id	sid	tid	token	lemma	pos
ejpam-4577	1	1	european	european	PROPN
ejpam-4577	1	2	journal	journal	PROPN
ejpam-4577	1	3	of	of	ADP
ejpam-4577	1	4	pure	pure	ADJ
ejpam-4577	1	5	and	and	CCONJ
ejpam-4577	1	6	applied	apply	VERB
ejpam-4577	1	7	mathematics	mathematic	NOUN
ejpam-4577	1	8	vol	vol	NOUN
ejpam-4577	1	9	.	.	PROPN
ejpam-4577	2	1	15	15	NUM
ejpam-4577	2	2	,	,	PUNCT
ejpam-4577	2	3	no	no	INTJ
ejpam-4577	2	4	.	.	NOUN
ejpam-4577	2	5	4	4	NUM
ejpam-4577	2	6	,	,	PUNCT
ejpam-4577	2	7	2022	2022	NUM
ejpam-4577	2	8	,	,	PUNCT
ejpam-4577	2	9	1783	1783	NUM
ejpam-4577	2	10	-	-	SYM
ejpam-4577	2	11	1796	1796	NUM
ejpam-4577	2	12	issn	issn	VERB
ejpam-4577	2	13	1307	1307	NUM
ejpam-4577	2	14	-	-	SYM
ejpam-4577	2	15	5543	5543	NUM
ejpam-4577	2	16	–	–	PUNCT
ejpam-4577	2	17	ejpam.com	ejpam.com	X
ejpam-4577	2	18	published	publish	VERB
ejpam-4577	2	19	by	by	ADP
ejpam-4577	2	20	new	new	PROPN
ejpam-4577	2	21	york	york	PROPN
ejpam-4577	2	22	business	business	PROPN
ejpam-4577	2	23	global	global	PROPN
ejpam-4577	2	24	hop	hop	PROPN
ejpam-4577	2	25	independent	independent	PROPN
ejpam-4577	2	26	hop	hop	NOUN
ejpam-4577	2	27	domination	domination	NOUN
ejpam-4577	2	28	in	in	ADP
ejpam-4577	2	29	graphs	graph	NOUN
ejpam-4577	2	30	javier	javier	PROPN
ejpam-4577	2	31	a.	a.	PROPN
ejpam-4577	2	32	hassan	hassan	PROPN
ejpam-4577	2	33	1	1	NUM
ejpam-4577	2	34	,	,	PUNCT
ejpam-4577	2	35	sergio	sergio	PROPN
ejpam-4577	2	36	r.	r.	PROPN
ejpam-4577	2	37	canoy	canoy	PROPN
ejpam-4577	2	38	,	,	PUNCT
ejpam-4577	2	39	jr.1,∗	jr.1,∗	PROPN
ejpam-4577	2	40	1	1	NUM
ejpam-4577	2	41	department	department	NOUN
ejpam-4577	2	42	of	of	ADP
ejpam-4577	2	43	mathematics	mathematic	NOUN
ejpam-4577	2	44	and	and	CCONJ
ejpam-4577	2	45	statistics	statistic	NOUN
ejpam-4577	2	46	,	,	PUNCT
ejpam-4577	2	47	college	college	NOUN
ejpam-4577	2	48	of	of	ADP
ejpam-4577	2	49	science	science	NOUN
ejpam-4577	2	50	and	and	CCONJ
ejpam-4577	2	51	mathematics	mathematic	NOUN
ejpam-4577	2	52	,	,	PUNCT
ejpam-4577	2	53	center	center	NOUN
ejpam-4577	2	54	for	for	ADP
ejpam-4577	2	55	graph	graph	NOUN
ejpam-4577	2	56	theory	theory	NOUN
ejpam-4577	2	57	,	,	PUNCT
ejpam-4577	2	58	premier	premier	PROPN
ejpam-4577	2	59	research	research	PROPN
ejpam-4577	2	60	institute	institute	PROPN
ejpam-4577	2	61	of	of	ADP
ejpam-4577	2	62	science	science	NOUN
ejpam-4577	2	63	and	and	CCONJ
ejpam-4577	2	64	mathematics	mathematic	NOUN
ejpam-4577	2	65	,	,	PUNCT
ejpam-4577	2	66	msu	msu	PROPN
ejpam-4577	2	67	-	-	PUNCT
ejpam-4577	2	68	iligan	iligan	PROPN
ejpam-4577	2	69	institute	institute	PROPN
ejpam-4577	2	70	of	of	ADP
ejpam-4577	2	71	technology	technology	PROPN
ejpam-4577	2	72	,	,	PUNCT
ejpam-4577	2	73	9200	9200	NUM
ejpam-4577	2	74	iligan	iligan	ADJ
ejpam-4577	2	75	city	city	NOUN
ejpam-4577	2	76	,	,	PUNCT
ejpam-4577	2	77	philippines	philippine	NOUN
ejpam-4577	2	78	abstract	abstract	ADJ
ejpam-4577	2	79	.	.	PUNCT
ejpam-4577	3	1	let	let	VERB
ejpam-4577	3	2	g	g	PRON
ejpam-4577	3	3	be	be	AUX
ejpam-4577	3	4	an	an	DET
ejpam-4577	3	5	undirected	undirected	ADJ
ejpam-4577	3	6	graph	graph	NOUN
ejpam-4577	3	7	with	with	ADP
ejpam-4577	3	8	vertex	vertex	NOUN
ejpam-4577	3	9	and	and	CCONJ
ejpam-4577	3	10	edge	edge	NOUN
ejpam-4577	3	11	sets	set	NOUN
ejpam-4577	3	12	v	v	ADP
ejpam-4577	3	13	(	(	PUNCT
ejpam-4577	3	14	g	g	NOUN
ejpam-4577	3	15	)	)	PUNCT
ejpam-4577	3	16	and	and	CCONJ
ejpam-4577	3	17	e(g	e(g	PROPN
ejpam-4577	3	18	)	)	PUNCT
ejpam-4577	3	19	,	,	PUNCT
ejpam-4577	3	20	respectively	respectively	ADV
ejpam-4577	3	21	.	.	PUNCT
ejpam-4577	4	1	a	a	DET
ejpam-4577	4	2	set	set	NOUN
ejpam-4577	4	3	s	s	NOUN
ejpam-4577	4	4	⊆	⊆	NUM
ejpam-4577	4	5	v	v	NOUN
ejpam-4577	4	6	(	(	PUNCT
ejpam-4577	4	7	g	g	NOUN
ejpam-4577	4	8	)	)	PUNCT
ejpam-4577	4	9	is	be	AUX
ejpam-4577	4	10	called	call	VERB
ejpam-4577	4	11	a	a	DET
ejpam-4577	4	12	hop	hop	NOUN
ejpam-4577	4	13	independent	independent	ADJ
ejpam-4577	4	14	hop	hop	NOUN
ejpam-4577	4	15	dominating	dominating	NOUN
ejpam-4577	4	16	set	set	NOUN
ejpam-4577	4	17	of	of	ADP
ejpam-4577	4	18	g	g	PROPN
ejpam-4577	4	19	if	if	SCONJ
ejpam-4577	4	20	s	s	VERB
ejpam-4577	4	21	is	be	AUX
ejpam-4577	4	22	both	both	PRON
ejpam-4577	4	23	hop	hop	ADV
ejpam-4577	4	24	independent	independent	ADJ
ejpam-4577	4	25	and	and	CCONJ
ejpam-4577	4	26	hop	hop	NOUN
ejpam-4577	4	27	dominating	dominating	NOUN
ejpam-4577	4	28	set	set	NOUN
ejpam-4577	4	29	of	of	ADP
ejpam-4577	4	30	g.	g.	PROPN
ejpam-4577	4	31	the	the	DET
ejpam-4577	4	32	minimum	minimum	ADJ
ejpam-4577	4	33	cardinality	cardinality	NOUN
ejpam-4577	4	34	of	of	ADP
ejpam-4577	4	35	hop	hop	PROPN
ejpam-4577	4	36	independent	independent	ADJ
ejpam-4577	4	37	hop	hop	NOUN
ejpam-4577	4	38	dominating	dominating	NOUN
ejpam-4577	4	39	set	set	NOUN
ejpam-4577	4	40	of	of	ADP
ejpam-4577	4	41	g	g	NOUN
ejpam-4577	4	42	,	,	PUNCT
ejpam-4577	4	43	denoted	denote	VERB
ejpam-4577	4	44	by	by	ADP
ejpam-4577	4	45	γhih(g	γhih(g	NOUN
ejpam-4577	4	46	)	)	PUNCT
ejpam-4577	4	47	,	,	PUNCT
ejpam-4577	4	48	is	be	AUX
ejpam-4577	4	49	called	call	VERB
ejpam-4577	4	50	the	the	DET
ejpam-4577	4	51	hop	hop	NOUN
ejpam-4577	4	52	independent	independent	ADJ
ejpam-4577	4	53	hop	hop	NOUN
ejpam-4577	4	54	domination	domination	NOUN
ejpam-4577	4	55	number	number	NOUN
ejpam-4577	4	56	of	of	ADP
ejpam-4577	4	57	g.	g.	PROPN
ejpam-4577	4	58	in	in	ADP
ejpam-4577	4	59	this	this	DET
ejpam-4577	4	60	paper	paper	NOUN
ejpam-4577	4	61	,	,	PUNCT
ejpam-4577	4	62	we	we	PRON
ejpam-4577	4	63	show	show	VERB
ejpam-4577	4	64	that	that	SCONJ
ejpam-4577	4	65	the	the	DET
ejpam-4577	4	66	hop	hop	NOUN
ejpam-4577	4	67	independent	independent	ADJ
ejpam-4577	4	68	hop	hop	NOUN
ejpam-4577	4	69	domination	domination	NOUN
ejpam-4577	4	70	number	number	NOUN
ejpam-4577	4	71	of	of	ADP
ejpam-4577	4	72	a	a	DET
ejpam-4577	4	73	graph	graph	NOUN
ejpam-4577	4	74	g	g	NOUN
ejpam-4577	4	75	lies	lie	NOUN
ejpam-4577	4	76	between	between	ADP
ejpam-4577	4	77	the	the	DET
ejpam-4577	4	78	hop	hop	NOUN
ejpam-4577	4	79	domination	domination	NOUN
ejpam-4577	4	80	number	number	NOUN
ejpam-4577	4	81	and	and	CCONJ
ejpam-4577	4	82	the	the	DET
ejpam-4577	4	83	hop	hop	NOUN
ejpam-4577	4	84	independence	independence	NOUN
ejpam-4577	4	85	number	number	NOUN
ejpam-4577	4	86	of	of	ADP
ejpam-4577	4	87	graph	graph	NOUN
ejpam-4577	4	88	g.	g.	PROPN
ejpam-4577	4	89	we	we	PRON
ejpam-4577	4	90	characterize	characterize	VERB
ejpam-4577	4	91	these	these	DET
ejpam-4577	4	92	types	type	NOUN
ejpam-4577	4	93	of	of	ADP
ejpam-4577	4	94	sets	set	NOUN
ejpam-4577	4	95	in	in	ADP
ejpam-4577	4	96	the	the	DET
ejpam-4577	4	97	shadow	shadow	NOUN
ejpam-4577	4	98	graph	graph	NOUN
ejpam-4577	4	99	,	,	PUNCT
ejpam-4577	4	100	join	join	NOUN
ejpam-4577	4	101	,	,	PUNCT
ejpam-4577	4	102	corona	corona	PROPN
ejpam-4577	4	103	,	,	PUNCT
ejpam-4577	4	104	and	and	CCONJ
ejpam-4577	4	105	lexicographic	lexicographic	ADJ
ejpam-4577	4	106	product	product	NOUN
ejpam-4577	4	107	of	of	ADP
ejpam-4577	4	108	two	two	NUM
ejpam-4577	4	109	graphs	graph	NOUN
ejpam-4577	4	110	.	.	PUNCT
ejpam-4577	5	1	moreover	moreover	ADV
ejpam-4577	5	2	,	,	PUNCT
ejpam-4577	5	3	either	either	CCONJ
ejpam-4577	5	4	exact	exact	ADJ
ejpam-4577	5	5	values	value	NOUN
ejpam-4577	5	6	or	or	CCONJ
ejpam-4577	5	7	bounds	bound	NOUN
ejpam-4577	5	8	of	of	ADP
ejpam-4577	5	9	the	the	DET
ejpam-4577	5	10	hop	hop	NOUN
ejpam-4577	5	11	independent	independent	ADJ
ejpam-4577	5	12	hop	hop	NOUN
ejpam-4577	5	13	domination	domination	NOUN
ejpam-4577	5	14	numbers	number	NOUN
ejpam-4577	5	15	of	of	ADP
ejpam-4577	5	16	these	these	DET
ejpam-4577	5	17	graphs	graph	NOUN
ejpam-4577	5	18	are	be	AUX
ejpam-4577	5	19	given	give	VERB
ejpam-4577	5	20	.	.	PUNCT
ejpam-4577	6	1	2020	2020	NUM
ejpam-4577	6	2	mathematics	mathematic	NOUN
ejpam-4577	6	3	subject	subject	NOUN
ejpam-4577	6	4	classifications	classification	NOUN
ejpam-4577	6	5	:	:	PUNCT
ejpam-4577	6	6	05c69	05c69	X
ejpam-4577	6	7	key	key	ADJ
ejpam-4577	6	8	words	word	NOUN
ejpam-4577	6	9	and	and	CCONJ
ejpam-4577	6	10	phrases	phrase	NOUN
ejpam-4577	6	11	:	:	PUNCT
ejpam-4577	6	12	hop	hop	NOUN
ejpam-4577	6	13	domination	domination	NOUN
ejpam-4577	6	14	,	,	PUNCT
ejpam-4577	6	15	hop	hop	NOUN
ejpam-4577	6	16	domination	domination	NOUN
ejpam-4577	6	17	number	number	NOUN
ejpam-4577	6	18	,	,	PUNCT
ejpam-4577	6	19	hop	hop	NOUN
ejpam-4577	6	20	independent	independent	ADJ
ejpam-4577	6	21	set	set	NOUN
ejpam-4577	6	22	,	,	PUNCT
ejpam-4577	6	23	hop	hop	ADJ
ejpam-4577	6	24	independence	independence	NOUN
ejpam-4577	6	25	number	number	NOUN
ejpam-4577	6	26	,	,	PUNCT
ejpam-4577	6	27	hop	hop	NOUN
ejpam-4577	6	28	independent	independent	ADJ
ejpam-4577	6	29	hop	hop	NOUN
ejpam-4577	6	30	domination	domination	NOUN
ejpam-4577	6	31	number	number	NOUN
ejpam-4577	6	32	1	1	NUM
ejpam-4577	6	33	.	.	PUNCT
ejpam-4577	6	34	introduction	introduction	NOUN
ejpam-4577	6	35	since	since	SCONJ
ejpam-4577	6	36	its	its	PRON
ejpam-4577	6	37	introduction	introduction	NOUN
ejpam-4577	6	38	in	in	ADP
ejpam-4577	6	39	2015	2015	NUM
ejpam-4577	6	40	(	(	PUNCT
ejpam-4577	6	41	see	see	VERB
ejpam-4577	6	42	[	[	X
ejpam-4577	6	43	10	10	NUM
ejpam-4577	6	44	]	]	NUM
ejpam-4577	6	45	)	)	PUNCT
ejpam-4577	6	46	,	,	PUNCT
ejpam-4577	6	47	hop	hop	NOUN
ejpam-4577	6	48	domination	domination	NOUN
ejpam-4577	6	49	has	have	AUX
ejpam-4577	6	50	been	be	AUX
ejpam-4577	6	51	one	one	NUM
ejpam-4577	6	52	of	of	ADP
ejpam-4577	6	53	the	the	DET
ejpam-4577	6	54	topics	topic	NOUN
ejpam-4577	6	55	of	of	ADP
ejpam-4577	6	56	research	research	NOUN
ejpam-4577	6	57	or	or	CCONJ
ejpam-4577	6	58	investigation	investigation	NOUN
ejpam-4577	6	59	in	in	ADP
ejpam-4577	6	60	the	the	DET
ejpam-4577	6	61	area	area	NOUN
ejpam-4577	6	62	.	.	PUNCT
ejpam-4577	7	1	to	to	ADP
ejpam-4577	7	2	date	date	NOUN
ejpam-4577	7	3	,	,	PUNCT
ejpam-4577	7	4	a	a	DET
ejpam-4577	7	5	number	number	NOUN
ejpam-4577	7	6	of	of	ADP
ejpam-4577	7	7	variants	variant	NOUN
ejpam-4577	7	8	of	of	ADP
ejpam-4577	7	9	hop	hop	NOUN
ejpam-4577	7	10	domination	domination	NOUN
ejpam-4577	7	11	have	have	AUX
ejpam-4577	7	12	been	be	AUX
ejpam-4577	7	13	introduced	introduce	VERB
ejpam-4577	7	14	and	and	CCONJ
ejpam-4577	7	15	studied	study	VERB
ejpam-4577	7	16	.	.	PUNCT
ejpam-4577	8	1	the	the	DET
ejpam-4577	8	2	newly	newly	ADV
ejpam-4577	8	3	defined	define	VERB
ejpam-4577	8	4	variations	variation	NOUN
ejpam-4577	8	5	and	and	CCONJ
ejpam-4577	8	6	parameters	parameter	NOUN
ejpam-4577	8	7	are	be	AUX
ejpam-4577	8	8	studied	study	VERB
ejpam-4577	8	9	in	in	ADP
ejpam-4577	8	10	many	many	ADJ
ejpam-4577	8	11	classes	class	NOUN
ejpam-4577	8	12	of	of	ADP
ejpam-4577	8	13	graphs	graph	NOUN
ejpam-4577	8	14	including	include	VERB
ejpam-4577	8	15	those	those	PRON
ejpam-4577	8	16	which	which	PRON
ejpam-4577	8	17	result	result	VERB
ejpam-4577	8	18	from	from	ADP
ejpam-4577	8	19	some	some	DET
ejpam-4577	8	20	binary	binary	ADJ
ejpam-4577	8	21	operations	operation	NOUN
ejpam-4577	8	22	(	(	PUNCT
ejpam-4577	8	23	see	see	VERB
ejpam-4577	8	24	[	[	X
ejpam-4577	8	25	1	1	NUM
ejpam-4577	8	26	]	]	PUNCT
ejpam-4577	8	27	,	,	PUNCT
ejpam-4577	8	28	[	[	X
ejpam-4577	8	29	2	2	NUM
ejpam-4577	8	30	]	]	PUNCT
ejpam-4577	8	31	,	,	PUNCT
ejpam-4577	8	32	[	[	X
ejpam-4577	8	33	4	4	NUM
ejpam-4577	8	34	]	]	PUNCT
ejpam-4577	8	35	,	,	PUNCT
ejpam-4577	8	36	[	[	X
ejpam-4577	8	37	5	5	NUM
ejpam-4577	8	38	]	]	PUNCT
ejpam-4577	8	39	,	,	PUNCT
ejpam-4577	9	1	[	[	X
ejpam-4577	9	2	6	6	NUM
ejpam-4577	9	3	]	]	PUNCT
ejpam-4577	9	4	,	,	PUNCT
ejpam-4577	9	5	[	[	X
ejpam-4577	9	6	7	7	NUM
ejpam-4577	9	7	]	]	PUNCT
ejpam-4577	9	8	,	,	PUNCT
ejpam-4577	9	9	[	[	X
ejpam-4577	9	10	9	9	NUM
ejpam-4577	9	11	]	]	PUNCT
ejpam-4577	9	12	,	,	PUNCT
ejpam-4577	9	13	and	and	CCONJ
ejpam-4577	9	14	[	[	X
ejpam-4577	9	15	11	11	NUM
ejpam-4577	9	16	]	]	NUM
ejpam-4577	9	17	)	)	PUNCT
ejpam-4577	9	18	.	.	PUNCT
ejpam-4577	10	1	recently	recently	ADV
ejpam-4577	10	2	,	,	PUNCT
ejpam-4577	10	3	hassan	hassan	PROPN
ejpam-4577	10	4	et	et	PROPN
ejpam-4577	10	5	al	al	PROPN
ejpam-4577	10	6	.	.	PUNCT
ejpam-4577	11	1	[	[	X
ejpam-4577	11	2	3	3	X
ejpam-4577	11	3	]	]	PUNCT
ejpam-4577	11	4	introduced	introduce	VERB
ejpam-4577	11	5	the	the	DET
ejpam-4577	11	6	concept	concept	NOUN
ejpam-4577	11	7	of	of	ADP
ejpam-4577	11	8	hop	hop	NOUN
ejpam-4577	11	9	independent	independent	ADJ
ejpam-4577	11	10	set	set	NOUN
ejpam-4577	11	11	in	in	ADP
ejpam-4577	11	12	a	a	DET
ejpam-4577	11	13	graph	graph	NOUN
ejpam-4577	11	14	and	and	CCONJ
ejpam-4577	11	15	defined	define	VERB
ejpam-4577	11	16	the	the	DET
ejpam-4577	11	17	parameter	parameter	NOUN
ejpam-4577	11	18	called	call	VERB
ejpam-4577	11	19	hop	hop	PROPN
ejpam-4577	11	20	independence	independence	NOUN
ejpam-4577	11	21	number	number	NOUN
ejpam-4577	11	22	of	of	ADP
ejpam-4577	11	23	a	a	DET
ejpam-4577	11	24	graph	graph	NOUN
ejpam-4577	11	25	.	.	PUNCT
ejpam-4577	12	1	the	the	DET
ejpam-4577	12	2	hop	hop	NOUN
ejpam-4577	12	3	independence	independence	NOUN
ejpam-4577	12	4	number	number	NOUN
ejpam-4577	12	5	may	may	AUX
ejpam-4577	12	6	be	be	AUX
ejpam-4577	12	7	equal	equal	ADJ
ejpam-4577	12	8	or	or	CCONJ
ejpam-4577	12	9	less	less	ADJ
ejpam-4577	12	10	or	or	CCONJ
ejpam-4577	12	11	greater	great	ADJ
ejpam-4577	12	12	than	than	ADP
ejpam-4577	12	13	the	the	DET
ejpam-4577	12	14	independence	independence	NOUN
ejpam-4577	12	15	number	number	NOUN
ejpam-4577	12	16	of	of	ADP
ejpam-4577	12	17	graph	graph	NOUN
ejpam-4577	12	18	.	.	PUNCT
ejpam-4577	13	1	a	a	DET
ejpam-4577	13	2	result	result	NOUN
ejpam-4577	13	3	in	in	ADP
ejpam-4577	13	4	[	[	X
ejpam-4577	13	5	3	3	X
ejpam-4577	13	6	]	]	PUNCT
ejpam-4577	13	7	shows	show	VERB
ejpam-4577	13	8	that	that	SCONJ
ejpam-4577	13	9	the	the	DET
ejpam-4577	13	10	absolute	absolute	ADJ
ejpam-4577	13	11	difference	difference	NOUN
ejpam-4577	13	12	between	between	ADP
ejpam-4577	13	13	the	the	DET
ejpam-4577	13	14	independence	independence	NOUN
ejpam-4577	13	15	number	number	NOUN
ejpam-4577	13	16	and	and	CCONJ
ejpam-4577	13	17	the	the	DET
ejpam-4577	13	18	hop	hop	NOUN
ejpam-4577	13	19	independence	independence	NOUN
ejpam-4577	13	20	number	number	NOUN
ejpam-4577	13	21	of	of	ADP
ejpam-4577	13	22	a	a	DET
ejpam-4577	13	23	graph	graph	NOUN
ejpam-4577	13	24	can	can	AUX
ejpam-4577	13	25	be	be	AUX
ejpam-4577	13	26	made	make	VERB
ejpam-4577	13	27	arbitrarily	arbitrarily	ADV
ejpam-4577	13	28	large	large	ADJ
ejpam-4577	13	29	.	.	PUNCT
ejpam-4577	14	1	moreover	moreover	ADV
ejpam-4577	14	2	,	,	PUNCT
ejpam-4577	14	3	it	it	PRON
ejpam-4577	14	4	was	be	AUX
ejpam-4577	14	5	pointed	point	VERB
ejpam-4577	14	6	out	out	ADP
ejpam-4577	14	7	that	that	SCONJ
ejpam-4577	14	8	the	the	DET
ejpam-4577	14	9	maximum	maximum	ADJ
ejpam-4577	14	10	hop	hop	NOUN
ejpam-4577	14	11	independent	independent	ADJ
ejpam-4577	14	12	set	set	NOUN
ejpam-4577	14	13	in	in	ADP
ejpam-4577	14	14	a	a	DET
ejpam-4577	14	15	graph	graph	NOUN
ejpam-4577	14	16	g	g	NOUN
ejpam-4577	14	17	forms	form	NOUN
ejpam-4577	14	18	a	a	DET
ejpam-4577	14	19	hop	hop	NOUN
ejpam-4577	14	20	dominating	dominating	NOUN
ejpam-4577	14	21	set	set	NOUN
ejpam-4577	14	22	,	,	PUNCT
ejpam-4577	14	23	that	that	ADV
ejpam-4577	14	24	is	is	ADV
ejpam-4577	14	25	,	,	PUNCT
ejpam-4577	14	26	the	the	DET
ejpam-4577	14	27	hop	hop	NOUN
ejpam-4577	14	28	independence	independence	NOUN
ejpam-4577	14	29	number	number	NOUN
ejpam-4577	14	30	of	of	ADP
ejpam-4577	14	31	a	a	DET
ejpam-4577	14	32	graph	graph	NOUN
ejpam-4577	14	33	g	g	NOUN
ejpam-4577	14	34	is	be	AUX
ejpam-4577	14	35	at	at	ADP
ejpam-4577	14	36	least	least	ADJ
ejpam-4577	14	37	equal	equal	ADJ
ejpam-4577	14	38	to	to	ADP
ejpam-4577	14	39	the	the	DET
ejpam-4577	14	40	hop	hop	NOUN
ejpam-4577	14	41	domination	domination	NOUN
ejpam-4577	14	42	∗corresponding	∗corresponde	VERB
ejpam-4577	14	43	author	author	NOUN
ejpam-4577	14	44	.	.	PUNCT
ejpam-4577	15	1	doi	doi	NOUN
ejpam-4577	15	2	:	:	PUNCT
ejpam-4577	15	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4577	https://doi.org/10.29020/nybg.ejpam.v15i4.4577	PROPN
ejpam-4577	15	4	email	email	NOUN
ejpam-4577	15	5	addresses	address	VERB
ejpam-4577	15	6	:	:	PUNCT
ejpam-4577	16	1	javier.hassan@g.msuiit.edu.ph	javier.hassan@g.msuiit.edu.ph	PROPN
ejpam-4577	16	2	(	(	PUNCT
ejpam-4577	16	3	j.	j.	PROPN
ejpam-4577	16	4	hassan	hassan	PROPN
ejpam-4577	16	5	)	)	PUNCT
ejpam-4577	16	6	,	,	PUNCT
ejpam-4577	16	7	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4577	16	8	(	(	PUNCT
ejpam-4577	16	9	s.	s.	PROPN
ejpam-4577	16	10	canoy	canoy	PROPN
ejpam-4577	16	11	)	)	PUNCT
ejpam-4577	16	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4577	16	13	1783	1783	NUM
ejpam-4577	17	1	©	©	ADP
ejpam-4577	17	2	2022	2022	NUM
ejpam-4577	17	3	ejpam	ejpam	VERB
ejpam-4577	17	4	all	all	DET
ejpam-4577	17	5	rights	right	NOUN
ejpam-4577	17	6	reserved	reserve	VERB
ejpam-4577	17	7	.	.	PUNCT
ejpam-4577	18	1	j.	j.	PROPN
ejpam-4577	18	2	hassan	hassan	PROPN
ejpam-4577	18	3	,	,	PUNCT
ejpam-4577	18	4	s.	s.	PROPN
ejpam-4577	18	5	canoy	canoy	PROPN
ejpam-4577	18	6	/	/	SYM
ejpam-4577	18	7	eur	eur	PROPN
ejpam-4577	18	8	.	.	PUNCT
ejpam-4577	19	1	j.	j.	PROPN
ejpam-4577	19	2	pure	pure	PROPN
ejpam-4577	19	3	appl	appl	PROPN
ejpam-4577	19	4	.	.	PROPN
ejpam-4577	19	5	math	math	PROPN
ejpam-4577	19	6	,	,	PUNCT
ejpam-4577	19	7	15	15	NUM
ejpam-4577	19	8	(	(	PUNCT
ejpam-4577	19	9	4	4	NUM
ejpam-4577	19	10	)	)	PUNCT
ejpam-4577	19	11	(	(	PUNCT
ejpam-4577	19	12	2022	2022	NUM
ejpam-4577	19	13	)	)	PUNCT
ejpam-4577	19	14	,	,	PUNCT
ejpam-4577	19	15	1783	1783	NUM
ejpam-4577	19	16	-	-	SYM
ejpam-4577	19	17	1796	1796	NUM
ejpam-4577	19	18	1784	1784	NUM
ejpam-4577	19	19	number	number	NOUN
ejpam-4577	19	20	of	of	ADP
ejpam-4577	19	21	g.	g.	PROPN
ejpam-4577	19	22	this	this	DET
ejpam-4577	19	23	observation	observation	NOUN
ejpam-4577	19	24	,	,	PUNCT
ejpam-4577	19	25	the	the	DET
ejpam-4577	19	26	way	way	NOUN
ejpam-4577	19	27	the	the	DET
ejpam-4577	19	28	variation	variation	NOUN
ejpam-4577	19	29	“	"	PUNCT
ejpam-4577	19	30	independent	independent	ADJ
ejpam-4577	19	31	domination	domination	NOUN
ejpam-4577	19	32	”	"	PUNCT
ejpam-4577	19	33	for	for	ADP
ejpam-4577	19	34	the	the	DET
ejpam-4577	19	35	standard	standard	ADJ
ejpam-4577	19	36	domination	domination	NOUN
ejpam-4577	19	37	concept	concept	NOUN
ejpam-4577	19	38	was	be	AUX
ejpam-4577	19	39	introduced	introduce	VERB
ejpam-4577	19	40	,	,	PUNCT
ejpam-4577	19	41	and	and	CCONJ
ejpam-4577	19	42	the	the	DET
ejpam-4577	19	43	possible	possible	ADJ
ejpam-4577	19	44	future	future	ADJ
ejpam-4577	19	45	applications	application	NOUN
ejpam-4577	19	46	it	it	PRON
ejpam-4577	19	47	may	may	AUX
ejpam-4577	19	48	offer	offer	VERB
ejpam-4577	19	49	researchers	researcher	NOUN
ejpam-4577	19	50	in	in	ADP
ejpam-4577	19	51	the	the	DET
ejpam-4577	19	52	field	field	NOUN
ejpam-4577	19	53	,	,	PUNCT
ejpam-4577	19	54	are	be	AUX
ejpam-4577	19	55	some	some	PRON
ejpam-4577	19	56	of	of	ADP
ejpam-4577	19	57	the	the	DET
ejpam-4577	19	58	motivations	motivation	NOUN
ejpam-4577	19	59	the	the	DET
ejpam-4577	19	60	authors	author	NOUN
ejpam-4577	19	61	have	have	VERB
ejpam-4577	19	62	for	for	ADP
ejpam-4577	19	63	introducing	introduce	VERB
ejpam-4577	19	64	and	and	CCONJ
ejpam-4577	19	65	studying	study	VERB
ejpam-4577	19	66	hop	hop	NOUN
ejpam-4577	19	67	independent	independent	ADJ
ejpam-4577	19	68	hop	hop	NOUN
ejpam-4577	19	69	domination	domination	NOUN
ejpam-4577	19	70	in	in	ADP
ejpam-4577	19	71	a	a	DET
ejpam-4577	19	72	graph	graph	NOUN
ejpam-4577	19	73	.	.	PUNCT
ejpam-4577	20	1	the	the	DET
ejpam-4577	20	2	newly	newly	ADV
ejpam-4577	20	3	defined	define	VERB
ejpam-4577	20	4	concept	concept	NOUN
ejpam-4577	20	5	and	and	CCONJ
ejpam-4577	20	6	the	the	DET
ejpam-4577	20	7	corresponding	corresponding	ADJ
ejpam-4577	20	8	parameter	parameter	NOUN
ejpam-4577	20	9	will	will	AUX
ejpam-4577	20	10	be	be	AUX
ejpam-4577	20	11	studied	study	VERB
ejpam-4577	20	12	initially	initially	ADV
ejpam-4577	20	13	for	for	ADP
ejpam-4577	20	14	some	some	DET
ejpam-4577	20	15	graphs	graph	NOUN
ejpam-4577	20	16	including	include	VERB
ejpam-4577	20	17	those	those	PRON
ejpam-4577	20	18	that	that	PRON
ejpam-4577	20	19	result	result	VERB
ejpam-4577	20	20	from	from	ADP
ejpam-4577	20	21	some	some	DET
ejpam-4577	20	22	binary	binary	ADJ
ejpam-4577	20	23	operations	operation	NOUN
ejpam-4577	20	24	.	.	PUNCT
ejpam-4577	21	1	2	2	X
ejpam-4577	21	2	.	.	X
ejpam-4577	21	3	terminology	terminology	NOUN
ejpam-4577	21	4	and	and	CCONJ
ejpam-4577	21	5	notation	notation	NOUN
ejpam-4577	21	6	two	two	NUM
ejpam-4577	21	7	vertices	vertex	NOUN
ejpam-4577	21	8	u	u	NOUN
ejpam-4577	21	9	,	,	PUNCT
ejpam-4577	21	10	v	v	NOUN
ejpam-4577	21	11	of	of	ADP
ejpam-4577	21	12	a	a	DET
ejpam-4577	21	13	graph	graph	NOUN
ejpam-4577	21	14	g	g	NOUN
ejpam-4577	21	15	are	be	AUX
ejpam-4577	21	16	adjacent	adjacent	ADJ
ejpam-4577	21	17	,	,	PUNCT
ejpam-4577	21	18	or	or	CCONJ
ejpam-4577	21	19	neighbors	neighbor	NOUN
ejpam-4577	21	20	,	,	PUNCT
ejpam-4577	21	21	if	if	SCONJ
ejpam-4577	21	22	uv	uv	NOUN
ejpam-4577	21	23	is	be	AUX
ejpam-4577	21	24	an	an	DET
ejpam-4577	21	25	edge	edge	NOUN
ejpam-4577	21	26	of	of	ADP
ejpam-4577	21	27	g.	g.	PROPN
ejpam-4577	21	28	moreover	moreover	ADV
ejpam-4577	21	29	,	,	PUNCT
ejpam-4577	21	30	an	an	DET
ejpam-4577	21	31	edge	edge	NOUN
ejpam-4577	21	32	uv	uv	NOUN
ejpam-4577	21	33	of	of	ADP
ejpam-4577	21	34	g	g	PROPN
ejpam-4577	21	35	is	be	AUX
ejpam-4577	21	36	incident	incident	NOUN
ejpam-4577	21	37	to	to	ADP
ejpam-4577	21	38	two	two	NUM
ejpam-4577	21	39	vertices	vertex	NOUN
ejpam-4577	21	40	u	u	NOUN
ejpam-4577	21	41	,	,	PUNCT
ejpam-4577	21	42	v	v	NOUN
ejpam-4577	21	43	of	of	ADP
ejpam-4577	21	44	g.	g.	PROPN
ejpam-4577	21	45	the	the	DET
ejpam-4577	21	46	set	set	NOUN
ejpam-4577	21	47	of	of	ADP
ejpam-4577	21	48	neighbors	neighbor	NOUN
ejpam-4577	21	49	of	of	ADP
ejpam-4577	21	50	a	a	DET
ejpam-4577	21	51	vertex	vertex	NOUN
ejpam-4577	21	52	u	u	NOUN
ejpam-4577	21	53	in	in	ADP
ejpam-4577	21	54	g	g	NOUN
ejpam-4577	21	55	,	,	PUNCT
ejpam-4577	21	56	denoted	denote	VERB
ejpam-4577	21	57	by	by	ADP
ejpam-4577	21	58	ng(u	ng(u	NOUN
ejpam-4577	21	59	)	)	PUNCT
ejpam-4577	21	60	,	,	PUNCT
ejpam-4577	21	61	is	be	AUX
ejpam-4577	21	62	called	call	VERB
ejpam-4577	21	63	the	the	DET
ejpam-4577	21	64	open	open	ADJ
ejpam-4577	21	65	neighborhood	neighborhood	NOUN
ejpam-4577	21	66	of	of	ADP
ejpam-4577	21	67	u	u	PROPN
ejpam-4577	21	68	in	in	ADP
ejpam-4577	21	69	g.	g.	PROPN
ejpam-4577	21	70	the	the	DET
ejpam-4577	21	71	closed	close	VERB
ejpam-4577	21	72	neighborhood	neighborhood	NOUN
ejpam-4577	21	73	of	of	ADP
ejpam-4577	21	74	u	u	NOUN
ejpam-4577	21	75	in	in	ADP
ejpam-4577	21	76	g	g	PROPN
ejpam-4577	21	77	is	be	AUX
ejpam-4577	21	78	the	the	DET
ejpam-4577	21	79	set	set	NOUN
ejpam-4577	21	80	ng[u	ng[u	PROPN
ejpam-4577	21	81	]	]	X
ejpam-4577	21	82	=	=	SYM
ejpam-4577	21	83	ng(u	ng(u	PROPN
ejpam-4577	21	84	)	)	PUNCT
ejpam-4577	21	85	∪	∪	NOUN
ejpam-4577	21	86	{	{	PUNCT
ejpam-4577	21	87	u	u	NOUN
ejpam-4577	21	88	}	}	PUNCT
ejpam-4577	21	89	.	.	PUNCT
ejpam-4577	22	1	if	if	SCONJ
ejpam-4577	22	2	x	x	PROPN
ejpam-4577	22	3	⊆	⊆	NUM
ejpam-4577	22	4	v	v	X
ejpam-4577	22	5	(	(	PUNCT
ejpam-4577	22	6	g	g	NOUN
ejpam-4577	22	7	)	)	PUNCT
ejpam-4577	22	8	,	,	PUNCT
ejpam-4577	22	9	the	the	DET
ejpam-4577	22	10	open	open	ADJ
ejpam-4577	22	11	neighborhood	neighborhood	NOUN
ejpam-4577	22	12	of	of	ADP
ejpam-4577	22	13	x	x	PUNCT
ejpam-4577	22	14	in	in	ADP
ejpam-4577	22	15	g	g	PROPN
ejpam-4577	22	16	is	be	AUX
ejpam-4577	22	17	the	the	DET
ejpam-4577	22	18	set	set	NOUN
ejpam-4577	22	19	ng(x	ng(x	NUM
ejpam-4577	22	20	)	)	PUNCT
ejpam-4577	23	1	=	=	SYM
ejpam-4577	23	2	⋃	⋃	NOUN
ejpam-4577	23	3	u∈x	u∈x	NOUN
ejpam-4577	23	4	ng(u	ng(u	NOUN
ejpam-4577	23	5	)	)	PUNCT
ejpam-4577	23	6	.	.	PUNCT
ejpam-4577	24	1	the	the	DET
ejpam-4577	24	2	closed	closed	ADJ
ejpam-4577	24	3	neighborhood	neighborhood	NOUN
ejpam-4577	24	4	of	of	ADP
ejpam-4577	24	5	x	x	PUNCT
ejpam-4577	24	6	in	in	ADP
ejpam-4577	24	7	g	g	PROPN
ejpam-4577	24	8	is	be	AUX
ejpam-4577	24	9	the	the	DET
ejpam-4577	24	10	set	set	NOUN
ejpam-4577	24	11	ng[x	ng[x	PROPN
ejpam-4577	24	12	]	]	X
ejpam-4577	24	13	=	=	PUNCT
ejpam-4577	24	14	ng(x	ng(x	X
ejpam-4577	24	15	)	)	PUNCT
ejpam-4577	24	16	∪x	∪x	X
ejpam-4577	24	17	.	.	PUNCT
ejpam-4577	25	1	let	let	VERB
ejpam-4577	25	2	g	g	PRON
ejpam-4577	25	3	be	be	AUX
ejpam-4577	25	4	a	a	DET
ejpam-4577	25	5	graph	graph	NOUN
ejpam-4577	25	6	.	.	PUNCT
ejpam-4577	26	1	a	a	DET
ejpam-4577	26	2	set	set	NOUN
ejpam-4577	26	3	d	d	NOUN
ejpam-4577	26	4	⊆	⊆	NUM
ejpam-4577	26	5	v	v	ADP
ejpam-4577	26	6	(	(	PUNCT
ejpam-4577	26	7	g	g	NOUN
ejpam-4577	26	8	)	)	PUNCT
ejpam-4577	26	9	is	be	AUX
ejpam-4577	26	10	a	a	DET
ejpam-4577	26	11	dominating	dominating	NOUN
ejpam-4577	26	12	set	set	NOUN
ejpam-4577	26	13	of	of	ADP
ejpam-4577	26	14	g	g	PROPN
ejpam-4577	26	15	if	if	SCONJ
ejpam-4577	26	16	for	for	ADP
ejpam-4577	26	17	every	every	DET
ejpam-4577	26	18	v	v	NUM
ejpam-4577	26	19	∈	∈	NOUN
ejpam-4577	26	20	v	v	NOUN
ejpam-4577	26	21	(	(	PUNCT
ejpam-4577	26	22	g	g	NOUN
ejpam-4577	26	23	)	)	PUNCT
ejpam-4577	26	24	\d	\d	NOUN
ejpam-4577	26	25	,	,	PUNCT
ejpam-4577	26	26	there	there	PRON
ejpam-4577	26	27	exists	exist	VERB
ejpam-4577	26	28	u	u	NOUN
ejpam-4577	26	29	∈	∈	PROPN
ejpam-4577	26	30	d	d	ADP
ejpam-4577	26	31	such	such	ADJ
ejpam-4577	26	32	that	that	DET
ejpam-4577	26	33	uv	uv	PROPN
ejpam-4577	26	34	∈	∈	PROPN
ejpam-4577	26	35	e(g	e(g	PROPN
ejpam-4577	26	36	)	)	PUNCT
ejpam-4577	26	37	,	,	PUNCT
ejpam-4577	26	38	that	that	ADV
ejpam-4577	26	39	is	is	ADV
ejpam-4577	26	40	,	,	PUNCT
ejpam-4577	26	41	ng[d	ng[d	PROPN
ejpam-4577	26	42	]	]	PUNCT
ejpam-4577	26	43	=	=	SYM
ejpam-4577	26	44	v	v	X
ejpam-4577	26	45	(	(	PUNCT
ejpam-4577	26	46	g	g	NOUN
ejpam-4577	26	47	)	)	PUNCT
ejpam-4577	26	48	.	.	PUNCT
ejpam-4577	27	1	the	the	DET
ejpam-4577	27	2	domination	domination	NOUN
ejpam-4577	27	3	number	number	NOUN
ejpam-4577	27	4	of	of	ADP
ejpam-4577	27	5	g	g	NOUN
ejpam-4577	27	6	,	,	PUNCT
ejpam-4577	27	7	denoted	denote	VERB
ejpam-4577	27	8	by	by	ADP
ejpam-4577	27	9	γ(g	γ(g	PROPN
ejpam-4577	27	10	)	)	PUNCT
ejpam-4577	27	11	,	,	PUNCT
ejpam-4577	27	12	is	be	AUX
ejpam-4577	27	13	the	the	DET
ejpam-4577	27	14	minimum	minimum	ADJ
ejpam-4577	27	15	cardinality	cardinality	NOUN
ejpam-4577	27	16	of	of	ADP
ejpam-4577	27	17	a	a	DET
ejpam-4577	27	18	dominating	dominating	NOUN
ejpam-4577	27	19	set	set	NOUN
ejpam-4577	27	20	of	of	ADP
ejpam-4577	27	21	g.	g.	PROPN
ejpam-4577	27	22	any	any	DET
ejpam-4577	27	23	dominating	dominating	NOUN
ejpam-4577	27	24	set	set	NOUN
ejpam-4577	27	25	d	d	NOUN
ejpam-4577	27	26	of	of	ADP
ejpam-4577	27	27	g	g	NOUN
ejpam-4577	27	28	with	with	ADP
ejpam-4577	27	29	cardinality	cardinality	PROPN
ejpam-4577	27	30	γ(g	γ(g	PROPN
ejpam-4577	27	31	)	)	PUNCT
ejpam-4577	27	32	,	,	PUNCT
ejpam-4577	27	33	is	be	AUX
ejpam-4577	27	34	called	call	VERB
ejpam-4577	27	35	a	a	DET
ejpam-4577	27	36	γ	γ	NOUN
ejpam-4577	27	37	-	-	PUNCT
ejpam-4577	27	38	set	set	NOUN
ejpam-4577	27	39	of	of	ADP
ejpam-4577	27	40	g.	g.	PROPN
ejpam-4577	27	41	let	let	VERB
ejpam-4577	27	42	g	g	NOUN
ejpam-4577	27	43	be	be	AUX
ejpam-4577	27	44	a	a	DET
ejpam-4577	27	45	graph	graph	NOUN
ejpam-4577	27	46	.	.	PUNCT
ejpam-4577	28	1	a	a	DET
ejpam-4577	28	2	set	set	NOUN
ejpam-4577	28	3	d	d	NOUN
ejpam-4577	28	4	⊆	⊆	NUM
ejpam-4577	28	5	v	v	ADP
ejpam-4577	28	6	(	(	PUNCT
ejpam-4577	28	7	g	g	NOUN
ejpam-4577	28	8	)	)	PUNCT
ejpam-4577	28	9	is	be	AUX
ejpam-4577	28	10	a	a	DET
ejpam-4577	28	11	total	total	ADJ
ejpam-4577	28	12	dominating	dominating	NOUN
ejpam-4577	28	13	set	set	NOUN
ejpam-4577	28	14	of	of	ADP
ejpam-4577	28	15	g	g	PROPN
ejpam-4577	28	16	if	if	SCONJ
ejpam-4577	28	17	for	for	ADP
ejpam-4577	28	18	every	every	DET
ejpam-4577	28	19	v	v	NUM
ejpam-4577	28	20	∈	∈	NOUN
ejpam-4577	28	21	v	v	NOUN
ejpam-4577	28	22	(	(	PUNCT
ejpam-4577	28	23	g	g	NOUN
ejpam-4577	28	24	)	)	PUNCT
ejpam-4577	28	25	,	,	PUNCT
ejpam-4577	28	26	there	there	PRON
ejpam-4577	28	27	exists	exist	VERB
ejpam-4577	28	28	u	u	NOUN
ejpam-4577	28	29	∈	∈	PROPN
ejpam-4577	28	30	d	d	ADP
ejpam-4577	28	31	such	such	ADJ
ejpam-4577	28	32	that	that	DET
ejpam-4577	28	33	uv	uv	PROPN
ejpam-4577	28	34	∈	∈	PROPN
ejpam-4577	28	35	e(g	e(g	PROPN
ejpam-4577	28	36	)	)	PUNCT
ejpam-4577	28	37	,	,	PUNCT
ejpam-4577	28	38	that	that	ADV
ejpam-4577	28	39	is	is	ADV
ejpam-4577	28	40	,	,	PUNCT
ejpam-4577	28	41	ng(d	ng(d	PUNCT
ejpam-4577	28	42	)	)	PUNCT
ejpam-4577	28	43	=	=	SYM
ejpam-4577	28	44	v	v	X
ejpam-4577	28	45	(	(	PUNCT
ejpam-4577	28	46	g	g	NOUN
ejpam-4577	28	47	)	)	PUNCT
ejpam-4577	28	48	.	.	PUNCT
ejpam-4577	29	1	the	the	DET
ejpam-4577	29	2	total	total	ADJ
ejpam-4577	29	3	domination	domination	NOUN
ejpam-4577	29	4	number	number	NOUN
ejpam-4577	29	5	of	of	ADP
ejpam-4577	29	6	g	g	NOUN
ejpam-4577	29	7	,	,	PUNCT
ejpam-4577	29	8	denoted	denote	VERB
ejpam-4577	29	9	by	by	ADP
ejpam-4577	29	10	γt(g	γt(g	NOUN
ejpam-4577	29	11	)	)	PUNCT
ejpam-4577	29	12	,	,	PUNCT
ejpam-4577	29	13	is	be	AUX
ejpam-4577	29	14	the	the	DET
ejpam-4577	29	15	minimum	minimum	ADJ
ejpam-4577	29	16	cardinality	cardinality	NOUN
ejpam-4577	29	17	of	of	ADP
ejpam-4577	29	18	a	a	DET
ejpam-4577	29	19	total	total	ADJ
ejpam-4577	29	20	dominating	dominating	NOUN
ejpam-4577	29	21	set	set	NOUN
ejpam-4577	29	22	of	of	ADP
ejpam-4577	29	23	g.	g.	PROPN
ejpam-4577	29	24	any	any	DET
ejpam-4577	29	25	total	total	ADJ
ejpam-4577	29	26	dominating	dominating	NOUN
ejpam-4577	29	27	set	set	VERB
ejpam-4577	29	28	with	with	ADP
ejpam-4577	29	29	cardinality	cardinality	NOUN
ejpam-4577	29	30	equal	equal	ADJ
ejpam-4577	29	31	to	to	ADP
ejpam-4577	29	32	γt(g	γt(g	NOUN
ejpam-4577	29	33	)	)	PUNCT
ejpam-4577	29	34	is	be	AUX
ejpam-4577	29	35	called	call	VERB
ejpam-4577	29	36	a	a	DET
ejpam-4577	29	37	γt	γt	NOUN
ejpam-4577	29	38	-	-	NOUN
ejpam-4577	29	39	set	set	NOUN
ejpam-4577	29	40	.	.	PUNCT
ejpam-4577	30	1	a	a	DET
ejpam-4577	30	2	vertex	vertex	NOUN
ejpam-4577	30	3	v	v	NOUN
ejpam-4577	30	4	in	in	ADP
ejpam-4577	30	5	g	g	PROPN
ejpam-4577	30	6	is	be	AUX
ejpam-4577	30	7	a	a	DET
ejpam-4577	30	8	hop	hop	NOUN
ejpam-4577	30	9	neighbor	neighbor	NOUN
ejpam-4577	30	10	of	of	ADP
ejpam-4577	30	11	vertex	vertex	NOUN
ejpam-4577	30	12	u	u	NOUN
ejpam-4577	30	13	in	in	ADP
ejpam-4577	30	14	g	g	PROPN
ejpam-4577	30	15	if	if	SCONJ
ejpam-4577	30	16	dg(u	dg(u	NOUN
ejpam-4577	30	17	,	,	PUNCT
ejpam-4577	30	18	v	v	NOUN
ejpam-4577	30	19	)	)	PUNCT
ejpam-4577	30	20	=	=	SYM
ejpam-4577	30	21	2	2	X
ejpam-4577	30	22	.	.	X
ejpam-4577	31	1	the	the	DET
ejpam-4577	31	2	set	set	ADJ
ejpam-4577	31	3	n2	n2	ADJ
ejpam-4577	31	4	g(u	g(u	PROPN
ejpam-4577	31	5	)	)	PUNCT
ejpam-4577	31	6	=	=	PRON
ejpam-4577	31	7	{	{	PUNCT
ejpam-4577	31	8	v	v	NUM
ejpam-4577	31	9	∈	∈	NOUN
ejpam-4577	31	10	v	v	NOUN
ejpam-4577	31	11	(	(	PUNCT
ejpam-4577	31	12	g	g	NOUN
ejpam-4577	31	13	)	)	PUNCT
ejpam-4577	31	14	:	:	PUNCT
ejpam-4577	31	15	dg(v	dg(v	X
ejpam-4577	31	16	,	,	PUNCT
ejpam-4577	31	17	u	u	NOUN
ejpam-4577	31	18	)	)	PUNCT
ejpam-4577	31	19	=	=	SYM
ejpam-4577	31	20	2	2	X
ejpam-4577	31	21	}	}	PUNCT
ejpam-4577	31	22	is	be	AUX
ejpam-4577	31	23	called	call	VERB
ejpam-4577	31	24	the	the	DET
ejpam-4577	31	25	open	open	ADJ
ejpam-4577	31	26	hop	hop	NOUN
ejpam-4577	31	27	neighborhood	neighborhood	NOUN
ejpam-4577	31	28	of	of	ADP
ejpam-4577	31	29	u.	u.	PROPN
ejpam-4577	31	30	the	the	DET
ejpam-4577	31	31	closed	closed	ADJ
ejpam-4577	31	32	hop	hop	NOUN
ejpam-4577	31	33	neighborhood	neighborhood	NOUN
ejpam-4577	31	34	of	of	ADP
ejpam-4577	31	35	u	u	PROPN
ejpam-4577	31	36	in	in	ADP
ejpam-4577	31	37	g	g	PROPN
ejpam-4577	31	38	is	be	AUX
ejpam-4577	31	39	given	give	VERB
ejpam-4577	31	40	by	by	ADP
ejpam-4577	31	41	n2	n2	PROPN
ejpam-4577	31	42	g[u	g[u	PROPN
ejpam-4577	31	43	]	]	X
ejpam-4577	31	44	=	=	SYM
ejpam-4577	31	45	n2	n2	ADJ
ejpam-4577	31	46	g(u	g(u	PROPN
ejpam-4577	31	47	)	)	PUNCT
ejpam-4577	31	48	∪	∪	NOUN
ejpam-4577	31	49	{	{	PUNCT
ejpam-4577	31	50	u	u	NOUN
ejpam-4577	31	51	}	}	PUNCT
ejpam-4577	31	52	.	.	PUNCT
ejpam-4577	32	1	the	the	DET
ejpam-4577	32	2	open	open	ADJ
ejpam-4577	32	3	hop	hop	NOUN
ejpam-4577	32	4	neighborhood	neighborhood	NOUN
ejpam-4577	32	5	of	of	ADP
ejpam-4577	32	6	x	x	PROPN
ejpam-4577	32	7	⊆	⊆	NUM
ejpam-4577	32	8	v	v	ADP
ejpam-4577	32	9	(	(	PUNCT
ejpam-4577	32	10	g	g	NOUN
ejpam-4577	32	11	)	)	PUNCT
ejpam-4577	32	12	is	be	AUX
ejpam-4577	32	13	the	the	DET
ejpam-4577	32	14	set	set	ADJ
ejpam-4577	32	15	n2	n2	ADJ
ejpam-4577	32	16	g(x	g(x	NOUN
ejpam-4577	32	17	)	)	PUNCT
ejpam-4577	33	1	=	=	SYM
ejpam-4577	33	2	⋃	⋃	NOUN
ejpam-4577	33	3	u∈x	u∈x	ADJ
ejpam-4577	33	4	n2	n2	NOUN
ejpam-4577	33	5	g(u	g(u	PROPN
ejpam-4577	33	6	)	)	PUNCT
ejpam-4577	33	7	.	.	PUNCT
ejpam-4577	34	1	the	the	DET
ejpam-4577	34	2	closed	closed	ADJ
ejpam-4577	34	3	hop	hop	NOUN
ejpam-4577	34	4	neighborhood	neighborhood	NOUN
ejpam-4577	34	5	of	of	ADP
ejpam-4577	34	6	x	x	PUNCT
ejpam-4577	34	7	in	in	ADP
ejpam-4577	34	8	g	g	PROPN
ejpam-4577	34	9	is	be	AUX
ejpam-4577	34	10	the	the	DET
ejpam-4577	34	11	set	set	ADJ
ejpam-4577	34	12	n2	n2	NOUN
ejpam-4577	34	13	g[x	g[x	PROPN
ejpam-4577	34	14	]	]	X
ejpam-4577	34	15	=	=	SYM
ejpam-4577	34	16	n2	n2	PROPN
ejpam-4577	34	17	g(x	g(x	NOUN
ejpam-4577	34	18	)	)	PUNCT
ejpam-4577	34	19	∪x	∪x	NUM
ejpam-4577	34	20	.	.	PUNCT
ejpam-4577	35	1	a	a	DET
ejpam-4577	35	2	set	set	NOUN
ejpam-4577	35	3	s	s	NOUN
ejpam-4577	35	4	⊆	⊆	NUM
ejpam-4577	35	5	v	v	NOUN
ejpam-4577	35	6	(	(	PUNCT
ejpam-4577	35	7	g	g	NOUN
ejpam-4577	35	8	)	)	PUNCT
