id	sid	tid	token	lemma	pos
ejpam-4684	1	1	european	european	PROPN
ejpam-4684	1	2	journal	journal	PROPN
ejpam-4684	1	3	of	of	ADP
ejpam-4684	1	4	pure	pure	ADJ
ejpam-4684	1	5	and	and	CCONJ
ejpam-4684	1	6	applied	apply	VERB
ejpam-4684	1	7	mathematics	mathematic	NOUN
ejpam-4684	1	8	vol	vol	NOUN
ejpam-4684	1	9	.	.	PUNCT
ejpam-4684	2	1	16	16	NUM
ejpam-4684	2	2	,	,	PUNCT
ejpam-4684	2	3	no	no	INTJ
ejpam-4684	2	4	.	.	NOUN
ejpam-4684	2	5	3	3	NUM
ejpam-4684	2	6	,	,	PUNCT
ejpam-4684	2	7	2023	2023	NUM
ejpam-4684	2	8	,	,	PUNCT
ejpam-4684	2	9	1848	1848	NUM
ejpam-4684	2	10	-	-	SYM
ejpam-4684	2	11	1861	1861	NUM
ejpam-4684	2	12	issn	issn	PROPN
ejpam-4684	2	13	1307	1307	NUM
ejpam-4684	2	14	-	-	SYM
ejpam-4684	2	15	5543	5543	NUM
ejpam-4684	2	16	–	–	PUNCT
ejpam-4684	2	17	ejpam.com	ejpam.com	X
ejpam-4684	2	18	published	publish	VERB
ejpam-4684	2	19	by	by	ADP
ejpam-4684	2	20	new	new	PROPN
ejpam-4684	2	21	york	york	PROPN
ejpam-4684	2	22	business	business	PROPN
ejpam-4684	2	23	global	global	ADJ
ejpam-4684	2	24	some	some	DET
ejpam-4684	2	25	properties	property	NOUN
ejpam-4684	2	26	and	and	CCONJ
ejpam-4684	2	27	realization	realization	NOUN
ejpam-4684	2	28	problems	problem	NOUN
ejpam-4684	2	29	involving	involve	VERB
ejpam-4684	2	30	connected	connected	ADJ
ejpam-4684	2	31	outer	outer	ADJ
ejpam-4684	2	32	-	-	PUNCT
ejpam-4684	2	33	hop	hop	NOUN
ejpam-4684	2	34	independent	independent	ADJ
ejpam-4684	2	35	hop	hop	NOUN
ejpam-4684	2	36	domination	domination	NOUN
ejpam-4684	2	37	in	in	ADP
ejpam-4684	2	38	graphs	graph	NOUN
ejpam-4684	2	39	javier	javier	PROPN
ejpam-4684	2	40	a.	a.	PROPN
ejpam-4684	2	41	hassan1,∗	hassan1,∗	PROPN
ejpam-4684	2	42	,	,	PUNCT
ejpam-4684	2	43	abdurajan	abdurajan	PROPN
ejpam-4684	2	44	b.	b.	PROPN
ejpam-4684	2	45	lintasan1	lintasan1	PROPN
ejpam-4684	2	46	,	,	PUNCT
ejpam-4684	2	47	nurijam	nurijam	PROPN
ejpam-4684	2	48	hanna	hanna	PROPN
ejpam-4684	2	49	m.	m.	PROPN
ejpam-4684	2	50	mohammad1	mohammad1	NOUN
ejpam-4684	2	51	1	1	NUM
ejpam-4684	2	52	mathematics	mathematic	NOUN
ejpam-4684	2	53	and	and	CCONJ
ejpam-4684	2	54	sciences	sciences	PROPN
ejpam-4684	2	55	department	department	PROPN
ejpam-4684	2	56	,	,	PUNCT
ejpam-4684	2	57	college	college	NOUN
ejpam-4684	2	58	of	of	ADP
ejpam-4684	2	59	arts	art	NOUN
ejpam-4684	2	60	and	and	CCONJ
ejpam-4684	2	61	sciences	science	NOUN
ejpam-4684	2	62	,	,	PUNCT
ejpam-4684	2	63	msu	msu	PROPN
ejpam-4684	2	64	tawi	tawi	PROPN
ejpam-4684	2	65	-	-	PUNCT
ejpam-4684	2	66	tawi	tawi	PROPN
ejpam-4684	2	67	college	college	PROPN
ejpam-4684	2	68	of	of	ADP
ejpam-4684	2	69	technology	technology	NOUN
ejpam-4684	2	70	and	and	CCONJ
ejpam-4684	2	71	oceanography	oceanography	NOUN
ejpam-4684	2	72	,	,	PUNCT
ejpam-4684	2	73	bongao	bongao	NOUN
ejpam-4684	2	74	,	,	PUNCT
ejpam-4684	2	75	tawi	tawi	NOUN
ejpam-4684	2	76	-	-	PUNCT
ejpam-4684	2	77	tawi	tawi	NOUN
ejpam-4684	2	78	,	,	PUNCT
ejpam-4684	2	79	philippines	philippine	NOUN
ejpam-4684	2	80	abstract	abstract	ADJ
ejpam-4684	2	81	.	.	PUNCT
ejpam-4684	3	1	in	in	ADP
ejpam-4684	3	2	this	this	DET
ejpam-4684	3	3	paper	paper	NOUN
ejpam-4684	3	4	,	,	PUNCT
ejpam-4684	3	5	we	we	PRON
ejpam-4684	3	6	construct	construct	VERB
ejpam-4684	3	7	a	a	DET
ejpam-4684	3	8	realization	realization	NOUN
ejpam-4684	3	9	problems	problem	NOUN
ejpam-4684	3	10	involving	involve	VERB
ejpam-4684	3	11	connected	connected	ADJ
ejpam-4684	3	12	outer	outer	ADJ
ejpam-4684	3	13	-	-	PUNCT
ejpam-4684	3	14	hop	hop	NOUN
ejpam-4684	3	15	independent	independent	ADJ
ejpam-4684	3	16	hop	hop	NOUN
ejpam-4684	3	17	domination	domination	NOUN
ejpam-4684	3	18	and	and	CCONJ
ejpam-4684	3	19	we	we	PRON
ejpam-4684	3	20	determine	determine	VERB
ejpam-4684	3	21	its	its	PRON
ejpam-4684	3	22	connections	connection	NOUN
ejpam-4684	3	23	with	with	ADP
ejpam-4684	3	24	other	other	ADJ
ejpam-4684	3	25	known	know	VERB
ejpam-4684	3	26	parameters	parameter	NOUN
ejpam-4684	3	27	in	in	ADP
ejpam-4684	3	28	graph	graph	NOUN
ejpam-4684	3	29	theory	theory	NOUN
ejpam-4684	3	30	.	.	PUNCT
ejpam-4684	4	1	in	in	ADP
ejpam-4684	4	2	particular	particular	ADJ
ejpam-4684	4	3	,	,	PUNCT
ejpam-4684	4	4	given	give	VERB
ejpam-4684	4	5	two	two	NUM
ejpam-4684	4	6	positive	positive	ADJ
ejpam-4684	4	7	integers	integer	NOUN
ejpam-4684	4	8	a	a	PRON
ejpam-4684	4	9	and	and	CCONJ
ejpam-4684	4	10	b	b	NOUN
ejpam-4684	4	11	with	with	ADP
ejpam-4684	4	12	2	2	NUM
ejpam-4684	4	13	≤	≤	NOUN
ejpam-4684	4	14	a	a	DET
ejpam-4684	4	15	≤	≤	NUM
ejpam-4684	4	16	b	b	NOUN
ejpam-4684	4	17	are	be	AUX
ejpam-4684	4	18	realizable	realizable	ADJ
ejpam-4684	4	19	as	as	ADP
ejpam-4684	4	20	the	the	DET
ejpam-4684	4	21	connected	connected	ADJ
ejpam-4684	4	22	hop	hop	NOUN
ejpam-4684	4	23	domination	domination	NOUN
ejpam-4684	4	24	,	,	PUNCT
ejpam-4684	4	25	connected	connected	ADJ
ejpam-4684	4	26	outer	outer	ADJ
ejpam-4684	4	27	-	-	PUNCT
ejpam-4684	4	28	hop	hop	NOUN
ejpam-4684	4	29	independent	independent	ADJ
ejpam-4684	4	30	hop	hop	NOUN
ejpam-4684	4	31	domination	domination	NOUN
ejpam-4684	4	32	,	,	PUNCT
ejpam-4684	4	33	and	and	CCONJ
ejpam-4684	4	34	connected	connected	ADJ
ejpam-4684	4	35	outer	outer	ADJ
ejpam-4684	4	36	-	-	PUNCT
ejpam-4684	4	37	independent	independent	ADJ
ejpam-4684	4	38	hop	hop	NOUN
ejpam-4684	4	39	domination	domination	NOUN
ejpam-4684	4	40	numbers	number	NOUN
ejpam-4684	4	41	,	,	PUNCT
ejpam-4684	4	42	respectively	respectively	ADV
ejpam-4684	4	43	,	,	PUNCT
ejpam-4684	4	44	of	of	ADP
ejpam-4684	4	45	a	a	DET
ejpam-4684	4	46	connected	connected	ADJ
ejpam-4684	4	47	graph	graph	NOUN
ejpam-4684	4	48	.	.	PUNCT
ejpam-4684	5	1	in	in	ADP
ejpam-4684	5	2	addition	addition	NOUN
ejpam-4684	5	3	,	,	PUNCT
ejpam-4684	5	4	we	we	PRON
ejpam-4684	5	5	characterize	characterize	VERB
ejpam-4684	5	6	the	the	DET
ejpam-4684	5	7	connected	connected	ADJ
ejpam-4684	5	8	outer	outer	ADJ
ejpam-4684	5	9	-	-	PUNCT
ejpam-4684	5	10	hop	hop	NOUN
ejpam-4684	5	11	independent	independent	ADJ
ejpam-4684	5	12	hop	hop	NOUN
ejpam-4684	5	13	dominating	dominating	NOUN
ejpam-4684	5	14	sets	set	NOUN
ejpam-4684	5	15	in	in	ADP
ejpam-4684	5	16	some	some	DET
ejpam-4684	5	17	families	family	NOUN
ejpam-4684	5	18	of	of	ADP
ejpam-4684	5	19	graphs	graph	NOUN
ejpam-4684	5	20	,	,	PUNCT
ejpam-4684	5	21	join	join	VERB
ejpam-4684	5	22	and	and	CCONJ
ejpam-4684	5	23	corona	corona	NOUN
ejpam-4684	5	24	of	of	ADP
ejpam-4684	5	25	two	two	NUM
ejpam-4684	5	26	graphs	graph	NOUN
ejpam-4684	5	27	,	,	PUNCT
ejpam-4684	5	28	and	and	CCONJ
ejpam-4684	5	29	we	we	PRON
ejpam-4684	5	30	use	use	VERB
ejpam-4684	5	31	these	these	DET
ejpam-4684	5	32	results	result	NOUN
ejpam-4684	5	33	to	to	PART
ejpam-4684	5	34	derive	derive	VERB
ejpam-4684	5	35	formulas	formula	NOUN
ejpam-4684	5	36	for	for	ADP
ejpam-4684	5	37	the	the	DET
ejpam-4684	5	38	parameters	parameter	NOUN
ejpam-4684	5	39	of	of	ADP
ejpam-4684	5	40	these	these	DET
ejpam-4684	5	41	graphs	graph	NOUN
ejpam-4684	5	42	.	.	PUNCT
ejpam-4684	6	1	2020	2020	NUM
ejpam-4684	6	2	mathematics	mathematic	NOUN
ejpam-4684	6	3	subject	subject	NOUN
ejpam-4684	6	4	classifications	classification	NOUN
ejpam-4684	6	5	:	:	PUNCT
ejpam-4684	6	6	05c69	05c69	X
ejpam-4684	6	7	key	key	ADJ
ejpam-4684	6	8	words	word	NOUN
ejpam-4684	6	9	and	and	CCONJ
ejpam-4684	6	10	phrases	phrase	NOUN
ejpam-4684	6	11	:	:	PUNCT
ejpam-4684	6	12	hop	hop	NOUN
ejpam-4684	6	13	independent	independent	ADJ
ejpam-4684	6	14	set	set	NOUN
ejpam-4684	6	15	,	,	PUNCT
ejpam-4684	6	16	connected	connected	ADJ
ejpam-4684	6	17	outer	outer	ADJ
ejpam-4684	6	18	-	-	PUNCT
ejpam-4684	6	19	hop	hop	NOUN
ejpam-4684	6	20	independent	independent	ADJ
ejpam-4684	6	21	hop	hop	NOUN
ejpam-4684	6	22	dominating	dominating	NOUN
ejpam-4684	6	23	set	set	NOUN
ejpam-4684	6	24	,	,	PUNCT
ejpam-4684	6	25	connected	connected	ADJ
ejpam-4684	6	26	outer	outer	ADJ
ejpam-4684	6	27	-	-	PUNCT
ejpam-4684	6	28	hop	hop	NOUN
ejpam-4684	6	29	independent	independent	ADJ
ejpam-4684	6	30	hop	hop	NOUN
ejpam-4684	6	31	domination	domination	NOUN
ejpam-4684	6	32	number	number	NOUN
ejpam-4684	6	33	1	1	NUM
ejpam-4684	6	34	.	.	PUNCT
ejpam-4684	7	1	introduction	introduction	NOUN
ejpam-4684	7	2	hop	hop	PROPN
ejpam-4684	7	3	domination	domination	NOUN
ejpam-4684	7	4	has	have	AUX
ejpam-4684	7	5	been	be	AUX
ejpam-4684	7	6	one	one	NUM
ejpam-4684	7	7	of	of	ADP
ejpam-4684	7	8	the	the	DET
ejpam-4684	7	9	widely	widely	ADV
ejpam-4684	7	10	studied	study	VERB
ejpam-4684	7	11	topics	topic	NOUN
ejpam-4684	7	12	of	of	ADP
ejpam-4684	7	13	research	research	NOUN
ejpam-4684	7	14	in	in	ADP
ejpam-4684	7	15	graph	graph	NOUN
ejpam-4684	7	16	theory	theory	NOUN
ejpam-4684	7	17	.	.	PUNCT
ejpam-4684	8	1	several	several	ADJ
ejpam-4684	8	2	mathematicians	mathematician	NOUN
ejpam-4684	8	3	have	have	AUX
ejpam-4684	8	4	investigated	investigate	VERB
ejpam-4684	8	5	this	this	DET
ejpam-4684	8	6	concept	concept	NOUN
ejpam-4684	8	7	and	and	CCONJ
ejpam-4684	8	8	introduced	introduce	VERB
ejpam-4684	8	9	variants	variant	NOUN
ejpam-4684	8	10	because	because	SCONJ
ejpam-4684	8	11	of	of	ADP
ejpam-4684	8	12	its	its	PRON
ejpam-4684	8	13	nice	nice	ADJ
ejpam-4684	8	14	application	application	NOUN
ejpam-4684	8	15	to	to	ADP
ejpam-4684	8	16	different	different	ADJ
ejpam-4684	8	17	fields	field	NOUN
ejpam-4684	8	18	and	and	CCONJ
ejpam-4684	8	19	in	in	ADP
ejpam-4684	8	20	networks	network	NOUN
ejpam-4684	8	21	.	.	PUNCT
ejpam-4684	9	1	some	some	DET
ejpam-4684	9	2	newly	newly	ADV
ejpam-4684	9	3	defined	define	VERB
ejpam-4684	9	4	variations	variation	NOUN
ejpam-4684	9	5	are	be	AUX
ejpam-4684	9	6	studied	study	VERB
ejpam-4684	9	7	in	in	ADP
ejpam-4684	9	8	many	many	ADJ
ejpam-4684	9	9	classes	class	NOUN
ejpam-4684	9	10	of	of	ADP
ejpam-4684	9	11	graphs	graph	NOUN
ejpam-4684	9	12	(	(	PUNCT
ejpam-4684	9	13	see	see	VERB
ejpam-4684	9	14	[	[	X
ejpam-4684	9	15	3–5	3–5	NUM
ejpam-4684	9	16	,	,	PUNCT
ejpam-4684	9	17	7–12	7–12	PROPN
ejpam-4684	9	18	,	,	PUNCT
ejpam-4684	9	19	14	14	NUM
ejpam-4684	9	20	]	]	PUNCT
ejpam-4684	9	21	)	)	PUNCT
ejpam-4684	9	22	.	.	PUNCT
ejpam-4684	10	1	in	in	ADP
ejpam-4684	10	2	2021	2021	NUM
ejpam-4684	10	3	,	,	PUNCT
ejpam-4684	10	4	nanding	nande	VERB
ejpam-4684	10	5	et	et	PROPN
ejpam-4684	10	6	al	al	PROPN
ejpam-4684	10	7	.	.	PUNCT
ejpam-4684	11	1	[	[	X
ejpam-4684	11	2	12	12	NUM
ejpam-4684	11	3	]	]	PUNCT
ejpam-4684	11	4	introduced	introduce	VERB
ejpam-4684	11	5	and	and	CCONJ
ejpam-4684	11	6	studied	study	VERB
ejpam-4684	11	7	the	the	DET
ejpam-4684	11	8	concept	concept	NOUN
ejpam-4684	11	9	called	call	VERB
ejpam-4684	11	10	connected	connected	ADJ
ejpam-4684	11	11	outerindependent	outerindependent	ADJ
ejpam-4684	11	12	hop	hop	NOUN
ejpam-4684	11	13	domination	domination	NOUN
ejpam-4684	11	14	in	in	ADP
ejpam-4684	11	15	a	a	DET
ejpam-4684	11	16	graph	graph	NOUN
ejpam-4684	11	17	.	.	PUNCT
ejpam-4684	12	1	they	they	PRON
ejpam-4684	12	2	characterized	characterize	VERB
ejpam-4684	12	3	this	this	DET
ejpam-4684	12	4	newly	newly	ADV
ejpam-4684	12	5	defined	define	VERB
ejpam-4684	12	6	sets	set	NOUN
ejpam-4684	12	7	on	on	ADP
ejpam-4684	12	8	graphs	graph	NOUN
ejpam-4684	12	9	under	under	ADP
ejpam-4684	12	10	some	some	DET
ejpam-4684	12	11	binary	binary	ADJ
ejpam-4684	12	12	operations	operation	NOUN
ejpam-4684	12	13	and	and	CCONJ
ejpam-4684	12	14	obtained	obtain	VERB
ejpam-4684	12	15	some	some	DET
ejpam-4684	12	16	nice	nice	ADJ
ejpam-4684	12	17	formulas	formula	NOUN
ejpam-4684	12	18	and	and	CCONJ
ejpam-4684	12	19	bounds	bound	NOUN
ejpam-4684	12	20	.	.	PUNCT
ejpam-4684	13	1	recently	recently	ADV
ejpam-4684	13	2	,	,	PUNCT
ejpam-4684	13	3	hassan	hassan	PROPN
ejpam-4684	13	4	et	et	PROPN
ejpam-4684	13	5	al	al	PROPN
ejpam-4684	13	6	.	.	PUNCT
ejpam-4684	14	1	[	[	X
ejpam-4684	14	2	6	6	NUM
ejpam-4684	14	3	]	]	PUNCT
ejpam-4684	14	4	introduced	introduce	VERB
ejpam-4684	14	5	the	the	DET
ejpam-4684	14	6	concept	concept	NOUN
ejpam-4684	14	7	of	of	ADP
ejpam-4684	14	8	hop	hop	NOUN
ejpam-4684	14	9	independent	independent	ADJ
ejpam-4684	14	10	set	set	NOUN
ejpam-4684	14	11	in	in	ADP
ejpam-4684	14	12	a	a	DET
ejpam-4684	14	13	graph	graph	NOUN
ejpam-4684	14	14	and	and	CCONJ
ejpam-4684	14	15	defined	define	VERB
ejpam-4684	14	16	the	the	DET
ejpam-4684	14	17	parameter	parameter	NOUN
ejpam-4684	14	18	called	call	VERB
ejpam-4684	14	19	hop	hop	PROPN
ejpam-4684	14	20	independence	independence	NOUN
ejpam-4684	14	21	number	number	NOUN
ejpam-4684	14	22	.	.	PUNCT
ejpam-4684	15	1	the	the	DET
ejpam-4684	15	2	authors	author	NOUN
ejpam-4684	15	3	have	have	AUX
ejpam-4684	15	4	shown	show	VERB
ejpam-4684	15	5	that	that	SCONJ
ejpam-4684	15	6	the	the	DET
ejpam-4684	15	7	hop	hop	NOUN
ejpam-4684	15	8	independence	independence	NOUN
ejpam-4684	15	9	number	number	NOUN
ejpam-4684	15	10	is	be	AUX
ejpam-4684	15	11	incomparable	incomparable	ADJ
ejpam-4684	15	12	with	with	ADP
ejpam-4684	15	13	the	the	DET
ejpam-4684	15	14	standard	standard	ADJ
ejpam-4684	15	15	independence	independence	NOUN
ejpam-4684	15	16	number	number	NOUN
ejpam-4684	15	17	∗corresponding	∗corresponde	VERB
ejpam-4684	15	18	author	author	NOUN
ejpam-4684	15	19	.	.	PUNCT
ejpam-4684	16	1	doi	doi	NOUN
ejpam-4684	16	2	:	:	PUNCT
ejpam-4684	16	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4684	https://doi.org/10.29020/nybg.ejpam.v16i3.4684	PRON
ejpam-4684	16	4	email	email	NOUN
ejpam-4684	16	5	addresses	address	NOUN
ejpam-4684	16	6	:	:	PUNCT
ejpam-4684	16	7	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-4684	16	8	(	(	PUNCT
ejpam-4684	16	9	j.	j.	PROPN
ejpam-4684	16	10	hassan	hassan	PROPN
ejpam-4684	16	11	)	)	PUNCT
ejpam-4684	16	12	,	,	PUNCT
ejpam-4684	16	13	abdurajanlintasan@msutawi-tawi.edu.ph	abdurajanlintasan@msutawi-tawi.edu.ph	PROPN
ejpam-4684	16	14	(	(	PUNCT
ejpam-4684	16	15	a.	a.	NOUN
ejpam-4684	16	16	lintasan	lintasan	PROPN
ejpam-4684	16	17	)	)	PUNCT
ejpam-4684	16	18	,	,	PUNCT
ejpam-4684	16	19	hannamohammad@msutawi-tawi.edu.ph	hannamohammad@msutawi-tawi.edu.ph	PROPN
ejpam-4684	16	20	(	(	PUNCT
ejpam-4684	16	21	n.h	n.h	PROPN
ejpam-4684	16	22	.	.	PUNCT
ejpam-4684	17	1	mohammad	mohammad	PROPN
ejpam-4684	17	2	)	)	PUNCT
ejpam-4684	17	3	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4684	17	4	1848	1848	NUM
ejpam-4684	18	1	©	©	ADP
ejpam-4684	18	2	2023	2023	NUM
ejpam-4684	18	3	ejpam	ejpam	NOUN
ejpam-4684	18	4	all	all	DET
ejpam-4684	18	5	rights	right	NOUN
ejpam-4684	18	6	reserved	reserve	VERB
ejpam-4684	18	7	.	.	PUNCT
ejpam-4684	19	1	j.	j.	PROPN
ejpam-4684	19	2	hassan	hassan	PROPN
ejpam-4684	19	3	,	,	PUNCT
ejpam-4684	19	4	a.	a.	PROPN
ejpam-4684	19	5	lintasan	lintasan	NOUN
ejpam-4684	19	6	,	,	PUNCT
ejpam-4684	19	7	n.	n.	PROPN
ejpam-4684	19	8	h.	h.	PROPN
ejpam-4684	19	9	mohammad	mohammad	PROPN
ejpam-4684	19	10	/	/	PUNCT
ejpam-4684	19	11	eur	eur	PROPN
ejpam-4684	19	12	.	.	PUNCT
ejpam-4684	20	1	j.	j.	PROPN
ejpam-4684	20	2	pure	pure	PROPN
ejpam-4684	20	3	appl	appl	PROPN
ejpam-4684	20	4	.	.	PROPN
ejpam-4684	20	5	math	math	PROPN
ejpam-4684	20	6	,	,	PUNCT
ejpam-4684	20	7	16	16	NUM
ejpam-4684	20	8	(	(	PUNCT
ejpam-4684	20	9	3	3	NUM
ejpam-4684	20	10	)	)	PUNCT
ejpam-4684	20	11	(	(	PUNCT
ejpam-4684	20	12	2023	2023	NUM
ejpam-4684	20	13	)	)	PUNCT
ejpam-4684	20	14	,	,	PUNCT
ejpam-4684	20	15	1848	1848	NUM
ejpam-4684	20	16	-	-	SYM
ejpam-4684	20	17	1861	1861	NUM
ejpam-4684	20	18	1849	1849	NUM
ejpam-4684	20	19	of	of	ADP
ejpam-4684	20	20	a	a	DET
ejpam-4684	20	21	graph	graph	NOUN
ejpam-4684	20	22	.	.	PUNCT
ejpam-4684	21	1	in	in	ADP
ejpam-4684	21	2	fact	fact	NOUN
ejpam-4684	21	3	,	,	PUNCT
ejpam-4684	21	4	the	the	DET
ejpam-4684	21	5	authors	author	NOUN
ejpam-4684	21	6	have	have	AUX
ejpam-4684	21	7	shown	show	VERB
ejpam-4684	21	8	that	that	SCONJ
ejpam-4684	21	9	the	the	DET
ejpam-4684	21	10	absolute	absolute	ADJ
ejpam-4684	21	11	difference	difference	NOUN
ejpam-4684	21	12	between	between	ADP
ejpam-4684	21	13	the	the	DET
ejpam-4684	21	14	hop	hop	NOUN
ejpam-4684	21	15	independence	independence	NOUN
ejpam-4684	21	16	number	number	NOUN
ejpam-4684	21	17	and	and	CCONJ
ejpam-4684	21	18	the	the	DET
ejpam-4684	21	19	independence	independence	NOUN
ejpam-4684	21	20	number	number	NOUN
ejpam-4684	21	21	of	of	ADP
ejpam-4684	21	22	a	a	DET
ejpam-4684	21	23	graph	graph	NOUN
ejpam-4684	21	24	can	can	AUX
ejpam-4684	21	25	be	be	AUX
ejpam-4684	21	26	made	make	VERB
ejpam-4684	21	27	arbitrarily	arbitrarily	ADV
ejpam-4684	21	28	large	large	ADJ
ejpam-4684	21	29	.	.	PUNCT
ejpam-4684	22	1	motivated	motivate	VERB
ejpam-4684	22	2	by	by	ADP
ejpam-4684	22	3	the	the	DET
ejpam-4684	22	4	aforementioned	aforementioned	ADJ
ejpam-4684	22	5	studies	study	NOUN
ejpam-4684	22	6	,	,	PUNCT
ejpam-4684	22	7	the	the	DET
ejpam-4684	22	8	concept	concept	NOUN
ejpam-4684	22	9	of	of	ADP
ejpam-4684	22	10	connected	connected	ADJ
ejpam-4684	22	11	outer	outer	ADJ
ejpam-4684	22	12	-	-	PUNCT
ejpam-4684	22	13	hop	hop	NOUN
ejpam-4684	22	14	independent	independent	ADJ
ejpam-4684	22	15	hop	hop	NOUN
ejpam-4684	22	16	domination	domination	NOUN
ejpam-4684	22	17	in	in	ADP
ejpam-4684	22	18	a	a	DET
ejpam-4684	22	19	graph	graph	NOUN
ejpam-4684	22	20	will	will	AUX
ejpam-4684	22	21	be	be	AUX
ejpam-4684	22	22	introduced	introduce	VERB
ejpam-4684	22	23	and	and	CCONJ
ejpam-4684	22	24	investigated	investigate	VERB
ejpam-4684	22	25	in	in	ADP
ejpam-4684	22	26	this	this	DET
ejpam-4684	22	27	study	study	NOUN
ejpam-4684	22	28	.	.	PUNCT
ejpam-4684	23	1	some	some	DET
ejpam-4684	23	2	properties	property	NOUN
ejpam-4684	23	3	and	and	CCONJ
ejpam-4684	23	4	realization	realization	NOUN
ejpam-4684	23	5	results	result	NOUN
ejpam-4684	23	6	involving	involve	VERB
ejpam-4684	23	7	this	this	DET
ejpam-4684	23	8	parameter	parameter	NOUN
ejpam-4684	23	9	will	will	AUX
ejpam-4684	23	10	be	be	AUX
ejpam-4684	23	11	formulated	formulate	VERB
ejpam-4684	23	12	.	.	PUNCT
ejpam-4684	24	1	moreover	moreover	ADV
ejpam-4684	24	2	,	,	PUNCT
ejpam-4684	24	3	exact	exact	ADJ
ejpam-4684	24	4	values	value	NOUN
ejpam-4684	24	5	or	or	CCONJ
ejpam-4684	24	6	bounds	bound	NOUN
ejpam-4684	24	7	for	for	ADP
ejpam-4684	24	8	the	the	DET
ejpam-4684	24	9	parameter	parameter	NOUN
ejpam-4684	24	10	will	will	AUX
ejpam-4684	24	11	be	be	AUX
ejpam-4684	24	12	given	give	VERB
ejpam-4684	24	13	for	for	ADP
ejpam-4684	24	14	some	some	DET
ejpam-4684	24	15	families	family	NOUN
ejpam-4684	24	16	of	of	ADP
ejpam-4684	24	17	graphs	graph	NOUN
ejpam-4684	24	18	,	,	PUNCT
ejpam-4684	24	19	join	join	NOUN
ejpam-4684	24	20	,	,	PUNCT
ejpam-4684	24	21	and	and	CCONJ
ejpam-4684	24	22	corona	corona	NOUN
ejpam-4684	24	23	of	of	ADP
ejpam-4684	24	24	two	two	NUM
ejpam-4684	24	25	graphs	graph	NOUN
ejpam-4684	24	26	.	.	PUNCT
ejpam-4684	25	1	just	just	ADV
ejpam-4684	25	2	like	like	ADP
ejpam-4684	25	3	hop	hop	NOUN
ejpam-4684	25	4	domination	domination	NOUN
ejpam-4684	25	5	,	,	PUNCT
ejpam-4684	25	6	we	we	PRON
ejpam-4684	25	7	believe	believe	VERB
ejpam-4684	25	8	that	that	SCONJ
ejpam-4684	25	9	this	this	DET
ejpam-4684	25	10	new	new	ADJ
ejpam-4684	25	11	parameter	parameter	NOUN
ejpam-4684	25	12	will	will	AUX
ejpam-4684	25	13	yield	yield	VERB
ejpam-4684	25	14	significant	significant	ADJ
ejpam-4684	25	15	results	result	NOUN
ejpam-4684	25	16	in	in	ADP
ejpam-4684	25	17	the	the	DET
ejpam-4684	25	18	topic	topic	NOUN
ejpam-4684	25	19	of	of	ADP
ejpam-4684	25	20	domination	domination	NOUN
ejpam-4684	25	21	and	and	CCONJ
ejpam-4684	25	22	can	can	AUX
ejpam-4684	25	23	lead	lead	VERB
ejpam-4684	25	24	to	to	ADP
ejpam-4684	25	25	other	other	ADJ
ejpam-4684	25	26	interesting	interesting	ADJ
ejpam-4684	25	27	research	research	NOUN
ejpam-4684	25	28	directions	direction	NOUN
ejpam-4684	25	29	in	in	ADP
ejpam-4684	25	30	the	the	DET
ejpam-4684	25	31	future	future	NOUN
ejpam-4684	25	32	.	.	PUNCT
ejpam-4684	26	1	2	2	X
ejpam-4684	26	2	.	.	X
ejpam-4684	26	3	terminology	terminology	NOUN
ejpam-4684	26	4	and	and	CCONJ
ejpam-4684	26	5	notation	notation	NOUN
ejpam-4684	26	6	let	let	VERB
ejpam-4684	26	7	g	g	PRON
ejpam-4684	26	8	be	be	AUX
ejpam-4684	26	9	a	a	DET
ejpam-4684	26	10	simple	simple	ADJ
ejpam-4684	26	11	graph	graph	NOUN
ejpam-4684	26	12	.	.	PUNCT
ejpam-4684	27	1	then	then	ADV
ejpam-4684	27	2	s	s	VERB
ejpam-4684	27	3	⊆	⊆	NUM
ejpam-4684	27	4	v	v	NOUN
ejpam-4684	27	5	(	(	PUNCT
ejpam-4684	27	6	g	g	NOUN
ejpam-4684	27	7	)	)	PUNCT
ejpam-4684	27	8	is	be	AUX
ejpam-4684	27	9	a	a	DET
ejpam-4684	27	10	clique	clique	NOUN
ejpam-4684	27	11	if	if	SCONJ
ejpam-4684	27	12	the	the	DET
ejpam-4684	27	13	subgraph	subgraph	NOUN
ejpam-4684	27	14	⟨s⟩	⟨s⟩	PROPN
ejpam-4684	27	15	induced	induce	VERB
ejpam-4684	27	16	by	by	ADP
ejpam-4684	27	17	s	s	PROPN
ejpam-4684	27	18	is	be	AUX
ejpam-4684	27	19	complete	complete	ADJ
ejpam-4684	27	20	.	.	PUNCT
ejpam-4684	28	1	the	the	DET
ejpam-4684	28	2	maximum	maximum	ADJ
ejpam-4684	28	3	cardinality	cardinality	NOUN
ejpam-4684	28	4	of	of	ADP
ejpam-4684	28	5	a	a	DET
ejpam-4684	28	6	clique	clique	NOUN
ejpam-4684	28	7	set	set	VERB
ejpam-4684	28	8	in	in	ADP
ejpam-4684	28	9	g	g	NOUN
ejpam-4684	28	10	,	,	PUNCT
ejpam-4684	28	11	denoted	denote	VERB
ejpam-4684	28	12	by	by	ADP
ejpam-4684	28	13	ω(g	ω(g	NOUN
ejpam-4684	28	14	)	)	PUNCT
ejpam-4684	28	15	,	,	PUNCT
ejpam-4684	28	16	is	be	AUX
ejpam-4684	28	17	called	call	VERB
ejpam-4684	28	18	a	a	DET
ejpam-4684	28	19	clique	clique	ADJ
ejpam-4684	28	20	number	number	NOUN
ejpam-4684	28	21	of	of	ADP
ejpam-4684	28	22	g.	g.	PROPN
ejpam-4684	28	23	any	any	DET
ejpam-4684	28	24	clique	clique	NOUN
ejpam-4684	28	25	set	set	VERB
ejpam-4684	28	26	with	with	ADP
ejpam-4684	28	27	cardinality	cardinality	NOUN
ejpam-4684	28	28	equal	equal	ADJ
ejpam-4684	28	29	to	to	ADP
ejpam-4684	28	30	ω(g	ω(g	NOUN
ejpam-4684	28	31	)	)	PUNCT
ejpam-4684	28	32	is	be	AUX
ejpam-4684	28	33	called	call	VERB
ejpam-4684	28	34	a	a	DET
ejpam-4684	28	35	ω	ω	NOUN
ejpam-4684	28	36	-	-	PUNCT
ejpam-4684	28	37	set	set	NOUN
ejpam-4684	28	38	.	.	PUNCT
ejpam-4684	29	1	a	a	DET
ejpam-4684	29	2	subset	subset	NOUN
ejpam-4684	29	3	d	d	NOUN
ejpam-4684	29	4	of	of	ADP
ejpam-4684	29	5	v	v	NOUN
ejpam-4684	29	6	(	(	PUNCT
ejpam-4684	29	7	g	g	NOUN
ejpam-4684	29	8	)	)	PUNCT
ejpam-4684	29	9	is	be	AUX
ejpam-4684	29	10	called	call	VERB
ejpam-4684	29	11	a	a	DET
ejpam-4684	29	12	pointwise	pointwise	ADJ
ejpam-4684	29	13	non	non	ADJ
ejpam-4684	29	14	-	-	ADJ
ejpam-4684	29	15	dominating	dominating	ADJ
ejpam-4684	29	16	set	set	NOUN
ejpam-4684	29	17	of	of	ADP
ejpam-4684	29	18	g	g	PROPN
ejpam-4684	29	19	if	if	SCONJ
ejpam-4684	29	20	for	for	ADP
ejpam-4684	29	21	each	each	DET
ejpam-4684	29	22	v	v	NUM
ejpam-4684	29	23	∈	∈	PROPN
ejpam-4684	29	24	v	v	NOUN
ejpam-4684	29	25	(	(	PUNCT
ejpam-4684	29	26	g	g	NOUN
ejpam-4684	29	27	)	)	PUNCT
ejpam-4684	29	28	\d	\d	NOUN
ejpam-4684	29	29	,	,	PUNCT
ejpam-4684	29	30	there	there	PRON
ejpam-4684	29	31	exists	exist	VERB
ejpam-4684	29	32	u	u	NOUN
ejpam-4684	29	33	∈	∈	PROPN
ejpam-4684	29	34	d	d	ADP
ejpam-4684	29	35	such	such	ADJ
ejpam-4684	29	36	that	that	DET
ejpam-4684	29	37	v	v	NOUN
ejpam-4684	29	38	/∈	/∈	PUNCT
ejpam-4684	29	39	ng(u	ng(u	NOUN
ejpam-4684	29	40	)	)	PUNCT
ejpam-4684	29	41	.	.	PUNCT
ejpam-4684	30	1	a	a	DET
ejpam-4684	30	2	subset	subset	NOUN
ejpam-4684	30	3	d	d	NOUN
ejpam-4684	30	4	of	of	ADP
ejpam-4684	30	5	v	v	NOUN
ejpam-4684	30	6	(	(	PUNCT
ejpam-4684	30	7	g	g	NOUN
ejpam-4684	30	8	)	)	PUNCT
ejpam-4684	30	9	is	be	AUX
ejpam-4684	30	10	independent	independent	ADJ
ejpam-4684	30	11	if	if	SCONJ
ejpam-4684	30	12	for	for	ADP
ejpam-4684	30	13	every	every	DET
ejpam-4684	30	14	pair	pair	NOUN
ejpam-4684	30	15	of	of	ADP
ejpam-4684	30	16	distinct	distinct	ADJ
ejpam-4684	30	17	vertices	vertex	NOUN
ejpam-4684	30	18	v	v	ADP
ejpam-4684	30	19	,	,	PUNCT
ejpam-4684	30	20	w	w	PROPN
ejpam-4684	30	21	∈	∈	PROPN
ejpam-4684	30	22	d	d	X
ejpam-4684	30	23	,	,	PUNCT
ejpam-4684	30	24	we	we	PRON
ejpam-4684	30	25	have	have	VERB
ejpam-4684	30	26	dg(v	dg(v	NOUN
ejpam-4684	30	27	,	,	PUNCT
ejpam-4684	30	28	w	w	NOUN
ejpam-4684	30	29	)	)	PUNCT
ejpam-4684	30	30	̸=	̸=	PROPN
ejpam-4684	30	31	1	1	NUM
ejpam-4684	30	32	.	.	PUNCT
ejpam-4684	31	1	the	the	DET
ejpam-4684	31	2	maximum	maximum	ADJ
ejpam-4684	31	3	cardinality	cardinality	NOUN
ejpam-4684	31	4	of	of	ADP
ejpam-4684	31	5	an	an	DET
ejpam-4684	31	6	independent	independent	ADJ
ejpam-4684	31	7	set	set	NOUN
ejpam-4684	31	8	in	in	ADP
ejpam-4684	31	9	g	g	NOUN
ejpam-4684	31	10	,	,	PUNCT
ejpam-4684	31	11	denoted	denote	VERB
ejpam-4684	31	12	by	by	ADP
ejpam-4684	31	13	α(g	α(g	NOUN
ejpam-4684	31	14	)	)	PUNCT
ejpam-4684	31	15	,	,	PUNCT
ejpam-4684	31	16	is	be	AUX
ejpam-4684	31	17	called	call	VERB
ejpam-4684	31	18	the	the	DET
ejpam-4684	31	19	independence	independence	NOUN
ejpam-4684	31	20	number	number	NOUN
ejpam-4684	31	21	of	of	ADP
ejpam-4684	31	22	g.	g.	PROPN
ejpam-4684	31	23	any	any	DET
ejpam-4684	31	24	independent	independent	ADJ
ejpam-4684	31	25	set	set	NOUN
ejpam-4684	31	26	with	with	ADP
ejpam-4684	31	27	cardinality	cardinality	NOUN
ejpam-4684	31	28	equal	equal	ADJ
ejpam-4684	31	29	to	to	ADP
ejpam-4684	31	30	α(g	α(g	NUM
ejpam-4684	31	31	)	)	PUNCT
ejpam-4684	31	32	is	be	AUX
ejpam-4684	31	33	called	call	VERB
ejpam-4684	31	34	an	an	DET
ejpam-4684	31	35	α	α	NOUN
ejpam-4684	31	36	-	-	PUNCT
ejpam-4684	31	37	set	set	NOUN
ejpam-4684	31	38	.	.	PUNCT
ejpam-4684	32	1	a	a	DET
ejpam-4684	32	2	vertex	vertex	NOUN
ejpam-4684	32	3	v	v	NOUN
ejpam-4684	32	4	in	in	ADP
ejpam-4684	32	5	g	g	PROPN
ejpam-4684	32	6	is	be	AUX
ejpam-4684	32	7	a	a	DET
ejpam-4684	32	8	hop	hop	NOUN
ejpam-4684	32	9	neighbor	neighbor	NOUN
ejpam-4684	32	10	of	of	ADP
ejpam-4684	32	11	vertex	vertex	NOUN
ejpam-4684	32	12	u	u	NOUN
ejpam-4684	32	13	in	in	ADP
ejpam-4684	32	14	g	g	PROPN
ejpam-4684	32	15	if	if	SCONJ
ejpam-4684	32	16	dg(u	dg(u	NOUN
ejpam-4684	32	17	,	,	PUNCT
ejpam-4684	32	18	v	v	NOUN
ejpam-4684	32	19	)	)	PUNCT
ejpam-4684	32	20	=	=	SYM
ejpam-4684	32	21	2	2	X
ejpam-4684	32	22	.	.	X
ejpam-4684	33	1	the	the	DET
ejpam-4684	33	2	set	set	ADJ
ejpam-4684	33	3	n2	n2	ADJ
ejpam-4684	33	4	g(u	g(u	PROPN
ejpam-4684	33	5	)	)	PUNCT
ejpam-4684	33	6	=	=	PRON
ejpam-4684	33	7	{	{	PUNCT
ejpam-4684	33	8	v	v	NUM
ejpam-4684	33	9	∈	∈	NOUN
ejpam-4684	33	10	v	v	NOUN
ejpam-4684	33	11	(	(	PUNCT
ejpam-4684	33	12	g	g	NOUN
ejpam-4684	33	13	)	)	PUNCT
ejpam-4684	33	14	:	:	PUNCT
ejpam-4684	33	15	dg(v	dg(v	X
ejpam-4684	33	16	,	,	PUNCT
ejpam-4684	33	17	u	u	NOUN
ejpam-4684	33	18	)	)	PUNCT
ejpam-4684	33	19	=	=	SYM
ejpam-4684	33	20	2	2	X
ejpam-4684	33	21	}	}	PUNCT
ejpam-4684	33	22	is	be	AUX
ejpam-4684	33	23	called	call	VERB
ejpam-4684	33	24	the	the	DET
ejpam-4684	33	25	open	open	ADJ
ejpam-4684	33	26	hop	hop	NOUN
ejpam-4684	33	27	neighborhood	neighborhood	NOUN
ejpam-4684	33	28	of	of	ADP
ejpam-4684	33	29	u.	u.	PROPN
ejpam-4684	33	30	the	the	DET
ejpam-4684	33	31	closed	closed	ADJ
ejpam-4684	33	32	hop	hop	NOUN
ejpam-4684	33	33	neighborhood	neighborhood	NOUN
ejpam-4684	33	34	of	of	ADP
ejpam-4684	33	35	u	u	PROPN
ejpam-4684	33	36	in	in	ADP
ejpam-4684	33	37	g	g	PROPN
ejpam-4684	33	38	is	be	AUX
ejpam-4684	33	39	given	give	VERB
ejpam-4684	33	40	by	by	ADP
ejpam-4684	33	41	n2	n2	PROPN
ejpam-4684	33	42	g[u	g[u	PROPN
ejpam-4684	33	43	]	]	X
ejpam-4684	33	44	=	=	SYM
ejpam-4684	33	45	n2	n2	ADJ
ejpam-4684	33	46	g(u	g(u	PROPN
ejpam-4684	33	47	)	)	PUNCT
ejpam-4684	33	48	∪	∪	NOUN
ejpam-4684	33	49	{	{	PUNCT
ejpam-4684	33	50	u	u	NOUN
ejpam-4684	33	51	}	}	PUNCT
ejpam-4684	33	52	.	.	PUNCT
ejpam-4684	34	1	the	the	DET
ejpam-4684	34	2	open	open	ADJ
ejpam-4684	34	3	hop	hop	NOUN
ejpam-4684	34	4	neighborhood	neighborhood	NOUN
ejpam-4684	34	5	of	of	ADP
ejpam-4684	34	6	x	x	PROPN
ejpam-4684	34	7	⊆	⊆	NUM
ejpam-4684	34	8	v	v	ADP
ejpam-4684	34	9	(	(	PUNCT
ejpam-4684	34	10	g	g	NOUN
ejpam-4684	34	11	)	)	PUNCT
ejpam-4684	34	12	is	be	AUX
ejpam-4684	34	13	the	the	DET
ejpam-4684	34	14	set	set	ADJ
ejpam-4684	34	15	n2	n2	ADJ
ejpam-4684	34	16	g(x	g(x	NOUN
ejpam-4684	34	17	)	)	PUNCT
ejpam-4684	35	1	=	=	SYM
ejpam-4684	35	2	⋃	⋃	NOUN
ejpam-4684	35	3	u∈x	u∈x	ADJ
ejpam-4684	35	4	n2	n2	NOUN
ejpam-4684	35	5	g(u	g(u	PROPN
ejpam-4684	35	6	)	)	PUNCT
ejpam-4684	35	7	.	.	PUNCT
ejpam-4684	36	1	the	the	DET
ejpam-4684	36	2	closed	closed	ADJ
ejpam-4684	36	3	hop	hop	NOUN
ejpam-4684	36	4	neighborhood	neighborhood	NOUN
ejpam-4684	36	5	of	of	ADP
ejpam-4684	36	6	x	x	PUNCT
ejpam-4684	36	7	in	in	ADP
ejpam-4684	36	8	g	g	PROPN
ejpam-4684	36	9	is	be	AUX
ejpam-4684	36	10	the	the	DET
ejpam-4684	36	11	set	set	ADJ
ejpam-4684	36	12	n2	n2	NOUN
ejpam-4684	36	13	g[x	g[x	PROPN
ejpam-4684	36	14	]	]	X
ejpam-4684	36	15	=	=	SYM
ejpam-4684	36	16	n2	n2	PROPN
ejpam-4684	36	17	g(x	g(x	NOUN
ejpam-4684	36	18	)	)	PUNCT
ejpam-4684	36	19	∪x	∪x	NUM
ejpam-4684	36	20	.	.	PUNCT
ejpam-4684	37	1	a	a	DET
ejpam-4684	37	2	subset	subset	NOUN
ejpam-4684	37	3	s	s	X
ejpam-4684	37	4	of	of	ADP
ejpam-4684	37	5	v	v	NOUN
