ejpam-4766	282	21	g	g	PROPN
ejpam-4766	282	22	◦	◦	NOUN
ejpam-4766	282	23	h	h	NOUN
ejpam-4766	282	24	if	if	SCONJ
ejpam-4766	283	1	and	and	CCONJ
ejpam-4766	283	2	only	only	ADV
ejpam-4766	283	3	if	if	SCONJ
ejpam-4766	283	4	d	d	PROPN
ejpam-4766	283	5	=	=	SYM
ejpam-4766	283	6	v	v	X
ejpam-4766	283	7	(	(	PUNCT
ejpam-4766	283	8	g	g	NOUN
ejpam-4766	283	9	)	)	PUNCT
ejpam-4766	283	10	∪	∪	NOUN
ejpam-4766	283	11	(	(	PUNCT
ejpam-4766	283	12	⋃	⋃	ADJ
ejpam-4766	283	13	v∈v	v∈v	NOUN
ejpam-4766	283	14	(	(	PUNCT
ejpam-4766	283	15	g)dv	g)dv	PROPN
ejpam-4766	283	16	)	)	PUNCT
ejpam-4766	283	17	,	,	PUNCT
ejpam-4766	283	18	where	where	SCONJ
ejpam-4766	283	19	dv	dv	PROPN
ejpam-4766	283	20	⊆	⊆	NUM
ejpam-4766	283	21	v	v	PROPN
ejpam-4766	283	22	(	(	PUNCT
ejpam-4766	283	23	hv	hv	NOUN
ejpam-4766	283	24	)	)	PUNCT
ejpam-4766	283	25	such	such	ADJ
ejpam-4766	283	26	that	that	SCONJ
ejpam-4766	283	27	dv	dv	PROPN
ejpam-4766	283	28	=	=	PROPN
ejpam-4766	283	29	∅	∅	NOUN
ejpam-4766	283	30	or	or	CCONJ
ejpam-4766	283	31	dv	dv	PROPN
ejpam-4766	283	32	̸=	̸=	PROPN
ejpam-4766	283	33	∅	∅	NOUN
ejpam-4766	283	34	for	for	ADP
ejpam-4766	283	35	each	each	DET
ejpam-4766	283	36	v	v	NUM
ejpam-4766	283	37	∈	∈	PROPN
ejpam-4766	283	38	v	v	NOUN
ejpam-4766	283	39	(	(	PUNCT
ejpam-4766	283	40	g	g	NOUN
ejpam-4766	283	41	)	)	PUNCT
ejpam-4766	283	42	.	.	PUNCT
ejpam-4766	284	1	proof	proof	NOUN
ejpam-4766	284	2	.	.	PUNCT
ejpam-4766	285	1	assume	assume	VERB
ejpam-4766	285	2	that	that	SCONJ
ejpam-4766	285	3	d	d	NOUN
ejpam-4766	285	4	is	be	AUX
ejpam-4766	285	5	a	a	DET
ejpam-4766	285	6	connected	connected	ADJ
ejpam-4766	285	7	outer	outer	ADJ
ejpam-4766	285	8	-	-	PUNCT
ejpam-4766	285	9	hop	hop	NOUN
ejpam-4766	285	10	independent	independent	ADJ
ejpam-4766	285	11	dominating	dominating	NOUN
ejpam-4766	285	12	set	set	VERB
ejpam-4766	285	13	in	in	ADP
ejpam-4766	285	14	g	g	PROPN
ejpam-4766	285	15	◦	◦	NOUN
ejpam-4766	285	16	h	h	NOUN
ejpam-4766	285	17	and	and	CCONJ
ejpam-4766	285	18	let	let	VERB
ejpam-4766	285	19	dv	dv	PROPN
ejpam-4766	285	20	=	=	PROPN
ejpam-4766	285	21	v	v	PROPN
ejpam-4766	285	22	(	(	PUNCT
ejpam-4766	285	23	hv	hv	NOUN
ejpam-4766	285	24	)	)	PUNCT
ejpam-4766	285	25	∩	∩	PROPN
ejpam-4766	285	26	d	d	NOUN
ejpam-4766	285	27	for	for	ADP
ejpam-4766	285	28	each	each	DET
ejpam-4766	285	29	v	v	NUM
ejpam-4766	285	30	∈	∈	PROPN
ejpam-4766	285	31	v	v	NOUN
ejpam-4766	285	32	(	(	PUNCT
ejpam-4766	285	33	g	g	NOUN
ejpam-4766	285	34	)	)	PUNCT
ejpam-4766	285	35	.	.	PUNCT
ejpam-4766	286	1	since	since	SCONJ
ejpam-4766	286	2	⟨d⟩	⟨d⟩	PROPN
ejpam-4766	286	3	is	be	AUX
ejpam-4766	286	4	connected	connect	VERB
ejpam-4766	286	5	,	,	PUNCT
ejpam-4766	286	6	it	it	PRON
ejpam-4766	286	7	follows	follow	VERB
ejpam-4766	286	8	that	that	SCONJ
ejpam-4766	286	9	d	d	PROPN
ejpam-4766	286	10	=	=	SYM
ejpam-4766	286	11	v	v	NOUN
ejpam-4766	286	12	(	(	PUNCT
ejpam-4766	286	13	g)∪	g)∪	VERB
ejpam-4766	286	14	(	(	PUNCT
ejpam-4766	286	15	⋃	⋃	ADJ
ejpam-4766	286	16	v∈v	v∈v	NOUN
ejpam-4766	286	17	(	(	PUNCT
ejpam-4766	286	18	g)dv	g)dv	PROPN
ejpam-4766	286	19	)	)	PUNCT
ejpam-4766	286	20	.	.	PUNCT
ejpam-4766	287	1	since	since	SCONJ
ejpam-4766	287	2	h	h	NOUN
ejpam-4766	287	3	is	be	AUX
ejpam-4766	287	4	complete	complete	ADJ
ejpam-4766	287	5	,	,	PUNCT
ejpam-4766	287	6	either	either	CCONJ
ejpam-4766	287	7	dv	dv	PROPN
ejpam-4766	287	8	=	=	PROPN
ejpam-4766	287	9	∅	∅	NOUN
ejpam-4766	287	10	or	or	CCONJ
ejpam-4766	287	11	dv	dv	PROPN
ejpam-4766	287	12	̸=	̸=	PROPN
ejpam-4766	287	13	∅	∅	NOUN
ejpam-4766	287	14	holds	hold	VERB
ejpam-4766	287	15	for	for	ADP
ejpam-4766	287	16	each	each	DET
ejpam-4766	287	17	v	v	NUM
ejpam-4766	287	18	∈	∈	PROPN
ejpam-4766	287	19	v	v	NOUN
ejpam-4766	287	20	(	(	PUNCT
ejpam-4766	287	21	g	g	NOUN
ejpam-4766	287	22	)	)	PUNCT
ejpam-4766	287	23	.	.	PUNCT
ejpam-4766	288	1	conversely	conversely	ADV
ejpam-4766	288	2	,	,	PUNCT
