id	sid	tid	token	lemma	pos
ejpam-5342	1	1	european	european	PROPN
ejpam-5342	1	2	journal	journal	PROPN
ejpam-5342	1	3	of	of	ADP
ejpam-5342	1	4	pure	pure	ADJ
ejpam-5342	1	5	and	and	CCONJ
ejpam-5342	1	6	applied	apply	VERB
ejpam-5342	1	7	mathematics	mathematic	NOUN
ejpam-5342	1	8	vol	vol	NOUN
ejpam-5342	1	9	.	.	PROPN
ejpam-5342	2	1	17	17	NUM
ejpam-5342	2	2	,	,	PUNCT
ejpam-5342	2	3	no	no	INTJ
ejpam-5342	2	4	.	.	NOUN
ejpam-5342	2	5	4	4	NUM
ejpam-5342	2	6	,	,	PUNCT
ejpam-5342	2	7	2024	2024	NUM
ejpam-5342	2	8	,	,	PUNCT
ejpam-5342	2	9	2505	2505	NUM
ejpam-5342	2	10	-	-	SYM
ejpam-5342	2	11	2515	2515	NUM
ejpam-5342	2	12	issn	issn	PROPN
ejpam-5342	2	13	1307	1307	NUM
ejpam-5342	2	14	-	-	SYM
ejpam-5342	2	15	5543	5543	NUM
ejpam-5342	2	16	–	–	PUNCT
ejpam-5342	3	1	ejpam.com	ejpam.com	X
ejpam-5342	3	2	published	publish	VERB
ejpam-5342	3	3	by	by	ADP
ejpam-5342	3	4	new	new	PROPN
ejpam-5342	3	5	york	york	PROPN
ejpam-5342	3	6	business	business	PROPN
ejpam-5342	3	7	global	global	PROPN
ejpam-5342	3	8	connected	connect	VERB
ejpam-5342	3	9	co	co	ADJ
ejpam-5342	3	10	-	-	ADJ
ejpam-5342	3	11	independent	independent	ADJ
ejpam-5342	3	12	hop	hop	NOUN
ejpam-5342	3	13	domination	domination	NOUN
ejpam-5342	3	14	in	in	ADP
ejpam-5342	3	15	the	the	DET
ejpam-5342	3	16	edge	edge	NOUN
ejpam-5342	3	17	corona	corona	NOUN
ejpam-5342	3	18	and	and	CCONJ
ejpam-5342	3	19	complementary	complementary	ADJ
ejpam-5342	3	20	prism	prism	NOUN
ejpam-5342	3	21	of	of	ADP
ejpam-5342	3	22	graphs	graph	NOUN
ejpam-5342	3	23	sandra	sandra	PROPN
ejpam-5342	3	24	a.	a.	PROPN
ejpam-5342	3	25	nanding1,2,∗	nanding1,2,∗	PROPN
ejpam-5342	3	26	,	,	PUNCT
ejpam-5342	3	27	helen	helen	PROPN
ejpam-5342	3	28	m.	m.	PROPN
ejpam-5342	3	29	rara2	rara2	PROPN
ejpam-5342	3	30	,	,	PUNCT
ejpam-5342	3	31	imelda	imelda	PROPN
ejpam-5342	3	32	s.	s.	PROPN
ejpam-5342	3	33	aniversaro2	aniversaro2	PROPN
ejpam-5342	3	34	1	1	NUM
ejpam-5342	3	35	department	department	NOUN
ejpam-5342	3	36	of	of	ADP
ejpam-5342	3	37	mathematics	mathematic	NOUN
ejpam-5342	3	38	and	and	CCONJ
ejpam-5342	3	39	statistics	statistic	NOUN
ejpam-5342	3	40	,	,	PUNCT
ejpam-5342	3	41	college	college	NOUN
ejpam-5342	3	42	of	of	ADP
ejpam-5342	3	43	science	science	NOUN
ejpam-5342	3	44	and	and	CCONJ
ejpam-5342	3	45	mathematics	mathematic	NOUN
ejpam-5342	3	46	,	,	PUNCT
ejpam-5342	3	47	university	university	NOUN
ejpam-5342	3	48	of	of	ADP
ejpam-5342	3	49	southern	southern	ADJ
ejpam-5342	3	50	mindanao	mindanao	PROPN
ejpam-5342	3	51	,	,	PUNCT
ejpam-5342	3	52	9407	9407	NUM
ejpam-5342	3	53	kabacan	kabacan	NOUN
ejpam-5342	3	54	,	,	PUNCT
ejpam-5342	3	55	cotabato	cotabato	PROPN
ejpam-5342	3	56	,	,	PUNCT
ejpam-5342	3	57	philippines	philippine	NOUN
ejpam-5342	3	58	2	2	NUM
ejpam-5342	3	59	department	department	NOUN
ejpam-5342	3	60	of	of	ADP
ejpam-5342	3	61	mathematics	mathematic	NOUN
ejpam-5342	3	62	and	and	CCONJ
ejpam-5342	3	63	statistics	statistic	NOUN
ejpam-5342	3	64	,	,	PUNCT
ejpam-5342	3	65	college	college	NOUN
ejpam-5342	3	66	of	of	ADP
ejpam-5342	3	67	science	science	NOUN
ejpam-5342	3	68	and	and	CCONJ
ejpam-5342	3	69	mathematics	mathematic	NOUN
ejpam-5342	3	70	,	,	PUNCT
ejpam-5342	3	71	mindanao	mindanao	PROPN
ejpam-5342	3	72	state	state	PROPN
ejpam-5342	3	73	university	university	PROPN
ejpam-5342	3	74	-	-	PUNCT
ejpam-5342	3	75	iligan	iligan	PROPN
ejpam-5342	3	76	institute	institute	PROPN
ejpam-5342	3	77	of	of	ADP
ejpam-5342	3	78	technology	technology	PROPN
ejpam-5342	3	79	,	,	PUNCT
ejpam-5342	3	80	9200	9200	NUM
ejpam-5342	3	81	iligan	iligan	ADJ
ejpam-5342	3	82	city	city	NOUN
ejpam-5342	3	83	,	,	PUNCT
ejpam-5342	3	84	philippines	philippine	NOUN
ejpam-5342	3	85	abstract	abstract	ADJ
ejpam-5342	3	86	.	.	PUNCT
ejpam-5342	4	1	let	let	VERB
ejpam-5342	4	2	g	g	PRON
ejpam-5342	4	3	be	be	AUX
ejpam-5342	4	4	a	a	DET
ejpam-5342	4	5	connected	connected	ADJ
ejpam-5342	4	6	graph	graph	NOUN
ejpam-5342	4	7	.	.	PUNCT
ejpam-5342	5	1	a	a	DET
ejpam-5342	5	2	subset	subset	NOUN
ejpam-5342	5	3	s	s	NOUN
ejpam-5342	5	4	of	of	ADP
ejpam-5342	5	5	v	v	NOUN
ejpam-5342	5	6	(	(	PUNCT
ejpam-5342	5	7	g	g	NOUN
ejpam-5342	5	8	)	)	PUNCT
ejpam-5342	5	9	is	be	AUX
ejpam-5342	5	10	a	a	DET
ejpam-5342	5	11	connected	connected	ADJ
ejpam-5342	5	12	co	co	NOUN
ejpam-5342	5	13	-	-	ADJ
ejpam-5342	5	14	independent	independent	ADJ
ejpam-5342	5	15	hop	hop	NOUN
ejpam-5342	5	16	dominating	dominating	NOUN
ejpam-5342	5	17	set	set	VERB
ejpam-5342	5	18	in	in	ADP
ejpam-5342	5	19	g	g	PROPN
ejpam-5342	5	20	if	if	SCONJ
ejpam-5342	5	21	the	the	DET
ejpam-5342	5	22	subgraph	subgraph	NOUN
ejpam-5342	5	23	induced	induce	VERB
ejpam-5342	5	24	by	by	ADP
ejpam-5342	5	25	s	s	PROPN
ejpam-5342	5	26	is	be	AUX
ejpam-5342	5	27	connected	connect	VERB
ejpam-5342	5	28	and	and	CCONJ
ejpam-5342	5	29	v	v	NOUN
ejpam-5342	5	30	(	(	PUNCT
ejpam-5342	5	31	g)\s	g)\s	NOUN
ejpam-5342	5	32	is	be	AUX
ejpam-5342	5	33	an	an	DET
ejpam-5342	5	34	independent	independent	ADJ
ejpam-5342	5	35	set	set	NOUN
ejpam-5342	5	36	where	where	SCONJ
ejpam-5342	5	37	for	for	ADP
ejpam-5342	5	38	each	each	DET
ejpam-5342	5	39	v	v	NUM
ejpam-5342	5	40	∈	∈	NOUN
ejpam-5342	5	41	v	v	NOUN
ejpam-5342	5	42	(	(	PUNCT
ejpam-5342	5	43	g)\s	g)\s	NOUN
ejpam-5342	5	44	,	,	PUNCT
ejpam-5342	5	45	there	there	PRON
ejpam-5342	5	46	exists	exist	VERB
ejpam-5342	5	47	a	a	DET
ejpam-5342	5	48	vertex	vertex	NOUN
ejpam-5342	5	49	u	u	NOUN
ejpam-5342	5	50	∈	∈	NOUN
ejpam-5342	5	51	s	s	VERB
ejpam-5342	5	52	such	such	ADJ
ejpam-5342	5	53	that	that	DET
ejpam-5342	5	54	dg(u	dg(u	ADJ
ejpam-5342	5	55	,	,	PUNCT
ejpam-5342	5	56	v	v	NOUN
ejpam-5342	5	57	)	)	PUNCT
ejpam-5342	6	1	=	=	SYM
ejpam-5342	6	2	2	2	X
ejpam-5342	6	3	.	.	X
ejpam-5342	6	4	the	the	DET
ejpam-5342	6	5	smallest	small	ADJ
ejpam-5342	6	6	cardinality	cardinality	NOUN
ejpam-5342	6	7	of	of	ADP
ejpam-5342	6	8	such	such	DET
ejpam-5342	6	9	an	an	DET
ejpam-5342	6	10	s	s	NOUN
ejpam-5342	6	11	is	be	AUX
ejpam-5342	6	12	called	call	VERB
ejpam-5342	6	13	the	the	DET
ejpam-5342	6	14	connected	connected	ADJ
ejpam-5342	6	15	co	co	NOUN
ejpam-5342	6	16	-	-	ADJ
ejpam-5342	6	17	independent	independent	ADJ
ejpam-5342	6	18	hop	hop	NOUN
ejpam-5342	6	19	domination	domination	NOUN
ejpam-5342	6	20	number	number	NOUN
ejpam-5342	6	21	of	of	ADP
ejpam-5342	6	22	g.	g.	PROPN
ejpam-5342	6	23	here	here	ADV
ejpam-5342	6	24	,	,	PUNCT
ejpam-5342	6	25	authors	author	NOUN
ejpam-5342	6	26	presented	present	VERB
ejpam-5342	6	27	the	the	DET
ejpam-5342	6	28	characterizations	characterization	NOUN
ejpam-5342	6	29	of	of	ADP
ejpam-5342	6	30	the	the	DET
ejpam-5342	6	31	connected	connected	ADJ
ejpam-5342	6	32	co	co	NOUN
ejpam-5342	6	33	-	-	ADJ
ejpam-5342	6	34	independent	independent	ADJ
ejpam-5342	6	35	hop	hop	NOUN
ejpam-5342	6	36	dominating	dominating	NOUN
ejpam-5342	6	37	sets	set	NOUN
ejpam-5342	6	38	in	in	ADP
ejpam-5342	6	39	the	the	DET
ejpam-5342	6	40	edge	edge	NOUN
ejpam-5342	6	41	corona	corona	NOUN
ejpam-5342	6	42	and	and	CCONJ
ejpam-5342	6	43	complementary	complementary	ADJ
ejpam-5342	6	44	prism	prism	NOUN
ejpam-5342	6	45	of	of	ADP
ejpam-5342	6	46	graphs	graph	NOUN
ejpam-5342	6	47	and	and	CCONJ
ejpam-5342	6	48	determines	determine	VERB
ejpam-5342	6	49	the	the	DET
ejpam-5342	6	50	exact	exact	ADJ
ejpam-5342	6	51	values	value	NOUN
ejpam-5342	6	52	of	of	ADP
ejpam-5342	6	53	their	their	PRON
ejpam-5342	6	54	corresponding	corresponding	ADJ
ejpam-5342	6	55	connected	connect	VERB
ejpam-5342	6	56	co	co	ADJ
ejpam-5342	6	57	-	-	ADJ
ejpam-5342	6	58	independent	independent	ADJ
ejpam-5342	6	59	hop	hop	NOUN
ejpam-5342	6	60	domination	domination	NOUN
ejpam-5342	6	61	number	number	NOUN
ejpam-5342	6	62	.	.	PUNCT
ejpam-5342	7	1	2020	2020	NUM
ejpam-5342	7	2	mathematics	mathematic	NOUN
ejpam-5342	7	3	subject	subject	NOUN
ejpam-5342	7	4	classifications	classification	NOUN
ejpam-5342	7	5	:	:	PUNCT
ejpam-5342	7	6	05c69	05c69	X
ejpam-5342	7	7	key	key	ADJ
ejpam-5342	7	8	words	word	NOUN
ejpam-5342	7	9	and	and	CCONJ
ejpam-5342	7	10	phrases	phrase	NOUN
ejpam-5342	7	11	:	:	PUNCT
ejpam-5342	7	12	strictly	strictly	ADV
ejpam-5342	7	13	co	co	ADJ
ejpam-5342	7	14	-	-	ADJ
ejpam-5342	7	15	independent	independent	ADJ
ejpam-5342	7	16	set	set	NOUN
ejpam-5342	7	17	,	,	PUNCT
ejpam-5342	7	18	connected	connected	ADJ
ejpam-5342	7	19	co	co	ADJ
ejpam-5342	7	20	-	-	ADJ
ejpam-5342	7	21	independent	independent	ADJ
ejpam-5342	7	22	hop	hop	NOUN
ejpam-5342	7	23	dominating	dominating	NOUN
ejpam-5342	7	24	set	set	NOUN
ejpam-5342	7	25	,	,	PUNCT
ejpam-5342	7	26	connected	connected	ADJ
ejpam-5342	7	27	co	co	ADJ
ejpam-5342	7	28	-	-	ADJ
ejpam-5342	7	29	independent	independent	ADJ
ejpam-5342	7	30	hop	hop	NOUN
ejpam-5342	7	31	domination	domination	NOUN
ejpam-5342	7	32	number	number	NOUN
ejpam-5342	7	33	,	,	PUNCT
ejpam-5342	7	34	edge	edge	NOUN
ejpam-5342	7	35	corona	corona	NOUN
ejpam-5342	7	36	,	,	PUNCT
ejpam-5342	7	37	complementary	complementary	ADJ
ejpam-5342	7	38	prism	prism	NOUN
ejpam-5342	7	39	1	1	NUM
ejpam-5342	7	40	.	.	PUNCT
ejpam-5342	8	1	introduction	introduction	NOUN
ejpam-5342	8	2	domination	domination	NOUN
ejpam-5342	8	3	in	in	ADP
ejpam-5342	8	4	graphs	graph	NOUN
ejpam-5342	8	5	was	be	AUX
ejpam-5342	8	6	first	first	ADV
ejpam-5342	8	7	introduced	introduce	VERB
ejpam-5342	8	8	by	by	ADP
ejpam-5342	8	9	c.	c.	PROPN
ejpam-5342	8	10	berge	berge	PROPN
ejpam-5342	8	11	in	in	ADP
ejpam-5342	8	12	1958	1958	NUM
ejpam-5342	8	13	[	[	X
ejpam-5342	8	14	2	2	NUM
ejpam-5342	8	15	]	]	PUNCT
ejpam-5342	8	16	.	.	PUNCT
ejpam-5342	9	1	there	there	PRON
ejpam-5342	9	2	are	be	VERB
ejpam-5342	9	3	now	now	ADV
ejpam-5342	9	4	many	many	ADJ
ejpam-5342	9	5	studies	study	NOUN
ejpam-5342	9	6	involving	involve	VERB
ejpam-5342	9	7	domination	domination	NOUN
ejpam-5342	9	8	and	and	CCONJ
ejpam-5342	9	9	its	its	PRON
ejpam-5342	9	10	variations	variation	NOUN
ejpam-5342	9	11	.	.	PUNCT
ejpam-5342	10	1	one	one	NUM
ejpam-5342	10	2	of	of	ADP
ejpam-5342	10	3	its	its	PRON
ejpam-5342	10	4	variation	variation	NOUN
ejpam-5342	10	5	is	be	AUX
ejpam-5342	10	6	the	the	DET
ejpam-5342	10	7	connected	connected	ADJ
ejpam-5342	10	8	coindependent	coindependent	NOUN
ejpam-5342	10	9	domination	domination	NOUN
ejpam-5342	10	10	number	number	NOUN
ejpam-5342	10	11	of	of	ADP
ejpam-5342	10	12	graphs	graph	NOUN
ejpam-5342	10	13	introduced	introduce	VERB
ejpam-5342	10	14	by	by	ADP
ejpam-5342	10	15	gayathri	gayathri	PROPN
ejpam-5342	10	16	and	and	CCONJ
ejpam-5342	10	17	kaspar	kaspar	NOUN
ejpam-5342	10	18	in	in	ADP
ejpam-5342	10	19	2010	2010	NUM
ejpam-5342	10	20	[	[	X
ejpam-5342	10	21	3	3	NUM
ejpam-5342	10	22	]	]	PUNCT
ejpam-5342	10	23	and	and	CCONJ
ejpam-5342	10	24	further	far	ADV
ejpam-5342	10	25	studied	study	VERB
ejpam-5342	10	26	in	in	ADP
ejpam-5342	10	27	[	[	X
ejpam-5342	10	28	1	1	NUM
ejpam-5342	10	29	,	,	PUNCT
ejpam-5342	10	30	10	10	NUM
ejpam-5342	10	31	]	]	PUNCT
ejpam-5342	10	32	.	.	PUNCT
ejpam-5342	11	1	recently	recently	ADV
ejpam-5342	11	2	,	,	PUNCT
ejpam-5342	11	3	natarajan	natarajan	PROPN
ejpam-5342	11	4	and	and	CCONJ
ejpam-5342	11	5	ayyaswamy	ayyaswamy	PROPN
ejpam-5342	11	6	[	[	X
ejpam-5342	11	7	7	7	NUM
ejpam-5342	11	8	]	]	PUNCT
ejpam-5342	11	9	introduced	introduce	VERB
ejpam-5342	11	10	and	and	CCONJ
ejpam-5342	11	11	studied	study	VERB
ejpam-5342	11	12	the	the	DET
ejpam-5342	11	13	concept	concept	NOUN
ejpam-5342	11	14	of	of	ADP
ejpam-5342	11	15	hop	hop	NOUN
ejpam-5342	11	16	domination	domination	NOUN
ejpam-5342	11	17	in	in	ADP
ejpam-5342	11	18	graphs	graph	NOUN
ejpam-5342	11	19	.	.	PUNCT
ejpam-5342	12	1	hop	hop	PROPN
ejpam-5342	12	2	domination	domination	NOUN
ejpam-5342	12	3	in	in	ADP
ejpam-5342	12	4	graphs	graph	NOUN
ejpam-5342	12	5	were	be	AUX
ejpam-5342	12	6	also	also	ADV
ejpam-5342	12	7	studied	study	VERB
ejpam-5342	12	8	in	in	ADP
ejpam-5342	12	9	[	[	X
ejpam-5342	12	10	5	5	NUM
ejpam-5342	12	11	,	,	PUNCT
ejpam-5342	12	12	6	6	NUM
ejpam-5342	12	13	,	,	PUNCT
ejpam-5342	12	14	8	8	NUM
ejpam-5342	12	15	,	,	PUNCT
ejpam-5342	12	16	9	9	NUM
ejpam-5342	12	17	,	,	PUNCT
ejpam-5342	12	18	11	11	NUM
ejpam-5342	12	19	]	]	PUNCT
ejpam-5342	12	20	.	.	PUNCT
ejpam-5342	13	1	in	in	ADP
ejpam-5342	13	2	[	[	X
ejpam-5342	13	3	6	6	NUM
ejpam-5342	13	4	]	]	PUNCT
ejpam-5342	13	5	,	,	PUNCT
ejpam-5342	13	6	the	the	DET
ejpam-5342	13	7	connected	connected	ADJ
ejpam-5342	13	8	co	co	NOUN
ejpam-5342	13	9	-	-	ADJ
ejpam-5342	13	10	independent	independent	ADJ
ejpam-5342	13	11	hop	hop	NOUN
ejpam-5342	13	12	dominating	dominating	NOUN
ejpam-5342	13	13	sets	set	NOUN
ejpam-5342	13	14	of	of	ADP
ejpam-5342	13	15	a	a	DET
ejpam-5342	13	16	graph	graph	NOUN
ejpam-5342	13	17	is	be	AUX
ejpam-5342	13	18	defined	define	VERB
ejpam-5342	13	19	and	and	CCONJ
ejpam-5342	13	20	studied	study	VERB
ejpam-5342	13	21	under	under	ADP
ejpam-5342	13	22	the	the	DET
ejpam-5342	13	23	join	join	NOUN
ejpam-5342	13	24	,	,	PUNCT
ejpam-5342	13	25	corona	corona	NOUN
ejpam-5342	13	26	and	and	CCONJ
ejpam-5342	13	27	lexicographic	lexicographic	ADJ
ejpam-5342	13	28	product	product	NOUN
ejpam-5342	13	29	of	of	ADP
ejpam-5342	13	30	graphs	graph	NOUN
ejpam-5342	13	31	.	.	PUNCT
ejpam-5342	14	1	∗corresponding	∗corresponde	VERB
ejpam-5342	14	2	author	author	NOUN
ejpam-5342	14	3	.	.	PUNCT
ejpam-5342	15	1	doi	doi	NOUN
ejpam-5342	15	2	:	:	PUNCT
ejpam-5342	15	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5342	https://doi.org/10.29020/nybg.ejpam.v17i4.5342	ADJ
ejpam-5342	15	4	email	email	NOUN
ejpam-5342	15	5	addresses	address	VERB
ejpam-5342	15	6	:	:	PUNCT
ejpam-5342	15	7	nsnanding@usm.edu.ph	nsnanding@usm.edu.ph	PROPN
ejpam-5342	15	8	(	(	PUNCT
ejpam-5342	15	9	s.	s.	PROPN
ejpam-5342	15	10	a.	a.	PROPN
ejpam-5342	15	11	nanding	nanding	PROPN
ejpam-5342	15	12	)	)	PUNCT
ejpam-5342	15	13	,	,	PUNCT
ejpam-5342	15	14	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-5342	15	15	(	(	PUNCT
ejpam-5342	15	16	h.	h.	PROPN
ejpam-5342	15	17	m.	m.	PROPN
ejpam-5342	15	18	rara	rara	PROPN
ejpam-5342	15	19	)	)	PUNCT
ejpam-5342	15	20	,	,	PUNCT
ejpam-5342	15	21	imelda.aniversario@g.msuiit.edu.ph	imelda.aniversario@g.msuiit.edu.ph	PROPN
ejpam-5342	15	22	(	(	PUNCT
ejpam-5342	15	23	i.	i.	PROPN
ejpam-5342	15	24	s.	s.	PROPN
ejpam-5342	15	25	aniversario	aniversario	PROPN
ejpam-5342	15	26	)	)	PUNCT
ejpam-5342	15	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5342	15	28	2505	2505	NUM
ejpam-5342	15	29	copyright	copyright	NOUN
ejpam-5342	15	30	:	:	PUNCT
ejpam-5342	15	31	©	©	PROPN
ejpam-5342	15	32	2024	2024	NUM
ejpam-5342	15	33	the	the	DET
ejpam-5342	15	34	author(s	author(s	NOUN
ejpam-5342	15	35	)	)	PUNCT
ejpam-5342	15	36	.	.	PUNCT
ejpam-5342	16	1	(	(	PUNCT
ejpam-5342	16	2	cc	cc	NOUN
ejpam-5342	16	3	by	by	ADP
ejpam-5342	16	4	-	-	PUNCT
ejpam-5342	16	5	nc	nc	PROPN
ejpam-5342	16	6	4.0	4.0	NUM
ejpam-5342	16	7	)	)	PUNCT
ejpam-5342	16	8	s.	s.	PROPN
ejpam-5342	16	9	a.	a.	PROPN
ejpam-5342	16	10	nanding	nanding	PROPN
ejpam-5342	16	11	,	,	PUNCT
ejpam-5342	16	12	h.	h.	PROPN
ejpam-5342	16	13	m.	m.	PROPN
ejpam-5342	16	14	rara	rara	PROPN
ejpam-5342	16	15	,	,	PUNCT
ejpam-5342	16	16	i.	i.	PROPN
ejpam-5342	16	17	s.	s.	PROPN
ejpam-5342	16	18	aniversario	aniversario	PROPN
ejpam-5342	16	19	/	/	SYM
ejpam-5342	16	20	eur	eur	PROPN
ejpam-5342	16	21	.	.	PUNCT
ejpam-5342	17	1	j.	j.	PROPN
ejpam-5342	17	2	pure	pure	PROPN
ejpam-5342	17	3	appl	appl	PROPN
ejpam-5342	17	4	.	.	PROPN
ejpam-5342	17	5	math	math	PROPN
ejpam-5342	17	6	,	,	PUNCT
ejpam-5342	17	7	17	17	NUM
ejpam-5342	17	8	(	(	PUNCT
ejpam-5342	17	9	4	4	NUM
ejpam-5342	17	10	)	)	PUNCT
ejpam-5342	17	11	(	(	PUNCT
ejpam-5342	17	12	2024	2024	NUM
ejpam-5342	17	13	)	)	PUNCT
ejpam-5342	17	14	,	,	PUNCT
ejpam-5342	17	15	2505	2505	NUM
ejpam-5342	17	16	-	-	SYM
ejpam-5342	17	17	2515	2515	NUM
ejpam-5342	17	18	2506	2506	NUM
ejpam-5342	17	19	2	2	NUM
ejpam-5342	17	20	.	.	PUNCT
ejpam-5342	17	21	preliminaries	preliminary	NOUN
ejpam-5342	17	22	all	all	DET
ejpam-5342	17	23	graphs	graph	NOUN
ejpam-5342	17	24	considered	consider	VERB
ejpam-5342	17	25	in	in	ADP
ejpam-5342	17	26	this	this	DET
ejpam-5342	17	27	study	study	NOUN
ejpam-5342	17	28	are	be	AUX
ejpam-5342	17	29	finite	finite	ADJ
ejpam-5342	17	30	,	,	PUNCT
ejpam-5342	17	31	simple	simple	ADJ
ejpam-5342	17	32	,	,	PUNCT
ejpam-5342	17	33	undirected	undirected	ADJ
ejpam-5342	17	34	and	and	CCONJ
ejpam-5342	17	35	connected	connected	ADJ
ejpam-5342	17	36	.	.	PUNCT
ejpam-5342	18	1	some	some	DET
ejpam-5342	18	2	necessary	necessary	ADJ
ejpam-5342	18	3	definitions	definition	NOUN
ejpam-5342	18	4	are	be	AUX
ejpam-5342	18	5	presented	present	VERB
ejpam-5342	18	6	in	in	ADP
ejpam-5342	18	7	this	this	DET
ejpam-5342	18	8	section	section	NOUN
ejpam-5342	18	9	.	.	PUNCT
ejpam-5342	19	1	readers	reader	NOUN
ejpam-5342	19	2	are	be	AUX
ejpam-5342	19	3	referred	refer	VERB
ejpam-5342	19	4	to	to	ADP
ejpam-5342	19	5	[	[	X
ejpam-5342	19	6	4	4	X
ejpam-5342	19	7	]	]	PUNCT
ejpam-5342	19	8	for	for	ADP
ejpam-5342	19	9	elementary	elementary	ADJ
ejpam-5342	19	10	graph	graph	NOUN
ejpam-5342	19	11	theoretic	theoretic	ADJ
ejpam-5342	19	12	concepts	concept	NOUN
ejpam-5342	19	13	.	.	PUNCT
ejpam-5342	20	1	definition	definition	NOUN
ejpam-5342	20	2	1	1	NUM
ejpam-5342	20	3	.	.	PUNCT
ejpam-5342	21	1	an	an	DET
ejpam-5342	21	2	independent	independent	ADJ
ejpam-5342	21	3	set	set	NOUN
ejpam-5342	21	4	s	s	NOUN
ejpam-5342	21	5	in	in	ADP
ejpam-5342	21	6	a	a	DET
ejpam-5342	21	7	graph	graph	NOUN
ejpam-5342	21	8	g	g	NOUN
ejpam-5342	21	9	is	be	AUX
ejpam-5342	21	10	a	a	DET
ejpam-5342	21	11	subset	subset	NOUN
ejpam-5342	21	12	of	of	ADP
ejpam-5342	21	13	the	the	DET
ejpam-5342	21	14	vertex	vertex	NOUN
ejpam-5342	21	15	-	-	PUNCT
ejpam-5342	21	16	set	set	NOUN
ejpam-5342	21	17	of	of	ADP
ejpam-5342	21	18	g	g	NOUN
ejpam-5342	21	19	such	such	ADJ
ejpam-5342	21	20	that	that	SCONJ
ejpam-5342	21	21	no	no	DET
ejpam-5342	21	22	two	two	NUM
ejpam-5342	21	23	vertices	vertex	NOUN
ejpam-5342	21	24	in	in	ADP
ejpam-5342	21	25	s	s	NOUN
ejpam-5342	21	26	are	be	AUX
ejpam-5342	21	27	adjacent	adjacent	ADJ
ejpam-5342	21	28	in	in	ADP
ejpam-5342	21	29	g.	g.	PROPN
ejpam-5342	21	30	the	the	DET
ejpam-5342	21	31	cardinality	cardinality	NOUN
ejpam-5342	21	32	of	of	ADP
ejpam-5342	21	33	a	a	DET
ejpam-5342	21	34	maximum	maximum	ADJ
ejpam-5342	21	35	independent	independent	ADJ
ejpam-5342	21	36	set	set	NOUN
ejpam-5342	21	37	is	be	AUX
ejpam-5342	21	38	called	call	VERB