ejpam-4577	35	9	is	be	AUX
ejpam-4577	35	10	a	a	DET
ejpam-4577	35	11	hop	hop	NOUN
ejpam-4577	35	12	dominating	dominating	NOUN
ejpam-4577	35	13	set	set	NOUN
ejpam-4577	35	14	of	of	ADP
ejpam-4577	35	15	g	g	PROPN
ejpam-4577	35	16	if	if	SCONJ
ejpam-4577	35	17	n2	n2	ADJ
ejpam-4577	35	18	g[s	g[s	PROPN
ejpam-4577	35	19	]	]	X
ejpam-4577	35	20	=	=	SYM
ejpam-4577	35	21	v	v	NOUN
ejpam-4577	35	22	(	(	PUNCT
ejpam-4577	35	23	g	g	NOUN
ejpam-4577	35	24	)	)	PUNCT
ejpam-4577	35	25	,	,	PUNCT
ejpam-4577	35	26	that	that	ADV
ejpam-4577	35	27	is	is	ADV
ejpam-4577	35	28	,	,	PUNCT
ejpam-4577	35	29	for	for	ADP
ejpam-4577	35	30	every	every	DET
ejpam-4577	35	31	v	v	NUM
ejpam-4577	35	32	∈	∈	NOUN
ejpam-4577	35	33	v	v	NOUN
ejpam-4577	35	34	(	(	PUNCT
ejpam-4577	35	35	g)\s	g)\s	NOUN
ejpam-4577	35	36	,	,	PUNCT
ejpam-4577	35	37	there	there	PRON
ejpam-4577	35	38	exists	exist	VERB
ejpam-4577	35	39	u	u	PROPN
ejpam-4577	35	40	∈	∈	PROPN
ejpam-4577	35	41	s	s	VERB
ejpam-4577	35	42	such	such	ADJ
ejpam-4577	35	43	that	that	DET
ejpam-4577	35	44	dg(u	dg(u	ADJ
ejpam-4577	35	45	,	,	PUNCT
ejpam-4577	35	46	v	v	NOUN
ejpam-4577	35	47	)	)	PUNCT
ejpam-4577	36	1	=	=	SYM
ejpam-4577	36	2	2	2	X
ejpam-4577	36	3	.	.	PUNCT
ejpam-4577	37	1	the	the	DET
ejpam-4577	37	2	minimum	minimum	ADJ
ejpam-4577	37	3	cardinality	cardinality	NOUN
ejpam-4577	37	4	among	among	ADP
ejpam-4577	37	5	all	all	DET
ejpam-4577	37	6	hop	hop	NOUN
ejpam-4577	37	7	dominating	dominating	NOUN
ejpam-4577	37	8	sets	set	NOUN
ejpam-4577	37	9	of	of	ADP
ejpam-4577	37	10	g	g	NOUN
ejpam-4577	37	11	,	,	PUNCT
ejpam-4577	37	12	denoted	denote	VERB
ejpam-4577	37	13	by	by	ADP
ejpam-4577	37	14	γh(g	γh(g	NOUN
ejpam-4577	37	15	)	)	PUNCT
ejpam-4577	37	16	,	,	PUNCT
ejpam-4577	37	17	is	be	AUX
ejpam-4577	37	18	called	call	VERB
ejpam-4577	37	19	the	the	DET
ejpam-4577	37	20	hop	hop	NOUN
ejpam-4577	37	21	domination	domination	NOUN
ejpam-4577	37	22	number	number	NOUN
ejpam-4577	37	23	of	of	ADP
ejpam-4577	37	24	g.	g.	PROPN
ejpam-4577	37	25	any	any	DET
ejpam-4577	37	26	hop	hop	NOUN
ejpam-4577	37	27	dominating	dominating	NOUN
ejpam-4577	37	28	set	set	VERB
ejpam-4577	37	29	with	with	ADP
ejpam-4577	37	30	cardinality	cardinality	NOUN
ejpam-4577	37	31	equal	equal	ADJ
ejpam-4577	37	32	to	to	ADP
ejpam-4577	37	33	γh(g	γh(g	NOUN
ejpam-4577	37	34	)	)	PUNCT
ejpam-4577	37	35	is	be	AUX
ejpam-4577	37	36	called	call	VERB
ejpam-4577	37	37	a	a	DET
ejpam-4577	37	38	γh	γh	ADV
ejpam-4577	37	39	-	-	PUNCT
ejpam-4577	37	40	set	set	NOUN
ejpam-4577	37	41	.	.	PUNCT
ejpam-4577	38	1	a	a	DET
ejpam-4577	38	2	nonempty	nonempty	ADV
ejpam-4577	38	3	set	set	VERB
ejpam-4577	38	4	s	s	PROPN
ejpam-4577	38	5	⊆	⊆	NUM
ejpam-4577	38	6	v	v	NOUN
ejpam-4577	38	7	(	(	PUNCT
ejpam-4577	38	8	g	g	NOUN
ejpam-4577	38	9	)	)	PUNCT
ejpam-4577	38	10	is	be	AUX
ejpam-4577	38	11	a	a	DET
ejpam-4577	38	12	hop	hop	NOUN
ejpam-4577	38	13	independent	independent	ADJ
ejpam-4577	38	14	set	set	NOUN
ejpam-4577	38	15	of	of	ADP
ejpam-4577	38	16	g	g	PROPN
ejpam-4577	38	17	if	if	SCONJ
ejpam-4577	38	18	dg(x	dg(x	NUM
ejpam-4577	38	19	,	,	PUNCT
ejpam-4577	38	20	y	y	NOUN
ejpam-4577	38	21	)	)	PUNCT
ejpam-4577	38	22	̸=	̸=	PROPN
ejpam-4577	38	23	2	2	NUM
ejpam-4577	38	24	for	for	ADP
ejpam-4577	38	25	any	any	DET
ejpam-4577	38	26	two	two	NUM
ejpam-4577	38	27	vertices	vertex	NOUN
ejpam-4577	38	28	x	x	X
ejpam-4577	38	29	,	,	PUNCT
ejpam-4577	38	30	y	y	PROPN
ejpam-4577	38	31	∈	∈	PROPN
ejpam-4577	38	32	s.	s.	PROPN
ejpam-4577	38	33	the	the	DET
ejpam-4577	38	34	hop	hop	PROPN
ejpam-4577	38	35	independence	independence	NOUN
ejpam-4577	38	36	number	number	NOUN
ejpam-4577	38	37	of	of	ADP
ejpam-4577	38	38	g	g	NOUN
ejpam-4577	38	39	,	,	PUNCT
ejpam-4577	38	40	denoted	denote	VERB
ejpam-4577	38	41	by	by	ADP
ejpam-4577	38	42	αh(g	αh(g	NOUN
ejpam-4577	38	43	)	)	PUNCT
ejpam-4577	38	44	,	,	PUNCT
ejpam-4577	38	45	is	be	AUX
ejpam-4577	38	46	the	the	DET
ejpam-4577	38	47	largest	large	ADJ
ejpam-4577	38	48	cardinality	cardinality	NOUN
ejpam-4577	38	49	of	of	ADP
ejpam-4577	38	50	a	a	DET
ejpam-4577	38	51	hop	hop	NOUN
ejpam-4577	38	52	independent	independent	ADJ
ejpam-4577	38	53	set	set	NOUN
ejpam-4577	38	54	of	of	ADP
ejpam-4577	38	55	g.	g.	PROPN
ejpam-4577	38	56	any	any	DET
ejpam-4577	38	57	hop	hop	NOUN
ejpam-4577	38	58	independent	independent	ADJ
ejpam-4577	38	59	set	set	NOUN
ejpam-4577	38	60	of	of	ADP
ejpam-4577	38	61	g	g	NOUN
ejpam-4577	38	62	with	with	ADP
ejpam-4577	38	63	cardinality	cardinality	NOUN
ejpam-4577	38	64	αh(g	αh(g	NOUN
ejpam-4577	38	65	)	)	PUNCT
ejpam-4577	38	66	is	be	AUX
ejpam-4577	38	67	called	call	VERB
ejpam-4577	38	68	an	an	DET
ejpam-4577	38	69	αh	αh	NOUN
ejpam-4577	38	70	-	-	PUNCT
ejpam-4577	38	71	set	set	NOUN
ejpam-4577	38	72	of	of	ADP
ejpam-4577	38	73	g.	g.	PROPN
ejpam-4577	38	74	a	a	DET
ejpam-4577	38	75	set	set	NOUN
ejpam-4577	38	76	s	s	PROPN
ejpam-4577	38	77	⊆	⊆	NUM
ejpam-4577	38	78	v	v	NOUN
ejpam-4577	38	79	(	(	PUNCT
ejpam-4577	38	80	g	g	NOUN
ejpam-4577	38	81	)	)	PUNCT
ejpam-4577	38	82	is	be	AUX
ejpam-4577	38	83	called	call	VERB
ejpam-4577	38	84	a	a	DET
ejpam-4577	38	85	hop	hop	NOUN
ejpam-4577	38	86	independent	independent	ADJ
ejpam-4577	38	87	hop	hop	NOUN
ejpam-4577	38	88	dominating	dominating	NOUN
ejpam-4577	38	89	set	set	NOUN
ejpam-4577	38	90	of	of	ADP
ejpam-4577	38	91	g	g	PROPN
ejpam-4577	38	92	if	if	SCONJ
ejpam-4577	38	93	s	s	VERB
ejpam-4577	38	94	is	be	AUX
ejpam-4577	38	95	both	both	PRON
ejpam-4577	38	96	hop	hop	ADV
ejpam-4577	38	97	independent	independent	ADJ
ejpam-4577	38	98	and	and	CCONJ
ejpam-4577	38	99	hop	hop	NOUN
ejpam-4577	38	100	dominating	dominating	NOUN
ejpam-4577	38	101	set	set	NOUN
ejpam-4577	38	102	of	of	ADP
ejpam-4577	38	103	g.	g.	PROPN
ejpam-4577	38	104	the	the	DET
ejpam-4577	38	105	minimum	minimum	ADJ
ejpam-4577	38	106	cardinality	cardinality	NOUN
ejpam-4577	38	107	of	of	ADP
ejpam-4577	38	108	a	a	DET
ejpam-4577	38	109	hop	hop	NOUN
ejpam-4577	38	110	independent	independent	ADJ
ejpam-4577	38	111	hop	hop	NOUN
ejpam-4577	38	112	dominating	dominating	NOUN
ejpam-4577	38	113	set	set	NOUN
ejpam-4577	38	114	of	of	ADP
ejpam-4577	38	115	g	g	NOUN
ejpam-4577	38	116	,	,	PUNCT
ejpam-4577	38	117	denoted	denote	VERB
ejpam-4577	38	118	by	by	ADP
ejpam-4577	38	119	γhih(g	γhih(g	NOUN
ejpam-4577	38	120	)	)	PUNCT
ejpam-4577	38	121	,	,	PUNCT
ejpam-4577	38	122	is	be	AUX
ejpam-4577	38	123	called	call	VERB
ejpam-4577	38	124	the	the	DET
ejpam-4577	38	125	hop	hop	NOUN
ejpam-4577	38	126	independent	independent	ADJ
ejpam-4577	38	127	hop	hop	NOUN
ejpam-4577	38	128	domination	domination	NOUN
ejpam-4577	38	129	number	number	NOUN
ejpam-4577	38	130	of	of	ADP
ejpam-4577	38	131	g.	g.	PROPN
ejpam-4577	38	132	any	any	DET
ejpam-4577	38	133	hop	hop	NOUN
ejpam-4577	38	134	independent	independent	ADJ
ejpam-4577	38	135	hop	hop	NOUN
ejpam-4577	38	136	dominating	dominating	NOUN
ejpam-4577	38	137	set	set	NOUN
ejpam-4577	38	138	of	of	ADP
ejpam-4577	38	139	g	g	NOUN
ejpam-4577	38	140	with	with	ADP
ejpam-4577	38	141	cardinality	cardinality	PROPN
ejpam-4577	38	142	γhih(g	γhih(g	PROPN
ejpam-4577	38	143	)	)	PUNCT
ejpam-4577	38	144	is	be	AUX
ejpam-4577	38	145	called	call	VERB
ejpam-4577	38	146	a	a	DET
ejpam-4577	38	147	γhih	γhih	NOUN
ejpam-4577	38	148	-	-	PUNCT
ejpam-4577	38	149	set	set	NOUN
ejpam-4577	38	150	of	of	ADP
ejpam-4577	38	151	g.	g.	PROPN
ejpam-4577	38	152	j.	j.	PROPN
ejpam-4577	38	153	hassan	hassan	PROPN
ejpam-4577	38	154	,	,	PUNCT
ejpam-4577	38	155	s.	s.	PROPN
ejpam-4577	38	156	canoy	canoy	PROPN
ejpam-4577	38	157	/	/	SYM
ejpam-4577	38	158	eur	eur	PROPN
ejpam-4577	38	159	.	.	PUNCT
ejpam-4577	39	1	j.	j.	PROPN
ejpam-4577	39	2	pure	pure	PROPN
ejpam-4577	39	3	appl	appl	PROPN
ejpam-4577	39	4	.	.	PROPN
ejpam-4577	39	5	math	math	PROPN
ejpam-4577	39	6	,	,	PUNCT
ejpam-4577	39	7	15	15	NUM
ejpam-4577	39	8	(	(	PUNCT
ejpam-4577	39	9	4	4	NUM
ejpam-4577	39	10	)	)	PUNCT
ejpam-4577	39	11	(	(	PUNCT
ejpam-4577	39	12	2022	2022	NUM
ejpam-4577	39	13	)	)	PUNCT
ejpam-4577	39	14	,	,	PUNCT
ejpam-4577	39	15	1783	1783	NUM
ejpam-4577	39	16	-	-	SYM
ejpam-4577	39	17	1796	1796	NUM
ejpam-4577	39	18	1785	1785	NUM
ejpam-4577	39	19	a	a	DET
ejpam-4577	39	20	set	set	NOUN
ejpam-4577	39	21	s	s	NOUN
ejpam-4577	39	22	⊆	⊆	NUM
ejpam-4577	39	23	v	v	NOUN
ejpam-4577	39	24	(	(	PUNCT
ejpam-4577	39	25	g	g	NOUN
ejpam-4577	39	26	)	)	PUNCT
ejpam-4577	39	27	is	be	AUX
ejpam-4577	39	28	a	a	DET
ejpam-4577	39	29	clique	clique	NOUN
ejpam-4577	39	30	if	if	SCONJ
ejpam-4577	39	31	the	the	DET
ejpam-4577	39	32	subgraph	subgraph	NOUN
ejpam-4577	39	33	⟨s⟩	⟨s⟩	PROPN
ejpam-4577	39	34	induced	induce	VERB
ejpam-4577	39	35	by	by	ADP
ejpam-4577	39	36	s	s	PROPN
ejpam-4577	39	37	is	be	AUX
ejpam-4577	39	38	a	a	DET
ejpam-4577	39	39	complete	complete	ADJ
ejpam-4577	39	40	graph	graph	NOUN
ejpam-4577	39	41	.	.	PUNCT
ejpam-4577	40	1	the	the	DET
ejpam-4577	40	2	maximum	maximum	ADJ
ejpam-4577	40	3	cardinality	cardinality	NOUN
ejpam-4577	40	4	of	of	ADP
ejpam-4577	40	5	a	a	DET
ejpam-4577	40	6	clique	clique	NOUN
ejpam-4577	40	7	of	of	ADP
ejpam-4577	40	8	g	g	NOUN
ejpam-4577	40	9	,	,	PUNCT
ejpam-4577	40	10	denoted	denote	VERB
ejpam-4577	40	11	by	by	ADP
ejpam-4577	40	12	ω(g	ω(g	NOUN
ejpam-4577	40	13	)	)	PUNCT
ejpam-4577	40	14	,	,	PUNCT
ejpam-4577	40	15	is	be	AUX
ejpam-4577	40	16	called	call	VERB
ejpam-4577	40	17	the	the	DET
ejpam-4577	40	18	clique	clique	ADJ
ejpam-4577	40	19	number	number	NOUN
ejpam-4577	40	20	of	of	ADP
ejpam-4577	40	21	g.	g.	PROPN
ejpam-4577	40	22	a	a	DET
ejpam-4577	40	23	set	set	NOUN
ejpam-4577	40	24	c	c	NOUN
ejpam-4577	40	25	⊆	⊆	NUM
ejpam-4577	40	26	v	v	NOUN
ejpam-4577	40	27	(	(	PUNCT
ejpam-4577	40	28	g	g	NOUN
ejpam-4577	40	29	)	)	PUNCT
ejpam-4577	40	30	is	be	AUX
ejpam-4577	40	31	a	a	DET
ejpam-4577	40	32	pointwise	pointwise	ADJ
ejpam-4577	40	33	non	non	ADJ
ejpam-4577	40	34	-	-	ADJ
ejpam-4577	40	35	dominating	dominating	ADJ
ejpam-4577	40	36	set	set	NOUN
ejpam-4577	40	37	if	if	SCONJ
ejpam-4577	40	38	for	for	ADP
ejpam-4577	40	39	every	every	DET
ejpam-4577	40	40	v	v	NUM
ejpam-4577	40	41	∈	∈	NOUN
ejpam-4577	40	42	v	v	NOUN
ejpam-4577	40	43	(	(	PUNCT
ejpam-4577	40	44	g	g	NOUN
ejpam-4577	40	45	)	)	PUNCT
ejpam-4577	40	46	\c	\c	NOUN
ejpam-4577	40	47	,	,	PUNCT
ejpam-4577	40	48	there	there	PRON
ejpam-4577	40	49	exists	exist	VERB
ejpam-4577	40	50	u	u	PROPN
ejpam-4577	40	51	∈	∈	PROPN
ejpam-4577	40	52	c	c	NOUN
ejpam-4577	40	53	such	such	ADJ
ejpam-4577	40	54	that	that	DET
ejpam-4577	40	55	v	v	NOUN
ejpam-4577	40	56	/∈	/∈	PUNCT
ejpam-4577	40	57	ng(u	ng(u	NOUN
ejpam-4577	40	58	)	)	PUNCT
ejpam-4577	40	59	.	.	PUNCT
ejpam-4577	41	1	the	the	DET
ejpam-4577	41	2	minimum	minimum	ADJ
ejpam-4577	41	3	cardinality	cardinality	NOUN
ejpam-4577	41	4	of	of	ADP
ejpam-4577	41	5	a	a	DET
ejpam-4577	41	6	pointwise	pointwise	ADJ
ejpam-4577	41	7	non	non	ADJ
ejpam-4577	41	8	-	-	ADJ
ejpam-4577	41	9	dominating	dominating	ADJ
ejpam-4577	41	10	set	set	NOUN
ejpam-4577	41	11	of	of	ADP
ejpam-4577	41	12	g	g	NOUN
ejpam-4577	41	13	,	,	PUNCT
ejpam-4577	41	14	denoted	denote	VERB
ejpam-4577	41	15	by	by	ADP
ejpam-4577	41	16	pnd(g	pnd(g	PROPN
ejpam-4577	41	17	)	)	PUNCT
ejpam-4577	41	18	,	,	PUNCT
ejpam-4577	41	19	is	be	AUX
ejpam-4577	41	20	called	call	VERB
ejpam-4577	41	21	a	a	DET
ejpam-4577	41	22	pointwise	pointwise	ADJ
ejpam-4577	41	23	non	non	ADJ
ejpam-4577	41	24	-	-	ADJ
ejpam-4577	41	25	domination	domination	ADJ
ejpam-4577	41	26	number	number	NOUN
ejpam-4577	41	27	of	of	ADP
ejpam-4577	41	28	g.	g.	PROPN
ejpam-4577	41	29	a	a	DET
ejpam-4577	41	30	set	set	NOUN
ejpam-4577	41	31	s	s	PROPN
ejpam-4577	41	32	⊆	⊆	NUM
ejpam-4577	41	33	v	v	NOUN
ejpam-4577	41	34	(	(	PUNCT
ejpam-4577	41	35	g	g	NOUN
ejpam-4577	41	36	)	)	PUNCT
ejpam-4577	41	37	is	be	AUX
ejpam-4577	41	38	a	a	DET
ejpam-4577	41	39	clique	clique	NOUN
ejpam-4577	41	40	pointwise	pointwise	PROPN
ejpam-4577	41	41	non	non	ADJ
ejpam-4577	41	42	-	-	ADJ
ejpam-4577	41	43	dominating	dominating	ADJ
ejpam-4577	41	44	set	set	NOUN
ejpam-4577	41	45	if	if	SCONJ
ejpam-4577	41	46	s	s	VERB
ejpam-4577	41	47	is	be	AUX
ejpam-4577	41	48	both	both	PRON
ejpam-4577	41	49	a	a	DET
ejpam-4577	41	50	clique	clique	NOUN
ejpam-4577	41	51	and	and	CCONJ
ejpam-4577	41	52	a	a	DET
ejpam-4577	41	53	pointwise	pointwise	ADJ
ejpam-4577	41	54	non	non	ADJ
ejpam-4577	41	55	-	-	ADJ
ejpam-4577	41	56	dominating	dominating	ADJ
ejpam-4577	41	57	set	set	NOUN
ejpam-4577	41	58	of	of	ADP
ejpam-4577	41	59	g.	g.	PROPN
ejpam-4577	41	60	the	the	DET
ejpam-4577	41	61	smallest	small	ADJ
ejpam-4577	41	62	cardinality	cardinality	NOUN
ejpam-4577	41	63	of	of	ADP
ejpam-4577	41	64	a	a	DET
ejpam-4577	41	65	clique	clique	NOUN
ejpam-4577	41	66	pointwise	pointwise	NOUN
ejpam-4577	41	67	nondominating	nondominate	VERB
ejpam-4577	41	68	set	set	NOUN
ejpam-4577	41	69	of	of	ADP
ejpam-4577	41	70	g	g	NOUN
ejpam-4577	41	71	,	,	PUNCT
ejpam-4577	41	72	denoted	denote	VERB
ejpam-4577	41	73	by	by	ADP
ejpam-4577	41	74	cpnd(g	cpnd(g	PROPN
ejpam-4577	41	75	)	)	PUNCT
ejpam-4577	41	76	,	,	PUNCT
ejpam-4577	41	77	is	be	AUX
ejpam-4577	41	78	called	call	VERB
ejpam-4577	41	79	the	the	DET
ejpam-4577	41	80	clique	clique	NOUN
ejpam-4577	41	81	pointwise	pointwise	PROPN
ejpam-4577	41	82	non	non	ADJ
ejpam-4577	41	83	-	-	ADJ
ejpam-4577	41	84	domination	domination	ADJ
ejpam-4577	41	85	number	number	NOUN
ejpam-4577	41	86	of	of	ADP
ejpam-4577	41	87	g.	g.	PROPN
ejpam-4577	41	88	any	any	DET
ejpam-4577	41	89	clique	clique	NOUN
ejpam-4577	41	90	pointwise	pointwise	PROPN
ejpam-4577	41	91	non	non	ADJ
ejpam-4577	41	92	-	-	ADJ
ejpam-4577	41	93	dominating	dominating	ADJ
ejpam-4577	41	94	set	set	NOUN
ejpam-4577	41	95	of	of	ADP
ejpam-4577	41	96	g	g	PROPN
ejpam-4577	41	97	with	with	ADP
ejpam-4577	41	98	cardinality	cardinality	NOUN
ejpam-4577	41	99	cpnd(g	cpnd(g	PROPN
ejpam-4577	41	100	)	)	PUNCT
ejpam-4577	41	101	is	be	AUX
ejpam-4577	41	102	called	call	VERB
ejpam-4577	41	103	a	a	DET
ejpam-4577	41	104	cpnd	cpnd	NOUN
ejpam-4577	41	105	-	-	PUNCT
ejpam-4577	41	106	set	set	NOUN
ejpam-4577	41	107	of	of	ADP
ejpam-4577	41	108	g.	g.	PROPN
ejpam-4577	41	109	a	a	DET
ejpam-4577	41	110	total	total	ADJ
ejpam-4577	41	111	dominating	dominating	NOUN
ejpam-4577	41	112	set	set	NOUN
ejpam-4577	41	113	d	d	PROPN
ejpam-4577	41	114	⊆	⊆	NUM
ejpam-4577	41	115	v	v	ADP
ejpam-4577	41	116	(	(	PUNCT
ejpam-4577	41	117	g	g	NOUN
ejpam-4577	41	118	)	)	PUNCT
ejpam-4577	41	119	is	be	AUX
ejpam-4577	41	120	called	call	VERB
ejpam-4577	41	121	a	a	DET
ejpam-4577	41	122	total	total	ADJ
ejpam-4577	41	123	dominating	dominating	NOUN
ejpam-4577	41	124	hop	hop	NOUN
ejpam-4577	41	125	independent	independent	ADJ
ejpam-4577	41	126	hop	hop	NOUN
ejpam-4577	41	127	dominating	dominating	NOUN
ejpam-4577	41	128	set	set	NOUN
ejpam-4577	41	129	if	if	SCONJ
ejpam-4577	41	130	it	it	PRON
ejpam-4577	41	131	is	be	AUX
ejpam-4577	41	132	a	a	DET
ejpam-4577	41	133	hop	hop	NOUN
ejpam-4577	41	134	independent	independent	ADJ
ejpam-4577	41	135	hop	hop	NOUN
ejpam-4577	41	136	dominating	dominating	NOUN
ejpam-4577	41	137	set	set	NOUN
ejpam-4577	41	138	.	.	PUNCT
ejpam-4577	42	1	the	the	DET
ejpam-4577	42	2	minimum	minimum	ADJ
ejpam-4577	42	3	cardinality	cardinality	NOUN
ejpam-4577	42	4	of	of	ADP
ejpam-4577	42	5	a	a	DET
ejpam-4577	42	6	total	total	ADJ
ejpam-4577	42	7	dominating	dominating	NOUN
ejpam-4577	42	8	hop	hop	NOUN
ejpam-4577	42	9	independent	independent	ADJ
ejpam-4577	42	10	hop	hop	NOUN
ejpam-4577	42	11	dominating	dominating	NOUN
ejpam-4577	42	12	set	set	NOUN
ejpam-4577	42	13	of	of	ADP
ejpam-4577	42	14	g	g	PROPN
ejpam-4577	42	15	is	be	AUX
ejpam-4577	42	16	denoted	denote	VERB
ejpam-4577	42	17	by	by	ADP
ejpam-4577	42	18	γhiht	γhiht	NOUN
ejpam-4577	42	19	(	(	PUNCT
ejpam-4577	42	20	g	g	NOUN
ejpam-4577	42	21	)	)	PUNCT
ejpam-4577	42	22	.	.	PUNCT
ejpam-4577	43	1	any	any	DET
ejpam-4577	43	2	total	total	ADJ
ejpam-4577	43	3	dominating	dominating	NOUN
ejpam-4577	43	4	hop	hop	NOUN
ejpam-4577	43	5	independent	independent	ADJ
ejpam-4577	43	6	hop	hop	NOUN
ejpam-4577	43	7	dominating	dominating	NOUN
ejpam-4577	43	8	set	set	NOUN
ejpam-4577	43	9	d	d	NOUN
ejpam-4577	43	10	with	with	ADP
ejpam-4577	43	11	cardinality	cardinality	NOUN
ejpam-4577	43	12	γhiht	γhiht	NOUN
ejpam-4577	43	13	(	(	PUNCT
ejpam-4577	43	14	g	g	NOUN
ejpam-4577	43	15	)	)	PUNCT
ejpam-4577	43	16	is	be	AUX
ejpam-4577	43	17	referred	refer	VERB
ejpam-4577	43	18	to	to	ADP
ejpam-4577	43	19	as	as	ADP
ejpam-4577	43	20	a	a	DET
ejpam-4577	43	21	γhiht	γhiht	ADJ
ejpam-4577	43	22	-set	-set	ADJ
ejpam-4577	43	23	.	.	PUNCT
ejpam-4577	44	1	the	the	DET
ejpam-4577	44	2	shadow	shadow	NOUN
ejpam-4577	44	3	graph	graph	NOUN
ejpam-4577	44	4	s(g	s(g	PROPN
ejpam-4577	44	5	)	)	PUNCT
ejpam-4577	44	6	of	of	ADP
ejpam-4577	44	7	graph	graph	NOUN
ejpam-4577	44	8	g	g	PROPN
ejpam-4577	44	9	is	be	AUX
ejpam-4577	44	10	constructed	construct	VERB
ejpam-4577	44	11	by	by	ADP
ejpam-4577	44	12	taking	take	VERB
ejpam-4577	44	13	two	two	NUM
ejpam-4577	44	14	copies	copy	NOUN
ejpam-4577	44	15	of	of	ADP
ejpam-4577	44	16	g	g	NOUN
ejpam-4577	44	17	,	,	PUNCT
ejpam-4577	44	18	say	say	VERB
ejpam-4577	44	19	g1	g1	PROPN
ejpam-4577	44	20	and	and	CCONJ
ejpam-4577	44	21	g2	g2	PROPN
ejpam-4577	44	22	,	,	PUNCT
ejpam-4577	44	23	and	and	CCONJ
ejpam-4577	44	24	then	then	ADV
ejpam-4577	44	25	joining	join	VERB
ejpam-4577	44	26	each	each	DET
ejpam-4577	44	27	vertex	vertex	NOUN
ejpam-4577	44	28	u	u	PROPN
ejpam-4577	44	29	∈	∈	PROPN
ejpam-4577	44	30	g1	g1	PROPN
ejpam-4577	44	31	to	to	ADP
ejpam-4577	44	32	the	the	DET
ejpam-4577	44	33	neighbors	neighbor	NOUN
ejpam-4577	44	34	of	of	ADP
ejpam-4577	44	35	its	its	PRON
ejpam-4577	44	36	corresponding	corresponding	ADJ
ejpam-4577	44	37	vertex	vertex	NOUN
ejpam-4577	44	38	u′	u′	PROPN
ejpam-4577	44	39	∈	∈	PROPN
ejpam-4577	44	40	g2	g2	PROPN
ejpam-4577	44	41	.	.	PUNCT
ejpam-4577	45	1	let	let	VERB
ejpam-4577	45	2	g	g	NOUN
ejpam-4577	45	3	and	and	CCONJ
ejpam-4577	45	4	h	h	NOUN
ejpam-4577	45	5	be	be	VERB
ejpam-4577	45	6	any	any	DET
ejpam-4577	45	7	two	two	NUM
ejpam-4577	45	8	graphs	graph	NOUN
ejpam-4577	45	9	.	.	PUNCT
ejpam-4577	46	1	the	the	DET
ejpam-4577	46	2	join	join	NOUN
ejpam-4577	46	3	g	g	PROPN
ejpam-4577	46	4	+	+	CCONJ
ejpam-4577	46	5	h	h	NOUN
ejpam-4577	46	6	is	be	AUX
ejpam-4577	46	7	the	the	DET
ejpam-4577	46	8	graph	graph	NOUN
ejpam-4577	46	9	with	with	ADP
ejpam-4577	46	10	vertex	vertex	NOUN
ejpam-4577	46	11	set	set	VERB
ejpam-4577	46	12	v	v	NOUN
ejpam-4577	46	13	(	(	PUNCT
ejpam-4577	46	14	g+h	g+h	NOUN
ejpam-4577	46	15	)	)	PUNCT
ejpam-4577	46	16	=	=	SYM
ejpam-4577	46	17	v	v	NOUN
ejpam-4577	46	18	(	(	PUNCT
ejpam-4577	46	19	g)∪	g)∪	VERB
ejpam-4577	46	20	v	v	NUM
ejpam-4577	46	21	(	(	PUNCT
ejpam-4577	46	22	h	h	NOUN
ejpam-4577	46	23	)	)	PUNCT
ejpam-4577	46	24	and	and	CCONJ
ejpam-4577	46	25	edge	edge	NOUN
ejpam-4577	46	26	set	set	VERB
ejpam-4577	46	27	e(g+h	e(g+h	NUM
ejpam-4577	46	28	)	)	PUNCT
ejpam-4577	47	1	=	=	SYM
ejpam-4577	47	2	e(g)∪e(h)∪	e(g)∪e(h)∪	NOUN
ejpam-4577	47	3	{	{	PUNCT
ejpam-4577	47	4	uv	uv	NOUN
ejpam-4577	47	5	:	:	PUNCT
ejpam-4577	47	6	u	u	PROPN
ejpam-4577	47	7	∈	∈	PROPN
ejpam-4577	47	8	v	v	ADP
ejpam-4577	47	9	(	(	PUNCT
ejpam-4577	47	10	g	g	NOUN
ejpam-4577	47	11	)	)	PUNCT
ejpam-4577	47	12	,	,	PUNCT
ejpam-4577	47	13	v	v	X
ejpam-4577	47	14	∈	∈	PROPN
ejpam-4577	47	15	v	v	NOUN
ejpam-4577	47	16	(	(	PUNCT
ejpam-4577	47	17	h	h	NOUN
ejpam-4577	47	18	)	)	PUNCT
ejpam-4577	47	19	}	}	PUNCT
ejpam-4577	47	20	.	.	PUNCT
ejpam-4577	48	1	the	the	DET
ejpam-4577	48	2	corona	corona	NOUN
ejpam-4577	48	3	g	g	PROPN
ejpam-4577	48	4	◦	◦	NOUN
ejpam-4577	48	5	h	h	NOUN
ejpam-4577	48	6	is	be	AUX
ejpam-4577	48	7	the	the	DET
ejpam-4577	48	8	graph	graph	NOUN
ejpam-4577	48	9	obtained	obtain	VERB
ejpam-4577	48	10	by	by	ADP
ejpam-4577	48	11	taking	take	VERB
ejpam-4577	48	12	one	one	NUM
ejpam-4577	48	13	copy	copy	NOUN
ejpam-4577	48	14	of	of	ADP
ejpam-4577	48	15	g	g	PROPN
ejpam-4577	48	16	and	and	CCONJ
ejpam-4577	48	17	|v	|v	PROPN
ejpam-4577	48	18	(	(	PUNCT
ejpam-4577	48	19	g)|	g)|	NOUN
ejpam-4577	48	20	copies	copy	NOUN
ejpam-4577	48	21	of	of	ADP
ejpam-4577	48	22	h	h	NOUN
ejpam-4577	48	23	,	,	PUNCT
ejpam-4577	48	24	and	and	CCONJ
ejpam-4577	48	25	then	then	ADV
ejpam-4577	48	26	joining	join	VERB
ejpam-4577	48	27	the	the	DET
ejpam-4577	48	28	ith	ith	PROPN
ejpam-4577	48	29	vertex	vertex	NOUN
ejpam-4577	48	30	of	of	ADP
ejpam-4577	48	31	g	g	NOUN
ejpam-4577	48	32	to	to	ADP
ejpam-4577	48	33	every	every	DET
ejpam-4577	48	34	vertex	vertex	NOUN
ejpam-4577	48	35	of	of	ADP
ejpam-4577	48	36	the	the	DET
ejpam-4577	48	37	ith	ith	PROPN
ejpam-4577	48	38	copy	copy	NOUN
ejpam-4577	48	39	of	of	ADP
ejpam-4577	48	40	h.	h.	PROPN
ejpam-4577	48	41	we	we	PRON
ejpam-4577	48	42	denote	denote	VERB
ejpam-4577	48	43	by	by	ADP
ejpam-4577	48	44	hv	hv	PROPN
ejpam-4577	49	1	the	the	DET
ejpam-4577	49	2	copy	copy	NOUN
ejpam-4577	49	3	of	of	ADP
ejpam-4577	49	4	h	h	NOUN
ejpam-4577	49	5	in	in	ADP
ejpam-4577	49	6	g	g	PROPN
ejpam-4577	49	7	◦	◦	NOUN
ejpam-4577	49	8	h	h	NOUN
ejpam-4577	49	9	corresponding	correspond	VERB
ejpam-4577	49	10	to	to	ADP
ejpam-4577	49	11	the	the	DET
ejpam-4577	49	12	vertex	vertex	NOUN
ejpam-4577	49	13	v	v	ADP
ejpam-4577	49	14	∈	∈	PROPN
ejpam-4577	49	15	g	g	NOUN
ejpam-4577	49	16	and	and	CCONJ
ejpam-4577	49	17	write	write	VERB
ejpam-4577	49	18	v	v	ADP
ejpam-4577	49	19	+	+	CCONJ
ejpam-4577	49	20	hv	hv	NOUN
ejpam-4577	49	21	for	for	ADP
ejpam-4577	49	22	⟨{v}⟩	⟨{v}⟩	NOUN
ejpam-4577	49	23	+	+	X
ejpam-4577	49	24	hv	hv	X
ejpam-4577	49	25	.	.	PUNCT
ejpam-4577	50	1	the	the	DET
ejpam-4577	50	2	lexicographic	lexicographic	ADJ
ejpam-4577	50	3	product	product	NOUN
ejpam-4577	50	4	g[h	g[h	PROPN
ejpam-4577	50	5	]	]	PUNCT
ejpam-4577	50	6	is	be	AUX
ejpam-4577	50	7	the	the	DET
ejpam-4577	50	8	graph	graph	NOUN
ejpam-4577	50	9	with	with	ADP
ejpam-4577	50	10	vertex	vertex	NOUN
ejpam-4577	50	11	set	set	VERB
ejpam-4577	50	12	v	v	NOUN
ejpam-4577	50	13	(	(	PUNCT
ejpam-4577	50	14	g[h	g[h	PROPN
ejpam-4577	50	15	]	]	PUNCT
ejpam-4577	50	16	)	)	PUNCT
ejpam-4577	50	17	=	=	SYM
ejpam-4577	50	18	v	v	X
ejpam-4577	50	19	(	(	PUNCT
ejpam-4577	50	20	g	g	NOUN
ejpam-4577	50	21	)	)	PUNCT
ejpam-4577	50	22	×	×	NOUN
ejpam-4577	50	23	v	v	NOUN
ejpam-4577	50	24	(	(	PUNCT
ejpam-4577	50	25	h	h	NOUN
ejpam-4577	50	26	)	)	PUNCT
ejpam-4577	50	27	and	and	CCONJ
ejpam-4577	50	28	(	(	PUNCT
ejpam-4577	50	29	v	v	NOUN
ejpam-4577	50	30	,	,	PUNCT
ejpam-4577	50	31	a)(u	a)(u	ADJ
ejpam-4577	50	32	,	,	PUNCT
ejpam-4577	50	33	b	b	X
ejpam-4577	50	34	)	)	PUNCT
ejpam-4577	50	35	∈	∈	NOUN
ejpam-4577	50	36	e(g[h	e(g[h	NOUN
ejpam-4577	50	37	]	]	PUNCT
ejpam-4577	50	38	)	)	PUNCT
ejpam-4577	50	39	if	if	SCONJ
ejpam-4577	50	40	and	and	CCONJ
ejpam-4577	50	41	only	only	ADV
ejpam-4577	50	42	if	if	SCONJ
ejpam-4577	50	43	either	either	DET
ejpam-4577	50	44	uv	uv	PROPN
ejpam-4577	50	45	∈	∈	PROPN
ejpam-4577	50	46	e(g	e(g	PROPN
ejpam-4577	50	47	)	)	PUNCT
ejpam-4577	50	48	or	or	CCONJ
ejpam-4577	50	49	u	u	X
ejpam-4577	50	50	=	=	PROPN
ejpam-4577	50	51	v	v	PROPN
ejpam-4577	50	52	and	and	CCONJ
ejpam-4577	50	53	ab	ab	PROPN
ejpam-4577	50	54	∈	∈	PROPN
ejpam-4577	50	55	e(h	e(h	PROPN
ejpam-4577	50	56	)	)	PUNCT
ejpam-4577	50	57	.	.	PUNCT
ejpam-4577	51	1	note	note	VERB
ejpam-4577	51	2	that	that	SCONJ
ejpam-4577	51	3	any	any	DET
ejpam-4577	51	4	non	non	ADJ
ejpam-4577	51	5	-	-	ADJ
ejpam-4577	51	6	empty	empty	ADJ
ejpam-4577	51	7	set	set	NOUN
ejpam-4577	51	8	c	c	NOUN
ejpam-4577	51	9	⊆	⊆	NUM
ejpam-4577	51	10	v	v	NOUN
ejpam-4577	51	11	(	(	PUNCT
ejpam-4577	51	12	g)×	g)×	NOUN
ejpam-4577	51	13	v	v	NOUN
ejpam-4577	51	14	(	(	PUNCT
ejpam-4577	51	15	h	h	NOUN
ejpam-4577	51	16	)	)	PUNCT
ejpam-4577	51	17	can	can	AUX
ejpam-4577	51	18	be	be	AUX
ejpam-4577	51	19	written	write	VERB
ejpam-4577	51	20	as	as	ADP
ejpam-4577	51	21	c	c	NOUN
ejpam-4577	51	22	=	=	PUNCT
ejpam-4577	51	23	⋃	⋃	PROPN
ejpam-4577	51	24	x∈s	x∈s	NOUN
ejpam-4577	52	1	[	[	X
ejpam-4577	52	2	{	{	PUNCT
ejpam-4577	52	3	x}×	x}×	PROPN
ejpam-4577	52	4	tx	tx	PROPN
ejpam-4577	52	5	]	]	X
ejpam-4577	52	6	,	,	PUNCT
ejpam-4577	52	7	where	where	SCONJ
ejpam-4577	52	8	s	s	VERB
ejpam-4577	52	9	⊆	⊆	NUM
ejpam-4577	52	10	v	v	NOUN
ejpam-4577	52	11	(	(	PUNCT
ejpam-4577	52	12	g	g	NOUN
ejpam-4577	52	13	)	)	PUNCT
ejpam-4577	52	14	and	and	CCONJ
ejpam-4577	52	15	tx	tx	VERB
ejpam-4577	52	16	⊆	⊆	NUM
ejpam-4577	52	17	v	v	NOUN
ejpam-4577	52	18	(	(	PUNCT
ejpam-4577	52	19	h	h	NOUN
ejpam-4577	52	20	)	)	PUNCT
ejpam-4577	52	21	for	for	ADP
ejpam-4577	52	22	each	each	DET
ejpam-4577	52	23	x	x	PROPN
ejpam-4577	52	24	∈	∈	PROPN
ejpam-4577	52	25	s.	s.	PROPN
ejpam-4577	52	26	specifically	specifically	ADV
ejpam-4577	52	27	,	,	PUNCT
ejpam-4577	52	28	tx	tx	PROPN
ejpam-4577	52	29	=	=	PUNCT
ejpam-4577	52	30	{	{	PUNCT
ejpam-4577	52	31	a	a	DET
ejpam-4577	52	32	∈	∈	PROPN
ejpam-4577	52	33	v	v	ADP
ejpam-4577	52	34	(	(	PUNCT
ejpam-4577	52	35	h	h	NOUN
ejpam-4577	52	36	)	)	PUNCT
ejpam-4577	52	37	:	:	PUNCT
ejpam-4577	52	38	(	(	PUNCT
ejpam-4577	52	39	x	x	X
ejpam-4577	52	40	,	,	PUNCT
ejpam-4577	52	41	a	a	PRON
ejpam-4577	52	42	)	)	PUNCT
ejpam-4577	52	43	∈	∈	PROPN
ejpam-4577	52	44	c	c	NOUN
ejpam-4577	52	45	}	}	PUNCT
ejpam-4577	52	46	for	for	ADP
ejpam-4577	52	47	each	each	DET
ejpam-4577	52	48	x	x	PROPN
ejpam-4577	52	49	∈	∈	PROPN
ejpam-4577	52	50	s.	s.	PROPN
ejpam-4577	52	51	3	3	X
ejpam-4577	52	52	.	.	PROPN
ejpam-4577	52	53	results	result	NOUN
ejpam-4577	52	54	proposition	proposition	NOUN
ejpam-4577	52	55	1	1	X
ejpam-4577	52	56	.	.	PUNCT
ejpam-4577	53	1	let	let	VERB
ejpam-4577	53	2	g	g	NOUN
ejpam-4577	53	3	be	be	AUX
ejpam-4577	53	4	any	any	DET
ejpam-4577	53	5	graph	graph	NOUN
ejpam-4577	53	6	on	on	ADP
ejpam-4577	53	7	n	n	DET
ejpam-4577	53	8	vertices	vertex	NOUN
ejpam-4577	53	9	.	.	PUNCT
ejpam-4577	54	1	then	then	ADV
ejpam-4577	54	2	γh(g	γh(g	PUNCT
ejpam-4577	54	3	)	)	PUNCT
ejpam-4577	54	4	≤	≤	NUM
ejpam-4577	54	5	γhih(g	γhih(g	ADP
ejpam-4577	54	6	)	)	PUNCT
ejpam-4577	54	7	≤	≤	NOUN
ejpam-4577	54	8	αh(g	αh(g	NOUN
ejpam-4577	54	9	)	)	PUNCT
ejpam-4577	54	10	.	.	PUNCT
ejpam-4577	55	1	proof	proof	NOUN
ejpam-4577	55	2	.	.	PUNCT
ejpam-4577	56	1	since	since	SCONJ
ejpam-4577	56	2	every	every	DET
ejpam-4577	56	3	hop	hop	NOUN
ejpam-4577	56	4	independent	independent	ADJ
ejpam-4577	56	5	hop	hop	NOUN
ejpam-4577	56	6	dominating	dominating	NOUN
ejpam-4577	56	7	set	set	NOUN
ejpam-4577	56	8	s	s	VERB
ejpam-4577	56	9	is	be	AUX
ejpam-4577	56	10	a	a	DET
ejpam-4577	56	11	hop	hop	NOUN
ejpam-4577	56	12	dominating	dominating	NOUN
ejpam-4577	56	13	set	set	NOUN
ejpam-4577	56	14	,	,	PUNCT
ejpam-4577	56	15	it	it	PRON
ejpam-4577	56	16	follows	follow	VERB
ejpam-4577	56	17	that	that	SCONJ
ejpam-4577	56	18	γh(g	γh(g	NOUN
ejpam-4577	56	19	)	)	PUNCT
ejpam-4577	56	20	≤	≤	NUM
ejpam-4577	56	21	γhih(g	γhih(g	NOUN
ejpam-4577	56	22	)	)	PUNCT
ejpam-4577	56	23	.	.	PUNCT
ejpam-4577	57	1	also	also	ADV
ejpam-4577	57	2	,	,	PUNCT
ejpam-4577	57	3	since	since	SCONJ
ejpam-4577	57	4	every	every	DET
ejpam-4577	57	5	αh	αh	NOUN
ejpam-4577	57	6	-	-	PUNCT
ejpam-4577	57	7	set	set	NOUN
ejpam-4577	57	8	is	be	AUX
ejpam-4577	57	9	a	a	DET
ejpam-4577	57	10	hop	hop	NOUN
ejpam-4577	57	11	independent	independent	ADJ
ejpam-4577	57	12	hop	hop	NOUN
ejpam-4577	57	13	dominating	dominating	NOUN
ejpam-4577	57	14	set	set	NOUN
ejpam-4577	57	15	,	,	PUNCT
ejpam-4577	57	16	the	the	DET
ejpam-4577	57	17	right	right	ADJ
ejpam-4577	57	18	inequality	inequality	NOUN
ejpam-4577	57	19	holds	hold	VERB
ejpam-4577	57	20	.	.	PUNCT
ejpam-4577	58	1	remark	remark	PROPN
ejpam-4577	58	2	1	1	NUM
ejpam-4577	58	3	.	.	PUNCT
ejpam-4577	59	1	the	the	DET
ejpam-4577	59	2	bounds	bound	NOUN
ejpam-4577	59	3	given	give	VERB
ejpam-4577	59	4	in	in	ADP
ejpam-4577	59	5	proposition	proposition	NOUN
ejpam-4577	59	6	1	1	NUM
ejpam-4577	59	7	are	be	AUX
ejpam-4577	59	8	tight	tight	ADJ
ejpam-4577	59	9	.	.	PUNCT
ejpam-4577	60	1	moreover	moreover	ADV
ejpam-4577	60	2	,	,	PUNCT
ejpam-4577	60	3	strict	strict	ADJ
ejpam-4577	60	4	inequalities	inequality	NOUN
ejpam-4577	60	5	can	can	AUX
ejpam-4577	60	6	also	also	ADV
ejpam-4577	60	7	be	be	AUX
ejpam-4577	60	8	attained	attain	VERB
ejpam-4577	60	9	.	.	PUNCT
ejpam-4577	61	1	j.	j.	PROPN
ejpam-4577	61	2	hassan	hassan	PROPN
ejpam-4577	61	3	,	,	PUNCT
ejpam-4577	61	4	s.	s.	PROPN
ejpam-4577	61	5	canoy	canoy	PROPN
ejpam-4577	61	6	/	/	SYM
ejpam-4577	61	7	eur	eur	PROPN
ejpam-4577	61	8	.	.	PUNCT
ejpam-4577	62	1	j.	j.	PROPN
ejpam-4577	62	2	pure	pure	PROPN
ejpam-4577	62	3	appl	appl	PROPN
ejpam-4577	62	4	.	.	PROPN
ejpam-4577	62	5	math	math	PROPN
ejpam-4577	62	6	,	,	PUNCT
ejpam-4577	62	7	15	15	NUM
ejpam-4577	62	8	(	(	PUNCT
ejpam-4577	62	9	4	4	NUM
ejpam-4577	62	10	)	)	PUNCT
ejpam-4577	62	11	(	(	PUNCT
ejpam-4577	62	12	2022	2022	NUM
ejpam-4577	62	13	)	)	PUNCT
ejpam-4577	62	14	,	,	PUNCT
ejpam-4577	62	15	1783	1783	NUM
ejpam-4577	62	16	-	-	SYM
ejpam-4577	62	17	1796	1796	NUM
ejpam-4577	62	18	1786	1786	NUM
ejpam-4577	62	19	to	to	PART
ejpam-4577	62	20	see	see	VERB
ejpam-4577	62	21	this	this	PRON
ejpam-4577	62	22	,	,	PUNCT
ejpam-4577	62	23	consider	consider	VERB
ejpam-4577	62	24	g	g	NOUN
ejpam-4577	62	25	=	=	NOUN
ejpam-4577	62	26	c4	c4	NOUN
ejpam-4577	62	27	.	.	PUNCT
ejpam-4577	63	1	then	then	ADV
ejpam-4577	63	2	γh(g	γh(g	NOUN
ejpam-4577	63	3	)	)	PUNCT
ejpam-4577	63	4	=	=	PUNCT
ejpam-4577	63	5	γhih(g	γhih(g	NOUN
ejpam-4577	63	6	)	)	PUNCT
ejpam-4577	63	7	=	=	NOUN
ejpam-4577	63	8	αh(g	αh(g	NOUN
ejpam-4577	63	9	)	)	PUNCT
ejpam-4577	63	10	=	=	SYM
ejpam-4577	64	1	2	2	X
ejpam-4577	64	2	.	.	X
ejpam-4577	64	3	for	for	ADP
ejpam-4577	64	4	the	the	DET
ejpam-4577	64	5	strict	strict	ADJ
ejpam-4577	64	6	inequalities	inequality	NOUN
ejpam-4577	64	7	,	,	PUNCT
ejpam-4577	64	8	let	let	VERB
ejpam-4577	64	9	s1	s1	PROPN
ejpam-4577	64	10	=	=	PUNCT
ejpam-4577	64	11	{	{	PUNCT
ejpam-4577	64	12	c	c	NOUN
ejpam-4577	64	13	,	,	PUNCT
ejpam-4577	64	14	e	e	NOUN
ejpam-4577	64	15	,	,	PUNCT
ejpam-4577	64	16	g	g	NOUN
ejpam-4577	64	17	}	}	PUNCT
ejpam-4577	64	18	(	(	PUNCT
ejpam-4577	64	19	see	see	VERB
ejpam-4577	64	20	figure	figure	NOUN
ejpam-4577	64	21	1	1	NUM
ejpam-4577	64	22	)	)	PUNCT
ejpam-4577	64	23	.	.	PUNCT
ejpam-4577	65	1	then	then	ADV
ejpam-4577	65	2	s1	s1	PROPN
ejpam-4577	65	3	is	be	AUX
ejpam-4577	65	4	a	a	DET
ejpam-4577	65	5	minimum	minimum	ADJ
ejpam-4577	65	6	hop	hop	NOUN
ejpam-4577	65	7	dominating	dominating	NOUN
ejpam-4577	65	8	set	set	NOUN
ejpam-4577	65	9	of	of	ADP
ejpam-4577	65	10	g.	g.	PROPN
ejpam-4577	65	11	since	since	SCONJ
ejpam-4577	65	12	dg(c	dg(c	PROPN
ejpam-4577	65	13	,	,	PUNCT
ejpam-4577	65	14	g	g	NOUN
ejpam-4577	65	15	)	)	PUNCT
ejpam-4577	65	16	=	=	SYM
ejpam-4577	65	17	2	2	NUM
ejpam-4577	65	18	,	,	PUNCT
ejpam-4577	65	19	it	it	PRON
ejpam-4577	65	20	follows	follow	VERB
ejpam-4577	65	21	that	that	SCONJ
ejpam-4577	65	22	s1	s1	NOUN
ejpam-4577	65	23	is	be	AUX
ejpam-4577	65	24	not	not	PART
ejpam-4577	65	25	a	a	DET
ejpam-4577	65	26	hop	hop	NOUN
ejpam-4577	65	27	independent	independent	ADJ
ejpam-4577	65	28	set	set	NOUN
ejpam-4577	65	29	.	.	PUNCT
ejpam-4577	66	1	next	next	ADV
ejpam-4577	66	2	,	,	PUNCT
ejpam-4577	66	3	let	let	VERB
ejpam-4577	66	4	s2	s2	VERB
ejpam-4577	66	5	=	=	PRON
ejpam-4577	66	6	{	{	PUNCT
ejpam-4577	66	7	a	a	PRON
ejpam-4577	66	8	,	,	PUNCT
ejpam-4577	66	9	b	b	NOUN
ejpam-4577	66	10	,	,	PUNCT
ejpam-4577	66	11	g	g	NOUN
ejpam-4577	66	12	,	,	PUNCT
ejpam-4577	66	13	h}(see	h}(see	NOUN
ejpam-4577	66	14	figure	figure	NOUN
ejpam-4577	66	15	2	2	NUM
ejpam-4577	66	16	)	)	PUNCT
ejpam-4577	66	17	.	.	PUNCT
ejpam-4577	67	1	then	then	ADV
ejpam-4577	67	2	s2	s2	PROPN
ejpam-4577	67	3	is	be	AUX
ejpam-4577	67	4	a	a	DET
ejpam-4577	67	5	minimum	minimum	ADJ
ejpam-4577	67	6	hop	hop	NOUN
ejpam-4577	67	7	independent	independent	ADJ
ejpam-4577	67	8	hop	hop	NOUN
ejpam-4577	67	9	dominating	dominating	NOUN
ejpam-4577	67	10	set	set	NOUN
ejpam-4577	67	11	of	of	ADP
ejpam-4577	67	12	g.	g.	PROPN
ejpam-4577	67	13	however	however	ADV
ejpam-4577	67	14	,	,	PUNCT
ejpam-4577	67	15	s2	s2	PROPN
ejpam-4577	67	16	is	be	AUX
ejpam-4577	67	17	not	not	PART
ejpam-4577	67	18	a	a	DET
ejpam-4577	67	19	maximum	maximum	ADJ
ejpam-4577	67	20	hop	hop	NOUN
ejpam-4577	67	21	independent	independent	ADJ
ejpam-4577	67	22	set	set	NOUN
ejpam-4577	67	23	of	of	ADP
ejpam-4577	67	24	g.	g.	PROPN
ejpam-4577	67	25	in	in	ADP
ejpam-4577	67	26	fact	fact	NOUN
ejpam-4577	67	27	,	,	PUNCT
ejpam-4577	67	28	s3	s3	PROPN
ejpam-4577	67	29	=	=	SYM
ejpam-4577	67	30	{	{	PUNCT
ejpam-4577	67	31	a	a	PRON
ejpam-4577	67	32	,	,	PUNCT
ejpam-4577	67	33	b	b	PROPN
ejpam-4577	67	34	,	,	PUNCT
ejpam-4577	67	35	h	h	NOUN
ejpam-4577	67	36	,	,	PUNCT
ejpam-4577	67	37	i	i	PRON
ejpam-4577	67	38	,	,	PUNCT
ejpam-4577	67	39	j	j	PROPN
ejpam-4577	67	40	}	}	PUNCT
ejpam-4577	67	41	(	(	PUNCT
ejpam-4577	67	42	see	see	VERB
ejpam-4577	67	43	figure	figure	NOUN
ejpam-4577	67	44	3	3	NUM
ejpam-4577	67	45	)	)	PUNCT
ejpam-4577	67	46	is	be	AUX
ejpam-4577	67	47	a	a	DET
ejpam-4577	67	48	maximum	maximum	ADJ
ejpam-4577	67	49	hop	hop	NOUN
ejpam-4577	67	50	independent	independent	ADJ
ejpam-4577	67	51	set	set	NOUN
ejpam-4577	67	52	of	of	ADP
ejpam-4577	67	53	g.	g.	PROPN
ejpam-4577	67	54	consequently	consequently	ADV
ejpam-4577	67	55	,	,	PUNCT
ejpam-4577	67	56	γh(g	γh(g	NOUN
ejpam-4577	67	57	)	)	PUNCT
ejpam-4577	67	58	=	=	SYM
ejpam-4577	67	59	3	3	NUM
ejpam-4577	67	60	<	<	SYM
ejpam-4577	67	61	4	4	NUM
ejpam-4577	67	62	=	=	SYM
ejpam-4577	67	63	γhih(g	γhih(g	PROPN
ejpam-4577	67	64	)	)	PUNCT
ejpam-4577	67	65	<	<	X
ejpam-4577	67	66	5	5	NUM
ejpam-4577	67	67	=	=	NOUN
