id	sid	tid	token	lemma	pos
ejpam-4760	1	1	european	european	PROPN
ejpam-4760	1	2	journal	journal	PROPN
ejpam-4760	1	3	of	of	ADP
ejpam-4760	1	4	pure	pure	ADJ
ejpam-4760	1	5	and	and	CCONJ
ejpam-4760	1	6	applied	apply	VERB
ejpam-4760	1	7	mathematics	mathematic	NOUN
ejpam-4760	1	8	vol	vol	NOUN
ejpam-4760	1	9	.	.	PUNCT
ejpam-4760	2	1	16	16	NUM
ejpam-4760	2	2	,	,	PUNCT
ejpam-4760	2	3	no	no	INTJ
ejpam-4760	2	4	.	.	NOUN
ejpam-4760	2	5	2	2	NUM
ejpam-4760	2	6	,	,	PUNCT
ejpam-4760	2	7	2023	2023	NUM
ejpam-4760	2	8	,	,	PUNCT
ejpam-4760	2	9	1326	1326	NUM
ejpam-4760	2	10	-	-	SYM
ejpam-4760	2	11	1341	1341	NUM
ejpam-4760	2	12	issn	issn	PROPN
ejpam-4760	2	13	1307	1307	NUM
ejpam-4760	2	14	-	-	SYM
ejpam-4760	2	15	5543	5543	NUM
ejpam-4760	2	16	–	–	PUNCT
ejpam-4760	2	17	ejpam.com	ejpam.com	X
ejpam-4760	2	18	published	publish	VERB
ejpam-4760	2	19	by	by	ADP
ejpam-4760	2	20	new	new	PROPN
ejpam-4760	2	21	york	york	PROPN
ejpam-4760	2	22	business	business	PROPN
ejpam-4760	2	23	global	global	PROPN
ejpam-4760	2	24	perfect	perfect	PROPN
ejpam-4760	2	25	isolate	isolate	NOUN
ejpam-4760	2	26	domination	domination	NOUN
ejpam-4760	2	27	in	in	ADP
ejpam-4760	2	28	graphs	graph	NOUN
ejpam-4760	2	29	cris	cris	PROPN
ejpam-4760	2	30	l.	l.	PROPN
ejpam-4760	2	31	armada1,3,∗	armada1,3,∗	PROPN
ejpam-4760	2	32	,	,	PUNCT
ejpam-4760	2	33	jamil	jamil	PROPN
ejpam-4760	2	34	j.	j.	PROPN
ejpam-4760	2	35	hamja2	hamja2	PROPN
ejpam-4760	2	36	1	1	NUM
ejpam-4760	2	37	mathematics	mathematics	PROPN
ejpam-4760	2	38	department	department	NOUN
ejpam-4760	2	39	,	,	PUNCT
ejpam-4760	2	40	college	college	NOUN
ejpam-4760	2	41	of	of	ADP
ejpam-4760	2	42	arts	art	NOUN
ejpam-4760	2	43	and	and	CCONJ
ejpam-4760	2	44	sciences	science	NOUN
ejpam-4760	2	45	,	,	PUNCT
ejpam-4760	2	46	cebu	cebu	NOUN
ejpam-4760	2	47	normal	normal	ADJ
ejpam-4760	2	48	university	university	NOUN
ejpam-4760	2	49	,	,	PUNCT
ejpam-4760	2	50	cebu	cebu	NOUN
ejpam-4760	2	51	city	city	NOUN
ejpam-4760	2	52	,	,	PUNCT
ejpam-4760	2	53	philippines	philippine	NOUN
ejpam-4760	2	54	2	2	NUM
ejpam-4760	2	55	office	office	NOUN
ejpam-4760	2	56	of	of	ADP
ejpam-4760	2	57	the	the	DET
ejpam-4760	2	58	vice	vice	NOUN
ejpam-4760	2	59	chancellor	chancellor	NOUN
ejpam-4760	2	60	for	for	ADP
ejpam-4760	2	61	academic	academic	ADJ
ejpam-4760	2	62	affairs	affair	NOUN
ejpam-4760	2	63	,	,	PUNCT
ejpam-4760	2	64	msu	msu	PROPN
ejpam-4760	2	65	-	-	PUNCT
ejpam-4760	2	66	tawi	tawi	NOUN
ejpam-4760	2	67	-	-	PUNCT
ejpam-4760	2	68	tawi	tawi	NOUN
ejpam-4760	2	69	college	college	PROPN
ejpam-4760	2	70	of	of	ADP
ejpam-4760	2	71	technology	technology	NOUN
ejpam-4760	2	72	and	and	CCONJ
ejpam-4760	2	73	oceanography	oceanography	NOUN
ejpam-4760	2	74	,	,	PUNCT
ejpam-4760	2	75	7500	7500	NUM
ejpam-4760	2	76	tawi	tawi	NOUN
ejpam-4760	2	77	-	-	PUNCT
ejpam-4760	2	78	tawi	tawi	NOUN
ejpam-4760	2	79	,	,	PUNCT
ejpam-4760	2	80	philippines	philippine	NOUN
ejpam-4760	2	81	3	3	NUM
ejpam-4760	2	82	center	center	NOUN
ejpam-4760	2	83	for	for	ADP
ejpam-4760	2	84	research	research	NOUN
ejpam-4760	2	85	and	and	CCONJ
ejpam-4760	2	86	development	development	NOUN
ejpam-4760	2	87	,	,	PUNCT
ejpam-4760	2	88	cebu	cebu	NOUN
ejpam-4760	2	89	normal	normal	ADJ
ejpam-4760	2	90	university	university	NOUN
ejpam-4760	2	91	,	,	PUNCT
ejpam-4760	2	92	cebu	cebu	NOUN
ejpam-4760	2	93	city	city	NOUN
ejpam-4760	2	94	,	,	PUNCT
ejpam-4760	3	1	philippines	philippine	NOUN
ejpam-4760	3	2	abstract	abstract	ADJ
ejpam-4760	3	3	.	.	PUNCT
ejpam-4760	4	1	let	let	VERB
ejpam-4760	4	2	g	g	PROPN
ejpam-4760	4	3	=	=	SYM
ejpam-4760	4	4	(	(	PUNCT
ejpam-4760	4	5	v	v	NOUN
ejpam-4760	4	6	(	(	PUNCT
ejpam-4760	4	7	g	g	NOUN
ejpam-4760	4	8	)	)	PUNCT
ejpam-4760	4	9	,	,	PUNCT
ejpam-4760	4	10	e(g	e(g	PROPN
ejpam-4760	4	11	)	)	PUNCT
ejpam-4760	4	12	)	)	PUNCT
ejpam-4760	5	1	be	be	AUX
ejpam-4760	5	2	a	a	DET
ejpam-4760	5	3	simple	simple	ADJ
ejpam-4760	5	4	connected	connected	ADJ
ejpam-4760	5	5	graph	graph	NOUN
ejpam-4760	5	6	.	.	PUNCT
ejpam-4760	6	1	a	a	DET
ejpam-4760	6	2	set	set	NOUN
ejpam-4760	6	3	s	s	NOUN
ejpam-4760	6	4	⊆	⊆	NUM
ejpam-4760	6	5	v	v	NOUN
ejpam-4760	6	6	(	(	PUNCT
ejpam-4760	6	7	g	g	NOUN
ejpam-4760	6	8	)	)	PUNCT
ejpam-4760	6	9	is	be	AUX
ejpam-4760	6	10	said	say	VERB
ejpam-4760	6	11	to	to	PART
ejpam-4760	6	12	be	be	AUX
ejpam-4760	6	13	a	a	DET
ejpam-4760	6	14	perfect	perfect	ADJ
ejpam-4760	6	15	isolate	isolate	NOUN
ejpam-4760	6	16	dominating	dominating	NOUN
ejpam-4760	6	17	set	set	NOUN
ejpam-4760	6	18	of	of	ADP
ejpam-4760	6	19	g	g	PROPN
ejpam-4760	6	20	if	if	SCONJ
ejpam-4760	6	21	s	s	VERB
ejpam-4760	6	22	is	be	AUX
ejpam-4760	6	23	a	a	DET
ejpam-4760	6	24	perfect	perfect	ADJ
ejpam-4760	6	25	dominating	dominating	NOUN
ejpam-4760	6	26	set	set	NOUN
ejpam-4760	6	27	and	and	CCONJ
ejpam-4760	6	28	an	an	DET
ejpam-4760	6	29	isolate	isolate	NOUN
ejpam-4760	6	30	dominating	dominating	NOUN
ejpam-4760	6	31	set	set	NOUN
ejpam-4760	6	32	of	of	ADP
ejpam-4760	6	33	g.	g.	PROPN
ejpam-4760	6	34	the	the	DET
ejpam-4760	6	35	minimum	minimum	ADJ
ejpam-4760	6	36	cardinality	cardinality	NOUN
ejpam-4760	6	37	of	of	ADP
ejpam-4760	6	38	a	a	DET
ejpam-4760	6	39	perfect	perfect	ADJ
ejpam-4760	6	40	isolate	isolate	NOUN
ejpam-4760	6	41	dominating	dominating	NOUN
ejpam-4760	6	42	set	set	NOUN
ejpam-4760	6	43	of	of	ADP
ejpam-4760	6	44	g	g	PROPN
ejpam-4760	6	45	is	be	AUX
ejpam-4760	6	46	called	call	VERB
ejpam-4760	6	47	perfect	perfect	ADJ
ejpam-4760	6	48	isolate	isolate	NOUN
ejpam-4760	6	49	domination	domination	NOUN
ejpam-4760	6	50	number	number	NOUN
ejpam-4760	6	51	,	,	PUNCT
ejpam-4760	6	52	and	and	CCONJ
ejpam-4760	6	53	is	be	AUX
ejpam-4760	6	54	denoted	denote	VERB
ejpam-4760	6	55	by	by	ADP
ejpam-4760	6	56	γp0(g	γp0(g	NOUN
ejpam-4760	6	57	)	)	PUNCT
ejpam-4760	6	58	.	.	PUNCT
ejpam-4760	7	1	a	a	DET
ejpam-4760	7	2	perfect	perfect	ADJ
ejpam-4760	7	3	isolate	isolate	NOUN
ejpam-4760	7	4	dominating	dominate	VERB
ejpam-4760	7	5	set	set	NOUN
ejpam-4760	7	6	s	s	NOUN
ejpam-4760	7	7	with	with	ADP
ejpam-4760	7	8	|s|	|s|	PROPN
ejpam-4760	7	9	=	=	SYM
ejpam-4760	7	10	γp0(g	γp0(g	NOUN
ejpam-4760	7	11	)	)	PUNCT
ejpam-4760	7	12	is	be	AUX
ejpam-4760	7	13	said	say	VERB
ejpam-4760	7	14	to	to	PART
ejpam-4760	7	15	be	be	AUX
ejpam-4760	7	16	γp0	γp0	NOUN
ejpam-4760	7	17	-	-	PUNCT
ejpam-4760	7	18	set	set	NOUN
ejpam-4760	7	19	.	.	PUNCT
ejpam-4760	8	1	in	in	ADP
ejpam-4760	8	2	this	this	DET
ejpam-4760	8	3	paper	paper	NOUN
ejpam-4760	8	4	,	,	PUNCT
ejpam-4760	8	5	the	the	DET
ejpam-4760	8	6	author	author	NOUN
ejpam-4760	8	7	gives	give	VERB
ejpam-4760	8	8	a	a	DET
ejpam-4760	8	9	characterization	characterization	NOUN
ejpam-4760	8	10	of	of	ADP
ejpam-4760	8	11	perfect	perfect	ADJ
ejpam-4760	8	12	isolate	isolate	NOUN
ejpam-4760	8	13	dominating	dominate	VERB
ejpam-4760	8	14	set	set	NOUN
ejpam-4760	8	15	of	of	ADP
ejpam-4760	8	16	some	some	DET
ejpam-4760	8	17	graphs	graph	NOUN
ejpam-4760	8	18	and	and	CCONJ
ejpam-4760	8	19	graphs	graph	NOUN
ejpam-4760	8	20	obtained	obtain	VERB
ejpam-4760	8	21	from	from	ADP
ejpam-4760	8	22	the	the	DET
ejpam-4760	8	23	join	join	NOUN
ejpam-4760	8	24	,	,	PUNCT
ejpam-4760	8	25	corona	corona	NOUN
ejpam-4760	8	26	and	and	CCONJ
ejpam-4760	8	27	lexicographic	lexicographic	ADJ
ejpam-4760	8	28	product	product	NOUN
ejpam-4760	8	29	of	of	ADP
ejpam-4760	8	30	two	two	NUM
ejpam-4760	8	31	graphs	graph	NOUN
ejpam-4760	8	32	.	.	PUNCT
ejpam-4760	9	1	moreover	moreover	ADV
ejpam-4760	9	2	,	,	PUNCT
ejpam-4760	9	3	the	the	DET
ejpam-4760	9	4	perfect	perfect	ADJ
ejpam-4760	9	5	isolate	isolate	NOUN
ejpam-4760	9	6	domination	domination	NOUN
ejpam-4760	9	7	number	number	NOUN
ejpam-4760	9	8	of	of	ADP
ejpam-4760	9	9	the	the	DET
ejpam-4760	9	10	forenamed	forenamed	PROPN
ejpam-4760	9	11	graphs	graph	NOUN
ejpam-4760	9	12	is	be	AUX
ejpam-4760	9	13	determined	determine	VERB
ejpam-4760	9	14	and	and	CCONJ
ejpam-4760	9	15	also	also	ADV
ejpam-4760	9	16	,	,	PUNCT
ejpam-4760	9	17	graphs	graph	NOUN
ejpam-4760	9	18	having	have	VERB
ejpam-4760	9	19	no	no	DET
ejpam-4760	9	20	perfect	perfect	ADJ
ejpam-4760	9	21	isolate	isolate	NOUN
ejpam-4760	9	22	dominating	dominating	NOUN
ejpam-4760	9	23	set	set	NOUN
ejpam-4760	9	24	are	be	AUX
ejpam-4760	9	25	examined	examine	VERB
ejpam-4760	9	26	.	.	PUNCT
ejpam-4760	10	1	2020	2020	NUM
ejpam-4760	10	2	mathematics	mathematics	PROPN
ejpam-4760	10	3	subject	subject	NOUN
ejpam-4760	10	4	classifications	classification	NOUN
ejpam-4760	10	5	:	:	PUNCT
ejpam-4760	10	6	05c69,05c38,05c76	05c69,05c38,05c76	ADJ
ejpam-4760	10	7	key	key	ADJ
ejpam-4760	10	8	words	word	NOUN
ejpam-4760	10	9	and	and	CCONJ
ejpam-4760	10	10	phrases	phrase	NOUN
ejpam-4760	10	11	:	:	PUNCT
ejpam-4760	10	12	perfect	perfect	ADJ
ejpam-4760	10	13	domination	domination	NOUN
ejpam-4760	10	14	,	,	PUNCT
ejpam-4760	10	15	isolate	isolate	VERB
ejpam-4760	10	16	domination	domination	NOUN
ejpam-4760	10	17	,	,	PUNCT
ejpam-4760	10	18	perfect	perfect	ADJ
ejpam-4760	10	19	isolate	isolate	NOUN
ejpam-4760	10	20	domination	domination	NOUN
ejpam-4760	10	21	1	1	NUM
ejpam-4760	10	22	.	.	PUNCT
ejpam-4760	10	23	introduction	introduction	NOUN
ejpam-4760	10	24	in	in	ADP
ejpam-4760	10	25	1960	1960	NUM
ejpam-4760	10	26	,	,	PUNCT
ejpam-4760	10	27	the	the	DET
ejpam-4760	10	28	study	study	NOUN
ejpam-4760	10	29	of	of	ADP
ejpam-4760	10	30	domination	domination	NOUN
ejpam-4760	10	31	in	in	ADP
ejpam-4760	10	32	graphs	graph	NOUN
ejpam-4760	10	33	began	begin	VERB
ejpam-4760	10	34	and	and	CCONJ
ejpam-4760	10	35	it	it	PRON
ejpam-4760	10	36	became	become	VERB
ejpam-4760	10	37	the	the	DET
ejpam-4760	10	38	most	most	ADV
ejpam-4760	10	39	interesting	interesting	ADJ
ejpam-4760	10	40	topic	topic	NOUN
ejpam-4760	10	41	in	in	ADP
ejpam-4760	10	42	graph	graph	NOUN
ejpam-4760	10	43	theory	theory	NOUN
ejpam-4760	10	44	because	because	SCONJ
ejpam-4760	10	45	of	of	ADP
ejpam-4760	10	46	its	its	PRON
ejpam-4760	10	47	application	application	NOUN
ejpam-4760	10	48	in	in	ADP
ejpam-4760	10	49	networking	network	VERB
ejpam-4760	10	50	.	.	PUNCT
ejpam-4760	11	1	in	in	ADP
ejpam-4760	11	2	1990	1990	NUM
ejpam-4760	11	3	,	,	PUNCT
ejpam-4760	11	4	livingston	livingston	PROPN
ejpam-4760	11	5	and	and	CCONJ
ejpam-4760	11	6	stout	stout	NOUN
ejpam-4760	12	1	[	[	X
ejpam-4760	12	2	10	10	NUM
ejpam-4760	12	3	]	]	PUNCT
ejpam-4760	12	4	,	,	PUNCT
ejpam-4760	12	5	introduced	introduce	VERB
ejpam-4760	12	6	the	the	DET
ejpam-4760	12	7	concept	concept	NOUN
ejpam-4760	12	8	of	of	ADP
ejpam-4760	12	9	perfect	perfect	ADJ
ejpam-4760	12	10	dominating	dominating	NOUN
ejpam-4760	12	11	sets	set	NOUN
ejpam-4760	12	12	of	of	ADP
ejpam-4760	12	13	g	g	NOUN
ejpam-4760	12	14	,	,	PUNCT
ejpam-4760	12	15	denoted	denote	VERB
ejpam-4760	12	16	by	by	ADP
ejpam-4760	12	17	γp(g	γp(g	NOUN
ejpam-4760	12	18	)	)	PUNCT
ejpam-4760	12	19	.	.	PUNCT
ejpam-4760	13	1	they	they	PRON
ejpam-4760	13	2	studied	study	VERB
ejpam-4760	13	3	the	the	DET
ejpam-4760	13	4	existence	existence	NOUN
ejpam-4760	13	5	and	and	CCONJ
ejpam-4760	13	6	construction	construction	NOUN
ejpam-4760	13	7	of	of	ADP
ejpam-4760	13	8	perfect	perfect	ADJ
ejpam-4760	13	9	dominating	dominating	NOUN
ejpam-4760	13	10	sets	set	NOUN
ejpam-4760	13	11	in	in	ADP
ejpam-4760	13	12	families	family	NOUN
ejpam-4760	13	13	of	of	ADP
ejpam-4760	13	14	graphs	graph	NOUN
ejpam-4760	13	15	arising	arise	VERB
ejpam-4760	13	16	from	from	ADP
ejpam-4760	13	17	the	the	DET
ejpam-4760	13	18	interconnection	interconnection	NOUN
ejpam-4760	13	19	networks	network	NOUN
ejpam-4760	13	20	of	of	ADP
ejpam-4760	13	21	parallel	parallel	ADJ
ejpam-4760	13	22	computers	computer	NOUN
ejpam-4760	13	23	.	.	PUNCT
ejpam-4760	14	1	in	in	ADP
ejpam-4760	14	2	2014	2014	NUM
ejpam-4760	14	3	,	,	PUNCT
ejpam-4760	14	4	kwon	kwon	VERB
ejpam-4760	14	5	and	and	CCONJ
ejpam-4760	14	6	lee	lee	PROPN
ejpam-4760	15	1	[	[	X
ejpam-4760	15	2	9	9	NUM
ejpam-4760	15	3	]	]	PUNCT
ejpam-4760	15	4	investigated	investigate	VERB
ejpam-4760	15	5	some	some	DET
ejpam-4760	15	6	results	result	NOUN
ejpam-4760	15	7	related	relate	VERB
ejpam-4760	15	8	to	to	ADP
ejpam-4760	15	9	perfect	perfect	ADJ
ejpam-4760	15	10	domination	domination	NOUN
ejpam-4760	15	11	sets	set	NOUN
ejpam-4760	15	12	of	of	ADP
ejpam-4760	15	13	cayley	cayley	ADJ
ejpam-4760	15	14	graphs	graph	NOUN
ejpam-4760	15	15	.	.	PUNCT
ejpam-4760	16	1	in	in	ADP
ejpam-4760	16	2	2013	2013	NUM
ejpam-4760	16	3	,	,	PUNCT
ejpam-4760	16	4	hamid	hamid	PROPN
ejpam-4760	16	5	and	and	CCONJ
ejpam-4760	16	6	balamurugan	balamurugan	VERB
ejpam-4760	16	7	[	[	X
ejpam-4760	16	8	4	4	NUM
ejpam-4760	16	9	]	]	PUNCT
ejpam-4760	16	10	studied	study	VERB
ejpam-4760	16	11	the	the	DET
ejpam-4760	16	12	concept	concept	NOUN
ejpam-4760	16	13	of	of	ADP
ejpam-4760	16	14	isolate	isolate	ADJ
ejpam-4760	16	15	domination	domination	NOUN
ejpam-4760	16	16	in	in	ADP
ejpam-4760	16	17	graphs	graph	NOUN
ejpam-4760	16	18	.	.	PUNCT
ejpam-4760	17	1	in	in	ADP
ejpam-4760	17	2	2015	2015	NUM
ejpam-4760	17	3	,	,	PUNCT
ejpam-4760	17	4	ariola	ariola	PROPN
ejpam-4760	18	1	[	[	X
ejpam-4760	18	2	2	2	NUM
ejpam-4760	18	3	]	]	PUNCT
ejpam-4760	18	4	looked	look	VERB
ejpam-4760	18	5	at	at	ADP
ejpam-4760	18	6	another	another	DET
ejpam-4760	18	7	aspect	aspect	NOUN
ejpam-4760	18	8	of	of	ADP
ejpam-4760	18	9	the	the	DET
ejpam-4760	18	10	isolate	isolate	NOUN
ejpam-4760	18	11	dominating	dominating	NOUN
ejpam-4760	18	12	set	set	NOUN
ejpam-4760	18	13	and	and	CCONJ
ejpam-4760	18	14	characterized	characterize	VERB
ejpam-4760	18	15	the	the	DET
ejpam-4760	18	16	lower	low	ADJ
ejpam-4760	18	17	and	and	CCONJ
ejpam-4760	18	18	upper	upper	ADJ
ejpam-4760	18	19	bounds	bound	NOUN
ejpam-4760	18	20	of	of	ADP
ejpam-4760	18	21	the	the	DET
ejpam-4760	18	22	isolate	isolate	ADJ
ejpam-4760	18	23	domination	domination	NOUN
ejpam-4760	18	24	number	number	NOUN
ejpam-4760	18	25	and	and	CCONJ
ejpam-4760	18	26	those	those	DET
ejpam-4760	18	27	graphs	graph	NOUN
ejpam-4760	18	28	resulting	result	VERB
ejpam-4760	18	29	from	from	ADP
ejpam-4760	18	30	some	some	DET
ejpam-4760	18	31	binary	binary	ADJ
ejpam-4760	18	32	operations	operation	NOUN
ejpam-4760	18	33	such	such	ADJ
ejpam-4760	18	34	as	as	ADP
ejpam-4760	18	35	join	join	NOUN
ejpam-4760	18	36	and	and	CCONJ
ejpam-4760	18	37	corona	corona	PROPN
ejpam-4760	18	38	.	.	PUNCT
ejpam-4760	19	1	in	in	ADP
ejpam-4760	19	2	2016	2016	NUM
ejpam-4760	19	3	,	,	PUNCT
ejpam-4760	19	4	hamid	hamid	PROPN
ejpam-4760	19	5	and	and	CCONJ
ejpam-4760	19	6	balamurugan	balamurugan	VERB
ejpam-4760	19	7	[	[	X
ejpam-4760	19	8	4	4	NUM
ejpam-4760	19	9	]	]	PUNCT
ejpam-4760	19	10	extended	extend	VERB
ejpam-4760	19	11	these	these	DET
ejpam-4760	19	12	parameters	parameter	NOUN
ejpam-4760	19	13	isolate	isolate	VERB
ejpam-4760	19	14	domination	domination	NOUN
ejpam-4760	19	15	number	number	NOUN
ejpam-4760	19	16	γ0	γ0	NOUN
ejpam-4760	19	17	and	and	CCONJ
ejpam-4760	19	18	the	the	DET
ejpam-4760	19	19	upper	upper	ADJ
ejpam-4760	19	20	isolate	isolate	NOUN
ejpam-4760	19	21	domination	domination	NOUN
ejpam-4760	19	22	number	number	NOUN
ejpam-4760	19	23	γ0	γ0	PROPN
ejpam-4760	19	24	.	.	PUNCT
ejpam-4760	20	1	in	in	ADP
ejpam-4760	20	2	2017	2017	NUM
ejpam-4760	20	3	,	,	PUNCT
ejpam-4760	20	4	rad	rad	NOUN
ejpam-4760	21	1	[	[	X
ejpam-4760	21	2	11	11	NUM
ejpam-4760	21	3	]	]	PUNCT
ejpam-4760	21	4	studied	study	VERB
ejpam-4760	21	5	the	the	DET
ejpam-4760	21	6	complexity	complexity	NOUN
ejpam-4760	21	7	of	of	ADP
ejpam-4760	21	8	the	the	DET
ejpam-4760	21	9	∗corresponding	∗corresponde	VERB
ejpam-4760	21	10	author	author	NOUN
ejpam-4760	21	11	.	.	PUNCT
ejpam-4760	22	1	doi	doi	NOUN
ejpam-4760	22	2	:	:	PUNCT
ejpam-4760	22	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4760	https://doi.org/10.29020/nybg.ejpam.v16i2.4760	ADJ
ejpam-4760	22	4	email	email	NOUN
ejpam-4760	22	5	addresses	address	NOUN
ejpam-4760	22	6	:	:	PUNCT
ejpam-4760	22	7	armadac@cnu.edu.ph	armadac@cnu.edu.ph	PROPN
ejpam-4760	22	8	(	(	PUNCT
ejpam-4760	22	9	c.	c.	PROPN
ejpam-4760	22	10	armada	armada	PROPN
ejpam-4760	22	11	)	)	PUNCT
ejpam-4760	22	12	,	,	PUNCT
ejpam-4760	22	13	jamilhamja@msutawi-tawi.edu.ph	jamilhamja@msutawi-tawi.edu.ph	PROPN
ejpam-4760	22	14	(	(	PUNCT
ejpam-4760	22	15	,	,	PUNCT
ejpam-4760	22	16	j.	j.	PROPN
ejpam-4760	22	17	hamja	hamja	PROPN
ejpam-4760	22	18	)	)	PUNCT
ejpam-4760	22	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4760	22	20	1326	1326	NUM
ejpam-4760	23	1	©	©	ADP
ejpam-4760	23	2	2023	2023	NUM
ejpam-4760	23	3	ejpam	ejpam	NOUN
ejpam-4760	23	4	all	all	DET
ejpam-4760	23	5	rights	right	NOUN
ejpam-4760	23	6	reserved	reserve	VERB
ejpam-4760	23	7	.	.	PUNCT
ejpam-4760	24	1	c.	c.	PROPN
ejpam-4760	24	2	armada	armada	PROPN
ejpam-4760	24	3	,	,	PUNCT
ejpam-4760	24	4	j.	j.	PROPN
ejpam-4760	24	5	hamja	hamja	PROPN
ejpam-4760	24	6	/	/	SYM
ejpam-4760	24	7	eur	eur	PROPN
ejpam-4760	24	8	.	.	PUNCT
ejpam-4760	25	1	j.	j.	PROPN
ejpam-4760	25	2	pure	pure	PROPN
ejpam-4760	25	3	appl	appl	PROPN
ejpam-4760	25	4	.	.	PROPN
ejpam-4760	25	5	math	math	PROPN
ejpam-4760	25	6	,	,	PUNCT
ejpam-4760	25	7	16	16	NUM
ejpam-4760	25	8	(	(	PUNCT
ejpam-4760	25	9	2	2	NUM
ejpam-4760	25	10	)	)	PUNCT
ejpam-4760	25	11	(	(	PUNCT
ejpam-4760	25	12	2023	2023	NUM
ejpam-4760	25	13	)	)	PUNCT
ejpam-4760	25	14	,	,	PUNCT
ejpam-4760	25	15	1326	1326	NUM
ejpam-4760	25	16	-	-	SYM
ejpam-4760	25	17	1341	1341	NUM
ejpam-4760	25	18	1327	1327	NUM
ejpam-4760	25	19	isolate	isolate	NOUN
ejpam-4760	25	20	domination	domination	NOUN
ejpam-4760	25	21	in	in	ADP
ejpam-4760	25	22	graphs	graph	NOUN
ejpam-4760	25	23	,	,	PUNCT
ejpam-4760	25	24	and	and	CCONJ
ejpam-4760	25	25	obtain	obtain	VERB
ejpam-4760	25	26	several	several	ADJ
ejpam-4760	25	27	bounds	bound	NOUN
ejpam-4760	25	28	and	and	CCONJ
ejpam-4760	25	29	characterizations	characterization	NOUN
ejpam-4760	25	30	on	on	ADP
ejpam-4760	25	31	the	the	DET
ejpam-4760	25	32	isolate	isolate	ADJ
ejpam-4760	25	33	domination	domination	NOUN
ejpam-4760	25	34	number	number	NOUN
ejpam-4760	25	35	.	.	PUNCT
ejpam-4760	26	1	furthermore	furthermore	ADV
ejpam-4760	26	2	,	,	PUNCT
ejpam-4760	26	3	some	some	DET
ejpam-4760	26	4	variations	variation	NOUN
ejpam-4760	26	5	and	and	CCONJ
ejpam-4760	26	6	parameters	parameter	NOUN
ejpam-4760	26	7	of	of	ADP
ejpam-4760	26	8	domination	domination	NOUN
ejpam-4760	26	9	in	in	ADP
ejpam-4760	26	10	graphs	graph	NOUN
ejpam-4760	26	11	are	be	AUX
ejpam-4760	26	12	studied	study	VERB
ejpam-4760	26	13	in	in	ADP
ejpam-4760	26	14	many	many	ADJ
ejpam-4760	26	15	classes	class	NOUN
ejpam-4760	26	16	(	(	PUNCT
ejpam-4760	26	17	see	see	VERB
ejpam-4760	26	18	[	[	X
ejpam-4760	26	19	1	1	NUM
ejpam-4760	26	20	]	]	PUNCT
ejpam-4760	26	21	,	,	PUNCT
ejpam-4760	26	22	[	[	X
ejpam-4760	26	23	8	8	NUM
ejpam-4760	26	24	]	]	PUNCT
ejpam-4760	26	25	,	,	PUNCT
ejpam-4760	26	26	[	[	X
ejpam-4760	26	27	6	6	NUM
ejpam-4760	26	28	]	]	PUNCT
ejpam-4760	26	29	and	and	CCONJ
ejpam-4760	26	30	[	[	X
ejpam-4760	26	31	5	5	NUM
ejpam-4760	26	32	]	]	PUNCT
ejpam-4760	26	33	)	)	PUNCT
ejpam-4760	26	34	.	.	PUNCT
ejpam-4760	27	1	in	in	ADP
ejpam-4760	27	2	this	this	DET
ejpam-4760	27	3	paper	paper	NOUN
ejpam-4760	27	4	,	,	PUNCT
ejpam-4760	27	5	we	we	PRON
ejpam-4760	27	6	introduce	introduce	VERB
ejpam-4760	27	7	the	the	DET
ejpam-4760	27	8	concept	concept	NOUN
ejpam-4760	27	9	of	of	ADP
ejpam-4760	27	10	perfect	perfect	ADJ
ejpam-4760	27	11	isolate	isolate	NOUN
ejpam-4760	27	12	domination	domination	NOUN
ejpam-4760	27	13	number	number	NOUN
ejpam-4760	27	14	.	.	PUNCT
ejpam-4760	28	1	we	we	PRON
ejpam-4760	28	2	characterize	characterize	VERB
ejpam-4760	28	3	the	the	DET
ejpam-4760	28	4	perfect	perfect	ADJ
ejpam-4760	28	5	isolate	isolate	NOUN
ejpam-4760	28	6	dominating	dominating	NOUN
ejpam-4760	28	7	set	set	NOUN
ejpam-4760	28	8	and	and	CCONJ
ejpam-4760	28	9	determine	determine	VERB
ejpam-4760	28	10	the	the	DET
ejpam-4760	28	11	exact	exact	ADJ
ejpam-4760	28	12	values	value	NOUN
ejpam-4760	28	13	of	of	ADP
ejpam-4760	28	14	perfect	perfect	ADJ
ejpam-4760	28	15	isolate	isolate	NOUN
ejpam-4760	28	16	domination	domination	NOUN
ejpam-4760	28	17	number	number	NOUN
ejpam-4760	28	18	of	of	ADP
ejpam-4760	28	19	some	some	DET
ejpam-4760	28	20	special	special	ADJ
ejpam-4760	28	21	graphs	graph	NOUN
ejpam-4760	28	22	and	and	CCONJ
ejpam-4760	28	23	graphs	graph	NOUN
ejpam-4760	28	24	under	under	ADP
ejpam-4760	28	25	some	some	DET
ejpam-4760	28	26	binary	binary	ADJ
ejpam-4760	28	27	operations	operation	NOUN
ejpam-4760	28	28	such	such	ADJ
ejpam-4760	28	29	as	as	ADP
ejpam-4760	28	30	join	join	NOUN
ejpam-4760	28	31	,	,	PUNCT
ejpam-4760	28	32	corona	corona	NOUN
ejpam-4760	28	33	and	and	CCONJ
ejpam-4760	28	34	lexicographic	lexicographic	ADJ
ejpam-4760	28	35	product	product	NOUN
ejpam-4760	28	36	of	of	ADP
ejpam-4760	28	37	two	two	NUM
ejpam-4760	28	38	graphs	graph	NOUN
ejpam-4760	28	39	.	.	PUNCT
ejpam-4760	29	1	not	not	PART
ejpam-4760	29	2	all	all	DET
ejpam-4760	29	3	graphs	graph	NOUN
ejpam-4760	29	4	have	have	VERB
ejpam-4760	29	5	perfect	perfect	ADJ
ejpam-4760	29	6	isolate	isolate	NOUN
ejpam-4760	29	7	dominating	dominating	NOUN
ejpam-4760	29	8	set	set	NOUN
ejpam-4760	29	9	and	and	CCONJ
ejpam-4760	29	10	we	we	PRON
ejpam-4760	29	11	called	call	VERB
ejpam-4760	29	12	them	they	PRON
ejpam-4760	29	13	non	non	ADJ
ejpam-4760	29	14	-	-	ADJ
ejpam-4760	29	15	γp0	γp0	NOUN
ejpam-4760	29	16	-	-	PUNCT
ejpam-4760	29	17	graphs	graph	NOUN
ejpam-4760	29	18	.	.	PUNCT
ejpam-4760	30	1	2	2	X
ejpam-4760	30	2	.	.	X
ejpam-4760	30	3	terminology	terminology	NOUN
ejpam-4760	30	4	and	and	CCONJ
ejpam-4760	30	5	notation	notation	NOUN
ejpam-4760	30	6	this	this	DET
ejpam-4760	30	7	section	section	NOUN
ejpam-4760	30	8	contains	contain	VERB
ejpam-4760	30	9	definitions	definition	NOUN
ejpam-4760	30	10	that	that	PRON
ejpam-4760	30	11	are	be	AUX
ejpam-4760	30	12	needed	need	VERB
ejpam-4760	30	13	for	for	ADP
ejpam-4760	30	14	the	the	DET
ejpam-4760	30	15	study	study	NOUN
ejpam-4760	30	16	.	.	PUNCT
ejpam-4760	31	1	let	let	VERB
ejpam-4760	31	2	g	g	PROPN
ejpam-4760	31	3	=	=	SYM
ejpam-4760	31	4	(	(	PUNCT
ejpam-4760	31	5	v	v	NOUN
ejpam-4760	31	6	(	(	PUNCT
ejpam-4760	31	7	g	g	NOUN
ejpam-4760	31	8	)	)	PUNCT
ejpam-4760	31	9	,	,	PUNCT
ejpam-4760	31	10	e(g	e(g	PROPN
ejpam-4760	31	11	)	)	PUNCT
ejpam-4760	31	12	)	)	PUNCT
ejpam-4760	32	1	be	be	AUX
ejpam-4760	32	2	a	a	DET
ejpam-4760	32	3	simple	simple	ADJ
ejpam-4760	32	4	connected	connected	ADJ
ejpam-4760	32	5	graph	graph	NOUN
ejpam-4760	32	6	where	where	SCONJ
ejpam-4760	32	7	v	v	NOUN
ejpam-4760	32	8	(	(	PUNCT
ejpam-4760	32	9	g	g	NOUN
ejpam-4760	32	10	)	)	PUNCT
ejpam-4760	32	11	is	be	AUX
ejpam-4760	32	12	a	a	DET
ejpam-4760	32	13	vertex	vertex	NOUN
ejpam-4760	32	14	-	-	PUNCT
ejpam-4760	32	15	set	set	NOUN
ejpam-4760	32	16	of	of	ADP
ejpam-4760	32	17	g	g	PROPN
ejpam-4760	32	18	and	and	CCONJ
ejpam-4760	32	19	e(g	e(g	PROPN
ejpam-4760	32	20	)	)	PUNCT
ejpam-4760	32	21	is	be	AUX
ejpam-4760	32	22	an	an	DET
ejpam-4760	32	23	edge	edge	NOUN
ejpam-4760	32	24	-	-	PUNCT
ejpam-4760	32	25	set	set	NOUN
ejpam-4760	32	26	of	of	ADP
ejpam-4760	32	27	g.	g.	PROPN
ejpam-4760	32	28	the	the	DET
ejpam-4760	32	29	number	number	NOUN
ejpam-4760	32	30	of	of	ADP
ejpam-4760	32	31	edges	edge	NOUN
ejpam-4760	32	32	incident	incident	NOUN
ejpam-4760	32	33	with	with	ADP
ejpam-4760	32	34	v	v	PROPN
ejpam-4760	32	35	is	be	AUX
ejpam-4760	32	36	called	call	VERB
ejpam-4760	32	37	the	the	DET
ejpam-4760	32	38	degree	degree	NOUN
ejpam-4760	32	39	of	of	ADP
ejpam-4760	32	40	a	a	DET
ejpam-4760	32	41	vertex	vertex	NOUN
ejpam-4760	32	42	v	v	NOUN
ejpam-4760	32	43	and	and	CCONJ
ejpam-4760	32	44	is	be	AUX
ejpam-4760	32	45	denoted	denote	VERB
ejpam-4760	32	46	by	by	ADP
ejpam-4760	32	47	deg(v	deg(v	PROPN
ejpam-4760	32	48	)	)	PUNCT
ejpam-4760	32	49	.	.	PUNCT
ejpam-4760	33	1	the	the	DET
ejpam-4760	33	2	maximum	maximum	NOUN
ejpam-4760	33	3	of	of	ADP
ejpam-4760	33	4	{	{	PUNCT
ejpam-4760	33	5	deg(v	deg(v	PROPN
ejpam-4760	33	6	)	)	PUNCT
ejpam-4760	33	7	:	:	PUNCT
ejpam-4760	33	8	v	v	X
ejpam-4760	33	9	∈	∈	PROPN
ejpam-4760	33	10	v	v	NOUN
ejpam-4760	33	11	(	(	PUNCT
ejpam-4760	33	12	g	g	NOUN
ejpam-4760	33	13	)	)	PUNCT
ejpam-4760	33	14	}	}	PUNCT
ejpam-4760	33	15	is	be	AUX
ejpam-4760	33	16	denoted	denote	VERB
ejpam-4760	33	17	by	by	ADP
ejpam-4760	33	18	∆(g	∆(g	PROPN
ejpam-4760	33	19	)	)	PUNCT
ejpam-4760	33	20	.	.	PUNCT
ejpam-4760	34	1	the	the	DET
ejpam-4760	34	2	set	set	NOUN
ejpam-4760	34	3	of	of	ADP
ejpam-4760	34	4	neighbors	neighbor	NOUN
ejpam-4760	34	5	of	of	ADP
ejpam-4760	34	6	a	a	DET
ejpam-4760	34	7	vertex	vertex	NOUN
ejpam-4760	34	8	u	u	NOUN
ejpam-4760	34	9	in	in	ADP
ejpam-4760	34	10	g	g	PROPN
ejpam-4760	34	11	is	be	AUX
ejpam-4760	34	12	called	call	VERB
ejpam-4760	34	13	the	the	DET
ejpam-4760	34	14	open	open	ADJ
ejpam-4760	34	15	neighborhood	neighborhood	NOUN
ejpam-4760	34	16	of	of	ADP
ejpam-4760	34	17	u	u	NOUN
ejpam-4760	34	18	in	in	ADP
ejpam-4760	34	19	g	g	PROPN
ejpam-4760	34	20	and	and	CCONJ
ejpam-4760	34	21	is	be	AUX
ejpam-4760	34	22	denoted	denote	VERB
ejpam-4760	34	23	by	by	ADP
ejpam-4760	34	24	ng(u	ng(u	NOUN
ejpam-4760	34	25	)	)	PUNCT
ejpam-4760	34	26	=	=	PRON
ejpam-4760	34	27	{	{	PUNCT
ejpam-4760	34	28	v	v	NUM
ejpam-4760	34	29	∈	∈	NOUN
ejpam-4760	34	30	v	v	NOUN
ejpam-4760	34	31	(	(	PUNCT
ejpam-4760	34	32	g	g	NOUN
ejpam-4760	34	33	)	)	PUNCT
ejpam-4760	34	34	:	:	PUNCT
ejpam-4760	34	35	uv	uv	PROPN
ejpam-4760	34	36	∈	∈	PROPN
ejpam-4760	34	37	e(g	e(g	PROPN
ejpam-4760	34	38	)	)	PUNCT
ejpam-4760	34	39	}	}	PUNCT
ejpam-4760	34	40	.	.	PUNCT
ejpam-4760	35	1	the	the	DET
ejpam-4760	35	2	closed	closed	ADJ
ejpam-4760	35	3	neighborhood	neighborhood	NOUN
ejpam-4760	35	4	of	of	ADP
ejpam-4760	35	5	u	u	NOUN
ejpam-4760	35	6	in	in	ADP
ejpam-4760	35	7	g	g	PROPN
ejpam-4760	35	8	is	be	AUX
ejpam-4760	35	9	the	the	DET
ejpam-4760	35	10	set	set	NOUN
ejpam-4760	35	11	ng[u	ng[u	PROPN
ejpam-4760	35	12	]	]	X
ejpam-4760	35	13	=	=	SYM
ejpam-4760	35	14	ng(u	ng(u	PROPN
ejpam-4760	35	15	)	)	PUNCT
ejpam-4760	35	16	∪	∪	NOUN
ejpam-4760	35	17	{	{	PUNCT
ejpam-4760	35	18	u	u	NOUN
ejpam-4760	35	19	}	}	PUNCT
ejpam-4760	35	20	and	and	CCONJ
ejpam-4760	35	21	the	the	DET
ejpam-4760	35	22	closed	closed	ADJ
ejpam-4760	35	23	neighborhood	neighborhood	NOUN
ejpam-4760	35	24	of	of	ADP
ejpam-4760	35	25	a	a	DET
ejpam-4760	35	26	subset	subset	NOUN
ejpam-4760	35	27	s	s	NOUN
ejpam-4760	35	28	of	of	ADP
ejpam-4760	35	29	v	v	NOUN
ejpam-4760	35	30	(	(	PUNCT
ejpam-4760	35	31	g	g	NOUN
ejpam-4760	35	32	)	)	PUNCT
ejpam-4760	35	33	is	be	AUX
ejpam-4760	35	34	the	the	DET
ejpam-4760	35	35	set	set	VERB
ejpam-4760	35	36	ng[s	ng[	NOUN
ejpam-4760	35	37	]	]	PUNCT
ejpam-4760	35	38	=	=	SYM
ejpam-4760	36	1	n	n	PRON
ejpam-4760	37	1	[	[	X
ejpam-4760	37	2	s	s	X
ejpam-4760	37	3	]	]	X
ejpam-4760	37	4	=	=	SYM
ejpam-4760	37	5	∪v∈sng[v	∪v∈sng[v	X
ejpam-4760	37	6	]	]	PUNCT
ejpam-4760	37	7	.	.	PUNCT
ejpam-4760	38	1	the	the	DET
ejpam-4760	38	2	subgraph	subgraph	NOUN
ejpam-4760	38	3	induced	induce	VERB
ejpam-4760	38	4	by	by	ADP
ejpam-4760	38	5	a	a	DET
ejpam-4760	38	6	set	set	NOUN
ejpam-4760	38	7	s	s	NOUN
ejpam-4760	38	8	of	of	ADP
ejpam-4760	38	9	vertices	vertex	NOUN
ejpam-4760	38	10	of	of	ADP
ejpam-4760	38	11	a	a	DET
ejpam-4760	38	12	graph	graph	NOUN
ejpam-4760	38	13	g	g	NOUN
ejpam-4760	38	14	is	be	AUX
ejpam-4760	38	15	denoted	denote	VERB
ejpam-4760	38	16	by	by	ADP
ejpam-4760	38	17	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	38	18	with	with	ADP
ejpam-4760	38	19	v	v	PROPN
ejpam-4760	38	20	(	(	PUNCT
ejpam-4760	38	21	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	38	22	)	)	PUNCT
ejpam-4760	38	23	=	=	SYM
ejpam-4760	38	24	s	s	PROPN
ejpam-4760	38	25	and	and	CCONJ
ejpam-4760	38	26	e(⟨s⟩	e(⟨s⟩	ADJ
ejpam-4760	38	27	)	)	PUNCT
ejpam-4760	39	1	=	=	PRON
ejpam-4760	39	2	{	{	PUNCT
ejpam-4760	39	3	uv	uv	PROPN
ejpam-4760	39	4	∈	∈	PROPN
ejpam-4760	39	5	e(g	e(g	PROPN
ejpam-4760	39	6	)	)	PUNCT
ejpam-4760	39	7	:	:	PUNCT
ejpam-4760	40	1	u	u	NOUN
ejpam-4760	40	2	,	,	PUNCT
ejpam-4760	40	3	v	v	NOUN
ejpam-4760	40	4	∈	∈	NOUN
ejpam-4760	40	5	s	s	PART
ejpam-4760	40	6	}	}	PUNCT
ejpam-4760	40	7	,	,	PUNCT
ejpam-4760	40	8	harary	harary	NOUN
ejpam-4760	40	9	in	in	ADP
ejpam-4760	40	10	[	[	X
ejpam-4760	40	11	7	7	NUM
ejpam-4760	40	12	]	]	PUNCT
ejpam-4760	40	13	.	.	PUNCT
ejpam-4760	41	1	a	a	DET
ejpam-4760	41	2	set	set	NOUN
ejpam-4760	41	3	s	s	NOUN
ejpam-4760	41	4	⊆	⊆	NUM
ejpam-4760	41	5	v	v	NOUN
ejpam-4760	41	6	(	(	PUNCT
ejpam-4760	41	7	g	g	NOUN
ejpam-4760	41	8	)	)	PUNCT
ejpam-4760	41	9	is	be	AUX
ejpam-4760	41	10	said	say	VERB
ejpam-4760	41	11	to	to	PART
ejpam-4760	41	12	be	be	AUX
ejpam-4760	41	13	a	a	DET
ejpam-4760	41	14	dominating	dominating	NOUN
ejpam-4760	41	15	set	set	NOUN
ejpam-4760	41	16	if	if	SCONJ
ejpam-4760	41	17	n	n	PRON
ejpam-4760	41	18	[	[	X
ejpam-4760	41	19	s	s	X
ejpam-4760	41	20	]	]	X
ejpam-4760	41	21	=	=	SYM
ejpam-4760	41	22	v	v	NOUN
ejpam-4760	41	23	(	(	PUNCT
ejpam-4760	41	24	g	g	NOUN
ejpam-4760	41	25	)	)	PUNCT
ejpam-4760	41	26	.	.	PUNCT
ejpam-4760	42	1	a	a	DET
ejpam-4760	42	2	dominating	dominating	NOUN
ejpam-4760	42	3	set	set	NOUN
ejpam-4760	42	4	s	s	VERB
ejpam-4760	42	5	is	be	AUX
ejpam-4760	42	6	a	a	DET
ejpam-4760	42	7	minimal	minimal	ADJ
ejpam-4760	42	8	dominating	dominating	NOUN
ejpam-4760	42	9	set	set	NOUN
ejpam-4760	42	10	if	if	SCONJ
ejpam-4760	42	11	no	no	DET
ejpam-4760	42	12	proper	proper	ADJ
ejpam-4760	42	13	subset	subset	NOUN
ejpam-4760	42	14	s′	s′	VERB
ejpam-4760	42	15	⊂	⊂	ADJ
ejpam-4760	42	16	s	s	X
ejpam-4760	42	17	is	be	AUX
ejpam-4760	42	18	a	a	DET
ejpam-4760	42	19	dominating	dominating	NOUN
ejpam-4760	42	20	set	set	NOUN
ejpam-4760	42	21	.	.	PUNCT
ejpam-4760	43	1	the	the	DET
ejpam-4760	43	2	domination	domination	NOUN
ejpam-4760	43	3	number	number	PROPN
ejpam-4760	43	4	γ(g	γ(g	PROPN
ejpam-4760	43	5	)	)	PUNCT
ejpam-4760	43	6	of	of	ADP
ejpam-4760	43	7	a	a	DET
ejpam-4760	43	8	graph	graph	NOUN
ejpam-4760	43	9	g	g	NOUN
ejpam-4760	43	10	is	be	AUX
ejpam-4760	43	11	the	the	DET
ejpam-4760	43	12	minimum	minimum	ADJ
ejpam-4760	43	13	cardinality	cardinality	NOUN
ejpam-4760	43	14	of	of	ADP
ejpam-4760	43	15	a	a	DET
ejpam-4760	43	16	dominating	dominating	NOUN
ejpam-4760	43	17	set	set	NOUN
ejpam-4760	43	18	of	of	ADP
ejpam-4760	43	19	g.	g.	PROPN
ejpam-4760	43	20	a	a	DET
ejpam-4760	43	21	dominating	dominating	NOUN
ejpam-4760	43	22	set	set	NOUN
ejpam-4760	43	23	s	s	NOUN
ejpam-4760	43	24	with	with	ADP
ejpam-4760	43	25	|s|	|s|	PROPN
ejpam-4760	43	26	=	=	SYM
ejpam-4760	43	27	γ(g	γ(g	PROPN
ejpam-4760	43	28	)	)	PUNCT
ejpam-4760	43	29	is	be	AUX
ejpam-4760	43	30	said	say	VERB
ejpam-4760	43	31	to	to	PART
ejpam-4760	43	32	be	be	AUX
ejpam-4760	43	33	a	a	DET
ejpam-4760	43	34	γ	γ	NOUN
ejpam-4760	43	35	-	-	PUNCT
ejpam-4760	43	36	set	set	NOUN
ejpam-4760	43	37	.	.	PUNCT
ejpam-4760	44	1	a	a	DET
ejpam-4760	44	2	set	set	NOUN
ejpam-4760	44	3	s	s	NOUN
ejpam-4760	44	4	⊆	⊆	NUM
ejpam-4760	44	5	v	v	NOUN
ejpam-4760	44	6	(	(	PUNCT
ejpam-4760	44	7	g	g	NOUN
ejpam-4760	44	8	)	)	PUNCT
ejpam-4760	44	9	is	be	AUX
ejpam-4760	44	10	said	say	VERB
ejpam-4760	44	11	to	to	PART
ejpam-4760	44	12	be	be	AUX
ejpam-4760	44	13	a	a	DET
ejpam-4760	44	14	perfect	perfect	ADJ
ejpam-4760	44	15	dominating	dominating	NOUN
ejpam-4760	44	16	set	set	NOUN
ejpam-4760	44	17	if	if	SCONJ
ejpam-4760	44	18	each	each	DET
ejpam-4760	44	19	vertex	vertex	NOUN
ejpam-4760	44	20	v	v	ADP
ejpam-4760	44	21	∈	∈	PROPN
ejpam-4760	44	22	v	v	NOUN
ejpam-4760	44	23	(	(	PUNCT
ejpam-4760	44	24	g	g	NOUN
ejpam-4760	44	25	)	)	PUNCT
ejpam-4760	44	26	\	\	PROPN
ejpam-4760	45	1	s	s	PART
ejpam-4760	45	2	is	be	AUX
ejpam-4760	45	3	dominated	dominate	VERB
ejpam-4760	45	4	by	by	ADP
ejpam-4760	45	5	exactly	exactly	ADV
ejpam-4760	45	6	one	one	NUM
ejpam-4760	45	7	element	element	NOUN
ejpam-4760	45	8	in	in	ADP
ejpam-4760	45	9	s.	s.	PROPN
ejpam-4760	45	10	the	the	DET
ejpam-4760	45	11	minimum	minimum	ADJ
ejpam-4760	45	12	cardinality	cardinality	NOUN
ejpam-4760	45	13	of	of	ADP
ejpam-4760	45	14	a	a	DET
ejpam-4760	45	15	perfect	perfect	ADJ
ejpam-4760	45	16	dominating	dominating	NOUN
ejpam-4760	45	17	set	set	NOUN
ejpam-4760	45	18	of	of	ADP
ejpam-4760	45	19	g	g	PROPN
ejpam-4760	45	20	is	be	AUX
ejpam-4760	45	21	called	call	VERB
ejpam-4760	45	22	perfect	perfect	ADJ
ejpam-4760	45	23	domination	domination	NOUN
ejpam-4760	45	24	number	number	NOUN
ejpam-4760	45	25	,	,	PUNCT
ejpam-4760	45	26	and	and	CCONJ
ejpam-4760	45	27	is	be	AUX
ejpam-4760	45	28	denoted	denote	VERB
ejpam-4760	45	29	by	by	ADP
ejpam-4760	45	30	γp(g	γp(g	NOUN
ejpam-4760	45	31	)	)	PUNCT
ejpam-4760	45	32	.	.	PUNCT
ejpam-4760	46	1	a	a	DET
ejpam-4760	46	2	perfect	perfect	ADJ
ejpam-4760	46	3	dominating	dominating	NOUN
ejpam-4760	46	4	set	set	NOUN
ejpam-4760	46	5	s	s	NOUN
ejpam-4760	46	6	with	with	ADP
ejpam-4760	46	7	|s|	|s|	PROPN
ejpam-4760	46	8	=	=	SYM
ejpam-4760	46	9	γp(g	γp(g	X
ejpam-4760	46	10	)	)	PUNCT
ejpam-4760	46	11	is	be	AUX
ejpam-4760	46	12	said	say	VERB
ejpam-4760	46	13	to	to	PART
ejpam-4760	46	14	be	be	AUX
ejpam-4760	46	15	a	a	DET
ejpam-4760	46	16	γp	γp	NOUN
ejpam-4760	46	17	-	-	PUNCT
ejpam-4760	46	18	set	set	NOUN
ejpam-4760	46	19	.	.	PUNCT
ejpam-4760	47	1	a	a	DET
ejpam-4760	47	2	dominating	dominating	NOUN
ejpam-4760	47	3	set	set	NOUN
ejpam-4760	47	4	s	s	NOUN
ejpam-4760	47	5	⊆	⊆	NUM
ejpam-4760	47	6	g	g	NOUN
ejpam-4760	47	7	is	be	AUX
ejpam-4760	47	8	said	say	VERB
ejpam-4760	47	9	to	to	PART
ejpam-4760	47	10	be	be	AUX
ejpam-4760	47	11	an	an	DET
ejpam-4760	47	12	isolate	isolate	NOUN
ejpam-4760	47	13	dominating	dominating	NOUN
ejpam-4760	47	14	set	set	NOUN
ejpam-4760	47	15	of	of	ADP
ejpam-4760	47	16	g	g	PROPN
ejpam-4760	47	17	if	if	SCONJ
ejpam-4760	47	18	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	47	19	has	have	VERB
ejpam-4760	47	20	at	at	ADV
ejpam-4760	47	21	least	least	ADJ
ejpam-4760	47	22	one	one	NUM
ejpam-4760	47	23	isolated	isolated	ADJ
ejpam-4760	47	24	vertex	vertex	NOUN
ejpam-4760	47	25	.	.	PUNCT
ejpam-4760	48	1	an	an	DET
ejpam-4760	48	2	isolate	isolate	NOUN
ejpam-4760	48	3	dominating	dominating	NOUN
ejpam-4760	48	4	set	set	NOUN
ejpam-4760	48	5	s	s	PART
ejpam-4760	48	6	is	be	AUX
ejpam-4760	48	7	said	say	VERB
ejpam-4760	48	8	to	to	PART
ejpam-4760	48	9	be	be	AUX
ejpam-4760	48	10	a	a	DET
ejpam-4760	48	11	minimal	minimal	ADJ
ejpam-4760	48	12	isolate	isolate	NOUN
ejpam-4760	48	13	dominating	dominating	NOUN
ejpam-4760	48	14	set	set	NOUN
ejpam-4760	48	15	if	if	SCONJ
ejpam-4760	48	16	no	no	DET
ejpam-4760	48	17	proper	proper	ADJ
ejpam-4760	48	18	subset	subset	NOUN
ejpam-4760	48	19	of	of	ADP
ejpam-4760	48	20	s	s	PROPN
ejpam-4760	48	21	is	be	AUX
ejpam-4760	48	22	an	an	DET
ejpam-4760	48	23	isolate	isolate	ADJ
ejpam-4760	48	24	dominating	dominating	NOUN
ejpam-4760	48	25	set	set	NOUN
ejpam-4760	48	26	.	.	PUNCT
ejpam-4760	49	1	the	the	DET
ejpam-4760	49	2	minimum	minimum	ADJ
ejpam-4760	49	3	cardinality	cardinality	NOUN
ejpam-4760	49	4	of	of	ADP
ejpam-4760	49	5	a	a	DET
ejpam-4760	49	6	minimal	minimal	ADJ
ejpam-4760	49	7	isolate	isolate	NOUN