ejpam-4766	288	3	suppose	suppose	VERB
ejpam-4766	288	4	that	that	SCONJ
ejpam-4766	288	5	d	d	PROPN
ejpam-4766	288	6	=	=	SYM
ejpam-4766	288	7	v	v	PROPN
ejpam-4766	288	8	(	(	PUNCT
ejpam-4766	288	9	g	g	NOUN
ejpam-4766	288	10	)	)	PUNCT
ejpam-4766	288	11	∪	∪	NOUN
ejpam-4766	288	12	(	(	PUNCT
ejpam-4766	288	13	⋃	⋃	ADJ
ejpam-4766	288	14	v∈v	v∈v	NOUN
ejpam-4766	288	15	(	(	PUNCT
ejpam-4766	288	16	g)dv	g)dv	PROPN
ejpam-4766	288	17	)	)	PUNCT
ejpam-4766	288	18	,	,	PUNCT
ejpam-4766	288	19	where	where	SCONJ
ejpam-4766	288	20	dv	dv	PROPN
ejpam-4766	288	21	⊆	⊆	NUM
ejpam-4766	288	22	v	v	PROPN
ejpam-4766	288	23	(	(	PUNCT
ejpam-4766	288	24	hv	hv	PROPN
ejpam-4766	288	25	)	)	PUNCT
ejpam-4766	288	26	.	.	PUNCT
ejpam-4766	289	1	if	if	SCONJ
ejpam-4766	289	2	dv	dv	PROPN
ejpam-4766	289	3	=	=	PROPN
ejpam-4766	289	4	∅	∅	NOUN
ejpam-4766	289	5	for	for	ADP
ejpam-4766	289	6	each	each	DET
ejpam-4766	289	7	v	v	NUM
ejpam-4766	289	8	∈	∈	PROPN
ejpam-4766	289	9	v	v	NOUN
ejpam-4766	289	10	(	(	PUNCT
ejpam-4766	289	11	g	g	NOUN
ejpam-4766	289	12	)	)	PUNCT
ejpam-4766	289	13	,	,	PUNCT
ejpam-4766	289	14	then	then	ADV
ejpam-4766	289	15	d	d	PROPN
ejpam-4766	289	16	=	=	SYM
ejpam-4766	289	17	v	v	PROPN
ejpam-4766	289	18	(	(	PUNCT
ejpam-4766	289	19	g	g	NOUN
ejpam-4766	289	20	)	)	PUNCT
ejpam-4766	289	21	.	.	PUNCT
ejpam-4766	290	1	since	since	SCONJ
ejpam-4766	290	2	h	h	NOUN
ejpam-4766	290	3	is	be	AUX
ejpam-4766	290	4	complete	complete	ADJ
ejpam-4766	290	5	,	,	PUNCT
ejpam-4766	290	6	it	it	PRON
ejpam-4766	290	7	follows	follow	VERB
ejpam-4766	290	8	that	that	SCONJ
ejpam-4766	290	9	d	d	PROPN
ejpam-4766	290	10	=	=	SYM
ejpam-4766	290	11	v	v	PROPN
ejpam-4766	290	12	(	(	PUNCT
ejpam-4766	290	13	g	g	NOUN
ejpam-4766	290	14	)	)	PUNCT
ejpam-4766	290	15	is	be	AUX
ejpam-4766	290	16	connected	connect	VERB
ejpam-4766	290	17	outer	outer	ADJ
ejpam-4766	290	18	-	-	PUNCT
ejpam-4766	290	19	hop	hop	NOUN
ejpam-4766	290	20	independent	independent	ADJ
ejpam-4766	290	21	dominating	dominating	NOUN
ejpam-4766	290	22	set	set	VERB
ejpam-4766	290	23	in	in	ADP
ejpam-4766	290	24	g	g	PROPN
ejpam-4766	290	25	◦	◦	NOUN
ejpam-4766	290	26	h.	h.	NOUN
ejpam-4766	290	27	similarly	similarly	ADV
ejpam-4766	290	28	,	,	PUNCT
ejpam-4766	290	29	if	if	SCONJ
ejpam-4766	290	30	dv	dv	PROPN
ejpam-4766	290	31	̸=	̸=	PROPN
ejpam-4766	290	32	∅	∅	NOUN
ejpam-4766	290	33	for	for	ADP
ejpam-4766	290	34	each	each	DET
ejpam-4766	290	35	v	v	NUM
ejpam-4766	290	36	∈	∈	PROPN
ejpam-4766	290	37	v	v	NOUN
ejpam-4766	290	38	(	(	PUNCT
ejpam-4766	290	39	g	g	NOUN
ejpam-4766	290	40	)	)	PUNCT
ejpam-4766	290	41	,	,	PUNCT
ejpam-4766	290	42	then	then	ADV
ejpam-4766	290	43	d	d	X
ejpam-4766	290	44	connected	connected	ADJ
ejpam-4766	290	45	outer	outer	ADJ
ejpam-4766	290	46	-	-	PUNCT
ejpam-4766	290	47	hop	hop	NOUN
ejpam-4766	290	48	independent	independent	ADJ
ejpam-4766	290	49	dominating	dominating	NOUN
ejpam-4766	290	50	set	set	VERB
ejpam-4766	290	51	in	in	ADP
ejpam-4766	290	52	g	g	PROPN
ejpam-4766	290	53	◦	◦	NOUN
ejpam-4766	290	54	h.	h.	NOUN
ejpam-4766	290	55	the	the	DET
ejpam-4766	290	56	next	next	ADJ
ejpam-4766	290	57	result	result	NOUN
ejpam-4766	290	58	follows	follow	VERB
ejpam-4766	290	59	from	from	ADP
ejpam-4766	290	60	theorem	theorem	ADJ
ejpam-4766	290	61	7	7	NUM
ejpam-4766	290	62	.	.	PUNCT
ejpam-4766	290	63	corollary	corollary	ADJ
ejpam-4766	290	64	5	5	NUM
ejpam-4766	290	65	.	.	PUNCT
ejpam-4766	291	1	let	let	VERB
ejpam-4766	291	2	g	g	PRON
ejpam-4766	291	3	be	be	AUX
ejpam-4766	291	4	a	a	DET
ejpam-4766	291	5	non	non	ADJ
ejpam-4766	291	6	-	-	ADJ
ejpam-4766	291	7	trivial	trivial	ADJ
ejpam-4766	291	8	connected	connected	ADJ
ejpam-4766	291	9	graph	graph	NOUN
ejpam-4766	291	10	with	with	ADP
ejpam-4766	291	11	|v	|v	PROPN
ejpam-4766	291	12	(	(	PUNCT
ejpam-4766	291	13	g)|	g)|	NOUN
ejpam-4766	291	14	=	=	PUNCT
ejpam-4766	291	15	s	s	PROPN