ejpam-4577	67	68	αh(g	αh(g	NOUN
ejpam-4577	67	69	)	)	PUNCT
ejpam-4577	67	70	.	.	PUNCT
ejpam-4577	68	1	g	g	NOUN
ejpam-4577	68	2	:	:	PUNCT
ejpam-4577	69	1	c	c	PROPN
ejpam-4577	70	1	d	d	X
ejpam-4577	70	2	b	b	PROPN
ejpam-4577	70	3	ea	ea	X
ejpam-4577	70	4	f	f	PROPN
ejpam-4577	71	1	g	g	PROPN
ejpam-4577	71	2	h	h	NOUN
ejpam-4577	72	1	i	i	PRON
ejpam-4577	72	2	j	j	PROPN
ejpam-4577	72	3	figure	figure	VERB
ejpam-4577	72	4	1	1	NUM
ejpam-4577	72	5	:	:	PUNCT
ejpam-4577	72	6	a	a	DET
ejpam-4577	72	7	graph	graph	NOUN
ejpam-4577	72	8	g	g	NOUN
ejpam-4577	72	9	with	with	ADP
ejpam-4577	72	10	γh(g	γh(g	NOUN
ejpam-4577	72	11	)	)	PUNCT
ejpam-4577	72	12	<	<	X
ejpam-4577	73	1	γhih(g	γhih(g	NOUN
ejpam-4577	73	2	)	)	PUNCT
ejpam-4577	73	3	<	<	X
ejpam-4577	73	4	αh(g	αh(g	NOUN
ejpam-4577	73	5	)	)	PUNCT
ejpam-4577	73	6	g	g	NOUN
ejpam-4577	73	7	:	:	PUNCT
ejpam-4577	74	1	c	c	PROPN
ejpam-4577	75	1	d	d	X
ejpam-4577	75	2	b	b	PROPN
ejpam-4577	75	3	ea	ea	X
ejpam-4577	75	4	f	f	PROPN
ejpam-4577	76	1	g	g	PROPN
ejpam-4577	76	2	h	h	NOUN
ejpam-4577	77	1	i	i	PRON
ejpam-4577	77	2	j	j	PROPN
ejpam-4577	77	3	figure	figure	VERB
ejpam-4577	77	4	2	2	NUM
ejpam-4577	77	5	:	:	PUNCT
ejpam-4577	77	6	a	a	DET
ejpam-4577	77	7	graph	graph	NOUN
ejpam-4577	77	8	g	g	NOUN
ejpam-4577	77	9	with	with	ADP
ejpam-4577	77	10	γh(g	γh(g	NOUN
ejpam-4577	77	11	)	)	PUNCT
ejpam-4577	77	12	<	<	X
ejpam-4577	78	1	γhih(g	γhih(g	NOUN
ejpam-4577	78	2	)	)	PUNCT
ejpam-4577	78	3	<	<	X
ejpam-4577	78	4	αh(g	αh(g	NOUN
ejpam-4577	78	5	)	)	PUNCT
ejpam-4577	78	6	g	g	NOUN
ejpam-4577	78	7	:	:	PUNCT
ejpam-4577	79	1	c	c	PROPN
ejpam-4577	80	1	d	d	X
ejpam-4577	80	2	b	b	PROPN
ejpam-4577	80	3	ea	ea	X
ejpam-4577	80	4	f	f	PROPN
ejpam-4577	81	1	g	g	PROPN
ejpam-4577	81	2	h	h	NOUN
ejpam-4577	82	1	i	i	PRON
ejpam-4577	82	2	j	j	PROPN
ejpam-4577	82	3	figure	figure	VERB
ejpam-4577	82	4	3	3	NUM
ejpam-4577	82	5	:	:	PUNCT
ejpam-4577	82	6	a	a	DET
ejpam-4577	82	7	graph	graph	NOUN
ejpam-4577	82	8	g	g	NOUN
ejpam-4577	82	9	with	with	ADP
ejpam-4577	82	10	γh(g	γh(g	NOUN
ejpam-4577	82	11	)	)	PUNCT
ejpam-4577	82	12	<	<	X
ejpam-4577	83	1	γhih(g	γhih(g	NOUN
ejpam-4577	83	2	)	)	PUNCT
ejpam-4577	83	3	<	<	X
ejpam-4577	83	4	αh(g	αh(g	NOUN
ejpam-4577	83	5	)	)	PUNCT
ejpam-4577	83	6	theorem	theorem	NOUN
ejpam-4577	83	7	1	1	NUM
ejpam-4577	83	8	.	.	PUNCT
ejpam-4577	84	1	[	[	X
ejpam-4577	84	2	3	3	X
ejpam-4577	84	3	]	]	PUNCT
ejpam-4577	84	4	let	let	VERB
ejpam-4577	84	5	g	g	NOUN
ejpam-4577	84	6	be	be	AUX
ejpam-4577	84	7	any	any	DET
ejpam-4577	84	8	graph	graph	NOUN
ejpam-4577	84	9	on	on	ADP
ejpam-4577	84	10	n	n	DET
ejpam-4577	84	11	vertices	vertex	NOUN
ejpam-4577	84	12	.	.	PUNCT
ejpam-4577	85	1	then	then	ADV
ejpam-4577	85	2	s	s	VERB
ejpam-4577	85	3	is	be	AUX
ejpam-4577	85	4	a	a	DET
ejpam-4577	85	5	hop	hop	NOUN
ejpam-4577	85	6	independent	independent	ADJ
ejpam-4577	85	7	set	set	NOUN
ejpam-4577	85	8	of	of	ADP
ejpam-4577	85	9	g	g	PROPN
ejpam-4577	85	10	if	if	SCONJ
ejpam-4577	86	1	and	and	CCONJ
ejpam-4577	86	2	only	only	ADV
ejpam-4577	86	3	if	if	SCONJ
ejpam-4577	86	4	every	every	DET
ejpam-4577	86	5	component	component	NOUN
ejpam-4577	86	6	of	of	ADP
ejpam-4577	86	7	⟨s⟩	⟨s⟩	PROPN
ejpam-4577	86	8	is	be	AUX
ejpam-4577	86	9	complete	complete	ADJ
ejpam-4577	86	10	.	.	PUNCT
ejpam-4577	87	1	moreover	moreover	ADV
ejpam-4577	87	2	,	,	PUNCT
ejpam-4577	87	3	αh(g	αh(g	NOUN
ejpam-4577	87	4	)	)	PUNCT
ejpam-4577	87	5	=	=	SYM
ejpam-4577	88	1	n	n	NOUN
ejpam-4577	88	2	if	if	SCONJ
ejpam-4577	88	3	and	and	CCONJ
ejpam-4577	88	4	only	only	ADV
ejpam-4577	88	5	if	if	SCONJ
ejpam-4577	88	6	every	every	DET
ejpam-4577	88	7	component	component	NOUN
ejpam-4577	88	8	of	of	ADP
ejpam-4577	88	9	g	g	PROPN
ejpam-4577	88	10	is	be	AUX
ejpam-4577	88	11	complete	complete	ADJ
ejpam-4577	88	12	.	.	PUNCT
ejpam-4577	89	1	theorem	theorem	NOUN
ejpam-4577	89	2	2	2	NUM
ejpam-4577	89	3	.	.	PUNCT
ejpam-4577	90	1	let	let	VERB
ejpam-4577	90	2	g	g	PRON
ejpam-4577	90	3	be	be	AUX
ejpam-4577	90	4	a	a	DET
ejpam-4577	90	5	graph	graph	NOUN
ejpam-4577	90	6	.	.	PUNCT
ejpam-4577	91	1	then	then	ADV
ejpam-4577	91	2	γh(g	γh(g	NOUN
ejpam-4577	91	3	)	)	PUNCT
ejpam-4577	91	4	=	=	SYM
ejpam-4577	91	5	γhih(g	γhih(g	NOUN
ejpam-4577	91	6	)	)	PUNCT
ejpam-4577	91	7	if	if	SCONJ
ejpam-4577	91	8	and	and	CCONJ
ejpam-4577	91	9	only	only	ADV
ejpam-4577	91	10	if	if	SCONJ
ejpam-4577	91	11	g	g	PROPN
ejpam-4577	91	12	has	have	VERB
ejpam-4577	91	13	a	a	DET
ejpam-4577	91	14	γh	γh	ADV
ejpam-4577	91	15	-	-	PUNCT
ejpam-4577	91	16	set	set	NOUN
ejpam-4577	91	17	s	s	VERB
ejpam-4577	91	18	such	such	ADJ
ejpam-4577	91	19	that	that	SCONJ
ejpam-4577	91	20	every	every	DET
ejpam-4577	91	21	component	component	NOUN
ejpam-4577	91	22	of	of	ADP
ejpam-4577	91	23	⟨s⟩	⟨s⟩	PROPN
ejpam-4577	91	24	is	be	AUX
ejpam-4577	91	25	complete	complete	ADJ
ejpam-4577	91	26	.	.	PUNCT
ejpam-4577	92	1	proof	proof	NOUN
ejpam-4577	92	2	.	.	PUNCT
ejpam-4577	93	1	suppose	suppose	VERB
ejpam-4577	93	2	γh(g	γh(g	NOUN
ejpam-4577	93	3	)	)	PUNCT
ejpam-4577	94	1	=	=	SYM
ejpam-4577	94	2	γhih(g	γhih(g	NOUN
ejpam-4577	94	3	)	)	PUNCT
ejpam-4577	94	4	and	and	CCONJ
ejpam-4577	94	5	let	let	VERB
ejpam-4577	94	6	s	s	PRON
ejpam-4577	94	7	be	be	AUX
ejpam-4577	94	8	a	a	DET
ejpam-4577	94	9	γhih	γhih	NOUN
ejpam-4577	94	10	-	-	PUNCT
ejpam-4577	94	11	set	set	NOUN
ejpam-4577	94	12	of	of	ADP
ejpam-4577	94	13	g.	g.	PROPN
ejpam-4577	95	1	then	then	ADV
ejpam-4577	95	2	s	s	VERB
ejpam-4577	95	3	is	be	AUX
ejpam-4577	95	4	a	a	DET
ejpam-4577	95	5	hop	hop	NOUN
ejpam-4577	95	6	independent	independent	ADJ
ejpam-4577	95	7	set	set	NOUN
ejpam-4577	95	8	of	of	ADP
ejpam-4577	95	9	g.	g.	PROPN
ejpam-4577	95	10	hence	hence	ADV
ejpam-4577	95	11	,	,	PUNCT
ejpam-4577	95	12	by	by	ADP
ejpam-4577	95	13	theorem	theorem	NOUN
ejpam-4577	95	14	1	1	NUM
ejpam-4577	95	15	,	,	PUNCT
ejpam-4577	95	16	every	every	DET
ejpam-4577	95	17	component	component	NOUN
ejpam-4577	95	18	of	of	ADP
ejpam-4577	95	19	⟨s⟩	⟨s⟩	PROPN
ejpam-4577	95	20	is	be	AUX
ejpam-4577	95	21	complete	complete	ADJ
ejpam-4577	95	22	.	.	PUNCT
ejpam-4577	96	1	by	by	ADP
ejpam-4577	96	2	assumption	assumption	NOUN
ejpam-4577	96	3	,	,	PUNCT
ejpam-4577	96	4	s	s	PART
ejpam-4577	96	5	is	be	AUX
ejpam-4577	96	6	a	a	DET
ejpam-4577	96	7	γh	γh	ADV
ejpam-4577	96	8	-	-	PUNCT
ejpam-4577	96	9	set	set	NOUN
ejpam-4577	96	10	of	of	ADP
ejpam-4577	96	11	g.	g.	NOUN
ejpam-4577	96	12	conversely	conversely	ADV
ejpam-4577	96	13	,	,	PUNCT
ejpam-4577	96	14	suppose	suppose	VERB
ejpam-4577	96	15	g	g	PROPN
ejpam-4577	96	16	has	have	VERB
ejpam-4577	96	17	a	a	DET
ejpam-4577	96	18	γh	γh	ADV
ejpam-4577	96	19	-	-	PUNCT
ejpam-4577	96	20	set	set	NOUN
ejpam-4577	96	21	s	s	VERB
ejpam-4577	96	22	such	such	ADJ
ejpam-4577	96	23	that	that	SCONJ
ejpam-4577	96	24	every	every	DET
ejpam-4577	96	25	component	component	NOUN
ejpam-4577	96	26	of	of	ADP
ejpam-4577	96	27	⟨s⟩	⟨s⟩	PROPN
ejpam-4577	96	28	is	be	AUX
ejpam-4577	96	29	complete	complete	ADJ
ejpam-4577	96	30	.	.	PUNCT
ejpam-4577	97	1	then	then	ADV
ejpam-4577	97	2	by	by	ADP
ejpam-4577	97	3	theorem	theorem	NOUN
ejpam-4577	97	4	1	1	NUM
ejpam-4577	97	5	,	,	PUNCT
ejpam-4577	97	6	s	s	VERB
ejpam-4577	97	7	is	be	AUX
ejpam-4577	97	8	a	a	DET
ejpam-4577	97	9	hop	hop	NOUN
ejpam-4577	97	10	independent	independent	ADJ
ejpam-4577	97	11	set	set	NOUN
ejpam-4577	97	12	.	.	PUNCT
ejpam-4577	98	1	since	since	SCONJ
ejpam-4577	98	2	s	s	PROPN
ejpam-4577	98	3	is	be	AUX
ejpam-4577	98	4	a	a	DET
ejpam-4577	98	5	hop	hop	NOUN
ejpam-4577	98	6	dominating	dominating	NOUN
ejpam-4577	98	7	set	set	NOUN
ejpam-4577	98	8	,	,	PUNCT
ejpam-4577	98	9	it	it	PRON
ejpam-4577	98	10	follows	follow	VERB
ejpam-4577	98	11	that	that	SCONJ
ejpam-4577	98	12	s	s	VERB
ejpam-4577	98	13	is	be	AUX
ejpam-4577	98	14	a	a	DET
ejpam-4577	98	15	hop	hop	NOUN
ejpam-4577	98	16	independent	independent	ADJ
ejpam-4577	98	17	hop	hop	NOUN
ejpam-4577	98	18	dominating	dominating	NOUN
ejpam-4577	98	19	set	set	NOUN
ejpam-4577	98	20	.	.	PUNCT
ejpam-4577	99	1	hence	hence	ADV
ejpam-4577	99	2	,	,	PUNCT
ejpam-4577	99	3	γhih(g	γhih(g	PROPN
ejpam-4577	99	4	)	)	PUNCT
ejpam-4577	99	5	≤	≤	NUM
ejpam-4577	99	6	|s|	|s|	PROPN
ejpam-4577	99	7	=	=	NOUN
ejpam-4577	99	8	γh(g	γh(g	NOUN
ejpam-4577	99	9	)	)	PUNCT
ejpam-4577	99	10	.	.	PUNCT
ejpam-4577	100	1	by	by	ADP
ejpam-4577	100	2	proposition	proposition	NOUN
ejpam-4577	100	3	1	1	NUM
ejpam-4577	100	4	,	,	PUNCT
ejpam-4577	100	5	γh(g	γh(g	NOUN
ejpam-4577	100	6	)	)	PUNCT
ejpam-4577	100	7	=	=	SYM
ejpam-4577	100	8	γhih(g	γhih(g	PROPN
ejpam-4577	100	9	)	)	PUNCT
ejpam-4577	100	10	.	.	PUNCT
ejpam-4577	101	1	the	the	DET
ejpam-4577	101	2	next	next	ADJ
ejpam-4577	101	3	result	result	NOUN
ejpam-4577	101	4	is	be	AUX
ejpam-4577	101	5	immediate	immediate	ADJ
ejpam-4577	101	6	from	from	ADP
ejpam-4577	101	7	theorem	theorem	ADJ
ejpam-4577	101	8	2	2	NUM
ejpam-4577	101	9	.	.	PUNCT
ejpam-4577	101	10	j.	j.	PROPN
ejpam-4577	101	11	hassan	hassan	PROPN
ejpam-4577	101	12	,	,	PUNCT
ejpam-4577	101	13	s.	s.	PROPN
ejpam-4577	101	14	canoy	canoy	PROPN
ejpam-4577	101	15	/	/	SYM
ejpam-4577	101	16	eur	eur	PROPN
ejpam-4577	101	17	.	.	PUNCT
ejpam-4577	102	1	j.	j.	PROPN
ejpam-4577	102	2	pure	pure	PROPN
ejpam-4577	102	3	appl	appl	PROPN
ejpam-4577	102	4	.	.	PROPN
ejpam-4577	102	5	math	math	PROPN
ejpam-4577	102	6	,	,	PUNCT
ejpam-4577	102	7	15	15	NUM
ejpam-4577	102	8	(	(	PUNCT
ejpam-4577	102	9	4	4	NUM
ejpam-4577	102	10	)	)	PUNCT
ejpam-4577	102	11	(	(	PUNCT
ejpam-4577	102	12	2022	2022	NUM
ejpam-4577	102	13	)	)	PUNCT
ejpam-4577	102	14	,	,	PUNCT
ejpam-4577	102	15	1783	1783	NUM
ejpam-4577	102	16	-	-	SYM
ejpam-4577	102	17	1796	1796	NUM
ejpam-4577	102	18	1787	1787	NUM
ejpam-4577	102	19	corollary	corollary	NOUN
ejpam-4577	102	20	1	1	NUM
ejpam-4577	102	21	.	.	PUNCT
ejpam-4577	103	1	let	let	VERB
ejpam-4577	103	2	n	n	PRON
ejpam-4577	103	3	≥	≥	X
ejpam-4577	103	4	3	3	NUM
ejpam-4577	103	5	be	be	AUX
ejpam-4577	103	6	any	any	DET
ejpam-4577	103	7	positive	positive	ADJ
ejpam-4577	103	8	integer	integer	NOUN
ejpam-4577	103	9	.	.	PUNCT
ejpam-4577	104	1	then	then	ADV
ejpam-4577	104	2	(	(	PUNCT
ejpam-4577	104	3	i	i	NOUN
ejpam-4577	104	4	)	)	PUNCT
ejpam-4577	104	5	γhih(pn	γhih(pn	NOUN
ejpam-4577	104	6	)	)	PUNCT
ejpam-4577	104	7	=	=	SYM
ejpam-4577	104	8	γh(pn	γh(pn	VERB
ejpam-4577	104	9	)	)	PUNCT
ejpam-4577	104	10	and	and	CCONJ
ejpam-4577	104	11	(	(	PUNCT
ejpam-4577	104	12	ii	ii	NOUN
ejpam-4577	104	13	)	)	PUNCT
ejpam-4577	104	14	γhih(cn	γhih(cn	PROPN
ejpam-4577	104	15	)	)	PUNCT
ejpam-4577	104	16	=	=	SYM
ejpam-4577	104	17	γh(cn	γh(cn	PROPN
ejpam-4577	104	18	)	)	PUNCT
ejpam-4577	104	19	.	.	PUNCT
ejpam-4577	105	1	theorem	theorem	NOUN
ejpam-4577	105	2	3	3	X
ejpam-4577	105	3	.	.	PUNCT
ejpam-4577	106	1	let	let	VERB
ejpam-4577	106	2	g	g	NOUN
ejpam-4577	106	3	be	be	AUX
ejpam-4577	106	4	any	any	DET
ejpam-4577	106	5	graph	graph	NOUN
ejpam-4577	106	6	on	on	ADP
ejpam-4577	106	7	n	n	PRON
ejpam-4577	106	8	≥	≥	NUM
ejpam-4577	106	9	2	2	NUM
ejpam-4577	106	10	vertices	vertex	NOUN
ejpam-4577	106	11	.	.	PUNCT
ejpam-4577	107	1	then	then	ADV
ejpam-4577	107	2	2	2	NUM
ejpam-4577	107	3	≤	≤	NUM
ejpam-4577	107	4	γhih(g	γhih(g	PROPN
ejpam-4577	107	5	)	)	PUNCT
ejpam-4577	107	6	≤	≤	PROPN
ejpam-4577	107	7	n.	n.	NOUN
ejpam-4577	107	8	moreover	moreover	ADV
ejpam-4577	107	9	,	,	PUNCT
ejpam-4577	107	10	the	the	DET
ejpam-4577	107	11	following	follow	VERB
ejpam-4577	107	12	statements	statement	NOUN
ejpam-4577	107	13	hold	hold	VERB
ejpam-4577	107	14	.	.	PUNCT
ejpam-4577	108	1	(	(	PUNCT
ejpam-4577	108	2	i	i	NOUN
ejpam-4577	108	3	)	)	PUNCT
ejpam-4577	108	4	γhih(g	γhih(g	PROPN
ejpam-4577	108	5	)	)	PUNCT
ejpam-4577	108	6	=	=	SYM
ejpam-4577	108	7	2	2	NUM
ejpam-4577	108	8	if	if	SCONJ
ejpam-4577	108	9	and	and	CCONJ
ejpam-4577	108	10	only	only	ADV
ejpam-4577	108	11	if	if	SCONJ
ejpam-4577	108	12	γh(g	γh(g	NOUN
ejpam-4577	108	13	)	)	PUNCT
ejpam-4577	108	14	=	=	SYM
ejpam-4577	108	15	2	2	X
ejpam-4577	108	16	.	.	PUNCT
ejpam-4577	108	17	(	(	PUNCT
ejpam-4577	108	18	ii	ii	NOUN
ejpam-4577	108	19	)	)	PUNCT
ejpam-4577	108	20	γhih(g	γhih(g	PROPN
ejpam-4577	108	21	)	)	PUNCT
ejpam-4577	108	22	=	=	SYM
ejpam-4577	109	1	n	n	NOUN
ejpam-4577	109	2	if	if	SCONJ
ejpam-4577	109	3	and	and	CCONJ
ejpam-4577	109	4	only	only	ADV
ejpam-4577	109	5	if	if	SCONJ
ejpam-4577	109	6	every	every	DET
ejpam-4577	109	7	component	component	NOUN
ejpam-4577	109	8	c	c	NOUN
ejpam-4577	109	9	of	of	ADP
ejpam-4577	109	10	g	g	PROPN
ejpam-4577	109	11	is	be	AUX
ejpam-4577	109	12	complete	complete	ADJ
ejpam-4577	109	13	.	.	PUNCT
ejpam-4577	110	1	proof	proof	NOUN
ejpam-4577	110	2	.	.	PUNCT
ejpam-4577	111	1	clearly	clearly	ADV
ejpam-4577	111	2	,	,	PUNCT
ejpam-4577	111	3	2	2	NUM
ejpam-4577	111	4	≤	≤	NUM
ejpam-4577	111	5	γhih(g	γhih(g	PROPN
ejpam-4577	111	6	)	)	PUNCT
ejpam-4577	111	7	≤	≤	NOUN
ejpam-4577	111	8	n.	n.	NOUN
ejpam-4577	111	9	(	(	PUNCT
ejpam-4577	111	10	i	i	NOUN
ejpam-4577	111	11	)	)	PUNCT
ejpam-4577	111	12	suppose	suppose	VERB
ejpam-4577	111	13	γhih(g	γhih(g	ADP
ejpam-4577	111	14	)	)	PUNCT
ejpam-4577	111	15	=	=	SYM
ejpam-4577	111	16	2	2	X
ejpam-4577	111	17	.	.	PUNCT
ejpam-4577	111	18	by	by	ADP
ejpam-4577	111	19	proposition	proposition	NOUN
ejpam-4577	111	20	1	1	NUM
ejpam-4577	111	21	,	,	PUNCT
ejpam-4577	111	22	γh(g	γh(g	NOUN
ejpam-4577	111	23	)	)	PUNCT
ejpam-4577	111	24	≤	≤	NOUN
ejpam-4577	111	25	γhih(g	γhih(g	ADP
ejpam-4577	111	26	)	)	PUNCT
ejpam-4577	111	27	=	=	SYM
ejpam-4577	112	1	2	2	X
ejpam-4577	112	2	.	.	PUNCT
ejpam-4577	112	3	since	since	SCONJ
ejpam-4577	112	4	γh(g	γh(g	NOUN
ejpam-4577	112	5	)	)	PUNCT
ejpam-4577	112	6	≥	≥	NOUN
ejpam-4577	112	7	2	2	NUM
ejpam-4577	112	8	for	for	ADP
ejpam-4577	112	9	any	any	DET
ejpam-4577	112	10	graph	graph	NOUN
ejpam-4577	112	11	of	of	ADP
ejpam-4577	112	12	order	order	NOUN
ejpam-4577	112	13	n	n	PRON
ejpam-4577	112	14	≥	≥	NOUN
ejpam-4577	112	15	2	2	NUM
ejpam-4577	112	16	,	,	PUNCT
ejpam-4577	112	17	it	it	PRON
ejpam-4577	112	18	follows	follow	VERB
ejpam-4577	112	19	that	that	PRON
ejpam-4577	112	20	γh(g	γh(g	PUNCT
ejpam-4577	112	21	)	)	PUNCT
ejpam-4577	113	1	=	=	SYM
ejpam-4577	113	2	2	2	X
ejpam-4577	113	3	.	.	X
ejpam-4577	113	4	conversely	conversely	ADV
ejpam-4577	113	5	,	,	PUNCT
ejpam-4577	113	6	suppose	suppose	VERB
ejpam-4577	113	7	γh(g	γh(g	NOUN
ejpam-4577	113	8	)	)	PUNCT
ejpam-4577	113	9	=	=	SYM
ejpam-4577	113	10	2	2	X
ejpam-4577	113	11	,	,	PUNCT
ejpam-4577	113	12	say	say	VERB
ejpam-4577	113	13	s	s	X
ejpam-4577	113	14	=	=	PUNCT
ejpam-4577	113	15	{	{	PUNCT
ejpam-4577	113	16	a	a	DET
ejpam-4577	113	17	,	,	PUNCT
ejpam-4577	113	18	b	b	NOUN
ejpam-4577	113	19	}	}	PUNCT
ejpam-4577	113	20	is	be	AUX
ejpam-4577	113	21	a	a	DET
ejpam-4577	113	22	γh	γh	ADV
ejpam-4577	113	23	-	-	PUNCT
ejpam-4577	113	24	set	set	NOUN
ejpam-4577	113	25	.	.	PUNCT
ejpam-4577	114	1	suppose	suppose	VERB
ejpam-4577	114	2	,	,	PUNCT
ejpam-4577	114	3	on	on	ADP
ejpam-4577	114	4	the	the	DET
ejpam-4577	114	5	contrary	contrary	NOUN
ejpam-4577	114	6	,	,	PUNCT
ejpam-4577	114	7	that	that	PRON
ejpam-4577	114	8	s	s	VERB
ejpam-4577	114	9	is	be	AUX
ejpam-4577	114	10	not	not	PART
ejpam-4577	114	11	a	a	DET
ejpam-4577	114	12	hop	hop	NOUN
ejpam-4577	114	13	independent	independent	ADJ
ejpam-4577	114	14	set	set	NOUN
ejpam-4577	114	15	,	,	PUNCT
ejpam-4577	114	16	that	that	PRON
ejpam-4577	114	17	is	be	AUX
ejpam-4577	114	18	dg(a	dg(a	PROPN
ejpam-4577	114	19	,	,	PUNCT
ejpam-4577	114	20	b	b	X
ejpam-4577	114	21	)	)	PUNCT
ejpam-4577	115	1	=	=	SYM
ejpam-4577	115	2	2	2	X
ejpam-4577	115	3	.	.	PUNCT
ejpam-4577	115	4	then	then	ADV
ejpam-4577	115	5	there	there	PRON
ejpam-4577	115	6	exists	exist	VERB
ejpam-4577	115	7	x	x	X
ejpam-4577	115	8	∈	∈	PROPN
ejpam-4577	115	9	v	v	X
ejpam-4577	115	10	(	(	PUNCT
ejpam-4577	115	11	g	g	NOUN
ejpam-4577	115	12	)	)	PUNCT
ejpam-4577	115	13	such	such	ADJ
ejpam-4577	115	14	that	that	SCONJ
ejpam-4577	115	15	x	x	SYM
ejpam-4577	115	16	∈	∈	PROPN
ejpam-4577	115	17	ng(a)∩ng(b	ng(a)∩ng(b	PROPN
ejpam-4577	115	18	)	)	PUNCT
ejpam-4577	115	19	.	.	PUNCT
ejpam-4577	116	1	this	this	PRON
ejpam-4577	116	2	implies	imply	VERB
ejpam-4577	116	3	that	that	SCONJ
ejpam-4577	116	4	x	x	PROPN
ejpam-4577	116	5	/∈	/∈	PUNCT
ejpam-4577	116	6	n2	n2	ADJ
ejpam-4577	116	7	g(a)∪n2	g(a)∪n2	PROPN
ejpam-4577	116	8	g(b	g(b	PROPN
ejpam-4577	116	9	)	)	PUNCT
ejpam-4577	116	10	,	,	PUNCT
ejpam-4577	116	11	contrary	contrary	ADV
ejpam-4577	116	12	to	to	ADP
ejpam-4577	116	13	the	the	DET
ejpam-4577	116	14	assumption	assumption	NOUN
ejpam-4577	116	15	that	that	SCONJ
ejpam-4577	116	16	s	s	VERB
ejpam-4577	116	17	is	be	AUX
ejpam-4577	116	18	a	a	DET
ejpam-4577	116	19	hop	hop	NOUN
ejpam-4577	116	20	dominating	dominating	NOUN
ejpam-4577	116	21	set	set	NOUN
ejpam-4577	116	22	.	.	PUNCT
ejpam-4577	117	1	therefore	therefore	ADV
ejpam-4577	117	2	,	,	PUNCT
ejpam-4577	117	3	s	s	VERB
ejpam-4577	117	4	is	be	AUX
ejpam-4577	117	5	a	a	DET
ejpam-4577	117	6	hop	hop	NOUN
ejpam-4577	117	7	independent	independent	ADJ
ejpam-4577	117	8	set	set	NOUN
ejpam-4577	117	9	and	and	CCONJ
ejpam-4577	117	10	γhih(g	γhih(g	NOUN
ejpam-4577	117	11	)	)	PUNCT
ejpam-4577	117	12	≤	≤	NUM
ejpam-4577	117	13	2	2	NUM
ejpam-4577	117	14	.	.	PUNCT
ejpam-4577	118	1	consequently	consequently	ADV
ejpam-4577	118	2	,	,	PUNCT
ejpam-4577	118	3	γhih(g	γhih(g	NOUN
ejpam-4577	118	4	)	)	PUNCT
ejpam-4577	118	5	=	=	SYM
ejpam-4577	118	6	2	2	X
ejpam-4577	118	7	.	.	PUNCT
ejpam-4577	118	8	(	(	PUNCT
ejpam-4577	118	9	ii	ii	NOUN
ejpam-4577	118	10	)	)	PUNCT
ejpam-4577	118	11	suppose	suppose	VERB
ejpam-4577	118	12	γhih(g	γhih(g	ADP
ejpam-4577	118	13	)	)	PUNCT
ejpam-4577	118	14	=	=	VERB
ejpam-4577	119	1	n.	n.	NOUN
ejpam-4577	119	2	then	then	ADV
ejpam-4577	119	3	s	s	VERB
ejpam-4577	119	4	=	=	SYM
ejpam-4577	119	5	v	v	PROPN
ejpam-4577	119	6	(	(	PUNCT
ejpam-4577	119	7	g	g	NOUN
ejpam-4577	119	8	)	)	PUNCT
ejpam-4577	119	9	=	=	SYM
ejpam-4577	119	10	{	{	PUNCT
ejpam-4577	119	11	v1	v1	PROPN
ejpam-4577	119	12	,	,	PUNCT
ejpam-4577	119	13	.	.	PUNCT
ejpam-4577	119	14	.	.	PUNCT
ejpam-4577	119	15	.	.	PUNCT
ejpam-4577	120	1	,	,	PUNCT
ejpam-4577	120	2	vn	vn	PROPN
ejpam-4577	120	3	}	}	PUNCT
ejpam-4577	120	4	is	be	AUX
ejpam-4577	120	5	the	the	DET
ejpam-4577	120	6	only	only	ADJ
ejpam-4577	120	7	hop	hop	NOUN
ejpam-4577	120	8	independent	independent	ADJ
ejpam-4577	120	9	hop	hop	NOUN
ejpam-4577	120	10	dominating	dominating	NOUN
ejpam-4577	120	11	set	set	NOUN
ejpam-4577	120	12	of	of	ADP
ejpam-4577	120	13	g.	g.	PROPN
ejpam-4577	120	14	thus	thus	ADV
ejpam-4577	120	15	,	,	PUNCT
ejpam-4577	120	16	by	by	ADP
ejpam-4577	120	17	theorem	theorem	NOUN
ejpam-4577	120	18	1	1	NUM
ejpam-4577	120	19	,	,	PUNCT
ejpam-4577	120	20	every	every	DET
ejpam-4577	120	21	component	component	NOUN
ejpam-4577	120	22	of	of	ADP
ejpam-4577	120	23	⟨s⟩	⟨s⟩	PROPN
ejpam-4577	120	24	=	=	PUNCT
ejpam-4577	121	1	g	g	NOUN
ejpam-4577	121	2	is	be	AUX
ejpam-4577	121	3	complete	complete	ADJ
ejpam-4577	121	4	.	.	PUNCT
ejpam-4577	122	1	for	for	ADP
ejpam-4577	122	2	the	the	DET
ejpam-4577	122	3	converse	converse	NOUN
ejpam-4577	122	4	,	,	PUNCT
ejpam-4577	122	5	suppose	suppose	VERB
ejpam-4577	122	6	that	that	SCONJ
ejpam-4577	122	7	every	every	DET
ejpam-4577	122	8	component	component	NOUN
ejpam-4577	122	9	c	c	NOUN
ejpam-4577	122	10	of	of	ADP
ejpam-4577	122	11	g	g	PROPN
ejpam-4577	122	12	is	be	AUX
ejpam-4577	122	13	complete	complete	ADJ
ejpam-4577	122	14	.	.	PUNCT
ejpam-4577	123	1	then	then	ADV
ejpam-4577	123	2	by	by	ADP
ejpam-4577	123	3	proposition	proposition	NOUN
ejpam-4577	123	4	1	1	NUM
ejpam-4577	123	5	,	,	PUNCT
ejpam-4577	123	6	n	n	NOUN
ejpam-4577	123	7	=	=	NOUN
ejpam-4577	123	8	γh(g	γh(g	NOUN
ejpam-4577	123	9	)	)	PUNCT
ejpam-4577	123	10	≤	≤	NOUN
ejpam-4577	123	11	γhih(g	γhih(g	ADP
ejpam-4577	123	12	)	)	PUNCT
ejpam-4577	123	13	≤	≤	NOUN
ejpam-4577	123	14	αh(g	αh(g	NOUN
ejpam-4577	123	15	)	)	PUNCT
ejpam-4577	123	16	=	=	SYM
ejpam-4577	123	17	n.	n.	NOUN
ejpam-4577	123	18	hence	hence	ADV
ejpam-4577	123	19	,	,	PUNCT
ejpam-4577	123	20	γhih(g	γhih(g	NOUN
ejpam-4577	123	21	)	)	PUNCT
ejpam-4577	123	22	=	=	VERB
ejpam-4577	123	23	n.	n.	NOUN
ejpam-4577	123	24	the	the	DET
ejpam-4577	123	25	next	next	ADJ
ejpam-4577	123	26	result	result	NOUN
ejpam-4577	123	27	is	be	AUX
ejpam-4577	123	28	a	a	DET
ejpam-4577	123	29	direct	direct	ADJ
ejpam-4577	123	30	consequence	consequence	NOUN
ejpam-4577	123	31	of	of	ADP
ejpam-4577	123	32	theorem	theorem	ADJ
ejpam-4577	123	33	3	3	NUM
ejpam-4577	123	34	.	.	PUNCT
ejpam-4577	123	35	corollary	corollary	ADJ
ejpam-4577	123	36	2	2	NUM
ejpam-4577	123	37	.	.	PUNCT
ejpam-4577	124	1	let	let	VERB
ejpam-4577	124	2	n	n	PRON
ejpam-4577	124	3	be	be	AUX
ejpam-4577	124	4	a	a	DET
ejpam-4577	124	5	positive	positive	ADJ
ejpam-4577	124	6	integer	integer	NOUN
ejpam-4577	124	7	.	.	PUNCT
ejpam-4577	125	1	then	then	ADV
ejpam-4577	125	2	each	each	PRON
ejpam-4577	125	3	of	of	ADP
ejpam-4577	125	4	the	the	DET
ejpam-4577	125	5	following	following	ADJ
ejpam-4577	125	6	statements	statement	NOUN
ejpam-4577	125	7	holds	hold	VERB
ejpam-4577	125	8	.	.	PUNCT
ejpam-4577	126	1	(	(	PUNCT
ejpam-4577	126	2	i	i	NOUN
ejpam-4577	126	3	)	)	PUNCT
ejpam-4577	126	4	γhih(kn	γhih(kn	NOUN
ejpam-4577	126	5	)	)	PUNCT
ejpam-4577	126	6	=	=	SYM
ejpam-4577	126	7	n.	n.	NOUN
ejpam-4577	126	8	(	(	PUNCT
ejpam-4577	126	9	ii	ii	NOUN
ejpam-4577	126	10	)	)	PUNCT
ejpam-4577	126	11	γhih(kn	γhih(kn	NOUN
ejpam-4577	126	12	)	)	PUNCT
ejpam-4577	126	13	=	=	SYM
ejpam-4577	127	1	n.	n.	NOUN
ejpam-4577	127	2	(	(	PUNCT
ejpam-4577	127	3	iii	iii	NOUN
ejpam-4577	127	4	)	)	PUNCT
ejpam-4577	127	5	γhih(g	γhih(g	PROPN
ejpam-4577	127	6	)	)	PUNCT
ejpam-4577	127	7	+	+	NUM
ejpam-4577	127	8	γhih(g	γhih(g	X
ejpam-4577	127	9	)	)	PUNCT
ejpam-4577	127	10	=	=	SYM
ejpam-4577	127	11	2n	2n	NUM
ejpam-4577	127	12	if	if	SCONJ
ejpam-4577	127	13	g	g	PROPN
ejpam-4577	127	14	=	=	PROPN
ejpam-4577	127	15	kn	kn	PROPN
ejpam-4577	127	16	.	.	PUNCT
ejpam-4577	127	17	(	(	PUNCT
ejpam-4577	127	18	iv	iv	X
ejpam-4577	127	19	)	)	PUNCT
ejpam-4577	127	20	γhih(g	γhih(g	NOUN
ejpam-4577	127	21	)	)	PUNCT
ejpam-4577	127	22	≤	≤	NOUN
ejpam-4577	128	1	n	n	CCONJ
ejpam-4577	128	2	−	−	PROPN
ejpam-4577	128	3	1	1	NUM
ejpam-4577	128	4	if	if	SCONJ
ejpam-4577	128	5	g	g	PROPN
ejpam-4577	128	6	is	be	AUX
ejpam-4577	128	7	a	a	DET
ejpam-4577	128	8	graph	graph	NOUN
ejpam-4577	128	9	on	on	ADP
ejpam-4577	128	10	n	n	DET
ejpam-4577	128	11	vertices	vertex	NOUN
ejpam-4577	128	12	and	and	CCONJ
ejpam-4577	128	13	has	have	VERB
ejpam-4577	128	14	at	at	ADV
ejpam-4577	128	15	least	least	ADV
ejpam-4577	128	16	one	one	NUM
ejpam-4577	128	17	non	non	ADJ
ejpam-4577	128	18	-	-	ADJ
ejpam-4577	128	19	complete	complete	ADJ
ejpam-4577	128	20	component	component	NOUN
ejpam-4577	128	21	.	.	PUNCT
ejpam-4577	129	1	proposition	proposition	NOUN
ejpam-4577	129	2	2	2	NUM
ejpam-4577	129	3	.	.	PUNCT
ejpam-4577	130	1	let	let	VERB
ejpam-4577	130	2	g	g	PRON
ejpam-4577	130	3	be	be	AUX
ejpam-4577	130	4	a	a	DET
ejpam-4577	130	5	graph	graph	NOUN
ejpam-4577	130	6	on	on	ADP
ejpam-4577	130	7	n	n	PRON
ejpam-4577	130	8	≥	≥	NUM
ejpam-4577	130	9	3	3	NUM
ejpam-4577	130	10	vertices	vertex	NOUN
ejpam-4577	130	11	.	.	PUNCT
ejpam-4577	131	1	if	if	SCONJ
ejpam-4577	131	2	g	g	PROPN
ejpam-4577	131	3	has	have	VERB
ejpam-4577	131	4	at	at	ADV
ejpam-4577	131	5	least	least	ADV
ejpam-4577	131	6	one	one	NUM
ejpam-4577	131	7	non	non	ADJ
ejpam-4577	131	8	-	-	ADJ
ejpam-4577	131	9	complete	complete	ADJ
ejpam-4577	131	10	component	component	NOUN
ejpam-4577	131	11	,	,	PUNCT
ejpam-4577	131	12	then	then	ADV
ejpam-4577	131	13	(	(	PUNCT
ejpam-4577	131	14	i	i	NOUN
ejpam-4577	131	15	)	)	PUNCT
ejpam-4577	131	16	4	4	NUM
ejpam-4577	131	17	≤	≤	NUM
ejpam-4577	131	18	γhih(g	γhih(g	NOUN
ejpam-4577	131	19	)	)	PUNCT
ejpam-4577	131	20	+	+	NUM
ejpam-4577	131	21	γhih(g	γhih(g	NOUN
ejpam-4577	131	22	)	)	PUNCT
ejpam-4577	131	23	≤	≤	NOUN
ejpam-4577	131	24	2n−	2n−	NUM
ejpam-4577	131	25	1	1	NUM
ejpam-4577	131	26	,	,	PUNCT
ejpam-4577	131	27	and	and	CCONJ
ejpam-4577	131	28	(	(	PUNCT
ejpam-4577	131	29	ii	ii	NOUN
ejpam-4577	131	30	)	)	PUNCT
ejpam-4577	131	31	4	4	NUM
ejpam-4577	131	32	≤	≤	NUM
ejpam-4577	131	33	γhih(g	γhih(g	NOUN
ejpam-4577	131	34	)	)	PUNCT
ejpam-4577	131	35	·	·	PUNCT
ejpam-4577	132	1	γhih(g	γhih(g	ADP
ejpam-4577	132	2	)	)	PUNCT
ejpam-4577	132	3	≤	≤	NOUN
ejpam-4577	132	4	n2	n2	NOUN
ejpam-4577	132	5	−	−	PROPN
ejpam-4577	132	6	n.	n.	PROPN
ejpam-4577	132	7	j.	j.	PROPN
ejpam-4577	132	8	hassan	hassan	PROPN
ejpam-4577	132	9	,	,	PUNCT
ejpam-4577	132	10	s.	s.	PROPN
ejpam-4577	132	11	canoy	canoy	PROPN
ejpam-4577	132	12	/	/	SYM
ejpam-4577	132	13	eur	eur	PROPN
ejpam-4577	132	14	.	.	PUNCT
ejpam-4577	133	1	j.	j.	PROPN
ejpam-4577	133	2	pure	pure	PROPN
ejpam-4577	133	3	appl	appl	PROPN
ejpam-4577	133	4	.	.	PROPN
ejpam-4577	133	5	math	math	PROPN
ejpam-4577	133	6	,	,	PUNCT
ejpam-4577	133	7	15	15	NUM
ejpam-4577	133	8	(	(	PUNCT
ejpam-4577	133	9	4	4	NUM
ejpam-4577	133	10	)	)	PUNCT
ejpam-4577	133	11	(	(	PUNCT
ejpam-4577	133	12	2022	2022	NUM
ejpam-4577	133	13	)	)	PUNCT
ejpam-4577	133	14	,	,	PUNCT
ejpam-4577	133	15	1783	1783	NUM
ejpam-4577	133	16	-	-	SYM
ejpam-4577	133	17	1796	1796	NUM
ejpam-4577	133	18	1788	1788	NUM
ejpam-4577	133	19	proof	proof	NOUN
ejpam-4577	133	20	.	.	PUNCT
ejpam-4577	134	1	by	by	ADP
ejpam-4577	134	2	corollary	corollary	ADJ
ejpam-4577	134	3	2(iv	2(iv	NUM
ejpam-4577	134	4	)	)	PUNCT
ejpam-4577	134	5	,	,	PUNCT
ejpam-4577	134	6	γhih(g	γhih(g	NOUN
ejpam-4577	134	7	)	)	PUNCT
ejpam-4577	134	8	≤	≤	NOUN
ejpam-4577	134	9	n	n	CCONJ
ejpam-4577	134	10	−	−	PROPN
ejpam-4577	134	11	1	1	NUM
ejpam-4577	134	12	and	and	CCONJ
ejpam-4577	134	13	by	by	ADP
ejpam-4577	134	14	theorem	theorem	ADJ
ejpam-4577	134	15	3	3	NUM
ejpam-4577	134	16	,	,	PUNCT
ejpam-4577	134	17	γhih(g	γhih(g	NOUN
ejpam-4577	134	18	)	)	PUNCT
ejpam-4577	134	19	≤	≤	NOUN
ejpam-4577	134	20	n.	n.	NOUN
ejpam-4577	134	21	these	these	PRON
ejpam-4577	134	22	imply	imply	VERB
ejpam-4577	134	23	that	that	SCONJ
ejpam-4577	134	24	γhih(g)+γhih(g	γhih(g)+γhih(g	NOUN
ejpam-4577	134	25	)	)	PUNCT
ejpam-4577	134	26	≤	≤	NUM
ejpam-4577	134	27	n−1+n	n−1+n	NOUN
ejpam-4577	134	28	=	=	PROPN
ejpam-4577	134	29	2n−1	2n−1	PROPN
ejpam-4577	134	30	and	and	CCONJ
ejpam-4577	134	31	γhih(g)·γhih(g	γhih(g)·γhih(g	NOUN
ejpam-4577	134	32	)	)	PUNCT
ejpam-4577	134	33	≤	≤	NOUN
ejpam-4577	134	34	(	(	PUNCT
ejpam-4577	134	35	n−1)n	n−1)n	PROPN
ejpam-4577	134	36	=	=	SYM
ejpam-4577	134	37	n2−n	n2−n	PROPN
ejpam-4577	134	38	.	.	PUNCT
ejpam-4577	135	1	since	since	SCONJ
ejpam-4577	135	2	γhih(g	γhih(g	NOUN
ejpam-4577	135	3	)	)	PUNCT
ejpam-4577	135	4	≥	≥	NOUN
ejpam-4577	135	5	2	2	NUM
ejpam-4577	135	6	for	for	ADP
ejpam-4577	135	7	any	any	DET
ejpam-4577	135	8	graph	graph	NOUN
ejpam-4577	135	9	of	of	ADP
ejpam-4577	135	10	order	order	NOUN
ejpam-4577	135	11	at	at	ADV
ejpam-4577	135	12	least	least	ADV
ejpam-4577	135	13	2	2	NUM
ejpam-4577	135	14	,	,	PUNCT
ejpam-4577	135	15	the	the	DET
ejpam-4577	135	16	left	left	ADJ
ejpam-4577	135	17	inequalities	inequality	NOUN
ejpam-4577	135	18	follow	follow	VERB
ejpam-4577	135	19	.	.	PUNCT
ejpam-4577	136	1	theorem	theorem	ADJ
ejpam-4577	136	2	4	4	NUM
ejpam-4577	136	3	.	.	PUNCT
ejpam-4577	137	1	let	let	VERB
ejpam-4577	137	2	g	g	NOUN
ejpam-4577	137	3	be	be	AUX
ejpam-4577	137	4	any	any	DET
ejpam-4577	137	5	graph	graph	NOUN
ejpam-4577	137	6	of	of	ADP
ejpam-4577	137	7	order	order	NOUN
ejpam-4577	137	8	n	n	PRON
ejpam-4577	137	9	≥	≥	NOUN
ejpam-4577	137	10	3	3	NUM
ejpam-4577	137	11	.	.	PUNCT
ejpam-4577	137	12	then	then	ADV
ejpam-4577	137	13	γhih(g	γhih(g	ADP
ejpam-4577	137	14	)	)	PUNCT
ejpam-4577	138	1	=	=	PUNCT
ejpam-4577	138	2	n−	n−	NOUN
ejpam-4577	138	3	1	1	NUM
ejpam-4577	138	4	if	if	SCONJ
ejpam-4577	138	5	and	and	CCONJ
ejpam-4577	138	6	only	only	ADV
ejpam-4577	138	7	if	if	SCONJ
ejpam-4577	138	8	all	all	DET
ejpam-4577	138	9	but	but	SCONJ
ejpam-4577	138	10	one	one	NUM
ejpam-4577	138	11	component	component	NOUN
ejpam-4577	138	12	h	h	NOUN
ejpam-4577	138	13	of	of	ADP
ejpam-4577	138	14	g	g	PROPN
ejpam-4577	138	15	are	be	AUX
ejpam-4577	138	16	cliques	clique	NOUN
ejpam-4577	138	17	,	,	PUNCT
ejpam-4577	138	18	where	where	SCONJ
ejpam-4577	138	19	h	h	NOUN
ejpam-4577	138	20	=	=	SYM
ejpam-4577	138	21	k|v	k|v	PROPN
ejpam-4577	138	22	(	(	PUNCT
ejpam-4577	138	23	h)|	h)|	PROPN
ejpam-4577	138	24	\e	\e	PROPN
ejpam-4577	138	25	(	(	PUNCT
ejpam-4577	138	26	h	h	NOUN
ejpam-4577	138	27	is	be	AUX
ejpam-4577	138	28	obtained	obtain	VERB
ejpam-4577	138	29	from	from	ADP
ejpam-4577	138	30	k|v	k|v	PROPN
ejpam-4577	138	31	(	(	PUNCT
ejpam-4577	138	32	h)|	h)|	NOUN
ejpam-4577	138	33	by	by	ADP
ejpam-4577	138	34	deleting	delete	VERB
ejpam-4577	138	35	an	an	DET
ejpam-4577	138	36	edge	edge	NOUN
ejpam-4577	138	37	e	e	NOUN
ejpam-4577	138	38	)	)	PUNCT
ejpam-4577	138	39	.	.	PUNCT
ejpam-4577	139	1	proof	proof	NOUN
ejpam-4577	139	2	.	.	PUNCT
ejpam-4577	140	1	suppose	suppose	VERB
ejpam-4577	140	2	γhih(g	γhih(g	ADP
ejpam-4577	140	3	)	)	PUNCT
ejpam-4577	140	4	=	=	SYM
ejpam-4577	141	1	n−1	n−1	PROPN
ejpam-4577	141	2	.	.	PUNCT
ejpam-4577	142	1	let	let	VERB
ejpam-4577	142	2	s	s	AUX
ejpam-4577	142	3	=	=	X
ejpam-4577	142	4	v	v	PROPN
ejpam-4577	142	5	(	(	PUNCT
ejpam-4577	142	6	g)\{v	g)\{v	PROPN
ejpam-4577	142	7	}	}	PUNCT
ejpam-4577	142	8	be	be	AUX
ejpam-4577	142	9	a	a	DET
ejpam-4577	142	10	γhih	γhih	NOUN
ejpam-4577	142	11	-	-	PUNCT
ejpam-4577	142	12	set	set	NOUN
ejpam-4577	142	13	.	.	PUNCT
ejpam-4577	143	1	let	let	VERB
ejpam-4577	143	2	g1	g1	PROPN
ejpam-4577	143	3	,	,	PUNCT
ejpam-4577	143	4	g2	g2	PROPN
ejpam-4577	143	5	,	,	PUNCT
ejpam-4577	143	6	.	.	PUNCT
ejpam-4577	143	7	.	.	PUNCT
ejpam-4577	144	1	.	.	PUNCT
ejpam-4577	145	1	,	,	PUNCT
ejpam-4577	145	2	gk	gk	PROPN
ejpam-4577	145	3	be	be	AUX
ejpam-4577	145	4	the	the	DET
ejpam-4577	145	5	components	component	NOUN
ejpam-4577	145	6	of	of	ADP
ejpam-4577	145	7	⟨s⟩.	⟨s⟩.	PROPN
ejpam-4577	145	8	then	then	ADV
ejpam-4577	145	9	each	each	DET
ejpam-4577	145	10	gi	gi	NOUN
ejpam-4577	145	11	is	be	AUX
ejpam-4577	145	12	a	a	DET
ejpam-4577	145	13	clique	clique	NOUN
ejpam-4577	145	14	.	.	PUNCT
ejpam-4577	146	1	since	since	SCONJ
ejpam-4577	146	2	v	v	NUM
ejpam-4577	146	3	/∈	/∈	PUNCT
ejpam-4577	146	4	s	s	PART
ejpam-4577	146	5	and	and	CCONJ
ejpam-4577	146	6	s	s	VERB
ejpam-4577	146	7	is	be	AUX
ejpam-4577	146	8	a	a	DET
ejpam-4577	146	9	hop	hop	NOUN
ejpam-4577	146	10	dominating	dominating	NOUN
ejpam-4577	146	11	set	set	NOUN
ejpam-4577	146	12	,	,	PUNCT
ejpam-4577	146	13	there	there	PRON
ejpam-4577	146	14	exists	exist	VERB
ejpam-4577	146	15	w	w	PROPN
ejpam-4577	146	16	∈	∈	PROPN
ejpam-4577	146	17	s	s	VERB
ejpam-4577	146	18	such	such	ADJ
ejpam-4577	146	19	that	that	PRON
ejpam-4577	146	20	dg(v	dg(v	ADJ
ejpam-4577	146	21	,	,	PUNCT
ejpam-4577	146	22	w	w	NOUN
ejpam-4577	146	23	)	)	PUNCT
ejpam-4577	146	24	=	=	SYM
ejpam-4577	146	25	2	2	X
ejpam-4577	146	26	.	.	X
ejpam-4577	146	27	assume	assume	VERB
ejpam-4577	146	28	that	that	SCONJ
ejpam-4577	146	29	w	w	PROPN
ejpam-4577	146	30	∈	∈	PROPN
ejpam-4577	146	31	v	v	NOUN
ejpam-4577	146	32	(	(	PUNCT
ejpam-4577	146	33	g1	g1	PROPN
ejpam-4577	146	34	)	)	PUNCT
ejpam-4577	146	35	.	.	PUNCT
ejpam-4577	147	1	let	let	VERB
ejpam-4577	147	2	z	z	NOUN
ejpam-4577	147	3	∈	∈	PROPN
ejpam-4577	147	4	ng(v)∩ng(w	ng(v)∩ng(w	PROPN
ejpam-4577	147	5	)	)	PUNCT
ejpam-4577	147	6	.	.	PUNCT
ejpam-4577	148	1	then	then	ADV
ejpam-4577	148	2	z	z	PROPN
ejpam-4577	148	3	∈	∈	PROPN
ejpam-4577	148	4	v	v	X
ejpam-4577	148	5	(	(	PUNCT
ejpam-4577	148	6	g1	g1	PROPN
ejpam-4577	148	7	)	)	PUNCT
ejpam-4577	148	8	.	.	PUNCT
ejpam-4577	149	1	suppose	suppose	VERB
ejpam-4577	149	2	there	there	PRON
ejpam-4577	149	3	exists	exist	VERB
ejpam-4577	149	4	j	j	PROPN
ejpam-4577	149	5	̸=	̸=	PROPN
ejpam-4577	149	6	1	1	NUM
ejpam-4577	149	7	such	such	ADJ
ejpam-4577	149	8	that	that	SCONJ
ejpam-4577	149	9	vp	vp	PROPN
ejpam-4577	149	10	∈	∈	PROPN
ejpam-4577	149	11	e(g	e(g	PROPN
ejpam-4577	149	12	)	)	PUNCT
ejpam-4577	149	13	for	for	ADP
ejpam-4577	149	14	some	some	DET
ejpam-4577	149	15	p	p	NOUN
ejpam-4577	149	16	∈	∈	PROPN
ejpam-4577	149	17	v	v	NOUN
ejpam-4577	149	18	(	(	PUNCT
ejpam-4577	149	19	gj	gj	NOUN
ejpam-4577	149	20	)	)	PUNCT
ejpam-4577	149	21	.	.	PUNCT
ejpam-4577	150	1	then	then	ADV
ejpam-4577	150	2	s∗	s∗	PROPN
ejpam-4577	150	3	=	=	SYM
ejpam-4577	150	4	v	v	PROPN
ejpam-4577	150	5	(	(	PUNCT
ejpam-4577	150	6	g	g	NOUN
ejpam-4577	150	7	)	)	PUNCT
ejpam-4577	150	8	\	\	NOUN
ejpam-4577	150	9	{	{	PUNCT
ejpam-4577	150	10	v	v	NOUN
ejpam-4577	150	11	,	,	PUNCT
ejpam-4577	150	12	p	p	PRON
ejpam-4577	150	13	}	}	PUNCT
ejpam-4577	150	14	is	be	AUX
ejpam-4577	150	15	a	a	DET
ejpam-4577	150	16	hop	hop	NOUN
ejpam-4577	150	17	independent	independent	ADJ
ejpam-4577	150	18	hop	hop	NOUN
ejpam-4577	150	19	dominating	dominating	NOUN
ejpam-4577	150	20	set	set	NOUN
ejpam-4577	150	21	in	in	ADP
ejpam-4577	150	22	g	g	PROPN
ejpam-4577	150	23	,	,	PUNCT
ejpam-4577	150	24	contrary	contrary	ADV
ejpam-4577	150	25	to	to	ADP
ejpam-4577	150	26	the	the	DET
ejpam-4577	150	27	assumption	assumption	NOUN
ejpam-4577	150	28	that	that	SCONJ
ejpam-4577	150	29	γhih(g	γhih(g	ADP
ejpam-4577	150	30	)	)	PUNCT
ejpam-4577	150	31	=	=	SYM
ejpam-4577	151	1	n−1	n−1	PROPN
ejpam-4577	151	2	.	.	PUNCT
ejpam-4577	152	1	this	this	PRON
ejpam-4577	152	2	implies	imply	VERB
ejpam-4577	152	3	that	that	SCONJ
ejpam-4577	152	4	the	the	DET
ejpam-4577	152	5	components	component	NOUN
ejpam-4577	152	6	ofg	ofg	PROPN
ejpam-4577	152	7	are	be	AUX
ejpam-4577	152	8	⟨v	⟨v	NUM