ejpam-4760	49	8	dominating	dominating	NOUN
ejpam-4760	49	9	set	set	NOUN
ejpam-4760	49	10	of	of	ADP
ejpam-4760	49	11	g	g	PROPN
ejpam-4760	49	12	is	be	AUX
ejpam-4760	49	13	called	call	VERB
ejpam-4760	49	14	the	the	DET
ejpam-4760	49	15	isolate	isolate	ADJ
ejpam-4760	49	16	domination	domination	NOUN
ejpam-4760	49	17	number	number	NOUN
ejpam-4760	49	18	and	and	CCONJ
ejpam-4760	49	19	is	be	AUX
ejpam-4760	49	20	denoted	denote	VERB
ejpam-4760	49	21	by	by	ADP
ejpam-4760	49	22	γ0(g	γ0(g	NOUN
ejpam-4760	49	23	)	)	PUNCT
ejpam-4760	49	24	.	.	PUNCT
ejpam-4760	50	1	an	an	DET
ejpam-4760	50	2	isolate	isolate	NOUN
ejpam-4760	50	3	dominating	dominating	NOUN
ejpam-4760	50	4	set	set	NOUN
ejpam-4760	50	5	s	s	NOUN
ejpam-4760	50	6	with	with	ADP
ejpam-4760	50	7	|s|	|s|	NOUN
ejpam-4760	50	8	=	=	SYM
ejpam-4760	50	9	γ0(g	γ0(g	NOUN
ejpam-4760	50	10	)	)	PUNCT
ejpam-4760	50	11	is	be	AUX
ejpam-4760	50	12	said	say	VERB
ejpam-4760	50	13	to	to	PART
ejpam-4760	50	14	be	be	AUX
ejpam-4760	50	15	a	a	DET
ejpam-4760	50	16	γ0	γ0	NOUN
ejpam-4760	50	17	-	-	PUNCT
ejpam-4760	50	18	set	set	NOUN
ejpam-4760	50	19	.	.	PUNCT
ejpam-4760	51	1	a	a	DET
ejpam-4760	51	2	perfect	perfect	ADJ
ejpam-4760	51	3	dominating	dominating	NOUN
ejpam-4760	51	4	set	set	NOUN
ejpam-4760	51	5	s	s	PROPN
ejpam-4760	51	6	⊆	⊆	NUM
ejpam-4760	51	7	v	v	NOUN
ejpam-4760	51	8	(	(	PUNCT
ejpam-4760	51	9	g	g	NOUN
ejpam-4760	51	10	)	)	PUNCT
ejpam-4760	51	11	is	be	AUX
ejpam-4760	51	12	said	say	VERB
ejpam-4760	51	13	to	to	PART
ejpam-4760	51	14	be	be	AUX
ejpam-4760	51	15	a	a	DET
ejpam-4760	51	16	independent	independent	ADJ
ejpam-4760	51	17	perfect	perfect	ADJ
ejpam-4760	51	18	dominating	dominating	NOUN
ejpam-4760	51	19	set	set	NOUN
ejpam-4760	51	20	(	(	PUNCT
ejpam-4760	51	21	ipds	ipds	PROPN
ejpam-4760	51	22	)	)	PUNCT
ejpam-4760	51	23	if	if	SCONJ
ejpam-4760	51	24	no	no	DET
ejpam-4760	51	25	two	two	NUM
ejpam-4760	51	26	vertices	vertex	NOUN
ejpam-4760	51	27	in	in	ADP
ejpam-4760	51	28	s	s	NOUN
ejpam-4760	51	29	are	be	AUX
ejpam-4760	51	30	adjacent	adjacent	ADJ
ejpam-4760	51	31	.	.	PUNCT
ejpam-4760	52	1	the	the	DET
ejpam-4760	52	2	minimum	minimum	ADJ
ejpam-4760	52	3	cardinality	cardinality	NOUN
ejpam-4760	52	4	of	of	ADP
ejpam-4760	52	5	an	an	DET
ejpam-4760	52	6	independent	independent	ADJ
ejpam-4760	52	7	perfect	perfect	ADJ
ejpam-4760	52	8	dominating	dominating	NOUN
ejpam-4760	52	9	set	set	NOUN
ejpam-4760	52	10	of	of	ADP
ejpam-4760	52	11	g	g	PROPN
ejpam-4760	52	12	is	be	AUX
ejpam-4760	52	13	called	call	VERB
ejpam-4760	52	14	independent	independent	ADJ
ejpam-4760	52	15	perfect	perfect	ADJ
ejpam-4760	52	16	domination	domination	NOUN
ejpam-4760	52	17	number	number	NOUN
ejpam-4760	52	18	and	and	CCONJ
ejpam-4760	52	19	is	be	AUX
ejpam-4760	52	20	denoted	denote	VERB
ejpam-4760	52	21	by	by	ADP
ejpam-4760	52	22	γip(g	γip(g	NOUN
ejpam-4760	52	23	)	)	PUNCT
ejpam-4760	52	24	.	.	PUNCT
ejpam-4760	53	1	a	a	DET
ejpam-4760	53	2	perfect	perfect	ADJ
ejpam-4760	53	3	dominating	dominating	NOUN
ejpam-4760	53	4	set	set	NOUN
ejpam-4760	53	5	s	s	NOUN
ejpam-4760	53	6	with	with	ADP
ejpam-4760	53	7	|s|	|s|	PROPN
ejpam-4760	53	8	=	=	PUNCT
ejpam-4760	53	9	γip(g	γip(g	PROPN
ejpam-4760	53	10	)	)	PUNCT
ejpam-4760	53	11	is	be	AUX
ejpam-4760	53	12	said	say	VERB
ejpam-4760	53	13	to	to	PART
ejpam-4760	53	14	be	be	AUX
ejpam-4760	53	15	a	a	DET
ejpam-4760	53	16	γip	γip	NOUN
ejpam-4760	53	17	-	-	PUNCT
ejpam-4760	53	18	set	set	NOUN
ejpam-4760	53	19	.	.	PUNCT
ejpam-4760	54	1	c.	c.	PROPN
ejpam-4760	54	2	armada	armada	PROPN
ejpam-4760	54	3	,	,	PUNCT
ejpam-4760	54	4	j.	j.	PROPN
ejpam-4760	54	5	hamja	hamja	PROPN
ejpam-4760	54	6	/	/	SYM
ejpam-4760	54	7	eur	eur	PROPN
ejpam-4760	54	8	.	.	PUNCT
ejpam-4760	55	1	j.	j.	PROPN
ejpam-4760	55	2	pure	pure	PROPN
ejpam-4760	55	3	appl	appl	PROPN
ejpam-4760	55	4	.	.	PROPN
ejpam-4760	55	5	math	math	PROPN
ejpam-4760	55	6	,	,	PUNCT
ejpam-4760	55	7	16	16	NUM
ejpam-4760	55	8	(	(	PUNCT
ejpam-4760	55	9	2	2	NUM
ejpam-4760	55	10	)	)	PUNCT
ejpam-4760	55	11	(	(	PUNCT
ejpam-4760	55	12	2023	2023	NUM
ejpam-4760	55	13	)	)	PUNCT
ejpam-4760	55	14	,	,	PUNCT
ejpam-4760	55	15	1326	1326	NUM
ejpam-4760	55	16	-	-	SYM
ejpam-4760	55	17	1341	1341	NUM
ejpam-4760	55	18	1328	1328	NUM
ejpam-4760	55	19	a	a	DET
ejpam-4760	55	20	set	set	NOUN
ejpam-4760	55	21	s	s	NOUN
ejpam-4760	55	22	⊆	⊆	NUM
ejpam-4760	55	23	v	v	NOUN
ejpam-4760	55	24	(	(	PUNCT
ejpam-4760	55	25	g	g	NOUN
ejpam-4760	55	26	)	)	PUNCT
ejpam-4760	55	27	is	be	AUX
ejpam-4760	55	28	said	say	VERB
ejpam-4760	55	29	to	to	PART
ejpam-4760	55	30	be	be	AUX
ejpam-4760	55	31	a	a	DET
ejpam-4760	55	32	perfect	perfect	ADJ
ejpam-4760	55	33	isolate	isolate	NOUN
ejpam-4760	55	34	dominating	dominating	NOUN
ejpam-4760	55	35	set	set	NOUN
ejpam-4760	55	36	of	of	ADP
ejpam-4760	55	37	g	g	PROPN
ejpam-4760	55	38	if	if	SCONJ
ejpam-4760	55	39	s	s	VERB
ejpam-4760	55	40	is	be	AUX
ejpam-4760	55	41	a	a	DET
ejpam-4760	55	42	perfect	perfect	ADJ
ejpam-4760	55	43	dominating	dominating	NOUN
ejpam-4760	55	44	set	set	NOUN
ejpam-4760	55	45	and	and	CCONJ
ejpam-4760	55	46	the	the	DET
ejpam-4760	55	47	induced	induced	ADJ
ejpam-4760	55	48	subgraph	subgraph	NOUN
ejpam-4760	55	49	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	55	50	has	have	VERB
ejpam-4760	55	51	at	at	ADV
ejpam-4760	55	52	least	least	ADJ
ejpam-4760	55	53	one	one	NUM
ejpam-4760	55	54	isolated	isolated	ADJ
ejpam-4760	55	55	vertex	vertex	NOUN
ejpam-4760	55	56	.	.	PUNCT
ejpam-4760	56	1	the	the	DET
ejpam-4760	56	2	minimum	minimum	ADJ
ejpam-4760	56	3	cardinality	cardinality	NOUN
ejpam-4760	56	4	of	of	ADP
ejpam-4760	56	5	a	a	DET
ejpam-4760	56	6	perfect	perfect	ADJ
ejpam-4760	56	7	isolate	isolate	NOUN
ejpam-4760	56	8	dominating	dominating	NOUN
ejpam-4760	56	9	set	set	NOUN
ejpam-4760	56	10	of	of	ADP
ejpam-4760	56	11	g	g	PROPN
ejpam-4760	56	12	is	be	AUX
ejpam-4760	56	13	called	call	VERB
ejpam-4760	56	14	perfect	perfect	ADJ
ejpam-4760	56	15	isolate	isolate	NOUN
ejpam-4760	56	16	domination	domination	NOUN
ejpam-4760	56	17	number	number	NOUN
ejpam-4760	56	18	and	and	CCONJ
ejpam-4760	56	19	is	be	AUX
ejpam-4760	56	20	denoted	denote	VERB
ejpam-4760	56	21	by	by	ADP
ejpam-4760	56	22	γp0(g	γp0(g	NOUN
ejpam-4760	56	23	)	)	PUNCT
ejpam-4760	56	24	.	.	PUNCT
ejpam-4760	57	1	a	a	DET
ejpam-4760	57	2	perfect	perfect	ADJ
ejpam-4760	57	3	isolate	isolate	NOUN
ejpam-4760	57	4	dominating	dominate	VERB
ejpam-4760	57	5	set	set	NOUN
ejpam-4760	57	6	s	s	NOUN
ejpam-4760	57	7	with	with	ADP
ejpam-4760	57	8	|s|	|s|	PROPN
ejpam-4760	57	9	=	=	SYM
ejpam-4760	57	10	γp0(g	γp0(g	NOUN
ejpam-4760	57	11	)	)	PUNCT
ejpam-4760	57	12	is	be	AUX
ejpam-4760	57	13	said	say	VERB
ejpam-4760	57	14	to	to	PART
ejpam-4760	57	15	be	be	AUX
ejpam-4760	57	16	γp0	γp0	NOUN
ejpam-4760	57	17	-	-	PUNCT
ejpam-4760	57	18	set	set	NOUN
ejpam-4760	57	19	.	.	PUNCT
ejpam-4760	58	1	if	if	SCONJ
ejpam-4760	58	2	a	a	DET
ejpam-4760	58	3	graph	graph	NOUN
ejpam-4760	58	4	g	g	NOUN
ejpam-4760	58	5	has	have	VERB
ejpam-4760	58	6	no	no	DET
ejpam-4760	58	7	perfect	perfect	ADJ
ejpam-4760	58	8	isolate	isolate	NOUN
ejpam-4760	58	9	dominating	dominating	NOUN
ejpam-4760	58	10	set	set	NOUN
ejpam-4760	58	11	,	,	PUNCT
ejpam-4760	58	12	then	then	ADV
ejpam-4760	58	13	we	we	PRON
ejpam-4760	58	14	say	say	VERB
ejpam-4760	58	15	that	that	SCONJ
ejpam-4760	58	16	the	the	DET
ejpam-4760	58	17	graph	graph	NOUN
ejpam-4760	58	18	g	g	PROPN
ejpam-4760	58	19	is	be	AUX
ejpam-4760	58	20	a	a	DET
ejpam-4760	58	21	non	non	ADJ
ejpam-4760	58	22	-	-	ADJ
ejpam-4760	58	23	γp0	γp0	NOUN
ejpam-4760	58	24	-	-	PUNCT
ejpam-4760	58	25	graph	graph	NOUN
ejpam-4760	58	26	.	.	PUNCT
ejpam-4760	58	27	example	example	NOUN
ejpam-4760	59	1	1	1	NUM
ejpam-4760	59	2	.	.	PUNCT
ejpam-4760	59	3	let	let	VERB
ejpam-4760	59	4	g	g	NOUN
ejpam-4760	59	5	be	be	AUX
ejpam-4760	59	6	the	the	DET
ejpam-4760	59	7	graph	graph	NOUN
ejpam-4760	59	8	in	in	ADP
ejpam-4760	59	9	figure	figure	NOUN
ejpam-4760	59	10	1	1	NUM
ejpam-4760	59	11	and	and	CCONJ
ejpam-4760	59	12	s	s	NOUN
ejpam-4760	59	13	=	=	NOUN
ejpam-4760	59	14	{	{	PUNCT
ejpam-4760	59	15	v1	v1	PROPN
ejpam-4760	59	16	,	,	PUNCT
ejpam-4760	59	17	v2	v2	NOUN
ejpam-4760	59	18	,	,	PUNCT
ejpam-4760	59	19	v7	v7	NOUN
ejpam-4760	59	20	}	}	PUNCT
ejpam-4760	59	21	.	.	PUNCT
ejpam-4760	60	1	then	then	ADV
ejpam-4760	60	2	v1	v1	VERB
ejpam-4760	60	3	dominates	dominate	VERB
ejpam-4760	60	4	v3	v3	PROPN
ejpam-4760	60	5	,	,	PUNCT
ejpam-4760	60	6	v2	v2	PROPN
ejpam-4760	60	7	dominates	dominate	VERB
ejpam-4760	60	8	v4	v4	NOUN
ejpam-4760	60	9	,	,	PUNCT
ejpam-4760	60	10	while	while	SCONJ
ejpam-4760	60	11	v7	v7	NOUN
ejpam-4760	60	12	dominates	dominate	VERB
ejpam-4760	60	13	v5	v5	PROPN
ejpam-4760	60	14	and	and	CCONJ
ejpam-4760	60	15	v6	v6	NOUN
ejpam-4760	60	16	.	.	PUNCT
ejpam-4760	61	1	this	this	PRON
ejpam-4760	61	2	shows	show	VERB
ejpam-4760	61	3	that	that	SCONJ
ejpam-4760	61	4	for	for	ADP
ejpam-4760	61	5	all	all	DET
ejpam-4760	61	6	vertices	vertex	NOUN
ejpam-4760	61	7	v3	v3	PROPN
ejpam-4760	61	8	,	,	PUNCT
ejpam-4760	61	9	v4	v4	PROPN
ejpam-4760	61	10	,	,	PUNCT
ejpam-4760	61	11	v5	v5	PROPN
ejpam-4760	61	12	,	,	PUNCT
ejpam-4760	61	13	v6	v6	NOUN
ejpam-4760	61	14	are	be	AUX
ejpam-4760	61	15	elements	element	NOUN
ejpam-4760	61	16	in	in	ADP
ejpam-4760	61	17	v	v	NOUN
ejpam-4760	61	18	(	(	PUNCT
ejpam-4760	61	19	g	g	NOUN
ejpam-4760	61	20	)	)	PUNCT
ejpam-4760	61	21	\s	\s	NOUN
ejpam-4760	61	22	which	which	PRON
ejpam-4760	61	23	are	be	AUX
ejpam-4760	61	24	dominated	dominate	VERB
ejpam-4760	61	25	by	by	ADP
ejpam-4760	61	26	exactly	exactly	ADV
ejpam-4760	61	27	one	one	NUM
ejpam-4760	61	28	vertex	vertex	NOUN
ejpam-4760	61	29	in	in	ADP
ejpam-4760	61	30	s.	s.	PROPN
ejpam-4760	61	31	thus	thus	ADV
ejpam-4760	61	32	,	,	PUNCT
ejpam-4760	61	33	s	s	VERB
ejpam-4760	61	34	is	be	AUX
ejpam-4760	61	35	a	a	DET
ejpam-4760	61	36	perfect	perfect	ADJ
ejpam-4760	61	37	dominating	dominating	NOUN
ejpam-4760	61	38	set	set	NOUN
ejpam-4760	61	39	of	of	ADP
ejpam-4760	61	40	g.	g.	PROPN
ejpam-4760	61	41	observe	observe	VERB
ejpam-4760	61	42	further	far	ADV
ejpam-4760	61	43	that	that	SCONJ
ejpam-4760	61	44	v7	v7	NOUN
ejpam-4760	61	45	is	be	AUX
ejpam-4760	61	46	an	an	DET
ejpam-4760	61	47	isolated	isolated	ADJ
ejpam-4760	61	48	vertex	vertex	NOUN
ejpam-4760	61	49	of	of	ADP
ejpam-4760	61	50	the	the	DET
ejpam-4760	61	51	induced	induced	ADJ
ejpam-4760	61	52	subgraph	subgraph	NOUN
ejpam-4760	61	53	⟨s⟩.	⟨s⟩.	PROPN
ejpam-4760	61	54	therefore	therefore	ADV
ejpam-4760	61	55	,	,	PUNCT
ejpam-4760	61	56	s	s	VERB
ejpam-4760	61	57	is	be	AUX
ejpam-4760	61	58	a	a	DET
ejpam-4760	61	59	perfect	perfect	ADJ
ejpam-4760	61	60	isolate	isolate	NOUN
ejpam-4760	61	61	dominating	dominating	NOUN
ejpam-4760	61	62	set	set	NOUN
ejpam-4760	61	63	of	of	ADP
ejpam-4760	61	64	g	g	PROPN
ejpam-4760	61	65	and	and	CCONJ
ejpam-4760	61	66	γp0(g	γp0(g	NOUN
ejpam-4760	61	67	)	)	PUNCT
ejpam-4760	61	68	=	=	SYM
ejpam-4760	61	69	γp(g	γp(g	X
ejpam-4760	61	70	)	)	PUNCT
ejpam-4760	62	1	=	=	NOUN
ejpam-4760	62	2	|s|=	|s|=	DET
ejpam-4760	62	3	3	3	NUM
ejpam-4760	62	4	.	.	X
ejpam-4760	62	5	v1	v1	PROPN
ejpam-4760	62	6	v2	v2	PROPN
ejpam-4760	62	7	v3	v3	PROPN
ejpam-4760	62	8	v4	v4	PROPN
ejpam-4760	62	9	v5	v5	PROPN
ejpam-4760	62	10	v6	v6	NOUN
ejpam-4760	62	11	v7	v7	VERB
ejpam-4760	63	1	g	g	NOUN
ejpam-4760	63	2	:	:	PUNCT
ejpam-4760	63	3	figure	figure	NOUN
ejpam-4760	63	4	1	1	NUM
ejpam-4760	63	5	:	:	PUNCT
ejpam-4760	63	6	graph	graph	VERB
ejpam-4760	63	7	g	g	NOUN
ejpam-4760	63	8	with	with	ADP
ejpam-4760	63	9	γp0(g	γp0(g	NOUN
ejpam-4760	63	10	)	)	PUNCT
ejpam-4760	63	11	=	=	SYM
ejpam-4760	63	12	γp(g	γp(g	X
ejpam-4760	63	13	)	)	PUNCT
ejpam-4760	63	14	=	=	SYM
ejpam-4760	63	15	3	3	NUM
ejpam-4760	63	16	3	3	NUM
ejpam-4760	63	17	.	.	PUNCT
ejpam-4760	63	18	results	result	NOUN
ejpam-4760	63	19	this	this	DET
ejpam-4760	63	20	section	section	NOUN
ejpam-4760	63	21	contains	contain	VERB
ejpam-4760	63	22	some	some	DET
ejpam-4760	63	23	known	know	VERB
ejpam-4760	63	24	results	result	NOUN
ejpam-4760	63	25	involving	involve	VERB
ejpam-4760	63	26	the	the	DET
ejpam-4760	63	27	domination	domination	NOUN
ejpam-4760	63	28	number	number	NOUN
ejpam-4760	63	29	,	,	PUNCT
ejpam-4760	63	30	the	the	DET
ejpam-4760	63	31	perfect	perfect	ADJ
ejpam-4760	63	32	domination	domination	NOUN
ejpam-4760	63	33	number	number	NOUN
ejpam-4760	63	34	and	and	CCONJ
ejpam-4760	63	35	the	the	DET
ejpam-4760	63	36	isolate	isolate	ADJ
ejpam-4760	63	37	domination	domination	NOUN
ejpam-4760	63	38	number	number	NOUN
ejpam-4760	63	39	.	.	PUNCT
ejpam-4760	64	1	also	also	ADV
ejpam-4760	64	2	,	,	PUNCT
ejpam-4760	64	3	it	it	PRON
ejpam-4760	64	4	contains	contain	VERB
ejpam-4760	64	5	the	the	DET
ejpam-4760	64	6	the	the	DET
ejpam-4760	64	7	perfect	perfect	ADJ
ejpam-4760	64	8	isolate	isolate	NOUN
ejpam-4760	64	9	domination	domination	NOUN
ejpam-4760	64	10	number	number	NOUN
ejpam-4760	64	11	of	of	ADP
ejpam-4760	64	12	paths	path	NOUN
ejpam-4760	64	13	,	,	PUNCT
ejpam-4760	64	14	cycles	cycle	NOUN
ejpam-4760	64	15	,	,	PUNCT
ejpam-4760	64	16	complete	complete	ADJ
ejpam-4760	64	17	graphs	graph	NOUN
ejpam-4760	64	18	,	,	PUNCT
ejpam-4760	64	19	fans	fan	NOUN
ejpam-4760	64	20	,	,	PUNCT
ejpam-4760	64	21	wheels	wheel	NOUN
ejpam-4760	64	22	,	,	PUNCT
ejpam-4760	64	23	friendship	friendship	NOUN
ejpam-4760	64	24	graphs	graph	NOUN
ejpam-4760	64	25	,	,	PUNCT
ejpam-4760	64	26	windmill	windmill	NOUN
ejpam-4760	64	27	graphs	graph	NOUN
ejpam-4760	64	28	and	and	CCONJ
ejpam-4760	64	29	graphs	graph	NOUN
ejpam-4760	64	30	resulting	result	VERB
ejpam-4760	64	31	from	from	ADP
ejpam-4760	64	32	some	some	DET
ejpam-4760	64	33	binary	binary	ADJ
ejpam-4760	64	34	operations	operation	NOUN
ejpam-4760	64	35	.	.	PUNCT
ejpam-4760	65	1	furthermore	furthermore	ADV
ejpam-4760	65	2	,	,	PUNCT
ejpam-4760	65	3	some	some	DET
ejpam-4760	65	4	non	non	ADJ
ejpam-4760	65	5	-	-	ADJ
ejpam-4760	65	6	γp0	γp0	NOUN
ejpam-4760	65	7	-	-	PUNCT
ejpam-4760	65	8	graphs	graph	NOUN
ejpam-4760	65	9	are	be	AUX
ejpam-4760	65	10	shown	show	VERB
ejpam-4760	65	11	.	.	PUNCT
ejpam-4760	66	1	proposition	proposition	NOUN
ejpam-4760	66	2	1	1	NUM
ejpam-4760	66	3	.	.	PUNCT
ejpam-4760	67	1	[	[	X
ejpam-4760	67	2	8	8	NUM
ejpam-4760	67	3	]	]	PUNCT
ejpam-4760	67	4	for	for	ADP
ejpam-4760	67	5	paths	path	NOUN
ejpam-4760	67	6	and	and	CCONJ
ejpam-4760	67	7	cycles	cycle	NOUN
ejpam-4760	67	8	of	of	ADP
ejpam-4760	67	9	order	order	NOUN
ejpam-4760	67	10	n	n	CCONJ
ejpam-4760	67	11	,	,	PUNCT
ejpam-4760	67	12	γ0(pn	γ0(pn	PROPN
ejpam-4760	67	13	)	)	PUNCT
ejpam-4760	67	14	=	=	SYM
ejpam-4760	67	15	γ0(cn	γ0(cn	PROPN
ejpam-4760	67	16	)	)	PUNCT
ejpam-4760	68	1	=	=	PRON
ejpam-4760	68	2	⌈n3	⌈n3	VERB
ejpam-4760	68	3	⌉.	⌉.	ADV
ejpam-4760	68	4	proposition	proposition	NOUN
ejpam-4760	68	5	2	2	NUM
ejpam-4760	68	6	.	.	PUNCT
ejpam-4760	69	1	[	[	X
ejpam-4760	69	2	8	8	NUM
ejpam-4760	69	3	]	]	PUNCT
ejpam-4760	69	4	for	for	ADP
ejpam-4760	69	5	kn	kn	PROPN
ejpam-4760	69	6	,	,	PUNCT
ejpam-4760	69	7	sn−1	sn−1	PROPN
ejpam-4760	69	8	,	,	PUNCT
ejpam-4760	69	9	and	and	CCONJ
ejpam-4760	69	10	wn−1	wn−1	PROPN
ejpam-4760	69	11	be	be	AUX
ejpam-4760	69	12	complete	complete	ADJ
ejpam-4760	69	13	,	,	PUNCT
ejpam-4760	69	14	star	star	NOUN
ejpam-4760	69	15	,	,	PUNCT
ejpam-4760	69	16	and	and	CCONJ
ejpam-4760	69	17	wheel	wheel	NOUN
ejpam-4760	69	18	of	of	ADP
ejpam-4760	69	19	n	n	PRON
ejpam-4760	69	20	≥	≥	NUM
ejpam-4760	69	21	2	2	NUM
ejpam-4760	69	22	vertices	vertex	NOUN
ejpam-4760	69	23	,	,	PUNCT
ejpam-4760	69	24	respectively	respectively	ADV
ejpam-4760	69	25	.	.	PUNCT
ejpam-4760	70	1	then	then	ADV
ejpam-4760	70	2	γ0(kn	γ0(kn	NUM
ejpam-4760	70	3	)	)	PUNCT
ejpam-4760	70	4	=	=	SYM
ejpam-4760	70	5	γ0(sn−1	γ0(sn−1	X
ejpam-4760	70	6	)	)	PUNCT
ejpam-4760	70	7	=	=	SYM
ejpam-4760	70	8	γ0(wn−1	γ0(wn−1	X
ejpam-4760	70	9	)	)	PUNCT
ejpam-4760	70	10	=	=	SYM
ejpam-4760	70	11	1	1	X
ejpam-4760	70	12	.	.	X
ejpam-4760	70	13	theorem	theorem	NOUN
ejpam-4760	70	14	1	1	NUM
ejpam-4760	70	15	.	.	PUNCT
ejpam-4760	71	1	[	[	X
ejpam-4760	71	2	8	8	NUM
ejpam-4760	71	3	]	]	PUNCT
ejpam-4760	71	4	for	for	ADP
ejpam-4760	71	5	kn	kn	PROPN
ejpam-4760	71	6	,	,	PUNCT
ejpam-4760	71	7	sn−1	sn−1	PROPN
ejpam-4760	71	8	,	,	PUNCT
ejpam-4760	71	9	and	and	CCONJ
ejpam-4760	71	10	wn−1	wn−1	PROPN
ejpam-4760	71	11	be	be	AUX
ejpam-4760	71	12	complete	complete	ADJ
ejpam-4760	71	13	,	,	PUNCT
ejpam-4760	71	14	star	star	NOUN
ejpam-4760	71	15	,	,	PUNCT
ejpam-4760	71	16	and	and	CCONJ
ejpam-4760	71	17	wheel	wheel	NOUN
ejpam-4760	71	18	of	of	ADP
ejpam-4760	71	19	n	n	PRON
ejpam-4760	71	20	≥	≥	NUM
ejpam-4760	71	21	2	2	NUM
ejpam-4760	71	22	vertices	vertex	NOUN
ejpam-4760	71	23	,	,	PUNCT
ejpam-4760	71	24	respectively	respectively	ADV
ejpam-4760	71	25	.	.	PUNCT
ejpam-4760	72	1	then	then	ADV
ejpam-4760	72	2	γ0(kn	γ0(kn	NUM
ejpam-4760	72	3	)	)	PUNCT
ejpam-4760	72	4	=	=	SYM
ejpam-4760	72	5	γ0(sn−1	γ0(sn−1	X
ejpam-4760	72	6	)	)	PUNCT
ejpam-4760	72	7	=	=	SYM
ejpam-4760	72	8	γ0(wn−1	γ0(wn−1	X
ejpam-4760	72	9	)	)	PUNCT
ejpam-4760	72	10	=	=	SYM
ejpam-4760	72	11	1	1	X
ejpam-4760	72	12	.	.	PUNCT
ejpam-4760	72	13	c.	c.	PROPN
ejpam-4760	72	14	armada	armada	PROPN
ejpam-4760	72	15	,	,	PUNCT
ejpam-4760	72	16	j.	j.	PROPN
ejpam-4760	72	17	hamja	hamja	PROPN
ejpam-4760	72	18	/	/	SYM
ejpam-4760	72	19	eur	eur	PROPN
ejpam-4760	72	20	.	.	PUNCT
ejpam-4760	73	1	j.	j.	PROPN
ejpam-4760	73	2	pure	pure	PROPN
ejpam-4760	73	3	appl	appl	PROPN
ejpam-4760	73	4	.	.	PROPN
ejpam-4760	73	5	math	math	PROPN
ejpam-4760	73	6	,	,	PUNCT
ejpam-4760	73	7	16	16	NUM
ejpam-4760	73	8	(	(	PUNCT
ejpam-4760	73	9	2	2	NUM
ejpam-4760	73	10	)	)	PUNCT
ejpam-4760	73	11	(	(	PUNCT
ejpam-4760	73	12	2023	2023	NUM
ejpam-4760	73	13	)	)	PUNCT
ejpam-4760	73	14	,	,	PUNCT
ejpam-4760	73	15	1326	1326	NUM
ejpam-4760	73	16	-	-	SYM
ejpam-4760	73	17	1341	1341	NUM
ejpam-4760	73	18	1329	1329	NUM
ejpam-4760	73	19	corollary	corollary	NOUN
ejpam-4760	73	20	1	1	NUM
ejpam-4760	73	21	.	.	PUNCT
ejpam-4760	74	1	[	[	X
ejpam-4760	74	2	3	3	X
ejpam-4760	74	3	]	]	PUNCT
ejpam-4760	74	4	let	let	VERB
ejpam-4760	74	5	g	g	NOUN
ejpam-4760	74	6	and	and	CCONJ
ejpam-4760	74	7	h	h	NOUN
ejpam-4760	74	8	be	be	AUX
ejpam-4760	74	9	connected	connect	VERB
ejpam-4760	74	10	graphs	graph	NOUN
ejpam-4760	74	11	.	.	PUNCT
ejpam-4760	75	1	then	then	ADV
ejpam-4760	75	2	γ(g+h	γ(g+h	NUM
ejpam-4760	75	3	)	)	PUNCT
ejpam-4760	76	1	=	=	PRON
ejpam-4760	76	2	{	{	PUNCT
ejpam-4760	76	3	1	1	NUM
ejpam-4760	76	4	,	,	PUNCT
ejpam-4760	76	5	γ(g	γ(g	PROPN
ejpam-4760	76	6	)	)	PUNCT
ejpam-4760	76	7	=	=	SYM
ejpam-4760	76	8	1	1	NUM
ejpam-4760	76	9	or	or	CCONJ
ejpam-4760	76	10	γ(h	γ(h	NOUN
ejpam-4760	76	11	)	)	PUNCT
ejpam-4760	76	12	=	=	SYM
ejpam-4760	76	13	1	1	NUM
ejpam-4760	76	14	2	2	NUM
ejpam-4760	76	15	,	,	PUNCT
ejpam-4760	76	16	γ(g	γ(g	PROPN
ejpam-4760	76	17	)	)	PUNCT
ejpam-4760	76	18	̸=	̸=	PROPN
ejpam-4760	76	19	1	1	NUM
ejpam-4760	76	20	and	and	CCONJ
ejpam-4760	76	21	γ(h	γ(h	NOUN
ejpam-4760	76	22	)	)	PUNCT
ejpam-4760	76	23	̸=	̸=	PROPN
ejpam-4760	76	24	1	1	NUM
ejpam-4760	76	25	.	.	PUNCT
ejpam-4760	77	1	the	the	DET
ejpam-4760	77	2	next	next	ADJ
ejpam-4760	77	3	four	four	NUM
ejpam-4760	77	4	results	result	NOUN
ejpam-4760	77	5	follow	follow	VERB
ejpam-4760	77	6	directly	directly	ADV
ejpam-4760	77	7	from	from	ADP
ejpam-4760	77	8	the	the	DET
ejpam-4760	77	9	definition	definition	NOUN
ejpam-4760	77	10	of	of	ADP
ejpam-4760	77	11	perfect	perfect	ADJ
ejpam-4760	77	12	isolate	isolate	NOUN
ejpam-4760	77	13	dominating	dominating	NOUN
ejpam-4760	77	14	set	set	NOUN
ejpam-4760	77	15	.	.	PUNCT
ejpam-4760	78	1	proposition	proposition	NOUN
ejpam-4760	78	2	3	3	NUM
ejpam-4760	78	3	.	.	PUNCT
ejpam-4760	79	1	let	let	VERB
ejpam-4760	79	2	s	s	PRON
ejpam-4760	79	3	⊆	⊆	NUM
ejpam-4760	79	4	v	v	NOUN
ejpam-4760	79	5	(	(	PUNCT
ejpam-4760	79	6	g	g	NOUN
ejpam-4760	79	7	)	)	PUNCT
ejpam-4760	79	8	be	be	AUX
ejpam-4760	79	9	an	an	DET
ejpam-4760	79	10	isolate	isolate	NOUN
ejpam-4760	79	11	dominating	dominating	NOUN
ejpam-4760	79	12	set	set	NOUN
ejpam-4760	79	13	of	of	ADP
ejpam-4760	79	14	g.	g.	PROPN
ejpam-4760	80	1	then	then	ADV
ejpam-4760	80	2	s	s	VERB
ejpam-4760	80	3	is	be	AUX
ejpam-4760	80	4	a	a	DET
ejpam-4760	80	5	perfect	perfect	ADJ
ejpam-4760	80	6	isolate	isolate	NOUN
ejpam-4760	80	7	dominating	dominating	NOUN
ejpam-4760	80	8	set	set	NOUN
ejpam-4760	80	9	if	if	SCONJ
ejpam-4760	80	10	and	and	CCONJ
ejpam-4760	80	11	only	only	ADV
ejpam-4760	80	12	if	if	SCONJ
ejpam-4760	80	13	for	for	ADP
ejpam-4760	80	14	every	every	PRON
ejpam-4760	80	15	v	v	NUM
ejpam-4760	80	16	∈	∈	NOUN
ejpam-4760	80	17	v	v	NOUN
ejpam-4760	80	18	(	(	PUNCT
ejpam-4760	80	19	g	g	NOUN
ejpam-4760	80	20	)	)	PUNCT
ejpam-4760	80	21	\	\	PROPN
ejpam-4760	80	22	s	s	PROPN
ejpam-4760	80	23	,	,	PUNCT
ejpam-4760	80	24	ng(v	ng(v	PUNCT
ejpam-4760	80	25	)	)	PUNCT
ejpam-4760	80	26	∩	∩	NOUN
ejpam-4760	80	27	s	s	PART
ejpam-4760	80	28	=	=	SYM
ejpam-4760	80	29	{	{	PUNCT
ejpam-4760	80	30	u	u	NOUN
ejpam-4760	80	31	}	}	PUNCT
ejpam-4760	80	32	for	for	ADP
ejpam-4760	80	33	some	some	DET
ejpam-4760	80	34	u	u	PROPN
ejpam-4760	80	35	∈	∈	PROPN
ejpam-4760	80	36	s.	s.	PROPN
ejpam-4760	80	37	proposition	proposition	NOUN
ejpam-4760	80	38	4	4	X
ejpam-4760	80	39	.	.	PUNCT
ejpam-4760	81	1	if	if	SCONJ
ejpam-4760	81	2	s	s	NOUN
ejpam-4760	81	3	is	be	AUX
ejpam-4760	81	4	a	a	DET
ejpam-4760	81	5	dominating	dominating	NOUN
ejpam-4760	81	6	set	set	NOUN
ejpam-4760	81	7	or	or	CCONJ
ejpam-4760	81	8	a	a	DET
ejpam-4760	81	9	perfect	perfect	ADJ
ejpam-4760	81	10	dominating	dominating	NOUN
ejpam-4760	81	11	set	set	NOUN
ejpam-4760	81	12	or	or	CCONJ
ejpam-4760	81	13	an	an	DET
ejpam-4760	81	14	isolate	isolate	NOUN
ejpam-4760	81	15	dominating	dominating	NOUN
ejpam-4760	81	16	set	set	NOUN
ejpam-4760	81	17	of	of	ADP
ejpam-4760	81	18	g	g	NOUN
ejpam-4760	81	19	with	with	ADP
ejpam-4760	81	20	|s|	|s|	NOUN
ejpam-4760	81	21	=	=	SYM
ejpam-4760	81	22	1	1	NUM
ejpam-4760	81	23	,	,	PUNCT
ejpam-4760	81	24	then	then	ADV
ejpam-4760	81	25	s	s	VERB
ejpam-4760	81	26	is	be	AUX
ejpam-4760	81	27	a	a	DET
ejpam-4760	81	28	perfect	perfect	ADJ
ejpam-4760	81	29	isolate	isolate	NOUN
ejpam-4760	81	30	dominating	dominating	NOUN
ejpam-4760	81	31	set	set	NOUN
ejpam-4760	81	32	of	of	ADP
ejpam-4760	81	33	g.	g.	PROPN
ejpam-4760	81	34	in	in	ADP
ejpam-4760	81	35	particular	particular	ADJ
ejpam-4760	81	36	,	,	PUNCT
ejpam-4760	81	37	γ(g	γ(g	PROPN
ejpam-4760	81	38	)	)	PUNCT
ejpam-4760	81	39	=	=	SYM
ejpam-4760	81	40	γp(g	γp(g	X
ejpam-4760	81	41	)	)	PUNCT
ejpam-4760	81	42	=	=	SYM
ejpam-4760	82	1	γ0(g	γ0(g	X
ejpam-4760	82	2	)	)	PUNCT
ejpam-4760	82	3	=	=	SYM
ejpam-4760	82	4	1	1	NUM
ejpam-4760	82	5	if	if	SCONJ
ejpam-4760	82	6	and	and	CCONJ
ejpam-4760	82	7	only	only	ADV
ejpam-4760	82	8	if	if	SCONJ
ejpam-4760	82	9	γp0(g	γp0(g	NOUN
ejpam-4760	82	10	)	)	PUNCT
ejpam-4760	82	11	=	=	SYM
ejpam-4760	83	1	1	1	X
ejpam-4760	83	2	.	.	X
ejpam-4760	83	3	proposition	proposition	NOUN
ejpam-4760	83	4	5	5	NUM
ejpam-4760	83	5	.	.	PUNCT
ejpam-4760	84	1	if	if	SCONJ
ejpam-4760	84	2	γp(g	γp(g	NOUN
ejpam-4760	84	3	)	)	PUNCT
ejpam-4760	85	1	=	=	SYM
ejpam-4760	86	1	c	c	NOUN
ejpam-4760	86	2	where	where	SCONJ
ejpam-4760	86	3	c	c	PROPN
ejpam-4760	86	4	∈	∈	PROPN
ejpam-4760	86	5	z+	z+	NUM
ejpam-4760	86	6	and	and	CCONJ
ejpam-4760	86	7	if	if	SCONJ
ejpam-4760	86	8	s	s	VERB
ejpam-4760	86	9	is	be	AUX
ejpam-4760	86	10	a	a	DET
ejpam-4760	86	11	γp	γp	NOUN
ejpam-4760	86	12	-	-	PUNCT
ejpam-4760	86	13	set	set	NOUN
ejpam-4760	86	14	of	of	ADP
ejpam-4760	86	15	g	g	NOUN
ejpam-4760	86	16	such	such	ADJ
ejpam-4760	86	17	that	that	SCONJ
ejpam-4760	86	18	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	86	19	has	have	VERB
ejpam-4760	86	20	an	an	DET
ejpam-4760	86	21	isolated	isolated	ADJ
ejpam-4760	86	22	vertex	vertex	NOUN
ejpam-4760	86	23	,	,	PUNCT
ejpam-4760	86	24	then	then	ADV
ejpam-4760	86	25	γp0(g	γp0(g	NOUN
ejpam-4760	86	26	)	)	PUNCT
ejpam-4760	86	27	=	=	SYM
ejpam-4760	86	28	c.	c.	NOUN
ejpam-4760	86	29	proposition	proposition	NOUN
ejpam-4760	86	30	6	6	NUM
ejpam-4760	86	31	.	.	PUNCT
ejpam-4760	87	1	if	if	SCONJ
ejpam-4760	87	2	γ0(g	γ0(g	NOUN
ejpam-4760	87	3	)	)	PUNCT
ejpam-4760	88	1	=	=	SYM
ejpam-4760	89	1	c	c	NOUN
ejpam-4760	89	2	where	where	SCONJ
ejpam-4760	89	3	c	c	PROPN
ejpam-4760	89	4	∈	∈	PROPN
ejpam-4760	89	5	z+	z+	NUM
ejpam-4760	89	6	and	and	CCONJ
ejpam-4760	89	7	if	if	SCONJ
ejpam-4760	89	8	s	s	X
ejpam-4760	89	9	is	be	AUX
ejpam-4760	89	10	a	a	DET
ejpam-4760	89	11	γ0	γ0	NOUN
ejpam-4760	89	12	-	-	PUNCT
ejpam-4760	89	13	set	set	NOUN
ejpam-4760	89	14	of	of	ADP
ejpam-4760	89	15	g	g	NOUN
ejpam-4760	89	16	such	such	ADJ
ejpam-4760	89	17	that	that	SCONJ
ejpam-4760	89	18	every	every	DET
ejpam-4760	89	19	vertex	vertex	NOUN
ejpam-4760	89	20	v	v	ADP
ejpam-4760	89	21	∈	∈	PROPN
ejpam-4760	89	22	v	v	NOUN
ejpam-4760	89	23	(	(	PUNCT
ejpam-4760	89	24	g	g	NOUN
ejpam-4760	89	25	)	)	PUNCT
ejpam-4760	89	26	\	\	PROPN
ejpam-4760	90	1	s	s	PART
ejpam-4760	90	2	is	be	AUX
ejpam-4760	90	3	dominated	dominate	VERB
ejpam-4760	90	4	by	by	ADP
ejpam-4760	90	5	exactly	exactly	ADV
ejpam-4760	90	6	one	one	NUM
ejpam-4760	90	7	vertex	vertex	NOUN
ejpam-4760	90	8	in	in	ADP
ejpam-4760	90	9	s	s	PROPN
ejpam-4760	90	10	,	,	PUNCT
ejpam-4760	90	11	then	then	ADV
ejpam-4760	90	12	γp0(g	γp0(g	NOUN
ejpam-4760	90	13	)	)	PUNCT
ejpam-4760	90	14	=	=	SYM
ejpam-4760	90	15	c.	c.	NOUN
ejpam-4760	90	16	proposition	proposition	NOUN
ejpam-4760	90	17	7	7	NUM
ejpam-4760	90	18	.	.	PUNCT
ejpam-4760	91	1	let	let	VERB
ejpam-4760	91	2	g	g	NOUN
ejpam-4760	91	3	be	be	AUX
ejpam-4760	91	4	any	any	DET
ejpam-4760	91	5	graph	graph	NOUN
ejpam-4760	91	6	such	such	ADJ
ejpam-4760	91	7	that	that	SCONJ
ejpam-4760	91	8	g	g	PROPN
ejpam-4760	91	9	has	have	VERB
ejpam-4760	91	10	a	a	DET
ejpam-4760	91	11	perfect	perfect	ADJ
ejpam-4760	91	12	isolate	isolate	NOUN
ejpam-4760	91	13	dominating	dominating	NOUN
ejpam-4760	91	14	set	set	NOUN
ejpam-4760	91	15	.	.	PUNCT
ejpam-4760	92	1	then	then	ADV
ejpam-4760	92	2	γ0(g	γ0(g	NOUN
ejpam-4760	92	3	)	)	PUNCT
ejpam-4760	92	4	≤	≤	NUM
ejpam-4760	92	5	γp0(g	γp0(g	NOUN
ejpam-4760	92	6	)	)	PUNCT
ejpam-4760	92	7	.	.	PUNCT
ejpam-4760	93	1	theorem	theorem	NOUN
ejpam-4760	93	2	2	2	NUM
ejpam-4760	93	3	.	.	X
ejpam-4760	94	1	for	for	ADP
ejpam-4760	94	2	any	any	DET
ejpam-4760	94	3	positive	positive	ADJ
ejpam-4760	94	4	integers	integer	NOUN
ejpam-4760	94	5	a	a	PRON
ejpam-4760	94	6	and	and	CCONJ
ejpam-4760	94	7	b	b	NOUN
ejpam-4760	94	8	with	with	ADP
ejpam-4760	94	9	1	1	NUM
ejpam-4760	94	10	≤	≤	NOUN
ejpam-4760	94	11	a	a	DET
ejpam-4760	94	12	≤	≤	NUM
ejpam-4760	94	13	b	b	NOUN
ejpam-4760	94	14	,	,	PUNCT
ejpam-4760	94	15	there	there	PRON
ejpam-4760	94	16	exists	exist	VERB
ejpam-4760	94	17	a	a	DET
ejpam-4760	94	18	connected	connected	ADJ
ejpam-4760	94	19	graph	graph	NOUN
ejpam-4760	94	20	g	g	ADP
ejpam-4760	94	21	such	such	ADJ
ejpam-4760	94	22	that	that	SCONJ
ejpam-4760	94	23	γ0(g	γ0(g	NOUN
ejpam-4760	94	24	)	)	PUNCT
ejpam-4760	94	25	=	=	SYM
ejpam-4760	94	26	a	a	PROPN
ejpam-4760	94	27	and	and	CCONJ
ejpam-4760	94	28	γp0(g	γp0(g	NOUN
ejpam-4760	94	29	)	)	PUNCT
ejpam-4760	94	30	=	=	SYM
ejpam-4760	94	31	b.	b.	PROPN
ejpam-4760	94	32	proof	proof	NOUN
ejpam-4760	94	33	.	.	PUNCT
ejpam-4760	95	1	consider	consider	VERB
ejpam-4760	95	2	the	the	DET
ejpam-4760	95	3	following	follow	VERB
ejpam-4760	95	4	cases	case	NOUN
ejpam-4760	95	5	:	:	PUNCT
ejpam-4760	95	6	case	case	NOUN
ejpam-4760	95	7	1	1	NUM
ejpam-4760	95	8	:	:	PUNCT
ejpam-4760	95	9	a	a	DET
ejpam-4760	95	10	=	=	SYM
ejpam-4760	95	11	b	b	NOUN
ejpam-4760	95	12	let	let	VERB
ejpam-4760	95	13	g	g	PRON
ejpam-4760	95	14	be	be	AUX
ejpam-4760	95	15	the	the	DET
ejpam-4760	95	16	graph	graph	NOUN
ejpam-4760	95	17	shown	show	VERB
ejpam-4760	95	18	in	in	ADP
ejpam-4760	95	19	figure	figure	NOUN
ejpam-4760	95	20	2	2	NUM
ejpam-4760	95	21	.	.	PUNCT
ejpam-4760	96	1	clearly	clearly	ADV
ejpam-4760	96	2	,	,	PUNCT
ejpam-4760	96	3	the	the	DET
ejpam-4760	96	4	set	set	NOUN
ejpam-4760	96	5	s1	s1	NOUN
ejpam-4760	96	6	=	=	SYM
ejpam-4760	96	7	{	{	PUNCT
ejpam-4760	96	8	v1	v1	PROPN
ejpam-4760	96	9	,	,	PUNCT
ejpam-4760	96	10	v2	v2	PROPN
ejpam-4760	96	11	,	,	PUNCT
ejpam-4760	96	12	v3	v3	PROPN
ejpam-4760	96	13	,	,	PUNCT
ejpam-4760	96	14	.	.	PUNCT
ejpam-4760	96	15	.	.	PUNCT
ejpam-4760	96	16	.	.	PUNCT
ejpam-4760	97	1	,	,	PUNCT
ejpam-4760	97	2	va	va	X
ejpam-4760	97	3	}	}	PUNCT
ejpam-4760	97	4	is	be	AUX
ejpam-4760	97	5	both	both	DET
ejpam-4760	97	6	γ0	γ0	NOUN
ejpam-4760	97	7	-	-	PUNCT
ejpam-4760	97	8	set	set	VERB
ejpam-4760	97	9	and	and	CCONJ
ejpam-4760	97	10	γp0	γp0	NOUN
ejpam-4760	97	11	-	-	PUNCT
ejpam-4760	97	12	set	set	NOUN
ejpam-4760	97	13	of	of	ADP
ejpam-4760	97	14	g.	g.	PROPN
ejpam-4760	97	15	therefore	therefore	ADV
ejpam-4760	97	16	,	,	PUNCT
ejpam-4760	97	17	γ0(g	γ0(g	PROPN
ejpam-4760	97	18	)	)	PUNCT
ejpam-4760	97	19	=	=	SYM
ejpam-4760	97	20	γp0(g	γp0(g	NOUN
ejpam-4760	97	21	)	)	PUNCT
ejpam-4760	97	22	=	=	SYM
ejpam-4760	98	1	a	a	PROPN
ejpam-4760	98	2	=	=	X
ejpam-4760	98	3	b.	b.	PROPN
ejpam-4760	98	4	.	.	PUNCT
ejpam-4760	98	5	.	.	PUNCT
ejpam-4760	98	6	.	.	PUNCT
ejpam-4760	98	7	.	.	PUNCT
ejpam-4760	98	8	.	.	PUNCT
ejpam-4760	98	9	.	.	PUNCT
ejpam-4760	99	1	v1	v1	PROPN
ejpam-4760	99	2	v2	v2	PROPN
ejpam-4760	99	3	v3	v3	PROPN
ejpam-4760	99	4	va−1	va−1	PROPN
ejpam-4760	99	5	va	va	PROPN
ejpam-4760	99	6	u1	u1	PROPN
ejpam-4760	99	7	u2	u2	PROPN
ejpam-4760	99	8	u3	u3	PROPN
ejpam-4760	99	9	ua−1	ua−1	PROPN
ejpam-4760	99	10	ua	ua	PROPN
ejpam-4760	99	11	g	g	PROPN
ejpam-4760	99	12	:	:	PUNCT
ejpam-4760	99	13	figure	figure	NOUN
ejpam-4760	99	14	2	2	NUM
ejpam-4760	99	15	:	:	PUNCT
ejpam-4760	99	16	graph	graph	VERB
ejpam-4760	99	17	g	g	NOUN
ejpam-4760	99	18	with	with	ADP
ejpam-4760	99	19	γ0(g	γ0(g	NOUN
ejpam-4760	99	20	)	)	PUNCT
ejpam-4760	99	21	=	=	SYM
ejpam-4760	99	22	γp0(g	γp0(g	NOUN
ejpam-4760	99	23	)	)	PUNCT
ejpam-4760	99	24	=	=	PUNCT
ejpam-4760	99	25	a	a	DET
ejpam-4760	99	26	c.	c.	PROPN
ejpam-4760	99	27	armada	armada	PROPN
ejpam-4760	99	28	,	,	PUNCT
ejpam-4760	99	29	j.	j.	PROPN
ejpam-4760	99	30	hamja	hamja	PROPN
ejpam-4760	99	31	/	/	SYM
ejpam-4760	99	32	eur	eur	PROPN
ejpam-4760	99	33	.	.	PUNCT
ejpam-4760	100	1	j.	j.	PROPN
ejpam-4760	100	2	pure	pure	PROPN
ejpam-4760	100	3	appl	appl	PROPN
ejpam-4760	100	4	.	.	PROPN
ejpam-4760	100	5	math	math	PROPN
ejpam-4760	100	6	,	,	PUNCT
ejpam-4760	100	7	16	16	NUM
ejpam-4760	100	8	(	(	PUNCT
ejpam-4760	100	9	2	2	NUM
ejpam-4760	100	10	)	)	PUNCT
ejpam-4760	100	11	(	(	PUNCT
ejpam-4760	100	12	2023	2023	NUM
ejpam-4760	100	13	)	)	PUNCT
ejpam-4760	100	14	,	,	PUNCT
ejpam-4760	100	15	1326	1326	NUM
ejpam-4760	100	16	-	-	SYM
ejpam-4760	100	17	1341	1341	NUM
ejpam-4760	100	18	1330	1330	NUM
ejpam-4760	100	19	case	case	NOUN
ejpam-4760	100	20	2	2	NUM
ejpam-4760	100	21	:	:	PUNCT
ejpam-4760	100	22	a	a	DET
ejpam-4760	100	23	<	<	X
ejpam-4760	100	24	b.	b.	NOUN
ejpam-4760	100	25	let	let	VERB
ejpam-4760	100	26	g	g	NOUN
ejpam-4760	100	27	be	be	AUX
ejpam-4760	100	28	the	the	DET
ejpam-4760	100	29	graph	graph	NOUN
ejpam-4760	100	30	shown	show	VERB
ejpam-4760	100	31	in	in	ADP
ejpam-4760	100	32	figures	figure	NOUN
ejpam-4760	100	33	3	3	NUM
ejpam-4760	100	34	or	or	CCONJ
ejpam-4760	100	35	figure	figure	VERB
ejpam-4760	100	36	4	4	NUM
ejpam-4760	100	37	.	.	PUNCT
ejpam-4760	101	1	let	let	VERB
ejpam-4760	101	2	m	m	VERB
ejpam-4760	101	3	=	=	VERB
ejpam-4760	102	1	b	b	X
ejpam-4760	102	2	−	−	PROPN
ejpam-4760	102	3	a	a	DET
ejpam-4760	102	4	+	+	NUM
ejpam-4760	102	5	4	4	NUM
ejpam-4760	102	6	and	and	CCONJ
ejpam-4760	102	7	j	j	PROPN
ejpam-4760	102	8	,	,	PUNCT
ejpam-4760	102	9	k	k	PROPN
ejpam-4760	102	10	,	,	PUNCT
ejpam-4760	102	11	l	l	PROPN
ejpam-4760	102	12	∈	∈	PROPN
ejpam-4760	102	13	z+	z+	X
ejpam-4760	102	14	.	.	PUNCT
ejpam-4760	102	15	observe	observe	VERB
ejpam-4760	102	16	that	that	SCONJ
ejpam-4760	102	17	s1	s1	NOUN
ejpam-4760	102	18	=	=	PUNCT
ejpam-4760	102	19	{	{	PUNCT
ejpam-4760	102	20	v1	v1	PROPN
ejpam-4760	102	21	,	,	PUNCT
ejpam-4760	102	22	v2	v2	PROPN
ejpam-4760	102	23	,	,	PUNCT
ejpam-4760	102	24	v3	v3	PROPN
ejpam-4760	102	25	.	.	PUNCT
ejpam-4760	102	26	.	.	PUNCT
ejpam-4760	103	1	.	.	PUNCT
ejpam-4760	104	1	,	,	PUNCT
ejpam-4760	104	2	va−4	va−4	NOUN
ejpam-4760	104	3	}	}	PUNCT
ejpam-4760	104	4	∪	∪	NOUN
ejpam-4760	104	5	{	{	PUNCT
ejpam-4760	104	6	z1	z1	ADJ
ejpam-4760	104	7	,	,	PUNCT
ejpam-4760	104	8	z2	z2	PROPN
ejpam-4760	104	9	,	,	PUNCT
ejpam-4760	104	10	z3	z3	PROPN
ejpam-4760	104	11	,	,	PUNCT
ejpam-4760	104	12	zm	zm	PROPN
ejpam-4760	104	13	}	}	PUNCT
ejpam-4760	104	14	is	be	AUX
ejpam-4760	104	15	a	a	DET
ejpam-4760	104	16	γ0	γ0	NOUN
ejpam-4760	104	17	-	-	PUNCT
ejpam-4760	104	18	set	set	NOUN
ejpam-4760	104	19	of	of	ADP
ejpam-4760	104	20	g	g	NOUN
ejpam-4760	104	21	and	and	CCONJ
ejpam-4760	104	22	s2	s2	PROPN
ejpam-4760	104	23	=	=	SYM
ejpam-4760	104	24	{	{	PUNCT
ejpam-4760	104	25	v1	v1	PROPN
ejpam-4760	104	26	,	,	PUNCT
ejpam-4760	104	27	v2	v2	PROPN
ejpam-4760	104	28	,	,	PUNCT
ejpam-4760	104	29	v3	v3	PROPN
ejpam-4760	104	30	.	.	PUNCT
ejpam-4760	104	31	.	.	PUNCT
ejpam-4760	105	1	.	.	PUNCT
ejpam-4760	106	1	,	,	PUNCT
ejpam-4760	106	2	va−4	va−4	NOUN
ejpam-4760	106	3	}	}	PUNCT
ejpam-4760	106	4	∪	∪	NOUN
ejpam-4760	106	5	{	{	PUNCT
ejpam-4760	106	6	zi	zi	NOUN
ejpam-4760	106	7	:	:	PUNCT
ejpam-4760	107	1	i	i	NOUN
ejpam-4760	107	2	=	=	NOUN
ejpam-4760	107	3	1	1	NUM
ejpam-4760	107	4	,	,	PUNCT
ejpam-4760	107	5	2	2	NUM
ejpam-4760	107	6	,	,	PUNCT
ejpam-4760	107	7	.	.	PUNCT
ejpam-4760	107	8	.	.	PUNCT
ejpam-4760	107	9	.	.	PUNCT
ejpam-4760	108	1	,	,	PUNCT
ejpam-4760	108	2	m	m	AUX
ejpam-4760	108	3	}	}	PUNCT
ejpam-4760	108	4	is	be	AUX
ejpam-4760	108	5	a	a	DET
ejpam-4760	108	6	γp0	γp0	NOUN
ejpam-4760	108	7	-	-	PUNCT
ejpam-4760	108	8	set	set	NOUN
ejpam-4760	108	9	of	of	ADP
ejpam-4760	108	10	g.	g.	PROPN
ejpam-4760	109	1	it	it	PRON
ejpam-4760	109	2	follows	follow	VERB
ejpam-4760	109	3	that	that	SCONJ
ejpam-4760	109	4	γ0(g	γ0(g	AUX
ejpam-4760	109	5	)	)	PUNCT
ejpam-4760	109	6	=	=	SYM
ejpam-4760	109	7	|s1|	|s1|	NOUN
ejpam-4760	109	8	=	=	PUNCT
ejpam-4760	109	9	a	a	DET
ejpam-4760	109	10	−	−	PROPN
ejpam-4760	109	11	4	4	NUM
ejpam-4760	109	12	+	+	SYM
ejpam-4760	109	13	4	4	NUM
ejpam-4760	109	14	=	=	SYM
ejpam-4760	109	15	a	a	PRON
ejpam-4760	109	16	and	and	CCONJ
ejpam-4760	109	17	γp0(g	γp0(g	NOUN
ejpam-4760	109	18	)	)	PUNCT
ejpam-4760	110	1	=	=	SYM
ejpam-4760	110	2	|s2|	|s2|	NOUN
ejpam-4760	110	3	=	=	PUNCT
ejpam-4760	110	4	a	a	DET
ejpam-4760	110	5	−	−	PROPN
ejpam-4760	110	6	4	4	NUM
ejpam-4760	110	7	+	+	NOUN
ejpam-4760	110	8	m	m	NOUN
ejpam-4760	110	9	=	=	PUNCT
ejpam-4760	110	10	a	a	PRON
ejpam-4760	110	11	−	−	NOUN
ejpam-4760	110	12	4	4	NUM
ejpam-4760	110	13	+	+	CCONJ
ejpam-4760	110	14	(	(	PUNCT
ejpam-4760	110	15	b	b	X
ejpam-4760	110	16	−	−	NOUN
ejpam-4760	110	17	a	a	DET
ejpam-4760	110	18	+	+	NOUN
ejpam-4760	110	19	4	4	NUM
ejpam-4760	110	20	)	)	PUNCT
ejpam-4760	110	21	=	=	SYM
ejpam-4760	110	22	b.	b.	PROPN
ejpam-4760	110	23	therefore	therefore	ADV