ejpam-4766	291	16	and	and	CCONJ
ejpam-4766	291	17	h	h	NOUN
ejpam-4766	291	18	be	be	VERB
ejpam-4766	291	19	any	any	DET
ejpam-4766	291	20	complete	complete	ADJ
ejpam-4766	291	21	graph	graph	NOUN
ejpam-4766	291	22	.	.	PUNCT
ejpam-4766	292	1	then	then	ADV
ejpam-4766	292	2	γohic	γohic	ADJ
ejpam-4766	292	3	(	(	PUNCT
ejpam-4766	292	4	g	g	PROPN
ejpam-4766	292	5	◦	◦	NOUN
ejpam-4766	292	6	h	h	NOUN
ejpam-4766	292	7	)	)	PUNCT
ejpam-4766	292	8	=	=	VERB
ejpam-4766	293	1	s.	s.	PROPN
ejpam-4766	293	2	in	in	ADP
ejpam-4766	293	3	particular	particular	ADJ
ejpam-4766	293	4	,	,	PUNCT
ejpam-4766	293	5	we	we	PRON
ejpam-4766	293	6	have	have	VERB
ejpam-4766	293	7	(	(	PUNCT
ejpam-4766	293	8	i	i	NOUN
ejpam-4766	293	9	)	)	PUNCT
ejpam-4766	293	10	γohic	γohic	ADJ
ejpam-4766	293	11	(	(	PUNCT
ejpam-4766	293	12	pn	pn	PROPN
ejpam-4766	293	13	◦	◦	NOUN
ejpam-4766	293	14	km	km	NOUN
ejpam-4766	293	15	)	)	PUNCT
ejpam-4766	293	16	=	=	SYM
ejpam-4766	294	1	n	n	NOUN
ejpam-4766	294	2	=	=	SYM
ejpam-4766	294	3	γohic	γohic	ADJ
ejpam-4766	294	4	(	(	PUNCT
ejpam-4766	294	5	cn	cn	PROPN
ejpam-4766	294	6	◦	◦	PROPN
ejpam-4766	294	7	km	km	PROPN
ejpam-4766	294	8	)	)	PUNCT
ejpam-4766	294	9	for	for	ADP
ejpam-4766	294	10	all	all	DET
ejpam-4766	294	11	n	n	PRON
ejpam-4766	294	12	≥	≥	NOUN
ejpam-4766	294	13	3,m	3,m	NUM
ejpam-4766	294	14	≥	≥	NOUN
ejpam-4766	294	15	1	1	NUM
ejpam-4766	294	16	;	;	PUNCT
ejpam-4766	294	17	and	and	CCONJ
ejpam-4766	294	18	(	(	PUNCT
ejpam-4766	294	19	ii	ii	NOUN
ejpam-4766	294	20	)	)	PUNCT
ejpam-4766	294	21	γohic	γohic	ADJ
ejpam-4766	294	22	(	(	PUNCT
ejpam-4766	294	23	fn	fn	NOUN
ejpam-4766	294	24	◦	◦	NOUN
ejpam-4766	294	25	km	km	NOUN
ejpam-4766	294	26	)	)	PUNCT
ejpam-4766	294	27	=	=	PUNCT
ejpam-4766	294	28	n+	n+	PUNCT
ejpam-4766	294	29	1	1	NUM
ejpam-4766	294	30	=	=	SYM
ejpam-4766	294	31	γohic	γohic	ADJ
ejpam-4766	294	32	(	(	PUNCT
ejpam-4766	294	33	wn	wn	PROPN
ejpam-4766	294	34	◦	◦	PROPN
ejpam-4766	294	35	km	km	PROPN
ejpam-4766	294	36	)	)	PUNCT
ejpam-4766	294	37	for	for	ADP
ejpam-4766	294	38	all	all	DET
ejpam-4766	294	39	n	n	PRON
ejpam-4766	294	40	≥	≥	NOUN
ejpam-4766	294	41	3,m	3,m	NUM
ejpam-4766	294	42	≥	≥	NOUN
ejpam-4766	294	43	1	1	NUM
ejpam-4766	294	44	.	.	NOUN
ejpam-4766	294	45	4	4	NUM
ejpam-4766	294	46	.	.	X
ejpam-4766	294	47	conclusion	conclusion	VERB
ejpam-4766	294	48	the	the	DET
ejpam-4766	294	49	concept	concept	NOUN
ejpam-4766	294	50	of	of	ADP
ejpam-4766	294	51	connected	connected	ADJ
ejpam-4766	294	52	outer	outer	ADJ
ejpam-4766	294	53	-	-	PUNCT
ejpam-4766	294	54	hop	hop	NOUN
ejpam-4766	294	55	independent	independent	ADJ
ejpam-4766	294	56	domination	domination	NOUN
ejpam-4766	294	57	in	in	ADP
ejpam-4766	294	58	a	a	DET
ejpam-4766	294	59	graph	graph	NOUN
ejpam-4766	294	60	has	have	AUX
ejpam-4766	294	61	been	be	AUX
ejpam-4766	294	62	introduced	introduce	VERB
ejpam-4766	294	63	and	and	CCONJ
ejpam-4766	294	64	investigated	investigate	VERB
ejpam-4766	294	65	in	in	ADP
ejpam-4766	294	66	this	this	DET
ejpam-4766	294	67	study	study	NOUN
ejpam-4766	294	68	.	.	PUNCT
ejpam-4766	295	1	it	it	PRON
ejpam-4766	295	2	was	be	AUX
ejpam-4766	295	3	shown	show	VERB
ejpam-4766	295	4	that	that	SCONJ
ejpam-4766	295	5	the	the	DET
ejpam-4766	295	6	connected	connected	ADJ
ejpam-4766	295	7	outer	outer	ADJ
ejpam-4766	295	8	-	-	PUNCT
ejpam-4766	295	9	hop	hop	NOUN
ejpam-4766	295	10	independent	independent	ADJ
ejpam-4766	295	11	domination	domination	NOUN
ejpam-4766	295	12	number	number	NOUN
ejpam-4766	295	13	is	be	AUX
ejpam-4766	295	14	at	at	ADP
ejpam-4766	295	15	least	least	ADJ
ejpam-4766	295	16	equal	equal	ADJ
ejpam-4766	295	17	to	to	ADP
ejpam-4766	295	18	the	the	DET
ejpam-4766	295	19	connected	connected	ADJ
ejpam-4766	295	20	domination	domination	NOUN
ejpam-4766	295	21	number	number	NOUN
ejpam-4766	295	22	of	of	ADP
ejpam-4766	295	23	a	a	DET
ejpam-4766	295	24	graph	graph	NOUN