ejpam-4684	37	6	(	(	PUNCT
ejpam-4684	37	7	g	g	NOUN
ejpam-4684	37	8	)	)	PUNCT
ejpam-4684	37	9	is	be	AUX
ejpam-4684	37	10	a	a	DET
ejpam-4684	37	11	hop	hop	NOUN
ejpam-4684	37	12	dominating	dominating	NOUN
ejpam-4684	37	13	of	of	ADP
ejpam-4684	37	14	g	g	PROPN
ejpam-4684	37	15	if	if	SCONJ
ejpam-4684	37	16	n2	n2	ADJ
ejpam-4684	37	17	g[s	g[s	PROPN
ejpam-4684	37	18	]	]	X
ejpam-4684	37	19	=	=	SYM
ejpam-4684	37	20	v	v	NOUN
ejpam-4684	37	21	(	(	PUNCT
ejpam-4684	37	22	g	g	NOUN
ejpam-4684	37	23	)	)	PUNCT
ejpam-4684	37	24	,	,	PUNCT
ejpam-4684	37	25	that	that	ADV
ejpam-4684	37	26	is	is	ADV
ejpam-4684	37	27	,	,	PUNCT
ejpam-4684	37	28	for	for	ADP
ejpam-4684	37	29	every	every	DET
ejpam-4684	37	30	v	v	NUM
ejpam-4684	37	31	∈	∈	NOUN
ejpam-4684	37	32	v	v	NOUN
ejpam-4684	37	33	(	(	PUNCT
ejpam-4684	37	34	g)\s	g)\s	NOUN
ejpam-4684	37	35	,	,	PUNCT
ejpam-4684	37	36	there	there	PRON
ejpam-4684	37	37	exists	exist	VERB
ejpam-4684	37	38	u	u	PROPN
ejpam-4684	37	39	∈	∈	PROPN
ejpam-4684	37	40	s	s	VERB
ejpam-4684	37	41	such	such	ADJ
ejpam-4684	37	42	that	that	DET
ejpam-4684	37	43	dg(u	dg(u	ADJ
ejpam-4684	37	44	,	,	PUNCT
ejpam-4684	37	45	v	v	NOUN
ejpam-4684	37	46	)	)	PUNCT
ejpam-4684	38	1	=	=	SYM
ejpam-4684	38	2	2	2	X
ejpam-4684	38	3	.	.	PUNCT
ejpam-4684	39	1	the	the	DET
ejpam-4684	39	2	minimum	minimum	ADJ
ejpam-4684	39	3	cardinality	cardinality	NOUN
ejpam-4684	39	4	among	among	ADP
ejpam-4684	39	5	all	all	DET
ejpam-4684	39	6	hop	hop	NOUN
ejpam-4684	39	7	dominating	dominating	NOUN
ejpam-4684	39	8	sets	set	NOUN
ejpam-4684	39	9	of	of	ADP
ejpam-4684	39	10	g	g	NOUN
ejpam-4684	39	11	,	,	PUNCT
ejpam-4684	39	12	denoted	denote	VERB
ejpam-4684	39	13	by	by	ADP
ejpam-4684	39	14	γh(g	γh(g	NOUN
ejpam-4684	39	15	)	)	PUNCT
ejpam-4684	39	16	,	,	PUNCT
ejpam-4684	39	17	is	be	AUX
ejpam-4684	39	18	called	call	VERB
ejpam-4684	39	19	the	the	DET
ejpam-4684	39	20	hop	hop	NOUN
ejpam-4684	39	21	domination	domination	NOUN
ejpam-4684	39	22	number	number	NOUN
ejpam-4684	39	23	of	of	ADP
ejpam-4684	39	24	g.	g.	PROPN
ejpam-4684	39	25	any	any	DET
ejpam-4684	39	26	hop	hop	NOUN
ejpam-4684	39	27	dominating	dominating	NOUN
ejpam-4684	39	28	set	set	VERB
ejpam-4684	39	29	with	with	ADP
ejpam-4684	39	30	cardinality	cardinality	NOUN
ejpam-4684	39	31	equal	equal	ADJ
ejpam-4684	39	32	to	to	ADP
ejpam-4684	39	33	γh(g	γh(g	NOUN
ejpam-4684	39	34	)	)	PUNCT
ejpam-4684	39	35	is	be	AUX
ejpam-4684	39	36	called	call	VERB
ejpam-4684	39	37	a	a	DET
ejpam-4684	39	38	γh	γh	ADV
ejpam-4684	39	39	-	-	PUNCT
ejpam-4684	39	40	set	set	NOUN
ejpam-4684	39	41	.	.	PUNCT
ejpam-4684	40	1	a	a	DET
ejpam-4684	40	2	hop	hop	NOUN
ejpam-4684	40	3	dominating	dominating	NOUN
ejpam-4684	40	4	set	set	NOUN
ejpam-4684	40	5	d	d	PROPN
ejpam-4684	40	6	⊆	⊆	NUM
ejpam-4684	40	7	v	v	ADP
ejpam-4684	40	8	(	(	PUNCT
ejpam-4684	40	9	g	g	NOUN
ejpam-4684	40	10	)	)	PUNCT
ejpam-4684	40	11	is	be	AUX
ejpam-4684	40	12	called	call	VERB
ejpam-4684	40	13	a	a	DET
ejpam-4684	40	14	connected	connected	ADJ
ejpam-4684	40	15	hop	hop	NOUN
ejpam-4684	40	16	dominating	dominating	NOUN
ejpam-4684	40	17	if	if	SCONJ
ejpam-4684	40	18	the	the	DET
ejpam-4684	40	19	subgraph	subgraph	NOUN
ejpam-4684	40	20	⟨d⟩	⟨d⟩	PROPN
ejpam-4684	40	21	induced	induce	VERB
ejpam-4684	40	22	by	by	ADP
ejpam-4684	40	23	d	d	PROPN
ejpam-4684	40	24	is	be	AUX
ejpam-4684	40	25	connected	connect	VERB
ejpam-4684	40	26	.	.	PUNCT
ejpam-4684	41	1	the	the	DET
ejpam-4684	41	2	minimum	minimum	ADJ
ejpam-4684	41	3	cardinality	cardinality	NOUN
ejpam-4684	41	4	among	among	ADP
ejpam-4684	41	5	all	all	DET
ejpam-4684	41	6	connected	connect	VERB
ejpam-4684	41	7	hop	hop	NOUN
ejpam-4684	41	8	dominating	dominating	NOUN
ejpam-4684	41	9	sets	set	NOUN
ejpam-4684	41	10	of	of	ADP
ejpam-4684	41	11	g	g	NOUN
ejpam-4684	41	12	,	,	PUNCT
ejpam-4684	41	13	denoted	denote	VERB
ejpam-4684	41	14	by	by	ADP
ejpam-4684	41	15	γch(g	γch(g	NOUN
ejpam-4684	41	16	)	)	PUNCT
ejpam-4684	41	17	,	,	PUNCT
ejpam-4684	41	18	is	be	AUX
ejpam-4684	41	19	called	call	VERB
ejpam-4684	41	20	the	the	DET
ejpam-4684	41	21	connected	connect	VERB
ejpam-4684	41	22	hop	hop	NOUN
ejpam-4684	41	23	domination	domination	NOUN
ejpam-4684	41	24	number	number	NOUN
ejpam-4684	41	25	of	of	ADP
ejpam-4684	41	26	g.	g.	PROPN
ejpam-4684	41	27	any	any	DET
ejpam-4684	41	28	connected	connect	VERB
ejpam-4684	41	29	hop	hop	NOUN
ejpam-4684	41	30	dominating	dominating	NOUN
ejpam-4684	41	31	set	set	VERB
ejpam-4684	41	32	with	with	ADP
ejpam-4684	41	33	cardinality	cardinality	NOUN
ejpam-4684	41	34	equal	equal	ADJ
ejpam-4684	41	35	to	to	ADP
ejpam-4684	41	36	γch(g	γch(g	NOUN
ejpam-4684	41	37	)	)	PUNCT
ejpam-4684	41	38	is	be	AUX
ejpam-4684	41	39	called	call	VERB
ejpam-4684	41	40	a	a	DET
ejpam-4684	41	41	γch	γch	NOUN
ejpam-4684	41	42	-	-	PUNCT
ejpam-4684	41	43	set	set	NOUN
ejpam-4684	41	44	.	.	PUNCT
ejpam-4684	42	1	a	a	DET
ejpam-4684	42	2	connected	connected	ADJ
ejpam-4684	42	3	hop	hop	NOUN
ejpam-4684	42	4	dominating	dominating	NOUN
ejpam-4684	42	5	set	set	NOUN
ejpam-4684	42	6	c	c	PROPN
ejpam-4684	42	7	⊆	⊆	NUM
ejpam-4684	42	8	v	v	NOUN
ejpam-4684	42	9	(	(	PUNCT
ejpam-4684	42	10	g	g	NOUN
ejpam-4684	42	11	)	)	PUNCT
ejpam-4684	42	12	is	be	AUX
ejpam-4684	42	13	called	call	VERB
ejpam-4684	42	14	a	a	DET
ejpam-4684	42	15	connected	connected	ADJ
ejpam-4684	42	16	outer	outer	ADJ
ejpam-4684	42	17	-	-	PUNCT
ejpam-4684	42	18	independent	independent	ADJ
ejpam-4684	42	19	hop	hop	NOUN
ejpam-4684	42	20	dominating	dominating	NOUN
ejpam-4684	42	21	if	if	SCONJ
ejpam-4684	42	22	v	v	NOUN
ejpam-4684	42	23	(	(	PUNCT
ejpam-4684	42	24	g)\c	g)\c	NOUN
ejpam-4684	42	25	is	be	AUX
ejpam-4684	42	26	an	an	DET
ejpam-4684	42	27	independent	independent	ADJ
ejpam-4684	42	28	set	set	NOUN
ejpam-4684	42	29	ing	ing	NOUN
ejpam-4684	42	30	.	.	PUNCT
ejpam-4684	43	1	the	the	DET
ejpam-4684	43	2	minimum	minimum	ADJ
ejpam-4684	43	3	cardinality	cardinality	NOUN
ejpam-4684	43	4	of	of	ADP
ejpam-4684	43	5	a	a	DET
ejpam-4684	43	6	connected	connected	ADJ
ejpam-4684	43	7	outer	outer	ADJ
ejpam-4684	43	8	-	-	PUNCT
ejpam-4684	43	9	independent	independent	ADJ
ejpam-4684	43	10	hop	hop	NOUN
ejpam-4684	43	11	dominating	dominating	NOUN
ejpam-4684	43	12	set	set	NOUN
ejpam-4684	43	13	in	in	ADP
ejpam-4684	43	14	g	g	NOUN
ejpam-4684	43	15	,	,	PUNCT
ejpam-4684	43	16	denoted	denote	VERB
ejpam-4684	43	17	by	by	ADP
ejpam-4684	43	18	γoich(g	γoich(g	NOUN
ejpam-4684	43	19	)	)	PUNCT
ejpam-4684	43	20	,	,	PUNCT
ejpam-4684	43	21	is	be	AUX
ejpam-4684	43	22	called	call	VERB
ejpam-4684	43	23	the	the	DET
ejpam-4684	43	24	connected	connected	ADJ
ejpam-4684	43	25	outer	outer	ADJ
ejpam-4684	43	26	-	-	PUNCT
ejpam-4684	43	27	independent	independent	ADJ
ejpam-4684	43	28	hop	hop	NOUN
ejpam-4684	43	29	domination	domination	NOUN
ejpam-4684	43	30	number	number	NOUN
ejpam-4684	43	31	of	of	ADP
ejpam-4684	43	32	g.	g.	PROPN
ejpam-4684	43	33	any	any	DET
ejpam-4684	43	34	connected	connected	ADJ
ejpam-4684	43	35	outer	outer	ADJ
ejpam-4684	43	36	-	-	PUNCT
ejpam-4684	43	37	independent	independent	ADJ
ejpam-4684	43	38	hop	hop	NOUN
ejpam-4684	43	39	dominating	dominating	NOUN
ejpam-4684	43	40	set	set	VERB
ejpam-4684	43	41	with	with	ADP
ejpam-4684	43	42	cardinality	cardinality	NOUN
ejpam-4684	43	43	equal	equal	ADJ
ejpam-4684	43	44	to	to	ADP
ejpam-4684	43	45	γoich(g	γoich(g	NOUN
ejpam-4684	43	46	)	)	PUNCT
ejpam-4684	43	47	is	be	AUX
ejpam-4684	43	48	called	call	VERB
ejpam-4684	43	49	a	a	DET
ejpam-4684	43	50	γoich	γoich	NOUN
ejpam-4684	43	51	-	-	PUNCT
ejpam-4684	43	52	set	set	NOUN
ejpam-4684	43	53	.	.	PUNCT
ejpam-4684	44	1	a	a	DET
ejpam-4684	44	2	subset	subset	NOUN
ejpam-4684	44	3	d	d	NOUN
ejpam-4684	44	4	of	of	ADP
ejpam-4684	44	5	v	v	NOUN
ejpam-4684	44	6	(	(	PUNCT
ejpam-4684	44	7	g	g	NOUN
ejpam-4684	44	8	)	)	PUNCT
ejpam-4684	44	9	is	be	AUX
ejpam-4684	44	10	hop	hop	ADV
ejpam-4684	44	11	independent	independent	ADJ
ejpam-4684	44	12	if	if	SCONJ
ejpam-4684	44	13	for	for	ADP
ejpam-4684	44	14	every	every	DET
ejpam-4684	44	15	pair	pair	NOUN
ejpam-4684	44	16	of	of	ADP
ejpam-4684	44	17	distinct	distinct	ADJ
ejpam-4684	44	18	vertices	vertex	NOUN
ejpam-4684	44	19	v	v	ADP
ejpam-4684	44	20	,	,	PUNCT
ejpam-4684	45	1	w	w	PROPN
ejpam-4684	45	2	∈	∈	PROPN
ejpam-4684	45	3	d	d	PROPN
ejpam-4684	45	4	,	,	PUNCT
ejpam-4684	45	5	j.	j.	PROPN
ejpam-4684	45	6	hassan	hassan	PROPN
ejpam-4684	45	7	,	,	PUNCT
ejpam-4684	45	8	a.	a.	PROPN
ejpam-4684	45	9	lintasan	lintasan	NOUN
ejpam-4684	45	10	,	,	PUNCT
ejpam-4684	45	11	n.	n.	PROPN
ejpam-4684	45	12	h.	h.	PROPN
ejpam-4684	45	13	mohammad	mohammad	PROPN
ejpam-4684	45	14	/	/	PUNCT
ejpam-4684	45	15	eur	eur	PROPN
ejpam-4684	45	16	.	.	PUNCT
ejpam-4684	46	1	j.	j.	PROPN
ejpam-4684	46	2	pure	pure	PROPN
ejpam-4684	46	3	appl	appl	PROPN
ejpam-4684	46	4	.	.	PROPN
ejpam-4684	46	5	math	math	PROPN
ejpam-4684	46	6	,	,	PUNCT
ejpam-4684	46	7	16	16	NUM
ejpam-4684	46	8	(	(	PUNCT
ejpam-4684	46	9	3	3	NUM
ejpam-4684	46	10	)	)	PUNCT
ejpam-4684	46	11	(	(	PUNCT
ejpam-4684	46	12	2023	2023	NUM
ejpam-4684	46	13	)	)	PUNCT
ejpam-4684	46	14	,	,	PUNCT
ejpam-4684	46	15	1848	1848	NUM
ejpam-4684	46	16	-	-	SYM
ejpam-4684	46	17	1861	1861	NUM
ejpam-4684	46	18	1850	1850	NUM
ejpam-4684	46	19	we	we	PRON
ejpam-4684	46	20	have	have	VERB
ejpam-4684	46	21	dg(v	dg(v	NOUN
ejpam-4684	46	22	,	,	PUNCT
ejpam-4684	46	23	w	w	NOUN
ejpam-4684	46	24	)	)	PUNCT
ejpam-4684	46	25	̸=	̸=	PROPN
ejpam-4684	46	26	2	2	NUM
ejpam-4684	46	27	.	.	PUNCT
ejpam-4684	47	1	the	the	DET
ejpam-4684	47	2	maximum	maximum	ADJ
ejpam-4684	47	3	cardinality	cardinality	NOUN
ejpam-4684	47	4	of	of	ADP
ejpam-4684	47	5	a	a	DET
ejpam-4684	47	6	hop	hop	NOUN
ejpam-4684	47	7	independent	independent	ADJ
ejpam-4684	47	8	set	set	NOUN
ejpam-4684	47	9	in	in	ADP
ejpam-4684	47	10	g	g	NOUN
ejpam-4684	47	11	,	,	PUNCT
ejpam-4684	47	12	denoted	denote	VERB
ejpam-4684	47	13	by	by	ADP
ejpam-4684	47	14	αh(g	αh(g	NOUN
ejpam-4684	47	15	)	)	PUNCT
ejpam-4684	47	16	,	,	PUNCT
ejpam-4684	47	17	is	be	AUX
ejpam-4684	47	18	called	call	VERB
ejpam-4684	47	19	the	the	DET
ejpam-4684	47	20	hop	hop	NOUN
ejpam-4684	47	21	independence	independence	NOUN
ejpam-4684	47	22	number	number	NOUN
ejpam-4684	47	23	of	of	ADP
ejpam-4684	47	24	g.	g.	PROPN
ejpam-4684	47	25	any	any	DET
ejpam-4684	47	26	hop	hop	NOUN
ejpam-4684	47	27	independent	independent	ADJ
ejpam-4684	47	28	set	set	NOUN
ejpam-4684	47	29	with	with	ADP
ejpam-4684	47	30	cardinality	cardinality	NOUN
ejpam-4684	47	31	equal	equal	ADJ
ejpam-4684	47	32	to	to	ADP
ejpam-4684	47	33	αh(g	αh(g	NOUN
ejpam-4684	47	34	)	)	PUNCT
ejpam-4684	47	35	is	be	AUX
ejpam-4684	47	36	called	call	VERB
ejpam-4684	47	37	an	an	DET
ejpam-4684	47	38	αh	αh	NOUN
ejpam-4684	47	39	-	-	PUNCT
ejpam-4684	47	40	set	set	NOUN
ejpam-4684	47	41	.	.	PUNCT
ejpam-4684	48	1	let	let	VERB
ejpam-4684	48	2	g	g	NOUN
ejpam-4684	48	3	and	and	CCONJ
ejpam-4684	48	4	h	h	NOUN
ejpam-4684	48	5	be	be	VERB
ejpam-4684	48	6	two	two	NUM
ejpam-4684	48	7	graphs	graph	NOUN
ejpam-4684	48	8	.	.	PUNCT
ejpam-4684	49	1	the	the	DET
ejpam-4684	49	2	join	join	NOUN
ejpam-4684	49	3	of	of	ADP
ejpam-4684	49	4	g	g	PROPN
ejpam-4684	49	5	and	and	CCONJ
ejpam-4684	49	6	h	h	NOUN
ejpam-4684	49	7	,	,	PUNCT
ejpam-4684	49	8	denoted	denote	VERB
ejpam-4684	49	9	by	by	ADP
ejpam-4684	49	10	g	g	PROPN
ejpam-4684	49	11	+	+	CCONJ
ejpam-4684	49	12	h	h	NOUN
ejpam-4684	49	13	is	be	AUX
ejpam-4684	49	14	the	the	DET
ejpam-4684	49	15	graph	graph	NOUN
ejpam-4684	49	16	with	with	ADP
ejpam-4684	49	17	vertex	vertex	NOUN
ejpam-4684	49	18	set	set	VERB
ejpam-4684	49	19	v	v	NOUN
ejpam-4684	49	20	(	(	PUNCT
ejpam-4684	49	21	g+h	g+h	NOUN
ejpam-4684	49	22	)	)	PUNCT
ejpam-4684	49	23	=	=	SYM
ejpam-4684	49	24	v	v	X
ejpam-4684	49	25	(	(	PUNCT
ejpam-4684	49	26	g)∪v	g)∪v	NOUN
ejpam-4684	49	27	(	(	PUNCT
ejpam-4684	49	28	h	h	NOUN
ejpam-4684	49	29	)	)	PUNCT
ejpam-4684	49	30	and	and	CCONJ
ejpam-4684	49	31	edge	edge	NOUN
ejpam-4684	49	32	set	set	VERB
ejpam-4684	49	33	e(g+h	e(g+h	NUM
ejpam-4684	49	34	)	)	PUNCT
ejpam-4684	50	1	=	=	SYM
ejpam-4684	50	2	e(g)∪e(h)∪{uv	e(g)∪e(h)∪{uv	X
ejpam-4684	50	3	:	:	PUNCT
ejpam-4684	50	4	u	u	PROPN
ejpam-4684	50	5	∈	∈	PROPN
ejpam-4684	50	6	v	v	NOUN
ejpam-4684	50	7	(	(	PUNCT
ejpam-4684	50	8	g	g	NOUN
ejpam-4684	50	9	)	)	PUNCT
ejpam-4684	50	10	,	,	PUNCT
ejpam-4684	50	11	v	v	X
ejpam-4684	50	12	∈	∈	PROPN
ejpam-4684	50	13	v	v	NOUN
ejpam-4684	50	14	(	(	PUNCT
ejpam-4684	50	15	h	h	NOUN
ejpam-4684	50	16	)	)	PUNCT
ejpam-4684	50	17	}	}	PUNCT
ejpam-4684	50	18	.	.	PUNCT
ejpam-4684	51	1	the	the	DET
ejpam-4684	51	2	corona	corona	NOUN
ejpam-4684	51	3	g	g	PROPN
ejpam-4684	51	4	and	and	CCONJ
ejpam-4684	51	5	h	h	NOUN
ejpam-4684	51	6	,	,	PUNCT
ejpam-4684	51	7	denoted	denote	VERB
ejpam-4684	51	8	by	by	ADP
ejpam-4684	51	9	g	g	PROPN
ejpam-4684	51	10	◦	◦	NOUN
ejpam-4684	51	11	h	h	NOUN
ejpam-4684	51	12	,	,	PUNCT
ejpam-4684	51	13	the	the	DET
ejpam-4684	51	14	graph	graph	NOUN
ejpam-4684	51	15	obtained	obtain	VERB
ejpam-4684	51	16	by	by	ADP
ejpam-4684	51	17	taking	take	VERB
ejpam-4684	51	18	one	one	NUM
ejpam-4684	51	19	copy	copy	NOUN
ejpam-4684	51	20	of	of	ADP
ejpam-4684	51	21	g	g	PROPN
ejpam-4684	51	22	and	and	CCONJ
ejpam-4684	51	23	|v	|v	PROPN
ejpam-4684	51	24	(	(	PUNCT
ejpam-4684	51	25	g)|	g)|	NOUN
ejpam-4684	51	26	copies	copy	NOUN
ejpam-4684	51	27	of	of	ADP
ejpam-4684	51	28	h	h	NOUN
ejpam-4684	51	29	,	,	PUNCT
ejpam-4684	51	30	and	and	CCONJ
ejpam-4684	51	31	then	then	ADV
ejpam-4684	51	32	joining	join	VERB
ejpam-4684	51	33	the	the	DET
ejpam-4684	51	34	ith	ith	PROPN
ejpam-4684	51	35	vertex	vertex	NOUN
ejpam-4684	51	36	of	of	ADP
ejpam-4684	51	37	g	g	NOUN
ejpam-4684	51	38	to	to	ADP
ejpam-4684	51	39	every	every	DET
ejpam-4684	51	40	vertex	vertex	NOUN
ejpam-4684	51	41	of	of	ADP
ejpam-4684	51	42	the	the	DET
ejpam-4684	51	43	ith	ith	PROPN
ejpam-4684	51	44	copy	copy	NOUN
ejpam-4684	51	45	of	of	ADP
ejpam-4684	51	46	h.	h.	PROPN
ejpam-4684	51	47	we	we	PRON
ejpam-4684	51	48	denote	denote	VERB
ejpam-4684	51	49	by	by	ADP
ejpam-4684	51	50	hv	hv	PROPN
ejpam-4684	51	51	the	the	DET
ejpam-4684	51	52	copy	copy	NOUN
ejpam-4684	51	53	of	of	ADP
ejpam-4684	51	54	h	h	NOUN
ejpam-4684	51	55	in	in	ADP
ejpam-4684	51	56	g	g	PROPN
ejpam-4684	51	57	◦	◦	NOUN
ejpam-4684	51	58	h	h	NOUN
ejpam-4684	51	59	corresponding	correspond	VERB
ejpam-4684	51	60	to	to	ADP
ejpam-4684	51	61	the	the	DET
ejpam-4684	51	62	vertex	vertex	NOUN
ejpam-4684	51	63	v	v	ADP
ejpam-4684	51	64	∈	∈	PROPN
ejpam-4684	51	65	g	g	NOUN
ejpam-4684	51	66	and	and	CCONJ
ejpam-4684	51	67	write	write	VERB
ejpam-4684	51	68	v	v	ADP
ejpam-4684	51	69	+	+	PROPN
ejpam-4684	51	70	hv	hv	NOUN
ejpam-4684	51	71	for	for	ADP
ejpam-4684	51	72	⟨{v}+hv⟩.	⟨{v}+hv⟩.	X
ejpam-4684	51	73	3	3	X
ejpam-4684	51	74	.	.	X
ejpam-4684	51	75	results	result	NOUN
ejpam-4684	51	76	we	we	PRON
ejpam-4684	51	77	begin	begin	VERB
ejpam-4684	51	78	this	this	DET
ejpam-4684	51	79	section	section	NOUN
ejpam-4684	51	80	by	by	ADP
ejpam-4684	51	81	introducing	introduce	VERB
ejpam-4684	51	82	the	the	DET
ejpam-4684	51	83	concept	concept	NOUN
ejpam-4684	51	84	called	call	VERB
ejpam-4684	51	85	connected	connected	ADJ
ejpam-4684	51	86	outer	outer	ADJ
ejpam-4684	51	87	-	-	PUNCT
ejpam-4684	51	88	hop	hop	NOUN
ejpam-4684	51	89	independent	independent	ADJ
ejpam-4684	51	90	hop	hop	NOUN
ejpam-4684	51	91	domination	domination	NOUN
ejpam-4684	51	92	in	in	ADP
ejpam-4684	51	93	a	a	DET
ejpam-4684	51	94	graph	graph	NOUN
ejpam-4684	51	95	.	.	PUNCT
ejpam-4684	52	1	definition	definition	NOUN
ejpam-4684	52	2	1	1	NUM
ejpam-4684	52	3	.	.	PUNCT
ejpam-4684	53	1	letg	letg	PROPN
ejpam-4684	53	2	be	be	VERB
ejpam-4684	53	3	a	a	DET
ejpam-4684	53	4	connected	connected	ADJ
ejpam-4684	53	5	graph	graph	NOUN
ejpam-4684	53	6	.	.	PUNCT
ejpam-4684	54	1	a	a	DET
ejpam-4684	54	2	subset	subset	NOUN
ejpam-4684	54	3	c	c	NOUN
ejpam-4684	54	4	of	of	ADP
ejpam-4684	54	5	v	v	PROPN
ejpam-4684	54	6	(	(	PUNCT
ejpam-4684	54	7	g	g	NOUN
ejpam-4684	54	8	)	)	PUNCT
ejpam-4684	54	9	is	be	AUX
ejpam-4684	54	10	called	call	VERB
ejpam-4684	54	11	a	a	DET
ejpam-4684	54	12	connected	connected	ADJ
ejpam-4684	54	13	outerhop	outerhop	NOUN
ejpam-4684	54	14	independent	independent	ADJ
ejpam-4684	54	15	hop	hop	NOUN
ejpam-4684	54	16	dominating	dominating	NOUN
ejpam-4684	54	17	if	if	SCONJ
ejpam-4684	54	18	c	c	PROPN
ejpam-4684	54	19	is	be	AUX
ejpam-4684	54	20	a	a	DET
ejpam-4684	54	21	connected	connected	ADJ
ejpam-4684	54	22	hop	hop	NOUN
ejpam-4684	54	23	dominating	dominating	NOUN
ejpam-4684	54	24	set	set	NOUN
ejpam-4684	54	25	and	and	CCONJ
ejpam-4684	54	26	v	v	NOUN
ejpam-4684	54	27	(	(	PUNCT
ejpam-4684	54	28	g)\c	g)\c	NOUN
ejpam-4684	54	29	is	be	AUX
ejpam-4684	54	30	a	a	DET
ejpam-4684	54	31	hop	hop	NOUN
ejpam-4684	54	32	independent	independent	ADJ
ejpam-4684	54	33	set	set	NOUN
ejpam-4684	54	34	in	in	ADP
ejpam-4684	54	35	g.	g.	PROPN
ejpam-4684	54	36	the	the	DET
ejpam-4684	54	37	minimum	minimum	ADJ
ejpam-4684	54	38	cardinality	cardinality	NOUN
ejpam-4684	54	39	of	of	ADP
ejpam-4684	54	40	a	a	DET
ejpam-4684	54	41	connected	connected	ADJ
ejpam-4684	54	42	outer	outer	ADJ
ejpam-4684	54	43	-	-	PUNCT
ejpam-4684	54	44	hop	hop	NOUN
ejpam-4684	54	45	independent	independent	ADJ
ejpam-4684	54	46	hop	hop	NOUN
ejpam-4684	54	47	dominating	dominating	NOUN
ejpam-4684	54	48	set	set	NOUN
ejpam-4684	54	49	in	in	ADP
ejpam-4684	54	50	g	g	NOUN
ejpam-4684	54	51	,	,	PUNCT
ejpam-4684	54	52	denoted	denote	VERB
ejpam-4684	54	53	by	by	ADP
ejpam-4684	54	54	,	,	PUNCT
ejpam-4684	54	55	γohich	γohich	PROPN
ejpam-4684	54	56	(	(	PUNCT
ejpam-4684	54	57	g	g	NOUN
ejpam-4684	54	58	)	)	PUNCT
ejpam-4684	54	59	is	be	AUX
ejpam-4684	54	60	called	call	VERB
ejpam-4684	54	61	the	the	DET
ejpam-4684	54	62	connected	connected	ADJ
ejpam-4684	54	63	outer	outer	ADJ
ejpam-4684	54	64	-	-	PUNCT
ejpam-4684	54	65	hop	hop	NOUN
ejpam-4684	54	66	independent	independent	ADJ
ejpam-4684	54	67	hop	hop	NOUN
ejpam-4684	54	68	domination	domination	NOUN
ejpam-4684	54	69	number	number	NOUN
ejpam-4684	54	70	of	of	ADP
ejpam-4684	54	71	g.	g.	PROPN
ejpam-4684	54	72	any	any	DET
ejpam-4684	54	73	connected	connected	ADJ
ejpam-4684	54	74	outer	outer	ADJ
ejpam-4684	54	75	-	-	PUNCT
ejpam-4684	54	76	hop	hop	NOUN
ejpam-4684	54	77	independent	independent	ADJ
ejpam-4684	54	78	hop	hop	NOUN
ejpam-4684	54	79	dominating	dominating	NOUN
ejpam-4684	54	80	set	set	VERB
ejpam-4684	54	81	with	with	ADP
ejpam-4684	54	82	cardinality	cardinality	NOUN
ejpam-4684	54	83	equal	equal	ADJ
ejpam-4684	54	84	to	to	ADP
ejpam-4684	54	85	γohich	γohich	PROPN
ejpam-4684	54	86	(	(	PUNCT
ejpam-4684	54	87	g	g	NOUN
ejpam-4684	54	88	)	)	PUNCT
ejpam-4684	54	89	is	be	AUX
ejpam-4684	54	90	called	call	VERB
ejpam-4684	54	91	a	a	DET
ejpam-4684	54	92	γohich	γohich	NOUN
ejpam-4684	54	93	-set	-set	PUNCT
ejpam-4684	54	94	of	of	ADP
ejpam-4684	54	95	g.	g.	PROPN
ejpam-4684	54	96	proposition	proposition	PROPN
ejpam-4684	54	97	1	1	NUM
ejpam-4684	54	98	.	.	PUNCT
ejpam-4684	55	1	let	let	VERB
ejpam-4684	55	2	g	g	PRON
ejpam-4684	55	3	be	be	AUX
ejpam-4684	55	4	a	a	DET
ejpam-4684	55	5	connected	connected	ADJ
ejpam-4684	55	6	graph	graph	NOUN
ejpam-4684	55	7	.	.	PUNCT
ejpam-4684	56	1	then	then	ADV
ejpam-4684	56	2	γch(g	γch(g	NOUN
ejpam-4684	56	3	)	)	PUNCT
ejpam-4684	56	4	≤	≤	NOUN
ejpam-4684	57	1	γohich	γohich	PRON
ejpam-4684	57	2	(	(	PUNCT
ejpam-4684	57	3	g	g	NOUN
ejpam-4684	57	4	)	)	PUNCT
ejpam-4684	57	5	,	,	PUNCT
ejpam-4684	57	6	and	and	CCONJ
ejpam-4684	57	7	this	this	DET
ejpam-4684	57	8	bound	bind	VERB
ejpam-4684	57	9	is	be	AUX
ejpam-4684	57	10	sharp	sharp	ADJ
ejpam-4684	57	11	.	.	PUNCT
ejpam-4684	58	1	proof	proof	NOUN
ejpam-4684	58	2	.	.	PUNCT
ejpam-4684	59	1	let	let	VERB
ejpam-4684	59	2	c	c	PRON
ejpam-4684	59	3	be	be	AUX
ejpam-4684	59	4	a	a	DET
ejpam-4684	59	5	γohich	γohich	NOUN
ejpam-4684	59	6	-set	-set	ADJ
ejpam-4684	59	7	of	of	ADP
ejpam-4684	59	8	g.	g.	PROPN
ejpam-4684	59	9	then	then	ADV
ejpam-4684	59	10	c	c	PROPN
ejpam-4684	59	11	is	be	AUX
ejpam-4684	59	12	a	a	DET
ejpam-4684	59	13	connected	connected	ADJ
ejpam-4684	59	14	hop	hop	NOUN
ejpam-4684	59	15	dominating	dominating	NOUN
ejpam-4684	59	16	set	set	NOUN
ejpam-4684	59	17	in	in	ADP
ejpam-4684	59	18	g	g	PROPN
ejpam-4684	59	19	(	(	PUNCT
ejpam-4684	59	20	by	by	ADP
ejpam-4684	59	21	definition	definition	NOUN
ejpam-4684	59	22	)	)	PUNCT
ejpam-4684	59	23	.	.	PUNCT
ejpam-4684	60	1	since	since	SCONJ
ejpam-4684	60	2	γch(g	γch(g	NOUN
ejpam-4684	60	3	)	)	PUNCT
ejpam-4684	60	4	is	be	AUX
ejpam-4684	60	5	the	the	DET
ejpam-4684	60	6	minimum	minimum	ADJ
ejpam-4684	60	7	cardinality	cardinality	NOUN
ejpam-4684	60	8	among	among	ADP
ejpam-4684	60	9	all	all	DET
ejpam-4684	60	10	connected	connect	VERB
ejpam-4684	60	11	hop	hop	NOUN
ejpam-4684	60	12	dominating	dominating	NOUN
ejpam-4684	60	13	sets	set	NOUN
ejpam-4684	60	14	in	in	ADP
ejpam-4684	60	15	g	g	NOUN
ejpam-4684	60	16	,	,	PUNCT
ejpam-4684	60	17	it	it	PRON
ejpam-4684	60	18	follows	follow	VERB
ejpam-4684	60	19	that	that	SCONJ
ejpam-4684	60	20	γohich	γohich	PROPN
ejpam-4684	60	21	(	(	PUNCT
ejpam-4684	60	22	g	g	NOUN
ejpam-4684	60	23	)	)	PUNCT
ejpam-4684	60	24	=	=	SYM
ejpam-4684	60	25	|c|	|c|	PROPN
ejpam-4684	60	26	≥	≥	NOUN
ejpam-4684	60	27	γch(g	γch(g	NOUN
ejpam-4684	60	28	)	)	PUNCT
ejpam-4684	60	29	.	.	PUNCT
ejpam-4684	61	1	to	to	PART
ejpam-4684	61	2	see	see	VERB
ejpam-4684	61	3	that	that	SCONJ
ejpam-4684	61	4	the	the	DET
ejpam-4684	61	5	bound	bind	VERB
ejpam-4684	61	6	is	be	AUX
ejpam-4684	61	7	sharp	sharp	ADJ
ejpam-4684	61	8	,	,	PUNCT
ejpam-4684	61	9	consider	consider	VERB
ejpam-4684	61	10	g	g	NOUN
ejpam-4684	61	11	=	=	NOUN
ejpam-4684	61	12	p7	p7	NOUN
ejpam-4684	61	13	=	=	PUNCT
ejpam-4684	61	14	[	[	X
ejpam-4684	61	15	v1	v1	NOUN
ejpam-4684	61	16	,	,	PUNCT
ejpam-4684	61	17	v2	v2	NOUN
ejpam-4684	61	18	,	,	PUNCT
ejpam-4684	61	19	.	.	PUNCT
ejpam-4684	61	20	.	.	PUNCT
ejpam-4684	62	1	.	.	PUNCT
ejpam-4684	63	1	,	,	PUNCT
ejpam-4684	63	2	v7	v7	VERB
ejpam-4684	63	3	]	]	PUNCT
ejpam-4684	63	4	.	.	PUNCT
ejpam-4684	64	1	let	let	VERB
ejpam-4684	64	2	s	s	PRON
ejpam-4684	64	3	=	=	PUNCT
ejpam-4684	64	4	{	{	PUNCT
ejpam-4684	64	5	v3	v3	PROPN
ejpam-4684	64	6	,	,	PUNCT
ejpam-4684	64	7	v4	v4	PROPN
ejpam-4684	64	8	,	,	PUNCT
ejpam-4684	64	9	v5	v5	PROPN
ejpam-4684	64	10	}	}	PUNCT
ejpam-4684	64	11	.	.	PUNCT
ejpam-4684	65	1	observe	observe	VERB
ejpam-4684	65	2	that	that	SCONJ
ejpam-4684	65	3	⟨s⟩	⟨s⟩	PROPN
ejpam-4684	65	4	is	be	AUX
ejpam-4684	65	5	connected	connect	VERB
ejpam-4684	65	6	and	and	CCONJ
ejpam-4684	65	7	n2	n2	ADJ
ejpam-4684	65	8	g[s	g[s	PROPN
ejpam-4684	65	9	]	]	X
ejpam-4684	65	10	=	=	SYM
ejpam-4684	65	11	v	v	NOUN
ejpam-4684	65	12	(	(	PUNCT
ejpam-4684	65	13	g	g	NOUN
ejpam-4684	65	14	)	)	PUNCT
ejpam-4684	65	15	.	.	PUNCT
ejpam-4684	66	1	this	this	PRON
ejpam-4684	66	2	means	mean	VERB
ejpam-4684	66	3	that	that	SCONJ
ejpam-4684	66	4	s	s	VERB
ejpam-4684	66	5	is	be	AUX
ejpam-4684	66	6	a	a	DET
ejpam-4684	66	7	connected	connected	ADJ
ejpam-4684	66	8	hop	hop	NOUN
ejpam-4684	66	9	dominating	dominating	NOUN
ejpam-4684	66	10	in	in	ADP
ejpam-4684	66	11	g.	g.	PROPN
ejpam-4684	66	12	since	since	SCONJ
ejpam-4684	66	13	any	any	DET
ejpam-4684	66	14	connected	connect	VERB
ejpam-4684	66	15	hop	hop	NOUN
ejpam-4684	66	16	dominating	dominating	NOUN
ejpam-4684	66	17	set	set	NOUN
ejpam-4684	66	18	in	in	ADP
ejpam-4684	66	19	g	g	PROPN
ejpam-4684	66	20	contains	contain	VERB
ejpam-4684	66	21	s	s	PROPN
ejpam-4684	66	22	,	,	PUNCT
ejpam-4684	66	23	s	s	PART
ejpam-4684	66	24	is	be	AUX
ejpam-4684	66	25	the	the	DET
ejpam-4684	66	26	minimum	minimum	ADJ
ejpam-4684	66	27	connected	connect	VERB
ejpam-4684	66	28	hop	hop	NOUN
ejpam-4684	66	29	dominating	dominating	NOUN
ejpam-4684	66	30	set	set	VERB
ejpam-4684	66	31	in	in	ADP
ejpam-4684	66	32	g.	g.	PROPN
ejpam-4684	66	33	hence	hence	ADV
ejpam-4684	66	34	,	,	PUNCT
ejpam-4684	66	35	γch(p7	γch(p7	PROPN
ejpam-4684	66	36	)	)	PUNCT
ejpam-4684	66	37	=	=	SYM
ejpam-4684	67	1	3	3	X
ejpam-4684	67	2	.	.	PUNCT
ejpam-4684	68	1	moreover	moreover	ADV
ejpam-4684	68	2	,	,	PUNCT
ejpam-4684	68	3	since	since	SCONJ
ejpam-4684	68	4	dg(a	dg(a	X
ejpam-4684	68	5	,	,	PUNCT
ejpam-4684	68	6	b	b	X
ejpam-4684	68	7	)	)	PUNCT
ejpam-4684	68	8	̸=	̸=	PROPN
ejpam-4684	68	9	2	2	NUM
ejpam-4684	68	10	for	for	ADP
ejpam-4684	68	11	every	every	DET
ejpam-4684	68	12	a	a	PROPN
ejpam-4684	68	13	,	,	PUNCT
ejpam-4684	68	14	b	b	PROPN
ejpam-4684	68	15	∈	∈	PROPN
ejpam-4684	68	16	v	v	NOUN
ejpam-4684	68	17	(	(	PUNCT
ejpam-4684	68	18	g)\s	g)\s	NOUN
ejpam-4684	68	19	,	,	PUNCT
ejpam-4684	68	20	it	it	PRON
ejpam-4684	68	21	follows	follow	VERB
ejpam-4684	68	22	that	that	SCONJ
ejpam-4684	68	23	s	s	VERB
ejpam-4684	68	24	is	be	AUX
ejpam-4684	68	25	the	the	DET
ejpam-4684	68	26	minimum	minimum	ADJ
ejpam-4684	68	27	connected	connect	VERB
ejpam-4684	68	28	outer	outer	ADJ
ejpam-4684	68	29	-	-	PUNCT
ejpam-4684	68	30	hop	hop	NOUN
ejpam-4684	68	31	independent	independent	ADJ
ejpam-4684	68	32	hop	hop	NOUN
ejpam-4684	68	33	dominating	dominating	NOUN
ejpam-4684	68	34	set	set	VERB
ejpam-4684	68	35	in	in	ADP
ejpam-4684	68	36	g.	g.	PROPN
ejpam-4684	68	37	consequently	consequently	ADV
ejpam-4684	68	38	,	,	PUNCT
ejpam-4684	68	39	γch(p7	γch(p7	PROPN
ejpam-4684	68	40	)	)	PUNCT
ejpam-4684	68	41	=	=	SYM
ejpam-4684	68	42	3	3	X
ejpam-4684	68	43	=	=	SYM
ejpam-4684	68	44	γohich	γohich	PROPN
ejpam-4684	68	45	(	(	PUNCT
ejpam-4684	68	46	p7	p7	PROPN
ejpam-4684	68	47	)	)	PUNCT
ejpam-4684	68	48	.	.	PUNCT
ejpam-4684	69	1	theorem	theorem	NOUN
ejpam-4684	69	2	1	1	X
ejpam-4684	69	3	.	.	PUNCT
ejpam-4684	70	1	let	let	VERB
ejpam-4684	70	2	g	g	PRON
ejpam-4684	70	3	be	be	AUX
ejpam-4684	70	4	a	a	DET
ejpam-4684	70	5	connected	connected	ADJ
ejpam-4684	70	6	graph	graph	NOUN
ejpam-4684	70	7	with	with	ADP
ejpam-4684	70	8	|v	|v	PROPN
ejpam-4684	70	9	(	(	PUNCT
ejpam-4684	70	10	g)|	g)|	NOUN
ejpam-4684	70	11	=	=	PUNCT
ejpam-4684	70	12	n	n	NOUN
ejpam-4684	70	13	≥	≥	NOUN
ejpam-4684	70	14	1	1	NUM
ejpam-4684	70	15	.	.	PUNCT
ejpam-4684	71	1	then	then	ADV
ejpam-4684	71	2	each	each	PRON
ejpam-4684	71	3	of	of	ADP
ejpam-4684	71	4	the	the	DET
ejpam-4684	71	5	following	following	NOUN
ejpam-4684	71	6	is	be	AUX
ejpam-4684	71	7	true	true	ADJ
ejpam-4684	71	8	.	.	PUNCT
ejpam-4684	72	1	(	(	PUNCT
ejpam-4684	72	2	i	i	NOUN
ejpam-4684	72	3	)	)	PUNCT
ejpam-4684	72	4	1	1	NUM
ejpam-4684	72	5	≤	≤	NUM
ejpam-4684	72	6	γohich	γohich	PRON
ejpam-4684	72	7	(	(	PUNCT
ejpam-4684	72	8	g	g	NOUN
ejpam-4684	72	9	)	)	PUNCT
ejpam-4684	72	10	≤	≤	NOUN
ejpam-4684	72	11	n.	n.	NOUN
ejpam-4684	72	12	(	(	PUNCT
ejpam-4684	72	13	ii	ii	PROPN
ejpam-4684	72	14	)	)	PUNCT
ejpam-4684	72	15	γohich	γohich	PROPN
ejpam-4684	72	16	(	(	PUNCT
ejpam-4684	72	17	g	g	NOUN
ejpam-4684	72	18	)	)	PUNCT
ejpam-4684	72	19	=	=	SYM
ejpam-4684	72	20	1	1	NUM
ejpam-4684	72	21	if	if	SCONJ
ejpam-4684	72	22	and	and	CCONJ
ejpam-4684	72	23	only	only	ADV
ejpam-4684	72	24	if	if	SCONJ
ejpam-4684	72	25	g	g	PROPN
ejpam-4684	72	26	is	be	AUX
ejpam-4684	72	27	trivial	trivial	ADJ
ejpam-4684	72	28	.	.	PUNCT
ejpam-4684	73	1	(	(	PUNCT
ejpam-4684	73	2	iii	iii	X
ejpam-4684	73	3	)	)	PUNCT
ejpam-4684	73	4	γohich	γohich	PROPN
ejpam-4684	73	5	(	(	PUNCT
ejpam-4684	73	6	g	g	NOUN
ejpam-4684	73	7	)	)	PUNCT
ejpam-4684	73	8	=	=	SYM
ejpam-4684	74	1	n	n	NOUN
ejpam-4684	74	2	if	if	SCONJ
ejpam-4684	74	3	and	and	CCONJ
ejpam-4684	74	4	only	only	ADV
ejpam-4684	74	5	if	if	SCONJ
ejpam-4684	74	6	g	g	PROPN
ejpam-4684	74	7	is	be	AUX
ejpam-4684	74	8	complete	complete	ADJ
ejpam-4684	74	9	.	.	PUNCT
ejpam-4684	75	1	j.	j.	PROPN
ejpam-4684	75	2	hassan	hassan	PROPN
ejpam-4684	75	3	,	,	PUNCT
ejpam-4684	75	4	a.	a.	PROPN
ejpam-4684	75	5	lintasan	lintasan	NOUN
ejpam-4684	75	6	,	,	PUNCT
ejpam-4684	75	7	n.	n.	PROPN
ejpam-4684	75	8	h.	h.	PROPN
ejpam-4684	75	9	mohammad	mohammad	PROPN
ejpam-4684	75	10	/	/	PUNCT
ejpam-4684	75	11	eur	eur	PROPN
ejpam-4684	75	12	.	.	PUNCT
ejpam-4684	76	1	j.	j.	PROPN
ejpam-4684	76	2	pure	pure	PROPN
ejpam-4684	76	3	appl	appl	PROPN
ejpam-4684	76	4	.	.	PROPN
ejpam-4684	76	5	math	math	PROPN
ejpam-4684	76	6	,	,	PUNCT
ejpam-4684	76	7	16	16	NUM
ejpam-4684	76	8	(	(	PUNCT
ejpam-4684	76	9	3	3	NUM
ejpam-4684	76	10	)	)	PUNCT
ejpam-4684	76	11	(	(	PUNCT
ejpam-4684	76	12	2023	2023	NUM
ejpam-4684	76	13	)	)	PUNCT
ejpam-4684	76	14	,	,	PUNCT
ejpam-4684	76	15	1848	1848	NUM
ejpam-4684	76	16	-	-	SYM
ejpam-4684	76	17	1861	1861	NUM
ejpam-4684	76	18	1851	1851	NUM
ejpam-4684	76	19	proof	proof	NOUN
ejpam-4684	76	20	.	.	PUNCT
ejpam-4684	77	1	(	(	PUNCT
ejpam-4684	77	2	i	i	NOUN
ejpam-4684	77	3	)	)	PUNCT
ejpam-4684	77	4	since	since	SCONJ
ejpam-4684	77	5	an	an	DET
ejpam-4684	77	6	empty	empty	ADJ
ejpam-4684	77	7	set	set	NOUN
ejpam-4684	77	8	can	can	AUX
ejpam-4684	77	9	not	not	PART
ejpam-4684	77	10	be	be	AUX
ejpam-4684	77	11	a	a	DET