ejpam-5342	21	39	the	the	DET
ejpam-5342	21	40	independence	independence	NOUN
ejpam-5342	21	41	number	number	NOUN
ejpam-5342	21	42	of	of	ADP
ejpam-5342	21	43	g	g	NOUN
ejpam-5342	21	44	and	and	CCONJ
ejpam-5342	21	45	is	be	AUX
ejpam-5342	21	46	denoted	denote	VERB
ejpam-5342	21	47	by	by	ADP
ejpam-5342	21	48	β(g	β(g	PROPN
ejpam-5342	21	49	)	)	PUNCT
ejpam-5342	21	50	.	.	PUNCT
ejpam-5342	22	1	an	an	DET
ejpam-5342	22	2	independent	independent	ADJ
ejpam-5342	22	3	set	set	NOUN
ejpam-5342	22	4	s	s	PROPN
ejpam-5342	22	5	⊆	⊆	NUM
ejpam-5342	22	6	v	v	NOUN
ejpam-5342	22	7	(	(	PUNCT
ejpam-5342	22	8	g	g	NOUN
ejpam-5342	22	9	)	)	PUNCT
ejpam-5342	22	10	with	with	ADP
ejpam-5342	22	11	|s|	|s|	PROPN
ejpam-5342	22	12	=	=	SYM
ejpam-5342	22	13	β(g	β(g	PROPN
ejpam-5342	22	14	)	)	PUNCT
ejpam-5342	22	15	is	be	AUX
ejpam-5342	22	16	called	call	VERB
ejpam-5342	22	17	a	a	DET
ejpam-5342	22	18	β	β	NOUN
ejpam-5342	22	19	-	-	NOUN
ejpam-5342	22	20	set	set	NOUN
ejpam-5342	22	21	of	of	ADP
ejpam-5342	22	22	g.	g.	PROPN
ejpam-5342	22	23	definition	definition	NOUN
ejpam-5342	22	24	2	2	NUM
ejpam-5342	22	25	.	.	PUNCT
ejpam-5342	22	26	a	a	DET
ejpam-5342	22	27	perfect	perfect	ADJ
ejpam-5342	22	28	matching	matching	NOUN
ejpam-5342	22	29	of	of	ADP
ejpam-5342	22	30	a	a	DET
ejpam-5342	22	31	graph	graph	NOUN
ejpam-5342	22	32	is	be	AUX
ejpam-5342	22	33	a	a	DET
ejpam-5342	22	34	matching	matching	NOUN
ejpam-5342	22	35	(	(	PUNCT
ejpam-5342	22	36	i.e.	i.e.	X
ejpam-5342	22	37	,	,	PUNCT
ejpam-5342	22	38	an	an	DET
ejpam-5342	22	39	independent	independent	ADJ
ejpam-5342	22	40	edge	edge	NOUN
ejpam-5342	22	41	set	set	NOUN
ejpam-5342	22	42	)	)	PUNCT
ejpam-5342	22	43	in	in	ADP
ejpam-5342	22	44	which	which	PRON
ejpam-5342	22	45	every	every	DET
ejpam-5342	22	46	vertex	vertex	NOUN
ejpam-5342	22	47	of	of	ADP
ejpam-5342	22	48	the	the	DET
ejpam-5342	22	49	graph	graph	NOUN
ejpam-5342	22	50	is	be	AUX
ejpam-5342	22	51	incident	incident	NOUN
ejpam-5342	22	52	to	to	ADP
ejpam-5342	22	53	exactly	exactly	ADV
ejpam-5342	22	54	one	one	NUM
ejpam-5342	22	55	edge	edge	NOUN
ejpam-5342	22	56	of	of	ADP
ejpam-5342	22	57	the	the	DET
ejpam-5342	22	58	matching	matching	NOUN
ejpam-5342	22	59	.	.	PUNCT
ejpam-5342	23	1	definition	definition	NOUN
ejpam-5342	23	2	3	3	NUM
ejpam-5342	23	3	.	.	PUNCT
ejpam-5342	24	1	a	a	DET
ejpam-5342	24	2	dominating	dominating	NOUN
ejpam-5342	24	3	set	set	NOUN
ejpam-5342	24	4	d	d	PROPN
ejpam-5342	24	5	⊆	⊆	NUM
ejpam-5342	24	6	v	v	ADP
ejpam-5342	24	7	(	(	PUNCT
ejpam-5342	24	8	g	g	NOUN
ejpam-5342	24	9	)	)	PUNCT
ejpam-5342	24	10	is	be	AUX
ejpam-5342	24	11	called	call	VERB
ejpam-5342	24	12	a	a	DET
ejpam-5342	24	13	connected	connected	ADJ
ejpam-5342	24	14	co	co	ADJ
ejpam-5342	24	15	-	-	ADJ
ejpam-5342	24	16	independent	independent	ADJ
ejpam-5342	24	17	dominating	dominating	NOUN
ejpam-5342	24	18	set	set	NOUN
ejpam-5342	24	19	of	of	ADP
ejpam-5342	24	20	g	g	PROPN
ejpam-5342	24	21	if	if	SCONJ
ejpam-5342	24	22	d	d	PROPN
ejpam-5342	24	23	is	be	AUX
ejpam-5342	24	24	a	a	DET
ejpam-5342	24	25	connected	connected	ADJ
ejpam-5342	24	26	dominating	dominating	NOUN
ejpam-5342	24	27	set	set	NOUN
ejpam-5342	24	28	of	of	ADP
ejpam-5342	24	29	g	g	PROPN
ejpam-5342	24	30	and	and	CCONJ
ejpam-5342	24	31	v	v	NOUN
ejpam-5342	24	32	(	(	PUNCT
ejpam-5342	24	33	g	g	NOUN
ejpam-5342	24	34	)	)	PUNCT
ejpam-5342	24	35	\d	\d	NOUN
ejpam-5342	24	36	is	be	AUX
ejpam-5342	24	37	an	an	DET
ejpam-5342	24	38	independent	independent	ADJ
ejpam-5342	24	39	set	set	NOUN
ejpam-5342	24	40	.	.	PUNCT
ejpam-5342	25	1	the	the	DET
ejpam-5342	25	2	cardinality	cardinality	NOUN
ejpam-5342	25	3	of	of	ADP
ejpam-5342	25	4	such	such	DET
ejpam-5342	25	5	a	a	DET
ejpam-5342	25	6	minimum	minimum	NOUN
ejpam-5342	25	7	set	set	NOUN
ejpam-5342	25	8	d	d	NOUN
ejpam-5342	25	9	is	be	AUX
ejpam-5342	25	10	called	call	VERB
ejpam-5342	25	11	a	a	DET
ejpam-5342	25	12	connected	connected	ADJ
ejpam-5342	25	13	co	co	ADJ
ejpam-5342	25	14	-	-	ADJ
ejpam-5342	25	15	independent	independent	ADJ
ejpam-5342	25	16	domination	domination	NOUN
ejpam-5342	25	17	number	number	NOUN
ejpam-5342	25	18	of	of	ADP
ejpam-5342	25	19	g	g	PROPN
ejpam-5342	25	20	denoted	denote	VERB
ejpam-5342	25	21	by	by	ADP
ejpam-5342	25	22	γc	γc	PROPN
ejpam-5342	25	23	,	,	PUNCT
ejpam-5342	25	24	coi(g	coi(g	PROPN
ejpam-5342	25	25	)	)	PUNCT
ejpam-5342	25	26	.	.	PUNCT
ejpam-5342	26	1	a	a	DET
ejpam-5342	26	2	connected	connected	ADJ
ejpam-5342	26	3	co	co	ADJ
ejpam-5342	26	4	-	-	ADJ
ejpam-5342	26	5	independent	independent	ADJ
ejpam-5342	26	6	dominating	dominating	NOUN
ejpam-5342	26	7	set	set	NOUN
ejpam-5342	26	8	d	d	NOUN
ejpam-5342	26	9	with	with	ADP
ejpam-5342	26	10	|d|	|d|	PROPN
ejpam-5342	26	11	=	=	SYM
ejpam-5342	26	12	γc	γc	PROPN
ejpam-5342	26	13	,	,	PUNCT
ejpam-5342	26	14	coi(g	coi(g	PROPN
ejpam-5342	26	15	)	)	PUNCT
ejpam-5342	26	16	is	be	AUX
ejpam-5342	26	17	called	call	VERB
ejpam-5342	26	18	a	a	DET
ejpam-5342	26	19	γc	γc	PROPN
ejpam-5342	26	20	,	,	PUNCT
ejpam-5342	26	21	coi	coi	NOUN
ejpam-5342	26	22	-	-	PUNCT
ejpam-5342	26	23	set	set	NOUN
ejpam-5342	26	24	of	of	ADP
ejpam-5342	26	25	g.	g.	PROPN
ejpam-5342	26	26	definition	definition	NOUN
ejpam-5342	26	27	4	4	NUM
ejpam-5342	26	28	.	.	PUNCT
ejpam-5342	27	1	a	a	DET
ejpam-5342	27	2	set	set	NOUN
ejpam-5342	27	3	s	s	NOUN
ejpam-5342	27	4	⊆	⊆	NUM
ejpam-5342	27	5	v	v	NOUN
ejpam-5342	27	6	(	(	PUNCT
ejpam-5342	27	7	g	g	NOUN
ejpam-5342	27	8	)	)	PUNCT
ejpam-5342	27	9	is	be	AUX
ejpam-5342	27	10	a	a	DET
ejpam-5342	27	11	hop	hop	NOUN
ejpam-5342	27	12	dominating	dominating	NOUN
ejpam-5342	27	13	set	set	NOUN
ejpam-5342	27	14	of	of	ADP
ejpam-5342	27	15	g	g	PROPN
ejpam-5342	27	16	if	if	SCONJ
ejpam-5342	27	17	for	for	ADP
ejpam-5342	27	18	every	every	DET
ejpam-5342	27	19	v	v	NUM
ejpam-5342	27	20	∈	∈	NOUN
ejpam-5342	27	21	v	v	NOUN
ejpam-5342	27	22	(	(	PUNCT
ejpam-5342	27	23	g)\s	g)\s	NOUN
ejpam-5342	27	24	,	,	PUNCT
ejpam-5342	27	25	there	there	PRON
ejpam-5342	27	26	exists	exist	VERB
ejpam-5342	27	27	u	u	PROPN
ejpam-5342	27	28	∈	∈	PROPN
ejpam-5342	27	29	s	s	VERB
ejpam-5342	27	30	such	such	ADJ
ejpam-5342	27	31	that	that	DET
ejpam-5342	27	32	dg(u	dg(u	ADJ
ejpam-5342	27	33	,	,	PUNCT
ejpam-5342	27	34	v	v	NOUN
ejpam-5342	27	35	)	)	PUNCT
ejpam-5342	28	1	=	=	SYM
ejpam-5342	28	2	2	2	X
ejpam-5342	28	3	.	.	PUNCT
ejpam-5342	29	1	the	the	DET
ejpam-5342	29	2	minimum	minimum	ADJ
ejpam-5342	29	3	cardinality	cardinality	NOUN
ejpam-5342	29	4	of	of	ADP
ejpam-5342	29	5	a	a	DET
ejpam-5342	29	6	hop	hop	NOUN
ejpam-5342	29	7	dominating	dominating	NOUN
ejpam-5342	29	8	set	set	NOUN
ejpam-5342	29	9	of	of	ADP
ejpam-5342	29	10	g	g	NOUN
ejpam-5342	29	11	,	,	PUNCT
ejpam-5342	29	12	denoted	denote	VERB
ejpam-5342	29	13	by	by	ADP
ejpam-5342	29	14	γh(g	γh(g	NOUN
ejpam-5342	29	15	)	)	PUNCT
ejpam-5342	29	16	,	,	PUNCT
ejpam-5342	29	17	is	be	AUX
ejpam-5342	29	18	called	call	VERB
ejpam-5342	29	19	the	the	DET
ejpam-5342	29	20	hop	hop	NOUN
ejpam-5342	29	21	domination	domination	NOUN
ejpam-5342	29	22	number	number	NOUN
ejpam-5342	29	23	of	of	ADP
ejpam-5342	29	24	g.	g.	PROPN
ejpam-5342	29	25	any	any	DET
ejpam-5342	29	26	hop	hop	NOUN
ejpam-5342	29	27	dominating	dominating	NOUN
ejpam-5342	29	28	set	set	VERB
ejpam-5342	29	29	with	with	ADP
ejpam-5342	29	30	cardinality	cardinality	NOUN
ejpam-5342	29	31	equal	equal	ADJ
ejpam-5342	29	32	to	to	ADP
ejpam-5342	29	33	γh(g	γh(g	NOUN
ejpam-5342	29	34	)	)	PUNCT
ejpam-5342	29	35	is	be	AUX
ejpam-5342	29	36	called	call	VERB
ejpam-5342	29	37	a	a	DET
ejpam-5342	29	38	γh	γh	ADV
ejpam-5342	29	39	-	-	PUNCT
ejpam-5342	29	40	set	set	NOUN
ejpam-5342	29	41	.	.	PUNCT
ejpam-5342	30	1	definition	definition	NOUN
ejpam-5342	30	2	5	5	NUM
ejpam-5342	30	3	.	.	PUNCT
ejpam-5342	31	1	a	a	DET
ejpam-5342	31	2	vertex	vertex	NOUN
ejpam-5342	31	3	v	v	NOUN
ejpam-5342	31	4	in	in	ADP
ejpam-5342	31	5	g	g	PROPN
ejpam-5342	31	6	is	be	AUX
ejpam-5342	31	7	a	a	DET
ejpam-5342	31	8	hop	hop	NOUN
ejpam-5342	31	9	neighbor	neighbor	NOUN
ejpam-5342	31	10	of	of	ADP
ejpam-5342	31	11	vertex	vertex	NOUN
ejpam-5342	31	12	u	u	NOUN
ejpam-5342	31	13	in	in	ADP
ejpam-5342	31	14	g	g	PROPN
ejpam-5342	31	15	if	if	SCONJ
ejpam-5342	31	16	dg(u	dg(u	NOUN
ejpam-5342	31	17	,	,	PUNCT
ejpam-5342	31	18	v	v	NOUN
ejpam-5342	31	19	)	)	PUNCT
ejpam-5342	31	20	=	=	SYM
ejpam-5342	31	21	2	2	X
ejpam-5342	31	22	.	.	X
ejpam-5342	32	1	the	the	DET
ejpam-5342	32	2	set	set	NOUN
ejpam-5342	32	3	ng(u	ng(u	NOUN
ejpam-5342	32	4	,	,	PUNCT
ejpam-5342	32	5	2	2	NUM
ejpam-5342	32	6	)	)	PUNCT
ejpam-5342	32	7	=	=	PRON
ejpam-5342	32	8	{	{	PUNCT
ejpam-5342	32	9	v	v	NUM
ejpam-5342	32	10	∈	∈	NOUN
ejpam-5342	32	11	v	v	NOUN
ejpam-5342	32	12	(	(	PUNCT
ejpam-5342	32	13	g	g	NOUN
ejpam-5342	32	14	)	)	PUNCT
ejpam-5342	32	15	:	:	PUNCT
ejpam-5342	32	16	dg(v	dg(v	X
ejpam-5342	32	17	,	,	PUNCT
ejpam-5342	32	18	u	u	NOUN
ejpam-5342	32	19	)	)	PUNCT
ejpam-5342	32	20	=	=	SYM
ejpam-5342	32	21	2	2	X
ejpam-5342	32	22	}	}	PUNCT
ejpam-5342	32	23	is	be	AUX
ejpam-5342	32	24	called	call	VERB
ejpam-5342	32	25	the	the	DET
ejpam-5342	32	26	open	open	ADJ
ejpam-5342	32	27	hop	hop	NOUN
ejpam-5342	32	28	neighborhood	neighborhood	NOUN
ejpam-5342	32	29	of	of	ADP
ejpam-5342	32	30	u.	u.	PROPN
ejpam-5342	32	31	the	the	DET
ejpam-5342	32	32	closed	closed	ADJ
ejpam-5342	32	33	hop	hop	NOUN
ejpam-5342	32	34	neighborhood	neighborhood	NOUN
ejpam-5342	32	35	of	of	ADP
ejpam-5342	32	36	u	u	PROPN
ejpam-5342	32	37	in	in	ADP
ejpam-5342	32	38	g	g	PROPN
ejpam-5342	32	39	is	be	AUX
ejpam-5342	32	40	given	give	VERB
ejpam-5342	32	41	by	by	ADP
ejpam-5342	32	42	ng[u	ng[u	PROPN
ejpam-5342	32	43	,	,	PUNCT
ejpam-5342	32	44	2	2	NUM
ejpam-5342	32	45	]	]	PUNCT
ejpam-5342	32	46	=	=	PUNCT
ejpam-5342	32	47	ng(u	ng(u	NOUN
ejpam-5342	32	48	,	,	PUNCT
ejpam-5342	32	49	2	2	X
ejpam-5342	32	50	)	)	PUNCT
ejpam-5342	32	51	∪	∪	NOUN
ejpam-5342	32	52	{	{	PUNCT
ejpam-5342	32	53	u	u	NOUN
ejpam-5342	32	54	}	}	PUNCT
ejpam-5342	32	55	.	.	PUNCT
ejpam-5342	33	1	the	the	DET
ejpam-5342	33	2	open	open	ADJ
ejpam-5342	33	3	hop	hop	NOUN
ejpam-5342	33	4	neighborhood	neighborhood	NOUN
ejpam-5342	33	5	of	of	ADP
ejpam-5342	33	6	x	x	PROPN
ejpam-5342	33	7	⊆	⊆	NUM
ejpam-5342	33	8	v	v	ADP
ejpam-5342	33	9	(	(	PUNCT
ejpam-5342	33	10	g	g	NOUN
ejpam-5342	33	11	)	)	PUNCT
ejpam-5342	33	12	is	be	AUX
ejpam-5342	33	13	the	the	DET
ejpam-5342	33	14	set	set	NOUN
ejpam-5342	33	15	ng(x	ng(x	NUM
ejpam-5342	33	16	,	,	PUNCT
ejpam-5342	33	17	2	2	X
ejpam-5342	33	18	)	)	PUNCT
ejpam-5342	33	19	=	=	NOUN
ejpam-5342	33	20	⋃	⋃	NOUN
ejpam-5342	33	21	u∈x	u∈x	ADJ
ejpam-5342	33	22	ng(u	ng(u	NOUN
ejpam-5342	33	23	,	,	PUNCT
ejpam-5342	33	24	2	2	NUM
ejpam-5342	33	25	)	)	PUNCT
ejpam-5342	33	26	.	.	PUNCT
ejpam-5342	34	1	the	the	DET
ejpam-5342	34	2	closed	closed	ADJ
ejpam-5342	34	3	hop	hop	NOUN
ejpam-5342	34	4	neighborhood	neighborhood	NOUN
ejpam-5342	34	5	of	of	ADP
ejpam-5342	34	6	x	x	PUNCT
ejpam-5342	34	7	in	in	ADP
ejpam-5342	34	8	g	g	PROPN
ejpam-5342	34	9	is	be	AUX
ejpam-5342	34	10	the	the	DET
ejpam-5342	34	11	set	set	PROPN
ejpam-5342	34	12	ng[x	ng[x	PROPN
ejpam-5342	34	13	,	,	PUNCT
ejpam-5342	34	14	2	2	NUM
ejpam-5342	34	15	]	]	PUNCT
ejpam-5342	34	16	=	=	SYM
ejpam-5342	34	17	ng(x	ng(x	X
ejpam-5342	34	18	,	,	PUNCT
ejpam-5342	34	19	2	2	NUM
ejpam-5342	34	20	)	)	PUNCT
ejpam-5342	34	21	∪x	∪x	NOUN
ejpam-5342	34	22	.	.	PUNCT
ejpam-5342	35	1	definition	definition	NOUN
ejpam-5342	35	2	6	6	NUM
ejpam-5342	35	3	.	.	PUNCT
ejpam-5342	36	1	a	a	DET
ejpam-5342	36	2	set	set	NOUN
ejpam-5342	36	3	s	s	NOUN
ejpam-5342	36	4	⊆	⊆	NUM
ejpam-5342	36	5	v	v	NOUN
ejpam-5342	36	6	(	(	PUNCT
ejpam-5342	36	7	g	g	NOUN
ejpam-5342	36	8	)	)	PUNCT
ejpam-5342	36	9	is	be	AUX
ejpam-5342	36	10	a	a	DET
ejpam-5342	36	11	connected	connected	ADJ
ejpam-5342	36	12	co	co	ADJ
ejpam-5342	36	13	-	-	ADJ
ejpam-5342	36	14	independent	independent	ADJ
ejpam-5342	36	15	set	set	NOUN
ejpam-5342	36	16	of	of	ADP
ejpam-5342	36	17	g	g	PROPN
ejpam-5342	36	18	if	if	SCONJ
ejpam-5342	36	19	⟨s⟩	⟨s⟩	PROPN
ejpam-5342	36	20	is	be	AUX
ejpam-5342	36	21	connected	connect	VERB
ejpam-5342	36	22	and	and	CCONJ
ejpam-5342	36	23	v	v	X
ejpam-5342	36	24	(	(	PUNCT
ejpam-5342	36	25	g)\s	g)\s	NOUN
ejpam-5342	36	26	is	be	AUX
ejpam-5342	36	27	independent	independent	ADJ
ejpam-5342	36	28	.	.	PUNCT
ejpam-5342	37	1	definition	definition	NOUN
ejpam-5342	37	2	7	7	NUM
ejpam-5342	37	3	.	.	PUNCT
ejpam-5342	38	1	a	a	DET
ejpam-5342	38	2	subset	subset	NOUN
ejpam-5342	38	3	s	s	X
ejpam-5342	38	4	of	of	ADP
ejpam-5342	38	5	v	v	NOUN
ejpam-5342	38	6	(	(	PUNCT
ejpam-5342	38	7	g	g	NOUN
ejpam-5342	38	8	)	)	PUNCT
ejpam-5342	38	9	is	be	AUX
ejpam-5342	38	10	a	a	DET
ejpam-5342	38	11	strictly	strictly	ADV
ejpam-5342	38	12	co	co	ADJ
ejpam-5342	38	13	-	-	ADJ
ejpam-5342	38	14	independent	independent	ADJ
ejpam-5342	38	15	set	set	NOUN
ejpam-5342	38	16	of	of	ADP
ejpam-5342	38	17	g	g	PROPN
ejpam-5342	38	18	if	if	SCONJ
ejpam-5342	38	19	v	v	X
ejpam-5342	38	20	(	(	PUNCT
ejpam-5342	38	21	g)\s	g)\s	NOUN
ejpam-5342	38	22	is	be	AUX
ejpam-5342	38	23	an	an	DET
ejpam-5342	38	24	independent	independent	ADJ
ejpam-5342	38	25	set	set	NOUN
ejpam-5342	38	26	and	and	CCONJ
ejpam-5342	38	27	ng(v	ng(v	NUM
ejpam-5342	38	28	)	)	PUNCT
ejpam-5342	38	29	∩	∩	NOUN
ejpam-5342	38	30	s	s	PART
ejpam-5342	38	31	̸=	̸=	PROPN
ejpam-5342	38	32	s	s	PART
ejpam-5342	38	33	for	for	ADP
ejpam-5342	38	34	all	all	PRON
ejpam-5342	38	35	v	v	ADP
ejpam-5342	38	36	∈	∈	NOUN
ejpam-5342	38	37	v	v	NOUN
ejpam-5342	38	38	(	(	PUNCT
ejpam-5342	38	39	g)\s	g)\s	NOUN
ejpam-5342	38	40	.	.	PUNCT
ejpam-5342	39	1	the	the	DET
ejpam-5342	39	2	minimum	minimum	ADJ
ejpam-5342	39	3	cardinality	cardinality	NOUN
ejpam-5342	39	4	of	of	ADP
ejpam-5342	39	5	a	a	DET
ejpam-5342	39	6	strictly	strictly	ADV
ejpam-5342	39	7	co	co	ADJ
ejpam-5342	39	8	-	-	ADJ
ejpam-5342	39	9	independent	independent	ADJ
ejpam-5342	39	10	set	set	NOUN
ejpam-5342	39	11	in	in	ADP
ejpam-5342	39	12	g	g	NOUN
ejpam-5342	39	13	,	,	PUNCT
ejpam-5342	39	14	denoted	denote	VERB
ejpam-5342	39	15	by	by	ADP
ejpam-5342	39	16	sci(g	sci(g	PROPN
ejpam-5342	39	17	)	)	PUNCT
ejpam-5342	39	18	is	be	AUX
ejpam-5342	39	19	called	call	VERB
ejpam-5342	39	20	the	the	DET
ejpam-5342	39	21	strictly	strictly	ADV
ejpam-5342	39	22	co	co	ADJ
ejpam-5342	39	23	-	-	ADJ
ejpam-5342	39	24	independent	independent	ADJ
ejpam-5342	39	25	number	number	NOUN
ejpam-5342	39	26	of	of	ADP
ejpam-5342	39	27	g.	g.	PROPN
ejpam-5342	39	28	a	a	DET
ejpam-5342	39	29	strictly	strictly	ADV
ejpam-5342	39	30	co	co	ADJ
ejpam-5342	39	31	-	-	ADJ
ejpam-5342	39	32	independent	independent	ADJ
ejpam-5342	39	33	set	set	NOUN
ejpam-5342	39	34	s	s	NOUN
ejpam-5342	39	35	with	with	ADP
ejpam-5342	39	36	|s|	|s|	NOUN
ejpam-5342	39	37	=	=	PUNCT
ejpam-5342	39	38	sci(g	sci(g	PROPN
ejpam-5342	39	39	)	)	PUNCT
ejpam-5342	39	40	is	be	AUX
ejpam-5342	39	41	called	call	VERB
ejpam-5342	39	42	an	an	DET
ejpam-5342	39	43	sci	sci	PROPN
ejpam-5342	39	44	-	-	PUNCT
ejpam-5342	39	45	set	set	NOUN
ejpam-5342	39	46	of	of	ADP
ejpam-5342	39	47	g.	g.	PROPN
ejpam-5342	39	48	definition	definition	NOUN
ejpam-5342	39	49	8	8	NUM
ejpam-5342	39	50	.	.	PUNCT
ejpam-5342	40	1	let	let	VERB
ejpam-5342	40	2	g	g	PRON
ejpam-5342	40	3	be	be	AUX
ejpam-5342	40	4	a	a	DET
ejpam-5342	40	5	connected	connected	ADJ
ejpam-5342	40	6	graph	graph	NOUN
ejpam-5342	40	7	.	.	PUNCT
ejpam-5342	41	1	a	a	DET
ejpam-5342	41	2	hop	hop	NOUN
ejpam-5342	41	3	dominating	dominating	NOUN
ejpam-5342	41	4	set	set	NOUN
ejpam-5342	41	5	s	s	PROPN
ejpam-5342	41	6	⊆	⊆	NUM
ejpam-5342	41	7	v	v	NOUN
ejpam-5342	41	8	(	(	PUNCT
ejpam-5342	41	9	g	g	NOUN
ejpam-5342	41	10	)	)	PUNCT
ejpam-5342	41	11	is	be	AUX
ejpam-5342	41	12	a	a	DET
ejpam-5342	41	13	connected	connected	ADJ
ejpam-5342	41	14	co	co	NOUN
ejpam-5342	41	15	-	-	ADJ
ejpam-5342	41	16	independent	independent	ADJ
ejpam-5342	41	17	hop	hop	NOUN
ejpam-5342	41	18	dominating	dominating	NOUN
ejpam-5342	41	19	set	set	NOUN
ejpam-5342	41	20	of	of	ADP
ejpam-5342	41	21	g	g	PROPN
ejpam-5342	41	22	if	if	SCONJ
ejpam-5342	41	23	⟨s⟩	⟨s⟩	PROPN
ejpam-5342	41	24	is	be	AUX
ejpam-5342	41	25	connected	connect	VERB
ejpam-5342	41	26	and	and	CCONJ
ejpam-5342	41	27	v	v	NOUN
ejpam-5342	41	28	(	(	PUNCT
ejpam-5342	41	29	g)\s	g)\s	NOUN
ejpam-5342	41	30	is	be	AUX
ejpam-5342	41	31	an	an	DET
ejpam-5342	41	32	independent	independent	ADJ
ejpam-5342	41	33	set	set	NOUN
ejpam-5342	41	34	.	.	PUNCT
ejpam-5342	42	1	the	the	DET
ejpam-5342	42	2	minimum	minimum	ADJ
ejpam-5342	42	3	cardinality	cardinality	NOUN
ejpam-5342	42	4	of	of	ADP
ejpam-5342	42	5	a	a	DET
ejpam-5342	42	6	connected	connected	ADJ
ejpam-5342	42	7	co	co	NOUN
ejpam-5342	42	8	-	-	ADJ
ejpam-5342	42	9	independent	independent	ADJ
ejpam-5342	42	10	hop	hop	NOUN
ejpam-5342	42	11	dominating	dominating	NOUN
ejpam-5342	42	12	set	set	NOUN
ejpam-5342	42	13	of	of	ADP
ejpam-5342	42	14	g	g	NOUN
ejpam-5342	42	15	,	,	PUNCT
ejpam-5342	42	16	denoted	denote	VERB
ejpam-5342	42	17	by	by	ADP
ejpam-5342	42	18	γch	γch	NOUN
ejpam-5342	42	19	,	,	PUNCT
ejpam-5342	42	20	coi(g	coi(g	PROPN
ejpam-5342	42	21	)	)	PUNCT
ejpam-5342	42	22	,	,	PUNCT
ejpam-5342	42	23	is	be	AUX
ejpam-5342	42	24	called	call	VERB
ejpam-5342	42	25	the	the	DET
ejpam-5342	42	26	connected	connected	ADJ
ejpam-5342	42	27	co	co	NOUN
ejpam-5342	42	28	-	-	ADJ
ejpam-5342	42	29	independent	independent	ADJ
ejpam-5342	42	30	hop	hop	NOUN
ejpam-5342	42	31	domination	domination	NOUN
ejpam-5342	42	32	number	number	NOUN
ejpam-5342	42	33	of	of	ADP
ejpam-5342	42	34	g.	g.	PROPN
ejpam-5342	42	35	a	a	DET
ejpam-5342	42	36	connected	connected	ADJ
ejpam-5342	42	37	co	co	NOUN
ejpam-5342	42	38	-	-	ADJ
ejpam-5342	42	39	independent	independent	ADJ
ejpam-5342	42	40	hop	hop	NOUN
ejpam-5342	42	41	dominating	dominating	NOUN
ejpam-5342	42	42	set	set	NOUN
ejpam-5342	42	43	s	s	NOUN
ejpam-5342	42	44	with	with	ADP
ejpam-5342	42	45	|s|	|s|	NOUN
ejpam-5342	42	46	=	=	SYM
ejpam-5342	42	47	γch	γch	NOUN
ejpam-5342	42	48	,	,	PUNCT
ejpam-5342	42	49	coi(g	coi(g	PROPN
ejpam-5342	42	50	)	)	PUNCT
ejpam-5342	42	51	is	be	AUX
ejpam-5342	42	52	called	call	VERB
ejpam-5342	42	53	a	a	DET
ejpam-5342	42	54	γch	γch	NOUN
ejpam-5342	42	55	,	,	PUNCT
ejpam-5342	42	56	coi	coi	NOUN
ejpam-5342	42	57	-	-	PUNCT
ejpam-5342	42	58	set	set	NOUN
ejpam-5342	42	59	of	of	ADP
ejpam-5342	42	60	g.	g.	PROPN
ejpam-5342	42	61	s.	s.	PROPN
ejpam-5342	42	62	a.	a.	PROPN
ejpam-5342	42	63	nanding	nanding	PROPN