ejpam-4766	295	25	.	.	PUNCT
ejpam-4766	296	1	connected	connected	ADJ
ejpam-4766	296	2	outer	outer	ADJ
ejpam-4766	296	3	-	-	PUNCT
ejpam-4766	296	4	hop	hop	NOUN
ejpam-4766	296	5	independent	independent	ADJ
ejpam-4766	296	6	dominating	dominating	NOUN
ejpam-4766	296	7	sets	set	NOUN
ejpam-4766	296	8	in	in	ADP
ejpam-4766	296	9	some	some	DET
ejpam-4766	296	10	special	special	ADJ
ejpam-4766	296	11	graphs	graph	NOUN
ejpam-4766	296	12	,	,	PUNCT
ejpam-4766	296	13	join	join	VERB
ejpam-4766	296	14	and	and	CCONJ
ejpam-4766	296	15	corona	corona	NOUN
ejpam-4766	296	16	of	of	ADP
ejpam-4766	296	17	two	two	NUM
ejpam-4766	296	18	graphs	graph	NOUN
ejpam-4766	296	19	have	have	AUX
ejpam-4766	296	20	been	be	AUX
ejpam-4766	296	21	characterized	characterize	VERB
ejpam-4766	296	22	.	.	PUNCT
ejpam-4766	297	1	this	this	DET
ejpam-4766	297	2	results	result	NOUN
ejpam-4766	297	3	have	have	AUX
ejpam-4766	297	4	been	be	AUX
ejpam-4766	297	5	used	use	VERB
ejpam-4766	297	6	in	in	ADP
ejpam-4766	297	7	determining	determine	VERB
ejpam-4766	297	8	the	the	DET
ejpam-4766	297	9	exact	exact	ADJ
ejpam-4766	297	10	values	value	NOUN
ejpam-4766	297	11	or	or	CCONJ
ejpam-4766	297	12	bounds	bound	NOUN
ejpam-4766	297	13	of	of	ADP
ejpam-4766	297	14	the	the	DET
ejpam-4766	297	15	parameter	parameter	NOUN
ejpam-4766	297	16	of	of	ADP
ejpam-4766	297	17	each	each	PRON
ejpam-4766	297	18	of	of	ADP
ejpam-4766	297	19	these	these	DET
ejpam-4766	297	20	graphs	graph	NOUN
ejpam-4766	297	21	.	.	PUNCT
ejpam-4766	298	1	moreover	moreover	ADV
ejpam-4766	298	2	,	,	PUNCT
ejpam-4766	298	3	realization	realization	NOUN
ejpam-4766	298	4	results	result	NOUN
ejpam-4766	298	5	involving	involve	VERB
ejpam-4766	298	6	connected	connect	VERB
ejpam-4766	298	7	outer	outer	ADJ
ejpam-4766	298	8	-	-	PUNCT
ejpam-4766	298	9	hop	hop	NOUN
ejpam-4766	298	10	independent	independent	ADJ
ejpam-4766	298	11	domination	domination	NOUN
ejpam-4766	298	12	have	have	AUX
ejpam-4766	298	13	been	be	AUX
ejpam-4766	298	14	presented	present	VERB
ejpam-4766	298	15	and	and	CCONJ
ejpam-4766	298	16	its	its	PRON
ejpam-4766	298	17	relationships	relationship	NOUN
ejpam-4766	298	18	with	with	ADP
ejpam-4766	298	19	other	other	ADJ
ejpam-4766	298	20	known	know	VERB
ejpam-4766	298	21	parameters	parameter	NOUN
ejpam-4766	298	22	have	have	AUX
ejpam-4766	298	23	been	be	AUX
ejpam-4766	298	24	determined	determine	VERB
ejpam-4766	298	25	.	.	PUNCT
ejpam-4766	299	1	interested	interested	ADJ
ejpam-4766	299	2	researchers	researcher	NOUN
ejpam-4766	299	3	may	may	AUX
ejpam-4766	299	4	study	study	VERB
ejpam-4766	299	5	this	this	DET
ejpam-4766	299	6	concept	concept	NOUN
ejpam-4766	299	7	in	in	ADP
ejpam-4766	299	8	some	some	DET
ejpam-4766	299	9	product	product	NOUN
ejpam-4766	299	10	of	of	ADP
ejpam-4766	299	11	graphs	graph	NOUN
ejpam-4766	299	12	which	which	PRON
ejpam-4766	299	13	were	be	AUX
ejpam-4766	299	14	not	not	PART
ejpam-4766	299	15	considered	consider	VERB
ejpam-4766	299	16	in	in	ADP
ejpam-4766	299	17	this	this	DET
ejpam-4766	299	18	paper	paper	NOUN
ejpam-4766	299	19	.	.	PUNCT
ejpam-4766	300	1	furthermore	furthermore	ADV
ejpam-4766	300	2	,	,	PUNCT
ejpam-4766	300	3	they	they	PRON
ejpam-4766	300	4	may	may	AUX
ejpam-4766	300	5	consider	consider	VERB
ejpam-4766	300	6	and	and	CCONJ
ejpam-4766	300	7	study	study	VERB
ejpam-4766	300	8	its	its	PRON
ejpam-4766	300	9	bounds	bound	NOUN
ejpam-4766	300	10	with	with	ADP
ejpam-4766	300	11	respect	respect	NOUN
ejpam-4766	300	12	to	to	ADP
ejpam-4766	300	13	the	the	DET
ejpam-4766	300	14	other	other	ADJ
ejpam-4766	300	15	known	know	VERB
ejpam-4766	300	16	parameters	parameter	NOUN
ejpam-4766	300	17	in	in	ADP
ejpam-4766	300	18	graph	graph	NOUN
ejpam-4766	300	19	theory	theory	NOUN
ejpam-4766	300	20	.	.	PUNCT
ejpam-4766	301	1	references	reference	NOUN
ejpam-4766	301	2	1828	1828	NUM