ejpam-4577	152	9	(	(	PUNCT
ejpam-4577	152	10	g1)∪{v}⟩	g1)∪{v}⟩	PROPN
ejpam-4577	152	11	,	,	PUNCT
ejpam-4577	152	12	g2	g2	PROPN
ejpam-4577	152	13	,	,	PUNCT
ejpam-4577	152	14	.	.	PUNCT
ejpam-4577	152	15	.	.	PUNCT
ejpam-4577	153	1	.	.	PUNCT
ejpam-4577	154	1	,	,	PUNCT
ejpam-4577	154	2	gk	gk	PROPN
ejpam-4577	154	3	.	.	PUNCT
ejpam-4577	155	1	now	now	ADV
ejpam-4577	155	2	,	,	PUNCT
ejpam-4577	155	3	we	we	PRON
ejpam-4577	155	4	will	will	AUX
ejpam-4577	155	5	show	show	VERB
ejpam-4577	155	6	that	that	SCONJ
ejpam-4577	155	7	xv	xv	PROPN
ejpam-4577	155	8	∈	∈	PROPN
ejpam-4577	155	9	e(g	e(g	PROPN
ejpam-4577	155	10	)	)	PUNCT
ejpam-4577	155	11	for	for	ADP
ejpam-4577	155	12	every	every	DET
ejpam-4577	155	13	x	x	SYM
ejpam-4577	155	14	∈	∈	PROPN
ejpam-4577	155	15	v	v	NOUN
ejpam-4577	155	16	(	(	PUNCT
ejpam-4577	155	17	g1	g1	PROPN
ejpam-4577	155	18	)	)	PUNCT
ejpam-4577	155	19	\	\	NOUN
ejpam-4577	155	20	{	{	PUNCT
ejpam-4577	155	21	w	w	NOUN
ejpam-4577	155	22	}	}	PUNCT
ejpam-4577	155	23	.	.	PUNCT
ejpam-4577	156	1	suppose	suppose	VERB
ejpam-4577	156	2	there	there	PRON
ejpam-4577	156	3	exists	exist	VERB
ejpam-4577	156	4	q	q	PROPN
ejpam-4577	156	5	∈	∈	PROPN
ejpam-4577	156	6	v	v	NOUN
ejpam-4577	156	7	(	(	PUNCT
ejpam-4577	156	8	g1	g1	PROPN
ejpam-4577	156	9	)	)	PUNCT
ejpam-4577	156	10	\	\	PROPN
ejpam-4577	156	11	{	{	PUNCT
ejpam-4577	156	12	w	w	NOUN
ejpam-4577	156	13	}	}	PUNCT
ejpam-4577	156	14	such	such	ADJ
ejpam-4577	156	15	that	that	SCONJ
ejpam-4577	156	16	qv	qv	PROPN
ejpam-4577	156	17	/∈	/∈	PUNCT
ejpam-4577	156	18	e(g	e(g	PROPN
ejpam-4577	156	19	)	)	PUNCT
ejpam-4577	156	20	.	.	PUNCT
ejpam-4577	157	1	then	then	ADV
ejpam-4577	157	2	dg(q	dg(q	NUM
ejpam-4577	157	3	,	,	PUNCT
ejpam-4577	157	4	v	v	NOUN
ejpam-4577	157	5	)	)	PUNCT
ejpam-4577	157	6	=	=	SYM
ejpam-4577	157	7	2	2	X
ejpam-4577	157	8	.	.	PUNCT
ejpam-4577	157	9	let	let	VERB
ejpam-4577	157	10	d	d	NOUN
ejpam-4577	157	11	=	=	PRON
ejpam-4577	157	12	{	{	PUNCT
ejpam-4577	157	13	t	t	NOUN
ejpam-4577	157	14	∈	∈	PROPN
ejpam-4577	157	15	v	v	PROPN
ejpam-4577	157	16	(	(	PUNCT
ejpam-4577	157	17	g1	g1	PROPN
ejpam-4577	157	18	)	)	PUNCT
ejpam-4577	157	19	:	:	PUNCT
ejpam-4577	157	20	vt	vt	PROPN
ejpam-4577	157	21	/∈	/∈	PROPN
ejpam-4577	157	22	e(g	e(g	PROPN
ejpam-4577	157	23	)	)	PUNCT
ejpam-4577	157	24	}	}	PUNCT
ejpam-4577	157	25	.	.	PUNCT
ejpam-4577	158	1	then	then	ADV
ejpam-4577	158	2	|d|	|d|	PROPN
ejpam-4577	158	3	≥	≥	NUM
ejpam-4577	158	4	2	2	NUM
ejpam-4577	158	5	and	and	CCONJ
ejpam-4577	158	6	⟨v	⟨v	NUM
ejpam-4577	158	7	(	(	PUNCT
ejpam-4577	158	8	g1	g1	PROPN
ejpam-4577	158	9	)	)	PUNCT
ejpam-4577	158	10	\	\	NOUN
ejpam-4577	158	11	d⟩	d⟩	NOUN
ejpam-4577	158	12	is	be	AUX
ejpam-4577	158	13	a	a	DET
ejpam-4577	158	14	clique	clique	NOUN
ejpam-4577	158	15	.	.	PUNCT
ejpam-4577	159	1	notice	notice	VERB
ejpam-4577	159	2	that	that	SCONJ
ejpam-4577	159	3	dg(v	dg(v	NOUN
ejpam-4577	159	4	,	,	PUNCT
ejpam-4577	159	5	t	t	NOUN
ejpam-4577	159	6	)	)	PUNCT
ejpam-4577	159	7	=	=	SYM
ejpam-4577	159	8	2	2	NUM
ejpam-4577	159	9	for	for	ADP
ejpam-4577	159	10	every	every	DET
ejpam-4577	159	11	t	t	PROPN
ejpam-4577	159	12	∈	∈	PROPN
ejpam-4577	159	13	d.	d.	PROPN
ejpam-4577	159	14	now	now	ADV
ejpam-4577	159	15	,	,	PUNCT
ejpam-4577	159	16	let	let	VERB
ejpam-4577	159	17	s′	s′	ADJ
ejpam-4577	159	18	=	=	SYM
ejpam-4577	159	19	v	v	ADJ
ejpam-4577	159	20	(	(	PUNCT
ejpam-4577	159	21	g	g	NOUN
ejpam-4577	159	22	)	)	PUNCT
ejpam-4577	159	23	\	\	PROPN
ejpam-4577	159	24	d.	d.	PROPN
ejpam-4577	159	25	then	then	ADV
ejpam-4577	159	26	s′	s′	PROPN
ejpam-4577	159	27	is	be	AUX
ejpam-4577	159	28	a	a	DET
ejpam-4577	159	29	hop	hop	NOUN
ejpam-4577	159	30	dominating	dominating	NOUN
ejpam-4577	159	31	set	set	NOUN
ejpam-4577	159	32	.	.	PUNCT
ejpam-4577	160	1	since	since	SCONJ
ejpam-4577	160	2	the	the	DET
ejpam-4577	160	3	components	component	NOUN
ejpam-4577	160	4	of	of	ADP
ejpam-4577	160	5	⟨s′⟩	⟨s′⟩	PROPN
ejpam-4577	160	6	are	be	AUX
ejpam-4577	160	7	⟨v	⟨v	NUM
ejpam-4577	160	8	(	(	PUNCT
ejpam-4577	160	9	g1	g1	PROPN
ejpam-4577	160	10	)	)	PUNCT
ejpam-4577	160	11	\	\	PROPN
ejpam-4577	160	12	d⟩	d⟩	NOUN
ejpam-4577	160	13	,	,	PUNCT
ejpam-4577	160	14	g2	g2	PROPN
ejpam-4577	160	15	,	,	PUNCT
ejpam-4577	160	16	.	.	PUNCT
ejpam-4577	160	17	.	.	PUNCT
ejpam-4577	161	1	.	.	PUNCT
ejpam-4577	162	1	,	,	PUNCT
ejpam-4577	162	2	gk	gk	INTJ
ejpam-4577	162	3	,	,	PUNCT
ejpam-4577	162	4	it	it	PRON
ejpam-4577	162	5	follows	follow	VERB
ejpam-4577	162	6	that	that	SCONJ
ejpam-4577	162	7	s′	s′	ADJ
ejpam-4577	162	8	is	be	AUX
ejpam-4577	162	9	a	a	DET
ejpam-4577	162	10	hop	hop	NOUN
ejpam-4577	162	11	independent	independent	ADJ
ejpam-4577	162	12	set	set	NOUN
ejpam-4577	162	13	.	.	PUNCT
ejpam-4577	163	1	hence	hence	ADV
ejpam-4577	163	2	,	,	PUNCT
ejpam-4577	163	3	γhih(g	γhih(g	NOUN
ejpam-4577	163	4	)	)	PUNCT
ejpam-4577	163	5	≤	≤	NOUN
ejpam-4577	163	6	|s′|	|s′|	NOUN
ejpam-4577	163	7	=	=	SYM
ejpam-4577	163	8	n	n	CCONJ
ejpam-4577	163	9	−	−	PROPN
ejpam-4577	163	10	|d|	|d|	PROPN
ejpam-4577	163	11	≤	≤	PROPN
ejpam-4577	163	12	n	n	CCONJ
ejpam-4577	163	13	−	−	PROPN
ejpam-4577	163	14	2	2	NUM
ejpam-4577	163	15	,	,	PUNCT
ejpam-4577	163	16	a	a	DET
ejpam-4577	163	17	contradiction	contradiction	NOUN
ejpam-4577	163	18	.	.	PUNCT
ejpam-4577	164	1	hence	hence	ADV
ejpam-4577	164	2	,	,	PUNCT
ejpam-4577	164	3	xv	xv	PROPN
ejpam-4577	164	4	∈	∈	PROPN
ejpam-4577	164	5	e(g	e(g	PROPN
ejpam-4577	164	6	)	)	PUNCT
ejpam-4577	165	1	for	for	ADP
ejpam-4577	165	2	every	every	DET
ejpam-4577	165	3	x	x	SYM
ejpam-4577	165	4	∈	∈	PROPN
ejpam-4577	165	5	v	v	NOUN
ejpam-4577	165	6	(	(	PUNCT
ejpam-4577	165	7	g1	g1	PROPN
ejpam-4577	165	8	)	)	PUNCT
ejpam-4577	165	9	\	\	NOUN
ejpam-4577	165	10	{	{	PUNCT
ejpam-4577	165	11	w	w	NOUN
ejpam-4577	165	12	}	}	PUNCT
ejpam-4577	165	13	.	.	PUNCT
ejpam-4577	166	1	this	this	PRON
ejpam-4577	166	2	implies	imply	VERB
ejpam-4577	166	3	that	that	SCONJ
ejpam-4577	166	4	h	h	NOUN
ejpam-4577	166	5	=	=	SYM
ejpam-4577	166	6	⟨v	⟨v	PUNCT
ejpam-4577	166	7	(	(	PUNCT
ejpam-4577	166	8	g1)∪	g1)∪	NOUN
ejpam-4577	166	9	{	{	PUNCT
ejpam-4577	166	10	v}⟩	v}⟩	PROPN
ejpam-4577	166	11	=	=	SYM
ejpam-4577	166	12	kv	kv	PROPN
ejpam-4577	166	13	(	(	PUNCT
ejpam-4577	166	14	h	h	NOUN
ejpam-4577	166	15	)	)	PUNCT
ejpam-4577	166	16	\	\	NOUN
ejpam-4577	167	1	e	e	NOUN
ejpam-4577	167	2	,	,	PUNCT
ejpam-4577	167	3	where	where	SCONJ
ejpam-4577	167	4	e	e	PROPN
ejpam-4577	167	5	=	=	PROPN
ejpam-4577	167	6	vw	vw	PROPN
ejpam-4577	167	7	.	.	PUNCT
ejpam-4577	168	1	the	the	DET
ejpam-4577	168	2	converse	converse	NOUN
ejpam-4577	168	3	is	be	AUX
ejpam-4577	168	4	clear	clear	ADJ
ejpam-4577	168	5	.	.	PUNCT
ejpam-4577	169	1	the	the	DET
ejpam-4577	169	2	next	next	ADJ
ejpam-4577	169	3	result	result	NOUN
ejpam-4577	169	4	follows	follow	VERB
ejpam-4577	169	5	from	from	ADP
ejpam-4577	169	6	theorem	theorem	ADJ
ejpam-4577	169	7	4	4	NUM
ejpam-4577	169	8	.	.	PUNCT
ejpam-4577	169	9	corollary	corollary	ADJ
ejpam-4577	169	10	3	3	X
ejpam-4577	169	11	.	.	PUNCT
ejpam-4577	170	1	let	let	VERB
ejpam-4577	170	2	g	g	PRON
ejpam-4577	170	3	be	be	AUX
ejpam-4577	170	4	a	a	DET
ejpam-4577	170	5	connected	connected	ADJ
ejpam-4577	170	6	graph	graph	NOUN
ejpam-4577	170	7	of	of	ADP
ejpam-4577	170	8	order	order	NOUN
ejpam-4577	170	9	n	n	PRON
ejpam-4577	170	10	≥	≥	NOUN
ejpam-4577	170	11	3	3	NUM
ejpam-4577	170	12	.	.	PUNCT
ejpam-4577	170	13	then	then	ADV
ejpam-4577	170	14	γhih(g	γhih(g	ADP
ejpam-4577	170	15	)	)	PUNCT
ejpam-4577	170	16	=	=	SYM
ejpam-4577	170	17	n	n	CCONJ
ejpam-4577	170	18	−	−	PROPN
ejpam-4577	170	19	1	1	NUM
ejpam-4577	170	20	if	if	SCONJ
ejpam-4577	170	21	and	and	CCONJ
ejpam-4577	170	22	only	only	ADV
ejpam-4577	170	23	if	if	SCONJ
ejpam-4577	170	24	g	g	PROPN
ejpam-4577	170	25	=	=	SYM
ejpam-4577	170	26	kn	kn	PROPN
ejpam-4577	170	27	\	\	PROPN
ejpam-4577	170	28	e	e	NOUN
ejpam-4577	170	29	for	for	ADP
ejpam-4577	170	30	some	some	DET
ejpam-4577	170	31	e	e	PROPN
ejpam-4577	170	32	∈	∈	PROPN
ejpam-4577	170	33	e(kn	e(kn	NUM
ejpam-4577	170	34	)	)	PUNCT
ejpam-4577	170	35	.	.	PUNCT
ejpam-4577	171	1	theorem	theorem	NOUN
ejpam-4577	171	2	5	5	NUM
ejpam-4577	171	3	.	.	PUNCT
ejpam-4577	172	1	let	let	VERB
ejpam-4577	172	2	g	g	PRON
ejpam-4577	172	3	be	be	AUX
ejpam-4577	172	4	a	a	DET
ejpam-4577	172	5	non	non	ADJ
ejpam-4577	172	6	-	-	ADJ
ejpam-4577	172	7	trivial	trivial	ADJ
ejpam-4577	172	8	connected	connected	ADJ
ejpam-4577	172	9	graph	graph	NOUN
ejpam-4577	172	10	.	.	PUNCT
ejpam-4577	173	1	then	then	ADV
ejpam-4577	173	2	s	s	VERB
ejpam-4577	173	3	is	be	AUX
ejpam-4577	173	4	a	a	DET
ejpam-4577	173	5	hop	hop	NOUN
ejpam-4577	173	6	independent	independent	ADJ
ejpam-4577	173	7	hop	hop	NOUN
ejpam-4577	173	8	dominating	dominating	NOUN
ejpam-4577	173	9	set	set	NOUN
ejpam-4577	173	10	of	of	ADP
ejpam-4577	173	11	s(g	s(g	PROPN
ejpam-4577	173	12	)	)	PUNCT
ejpam-4577	173	13	if	if	SCONJ
ejpam-4577	173	14	and	and	CCONJ
ejpam-4577	173	15	only	only	ADV
ejpam-4577	173	16	if	if	SCONJ
ejpam-4577	173	17	one	one	NUM
ejpam-4577	173	18	of	of	ADP
ejpam-4577	173	19	the	the	DET
ejpam-4577	173	20	following	follow	VERB
ejpam-4577	173	21	conditions	condition	NOUN
ejpam-4577	173	22	holds	hold	VERB
ejpam-4577	173	23	:	:	PUNCT
ejpam-4577	173	24	(	(	PUNCT
ejpam-4577	173	25	i	i	NOUN
ejpam-4577	173	26	)	)	PUNCT
ejpam-4577	173	27	s	s	VERB
ejpam-4577	173	28	is	be	AUX
ejpam-4577	173	29	a	a	DET
ejpam-4577	173	30	hop	hop	NOUN
ejpam-4577	173	31	independent	independent	ADJ
ejpam-4577	173	32	hop	hop	NOUN
ejpam-4577	173	33	dominating	dominating	NOUN
ejpam-4577	173	34	set	set	VERB
ejpam-4577	173	35	in	in	ADP
ejpam-4577	173	36	g1	g1	PROPN
ejpam-4577	173	37	.	.	PUNCT
ejpam-4577	174	1	(	(	PUNCT
ejpam-4577	174	2	ii	ii	X
ejpam-4577	174	3	)	)	PUNCT
ejpam-4577	174	4	s	s	VERB
ejpam-4577	174	5	is	be	AUX
ejpam-4577	174	6	a	a	DET
ejpam-4577	174	7	hop	hop	NOUN
ejpam-4577	174	8	independent	independent	ADJ
ejpam-4577	174	9	hop	hop	NOUN
ejpam-4577	174	10	dominating	dominating	NOUN
ejpam-4577	174	11	set	set	NOUN
ejpam-4577	174	12	in	in	ADP
ejpam-4577	174	13	g2	g2	PROPN
ejpam-4577	174	14	.	.	PUNCT
ejpam-4577	175	1	(	(	PUNCT
ejpam-4577	175	2	iii	iii	X
ejpam-4577	175	3	)	)	PUNCT
ejpam-4577	175	4	s	s	PART
ejpam-4577	175	5	=	=	NOUN
ejpam-4577	175	6	sg1	sg1	NOUN
ejpam-4577	175	7	∪	∪	VERB
ejpam-4577	175	8	sg2	sg2	PROPN
ejpam-4577	175	9	such	such	ADJ
ejpam-4577	175	10	that	that	SCONJ
ejpam-4577	175	11	sg1	sg1	NOUN
ejpam-4577	175	12	∪	∪	ADP
ejpam-4577	175	13	s′	s′	ADJ
ejpam-4577	175	14	g2	g2	PROPN
ejpam-4577	175	15	and	and	CCONJ
ejpam-4577	175	16	s′	s′	ADJ
ejpam-4577	175	17	g1	g1	PROPN
ejpam-4577	175	18	∪	∪	ADP
ejpam-4577	175	19	sg2	sg2	PROPN
ejpam-4577	175	20	are	be	AUX
ejpam-4577	175	21	hop	hop	ADV
ejpam-4577	175	22	independent	independent	ADJ
ejpam-4577	175	23	hop	hop	NOUN
ejpam-4577	175	24	dominating	dominating	NOUN
ejpam-4577	175	25	sets	set	NOUN
ejpam-4577	175	26	in	in	ADP
ejpam-4577	175	27	g1	g1	PROPN
ejpam-4577	175	28	and	and	CCONJ
ejpam-4577	175	29	g2	g2	PROPN
ejpam-4577	175	30	,	,	PUNCT
ejpam-4577	175	31	respectively	respectively	ADV
ejpam-4577	175	32	,	,	PUNCT
ejpam-4577	175	33	where	where	SCONJ
ejpam-4577	175	34	s	s	AUX
ejpam-4577	175	35	′	′	NUM
ejpam-4577	175	36	g2	g2	PROPN
ejpam-4577	175	37	=	=	PRON
ejpam-4577	175	38	{	{	PUNCT
ejpam-4577	175	39	a	a	PRON
ejpam-4577	175	40	∈	∈	PROPN
ejpam-4577	175	41	v	v	NOUN
ejpam-4577	175	42	(	(	PUNCT
ejpam-4577	175	43	g1	g1	PROPN
ejpam-4577	175	44	)	)	PUNCT
ejpam-4577	175	45	:	:	PUNCT
ejpam-4577	175	46	a	a	DET
ejpam-4577	175	47	′	′	NUM
ejpam-4577	175	48	∈	∈	PROPN
ejpam-4577	175	49	sg2	sg2	PROPN
ejpam-4577	175	50	}	}	PUNCT
ejpam-4577	175	51	and	and	CCONJ
ejpam-4577	175	52	s′	s′	ADJ
ejpam-4577	175	53	g1	g1	PROPN
ejpam-4577	175	54	=	=	PUNCT
ejpam-4577	175	55	{	{	PUNCT
ejpam-4577	175	56	a	a	DET
ejpam-4577	175	57	∈	∈	PROPN
ejpam-4577	175	58	v	v	NOUN
ejpam-4577	175	59	(	(	PUNCT
ejpam-4577	175	60	g2	g2	PROPN
ejpam-4577	175	61	)	)	PUNCT
ejpam-4577	175	62	:	:	PUNCT
ejpam-4577	175	63	a	a	DET
ejpam-4577	175	64	′	′	NUM
ejpam-4577	175	65	∈	∈	NOUN
ejpam-4577	175	66	sg1	sg1	NOUN
ejpam-4577	175	67	}	}	PUNCT
ejpam-4577	175	68	.	.	PUNCT
ejpam-4577	176	1	proof	proof	NOUN
ejpam-4577	176	2	.	.	PUNCT
ejpam-4577	177	1	let	let	VERB
ejpam-4577	177	2	s	s	PRON
ejpam-4577	177	3	be	be	AUX
ejpam-4577	177	4	a	a	DET
ejpam-4577	177	5	hop	hop	NOUN
ejpam-4577	177	6	independent	independent	ADJ
ejpam-4577	177	7	hop	hop	NOUN
ejpam-4577	177	8	dominating	dominating	NOUN
ejpam-4577	177	9	set	set	NOUN
ejpam-4577	177	10	of	of	ADP
ejpam-4577	177	11	s(g	s(g	PROPN
ejpam-4577	177	12	)	)	PUNCT
ejpam-4577	177	13	.	.	PUNCT
ejpam-4577	178	1	set	set	VERB
ejpam-4577	178	2	sg1	sg1	NOUN
ejpam-4577	178	3	=	=	SYM
ejpam-4577	178	4	s	s	PART
ejpam-4577	178	5	∩v	∩v	NOUN
ejpam-4577	178	6	(	(	PUNCT
ejpam-4577	178	7	g1	g1	PROPN
ejpam-4577	178	8	)	)	PUNCT
ejpam-4577	178	9	and	and	CCONJ
ejpam-4577	178	10	sg2	sg2	PROPN
ejpam-4577	178	11	=	=	PROPN
ejpam-4577	178	12	s	s	PROPN
ejpam-4577	178	13	∩	∩	ADJ
ejpam-4577	178	14	v	v	X
ejpam-4577	178	15	(	(	PUNCT
ejpam-4577	178	16	g2	g2	PROPN
ejpam-4577	178	17	)	)	PUNCT
ejpam-4577	178	18	.	.	PUNCT
ejpam-4577	179	1	if	if	SCONJ
ejpam-4577	179	2	sg2	sg2	PROPN
ejpam-4577	179	3	=	=	SYM
ejpam-4577	179	4	∅	∅	NOUN
ejpam-4577	179	5	,	,	PUNCT
ejpam-4577	179	6	then	then	ADV
ejpam-4577	179	7	s	s	PART
ejpam-4577	179	8	=	=	NOUN
ejpam-4577	179	9	sg1	sg1	PROPN
ejpam-4577	179	10	is	be	AUX
ejpam-4577	179	11	a	a	DET
ejpam-4577	179	12	hop	hop	NOUN
ejpam-4577	179	13	independent	independent	ADJ
ejpam-4577	179	14	hop	hop	NOUN
ejpam-4577	179	15	dominating	dominating	NOUN
ejpam-4577	179	16	set	set	NOUN
ejpam-4577	179	17	of	of	ADP
ejpam-4577	179	18	g1	g1	PROPN
ejpam-4577	179	19	.	.	PUNCT
ejpam-4577	180	1	if	if	SCONJ
ejpam-4577	180	2	sg1	sg1	NOUN
ejpam-4577	180	3	=	=	SYM
ejpam-4577	180	4	∅	∅	NOUN
ejpam-4577	180	5	,	,	PUNCT
ejpam-4577	180	6	then	then	ADV
ejpam-4577	180	7	s	s	PART
ejpam-4577	180	8	=	=	PUNCT
ejpam-4577	180	9	sg2	sg2	PROPN
ejpam-4577	180	10	is	be	AUX
ejpam-4577	180	11	a	a	DET
ejpam-4577	180	12	hop	hop	NOUN
ejpam-4577	180	13	independent	independent	ADJ
ejpam-4577	180	14	hop	hop	NOUN
ejpam-4577	180	15	dominating	dominating	NOUN
ejpam-4577	180	16	set	set	NOUN
ejpam-4577	180	17	of	of	ADP
ejpam-4577	180	18	g2	g2	PROPN
ejpam-4577	180	19	.	.	PUNCT
ejpam-4577	181	1	hence	hence	ADV
ejpam-4577	181	2	,	,	PUNCT
ejpam-4577	181	3	(	(	PUNCT
ejpam-4577	181	4	i	i	NOUN
ejpam-4577	181	5	)	)	PUNCT
ejpam-4577	181	6	or	or	CCONJ
ejpam-4577	181	7	(	(	PUNCT
ejpam-4577	181	8	ii	ii	NOUN
ejpam-4577	181	9	)	)	PUNCT
ejpam-4577	181	10	holds	hold	VERB
ejpam-4577	181	11	.	.	PUNCT
ejpam-4577	182	1	next	next	ADV
ejpam-4577	182	2	,	,	PUNCT
ejpam-4577	182	3	suppose	suppose	VERB
ejpam-4577	182	4	sg1	sg1	PROPN
ejpam-4577	182	5	and	and	CCONJ
ejpam-4577	182	6	sg2	sg2	PROPN
ejpam-4577	182	7	are	be	AUX
ejpam-4577	182	8	both	both	PRON
ejpam-4577	182	9	non	non	ADJ
ejpam-4577	182	10	-	-	ADJ
ejpam-4577	182	11	empty	empty	ADJ
ejpam-4577	182	12	.	.	PUNCT
ejpam-4577	183	1	let	let	VERB
ejpam-4577	183	2	s′	s′	ADJ
ejpam-4577	183	3	g2	g2	PROPN
ejpam-4577	183	4	=	=	PRON
ejpam-4577	183	5	{	{	PUNCT
ejpam-4577	183	6	a	a	PRON
ejpam-4577	183	7	∈	∈	PROPN
ejpam-4577	183	8	v	v	NOUN
ejpam-4577	183	9	(	(	PUNCT
ejpam-4577	183	10	g1	g1	PROPN
ejpam-4577	183	11	)	)	PUNCT
ejpam-4577	183	12	:	:	PUNCT
ejpam-4577	183	13	a′	a′	PROPN
ejpam-4577	183	14	∈	∈	PROPN
ejpam-4577	183	15	sg2	sg2	PROPN
ejpam-4577	183	16	}	}	PUNCT
ejpam-4577	183	17	.	.	PUNCT
ejpam-4577	184	1	suppose	suppose	VERB
ejpam-4577	184	2	sg1	sg1	NOUN
ejpam-4577	184	3	∪	∪	ADP
ejpam-4577	184	4	s′	s′	ADJ
ejpam-4577	184	5	g2	g2	PROPN
ejpam-4577	184	6	is	be	AUX
ejpam-4577	184	7	not	not	PART
ejpam-4577	184	8	a	a	DET
ejpam-4577	184	9	hop	hop	NOUN
ejpam-4577	184	10	independent	independent	ADJ
ejpam-4577	184	11	set	set	NOUN
ejpam-4577	184	12	in	in	ADP
ejpam-4577	184	13	g1	g1	PROPN
ejpam-4577	184	14	.	.	PUNCT
ejpam-4577	185	1	then	then	ADV
ejpam-4577	185	2	there	there	PRON
ejpam-4577	185	3	exist	exist	VERB
ejpam-4577	185	4	p	p	PRON
ejpam-4577	185	5	,	,	PUNCT
ejpam-4577	185	6	q	q	PUNCT
ejpam-4577	185	7	∈	∈	PROPN
ejpam-4577	185	8	sg1	sg1	NOUN
ejpam-4577	185	9	∪	∪	VERB
ejpam-4577	185	10	s′	s′	ADJ
ejpam-4577	185	11	g2	g2	PROPN
ejpam-4577	185	12	such	such	ADJ
ejpam-4577	185	13	that	that	SCONJ
ejpam-4577	185	14	dg1(p	dg1(p	PROPN
ejpam-4577	185	15	,	,	PUNCT
ejpam-4577	185	16	q	q	NOUN
ejpam-4577	185	17	)	)	PUNCT
ejpam-4577	185	18	=	=	SYM
ejpam-4577	185	19	2	2	NUM
ejpam-4577	185	20	=	=	SYM
ejpam-4577	185	21	ds(g)(p	ds(g)(p	NUM
ejpam-4577	185	22	,	,	PUNCT
ejpam-4577	185	23	q	q	NOUN
ejpam-4577	185	24	)	)	PUNCT
ejpam-4577	185	25	.	.	PUNCT
ejpam-4577	186	1	since	since	SCONJ
ejpam-4577	186	2	sg1	sg1	PROPN
ejpam-4577	186	3	j.	j.	PROPN
ejpam-4577	186	4	hassan	hassan	PROPN
ejpam-4577	186	5	,	,	PUNCT
ejpam-4577	186	6	s.	s.	PROPN
ejpam-4577	186	7	canoy	canoy	PROPN
ejpam-4577	186	8	/	/	SYM
ejpam-4577	186	9	eur	eur	PROPN
ejpam-4577	186	10	.	.	PUNCT
ejpam-4577	187	1	j.	j.	PROPN
ejpam-4577	187	2	pure	pure	PROPN
ejpam-4577	187	3	appl	appl	PROPN
ejpam-4577	187	4	.	.	PROPN
ejpam-4577	187	5	math	math	PROPN
ejpam-4577	187	6	,	,	PUNCT
ejpam-4577	187	7	15	15	NUM
ejpam-4577	187	8	(	(	PUNCT
ejpam-4577	187	9	4	4	NUM
ejpam-4577	187	10	)	)	PUNCT
ejpam-4577	187	11	(	(	PUNCT
ejpam-4577	187	12	2022	2022	NUM
ejpam-4577	187	13	)	)	PUNCT
ejpam-4577	187	14	,	,	PUNCT
ejpam-4577	187	15	1783	1783	NUM
ejpam-4577	187	16	-	-	SYM
ejpam-4577	187	17	1796	1796	NUM
ejpam-4577	187	18	1789	1789	NUM
ejpam-4577	187	19	and	and	CCONJ
ejpam-4577	187	20	sg2	sg2	PROPN
ejpam-4577	187	21	are	be	AUX
ejpam-4577	187	22	hop	hop	ADV
ejpam-4577	187	23	independent	independent	ADJ
ejpam-4577	187	24	sets	set	NOUN
ejpam-4577	187	25	,	,	PUNCT
ejpam-4577	187	26	we	we	PRON
ejpam-4577	187	27	may	may	AUX
ejpam-4577	187	28	assume	assume	VERB
ejpam-4577	187	29	that	that	SCONJ
ejpam-4577	187	30	p	p	PROPN
ejpam-4577	187	31	∈	∈	PROPN
ejpam-4577	187	32	sg1	sg1	NOUN
ejpam-4577	187	33	and	and	CCONJ
ejpam-4577	187	34	q	q	NOUN
ejpam-4577	187	35	∈	∈	PROPN
ejpam-4577	187	36	s′	s′	NUM
ejpam-4577	187	37	g2	g2	PROPN
ejpam-4577	187	38	.	.	PUNCT
ejpam-4577	188	1	then	then	ADV
ejpam-4577	188	2	q′	q′	PUNCT
ejpam-4577	188	3	∈	∈	PROPN
ejpam-4577	188	4	sg2	sg2	PROPN
ejpam-4577	188	5	and	and	CCONJ
ejpam-4577	188	6	ds(g)(p	ds(g)(p	PROPN
ejpam-4577	188	7	,	,	PUNCT
ejpam-4577	188	8	q	q	NOUN
ejpam-4577	188	9	′	′	NOUN
ejpam-4577	188	10	)	)	PUNCT
ejpam-4577	188	11	=	=	SYM
ejpam-4577	188	12	2	2	NUM
ejpam-4577	188	13	,	,	PUNCT
ejpam-4577	188	14	contrary	contrary	ADV
ejpam-4577	188	15	to	to	ADP
ejpam-4577	188	16	the	the	DET
ejpam-4577	188	17	assumption	assumption	NOUN
ejpam-4577	188	18	that	that	SCONJ
ejpam-4577	188	19	s	s	VERB
ejpam-4577	188	20	is	be	AUX
ejpam-4577	188	21	a	a	DET
ejpam-4577	188	22	hop	hop	NOUN
ejpam-4577	188	23	independent	independent	ADJ
ejpam-4577	188	24	set	set	NOUN
ejpam-4577	188	25	.	.	PUNCT
ejpam-4577	189	1	thus	thus	ADV
ejpam-4577	189	2	,	,	PUNCT
ejpam-4577	189	3	sg1	sg1	PROPN
ejpam-4577	189	4	∪	∪	ADP
ejpam-4577	189	5	s′	s′	ADJ
ejpam-4577	189	6	g2	g2	PROPN
ejpam-4577	189	7	is	be	AUX
ejpam-4577	189	8	a	a	DET
ejpam-4577	189	9	hop	hop	NOUN
ejpam-4577	189	10	independent	independent	ADJ
ejpam-4577	189	11	set	set	NOUN
ejpam-4577	189	12	.	.	PUNCT
ejpam-4577	190	1	next	next	ADV
ejpam-4577	190	2	,	,	PUNCT
ejpam-4577	190	3	let	let	VERB
ejpam-4577	190	4	x	x	PUNCT
ejpam-4577	190	5	∈	∈	PROPN
ejpam-4577	190	6	v	v	NOUN
ejpam-4577	190	7	(	(	PUNCT
ejpam-4577	190	8	g1	g1	PROPN
ejpam-4577	190	9	)	)	PUNCT
ejpam-4577	190	10	\	\	PROPN
ejpam-4577	190	11	sg1	sg1	NOUN
ejpam-4577	190	12	∪	∪	ADP
ejpam-4577	190	13	s′	s′	ADJ
ejpam-4577	190	14	g2	g2	PROPN
ejpam-4577	190	15	.	.	PUNCT
ejpam-4577	191	1	then	then	ADV
ejpam-4577	191	2	x	x	SYM
ejpam-4577	191	3	∈	∈	PROPN
ejpam-4577	191	4	v	v	X
ejpam-4577	191	5	(	(	PUNCT
ejpam-4577	191	6	s(g	s(g	PROPN
ejpam-4577	191	7	)	)	PUNCT
ejpam-4577	191	8	)	)	PUNCT
ejpam-4577	191	9	\	\	PROPN
ejpam-4577	192	1	s.	s.	PROPN
ejpam-4577	192	2	since	since	SCONJ
ejpam-4577	192	3	s	s	PROPN
ejpam-4577	192	4	is	be	AUX
ejpam-4577	192	5	a	a	DET
ejpam-4577	192	6	hop	hop	NOUN
ejpam-4577	192	7	dominating	dominating	NOUN
ejpam-4577	192	8	of	of	ADP
ejpam-4577	192	9	s(g	s(g	PROPN
ejpam-4577	192	10	)	)	PUNCT
ejpam-4577	192	11	,	,	PUNCT
ejpam-4577	192	12	there	there	PRON
ejpam-4577	192	13	exists	exist	VERB
ejpam-4577	192	14	y	y	PROPN
ejpam-4577	192	15	∈	∈	PROPN
ejpam-4577	192	16	s	s	VERB
ejpam-4577	192	17	such	such	ADJ
ejpam-4577	192	18	that	that	DET
ejpam-4577	192	19	ds(g)(x	ds(g)(x	NOUN
ejpam-4577	192	20	,	,	PUNCT
ejpam-4577	192	21	y	y	NOUN
ejpam-4577	192	22	)	)	PUNCT
ejpam-4577	192	23	=	=	SYM
ejpam-4577	193	1	2	2	X
ejpam-4577	193	2	.	.	X
ejpam-4577	194	1	if	if	SCONJ
ejpam-4577	194	2	y	y	PROPN
ejpam-4577	194	3	∈	∈	PROPN
ejpam-4577	194	4	sg1	sg1	NOUN
ejpam-4577	194	5	,	,	PUNCT
ejpam-4577	194	6	then	then	ADV
ejpam-4577	194	7	we	we	PRON
ejpam-4577	194	8	are	be	AUX
ejpam-4577	194	9	done	do	VERB
ejpam-4577	194	10	.	.	PUNCT
ejpam-4577	195	1	suppose	suppose	VERB
ejpam-4577	195	2	y	y	PROPN
ejpam-4577	195	3	∈	∈	PROPN
ejpam-4577	195	4	sg2	sg2	PROPN
ejpam-4577	195	5	,	,	PUNCT
ejpam-4577	195	6	say	say	VERB
ejpam-4577	195	7	y	y	PROPN
ejpam-4577	195	8	=	=	SYM
ejpam-4577	195	9	z′	z′	PROPN
ejpam-4577	195	10	,	,	PUNCT
ejpam-4577	195	11	where	where	SCONJ
ejpam-4577	195	12	z	z	PROPN
ejpam-4577	195	13	∈	∈	PROPN
ejpam-4577	195	14	v	v	NOUN
ejpam-4577	195	15	(	(	PUNCT
ejpam-4577	195	16	g1	g1	PROPN
ejpam-4577	195	17	)	)	PUNCT
ejpam-4577	195	18	.	.	PUNCT
ejpam-4577	196	1	then	then	ADV
ejpam-4577	196	2	z	z	PROPN
ejpam-4577	196	3	∈	∈	PROPN
ejpam-4577	196	4	s′	s′	VERB
ejpam-4577	196	5	g2	g2	PROPN
ejpam-4577	196	6	and	and	CCONJ
ejpam-4577	196	7	ds(g)(x	ds(g)(x	PROPN
ejpam-4577	196	8	,	,	PUNCT
ejpam-4577	196	9	z	z	NOUN
ejpam-4577	196	10	)	)	PUNCT
ejpam-4577	196	11	=	=	SYM
ejpam-4577	196	12	dg1(x	dg1(x	PROPN
ejpam-4577	196	13	,	,	PUNCT
ejpam-4577	196	14	z	z	NOUN
ejpam-4577	196	15	)	)	PUNCT
ejpam-4577	196	16	=	=	SYM
ejpam-4577	196	17	2	2	X
ejpam-4577	196	18	.	.	PUNCT
ejpam-4577	196	19	therefore	therefore	ADV
ejpam-4577	196	20	,	,	PUNCT
ejpam-4577	196	21	sg1	sg1	PROPN
ejpam-4577	196	22	∪	∪	ADP
ejpam-4577	196	23	s′	s′	ADJ
ejpam-4577	196	24	g2	g2	PROPN
ejpam-4577	196	25	is	be	AUX
ejpam-4577	196	26	a	a	DET
ejpam-4577	196	27	hop	hop	NOUN
ejpam-4577	196	28	dominating	dominating	NOUN
ejpam-4577	196	29	set	set	NOUN
ejpam-4577	196	30	.	.	PUNCT
ejpam-4577	197	1	consequently	consequently	ADV
ejpam-4577	197	2	,	,	PUNCT
ejpam-4577	197	3	sg1	sg1	PROPN
ejpam-4577	197	4	∪	∪	ADP
ejpam-4577	197	5	s′	s′	ADJ
ejpam-4577	197	6	g2	g2	PROPN
ejpam-4577	197	7	is	be	AUX
ejpam-4577	197	8	a	a	DET
ejpam-4577	197	9	hop	hop	NOUN
ejpam-4577	197	10	independent	independent	ADJ
ejpam-4577	197	11	hop	hop	NOUN
ejpam-4577	197	12	dominating	dominating	NOUN
ejpam-4577	197	13	set	set	NOUN
ejpam-4577	197	14	of	of	ADP
ejpam-4577	197	15	g1	g1	PROPN
ejpam-4577	197	16	.	.	PUNCT
ejpam-4577	198	1	similarly	similarly	ADV
ejpam-4577	198	2	,	,	PUNCT
ejpam-4577	198	3	s′	s′	ADJ
ejpam-4577	198	4	g1	g1	PROPN
ejpam-4577	198	5	∪	∪	ADP
ejpam-4577	198	6	sg2	sg2	PROPN
ejpam-4577	198	7	is	be	AUX
ejpam-4577	198	8	a	a	DET
ejpam-4577	198	9	hop	hop	NOUN
ejpam-4577	198	10	independent	independent	ADJ
ejpam-4577	198	11	hop	hop	NOUN
ejpam-4577	198	12	dominating	dominating	NOUN
ejpam-4577	198	13	set	set	NOUN
ejpam-4577	198	14	of	of	ADP
ejpam-4577	198	15	g2	g2	PROPN
ejpam-4577	198	16	.	.	PUNCT
ejpam-4577	199	1	hence	hence	ADV
ejpam-4577	199	2	,	,	PUNCT
ejpam-4577	199	3	(	(	PUNCT
ejpam-4577	199	4	iii	iii	NOUN
ejpam-4577	199	5	)	)	PUNCT
ejpam-4577	199	6	holds	hold	VERB
ejpam-4577	199	7	.	.	PUNCT
ejpam-4577	200	1	for	for	ADP
ejpam-4577	200	2	the	the	DET
ejpam-4577	200	3	converse	converse	NOUN
ejpam-4577	200	4	,	,	PUNCT
ejpam-4577	200	5	suppose	suppose	VERB
ejpam-4577	200	6	(	(	PUNCT
ejpam-4577	200	7	i	i	NOUN
ejpam-4577	200	8	)	)	PUNCT
ejpam-4577	200	9	holds	hold	VERB
ejpam-4577	200	10	.	.	PUNCT
ejpam-4577	201	1	then	then	ADV
ejpam-4577	201	2	s	s	VERB
ejpam-4577	201	3	is	be	AUX
ejpam-4577	201	4	a	a	DET
ejpam-4577	201	5	hop	hop	NOUN
ejpam-4577	201	6	independent	independent	ADJ
ejpam-4577	201	7	set	set	NOUN
ejpam-4577	201	8	of	of	ADP
ejpam-4577	201	9	s(g	s(g	PROPN
ejpam-4577	201	10	)	)	PUNCT
ejpam-4577	201	11	.	.	PUNCT
ejpam-4577	202	1	let	let	VERB
ejpam-4577	202	2	a	a	DET
ejpam-4577	202	3	∈	∈	PROPN
ejpam-4577	202	4	v	v	NOUN
ejpam-4577	202	5	(	(	PUNCT
ejpam-4577	202	6	s(g	s(g	PROPN
ejpam-4577	202	7	)	)	PUNCT
ejpam-4577	202	8	)	)	PUNCT
ejpam-4577	203	1	\	\	PUNCT
ejpam-4577	203	2	s.	s.	PROPN
ejpam-4577	203	3	if	if	SCONJ
ejpam-4577	203	4	a	a	DET
ejpam-4577	203	5	∈	∈	PROPN
ejpam-4577	203	6	v	v	NOUN
ejpam-4577	203	7	(	(	PUNCT
ejpam-4577	203	8	g1	g1	PROPN
ejpam-4577	203	9	)	)	PUNCT
ejpam-4577	203	10	\	\	PROPN
ejpam-4577	203	11	s	s	X
ejpam-4577	203	12	,	,	PUNCT
ejpam-4577	203	13	then	then	ADV
ejpam-4577	203	14	there	there	PRON
ejpam-4577	203	15	exists	exist	VERB
ejpam-4577	203	16	b	b	PROPN
ejpam-4577	203	17	∈	∈	PROPN
ejpam-4577	203	18	s	s	VERB
ejpam-4577	203	19	such	such	ADJ
ejpam-4577	203	20	that	that	SCONJ
ejpam-4577	203	21	dg1(a	dg1(a	PROPN
ejpam-4577	203	22	,	,	PUNCT
ejpam-4577	203	23	b	b	NOUN
ejpam-4577	203	24	)	)	PUNCT
ejpam-4577	203	25	=	=	PUNCT
ejpam-4577	203	26	ds(g)(a	ds(g)(a	PROPN
ejpam-4577	203	27	,	,	PUNCT
ejpam-4577	203	28	b	b	NOUN
ejpam-4577	203	29	)	)	PUNCT
ejpam-4577	203	30	=	=	SYM
ejpam-4577	203	31	2	2	X
ejpam-4577	203	32	.	.	PUNCT
ejpam-4577	203	33	suppose	suppose	VERB
ejpam-4577	203	34	a	a	DET
ejpam-4577	203	35	∈	∈	PROPN
ejpam-4577	203	36	v	v	NOUN
ejpam-4577	203	37	(	(	PUNCT
ejpam-4577	203	38	g2	g2	PROPN
ejpam-4577	203	39	)	)	PUNCT
ejpam-4577	203	40	,	,	PUNCT
ejpam-4577	203	41	say	say	VERB
ejpam-4577	203	42	a	a	DET
ejpam-4577	203	43	=	=	NOUN
ejpam-4577	203	44	v′	v′	NOUN
ejpam-4577	203	45	,	,	PUNCT
ejpam-4577	203	46	where	where	SCONJ
ejpam-4577	203	47	v	v	X
ejpam-4577	203	48	∈	∈	PROPN
ejpam-4577	203	49	v	v	NOUN
ejpam-4577	203	50	(	(	PUNCT
ejpam-4577	203	51	g1	g1	PROPN
ejpam-4577	203	52	)	)	PUNCT
ejpam-4577	203	53	.	.	PUNCT
ejpam-4577	204	1	if	if	SCONJ
ejpam-4577	204	2	v	v	NUM
ejpam-4577	204	3	∈	∈	PROPN
ejpam-4577	204	4	s	s	NOUN
ejpam-4577	204	5	,	,	PUNCT
ejpam-4577	204	6	then	then	ADV
ejpam-4577	204	7	dg1(a	dg1(a	PROPN
ejpam-4577	204	8	,	,	PUNCT
ejpam-4577	204	9	v	v	NOUN
ejpam-4577	204	10	)	)	PUNCT
ejpam-4577	204	11	=	=	PUNCT
ejpam-4577	204	12	ds(g)(a	ds(g)(a	PROPN
ejpam-4577	204	13	,	,	PUNCT
ejpam-4577	204	14	v	v	NOUN
ejpam-4577	204	15	)	)	PUNCT
ejpam-4577	204	16	=	=	SYM
ejpam-4577	204	17	2	2	X
ejpam-4577	204	18	.	.	X
ejpam-4577	205	1	if	if	SCONJ
ejpam-4577	205	2	v	v	NUM
ejpam-4577	205	3	/∈	/∈	SYM
ejpam-4577	206	1	s	s	X
ejpam-4577	206	2	,	,	PUNCT
ejpam-4577	206	3	then	then	ADV
ejpam-4577	206	4	there	there	PRON
ejpam-4577	206	5	exists	exist	VERB
ejpam-4577	206	6	w	w	PROPN
ejpam-4577	206	7	∈	∈	PROPN
ejpam-4577	206	8	s	s	VERB
ejpam-4577	206	9	such	such	ADJ
ejpam-4577	207	1	that	that	PRON
ejpam-4577	207	2	dg1(v	dg1(v	PROPN
ejpam-4577	207	3	,	,	PUNCT
ejpam-4577	207	4	w	w	PROPN
ejpam-4577	207	5	)	)	PUNCT
ejpam-4577	207	6	=	=	SYM
ejpam-4577	207	7	2	2	X
ejpam-4577	207	8	.	.	PUNCT
ejpam-4577	207	9	it	it	PRON
ejpam-4577	207	10	follows	follow	VERB
ejpam-4577	207	11	that	that	SCONJ
ejpam-4577	207	12	ds(g)(a	ds(g)(a	NOUN
ejpam-4577	207	13	,	,	PUNCT
ejpam-4577	207	14	w	w	NOUN
ejpam-4577	207	15	)	)	PUNCT
ejpam-4577	207	16	=	=	SYM
ejpam-4577	207	17	ds(g)(v	ds(g)(v	NOUN
ejpam-4577	207	18	′	′	NOUN
ejpam-4577	207	19	,	,	PUNCT
ejpam-4577	207	20	w	w	NOUN
ejpam-4577	207	21	)	)	PUNCT
ejpam-4577	207	22	=	=	SYM
ejpam-4577	207	23	2	2	X
ejpam-4577	207	24	.	.	X
ejpam-4577	207	25	therefore	therefore	ADV
ejpam-4577	207	26	,	,	PUNCT
ejpam-4577	207	27	s	s	VERB
ejpam-4577	207	28	is	be	AUX
ejpam-4577	207	29	a	a	DET
ejpam-4577	207	30	hop	hop	NOUN
ejpam-4577	207	31	independent	independent	ADJ
ejpam-4577	207	32	hop	hop	NOUN
ejpam-4577	207	33	dominating	dominating	NOUN
ejpam-4577	207	34	set	set	NOUN
ejpam-4577	207	35	of	of	ADP
ejpam-4577	207	36	s(g	s(g	PROPN
ejpam-4577	207	37	)	)	PUNCT
ejpam-4577	207	38	.	.	PUNCT
ejpam-4577	208	1	similarly	similarly	ADV
ejpam-4577	208	2	,	,	PUNCT
ejpam-4577	208	3	if	if	SCONJ
ejpam-4577	208	4	(	(	PUNCT
ejpam-4577	208	5	ii	ii	NOUN
ejpam-4577	208	6	)	)	PUNCT
ejpam-4577	208	7	holds	hold	VERB
ejpam-4577	208	8	,	,	PUNCT
ejpam-4577	208	9	then	then	ADV
ejpam-4577	208	10	s	s	VERB
ejpam-4577	208	11	is	be	AUX
ejpam-4577	208	12	a	a	DET
ejpam-4577	208	13	hop	hop	NOUN
ejpam-4577	208	14	independent	independent	ADJ
ejpam-4577	208	15	hop	hop	NOUN
ejpam-4577	208	16	dominating	dominating	NOUN
ejpam-4577	208	17	set	set	NOUN
ejpam-4577	208	18	of	of	ADP
ejpam-4577	208	19	s(g	s(g	PROPN
ejpam-4577	208	20	)	)	PUNCT
ejpam-4577	208	21	.	.	PUNCT
ejpam-4577	209	1	now	now	ADV
ejpam-4577	209	2	,	,	PUNCT
ejpam-4577	209	3	suppose	suppose	VERB
ejpam-4577	209	4	(	(	PUNCT
ejpam-4577	209	5	iii	iii	NOUN
ejpam-4577	209	6	)	)	PUNCT
ejpam-4577	209	7	holds	hold	VERB
ejpam-4577	209	8	.	.	PUNCT
ejpam-4577	210	1	suppose	suppose	VERB
ejpam-4577	210	2	further	far	ADV
ejpam-4577	210	3	that	that	PRON
ejpam-4577	210	4	s	s	PART
ejpam-4577	210	5	=	=	NOUN
ejpam-4577	210	6	sg1	sg1	NOUN
ejpam-4577	210	7	∪sg2	∪sg2	PROPN
ejpam-4577	210	8	is	be	AUX
ejpam-4577	210	9	not	not	PART
ejpam-4577	210	10	a	a	DET
ejpam-4577	210	11	hop	hop	NOUN
ejpam-4577	210	12	independent	independent	ADJ
ejpam-4577	210	13	set	set	NOUN
ejpam-4577	210	14	in	in	ADP
ejpam-4577	210	15	s(g	s(g	PROPN
ejpam-4577	210	16	)	)	PUNCT
ejpam-4577	210	17	.	.	PUNCT
ejpam-4577	211	1	then	then	ADV
ejpam-4577	211	2	there	there	PRON
ejpam-4577	211	3	exist	exist	VERB
ejpam-4577	211	4	a	a	DET
ejpam-4577	211	5	,	,	PUNCT
ejpam-4577	211	6	b	b	X
ejpam-4577	211	7	∈	∈	NOUN
ejpam-4577	211	8	s	s	VERB
ejpam-4577	211	9	such	such	ADJ
ejpam-4577	211	10	that	that	DET
ejpam-4577	211	11	ds(g)(a	ds(g)(a	NOUN
ejpam-4577	211	12	,	,	PUNCT
ejpam-4577	211	13	b	b	X
ejpam-4577	211	14	)	)	PUNCT
ejpam-4577	211	15	=	=	SYM
ejpam-4577	211	16	2	2	X
ejpam-4577	211	17	.	.	PUNCT
ejpam-4577	211	18	since	since	SCONJ
ejpam-4577	211	19	sg1	sg1	PROPN
ejpam-4577	211	20	and	and	CCONJ
ejpam-4577	211	21	sg2	sg2	PROPN
ejpam-4577	211	22	are	be	AUX
ejpam-4577	211	23	hop	hop	ADV
ejpam-4577	211	24	independent	independent	ADJ
ejpam-4577	211	25	sets	set	NOUN
ejpam-4577	211	26	,	,	PUNCT
ejpam-4577	211	27	we	we	PRON
ejpam-4577	211	28	may	may	AUX
ejpam-4577	211	29	assume	assume	VERB
ejpam-4577	211	30	that	that	SCONJ
ejpam-4577	211	31	a	a	DET
ejpam-4577	211	32	∈	∈	PROPN
ejpam-4577	211	33	sg1	sg1	NOUN
ejpam-4577	211	34	and	and	CCONJ
ejpam-4577	211	35	b	b	PROPN
ejpam-4577	211	36	∈	∈	PROPN
ejpam-4577	211	37	sg2	sg2	PROPN
ejpam-4577	211	38	.	.	PUNCT
ejpam-4577	212	1	then	then	ADV
ejpam-4577	212	2	dg2(a	dg2(a	PROPN
ejpam-4577	212	3	′	′	NOUN
ejpam-4577	212	4	,	,	PUNCT
ejpam-4577	212	5	b	b	NOUN
ejpam-4577	212	6	)	)	PUNCT
ejpam-4577	212	7	=	=	SYM
ejpam-4577	212	8	2	2	NUM
ejpam-4577	212	9	,	,	PUNCT
ejpam-4577	212	10	contrary	contrary	ADV
ejpam-4577	212	11	to	to	ADP
ejpam-4577	212	12	the	the	DET
ejpam-4577	212	13	assumption	assumption	NOUN
ejpam-4577	212	14	that	that	SCONJ
ejpam-4577	212	15	s′	s′	VERB
ejpam-4577	212	16	g1	g1	PROPN
ejpam-4577	212	17	∪sg2	∪sg2	PROPN
ejpam-4577	212	18	is	be	AUX
ejpam-4577	212	19	a	a	DET
ejpam-4577	212	20	hop	hop	NOUN
ejpam-4577	212	21	independent	independent	ADJ
ejpam-4577	212	22	set	set	NOUN
ejpam-4577	212	23	in	in	ADP
ejpam-4577	212	24	g2	g2	PROPN
ejpam-4577	212	25	.	.	PUNCT
ejpam-4577	213	1	therefore	therefore	ADV
ejpam-4577	213	2	,	,	PUNCT
ejpam-4577	213	3	s	s	VERB
ejpam-4577	213	4	is	be	AUX
ejpam-4577	213	5	a	a	DET
ejpam-4577	213	6	hop	hop	NOUN
ejpam-4577	213	7	independent	independent	ADJ
ejpam-4577	213	8	set	set	NOUN
ejpam-4577	213	9	s(g	s(g	PROPN
ejpam-4577	213	10	)	)	PUNCT
ejpam-4577	213	11	.	.	PUNCT
ejpam-4577	214	1	next	next	ADV
ejpam-4577	214	2	,	,	PUNCT
ejpam-4577	214	3	let	let	VERB
ejpam-4577	214	4	y	y	PROPN
ejpam-4577	214	5	∈	∈	PROPN
ejpam-4577	214	6	v	v	X
ejpam-4577	214	7	(	(	PUNCT
ejpam-4577	214	8	s(g	s(g	PROPN
ejpam-4577	214	9	)	)	PUNCT
ejpam-4577	214	10	)	)	PUNCT
ejpam-4577	214	11	\	\	PUNCT
ejpam-4577	215	1	s.	s.	PROPN
ejpam-4577	215	2	then	then	ADV
ejpam-4577	215	3	y	y	PROPN
ejpam-4577	215	4	/∈	/∈	PUNCT
ejpam-4577	215	5	sg1	sg1	PROPN
ejpam-4577	215	6	∪	∪	ADP
ejpam-4577	215	7	sg2	sg2	PROPN
ejpam-4577	215	8	.	.	PUNCT
ejpam-4577	216	1	suppose	suppose	VERB
ejpam-4577	216	2	y	y	PROPN
ejpam-4577	216	3	∈	∈	PROPN
ejpam-4577	216	4	v	v	PROPN
ejpam-4577	216	5	(	(	PUNCT
ejpam-4577	216	6	g2	g2	PROPN
ejpam-4577	216	7	)	)	PUNCT
ejpam-4577	216	8	\	\	PROPN
ejpam-4577	217	1	sg2	sg2	PROPN
ejpam-4577	217	2	,	,	PUNCT
ejpam-4577	217	3	say	say	VERB
ejpam-4577	217	4	y	y	PROPN
ejpam-4577	217	5	=	=	SYM
ejpam-4577	217	6	z′	z′	PROPN
ejpam-4577	217	7	,	,	PUNCT
ejpam-4577	217	8	where	where	SCONJ
ejpam-4577	217	9	z	z	PROPN
ejpam-4577	217	10	∈	∈	PROPN
ejpam-4577	217	11	v	v	NOUN
ejpam-4577	217	12	(	(	PUNCT
ejpam-4577	217	13	g1	g1	PROPN
ejpam-4577	217	14	)	)	PUNCT
ejpam-4577	217	15	.	.	PUNCT
ejpam-4577	218	1	then	then	ADV
ejpam-4577	218	2	z	z	PROPN
ejpam-4577	218	3	/∈	/∈	PUNCT
ejpam-4577	218	4	s′	s′	VERB
ejpam-4577	218	5	g2	g2	PROPN
ejpam-4577	218	6	.	.	PUNCT
ejpam-4577	219	1	if	if	SCONJ
ejpam-4577	219	2	z	z	NOUN
ejpam-4577	219	3	∈	∈	PROPN