ejpam-4760	110	24	,	,	PUNCT
ejpam-4760	110	25	γ0(g	γ0(g	X
ejpam-4760	110	26	)	)	PUNCT
ejpam-4760	110	27	=	=	PUNCT
ejpam-4760	110	28	a	a	DET
ejpam-4760	110	29	<	<	X
ejpam-4760	110	30	b	b	X
ejpam-4760	110	31	=	=	SYM
ejpam-4760	110	32	γp0(g	γp0(g	PROPN
ejpam-4760	110	33	)	)	PUNCT
ejpam-4760	110	34	.	.	PUNCT
ejpam-4760	110	35	.	.	PUNCT
ejpam-4760	110	36	.	.	PUNCT
ejpam-4760	110	37	.	.	PUNCT
ejpam-4760	111	1	u1	u1	PROPN
ejpam-4760	111	2	u2	u2	PROPN
ejpam-4760	111	3	u3	u3	PROPN
ejpam-4760	111	4	ua−4	ua−4	PROPN
ejpam-4760	111	5	ua	ua	NOUN
ejpam-4760	111	6	v1	v1	PROPN
ejpam-4760	111	7	v2	v2	PROPN
ejpam-4760	111	8	v3	v3	PROPN
ejpam-4760	111	9	va−4	va−4	PROPN
ejpam-4760	111	10	g	g	PROPN
ejpam-4760	111	11	:	:	PUNCT
ejpam-4760	111	12	.	.	PUNCT
ejpam-4760	111	13	.	.	PUNCT
ejpam-4760	111	14	.	.	PUNCT
ejpam-4760	111	15	.	.	PUNCT
ejpam-4760	111	16	.	.	PUNCT
ejpam-4760	111	17	.	.	PUNCT
ejpam-4760	111	18	...	...	PUNCT
ejpam-4760	112	1	w1	w1	NOUN
ejpam-4760	112	2	w2	w2	NOUN
ejpam-4760	112	3	wj	wj	PROPN
ejpam-4760	113	1	x1	x1	PROPN
ejpam-4760	114	1	x2	x2	PROPN
ejpam-4760	114	2	xk	xk	PROPN
ejpam-4760	114	3	y1y2yl	y1y2yl	PROPN
ejpam-4760	114	4	z1	z1	PROPN
ejpam-4760	114	5	z2	z2	PROPN
ejpam-4760	114	6	zm−1	zm−1	PROPN
ejpam-4760	114	7	.	.	PUNCT
ejpam-4760	114	8	.	.	PUNCT
ejpam-4760	114	9	.	.	PUNCT
ejpam-4760	115	1	z3	z3	PROPN
ejpam-4760	115	2	z4	z4	PROPN
ejpam-4760	115	3	z5	z5	PROPN
ejpam-4760	115	4	zm	zm	PROPN
ejpam-4760	115	5	..	..	PUNCT
ejpam-4760	115	6	.	.	PUNCT
ejpam-4760	116	1	figure	figure	VERB
ejpam-4760	116	2	3	3	NUM
ejpam-4760	116	3	:	:	PUNCT
ejpam-4760	116	4	graph	graph	VERB
ejpam-4760	116	5	g	g	NOUN
ejpam-4760	116	6	with	with	ADP
ejpam-4760	116	7	γ0(g	γ0(g	NOUN
ejpam-4760	116	8	)	)	PUNCT
ejpam-4760	116	9	=	=	SYM
ejpam-4760	116	10	a	a	PRON
ejpam-4760	116	11	.	.	PUNCT
ejpam-4760	116	12	.	.	PUNCT
ejpam-4760	116	13	.	.	PUNCT
ejpam-4760	117	1	u1	u1	PROPN
ejpam-4760	117	2	u2	u2	PROPN
ejpam-4760	117	3	u3	u3	PROPN
ejpam-4760	117	4	ua−4	ua−4	PROPN
ejpam-4760	117	5	ua	ua	NOUN
ejpam-4760	117	6	v1	v1	PROPN
ejpam-4760	117	7	v2	v2	PROPN
ejpam-4760	117	8	v3	v3	PROPN
ejpam-4760	117	9	va−4	va−4	PROPN
ejpam-4760	117	10	g	g	PROPN
ejpam-4760	117	11	:	:	PUNCT
ejpam-4760	117	12	.	.	PUNCT
ejpam-4760	117	13	.	.	PUNCT
ejpam-4760	117	14	.	.	PUNCT
ejpam-4760	117	15	.	.	PUNCT
ejpam-4760	117	16	.	.	PUNCT
ejpam-4760	117	17	.	.	PUNCT
ejpam-4760	117	18	...	...	PUNCT
ejpam-4760	118	1	w1	w1	NOUN
ejpam-4760	118	2	w2	w2	NOUN
ejpam-4760	118	3	wj	wj	PROPN
ejpam-4760	119	1	x1	x1	PROPN
ejpam-4760	120	1	x2	x2	PROPN
ejpam-4760	120	2	xk	xk	PROPN
ejpam-4760	120	3	y1y2yl	y1y2yl	PROPN
ejpam-4760	120	4	z1	z1	PROPN
ejpam-4760	120	5	z2	z2	PROPN
ejpam-4760	120	6	zm−1	zm−1	PROPN
ejpam-4760	120	7	.	.	PUNCT
ejpam-4760	120	8	.	.	PUNCT
ejpam-4760	120	9	.	.	PUNCT
ejpam-4760	121	1	z3	z3	PROPN
ejpam-4760	121	2	z4	z4	PROPN
ejpam-4760	121	3	z5	z5	PROPN
ejpam-4760	121	4	zm	zm	PROPN
ejpam-4760	121	5	..	..	PUNCT
ejpam-4760	121	6	.	.	PUNCT
ejpam-4760	122	1	figure	figure	VERB
ejpam-4760	122	2	4	4	NUM
ejpam-4760	122	3	:	:	PUNCT
ejpam-4760	122	4	graph	graph	VERB
ejpam-4760	122	5	g	g	NOUN
ejpam-4760	122	6	with	with	ADP
ejpam-4760	122	7	γp0(g	γp0(g	NOUN
ejpam-4760	122	8	)	)	PUNCT
ejpam-4760	123	1	=	=	SYM
ejpam-4760	123	2	b	b	PROPN
ejpam-4760	123	3	this	this	PRON
ejpam-4760	123	4	proves	prove	VERB
ejpam-4760	123	5	the	the	DET
ejpam-4760	123	6	assertion	assertion	NOUN
ejpam-4760	123	7	.	.	PUNCT
ejpam-4760	124	1	c.	c.	PROPN
ejpam-4760	124	2	armada	armada	PROPN
ejpam-4760	124	3	,	,	PUNCT
ejpam-4760	124	4	j.	j.	PROPN
ejpam-4760	124	5	hamja	hamja	PROPN
ejpam-4760	124	6	/	/	SYM
ejpam-4760	124	7	eur	eur	PROPN
ejpam-4760	124	8	.	.	PUNCT
ejpam-4760	125	1	j.	j.	PROPN
ejpam-4760	125	2	pure	pure	PROPN
ejpam-4760	125	3	appl	appl	PROPN
ejpam-4760	125	4	.	.	PROPN
ejpam-4760	125	5	math	math	PROPN
ejpam-4760	125	6	,	,	PUNCT
ejpam-4760	125	7	16	16	NUM
ejpam-4760	125	8	(	(	PUNCT
ejpam-4760	125	9	2	2	NUM
ejpam-4760	125	10	)	)	PUNCT
ejpam-4760	125	11	(	(	PUNCT
ejpam-4760	125	12	2023	2023	NUM
ejpam-4760	125	13	)	)	PUNCT
ejpam-4760	125	14	,	,	PUNCT
ejpam-4760	125	15	1326	1326	NUM
ejpam-4760	125	16	-	-	SYM
ejpam-4760	125	17	1341	1341	NUM
ejpam-4760	125	18	1331	1331	NUM
ejpam-4760	125	19	corollary	corollary	NOUN
ejpam-4760	125	20	2	2	NUM
ejpam-4760	125	21	.	.	PUNCT
ejpam-4760	126	1	the	the	DET
ejpam-4760	126	2	difference	difference	NOUN
ejpam-4760	126	3	γp0γ0	γp0γ0	PUNCT
ejpam-4760	126	4	can	can	AUX
ejpam-4760	126	5	be	be	AUX
ejpam-4760	126	6	made	make	VERB
ejpam-4760	126	7	arbitrarily	arbitrarily	ADV
ejpam-4760	126	8	large	large	ADJ
ejpam-4760	126	9	.	.	PUNCT
ejpam-4760	127	1	the	the	DET
ejpam-4760	127	2	next	next	ADJ
ejpam-4760	127	3	result	result	NOUN
ejpam-4760	127	4	follows	follow	VERB
ejpam-4760	127	5	from	from	ADP
ejpam-4760	127	6	proposition	proposition	NOUN
ejpam-4760	127	7	1	1	NUM
ejpam-4760	127	8	and	and	CCONJ
ejpam-4760	127	9	proposition	proposition	NOUN
ejpam-4760	127	10	4	4	NUM
ejpam-4760	127	11	.	.	PUNCT
ejpam-4760	127	12	corollary	corollary	ADJ
ejpam-4760	127	13	3	3	X
ejpam-4760	127	14	.	.	PUNCT
ejpam-4760	128	1	let	let	VERB
ejpam-4760	128	2	g	g	PRON
ejpam-4760	128	3	be	be	AUX
ejpam-4760	128	4	a	a	DET
ejpam-4760	128	5	simple	simple	ADJ
ejpam-4760	128	6	connected	connected	ADJ
ejpam-4760	128	7	graph	graph	NOUN
ejpam-4760	128	8	of	of	ADP
ejpam-4760	128	9	order	order	NOUN
ejpam-4760	128	10	3	3	NUM
ejpam-4760	128	11	,	,	PUNCT
ejpam-4760	128	12	that	that	ADV
ejpam-4760	128	13	is	is	ADV
ejpam-4760	128	14	,	,	PUNCT
ejpam-4760	128	15	either	either	CCONJ
ejpam-4760	128	16	g	g	PROPN
ejpam-4760	128	17	=	=	PROPN
ejpam-4760	128	18	p3	p3	PROPN
ejpam-4760	128	19	or	or	CCONJ
ejpam-4760	128	20	g	g	PROPN
ejpam-4760	128	21	=	=	PROPN
ejpam-4760	128	22	c3	c3	PROPN
ejpam-4760	128	23	.	.	PUNCT
ejpam-4760	129	1	then	then	ADV
ejpam-4760	129	2	γp0(g	γp0(g	X
ejpam-4760	129	3	)	)	PUNCT
ejpam-4760	129	4	=	=	SYM
ejpam-4760	130	1	1	1	X
ejpam-4760	130	2	.	.	X
ejpam-4760	130	3	theorem	theorem	NOUN
ejpam-4760	130	4	3	3	X
ejpam-4760	130	5	.	.	PUNCT
ejpam-4760	131	1	let	let	VERB
ejpam-4760	131	2	g	g	PRON
ejpam-4760	131	3	be	be	AUX
ejpam-4760	131	4	a	a	DET
ejpam-4760	131	5	connected	connected	ADJ
ejpam-4760	131	6	graph	graph	NOUN
ejpam-4760	131	7	of	of	ADP
ejpam-4760	131	8	order	order	NOUN
ejpam-4760	131	9	n	n	PRON
ejpam-4760	131	10	≥	≥	NOUN
ejpam-4760	131	11	2	2	NUM
ejpam-4760	131	12	.	.	PUNCT
ejpam-4760	131	13	then	then	ADV
ejpam-4760	131	14	γp0(g	γp0(g	NOUN
ejpam-4760	131	15	)	)	PUNCT
ejpam-4760	131	16	=	=	SYM
ejpam-4760	131	17	1	1	NUM
ejpam-4760	131	18	if	if	SCONJ
ejpam-4760	131	19	and	and	CCONJ
ejpam-4760	131	20	only	only	ADV
ejpam-4760	131	21	if	if	SCONJ
ejpam-4760	131	22	∆(g	∆(g	NOUN
ejpam-4760	131	23	)	)	PUNCT
ejpam-4760	131	24	=	=	SYM
ejpam-4760	132	1	n−	n−	NOUN
ejpam-4760	132	2	1	1	NUM
ejpam-4760	132	3	.	.	PUNCT
ejpam-4760	133	1	proof	proof	NOUN
ejpam-4760	133	2	.	.	PUNCT
ejpam-4760	134	1	suppose	suppose	VERB
ejpam-4760	134	2	that	that	SCONJ
ejpam-4760	134	3	γp0(g	γp0(g	NOUN
ejpam-4760	134	4	)	)	PUNCT
ejpam-4760	134	5	=	=	SYM
ejpam-4760	135	1	1	1	X
ejpam-4760	135	2	.	.	PUNCT
ejpam-4760	135	3	let	let	VERB
ejpam-4760	135	4	s	s	AUX
ejpam-4760	135	5	=	=	PUNCT
ejpam-4760	135	6	{	{	PUNCT
ejpam-4760	135	7	u	u	NOUN
ejpam-4760	135	8	}	}	PUNCT
ejpam-4760	135	9	be	be	VERB
ejpam-4760	135	10	the	the	DET
ejpam-4760	135	11	perfect	perfect	ADJ
ejpam-4760	135	12	isolate	isolate	NOUN
ejpam-4760	135	13	dominating	dominate	VERB
ejpam-4760	135	14	set	set	NOUN
ejpam-4760	135	15	of	of	ADP
ejpam-4760	135	16	g.	g.	PROPN
ejpam-4760	135	17	if	if	SCONJ
ejpam-4760	135	18	g	g	PROPN
ejpam-4760	135	19	is	be	AUX
ejpam-4760	135	20	trivial	trivial	ADJ
ejpam-4760	135	21	,	,	PUNCT
ejpam-4760	135	22	then	then	ADV
ejpam-4760	135	23	deg(u	deg(u	PROPN
ejpam-4760	135	24	)	)	PUNCT
ejpam-4760	135	25	=	=	SYM
ejpam-4760	136	1	0	0	X
ejpam-4760	136	2	.	.	PUNCT
ejpam-4760	137	1	so	so	ADV
ejpam-4760	137	2	,	,	PUNCT
ejpam-4760	137	3	we	we	PRON
ejpam-4760	137	4	are	be	AUX
ejpam-4760	137	5	done	do	VERB
ejpam-4760	137	6	.	.	PUNCT
ejpam-4760	138	1	assume	assume	VERB
ejpam-4760	138	2	that	that	SCONJ
ejpam-4760	138	3	g	g	PROPN
ejpam-4760	138	4	is	be	AUX
ejpam-4760	138	5	nontrivial	nontrivial	ADJ
ejpam-4760	138	6	.	.	PUNCT
ejpam-4760	139	1	then	then	ADV
ejpam-4760	139	2	every	every	DET
ejpam-4760	139	3	vertex	vertex	NOUN
ejpam-4760	139	4	v	v	ADP
ejpam-4760	139	5	∈	∈	PROPN
ejpam-4760	139	6	v	v	NOUN
ejpam-4760	139	7	(	(	PUNCT
ejpam-4760	139	8	g	g	NOUN
ejpam-4760	139	9	)	)	PUNCT
ejpam-4760	139	10	\	\	PROPN
ejpam-4760	140	1	s	s	PART
ejpam-4760	140	2	is	be	AUX
ejpam-4760	140	3	adjacent	adjacent	ADJ
ejpam-4760	140	4	to	to	ADP
ejpam-4760	140	5	u	u	PROPN
ejpam-4760	140	6	∈	∈	PROPN
ejpam-4760	140	7	s.	s.	PROPN
ejpam-4760	140	8	hence	hence	ADV
ejpam-4760	140	9	,	,	PUNCT
ejpam-4760	140	10	deg(u	deg(u	PROPN
ejpam-4760	140	11	)	)	PUNCT
ejpam-4760	140	12	=	=	SYM
ejpam-4760	141	1	n	n	CCONJ
ejpam-4760	141	2	−	−	NOUN
ejpam-4760	141	3	1	1	NUM
ejpam-4760	141	4	since	since	SCONJ
ejpam-4760	141	5	|v	|v	PROPN
ejpam-4760	141	6	(	(	PUNCT
ejpam-4760	141	7	g)|=	g)|=	PROPN
ejpam-4760	141	8	n.	n.	PROPN
ejpam-4760	141	9	therefore	therefore	ADV
ejpam-4760	141	10	,	,	PUNCT
ejpam-4760	141	11	∆(g	∆(g	NOUN
ejpam-4760	141	12	)	)	PUNCT
ejpam-4760	141	13	=	=	SYM
ejpam-4760	141	14	n−	n−	NOUN
ejpam-4760	141	15	1	1	NUM
ejpam-4760	141	16	.	.	PUNCT
ejpam-4760	142	1	for	for	ADP
ejpam-4760	142	2	the	the	DET
ejpam-4760	142	3	converse	converse	NOUN
ejpam-4760	142	4	,	,	PUNCT
ejpam-4760	142	5	let	let	VERB
ejpam-4760	142	6	∆(g	∆(g	NOUN
ejpam-4760	142	7	)	)	PUNCT
ejpam-4760	143	1	=	=	PUNCT
ejpam-4760	143	2	n−	n−	NOUN
ejpam-4760	143	3	1	1	NUM
ejpam-4760	143	4	.	.	PUNCT
ejpam-4760	144	1	then	then	ADV
ejpam-4760	144	2	there	there	PRON
ejpam-4760	144	3	exists	exist	VERB
ejpam-4760	144	4	a	a	DET
ejpam-4760	144	5	vertex	vertex	NOUN
ejpam-4760	144	6	u	u	NOUN
ejpam-4760	144	7	∈	∈	PROPN
ejpam-4760	144	8	v	v	ADP
ejpam-4760	144	9	(	(	PUNCT
ejpam-4760	144	10	g	g	NOUN
ejpam-4760	144	11	)	)	PUNCT
ejpam-4760	144	12	such	such	ADJ
ejpam-4760	144	13	that	that	SCONJ
ejpam-4760	144	14	deg(u	deg(u	PROPN
ejpam-4760	144	15	)	)	PUNCT
ejpam-4760	144	16	=	=	SYM
ejpam-4760	144	17	n	n	CCONJ
ejpam-4760	144	18	−	−	PROPN
ejpam-4760	144	19	1	1	NUM
ejpam-4760	144	20	.	.	PUNCT
ejpam-4760	145	1	since	since	SCONJ
ejpam-4760	145	2	every	every	DET
ejpam-4760	145	3	vertex	vertex	NOUN
ejpam-4760	145	4	v	v	ADP
ejpam-4760	145	5	∈	∈	NOUN
ejpam-4760	145	6	v	v	NOUN
ejpam-4760	145	7	(	(	PUNCT
ejpam-4760	145	8	g	g	NOUN
ejpam-4760	145	9	)	)	PUNCT
ejpam-4760	145	10	\	\	NOUN
ejpam-4760	145	11	{	{	PUNCT
ejpam-4760	145	12	u	u	NOUN
ejpam-4760	145	13	}	}	PUNCT
ejpam-4760	145	14	is	be	AUX
ejpam-4760	145	15	dominated	dominate	VERB
ejpam-4760	145	16	by	by	ADP
ejpam-4760	145	17	exactly	exactly	ADV
ejpam-4760	145	18	one	one	NUM
ejpam-4760	145	19	vertex	vertex	NOUN
ejpam-4760	145	20	u	u	NOUN
ejpam-4760	145	21	,	,	PUNCT
ejpam-4760	145	22	s	s	PART
ejpam-4760	145	23	=	=	PUNCT
ejpam-4760	145	24	{	{	PUNCT
ejpam-4760	145	25	u	u	NOUN
ejpam-4760	145	26	}	}	PUNCT
ejpam-4760	145	27	is	be	AUX
ejpam-4760	145	28	a	a	DET
ejpam-4760	145	29	perfect	perfect	ADJ
ejpam-4760	145	30	dominating	dominating	NOUN
ejpam-4760	145	31	set	set	NOUN
ejpam-4760	145	32	of	of	ADP
ejpam-4760	145	33	g.	g.	PROPN
ejpam-4760	145	34	by	by	ADP
ejpam-4760	145	35	proposition	proposition	NOUN
ejpam-4760	145	36	4	4	NUM
ejpam-4760	145	37	,	,	PUNCT
ejpam-4760	145	38	γp0(g	γp0(g	NOUN
ejpam-4760	145	39	)	)	PUNCT
ejpam-4760	145	40	=	=	SYM
ejpam-4760	145	41	|s|	|s|	NOUN
ejpam-4760	145	42	=	=	SYM
ejpam-4760	145	43	1	1	NUM
ejpam-4760	145	44	.	.	PUNCT
ejpam-4760	146	1	the	the	DET
ejpam-4760	146	2	next	next	ADJ
ejpam-4760	146	3	result	result	NOUN
ejpam-4760	146	4	follows	follow	VERB
ejpam-4760	146	5	from	from	ADP
ejpam-4760	146	6	theorem	theorem	ADJ
ejpam-4760	146	7	3	3	NUM
ejpam-4760	146	8	since	since	SCONJ
ejpam-4760	146	9	∆(kn	∆(kn	NUM
ejpam-4760	146	10	)	)	PUNCT
ejpam-4760	147	1	=	=	PUNCT
ejpam-4760	147	2	n−	n−	NOUN
ejpam-4760	147	3	1	1	NUM
ejpam-4760	147	4	.	.	PUNCT
ejpam-4760	147	5	corollary	corollary	ADJ
ejpam-4760	147	6	4	4	NUM
ejpam-4760	147	7	.	.	PUNCT
ejpam-4760	148	1	for	for	ADP
ejpam-4760	148	2	the	the	DET
ejpam-4760	148	3	complete	complete	ADJ
ejpam-4760	148	4	graph	graph	NOUN
ejpam-4760	148	5	kn	kn	PROPN
ejpam-4760	148	6	,	,	PUNCT
ejpam-4760	148	7	where	where	SCONJ
ejpam-4760	148	8	n	n	PRON
ejpam-4760	148	9	≥	≥	NOUN
ejpam-4760	148	10	1	1	NUM
ejpam-4760	148	11	,	,	PUNCT
ejpam-4760	148	12	γp0(kn	γp0(kn	NUM
ejpam-4760	148	13	)	)	PUNCT
ejpam-4760	148	14	=	=	SYM
ejpam-4760	148	15	1	1	X
ejpam-4760	148	16	.	.	X
ejpam-4760	148	17	theorem	theorem	NOUN
ejpam-4760	148	18	4	4	NUM
ejpam-4760	148	19	.	.	PUNCT
ejpam-4760	149	1	let	let	VERB
ejpam-4760	149	2	g	g	NOUN
ejpam-4760	149	3	be	be	AUX
ejpam-4760	149	4	connected	connect	VERB
ejpam-4760	149	5	graph	graph	NOUN
ejpam-4760	149	6	of	of	ADP
ejpam-4760	149	7	order	order	NOUN
ejpam-4760	149	8	n	n	PRON
ejpam-4760	149	9	≥	≥	NOUN
ejpam-4760	149	10	4	4	NUM
ejpam-4760	149	11	.	.	PUNCT
ejpam-4760	149	12	then	then	ADV
ejpam-4760	149	13	γp0(g	γp0(g	NOUN
ejpam-4760	149	14	)	)	PUNCT
ejpam-4760	149	15	=	=	SYM
ejpam-4760	149	16	2	2	NUM
ejpam-4760	149	17	if	if	SCONJ
ejpam-4760	149	18	and	and	CCONJ
ejpam-4760	149	19	only	only	ADV
ejpam-4760	149	20	if	if	SCONJ
ejpam-4760	149	21	there	there	PRON
ejpam-4760	149	22	exists	exist	VERB
ejpam-4760	149	23	two	two	NUM
ejpam-4760	149	24	vertices	vertex	NOUN
ejpam-4760	149	25	x	x	X
ejpam-4760	149	26	,	,	PUNCT
ejpam-4760	149	27	y	y	PROPN
ejpam-4760	149	28	∈	∈	PROPN
ejpam-4760	149	29	s	s	PART
ejpam-4760	149	30	⊆	⊆	NUM
ejpam-4760	149	31	v	v	NOUN
ejpam-4760	149	32	(	(	PUNCT
ejpam-4760	149	33	g	g	NOUN
ejpam-4760	149	34	)	)	PUNCT
ejpam-4760	149	35	such	such	ADJ
ejpam-4760	149	36	that	that	DET
ejpam-4760	149	37	ng(x	ng(x	NUM
ejpam-4760	149	38	)	)	PUNCT
ejpam-4760	149	39	∩	∩	NOUN
ejpam-4760	149	40	ng(y	ng(y	NOUN
ejpam-4760	149	41	)	)	PUNCT
ejpam-4760	149	42	=	=	NOUN
ejpam-4760	149	43	∅	∅	NOUN
ejpam-4760	149	44	and	and	CCONJ
ejpam-4760	149	45	ng[x	ng[x	PROPN
ejpam-4760	149	46	]	]	X
ejpam-4760	149	47	∪ng[y	∪ng[y	PROPN
ejpam-4760	149	48	]	]	X
ejpam-4760	149	49	=	=	SYM
ejpam-4760	149	50	v	v	X
ejpam-4760	149	51	(	(	PUNCT
ejpam-4760	149	52	g	g	NOUN
ejpam-4760	149	53	)	)	PUNCT
ejpam-4760	149	54	.	.	PUNCT
ejpam-4760	150	1	proof	proof	NOUN
ejpam-4760	150	2	.	.	PUNCT
ejpam-4760	151	1	suppose	suppose	VERB
ejpam-4760	151	2	that	that	SCONJ
ejpam-4760	151	3	γp0(g	γp0(g	NOUN
ejpam-4760	151	4	)	)	PUNCT
ejpam-4760	151	5	=	=	SYM
ejpam-4760	152	1	2	2	X
ejpam-4760	152	2	.	.	X
ejpam-4760	152	3	let	let	VERB
ejpam-4760	152	4	s	s	PRON
ejpam-4760	152	5	⊆	⊆	NUM
ejpam-4760	152	6	v	v	NOUN
ejpam-4760	152	7	(	(	PUNCT
ejpam-4760	152	8	g	g	NOUN
ejpam-4760	152	9	)	)	PUNCT
ejpam-4760	152	10	be	be	AUX
ejpam-4760	152	11	a	a	DET
ejpam-4760	152	12	perfect	perfect	ADJ
ejpam-4760	152	13	isolate	isolate	NOUN
ejpam-4760	152	14	dominating	dominating	NOUN
ejpam-4760	152	15	set	set	NOUN
ejpam-4760	152	16	of	of	ADP
ejpam-4760	152	17	g.	g.	PROPN
ejpam-4760	152	18	then	then	ADV
ejpam-4760	152	19	|s|	|s|	PROPN
ejpam-4760	152	20	=	=	SYM
ejpam-4760	152	21	2	2	NUM
ejpam-4760	153	1	and	and	CCONJ
ejpam-4760	153	2	so	so	ADV
ejpam-4760	153	3	,	,	PUNCT
ejpam-4760	153	4	there	there	PRON
ejpam-4760	153	5	exist	exist	VERB
ejpam-4760	153	6	two	two	NUM
ejpam-4760	153	7	vertices	vertex	NOUN
ejpam-4760	153	8	x	x	X
ejpam-4760	153	9	,	,	PUNCT
ejpam-4760	153	10	y	y	PROPN
ejpam-4760	153	11	∈	∈	PROPN
ejpam-4760	153	12	s	s	X
ejpam-4760	153	13	which	which	PRON
ejpam-4760	153	14	are	be	AUX
ejpam-4760	153	15	isolated	isolate	VERB
ejpam-4760	153	16	vertices	vertex	NOUN
ejpam-4760	153	17	in	in	ADP
ejpam-4760	153	18	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	153	19	such	such	ADJ
ejpam-4760	153	20	that	that	SCONJ
ejpam-4760	153	21	each	each	DET
ejpam-4760	153	22	vertex	vertex	NOUN
ejpam-4760	153	23	v	v	ADP
ejpam-4760	153	24	∈	∈	NOUN
ejpam-4760	153	25	v	v	NOUN
ejpam-4760	153	26	(	(	PUNCT
ejpam-4760	153	27	g)\s	g)\s	NOUN
ejpam-4760	153	28	is	be	AUX
ejpam-4760	153	29	dominated	dominate	VERB
ejpam-4760	153	30	only	only	ADV
ejpam-4760	153	31	by	by	ADP
ejpam-4760	153	32	either	either	CCONJ
ejpam-4760	153	33	x	x	SYM
ejpam-4760	153	34	or	or	CCONJ
ejpam-4760	153	35	y	y	PROPN
ejpam-4760	153	36	but	but	CCONJ
ejpam-4760	153	37	not	not	PART
ejpam-4760	153	38	both	both	PRON
ejpam-4760	153	39	.	.	PUNCT
ejpam-4760	154	1	thus	thus	ADV
ejpam-4760	154	2	,	,	PUNCT
ejpam-4760	154	3	ng(x	ng(x	NUM
ejpam-4760	154	4	)	)	PUNCT
ejpam-4760	154	5	∩ng(y	∩ng(y	PROPN
ejpam-4760	154	6	)	)	PUNCT
ejpam-4760	154	7	=	=	NOUN
ejpam-4760	154	8	∅	∅	NOUN
ejpam-4760	154	9	and	and	CCONJ
ejpam-4760	154	10	ng[s	ng[	NOUN
ejpam-4760	154	11	]	]	PUNCT
ejpam-4760	154	12	=	=	SYM
ejpam-4760	154	13	ng[x	ng[x	PROPN
ejpam-4760	154	14	]	]	PUNCT
ejpam-4760	154	15	∪ng[y	∪ng[y	PROPN
ejpam-4760	154	16	]	]	X
ejpam-4760	154	17	=	=	SYM
ejpam-4760	154	18	v	v	X
ejpam-4760	154	19	(	(	PUNCT
ejpam-4760	154	20	g	g	NOUN
ejpam-4760	154	21	)	)	PUNCT
ejpam-4760	154	22	.	.	PUNCT
ejpam-4760	155	1	for	for	ADP
ejpam-4760	155	2	the	the	DET
ejpam-4760	155	3	converse	converse	NOUN
ejpam-4760	155	4	,	,	PUNCT
ejpam-4760	155	5	suppose	suppose	VERB
ejpam-4760	155	6	that	that	SCONJ
ejpam-4760	155	7	ng(x	ng(x	NUM
ejpam-4760	155	8	)	)	PUNCT
ejpam-4760	155	9	∩	∩	NOUN
ejpam-4760	155	10	ng(y	ng(y	NOUN
ejpam-4760	155	11	)	)	PUNCT
ejpam-4760	155	12	=	=	NOUN
ejpam-4760	155	13	∅	∅	NOUN
ejpam-4760	155	14	and	and	CCONJ
ejpam-4760	155	15	ng[x	ng[x	PROPN
ejpam-4760	155	16	]	]	PUNCT
ejpam-4760	155	17	∪	∪	ADP
ejpam-4760	155	18	ng[y	ng[y	PROPN
ejpam-4760	155	19	]	]	X
ejpam-4760	155	20	=	=	SYM
ejpam-4760	155	21	v	v	X
ejpam-4760	155	22	(	(	PUNCT
ejpam-4760	155	23	g	g	NOUN
ejpam-4760	155	24	)	)	PUNCT
ejpam-4760	155	25	.	.	PUNCT
ejpam-4760	156	1	it	it	PRON
ejpam-4760	156	2	follows	follow	VERB
ejpam-4760	156	3	that	that	SCONJ
ejpam-4760	156	4	the	the	DET
ejpam-4760	156	5	graph	graph	NOUN
ejpam-4760	156	6	g	g	PROPN
ejpam-4760	156	7	can	can	AUX
ejpam-4760	156	8	not	not	PART
ejpam-4760	156	9	be	be	AUX
ejpam-4760	156	10	dominated	dominate	VERB
ejpam-4760	156	11	by	by	ADP
ejpam-4760	156	12	1	1	NUM
ejpam-4760	156	13	vertex	vertex	NOUN
ejpam-4760	156	14	only	only	ADV
ejpam-4760	156	15	,	,	PUNCT
ejpam-4760	156	16	that	that	ADV
ejpam-4760	156	17	is	is	ADV
ejpam-4760	156	18	,	,	PUNCT
ejpam-4760	156	19	γp0(g	γp0(g	NOUN
ejpam-4760	156	20	)	)	PUNCT
ejpam-4760	156	21	>	>	X
ejpam-4760	156	22	1	1	NUM
ejpam-4760	156	23	and	and	CCONJ
ejpam-4760	156	24	each	each	DET
ejpam-4760	156	25	vertex	vertex	NOUN
ejpam-4760	156	26	v	v	ADP
ejpam-4760	156	27	∈	∈	NOUN
ejpam-4760	156	28	v	v	NOUN
ejpam-4760	156	29	(	(	PUNCT
ejpam-4760	156	30	g)\s	g)\s	NOUN
ejpam-4760	156	31	is	be	AUX
ejpam-4760	156	32	dominated	dominate	VERB
ejpam-4760	156	33	only	only	ADV
ejpam-4760	156	34	by	by	ADP
ejpam-4760	156	35	either	either	CCONJ
ejpam-4760	156	36	x	x	SYM
ejpam-4760	156	37	or	or	CCONJ
ejpam-4760	156	38	y	y	PROPN
ejpam-4760	156	39	but	but	CCONJ
ejpam-4760	156	40	not	not	PART
ejpam-4760	156	41	both	both	PRON
ejpam-4760	156	42	and	and	CCONJ
ejpam-4760	156	43	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	156	44	has	have	VERB
ejpam-4760	156	45	two	two	NUM
ejpam-4760	156	46	isolated	isolated	ADJ
ejpam-4760	156	47	vertices	vertex	NOUN
ejpam-4760	156	48	.	.	PUNCT
ejpam-4760	157	1	clearly	clearly	ADV
ejpam-4760	157	2	,	,	PUNCT
ejpam-4760	157	3	s	s	VERB
ejpam-4760	157	4	=	=	PUNCT
ejpam-4760	157	5	{	{	PUNCT
ejpam-4760	157	6	x	x	PROPN
ejpam-4760	157	7	,	,	PUNCT
ejpam-4760	157	8	y	y	PRON
ejpam-4760	157	9	}	}	PUNCT
ejpam-4760	157	10	is	be	AUX
ejpam-4760	157	11	a	a	DET
ejpam-4760	157	12	perfect	perfect	ADJ
ejpam-4760	157	13	isolate	isolate	NOUN
ejpam-4760	157	14	dominating	dominating	NOUN
ejpam-4760	157	15	set	set	NOUN
ejpam-4760	157	16	of	of	ADP
ejpam-4760	157	17	g.	g.	PROPN
ejpam-4760	157	18	therefore	therefore	ADV
ejpam-4760	157	19	,	,	PUNCT
ejpam-4760	157	20	γp0(g	γp0(g	X
ejpam-4760	157	21	)	)	PUNCT
ejpam-4760	157	22	=	=	SYM
ejpam-4760	157	23	|s|	|s|	NOUN
ejpam-4760	157	24	=	=	SYM
ejpam-4760	157	25	2	2	X
ejpam-4760	157	26	.	.	PUNCT
ejpam-4760	157	27	theorem	theorem	NOUN
ejpam-4760	157	28	5	5	NUM
ejpam-4760	157	29	.	.	X
ejpam-4760	158	1	for	for	ADP
ejpam-4760	158	2	any	any	DET
ejpam-4760	158	3	path	path	NOUN
ejpam-4760	158	4	pn	pn	NOUN
ejpam-4760	158	5	of	of	ADP
ejpam-4760	158	6	order	order	NOUN
ejpam-4760	158	7	n	n	PRON
ejpam-4760	158	8	≥	≥	NOUN
ejpam-4760	158	9	1	1	NUM
ejpam-4760	158	10	,	,	PUNCT
ejpam-4760	158	11	γp0(pn	γp0(pn	NUM
ejpam-4760	158	12	)	)	PUNCT
ejpam-4760	158	13	=	=	PUNCT
ejpam-4760	158	14	⌈n	⌈n	NOUN
ejpam-4760	158	15	3	3	NUM
ejpam-4760	158	16	⌉	⌉	X
ejpam-4760	158	17	.	.	PUNCT
ejpam-4760	159	1	proof	proof	NOUN
ejpam-4760	159	2	.	.	PUNCT
ejpam-4760	160	1	suppose	suppose	VERB
ejpam-4760	160	2	that	that	SCONJ
ejpam-4760	160	3	v	v	INTJ
ejpam-4760	160	4	(	(	PUNCT
ejpam-4760	160	5	pn	pn	NOUN
ejpam-4760	160	6	)	)	PUNCT
ejpam-4760	160	7	=	=	SYM
ejpam-4760	160	8	{	{	PUNCT
ejpam-4760	160	9	u1	u1	NOUN
ejpam-4760	160	10	,	,	PUNCT
ejpam-4760	160	11	u2	u2	NOUN
ejpam-4760	160	12	,	,	PUNCT
ejpam-4760	160	13	.	.	PUNCT
ejpam-4760	160	14	.	.	PUNCT
ejpam-4760	161	1	.	.	PUNCT
ejpam-4760	162	1	,	,	PUNCT
ejpam-4760	162	2	un−1	un−1	PROPN
ejpam-4760	162	3	,	,	PUNCT
ejpam-4760	162	4	un	un	ADJ
ejpam-4760	162	5	}	}	PUNCT
ejpam-4760	162	6	such	such	ADJ
ejpam-4760	162	7	that	that	DET
ejpam-4760	162	8	deg(u1	deg(u1	NOUN
ejpam-4760	162	9	)	)	PUNCT
ejpam-4760	162	10	=	=	SYM
ejpam-4760	162	11	deg(un	deg(un	NOUN
ejpam-4760	162	12	)	)	PUNCT
ejpam-4760	162	13	=	=	SYM
ejpam-4760	162	14	1	1	NUM
ejpam-4760	162	15	and	and	CCONJ
ejpam-4760	162	16	deg(ui	deg(ui	PROPN
ejpam-4760	162	17	)	)	PUNCT
ejpam-4760	162	18	=	=	SYM
ejpam-4760	162	19	2	2	NUM
ejpam-4760	162	20	for	for	ADP
ejpam-4760	162	21	all	all	DET
ejpam-4760	162	22	i	i	PRON
ejpam-4760	162	23	=	=	NOUN
ejpam-4760	162	24	2	2	NUM
ejpam-4760	162	25	,	,	PUNCT
ejpam-4760	162	26	3	3	NUM
ejpam-4760	162	27	,	,	PUNCT
ejpam-4760	162	28	.	.	PUNCT
ejpam-4760	162	29	.	.	PUNCT
ejpam-4760	163	1	.	.	PUNCT
ejpam-4760	164	1	,	,	PUNCT
ejpam-4760	165	1	n	n	CCONJ
ejpam-4760	165	2	−	−	PROPN
ejpam-4760	166	1	1	1	X
ejpam-4760	166	2	.	.	X
ejpam-4760	166	3	note	note	VERB
ejpam-4760	166	4	that	that	SCONJ
ejpam-4760	166	5	by	by	ADP
ejpam-4760	166	6	proposition	proposition	NOUN
ejpam-4760	166	7	1	1	NUM
ejpam-4760	166	8	,	,	PUNCT
ejpam-4760	166	9	γ0(pn	γ0(pn	NUM
ejpam-4760	166	10	)	)	PUNCT
ejpam-4760	166	11	=	=	VERB
ejpam-4760	166	12	⌈n3	⌈n3	AUX
ejpam-4760	166	13	⌉.	⌉.	ADV
ejpam-4760	166	14	consider	consider	VERB
ejpam-4760	166	15	the	the	DET
ejpam-4760	166	16	following	follow	VERB
ejpam-4760	166	17	cases	case	NOUN
ejpam-4760	166	18	:	:	PUNCT
ejpam-4760	166	19	c.	c.	PROPN
ejpam-4760	166	20	armada	armada	PROPN
ejpam-4760	166	21	,	,	PUNCT
ejpam-4760	166	22	j.	j.	PROPN
ejpam-4760	166	23	hamja	hamja	PROPN
ejpam-4760	166	24	/	/	SYM
ejpam-4760	166	25	eur	eur	PROPN
ejpam-4760	166	26	.	.	PUNCT
ejpam-4760	167	1	j.	j.	PROPN
ejpam-4760	167	2	pure	pure	PROPN
ejpam-4760	167	3	appl	appl	PROPN
ejpam-4760	167	4	.	.	PROPN
ejpam-4760	167	5	math	math	PROPN
ejpam-4760	167	6	,	,	PUNCT
ejpam-4760	167	7	16	16	NUM
ejpam-4760	167	8	(	(	PUNCT
ejpam-4760	167	9	2	2	NUM
ejpam-4760	167	10	)	)	PUNCT
ejpam-4760	167	11	(	(	PUNCT
ejpam-4760	167	12	2023	2023	NUM
ejpam-4760	167	13	)	)	PUNCT
ejpam-4760	167	14	,	,	PUNCT
ejpam-4760	167	15	1326	1326	NUM
ejpam-4760	167	16	-	-	SYM
ejpam-4760	167	17	1341	1341	NUM
ejpam-4760	167	18	1332	1332	NUM
ejpam-4760	167	19	case	case	NOUN
ejpam-4760	167	20	1	1	NUM
ejpam-4760	167	21	:	:	PUNCT
ejpam-4760	167	22	suppose	suppose	VERB
ejpam-4760	167	23	that	that	SCONJ
ejpam-4760	167	24	n	n	PROPN
ejpam-4760	167	25	≡	≡	PROPN
ejpam-4760	167	26	0	0	PUNCT
ejpam-4760	168	1	(	(	PUNCT
ejpam-4760	168	2	mod	mod	NOUN
ejpam-4760	168	3	3	3	NUM
ejpam-4760	168	4	)	)	PUNCT
ejpam-4760	168	5	.	.	PUNCT
ejpam-4760	169	1	if	if	SCONJ
ejpam-4760	169	2	n	n	NUM
ejpam-4760	169	3	=	=	SYM
ejpam-4760	169	4	3	3	NUM
ejpam-4760	169	5	,	,	PUNCT
ejpam-4760	169	6	by	by	ADP
ejpam-4760	169	7	corollary	corollary	ADJ
ejpam-4760	169	8	3	3	NUM
ejpam-4760	169	9	,	,	PUNCT
ejpam-4760	169	10	γp0(p3	γp0(p3	ADV
ejpam-4760	169	11	)	)	PUNCT
ejpam-4760	169	12	=	=	SYM
ejpam-4760	169	13	1	1	NUM
ejpam-4760	169	14	=	=	SYM
ejpam-4760	169	15	⌈33⌉.	⌈33⌉.	PROPN
ejpam-4760	169	16	suppose	suppose	VERB
ejpam-4760	169	17	that	that	SCONJ
ejpam-4760	169	18	n	n	PROPN
ejpam-4760	169	19	>	>	X
ejpam-4760	169	20	3	3	X
ejpam-4760	169	21	.	.	PUNCT
ejpam-4760	170	1	let	let	VERB
ejpam-4760	170	2	r	r	NOUN
ejpam-4760	170	3	=	=	SYM
ejpam-4760	170	4	n	n	NUM
ejpam-4760	170	5	3	3	NUM
ejpam-4760	170	6	and	and	CCONJ
ejpam-4760	170	7	j	j	PROPN
ejpam-4760	170	8	=	=	SYM
ejpam-4760	170	9	1	1	NUM
ejpam-4760	170	10	,	,	PUNCT
ejpam-4760	170	11	2	2	NUM
ejpam-4760	170	12	,	,	PUNCT
ejpam-4760	170	13	.	.	PUNCT
ejpam-4760	170	14	.	.	PUNCT
ejpam-4760	171	1	.	.	PUNCT
ejpam-4760	172	1	,	,	PUNCT
ejpam-4760	172	2	r	r	NOUN
ejpam-4760	172	3	−	−	PROPN
ejpam-4760	172	4	1	1	NUM
ejpam-4760	172	5	,	,	PUNCT
ejpam-4760	172	6	r.	r.	PROPN
ejpam-4760	172	7	group	group	PROPN
ejpam-4760	172	8	the	the	DET
ejpam-4760	172	9	vertices	vertex	NOUN
ejpam-4760	172	10	of	of	ADP
ejpam-4760	172	11	pn	pn	NOUN
ejpam-4760	172	12	into	into	ADP
ejpam-4760	172	13	r	r	NOUN
ejpam-4760	172	14	disjoint	disjoint	NOUN
ejpam-4760	172	15	subsets	subset	NOUN
ejpam-4760	172	16	sj	sj	NOUN
ejpam-4760	172	17	s1	s1	PROPN
ejpam-4760	172	18	=	=	PUNCT
ejpam-4760	172	19	{	{	PUNCT
ejpam-4760	172	20	u1	u1	NOUN
ejpam-4760	172	21	,	,	PUNCT
ejpam-4760	172	22	u2	u2	NOUN
ejpam-4760	172	23	,	,	PUNCT
ejpam-4760	172	24	u3	u3	NOUN
ejpam-4760	172	25	}	}	PUNCT
ejpam-4760	172	26	s2	s2	NOUN
ejpam-4760	172	27	=	=	SYM
ejpam-4760	172	28	{	{	PUNCT
ejpam-4760	172	29	u4	u4	PROPN
ejpam-4760	172	30	,	,	PUNCT
ejpam-4760	172	31	u5	u5	PROPN
ejpam-4760	172	32	,	,	PUNCT
ejpam-4760	172	33	u6	u6	ADJ
ejpam-4760	172	34	}	}	PUNCT
ejpam-4760	172	35	s3	s3	NOUN
ejpam-4760	172	36	=	=	SYM
ejpam-4760	172	37	{	{	PUNCT
ejpam-4760	172	38	u7	u7	PROPN
ejpam-4760	172	39	,	,	PUNCT
ejpam-4760	172	40	u8	u8	PROPN
ejpam-4760	172	41	,	,	PUNCT
ejpam-4760	172	42	u9	u9	PROPN
ejpam-4760	172	43	}	}	PUNCT
ejpam-4760	172	44	s4	s4	PROPN
ejpam-4760	172	45	=	=	SYM
ejpam-4760	172	46	{	{	PUNCT
ejpam-4760	172	47	u10	u10	PROPN
ejpam-4760	172	48	,	,	PUNCT
ejpam-4760	172	49	u11	u11	PROPN
ejpam-4760	172	50	,	,	PUNCT
ejpam-4760	172	51	u12	u12	PROPN
ejpam-4760	172	52	}	}	PUNCT
ejpam-4760	172	53	...	...	PUNCT
ejpam-4760	173	1	sr−1	sr−1	PROPN
ejpam-4760	173	2	=	=	SYM
ejpam-4760	173	3	{	{	PUNCT
ejpam-4760	173	4	un−5	un−5	PROPN
ejpam-4760	173	5	,	,	PUNCT
ejpam-4760	173	6	un−4	un−4	NOUN
ejpam-4760	173	7	,	,	PUNCT
ejpam-4760	173	8	un−3	un−3	ADJ
ejpam-4760	173	9	}	}	PUNCT
ejpam-4760	173	10	sr	sr	NOUN
ejpam-4760	173	11	=	=	SYM
ejpam-4760	173	12	{	{	PUNCT
ejpam-4760	173	13	un−2	un−2	PROPN
ejpam-4760	173	14	,	,	PUNCT
ejpam-4760	173	15	un−1	un−1	PROPN
ejpam-4760	173	16	,	,	PUNCT
ejpam-4760	173	17	un	un	ADJ
ejpam-4760	173	18	}	}	PUNCT
ejpam-4760	173	19	clearly	clearly	ADV
ejpam-4760	173	20	,	,	PUNCT
ejpam-4760	173	21	the	the	DET
ejpam-4760	173	22	set	set	NOUN
ejpam-4760	173	23	s	s	PART
ejpam-4760	173	24	=	=	PUNCT
ejpam-4760	173	25	{	{	PUNCT
ejpam-4760	173	26	u2	u2	PROPN
ejpam-4760	173	27	,	,	PUNCT
ejpam-4760	173	28	u5	u5	PROPN
ejpam-4760	173	29	,	,	PUNCT
ejpam-4760	173	30	u8	u8	PROPN
ejpam-4760	173	31	,	,	PUNCT
ejpam-4760	173	32	u11	u11	PROPN
ejpam-4760	173	33	,	,	PUNCT
ejpam-4760	173	34	.	.	PUNCT
ejpam-4760	173	35	.	.	PUNCT
ejpam-4760	173	36	.	.	PUNCT
ejpam-4760	174	1	,	,	PUNCT
ejpam-4760	174	2	un−4	un−4	NOUN
ejpam-4760	174	3	,	,	PUNCT
ejpam-4760	174	4	un−1	un−1	ADJ
ejpam-4760	174	5	}	}	PUNCT
ejpam-4760	174	6	is	be	AUX
ejpam-4760	174	7	a	a	DET
ejpam-4760	174	8	γ0	γ0	NOUN
ejpam-4760	174	9	-	-	PUNCT
ejpam-4760	174	10	set	set	NOUN
ejpam-4760	174	11	of	of	ADP
ejpam-4760	174	12	pn	pn	PROPN
ejpam-4760	174	13	since	since	SCONJ
ejpam-4760	174	14	n	n	PROPN
ejpam-4760	174	15	[	[	X
ejpam-4760	174	16	s	s	X
ejpam-4760	174	17	]	]	X
ejpam-4760	174	18	=	=	SYM
ejpam-4760	174	19	v	v	X
ejpam-4760	174	20	(	(	PUNCT
ejpam-4760	174	21	pn	pn	NOUN
ejpam-4760	174	22	)	)	PUNCT
ejpam-4760	174	23	,	,	PUNCT
ejpam-4760	174	24	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	174	25	has	have	AUX
ejpam-4760	174	26	isolated	isolate	VERB
ejpam-4760	174	27	vertices	vertex	NOUN
ejpam-4760	174	28	and	and	CCONJ
ejpam-4760	174	29	|s|	|s|	NOUN
ejpam-4760	174	30	=	=	SYM
ejpam-4760	174	31	⌈n3	⌈n3	X
ejpam-4760	174	32	⌉	⌉	X
ejpam-4760	174	33	by	by	ADP
ejpam-4760	174	34	proposition	proposition	NOUN
ejpam-4760	174	35	1	1	NUM
ejpam-4760	174	36	.	.	PUNCT
ejpam-4760	175	1	clearly	clearly	ADV
ejpam-4760	175	2	,	,	PUNCT
ejpam-4760	175	3	all	all	DET
ejpam-4760	175	4	other	other	ADJ
ejpam-4760	175	5	vertices	vertex	NOUN
ejpam-4760	175	6	ui	ui	PROPN
ejpam-4760	175	7	∈	∈	PROPN
ejpam-4760	175	8	v	v	NOUN
ejpam-4760	175	9	(	(	PUNCT
ejpam-4760	175	10	pn	pn	NOUN
ejpam-4760	175	11	)	)	PUNCT
ejpam-4760	175	12	\	\	PROPN
ejpam-4760	175	13	s	s	PART
ejpam-4760	175	14	for	for	ADP
ejpam-4760	175	15	all	all	DET
ejpam-4760	175	16	i	i	PRON
ejpam-4760	175	17	=	=	NOUN
ejpam-4760	175	18	1	1	NUM
ejpam-4760	175	19	,	,	PUNCT
ejpam-4760	175	20	3	3	NUM
ejpam-4760	175	21	,	,	PUNCT
ejpam-4760	175	22	4	4	NUM
ejpam-4760	175	23	,	,	PUNCT
ejpam-4760	175	24	6	6	NUM
ejpam-4760	175	25	,	,	PUNCT
ejpam-4760	175	26	.	.	PUNCT
ejpam-4760	175	27	.	.	PUNCT
ejpam-4760	176	1	.	.	PUNCT
ejpam-4760	177	1	,	,	PUNCT
ejpam-4760	178	1	n	n	CCONJ
ejpam-4760	178	2	−	−	PROPN
ejpam-4760	178	3	5	5	NUM
ejpam-4760	178	4	,	,	PUNCT
ejpam-4760	178	5	n	n	CCONJ
ejpam-4760	178	6	−	−	PROPN
ejpam-4760	178	7	3	3	NUM
ejpam-4760	178	8	,	,	PUNCT
ejpam-4760	178	9	n	n	CCONJ
ejpam-4760	178	10	−	−	PROPN
ejpam-4760	178	11	2	2	NUM
ejpam-4760	178	12	,	,	PUNCT
ejpam-4760	178	13	n	n	PRON
ejpam-4760	178	14	are	be	AUX
ejpam-4760	178	15	dominated	dominate	VERB
ejpam-4760	178	16	by	by	ADP
ejpam-4760	178	17	exactly	exactly	ADV
ejpam-4760	178	18	one	one	NUM
ejpam-4760	178	19	vertex	vertex	NOUN
ejpam-4760	178	20	in	in	ADP
ejpam-4760	178	21	s.	s.	PROPN
ejpam-4760	178	22	by	by	ADP
ejpam-4760	178	23	proposition	proposition	NOUN
ejpam-4760	178	24	6	6	NUM
ejpam-4760	178	25	,	,	PUNCT
ejpam-4760	178	26	γp0(pn	γp0(pn	NUM
ejpam-4760	178	27	)	)	PUNCT
ejpam-4760	178	28	=	=	VERB
ejpam-4760	178	29	⌈n3	⌈n3	VERB
ejpam-4760	178	30	⌉.	⌉.	ADV
ejpam-4760	178	31	case	case	NOUN
ejpam-4760	178	32	2	2	NUM
ejpam-4760	178	33	:	:	PUNCT
ejpam-4760	178	34	suppose	suppose	VERB
ejpam-4760	178	35	that	that	SCONJ
ejpam-4760	178	36	n	n	X
ejpam-4760	178	37	≡	≡	PROPN
ejpam-4760	178	38	1	1	NUM
ejpam-4760	178	39	(	(	PUNCT
ejpam-4760	178	40	mod	mod	NOUN
ejpam-4760	178	41	3	3	NUM
ejpam-4760	178	42	)	)	PUNCT
ejpam-4760	178	43	.	.	PUNCT
ejpam-4760	179	1	if	if	SCONJ
ejpam-4760	179	2	n	n	NOUN
ejpam-4760	179	3	=	=	SYM
ejpam-4760	179	4	1	1	NUM
ejpam-4760	179	5	,	,	PUNCT
ejpam-4760	179	6	then	then	ADV
ejpam-4760	179	7	γp0(p1	γp0(p1	VERB
ejpam-4760	179	8	)	)	PUNCT
ejpam-4760	179	9	=	=	SYM
ejpam-4760	179	10	1	1	NUM
ejpam-4760	179	11	=	=	SYM
ejpam-4760	179	12	⌈13⌉.	⌈13⌉.	PROPN
ejpam-4760	179	13	suppose	suppose	VERB
ejpam-4760	179	14	that	that	SCONJ
ejpam-4760	179	15	n	n	NOUN
ejpam-4760	179	16	=	=	SYM
ejpam-4760	179	17	4	4	X
ejpam-4760	179	18	.	.	PUNCT
ejpam-4760	179	19	clearly	clearly	ADV
ejpam-4760	179	20	,	,	PUNCT
ejpam-4760	179	21	s	s	PART
ejpam-4760	179	22	=	=	PUNCT
ejpam-4760	179	23	{	{	PUNCT
ejpam-4760	179	24	u1	u1	PROPN
ejpam-4760	179	25	,	,	PUNCT
ejpam-4760	179	26	u4	u4	PROPN
ejpam-4760	179	27	}	}	PUNCT
ejpam-4760	179	28	is	be	AUX
ejpam-4760	179	29	a	a	DET
ejpam-4760	179	30	γ0	γ0	NOUN
ejpam-4760	179	31	-	-	PUNCT
ejpam-4760	179	32	set	set	NOUN
ejpam-4760	179	33	of	of	ADP
ejpam-4760	179	34	p4	p4	NOUN
ejpam-4760	179	35	since	since	SCONJ
ejpam-4760	179	36	|s|	|s|	NOUN
ejpam-4760	179	37	=	=	SYM
ejpam-4760	179	38	⌈43⌉	⌈43⌉	NOUN
ejpam-4760	179	39	=	=	SYM
ejpam-4760	179	40	2	2	X
ejpam-4760	179	41	.	.	PUNCT
ejpam-4760	179	42	clearly	clearly	ADV
ejpam-4760	179	43	,	,	PUNCT
ejpam-4760	179	44	n(u1	n(u1	NOUN
ejpam-4760	179	45	)	)	PUNCT
ejpam-4760	179	46	∩	∩	NOUN
ejpam-4760	179	47	n(u4	n(u4	NOUN
ejpam-4760	179	48	)	)	PUNCT
ejpam-4760	179	49	=	=	SYM
ejpam-4760	179	50	∅	∅	NOUN
ejpam-4760	179	51	and	and	CCONJ
ejpam-4760	179	52	n	n	CCONJ
ejpam-4760	179	53	[	[	X
ejpam-4760	179	54	u1	u1	NOUN
ejpam-4760	179	55	]	]	PUNCT
ejpam-4760	179	56	∪	∪	ADP
ejpam-4760	179	57	n	n	PRON
ejpam-4760	179	58	[	[	X
ejpam-4760	179	59	u4	u4	X
ejpam-4760	179	60	]	]	X
ejpam-4760	179	61	=	=	SYM
ejpam-4760	179	62	v	v	NOUN
ejpam-4760	179	63	(	(	PUNCT
ejpam-4760	179	64	p4	p4	ADJ
ejpam-4760	179	65	)	)	PUNCT
ejpam-4760	179	66	.	.	PUNCT
ejpam-4760	180	1	by	by	ADP
ejpam-4760	180	2	theorem	theorem	ADJ
ejpam-4760	180	3	4	4	NUM
ejpam-4760	180	4	,	,	PUNCT
ejpam-4760	180	5	γp0(p4	γp0(p4	NOUN
ejpam-4760	180	6	)	)	PUNCT
ejpam-4760	180	7	=	=	SYM
ejpam-4760	180	8	2	2	NUM
ejpam-4760	180	9	=	=	SYM
ejpam-4760	180	10	⌈43⌉.	⌈43⌉.	PROPN
ejpam-4760	180	11	suppose	suppose	VERB
ejpam-4760	180	12	that	that	SCONJ
ejpam-4760	180	13	n	n	PROPN
ejpam-4760	180	14	>	>	X
ejpam-4760	180	15	4	4	X
ejpam-4760	180	16	.	.	PUNCT
ejpam-4760	181	1	let	let	VERB
ejpam-4760	181	2	r	r	NOUN
ejpam-4760	181	3	=	=	PUNCT
ejpam-4760	181	4	n+2	n+2	NUM
ejpam-4760	181	5	3	3	NUM
ejpam-4760	181	6	and	and	CCONJ
ejpam-4760	181	7	j	j	PROPN
ejpam-4760	181	8	=	=	SYM
ejpam-4760	181	9	1	1	NUM
ejpam-4760	181	10	,	,	PUNCT
ejpam-4760	181	11	2	2	NUM
ejpam-4760	181	12	,	,	PUNCT
ejpam-4760	181	13	.	.	PUNCT
ejpam-4760	181	14	.	.	PUNCT
ejpam-4760	182	1	.	.	PUNCT
ejpam-4760	183	1	,	,	PUNCT
ejpam-4760	183	2	r	r	NOUN
ejpam-4760	183	3	−	−	PROPN
ejpam-4760	183	4	1	1	NUM
ejpam-4760	183	5	,	,	PUNCT
ejpam-4760	183	6	r.	r.	PROPN
ejpam-4760	183	7	group	group	PROPN
ejpam-4760	183	8	the	the	DET
ejpam-4760	183	9	vertices	vertex	NOUN
ejpam-4760	183	10	of	of	ADP
ejpam-4760	183	11	pn	pn	NOUN
ejpam-4760	183	12	into	into	ADP
ejpam-4760	183	13	r	r	NOUN
ejpam-4760	183	14	disjoint	disjoint	NOUN
ejpam-4760	183	15	subsets	subset	NOUN
ejpam-4760	183	16	sj	sj	NOUN
ejpam-4760	183	17	s1	s1	PROPN
ejpam-4760	183	18	=	=	PUNCT
ejpam-4760	183	19	{	{	PUNCT
ejpam-4760	183	20	u1	u1	NOUN
ejpam-4760	183	21	}	}	PUNCT
ejpam-4760	183	22	s2	s2	NOUN
ejpam-4760	183	23	=	=	SYM
ejpam-4760	183	24	{	{	PUNCT
ejpam-4760	183	25	u2	u2	PROPN
ejpam-4760	183	26	,	,	PUNCT
ejpam-4760	183	27	u3	u3	NOUN
ejpam-4760	183	28	,	,	PUNCT
ejpam-4760	183	29	u4	u4	PROPN
ejpam-4760	183	30	}	}	PUNCT
ejpam-4760	183	31	s3	s3	NOUN
ejpam-4760	183	32	=	=	SYM
ejpam-4760	183	33	{	{	PUNCT
ejpam-4760	183	34	u5	u5	PROPN