ejpam-4766	301	3	acknowledgements	acknowledgement	NOUN
ejpam-4766	301	4	the	the	DET
ejpam-4766	301	5	authors	author	NOUN
ejpam-4766	301	6	would	would	AUX
ejpam-4766	301	7	like	like	VERB
ejpam-4766	301	8	to	to	PART
ejpam-4766	301	9	thank	thank	VERB
ejpam-4766	301	10	the	the	DET
ejpam-4766	301	11	referees	referee	NOUN
ejpam-4766	301	12	for	for	ADP
ejpam-4766	301	13	their	their	PRON
ejpam-4766	301	14	invaluable	invaluable	ADJ
ejpam-4766	301	15	comments	comment	NOUN
ejpam-4766	301	16	and	and	CCONJ
ejpam-4766	301	17	suggestions	suggestion	NOUN
ejpam-4766	301	18	that	that	PRON
ejpam-4766	301	19	led	lead	VERB
ejpam-4766	301	20	to	to	ADP
ejpam-4766	301	21	the	the	DET
ejpam-4766	301	22	improvement	improvement	NOUN
ejpam-4766	301	23	of	of	ADP
ejpam-4766	301	24	the	the	DET
ejpam-4766	301	25	paper	paper	NOUN
ejpam-4766	301	26	.	.	PUNCT
ejpam-4766	302	1	also	also	ADV
ejpam-4766	302	2	,	,	PUNCT
ejpam-4766	302	3	the	the	DET
ejpam-4766	302	4	authors	author	NOUN
ejpam-4766	302	5	would	would	AUX
ejpam-4766	302	6	like	like	VERB
ejpam-4766	302	7	to	to	PART
ejpam-4766	302	8	thank	thank	VERB
ejpam-4766	302	9	mindanao	mindanao	PROPN
ejpam-4766	302	10	state	state	PROPN
ejpam-4766	302	11	university	university	PROPN
ejpam-4766	302	12	tawi	tawi	PROPN
ejpam-4766	302	13	-	-	PUNCT
ejpam-4766	302	14	tawi	tawi	PROPN
ejpam-4766	302	15	college	college	PROPN
ejpam-4766	302	16	of	of	ADP
ejpam-4766	302	17	technology	technology	NOUN
ejpam-4766	302	18	and	and	CCONJ
ejpam-4766	302	19	oceanography	oceanography	NOUN
ejpam-4766	302	20	for	for	ADP
ejpam-4766	302	21	funding	fund	VERB
ejpam-4766	302	22	this	this	DET
ejpam-4766	302	23	research	research	NOUN
ejpam-4766	302	24	.	.	PUNCT
ejpam-4766	303	1	references	reference	NOUN
ejpam-4766	303	2	[	[	X
ejpam-4766	303	3	1	1	NUM
ejpam-4766	303	4	]	]	X
ejpam-4766	303	5	c.e	c.e	PROPN
ejpam-4766	303	6	.	.	PROPN
ejpam-4766	303	7	adame	adame	PROPN
ejpam-4766	303	8	and	and	CCONJ
ejpam-4766	303	9	c.l	c.l	PROPN
ejpam-4766	303	10	.	.	PROPN
ejpam-4766	303	11	garita	garita	PROPN
ejpam-4766	303	12	.	.	PUNCT
ejpam-4766	304	1	total	total	ADJ
ejpam-4766	304	2	domination	domination	NOUN
ejpam-4766	304	3	on	on	ADP
ejpam-4766	304	4	some	some	DET
ejpam-4766	304	5	graph	graph	NOUN
ejpam-4766	304	6	operators	operator	NOUN
ejpam-4766	304	7	.	.	PUNCT
ejpam-4766	305	1	mathematics	mathematic	NOUN
ejpam-4766	305	2	,	,	PUNCT
ejpam-4766	305	3	9:1–9	9:1–9	NUM
ejpam-4766	305	4	,	,	PUNCT
ejpam-4766	305	5	2021	2021	NUM
ejpam-4766	305	6	.	.	PUNCT
ejpam-4766	306	1	[	[	X
ejpam-4766	306	2	2	2	NUM
ejpam-4766	306	3	]	]	X
ejpam-4766	306	4	r.c	r.c	PROPN
ejpam-4766	306	5	.	.	PROPN
ejpam-4766	306	6	brigham	brigham	PROPN
ejpam-4766	306	7	,	,	PUNCT
ejpam-4766	306	8	orlando	orlando	PROPN
ejpam-4766	306	9	g.	g.	PROPN
ejpam-4766	306	10	chartrand	chartrand	PROPN
ejpam-4766	306	11	,	,	PUNCT
ejpam-4766	306	12	r.d	r.d	PROPN
ejpam-4766	306	13	.	.	PROPN
ejpam-4766	306	14	dutton	dutton	PROPN
ejpam-4766	306	15	,	,	PUNCT
ejpam-4766	306	16	and	and	CCONJ
ejpam-4766	306	17	p.	p.	PROPN
ejpam-4766	306	18	chang	chang	PROPN
ejpam-4766	306	19	.	.	PUNCT
ejpam-4766	307	1	resolving	resolve	VERB
ejpam-4766	307	2	domination	domination	NOUN
ejpam-4766	307	3	in	in	ADP
ejpam-4766	307	4	graphs	graph	NOUN
ejpam-4766	307	5	.	.	PUNCT
ejpam-4766	308	1	mathematica	mathematica	PROPN
ejpam-4766	308	2	bohemica	bohemica	PROPN
ejpam-4766	308	3	.	.	PUNCT
ejpam-4766	308	4	,	,	PUNCT
ejpam-4766	308	5	25(1):25–36	25(1):25–36	NUM
ejpam-4766	308	6	,	,	PUNCT
ejpam-4766	308	7	2003	2003	NUM
ejpam-4766	308	8	.	.	PUNCT
ejpam-4766	309	1	[	[	X
ejpam-4766	309	2	3	3	X
ejpam-4766	309	3	]	]	X
ejpam-4766	309	4	b.	b.	PROPN
ejpam-4766	309	5	gayathri	gayathri	PROPN
ejpam-4766	309	6	and	and	CCONJ
ejpam-4766	309	7	s.	s.	PROPN
ejpam-4766	309	8	kaspar	kaspar	PROPN
ejpam-4766	309	9	.	.	PUNCT
ejpam-4766	310	1	connected	connect	VERB