ejpam-4684	77	12	connected	connected	ADJ
ejpam-4684	77	13	outer	outer	ADJ
ejpam-4684	77	14	-	-	PUNCT
ejpam-4684	77	15	hop	hop	NOUN
ejpam-4684	77	16	independent	independent	ADJ
ejpam-4684	77	17	hop	hop	NOUN
ejpam-4684	77	18	dominating	dominating	NOUN
ejpam-4684	77	19	set	set	NOUN
ejpam-4684	77	20	in	in	ADP
ejpam-4684	77	21	g	g	PROPN
ejpam-4684	77	22	,	,	PUNCT
ejpam-4684	77	23	we	we	PRON
ejpam-4684	77	24	have	have	VERB
ejpam-4684	77	25	γohich	γohich	PROPN
ejpam-4684	77	26	(	(	PUNCT
ejpam-4684	77	27	g	g	NOUN
ejpam-4684	77	28	)	)	PUNCT
ejpam-4684	77	29	≥	≥	NOUN
ejpam-4684	77	30	1	1	NUM
ejpam-4684	77	31	.	.	PUNCT
ejpam-4684	78	1	moreover	moreover	ADV
ejpam-4684	78	2	,	,	PUNCT
ejpam-4684	78	3	since	since	SCONJ
ejpam-4684	78	4	any	any	DET
ejpam-4684	78	5	connected	connected	ADJ
ejpam-4684	78	6	outer	outer	ADJ
ejpam-4684	78	7	-	-	PUNCT
ejpam-4684	78	8	hop	hop	NOUN
ejpam-4684	78	9	independent	independent	ADJ
ejpam-4684	78	10	hop	hop	NOUN
ejpam-4684	78	11	dominating	dominating	NOUN
ejpam-4684	78	12	set	set	NOUN
ejpam-4684	78	13	in	in	ADP
ejpam-4684	78	14	g	g	PROPN
ejpam-4684	78	15	is	be	AUX
ejpam-4684	78	16	contained	contain	VERB
ejpam-4684	78	17	in	in	ADP
ejpam-4684	78	18	v	v	NUM
ejpam-4684	78	19	(	(	PUNCT
ejpam-4684	78	20	g	g	NOUN
ejpam-4684	78	21	)	)	PUNCT
ejpam-4684	78	22	,	,	PUNCT
ejpam-4684	78	23	we	we	PRON
ejpam-4684	78	24	have	have	VERB
ejpam-4684	78	25	γohich	γohich	PROPN
ejpam-4684	78	26	(	(	PUNCT
ejpam-4684	78	27	g	g	NOUN
ejpam-4684	78	28	)	)	PUNCT
ejpam-4684	78	29	≤	≤	NOUN
ejpam-4684	78	30	n.	n.	NOUN
ejpam-4684	78	31	consequently	consequently	ADV
ejpam-4684	78	32	,	,	PUNCT
ejpam-4684	78	33	1	1	NUM
ejpam-4684	78	34	≤	≤	NUM
ejpam-4684	78	35	γohich	γohich	PROPN
ejpam-4684	78	36	(	(	PUNCT
ejpam-4684	78	37	g	g	NOUN
ejpam-4684	78	38	)	)	PUNCT
ejpam-4684	78	39	≤	≤	NOUN
ejpam-4684	78	40	n.	n.	NOUN
ejpam-4684	78	41	(	(	PUNCT
ejpam-4684	78	42	ii	ii	PROPN
ejpam-4684	78	43	)	)	PUNCT
ejpam-4684	78	44	suppose	suppose	VERB
ejpam-4684	78	45	γohich	γohich	PROPN
ejpam-4684	78	46	(	(	PUNCT
ejpam-4684	78	47	g	g	NOUN
ejpam-4684	78	48	)	)	PUNCT
ejpam-4684	78	49	=	=	SYM
ejpam-4684	78	50	1	1	X
ejpam-4684	78	51	.	.	PUNCT
ejpam-4684	78	52	suppose	suppose	VERB
ejpam-4684	78	53	that	that	SCONJ
ejpam-4684	78	54	g	g	PROPN
ejpam-4684	78	55	is	be	AUX
ejpam-4684	78	56	non	non	ADJ
ejpam-4684	78	57	-	-	ADJ
ejpam-4684	78	58	trivial	trivial	ADJ
ejpam-4684	78	59	.	.	PUNCT
ejpam-4684	79	1	then	then	ADV
ejpam-4684	79	2	g	g	PROPN
ejpam-4684	79	3	is	be	AUX
ejpam-4684	79	4	either	either	CCONJ
ejpam-4684	79	5	connected	connect	VERB
ejpam-4684	79	6	or	or	CCONJ
ejpam-4684	79	7	disconnected	disconnected	ADJ
ejpam-4684	79	8	.	.	PUNCT
ejpam-4684	80	1	if	if	SCONJ
ejpam-4684	80	2	g	g	PROPN
ejpam-4684	80	3	is	be	AUX
ejpam-4684	80	4	connected	connect	VERB
ejpam-4684	80	5	,	,	PUNCT
ejpam-4684	80	6	then	then	ADV
ejpam-4684	80	7	there	there	PRON
ejpam-4684	80	8	exist	exist	VERB
ejpam-4684	80	9	a	a	DET
ejpam-4684	80	10	,	,	PUNCT
ejpam-4684	80	11	b	b	PROPN
ejpam-4684	80	12	∈	∈	PROPN
ejpam-4684	80	13	v	v	NOUN
ejpam-4684	80	14	(	(	PUNCT
ejpam-4684	80	15	g	g	NOUN
ejpam-4684	80	16	)	)	PUNCT
ejpam-4684	80	17	such	such	ADJ
ejpam-4684	80	18	that	that	SCONJ
ejpam-4684	80	19	dg(a	dg(a	PROPN
ejpam-4684	80	20	,	,	PUNCT
ejpam-4684	80	21	b	b	X
ejpam-4684	80	22	)	)	PUNCT
ejpam-4684	80	23	=	=	SYM
ejpam-4684	81	1	1	1	X
ejpam-4684	81	2	.	.	PUNCT
ejpam-4684	82	1	this	this	PRON
ejpam-4684	82	2	means	mean	VERB
ejpam-4684	82	3	that	that	SCONJ
ejpam-4684	82	4	a	a	DET
ejpam-4684	82	5	/∈	/∈	ADJ
ejpam-4684	82	6	n2	n2	NOUN
ejpam-4684	82	7	g[b	g[b	PROPN
ejpam-4684	82	8	]	]	PUNCT
ejpam-4684	82	9	and	and	CCONJ
ejpam-4684	82	10	b	b	PROPN
ejpam-4684	82	11	/∈	/∈	PUNCT
ejpam-4684	82	12	n2	n2	ADJ
ejpam-4684	82	13	g[a	g[a	PROPN
ejpam-4684	82	14	]	]	X
ejpam-4684	82	15	,	,	PUNCT
ejpam-4684	82	16	showing	show	VERB
ejpam-4684	82	17	that	that	SCONJ
ejpam-4684	82	18	a	a	DET
ejpam-4684	82	19	singleton	singleton	NOUN
ejpam-4684	82	20	set	set	NOUN
ejpam-4684	82	21	is	be	AUX
ejpam-4684	82	22	not	not	PART
ejpam-4684	82	23	the	the	DET
ejpam-4684	82	24	minimum	minimum	ADJ
ejpam-4684	82	25	connected	connected	ADJ
ejpam-4684	82	26	outer	outer	ADJ
ejpam-4684	82	27	-	-	PUNCT
ejpam-4684	82	28	hop	hop	NOUN
ejpam-4684	82	29	independent	independent	ADJ
ejpam-4684	82	30	hop	hop	NOUN
ejpam-4684	82	31	dominating	dominating	NOUN
ejpam-4684	82	32	set	set	VERB
ejpam-4684	82	33	in	in	ADP
ejpam-4684	82	34	g.	g.	PROPN
ejpam-4684	82	35	thus	thus	ADV
ejpam-4684	82	36	,	,	PUNCT
ejpam-4684	82	37	γohich	γohich	PROPN
ejpam-4684	82	38	(	(	PUNCT
ejpam-4684	82	39	g	g	NOUN
ejpam-4684	82	40	)	)	PUNCT
ejpam-4684	82	41	>	>	X
ejpam-4684	82	42	1	1	NUM
ejpam-4684	82	43	,	,	PUNCT
ejpam-4684	82	44	a	a	DET
ejpam-4684	82	45	contradiction	contradiction	NOUN
ejpam-4684	82	46	.	.	PUNCT
ejpam-4684	83	1	suppose	suppose	VERB
ejpam-4684	83	2	that	that	SCONJ
ejpam-4684	83	3	g1	g1	PROPN
ejpam-4684	83	4	,	,	PUNCT
ejpam-4684	83	5	.	.	PUNCT
ejpam-4684	83	6	.	.	PUNCT
ejpam-4684	84	1	.	.	PUNCT
ejpam-4684	85	1	,	,	PUNCT
ejpam-4684	85	2	gk	gk	PROPN
ejpam-4684	85	3	,	,	PUNCT
ejpam-4684	85	4	k	k	PROPN
ejpam-4684	85	5	≥	≥	NUM
ejpam-4684	85	6	2	2	NUM
ejpam-4684	85	7	are	be	AUX
ejpam-4684	85	8	the	the	DET
ejpam-4684	85	9	components	component	NOUN
ejpam-4684	85	10	of	of	ADP
ejpam-4684	85	11	g	g	NOUN
ejpam-4684	85	12	and	and	CCONJ
ejpam-4684	85	13	let	let	VERB
ejpam-4684	85	14	s	s	PRON
ejpam-4684	85	15	be	be	AUX
ejpam-4684	85	16	a	a	DET
ejpam-4684	85	17	connected	connected	ADJ
ejpam-4684	85	18	outer	outer	ADJ
ejpam-4684	85	19	-	-	PUNCT
ejpam-4684	85	20	hop	hop	NOUN
ejpam-4684	85	21	independent	independent	ADJ
ejpam-4684	85	22	hop	hop	NOUN
ejpam-4684	85	23	dominating	dominating	NOUN
ejpam-4684	85	24	set	set	NOUN
ejpam-4684	85	25	of	of	ADP
ejpam-4684	85	26	g.	g.	PROPN
ejpam-4684	85	27	then	then	ADV
ejpam-4684	85	28	s	s	VERB
ejpam-4684	85	29	=	=	NOUN
ejpam-4684	85	30	s1∪	s1∪	NOUN
ejpam-4684	85	31	.	.	PUNCT
ejpam-4684	85	32	.	.	PUNCT
ejpam-4684	86	1	.∪sk	.∪sk	PROPN
ejpam-4684	86	2	,	,	PUNCT
ejpam-4684	86	3	where	where	SCONJ
ejpam-4684	86	4	si	si	PROPN
ejpam-4684	86	5	is	be	AUX
ejpam-4684	86	6	a	a	DET
ejpam-4684	86	7	connected	connected	ADJ
ejpam-4684	86	8	outer	outer	ADJ
ejpam-4684	86	9	-	-	PUNCT
ejpam-4684	86	10	hop	hop	NOUN
ejpam-4684	86	11	independent	independent	ADJ
ejpam-4684	86	12	hop	hop	NOUN
ejpam-4684	86	13	dominating	dominating	NOUN
ejpam-4684	86	14	set	set	NOUN
ejpam-4684	86	15	of	of	ADP
ejpam-4684	86	16	gi	gi	NOUN
ejpam-4684	86	17	for	for	ADP
ejpam-4684	86	18	each	each	DET
ejpam-4684	86	19	i	i	PRON
ejpam-4684	86	20	∈	∈	PROPN
ejpam-4684	86	21	{	{	PUNCT
ejpam-4684	86	22	1	1	NUM
ejpam-4684	86	23	,	,	PUNCT
ejpam-4684	86	24	.	.	PUNCT
ejpam-4684	86	25	.	.	PUNCT
ejpam-4684	86	26	.	.	PUNCT
ejpam-4684	87	1	,	,	PUNCT
ejpam-4684	87	2	k	k	X
ejpam-4684	87	3	}	}	PUNCT
ejpam-4684	87	4	.	.	PUNCT
ejpam-4684	88	1	since	since	SCONJ
ejpam-4684	88	2	k	k	PROPN
ejpam-4684	88	3	≥	≥	NUM
ejpam-4684	88	4	2	2	NUM
ejpam-4684	88	5	,	,	PUNCT
ejpam-4684	88	6	we	we	PRON
ejpam-4684	88	7	have	have	VERB
ejpam-4684	88	8	γohich	γohich	PROPN
ejpam-4684	88	9	(	(	PUNCT
ejpam-4684	88	10	g	g	NOUN
ejpam-4684	88	11	)	)	PUNCT
ejpam-4684	88	12	≥	≥	NOUN
ejpam-4684	88	13	2	2	NUM
ejpam-4684	88	14	,	,	PUNCT
ejpam-4684	88	15	a	a	DET
ejpam-4684	88	16	contradiction	contradiction	NOUN
ejpam-4684	88	17	.	.	PUNCT
ejpam-4684	89	1	therefore	therefore	ADV
ejpam-4684	89	2	,	,	PUNCT
ejpam-4684	89	3	g	g	PROPN
ejpam-4684	89	4	must	must	AUX
ejpam-4684	89	5	be	be	AUX
ejpam-4684	89	6	a	a	DET
ejpam-4684	89	7	trivial	trivial	ADJ
ejpam-4684	89	8	graph	graph	NOUN
ejpam-4684	89	9	.	.	PUNCT
ejpam-4684	90	1	the	the	DET
ejpam-4684	90	2	converse	converse	NOUN
ejpam-4684	90	3	is	be	AUX
ejpam-4684	90	4	clear	clear	ADJ
ejpam-4684	90	5	.	.	PUNCT
ejpam-4684	91	1	(	(	PUNCT
ejpam-4684	91	2	iii	iii	X
ejpam-4684	91	3	)	)	PUNCT
ejpam-4684	91	4	let	let	VERB
ejpam-4684	91	5	γohich	γohich	PROPN
ejpam-4684	91	6	(	(	PUNCT
ejpam-4684	91	7	g	g	NOUN
ejpam-4684	91	8	)	)	PUNCT
ejpam-4684	91	9	=	=	VERB
ejpam-4684	91	10	n.	n.	NOUN
ejpam-4684	91	11	suppose	suppose	VERB
ejpam-4684	91	12	further	far	ADV
ejpam-4684	91	13	that	that	SCONJ
ejpam-4684	91	14	g	g	PROPN
ejpam-4684	91	15	is	be	AUX
ejpam-4684	91	16	non	non	ADJ
ejpam-4684	91	17	-	-	ADJ
ejpam-4684	91	18	complete	complete	ADJ
ejpam-4684	91	19	.	.	PUNCT
ejpam-4684	92	1	let	let	VERB
ejpam-4684	92	2	x	x	PRON
ejpam-4684	92	3	,	,	PUNCT
ejpam-4684	92	4	y	y	PROPN
ejpam-4684	92	5	∈	∈	PROPN
ejpam-4684	92	6	v	v	ADP
ejpam-4684	92	7	(	(	PUNCT
ejpam-4684	92	8	g	g	NOUN
ejpam-4684	92	9	)	)	PUNCT
ejpam-4684	92	10	such	such	ADJ
ejpam-4684	92	11	that	that	DET
ejpam-4684	92	12	dg(x	dg(x	PROPN
ejpam-4684	92	13	,	,	PUNCT
ejpam-4684	92	14	y	y	NOUN
ejpam-4684	92	15	)	)	PUNCT
ejpam-4684	92	16	=	=	SYM
ejpam-4684	92	17	∆(g	∆(g	PROPN
ejpam-4684	92	18	)	)	PUNCT
ejpam-4684	92	19	,	,	PUNCT
ejpam-4684	92	20	∆(g	∆(g	PROPN
ejpam-4684	92	21	)	)	PUNCT
ejpam-4684	92	22	is	be	AUX
ejpam-4684	92	23	the	the	DET
ejpam-4684	92	24	maximum	maximum	ADJ
ejpam-4684	92	25	degree	degree	NOUN
ejpam-4684	92	26	of	of	ADP
ejpam-4684	92	27	g.	g.	PROPN
ejpam-4684	92	28	this	this	PRON
ejpam-4684	92	29	means	mean	VERB
ejpam-4684	92	30	that	that	SCONJ
ejpam-4684	92	31	x	x	X
ejpam-4684	92	32	,	,	PUNCT
ejpam-4684	92	33	y	y	PROPN
ejpam-4684	92	34	are	be	AUX
ejpam-4684	92	35	non	non	ADJ
ejpam-4684	92	36	-	-	ADJ
ejpam-4684	92	37	cut	cut	ADJ
ejpam-4684	92	38	vertices	vertex	NOUN
ejpam-4684	92	39	of	of	ADP
ejpam-4684	92	40	g.	g.	PROPN
ejpam-4684	92	41	moreover	moreover	ADV
ejpam-4684	92	42	,	,	PUNCT
ejpam-4684	92	43	since	since	SCONJ
ejpam-4684	92	44	g	g	PROPN
ejpam-4684	92	45	is	be	AUX
ejpam-4684	92	46	non	non	ADJ
ejpam-4684	92	47	-	-	ADJ
ejpam-4684	92	48	complete	complete	ADJ
ejpam-4684	92	49	,	,	PUNCT
ejpam-4684	92	50	dg(x	dg(x	NUM
ejpam-4684	92	51	,	,	PUNCT
ejpam-4684	92	52	y	y	PROPN
ejpam-4684	92	53	)	)	PUNCT
ejpam-4684	92	54	≥	≥	NOUN
ejpam-4684	92	55	2	2	NUM
ejpam-4684	92	56	.	.	PUNCT
ejpam-4684	93	1	now	now	ADV
ejpam-4684	93	2	,	,	PUNCT
ejpam-4684	93	3	let	let	VERB
ejpam-4684	93	4	s′	s′	ADJ
ejpam-4684	93	5	=	=	PUNCT
ejpam-4684	93	6	{	{	PUNCT
ejpam-4684	93	7	v	v	NOUN
ejpam-4684	93	8	(	(	PUNCT
ejpam-4684	93	9	g)\{x	g)\{x	PROPN
ejpam-4684	93	10	}	}	PUNCT
ejpam-4684	93	11	.	.	PUNCT
ejpam-4684	94	1	then	then	ADV
ejpam-4684	94	2	s′	s′	PROPN
ejpam-4684	94	3	is	be	AUX
ejpam-4684	94	4	a	a	DET
ejpam-4684	94	5	connected	connected	ADJ
ejpam-4684	94	6	outer	outer	ADJ
ejpam-4684	94	7	-	-	PUNCT
ejpam-4684	94	8	hop	hop	NOUN
ejpam-4684	94	9	independent	independent	ADJ
ejpam-4684	94	10	hop	hop	NOUN
ejpam-4684	94	11	dominating	dominating	NOUN
ejpam-4684	94	12	set	set	VERB
ejpam-4684	94	13	ing	ing	NOUN
ejpam-4684	94	14	.	.	PUNCT
ejpam-4684	95	1	thus	thus	ADV
ejpam-4684	95	2	,	,	PUNCT
ejpam-4684	95	3	γohich	γohich	PRON
ejpam-4684	95	4	(	(	PUNCT
ejpam-4684	95	5	g	g	NOUN
ejpam-4684	95	6	)	)	PUNCT
ejpam-4684	95	7	≤	≤	NUM
ejpam-4684	95	8	n−	n−	NOUN
ejpam-4684	95	9	1	1	NUM
ejpam-4684	95	10	,	,	PUNCT
ejpam-4684	95	11	a	a	DET
ejpam-4684	95	12	contradiction	contradiction	NOUN
ejpam-4684	95	13	.	.	PUNCT
ejpam-4684	96	1	therefore	therefore	ADV
ejpam-4684	96	2	,	,	PUNCT
ejpam-4684	96	3	g	g	PROPN
ejpam-4684	96	4	is	be	AUX
ejpam-4684	96	5	complete	complete	ADJ
ejpam-4684	96	6	.	.	PUNCT
ejpam-4684	97	1	conversely	conversely	ADV
ejpam-4684	97	2	,	,	PUNCT
ejpam-4684	97	3	suppose	suppose	VERB
ejpam-4684	97	4	g	g	PROPN
ejpam-4684	97	5	is	be	AUX
ejpam-4684	97	6	complete	complete	ADJ
ejpam-4684	97	7	.	.	PUNCT
ejpam-4684	98	1	then	then	ADV
ejpam-4684	98	2	n2	n2	PROPN
ejpam-4684	98	3	g[a	g[a	PROPN
ejpam-4684	98	4	]	]	X
ejpam-4684	98	5	=	=	X
ejpam-4684	98	6	{	{	PUNCT
ejpam-4684	98	7	a	a	NOUN
ejpam-4684	98	8	}	}	PUNCT
ejpam-4684	98	9	for	for	ADP
ejpam-4684	98	10	every	every	DET
ejpam-4684	98	11	a	a	DET
ejpam-4684	98	12	∈	∈	PROPN
ejpam-4684	98	13	v	v	NOUN
ejpam-4684	98	14	(	(	PUNCT
ejpam-4684	98	15	g	g	NOUN
ejpam-4684	98	16	)	)	PUNCT
ejpam-4684	98	17	.	.	PUNCT
ejpam-4684	99	1	let	let	VERB
ejpam-4684	99	2	s	s	PRON
ejpam-4684	99	3	=	=	X
ejpam-4684	99	4	v	v	ADJ
ejpam-4684	99	5	(	(	PUNCT
ejpam-4684	99	6	g	g	NOUN
ejpam-4684	99	7	)	)	PUNCT
ejpam-4684	99	8	=	=	SYM
ejpam-4684	99	9	{	{	PUNCT
ejpam-4684	99	10	a1	a1	PROPN
ejpam-4684	99	11	,	,	PUNCT
ejpam-4684	99	12	a2	a2	PROPN
ejpam-4684	99	13	,	,	PUNCT
ejpam-4684	99	14	.	.	PUNCT
ejpam-4684	99	15	.	.	PUNCT
ejpam-4684	100	1	.	.	PUNCT
ejpam-4684	101	1	,	,	PUNCT
ejpam-4684	101	2	an	an	PRON
ejpam-4684	101	3	}	}	PUNCT
ejpam-4684	101	4	.	.	PUNCT
ejpam-4684	102	1	then	then	ADV
ejpam-4684	102	2	s	s	VERB
ejpam-4684	102	3	is	be	AUX
ejpam-4684	102	4	the	the	DET
ejpam-4684	102	5	minimum	minimum	ADJ
ejpam-4684	102	6	connected	connect	VERB
ejpam-4684	102	7	outer	outer	ADJ
ejpam-4684	102	8	-	-	PUNCT
ejpam-4684	102	9	hop	hop	NOUN
ejpam-4684	102	10	independent	independent	ADJ
ejpam-4684	102	11	hop	hop	NOUN
ejpam-4684	102	12	dominating	dominating	NOUN
ejpam-4684	102	13	set	set	NOUN
ejpam-4684	102	14	of	of	ADP
ejpam-4684	102	15	g.	g.	PROPN
ejpam-4684	102	16	thus	thus	ADV
ejpam-4684	102	17	,	,	PUNCT
ejpam-4684	102	18	γohich	γohich	PROPN
ejpam-4684	102	19	(	(	PUNCT
ejpam-4684	102	20	g	g	NOUN
ejpam-4684	102	21	)	)	PUNCT
ejpam-4684	102	22	=	=	VERB
ejpam-4684	102	23	n.	n.	NOUN
ejpam-4684	102	24	the	the	DET
ejpam-4684	102	25	next	next	ADJ
ejpam-4684	102	26	result	result	NOUN
ejpam-4684	102	27	follows	follow	VERB
ejpam-4684	102	28	from	from	ADP
ejpam-4684	102	29	theorem	theorem	ADJ
ejpam-4684	102	30	1	1	NUM
ejpam-4684	102	31	.	.	PUNCT
ejpam-4684	102	32	corollary	corollary	ADJ
ejpam-4684	102	33	1	1	NUM
ejpam-4684	102	34	.	.	PUNCT
ejpam-4684	103	1	let	let	VERB
ejpam-4684	103	2	g	g	PRON
ejpam-4684	103	3	be	be	AUX
ejpam-4684	103	4	a	a	DET
ejpam-4684	103	5	connected	connected	ADJ
ejpam-4684	103	6	graph	graph	NOUN
ejpam-4684	103	7	on	on	ADP
ejpam-4684	103	8	n	n	PRON
ejpam-4684	103	9	≥	≥	NUM
ejpam-4684	103	10	2	2	NUM
ejpam-4684	103	11	vertices	vertex	NOUN
ejpam-4684	103	12	.	.	PUNCT
ejpam-4684	104	1	then	then	ADV
ejpam-4684	104	2	(	(	PUNCT
ejpam-4684	104	3	i	i	NOUN
ejpam-4684	104	4	)	)	PUNCT
ejpam-4684	104	5	γohich	γohich	PROPN
ejpam-4684	104	6	(	(	PUNCT
ejpam-4684	104	7	g	g	NOUN
ejpam-4684	104	8	)	)	PUNCT
ejpam-4684	104	9	=	=	SYM
ejpam-4684	105	1	n	n	NOUN
ejpam-4684	105	2	if	if	SCONJ
ejpam-4684	105	3	and	and	CCONJ
ejpam-4684	105	4	only	only	ADV
ejpam-4684	105	5	if	if	SCONJ
ejpam-4684	105	6	g	g	PROPN
ejpam-4684	105	7	=	=	PROPN
ejpam-4684	105	8	kn	kn	PROPN
ejpam-4684	105	9	.	.	PUNCT
ejpam-4684	106	1	(	(	PUNCT
ejpam-4684	106	2	ii	ii	NOUN
ejpam-4684	106	3	)	)	PUNCT
ejpam-4684	106	4	2	2	NUM
ejpam-4684	106	5	≤	≤	NUM
ejpam-4684	106	6	γohich	γohich	PRON
ejpam-4684	106	7	(	(	PUNCT
ejpam-4684	106	8	g	g	NOUN
ejpam-4684	106	9	)	)	PUNCT
ejpam-4684	106	10	≤	≤	NUM
ejpam-4684	107	1	n−	n−	NOUN
ejpam-4684	107	2	1	1	NUM
ejpam-4684	107	3	if	if	SCONJ
ejpam-4684	107	4	and	and	CCONJ
ejpam-4684	107	5	only	only	ADV
ejpam-4684	107	6	if	if	SCONJ
ejpam-4684	107	7	g	g	PROPN
ejpam-4684	107	8	is	be	AUX
ejpam-4684	107	9	non	non	ADJ
ejpam-4684	107	10	-	-	ADJ
ejpam-4684	107	11	complete	complete	ADJ
ejpam-4684	107	12	graph	graph	NOUN
ejpam-4684	107	13	.	.	PUNCT
ejpam-4684	108	1	(	(	PUNCT
ejpam-4684	108	2	iii	iii	NOUN
ejpam-4684	108	3	)	)	PUNCT
ejpam-4684	108	4	4	4	NUM
ejpam-4684	108	5	≤	≤	NOUN
ejpam-4684	108	6	γohich	γohich	PROPN
ejpam-4684	108	7	(	(	PUNCT
ejpam-4684	108	8	g)+γohich	g)+γohich	X
ejpam-4684	108	9	(	(	PUNCT
ejpam-4684	108	10	g′	g′	NOUN
ejpam-4684	108	11	)	)	PUNCT
ejpam-4684	108	12	≤	≤	NOUN
ejpam-4684	108	13	2n−2	2n−2	NUM
ejpam-4684	108	14	if	if	SCONJ
ejpam-4684	108	15	and	and	CCONJ
ejpam-4684	108	16	only	only	ADV
ejpam-4684	108	17	if	if	SCONJ
ejpam-4684	108	18	g	g	PROPN
ejpam-4684	108	19	and	and	CCONJ
ejpam-4684	108	20	g′	g′	NOUN
ejpam-4684	108	21	are	be	AUX
ejpam-4684	108	22	two	two	NUM
ejpam-4684	108	23	non	non	ADJ
ejpam-4684	108	24	-	-	ADJ
ejpam-4684	108	25	complete	complete	ADJ
ejpam-4684	108	26	graphs	graph	NOUN
ejpam-4684	108	27	.	.	PUNCT
ejpam-4684	109	1	(	(	PUNCT
ejpam-4684	109	2	iv	iv	X
ejpam-4684	109	3	)	)	PUNCT
ejpam-4684	109	4	4	4	NUM
ejpam-4684	109	5	≤	≤	NUM
ejpam-4684	109	6	γohich	γohich	PROPN
ejpam-4684	109	7	(	(	PUNCT
ejpam-4684	109	8	h	h	NOUN
ejpam-4684	109	9	)	)	PUNCT
ejpam-4684	109	10	·	·	PUNCT
ejpam-4684	110	1	γohich	γohich	PROPN
ejpam-4684	110	2	(	(	PUNCT
ejpam-4684	110	3	j	j	NOUN
ejpam-4684	110	4	)	)	PUNCT
ejpam-4684	110	5	≤	≤	NOUN
ejpam-4684	110	6	n2	n2	NOUN
ejpam-4684	110	7	−	−	PROPN
ejpam-4684	110	8	2n	2n	NUM
ejpam-4684	111	1	+	+	CCONJ
ejpam-4684	111	2	1	1	NUM
ejpam-4684	111	3	if	if	SCONJ
ejpam-4684	111	4	and	and	CCONJ
ejpam-4684	111	5	only	only	ADV
ejpam-4684	111	6	if	if	SCONJ
ejpam-4684	111	7	h	h	NOUN
ejpam-4684	111	8	and	and	CCONJ
ejpam-4684	111	9	j	j	PROPN
ejpam-4684	111	10	are	be	AUX
ejpam-4684	111	11	two	two	NUM
ejpam-4684	111	12	non	non	ADJ
ejpam-4684	111	13	-	-	ADJ
ejpam-4684	111	14	complete	complete	ADJ
ejpam-4684	111	15	graphs	graph	NOUN
ejpam-4684	111	16	.	.	PUNCT
ejpam-4684	112	1	theorem	theorem	NOUN
ejpam-4684	112	2	2	2	NUM
ejpam-4684	112	3	.	.	PUNCT
ejpam-4684	113	1	let	let	VERB
ejpam-4684	113	2	g	g	PRON
ejpam-4684	113	3	be	be	AUX
ejpam-4684	113	4	a	a	DET
ejpam-4684	113	5	connected	connected	ADJ
ejpam-4684	113	6	graph	graph	NOUN
ejpam-4684	113	7	.	.	PUNCT
ejpam-4684	114	1	then	then	ADV
ejpam-4684	114	2	γohich	γohich	PROPN
ejpam-4684	114	3	(	(	PUNCT
ejpam-4684	114	4	g	g	NOUN
ejpam-4684	114	5	)	)	PUNCT
ejpam-4684	114	6	=	=	SYM
ejpam-4684	114	7	γch(g	γch(g	NOUN
ejpam-4684	114	8	)	)	PUNCT
ejpam-4684	114	9	if	if	SCONJ
ejpam-4684	114	10	and	and	CCONJ
ejpam-4684	114	11	only	only	ADV
ejpam-4684	114	12	if	if	SCONJ
ejpam-4684	114	13	g	g	PROPN
ejpam-4684	114	14	has	have	VERB
ejpam-4684	114	15	a	a	DET
ejpam-4684	114	16	γch	γch	NOUN
ejpam-4684	114	17	-	-	PUNCT
ejpam-4684	114	18	set	set	VERB
ejpam-4684	114	19	d	d	NOUN
ejpam-4684	114	20	such	such	ADJ
ejpam-4684	114	21	that	that	DET
ejpam-4684	114	22	v	v	NOUN
ejpam-4684	114	23	(	(	PUNCT
ejpam-4684	114	24	g	g	NOUN
ejpam-4684	114	25	)	)	PUNCT
ejpam-4684	114	26	\d	\d	NOUN
ejpam-4684	114	27	is	be	AUX
ejpam-4684	114	28	a	a	DET
ejpam-4684	114	29	hop	hop	NOUN
ejpam-4684	114	30	independent	independent	ADJ
ejpam-4684	114	31	set	set	NOUN
ejpam-4684	114	32	in	in	ADP
ejpam-4684	114	33	g.	g.	PROPN
ejpam-4684	114	34	proof	proof	PROPN
ejpam-4684	114	35	.	.	PUNCT
ejpam-4684	115	1	suppose	suppose	VERB
ejpam-4684	115	2	γohich	γohich	PROPN
ejpam-4684	115	3	(	(	PUNCT
ejpam-4684	115	4	g	g	NOUN
ejpam-4684	115	5	)	)	PUNCT
ejpam-4684	115	6	=	=	SYM
ejpam-4684	115	7	γch(g	γch(g	NOUN
ejpam-4684	115	8	)	)	PUNCT
ejpam-4684	115	9	.	.	PUNCT
ejpam-4684	116	1	let	let	VERB
ejpam-4684	116	2	d	d	PRON
ejpam-4684	116	3	be	be	AUX
ejpam-4684	116	4	a	a	DET
ejpam-4684	116	5	γohich	γohich	NOUN
ejpam-4684	116	6	-set	-set	ADJ
ejpam-4684	116	7	of	of	ADP
ejpam-4684	116	8	g.	g.	PROPN
ejpam-4684	116	9	then	then	ADV
ejpam-4684	116	10	v	v	X
ejpam-4684	116	11	(	(	PUNCT
ejpam-4684	116	12	g	g	NOUN
ejpam-4684	116	13	)	)	PUNCT
ejpam-4684	116	14	\d	\d	NOUN
ejpam-4684	116	15	is	be	AUX
ejpam-4684	116	16	a	a	DET
ejpam-4684	116	17	hop	hop	NOUN
ejpam-4684	116	18	independent	independent	ADJ
ejpam-4684	116	19	set	set	NOUN
ejpam-4684	116	20	in	in	ADP
ejpam-4684	116	21	g.	g.	PROPN
ejpam-4684	116	22	since	since	SCONJ
ejpam-4684	116	23	d	d	PROPN
ejpam-4684	116	24	is	be	AUX
ejpam-4684	116	25	a	a	DET
ejpam-4684	116	26	connected	connected	ADJ
ejpam-4684	116	27	hop	hop	NOUN
ejpam-4684	116	28	dominating	dominating	NOUN
ejpam-4684	116	29	set	set	NOUN
ejpam-4684	116	30	and	and	CCONJ
ejpam-4684	116	31	γohich	γohich	PROPN
ejpam-4684	116	32	(	(	PUNCT
ejpam-4684	116	33	g	g	NOUN
ejpam-4684	116	34	)	)	PUNCT
ejpam-4684	116	35	=	=	SYM
ejpam-4684	116	36	γch(g	γch(g	PROPN
ejpam-4684	116	37	)	)	PUNCT
ejpam-4684	116	38	=	=	SYM
ejpam-4684	116	39	|d|	|d|	PROPN
ejpam-4684	116	40	,	,	PUNCT
ejpam-4684	116	41	it	it	PRON
ejpam-4684	116	42	follows	follow	VERB
ejpam-4684	116	43	that	that	SCONJ
ejpam-4684	116	44	d	d	NOUN
ejpam-4684	116	45	is	be	AUX
ejpam-4684	116	46	a	a	DET
ejpam-4684	116	47	γch	γch	NOUN
ejpam-4684	116	48	-	-	PUNCT
ejpam-4684	116	49	set	set	NOUN
ejpam-4684	116	50	of	of	ADP
ejpam-4684	116	51	g.	g.	PROPN
ejpam-4684	116	52	j.	j.	PROPN
ejpam-4684	116	53	hassan	hassan	PROPN
ejpam-4684	116	54	,	,	PUNCT
ejpam-4684	116	55	a.	a.	PROPN
ejpam-4684	116	56	lintasan	lintasan	NOUN
ejpam-4684	116	57	,	,	PUNCT
ejpam-4684	116	58	n.	n.	PROPN
ejpam-4684	116	59	h.	h.	PROPN
ejpam-4684	116	60	mohammad	mohammad	PROPN
ejpam-4684	116	61	/	/	PUNCT
ejpam-4684	116	62	eur	eur	PROPN
ejpam-4684	116	63	.	.	PUNCT
ejpam-4684	117	1	j.	j.	PROPN
ejpam-4684	117	2	pure	pure	PROPN
ejpam-4684	117	3	appl	appl	PROPN
ejpam-4684	117	4	.	.	PROPN
ejpam-4684	117	5	math	math	PROPN
ejpam-4684	117	6	,	,	PUNCT
ejpam-4684	117	7	16	16	NUM
ejpam-4684	117	8	(	(	PUNCT
ejpam-4684	117	9	3	3	NUM
ejpam-4684	117	10	)	)	PUNCT
ejpam-4684	117	11	(	(	PUNCT
ejpam-4684	117	12	2023	2023	NUM
ejpam-4684	117	13	)	)	PUNCT
ejpam-4684	117	14	,	,	PUNCT
ejpam-4684	117	15	1848	1848	NUM
ejpam-4684	117	16	-	-	SYM
ejpam-4684	117	17	1861	1861	NUM
ejpam-4684	117	18	1852	1852	NUM
ejpam-4684	117	19	conversely	conversely	ADV
ejpam-4684	117	20	,	,	PUNCT
ejpam-4684	117	21	suppose	suppose	VERB
ejpam-4684	117	22	g	g	PROPN
ejpam-4684	117	23	has	have	VERB
ejpam-4684	117	24	a	a	DET
ejpam-4684	117	25	γch	γch	NOUN
ejpam-4684	117	26	-	-	PUNCT
ejpam-4684	117	27	set	set	VERB
ejpam-4684	117	28	d	d	NOUN
ejpam-4684	117	29	such	such	ADJ
ejpam-4684	117	30	that	that	DET
ejpam-4684	117	31	v	v	NOUN
ejpam-4684	117	32	(	(	PUNCT
ejpam-4684	117	33	g	g	NOUN
ejpam-4684	117	34	)	)	PUNCT
ejpam-4684	117	35	\	\	PUNCT
ejpam-4684	118	1	d	d	NOUN
ejpam-4684	118	2	is	be	AUX
ejpam-4684	118	3	a	a	DET
ejpam-4684	118	4	hop	hop	NOUN
ejpam-4684	118	5	independent	independent	ADJ
ejpam-4684	118	6	set	set	NOUN
ejpam-4684	118	7	in	in	ADP
ejpam-4684	118	8	g.	g.	PROPN
ejpam-4684	119	1	then	then	ADV
ejpam-4684	119	2	d	d	PROPN
ejpam-4684	119	3	is	be	AUX
ejpam-4684	119	4	a	a	DET
ejpam-4684	119	5	connected	connected	ADJ
ejpam-4684	119	6	outer	outer	ADJ
ejpam-4684	119	7	-	-	PUNCT
ejpam-4684	119	8	hop	hop	NOUN
ejpam-4684	119	9	independent	independent	ADJ
ejpam-4684	119	10	hop	hop	NOUN
ejpam-4684	119	11	dominating	dominating	NOUN
ejpam-4684	119	12	set	set	VERB
ejpam-4684	119	13	in	in	ADP
ejpam-4684	119	14	g.	g.	PROPN
ejpam-4684	119	15	hence	hence	ADV
ejpam-4684	119	16	,	,	PUNCT
ejpam-4684	119	17	γohich	γohich	PROPN
ejpam-4684	119	18	(	(	PUNCT
ejpam-4684	119	19	g	g	NOUN
ejpam-4684	119	20	)	)	PUNCT
ejpam-4684	119	21	≤	≤	NOUN
ejpam-4684	119	22	|d|	|d|	PROPN
ejpam-4684	119	23	=	=	SYM
ejpam-4684	119	24	γch(g	γch(g	PROPN
ejpam-4684	119	25	)	)	PUNCT
ejpam-4684	119	26	.	.	PUNCT
ejpam-4684	120	1	by	by	ADP
ejpam-4684	120	2	proposition	proposition	NOUN
ejpam-4684	120	3	1	1	NUM
ejpam-4684	120	4	,	,	PUNCT
ejpam-4684	120	5	γohich	γohich	PRON
ejpam-4684	120	6	(	(	PUNCT
ejpam-4684	120	7	g	g	NOUN
ejpam-4684	120	8	)	)	PUNCT
ejpam-4684	120	9	=	=	SYM
ejpam-4684	120	10	|d|	|d|	PROPN
ejpam-4684	120	11	=	=	SYM
ejpam-4684	120	12	γch(g	γch(g	PROPN
ejpam-4684	120	13	)	)	PUNCT
ejpam-4684	120	14	.	.	PUNCT
ejpam-4684	121	1	the	the	DET
ejpam-4684	121	2	next	next	ADJ
ejpam-4684	121	3	result	result	NOUN
ejpam-4684	121	4	is	be	AUX
ejpam-4684	121	5	a	a	DET
ejpam-4684	121	6	realization	realization	NOUN
ejpam-4684	121	7	problem	problem	NOUN
ejpam-4684	121	8	involving	involve	VERB
ejpam-4684	121	9	connected	connected	ADJ
ejpam-4684	121	10	outer	outer	ADJ
ejpam-4684	121	11	-	-	PUNCT
ejpam-4684	121	12	hop	hop	NOUN
ejpam-4684	121	13	independent	independent	ADJ
ejpam-4684	121	14	hop	hop	NOUN
ejpam-4684	121	15	domination	domination	NOUN
ejpam-4684	121	16	and	and	CCONJ
ejpam-4684	121	17	connected	connect	VERB
ejpam-4684	121	18	hop	hop	NOUN
ejpam-4684	121	19	domination	domination	NOUN
ejpam-4684	121	20	.	.	PUNCT
ejpam-4684	122	1	theorem	theorem	NOUN
ejpam-4684	122	2	3	3	X
ejpam-4684	122	3	.	.	PUNCT
ejpam-4684	123	1	let	let	VERB
ejpam-4684	123	2	a	a	PRON
ejpam-4684	123	3	and	and	CCONJ
ejpam-4684	123	4	b	b	NOUN
ejpam-4684	123	5	be	be	AUX
ejpam-4684	123	6	positive	positive	ADJ
ejpam-4684	123	7	integers	integer	NOUN
ejpam-4684	123	8	such	such	ADJ
ejpam-4684	123	9	that	that	SCONJ
ejpam-4684	123	10	2	2	NUM
ejpam-4684	123	11	≤	≤	NUM
ejpam-4684	123	12	a	a	DET
ejpam-4684	123	13	≤	≤	PROPN
ejpam-4684	123	14	b.	b.	NOUN
ejpam-4684	124	1	then	then	ADV
ejpam-4684	124	2	there	there	PRON
ejpam-4684	124	3	exists	exist	VERB
ejpam-4684	124	4	a	a	DET
ejpam-4684	124	5	connected	connected	ADJ
ejpam-4684	124	6	graph	graph	NOUN
ejpam-4684	124	7	g	g	ADP
ejpam-4684	124	8	such	such	ADJ
ejpam-4684	124	9	that	that	DET
ejpam-4684	124	10	γch(g	γch(g	NOUN
ejpam-4684	124	11	)	)	PUNCT
ejpam-4684	124	12	=	=	SYM
ejpam-4684	124	13	a	a	PROPN
ejpam-4684	124	14	and	and	CCONJ
ejpam-4684	124	15	γohich	γohich	PROPN
ejpam-4684	124	16	(	(	PUNCT
ejpam-4684	124	17	g	g	NOUN
ejpam-4684	124	18	)	)	PUNCT
ejpam-4684	124	19	=	=	SYM
ejpam-4684	124	20	b.	b.	NOUN
ejpam-4684	124	21	proof	proof	NOUN
ejpam-4684	124	22	.	.	PUNCT
ejpam-4684	125	1	for	for	ADP
ejpam-4684	125	2	a	a	DET
ejpam-4684	125	3	=	=	SYM
ejpam-4684	125	4	b	b	NOUN
ejpam-4684	125	5	,	,	PUNCT
ejpam-4684	125	6	consider	consider	VERB
ejpam-4684	125	7	the	the	DET
ejpam-4684	125	8	following	follow	VERB
ejpam-4684	125	9	two	two	NUM
ejpam-4684	125	10	cases	case	NOUN
ejpam-4684	125	11	:	:	PUNCT
ejpam-4684	125	12	case	case	NOUN
ejpam-4684	125	13	1	1	NUM
ejpam-4684	125	14	:	:	PUNCT
ejpam-4684	125	15	a	a	DET
ejpam-4684	125	16	=	=	SYM
ejpam-4684	125	17	2	2	NUM
ejpam-4684	125	18	consider	consider	VERB
ejpam-4684	125	19	ka	ka	PROPN
ejpam-4684	125	20	.	.	PUNCT
ejpam-4684	126	1	then	then	ADV
ejpam-4684	126	2	by	by	ADP
ejpam-4684	126	3	corollary	corollary	ADJ
ejpam-4684	126	4	1	1	NUM
ejpam-4684	126	5	,	,	PUNCT
ejpam-4684	126	6	γohich	γohich	PROPN
ejpam-4684	126	7	(	(	PUNCT
ejpam-4684	126	8	ka	ka	PROPN
ejpam-4684	126	9	)	)	PUNCT
ejpam-4684	126	10	=	=	SYM
ejpam-4684	126	11	a.	a.	NOUN
ejpam-4684	126	12	since	since	SCONJ
ejpam-4684	126	13	γch(ka	γch(ka	NOUN
ejpam-4684	126	14	)	)	PUNCT
ejpam-4684	127	1	=	=	SYM
ejpam-4684	127	2	a	a	X
ejpam-4684	127	3	,	,	PUNCT
ejpam-4684	127	4	we	we	PRON
ejpam-4684	127	5	have	have	VERB
ejpam-4684	127	6	γohich	γohich	PROPN
ejpam-4684	127	7	(	(	PUNCT
ejpam-4684	127	8	ka	ka	PROPN
ejpam-4684	127	9	)	)	PUNCT
ejpam-4684	127	10	=	=	SYM
ejpam-4684	127	11	a	a	DET
ejpam-4684	127	12	=	=	NOUN
ejpam-4684	127	13	γch(ka	γch(ka	NOUN
ejpam-4684	127	14	)	)	PUNCT
ejpam-4684	127	15	.	.	PUNCT
ejpam-4684	128	1	case	case	NOUN
ejpam-4684	128	2	2	2	NUM
ejpam-4684	128	3	:	:	PUNCT
ejpam-4684	128	4	a	a	DET
ejpam-4684	128	5	≥	≥	NOUN
ejpam-4684	128	6	3	3	NUM
ejpam-4684	128	7	consider	consider	VERB
ejpam-4684	128	8	the	the	DET
ejpam-4684	128	9	graph	graph	NOUN
ejpam-4684	128	10	g	g	NOUN
ejpam-4684	128	11	in	in	ADP
ejpam-4684	128	12	figure	figure	NOUN
ejpam-4684	128	13	1	1	NUM
ejpam-4684	128	14	.	.	PUNCT
ejpam-4684	129	1	let	let	VERB
ejpam-4684	129	2	d	d	NOUN
ejpam-4684	129	3	=	=	PUNCT
ejpam-4684	129	4	{	{	PUNCT
ejpam-4684	129	5	d1	d1	PROPN
ejpam-4684	129	6	,	,	PUNCT
ejpam-4684	129	7	d2	d2	PROPN
ejpam-4684	129	8	,	,	PUNCT
ejpam-4684	129	9	.	.	PUNCT
ejpam-4684	129	10	.	.	PUNCT
ejpam-4684	130	1	.	.	PUNCT
ejpam-4684	131	1	,	,	PUNCT
ejpam-4684	131	2	da	da	ADJ
ejpam-4684	131	3	}	}	PUNCT
ejpam-4684	131	4	.	.	PUNCT
ejpam-4684	132	1	then	then	ADV
ejpam-4684	132	2	d	d	PROPN
ejpam-4684	132	3	is	be	AUX
ejpam-4684	132	4	both	both	PRON
ejpam-4684	132	5	connected	connect	VERB
ejpam-4684	132	6	hop	hop	NOUN
ejpam-4684	132	7	dominating	dominating	NOUN
ejpam-4684	132	8	and	and	CCONJ
ejpam-4684	132	9	connected	connected	ADJ
ejpam-4684	132	10	outer	outer	ADJ
ejpam-4684	132	11	-	-	PUNCT
ejpam-4684	132	12	hop	hop	NOUN
ejpam-4684	132	13	independent	independent	ADJ
ejpam-4684	132	14	hop	hop	NOUN
ejpam-4684	132	15	dominating	dominating	NOUN
ejpam-4684	132	16	of	of	ADP
ejpam-4684	132	17	g.	g.	PROPN
ejpam-4684	132	18	observe	observe	VERB
ejpam-4684	132	19	that	that	SCONJ
ejpam-4684	132	20	every	every	DET
ejpam-4684	132	21	connected	connect	VERB
ejpam-4684	132	22	hop	hop	NOUN
ejpam-4684	132	23	dominating	dominating	NOUN
ejpam-4684	132	24	(	(	PUNCT
ejpam-4684	132	25	resp	resp	NOUN
ejpam-4684	132	26	.	.	PUNCT
ejpam-4684	133	1	connected	connected	ADJ
ejpam-4684	133	2	outer	outer	ADJ
ejpam-4684	133	3	-	-	PUNCT
ejpam-4684	133	4	hop	hop	NOUN
ejpam-4684	133	5	independent	independent	ADJ
ejpam-4684	133	6	hop	hop	NOUN