ejpam-4760	183	35	,	,	PUNCT
ejpam-4760	183	36	u6	u6	PROPN
ejpam-4760	183	37	,	,	PUNCT
ejpam-4760	183	38	u7	u7	PROPN
ejpam-4760	183	39	}	}	PUNCT
ejpam-4760	183	40	s4	s4	PROPN
ejpam-4760	183	41	=	=	SYM
ejpam-4760	183	42	{	{	PUNCT
ejpam-4760	183	43	u8	u8	PROPN
ejpam-4760	183	44	,	,	PUNCT
ejpam-4760	183	45	u9	u9	PROPN
ejpam-4760	183	46	,	,	PUNCT
ejpam-4760	183	47	u10	u10	PROPN
ejpam-4760	183	48	}	}	PUNCT
ejpam-4760	183	49	...	...	PUNCT
ejpam-4760	184	1	sr−1	sr−1	PROPN
ejpam-4760	184	2	=	=	SYM
ejpam-4760	184	3	{	{	PUNCT
ejpam-4760	184	4	un−5	un−5	PROPN
ejpam-4760	184	5	,	,	PUNCT
ejpam-4760	184	6	un−4	un−4	NOUN
ejpam-4760	184	7	,	,	PUNCT
ejpam-4760	184	8	un−3	un−3	ADJ
ejpam-4760	184	9	}	}	PUNCT
ejpam-4760	184	10	sr	sr	NOUN
ejpam-4760	184	11	=	=	SYM
ejpam-4760	184	12	{	{	PUNCT
ejpam-4760	184	13	un−2	un−2	PROPN
ejpam-4760	184	14	,	,	PUNCT
ejpam-4760	184	15	un−1	un−1	PROPN
ejpam-4760	184	16	,	,	PUNCT
ejpam-4760	184	17	un	un	ADJ
ejpam-4760	184	18	}	}	PUNCT
ejpam-4760	184	19	clearly	clearly	ADV
ejpam-4760	184	20	,	,	PUNCT
ejpam-4760	184	21	the	the	DET
ejpam-4760	184	22	set	set	NOUN
ejpam-4760	184	23	s	s	PART
ejpam-4760	184	24	=	=	NOUN
ejpam-4760	184	25	{	{	PUNCT
ejpam-4760	184	26	u1	u1	PROPN
ejpam-4760	184	27	,	,	PUNCT
ejpam-4760	184	28	u4	u4	PROPN
ejpam-4760	184	29	,	,	PUNCT
ejpam-4760	184	30	u7	u7	PROPN
ejpam-4760	184	31	,	,	PUNCT
ejpam-4760	184	32	u10	u10	PROPN
ejpam-4760	184	33	,	,	PUNCT
ejpam-4760	184	34	.	.	PUNCT
ejpam-4760	184	35	.	.	PUNCT
ejpam-4760	184	36	.	.	PUNCT
ejpam-4760	185	1	,	,	PUNCT
ejpam-4760	185	2	un−3	un−3	PROPN
ejpam-4760	185	3	,	,	PUNCT
ejpam-4760	185	4	un	un	ADJ
ejpam-4760	185	5	}	}	PUNCT
ejpam-4760	185	6	is	be	AUX
ejpam-4760	185	7	a	a	DET
ejpam-4760	185	8	γ0	γ0	NOUN
ejpam-4760	185	9	-	-	PUNCT
ejpam-4760	185	10	set	set	NOUN
ejpam-4760	185	11	of	of	ADP
ejpam-4760	185	12	pn	pn	PROPN
ejpam-4760	185	13	since	since	SCONJ
ejpam-4760	185	14	n	n	PROPN
ejpam-4760	185	15	[	[	X
ejpam-4760	185	16	s	s	X
ejpam-4760	185	17	]	]	X
ejpam-4760	185	18	=	=	SYM
ejpam-4760	185	19	v	v	X
ejpam-4760	185	20	(	(	PUNCT
ejpam-4760	185	21	pn	pn	NOUN
ejpam-4760	185	22	)	)	PUNCT
ejpam-4760	185	23	,	,	PUNCT
ejpam-4760	185	24	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	185	25	has	have	AUX
ejpam-4760	185	26	isolated	isolate	VERB
ejpam-4760	185	27	vertices	vertex	NOUN
ejpam-4760	185	28	and	and	CCONJ
ejpam-4760	185	29	|s|	|s|	NOUN
ejpam-4760	185	30	=	=	SYM
ejpam-4760	185	31	⌈n3	⌈n3	X
ejpam-4760	185	32	⌉	⌉	X
ejpam-4760	185	33	by	by	ADP
ejpam-4760	185	34	proposition	proposition	NOUN
ejpam-4760	185	35	1	1	NUM
ejpam-4760	185	36	.	.	PUNCT
ejpam-4760	186	1	clearly	clearly	ADV
ejpam-4760	186	2	,	,	PUNCT
ejpam-4760	186	3	all	all	DET
ejpam-4760	186	4	other	other	ADJ
ejpam-4760	186	5	vertices	vertex	NOUN
ejpam-4760	186	6	ui	ui	PROPN
ejpam-4760	186	7	∈	∈	PROPN
ejpam-4760	186	8	v	v	NOUN
ejpam-4760	186	9	(	(	PUNCT
ejpam-4760	186	10	pn	pn	NOUN
ejpam-4760	186	11	)	)	PUNCT
ejpam-4760	186	12	\	\	PROPN
ejpam-4760	186	13	s	s	PART
ejpam-4760	186	14	for	for	ADP
ejpam-4760	186	15	all	all	DET
ejpam-4760	186	16	i	i	PRON
ejpam-4760	186	17	=	=	NOUN
ejpam-4760	186	18	2	2	NUM
ejpam-4760	186	19	,	,	PUNCT
ejpam-4760	186	20	3	3	NUM
ejpam-4760	186	21	,	,	PUNCT
ejpam-4760	186	22	5	5	NUM
ejpam-4760	186	23	,	,	PUNCT
ejpam-4760	186	24	6	6	NUM
ejpam-4760	186	25	,	,	PUNCT
ejpam-4760	186	26	.	.	PUNCT
ejpam-4760	186	27	.	.	PUNCT
ejpam-4760	187	1	.	.	PUNCT
ejpam-4760	188	1	,	,	PUNCT
ejpam-4760	189	1	n	n	CCONJ
ejpam-4760	189	2	−	−	PROPN
ejpam-4760	189	3	5	5	NUM
ejpam-4760	189	4	,	,	PUNCT
ejpam-4760	189	5	n	n	CCONJ
ejpam-4760	189	6	−	−	PROPN
ejpam-4760	189	7	4	4	NUM
ejpam-4760	189	8	,	,	PUNCT
ejpam-4760	189	9	n	n	CCONJ
ejpam-4760	189	10	−	−	PROPN
ejpam-4760	189	11	2	2	NUM
ejpam-4760	189	12	,	,	PUNCT
ejpam-4760	189	13	n	n	CCONJ
ejpam-4760	189	14	−	−	PROPN
ejpam-4760	189	15	1	1	NUM
ejpam-4760	189	16	are	be	AUX
ejpam-4760	189	17	dominated	dominate	VERB
ejpam-4760	189	18	by	by	ADP
ejpam-4760	189	19	exactly	exactly	ADV
ejpam-4760	189	20	one	one	NUM
ejpam-4760	189	21	vertex	vertex	NOUN
ejpam-4760	189	22	in	in	ADP
ejpam-4760	189	23	s.	s.	PROPN
ejpam-4760	189	24	by	by	ADP
ejpam-4760	189	25	proposition	proposition	NOUN
ejpam-4760	189	26	6	6	NUM
ejpam-4760	189	27	,	,	PUNCT
ejpam-4760	189	28	γp0(pn	γp0(pn	NUM
ejpam-4760	189	29	)	)	PUNCT
ejpam-4760	189	30	=	=	VERB
ejpam-4760	189	31	⌈n3	⌈n3	VERB
ejpam-4760	189	32	⌉.	⌉.	ADV
ejpam-4760	189	33	case	case	NOUN
ejpam-4760	189	34	3	3	X
ejpam-4760	189	35	:	:	PUNCT
ejpam-4760	189	36	suppose	suppose	VERB
ejpam-4760	189	37	that	that	SCONJ
ejpam-4760	189	38	n	n	NUM
ejpam-4760	189	39	≡	≡	PROPN
ejpam-4760	189	40	2	2	NUM
ejpam-4760	189	41	(	(	PUNCT
ejpam-4760	189	42	mod	mod	NOUN
ejpam-4760	189	43	3	3	NUM
ejpam-4760	189	44	)	)	PUNCT
ejpam-4760	189	45	.	.	PUNCT
ejpam-4760	190	1	suppose	suppose	VERB
ejpam-4760	190	2	that	that	SCONJ
ejpam-4760	190	3	n	n	PROPN
ejpam-4760	190	4	=	=	SYM
ejpam-4760	190	5	2	2	X
ejpam-4760	190	6	.	.	PUNCT
ejpam-4760	190	7	clearly	clearly	ADV
ejpam-4760	190	8	,	,	PUNCT
ejpam-4760	190	9	∆(p2	∆(p2	VERB
ejpam-4760	190	10	)	)	PUNCT
ejpam-4760	190	11	=	=	SYM
ejpam-4760	190	12	1	1	X
ejpam-4760	190	13	.	.	PUNCT
ejpam-4760	190	14	by	by	ADP
ejpam-4760	190	15	theorem	theorem	NOUN
ejpam-4760	190	16	3	3	NUM
ejpam-4760	190	17	,	,	PUNCT
ejpam-4760	190	18	γp0(p2	γp0(p2	ADJ
ejpam-4760	190	19	)	)	PUNCT
ejpam-4760	190	20	=	=	SYM
ejpam-4760	190	21	1	1	NUM
ejpam-4760	190	22	=	=	SYM
ejpam-4760	190	23	⌈23⌉.	⌈23⌉.	PROPN
ejpam-4760	190	24	suppose	suppose	VERB
ejpam-4760	190	25	that	that	SCONJ
ejpam-4760	190	26	n	n	PROPN
ejpam-4760	190	27	>	>	X
ejpam-4760	190	28	2	2	X
ejpam-4760	190	29	.	.	PUNCT
ejpam-4760	191	1	let	let	VERB
ejpam-4760	191	2	r	r	NOUN
ejpam-4760	191	3	=	=	SYM
ejpam-4760	191	4	n+1	n+1	PROPN
ejpam-4760	191	5	3	3	NUM
ejpam-4760	191	6	and	and	CCONJ
ejpam-4760	191	7	j	j	PROPN
ejpam-4760	191	8	=	=	SYM
ejpam-4760	191	9	1	1	NUM
ejpam-4760	191	10	,	,	PUNCT
ejpam-4760	191	11	2	2	NUM
ejpam-4760	191	12	,	,	PUNCT
ejpam-4760	191	13	.	.	PUNCT
ejpam-4760	191	14	.	.	PUNCT
ejpam-4760	192	1	.	.	PUNCT
ejpam-4760	193	1	,	,	PUNCT
ejpam-4760	193	2	r−1	r−1	PROPN
ejpam-4760	193	3	,	,	PUNCT
ejpam-4760	193	4	r.	r.	PROPN
ejpam-4760	193	5	group	group	PROPN
ejpam-4760	193	6	the	the	DET
ejpam-4760	193	7	vertices	vertex	NOUN
ejpam-4760	193	8	of	of	ADP
ejpam-4760	193	9	pn	pn	NOUN
ejpam-4760	193	10	into	into	ADP
ejpam-4760	193	11	r	r	NOUN
ejpam-4760	193	12	disjoint	disjoint	NOUN
ejpam-4760	193	13	subsets	subset	NOUN
ejpam-4760	193	14	sj	sj	PROPN
ejpam-4760	193	15	c.	c.	PROPN
ejpam-4760	193	16	armada	armada	PROPN
ejpam-4760	193	17	,	,	PUNCT
ejpam-4760	193	18	j.	j.	PROPN
ejpam-4760	193	19	hamja	hamja	PROPN
ejpam-4760	193	20	/	/	SYM
ejpam-4760	193	21	eur	eur	PROPN
ejpam-4760	193	22	.	.	PUNCT
ejpam-4760	194	1	j.	j.	PROPN
ejpam-4760	194	2	pure	pure	PROPN
ejpam-4760	194	3	appl	appl	PROPN
ejpam-4760	194	4	.	.	PROPN
ejpam-4760	194	5	math	math	PROPN
ejpam-4760	194	6	,	,	PUNCT
ejpam-4760	194	7	16	16	NUM
ejpam-4760	194	8	(	(	PUNCT
ejpam-4760	194	9	2	2	NUM
ejpam-4760	194	10	)	)	PUNCT
ejpam-4760	194	11	(	(	PUNCT
ejpam-4760	194	12	2023	2023	NUM
ejpam-4760	194	13	)	)	PUNCT
ejpam-4760	194	14	,	,	PUNCT
ejpam-4760	194	15	1326	1326	NUM
ejpam-4760	194	16	-	-	SYM
ejpam-4760	194	17	1341	1341	NUM
ejpam-4760	194	18	1333	1333	NUM
ejpam-4760	194	19	s1	s1	NOUN
ejpam-4760	194	20	=	=	SYM
ejpam-4760	194	21	{	{	PUNCT
ejpam-4760	194	22	u1	u1	NOUN
ejpam-4760	194	23	,	,	PUNCT
ejpam-4760	194	24	u2	u2	NOUN
ejpam-4760	194	25	}	}	PUNCT
ejpam-4760	194	26	s2	s2	NOUN
ejpam-4760	194	27	=	=	SYM
ejpam-4760	194	28	{	{	PUNCT
ejpam-4760	194	29	u3	u3	PROPN
ejpam-4760	194	30	,	,	PUNCT
ejpam-4760	194	31	u4	u4	PROPN
ejpam-4760	194	32	,	,	PUNCT
ejpam-4760	194	33	u5	u5	PROPN
ejpam-4760	194	34	}	}	PUNCT
ejpam-4760	194	35	s3	s3	NOUN
ejpam-4760	194	36	=	=	SYM
ejpam-4760	194	37	{	{	PUNCT
ejpam-4760	194	38	u6	u6	PROPN
ejpam-4760	194	39	,	,	PUNCT
ejpam-4760	194	40	u7	u7	PROPN
ejpam-4760	194	41	,	,	PUNCT
ejpam-4760	194	42	u8	u8	PROPN
ejpam-4760	194	43	}	}	PUNCT
ejpam-4760	194	44	s4	s4	PROPN
ejpam-4760	194	45	=	=	SYM
ejpam-4760	194	46	{	{	PUNCT
ejpam-4760	194	47	u9	u9	PROPN
ejpam-4760	194	48	,	,	PUNCT
ejpam-4760	194	49	u10	u10	PROPN
ejpam-4760	194	50	,	,	PUNCT
ejpam-4760	194	51	u11	u11	PROPN
ejpam-4760	194	52	}	}	PUNCT
ejpam-4760	194	53	...	...	PUNCT
ejpam-4760	195	1	sr−1	sr−1	PROPN
ejpam-4760	195	2	=	=	SYM
ejpam-4760	195	3	{	{	PUNCT
ejpam-4760	195	4	un−5	un−5	PROPN
ejpam-4760	195	5	,	,	PUNCT
ejpam-4760	195	6	un−4	un−4	NOUN
ejpam-4760	195	7	,	,	PUNCT
ejpam-4760	195	8	un−3	un−3	ADJ
ejpam-4760	195	9	}	}	PUNCT
ejpam-4760	195	10	sr	sr	NOUN
ejpam-4760	195	11	=	=	SYM
ejpam-4760	195	12	{	{	PUNCT
ejpam-4760	195	13	un−2	un−2	PROPN
ejpam-4760	195	14	,	,	PUNCT
ejpam-4760	195	15	un−1	un−1	PROPN
ejpam-4760	195	16	,	,	PUNCT
ejpam-4760	195	17	un	un	ADJ
ejpam-4760	195	18	}	}	PUNCT
ejpam-4760	195	19	clearly	clearly	ADV
ejpam-4760	195	20	,	,	PUNCT
ejpam-4760	195	21	the	the	DET
ejpam-4760	195	22	set	set	NOUN
ejpam-4760	195	23	s	s	PART
ejpam-4760	195	24	=	=	NOUN
ejpam-4760	195	25	{	{	PUNCT
ejpam-4760	195	26	u1	u1	PROPN
ejpam-4760	195	27	,	,	PUNCT
ejpam-4760	195	28	u4	u4	PROPN
ejpam-4760	195	29	,	,	PUNCT
ejpam-4760	195	30	u7	u7	PROPN
ejpam-4760	195	31	,	,	PUNCT
ejpam-4760	195	32	u10	u10	PROPN
ejpam-4760	195	33	,	,	PUNCT
ejpam-4760	195	34	.	.	PUNCT
ejpam-4760	195	35	.	.	PUNCT
ejpam-4760	195	36	.	.	PUNCT
ejpam-4760	196	1	,	,	PUNCT
ejpam-4760	196	2	un−4	un−4	NOUN
ejpam-4760	196	3	,	,	PUNCT
ejpam-4760	196	4	un−1	un−1	ADJ
ejpam-4760	196	5	}	}	PUNCT
ejpam-4760	196	6	is	be	AUX
ejpam-4760	196	7	a	a	DET
ejpam-4760	196	8	γ0	γ0	NOUN
ejpam-4760	196	9	-	-	PUNCT
ejpam-4760	196	10	set	set	NOUN
ejpam-4760	196	11	of	of	ADP
ejpam-4760	196	12	pn	pn	PROPN
ejpam-4760	196	13	since	since	SCONJ
ejpam-4760	196	14	n	n	PROPN
ejpam-4760	196	15	[	[	X
ejpam-4760	196	16	s	s	X
ejpam-4760	196	17	]	]	X
ejpam-4760	196	18	=	=	SYM
ejpam-4760	196	19	v	v	X
ejpam-4760	196	20	(	(	PUNCT
ejpam-4760	196	21	pn	pn	NOUN
ejpam-4760	196	22	)	)	PUNCT
ejpam-4760	196	23	,	,	PUNCT
ejpam-4760	196	24	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	196	25	has	have	AUX
ejpam-4760	196	26	isolated	isolate	VERB
ejpam-4760	196	27	vertices	vertex	NOUN
ejpam-4760	196	28	and	and	CCONJ
ejpam-4760	196	29	|s|	|s|	NOUN
ejpam-4760	196	30	=	=	SYM
ejpam-4760	196	31	⌈n3	⌈n3	X
ejpam-4760	196	32	⌉	⌉	X
ejpam-4760	196	33	by	by	ADP
ejpam-4760	196	34	proposition	proposition	NOUN
ejpam-4760	196	35	1	1	NUM
ejpam-4760	196	36	.	.	PUNCT
ejpam-4760	197	1	clearly	clearly	ADV
ejpam-4760	197	2	,	,	PUNCT
ejpam-4760	197	3	all	all	DET
ejpam-4760	197	4	other	other	ADJ
ejpam-4760	197	5	vertices	vertex	NOUN
ejpam-4760	197	6	ui	ui	PROPN
ejpam-4760	197	7	∈	∈	PROPN
ejpam-4760	197	8	v	v	NOUN
ejpam-4760	197	9	(	(	PUNCT
ejpam-4760	197	10	pn	pn	NOUN
ejpam-4760	197	11	)	)	PUNCT
ejpam-4760	197	12	\	\	PROPN
ejpam-4760	197	13	s	s	PART
ejpam-4760	197	14	for	for	ADP
ejpam-4760	197	15	all	all	DET
ejpam-4760	197	16	i	i	PRON
ejpam-4760	197	17	=	=	NOUN
ejpam-4760	197	18	2	2	NUM
ejpam-4760	197	19	,	,	PUNCT
ejpam-4760	197	20	3	3	NUM
ejpam-4760	197	21	,	,	PUNCT
ejpam-4760	197	22	5	5	NUM
ejpam-4760	197	23	,	,	PUNCT
ejpam-4760	197	24	6	6	NUM
ejpam-4760	197	25	,	,	PUNCT
ejpam-4760	197	26	.	.	PUNCT
ejpam-4760	197	27	.	.	PUNCT
ejpam-4760	198	1	.	.	PUNCT
ejpam-4760	199	1	,	,	PUNCT
ejpam-4760	200	1	n	n	CCONJ
ejpam-4760	200	2	−	−	PROPN
ejpam-4760	200	3	5	5	NUM
ejpam-4760	200	4	,	,	PUNCT
ejpam-4760	200	5	n	n	CCONJ
ejpam-4760	200	6	−	−	PROPN
ejpam-4760	200	7	3	3	NUM
ejpam-4760	200	8	,	,	PUNCT
ejpam-4760	200	9	n	n	CCONJ
ejpam-4760	200	10	−	−	PROPN
ejpam-4760	200	11	2	2	NUM
ejpam-4760	200	12	,	,	PUNCT
ejpam-4760	200	13	n	n	PRON
ejpam-4760	200	14	are	be	AUX
ejpam-4760	200	15	dominated	dominate	VERB
ejpam-4760	200	16	by	by	ADP
ejpam-4760	200	17	exactly	exactly	ADV
ejpam-4760	200	18	one	one	NUM
ejpam-4760	200	19	vertex	vertex	NOUN
ejpam-4760	200	20	in	in	ADP
ejpam-4760	200	21	s.	s.	PROPN
ejpam-4760	200	22	by	by	ADP
ejpam-4760	200	23	proposition	proposition	NOUN
ejpam-4760	200	24	6	6	NUM
ejpam-4760	200	25	,	,	PUNCT
ejpam-4760	200	26	γp0(pn	γp0(pn	NUM
ejpam-4760	200	27	)	)	PUNCT
ejpam-4760	200	28	=	=	PRON
ejpam-4760	201	1	⌈n3	⌈n3	X
ejpam-4760	201	2	⌉.	⌉.	ADV
ejpam-4760	201	3	therefore	therefore	ADV
ejpam-4760	201	4	,	,	PUNCT
ejpam-4760	201	5	in	in	ADP
ejpam-4760	201	6	any	any	DET
ejpam-4760	201	7	case	case	NOUN
ejpam-4760	201	8	,	,	PUNCT
ejpam-4760	201	9	γp0(pn	γp0(pn	NUM
ejpam-4760	201	10	)	)	PUNCT
ejpam-4760	201	11	=	=	VERB
ejpam-4760	201	12	⌈n3	⌈n3	ADJ
ejpam-4760	201	13	⌉.	⌉.	ADV
ejpam-4760	201	14	theorem	theorem	ADJ
ejpam-4760	201	15	6	6	NUM
ejpam-4760	201	16	.	.	PUNCT
ejpam-4760	202	1	for	for	ADP
ejpam-4760	202	2	a	a	DET
ejpam-4760	202	3	cycle	cycle	NOUN
ejpam-4760	202	4	cn	cn	NOUN
ejpam-4760	202	5	of	of	ADP
ejpam-4760	202	6	order	order	NOUN
ejpam-4760	202	7	n	n	NOUN
ejpam-4760	202	8	=	=	SYM
ejpam-4760	202	9	3	3	NUM
ejpam-4760	202	10	or	or	CCONJ
ejpam-4760	202	11	n	n	PRON
ejpam-4760	202	12	≥	≥	NOUN
ejpam-4760	202	13	6	6	NUM
ejpam-4760	202	14	,	,	PUNCT
ejpam-4760	202	15	γp0(cn	γp0(cn	NUM
ejpam-4760	202	16	)	)	PUNCT
ejpam-4760	202	17	=	=	PRON
ejpam-4760	202	18	{	{	PUNCT
ejpam-4760	202	19	⌈	⌈	PROPN
ejpam-4760	202	20	n	n	CCONJ
ejpam-4760	202	21	3	3	NUM
ejpam-4760	202	22	⌉	⌉	NOUN
ejpam-4760	202	23	+	+	ADJ
ejpam-4760	202	24	1	1	NUM
ejpam-4760	202	25	,	,	PUNCT
ejpam-4760	202	26	if	if	SCONJ
ejpam-4760	202	27	n	n	PRON
ejpam-4760	202	28	≡	≡	PROPN
ejpam-4760	202	29	2	2	NUM
ejpam-4760	202	30	(	(	PUNCT
ejpam-4760	202	31	mod	mod	NOUN
ejpam-4760	202	32	3)⌈	3)⌈	NUM
ejpam-4760	202	33	n	n	NUM
ejpam-4760	202	34	3	3	NUM
ejpam-4760	202	35	⌉	⌉	NOUN
ejpam-4760	202	36	,	,	PUNCT
ejpam-4760	202	37	if	if	SCONJ
ejpam-4760	202	38	n	n	X
ejpam-4760	202	39	̸≡	̸≡	VERB
ejpam-4760	202	40	2	2	NUM
ejpam-4760	202	41	(	(	PUNCT
ejpam-4760	202	42	mod	mod	NOUN
ejpam-4760	202	43	3	3	NUM
ejpam-4760	202	44	)	)	PUNCT
ejpam-4760	202	45	proof	proof	NOUN
ejpam-4760	202	46	.	.	PUNCT
ejpam-4760	202	47	suppose	suppose	VERB
ejpam-4760	202	48	that	that	SCONJ
ejpam-4760	202	49	v	v	INTJ
ejpam-4760	202	50	(	(	PUNCT
ejpam-4760	202	51	cn	cn	PROPN
ejpam-4760	202	52	)	)	PUNCT
ejpam-4760	202	53	=	=	SYM
ejpam-4760	202	54	{	{	PUNCT
ejpam-4760	202	55	u1	u1	NOUN
ejpam-4760	202	56	,	,	PUNCT
ejpam-4760	202	57	u2	u2	NOUN
ejpam-4760	202	58	,	,	PUNCT
ejpam-4760	202	59	.	.	PUNCT
ejpam-4760	202	60	.	.	PUNCT
ejpam-4760	203	1	.	.	PUNCT
ejpam-4760	204	1	,	,	PUNCT
ejpam-4760	204	2	un−1	un−1	PROPN
ejpam-4760	204	3	,	,	PUNCT
ejpam-4760	204	4	un	un	ADJ
ejpam-4760	204	5	}	}	PUNCT
ejpam-4760	204	6	such	such	ADJ
ejpam-4760	204	7	that	that	SCONJ
ejpam-4760	204	8	deg(ui	deg(ui	X
ejpam-4760	204	9	)	)	PUNCT
ejpam-4760	204	10	=	=	SYM
ejpam-4760	204	11	2	2	NUM
ejpam-4760	204	12	for	for	ADP
ejpam-4760	204	13	all	all	DET
ejpam-4760	204	14	i	i	PRON
ejpam-4760	204	15	=	=	NOUN
ejpam-4760	204	16	1	1	NUM
ejpam-4760	204	17	,	,	PUNCT
ejpam-4760	204	18	2	2	NUM
ejpam-4760	204	19	,	,	PUNCT
ejpam-4760	204	20	3	3	NUM
ejpam-4760	204	21	,	,	PUNCT
ejpam-4760	204	22	.	.	PUNCT
ejpam-4760	204	23	.	.	PUNCT
ejpam-4760	205	1	.	.	PUNCT
ejpam-4760	206	1	,	,	PUNCT
ejpam-4760	206	2	n−	n−	NOUN
ejpam-4760	206	3	1	1	NUM
ejpam-4760	206	4	,	,	PUNCT
ejpam-4760	206	5	n.	n.	NOUN
ejpam-4760	206	6	by	by	ADP
ejpam-4760	206	7	proposition	proposition	NOUN
ejpam-4760	206	8	1	1	NUM
ejpam-4760	206	9	,	,	PUNCT
ejpam-4760	206	10	γ0(cn	γ0(cn	PROPN
ejpam-4760	206	11	)	)	PUNCT
ejpam-4760	207	1	=	=	PRON
ejpam-4760	207	2	⌈n3	⌈n3	VERB
ejpam-4760	207	3	⌉.	⌉.	ADV
ejpam-4760	207	4	consider	consider	VERB
ejpam-4760	207	5	the	the	DET
ejpam-4760	207	6	following	follow	VERB
ejpam-4760	207	7	cases	case	NOUN
ejpam-4760	207	8	:	:	PUNCT
ejpam-4760	207	9	case	case	NOUN
ejpam-4760	207	10	1	1	NUM
ejpam-4760	207	11	:	:	PUNCT
ejpam-4760	207	12	suppose	suppose	VERB
ejpam-4760	207	13	that	that	SCONJ
ejpam-4760	207	14	n	n	PROPN
ejpam-4760	207	15	≡	≡	PROPN
ejpam-4760	207	16	0	0	PUNCT
ejpam-4760	208	1	(	(	PUNCT
ejpam-4760	208	2	mod	mod	NOUN
ejpam-4760	208	3	3	3	NUM
ejpam-4760	208	4	)	)	PUNCT
ejpam-4760	208	5	.	.	PUNCT
ejpam-4760	209	1	if	if	SCONJ
ejpam-4760	209	2	n	n	NUM
ejpam-4760	209	3	=	=	SYM
ejpam-4760	209	4	3	3	NUM
ejpam-4760	209	5	,	,	PUNCT
ejpam-4760	209	6	by	by	ADP
ejpam-4760	209	7	corollary	corollary	ADJ
ejpam-4760	209	8	3	3	NUM
ejpam-4760	209	9	,	,	PUNCT
ejpam-4760	209	10	γp0(c3	γp0(c3	NUM
ejpam-4760	209	11	)	)	PUNCT
ejpam-4760	209	12	=	=	SYM
ejpam-4760	209	13	1	1	NUM
ejpam-4760	209	14	=	=	SYM
ejpam-4760	209	15	⌈33⌉.	⌈33⌉.	PROPN
ejpam-4760	209	16	suppose	suppose	VERB
ejpam-4760	209	17	that	that	SCONJ
ejpam-4760	209	18	n	n	PROPN
ejpam-4760	209	19	>	>	X
ejpam-4760	209	20	3	3	X
ejpam-4760	209	21	.	.	PUNCT
ejpam-4760	210	1	let	let	VERB
ejpam-4760	210	2	r	r	NOUN
ejpam-4760	210	3	=	=	SYM
ejpam-4760	210	4	n	n	NUM
ejpam-4760	210	5	3	3	NUM
ejpam-4760	210	6	and	and	CCONJ
ejpam-4760	210	7	j	j	PROPN
ejpam-4760	210	8	=	=	SYM
ejpam-4760	210	9	1	1	NUM
ejpam-4760	210	10	,	,	PUNCT
ejpam-4760	210	11	2	2	NUM
ejpam-4760	210	12	,	,	PUNCT
ejpam-4760	210	13	.	.	PUNCT
ejpam-4760	210	14	.	.	PUNCT
ejpam-4760	211	1	.	.	PUNCT
ejpam-4760	212	1	,	,	PUNCT
ejpam-4760	212	2	r	r	NOUN
ejpam-4760	212	3	−	−	PROPN
ejpam-4760	212	4	1	1	NUM
ejpam-4760	212	5	,	,	PUNCT
ejpam-4760	212	6	r.	r.	PROPN
ejpam-4760	212	7	group	group	PROPN
ejpam-4760	212	8	the	the	DET
ejpam-4760	212	9	vertices	vertex	NOUN
ejpam-4760	212	10	of	of	ADP
ejpam-4760	212	11	cn	cn	PROPN
ejpam-4760	212	12	into	into	ADP
ejpam-4760	212	13	r	r	NOUN
ejpam-4760	212	14	disjoint	disjoint	NOUN
ejpam-4760	212	15	subsets	subset	NOUN
ejpam-4760	212	16	tj	tj	PROPN
ejpam-4760	212	17	t1	t1	PROPN
ejpam-4760	212	18	=	=	PUNCT
ejpam-4760	212	19	{	{	PUNCT
ejpam-4760	212	20	u1	u1	NOUN
ejpam-4760	212	21	,	,	PUNCT
ejpam-4760	212	22	u2	u2	NOUN
ejpam-4760	212	23	,	,	PUNCT
ejpam-4760	212	24	u3	u3	NOUN
ejpam-4760	212	25	}	}	PUNCT
ejpam-4760	212	26	t2	t2	NOUN
ejpam-4760	212	27	=	=	SYM
ejpam-4760	212	28	{	{	PUNCT
ejpam-4760	212	29	u4	u4	PROPN
ejpam-4760	212	30	,	,	PUNCT
ejpam-4760	212	31	u5	u5	PROPN
ejpam-4760	212	32	,	,	PUNCT
ejpam-4760	212	33	u6	u6	NOUN
ejpam-4760	212	34	}	}	PUNCT
ejpam-4760	212	35	t3	t3	NOUN
ejpam-4760	212	36	=	=	SYM
ejpam-4760	212	37	{	{	PUNCT
ejpam-4760	212	38	u7	u7	PROPN
ejpam-4760	212	39	,	,	PUNCT
ejpam-4760	212	40	u8	u8	PROPN
ejpam-4760	212	41	,	,	PUNCT
ejpam-4760	212	42	u9	u9	PROPN
ejpam-4760	212	43	}	}	PUNCT
ejpam-4760	212	44	t4	t4	PROPN
ejpam-4760	212	45	=	=	SYM
ejpam-4760	212	46	{	{	PUNCT
ejpam-4760	212	47	u10	u10	PROPN
ejpam-4760	212	48	,	,	PUNCT
ejpam-4760	212	49	u11	u11	PROPN
ejpam-4760	212	50	,	,	PUNCT
ejpam-4760	212	51	u12	u12	PROPN
ejpam-4760	212	52	}	}	PUNCT
ejpam-4760	212	53	...	...	PUNCT
ejpam-4760	213	1	tr−1	tr−1	PROPN
ejpam-4760	213	2	=	=	PUNCT
ejpam-4760	213	3	{	{	PUNCT
ejpam-4760	213	4	un−5	un−5	PROPN
ejpam-4760	213	5	,	,	PUNCT
ejpam-4760	213	6	un−4	un−4	NOUN
ejpam-4760	213	7	,	,	PUNCT
ejpam-4760	213	8	un−3	un−3	ADJ
ejpam-4760	213	9	}	}	PUNCT
ejpam-4760	213	10	tr	tr	VERB
ejpam-4760	213	11	=	=	NOUN
ejpam-4760	213	12	{	{	PUNCT
ejpam-4760	213	13	un−2	un−2	PROPN
ejpam-4760	213	14	,	,	PUNCT
ejpam-4760	213	15	un−1	un−1	PROPN
ejpam-4760	213	16	,	,	PUNCT
ejpam-4760	213	17	un	un	ADJ
ejpam-4760	213	18	}	}	PUNCT
ejpam-4760	213	19	clearly	clearly	ADV
ejpam-4760	213	20	,	,	PUNCT
ejpam-4760	213	21	the	the	DET
ejpam-4760	213	22	set	set	NOUN
ejpam-4760	213	23	s	s	PART
ejpam-4760	213	24	=	=	PUNCT
ejpam-4760	213	25	{	{	PUNCT
ejpam-4760	213	26	u2	u2	PROPN
ejpam-4760	213	27	,	,	PUNCT
ejpam-4760	213	28	u5	u5	PROPN
ejpam-4760	213	29	,	,	PUNCT
ejpam-4760	213	30	u8	u8	PROPN
ejpam-4760	213	31	,	,	PUNCT
ejpam-4760	213	32	u11	u11	PROPN
ejpam-4760	213	33	,	,	PUNCT
ejpam-4760	213	34	.	.	PUNCT
ejpam-4760	213	35	.	.	PUNCT
ejpam-4760	213	36	.	.	PUNCT
ejpam-4760	214	1	,	,	PUNCT
ejpam-4760	214	2	un−4	un−4	NOUN
ejpam-4760	214	3	,	,	PUNCT
ejpam-4760	214	4	un−1	un−1	ADJ
ejpam-4760	214	5	}	}	PUNCT
ejpam-4760	214	6	is	be	AUX
ejpam-4760	214	7	a	a	DET
ejpam-4760	214	8	γ0	γ0	NOUN
ejpam-4760	214	9	-	-	PUNCT
ejpam-4760	214	10	set	set	NOUN
ejpam-4760	214	11	of	of	ADP
ejpam-4760	214	12	cn	cn	PROPN
ejpam-4760	214	13	since	since	SCONJ
ejpam-4760	214	14	n	n	PROPN
ejpam-4760	214	15	[	[	X
ejpam-4760	214	16	s	s	X
ejpam-4760	214	17	]	]	X
ejpam-4760	214	18	=	=	SYM
ejpam-4760	214	19	v	v	X
ejpam-4760	214	20	(	(	PUNCT
ejpam-4760	214	21	cn	cn	PROPN
ejpam-4760	214	22	)	)	PUNCT
ejpam-4760	214	23	,	,	PUNCT
ejpam-4760	214	24	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	214	25	has	have	AUX
ejpam-4760	214	26	isolated	isolate	VERB
ejpam-4760	214	27	vertices	vertex	NOUN
ejpam-4760	214	28	and	and	CCONJ
ejpam-4760	214	29	|s|	|s|	NOUN
ejpam-4760	214	30	=	=	SYM
ejpam-4760	214	31	⌈n3	⌈n3	X
ejpam-4760	214	32	⌉	⌉	X
ejpam-4760	214	33	by	by	ADP
ejpam-4760	214	34	proposition	proposition	NOUN
ejpam-4760	214	35	1	1	NUM
ejpam-4760	214	36	.	.	PUNCT
ejpam-4760	215	1	clearly	clearly	ADV
ejpam-4760	215	2	,	,	PUNCT
ejpam-4760	215	3	all	all	DET
ejpam-4760	215	4	other	other	ADJ
ejpam-4760	215	5	vertices	vertex	NOUN
ejpam-4760	215	6	ui	ui	PROPN
ejpam-4760	215	7	∈	∈	PROPN
ejpam-4760	215	8	v	v	ADP
ejpam-4760	215	9	(	(	PUNCT
ejpam-4760	215	10	cn	cn	PROPN
ejpam-4760	215	11	)	)	PUNCT
ejpam-4760	215	12	\	\	PROPN
ejpam-4760	215	13	s	s	PART
ejpam-4760	215	14	for	for	ADP
ejpam-4760	215	15	all	all	DET
ejpam-4760	215	16	i	i	PRON
ejpam-4760	215	17	=	=	NOUN
ejpam-4760	215	18	1	1	NUM
ejpam-4760	215	19	,	,	PUNCT
ejpam-4760	215	20	3	3	NUM
ejpam-4760	215	21	,	,	PUNCT
ejpam-4760	215	22	4	4	NUM
ejpam-4760	215	23	,	,	PUNCT
ejpam-4760	215	24	6	6	NUM
ejpam-4760	215	25	,	,	PUNCT
ejpam-4760	215	26	.	.	PUNCT
ejpam-4760	215	27	.	.	PUNCT
ejpam-4760	216	1	.	.	PUNCT
ejpam-4760	217	1	,	,	PUNCT
ejpam-4760	217	2	n−	n−	NOUN
ejpam-4760	217	3	5	5	NUM
ejpam-4760	217	4	,	,	PUNCT
ejpam-4760	217	5	n−	n−	NOUN
ejpam-4760	217	6	3	3	NUM
ejpam-4760	217	7	,	,	PUNCT
ejpam-4760	217	8	n−	n−	NOUN
ejpam-4760	217	9	2	2	NUM
ejpam-4760	217	10	,	,	PUNCT
ejpam-4760	217	11	n	n	PRON
ejpam-4760	217	12	are	be	AUX
ejpam-4760	217	13	dominated	dominate	VERB
ejpam-4760	217	14	by	by	ADP
ejpam-4760	217	15	exactly	exactly	ADV
ejpam-4760	217	16	one	one	NUM
ejpam-4760	217	17	vertex	vertex	NOUN
ejpam-4760	217	18	in	in	ADP
ejpam-4760	217	19	s.	s.	PROPN
ejpam-4760	217	20	by	by	ADP
ejpam-4760	217	21	proposition	proposition	NOUN
ejpam-4760	217	22	6	6	NUM
ejpam-4760	217	23	,	,	PUNCT
ejpam-4760	217	24	γp0(cn	γp0(cn	NUM
ejpam-4760	217	25	)	)	PUNCT
ejpam-4760	218	1	=	=	PRON
ejpam-4760	218	2	⌈n3	⌈n3	VERB
ejpam-4760	218	3	⌉.	⌉.	ADJ
ejpam-4760	218	4	c.	c.	PROPN
ejpam-4760	218	5	armada	armada	PROPN
ejpam-4760	218	6	,	,	PUNCT
ejpam-4760	218	7	j.	j.	PROPN
ejpam-4760	218	8	hamja	hamja	PROPN
ejpam-4760	218	9	/	/	SYM
ejpam-4760	218	10	eur	eur	PROPN
ejpam-4760	218	11	.	.	PUNCT
ejpam-4760	219	1	j.	j.	PROPN
ejpam-4760	219	2	pure	pure	PROPN
ejpam-4760	219	3	appl	appl	PROPN
ejpam-4760	219	4	.	.	PROPN
ejpam-4760	219	5	math	math	PROPN
ejpam-4760	219	6	,	,	PUNCT
ejpam-4760	219	7	16	16	NUM
ejpam-4760	219	8	(	(	PUNCT
ejpam-4760	219	9	2	2	NUM
ejpam-4760	219	10	)	)	PUNCT
ejpam-4760	219	11	(	(	PUNCT
ejpam-4760	219	12	2023	2023	NUM
ejpam-4760	219	13	)	)	PUNCT
ejpam-4760	219	14	,	,	PUNCT
ejpam-4760	219	15	1326	1326	NUM
ejpam-4760	219	16	-	-	SYM
ejpam-4760	219	17	1341	1341	NUM
ejpam-4760	219	18	1334	1334	NUM
ejpam-4760	219	19	case	case	NOUN
ejpam-4760	219	20	2	2	NUM
ejpam-4760	219	21	:	:	PUNCT
ejpam-4760	219	22	suppose	suppose	VERB
ejpam-4760	219	23	that	that	SCONJ
ejpam-4760	219	24	n	n	X
ejpam-4760	219	25	≡	≡	PROPN
ejpam-4760	219	26	1	1	NUM
ejpam-4760	219	27	(	(	PUNCT
ejpam-4760	219	28	mod	mod	NOUN
ejpam-4760	219	29	3	3	NUM
ejpam-4760	219	30	)	)	PUNCT
ejpam-4760	219	31	.	.	PUNCT
ejpam-4760	220	1	suppose	suppose	VERB
ejpam-4760	220	2	that	that	SCONJ
ejpam-4760	220	3	n	n	NOUN
ejpam-4760	220	4	=	=	SYM
ejpam-4760	220	5	7	7	X
ejpam-4760	220	6	.	.	PUNCT
ejpam-4760	220	7	by	by	ADP
ejpam-4760	220	8	proposition	proposition	NOUN
ejpam-4760	220	9	1	1	NUM
ejpam-4760	220	10	,	,	PUNCT
ejpam-4760	220	11	γ0(c7	γ0(c7	NOUN
ejpam-4760	220	12	)	)	PUNCT
ejpam-4760	220	13	=	=	SYM
ejpam-4760	221	1	3	3	X
ejpam-4760	221	2	.	.	PUNCT
ejpam-4760	221	3	clearly	clearly	ADV
ejpam-4760	221	4	,	,	PUNCT
ejpam-4760	221	5	s	s	PART
ejpam-4760	221	6	=	=	PUNCT
ejpam-4760	221	7	{	{	PUNCT
ejpam-4760	221	8	u1	u1	NOUN
ejpam-4760	221	9	,	,	PUNCT
ejpam-4760	221	10	u2	u2	PROPN
ejpam-4760	221	11	,	,	PUNCT
ejpam-4760	221	12	u5	u5	PROPN
ejpam-4760	221	13	}	}	PUNCT
ejpam-4760	221	14	is	be	AUX
ejpam-4760	221	15	a	a	DET
ejpam-4760	221	16	γ0	γ0	NOUN
ejpam-4760	221	17	-	-	PUNCT
ejpam-4760	221	18	set	set	NOUN
ejpam-4760	221	19	since	since	SCONJ
ejpam-4760	221	20	n	n	PRON
ejpam-4760	221	21	[	[	X
ejpam-4760	221	22	s	s	X
ejpam-4760	221	23	]	]	X
ejpam-4760	221	24	=	=	SYM
ejpam-4760	221	25	v	v	X
ejpam-4760	221	26	(	(	PUNCT
ejpam-4760	221	27	c7	c7	PROPN
ejpam-4760	221	28	)	)	PUNCT
ejpam-4760	221	29	,	,	PUNCT
ejpam-4760	221	30	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	221	31	has	have	VERB
ejpam-4760	221	32	an	an	DET
ejpam-4760	221	33	isolated	isolated	ADJ
ejpam-4760	221	34	vertex	vertex	NOUN
ejpam-4760	221	35	u5	u5	NOUN
ejpam-4760	221	36	and	and	CCONJ
ejpam-4760	221	37	|s|	|s|	PROPN
ejpam-4760	221	38	=	=	SYM
ejpam-4760	221	39	3	3	X
ejpam-4760	221	40	.	.	PUNCT
ejpam-4760	222	1	also	also	ADV
ejpam-4760	222	2	,	,	PUNCT
ejpam-4760	222	3	u3	u3	PROPN
ejpam-4760	222	4	,	,	PUNCT
ejpam-4760	222	5	u4	u4	PROPN
ejpam-4760	222	6	,	,	PUNCT
ejpam-4760	222	7	u6	u6	PROPN
ejpam-4760	222	8	,	,	PUNCT
ejpam-4760	222	9	u7	u7	PROPN
ejpam-4760	222	10	∈	∈	PROPN
ejpam-4760	222	11	v	v	PROPN
ejpam-4760	222	12	(	(	PUNCT
ejpam-4760	222	13	c7	c7	PROPN
ejpam-4760	222	14	)	)	PUNCT
ejpam-4760	222	15	\	\	PROPN
ejpam-4760	223	1	s	s	PART
ejpam-4760	223	2	are	be	AUX
ejpam-4760	223	3	dominated	dominate	VERB
ejpam-4760	223	4	by	by	ADP
ejpam-4760	223	5	exactly	exactly	ADV
ejpam-4760	223	6	one	one	NUM
ejpam-4760	223	7	vertex	vertex	NOUN
ejpam-4760	223	8	in	in	ADP
ejpam-4760	223	9	s.	s.	PROPN
ejpam-4760	223	10	by	by	ADP
ejpam-4760	223	11	proposition	proposition	NOUN
ejpam-4760	223	12	6	6	NUM
ejpam-4760	223	13	,	,	PUNCT
ejpam-4760	223	14	γp0(c7	γp0(c7	NUM
ejpam-4760	223	15	)	)	PUNCT
ejpam-4760	223	16	=	=	SYM
ejpam-4760	223	17	3	3	NUM
ejpam-4760	223	18	=	=	PUNCT
ejpam-4760	223	19	⌈73⌉.	⌈73⌉.	VERB
ejpam-4760	223	20	suppose	suppose	VERB
ejpam-4760	223	21	that	that	SCONJ
ejpam-4760	223	22	n	n	PROPN
ejpam-4760	223	23	>	>	X
ejpam-4760	223	24	7	7	X
ejpam-4760	223	25	.	.	PUNCT
ejpam-4760	224	1	let	let	VERB
ejpam-4760	224	2	r	r	NOUN
ejpam-4760	224	3	=	=	PUNCT
ejpam-4760	224	4	n+2	n+2	NUM
ejpam-4760	224	5	3	3	NUM
ejpam-4760	224	6	and	and	CCONJ
ejpam-4760	224	7	j	j	PROPN
ejpam-4760	224	8	=	=	SYM
ejpam-4760	224	9	1	1	NUM
ejpam-4760	224	10	,	,	PUNCT
ejpam-4760	224	11	2	2	NUM
ejpam-4760	224	12	,	,	PUNCT
ejpam-4760	224	13	.	.	PUNCT
ejpam-4760	224	14	.	.	PUNCT
ejpam-4760	225	1	.	.	PUNCT
ejpam-4760	226	1	,	,	PUNCT
ejpam-4760	226	2	r	r	NOUN
ejpam-4760	226	3	−	−	PROPN
ejpam-4760	226	4	1	1	NUM
ejpam-4760	226	5	,	,	PUNCT
ejpam-4760	226	6	r.	r.	PROPN
ejpam-4760	226	7	group	group	PROPN
ejpam-4760	226	8	the	the	DET
ejpam-4760	226	9	vertices	vertex	NOUN
ejpam-4760	226	10	of	of	ADP
ejpam-4760	226	11	cn	cn	PROPN
ejpam-4760	226	12	into	into	ADP
ejpam-4760	226	13	r	r	NOUN
ejpam-4760	226	14	disjoint	disjoint	NOUN
ejpam-4760	226	15	subsets	subset	NOUN
ejpam-4760	226	16	tj	tj	PROPN
ejpam-4760	226	17	t1	t1	PROPN
ejpam-4760	226	18	=	=	PUNCT
ejpam-4760	226	19	{	{	PUNCT
ejpam-4760	226	20	u1	u1	NOUN
ejpam-4760	226	21	}	}	PUNCT
ejpam-4760	226	22	t2	t2	NOUN
ejpam-4760	226	23	=	=	SYM
ejpam-4760	226	24	{	{	PUNCT
ejpam-4760	226	25	u2	u2	PROPN
ejpam-4760	226	26	,	,	PUNCT
ejpam-4760	226	27	u3	u3	NOUN
ejpam-4760	226	28	,	,	PUNCT
ejpam-4760	226	29	u4	u4	PROPN
ejpam-4760	226	30	}	}	PUNCT
ejpam-4760	226	31	t3	t3	NOUN
ejpam-4760	226	32	=	=	SYM
ejpam-4760	226	33	{	{	PUNCT
ejpam-4760	226	34	u5	u5	PROPN
ejpam-4760	226	35	,	,	PUNCT
ejpam-4760	226	36	u6	u6	PROPN
ejpam-4760	226	37	,	,	PUNCT
ejpam-4760	226	38	u7	u7	PROPN
ejpam-4760	226	39	}	}	PUNCT
ejpam-4760	226	40	t4	t4	PROPN
ejpam-4760	226	41	=	=	PROPN
ejpam-4760	226	42	{	{	PUNCT
ejpam-4760	226	43	u8	u8	PROPN
ejpam-4760	226	44	,	,	PUNCT
ejpam-4760	226	45	u9	u9	PROPN
ejpam-4760	226	46	,	,	PUNCT
ejpam-4760	226	47	u10	u10	PROPN
ejpam-4760	226	48	}	}	PUNCT
ejpam-4760	226	49	...	...	PUNCT
ejpam-4760	227	1	tr−1	tr−1	PROPN
ejpam-4760	227	2	=	=	PUNCT
ejpam-4760	227	3	{	{	PUNCT
ejpam-4760	227	4	un−5	un−5	PROPN
ejpam-4760	227	5	,	,	PUNCT
ejpam-4760	227	6	un−4	un−4	NOUN
ejpam-4760	227	7	,	,	PUNCT
ejpam-4760	227	8	un−3	un−3	ADJ
ejpam-4760	227	9	}	}	PUNCT
ejpam-4760	227	10	tr	tr	VERB
ejpam-4760	227	11	=	=	NOUN
ejpam-4760	227	12	{	{	PUNCT
ejpam-4760	227	13	un−2	un−2	PROPN
ejpam-4760	227	14	,	,	PUNCT
ejpam-4760	227	15	un−1	un−1	PROPN
ejpam-4760	227	16	,	,	PUNCT
ejpam-4760	227	17	un	un	ADJ
ejpam-4760	227	18	}	}	PUNCT
ejpam-4760	227	19	clearly	clearly	ADV
ejpam-4760	227	20	,	,	PUNCT
ejpam-4760	227	21	the	the	DET
ejpam-4760	227	22	set	set	NOUN
ejpam-4760	227	23	s	s	PART
ejpam-4760	227	24	=	=	NOUN
ejpam-4760	227	25	{	{	PUNCT
ejpam-4760	227	26	u1	u1	NOUN
ejpam-4760	227	27	,	,	PUNCT
ejpam-4760	227	28	u2	u2	PROPN
ejpam-4760	227	29	,	,	PUNCT
ejpam-4760	227	30	u5	u5	PROPN
ejpam-4760	227	31	,	,	PUNCT
ejpam-4760	227	32	u8	u8	PROPN
ejpam-4760	227	33	,	,	PUNCT
ejpam-4760	227	34	.	.	PUNCT
ejpam-4760	227	35	.	.	PUNCT
ejpam-4760	227	36	.	.	PUNCT
ejpam-4760	228	1	,	,	PUNCT
ejpam-4760	228	2	un−5	un−5	PROPN
ejpam-4760	228	3	,	,	PUNCT
ejpam-4760	228	4	un−2	un−2	PROPN
ejpam-4760	228	5	}	}	PUNCT
ejpam-4760	228	6	is	be	AUX
ejpam-4760	228	7	a	a	DET
ejpam-4760	228	8	γ0	γ0	NOUN
ejpam-4760	228	9	-	-	PUNCT
ejpam-4760	228	10	set	set	NOUN
ejpam-4760	228	11	of	of	ADP
ejpam-4760	228	12	cn	cn	PROPN
ejpam-4760	228	13	since	since	SCONJ
ejpam-4760	228	14	n	n	PROPN
ejpam-4760	228	15	[	[	X
ejpam-4760	228	16	s	s	X
ejpam-4760	228	17	]	]	X
ejpam-4760	228	18	=	=	SYM
ejpam-4760	228	19	v	v	X
ejpam-4760	228	20	(	(	PUNCT
ejpam-4760	228	21	cn	cn	PROPN
ejpam-4760	228	22	)	)	PUNCT
ejpam-4760	228	23	,	,	PUNCT
ejpam-4760	228	24	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	228	25	has	have	AUX
ejpam-4760	228	26	isolated	isolate	VERB
ejpam-4760	228	27	vertices	vertex	NOUN
ejpam-4760	228	28	and	and	CCONJ
ejpam-4760	228	29	|s|	|s|	NOUN
ejpam-4760	228	30	=	=	SYM
ejpam-4760	228	31	⌈n3	⌈n3	X
ejpam-4760	228	32	⌉	⌉	X
ejpam-4760	228	33	by	by	ADP
ejpam-4760	228	34	proposition	proposition	NOUN
ejpam-4760	228	35	1	1	NUM
ejpam-4760	228	36	.	.	PUNCT
ejpam-4760	229	1	clearly	clearly	ADV
ejpam-4760	229	2	,	,	PUNCT
ejpam-4760	229	3	all	all	DET
ejpam-4760	229	4	other	other	ADJ
ejpam-4760	229	5	vertices	vertex	NOUN
ejpam-4760	229	6	ui	ui	PROPN
ejpam-4760	229	7	∈	∈	PROPN
ejpam-4760	229	8	v	v	ADP
ejpam-4760	229	9	(	(	PUNCT
ejpam-4760	229	10	cn	cn	PROPN
ejpam-4760	229	11	)	)	PUNCT
ejpam-4760	229	12	\	\	PROPN
ejpam-4760	229	13	s	s	PART
ejpam-4760	229	14	for	for	ADP
ejpam-4760	229	15	all	all	DET
ejpam-4760	229	16	i	i	PRON
ejpam-4760	229	17	=	=	NOUN
ejpam-4760	229	18	3	3	NUM
ejpam-4760	229	19	,	,	PUNCT
ejpam-4760	229	20	4	4	NUM
ejpam-4760	229	21	,	,	PUNCT
ejpam-4760	229	22	6	6	NUM
ejpam-4760	229	23	,	,	PUNCT
ejpam-4760	229	24	7	7	NUM
ejpam-4760	229	25	,	,	PUNCT
ejpam-4760	229	26	.	.	PUNCT
ejpam-4760	229	27	.	.	PUNCT
ejpam-4760	230	1	.	.	PUNCT
ejpam-4760	231	1	,	,	PUNCT
ejpam-4760	231	2	n−	n−	NOUN
ejpam-4760	231	3	4	4	NUM
ejpam-4760	231	4	,	,	PUNCT
ejpam-4760	231	5	n−	n−	NOUN
ejpam-4760	231	6	3	3	NUM
ejpam-4760	231	7	,	,	PUNCT
ejpam-4760	231	8	n−	n−	NOUN
ejpam-4760	231	9	1	1	NUM
ejpam-4760	231	10	,	,	PUNCT
ejpam-4760	231	11	n	n	PRON
ejpam-4760	231	12	are	be	AUX
ejpam-4760	231	13	dominated	dominate	VERB
ejpam-4760	231	14	by	by	ADP
ejpam-4760	231	15	exactly	exactly	ADV
ejpam-4760	231	16	one	one	NUM
ejpam-4760	231	17	vertex	vertex	NOUN
ejpam-4760	231	18	in	in	ADP
ejpam-4760	231	19	s.	s.	PROPN
ejpam-4760	231	20	by	by	ADP
ejpam-4760	231	21	proposition	proposition	NOUN
ejpam-4760	231	22	6	6	NUM
ejpam-4760	231	23	,	,	PUNCT
ejpam-4760	231	24	γp0(cn	γp0(cn	NUM
ejpam-4760	231	25	)	)	PUNCT
ejpam-4760	232	1	=	=	VERB
ejpam-4760	232	2	⌈n3	⌈n3	VERB
ejpam-4760	232	3	⌉.	⌉.	ADV
ejpam-4760	232	4	case	case	NOUN
ejpam-4760	232	5	3	3	X
ejpam-4760	232	6	:	:	PUNCT
ejpam-4760	232	7	suppose	suppose	VERB
ejpam-4760	232	8	that	that	SCONJ
ejpam-4760	232	9	n	n	NUM
ejpam-4760	232	10	≡	≡	PROPN
ejpam-4760	232	11	2	2	NUM
ejpam-4760	232	12	(	(	PUNCT
ejpam-4760	232	13	mod	mod	NOUN
ejpam-4760	232	14	3	3	NUM
ejpam-4760	232	15	)	)	PUNCT
ejpam-4760	232	16	.	.	PUNCT
ejpam-4760	233	1	suppose	suppose	VERB
ejpam-4760	233	2	that	that	SCONJ
ejpam-4760	233	3	n	n	PROPN
ejpam-4760	233	4	=	=	SYM
ejpam-4760	233	5	8	8	NUM
ejpam-4760	233	6	.	.	PUNCT
ejpam-4760	234	1	clearly	clearly	ADV
ejpam-4760	234	2	,	,	PUNCT
ejpam-4760	234	3	s	s	PART
ejpam-4760	234	4	=	=	PUNCT
ejpam-4760	234	5	{	{	PUNCT
ejpam-4760	234	6	u1	u1	NOUN
ejpam-4760	234	7	,	,	PUNCT
ejpam-4760	234	8	u3	u3	NOUN
ejpam-4760	234	9	,	,	PUNCT
ejpam-4760	234	10	u6	u6	PROPN
ejpam-4760	234	11	}	}	PUNCT
ejpam-4760	234	12	is	be	AUX
ejpam-4760	234	13	a	a	DET
ejpam-4760	234	14	γ0	γ0	NOUN
ejpam-4760	234	15	-	-	PUNCT
ejpam-4760	234	16	set	set	NOUN
ejpam-4760	234	17	of	of	ADP
ejpam-4760	234	18	c8	c8	PROPN
ejpam-4760	234	19	since	since	SCONJ
ejpam-4760	234	20	n	n	PROPN
ejpam-4760	234	21	[	[	X
ejpam-4760	234	22	s	s	X
ejpam-4760	234	23	]	]	X
ejpam-4760	234	24	=	=	SYM
ejpam-4760	234	25	v	v	X
ejpam-4760	234	26	(	(	PUNCT
ejpam-4760	234	27	c8	c8	PROPN
ejpam-4760	234	28	)	)	PUNCT
ejpam-4760	234	29	and	and	CCONJ
ejpam-4760	234	30	|s|	|s|	PROPN
ejpam-4760	234	31	=	=	SYM
ejpam-4760	234	32	⌈83⌉	⌈83⌉	PROPN
ejpam-4760	234	33	=	=	SYM
ejpam-4760	234	34	3	3	X
ejpam-4760	234	35	.	.	X
ejpam-4760	234	36	note	note	VERB
ejpam-4760	234	37	that	that	SCONJ
ejpam-4760	234	38	u2	u2	NOUN
ejpam-4760	234	39	is	be	AUX
ejpam-4760	234	40	dominated	dominate	VERB
ejpam-4760	234	41	by	by	ADP
ejpam-4760	234	42	both	both	DET
ejpam-4760	234	43	u1	u1	NOUN
ejpam-4760	234	44	and	and	CCONJ
ejpam-4760	234	45	u3	u3	NOUN
ejpam-4760	234	46	.	.	PUNCT
ejpam-4760	235	1	hence	hence	ADV
ejpam-4760	235	2	,	,	PUNCT
ejpam-4760	235	3	s	s	VERB
ejpam-4760	235	4	is	be	AUX
ejpam-4760	235	5	not	not	PART
ejpam-4760	235	6	a	a	DET
ejpam-4760	235	7	perfect	perfect	ADJ
ejpam-4760	235	8	dominating	dominating	NOUN
ejpam-4760	235	9	set	set	NOUN
ejpam-4760	235	10	.	.	PUNCT
ejpam-4760	236	1	let	let	VERB
ejpam-4760	236	2	t	t	NOUN
ejpam-4760	236	3	=	=	SYM
ejpam-4760	236	4	s	s	PART
ejpam-4760	236	5	∪	∪	X
ejpam-4760	236	6	{	{	PUNCT
ejpam-4760	236	7	u2	u2	PROPN
ejpam-4760	236	8	}	}	PUNCT
ejpam-4760	236	9	=	=	SYM
ejpam-4760	236	10	{	{	PUNCT