ejpam-4766	310	2	co	co	ADJ
ejpam-4766	310	3	-	-	ADJ
ejpam-4766	310	4	independent	independent	ADJ
ejpam-4766	310	5	domination	domination	NOUN
ejpam-4766	310	6	of	of	ADP
ejpam-4766	310	7	a	a	DET
ejpam-4766	310	8	graph	graph	NOUN
ejpam-4766	310	9	.	.	PUNCT
ejpam-4766	311	1	int	int	NOUN
ejpam-4766	311	2	.	.	PUNCT
ejpam-4766	312	1	j.	j.	PROPN
ejpam-4766	312	2	contemp	contemp	PROPN
ejpam-4766	312	3	.	.	PUNCT
ejpam-4766	313	1	math	math	NOUN
ejpam-4766	313	2	.	.	PUNCT
ejpam-4766	314	1	sciences	science	NOUN
ejpam-4766	314	2	,	,	PUNCT
ejpam-4766	314	3	,	,	PUNCT
ejpam-4766	314	4	9(6):423–429	9(6):423–429	NUM
ejpam-4766	314	5	,	,	PUNCT
ejpam-4766	314	6	2011	2011	NUM
ejpam-4766	314	7	.	.	PUNCT
ejpam-4766	315	1	[	[	X
ejpam-4766	315	2	4	4	X
ejpam-4766	315	3	]	]	PUNCT
ejpam-4766	315	4	j.	j.	PROPN
ejpam-4766	315	5	hassan	hassan	PROPN
ejpam-4766	315	6	and	and	CCONJ
ejpam-4766	315	7	s.	s.	PROPN
ejpam-4766	315	8	canoy	canoy	PROPN
ejpam-4766	315	9	jr	jr	PROPN
ejpam-4766	315	10	.	.	PUNCT
ejpam-4766	316	1	grundy	grundy	PROPN
ejpam-4766	316	2	hop	hop	PROPN
ejpam-4766	316	3	domination	domination	PROPN
ejpam-4766	316	4	in	in	ADP
ejpam-4766	316	5	graphs	graph	NOUN
ejpam-4766	316	6	.	.	PUNCT
ejpam-4766	317	1	eur	eur	PROPN
ejpam-4766	317	2	.	.	PUNCT
ejpam-4766	318	1	j.	j.	PROPN
ejpam-4766	318	2	pure	pure	PROPN
ejpam-4766	318	3	appl	appl	PROPN
ejpam-4766	318	4	.	.	PUNCT
ejpam-4766	318	5	math	math	PROPN
ejpam-4766	318	6	.	.	PUNCT
ejpam-4766	318	7	,	,	PUNCT
ejpam-4766	318	8	15(4):1623–1636	15(4):1623–1636	NUM
ejpam-4766	318	9	,	,	PUNCT
ejpam-4766	318	10	2022	2022	NUM
ejpam-4766	318	11	.	.	PUNCT
ejpam-4766	319	1	[	[	X
ejpam-4766	319	2	5	5	X
ejpam-4766	319	3	]	]	PUNCT
ejpam-4766	319	4	j.	j.	PROPN
ejpam-4766	319	5	hassan	hassan	PROPN
ejpam-4766	319	6	and	and	CCONJ
ejpam-4766	319	7	s.	s.	PROPN
ejpam-4766	319	8	canoy	canoy	PROPN
ejpam-4766	319	9	jr	jr	PROPN
ejpam-4766	319	10	.	.	PROPN
ejpam-4766	319	11	hop	hop	PROPN
ejpam-4766	319	12	independent	independent	ADJ
ejpam-4766	319	13	hop	hop	NOUN
ejpam-4766	319	14	domination	domination	NOUN
ejpam-4766	319	15	in	in	ADP
ejpam-4766	319	16	graphs	graph	NOUN
ejpam-4766	319	17	.	.	PUNCT
ejpam-4766	320	1	eur	eur	PROPN
ejpam-4766	320	2	.	.	PUNCT
ejpam-4766	321	1	j.	j.	PROPN
ejpam-4766	321	2	pure	pure	PROPN
ejpam-4766	321	3	appl	appl	PROPN
ejpam-4766	321	4	.	.	PUNCT
ejpam-4766	321	5	math	math	PROPN
ejpam-4766	321	6	.	.	PUNCT
ejpam-4766	321	7	,	,	PUNCT
ejpam-4766	321	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-4766	321	9	,	,	PUNCT
ejpam-4766	321	10	2022	2022	NUM
ejpam-4766	321	11	.	.	PUNCT
ejpam-4766	322	1	[	[	X
ejpam-4766	322	2	6	6	NUM
ejpam-4766	322	3	]	]	PUNCT
ejpam-4766	322	4	j.	j.	PROPN
ejpam-4766	322	5	hassan	hassan	PROPN
ejpam-4766	322	6	and	and	CCONJ
ejpam-4766	322	7	s.	s.	PROPN
ejpam-4766	322	8	canoy	canoy	PROPN
ejpam-4766	322	9	jr	jr	PROPN
ejpam-4766	322	10	.	.	PROPN
ejpam-4766	322	11	connected	connect	VERB
ejpam-4766	322	12	grundy	grundy	PROPN
ejpam-4766	322	13	hop	hop	NOUN
ejpam-4766	322	14	dominating	dominate	VERB
ejpam-4766	322	15	sequences	sequence	NOUN
ejpam-4766	322	16	in	in	ADP
ejpam-4766	322	17	graphs	graph	NOUN
ejpam-4766	322	18	.	.	PUNCT
ejpam-4766	323	1	eur	eur	PROPN
ejpam-4766	323	2	.	.	PUNCT
ejpam-4766	324	1	j.	j.	PROPN
ejpam-4766	324	2	pure	pure	PROPN
ejpam-4766	324	3	appl	appl	PROPN
ejpam-4766	324	4	.	.	PUNCT
ejpam-4766	324	5	math	math	PROPN
ejpam-4766	324	6	.	.	PUNCT
ejpam-4766	324	7	,	,	PUNCT
ejpam-4766	325	1	16(2):1212–1227	16(2):1212–1227	NUM
ejpam-4766	325	2	,	,	PUNCT
ejpam-4766	325	3	2023	2023	NUM
ejpam-4766	325	4	.	.	PUNCT
ejpam-4766	326	1	[	[	X
ejpam-4766	326	2	7	7	X
ejpam-4766	326	3	]	]	PUNCT
ejpam-4766	326	4	j.	j.	PROPN
ejpam-4766	326	5	hassan	hassan	PROPN
ejpam-4766	326	6	,	,	PUNCT
ejpam-4766	326	7	s.	s.	PROPN
ejpam-4766	326	8	canoy	canoy	PROPN