ejpam-4577	219	4	sg1	sg1	NOUN
ejpam-4577	219	5	,	,	PUNCT
ejpam-4577	219	6	then	then	ADV
ejpam-4577	219	7	ds(g)(y	ds(g)(y	ADJ
ejpam-4577	219	8	,	,	PUNCT
ejpam-4577	219	9	z	z	NOUN
ejpam-4577	219	10	)	)	PUNCT
ejpam-4577	219	11	=	=	VERB
ejpam-4577	219	12	ds(g)(z	ds(g)(z	VERB
ejpam-4577	219	13	′	′	NUM
ejpam-4577	219	14	,	,	PUNCT
ejpam-4577	219	15	z	z	NOUN
ejpam-4577	219	16	)	)	PUNCT
ejpam-4577	219	17	=	=	SYM
ejpam-4577	219	18	2	2	X
ejpam-4577	219	19	.	.	X
ejpam-4577	219	20	suppose	suppose	VERB
ejpam-4577	219	21	z	z	NOUN
ejpam-4577	219	22	/∈	/∈	PUNCT
ejpam-4577	219	23	sg1	sg1	PROPN
ejpam-4577	219	24	.	.	PUNCT
ejpam-4577	220	1	since	since	SCONJ
ejpam-4577	220	2	sg1	sg1	PROPN
ejpam-4577	220	3	∪	∪	ADP
ejpam-4577	220	4	s′	s′	ADJ
ejpam-4577	220	5	g2	g2	PROPN
ejpam-4577	220	6	is	be	AUX
ejpam-4577	220	7	a	a	DET
ejpam-4577	220	8	hop	hop	NOUN
ejpam-4577	220	9	dominating	dominating	NOUN
ejpam-4577	220	10	set	set	NOUN
ejpam-4577	220	11	of	of	ADP
ejpam-4577	220	12	g1	g1	NOUN
ejpam-4577	220	13	,	,	PUNCT
ejpam-4577	220	14	there	there	PRON
ejpam-4577	220	15	exists	exist	VERB
ejpam-4577	220	16	p	p	PROPN
ejpam-4577	220	17	∈	∈	PROPN
ejpam-4577	220	18	sg1	sg1	NOUN
ejpam-4577	220	19	∪	∪	ADJ
ejpam-4577	220	20	s′	s′	ADJ
ejpam-4577	220	21	g2	g2	PROPN
ejpam-4577	220	22	such	such	ADJ
ejpam-4577	220	23	that	that	SCONJ
ejpam-4577	220	24	dg1(p	dg1(p	PROPN
ejpam-4577	220	25	,	,	PUNCT
ejpam-4577	220	26	z	z	NOUN
ejpam-4577	220	27	)	)	PUNCT
ejpam-4577	220	28	=	=	SYM
ejpam-4577	220	29	2	2	NUM
ejpam-4577	220	30	=	=	SYM
ejpam-4577	220	31	ds(g)(p	ds(g)(p	NUM
ejpam-4577	220	32	,	,	PUNCT
ejpam-4577	220	33	z	z	NOUN
ejpam-4577	220	34	)	)	PUNCT
ejpam-4577	220	35	.	.	PUNCT
ejpam-4577	221	1	if	if	SCONJ
ejpam-4577	221	2	p	p	PROPN
ejpam-4577	221	3	∈	∈	PROPN
ejpam-4577	221	4	sg1	sg1	NOUN
ejpam-4577	221	5	,	,	PUNCT
ejpam-4577	221	6	then	then	ADV
ejpam-4577	221	7	p	p	PROPN
ejpam-4577	221	8	∈	∈	PROPN
ejpam-4577	221	9	s	s	X
ejpam-4577	221	10	and	and	CCONJ
ejpam-4577	221	11	ds(g)(p	ds(g)(p	NOUN
ejpam-4577	221	12	,	,	PUNCT
ejpam-4577	221	13	z	z	NOUN
ejpam-4577	221	14	′	′	NOUN
ejpam-4577	221	15	)	)	PUNCT
ejpam-4577	221	16	=	=	SYM
ejpam-4577	222	1	2	2	X
ejpam-4577	222	2	.	.	X
ejpam-4577	223	1	if	if	SCONJ
ejpam-4577	223	2	p	p	PROPN
ejpam-4577	223	3	∈	∈	PROPN
ejpam-4577	223	4	s′	s′	ADJ
ejpam-4577	223	5	g2	g2	PROPN
ejpam-4577	223	6	,	,	PUNCT
ejpam-4577	223	7	then	then	ADV
ejpam-4577	223	8	p′	p′	PROPN
ejpam-4577	223	9	∈	∈	PROPN
ejpam-4577	223	10	sg2	sg2	PROPN
ejpam-4577	223	11	⊆	⊆	NUM
ejpam-4577	223	12	s	s	NOUN
ejpam-4577	223	13	and	and	CCONJ
ejpam-4577	223	14	dg2(p	dg2(p	PROPN
ejpam-4577	223	15	′	′	NUM
ejpam-4577	223	16	,	,	PUNCT
ejpam-4577	223	17	z′	z′	NUM
ejpam-4577	223	18	)	)	PUNCT
ejpam-4577	223	19	=	=	SYM
ejpam-4577	223	20	ds(g)(p	ds(g)(p	NOUN
ejpam-4577	223	21	′	′	NUM
ejpam-4577	223	22	,	,	PUNCT
ejpam-4577	223	23	z′	z′	NUM
ejpam-4577	223	24	)	)	PUNCT
ejpam-4577	223	25	=	=	SYM
ejpam-4577	224	1	2	2	X
ejpam-4577	224	2	.	.	X
ejpam-4577	224	3	therefore	therefore	ADV
ejpam-4577	224	4	,	,	PUNCT
ejpam-4577	224	5	s	s	VERB
ejpam-4577	224	6	is	be	AUX
ejpam-4577	224	7	a	a	DET
ejpam-4577	224	8	hop	hop	NOUN
ejpam-4577	224	9	dominating	dominating	NOUN
ejpam-4577	224	10	set	set	NOUN
ejpam-4577	224	11	of	of	ADP
ejpam-4577	224	12	s(g	s(g	PROPN
ejpam-4577	224	13	)	)	PUNCT
ejpam-4577	224	14	.	.	PUNCT
ejpam-4577	225	1	consequently	consequently	ADV
ejpam-4577	225	2	,	,	PUNCT
ejpam-4577	225	3	s	s	VERB
ejpam-4577	225	4	is	be	AUX
ejpam-4577	225	5	a	a	DET
ejpam-4577	225	6	hop	hop	NOUN
ejpam-4577	225	7	independent	independent	ADJ
ejpam-4577	225	8	hop	hop	NOUN
ejpam-4577	225	9	dominating	dominating	NOUN
ejpam-4577	225	10	set	set	NOUN
ejpam-4577	225	11	of	of	ADP
ejpam-4577	225	12	s(g	s(g	PROPN
ejpam-4577	225	13	)	)	PUNCT
ejpam-4577	225	14	.	.	PUNCT
ejpam-4577	226	1	corollary	corollary	ADJ
ejpam-4577	226	2	4	4	NUM
ejpam-4577	226	3	.	.	PUNCT
ejpam-4577	227	1	let	let	VERB
ejpam-4577	227	2	g	g	PRON
ejpam-4577	227	3	be	be	AUX
ejpam-4577	227	4	a	a	DET
ejpam-4577	227	5	non	non	ADJ
ejpam-4577	227	6	-	-	ADJ
ejpam-4577	227	7	trivial	trivial	ADJ
ejpam-4577	227	8	connected	connected	ADJ
ejpam-4577	227	9	graph	graph	NOUN
ejpam-4577	227	10	.	.	PUNCT
ejpam-4577	228	1	then	then	ADV
ejpam-4577	228	2	γhih(s(g	γhih(s(g	NUM
ejpam-4577	228	3	)	)	PUNCT
ejpam-4577	228	4	)	)	PUNCT
ejpam-4577	229	1	=	=	PUNCT
ejpam-4577	229	2	γhih(g	γhih(g	NOUN
ejpam-4577	229	3	)	)	PUNCT
ejpam-4577	229	4	.	.	PUNCT
ejpam-4577	230	1	in	in	ADP
ejpam-4577	230	2	particular	particular	ADJ
ejpam-4577	230	3	,	,	PUNCT
ejpam-4577	230	4	we	we	PRON
ejpam-4577	230	5	have	have	VERB
ejpam-4577	230	6	(	(	PUNCT
ejpam-4577	230	7	i	i	NOUN
ejpam-4577	230	8	)	)	PUNCT
ejpam-4577	230	9	γhih(s(kn	γhih(s(kn	PROPN
ejpam-4577	230	10	)	)	PUNCT
ejpam-4577	230	11	)	)	PUNCT
ejpam-4577	231	1	=	=	SYM
ejpam-4577	231	2	γhih(kn	γhih(kn	NOUN
ejpam-4577	231	3	)	)	PUNCT
ejpam-4577	231	4	=	=	SYM
ejpam-4577	231	5	n	n	CCONJ
ejpam-4577	231	6	for	for	ADP
ejpam-4577	231	7	every	every	DET
ejpam-4577	231	8	n	n	PRON
ejpam-4577	231	9	≥	≥	NOUN
ejpam-4577	231	10	2	2	NUM
ejpam-4577	231	11	,	,	PUNCT
ejpam-4577	231	12	(	(	PUNCT
ejpam-4577	231	13	ii	ii	NOUN
ejpam-4577	231	14	)	)	PUNCT
ejpam-4577	231	15	γhih(s(pn	γhih(s(pn	PROPN
ejpam-4577	231	16	)	)	PUNCT
ejpam-4577	231	17	)	)	PUNCT
ejpam-4577	232	1	=	=	SYM
ejpam-4577	232	2	γhih(pn	γhih(pn	NOUN
ejpam-4577	232	3	)	)	PUNCT
ejpam-4577	232	4	=	=	SYM
ejpam-4577	232	5	γh(pn	γh(pn	VERB
ejpam-4577	232	6	)	)	PUNCT
ejpam-4577	232	7	for	for	ADP
ejpam-4577	232	8	every	every	DET
ejpam-4577	232	9	n	n	PRON
ejpam-4577	232	10	≥	≥	NOUN
ejpam-4577	232	11	2	2	NUM
ejpam-4577	232	12	,	,	PUNCT
ejpam-4577	232	13	and	and	CCONJ
ejpam-4577	232	14	(	(	PUNCT
ejpam-4577	232	15	iii	iii	NOUN
ejpam-4577	232	16	)	)	PUNCT
ejpam-4577	232	17	γhih(s(cn	γhih(s(cn	NUM
ejpam-4577	232	18	)	)	PUNCT
ejpam-4577	232	19	)	)	PUNCT
ejpam-4577	233	1	=	=	SYM
ejpam-4577	233	2	γhih(cn	γhih(cn	PROPN
ejpam-4577	233	3	)	)	PUNCT
ejpam-4577	233	4	=	=	SYM
ejpam-4577	233	5	γh(cn	γh(cn	PROPN
ejpam-4577	233	6	)	)	PUNCT
ejpam-4577	233	7	for	for	ADP
ejpam-4577	233	8	evey	evey	NOUN
ejpam-4577	233	9	n	n	PRON
ejpam-4577	233	10	≥	≥	NOUN
ejpam-4577	233	11	3	3	NUM
ejpam-4577	233	12	.	.	PUNCT
ejpam-4577	233	13	proof	proof	NOUN
ejpam-4577	233	14	.	.	PUNCT
ejpam-4577	234	1	let	let	VERB
ejpam-4577	234	2	s	s	PRON
ejpam-4577	234	3	be	be	AUX
ejpam-4577	234	4	a	a	DET
ejpam-4577	234	5	γhih	γhih	NOUN
ejpam-4577	234	6	-	-	PUNCT
ejpam-4577	234	7	set	set	NOUN
ejpam-4577	234	8	of	of	ADP
ejpam-4577	234	9	g.	g.	PROPN
ejpam-4577	234	10	then	then	ADV
ejpam-4577	234	11	by	by	ADP
ejpam-4577	234	12	theorem	theorem	NOUN
ejpam-4577	234	13	5	5	NUM
ejpam-4577	234	14	,	,	PUNCT
ejpam-4577	234	15	s	s	VERB
ejpam-4577	234	16	is	be	AUX
ejpam-4577	234	17	a	a	DET
ejpam-4577	234	18	hop	hop	NOUN
ejpam-4577	234	19	independent	independent	ADJ
ejpam-4577	234	20	hop	hop	NOUN
ejpam-4577	234	21	dominating	dominating	NOUN
ejpam-4577	234	22	set	set	NOUN
ejpam-4577	234	23	of	of	ADP
ejpam-4577	234	24	s(g	s(g	PROPN
ejpam-4577	234	25	)	)	PUNCT
ejpam-4577	234	26	.	.	PUNCT
ejpam-4577	235	1	thus	thus	ADV
ejpam-4577	235	2	,	,	PUNCT
ejpam-4577	235	3	γhih(s(g	γhih(s(g	NUM
ejpam-4577	235	4	)	)	PUNCT
ejpam-4577	235	5	)	)	PUNCT
ejpam-4577	235	6	≤	≤	NUM
ejpam-4577	235	7	|s|	|s|	PROPN
ejpam-4577	235	8	=	=	PUNCT
ejpam-4577	235	9	γhih(g	γhih(g	PROPN
ejpam-4577	235	10	)	)	PUNCT
ejpam-4577	235	11	.	.	PUNCT
ejpam-4577	236	1	j.	j.	PROPN
ejpam-4577	236	2	hassan	hassan	PROPN
ejpam-4577	236	3	,	,	PUNCT
ejpam-4577	236	4	s.	s.	PROPN
ejpam-4577	236	5	canoy	canoy	PROPN
ejpam-4577	236	6	/	/	SYM
ejpam-4577	236	7	eur	eur	PROPN
ejpam-4577	236	8	.	.	PUNCT
ejpam-4577	237	1	j.	j.	PROPN
ejpam-4577	237	2	pure	pure	PROPN
ejpam-4577	237	3	appl	appl	PROPN
ejpam-4577	237	4	.	.	PROPN
ejpam-4577	237	5	math	math	PROPN
ejpam-4577	237	6	,	,	PUNCT
ejpam-4577	237	7	15	15	NUM
ejpam-4577	237	8	(	(	PUNCT
ejpam-4577	237	9	4	4	NUM
ejpam-4577	237	10	)	)	PUNCT
ejpam-4577	237	11	(	(	PUNCT
ejpam-4577	237	12	2022	2022	NUM
ejpam-4577	237	13	)	)	PUNCT
ejpam-4577	237	14	,	,	PUNCT
ejpam-4577	237	15	1783	1783	NUM
ejpam-4577	237	16	-	-	SYM
ejpam-4577	237	17	1796	1796	NUM
ejpam-4577	237	18	1790	1790	NUM
ejpam-4577	237	19	on	on	ADP
ejpam-4577	237	20	the	the	DET
ejpam-4577	237	21	other	other	ADJ
ejpam-4577	237	22	hand	hand	NOUN
ejpam-4577	237	23	,	,	PUNCT
ejpam-4577	237	24	suppose	suppose	VERB
ejpam-4577	237	25	s∗	s∗	PROPN
ejpam-4577	237	26	is	be	AUX
ejpam-4577	237	27	a	a	DET
ejpam-4577	237	28	γhih	γhih	NOUN
ejpam-4577	237	29	-	-	PUNCT
ejpam-4577	237	30	set	set	NOUN
ejpam-4577	237	31	of	of	ADP
ejpam-4577	237	32	s(g	s(g	PROPN
ejpam-4577	237	33	)	)	PUNCT
ejpam-4577	237	34	.	.	PUNCT
ejpam-4577	238	1	if	if	SCONJ
ejpam-4577	238	2	s∗	s∗	PROPN
ejpam-4577	238	3	is	be	AUX
ejpam-4577	238	4	of	of	ADP
ejpam-4577	238	5	type	type	NOUN
ejpam-4577	238	6	(	(	PUNCT
ejpam-4577	238	7	i	i	NOUN
ejpam-4577	238	8	)	)	PUNCT
ejpam-4577	238	9	or	or	CCONJ
ejpam-4577	238	10	(	(	PUNCT
ejpam-4577	238	11	ii	ii	NOUN
ejpam-4577	238	12	)	)	PUNCT
ejpam-4577	238	13	,	,	PUNCT
ejpam-4577	238	14	then	then	ADV
ejpam-4577	238	15	s∗	s∗	PROPN
ejpam-4577	238	16	is	be	AUX
ejpam-4577	238	17	a	a	DET
ejpam-4577	238	18	hop	hop	NOUN
ejpam-4577	238	19	independent	independent	ADJ
ejpam-4577	238	20	hop	hop	NOUN
ejpam-4577	238	21	dominating	dominating	NOUN
ejpam-4577	238	22	set	set	NOUN
ejpam-4577	238	23	of	of	ADP
ejpam-4577	238	24	g	g	NOUN
ejpam-4577	238	25	by	by	ADP
ejpam-4577	238	26	(	(	PUNCT
ejpam-4577	238	27	i	i	NOUN
ejpam-4577	238	28	)	)	PUNCT
ejpam-4577	238	29	and	and	CCONJ
ejpam-4577	238	30	(	(	PUNCT
ejpam-4577	238	31	ii	ii	NOUN
ejpam-4577	238	32	)	)	PUNCT
ejpam-4577	238	33	of	of	ADP
ejpam-4577	238	34	theorem	theorem	NOUN
ejpam-4577	238	35	5	5	NUM
ejpam-4577	238	36	.	.	PUNCT
ejpam-4577	238	37	hence	hence	ADV
ejpam-4577	238	38	,	,	PUNCT
ejpam-4577	238	39	γhih(s(g	γhih(s(g	NUM
ejpam-4577	238	40	)	)	PUNCT
ejpam-4577	238	41	)	)	PUNCT
ejpam-4577	239	1	=	=	PRON
ejpam-4577	239	2	|s∗|	|s∗|	NUM
ejpam-4577	239	3	≥	≥	NUM
ejpam-4577	239	4	γhih(g	γhih(g	NOUN
ejpam-4577	239	5	)	)	PUNCT
ejpam-4577	239	6	.	.	PUNCT
ejpam-4577	240	1	suppose	suppose	VERB
ejpam-4577	240	2	s∗	s∗	PROPN
ejpam-4577	240	3	is	be	AUX
ejpam-4577	240	4	of	of	ADP
ejpam-4577	240	5	type	type	NOUN
ejpam-4577	240	6	(	(	PUNCT
ejpam-4577	240	7	iii	iii	NOUN
ejpam-4577	240	8	)	)	PUNCT
ejpam-4577	240	9	,	,	PUNCT
ejpam-4577	240	10	say	say	VERB
ejpam-4577	240	11	s∗	s∗	PROPN
ejpam-4577	240	12	=	=	SYM
ejpam-4577	240	13	sg1	sg1	PROPN
ejpam-4577	240	14	∪	∪	PROPN
ejpam-4577	240	15	sg2	sg2	PROPN
ejpam-4577	240	16	.	.	PUNCT
ejpam-4577	241	1	then	then	ADV
ejpam-4577	241	2	s∗	s∗	VERB
ejpam-4577	241	3	g	g	PROPN
ejpam-4577	241	4	=	=	PUNCT
ejpam-4577	241	5	sg1	sg1	PROPN
ejpam-4577	241	6	∪	∪	ADJ
ejpam-4577	241	7	s′	s′	ADJ
ejpam-4577	241	8	g2	g2	PROPN
ejpam-4577	241	9	is	be	AUX
ejpam-4577	241	10	a	a	DET
ejpam-4577	241	11	hop	hop	NOUN
ejpam-4577	241	12	independent	independent	ADJ
ejpam-4577	241	13	hop	hop	NOUN
ejpam-4577	241	14	dominating	dominating	NOUN
ejpam-4577	241	15	set	set	NOUN
ejpam-4577	241	16	of	of	ADP
ejpam-4577	241	17	g1	g1	NOUN
ejpam-4577	241	18	by	by	ADP
ejpam-4577	241	19	theorem	theorem	ADJ
ejpam-4577	241	20	5(iii	5(iii	NUM
ejpam-4577	241	21	)	)	PUNCT
ejpam-4577	241	22	.	.	PUNCT
ejpam-4577	242	1	this	this	PRON
ejpam-4577	242	2	implies	imply	VERB
ejpam-4577	242	3	that	that	SCONJ
ejpam-4577	242	4	γhih(s(g	γhih(s(g	NOUN
ejpam-4577	242	5	)	)	PUNCT
ejpam-4577	242	6	)	)	PUNCT
ejpam-4577	243	1	=	=	NOUN
ejpam-4577	243	2	|s∗|	|s∗|	NOUN
ejpam-4577	243	3	=	=	PUNCT
ejpam-4577	243	4	|s∗	|s∗	PROPN
ejpam-4577	243	5	g|	g|	PROPN
ejpam-4577	243	6	≥	≥	NOUN
ejpam-4577	243	7	γhih(g	γhih(g	PROPN
ejpam-4577	243	8	)	)	PUNCT
ejpam-4577	243	9	.	.	PUNCT
ejpam-4577	244	1	consequently	consequently	ADV
ejpam-4577	244	2	,	,	PUNCT
ejpam-4577	244	3	γhih(s(g	γhih(s(g	NUM
ejpam-4577	244	4	)	)	PUNCT
ejpam-4577	244	5	)	)	PUNCT
ejpam-4577	245	1	=	=	PUNCT
ejpam-4577	245	2	γhih(g	γhih(g	NOUN
ejpam-4577	245	3	)	)	PUNCT
ejpam-4577	245	4	.	.	PUNCT
ejpam-4577	246	1	statements	statement	NOUN
ejpam-4577	246	2	(	(	PUNCT
ejpam-4577	246	3	i	i	NOUN
ejpam-4577	246	4	)	)	PUNCT
ejpam-4577	246	5	,	,	PUNCT
ejpam-4577	246	6	(	(	PUNCT
ejpam-4577	246	7	ii	ii	NOUN
ejpam-4577	246	8	)	)	PUNCT
ejpam-4577	246	9	and	and	CCONJ
ejpam-4577	246	10	(	(	PUNCT
ejpam-4577	246	11	iii	iii	X
ejpam-4577	246	12	)	)	PUNCT
ejpam-4577	246	13	follow	follow	VERB
ejpam-4577	246	14	from	from	ADP
ejpam-4577	246	15	corollary	corollary	ADJ
ejpam-4577	246	16	1	1	NUM
ejpam-4577	246	17	,	,	PUNCT
ejpam-4577	246	18	theorem	theorem	VERB
ejpam-4577	246	19	3	3	NUM
ejpam-4577	246	20	and	and	CCONJ
ejpam-4577	246	21	theorem	theorem	VERB
ejpam-4577	246	22	5	5	NUM
ejpam-4577	246	23	.	.	PUNCT
ejpam-4577	247	1	lemma	lemma	PROPN
ejpam-4577	247	2	1	1	NUM
ejpam-4577	247	3	.	.	PUNCT
ejpam-4577	248	1	[	[	X
ejpam-4577	248	2	8	8	NUM
ejpam-4577	248	3	]	]	PUNCT
ejpam-4577	248	4	let	let	VERB
ejpam-4577	248	5	g	g	PRON
ejpam-4577	248	6	be	be	AUX
ejpam-4577	248	7	a	a	DET
ejpam-4577	248	8	graph	graph	NOUN
ejpam-4577	248	9	of	of	ADP
ejpam-4577	248	10	order	order	NOUN
ejpam-4577	248	11	n.	n.	NOUN
ejpam-4577	248	12	then	then	ADV
ejpam-4577	248	13	every	every	DET
ejpam-4577	248	14	component	component	NOUN
ejpam-4577	248	15	of	of	ADP
ejpam-4577	248	16	s(g	s(g	PROPN
ejpam-4577	248	17	)	)	PUNCT
ejpam-4577	248	18	is	be	AUX
ejpam-4577	248	19	a	a	DET
ejpam-4577	248	20	complete	complete	ADJ
ejpam-4577	248	21	graph	graph	NOUN
ejpam-4577	248	22	if	if	SCONJ
ejpam-4577	248	23	and	and	CCONJ
ejpam-4577	248	24	only	only	ADV
ejpam-4577	248	25	if	if	SCONJ
ejpam-4577	248	26	g	g	PROPN
ejpam-4577	248	27	=	=	PROPN
ejpam-4577	248	28	kn	kn	PROPN
ejpam-4577	248	29	.	.	PUNCT
ejpam-4577	248	30	theorem	theorem	VERB
ejpam-4577	248	31	6	6	NUM
ejpam-4577	248	32	.	.	PUNCT
ejpam-4577	249	1	let	let	VERB
ejpam-4577	249	2	g	g	PRON
ejpam-4577	249	3	be	be	AUX
ejpam-4577	249	4	a	a	DET
ejpam-4577	249	5	graph	graph	NOUN
ejpam-4577	249	6	on	on	ADP
ejpam-4577	249	7	n	n	DET
ejpam-4577	249	8	vertices	vertex	NOUN
ejpam-4577	249	9	.	.	PUNCT
ejpam-4577	250	1	then	then	ADV
ejpam-4577	250	2	2	2	NUM
ejpam-4577	250	3	≤	≤	NOUN
ejpam-4577	250	4	γhih(s(g	γhih(s(g	NOUN
ejpam-4577	250	5	)	)	PUNCT
ejpam-4577	250	6	)	)	PUNCT
ejpam-4577	250	7	≤	≤	NUM
ejpam-4577	250	8	2n	2n	NUM
ejpam-4577	250	9	.	.	PUNCT
ejpam-4577	251	1	moreover	moreover	ADV
ejpam-4577	251	2	,	,	PUNCT
ejpam-4577	251	3	γhih(s(g	γhih(s(g	NUM
ejpam-4577	251	4	)	)	PUNCT
ejpam-4577	251	5	)	)	PUNCT
ejpam-4577	252	1	=	=	SYM
ejpam-4577	252	2	2n	2n	NUM
ejpam-4577	253	1	if	if	SCONJ
ejpam-4577	253	2	and	and	CCONJ
ejpam-4577	253	3	only	only	ADV
ejpam-4577	253	4	if	if	SCONJ
ejpam-4577	253	5	g	g	PROPN
ejpam-4577	253	6	=	=	PROPN
ejpam-4577	253	7	kn	kn	PROPN
ejpam-4577	253	8	.	.	PUNCT
ejpam-4577	253	9	proof	proof	NOUN
ejpam-4577	253	10	.	.	PUNCT
ejpam-4577	254	1	since	since	SCONJ
ejpam-4577	254	2	2	2	NUM
ejpam-4577	254	3	≤	≤	NUM
ejpam-4577	254	4	|v	|v	X
ejpam-4577	254	5	(	(	PUNCT
ejpam-4577	254	6	s(g))|	s(g))|	PROPN
ejpam-4577	254	7	≤	≤	NOUN
ejpam-4577	254	8	2n	2n	NUM
ejpam-4577	254	9	,	,	PUNCT
ejpam-4577	254	10	it	it	PRON
ejpam-4577	254	11	follows	follow	VERB
ejpam-4577	254	12	that	that	SCONJ
ejpam-4577	254	13	2	2	NUM
ejpam-4577	254	14	≤	≤	NOUN
ejpam-4577	254	15	γhih(s(g	γhih(s(g	NOUN
ejpam-4577	254	16	)	)	PUNCT
ejpam-4577	254	17	)	)	PUNCT
ejpam-4577	254	18	≤	≤	NUM
ejpam-4577	254	19	2n	2n	NUM
ejpam-4577	254	20	by	by	ADP
ejpam-4577	254	21	theorem	theorem	NOUN
ejpam-4577	254	22	3	3	NUM
ejpam-4577	254	23	.	.	PUNCT
ejpam-4577	254	24	suppose	suppose	VERB
ejpam-4577	254	25	γhih(s(g	γhih(s(g	NOUN
ejpam-4577	254	26	)	)	PUNCT
ejpam-4577	254	27	)	)	PUNCT
ejpam-4577	255	1	=	=	SYM
ejpam-4577	255	2	2n	2n	X
ejpam-4577	255	3	.	.	PUNCT
ejpam-4577	256	1	then	then	ADV
ejpam-4577	256	2	every	every	DET
ejpam-4577	256	3	component	component	NOUN
ejpam-4577	256	4	of	of	ADP
ejpam-4577	256	5	s(g	s(g	PROPN
ejpam-4577	256	6	)	)	PUNCT
ejpam-4577	256	7	is	be	AUX
ejpam-4577	256	8	a	a	DET
ejpam-4577	256	9	complete	complete	ADJ
ejpam-4577	256	10	graph	graph	NOUN
ejpam-4577	256	11	by	by	ADP
ejpam-4577	256	12	theorem	theorem	NOUN
ejpam-4577	256	13	3	3	NUM
ejpam-4577	256	14	.	.	PUNCT
ejpam-4577	257	1	hence	hence	ADV
ejpam-4577	257	2	,	,	PUNCT
ejpam-4577	257	3	g	g	PROPN
ejpam-4577	257	4	=	=	PUNCT
ejpam-4577	257	5	kn	kn	PROPN
ejpam-4577	257	6	by	by	ADP
ejpam-4577	257	7	lemma	lemma	PROPN
ejpam-4577	257	8	1	1	NUM
ejpam-4577	257	9	.	.	PUNCT
ejpam-4577	258	1	for	for	ADP
ejpam-4577	258	2	the	the	DET
ejpam-4577	258	3	converse	converse	NOUN
ejpam-4577	258	4	,	,	PUNCT
ejpam-4577	258	5	suppose	suppose	VERB
ejpam-4577	258	6	g	g	PROPN
ejpam-4577	258	7	=	=	PROPN
ejpam-4577	258	8	kn	kn	PROPN
ejpam-4577	258	9	.	.	PUNCT
ejpam-4577	259	1	then	then	ADV
ejpam-4577	259	2	s(g	s(g	PROPN
ejpam-4577	259	3	)	)	PUNCT
ejpam-4577	259	4	=	=	SYM
ejpam-4577	259	5	k2n	k2n	PROPN
ejpam-4577	259	6	.	.	PUNCT
ejpam-4577	260	1	hence	hence	ADV
ejpam-4577	260	2	,	,	PUNCT
ejpam-4577	260	3	γhih(s(g	γhih(s(g	NUM
ejpam-4577	260	4	)	)	PUNCT
ejpam-4577	260	5	)	)	PUNCT
ejpam-4577	261	1	=	=	PUNCT
ejpam-4577	261	2	2n	2n	NUM
ejpam-4577	261	3	by	by	ADP
ejpam-4577	261	4	theorem	theorem	NOUN
ejpam-4577	261	5	3	3	NUM
ejpam-4577	261	6	.	.	PUNCT
ejpam-4577	261	7	theorem	theorem	NOUN
ejpam-4577	261	8	7	7	NUM
ejpam-4577	261	9	.	.	PUNCT
ejpam-4577	262	1	let	let	VERB
ejpam-4577	262	2	g	g	PRON
ejpam-4577	262	3	be	be	AUX
ejpam-4577	262	4	a	a	DET
ejpam-4577	262	5	graph	graph	NOUN
ejpam-4577	262	6	of	of	ADP
ejpam-4577	262	7	order	order	NOUN
ejpam-4577	262	8	n.	n.	NOUN
ejpam-4577	263	1	then	then	ADV
ejpam-4577	263	2	1	1	NUM
ejpam-4577	263	3	≤	≤	NUM
ejpam-4577	263	4	cpnd(g	cpnd(g	NOUN
ejpam-4577	263	5	)	)	PUNCT
ejpam-4577	263	6	≤	≤	NOUN
ejpam-4577	263	7	n.	n.	NOUN
ejpam-4577	263	8	moreover	moreover	ADV
ejpam-4577	263	9	,	,	PUNCT
ejpam-4577	263	10	(	(	PUNCT
ejpam-4577	263	11	i	i	NOUN
ejpam-4577	263	12	)	)	PUNCT
ejpam-4577	263	13	cpnd(g	cpnd(g	NOUN
ejpam-4577	263	14	)	)	PUNCT
ejpam-4577	263	15	=	=	SYM
ejpam-4577	263	16	1	1	NUM
ejpam-4577	263	17	if	if	SCONJ
ejpam-4577	263	18	and	and	CCONJ
ejpam-4577	263	19	only	only	ADV
ejpam-4577	263	20	if	if	SCONJ
ejpam-4577	263	21	g	g	PROPN
ejpam-4577	263	22	has	have	VERB
ejpam-4577	263	23	an	an	DET
ejpam-4577	263	24	isolated	isolated	ADJ
ejpam-4577	263	25	vertex	vertex	NOUN
ejpam-4577	263	26	.	.	PUNCT
ejpam-4577	264	1	(	(	PUNCT
ejpam-4577	264	2	ii	ii	NOUN
ejpam-4577	264	3	)	)	PUNCT
ejpam-4577	264	4	cpnd(g	cpnd(g	NOUN
ejpam-4577	264	5	)	)	PUNCT
ejpam-4577	264	6	=	=	SYM
ejpam-4577	264	7	2	2	NUM
ejpam-4577	264	8	if	if	SCONJ
ejpam-4577	264	9	and	and	CCONJ
ejpam-4577	264	10	only	only	ADV
ejpam-4577	264	11	if	if	SCONJ
ejpam-4577	264	12	g	g	PROPN
ejpam-4577	264	13	has	have	VERB
ejpam-4577	264	14	no	no	DET
ejpam-4577	264	15	isolated	isolated	ADJ
ejpam-4577	264	16	vertex	vertex	NOUN
ejpam-4577	264	17	and	and	CCONJ
ejpam-4577	264	18	there	there	PRON
ejpam-4577	264	19	exist	exist	VERB
ejpam-4577	264	20	adjacent	adjacent	ADJ
ejpam-4577	264	21	vertices	vertex	NOUN
ejpam-4577	264	22	x	x	PUNCT
ejpam-4577	264	23	and	and	CCONJ
ejpam-4577	264	24	y	y	PROPN
ejpam-4577	264	25	of	of	ADP
ejpam-4577	264	26	g	g	PROPN
ejpam-4577	264	27	such	such	ADJ
ejpam-4577	264	28	that	that	PRON
ejpam-4577	264	29	ng(x	ng(x	NUM
ejpam-4577	264	30	)	)	PUNCT
ejpam-4577	264	31	∩ng(y	∩ng(y	PROPN
ejpam-4577	264	32	)	)	PUNCT
ejpam-4577	265	1	=	=	PUNCT
ejpam-4577	265	2	∅.	∅.	PRON
ejpam-4577	265	3	(	(	PUNCT
ejpam-4577	265	4	iii	iii	NOUN
ejpam-4577	265	5	)	)	PUNCT
ejpam-4577	265	6	cpnd(g	cpnd(g	NOUN
ejpam-4577	265	7	)	)	PUNCT
ejpam-4577	265	8	=	=	SYM
ejpam-4577	266	1	n	n	NOUN
ejpam-4577	266	2	if	if	SCONJ
ejpam-4577	266	3	and	and	CCONJ
ejpam-4577	266	4	only	only	ADV
ejpam-4577	266	5	if	if	SCONJ
ejpam-4577	266	6	g	g	PROPN
ejpam-4577	266	7	is	be	AUX
ejpam-4577	266	8	a	a	DET
ejpam-4577	266	9	complete	complete	ADJ
ejpam-4577	266	10	graph	graph	NOUN
ejpam-4577	266	11	.	.	PUNCT
ejpam-4577	267	1	proof	proof	NOUN
ejpam-4577	267	2	.	.	PUNCT
ejpam-4577	268	1	celarly	celarly	ADV
ejpam-4577	268	2	,	,	PUNCT
ejpam-4577	268	3	1	1	NUM
ejpam-4577	268	4	≤	≤	NUM
ejpam-4577	268	5	cpnd(g	cpnd(g	NOUN
ejpam-4577	268	6	)	)	PUNCT
ejpam-4577	268	7	≤	≤	NOUN
ejpam-4577	268	8	n.	n.	NOUN
ejpam-4577	268	9	(	(	PUNCT
ejpam-4577	268	10	i	i	NOUN
ejpam-4577	268	11	)	)	PUNCT
ejpam-4577	268	12	suppose	suppose	VERB
ejpam-4577	268	13	cpnd(g	cpnd(g	NOUN
ejpam-4577	268	14	)	)	PUNCT
ejpam-4577	268	15	=	=	SYM
ejpam-4577	268	16	1	1	X
ejpam-4577	268	17	,	,	PUNCT
ejpam-4577	268	18	say	say	VERB
ejpam-4577	268	19	{	{	PUNCT
ejpam-4577	268	20	p	p	X
ejpam-4577	268	21	}	}	PUNCT
ejpam-4577	268	22	is	be	AUX
ejpam-4577	268	23	a	a	DET
ejpam-4577	268	24	cpnd	cpnd	NOUN
ejpam-4577	268	25	-	-	PUNCT
ejpam-4577	268	26	set	set	NOUN
ejpam-4577	268	27	of	of	ADP
ejpam-4577	268	28	g.	g.	PROPN
ejpam-4577	268	29	clearly	clearly	ADV
ejpam-4577	268	30	,	,	PUNCT
ejpam-4577	268	31	p	p	PROPN
ejpam-4577	268	32	is	be	AUX
ejpam-4577	268	33	an	an	DET
ejpam-4577	268	34	isolated	isolated	ADJ
ejpam-4577	268	35	vertex	vertex	NOUN
ejpam-4577	268	36	of	of	ADP
ejpam-4577	268	37	g.	g.	PROPN
ejpam-4577	268	38	conversely	conversely	ADV
ejpam-4577	268	39	,	,	PUNCT
ejpam-4577	268	40	suppose	suppose	VERB
ejpam-4577	268	41	g	g	PROPN
ejpam-4577	268	42	has	have	VERB
ejpam-4577	268	43	an	an	DET
ejpam-4577	268	44	isolated	isolated	ADJ
ejpam-4577	268	45	vertex	vertex	NOUN
ejpam-4577	268	46	,	,	PUNCT
ejpam-4577	268	47	say	say	VERB
ejpam-4577	268	48	a.	a.	NOUN
ejpam-4577	268	49	then	then	ADV
ejpam-4577	268	50	{	{	PUNCT
ejpam-4577	268	51	a	a	PRON
ejpam-4577	268	52	}	}	PUNCT
ejpam-4577	268	53	is	be	AUX
ejpam-4577	268	54	a	a	DET
ejpam-4577	268	55	cpnd	cpnd	NOUN
ejpam-4577	268	56	-	-	PUNCT
ejpam-4577	268	57	set	set	NOUN
ejpam-4577	268	58	of	of	ADP
ejpam-4577	268	59	g.	g.	PROPN
ejpam-4577	268	60	hence	hence	ADV
ejpam-4577	268	61	,	,	PUNCT
ejpam-4577	268	62	cpnd(g	cpnd(g	NOUN
ejpam-4577	268	63	)	)	PUNCT
ejpam-4577	268	64	=	=	SYM
ejpam-4577	269	1	1	1	X
ejpam-4577	269	2	.	.	PUNCT
ejpam-4577	269	3	(	(	PUNCT
ejpam-4577	269	4	ii	ii	NOUN
ejpam-4577	269	5	)	)	PUNCT
ejpam-4577	269	6	suppose	suppose	VERB
ejpam-4577	269	7	cpnd(g	cpnd(g	NOUN
ejpam-4577	269	8	)	)	PUNCT
ejpam-4577	269	9	=	=	SYM
ejpam-4577	269	10	2	2	NUM
ejpam-4577	269	11	,	,	PUNCT
ejpam-4577	269	12	say	say	VERB
ejpam-4577	269	13	c	c	NOUN
ejpam-4577	269	14	=	=	SYM
ejpam-4577	269	15	{	{	PUNCT
ejpam-4577	269	16	x	x	PROPN
ejpam-4577	269	17	,	,	PUNCT
ejpam-4577	269	18	y	y	PRON
ejpam-4577	269	19	}	}	PUNCT
ejpam-4577	269	20	is	be	AUX
ejpam-4577	269	21	a	a	DET
ejpam-4577	269	22	clique	clique	NOUN
ejpam-4577	269	23	pointwise	pointwise	PROPN
ejpam-4577	269	24	non	non	ADJ
ejpam-4577	269	25	-	-	ADJ
ejpam-4577	269	26	dominating	dominating	ADJ
ejpam-4577	269	27	set	set	NOUN
ejpam-4577	269	28	of	of	ADP
ejpam-4577	269	29	g.	g.	PROPN
ejpam-4577	269	30	then	then	ADV
ejpam-4577	269	31	x	x	X
ejpam-4577	269	32	and	and	CCONJ
ejpam-4577	269	33	y	y	PROPN
ejpam-4577	269	34	are	be	AUX
ejpam-4577	269	35	adjacent	adjacent	ADJ
ejpam-4577	269	36	.	.	PUNCT
ejpam-4577	270	1	by	by	ADP
ejpam-4577	270	2	(	(	PUNCT
ejpam-4577	270	3	i	i	NOUN
ejpam-4577	270	4	)	)	PUNCT
ejpam-4577	270	5	,	,	PUNCT
ejpam-4577	270	6	g	g	PROPN
ejpam-4577	270	7	has	have	VERB
ejpam-4577	270	8	no	no	DET
ejpam-4577	270	9	isolated	isolated	ADJ
ejpam-4577	270	10	vertex	vertex	NOUN
ejpam-4577	270	11	.	.	PUNCT
ejpam-4577	271	1	now	now	ADV
ejpam-4577	271	2	,	,	PUNCT
ejpam-4577	271	3	suppose	suppose	VERB
ejpam-4577	271	4	that	that	SCONJ
ejpam-4577	271	5	ng(x	ng(x	NUM
ejpam-4577	271	6	)	)	PUNCT
ejpam-4577	271	7	∩	∩	NOUN
ejpam-4577	271	8	ng(y	ng(y	NOUN
ejpam-4577	271	9	)	)	PUNCT
ejpam-4577	271	10	̸=	̸=	PROPN
ejpam-4577	271	11	∅.	∅.	ADV
ejpam-4577	271	12	let	let	VERB
ejpam-4577	271	13	a	a	DET
ejpam-4577	271	14	∈	∈	PROPN
ejpam-4577	271	15	ng(x	ng(x	NUM
ejpam-4577	271	16	)	)	PUNCT
ejpam-4577	271	17	∩	∩	NOUN
ejpam-4577	271	18	ng(y	ng(y	NOUN
ejpam-4577	271	19	)	)	PUNCT
ejpam-4577	271	20	.	.	PUNCT
ejpam-4577	272	1	then	then	ADV
ejpam-4577	272	2	a	a	DET
ejpam-4577	272	3	∈	∈	PROPN
ejpam-4577	272	4	v	v	ADP
ejpam-4577	272	5	(	(	PUNCT
ejpam-4577	272	6	g	g	NOUN
ejpam-4577	272	7	)	)	PUNCT
ejpam-4577	272	8	\	\	PROPN
ejpam-4577	272	9	c.	c.	NOUN
ejpam-4577	272	10	since	since	SCONJ
ejpam-4577	272	11	a	a	PRON
ejpam-4577	272	12	is	be	AUX
ejpam-4577	272	13	adjacent	adjacent	ADJ
ejpam-4577	272	14	to	to	ADP
ejpam-4577	272	15	both	both	PRON
ejpam-4577	272	16	x	x	PROPN
ejpam-4577	272	17	and	and	CCONJ
ejpam-4577	272	18	y	y	PROPN
ejpam-4577	272	19	,	,	PUNCT
ejpam-4577	272	20	it	it	PRON
ejpam-4577	272	21	follows	follow	VERB
ejpam-4577	272	22	that	that	SCONJ
ejpam-4577	272	23	c	c	PROPN
ejpam-4577	272	24	is	be	AUX
ejpam-4577	272	25	not	not	PART
ejpam-4577	272	26	a	a	DET
ejpam-4577	272	27	pointwise	pointwise	ADJ
ejpam-4577	272	28	non	non	ADJ
ejpam-4577	272	29	-	-	ADJ
ejpam-4577	272	30	dominating	dominating	ADJ
ejpam-4577	272	31	set	set	NOUN
ejpam-4577	272	32	,	,	PUNCT
ejpam-4577	272	33	a	a	DET
ejpam-4577	272	34	contradiction	contradiction	NOUN
ejpam-4577	272	35	.	.	PUNCT
ejpam-4577	273	1	hence	hence	ADV
ejpam-4577	273	2	,	,	PUNCT
ejpam-4577	273	3	ng(x	ng(x	NUM
ejpam-4577	273	4	)	)	PUNCT
ejpam-4577	273	5	∩ng(y	∩ng(y	PROPN
ejpam-4577	273	6	)	)	PUNCT
ejpam-4577	273	7	=	=	NOUN
ejpam-4577	273	8	∅.	∅.	VERB
ejpam-4577	273	9	conversely	conversely	ADV
ejpam-4577	273	10	,	,	PUNCT
ejpam-4577	273	11	suppose	suppose	VERB
ejpam-4577	273	12	g	g	PROPN
ejpam-4577	273	13	has	have	VERB
ejpam-4577	273	14	no	no	DET
ejpam-4577	273	15	isolated	isolated	ADJ
ejpam-4577	273	16	vertex	vertex	NOUN
ejpam-4577	273	17	and	and	CCONJ
ejpam-4577	273	18	there	there	PRON
ejpam-4577	273	19	exist	exist	VERB
ejpam-4577	273	20	adjacent	adjacent	ADJ
ejpam-4577	273	21	vertices	vertex	NOUN
ejpam-4577	273	22	x	x	PUNCT
ejpam-4577	273	23	and	and	CCONJ
ejpam-4577	273	24	y	y	PROPN
ejpam-4577	273	25	of	of	ADP
ejpam-4577	273	26	g	g	PROPN
ejpam-4577	273	27	such	such	ADJ
ejpam-4577	273	28	that	that	PRON
ejpam-4577	273	29	ng(x	ng(x	NUM
ejpam-4577	273	30	)	)	PUNCT
ejpam-4577	273	31	∩ng(y	∩ng(y	PROPN
ejpam-4577	273	32	)	)	PUNCT
ejpam-4577	273	33	=	=	VERB
ejpam-4577	273	34	∅.	∅.	AUX
ejpam-4577	273	35	let	let	VERB
ejpam-4577	273	36	c	c	NOUN
ejpam-4577	273	37	=	=	PRON
ejpam-4577	273	38	{	{	PUNCT
ejpam-4577	273	39	x	x	PROPN
ejpam-4577	273	40	,	,	PUNCT
ejpam-4577	273	41	y	y	PROPN
ejpam-4577	273	42	}	}	PUNCT
ejpam-4577	273	43	and	and	CCONJ
ejpam-4577	273	44	a	a	DET
ejpam-4577	273	45	∈	∈	NOUN
ejpam-4577	273	46	v	v	ADP
ejpam-4577	273	47	(	(	PUNCT
ejpam-4577	273	48	g	g	NOUN
ejpam-4577	273	49	)	)	PUNCT
ejpam-4577	273	50	\c	\c	NOUN
ejpam-4577	273	51	.	.	PUNCT
ejpam-4577	274	1	by	by	ADP
ejpam-4577	274	2	assumption	assumption	NOUN
ejpam-4577	274	3	,	,	PUNCT
ejpam-4577	274	4	a	a	PRON
ejpam-4577	274	5	is	be	AUX
ejpam-4577	274	6	not	not	PART
ejpam-4577	274	7	adjacent	adjacent	ADJ
ejpam-4577	274	8	to	to	ADP
ejpam-4577	274	9	x	x	PUNCT
ejpam-4577	274	10	or	or	CCONJ
ejpam-4577	274	11	y.	y.	NOUN
ejpam-4577	274	12	this	this	PRON
ejpam-4577	274	13	implies	imply	VERB
ejpam-4577	274	14	that	that	SCONJ
ejpam-4577	274	15	c	c	PROPN
ejpam-4577	274	16	is	be	AUX
ejpam-4577	274	17	a	a	DET
ejpam-4577	274	18	clique	clique	NOUN
ejpam-4577	274	19	pointwise	pointwise	PROPN
ejpam-4577	274	20	non	non	ADJ
ejpam-4577	274	21	-	-	ADJ
ejpam-4577	274	22	dominating	dominating	ADJ
ejpam-4577	274	23	set	set	NOUN
ejpam-4577	274	24	,	,	PUNCT
ejpam-4577	274	25	and	and	CCONJ
ejpam-4577	274	26	so	so	ADV
ejpam-4577	274	27	cpnd(g	cpnd(g	ADJ
ejpam-4577	274	28	)	)	PUNCT
ejpam-4577	274	29	≤	≤	NOUN
ejpam-4577	274	30	2	2	NUM
ejpam-4577	274	31	.	.	PUNCT
ejpam-4577	275	1	since	since	SCONJ
ejpam-4577	275	2	g	g	PROPN
ejpam-4577	275	3	has	have	VERB
ejpam-4577	275	4	no	no	DET
ejpam-4577	275	5	isolated	isolated	ADJ
ejpam-4577	275	6	vertex	vertex	NOUN
ejpam-4577	275	7	,	,	PUNCT
ejpam-4577	275	8	cpnd(g	cpnd(g	NOUN
ejpam-4577	275	9	)	)	PUNCT
ejpam-4577	275	10	≥	≥	NOUN
ejpam-4577	275	11	2	2	NUM
ejpam-4577	275	12	.	.	PUNCT
ejpam-4577	275	13	consequently	consequently	ADV
ejpam-4577	275	14	,	,	PUNCT
ejpam-4577	275	15	cpnd(g	cpnd(g	NOUN
ejpam-4577	275	16	)	)	PUNCT
ejpam-4577	275	17	=	=	SYM
ejpam-4577	275	18	2	2	X
ejpam-4577	275	19	.	.	PUNCT
ejpam-4577	275	20	(	(	PUNCT
ejpam-4577	275	21	iii	iii	NOUN
ejpam-4577	275	22	)	)	PUNCT
ejpam-4577	275	23	suppose	suppose	VERB
ejpam-4577	275	24	cpnd(g	cpnd(g	NOUN
ejpam-4577	275	25	)	)	PUNCT
ejpam-4577	275	26	=	=	VERB
ejpam-4577	276	1	n.	n.	NOUN
ejpam-4577	276	2	then	then	ADV
ejpam-4577	276	3	c	c	X
ejpam-4577	276	4	=	=	SYM
ejpam-4577	276	5	v	v	PROPN
ejpam-4577	276	6	(	(	PUNCT
ejpam-4577	276	7	g	g	NOUN
ejpam-4577	276	8	)	)	PUNCT
ejpam-4577	276	9	is	be	AUX
ejpam-4577	276	10	the	the	DET
ejpam-4577	276	11	only	only	ADJ
ejpam-4577	276	12	clique	clique	NOUN
ejpam-4577	276	13	pointwise	pointwise	PROPN
ejpam-4577	276	14	nondominating	nondominate	VERB
ejpam-4577	276	15	set	set	NOUN
ejpam-4577	276	16	of	of	ADP
ejpam-4577	276	17	g.	g.	PROPN
ejpam-4577	276	18	it	it	PRON
ejpam-4577	276	19	follows	follow	VERB
ejpam-4577	276	20	that	that	SCONJ
ejpam-4577	276	21	g	g	PROPN
ejpam-4577	276	22	is	be	AUX
ejpam-4577	276	23	a	a	DET
ejpam-4577	276	24	complete	complete	ADJ
ejpam-4577	276	25	graph	graph	NOUN
ejpam-4577	276	26	.	.	PUNCT
ejpam-4577	277	1	the	the	DET
ejpam-4577	277	2	converse	converse	NOUN
ejpam-4577	277	3	is	be	AUX
ejpam-4577	277	4	clear	clear	ADJ
ejpam-4577	277	5	.	.	PUNCT
ejpam-4577	278	1	the	the	DET
ejpam-4577	278	2	next	next	ADJ
ejpam-4577	278	3	result	result	NOUN
ejpam-4577	278	4	follows	follow	VERB
ejpam-4577	278	5	immediately	immediately	ADV
ejpam-4577	278	6	from	from	ADP
ejpam-4577	278	7	theorem	theorem	ADJ
ejpam-4577	278	8	7(ii	7(ii	PROPN
ejpam-4577	278	9	)	)	PUNCT
ejpam-4577	278	10	.	.	PUNCT
ejpam-4577	279	1	j.	j.	PROPN
ejpam-4577	279	2	hassan	hassan	PROPN
ejpam-4577	279	3	,	,	PUNCT
ejpam-4577	279	4	s.	s.	PROPN
ejpam-4577	279	5	canoy	canoy	PROPN
ejpam-4577	279	6	/	/	SYM
ejpam-4577	279	7	eur	eur	PROPN
ejpam-4577	279	8	.	.	PUNCT
ejpam-4577	280	1	j.	j.	PROPN
ejpam-4577	280	2	pure	pure	PROPN
ejpam-4577	280	3	appl	appl	PROPN
ejpam-4577	280	4	.	.	PROPN
ejpam-4577	280	5	math	math	PROPN
ejpam-4577	280	6	,	,	PUNCT
ejpam-4577	280	7	15	15	NUM
ejpam-4577	280	8	(	(	PUNCT
ejpam-4577	280	9	4	4	NUM
ejpam-4577	280	10	)	)	PUNCT
ejpam-4577	280	11	(	(	PUNCT
ejpam-4577	280	12	2022	2022	NUM
ejpam-4577	280	13	)	)	PUNCT
ejpam-4577	280	14	,	,	PUNCT
ejpam-4577	280	15	1783	1783	NUM
ejpam-4577	280	16	-	-	SYM
ejpam-4577	280	17	1796	1796	NUM
ejpam-4577	280	18	1791	1791	NUM
ejpam-4577	280	19	corollary	corollary	NOUN
ejpam-4577	280	20	5	5	NUM
ejpam-4577	280	21	.	.	PUNCT
ejpam-4577	281	1	let	let	VERB
ejpam-4577	281	2	n	n	PRON
ejpam-4577	281	3	be	be	AUX
ejpam-4577	281	4	any	any	DET
ejpam-4577	281	5	positive	positive	ADJ
ejpam-4577	281	6	integer	integer	NOUN
ejpam-4577	281	7	.	.	PUNCT
ejpam-4577	282	1	then	then	ADV
ejpam-4577	282	2	(	(	PUNCT
ejpam-4577	282	3	i	i	NOUN
ejpam-4577	282	4	)	)	PUNCT
ejpam-4577	282	5	cpnd(pn	cpnd(pn	PROPN
ejpam-4577	282	6	)	)	PUNCT
ejpam-4577	282	7	=	=	SYM
ejpam-4577	282	8	2	2	NUM
ejpam-4577	282	9	for	for	ADP
ejpam-4577	282	10	any	any	DET
ejpam-4577	282	11	n	n	PRON
ejpam-4577	282	12	≥	≥	NOUN
ejpam-4577	282	13	2	2	NUM
ejpam-4577	282	14	.	.	PUNCT
ejpam-4577	282	15	(	(	PUNCT
ejpam-4577	282	16	ii	ii	NOUN
ejpam-4577	282	17	)	)	PUNCT
ejpam-4577	282	18	cpnd(cn	cpnd(cn	NOUN
ejpam-4577	282	19	)	)	PUNCT
ejpam-4577	282	20	=	=	SYM
ejpam-4577	282	21	2	2	NUM
ejpam-4577	282	22	for	for	ADP
ejpam-4577	282	23	any	any	DET
ejpam-4577	282	24	n	n	PRON
ejpam-4577	282	25	≥	≥	NOUN
ejpam-4577	282	26	4	4	NUM
ejpam-4577	282	27	.	.	PUNCT
ejpam-4577	282	28	theorem	theorem	VERB
ejpam-4577	282	29	8	8	NUM
ejpam-4577	282	30	.	.	PUNCT
ejpam-4577	283	1	[	[	X
ejpam-4577	283	2	7	7	X
ejpam-4577	283	3	]	]	X
ejpam-4577	283	4	let	let	VERB
ejpam-4577	283	5	g	g	NOUN
ejpam-4577	283	6	and	and	CCONJ
ejpam-4577	283	7	h	h	NOUN
ejpam-4577	283	8	be	be	VERB
ejpam-4577	283	9	any	any	DET
ejpam-4577	283	10	two	two	NUM
ejpam-4577	283	11	graphs	graph	NOUN
ejpam-4577	283	12	.	.	PUNCT
ejpam-4577	284	1	a	a	DET
ejpam-4577	284	2	set	set	NOUN
ejpam-4577	284	3	s	s	NOUN
ejpam-4577	284	4	⊆	⊆	NUM
ejpam-4577	284	5	v	v	NOUN
ejpam-4577	284	6	(	(	PUNCT
ejpam-4577	284	7	g+h	g+h	PROPN
ejpam-4577	284	8	)	)	PUNCT
ejpam-4577	284	9	is	be	AUX
ejpam-4577	284	10	hop	hop	NOUN
ejpam-4577	284	11	dominating	dominate	VERB
ejpam-4577	284	12	set	set	NOUN
ejpam-4577	284	13	of	of	ADP
ejpam-4577	284	14	g+h	g+h	PROPN
ejpam-4577	284	15	if	if	SCONJ
ejpam-4577	285	1	and	and	CCONJ
ejpam-4577	285	2	only	only	ADV
ejpam-4577	285	3	if	if	SCONJ
ejpam-4577	285	4	s	s	NOUN
ejpam-4577	285	5	=	=	PUNCT
ejpam-4577	285	6	sg	sg	PROPN
ejpam-4577	285	7	∪sh	∪sh	NOUN
ejpam-4577	285	8	,	,	PUNCT
ejpam-4577	285	9	where	where	SCONJ
ejpam-4577	285	10	sg	sg	PROPN
ejpam-4577	285	11	and	and	CCONJ
ejpam-4577	285	12	sh	sh	PROPN
ejpam-4577	285	13	are	be	AUX
ejpam-4577	285	14	pointwise	pointwise	PROPN
ejpam-4577	285	15	non	non	ADJ
ejpam-4577	285	16	-	-	ADJ
ejpam-4577	285	17	dominating	dominating	ADJ
ejpam-4577	285	18	sets	set	NOUN
ejpam-4577	285	19	of	of	ADP
ejpam-4577	285	20	g	g	PROPN
ejpam-4577	285	21	and	and	CCONJ