ejpam-4760	236	11	u1	u1	NOUN
ejpam-4760	236	12	,	,	PUNCT
ejpam-4760	236	13	u2	u2	NOUN
ejpam-4760	236	14	,	,	PUNCT
ejpam-4760	236	15	u3	u3	NOUN
ejpam-4760	236	16	,	,	PUNCT
ejpam-4760	236	17	u6	u6	NOUN
ejpam-4760	236	18	}	}	PUNCT
ejpam-4760	236	19	.	.	PUNCT
ejpam-4760	237	1	clearly	clearly	ADV
ejpam-4760	237	2	,	,	PUNCT
ejpam-4760	237	3	|t	|t	PROPN
ejpam-4760	237	4	|	|	ADV
ejpam-4760	237	5	=	=	SYM
ejpam-4760	237	6	4	4	NUM
ejpam-4760	237	7	=	=	X
ejpam-4760	238	1	⌈83⌉	⌈83⌉	PROPN
ejpam-4760	238	2	+	+	NUM
ejpam-4760	238	3	1	1	NUM
ejpam-4760	238	4	and	and	CCONJ
ejpam-4760	238	5	u4	u4	PROPN
ejpam-4760	238	6	,	,	PUNCT
ejpam-4760	238	7	u5	u5	PROPN
ejpam-4760	238	8	,	,	PUNCT
ejpam-4760	238	9	u7	u7	PROPN
ejpam-4760	238	10	,	,	PUNCT
ejpam-4760	238	11	u8	u8	PROPN
ejpam-4760	238	12	∈	∈	PROPN
ejpam-4760	238	13	v	v	NOUN
ejpam-4760	238	14	(	(	PUNCT
ejpam-4760	238	15	c8	c8	PROPN
ejpam-4760	238	16	)	)	PUNCT
ejpam-4760	238	17	\	\	PROPN
ejpam-4760	239	1	t	t	PROPN
ejpam-4760	239	2	are	be	AUX
ejpam-4760	239	3	dominated	dominate	VERB
ejpam-4760	239	4	by	by	ADP
ejpam-4760	239	5	exactly	exactly	ADV
ejpam-4760	239	6	one	one	NUM
ejpam-4760	239	7	vertex	vertex	NOUN
ejpam-4760	239	8	in	in	ADP
ejpam-4760	239	9	t	t	PROPN
ejpam-4760	239	10	.	.	PUNCT
ejpam-4760	240	1	clearly	clearly	ADV
ejpam-4760	240	2	,	,	PUNCT
ejpam-4760	240	3	t	t	PROPN
ejpam-4760	240	4	is	be	AUX
ejpam-4760	240	5	a	a	DET
ejpam-4760	240	6	γp0	γp0	NOUN
ejpam-4760	240	7	-	-	PUNCT
ejpam-4760	240	8	set	set	NOUN
ejpam-4760	240	9	in	in	ADP
ejpam-4760	240	10	c8	c8	PROPN
ejpam-4760	240	11	and	and	CCONJ
ejpam-4760	240	12	so	so	ADV
ejpam-4760	240	13	,	,	PUNCT
ejpam-4760	240	14	γp0(c8	γp0(c8	PROPN
ejpam-4760	240	15	)	)	PUNCT
ejpam-4760	240	16	=	=	SYM
ejpam-4760	241	1	4	4	NUM
ejpam-4760	241	2	=	=	X
ejpam-4760	241	3	⌈83⌉	⌈83⌉	PROPN
ejpam-4760	241	4	+	+	NOUN
ejpam-4760	241	5	1	1	X
ejpam-4760	241	6	.	.	PUNCT
ejpam-4760	241	7	suppose	suppose	VERB
ejpam-4760	241	8	that	that	SCONJ
ejpam-4760	241	9	n	n	PROPN
ejpam-4760	241	10	>	>	X
ejpam-4760	241	11	8	8	NUM
ejpam-4760	241	12	.	.	PUNCT
ejpam-4760	242	1	let	let	VERB
ejpam-4760	242	2	r	r	NOUN
ejpam-4760	242	3	=	=	SYM
ejpam-4760	242	4	n+1	n+1	PROPN
ejpam-4760	242	5	3	3	NUM
ejpam-4760	242	6	and	and	CCONJ
ejpam-4760	242	7	j	j	PROPN
ejpam-4760	242	8	=	=	SYM
ejpam-4760	242	9	1	1	NUM
ejpam-4760	242	10	,	,	PUNCT
ejpam-4760	242	11	2	2	NUM
ejpam-4760	242	12	,	,	PUNCT
ejpam-4760	242	13	.	.	PUNCT
ejpam-4760	242	14	.	.	PUNCT
ejpam-4760	243	1	.	.	PUNCT
ejpam-4760	244	1	,	,	PUNCT
ejpam-4760	244	2	r	r	NOUN
ejpam-4760	244	3	−	−	PROPN
ejpam-4760	244	4	1	1	NUM
ejpam-4760	244	5	,	,	PUNCT
ejpam-4760	244	6	r.	r.	PROPN
ejpam-4760	244	7	group	group	PROPN
ejpam-4760	244	8	the	the	DET
ejpam-4760	244	9	vertices	vertex	NOUN
ejpam-4760	244	10	of	of	ADP
ejpam-4760	244	11	cn	cn	PROPN
ejpam-4760	244	12	into	into	ADP
ejpam-4760	244	13	r	r	NOUN
ejpam-4760	244	14	disjoint	disjoint	NOUN
ejpam-4760	244	15	subsets	subset	NOUN
ejpam-4760	244	16	tj	tj	PROPN
ejpam-4760	244	17	t1	t1	PROPN
ejpam-4760	244	18	=	=	PUNCT
ejpam-4760	244	19	{	{	PUNCT
ejpam-4760	244	20	u1	u1	NOUN
ejpam-4760	244	21	,	,	PUNCT
ejpam-4760	244	22	u2	u2	NOUN
ejpam-4760	244	23	}	}	PUNCT
ejpam-4760	244	24	t2	t2	NOUN
ejpam-4760	244	25	=	=	SYM
ejpam-4760	244	26	{	{	PUNCT
ejpam-4760	244	27	u3	u3	PROPN
ejpam-4760	244	28	,	,	PUNCT
ejpam-4760	244	29	u4	u4	PROPN
ejpam-4760	244	30	,	,	PUNCT
ejpam-4760	244	31	u5	u5	PROPN
ejpam-4760	244	32	}	}	PUNCT
ejpam-4760	244	33	t3	t3	NOUN
ejpam-4760	244	34	=	=	SYM
ejpam-4760	244	35	{	{	PUNCT
ejpam-4760	244	36	u6	u6	PROPN
ejpam-4760	244	37	,	,	PUNCT
ejpam-4760	244	38	u7	u7	PROPN
ejpam-4760	244	39	,	,	PUNCT
ejpam-4760	244	40	u8	u8	PROPN
ejpam-4760	244	41	}	}	PUNCT
ejpam-4760	244	42	t4	t4	PROPN
ejpam-4760	244	43	=	=	PROPN
ejpam-4760	244	44	{	{	PUNCT
ejpam-4760	244	45	u9	u9	PROPN
ejpam-4760	244	46	,	,	PUNCT
ejpam-4760	244	47	u10	u10	PROPN
ejpam-4760	244	48	,	,	PUNCT
ejpam-4760	244	49	u11	u11	PROPN
ejpam-4760	244	50	}	}	PUNCT
ejpam-4760	244	51	...	...	PUNCT
ejpam-4760	245	1	tr−1	tr−1	PROPN
ejpam-4760	245	2	=	=	PUNCT
ejpam-4760	245	3	{	{	PUNCT
ejpam-4760	245	4	un−5	un−5	PROPN
ejpam-4760	245	5	,	,	PUNCT
ejpam-4760	245	6	un−4	un−4	NOUN
ejpam-4760	245	7	,	,	PUNCT
ejpam-4760	245	8	un−3	un−3	ADJ
ejpam-4760	245	9	}	}	PUNCT
ejpam-4760	245	10	tr	tr	VERB
ejpam-4760	245	11	=	=	NOUN
ejpam-4760	245	12	{	{	PUNCT
ejpam-4760	245	13	un−2	un−2	PROPN
ejpam-4760	245	14	,	,	PUNCT
ejpam-4760	245	15	un−1	un−1	PROPN
ejpam-4760	245	16	,	,	PUNCT
ejpam-4760	245	17	un	un	ADJ
ejpam-4760	245	18	}	}	PUNCT
ejpam-4760	245	19	clearly	clearly	ADV
ejpam-4760	245	20	,	,	PUNCT
ejpam-4760	245	21	the	the	DET
ejpam-4760	245	22	set	set	NOUN
ejpam-4760	245	23	s	s	PART
ejpam-4760	245	24	=	=	NOUN
ejpam-4760	245	25	{	{	PUNCT
ejpam-4760	245	26	u1	u1	NOUN
ejpam-4760	245	27	,	,	PUNCT
ejpam-4760	245	28	u3	u3	NOUN
ejpam-4760	245	29	,	,	PUNCT
ejpam-4760	245	30	u6	u6	NOUN
ejpam-4760	245	31	,	,	PUNCT
ejpam-4760	245	32	u9	u9	PROPN
ejpam-4760	245	33	,	,	PUNCT
ejpam-4760	245	34	u12	u12	PROPN
ejpam-4760	245	35	,	,	PUNCT
ejpam-4760	245	36	.	.	PUNCT
ejpam-4760	245	37	.	.	PUNCT
ejpam-4760	245	38	.	.	PUNCT
ejpam-4760	246	1	,	,	PUNCT
ejpam-4760	246	2	un−5	un−5	PROPN
ejpam-4760	246	3	,	,	PUNCT
ejpam-4760	246	4	un−2	un−2	PROPN
ejpam-4760	246	5	}	}	PUNCT
ejpam-4760	246	6	is	be	AUX
ejpam-4760	246	7	a	a	DET
ejpam-4760	246	8	γ0	γ0	NOUN
ejpam-4760	246	9	-	-	PUNCT
ejpam-4760	246	10	set	set	NOUN
ejpam-4760	246	11	of	of	ADP
ejpam-4760	246	12	cn	cn	PROPN
ejpam-4760	246	13	since	since	SCONJ
ejpam-4760	246	14	n	n	PROPN
ejpam-4760	246	15	[	[	X
ejpam-4760	246	16	s	s	X
ejpam-4760	246	17	]	]	X
ejpam-4760	246	18	=	=	SYM
ejpam-4760	246	19	v	v	NOUN
ejpam-4760	246	20	(	(	PUNCT
ejpam-4760	246	21	g	g	NOUN
ejpam-4760	246	22	)	)	PUNCT
ejpam-4760	246	23	,	,	PUNCT
ejpam-4760	246	24	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	246	25	has	have	AUX
ejpam-4760	246	26	isolated	isolate	VERB
ejpam-4760	246	27	vertices	vertex	NOUN
ejpam-4760	246	28	and	and	CCONJ
ejpam-4760	246	29	|s|	|s|	NOUN
ejpam-4760	246	30	=	=	SYM
ejpam-4760	246	31	⌈n3	⌈n3	X
ejpam-4760	246	32	⌉	⌉	X
ejpam-4760	246	33	by	by	ADP
ejpam-4760	246	34	proposition	proposition	NOUN
ejpam-4760	246	35	1	1	NUM
ejpam-4760	246	36	.	.	PUNCT
ejpam-4760	247	1	clearly	clearly	ADV
ejpam-4760	247	2	,	,	PUNCT
ejpam-4760	247	3	u2	u2	PROPN
ejpam-4760	247	4	is	be	AUX
ejpam-4760	247	5	dominated	dominate	VERB
ejpam-4760	247	6	by	by	ADP
ejpam-4760	247	7	both	both	DET
ejpam-4760	247	8	u1	u1	NOUN
ejpam-4760	247	9	and	and	CCONJ
ejpam-4760	247	10	u3	u3	NOUN
ejpam-4760	247	11	.	.	PUNCT
ejpam-4760	248	1	hence	hence	ADV
ejpam-4760	248	2	,	,	PUNCT
ejpam-4760	248	3	s	s	VERB
ejpam-4760	248	4	is	be	AUX
ejpam-4760	248	5	not	not	PART
ejpam-4760	248	6	a	a	DET
ejpam-4760	248	7	perfect	perfect	ADJ
ejpam-4760	248	8	dominating	dominating	NOUN
ejpam-4760	248	9	set	set	NOUN
ejpam-4760	248	10	.	.	PUNCT
ejpam-4760	249	1	let	let	VERB
ejpam-4760	249	2	t	t	NOUN
ejpam-4760	249	3	=	=	SYM
ejpam-4760	249	4	s	s	PART
ejpam-4760	249	5	∪	∪	X
ejpam-4760	249	6	{	{	PUNCT
ejpam-4760	249	7	u2	u2	PROPN
ejpam-4760	249	8	}	}	PUNCT
ejpam-4760	249	9	=	=	SYM
ejpam-4760	249	10	{	{	PUNCT
ejpam-4760	249	11	u1	u1	NOUN
ejpam-4760	249	12	,	,	PUNCT
ejpam-4760	249	13	u2	u2	NOUN
ejpam-4760	249	14	,	,	PUNCT
ejpam-4760	249	15	u3	u3	NOUN
ejpam-4760	249	16	,	,	PUNCT
ejpam-4760	249	17	u6	u6	NOUN
ejpam-4760	249	18	,	,	PUNCT
ejpam-4760	249	19	.	.	PUNCT
ejpam-4760	249	20	.	.	PUNCT
ejpam-4760	250	1	.	.	PUNCT
ejpam-4760	251	1	,	,	PUNCT
ejpam-4760	252	1	un−5	un−5	PROPN
ejpam-4760	252	2	,	,	PUNCT
ejpam-4760	252	3	un−2	un−2	PROPN
ejpam-4760	252	4	}	}	PUNCT
ejpam-4760	252	5	.	.	PUNCT
ejpam-4760	253	1	clearly	clearly	ADV
ejpam-4760	253	2	,	,	PUNCT
ejpam-4760	253	3	|t	|t	VERB
ejpam-4760	253	4	|	|	ADV
ejpam-4760	253	5	=	=	SYM
ejpam-4760	254	1	⌈83⌉	⌈83⌉	PROPN
ejpam-4760	255	1	+	+	NUM
ejpam-4760	255	2	1	1	NUM
ejpam-4760	255	3	and	and	CCONJ
ejpam-4760	255	4	all	all	DET
ejpam-4760	255	5	other	other	ADJ
ejpam-4760	255	6	vertices	vertex	NOUN
ejpam-4760	255	7	ui	ui	PROPN
ejpam-4760	255	8	∈	∈	PROPN
ejpam-4760	255	9	v	v	ADP
ejpam-4760	255	10	(	(	PUNCT
ejpam-4760	255	11	cn	cn	PROPN
ejpam-4760	255	12	)	)	PUNCT
ejpam-4760	255	13	\	\	PROPN
ejpam-4760	255	14	t	t	PROPN
ejpam-4760	255	15	for	for	ADP
ejpam-4760	255	16	all	all	DET
ejpam-4760	255	17	i	i	NOUN
ejpam-4760	255	18	=	=	NOUN
ejpam-4760	255	19	4	4	NUM
ejpam-4760	255	20	,	,	PUNCT
ejpam-4760	255	21	5	5	NUM
ejpam-4760	255	22	,	,	PUNCT
ejpam-4760	255	23	7	7	NUM
ejpam-4760	255	24	,	,	PUNCT
ejpam-4760	255	25	8	8	NUM
ejpam-4760	255	26	,	,	PUNCT
ejpam-4760	255	27	.	.	PUNCT
ejpam-4760	255	28	.	.	PUNCT
ejpam-4760	255	29	.	.	PUNCT
ejpam-4760	255	30	,	,	PUNCT
ejpam-4760	256	1	n	n	CCONJ
ejpam-4760	256	2	−	−	PROPN
ejpam-4760	256	3	4	4	NUM
ejpam-4760	256	4	,	,	PUNCT
ejpam-4760	256	5	n	n	CCONJ
ejpam-4760	256	6	−	−	PROPN
ejpam-4760	256	7	3	3	NUM
ejpam-4760	256	8	,	,	PUNCT
ejpam-4760	256	9	n	n	CCONJ
ejpam-4760	256	10	−	−	PROPN
ejpam-4760	256	11	1	1	NUM
ejpam-4760	256	12	,	,	PUNCT
ejpam-4760	256	13	n	n	PRON
ejpam-4760	256	14	are	be	AUX
ejpam-4760	256	15	dominated	dominate	VERB
ejpam-4760	256	16	by	by	ADP
ejpam-4760	256	17	exactly	exactly	ADV
ejpam-4760	256	18	one	one	NUM
ejpam-4760	256	19	vertex	vertex	NOUN
ejpam-4760	256	20	in	in	ADP
ejpam-4760	256	21	t	t	PROPN
ejpam-4760	256	22	.	.	PUNCT
ejpam-4760	257	1	clearly	clearly	ADV
ejpam-4760	257	2	,	,	PUNCT
ejpam-4760	257	3	t	t	PROPN
ejpam-4760	257	4	is	be	AUX
ejpam-4760	257	5	a	a	DET
ejpam-4760	257	6	γp0	γp0	NOUN
ejpam-4760	257	7	-	-	PUNCT
ejpam-4760	257	8	set	set	NOUN
ejpam-4760	257	9	in	in	ADP
ejpam-4760	257	10	cn	cn	PROPN
ejpam-4760	257	11	and	and	CCONJ
ejpam-4760	257	12	so	so	ADV
ejpam-4760	257	13	,	,	PUNCT
ejpam-4760	257	14	γp0(cn	γp0(cn	PROPN
ejpam-4760	257	15	)	)	PUNCT
ejpam-4760	258	1	=	=	AUX
ejpam-4760	258	2	⌈n3	⌈n3	X
ejpam-4760	258	3	⌉+	⌉+	NUM
ejpam-4760	259	1	1	1	X
ejpam-4760	259	2	.	.	PUNCT
ejpam-4760	259	3	c.	c.	PROPN
ejpam-4760	259	4	armada	armada	PROPN
ejpam-4760	259	5	,	,	PUNCT
ejpam-4760	259	6	j.	j.	PROPN
ejpam-4760	259	7	hamja	hamja	PROPN
ejpam-4760	259	8	/	/	SYM
ejpam-4760	259	9	eur	eur	PROPN
ejpam-4760	259	10	.	.	PUNCT
ejpam-4760	260	1	j.	j.	PROPN
ejpam-4760	260	2	pure	pure	PROPN
ejpam-4760	260	3	appl	appl	PROPN
ejpam-4760	260	4	.	.	PROPN
ejpam-4760	260	5	math	math	PROPN
ejpam-4760	260	6	,	,	PUNCT
ejpam-4760	260	7	16	16	NUM
ejpam-4760	260	8	(	(	PUNCT
ejpam-4760	260	9	2	2	NUM
ejpam-4760	260	10	)	)	PUNCT
ejpam-4760	260	11	(	(	PUNCT
ejpam-4760	260	12	2023	2023	NUM
ejpam-4760	260	13	)	)	PUNCT
ejpam-4760	260	14	,	,	PUNCT
ejpam-4760	260	15	1326	1326	NUM
ejpam-4760	260	16	-	-	SYM
ejpam-4760	260	17	1341	1341	NUM
ejpam-4760	260	18	1335	1335	NUM
ejpam-4760	260	19	by	by	ADP
ejpam-4760	260	20	proposition	proposition	NOUN
ejpam-4760	260	21	1	1	NUM
ejpam-4760	260	22	and	and	CCONJ
ejpam-4760	260	23	theorem	theorem	VERB
ejpam-4760	260	24	6	6	NUM
ejpam-4760	260	25	,	,	PUNCT
ejpam-4760	260	26	γ0(cn	γ0(cn	PROPN
ejpam-4760	260	27	)	)	PUNCT
ejpam-4760	260	28	≤	≤	NUM
ejpam-4760	260	29	γp0(cn	γp0(cn	NOUN
ejpam-4760	260	30	)	)	PUNCT
ejpam-4760	260	31	for	for	ADP
ejpam-4760	260	32	n	n	NOUN
ejpam-4760	260	33	=	=	SYM
ejpam-4760	260	34	3	3	NUM
ejpam-4760	260	35	or	or	CCONJ
ejpam-4760	260	36	n	n	PRON
ejpam-4760	260	37	≥	≥	NOUN
ejpam-4760	260	38	6	6	NUM
ejpam-4760	260	39	.	.	PUNCT
ejpam-4760	260	40	theorem	theorem	VERB
ejpam-4760	260	41	7	7	NUM
ejpam-4760	260	42	.	.	PUNCT
ejpam-4760	261	1	the	the	DET
ejpam-4760	261	2	cycle	cycle	NOUN
ejpam-4760	261	3	graphs	graph	NOUN
ejpam-4760	261	4	c4	c4	NOUN
ejpam-4760	261	5	and	and	CCONJ
ejpam-4760	261	6	c5	c5	PROPN
ejpam-4760	261	7	are	be	AUX
ejpam-4760	261	8	non	non	ADJ
ejpam-4760	261	9	-	-	ADJ
ejpam-4760	261	10	γp0	γp0	NOUN
ejpam-4760	261	11	-	-	PUNCT
ejpam-4760	261	12	graphs	graph	NOUN
ejpam-4760	261	13	.	.	PUNCT
ejpam-4760	262	1	proof	proof	NOUN
ejpam-4760	262	2	.	.	PUNCT
ejpam-4760	263	1	let	let	VERB
ejpam-4760	263	2	v	v	X
ejpam-4760	263	3	(	(	PUNCT
ejpam-4760	263	4	c4	c4	NOUN
ejpam-4760	263	5	)	)	PUNCT
ejpam-4760	263	6	=	=	SYM
ejpam-4760	263	7	{	{	PUNCT
ejpam-4760	263	8	u1	u1	NOUN
ejpam-4760	263	9	,	,	PUNCT
ejpam-4760	263	10	u2	u2	NOUN
ejpam-4760	263	11	,	,	PUNCT
ejpam-4760	263	12	u3	u3	NOUN
ejpam-4760	263	13	,	,	PUNCT
ejpam-4760	263	14	u4	u4	PROPN
ejpam-4760	263	15	}	}	PUNCT
ejpam-4760	263	16	and	and	CCONJ
ejpam-4760	263	17	v	v	NOUN
ejpam-4760	263	18	(	(	PUNCT
ejpam-4760	263	19	c5	c5	PROPN
ejpam-4760	263	20	)	)	PUNCT
ejpam-4760	263	21	=	=	PRON
ejpam-4760	263	22	{	{	PUNCT
ejpam-4760	263	23	u1	u1	NOUN
ejpam-4760	263	24	,	,	PUNCT
ejpam-4760	263	25	u2	u2	NOUN
ejpam-4760	263	26	,	,	PUNCT
ejpam-4760	263	27	u3	u3	PROPN
ejpam-4760	263	28	,	,	PUNCT
ejpam-4760	263	29	u4	u4	PROPN
ejpam-4760	263	30	,	,	PUNCT
ejpam-4760	263	31	u5	u5	PROPN
ejpam-4760	263	32	}	}	PUNCT
ejpam-4760	263	33	.	.	PUNCT
ejpam-4760	264	1	for	for	ADP
ejpam-4760	264	2	the	the	DET
ejpam-4760	264	3	graph	graph	NOUN
ejpam-4760	264	4	c4	c4	NOUN
ejpam-4760	264	5	,	,	PUNCT
ejpam-4760	264	6	clearly	clearly	ADV
ejpam-4760	264	7	,	,	PUNCT
ejpam-4760	264	8	the	the	DET
ejpam-4760	264	9	sets	set	NOUN
ejpam-4760	264	10	s1	s1	NOUN
ejpam-4760	264	11	=	=	SYM
ejpam-4760	264	12	{	{	PUNCT
ejpam-4760	264	13	u1	u1	NOUN
ejpam-4760	264	14	,	,	PUNCT
ejpam-4760	264	15	u2	u2	PROPN
ejpam-4760	264	16	}	}	PUNCT
ejpam-4760	264	17	,	,	PUNCT
ejpam-4760	264	18	s2	s2	X
ejpam-4760	264	19	=	=	SYM
ejpam-4760	264	20	{	{	PUNCT
ejpam-4760	264	21	u2	u2	NOUN
ejpam-4760	264	22	,	,	PUNCT
ejpam-4760	264	23	u3	u3	NOUN
ejpam-4760	264	24	}	}	PUNCT
ejpam-4760	264	25	,	,	PUNCT
ejpam-4760	264	26	s3	s3	PROPN
ejpam-4760	264	27	=	=	SYM
ejpam-4760	264	28	{	{	PUNCT
ejpam-4760	264	29	u3	u3	PROPN
ejpam-4760	264	30	,	,	PUNCT
ejpam-4760	264	31	u4	u4	PROPN
ejpam-4760	264	32	}	}	PUNCT
ejpam-4760	264	33	,	,	PUNCT
ejpam-4760	264	34	and	and	CCONJ
ejpam-4760	264	35	s4	s4	PROPN
ejpam-4760	264	36	=	=	SYM
ejpam-4760	264	37	{	{	PUNCT
ejpam-4760	264	38	u1	u1	PROPN
ejpam-4760	264	39	,	,	PUNCT
ejpam-4760	264	40	u4	u4	PROPN
ejpam-4760	264	41	}	}	PUNCT
ejpam-4760	264	42	are	be	AUX
ejpam-4760	264	43	perfect	perfect	ADJ
ejpam-4760	264	44	dominating	dominating	NOUN
ejpam-4760	264	45	sets	set	NOUN
ejpam-4760	264	46	(	(	PUNCT
ejpam-4760	264	47	γp	γp	NOUN
ejpam-4760	264	48	-	-	PUNCT
ejpam-4760	264	49	sets	set	NOUN
ejpam-4760	264	50	)	)	PUNCT
ejpam-4760	264	51	of	of	ADP
ejpam-4760	264	52	c4	c4	NOUN
ejpam-4760	264	53	but	but	CCONJ
ejpam-4760	264	54	none	none	NOUN
ejpam-4760	264	55	of	of	ADP
ejpam-4760	264	56	them	they	PRON
ejpam-4760	264	57	are	be	AUX
ejpam-4760	264	58	isolate	isolate	VERB
ejpam-4760	264	59	dominating	dominating	NOUN
ejpam-4760	264	60	sets	set	NOUN
ejpam-4760	264	61	since	since	SCONJ
ejpam-4760	264	62	⟨si⟩	⟨si⟩	NOUN
ejpam-4760	264	63	has	have	VERB
ejpam-4760	264	64	no	no	DET
ejpam-4760	264	65	isolated	isolated	ADJ
ejpam-4760	264	66	vertex	vertex	NOUN
ejpam-4760	264	67	for	for	ADP
ejpam-4760	264	68	all	all	DET
ejpam-4760	264	69	i	i	PRON
ejpam-4760	264	70	=	=	NOUN
ejpam-4760	264	71	1	1	NUM
ejpam-4760	264	72	,	,	PUNCT
ejpam-4760	264	73	2	2	NUM
ejpam-4760	264	74	,	,	PUNCT
ejpam-4760	264	75	3	3	NUM
ejpam-4760	264	76	,	,	PUNCT
ejpam-4760	264	77	4	4	NUM
ejpam-4760	264	78	.	.	PUNCT
ejpam-4760	265	1	also	also	ADV
ejpam-4760	265	2	,	,	PUNCT
ejpam-4760	265	3	the	the	DET
ejpam-4760	265	4	sets	set	NOUN
ejpam-4760	265	5	t1	t1	NOUN
ejpam-4760	265	6	=	=	PUNCT
ejpam-4760	265	7	{	{	PUNCT
ejpam-4760	265	8	u1	u1	NOUN
ejpam-4760	265	9	,	,	PUNCT
ejpam-4760	265	10	u3	u3	NOUN
ejpam-4760	265	11	}	}	PUNCT
ejpam-4760	265	12	and	and	CCONJ
ejpam-4760	265	13	t2	t2	PROPN
ejpam-4760	265	14	=	=	SYM
ejpam-4760	265	15	{	{	PUNCT
ejpam-4760	265	16	u2	u2	PROPN
ejpam-4760	265	17	,	,	PUNCT
ejpam-4760	265	18	u4	u4	PROPN
ejpam-4760	265	19	}	}	PUNCT
ejpam-4760	265	20	are	be	AUX
ejpam-4760	265	21	isolate	isolate	ADJ
ejpam-4760	265	22	dominating	dominating	NOUN
ejpam-4760	265	23	sets	set	NOUN
ejpam-4760	265	24	(	(	PUNCT
ejpam-4760	265	25	γ0	γ0	NOUN
ejpam-4760	265	26	-	-	PUNCT
ejpam-4760	265	27	sets	set	NOUN
ejpam-4760	265	28	)	)	PUNCT
ejpam-4760	265	29	of	of	ADP
ejpam-4760	265	30	c4	c4	NOUN
ejpam-4760	265	31	by	by	ADP
ejpam-4760	265	32	proposition	proposition	NOUN
ejpam-4760	265	33	1	1	NUM
ejpam-4760	265	34	but	but	CCONJ
ejpam-4760	265	35	none	none	NOUN
ejpam-4760	265	36	of	of	ADP
ejpam-4760	265	37	them	they	PRON
ejpam-4760	265	38	are	be	AUX
ejpam-4760	265	39	perfect	perfect	ADJ
ejpam-4760	265	40	dominating	dominating	NOUN
ejpam-4760	265	41	sets	set	NOUN
ejpam-4760	265	42	since	since	SCONJ
ejpam-4760	265	43	all	all	DET
ejpam-4760	265	44	vertices	vertex	NOUN
ejpam-4760	265	45	in	in	ADP
ejpam-4760	265	46	v	v	NOUN
ejpam-4760	265	47	(	(	PUNCT
ejpam-4760	265	48	c4	c4	NOUN
ejpam-4760	265	49	)	)	PUNCT
ejpam-4760	265	50	\tj	\tj	PROPN
ejpam-4760	265	51	are	be	AUX
ejpam-4760	265	52	dominated	dominate	VERB
ejpam-4760	265	53	by	by	ADP
ejpam-4760	265	54	two	two	NUM
ejpam-4760	265	55	vertices	vertex	NOUN
ejpam-4760	265	56	in	in	ADP
ejpam-4760	265	57	tj	tj	NOUN
ejpam-4760	265	58	for	for	ADP
ejpam-4760	265	59	all	all	DET
ejpam-4760	265	60	j	j	NOUN
ejpam-4760	265	61	=	=	SYM
ejpam-4760	265	62	1	1	NUM
ejpam-4760	265	63	,	,	PUNCT
ejpam-4760	265	64	2	2	NUM
ejpam-4760	265	65	.	.	PUNCT
ejpam-4760	265	66	choosing	choose	VERB
ejpam-4760	265	67	3	3	NUM
ejpam-4760	265	68	vertices	vertex	NOUN
ejpam-4760	265	69	or	or	CCONJ
ejpam-4760	265	70	4	4	NUM
ejpam-4760	265	71	vertices	vertex	NOUN
ejpam-4760	265	72	in	in	ADP
ejpam-4760	265	73	c4	c4	NOUN
ejpam-4760	265	74	for	for	ADP
ejpam-4760	265	75	γp0	γp0	NOUN
ejpam-4760	265	76	-	-	PUNCT
ejpam-4760	265	77	sets	set	NOUN
ejpam-4760	265	78	is	be	AUX
ejpam-4760	265	79	not	not	PART
ejpam-4760	265	80	possible	possible	ADJ
ejpam-4760	265	81	since	since	SCONJ
ejpam-4760	265	82	their	their	PRON
ejpam-4760	265	83	induced	induced	ADJ
ejpam-4760	265	84	subgraphs	subgraphs	NOUN
ejpam-4760	265	85	has	have	VERB
ejpam-4760	265	86	no	no	DET
ejpam-4760	265	87	isolated	isolated	ADJ
ejpam-4760	265	88	vertex	vertex	NOUN
ejpam-4760	265	89	.	.	PUNCT
ejpam-4760	266	1	thus	thus	ADV
ejpam-4760	266	2	,	,	PUNCT
ejpam-4760	266	3	in	in	ADP
ejpam-4760	266	4	any	any	DET
ejpam-4760	266	5	case	case	NOUN
ejpam-4760	266	6	,	,	PUNCT
ejpam-4760	266	7	c4	c4	NOUN
ejpam-4760	266	8	contains	contain	VERB
ejpam-4760	266	9	a	a	DET
ejpam-4760	266	10	perfect	perfect	ADJ
ejpam-4760	266	11	dominating	dominating	NOUN
ejpam-4760	266	12	set	set	NOUN
ejpam-4760	266	13	or	or	CCONJ
ejpam-4760	266	14	an	an	DET
ejpam-4760	266	15	isolate	isolate	NOUN
ejpam-4760	266	16	dominating	dominating	NOUN
ejpam-4760	266	17	set	set	NOUN
ejpam-4760	266	18	but	but	CCONJ
ejpam-4760	266	19	not	not	PART
ejpam-4760	266	20	both	both	PRON
ejpam-4760	266	21	.	.	PUNCT
ejpam-4760	267	1	therefore	therefore	ADV
ejpam-4760	267	2	,	,	PUNCT
ejpam-4760	267	3	c4	c4	NOUN
ejpam-4760	267	4	is	be	AUX
ejpam-4760	267	5	a	a	DET
ejpam-4760	267	6	non	non	ADJ
ejpam-4760	267	7	-	-	ADJ
ejpam-4760	267	8	γp0	γp0	NOUN
ejpam-4760	267	9	-	-	PUNCT
ejpam-4760	267	10	graph	graph	NOUN
ejpam-4760	267	11	.	.	PUNCT
ejpam-4760	268	1	for	for	ADP
ejpam-4760	268	2	the	the	DET
ejpam-4760	268	3	graph	graph	NOUN
ejpam-4760	268	4	c5	c5	PROPN
ejpam-4760	268	5	,	,	PUNCT
ejpam-4760	268	6	clearly	clearly	ADV
ejpam-4760	268	7	,	,	PUNCT
ejpam-4760	268	8	the	the	DET
ejpam-4760	268	9	sets	set	NOUN
ejpam-4760	268	10	s1	s1	NOUN
ejpam-4760	268	11	=	=	SYM
ejpam-4760	268	12	{	{	PUNCT
ejpam-4760	268	13	u1	u1	NOUN
ejpam-4760	268	14	,	,	PUNCT
ejpam-4760	268	15	u2	u2	NOUN
ejpam-4760	268	16	,	,	PUNCT
ejpam-4760	268	17	u3	u3	NOUN
ejpam-4760	268	18	}	}	PUNCT
ejpam-4760	268	19	,	,	PUNCT
ejpam-4760	268	20	s2	s2	X
ejpam-4760	268	21	=	=	SYM
ejpam-4760	268	22	{	{	PUNCT
ejpam-4760	268	23	u2	u2	PROPN
ejpam-4760	268	24	,	,	PUNCT
ejpam-4760	268	25	u3	u3	NOUN
ejpam-4760	268	26	,	,	PUNCT
ejpam-4760	268	27	u4	u4	PROPN
ejpam-4760	268	28	}	}	PUNCT
ejpam-4760	268	29	,	,	PUNCT
ejpam-4760	268	30	s3	s3	PROPN
ejpam-4760	268	31	=	=	SYM
ejpam-4760	268	32	{	{	PUNCT
ejpam-4760	268	33	u3	u3	PROPN
ejpam-4760	268	34	,	,	PUNCT
ejpam-4760	268	35	u4	u4	PROPN
ejpam-4760	268	36	,	,	PUNCT
ejpam-4760	268	37	u5	u5	PROPN
ejpam-4760	268	38	}	}	PUNCT
ejpam-4760	268	39	,	,	PUNCT
ejpam-4760	268	40	s4	s4	PROPN
ejpam-4760	268	41	=	=	SYM
ejpam-4760	268	42	{	{	PUNCT
ejpam-4760	268	43	u4	u4	PROPN
ejpam-4760	268	44	,	,	PUNCT
ejpam-4760	268	45	u5	u5	PROPN
ejpam-4760	268	46	,	,	PUNCT
ejpam-4760	268	47	u1	u1	NOUN
ejpam-4760	268	48	}	}	PUNCT
ejpam-4760	268	49	,	,	PUNCT
ejpam-4760	268	50	and	and	CCONJ
ejpam-4760	268	51	s5	s5	PROPN
ejpam-4760	268	52	=	=	PUNCT
ejpam-4760	268	53	{	{	PUNCT
ejpam-4760	268	54	u5	u5	PROPN
ejpam-4760	268	55	,	,	PUNCT
ejpam-4760	268	56	u1	u1	NOUN
ejpam-4760	268	57	,	,	PUNCT
ejpam-4760	268	58	u2	u2	PROPN
ejpam-4760	268	59	}	}	PUNCT
ejpam-4760	268	60	are	be	AUX
ejpam-4760	268	61	perfect	perfect	ADJ
ejpam-4760	268	62	dominating	dominating	NOUN
ejpam-4760	268	63	sets	set	NOUN
ejpam-4760	268	64	(	(	PUNCT
ejpam-4760	268	65	γp	γp	NOUN
ejpam-4760	268	66	-	-	PUNCT
ejpam-4760	268	67	sets	set	NOUN
ejpam-4760	268	68	)	)	PUNCT
ejpam-4760	268	69	of	of	ADP
ejpam-4760	268	70	c5	c5	PROPN
ejpam-4760	268	71	but	but	CCONJ
ejpam-4760	268	72	none	none	NOUN
ejpam-4760	268	73	of	of	ADP
ejpam-4760	268	74	them	they	PRON
ejpam-4760	268	75	are	be	AUX
ejpam-4760	268	76	isolate	isolate	VERB
ejpam-4760	268	77	dominating	dominating	NOUN
ejpam-4760	268	78	sets	set	NOUN
ejpam-4760	268	79	since	since	SCONJ
ejpam-4760	268	80	⟨si⟩	⟨si⟩	NOUN
ejpam-4760	268	81	has	have	VERB
ejpam-4760	268	82	no	no	DET
ejpam-4760	268	83	isolated	isolated	ADJ
ejpam-4760	268	84	vertex	vertex	NOUN
ejpam-4760	268	85	for	for	ADP
ejpam-4760	268	86	all	all	DET
ejpam-4760	268	87	i	i	PRON
ejpam-4760	268	88	=	=	NOUN
ejpam-4760	268	89	1	1	NUM
ejpam-4760	268	90	,	,	PUNCT
ejpam-4760	268	91	2	2	NUM
ejpam-4760	268	92	,	,	PUNCT
ejpam-4760	268	93	3	3	NUM
ejpam-4760	268	94	,	,	PUNCT
ejpam-4760	268	95	4	4	NUM
ejpam-4760	268	96	,	,	PUNCT
ejpam-4760	268	97	5	5	NUM
ejpam-4760	268	98	.	.	PUNCT
ejpam-4760	269	1	also	also	ADV
ejpam-4760	269	2	,	,	PUNCT
ejpam-4760	269	3	the	the	DET
ejpam-4760	269	4	sets	set	NOUN
ejpam-4760	269	5	t1	t1	NOUN
ejpam-4760	269	6	=	=	PUNCT
ejpam-4760	269	7	{	{	PUNCT
ejpam-4760	269	8	u1	u1	NOUN
ejpam-4760	269	9	,	,	PUNCT
ejpam-4760	269	10	u3	u3	PROPN
ejpam-4760	269	11	}	}	PUNCT
ejpam-4760	269	12	,	,	PUNCT
ejpam-4760	269	13	t2	t2	NOUN
ejpam-4760	269	14	=	=	SYM
ejpam-4760	269	15	{	{	PUNCT
ejpam-4760	269	16	u1	u1	PROPN
ejpam-4760	269	17	,	,	PUNCT
ejpam-4760	269	18	u4	u4	PROPN
ejpam-4760	269	19	}	}	PUNCT
ejpam-4760	269	20	,	,	PUNCT
ejpam-4760	269	21	t3	t3	PROPN
ejpam-4760	269	22	=	=	PUNCT
ejpam-4760	269	23	{	{	PUNCT
ejpam-4760	269	24	u2	u2	PROPN
ejpam-4760	269	25	,	,	PUNCT
ejpam-4760	269	26	u4	u4	PROPN
ejpam-4760	269	27	}	}	PUNCT
ejpam-4760	269	28	,	,	PUNCT
ejpam-4760	269	29	t4	t4	PROPN
ejpam-4760	269	30	=	=	PROPN
ejpam-4760	269	31	{	{	PUNCT
ejpam-4760	269	32	u2	u2	PROPN
ejpam-4760	269	33	,	,	PUNCT
ejpam-4760	269	34	u5	u5	PROPN
ejpam-4760	269	35	}	}	PUNCT
ejpam-4760	269	36	and	and	CCONJ
ejpam-4760	269	37	t5	t5	PROPN
ejpam-4760	269	38	=	=	SYM
ejpam-4760	269	39	{	{	PUNCT
ejpam-4760	269	40	u3	u3	PROPN
ejpam-4760	269	41	,	,	PUNCT
ejpam-4760	269	42	u5	u5	PROPN
ejpam-4760	269	43	}	}	PUNCT
ejpam-4760	269	44	are	be	AUX
ejpam-4760	269	45	isolate	isolate	VERB
ejpam-4760	269	46	dominating	dominating	NOUN
ejpam-4760	269	47	sets	set	NOUN
ejpam-4760	269	48	(	(	PUNCT
ejpam-4760	269	49	γ0	γ0	NOUN
ejpam-4760	269	50	-	-	PUNCT
ejpam-4760	269	51	sets	set	NOUN
ejpam-4760	269	52	)	)	PUNCT
ejpam-4760	269	53	of	of	ADP
ejpam-4760	269	54	c5	c5	PROPN
ejpam-4760	269	55	by	by	ADP
ejpam-4760	269	56	proposition	proposition	NOUN
ejpam-4760	269	57	1	1	NUM
ejpam-4760	269	58	but	but	CCONJ
ejpam-4760	269	59	none	none	NOUN
ejpam-4760	269	60	of	of	ADP
ejpam-4760	269	61	them	they	PRON
ejpam-4760	269	62	are	be	AUX
ejpam-4760	269	63	perfect	perfect	ADJ
ejpam-4760	269	64	dominating	dominating	NOUN
ejpam-4760	269	65	sets	set	NOUN
ejpam-4760	269	66	since	since	SCONJ
ejpam-4760	269	67	some	some	DET
ejpam-4760	269	68	vertices	vertex	NOUN
ejpam-4760	269	69	in	in	ADP
ejpam-4760	269	70	v	v	NOUN
ejpam-4760	269	71	(	(	PUNCT
ejpam-4760	269	72	c5)\tj	c5)\tj	NOUN
ejpam-4760	269	73	are	be	AUX
ejpam-4760	269	74	dominated	dominate	VERB
ejpam-4760	269	75	by	by	ADP
ejpam-4760	269	76	two	two	NUM
ejpam-4760	269	77	vertices	vertex	NOUN
ejpam-4760	269	78	in	in	ADP
ejpam-4760	269	79	tj	tj	NOUN
ejpam-4760	269	80	for	for	ADP
ejpam-4760	269	81	all	all	DET
ejpam-4760	269	82	j	j	NOUN
ejpam-4760	269	83	=	=	SYM
ejpam-4760	269	84	1	1	NUM
ejpam-4760	269	85	,	,	PUNCT
ejpam-4760	269	86	2	2	NUM
ejpam-4760	269	87	,	,	PUNCT
ejpam-4760	269	88	3	3	NUM
ejpam-4760	269	89	,	,	PUNCT
ejpam-4760	269	90	4	4	NUM
ejpam-4760	269	91	,	,	PUNCT
ejpam-4760	269	92	5	5	NUM
ejpam-4760	269	93	.	.	X
ejpam-4760	269	94	note	note	VERB
ejpam-4760	269	95	that	that	SCONJ
ejpam-4760	269	96	the	the	DET
ejpam-4760	269	97	sets	set	NOUN
ejpam-4760	269	98	r1	r1	NOUN
ejpam-4760	269	99	=	=	SYM
ejpam-4760	269	100	{	{	PUNCT
ejpam-4760	269	101	u1	u1	NOUN
ejpam-4760	269	102	,	,	PUNCT
ejpam-4760	269	103	u3	u3	PROPN
ejpam-4760	269	104	,	,	PUNCT
ejpam-4760	269	105	u5	u5	PROPN
ejpam-4760	269	106	}	}	PUNCT
ejpam-4760	269	107	,	,	PUNCT
ejpam-4760	269	108	r2	r2	PROPN
ejpam-4760	269	109	=	=	SYM
ejpam-4760	269	110	{	{	PUNCT
ejpam-4760	269	111	u1	u1	NOUN
ejpam-4760	269	112	,	,	PUNCT
ejpam-4760	269	113	u3	u3	PROPN
ejpam-4760	269	114	,	,	PUNCT
ejpam-4760	269	115	u4	u4	PROPN
ejpam-4760	269	116	}	}	PUNCT
ejpam-4760	269	117	,	,	PUNCT
ejpam-4760	269	118	r3	r3	PROPN
ejpam-4760	269	119	=	=	SYM
ejpam-4760	269	120	{	{	PUNCT
ejpam-4760	269	121	u2	u2	PROPN
ejpam-4760	269	122	,	,	PUNCT
ejpam-4760	269	123	u3	u3	NOUN
ejpam-4760	269	124	,	,	PUNCT
ejpam-4760	269	125	u5	u5	PROPN
ejpam-4760	269	126	}	}	PUNCT
ejpam-4760	269	127	,	,	PUNCT
ejpam-4760	269	128	r4	r4	NOUN
ejpam-4760	269	129	=	=	PUNCT
ejpam-4760	269	130	{	{	PUNCT
ejpam-4760	269	131	u2	u2	PROPN
ejpam-4760	269	132	,	,	PUNCT
ejpam-4760	269	133	u4	u4	PROPN
ejpam-4760	269	134	,	,	PUNCT
ejpam-4760	269	135	u5	u5	PROPN
ejpam-4760	269	136	}	}	PUNCT
ejpam-4760	269	137	,	,	PUNCT
ejpam-4760	269	138	and	and	CCONJ
ejpam-4760	269	139	r5	r5	PROPN
ejpam-4760	269	140	=	=	SYM
ejpam-4760	269	141	{	{	PUNCT
ejpam-4760	269	142	u1	u1	NOUN
ejpam-4760	269	143	,	,	PUNCT
ejpam-4760	269	144	u2	u2	PROPN
ejpam-4760	269	145	,	,	PUNCT
ejpam-4760	269	146	u4	u4	PROPN
ejpam-4760	269	147	}	}	PUNCT
ejpam-4760	269	148	are	be	AUX
ejpam-4760	269	149	isolate	isolate	ADJ
ejpam-4760	269	150	dominating	dominating	NOUN
ejpam-4760	269	151	sets	set	NOUN
ejpam-4760	269	152	but	but	CCONJ
ejpam-4760	269	153	none	none	NOUN
ejpam-4760	269	154	of	of	ADP
ejpam-4760	269	155	them	they	PRON
ejpam-4760	269	156	are	be	AUX
ejpam-4760	269	157	perfect	perfect	ADJ
ejpam-4760	269	158	dominating	dominating	NOUN
ejpam-4760	269	159	sets	set	NOUN
ejpam-4760	269	160	since	since	SCONJ
ejpam-4760	269	161	all	all	DET
ejpam-4760	269	162	vertices	vertex	NOUN
ejpam-4760	269	163	in	in	ADP
ejpam-4760	269	164	v	v	PROPN
ejpam-4760	269	165	(	(	PUNCT
ejpam-4760	269	166	c5	c5	PROPN
ejpam-4760	269	167	)	)	PUNCT
ejpam-4760	269	168	\	\	PROPN
ejpam-4760	269	169	rk	rk	NOUN
ejpam-4760	269	170	are	be	AUX
ejpam-4760	269	171	dominated	dominate	VERB
ejpam-4760	269	172	by	by	ADP
ejpam-4760	269	173	two	two	NUM
ejpam-4760	269	174	vertices	vertex	NOUN
ejpam-4760	269	175	in	in	ADP
ejpam-4760	269	176	rk	rk	NOUN
ejpam-4760	269	177	for	for	ADP
ejpam-4760	269	178	all	all	PRON
ejpam-4760	269	179	k	k	NOUN
ejpam-4760	269	180	=	=	SYM
ejpam-4760	269	181	1	1	NUM
ejpam-4760	269	182	,	,	PUNCT
ejpam-4760	269	183	2	2	NUM
ejpam-4760	269	184	,	,	PUNCT
ejpam-4760	269	185	3	3	NUM
ejpam-4760	269	186	,	,	PUNCT
ejpam-4760	269	187	4	4	NUM
ejpam-4760	269	188	,	,	PUNCT
ejpam-4760	269	189	5	5	NUM
ejpam-4760	269	190	.	.	PUNCT
ejpam-4760	269	191	choosing	choose	VERB
ejpam-4760	269	192	4	4	NUM
ejpam-4760	269	193	or	or	CCONJ
ejpam-4760	269	194	5	5	NUM
ejpam-4760	269	195	vertices	vertex	NOUN
ejpam-4760	269	196	in	in	ADP
ejpam-4760	269	197	c5	c5	PROPN
ejpam-4760	269	198	for	for	ADP
ejpam-4760	269	199	γp0	γp0	NOUN
ejpam-4760	269	200	-	-	PUNCT
ejpam-4760	269	201	sets	set	NOUN
ejpam-4760	269	202	is	be	AUX
ejpam-4760	269	203	not	not	PART
ejpam-4760	269	204	possible	possible	ADJ
ejpam-4760	269	205	since	since	SCONJ
ejpam-4760	269	206	their	their	PRON
ejpam-4760	269	207	induced	induced	ADJ
ejpam-4760	269	208	subgraphs	subgraphs	NOUN
ejpam-4760	269	209	has	have	VERB
ejpam-4760	269	210	no	no	DET
ejpam-4760	269	211	isolated	isolated	ADJ
ejpam-4760	269	212	vertex	vertex	NOUN
ejpam-4760	269	213	.	.	PUNCT
ejpam-4760	270	1	thus	thus	ADV
ejpam-4760	270	2	,	,	PUNCT
ejpam-4760	270	3	in	in	ADP
ejpam-4760	270	4	any	any	DET
ejpam-4760	270	5	case	case	NOUN
ejpam-4760	270	6	,	,	PUNCT
ejpam-4760	270	7	c5	c5	PROPN
ejpam-4760	270	8	contains	contain	VERB
ejpam-4760	270	9	a	a	DET
ejpam-4760	270	10	perfect	perfect	ADJ
ejpam-4760	270	11	dominating	dominating	NOUN
ejpam-4760	270	12	set	set	NOUN
ejpam-4760	270	13	or	or	CCONJ
ejpam-4760	270	14	an	an	DET
ejpam-4760	270	15	isolate	isolate	NOUN
ejpam-4760	270	16	dominating	dominating	NOUN
ejpam-4760	270	17	set	set	NOUN
ejpam-4760	270	18	but	but	CCONJ
ejpam-4760	270	19	not	not	PART
ejpam-4760	270	20	both	both	PRON
ejpam-4760	270	21	.	.	PUNCT
ejpam-4760	271	1	therefore	therefore	ADV
ejpam-4760	271	2	,	,	PUNCT
ejpam-4760	271	3	c5	c5	PROPN
ejpam-4760	271	4	is	be	AUX
ejpam-4760	271	5	a	a	DET
ejpam-4760	271	6	non	non	ADJ
ejpam-4760	271	7	-	-	ADJ
ejpam-4760	271	8	γp0	γp0	NOUN
ejpam-4760	271	9	-	-	PUNCT
ejpam-4760	271	10	graph	graph	NOUN
ejpam-4760	271	11	.	.	PUNCT
ejpam-4760	272	1	4	4	X
ejpam-4760	272	2	.	.	X
ejpam-4760	272	3	the	the	DET
ejpam-4760	272	4	perfect	perfect	ADJ
ejpam-4760	272	5	isolate	isolate	NOUN
ejpam-4760	272	6	dominating	dominating	NOUN
ejpam-4760	272	7	set	set	VERB
ejpam-4760	272	8	in	in	ADP
ejpam-4760	272	9	the	the	DET
ejpam-4760	272	10	join	join	NOUN
ejpam-4760	272	11	of	of	ADP
ejpam-4760	272	12	graphs	graph	NOUN
ejpam-4760	272	13	this	this	DET
ejpam-4760	272	14	section	section	NOUN
ejpam-4760	272	15	contains	contain	VERB
ejpam-4760	272	16	results	result	NOUN
ejpam-4760	272	17	when	when	SCONJ
ejpam-4760	272	18	the	the	DET
ejpam-4760	272	19	join	join	NOUN
ejpam-4760	272	20	g+h	g+h	PROPN
ejpam-4760	272	21	has	have	VERB
ejpam-4760	272	22	a	a	DET
ejpam-4760	272	23	γp0	γp0	NOUN
ejpam-4760	272	24	-	-	PUNCT
ejpam-4760	272	25	set	set	VERB
ejpam-4760	272	26	or	or	CCONJ
ejpam-4760	272	27	has	have	VERB
ejpam-4760	272	28	no	no	DET
ejpam-4760	272	29	γp0	γp0	NOUN
ejpam-4760	272	30	-	-	PUNCT
ejpam-4760	272	31	set	set	VERB
ejpam-4760	272	32	and	and	CCONJ
ejpam-4760	272	33	its	its	PRON
ejpam-4760	272	34	perfect	perfect	ADJ
ejpam-4760	272	35	isolate	isolate	NOUN
ejpam-4760	272	36	domination	domination	NOUN
ejpam-4760	272	37	number	number	NOUN
ejpam-4760	272	38	.	.	PUNCT
ejpam-4760	273	1	the	the	DET
ejpam-4760	273	2	join	join	NOUN
ejpam-4760	273	3	of	of	ADP
ejpam-4760	273	4	two	two	NUM
ejpam-4760	273	5	graphs	graph	NOUN
ejpam-4760	273	6	g	g	NOUN
ejpam-4760	273	7	and	and	CCONJ
ejpam-4760	273	8	h	h	NOUN
ejpam-4760	273	9	,	,	PUNCT
ejpam-4760	273	10	denoted	denote	VERB
ejpam-4760	273	11	by	by	ADP
ejpam-4760	273	12	g	g	PROPN
ejpam-4760	273	13	+	+	PROPN
ejpam-4760	273	14	h	h	NOUN
ejpam-4760	273	15	,	,	PUNCT
ejpam-4760	273	16	is	be	AUX
ejpam-4760	273	17	the	the	DET
ejpam-4760	273	18	graph	graph	NOUN
ejpam-4760	273	19	with	with	ADP
ejpam-4760	273	20	v	v	NOUN
ejpam-4760	273	21	(	(	PUNCT
ejpam-4760	273	22	g+h	g+h	NOUN
ejpam-4760	273	23	)	)	PUNCT
ejpam-4760	273	24	=	=	SYM
ejpam-4760	273	25	v	v	X
ejpam-4760	273	26	(	(	PUNCT
ejpam-4760	273	27	g	g	NOUN
ejpam-4760	273	28	)	)	PUNCT
ejpam-4760	273	29	∪	∪	NOUN
ejpam-4760	273	30	v	v	NOUN
ejpam-4760	273	31	(	(	PUNCT
ejpam-4760	273	32	h	h	NOUN
ejpam-4760	273	33	)	)	PUNCT
ejpam-4760	273	34	and	and	CCONJ
ejpam-4760	273	35	e(g+h	e(g+h	NUM
ejpam-4760	273	36	)	)	PUNCT
ejpam-4760	273	37	=	=	SYM
ejpam-4760	273	38	e(g	e(g	PROPN
ejpam-4760	273	39	)	)	PUNCT
ejpam-4760	273	40	∪e(h	∪e(h	PROPN
ejpam-4760	273	41	)	)	PUNCT
ejpam-4760	273	42	∪	∪	NOUN
ejpam-4760	273	43	{	{	PUNCT
ejpam-4760	273	44	uv	uv	NOUN
ejpam-4760	273	45	:	:	PUNCT
ejpam-4760	273	46	u	u	PROPN
ejpam-4760	273	47	∈	∈	PROPN
ejpam-4760	273	48	v	v	ADP
ejpam-4760	273	49	(	(	PUNCT
ejpam-4760	273	50	g	g	NOUN
ejpam-4760	273	51	)	)	PUNCT
ejpam-4760	273	52	,	,	PUNCT
ejpam-4760	273	53	v	v	X
ejpam-4760	273	54	∈	∈	PROPN
ejpam-4760	273	55	v	v	NOUN
ejpam-4760	273	56	(	(	PUNCT
ejpam-4760	273	57	h	h	NOUN
ejpam-4760	273	58	)	)	PUNCT
ejpam-4760	273	59	}	}	PUNCT
ejpam-4760	273	60	.	.	PUNCT
ejpam-4760	274	1	theorem	theorem	ADJ
ejpam-4760	274	2	8	8	NUM
ejpam-4760	274	3	.	.	PUNCT
ejpam-4760	275	1	let	let	VERB
ejpam-4760	275	2	g	g	NOUN
ejpam-4760	276	1	and	and	CCONJ
ejpam-4760	276	2	h	h	NOUN
ejpam-4760	276	3	be	be	VERB
ejpam-4760	276	4	any	any	DET
ejpam-4760	276	5	graphs	graph	NOUN
ejpam-4760	276	6	with	with	ADP
ejpam-4760	276	7	γ(g	γ(g	PROPN
ejpam-4760	276	8	)	)	PUNCT
ejpam-4760	277	1	=	=	SYM
ejpam-4760	277	2	1	1	NUM
ejpam-4760	277	3	or	or	CCONJ
ejpam-4760	277	4	γ(h	γ(h	NOUN
ejpam-4760	277	5	)	)	PUNCT
ejpam-4760	277	6	=	=	SYM
ejpam-4760	278	1	1	1	X
ejpam-4760	278	2	.	.	PUNCT
ejpam-4760	278	3	then	then	ADV
ejpam-4760	278	4	γp0(g+h	γp0(g+h	VERB
ejpam-4760	278	5	)	)	PUNCT
ejpam-4760	279	1	=	=	SYM
ejpam-4760	279	2	1	1	X
ejpam-4760	279	3	.	.	PUNCT
ejpam-4760	279	4	proof	proof	NOUN
ejpam-4760	279	5	.	.	PUNCT
ejpam-4760	280	1	by	by	ADP
ejpam-4760	280	2	corollary	corollary	ADJ
ejpam-4760	280	3	1	1	NUM
ejpam-4760	280	4	,	,	PUNCT
ejpam-4760	280	5	γ(g+h	γ(g+h	NUM
ejpam-4760	280	6	)	)	PUNCT
ejpam-4760	280	7	=	=	SYM
ejpam-4760	280	8	1	1	X
ejpam-4760	280	9	.	.	PUNCT
ejpam-4760	280	10	by	by	ADP
ejpam-4760	280	11	proposition	proposition	NOUN
ejpam-4760	280	12	4	4	NUM
ejpam-4760	280	13	,	,	PUNCT
ejpam-4760	280	14	γp0(g+h	γp0(g+h	NOUN
ejpam-4760	280	15	)	)	PUNCT
ejpam-4760	280	16	=	=	SYM
ejpam-4760	280	17	1	1	X
ejpam-4760	280	18	.	.	PUNCT
ejpam-4760	281	1	the	the	DET
ejpam-4760	281	2	next	next	ADJ
ejpam-4760	281	3	result	result	NOUN
ejpam-4760	281	4	follows	follow	VERB
ejpam-4760	281	5	from	from	ADP
ejpam-4760	281	6	theorem	theorem	ADJ
ejpam-4760	281	7	8	8	NUM
ejpam-4760	281	8	since	since	SCONJ
ejpam-4760	281	9	γ(k1	γ(k1	PROPN
ejpam-4760	281	10	)	)	PUNCT
ejpam-4760	281	11	=	=	SYM
ejpam-4760	281	12	γ(p2	γ(p2	X
ejpam-4760	281	13	)	)	PUNCT
ejpam-4760	281	14	=	=	SYM
ejpam-4760	281	15	γ(p3	γ(p3	X
ejpam-4760	281	16	)	)	PUNCT
ejpam-4760	281	17	=	=	PUNCT
ejpam-4760	281	18	γ(c3	γ(c3	PRON
ejpam-4760	281	19	)	)	PUNCT
ejpam-4760	282	1	=	=	SYM