ejpam-5342	42	64	,	,	PUNCT
ejpam-5342	42	65	h.	h.	PROPN
ejpam-5342	42	66	m.	m.	PROPN
ejpam-5342	42	67	rara	rara	PROPN
ejpam-5342	42	68	,	,	PUNCT
ejpam-5342	42	69	i.	i.	PROPN
ejpam-5342	42	70	s.	s.	PROPN
ejpam-5342	42	71	aniversario	aniversario	PROPN
ejpam-5342	42	72	/	/	SYM
ejpam-5342	42	73	eur	eur	PROPN
ejpam-5342	42	74	.	.	PUNCT
ejpam-5342	43	1	j.	j.	PROPN
ejpam-5342	43	2	pure	pure	PROPN
ejpam-5342	43	3	appl	appl	PROPN
ejpam-5342	43	4	.	.	PROPN
ejpam-5342	43	5	math	math	PROPN
ejpam-5342	43	6	,	,	PUNCT
ejpam-5342	43	7	17	17	NUM
ejpam-5342	43	8	(	(	PUNCT
ejpam-5342	43	9	4	4	NUM
ejpam-5342	43	10	)	)	PUNCT
ejpam-5342	43	11	(	(	PUNCT
ejpam-5342	43	12	2024	2024	NUM
ejpam-5342	43	13	)	)	PUNCT
ejpam-5342	43	14	,	,	PUNCT
ejpam-5342	43	15	2505	2505	NUM
ejpam-5342	43	16	-	-	SYM
ejpam-5342	43	17	2515	2515	NUM
ejpam-5342	43	18	2507	2507	NUM
ejpam-5342	43	19	example	example	NOUN
ejpam-5342	43	20	1	1	X
ejpam-5342	43	21	.	.	PUNCT
ejpam-5342	44	1	let	let	VERB
ejpam-5342	44	2	p8	p8	VERB
ejpam-5342	44	3	=	=	PUNCT
ejpam-5342	45	1	[	[	X
ejpam-5342	45	2	a	a	PRON
ejpam-5342	45	3	,	,	PUNCT
ejpam-5342	45	4	b	b	NOUN
ejpam-5342	45	5	,	,	PUNCT
ejpam-5342	45	6	c	c	NOUN
ejpam-5342	45	7	,	,	PUNCT
ejpam-5342	45	8	d	d	NOUN
ejpam-5342	45	9	,	,	PUNCT
ejpam-5342	45	10	e	e	NOUN
ejpam-5342	45	11	,	,	PUNCT
ejpam-5342	45	12	f	f	PROPN
ejpam-5342	45	13	,	,	PUNCT
ejpam-5342	45	14	g	g	PROPN
ejpam-5342	45	15	,	,	PUNCT
ejpam-5342	45	16	h	h	NOUN
ejpam-5342	45	17	]	]	X
ejpam-5342	45	18	.	.	PUNCT
ejpam-5342	46	1	then	then	ADV
ejpam-5342	46	2	s1	s1	PROPN
ejpam-5342	46	3	=	=	PUNCT
ejpam-5342	46	4	{	{	PUNCT
ejpam-5342	46	5	c	c	NOUN
ejpam-5342	46	6	,	,	PUNCT
ejpam-5342	46	7	d	d	NOUN
ejpam-5342	46	8	,	,	PUNCT
ejpam-5342	46	9	g	g	PROPN
ejpam-5342	46	10	,	,	PUNCT
ejpam-5342	46	11	h	h	NOUN
ejpam-5342	46	12	}	}	PUNCT
ejpam-5342	46	13	,	,	PUNCT
ejpam-5342	46	14	s2	s2	X
ejpam-5342	46	15	=	=	PUNCT
ejpam-5342	46	16	{	{	PUNCT
ejpam-5342	46	17	c	c	NOUN
ejpam-5342	46	18	,	,	PUNCT
ejpam-5342	46	19	d	d	NOUN
ejpam-5342	46	20	,	,	PUNCT
ejpam-5342	46	21	e	e	NOUN
ejpam-5342	46	22	,	,	PUNCT
ejpam-5342	46	23	f	f	NOUN
ejpam-5342	46	24	}	}	PUNCT
ejpam-5342	46	25	and	and	CCONJ
ejpam-5342	46	26	s3	s3	PROPN
ejpam-5342	46	27	=	=	SYM
ejpam-5342	46	28	{	{	PUNCT
ejpam-5342	46	29	b	b	PROPN
ejpam-5342	46	30	,	,	PUNCT
ejpam-5342	46	31	c	c	NOUN
ejpam-5342	46	32	,	,	PUNCT
ejpam-5342	46	33	d	d	NOUN
ejpam-5342	46	34	,	,	PUNCT
ejpam-5342	46	35	e	e	NOUN
ejpam-5342	46	36	,	,	PUNCT
ejpam-5342	46	37	f	f	X
ejpam-5342	46	38	,	,	PUNCT
ejpam-5342	46	39	g	g	NOUN
ejpam-5342	46	40	}	}	PUNCT
ejpam-5342	46	41	are	be	AUX
ejpam-5342	46	42	hop	hop	NOUN
ejpam-5342	46	43	dominating	dominating	NOUN
ejpam-5342	46	44	sets	set	NOUN
ejpam-5342	46	45	of	of	ADP
ejpam-5342	46	46	p8	p8	PROPN
ejpam-5342	46	47	.	.	PUNCT
ejpam-5342	47	1	⟨s1⟩	⟨s1⟩	NOUN
ejpam-5342	47	2	is	be	AUX
ejpam-5342	47	3	not	not	PART
ejpam-5342	47	4	connected	connect	VERB
ejpam-5342	47	5	while	while	SCONJ
ejpam-5342	47	6	⟨s2⟩	⟨s2⟩	NOUN
ejpam-5342	47	7	and	and	CCONJ
ejpam-5342	47	8	⟨s3⟩	⟨s3⟩	NOUN
ejpam-5342	47	9	are	be	AUX
ejpam-5342	47	10	connected	connect	VERB
ejpam-5342	47	11	.	.	PUNCT
ejpam-5342	48	1	however	however	ADV
ejpam-5342	48	2	,	,	PUNCT
ejpam-5342	48	3	s2	s2	PROPN
ejpam-5342	48	4	is	be	AUX
ejpam-5342	48	5	not	not	PART
ejpam-5342	48	6	a	a	DET
ejpam-5342	48	7	connected	connected	ADJ
ejpam-5342	48	8	co	co	ADJ
ejpam-5342	48	9	-	-	ADJ
ejpam-5342	48	10	independent	independent	ADJ
ejpam-5342	48	11	dominating	dominating	NOUN
ejpam-5342	48	12	set	set	NOUN
ejpam-5342	48	13	since	since	SCONJ
ejpam-5342	48	14	v	v	NOUN
ejpam-5342	48	15	(	(	PUNCT
ejpam-5342	48	16	g)\s2	g)\s2	PROPN
ejpam-5342	48	17	is	be	AUX
ejpam-5342	48	18	not	not	PART
ejpam-5342	48	19	an	an	DET
ejpam-5342	48	20	independent	independent	ADJ
ejpam-5342	48	21	set	set	NOUN
ejpam-5342	48	22	while	while	SCONJ
ejpam-5342	48	23	s3	s3	PROPN
ejpam-5342	48	24	is	be	AUX
ejpam-5342	48	25	a	a	DET
ejpam-5342	48	26	connected	connected	ADJ
ejpam-5342	48	27	co	co	ADJ
ejpam-5342	48	28	-	-	ADJ
ejpam-5342	48	29	independent	independent	ADJ
ejpam-5342	48	30	dominating	dominating	NOUN
ejpam-5342	48	31	set	set	NOUN
ejpam-5342	48	32	because	because	SCONJ
ejpam-5342	48	33	v	v	PROPN
ejpam-5342	48	34	(	(	PUNCT
ejpam-5342	48	35	g)\s3	g)\s3	INTJ
ejpam-5342	48	36	is	be	AUX
ejpam-5342	48	37	an	an	DET
ejpam-5342	48	38	independent	independent	ADJ
ejpam-5342	48	39	set	set	NOUN
ejpam-5342	48	40	.	.	PUNCT
ejpam-5342	49	1	thus	thus	ADV
ejpam-5342	49	2	,	,	PUNCT
ejpam-5342	49	3	s3	s3	PROPN
ejpam-5342	49	4	is	be	AUX
ejpam-5342	49	5	a	a	DET
ejpam-5342	49	6	connected	connected	ADJ
ejpam-5342	49	7	co	co	NOUN
ejpam-5342	49	8	-	-	ADJ
ejpam-5342	49	9	independent	independent	ADJ
ejpam-5342	49	10	hop	hop	NOUN
ejpam-5342	49	11	dominating	dominating	NOUN
ejpam-5342	49	12	set	set	NOUN
ejpam-5342	49	13	.	.	PUNCT
ejpam-5342	50	1	it	it	PRON
ejpam-5342	50	2	can	can	AUX
ejpam-5342	50	3	be	be	AUX
ejpam-5342	50	4	verified	verify	VERB
ejpam-5342	50	5	that	that	SCONJ
ejpam-5342	50	6	γch	γch	NOUN
ejpam-5342	50	7	,	,	PUNCT
ejpam-5342	50	8	coi(p8	coi(p8	PROPN
ejpam-5342	50	9	)	)	PUNCT
ejpam-5342	50	10	=	=	NOUN
ejpam-5342	50	11	6	6	X
ejpam-5342	50	12	.	.	PUNCT
ejpam-5342	50	13	definition	definition	NOUN
ejpam-5342	50	14	9	9	NUM
ejpam-5342	50	15	.	.	PUNCT
ejpam-5342	51	1	for	for	ADP
ejpam-5342	51	2	every	every	DET
ejpam-5342	51	3	u	u	NOUN
ejpam-5342	51	4	,	,	PUNCT
ejpam-5342	51	5	v	v	PROPN
ejpam-5342	51	6	∈	∈	PROPN
ejpam-5342	51	7	v	v	NOUN
ejpam-5342	51	8	(	(	PUNCT
ejpam-5342	51	9	g	g	NOUN
ejpam-5342	51	10	)	)	PUNCT
ejpam-5342	51	11	such	such	ADJ
ejpam-5342	51	12	that	that	SCONJ
ejpam-5342	51	13	uv	uv	PROPN
ejpam-5342	51	14	∈	∈	PROPN
ejpam-5342	51	15	e(g	e(g	PROPN
ejpam-5342	51	16	)	)	PUNCT
ejpam-5342	51	17	,	,	PUNCT
ejpam-5342	51	18	denote	denote	VERB
ejpam-5342	51	19	by	by	ADP
ejpam-5342	51	20	huv	huv	PROPN
ejpam-5342	51	21	the	the	DET
ejpam-5342	51	22	copy	copy	NOUN
ejpam-5342	51	23	of	of	ADP
ejpam-5342	51	24	h	h	NOUN
ejpam-5342	51	25	whose	whose	DET
ejpam-5342	51	26	vertices	vertex	NOUN
ejpam-5342	51	27	are	be	AUX
ejpam-5342	51	28	attached	attach	VERB
ejpam-5342	51	29	one	one	NUM
ejpam-5342	51	30	by	by	ADP
ejpam-5342	51	31	one	one	NUM
ejpam-5342	51	32	to	to	ADP
ejpam-5342	51	33	the	the	DET
ejpam-5342	51	34	end	end	NOUN
ejpam-5342	51	35	vertices	vertice	VERB
ejpam-5342	51	36	u	u	NOUN
ejpam-5342	51	37	and	and	CCONJ
ejpam-5342	51	38	v	v	NOUN
ejpam-5342	51	39	of	of	ADP
ejpam-5342	51	40	each	each	DET
ejpam-5342	51	41	edge	edge	NOUN
ejpam-5342	51	42	uv	uv	NOUN
ejpam-5342	51	43	of	of	ADP
ejpam-5342	51	44	g	g	PROPN
ejpam-5342	51	45	and	and	CCONJ
ejpam-5342	51	46	a	a	DET
ejpam-5342	51	47	set	set	VERB
ejpam-5342	51	48	suv	suv	NOUN
ejpam-5342	51	49	⊆	⊆	NUM
ejpam-5342	51	50	huv	huv	PROPN
ejpam-5342	51	51	.	.	PUNCT
ejpam-5342	52	1	3	3	X
ejpam-5342	52	2	.	.	NOUN
ejpam-5342	52	3	results	result	VERB
ejpam-5342	52	4	3.1	3.1	NUM
ejpam-5342	52	5	.	.	PUNCT
ejpam-5342	53	1	preliminary	preliminary	ADJ
ejpam-5342	53	2	results	result	NOUN
ejpam-5342	53	3	it	it	PRON
ejpam-5342	53	4	is	be	AUX
ejpam-5342	53	5	worth	worth	ADJ
ejpam-5342	53	6	mentioning	mention	VERB
ejpam-5342	53	7	that	that	SCONJ
ejpam-5342	53	8	every	every	DET
ejpam-5342	53	9	connected	connected	ADJ
ejpam-5342	53	10	graphg	graphg	NOUN
ejpam-5342	53	11	admits	admit	VERB
ejpam-5342	53	12	a	a	DET
ejpam-5342	53	13	connected	connected	ADJ
ejpam-5342	53	14	co	co	NOUN
ejpam-5342	53	15	-	-	ADJ
ejpam-5342	53	16	independent	independent	ADJ
ejpam-5342	53	17	hop	hop	NOUN
ejpam-5342	53	18	dominating	dominating	NOUN
ejpam-5342	53	19	set	set	NOUN
ejpam-5342	53	20	.	.	PUNCT
ejpam-5342	54	1	indeed	indeed	ADV
ejpam-5342	54	2	,	,	PUNCT
ejpam-5342	54	3	the	the	DET
ejpam-5342	54	4	vertex	vertex	NOUN
ejpam-5342	54	5	-	-	PUNCT
ejpam-5342	54	6	set	set	VERB
ejpam-5342	54	7	v	v	NOUN
ejpam-5342	54	8	(	(	PUNCT
ejpam-5342	54	9	g	g	NOUN
ejpam-5342	54	10	)	)	PUNCT
ejpam-5342	54	11	of	of	ADP
ejpam-5342	54	12	g	g	PROPN
ejpam-5342	54	13	is	be	AUX
ejpam-5342	54	14	a	a	DET
ejpam-5342	54	15	connected	connected	ADJ
ejpam-5342	54	16	co	co	NOUN
ejpam-5342	54	17	-	-	ADJ
ejpam-5342	54	18	independent	independent	ADJ
ejpam-5342	54	19	hop	hop	NOUN
ejpam-5342	54	20	dominating	dominating	NOUN
ejpam-5342	54	21	set	set	NOUN
ejpam-5342	54	22	.	.	PUNCT
ejpam-5342	55	1	as	as	ADP
ejpam-5342	55	2	a	a	DET
ejpam-5342	55	3	simple	simple	ADJ
ejpam-5342	55	4	observation	observation	NOUN
ejpam-5342	55	5	,	,	PUNCT
ejpam-5342	55	6	we	we	PRON
ejpam-5342	55	7	state	state	VERB
ejpam-5342	55	8	the	the	DET
ejpam-5342	55	9	following	following	NOUN
ejpam-5342	55	10	.	.	PUNCT
ejpam-5342	56	1	remark	remark	NOUN
ejpam-5342	56	2	1	1	NUM
ejpam-5342	56	3	.	.	PUNCT
ejpam-5342	57	1	every	every	DET
ejpam-5342	57	2	connected	connected	ADJ
ejpam-5342	57	3	co	co	NOUN
ejpam-5342	57	4	-	-	ADJ
ejpam-5342	57	5	independent	independent	ADJ
ejpam-5342	57	6	hop	hop	NOUN
ejpam-5342	57	7	dominating	dominating	NOUN
ejpam-5342	57	8	set	set	VERB
ejpam-5342	57	9	in	in	ADP
ejpam-5342	57	10	a	a	DET
ejpam-5342	57	11	connected	connected	ADJ
ejpam-5342	57	12	graph	graph	NOUN
ejpam-5342	57	13	g	g	PROPN
ejpam-5342	57	14	is	be	AUX
ejpam-5342	57	15	a	a	DET
ejpam-5342	57	16	hop	hop	NOUN
ejpam-5342	57	17	dominating	dominating	NOUN
ejpam-5342	57	18	set	set	NOUN
ejpam-5342	57	19	.	.	PUNCT
ejpam-5342	58	1	hence	hence	ADV
ejpam-5342	58	2	,	,	PUNCT
ejpam-5342	58	3	γh(g	γh(g	NOUN
ejpam-5342	58	4	)	)	PUNCT
ejpam-5342	58	5	≤	≤	NUM
ejpam-5342	58	6	γch	γch	NOUN
ejpam-5342	58	7	,	,	PUNCT
ejpam-5342	58	8	coi(g	coi(g	PROPN
ejpam-5342	58	9	)	)	PUNCT
ejpam-5342	58	10	.	.	PUNCT
ejpam-5342	59	1	remark	remark	NOUN
ejpam-5342	59	2	2	2	NUM
ejpam-5342	59	3	.	.	PUNCT
ejpam-5342	60	1	let	let	VERB
ejpam-5342	60	2	g	g	PRON
ejpam-5342	60	3	be	be	AUX
ejpam-5342	60	4	a	a	DET
ejpam-5342	60	5	connected	connected	ADJ
ejpam-5342	60	6	graph	graph	NOUN
ejpam-5342	60	7	of	of	ADP
ejpam-5342	60	8	order	order	NOUN
ejpam-5342	60	9	n.	n.	NOUN
ejpam-5342	60	10	then	then	ADV
ejpam-5342	60	11	1	1	NUM
ejpam-5342	60	12	≤	≤	NOUN
ejpam-5342	60	13	γch	γch	NOUN
ejpam-5342	60	14	,	,	PUNCT
ejpam-5342	60	15	coi(g	coi(g	PROPN
ejpam-5342	60	16	)	)	PUNCT
ejpam-5342	60	17	≤	≤	PUNCT
ejpam-5342	60	18	n.	n.	NOUN
ejpam-5342	60	19	moreover	moreover	ADV
ejpam-5342	60	20	,	,	PUNCT
ejpam-5342	60	21	γch	γch	NOUN
ejpam-5342	60	22	,	,	PUNCT
ejpam-5342	60	23	coi(g	coi(g	PROPN
ejpam-5342	60	24	)	)	PUNCT
ejpam-5342	61	1	=	=	PUNCT
ejpam-5342	61	2	1	1	NUM
ejpam-5342	61	3	if	if	SCONJ
ejpam-5342	61	4	and	and	CCONJ
ejpam-5342	61	5	only	only	ADV
ejpam-5342	61	6	if	if	SCONJ
ejpam-5342	61	7	g	g	PROPN
ejpam-5342	61	8	=	=	SYM
ejpam-5342	61	9	k1	k1	PROPN
ejpam-5342	61	10	.	.	PUNCT
ejpam-5342	61	11	example	example	NOUN
ejpam-5342	62	1	2	2	NUM
ejpam-5342	62	2	.	.	PUNCT
ejpam-5342	62	3	the	the	DET
ejpam-5342	62	4	formulas	formula	NOUN
ejpam-5342	62	5	below	below	ADV
ejpam-5342	62	6	give	give	VERB
ejpam-5342	62	7	the	the	DET
ejpam-5342	62	8	connected	connected	ADJ
ejpam-5342	62	9	co	co	NOUN
ejpam-5342	62	10	-	-	ADJ
ejpam-5342	62	11	independent	independent	ADJ
ejpam-5342	62	12	hop	hop	NOUN
ejpam-5342	62	13	domination	domination	NOUN
ejpam-5342	62	14	number	number	NOUN
ejpam-5342	62	15	of	of	ADP
ejpam-5342	62	16	the	the	DET
ejpam-5342	62	17	path	path	NOUN
ejpam-5342	62	18	pn	pn	NOUN
ejpam-5342	62	19	and	and	CCONJ
ejpam-5342	62	20	cycle	cycle	NOUN
ejpam-5342	62	21	cn	cn	PROPN
ejpam-5342	62	22	.	.	PUNCT
ejpam-5342	62	23	γch	γch	NOUN
ejpam-5342	62	24	,	,	PUNCT
ejpam-5342	62	25	coi(pn	coi(pn	NOUN
ejpam-5342	62	26	)	)	PUNCT
ejpam-5342	62	27	=	=	SYM
ejpam-5342	63	1			NOUN
ejpam-5342	63	2	1	1	NUM
ejpam-5342	63	3	if	if	SCONJ
ejpam-5342	63	4	n	n	NOUN
ejpam-5342	63	5	=	=	SYM
ejpam-5342	63	6	1	1	NUM
ejpam-5342	63	7	2	2	NUM
ejpam-5342	63	8	if	if	SCONJ
ejpam-5342	63	9	n	n	NOUN
ejpam-5342	63	10	=	=	SYM
ejpam-5342	63	11	2	2	NUM
ejpam-5342	63	12	,	,	PUNCT
ejpam-5342	63	13	3	3	NUM
ejpam-5342	63	14	n−	n−	NOUN
ejpam-5342	63	15	2	2	NUM
ejpam-5342	63	16	if	if	SCONJ
ejpam-5342	63	17	n	n	PRON
ejpam-5342	63	18	≥	≥	NOUN
ejpam-5342	63	19	4	4	NUM
ejpam-5342	63	20	γch	γch	NOUN
ejpam-5342	63	21	,	,	PUNCT
ejpam-5342	63	22	coi(cn	coi(cn	NUM
ejpam-5342	63	23	)	)	PUNCT
ejpam-5342	63	24	=	=	PRON
ejpam-5342	63	25	{	{	PUNCT
ejpam-5342	63	26	3	3	NUM
ejpam-5342	63	27	if	if	SCONJ
ejpam-5342	63	28	n	n	NOUN
ejpam-5342	63	29	=	=	SYM
ejpam-5342	63	30	3	3	NUM
ejpam-5342	63	31	n−	n−	NOUN
ejpam-5342	63	32	1	1	NUM
ejpam-5342	63	33	if	if	SCONJ
ejpam-5342	63	34	n	n	PRON
ejpam-5342	63	35	≥	≥	VERB
ejpam-5342	63	36	4	4	NUM
ejpam-5342	63	37	remark	remark	NOUN
ejpam-5342	63	38	3	3	NUM
ejpam-5342	63	39	.	.	PUNCT
ejpam-5342	64	1	if	if	SCONJ
ejpam-5342	64	2	g	g	PROPN
ejpam-5342	64	3	is	be	AUX
ejpam-5342	64	4	a	a	DET
ejpam-5342	64	5	complete	complete	ADJ
ejpam-5342	64	6	graph	graph	NOUN
ejpam-5342	64	7	,	,	PUNCT
ejpam-5342	64	8	then	then	ADV
ejpam-5342	64	9	γch	γch	VERB
ejpam-5342	64	10	,	,	PUNCT
ejpam-5342	64	11	coi(g	coi(g	PROPN
ejpam-5342	64	12	)	)	PUNCT
ejpam-5342	64	13	=	=	SYM
ejpam-5342	64	14	n.	n.	NOUN
ejpam-5342	64	15	theorem	theorem	NOUN
ejpam-5342	64	16	1	1	X
ejpam-5342	64	17	.	.	PUNCT
ejpam-5342	65	1	let	let	VERB
ejpam-5342	65	2	g	g	PRON
ejpam-5342	65	3	be	be	AUX
ejpam-5342	65	4	a	a	DET
ejpam-5342	65	5	connected	connected	ADJ
ejpam-5342	65	6	graph	graph	NOUN
ejpam-5342	65	7	of	of	ADP
ejpam-5342	65	8	order	order	NOUN
ejpam-5342	65	9	n	n	PRON
ejpam-5342	65	10	≥	≥	NOUN
ejpam-5342	65	11	3	3	NUM
ejpam-5342	65	12	.	.	PUNCT
ejpam-5342	66	1	then	then	ADV
ejpam-5342	66	2	γch	γch	VERB
ejpam-5342	66	3	,	,	PUNCT
ejpam-5342	66	4	coi(g	coi(g	PROPN
ejpam-5342	66	5	)	)	PUNCT
ejpam-5342	66	6	=	=	SYM
ejpam-5342	66	7	2	2	NUM
ejpam-5342	66	8	if	if	SCONJ
ejpam-5342	66	9	and	and	CCONJ
ejpam-5342	66	10	only	only	ADV
ejpam-5342	66	11	if	if	SCONJ
ejpam-5342	66	12	there	there	PRON
ejpam-5342	66	13	exist	exist	VERB
ejpam-5342	66	14	adjacent	adjacent	ADJ
ejpam-5342	66	15	vertices	vertex	NOUN
ejpam-5342	66	16	x	x	PUNCT
ejpam-5342	66	17	and	and	CCONJ
ejpam-5342	66	18	y	y	PROPN
ejpam-5342	66	19	of	of	ADP
ejpam-5342	66	20	g	g	PROPN
ejpam-5342	66	21	such	such	ADJ
ejpam-5342	66	22	that	that	PRON
ejpam-5342	66	23	for	for	ADP
ejpam-5342	66	24	each	each	DET
ejpam-5342	66	25	z	z	NOUN
ejpam-5342	66	26	∈	∈	PROPN
ejpam-5342	66	27	v	v	NOUN
ejpam-5342	66	28	(	(	PUNCT
ejpam-5342	66	29	g)\{x	g)\{x	PROPN
ejpam-5342	66	30	,	,	PUNCT
ejpam-5342	66	31	y	y	NOUN
ejpam-5342	66	32	}	}	PUNCT
ejpam-5342	66	33	,	,	PUNCT
ejpam-5342	66	34	ng(z	ng(z	NUM
ejpam-5342	66	35	)	)	PUNCT
ejpam-5342	66	36	=	=	PRON
ejpam-5342	67	1	{	{	PUNCT
ejpam-5342	67	2	x	x	NOUN
ejpam-5342	67	3	}	}	PUNCT
ejpam-5342	67	4	or	or	CCONJ
ejpam-5342	67	5	ng(z	ng(z	NUM
ejpam-5342	67	6	)	)	PUNCT
ejpam-5342	68	1	=	=	PRON
ejpam-5342	68	2	{	{	PUNCT
ejpam-5342	68	3	y	y	NOUN
ejpam-5342	68	4	}	}	PUNCT
ejpam-5342	68	5	and	and	CCONJ
ejpam-5342	68	6	z	z	NOUN
ejpam-5342	68	7	/∈	/∈	PUNCT
ejpam-5342	68	8	ng(x	ng(x	NUM
ejpam-5342	68	9	)	)	PUNCT
ejpam-5342	68	10	∩ng(y	∩ng(y	PROPN
ejpam-5342	68	11	)	)	PUNCT
ejpam-5342	68	12	.	.	PUNCT
ejpam-5342	69	1	proof	proof	NOUN
ejpam-5342	69	2	:	:	PUNCT
ejpam-5342	69	3	suppose	suppose	VERB
ejpam-5342	69	4	γch	γch	NOUN
ejpam-5342	69	5	,	,	PUNCT
ejpam-5342	69	6	coi(g	coi(g	PROPN
ejpam-5342	69	7	)	)	PUNCT
ejpam-5342	69	8	=	=	SYM
ejpam-5342	70	1	2	2	X
ejpam-5342	70	2	.	.	X
ejpam-5342	70	3	let	let	VERB
ejpam-5342	70	4	s	s	VERB
ejpam-5342	70	5	=	=	PUNCT
ejpam-5342	70	6	{	{	PUNCT
ejpam-5342	70	7	x	x	PROPN
ejpam-5342	70	8	,	,	PUNCT
ejpam-5342	70	9	y	y	PROPN
ejpam-5342	70	10	}	}	PUNCT
ejpam-5342	70	11	be	be	AUX
ejpam-5342	70	12	γch	γch	NOUN
ejpam-5342	70	13	,	,	PUNCT
ejpam-5342	70	14	coi	coi	NOUN
ejpam-5342	70	15	-	-	PUNCT
ejpam-5342	70	16	set	set	NOUN
ejpam-5342	70	17	of	of	ADP
ejpam-5342	70	18	g.	g.	PROPN
ejpam-5342	70	19	since	since	SCONJ
ejpam-5342	70	20	s	s	PRON
ejpam-5342	70	21	is	be	AUX
ejpam-5342	70	22	connected	connect	VERB
ejpam-5342	70	23	,	,	PUNCT
ejpam-5342	70	24	xy	xy	PROPN
ejpam-5342	70	25	∈	∈	PROPN
ejpam-5342	70	26	e(g	e(g	PROPN
ejpam-5342	70	27	)	)	PUNCT
ejpam-5342	70	28	.	.	PUNCT
ejpam-5342	71	1	let	let	VERB
ejpam-5342	71	2	z	z	NOUN
ejpam-5342	71	3	∈	∈	PROPN
ejpam-5342	71	4	v	v	PROPN
ejpam-5342	71	5	(	(	PUNCT
ejpam-5342	71	6	g)\{x	g)\{x	PROPN
ejpam-5342	71	7	,	,	PUNCT
ejpam-5342	71	8	y	y	NOUN
ejpam-5342	71	9	}	}	PUNCT
ejpam-5342	71	10	.	.	PUNCT
ejpam-5342	72	1	then	then	ADV
ejpam-5342	72	2	z	z	PROPN
ejpam-5342	72	3	/∈	/∈	PUNCT
ejpam-5342	72	4	s.	s.	PROPN
ejpam-5342	72	5	since	since	SCONJ
ejpam-5342	72	6	s	s	PROPN
ejpam-5342	72	7	is	be	AUX
ejpam-5342	72	8	a	a	DET
ejpam-5342	72	9	hop	hop	NOUN
ejpam-5342	72	10	dominating	dominating	NOUN
ejpam-5342	72	11	set	set	NOUN
ejpam-5342	72	12	of	of	ADP
ejpam-5342	72	13	g	g	PROPN
ejpam-5342	72	14	,	,	PUNCT
ejpam-5342	72	15	z	z	PROPN
ejpam-5342	72	16	∈	∈	PROPN
ejpam-5342	72	17	ng(x	ng(x	NUM
ejpam-5342	72	18	,	,	PUNCT
ejpam-5342	72	19	2	2	X
ejpam-5342	72	20	)	)	PUNCT
ejpam-5342	72	21	∪	∪	ADP
ejpam-5342	72	22	ng(y	ng(y	NOUN
ejpam-5342	72	23	,	,	PUNCT
ejpam-5342	72	24	2	2	NUM
ejpam-5342	72	25	)	)	PUNCT
ejpam-5342	72	26	.	.	PUNCT
ejpam-5342	73	1	suppose	suppose	VERB
ejpam-5342	73	2	z	z	PROPN
ejpam-5342	73	3	∈	∈	PROPN
ejpam-5342	73	4	ng(x	ng(x	NUM
ejpam-5342	73	5	,	,	PUNCT
ejpam-5342	73	6	2	2	NUM
ejpam-5342	73	7	)	)	PUNCT
ejpam-5342	73	8	.	.	PUNCT
ejpam-5342	74	1	then	then	ADV
ejpam-5342	74	2	there	there	PRON
ejpam-5342	74	3	exist	exist	VERB
ejpam-5342	74	4	w	w	PROPN
ejpam-5342	74	5	∈	∈	PROPN
ejpam-5342	74	6	ng(z	ng(z	NUM
ejpam-5342	74	7	)	)	PUNCT
ejpam-5342	74	8	∩	∩	NOUN
ejpam-5342	74	9	ng(x	ng(x	NUM
ejpam-5342	74	10	)	)	PUNCT
ejpam-5342	74	11	.	.	PUNCT
ejpam-5342	75	1	since	since	SCONJ
ejpam-5342	75	2	v	v	NOUN
ejpam-5342	75	3	(	(	PUNCT
ejpam-5342	75	4	g)\s	g)\s	NOUN
ejpam-5342	75	5	is	be	AUX
ejpam-5342	75	6	an	an	DET
ejpam-5342	75	7	independent	independent	ADJ
ejpam-5342	75	8	set	set	NOUN
ejpam-5342	75	9	,	,	PUNCT
ejpam-5342	75	10	w	w	PROPN
ejpam-5342	75	11	∈	∈	PROPN
ejpam-5342	75	12	s.	s.	PROPN
ejpam-5342	75	13	thus	thus	ADV
ejpam-5342	75	14	,	,	PUNCT
ejpam-5342	75	15	w	w	PROPN
ejpam-5342	75	16	=	=	SYM
ejpam-5342	75	17	y	y	PROPN
ejpam-5342	75	18	,	,	PUNCT
ejpam-5342	75	19	that	that	ADV
ejpam-5342	75	20	is	is	ADV