ejpam-4766	326	9	jr	jr	PROPN
ejpam-4766	326	10	,	,	PUNCT
ejpam-4766	326	11	and	and	CCONJ
ejpam-4766	326	12	a.	a.	PROPN
ejpam-4766	326	13	aradais	aradais	PROPN
ejpam-4766	326	14	.	.	PUNCT
ejpam-4766	327	1	hop	hop	PROPN
ejpam-4766	327	2	independent	independent	ADJ
ejpam-4766	327	3	sets	set	NOUN
ejpam-4766	327	4	in	in	ADP
ejpam-4766	327	5	graphs	graph	NOUN
ejpam-4766	327	6	.	.	PUNCT
ejpam-4766	328	1	eur	eur	PROPN
ejpam-4766	328	2	.	.	PUNCT
ejpam-4766	329	1	j.	j.	PROPN
ejpam-4766	329	2	pure	pure	PROPN
ejpam-4766	329	3	appl	appl	PROPN
ejpam-4766	329	4	.	.	PUNCT
ejpam-4766	329	5	math	math	PROPN
ejpam-4766	329	6	.	.	PUNCT
ejpam-4766	329	7	,	,	PUNCT
ejpam-4766	329	8	15(2):467–477	15(2):467–477	PROPN
ejpam-4766	329	9	,	,	PUNCT
ejpam-4766	329	10	2022	2022	NUM
ejpam-4766	329	11	.	.	PUNCT
ejpam-4766	330	1	[	[	X
ejpam-4766	330	2	8	8	X
ejpam-4766	330	3	]	]	X
ejpam-4766	330	4	j.	j.	PROPN
ejpam-4766	330	5	hassan	hassan	PROPN
ejpam-4766	330	6	,	,	PUNCT
ejpam-4766	330	7	s.	s.	PROPN
ejpam-4766	330	8	canoy	canoy	PROPN
ejpam-4766	330	9	jr	jr	PROPN
ejpam-4766	330	10	.	.	PROPN
ejpam-4766	330	11	,	,	PUNCT
ejpam-4766	330	12	and	and	CCONJ
ejpam-4766	330	13	chrisley	chrisley	PROPN
ejpam-4766	330	14	jade	jade	NOUN
ejpam-4766	330	15	saromines	saromine	NOUN
ejpam-4766	330	16	.	.	PUNCT
ejpam-4766	331	1	convex	convex	VERB
ejpam-4766	331	2	hop	hop	NOUN
ejpam-4766	331	3	domination	domination	NOUN
ejpam-4766	331	4	in	in	ADP
ejpam-4766	331	5	graphs	graph	NOUN
ejpam-4766	331	6	.	.	PUNCT
ejpam-4766	332	1	eur	eur	PROPN
ejpam-4766	332	2	.	.	PUNCT
ejpam-4766	333	1	j.	j.	PROPN
ejpam-4766	333	2	pure	pure	PROPN
ejpam-4766	333	3	appl	appl	PROPN
ejpam-4766	333	4	.	.	PUNCT
ejpam-4766	333	5	math	math	PROPN
ejpam-4766	333	6	.	.	PUNCT
ejpam-4766	333	7	,	,	PUNCT
ejpam-4766	333	8	16(1):319–335	16(1):319–335	NOUN
ejpam-4766	333	9	,	,	PUNCT
ejpam-4766	333	10	2023	2023	NUM
ejpam-4766	333	11	.	.	PUNCT
ejpam-4766	334	1	[	[	X
ejpam-4766	334	2	9	9	NUM
ejpam-4766	334	3	]	]	PUNCT
ejpam-4766	334	4	s.	s.	PROPN
ejpam-4766	334	5	canoy	canoy	PROPN
ejpam-4766	334	6	jr	jr	PROPN
ejpam-4766	334	7	.	.	PROPN
ejpam-4766	334	8	and	and	CCONJ
ejpam-4766	334	9	s.	s.	PROPN
ejpam-4766	334	10	arriola	arriola	PROPN
ejpam-4766	334	11	.	.	PUNCT
ejpam-4766	335	1	(	(	PUNCT
ejpam-4766	335	2	1	1	NUM
ejpam-4766	335	3	,	,	PUNCT
ejpam-4766	335	4	2)*-domination	2)*-domination	NUM
ejpam-4766	335	5	in	in	ADP
ejpam-4766	335	6	graphs	graph	NOUN
ejpam-4766	335	7	.	.	PUNCT
ejpam-4766	336	1	advances	advance	NOUN
ejpam-4766	336	2	and	and	CCONJ
ejpam-4766	336	3	application	application	NOUN
ejpam-4766	336	4	in	in	ADP
ejpam-4766	336	5	discrete	discrete	ADJ
ejpam-4766	336	6	mathematics	mathematic	NOUN
ejpam-4766	336	7	,	,	PUNCT
ejpam-4766	336	8	18(2):179–190	18(2):179–190	NUM
ejpam-4766	336	9	,	,	PUNCT
ejpam-4766	336	10	2017	2017	NUM
ejpam-4766	336	11	.	.	PUNCT
ejpam-4766	337	1	[	[	X
ejpam-4766	337	2	10	10	NUM
ejpam-4766	337	3	]	]	X
ejpam-4766	337	4	s.	s.	PROPN
ejpam-4766	337	5	canoy	canoy	PROPN
ejpam-4766	337	6	jr	jr	PROPN
ejpam-4766	337	7	and	and	CCONJ
ejpam-4766	337	8	j.	j.	PROPN
ejpam-4766	337	9	hassan	hassan	PROPN
ejpam-4766	337	10	.	.	PUNCT
ejpam-4766	338	1	weakly	weakly	ADJ
ejpam-4766	338	2	convex	convex	VERB
ejpam-4766	338	3	hop	hop	NOUN
ejpam-4766	338	4	dominating	dominating	NOUN
ejpam-4766	338	5	sets	set	NOUN
ejpam-4766	338	6	in	in	ADP
ejpam-4766	338	7	graphs	graph	NOUN
ejpam-4766	338	8	.	.	PUNCT
ejpam-4766	339	1	eur	eur	PROPN
ejpam-4766	339	2	.	.	PUNCT
ejpam-4766	340	1	j.	j.	PROPN
ejpam-4766	340	2	pure	pure	PROPN
ejpam-4766	340	3	appl	appl	PROPN
ejpam-4766	340	4	.	.	PUNCT
ejpam-4766	340	5	math	math	PROPN
ejpam-4766	340	6	.	.	PUNCT
ejpam-4766	340	7	,	,	PUNCT
ejpam-4766	340	8	16(2):1196–1211	16(2):1196–1211	NUM
ejpam-4766	340	9	,	,	PUNCT
ejpam-4766	340	10	2023	2023	NUM
ejpam-4766	340	11	.	.	PUNCT