ejpam-4760	282	2	1	1	X
ejpam-4760	282	3	.	.	PUNCT
ejpam-4760	282	4	c.	c.	PROPN
ejpam-4760	282	5	armada	armada	PROPN
ejpam-4760	282	6	,	,	PUNCT
ejpam-4760	282	7	j.	j.	PROPN
ejpam-4760	282	8	hamja	hamja	PROPN
ejpam-4760	282	9	/	/	SYM
ejpam-4760	282	10	eur	eur	PROPN
ejpam-4760	282	11	.	.	PUNCT
ejpam-4760	283	1	j.	j.	PROPN
ejpam-4760	283	2	pure	pure	PROPN
ejpam-4760	283	3	appl	appl	PROPN
ejpam-4760	283	4	.	.	PROPN
ejpam-4760	283	5	math	math	PROPN
ejpam-4760	283	6	,	,	PUNCT
ejpam-4760	283	7	16	16	NUM
ejpam-4760	283	8	(	(	PUNCT
ejpam-4760	283	9	2	2	NUM
ejpam-4760	283	10	)	)	PUNCT
ejpam-4760	283	11	(	(	PUNCT
ejpam-4760	283	12	2023	2023	NUM
ejpam-4760	283	13	)	)	PUNCT
ejpam-4760	283	14	,	,	PUNCT
ejpam-4760	283	15	1326	1326	NUM
ejpam-4760	283	16	-	-	SYM
ejpam-4760	283	17	1341	1341	NUM
ejpam-4760	283	18	1336	1336	NUM
ejpam-4760	283	19	corollary	corollary	NOUN
ejpam-4760	283	20	5	5	NUM
ejpam-4760	283	21	.	.	PUNCT
ejpam-4760	284	1	the	the	DET
ejpam-4760	284	2	following	follow	VERB
ejpam-4760	284	3	are	be	AUX
ejpam-4760	284	4	graphs	graph	NOUN
ejpam-4760	284	5	having	have	VERB
ejpam-4760	284	6	γp0(g	γp0(g	NOUN
ejpam-4760	284	7	)	)	PUNCT
ejpam-4760	284	8	=	=	SYM
ejpam-4760	284	9	1	1	X
ejpam-4760	284	10	.	.	PUNCT
ejpam-4760	284	11	i.	i.	PROPN
ejpam-4760	284	12	star	star	PROPN
ejpam-4760	284	13	graph	graph	VERB
ejpam-4760	284	14	sn	sn	PROPN
ejpam-4760	284	15	=	=	SYM
ejpam-4760	284	16	k1	k1	PROPN
ejpam-4760	285	1	+	+	PROPN
ejpam-4760	285	2	kn	kn	PROPN
ejpam-4760	285	3	,	,	PUNCT
ejpam-4760	285	4	n	n	PRON
ejpam-4760	285	5	≥	≥	NUM
ejpam-4760	285	6	2	2	NUM
ejpam-4760	285	7	ii	ii	NOUN
ejpam-4760	285	8	.	.	PUNCT
ejpam-4760	286	1	fan	fan	PROPN
ejpam-4760	286	2	graph	graph	NOUN
ejpam-4760	286	3	fn	fn	NOUN
ejpam-4760	286	4	=	=	SYM
ejpam-4760	286	5	k1	k1	PROPN
ejpam-4760	286	6	+	+	CCONJ
ejpam-4760	286	7	pn	pn	PROPN
ejpam-4760	286	8	,	,	PUNCT
ejpam-4760	286	9	n	n	PRON
ejpam-4760	286	10	≥	≥	NOUN
ejpam-4760	286	11	2	2	NUM
ejpam-4760	286	12	iii	iii	NOUN
ejpam-4760	286	13	.	.	PROPN
ejpam-4760	286	14	wheel	wheel	PROPN
ejpam-4760	286	15	graph	graph	NOUN
ejpam-4760	286	16	wn	wn	PROPN
ejpam-4760	286	17	=	=	PROPN
ejpam-4760	286	18	k1	k1	PROPN
ejpam-4760	287	1	+	+	CCONJ
ejpam-4760	287	2	cn	cn	PROPN
ejpam-4760	287	3	,	,	PUNCT
ejpam-4760	287	4	n	n	CCONJ
ejpam-4760	287	5	≥	≥	NUM
ejpam-4760	287	6	3	3	NUM
ejpam-4760	287	7	iv	iv	NUM
ejpam-4760	287	8	.	.	PUNCT
ejpam-4760	287	9	friendship	friendship	NOUN
ejpam-4760	287	10	graph	graph	NOUN
ejpam-4760	287	11	fn	fn	NOUN
ejpam-4760	287	12	=	=	NOUN
ejpam-4760	287	13	k1	k1	PROPN
ejpam-4760	287	14	+	+	CCONJ
ejpam-4760	287	15	np2	np2	PROPN
ejpam-4760	287	16	,	,	PUNCT
ejpam-4760	287	17	n	n	PRON
ejpam-4760	287	18	≥	≥	NOUN
ejpam-4760	287	19	2	2	NUM
ejpam-4760	287	20	v.	v.	ADP
ejpam-4760	287	21	windmill	windmill	NOUN
ejpam-4760	287	22	graph	graph	NOUN
ejpam-4760	287	23	wm	wm	PROPN
ejpam-4760	287	24	n	n	PROPN
ejpam-4760	287	25	=	=	PROPN
ejpam-4760	287	26	k1	k1	PROPN
ejpam-4760	288	1	+	+	PROPN
ejpam-4760	288	2	mkn−1	mkn−1	PROPN
ejpam-4760	288	3	,	,	PUNCT
ejpam-4760	288	4	n	n	PRON
ejpam-4760	288	5	≥	≥	NOUN
ejpam-4760	288	6	3	3	NUM
ejpam-4760	288	7	and	and	CCONJ
ejpam-4760	288	8	m	m	PROPN
ejpam-4760	288	9	≥	≥	NUM
ejpam-4760	288	10	2	2	NUM
ejpam-4760	288	11	vi	vi	NOUN
ejpam-4760	288	12	.	.	PROPN
ejpam-4760	289	1	complete	complete	ADJ
ejpam-4760	289	2	bipartite	bipartite	PROPN
ejpam-4760	289	3	graph	graph	NOUN
ejpam-4760	289	4	km	km	PROPN
ejpam-4760	289	5	,	,	PUNCT
ejpam-4760	289	6	n	n	NOUN
ejpam-4760	289	7	=	=	SYM
ejpam-4760	289	8	km	km	PROPN
ejpam-4760	289	9	+	+	PROPN
ejpam-4760	289	10	kn	kn	PROPN
ejpam-4760	289	11	,	,	PUNCT
ejpam-4760	289	12	either	either	CCONJ
ejpam-4760	289	13	m	m	PROPN
ejpam-4760	289	14	=	=	SYM
ejpam-4760	289	15	1	1	NUM
ejpam-4760	289	16	or	or	CCONJ
ejpam-4760	289	17	n	n	NOUN
ejpam-4760	289	18	=	=	SYM
ejpam-4760	289	19	1	1	X
ejpam-4760	289	20	.	.	X
ejpam-4760	290	1	vii	vii	AUX
ejpam-4760	290	2	.	.	PROPN
ejpam-4760	290	3	generalized	generalize	VERB
ejpam-4760	290	4	fan	fan	PROPN
ejpam-4760	290	5	graph	graph	PROPN
ejpam-4760	290	6	fm	fm	PROPN
ejpam-4760	290	7	,	,	PUNCT
ejpam-4760	290	8	n	n	NOUN
ejpam-4760	290	9	=	=	SYM
ejpam-4760	290	10	km	km	PROPN
ejpam-4760	290	11	+	+	CCONJ
ejpam-4760	290	12	pn	pn	PROPN
ejpam-4760	290	13	,	,	PUNCT
ejpam-4760	290	14	m	m	VERB
ejpam-4760	290	15	≥	≥	NOUN
ejpam-4760	290	16	1	1	NUM
ejpam-4760	290	17	and	and	CCONJ
ejpam-4760	290	18	n	n	CCONJ
ejpam-4760	290	19	=	=	SYM
ejpam-4760	290	20	2	2	NUM
ejpam-4760	290	21	,	,	PUNCT
ejpam-4760	290	22	3	3	NUM
ejpam-4760	290	23	viii	viii	NOUN
ejpam-4760	290	24	.	.	PUNCT
ejpam-4760	291	1	generalized	generalize	VERB
ejpam-4760	291	2	wheel	wheel	NOUN
ejpam-4760	291	3	graph	graph	NOUN
ejpam-4760	291	4	wm,3	wm,3	NOUN
ejpam-4760	291	5	=	=	PROPN
ejpam-4760	291	6	km	km	NOUN
ejpam-4760	291	7	+	+	CCONJ
ejpam-4760	291	8	c3	c3	PROPN
ejpam-4760	291	9	,	,	PUNCT
ejpam-4760	291	10	m	m	VERB
ejpam-4760	291	11	≥	≥	NOUN
ejpam-4760	291	12	1	1	NUM
ejpam-4760	291	13	.	.	PUNCT
ejpam-4760	291	14	theorem	theorem	NOUN
ejpam-4760	291	15	9	9	NUM
ejpam-4760	291	16	.	.	PUNCT
ejpam-4760	292	1	let	let	VERB
ejpam-4760	292	2	g	g	NOUN
ejpam-4760	293	1	and	and	CCONJ
ejpam-4760	293	2	h	h	NOUN
ejpam-4760	293	3	be	be	VERB
ejpam-4760	293	4	any	any	DET
ejpam-4760	293	5	graphs	graph	NOUN
ejpam-4760	293	6	with	with	ADP
ejpam-4760	293	7	γ(g	γ(g	PROPN
ejpam-4760	293	8	)	)	PUNCT
ejpam-4760	293	9	≥	≥	NOUN
ejpam-4760	293	10	2	2	NUM
ejpam-4760	293	11	and	and	CCONJ
ejpam-4760	293	12	γ(h	γ(h	NOUN
ejpam-4760	293	13	)	)	PUNCT
ejpam-4760	293	14	≥	≥	NOUN
ejpam-4760	294	1	2	2	NUM
ejpam-4760	294	2	.	.	PUNCT
ejpam-4760	294	3	then	then	ADV
ejpam-4760	294	4	the	the	DET
ejpam-4760	294	5	graph	graph	NOUN
ejpam-4760	294	6	g+h	g+h	PROPN
ejpam-4760	294	7	is	be	AUX
ejpam-4760	294	8	a	a	DET
ejpam-4760	294	9	non	non	ADJ
ejpam-4760	294	10	-	-	ADJ
ejpam-4760	294	11	γp0	γp0	NOUN
ejpam-4760	294	12	-	-	PUNCT
ejpam-4760	294	13	graph	graph	NOUN
ejpam-4760	294	14	.	.	PUNCT
ejpam-4760	295	1	proof	proof	NOUN
ejpam-4760	295	2	.	.	PUNCT
ejpam-4760	296	1	by	by	ADP
ejpam-4760	296	2	corollary	corollary	ADJ
ejpam-4760	296	3	1	1	NUM
ejpam-4760	296	4	,	,	PUNCT
ejpam-4760	296	5	γ(g+h	γ(g+h	NUM
ejpam-4760	296	6	)	)	PUNCT
ejpam-4760	296	7	=	=	SYM
ejpam-4760	296	8	2	2	X
ejpam-4760	296	9	.	.	X
ejpam-4760	296	10	let	let	VERB
ejpam-4760	296	11	s	s	PRON
ejpam-4760	296	12	be	be	AUX
ejpam-4760	296	13	a	a	DET
ejpam-4760	296	14	γp0	γp0	NOUN
ejpam-4760	296	15	-	-	PUNCT
ejpam-4760	296	16	set	set	NOUN
ejpam-4760	296	17	of	of	ADP
ejpam-4760	296	18	g+h	g+h	PROPN
ejpam-4760	296	19	.	.	PUNCT
ejpam-4760	297	1	by	by	ADP
ejpam-4760	297	2	proposition	proposition	NOUN
ejpam-4760	297	3	4	4	NUM
ejpam-4760	297	4	,	,	PUNCT
ejpam-4760	297	5	γp0(g+h	γp0(g+h	PROPN
ejpam-4760	297	6	)	)	PUNCT
ejpam-4760	297	7	>	>	X
ejpam-4760	297	8	1	1	X
ejpam-4760	297	9	.	.	PUNCT
ejpam-4760	297	10	thus	thus	ADV
ejpam-4760	297	11	,	,	PUNCT
ejpam-4760	297	12	|s|	|s|	VERB
ejpam-4760	297	13	>	>	ADP
ejpam-4760	297	14	1	1	X
ejpam-4760	297	15	.	.	PUNCT
ejpam-4760	297	16	suppose	suppose	VERB
ejpam-4760	297	17	that	that	SCONJ
ejpam-4760	297	18	x	x	NOUN
ejpam-4760	297	19	,	,	PUNCT
ejpam-4760	297	20	y	y	PROPN
ejpam-4760	297	21	∈	∈	PROPN
ejpam-4760	297	22	s.	s.	PROPN
ejpam-4760	297	23	consider	consider	VERB
ejpam-4760	297	24	the	the	DET
ejpam-4760	297	25	following	follow	VERB
ejpam-4760	297	26	cases	case	NOUN
ejpam-4760	297	27	:	:	PUNCT
ejpam-4760	297	28	case	case	NOUN
ejpam-4760	297	29	1	1	NUM
ejpam-4760	297	30	:	:	PUNCT
ejpam-4760	297	31	x	x	X
ejpam-4760	297	32	,	,	PUNCT
ejpam-4760	297	33	y	y	PROPN
ejpam-4760	297	34	∈	∈	PROPN
ejpam-4760	297	35	s	s	PART
ejpam-4760	297	36	⊆	⊆	NUM
ejpam-4760	297	37	v	v	NOUN
ejpam-4760	297	38	(	(	PUNCT
ejpam-4760	297	39	g	g	NOUN
ejpam-4760	297	40	)	)	PUNCT
ejpam-4760	297	41	.	.	PUNCT
ejpam-4760	298	1	clearly	clearly	ADV
ejpam-4760	298	2	,	,	PUNCT
ejpam-4760	298	3	for	for	ADP
ejpam-4760	298	4	all	all	DET
ejpam-4760	298	5	z	z	NOUN
ejpam-4760	298	6	∈	∈	PROPN
ejpam-4760	298	7	v	v	ADP
ejpam-4760	298	8	(	(	PUNCT
ejpam-4760	298	9	h	h	NOUN
ejpam-4760	298	10	)	)	PUNCT
ejpam-4760	298	11	,	,	PUNCT
ejpam-4760	298	12	z	z	PROPN
ejpam-4760	298	13	is	be	AUX
ejpam-4760	298	14	dominated	dominate	VERB
ejpam-4760	298	15	in	in	ADP
ejpam-4760	298	16	g	g	PROPN
ejpam-4760	298	17	+	+	CCONJ
ejpam-4760	298	18	h	h	NOUN
ejpam-4760	298	19	by	by	ADP
ejpam-4760	298	20	the	the	DET
ejpam-4760	298	21	two	two	NUM
ejpam-4760	298	22	vertices	vertex	NOUN
ejpam-4760	298	23	x	x	PUNCT
ejpam-4760	298	24	and	and	CCONJ
ejpam-4760	298	25	y	y	PROPN
ejpam-4760	298	26	in	in	ADP
ejpam-4760	298	27	s	s	PRON
ejpam-4760	298	28	.	.	PUNCT
ejpam-4760	299	1	thus	thus	ADV
ejpam-4760	299	2	,	,	PUNCT
ejpam-4760	299	3	s	s	VERB
ejpam-4760	299	4	is	be	AUX
ejpam-4760	299	5	not	not	PART
ejpam-4760	299	6	a	a	DET
ejpam-4760	299	7	perfect	perfect	ADJ
ejpam-4760	299	8	dominating	dominating	NOUN
ejpam-4760	299	9	set	set	NOUN
ejpam-4760	299	10	of	of	ADP
ejpam-4760	299	11	g+h	g+h	PROPN
ejpam-4760	299	12	.	.	PUNCT
ejpam-4760	300	1	thus	thus	ADV
ejpam-4760	300	2	,	,	PUNCT
ejpam-4760	300	3	s	s	VERB
ejpam-4760	300	4	is	be	AUX
ejpam-4760	300	5	not	not	PART
ejpam-4760	300	6	a	a	DET
ejpam-4760	300	7	γp0	γp0	NOUN
ejpam-4760	300	8	-	-	PUNCT
ejpam-4760	300	9	set	set	NOUN
ejpam-4760	300	10	of	of	ADP
ejpam-4760	300	11	g+h	g+h	PROPN
ejpam-4760	300	12	.	.	PUNCT
ejpam-4760	301	1	this	this	PRON
ejpam-4760	301	2	is	be	AUX
ejpam-4760	301	3	a	a	DET
ejpam-4760	301	4	contradiction	contradiction	NOUN
ejpam-4760	301	5	.	.	PUNCT
ejpam-4760	302	1	similarly	similarly	ADV
ejpam-4760	302	2	,	,	PUNCT
ejpam-4760	302	3	if	if	SCONJ
ejpam-4760	302	4	x	x	X
ejpam-4760	302	5	,	,	PUNCT
ejpam-4760	302	6	y	y	PROPN
ejpam-4760	302	7	∈	∈	PROPN
ejpam-4760	302	8	s	s	PART
ejpam-4760	302	9	⊆	⊆	NUM
ejpam-4760	302	10	v	v	NOUN
ejpam-4760	302	11	(	(	PUNCT
ejpam-4760	302	12	h	h	NOUN
ejpam-4760	302	13	)	)	PUNCT
ejpam-4760	302	14	,	,	PUNCT
ejpam-4760	302	15	then	then	ADV
ejpam-4760	302	16	s	s	VERB
ejpam-4760	302	17	is	be	AUX
ejpam-4760	302	18	not	not	PART
ejpam-4760	302	19	γp0	γp0	NOUN
ejpam-4760	302	20	-	-	PUNCT
ejpam-4760	302	21	set	set	NOUN
ejpam-4760	302	22	of	of	ADP
ejpam-4760	302	23	g+h	g+h	PROPN
ejpam-4760	302	24	.	.	PUNCT
ejpam-4760	303	1	this	this	PRON
ejpam-4760	303	2	is	be	AUX
ejpam-4760	303	3	a	a	DET
ejpam-4760	303	4	contradiction	contradiction	NOUN
ejpam-4760	303	5	.	.	PUNCT
ejpam-4760	304	1	therefore	therefore	ADV
ejpam-4760	304	2	,	,	PUNCT
ejpam-4760	304	3	having	have	VERB
ejpam-4760	304	4	two	two	NUM
ejpam-4760	304	5	vertices	vertex	NOUN
ejpam-4760	304	6	in	in	ADP
ejpam-4760	304	7	v	v	ADP
ejpam-4760	304	8	(	(	PUNCT
ejpam-4760	304	9	g	g	NOUN
ejpam-4760	304	10	)	)	PUNCT
ejpam-4760	304	11	or	or	CCONJ
ejpam-4760	304	12	in	in	ADP
ejpam-4760	304	13	v	v	NUM
ejpam-4760	304	14	(	(	PUNCT
ejpam-4760	304	15	h	h	NOUN
ejpam-4760	304	16	)	)	PUNCT
ejpam-4760	304	17	is	be	AUX
ejpam-4760	304	18	not	not	PART
ejpam-4760	304	19	possible	possible	ADJ
ejpam-4760	304	20	for	for	SCONJ
ejpam-4760	304	21	a	a	DET
ejpam-4760	304	22	set	set	NOUN
ejpam-4760	304	23	s	s	VERB
ejpam-4760	304	24	to	to	PART
ejpam-4760	304	25	be	be	AUX
ejpam-4760	304	26	a	a	DET
ejpam-4760	304	27	γp0	γp0	NOUN
ejpam-4760	304	28	-	-	PUNCT
ejpam-4760	304	29	set	set	NOUN
ejpam-4760	304	30	of	of	ADP
ejpam-4760	304	31	g+h	g+h	PROPN
ejpam-4760	304	32	.	.	PUNCT
ejpam-4760	305	1	case	case	NOUN
ejpam-4760	305	2	2	2	NUM
ejpam-4760	305	3	:	:	PUNCT
ejpam-4760	305	4	x	x	X
ejpam-4760	305	5	,	,	PUNCT
ejpam-4760	305	6	y	y	PROPN
ejpam-4760	305	7	∈	∈	PROPN
ejpam-4760	305	8	s	s	VERB
ejpam-4760	305	9	such	such	ADJ
ejpam-4760	305	10	that	that	SCONJ
ejpam-4760	305	11	x	x	SYM
ejpam-4760	305	12	∈	∈	NOUN
ejpam-4760	305	13	v	v	X
ejpam-4760	305	14	(	(	PUNCT
ejpam-4760	305	15	g	g	NOUN
ejpam-4760	305	16	)	)	PUNCT
ejpam-4760	305	17	and	and	CCONJ
ejpam-4760	305	18	y	y	PROPN
ejpam-4760	305	19	∈	∈	PROPN
ejpam-4760	305	20	v	v	ADP
ejpam-4760	305	21	(	(	PUNCT
ejpam-4760	305	22	h	h	NOUN
ejpam-4760	305	23	)	)	PUNCT
ejpam-4760	305	24	.	.	PUNCT
ejpam-4760	306	1	clearly	clearly	ADV
ejpam-4760	306	2	,	,	PUNCT
ejpam-4760	306	3	the	the	DET
ejpam-4760	306	4	induced	induced	ADJ
ejpam-4760	306	5	subgraph	subgraph	NOUN
ejpam-4760	306	6	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	306	7	has	have	VERB
ejpam-4760	306	8	no	no	DET
ejpam-4760	306	9	isolated	isolated	ADJ
ejpam-4760	306	10	vertex	vertex	NOUN
ejpam-4760	306	11	since	since	SCONJ
ejpam-4760	306	12	xy	xy	PROPN
ejpam-4760	306	13	∈	∈	PROPN
ejpam-4760	306	14	e(g+h	e(g+h	NUM
ejpam-4760	306	15	)	)	PUNCT
ejpam-4760	306	16	.	.	PUNCT
ejpam-4760	307	1	hence	hence	ADV
ejpam-4760	307	2	,	,	PUNCT
ejpam-4760	307	3	s	s	VERB
ejpam-4760	307	4	is	be	AUX
ejpam-4760	307	5	not	not	PART
ejpam-4760	307	6	an	an	DET
ejpam-4760	307	7	isolate	isolate	NOUN
ejpam-4760	307	8	dominating	dominating	NOUN
ejpam-4760	307	9	set	set	NOUN
ejpam-4760	307	10	of	of	ADP
ejpam-4760	307	11	g+h	g+h	PROPN
ejpam-4760	307	12	.	.	PUNCT
ejpam-4760	308	1	thus	thus	ADV
ejpam-4760	308	2	,	,	PUNCT
ejpam-4760	308	3	s	s	VERB
ejpam-4760	308	4	is	be	AUX
ejpam-4760	308	5	not	not	PART
ejpam-4760	308	6	a	a	DET
ejpam-4760	308	7	γp0	γp0	NOUN
ejpam-4760	308	8	-	-	PUNCT
ejpam-4760	308	9	set	set	NOUN
ejpam-4760	308	10	of	of	ADP
ejpam-4760	308	11	g+h	g+h	PROPN
ejpam-4760	308	12	,	,	PUNCT
ejpam-4760	308	13	a	a	DET
ejpam-4760	308	14	contradiction	contradiction	NOUN
ejpam-4760	308	15	.	.	PUNCT
ejpam-4760	309	1	furthermore	furthermore	ADV
ejpam-4760	309	2	,	,	PUNCT
ejpam-4760	309	3	adding	add	VERB
ejpam-4760	309	4	a	a	DET
ejpam-4760	309	5	vertex	vertex	NOUN
ejpam-4760	309	6	in	in	ADP
ejpam-4760	309	7	s	s	PROPN
ejpam-4760	309	8	which	which	PRON
ejpam-4760	309	9	is	be	AUX
ejpam-4760	309	10	either	either	CCONJ
ejpam-4760	309	11	from	from	ADP
ejpam-4760	309	12	v	v	NUM
ejpam-4760	309	13	(	(	PUNCT
ejpam-4760	309	14	g	g	NOUN
ejpam-4760	309	15	)	)	PUNCT
ejpam-4760	309	16	or	or	CCONJ
ejpam-4760	309	17	v	v	NOUN
ejpam-4760	309	18	(	(	PUNCT
ejpam-4760	309	19	h	h	NOUN
ejpam-4760	309	20	)	)	PUNCT
ejpam-4760	309	21	is	be	AUX
ejpam-4760	309	22	not	not	PART
ejpam-4760	309	23	possible	possible	ADJ
ejpam-4760	309	24	by	by	ADP
ejpam-4760	309	25	case	case	NOUN
ejpam-4760	309	26	1	1	NUM
ejpam-4760	309	27	.	.	PUNCT
ejpam-4760	310	1	hence	hence	ADV
ejpam-4760	310	2	,	,	PUNCT
ejpam-4760	310	3	in	in	ADP
ejpam-4760	310	4	any	any	DET
ejpam-4760	310	5	case	case	NOUN
ejpam-4760	310	6	,	,	PUNCT
ejpam-4760	310	7	s	s	VERB
ejpam-4760	310	8	is	be	AUX
ejpam-4760	310	9	not	not	PART
ejpam-4760	310	10	a	a	DET
ejpam-4760	310	11	γp0	γp0	NOUN
ejpam-4760	310	12	-	-	PUNCT
ejpam-4760	310	13	set	set	NOUN
ejpam-4760	310	14	of	of	ADP
ejpam-4760	310	15	g	g	PROPN
ejpam-4760	310	16	+	+	CCONJ
ejpam-4760	310	17	h.	h.	PROPN
ejpam-4760	310	18	therefore	therefore	ADV
ejpam-4760	310	19	,	,	PUNCT
ejpam-4760	310	20	the	the	DET
ejpam-4760	310	21	graph	graph	NOUN
ejpam-4760	310	22	g	g	PROPN
ejpam-4760	310	23	+	+	CCONJ
ejpam-4760	310	24	h	h	NOUN
ejpam-4760	310	25	is	be	AUX
ejpam-4760	310	26	a	a	DET
ejpam-4760	310	27	non	non	ADJ
ejpam-4760	310	28	-	-	ADJ
ejpam-4760	310	29	γp0	γp0	NOUN
ejpam-4760	310	30	-	-	PUNCT
ejpam-4760	310	31	graph	graph	NOUN
ejpam-4760	310	32	if	if	SCONJ
ejpam-4760	310	33	γ(g	γ(g	PROPN
ejpam-4760	310	34	)	)	PUNCT
ejpam-4760	310	35	≥	≥	NOUN
ejpam-4760	310	36	2	2	NUM
ejpam-4760	310	37	and	and	CCONJ
ejpam-4760	310	38	γ(h	γ(h	NOUN
ejpam-4760	310	39	)	)	PUNCT
ejpam-4760	310	40	≥	≥	NOUN
ejpam-4760	310	41	2	2	NUM
ejpam-4760	310	42	.	.	PUNCT
ejpam-4760	311	1	the	the	DET
ejpam-4760	311	2	next	next	ADJ
ejpam-4760	311	3	result	result	NOUN
ejpam-4760	311	4	follows	follow	VERB
ejpam-4760	311	5	from	from	ADP
ejpam-4760	311	6	theorem	theorem	ADJ
ejpam-4760	311	7	9	9	NUM
ejpam-4760	311	8	.	.	PUNCT
ejpam-4760	311	9	corollary	corollary	ADJ
ejpam-4760	311	10	6	6	NUM
ejpam-4760	311	11	.	.	PUNCT
ejpam-4760	312	1	the	the	DET
ejpam-4760	312	2	following	follow	VERB
ejpam-4760	312	3	graphs	graph	NOUN
ejpam-4760	312	4	are	be	AUX
ejpam-4760	312	5	non	non	ADJ
ejpam-4760	312	6	-	-	ADJ
ejpam-4760	312	7	γp0	γp0	NOUN
ejpam-4760	312	8	-	-	PUNCT
ejpam-4760	312	9	graphs	graph	NOUN
ejpam-4760	312	10	.	.	PUNCT
ejpam-4760	313	1	i.	i.	PROPN
ejpam-4760	313	2	complete	complete	PROPN
ejpam-4760	313	3	bipartite	bipartite	PROPN
ejpam-4760	313	4	graph	graph	NOUN
ejpam-4760	313	5	km	km	PROPN
ejpam-4760	313	6	,	,	PUNCT
ejpam-4760	313	7	n	n	NOUN
ejpam-4760	313	8	=	=	SYM
ejpam-4760	313	9	km	km	PROPN
ejpam-4760	314	1	+	+	PROPN
ejpam-4760	314	2	kn	kn	PROPN
ejpam-4760	314	3	,	,	PUNCT
ejpam-4760	314	4	m	m	PROPN
ejpam-4760	314	5	≥	≥	NOUN
ejpam-4760	314	6	2	2	NUM
ejpam-4760	314	7	and	and	CCONJ
ejpam-4760	314	8	n	n	PRON
ejpam-4760	314	9	≥	≥	NUM
ejpam-4760	314	10	2	2	NUM
ejpam-4760	314	11	.	.	X
ejpam-4760	314	12	ii	ii	PROPN
ejpam-4760	314	13	.	.	PUNCT
ejpam-4760	315	1	generalized	generalize	VERB
ejpam-4760	315	2	fan	fan	PROPN
ejpam-4760	315	3	graph	graph	PROPN
ejpam-4760	315	4	fm	fm	PROPN
ejpam-4760	315	5	,	,	PUNCT
ejpam-4760	315	6	n	n	NOUN
ejpam-4760	315	7	=	=	SYM
ejpam-4760	315	8	km	km	PROPN
ejpam-4760	315	9	+	+	CCONJ
ejpam-4760	315	10	pn	pn	PROPN
ejpam-4760	315	11	,	,	PUNCT
ejpam-4760	315	12	m	m	VERB
ejpam-4760	315	13	≥	≥	NOUN
ejpam-4760	315	14	2	2	NUM
ejpam-4760	315	15	and	and	CCONJ
ejpam-4760	315	16	n	n	PRON
ejpam-4760	315	17	≥	≥	NOUN
ejpam-4760	315	18	4	4	NUM
ejpam-4760	315	19	iii	iii	NOUN
ejpam-4760	315	20	.	.	NOUN
ejpam-4760	315	21	generalized	generalize	VERB
ejpam-4760	315	22	wheel	wheel	NOUN
ejpam-4760	315	23	graph	graph	NOUN
ejpam-4760	315	24	wm	wm	PROPN
ejpam-4760	315	25	,	,	PUNCT
ejpam-4760	315	26	n	n	NOUN
ejpam-4760	315	27	=	=	SYM
ejpam-4760	315	28	km	km	PROPN
ejpam-4760	315	29	+	+	CCONJ
ejpam-4760	315	30	cn	cn	PROPN
ejpam-4760	315	31	,	,	PUNCT
ejpam-4760	315	32	m	m	PROPN
ejpam-4760	315	33	≥	≥	NOUN
ejpam-4760	315	34	2	2	NUM
ejpam-4760	315	35	and	and	CCONJ
ejpam-4760	315	36	n	n	PRON
ejpam-4760	315	37	≥	≥	NOUN
ejpam-4760	315	38	4	4	NUM
ejpam-4760	315	39	c.	c.	PROPN
ejpam-4760	315	40	armada	armada	PROPN
ejpam-4760	315	41	,	,	PUNCT
ejpam-4760	315	42	j.	j.	PROPN
ejpam-4760	315	43	hamja	hamja	PROPN
ejpam-4760	315	44	/	/	SYM
ejpam-4760	315	45	eur	eur	PROPN
ejpam-4760	315	46	.	.	PUNCT
ejpam-4760	316	1	j.	j.	PROPN
ejpam-4760	316	2	pure	pure	PROPN
ejpam-4760	316	3	appl	appl	PROPN
ejpam-4760	316	4	.	.	PROPN
ejpam-4760	316	5	math	math	PROPN
ejpam-4760	316	6	,	,	PUNCT
ejpam-4760	316	7	16	16	NUM
ejpam-4760	316	8	(	(	PUNCT
ejpam-4760	316	9	2	2	NUM
ejpam-4760	316	10	)	)	PUNCT
ejpam-4760	316	11	(	(	PUNCT
ejpam-4760	316	12	2023	2023	NUM
ejpam-4760	316	13	)	)	PUNCT
ejpam-4760	316	14	,	,	PUNCT
ejpam-4760	316	15	1326	1326	NUM
ejpam-4760	316	16	-	-	SYM
ejpam-4760	316	17	1341	1341	NUM
ejpam-4760	316	18	1337	1337	NUM
ejpam-4760	316	19	5	5	NUM
ejpam-4760	316	20	.	.	PUNCT
ejpam-4760	317	1	the	the	DET
ejpam-4760	317	2	perfect	perfect	ADJ
ejpam-4760	317	3	isolate	isolate	NOUN
ejpam-4760	317	4	dominating	dominating	NOUN
ejpam-4760	317	5	set	set	VERB
ejpam-4760	317	6	in	in	ADP
ejpam-4760	317	7	the	the	DET
ejpam-4760	317	8	corona	corona	NOUN
ejpam-4760	317	9	of	of	ADP
ejpam-4760	317	10	graphs	graph	NOUN
ejpam-4760	317	11	this	this	DET
ejpam-4760	317	12	section	section	NOUN
ejpam-4760	317	13	contains	contain	VERB
ejpam-4760	317	14	results	result	NOUN
ejpam-4760	317	15	when	when	SCONJ
ejpam-4760	317	16	the	the	DET
ejpam-4760	317	17	corona	corona	NOUN
ejpam-4760	317	18	g	g	PROPN
ejpam-4760	318	1	+	+	CCONJ
ejpam-4760	318	2	h	h	NOUN
ejpam-4760	318	3	has	have	VERB
ejpam-4760	318	4	a	a	DET
ejpam-4760	318	5	γp0	γp0	NOUN
ejpam-4760	318	6	-	-	PUNCT
ejpam-4760	318	7	set	set	VERB
ejpam-4760	318	8	or	or	CCONJ
ejpam-4760	318	9	has	have	VERB
ejpam-4760	318	10	no	no	DET
ejpam-4760	318	11	γp0	γp0	NOUN
ejpam-4760	318	12	-	-	PUNCT
ejpam-4760	318	13	set	set	VERB
ejpam-4760	318	14	and	and	CCONJ
ejpam-4760	318	15	its	its	PRON
ejpam-4760	318	16	perfect	perfect	ADJ
ejpam-4760	318	17	isolate	isolate	NOUN
ejpam-4760	318	18	domination	domination	NOUN
ejpam-4760	318	19	number	number	NOUN
ejpam-4760	318	20	.	.	PUNCT
ejpam-4760	319	1	the	the	DET
ejpam-4760	319	2	corona	corona	NOUN
ejpam-4760	319	3	of	of	ADP
ejpam-4760	319	4	graphs	graph	NOUN
ejpam-4760	319	5	g	g	PROPN
ejpam-4760	319	6	and	and	CCONJ
ejpam-4760	319	7	h	h	NOUN
ejpam-4760	319	8	,	,	PUNCT
ejpam-4760	319	9	g	g	PROPN
ejpam-4760	319	10	◦	◦	NOUN
ejpam-4760	319	11	h	h	NOUN
ejpam-4760	319	12	,	,	PUNCT
ejpam-4760	319	13	is	be	AUX
ejpam-4760	319	14	the	the	DET
ejpam-4760	319	15	graph	graph	NOUN
ejpam-4760	319	16	obtained	obtain	VERB
ejpam-4760	319	17	by	by	ADP
ejpam-4760	319	18	taking	take	VERB
ejpam-4760	319	19	one	one	NUM
ejpam-4760	319	20	copy	copy	NOUN
ejpam-4760	319	21	of	of	ADP
ejpam-4760	319	22	g	g	PROPN
ejpam-4760	319	23	and	and	CCONJ
ejpam-4760	319	24	|v	|v	PROPN
ejpam-4760	319	25	(	(	PUNCT
ejpam-4760	319	26	g)|	g)|	NOUN
ejpam-4760	319	27	copies	copy	NOUN
ejpam-4760	319	28	of	of	ADP
ejpam-4760	319	29	h	h	NOUN
ejpam-4760	319	30	,	,	PUNCT
ejpam-4760	319	31	and	and	CCONJ
ejpam-4760	319	32	then	then	ADV
ejpam-4760	319	33	joining	join	VERB
ejpam-4760	319	34	the	the	DET
ejpam-4760	319	35	ith	ith	PROPN
ejpam-4760	319	36	vertex	vertex	NOUN
ejpam-4760	319	37	of	of	ADP
ejpam-4760	319	38	g	g	NOUN
ejpam-4760	319	39	to	to	ADP
ejpam-4760	319	40	every	every	DET
ejpam-4760	319	41	vertex	vertex	NOUN
ejpam-4760	319	42	of	of	ADP
ejpam-4760	319	43	the	the	DET
ejpam-4760	319	44	ith	ith	PROPN
ejpam-4760	319	45	copy	copy	NOUN
ejpam-4760	319	46	of	of	ADP
ejpam-4760	319	47	h.	h.	PROPN
ejpam-4760	319	48	for	for	ADP
ejpam-4760	319	49	every	every	DET
ejpam-4760	319	50	v	v	NUM
ejpam-4760	319	51	∈	∈	PROPN
ejpam-4760	319	52	v	v	NOUN
ejpam-4760	319	53	(	(	PUNCT
ejpam-4760	319	54	g	g	NOUN
ejpam-4760	319	55	)	)	PUNCT
ejpam-4760	319	56	,	,	PUNCT
ejpam-4760	319	57	denote	denote	VERB
ejpam-4760	319	58	by	by	ADP
ejpam-4760	319	59	hv	hv	PROPN
ejpam-4760	319	60	the	the	DET
ejpam-4760	319	61	copy	copy	NOUN
ejpam-4760	319	62	of	of	ADP
ejpam-4760	319	63	h	h	NOUN
ejpam-4760	319	64	whose	whose	DET
ejpam-4760	319	65	vertices	vertex	NOUN
ejpam-4760	319	66	are	be	AUX
ejpam-4760	319	67	attached	attach	VERB
ejpam-4760	319	68	one	one	NUM
ejpam-4760	319	69	by	by	ADP
ejpam-4760	319	70	one	one	NUM
ejpam-4760	319	71	to	to	ADP
ejpam-4760	319	72	the	the	DET
ejpam-4760	319	73	vertex	vertex	NOUN
ejpam-4760	319	74	v.	v.	ADP
ejpam-4760	319	75	subsequently	subsequently	ADV
ejpam-4760	319	76	,	,	PUNCT
ejpam-4760	319	77	denote	denote	VERB
ejpam-4760	319	78	by	by	ADP
ejpam-4760	319	79	v	v	PRON
ejpam-4760	319	80	+	+	CCONJ
ejpam-4760	319	81	hv	hv	NOUN
ejpam-4760	319	82	the	the	DET
ejpam-4760	319	83	subgraph	subgraph	NOUN
ejpam-4760	319	84	of	of	ADP
ejpam-4760	319	85	the	the	DET
ejpam-4760	319	86	corona	corona	NOUN
ejpam-4760	319	87	g	g	PROPN
ejpam-4760	319	88	◦	◦	NOUN
ejpam-4760	319	89	h	h	NOUN
ejpam-4760	319	90	corresponding	correspond	VERB
ejpam-4760	319	91	to	to	ADP
ejpam-4760	319	92	the	the	DET
ejpam-4760	319	93	join	join	NOUN
ejpam-4760	319	94	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4760	319	95	,	,	PUNCT
ejpam-4760	319	96	v	v	PROPN
ejpam-4760	319	97	∈	∈	PROPN
ejpam-4760	319	98	v	v	NOUN
ejpam-4760	319	99	(	(	PUNCT
ejpam-4760	319	100	g	g	NOUN
ejpam-4760	319	101	)	)	PUNCT
ejpam-4760	319	102	,	,	PUNCT
ejpam-4760	319	103	harary	harary	NOUN
ejpam-4760	319	104	in	in	ADP
ejpam-4760	319	105	[	[	X
ejpam-4760	319	106	7	7	NUM
ejpam-4760	319	107	]	]	PUNCT
ejpam-4760	319	108	.	.	PUNCT
ejpam-4760	320	1	theorem	theorem	ADJ
ejpam-4760	320	2	10	10	NUM
ejpam-4760	320	3	.	.	PUNCT
ejpam-4760	321	1	let	let	VERB
ejpam-4760	321	2	g	g	PRON
ejpam-4760	321	3	be	be	AUX
ejpam-4760	321	4	a	a	DET
ejpam-4760	321	5	connected	connected	ADJ
ejpam-4760	321	6	graph	graph	NOUN
ejpam-4760	321	7	and	and	CCONJ
ejpam-4760	321	8	h	h	NOUN
ejpam-4760	321	9	be	be	AUX
ejpam-4760	321	10	any	any	DET
ejpam-4760	321	11	graph	graph	NOUN
ejpam-4760	321	12	.	.	PUNCT
ejpam-4760	322	1	then	then	ADV
ejpam-4760	322	2	a	a	DET
ejpam-4760	322	3	subset	subset	NOUN
ejpam-4760	322	4	s	s	X
ejpam-4760	322	5	of	of	ADP
ejpam-4760	322	6	v	v	NOUN
ejpam-4760	322	7	(	(	PUNCT
ejpam-4760	322	8	g	g	PROPN
ejpam-4760	322	9	◦	◦	NOUN
ejpam-4760	322	10	h	h	NOUN
ejpam-4760	322	11	)	)	PUNCT
ejpam-4760	322	12	is	be	AUX
ejpam-4760	322	13	a	a	DET
ejpam-4760	322	14	perfect	perfect	ADJ
ejpam-4760	322	15	isolate	isolate	NOUN
ejpam-4760	322	16	dominating	dominating	NOUN
ejpam-4760	322	17	set	set	NOUN
ejpam-4760	322	18	of	of	ADP
ejpam-4760	322	19	g	g	PROPN
ejpam-4760	322	20	◦	◦	NOUN
ejpam-4760	322	21	h	h	NOUN
ejpam-4760	322	22	if	if	SCONJ
ejpam-4760	323	1	and	and	CCONJ
ejpam-4760	323	2	only	only	ADV
ejpam-4760	323	3	if	if	SCONJ
ejpam-4760	323	4	for	for	ADP
ejpam-4760	323	5	every	every	DET
ejpam-4760	323	6	v	v	NUM
ejpam-4760	323	7	∈	∈	NOUN
ejpam-4760	323	8	v	v	NOUN
ejpam-4760	323	9	(	(	PUNCT
ejpam-4760	323	10	g	g	NOUN
ejpam-4760	323	11	)	)	PUNCT
ejpam-4760	323	12	,	,	PUNCT
ejpam-4760	323	13	s	s	VERB
ejpam-4760	323	14	=	=	PUNCT
ejpam-4760	323	15	⋃	⋃	NOUN
ejpam-4760	323	16	v∈v	v∈v	NOUN
ejpam-4760	323	17	(	(	PUNCT
ejpam-4760	323	18	g	g	NOUN
ejpam-4760	323	19	)	)	PUNCT
ejpam-4760	323	20	sv	sv	PROPN
ejpam-4760	323	21	where	where	SCONJ
ejpam-4760	323	22	sv	sv	PROPN
ejpam-4760	323	23	is	be	AUX
ejpam-4760	323	24	a	a	DET
ejpam-4760	323	25	minimal	minimal	ADJ
ejpam-4760	323	26	dominating	dominating	NOUN
ejpam-4760	323	27	set	set	NOUN
ejpam-4760	323	28	of	of	ADP
ejpam-4760	323	29	hv	hv	PROPN
ejpam-4760	323	30	and	and	CCONJ
ejpam-4760	323	31	γ(h	γ(h	NOUN
ejpam-4760	323	32	)	)	PUNCT
ejpam-4760	323	33	=	=	SYM
ejpam-4760	324	1	1	1	X
ejpam-4760	324	2	.	.	PUNCT
ejpam-4760	324	3	proof	proof	NOUN
ejpam-4760	324	4	.	.	PUNCT
ejpam-4760	325	1	let	let	VERB
ejpam-4760	325	2	s	s	PRON
ejpam-4760	325	3	be	be	AUX
ejpam-4760	325	4	a	a	DET
ejpam-4760	325	5	perfect	perfect	ADJ
ejpam-4760	325	6	isolate	isolate	NOUN
ejpam-4760	325	7	dominating	dominating	NOUN
ejpam-4760	325	8	set	set	NOUN
ejpam-4760	325	9	of	of	ADP
ejpam-4760	325	10	g	g	PROPN
ejpam-4760	325	11	◦	◦	PROPN
ejpam-4760	325	12	h.	h.	PROPN
ejpam-4760	325	13	suppose	suppose	VERB
ejpam-4760	325	14	that	that	SCONJ
ejpam-4760	325	15	s	s	VERB
ejpam-4760	325	16	=	=	SYM
ejpam-4760	325	17	v	v	X
ejpam-4760	325	18	(	(	PUNCT
ejpam-4760	325	19	g	g	NOUN
ejpam-4760	325	20	)	)	PUNCT
ejpam-4760	325	21	.	.	PUNCT
ejpam-4760	326	1	clearly	clearly	ADV
ejpam-4760	326	2	,	,	PUNCT
ejpam-4760	326	3	s	s	VERB
ejpam-4760	326	4	is	be	AUX
ejpam-4760	326	5	a	a	DET
ejpam-4760	326	6	perfect	perfect	ADJ
ejpam-4760	326	7	dominating	dominating	NOUN
ejpam-4760	326	8	set	set	NOUN
ejpam-4760	326	9	since	since	SCONJ
ejpam-4760	326	10	n	n	PRON
ejpam-4760	326	11	[	[	X
ejpam-4760	326	12	s	s	X
ejpam-4760	326	13	]	]	X
ejpam-4760	326	14	=	=	SYM
ejpam-4760	326	15	v	v	NOUN
ejpam-4760	326	16	(	(	PUNCT
ejpam-4760	326	17	g	g	PROPN
ejpam-4760	326	18	◦	◦	NOUN
ejpam-4760	326	19	h	h	NOUN
ejpam-4760	326	20	)	)	PUNCT
ejpam-4760	326	21	and	and	CCONJ
ejpam-4760	326	22	every	every	DET
ejpam-4760	326	23	vertex	vertex	NOUN
ejpam-4760	326	24	in	in	ADP
ejpam-4760	326	25	v	v	PROPN
ejpam-4760	326	26	(	(	PUNCT
ejpam-4760	326	27	hv	hv	X
ejpam-4760	326	28	)	)	PUNCT
ejpam-4760	326	29	is	be	AUX
ejpam-4760	326	30	dominated	dominate	VERB
ejpam-4760	326	31	by	by	ADP
ejpam-4760	326	32	exactly	exactly	ADV
ejpam-4760	326	33	one	one	NUM
ejpam-4760	326	34	vertex	vertex	NOUN
ejpam-4760	326	35	v	v	ADP
ejpam-4760	326	36	∈	∈	NOUN
ejpam-4760	326	37	v	v	NOUN
ejpam-4760	326	38	(	(	PUNCT
ejpam-4760	326	39	g	g	NOUN
ejpam-4760	326	40	)	)	PUNCT
ejpam-4760	326	41	but	but	CCONJ
ejpam-4760	326	42	s	s	NOUN
ejpam-4760	326	43	is	be	AUX
ejpam-4760	326	44	not	not	PART
ejpam-4760	326	45	an	an	DET
ejpam-4760	326	46	isolate	isolate	NOUN
ejpam-4760	326	47	dominating	dominating	NOUN
ejpam-4760	326	48	set	set	NOUN
ejpam-4760	326	49	since	since	SCONJ
ejpam-4760	326	50	g	g	PROPN
ejpam-4760	326	51	is	be	AUX
ejpam-4760	326	52	connected	connect	VERB
ejpam-4760	326	53	,	,	PUNCT
ejpam-4760	326	54	a	a	DET
ejpam-4760	326	55	contradiction	contradiction	NOUN
ejpam-4760	326	56	.	.	PUNCT
ejpam-4760	327	1	hence	hence	ADV
ejpam-4760	327	2	,	,	PUNCT
ejpam-4760	327	3	s	s	VERB
ejpam-4760	327	4	̸=	̸=	PROPN
ejpam-4760	327	5	v	v	NOUN
ejpam-4760	327	6	(	(	PUNCT
ejpam-4760	327	7	g	g	NOUN
ejpam-4760	327	8	)	)	PUNCT
ejpam-4760	327	9	.	.	PUNCT
ejpam-4760	328	1	thus	thus	ADV
ejpam-4760	328	2	,	,	PUNCT
ejpam-4760	328	3	there	there	PRON
ejpam-4760	328	4	exists	exist	VERB
ejpam-4760	328	5	v	v	ADP
ejpam-4760	328	6	∈	∈	PROPN
ejpam-4760	328	7	v	v	NOUN
ejpam-4760	328	8	(	(	PUNCT
ejpam-4760	328	9	g	g	NOUN
ejpam-4760	328	10	)	)	PUNCT
ejpam-4760	328	11	⊆	⊆	NUM
ejpam-4760	328	12	v	v	NOUN
ejpam-4760	328	13	(	(	PUNCT
ejpam-4760	328	14	g	g	PROPN
ejpam-4760	328	15	◦	◦	NOUN
ejpam-4760	328	16	h	h	NOUN
ejpam-4760	328	17	)	)	PUNCT
ejpam-4760	328	18	such	such	ADJ
ejpam-4760	328	19	that	that	PRON
ejpam-4760	328	20	v	v	NOUN
ejpam-4760	328	21	/∈	/∈	PUNCT
ejpam-4760	328	22	s	s	X
ejpam-4760	328	23	,	,	PUNCT
ejpam-4760	328	24	s	s	AUX
ejpam-4760	328	25	contain	contain	VERB
ejpam-4760	328	26	a	a	DET
ejpam-4760	328	27	vertex	vertex	NOUN
ejpam-4760	328	28	or	or	CCONJ
ejpam-4760	328	29	vertices	vertex	NOUN
ejpam-4760	328	30	that	that	PRON
ejpam-4760	328	31	dominates	dominate	VERB
ejpam-4760	328	32	hv	hv	PRON
ejpam-4760	328	33	.	.	PUNCT
ejpam-4760	329	1	let	let	VERB
ejpam-4760	329	2	sv	sv	INTJ
ejpam-4760	329	3	be	be	AUX
ejpam-4760	329	4	a	a	DET
ejpam-4760	329	5	dominating	dominating	NOUN
ejpam-4760	329	6	set	set	NOUN
ejpam-4760	329	7	of	of	ADP
ejpam-4760	329	8	hv	hv	PROPN
ejpam-4760	329	9	and	and	CCONJ
ejpam-4760	329	10	sv	sv	PROPN
ejpam-4760	330	1	⊆	⊆	NUM
ejpam-4760	330	2	s.	s.	PROPN
ejpam-4760	330	3	also	also	ADV
ejpam-4760	330	4	,	,	PUNCT
ejpam-4760	330	5	suppose	suppose	VERB
ejpam-4760	330	6	that	that	SCONJ
ejpam-4760	330	7	there	there	PRON
ejpam-4760	330	8	exists	exist	VERB
ejpam-4760	330	9	y	y	PROPN
ejpam-4760	330	10	∈	∈	PROPN
ejpam-4760	330	11	v	v	ADP
ejpam-4760	330	12	(	(	PUNCT
ejpam-4760	330	13	g	g	NOUN
ejpam-4760	330	14	)	)	PUNCT
ejpam-4760	330	15	such	such	ADJ
ejpam-4760	330	16	that	that	SCONJ
ejpam-4760	330	17	y	y	PROPN
ejpam-4760	330	18	∈	∈	PROPN
ejpam-4760	330	19	s	s	PART
ejpam-4760	330	20	and	and	CCONJ
ejpam-4760	330	21	vy	vy	PROPN
ejpam-4760	330	22	∈	∈	PROPN
ejpam-4760	330	23	e(g	e(g	PROPN
ejpam-4760	330	24	)	)	PUNCT
ejpam-4760	330	25	⊆	⊆	NUM
ejpam-4760	330	26	e(g	e(g	PROPN
ejpam-4760	330	27	◦	◦	NOUN
ejpam-4760	330	28	h	h	NOUN
ejpam-4760	330	29	)	)	PUNCT
ejpam-4760	330	30	.	.	PUNCT
ejpam-4760	331	1	clearly	clearly	ADV
ejpam-4760	331	2	,	,	PUNCT
ejpam-4760	331	3	v	v	PROPN
ejpam-4760	331	4	∈	∈	PROPN
ejpam-4760	331	5	v	v	NOUN
ejpam-4760	331	6	(	(	PUNCT
ejpam-4760	331	7	g	g	PROPN
ejpam-4760	331	8	◦	◦	NOUN
ejpam-4760	331	9	h	h	NOUN
ejpam-4760	331	10	)	)	PUNCT
ejpam-4760	331	11	\	\	PROPN
ejpam-4760	332	1	s	s	PART
ejpam-4760	332	2	is	be	AUX
ejpam-4760	332	3	dominated	dominate	VERB
ejpam-4760	332	4	by	by	ADP
ejpam-4760	332	5	y	y	PROPN
ejpam-4760	332	6	and	and	CCONJ
ejpam-4760	332	7	a	a	DET
ejpam-4760	332	8	vertex	vertex	NOUN
ejpam-4760	332	9	in	in	ADP
ejpam-4760	332	10	sv	sv	PROPN
ejpam-4760	332	11	,	,	PUNCT
ejpam-4760	332	12	a	a	DET
ejpam-4760	332	13	contradiction	contradiction	NOUN
ejpam-4760	332	14	since	since	SCONJ
ejpam-4760	332	15	s	s	NOUN
ejpam-4760	332	16	is	be	AUX
ejpam-4760	332	17	a	a	DET
ejpam-4760	332	18	perfect	perfect	ADJ
ejpam-4760	332	19	dominating	dominating	NOUN
ejpam-4760	332	20	set	set	NOUN
ejpam-4760	332	21	.	.	PUNCT
ejpam-4760	333	1	since	since	SCONJ
ejpam-4760	333	2	y	y	PROPN
ejpam-4760	333	3	is	be	AUX
ejpam-4760	333	4	arbitrary	arbitrary	ADJ
ejpam-4760	333	5	,	,	PUNCT
ejpam-4760	333	6	for	for	ADP
ejpam-4760	333	7	all	all	DET
ejpam-4760	333	8	y	y	PROPN
ejpam-4760	333	9	∈	∈	PROPN
ejpam-4760	333	10	v	v	NOUN
ejpam-4760	333	11	(	(	PUNCT
ejpam-4760	333	12	g	g	NOUN
ejpam-4760	333	13	)	)	PUNCT
ejpam-4760	333	14	,	,	PUNCT
ejpam-4760	333	15	y	y	PROPN
ejpam-4760	333	16	must	must	AUX
ejpam-4760	333	17	not	not	PART
ejpam-4760	333	18	be	be	AUX
ejpam-4760	333	19	an	an	DET
ejpam-4760	333	20	element	element	NOUN
ejpam-4760	333	21	in	in	ADP
ejpam-4760	333	22	s	s	PROPN
ejpam-4760	333	23	,	,	PUNCT
ejpam-4760	333	24	that	that	ADV
ejpam-4760	333	25	is	is	ADV
ejpam-4760	333	26	,	,	PUNCT
ejpam-4760	333	27	s	s	VERB
ejpam-4760	333	28	must	must	AUX
ejpam-4760	333	29	not	not	PART
ejpam-4760	333	30	contain	contain	VERB
ejpam-4760	333	31	a	a	DET
ejpam-4760	333	32	vertex	vertex	NOUN
ejpam-4760	333	33	in	in	ADP
ejpam-4760	333	34	v	v	NOUN
ejpam-4760	333	35	(	(	PUNCT
ejpam-4760	333	36	g	g	NOUN
ejpam-4760	333	37	)	)	PUNCT
ejpam-4760	333	38	.	.	PUNCT
ejpam-4760	334	1	hence	hence	ADV
ejpam-4760	334	2	,	,	PUNCT
ejpam-4760	334	3	s	s	PART
ejpam-4760	334	4	=	=	SYM
ejpam-4760	334	5	∪v∈v	∪v∈v	X
ejpam-4760	334	6	(	(	PUNCT
ejpam-4760	334	7	g)sv	g)sv	PROPN
ejpam-4760	334	8	such	such	ADJ
ejpam-4760	334	9	that	that	SCONJ
ejpam-4760	334	10	sv	sv	PROPN
ejpam-4760	334	11	is	be	AUX
ejpam-4760	334	12	a	a	DET
ejpam-4760	334	13	dominating	dominating	NOUN
ejpam-4760	334	14	set	set	VERB
ejpam-4760	334	15	in	in	ADP
ejpam-4760	334	16	hv	hv	PROPN
ejpam-4760	334	17	.	.	PUNCT
ejpam-4760	334	18	suppose	suppose	VERB
ejpam-4760	334	19	that	that	SCONJ
ejpam-4760	334	20	sv	sv	PROPN
ejpam-4760	334	21	contains	contain	VERB
ejpam-4760	334	22	two	two	NUM
ejpam-4760	334	23	or	or	CCONJ
ejpam-4760	334	24	more	more	ADJ
ejpam-4760	334	25	vertices	vertex	NOUN
ejpam-4760	334	26	,	,	PUNCT
ejpam-4760	334	27	say	say	VERB
ejpam-4760	334	28	x	x	PUNCT
ejpam-4760	334	29	and	and	CCONJ
ejpam-4760	334	30	z	z	NOUN
ejpam-4760	334	31	,	,	PUNCT
ejpam-4760	334	32	where	where	SCONJ
ejpam-4760	334	33	x	x	X
ejpam-4760	334	34	,	,	PUNCT
ejpam-4760	334	35	z	z	PROPN
ejpam-4760	334	36	∈	∈	PROPN
ejpam-4760	334	37	v	v	ADP
ejpam-4760	334	38	(	(	PUNCT
ejpam-4760	334	39	hv	hv	PROPN
ejpam-4760	334	40	)	)	PUNCT
ejpam-4760	334	41	.	.	PUNCT
ejpam-4760	335	1	thus	thus	ADV
ejpam-4760	335	2	,	,	PUNCT
ejpam-4760	335	3	v	v	PROPN
ejpam-4760	335	4	∈	∈	PROPN
ejpam-4760	335	5	v	v	NOUN
ejpam-4760	335	6	(	(	PUNCT
ejpam-4760	335	7	g	g	PROPN
ejpam-4760	335	8	◦	◦	NOUN
ejpam-4760	335	9	h	h	NOUN
ejpam-4760	335	10	)	)	PUNCT
ejpam-4760	335	11	\	\	PROPN
ejpam-4760	336	1	s	s	PART
ejpam-4760	336	2	is	be	AUX
ejpam-4760	336	3	dominated	dominate	VERB
ejpam-4760	336	4	by	by	ADP
ejpam-4760	336	5	x	x	PUNCT
ejpam-4760	336	6	and	and	CCONJ
ejpam-4760	336	7	z	z	PROPN
ejpam-4760	336	8	in	in	ADP
ejpam-4760	336	9	sv	sv	PROPN
ejpam-4760	336	10	⊆	⊆	NUM
ejpam-4760	336	11	s	s	PROPN
ejpam-4760	336	12	,	,	PUNCT
ejpam-4760	336	13	a	a	DET
ejpam-4760	336	14	contradiction	contradiction	NOUN
ejpam-4760	336	15	since	since	SCONJ
ejpam-4760	336	16	s	s	NOUN
ejpam-4760	336	17	is	be	AUX