ejpam-5342	75	21	,	,	PUNCT
ejpam-5342	75	22	ng(z	ng(z	PROPN
ejpam-5342	75	23	)	)	PUNCT
ejpam-5342	75	24	=	=	PRON
ejpam-5342	76	1	{	{	PUNCT
ejpam-5342	76	2	y	y	NOUN
ejpam-5342	76	3	}	}	PUNCT
ejpam-5342	76	4	.	.	PUNCT
ejpam-5342	77	1	similarly	similarly	ADV
ejpam-5342	77	2	,	,	PUNCT
ejpam-5342	77	3	s.	s.	PROPN
ejpam-5342	77	4	a.	a.	PROPN
ejpam-5342	77	5	nanding	nanding	PROPN
ejpam-5342	77	6	,	,	PUNCT
ejpam-5342	77	7	h.	h.	PROPN
ejpam-5342	77	8	m.	m.	PROPN
ejpam-5342	77	9	rara	rara	PROPN
ejpam-5342	77	10	,	,	PUNCT
ejpam-5342	77	11	i.	i.	PROPN
ejpam-5342	77	12	s.	s.	PROPN
ejpam-5342	77	13	aniversario	aniversario	PROPN
ejpam-5342	77	14	/	/	SYM
ejpam-5342	77	15	eur	eur	PROPN
ejpam-5342	77	16	.	.	PUNCT
ejpam-5342	78	1	j.	j.	PROPN
ejpam-5342	78	2	pure	pure	PROPN
ejpam-5342	78	3	appl	appl	PROPN
ejpam-5342	78	4	.	.	PROPN
ejpam-5342	78	5	math	math	PROPN
ejpam-5342	78	6	,	,	PUNCT
ejpam-5342	78	7	17	17	NUM
ejpam-5342	78	8	(	(	PUNCT
ejpam-5342	78	9	4	4	NUM
ejpam-5342	78	10	)	)	PUNCT
ejpam-5342	78	11	(	(	PUNCT
ejpam-5342	78	12	2024	2024	NUM
ejpam-5342	78	13	)	)	PUNCT
ejpam-5342	78	14	,	,	PUNCT
ejpam-5342	78	15	2505	2505	NUM
ejpam-5342	78	16	-	-	SYM
ejpam-5342	78	17	2515	2515	NUM
ejpam-5342	78	18	2508	2508	NUM
ejpam-5342	78	19	if	if	SCONJ
ejpam-5342	78	20	z	z	NOUN
ejpam-5342	78	21	∈	∈	PROPN
ejpam-5342	78	22	ng(y	ng(y	NOUN
ejpam-5342	78	23	,	,	PUNCT
ejpam-5342	78	24	2	2	NUM
ejpam-5342	78	25	)	)	PUNCT
ejpam-5342	78	26	,	,	PUNCT
ejpam-5342	78	27	then	then	ADV
ejpam-5342	78	28	ng(z	ng(z	NUM
ejpam-5342	78	29	)	)	PUNCT
ejpam-5342	78	30	=	=	PRON
ejpam-5342	78	31	{	{	PUNCT
ejpam-5342	78	32	x	x	NOUN
ejpam-5342	78	33	}	}	PUNCT
ejpam-5342	78	34	.	.	PUNCT
ejpam-5342	79	1	since	since	SCONJ
ejpam-5342	79	2	z	z	PROPN
ejpam-5342	79	3	∈	∈	PROPN
ejpam-5342	79	4	ng(x	ng(x	NUM
ejpam-5342	79	5	,	,	PUNCT
ejpam-5342	79	6	2	2	X
ejpam-5342	79	7	)	)	PUNCT
ejpam-5342	79	8	∪ng(y	∪ng(y	PROPN
ejpam-5342	79	9	,	,	PUNCT
ejpam-5342	79	10	2	2	NUM
ejpam-5342	79	11	)	)	PUNCT
ejpam-5342	79	12	,	,	PUNCT
ejpam-5342	79	13	z	z	NOUN
ejpam-5342	79	14	/∈	/∈	PUNCT
ejpam-5342	79	15	ng(x	ng(x	NUM
ejpam-5342	79	16	)	)	PUNCT
ejpam-5342	79	17	∩ng(y	∩ng(y	PROPN
ejpam-5342	79	18	)	)	PUNCT
ejpam-5342	79	19	.	.	PUNCT
ejpam-5342	80	1	conversely	conversely	ADV
ejpam-5342	80	2	,	,	PUNCT
ejpam-5342	80	3	suppose	suppose	VERB
ejpam-5342	80	4	that	that	SCONJ
ejpam-5342	80	5	there	there	PRON
ejpam-5342	80	6	exist	exist	VERB
ejpam-5342	80	7	adjacent	adjacent	ADJ
ejpam-5342	80	8	vertices	vertex	NOUN
ejpam-5342	80	9	x	x	PUNCT
ejpam-5342	80	10	and	and	CCONJ
ejpam-5342	80	11	y	y	PROPN
ejpam-5342	80	12	of	of	ADP
ejpam-5342	80	13	g	g	PROPN
ejpam-5342	80	14	satisfying	satisfy	VERB
ejpam-5342	80	15	the	the	DET
ejpam-5342	80	16	given	give	VERB
ejpam-5342	80	17	condition	condition	NOUN
ejpam-5342	80	18	.	.	PUNCT
ejpam-5342	81	1	let	let	VERB
ejpam-5342	81	2	s	s	PRON
ejpam-5342	81	3	=	=	PUNCT
ejpam-5342	81	4	{	{	PUNCT
ejpam-5342	81	5	x	x	PROPN
ejpam-5342	81	6	,	,	PUNCT
ejpam-5342	81	7	y	y	PROPN
ejpam-5342	81	8	}	}	PUNCT
ejpam-5342	81	9	.	.	PUNCT
ejpam-5342	82	1	since	since	SCONJ
ejpam-5342	82	2	xy	xy	PROPN
ejpam-5342	82	3	∈	∈	PROPN
ejpam-5342	82	4	e(g	e(g	PROPN
ejpam-5342	82	5	)	)	PUNCT
ejpam-5342	82	6	,	,	PUNCT
ejpam-5342	82	7	s	s	VERB
ejpam-5342	82	8	is	be	AUX
ejpam-5342	82	9	connected	connect	VERB
ejpam-5342	82	10	.	.	PUNCT
ejpam-5342	83	1	let	let	VERB
ejpam-5342	83	2	z	z	NOUN
ejpam-5342	83	3	∈	∈	PROPN
ejpam-5342	83	4	v	v	NOUN
ejpam-5342	83	5	(	(	PUNCT
ejpam-5342	83	6	g)\s	g)\s	NOUN
ejpam-5342	83	7	.	.	PUNCT
ejpam-5342	84	1	if	if	SCONJ
ejpam-5342	84	2	ng(z	ng(z	NUM
ejpam-5342	84	3	)	)	PUNCT
ejpam-5342	85	1	=	=	PRON
ejpam-5342	85	2	{	{	PUNCT
ejpam-5342	85	3	x	x	NOUN
ejpam-5342	85	4	}	}	PUNCT
ejpam-5342	85	5	,	,	PUNCT
ejpam-5342	85	6	then	then	ADV
ejpam-5342	85	7	since	since	SCONJ
ejpam-5342	85	8	xy	xy	PROPN
ejpam-5342	85	9	∈	∈	PROPN
ejpam-5342	85	10	e(g	e(g	PROPN
ejpam-5342	85	11	)	)	PUNCT
ejpam-5342	85	12	,	,	PUNCT
ejpam-5342	85	13	dg(y	dg(y	ADJ
ejpam-5342	85	14	,	,	PUNCT
ejpam-5342	85	15	z	z	NOUN
ejpam-5342	85	16	)	)	PUNCT
ejpam-5342	85	17	=	=	SYM
ejpam-5342	85	18	2	2	X
ejpam-5342	85	19	.	.	PUNCT
ejpam-5342	85	20	while	while	SCONJ
ejpam-5342	85	21	on	on	ADP
ejpam-5342	85	22	the	the	DET
ejpam-5342	85	23	other	other	ADJ
ejpam-5342	85	24	hand	hand	NOUN
ejpam-5342	85	25	,	,	PUNCT
ejpam-5342	85	26	if	if	SCONJ
ejpam-5342	85	27	ng(z	ng(z	NUM
ejpam-5342	85	28	)	)	PUNCT
ejpam-5342	86	1	=	=	PRON
ejpam-5342	86	2	{	{	PUNCT
ejpam-5342	86	3	y	y	NOUN
ejpam-5342	86	4	}	}	PUNCT
ejpam-5342	86	5	,	,	PUNCT
ejpam-5342	86	6	then	then	ADV
ejpam-5342	86	7	dg(x	dg(x	NUM
ejpam-5342	86	8	,	,	PUNCT
ejpam-5342	86	9	z	z	X
ejpam-5342	86	10	)	)	PUNCT
ejpam-5342	86	11	=	=	SYM
ejpam-5342	86	12	2	2	X
ejpam-5342	86	13	.	.	PUNCT
ejpam-5342	86	14	thus	thus	ADV
ejpam-5342	86	15	,	,	PUNCT
ejpam-5342	86	16	s	s	VERB
ejpam-5342	86	17	is	be	AUX
ejpam-5342	86	18	a	a	DET
ejpam-5342	86	19	hop	hop	NOUN
ejpam-5342	86	20	dominating	dominating	NOUN
ejpam-5342	86	21	set	set	NOUN
ejpam-5342	86	22	of	of	ADP
ejpam-5342	86	23	g.	g.	PROPN
ejpam-5342	86	24	since	since	SCONJ
ejpam-5342	86	25	ng(z	ng(z	NUM
ejpam-5342	86	26	)	)	PUNCT
ejpam-5342	87	1	=	=	PRON
ejpam-5342	87	2	{	{	PUNCT
ejpam-5342	87	3	x	x	NOUN
ejpam-5342	87	4	}	}	PUNCT
ejpam-5342	87	5	or	or	CCONJ
ejpam-5342	87	6	ng(z	ng(z	NUM
ejpam-5342	87	7	)	)	PUNCT
ejpam-5342	88	1	=	=	PRON
ejpam-5342	88	2	{	{	PUNCT
ejpam-5342	88	3	y	y	NOUN
ejpam-5342	88	4	}	}	PUNCT
ejpam-5342	88	5	,	,	PUNCT
ejpam-5342	88	6	v	v	X
ejpam-5342	88	7	(	(	PUNCT
ejpam-5342	88	8	g)\s	g)\s	NOUN
ejpam-5342	88	9	is	be	AUX
ejpam-5342	88	10	an	an	DET
ejpam-5342	88	11	independent	independent	ADJ
ejpam-5342	88	12	set	set	NOUN
ejpam-5342	88	13	.	.	PUNCT
ejpam-5342	89	1	therefore	therefore	ADV
ejpam-5342	89	2	,	,	PUNCT
ejpam-5342	89	3	s	s	VERB
ejpam-5342	89	4	is	be	AUX
ejpam-5342	89	5	a	a	DET
ejpam-5342	89	6	connected	connected	ADJ
ejpam-5342	89	7	co	co	NOUN
ejpam-5342	89	8	-	-	ADJ
ejpam-5342	89	9	independent	independent	ADJ
ejpam-5342	89	10	hop	hop	NOUN
ejpam-5342	89	11	dominating	dominating	NOUN
ejpam-5342	89	12	set	set	NOUN
ejpam-5342	89	13	of	of	ADP
ejpam-5342	89	14	g.	g.	PROPN
ejpam-5342	90	1	so	so	ADV
ejpam-5342	90	2	,	,	PUNCT
ejpam-5342	90	3	γch	γch	NOUN
ejpam-5342	90	4	,	,	PUNCT
ejpam-5342	90	5	coi(g	coi(g	PROPN
ejpam-5342	90	6	)	)	PUNCT
ejpam-5342	90	7	≤	≤	NUM
ejpam-5342	90	8	|s|	|s|	PROPN
ejpam-5342	90	9	=	=	SYM
ejpam-5342	90	10	2	2	NUM
ejpam-5342	90	11	.	.	PUNCT
ejpam-5342	91	1	but	but	CCONJ
ejpam-5342	91	2	g	g	PROPN
ejpam-5342	91	3	is	be	AUX
ejpam-5342	91	4	nontrivial	nontrivial	ADJ
ejpam-5342	91	5	.	.	PUNCT
ejpam-5342	92	1	hence	hence	ADV
ejpam-5342	92	2	,	,	PUNCT
ejpam-5342	92	3	γch	γch	NOUN
ejpam-5342	92	4	,	,	PUNCT
ejpam-5342	92	5	coi(g	coi(g	PROPN
ejpam-5342	92	6	)	)	PUNCT
ejpam-5342	92	7	̸=	̸=	NOUN
ejpam-5342	92	8	1	1	NUM
ejpam-5342	92	9	and	and	CCONJ
ejpam-5342	92	10	so	so	ADV
ejpam-5342	92	11	γch	γch	ADV
ejpam-5342	92	12	,	,	PUNCT
ejpam-5342	92	13	coi(g	coi(g	PROPN
ejpam-5342	92	14	)	)	PUNCT
ejpam-5342	92	15	=	=	SYM
ejpam-5342	92	16	2	2	X
ejpam-5342	92	17	.	.	NOUN
ejpam-5342	92	18	example	example	NOUN
ejpam-5342	93	1	3	3	NUM
ejpam-5342	93	2	.	.	PUNCT
ejpam-5342	94	1	the	the	DET
ejpam-5342	94	2	graph	graph	NOUN
ejpam-5342	94	3	p2	p2	PROPN
ejpam-5342	94	4	◦	◦	NOUN
ejpam-5342	94	5	kn	kn	PROPN
ejpam-5342	94	6	in	in	ADP
ejpam-5342	94	7	figure	figure	NOUN
ejpam-5342	94	8	1	1	NUM
ejpam-5342	94	9	has	have	AUX
ejpam-5342	94	10	γch	γch	AUX
ejpam-5342	94	11	,	,	PUNCT
ejpam-5342	94	12	coi(p2	coi(p2	ADJ
ejpam-5342	94	13	◦	◦	NOUN
ejpam-5342	94	14	kn	kn	NOUN
ejpam-5342	94	15	)	)	PUNCT
ejpam-5342	94	16	=	=	SYM
ejpam-5342	94	17	2	2	X
ejpam-5342	94	18	.	.	X
ejpam-5342	94	19	figure	figure	NOUN
ejpam-5342	94	20	1	1	NUM
ejpam-5342	94	21	:	:	PUNCT
ejpam-5342	94	22	p2	p2	PROPN
ejpam-5342	94	23	◦	◦	PROPN
ejpam-5342	94	24	kn	kn	PROPN
ejpam-5342	94	25	theorem	theorem	NOUN
ejpam-5342	94	26	2	2	X
ejpam-5342	94	27	.	.	PUNCT
ejpam-5342	95	1	let	let	VERB
ejpam-5342	95	2	g	g	PRON
ejpam-5342	95	3	be	be	AUX
ejpam-5342	95	4	a	a	DET
ejpam-5342	95	5	connected	connected	ADJ
ejpam-5342	95	6	graph	graph	NOUN
ejpam-5342	95	7	of	of	ADP
ejpam-5342	95	8	order	order	NOUN
ejpam-5342	95	9	n	n	PRON
ejpam-5342	95	10	≥	≥	NOUN
ejpam-5342	95	11	2	2	NUM
ejpam-5342	95	12	.	.	PUNCT
ejpam-5342	96	1	then	then	ADV
ejpam-5342	96	2	γch	γch	VERB
ejpam-5342	96	3	,	,	PUNCT
ejpam-5342	96	4	coi(g	coi(g	PROPN
ejpam-5342	96	5	)	)	PUNCT
ejpam-5342	97	1	=	=	SYM
ejpam-5342	98	1	n	n	NOUN
ejpam-5342	98	2	if	if	SCONJ
ejpam-5342	98	3	and	and	CCONJ
ejpam-5342	98	4	only	only	ADV
ejpam-5342	98	5	if	if	SCONJ
ejpam-5342	98	6	g	g	PROPN
ejpam-5342	98	7	is	be	AUX
ejpam-5342	98	8	complete	complete	ADJ
ejpam-5342	98	9	.	.	PUNCT
ejpam-5342	99	1	proof	proof	NOUN
ejpam-5342	99	2	:	:	PUNCT
ejpam-5342	99	3	suppose	suppose	VERB
ejpam-5342	99	4	γch	γch	NOUN
ejpam-5342	99	5	,	,	PUNCT
ejpam-5342	99	6	coi(g	coi(g	PROPN
ejpam-5342	99	7	)	)	PUNCT
ejpam-5342	100	1	=	=	SYM
ejpam-5342	100	2	n.	n.	NOUN
ejpam-5342	100	3	suppose	suppose	VERB
ejpam-5342	100	4	that	that	SCONJ
ejpam-5342	100	5	g	g	PROPN
ejpam-5342	100	6	is	be	AUX
ejpam-5342	100	7	not	not	PART
ejpam-5342	100	8	complete	complete	ADJ
ejpam-5342	100	9	.	.	PUNCT
ejpam-5342	101	1	then	then	ADV
ejpam-5342	101	2	there	there	PRON
ejpam-5342	101	3	exist	exist	VERB
ejpam-5342	101	4	distinct	distinct	ADJ
ejpam-5342	101	5	vertices	vertex	NOUN
ejpam-5342	101	6	u	u	NOUN
ejpam-5342	101	7	,	,	PUNCT
ejpam-5342	101	8	v	v	NOUN
ejpam-5342	101	9	∈	∈	PROPN
ejpam-5342	101	10	v	v	NOUN
ejpam-5342	101	11	(	(	PUNCT
ejpam-5342	101	12	g	g	NOUN
ejpam-5342	101	13	)	)	PUNCT
ejpam-5342	101	14	such	such	ADJ
ejpam-5342	101	15	that	that	SCONJ
ejpam-5342	101	16	dg(u	dg(u	ADJ
ejpam-5342	101	17	,	,	PUNCT
ejpam-5342	101	18	v	v	NOUN
ejpam-5342	101	19	)	)	PUNCT
ejpam-5342	101	20	=	=	SYM
ejpam-5342	101	21	2	2	X
ejpam-5342	101	22	.	.	X
ejpam-5342	101	23	let	let	VERB
ejpam-5342	101	24	s	s	NOUN
ejpam-5342	101	25	=	=	X
ejpam-5342	101	26	v	v	X
ejpam-5342	101	27	(	(	PUNCT
ejpam-5342	101	28	g)\{u	g)\{u	PROPN
ejpam-5342	101	29	}	}	PUNCT
ejpam-5342	101	30	.	.	PUNCT
ejpam-5342	102	1	then	then	ADV
ejpam-5342	102	2	s	s	VERB
ejpam-5342	102	3	is	be	AUX
ejpam-5342	102	4	a	a	DET
ejpam-5342	102	5	connected	connected	ADJ
ejpam-5342	102	6	co	co	NOUN
ejpam-5342	102	7	-	-	ADJ
ejpam-5342	102	8	independent	independent	ADJ
ejpam-5342	102	9	hop	hop	NOUN
ejpam-5342	102	10	dominating	dominating	NOUN
ejpam-5342	102	11	set	set	NOUN
ejpam-5342	102	12	of	of	ADP
ejpam-5342	102	13	g.	g.	PROPN
ejpam-5342	102	14	therefore	therefore	ADV
ejpam-5342	102	15	,	,	PUNCT
ejpam-5342	102	16	γch	γch	NOUN
ejpam-5342	102	17	,	,	PUNCT
ejpam-5342	102	18	coi(g	coi(g	PROPN
ejpam-5342	102	19	)	)	PUNCT
ejpam-5342	102	20	≤	≤	NUM
ejpam-5342	102	21	|s|	|s|	PROPN
ejpam-5342	102	22	=	=	SYM
ejpam-5342	102	23	n−	n−	NOUN
ejpam-5342	102	24	1	1	NUM
ejpam-5342	102	25	,	,	PUNCT
ejpam-5342	102	26	a	a	DET
ejpam-5342	102	27	contradiction	contradiction	NOUN
ejpam-5342	102	28	.	.	PUNCT
ejpam-5342	103	1	thus	thus	ADV
ejpam-5342	103	2	,	,	PUNCT
ejpam-5342	103	3	g	g	PROPN
ejpam-5342	103	4	is	be	AUX
ejpam-5342	103	5	a	a	DET
ejpam-5342	103	6	complete	complete	ADJ
ejpam-5342	103	7	graph	graph	NOUN
ejpam-5342	103	8	.	.	PUNCT
ejpam-5342	104	1	conversely	conversely	ADV
ejpam-5342	104	2	,	,	PUNCT
ejpam-5342	104	3	by	by	ADP
ejpam-5342	104	4	remark	remark	NOUN
ejpam-5342	104	5	3	3	NUM
ejpam-5342	104	6	,	,	PUNCT
ejpam-5342	104	7	γch	γch	NOUN
ejpam-5342	104	8	,	,	PUNCT
ejpam-5342	104	9	coi(kn	coi(kn	NUM
ejpam-5342	104	10	)	)	PUNCT
ejpam-5342	104	11	=	=	PUNCT
ejpam-5342	104	12	n.	n.	NOUN
ejpam-5342	104	13	3.2	3.2	NUM
ejpam-5342	104	14	.	.	PUNCT
ejpam-5342	105	1	connected	connect	VERB
ejpam-5342	105	2	co	co	ADJ
ejpam-5342	105	3	-	-	ADJ
ejpam-5342	105	4	independent	independent	ADJ
ejpam-5342	105	5	hop	hop	NOUN
ejpam-5342	105	6	domination	domination	NOUN
ejpam-5342	105	7	in	in	ADP
ejpam-5342	105	8	the	the	DET
ejpam-5342	105	9	edge	edge	NOUN
ejpam-5342	105	10	corona	corona	NOUN
ejpam-5342	105	11	of	of	ADP
ejpam-5342	105	12	graphs	graph	NOUN
ejpam-5342	105	13	the	the	DET
ejpam-5342	105	14	edge	edge	NOUN
ejpam-5342	105	15	corona	corona	NOUN
ejpam-5342	105	16	g	g	PROPN
ejpam-5342	105	17	⋄h	⋄h	NOUN
ejpam-5342	105	18	of	of	ADP
ejpam-5342	105	19	g	g	PROPN
ejpam-5342	105	20	and	and	CCONJ
ejpam-5342	105	21	h	h	NOUN
ejpam-5342	105	22	is	be	AUX
ejpam-5342	105	23	the	the	DET
ejpam-5342	105	24	graph	graph	NOUN
ejpam-5342	105	25	obtained	obtain	VERB
ejpam-5342	105	26	by	by	ADP
ejpam-5342	105	27	taking	take	VERB
ejpam-5342	105	28	one	one	NUM
ejpam-5342	105	29	copy	copy	NOUN
ejpam-5342	105	30	of	of	ADP
ejpam-5342	105	31	g	g	PROPN
ejpam-5342	105	32	and	and	CCONJ
ejpam-5342	105	33	|e(g)|	|e(g)|	ADJ
ejpam-5342	105	34	copies	copy	NOUN
ejpam-5342	105	35	of	of	ADP
ejpam-5342	105	36	h	h	NOUN
ejpam-5342	105	37	and	and	CCONJ
ejpam-5342	105	38	joining	join	VERB
ejpam-5342	105	39	each	each	PRON
ejpam-5342	105	40	of	of	ADP
ejpam-5342	105	41	the	the	DET
ejpam-5342	105	42	end	end	NOUN
ejpam-5342	105	43	vertices	vertice	VERB
ejpam-5342	105	44	u	u	NOUN
ejpam-5342	105	45	and	and	CCONJ
ejpam-5342	105	46	v	v	NOUN
ejpam-5342	105	47	of	of	ADP
ejpam-5342	105	48	each	each	DET
ejpam-5342	105	49	edge	edge	NOUN
ejpam-5342	105	50	uv	uv	NOUN
ejpam-5342	105	51	of	of	ADP
ejpam-5342	105	52	g	g	NOUN
ejpam-5342	105	53	to	to	ADP
ejpam-5342	105	54	every	every	DET
ejpam-5342	105	55	vertex	vertex	NOUN
ejpam-5342	105	56	of	of	ADP
ejpam-5342	105	57	the	the	DET
ejpam-5342	105	58	copy	copy	NOUN
ejpam-5342	105	59	huv	huv	PROPN
ejpam-5342	105	60	of	of	ADP
ejpam-5342	105	61	h.	h.	PROPN
ejpam-5342	105	62	example	example	PROPN
ejpam-5342	106	1	4	4	X
ejpam-5342	106	2	.	.	PUNCT
ejpam-5342	106	3	let	let	VERB
ejpam-5342	106	4	g	g	PROPN
ejpam-5342	106	5	=	=	PROPN
ejpam-5342	106	6	c3	c3	PROPN
ejpam-5342	106	7	and	and	CCONJ
ejpam-5342	106	8	h	h	NOUN
ejpam-5342	106	9	=	=	SYM
ejpam-5342	106	10	k2	k2	PROPN
ejpam-5342	106	11	.	.	PUNCT
ejpam-5342	107	1	the	the	DET
ejpam-5342	107	2	edge	edge	NOUN
ejpam-5342	107	3	corona	corona	NOUN
ejpam-5342	107	4	of	of	ADP
ejpam-5342	107	5	g	g	PROPN
ejpam-5342	107	6	⋄h	⋄h	PROPN
ejpam-5342	107	7	and	and	CCONJ
ejpam-5342	107	8	h	h	NOUN
ejpam-5342	107	9	⋄g	⋄g	ADP
ejpam-5342	107	10	are	be	AUX
ejpam-5342	107	11	shown	show	VERB
ejpam-5342	107	12	in	in	ADP
ejpam-5342	107	13	figure	figure	NOUN
ejpam-5342	107	14	2	2	NUM
ejpam-5342	107	15	.	.	PUNCT
ejpam-5342	107	16	figure	figure	NOUN
ejpam-5342	107	17	2	2	NUM
ejpam-5342	107	18	:	:	PUNCT
ejpam-5342	107	19	edge	edge	NOUN
ejpam-5342	107	20	corona	corona	NOUN
ejpam-5342	107	21	c4	c4	PROPN
ejpam-5342	107	22	⋄k2	⋄k2	ADP
ejpam-5342	107	23	and	and	CCONJ
ejpam-5342	107	24	k2	k2	PROPN
ejpam-5342	107	25	⋄	⋄	PROPN
ejpam-5342	107	26	c4	c4	NOUN
ejpam-5342	107	27	s.	s.	PROPN
ejpam-5342	107	28	a.	a.	PROPN
ejpam-5342	107	29	nanding	nanding	PROPN
ejpam-5342	107	30	,	,	PUNCT
ejpam-5342	107	31	h.	h.	PROPN
ejpam-5342	107	32	m.	m.	PROPN
ejpam-5342	107	33	rara	rara	PROPN
ejpam-5342	107	34	,	,	PUNCT
ejpam-5342	107	35	i.	i.	PROPN
ejpam-5342	107	36	s.	s.	PROPN
ejpam-5342	107	37	aniversario	aniversario	PROPN
ejpam-5342	107	38	/	/	SYM
ejpam-5342	107	39	eur	eur	PROPN
ejpam-5342	107	40	.	.	PUNCT
ejpam-5342	108	1	j.	j.	PROPN
ejpam-5342	108	2	pure	pure	PROPN
ejpam-5342	108	3	appl	appl	PROPN
ejpam-5342	108	4	.	.	PROPN
ejpam-5342	108	5	math	math	PROPN
ejpam-5342	108	6	,	,	PUNCT
ejpam-5342	108	7	17	17	NUM
ejpam-5342	108	8	(	(	PUNCT
ejpam-5342	108	9	4	4	NUM
ejpam-5342	108	10	)	)	PUNCT
ejpam-5342	108	11	(	(	PUNCT
ejpam-5342	108	12	2024	2024	NUM
ejpam-5342	108	13	)	)	PUNCT
ejpam-5342	108	14	,	,	PUNCT
ejpam-5342	108	15	2505	2505	NUM
ejpam-5342	108	16	-	-	SYM
ejpam-5342	108	17	2515	2515	NUM
ejpam-5342	108	18	2509	2509	NUM
ejpam-5342	108	19	remark	remark	NOUN
ejpam-5342	108	20	4	4	NUM
ejpam-5342	108	21	.	.	PUNCT
ejpam-5342	109	1	if	if	SCONJ
ejpam-5342	109	2	g	g	PROPN
ejpam-5342	109	3	is	be	AUX
ejpam-5342	109	4	a	a	DET
ejpam-5342	109	5	connected	connected	ADJ
ejpam-5342	109	6	graph	graph	NOUN
ejpam-5342	109	7	of	of	ADP
ejpam-5342	109	8	order	order	NOUN
ejpam-5342	109	9	2	2	NUM
ejpam-5342	109	10	and	and	CCONJ
ejpam-5342	109	11	h	h	NOUN
ejpam-5342	109	12	is	be	AUX
ejpam-5342	109	13	any	any	DET
ejpam-5342	109	14	graph	graph	NOUN
ejpam-5342	109	15	,	,	PUNCT
ejpam-5342	109	16	then	then	ADV
ejpam-5342	109	17	g⋄h	g⋄h	X
ejpam-5342	109	18	=	=	SYM
ejpam-5342	109	19	g+h	g+h	PROPN
ejpam-5342	109	20	.	.	PUNCT
ejpam-5342	110	1	theorem	theorem	NOUN
ejpam-5342	110	2	3	3	X
ejpam-5342	110	3	.	.	PUNCT
ejpam-5342	111	1	let	let	VERB
ejpam-5342	111	2	g	g	PRON
ejpam-5342	111	3	be	be	AUX
ejpam-5342	111	4	a	a	DET
ejpam-5342	111	5	connected	connected	ADJ
ejpam-5342	111	6	graph	graph	NOUN
ejpam-5342	111	7	of	of	ADP
ejpam-5342	111	8	order	order	NOUN
ejpam-5342	111	9	n	n	PRON
ejpam-5342	111	10	≥	≥	NOUN
ejpam-5342	111	11	3	3	NUM
ejpam-5342	111	12	and	and	CCONJ
ejpam-5342	111	13	h	h	NOUN
ejpam-5342	111	14	be	be	VERB
ejpam-5342	111	15	any	any	DET
ejpam-5342	111	16	graph	graph	NOUN
ejpam-5342	111	17	.	.	PUNCT
ejpam-5342	112	1	then	then	ADV
ejpam-5342	112	2	c	c	PROPN
ejpam-5342	112	3	⊆	⊆	NUM
ejpam-5342	112	4	v	v	NOUN
ejpam-5342	112	5	(	(	PUNCT
ejpam-5342	112	6	g	g	PROPN
ejpam-5342	112	7	⋄h	⋄h	PROPN
ejpam-5342	112	8	)	)	PUNCT
ejpam-5342	112	9	is	be	AUX
ejpam-5342	112	10	a	a	DET
ejpam-5342	112	11	connected	connected	ADJ
ejpam-5342	112	12	co	co	NOUN
ejpam-5342	112	13	-	-	ADJ
ejpam-5342	112	14	independent	independent	ADJ
ejpam-5342	112	15	hop	hop	NOUN
ejpam-5342	112	16	dominating	dominating	NOUN
ejpam-5342	112	17	set	set	NOUN
ejpam-5342	112	18	of	of	ADP
ejpam-5342	112	19	g	g	PROPN
ejpam-5342	112	20	⋄h	⋄h	X
ejpam-5342	112	21	if	if	SCONJ
ejpam-5342	113	1	and	and	CCONJ
ejpam-5342	113	2	only	only	ADV
ejpam-5342	113	3	if	if	SCONJ
ejpam-5342	113	4	c	c	X
ejpam-5342	113	5	=	=	PUNCT
ejpam-5342	113	6	a	a	DET
ejpam-5342	113	7	∪	∪	X
ejpam-5342	113	8	(	(	PUNCT
ejpam-5342	113	9	⋃	⋃	NOUN
ejpam-5342	113	10	uv∈e(g	uv∈e(g	NOUN
ejpam-5342	113	11	)	)	PUNCT
ejpam-5342	113	12	suv	suv	NOUN
ejpam-5342	113	13	)	)	PUNCT
ejpam-5342	113	14	where	where	SCONJ
ejpam-5342	113	15	(	(	PUNCT
ejpam-5342	113	16	i	i	NOUN
ejpam-5342	113	17	)	)	PUNCT