ejpam-4577	285	22	h	h	NOUN
ejpam-4577	285	23	,	,	PUNCT
ejpam-4577	285	24	respectively	respectively	ADV
ejpam-4577	285	25	.	.	PUNCT
ejpam-4577	285	26	theorem	theorem	VERB
ejpam-4577	285	27	9	9	NUM
ejpam-4577	285	28	.	.	PUNCT
ejpam-4577	286	1	[	[	X
ejpam-4577	286	2	3	3	X
ejpam-4577	286	3	]	]	PUNCT
ejpam-4577	286	4	let	let	VERB
ejpam-4577	286	5	g	g	NOUN
ejpam-4577	286	6	and	and	CCONJ
ejpam-4577	286	7	h	h	PROPN
ejpam-4577	286	8	be	be	AUX
ejpam-4577	286	9	graphs	graph	NOUN
ejpam-4577	286	10	.	.	PUNCT
ejpam-4577	287	1	then	then	ADV
ejpam-4577	287	2	s	s	VERB
ejpam-4577	287	3	is	be	AUX
ejpam-4577	287	4	a	a	DET
ejpam-4577	287	5	non	non	ADJ
ejpam-4577	287	6	-	-	ADJ
ejpam-4577	287	7	empty	empty	ADJ
ejpam-4577	287	8	hop	hop	NOUN
ejpam-4577	287	9	independent	independent	ADJ
ejpam-4577	287	10	set	set	NOUN
ejpam-4577	287	11	of	of	ADP
ejpam-4577	287	12	g+h	g+h	PROPN
ejpam-4577	287	13	if	if	SCONJ
ejpam-4577	287	14	and	and	CCONJ
ejpam-4577	287	15	only	only	ADV
ejpam-4577	287	16	if	if	SCONJ
ejpam-4577	287	17	one	one	NUM
ejpam-4577	287	18	of	of	ADP
ejpam-4577	287	19	the	the	DET
ejpam-4577	287	20	following	following	ADJ
ejpam-4577	287	21	statements	statement	NOUN
ejpam-4577	287	22	holds	hold	VERB
ejpam-4577	287	23	:	:	PUNCT
ejpam-4577	287	24	(	(	PUNCT
ejpam-4577	287	25	i	i	NOUN
ejpam-4577	287	26	)	)	PUNCT
ejpam-4577	287	27	s	s	AUX
ejpam-4577	287	28	is	be	AUX
ejpam-4577	287	29	a	a	DET
ejpam-4577	287	30	clique	clique	NOUN
ejpam-4577	287	31	in	in	ADP
ejpam-4577	287	32	g.	g.	PROPN
ejpam-4577	287	33	(	(	PUNCT
ejpam-4577	287	34	ii	ii	PROPN
ejpam-4577	287	35	)	)	PUNCT
ejpam-4577	287	36	s	s	VERB
ejpam-4577	287	37	is	be	AUX
ejpam-4577	287	38	a	a	DET
ejpam-4577	287	39	clique	clique	NOUN
ejpam-4577	287	40	in	in	ADP
ejpam-4577	287	41	h	h	PROPN
ejpam-4577	287	42	(	(	PUNCT
ejpam-4577	287	43	iii	iii	NOUN
ejpam-4577	287	44	)	)	PUNCT
ejpam-4577	287	45	s	s	PART
ejpam-4577	287	46	∩	∩	ADJ
ejpam-4577	287	47	v	v	X
ejpam-4577	287	48	(	(	PUNCT
ejpam-4577	287	49	g	g	NOUN
ejpam-4577	287	50	)	)	PUNCT
ejpam-4577	287	51	and	and	CCONJ
ejpam-4577	287	52	s	s	VERB
ejpam-4577	287	53	∩	∩	ADJ
ejpam-4577	287	54	v	v	ADJ
ejpam-4577	287	55	(	(	PUNCT
ejpam-4577	287	56	g	g	NOUN
ejpam-4577	287	57	)	)	PUNCT
ejpam-4577	287	58	are	be	AUX
ejpam-4577	287	59	cliques	clique	NOUN
ejpam-4577	287	60	in	in	ADP
ejpam-4577	287	61	g	g	PROPN
ejpam-4577	287	62	and	and	CCONJ
ejpam-4577	287	63	h	h	NOUN
ejpam-4577	287	64	,	,	PUNCT
ejpam-4577	287	65	respectively	respectively	ADV
ejpam-4577	287	66	.	.	PUNCT
ejpam-4577	288	1	theorem	theorem	VERB
ejpam-4577	288	2	10	10	NUM
ejpam-4577	288	3	.	.	PUNCT
ejpam-4577	289	1	let	let	VERB
ejpam-4577	289	2	g	g	NOUN
ejpam-4577	289	3	and	and	CCONJ
ejpam-4577	289	4	h	h	NOUN
ejpam-4577	289	5	be	be	VERB
ejpam-4577	289	6	two	two	NUM
ejpam-4577	289	7	graphs	graph	NOUN
ejpam-4577	289	8	.	.	PUNCT
ejpam-4577	290	1	a	a	DET
ejpam-4577	290	2	set	set	NOUN
ejpam-4577	290	3	s	s	NOUN
ejpam-4577	290	4	⊆	⊆	NUM
ejpam-4577	290	5	v	v	NOUN
ejpam-4577	290	6	(	(	PUNCT
ejpam-4577	290	7	g	g	PROPN
ejpam-4577	290	8	+	+	NOUN
ejpam-4577	290	9	h	h	NOUN
ejpam-4577	290	10	)	)	PUNCT
ejpam-4577	290	11	is	be	AUX
ejpam-4577	290	12	a	a	DET
ejpam-4577	290	13	hop	hop	NOUN
ejpam-4577	290	14	independent	independent	ADJ
ejpam-4577	290	15	hop	hop	NOUN
ejpam-4577	290	16	dominating	dominating	NOUN
ejpam-4577	290	17	set	set	NOUN
ejpam-4577	290	18	of	of	ADP
ejpam-4577	290	19	g	g	PROPN
ejpam-4577	291	1	+	+	CCONJ
ejpam-4577	291	2	h	h	NOUN
ejpam-4577	291	3	if	if	SCONJ
ejpam-4577	291	4	and	and	CCONJ
ejpam-4577	291	5	only	only	ADV
ejpam-4577	291	6	if	if	SCONJ
ejpam-4577	291	7	s	s	VERB
ejpam-4577	291	8	=	=	PUNCT
ejpam-4577	291	9	sg	sg	X
ejpam-4577	291	10	∪	∪	ADJ
ejpam-4577	291	11	sh	sh	PROPN
ejpam-4577	291	12	,	,	PUNCT
ejpam-4577	291	13	where	where	SCONJ
ejpam-4577	291	14	sg	sg	PROPN
ejpam-4577	291	15	and	and	CCONJ
ejpam-4577	291	16	sh	sh	PROPN
ejpam-4577	291	17	are	be	AUX
ejpam-4577	291	18	clique	clique	PROPN
ejpam-4577	291	19	pointwise	pointwise	PROPN
ejpam-4577	291	20	non	non	ADJ
ejpam-4577	291	21	-	-	ADJ
ejpam-4577	291	22	dominating	dominating	ADJ
ejpam-4577	291	23	sets	set	NOUN
ejpam-4577	291	24	of	of	ADP
ejpam-4577	291	25	g	g	PROPN
ejpam-4577	291	26	and	and	CCONJ
ejpam-4577	291	27	h	h	NOUN
ejpam-4577	291	28	,	,	PUNCT
ejpam-4577	291	29	respectively	respectively	ADV
ejpam-4577	291	30	.	.	PUNCT
ejpam-4577	292	1	proof	proof	NOUN
ejpam-4577	292	2	.	.	PUNCT
ejpam-4577	293	1	suppose	suppose	VERB
ejpam-4577	293	2	s	s	PRON
ejpam-4577	293	3	is	be	AUX
ejpam-4577	293	4	a	a	DET
ejpam-4577	293	5	hop	hop	NOUN
ejpam-4577	293	6	independent	independent	ADJ
ejpam-4577	293	7	hop	hop	NOUN
ejpam-4577	293	8	dominating	dominating	NOUN
ejpam-4577	293	9	set	set	NOUN
ejpam-4577	293	10	of	of	ADP
ejpam-4577	293	11	g	g	PROPN
ejpam-4577	293	12	+	+	PROPN
ejpam-4577	293	13	h.	h.	PROPN
ejpam-4577	293	14	then	then	ADV
ejpam-4577	293	15	sg	sg	PROPN
ejpam-4577	293	16	and	and	CCONJ
ejpam-4577	293	17	sh	sh	PROPN
ejpam-4577	293	18	are	be	AUX
ejpam-4577	293	19	both	both	PRON
ejpam-4577	293	20	non	non	ADJ
ejpam-4577	293	21	-	-	ADJ
ejpam-4577	293	22	empty	empty	ADJ
ejpam-4577	293	23	.	.	PUNCT
ejpam-4577	294	1	since	since	SCONJ
ejpam-4577	294	2	s	s	PROPN
ejpam-4577	294	3	is	be	AUX
ejpam-4577	294	4	a	a	DET
ejpam-4577	294	5	hop	hop	NOUN
ejpam-4577	294	6	dominating	dominating	NOUN
ejpam-4577	294	7	set	set	NOUN
ejpam-4577	294	8	,	,	PUNCT
ejpam-4577	294	9	sg	sg	PROPN
ejpam-4577	294	10	and	and	CCONJ
ejpam-4577	294	11	sh	sh	PROPN
ejpam-4577	294	12	are	be	AUX
ejpam-4577	294	13	pointwise	pointwise	NUM
ejpam-4577	294	14	nondominating	nondominate	VERB
ejpam-4577	294	15	sets	set	NOUN
ejpam-4577	294	16	of	of	ADP
ejpam-4577	294	17	g	g	PROPN
ejpam-4577	294	18	and	and	CCONJ
ejpam-4577	294	19	h	h	NOUN
ejpam-4577	294	20	,	,	PUNCT
ejpam-4577	294	21	respectively	respectively	ADV
ejpam-4577	294	22	by	by	ADP
ejpam-4577	294	23	theorem	theorem	NOUN
ejpam-4577	294	24	8	8	NUM
ejpam-4577	294	25	.	.	PUNCT
ejpam-4577	295	1	since	since	SCONJ
ejpam-4577	295	2	s	s	PROPN
ejpam-4577	295	3	is	be	AUX
ejpam-4577	295	4	a	a	DET
ejpam-4577	295	5	hop	hop	NOUN
ejpam-4577	295	6	independent	independent	ADJ
ejpam-4577	295	7	set	set	NOUN
ejpam-4577	295	8	,	,	PUNCT
ejpam-4577	295	9	sg	sg	PROPN
ejpam-4577	295	10	and	and	CCONJ
ejpam-4577	295	11	sh	sh	PROPN
ejpam-4577	295	12	are	be	AUX
ejpam-4577	295	13	cliques	clique	NOUN
ejpam-4577	295	14	in	in	ADP
ejpam-4577	295	15	g	g	PROPN
ejpam-4577	295	16	and	and	CCONJ
ejpam-4577	295	17	h	h	NOUN
ejpam-4577	295	18	,	,	PUNCT
ejpam-4577	295	19	respectively	respectively	ADV
ejpam-4577	295	20	,	,	PUNCT
ejpam-4577	295	21	by	by	ADP
ejpam-4577	295	22	theorem	theorem	NOUN
ejpam-4577	295	23	9	9	NUM
ejpam-4577	295	24	.	.	PUNCT
ejpam-4577	296	1	therefore	therefore	ADV
ejpam-4577	296	2	,	,	PUNCT
ejpam-4577	296	3	sg	sg	PROPN
ejpam-4577	296	4	and	and	CCONJ
ejpam-4577	296	5	sh	sh	PROPN
ejpam-4577	296	6	are	be	AUX
ejpam-4577	296	7	clique	clique	PROPN
ejpam-4577	296	8	pointwise	pointwise	PROPN
ejpam-4577	296	9	non	non	ADJ
ejpam-4577	296	10	-	-	ADJ
ejpam-4577	296	11	dominating	dominating	ADJ
ejpam-4577	296	12	sets	set	NOUN
ejpam-4577	296	13	of	of	ADP
ejpam-4577	296	14	g	g	PROPN
ejpam-4577	296	15	and	and	CCONJ
ejpam-4577	296	16	h	h	NOUN
ejpam-4577	296	17	,	,	PUNCT
ejpam-4577	296	18	respectively	respectively	ADV
ejpam-4577	296	19	.	.	PUNCT
ejpam-4577	297	1	conversely	conversely	ADV
ejpam-4577	297	2	,	,	PUNCT
ejpam-4577	297	3	suppose	suppose	VERB
ejpam-4577	297	4	that	that	SCONJ
ejpam-4577	297	5	s	s	VERB
ejpam-4577	297	6	=	=	PUNCT
ejpam-4577	297	7	sg	sg	X
ejpam-4577	297	8	∪	∪	ADJ
ejpam-4577	297	9	sh	sh	PROPN
ejpam-4577	297	10	,	,	PUNCT
ejpam-4577	297	11	where	where	SCONJ
ejpam-4577	297	12	sg	sg	PROPN
ejpam-4577	297	13	and	and	CCONJ
ejpam-4577	297	14	sh	sh	PROPN
ejpam-4577	297	15	are	be	AUX
ejpam-4577	297	16	clique	clique	ADJ
ejpam-4577	297	17	pointwise	pointwise	PROPN
ejpam-4577	297	18	nondominating	nondominate	VERB
ejpam-4577	297	19	sets	set	NOUN
ejpam-4577	297	20	of	of	ADP
ejpam-4577	297	21	g	g	PROPN
ejpam-4577	297	22	and	and	CCONJ
ejpam-4577	297	23	h	h	NOUN
ejpam-4577	297	24	,	,	PUNCT
ejpam-4577	297	25	respectively	respectively	ADV
ejpam-4577	297	26	.	.	PUNCT
ejpam-4577	298	1	since	since	SCONJ
ejpam-4577	298	2	sg	sg	PROPN
ejpam-4577	298	3	and	and	CCONJ
ejpam-4577	298	4	sh	sh	PROPN
ejpam-4577	298	5	are	be	AUX
ejpam-4577	298	6	pointwise	pointwise	PROPN
ejpam-4577	298	7	non	non	ADJ
ejpam-4577	298	8	-	-	ADJ
ejpam-4577	298	9	dominating	dominating	ADJ
ejpam-4577	298	10	sets	set	NOUN
ejpam-4577	298	11	,	,	PUNCT
ejpam-4577	298	12	s	s	PART
ejpam-4577	298	13	=	=	PUNCT
ejpam-4577	298	14	sg	sg	PROPN
ejpam-4577	298	15	∪	∪	NOUN
ejpam-4577	298	16	sh	sh	PROPN
ejpam-4577	298	17	is	be	AUX
ejpam-4577	298	18	a	a	DET
ejpam-4577	298	19	hop	hop	NOUN
ejpam-4577	298	20	dominating	dominating	NOUN
ejpam-4577	298	21	set	set	NOUN
ejpam-4577	298	22	of	of	ADP
ejpam-4577	298	23	g+h	g+h	PROPN
ejpam-4577	298	24	by	by	ADP
ejpam-4577	298	25	theorem	theorem	NOUN
ejpam-4577	298	26	8	8	NUM
ejpam-4577	298	27	.	.	PUNCT
ejpam-4577	299	1	since	since	SCONJ
ejpam-4577	299	2	sg	sg	PROPN
ejpam-4577	299	3	and	and	CCONJ
ejpam-4577	299	4	sh	sh	PROPN
ejpam-4577	299	5	are	be	AUX
ejpam-4577	299	6	cliques	clique	NOUN
ejpam-4577	299	7	,	,	PUNCT
ejpam-4577	299	8	it	it	PRON
ejpam-4577	299	9	follows	follow	VERB
ejpam-4577	299	10	that	that	PRON
ejpam-4577	299	11	s	s	VERB
ejpam-4577	299	12	=	=	PUNCT
ejpam-4577	299	13	sg	sg	PROPN
ejpam-4577	299	14	∪	∪	NOUN
ejpam-4577	299	15	sh	sh	PROPN
ejpam-4577	299	16	is	be	AUX
ejpam-4577	299	17	a	a	DET
ejpam-4577	299	18	hop	hop	NOUN
ejpam-4577	299	19	independent	independent	ADJ
ejpam-4577	299	20	set	set	NOUN
ejpam-4577	299	21	of	of	ADP
ejpam-4577	299	22	g	g	PROPN
ejpam-4577	299	23	+	+	CCONJ
ejpam-4577	299	24	h	h	NOUN
ejpam-4577	299	25	by	by	ADP
ejpam-4577	299	26	theorem	theorem	NOUN
ejpam-4577	299	27	9	9	NUM
ejpam-4577	299	28	.	.	PUNCT
ejpam-4577	299	29	consequently	consequently	ADV
ejpam-4577	299	30	,	,	PUNCT
ejpam-4577	299	31	s	s	VERB
ejpam-4577	299	32	=	=	PUNCT
ejpam-4577	299	33	sg	sg	PROPN
ejpam-4577	299	34	∪	∪	NOUN
ejpam-4577	299	35	sh	sh	PROPN
ejpam-4577	299	36	is	be	AUX
ejpam-4577	299	37	a	a	DET
ejpam-4577	299	38	hop	hop	NOUN
ejpam-4577	299	39	independent	independent	ADJ
ejpam-4577	299	40	hop	hop	NOUN
ejpam-4577	299	41	dominating	dominating	NOUN
ejpam-4577	299	42	set	set	NOUN
ejpam-4577	299	43	of	of	ADP
ejpam-4577	299	44	g+h	g+h	PROPN
ejpam-4577	299	45	.	.	PUNCT
ejpam-4577	300	1	the	the	DET
ejpam-4577	300	2	next	next	ADJ
ejpam-4577	300	3	result	result	NOUN
ejpam-4577	300	4	follows	follow	VERB
ejpam-4577	300	5	from	from	ADP
ejpam-4577	300	6	theorem	theorem	ADJ
ejpam-4577	300	7	7	7	NUM
ejpam-4577	300	8	,	,	PUNCT
ejpam-4577	300	9	corollary	corollary	ADJ
ejpam-4577	300	10	5	5	NUM
ejpam-4577	300	11	and	and	CCONJ
ejpam-4577	300	12	theorem	theorem	VERB
ejpam-4577	300	13	10	10	NUM
ejpam-4577	300	14	.	.	PUNCT
ejpam-4577	301	1	corollary	corollary	ADJ
ejpam-4577	301	2	6	6	NUM
ejpam-4577	301	3	.	.	PUNCT
ejpam-4577	302	1	let	let	VERB
ejpam-4577	302	2	g	g	NOUN
ejpam-4577	302	3	and	and	CCONJ
ejpam-4577	302	4	h	h	PROPN
ejpam-4577	302	5	be	be	AUX
ejpam-4577	302	6	graphs	graph	NOUN
ejpam-4577	302	7	.	.	PUNCT
ejpam-4577	303	1	then	then	ADV
ejpam-4577	303	2	γhih(g	γhih(g	ADP
ejpam-4577	303	3	+	+	CCONJ
ejpam-4577	303	4	h	h	NOUN
ejpam-4577	303	5	)	)	PUNCT
ejpam-4577	303	6	=	=	PUNCT
ejpam-4577	303	7	cpnd(g	cpnd(g	NOUN
ejpam-4577	303	8	)	)	PUNCT
ejpam-4577	303	9	+	+	CCONJ
ejpam-4577	303	10	cpnd(h	cpnd(h	NOUN
ejpam-4577	303	11	)	)	PUNCT
ejpam-4577	303	12	.	.	PUNCT
ejpam-4577	304	1	in	in	ADP
ejpam-4577	304	2	particular	particular	ADJ
ejpam-4577	304	3	,	,	PUNCT
ejpam-4577	304	4	we	we	PRON
ejpam-4577	304	5	have	have	VERB
ejpam-4577	304	6	(	(	PUNCT
ejpam-4577	304	7	i	i	NOUN
ejpam-4577	304	8	)	)	PUNCT
ejpam-4577	304	9	γhih(kn	γhih(kn	VERB
ejpam-4577	304	10	+	+	NOUN
ejpam-4577	304	11	h	h	NOUN
ejpam-4577	304	12	)	)	PUNCT
ejpam-4577	304	13	=	=	PUNCT
ejpam-4577	305	1	n+	n+	PUNCT
ejpam-4577	305	2	cpnd(h	cpnd(h	NOUN
ejpam-4577	305	3	)	)	PUNCT
ejpam-4577	305	4	for	for	ADP
ejpam-4577	305	5	all	all	DET
ejpam-4577	305	6	n	n	PRON
ejpam-4577	305	7	≥	≥	NOUN
ejpam-4577	305	8	1	1	NUM
ejpam-4577	305	9	,	,	PUNCT
ejpam-4577	305	10	(	(	PUNCT
ejpam-4577	305	11	ii	ii	NOUN
ejpam-4577	305	12	)	)	PUNCT
ejpam-4577	305	13	γhih(g+h	γhih(g+h	NOUN
ejpam-4577	305	14	)	)	PUNCT
ejpam-4577	306	1	=	=	SYM
ejpam-4577	306	2	2	2	NUM
ejpam-4577	306	3	if	if	SCONJ
ejpam-4577	306	4	g	g	PROPN
ejpam-4577	306	5	and	and	CCONJ
ejpam-4577	306	6	h	h	NOUN
ejpam-4577	306	7	contain	contain	VERB
ejpam-4577	306	8	isolated	isolated	ADJ
ejpam-4577	306	9	vertices	vertex	NOUN
ejpam-4577	306	10	,	,	PUNCT
ejpam-4577	306	11	(	(	PUNCT
ejpam-4577	306	12	iii	iii	X
ejpam-4577	306	13	)	)	PUNCT
ejpam-4577	306	14	γhih(wn	γhih(wn	NOUN
ejpam-4577	306	15	)	)	PUNCT
ejpam-4577	306	16	=	=	PUNCT
ejpam-4577	306	17	γhih(k1	γhih(k1	NOUN
ejpam-4577	306	18	+	+	X
ejpam-4577	306	19	cn	cn	ADJ
ejpam-4577	306	20	)	)	PUNCT
ejpam-4577	306	21	=	=	SYM
ejpam-4577	306	22	3	3	NUM
ejpam-4577	306	23	for	for	ADP
ejpam-4577	306	24	all	all	DET
ejpam-4577	306	25	n	n	PRON
ejpam-4577	306	26	≥	≥	NOUN
ejpam-4577	306	27	4	4	NUM
ejpam-4577	306	28	,	,	PUNCT
ejpam-4577	306	29	(	(	PUNCT
ejpam-4577	306	30	iv	iv	X
ejpam-4577	306	31	)	)	PUNCT
ejpam-4577	306	32	γhih(fn	γhih(fn	NOUN
ejpam-4577	306	33	)	)	PUNCT
ejpam-4577	306	34	=	=	PUNCT
ejpam-4577	306	35	γhih(k1	γhih(k1	NOUN
ejpam-4577	306	36	+	+	CCONJ
ejpam-4577	306	37	pn	pn	NOUN
ejpam-4577	306	38	)	)	PUNCT
ejpam-4577	306	39	=	=	SYM
ejpam-4577	306	40	3	3	NUM
ejpam-4577	306	41	for	for	ADP
ejpam-4577	306	42	all	all	DET
ejpam-4577	306	43	n	n	PRON
ejpam-4577	306	44	≥	≥	NOUN
ejpam-4577	306	45	2	2	NUM
ejpam-4577	306	46	,	,	PUNCT
ejpam-4577	306	47	(	(	PUNCT
ejpam-4577	306	48	v	v	NOUN
ejpam-4577	306	49	)	)	PUNCT
ejpam-4577	306	50	γhih(kn	γhih(kn	NOUN
ejpam-4577	306	51	+	+	NOUN
ejpam-4577	306	52	km	km	NOUN
ejpam-4577	306	53	)	)	PUNCT
ejpam-4577	306	54	=	=	PUNCT
ejpam-4577	307	1	n+m	n+m	PROPN
ejpam-4577	307	2	for	for	ADP
ejpam-4577	307	3	all	all	DET
ejpam-4577	307	4	n	n	CCONJ
ejpam-4577	307	5	,	,	PUNCT
ejpam-4577	307	6	m	m	VERB
ejpam-4577	307	7	≥	≥	NOUN
ejpam-4577	307	8	1	1	NUM
ejpam-4577	307	9	,	,	PUNCT
ejpam-4577	307	10	j.	j.	PROPN
ejpam-4577	307	11	hassan	hassan	PROPN
ejpam-4577	307	12	,	,	PUNCT
ejpam-4577	307	13	s.	s.	PROPN
ejpam-4577	307	14	canoy	canoy	PROPN
ejpam-4577	307	15	/	/	SYM
ejpam-4577	307	16	eur	eur	PROPN
ejpam-4577	307	17	.	.	PUNCT
ejpam-4577	308	1	j.	j.	PROPN
ejpam-4577	308	2	pure	pure	PROPN
ejpam-4577	308	3	appl	appl	PROPN
ejpam-4577	308	4	.	.	PROPN
ejpam-4577	308	5	math	math	PROPN
ejpam-4577	308	6	,	,	PUNCT
ejpam-4577	308	7	15	15	NUM
ejpam-4577	308	8	(	(	PUNCT
ejpam-4577	308	9	4	4	NUM
ejpam-4577	308	10	)	)	PUNCT
ejpam-4577	308	11	(	(	PUNCT
ejpam-4577	308	12	2022	2022	NUM
ejpam-4577	308	13	)	)	PUNCT
ejpam-4577	308	14	,	,	PUNCT
ejpam-4577	308	15	1783	1783	NUM
ejpam-4577	308	16	-	-	SYM
ejpam-4577	308	17	1796	1796	NUM
ejpam-4577	308	18	1792	1792	NUM
ejpam-4577	308	19	(	(	PUNCT
ejpam-4577	308	20	vi	vi	NOUN
ejpam-4577	308	21	)	)	PUNCT
ejpam-4577	308	22	γhih(pn	γhih(pn	NOUN
ejpam-4577	308	23	+	+	CCONJ
ejpam-4577	308	24	pm	pm	NOUN
ejpam-4577	308	25	)	)	PUNCT
ejpam-4577	308	26	=	=	SYM
ejpam-4577	308	27	4	4	NUM
ejpam-4577	308	28	for	for	ADP
ejpam-4577	308	29	all	all	DET
ejpam-4577	308	30	n	n	CCONJ
ejpam-4577	308	31	,	,	PUNCT
ejpam-4577	308	32	m	m	VERB
ejpam-4577	308	33	≥	≥	NOUN
ejpam-4577	308	34	2	2	NUM
ejpam-4577	308	35	,	,	PUNCT
ejpam-4577	308	36	(	(	PUNCT
ejpam-4577	308	37	vii	vii	PROPN
ejpam-4577	308	38	)	)	PUNCT
ejpam-4577	308	39	γhih(cn	γhih(cn	PROPN
ejpam-4577	308	40	+	+	CCONJ
ejpam-4577	308	41	cm	cm	NOUN
ejpam-4577	308	42	)	)	PUNCT
ejpam-4577	308	43	=	=	SYM
ejpam-4577	308	44	4	4	NUM
ejpam-4577	308	45	for	for	ADP
ejpam-4577	308	46	all	all	DET
ejpam-4577	308	47	n	n	CCONJ
ejpam-4577	308	48	,	,	PUNCT
ejpam-4577	308	49	m	m	VERB
ejpam-4577	308	50	≥	≥	NOUN
ejpam-4577	308	51	4	4	NUM
ejpam-4577	308	52	,	,	PUNCT
ejpam-4577	308	53	and	and	CCONJ
ejpam-4577	308	54	(	(	PUNCT
ejpam-4577	308	55	viii	viii	NOUN
ejpam-4577	308	56	)	)	PUNCT
ejpam-4577	308	57	γhih(k1,n	γhih(k1,n	NOUN
ejpam-4577	308	58	)	)	PUNCT
ejpam-4577	309	1	=	=	PUNCT
ejpam-4577	309	2	γhih(k1	γhih(k1	ADP
ejpam-4577	309	3	+	+	PROPN
ejpam-4577	309	4	kn	kn	NOUN
ejpam-4577	309	5	)	)	PUNCT
ejpam-4577	309	6	=	=	SYM
ejpam-4577	309	7	2	2	NUM
ejpam-4577	309	8	for	for	ADP
ejpam-4577	309	9	all	all	PRON
ejpam-4577	309	10	n	n	PRON
ejpam-4577	309	11	≥	≥	NUM
ejpam-4577	309	12	1	1	NUM
ejpam-4577	309	13	.	.	PUNCT
ejpam-4577	309	14	theorem	theorem	VERB
ejpam-4577	309	15	11	11	NUM
ejpam-4577	309	16	.	.	PUNCT
ejpam-4577	310	1	[	[	X
ejpam-4577	310	2	3	3	X
ejpam-4577	310	3	]	]	PUNCT
ejpam-4577	310	4	let	let	VERB
ejpam-4577	310	5	g	g	PRON
ejpam-4577	310	6	be	be	AUX
ejpam-4577	310	7	a	a	DET
ejpam-4577	310	8	non	non	ADJ
ejpam-4577	310	9	-	-	ADJ
ejpam-4577	310	10	trivial	trivial	ADJ
ejpam-4577	310	11	connected	connected	ADJ
ejpam-4577	310	12	graph	graph	NOUN
ejpam-4577	310	13	and	and	CCONJ
ejpam-4577	310	14	let	let	VERB
ejpam-4577	310	15	h	h	NOUN
ejpam-4577	310	16	be	be	AUX
ejpam-4577	310	17	any	any	DET
ejpam-4577	310	18	graph	graph	NOUN
ejpam-4577	310	19	.	.	PUNCT
ejpam-4577	311	1	then	then	ADV
ejpam-4577	311	2	s	s	VERB
ejpam-4577	311	3	is	be	AUX
ejpam-4577	311	4	a	a	DET
ejpam-4577	311	5	hop	hop	NOUN
ejpam-4577	311	6	independent	independent	ADJ
ejpam-4577	311	7	set	set	NOUN
ejpam-4577	311	8	in	in	ADP
ejpam-4577	311	9	g	g	PROPN
ejpam-4577	311	10	◦	◦	NOUN
ejpam-4577	311	11	h	h	NOUN
ejpam-4577	311	12	if	if	SCONJ
ejpam-4577	312	1	and	and	CCONJ
ejpam-4577	312	2	only	only	ADV
ejpam-4577	312	3	if	if	SCONJ
ejpam-4577	312	4	s	s	VERB
ejpam-4577	312	5	=	=	NOUN
ejpam-4577	312	6	a	a	DET
ejpam-4577	312	7	∪	∪	X
ejpam-4577	312	8	(	(	PUNCT
ejpam-4577	312	9	∪v∈v	∪v∈v	X
ejpam-4577	312	10	(	(	PUNCT
ejpam-4577	312	11	g)sv	g)sv	PROPN
ejpam-4577	312	12	)	)	PUNCT
ejpam-4577	312	13	and	and	CCONJ
ejpam-4577	312	14	satisfies	satisfy	VERB
ejpam-4577	312	15	the	the	DET
ejpam-4577	312	16	following	follow	VERB
ejpam-4577	312	17	conditions	condition	NOUN
ejpam-4577	312	18	:	:	PUNCT
ejpam-4577	312	19	(	(	PUNCT
ejpam-4577	312	20	i	i	NOUN
ejpam-4577	312	21	)	)	PUNCT
ejpam-4577	312	22	a	a	PRON
ejpam-4577	312	23	is	be	AUX
ejpam-4577	312	24	a	a	DET
ejpam-4577	312	25	hop	hop	NOUN
ejpam-4577	312	26	independent	independent	ADJ
ejpam-4577	312	27	set	set	NOUN
ejpam-4577	312	28	of	of	ADP
ejpam-4577	312	29	g.	g.	PROPN
ejpam-4577	312	30	(	(	PUNCT
ejpam-4577	312	31	ii	ii	PROPN
ejpam-4577	312	32	)	)	PUNCT
ejpam-4577	312	33	sv	sv	PROPN
ejpam-4577	312	34	is	be	AUX
ejpam-4577	312	35	empty	empty	ADJ
ejpam-4577	312	36	or	or	CCONJ
ejpam-4577	312	37	a	a	DET
ejpam-4577	312	38	clique	clique	NOUN
ejpam-4577	312	39	in	in	ADP
ejpam-4577	312	40	hv	hv	PROPN
ejpam-4577	312	41	for	for	ADP
ejpam-4577	312	42	each	each	DET
ejpam-4577	312	43	v	v	NUM
ejpam-4577	312	44	∈	∈	PROPN
ejpam-4577	312	45	v	v	NOUN
ejpam-4577	312	46	(	(	PUNCT
ejpam-4577	312	47	g	g	NOUN
ejpam-4577	312	48	)	)	PUNCT
ejpam-4577	312	49	\ng(a	\ng(a	PROPN
ejpam-4577	312	50	)	)	PUNCT
ejpam-4577	312	51	.	.	PUNCT
ejpam-4577	313	1	(	(	PUNCT
ejpam-4577	313	2	iii	iii	X
ejpam-4577	313	3	)	)	PUNCT
ejpam-4577	313	4	sv	sv	NOUN
ejpam-4577	314	1	=	=	NOUN
ejpam-4577	314	2	∅	∅	NOUN
ejpam-4577	314	3	for	for	ADP
ejpam-4577	314	4	each	each	DET
ejpam-4577	314	5	v	v	ADP
ejpam-4577	314	6	∈	∈	PROPN
ejpam-4577	314	7	ng(a	ng(a	NOUN
ejpam-4577	314	8	)	)	PUNCT
ejpam-4577	314	9	.	.	PUNCT
ejpam-4577	315	1	theorem	theorem	NOUN
ejpam-4577	315	2	12	12	NUM
ejpam-4577	315	3	.	.	PUNCT
ejpam-4577	316	1	[	[	X
ejpam-4577	316	2	7	7	X
ejpam-4577	316	3	]	]	X
ejpam-4577	316	4	let	let	VERB
ejpam-4577	316	5	g	g	NOUN
ejpam-4577	316	6	and	and	CCONJ
ejpam-4577	316	7	h	h	NOUN
ejpam-4577	316	8	be	be	VERB
ejpam-4577	316	9	any	any	DET
ejpam-4577	316	10	two	two	NUM
ejpam-4577	316	11	graphs	graph	NOUN
ejpam-4577	316	12	.	.	PUNCT
ejpam-4577	317	1	a	a	DET
ejpam-4577	317	2	set	set	NOUN
ejpam-4577	317	3	c	c	NOUN
ejpam-4577	317	4	⊆	⊆	NUM
ejpam-4577	317	5	v	v	NOUN
ejpam-4577	317	6	(	(	PUNCT
ejpam-4577	317	7	g	g	NOUN
ejpam-4577	317	8	)	)	PUNCT
ejpam-4577	317	9	is	be	AUX
ejpam-4577	317	10	a	a	DET
ejpam-4577	317	11	hop	hop	NOUN
ejpam-4577	317	12	dominating	dominating	NOUN
ejpam-4577	317	13	set	set	NOUN
ejpam-4577	317	14	of	of	ADP
ejpam-4577	317	15	g	g	PROPN
ejpam-4577	317	16	◦	◦	NOUN
ejpam-4577	317	17	h	h	NOUN
ejpam-4577	317	18	if	if	SCONJ
ejpam-4577	318	1	and	and	CCONJ
ejpam-4577	318	2	only	only	ADV
ejpam-4577	318	3	if	if	SCONJ
ejpam-4577	318	4	c	c	PROPN
ejpam-4577	318	5	=	=	SYM
ejpam-4577	318	6	a∪	a∪	PROPN
ejpam-4577	318	7	(	(	PUNCT
ejpam-4577	318	8	∪v∈v	∪v∈v	X
ejpam-4577	318	9	(	(	PUNCT
ejpam-4577	318	10	g)∩ng(a)sv)∪	g)∩ng(a)sv)∪	X
ejpam-4577	318	11	(	(	PUNCT
ejpam-4577	318	12	∪w∈v	∪w∈v	PROPN
ejpam-4577	318	13	(	(	PUNCT
ejpam-4577	318	14	g)\ng(a)ew	g)\ng(a)ew	PROPN
ejpam-4577	318	15	)	)	PUNCT
ejpam-4577	318	16	and	and	CCONJ
ejpam-4577	318	17	satisfies	satisfy	VERB
ejpam-4577	318	18	the	the	DET
ejpam-4577	318	19	following	follow	VERB
ejpam-4577	318	20	conditions	condition	NOUN
ejpam-4577	318	21	:	:	PUNCT
ejpam-4577	318	22	(	(	PUNCT
ejpam-4577	318	23	i	i	NOUN
ejpam-4577	318	24	)	)	PUNCT
ejpam-4577	318	25	a	a	DET
ejpam-4577	318	26	⊆	⊆	NUM
ejpam-4577	318	27	v	v	NOUN
ejpam-4577	318	28	(	(	PUNCT
ejpam-4577	318	29	g	g	NOUN
ejpam-4577	318	30	)	)	PUNCT
ejpam-4577	318	31	such	such	ADJ
ejpam-4577	318	32	that	that	PRON
ejpam-4577	318	33	for	for	ADP
ejpam-4577	318	34	each	each	DET
ejpam-4577	318	35	w	w	PROPN
ejpam-4577	318	36	∈	∈	PROPN
ejpam-4577	318	37	v	v	ADP
ejpam-4577	318	38	(	(	PUNCT
ejpam-4577	318	39	g	g	NOUN
ejpam-4577	318	40	)	)	PUNCT
ejpam-4577	318	41	\a	\a	ADJ
ejpam-4577	318	42	,	,	PUNCT
ejpam-4577	318	43	there	there	PRON
ejpam-4577	318	44	exists	exist	VERB
ejpam-4577	318	45	x	x	X
ejpam-4577	318	46	∈	∈	PROPN
ejpam-4577	318	47	a	a	PRON
ejpam-4577	318	48	with	with	ADP
ejpam-4577	318	49	dg(w	dg(w	NOUN
ejpam-4577	318	50	,	,	PUNCT
ejpam-4577	318	51	x	x	X
ejpam-4577	318	52	)	)	PUNCT
ejpam-4577	318	53	=	=	SYM
ejpam-4577	318	54	2	2	NUM
ejpam-4577	318	55	or	or	CCONJ
ejpam-4577	318	56	there	there	PRON
ejpam-4577	318	57	exists	exist	VERB
ejpam-4577	318	58	y	y	PROPN
ejpam-4577	318	59	∈	∈	PROPN
ejpam-4577	318	60	v	v	ADP
ejpam-4577	318	61	(	(	PUNCT
ejpam-4577	318	62	g	g	NOUN
ejpam-4577	318	63	)	)	PUNCT
ejpam-4577	318	64	∩ng(w	∩ng(w	PROPN
ejpam-4577	318	65	)	)	PUNCT
ejpam-4577	318	66	with	with	ADP
ejpam-4577	318	67	v	v	NUM
ejpam-4577	318	68	(	(	PUNCT
ejpam-4577	318	69	hy	hy	NOUN
ejpam-4577	318	70	)	)	PUNCT
ejpam-4577	318	71	∩	∩	NOUN
ejpam-4577	318	72	c	c	PROPN
ejpam-4577	318	73	̸=	̸=	PROPN
ejpam-4577	318	74	∅.	∅.	PROPN
ejpam-4577	318	75	(	(	PUNCT
ejpam-4577	318	76	ii	ii	NOUN
ejpam-4577	318	77	)	)	PUNCT
ejpam-4577	318	78	sv	sv	VERB
ejpam-4577	319	1	⊆	⊆	NUM
ejpam-4577	319	2	v	v	X
ejpam-4577	319	3	(	(	PUNCT
ejpam-4577	319	4	hv	hv	PROPN
ejpam-4577	319	5	)	)	PUNCT
ejpam-4577	319	6	for	for	ADP
ejpam-4577	319	7	each	each	DET
ejpam-4577	319	8	v	v	NUM
ejpam-4577	319	9	∈	∈	PROPN
ejpam-4577	319	10	v	v	NOUN
ejpam-4577	319	11	(	(	PUNCT
ejpam-4577	319	12	g	g	NOUN
ejpam-4577	319	13	)	)	PUNCT
ejpam-4577	319	14	∩ng(a	∩ng(a	NOUN
ejpam-4577	319	15	)	)	PUNCT
ejpam-4577	319	16	.	.	PUNCT
ejpam-4577	320	1	(	(	PUNCT
ejpam-4577	320	2	iii	iii	X
ejpam-4577	320	3	)	)	PUNCT
ejpam-4577	320	4	ew	ew	NOUN
ejpam-4577	320	5	⊆	⊆	NUM
ejpam-4577	320	6	v	v	NOUN
ejpam-4577	320	7	(	(	PUNCT
ejpam-4577	320	8	hw	hw	NOUN
ejpam-4577	320	9	)	)	PUNCT
ejpam-4577	320	10	is	be	AUX
ejpam-4577	320	11	a	a	DET
ejpam-4577	320	12	pointwise	pointwise	ADJ
ejpam-4577	320	13	non	non	ADJ
ejpam-4577	320	14	-	-	ADJ
ejpam-4577	320	15	dominating	dominating	ADJ
ejpam-4577	320	16	set	set	NOUN
ejpam-4577	320	17	of	of	ADP
ejpam-4577	320	18	hw	hw	PRON
ejpam-4577	320	19	for	for	ADP
ejpam-4577	320	20	each	each	DET
ejpam-4577	320	21	w	w	PROPN
ejpam-4577	320	22	∈	∈	PROPN
ejpam-4577	320	23	v	v	ADP
ejpam-4577	320	24	(	(	PUNCT
ejpam-4577	320	25	g	g	NOUN
ejpam-4577	320	26	)	)	PUNCT
ejpam-4577	320	27	\ng(a	\ng(a	PROPN
ejpam-4577	320	28	)	)	PUNCT
ejpam-4577	320	29	.	.	PUNCT
ejpam-4577	321	1	theorem	theorem	NOUN
ejpam-4577	321	2	13	13	NUM
ejpam-4577	321	3	.	.	PUNCT
ejpam-4577	322	1	let	let	VERB
ejpam-4577	322	2	g	g	PRON
ejpam-4577	322	3	be	be	AUX
ejpam-4577	322	4	a	a	DET
ejpam-4577	322	5	non	non	ADJ
ejpam-4577	322	6	-	-	ADJ
ejpam-4577	322	7	trivial	trivial	ADJ
ejpam-4577	322	8	connected	connected	ADJ
ejpam-4577	322	9	graph	graph	NOUN
ejpam-4577	322	10	and	and	CCONJ
ejpam-4577	322	11	let	let	VERB
ejpam-4577	322	12	h	h	NOUN
ejpam-4577	322	13	be	be	AUX
ejpam-4577	322	14	any	any	DET
ejpam-4577	322	15	graph	graph	NOUN
ejpam-4577	322	16	.	.	PUNCT
ejpam-4577	323	1	then	then	ADV
ejpam-4577	323	2	c	c	PROPN
ejpam-4577	323	3	is	be	AUX
ejpam-4577	323	4	a	a	DET
ejpam-4577	323	5	hop	hop	NOUN
ejpam-4577	323	6	independent	independent	ADJ
ejpam-4577	323	7	hop	hop	NOUN
ejpam-4577	323	8	dominating	dominating	NOUN
ejpam-4577	323	9	set	set	NOUN
ejpam-4577	323	10	of	of	ADP
ejpam-4577	323	11	g	g	PROPN
ejpam-4577	323	12	◦	◦	NOUN
ejpam-4577	323	13	h	h	NOUN
ejpam-4577	324	1	if	if	SCONJ
ejpam-4577	325	1	and	and	CCONJ
ejpam-4577	325	2	only	only	ADV
ejpam-4577	325	3	if	if	SCONJ
ejpam-4577	325	4	c	c	X
ejpam-4577	325	5	=	=	PUNCT
ejpam-4577	325	6	a	a	DET
ejpam-4577	325	7	∪	∪	X
ejpam-4577	325	8	(	(	PUNCT
ejpam-4577	325	9	∪v∈v	∪v∈v	X
ejpam-4577	325	10	(	(	PUNCT
ejpam-4577	325	11	g)cv	g)cv	PROPN
ejpam-4577	325	12	)	)	PUNCT
ejpam-4577	325	13	,	,	PUNCT
ejpam-4577	325	14	where	where	SCONJ
ejpam-4577	325	15	a	a	DET
ejpam-4577	325	16	⊆	⊆	NUM
ejpam-4577	325	17	v	v	NOUN
ejpam-4577	325	18	(	(	PUNCT
ejpam-4577	325	19	g	g	NOUN
ejpam-4577	325	20	)	)	PUNCT
ejpam-4577	325	21	,	,	PUNCT
ejpam-4577	325	22	cv	cv	PROPN
ejpam-4577	325	23	⊆	⊆	NUM
ejpam-4577	325	24	v	v	PROPN
ejpam-4577	325	25	(	(	PUNCT
ejpam-4577	325	26	hv	hv	PROPN
ejpam-4577	325	27	)	)	PUNCT
ejpam-4577	325	28	for	for	ADP
ejpam-4577	325	29	each	each	DET
ejpam-4577	325	30	v	v	NUM
ejpam-4577	325	31	∈	∈	PROPN
ejpam-4577	325	32	v	v	NOUN
ejpam-4577	325	33	(	(	PUNCT
ejpam-4577	325	34	g	g	NOUN
ejpam-4577	325	35	)	)	PUNCT
ejpam-4577	325	36	,	,	PUNCT
ejpam-4577	325	37	and	and	CCONJ
ejpam-4577	325	38	satisfies	satisfy	VERB
ejpam-4577	325	39	the	the	DET
ejpam-4577	325	40	following	follow	VERB
ejpam-4577	325	41	conditions	condition	NOUN
ejpam-4577	325	42	:	:	PUNCT
ejpam-4577	325	43	(	(	PUNCT
ejpam-4577	325	44	i	i	NOUN
ejpam-4577	325	45	)	)	PUNCT
ejpam-4577	325	46	a	a	DET
ejpam-4577	325	47	=	=	NOUN
ejpam-4577	325	48	∅	∅	NOUN
ejpam-4577	325	49	or	or	CCONJ
ejpam-4577	325	50	a	a	PRON
ejpam-4577	325	51	is	be	AUX
ejpam-4577	325	52	a	a	DET
ejpam-4577	325	53	hop	hop	NOUN
ejpam-4577	325	54	independent	independent	ADJ
ejpam-4577	325	55	set	set	NOUN
ejpam-4577	325	56	of	of	ADP
ejpam-4577	325	57	g.	g.	PROPN
ejpam-4577	325	58	(	(	PUNCT
ejpam-4577	325	59	ii	ii	PROPN
ejpam-4577	325	60	)	)	PUNCT
ejpam-4577	325	61	cy	cy	NOUN
ejpam-4577	325	62	=	=	PUNCT
ejpam-4577	325	63	∅	∅	NOUN
ejpam-4577	325	64	for	for	ADP
ejpam-4577	325	65	each	each	DET
ejpam-4577	325	66	y	y	PROPN
ejpam-4577	325	67	∈	∈	PROPN
ejpam-4577	325	68	ng(a	ng(a	NOUN
ejpam-4577	325	69	)	)	PUNCT
ejpam-4577	325	70	.	.	PUNCT
ejpam-4577	326	1	(	(	PUNCT
ejpam-4577	326	2	iii	iii	X
ejpam-4577	326	3	)	)	PUNCT
ejpam-4577	326	4	for	for	ADP
ejpam-4577	326	5	each	each	DET
ejpam-4577	326	6	v	v	NUM
ejpam-4577	326	7	∈	∈	NOUN
ejpam-4577	326	8	v	v	NOUN
ejpam-4577	326	9	(	(	PUNCT
ejpam-4577	326	10	g)\n2	g)\n2	NOUN
ejpam-4577	326	11	g[a	g[a	PROPN
ejpam-4577	326	12	]	]	X
ejpam-4577	326	13	,	,	PUNCT
ejpam-4577	326	14	there	there	PRON
ejpam-4577	326	15	exists	exist	VERB
ejpam-4577	326	16	w	w	PROPN
ejpam-4577	326	17	∈	∈	PROPN
ejpam-4577	326	18	ng(v	ng(v	PUNCT
ejpam-4577	326	19	)	)	PUNCT
ejpam-4577	326	20	such	such	ADJ
ejpam-4577	326	21	that	that	SCONJ
ejpam-4577	326	22	cw	cw	NOUN
ejpam-4577	326	23	is	be	AUX
ejpam-4577	326	24	a	a	DET
ejpam-4577	326	25	hop	hop	NOUN
ejpam-4577	326	26	independent	independent	ADJ
ejpam-4577	326	27	set	set	NOUN
ejpam-4577	326	28	of	of	ADP
ejpam-4577	326	29	hw	hw	PRON
ejpam-4577	326	30	.	.	PUNCT
ejpam-4577	327	1	(	(	PUNCT
ejpam-4577	327	2	iv	iv	X
ejpam-4577	327	3	)	)	PUNCT
ejpam-4577	327	4	for	for	ADP
ejpam-4577	327	5	each	each	DET
ejpam-4577	327	6	v	v	NUM
ejpam-4577	327	7	∈	∈	PROPN
ejpam-4577	327	8	v	v	NOUN
ejpam-4577	327	9	(	(	PUNCT
ejpam-4577	327	10	g	g	NOUN
ejpam-4577	327	11	)	)	PUNCT
ejpam-4577	327	12	\ng(a	\ng(a	PROPN
ejpam-4577	327	13	)	)	PUNCT
ejpam-4577	327	14	,	,	PUNCT
ejpam-4577	327	15	cv	cv	PROPN
ejpam-4577	327	16	is	be	AUX
ejpam-4577	327	17	a	a	DET
ejpam-4577	327	18	clique	clique	NOUN
ejpam-4577	327	19	pointwise	pointwise	PROPN
ejpam-4577	327	20	non	non	ADJ
ejpam-4577	327	21	-	-	ADJ
ejpam-4577	327	22	dominating	dominating	ADJ
ejpam-4577	327	23	set	set	NOUN
ejpam-4577	327	24	.	.	PUNCT
ejpam-4577	328	1	proof	proof	NOUN
ejpam-4577	328	2	.	.	PUNCT
ejpam-4577	329	1	suppose	suppose	VERB
ejpam-4577	329	2	c	c	NOUN
ejpam-4577	329	3	is	be	AUX
ejpam-4577	329	4	a	a	DET
ejpam-4577	329	5	hop	hop	NOUN
ejpam-4577	329	6	independent	independent	ADJ
ejpam-4577	329	7	hop	hop	NOUN
ejpam-4577	329	8	dominating	dominating	NOUN
ejpam-4577	329	9	set	set	NOUN
ejpam-4577	329	10	of	of	ADP
ejpam-4577	329	11	g	g	PROPN
ejpam-4577	329	12	◦	◦	NOUN
ejpam-4577	329	13	h.	h.	NOUN
ejpam-4577	329	14	let	let	VERB
ejpam-4577	329	15	a	a	DET
ejpam-4577	329	16	=	=	SYM
ejpam-4577	329	17	c∩v	c∩v	NOUN
ejpam-4577	329	18	(	(	PUNCT
ejpam-4577	329	19	g	g	NOUN
ejpam-4577	329	20	)	)	PUNCT
ejpam-4577	329	21	and	and	CCONJ
ejpam-4577	329	22	cv	cv	PROPN
ejpam-4577	329	23	=	=	SYM
ejpam-4577	329	24	c	c	PROPN
ejpam-4577	329	25	∩	∩	X
ejpam-4577	329	26	v	v	X
ejpam-4577	329	27	(	(	PUNCT
ejpam-4577	329	28	hv	hv	PROPN
ejpam-4577	329	29	)	)	PUNCT
ejpam-4577	329	30	for	for	ADP
ejpam-4577	329	31	each	each	DET
ejpam-4577	329	32	v	v	NUM
ejpam-4577	329	33	∈	∈	PROPN
ejpam-4577	329	34	v	v	NOUN
ejpam-4577	329	35	(	(	PUNCT
ejpam-4577	329	36	g	g	NOUN
ejpam-4577	329	37	)	)	PUNCT
ejpam-4577	329	38	.	.	PUNCT
ejpam-4577	330	1	suppose	suppose	VERB
ejpam-4577	330	2	further	far	ADV
ejpam-4577	330	3	that	that	SCONJ
ejpam-4577	330	4	a	a	DET
ejpam-4577	330	5	̸=	̸=	PROPN
ejpam-4577	330	6	∅.	∅.	NOUN
ejpam-4577	330	7	since	since	SCONJ
ejpam-4577	330	8	c	c	PROPN
ejpam-4577	330	9	is	be	AUX
ejpam-4577	330	10	a	a	DET
ejpam-4577	330	11	hop	hop	NOUN
ejpam-4577	330	12	independent	independent	ADJ
ejpam-4577	330	13	set	set	NOUN
ejpam-4577	330	14	,	,	PUNCT
ejpam-4577	330	15	a	a	PRON
ejpam-4577	330	16	is	be	AUX
ejpam-4577	330	17	a	a	DET
ejpam-4577	330	18	hop	hop	NOUN
ejpam-4577	330	19	independent	independent	ADJ
ejpam-4577	330	20	set	set	NOUN
ejpam-4577	330	21	of	of	ADP
ejpam-4577	330	22	g	g	NOUN
ejpam-4577	330	23	by	by	ADP
ejpam-4577	330	24	theorem	theorem	NOUN
ejpam-4577	330	25	11(i	11(i	NUM
ejpam-4577	330	26	)	)	PUNCT
ejpam-4577	330	27	.	.	PUNCT
ejpam-4577	331	1	this	this	PRON
ejpam-4577	331	2	shows	show	VERB
ejpam-4577	331	3	that	that	SCONJ
ejpam-4577	331	4	(	(	PUNCT
ejpam-4577	331	5	i	i	NOUN
ejpam-4577	331	6	)	)	PUNCT
ejpam-4577	331	7	holds	hold	VERB
ejpam-4577	331	8	.	.	PUNCT
ejpam-4577	332	1	clearly	clearly	ADV
ejpam-4577	332	2	,	,	PUNCT
ejpam-4577	332	3	(	(	PUNCT
ejpam-4577	332	4	ii	ii	NOUN
ejpam-4577	332	5	)	)	PUNCT
ejpam-4577	332	6	holds	hold	VERB
ejpam-4577	332	7	by	by	ADP
ejpam-4577	332	8	theorem	theorem	NOUN
ejpam-4577	332	9	11(iii	11(iii	NUM
ejpam-4577	332	10	)	)	PUNCT
ejpam-4577	332	11	.	.	PUNCT
ejpam-4577	333	1	next	next	ADV
ejpam-4577	333	2	,	,	PUNCT
ejpam-4577	333	3	let	let	VERB
ejpam-4577	333	4	v	v	NUM
ejpam-4577	333	5	∈	∈	PROPN
ejpam-4577	333	6	v	v	NOUN
ejpam-4577	333	7	(	(	PUNCT
ejpam-4577	333	8	g	g	NOUN
ejpam-4577	333	9	)	)	PUNCT
ejpam-4577	333	10	\	\	NOUN
ejpam-4577	333	11	n2	n2	ADJ
ejpam-4577	333	12	g[a	g[a	PROPN
ejpam-4577	333	13	]	]	PUNCT
ejpam-4577	333	14	.	.	PUNCT
ejpam-4577	334	1	then	then	ADV
ejpam-4577	334	2	v	v	X
ejpam-4577	334	3	/∈	/∈	PUNCT
ejpam-4577	334	4	a	a	DET
ejpam-4577	334	5	and	and	CCONJ
ejpam-4577	334	6	dg(u	dg(u	X
ejpam-4577	334	7	,	,	PUNCT
ejpam-4577	334	8	v	v	NOUN
ejpam-4577	334	9	)	)	PUNCT
ejpam-4577	334	10	̸=	̸=	PROPN
ejpam-4577	334	11	2	2	NUM
ejpam-4577	334	12	for	for	ADP
ejpam-4577	334	13	every	every	DET
ejpam-4577	334	14	u	u	PROPN
ejpam-4577	334	15	∈	∈	PROPN
ejpam-4577	334	16	a.	a.	NOUN
ejpam-4577	334	17	since	since	SCONJ
ejpam-4577	334	18	c	c	PROPN
ejpam-4577	334	19	is	be	AUX
ejpam-4577	334	20	a	a	DET
ejpam-4577	334	21	hop	hop	NOUN
ejpam-4577	334	22	dominating	dominating	NOUN
ejpam-4577	334	23	set	set	NOUN
ejpam-4577	334	24	of	of	ADP
ejpam-4577	334	25	g	g	PROPN
ejpam-4577	334	26	◦	◦	NOUN
ejpam-4577	334	27	h	h	NOUN
ejpam-4577	334	28	,	,	PUNCT
ejpam-4577	334	29	there	there	PRON
ejpam-4577	334	30	exists	exist	VERB
ejpam-4577	334	31	x	x	X
ejpam-4577	334	32	∈	∈	PROPN
ejpam-4577	334	33	c	c	NOUN
ejpam-4577	334	34	such	such	ADJ
ejpam-4577	334	35	that	that	SCONJ
ejpam-4577	334	36	dg	dg	VERB
ejpam-4577	334	37	◦	◦	NOUN
ejpam-4577	334	38	h(x	h(x	PROPN
ejpam-4577	334	39	,	,	PUNCT
ejpam-4577	334	40	v	v	NOUN
ejpam-4577	334	41	)	)	PUNCT
ejpam-4577	334	42	=	=	SYM
ejpam-4577	335	1	2	2	X