ejpam-4684	133	7	dominating	dominating	NOUN
ejpam-4684	133	8	)	)	PUNCT
ejpam-4684	134	1	set	set	NOUN
ejpam-4684	134	2	of	of	ADP
ejpam-4684	134	3	g	g	PROPN
ejpam-4684	134	4	contains	contain	VERB
ejpam-4684	134	5	d.	d.	PROPN
ejpam-4684	134	6	this	this	PRON
ejpam-4684	134	7	follows	follow	VERB
ejpam-4684	134	8	that	that	SCONJ
ejpam-4684	134	9	d	d	NOUN
ejpam-4684	134	10	is	be	AUX
ejpam-4684	134	11	both	both	PRON
ejpam-4684	134	12	a	a	DET
ejpam-4684	134	13	γch	γch	NOUN
ejpam-4684	134	14	-	-	PUNCT
ejpam-4684	134	15	set	set	VERB
ejpam-4684	134	16	and	and	CCONJ
ejpam-4684	134	17	a	a	DET
ejpam-4684	134	18	γohich	γohich	NOUN
ejpam-4684	134	19	-set	-set	PUNCT
ejpam-4684	134	20	of	of	ADP
ejpam-4684	134	21	g.	g.	PROPN
ejpam-4684	134	22	thus	thus	ADV
ejpam-4684	134	23	,	,	PUNCT
ejpam-4684	134	24	γch(g	γch(g	NOUN
ejpam-4684	134	25	)	)	PUNCT
ejpam-4684	134	26	=	=	PUNCT
ejpam-4684	134	27	a	a	DET
ejpam-4684	134	28	=	=	X
ejpam-4684	134	29	γohich	γohich	X
ejpam-4684	134	30	(	(	PUNCT
ejpam-4684	134	31	g	g	NOUN
ejpam-4684	134	32	)	)	PUNCT
ejpam-4684	134	33	.	.	PUNCT
ejpam-4684	135	1	g	g	NOUN
ejpam-4684	135	2	:	:	PUNCT
ejpam-4684	135	3	d2d1	d2d1	VERB
ejpam-4684	135	4	.	.	PUNCT
ejpam-4684	135	5	.	.	PUNCT
ejpam-4684	135	6	.	.	PUNCT
ejpam-4684	136	1	dada−1d3	dada−1d3	PRON
ejpam-4684	136	2	figure	figure	VERB
ejpam-4684	136	3	1	1	NUM
ejpam-4684	136	4	:	:	PUNCT
ejpam-4684	136	5	a	a	DET
ejpam-4684	136	6	graph	graph	NOUN
ejpam-4684	136	7	g	g	NOUN
ejpam-4684	136	8	with	with	ADP
ejpam-4684	136	9	γch(g	γch(g	NOUN
ejpam-4684	136	10	)	)	PUNCT
ejpam-4684	136	11	=	=	PUNCT
ejpam-4684	137	1	γohi	γohi	PROPN
ejpam-4684	137	2	ch	ch	NOUN
ejpam-4684	137	3	(	(	PUNCT
ejpam-4684	137	4	g	g	NOUN
ejpam-4684	137	5	)	)	PUNCT
ejpam-4684	137	6	suppose	suppose	VERB
ejpam-4684	137	7	a	a	DET
ejpam-4684	137	8	<	<	X
ejpam-4684	137	9	b.	b.	NOUN
ejpam-4684	137	10	let	let	VERB
ejpam-4684	137	11	m	m	VERB
ejpam-4684	137	12	=	=	VERB
ejpam-4684	138	1	b	b	X
ejpam-4684	138	2	−	−	PROPN
ejpam-4684	138	3	a	a	PRON
ejpam-4684	139	1	and	and	CCONJ
ejpam-4684	139	2	consider	consider	VERB
ejpam-4684	139	3	the	the	DET
ejpam-4684	139	4	graph	graph	NOUN
ejpam-4684	139	5	g′	g′	NOUN
ejpam-4684	139	6	given	give	VERB
ejpam-4684	139	7	in	in	ADP
ejpam-4684	139	8	figure	figure	NOUN
ejpam-4684	139	9	2	2	NUM
ejpam-4684	139	10	.	.	PUNCT
ejpam-4684	140	1	let	let	VERB
ejpam-4684	140	2	d1	d1	PROPN
ejpam-4684	140	3	=	=	PUNCT
ejpam-4684	140	4	{	{	PUNCT
ejpam-4684	140	5	x1	x1	PROPN
ejpam-4684	140	6	,	,	PUNCT
ejpam-4684	140	7	x2	x2	PROPN
ejpam-4684	140	8	,	,	PUNCT
ejpam-4684	140	9	.	.	PUNCT
ejpam-4684	140	10	.	.	PUNCT
ejpam-4684	141	1	.	.	PUNCT
ejpam-4684	142	1	,	,	PUNCT
ejpam-4684	142	2	xa	xa	PROPN
ejpam-4684	142	3	}	}	PUNCT
ejpam-4684	142	4	and	and	CCONJ
ejpam-4684	142	5	d2	d2	PROPN
ejpam-4684	142	6	=	=	SYM
ejpam-4684	142	7	{	{	PUNCT
ejpam-4684	142	8	x1	x1	PROPN
ejpam-4684	142	9	,	,	PUNCT
ejpam-4684	142	10	x2	x2	PROPN
ejpam-4684	142	11	,	,	PUNCT
ejpam-4684	142	12	.	.	PUNCT
ejpam-4684	142	13	.	.	PUNCT
ejpam-4684	143	1	.	.	PUNCT
ejpam-4684	144	1	,	,	PUNCT
ejpam-4684	144	2	xa	xa	PROPN
ejpam-4684	144	3	,	,	PUNCT
ejpam-4684	144	4	y1	y1	PROPN
ejpam-4684	144	5	,	,	PUNCT
ejpam-4684	144	6	y2	y2	PROPN
ejpam-4684	144	7	,	,	PUNCT
ejpam-4684	144	8	.	.	PUNCT
ejpam-4684	144	9	.	.	PUNCT
ejpam-4684	144	10	.	.	PUNCT
ejpam-4684	145	1	,	,	PUNCT
ejpam-4684	145	2	ym	ym	PROPN
ejpam-4684	145	3	}	}	PUNCT
ejpam-4684	145	4	.	.	PUNCT
ejpam-4684	146	1	then	then	ADV
ejpam-4684	146	2	n	n	NUM
ejpam-4684	146	3	′2	′2	X
ejpam-4684	146	4	g	g	NOUN
ejpam-4684	147	1	[	[	X
ejpam-4684	147	2	d1	d1	NOUN
ejpam-4684	147	3	]	]	X
ejpam-4684	147	4	=	=	SYM
ejpam-4684	147	5	v	v	X
ejpam-4684	147	6	(	(	PUNCT
ejpam-4684	147	7	g′	g′	NOUN
ejpam-4684	147	8	)	)	PUNCT
ejpam-4684	147	9	and	and	CCONJ
ejpam-4684	147	10	n	n	CCONJ
ejpam-4684	147	11	′2	′2	X
ejpam-4684	147	12	g	g	PROPN
ejpam-4684	147	13	[	[	X
ejpam-4684	147	14	d2	d2	X
ejpam-4684	147	15	]	]	X
ejpam-4684	147	16	=	=	SYM
ejpam-4684	147	17	v	v	X
ejpam-4684	147	18	(	(	PUNCT
ejpam-4684	147	19	g′	g′	NOUN
ejpam-4684	147	20	)	)	PUNCT
ejpam-4684	147	21	.	.	PUNCT
ejpam-4684	148	1	since	since	SCONJ
ejpam-4684	148	2	⟨d1⟩	⟨d1⟩	PROPN
ejpam-4684	148	3	and	and	CCONJ
ejpam-4684	148	4	⟨d2⟩	⟨d2⟩	NOUN
ejpam-4684	148	5	are	be	AUX
ejpam-4684	148	6	connected	connect	VERB
ejpam-4684	148	7	,	,	PUNCT
ejpam-4684	148	8	it	it	PRON
ejpam-4684	148	9	follows	follow	VERB
ejpam-4684	148	10	that	that	SCONJ
ejpam-4684	148	11	d1	d1	PROPN
ejpam-4684	148	12	and	and	CCONJ
ejpam-4684	148	13	d2	d2	PROPN
ejpam-4684	148	14	are	be	AUX
ejpam-4684	148	15	both	both	PRON
ejpam-4684	148	16	connected	connect	VERB
ejpam-4684	148	17	hop	hop	NOUN
ejpam-4684	148	18	dominating	dominating	NOUN
ejpam-4684	148	19	sets	set	NOUN
ejpam-4684	148	20	of	of	ADP
ejpam-4684	148	21	g′.	g′.	NOUN
ejpam-4684	148	22	moreover	moreover	ADV
ejpam-4684	148	23	,	,	PUNCT
ejpam-4684	148	24	since	since	SCONJ
ejpam-4684	148	25	any	any	DET
ejpam-4684	148	26	connected	connected	ADJ
ejpam-4684	148	27	hop	hop	NOUN
ejpam-4684	148	28	dominating	dominating	NOUN
ejpam-4684	148	29	(	(	PUNCT
ejpam-4684	148	30	resp	resp	NOUN
ejpam-4684	148	31	.	.	PUNCT
ejpam-4684	149	1	connected	connected	ADJ
ejpam-4684	149	2	outer	outer	ADJ
ejpam-4684	149	3	-	-	PUNCT
ejpam-4684	149	4	hop	hop	NOUN
ejpam-4684	149	5	independent	independent	ADJ
ejpam-4684	149	6	hop	hop	NOUN
ejpam-4684	149	7	dominating	dominating	NOUN
ejpam-4684	149	8	)	)	PUNCT
ejpam-4684	150	1	set	set	NOUN
ejpam-4684	150	2	d	d	NOUN
ejpam-4684	150	3	contains	contain	VERB
ejpam-4684	150	4	d1	d1	PROPN
ejpam-4684	150	5	(	(	PUNCT
ejpam-4684	150	6	resp	resp	NOUN
ejpam-4684	150	7	.	.	PUNCT
ejpam-4684	151	1	d2	d2	PROPN
ejpam-4684	151	2	)	)	PUNCT
ejpam-4684	151	3	,	,	PUNCT
ejpam-4684	151	4	d1	d1	PROPN
ejpam-4684	151	5	and	and	CCONJ
ejpam-4684	151	6	d2	d2	PROPN
ejpam-4684	151	7	are	be	AUX
ejpam-4684	151	8	γch	γch	VERB
ejpam-4684	151	9	-	-	PUNCT
ejpam-4684	151	10	set	set	VERB
ejpam-4684	151	11	and	and	CCONJ
ejpam-4684	151	12	γohich	γohich	PRON
ejpam-4684	151	13	-set	-set	PUNCT
ejpam-4684	151	14	of	of	ADP
ejpam-4684	151	15	g	g	NOUN
ejpam-4684	151	16	,	,	PUNCT
ejpam-4684	151	17	respectively	respectively	ADV
ejpam-4684	151	18	.	.	PUNCT
ejpam-4684	152	1	consequently	consequently	ADV
ejpam-4684	152	2	,	,	PUNCT
ejpam-4684	152	3	γch(g	γch(g	NOUN
ejpam-4684	152	4	′	′	NUM
ejpam-4684	152	5	)	)	PUNCT
ejpam-4684	152	6	=	=	PUNCT
ejpam-4684	152	7	a	a	PROPN
ejpam-4684	152	8	and	and	CCONJ
ejpam-4684	152	9	γohich	γohich	PROPN
ejpam-4684	152	10	(	(	PUNCT
ejpam-4684	152	11	g′	g′	NOUN
ejpam-4684	152	12	)	)	PUNCT
ejpam-4684	153	1	=	=	PUNCT
ejpam-4684	153	2	m+	m+	NUM
ejpam-4684	153	3	a	a	DET
ejpam-4684	153	4	=	=	SYM
ejpam-4684	153	5	b	b	NOUN
ejpam-4684	153	6	,	,	PUNCT
ejpam-4684	153	7	that	that	PRON
ejpam-4684	153	8	is	be	AUX
ejpam-4684	153	9	γch(g	γch(g	NOUN
ejpam-4684	153	10	′	′	NUM
ejpam-4684	153	11	)	)	PUNCT
ejpam-4684	153	12	=	=	PUNCT
ejpam-4684	154	1	a	a	DET
ejpam-4684	154	2	<	<	X
ejpam-4684	154	3	b	b	PROPN
ejpam-4684	154	4	=	=	X
ejpam-4684	154	5	γohich	γohich	PROPN
ejpam-4684	154	6	(	(	PUNCT
ejpam-4684	154	7	g′	g′	NOUN
ejpam-4684	154	8	)	)	PUNCT
ejpam-4684	154	9	.	.	PUNCT
ejpam-4684	155	1	j.	j.	PROPN
ejpam-4684	155	2	hassan	hassan	PROPN
ejpam-4684	155	3	,	,	PUNCT
ejpam-4684	155	4	a.	a.	PROPN
ejpam-4684	155	5	lintasan	lintasan	NOUN
ejpam-4684	155	6	,	,	PUNCT
ejpam-4684	155	7	n.	n.	PROPN
ejpam-4684	155	8	h.	h.	PROPN
ejpam-4684	155	9	mohammad	mohammad	PROPN
ejpam-4684	155	10	/	/	PUNCT
ejpam-4684	155	11	eur	eur	PROPN
ejpam-4684	155	12	.	.	PUNCT
ejpam-4684	156	1	j.	j.	PROPN
ejpam-4684	156	2	pure	pure	PROPN
ejpam-4684	156	3	appl	appl	PROPN
ejpam-4684	156	4	.	.	PROPN
ejpam-4684	156	5	math	math	PROPN
ejpam-4684	156	6	,	,	PUNCT
ejpam-4684	156	7	16	16	NUM
ejpam-4684	156	8	(	(	PUNCT
ejpam-4684	156	9	3	3	NUM
ejpam-4684	156	10	)	)	PUNCT
ejpam-4684	156	11	(	(	PUNCT
ejpam-4684	156	12	2023	2023	NUM
ejpam-4684	156	13	)	)	PUNCT
ejpam-4684	156	14	,	,	PUNCT
ejpam-4684	156	15	1848	1848	NUM
ejpam-4684	156	16	-	-	SYM
ejpam-4684	156	17	1861	1861	NUM
ejpam-4684	156	18	1853	1853	NUM
ejpam-4684	156	19	xa−1	xa−1	PROPN
ejpam-4684	156	20	g′	g′	PROPN
ejpam-4684	156	21	:	:	PUNCT
ejpam-4684	157	1	x2x1	x2x1	INTJ
ejpam-4684	157	2	xa	xa	PROPN
ejpam-4684	157	3	.	.	PUNCT
ejpam-4684	157	4	.	.	PUNCT
ejpam-4684	157	5	.	.	PUNCT
ejpam-4684	158	1	y1	y1	INTJ
ejpam-4684	158	2	y2	y2	INTJ
ejpam-4684	159	1	ym	ym	INTJ
ejpam-4684	159	2	.	.	PUNCT
ejpam-4684	159	3	.	.	PUNCT
ejpam-4684	159	4	.	.	PUNCT
ejpam-4684	160	1	figure	figure	VERB
ejpam-4684	160	2	2	2	NUM
ejpam-4684	160	3	:	:	PUNCT
ejpam-4684	160	4	a	a	DET
ejpam-4684	160	5	graph	graph	NOUN
ejpam-4684	160	6	g′	g′	NOUN
ejpam-4684	160	7	with	with	ADP
ejpam-4684	160	8	γch(g	γch(g	NOUN
ejpam-4684	160	9	′	′	NUM
ejpam-4684	160	10	)	)	PUNCT
ejpam-4684	160	11	<	<	X
ejpam-4684	160	12	γohi	γohi	PROPN
ejpam-4684	160	13	ch	ch	PROPN
ejpam-4684	160	14	(	(	PUNCT
ejpam-4684	160	15	g′	g′	NOUN
ejpam-4684	160	16	)	)	PUNCT
ejpam-4684	160	17	corollary	corollary	NOUN
ejpam-4684	161	1	2	2	NUM
ejpam-4684	161	2	.	.	PUNCT
ejpam-4684	162	1	let	let	VERB
ejpam-4684	162	2	n	n	PRON
ejpam-4684	162	3	be	be	AUX
ejpam-4684	162	4	a	a	DET
ejpam-4684	162	5	positive	positive	ADJ
ejpam-4684	162	6	integer	integer	NOUN
ejpam-4684	162	7	.	.	PUNCT
ejpam-4684	163	1	then	then	ADV
ejpam-4684	163	2	there	there	PRON
ejpam-4684	163	3	exists	exist	VERB
ejpam-4684	163	4	a	a	DET
ejpam-4684	163	5	connected	connected	ADJ
ejpam-4684	163	6	graph	graph	NOUN
ejpam-4684	163	7	g	g	ADP
ejpam-4684	163	8	such	such	ADJ
ejpam-4684	163	9	that	that	DET
ejpam-4684	163	10	γohich	γohich	PROPN
ejpam-4684	163	11	(	(	PUNCT
ejpam-4684	163	12	g)−	g)−	PROPN
ejpam-4684	163	13	γch(g	γch(g	PROPN
ejpam-4684	163	14	)	)	PUNCT
ejpam-4684	163	15	=	=	PUNCT
ejpam-4684	164	1	n.	n.	NOUN
ejpam-4684	164	2	in	in	ADP
ejpam-4684	164	3	other	other	ADJ
ejpam-4684	164	4	words	word	NOUN
ejpam-4684	164	5	,	,	PUNCT
ejpam-4684	164	6	γohich	γohich	PROPN
ejpam-4684	164	7	(	(	PUNCT
ejpam-4684	164	8	g)−	g)−	PROPN
ejpam-4684	164	9	γch(g	γch(g	NOUN
ejpam-4684	164	10	)	)	PUNCT
ejpam-4684	164	11	can	can	AUX
ejpam-4684	164	12	be	be	AUX
ejpam-4684	164	13	made	make	VERB
ejpam-4684	164	14	arbitrarily	arbitrarily	ADV
ejpam-4684	164	15	large	large	ADJ
ejpam-4684	164	16	.	.	PUNCT
ejpam-4684	165	1	the	the	DET
ejpam-4684	165	2	next	next	ADJ
ejpam-4684	165	3	result	result	NOUN
ejpam-4684	165	4	is	be	AUX
ejpam-4684	165	5	a	a	DET
ejpam-4684	165	6	realization	realization	NOUN
ejpam-4684	165	7	problem	problem	NOUN
ejpam-4684	165	8	involving	involve	VERB
ejpam-4684	165	9	connected	connected	ADJ
ejpam-4684	165	10	outer	outer	ADJ
ejpam-4684	165	11	-	-	PUNCT
ejpam-4684	165	12	independent	independent	ADJ
ejpam-4684	165	13	hop	hop	NOUN
ejpam-4684	165	14	domination	domination	NOUN
ejpam-4684	165	15	and	and	CCONJ
ejpam-4684	165	16	connected	connected	ADJ
ejpam-4684	165	17	outer	outer	ADJ
ejpam-4684	165	18	-	-	PUNCT
ejpam-4684	165	19	hop	hop	NOUN
ejpam-4684	165	20	independent	independent	ADJ
ejpam-4684	165	21	hop	hop	NOUN
ejpam-4684	165	22	domination	domination	NOUN
ejpam-4684	165	23	.	.	PUNCT
ejpam-4684	166	1	theorem	theorem	ADJ
ejpam-4684	166	2	4	4	NUM
ejpam-4684	166	3	.	.	PUNCT
ejpam-4684	167	1	let	let	VERB
ejpam-4684	167	2	a	a	PRON
ejpam-4684	167	3	and	and	CCONJ
ejpam-4684	167	4	b	b	NOUN
ejpam-4684	167	5	be	be	AUX
ejpam-4684	167	6	positive	positive	ADJ
ejpam-4684	167	7	integers	integer	NOUN
ejpam-4684	167	8	such	such	ADJ
ejpam-4684	167	9	that	that	SCONJ
ejpam-4684	167	10	2	2	NUM
ejpam-4684	167	11	≤	≤	NUM
ejpam-4684	167	12	a	a	DET
ejpam-4684	167	13	≤	≤	PROPN
ejpam-4684	167	14	b.	b.	NOUN
ejpam-4684	168	1	then	then	ADV
ejpam-4684	168	2	(	(	PUNCT
ejpam-4684	168	3	i	i	NOUN
ejpam-4684	168	4	)	)	PUNCT
ejpam-4684	168	5	there	there	PRON
ejpam-4684	168	6	exists	exist	VERB
ejpam-4684	168	7	a	a	DET
ejpam-4684	168	8	connected	connected	ADJ
ejpam-4684	168	9	graph	graph	NOUN
ejpam-4684	168	10	g	g	ADP
ejpam-4684	168	11	such	such	ADJ
ejpam-4684	168	12	that	that	DET
ejpam-4684	168	13	γohich	γohich	PROPN
ejpam-4684	168	14	(	(	PUNCT
ejpam-4684	168	15	g	g	NOUN
ejpam-4684	168	16	)	)	PUNCT
ejpam-4684	168	17	=	=	SYM
ejpam-4684	168	18	a	a	PRON
ejpam-4684	168	19	and	and	CCONJ
ejpam-4684	168	20	γoich(g	γoich(g	PROPN
ejpam-4684	168	21	)	)	PUNCT
ejpam-4684	168	22	=	=	SYM
ejpam-4684	168	23	b.	b.	PROPN
ejpam-4684	168	24	(	(	PUNCT
ejpam-4684	168	25	ii	ii	PROPN
ejpam-4684	168	26	)	)	PUNCT
ejpam-4684	168	27	there	there	PRON
ejpam-4684	168	28	exists	exist	VERB
ejpam-4684	168	29	a	a	DET
ejpam-4684	168	30	connected	connected	ADJ
ejpam-4684	168	31	graph	graph	NOUN
ejpam-4684	168	32	g	g	ADP
ejpam-4684	168	33	such	such	ADJ
ejpam-4684	168	34	that	that	DET
ejpam-4684	168	35	γoich(g	γoich(g	NOUN
ejpam-4684	168	36	)	)	PUNCT
ejpam-4684	168	37	=	=	PUNCT
ejpam-4684	168	38	a	a	PROPN
ejpam-4684	168	39	and	and	CCONJ
ejpam-4684	168	40	γohich	γohich	PROPN
ejpam-4684	168	41	(	(	PUNCT
ejpam-4684	168	42	g	g	NOUN
ejpam-4684	168	43	)	)	PUNCT
ejpam-4684	169	1	=	=	SYM
ejpam-4684	169	2	b.	b.	NOUN
ejpam-4684	169	3	proof	proof	NOUN
ejpam-4684	169	4	.	.	PUNCT
ejpam-4684	170	1	(	(	PUNCT
ejpam-4684	170	2	i	i	NOUN
ejpam-4684	170	3	)	)	PUNCT
ejpam-4684	170	4	for	for	ADP
ejpam-4684	170	5	a	a	DET
ejpam-4684	170	6	=	=	SYM
ejpam-4684	170	7	b	b	NOUN
ejpam-4684	170	8	,	,	PUNCT
ejpam-4684	170	9	consider	consider	VERB
ejpam-4684	170	10	g	g	PROPN
ejpam-4684	170	11	=	=	SYM
ejpam-4684	170	12	ka	ka	PROPN
ejpam-4684	170	13	.	.	PUNCT
ejpam-4684	171	1	then	then	ADV
ejpam-4684	171	2	γoich(g	γoich(g	VERB
ejpam-4684	171	3	)	)	PUNCT
ejpam-4684	171	4	=	=	PUNCT
ejpam-4684	171	5	a	a	DET
ejpam-4684	171	6	=	=	PUNCT
ejpam-4684	171	7	γohich	γohich	PROPN
ejpam-4684	171	8	.	.	PUNCT
ejpam-4684	172	1	suppose	suppose	VERB
ejpam-4684	172	2	a	a	DET
ejpam-4684	172	3	<	<	X
ejpam-4684	172	4	b.	b.	NOUN
ejpam-4684	172	5	let	let	VERB
ejpam-4684	172	6	m	m	VERB
ejpam-4684	172	7	=	=	VERB
ejpam-4684	173	1	b	b	X
ejpam-4684	173	2	−	−	PROPN
ejpam-4684	173	3	a	a	PRON
ejpam-4684	174	1	and	and	CCONJ
ejpam-4684	174	2	consider	consider	VERB
ejpam-4684	174	3	the	the	DET
ejpam-4684	174	4	graph	graph	NOUN
ejpam-4684	174	5	j	j	PROPN
ejpam-4684	174	6	in	in	ADP
ejpam-4684	174	7	figure	figure	NOUN
ejpam-4684	174	8	3	3	NUM
ejpam-4684	174	9	.	.	PUNCT
ejpam-4684	175	1	let	let	VERB
ejpam-4684	175	2	s1	s1	PROPN
ejpam-4684	175	3	=	=	SYM
ejpam-4684	175	4	{	{	PUNCT
ejpam-4684	175	5	v1	v1	PROPN
ejpam-4684	175	6	,	,	PUNCT
ejpam-4684	175	7	v2	v2	PROPN
ejpam-4684	175	8	,	,	PUNCT
ejpam-4684	175	9	.	.	PUNCT
ejpam-4684	175	10	.	.	PUNCT
ejpam-4684	176	1	.	.	PUNCT
ejpam-4684	177	1	,	,	PUNCT
ejpam-4684	177	2	va	va	NOUN
ejpam-4684	177	3	}	}	PUNCT
ejpam-4684	177	4	and	and	CCONJ
ejpam-4684	177	5	s2	s2	VERB
ejpam-4684	177	6	=	=	SYM
ejpam-4684	177	7	{	{	PUNCT
ejpam-4684	177	8	v1	v1	PROPN
ejpam-4684	177	9	,	,	PUNCT
ejpam-4684	177	10	v2	v2	PROPN
ejpam-4684	177	11	,	,	PUNCT
ejpam-4684	177	12	.	.	PUNCT
ejpam-4684	177	13	.	.	PUNCT
ejpam-4684	178	1	.	.	PUNCT
ejpam-4684	179	1	,	,	PUNCT
ejpam-4684	179	2	va	va	NOUN
ejpam-4684	179	3	,	,	PUNCT
ejpam-4684	179	4	y1	y1	PROPN
ejpam-4684	179	5	,	,	PUNCT
ejpam-4684	179	6	y2	y2	PROPN
ejpam-4684	179	7	,	,	PUNCT
ejpam-4684	179	8	.	.	PUNCT
ejpam-4684	179	9	.	.	PUNCT
ejpam-4684	180	1	.	.	PUNCT
ejpam-4684	181	1	,	,	PUNCT
ejpam-4684	181	2	ym	ym	PROPN
ejpam-4684	181	3	}	}	PUNCT
ejpam-4684	181	4	.	.	PUNCT
ejpam-4684	182	1	then	then	ADV
ejpam-4684	182	2	s1	s1	PROPN
ejpam-4684	182	3	and	and	CCONJ
ejpam-4684	182	4	s2	s2	PROPN
ejpam-4684	182	5	are	be	AUX
ejpam-4684	182	6	γohich	γohich	NOUN
ejpam-4684	182	7	-set	-set	ADJ
ejpam-4684	182	8	and	and	CCONJ
ejpam-4684	182	9	γoich	γoich	NOUN
ejpam-4684	182	10	-	-	PUNCT
ejpam-4684	182	11	set	set	NOUN
ejpam-4684	182	12	of	of	ADP
ejpam-4684	182	13	j	j	PROPN
ejpam-4684	182	14	,	,	PUNCT
ejpam-4684	182	15	respectively	respectively	ADV
ejpam-4684	182	16	.	.	PUNCT
ejpam-4684	183	1	hence	hence	ADV
ejpam-4684	183	2	,	,	PUNCT
ejpam-4684	183	3	γ	γ	X
ejpam-4684	183	4	ohi	ohi	PROPN
ejpam-4684	183	5	ch	ch	PROPN
ejpam-4684	183	6	(	(	PUNCT
ejpam-4684	183	7	j	j	PROPN
ejpam-4684	183	8	)	)	PUNCT
ejpam-4684	183	9	=	=	PUNCT
ejpam-4684	183	10	a	a	PRON
ejpam-4684	183	11	and	and	CCONJ
ejpam-4684	183	12	γoich(j	γoich(j	NOUN
ejpam-4684	183	13	)	)	PUNCT
ejpam-4684	184	1	=	=	VERB
ejpam-4684	184	2	m+	m+	NUM
ejpam-4684	184	3	a	a	DET
ejpam-4684	184	4	=	=	PROPN
ejpam-4684	184	5	b.	b.	PROPN
ejpam-4684	184	6	j.	j.	PROPN
ejpam-4684	184	7	hassan	hassan	PROPN
ejpam-4684	184	8	,	,	PUNCT
ejpam-4684	184	9	a.	a.	PROPN
ejpam-4684	184	10	lintasan	lintasan	NOUN
ejpam-4684	184	11	,	,	PUNCT
ejpam-4684	184	12	n.	n.	PROPN
ejpam-4684	184	13	h.	h.	PROPN
ejpam-4684	184	14	mohammad	mohammad	PROPN
ejpam-4684	184	15	/	/	PUNCT
ejpam-4684	184	16	eur	eur	PROPN
ejpam-4684	184	17	.	.	PUNCT
ejpam-4684	185	1	j.	j.	PROPN
ejpam-4684	185	2	pure	pure	PROPN
ejpam-4684	185	3	appl	appl	PROPN
ejpam-4684	185	4	.	.	PROPN
ejpam-4684	185	5	math	math	PROPN
ejpam-4684	185	6	,	,	PUNCT
ejpam-4684	185	7	16	16	NUM
ejpam-4684	185	8	(	(	PUNCT
ejpam-4684	185	9	3	3	NUM
ejpam-4684	185	10	)	)	PUNCT
ejpam-4684	185	11	(	(	PUNCT
ejpam-4684	185	12	2023	2023	NUM
ejpam-4684	185	13	)	)	PUNCT
ejpam-4684	185	14	,	,	PUNCT
ejpam-4684	185	15	1848	1848	NUM
ejpam-4684	185	16	-	-	SYM
ejpam-4684	185	17	1861	1861	NUM
ejpam-4684	185	18	1854	1854	NUM
ejpam-4684	185	19	.	.	PUNCT
ejpam-4684	185	20	.	.	PUNCT
ejpam-4684	185	21	.	.	PUNCT
ejpam-4684	186	1	v1	v1	VERB
ejpam-4684	186	2	v2	v2	PROPN
ejpam-4684	186	3	va−1	va−1	NOUN
ejpam-4684	186	4	va	va	NOUN
ejpam-4684	186	5	y1	y1	PROPN
ejpam-4684	186	6	w	w	PROPN
ejpam-4684	186	7	ym	ym	INTJ
ejpam-4684	186	8	.	.	PUNCT
ejpam-4684	186	9	.	.	PUNCT
ejpam-4684	186	10	.	.	PUNCT
ejpam-4684	187	1	j	j	NOUN
ejpam-4684	187	2	:	:	PUNCT
ejpam-4684	187	3	va−2	va−2	PROPN
ejpam-4684	187	4	figure	figure	NOUN
ejpam-4684	187	5	3	3	NUM
ejpam-4684	187	6	:	:	PUNCT
ejpam-4684	187	7	a	a	DET
ejpam-4684	187	8	graph	graph	NOUN
ejpam-4684	187	9	j	j	PROPN
ejpam-4684	187	10	with	with	ADP
ejpam-4684	187	11	γohi	γohi	PROPN
ejpam-4684	187	12	ch	ch	PROPN
ejpam-4684	187	13	(	(	PUNCT
ejpam-4684	187	14	j	j	PROPN
ejpam-4684	187	15	)	)	PUNCT
ejpam-4684	187	16	<	<	X
ejpam-4684	187	17	γoi	γoi	PROPN
ejpam-4684	187	18	ch(j	ch(j	NOUN
ejpam-4684	187	19	)	)	PUNCT
ejpam-4684	187	20	(	(	PUNCT
ejpam-4684	187	21	ii	ii	NOUN
ejpam-4684	187	22	)	)	PUNCT
ejpam-4684	187	23	for	for	ADP
ejpam-4684	187	24	a	a	DET
ejpam-4684	187	25	=	=	SYM
ejpam-4684	187	26	b	b	NOUN
ejpam-4684	187	27	,	,	PUNCT
ejpam-4684	187	28	consider	consider	VERB
ejpam-4684	187	29	g	g	PROPN
ejpam-4684	187	30	=	=	SYM
ejpam-4684	187	31	ka	ka	PROPN
ejpam-4684	187	32	.	.	PUNCT
ejpam-4684	188	1	then	then	ADV
ejpam-4684	188	2	γohich	γohich	PROPN
ejpam-4684	188	3	(	(	PUNCT
ejpam-4684	188	4	g	g	NOUN
ejpam-4684	188	5	)	)	PUNCT
ejpam-4684	188	6	=	=	SYM
ejpam-4684	188	7	a	a	DET
ejpam-4684	188	8	=	=	PUNCT
ejpam-4684	188	9	γoich(g	γoich(g	NOUN
ejpam-4684	188	10	)	)	PUNCT
ejpam-4684	188	11	.	.	PUNCT
ejpam-4684	189	1	suppose	suppose	VERB
ejpam-4684	189	2	a	a	DET
ejpam-4684	189	3	<	<	X
ejpam-4684	189	4	b.	b.	NOUN
ejpam-4684	189	5	let	let	VERB
ejpam-4684	189	6	m	m	VERB
ejpam-4684	189	7	=	=	VERB
ejpam-4684	190	1	b	b	X
ejpam-4684	190	2	−	−	PROPN
ejpam-4684	190	3	a	a	PRON
ejpam-4684	191	1	and	and	CCONJ
ejpam-4684	191	2	consider	consider	VERB
ejpam-4684	191	3	the	the	DET
ejpam-4684	191	4	graph	graph	NOUN
ejpam-4684	191	5	h	h	NOUN
ejpam-4684	191	6	in	in	ADP
ejpam-4684	191	7	figure	figure	NOUN
ejpam-4684	191	8	4	4	NUM
ejpam-4684	191	9	.	.	PUNCT
ejpam-4684	192	1	let	let	VERB
ejpam-4684	192	2	d1	d1	PROPN
ejpam-4684	192	3	=	=	PUNCT
ejpam-4684	192	4	{	{	PUNCT
ejpam-4684	192	5	x1	x1	PROPN
ejpam-4684	192	6	,	,	PUNCT
ejpam-4684	192	7	x2	x2	PROPN
ejpam-4684	192	8	,	,	PUNCT
ejpam-4684	192	9	.	.	PUNCT
ejpam-4684	192	10	.	.	PUNCT
ejpam-4684	193	1	.	.	PUNCT
ejpam-4684	194	1	,	,	PUNCT
ejpam-4684	194	2	xa	xa	PROPN
ejpam-4684	194	3	}	}	PUNCT
ejpam-4684	194	4	and	and	CCONJ
ejpam-4684	194	5	d2	d2	PROPN
ejpam-4684	194	6	=	=	SYM
ejpam-4684	194	7	{	{	PUNCT
ejpam-4684	194	8	x1	x1	PROPN
ejpam-4684	194	9	,	,	PUNCT
ejpam-4684	194	10	x2	x2	PROPN
ejpam-4684	194	11	,	,	PUNCT
ejpam-4684	194	12	.	.	PUNCT
ejpam-4684	194	13	.	.	PUNCT
ejpam-4684	195	1	.	.	PUNCT
ejpam-4684	196	1	,	,	PUNCT
ejpam-4684	196	2	xa	xa	PROPN
ejpam-4684	196	3	,	,	PUNCT
ejpam-4684	196	4	y1	y1	PROPN
ejpam-4684	196	5	,	,	PUNCT
ejpam-4684	196	6	y2	y2	PROPN
ejpam-4684	196	7	,	,	PUNCT
ejpam-4684	196	8	.	.	PUNCT
ejpam-4684	196	9	.	.	PUNCT
ejpam-4684	196	10	.	.	PUNCT
ejpam-4684	197	1	,	,	PUNCT
ejpam-4684	197	2	ym	ym	PROPN
ejpam-4684	197	3	}	}	PUNCT
ejpam-4684	197	4	.	.	PUNCT
ejpam-4684	198	1	then	then	ADV
ejpam-4684	198	2	d1	d1	PROPN
ejpam-4684	198	3	and	and	CCONJ
ejpam-4684	198	4	d2	d2	PROPN
ejpam-4684	198	5	are	be	AUX
ejpam-4684	198	6	γoich	γoich	ADV
ejpam-4684	198	7	-	-	PUNCT
ejpam-4684	198	8	set	set	VERB
ejpam-4684	198	9	and	and	CCONJ
ejpam-4684	198	10	γohich	γohich	PRON
ejpam-4684	198	11	-set	-set	PUNCT
ejpam-4684	198	12	of	of	ADP
ejpam-4684	198	13	h	h	NOUN
ejpam-4684	198	14	,	,	PUNCT
ejpam-4684	198	15	respectively	respectively	ADV
ejpam-4684	198	16	.	.	PUNCT
ejpam-4684	199	1	hence	hence	ADV
ejpam-4684	199	2	,	,	PUNCT
ejpam-4684	199	3	γoich(h	γoich(h	PROPN
ejpam-4684	199	4	)	)	PUNCT
ejpam-4684	199	5	=	=	SYM
ejpam-4684	199	6	a	a	PROPN
ejpam-4684	199	7	and	and	CCONJ
ejpam-4684	199	8	γohich	γohich	PROPN
ejpam-4684	199	9	(	(	PUNCT
ejpam-4684	199	10	h	h	NOUN
ejpam-4684	199	11	)	)	PUNCT
ejpam-4684	199	12	=	=	VERB
ejpam-4684	200	1	m+	m+	NUM
ejpam-4684	200	2	a	a	DET
ejpam-4684	200	3	=	=	X
ejpam-4684	200	4	b.	b.	PROPN
ejpam-4684	200	5	xa−2	xa−2	PROPN
ejpam-4684	200	6	h	h	NOUN
ejpam-4684	200	7	:	:	PUNCT
ejpam-4684	201	1	x2x1	x2x1	X
ejpam-4684	201	2	xa	xa	PROPN
ejpam-4684	201	3	.	.	PUNCT
ejpam-4684	201	4	.	.	PUNCT
ejpam-4684	201	5	.	.	PUNCT
ejpam-4684	202	1	y1	y1	INTJ
ejpam-4684	202	2	y2	y2	INTJ
ejpam-4684	203	1	ym	ym	INTJ
ejpam-4684	203	2	.	.	PUNCT
ejpam-4684	203	3	.	.	PUNCT
ejpam-4684	203	4	.	.	PUNCT
ejpam-4684	204	1	w	w	PROPN
ejpam-4684	204	2	aa−1	aa−1	NOUN
ejpam-4684	204	3	figure	figure	NOUN
ejpam-4684	204	4	4	4	NUM
ejpam-4684	204	5	:	:	PUNCT
ejpam-4684	204	6	a	a	DET
ejpam-4684	204	7	graph	graph	NOUN
ejpam-4684	204	8	h	h	NOUN
ejpam-4684	204	9	with	with	ADP
ejpam-4684	204	10	γoi	γoi	NOUN
ejpam-4684	204	11	ch(h	ch(h	VERB
ejpam-4684	204	12	)	)	PUNCT
ejpam-4684	204	13	<	<	X
ejpam-4684	204	14	γohi	γohi	PROPN
ejpam-4684	204	15	ch	ch	PROPN
ejpam-4684	204	16	(	(	PUNCT
ejpam-4684	204	17	h	h	NOUN
ejpam-4684	204	18	)	)	PUNCT
ejpam-4684	204	19	corollary	corollary	ADJ
ejpam-4684	204	20	3	3	NUM
ejpam-4684	204	21	.	.	PUNCT
ejpam-4684	205	1	let	let	VERB
ejpam-4684	205	2	n	n	PRON
ejpam-4684	205	3	be	be	AUX
ejpam-4684	205	4	a	a	DET
ejpam-4684	205	5	positive	positive	ADJ
ejpam-4684	205	6	integer	integer	NOUN
ejpam-4684	205	7	.	.	PUNCT
ejpam-4684	206	1	then	then	ADV
ejpam-4684	206	2	each	each	PRON
ejpam-4684	206	3	of	of	ADP
ejpam-4684	206	4	the	the	DET
ejpam-4684	206	5	following	following	ADJ
ejpam-4684	206	6	statements	statement	NOUN
ejpam-4684	206	7	holds	hold	VERB
ejpam-4684	206	8	.	.	PUNCT
ejpam-4684	207	1	(	(	PUNCT
ejpam-4684	207	2	i	i	NOUN
ejpam-4684	207	3	)	)	PUNCT
ejpam-4684	207	4	there	there	PRON
ejpam-4684	207	5	exists	exist	VERB
ejpam-4684	207	6	a	a	DET
ejpam-4684	207	7	connected	connected	ADJ
ejpam-4684	207	8	graph	graph	NOUN
ejpam-4684	207	9	g	g	ADP
ejpam-4684	207	10	such	such	ADJ
ejpam-4684	207	11	that	that	PRON
ejpam-4684	207	12	γoich(g)−	γoich(g)−	PROPN
ejpam-4684	207	13	γohich	γohich	PROPN
ejpam-4684	207	14	(	(	PUNCT
ejpam-4684	207	15	g	g	NOUN
ejpam-4684	207	16	)	)	PUNCT
ejpam-4684	207	17	=	=	VERB
ejpam-4684	207	18	n.	n.	NOUN
ejpam-4684	207	19	(	(	PUNCT
ejpam-4684	207	20	ii	ii	NOUN
ejpam-4684	207	21	)	)	PUNCT
ejpam-4684	207	22	there	there	PRON
ejpam-4684	207	23	exists	exist	VERB
ejpam-4684	207	24	a	a	DET
ejpam-4684	207	25	connected	connected	ADJ
ejpam-4684	207	26	graph	graph	NOUN
ejpam-4684	207	27	g	g	ADP
ejpam-4684	207	28	such	such	ADJ
ejpam-4684	207	29	that	that	DET
ejpam-4684	207	30	γohich	γohich	PROPN
ejpam-4684	207	31	(	(	PUNCT
ejpam-4684	207	32	g)−	g)−	PROPN
ejpam-4684	207	33	γoich(g	γoich(g	PROPN
ejpam-4684	207	34	)	)	PUNCT
ejpam-4684	207	35	=	=	VERB
ejpam-4684	208	1	n.	n.	NOUN
ejpam-4684	208	2	in	in	ADP
ejpam-4684	208	3	other	other	ADJ
ejpam-4684	208	4	words	word	NOUN
ejpam-4684	208	5	,	,	PUNCT
ejpam-4684	208	6	the	the	DET
ejpam-4684	208	7	absolute	absolute	ADJ
ejpam-4684	208	8	difference	difference	NOUN
ejpam-4684	208	9	|γoich(g)−γohich	|γoich(g)−γohich	ADP
ejpam-4684	208	10	(	(	PUNCT
ejpam-4684	208	11	g)|	g)|	NOUN
ejpam-4684	208	12	can	can	AUX
ejpam-4684	208	13	be	be	AUX
ejpam-4684	208	14	made	make	VERB
ejpam-4684	208	15	arbitrarily	arbitrarily	ADV
ejpam-4684	208	16	large	large	ADJ
ejpam-4684	208	17	.	.	PUNCT
ejpam-4684	209	1	j.	j.	PROPN
ejpam-4684	209	2	hassan	hassan	PROPN
ejpam-4684	209	3	,	,	PUNCT
ejpam-4684	209	4	a.	a.	PROPN
ejpam-4684	209	5	lintasan	lintasan	NOUN
ejpam-4684	209	6	,	,	PUNCT
ejpam-4684	209	7	n.	n.	PROPN
ejpam-4684	209	8	h.	h.	PROPN
ejpam-4684	209	9	mohammad	mohammad	PROPN
ejpam-4684	209	10	/	/	PUNCT
ejpam-4684	209	11	eur	eur	PROPN
ejpam-4684	209	12	.	.	PUNCT
ejpam-4684	210	1	j.	j.	PROPN
ejpam-4684	210	2	pure	pure	PROPN
ejpam-4684	210	3	appl	appl	PROPN
ejpam-4684	210	4	.	.	PROPN
ejpam-4684	210	5	math	math	PROPN
ejpam-4684	210	6	,	,	PUNCT
ejpam-4684	210	7	16	16	NUM
ejpam-4684	210	8	(	(	PUNCT
ejpam-4684	210	9	3	3	NUM
ejpam-4684	210	10	)	)	PUNCT
ejpam-4684	210	11	(	(	PUNCT
ejpam-4684	210	12	2023	2023	NUM
ejpam-4684	210	13	)	)	PUNCT
ejpam-4684	210	14	,	,	PUNCT
ejpam-4684	210	15	1848	1848	NUM
ejpam-4684	210	16	-	-	SYM
ejpam-4684	210	17	1861	1861	NUM
ejpam-4684	210	18	1855	1855	NUM
ejpam-4684	210	19	proposition	proposition	NOUN
ejpam-4684	210	20	2	2	NUM
ejpam-4684	210	21	.	.	X
ejpam-4684	211	1	for	for	ADP
ejpam-4684	211	2	any	any	DET
ejpam-4684	211	3	positive	positive	ADJ
ejpam-4684	211	4	integer	integer	NOUN
ejpam-4684	211	5	n	n	PRON
ejpam-4684	211	6	≥	≥	NOUN
ejpam-4684	211	7	1	1	NUM
ejpam-4684	211	8	,	,	PUNCT
ejpam-4684	211	9	γohi	γohi	PROPN
ejpam-4684	211	10	ch	ch	PROPN
ejpam-4684	211	11	(	(	PUNCT
ejpam-4684	211	12	pn	pn	NOUN
ejpam-4684	211	13	)	)	PUNCT
ejpam-4684	211	14	=	=	PUNCT
ejpam-4684	212	1			NOUN
ejpam-4684	212	2	1	1	NUM
ejpam-4684	212	3	if	if	SCONJ
ejpam-4684	212	4	n	n	NOUN
ejpam-4684	212	5	=	=	SYM
ejpam-4684	212	6	1	1	NUM
ejpam-4684	212	7	2	2	NUM
ejpam-4684	212	8	if	if	SCONJ
ejpam-4684	212	9	n	n	NOUN
ejpam-4684	212	10	=	=	SYM
ejpam-4684	212	11	2	2	NUM
ejpam-4684	212	12	,	,	PUNCT
ejpam-4684	212	13	3	3	NUM
ejpam-4684	212	14	,	,	PUNCT
ejpam-4684	212	15	4	4	NUM
ejpam-4684	212	16	,	,	PUNCT
ejpam-4684	212	17	5	5	NUM
ejpam-4684	212	18	n−	n−	NOUN
ejpam-4684	212	19	4	4	NUM
ejpam-4684	212	20	if	if	SCONJ
ejpam-4684	212	21	n	n	PRON
ejpam-4684	212	22	≥	≥	VERB
ejpam-4684	212	23	6	6	NUM
ejpam-4684	212	24	proof	proof	NOUN
ejpam-4684	212	25	.	.	PUNCT
ejpam-4684	213	1	clearly	clearly	ADV
ejpam-4684	213	2	,	,	PUNCT
ejpam-4684	213	3	γohich	γohich	PROPN
ejpam-4684	213	4	(	(	PUNCT
ejpam-4684	213	5	p1	p1	PROPN
ejpam-4684	213	6	)	)	PUNCT
ejpam-4684	213	7	=	=	SYM
ejpam-4684	213	8	1	1	NUM
ejpam-4684	213	9	and	and	CCONJ
ejpam-4684	213	10	γohich	γohich	PROPN
ejpam-4684	213	11	(	(	PUNCT
ejpam-4684	213	12	pn	pn	PROPN
ejpam-4684	213	13	)	)	PUNCT
ejpam-4684	213	14	=	=	SYM
ejpam-4684	213	15	2	2	NUM
ejpam-4684	213	16	for	for	ADP
ejpam-4684	213	17	n	n	NOUN
ejpam-4684	213	18	=	=	SYM
ejpam-4684	213	19	3	3	NUM
ejpam-4684	213	20	,	,	PUNCT
ejpam-4684	213	21	4	4	NUM
ejpam-4684	213	22	,	,	PUNCT
ejpam-4684	213	23	5	5	NUM
ejpam-4684	213	24	.	.	PUNCT
ejpam-4684	213	25	suppose	suppose	VERB
ejpam-4684	213	26	that	that	SCONJ
ejpam-4684	213	27	n	n	PROPN
ejpam-4684	213	28	≥	≥	NUM
ejpam-4684	213	29	6	6	NUM
ejpam-4684	213	30	.	.	PUNCT
ejpam-4684	214	1	let	let	VERB
ejpam-4684	214	2	pn	pn	VERB
ejpam-4684	214	3	=	=	PUNCT
ejpam-4684	215	1	[	[	X
ejpam-4684	215	2	v1	v1	NOUN
ejpam-4684	215	3	,	,	PUNCT
ejpam-4684	215	4	v2	v2	NOUN
ejpam-4684	215	5	,	,	PUNCT
ejpam-4684	215	6	.	.	PUNCT
ejpam-4684	215	7	.	.	PUNCT
ejpam-4684	215	8	.	.	PUNCT
ejpam-4684	216	1	,	,	PUNCT
ejpam-4684	216	2	vn	vn	X
ejpam-4684	216	3	]	]	PUNCT
ejpam-4684	216	4	and	and	CCONJ
ejpam-4684	216	5	d	d	NOUN
ejpam-4684	216	6	=	=	SYM
ejpam-4684	216	7	{	{	PUNCT
ejpam-4684	216	8	v3	v3	PROPN
ejpam-4684	216	9	,	,	PUNCT
ejpam-4684	216	10	v4	v4	PROPN
ejpam-4684	216	11	·	·	PUNCT
ejpam-4684	216	12	·	·	PUNCT
ejpam-4684	216	13	·	·	PUNCT