ejpam-4766	341	1	[	[	X
ejpam-4766	341	2	11	11	NUM
ejpam-4766	341	3	]	]	PUNCT
ejpam-4766	341	4	m.	m.	NOUN
ejpam-4766	341	5	livingston	livingston	PROPN
ejpam-4766	341	6	and	and	CCONJ
ejpam-4766	341	7	q.f	q.f	PROPN
ejpam-4766	341	8	stout	stout	PROPN
ejpam-4766	341	9	.	.	PUNCT
ejpam-4766	342	1	perfect	perfect	ADJ
ejpam-4766	342	2	dominating	dominating	NOUN
ejpam-4766	342	3	sets	set	NOUN
ejpam-4766	342	4	,	,	PUNCT
ejpam-4766	342	5	.	.	PUNCT
ejpam-4766	343	1	in	in	ADP
ejpam-4766	343	2	congressus	congressus	PROPN
ejpam-4766	343	3	numerantum	numerantum	PROPN
ejpam-4766	343	4	.	.	PUNCT
ejpam-4766	343	5	,	,	PUNCT
ejpam-4766	343	6	79:187–203	79:187–203	NUM
ejpam-4766	343	7	,	,	PUNCT
ejpam-4766	343	8	1990	1990	NUM
ejpam-4766	343	9	.	.	PUNCT
ejpam-4766	344	1	[	[	X
ejpam-4766	344	2	12	12	NUM
ejpam-4766	344	3	]	]	X
ejpam-4766	344	4	e.	e.	PROPN
ejpam-4766	344	5	sampathkumar	sampathkumar	PROPN
ejpam-4766	344	6	and	and	CCONJ
ejpam-4766	344	7	h.b	h.b	PROPN
ejpam-4766	344	8	.	.	PROPN
ejpam-4766	344	9	walikar	walikar	PROPN
ejpam-4766	344	10	.	.	PUNCT
ejpam-4766	345	1	the	the	DET
ejpam-4766	345	2	connected	connected	ADJ
ejpam-4766	345	3	domination	domination	NOUN
ejpam-4766	345	4	number	number	NOUN
ejpam-4766	345	5	of	of	ADP
ejpam-4766	345	6	a	a	DET
ejpam-4766	345	7	graph	graph	NOUN
ejpam-4766	345	8	.	.	PUNCT
ejpam-4766	345	9	jour	jour	PROPN
ejpam-4766	345	10	.	.	PUNCT
ejpam-4766	345	11	math	math	PROPN
ejpam-4766	345	12	.	.	PUNCT
ejpam-4766	346	1	phy	phy	PROPN
ejpam-4766	346	2	.	.	PUNCT
ejpam-4766	347	1	sci	sci	PROPN
ejpam-4766	347	2	.	.	PROPN
ejpam-4766	347	3	,	,	PUNCT
ejpam-4766	347	4	13(6	13(6	PROPN
ejpam-4766	347	5	)	)	PUNCT
ejpam-4766	347	6	,	,	PUNCT
ejpam-4766	347	7	1979	1979	NUM
ejpam-4766	347	8	.	.	PUNCT
ejpam-4766	348	1	[	[	X
ejpam-4766	348	2	13	13	NUM
ejpam-4766	348	3	]	]	PUNCT
ejpam-4766	348	4	a.	a.	NOUN
ejpam-4766	348	5	sugumaran	sugumaran	NOUN
ejpam-4766	348	6	and	and	CCONJ
ejpam-4766	348	7	e.	e.	PROPN
ejpam-4766	348	8	jayachandran	jayachandran	PROPN
ejpam-4766	348	9	.	.	PUNCT
ejpam-4766	349	1	domination	domination	NOUN
ejpam-4766	349	2	number	number	NOUN
ejpam-4766	349	3	of	of	ADP
ejpam-4766	349	4	some	some	DET
ejpam-4766	349	5	graphs	graph	NOUN
ejpam-4766	349	6	.	.	PUNCT
ejpam-4766	350	1	int’l	int’l	NUM
ejpam-4766	350	2	.	.	PUNCT
ejpam-4766	350	3	jour	jour	AUX
ejpam-4766	350	4	.	.	PUNCT
ejpam-4766	350	5	scientific	scientific	ADJ
ejpam-4766	350	6	.	.	PUNCT
ejpam-4766	351	1	dev’t	dev’t	NOUN
ejpam-4766	351	2	and	and	CCONJ
ejpam-4766	351	3	research	research	NOUN
ejpam-4766	351	4	.	.	PUNCT
ejpam-4766	351	5	,	,	PUNCT
ejpam-4766	351	6	11(3):386–391	11(3):386–391	NUM
ejpam-4766	351	7	,	,	PUNCT
ejpam-4766	351	8	2018	2018	NUM
ejpam-4766	351	9	.	.	PUNCT
ejpam-4766	352	1	references	reference	NOUN
ejpam-4766	352	2	1829	1829	NUM
ejpam-4766	353	1	[	[	X
ejpam-4766	353	2	14	14	NUM
ejpam-4766	353	3	]	]	X
ejpam-4766	353	4	s.k	s.k	PROPN
ejpam-4766	353	5	.	.	PROPN
ejpam-4766	353	6	vaidya	vaidya	PROPN
ejpam-4766	353	7	and	and	CCONJ
ejpam-4766	353	8	s.h	s.h	PROPN
ejpam-4766	353	9	.	.	PROPN
ejpam-4766	353	10	karkar	karkar	PROPN
ejpam-4766	353	11	.	.	PUNCT
ejpam-4766	354	1	on	on	ADP
ejpam-4766	354	2	the	the	DET
ejpam-4766	354	3	strong	strong	ADJ
ejpam-4766	354	4	domination	domination	NOUN
ejpam-4766	354	5	number	number	NOUN
ejpam-4766	354	6	of	of	ADP
ejpam-4766	354	7	graphs	graph	NOUN
ejpam-4766	354	8	.	.	PUNCT
ejpam-4766	355	1	applications	application	NOUN
ejpam-4766	355	2	and	and	CCONJ
ejpam-4766	355	3	applied	apply	VERB
ejpam-4766	355	4	mathematics	mathematic	NOUN
ejpam-4766	355	5	(	(	PUNCT
ejpam-4766	355	6	aam	aam	PROPN
ejpam-4766	355	7	)	)	PUNCT
ejpam-4766	355	8	.	.	PUNCT
ejpam-4766	355	9	,	,	PUNCT
ejpam-4766	355	10	12(1):604–612	12(1):604–612	PROPN
ejpam-4766	355	11	,	,	PUNCT
ejpam-4766	355	12	2017	2017	NUM
ejpam-4766	355	13	.	.	PUNCT