ejpam-4577	335	2	.	.	PUNCT
ejpam-4577	335	3	it	it	PRON
ejpam-4577	335	4	follows	follow	VERB
ejpam-4577	335	5	that	that	SCONJ
ejpam-4577	335	6	x	x	PUNCT
ejpam-4577	335	7	∈	∈	PROPN
ejpam-4577	335	8	cw	cw	NOUN
ejpam-4577	335	9	for	for	ADP
ejpam-4577	335	10	some	some	DET
ejpam-4577	335	11	w	w	PROPN
ejpam-4577	335	12	∈	∈	PROPN
ejpam-4577	335	13	ng(v	ng(v	NOUN
ejpam-4577	335	14	)	)	PUNCT
ejpam-4577	335	15	.	.	PUNCT
ejpam-4577	336	1	since	since	SCONJ
ejpam-4577	336	2	c	c	PROPN
ejpam-4577	336	3	is	be	AUX
ejpam-4577	336	4	a	a	DET
ejpam-4577	336	5	hop	hop	NOUN
ejpam-4577	336	6	independent	independent	ADJ
ejpam-4577	336	7	set	set	NOUN
ejpam-4577	336	8	,	,	PUNCT
ejpam-4577	336	9	it	it	PRON
ejpam-4577	336	10	follows	follow	VERB
ejpam-4577	336	11	that	that	SCONJ
ejpam-4577	336	12	cw	cw	NOUN
ejpam-4577	336	13	is	be	AUX
ejpam-4577	336	14	a	a	DET
ejpam-4577	336	15	hop	hop	NOUN
ejpam-4577	336	16	independent	independent	ADJ
ejpam-4577	336	17	set	set	NOUN
ejpam-4577	336	18	of	of	ADP
ejpam-4577	336	19	hw	hw	PRON
ejpam-4577	336	20	,	,	PUNCT
ejpam-4577	336	21	showing	show	VERB
ejpam-4577	336	22	that	that	SCONJ
ejpam-4577	336	23	(	(	PUNCT
ejpam-4577	336	24	iii	iii	NOUN
ejpam-4577	336	25	)	)	PUNCT
ejpam-4577	336	26	holds	hold	VERB
ejpam-4577	336	27	.	.	PUNCT
ejpam-4577	337	1	property	property	NOUN
ejpam-4577	337	2	(	(	PUNCT
ejpam-4577	337	3	iv	iv	X
ejpam-4577	337	4	)	)	PUNCT
ejpam-4577	337	5	follows	follow	VERB
ejpam-4577	337	6	immediately	immediately	ADV
ejpam-4577	337	7	from	from	ADP
ejpam-4577	337	8	theorem	theorem	ADJ
ejpam-4577	337	9	11(ii	11(ii	NUM
ejpam-4577	337	10	)	)	PUNCT
ejpam-4577	337	11	and	and	CCONJ
ejpam-4577	337	12	theorem	theorem	VERB
ejpam-4577	337	13	12(iii	12(iii	NUM
ejpam-4577	337	14	)	)	PUNCT
ejpam-4577	337	15	.	.	PUNCT
ejpam-4577	338	1	j.	j.	PROPN
ejpam-4577	338	2	hassan	hassan	PROPN
ejpam-4577	338	3	,	,	PUNCT
ejpam-4577	338	4	s.	s.	PROPN
ejpam-4577	338	5	canoy	canoy	PROPN
ejpam-4577	338	6	/	/	SYM
ejpam-4577	338	7	eur	eur	PROPN
ejpam-4577	338	8	.	.	PUNCT
ejpam-4577	339	1	j.	j.	PROPN
ejpam-4577	339	2	pure	pure	PROPN
ejpam-4577	339	3	appl	appl	PROPN
ejpam-4577	339	4	.	.	PROPN
ejpam-4577	339	5	math	math	PROPN
ejpam-4577	339	6	,	,	PUNCT
ejpam-4577	339	7	15	15	NUM
ejpam-4577	339	8	(	(	PUNCT
ejpam-4577	339	9	4	4	NUM
ejpam-4577	339	10	)	)	PUNCT
ejpam-4577	339	11	(	(	PUNCT
ejpam-4577	339	12	2022	2022	NUM
ejpam-4577	339	13	)	)	PUNCT
ejpam-4577	339	14	,	,	PUNCT
ejpam-4577	339	15	1783	1783	NUM
ejpam-4577	339	16	-	-	SYM
ejpam-4577	339	17	1796	1796	NUM
ejpam-4577	339	18	1793	1793	NUM
ejpam-4577	339	19	for	for	ADP
ejpam-4577	339	20	the	the	DET
ejpam-4577	339	21	converse	converse	NOUN
ejpam-4577	339	22	,	,	PUNCT
ejpam-4577	339	23	suppose	suppose	VERB
ejpam-4577	339	24	that	that	SCONJ
ejpam-4577	339	25	c	c	PROPN
ejpam-4577	339	26	has	have	VERB
ejpam-4577	339	27	the	the	DET
ejpam-4577	339	28	given	give	VERB
ejpam-4577	339	29	form	form	NOUN
ejpam-4577	339	30	and	and	CCONJ
ejpam-4577	339	31	satisfies	satisfie	NOUN
ejpam-4577	339	32	conditions	condition	NOUN
ejpam-4577	339	33	(	(	PUNCT
ejpam-4577	339	34	i	i	NOUN
ejpam-4577	339	35	)	)	PUNCT
ejpam-4577	339	36	,	,	PUNCT
ejpam-4577	339	37	(	(	PUNCT
ejpam-4577	339	38	ii	ii	NOUN
ejpam-4577	339	39	)	)	PUNCT
ejpam-4577	339	40	,	,	PUNCT
ejpam-4577	339	41	(	(	PUNCT
ejpam-4577	339	42	iii	iii	NOUN
ejpam-4577	339	43	)	)	PUNCT
ejpam-4577	339	44	and	and	CCONJ
ejpam-4577	339	45	(	(	PUNCT
ejpam-4577	339	46	iv	iv	X
ejpam-4577	339	47	)	)	PUNCT
ejpam-4577	339	48	.	.	PUNCT
ejpam-4577	340	1	then	then	ADV
ejpam-4577	340	2	by	by	ADP
ejpam-4577	340	3	theorem	theorem	NOUN
ejpam-4577	340	4	11	11	NUM
ejpam-4577	340	5	,	,	PUNCT
ejpam-4577	340	6	c	c	PROPN
ejpam-4577	340	7	is	be	AUX
ejpam-4577	340	8	a	a	DET
ejpam-4577	340	9	hop	hop	NOUN
ejpam-4577	340	10	independent	independent	ADJ
ejpam-4577	340	11	set	set	NOUN
ejpam-4577	340	12	of	of	ADP
ejpam-4577	340	13	g	g	PROPN
ejpam-4577	340	14	◦	◦	PROPN
ejpam-4577	340	15	h.	h.	PROPN
ejpam-4577	340	16	next	next	ADV
ejpam-4577	340	17	,	,	PUNCT
ejpam-4577	340	18	let	let	VERB
ejpam-4577	340	19	a	a	DET
ejpam-4577	340	20	∈	∈	PROPN
ejpam-4577	340	21	v	v	NOUN
ejpam-4577	340	22	(	(	PUNCT
ejpam-4577	340	23	g	g	PROPN
ejpam-4577	340	24	◦	◦	NOUN
ejpam-4577	340	25	h	h	NOUN
ejpam-4577	340	26	)	)	PUNCT
ejpam-4577	340	27	\	\	PROPN
ejpam-4577	340	28	c	c	NOUN
ejpam-4577	340	29	and	and	CCONJ
ejpam-4577	340	30	v	v	ADP
ejpam-4577	340	31	∈	∈	NOUN
ejpam-4577	340	32	v	v	NOUN
ejpam-4577	340	33	(	(	PUNCT
ejpam-4577	340	34	g	g	NOUN
ejpam-4577	340	35	)	)	PUNCT
ejpam-4577	340	36	such	such	ADJ
ejpam-4577	340	37	that	that	SCONJ
ejpam-4577	340	38	a	a	DET
ejpam-4577	340	39	∈	∈	PROPN
ejpam-4577	340	40	v	v	NOUN
ejpam-4577	340	41	(	(	PUNCT
ejpam-4577	340	42	v	v	PROPN
ejpam-4577	340	43	+	+	PROPN
ejpam-4577	340	44	hv	hv	NOUN
ejpam-4577	340	45	)	)	PUNCT
ejpam-4577	340	46	.	.	PUNCT
ejpam-4577	341	1	consider	consider	VERB
ejpam-4577	341	2	the	the	DET
ejpam-4577	341	3	following	follow	VERB
ejpam-4577	341	4	cases	case	NOUN
ejpam-4577	341	5	:	:	PUNCT
ejpam-4577	341	6	case	case	NOUN
ejpam-4577	341	7	1	1	NUM
ejpam-4577	341	8	:	:	PUNCT
ejpam-4577	341	9	a	a	PRON
ejpam-4577	341	10	=	=	X
ejpam-4577	342	1	v.	v.	ADP
ejpam-4577	342	2	then	then	ADV
ejpam-4577	342	3	a	a	DET
ejpam-4577	342	4	∈	∈	PROPN
ejpam-4577	342	5	v	v	NOUN
ejpam-4577	342	6	(	(	PUNCT
ejpam-4577	342	7	g)\a	g)\a	NOUN
ejpam-4577	342	8	.	.	PUNCT
ejpam-4577	343	1	if	if	SCONJ
ejpam-4577	343	2	a	a	DET
ejpam-4577	343	3	∈	∈	PROPN
ejpam-4577	343	4	n2	n2	NOUN
ejpam-4577	343	5	g(a	g(a	PROPN
ejpam-4577	343	6	)	)	PUNCT
ejpam-4577	343	7	,	,	PUNCT
ejpam-4577	343	8	then	then	ADV
ejpam-4577	343	9	dg(a	dg(a	NUM
ejpam-4577	343	10	,	,	PUNCT
ejpam-4577	343	11	b	b	X
ejpam-4577	343	12	)	)	PUNCT
ejpam-4577	343	13	=	=	SYM
ejpam-4577	343	14	dg	dg	PROPN
ejpam-4577	343	15	◦	◦	PROPN
ejpam-4577	343	16	h(a	h(a	PROPN
ejpam-4577	343	17	,	,	PUNCT
ejpam-4577	343	18	b	b	NOUN
ejpam-4577	343	19	)	)	PUNCT
ejpam-4577	343	20	=	=	SYM
ejpam-4577	343	21	2	2	NUM
ejpam-4577	343	22	for	for	ADP
ejpam-4577	343	23	some	some	DET
ejpam-4577	343	24	b	b	NOUN
ejpam-4577	343	25	∈	∈	PROPN
ejpam-4577	343	26	a	a	DET
ejpam-4577	343	27	⊆	⊆	NUM
ejpam-4577	343	28	c.	c.	NOUN
ejpam-4577	343	29	if	if	SCONJ
ejpam-4577	343	30	a	a	DET
ejpam-4577	343	31	/∈	/∈	PROPN
ejpam-4577	343	32	n2	n2	NOUN
ejpam-4577	343	33	g(a	g(a	PROPN
ejpam-4577	343	34	)	)	PUNCT
ejpam-4577	344	1	,	,	PUNCT
ejpam-4577	344	2	then	then	ADV
ejpam-4577	344	3	there	there	PRON
ejpam-4577	344	4	exists	exist	VERB
ejpam-4577	344	5	w	w	PROPN
ejpam-4577	344	6	∈	∈	PROPN
ejpam-4577	344	7	ng(a	ng(a	NOUN
ejpam-4577	344	8	)	)	PUNCT
ejpam-4577	344	9	such	such	ADJ
ejpam-4577	344	10	that	that	SCONJ
ejpam-4577	344	11	cw	cw	NOUN
ejpam-4577	344	12	is	be	AUX
ejpam-4577	344	13	a	a	DET
ejpam-4577	344	14	hop	hop	NOUN
ejpam-4577	344	15	independent	independent	ADJ
ejpam-4577	344	16	set	set	VERB
ejpam-4577	344	17	by	by	ADP
ejpam-4577	344	18	(	(	PUNCT
ejpam-4577	344	19	iii	iii	NOUN
ejpam-4577	344	20	)	)	PUNCT
ejpam-4577	344	21	.	.	PUNCT
ejpam-4577	345	1	choose	choose	VERB
ejpam-4577	345	2	any	any	DET
ejpam-4577	345	3	p	p	PROPN
ejpam-4577	345	4	∈	∈	PROPN
ejpam-4577	345	5	cw	cw	NOUN
ejpam-4577	345	6	.	.	PUNCT
ejpam-4577	346	1	then	then	ADV
ejpam-4577	346	2	p	p	PROPN
ejpam-4577	346	3	∈	∈	PROPN
ejpam-4577	346	4	c	c	PROPN
ejpam-4577	346	5	and	and	CCONJ
ejpam-4577	346	6	dg	dg	PROPN
ejpam-4577	346	7	◦	◦	PROPN
ejpam-4577	346	8	h(a	h(a	PROPN
ejpam-4577	346	9	,	,	PUNCT
ejpam-4577	346	10	p	p	NOUN
ejpam-4577	346	11	)	)	PUNCT
ejpam-4577	346	12	=	=	SYM
ejpam-4577	346	13	2	2	X
ejpam-4577	346	14	.	.	X
ejpam-4577	346	15	case	case	NOUN
ejpam-4577	346	16	2	2	NUM
ejpam-4577	346	17	:	:	PUNCT
ejpam-4577	346	18	a	a	DET
ejpam-4577	346	19	̸=	̸=	PROPN
ejpam-4577	346	20	v.	v.	CCONJ
ejpam-4577	347	1	then	then	ADV
ejpam-4577	347	2	a	a	DET
ejpam-4577	347	3	∈	∈	PROPN
ejpam-4577	347	4	v	v	ADP
ejpam-4577	347	5	(	(	PUNCT
ejpam-4577	347	6	hv	hv	PROPN
ejpam-4577	347	7	)	)	PUNCT
ejpam-4577	347	8	\	\	PROPN
ejpam-4577	347	9	cv	cv	PROPN
ejpam-4577	347	10	.	.	PUNCT
ejpam-4577	348	1	if	if	SCONJ
ejpam-4577	348	2	v	v	NUM
ejpam-4577	348	3	∈	∈	PROPN
ejpam-4577	348	4	ng(a	ng(a	NOUN
ejpam-4577	348	5	)	)	PUNCT
ejpam-4577	348	6	,	,	PUNCT
ejpam-4577	348	7	say	say	VERB
ejpam-4577	348	8	cv	cv	PROPN
ejpam-4577	348	9	∈	∈	PROPN
ejpam-4577	348	10	e(g	e(g	PROPN
ejpam-4577	348	11	◦	◦	PROPN
ejpam-4577	348	12	h	h	NOUN
ejpam-4577	348	13	)	)	PUNCT
ejpam-4577	348	14	for	for	ADP
ejpam-4577	348	15	some	some	DET
ejpam-4577	348	16	c	c	NOUN
ejpam-4577	348	17	∈	∈	PROPN
ejpam-4577	348	18	a	a	DET
ejpam-4577	348	19	⊆	⊆	NUM
ejpam-4577	348	20	c	c	NOUN
ejpam-4577	348	21	,	,	PUNCT
ejpam-4577	348	22	then	then	ADV
ejpam-4577	348	23	dg(c	dg(c	PROPN
ejpam-4577	348	24	,	,	PUNCT
ejpam-4577	348	25	a	a	PRON
ejpam-4577	348	26	)	)	PUNCT
ejpam-4577	348	27	=	=	SYM
ejpam-4577	348	28	2	2	X
ejpam-4577	348	29	.	.	PUNCT
ejpam-4577	348	30	suppose	suppose	VERB
ejpam-4577	348	31	v	v	X
ejpam-4577	348	32	/∈	/∈	PUNCT
ejpam-4577	348	33	ng(a	ng(a	NUM
ejpam-4577	348	34	)	)	PUNCT
ejpam-4577	348	35	.	.	PUNCT
ejpam-4577	349	1	by	by	ADP
ejpam-4577	349	2	(	(	PUNCT
ejpam-4577	349	3	iv	iv	X
ejpam-4577	349	4	)	)	PUNCT
ejpam-4577	349	5	,	,	PUNCT
ejpam-4577	349	6	there	there	PRON
ejpam-4577	349	7	exists	exist	VERB
ejpam-4577	349	8	q	q	PROPN
ejpam-4577	349	9	∈	∈	PROPN
ejpam-4577	349	10	cv	cv	PROPN
ejpam-4577	350	1	⊆	⊆	NUM
ejpam-4577	350	2	c	c	NOUN
ejpam-4577	350	3	such	such	ADJ
ejpam-4577	350	4	that	that	SCONJ
ejpam-4577	350	5	dg	dg	VERB
ejpam-4577	350	6	◦	◦	NOUN
ejpam-4577	350	7	h(q	h(q	ADV
ejpam-4577	350	8	,	,	PUNCT
ejpam-4577	350	9	a	a	PRON
ejpam-4577	350	10	)	)	PUNCT
ejpam-4577	350	11	=	=	SYM
ejpam-4577	350	12	2	2	X
ejpam-4577	350	13	.	.	PUNCT
ejpam-4577	350	14	thus	thus	ADV
ejpam-4577	350	15	,	,	PUNCT
ejpam-4577	350	16	c	c	PROPN
ejpam-4577	350	17	is	be	AUX
ejpam-4577	350	18	a	a	DET
ejpam-4577	350	19	hop	hop	NOUN
ejpam-4577	350	20	dominating	dominating	NOUN
ejpam-4577	350	21	set	set	NOUN
ejpam-4577	350	22	.	.	PUNCT
ejpam-4577	351	1	therefore	therefore	ADV
ejpam-4577	351	2	,	,	PUNCT
ejpam-4577	351	3	c	c	PROPN
ejpam-4577	351	4	is	be	AUX
ejpam-4577	351	5	a	a	DET
ejpam-4577	351	6	hop	hop	NOUN
ejpam-4577	351	7	independent	independent	ADJ
ejpam-4577	351	8	hop	hop	NOUN
ejpam-4577	351	9	dominating	dominating	NOUN
ejpam-4577	351	10	set	set	VERB
ejpam-4577	351	11	in	in	ADP
ejpam-4577	351	12	g	g	PROPN
ejpam-4577	351	13	◦	◦	NOUN
ejpam-4577	351	14	h.	h.	NOUN
ejpam-4577	351	15	consider	consider	VERB
ejpam-4577	351	16	the	the	DET
ejpam-4577	351	17	following	follow	VERB
ejpam-4577	351	18	families	family	NOUN
ejpam-4577	351	19	of	of	ADP
ejpam-4577	351	20	graphs	graph	NOUN
ejpam-4577	351	21	:	:	PUNCT
ejpam-4577	351	22	g1	g1	PROPN
ejpam-4577	351	23	=	=	SYM
ejpam-4577	351	24	{	{	PUNCT
ejpam-4577	351	25	g	g	NOUN
ejpam-4577	351	26	:	:	PUNCT
ejpam-4577	351	27	g	g	PROPN
ejpam-4577	351	28	admits	admit	VERB
ejpam-4577	351	29	a	a	DET
ejpam-4577	351	30	dominating	dominating	NOUN
ejpam-4577	351	31	hop	hop	NOUN
ejpam-4577	351	32	independent	independent	ADJ
ejpam-4577	351	33	hop	hop	NOUN
ejpam-4577	351	34	dominating	dominating	NOUN
ejpam-4577	351	35	set	set	NOUN
ejpam-4577	351	36	}	}	PUNCT
ejpam-4577	351	37	and	and	CCONJ
ejpam-4577	351	38	g2	g2	PROPN
ejpam-4577	351	39	=	=	PRON
ejpam-4577	351	40	{	{	PUNCT
ejpam-4577	351	41	g	g	NOUN
ejpam-4577	351	42	:	:	PUNCT
ejpam-4577	351	43	g	g	PROPN
ejpam-4577	351	44	admits	admit	VERB
ejpam-4577	351	45	a	a	DET
ejpam-4577	351	46	total	total	ADJ
ejpam-4577	351	47	dominating	dominating	NOUN
ejpam-4577	351	48	hop	hop	NOUN
ejpam-4577	351	49	independent	independent	ADJ
ejpam-4577	351	50	hop	hop	NOUN
ejpam-4577	351	51	dominating	dominating	NOUN
ejpam-4577	351	52	set	set	NOUN
ejpam-4577	351	53	}	}	PUNCT
ejpam-4577	351	54	.	.	PUNCT
ejpam-4577	352	1	let	let	VERB
ejpam-4577	352	2	g	g	PRON
ejpam-4577	352	3	be	be	AUX
ejpam-4577	352	4	a	a	DET
ejpam-4577	352	5	graph	graph	NOUN
ejpam-4577	352	6	.	.	PUNCT
ejpam-4577	353	1	denote	denote	VERB
ejpam-4577	353	2	by	by	ADP
ejpam-4577	353	3	h	h	NOUN
ejpam-4577	353	4	=	=	PUNCT
ejpam-4577	353	5	{	{	PUNCT
ejpam-4577	353	6	a	a	X
ejpam-4577	353	7	:	:	PUNCT
ejpam-4577	353	8	a	a	PRON
ejpam-4577	353	9	is	be	AUX
ejpam-4577	353	10	a	a	DET
ejpam-4577	353	11	hop	hop	NOUN
ejpam-4577	353	12	independent	independent	ADJ
ejpam-4577	353	13	hop	hop	NOUN
ejpam-4577	353	14	dominating	dominating	NOUN
ejpam-4577	353	15	set	set	NOUN
ejpam-4577	353	16	of	of	ADP
ejpam-4577	353	17	g	g	NOUN
ejpam-4577	353	18	}	}	PUNCT
ejpam-4577	353	19	,	,	PUNCT
ejpam-4577	353	20	h1	h1	VERB
ejpam-4577	353	21	g	g	NOUN
ejpam-4577	353	22	=	=	PUNCT
ejpam-4577	353	23	{	{	PUNCT
ejpam-4577	353	24	b	b	NOUN
ejpam-4577	353	25	:	:	PUNCT
ejpam-4577	353	26	b	b	NOUN
ejpam-4577	353	27	is	be	AUX
ejpam-4577	353	28	a	a	DET
ejpam-4577	353	29	dominating	dominating	NOUN
ejpam-4577	353	30	hop	hop	NOUN
ejpam-4577	353	31	independent	independent	ADJ
ejpam-4577	353	32	hop	hop	NOUN
ejpam-4577	353	33	dominating	dominating	NOUN
ejpam-4577	353	34	set	set	NOUN
ejpam-4577	353	35	of	of	ADP
ejpam-4577	353	36	g	g	NOUN
ejpam-4577	353	37	}	}	PUNCT
ejpam-4577	353	38	ifg	ifg	VERB
ejpam-4577	353	39	∈	∈	NOUN
ejpam-4577	353	40	g1	g1	NOUN
ejpam-4577	353	41	,	,	PUNCT
ejpam-4577	353	42	and	and	CCONJ
ejpam-4577	353	43	h2	h2	NOUN
ejpam-4577	353	44	g	g	NOUN
ejpam-4577	353	45	=	=	PUNCT
ejpam-4577	353	46	{	{	PUNCT
ejpam-4577	353	47	t	t	NOUN
ejpam-4577	353	48	:	:	PUNCT
ejpam-4577	353	49	t	t	PROPN
ejpam-4577	353	50	is	be	AUX
ejpam-4577	353	51	a	a	DET
ejpam-4577	353	52	total	total	ADJ
ejpam-4577	353	53	dominating	dominating	NOUN
ejpam-4577	353	54	hop	hop	NOUN
ejpam-4577	353	55	independent	independent	ADJ
ejpam-4577	353	56	hop	hop	NOUN
ejpam-4577	353	57	dominating	dominating	NOUN
ejpam-4577	353	58	set	set	NOUN
ejpam-4577	353	59	of	of	ADP
ejpam-4577	353	60	g	g	NOUN
ejpam-4577	353	61	}	}	PUNCT
ejpam-4577	353	62	ifg	ifg	VERB
ejpam-4577	353	63	∈	∈	PROPN
ejpam-4577	353	64	g2	g2	PROPN
ejpam-4577	353	65	.	.	PUNCT
ejpam-4577	354	1	corollary	corollary	ADJ
ejpam-4577	354	2	7	7	NUM
ejpam-4577	354	3	.	.	PUNCT
ejpam-4577	355	1	let	let	VERB
ejpam-4577	355	2	g	g	PRON
ejpam-4577	355	3	be	be	AUX
ejpam-4577	355	4	a	a	DET
ejpam-4577	355	5	non	non	ADJ
ejpam-4577	355	6	-	-	ADJ
ejpam-4577	355	7	trivial	trivial	ADJ
ejpam-4577	355	8	connected	connected	ADJ
ejpam-4577	355	9	graph	graph	NOUN
ejpam-4577	355	10	and	and	CCONJ
ejpam-4577	355	11	let	let	VERB
ejpam-4577	355	12	h	h	NOUN
ejpam-4577	355	13	be	be	AUX
ejpam-4577	355	14	any	any	DET
ejpam-4577	355	15	graph	graph	NOUN
ejpam-4577	355	16	.	.	PUNCT
ejpam-4577	356	1	then	then	ADV
ejpam-4577	356	2	γhih(g	γhih(g	PRON
ejpam-4577	356	3	◦	◦	NOUN
ejpam-4577	356	4	h	h	NOUN
ejpam-4577	356	5	)	)	PUNCT
ejpam-4577	356	6	≤	≤	NOUN
ejpam-4577	357	1	min{|a|+	min{|a|+	VERB
ejpam-4577	357	2	|v	|v	X
ejpam-4577	357	3	(	(	PUNCT
ejpam-4577	357	4	g	g	NOUN
ejpam-4577	357	5	)	)	PUNCT
ejpam-4577	357	6	\ng(a)|cpnd(h	\ng(a)|cpnd(h	NOUN
ejpam-4577	357	7	)	)	PUNCT
ejpam-4577	357	8	:	:	PUNCT
ejpam-4577	357	9	a	a	DET
ejpam-4577	357	10	∈	∈	PROPN
ejpam-4577	357	11	h	h	NOUN
ejpam-4577	357	12	}	}	PUNCT
ejpam-4577	357	13	.	.	PUNCT
ejpam-4577	358	1	in	in	ADP
ejpam-4577	358	2	particular	particular	ADJ
ejpam-4577	358	3	,	,	PUNCT
ejpam-4577	358	4	we	we	PRON
ejpam-4577	358	5	have	have	VERB
ejpam-4577	358	6	(	(	PUNCT
ejpam-4577	358	7	i	i	NOUN
ejpam-4577	358	8	)	)	PUNCT
ejpam-4577	358	9	γhih(g	γhih(g	PROPN
ejpam-4577	358	10	◦	◦	NOUN
ejpam-4577	358	11	h	h	NOUN
ejpam-4577	358	12	)	)	PUNCT
ejpam-4577	358	13	≤	≤	NUM
ejpam-4577	358	14	min{|b|+	min{|b|+	PROPN
ejpam-4577	358	15	|b	|b	NOUN
ejpam-4577	358	16	\ng(b)|cpnd(h	\ng(b)|cpnd(h	NOUN
ejpam-4577	358	17	)	)	PUNCT
ejpam-4577	358	18	:	:	PUNCT
ejpam-4577	359	1	b	b	X
ejpam-4577	359	2	∈	∈	PROPN
ejpam-4577	359	3	h1	h1	VERB
ejpam-4577	359	4	g	g	NOUN
ejpam-4577	359	5	}	}	PUNCT
ejpam-4577	359	6	if	if	SCONJ
ejpam-4577	359	7	g	g	PROPN
ejpam-4577	359	8	∈	∈	PROPN
ejpam-4577	359	9	g1	g1	NOUN
ejpam-4577	359	10	,	,	PUNCT
ejpam-4577	359	11	and	and	CCONJ
ejpam-4577	359	12	(	(	PUNCT
ejpam-4577	359	13	ii	ii	NOUN
ejpam-4577	359	14	)	)	PUNCT
ejpam-4577	359	15	γhih(g	γhih(g	PROPN
ejpam-4577	359	16	◦	◦	NOUN
ejpam-4577	359	17	h	h	NOUN
ejpam-4577	359	18	)	)	PUNCT
ejpam-4577	359	19	≤	≤	NOUN
ejpam-4577	359	20	γhiht	γhiht	NOUN
ejpam-4577	359	21	(	(	PUNCT
ejpam-4577	359	22	g	g	NOUN
ejpam-4577	359	23	)	)	PUNCT
ejpam-4577	359	24	if	if	SCONJ
ejpam-4577	359	25	g	g	PROPN
ejpam-4577	359	26	∈	∈	PROPN
ejpam-4577	359	27	g2	g2	PROPN
ejpam-4577	359	28	g.	g.	PROPN
ejpam-4577	359	29	proof	proof	PROPN
ejpam-4577	359	30	.	.	PUNCT
ejpam-4577	360	1	let	let	VERB
ejpam-4577	360	2	a	a	DET
ejpam-4577	360	3	∈	∈	PROPN
ejpam-4577	360	4	h.	h.	NOUN
ejpam-4577	360	5	for	for	ADP
ejpam-4577	360	6	each	each	PRON
ejpam-4577	360	7	v	v	NUM
ejpam-4577	360	8	∈	∈	PROPN
ejpam-4577	360	9	v	v	NOUN
ejpam-4577	360	10	(	(	PUNCT
ejpam-4577	360	11	g	g	NOUN
ejpam-4577	360	12	)	)	PUNCT
ejpam-4577	360	13	\	\	NOUN
ejpam-4577	360	14	ng(a	ng(a	NOUN
ejpam-4577	360	15	)	)	PUNCT
ejpam-4577	360	16	,	,	PUNCT
ejpam-4577	360	17	let	let	VERB
ejpam-4577	360	18	cv	cv	PROPN
ejpam-4577	360	19	be	be	AUX
ejpam-4577	360	20	a	a	DET
ejpam-4577	360	21	cpnd	cpnd	NOUN
ejpam-4577	360	22	-	-	PUNCT
ejpam-4577	360	23	set	set	NOUN
ejpam-4577	360	24	of	of	ADP
ejpam-4577	360	25	hv	hv	PROPN
ejpam-4577	360	26	.	.	PUNCT
ejpam-4577	361	1	then	then	ADV
ejpam-4577	361	2	c	c	X
ejpam-4577	361	3	=	=	SYM
ejpam-4577	361	4	a∪(∪v∈v	a∪(∪v∈v	PROPN
ejpam-4577	361	5	(	(	PUNCT
ejpam-4577	361	6	g)\ng(a)cv	g)\ng(a)cv	PROPN
ejpam-4577	361	7	)	)	PUNCT
ejpam-4577	361	8	is	be	AUX
ejpam-4577	361	9	a	a	DET
ejpam-4577	361	10	hop	hop	NOUN
ejpam-4577	361	11	independent	independent	ADJ
ejpam-4577	361	12	hop	hop	NOUN
ejpam-4577	361	13	dominating	dominating	NOUN
ejpam-4577	361	14	set	set	NOUN
ejpam-4577	361	15	of	of	ADP
ejpam-4577	361	16	g	g	PROPN
ejpam-4577	361	17	◦	◦	NOUN
ejpam-4577	361	18	h	h	NOUN
ejpam-4577	361	19	by	by	ADP
ejpam-4577	361	20	theorem	theorem	NOUN
ejpam-4577	361	21	13	13	NUM
ejpam-4577	361	22	.	.	PUNCT
ejpam-4577	362	1	thus	thus	ADV
ejpam-4577	362	2	,	,	PUNCT
ejpam-4577	362	3	γhih(g	γhih(g	DET
ejpam-4577	362	4	◦	◦	NOUN
ejpam-4577	362	5	h	h	NOUN
ejpam-4577	362	6	)	)	PUNCT
ejpam-4577	362	7	≤	≤	NOUN
ejpam-4577	362	8	|c|	|c|	PROPN
ejpam-4577	362	9	=	=	PRON
ejpam-4577	362	10	|a|+	|a|+	VERB
ejpam-4577	362	11	∑	∑	PUNCT
ejpam-4577	362	12	v∈v	v∈v	NOUN
ejpam-4577	362	13	(	(	PUNCT
ejpam-4577	362	14	g)\ng(a	g)\ng(a	NOUN
ejpam-4577	362	15	)	)	PUNCT
ejpam-4577	362	16	|cv|	|cv|	X
ejpam-4577	363	1	=	=	PUNCT
ejpam-4577	363	2	|a|+	|a|+	VERB
ejpam-4577	363	3	|v	|v	X
ejpam-4577	363	4	(	(	PUNCT
ejpam-4577	363	5	g	g	NOUN
ejpam-4577	363	6	)	)	PUNCT
ejpam-4577	363	7	\ng(a)|cpnd(h	\ng(a)|cpnd(h	NOUN
ejpam-4577	363	8	)	)	PUNCT
ejpam-4577	363	9	.	.	PUNCT
ejpam-4577	364	1	since	since	SCONJ
ejpam-4577	364	2	a	a	PRON
ejpam-4577	364	3	is	be	AUX
ejpam-4577	364	4	arbitrary	arbitrary	ADJ
ejpam-4577	364	5	,	,	PUNCT
ejpam-4577	364	6	it	it	PRON
ejpam-4577	364	7	follows	follow	VERB
ejpam-4577	364	8	that	that	SCONJ
ejpam-4577	364	9	γhih(g	γhih(g	ADP
ejpam-4577	364	10	◦	◦	NOUN
ejpam-4577	364	11	h	h	NOUN
ejpam-4577	364	12	)	)	PUNCT
ejpam-4577	364	13	≤	≤	NOUN
ejpam-4577	364	14	min{|a|+	min{|a|+	VERB
ejpam-4577	364	15	|v	|v	X
ejpam-4577	364	16	(	(	PUNCT
ejpam-4577	364	17	g	g	NOUN
ejpam-4577	364	18	)	)	PUNCT
ejpam-4577	364	19	\ng(a)|cpnd(h	\ng(a)|cpnd(h	NOUN
ejpam-4577	364	20	)	)	PUNCT
ejpam-4577	364	21	:	:	PUNCT
ejpam-4577	364	22	a	a	DET
ejpam-4577	364	23	∈	∈	PROPN
ejpam-4577	364	24	h	h	NOUN
ejpam-4577	364	25	}	}	PUNCT
ejpam-4577	364	26	.	.	PUNCT
ejpam-4577	365	1	j.	j.	PROPN
ejpam-4577	365	2	hassan	hassan	PROPN
ejpam-4577	365	3	,	,	PUNCT
ejpam-4577	365	4	s.	s.	PROPN
ejpam-4577	365	5	canoy	canoy	PROPN
ejpam-4577	365	6	/	/	SYM
ejpam-4577	365	7	eur	eur	PROPN
ejpam-4577	365	8	.	.	PUNCT
ejpam-4577	366	1	j.	j.	PROPN
ejpam-4577	366	2	pure	pure	PROPN
ejpam-4577	366	3	appl	appl	PROPN
ejpam-4577	366	4	.	.	PROPN
ejpam-4577	366	5	math	math	PROPN
ejpam-4577	366	6	,	,	PUNCT
ejpam-4577	366	7	15	15	NUM
ejpam-4577	366	8	(	(	PUNCT
ejpam-4577	366	9	4	4	NUM
ejpam-4577	366	10	)	)	PUNCT
ejpam-4577	366	11	(	(	PUNCT
ejpam-4577	366	12	2022	2022	NUM
ejpam-4577	366	13	)	)	PUNCT
ejpam-4577	366	14	,	,	PUNCT
ejpam-4577	366	15	1783	1783	NUM
ejpam-4577	366	16	-	-	SYM
ejpam-4577	366	17	1796	1796	NUM
ejpam-4577	366	18	1794	1794	NUM
ejpam-4577	366	19	let	let	VERB
ejpam-4577	366	20	g	g	PROPN
ejpam-4577	366	21	∈	∈	PROPN
ejpam-4577	366	22	g1	g1	NOUN
ejpam-4577	366	23	and	and	CCONJ
ejpam-4577	366	24	let	let	VERB
ejpam-4577	366	25	b	b	X
ejpam-4577	366	26	∈	∈	PROPN
ejpam-4577	366	27	h1	h1	PROPN
ejpam-4577	366	28	g.	g.	PROPN
ejpam-4577	366	29	since	since	SCONJ
ejpam-4577	366	30	b	b	PROPN
ejpam-4577	366	31	is	be	AUX
ejpam-4577	366	32	a	a	DET
ejpam-4577	366	33	dominating	dominating	NOUN
ejpam-4577	366	34	set	set	NOUN
ejpam-4577	366	35	,	,	PUNCT
ejpam-4577	366	36	it	it	PRON
ejpam-4577	366	37	follows	follow	VERB
ejpam-4577	366	38	that	that	SCONJ
ejpam-4577	366	39	v	v	X
ejpam-4577	366	40	(	(	PUNCT
ejpam-4577	366	41	g	g	NOUN
ejpam-4577	366	42	)	)	PUNCT
ejpam-4577	366	43	\ng(b	\ng(b	NOUN
ejpam-4577	366	44	)	)	PUNCT
ejpam-4577	366	45	=	=	SYM
ejpam-4577	366	46	b	b	X
ejpam-4577	366	47	\ng(b	\ng(b	NOUN
ejpam-4577	366	48	)	)	PUNCT
ejpam-4577	366	49	.	.	PUNCT
ejpam-4577	367	1	hence	hence	ADV
ejpam-4577	367	2	,	,	PUNCT
ejpam-4577	367	3	(	(	PUNCT
ejpam-4577	367	4	i	i	NOUN
ejpam-4577	367	5	)	)	PUNCT
ejpam-4577	367	6	follows	follow	VERB
ejpam-4577	367	7	from	from	ADP
ejpam-4577	367	8	the	the	DET
ejpam-4577	367	9	first	first	ADJ
ejpam-4577	367	10	inequality	inequality	NOUN
ejpam-4577	367	11	.	.	PUNCT
ejpam-4577	368	1	next	next	ADV
ejpam-4577	368	2	,	,	PUNCT
ejpam-4577	368	3	let	let	VERB
ejpam-4577	368	4	g	g	PROPN
ejpam-4577	368	5	∈	∈	PROPN
ejpam-4577	368	6	g2	g2	PROPN
ejpam-4577	368	7	and	and	CCONJ
ejpam-4577	368	8	let	let	VERB
ejpam-4577	368	9	t	t	PROPN
ejpam-4577	368	10	∈	∈	PROPN
ejpam-4577	368	11	h2	h2	PROPN
ejpam-4577	368	12	g.	g.	PROPN
ejpam-4577	368	13	since	since	SCONJ
ejpam-4577	368	14	t	t	PROPN
ejpam-4577	368	15	is	be	AUX
ejpam-4577	368	16	a	a	DET
ejpam-4577	368	17	total	total	ADJ
ejpam-4577	368	18	dominating	dominating	NOUN
ejpam-4577	368	19	set	set	NOUN
ejpam-4577	368	20	of	of	ADP
ejpam-4577	368	21	g	g	PROPN
ejpam-4577	368	22	,	,	PUNCT
ejpam-4577	368	23	it	it	PRON
ejpam-4577	368	24	follows	follow	VERB
ejpam-4577	368	25	that	that	SCONJ
ejpam-4577	368	26	v	v	X
ejpam-4577	368	27	(	(	PUNCT
ejpam-4577	368	28	g	g	NOUN
ejpam-4577	368	29	)	)	PUNCT
ejpam-4577	368	30	=	=	SYM
ejpam-4577	368	31	ng(t	ng(t	PRON
ejpam-4577	368	32	)	)	PUNCT
ejpam-4577	368	33	.	.	PUNCT
ejpam-4577	369	1	thus	thus	ADV
ejpam-4577	369	2	,	,	PUNCT
ejpam-4577	369	3	γhih(g	γhih(g	PRON
ejpam-4577	369	4	◦	◦	NOUN
ejpam-4577	369	5	h	h	NOUN
ejpam-4577	369	6	)	)	PUNCT
ejpam-4577	369	7	≤	≤	NOUN
ejpam-4577	369	8	min{|t	min{|t	PROPN
ejpam-4577	370	1	|	|	ADV
ejpam-4577	370	2	:	:	PUNCT
ejpam-4577	370	3	t	t	PROPN
ejpam-4577	370	4	∈	∈	PROPN
ejpam-4577	370	5	h2	h2	PROPN
ejpam-4577	370	6	g	g	NOUN
ejpam-4577	370	7	}	}	PUNCT
ejpam-4577	370	8	=	=	PUNCT
ejpam-4577	370	9	γhiht	γhiht	NOUN
ejpam-4577	370	10	(	(	PUNCT
ejpam-4577	370	11	g	g	NOUN
ejpam-4577	370	12	)	)	PUNCT
ejpam-4577	370	13	by	by	ADP
ejpam-4577	370	14	the	the	DET
ejpam-4577	370	15	first	first	ADJ
ejpam-4577	370	16	inequality	inequality	NOUN
ejpam-4577	370	17	.	.	PUNCT
ejpam-4577	371	1	hence	hence	ADV
ejpam-4577	371	2	,	,	PUNCT
ejpam-4577	371	3	(	(	PUNCT
ejpam-4577	371	4	ii	ii	NOUN
ejpam-4577	371	5	)	)	PUNCT
ejpam-4577	371	6	holds	hold	VERB
ejpam-4577	371	7	.	.	PUNCT
ejpam-4577	372	1	theorem	theorem	VERB
ejpam-4577	372	2	14	14	NUM
ejpam-4577	372	3	.	.	PUNCT
ejpam-4577	373	1	[	[	X
ejpam-4577	373	2	3	3	X
ejpam-4577	373	3	]	]	PUNCT
ejpam-4577	373	4	let	let	VERB
ejpam-4577	373	5	g	g	NOUN
ejpam-4577	373	6	and	and	CCONJ
ejpam-4577	373	7	h	h	PROPN
ejpam-4577	373	8	be	be	VERB
ejpam-4577	373	9	non	non	ADJ
ejpam-4577	373	10	-	-	ADJ
ejpam-4577	373	11	trivial	trivial	ADJ
ejpam-4577	373	12	connected	connected	ADJ
ejpam-4577	373	13	graphs	graph	NOUN
ejpam-4577	373	14	.	.	PUNCT
ejpam-4577	374	1	then	then	ADV
ejpam-4577	374	2	c	c	NOUN
ejpam-4577	374	3	=	=	PUNCT
ejpam-4577	374	4	⋃	⋃	PROPN
ejpam-4577	374	5	x∈s	x∈s	NOUN
ejpam-4577	375	1	[	[	X
ejpam-4577	375	2	{	{	PUNCT
ejpam-4577	375	3	x}×tx	x}×tx	X
ejpam-4577	375	4	]	]	X
ejpam-4577	375	5	,	,	PUNCT
ejpam-4577	375	6	where	where	SCONJ
ejpam-4577	375	7	s	s	VERB
ejpam-4577	375	8	⊆	⊆	NUM
ejpam-4577	375	9	v	v	NOUN
ejpam-4577	375	10	(	(	PUNCT
ejpam-4577	375	11	g	g	NOUN
ejpam-4577	375	12	)	)	PUNCT
ejpam-4577	375	13	and	and	CCONJ
ejpam-4577	375	14	tx	tx	VERB
ejpam-4577	375	15	⊆	⊆	NUM
ejpam-4577	375	16	v	v	NOUN
ejpam-4577	375	17	(	(	PUNCT
ejpam-4577	375	18	h	h	NOUN
ejpam-4577	375	19	)	)	PUNCT
ejpam-4577	375	20	for	for	ADP
ejpam-4577	375	21	each	each	DET
ejpam-4577	375	22	x	x	SYM
ejpam-4577	375	23	∈	∈	PROPN
ejpam-4577	375	24	s	s	NOUN
ejpam-4577	375	25	,	,	PUNCT
ejpam-4577	375	26	is	be	AUX
ejpam-4577	375	27	a	a	DET
ejpam-4577	375	28	hop	hop	NOUN
ejpam-4577	375	29	independent	independent	ADJ
ejpam-4577	375	30	set	set	NOUN
ejpam-4577	375	31	of	of	ADP
ejpam-4577	375	32	g[h	g[h	NOUN
ejpam-4577	375	33	]	]	PUNCT
ejpam-4577	375	34	if	if	SCONJ
ejpam-4577	375	35	and	and	CCONJ
ejpam-4577	375	36	only	only	ADV
ejpam-4577	375	37	if	if	SCONJ
ejpam-4577	375	38	the	the	DET
ejpam-4577	375	39	following	follow	VERB
ejpam-4577	375	40	conditions	condition	NOUN
ejpam-4577	375	41	hold	hold	VERB
ejpam-4577	375	42	.	.	PUNCT
ejpam-4577	376	1	(	(	PUNCT
ejpam-4577	376	2	i	i	NOUN
ejpam-4577	376	3	)	)	PUNCT
ejpam-4577	376	4	s	s	VERB
ejpam-4577	376	5	is	be	AUX
ejpam-4577	376	6	a	a	DET
ejpam-4577	376	7	hop	hop	NOUN
ejpam-4577	376	8	independent	independent	ADJ
ejpam-4577	376	9	set	set	NOUN
ejpam-4577	376	10	of	of	ADP
ejpam-4577	376	11	g.	g.	PROPN
ejpam-4577	376	12	(	(	PUNCT
ejpam-4577	376	13	ii	ii	PROPN
ejpam-4577	376	14	)	)	PUNCT
ejpam-4577	376	15	tx	tx	PROPN
ejpam-4577	376	16	is	be	AUX
ejpam-4577	376	17	a	a	DET
ejpam-4577	376	18	clique	clique	NOUN
ejpam-4577	376	19	in	in	ADP
ejpam-4577	376	20	h	h	NOUN
ejpam-4577	376	21	for	for	ADP
ejpam-4577	376	22	each	each	PRON
ejpam-4577	376	23	x	x	SYM
ejpam-4577	376	24	∈	∈	PROPN
ejpam-4577	376	25	s.	s.	PROPN
ejpam-4577	376	26	theorem	theorem	VERB
ejpam-4577	376	27	15	15	NUM
ejpam-4577	376	28	.	.	PUNCT
ejpam-4577	377	1	[	[	X
ejpam-4577	377	2	7	7	X
ejpam-4577	377	3	]	]	X
ejpam-4577	377	4	let	let	VERB
ejpam-4577	377	5	g	g	NOUN
ejpam-4577	377	6	and	and	CCONJ
ejpam-4577	377	7	h	h	NOUN
ejpam-4577	377	8	be	be	AUX
ejpam-4577	377	9	connected	connect	VERB
ejpam-4577	377	10	non	non	ADJ
ejpam-4577	377	11	-	-	ADJ
ejpam-4577	377	12	trivial	trivial	ADJ
ejpam-4577	377	13	graphs	graph	NOUN
ejpam-4577	377	14	.	.	PUNCT
ejpam-4577	378	1	a	a	DET
ejpam-4577	378	2	subset	subset	NOUN
ejpam-4577	378	3	c	c	NOUN
ejpam-4577	378	4	⋃	⋃	PROPN
ejpam-4577	378	5	x∈s	x∈s	PROPN
ejpam-4577	379	1	[	[	X
ejpam-4577	379	2	{	{	PUNCT
ejpam-4577	379	3	x}×tx	x}×tx	X
ejpam-4577	379	4	]	]	X
ejpam-4577	379	5	of	of	ADP
ejpam-4577	379	6	v	v	NOUN
ejpam-4577	379	7	(	(	PUNCT
ejpam-4577	379	8	g[h	g[h	PROPN
ejpam-4577	379	9	]	]	PUNCT
ejpam-4577	379	10	is	be	AUX
ejpam-4577	379	11	a	a	DET
ejpam-4577	379	12	hop	hop	NOUN
ejpam-4577	379	13	dominating	dominating	NOUN
ejpam-4577	379	14	set	set	NOUN
ejpam-4577	379	15	of	of	ADP
ejpam-4577	379	16	g[h	g[h	PROPN
ejpam-4577	379	17	]	]	PUNCT
ejpam-4577	379	18	if	if	SCONJ
ejpam-4577	379	19	and	and	CCONJ
ejpam-4577	379	20	only	only	ADV
ejpam-4577	379	21	if	if	SCONJ
ejpam-4577	379	22	the	the	DET
ejpam-4577	379	23	following	follow	VERB
ejpam-4577	379	24	conditions	condition	NOUN
ejpam-4577	379	25	hold	hold	VERB
ejpam-4577	379	26	.	.	PUNCT
ejpam-4577	380	1	(	(	PUNCT
ejpam-4577	380	2	i	i	NOUN
ejpam-4577	380	3	)	)	PUNCT
ejpam-4577	380	4	s	s	VERB
ejpam-4577	380	5	is	be	AUX
ejpam-4577	380	6	a	a	DET
ejpam-4577	380	7	hop	hop	NOUN
ejpam-4577	380	8	dominating	dominating	NOUN
ejpam-4577	380	9	set	set	NOUN
ejpam-4577	380	10	of	of	ADP
ejpam-4577	380	11	g.	g.	PROPN
ejpam-4577	380	12	(	(	PUNCT
ejpam-4577	380	13	ii	ii	PROPN
ejpam-4577	380	14	)	)	PUNCT
ejpam-4577	380	15	tx	tx	PROPN
ejpam-4577	380	16	is	be	AUX
ejpam-4577	380	17	a	a	DET
ejpam-4577	380	18	pointwise	pointwise	ADJ
ejpam-4577	380	19	non	non	ADJ
ejpam-4577	380	20	-	-	ADJ
ejpam-4577	380	21	dominating	dominating	ADJ
ejpam-4577	380	22	set	set	NOUN
ejpam-4577	380	23	of	of	ADP
ejpam-4577	380	24	h	h	NOUN
ejpam-4577	380	25	for	for	ADP
ejpam-4577	380	26	each	each	DET
ejpam-4577	380	27	x	x	SYM
ejpam-4577	380	28	∈	∈	PROPN
ejpam-4577	380	29	s	s	VERB
ejpam-4577	380	30	with	with	ADP
ejpam-4577	380	31	|n2	|n2	PROPN
ejpam-4577	380	32	g(x	g(x	NOUN
ejpam-4577	380	33	)	)	PUNCT
ejpam-4577	380	34	∩	∩	NOUN
ejpam-4577	380	35	s|	s|	VERB
ejpam-4577	380	36	=	=	SYM
ejpam-4577	381	1	0	0	X
ejpam-4577	381	2	.	.	PUNCT
ejpam-4577	381	3	theorem	theorem	VERB
ejpam-4577	381	4	16	16	NUM
ejpam-4577	381	5	.	.	PUNCT
ejpam-4577	382	1	let	let	VERB
ejpam-4577	382	2	g	g	NOUN
ejpam-4577	382	3	and	and	CCONJ
ejpam-4577	382	4	h	h	PROPN
ejpam-4577	382	5	be	be	VERB
ejpam-4577	382	6	non	non	ADJ
ejpam-4577	382	7	-	-	ADJ
ejpam-4577	382	8	trivial	trivial	ADJ
ejpam-4577	382	9	connected	connected	ADJ
ejpam-4577	382	10	graphs	graph	NOUN
ejpam-4577	382	11	.	.	PUNCT
ejpam-4577	383	1	then	then	ADV
ejpam-4577	383	2	c	c	X
ejpam-4577	383	3	=	=	PUNCT
ejpam-4577	383	4	⋃	⋃	NOUN
ejpam-4577	383	5	x∈a	x∈a	NOUN
ejpam-4577	383	6	[	[	X
ejpam-4577	383	7	{	{	PUNCT
ejpam-4577	383	8	x	x	NOUN
ejpam-4577	383	9	}	}	PUNCT
ejpam-4577	383	10	×	×	PROPN
ejpam-4577	383	11	tx	tx	PROPN
ejpam-4577	383	12	]	]	X
ejpam-4577	383	13	,	,	PUNCT
ejpam-4577	383	14	where	where	SCONJ
ejpam-4577	383	15	a	a	DET
ejpam-4577	383	16	⊆	⊆	NUM
ejpam-4577	383	17	v	v	NOUN
ejpam-4577	383	18	(	(	PUNCT
ejpam-4577	383	19	g	g	NOUN
ejpam-4577	383	20	)	)	PUNCT
ejpam-4577	383	21	and	and	CCONJ
ejpam-4577	383	22	tx	tx	VERB
ejpam-4577	383	23	⊆	⊆	NUM
ejpam-4577	383	24	v	v	NOUN
ejpam-4577	383	25	(	(	PUNCT
ejpam-4577	383	26	h	h	NOUN
ejpam-4577	383	27	)	)	PUNCT
ejpam-4577	383	28	for	for	ADP
ejpam-4577	383	29	each	each	DET
ejpam-4577	383	30	x	x	SYM
ejpam-4577	383	31	∈	∈	PROPN
ejpam-4577	383	32	a	a	PRON
ejpam-4577	383	33	,	,	PUNCT
ejpam-4577	383	34	is	be	AUX
ejpam-4577	383	35	a	a	DET
ejpam-4577	383	36	hop	hop	NOUN
ejpam-4577	383	37	independent	independent	ADJ
ejpam-4577	383	38	hop	hop	NOUN
ejpam-4577	383	39	dominating	dominating	NOUN
ejpam-4577	383	40	set	set	NOUN
ejpam-4577	383	41	of	of	ADP
ejpam-4577	383	42	g[h	g[h	PROPN
ejpam-4577	383	43	]	]	PUNCT
ejpam-4577	383	44	if	if	SCONJ
ejpam-4577	383	45	and	and	CCONJ
ejpam-4577	383	46	only	only	ADV
ejpam-4577	383	47	if	if	SCONJ
ejpam-4577	383	48	the	the	DET
ejpam-4577	383	49	following	follow	VERB
ejpam-4577	383	50	conditions	condition	NOUN
ejpam-4577	383	51	hold	hold	VERB
ejpam-4577	383	52	.	.	PUNCT
ejpam-4577	384	1	(	(	PUNCT
ejpam-4577	384	2	i	i	NOUN
ejpam-4577	384	3	)	)	PUNCT
ejpam-4577	384	4	a	a	PRON
ejpam-4577	384	5	is	be	AUX
ejpam-4577	384	6	a	a	DET
ejpam-4577	384	7	hop	hop	NOUN
ejpam-4577	384	8	independent	independent	ADJ
ejpam-4577	384	9	hop	hop	NOUN
ejpam-4577	384	10	dominating	dominating	NOUN
ejpam-4577	384	11	set	set	NOUN
ejpam-4577	384	12	of	of	ADP
ejpam-4577	384	13	g.	g.	PROPN
ejpam-4577	384	14	(	(	PUNCT
ejpam-4577	384	15	ii	ii	PROPN
ejpam-4577	384	16	)	)	PUNCT
ejpam-4577	384	17	tx	tx	PROPN
ejpam-4577	384	18	is	be	AUX
ejpam-4577	384	19	a	a	DET
ejpam-4577	384	20	clique	clique	NOUN
ejpam-4577	384	21	pointwise	pointwise	PROPN
ejpam-4577	384	22	non	non	ADJ
ejpam-4577	384	23	-	-	ADJ
ejpam-4577	384	24	dominating	dominating	ADJ
ejpam-4577	384	25	set	set	NOUN
ejpam-4577	384	26	in	in	ADP
ejpam-4577	384	27	h	h	NOUN
ejpam-4577	384	28	for	for	ADP
ejpam-4577	384	29	each	each	DET
ejpam-4577	384	30	x	x	SYM
ejpam-4577	384	31	∈	∈	NOUN
ejpam-4577	384	32	a.	a.	NOUN
ejpam-4577	384	33	proof	proof	NOUN
ejpam-4577	384	34	.	.	PUNCT
ejpam-4577	385	1	suppose	suppose	VERB
ejpam-4577	385	2	c	c	NOUN
ejpam-4577	385	3	=	=	PUNCT
ejpam-4577	385	4	⋃	⋃	NOUN
ejpam-4577	385	5	x∈a	x∈a	NOUN
ejpam-4577	385	6	[	[	X
ejpam-4577	385	7	{	{	PUNCT
ejpam-4577	385	8	x	x	NOUN
ejpam-4577	385	9	}	}	PUNCT
ejpam-4577	385	10	×	×	PROPN
ejpam-4577	385	11	tx	tx	PROPN
ejpam-4577	385	12	]	]	PUNCT
ejpam-4577	385	13	is	be	AUX
ejpam-4577	385	14	a	a	DET
ejpam-4577	385	15	hop	hop	NOUN
ejpam-4577	385	16	independent	independent	ADJ
ejpam-4577	385	17	hop	hop	NOUN
ejpam-4577	385	18	dominating	dominating	NOUN
ejpam-4577	385	19	set	set	NOUN
ejpam-4577	385	20	of	of	ADP
ejpam-4577	385	21	g[h	g[h	NOUN
ejpam-4577	385	22	]	]	PUNCT
ejpam-4577	385	23	.	.	PUNCT
ejpam-4577	386	1	since	since	SCONJ
ejpam-4577	386	2	c	c	PROPN
ejpam-4577	386	3	is	be	AUX
ejpam-4577	386	4	a	a	DET
ejpam-4577	386	5	hop	hop	NOUN
ejpam-4577	386	6	independent	independent	ADJ
ejpam-4577	386	7	set	set	NOUN
ejpam-4577	386	8	,	,	PUNCT
ejpam-4577	386	9	it	it	PRON
ejpam-4577	386	10	follows	follow	VERB
ejpam-4577	386	11	that	that	SCONJ
ejpam-4577	386	12	a	a	PRON
ejpam-4577	386	13	is	be	AUX
ejpam-4577	386	14	a	a	DET
ejpam-4577	386	15	hop	hop	NOUN
ejpam-4577	386	16	independent	independent	ADJ
ejpam-4577	386	17	set	set	NOUN
ejpam-4577	386	18	of	of	ADP