ejpam-4684	216	14	,	,	PUNCT
ejpam-4684	216	15	vn−3	vn−3	PROPN
ejpam-4684	216	16	,	,	PUNCT
ejpam-4684	216	17	vn−2	vn−2	PROPN
ejpam-4684	216	18	}	}	PUNCT
ejpam-4684	216	19	.	.	PUNCT
ejpam-4684	217	1	then	then	ADV
ejpam-4684	217	2	n2	n2	PROPN
ejpam-4684	217	3	pn	pn	PROPN
ejpam-4684	218	1	[	[	X
ejpam-4684	218	2	d	d	X
ejpam-4684	218	3	]	]	X
ejpam-4684	218	4	=	=	SYM
ejpam-4684	218	5	v	v	X
ejpam-4684	218	6	(	(	PUNCT
ejpam-4684	218	7	pn	pn	NOUN
ejpam-4684	218	8	)	)	PUNCT
ejpam-4684	218	9	and	and	CCONJ
ejpam-4684	218	10	⟨d⟩	⟨d⟩	PROPN
ejpam-4684	218	11	is	be	AUX
ejpam-4684	218	12	connected	connect	VERB
ejpam-4684	218	13	.	.	PUNCT
ejpam-4684	219	1	thus	thus	ADV
ejpam-4684	219	2	,	,	PUNCT
ejpam-4684	219	3	d	d	PRON
ejpam-4684	219	4	is	be	AUX
ejpam-4684	219	5	a	a	DET
ejpam-4684	219	6	connected	connected	ADJ
ejpam-4684	219	7	hop	hop	NOUN
ejpam-4684	219	8	dominating	dominating	NOUN
ejpam-4684	219	9	set	set	NOUN
ejpam-4684	219	10	of	of	ADP
ejpam-4684	219	11	pn	pn	PROPN
ejpam-4684	219	12	.	.	PUNCT
ejpam-4684	220	1	since	since	SCONJ
ejpam-4684	220	2	n	n	PROPN
ejpam-4684	220	3	≥	≥	NUM
ejpam-4684	220	4	6	6	NUM
ejpam-4684	220	5	,	,	PUNCT
ejpam-4684	220	6	it	it	PRON
ejpam-4684	220	7	follows	follow	VERB
ejpam-4684	220	8	that	that	SCONJ
ejpam-4684	220	9	dpn(a	dpn(a	PROPN
ejpam-4684	220	10	,	,	PUNCT
ejpam-4684	220	11	b	b	NOUN
ejpam-4684	220	12	)	)	PUNCT
ejpam-4684	220	13	̸=	̸=	PROPN
ejpam-4684	220	14	2	2	NUM
ejpam-4684	220	15	for	for	ADP
ejpam-4684	220	16	every	every	DET
ejpam-4684	220	17	a	a	PROPN
ejpam-4684	220	18	,	,	PUNCT
ejpam-4684	220	19	b	b	PROPN
ejpam-4684	220	20	∈	∈	PROPN
ejpam-4684	220	21	v	v	NOUN
ejpam-4684	220	22	(	(	PUNCT
ejpam-4684	220	23	pn	pn	NOUN
ejpam-4684	220	24	)	)	PUNCT
ejpam-4684	220	25	\d	\d	NOUN
ejpam-4684	220	26	.	.	PUNCT
ejpam-4684	221	1	hence	hence	ADV
ejpam-4684	221	2	,	,	PUNCT
ejpam-4684	221	3	v	v	PROPN
ejpam-4684	221	4	(	(	PUNCT
ejpam-4684	221	5	pn	pn	NOUN
ejpam-4684	221	6	)	)	PUNCT
ejpam-4684	221	7	\d	\d	NOUN
ejpam-4684	221	8	is	be	AUX
ejpam-4684	221	9	a	a	DET
ejpam-4684	221	10	hop	hop	NOUN
ejpam-4684	221	11	independent	independent	ADJ
ejpam-4684	221	12	set	set	NOUN
ejpam-4684	221	13	of	of	ADP
ejpam-4684	221	14	pn	pn	PROPN
ejpam-4684	221	15	,	,	PUNCT
ejpam-4684	221	16	showing	show	VERB
ejpam-4684	221	17	that	that	SCONJ
ejpam-4684	221	18	d	d	NOUN
ejpam-4684	221	19	is	be	AUX
ejpam-4684	221	20	a	a	DET
ejpam-4684	221	21	connected	connected	ADJ
ejpam-4684	221	22	outer	outer	ADJ
ejpam-4684	221	23	-	-	PUNCT
ejpam-4684	221	24	hop	hop	NOUN
ejpam-4684	221	25	independent	independent	ADJ
ejpam-4684	221	26	hop	hop	NOUN
ejpam-4684	221	27	dominating	dominating	NOUN
ejpam-4684	221	28	set	set	NOUN
ejpam-4684	221	29	of	of	ADP
ejpam-4684	221	30	pn	pn	PROPN
ejpam-4684	221	31	,	,	PUNCT
ejpam-4684	221	32	and	and	CCONJ
ejpam-4684	221	33	so	so	ADV
ejpam-4684	221	34	γohich	γohich	PROPN
ejpam-4684	221	35	(	(	PUNCT
ejpam-4684	221	36	pn	pn	NOUN
ejpam-4684	221	37	)	)	PUNCT
ejpam-4684	221	38	≤	≤	NOUN
ejpam-4684	221	39	n−	n−	NOUN
ejpam-4684	221	40	4	4	NUM
ejpam-4684	221	41	for	for	ADP
ejpam-4684	221	42	all	all	DET
ejpam-4684	221	43	n	n	PRON
ejpam-4684	221	44	≥	≥	NOUN
ejpam-4684	221	45	6	6	NUM
ejpam-4684	221	46	.	.	PUNCT
ejpam-4684	222	1	on	on	ADP
ejpam-4684	222	2	the	the	DET
ejpam-4684	222	3	other	other	ADJ
ejpam-4684	222	4	hand	hand	NOUN
ejpam-4684	222	5	,	,	PUNCT
ejpam-4684	222	6	observe	observe	VERB
ejpam-4684	222	7	that	that	SCONJ
ejpam-4684	222	8	any	any	DET
ejpam-4684	222	9	connected	connected	ADJ
ejpam-4684	222	10	outer	outer	ADJ
ejpam-4684	222	11	-	-	PUNCT
ejpam-4684	222	12	hop	hop	NOUN
ejpam-4684	222	13	independent	independent	ADJ
ejpam-4684	222	14	hop	hop	NOUN
ejpam-4684	222	15	dominating	dominating	NOUN
ejpam-4684	222	16	set	set	NOUN
ejpam-4684	222	17	s	s	PROPN
ejpam-4684	222	18	in	in	ADP
ejpam-4684	222	19	pn	pn	PROPN
ejpam-4684	222	20	contains	contain	VERB
ejpam-4684	222	21	d.	d.	PROPN
ejpam-4684	222	22	therefore	therefore	ADV
ejpam-4684	222	23	,	,	PUNCT
ejpam-4684	222	24	γohich	γohich	PROPN
ejpam-4684	222	25	(	(	PUNCT
ejpam-4684	222	26	pn	pn	NOUN
ejpam-4684	222	27	)	)	PUNCT
ejpam-4684	222	28	=	=	SYM
ejpam-4684	222	29	n	n	CCONJ
ejpam-4684	222	30	−	−	NOUN
ejpam-4684	222	31	4	4	NUM
ejpam-4684	222	32	for	for	ADP
ejpam-4684	222	33	all	all	DET
ejpam-4684	222	34	n	n	PRON
ejpam-4684	222	35	≥	≥	NUM
ejpam-4684	222	36	6	6	NUM
ejpam-4684	222	37	.	.	PUNCT
ejpam-4684	222	38	proposition	proposition	NOUN
ejpam-4684	222	39	3	3	NUM
ejpam-4684	222	40	.	.	X
ejpam-4684	223	1	for	for	ADP
ejpam-4684	223	2	any	any	DET
ejpam-4684	223	3	positive	positive	ADJ
ejpam-4684	223	4	integer	integer	NOUN
ejpam-4684	223	5	n	n	PRON
ejpam-4684	223	6	≥	≥	NOUN
ejpam-4684	223	7	3	3	NUM
ejpam-4684	223	8	,	,	PUNCT
ejpam-4684	223	9	γohi	γohi	PROPN
ejpam-4684	223	10	ch	ch	PROPN
ejpam-4684	223	11	(	(	PUNCT
ejpam-4684	223	12	cn	cn	PROPN
ejpam-4684	223	13	)	)	PUNCT
ejpam-4684	223	14	=	=	PRON
ejpam-4684	223	15	{	{	PUNCT
ejpam-4684	223	16	3	3	NUM
ejpam-4684	223	17	if	if	SCONJ
ejpam-4684	223	18	n	n	NOUN
ejpam-4684	223	19	=	=	SYM
ejpam-4684	223	20	3	3	NUM
ejpam-4684	223	21	n−	n−	NOUN
ejpam-4684	223	22	2	2	NUM
ejpam-4684	223	23	if	if	SCONJ
ejpam-4684	223	24	n	n	PRON
ejpam-4684	223	25	≥	≥	VERB
ejpam-4684	223	26	4	4	NUM
ejpam-4684	223	27	proof	proof	NOUN
ejpam-4684	223	28	.	.	PUNCT
ejpam-4684	224	1	clearly	clearly	ADV
ejpam-4684	224	2	,	,	PUNCT
ejpam-4684	224	3	γohich	γohich	PROPN
ejpam-4684	224	4	(	(	PUNCT
ejpam-4684	224	5	c3	c3	PROPN
ejpam-4684	224	6	)	)	PUNCT
ejpam-4684	224	7	=	=	SYM
ejpam-4684	224	8	3	3	X
ejpam-4684	224	9	.	.	X
ejpam-4684	224	10	suppose	suppose	VERB
ejpam-4684	224	11	n	n	PRON
ejpam-4684	224	12	≥	≥	NUM
ejpam-4684	224	13	4	4	NUM
ejpam-4684	224	14	.	.	PUNCT
ejpam-4684	225	1	let	let	VERB
ejpam-4684	225	2	cn	cn	PROPN
ejpam-4684	225	3	=	=	PUNCT
ejpam-4684	226	1	[	[	X
ejpam-4684	226	2	v1	v1	NOUN
ejpam-4684	226	3	,	,	PUNCT
ejpam-4684	226	4	v2	v2	NOUN
ejpam-4684	226	5	,	,	PUNCT
ejpam-4684	226	6	.	.	PUNCT
ejpam-4684	226	7	.	.	PUNCT
ejpam-4684	226	8	.	.	PUNCT
ejpam-4684	227	1	,	,	PUNCT
ejpam-4684	227	2	vn	vn	X
ejpam-4684	227	3	,	,	PUNCT
ejpam-4684	227	4	v1	v1	PROPN
ejpam-4684	227	5	]	]	PUNCT
ejpam-4684	227	6	and	and	CCONJ
ejpam-4684	227	7	consider	consider	VERB
ejpam-4684	227	8	d∗	d∗	NOUN
ejpam-4684	227	9	=	=	SYM
ejpam-4684	227	10	{	{	PUNCT
ejpam-4684	227	11	v1	v1	PROPN
ejpam-4684	227	12	,	,	PUNCT
ejpam-4684	227	13	v2	v2	PROPN
ejpam-4684	227	14	,	,	PUNCT
ejpam-4684	227	15	.	.	PUNCT
ejpam-4684	227	16	.	.	PUNCT
ejpam-4684	228	1	.	.	PUNCT
ejpam-4684	229	1	,	,	PUNCT
ejpam-4684	229	2	vn−2	vn−2	PROPN
ejpam-4684	229	3	}	}	PUNCT
ejpam-4684	229	4	.	.	PUNCT
ejpam-4684	230	1	then	then	ADV
ejpam-4684	230	2	n2	n2	PROPN
ejpam-4684	230	3	cn	cn	PROPN
ejpam-4684	231	1	[	[	X
ejpam-4684	231	2	d∗	d∗	X
ejpam-4684	231	3	]	]	X
ejpam-4684	231	4	=	=	SYM
ejpam-4684	231	5	v	v	X
ejpam-4684	231	6	(	(	PUNCT
ejpam-4684	231	7	cn	cn	PROPN
ejpam-4684	231	8	)	)	PUNCT
ejpam-4684	231	9	and	and	CCONJ
ejpam-4684	231	10	⟨d∗⟩	⟨d∗⟩	PROPN
ejpam-4684	231	11	is	be	AUX
ejpam-4684	231	12	connected	connect	VERB
ejpam-4684	231	13	.	.	PUNCT
ejpam-4684	232	1	thus	thus	ADV
ejpam-4684	232	2	,	,	PUNCT
ejpam-4684	232	3	d∗	d∗	PROPN
ejpam-4684	232	4	is	be	AUX
ejpam-4684	232	5	a	a	DET
ejpam-4684	232	6	connected	connected	ADJ
ejpam-4684	232	7	hop	hop	NOUN
ejpam-4684	232	8	dominating	dominating	NOUN
ejpam-4684	232	9	set	set	NOUN
ejpam-4684	232	10	of	of	ADP
ejpam-4684	232	11	cn	cn	PROPN
ejpam-4684	232	12	.	.	PUNCT
ejpam-4684	233	1	since	since	SCONJ
ejpam-4684	233	2	dcn(vn−1	dcn(vn−1	PROPN
ejpam-4684	233	3	,	,	PUNCT
ejpam-4684	233	4	vn	vn	NOUN
ejpam-4684	233	5	)	)	PUNCT
ejpam-4684	234	1	=	=	SYM
ejpam-4684	234	2	1	1	NUM
ejpam-4684	234	3	,	,	PUNCT
ejpam-4684	234	4	it	it	PRON
ejpam-4684	234	5	follows	follow	VERB
ejpam-4684	234	6	that	that	SCONJ
ejpam-4684	234	7	d∗	d∗	PROPN
ejpam-4684	234	8	is	be	AUX
ejpam-4684	234	9	a	a	DET
ejpam-4684	234	10	connected	connected	ADJ
ejpam-4684	234	11	outer	outer	ADJ
ejpam-4684	234	12	-	-	PUNCT
ejpam-4684	234	13	hop	hop	NOUN
ejpam-4684	234	14	independent	independent	ADJ
ejpam-4684	234	15	hop	hop	NOUN
ejpam-4684	234	16	dominating	dominating	NOUN
ejpam-4684	234	17	set	set	NOUN
ejpam-4684	234	18	of	of	ADP
ejpam-4684	234	19	cn	cn	PROPN
ejpam-4684	234	20	.	.	PUNCT
ejpam-4684	235	1	since	since	SCONJ
ejpam-4684	235	2	the	the	DET
ejpam-4684	235	3	maximum	maximum	ADJ
ejpam-4684	235	4	connected	connected	ADJ
ejpam-4684	235	5	hop	hop	NOUN
ejpam-4684	235	6	independent	independent	ADJ
ejpam-4684	235	7	set	set	NOUN
ejpam-4684	235	8	in	in	ADP
ejpam-4684	235	9	cn	cn	PROPN
ejpam-4684	235	10	is	be	AUX
ejpam-4684	235	11	of	of	ADP
ejpam-4684	235	12	cardinality	cardinality	NOUN
ejpam-4684	235	13	2	2	NUM
ejpam-4684	235	14	,	,	PUNCT
ejpam-4684	235	15	it	it	PRON
ejpam-4684	235	16	follows	follow	VERB
ejpam-4684	235	17	that	that	SCONJ
ejpam-4684	235	18	d∗	d∗	PROPN
ejpam-4684	235	19	is	be	AUX
ejpam-4684	235	20	a	a	DET
ejpam-4684	235	21	γohich	γohich	NOUN
ejpam-4684	235	22	-set	-set	ADJ
ejpam-4684	235	23	of	of	ADP
ejpam-4684	235	24	cn	cn	PROPN
ejpam-4684	235	25	.	.	PUNCT
ejpam-4684	236	1	therefore	therefore	ADV
ejpam-4684	236	2	,	,	PUNCT
ejpam-4684	236	3	γ	γ	X
ejpam-4684	236	4	ohi	ohi	PROPN
ejpam-4684	236	5	ch	ch	PROPN
ejpam-4684	236	6	(	(	PUNCT
ejpam-4684	236	7	cn	cn	PROPN
ejpam-4684	236	8	)	)	PUNCT
ejpam-4684	236	9	=	=	PUNCT
ejpam-4684	236	10	n−	n−	NOUN
ejpam-4684	236	11	2	2	NUM
ejpam-4684	236	12	for	for	ADP
ejpam-4684	236	13	all	all	DET
ejpam-4684	236	14	n	n	PRON
ejpam-4684	236	15	≥	≥	NUM
ejpam-4684	236	16	4	4	NUM
ejpam-4684	236	17	.	.	PUNCT
ejpam-4684	236	18	theorem	theorem	NOUN
ejpam-4684	236	19	5	5	NUM
ejpam-4684	236	20	.	.	PUNCT
ejpam-4684	237	1	let	let	VERB
ejpam-4684	237	2	g	g	NOUN
ejpam-4684	237	3	be	be	AUX
ejpam-4684	237	4	any	any	DET
ejpam-4684	237	5	connected	connected	ADJ
ejpam-4684	237	6	graph	graph	NOUN
ejpam-4684	237	7	of	of	ADP
ejpam-4684	237	8	order	order	NOUN
ejpam-4684	237	9	n	n	PRON
ejpam-4684	237	10	≥	≥	NOUN
ejpam-4684	237	11	1	1	NUM
ejpam-4684	237	12	.	.	PUNCT
ejpam-4684	238	1	then	then	ADV
ejpam-4684	238	2	γohich	γohich	PROPN
ejpam-4684	238	3	(	(	PUNCT
ejpam-4684	238	4	g	g	NOUN
ejpam-4684	238	5	)	)	PUNCT
ejpam-4684	238	6	≥	≥	NOUN
ejpam-4684	238	7	n−	n−	NOUN
ejpam-4684	238	8	αh(g	αh(g	NOUN
ejpam-4684	238	9	)	)	PUNCT
ejpam-4684	238	10	.	.	PUNCT
ejpam-4684	239	1	proof	proof	NOUN
ejpam-4684	239	2	.	.	PUNCT
ejpam-4684	240	1	letd	letd	PROPN
ejpam-4684	240	2	be	be	AUX
ejpam-4684	240	3	a	a	DET
ejpam-4684	240	4	γohich	γohich	NOUN
ejpam-4684	240	5	-set	-set	ADJ
ejpam-4684	240	6	of	of	ADP
ejpam-4684	240	7	g.	g.	PROPN
ejpam-4684	240	8	then	then	ADV
ejpam-4684	240	9	γohich	γohich	PROPN
ejpam-4684	240	10	(	(	PUNCT
ejpam-4684	240	11	g	g	NOUN
ejpam-4684	240	12	)	)	PUNCT
ejpam-4684	240	13	=	=	SYM
ejpam-4684	240	14	|d|	|d|	PROPN
ejpam-4684	240	15	and	and	CCONJ
ejpam-4684	240	16	v	v	PROPN
ejpam-4684	240	17	(	(	PUNCT
ejpam-4684	240	18	g)\d	g)\d	NOUN
ejpam-4684	240	19	is	be	AUX
ejpam-4684	240	20	a	a	DET
ejpam-4684	240	21	hop	hop	NOUN
ejpam-4684	240	22	independent	independent	ADJ
ejpam-4684	240	23	set	set	NOUN
ejpam-4684	240	24	in	in	ADP
ejpam-4684	240	25	g	g	PROPN
ejpam-4684	240	26	(	(	PUNCT
ejpam-4684	240	27	by	by	ADP
ejpam-4684	240	28	definition	definition	NOUN
ejpam-4684	240	29	)	)	PUNCT
ejpam-4684	240	30	.	.	PUNCT
ejpam-4684	241	1	it	it	PRON
ejpam-4684	241	2	follows	follow	VERB
ejpam-4684	241	3	that	that	SCONJ
ejpam-4684	241	4	αh(g	αh(g	NOUN
ejpam-4684	241	5	)	)	PUNCT
ejpam-4684	241	6	≥	≥	NOUN
ejpam-4684	241	7	|v	|v	NOUN
ejpam-4684	241	8	(	(	PUNCT
ejpam-4684	241	9	g	g	NOUN
ejpam-4684	241	10	)	)	PUNCT
ejpam-4684	241	11	\d|	\d|	NOUN
ejpam-4684	241	12	.	.	PUNCT
ejpam-4684	242	1	hence	hence	ADV
ejpam-4684	242	2	,	,	PUNCT
ejpam-4684	242	3	n−	n−	NOUN
ejpam-4684	242	4	αh(g	αh(g	NOUN
ejpam-4684	242	5	)	)	PUNCT
ejpam-4684	242	6	≤	≤	NUM
ejpam-4684	242	7	n−	n−	PROPN
ejpam-4684	242	8	|v	|v	PROPN
ejpam-4684	242	9	(	(	PUNCT
ejpam-4684	242	10	g	g	NOUN
ejpam-4684	242	11	)	)	PUNCT
ejpam-4684	242	12	\d|	\d|	NOUN
ejpam-4684	242	13	=	=	PUNCT
ejpam-4684	242	14	n−	n−	NOUN
ejpam-4684	242	15	n+	n+	X
ejpam-4684	242	16	|d|	|d|	PROPN
ejpam-4684	242	17	=	=	SYM
ejpam-4684	242	18	|d|	|d|	PROPN
ejpam-4684	242	19	=	=	SYM
ejpam-4684	242	20	γohich	γohich	PROPN
ejpam-4684	242	21	(	(	PUNCT
ejpam-4684	242	22	g	g	NOUN
ejpam-4684	242	23	)	)	PUNCT
ejpam-4684	242	24	.	.	PUNCT
ejpam-4684	243	1	remark	remark	PROPN
ejpam-4684	243	2	1	1	NUM
ejpam-4684	243	3	.	.	PUNCT
ejpam-4684	244	1	the	the	DET
ejpam-4684	244	2	bound	bind	VERB
ejpam-4684	244	3	in	in	ADP
ejpam-4684	244	4	theorem	theorem	NOUN
ejpam-4684	244	5	5	5	NUM
ejpam-4684	244	6	is	be	AUX
ejpam-4684	244	7	sharp	sharp	ADJ
ejpam-4684	244	8	.	.	PUNCT
ejpam-4684	245	1	moreover	moreover	ADV
ejpam-4684	245	2	,	,	PUNCT
ejpam-4684	245	3	strict	strict	ADJ
ejpam-4684	245	4	inequality	inequality	NOUN
ejpam-4684	245	5	can	can	AUX
ejpam-4684	245	6	be	be	AUX
ejpam-4684	245	7	attained	attain	VERB
ejpam-4684	245	8	.	.	PUNCT
ejpam-4684	246	1	for	for	ADP
ejpam-4684	246	2	sharpness	sharpness	NOUN
ejpam-4684	246	3	,	,	PUNCT
ejpam-4684	246	4	consider	consider	VERB
ejpam-4684	246	5	the	the	DET
ejpam-4684	246	6	graph	graph	NOUN
ejpam-4684	246	7	g	g	NOUN
ejpam-4684	246	8	in	in	ADP
ejpam-4684	246	9	figure	figure	NOUN
ejpam-4684	246	10	5	5	NUM
ejpam-4684	246	11	.	.	PUNCT
ejpam-4684	247	1	let	let	VERB
ejpam-4684	247	2	s	s	PRON
ejpam-4684	247	3	=	=	X
ejpam-4684	247	4	{	{	PUNCT
ejpam-4684	247	5	c	c	NOUN
ejpam-4684	247	6	,	,	PUNCT
ejpam-4684	247	7	d	d	NOUN
ejpam-4684	247	8	,	,	PUNCT
ejpam-4684	247	9	e	e	NOUN
ejpam-4684	247	10	}	}	PUNCT
ejpam-4684	247	11	.	.	PUNCT
ejpam-4684	248	1	then	then	ADV
ejpam-4684	248	2	s	s	VERB
ejpam-4684	248	3	is	be	AUX
ejpam-4684	248	4	a	a	DET
ejpam-4684	248	5	minimum	minimum	NOUN
ejpam-4684	248	6	connected	connect	VERB
ejpam-4684	248	7	hop	hop	NOUN
ejpam-4684	248	8	dominating	dominating	NOUN
ejpam-4684	248	9	set	set	NOUN
ejpam-4684	248	10	of	of	ADP
ejpam-4684	248	11	g.	g.	PROPN
ejpam-4684	248	12	notice	notice	VERB
ejpam-4684	248	13	that	that	SCONJ
ejpam-4684	248	14	v	v	X
ejpam-4684	248	15	(	(	PUNCT
ejpam-4684	248	16	g	g	NOUN
ejpam-4684	248	17	)	)	PUNCT
ejpam-4684	248	18	\s	\s	NOUN
ejpam-4684	248	19	is	be	AUX
ejpam-4684	248	20	a	a	DET
ejpam-4684	248	21	hop	hop	NOUN
ejpam-4684	248	22	independent	independent	ADJ
ejpam-4684	248	23	set	set	NOUN
ejpam-4684	248	24	.	.	PUNCT
ejpam-4684	249	1	it	it	PRON
ejpam-4684	249	2	follows	follow	VERB
ejpam-4684	249	3	that	that	SCONJ
ejpam-4684	249	4	s	s	VERB
ejpam-4684	249	5	is	be	AUX
ejpam-4684	249	6	a	a	DET
ejpam-4684	249	7	minimum	minimum	ADJ
ejpam-4684	249	8	connected	connect	VERB
ejpam-4684	249	9	outer	outer	ADJ
ejpam-4684	249	10	-	-	PUNCT
ejpam-4684	249	11	hop	hop	NOUN
ejpam-4684	249	12	independent	independent	ADJ
ejpam-4684	249	13	hop	hop	NOUN
ejpam-4684	249	14	dominating	dominating	NOUN
ejpam-4684	249	15	set	set	NOUN
ejpam-4684	249	16	of	of	ADP
ejpam-4684	249	17	g.	g.	PROPN
ejpam-4684	249	18	thus	thus	ADV
ejpam-4684	249	19	,	,	PUNCT
ejpam-4684	249	20	γohich	γohich	PROPN
ejpam-4684	249	21	(	(	PUNCT
ejpam-4684	249	22	g	g	NOUN
ejpam-4684	249	23	)	)	PUNCT
ejpam-4684	249	24	=	=	SYM
ejpam-4684	250	1	3	3	X
ejpam-4684	250	2	.	.	PUNCT
ejpam-4684	251	1	next	next	ADV
ejpam-4684	251	2	,	,	PUNCT
ejpam-4684	251	3	let	let	VERB
ejpam-4684	251	4	s′	s′	ADJ
ejpam-4684	251	5	=	=	PUNCT
ejpam-4684	251	6	{	{	PUNCT
ejpam-4684	251	7	b	b	NOUN
ejpam-4684	251	8	,	,	PUNCT
ejpam-4684	251	9	c	c	X
ejpam-4684	251	10	,	,	PUNCT
ejpam-4684	251	11	f	f	PROPN
ejpam-4684	251	12	,	,	PUNCT
ejpam-4684	251	13	g	g	PROPN
ejpam-4684	251	14	,	,	PUNCT
ejpam-4684	251	15	h	h	NOUN
ejpam-4684	251	16	}	}	PUNCT
ejpam-4684	251	17	.	.	PUNCT
ejpam-4684	252	1	then	then	ADV
ejpam-4684	252	2	s	s	VERB
ejpam-4684	252	3	is	be	AUX
ejpam-4684	252	4	the	the	DET
ejpam-4684	252	5	maximum	maximum	ADJ
ejpam-4684	252	6	hop	hop	NOUN
ejpam-4684	252	7	independent	independent	ADJ
ejpam-4684	252	8	set	set	NOUN
ejpam-4684	252	9	of	of	ADP
ejpam-4684	252	10	g.	g.	PROPN
ejpam-4684	252	11	consequently	consequently	ADV
ejpam-4684	252	12	,	,	PUNCT
ejpam-4684	252	13	|v	|v	PROPN
ejpam-4684	252	14	(	(	PUNCT
ejpam-4684	252	15	g)|	g)|	NOUN
ejpam-4684	252	16	−	−	NOUN
ejpam-4684	252	17	αh(g	αh(g	NOUN
ejpam-4684	252	18	)	)	PUNCT
ejpam-4684	252	19	=	=	SYM
ejpam-4684	252	20	8−	8−	NUM
ejpam-4684	252	21	5	5	NUM
ejpam-4684	252	22	=	=	SYM
ejpam-4684	252	23	3	3	NUM
ejpam-4684	252	24	=	=	SYM
ejpam-4684	252	25	γohich	γohich	X
ejpam-4684	252	26	(	(	PUNCT
ejpam-4684	252	27	g	g	NOUN
ejpam-4684	252	28	)	)	PUNCT
ejpam-4684	252	29	.	.	PUNCT
ejpam-4684	253	1	j.	j.	PROPN
ejpam-4684	253	2	hassan	hassan	PROPN
ejpam-4684	253	3	,	,	PUNCT
ejpam-4684	253	4	a.	a.	PROPN
ejpam-4684	253	5	lintasan	lintasan	NOUN
ejpam-4684	253	6	,	,	PUNCT
ejpam-4684	253	7	n.	n.	PROPN
ejpam-4684	253	8	h.	h.	PROPN
ejpam-4684	253	9	mohammad	mohammad	PROPN
ejpam-4684	253	10	/	/	PUNCT
ejpam-4684	253	11	eur	eur	PROPN
ejpam-4684	253	12	.	.	PUNCT
ejpam-4684	254	1	j.	j.	PROPN
ejpam-4684	254	2	pure	pure	PROPN
ejpam-4684	254	3	appl	appl	PROPN
ejpam-4684	254	4	.	.	PROPN
ejpam-4684	254	5	math	math	PROPN
ejpam-4684	254	6	,	,	PUNCT
ejpam-4684	254	7	16	16	NUM
ejpam-4684	254	8	(	(	PUNCT
ejpam-4684	254	9	3	3	NUM
ejpam-4684	254	10	)	)	PUNCT
ejpam-4684	254	11	(	(	PUNCT
ejpam-4684	254	12	2023	2023	NUM
ejpam-4684	254	13	)	)	PUNCT
ejpam-4684	254	14	,	,	PUNCT
ejpam-4684	254	15	1848	1848	NUM
ejpam-4684	254	16	-	-	SYM
ejpam-4684	254	17	1861	1861	NUM
ejpam-4684	254	18	1856	1856	NUM
ejpam-4684	254	19	g	g	NOUN
ejpam-4684	254	20	:	:	PUNCT
ejpam-4684	254	21	a	a	DET
ejpam-4684	254	22	b	b	X
ejpam-4684	254	23	c	c	NOUN
ejpam-4684	254	24	d	d	X
ejpam-4684	254	25	e	e	X
ejpam-4684	254	26	f	f	PROPN
ejpam-4684	254	27	g	g	PROPN
ejpam-4684	254	28	h	h	NOUN
ejpam-4684	254	29	figure	figure	NOUN
ejpam-4684	254	30	5	5	NUM
ejpam-4684	254	31	:	:	PUNCT
ejpam-4684	254	32	a	a	DET
ejpam-4684	254	33	graph	graph	NOUN
ejpam-4684	254	34	g	g	NOUN
ejpam-4684	254	35	with	with	ADP
ejpam-4684	254	36	γohi	γohi	PROPN
ejpam-4684	254	37	ch	ch	PROPN
ejpam-4684	254	38	(	(	PUNCT
ejpam-4684	254	39	g	g	NOUN
ejpam-4684	254	40	)	)	PUNCT
ejpam-4684	254	41	=	=	SYM
ejpam-4684	255	1	|v	|v	PROPN
ejpam-4684	255	2	(	(	PUNCT
ejpam-4684	255	3	g)|	g)|	NOUN
ejpam-4684	255	4	−	−	NOUN
ejpam-4684	255	5	αh(g	αh(g	NOUN
ejpam-4684	255	6	)	)	PUNCT
ejpam-4684	255	7	for	for	ADP
ejpam-4684	255	8	strict	strict	ADJ
ejpam-4684	255	9	inequality	inequality	NOUN
ejpam-4684	255	10	,	,	PUNCT
ejpam-4684	255	11	consider	consider	VERB
ejpam-4684	255	12	k7	k7	PROPN
ejpam-4684	255	13	.	.	PUNCT
ejpam-4684	256	1	then	then	ADV
ejpam-4684	256	2	γohich	γohich	PROPN
ejpam-4684	256	3	(	(	PUNCT
ejpam-4684	256	4	k7	k7	PROPN
ejpam-4684	256	5	)	)	PUNCT
ejpam-4684	256	6	=	=	SYM
ejpam-4684	256	7	7	7	NUM
ejpam-4684	256	8	=	=	SYM
ejpam-4684	256	9	αh(k7	αh(k7	NUM
ejpam-4684	256	10	)	)	PUNCT
ejpam-4684	256	11	.	.	PUNCT
ejpam-4684	257	1	thus	thus	ADV
ejpam-4684	257	2	,	,	PUNCT
ejpam-4684	257	3	γohich	γohich	PROPN
ejpam-4684	257	4	(	(	PUNCT
ejpam-4684	257	5	k7	k7	PROPN
ejpam-4684	257	6	)	)	PUNCT
ejpam-4684	257	7	=	=	PUNCT
ejpam-4684	257	8	7	7	NUM
ejpam-4684	257	9	>	>	X
ejpam-4684	257	10	(	(	PUNCT
ejpam-4684	257	11	7−	7−	NUM
ejpam-4684	257	12	αh(k7	αh(k7	NUM
ejpam-4684	257	13	)	)	PUNCT
ejpam-4684	257	14	)	)	PUNCT
ejpam-4684	258	1	=	=	PUNCT
ejpam-4684	259	1	7−	7−	NUM
ejpam-4684	259	2	7	7	NUM
ejpam-4684	259	3	=	=	SYM
ejpam-4684	259	4	0	0	NUM
ejpam-4684	259	5	.	.	PUNCT
ejpam-4684	260	1	the	the	DET
ejpam-4684	260	2	following	follow	VERB
ejpam-4684	260	3	concept	concept	NOUN
ejpam-4684	260	4	will	will	AUX
ejpam-4684	260	5	be	be	AUX
ejpam-4684	260	6	used	use	VERB
ejpam-4684	260	7	in	in	ADP
ejpam-4684	260	8	characterizing	characterize	VERB
ejpam-4684	260	9	the	the	DET
ejpam-4684	260	10	connected	connected	ADJ
ejpam-4684	260	11	outer	outer	ADJ
ejpam-4684	260	12	-	-	PUNCT
ejpam-4684	260	13	hop	hop	NOUN
ejpam-4684	260	14	independent	independent	ADJ
ejpam-4684	260	15	hop	hop	NOUN
ejpam-4684	260	16	dominating	dominating	NOUN
ejpam-4684	260	17	sets	set	NOUN
ejpam-4684	260	18	in	in	ADP
ejpam-4684	260	19	the	the	DET
ejpam-4684	260	20	join	join	NOUN
ejpam-4684	260	21	of	of	ADP
ejpam-4684	260	22	two	two	NUM
ejpam-4684	260	23	graphs	graph	NOUN
ejpam-4684	260	24	.	.	PUNCT
ejpam-4684	261	1	definition	definition	NOUN
ejpam-4684	261	2	2	2	NUM
ejpam-4684	261	3	.	.	PUNCT
ejpam-4684	262	1	let	let	VERB
ejpam-4684	262	2	g	g	PRON
ejpam-4684	262	3	be	be	AUX
ejpam-4684	262	4	a	a	DET
ejpam-4684	262	5	non	non	ADJ
ejpam-4684	262	6	-	-	ADJ
ejpam-4684	262	7	complete	complete	ADJ
ejpam-4684	262	8	graph	graph	NOUN
ejpam-4684	262	9	.	.	PUNCT
ejpam-4684	263	1	then	then	ADV
ejpam-4684	263	2	d	d	PROPN
ejpam-4684	263	3	⊆	⊆	NUM
ejpam-4684	263	4	v	v	ADP
ejpam-4684	263	5	(	(	PUNCT
ejpam-4684	263	6	g	g	NOUN
ejpam-4684	263	7	)	)	PUNCT
ejpam-4684	263	8	is	be	AUX
ejpam-4684	263	9	called	call	VERB
ejpam-4684	263	10	an	an	DET
ejpam-4684	263	11	outer	outer	ADJ
ejpam-4684	263	12	-	-	PUNCT
ejpam-4684	263	13	clique	clique	NOUN
ejpam-4684	263	14	pointwise	pointwise	PROPN
ejpam-4684	263	15	non	non	ADJ
ejpam-4684	263	16	-	-	ADJ
ejpam-4684	263	17	dominating	dominating	ADJ
ejpam-4684	263	18	set	set	NOUN
ejpam-4684	263	19	in	in	ADP
ejpam-4684	263	20	g	g	PROPN
ejpam-4684	263	21	if	if	SCONJ
ejpam-4684	263	22	d	d	PROPN
ejpam-4684	263	23	is	be	AUX
ejpam-4684	263	24	pointwise	pointwise	PROPN
ejpam-4684	263	25	non	non	ADJ
ejpam-4684	263	26	-	-	ADJ
ejpam-4684	263	27	dominating	dominating	ADJ
ejpam-4684	263	28	set	set	NOUN
ejpam-4684	263	29	and	and	CCONJ
ejpam-4684	263	30	v	v	NOUN
ejpam-4684	263	31	(	(	PUNCT
ejpam-4684	263	32	g	g	NOUN
ejpam-4684	263	33	)	)	PUNCT
ejpam-4684	263	34	\d	\d	NOUN
ejpam-4684	263	35	is	be	AUX
ejpam-4684	263	36	clique	clique	NOUN
ejpam-4684	263	37	set	set	NOUN
ejpam-4684	263	38	in	in	ADP
ejpam-4684	263	39	g.	g.	PROPN
ejpam-4684	263	40	the	the	DET
ejpam-4684	263	41	smallest	small	ADJ
ejpam-4684	263	42	cardinality	cardinality	NOUN
ejpam-4684	263	43	of	of	ADP
ejpam-4684	263	44	an	an	DET
ejpam-4684	263	45	outer	outer	ADJ
ejpam-4684	263	46	-	-	PUNCT
ejpam-4684	263	47	clique	clique	NOUN
ejpam-4684	263	48	pointwise	pointwise	PROPN
ejpam-4684	263	49	non	non	ADJ
ejpam-4684	263	50	-	-	ADJ
ejpam-4684	263	51	dominating	dominating	ADJ
ejpam-4684	263	52	set	set	NOUN
ejpam-4684	263	53	of	of	ADP
ejpam-4684	263	54	g	g	NOUN
ejpam-4684	263	55	,	,	PUNCT
ejpam-4684	263	56	denoted	denote	VERB
ejpam-4684	263	57	by	by	ADP
ejpam-4684	263	58	ocpnd(g	ocpnd(g	NOUN
ejpam-4684	263	59	)	)	PUNCT
ejpam-4684	263	60	,	,	PUNCT
ejpam-4684	263	61	is	be	AUX
ejpam-4684	263	62	called	call	VERB
ejpam-4684	263	63	the	the	DET
ejpam-4684	263	64	outer	outer	ADJ
ejpam-4684	263	65	-	-	PUNCT
ejpam-4684	263	66	clique	clique	NOUN
ejpam-4684	263	67	pointwise	pointwise	PROPN
ejpam-4684	263	68	non	non	ADJ
ejpam-4684	263	69	-	-	ADJ
ejpam-4684	263	70	domination	domination	ADJ
ejpam-4684	263	71	number	number	NOUN
ejpam-4684	263	72	of	of	ADP
ejpam-4684	263	73	g.	g.	PROPN
ejpam-4684	263	74	any	any	DET
ejpam-4684	263	75	outer	outer	ADJ
ejpam-4684	263	76	-	-	PUNCT
ejpam-4684	263	77	clique	clique	NOUN
ejpam-4684	263	78	pointwise	pointwise	PROPN
ejpam-4684	263	79	non	non	ADJ
ejpam-4684	263	80	-	-	ADJ
ejpam-4684	263	81	dominating	dominating	ADJ
ejpam-4684	263	82	set	set	NOUN
ejpam-4684	263	83	d	d	NOUN
ejpam-4684	263	84	of	of	ADP
ejpam-4684	263	85	g	g	NOUN
ejpam-4684	263	86	with	with	ADP
ejpam-4684	263	87	|d|	|d|	PROPN
ejpam-4684	263	88	=	=	SYM
ejpam-4684	263	89	ocpnd(g	ocpnd(g	PROPN
ejpam-4684	263	90	)	)	PUNCT
ejpam-4684	263	91	,	,	PUNCT
ejpam-4684	263	92	is	be	AUX
ejpam-4684	263	93	called	call	VERB
ejpam-4684	263	94	an	an	DET
ejpam-4684	263	95	ocpnd	ocpnd	NOUN
ejpam-4684	263	96	-	-	PUNCT
ejpam-4684	263	97	set	set	NOUN
ejpam-4684	263	98	of	of	ADP
ejpam-4684	263	99	g.	g.	PROPN
ejpam-4684	263	100	example	example	NOUN
ejpam-4684	264	1	1	1	X
ejpam-4684	264	2	.	.	X
ejpam-4684	264	3	consider	consider	VERB
ejpam-4684	264	4	the	the	DET
ejpam-4684	264	5	graph	graph	NOUN
ejpam-4684	264	6	g	g	NOUN
ejpam-4684	264	7	in	in	ADP
ejpam-4684	264	8	figure	figure	NOUN
ejpam-4684	264	9	6	6	NUM
ejpam-4684	264	10	.	.	PUNCT
ejpam-4684	265	1	let	let	VERB
ejpam-4684	265	2	o	o	NOUN
ejpam-4684	265	3	=	=	PUNCT
ejpam-4684	265	4	{	{	PUNCT
ejpam-4684	265	5	a1	a1	PROPN
ejpam-4684	265	6	,	,	PUNCT
ejpam-4684	265	7	a2	a2	PROPN
ejpam-4684	265	8	,	,	PUNCT
ejpam-4684	265	9	a5	a5	NOUN
ejpam-4684	265	10	,	,	PUNCT
ejpam-4684	265	11	a6	a6	NOUN
ejpam-4684	265	12	}	}	PUNCT
ejpam-4684	265	13	.	.	PUNCT
ejpam-4684	266	1	then	then	ADV
ejpam-4684	266	2	o	o	NOUN
ejpam-4684	266	3	is	be	AUX
ejpam-4684	266	4	a	a	DET
ejpam-4684	266	5	pointwise	pointwise	ADJ
ejpam-4684	266	6	non	non	ADJ
ejpam-4684	266	7	-	-	ADJ
ejpam-4684	266	8	dominating	dominating	ADJ
ejpam-4684	266	9	set	set	NOUN
ejpam-4684	266	10	of	of	ADP
ejpam-4684	266	11	g.	g.	PROPN
ejpam-4684	266	12	since	since	SCONJ
ejpam-4684	266	13	⟨v	⟨v	PROPN
ejpam-4684	266	14	(	(	PUNCT
ejpam-4684	266	15	g	g	NOUN
ejpam-4684	266	16	)	)	PUNCT
ejpam-4684	266	17	\	\	NOUN
ejpam-4684	266	18	o⟩	o⟩	X
ejpam-4684	267	1	∼=	∼=	PART
ejpam-4684	267	2	k4	k4	NOUN
ejpam-4684	267	3	,	,	PUNCT
ejpam-4684	267	4	it	it	PRON
ejpam-4684	267	5	follows	follow	VERB
ejpam-4684	267	6	that	that	SCONJ
ejpam-4684	267	7	v	v	X
ejpam-4684	267	8	(	(	PUNCT
ejpam-4684	267	9	g	g	NOUN
ejpam-4684	267	10	)	)	PUNCT
ejpam-4684	267	11	\	\	NOUN
ejpam-4684	268	1	o	o	NOUN
ejpam-4684	268	2	is	be	AUX
ejpam-4684	268	3	clique	clique	ADJ
ejpam-4684	268	4	in	in	ADP
ejpam-4684	268	5	g.	g.	PROPN
ejpam-4684	268	6	thus	thus	ADV
ejpam-4684	268	7	,	,	PUNCT
ejpam-4684	268	8	o	o	PROPN
ejpam-4684	268	9	is	be	AUX
ejpam-4684	268	10	an	an	DET
ejpam-4684	268	11	outer	outer	ADJ
ejpam-4684	268	12	-	-	PUNCT
ejpam-4684	268	13	clique	clique	NOUN
ejpam-4684	268	14	pointwise	pointwise	PROPN
ejpam-4684	268	15	non	non	ADJ
ejpam-4684	268	16	-	-	ADJ
ejpam-4684	268	17	dominating	dominating	ADJ
ejpam-4684	268	18	set	set	NOUN
ejpam-4684	268	19	of	of	ADP
ejpam-4684	268	20	g.	g.	PROPN
ejpam-4684	268	21	next	next	ADV
ejpam-4684	268	22	,	,	PUNCT
ejpam-4684	268	23	let	let	VERB
ejpam-4684	268	24	o′	o′	X
ejpam-4684	268	25	=	=	PUNCT
ejpam-4684	268	26	{	{	PUNCT
ejpam-4684	268	27	a1	a1	PROPN
ejpam-4684	268	28	,	,	PUNCT
ejpam-4684	268	29	a2	a2	PROPN
ejpam-4684	268	30	,	,	PUNCT
ejpam-4684	268	31	a6	a6	NOUN
ejpam-4684	268	32	}	}	PUNCT
ejpam-4684	268	33	.	.	PUNCT
ejpam-4684	269	1	then	then	ADV
ejpam-4684	269	2	o′	o′	PROPN
ejpam-4684	269	3	is	be	AUX
ejpam-4684	269	4	a	a	DET
ejpam-4684	269	5	pointwise	pointwise	ADJ
ejpam-4684	269	6	non	non	ADJ
ejpam-4684	269	7	-	-	ADJ
ejpam-4684	269	8	dominating	dominating	NOUN
ejpam-4684	269	9	of	of	ADP
ejpam-4684	269	10	g.	g.	PROPN
ejpam-4684	269	11	however	however	ADV
ejpam-4684	269	12	,	,	PUNCT
ejpam-4684	269	13	o′	o′	PROPN
ejpam-4684	269	14	is	be	AUX
ejpam-4684	269	15	not	not	PART
ejpam-4684	269	16	an	an	DET
ejpam-4684	269	17	outer	outer	ADJ
ejpam-4684	269	18	-	-	PUNCT
ejpam-4684	269	19	clique	clique	NOUN
ejpam-4684	269	20	pointwise	pointwise	PROPN
ejpam-4684	269	21	non	non	ADJ
ejpam-4684	269	22	-	-	ADJ
ejpam-4684	269	23	dominating	dominating	ADJ
ejpam-4684	269	24	set	set	NOUN
ejpam-4684	269	25	of	of	ADP
ejpam-4684	269	26	g	g	PROPN
ejpam-4684	269	27	since	since	SCONJ
ejpam-4684	269	28	v	v	NOUN
ejpam-4684	269	29	(	(	PUNCT
ejpam-4684	269	30	g)\o′	g)\o′	NOUN
ejpam-4684	269	31	=	=	NOUN
ejpam-4684	269	32	{	{	PUNCT
ejpam-4684	269	33	a3	a3	NOUN
ejpam-4684	269	34	,	,	PUNCT
ejpam-4684	269	35	a4	a4	PROPN
ejpam-4684	269	36	,	,	PUNCT
ejpam-4684	269	37	a5	a5	PROPN
ejpam-4684	269	38	,	,	PUNCT
ejpam-4684	269	39	a7	a7	PROPN
ejpam-4684	269	40	,	,	PUNCT
ejpam-4684	269	41	a8	a8	PROPN
ejpam-4684	269	42	}	}	PUNCT
ejpam-4684	269	43	is	be	AUX
ejpam-4684	269	44	not	not	PART
ejpam-4684	269	45	clique	clique	ADJ
ejpam-4684	269	46	in	in	ADP
ejpam-4684	269	47	g.	g.	PROPN
ejpam-4684	269	48	moreover	moreover	ADV
ejpam-4684	269	49	,	,	PUNCT
ejpam-4684	269	50	since	since	SCONJ
ejpam-4684	269	51	b	b	PROPN
ejpam-4684	269	52	=	=	SYM
ejpam-4684	269	53	{	{	PUNCT
ejpam-4684	269	54	a3	a3	NOUN
ejpam-4684	269	55	,	,	PUNCT
ejpam-4684	269	56	a4	a4	PROPN
ejpam-4684	269	57	,	,	PUNCT
ejpam-4684	269	58	a7	a7	PROPN
ejpam-4684	269	59	,	,	PUNCT
ejpam-4684	269	60	a8	a8	PROPN
ejpam-4684	269	61	}	}	PUNCT
ejpam-4684	269	62	is	be	AUX
ejpam-4684	269	63	the	the	DET
ejpam-4684	269	64	maximum	maximum	ADJ
ejpam-4684	269	65	clique	clique	NOUN
ejpam-4684	269	66	set	set	NOUN
ejpam-4684	269	67	in	in	ADP
ejpam-4684	269	68	g	g	PROPN