ejpam-4760	336	18	a	a	DET
ejpam-4760	336	19	perfect	perfect	ADJ
ejpam-4760	336	20	dominating	dominating	NOUN
ejpam-4760	336	21	set	set	NOUN
ejpam-4760	336	22	.	.	PUNCT
ejpam-4760	337	1	thus	thus	ADV
ejpam-4760	337	2	,	,	PUNCT
ejpam-4760	337	3	|sv|	|sv|	PROPN
ejpam-4760	337	4	=	=	SYM
ejpam-4760	337	5	1	1	NUM
ejpam-4760	337	6	,	,	PUNCT
ejpam-4760	337	7	and	and	CCONJ
ejpam-4760	337	8	so	so	ADV
ejpam-4760	337	9	,	,	PUNCT
ejpam-4760	337	10	sv	sv	PROPN
ejpam-4760	337	11	is	be	AUX
ejpam-4760	337	12	a	a	DET
ejpam-4760	337	13	minimal	minimal	ADJ
ejpam-4760	337	14	dominating	dominating	NOUN
ejpam-4760	337	15	set	set	NOUN
ejpam-4760	337	16	of	of	ADP
ejpam-4760	337	17	hv	hv	PROPN
ejpam-4760	337	18	and	and	CCONJ
ejpam-4760	337	19	γ(h	γ(h	NOUN
ejpam-4760	337	20	)	)	PUNCT
ejpam-4760	337	21	=	=	SYM
ejpam-4760	338	1	1	1	X
ejpam-4760	338	2	.	.	PUNCT
ejpam-4760	338	3	conversely	conversely	ADV
ejpam-4760	338	4	,	,	PUNCT
ejpam-4760	338	5	suppose	suppose	VERB
ejpam-4760	338	6	that	that	SCONJ
ejpam-4760	338	7	for	for	ADP
ejpam-4760	338	8	every	every	DET
ejpam-4760	338	9	v	v	NUM
ejpam-4760	338	10	∈	∈	NOUN
ejpam-4760	338	11	v	v	NOUN
ejpam-4760	338	12	(	(	PUNCT
ejpam-4760	338	13	g	g	NOUN
ejpam-4760	338	14	)	)	PUNCT
ejpam-4760	338	15	,	,	PUNCT
ejpam-4760	338	16	s	s	VERB
ejpam-4760	338	17	=	=	SYM
ejpam-4760	338	18	∪v∈v	∪v∈v	X
ejpam-4760	338	19	(	(	PUNCT
ejpam-4760	338	20	g)sv	g)sv	PROPN
ejpam-4760	338	21	where	where	SCONJ
ejpam-4760	338	22	sv	sv	PROPN
ejpam-4760	338	23	is	be	AUX
ejpam-4760	338	24	a	a	DET
ejpam-4760	338	25	minimal	minimal	ADJ
ejpam-4760	338	26	dominating	dominating	NOUN
ejpam-4760	338	27	set	set	NOUN
ejpam-4760	338	28	of	of	ADP
ejpam-4760	338	29	hv	hv	PROPN
ejpam-4760	338	30	and	and	CCONJ
ejpam-4760	338	31	γ(h	γ(h	NOUN
ejpam-4760	338	32	)	)	PUNCT
ejpam-4760	338	33	=	=	SYM
ejpam-4760	339	1	1	1	X
ejpam-4760	339	2	.	.	PUNCT
ejpam-4760	339	3	clearly	clearly	ADV
ejpam-4760	339	4	,	,	PUNCT
ejpam-4760	339	5	n	n	PROPN
ejpam-4760	339	6	[	[	X
ejpam-4760	339	7	s	s	X
ejpam-4760	339	8	]	]	X
ejpam-4760	339	9	=	=	SYM
ejpam-4760	339	10	v	v	NOUN
ejpam-4760	339	11	(	(	PUNCT
ejpam-4760	339	12	g	g	PROPN
ejpam-4760	339	13	◦	◦	NOUN
ejpam-4760	339	14	h	h	NOUN
ejpam-4760	339	15	)	)	PUNCT
ejpam-4760	339	16	and	and	CCONJ
ejpam-4760	339	17	for	for	ADP
ejpam-4760	339	18	every	every	DET
ejpam-4760	339	19	vertex	vertex	NOUN
ejpam-4760	339	20	v	v	ADP
ejpam-4760	339	21	∈	∈	NOUN
ejpam-4760	339	22	v	v	NOUN
ejpam-4760	339	23	(	(	PUNCT
ejpam-4760	339	24	g	g	NOUN
ejpam-4760	339	25	)	)	PUNCT
ejpam-4760	339	26	=	=	NOUN
ejpam-4760	339	27	v	v	NOUN
ejpam-4760	339	28	(	(	PUNCT
ejpam-4760	339	29	g	g	PROPN
ejpam-4760	339	30	◦	◦	NOUN
ejpam-4760	339	31	h	h	NOUN
ejpam-4760	339	32	)	)	PUNCT
ejpam-4760	339	33	\	\	PROPN
ejpam-4760	340	1	s	s	X
ejpam-4760	340	2	,	,	PUNCT
ejpam-4760	340	3	v	v	NOUN
ejpam-4760	340	4	is	be	AUX
ejpam-4760	340	5	dominated	dominate	VERB
ejpam-4760	340	6	by	by	ADP
ejpam-4760	340	7	exactly	exactly	ADV
ejpam-4760	340	8	one	one	NUM
ejpam-4760	340	9	vertex	vertex	NOUN
ejpam-4760	340	10	in	in	ADP
ejpam-4760	340	11	sv	sv	PROPN
ejpam-4760	340	12	⊆	⊆	NUM
ejpam-4760	340	13	s.	s.	PROPN
ejpam-4760	340	14	thus	thus	ADV
ejpam-4760	340	15	,	,	PUNCT
ejpam-4760	340	16	s	s	VERB
ejpam-4760	340	17	is	be	AUX
ejpam-4760	340	18	a	a	DET
ejpam-4760	340	19	perfect	perfect	ADJ
ejpam-4760	340	20	dominating	dominating	NOUN
ejpam-4760	340	21	set	set	NOUN
ejpam-4760	340	22	.	.	PUNCT
ejpam-4760	341	1	also	also	ADV
ejpam-4760	341	2	,	,	PUNCT
ejpam-4760	341	3	since	since	SCONJ
ejpam-4760	341	4	any	any	DET
ejpam-4760	341	5	two	two	NUM
ejpam-4760	341	6	vertices	vertex	NOUN
ejpam-4760	341	7	in	in	ADP
ejpam-4760	341	8	s	s	PROPN
ejpam-4760	341	9	is	be	AUX
ejpam-4760	341	10	not	not	PART
ejpam-4760	341	11	adjacent	adjacent	ADJ
ejpam-4760	341	12	in	in	ADP
ejpam-4760	341	13	g	g	PROPN
ejpam-4760	341	14	◦	◦	NOUN
ejpam-4760	341	15	h	h	NOUN
ejpam-4760	341	16	,	,	PUNCT
ejpam-4760	341	17	⟨s⟩	⟨s⟩	PROPN
ejpam-4760	341	18	has	have	AUX
ejpam-4760	341	19	isolated	isolate	VERB
ejpam-4760	341	20	vertices	vertex	NOUN
ejpam-4760	341	21	.	.	PUNCT
ejpam-4760	342	1	thus	thus	ADV
ejpam-4760	342	2	,	,	PUNCT
ejpam-4760	342	3	s	s	X
ejpam-4760	342	4	is	be	AUX
ejpam-4760	342	5	also	also	ADV
ejpam-4760	342	6	an	an	DET
ejpam-4760	342	7	isolate	isolate	ADJ
ejpam-4760	342	8	dominating	dominating	NOUN
ejpam-4760	342	9	set	set	NOUN
ejpam-4760	342	10	.	.	PUNCT
ejpam-4760	343	1	therefore	therefore	ADV
ejpam-4760	343	2	,	,	PUNCT
ejpam-4760	343	3	s	s	VERB
ejpam-4760	343	4	⊆	⊆	NUM
ejpam-4760	343	5	v	v	NOUN
ejpam-4760	343	6	(	(	PUNCT
ejpam-4760	343	7	g	g	PROPN
ejpam-4760	343	8	◦	◦	NOUN
ejpam-4760	343	9	h	h	NOUN
ejpam-4760	343	10	)	)	PUNCT
ejpam-4760	343	11	is	be	AUX
ejpam-4760	343	12	a	a	DET
ejpam-4760	343	13	perfect	perfect	ADJ
ejpam-4760	343	14	isolate	isolate	NOUN
ejpam-4760	343	15	dominating	dominating	NOUN
ejpam-4760	343	16	set	set	NOUN
ejpam-4760	343	17	of	of	ADP
ejpam-4760	343	18	g	g	PROPN
ejpam-4760	343	19	◦	◦	PROPN
ejpam-4760	343	20	h.	h.	NOUN
ejpam-4760	343	21	the	the	DET
ejpam-4760	343	22	next	next	ADJ
ejpam-4760	343	23	two	two	NUM
ejpam-4760	343	24	results	result	NOUN
ejpam-4760	343	25	follow	follow	VERB
ejpam-4760	343	26	from	from	ADP
ejpam-4760	343	27	theorem	theorem	ADJ
ejpam-4760	343	28	10	10	NUM
ejpam-4760	343	29	.	.	PUNCT
ejpam-4760	343	30	corollary	corollary	ADJ
ejpam-4760	343	31	7	7	NUM
ejpam-4760	343	32	.	.	PUNCT
ejpam-4760	344	1	let	let	VERB
ejpam-4760	344	2	g	g	PRON
ejpam-4760	344	3	be	be	AUX
ejpam-4760	344	4	a	a	DET
ejpam-4760	344	5	connected	connected	ADJ
ejpam-4760	344	6	graph	graph	NOUN
ejpam-4760	344	7	of	of	ADP
ejpam-4760	344	8	order	order	NOUN
ejpam-4760	344	9	n	n	NOUN
ejpam-4760	345	1	and	and	CCONJ
ejpam-4760	345	2	h	h	NOUN
ejpam-4760	345	3	be	be	AUX
ejpam-4760	345	4	any	any	DET
ejpam-4760	345	5	graph	graph	NOUN
ejpam-4760	345	6	where	where	SCONJ
ejpam-4760	345	7	γ(h	γ(h	NOUN
ejpam-4760	345	8	)	)	PUNCT
ejpam-4760	345	9	=	=	SYM
ejpam-4760	346	1	1	1	X
ejpam-4760	346	2	.	.	X
ejpam-4760	346	3	then	then	ADV
ejpam-4760	346	4	γp0(g	γp0(g	PROPN
ejpam-4760	346	5	◦	◦	PROPN
ejpam-4760	346	6	h	h	NOUN
ejpam-4760	346	7	)	)	PUNCT
ejpam-4760	346	8	=	=	VERB
ejpam-4760	346	9	n.	n.	NOUN
ejpam-4760	346	10	corollary	corollary	NOUN
ejpam-4760	346	11	8	8	NUM
ejpam-4760	346	12	.	.	PUNCT
ejpam-4760	347	1	let	let	VERB
ejpam-4760	347	2	g	g	PRON
ejpam-4760	347	3	be	be	AUX
ejpam-4760	347	4	a	a	DET
ejpam-4760	347	5	connected	connected	ADJ
ejpam-4760	347	6	graph	graph	NOUN
ejpam-4760	347	7	and	and	CCONJ
ejpam-4760	347	8	h	h	NOUN
ejpam-4760	347	9	be	be	AUX
ejpam-4760	347	10	any	any	DET
ejpam-4760	347	11	graph	graph	NOUN
ejpam-4760	347	12	where	where	SCONJ
ejpam-4760	347	13	γ(h	γ(h	NOUN
ejpam-4760	347	14	)	)	PUNCT
ejpam-4760	347	15	≥	≥	NOUN
ejpam-4760	348	1	2	2	NUM
ejpam-4760	348	2	.	.	PUNCT
ejpam-4760	348	3	then	then	ADV
ejpam-4760	348	4	g	g	PROPN
ejpam-4760	348	5	◦	◦	NOUN
ejpam-4760	348	6	h	h	NOUN
ejpam-4760	348	7	is	be	AUX
ejpam-4760	348	8	a	a	DET
ejpam-4760	348	9	non	non	ADJ
ejpam-4760	348	10	-	-	ADJ
ejpam-4760	348	11	γp0	γp0	NOUN
ejpam-4760	348	12	-	-	PUNCT
ejpam-4760	348	13	graph	graph	NOUN
ejpam-4760	348	14	.	.	PUNCT
ejpam-4760	349	1	c.	c.	PROPN
ejpam-4760	349	2	armada	armada	PROPN
ejpam-4760	349	3	,	,	PUNCT
ejpam-4760	349	4	j.	j.	PROPN
ejpam-4760	349	5	hamja	hamja	PROPN
ejpam-4760	349	6	/	/	SYM
ejpam-4760	349	7	eur	eur	PROPN
ejpam-4760	349	8	.	.	PUNCT
ejpam-4760	350	1	j.	j.	PROPN
ejpam-4760	350	2	pure	pure	PROPN
ejpam-4760	350	3	appl	appl	PROPN
ejpam-4760	350	4	.	.	PROPN
ejpam-4760	350	5	math	math	PROPN
ejpam-4760	350	6	,	,	PUNCT
ejpam-4760	350	7	16	16	NUM
ejpam-4760	350	8	(	(	PUNCT
ejpam-4760	350	9	2	2	NUM
ejpam-4760	350	10	)	)	PUNCT
ejpam-4760	350	11	(	(	PUNCT
ejpam-4760	350	12	2023	2023	NUM
ejpam-4760	350	13	)	)	PUNCT
ejpam-4760	350	14	,	,	PUNCT
ejpam-4760	350	15	1326	1326	NUM
ejpam-4760	350	16	-	-	SYM
ejpam-4760	350	17	1341	1341	NUM
ejpam-4760	350	18	1338	1338	NUM
ejpam-4760	350	19	the	the	DET
ejpam-4760	350	20	next	next	ADJ
ejpam-4760	350	21	two	two	NUM
ejpam-4760	350	22	results	result	NOUN
ejpam-4760	350	23	follow	follow	VERB
ejpam-4760	350	24	from	from	ADP
ejpam-4760	350	25	corollary	corollary	ADJ
ejpam-4760	350	26	7	7	NUM
ejpam-4760	350	27	.	.	PUNCT
ejpam-4760	350	28	corollary	corollary	ADJ
ejpam-4760	350	29	9	9	NUM
ejpam-4760	350	30	.	.	PUNCT
ejpam-4760	351	1	let	let	VERB
ejpam-4760	351	2	g	g	PRON
ejpam-4760	351	3	be	be	AUX
ejpam-4760	351	4	a	a	DET
ejpam-4760	351	5	connected	connected	ADJ
ejpam-4760	351	6	graph	graph	NOUN
ejpam-4760	351	7	and	and	CCONJ
ejpam-4760	351	8	kn	kn	PROPN
ejpam-4760	351	9	be	be	AUX
ejpam-4760	351	10	a	a	DET
ejpam-4760	351	11	complete	complete	ADJ
ejpam-4760	351	12	graph	graph	NOUN
ejpam-4760	351	13	.	.	PUNCT
ejpam-4760	352	1	then	then	ADV
ejpam-4760	352	2	γp0(g	γp0(g	PROPN
ejpam-4760	352	3	◦	◦	PROPN
ejpam-4760	352	4	kn	kn	PROPN
ejpam-4760	352	5	)	)	PUNCT
ejpam-4760	352	6	=	=	SYM
ejpam-4760	352	7	|v	|v	PROPN
ejpam-4760	352	8	(	(	PUNCT
ejpam-4760	352	9	g)|	g)|	PROPN
ejpam-4760	352	10	.	.	PUNCT
ejpam-4760	352	11	corollary	corollary	ADJ
ejpam-4760	352	12	10	10	NUM
ejpam-4760	352	13	.	.	PUNCT
ejpam-4760	353	1	let	let	VERB
ejpam-4760	353	2	g	g	PRON
ejpam-4760	353	3	be	be	AUX
ejpam-4760	353	4	a	a	DET
ejpam-4760	353	5	connected	connected	ADJ
ejpam-4760	353	6	graph	graph	NOUN
ejpam-4760	353	7	and	and	CCONJ
ejpam-4760	353	8	h	h	NOUN
ejpam-4760	353	9	be	be	AUX
ejpam-4760	353	10	any	any	DET
ejpam-4760	353	11	graph	graph	NOUN
ejpam-4760	353	12	described	describe	VERB
ejpam-4760	353	13	in	in	ADP
ejpam-4760	353	14	corollary	corollary	ADJ
ejpam-4760	353	15	5	5	NUM
ejpam-4760	353	16	.	.	PUNCT
ejpam-4760	354	1	then	then	ADV
ejpam-4760	354	2	γp0(g	γp0(g	PROPN
ejpam-4760	354	3	◦	◦	PROPN
ejpam-4760	354	4	h	h	NOUN
ejpam-4760	354	5	)	)	PUNCT
ejpam-4760	354	6	=	=	SYM
ejpam-4760	354	7	|v	|v	PROPN
ejpam-4760	354	8	(	(	PUNCT
ejpam-4760	354	9	g)|	g)|	NOUN
ejpam-4760	354	10	.	.	PUNCT
ejpam-4760	355	1	the	the	DET
ejpam-4760	355	2	next	next	ADJ
ejpam-4760	355	3	result	result	NOUN
ejpam-4760	355	4	follows	follow	VERB
ejpam-4760	355	5	from	from	ADP
ejpam-4760	355	6	corollary	corollary	ADJ
ejpam-4760	355	7	8	8	NUM
ejpam-4760	355	8	.	.	PUNCT
ejpam-4760	356	1	corollary	corollary	ADJ
ejpam-4760	356	2	11	11	NUM
ejpam-4760	356	3	.	.	PUNCT
ejpam-4760	357	1	let	let	VERB
ejpam-4760	357	2	g	g	PRON
ejpam-4760	357	3	be	be	AUX
ejpam-4760	357	4	a	a	DET
ejpam-4760	357	5	connected	connected	ADJ
ejpam-4760	357	6	graph	graph	NOUN
ejpam-4760	357	7	and	and	CCONJ
ejpam-4760	357	8	h	h	NOUN
ejpam-4760	357	9	be	be	AUX
ejpam-4760	357	10	any	any	DET
ejpam-4760	357	11	graph	graph	NOUN
ejpam-4760	357	12	described	describe	VERB
ejpam-4760	357	13	in	in	ADP
ejpam-4760	357	14	corollary	corollary	ADJ
ejpam-4760	357	15	6	6	NUM
ejpam-4760	357	16	.	.	PUNCT
ejpam-4760	358	1	then	then	ADV
ejpam-4760	358	2	g	g	PROPN
ejpam-4760	358	3	◦	◦	NOUN
ejpam-4760	358	4	h	h	NOUN
ejpam-4760	358	5	is	be	AUX
ejpam-4760	358	6	non	non	ADJ
ejpam-4760	358	7	-	-	ADJ
ejpam-4760	358	8	γp0	γp0	NOUN
ejpam-4760	358	9	-	-	PUNCT
ejpam-4760	358	10	graphs	graph	NOUN
ejpam-4760	358	11	.	.	PUNCT
ejpam-4760	359	1	the	the	DET
ejpam-4760	359	2	next	next	ADJ
ejpam-4760	359	3	result	result	NOUN
ejpam-4760	359	4	follows	follow	VERB
ejpam-4760	359	5	from	from	ADP
ejpam-4760	359	6	corollary	corollary	ADJ
ejpam-4760	359	7	7	7	NUM
ejpam-4760	359	8	and	and	CCONJ
ejpam-4760	359	9	corollary	corollary	ADJ
ejpam-4760	359	10	8	8	NUM
ejpam-4760	359	11	.	.	PUNCT
ejpam-4760	360	1	corollary	corollary	ADJ
ejpam-4760	360	2	12	12	NUM
ejpam-4760	360	3	.	.	PUNCT
ejpam-4760	361	1	let	let	VERB
ejpam-4760	361	2	g	g	PRON
ejpam-4760	361	3	be	be	AUX
ejpam-4760	361	4	a	a	DET
ejpam-4760	361	5	connected	connected	ADJ
ejpam-4760	361	6	graph	graph	NOUN
ejpam-4760	361	7	.	.	PUNCT
ejpam-4760	362	1	then	then	ADV
ejpam-4760	362	2	for	for	ADP
ejpam-4760	362	3	n	n	PRON
ejpam-4760	362	4	≥	≥	NOUN
ejpam-4760	362	5	4	4	NUM
ejpam-4760	362	6	,	,	PUNCT
ejpam-4760	362	7	g	g	PROPN
ejpam-4760	362	8	◦	◦	NOUN
ejpam-4760	362	9	pn	pn	NOUN
ejpam-4760	362	10	and	and	CCONJ
ejpam-4760	362	11	g	g	PROPN
ejpam-4760	362	12	◦	◦	NOUN
ejpam-4760	362	13	cn	cn	PROPN
ejpam-4760	362	14	are	be	AUX
ejpam-4760	362	15	non	non	ADJ
ejpam-4760	362	16	-	-	ADJ
ejpam-4760	362	17	γp0	γp0	NOUN
ejpam-4760	362	18	-	-	PUNCT
ejpam-4760	362	19	graphs	graph	NOUN
ejpam-4760	362	20	and	and	CCONJ
ejpam-4760	362	21	for	for	ADP
ejpam-4760	362	22	n	n	X
ejpam-4760	362	23	<	<	X
ejpam-4760	362	24	4	4	NUM
ejpam-4760	362	25	,	,	PUNCT
ejpam-4760	362	26	γp0(g	γp0(g	NOUN
ejpam-4760	362	27	◦	◦	NOUN
ejpam-4760	362	28	pn	pn	NOUN
ejpam-4760	362	29	)	)	PUNCT
ejpam-4760	362	30	=	=	PUNCT
ejpam-4760	362	31	γp0(g	γp0(g	PROPN
ejpam-4760	362	32	◦	◦	PROPN
ejpam-4760	362	33	c3	c3	NOUN
ejpam-4760	362	34	)	)	PUNCT
ejpam-4760	363	1	=	=	SYM
ejpam-4760	363	2	|v	|v	PROPN
ejpam-4760	363	3	(	(	PUNCT
ejpam-4760	363	4	g)|	g)|	NOUN
ejpam-4760	363	5	.	.	PUNCT
ejpam-4760	363	6	6	6	NUM
ejpam-4760	363	7	.	.	PUNCT
ejpam-4760	364	1	the	the	DET
ejpam-4760	364	2	perfect	perfect	ADJ
ejpam-4760	364	3	isolate	isolate	NOUN
ejpam-4760	364	4	dominating	dominating	NOUN
ejpam-4760	364	5	set	set	VERB
ejpam-4760	364	6	in	in	ADP
ejpam-4760	364	7	the	the	DET
ejpam-4760	364	8	lexicographic	lexicographic	ADJ
ejpam-4760	364	9	product	product	NOUN
ejpam-4760	364	10	of	of	ADP
ejpam-4760	364	11	graphs	graph	NOUN
ejpam-4760	364	12	this	this	DET
ejpam-4760	364	13	section	section	NOUN
ejpam-4760	364	14	contains	contain	VERB
ejpam-4760	364	15	results	result	NOUN
ejpam-4760	364	16	when	when	SCONJ
ejpam-4760	364	17	the	the	DET
ejpam-4760	364	18	lexicographic	lexicographic	ADJ
ejpam-4760	364	19	product	product	NOUN
ejpam-4760	364	20	g[h	g[h	PROPN
ejpam-4760	364	21	]	]	PUNCT
ejpam-4760	364	22	has	have	VERB
ejpam-4760	364	23	a	a	DET
ejpam-4760	364	24	γp0	γp0	NOUN
ejpam-4760	364	25	-	-	PUNCT
ejpam-4760	364	26	set	set	VERB
ejpam-4760	364	27	or	or	CCONJ
ejpam-4760	364	28	has	have	VERB
ejpam-4760	364	29	no	no	DET
ejpam-4760	364	30	γp0	γp0	NOUN
ejpam-4760	364	31	-	-	PUNCT
ejpam-4760	364	32	set	set	VERB
ejpam-4760	364	33	and	and	CCONJ
ejpam-4760	364	34	its	its	PRON
ejpam-4760	364	35	perfect	perfect	ADJ
ejpam-4760	364	36	isolate	isolate	NOUN
ejpam-4760	364	37	domination	domination	NOUN
ejpam-4760	364	38	number	number	NOUN
ejpam-4760	364	39	.	.	PUNCT
ejpam-4760	365	1	the	the	DET
ejpam-4760	365	2	lexicographic	lexicographic	ADJ
ejpam-4760	365	3	product	product	NOUN
ejpam-4760	365	4	or	or	CCONJ
ejpam-4760	365	5	composition	composition	NOUN
ejpam-4760	365	6	of	of	ADP
ejpam-4760	365	7	two	two	NUM
ejpam-4760	365	8	graphs	graph	NOUN
ejpam-4760	365	9	g	g	NOUN
ejpam-4760	365	10	and	and	CCONJ
ejpam-4760	365	11	h	h	NOUN
ejpam-4760	365	12	is	be	AUX
ejpam-4760	365	13	the	the	DET
ejpam-4760	365	14	graph	graph	NOUN
ejpam-4760	365	15	g[h	g[h	PROPN
ejpam-4760	365	16	]	]	PUNCT
ejpam-4760	365	17	with	with	ADP
ejpam-4760	365	18	vertex	vertex	NOUN
ejpam-4760	365	19	set	set	VERB
ejpam-4760	365	20	v	v	NOUN
ejpam-4760	365	21	(	(	PUNCT
ejpam-4760	365	22	g[h	g[h	PROPN
ejpam-4760	365	23	]	]	PUNCT
ejpam-4760	365	24	)	)	PUNCT
ejpam-4760	365	25	=	=	SYM
ejpam-4760	365	26	v	v	X
ejpam-4760	365	27	(	(	PUNCT
ejpam-4760	365	28	g	g	NOUN
ejpam-4760	365	29	)	)	PUNCT
ejpam-4760	365	30	×	×	NOUN
ejpam-4760	365	31	v	v	NOUN
ejpam-4760	365	32	(	(	PUNCT
ejpam-4760	365	33	h	h	NOUN
ejpam-4760	365	34	)	)	PUNCT
ejpam-4760	365	35	and	and	CCONJ
ejpam-4760	365	36	edge	edge	VERB
ejpam-4760	365	37	set	set	VERB
ejpam-4760	365	38	e(g[h	e(g[h	NOUN
ejpam-4760	365	39	]	]	PUNCT
ejpam-4760	365	40	)	)	PUNCT
ejpam-4760	365	41	satisfying	satisfy	VERB
ejpam-4760	365	42	the	the	DET
ejpam-4760	365	43	following	follow	VERB
ejpam-4760	365	44	conditions	condition	NOUN
ejpam-4760	365	45	:	:	PUNCT
ejpam-4760	365	46	(	(	PUNCT
ejpam-4760	365	47	x	x	X
ejpam-4760	365	48	,	,	PUNCT
ejpam-4760	365	49	u)(y	u)(y	PROPN
ejpam-4760	365	50	,	,	PUNCT
ejpam-4760	365	51	v	v	NOUN
ejpam-4760	365	52	)	)	PUNCT
ejpam-4760	365	53	∈	∈	NOUN
ejpam-4760	365	54	e(g[h	e(g[h	NOUN
ejpam-4760	365	55	]	]	PUNCT
ejpam-4760	365	56	)	)	PUNCT
ejpam-4760	365	57	if	if	SCONJ
ejpam-4760	365	58	and	and	CCONJ
ejpam-4760	365	59	only	only	ADV
ejpam-4760	365	60	if	if	SCONJ
ejpam-4760	365	61	xy	xy	PROPN
ejpam-4760	365	62	∈	∈	PROPN
ejpam-4760	365	63	e(g	e(g	PROPN
ejpam-4760	365	64	)	)	PUNCT
ejpam-4760	365	65	or	or	CCONJ
ejpam-4760	365	66	x	x	X
ejpam-4760	365	67	=	=	SYM
ejpam-4760	365	68	y	y	PROPN
ejpam-4760	365	69	and	and	CCONJ
ejpam-4760	365	70	uv	uv	PROPN
ejpam-4760	365	71	∈	∈	PROPN
ejpam-4760	365	72	e(h	e(h	PROPN
ejpam-4760	365	73	)	)	PUNCT
ejpam-4760	365	74	.	.	PUNCT
ejpam-4760	366	1	any	any	DET
ejpam-4760	366	2	subset	subset	NOUN
ejpam-4760	366	3	c	c	NOUN
ejpam-4760	366	4	of	of	ADP
ejpam-4760	366	5	v	v	PROPN
ejpam-4760	366	6	(	(	PUNCT
ejpam-4760	366	7	g[h	g[h	PROPN
ejpam-4760	366	8	]	]	PUNCT
ejpam-4760	366	9	)	)	PUNCT
ejpam-4760	366	10	can	can	AUX
ejpam-4760	366	11	be	be	AUX
ejpam-4760	366	12	expressed	express	VERB
ejpam-4760	366	13	as	as	ADP
ejpam-4760	366	14	c	c	NOUN
ejpam-4760	366	15	=	=	SYM
ejpam-4760	366	16	⋃	⋃	PROPN
ejpam-4760	366	17	x∈s	x∈s	NOUN
ejpam-4760	366	18	(	(	PUNCT
ejpam-4760	366	19	{	{	PUNCT
ejpam-4760	366	20	x	x	NOUN
ejpam-4760	366	21	}	}	PUNCT
ejpam-4760	366	22	×	×	PROPN
ejpam-4760	366	23	tx	tx	PROPN
ejpam-4760	366	24	)	)	PUNCT
ejpam-4760	366	25	where	where	SCONJ
ejpam-4760	366	26	s	s	VERB
ejpam-4760	366	27	⊆	⊆	NUM
ejpam-4760	366	28	v	v	NOUN
ejpam-4760	366	29	(	(	PUNCT
ejpam-4760	366	30	g	g	NOUN
ejpam-4760	366	31	)	)	PUNCT
ejpam-4760	366	32	and	and	CCONJ
ejpam-4760	366	33	tx	tx	VERB
ejpam-4760	366	34	⊆	⊆	NUM
ejpam-4760	366	35	v	v	NOUN
ejpam-4760	366	36	(	(	PUNCT
ejpam-4760	366	37	h	h	NOUN
ejpam-4760	366	38	)	)	PUNCT
ejpam-4760	366	39	for	for	ADP
ejpam-4760	366	40	each	each	DET
ejpam-4760	366	41	x	x	SYM
ejpam-4760	366	42	∈	∈	PROPN
ejpam-4760	366	43	s.	s.	PROPN
ejpam-4760	366	44	s	s	PART
ejpam-4760	366	45	is	be	AUX
ejpam-4760	366	46	called	call	VERB
ejpam-4760	366	47	as	as	SCONJ
ejpam-4760	366	48	g	g	NOUN
ejpam-4760	366	49	-	-	PUNCT
ejpam-4760	366	50	projection	projection	NOUN
ejpam-4760	366	51	of	of	ADP
ejpam-4760	366	52	c	c	PROPN
ejpam-4760	366	53	and	and	CCONJ
ejpam-4760	366	54	∪x∈stx	∪x∈stx	NOUN
ejpam-4760	366	55	is	be	AUX
ejpam-4760	366	56	called	call	VERB
ejpam-4760	366	57	as	as	SCONJ
ejpam-4760	366	58	the	the	DET
ejpam-4760	366	59	h	h	NOUN
ejpam-4760	366	60	-	-	PUNCT
ejpam-4760	366	61	projection	projection	NOUN
ejpam-4760	366	62	of	of	ADP
ejpam-4760	366	63	c.	c.	PROPN
ejpam-4760	366	64	theorem	theorem	VERB
ejpam-4760	366	65	11	11	NUM
ejpam-4760	366	66	.	.	PUNCT
ejpam-4760	367	1	let	let	VERB
ejpam-4760	367	2	g	g	NOUN
ejpam-4760	367	3	and	and	CCONJ
ejpam-4760	367	4	h	h	NOUN
ejpam-4760	367	5	be	be	AUX
ejpam-4760	367	6	connected	connect	VERB
ejpam-4760	367	7	nontrivial	nontrivial	ADJ
ejpam-4760	367	8	graphs	graph	NOUN
ejpam-4760	367	9	.	.	PUNCT
ejpam-4760	368	1	a	a	DET
ejpam-4760	368	2	subset	subset	NOUN
ejpam-4760	368	3	c	c	NOUN
ejpam-4760	368	4	=	=	PUNCT
ejpam-4760	368	5	⋃	⋃	PROPN
ejpam-4760	368	6	x∈s	x∈s	NOUN
ejpam-4760	368	7	(	(	PUNCT
ejpam-4760	368	8	{	{	PUNCT
ejpam-4760	368	9	x	x	NOUN
ejpam-4760	368	10	}	}	PUNCT
ejpam-4760	368	11	×	×	PROPN
ejpam-4760	368	12	tx	tx	PROPN
ejpam-4760	368	13	)	)	PUNCT
ejpam-4760	368	14	of	of	ADP
ejpam-4760	368	15	v	v	NOUN
ejpam-4760	368	16	(	(	PUNCT
ejpam-4760	368	17	g[h	g[h	PROPN
ejpam-4760	368	18	]	]	PUNCT
ejpam-4760	368	19	)	)	PUNCT
ejpam-4760	368	20	where	where	SCONJ
ejpam-4760	368	21	s	s	VERB
ejpam-4760	368	22	⊆	⊆	NUM
ejpam-4760	368	23	v	v	NOUN
ejpam-4760	368	24	(	(	PUNCT
ejpam-4760	368	25	g	g	NOUN
ejpam-4760	368	26	)	)	PUNCT
ejpam-4760	368	27	and	and	CCONJ
ejpam-4760	368	28	tx	tx	VERB
ejpam-4760	368	29	⊆	⊆	NUM
ejpam-4760	368	30	v	v	NOUN
ejpam-4760	368	31	(	(	PUNCT
ejpam-4760	368	32	h	h	NOUN
ejpam-4760	368	33	)	)	PUNCT
ejpam-4760	368	34	for	for	ADP
ejpam-4760	368	35	each	each	DET
ejpam-4760	368	36	x	x	SYM
ejpam-4760	368	37	∈	∈	PROPN
ejpam-4760	368	38	s	s	NOUN
ejpam-4760	368	39	,	,	PUNCT
ejpam-4760	368	40	is	be	AUX
ejpam-4760	368	41	a	a	DET
ejpam-4760	368	42	perfect	perfect	ADJ
ejpam-4760	368	43	isolate	isolate	NOUN
ejpam-4760	368	44	dominating	dominating	NOUN
ejpam-4760	368	45	set	set	NOUN
ejpam-4760	368	46	of	of	ADP
ejpam-4760	368	47	g[h	g[h	PROPN
ejpam-4760	368	48	]	]	PUNCT
ejpam-4760	368	49	if	if	SCONJ
ejpam-4760	368	50	and	and	CCONJ
ejpam-4760	368	51	only	only	ADV
ejpam-4760	368	52	if	if	SCONJ
ejpam-4760	368	53	s	s	NOUN
ejpam-4760	368	54	is	be	AUX
ejpam-4760	368	55	an	an	DET
ejpam-4760	368	56	independent	independent	ADJ
ejpam-4760	368	57	perfect	perfect	ADJ
ejpam-4760	368	58	dominating	dominating	NOUN
ejpam-4760	368	59	set	set	NOUN
ejpam-4760	368	60	(	(	PUNCT
ejpam-4760	368	61	ipds	ipds	PROPN
ejpam-4760	368	62	)	)	PUNCT
ejpam-4760	368	63	and	and	CCONJ
ejpam-4760	368	64	tx	tx	PROPN
ejpam-4760	368	65	is	be	AUX
ejpam-4760	368	66	a	a	DET
ejpam-4760	368	67	dominating	dominating	NOUN
ejpam-4760	368	68	set	set	NOUN
ejpam-4760	368	69	of	of	ADP
ejpam-4760	368	70	h	h	NOUN
ejpam-4760	368	71	with	with	ADP
ejpam-4760	368	72	|tx|	|tx|	NOUN
ejpam-4760	368	73	=	=	SYM
ejpam-4760	368	74	1	1	NUM
ejpam-4760	368	75	for	for	ADP
ejpam-4760	368	76	all	all	DET
ejpam-4760	368	77	x	x	SYM
ejpam-4760	368	78	∈	∈	PROPN
ejpam-4760	368	79	s.	s.	PROPN
ejpam-4760	368	80	proof	proof	PROPN
ejpam-4760	368	81	.	.	PUNCT
ejpam-4760	369	1	suppose	suppose	VERB
ejpam-4760	369	2	that	that	SCONJ
ejpam-4760	369	3	c	c	PROPN
ejpam-4760	369	4	is	be	AUX
ejpam-4760	369	5	a	a	DET
ejpam-4760	369	6	perfect	perfect	ADJ
ejpam-4760	369	7	isolate	isolate	NOUN
ejpam-4760	369	8	dominating	dominating	NOUN
ejpam-4760	369	9	set	set	NOUN
ejpam-4760	369	10	of	of	ADP
ejpam-4760	369	11	g[h	g[h	PROPN
ejpam-4760	369	12	]	]	PUNCT
ejpam-4760	369	13	.	.	PUNCT
ejpam-4760	370	1	let	let	VERB
ejpam-4760	370	2	u	u	PRON
ejpam-4760	370	3	∈	∈	PROPN
ejpam-4760	370	4	v	v	ADP
ejpam-4760	370	5	(	(	PUNCT
ejpam-4760	370	6	g	g	NOUN
ejpam-4760	370	7	)	)	PUNCT
ejpam-4760	370	8	\	\	PUNCT
ejpam-4760	371	1	s.	s.	PROPN
ejpam-4760	371	2	pick	pick	VERB
ejpam-4760	371	3	any	any	DET
ejpam-4760	371	4	v	v	NOUN
ejpam-4760	371	5	∈	∈	PROPN
ejpam-4760	371	6	v	v	NOUN
ejpam-4760	371	7	(	(	PUNCT
ejpam-4760	371	8	h	h	NOUN
ejpam-4760	371	9	)	)	PUNCT
ejpam-4760	371	10	.	.	PUNCT
ejpam-4760	372	1	since	since	SCONJ
ejpam-4760	372	2	c	c	PROPN
ejpam-4760	372	3	is	be	AUX
ejpam-4760	372	4	a	a	DET
ejpam-4760	372	5	perfect	perfect	ADJ
ejpam-4760	372	6	dominating	dominating	NOUN
ejpam-4760	372	7	set	set	NOUN
ejpam-4760	372	8	,	,	PUNCT
ejpam-4760	372	9	there	there	PRON
ejpam-4760	372	10	exists	exist	VERB
ejpam-4760	372	11	(	(	PUNCT
ejpam-4760	372	12	y	y	NOUN
ejpam-4760	372	13	,	,	PUNCT
ejpam-4760	372	14	z	z	NOUN
ejpam-4760	372	15	)	)	PUNCT
ejpam-4760	372	16	∈	∈	PROPN
ejpam-4760	372	17	c	c	NOUN
ejpam-4760	372	18	such	such	ADJ
ejpam-4760	372	19	that	that	SCONJ
ejpam-4760	372	20	ng[h](u	ng[h](u	PROPN
ejpam-4760	372	21	,	,	PUNCT
ejpam-4760	372	22	v	v	NOUN
ejpam-4760	372	23	)	)	PUNCT
ejpam-4760	372	24	∩	∩	NOUN
ejpam-4760	372	25	c	c	NOUN
ejpam-4760	372	26	=	=	SYM
ejpam-4760	372	27	{	{	PUNCT
ejpam-4760	372	28	(	(	PUNCT
ejpam-4760	372	29	y	y	PROPN
ejpam-4760	372	30	,	,	PUNCT
ejpam-4760	372	31	z	z	NOUN
ejpam-4760	372	32	)	)	PUNCT
ejpam-4760	372	33	}	}	PUNCT
ejpam-4760	372	34	.	.	PUNCT
ejpam-4760	373	1	this	this	PRON
ejpam-4760	373	2	implies	imply	VERB
ejpam-4760	373	3	that	that	SCONJ
ejpam-4760	373	4	ng(u	ng(u	NOUN
ejpam-4760	373	5	)	)	PUNCT
ejpam-4760	373	6	∩	∩	NOUN
ejpam-4760	373	7	s	s	PART
ejpam-4760	373	8	=	=	PUNCT
ejpam-4760	373	9	{	{	PUNCT
ejpam-4760	373	10	y	y	NOUN
ejpam-4760	373	11	}	}	PUNCT
ejpam-4760	373	12	.	.	PUNCT
ejpam-4760	374	1	this	this	PRON
ejpam-4760	374	2	implies	imply	VERB
ejpam-4760	374	3	that	that	SCONJ
ejpam-4760	374	4	every	every	DET
ejpam-4760	374	5	u	u	PROPN
ejpam-4760	374	6	∈	∈	PROPN
ejpam-4760	374	7	v	v	NOUN
ejpam-4760	374	8	(	(	PUNCT
ejpam-4760	374	9	g	g	NOUN
ejpam-4760	374	10	)	)	PUNCT
ejpam-4760	374	11	\	\	PROPN
ejpam-4760	374	12	s	s	PART
ejpam-4760	374	13	is	be	AUX
ejpam-4760	374	14	dominated	dominate	VERB
ejpam-4760	374	15	by	by	ADP
ejpam-4760	374	16	exactly	exactly	ADV
ejpam-4760	374	17	one	one	NUM
ejpam-4760	374	18	vertex	vertex	NOUN
ejpam-4760	374	19	in	in	ADP
ejpam-4760	374	20	s	s	PRON
ejpam-4760	374	21	and	and	CCONJ
ejpam-4760	374	22	so	so	ADV
ejpam-4760	374	23	,	,	PUNCT
ejpam-4760	374	24	s	s	VERB
ejpam-4760	374	25	is	be	AUX
ejpam-4760	374	26	a	a	DET
ejpam-4760	374	27	perfect	perfect	ADJ
ejpam-4760	374	28	dominating	dominating	NOUN
ejpam-4760	374	29	set	set	NOUN
ejpam-4760	374	30	.	.	PUNCT
ejpam-4760	375	1	suppose	suppose	VERB
ejpam-4760	375	2	that	that	SCONJ
ejpam-4760	375	3	p	p	X
ejpam-4760	375	4	,	,	PUNCT
ejpam-4760	375	5	q	q	PROPN
ejpam-4760	375	6	∈	∈	PROPN
ejpam-4760	375	7	s	s	VERB
ejpam-4760	375	8	such	such	ADJ
ejpam-4760	375	9	that	that	DET
ejpam-4760	375	10	pq	pq	PROPN
ejpam-4760	375	11	∈	∈	PROPN
ejpam-4760	375	12	e(g	e(g	PROPN
ejpam-4760	375	13	)	)	PUNCT
ejpam-4760	375	14	.	.	PUNCT
ejpam-4760	376	1	since	since	SCONJ
ejpam-4760	376	2	h	h	NOUN
ejpam-4760	376	3	is	be	AUX
ejpam-4760	376	4	connected	connect	VERB
ejpam-4760	376	5	,	,	PUNCT
ejpam-4760	376	6	there	there	PRON
ejpam-4760	376	7	exists	exist	VERB
ejpam-4760	376	8	vertices	vertice	VERB
ejpam-4760	376	9	c.	c.	PROPN
ejpam-4760	376	10	armada	armada	PROPN
ejpam-4760	376	11	,	,	PUNCT
ejpam-4760	376	12	j.	j.	PROPN
ejpam-4760	376	13	hamja	hamja	PROPN
ejpam-4760	376	14	/	/	SYM
ejpam-4760	376	15	eur	eur	PROPN
ejpam-4760	376	16	.	.	PUNCT
ejpam-4760	377	1	j.	j.	PROPN
ejpam-4760	377	2	pure	pure	PROPN
ejpam-4760	377	3	appl	appl	PROPN
ejpam-4760	377	4	.	.	PROPN
ejpam-4760	377	5	math	math	PROPN
ejpam-4760	377	6	,	,	PUNCT
ejpam-4760	377	7	16	16	NUM
ejpam-4760	377	8	(	(	PUNCT
ejpam-4760	377	9	2	2	NUM
ejpam-4760	377	10	)	)	PUNCT
ejpam-4760	377	11	(	(	PUNCT
ejpam-4760	377	12	2023	2023	NUM
ejpam-4760	377	13	)	)	PUNCT
ejpam-4760	377	14	,	,	PUNCT
ejpam-4760	377	15	1326	1326	NUM
ejpam-4760	377	16	-	-	SYM
ejpam-4760	377	17	1341	1341	NUM
ejpam-4760	377	18	1339	1339	NUM
ejpam-4760	377	19	m	m	NOUN
ejpam-4760	377	20	,	,	PUNCT
ejpam-4760	377	21	n	n	PROPN
ejpam-4760	377	22	∈	∈	NOUN
ejpam-4760	377	23	v	v	NOUN
ejpam-4760	377	24	(	(	PUNCT
ejpam-4760	377	25	h	h	NOUN
ejpam-4760	377	26	)	)	PUNCT
ejpam-4760	377	27	such	such	ADJ
ejpam-4760	377	28	that	that	SCONJ
ejpam-4760	377	29	mn	mn	PROPN
ejpam-4760	377	30	∈	∈	PROPN
ejpam-4760	377	31	e(h	e(h	PROPN
ejpam-4760	377	32	)	)	PUNCT
ejpam-4760	377	33	,	,	PUNCT
ejpam-4760	377	34	(	(	PUNCT
ejpam-4760	377	35	p	p	X
ejpam-4760	377	36	,	,	PUNCT
ejpam-4760	377	37	m)(q	m)(q	PROPN
ejpam-4760	377	38	,	,	PUNCT
ejpam-4760	377	39	m	m	NOUN
ejpam-4760	377	40	)	)	PUNCT
ejpam-4760	377	41	∈	∈	NOUN
ejpam-4760	377	42	e(g[h	e(g[h	NOUN
ejpam-4760	377	43	]	]	PUNCT
ejpam-4760	377	44	)	)	PUNCT
ejpam-4760	377	45	and	and	CCONJ
ejpam-4760	377	46	(	(	PUNCT
ejpam-4760	377	47	p	p	X
ejpam-4760	377	48	,	,	PUNCT
ejpam-4760	377	49	m	m	NOUN
ejpam-4760	377	50	)	)	PUNCT
ejpam-4760	377	51	,	,	PUNCT
ejpam-4760	377	52	(	(	PUNCT
ejpam-4760	377	53	q	q	X
ejpam-4760	377	54	,	,	PUNCT
ejpam-4760	377	55	m	m	NOUN
ejpam-4760	377	56	)	)	PUNCT
ejpam-4760	377	57	∈	∈	PROPN
ejpam-4760	378	1	c	c	NOUN
ejpam-4760	378	2	,	,	PUNCT
ejpam-4760	378	3	a	a	DET
ejpam-4760	378	4	contradiction	contradiction	NOUN
ejpam-4760	378	5	since	since	SCONJ
ejpam-4760	378	6	the	the	DET
ejpam-4760	378	7	vertices	vertex	NOUN
ejpam-4760	378	8	(	(	PUNCT
ejpam-4760	378	9	p	p	NOUN
ejpam-4760	378	10	,	,	PUNCT
ejpam-4760	378	11	n	n	CCONJ
ejpam-4760	378	12	)	)	PUNCT
ejpam-4760	378	13	and	and	CCONJ
ejpam-4760	378	14	(	(	PUNCT
ejpam-4760	378	15	q	q	NOUN
ejpam-4760	378	16	,	,	PUNCT
ejpam-4760	378	17	n	n	CCONJ
ejpam-4760	378	18	)	)	PUNCT
ejpam-4760	378	19	are	be	AUX
ejpam-4760	378	20	both	both	PRON
ejpam-4760	378	21	dominated	dominate	VERB
ejpam-4760	378	22	by	by	ADP
ejpam-4760	378	23	the	the	DET
ejpam-4760	378	24	two	two	NUM
ejpam-4760	378	25	vertices	vertex	NOUN
ejpam-4760	378	26	(	(	PUNCT
ejpam-4760	378	27	p	p	X
ejpam-4760	378	28	,	,	PUNCT
ejpam-4760	378	29	m	m	NOUN
ejpam-4760	378	30	)	)	PUNCT
ejpam-4760	378	31	and	and	CCONJ
ejpam-4760	378	32	(	(	PUNCT
ejpam-4760	378	33	q	q	X
ejpam-4760	378	34	,	,	PUNCT
ejpam-4760	378	35	m	m	NOUN
ejpam-4760	378	36	)	)	PUNCT
ejpam-4760	378	37	in	in	ADP
ejpam-4760	378	38	c.	c.	PROPN
ejpam-4760	378	39	hence	hence	ADV
ejpam-4760	378	40	,	,	PUNCT
ejpam-4760	378	41	for	for	ADP
ejpam-4760	378	42	any	any	DET
ejpam-4760	378	43	two	two	NUM
ejpam-4760	378	44	vertices	vertex	NOUN
ejpam-4760	378	45	p	p	NOUN
ejpam-4760	378	46	,	,	PUNCT
ejpam-4760	378	47	q	q	PROPN
ejpam-4760	378	48	∈	∈	PROPN
ejpam-4760	378	49	s	s	NOUN
ejpam-4760	378	50	,	,	PUNCT
ejpam-4760	378	51	pq	pq	PROPN
ejpam-4760	378	52	/∈	/∈	PUNCT
ejpam-4760	378	53	e(g	e(g	PROPN
ejpam-4760	378	54	)	)	PUNCT
ejpam-4760	378	55	.	.	PUNCT
ejpam-4760	379	1	thus	thus	ADV
ejpam-4760	379	2	,	,	PUNCT
ejpam-4760	379	3	s	s	VERB
ejpam-4760	379	4	is	be	AUX
ejpam-4760	379	5	an	an	DET
ejpam-4760	379	6	independent	independent	ADJ
ejpam-4760	379	7	set	set	NOUN
ejpam-4760	379	8	.	.	PUNCT
ejpam-4760	380	1	let	let	VERB
ejpam-4760	380	2	x	x	PUNCT
ejpam-4760	380	3	∈	∈	NOUN
ejpam-4760	380	4	s	s	PART
ejpam-4760	380	5	and	and	CCONJ
ejpam-4760	380	6	suppose	suppose	VERB
ejpam-4760	380	7	that	that	SCONJ
ejpam-4760	380	8	|tx|	|tx|	PROPN
ejpam-4760	380	9	≥	≥	NUM
ejpam-4760	380	10	2	2	X
ejpam-4760	380	11	.	.	PUNCT
ejpam-4760	381	1	let	let	VERB
ejpam-4760	381	2	c	c	X
ejpam-4760	381	3	,	,	PUNCT
ejpam-4760	381	4	d	d	PROPN
ejpam-4760	381	5	∈	∈	PROPN
ejpam-4760	381	6	tx	tx	VERB
ejpam-4760	381	7	such	such	ADJ
ejpam-4760	381	8	that	that	SCONJ
ejpam-4760	381	9	c	c	PROPN
ejpam-4760	381	10	̸=	̸=	PROPN
ejpam-4760	381	11	d.	d.	PROPN
ejpam-4760	381	12	thus	thus	ADV
ejpam-4760	381	13	,	,	PUNCT
ejpam-4760	381	14	(	(	PUNCT
ejpam-4760	381	15	x	x	NOUN
ejpam-4760	381	16	,	,	PUNCT
ejpam-4760	381	17	c	c	NOUN
ejpam-4760	381	18	)	)	PUNCT
ejpam-4760	381	19	,	,	PUNCT
ejpam-4760	381	20	(	(	PUNCT
ejpam-4760	381	21	x	x	X
ejpam-4760	381	22	,	,	PUNCT
ejpam-4760	381	23	d	d	NOUN
ejpam-4760	381	24	)	)	PUNCT
ejpam-4760	381	25	∈	∈	PROPN
ejpam-4760	381	26	c.	c.	NOUN
ejpam-4760	381	27	let	let	VERB
ejpam-4760	381	28	e	e	NOUN
ejpam-4760	381	29	∈	∈	PROPN
ejpam-4760	381	30	v	v	ADP
ejpam-4760	381	31	(	(	PUNCT
ejpam-4760	381	32	g	g	NOUN
ejpam-4760	381	33	)	)	PUNCT
ejpam-4760	381	34	such	such	ADJ
ejpam-4760	381	35	that	that	SCONJ
ejpam-4760	381	36	xe	xe	PROPN
ejpam-4760	381	37	∈	∈	PROPN
ejpam-4760	381	38	e(g	e(g	PROPN
ejpam-4760	381	39	)	)	PUNCT
ejpam-4760	381	40	.	.	PUNCT
ejpam-4760	382	1	since	since	SCONJ
ejpam-4760	382	2	s	s	PROPN
ejpam-4760	382	3	is	be	AUX
ejpam-4760	382	4	independent	independent	ADJ
ejpam-4760	382	5	,	,	PUNCT
ejpam-4760	382	6	e	e	PROPN
ejpam-4760	382	7	/∈	/∈	PUNCT
ejpam-4760	382	8	s.	s.	PROPN
ejpam-4760	382	9	clearly	clearly	ADV
ejpam-4760	382	10	,	,	PUNCT
ejpam-4760	382	11	(	(	PUNCT
ejpam-4760	382	12	e	e	NOUN
ejpam-4760	382	13	,	,	PUNCT
ejpam-4760	382	14	c	c	NOUN
ejpam-4760	382	15	)	)	PUNCT
ejpam-4760	382	16	/∈	/∈	PUNCT
ejpam-4760	383	1	c	c	NOUN
ejpam-4760	383	2	and	and	CCONJ
ejpam-4760	383	3	(	(	PUNCT
ejpam-4760	383	4	e	e	NOUN
ejpam-4760	383	5	,	,	PUNCT
ejpam-4760	383	6	c	c	NOUN
ejpam-4760	383	7	)	)	PUNCT
ejpam-4760	383	8	is	be	AUX
ejpam-4760	383	9	dominated	dominate	VERB
ejpam-4760	383	10	by	by	ADP
ejpam-4760	383	11	the	the	DET
ejpam-4760	383	12	two	two	NUM
ejpam-4760	383	13	vertices	vertex	NOUN
ejpam-4760	383	14	(	(	PUNCT
ejpam-4760	383	15	x	x	X
ejpam-4760	383	16	,	,	PUNCT
ejpam-4760	383	17	c	c	NOUN
ejpam-4760	383	18	)	)	PUNCT
ejpam-4760	383	19	and	and	CCONJ
ejpam-4760	383	20	(	(	PUNCT
ejpam-4760	383	21	x	x	X
ejpam-4760	383	22	,	,	PUNCT
ejpam-4760	383	23	d	d	NOUN
ejpam-4760	383	24	)	)	PUNCT
ejpam-4760	383	25	in	in	ADP
ejpam-4760	383	26	c	c	NOUN
ejpam-4760	383	27	,	,	PUNCT
ejpam-4760	383	28	a	a	DET
ejpam-4760	383	29	contradiction	contradiction	NOUN
ejpam-4760	383	30	since	since	SCONJ
ejpam-4760	383	31	c	c	PROPN
ejpam-4760	383	32	is	be	AUX
ejpam-4760	383	33	a	a	DET
ejpam-4760	383	34	perfect	perfect	ADJ
ejpam-4760	383	35	dominating	dominating	NOUN
ejpam-4760	383	36	set	set	NOUN
ejpam-4760	383	37	.	.	PUNCT
ejpam-4760	384	1	hence	hence	ADV
ejpam-4760	384	2	,	,	PUNCT
ejpam-4760	384	3	|tx|	|tx|	X
ejpam-4760	384	4	=	=	SYM
ejpam-4760	384	5	1	1	NUM
ejpam-4760	384	6	for	for	ADP
ejpam-4760	384	7	each	each	DET
ejpam-4760	384	8	x	x	PROPN
ejpam-4760	384	9	∈	∈	PROPN
ejpam-4760	384	10	s.	s.	PROPN
ejpam-4760	384	11	furthermore	furthermore	ADV
ejpam-4760	384	12	,	,	PUNCT
ejpam-4760	384	13	since	since	SCONJ
ejpam-4760	384	14	s	s	NOUN
ejpam-4760	384	15	is	be	AUX
ejpam-4760	384	16	an	an	DET
ejpam-4760	384	17	independent	independent	ADJ
ejpam-4760	384	18	dominating	dominating	NOUN
ejpam-4760	384	19	set	set	NOUN
ejpam-4760	384	20	and	and	CCONJ
ejpam-4760	384	21	c	c	NOUN
ejpam-4760	384	22	is	be	AUX
ejpam-4760	384	23	a	a	DET
ejpam-4760	384	24	dominating	dominating	NOUN
ejpam-4760	384	25	set	set	NOUN
ejpam-4760	384	26	,	,	PUNCT
ejpam-4760	384	27	tx	tx	PROPN
ejpam-4760	384	28	is	be	AUX
ejpam-4760	384	29	a	a	DET
ejpam-4760	384	30	dominating	dominating	NOUN
ejpam-4760	384	31	set	set	VERB
ejpam-4760	384	32	in	in	ADP
ejpam-4760	384	33	h	h	NOUN
ejpam-4760	384	34	for	for	ADP
ejpam-4760	384	35	each	each	DET
ejpam-4760	384	36	x	x	SYM
ejpam-4760	384	37	∈	∈	PROPN
ejpam-4760	384	38	s.	s.	PROPN
ejpam-4760	384	39	conversely	conversely	ADV
ejpam-4760	384	40	,	,	PUNCT
ejpam-4760	384	41	suppose	suppose	VERB
ejpam-4760	384	42	that	that	SCONJ
ejpam-4760	384	43	s	s	VERB
ejpam-4760	384	44	is	be	AUX
ejpam-4760	384	45	an	an	DET
ejpam-4760	384	46	independent	independent	ADJ
ejpam-4760	384	47	perfect	perfect	ADJ
ejpam-4760	384	48	dominating	dominating	NOUN
ejpam-4760	384	49	set	set	NOUN
ejpam-4760	384	50	(	(	PUNCT
ejpam-4760	384	51	ipds	ipds	PROPN
ejpam-4760	384	52	)	)	PUNCT
ejpam-4760	384	53	and	and	CCONJ
ejpam-4760	384	54	tx	tx	PROPN
ejpam-4760	384	55	is	be	AUX
ejpam-4760	384	56	a	a	DET
ejpam-4760	384	57	dominating	dominating	NOUN
ejpam-4760	384	58	set	set	NOUN
ejpam-4760	384	59	of	of	ADP
ejpam-4760	384	60	h	h	NOUN
ejpam-4760	384	61	with	with	ADP
ejpam-4760	384	62	|tx|	|tx|	NOUN
ejpam-4760	384	63	=	=	SYM
ejpam-4760	384	64	1	1	NUM
ejpam-4760	384	65	for	for	SCONJ
ejpam-4760	384	66	all	all	DET
ejpam-4760	384	67	x	x	SYM
ejpam-4760	384	68	∈	∈	PROPN
ejpam-4760	384	69	s.	s.	PROPN
ejpam-4760	384	70	let	let	VERB
ejpam-4760	384	71	tx	tx	VERB
ejpam-4760	384	72	=	=	PUNCT
ejpam-4760	384	73	{	{	PUNCT
ejpam-4760	384	74	t	t	X
ejpam-4760	384	75	}	}	PUNCT
ejpam-4760	384	76	such	such	ADJ
ejpam-4760	384	77	that	that	SCONJ
ejpam-4760	384	78	t	t	PROPN