ejpam-4577	386	19	g	g	NOUN
ejpam-4577	386	20	by	by	ADP
ejpam-4577	386	21	theorem	theorem	NOUN
ejpam-4577	386	22	14	14	NUM
ejpam-4577	386	23	.	.	PUNCT
ejpam-4577	387	1	moreover	moreover	ADV
ejpam-4577	387	2	,	,	PUNCT
ejpam-4577	387	3	since	since	SCONJ
ejpam-4577	387	4	c	c	PROPN
ejpam-4577	387	5	is	be	AUX
ejpam-4577	387	6	a	a	DET
ejpam-4577	387	7	hop	hop	NOUN
ejpam-4577	387	8	dominating	dominating	NOUN
ejpam-4577	387	9	set	set	NOUN
ejpam-4577	387	10	of	of	ADP
ejpam-4577	387	11	g	g	PROPN
ejpam-4577	387	12	,	,	PUNCT
ejpam-4577	387	13	a	a	PRON
ejpam-4577	387	14	is	be	AUX
ejpam-4577	387	15	a	a	DET
ejpam-4577	387	16	hop	hop	NOUN
ejpam-4577	387	17	dominating	dominating	NOUN
ejpam-4577	387	18	set	set	VERB
ejpam-4577	387	19	by	by	ADP
ejpam-4577	387	20	theorem	theorem	NOUN
ejpam-4577	387	21	15	15	NUM
ejpam-4577	387	22	.	.	PUNCT
ejpam-4577	388	1	hence	hence	ADV
ejpam-4577	388	2	,	,	PUNCT
ejpam-4577	388	3	(	(	PUNCT
ejpam-4577	388	4	i	i	NOUN
ejpam-4577	388	5	)	)	PUNCT
ejpam-4577	388	6	holds	hold	VERB
ejpam-4577	388	7	.	.	PUNCT
ejpam-4577	389	1	also	also	ADV
ejpam-4577	389	2	,	,	PUNCT
ejpam-4577	389	3	by	by	ADP
ejpam-4577	389	4	theorem	theorem	ADJ
ejpam-4577	389	5	14	14	NUM
ejpam-4577	389	6	and	and	CCONJ
ejpam-4577	389	7	theorem	theorem	VERB
ejpam-4577	389	8	15	15	NUM
ejpam-4577	389	9	,	,	PUNCT
ejpam-4577	389	10	tx	tx	PROPN
ejpam-4577	389	11	is	be	AUX
ejpam-4577	389	12	a	a	DET
ejpam-4577	389	13	clique	clique	NOUN
ejpam-4577	389	14	pointwise	pointwise	PROPN
ejpam-4577	389	15	non	non	ADJ
ejpam-4577	389	16	-	-	ADJ
ejpam-4577	389	17	dominating	dominating	ADJ
ejpam-4577	389	18	set	set	NOUN
ejpam-4577	389	19	of	of	ADP
ejpam-4577	389	20	h	h	NOUN
ejpam-4577	389	21	for	for	ADP
ejpam-4577	389	22	each	each	DET
ejpam-4577	389	23	x	x	SYM
ejpam-4577	389	24	∈	∈	PROPN
ejpam-4577	389	25	a	a	PRON
ejpam-4577	389	26	,	,	PUNCT
ejpam-4577	389	27	respectively	respectively	ADV
ejpam-4577	389	28	.	.	PUNCT
ejpam-4577	390	1	hence	hence	ADV
ejpam-4577	390	2	,	,	PUNCT
ejpam-4577	390	3	(	(	PUNCT
ejpam-4577	390	4	ii	ii	NOUN
ejpam-4577	390	5	)	)	PUNCT
ejpam-4577	390	6	holds	hold	VERB
ejpam-4577	390	7	.	.	PUNCT
ejpam-4577	391	1	conversely	conversely	ADV
ejpam-4577	391	2	,	,	PUNCT
ejpam-4577	391	3	suppose	suppose	VERB
ejpam-4577	391	4	that	that	SCONJ
ejpam-4577	391	5	c	c	NOUN
ejpam-4577	391	6	=	=	PUNCT
ejpam-4577	391	7	⋃	⋃	PROPN
ejpam-4577	391	8	x∈b	x∈b	NOUN
ejpam-4577	392	1	[	[	X
ejpam-4577	392	2	{	{	PUNCT
ejpam-4577	392	3	x}×tx	x}×tx	X
ejpam-4577	392	4	]	]	X
ejpam-4577	392	5	and	and	CCONJ
ejpam-4577	392	6	satisfies	satisfie	NOUN
ejpam-4577	392	7	(	(	PUNCT
ejpam-4577	392	8	i	i	NOUN
ejpam-4577	392	9	)	)	PUNCT
ejpam-4577	392	10	and	and	CCONJ
ejpam-4577	392	11	(	(	PUNCT
ejpam-4577	392	12	ii	ii	NOUN
ejpam-4577	392	13	)	)	PUNCT
ejpam-4577	392	14	.	.	PUNCT
ejpam-4577	393	1	then	then	ADV
ejpam-4577	393	2	by	by	ADP
ejpam-4577	393	3	theorem	theorem	ADJ
ejpam-4577	393	4	14	14	NUM
ejpam-4577	393	5	and	and	CCONJ
ejpam-4577	393	6	theorem	theorem	VERB
ejpam-4577	393	7	15	15	NUM
ejpam-4577	393	8	,	,	PUNCT
ejpam-4577	393	9	c	c	PROPN
ejpam-4577	393	10	is	be	AUX
ejpam-4577	393	11	a	a	DET
ejpam-4577	393	12	hop	hop	NOUN
ejpam-4577	393	13	independent	independent	ADJ
ejpam-4577	393	14	hop	hop	NOUN
ejpam-4577	393	15	dominating	dominating	NOUN
ejpam-4577	393	16	set	set	NOUN
ejpam-4577	393	17	of	of	ADP
ejpam-4577	393	18	g[h	g[h	PROPN
ejpam-4577	393	19	]	]	PUNCT
ejpam-4577	393	20	.	.	PUNCT
ejpam-4577	394	1	j.	j.	PROPN
ejpam-4577	394	2	hassan	hassan	PROPN
ejpam-4577	394	3	,	,	PUNCT
ejpam-4577	394	4	s.	s.	PROPN
ejpam-4577	394	5	canoy	canoy	PROPN
ejpam-4577	394	6	/	/	SYM
ejpam-4577	394	7	eur	eur	PROPN
ejpam-4577	394	8	.	.	PUNCT
ejpam-4577	395	1	j.	j.	PROPN
ejpam-4577	395	2	pure	pure	PROPN
ejpam-4577	395	3	appl	appl	PROPN
ejpam-4577	395	4	.	.	PROPN
ejpam-4577	395	5	math	math	PROPN
ejpam-4577	395	6	,	,	PUNCT
ejpam-4577	395	7	15	15	NUM
ejpam-4577	395	8	(	(	PUNCT
ejpam-4577	395	9	4	4	NUM
ejpam-4577	395	10	)	)	PUNCT
ejpam-4577	395	11	(	(	PUNCT
ejpam-4577	395	12	2022	2022	NUM
ejpam-4577	395	13	)	)	PUNCT
ejpam-4577	395	14	,	,	PUNCT
ejpam-4577	395	15	1783	1783	NUM
ejpam-4577	395	16	-	-	SYM
ejpam-4577	395	17	1796	1796	NUM
ejpam-4577	395	18	1795	1795	NUM
ejpam-4577	395	19	corollary	corollary	ADJ
ejpam-4577	395	20	8	8	NUM
ejpam-4577	395	21	.	.	PUNCT
ejpam-4577	396	1	let	let	VERB
ejpam-4577	396	2	g	g	NOUN
ejpam-4577	396	3	and	and	CCONJ
ejpam-4577	396	4	h	h	PROPN
ejpam-4577	396	5	be	be	VERB
ejpam-4577	396	6	non	non	ADJ
ejpam-4577	396	7	-	-	ADJ
ejpam-4577	396	8	trivial	trivial	ADJ
ejpam-4577	396	9	connected	connected	ADJ
ejpam-4577	396	10	graphs	graph	NOUN
ejpam-4577	396	11	.	.	PUNCT
ejpam-4577	397	1	then	then	ADV
ejpam-4577	397	2	γhih(g[h	γhih(g[h	ADV
ejpam-4577	397	3	]	]	X
ejpam-4577	397	4	)	)	PUNCT
ejpam-4577	397	5	=	=	SYM
ejpam-4577	397	6	γhih(g)cpnd(h	γhih(g)cpnd(h	NOUN
ejpam-4577	397	7	)	)	PUNCT
ejpam-4577	397	8	.	.	PUNCT
ejpam-4577	398	1	in	in	ADP
ejpam-4577	398	2	particular	particular	ADJ
ejpam-4577	398	3	,	,	PUNCT
ejpam-4577	398	4	we	we	PRON
ejpam-4577	398	5	have	have	VERB
ejpam-4577	398	6	(	(	PUNCT
ejpam-4577	398	7	i	i	NOUN
ejpam-4577	398	8	)	)	PUNCT
ejpam-4577	398	9	γhih(kn[km	γhih(kn[km	PROPN
ejpam-4577	398	10	]	]	X
ejpam-4577	398	11	)	)	PUNCT
ejpam-4577	399	1	=	=	SYM
ejpam-4577	399	2	γhih(kn)cpnd(km	γhih(kn)cpnd(km	NOUN
ejpam-4577	399	3	)	)	PUNCT
ejpam-4577	399	4	=	=	SYM
ejpam-4577	399	5	nm	nm	NOUN
ejpam-4577	399	6	for	for	ADP
ejpam-4577	399	7	any	any	DET
ejpam-4577	399	8	n	n	CCONJ
ejpam-4577	399	9	,	,	PUNCT
ejpam-4577	399	10	m	m	VERB
ejpam-4577	399	11	≥	≥	NOUN
ejpam-4577	399	12	1	1	NUM
ejpam-4577	399	13	,	,	PUNCT
ejpam-4577	399	14	(	(	PUNCT
ejpam-4577	399	15	ii	ii	NOUN
ejpam-4577	399	16	)	)	PUNCT
ejpam-4577	399	17	γhih(kn[pm	γhih(kn[pm	PROPN
ejpam-4577	399	18	]	]	PUNCT
ejpam-4577	399	19	)	)	PUNCT
ejpam-4577	399	20	=	=	SYM
ejpam-4577	399	21	γhih(kn)cpnd(pm	γhih(kn)cpnd(pm	NOUN
ejpam-4577	399	22	)	)	PUNCT
ejpam-4577	399	23	=	=	SYM
ejpam-4577	399	24	2n	2n	NUM
ejpam-4577	399	25	for	for	ADP
ejpam-4577	399	26	any	any	DET
ejpam-4577	399	27	n	n	PRON
ejpam-4577	399	28	≥	≥	NOUN
ejpam-4577	399	29	1,m	1,m	X
ejpam-4577	399	30	≥	≥	NUM
ejpam-4577	399	31	3	3	NUM
ejpam-4577	399	32	,	,	PUNCT
ejpam-4577	399	33	(	(	PUNCT
ejpam-4577	399	34	iii	iii	NOUN
ejpam-4577	399	35	)	)	PUNCT
ejpam-4577	399	36	γhih(kn[cm	γhih(kn[cm	NOUN
ejpam-4577	399	37	]	]	X
ejpam-4577	399	38	)	)	PUNCT
ejpam-4577	399	39	=	=	SYM
ejpam-4577	399	40	γhih(kn)cpnd(cm	γhih(kn)cpnd(cm	NOUN
ejpam-4577	399	41	)	)	PUNCT
ejpam-4577	400	1	=	=	SYM
ejpam-4577	400	2	2n	2n	NUM
ejpam-4577	400	3	for	for	ADP
ejpam-4577	400	4	any	any	DET
ejpam-4577	400	5	n	n	PRON
ejpam-4577	400	6	≥	≥	NOUN
ejpam-4577	400	7	1,m	1,m	X
ejpam-4577	400	8	≥	≥	NUM
ejpam-4577	400	9	4	4	NUM
ejpam-4577	400	10	,	,	PUNCT
ejpam-4577	400	11	(	(	PUNCT
ejpam-4577	400	12	iv	iv	X
ejpam-4577	400	13	)	)	PUNCT
ejpam-4577	400	14	γhih(pn[pm	γhih(pn[pm	PROPN
ejpam-4577	400	15	]	]	PUNCT
ejpam-4577	400	16	)	)	PUNCT
ejpam-4577	400	17	=	=	SYM
ejpam-4577	400	18	γhih(pn)cpnd(pm	γhih(pn)cpnd(pm	NOUN
ejpam-4577	400	19	)	)	PUNCT
ejpam-4577	400	20	=	=	SYM
ejpam-4577	400	21	2γh(pn	2γh(pn	NUM
ejpam-4577	400	22	)	)	PUNCT
ejpam-4577	400	23	for	for	ADP
ejpam-4577	400	24	any	any	DET
ejpam-4577	400	25	n	n	CCONJ
ejpam-4577	400	26	,	,	PUNCT
ejpam-4577	400	27	m	m	VERB
ejpam-4577	400	28	≥	≥	NOUN
ejpam-4577	400	29	3	3	NUM
ejpam-4577	400	30	,	,	PUNCT
ejpam-4577	400	31	and	and	CCONJ
ejpam-4577	400	32	(	(	PUNCT
ejpam-4577	400	33	v	v	NOUN
ejpam-4577	400	34	)	)	PUNCT
ejpam-4577	400	35	γhih(cn[cm	γhih(cn[cm	NOUN
ejpam-4577	400	36	]	]	X
ejpam-4577	400	37	)	)	PUNCT
ejpam-4577	400	38	=	=	SYM
ejpam-4577	400	39	γhih(cn)cpnd(cm	γhih(cn)cpnd(cm	NOUN
ejpam-4577	400	40	)	)	PUNCT
ejpam-4577	400	41	=	=	SYM
ejpam-4577	400	42	2γh(cn	2γh(cn	NUM
ejpam-4577	400	43	)	)	PUNCT
ejpam-4577	400	44	for	for	ADP
ejpam-4577	400	45	any	any	DET
ejpam-4577	400	46	n	n	CCONJ
ejpam-4577	400	47	,	,	PUNCT
ejpam-4577	400	48	m	m	VERB
ejpam-4577	400	49	≥	≥	NOUN
ejpam-4577	400	50	4	4	NUM
ejpam-4577	400	51	.	.	PUNCT
ejpam-4577	401	1	proof	proof	NOUN
ejpam-4577	401	2	.	.	PUNCT
ejpam-4577	402	1	let	let	VERB
ejpam-4577	402	2	a	a	PRON
ejpam-4577	402	3	be	be	AUX
ejpam-4577	402	4	a	a	DET
ejpam-4577	402	5	γhih	γhih	NOUN
ejpam-4577	402	6	-	-	PUNCT
ejpam-4577	402	7	set	set	NOUN
ejpam-4577	402	8	of	of	ADP
ejpam-4577	402	9	g	g	NOUN
ejpam-4577	402	10	and	and	CCONJ
ejpam-4577	402	11	let	let	VERB
ejpam-4577	402	12	t	t	PROPN
ejpam-4577	402	13	be	be	AUX
ejpam-4577	402	14	a	a	DET
ejpam-4577	402	15	cpnd	cpnd	NOUN
ejpam-4577	402	16	-	-	PUNCT
ejpam-4577	402	17	set	set	NOUN
ejpam-4577	402	18	of	of	ADP
ejpam-4577	402	19	h.	h.	NOUN
ejpam-4577	402	20	for	for	ADP
ejpam-4577	402	21	each	each	DET
ejpam-4577	402	22	x	x	PROPN
ejpam-4577	402	23	∈	∈	PROPN
ejpam-4577	402	24	a	a	PRON
ejpam-4577	402	25	,	,	PUNCT
ejpam-4577	402	26	set	set	VERB
ejpam-4577	402	27	tx	tx	PROPN
ejpam-4577	402	28	=	=	SYM
ejpam-4577	402	29	t	t	PROPN
ejpam-4577	402	30	.	.	PUNCT
ejpam-4577	403	1	then	then	ADV
ejpam-4577	403	2	c	c	X
ejpam-4577	403	3	=	=	PUNCT
ejpam-4577	403	4	⋃	⋃	NOUN
ejpam-4577	403	5	x∈a	x∈a	NOUN
ejpam-4577	403	6	[	[	X
ejpam-4577	403	7	{	{	PUNCT
ejpam-4577	403	8	x	x	NOUN
ejpam-4577	403	9	}	}	PUNCT
ejpam-4577	403	10	×	×	NOUN
ejpam-4577	403	11	tx	tx	PROPN
ejpam-4577	403	12	]	]	X
ejpam-4577	403	13	=	=	PUNCT
ejpam-4577	403	14	a	a	DET
ejpam-4577	403	15	×	×	PROPN
ejpam-4577	403	16	t	t	NOUN
ejpam-4577	403	17	is	be	AUX
ejpam-4577	403	18	a	a	DET
ejpam-4577	403	19	hop	hop	NOUN
ejpam-4577	403	20	independent	independent	ADJ
ejpam-4577	403	21	hop	hop	NOUN
ejpam-4577	403	22	dominating	dominating	NOUN
ejpam-4577	403	23	set	set	NOUN
ejpam-4577	403	24	of	of	ADP
ejpam-4577	403	25	g[h	g[h	PROPN
ejpam-4577	403	26	]	]	PUNCT
ejpam-4577	403	27	by	by	ADP
ejpam-4577	403	28	theorem	theorem	NOUN
ejpam-4577	403	29	16	16	NUM
ejpam-4577	403	30	.	.	PUNCT
ejpam-4577	404	1	hence	hence	ADV
ejpam-4577	404	2	,	,	PUNCT
ejpam-4577	404	3	γhih(g[h	γhih(g[h	PROPN
ejpam-4577	404	4	]	]	PUNCT
ejpam-4577	404	5	)	)	PUNCT
ejpam-4577	404	6	≤	≤	NUM
ejpam-4577	404	7	|c|	|c|	PROPN
ejpam-4577	404	8	=	=	SYM
ejpam-4577	404	9	γhih(g)cpnd(h	γhih(g)cpnd(h	NOUN
ejpam-4577	404	10	)	)	PUNCT
ejpam-4577	404	11	.	.	PUNCT
ejpam-4577	405	1	on	on	ADP
ejpam-4577	405	2	the	the	DET
ejpam-4577	405	3	other	other	ADJ
ejpam-4577	405	4	hand	hand	NOUN
ejpam-4577	405	5	,	,	PUNCT
ejpam-4577	405	6	if	if	SCONJ
ejpam-4577	405	7	c	c	NOUN
ejpam-4577	405	8	′	′	NOUN
ejpam-4577	405	9	=	=	PUNCT
ejpam-4577	405	10	⋃	⋃	PROPN
ejpam-4577	405	11	x∈a′	x∈a′	PROPN
ejpam-4577	406	1	[	[	X
ejpam-4577	406	2	{	{	PUNCT
ejpam-4577	406	3	x	x	NOUN
ejpam-4577	406	4	}	}	PUNCT
ejpam-4577	406	5	×	×	NOUN
ejpam-4577	406	6	rx	rx	NOUN
ejpam-4577	406	7	]	]	PUNCT
ejpam-4577	406	8	is	be	AUX
ejpam-4577	406	9	a	a	DET
ejpam-4577	406	10	γhih	γhih	NOUN
ejpam-4577	406	11	-	-	PUNCT
ejpam-4577	406	12	set	set	NOUN
ejpam-4577	406	13	of	of	ADP
ejpam-4577	406	14	g[h	g[h	PROPN
ejpam-4577	406	15	]	]	PUNCT
ejpam-4577	406	16	,	,	PUNCT
ejpam-4577	406	17	then	then	ADV
ejpam-4577	406	18	a′	a′	PROPN
ejpam-4577	406	19	is	be	AUX
ejpam-4577	406	20	a	a	DET
ejpam-4577	406	21	hop	hop	NOUN
ejpam-4577	406	22	independent	independent	ADJ
ejpam-4577	406	23	hop	hop	NOUN
ejpam-4577	406	24	dominating	dominating	NOUN
ejpam-4577	406	25	set	set	NOUN
ejpam-4577	406	26	of	of	ADP
ejpam-4577	406	27	g	g	PROPN
ejpam-4577	406	28	and	and	CCONJ
ejpam-4577	406	29	rx	rx	VERB
ejpam-4577	406	30	is	be	AUX
ejpam-4577	406	31	a	a	DET
ejpam-4577	406	32	clique	clique	NOUN
ejpam-4577	406	33	pointwise	pointwise	PROPN
ejpam-4577	406	34	non	non	ADJ
ejpam-4577	406	35	-	-	ADJ
ejpam-4577	406	36	dominating	dominating	ADJ
ejpam-4577	406	37	set	set	NOUN
ejpam-4577	406	38	of	of	ADP
ejpam-4577	406	39	h	h	NOUN
ejpam-4577	406	40	for	for	ADP
ejpam-4577	406	41	every	every	DET
ejpam-4577	406	42	x	x	PROPN
ejpam-4577	406	43	∈	∈	PROPN
ejpam-4577	406	44	a′	a′	NOUN
ejpam-4577	406	45	by	by	ADP
ejpam-4577	406	46	theorem	theorem	NOUN
ejpam-4577	406	47	16	16	NUM
ejpam-4577	406	48	.	.	PUNCT
ejpam-4577	407	1	hence	hence	ADV
ejpam-4577	407	2	,	,	PUNCT
ejpam-4577	407	3	γhih(g[h	γhih(g[h	PROPN
ejpam-4577	407	4	]	]	PUNCT
ejpam-4577	407	5	)	)	PUNCT
ejpam-4577	408	1	=	=	SYM
ejpam-4577	408	2	|c	|c	VERB
ejpam-4577	408	3	′|	′|	NUM
ejpam-4577	408	4	=	=	SYM
ejpam-4577	408	5	∑	∑	PUNCT
ejpam-4577	408	6	x∈a′	x∈a′	PROPN
ejpam-4577	408	7	|rx|	|rx|	PROPN
ejpam-4577	408	8	≥	≥	NUM
ejpam-4577	408	9	|a′|cpnd(h	|a′|cpnd(h	NUM
ejpam-4577	408	10	)	)	PUNCT
ejpam-4577	408	11	≥	≥	NOUN
ejpam-4577	408	12	γhih(g)cpnd(h	γhih(g)cpnd(h	NOUN
ejpam-4577	408	13	)	)	PUNCT
ejpam-4577	408	14	.	.	PUNCT
ejpam-4577	409	1	consequently	consequently	ADV
ejpam-4577	409	2	,	,	PUNCT
ejpam-4577	409	3	γhih(g[h	γhih(g[h	PROPN
ejpam-4577	409	4	]	]	PUNCT
ejpam-4577	409	5	)	)	PUNCT
ejpam-4577	409	6	=	=	SYM
ejpam-4577	409	7	γhih(g)cpnd(h	γhih(g)cpnd(h	NOUN
ejpam-4577	409	8	)	)	PUNCT
ejpam-4577	409	9	.	.	PUNCT
ejpam-4577	410	1	the	the	DET
ejpam-4577	410	2	assertions	assertion	NOUN
ejpam-4577	410	3	in	in	ADP
ejpam-4577	410	4	(	(	PUNCT
ejpam-4577	410	5	i	i	NOUN
ejpam-4577	410	6	)	)	PUNCT
ejpam-4577	410	7	,	,	PUNCT
ejpam-4577	410	8	(	(	PUNCT
ejpam-4577	410	9	ii	ii	NOUN
ejpam-4577	410	10	)	)	PUNCT
ejpam-4577	410	11	,	,	PUNCT
ejpam-4577	410	12	(	(	PUNCT
ejpam-4577	410	13	iii	iii	NOUN
ejpam-4577	410	14	)	)	PUNCT
ejpam-4577	410	15	,	,	PUNCT
ejpam-4577	410	16	(	(	PUNCT
ejpam-4577	410	17	iv	iv	X
ejpam-4577	410	18	)	)	PUNCT
ejpam-4577	410	19	and	and	CCONJ
ejpam-4577	410	20	(	(	PUNCT
ejpam-4577	410	21	v	v	NOUN
ejpam-4577	410	22	)	)	PUNCT
ejpam-4577	410	23	follow	follow	VERB
ejpam-4577	410	24	from	from	ADP
ejpam-4577	410	25	theorem	theorem	ADJ
ejpam-4577	410	26	2	2	NUM
ejpam-4577	410	27	,	,	PUNCT
ejpam-4577	410	28	corollary	corollary	ADJ
ejpam-4577	410	29	1	1	NUM
ejpam-4577	410	30	,	,	PUNCT
ejpam-4577	410	31	theorem	theorem	VERB
ejpam-4577	410	32	7	7	NUM
ejpam-4577	410	33	,	,	PUNCT
ejpam-4577	410	34	corollary	corollary	ADJ
ejpam-4577	410	35	5	5	NUM
ejpam-4577	410	36	,	,	PUNCT
ejpam-4577	410	37	and	and	CCONJ
ejpam-4577	410	38	the	the	DET
ejpam-4577	410	39	first	first	ADJ
ejpam-4577	410	40	part	part	NOUN
ejpam-4577	410	41	.	.	PUNCT
ejpam-4577	411	1	4	4	X
ejpam-4577	411	2	.	.	X
ejpam-4577	411	3	conclusion	conclusion	VERB
ejpam-4577	411	4	the	the	DET
ejpam-4577	411	5	concept	concept	NOUN
ejpam-4577	411	6	of	of	ADP
ejpam-4577	411	7	hop	hop	PROPN
ejpam-4577	411	8	independent	independent	ADJ
ejpam-4577	411	9	hop	hop	NOUN
ejpam-4577	411	10	domination	domination	NOUN
ejpam-4577	411	11	has	have	AUX
ejpam-4577	411	12	been	be	AUX
ejpam-4577	411	13	introduced	introduce	VERB
ejpam-4577	411	14	and	and	CCONJ
ejpam-4577	411	15	initially	initially	ADV
ejpam-4577	411	16	investigated	investigate	VERB
ejpam-4577	411	17	in	in	ADP
ejpam-4577	411	18	this	this	DET
ejpam-4577	411	19	study	study	NOUN
ejpam-4577	411	20	.	.	PUNCT
ejpam-4577	412	1	as	as	SCONJ
ejpam-4577	412	2	pointed	point	VERB
ejpam-4577	412	3	out	out	ADP
ejpam-4577	412	4	,	,	PUNCT
ejpam-4577	412	5	every	every	DET
ejpam-4577	412	6	graph	graph	NOUN
ejpam-4577	412	7	admits	admit	VERB
ejpam-4577	412	8	a	a	DET
ejpam-4577	412	9	hop	hop	NOUN
ejpam-4577	412	10	independent	independent	ADJ
ejpam-4577	412	11	hop	hop	NOUN
ejpam-4577	412	12	dominating	dominating	NOUN
ejpam-4577	412	13	set	set	NOUN
ejpam-4577	412	14	and	and	CCONJ
ejpam-4577	412	15	the	the	DET
ejpam-4577	412	16	hop	hop	NOUN
ejpam-4577	412	17	independent	independent	ADJ
ejpam-4577	412	18	hop	hop	NOUN
ejpam-4577	412	19	domination	domination	NOUN
ejpam-4577	412	20	number	number	NOUN
ejpam-4577	412	21	of	of	ADP
ejpam-4577	412	22	a	a	DET
ejpam-4577	412	23	graph	graph	NOUN
ejpam-4577	412	24	lies	lie	VERB
ejpam-4577	412	25	between	between	ADP
ejpam-4577	412	26	the	the	DET
ejpam-4577	412	27	hop	hop	NOUN
ejpam-4577	412	28	domination	domination	NOUN
ejpam-4577	412	29	number	number	NOUN
ejpam-4577	412	30	and	and	CCONJ
ejpam-4577	412	31	the	the	DET
ejpam-4577	412	32	hop	hop	NOUN
ejpam-4577	412	33	independence	independence	NOUN
ejpam-4577	412	34	number	number	NOUN
ejpam-4577	412	35	of	of	ADP
ejpam-4577	412	36	the	the	DET
ejpam-4577	412	37	graph	graph	NOUN
ejpam-4577	412	38	.	.	PUNCT
ejpam-4577	413	1	graphs	graph	NOUN
ejpam-4577	413	2	which	which	PRON
ejpam-4577	413	3	attained	attain	VERB
ejpam-4577	413	4	some	some	DET
ejpam-4577	413	5	specific	specific	ADJ
ejpam-4577	413	6	values	value	NOUN
ejpam-4577	413	7	for	for	ADP
ejpam-4577	413	8	their	their	PRON
ejpam-4577	413	9	hop	hop	NOUN
ejpam-4577	413	10	independent	independent	ADJ
ejpam-4577	413	11	hop	hop	NOUN
ejpam-4577	413	12	domination	domination	NOUN
ejpam-4577	413	13	number	number	NOUN
ejpam-4577	413	14	have	have	AUX
ejpam-4577	413	15	been	be	AUX
ejpam-4577	413	16	characterized	characterize	VERB
ejpam-4577	413	17	.	.	PUNCT
ejpam-4577	414	1	necessary	necessary	ADJ
ejpam-4577	414	2	and	and	CCONJ
ejpam-4577	414	3	sufficient	sufficient	ADJ
ejpam-4577	414	4	conditions	condition	NOUN
ejpam-4577	414	5	for	for	ADP
ejpam-4577	414	6	a	a	DET
ejpam-4577	414	7	subset	subset	NOUN
ejpam-4577	414	8	in	in	ADP
ejpam-4577	414	9	the	the	DET
ejpam-4577	414	10	shadow	shadow	NOUN
ejpam-4577	414	11	graph	graph	NOUN
ejpam-4577	414	12	,	,	PUNCT
ejpam-4577	414	13	join	join	NOUN
ejpam-4577	414	14	,	,	PUNCT
ejpam-4577	414	15	corona	corona	PROPN
ejpam-4577	414	16	,	,	PUNCT
ejpam-4577	414	17	and	and	CCONJ
ejpam-4577	414	18	lexicographic	lexicographic	ADJ
ejpam-4577	414	19	product	product	NOUN
ejpam-4577	414	20	of	of	ADP
ejpam-4577	414	21	two	two	NUM
ejpam-4577	414	22	graphs	graph	NOUN
ejpam-4577	414	23	have	have	AUX
ejpam-4577	414	24	been	be	AUX
ejpam-4577	414	25	obtained	obtain	VERB
ejpam-4577	414	26	.	.	PUNCT
ejpam-4577	415	1	these	these	DET
ejpam-4577	415	2	characterizations	characterization	NOUN
ejpam-4577	415	3	have	have	AUX
ejpam-4577	415	4	been	be	AUX
ejpam-4577	415	5	used	use	VERB
ejpam-4577	415	6	to	to	PART
ejpam-4577	415	7	obtain	obtain	VERB
ejpam-4577	415	8	bounds	bound	NOUN
ejpam-4577	415	9	or	or	CCONJ
ejpam-4577	415	10	exact	exact	ADJ
ejpam-4577	415	11	value	value	NOUN
ejpam-4577	415	12	of	of	ADP
ejpam-4577	415	13	the	the	DET
ejpam-4577	415	14	hop	hop	NOUN
ejpam-4577	415	15	independent	independent	ADJ
ejpam-4577	415	16	hop	hop	NOUN
ejpam-4577	415	17	domination	domination	NOUN
ejpam-4577	415	18	number	number	NOUN
ejpam-4577	415	19	of	of	ADP
ejpam-4577	415	20	each	each	PRON
ejpam-4577	415	21	of	of	ADP
ejpam-4577	415	22	these	these	DET
ejpam-4577	415	23	graphs	graph	NOUN
ejpam-4577	415	24	.	.	PUNCT
ejpam-4577	416	1	it	it	PRON
ejpam-4577	416	2	may	may	AUX
ejpam-4577	416	3	be	be	AUX
ejpam-4577	416	4	interesting	interesting	ADJ
ejpam-4577	416	5	to	to	PART
ejpam-4577	416	6	find	find	VERB
ejpam-4577	416	7	bounds	bound	NOUN
ejpam-4577	416	8	for	for	ADP
ejpam-4577	416	9	this	this	DET
ejpam-4577	416	10	newly	newly	ADV
ejpam-4577	416	11	defined	define	VERB
ejpam-4577	416	12	parameter	parameter	NOUN
ejpam-4577	416	13	in	in	ADP
ejpam-4577	416	14	terms	term	NOUN
ejpam-4577	416	15	of	of	ADP
ejpam-4577	416	16	other	other	ADJ
ejpam-4577	416	17	known	know	VERB
ejpam-4577	416	18	parameters	parameter	NOUN
ejpam-4577	416	19	,	,	PUNCT
ejpam-4577	416	20	investigate	investigate	VERB
ejpam-4577	416	21	the	the	DET
ejpam-4577	416	22	concept	concept	NOUN
ejpam-4577	416	23	for	for	ADP
ejpam-4577	416	24	trees	tree	NOUN
ejpam-4577	416	25	and	and	CCONJ
ejpam-4577	416	26	other	other	ADJ
ejpam-4577	416	27	interesting	interesting	ADJ
ejpam-4577	416	28	graphs	graph	NOUN
ejpam-4577	416	29	,	,	PUNCT
ejpam-4577	416	30	and	and	CCONJ
ejpam-4577	416	31	determine	determine	VERB
ejpam-4577	416	32	the	the	DET
ejpam-4577	416	33	complexity	complexity	NOUN
ejpam-4577	416	34	of	of	ADP
ejpam-4577	416	35	the	the	DET
ejpam-4577	416	36	hop	hop	NOUN
ejpam-4577	416	37	independent	independent	ADJ
ejpam-4577	416	38	hop	hop	PROPN
ejpam-4577	416	39	domination	domination	PROPN
ejpam-4577	416	40	problem	problem	NOUN
ejpam-4577	416	41	.	.	PUNCT
ejpam-4577	417	1	references	reference	NOUN
ejpam-4577	417	2	1796	1796	NUM
ejpam-4577	417	3	acknowledgements	acknowledgement	NOUN
ejpam-4577	417	4	the	the	DET
ejpam-4577	417	5	authors	author	NOUN
ejpam-4577	417	6	would	would	AUX
ejpam-4577	417	7	like	like	VERB
ejpam-4577	417	8	to	to	PART
ejpam-4577	417	9	thank	thank	VERB
ejpam-4577	417	10	the	the	DET
ejpam-4577	417	11	department	department	NOUN
ejpam-4577	417	12	of	of	ADP
ejpam-4577	417	13	science	science	NOUN
ejpam-4577	417	14	and	and	CCONJ
ejpam-4577	417	15	technology	technology	NOUN
ejpam-4577	417	16	accelerated	accelerate	VERB
ejpam-4577	417	17	science	science	NOUN
ejpam-4577	417	18	and	and	CCONJ
ejpam-4577	417	19	technology	technology	NOUN
ejpam-4577	417	20	human	human	ADJ
ejpam-4577	417	21	resource	resource	NOUN
ejpam-4577	417	22	development	development	NOUN
ejpam-4577	417	23	program	program	NOUN
ejpam-4577	417	24	(	(	PUNCT
ejpam-4577	417	25	dost	dost	NOUN
ejpam-4577	417	26	-	-	PUNCT
ejpam-4577	417	27	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-4577	417	28	and	and	CCONJ
ejpam-4577	417	29	msu	msu	PROPN
ejpam-4577	417	30	-	-	PUNCT
ejpam-4577	417	31	iligan	iligan	PROPN
ejpam-4577	417	32	institute	institute	PROPN
ejpam-4577	417	33	of	of	ADP
ejpam-4577	417	34	technology	technology	NOUN
ejpam-4577	417	35	for	for	ADP
ejpam-4577	417	36	funding	fund	VERB
ejpam-4577	417	37	this	this	DET
ejpam-4577	417	38	research	research	NOUN
ejpam-4577	417	39	.	.	PUNCT
ejpam-4577	418	1	references	reference	NOUN
ejpam-4577	418	2	[	[	X
ejpam-4577	418	3	1	1	NUM
ejpam-4577	418	4	]	]	PUNCT
ejpam-4577	418	5	s.	s.	PROPN
ejpam-4577	418	6	ayyaswamy	ayyaswamy	PROPN
ejpam-4577	418	7	,	,	PUNCT
ejpam-4577	418	8	b.	b.	PROPN
ejpam-4577	418	9	krishnakumari	krishnakumari	PROPN
ejpam-4577	418	10	,	,	PUNCT
ejpam-4577	418	11	b.	b.	PROPN
ejpam-4577	418	12	natarjan	natarjan	PROPN
ejpam-4577	418	13	,	,	PUNCT
ejpam-4577	418	14	and	and	CCONJ
ejpam-4577	418	15	y.	y.	PROPN
ejpam-4577	418	16	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4577	418	17	.	.	PUNCT
ejpam-4577	419	1	bounds	bound	NOUN
ejpam-4577	419	2	on	on	ADP
ejpam-4577	419	3	the	the	DET
ejpam-4577	419	4	hop	hop	NOUN
ejpam-4577	419	5	domination	domination	NOUN
ejpam-4577	419	6	number	number	NOUN
ejpam-4577	419	7	of	of	ADP
ejpam-4577	419	8	a	a	DET
ejpam-4577	419	9	tree	tree	NOUN
ejpam-4577	419	10	.	.	PUNCT
ejpam-4577	420	1	proceedings	proceeding	NOUN
ejpam-4577	420	2	-	-	PUNCT
ejpam-4577	420	3	mathematical	mathematical	ADJ
ejpam-4577	420	4	sciences	science	NOUN
ejpam-4577	420	5	.	.	PUNCT
ejpam-4577	420	6	,	,	PUNCT
ejpam-4577	420	7	125(4):449–455	125(4):449–455	ADP
ejpam-4577	420	8	,	,	PUNCT
ejpam-4577	420	9	2015	2015	NUM
ejpam-4577	420	10	.	.	PUNCT
ejpam-4577	421	1	[	[	X
ejpam-4577	421	2	2	2	NUM
ejpam-4577	421	3	]	]	PUNCT
ejpam-4577	421	4	s.	s.	PROPN
ejpam-4577	421	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4577	421	6	,	,	PUNCT
ejpam-4577	421	7	c.	c.	PROPN
ejpam-4577	421	8	natarajan	natarajan	PROPN
ejpam-4577	421	9	,	,	PUNCT
ejpam-4577	421	10	and	and	CCONJ
ejpam-4577	421	11	g.	g.	PROPN
ejpam-4577	421	12	sathiamoorphy	sathiamoorphy	PROPN
ejpam-4577	421	13	.	.	PUNCT
ejpam-4577	422	1	a	a	DET
ejpam-4577	422	2	note	note	NOUN
ejpam-4577	422	3	on	on	ADP
ejpam-4577	422	4	hop	hop	NOUN
ejpam-4577	422	5	domination	domination	NOUN
ejpam-4577	422	6	number	number	NOUN
ejpam-4577	422	7	of	of	ADP
ejpam-4577	422	8	some	some	DET
ejpam-4577	422	9	special	special	ADJ
ejpam-4577	422	10	families	family	NOUN
ejpam-4577	422	11	of	of	ADP
ejpam-4577	422	12	graphs	graph	NOUN
ejpam-4577	422	13	.	.	PUNCT
ejpam-4577	423	1	international	international	ADJ
ejpam-4577	423	2	journal	journal	NOUN
ejpam-4577	423	3	of	of	ADP
ejpam-4577	423	4	pure	pure	ADJ
ejpam-4577	423	5	and	and	CCONJ
ejpam-4577	423	6	applied	applied	ADJ
ejpam-4577	423	7	mathematics	mathematic	NOUN
ejpam-4577	423	8	.	.	PUNCT
ejpam-4577	423	9	,	,	PUNCT
ejpam-4577	423	10	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-4577	423	11	,	,	PUNCT
ejpam-4577	423	12	2018	2018	NUM
ejpam-4577	423	13	.	.	PUNCT
ejpam-4577	424	1	[	[	X
ejpam-4577	424	2	3	3	X
ejpam-4577	424	3	]	]	PUNCT
ejpam-4577	424	4	j.	j.	PROPN
ejpam-4577	424	5	hassan	hassan	PROPN
ejpam-4577	424	6	,	,	PUNCT
ejpam-4577	424	7	s.	s.	PROPN
ejpam-4577	424	8	canoy	canoy	PROPN
ejpam-4577	424	9	jr	jr	PROPN
ejpam-4577	424	10	.	.	PROPN
ejpam-4577	424	11	,	,	PUNCT
ejpam-4577	424	12	and	and	CCONJ
ejpam-4577	424	13	a.	a.	PROPN
ejpam-4577	424	14	aradais	aradais	PROPN
ejpam-4577	424	15	.	.	PUNCT
ejpam-4577	425	1	hop	hop	PROPN
ejpam-4577	425	2	independent	independent	ADJ
ejpam-4577	425	3	sets	set	NOUN
ejpam-4577	425	4	in	in	ADP
ejpam-4577	425	5	graphs	graph	NOUN
ejpam-4577	425	6	.	.	PUNCT
ejpam-4577	426	1	eur	eur	PROPN
ejpam-4577	426	2	.	.	PUNCT
ejpam-4577	427	1	j.	j.	PROPN
ejpam-4577	427	2	pure	pure	PROPN
ejpam-4577	427	3	appl	appl	PROPN
ejpam-4577	427	4	.	.	PUNCT
ejpam-4577	427	5	math	math	PROPN
ejpam-4577	427	6	.	.	PUNCT
ejpam-4577	427	7	,	,	PUNCT
ejpam-4577	427	8	15(2):467–477	15(2):467–477	PROPN
ejpam-4577	427	9	,	,	PUNCT
ejpam-4577	427	10	2022	2022	NUM
ejpam-4577	427	11	.	.	PUNCT
ejpam-4577	428	1	[	[	X
ejpam-4577	428	2	4	4	NUM
ejpam-4577	428	3	]	]	X
ejpam-4577	428	4	m.	m.	NOUN
ejpam-4577	428	5	henning	henning	PROPN
ejpam-4577	428	6	and	and	CCONJ
ejpam-4577	428	7	n.	n.	PROPN
ejpam-4577	428	8	rad	rad	PROPN
ejpam-4577	428	9	.	.	PROPN
ejpam-4577	429	1	on	on	ADP
ejpam-4577	429	2	2	2	NUM
ejpam-4577	429	3	-	-	PUNCT
ejpam-4577	429	4	step	step	NOUN
ejpam-4577	429	5	and	and	CCONJ
ejpam-4577	429	6	hop	hop	NOUN
ejpam-4577	429	7	dominating	dominating	NOUN
ejpam-4577	429	8	sets	set	NOUN
ejpam-4577	429	9	in	in	ADP
ejpam-4577	429	10	graphs	graph	NOUN
ejpam-4577	429	11	.	.	PUNCT
ejpam-4577	430	1	graphs	graph	NOUN
ejpam-4577	430	2	and	and	CCONJ
ejpam-4577	430	3	combinatorics	combinatoric	NOUN
ejpam-4577	430	4	.	.	PUNCT
ejpam-4577	430	5	,	,	PUNCT
ejpam-4577	430	6	33(4):913–927	33(4):913–927	PROPN
ejpam-4577	430	7	,	,	PUNCT
ejpam-4577	430	8	2017	2017	NUM
ejpam-4577	430	9	.	.	PUNCT
ejpam-4577	431	1	[	[	X
ejpam-4577	431	2	5	5	X
ejpam-4577	431	3	]	]	PUNCT
ejpam-4577	431	4	s.	s.	PROPN
ejpam-4577	431	5	canoy	canoy	PROPN
ejpam-4577	431	6	jr	jr	PROPN
ejpam-4577	431	7	.	.	PROPN
ejpam-4577	431	8	and	and	CCONJ
ejpam-4577	431	9	g.	g.	PROPN
ejpam-4577	431	10	malacas	malacas	PROPN
ejpam-4577	431	11	.	.	PUNCT
ejpam-4577	432	1	determining	determine	VERB
ejpam-4577	432	2	the	the	DET
ejpam-4577	432	3	intruder	intruder	NOUN
ejpam-4577	432	4	’s	’s	PART
ejpam-4577	432	5	location	location	NOUN
ejpam-4577	432	6	in	in	ADP
ejpam-4577	432	7	a	a	DET
ejpam-4577	432	8	given	give	VERB
ejpam-4577	432	9	network	network	NOUN
ejpam-4577	432	10	:	:	PUNCT
ejpam-4577	432	11	locating	locate	VERB
ejpam-4577	432	12	-	-	PUNCT
ejpam-4577	432	13	dominating	dominating	NOUN
ejpam-4577	432	14	sets	set	NOUN
ejpam-4577	432	15	in	in	ADP
ejpam-4577	432	16	a	a	DET
ejpam-4577	432	17	graph	graph	NOUN
ejpam-4577	432	18	.	.	PUNCT
ejpam-4577	433	1	nrcp	nrcp	PROPN
ejpam-4577	433	2	research	research	PROPN
ejpam-4577	433	3	journal	journal	PROPN
ejpam-4577	433	4	.	.	PUNCT
ejpam-4577	433	5	,	,	PUNCT
ejpam-4577	433	6	13(1):1–8	13(1):1–8	NUM
ejpam-4577	433	7	,	,	PUNCT
ejpam-4577	433	8	2013	2013	NUM
ejpam-4577	433	9	.	.	PUNCT
ejpam-4577	434	1	[	[	X
ejpam-4577	434	2	6	6	X
ejpam-4577	434	3	]	]	PUNCT
ejpam-4577	434	4	s.	s.	PROPN
ejpam-4577	434	5	canoy	canoy	PROPN
ejpam-4577	434	6	jr	jr	PROPN
ejpam-4577	434	7	.	.	PROPN
ejpam-4577	434	8	and	and	CCONJ
ejpam-4577	434	9	g.	g.	PROPN
ejpam-4577	434	10	malacas	malacas	PROPN
ejpam-4577	434	11	.	.	PUNCT
ejpam-4577	435	1	differentiating	differentiate	VERB
ejpam-4577	435	2	-	-	PUNCT
ejpam-4577	435	3	dominating	dominating	NOUN
ejpam-4577	435	4	sets	set	NOUN
ejpam-4577	435	5	in	in	ADP
ejpam-4577	435	6	graphs	graph	NOUN
ejpam-4577	435	7	under	under	ADP
ejpam-4577	435	8	binary	binary	ADJ
ejpam-4577	435	9	operations	operation	NOUN
ejpam-4577	435	10	.	.	PUNCT
ejpam-4577	436	1	tamkang	tamkang	PROPN
ejpam-4577	436	2	j.	j.	PROPN
ejpam-4577	436	3	math	math	PROPN
ejpam-4577	436	4	.	.	PUNCT
ejpam-4577	436	5	,	,	PUNCT
ejpam-4577	436	6	46(1):51–60	46(1):51–60	NOUN
ejpam-4577	436	7	,	,	PUNCT
ejpam-4577	436	8	2015	2015	NUM
ejpam-4577	436	9	.	.	PUNCT
ejpam-4577	437	1	[	[	X
ejpam-4577	437	2	7	7	X
ejpam-4577	437	3	]	]	X
ejpam-4577	437	4	s.	s.	PROPN
ejpam-4577	437	5	canoy	canoy	PROPN
ejpam-4577	437	6	jr	jr	PROPN
ejpam-4577	437	7	.	.	PROPN
ejpam-4577	437	8	,	,	PUNCT
ejpam-4577	437	9	r.	r.	PROPN
ejpam-4577	437	10	mollejon	mollejon	NOUN
ejpam-4577	437	11	,	,	PUNCT
ejpam-4577	437	12	and	and	CCONJ
ejpam-4577	437	13	j.	j.	PROPN
ejpam-4577	437	14	g.	g.	PROPN
ejpam-4577	437	15	canoy	canoy	PROPN
ejpam-4577	437	16	.	.	PUNCT
ejpam-4577	438	1	hop	hop	PROPN
ejpam-4577	438	2	dominating	dominating	NOUN
ejpam-4577	438	3	sets	set	NOUN
ejpam-4577	438	4	in	in	ADP
ejpam-4577	438	5	graphs	graph	NOUN
ejpam-4577	438	6	under	under	ADP
ejpam-4577	438	7	binary	binary	ADJ
ejpam-4577	438	8	operations	operation	NOUN
ejpam-4577	438	9	.	.	PUNCT
ejpam-4577	439	1	eur	eur	PROPN
ejpam-4577	439	2	.	.	PUNCT
ejpam-4577	440	1	j.	j.	PROPN
ejpam-4577	440	2	pure	pure	PROPN
ejpam-4577	440	3	appl	appl	PROPN
ejpam-4577	440	4	.	.	PUNCT
ejpam-4577	440	5	math	math	PROPN
ejpam-4577	440	6	.	.	PUNCT
ejpam-4577	440	7	,	,	PUNCT
ejpam-4577	441	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4577	441	2	,	,	PUNCT
ejpam-4577	441	3	2019	2019	NUM
ejpam-4577	441	4	.	.	PUNCT
ejpam-4577	442	1	[	[	X
ejpam-4577	442	2	8	8	X
ejpam-4577	442	3	]	]	X
ejpam-4577	442	4	s.	s.	PROPN
ejpam-4577	442	5	canoy	canoy	PROPN
ejpam-4577	442	6	jr	jr	PROPN
ejpam-4577	442	7	.	.	PROPN
ejpam-4577	442	8	and	and	CCONJ
ejpam-4577	442	9	g.	g.	PROPN
ejpam-4577	442	10	salasalan	salasalan	NOUN
ejpam-4577	442	11	.	.	PUNCT
ejpam-4577	443	1	revisiting	revisit	VERB
ejpam-4577	443	2	domination	domination	NOUN
ejpam-4577	443	3	,	,	PUNCT
ejpam-4577	443	4	hop	hop	NOUN
ejpam-4577	443	5	domination	domination	NOUN
ejpam-4577	443	6	,	,	PUNCT
ejpam-4577	443	7	and	and	CCONJ
ejpam-4577	443	8	global	global	ADJ
ejpam-4577	443	9	hop	hop	NOUN
ejpam-4577	443	10	domination	domination	NOUN
ejpam-4577	443	11	in	in	ADP
ejpam-4577	443	12	graphs	graph	NOUN
ejpam-4577	443	13	.	.	PUNCT
ejpam-4577	444	1	eur	eur	PROPN
ejpam-4577	444	2	.	.	PUNCT
ejpam-4577	445	1	j.	j.	PROPN
ejpam-4577	445	2	pure	pure	PROPN
ejpam-4577	445	3	appl	appl	PROPN
ejpam-4577	445	4	.	.	PUNCT
ejpam-4577	445	5	math	math	PROPN
ejpam-4577	445	6	.	.	PUNCT
ejpam-4577	445	7	,	,	PUNCT
ejpam-4577	445	8	14:1415–1428	14:1415–1428	NUM
ejpam-4577	445	9	,	,	PUNCT
ejpam-4577	445	10	2021	2021	NUM
ejpam-4577	445	11	.	.	PUNCT
ejpam-4577	446	1	[	[	X
ejpam-4577	446	2	9	9	NUM
ejpam-4577	446	3	]	]	PUNCT
ejpam-4577	446	4	s.	s.	PROPN
ejpam-4577	446	5	canoy	canoy	PROPN
ejpam-4577	446	6	jr	jr	PROPN
ejpam-4577	446	7	.	.	PROPN
ejpam-4577	446	8	and	and	CCONJ
ejpam-4577	446	9	g.	g.	PROPN
ejpam-4577	446	10	salasalan	salasalan	NOUN
ejpam-4577	446	11	.	.	PUNCT
ejpam-4577	447	1	locating	locate	VERB
ejpam-4577	447	2	-	-	PUNCT
ejpam-4577	447	3	hop	hop	NOUN
ejpam-4577	447	4	domination	domination	NOUN
ejpam-4577	447	5	in	in	ADP
ejpam-4577	447	6	graphs	graph	NOUN
ejpam-4577	447	7	.	.	PUNCT
ejpam-4577	448	1	kyungpook	kyungpook	PROPN
ejpam-4577	448	2	mathematical	mathematical	PROPN
ejpam-4577	448	3	journal	journal	PROPN
ejpam-4577	448	4	.	.	PUNCT
ejpam-4577	448	5	,	,	PUNCT
ejpam-4577	448	6	62:193–204	62:193–204	NUM
ejpam-4577	448	7	,	,	PUNCT
ejpam-4577	448	8	2022	2022	NUM
ejpam-4577	448	9	.	.	PUNCT
ejpam-4577	449	1	[	[	X
ejpam-4577	449	2	10	10	NUM
ejpam-4577	449	3	]	]	X
ejpam-4577	449	4	c.	c.	PROPN
ejpam-4577	449	5	natarajan	natarajan	PROPN
ejpam-4577	449	6	and	and	CCONJ
ejpam-4577	449	7	s.	s.	PROPN
ejpam-4577	449	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4577	449	9	.	.	PUNCT
ejpam-4577	450	1	hop	hop	PROPN
ejpam-4577	450	2	domination	domination	NOUN
ejpam-4577	450	3	in	in	ADP
ejpam-4577	450	4	graphs	graphs	PROPN
ejpam-4577	450	5	ii	ii	PROPN
ejpam-4577	450	6	.	.	PUNCT
ejpam-4577	450	7	versita	versita	PROPN
ejpam-4577	450	8	,	,	PUNCT
ejpam-4577	450	9	23(2):187	23(2):187	NUM
ejpam-4577	450	10	–	–	PUNCT
ejpam-4577	450	11	199	199	NUM
ejpam-4577	450	12	,	,	PUNCT
ejpam-4577	450	13	2015	2015	NUM
ejpam-4577	450	14	.	.	PUNCT
ejpam-4577	451	1	[	[	X
ejpam-4577	451	2	11	11	NUM
ejpam-4577	451	3	]	]	X
ejpam-4577	451	4	g.	g.	NOUN
ejpam-4577	451	5	salasalan	salasalan	NOUN
ejpam-4577	451	6	and	and	CCONJ
ejpam-4577	451	7	s.	s.	PROPN
ejpam-4577	451	8	canoy	canoy	PROPN
ejpam-4577	451	9	jr	jr	PROPN
ejpam-4577	451	10	.	.	PROPN
ejpam-4577	451	11	global	global	PROPN
ejpam-4577	451	12	hop	hop	PROPN
ejpam-4577	451	13	domination	domination	PROPN
ejpam-4577	451	14	numbers	number	NOUN
ejpam-4577	451	15	of	of	ADP
ejpam-4577	451	16	graphs	graph	NOUN
ejpam-4577	451	17	.	.	PUNCT
ejpam-4577	452	1	eur	eur	PROPN
ejpam-4577	452	2	.	.	PUNCT
ejpam-4577	453	1	j.	j.	PROPN
ejpam-4577	453	2	pure	pure	PROPN
ejpam-4577	453	3	appl	appl	PROPN
ejpam-4577	453	4	.	.	PUNCT
ejpam-4577	453	5	math	math	PROPN
ejpam-4577	453	6	.	.	PUNCT
ejpam-4577	453	7	,	,	PUNCT
ejpam-4577	453	8	14(1):112–125	14(1):112–125	NUM
ejpam-4577	453	9	,	,	PUNCT
ejpam-4577	453	10	2021	2021	NUM
ejpam-4577	453	11	.	.	PUNCT