ejpam-4684	269	69	,	,	PUNCT
ejpam-4684	269	70	it	it	PRON
ejpam-4684	269	71	follows	follow	VERB
ejpam-4684	269	72	that	that	PRON
ejpam-4684	269	73	ocpnd(g	ocpnd(g	ADP
ejpam-4684	269	74	)	)	PUNCT
ejpam-4684	269	75	=	=	SYM
ejpam-4684	270	1	4	4	X
ejpam-4684	270	2	.	.	PUNCT
ejpam-4684	270	3	j.	j.	PROPN
ejpam-4684	270	4	hassan	hassan	PROPN
ejpam-4684	270	5	,	,	PUNCT
ejpam-4684	270	6	a.	a.	PROPN
ejpam-4684	270	7	lintasan	lintasan	NOUN
ejpam-4684	270	8	,	,	PUNCT
ejpam-4684	270	9	n.	n.	PROPN
ejpam-4684	270	10	h.	h.	PROPN
ejpam-4684	270	11	mohammad	mohammad	PROPN
ejpam-4684	270	12	/	/	PUNCT
ejpam-4684	270	13	eur	eur	PROPN
ejpam-4684	270	14	.	.	PUNCT
ejpam-4684	271	1	j.	j.	PROPN
ejpam-4684	271	2	pure	pure	PROPN
ejpam-4684	271	3	appl	appl	PROPN
ejpam-4684	271	4	.	.	PROPN
ejpam-4684	271	5	math	math	PROPN
ejpam-4684	271	6	,	,	PUNCT
ejpam-4684	271	7	16	16	NUM
ejpam-4684	271	8	(	(	PUNCT
ejpam-4684	271	9	3	3	NUM
ejpam-4684	271	10	)	)	PUNCT
ejpam-4684	271	11	(	(	PUNCT
ejpam-4684	271	12	2023	2023	NUM
ejpam-4684	271	13	)	)	PUNCT
ejpam-4684	271	14	,	,	PUNCT
ejpam-4684	271	15	1848	1848	NUM
ejpam-4684	271	16	-	-	SYM
ejpam-4684	271	17	1861	1861	NUM
ejpam-4684	271	18	1857	1857	NUM
ejpam-4684	271	19	a1	a1	NOUN
ejpam-4684	271	20	a2	a2	PROPN
ejpam-4684	271	21	a3	a3	NOUN
ejpam-4684	271	22	a4	a4	PROPN
ejpam-4684	271	23	g	g	NOUN
ejpam-4684	271	24	:	:	PUNCT
ejpam-4684	271	25	a5	a5	PROPN
ejpam-4684	271	26	a6	a6	PROPN
ejpam-4684	271	27	a7	a7	PROPN
ejpam-4684	271	28	a8	a8	PROPN
ejpam-4684	271	29	figure	figure	NOUN
ejpam-4684	271	30	6	6	NUM
ejpam-4684	271	31	:	:	PUNCT
ejpam-4684	271	32	a	a	DET
ejpam-4684	271	33	graph	graph	NOUN
ejpam-4684	271	34	g	g	NOUN
ejpam-4684	271	35	with	with	ADP
ejpam-4684	271	36	ocpnd(g	ocpnd(g	NOUN
ejpam-4684	271	37	)	)	PUNCT
ejpam-4684	271	38	=	=	SYM
ejpam-4684	271	39	4	4	NUM
ejpam-4684	271	40	theorem	theorem	NOUN
ejpam-4684	271	41	6	6	NUM
ejpam-4684	271	42	.	.	PUNCT
ejpam-4684	272	1	let	let	VERB
ejpam-4684	272	2	g	g	NOUN
ejpam-4684	272	3	and	and	CCONJ
ejpam-4684	272	4	h	h	NOUN
ejpam-4684	272	5	be	be	VERB
ejpam-4684	272	6	two	two	NUM
ejpam-4684	272	7	non	non	ADJ
ejpam-4684	272	8	-	-	ADJ
ejpam-4684	272	9	complete	complete	ADJ
ejpam-4684	272	10	graphs	graph	NOUN
ejpam-4684	272	11	.	.	PUNCT
ejpam-4684	273	1	then	then	ADV
ejpam-4684	273	2	c	c	PROPN
ejpam-4684	273	3	⊆	⊆	NUM
ejpam-4684	273	4	v	v	NOUN
ejpam-4684	273	5	(	(	PUNCT
ejpam-4684	273	6	g+h	g+h	PROPN
ejpam-4684	273	7	)	)	PUNCT
ejpam-4684	273	8	is	be	AUX
ejpam-4684	273	9	a	a	DET
ejpam-4684	273	10	connected	connected	ADJ
ejpam-4684	273	11	outer	outer	ADJ
ejpam-4684	273	12	-	-	PUNCT
ejpam-4684	273	13	hop	hop	NOUN
ejpam-4684	273	14	independent	independent	ADJ
ejpam-4684	273	15	hop	hop	NOUN
ejpam-4684	273	16	dominating	dominating	NOUN
ejpam-4684	273	17	of	of	ADP
ejpam-4684	273	18	g	g	PROPN
ejpam-4684	273	19	+	+	PROPN
ejpam-4684	273	20	h	h	NOUN
ejpam-4684	273	21	if	if	SCONJ
ejpam-4684	274	1	and	and	CCONJ
ejpam-4684	274	2	only	only	ADV
ejpam-4684	274	3	if	if	SCONJ
ejpam-4684	274	4	c	c	NOUN
ejpam-4684	274	5	=	=	NOUN
ejpam-4684	274	6	cg	cg	NOUN
ejpam-4684	274	7	∪	∪	NOUN
ejpam-4684	274	8	ch	ch	NOUN
ejpam-4684	274	9	,	,	PUNCT
ejpam-4684	274	10	where	where	SCONJ
ejpam-4684	274	11	cg	cg	NOUN
ejpam-4684	274	12	and	and	CCONJ
ejpam-4684	274	13	ch	ch	NOUN
ejpam-4684	274	14	are	be	AUX
ejpam-4684	274	15	outer	outer	ADJ
ejpam-4684	274	16	-	-	PUNCT
ejpam-4684	274	17	clique	clique	NOUN
ejpam-4684	274	18	pointwise	pointwise	PROPN
ejpam-4684	274	19	non	non	ADJ
ejpam-4684	274	20	-	-	ADJ
ejpam-4684	274	21	dominating	dominating	ADJ
ejpam-4684	274	22	sets	set	NOUN
ejpam-4684	274	23	of	of	ADP
ejpam-4684	274	24	g	g	PROPN
ejpam-4684	274	25	and	and	CCONJ
ejpam-4684	274	26	h	h	NOUN
ejpam-4684	274	27	,	,	PUNCT
ejpam-4684	274	28	respectively	respectively	ADV
ejpam-4684	274	29	.	.	PUNCT
ejpam-4684	275	1	proof	proof	NOUN
ejpam-4684	275	2	.	.	PUNCT
ejpam-4684	276	1	suppose	suppose	VERB
ejpam-4684	276	2	c	c	SYM
ejpam-4684	276	3	⊆	⊆	NUM
ejpam-4684	276	4	v	v	NOUN
ejpam-4684	276	5	(	(	PUNCT
ejpam-4684	276	6	g+h	g+h	NOUN
ejpam-4684	276	7	)	)	PUNCT
ejpam-4684	276	8	be	be	AUX
ejpam-4684	276	9	a	a	DET
ejpam-4684	276	10	connected	connected	ADJ
ejpam-4684	276	11	outer	outer	ADJ
ejpam-4684	276	12	-	-	PUNCT
ejpam-4684	276	13	hop	hop	NOUN
ejpam-4684	276	14	independent	independent	ADJ
ejpam-4684	276	15	hop	hop	NOUN
ejpam-4684	276	16	dominating	dominating	NOUN
ejpam-4684	276	17	set	set	NOUN
ejpam-4684	276	18	of	of	ADP
ejpam-4684	276	19	g	g	PROPN
ejpam-4684	276	20	+	+	CCONJ
ejpam-4684	276	21	h.	h.	PROPN
ejpam-4684	276	22	let	let	VERB
ejpam-4684	276	23	cg	cg	NOUN
ejpam-4684	276	24	=	=	NOUN
ejpam-4684	276	25	v	v	X
ejpam-4684	276	26	(	(	PUNCT
ejpam-4684	276	27	g	g	NOUN
ejpam-4684	276	28	)	)	PUNCT
ejpam-4684	276	29	∩	∩	NOUN
ejpam-4684	276	30	c	c	NOUN
ejpam-4684	276	31	and	and	CCONJ
ejpam-4684	277	1	ch	ch	NOUN
ejpam-4684	277	2	=	=	SYM
ejpam-4684	277	3	v	v	PROPN
ejpam-4684	277	4	(	(	PUNCT
ejpam-4684	277	5	h	h	NOUN
ejpam-4684	277	6	)	)	PUNCT
ejpam-4684	277	7	∩	∩	ADJ
ejpam-4684	277	8	c.	c.	PROPN
ejpam-4684	277	9	assume	assume	VERB
ejpam-4684	277	10	that	that	SCONJ
ejpam-4684	277	11	cg	cg	NOUN
ejpam-4684	277	12	=	=	PUNCT
ejpam-4684	277	13	∅.	∅.	NOUN
ejpam-4684	277	14	then	then	ADV
ejpam-4684	278	1	c	c	AUX
ejpam-4684	278	2	=	=	NOUN
ejpam-4684	278	3	ch	ch	NOUN
ejpam-4684	278	4	.	.	PUNCT
ejpam-4684	279	1	observe	observe	VERB
ejpam-4684	279	2	that	that	PRON
ejpam-4684	279	3	v	v	NOUN
ejpam-4684	279	4	(	(	PUNCT
ejpam-4684	279	5	g	g	NOUN
ejpam-4684	279	6	)	)	PUNCT
ejpam-4684	279	7	⊆	⊆	NUM
ejpam-4684	279	8	ng+h(c	ng+h(c	PROPN
ejpam-4684	279	9	)	)	PUNCT
ejpam-4684	279	10	.	.	PUNCT
ejpam-4684	280	1	it	it	PRON
ejpam-4684	280	2	follows	follow	VERB
ejpam-4684	280	3	that	that	SCONJ
ejpam-4684	280	4	v	v	X
ejpam-4684	280	5	(	(	PUNCT
ejpam-4684	280	6	g	g	NOUN
ejpam-4684	280	7	)	)	PUNCT
ejpam-4684	280	8	/∈	/∈	PUNCT
ejpam-4684	281	1	n2	n2	NOUN
ejpam-4684	281	2	g+h	g+h	PROPN
ejpam-4684	282	1	[	[	X
ejpam-4684	282	2	c	c	X
ejpam-4684	282	3	]	]	X
ejpam-4684	282	4	,	,	PUNCT
ejpam-4684	282	5	a	a	DET
ejpam-4684	282	6	contradiction	contradiction	NOUN
ejpam-4684	282	7	.	.	PUNCT
ejpam-4684	283	1	hence	hence	ADV
ejpam-4684	283	2	,	,	PUNCT
ejpam-4684	283	3	cg	cg	PROPN
ejpam-4684	283	4	̸=	̸=	PROPN
ejpam-4684	283	5	∅.	∅.	PRON
ejpam-4684	283	6	similarly	similarly	ADV
ejpam-4684	283	7	,	,	PUNCT
ejpam-4684	283	8	ch	ch	NOUN
ejpam-4684	283	9	̸=	̸=	PROPN
ejpam-4684	283	10	∅.	∅.	ADP
ejpam-4684	283	11	now	now	ADV
ejpam-4684	283	12	,	,	PUNCT
ejpam-4684	283	13	let	let	VERB
ejpam-4684	283	14	a	a	DET
ejpam-4684	283	15	∈	∈	PROPN
ejpam-4684	283	16	v	v	NOUN
ejpam-4684	283	17	(	(	PUNCT
ejpam-4684	283	18	g	g	NOUN
ejpam-4684	283	19	)	)	PUNCT
ejpam-4684	283	20	\	\	PROPN
ejpam-4684	283	21	cg	cg	NOUN
ejpam-4684	283	22	.	.	PUNCT
ejpam-4684	284	1	since	since	SCONJ
ejpam-4684	284	2	c	c	PROPN
ejpam-4684	284	3	is	be	AUX
ejpam-4684	284	4	a	a	DET
ejpam-4684	284	5	hop	hop	NOUN
ejpam-4684	284	6	dominating	dominating	NOUN
ejpam-4684	284	7	set	set	NOUN
ejpam-4684	284	8	,	,	PUNCT
ejpam-4684	284	9	there	there	PRON
ejpam-4684	284	10	exists	exist	VERB
ejpam-4684	284	11	b	b	PROPN
ejpam-4684	284	12	∈	∈	PROPN
ejpam-4684	284	13	c	c	NOUN
ejpam-4684	284	14	such	such	ADJ
ejpam-4684	284	15	that	that	DET
ejpam-4684	284	16	dg+h(a	dg+h(a	NOUN
ejpam-4684	284	17	,	,	PUNCT
ejpam-4684	284	18	b	b	NOUN
ejpam-4684	284	19	)	)	PUNCT
ejpam-4684	284	20	=	=	SYM
ejpam-4684	284	21	2	2	X
ejpam-4684	284	22	.	.	PUNCT
ejpam-4684	285	1	thus	thus	ADV
ejpam-4684	285	2	,	,	PUNCT
ejpam-4684	285	3	b	b	X
ejpam-4684	285	4	∈	∈	PROPN
ejpam-4684	285	5	cg	cg	NOUN
ejpam-4684	285	6	and	and	CCONJ
ejpam-4684	285	7	a	a	DET
ejpam-4684	285	8	/∈	/∈	NOUN
ejpam-4684	285	9	ng(b	ng(b	NUM
ejpam-4684	285	10	)	)	PUNCT
ejpam-4684	285	11	.	.	PUNCT
ejpam-4684	286	1	this	this	PRON
ejpam-4684	286	2	means	mean	VERB
ejpam-4684	286	3	that	that	SCONJ
ejpam-4684	286	4	cg	cg	NOUN
ejpam-4684	286	5	is	be	AUX
ejpam-4684	286	6	a	a	DET
ejpam-4684	286	7	pointwise	pointwise	ADJ
ejpam-4684	286	8	non	non	ADJ
ejpam-4684	286	9	-	-	ADJ
ejpam-4684	286	10	dominating	dominating	ADJ
ejpam-4684	286	11	set	set	NOUN
ejpam-4684	286	12	of	of	ADP
ejpam-4684	286	13	g.	g.	PROPN
ejpam-4684	286	14	since	since	SCONJ
ejpam-4684	286	15	v	v	PROPN
ejpam-4684	286	16	(	(	PUNCT
ejpam-4684	286	17	g+h	g+h	NOUN
ejpam-4684	286	18	)	)	PUNCT
ejpam-4684	286	19	\c	\c	NOUN
ejpam-4684	286	20	is	be	AUX
ejpam-4684	286	21	a	a	DET
ejpam-4684	286	22	hop	hop	NOUN
ejpam-4684	286	23	independent	independent	ADJ
ejpam-4684	286	24	set	set	NOUN
ejpam-4684	286	25	of	of	ADP
ejpam-4684	286	26	g+h	g+h	PROPN
ejpam-4684	286	27	,	,	PUNCT
ejpam-4684	286	28	it	it	PRON
ejpam-4684	286	29	follows	follow	VERB
ejpam-4684	286	30	that	that	SCONJ
ejpam-4684	286	31	v	v	ADP
ejpam-4684	286	32	(	(	PUNCT
ejpam-4684	286	33	g	g	NOUN
ejpam-4684	286	34	)	)	PUNCT
ejpam-4684	286	35	\cg	\cg	NUM
ejpam-4684	286	36	is	be	AUX
ejpam-4684	286	37	a	a	DET
ejpam-4684	286	38	clique	clique	NOUN
ejpam-4684	286	39	set	set	NOUN
ejpam-4684	286	40	of	of	ADP
ejpam-4684	286	41	g.	g.	PROPN
ejpam-4684	286	42	hence	hence	ADV
ejpam-4684	286	43	,	,	PUNCT
ejpam-4684	286	44	cg	cg	NOUN
ejpam-4684	286	45	is	be	AUX
ejpam-4684	286	46	an	an	DET
ejpam-4684	286	47	outer	outer	ADJ
ejpam-4684	286	48	-	-	PUNCT
ejpam-4684	286	49	clique	clique	NOUN
ejpam-4684	286	50	pointwise	pointwise	PROPN
ejpam-4684	286	51	non	non	ADJ
ejpam-4684	286	52	-	-	ADJ
ejpam-4684	286	53	dominating	dominating	ADJ
ejpam-4684	286	54	set	set	NOUN
ejpam-4684	286	55	of	of	ADP
ejpam-4684	286	56	g.	g.	PROPN
ejpam-4684	286	57	similarly	similarly	ADV
ejpam-4684	286	58	,	,	PUNCT
ejpam-4684	286	59	ch	ch	NOUN
ejpam-4684	286	60	is	be	AUX
ejpam-4684	286	61	an	an	DET
ejpam-4684	286	62	outer	outer	ADJ
ejpam-4684	286	63	-	-	PUNCT
ejpam-4684	286	64	clique	clique	NOUN
ejpam-4684	286	65	pointwise	pointwise	PROPN
ejpam-4684	286	66	non	non	ADJ
ejpam-4684	286	67	-	-	ADJ
ejpam-4684	286	68	dominating	dominating	ADJ
ejpam-4684	286	69	set	set	NOUN
ejpam-4684	286	70	of	of	ADP
ejpam-4684	286	71	h.	h.	NOUN
ejpam-4684	286	72	conversely	conversely	ADV
ejpam-4684	286	73	,	,	PUNCT
ejpam-4684	286	74	suppose	suppose	VERB
ejpam-4684	286	75	c	c	NOUN
ejpam-4684	286	76	=	=	SYM
ejpam-4684	286	77	cg	cg	PROPN
ejpam-4684	286	78	∪ch	∪ch	PROPN
ejpam-4684	286	79	,	,	PUNCT
ejpam-4684	286	80	where	where	SCONJ
ejpam-4684	286	81	cg	cg	NOUN
ejpam-4684	286	82	and	and	CCONJ
ejpam-4684	286	83	ch	ch	NOUN
ejpam-4684	286	84	are	be	AUX
ejpam-4684	286	85	outer	outer	ADJ
ejpam-4684	286	86	-	-	PUNCT
ejpam-4684	286	87	clique	clique	NOUN
ejpam-4684	286	88	pointwise	pointwise	NOUN
ejpam-4684	286	89	nondominating	nondominate	VERB
ejpam-4684	286	90	sets	set	NOUN
ejpam-4684	286	91	in	in	ADP
ejpam-4684	286	92	g	g	PROPN
ejpam-4684	286	93	and	and	CCONJ
ejpam-4684	286	94	h	h	NOUN
ejpam-4684	286	95	,	,	PUNCT
ejpam-4684	286	96	respectively	respectively	ADV
ejpam-4684	286	97	.	.	PUNCT
ejpam-4684	287	1	clearly	clearly	ADV
ejpam-4684	287	2	,	,	PUNCT
ejpam-4684	287	3	⟨c⟩	⟨c⟩	PROPN
ejpam-4684	287	4	is	be	AUX
ejpam-4684	287	5	connected	connect	VERB
ejpam-4684	287	6	and	and	CCONJ
ejpam-4684	287	7	v	v	ADJ
ejpam-4684	287	8	(	(	PUNCT
ejpam-4684	287	9	g	g	PROPN
ejpam-4684	287	10	+	+	NOUN
ejpam-4684	287	11	h	h	NOUN
ejpam-4684	287	12	)	)	PUNCT
ejpam-4684	287	13	\	\	PUNCT
ejpam-4684	288	1	c	c	NOUN
ejpam-4684	288	2	is	be	AUX
ejpam-4684	288	3	a	a	DET
ejpam-4684	288	4	hop	hop	NOUN
ejpam-4684	288	5	independent	independent	ADJ
ejpam-4684	288	6	set	set	NOUN
ejpam-4684	288	7	.	.	PUNCT
ejpam-4684	289	1	now	now	ADV
ejpam-4684	289	2	,	,	PUNCT
ejpam-4684	289	3	let	let	VERB
ejpam-4684	289	4	a	a	DET
ejpam-4684	289	5	∈	∈	NOUN
ejpam-4684	289	6	v	v	NOUN
ejpam-4684	289	7	(	(	PUNCT
ejpam-4684	289	8	g	g	PROPN
ejpam-4684	289	9	+	+	NOUN
ejpam-4684	289	10	h	h	NOUN
ejpam-4684	289	11	)	)	PUNCT
ejpam-4684	289	12	\	\	PROPN
ejpam-4684	289	13	c.	c.	PROPN
ejpam-4684	289	14	suppose	suppose	VERB
ejpam-4684	289	15	a	a	DET
ejpam-4684	289	16	∈	∈	PROPN
ejpam-4684	289	17	v	v	NOUN
ejpam-4684	289	18	(	(	PUNCT
ejpam-4684	289	19	g	g	NOUN
ejpam-4684	289	20	)	)	PUNCT
ejpam-4684	289	21	.	.	PUNCT
ejpam-4684	290	1	since	since	SCONJ
ejpam-4684	290	2	cg	cg	NOUN
ejpam-4684	290	3	is	be	AUX
ejpam-4684	290	4	a	a	DET
ejpam-4684	290	5	pointwise	pointwise	ADJ
ejpam-4684	290	6	non	non	ADJ
ejpam-4684	290	7	-	-	ADJ
ejpam-4684	290	8	dominating	dominating	ADJ
ejpam-4684	290	9	set	set	NOUN
ejpam-4684	290	10	of	of	ADP
ejpam-4684	290	11	g	g	NOUN
ejpam-4684	290	12	,	,	PUNCT
ejpam-4684	290	13	there	there	PRON
ejpam-4684	290	14	exists	exist	VERB
ejpam-4684	290	15	b	b	PROPN
ejpam-4684	290	16	∈	∈	PROPN
ejpam-4684	290	17	cg	cg	NOUN
ejpam-4684	290	18	\ng(a	\ng(a	PROPN
ejpam-4684	290	19	)	)	PUNCT
ejpam-4684	290	20	.	.	PUNCT
ejpam-4684	291	1	thus	thus	ADV
ejpam-4684	291	2	,	,	PUNCT
ejpam-4684	291	3	dg+h(a	dg+h(a	PROPN
ejpam-4684	291	4	,	,	PUNCT
ejpam-4684	291	5	b	b	NOUN
ejpam-4684	291	6	)	)	PUNCT
ejpam-4684	291	7	=	=	SYM
ejpam-4684	291	8	2	2	X
ejpam-4684	291	9	.	.	X
ejpam-4684	291	10	similarly	similarly	ADV
ejpam-4684	291	11	,	,	PUNCT
ejpam-4684	291	12	when	when	SCONJ
ejpam-4684	291	13	a	a	DET
ejpam-4684	291	14	∈	∈	PROPN
ejpam-4684	291	15	v	v	NOUN
ejpam-4684	291	16	(	(	PUNCT
ejpam-4684	291	17	h	h	NOUN
ejpam-4684	291	18	)	)	PUNCT
ejpam-4684	291	19	.	.	PUNCT
ejpam-4684	292	1	therefore	therefore	ADV
ejpam-4684	292	2	,	,	PUNCT
ejpam-4684	292	3	c	c	PROPN
ejpam-4684	292	4	is	be	AUX
ejpam-4684	292	5	a	a	DET
ejpam-4684	292	6	hop	hop	NOUN
ejpam-4684	292	7	dominating	dominating	NOUN
ejpam-4684	292	8	set	set	NOUN
ejpam-4684	292	9	of	of	ADP
ejpam-4684	292	10	g+h	g+h	PROPN
ejpam-4684	292	11	.	.	PUNCT
ejpam-4684	293	1	consequently	consequently	ADV
ejpam-4684	293	2	,	,	PUNCT
ejpam-4684	293	3	s	s	VERB
ejpam-4684	293	4	is	be	AUX
ejpam-4684	293	5	a	a	DET
ejpam-4684	293	6	connected	connected	ADJ
ejpam-4684	293	7	outer	outer	ADJ
ejpam-4684	293	8	-	-	PUNCT
ejpam-4684	293	9	hop	hop	NOUN
ejpam-4684	293	10	independent	independent	ADJ
ejpam-4684	293	11	hop	hop	NOUN
ejpam-4684	293	12	dominating	dominating	NOUN
ejpam-4684	293	13	set	set	NOUN
ejpam-4684	293	14	of	of	ADP
ejpam-4684	293	15	g+h	g+h	PROPN
ejpam-4684	293	16	.	.	PUNCT
ejpam-4684	294	1	corollary	corollary	ADJ
ejpam-4684	294	2	4	4	NUM
ejpam-4684	294	3	.	.	PUNCT
ejpam-4684	295	1	let	let	VERB
ejpam-4684	295	2	g	g	NOUN
ejpam-4684	295	3	and	and	CCONJ
ejpam-4684	295	4	h	h	NOUN
ejpam-4684	295	5	be	be	VERB
ejpam-4684	295	6	two	two	NUM
ejpam-4684	295	7	non	non	ADJ
ejpam-4684	295	8	-	-	ADJ
ejpam-4684	295	9	complete	complete	ADJ
ejpam-4684	295	10	graphs	graph	NOUN
ejpam-4684	295	11	.	.	PUNCT
ejpam-4684	296	1	then	then	ADV
ejpam-4684	296	2	γohich	γohich	PROPN
ejpam-4684	296	3	(	(	PUNCT
ejpam-4684	296	4	g+h	g+h	PROPN
ejpam-4684	296	5	)	)	PUNCT
ejpam-4684	296	6	=	=	SYM
ejpam-4684	296	7	ocpnd(g	ocpnd(g	X
ejpam-4684	296	8	)	)	PUNCT
ejpam-4684	296	9	+	+	NOUN
ejpam-4684	296	10	ocpnd(h	ocpnd(h	NUM
ejpam-4684	296	11	)	)	PUNCT
ejpam-4684	296	12	.	.	PUNCT
ejpam-4684	297	1	proof	proof	NOUN
ejpam-4684	297	2	.	.	PUNCT
ejpam-4684	298	1	suppose	suppose	VERB
ejpam-4684	298	2	c	c	SYM
ejpam-4684	298	3	⊆	⊆	NUM
ejpam-4684	298	4	v	v	NOUN
ejpam-4684	298	5	(	(	PUNCT
ejpam-4684	298	6	g+h	g+h	PROPN
ejpam-4684	298	7	)	)	PUNCT
ejpam-4684	298	8	is	be	AUX
ejpam-4684	298	9	a	a	DET
ejpam-4684	298	10	γohich	γohich	NOUN
ejpam-4684	298	11	-set	-set	ADJ
ejpam-4684	298	12	ofg+h	ofg+h	PROPN
ejpam-4684	298	13	.	.	PUNCT
ejpam-4684	298	14	then	then	ADV
ejpam-4684	298	15	by	by	ADP
ejpam-4684	298	16	theorem	theorem	NOUN
ejpam-4684	298	17	6	6	NUM
ejpam-4684	298	18	,	,	PUNCT
ejpam-4684	298	19	c	c	NOUN
ejpam-4684	298	20	=	=	SYM
ejpam-4684	298	21	cg∪ch	cg∪ch	PROPN
ejpam-4684	298	22	,	,	PUNCT
ejpam-4684	298	23	where	where	SCONJ
ejpam-4684	298	24	cg	cg	NOUN
ejpam-4684	298	25	and	and	CCONJ
ejpam-4684	298	26	ch	ch	NOUN
ejpam-4684	298	27	are	be	AUX
ejpam-4684	298	28	outer	outer	ADJ
ejpam-4684	298	29	-	-	PUNCT
ejpam-4684	298	30	clique	clique	NOUN
ejpam-4684	298	31	pointwise	pointwise	PROPN
ejpam-4684	298	32	non	non	ADJ
ejpam-4684	298	33	-	-	ADJ
ejpam-4684	298	34	dominating	dominating	ADJ
ejpam-4684	298	35	sets	set	NOUN
ejpam-4684	298	36	of	of	ADP
ejpam-4684	298	37	g	g	NOUN
ejpam-4684	298	38	andh	andh	NOUN
ejpam-4684	298	39	,	,	PUNCT
ejpam-4684	298	40	respectively	respectively	ADV
ejpam-4684	298	41	.	.	PUNCT
ejpam-4684	299	1	thus	thus	ADV
ejpam-4684	299	2	,	,	PUNCT
ejpam-4684	299	3	γohich	γohich	PROPN
ejpam-4684	299	4	(	(	PUNCT
ejpam-4684	299	5	g+h	g+h	NOUN
ejpam-4684	299	6	)	)	PUNCT
ejpam-4684	300	1	=	=	SYM
ejpam-4684	300	2	|c|	|c|	PROPN
ejpam-4684	300	3	=	=	PUNCT
ejpam-4684	300	4	|cg|+	|cg|+	NOUN
ejpam-4684	300	5	|ch	|ch	PROPN
ejpam-4684	300	6	|	|	ADV
ejpam-4684	300	7	≥	≥	NOUN
ejpam-4684	300	8	ocpnd(g	ocpnd(g	ADP
ejpam-4684	300	9	)	)	PUNCT
ejpam-4684	300	10	+	+	NOUN
ejpam-4684	300	11	ocpnd(h	ocpnd(h	NUM
ejpam-4684	300	12	)	)	PUNCT
ejpam-4684	300	13	.	.	PUNCT
ejpam-4684	301	1	on	on	ADP
ejpam-4684	301	2	the	the	DET
ejpam-4684	301	3	other	other	ADJ
ejpam-4684	301	4	hand	hand	NOUN
ejpam-4684	301	5	,	,	PUNCT
ejpam-4684	301	6	let	let	VERB
ejpam-4684	301	7	cg	cg	NOUN
ejpam-4684	301	8	and	and	CCONJ
ejpam-4684	301	9	ch	ch	NOUN
ejpam-4684	301	10	be	be	AUX
ejpam-4684	301	11	ocpnd	ocpnd	NOUN
ejpam-4684	301	12	-	-	PUNCT
ejpam-4684	301	13	sets	set	NOUN
ejpam-4684	301	14	of	of	ADP
ejpam-4684	301	15	g	g	PROPN
ejpam-4684	301	16	and	and	CCONJ
ejpam-4684	301	17	h	h	NOUN
ejpam-4684	301	18	,	,	PUNCT
ejpam-4684	301	19	respectively	respectively	ADV
ejpam-4684	301	20	.	.	PUNCT
ejpam-4684	302	1	then	then	ADV
ejpam-4684	302	2	by	by	ADP
ejpam-4684	302	3	j.	j.	PROPN
ejpam-4684	302	4	hassan	hassan	PROPN
ejpam-4684	302	5	,	,	PUNCT
ejpam-4684	302	6	a.	a.	PROPN
ejpam-4684	302	7	lintasan	lintasan	NOUN
ejpam-4684	302	8	,	,	PUNCT
ejpam-4684	302	9	n.	n.	PROPN
ejpam-4684	302	10	h.	h.	PROPN
ejpam-4684	302	11	mohammad	mohammad	PROPN
ejpam-4684	302	12	/	/	PUNCT
ejpam-4684	302	13	eur	eur	PROPN
ejpam-4684	302	14	.	.	PUNCT
ejpam-4684	303	1	j.	j.	PROPN
ejpam-4684	303	2	pure	pure	PROPN
ejpam-4684	303	3	appl	appl	PROPN
ejpam-4684	303	4	.	.	PROPN
ejpam-4684	303	5	math	math	PROPN
ejpam-4684	303	6	,	,	PUNCT
ejpam-4684	303	7	16	16	NUM
ejpam-4684	303	8	(	(	PUNCT
ejpam-4684	303	9	3	3	NUM
ejpam-4684	303	10	)	)	PUNCT
ejpam-4684	303	11	(	(	PUNCT
ejpam-4684	303	12	2023	2023	NUM
ejpam-4684	303	13	)	)	PUNCT
ejpam-4684	303	14	,	,	PUNCT
ejpam-4684	303	15	1848	1848	NUM
ejpam-4684	303	16	-	-	SYM
ejpam-4684	303	17	1861	1861	NUM
ejpam-4684	303	18	1858	1858	NUM
ejpam-4684	303	19	theorem	theorem	NOUN
ejpam-4684	303	20	6	6	NUM
ejpam-4684	303	21	,	,	PUNCT
ejpam-4684	303	22	c	c	NOUN
ejpam-4684	304	1	=	=	PUNCT
ejpam-4684	304	2	cg	cg	NOUN
ejpam-4684	304	3	∪	∪	NOUN
ejpam-4684	304	4	ch	ch	NOUN
ejpam-4684	304	5	is	be	AUX
ejpam-4684	304	6	a	a	DET
ejpam-4684	304	7	connected	connected	ADJ
ejpam-4684	304	8	outer	outer	ADJ
ejpam-4684	304	9	-	-	PUNCT
ejpam-4684	304	10	hop	hop	NOUN
ejpam-4684	304	11	independent	independent	ADJ
ejpam-4684	304	12	hop	hop	NOUN
ejpam-4684	304	13	dominating	dominating	NOUN
ejpam-4684	304	14	set	set	NOUN
ejpam-4684	304	15	of	of	ADP
ejpam-4684	304	16	g+h	g+h	PROPN
ejpam-4684	304	17	.	.	PUNCT
ejpam-4684	305	1	hence	hence	ADV
ejpam-4684	305	2	,	,	PUNCT
ejpam-4684	305	3	ocpnd(g	ocpnd(g	ADV
ejpam-4684	305	4	)	)	PUNCT
ejpam-4684	305	5	+	+	NUM
ejpam-4684	306	1	ocpnd(h	ocpnd(h	NUM
ejpam-4684	306	2	)	)	PUNCT
ejpam-4684	306	3	=	=	SYM
ejpam-4684	306	4	|cg|+	|cg|+	X
ejpam-4684	306	5	|ch	|ch	PROPN
ejpam-4684	306	6	|	|	NOUN
ejpam-4684	306	7	=	=	SYM
ejpam-4684	306	8	|c|	|c|	PROPN
ejpam-4684	306	9	≥	≥	PRON
ejpam-4684	306	10	γohich	γohich	PROPN
ejpam-4684	306	11	(	(	PUNCT
ejpam-4684	306	12	g+h	g+h	PROPN
ejpam-4684	306	13	)	)	PUNCT
ejpam-4684	306	14	.	.	PUNCT
ejpam-4684	307	1	therefore	therefore	ADV
ejpam-4684	307	2	,	,	PUNCT
ejpam-4684	307	3	γohich	γohich	PROPN
ejpam-4684	307	4	(	(	PUNCT
ejpam-4684	307	5	g+h	g+h	NOUN
ejpam-4684	307	6	)	)	PUNCT
ejpam-4684	307	7	=	=	SYM
ejpam-4684	307	8	ocpnd(g	ocpnd(g	X
ejpam-4684	307	9	)	)	PUNCT
ejpam-4684	307	10	+	+	NOUN
ejpam-4684	307	11	ocpnd(h	ocpnd(h	NUM
ejpam-4684	307	12	)	)	PUNCT
ejpam-4684	307	13	.	.	PUNCT
ejpam-4684	308	1	theorem	theorem	ADJ
ejpam-4684	308	2	7	7	NUM
ejpam-4684	308	3	.	.	PUNCT
ejpam-4684	309	1	let	let	VERB
ejpam-4684	309	2	g	g	PRON
ejpam-4684	309	3	be	be	AUX
ejpam-4684	309	4	a	a	DET
ejpam-4684	309	5	complete	complete	ADJ
ejpam-4684	309	6	graph	graph	NOUN
ejpam-4684	309	7	and	and	CCONJ
ejpam-4684	309	8	h	h	NOUN
ejpam-4684	309	9	be	be	AUX
ejpam-4684	309	10	non	non	ADJ
ejpam-4684	309	11	-	-	ADJ
ejpam-4684	309	12	complete	complete	ADJ
ejpam-4684	309	13	graph	graph	NOUN
ejpam-4684	309	14	.	.	PUNCT
ejpam-4684	310	1	then	then	ADV
ejpam-4684	310	2	t	t	PROPN
ejpam-4684	310	3	⊆	⊆	NUM
ejpam-4684	310	4	v	v	NOUN
ejpam-4684	310	5	(	(	PUNCT
ejpam-4684	310	6	g	g	PROPN
ejpam-4684	310	7	+	+	NOUN
ejpam-4684	310	8	h	h	NOUN
ejpam-4684	310	9	)	)	PUNCT
ejpam-4684	310	10	is	be	AUX
ejpam-4684	310	11	a	a	DET
ejpam-4684	310	12	connected	connected	ADJ
ejpam-4684	310	13	outer	outer	ADJ
ejpam-4684	310	14	-	-	PUNCT
ejpam-4684	310	15	hop	hop	NOUN
ejpam-4684	310	16	independent	independent	ADJ
ejpam-4684	310	17	hop	hop	NOUN
ejpam-4684	310	18	dominating	dominating	NOUN
ejpam-4684	310	19	set	set	VERB
ejpam-4684	310	20	in	in	ADP
ejpam-4684	310	21	g	g	PROPN
ejpam-4684	311	1	+	+	NOUN
ejpam-4684	311	2	h	h	NOUN
ejpam-4684	311	3	if	if	SCONJ
ejpam-4684	311	4	and	and	CCONJ
ejpam-4684	311	5	only	only	ADV
ejpam-4684	311	6	if	if	SCONJ
ejpam-4684	311	7	t	t	NOUN
ejpam-4684	311	8	=	=	SYM
ejpam-4684	311	9	v	v	PROPN
ejpam-4684	311	10	(	(	PUNCT
ejpam-4684	311	11	g	g	NOUN
ejpam-4684	311	12	)	)	PUNCT
ejpam-4684	311	13	∪	∪	ADP
ejpam-4684	311	14	th	th	NOUN
ejpam-4684	311	15	,	,	PUNCT
ejpam-4684	311	16	where	where	SCONJ
ejpam-4684	311	17	th	th	X
ejpam-4684	311	18	is	be	AUX
ejpam-4684	311	19	an	an	DET
ejpam-4684	311	20	outer	outer	ADJ
ejpam-4684	311	21	-	-	PUNCT
ejpam-4684	311	22	clique	clique	NOUN
ejpam-4684	311	23	pointwise	pointwise	PROPN
ejpam-4684	311	24	non	non	ADJ
ejpam-4684	311	25	-	-	ADJ
ejpam-4684	311	26	dominating	dominating	ADJ
ejpam-4684	311	27	set	set	NOUN
ejpam-4684	311	28	of	of	ADP
ejpam-4684	311	29	h.	h.	PROPN
ejpam-4684	311	30	proof	proof	NOUN
ejpam-4684	311	31	.	.	PUNCT
ejpam-4684	312	1	suppose	suppose	VERB
ejpam-4684	312	2	that	that	SCONJ
ejpam-4684	312	3	t	t	NOUN
ejpam-4684	312	4	=	=	SYM
ejpam-4684	312	5	v	v	PROPN
ejpam-4684	312	6	(	(	PUNCT
ejpam-4684	312	7	g	g	NOUN
ejpam-4684	312	8	)	)	PUNCT
ejpam-4684	312	9	∪	∪	ADP
ejpam-4684	312	10	th	th	X
ejpam-4684	312	11	is	be	AUX
ejpam-4684	312	12	a	a	DET
ejpam-4684	312	13	connected	connected	ADJ
ejpam-4684	312	14	outer	outer	ADJ
ejpam-4684	312	15	-	-	PUNCT
ejpam-4684	312	16	hop	hop	NOUN
ejpam-4684	312	17	independent	independent	ADJ
ejpam-4684	312	18	hop	hop	NOUN
ejpam-4684	312	19	dominating	dominating	NOUN
ejpam-4684	312	20	set	set	VERB
ejpam-4684	312	21	in	in	ADP
ejpam-4684	312	22	g	g	PROPN
ejpam-4684	312	23	+	+	CCONJ
ejpam-4684	312	24	h.	h.	PROPN
ejpam-4684	312	25	since	since	SCONJ
ejpam-4684	312	26	g	g	PROPN
ejpam-4684	312	27	is	be	AUX
ejpam-4684	312	28	complete	complete	ADJ
ejpam-4684	312	29	,	,	PUNCT
ejpam-4684	312	30	it	it	PRON
ejpam-4684	312	31	follows	follow	VERB
ejpam-4684	312	32	that	that	SCONJ
ejpam-4684	312	33	t	t	NOUN
ejpam-4684	312	34	=	=	SYM
ejpam-4684	312	35	v	v	PROPN
ejpam-4684	312	36	(	(	PUNCT
ejpam-4684	312	37	g	g	NOUN
ejpam-4684	312	38	)	)	PUNCT
ejpam-4684	312	39	∪	∪	ADP
ejpam-4684	312	40	th	th	NOUN
ejpam-4684	312	41	,	,	PUNCT
ejpam-4684	312	42	where	where	SCONJ
ejpam-4684	312	43	th	th	X
ejpam-4684	312	44	̸=	̸=	PROPN
ejpam-4684	312	45	∅.	∅.	ADV
ejpam-4684	312	46	since	since	SCONJ
ejpam-4684	312	47	t	t	PROPN
ejpam-4684	312	48	is	be	AUX
ejpam-4684	312	49	a	a	DET
ejpam-4684	312	50	hop	hop	NOUN
ejpam-4684	312	51	dominating	dominating	NOUN
ejpam-4684	312	52	,	,	PUNCT
ejpam-4684	312	53	th	th	X
ejpam-4684	312	54	must	must	AUX
ejpam-4684	312	55	be	be	AUX
ejpam-4684	312	56	a	a	DET
ejpam-4684	312	57	pointwise	pointwise	ADJ
ejpam-4684	312	58	non	non	ADJ
ejpam-4684	312	59	-	-	ADJ
ejpam-4684	312	60	dominating	dominating	ADJ
ejpam-4684	312	61	set	set	NOUN
ejpam-4684	312	62	in	in	ADP
ejpam-4684	312	63	h.	h.	PROPN
ejpam-4684	313	1	if	if	SCONJ
ejpam-4684	313	2	v	v	X
ejpam-4684	313	3	(	(	PUNCT
ejpam-4684	313	4	h	h	NOUN
ejpam-4684	313	5	)	)	PUNCT
ejpam-4684	313	6	\	\	PUNCT
ejpam-4684	313	7	th	th	X
ejpam-4684	313	8	is	be	AUX
ejpam-4684	313	9	not	not	PART
ejpam-4684	313	10	clique	clique	ADJ
ejpam-4684	313	11	in	in	ADP
ejpam-4684	313	12	h	h	NOUN
ejpam-4684	313	13	,	,	PUNCT
ejpam-4684	313	14	then	then	ADV
ejpam-4684	313	15	there	there	PRON
ejpam-4684	313	16	exist	exist	VERB
ejpam-4684	313	17	a	a	DET
ejpam-4684	313	18	,	,	PUNCT
ejpam-4684	313	19	b	b	PROPN
ejpam-4684	313	20	∈	∈	PROPN
ejpam-4684	313	21	v	v	ADP
ejpam-4684	313	22	(	(	PUNCT
ejpam-4684	313	23	h	h	NOUN
ejpam-4684	313	24	)	)	PUNCT
ejpam-4684	313	25	\	\	NOUN
ejpam-4684	314	1	th	th	X
ejpam-4684	314	2	⊆	⊆	NUM
ejpam-4684	314	3	v	v	NOUN
ejpam-4684	314	4	(	(	PUNCT
ejpam-4684	314	5	g+h	g+h	NOUN
ejpam-4684	314	6	)	)	PUNCT
ejpam-4684	314	7	\	\	PROPN
ejpam-4684	315	1	t	t	NOUN
ejpam-4684	315	2	such	such	ADJ
ejpam-4684	315	3	that	that	DET
ejpam-4684	315	4	dh(a	dh(a	ADJ
ejpam-4684	315	5	,	,	PUNCT
ejpam-4684	315	6	b	b	NOUN
ejpam-4684	315	7	)	)	PUNCT
ejpam-4684	315	8	≥	≥	NOUN
ejpam-4684	315	9	2	2	NUM
ejpam-4684	315	10	.	.	PUNCT
ejpam-4684	316	1	it	it	PRON
ejpam-4684	316	2	follows	follow	VERB
ejpam-4684	316	3	that	that	PRON
ejpam-4684	316	4	dg+h(a	dg+h(a	NOUN
ejpam-4684	316	5	,	,	PUNCT
ejpam-4684	316	6	b	b	NOUN
ejpam-4684	316	7	)	)	PUNCT
ejpam-4684	316	8	=	=	SYM
ejpam-4684	316	9	2	2	NUM
ejpam-4684	316	10	,	,	PUNCT
ejpam-4684	316	11	a	a	DET
ejpam-4684	316	12	contradiction	contradiction	NOUN
ejpam-4684	316	13	to	to	ADP
ejpam-4684	316	14	the	the	DET
ejpam-4684	316	15	fact	fact	NOUN
ejpam-4684	316	16	that	that	SCONJ
ejpam-4684	316	17	v	v	X
ejpam-4684	316	18	(	(	PUNCT
ejpam-4684	316	19	g	g	PROPN
ejpam-4684	316	20	+	+	NOUN
ejpam-4684	316	21	h	h	NOUN
ejpam-4684	316	22	)	)	PUNCT
ejpam-4684	316	23	\	\	PROPN
ejpam-4684	316	24	t	t	PROPN
ejpam-4684	316	25	is	be	AUX
ejpam-4684	316	26	a	a	DET
ejpam-4684	316	27	hop	hop	NOUN
ejpam-4684	316	28	independent	independent	ADJ
ejpam-4684	316	29	in	in	ADP
ejpam-4684	316	30	g	g	PROPN
ejpam-4684	316	31	+	+	PROPN
ejpam-4684	316	32	h.	h.	PROPN
ejpam-4684	316	33	thus	thus	ADV
ejpam-4684	316	34	,	,	PUNCT
ejpam-4684	316	35	th	th	X
ejpam-4684	316	36	is	be	AUX
ejpam-4684	316	37	an	an	DET
ejpam-4684	316	38	outer	outer	ADJ
ejpam-4684	316	39	-	-	PUNCT
ejpam-4684	316	40	clique	clique	NOUN
ejpam-4684	316	41	pointwise	pointwise	PROPN
ejpam-4684	316	42	non	non	ADJ
ejpam-4684	316	43	-	-	ADJ
ejpam-4684	316	44	dominating	dominating	ADJ
ejpam-4684	316	45	set	set	NOUN
ejpam-4684	316	46	of	of	ADP
ejpam-4684	316	47	h.	h.	NOUN
ejpam-4684	316	48	conversely	conversely	ADV
ejpam-4684	316	49	,	,	PUNCT
ejpam-4684	316	50	assume	assume	VERB
ejpam-4684	316	51	that	that	SCONJ
ejpam-4684	316	52	t	t	NOUN
ejpam-4684	316	53	=	=	SYM
ejpam-4684	316	54	v	v	PROPN
ejpam-4684	316	55	(	(	PUNCT
ejpam-4684	316	56	g	g	NOUN
ejpam-4684	316	57	)	)	PUNCT
ejpam-4684	316	58	∪	∪	ADP
ejpam-4684	316	59	th	th	NOUN
ejpam-4684	316	60	,	,	PUNCT
ejpam-4684	316	61	where	where	SCONJ
ejpam-4684	316	62	th	th	X
ejpam-4684	316	63	is	be	AUX
ejpam-4684	316	64	an	an	DET
ejpam-4684	316	65	outer	outer	ADJ
ejpam-4684	316	66	-	-	PUNCT
ejpam-4684	316	67	clique	clique	NOUN
ejpam-4684	316	68	pointwise	pointwise	NOUN
ejpam-4684	316	69	nondominating	nondominate	VERB
ejpam-4684	316	70	set	set	NOUN
ejpam-4684	316	71	of	of	ADP
ejpam-4684	316	72	h.	h.	PROPN
ejpam-4684	316	73	then	then	ADV
ejpam-4684	316	74	t	t	PROPN
ejpam-4684	316	75	is	be	AUX
ejpam-4684	316	76	connected	connect	VERB
ejpam-4684	316	77	outer	outer	ADJ
ejpam-4684	316	78	-	-	PUNCT
ejpam-4684	316	79	hop	hop	NOUN
ejpam-4684	316	80	independent	independent	ADJ
ejpam-4684	316	81	hop	hop	NOUN
ejpam-4684	316	82	dominating	dominating	NOUN
ejpam-4684	316	83	set	set	VERB
ejpam-4684	316	84	in	in	ADP
ejpam-4684	316	85	g+h	g+h	PROPN
ejpam-4684	316	86	by	by	ADP
ejpam-4684	316	87	theorem	theorem	ADJ
ejpam-4684	316	88	6	6	NUM
ejpam-4684	316	89	.	.	PUNCT
ejpam-4684	316	90	corollary	corollary	ADJ
ejpam-4684	316	91	5	5	NUM
ejpam-4684	316	92	.	.	PUNCT
ejpam-4684	317	1	let	let	VERB
ejpam-4684	317	2	g	g	PRON
ejpam-4684	317	3	be	be	AUX
ejpam-4684	317	4	a	a	DET
ejpam-4684	317	5	complete	complete	ADJ
ejpam-4684	317	6	graph	graph	NOUN