ejpam-5342	113	18	a	a	DET
ejpam-5342	113	19	⊆	⊆	NUM
ejpam-5342	113	20	v	v	NOUN
ejpam-5342	113	21	(	(	PUNCT
ejpam-5342	113	22	g	g	NOUN
ejpam-5342	113	23	)	)	PUNCT
ejpam-5342	113	24	is	be	AUX
ejpam-5342	113	25	a	a	DET
ejpam-5342	113	26	connected	connected	ADJ
ejpam-5342	113	27	co	co	ADJ
ejpam-5342	113	28	-	-	ADJ
ejpam-5342	113	29	independent	independent	ADJ
ejpam-5342	113	30	set	set	NOUN
ejpam-5342	113	31	of	of	ADP
ejpam-5342	113	32	g	g	NOUN
ejpam-5342	113	33	containing	contain	VERB
ejpam-5342	113	34	all	all	DET
ejpam-5342	113	35	vertices	vertex	NOUN
ejpam-5342	113	36	incident	incident	NOUN
ejpam-5342	113	37	to	to	ADP
ejpam-5342	113	38	all	all	DET
ejpam-5342	113	39	the	the	DET
ejpam-5342	113	40	edges	edge	NOUN
ejpam-5342	113	41	of	of	ADP
ejpam-5342	113	42	g.	g.	PROPN
ejpam-5342	113	43	(	(	PUNCT
ejpam-5342	113	44	ii	ii	PROPN
ejpam-5342	113	45	)	)	PUNCT
ejpam-5342	113	46	suv	suv	NOUN
ejpam-5342	114	1	=	=	SYM
ejpam-5342	114	2	v	v	PROPN
ejpam-5342	114	3	(	(	PUNCT
ejpam-5342	114	4	huv	huv	PROPN
ejpam-5342	114	5	)	)	PUNCT
ejpam-5342	114	6	if	if	SCONJ
ejpam-5342	114	7	uv	uv	PROPN
ejpam-5342	114	8	∈	∈	PROPN
ejpam-5342	114	9	e(g	e(g	PROPN
ejpam-5342	114	10	)	)	PUNCT
ejpam-5342	114	11	such	such	ADJ
ejpam-5342	114	12	that	that	SCONJ
ejpam-5342	114	13	u	u	PROPN
ejpam-5342	114	14	∈	∈	PROPN
ejpam-5342	114	15	v	v	NOUN
ejpam-5342	114	16	(	(	PUNCT
ejpam-5342	114	17	g)\a	g)\a	NOUN
ejpam-5342	114	18	or	or	CCONJ
ejpam-5342	114	19	v	v	ADP
ejpam-5342	114	20	∈	∈	PROPN
ejpam-5342	114	21	v	v	NOUN
ejpam-5342	114	22	(	(	PUNCT
ejpam-5342	114	23	g)\a	g)\a	NOUN
ejpam-5342	114	24	.	.	PUNCT
ejpam-5342	114	25	(	(	PUNCT
ejpam-5342	114	26	iii	iii	NOUN
ejpam-5342	114	27	)	)	PUNCT
ejpam-5342	114	28	for	for	ADP
ejpam-5342	114	29	every	every	DET
ejpam-5342	114	30	a	a	PROPN
ejpam-5342	114	31	,	,	PUNCT
ejpam-5342	114	32	b	b	PROPN
ejpam-5342	114	33	∈	∈	PROPN
ejpam-5342	114	34	a	a	PRON
ejpam-5342	114	35	such	such	ADJ
ejpam-5342	114	36	that	that	SCONJ
ejpam-5342	114	37	ab	ab	PROPN
ejpam-5342	114	38	∈	∈	PROPN
ejpam-5342	114	39	e(g	e(g	PROPN
ejpam-5342	114	40	)	)	PUNCT
ejpam-5342	114	41	and	and	CCONJ
ejpam-5342	114	42	sab	sab	VERB
ejpam-5342	114	43	̸=	̸=	PROPN
ejpam-5342	114	44	v	v	PROPN
ejpam-5342	114	45	(	(	PUNCT
ejpam-5342	114	46	hab	hab	NOUN
ejpam-5342	114	47	)	)	PUNCT
ejpam-5342	114	48	,	,	PUNCT
ejpam-5342	114	49	v	v	X
ejpam-5342	114	50	(	(	PUNCT
ejpam-5342	114	51	hab)\sab	hab)\sab	PROPN
ejpam-5342	114	52	is	be	AUX
ejpam-5342	114	53	an	an	DET
ejpam-5342	114	54	independent	independent	ADJ
ejpam-5342	114	55	set	set	NOUN
ejpam-5342	114	56	in	in	ADP
ejpam-5342	114	57	hab	hab	NOUN
ejpam-5342	114	58	.	.	PUNCT
ejpam-5342	115	1	proof	proof	NOUN
ejpam-5342	115	2	:	:	PUNCT
ejpam-5342	115	3	suppose	suppose	VERB
ejpam-5342	115	4	that	that	SCONJ
ejpam-5342	115	5	c	c	PROPN
ejpam-5342	115	6	is	be	AUX
ejpam-5342	115	7	a	a	DET
ejpam-5342	115	8	connected	connected	ADJ
ejpam-5342	115	9	co	co	NOUN
ejpam-5342	115	10	-	-	ADJ
ejpam-5342	115	11	independent	independent	ADJ
ejpam-5342	115	12	hop	hop	NOUN
ejpam-5342	115	13	dominating	dominating	NOUN
ejpam-5342	115	14	set	set	NOUN
ejpam-5342	115	15	of	of	ADP
ejpam-5342	115	16	g⋄h	g⋄h	PROPN
ejpam-5342	115	17	.	.	PUNCT
ejpam-5342	116	1	let	let	VERB
ejpam-5342	116	2	a	a	DET
ejpam-5342	116	3	=	=	SYM
ejpam-5342	116	4	c∩v	c∩v	NOUN
ejpam-5342	116	5	(	(	PUNCT
ejpam-5342	116	6	g	g	NOUN
ejpam-5342	116	7	)	)	PUNCT
ejpam-5342	116	8	and	and	CCONJ
ejpam-5342	116	9	let	let	VERB
ejpam-5342	116	10	suv	suv	PROPN
ejpam-5342	116	11	=	=	PROPN
ejpam-5342	116	12	c∩v	c∩v	NOUN
ejpam-5342	116	13	(	(	PUNCT
ejpam-5342	116	14	huv	huv	PROPN
ejpam-5342	116	15	)	)	PUNCT
ejpam-5342	116	16	for	for	ADP
ejpam-5342	116	17	each	each	DET
ejpam-5342	116	18	uv	uv	PROPN
ejpam-5342	116	19	∈	∈	PROPN
ejpam-5342	116	20	e(g	e(g	PROPN
ejpam-5342	116	21	)	)	PUNCT
ejpam-5342	116	22	.	.	PUNCT
ejpam-5342	117	1	then	then	ADV
ejpam-5342	117	2	c	c	X
ejpam-5342	117	3	=	=	SYM
ejpam-5342	117	4	a∪	a∪	PROPN
ejpam-5342	117	5	(	(	PUNCT
ejpam-5342	117	6	⋃	⋃	ADP
ejpam-5342	117	7	uv∈v	uv∈v	NOUN
ejpam-5342	117	8	(	(	PUNCT
ejpam-5342	117	9	g	g	NOUN
ejpam-5342	117	10	)	)	PUNCT
ejpam-5342	117	11	suv	suv	NOUN
ejpam-5342	117	12	)	)	PUNCT
ejpam-5342	117	13	where	where	SCONJ
ejpam-5342	117	14	a	a	DET
ejpam-5342	117	15	⊆	⊆	NUM
ejpam-5342	117	16	v	v	NOUN
ejpam-5342	117	17	(	(	PUNCT
ejpam-5342	117	18	g	g	NOUN
ejpam-5342	117	19	)	)	PUNCT
ejpam-5342	117	20	.	.	PUNCT
ejpam-5342	118	1	first	first	ADV
ejpam-5342	118	2	,	,	PUNCT
ejpam-5342	118	3	we	we	PRON
ejpam-5342	118	4	show	show	VERB
ejpam-5342	118	5	that	that	SCONJ
ejpam-5342	118	6	⟨a⟩	⟨a⟩	PROPN
ejpam-5342	118	7	is	be	AUX
ejpam-5342	118	8	connected	connect	VERB
ejpam-5342	118	9	.	.	PUNCT
ejpam-5342	119	1	let	let	VERB
ejpam-5342	119	2	x	x	PRON
ejpam-5342	119	3	,	,	PUNCT
ejpam-5342	119	4	y	y	PROPN
ejpam-5342	119	5	∈	∈	PROPN
ejpam-5342	120	1	a	a	DET
ejpam-5342	120	2	with	with	ADP
ejpam-5342	120	3	x	x	PUNCT
ejpam-5342	120	4	̸=	̸=	PROPN
ejpam-5342	120	5	y.	y.	NOUN
ejpam-5342	120	6	if	if	SCONJ
ejpam-5342	120	7	xy	xy	PROPN
ejpam-5342	120	8	∈	∈	PROPN
ejpam-5342	120	9	e(g	e(g	PROPN
ejpam-5342	120	10	)	)	PUNCT
ejpam-5342	120	11	,	,	PUNCT
ejpam-5342	120	12	then	then	ADV
ejpam-5342	120	13	we	we	PRON
ejpam-5342	120	14	are	be	AUX
ejpam-5342	120	15	done	do	VERB
ejpam-5342	120	16	.	.	PUNCT
ejpam-5342	121	1	suppose	suppose	VERB
ejpam-5342	121	2	that	that	SCONJ
ejpam-5342	121	3	xy	xy	PROPN
ejpam-5342	121	4	/∈	/∈	PUNCT
ejpam-5342	121	5	e(g	e(g	PROPN
ejpam-5342	121	6	)	)	PUNCT
ejpam-5342	121	7	.	.	PUNCT
ejpam-5342	122	1	since	since	SCONJ
ejpam-5342	122	2	⟨c⟩	⟨c⟩	PROPN
ejpam-5342	122	3	is	be	AUX
ejpam-5342	122	4	connected	connect	VERB
ejpam-5342	122	5	and	and	CCONJ
ejpam-5342	122	6	x	x	X
ejpam-5342	122	7	,	,	PUNCT
ejpam-5342	122	8	y	y	PROPN
ejpam-5342	122	9	∈	∈	PROPN
ejpam-5342	122	10	c	c	X
ejpam-5342	122	11	,	,	PUNCT
ejpam-5342	122	12	there	there	PRON
ejpam-5342	122	13	exists	exist	VERB
ejpam-5342	122	14	an	an	DET
ejpam-5342	122	15	x	x	NOUN
ejpam-5342	122	16	-	-	NOUN
ejpam-5342	122	17	y	y	ADJ
ejpam-5342	122	18	path	path	NOUN
ejpam-5342	123	1	[	[	X
ejpam-5342	123	2	x1	x1	PROPN
ejpam-5342	123	3	,	,	PUNCT
ejpam-5342	123	4	x2	x2	PROPN
ejpam-5342	123	5	,	,	PUNCT
ejpam-5342	123	6	...	...	PUNCT
ejpam-5342	123	7	,	,	PUNCT
ejpam-5342	123	8	xn	xn	PROPN
ejpam-5342	123	9	]	]	X
ejpam-5342	123	10	in	in	ADP
ejpam-5342	123	11	⟨c⟩	⟨c⟩	PROPN
ejpam-5342	123	12	where	where	SCONJ
ejpam-5342	123	13	x	x	X
ejpam-5342	123	14	=	=	SYM
ejpam-5342	123	15	x1	x1	PROPN
ejpam-5342	123	16	,	,	PUNCT
ejpam-5342	123	17	y	y	PROPN
ejpam-5342	123	18	=	=	SYM
ejpam-5342	123	19	xn	xn	PROPN
ejpam-5342	123	20	and	and	CCONJ
ejpam-5342	123	21	n	n	CCONJ
ejpam-5342	123	22	>	>	X
ejpam-5342	123	23	2	2	X
ejpam-5342	123	24	.	.	PUNCT
ejpam-5342	124	1	if	if	SCONJ
ejpam-5342	124	2	xi	xi	PROPN
ejpam-5342	124	3	∈	∈	PROPN
ejpam-5342	124	4	a	a	PRON
ejpam-5342	124	5	for	for	ADP
ejpam-5342	124	6	all	all	PRON
ejpam-5342	124	7	i	i	PRON
ejpam-5342	124	8	∈	∈	PROPN
ejpam-5342	124	9	{	{	PUNCT
ejpam-5342	124	10	1	1	NUM
ejpam-5342	124	11	,	,	PUNCT
ejpam-5342	124	12	2	2	NUM
ejpam-5342	124	13	,	,	PUNCT
ejpam-5342	124	14	...	...	PUNCT
ejpam-5342	124	15	,	,	PUNCT
ejpam-5342	124	16	n	n	CCONJ
ejpam-5342	124	17	}	}	PUNCT
ejpam-5342	124	18	,	,	PUNCT
ejpam-5342	124	19	then	then	ADV
ejpam-5342	124	20	the	the	DET
ejpam-5342	124	21	path	path	NOUN
ejpam-5342	125	1	[	[	X
ejpam-5342	125	2	x1	x1	PROPN
ejpam-5342	125	3	,	,	PUNCT
ejpam-5342	125	4	x2	x2	PROPN
ejpam-5342	125	5	,	,	PUNCT
ejpam-5342	125	6	...	...	PUNCT
ejpam-5342	125	7	,	,	PUNCT
ejpam-5342	125	8	xn	xn	PROPN
ejpam-5342	125	9	]	]	X
ejpam-5342	125	10	is	be	AUX
ejpam-5342	125	11	in	in	ADP
ejpam-5342	125	12	a.	a.	NOUN
ejpam-5342	125	13	suppose	suppose	VERB
ejpam-5342	125	14	there	there	PRON
ejpam-5342	125	15	exists	exist	VERB
ejpam-5342	126	1	xi	xi	X
ejpam-5342	126	2	/∈	/∈	PUNCT
ejpam-5342	126	3	a.	a.	NOUN
ejpam-5342	126	4	then	then	ADV
ejpam-5342	126	5	xi	xi	PROPN
ejpam-5342	126	6	∈	∈	PROPN
ejpam-5342	126	7	suv	suv	PROPN
ejpam-5342	126	8	for	for	ADP
ejpam-5342	126	9	some	some	DET
ejpam-5342	126	10	edge	edge	NOUN
ejpam-5342	126	11	uv	uv	PROPN
ejpam-5342	126	12	∈	∈	PROPN
ejpam-5342	126	13	e(g	e(g	PROPN
ejpam-5342	126	14	)	)	PUNCT
ejpam-5342	126	15	.	.	PUNCT
ejpam-5342	127	1	by	by	ADP
ejpam-5342	127	2	definition	definition	NOUN
ejpam-5342	127	3	of	of	ADP
ejpam-5342	127	4	g	g	PROPN
ejpam-5342	127	5	⋄h	⋄h	PROPN
ejpam-5342	127	6	,	,	PUNCT
ejpam-5342	127	7	u	u	NOUN
ejpam-5342	127	8	,	,	PUNCT
ejpam-5342	127	9	v	v	NOUN
ejpam-5342	127	10	∈	∈	NOUN
ejpam-5342	127	11	a.	a.	NOUN
ejpam-5342	127	12	hence	hence	ADV
ejpam-5342	127	13	,	,	PUNCT
ejpam-5342	127	14	[	[	X
ejpam-5342	127	15	x1	x1	ADJ
ejpam-5342	127	16	,	,	PUNCT
ejpam-5342	127	17	...	...	PUNCT
ejpam-5342	127	18	,	,	PUNCT
ejpam-5342	127	19	u	u	NOUN
ejpam-5342	127	20	,	,	PUNCT
ejpam-5342	127	21	v	v	NOUN
ejpam-5342	127	22	,	,	PUNCT
ejpam-5342	127	23	...	...	PUNCT
ejpam-5342	127	24	,	,	PUNCT
ejpam-5342	127	25	xn	xn	PROPN
ejpam-5342	127	26	]	]	X
ejpam-5342	127	27	is	be	AUX
ejpam-5342	127	28	a	a	DET
ejpam-5342	127	29	path	path	NOUN
ejpam-5342	127	30	in	in	ADP
ejpam-5342	127	31	a	a	PRON
ejpam-5342	127	32	,	,	PUNCT
ejpam-5342	127	33	showing	show	VERB
ejpam-5342	127	34	that	that	SCONJ
ejpam-5342	127	35	⟨a⟩	⟨a⟩	PROPN
ejpam-5342	127	36	is	be	AUX
ejpam-5342	127	37	connected	connect	VERB
ejpam-5342	127	38	.	.	PUNCT
ejpam-5342	128	1	next	next	ADV
ejpam-5342	128	2	,	,	PUNCT
ejpam-5342	128	3	let	let	VERB
ejpam-5342	128	4	u	u	NOUN
ejpam-5342	128	5	,	,	PUNCT
ejpam-5342	128	6	v	v	PROPN
ejpam-5342	128	7	∈	∈	PROPN
ejpam-5342	128	8	v	v	NOUN
ejpam-5342	128	9	(	(	PUNCT
ejpam-5342	128	10	g)\a	g)\a	NOUN
ejpam-5342	128	11	with	with	ADP
ejpam-5342	128	12	u	u	NOUN
ejpam-5342	128	13	̸=	̸=	PROPN
ejpam-5342	128	14	v.	v.	ADP
ejpam-5342	128	15	then	then	ADV
ejpam-5342	128	16	u	u	PROPN
ejpam-5342	128	17	,	,	PUNCT
ejpam-5342	128	18	v	v	PROPN
ejpam-5342	128	19	∈	∈	PROPN
ejpam-5342	128	20	v	v	NOUN
ejpam-5342	128	21	(	(	PUNCT
ejpam-5342	128	22	g	g	PROPN
ejpam-5342	128	23	⋄	⋄	PROPN
ejpam-5342	128	24	h)\c	h)\c	NOUN
ejpam-5342	128	25	.	.	PUNCT
ejpam-5342	129	1	since	since	SCONJ
ejpam-5342	129	2	v	v	NOUN
ejpam-5342	129	3	(	(	PUNCT
ejpam-5342	129	4	g	g	PROPN
ejpam-5342	129	5	⋄	⋄	PROPN
ejpam-5342	129	6	h)\c	h)\c	NOUN
ejpam-5342	129	7	is	be	AUX
ejpam-5342	129	8	independent	independent	ADJ
ejpam-5342	129	9	,	,	PUNCT
ejpam-5342	129	10	uv	uv	NOUN
ejpam-5342	129	11	/∈	/∈	PUNCT
ejpam-5342	130	1	e(g	e(g	PROPN
ejpam-5342	130	2	⋄	⋄	PROPN
ejpam-5342	130	3	h	h	NOUN
ejpam-5342	130	4	)	)	PUNCT
ejpam-5342	130	5	.	.	PUNCT
ejpam-5342	131	1	since	since	SCONJ
ejpam-5342	131	2	u	u	NOUN
ejpam-5342	131	3	,	,	PUNCT
ejpam-5342	131	4	v	v	PROPN
ejpam-5342	131	5	∈	∈	PROPN
ejpam-5342	131	6	v	v	NOUN
ejpam-5342	131	7	(	(	PUNCT
ejpam-5342	131	8	g	g	NOUN
ejpam-5342	131	9	)	)	PUNCT
ejpam-5342	131	10	,	,	PUNCT
ejpam-5342	131	11	uv	uv	NOUN
ejpam-5342	131	12	/∈	/∈	PUNCT
ejpam-5342	131	13	e(g	e(g	PROPN
ejpam-5342	131	14	)	)	PUNCT
ejpam-5342	131	15	implying	imply	VERB
ejpam-5342	131	16	that	that	PRON
ejpam-5342	131	17	v	v	NOUN
ejpam-5342	131	18	(	(	PUNCT
ejpam-5342	131	19	g)\a	g)\a	NOUN
ejpam-5342	131	20	is	be	AUX
ejpam-5342	131	21	independent	independent	ADJ
ejpam-5342	131	22	.	.	PUNCT
ejpam-5342	132	1	now	now	ADV
ejpam-5342	132	2	,	,	PUNCT
ejpam-5342	132	3	suppose	suppose	VERB
ejpam-5342	132	4	v	v	PRON
ejpam-5342	132	5	is	be	AUX
ejpam-5342	132	6	a	a	DET
ejpam-5342	132	7	vertex	vertex	NOUN
ejpam-5342	132	8	incident	incident	NOUN
ejpam-5342	132	9	to	to	ADP
ejpam-5342	132	10	all	all	DET
ejpam-5342	132	11	the	the	DET
ejpam-5342	132	12	edges	edge	NOUN
ejpam-5342	132	13	of	of	ADP
ejpam-5342	132	14	g	g	NOUN
ejpam-5342	132	15	and	and	CCONJ
ejpam-5342	132	16	v	v	NOUN
ejpam-5342	132	17	/∈	/∈	PUNCT
ejpam-5342	133	1	a.	a.	NOUN
ejpam-5342	133	2	then	then	ADV
ejpam-5342	133	3	v	v	X
ejpam-5342	133	4	∈	∈	PROPN
ejpam-5342	133	5	ng(w)∩ng⋄h(p	ng(w)∩ng⋄h(p	NOUN
ejpam-5342	133	6	)	)	PUNCT
ejpam-5342	133	7	for	for	ADP
ejpam-5342	133	8	all	all	DET
ejpam-5342	133	9	w	w	PROPN
ejpam-5342	133	10	∈	∈	PROPN
ejpam-5342	133	11	v	v	ADP
ejpam-5342	133	12	(	(	PUNCT
ejpam-5342	133	13	g	g	NOUN
ejpam-5342	133	14	)	)	PUNCT
ejpam-5342	133	15	and	and	CCONJ
ejpam-5342	133	16	for	for	ADP
ejpam-5342	133	17	all	all	DET
ejpam-5342	133	18	p	p	NOUN
ejpam-5342	133	19	∈	∈	PROPN
ejpam-5342	133	20	v	v	ADP
ejpam-5342	133	21	(	(	PUNCT
ejpam-5342	133	22	hvw	hvw	NOUN
ejpam-5342	133	23	)	)	PUNCT
ejpam-5342	133	24	.	.	PUNCT
ejpam-5342	134	1	thus	thus	ADV
ejpam-5342	134	2	,	,	PUNCT
ejpam-5342	134	3	ng⋄h(v	ng⋄h(v	NOUN
ejpam-5342	134	4	,	,	PUNCT
ejpam-5342	134	5	2)∩c	2)∩c	NOUN
ejpam-5342	134	6	=	=	SYM
ejpam-5342	134	7	∅	∅	NOUN
ejpam-5342	134	8	,	,	PUNCT
ejpam-5342	134	9	a	a	DET
ejpam-5342	134	10	contradiction	contradiction	NOUN
ejpam-5342	134	11	since	since	SCONJ
ejpam-5342	134	12	c	c	PROPN
ejpam-5342	134	13	is	be	AUX
ejpam-5342	134	14	a	a	DET
ejpam-5342	134	15	hop	hop	NOUN
ejpam-5342	134	16	dominating	dominating	NOUN
ejpam-5342	134	17	set	set	NOUN
ejpam-5342	134	18	.	.	PUNCT
ejpam-5342	135	1	hence	hence	ADV
ejpam-5342	135	2	,	,	PUNCT
ejpam-5342	135	3	a	a	PRON
ejpam-5342	135	4	is	be	AUX
ejpam-5342	135	5	a	a	DET
ejpam-5342	135	6	connected	connected	ADJ
ejpam-5342	135	7	co	co	ADJ
ejpam-5342	135	8	-	-	ADJ
ejpam-5342	135	9	independent	independent	ADJ
ejpam-5342	135	10	set	set	NOUN
ejpam-5342	135	11	of	of	ADP
ejpam-5342	135	12	g	g	NOUN
ejpam-5342	135	13	containing	contain	VERB
ejpam-5342	135	14	all	all	DET
ejpam-5342	135	15	vertices	vertex	NOUN
ejpam-5342	135	16	incident	incident	NOUN
ejpam-5342	135	17	to	to	ADP
ejpam-5342	135	18	all	all	DET
ejpam-5342	135	19	edges	edge	NOUN
ejpam-5342	135	20	of	of	ADP
ejpam-5342	135	21	g	g	NOUN
ejpam-5342	135	22	,	,	PUNCT
ejpam-5342	135	23	showing	show	VERB
ejpam-5342	135	24	that	that	SCONJ
ejpam-5342	135	25	(	(	PUNCT
ejpam-5342	135	26	i	i	NOUN
ejpam-5342	135	27	)	)	PUNCT
ejpam-5342	135	28	holds	hold	VERB
ejpam-5342	135	29	.	.	PUNCT
ejpam-5342	136	1	let	let	VERB
ejpam-5342	136	2	uv	uv	PRON
ejpam-5342	136	3	∈	∈	PROPN
ejpam-5342	136	4	e(g	e(g	PROPN
ejpam-5342	136	5	)	)	PUNCT
ejpam-5342	136	6	with	with	ADP
ejpam-5342	136	7	u	u	PROPN
ejpam-5342	136	8	/∈	/∈	PROPN
ejpam-5342	136	9	a.	a.	PROPN
ejpam-5342	136	10	suppose	suppose	VERB
ejpam-5342	136	11	suv	suv	PROPN
ejpam-5342	136	12	̸=	̸=	PROPN
ejpam-5342	136	13	v	v	PROPN
ejpam-5342	136	14	(	(	PUNCT
ejpam-5342	136	15	huv	huv	PROPN
ejpam-5342	136	16	)	)	PUNCT
ejpam-5342	136	17	.	.	PUNCT
ejpam-5342	137	1	then	then	ADV
ejpam-5342	137	2	there	there	PRON
ejpam-5342	137	3	exists	exist	VERB
ejpam-5342	137	4	x	x	X
ejpam-5342	137	5	∈	∈	PROPN
ejpam-5342	137	6	v	v	NOUN
ejpam-5342	137	7	(	(	PUNCT
ejpam-5342	137	8	huv)\suv	huv)\suv	PROPN
ejpam-5342	137	9	.	.	PUNCT
ejpam-5342	138	1	hence	hence	ADV
ejpam-5342	138	2	,	,	PUNCT
ejpam-5342	138	3	x	x	X
ejpam-5342	138	4	,	,	PUNCT
ejpam-5342	138	5	u	u	PROPN
ejpam-5342	138	6	∈	∈	PROPN
ejpam-5342	138	7	v	v	NOUN
ejpam-5342	138	8	(	(	PUNCT
ejpam-5342	138	9	g	g	PROPN
ejpam-5342	138	10	⋄	⋄	PROPN
ejpam-5342	138	11	h)\c	h)\c	NOUN
ejpam-5342	138	12	and	and	CCONJ
ejpam-5342	138	13	xu	xu	PROPN
ejpam-5342	138	14	∈	∈	PROPN
ejpam-5342	139	1	e(g	e(g	PROPN
ejpam-5342	139	2	⋄	⋄	PROPN
ejpam-5342	139	3	h	h	NOUN
ejpam-5342	139	4	)	)	PUNCT
ejpam-5342	139	5	,	,	PUNCT
ejpam-5342	139	6	a	a	DET
ejpam-5342	139	7	contradiction	contradiction	NOUN
ejpam-5342	139	8	to	to	ADP
ejpam-5342	139	9	the	the	DET
ejpam-5342	139	10	independence	independence	NOUN
ejpam-5342	139	11	of	of	ADP
ejpam-5342	139	12	v	v	NOUN
ejpam-5342	139	13	(	(	PUNCT
ejpam-5342	139	14	g⋄h)\c	g⋄h)\c	NOUN
ejpam-5342	139	15	.	.	PUNCT
ejpam-5342	140	1	thus	thus	ADV
ejpam-5342	140	2	,	,	PUNCT
ejpam-5342	140	3	suv	suv	PROPN
ejpam-5342	140	4	=	=	SYM
ejpam-5342	140	5	v	v	PROPN
ejpam-5342	140	6	(	(	PUNCT
ejpam-5342	140	7	huv	huv	PROPN
ejpam-5342	140	8	)	)	PUNCT
ejpam-5342	140	9	and	and	CCONJ
ejpam-5342	140	10	(	(	PUNCT
ejpam-5342	140	11	ii	ii	NOUN
ejpam-5342	140	12	)	)	PUNCT
ejpam-5342	140	13	holds	hold	VERB
ejpam-5342	140	14	.	.	PUNCT
ejpam-5342	141	1	lastly	lastly	ADV
ejpam-5342	141	2	,	,	PUNCT
ejpam-5342	141	3	let	let	VERB
ejpam-5342	141	4	a	a	DET
ejpam-5342	141	5	,	,	PUNCT
ejpam-5342	141	6	b	b	PROPN
ejpam-5342	141	7	∈	∈	PROPN
ejpam-5342	141	8	a	a	DET
ejpam-5342	141	9	such	such	ADJ
ejpam-5342	141	10	that	that	SCONJ
ejpam-5342	141	11	ab	ab	PROPN
ejpam-5342	141	12	∈	∈	PROPN
ejpam-5342	141	13	e(g	e(g	PROPN
ejpam-5342	141	14	)	)	PUNCT
ejpam-5342	141	15	and	and	CCONJ
ejpam-5342	141	16	sab	sab	VERB
ejpam-5342	141	17	̸=	̸=	PROPN
ejpam-5342	141	18	v	v	PROPN
ejpam-5342	141	19	(	(	PUNCT
ejpam-5342	141	20	hab	hab	NOUN
ejpam-5342	141	21	)	)	PUNCT
ejpam-5342	141	22	.	.	PUNCT
ejpam-5342	142	1	since	since	SCONJ
ejpam-5342	142	2	v	v	NOUN
ejpam-5342	142	3	(	(	PUNCT
ejpam-5342	142	4	g	g	NOUN
ejpam-5342	142	5	⋄h)\c	⋄h)\c	PROPN
ejpam-5342	142	6	is	be	AUX
ejpam-5342	142	7	independent	independent	ADJ
ejpam-5342	142	8	and	and	CCONJ
ejpam-5342	142	9	(	(	PUNCT
ejpam-5342	142	10	v	v	NOUN
ejpam-5342	142	11	(	(	PUNCT
ejpam-5342	142	12	hab)\sab	hab)\sab	PROPN
ejpam-5342	142	13	)	)	PUNCT
ejpam-5342	142	14	⊆	⊆	NUM
ejpam-5342	142	15	v	v	NOUN
ejpam-5342	142	16	(	(	PUNCT
ejpam-5342	142	17	g	g	NOUN
ejpam-5342	142	18	⋄h)\c	⋄h)\c	PROPN
ejpam-5342	142	19	,	,	PUNCT
ejpam-5342	142	20	v	v	NUM
ejpam-5342	142	21	(	(	PUNCT
ejpam-5342	142	22	hab)\sab	hab)\sab	PROPN
ejpam-5342	142	23	is	be	AUX
ejpam-5342	142	24	an	an	DET
ejpam-5342	142	25	independent	independent	ADJ
ejpam-5342	142	26	set	set	NOUN
ejpam-5342	142	27	in	in	ADP
ejpam-5342	142	28	hab	hab	NOUN
ejpam-5342	142	29	.	.	PUNCT
ejpam-5342	143	1	hence	hence	ADV
ejpam-5342	143	2	,	,	PUNCT
ejpam-5342	143	3	(	(	PUNCT
ejpam-5342	143	4	iii	iii	NOUN
ejpam-5342	143	5	)	)	PUNCT
ejpam-5342	143	6	holds	hold	VERB
ejpam-5342	143	7	.	.	PUNCT
ejpam-5342	144	1	for	for	ADP
ejpam-5342	144	2	the	the	DET
ejpam-5342	144	3	converse	converse	NOUN
ejpam-5342	144	4	,	,	PUNCT
ejpam-5342	144	5	suppose	suppose	VERB
ejpam-5342	144	6	c	c	NOUN
ejpam-5342	144	7	=	=	PUNCT
ejpam-5342	144	8	a	a	DET
ejpam-5342	144	9	∪	∪	X
ejpam-5342	144	10	(	(	PUNCT
ejpam-5342	144	11	⋃	⋃	NOUN
ejpam-5342	144	12	uv∈e(g	uv∈e(g	NOUN
ejpam-5342	144	13	)	)	PUNCT