ejpam-4760	384	79	dominates	dominate	VERB
ejpam-4760	384	80	all	all	DET
ejpam-4760	384	81	other	other	ADJ
ejpam-4760	384	82	vertices	vertex	NOUN
ejpam-4760	384	83	of	of	ADP
ejpam-4760	384	84	h.	h.	NOUN
ejpam-4760	384	85	let	let	VERB
ejpam-4760	384	86	(	(	PUNCT
ejpam-4760	384	87	p	p	X
ejpam-4760	384	88	,	,	PUNCT
ejpam-4760	384	89	q	q	NOUN
ejpam-4760	384	90	)	)	PUNCT
ejpam-4760	384	91	∈	∈	NOUN
ejpam-4760	384	92	v	v	NOUN
ejpam-4760	384	93	(	(	PUNCT
ejpam-4760	384	94	g[h	g[h	PROPN
ejpam-4760	384	95	]	]	PUNCT
ejpam-4760	384	96	)	)	PUNCT
ejpam-4760	384	97	\	\	PROPN
ejpam-4760	384	98	c	c	NOUN
ejpam-4760	384	99	and	and	CCONJ
ejpam-4760	384	100	consider	consider	VERB
ejpam-4760	384	101	the	the	DET
ejpam-4760	384	102	following	follow	VERB
ejpam-4760	384	103	cases	case	NOUN
ejpam-4760	384	104	:	:	PUNCT
ejpam-4760	384	105	case	case	NOUN
ejpam-4760	384	106	1	1	NUM
ejpam-4760	384	107	:	:	PUNCT
ejpam-4760	384	108	p	p	X
ejpam-4760	384	109	/∈	/∈	PUNCT
ejpam-4760	384	110	s.	s.	PROPN
ejpam-4760	384	111	since	since	SCONJ
ejpam-4760	384	112	s	s	PROPN
ejpam-4760	384	113	is	be	AUX
ejpam-4760	384	114	a	a	DET
ejpam-4760	384	115	perfect	perfect	ADJ
ejpam-4760	384	116	dominating	dominating	NOUN
ejpam-4760	384	117	set	set	NOUN
ejpam-4760	384	118	,	,	PUNCT
ejpam-4760	384	119	there	there	PRON
ejpam-4760	384	120	exists	exist	VERB
ejpam-4760	384	121	x	x	X
ejpam-4760	384	122	∈	∈	PROPN
ejpam-4760	384	123	s	s	VERB
ejpam-4760	384	124	such	such	ADJ
ejpam-4760	384	125	that	that	PRON
ejpam-4760	384	126	s	s	VERB
ejpam-4760	384	127	∩ng(p	∩ng(p	NOUN
ejpam-4760	384	128	)	)	PUNCT
ejpam-4760	384	129	=	=	SYM
ejpam-4760	384	130	{	{	PUNCT
ejpam-4760	384	131	x	x	NOUN
ejpam-4760	384	132	}	}	PUNCT
ejpam-4760	384	133	.	.	PUNCT
ejpam-4760	385	1	then	then	ADV
ejpam-4760	385	2	{	{	PUNCT
ejpam-4760	385	3	(	(	PUNCT
ejpam-4760	385	4	x	x	NOUN
ejpam-4760	385	5	,	,	PUNCT
ejpam-4760	385	6	t	t	PROPN
ejpam-4760	385	7	)	)	PUNCT
ejpam-4760	385	8	}	}	PUNCT
ejpam-4760	385	9	=	=	SYM
ejpam-4760	385	10	ng[h]((p	ng[h]((p	NOUN
ejpam-4760	385	11	,	,	PUNCT
ejpam-4760	385	12	q))∩c	q))∩c	NOUN
ejpam-4760	385	13	,	,	PUNCT
ejpam-4760	385	14	that	that	ADV
ejpam-4760	385	15	is	is	ADV
ejpam-4760	385	16	,	,	PUNCT
ejpam-4760	385	17	the	the	DET
ejpam-4760	385	18	point	point	NOUN
ejpam-4760	385	19	(	(	PUNCT
ejpam-4760	385	20	p	p	X
ejpam-4760	385	21	,	,	PUNCT
ejpam-4760	385	22	q	q	NOUN
ejpam-4760	385	23	)	)	PUNCT
ejpam-4760	385	24	∈	∈	NOUN
ejpam-4760	385	25	v	v	NOUN
ejpam-4760	385	26	(	(	PUNCT
ejpam-4760	385	27	g[h])\c	g[h])\c	PROPN
ejpam-4760	385	28	is	be	AUX
ejpam-4760	385	29	dominated	dominate	VERB
ejpam-4760	385	30	by	by	ADP
ejpam-4760	385	31	exactly	exactly	ADV
ejpam-4760	385	32	one	one	NUM
ejpam-4760	385	33	vertex	vertex	NOUN
ejpam-4760	385	34	(	(	PUNCT
ejpam-4760	385	35	x	x	NOUN
ejpam-4760	385	36	,	,	PUNCT
ejpam-4760	385	37	t	t	PROPN
ejpam-4760	385	38	)	)	PUNCT
ejpam-4760	385	39	in	in	ADP
ejpam-4760	385	40	c.	c.	PROPN
ejpam-4760	385	41	hence	hence	ADV
ejpam-4760	385	42	,	,	PUNCT
ejpam-4760	385	43	c	c	PROPN
ejpam-4760	385	44	is	be	AUX
ejpam-4760	385	45	a	a	DET
ejpam-4760	385	46	perfect	perfect	ADJ
ejpam-4760	385	47	dominating	dominating	NOUN
ejpam-4760	385	48	set	set	NOUN
ejpam-4760	385	49	.	.	PUNCT
ejpam-4760	386	1	case	case	NOUN
ejpam-4760	386	2	2	2	NUM
ejpam-4760	386	3	:	:	PUNCT
ejpam-4760	386	4	p	p	X
ejpam-4760	386	5	∈	∈	PROPN
ejpam-4760	386	6	s.	s.	PROPN
ejpam-4760	386	7	since	since	SCONJ
ejpam-4760	386	8	tx	tx	PROPN
ejpam-4760	386	9	=	=	PUNCT
ejpam-4760	386	10	{	{	PUNCT
ejpam-4760	386	11	t	t	NOUN
ejpam-4760	386	12	}	}	PUNCT
ejpam-4760	386	13	and	and	CCONJ
ejpam-4760	386	14	s	s	VERB
ejpam-4760	386	15	is	be	AUX
ejpam-4760	386	16	a	a	DET
ejpam-4760	386	17	perfect	perfect	ADJ
ejpam-4760	386	18	dominating	dominating	NOUN
ejpam-4760	386	19	set	set	NOUN
ejpam-4760	386	20	,	,	PUNCT
ejpam-4760	386	21	{	{	PUNCT
ejpam-4760	386	22	(	(	PUNCT
ejpam-4760	386	23	p	p	X
ejpam-4760	386	24	,	,	PUNCT
ejpam-4760	386	25	t	t	PROPN
ejpam-4760	386	26	)	)	PUNCT
ejpam-4760	386	27	}	}	PUNCT
ejpam-4760	386	28	=	=	SYM
ejpam-4760	386	29	ng[h]((p	ng[h]((p	NOUN
ejpam-4760	386	30	,	,	PUNCT
ejpam-4760	386	31	q))∩c	q))∩c	NOUN
ejpam-4760	386	32	,	,	PUNCT
ejpam-4760	386	33	that	that	ADV
ejpam-4760	386	34	is	is	ADV
ejpam-4760	386	35	,	,	PUNCT
ejpam-4760	386	36	the	the	DET
ejpam-4760	386	37	point	point	NOUN
ejpam-4760	386	38	(	(	PUNCT
ejpam-4760	386	39	p	p	X
ejpam-4760	386	40	,	,	PUNCT
ejpam-4760	386	41	q	q	NOUN
ejpam-4760	386	42	)	)	PUNCT
ejpam-4760	386	43	∈	∈	NOUN
ejpam-4760	386	44	v	v	NOUN
ejpam-4760	386	45	(	(	PUNCT
ejpam-4760	386	46	g[h	g[h	PROPN
ejpam-4760	386	47	]	]	PUNCT
ejpam-4760	386	48	)	)	PUNCT
ejpam-4760	386	49	\	\	PUNCT
ejpam-4760	387	1	c	c	NOUN
ejpam-4760	387	2	is	be	AUX
ejpam-4760	387	3	dominated	dominate	VERB
ejpam-4760	387	4	by	by	ADP
ejpam-4760	387	5	exactly	exactly	ADV
ejpam-4760	387	6	one	one	NUM
ejpam-4760	387	7	vertex	vertex	NOUN
ejpam-4760	387	8	(	(	PUNCT
ejpam-4760	387	9	p	p	X
ejpam-4760	387	10	,	,	PUNCT
ejpam-4760	387	11	t	t	PROPN
ejpam-4760	387	12	)	)	PUNCT
ejpam-4760	387	13	in	in	ADP
ejpam-4760	387	14	c.	c.	PROPN
ejpam-4760	387	15	hence	hence	ADV
ejpam-4760	387	16	,	,	PUNCT
ejpam-4760	387	17	c	c	PROPN
ejpam-4760	387	18	is	be	AUX
ejpam-4760	387	19	a	a	DET
ejpam-4760	387	20	perfect	perfect	ADJ
ejpam-4760	387	21	dominating	dominating	NOUN
ejpam-4760	387	22	set	set	NOUN
ejpam-4760	387	23	.	.	PUNCT
ejpam-4760	388	1	since	since	SCONJ
ejpam-4760	388	2	s	s	NOUN
ejpam-4760	388	3	is	be	AUX
ejpam-4760	388	4	independent	independent	ADJ
ejpam-4760	388	5	set	set	NOUN
ejpam-4760	388	6	and	and	CCONJ
ejpam-4760	388	7	tx	tx	PROPN
ejpam-4760	388	8	is	be	AUX
ejpam-4760	388	9	a	a	DET
ejpam-4760	388	10	dominating	dominating	NOUN
ejpam-4760	388	11	set	set	VERB
ejpam-4760	388	12	with	with	ADP
ejpam-4760	388	13	|tx|	|tx|	NOUN
ejpam-4760	388	14	=	=	SYM
ejpam-4760	388	15	1	1	NUM
ejpam-4760	388	16	,	,	PUNCT
ejpam-4760	388	17	c	c	PROPN
ejpam-4760	388	18	is	be	AUX
ejpam-4760	388	19	also	also	ADV
ejpam-4760	388	20	independent	independent	ADJ
ejpam-4760	388	21	set	set	NOUN
ejpam-4760	388	22	and	and	CCONJ
ejpam-4760	388	23	so	so	ADV
ejpam-4760	388	24	,	,	PUNCT
ejpam-4760	388	25	⟨c⟩	⟨c⟩	PROPN
ejpam-4760	388	26	contains	contain	VERB
ejpam-4760	388	27	isolated	isolated	ADJ
ejpam-4760	388	28	vertices	vertex	NOUN
ejpam-4760	388	29	.	.	PUNCT
ejpam-4760	389	1	accordingly	accordingly	ADV
ejpam-4760	389	2	,	,	PUNCT
ejpam-4760	389	3	c	c	PROPN
ejpam-4760	389	4	is	be	AUX
ejpam-4760	389	5	a	a	DET
ejpam-4760	389	6	perfect	perfect	ADJ
ejpam-4760	389	7	isolate	isolate	NOUN
ejpam-4760	389	8	dominating	dominating	NOUN
ejpam-4760	389	9	set	set	NOUN
ejpam-4760	389	10	of	of	ADP
ejpam-4760	389	11	g[h	g[h	PROPN
ejpam-4760	389	12	]	]	PUNCT
ejpam-4760	389	13	.	.	PUNCT
ejpam-4760	390	1	the	the	DET
ejpam-4760	390	2	next	next	ADJ
ejpam-4760	390	3	two	two	NUM
ejpam-4760	390	4	results	result	NOUN
ejpam-4760	390	5	follow	follow	VERB
ejpam-4760	390	6	from	from	ADP
ejpam-4760	390	7	theorem	theorem	ADJ
ejpam-4760	390	8	11	11	NUM
ejpam-4760	390	9	.	.	PUNCT
ejpam-4760	391	1	corollary	corollary	ADJ
ejpam-4760	391	2	13	13	NUM
ejpam-4760	391	3	.	.	PUNCT
ejpam-4760	392	1	let	let	VERB
ejpam-4760	392	2	g	g	NOUN
ejpam-4760	392	3	and	and	CCONJ
ejpam-4760	392	4	h	h	NOUN
ejpam-4760	392	5	be	be	AUX
ejpam-4760	392	6	connected	connect	VERB
ejpam-4760	392	7	graphs	graph	NOUN
ejpam-4760	392	8	.	.	PUNCT
ejpam-4760	393	1	then	then	ADV
ejpam-4760	393	2	γp0(g[h	γp0(g[h	ADJ
ejpam-4760	393	3	]	]	X
ejpam-4760	393	4	)	)	PUNCT
ejpam-4760	394	1	=	=	SYM
ejpam-4760	394	2			NOUN
ejpam-4760	394	3	γp0(g	γp0(g	NOUN
ejpam-4760	394	4	)	)	PUNCT
ejpam-4760	394	5	,	,	PUNCT
ejpam-4760	394	6	if	if	SCONJ
ejpam-4760	394	7	h	h	NOUN
ejpam-4760	394	8	=	=	PROPN
ejpam-4760	394	9	k1	k1	PROPN
ejpam-4760	394	10	γp0(h	γp0(h	PROPN
ejpam-4760	394	11	)	)	PUNCT
ejpam-4760	394	12	,	,	PUNCT
ejpam-4760	394	13	if	if	SCONJ
ejpam-4760	394	14	g	g	PROPN
ejpam-4760	394	15	=	=	SYM
ejpam-4760	394	16	k1	k1	PROPN
ejpam-4760	394	17	γip(g	γip(g	PROPN
ejpam-4760	394	18	)	)	PUNCT
ejpam-4760	394	19	,	,	PUNCT
ejpam-4760	394	20	if	if	SCONJ
ejpam-4760	394	21	g	g	PROPN
ejpam-4760	394	22	has	have	VERB
ejpam-4760	394	23	an	an	DET
ejpam-4760	394	24	ipds	ipds	NOUN
ejpam-4760	394	25	and	and	CCONJ
ejpam-4760	394	26	γ(h	γ(h	NOUN
ejpam-4760	394	27	)	)	PUNCT
ejpam-4760	394	28	=	=	SYM
ejpam-4760	395	1	1	1	X
ejpam-4760	395	2	.	.	PUNCT
ejpam-4760	395	3	corollary	corollary	ADJ
ejpam-4760	395	4	14	14	NUM
ejpam-4760	395	5	.	.	PUNCT
ejpam-4760	396	1	let	let	VERB
ejpam-4760	396	2	g	g	NOUN
ejpam-4760	396	3	and	and	CCONJ
ejpam-4760	396	4	h	h	NOUN
ejpam-4760	396	5	be	be	AUX
ejpam-4760	396	6	connected	connect	VERB
ejpam-4760	396	7	graphs	graph	NOUN
ejpam-4760	396	8	.	.	PUNCT
ejpam-4760	397	1	then	then	ADV
ejpam-4760	397	2	g[h	g[h	VERB
ejpam-4760	397	3	]	]	PUNCT
ejpam-4760	397	4	is	be	AUX
ejpam-4760	397	5	a	a	DET
ejpam-4760	397	6	non	non	ADJ
ejpam-4760	397	7	-	-	ADJ
ejpam-4760	397	8	γp0	γp0	NOUN
ejpam-4760	397	9	-	-	PUNCT
ejpam-4760	397	10	graph	graph	NOUN
ejpam-4760	397	11	if	if	SCONJ
ejpam-4760	398	1	and	and	CCONJ
ejpam-4760	398	2	only	only	ADV
ejpam-4760	398	3	if	if	SCONJ
ejpam-4760	398	4	one	one	NUM
ejpam-4760	398	5	of	of	ADP
ejpam-4760	398	6	the	the	DET
ejpam-4760	398	7	two	two	NUM
ejpam-4760	398	8	cases	case	NOUN
ejpam-4760	398	9	is	be	AUX
ejpam-4760	398	10	satisfied	satisfied	ADJ
ejpam-4760	398	11	:	:	PUNCT
ejpam-4760	398	12	(	(	PUNCT
ejpam-4760	398	13	i	i	NOUN
ejpam-4760	398	14	)	)	PUNCT
ejpam-4760	398	15	γ(h	γ(h	PROPN
ejpam-4760	398	16	)	)	PUNCT
ejpam-4760	398	17	≥	≥	NOUN
ejpam-4760	398	18	2	2	NUM
ejpam-4760	398	19	(	(	PUNCT
ejpam-4760	398	20	ii	ii	NOUN
ejpam-4760	398	21	)	)	PUNCT
ejpam-4760	398	22	γ(h	γ(h	NOUN
ejpam-4760	398	23	)	)	PUNCT
ejpam-4760	398	24	=	=	SYM
ejpam-4760	399	1	1	1	NUM
ejpam-4760	399	2	and	and	CCONJ
ejpam-4760	399	3	g	g	PROPN
ejpam-4760	399	4	has	have	VERB
ejpam-4760	399	5	no	no	DET
ejpam-4760	399	6	independent	independent	ADJ
ejpam-4760	399	7	perfect	perfect	ADJ
ejpam-4760	399	8	dominating	dominating	NOUN
ejpam-4760	399	9	set	set	NOUN
ejpam-4760	399	10	.	.	PUNCT
ejpam-4760	400	1	the	the	DET
ejpam-4760	400	2	next	next	ADJ
ejpam-4760	400	3	two	two	NUM
ejpam-4760	400	4	results	result	NOUN
ejpam-4760	400	5	follow	follow	VERB
ejpam-4760	400	6	from	from	ADP
ejpam-4760	400	7	corollary	corollary	ADJ
ejpam-4760	400	8	13	13	NUM
ejpam-4760	400	9	.	.	PUNCT
ejpam-4760	401	1	c.	c.	PROPN
ejpam-4760	401	2	armada	armada	PROPN
ejpam-4760	401	3	,	,	PUNCT
ejpam-4760	401	4	j.	j.	PROPN
ejpam-4760	401	5	hamja	hamja	PROPN
ejpam-4760	401	6	/	/	SYM
ejpam-4760	401	7	eur	eur	PROPN
ejpam-4760	401	8	.	.	PUNCT
ejpam-4760	402	1	j.	j.	PROPN
ejpam-4760	402	2	pure	pure	PROPN
ejpam-4760	402	3	appl	appl	PROPN
ejpam-4760	402	4	.	.	PROPN
ejpam-4760	402	5	math	math	PROPN
ejpam-4760	402	6	,	,	PUNCT
ejpam-4760	402	7	16	16	NUM
ejpam-4760	402	8	(	(	PUNCT
ejpam-4760	402	9	2	2	NUM
ejpam-4760	402	10	)	)	PUNCT
ejpam-4760	402	11	(	(	PUNCT
ejpam-4760	402	12	2023	2023	NUM
ejpam-4760	402	13	)	)	PUNCT
ejpam-4760	402	14	,	,	PUNCT
ejpam-4760	402	15	1326	1326	NUM
ejpam-4760	402	16	-	-	SYM
ejpam-4760	402	17	1341	1341	NUM
ejpam-4760	402	18	1340	1340	NUM
ejpam-4760	402	19	corollary	corollary	NOUN
ejpam-4760	402	20	15	15	NUM
ejpam-4760	402	21	.	.	PUNCT
ejpam-4760	403	1	let	let	VERB
ejpam-4760	403	2	g	g	PRON
ejpam-4760	403	3	be	be	AUX
ejpam-4760	403	4	a	a	DET
ejpam-4760	403	5	connected	connected	ADJ
ejpam-4760	403	6	graph	graph	NOUN
ejpam-4760	403	7	such	such	ADJ
ejpam-4760	403	8	that	that	SCONJ
ejpam-4760	403	9	g	g	PROPN
ejpam-4760	403	10	has	have	VERB
ejpam-4760	403	11	an	an	DET
ejpam-4760	403	12	ipds	ipds	NOUN
ejpam-4760	403	13	and	and	CCONJ
ejpam-4760	403	14	kn	kn	PROPN
ejpam-4760	403	15	be	be	AUX
ejpam-4760	403	16	a	a	DET
ejpam-4760	403	17	complete	complete	ADJ
ejpam-4760	403	18	graph	graph	NOUN
ejpam-4760	403	19	.	.	PUNCT
ejpam-4760	404	1	then	then	ADV
ejpam-4760	404	2	γp0(g[kn	γp0(g[kn	PROPN
ejpam-4760	404	3	]	]	PUNCT
ejpam-4760	404	4	)	)	PUNCT
ejpam-4760	404	5	=	=	PRON
ejpam-4760	404	6	{	{	PUNCT
ejpam-4760	404	7	γp0(g	γp0(g	NOUN
ejpam-4760	404	8	)	)	PUNCT
ejpam-4760	404	9	,	,	PUNCT
ejpam-4760	404	10	if	if	SCONJ
ejpam-4760	404	11	n	n	CCONJ
ejpam-4760	404	12	=	=	SYM
ejpam-4760	404	13	1	1	NUM
ejpam-4760	404	14	γip(g	γip(g	NUM
ejpam-4760	404	15	)	)	PUNCT
ejpam-4760	404	16	,	,	PUNCT
ejpam-4760	404	17	if	if	SCONJ
ejpam-4760	404	18	n	n	PROPN
ejpam-4760	404	19	>	>	X
ejpam-4760	404	20	1	1	X
ejpam-4760	404	21	.	.	PUNCT
ejpam-4760	404	22	corollary	corollary	ADJ
ejpam-4760	404	23	16	16	NUM
ejpam-4760	404	24	.	.	PUNCT
ejpam-4760	405	1	let	let	VERB
ejpam-4760	405	2	g	g	PRON
ejpam-4760	405	3	be	be	AUX
ejpam-4760	405	4	a	a	DET
ejpam-4760	405	5	connected	connected	ADJ
ejpam-4760	405	6	graph	graph	NOUN
ejpam-4760	405	7	such	such	ADJ
ejpam-4760	405	8	that	that	SCONJ
ejpam-4760	405	9	g	g	PROPN
ejpam-4760	405	10	has	have	VERB
ejpam-4760	405	11	an	an	DET
ejpam-4760	405	12	ipds	ipds	NOUN
ejpam-4760	405	13	and	and	CCONJ
ejpam-4760	405	14	h	h	NOUN
ejpam-4760	405	15	be	be	VERB
ejpam-4760	405	16	any	any	DET
ejpam-4760	405	17	graph	graph	NOUN
ejpam-4760	405	18	described	describe	VERB
ejpam-4760	405	19	in	in	ADP
ejpam-4760	405	20	corollary	corollary	ADJ
ejpam-4760	405	21	5	5	NUM
ejpam-4760	405	22	.	.	PUNCT
ejpam-4760	405	23	then	then	ADV
ejpam-4760	405	24	γp0(g[h	γp0(g[h	ADJ
ejpam-4760	405	25	]	]	X
ejpam-4760	405	26	)	)	PUNCT
ejpam-4760	405	27	=	=	SYM
ejpam-4760	405	28	γip(g	γip(g	PROPN
ejpam-4760	405	29	)	)	PUNCT
ejpam-4760	405	30	.	.	PUNCT
ejpam-4760	406	1	the	the	DET
ejpam-4760	406	2	next	next	ADJ
ejpam-4760	406	3	result	result	NOUN
ejpam-4760	406	4	follows	follow	VERB
ejpam-4760	406	5	from	from	ADP
ejpam-4760	406	6	corollary	corollary	ADJ
ejpam-4760	406	7	14	14	NUM
ejpam-4760	406	8	(	(	PUNCT
ejpam-4760	406	9	ii	ii	NOUN
ejpam-4760	406	10	)	)	PUNCT
ejpam-4760	406	11	.	.	PUNCT
ejpam-4760	407	1	corollary	corollary	ADJ
ejpam-4760	407	2	17	17	NUM
ejpam-4760	407	3	.	.	PUNCT
ejpam-4760	408	1	let	let	VERB
ejpam-4760	408	2	g	g	PRON
ejpam-4760	408	3	be	be	AUX
ejpam-4760	408	4	a	a	DET
ejpam-4760	408	5	connected	connected	ADJ
ejpam-4760	408	6	graph	graph	NOUN
ejpam-4760	408	7	such	such	ADJ
ejpam-4760	408	8	that	that	SCONJ
ejpam-4760	408	9	g	g	PROPN
ejpam-4760	408	10	has	have	VERB
ejpam-4760	408	11	no	no	DET
ejpam-4760	408	12	ipds	ipds	NOUN
ejpam-4760	408	13	and	and	CCONJ
ejpam-4760	408	14	h	h	NOUN
ejpam-4760	408	15	be	be	VERB
ejpam-4760	408	16	any	any	DET
ejpam-4760	408	17	graph	graph	NOUN
ejpam-4760	408	18	.	.	PUNCT
ejpam-4760	409	1	then	then	ADV
ejpam-4760	409	2	g[h	g[h	VERB
ejpam-4760	409	3	]	]	PUNCT
ejpam-4760	409	4	is	be	AUX
ejpam-4760	409	5	non	non	ADJ
ejpam-4760	409	6	-	-	ADJ
ejpam-4760	409	7	γp0	γp0	NOUN
ejpam-4760	409	8	-	-	PUNCT
ejpam-4760	409	9	graphs	graph	NOUN
ejpam-4760	409	10	.	.	PUNCT
ejpam-4760	410	1	the	the	DET
ejpam-4760	410	2	next	next	ADJ
ejpam-4760	410	3	result	result	NOUN
ejpam-4760	410	4	follows	follow	VERB
ejpam-4760	410	5	from	from	ADP
ejpam-4760	410	6	corollary	corollary	ADJ
ejpam-4760	410	7	14	14	NUM
ejpam-4760	410	8	(	(	PUNCT
ejpam-4760	410	9	i	i	NOUN
ejpam-4760	410	10	)	)	PUNCT
ejpam-4760	410	11	.	.	PUNCT
ejpam-4760	411	1	corollary	corollary	ADJ
ejpam-4760	411	2	18	18	NUM
ejpam-4760	411	3	.	.	PUNCT
ejpam-4760	412	1	let	let	VERB
ejpam-4760	412	2	g	g	PRON
ejpam-4760	412	3	be	be	AUX
ejpam-4760	412	4	a	a	DET
ejpam-4760	412	5	connected	connected	ADJ
ejpam-4760	412	6	graph	graph	NOUN
ejpam-4760	412	7	and	and	CCONJ
ejpam-4760	412	8	h	h	NOUN
ejpam-4760	412	9	be	be	AUX
ejpam-4760	412	10	any	any	DET
ejpam-4760	412	11	graph	graph	NOUN
ejpam-4760	412	12	described	describe	VERB
ejpam-4760	412	13	in	in	ADP
ejpam-4760	412	14	corollary	corollary	ADJ
ejpam-4760	412	15	6	6	NUM
ejpam-4760	412	16	.	.	PUNCT
ejpam-4760	413	1	then	then	ADV
ejpam-4760	413	2	g[h	g[h	PROPN
ejpam-4760	413	3	]	]	PUNCT
ejpam-4760	413	4	is	be	AUX
ejpam-4760	413	5	non	non	ADJ
ejpam-4760	413	6	-	-	ADJ
ejpam-4760	413	7	γp0	γp0	NOUN
ejpam-4760	413	8	-	-	PUNCT
ejpam-4760	413	9	graphs	graph	NOUN
ejpam-4760	413	10	.	.	PUNCT
ejpam-4760	414	1	the	the	DET
ejpam-4760	414	2	next	next	ADJ
ejpam-4760	414	3	result	result	NOUN
ejpam-4760	414	4	follows	follow	VERB
ejpam-4760	414	5	from	from	ADP
ejpam-4760	414	6	corollary	corollary	ADJ
ejpam-4760	414	7	13	13	NUM
ejpam-4760	414	8	and	and	CCONJ
ejpam-4760	414	9	corollary	corollary	ADJ
ejpam-4760	414	10	14	14	NUM
ejpam-4760	414	11	.	.	PUNCT
ejpam-4760	415	1	corollary	corollary	ADJ
ejpam-4760	415	2	19	19	NUM
ejpam-4760	415	3	.	.	PUNCT
ejpam-4760	416	1	let	let	VERB
ejpam-4760	416	2	g	g	PRON
ejpam-4760	416	3	be	be	AUX
ejpam-4760	416	4	a	a	DET
ejpam-4760	416	5	connected	connected	ADJ
ejpam-4760	416	6	graph	graph	NOUN
ejpam-4760	416	7	such	such	ADJ
ejpam-4760	416	8	that	that	SCONJ
ejpam-4760	416	9	g	g	PROPN
ejpam-4760	416	10	has	have	VERB
ejpam-4760	416	11	an	an	DET
ejpam-4760	416	12	ipds	ipds	NOUN
ejpam-4760	416	13	.	.	PUNCT
ejpam-4760	417	1	then	then	ADV
ejpam-4760	417	2	for	for	ADP
ejpam-4760	417	3	n	n	PRON
ejpam-4760	417	4	≥	≥	NUM
ejpam-4760	417	5	4	4	NUM
ejpam-4760	417	6	,	,	PUNCT
ejpam-4760	417	7	g[pn	g[pn	PROPN
ejpam-4760	417	8	]	]	PUNCT
ejpam-4760	417	9	and	and	CCONJ
ejpam-4760	417	10	g[cn	g[cn	PROPN
ejpam-4760	417	11	]	]	PUNCT
ejpam-4760	417	12	are	be	AUX
ejpam-4760	417	13	non	non	ADJ
ejpam-4760	417	14	-	-	ADJ
ejpam-4760	417	15	γp0	γp0	NOUN
ejpam-4760	417	16	-	-	PUNCT
ejpam-4760	417	17	graphs	graph	NOUN
ejpam-4760	417	18	and	and	CCONJ
ejpam-4760	417	19	for	for	ADP
ejpam-4760	417	20	n	n	NOUN
ejpam-4760	417	21	=	=	SYM
ejpam-4760	417	22	2	2	NUM
ejpam-4760	417	23	,	,	PUNCT
ejpam-4760	417	24	3	3	NUM
ejpam-4760	417	25	,	,	PUNCT
ejpam-4760	417	26	γp0(g[pn	γp0(g[pn	PROPN
ejpam-4760	417	27	]	]	PUNCT
ejpam-4760	417	28	)	)	PUNCT
ejpam-4760	417	29	=	=	SYM
ejpam-4760	417	30	γp0(g[c3	γp0(g[c3	PROPN
ejpam-4760	417	31	]	]	PUNCT
ejpam-4760	417	32	)	)	PUNCT
ejpam-4760	417	33	=	=	SYM
ejpam-4760	417	34	γip(g	γip(g	PROPN
ejpam-4760	417	35	)	)	PUNCT
ejpam-4760	417	36	.	.	PUNCT
ejpam-4760	418	1	7	7	X
ejpam-4760	418	2	.	.	X
ejpam-4760	418	3	conclusion	conclusion	NOUN
ejpam-4760	418	4	the	the	DET
ejpam-4760	418	5	paper	paper	NOUN
ejpam-4760	418	6	has	have	AUX
ejpam-4760	418	7	introduced	introduce	VERB
ejpam-4760	418	8	the	the	DET
ejpam-4760	418	9	concept	concept	NOUN
ejpam-4760	418	10	of	of	ADP
ejpam-4760	418	11	perfect	perfect	ADJ
ejpam-4760	418	12	isolate	isolate	NOUN
ejpam-4760	418	13	dominating	dominating	NOUN
ejpam-4760	418	14	sets	set	NOUN
ejpam-4760	418	15	of	of	ADP
ejpam-4760	418	16	some	some	DET
ejpam-4760	418	17	graphs	graph	NOUN
ejpam-4760	418	18	resulting	result	VERB
ejpam-4760	418	19	from	from	ADP
ejpam-4760	418	20	some	some	DET
ejpam-4760	418	21	binary	binary	ADJ
ejpam-4760	418	22	operations	operation	NOUN
ejpam-4760	418	23	such	such	ADJ
ejpam-4760	418	24	as	as	ADP
ejpam-4760	418	25	join	join	NOUN
ejpam-4760	418	26	,	,	PUNCT
ejpam-4760	418	27	corona	corona	NOUN
ejpam-4760	418	28	,	,	PUNCT
ejpam-4760	418	29	and	and	CCONJ
ejpam-4760	418	30	lexicographic	lexicographic	ADJ
ejpam-4760	418	31	product	product	NOUN
ejpam-4760	418	32	of	of	ADP
ejpam-4760	418	33	two	two	NUM
ejpam-4760	418	34	graphs	graph	NOUN
ejpam-4760	418	35	.	.	PUNCT
ejpam-4760	419	1	the	the	DET
ejpam-4760	419	2	existence	existence	NOUN
ejpam-4760	419	3	of	of	ADP
ejpam-4760	419	4	the	the	DET
ejpam-4760	419	5	perfect	perfect	ADJ
ejpam-4760	419	6	isolate	isolate	NOUN
ejpam-4760	419	7	dominating	dominating	NOUN
ejpam-4760	419	8	sets	set	NOUN
ejpam-4760	419	9	of	of	ADP
ejpam-4760	419	10	some	some	DET
ejpam-4760	419	11	graphs	graph	NOUN
ejpam-4760	419	12	and	and	CCONJ
ejpam-4760	419	13	some	some	DET
ejpam-4760	419	14	binary	binary	ADJ
ejpam-4760	419	15	operations	operation	NOUN
ejpam-4760	419	16	are	be	AUX
ejpam-4760	419	17	examine	examine	ADJ
ejpam-4760	419	18	because	because	SCONJ
ejpam-4760	419	19	not	not	PART
ejpam-4760	419	20	all	all	DET
ejpam-4760	419	21	graphs	graph	NOUN
ejpam-4760	419	22	have	have	VERB
ejpam-4760	419	23	this	this	DET
ejpam-4760	419	24	set	set	NOUN
ejpam-4760	419	25	.	.	PUNCT
ejpam-4760	420	1	for	for	ADP
ejpam-4760	420	2	future	future	ADJ
ejpam-4760	420	3	investigation	investigation	NOUN
ejpam-4760	420	4	,	,	PUNCT
ejpam-4760	420	5	the	the	DET
ejpam-4760	420	6	authors	author	NOUN
ejpam-4760	420	7	recommend	recommend	VERB
ejpam-4760	420	8	to	to	PART
ejpam-4760	420	9	explore	explore	VERB
ejpam-4760	420	10	this	this	DET
ejpam-4760	420	11	parameter	parameter	NOUN
ejpam-4760	420	12	to	to	PART
ejpam-4760	420	13	determine	determine	VERB
ejpam-4760	420	14	the	the	DET
ejpam-4760	420	15	exact	exact	ADJ
ejpam-4760	420	16	values	value	NOUN
ejpam-4760	420	17	of	of	ADP
ejpam-4760	420	18	some	some	DET
ejpam-4760	420	19	graphs	graph	NOUN
ejpam-4760	420	20	and	and	CCONJ
ejpam-4760	420	21	some	some	DET
ejpam-4760	420	22	binary	binary	ADJ
ejpam-4760	420	23	operations	operation	NOUN
ejpam-4760	420	24	that	that	PRON
ejpam-4760	420	25	have	have	AUX
ejpam-4760	420	26	not	not	PART
ejpam-4760	420	27	discussed	discuss	VERB
ejpam-4760	420	28	in	in	ADP
ejpam-4760	420	29	the	the	DET
ejpam-4760	420	30	study	study	NOUN
ejpam-4760	420	31	.	.	PUNCT
ejpam-4760	421	1	moreover	moreover	ADV
ejpam-4760	421	2	,	,	PUNCT
ejpam-4760	421	3	look	look	VERB
ejpam-4760	421	4	for	for	SCONJ
ejpam-4760	421	5	the	the	DET
ejpam-4760	421	6	relationship	relationship	NOUN
ejpam-4760	421	7	with	with	ADP
ejpam-4760	421	8	other	other	ADJ
ejpam-4760	421	9	parameters	parameter	NOUN
ejpam-4760	421	10	of	of	ADP
ejpam-4760	421	11	domination	domination	NOUN
ejpam-4760	421	12	which	which	PRON
ejpam-4760	421	13	are	be	AUX
ejpam-4760	421	14	related	relate	VERB
ejpam-4760	421	15	to	to	ADP
ejpam-4760	421	16	this	this	DET
ejpam-4760	421	17	parameter	parameter	NOUN
ejpam-4760	421	18	.	.	PUNCT
ejpam-4760	422	1	acknowledgements	acknowledgement	NOUN
ejpam-4760	422	2	the	the	DET
ejpam-4760	422	3	authors	author	NOUN
ejpam-4760	422	4	would	would	AUX
ejpam-4760	422	5	like	like	VERB
ejpam-4760	422	6	to	to	PART
ejpam-4760	422	7	thank	thank	VERB
ejpam-4760	422	8	the	the	DET
ejpam-4760	422	9	anonymous	anonymous	ADJ
ejpam-4760	422	10	referees	referee	NOUN
ejpam-4760	422	11	for	for	ADP
ejpam-4760	422	12	their	their	PRON
ejpam-4760	422	13	comments	comment	NOUN
ejpam-4760	422	14	and	and	CCONJ
ejpam-4760	422	15	suggestions	suggestion	NOUN
ejpam-4760	422	16	which	which	PRON
ejpam-4760	422	17	led	lead	VERB
ejpam-4760	422	18	to	to	ADP
ejpam-4760	422	19	the	the	DET
ejpam-4760	422	20	betterment	betterment	NOUN
ejpam-4760	422	21	of	of	ADP
ejpam-4760	422	22	the	the	DET
ejpam-4760	422	23	paper	paper	NOUN
ejpam-4760	422	24	.	.	PUNCT
ejpam-4760	423	1	this	this	DET
ejpam-4760	423	2	study	study	NOUN
ejpam-4760	423	3	has	have	AUX
ejpam-4760	423	4	been	be	AUX
ejpam-4760	423	5	supported	support	VERB
ejpam-4760	423	6	by	by	ADP
ejpam-4760	423	7	mindanao	mindanao	PROPN
ejpam-4760	423	8	state	state	PROPN
ejpam-4760	423	9	university	university	PROPN
ejpam-4760	423	10	tawi	tawi	PROPN
ejpam-4760	423	11	-	-	PUNCT
ejpam-4760	423	12	tawi	tawi	PROPN
ejpam-4760	423	13	college	college	PROPN
ejpam-4760	423	14	of	of	ADP
ejpam-4760	423	15	technology	technology	NOUN
ejpam-4760	423	16	and	and	CCONJ
ejpam-4760	423	17	oceanography	oceanography	NOUN
ejpam-4760	423	18	and	and	CCONJ
ejpam-4760	423	19	the	the	DET
ejpam-4760	423	20	college	college	NOUN
ejpam-4760	423	21	of	of	ADP
ejpam-4760	423	22	arts	art	NOUN
ejpam-4760	423	23	and	and	CCONJ
ejpam-4760	423	24	sciences	science	NOUN
ejpam-4760	423	25	and	and	CCONJ
ejpam-4760	423	26	center	center	NOUN
ejpam-4760	423	27	for	for	ADP
ejpam-4760	423	28	research	research	NOUN
ejpam-4760	423	29	and	and	CCONJ
ejpam-4760	423	30	development	development	NOUN
ejpam-4760	423	31	of	of	ADP
ejpam-4760	423	32	cebu	cebu	PROPN
ejpam-4760	423	33	normal	normal	ADJ
ejpam-4760	423	34	university	university	NOUN
ejpam-4760	423	35	.	.	PUNCT
ejpam-4760	424	1	references	reference	NOUN
ejpam-4760	424	2	1341	1341	NUM
ejpam-4760	424	3	references	reference	NOUN
ejpam-4760	424	4	[	[	X
ejpam-4760	424	5	1	1	NUM
ejpam-4760	424	6	]	]	X
ejpam-4760	424	7	c.	c.	PROPN
ejpam-4760	424	8	armada	armada	PROPN
ejpam-4760	424	9	.	.	PUNCT
ejpam-4760	425	1	forcing	force	VERB
ejpam-4760	425	2	total	total	ADJ
ejpam-4760	425	3	dr	dr	PROPN
ejpam-4760	425	4	-	-	PUNCT
ejpam-4760	425	5	power	power	NOUN
ejpam-4760	425	6	domination	domination	NOUN
ejpam-4760	425	7	number	number	NOUN
ejpam-4760	425	8	of	of	ADP
ejpam-4760	425	9	graphs	graph	NOUN
ejpam-4760	425	10	under	under	ADP
ejpam-4760	425	11	some	some	DET
ejpam-4760	425	12	binary	binary	ADJ
ejpam-4760	425	13	operations	operation	NOUN
ejpam-4760	425	14	.	.	PUNCT
ejpam-4760	426	1	european	european	ADJ
ejpam-4760	426	2	journal	journal	PROPN
ejpam-4760	426	3	of	of	ADP
ejpam-4760	426	4	pure	pure	ADJ
ejpam-4760	426	5	and	and	CCONJ
ejpam-4760	426	6	applied	applied	ADJ
ejpam-4760	426	7	mathematics	mathematic	NOUN
ejpam-4760	426	8	,	,	PUNCT
ejpam-4760	426	9	14(3):1098	14(3):1098	NUM
ejpam-4760	426	10	–	–	PUNCT
ejpam-4760	426	11	1107	1107	NUM
ejpam-4760	426	12	,	,	PUNCT
ejpam-4760	426	13	2021	2021	NUM
ejpam-4760	426	14	.	.	PUNCT
ejpam-4760	427	1	[	[	X
ejpam-4760	427	2	2	2	NUM
ejpam-4760	427	3	]	]	X
ejpam-4760	427	4	b.	b.	PROPN
ejpam-4760	427	5	h.	h.	PROPN
ejpam-4760	427	6	arriola	arriola	PROPN
ejpam-4760	427	7	.	.	PUNCT
ejpam-4760	428	1	solate	solate	ADJ
ejpam-4760	428	2	domination	domination	NOUN
ejpam-4760	428	3	in	in	ADP
ejpam-4760	428	4	the	the	DET
ejpam-4760	428	5	join	join	NOUN
ejpam-4760	428	6	and	and	CCONJ
ejpam-4760	428	7	corona	corona	NOUN
ejpam-4760	428	8	of	of	ADP
ejpam-4760	428	9	graphs	graph	NOUN
ejpam-4760	428	10	i.	i.	PROPN
ejpam-4760	428	11	applied	apply	VERB
ejpam-4760	428	12	mathematical	mathematical	ADJ
ejpam-4760	428	13	sciences	sciences	PROPN
ejpam-4760	428	14	,	,	PUNCT
ejpam-4760	428	15	9(31):1543	9(31):1543	NUM
ejpam-4760	428	16	–	–	PUNCT
ejpam-4760	428	17	1549	1549	NUM
ejpam-4760	428	18	,	,	PUNCT
ejpam-4760	428	19	2015	2015	NUM
ejpam-4760	428	20	.	.	PUNCT
ejpam-4760	429	1	[	[	X
ejpam-4760	429	2	3	3	NUM
ejpam-4760	429	3	]	]	X
ejpam-4760	429	4	c.	c.	PROPN
ejpam-4760	429	5	go	go	VERB
ejpam-4760	429	6	c.	c.	PROPN
ejpam-4760	429	7	armada	armada	PROPN
ejpam-4760	429	8	,	,	PUNCT
ejpam-4760	429	9	s.	s.	PROPN
ejpam-4760	429	10	canoy	canoy	PROPN
ejpam-4760	429	11	jr	jr	PROPN
ejpam-4760	429	12	.	.	PUNCT
ejpam-4760	430	1	forcing	force	VERB
ejpam-4760	430	2	domination	domination	NOUN
ejpam-4760	430	3	numbers	number	NOUN
ejpam-4760	430	4	of	of	ADP
ejpam-4760	430	5	graphs	graph	NOUN
ejpam-4760	430	6	under	under	ADP
ejpam-4760	430	7	some	some	DET
ejpam-4760	430	8	binary	binary	ADJ
ejpam-4760	430	9	operations	operation	NOUN
ejpam-4760	430	10	.	.	PUNCT
ejpam-4760	431	1	advances	advance	NOUN
ejpam-4760	431	2	and	and	CCONJ
ejpam-4760	431	3	applications	application	NOUN
ejpam-4760	431	4	in	in	ADP
ejpam-4760	431	5	discrete	discrete	ADJ
ejpam-4760	431	6	mathematics	mathematic	NOUN
ejpam-4760	431	7	,	,	PUNCT
ejpam-4760	431	8	19:213–228	19:213–228	NUM
ejpam-4760	431	9	,	,	PUNCT
ejpam-4760	431	10	2018	2018	NUM
ejpam-4760	431	11	.	.	PUNCT
ejpam-4760	432	1	[	[	X
ejpam-4760	432	2	4	4	X
ejpam-4760	432	3	]	]	X
ejpam-4760	432	4	i.s	i.s	PROPN
ejpam-4760	432	5	.	.	PROPN
ejpam-4760	432	6	hamid	hamid	PROPN
ejpam-4760	432	7	and	and	CCONJ
ejpam-4760	432	8	s.balamurugan	s.balamurugan	PROPN
ejpam-4760	432	9	.	.	PUNCT
ejpam-4760	432	10	isolate	isolate	VERB
ejpam-4760	432	11	domination	domination	NOUN
ejpam-4760	432	12	in	in	ADP
ejpam-4760	432	13	graphs	graph	NOUN
ejpam-4760	432	14	.	.	PUNCT
ejpam-4760	433	1	arab	arab	PROPN
ejpam-4760	433	2	journal	journal	PROPN
ejpam-4760	433	3	mathematical	mathematical	PROPN
ejpam-4760	433	4	sciences	sciences	PROPN
ejpam-4760	433	5	,	,	PUNCT
ejpam-4760	433	6	pages	page	NOUN
ejpam-4760	433	7	232–241	232–241	NUM
ejpam-4760	433	8	.	.	PROPN
ejpam-4760	433	9	,	,	PUNCT
ejpam-4760	433	10	2016	2016	NUM
ejpam-4760	433	11	.	.	PUNCT
ejpam-4760	434	1	[	[	X
ejpam-4760	434	2	5	5	X
ejpam-4760	434	3	]	]	PUNCT
ejpam-4760	434	4	j.	j.	PROPN
ejpam-4760	434	5	hamja	hamja	PROPN
ejpam-4760	434	6	,	,	PUNCT
ejpam-4760	434	7	i.	i.	PROPN
ejpam-4760	434	8	aniversario	aniversario	PROPN
ejpam-4760	434	9	,	,	PUNCT
ejpam-4760	434	10	and	and	CCONJ
ejpam-4760	434	11	c.	c.	PROPN
ejpam-4760	434	12	merca	merca	PROPN
ejpam-4760	434	13	.	.	PUNCT
ejpam-4760	435	1	weakly	weakly	ADV
ejpam-4760	435	2	connected	connect	VERB
ejpam-4760	435	3	hop	hop	NOUN
ejpam-4760	435	4	domination	domination	NOUN
ejpam-4760	435	5	in	in	ADP
ejpam-4760	435	6	graphs	graph	NOUN
ejpam-4760	435	7	resulting	result	VERB
ejpam-4760	435	8	from	from	ADP
ejpam-4760	435	9	some	some	DET
ejpam-4760	435	10	binary	binary	ADJ
ejpam-4760	435	11	operations	operation	NOUN
ejpam-4760	435	12	.	.	PUNCT
ejpam-4760	436	1	europian	europian	ADJ
ejpam-4760	436	2	journal	journal	PROPN
ejpam-4760	436	3	of	of	ADP
ejpam-4760	436	4	pure	pure	ADJ
ejpam-4760	436	5	and	and	CCONJ
ejpam-4760	436	6	applied	applied	ADJ
ejpam-4760	436	7	mathematics	mathematic	NOUN
ejpam-4760	436	8	,	,	PUNCT
ejpam-4760	436	9	16(1):454–464	16(1):454–464	PROPN
ejpam-4760	436	10	.	.	PUNCT
ejpam-4760	436	11	,	,	PUNCT
ejpam-4760	436	12	2023	2023	NUM
ejpam-4760	436	13	.	.	PUNCT
ejpam-4760	437	1	[	[	X
ejpam-4760	437	2	6	6	NUM
ejpam-4760	437	3	]	]	PUNCT
ejpam-4760	437	4	j.	j.	PROPN
ejpam-4760	437	5	hamja	hamja	PROPN
ejpam-4760	437	6	,	,	PUNCT
ejpam-4760	437	7	i.	i.	PROPN
ejpam-4760	437	8	aniversario	aniversario	PROPN
ejpam-4760	437	9	,	,	PUNCT
ejpam-4760	437	10	and	and	CCONJ
ejpam-4760	437	11	h.	h.	PROPN
ejpam-4760	437	12	rara	rara	PROPN
ejpam-4760	437	13	.	.	PUNCT
ejpam-4760	438	1	on	on	ADP
ejpam-4760	438	2	weakly	weakly	ADJ
ejpam-4760	438	3	connected	connect	VERB
ejpam-4760	438	4	closed	close	VERB
ejpam-4760	438	5	geodetic	geodetic	ADJ
ejpam-4760	438	6	domination	domination	NOUN
ejpam-4760	438	7	in	in	ADP
ejpam-4760	438	8	graphs	graph	NOUN
ejpam-4760	438	9	under	under	ADP
ejpam-4760	438	10	some	some	DET
ejpam-4760	438	11	binary	binary	ADJ
ejpam-4760	438	12	operations	operation	NOUN
ejpam-4760	438	13	.	.	PUNCT
ejpam-4760	439	1	europian	europian	ADJ
ejpam-4760	439	2	journal	journal	PROPN
ejpam-4760	439	3	of	of	ADP
ejpam-4760	439	4	pure	pure	ADJ
ejpam-4760	439	5	and	and	CCONJ
ejpam-4760	439	6	applied	applied	ADJ
ejpam-4760	439	7	mathematics	mathematic	NOUN
ejpam-4760	439	8	,	,	PUNCT
ejpam-4760	439	9	15(2):736–752	15(2):736–752	PROPN
ejpam-4760	439	10	.	.	PROPN
ejpam-4760	439	11	,	,	PUNCT
ejpam-4760	439	12	2022	2022	NUM
ejpam-4760	439	13	.	.	PUNCT
ejpam-4760	440	1	[	[	X
ejpam-4760	440	2	7	7	X
ejpam-4760	440	3	]	]	X
ejpam-4760	440	4	f.	f.	PROPN
ejpam-4760	440	5	harary	harary	PROPN
ejpam-4760	440	6	.	.	PUNCT
ejpam-4760	441	1	graph	graph	NOUN
ejpam-4760	441	2	theory	theory	NOUN
ejpam-4760	441	3	.	.	PUNCT
ejpam-4760	442	1	addison	addison	PROPN
ejpam-4760	442	2	-	-	PUNCT
ejpam-4760	442	3	wesley	wesley	PROPN
ejpam-4760	442	4	publishing	publishing	PROPN
ejpam-4760	442	5	company	company	PROPN
ejpam-4760	442	6	,	,	PUNCT
ejpam-4760	442	7	inc	inc	PROPN
ejpam-4760	442	8	,	,	PUNCT
ejpam-4760	442	9	usa	usa	PROPN
ejpam-4760	442	10	,	,	PUNCT
ejpam-4760	442	11	1969	1969	NUM
ejpam-4760	442	12	.	.	PUNCT
ejpam-4760	443	1	[	[	X
ejpam-4760	443	2	8	8	X
ejpam-4760	443	3	]	]	X
ejpam-4760	443	4	t.w	t.w	PROPN
ejpam-4760	443	5	.	.	PROPN
ejpam-4760	443	6	haynes	haynes	PROPN
ejpam-4760	443	7	,	,	PUNCT
ejpam-4760	443	8	s.t	s.t	PROPN
ejpam-4760	443	9	.	.	PROPN
ejpam-4760	443	10	hedetniemi	hedetniemi	PROPN
ejpam-4760	443	11	,	,	PUNCT
ejpam-4760	443	12	and	and	CCONJ
ejpam-4760	443	13	p.j	p.j	PROPN
ejpam-4760	443	14	.	.	PROPN
ejpam-4760	443	15	slater	slater	PROPN
ejpam-4760	443	16	.	.	PUNCT
ejpam-4760	444	1	fundamentals	fundamental	NOUN
ejpam-4760	444	2	of	of	ADP
ejpam-4760	444	3	domination	domination	NOUN
ejpam-4760	444	4	in	in	ADP
ejpam-4760	444	5	graphs	graph	NOUN
ejpam-4760	444	6	.	.	PUNCT
ejpam-4760	445	1	marcel	marcel	PROPN
ejpam-4760	445	2	dekker	dekker	PROPN
ejpam-4760	445	3	,	,	PUNCT
ejpam-4760	445	4	new	new	PROPN
ejpam-4760	445	5	york	york	PROPN
ejpam-4760	445	6	,	,	PUNCT
ejpam-4760	445	7	1998	1998	NUM
ejpam-4760	445	8	.	.	PUNCT
ejpam-4760	446	1	[	[	X
ejpam-4760	446	2	9	9	X
ejpam-4760	446	3	]	]	X
ejpam-4760	446	4	y.	y.	PROPN
ejpam-4760	446	5	s.	s.	PROPN
ejpam-4760	446	6	kwon	kwon	PROPN
ejpam-4760	446	7	and	and	CCONJ
ejpam-4760	446	8	j.	j.	PROPN
ejpam-4760	446	9	lee	lee	PROPN
ejpam-4760	446	10	.	.	PROPN
ejpam-4760	446	11	perfect	perfect	ADJ
ejpam-4760	446	12	domination	domination	NOUN
ejpam-4760	446	13	sets	set	NOUN
ejpam-4760	446	14	in	in	ADP
ejpam-4760	446	15	cayley	cayley	ADJ
ejpam-4760	446	16	graphs	graph	NOUN
ejpam-4760	446	17	.	.	PUNCT
ejpam-4760	447	1	discrete	discrete	ADJ
ejpam-4760	447	2	applied	apply	VERB
ejpam-4760	447	3	mathematics	mathematic	NOUN
ejpam-4760	447	4	,	,	PUNCT
ejpam-4760	447	5	162:259–263	162:259–263	NUM
ejpam-4760	447	6	.	.	PUNCT
ejpam-4760	447	7	,	,	PUNCT
ejpam-4760	447	8	2014	2014	NUM
ejpam-4760	447	9	.	.	PUNCT
ejpam-4760	448	1	[	[	X
ejpam-4760	448	2	10	10	NUM
ejpam-4760	448	3	]	]	PUNCT
ejpam-4760	448	4	m.	m.	NOUN
ejpam-4760	448	5	livingston	livingston	PROPN
ejpam-4760	448	6	and	and	CCONJ
ejpam-4760	448	7	q.	q.	PROPN
ejpam-4760	448	8	f.	f.	PROPN
ejpam-4760	448	9	stout	stout	PROPN
ejpam-4760	448	10	.	.	PUNCT
ejpam-4760	449	1	perfect	perfect	ADJ
ejpam-4760	449	2	dominating	dominating	NOUN
ejpam-4760	449	3	sets	set	NOUN
ejpam-4760	449	4	.	.	PUNCT
ejpam-4760	450	1	congressus	congressus	PROPN
ejpam-4760	450	2	numerantium	numerantium	PROPN
ejpam-4760	450	3	,	,	PUNCT
ejpam-4760	450	4	79:187–203	79:187–203	PROPN
ejpam-4760	450	5	.	.	PUNCT
ejpam-4760	450	6	,	,	PUNCT
ejpam-4760	450	7	1990	1990	NUM
ejpam-4760	450	8	.	.	PUNCT
ejpam-4760	451	1	[	[	X
ejpam-4760	451	2	11	11	NUM
ejpam-4760	451	3	]	]	X
ejpam-4760	451	4	n.	n.	PROPN
ejpam-4760	451	5	j.	j.	PROPN
ejpam-4760	451	6	rad	rad	PROPN
ejpam-4760	451	7	.	.	PUNCT
ejpam-4760	452	1	some	some	DET
ejpam-4760	452	2	notes	note	NOUN
ejpam-4760	452	3	on	on	ADP
ejpam-4760	452	4	the	the	DET
ejpam-4760	452	5	isolate	isolate	ADJ
ejpam-4760	452	6	domination	domination	NOUN
ejpam-4760	452	7	in	in	ADP
ejpam-4760	452	8	graphs	graph	NOUN
ejpam-4760	452	9	.	.	PUNCT
ejpam-4760	453	1	akce	akce	PROPN
ejpam-4760	453	2	international	international	PROPN
ejpam-4760	453	3	journal	journal	NOUN
ejpam-4760	453	4	of	of	ADP
ejpam-4760	453	5	graphs	graph	NOUN
ejpam-4760	453	6	and	and	CCONJ
ejpam-4760	453	7	combinatorics	combinatoric	NOUN
ejpam-4760	453	8	,	,	PUNCT
ejpam-4760	453	9	14:112	14:112	NUM
ejpam-4760	453	10	–	–	PUNCT
ejpam-4760	453	11	117	117	NUM
ejpam-4760	453	12	.	.	NUM
ejpam-4760	453	13	,	,	PUNCT
ejpam-4760	453	14	2017	2017	NUM
ejpam-4760	453	15	.	.	PUNCT