ejpam-4684	317	7	and	and	CCONJ
ejpam-4684	317	8	h	h	NOUN
ejpam-4684	317	9	be	be	AUX
ejpam-4684	317	10	any	any	DET
ejpam-4684	317	11	non	non	ADJ
ejpam-4684	317	12	-	-	ADJ
ejpam-4684	317	13	complete	complete	ADJ
ejpam-4684	317	14	graph	graph	NOUN
ejpam-4684	317	15	.	.	PUNCT
ejpam-4684	318	1	then	then	ADV
ejpam-4684	318	2	γohich	γohich	PROPN
ejpam-4684	318	3	(	(	PUNCT
ejpam-4684	318	4	g+h	g+h	PROPN
ejpam-4684	318	5	)	)	PUNCT
ejpam-4684	319	1	=	=	SYM
ejpam-4684	319	2	|v	|v	PROPN
ejpam-4684	319	3	(	(	PUNCT
ejpam-4684	319	4	g)|+	g)|+	NOUN
ejpam-4684	319	5	ocpnd(h	ocpnd(h	PROPN
ejpam-4684	319	6	)	)	PUNCT
ejpam-4684	319	7	.	.	PUNCT
ejpam-4684	320	1	proof	proof	NOUN
ejpam-4684	320	2	.	.	PUNCT
ejpam-4684	321	1	suppose	suppose	VERB
ejpam-4684	321	2	t	t	PROPN
ejpam-4684	321	3	⊆	⊆	NUM
ejpam-4684	321	4	v	v	NOUN
ejpam-4684	321	5	(	(	PUNCT
ejpam-4684	321	6	g	g	PROPN
ejpam-4684	321	7	+	+	NOUN
ejpam-4684	321	8	h	h	NOUN
ejpam-4684	321	9	)	)	PUNCT
ejpam-4684	321	10	is	be	AUX
ejpam-4684	321	11	a	a	DET
ejpam-4684	321	12	γohich	γohich	NOUN
ejpam-4684	321	13	-set	-set	PUNCT
ejpam-4684	321	14	of	of	ADP
ejpam-4684	321	15	g	g	PROPN
ejpam-4684	321	16	+	+	CCONJ
ejpam-4684	321	17	h.	h.	PROPN
ejpam-4684	321	18	then	then	ADV
ejpam-4684	321	19	by	by	ADP
ejpam-4684	321	20	theorem	theorem	NOUN
ejpam-4684	321	21	7	7	NUM
ejpam-4684	321	22	,	,	PUNCT
ejpam-4684	321	23	t	t	NOUN
ejpam-4684	321	24	=	=	SYM
ejpam-4684	321	25	v	v	PROPN
ejpam-4684	321	26	(	(	PUNCT
ejpam-4684	321	27	g	g	NOUN
ejpam-4684	321	28	)	)	PUNCT
ejpam-4684	321	29	∪	∪	ADP
ejpam-4684	321	30	th	th	NOUN
ejpam-4684	321	31	,	,	PUNCT
ejpam-4684	321	32	where	where	SCONJ
ejpam-4684	321	33	th	th	X
ejpam-4684	321	34	is	be	AUX
ejpam-4684	321	35	an	an	DET
ejpam-4684	321	36	outer	outer	ADJ
ejpam-4684	321	37	-	-	PUNCT
ejpam-4684	321	38	clique	clique	NOUN
ejpam-4684	321	39	pointwise	pointwise	PROPN
ejpam-4684	321	40	non	non	ADJ
ejpam-4684	321	41	-	-	ADJ
ejpam-4684	321	42	dominating	dominating	ADJ
ejpam-4684	321	43	set	set	NOUN
ejpam-4684	321	44	of	of	ADP
ejpam-4684	321	45	h.	h.	PROPN
ejpam-4684	322	1	thus	thus	ADV
ejpam-4684	322	2	,	,	PUNCT
ejpam-4684	322	3	γohich	γohich	PROPN
ejpam-4684	322	4	(	(	PUNCT
ejpam-4684	322	5	g+h	g+h	PROPN
ejpam-4684	322	6	)	)	PUNCT
ejpam-4684	322	7	=	=	PRON
ejpam-4684	322	8	|t	|t	VERB
ejpam-4684	323	1	|	|	ADV
ejpam-4684	323	2	=	=	SYM
ejpam-4684	323	3	|v	|v	PROPN
ejpam-4684	323	4	(	(	PUNCT
ejpam-4684	323	5	g)|+	g)|+	NOUN
ejpam-4684	323	6	|th	|th	X
ejpam-4684	323	7	|	|	ADV
ejpam-4684	323	8	≥	≥	X
ejpam-4684	323	9	|v	|v	PROPN
ejpam-4684	323	10	(	(	PUNCT
ejpam-4684	323	11	g)|+	g)|+	NOUN
ejpam-4684	323	12	ocpnd(h	ocpnd(h	PROPN
ejpam-4684	323	13	)	)	PUNCT
ejpam-4684	323	14	.	.	PUNCT
ejpam-4684	324	1	on	on	ADP
ejpam-4684	324	2	the	the	DET
ejpam-4684	324	3	other	other	ADJ
ejpam-4684	324	4	hand	hand	NOUN
ejpam-4684	324	5	,	,	PUNCT
ejpam-4684	324	6	let	let	VERB
ejpam-4684	324	7	t	t	NOUN
ejpam-4684	324	8	=	=	SYM
ejpam-4684	324	9	v	v	PROPN
ejpam-4684	324	10	(	(	PUNCT
ejpam-4684	324	11	g	g	NOUN
ejpam-4684	324	12	)	)	PUNCT
ejpam-4684	324	13	∪	∪	ADP
ejpam-4684	324	14	th	th	NOUN
ejpam-4684	324	15	,	,	PUNCT
ejpam-4684	324	16	where	where	SCONJ
ejpam-4684	324	17	th	th	X
ejpam-4684	324	18	is	be	AUX
ejpam-4684	324	19	an	an	DET
ejpam-4684	324	20	ocpnd	ocpnd	NOUN
ejpam-4684	324	21	-	-	PUNCT
ejpam-4684	324	22	set	set	NOUN
ejpam-4684	324	23	of	of	ADP
ejpam-4684	324	24	h.	h.	PROPN
ejpam-4684	324	25	then	then	ADV
ejpam-4684	324	26	by	by	ADP
ejpam-4684	324	27	theorem	theorem	NOUN
ejpam-4684	324	28	7	7	NUM
ejpam-4684	324	29	,	,	PUNCT
ejpam-4684	324	30	t	t	NOUN
ejpam-4684	324	31	=	=	SYM
ejpam-4684	324	32	v	v	PROPN
ejpam-4684	324	33	(	(	PUNCT
ejpam-4684	324	34	g	g	NOUN
ejpam-4684	324	35	)	)	PUNCT
ejpam-4684	324	36	∪	∪	ADP
ejpam-4684	324	37	th	th	X
ejpam-4684	324	38	is	be	AUX
ejpam-4684	324	39	a	a	DET
ejpam-4684	324	40	connected	connected	ADJ
ejpam-4684	324	41	outer	outer	ADJ
ejpam-4684	324	42	-	-	PUNCT
ejpam-4684	324	43	hop	hop	NOUN
ejpam-4684	324	44	independent	independent	ADJ
ejpam-4684	324	45	hop	hop	NOUN
ejpam-4684	324	46	dominating	dominating	NOUN
ejpam-4684	324	47	set	set	NOUN
ejpam-4684	324	48	of	of	ADP
ejpam-4684	324	49	g+h	g+h	PROPN
ejpam-4684	324	50	.	.	PUNCT
ejpam-4684	325	1	hence	hence	ADV
ejpam-4684	325	2	,	,	PUNCT
ejpam-4684	325	3	|v	|v	PROPN
ejpam-4684	325	4	(	(	PUNCT
ejpam-4684	325	5	g)|+	g)|+	NOUN
ejpam-4684	325	6	ocpnd(h	ocpnd(h	NUM
ejpam-4684	325	7	)	)	PUNCT
ejpam-4684	325	8	=	=	SYM
ejpam-4684	325	9	|v	|v	PROPN
ejpam-4684	325	10	(	(	PUNCT
ejpam-4684	325	11	g)|+	g)|+	NOUN
ejpam-4684	325	12	|th	|th	X
ejpam-4684	325	13	|	|	ADV
ejpam-4684	325	14	=	=	PUNCT
ejpam-4684	325	15	|t	|t	PROPN
ejpam-4684	326	1	|	|	ADV
ejpam-4684	326	2	≥	≥	PRON
ejpam-4684	326	3	γohich	γohich	PROPN
ejpam-4684	326	4	(	(	PUNCT
ejpam-4684	326	5	g+h	g+h	PROPN
ejpam-4684	326	6	)	)	PUNCT
ejpam-4684	326	7	.	.	PUNCT
ejpam-4684	327	1	consequently	consequently	ADV
ejpam-4684	327	2	,	,	PUNCT
ejpam-4684	327	3	γohich	γohich	PROPN
ejpam-4684	327	4	(	(	PUNCT
ejpam-4684	327	5	g+h	g+h	NOUN
ejpam-4684	327	6	)	)	PUNCT
ejpam-4684	327	7	=	=	SYM
ejpam-4684	327	8	|v	|v	PROPN
ejpam-4684	327	9	(	(	PUNCT
ejpam-4684	327	10	g)|+	g)|+	NOUN
ejpam-4684	327	11	ocpnd(h	ocpnd(h	PROPN
ejpam-4684	327	12	)	)	PUNCT
ejpam-4684	327	13	.	.	PUNCT
ejpam-4684	328	1	j.	j.	PROPN
ejpam-4684	328	2	hassan	hassan	PROPN
ejpam-4684	328	3	,	,	PUNCT
ejpam-4684	328	4	a.	a.	PROPN
ejpam-4684	328	5	lintasan	lintasan	NOUN
ejpam-4684	328	6	,	,	PUNCT
ejpam-4684	328	7	n.	n.	PROPN
ejpam-4684	328	8	h.	h.	PROPN
ejpam-4684	328	9	mohammad	mohammad	PROPN
ejpam-4684	328	10	/	/	PUNCT
ejpam-4684	328	11	eur	eur	PROPN
ejpam-4684	328	12	.	.	PUNCT
ejpam-4684	329	1	j.	j.	PROPN
ejpam-4684	329	2	pure	pure	PROPN
ejpam-4684	329	3	appl	appl	PROPN
ejpam-4684	329	4	.	.	PROPN
ejpam-4684	329	5	math	math	PROPN
ejpam-4684	329	6	,	,	PUNCT
ejpam-4684	329	7	16	16	NUM
ejpam-4684	329	8	(	(	PUNCT
ejpam-4684	329	9	3	3	NUM
ejpam-4684	329	10	)	)	PUNCT
ejpam-4684	329	11	(	(	PUNCT
ejpam-4684	329	12	2023	2023	NUM
ejpam-4684	329	13	)	)	PUNCT
ejpam-4684	329	14	,	,	PUNCT
ejpam-4684	329	15	1848	1848	NUM
ejpam-4684	329	16	-	-	SYM
ejpam-4684	329	17	1861	1861	NUM
ejpam-4684	329	18	1859	1859	NUM
ejpam-4684	329	19	theorem	theorem	VERB
ejpam-4684	329	20	8	8	NUM
ejpam-4684	329	21	.	.	PUNCT
ejpam-4684	330	1	let	let	VERB
ejpam-4684	330	2	g	g	PRON
ejpam-4684	330	3	be	be	AUX
ejpam-4684	330	4	a	a	DET
ejpam-4684	330	5	non	non	ADJ
ejpam-4684	330	6	-	-	ADJ
ejpam-4684	330	7	trivial	trivial	ADJ
ejpam-4684	330	8	connected	connected	ADJ
ejpam-4684	330	9	graph	graph	NOUN
ejpam-4684	330	10	and	and	CCONJ
ejpam-4684	330	11	h	h	NOUN
ejpam-4684	330	12	be	be	AUX
ejpam-4684	330	13	any	any	DET
ejpam-4684	330	14	non	non	ADJ
ejpam-4684	330	15	-	-	ADJ
ejpam-4684	330	16	complete	complete	ADJ
ejpam-4684	330	17	graph	graph	NOUN
ejpam-4684	330	18	.	.	PUNCT
ejpam-4684	331	1	a	a	DET
ejpam-4684	331	2	set	set	NOUN
ejpam-4684	331	3	c	c	NOUN
ejpam-4684	331	4	⊆	⊆	NUM
ejpam-4684	331	5	v	v	NOUN
ejpam-4684	331	6	(	(	PUNCT
ejpam-4684	331	7	g	g	PROPN
ejpam-4684	331	8	◦	◦	NOUN
ejpam-4684	331	9	h	h	NOUN
ejpam-4684	331	10	)	)	PUNCT
ejpam-4684	331	11	is	be	AUX
ejpam-4684	331	12	a	a	DET
ejpam-4684	331	13	connected	connected	ADJ
ejpam-4684	331	14	outer	outer	ADJ
ejpam-4684	331	15	-	-	PUNCT
ejpam-4684	331	16	hop	hop	NOUN
ejpam-4684	331	17	independent	independent	ADJ
ejpam-4684	331	18	hop	hop	NOUN
ejpam-4684	331	19	dominating	dominating	NOUN
ejpam-4684	331	20	set	set	NOUN
ejpam-4684	331	21	of	of	ADP
ejpam-4684	331	22	g	g	PROPN
ejpam-4684	331	23	◦	◦	NOUN
ejpam-4684	331	24	h	h	NOUN
ejpam-4684	331	25	if	if	SCONJ
ejpam-4684	332	1	and	and	CCONJ
ejpam-4684	332	2	only	only	ADV
ejpam-4684	332	3	if	if	SCONJ
ejpam-4684	332	4	c	c	PROPN
ejpam-4684	332	5	=	=	SYM
ejpam-4684	332	6	v	v	PROPN
ejpam-4684	332	7	(	(	PUNCT
ejpam-4684	332	8	g	g	NOUN
ejpam-4684	332	9	)	)	PUNCT
ejpam-4684	332	10	∪	∪	NOUN
ejpam-4684	332	11	(	(	PUNCT
ejpam-4684	332	12	⋃	⋃	PROPN
ejpam-4684	332	13	a∈v	a∈v	NOUN
ejpam-4684	332	14	(	(	PUNCT
ejpam-4684	332	15	g)ca	g)ca	PROPN
ejpam-4684	332	16	)	)	PUNCT
ejpam-4684	332	17	,	,	PUNCT
ejpam-4684	332	18	where	where	SCONJ
ejpam-4684	332	19	ca	can	AUX
ejpam-4684	332	20	⊆	⊆	NUM
ejpam-4684	332	21	v	v	NOUN
ejpam-4684	332	22	(	(	PUNCT
ejpam-4684	332	23	ha	ha	INTJ
ejpam-4684	332	24	)	)	PUNCT
ejpam-4684	332	25	and	and	CCONJ
ejpam-4684	332	26	v	v	NOUN
ejpam-4684	332	27	(	(	PUNCT
ejpam-4684	332	28	ha	ha	INTJ
ejpam-4684	332	29	)	)	PUNCT
ejpam-4684	332	30	\	\	NOUN
ejpam-4684	332	31	ca	ca	NOUN
ejpam-4684	332	32	is	be	AUX
ejpam-4684	332	33	clique	clique	ADJ
ejpam-4684	332	34	in	in	ADP
ejpam-4684	332	35	ha	ha	INTJ
ejpam-4684	332	36	for	for	ADP
ejpam-4684	332	37	each	each	PRON
ejpam-4684	332	38	a	a	DET
ejpam-4684	332	39	∈	∈	PROPN
ejpam-4684	332	40	v	v	NOUN
ejpam-4684	332	41	(	(	PUNCT
ejpam-4684	332	42	g	g	NOUN
ejpam-4684	332	43	)	)	PUNCT
ejpam-4684	332	44	.	.	PUNCT
ejpam-4684	333	1	proof	proof	NOUN
ejpam-4684	333	2	.	.	PUNCT
ejpam-4684	334	1	suppose	suppose	VERB
ejpam-4684	334	2	c	c	SYM
ejpam-4684	334	3	⊆	⊆	NUM
ejpam-4684	334	4	v	v	NOUN
ejpam-4684	334	5	(	(	PUNCT
ejpam-4684	334	6	g	g	PROPN
ejpam-4684	334	7	◦	◦	NOUN
ejpam-4684	334	8	h	h	NOUN
ejpam-4684	334	9	)	)	PUNCT
ejpam-4684	334	10	is	be	AUX
ejpam-4684	334	11	a	a	DET
ejpam-4684	334	12	connected	connected	ADJ
ejpam-4684	334	13	outer	outer	ADJ
ejpam-4684	334	14	-	-	PUNCT
ejpam-4684	334	15	hop	hop	NOUN
ejpam-4684	334	16	independent	independent	ADJ
ejpam-4684	334	17	hop	hop	NOUN
ejpam-4684	334	18	dominating	dominating	NOUN
ejpam-4684	334	19	set	set	NOUN
ejpam-4684	334	20	of	of	ADP
ejpam-4684	334	21	g	g	PROPN
ejpam-4684	334	22	◦	◦	NOUN
ejpam-4684	334	23	h	h	NOUN
ejpam-4684	334	24	and	and	CCONJ
ejpam-4684	334	25	let	let	VERB
ejpam-4684	334	26	ca	can	AUX
ejpam-4684	334	27	=	=	PUNCT
ejpam-4684	334	28	v	v	PROPN
ejpam-4684	334	29	(	(	PUNCT
ejpam-4684	334	30	ha	ha	INTJ
ejpam-4684	334	31	)	)	PUNCT
ejpam-4684	334	32	∩	∩	NOUN
ejpam-4684	334	33	c	c	PROPN
ejpam-4684	334	34	for	for	ADP
ejpam-4684	334	35	each	each	DET
ejpam-4684	334	36	a	a	DET
ejpam-4684	334	37	∈	∈	PROPN
ejpam-4684	334	38	v	v	NOUN
ejpam-4684	334	39	(	(	PUNCT
ejpam-4684	334	40	g	g	NOUN
ejpam-4684	334	41	)	)	PUNCT
ejpam-4684	334	42	.	.	PUNCT
ejpam-4684	335	1	since	since	SCONJ
ejpam-4684	335	2	⟨c⟩	⟨c⟩	PROPN
ejpam-4684	335	3	is	be	AUX
ejpam-4684	335	4	connected	connect	VERB
ejpam-4684	335	5	,	,	PUNCT
ejpam-4684	335	6	it	it	PRON
ejpam-4684	335	7	follows	follow	VERB
ejpam-4684	335	8	that	that	SCONJ
ejpam-4684	335	9	c	c	PROPN
ejpam-4684	335	10	=	=	SYM
ejpam-4684	335	11	v	v	PROPN
ejpam-4684	335	12	(	(	PUNCT
ejpam-4684	335	13	g	g	NOUN
ejpam-4684	335	14	)	)	PUNCT
ejpam-4684	335	15	∪	∪	NOUN
ejpam-4684	335	16	(	(	PUNCT
ejpam-4684	335	17	⋃	⋃	PROPN
ejpam-4684	335	18	a∈v	a∈v	NOUN
ejpam-4684	335	19	(	(	PUNCT
ejpam-4684	335	20	g)ca	g)ca	PROPN
ejpam-4684	335	21	)	)	PUNCT
ejpam-4684	335	22	.	.	PUNCT
ejpam-4684	336	1	since	since	SCONJ
ejpam-4684	336	2	v	v	NOUN
ejpam-4684	336	3	(	(	PUNCT
ejpam-4684	336	4	g	g	PROPN
ejpam-4684	336	5	◦	◦	NOUN
ejpam-4684	336	6	h	h	NOUN
ejpam-4684	336	7	)	)	PUNCT
ejpam-4684	336	8	\	\	NOUN
ejpam-4684	336	9	c	c	NOUN
ejpam-4684	336	10	=	=	PUNCT
ejpam-4684	336	11	⋃	⋃	NOUN
ejpam-4684	336	12	a∈v	a∈v	NOUN
ejpam-4684	336	13	(	(	PUNCT
ejpam-4684	336	14	g)(v	g)(v	X
ejpam-4684	336	15	(	(	PUNCT
ejpam-4684	336	16	ha	ha	INTJ
ejpam-4684	336	17	)	)	PUNCT
ejpam-4684	336	18	\	\	NOUN
ejpam-4684	336	19	ca	can	AUX
ejpam-4684	336	20	)	)	PUNCT
ejpam-4684	336	21	is	be	AUX
ejpam-4684	336	22	a	a	DET
ejpam-4684	336	23	hop	hop	NOUN
ejpam-4684	336	24	independent	independent	ADJ
ejpam-4684	336	25	set	set	NOUN
ejpam-4684	336	26	of	of	ADP
ejpam-4684	336	27	g	g	PROPN
ejpam-4684	336	28	◦	◦	NOUN
ejpam-4684	336	29	h	h	NOUN
ejpam-4684	336	30	,	,	PUNCT
ejpam-4684	336	31	it	it	PRON
ejpam-4684	336	32	follows	follow	VERB
ejpam-4684	336	33	that	that	SCONJ
ejpam-4684	336	34	v	v	X
ejpam-4684	336	35	(	(	PUNCT
ejpam-4684	336	36	ha	ha	INTJ
ejpam-4684	336	37	)	)	PUNCT
ejpam-4684	336	38	\	\	NOUN
ejpam-4684	336	39	ca	can	AUX
ejpam-4684	336	40	is	be	AUX
ejpam-4684	336	41	a	a	DET
ejpam-4684	336	42	hop	hop	NOUN
ejpam-4684	336	43	independent	independent	ADJ
ejpam-4684	336	44	set	set	NOUN
ejpam-4684	336	45	of	of	ADP
ejpam-4684	336	46	ha	ha	INTJ
ejpam-4684	336	47	for	for	ADP
ejpam-4684	336	48	each	each	PRON
ejpam-4684	336	49	a	a	DET
ejpam-4684	336	50	∈	∈	PROPN
ejpam-4684	336	51	v	v	NOUN
ejpam-4684	336	52	(	(	PUNCT
ejpam-4684	336	53	g	g	NOUN
ejpam-4684	336	54	)	)	PUNCT
ejpam-4684	336	55	.	.	PUNCT
ejpam-4684	337	1	suppose	suppose	VERB
ejpam-4684	337	2	v	v	X
ejpam-4684	337	3	(	(	PUNCT
ejpam-4684	337	4	ha	ha	INTJ
ejpam-4684	337	5	)	)	PUNCT
ejpam-4684	337	6	\	\	NOUN
ejpam-4684	337	7	ca	can	AUX
ejpam-4684	337	8	is	be	AUX
ejpam-4684	337	9	not	not	PART
ejpam-4684	337	10	a	a	DET
ejpam-4684	337	11	clique	clique	NOUN
ejpam-4684	337	12	in	in	ADP
ejpam-4684	337	13	ha	ha	INTJ
ejpam-4684	337	14	for	for	ADP
ejpam-4684	337	15	some	some	PRON
ejpam-4684	337	16	a	a	DET
ejpam-4684	337	17	∈	∈	PROPN
ejpam-4684	337	18	v	v	NOUN
ejpam-4684	337	19	(	(	PUNCT
ejpam-4684	337	20	g	g	NOUN
ejpam-4684	337	21	)	)	PUNCT
ejpam-4684	337	22	.	.	PUNCT
ejpam-4684	338	1	then	then	ADV
ejpam-4684	338	2	there	there	PRON
ejpam-4684	338	3	exists	exist	VERB
ejpam-4684	338	4	u	u	NOUN
ejpam-4684	338	5	,	,	PUNCT
ejpam-4684	338	6	v	v	NOUN
ejpam-4684	338	7	∈	∈	PROPN
ejpam-4684	338	8	v	v	NOUN
ejpam-4684	338	9	(	(	PUNCT
ejpam-4684	338	10	ha	ha	INTJ
ejpam-4684	338	11	)	)	PUNCT
ejpam-4684	338	12	\ca	\ca	PROPN
ejpam-4684	338	13	⊆	⊆	NUM
ejpam-4684	338	14	v	v	NOUN
ejpam-4684	338	15	(	(	PUNCT
ejpam-4684	338	16	g	g	PROPN
ejpam-4684	338	17	◦	◦	NOUN
ejpam-4684	338	18	h	h	NOUN
ejpam-4684	338	19	)	)	PUNCT
ejpam-4684	338	20	\c	\c	ADP
ejpam-4684	338	21	such	such	ADJ
ejpam-4684	338	22	that	that	PRON
ejpam-4684	338	23	dha(u	dha(u	PROPN
ejpam-4684	338	24	,	,	PUNCT
ejpam-4684	338	25	v	v	NOUN
ejpam-4684	338	26	)	)	PUNCT
ejpam-4684	338	27	=	=	SYM
ejpam-4684	338	28	dg	dg	PROPN
ejpam-4684	338	29	◦	◦	NOUN
ejpam-4684	338	30	h(u	h(u	PROPN
ejpam-4684	338	31	,	,	PUNCT
ejpam-4684	338	32	v	v	NOUN
ejpam-4684	338	33	)	)	PUNCT
ejpam-4684	338	34	=	=	SYM
ejpam-4684	338	35	2	2	NUM
ejpam-4684	338	36	for	for	ADP
ejpam-4684	338	37	some	some	PRON
ejpam-4684	338	38	a	a	DET
ejpam-4684	338	39	∈	∈	PROPN
ejpam-4684	338	40	v	v	NOUN
ejpam-4684	338	41	(	(	PUNCT
ejpam-4684	338	42	g	g	NOUN
ejpam-4684	338	43	)	)	PUNCT
ejpam-4684	338	44	,	,	PUNCT
ejpam-4684	338	45	a	a	DET
ejpam-4684	338	46	contradiction	contradiction	NOUN
ejpam-4684	338	47	to	to	ADP
ejpam-4684	338	48	the	the	DET
ejpam-4684	338	49	fact	fact	NOUN
ejpam-4684	338	50	that	that	SCONJ
ejpam-4684	338	51	c	c	PROPN
ejpam-4684	338	52	is	be	AUX
ejpam-4684	338	53	a	a	DET
ejpam-4684	338	54	connected	connected	ADJ
ejpam-4684	338	55	outer	outer	ADJ
ejpam-4684	338	56	-	-	PUNCT
ejpam-4684	338	57	hop	hop	NOUN
ejpam-4684	338	58	independent	independent	ADJ
ejpam-4684	338	59	hop	hop	NOUN
ejpam-4684	338	60	dominating	dominating	NOUN
ejpam-4684	338	61	set	set	VERB
ejpam-4684	338	62	ofg	ofg	PROPN
ejpam-4684	338	63	◦	◦	NOUN
ejpam-4684	338	64	h.	h.	NOUN
ejpam-4684	338	65	therefore	therefore	ADV
ejpam-4684	338	66	,	,	PUNCT
ejpam-4684	338	67	v	v	PROPN
ejpam-4684	338	68	(	(	PUNCT
ejpam-4684	338	69	ha)\ca	ha)\ca	PROPN
ejpam-4684	338	70	is	be	AUX
ejpam-4684	338	71	clique	clique	ADJ
ejpam-4684	338	72	inha	inha	NOUN
ejpam-4684	338	73	for	for	ADP
ejpam-4684	338	74	every	every	DET
ejpam-4684	338	75	a	a	DET
ejpam-4684	338	76	∈	∈	PROPN
ejpam-4684	338	77	v	v	NOUN
ejpam-4684	338	78	(	(	PUNCT
ejpam-4684	338	79	g	g	NOUN
ejpam-4684	338	80	)	)	PUNCT
ejpam-4684	338	81	.	.	PUNCT
ejpam-4684	339	1	conversely	conversely	ADV
ejpam-4684	339	2	,	,	PUNCT
ejpam-4684	339	3	suppose	suppose	VERB
ejpam-4684	339	4	c	c	NOUN
ejpam-4684	339	5	=	=	SYM
ejpam-4684	339	6	v	v	PROPN
ejpam-4684	339	7	(	(	PUNCT
ejpam-4684	339	8	g)∪	g)∪	VERB
ejpam-4684	339	9	(	(	PUNCT
ejpam-4684	339	10	⋃	⋃	NOUN
ejpam-4684	339	11	a∈v	a∈v	NOUN
ejpam-4684	339	12	(	(	PUNCT
ejpam-4684	339	13	g)ca	g)ca	PROPN
ejpam-4684	339	14	)	)	PUNCT
ejpam-4684	339	15	,	,	PUNCT
ejpam-4684	339	16	where	where	SCONJ
ejpam-4684	339	17	ca	can	AUX
ejpam-4684	339	18	⊆	⊆	NUM
ejpam-4684	339	19	v	v	NOUN
ejpam-4684	339	20	(	(	PUNCT
ejpam-4684	339	21	ha	ha	INTJ
ejpam-4684	339	22	)	)	PUNCT
ejpam-4684	339	23	and	and	CCONJ
ejpam-4684	339	24	v	v	NOUN
ejpam-4684	339	25	(	(	PUNCT
ejpam-4684	339	26	ha	ha	INTJ
ejpam-4684	339	27	)	)	PUNCT
ejpam-4684	339	28	\ca	\ca	PROPN
ejpam-4684	339	29	is	be	AUX
ejpam-4684	339	30	clique	clique	NOUN
ejpam-4684	339	31	in	in	ADP
ejpam-4684	339	32	ha	ha	INTJ
ejpam-4684	339	33	for	for	ADP
ejpam-4684	339	34	each	each	PRON
ejpam-4684	339	35	a	a	DET
ejpam-4684	339	36	∈	∈	PROPN
ejpam-4684	339	37	v	v	NOUN
ejpam-4684	339	38	(	(	PUNCT
ejpam-4684	339	39	g	g	NOUN
ejpam-4684	339	40	)	)	PUNCT
ejpam-4684	339	41	.	.	PUNCT
ejpam-4684	340	1	clearly	clearly	ADV
ejpam-4684	340	2	,	,	PUNCT
ejpam-4684	340	3	c	c	PROPN
ejpam-4684	340	4	is	be	AUX
ejpam-4684	340	5	a	a	DET
ejpam-4684	340	6	connected	connected	ADJ
ejpam-4684	340	7	hop	hop	NOUN
ejpam-4684	340	8	dominating	dominating	NOUN
ejpam-4684	340	9	set	set	NOUN
ejpam-4684	340	10	of	of	ADP
ejpam-4684	340	11	g	g	PROPN
ejpam-4684	340	12	◦	◦	NOUN
ejpam-4684	340	13	h.	h.	PROPN
ejpam-4684	340	14	since	since	SCONJ
ejpam-4684	340	15	v	v	PROPN
ejpam-4684	340	16	(	(	PUNCT
ejpam-4684	340	17	ha	ha	INTJ
ejpam-4684	340	18	)	)	PUNCT
ejpam-4684	340	19	\	\	NOUN
ejpam-4684	340	20	ca	ca	NOUN
ejpam-4684	340	21	is	be	AUX
ejpam-4684	340	22	clique	clique	ADJ
ejpam-4684	340	23	in	in	ADP
ejpam-4684	340	24	ha	ha	INTJ
ejpam-4684	340	25	for	for	ADP
ejpam-4684	340	26	each	each	PRON
ejpam-4684	340	27	a	a	DET
ejpam-4684	340	28	∈	∈	PROPN
ejpam-4684	340	29	v	v	NOUN
ejpam-4684	340	30	(	(	PUNCT
ejpam-4684	340	31	g	g	NOUN
ejpam-4684	340	32	)	)	PUNCT
ejpam-4684	340	33	,	,	PUNCT
ejpam-4684	340	34	it	it	PRON
ejpam-4684	340	35	follows	follow	VERB
ejpam-4684	340	36	that	that	SCONJ
ejpam-4684	340	37	v	v	NOUN
ejpam-4684	340	38	(	(	PUNCT
ejpam-4684	340	39	g	g	PROPN
ejpam-4684	340	40	◦	◦	NOUN
ejpam-4684	340	41	h	h	NOUN
ejpam-4684	340	42	)	)	PUNCT
ejpam-4684	340	43	\	\	NOUN
ejpam-4684	341	1	c	c	NOUN
ejpam-4684	341	2	=	=	PUNCT
ejpam-4684	341	3	⋃	⋃	NOUN
ejpam-4684	341	4	a∈v	a∈v	NOUN
ejpam-4684	341	5	(	(	PUNCT
ejpam-4684	341	6	g	g	NOUN
ejpam-4684	341	7	)	)	PUNCT
ejpam-4684	341	8	(	(	PUNCT
ejpam-4684	341	9	v	v	X
ejpam-4684	341	10	(	(	PUNCT
ejpam-4684	341	11	ha	ha	INTJ
ejpam-4684	341	12	)	)	PUNCT
ejpam-4684	341	13	\	\	NOUN
ejpam-4684	341	14	ca	can	AUX
ejpam-4684	341	15	)	)	PUNCT
ejpam-4684	341	16	is	be	AUX
ejpam-4684	341	17	a	a	DET
ejpam-4684	341	18	hop	hop	NOUN
ejpam-4684	341	19	independent	independent	ADJ
ejpam-4684	341	20	set	set	NOUN
ejpam-4684	341	21	of	of	ADP
ejpam-4684	341	22	g	g	PROPN
ejpam-4684	341	23	◦	◦	PROPN
ejpam-4684	341	24	h.	h.	PROPN
ejpam-4684	341	25	therefore	therefore	ADV
ejpam-4684	341	26	,	,	PUNCT
ejpam-4684	341	27	c	c	PROPN
ejpam-4684	341	28	is	be	AUX
ejpam-4684	341	29	a	a	DET
ejpam-4684	341	30	connected	connected	ADJ
ejpam-4684	341	31	outer	outer	ADJ
ejpam-4684	341	32	-	-	PUNCT
ejpam-4684	341	33	hop	hop	NOUN
ejpam-4684	341	34	independent	independent	ADJ
ejpam-4684	341	35	hop	hop	NOUN
ejpam-4684	341	36	dominating	dominating	NOUN
ejpam-4684	341	37	set	set	NOUN
ejpam-4684	341	38	of	of	ADP
ejpam-4684	341	39	g	g	PROPN
ejpam-4684	341	40	◦	◦	NOUN
ejpam-4684	341	41	h.	h.	PROPN
ejpam-4684	341	42	corollary	corollary	ADJ
ejpam-4684	341	43	6	6	NUM
ejpam-4684	341	44	.	.	PUNCT
ejpam-4684	342	1	let	let	VERB
ejpam-4684	342	2	g	g	PRON
ejpam-4684	342	3	be	be	AUX
ejpam-4684	342	4	a	a	DET
ejpam-4684	342	5	non	non	ADJ
ejpam-4684	342	6	-	-	ADJ
ejpam-4684	342	7	trivial	trivial	ADJ
ejpam-4684	342	8	connected	connected	ADJ
ejpam-4684	342	9	graph	graph	NOUN
ejpam-4684	342	10	with	with	ADP
ejpam-4684	342	11	|v	|v	PROPN
ejpam-4684	342	12	(	(	PUNCT
ejpam-4684	342	13	g)|	g)|	NOUN
ejpam-4684	342	14	=	=	PUNCT
ejpam-4684	342	15	n	n	PROPN
ejpam-4684	342	16	and	and	CCONJ
ejpam-4684	342	17	h	h	NOUN
ejpam-4684	342	18	be	be	VERB
ejpam-4684	342	19	any	any	DET
ejpam-4684	342	20	noncomplete	noncomplete	ADJ
ejpam-4684	342	21	graph	graph	NOUN
ejpam-4684	342	22	with	with	ADP
ejpam-4684	342	23	|v	|v	PROPN
ejpam-4684	342	24	(	(	PUNCT
ejpam-4684	342	25	h)|	h)|	NOUN
ejpam-4684	342	26	=	=	PUNCT
ejpam-4684	342	27	m.	m.	NOUN
ejpam-4684	342	28	then	then	ADV
ejpam-4684	342	29	γohich	γohich	PROPN
ejpam-4684	342	30	(	(	PUNCT
ejpam-4684	342	31	g	g	PROPN
ejpam-4684	342	32	◦	◦	NOUN
ejpam-4684	342	33	h	h	NOUN
ejpam-4684	342	34	)	)	PUNCT
ejpam-4684	342	35	=	=	SYM
ejpam-4684	342	36	n	n	PROPN
ejpam-4684	342	37	+	+	CCONJ
ejpam-4684	342	38	n(m	n(m	PROPN
ejpam-4684	342	39	−	−	NOUN
ejpam-4684	342	40	ω(h	ω(h	NUM
ejpam-4684	342	41	)	)	PUNCT
ejpam-4684	342	42	)	)	PUNCT
ejpam-4684	342	43	.	.	PUNCT
ejpam-4684	343	1	in	in	ADP
ejpam-4684	343	2	particular	particular	ADJ
ejpam-4684	343	3	,	,	PUNCT
ejpam-4684	343	4	we	we	PRON
ejpam-4684	343	5	have	have	VERB
ejpam-4684	343	6	(	(	PUNCT
ejpam-4684	343	7	i	i	NOUN
ejpam-4684	343	8	)	)	PUNCT
ejpam-4684	343	9	γohich	γohich	PROPN
ejpam-4684	343	10	(	(	PUNCT
ejpam-4684	343	11	g	g	PROPN
ejpam-4684	343	12	◦	◦	NOUN
ejpam-4684	343	13	h	h	NOUN
ejpam-4684	343	14	)	)	PUNCT
ejpam-4684	343	15	=	=	PUNCT
ejpam-4684	344	1	n+	n+	PUNCT
ejpam-4684	344	2	n(m−	n(m−	PROPN
ejpam-4684	344	3	2	2	X
ejpam-4684	344	4	)	)	PUNCT
ejpam-4684	344	5	if	if	SCONJ
ejpam-4684	344	6	h	h	NOUN
ejpam-4684	344	7	=	=	SYM
ejpam-4684	344	8	pm	pm	PROPN
ejpam-4684	344	9	,	,	PUNCT
ejpam-4684	344	10	k1,m	k1,m	PROPN
ejpam-4684	344	11	for	for	ADP
ejpam-4684	344	12	all	all	DET
ejpam-4684	344	13	m	m	PROPN
ejpam-4684	344	14	≥	≥	NOUN
ejpam-4684	344	15	3	3	NUM
ejpam-4684	344	16	,	,	PUNCT
ejpam-4684	344	17	(	(	PUNCT
ejpam-4684	344	18	ii	ii	NOUN
ejpam-4684	344	19	)	)	PUNCT
ejpam-4684	344	20	γohich	γohich	PROPN
ejpam-4684	344	21	(	(	PUNCT
ejpam-4684	344	22	g	g	PROPN
ejpam-4684	344	23	◦	◦	NOUN
ejpam-4684	344	24	h	h	NOUN
ejpam-4684	344	25	)	)	PUNCT
ejpam-4684	345	1	=	=	PUNCT
ejpam-4684	345	2	n+	n+	PUNCT
ejpam-4684	345	3	n(m−	n(m−	PROPN
ejpam-4684	345	4	2	2	X
ejpam-4684	345	5	)	)	PUNCT
ejpam-4684	345	6	if	if	SCONJ
ejpam-4684	345	7	h	h	NOUN
ejpam-4684	345	8	=	=	NOUN
ejpam-4684	345	9	cm	cm	NOUN
ejpam-4684	345	10	for	for	ADP
ejpam-4684	345	11	all	all	DET
ejpam-4684	345	12	m	m	NOUN
ejpam-4684	345	13	≥	≥	NOUN
ejpam-4684	345	14	4	4	NUM
ejpam-4684	345	15	,	,	PUNCT
ejpam-4684	345	16	(	(	PUNCT
ejpam-4684	345	17	iii	iii	X
ejpam-4684	345	18	)	)	PUNCT
ejpam-4684	345	19	γohich	γohich	PROPN
ejpam-4684	345	20	(	(	PUNCT
ejpam-4684	345	21	g	g	PROPN
ejpam-4684	345	22	◦	◦	NOUN
ejpam-4684	345	23	wm	wm	PROPN
ejpam-4684	345	24	)	)	PUNCT
ejpam-4684	345	25	=	=	PUNCT
ejpam-4684	346	1	n+	n+	NUM
ejpam-4684	346	2	n(m−	n(m−	PROPN
ejpam-4684	346	3	3	3	NUM
ejpam-4684	346	4	)	)	PUNCT
ejpam-4684	346	5	for	for	ADP
ejpam-4684	346	6	all	all	DET
ejpam-4684	346	7	m	m	PROPN
ejpam-4684	346	8	≥	≥	NOUN
ejpam-4684	346	9	4	4	NUM
ejpam-4684	346	10	,	,	PUNCT
ejpam-4684	346	11	(	(	PUNCT
ejpam-4684	346	12	iv	iv	X
ejpam-4684	346	13	)	)	PUNCT
ejpam-4684	346	14	γohich	γohich	PROPN
ejpam-4684	346	15	(	(	PUNCT
ejpam-4684	346	16	g	g	PROPN
ejpam-4684	346	17	◦	◦	PROPN
ejpam-4684	346	18	fm	fm	NOUN
ejpam-4684	346	19	)	)	PUNCT
ejpam-4684	346	20	=	=	PRON
ejpam-4684	347	1	n+	n+	NUM
ejpam-4684	347	2	n(m−	n(m−	PROPN
ejpam-4684	347	3	3	3	NUM
ejpam-4684	347	4	)	)	PUNCT
ejpam-4684	347	5	for	for	ADP
ejpam-4684	347	6	all	all	DET
ejpam-4684	347	7	m	m	PROPN
ejpam-4684	347	8	≥	≥	NOUN
ejpam-4684	347	9	3	3	NUM
ejpam-4684	347	10	,	,	PUNCT
ejpam-4684	347	11	proof	proof	NOUN
ejpam-4684	347	12	.	.	PUNCT
ejpam-4684	348	1	let	let	VERB
ejpam-4684	348	2	c	c	PRON
ejpam-4684	348	3	be	be	AUX
ejpam-4684	348	4	a	a	DET
ejpam-4684	348	5	γohich	γohich	NOUN
ejpam-4684	348	6	-set	-set	ADV
ejpam-4684	348	7	ofg	ofg	PROPN
ejpam-4684	348	8	◦	◦	NOUN
ejpam-4684	348	9	h.	h.	NOUN
ejpam-4684	348	10	then	then	ADV
ejpam-4684	348	11	c	c	X
ejpam-4684	348	12	=	=	SYM
ejpam-4684	348	13	v	v	PROPN
ejpam-4684	348	14	(	(	PUNCT
ejpam-4684	348	15	g)∪	g)∪	NOUN
ejpam-4684	348	16	(	(	PUNCT
ejpam-4684	348	17	⋃	⋃	NOUN
ejpam-4684	348	18	v∈v	v∈v	NOUN
ejpam-4684	348	19	(	(	PUNCT
ejpam-4684	348	20	g)cv	g)cv	PROPN
ejpam-4684	348	21	)	)	PUNCT
ejpam-4684	348	22	,	,	PUNCT
ejpam-4684	348	23	where	where	SCONJ
ejpam-4684	348	24	cv	cv	PROPN
ejpam-4684	348	25	⊆	⊆	NUM
ejpam-4684	348	26	v	v	PROPN
ejpam-4684	348	27	(	(	PUNCT
ejpam-4684	348	28	hv	hv	NOUN
ejpam-4684	348	29	)	)	PUNCT
ejpam-4684	348	30	and	and	CCONJ
ejpam-4684	348	31	v	v	NOUN
ejpam-4684	348	32	(	(	PUNCT
ejpam-4684	348	33	hv	hv	PROPN
ejpam-4684	348	34	)	)	PUNCT
ejpam-4684	348	35	\	\	PROPN
ejpam-4684	348	36	cv	cv	PROPN
ejpam-4684	348	37	is	be	AUX
ejpam-4684	348	38	clique	clique	NOUN
ejpam-4684	348	39	in	in	ADP
ejpam-4684	348	40	hv	hv	PROPN
ejpam-4684	348	41	for	for	ADP
ejpam-4684	348	42	each	each	DET
ejpam-4684	348	43	v	v	NUM
ejpam-4684	348	44	∈	∈	PROPN
ejpam-4684	348	45	v	v	NOUN
ejpam-4684	348	46	(	(	PUNCT
ejpam-4684	348	47	g	g	NOUN
ejpam-4684	348	48	)	)	PUNCT
ejpam-4684	348	49	by	by	ADP
ejpam-4684	348	50	theorem	theorem	NOUN
ejpam-4684	348	51	8	8	NUM
ejpam-4684	348	52	.	.	PUNCT
ejpam-4684	349	1	hence	hence	ADV
ejpam-4684	349	2	,	,	PUNCT
ejpam-4684	349	3	γohich	γohich	PROPN
ejpam-4684	349	4	(	(	PUNCT
ejpam-4684	349	5	g	g	PROPN
ejpam-4684	349	6	◦	◦	NOUN
ejpam-4684	349	7	h	h	NOUN
ejpam-4684	349	8	)	)	PUNCT
ejpam-4684	349	9	=	=	SYM
ejpam-4684	349	10	|c|	|c|	PROPN
ejpam-4684	349	11	=	=	SYM
ejpam-4684	349	12	|v	|v	PROPN
ejpam-4684	349	13	(	(	PUNCT
ejpam-4684	349	14	g)|+	g)|+	NOUN
ejpam-4684	349	15	|	|	ADV
ejpam-4684	349	16	⋃	⋃	PUNCT
ejpam-4684	349	17	v∈v	v∈v	NOUN
ejpam-4684	349	18	(	(	PUNCT
ejpam-4684	349	19	g	g	NOUN
ejpam-4684	349	20	)	)	PUNCT
ejpam-4684	349	21	cv|	cv|	NOUN
ejpam-4684	349	22	=	=	SYM
ejpam-4684	349	23	v	v	NOUN
ejpam-4684	349	24	(	(	PUNCT
ejpam-4684	349	25	g	g	NOUN
ejpam-4684	349	26	)	)	PUNCT
ejpam-4684	349	27	+	+	CCONJ
ejpam-4684	349	28	∑	∑	PUNCT
ejpam-4684	349	29	v∈v	v∈v	NOUN
ejpam-4684	349	30	(	(	PUNCT
ejpam-4684	349	31	g	g	NOUN
ejpam-4684	349	32	)	)	PUNCT
ejpam-4684	349	33	|cv|	|cv|	NOUN
ejpam-4684	350	1	=	=	PUNCT
ejpam-4684	350	2	|v	|v	PROPN
ejpam-4684	350	3	(	(	PUNCT
ejpam-4684	350	4	g)|+	g)|+	PROPN
ejpam-4684	350	5	∑	∑	PUNCT
ejpam-4684	350	6	v∈v	v∈v	PROPN
ejpam-4684	350	7	(	(	PUNCT
ejpam-4684	350	8	g	g	NOUN
ejpam-4684	350	9	)	)	PUNCT
ejpam-4684	350	10	(	(	PUNCT
ejpam-4684	350	11	|v	|v	X
ejpam-4684	350	12	(	(	PUNCT
ejpam-4684	350	13	hv)|	hv)|	PROPN
ejpam-4684	350	14	−	−	PROPN
ejpam-4684	350	15	|v	|v	PROPN
ejpam-4684	350	16	(	(	PUNCT
ejpam-4684	350	17	hv	hv	PROPN
ejpam-4684	350	18	)	)	PUNCT
ejpam-4684	350	19	\	\	PROPN
ejpam-4684	350	20	cv|	cv|	NOUN
ejpam-4684	350	21	)	)	PUNCT
ejpam-4684	350	22	≥	≥	NOUN
ejpam-4684	350	23	|v	|v	X
ejpam-4684	350	24	(	(	PUNCT
ejpam-4684	350	25	g)|+	g)|+	PROPN
ejpam-4684	350	26	|v	|v	PROPN
ejpam-4684	350	27	(	(	PUNCT
ejpam-4684	350	28	g)|(m−	g)|(m−	PROPN
ejpam-4684	350	29	ω(h	ω(h	NUM
ejpam-4684	350	30	)	)	PUNCT
ejpam-4684	350	31	)	)	PUNCT
ejpam-4684	351	1	=	=	SYM
ejpam-4684	351	2	n+	n+	NUM
ejpam-4684	351	3	n(m−	n(m−	PROPN
ejpam-4684	351	4	ω(h	ω(h	NUM
ejpam-4684	351	5	)	)	PUNCT
ejpam-4684	351	6	)	)	PUNCT
ejpam-4684	351	7	.	.	PUNCT
ejpam-4684	352	1	j.	j.	PROPN
ejpam-4684	352	2	hassan	hassan	PROPN
ejpam-4684	352	3	,	,	PUNCT
ejpam-4684	352	4	a.	a.	PROPN
ejpam-4684	352	5	lintasan	lintasan	NOUN
ejpam-4684	352	6	,	,	PUNCT
ejpam-4684	352	7	n.	n.	PROPN
ejpam-4684	352	8	h.	h.	PROPN
ejpam-4684	352	9	mohammad	mohammad	PROPN
ejpam-4684	352	10	/	/	PUNCT
ejpam-4684	352	11	eur	eur	PROPN
ejpam-4684	352	12	.	.	PUNCT
ejpam-4684	353	1	j.	j.	PROPN
ejpam-4684	353	2	pure	pure	PROPN
ejpam-4684	353	3	appl	appl	PROPN
ejpam-4684	353	4	.	.	PROPN
ejpam-4684	353	5	math	math	PROPN
ejpam-4684	353	6	,	,	PUNCT
ejpam-4684	353	7	16	16	NUM
ejpam-4684	353	8	(	(	PUNCT
ejpam-4684	353	9	3	3	NUM
ejpam-4684	353	10	)	)	PUNCT
ejpam-4684	353	11	(	(	PUNCT
ejpam-4684	353	12	2023	2023	NUM
ejpam-4684	353	13	)	)	PUNCT
ejpam-4684	353	14	,	,	PUNCT
ejpam-4684	353	15	1848	1848	NUM
ejpam-4684	353	16	-	-	SYM
ejpam-4684	353	17	1861	1861	NUM
ejpam-4684	353	18	1860	1860	NUM
ejpam-4684	353	19	therefore	therefore	ADV
ejpam-4684	353	20	,	,	PUNCT
ejpam-4684	353	21	γohich	γohich	PRON
ejpam-4684	353	22	(	(	PUNCT
ejpam-4684	353	23	g	g	PROPN
ejpam-4684	353	24	◦	◦	NOUN
ejpam-4684	353	25	h	h	NOUN
ejpam-4684	353	26	)	)	PUNCT
ejpam-4684	353	27	≥	≥	NUM
ejpam-4684	353	28	n+	n+	PUNCT