ejpam-5342	144	14	suv	suv	NOUN
ejpam-5342	144	15	)	)	PUNCT
ejpam-5342	144	16	where	where	SCONJ
ejpam-5342	144	17	(	(	PUNCT
ejpam-5342	144	18	i	i	NOUN
ejpam-5342	144	19	)	)	PUNCT
ejpam-5342	144	20	,	,	PUNCT
ejpam-5342	144	21	(	(	PUNCT
ejpam-5342	144	22	ii	ii	NOUN
ejpam-5342	144	23	)	)	PUNCT
ejpam-5342	144	24	and	and	CCONJ
ejpam-5342	144	25	(	(	PUNCT
ejpam-5342	144	26	iii	iii	NOUN
ejpam-5342	144	27	)	)	PUNCT
ejpam-5342	144	28	hold	hold	NOUN
ejpam-5342	144	29	.	.	PUNCT
ejpam-5342	145	1	first	first	ADV
ejpam-5342	145	2	,	,	PUNCT
ejpam-5342	145	3	we	we	PRON
ejpam-5342	145	4	show	show	VERB
ejpam-5342	145	5	that	that	SCONJ
ejpam-5342	145	6	c	c	PROPN
ejpam-5342	145	7	is	be	AUX
ejpam-5342	145	8	connected	connect	VERB
ejpam-5342	145	9	.	.	PUNCT
ejpam-5342	146	1	let	let	VERB
ejpam-5342	146	2	u	u	NOUN
ejpam-5342	146	3	,	,	PUNCT
ejpam-5342	146	4	v	v	PROPN
ejpam-5342	146	5	∈	∈	NOUN
ejpam-5342	146	6	c	c	NOUN
ejpam-5342	146	7	with	with	ADP
ejpam-5342	146	8	u	u	NOUN
ejpam-5342	146	9	̸=	̸=	PROPN
ejpam-5342	146	10	v.	v.	ADV
ejpam-5342	146	11	if	if	SCONJ
ejpam-5342	146	12	uv	uv	PROPN
ejpam-5342	146	13	∈	∈	PROPN
ejpam-5342	146	14	e(g	e(g	PROPN
ejpam-5342	146	15	⋄	⋄	PROPN
ejpam-5342	146	16	h	h	NOUN
ejpam-5342	146	17	)	)	PUNCT
ejpam-5342	146	18	,	,	PUNCT
ejpam-5342	146	19	then	then	ADV
ejpam-5342	146	20	we	we	PRON
ejpam-5342	146	21	are	be	AUX
ejpam-5342	146	22	done	do	VERB
ejpam-5342	146	23	.	.	PUNCT
ejpam-5342	147	1	so	so	ADV
ejpam-5342	147	2	,	,	PUNCT
ejpam-5342	147	3	suppose	suppose	VERB
ejpam-5342	147	4	that	that	SCONJ
ejpam-5342	147	5	uv	uv	NOUN
ejpam-5342	147	6	/∈	/∈	PUNCT
ejpam-5342	147	7	e(g	e(g	PROPN
ejpam-5342	147	8	⋄h	⋄h	PROPN
ejpam-5342	147	9	)	)	PUNCT
ejpam-5342	147	10	.	.	PUNCT
ejpam-5342	148	1	consider	consider	VERB
ejpam-5342	148	2	the	the	DET
ejpam-5342	148	3	following	follow	VERB
ejpam-5342	148	4	cases	case	NOUN
ejpam-5342	148	5	.	.	PUNCT
ejpam-5342	149	1	case	case	NOUN
ejpam-5342	149	2	1	1	NUM
ejpam-5342	149	3	.	.	X
ejpam-5342	149	4	u	u	NOUN
ejpam-5342	149	5	,	,	PUNCT
ejpam-5342	149	6	v	v	PROPN
ejpam-5342	149	7	∈	∈	PRON
ejpam-5342	149	8	a	a	PRON
ejpam-5342	149	9	by	by	X
ejpam-5342	149	10	(	(	PUNCT
ejpam-5342	149	11	i	i	NOUN
ejpam-5342	149	12	)	)	PUNCT
ejpam-5342	149	13	,	,	PUNCT
ejpam-5342	149	14	⟨a⟩	⟨a⟩	PROPN
ejpam-5342	149	15	is	be	AUX
ejpam-5342	149	16	connected	connect	VERB
ejpam-5342	149	17	.	.	PUNCT
ejpam-5342	150	1	hence	hence	ADV
ejpam-5342	150	2	,	,	PUNCT
ejpam-5342	150	3	there	there	PRON
ejpam-5342	150	4	exists	exist	VERB
ejpam-5342	150	5	a	a	DET
ejpam-5342	150	6	u	u	NOUN
ejpam-5342	150	7	-	-	NOUN
ejpam-5342	150	8	v	v	ADJ
ejpam-5342	150	9	path	path	NOUN
ejpam-5342	150	10	p	p	X
ejpam-5342	151	1	[	[	X
ejpam-5342	151	2	u	u	NOUN
ejpam-5342	151	3	,	,	PUNCT
ejpam-5342	151	4	v	v	ADP
ejpam-5342	151	5	]	]	PUNCT
ejpam-5342	151	6	in	in	ADP
ejpam-5342	151	7	a.	a.	NOUN
ejpam-5342	151	8	since	since	SCONJ
ejpam-5342	151	9	a	a	DET
ejpam-5342	151	10	⊆	⊆	NUM
ejpam-5342	151	11	c	c	NOUN
ejpam-5342	151	12	,	,	PUNCT
ejpam-5342	151	13	the	the	DET
ejpam-5342	151	14	path	path	NOUN
ejpam-5342	151	15	p	p	X
ejpam-5342	152	1	[	[	X
ejpam-5342	152	2	u	u	NOUN
ejpam-5342	152	3	,	,	PUNCT
ejpam-5342	152	4	v	v	NOUN
ejpam-5342	152	5	]	]	PUNCT
ejpam-5342	152	6	is	be	AUX
ejpam-5342	152	7	in	in	ADP
ejpam-5342	152	8	c.	c.	NOUN
ejpam-5342	152	9	case	case	NOUN
ejpam-5342	152	10	2	2	NUM
ejpam-5342	152	11	.	.	X
ejpam-5342	152	12	u	u	PROPN
ejpam-5342	152	13	∈	∈	PROPN
ejpam-5342	152	14	a	a	PRON
ejpam-5342	152	15	and	and	CCONJ
ejpam-5342	152	16	v	v	NOUN
ejpam-5342	152	17	∈	∈	PROPN
ejpam-5342	152	18	sxy	sxy	PROPN
ejpam-5342	152	19	for	for	ADP
ejpam-5342	152	20	some	some	DET
ejpam-5342	152	21	xy	xy	PROPN
ejpam-5342	152	22	∈	∈	PROPN
ejpam-5342	152	23	e(g	e(g	PROPN
ejpam-5342	152	24	)	)	PUNCT
ejpam-5342	152	25	since	since	SCONJ
ejpam-5342	152	26	uv	uv	PROPN
ejpam-5342	152	27	/∈	/∈	PUNCT
ejpam-5342	152	28	e(g	e(g	PROPN
ejpam-5342	152	29	⋄	⋄	PROPN
ejpam-5342	152	30	h	h	NOUN
ejpam-5342	152	31	)	)	PUNCT
ejpam-5342	152	32	,	,	PUNCT
ejpam-5342	152	33	u	u	NOUN
ejpam-5342	152	34	̸=	̸=	PROPN
ejpam-5342	152	35	x	x	X
ejpam-5342	152	36	and	and	CCONJ
ejpam-5342	152	37	u	u	PROPN
ejpam-5342	152	38	̸=	̸=	PROPN
ejpam-5342	152	39	y.	y.	NOUN
ejpam-5342	152	40	since	since	SCONJ
ejpam-5342	152	41	v	v	NOUN
ejpam-5342	152	42	(	(	PUNCT
ejpam-5342	152	43	g)\a	g)\a	NOUN
ejpam-5342	152	44	is	be	AUX
ejpam-5342	152	45	independent	independent	ADJ
ejpam-5342	152	46	by	by	ADP
ejpam-5342	152	47	(	(	PUNCT
ejpam-5342	152	48	i	i	NOUN
ejpam-5342	152	49	)	)	PUNCT
ejpam-5342	152	50	,	,	PUNCT
ejpam-5342	152	51	x	x	PUNCT
ejpam-5342	152	52	∈	∈	PROPN
ejpam-5342	152	53	a	a	PRON
ejpam-5342	152	54	or	or	CCONJ
ejpam-5342	152	55	y	y	PROPN
ejpam-5342	152	56	∈	∈	PROPN
ejpam-5342	152	57	a	a	PRON
ejpam-5342	152	58	,	,	PUNCT
ejpam-5342	152	59	say	say	VERB
ejpam-5342	152	60	x	x	X
ejpam-5342	152	61	∈	∈	NOUN
ejpam-5342	152	62	a.	a.	NOUN
ejpam-5342	153	1	if	if	SCONJ
ejpam-5342	153	2	ux	ux	PROPN
ejpam-5342	153	3	∈	∈	PROPN
ejpam-5342	153	4	e(g	e(g	PROPN
ejpam-5342	153	5	)	)	PUNCT
ejpam-5342	153	6	,	,	PUNCT
ejpam-5342	153	7	then	then	ADV
ejpam-5342	153	8	the	the	DET
ejpam-5342	153	9	path	path	NOUN
ejpam-5342	154	1	[	[	X
ejpam-5342	154	2	u	u	NOUN
ejpam-5342	154	3	,	,	PUNCT
ejpam-5342	154	4	x	x	X
ejpam-5342	154	5	,	,	PUNCT
ejpam-5342	154	6	v	v	NOUN
ejpam-5342	154	7	]	]	PUNCT
ejpam-5342	154	8	is	be	AUX
ejpam-5342	154	9	a	a	DET
ejpam-5342	154	10	u	u	NOUN
ejpam-5342	154	11	-	-	NOUN
ejpam-5342	154	12	v	v	ADJ
ejpam-5342	154	13	path	path	NOUN
ejpam-5342	154	14	in	in	ADP
ejpam-5342	154	15	c.	c.	PROPN
ejpam-5342	154	16	suppose	suppose	VERB
ejpam-5342	154	17	ux	ux	PROPN
ejpam-5342	154	18	/∈	/∈	PUNCT
ejpam-5342	154	19	e(g	e(g	PROPN
ejpam-5342	154	20	)	)	PUNCT
ejpam-5342	154	21	.	.	PUNCT
ejpam-5342	155	1	since	since	SCONJ
ejpam-5342	155	2	⟨a⟩	⟨a⟩	PROPN
ejpam-5342	155	3	is	be	AUX
ejpam-5342	155	4	connected	connect	VERB
ejpam-5342	155	5	by	by	ADP
ejpam-5342	155	6	(	(	PUNCT
ejpam-5342	155	7	i	i	NOUN
ejpam-5342	155	8	)	)	PUNCT
ejpam-5342	155	9	and	and	CCONJ
ejpam-5342	155	10	u	u	NOUN
ejpam-5342	155	11	,	,	PUNCT
ejpam-5342	155	12	x	x	PROPN
ejpam-5342	155	13	∈	∈	PROPN
ejpam-5342	155	14	a	a	PRON
ejpam-5342	155	15	,	,	PUNCT
ejpam-5342	155	16	there	there	PRON
ejpam-5342	155	17	exists	exist	VERB
ejpam-5342	155	18	u	u	NOUN
ejpam-5342	155	19	-	-	ADJ
ejpam-5342	155	20	x	x	ADJ
ejpam-5342	155	21	path	path	NOUN
ejpam-5342	155	22	[	[	X
ejpam-5342	155	23	y1	y1	INTJ
ejpam-5342	155	24	,	,	PUNCT
ejpam-5342	155	25	y2	y2	PROPN
ejpam-5342	155	26	,	,	PUNCT
ejpam-5342	155	27	...	...	PUNCT
ejpam-5342	155	28	,	,	PUNCT
ejpam-5342	155	29	yk	yk	PROPN
ejpam-5342	155	30	]	]	PUNCT
ejpam-5342	155	31	s.	s.	PROPN
ejpam-5342	155	32	a.	a.	PROPN
ejpam-5342	155	33	nanding	nanding	PROPN
ejpam-5342	155	34	,	,	PUNCT
ejpam-5342	155	35	h.	h.	PROPN
ejpam-5342	155	36	m.	m.	PROPN
ejpam-5342	155	37	rara	rara	PROPN
ejpam-5342	155	38	,	,	PUNCT
ejpam-5342	155	39	i.	i.	PROPN
ejpam-5342	155	40	s.	s.	PROPN
ejpam-5342	155	41	aniversario	aniversario	PROPN
ejpam-5342	155	42	/	/	SYM
ejpam-5342	155	43	eur	eur	PROPN
ejpam-5342	155	44	.	.	PUNCT
ejpam-5342	156	1	j.	j.	PROPN
ejpam-5342	156	2	pure	pure	PROPN
ejpam-5342	156	3	appl	appl	PROPN
ejpam-5342	156	4	.	.	PROPN
ejpam-5342	156	5	math	math	PROPN
ejpam-5342	156	6	,	,	PUNCT
ejpam-5342	156	7	17	17	NUM
ejpam-5342	156	8	(	(	PUNCT
ejpam-5342	156	9	4	4	NUM
ejpam-5342	156	10	)	)	PUNCT
ejpam-5342	156	11	(	(	PUNCT
ejpam-5342	156	12	2024	2024	NUM
ejpam-5342	156	13	)	)	PUNCT
ejpam-5342	156	14	,	,	PUNCT
ejpam-5342	156	15	2505	2505	NUM
ejpam-5342	156	16	-	-	SYM
ejpam-5342	156	17	2515	2515	NUM
ejpam-5342	156	18	2510	2510	NUM
ejpam-5342	156	19	in	in	ADP
ejpam-5342	156	20	a	a	DET
ejpam-5342	156	21	where	where	SCONJ
ejpam-5342	156	22	u	u	NOUN
ejpam-5342	156	23	=	=	PROPN
ejpam-5342	156	24	y1	y1	PROPN
ejpam-5342	156	25	,	,	PUNCT
ejpam-5342	156	26	x	x	X
ejpam-5342	156	27	=	=	SYM
ejpam-5342	156	28	yk	yk	PROPN
ejpam-5342	156	29	and	and	CCONJ
ejpam-5342	156	30	k	k	X
ejpam-5342	156	31	>	>	X
ejpam-5342	156	32	2	2	X
ejpam-5342	156	33	.	.	PUNCT
ejpam-5342	157	1	hence	hence	ADV
ejpam-5342	157	2	,	,	PUNCT
ejpam-5342	157	3	the	the	DET
ejpam-5342	157	4	path	path	NOUN
ejpam-5342	157	5	[	[	X
ejpam-5342	157	6	y1	y1	INTJ
ejpam-5342	157	7	,	,	PUNCT
ejpam-5342	157	8	y2	y2	PROPN
ejpam-5342	157	9	,	,	PUNCT
ejpam-5342	157	10	...	...	PUNCT
ejpam-5342	157	11	,	,	PUNCT
ejpam-5342	157	12	yk	yk	PROPN
ejpam-5342	157	13	,	,	PUNCT
ejpam-5342	157	14	v	v	NOUN
ejpam-5342	157	15	]	]	X
ejpam-5342	157	16	is	be	AUX
ejpam-5342	157	17	a	a	DET
ejpam-5342	157	18	u	u	NOUN
ejpam-5342	157	19	-	-	NOUN
ejpam-5342	157	20	v	v	ADJ
ejpam-5342	157	21	path	path	NOUN
ejpam-5342	157	22	in	in	ADP
ejpam-5342	157	23	c.	c.	PROPN
ejpam-5342	157	24	case	case	NOUN
ejpam-5342	157	25	3	3	NUM
ejpam-5342	157	26	.	.	X
ejpam-5342	157	27	u	u	NOUN
ejpam-5342	157	28	,	,	PUNCT
ejpam-5342	157	29	v	v	NOUN
ejpam-5342	157	30	∈	∈	NOUN
ejpam-5342	157	31	spq	spq	NOUN
ejpam-5342	157	32	for	for	ADP
ejpam-5342	157	33	some	some	DET
ejpam-5342	157	34	edge	edge	NOUN
ejpam-5342	157	35	pq	pq	PROPN
ejpam-5342	157	36	∈	∈	PROPN
ejpam-5342	157	37	e(g	e(g	PROPN
ejpam-5342	157	38	)	)	PUNCT
ejpam-5342	157	39	.	.	PUNCT
ejpam-5342	158	1	since	since	SCONJ
ejpam-5342	158	2	v	v	NOUN
ejpam-5342	158	3	(	(	PUNCT
ejpam-5342	158	4	g)\a	g)\a	NOUN
ejpam-5342	158	5	is	be	AUX
ejpam-5342	158	6	independent	independent	ADJ
ejpam-5342	158	7	by	by	ADP
ejpam-5342	158	8	(	(	PUNCT
ejpam-5342	158	9	i	i	NOUN
ejpam-5342	158	10	)	)	PUNCT
ejpam-5342	158	11	,	,	PUNCT
ejpam-5342	158	12	p	p	PROPN
ejpam-5342	158	13	∈	∈	PROPN
ejpam-5342	158	14	a	a	PRON
ejpam-5342	158	15	or	or	CCONJ
ejpam-5342	158	16	q	q	PROPN
ejpam-5342	158	17	∈	∈	PROPN
ejpam-5342	158	18	a.	a.	NOUN
ejpam-5342	158	19	hence	hence	ADV
ejpam-5342	158	20	,	,	PUNCT
ejpam-5342	158	21	the	the	DET
ejpam-5342	158	22	path	path	NOUN
ejpam-5342	159	1	[	[	X
ejpam-5342	159	2	u	u	NOUN
ejpam-5342	159	3	,	,	PUNCT
ejpam-5342	159	4	p	p	X
ejpam-5342	159	5	,	,	PUNCT
ejpam-5342	159	6	v	v	NOUN
ejpam-5342	159	7	]	]	PUNCT
ejpam-5342	159	8	or	or	CCONJ
ejpam-5342	159	9	[	[	X
ejpam-5342	159	10	u	u	NOUN
ejpam-5342	159	11	,	,	PUNCT
ejpam-5342	159	12	q	q	INTJ
ejpam-5342	159	13	,	,	PUNCT
ejpam-5342	159	14	v	v	NOUN
ejpam-5342	159	15	]	]	PUNCT
ejpam-5342	159	16	is	be	AUX
ejpam-5342	159	17	in	in	ADP
ejpam-5342	159	18	c.	c.	NOUN
ejpam-5342	159	19	in	in	ADP
ejpam-5342	159	20	any	any	DET
ejpam-5342	159	21	case	case	NOUN
ejpam-5342	159	22	,	,	PUNCT
ejpam-5342	159	23	⟨c⟩	⟨c⟩	PROPN
ejpam-5342	159	24	is	be	AUX
ejpam-5342	159	25	connected	connect	VERB
ejpam-5342	159	26	.	.	PUNCT
ejpam-5342	160	1	next	next	ADV
ejpam-5342	160	2	,	,	PUNCT
ejpam-5342	160	3	we	we	PRON
ejpam-5342	160	4	show	show	VERB
ejpam-5342	160	5	that	that	SCONJ
ejpam-5342	160	6	v	v	NOUN
ejpam-5342	160	7	(	(	PUNCT
ejpam-5342	160	8	g	g	NOUN
ejpam-5342	160	9	⋄h)\c	⋄h)\c	PROPN
ejpam-5342	160	10	is	be	AUX
ejpam-5342	160	11	independent	independent	ADJ
ejpam-5342	160	12	.	.	PUNCT
ejpam-5342	161	1	let	let	VERB
ejpam-5342	161	2	p	p	PRON
ejpam-5342	161	3	,	,	PUNCT
ejpam-5342	161	4	q	q	PROPN
ejpam-5342	161	5	∈	∈	PROPN
ejpam-5342	161	6	v	v	NOUN
ejpam-5342	161	7	(	(	PUNCT
ejpam-5342	161	8	g	g	NOUN
ejpam-5342	161	9	⋄h)\c	⋄h)\c	VERB
ejpam-5342	161	10	with	with	ADP
ejpam-5342	161	11	p	p	PROPN
ejpam-5342	161	12	̸=	̸=	PROPN
ejpam-5342	161	13	q.	q.	NOUN
ejpam-5342	161	14	consider	consider	VERB
ejpam-5342	161	15	the	the	DET
ejpam-5342	161	16	following	follow	VERB
ejpam-5342	161	17	cases	case	NOUN
ejpam-5342	161	18	.	.	PUNCT
ejpam-5342	162	1	case	case	NOUN
ejpam-5342	162	2	1	1	NUM
ejpam-5342	162	3	.	.	PUNCT
ejpam-5342	163	1	p	p	PROPN
ejpam-5342	163	2	∈	∈	PROPN
ejpam-5342	163	3	v	v	NOUN
ejpam-5342	163	4	(	(	PUNCT
ejpam-5342	163	5	g)\a	g)\a	NOUN
ejpam-5342	163	6	and	and	CCONJ
ejpam-5342	163	7	q	q	NOUN
ejpam-5342	163	8	∈	∈	PROPN
ejpam-5342	163	9	v	v	NOUN
ejpam-5342	163	10	(	(	PUNCT
ejpam-5342	163	11	g)\a	g)\a	NOUN
ejpam-5342	163	12	since	since	SCONJ
ejpam-5342	163	13	v	v	NOUN
ejpam-5342	163	14	(	(	PUNCT
ejpam-5342	163	15	g)\a	g)\a	NOUN
ejpam-5342	163	16	is	be	AUX
ejpam-5342	163	17	independent	independent	ADJ
ejpam-5342	163	18	by	by	ADP
ejpam-5342	163	19	(	(	PUNCT
ejpam-5342	163	20	i	i	NOUN
ejpam-5342	163	21	)	)	PUNCT
ejpam-5342	163	22	,	,	PUNCT
ejpam-5342	163	23	pq	pq	PROPN
ejpam-5342	163	24	/∈	/∈	PUNCT
ejpam-5342	163	25	e(g	e(g	PROPN
ejpam-5342	163	26	)	)	PUNCT
ejpam-5342	163	27	.	.	PUNCT
ejpam-5342	164	1	thus	thus	ADV
ejpam-5342	164	2	,	,	PUNCT
ejpam-5342	164	3	pq	pq	INTJ
ejpam-5342	164	4	/∈	/∈	PUNCT
ejpam-5342	164	5	e(g	e(g	PROPN
ejpam-5342	164	6	⋄h	⋄h	PROPN
ejpam-5342	164	7	)	)	PUNCT
ejpam-5342	164	8	.	.	PUNCT
ejpam-5342	165	1	case	case	NOUN
ejpam-5342	165	2	2	2	NUM
ejpam-5342	165	3	.	.	PUNCT
ejpam-5342	166	1	p	p	PROPN
ejpam-5342	166	2	∈	∈	PROPN
ejpam-5342	166	3	v	v	NOUN
ejpam-5342	166	4	(	(	PUNCT
ejpam-5342	166	5	g)\a	g)\a	NOUN
ejpam-5342	166	6	,	,	PUNCT
ejpam-5342	166	7	q	q	PROPN
ejpam-5342	166	8	∈	∈	PROPN
ejpam-5342	166	9	v	v	NOUN
ejpam-5342	166	10	(	(	PUNCT
ejpam-5342	166	11	hxy)\sxy	hxy)\sxy	PROPN
ejpam-5342	166	12	for	for	ADP
ejpam-5342	166	13	some	some	DET
ejpam-5342	166	14	xy	xy	PROPN
ejpam-5342	166	15	∈	∈	PROPN
ejpam-5342	166	16	e(g	e(g	PROPN
ejpam-5342	166	17	)	)	PUNCT
ejpam-5342	166	18	since	since	SCONJ
ejpam-5342	166	19	sxy	sxy	PROPN
ejpam-5342	166	20	̸=	̸=	PROPN
ejpam-5342	166	21	v	v	ADP
ejpam-5342	166	22	(	(	PUNCT
ejpam-5342	166	23	hxy	hxy	NOUN
ejpam-5342	166	24	)	)	PUNCT
ejpam-5342	166	25	,	,	PUNCT
ejpam-5342	166	26	x	x	X
ejpam-5342	166	27	,	,	PUNCT
ejpam-5342	166	28	y	y	PROPN
ejpam-5342	166	29	∈	∈	PROPN
ejpam-5342	166	30	a	a	DET
ejpam-5342	166	31	by	by	ADP
ejpam-5342	166	32	(	(	PUNCT
ejpam-5342	166	33	ii	ii	NOUN
ejpam-5342	166	34	)	)	PUNCT
ejpam-5342	166	35	.	.	PUNCT
ejpam-5342	167	1	hence	hence	ADV
ejpam-5342	167	2	,	,	PUNCT
ejpam-5342	167	3	p	p	PROPN
ejpam-5342	167	4	̸=	̸=	PROPN
ejpam-5342	167	5	x	x	PUNCT
ejpam-5342	167	6	and	and	CCONJ
ejpam-5342	167	7	p	p	PROPN
ejpam-5342	167	8	̸=	̸=	PROPN
ejpam-5342	167	9	y.	y.	NOUN
ejpam-5342	167	10	by	by	ADP
ejpam-5342	167	11	definition	definition	NOUN
ejpam-5342	167	12	of	of	ADP
ejpam-5342	167	13	g	g	PROPN
ejpam-5342	167	14	⋄h	⋄h	PROPN
ejpam-5342	167	15	,	,	PUNCT
ejpam-5342	167	16	pq	pq	NOUN
ejpam-5342	167	17	/∈	/∈	PUNCT
ejpam-5342	167	18	e(g	e(g	PROPN
ejpam-5342	167	19	⋄h	⋄h	PROPN
ejpam-5342	167	20	)	)	PUNCT
ejpam-5342	167	21	.	.	PUNCT
ejpam-5342	168	1	case	case	NOUN
ejpam-5342	168	2	3	3	X
ejpam-5342	168	3	.	.	PUNCT
ejpam-5342	169	1	p	p	PROPN
ejpam-5342	169	2	∈	∈	PROPN
ejpam-5342	169	3	v	v	NOUN
ejpam-5342	169	4	(	(	PUNCT
ejpam-5342	169	5	hxy)\sxy	hxy)\sxy	PROPN
ejpam-5342	169	6	and	and	CCONJ
ejpam-5342	169	7	q	q	NOUN
ejpam-5342	169	8	∈	∈	PROPN
ejpam-5342	169	9	v	v	NOUN
ejpam-5342	169	10	(	(	PUNCT
ejpam-5342	169	11	hrs)\srs	hrs)\srs	NOUN
ejpam-5342	169	12	for	for	ADP
ejpam-5342	169	13	some	some	DET
ejpam-5342	169	14	distinct	distinct	ADJ
ejpam-5342	169	15	edges	edge	NOUN
ejpam-5342	169	16	xy	xy	NOUN
ejpam-5342	169	17	,	,	PUNCT
ejpam-5342	169	18	rs	rs	PROPN
ejpam-5342	169	19	∈	∈	PROPN
ejpam-5342	169	20	e(g	e(g	PROPN
ejpam-5342	169	21	)	)	PUNCT
ejpam-5342	169	22	then	then	ADV
ejpam-5342	169	23	,	,	PUNCT
ejpam-5342	169	24	by	by	ADP
ejpam-5342	169	25	definition	definition	NOUN
ejpam-5342	169	26	of	of	ADP
ejpam-5342	169	27	g	g	PROPN
ejpam-5342	169	28	⋄h	⋄h	PROPN
ejpam-5342	169	29	,	,	PUNCT
ejpam-5342	169	30	pq	pq	NOUN
ejpam-5342	169	31	/∈	/∈	PUNCT
ejpam-5342	169	32	e(g	e(g	PROPN
ejpam-5342	169	33	⋄h	⋄h	PROPN
ejpam-5342	169	34	)	)	PUNCT
ejpam-5342	169	35	.	.	PUNCT
ejpam-5342	170	1	case	case	NOUN
ejpam-5342	170	2	4	4	NUM
ejpam-5342	170	3	.	.	X
ejpam-5342	171	1	p	p	X
ejpam-5342	171	2	,	,	PUNCT
ejpam-5342	171	3	q	q	PROPN
ejpam-5342	171	4	∈	∈	PROPN
ejpam-5342	171	5	v	v	NOUN
ejpam-5342	171	6	(	(	PUNCT
ejpam-5342	171	7	hzt)\szt	hzt)\szt	NOUN
ejpam-5342	171	8	for	for	ADP
ejpam-5342	171	9	some	some	DET
ejpam-5342	171	10	edge	edge	NOUN
ejpam-5342	171	11	zt	zt	PROPN
ejpam-5342	171	12	∈	∈	PROPN
ejpam-5342	171	13	e(g	e(g	PROPN
ejpam-5342	171	14	)	)	PUNCT
ejpam-5342	171	15	since	since	SCONJ
ejpam-5342	171	16	v	v	NUM
ejpam-5342	171	17	(	(	PUNCT
ejpam-5342	171	18	hzt)\szt	hzt)\szt	PROPN
ejpam-5342	171	19	is	be	AUX
ejpam-5342	171	20	independent	independent	ADJ
ejpam-5342	171	21	by	by	ADP
ejpam-5342	171	22	(	(	PUNCT
ejpam-5342	171	23	iii	iii	NOUN
ejpam-5342	171	24	)	)	PUNCT
ejpam-5342	171	25	,	,	PUNCT
ejpam-5342	171	26	pq	pq	INTJ
ejpam-5342	171	27	/∈	/∈	PUNCT
ejpam-5342	171	28	e(g	e(g	PROPN
ejpam-5342	171	29	⋄h	⋄h	PROPN
ejpam-5342	171	30	)	)	PUNCT
ejpam-5342	171	31	.	.	PUNCT
ejpam-5342	172	1	therefore	therefore	ADV
ejpam-5342	172	2	,	,	PUNCT
ejpam-5342	172	3	in	in	ADP
ejpam-5342	172	4	any	any	DET
ejpam-5342	172	5	case	case	NOUN
ejpam-5342	172	6	,	,	PUNCT
ejpam-5342	172	7	v	v	NOUN
ejpam-5342	172	8	(	(	PUNCT
ejpam-5342	172	9	g	g	NOUN
ejpam-5342	172	10	⋄h)\c	⋄h)\c	PROPN
ejpam-5342	172	11	is	be	AUX
ejpam-5342	172	12	an	an	DET
ejpam-5342	172	13	independent	independent	ADJ
ejpam-5342	172	14	set	set	NOUN
ejpam-5342	172	15	in	in	ADP
ejpam-5342	172	16	g	g	PROPN
ejpam-5342	172	17	⋄h	⋄h	PROPN
ejpam-5342	172	18	.	.	PUNCT
ejpam-5342	173	1	lastly	lastly	ADV
ejpam-5342	173	2	,	,	PUNCT
ejpam-5342	173	3	we	we	PRON
ejpam-5342	173	4	show	show	VERB
ejpam-5342	173	5	that	that	SCONJ
ejpam-5342	173	6	c	c	PROPN
ejpam-5342	173	7	is	be	AUX
ejpam-5342	173	8	a	a	DET
ejpam-5342	173	9	hop	hop	NOUN
ejpam-5342	173	10	dominating	dominating	NOUN
ejpam-5342	173	11	set	set	NOUN
ejpam-5342	173	12	of	of	ADP
ejpam-5342	173	13	g	g	PROPN
ejpam-5342	173	14	⋄	⋄	PROPN
ejpam-5342	173	15	h.	h.	PROPN
ejpam-5342	173	16	let	let	VERB
ejpam-5342	173	17	u	u	PRON
ejpam-5342	173	18	∈	∈	PROPN
ejpam-5342	173	19	v	v	NOUN
ejpam-5342	173	20	(	(	PUNCT
ejpam-5342	173	21	g	g	PROPN
ejpam-5342	173	22	⋄	⋄	PROPN
ejpam-5342	173	23	h)\c	h)\c	NOUN
ejpam-5342	173	24	.	.	PUNCT
ejpam-5342	174	1	consider	consider	VERB
ejpam-5342	174	2	the	the	DET
ejpam-5342	174	3	following	follow	VERB
ejpam-5342	174	4	cases	case	NOUN
ejpam-5342	174	5	.	.	PUNCT
ejpam-5342	175	1	case	case	NOUN
ejpam-5342	175	2	1	1	NUM
ejpam-5342	175	3	.	.	PUNCT
ejpam-5342	176	1	u	u	PROPN
ejpam-5342	176	2	∈	∈	PROPN
ejpam-5342	176	3	v	v	NOUN
ejpam-5342	176	4	(	(	PUNCT
ejpam-5342	176	5	g)\a	g)\a	NOUN
ejpam-5342	176	6	let	let	VERB
ejpam-5342	176	7	degg(u	degg(u	NUM
ejpam-5342	176	8	)	)	PUNCT
ejpam-5342	176	9	=	=	SYM
ejpam-5342	177	1	1	1	X
ejpam-5342	177	2	.	.	PUNCT
ejpam-5342	177	3	since	since	SCONJ
ejpam-5342	177	4	|v	|v	PROPN
ejpam-5342	177	5	(	(	PUNCT
ejpam-5342	177	6	g)|	g)|	X
ejpam-5342	177	7	≥	≥	NOUN
ejpam-5342	177	8	3	3	NUM
ejpam-5342	177	9	,	,	PUNCT
ejpam-5342	177	10	there	there	PRON
ejpam-5342	177	11	exists	exist	VERB
ejpam-5342	177	12	vw	vw	PROPN
ejpam-5342	177	13	∈	∈	PROPN
ejpam-5342	177	14	e(g	e(g	PROPN
ejpam-5342	177	15	)	)	PUNCT
ejpam-5342	177	16	with	with	ADP
ejpam-5342	177	17	u	u	PROPN
ejpam-5342	177	18	∈	∈	PROPN
ejpam-5342	177	19	ng(v)\ng(w	ng(v)\ng(w	ADJ
ejpam-5342	177	20	)	)	PUNCT
ejpam-5342	177	21	or	or	CCONJ
ejpam-5342	177	22	u	u	PROPN
ejpam-5342	177	23	∈	∈	PROPN
ejpam-5342	177	24	ng(w)\ng(v	ng(w)\ng(v	NOUN
ejpam-5342	177	25	)	)	PUNCT
ejpam-5342	177	26	.	.	PUNCT
ejpam-5342	178	1	if	if	SCONJ
ejpam-5342	178	2	w	w	PROPN
ejpam-5342	178	3	∈	∈	PROPN
ejpam-5342	178	4	a	a	PRON
ejpam-5342	178	5	,	,	PUNCT
ejpam-5342	178	6	then	then	ADV
ejpam-5342	178	7	w	w	PROPN
ejpam-5342	178	8	∈	∈	PROPN
ejpam-5342	178	9	ng(u	ng(u	NOUN
ejpam-5342	178	10	,	,	PUNCT
ejpam-5342	178	11	2	2	NUM
ejpam-5342	178	12	)	)	PUNCT
ejpam-5342	178	13	∩	∩	ADJ
ejpam-5342	178	14	a.	a.	NOUN
ejpam-5342	178	15	if	if	SCONJ
ejpam-5342	178	16	w	w	PROPN
ejpam-5342	178	17	/∈	/∈	PROPN
ejpam-5342	178	18	a	a	PRON
ejpam-5342	178	19	,	,	PUNCT
ejpam-5342	178	20	then	then	ADV
ejpam-5342	178	21	svw	svw	VERB
ejpam-5342	178	22	=	=	SYM
ejpam-5342	178	23	v	v	ADJ
ejpam-5342	178	24	(	(	PUNCT
ejpam-5342	178	25	hvw	hvw	NOUN
ejpam-5342	178	26	)	)	PUNCT
ejpam-5342	178	27	by	by	ADP
ejpam-5342	178	28	(	(	PUNCT
ejpam-5342	178	29	ii	ii	NOUN
ejpam-5342	178	30	)	)	PUNCT
ejpam-5342	178	31	.	.	PUNCT
ejpam-5342	179	1	thus	thus	ADV
ejpam-5342	179	2	,	,	PUNCT
ejpam-5342	179	3	a	a	DET
ejpam-5342	179	4	vertex	vertex	NOUN
ejpam-5342	179	5	p	p	X
ejpam-5342	179	6	∈	∈	PROPN
ejpam-5342	179	7	ng⋄h(u	ng⋄h(u	PROPN
ejpam-5342	179	8	,	,	PUNCT
ejpam-5342	179	9	2	2	X
ejpam-5342	179	10	)	)	PUNCT
ejpam-5342	179	11	∩	∩	NOUN
ejpam-5342	179	12	svw	svw	NOUN
ejpam-5342	179	13	exists	exist	VERB
ejpam-5342	179	14	.	.	PUNCT
ejpam-5342	180	1	hence	hence	ADV
ejpam-5342	180	2	,	,	PUNCT
ejpam-5342	180	3	p	p	PROPN
ejpam-5342	180	4	∈	∈	PROPN
ejpam-5342	180	5	ng⋄h(u	ng⋄h(u	PROPN
ejpam-5342	180	6	,	,	PUNCT
ejpam-5342	180	7	2	2	X
ejpam-5342	180	8	)	)	PUNCT
ejpam-5342	180	9	∩	∩	ADJ
ejpam-5342	180	10	c.	c.	NOUN
ejpam-5342	180	11	case	case	NOUN
ejpam-5342	180	12	2	2	NUM
ejpam-5342	180	13	.	.	X
ejpam-5342	180	14	u	u	PROPN
ejpam-5342	180	15	∈	∈	PROPN
ejpam-5342	180	16	v	v	NOUN
ejpam-5342	180	17	(	(	PUNCT
ejpam-5342	180	18	hxy)\sxy	hxy)\sxy	PROPN
ejpam-5342	180	19	for	for	ADP
ejpam-5342	180	20	some	some	DET
ejpam-5342	180	21	xy	xy	PROPN
ejpam-5342	180	22	∈	∈	PROPN
ejpam-5342	180	23	e(g	e(g	PROPN
ejpam-5342	180	24	)	)	PUNCT
ejpam-5342	180	25	by	by	ADP
ejpam-5342	180	26	(	(	PUNCT
ejpam-5342	180	27	ii	ii	NOUN
ejpam-5342	180	28	)	)	PUNCT
ejpam-5342	180	29	,	,	PUNCT
ejpam-5342	180	30	x	x	X
ejpam-5342	180	31	,	,	PUNCT
ejpam-5342	180	32	y	y	PROPN
ejpam-5342	180	33	∈	∈	PROPN
ejpam-5342	180	34	a.	a.	NOUN
ejpam-5342	180	35	since	since	SCONJ
ejpam-5342	180	36	|v	|v	PROPN
ejpam-5342	180	37	(	(	PUNCT
ejpam-5342	180	38	g)|	g)|	X
ejpam-5342	180	39	≥	≥	NOUN
ejpam-5342	180	40	3	3	NUM
ejpam-5342	180	41	,	,	PUNCT
ejpam-5342	180	42	there	there	PRON
ejpam-5342	180	43	exist	exist	VERB
ejpam-5342	180	44	z	z	PROPN
ejpam-5342	180	45	∈	∈	PROPN
ejpam-5342	180	46	v	v	ADP
ejpam-5342	180	47	(	(	PUNCT
ejpam-5342	180	48	g	g	NOUN
ejpam-5342	180	49	)	)	PUNCT
ejpam-5342	180	50	∩ng(x	∩ng(x	NOUN
ejpam-5342	180	51	)	)	PUNCT
ejpam-5342	180	52	or	or	CCONJ
ejpam-5342	180	53	z	z	NOUN
ejpam-5342	180	54	∈	∈	PROPN
ejpam-5342	180	55	v	v	ADP
ejpam-5342	180	56	(	(	PUNCT
ejpam-5342	180	57	g	g	NOUN
ejpam-5342	180	58	)	)	PUNCT
ejpam-5342	180	59	∩ng(y	∩ng(y	PROPN
ejpam-5342	180	60	)	)	PUNCT
ejpam-5342	180	61	.	.	PUNCT
ejpam-5342	181	1	if	if	SCONJ
ejpam-5342	181	2	z	z	PROPN
ejpam-5342	181	3	∈	∈	PROPN
ejpam-5342	181	4	a	a	PRON
ejpam-5342	181	5	,	,	PUNCT
ejpam-5342	181	6	then	then	ADV
ejpam-5342	181	7	z	z	PROPN
ejpam-5342	181	8	∈	∈	PROPN
ejpam-5342	181	9	ng⋄h(u	ng⋄h(u	PROPN
ejpam-5342	181	10	,	,	PUNCT
ejpam-5342	181	11	2	2	X
ejpam-5342	181	12	)	)	PUNCT
ejpam-5342	181	13	∩	∩	ADJ
ejpam-5342	181	14	c.	c.	NOUN
ejpam-5342	181	15	if	if	SCONJ
ejpam-5342	181	16	z	z	PROPN
ejpam-5342	181	17	/∈	/∈	VERB
ejpam-5342	182	1	a	a	PRON
ejpam-5342	182	2	,	,	PUNCT
ejpam-5342	182	3	then	then	ADV
ejpam-5342	182	4	syz	syz	VERB
ejpam-5342	182	5	=	=	SYM
ejpam-5342	182	6	v	v	X
ejpam-5342	182	7	(	(	PUNCT
ejpam-5342	182	8	hyz	hyz	PROPN
ejpam-5342	182	9	)	)	PUNCT
ejpam-5342	182	10	.	.	PUNCT
ejpam-5342	183	1	hence	hence	ADV
ejpam-5342	183	2	,	,	PUNCT
ejpam-5342	183	3	a	a	DET
ejpam-5342	183	4	vertex	vertex	NOUN
ejpam-5342	183	5	w	w	PROPN
ejpam-5342	183	6	∈	∈	PROPN
ejpam-5342	183	7	ng⋄h(u	ng⋄h(u	PROPN
ejpam-5342	183	8	,	,	PUNCT
ejpam-5342	183	9	2	2	X
ejpam-5342	183	10	)	)	PUNCT
ejpam-5342	183	11	∩	∩	NOUN
ejpam-5342	183	12	syz	syz	VERB
ejpam-5342	183	13	or	or	CCONJ
ejpam-5342	183	14	w	w	PROPN
ejpam-5342	183	15	∈	∈	PROPN
ejpam-5342	183	16	ng⋄h(u	ng⋄h(u	PROPN
ejpam-5342	183	17	,	,	PUNCT
ejpam-5342	183	18	2	2	X
ejpam-5342	183	19	)	)	PUNCT
ejpam-5342	183	20	∩	∩	NOUN
ejpam-5342	183	21	sxz	sxz	PROPN
ejpam-5342	183	22	.	.	PUNCT
ejpam-5342	184	1	therefore	therefore	ADV
ejpam-5342	184	2	,	,	PUNCT
ejpam-5342	184	3	in	in	ADP
ejpam-5342	184	4	any	any	DET
ejpam-5342	184	5	case	case	NOUN
ejpam-5342	184	6	c	c	NOUN
ejpam-5342	184	7	is	be	AUX
ejpam-5342	184	8	a	a	DET
ejpam-5342	184	9	hop	hop	NOUN
ejpam-5342	184	10	dominating	dominating	NOUN
ejpam-5342	184	11	set	set	VERB
ejpam-5342	184	12	ofg⋄h	ofg⋄h	PROPN
ejpam-5342	184	13	.	.	PUNCT
ejpam-5342	185	1	accordingly	accordingly	ADV
ejpam-5342	185	2	,	,	PUNCT
ejpam-5342	185	3	c	c	PROPN
ejpam-5342	185	4	is	be	AUX
ejpam-5342	185	5	a	a	DET
ejpam-5342	185	6	connected	connected	ADJ
ejpam-5342	185	7	co	co	NOUN
ejpam-5342	185	8	-	-	ADJ
ejpam-5342	185	9	independent	independent	ADJ
ejpam-5342	185	10	hop	hop	NOUN
ejpam-5342	185	11	dominating	dominating	NOUN
ejpam-5342	185	12	set	set	NOUN
ejpam-5342	185	13	of	of	ADP
ejpam-5342	185	14	g	g	PROPN
ejpam-5342	185	15	⋄h	⋄h	PROPN
ejpam-5342	185	16	.	.	PUNCT
ejpam-5342	186	1	corollary	corollary	ADJ
ejpam-5342	186	2	1	1	NUM
ejpam-5342	186	3	.	.	PUNCT
ejpam-5342	187	1	let	let	VERB
ejpam-5342	187	2	g	g	PRON
ejpam-5342	187	3	be	be	AUX
ejpam-5342	187	4	a	a	DET
ejpam-5342	187	5	connected	connected	ADJ
ejpam-5342	187	6	graph	graph	NOUN
ejpam-5342	187	7	of	of	ADP
ejpam-5342	187	8	order	order	NOUN
ejpam-5342	187	9	n	n	PRON
ejpam-5342	187	10	≥	≥	NOUN
ejpam-5342	187	11	3	3	NUM
ejpam-5342	187	12	and	and	CCONJ
ejpam-5342	187	13	h	h	NOUN
ejpam-5342	187	14	be	be	VERB
ejpam-5342	187	15	any	any	DET
ejpam-5342	187	16	graph	graph	NOUN
ejpam-5342	187	17	of	of	ADP
ejpam-5342	187	18	size	size	NOUN
ejpam-5342	187	19	p	p	PROPN
ejpam-5342	187	20	and	and	CCONJ
ejpam-5342	187	21	of	of	ADP
ejpam-5342	187	22	order	order	NOUN
ejpam-5342	187	23	m.	m.	NOUN
ejpam-5342	187	24	then	then	ADV
ejpam-5342	187	25	γch	γch	VERB
ejpam-5342	187	26	,	,	PUNCT
ejpam-5342	187	27	coi(g	coi(g	PROPN
ejpam-5342	187	28	⋄h	⋄h	PROPN
ejpam-5342	187	29	)	)	PUNCT
ejpam-5342	187	30	=	=	PRON
ejpam-5342	187	31	n+	n+	X
ejpam-5342	187	32	p(m−	p(m−	NOUN
ejpam-5342	187	33	β(h	β(h	PROPN
ejpam-5342	187	34	)	)	PUNCT
ejpam-5342	187	35	)	)	PUNCT
ejpam-5342	187	36	.	.	PUNCT
ejpam-5342	188	1	proof	proof	NOUN
ejpam-5342	188	2	:	:	PUNCT
ejpam-5342	188	3	let	let	VERB
ejpam-5342	188	4	co	co	VERB
ejpam-5342	188	5	=	=	NOUN
ejpam-5342	188	6	a	a	DET
ejpam-5342	188	7	∪	∪	X
ejpam-5342	188	8	(	(	PUNCT
ejpam-5342	188	9	⋃	⋃	ADJ
ejpam-5342	188	10	uv∈v	uv∈v	NOUN
ejpam-5342	188	11	(	(	PUNCT
ejpam-5342	188	12	g	g	NOUN
ejpam-5342	188	13	)	)	PUNCT
ejpam-5342	188	14	suv	suv	PROPN
ejpam-5342	188	15	)	)	PUNCT
ejpam-5342	188	16	be	be	VERB
ejpam-5342	188	17	a	a	DET
ejpam-5342	188	18	γch	γch	NOUN
ejpam-5342	188	19	,	,	PUNCT
ejpam-5342	188	20	coi	coi	NOUN
ejpam-5342	188	21	-	-	PUNCT
ejpam-5342	188	22	set	set	NOUN
ejpam-5342	188	23	of	of	ADP
ejpam-5342	188	24	g	g	PROPN
ejpam-5342	188	25	⋄h	⋄h	PROPN
ejpam-5342	188	26	.	.	PUNCT
ejpam-5342	189	1	then	then	ADV
ejpam-5342	189	2	conditions	condition	NOUN
ejpam-5342	189	3	(	(	PUNCT
ejpam-5342	189	4	i	i	NOUN
ejpam-5342	189	5	)	)	PUNCT
ejpam-5342	189	6	,	,	PUNCT
ejpam-5342	189	7	(	(	PUNCT
ejpam-5342	189	8	ii	ii	NOUN
ejpam-5342	189	9	)	)	PUNCT
ejpam-5342	189	10	and	and	CCONJ
ejpam-5342	189	11	(	(	PUNCT
ejpam-5342	189	12	iii	iii	NOUN
ejpam-5342	189	13	)	)	PUNCT
ejpam-5342	189	14	of	of	ADP
ejpam-5342	189	15	theorem	theorem	ADJ
ejpam-5342	189	16	3	3	NUM
ejpam-5342	189	17	hold	hold	VERB
ejpam-5342	189	18	where	where	SCONJ
ejpam-5342	189	19	a	a	DET
ejpam-5342	189	20	=	=	SYM
ejpam-5342	189	21	v	v	NOUN
ejpam-5342	189	22	(	(	PUNCT
ejpam-5342	189	23	g	g	NOUN
ejpam-5342	189	24	)	)	PUNCT
ejpam-5342	189	25	and	and	CCONJ
ejpam-5342	189	26	suv	suv	PROPN
ejpam-5342	189	27	=	=	SYM
ejpam-5342	189	28	v	v	PROPN
ejpam-5342	189	29	(	(	PUNCT
ejpam-5342	189	30	huv)\s∗	huv)\s∗	PROPN
ejpam-5342	189	31	where	where	SCONJ
ejpam-5342	189	32	s∗	s∗	PROPN
ejpam-5342	189	33	is	be	AUX
ejpam-5342	189	34	any	any	DET
ejpam-5342	189	35	independent	independent	ADJ
ejpam-5342	189	36	set	set	NOUN
ejpam-5342	189	37	of	of	ADP
ejpam-5342	189	38	huv	huv	PROPN
ejpam-5342	189	39	.	.	PUNCT
ejpam-5342	190	1	thus	thus	ADV
ejpam-5342	190	2	,	,	PUNCT
ejpam-5342	190	3	γch	γch	NOUN
ejpam-5342	190	4	,	,	PUNCT
ejpam-5342	190	5	coi(g	coi(g	PROPN
ejpam-5342	190	6	⋄h	⋄h	PROPN
ejpam-5342	190	7	)	)	PUNCT
ejpam-5342	190	8	=	=	PUNCT
ejpam-5342	190	9	|a|+	|a|+	NOUN
ejpam-5342	190	10	p|suv|	p|suv|	NOUN
ejpam-5342	190	11	=	=	SYM
ejpam-5342	190	12	n+	n+	PROPN
ejpam-5342	190	13	p(|v	p(|v	PROPN
ejpam-5342	190	14	(	(	PUNCT
ejpam-5342	190	15	huv)|	huv)|	NOUN
ejpam-5342	190	16	−	−	NOUN
ejpam-5342	190	17	|s∗|	|s∗|	NUM
ejpam-5342	190	18	)	)	PUNCT
ejpam-5342	190	19	≥	≥	NOUN
ejpam-5342	190	20	n+	n+	PUNCT
ejpam-5342	190	21	p(m−	p(m−	NOUN
ejpam-5342	190	22	β(h	β(h	PROPN
ejpam-5342	190	23	)	)	PUNCT
ejpam-5342	190	24	)	)	PUNCT
ejpam-5342	190	25	.	.	PUNCT
ejpam-5342	191	1	let	let	VERB
ejpam-5342	191	2	t	t	NOUN
ejpam-5342	191	3	be	be	AUX
ejpam-5342	191	4	a	a	DET
ejpam-5342	191	5	β	β	NOUN
ejpam-5342	191	6	-	-	VERB
ejpam-5342	191	7	set	set	NOUN
ejpam-5342	191	8	of	of	ADP
ejpam-5342	191	9	h	h	NOUN
ejpam-5342	191	10	and	and	CCONJ
ejpam-5342	191	11	suv	suv	PROPN
ejpam-5342	191	12	=	=	SYM
ejpam-5342	191	13	v	v	PROPN
ejpam-5342	191	14	(	(	PUNCT
ejpam-5342	191	15	huv)\t	huv)\t	NOUN
ejpam-5342	191	16	for	for	ADP
ejpam-5342	191	17	each	each	DET
ejpam-5342	191	18	uv	uv	PROPN
ejpam-5342	191	19	∈	∈	PROPN
ejpam-5342	191	20	e(g	e(g	PROPN
ejpam-5342	191	21	)	)	PUNCT
ejpam-5342	191	22	.	.	PUNCT
ejpam-5342	192	1	then	then	ADV
ejpam-5342	192	2	c	c	X
ejpam-5342	192	3	=	=	SYM
ejpam-5342	192	4	v	v	PROPN
ejpam-5342	192	5	(	(	PUNCT
ejpam-5342	192	6	g	g	NOUN
ejpam-5342	192	7	)	)	PUNCT
ejpam-5342	192	8	∪	∪	NOUN
ejpam-5342	192	9	(	(	PUNCT
ejpam-5342	192	10	⋃	⋃	NOUN
ejpam-5342	192	11	uv∈e(g	uv∈e(g	NOUN
ejpam-5342	192	12	)	)	PUNCT
ejpam-5342	192	13	suv	suv	PROPN
ejpam-5342	192	14	)	)	PUNCT
ejpam-5342	192	15	is	be	AUX
ejpam-5342	192	16	a	a	DET
ejpam-5342	192	17	connected	connected	ADJ
ejpam-5342	192	18	co	co	NOUN
ejpam-5342	192	19	-	-	ADJ
ejpam-5342	192	20	independent	independent	ADJ
ejpam-5342	192	21	hop	hop	NOUN
ejpam-5342	192	22	dominating	dominating	NOUN
ejpam-5342	192	23	set	set	NOUN
ejpam-5342	192	24	of	of	ADP
ejpam-5342	192	25	g	g	PROPN
ejpam-5342	192	26	⋄h	⋄h	NOUN
ejpam-5342	192	27	by	by	ADP
ejpam-5342	192	28	theorem	theorem	NOUN
ejpam-5342	192	29	3	3	NUM
ejpam-5342	192	30	.	.	PUNCT
ejpam-5342	192	31	s.	s.	PROPN
ejpam-5342	192	32	a.	a.	PROPN
ejpam-5342	192	33	nanding	nanding	PROPN
ejpam-5342	192	34	,	,	PUNCT
ejpam-5342	192	35	h.	h.	PROPN
ejpam-5342	192	36	m.	m.	PROPN
ejpam-5342	192	37	rara	rara	PROPN
ejpam-5342	192	38	,	,	PUNCT
ejpam-5342	192	39	i.	i.	PROPN
ejpam-5342	192	40	s.	s.	PROPN
ejpam-5342	192	41	aniversario	aniversario	PROPN
ejpam-5342	192	42	/	/	SYM
ejpam-5342	192	43	eur	eur	PROPN
ejpam-5342	192	44	.	.	PUNCT
ejpam-5342	193	1	j.	j.	PROPN
ejpam-5342	193	2	pure	pure	PROPN
ejpam-5342	193	3	appl	appl	PROPN
ejpam-5342	193	4	.	.	PROPN
ejpam-5342	193	5	math	math	PROPN
ejpam-5342	193	6	,	,	PUNCT
ejpam-5342	193	7	17	17	NUM
ejpam-5342	193	8	(	(	PUNCT
ejpam-5342	193	9	4	4	NUM
ejpam-5342	193	10	)	)	PUNCT
ejpam-5342	193	11	(	(	PUNCT
ejpam-5342	193	12	2024	2024	NUM
ejpam-5342	193	13	)	)	PUNCT
ejpam-5342	193	14	,	,	PUNCT
ejpam-5342	193	15	2505	2505	NUM
ejpam-5342	193	16	-	-	SYM
ejpam-5342	193	17	2515	2515	NUM
ejpam-5342	193	18	2511	2511	NUM
ejpam-5342	193	19	hence	hence	ADV
ejpam-5342	193	20	,	,	PUNCT
ejpam-5342	193	21	γch	γch	NOUN
ejpam-5342	193	22	,	,	PUNCT
ejpam-5342	193	23	coi(g	coi(g	PROPN
ejpam-5342	193	24	⋄h	⋄h	PROPN
ejpam-5342	193	25	)	)	PUNCT
ejpam-5342	193	26	≤	≤	PROPN
ejpam-5342	193	27	|c|	|c|	PROPN
ejpam-5342	193	28	=	=	SYM
ejpam-5342	193	29	|v	|v	PROPN
ejpam-5342	193	30	(	(	PUNCT
ejpam-5342	193	31	g)|+	g)|+	NOUN
ejpam-5342	193	32	p|suv|	p|suv|	NOUN
ejpam-5342	193	33	=	=	SYM
ejpam-5342	193	34	n+	n+	X
ejpam-5342	193	35	p|v	p|v	X
ejpam-5342	193	36	(	(	PUNCT
ejpam-5342	193	37	huv)\t	huv)\t	NOUN
ejpam-5342	193	38	|	|	NOUN
ejpam-5342	193	39	=	=	SYM
ejpam-5342	193	40	n+	n+	X
ejpam-5342	193	41	p(m−	p(m−	NOUN
ejpam-5342	193	42	β(h	β(h	PROPN
ejpam-5342	193	43	)	)	PUNCT
ejpam-5342	193	44	)	)	PUNCT
ejpam-5342	193	45	.	.	PUNCT
ejpam-5342	194	1	therefore	therefore	ADV
ejpam-5342	194	2	,	,	PUNCT
ejpam-5342	194	3	γch	γch	NOUN
ejpam-5342	194	4	,	,	PUNCT
ejpam-5342	194	5	coi(g	coi(g	PROPN
ejpam-5342	194	6	⋄h	⋄h	PROPN
ejpam-5342	194	7	)	)	PUNCT
ejpam-5342	194	8	=	=	PRON
ejpam-5342	194	9	n+	n+	X
ejpam-5342	194	10	p(m−	p(m−	NOUN
ejpam-5342	194	11	β(h	β(h	PROPN
ejpam-5342	194	12	)	)	PUNCT
ejpam-5342	194	13	)	)	PUNCT
ejpam-5342	194	14	.	.	PUNCT
ejpam-5342	195	1	example	example	NOUN
ejpam-5342	196	1	5	5	NUM
ejpam-5342	196	2	.	.	PUNCT
ejpam-5342	197	1	the	the	DET
ejpam-5342	197	2	set	set	NOUN
ejpam-5342	197	3	of	of	ADP
ejpam-5342	197	4	shaded	shade	VERB
ejpam-5342	197	5	vertices	vertex	NOUN
ejpam-5342	197	6	in	in	ADP
ejpam-5342	197	7	the	the	DET
ejpam-5342	197	8	graph	graph	NOUN
ejpam-5342	197	9	of	of	ADP
ejpam-5342	197	10	p4	p4	ADJ
ejpam-5342	197	11	⋄	⋄	PROPN
ejpam-5342	197	12	p5	p5	NOUN
ejpam-5342	197	13	represents	represent	VERB
ejpam-5342	197	14	a	a	DET
ejpam-5342	197	15	connected	connected	ADJ
ejpam-5342	197	16	co	co	NOUN
ejpam-5342	197	17	-	-	ADJ
ejpam-5342	197	18	independent	independent	ADJ
ejpam-5342	197	19	hop	hop	NOUN
ejpam-5342	197	20	dominating	dominating	NOUN
ejpam-5342	197	21	set	set	NOUN
ejpam-5342	197	22	of	of	ADP
ejpam-5342	197	23	p4	p4	ADJ
ejpam-5342	197	24	⋄	⋄	PROPN
ejpam-5342	197	25	p5	p5	NOUN
ejpam-5342	197	26	.	.	PUNCT
ejpam-5342	198	1	by	by	ADP
ejpam-5342	198	2	corollary	corollary	ADJ
ejpam-5342	198	3	1	1	NUM
ejpam-5342	198	4	,	,	PUNCT
ejpam-5342	198	5	γch	γch	VERB
ejpam-5342	198	6	,	,	PUNCT
ejpam-5342	198	7	coi(p4	coi(p4	PROPN
ejpam-5342	198	8	⋄	⋄	PROPN
ejpam-5342	198	9	p5	p5	PROPN
ejpam-5342	198	10	)	)	PUNCT
ejpam-5342	199	1	=	=	PUNCT
ejpam-5342	200	1	10	10	NUM
ejpam-5342	200	2	.	.	X
ejpam-5342	200	3	3.3	3.3	NUM
ejpam-5342	200	4	.	.	PUNCT
ejpam-5342	201	1	connected	connect	VERB
ejpam-5342	201	2	co	co	ADJ
ejpam-5342	201	3	-	-	ADJ
ejpam-5342	201	4	independent	independent	ADJ
ejpam-5342	201	5	hop	hop	NOUN
ejpam-5342	201	6	domination	domination	NOUN
ejpam-5342	201	7	in	in	ADP
ejpam-5342	201	8	the	the	DET
ejpam-5342	201	9	complementary	complementary	ADJ
ejpam-5342	201	10	prism	prism	NOUN
ejpam-5342	201	11	for	for	ADP
ejpam-5342	201	12	a	a	DET
ejpam-5342	201	13	graph	graph	NOUN
ejpam-5342	201	14	g	g	NOUN
ejpam-5342	201	15	,	,	PUNCT
ejpam-5342	201	16	the	the	DET
ejpam-5342	201	17	complementary	complementary	ADJ
ejpam-5342	201	18	prism	prism	NOUN
ejpam-5342	201	19	,	,	PUNCT
ejpam-5342	201	20	denoted	denote	VERB
ejpam-5342	201	21	gg	gg	NOUN
ejpam-5342	201	22	,	,	PUNCT
ejpam-5342	201	23	is	be	AUX
ejpam-5342	201	24	formed	form	VERB
ejpam-5342	201	25	from	from	ADP
ejpam-5342	201	26	the	the	DET
ejpam-5342	201	27	disjoint	disjoint	PROPN
ejpam-5342	201	28	union	union	NOUN
ejpam-5342	201	29	of	of	ADP
ejpam-5342	201	30	g	g	PROPN
ejpam-5342	201	31	and	and	CCONJ
ejpam-5342	201	32	its	its	PRON
ejpam-5342	201	33	complement	complement	NOUN
ejpam-5342	201	34	g	g	NOUN
ejpam-5342	201	35	by	by	ADP
ejpam-5342	201	36	adding	add	VERB
ejpam-5342	201	37	a	a	DET
ejpam-5342	201	38	perfect	perfect	ADJ
ejpam-5342	201	39	matching	matching	NOUN
ejpam-5342	201	40	between	between	ADP
ejpam-5342	201	41	corresponding	corresponding	ADJ
ejpam-5342	201	42	vertices	vertex	NOUN
ejpam-5342	201	43	of	of	ADP
ejpam-5342	201	44	g	g	PROPN
ejpam-5342	201	45	and	and	CCONJ
ejpam-5342	201	46	g.	g.	NOUN
ejpam-5342	201	47	for	for	ADP
ejpam-5342	201	48	each	each	DET
ejpam-5342	201	49	v	v	NUM
ejpam-5342	201	50	∈	∈	PROPN
ejpam-5342	201	51	v	v	NOUN
ejpam-5342	201	52	(	(	PUNCT
ejpam-5342	201	53	g	g	NOUN
ejpam-5342	201	54	)	)	PUNCT
ejpam-5342	201	55	,	,	PUNCT
ejpam-5342	201	56	let	let	VERB
ejpam-5342	201	57	v	v	PART
ejpam-5342	201	58	denote	denote	VERB
ejpam-5342	201	59	the	the	DET
ejpam-5342	201	60	vertex	vertex	NOUN
ejpam-5342	201	61	corresponding	correspond	VERB
ejpam-5342	201	62	to	to	ADP
ejpam-5342	201	63	v	v	NOUN
ejpam-5342	201	64	in	in	ADP
ejpam-5342	201	65	g.	g.	PROPN
ejpam-5342	201	66	formally	formally	ADV
ejpam-5342	201	67	,	,	PUNCT
ejpam-5342	201	68	the	the	DET
ejpam-5342	201	69	graph	graph	NOUN
ejpam-5342	201	70	gg	gg	NOUN
ejpam-5342	201	71	is	be	AUX
ejpam-5342	201	72	formed	form	VERB
ejpam-5342	201	73	from	from	ADP
ejpam-5342	201	74	g∪g	g∪g	NOUN
ejpam-5342	201	75	by	by	ADP
ejpam-5342	201	76	adding	add	VERB
ejpam-5342	201	77	the	the	DET
ejpam-5342	201	78	edge	edge	NOUN
ejpam-5342	201	79	vv	vv	NOUN
ejpam-5342	201	80	for	for	ADP
ejpam-5342	201	81	every	every	DET
ejpam-5342	201	82	v	v	NUM
ejpam-5342	201	83	∈	∈	NOUN