ejpam-4684	353	29	n(m−	n(m−	PROPN
ejpam-4684	353	30	ω(h	ω(h	NUM
ejpam-4684	353	31	)	)	PUNCT
ejpam-4684	353	32	)	)	PUNCT
ejpam-4684	353	33	.	.	PUNCT
ejpam-4684	354	1	on	on	ADP
ejpam-4684	354	2	the	the	DET
ejpam-4684	354	3	other	other	ADJ
ejpam-4684	354	4	hand	hand	NOUN
ejpam-4684	354	5	,	,	PUNCT
ejpam-4684	354	6	for	for	ADP
ejpam-4684	354	7	each	each	DET
ejpam-4684	354	8	v	v	NUM
ejpam-4684	354	9	∈	∈	PROPN
ejpam-4684	354	10	v	v	NOUN
ejpam-4684	354	11	(	(	PUNCT
ejpam-4684	354	12	g	g	NOUN
ejpam-4684	354	13	)	)	PUNCT
ejpam-4684	354	14	,	,	PUNCT
ejpam-4684	354	15	let	let	VERB
ejpam-4684	354	16	cv	cv	PROPN
ejpam-4684	354	17	⊆	⊆	NUM
ejpam-4684	354	18	v	v	PROPN
ejpam-4684	354	19	(	(	PUNCT
ejpam-4684	354	20	hv	hv	NOUN
ejpam-4684	354	21	)	)	PUNCT
ejpam-4684	354	22	such	such	ADJ
ejpam-4684	354	23	that	that	PRON
ejpam-4684	354	24	v	v	NOUN
ejpam-4684	354	25	(	(	PUNCT
ejpam-4684	354	26	hv	hv	PROPN
ejpam-4684	354	27	)	)	PUNCT
ejpam-4684	354	28	\	\	PROPN
ejpam-4684	354	29	cv	cv	PROPN
ejpam-4684	354	30	is	be	AUX
ejpam-4684	354	31	a	a	DET
ejpam-4684	354	32	maximum	maximum	ADJ
ejpam-4684	354	33	clique	clique	NOUN
ejpam-4684	354	34	of	of	ADP
ejpam-4684	354	35	hv	hv	PROPN
ejpam-4684	354	36	.	.	PUNCT
ejpam-4684	355	1	then	then	ADV
ejpam-4684	355	2	by	by	ADP
ejpam-4684	355	3	theorem	theorem	NOUN
ejpam-4684	355	4	8	8	NUM
ejpam-4684	355	5	,	,	PUNCT
ejpam-4684	355	6	c	c	NOUN
ejpam-4684	355	7	=	=	SYM
ejpam-4684	355	8	v	v	PROPN
ejpam-4684	355	9	(	(	PUNCT
ejpam-4684	355	10	g	g	NOUN
ejpam-4684	355	11	)	)	PUNCT
ejpam-4684	355	12	∪	∪	NOUN
ejpam-4684	355	13	(	(	PUNCT
ejpam-4684	355	14	⋃	⋃	ADJ
ejpam-4684	355	15	v∈v	v∈v	NOUN
ejpam-4684	355	16	(	(	PUNCT
ejpam-4684	355	17	g)cv	g)cv	PROPN
ejpam-4684	355	18	)	)	PUNCT
ejpam-4684	355	19	is	be	AUX
ejpam-4684	355	20	a	a	DET
ejpam-4684	355	21	connected	connected	ADJ
ejpam-4684	355	22	outer	outer	ADJ
ejpam-4684	355	23	-	-	PUNCT
ejpam-4684	355	24	hop	hop	NOUN
ejpam-4684	355	25	independent	independent	ADJ
ejpam-4684	355	26	hop	hop	NOUN
ejpam-4684	355	27	dominating	dominating	NOUN
ejpam-4684	355	28	set	set	NOUN
ejpam-4684	355	29	of	of	ADP
ejpam-4684	355	30	g	g	PROPN
ejpam-4684	355	31	◦	◦	NOUN
ejpam-4684	355	32	h.	h.	PROPN
ejpam-4684	355	33	thus	thus	ADV
ejpam-4684	355	34	,	,	PUNCT
ejpam-4684	355	35	γohich	γohich	PRON
ejpam-4684	355	36	(	(	PUNCT
ejpam-4684	355	37	g	g	PROPN
ejpam-4684	355	38	◦	◦	NOUN
ejpam-4684	355	39	h	h	NOUN
ejpam-4684	355	40	)	)	PUNCT
ejpam-4684	355	41	≤	≤	NOUN
ejpam-4684	355	42	|c|	|c|	PROPN
ejpam-4684	355	43	=	=	SYM
ejpam-4684	355	44	|v	|v	PROPN
ejpam-4684	355	45	(	(	PUNCT
ejpam-4684	355	46	g)|+	g)|+	NOUN
ejpam-4684	355	47	|	|	ADV
ejpam-4684	355	48	⋃	⋃	PUNCT
ejpam-4684	355	49	v∈v	v∈v	NOUN
ejpam-4684	355	50	(	(	PUNCT
ejpam-4684	355	51	g	g	NOUN
ejpam-4684	355	52	)	)	PUNCT
ejpam-4684	355	53	cv|	cv|	NOUN
ejpam-4684	355	54	=	=	SYM
ejpam-4684	355	55	v	v	NOUN
ejpam-4684	355	56	(	(	PUNCT
ejpam-4684	355	57	g	g	NOUN
ejpam-4684	355	58	)	)	PUNCT
ejpam-4684	355	59	+	+	CCONJ
ejpam-4684	355	60	∑	∑	PUNCT
ejpam-4684	355	61	v∈v	v∈v	NOUN
ejpam-4684	355	62	(	(	PUNCT
ejpam-4684	355	63	g	g	NOUN
ejpam-4684	355	64	)	)	PUNCT
ejpam-4684	355	65	|cv|	|cv|	NOUN
ejpam-4684	356	1	=	=	PUNCT
ejpam-4684	356	2	|v	|v	PROPN
ejpam-4684	356	3	(	(	PUNCT
ejpam-4684	356	4	g)|+	g)|+	PROPN
ejpam-4684	356	5	∑	∑	PUNCT
ejpam-4684	356	6	v∈v	v∈v	PROPN
ejpam-4684	356	7	(	(	PUNCT
ejpam-4684	356	8	g	g	NOUN
ejpam-4684	356	9	)	)	PUNCT
ejpam-4684	356	10	(	(	PUNCT
ejpam-4684	356	11	|v	|v	X
ejpam-4684	356	12	(	(	PUNCT
ejpam-4684	356	13	hv)|	hv)|	PROPN
ejpam-4684	356	14	−	−	PROPN
ejpam-4684	356	15	|v	|v	PROPN
ejpam-4684	356	16	(	(	PUNCT
ejpam-4684	356	17	hv	hv	PROPN
ejpam-4684	356	18	)	)	PUNCT
ejpam-4684	356	19	\	\	NOUN
ejpam-4684	356	20	cv|	cv|	NOUN
ejpam-4684	356	21	)	)	PUNCT
ejpam-4684	356	22	=	=	SYM
ejpam-4684	356	23	|v	|v	PROPN
ejpam-4684	356	24	(	(	PUNCT
ejpam-4684	356	25	g)|+	g)|+	PROPN
ejpam-4684	356	26	|v	|v	PROPN
ejpam-4684	356	27	(	(	PUNCT
ejpam-4684	356	28	g)|(|v	g)|(|v	X
ejpam-4684	356	29	(	(	PUNCT
ejpam-4684	356	30	hv)|	hv)|	PROPN
ejpam-4684	356	31	−	−	NOUN
ejpam-4684	356	32	ω(h	ω(h	NUM
ejpam-4684	356	33	)	)	PUNCT
ejpam-4684	356	34	)	)	PUNCT
ejpam-4684	357	1	=	=	SYM
ejpam-4684	357	2	n+	n+	NUM
ejpam-4684	357	3	n(m−	n(m−	PROPN
ejpam-4684	357	4	ω(h	ω(h	NUM
ejpam-4684	357	5	)	)	PUNCT
ejpam-4684	357	6	)	)	PUNCT
ejpam-4684	357	7	.	.	PUNCT
ejpam-4684	358	1	consequently	consequently	ADV
ejpam-4684	358	2	,	,	PUNCT
ejpam-4684	358	3	γohich	γohich	PROPN
ejpam-4684	358	4	(	(	PUNCT
ejpam-4684	358	5	g	g	PROPN
ejpam-4684	358	6	◦	◦	NOUN
ejpam-4684	358	7	h	h	NOUN
ejpam-4684	358	8	)	)	PUNCT
ejpam-4684	358	9	=	=	PRON
ejpam-4684	358	10	n+	n+	PUNCT
ejpam-4684	358	11	n(m−	n(m−	PROPN
ejpam-4684	358	12	ω(h	ω(h	NUM
ejpam-4684	358	13	)	)	PUNCT
ejpam-4684	358	14	)	)	PUNCT
ejpam-4684	358	15	.	.	PUNCT
ejpam-4684	359	1	since	since	SCONJ
ejpam-4684	359	2	ω(pm	ω(pm	NOUN
ejpam-4684	359	3	)	)	PUNCT
ejpam-4684	359	4	=	=	SYM
ejpam-4684	359	5	ω(k1,m	ω(k1,m	NUM
ejpam-4684	359	6	)	)	PUNCT
ejpam-4684	359	7	=	=	SYM
ejpam-4684	359	8	2	2	NUM
ejpam-4684	359	9	for	for	ADP
ejpam-4684	359	10	all	all	DET
ejpam-4684	359	11	m	m	PROPN
ejpam-4684	359	12	≥	≥	NOUN
ejpam-4684	359	13	3	3	NUM
ejpam-4684	359	14	and	and	CCONJ
ejpam-4684	359	15	ω(cn	ω(cn	NUM
ejpam-4684	359	16	)	)	PUNCT
ejpam-4684	359	17	=	=	SYM
ejpam-4684	359	18	2	2	NUM
ejpam-4684	359	19	for	for	ADP
ejpam-4684	359	20	all	all	DET
ejpam-4684	359	21	m	m	PROPN
ejpam-4684	359	22	≥	≥	NOUN
ejpam-4684	359	23	4	4	NUM
ejpam-4684	359	24	,	,	PUNCT
ejpam-4684	359	25	statements	statement	NOUN
ejpam-4684	359	26	(	(	PUNCT
ejpam-4684	359	27	i	i	NOUN
ejpam-4684	359	28	)	)	PUNCT
ejpam-4684	359	29	and	and	CCONJ
ejpam-4684	359	30	(	(	PUNCT
ejpam-4684	359	31	ii	ii	NOUN
ejpam-4684	359	32	)	)	PUNCT
ejpam-4684	359	33	hold	hold	VERB
ejpam-4684	359	34	.	.	PUNCT
ejpam-4684	360	1	also	also	ADV
ejpam-4684	360	2	,	,	PUNCT
ejpam-4684	360	3	since	since	SCONJ
ejpam-4684	360	4	ω(wm	ω(wm	NOUN
ejpam-4684	360	5	)	)	PUNCT
ejpam-4684	360	6	=	=	SYM
ejpam-4684	360	7	3	3	NUM
ejpam-4684	360	8	for	for	ADP
ejpam-4684	360	9	all	all	DET
ejpam-4684	360	10	m	m	PROPN
ejpam-4684	360	11	≥	≥	NOUN
ejpam-4684	360	12	4	4	NUM
ejpam-4684	360	13	and	and	CCONJ
ejpam-4684	360	14	ω(fm	ω(fm	NUM
ejpam-4684	360	15	)	)	PUNCT
ejpam-4684	360	16	=	=	SYM
ejpam-4684	360	17	3	3	NUM
ejpam-4684	360	18	for	for	ADP
ejpam-4684	360	19	all	all	DET
ejpam-4684	360	20	m	m	PROPN
ejpam-4684	360	21	≥	≥	NOUN
ejpam-4684	360	22	3	3	NUM
ejpam-4684	360	23	,	,	PUNCT
ejpam-4684	360	24	statements	statement	NOUN
ejpam-4684	360	25	(	(	PUNCT
ejpam-4684	360	26	iii	iii	NOUN
ejpam-4684	360	27	)	)	PUNCT
ejpam-4684	360	28	and	and	CCONJ
ejpam-4684	360	29	(	(	PUNCT
ejpam-4684	360	30	iv	iv	X
ejpam-4684	360	31	)	)	PUNCT
ejpam-4684	360	32	hold	hold	NOUN
ejpam-4684	360	33	.	.	PUNCT
ejpam-4684	361	1	4	4	X
ejpam-4684	361	2	.	.	X
ejpam-4684	361	3	conclusion	conclusion	NOUN
ejpam-4684	361	4	this	this	DET
ejpam-4684	361	5	study	study	NOUN
ejpam-4684	361	6	has	have	AUX
ejpam-4684	361	7	initiated	initiate	VERB
ejpam-4684	361	8	the	the	DET
ejpam-4684	361	9	study	study	NOUN
ejpam-4684	361	10	of	of	ADP
ejpam-4684	361	11	the	the	DET
ejpam-4684	361	12	concept	concept	NOUN
ejpam-4684	361	13	called	call	VERB
ejpam-4684	361	14	connected	connected	ADJ
ejpam-4684	361	15	outer	outer	ADJ
ejpam-4684	361	16	-	-	PUNCT
ejpam-4684	361	17	hop	hop	NOUN
ejpam-4684	361	18	independent	independent	ADJ
ejpam-4684	361	19	hop	hop	NOUN
ejpam-4684	361	20	domination	domination	NOUN
ejpam-4684	361	21	in	in	ADP
ejpam-4684	361	22	a	a	DET
ejpam-4684	361	23	graph	graph	NOUN
ejpam-4684	361	24	.	.	PUNCT
ejpam-4684	362	1	it	it	PRON
ejpam-4684	362	2	was	be	AUX
ejpam-4684	362	3	shown	show	VERB
ejpam-4684	362	4	that	that	SCONJ
ejpam-4684	362	5	the	the	DET
ejpam-4684	362	6	connected	connected	ADJ
ejpam-4684	362	7	outer	outer	ADJ
ejpam-4684	362	8	-	-	PUNCT
ejpam-4684	362	9	hop	hop	NOUN
ejpam-4684	362	10	independent	independent	ADJ
ejpam-4684	362	11	hop	hop	NOUN
ejpam-4684	362	12	domination	domination	NOUN
ejpam-4684	362	13	number	number	NOUN
ejpam-4684	362	14	is	be	AUX
ejpam-4684	362	15	at	at	ADP
ejpam-4684	362	16	least	least	ADJ
ejpam-4684	362	17	equal	equal	ADJ
ejpam-4684	362	18	to	to	ADP
ejpam-4684	362	19	the	the	DET
ejpam-4684	362	20	connected	connect	VERB
ejpam-4684	362	21	hop	hop	NOUN
ejpam-4684	362	22	domination	domination	NOUN
ejpam-4684	362	23	number	number	NOUN
ejpam-4684	362	24	of	of	ADP
ejpam-4684	362	25	a	a	DET
ejpam-4684	362	26	graph	graph	NOUN
ejpam-4684	362	27	.	.	PUNCT
ejpam-4684	363	1	this	this	DET
ejpam-4684	363	2	study	study	NOUN
ejpam-4684	363	3	gave	give	VERB
ejpam-4684	363	4	some	some	DET
ejpam-4684	363	5	lower	low	ADJ
ejpam-4684	363	6	or	or	CCONJ
ejpam-4684	363	7	upper	upper	ADJ
ejpam-4684	363	8	bounds	bound	NOUN
ejpam-4684	363	9	on	on	ADP
ejpam-4684	363	10	the	the	DET
ejpam-4684	363	11	parameter	parameter	NOUN
ejpam-4684	363	12	of	of	ADP
ejpam-4684	363	13	some	some	DET
ejpam-4684	363	14	graphs	graph	NOUN
ejpam-4684	363	15	.	.	PUNCT
ejpam-4684	364	1	in	in	ADP
ejpam-4684	364	2	addition	addition	NOUN
ejpam-4684	364	3	,	,	PUNCT
ejpam-4684	364	4	exact	exact	ADJ
ejpam-4684	364	5	values	value	NOUN
ejpam-4684	364	6	of	of	ADP
ejpam-4684	364	7	the	the	DET
ejpam-4684	364	8	parameter	parameter	NOUN
ejpam-4684	364	9	have	have	AUX
ejpam-4684	364	10	been	be	AUX
ejpam-4684	364	11	obtained	obtain	VERB
ejpam-4684	364	12	for	for	ADP
ejpam-4684	364	13	some	some	DET
ejpam-4684	364	14	special	special	ADJ
ejpam-4684	364	15	graphs	graph	NOUN
ejpam-4684	364	16	and	and	CCONJ
ejpam-4684	364	17	graphs	graph	NOUN
ejpam-4684	364	18	under	under	ADP
ejpam-4684	364	19	some	some	DET
ejpam-4684	364	20	binary	binary	ADJ
ejpam-4684	364	21	operations	operation	NOUN
ejpam-4684	364	22	.	.	PUNCT
ejpam-4684	365	1	realization	realization	NOUN
ejpam-4684	365	2	results	result	NOUN
ejpam-4684	365	3	involving	involve	VERB
ejpam-4684	365	4	connected	connect	VERB
ejpam-4684	365	5	outerhop	outerhop	ADJ
ejpam-4684	365	6	independent	independent	ADJ
ejpam-4684	365	7	hop	hop	NOUN
ejpam-4684	365	8	domination	domination	NOUN
ejpam-4684	365	9	were	be	AUX
ejpam-4684	365	10	presented	present	VERB
ejpam-4684	365	11	.	.	PUNCT
ejpam-4684	366	1	interested	interested	ADJ
ejpam-4684	366	2	researchers	researcher	NOUN
ejpam-4684	366	3	may	may	AUX
ejpam-4684	366	4	consider	consider	VERB
ejpam-4684	366	5	and	and	CCONJ
ejpam-4684	366	6	investigate	investigate	VERB
ejpam-4684	366	7	this	this	DET
ejpam-4684	366	8	newly	newly	ADV
ejpam-4684	366	9	defined	define	VERB
ejpam-4684	366	10	parameter	parameter	NOUN
ejpam-4684	366	11	for	for	ADP
ejpam-4684	366	12	some	some	DET
ejpam-4684	366	13	products	product	NOUN
ejpam-4684	366	14	of	of	ADP
ejpam-4684	366	15	graphs	graph	NOUN
ejpam-4684	366	16	which	which	PRON
ejpam-4684	366	17	were	be	AUX
ejpam-4684	366	18	not	not	PART
ejpam-4684	366	19	considered	consider	VERB
ejpam-4684	366	20	in	in	ADP
ejpam-4684	366	21	this	this	DET
ejpam-4684	366	22	study	study	NOUN
ejpam-4684	366	23	.	.	PUNCT
ejpam-4684	367	1	they	they	PRON
ejpam-4684	367	2	may	may	AUX
ejpam-4684	367	3	also	also	ADV
ejpam-4684	367	4	consider	consider	VERB
ejpam-4684	367	5	and	and	CCONJ
ejpam-4684	367	6	study	study	VERB
ejpam-4684	367	7	the	the	DET
ejpam-4684	367	8	complexity	complexity	NOUN
ejpam-4684	367	9	of	of	ADP
ejpam-4684	367	10	this	this	DET
ejpam-4684	367	11	parameter	parameter	NOUN
ejpam-4684	367	12	.	.	PUNCT
ejpam-4684	368	1	acknowledgements	acknowledgement	NOUN
ejpam-4684	368	2	the	the	DET
ejpam-4684	368	3	authors	author	NOUN
ejpam-4684	368	4	would	would	AUX
ejpam-4684	368	5	like	like	VERB
ejpam-4684	368	6	to	to	PART
ejpam-4684	368	7	thank	thank	VERB
ejpam-4684	368	8	the	the	DET
ejpam-4684	368	9	referees	referee	NOUN
ejpam-4684	368	10	for	for	ADP
ejpam-4684	368	11	their	their	PRON
ejpam-4684	368	12	invaluable	invaluable	ADJ
ejpam-4684	368	13	comments	comment	NOUN
ejpam-4684	368	14	and	and	CCONJ
ejpam-4684	368	15	suggestions	suggestion	NOUN
ejpam-4684	368	16	that	that	PRON
ejpam-4684	368	17	led	lead	VERB
ejpam-4684	368	18	to	to	ADP
ejpam-4684	368	19	the	the	DET
ejpam-4684	368	20	improvement	improvement	NOUN
ejpam-4684	368	21	of	of	ADP
ejpam-4684	368	22	the	the	DET
ejpam-4684	368	23	paper	paper	NOUN
ejpam-4684	368	24	.	.	PUNCT
ejpam-4684	369	1	also	also	ADV
ejpam-4684	369	2	,	,	PUNCT
ejpam-4684	369	3	the	the	DET
ejpam-4684	369	4	authors	author	NOUN
ejpam-4684	369	5	would	would	AUX
ejpam-4684	369	6	like	like	VERB
ejpam-4684	369	7	to	to	PART
ejpam-4684	369	8	thank	thank	VERB
ejpam-4684	369	9	mindanao	mindanao	PROPN
ejpam-4684	369	10	state	state	PROPN
ejpam-4684	369	11	university	university	PROPN
ejpam-4684	369	12	tawi	tawi	PROPN
ejpam-4684	369	13	-	-	PUNCT
ejpam-4684	369	14	tawi	tawi	PROPN
ejpam-4684	369	15	college	college	PROPN
ejpam-4684	369	16	of	of	ADP
ejpam-4684	369	17	technology	technology	NOUN
ejpam-4684	369	18	and	and	CCONJ
ejpam-4684	369	19	oceanography	oceanography	NOUN
ejpam-4684	369	20	for	for	ADP
ejpam-4684	369	21	funding	fund	VERB
ejpam-4684	369	22	this	this	DET
ejpam-4684	369	23	research	research	NOUN
ejpam-4684	369	24	.	.	PUNCT
ejpam-4684	370	1	references	reference	NOUN
ejpam-4684	370	2	1861	1861	NUM
ejpam-4684	370	3	references	reference	NOUN
ejpam-4684	370	4	[	[	X
ejpam-4684	370	5	1	1	NUM
ejpam-4684	370	6	]	]	PUNCT
ejpam-4684	370	7	s.	s.	PROPN
ejpam-4684	370	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4684	370	9	and	and	CCONJ
ejpam-4684	370	10	b.	b.	PROPN
ejpam-4684	370	11	krishnakumari	krishnakumari	PROPN
ejpam-4684	370	12	and	and	CCONJ
ejpam-4684	370	13	b.	b.	PROPN
ejpam-4684	370	14	natarjan	natarjan	PROPN
ejpam-4684	370	15	and	and	CCONJ
ejpam-4684	370	16	y.	y.	PROPN
ejpam-4684	370	17	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4684	370	18	,	,	PUNCT
ejpam-4684	370	19	bounds	bound	VERB
ejpam-4684	370	20	on	on	ADP
ejpam-4684	370	21	the	the	DET
ejpam-4684	370	22	hop	hop	NOUN
ejpam-4684	370	23	domination	domination	NOUN
ejpam-4684	370	24	number	number	NOUN
ejpam-4684	370	25	of	of	ADP
ejpam-4684	370	26	a	a	DET
ejpam-4684	370	27	tree	tree	NOUN
ejpam-4684	370	28	.	.	PUNCT
ejpam-4684	371	1	,	,	PUNCT
ejpam-4684	371	2	proceedings	proceeding	NOUN
ejpam-4684	371	3	-	-	PUNCT
ejpam-4684	371	4	mathematical	mathematical	ADJ
ejpam-4684	371	5	sciences	science	NOUN
ejpam-4684	371	6	.	.	PUNCT
ejpam-4684	371	7	,	,	PUNCT
ejpam-4684	371	8	2015	2015	NUM
ejpam-4684	371	9	,	,	PUNCT
ejpam-4684	371	10	125(4	125(4	NUM
ejpam-4684	371	11	)	)	PUNCT
ejpam-4684	371	12	,	,	PUNCT
ejpam-4684	371	13	449	449	NUM
ejpam-4684	371	14	-	-	SYM
ejpam-4684	371	15	455	455	NUM
ejpam-4684	371	16	.	.	PUNCT
ejpam-4684	372	1	[	[	X
ejpam-4684	372	2	2	2	X
ejpam-4684	372	3	]	]	PUNCT
ejpam-4684	372	4	s.	s.	PROPN
ejpam-4684	372	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4684	372	6	and	and	CCONJ
ejpam-4684	372	7	c.	c.	PROPN
ejpam-4684	372	8	natarajan	natarajan	PROPN
ejpam-4684	372	9	and	and	CCONJ
ejpam-4684	372	10	g.	g.	PROPN
ejpam-4684	372	11	sathiamoorphy	sathiamoorphy	PROPN
ejpam-4684	372	12	,	,	PUNCT
ejpam-4684	372	13	a	a	DET
ejpam-4684	372	14	note	note	NOUN
ejpam-4684	372	15	on	on	ADP
ejpam-4684	372	16	hop	hop	NOUN
ejpam-4684	372	17	domination	domination	NOUN
ejpam-4684	372	18	number	number	NOUN
ejpam-4684	372	19	of	of	ADP
ejpam-4684	372	20	some	some	DET
ejpam-4684	372	21	special	special	ADJ
ejpam-4684	372	22	families	family	NOUN
ejpam-4684	372	23	of	of	ADP
ejpam-4684	372	24	graphs	graph	NOUN
ejpam-4684	372	25	.	.	PUNCT
ejpam-4684	373	1	,	,	PUNCT
ejpam-4684	373	2	international	international	ADJ
ejpam-4684	373	3	journal	journal	NOUN
ejpam-4684	373	4	of	of	ADP
ejpam-4684	373	5	pure	pure	ADJ
ejpam-4684	373	6	and	and	CCONJ
ejpam-4684	373	7	applied	applied	ADJ
ejpam-4684	373	8	mathematics	mathematic	NOUN
ejpam-4684	373	9	.	.	PUNCT
ejpam-4684	373	10	,	,	PUNCT
ejpam-4684	373	11	2018	2018	NUM
ejpam-4684	373	12	,	,	PUNCT
ejpam-4684	373	13	119	119	NUM
ejpam-4684	373	14	,	,	PUNCT
ejpam-4684	373	15	12	12	NUM
ejpam-4684	373	16	,	,	PUNCT
ejpam-4684	373	17	11465	11465	NUM
ejpam-4684	373	18	-	-	SYM
ejpam-4684	373	19	14171	14171	NUM
ejpam-4684	373	20	.	.	PUNCT
ejpam-4684	374	1	[	[	X
ejpam-4684	374	2	3	3	X
ejpam-4684	374	3	]	]	X
ejpam-4684	374	4	s.	s.	PROPN
ejpam-4684	374	5	canoy	canoy	PROPN
ejpam-4684	374	6	jr	jr	PROPN
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ejpam-4684	374	8	j.	j.	PROPN
ejpam-4684	374	9	hassan	hassan	PROPN
ejpam-4684	374	10	.	.	PROPN
ejpam-4684	374	11	,	,	PUNCT
ejpam-4684	374	12	weakly	weakly	ADV
ejpam-4684	374	13	convex	convex	ADJ
ejpam-4684	374	14	hop	hop	NOUN
ejpam-4684	374	15	dominating	dominating	NOUN
ejpam-4684	374	16	sets	set	NOUN
ejpam-4684	374	17	in	in	ADP
ejpam-4684	374	18	graphs	graph	NOUN
ejpam-4684	374	19	,	,	PUNCT
ejpam-4684	374	20	eur	eur	PROPN
ejpam-4684	374	21	.	.	PUNCT
ejpam-4684	375	1	j.	j.	PROPN
ejpam-4684	375	2	pure	pure	PROPN
ejpam-4684	375	3	appl	appl	PROPN
ejpam-4684	375	4	.	.	PUNCT
ejpam-4684	375	5	math	math	PROPN
ejpam-4684	375	6	.	.	PUNCT
ejpam-4684	375	7	,	,	PUNCT
ejpam-4684	375	8	2023	2023	NUM
ejpam-4684	375	9	,	,	PUNCT
ejpam-4684	375	10	16	16	NUM
ejpam-4684	375	11	,	,	PUNCT
ejpam-4684	375	12	2	2	NUM
ejpam-4684	375	13	,	,	PUNCT
ejpam-4684	375	14	1196	1196	NUM
ejpam-4684	375	15	-	-	SYM
ejpam-4684	375	16	1211	1211	NUM
ejpam-4684	375	17	.	.	PUNCT
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ejpam-4684	376	3	]	]	X
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ejpam-4684	376	5	canoy	canoy	PROPN
ejpam-4684	376	6	jr	jr	PROPN
ejpam-4684	376	7	.	.	PROPN
ejpam-4684	376	8	and	and	CCONJ
ejpam-4684	376	9	r.	r.	PROPN
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ejpam-4684	376	11	and	and	CCONJ
ejpam-4684	376	12	j.	j.	PROPN
ejpam-4684	376	13	g.	g.	PROPN
ejpam-4684	376	14	canoy	canoy	PROPN
ejpam-4684	376	15	,	,	PUNCT
ejpam-4684	376	16	hop	hop	NOUN
ejpam-4684	376	17	dominating	dominating	NOUN
ejpam-4684	376	18	sets	set	NOUN
ejpam-4684	376	19	in	in	ADP
ejpam-4684	376	20	graphs	graph	NOUN
ejpam-4684	376	21	under	under	ADP
ejpam-4684	376	22	binary	binary	ADJ
ejpam-4684	376	23	operations	operation	NOUN
ejpam-4684	376	24	.	.	PUNCT
ejpam-4684	377	1	,eur	,eur	PROPN
ejpam-4684	377	2	.	.	PUNCT
ejpam-4684	378	1	j.	j.	PROPN
ejpam-4684	378	2	pure	pure	PROPN
ejpam-4684	378	3	appl	appl	PROPN
ejpam-4684	378	4	.	.	PUNCT
ejpam-4684	378	5	math	math	PROPN
ejpam-4684	378	6	.	.	PUNCT
ejpam-4684	378	7	,	,	PUNCT
ejpam-4684	378	8	2019	2019	NUM
ejpam-4684	378	9	,	,	PUNCT
ejpam-4684	378	10	12	12	NUM
ejpam-4684	378	11	,	,	PUNCT
ejpam-4684	378	12	4	4	NUM
ejpam-4684	378	13	,	,	PUNCT
ejpam-4684	378	14	1455	1455	NUM
ejpam-4684	378	15	-	-	SYM
ejpam-4684	378	16	1463	1463	NUM
ejpam-4684	378	17	.	.	PUNCT
ejpam-4684	379	1	[	[	X
ejpam-4684	379	2	5	5	X
ejpam-4684	379	3	]	]	PUNCT
ejpam-4684	379	4	s.	s.	PROPN
ejpam-4684	379	5	canoy	canoy	PROPN
ejpam-4684	379	6	jr	jr	PROPN
ejpam-4684	379	7	.	.	PROPN
ejpam-4684	379	8	and	and	CCONJ
ejpam-4684	379	9	g.	g.	PROPN
ejpam-4684	379	10	salasalan	salasalan	NOUN
ejpam-4684	379	11	,	,	PUNCT
ejpam-4684	379	12	locating	locate	VERB
ejpam-4684	379	13	-	-	PUNCT
ejpam-4684	379	14	hop	hop	NOUN
ejpam-4684	379	15	domination	domination	NOUN
ejpam-4684	379	16	in	in	ADP
ejpam-4684	379	17	graphs	graph	NOUN
ejpam-4684	379	18	.	.	PUNCT
ejpam-4684	379	19	,	,	PUNCT
ejpam-4684	379	20	kyungpook	kyungpook	PROPN
ejpam-4684	379	21	mathematical	mathematical	ADJ
ejpam-4684	379	22	journal	journal	PROPN
ejpam-4684	379	23	.	.	PUNCT
ejpam-4684	379	24	,	,	PUNCT
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ejpam-4684	379	26	,	,	PUNCT
ejpam-4684	379	27	62	62	NUM
ejpam-4684	379	28	,	,	PUNCT
ejpam-4684	379	29	193	193	NUM
ejpam-4684	379	30	-	-	SYM
ejpam-4684	379	31	204	204	NUM
ejpam-4684	379	32	.	.	PUNCT
ejpam-4684	380	1	[	[	X
ejpam-4684	380	2	6	6	NUM
ejpam-4684	380	3	]	]	PUNCT
ejpam-4684	380	4	j.	j.	PROPN
ejpam-4684	380	5	hassan	hassan	PROPN
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ejpam-4684	380	7	s.	s.	PROPN
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ejpam-4684	380	9	jr	jr	PROPN
ejpam-4684	380	10	.	.	PROPN
ejpam-4684	380	11	and	and	CCONJ
ejpam-4684	380	12	a.	a.	PROPN
ejpam-4684	380	13	aradais	aradais	PROPN
ejpam-4684	380	14	,	,	PUNCT
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ejpam-4684	380	17	sets	set	NOUN
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ejpam-4684	380	19	graphs	graph	NOUN
ejpam-4684	380	20	.	.	PUNCT
ejpam-4684	380	21	,	,	PUNCT
ejpam-4684	380	22	eur	eur	PROPN
ejpam-4684	380	23	.	.	PUNCT
ejpam-4684	381	1	j.	j.	PROPN
ejpam-4684	381	2	pure	pure	PROPN
ejpam-4684	381	3	appl	appl	PROPN
ejpam-4684	381	4	.	.	PUNCT
ejpam-4684	381	5	math	math	PROPN
ejpam-4684	381	6	.	.	PUNCT
ejpam-4684	382	1	,2022	,2022	PROPN
ejpam-4684	382	2	,	,	PUNCT
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ejpam-4684	382	4	,	,	PUNCT
ejpam-4684	382	5	2	2	NUM
ejpam-4684	382	6	,	,	PUNCT
ejpam-4684	382	7	467	467	NUM
ejpam-4684	382	8	-	-	SYM
ejpam-4684	382	9	477	477	NUM
ejpam-4684	382	10	.	.	PUNCT
ejpam-4684	383	1	[	[	X
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ejpam-4684	383	3	]	]	PUNCT
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ejpam-4684	383	7	s.	s.	PROPN
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ejpam-4684	383	9	jr	jr	PROPN
ejpam-4684	383	10	.	.	PROPN
ejpam-4684	383	11	,	,	PUNCT
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ejpam-4684	383	13	hop	hop	PROPN
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ejpam-4684	383	15	in	in	ADP
ejpam-4684	383	16	graphs	graph	NOUN
ejpam-4684	383	17	,	,	PUNCT
ejpam-4684	383	18	eur	eur	PROPN
ejpam-4684	383	19	.	.	PUNCT
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ejpam-4684	384	3	appl	appl	PROPN
ejpam-4684	384	4	.	.	PUNCT
ejpam-4684	384	5	math	math	PROPN
ejpam-4684	384	6	.	.	PUNCT
ejpam-4684	385	1	,2022	,2022	PROPN
ejpam-4684	385	2	,	,	PUNCT
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ejpam-4684	385	4	,	,	PUNCT
ejpam-4684	385	5	4	4	NUM
ejpam-4684	385	6	,	,	PUNCT
ejpam-4684	385	7	1623	1623	NUM
ejpam-4684	385	8	-	-	SYM
ejpam-4684	385	9	1636	1636	NUM
ejpam-4684	385	10	.	.	PUNCT
ejpam-4684	386	1	[	[	X
ejpam-4684	386	2	8	8	X
ejpam-4684	386	3	]	]	PUNCT
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ejpam-4684	386	7	s.	s.	PROPN
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ejpam-4684	386	9	jr	jr	PROPN
ejpam-4684	386	10	.	.	PROPN
ejpam-4684	386	11	,	,	PUNCT
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ejpam-4684	386	14	hop	hop	NOUN
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ejpam-4684	386	16	in	in	ADP
ejpam-4684	386	17	graphs	graph	NOUN
ejpam-4684	386	18	.	.	PUNCT
ejpam-4684	386	19	,	,	PUNCT
ejpam-4684	386	20	eur	eur	PROPN
ejpam-4684	386	21	.	.	PUNCT
ejpam-4684	387	1	j.	j.	PROPN
ejpam-4684	387	2	pure	pure	PROPN
ejpam-4684	387	3	appl	appl	PROPN
ejpam-4684	387	4	.	.	PUNCT
ejpam-4684	387	5	math	math	PROPN
ejpam-4684	387	6	.	.	PUNCT
ejpam-4684	388	1	,2022	,2022	PROPN
ejpam-4684	388	2	,	,	PUNCT
ejpam-4684	388	3	15	15	NUM
ejpam-4684	388	4	,	,	PUNCT
ejpam-4684	388	5	4	4	NUM
ejpam-4684	388	6	,	,	PUNCT
ejpam-4684	388	7	1783	1783	NUM
ejpam-4684	388	8	-	-	SYM
ejpam-4684	388	9	1796	1796	NUM
ejpam-4684	388	10	.	.	PUNCT
ejpam-4684	389	1	[	[	X
ejpam-4684	389	2	9	9	NUM
ejpam-4684	389	3	]	]	PUNCT
ejpam-4684	389	4	j.	j.	PROPN
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ejpam-4684	389	7	s.	s.	PROPN
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ejpam-4684	389	15	,	,	PUNCT
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ejpam-4684	389	17	hop	hop	NOUN
ejpam-4684	389	18	domination	domination	NOUN
ejpam-4684	389	19	in	in	ADP
ejpam-4684	389	20	graphs	graph	NOUN
ejpam-4684	389	21	,	,	PUNCT
ejpam-4684	389	22	eur	eur	PROPN
ejpam-4684	389	23	.	.	PUNCT
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ejpam-4684	390	6	.	.	PUNCT
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ejpam-4684	391	2	,	,	PUNCT
ejpam-4684	391	3	16	16	NUM
ejpam-4684	391	4	,	,	PUNCT
ejpam-4684	391	5	1	1	NUM
ejpam-4684	391	6	,	,	PUNCT
ejpam-4684	391	7	319	319	NUM
ejpam-4684	391	8	-	-	SYM
ejpam-4684	391	9	335	335	NUM
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ejpam-4684	392	3	]	]	PUNCT
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ejpam-4684	392	16	sequences	sequence	NOUN
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ejpam-4684	392	18	graphs	graph	NOUN
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ejpam-4684	392	20	,	,	PUNCT
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ejpam-4684	392	22	.	.	PUNCT
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ejpam-4684	393	6	.	.	PUNCT
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ejpam-4684	394	2	,	,	PUNCT
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ejpam-4684	394	4	,	,	PUNCT
ejpam-4684	394	5	2	2	NUM
ejpam-4684	394	6	,	,	PUNCT
ejpam-4684	394	7	1212	1212	NUM
ejpam-4684	394	8	-	-	SYM
ejpam-4684	394	9	1227	1227	NUM
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ejpam-4684	395	8	rad	rad	PROPN
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ejpam-4684	395	15	hop	hop	NOUN
ejpam-4684	395	16	dominating	dominating	NOUN
ejpam-4684	395	17	sets	set	NOUN
ejpam-4684	395	18	in	in	ADP
ejpam-4684	395	19	graphs	graph	NOUN
ejpam-4684	395	20	.	.	PUNCT
ejpam-4684	395	21	,	,	PUNCT
ejpam-4684	395	22	graphs	graph	NOUN
ejpam-4684	395	23	and	and	CCONJ
ejpam-4684	395	24	combinatorics	combinatoric	NOUN
ejpam-4684	395	25	.	.	PROPN
ejpam-4684	395	26	,	,	PUNCT
ejpam-4684	395	27	2017	2017	NUM
ejpam-4684	395	28	,	,	PUNCT
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ejpam-4684	395	30	)	)	PUNCT
ejpam-4684	395	31	,	,	PUNCT
ejpam-4684	395	32	913	913	NUM
ejpam-4684	395	33	-	-	SYM
ejpam-4684	395	34	927	927	NUM
ejpam-4684	395	35	.	.	PUNCT
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ejpam-4684	396	2	12	12	NUM
ejpam-4684	396	3	]	]	PUNCT
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ejpam-4684	396	8	rara	rara	PROPN
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ejpam-4684	396	11	outer	outer	ADJ
ejpam-4684	396	12	-	-	PUNCT
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ejpam-4684	396	14	hop	hop	NOUN
ejpam-4684	396	15	domination	domination	NOUN
ejpam-4684	396	16	in	in	ADP
ejpam-4684	396	17	graphs	graph	NOUN
ejpam-4684	396	18	.	.	PUNCT
ejpam-4684	396	19	,	,	PUNCT
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ejpam-4684	396	21	.	.	PUNCT
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ejpam-4684	397	4	.	.	PUNCT
ejpam-4684	397	5	math	math	PROPN
ejpam-4684	397	6	.	.	PUNCT
ejpam-4684	398	1	,2021	,2021	PROPN
ejpam-4684	398	2	,	,	PUNCT
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ejpam-4684	398	4	,	,	PUNCT
ejpam-4684	398	5	4	4	NUM
ejpam-4684	398	6	,	,	PUNCT
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ejpam-4684	398	8	-	-	SYM
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ejpam-4684	398	10	.	.	PUNCT
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ejpam-4684	399	2	13	13	NUM
ejpam-4684	399	3	]	]	X
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ejpam-4684	399	18	,	,	PUNCT
ejpam-4684	399	19	2015	2015	NUM
ejpam-4684	399	20	,	,	PUNCT
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ejpam-4684	399	22	)	)	PUNCT
ejpam-4684	399	23	,	,	PUNCT
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ejpam-4684	399	25	-	-	SYM
ejpam-4684	399	26	199	199	NUM
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ejpam-4684	400	2	14	14	NUM
ejpam-4684	400	3	]	]	X
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ejpam-4684	400	7	s.	s.	PROPN
ejpam-4684	400	8	canoy	canoy	PROPN
ejpam-4684	400	9	jr	jr	PROPN
ejpam-4684	400	10	.	.	PROPN
ejpam-4684	400	11	,	,	PUNCT
ejpam-4684	400	12	global	global	ADJ
ejpam-4684	400	13	hop	hop	NOUN
ejpam-4684	400	14	domination	domination	PROPN
ejpam-4684	400	15	numbers	number	NOUN
ejpam-4684	400	16	of	of	ADP
ejpam-4684	400	17	graphs	graph	NOUN
ejpam-4684	400	18	.	.	PUNCT
ejpam-4684	400	19	,	,	PUNCT
ejpam-4684	400	20	eur	eur	PROPN
ejpam-4684	400	21	.	.	PUNCT
ejpam-4684	401	1	j.	j.	PROPN
ejpam-4684	401	2	pure	pure	PROPN
ejpam-4684	401	3	appl	appl	PROPN
ejpam-4684	401	4	.	.	PUNCT
ejpam-4684	401	5	math	math	PROPN
ejpam-4684	401	6	.	.	PUNCT
ejpam-4684	401	7	,	,	PUNCT
ejpam-4684	401	8	2021	2021	NUM
ejpam-4684	401	9	,	,	PUNCT
ejpam-4684	401	10	14(1	14(1	NUM
ejpam-4684	401	11	)	)	PUNCT
ejpam-4684	401	12	,	,	PUNCT
ejpam-4684	401	13	112	112	NUM
ejpam-4684	401	14	-	-	SYM
ejpam-4684	401	15	125	125	NUM
ejpam-4684	401	16	.	.	PUNCT