ejpam-5342	201	84	v	v	NOUN
ejpam-5342	201	85	(	(	PUNCT
ejpam-5342	201	86	g	g	NOUN
ejpam-5342	201	87	)	)	PUNCT
ejpam-5342	201	88	.	.	PUNCT
ejpam-5342	202	1	example	example	NOUN
ejpam-5342	203	1	6	6	NUM
ejpam-5342	203	2	.	.	PUNCT
ejpam-5342	203	3	consider	consider	VERB
ejpam-5342	203	4	the	the	DET
ejpam-5342	203	5	graphs	graph	NOUN
ejpam-5342	203	6	c4	c4	NOUN
ejpam-5342	203	7	,	,	PUNCT
ejpam-5342	203	8	c4	c4	NOUN
ejpam-5342	203	9	in	in	ADP
ejpam-5342	203	10	figure	figure	NOUN
ejpam-5342	203	11	3	3	NUM
ejpam-5342	203	12	.	.	PUNCT
ejpam-5342	204	1	in	in	ADP
ejpam-5342	204	2	the	the	DET
ejpam-5342	204	3	same	same	ADJ
ejpam-5342	204	4	figure	figure	NOUN
ejpam-5342	204	5	is	be	AUX
ejpam-5342	204	6	an	an	DET
ejpam-5342	204	7	illustration	illustration	NOUN
ejpam-5342	204	8	of	of	ADP
ejpam-5342	204	9	complementary	complementary	ADJ
ejpam-5342	204	10	prism	prism	NOUN
ejpam-5342	204	11	c4c4	c4c4	PROPN
ejpam-5342	204	12	.	.	PROPN
ejpam-5342	204	13	figure	figure	NOUN
ejpam-5342	204	14	3	3	NUM
ejpam-5342	204	15	:	:	PUNCT
ejpam-5342	204	16	(	(	PUNCT
ejpam-5342	204	17	1)cycle	1)cycle	NUM
ejpam-5342	204	18	c4	c4	NOUN
ejpam-5342	204	19	(	(	PUNCT
ejpam-5342	204	20	2)complement	2)complement	NUM
ejpam-5342	204	21	c4	c4	NOUN
ejpam-5342	204	22	of	of	ADP
ejpam-5342	204	23	c4	c4	NOUN
ejpam-5342	204	24	(	(	PUNCT
ejpam-5342	204	25	3)complementary	3)complementary	NUM
ejpam-5342	204	26	prism	prism	NOUN
ejpam-5342	204	27	c4c4	c4c4	PUNCT
ejpam-5342	204	28	theorem	theorem	NOUN
ejpam-5342	204	29	4	4	NUM
ejpam-5342	204	30	.	.	PUNCT
ejpam-5342	205	1	let	let	VERB
ejpam-5342	205	2	g	g	NOUN
ejpam-5342	205	3	be	be	AUX
ejpam-5342	205	4	either	either	CCONJ
ejpam-5342	205	5	a	a	DET
ejpam-5342	205	6	complete	complete	ADJ
ejpam-5342	205	7	graph	graph	NOUN
ejpam-5342	205	8	or	or	CCONJ
ejpam-5342	205	9	an	an	DET
ejpam-5342	205	10	empty	empty	ADJ
ejpam-5342	205	11	graph	graph	NOUN
ejpam-5342	205	12	of	of	ADP
ejpam-5342	205	13	order	order	NOUN
ejpam-5342	205	14	n	n	PRON
ejpam-5342	205	15	≥	≥	NOUN
ejpam-5342	205	16	2	2	NUM
ejpam-5342	205	17	.	.	PUNCT
ejpam-5342	206	1	then	then	ADV
ejpam-5342	206	2	s	s	VERB
ejpam-5342	206	3	⊆	⊆	NUM
ejpam-5342	206	4	v	v	NOUN
ejpam-5342	206	5	(	(	PUNCT
ejpam-5342	206	6	gg	gg	NOUN
ejpam-5342	206	7	)	)	PUNCT
ejpam-5342	206	8	is	be	AUX
ejpam-5342	206	9	a	a	DET
ejpam-5342	206	10	connected	connected	ADJ
ejpam-5342	206	11	co	co	NOUN
ejpam-5342	206	12	-	-	ADJ
ejpam-5342	206	13	independent	independent	ADJ
ejpam-5342	206	14	hop	hop	NOUN
ejpam-5342	206	15	dominating	dominating	NOUN
ejpam-5342	206	16	set	set	NOUN
ejpam-5342	206	17	of	of	ADP
ejpam-5342	206	18	gg	gg	PROPN
ejpam-5342	206	19	if	if	SCONJ
ejpam-5342	206	20	and	and	CCONJ
ejpam-5342	206	21	only	only	ADV
ejpam-5342	206	22	if	if	SCONJ
ejpam-5342	206	23	s	s	AUX
ejpam-5342	206	24	=	=	PUNCT
ejpam-5342	206	25	sg	sg	X
ejpam-5342	206	26	∪	∪	ADJ
ejpam-5342	206	27	sg	sg	NOUN
ejpam-5342	206	28	and	and	CCONJ
ejpam-5342	206	29	the	the	DET
ejpam-5342	206	30	following	follow	VERB
ejpam-5342	206	31	hold	hold	NOUN
ejpam-5342	206	32	:	:	PUNCT
ejpam-5342	206	33	(	(	PUNCT
ejpam-5342	206	34	i	i	NOUN
ejpam-5342	206	35	)	)	PUNCT
ejpam-5342	206	36	sg	sg	PROPN
ejpam-5342	206	37	=	=	SYM
ejpam-5342	206	38	v	v	PROPN
ejpam-5342	206	39	(	(	PUNCT
ejpam-5342	206	40	g	g	NOUN
ejpam-5342	206	41	)	)	PUNCT
ejpam-5342	206	42	and	and	CCONJ
ejpam-5342	206	43	sg	sg	ADP
ejpam-5342	206	44	⊆	⊆	NUM
ejpam-5342	206	45	v	v	NOUN
ejpam-5342	206	46	(	(	PUNCT
ejpam-5342	206	47	g	g	NOUN
ejpam-5342	206	48	)	)	PUNCT
ejpam-5342	206	49	if	if	SCONJ
ejpam-5342	206	50	g	g	PROPN
ejpam-5342	206	51	is	be	AUX
ejpam-5342	206	52	complete	complete	ADJ
ejpam-5342	206	53	and	and	CCONJ
ejpam-5342	206	54	(	(	PUNCT
ejpam-5342	206	55	ii	ii	NOUN
ejpam-5342	206	56	)	)	PUNCT
ejpam-5342	206	57	sg	sg	ADP
ejpam-5342	206	58	=	=	SYM
ejpam-5342	206	59	v	v	PROPN
ejpam-5342	206	60	(	(	PUNCT
ejpam-5342	206	61	g	g	NOUN
ejpam-5342	206	62	)	)	PUNCT
ejpam-5342	206	63	and	and	CCONJ
ejpam-5342	206	64	sg	sg	ADP
ejpam-5342	206	65	⊆	⊆	NUM
ejpam-5342	206	66	v	v	NOUN
ejpam-5342	206	67	(	(	PUNCT
ejpam-5342	206	68	g	g	NOUN
ejpam-5342	206	69	)	)	PUNCT
ejpam-5342	206	70	if	if	SCONJ
ejpam-5342	206	71	g	g	PROPN
ejpam-5342	206	72	is	be	AUX
ejpam-5342	206	73	an	an	DET
ejpam-5342	206	74	empty	empty	ADJ
ejpam-5342	206	75	graph	graph	NOUN
ejpam-5342	206	76	.	.	PUNCT
ejpam-5342	207	1	s.	s.	PROPN
ejpam-5342	207	2	a.	a.	PROPN
ejpam-5342	207	3	nanding	nanding	PROPN
ejpam-5342	207	4	,	,	PUNCT
ejpam-5342	207	5	h.	h.	PROPN
ejpam-5342	207	6	m.	m.	PROPN
ejpam-5342	207	7	rara	rara	PROPN
ejpam-5342	207	8	,	,	PUNCT
ejpam-5342	207	9	i.	i.	PROPN
ejpam-5342	207	10	s.	s.	PROPN
ejpam-5342	207	11	aniversario	aniversario	PROPN
ejpam-5342	207	12	/	/	SYM
ejpam-5342	207	13	eur	eur	PROPN
ejpam-5342	207	14	.	.	PUNCT
ejpam-5342	208	1	j.	j.	PROPN
ejpam-5342	208	2	pure	pure	PROPN
ejpam-5342	208	3	appl	appl	PROPN
ejpam-5342	208	4	.	.	PROPN
ejpam-5342	208	5	math	math	PROPN
ejpam-5342	208	6	,	,	PUNCT
ejpam-5342	208	7	17	17	NUM
ejpam-5342	208	8	(	(	PUNCT
ejpam-5342	208	9	4	4	NUM
ejpam-5342	208	10	)	)	PUNCT
ejpam-5342	208	11	(	(	PUNCT
ejpam-5342	208	12	2024	2024	NUM
ejpam-5342	208	13	)	)	PUNCT
ejpam-5342	208	14	,	,	PUNCT
ejpam-5342	208	15	2505	2505	NUM
ejpam-5342	208	16	-	-	SYM
ejpam-5342	208	17	2515	2515	NUM
ejpam-5342	208	18	2512	2512	NUM
ejpam-5342	208	19	proof	proof	NOUN
ejpam-5342	208	20	:	:	PUNCT
ejpam-5342	208	21	suppose	suppose	VERB
ejpam-5342	208	22	that	that	SCONJ
ejpam-5342	208	23	s	s	VERB
ejpam-5342	208	24	⊆	⊆	NUM
ejpam-5342	208	25	v	v	NOUN
ejpam-5342	208	26	(	(	PUNCT
ejpam-5342	208	27	gg	gg	NOUN
ejpam-5342	208	28	)	)	PUNCT
ejpam-5342	208	29	is	be	AUX
ejpam-5342	208	30	a	a	DET
ejpam-5342	208	31	connected	connected	ADJ
ejpam-5342	208	32	co	co	NOUN
ejpam-5342	208	33	-	-	ADJ
ejpam-5342	208	34	independent	independent	ADJ
ejpam-5342	208	35	hop	hop	NOUN
ejpam-5342	208	36	dominating	dominating	NOUN
ejpam-5342	208	37	set	set	NOUN
ejpam-5342	208	38	of	of	ADP
ejpam-5342	208	39	gg	gg	PROPN
ejpam-5342	208	40	.	.	PUNCT
ejpam-5342	209	1	let	let	VERB
ejpam-5342	209	2	sg	sg	VERB
ejpam-5342	209	3	=	=	SYM
ejpam-5342	209	4	s	s	PART
ejpam-5342	209	5	∩	∩	ADJ
ejpam-5342	209	6	v	v	X
ejpam-5342	209	7	(	(	PUNCT
ejpam-5342	209	8	g	g	NOUN
ejpam-5342	209	9	)	)	PUNCT
ejpam-5342	209	10	and	and	CCONJ
ejpam-5342	209	11	sg	sg	X
ejpam-5342	209	12	=	=	SYM
ejpam-5342	209	13	s	s	PROPN
ejpam-5342	209	14	∩	∩	ADJ
ejpam-5342	209	15	v	v	X
ejpam-5342	209	16	(	(	PUNCT
ejpam-5342	209	17	g	g	NOUN
ejpam-5342	209	18	)	)	PUNCT
ejpam-5342	209	19	.	.	PUNCT
ejpam-5342	210	1	then	then	ADV
ejpam-5342	210	2	s	s	VERB
ejpam-5342	210	3	=	=	PUNCT
ejpam-5342	210	4	sg	sg	X
ejpam-5342	210	5	∪	∪	ADJ
ejpam-5342	210	6	sg	sg	PROPN
ejpam-5342	210	7	.	.	PUNCT
ejpam-5342	211	1	let	let	VERB
ejpam-5342	211	2	g	g	PRON
ejpam-5342	211	3	be	be	AUX
ejpam-5342	211	4	a	a	DET
ejpam-5342	211	5	complete	complete	ADJ
ejpam-5342	211	6	graph	graph	NOUN
ejpam-5342	211	7	and	and	CCONJ
ejpam-5342	211	8	suppose	suppose	VERB
ejpam-5342	211	9	that	that	SCONJ
ejpam-5342	211	10	sg	sg	PROPN
ejpam-5342	211	11	̸=	̸=	PROPN
ejpam-5342	211	12	v	v	NOUN
ejpam-5342	211	13	(	(	PUNCT
ejpam-5342	211	14	g	g	NOUN
ejpam-5342	211	15	)	)	PUNCT
ejpam-5342	211	16	.	.	PUNCT
ejpam-5342	212	1	then	then	ADV
ejpam-5342	212	2	there	there	PRON
ejpam-5342	212	3	exists	exist	VERB
ejpam-5342	212	4	x	x	X
ejpam-5342	212	5	∈	∈	PROPN
ejpam-5342	212	6	v	v	NOUN
ejpam-5342	212	7	(	(	PUNCT
ejpam-5342	212	8	g)\sg	g)\sg	PROPN
ejpam-5342	212	9	.	.	PUNCT
ejpam-5342	212	10	since	since	SCONJ
ejpam-5342	212	11	v	v	NOUN
ejpam-5342	212	12	(	(	PUNCT
ejpam-5342	212	13	gg)\s	gg)\s	NOUN
ejpam-5342	212	14	is	be	AUX
ejpam-5342	212	15	independent	independent	ADJ
ejpam-5342	212	16	and	and	CCONJ
ejpam-5342	212	17	xx	xx	NUM
ejpam-5342	212	18	∈	∈	PROPN
ejpam-5342	212	19	e(gg	e(gg	PROPN
ejpam-5342	212	20	)	)	PUNCT
ejpam-5342	212	21	,	,	PUNCT
ejpam-5342	212	22	x	x	PUNCT
ejpam-5342	212	23	∈	∈	NOUN
ejpam-5342	212	24	v	v	ADP
ejpam-5342	212	25	(	(	PUNCT
ejpam-5342	212	26	g	g	NOUN
ejpam-5342	212	27	)	)	PUNCT
ejpam-5342	212	28	∩	∩	PROPN
ejpam-5342	212	29	sg	sg	PROPN
ejpam-5342	212	30	.	.	PUNCT
ejpam-5342	213	1	since	since	SCONJ
ejpam-5342	213	2	g	g	PROPN
ejpam-5342	213	3	is	be	AUX
ejpam-5342	213	4	complete	complete	ADJ
ejpam-5342	213	5	,	,	PUNCT
ejpam-5342	213	6	g	g	PROPN
ejpam-5342	213	7	is	be	AUX
ejpam-5342	213	8	an	an	DET
ejpam-5342	213	9	empty	empty	ADJ
ejpam-5342	213	10	graph	graph	NOUN
ejpam-5342	213	11	.	.	PUNCT
ejpam-5342	214	1	thus	thus	ADV
ejpam-5342	214	2	,	,	PUNCT
ejpam-5342	214	3	x	x	PRON
ejpam-5342	214	4	is	be	AUX
ejpam-5342	214	5	an	an	DET
ejpam-5342	214	6	isolated	isolated	ADJ
ejpam-5342	214	7	vertex	vertex	NOUN
ejpam-5342	214	8	of	of	ADP
ejpam-5342	214	9	g.	g.	PROPN
ejpam-5342	214	10	this	this	PRON
ejpam-5342	214	11	contradicts	contradict	VERB
ejpam-5342	214	12	the	the	DET
ejpam-5342	214	13	connectedness	connectedness	NOUN
ejpam-5342	214	14	of	of	ADP
ejpam-5342	214	15	s.	s.	PROPN
ejpam-5342	214	16	hence	hence	PROPN
ejpam-5342	214	17	,	,	PUNCT
ejpam-5342	214	18	sg	sg	PROPN
ejpam-5342	214	19	=	=	SYM
ejpam-5342	214	20	v	v	PROPN
ejpam-5342	214	21	(	(	PUNCT
ejpam-5342	214	22	g	g	NOUN
ejpam-5342	214	23	)	)	PUNCT
ejpam-5342	214	24	and	and	CCONJ
ejpam-5342	214	25	(	(	PUNCT
ejpam-5342	214	26	i	i	NOUN
ejpam-5342	214	27	)	)	PUNCT
ejpam-5342	214	28	holds	hold	VERB
ejpam-5342	214	29	.	.	PUNCT
ejpam-5342	215	1	for	for	ADP
ejpam-5342	215	2	(	(	PUNCT
ejpam-5342	215	3	ii	ii	NOUN
ejpam-5342	215	4	)	)	PUNCT
ejpam-5342	215	5	,	,	PUNCT
ejpam-5342	215	6	if	if	SCONJ
ejpam-5342	215	7	g	g	PROPN
ejpam-5342	215	8	is	be	AUX
ejpam-5342	215	9	an	an	DET
ejpam-5342	215	10	empty	empty	ADJ
ejpam-5342	215	11	graph	graph	NOUN
ejpam-5342	215	12	,	,	PUNCT
ejpam-5342	215	13	then	then	ADV
ejpam-5342	215	14	g	g	PROPN
ejpam-5342	215	15	is	be	AUX
ejpam-5342	215	16	a	a	DET
ejpam-5342	215	17	complete	complete	ADJ
ejpam-5342	215	18	graph	graph	NOUN
ejpam-5342	215	19	.	.	PUNCT
ejpam-5342	216	1	by	by	ADP
ejpam-5342	216	2	(	(	PUNCT
ejpam-5342	216	3	i	i	NOUN
ejpam-5342	216	4	)	)	PUNCT
ejpam-5342	216	5	,	,	PUNCT
ejpam-5342	216	6	sg	sg	PROPN
ejpam-5342	216	7	=	=	SYM
ejpam-5342	216	8	v	v	PROPN
ejpam-5342	216	9	(	(	PUNCT
ejpam-5342	216	10	g	g	NOUN
ejpam-5342	216	11	)	)	PUNCT
ejpam-5342	216	12	and	and	CCONJ
ejpam-5342	216	13	sg	sg	ADP
ejpam-5342	216	14	⊆	⊆	NUM
ejpam-5342	216	15	v	v	NOUN
ejpam-5342	216	16	(	(	PUNCT
ejpam-5342	216	17	g	g	NOUN
ejpam-5342	216	18	)	)	PUNCT
ejpam-5342	216	19	.	.	PUNCT
ejpam-5342	217	1	for	for	ADP
ejpam-5342	217	2	the	the	DET
ejpam-5342	217	3	converse	converse	NOUN
ejpam-5342	217	4	,	,	PUNCT
ejpam-5342	217	5	suppose	suppose	VERB
ejpam-5342	217	6	that	that	SCONJ
ejpam-5342	217	7	s	s	VERB
ejpam-5342	217	8	=	=	PUNCT
ejpam-5342	217	9	sg	sg	X
ejpam-5342	217	10	∪	∪	ADJ
ejpam-5342	217	11	sg	sg	PROPN
ejpam-5342	217	12	and	and	CCONJ
ejpam-5342	217	13	(	(	PUNCT
ejpam-5342	217	14	i	i	NOUN
ejpam-5342	217	15	)	)	PUNCT
ejpam-5342	217	16	and	and	CCONJ
ejpam-5342	217	17	(	(	PUNCT
ejpam-5342	217	18	ii	ii	NOUN
ejpam-5342	217	19	)	)	PUNCT
ejpam-5342	217	20	hold	hold	VERB
ejpam-5342	217	21	.	.	PUNCT
ejpam-5342	218	1	then	then	ADV
ejpam-5342	218	2	clearly	clearly	ADV
ejpam-5342	218	3	,	,	PUNCT
ejpam-5342	218	4	s	s	VERB
ejpam-5342	218	5	is	be	AUX
ejpam-5342	218	6	connected	connect	VERB
ejpam-5342	218	7	.	.	PUNCT
ejpam-5342	219	1	suppose	suppose	VERB
ejpam-5342	219	2	(	(	PUNCT
ejpam-5342	219	3	i	i	NOUN
ejpam-5342	219	4	)	)	PUNCT
ejpam-5342	219	5	holds	hold	VERB
ejpam-5342	219	6	.	.	PUNCT
ejpam-5342	220	1	then	then	ADV
ejpam-5342	220	2	v	v	X
ejpam-5342	220	3	(	(	PUNCT
ejpam-5342	220	4	gg)\s	gg)\s	NOUN
ejpam-5342	220	5	=	=	SYM
ejpam-5342	220	6	v	v	NOUN
ejpam-5342	220	7	(	(	PUNCT
ejpam-5342	220	8	g)\sg	g)\sg	PROPN
ejpam-5342	220	9	is	be	AUX
ejpam-5342	220	10	independent	independent	ADJ
ejpam-5342	220	11	since	since	SCONJ
ejpam-5342	220	12	g	g	PROPN
ejpam-5342	220	13	is	be	AUX
ejpam-5342	220	14	an	an	DET
ejpam-5342	220	15	empty	empty	ADJ
ejpam-5342	220	16	graph	graph	NOUN
ejpam-5342	220	17	.	.	PUNCT
ejpam-5342	221	1	let	let	VERB
ejpam-5342	221	2	x	x	SYM
ejpam-5342	221	3	∈	∈	PROPN
ejpam-5342	221	4	v	v	NOUN
ejpam-5342	221	5	(	(	PUNCT
ejpam-5342	221	6	gg)\s	gg)\s	NOUN
ejpam-5342	221	7	.	.	PUNCT
ejpam-5342	222	1	then	then	ADV
ejpam-5342	222	2	x	x	SYM
ejpam-5342	222	3	∈	∈	PROPN
ejpam-5342	222	4	v	v	X
ejpam-5342	222	5	(	(	PUNCT
ejpam-5342	222	6	g)\sg	g)\sg	PROPN
ejpam-5342	222	7	.	.	PROPN
ejpam-5342	222	8	hence	hence	ADV
ejpam-5342	222	9	,	,	PUNCT
ejpam-5342	222	10	x	x	PUNCT
ejpam-5342	222	11	=	=	PUNCT
ejpam-5342	222	12	p	p	NOUN
ejpam-5342	222	13	for	for	ADP
ejpam-5342	222	14	some	some	DET
ejpam-5342	222	15	p	p	NOUN
ejpam-5342	222	16	∈	∈	PROPN
ejpam-5342	222	17	v	v	NOUN
ejpam-5342	222	18	(	(	PUNCT
ejpam-5342	222	19	g	g	NOUN
ejpam-5342	222	20	)	)	PUNCT
ejpam-5342	222	21	.	.	PUNCT
ejpam-5342	223	1	since	since	SCONJ
ejpam-5342	223	2	g	g	PROPN
ejpam-5342	223	3	is	be	AUX
ejpam-5342	223	4	complete	complete	ADJ
ejpam-5342	223	5	,	,	PUNCT
ejpam-5342	223	6	py	py	PROPN
ejpam-5342	223	7	∈	∈	PROPN
ejpam-5342	223	8	e(g	e(g	PROPN
ejpam-5342	223	9	)	)	PUNCT
ejpam-5342	224	1	for	for	ADP
ejpam-5342	224	2	each	each	DET
ejpam-5342	224	3	y	y	PROPN
ejpam-5342	224	4	∈	∈	PROPN
ejpam-5342	224	5	v	v	NOUN
ejpam-5342	224	6	(	(	PUNCT
ejpam-5342	224	7	g)\{p	g)\{p	NOUN
ejpam-5342	224	8	}	}	PUNCT
ejpam-5342	224	9	.	.	PUNCT
ejpam-5342	225	1	since	since	SCONJ
ejpam-5342	225	2	xp	xp	PROPN
ejpam-5342	225	3	∈	∈	PROPN
ejpam-5342	225	4	e(gg	e(gg	PROPN
ejpam-5342	225	5	)	)	PUNCT
ejpam-5342	225	6	,	,	PUNCT
ejpam-5342	225	7	dgg(x	dgg(x	PROPN
ejpam-5342	225	8	,	,	PUNCT
ejpam-5342	225	9	y	y	NOUN
ejpam-5342	225	10	)	)	PUNCT
ejpam-5342	225	11	=	=	SYM
ejpam-5342	225	12	2	2	X
ejpam-5342	225	13	.	.	X
ejpam-5342	225	14	suppose	suppose	VERB
ejpam-5342	225	15	(	(	PUNCT
ejpam-5342	225	16	ii	ii	NOUN
ejpam-5342	225	17	)	)	PUNCT
ejpam-5342	225	18	holds	hold	VERB
ejpam-5342	225	19	.	.	PUNCT
ejpam-5342	226	1	then	then	ADV
ejpam-5342	226	2	v	v	X
ejpam-5342	226	3	(	(	PUNCT
ejpam-5342	226	4	gg)\s	gg)\s	NOUN
ejpam-5342	226	5	=	=	SYM
ejpam-5342	226	6	v	v	NOUN
ejpam-5342	226	7	(	(	PUNCT
ejpam-5342	226	8	g)\sg	g)\sg	PROPN
ejpam-5342	226	9	is	be	AUX
ejpam-5342	226	10	independent	independent	ADJ
ejpam-5342	226	11	since	since	SCONJ
ejpam-5342	226	12	g	g	PROPN
ejpam-5342	226	13	is	be	AUX
ejpam-5342	226	14	an	an	DET
ejpam-5342	226	15	empty	empty	ADJ
ejpam-5342	226	16	graph	graph	NOUN
ejpam-5342	226	17	.	.	PUNCT
ejpam-5342	227	1	let	let	VERB
ejpam-5342	227	2	z	z	NOUN
ejpam-5342	227	3	∈	∈	PROPN
ejpam-5342	227	4	v	v	NOUN
ejpam-5342	227	5	(	(	PUNCT
ejpam-5342	227	6	gg)\s	gg)\s	NOUN
ejpam-5342	227	7	.	.	PUNCT
ejpam-5342	228	1	then	then	ADV
ejpam-5342	228	2	z	z	PROPN
ejpam-5342	228	3	∈	∈	PROPN
ejpam-5342	228	4	v	v	ADP
ejpam-5342	228	5	(	(	PUNCT
ejpam-5342	228	6	g)\sg	g)\sg	PROPN
ejpam-5342	228	7	.	.	PUNCT
ejpam-5342	229	1	thus	thus	ADV
ejpam-5342	229	2	,	,	PUNCT
ejpam-5342	229	3	z	z	PROPN
ejpam-5342	229	4	∈	∈	PROPN
ejpam-5342	229	5	v	v	ADP
ejpam-5342	229	6	(	(	PUNCT
ejpam-5342	229	7	g	g	NOUN
ejpam-5342	229	8	)	)	PUNCT
ejpam-5342	229	9	∩	∩	NOUN
ejpam-5342	229	10	sg	sg	PROPN
ejpam-5342	229	11	since	since	SCONJ
ejpam-5342	229	12	zz	zz	PROPN
ejpam-5342	229	13	∈	∈	PROPN
ejpam-5342	229	14	e(gg	e(gg	PROPN
ejpam-5342	229	15	)	)	PUNCT
ejpam-5342	229	16	and	and	CCONJ
ejpam-5342	229	17	v	v	NOUN
ejpam-5342	229	18	(	(	PUNCT
ejpam-5342	229	19	gg)\s	gg)\s	NOUN
ejpam-5342	229	20	is	be	AUX
ejpam-5342	229	21	independent	independent	ADJ
ejpam-5342	229	22	.	.	PUNCT
ejpam-5342	230	1	since	since	SCONJ
ejpam-5342	230	2	g	g	PROPN
ejpam-5342	230	3	is	be	AUX
ejpam-5342	230	4	complete	complete	ADJ
ejpam-5342	230	5	,	,	PUNCT
ejpam-5342	230	6	qz	qz	PROPN
ejpam-5342	230	7	∈	∈	PROPN
ejpam-5342	230	8	e(g	e(g	PROPN
ejpam-5342	230	9	)	)	PUNCT
ejpam-5342	231	1	for	for	ADP
ejpam-5342	231	2	all	all	DET
ejpam-5342	231	3	q	q	PROPN
ejpam-5342	231	4	∈	∈	PROPN
ejpam-5342	231	5	v	v	NOUN
ejpam-5342	231	6	(	(	PUNCT
ejpam-5342	231	7	g)\{z	g)\{z	NOUN
ejpam-5342	231	8	}	}	PUNCT
ejpam-5342	231	9	.	.	PUNCT
ejpam-5342	232	1	it	it	PRON
ejpam-5342	232	2	follows	follow	VERB
ejpam-5342	232	3	that	that	SCONJ
ejpam-5342	232	4	dgg(z	dgg(z	NOUN
ejpam-5342	232	5	,	,	PUNCT
ejpam-5342	232	6	q	q	NOUN
ejpam-5342	232	7	)	)	PUNCT
ejpam-5342	232	8	=	=	SYM
ejpam-5342	232	9	2	2	NUM
ejpam-5342	232	10	and	and	CCONJ
ejpam-5342	232	11	q	q	ADJ
ejpam-5342	232	12	∈	∈	PROPN
ejpam-5342	232	13	v	v	NOUN
ejpam-5342	232	14	(	(	PUNCT
ejpam-5342	232	15	g)\{z	g)\{z	NOUN
ejpam-5342	232	16	}	}	PUNCT
ejpam-5342	232	17	.	.	PUNCT
ejpam-5342	233	1	therefore	therefore	ADV
ejpam-5342	233	2	,	,	PUNCT
ejpam-5342	233	3	in	in	ADP
ejpam-5342	233	4	any	any	DET
ejpam-5342	233	5	case	case	NOUN
ejpam-5342	233	6	,	,	PUNCT
ejpam-5342	233	7	s	s	VERB
ejpam-5342	233	8	is	be	AUX
ejpam-5342	233	9	a	a	DET
ejpam-5342	233	10	connected	connected	ADJ
ejpam-5342	233	11	co	co	NOUN
ejpam-5342	233	12	-	-	ADJ
ejpam-5342	233	13	independent	independent	ADJ
ejpam-5342	233	14	hop	hop	NOUN
ejpam-5342	233	15	dominating	dominating	NOUN
ejpam-5342	233	16	set	set	NOUN
ejpam-5342	233	17	of	of	ADP
ejpam-5342	233	18	gg	gg	PROPN
ejpam-5342	233	19	.	.	PUNCT
ejpam-5342	234	1	corollary	corollary	ADJ
ejpam-5342	234	2	2	2	NUM
ejpam-5342	234	3	.	.	PUNCT
ejpam-5342	235	1	let	let	VERB
ejpam-5342	235	2	g	g	NOUN
ejpam-5342	235	3	be	be	AUX
ejpam-5342	235	4	either	either	CCONJ
ejpam-5342	235	5	a	a	DET
ejpam-5342	235	6	complete	complete	ADJ
ejpam-5342	235	7	graph	graph	NOUN
ejpam-5342	235	8	or	or	CCONJ
ejpam-5342	235	9	an	an	DET
ejpam-5342	235	10	empty	empty	ADJ
ejpam-5342	235	11	graph	graph	NOUN
ejpam-5342	235	12	of	of	ADP
ejpam-5342	235	13	order	order	NOUN
ejpam-5342	235	14	n	n	PRON
ejpam-5342	235	15	≥	≥	NOUN
ejpam-5342	235	16	2	2	NUM
ejpam-5342	235	17	.	.	PUNCT
ejpam-5342	236	1	then	then	ADV
ejpam-5342	236	2	γch	γch	NOUN
ejpam-5342	236	3	,	,	PUNCT
ejpam-5342	236	4	coi(gg	coi(gg	NOUN
ejpam-5342	236	5	)	)	PUNCT
ejpam-5342	237	1	=	=	VERB
ejpam-5342	237	2	n.	n.	NOUN
ejpam-5342	237	3	proof	proof	NOUN
ejpam-5342	237	4	:	:	PUNCT
ejpam-5342	237	5	let	let	VERB
ejpam-5342	237	6	s	s	PRON
ejpam-5342	237	7	be	be	AUX
ejpam-5342	237	8	a	a	DET
ejpam-5342	237	9	γch	γch	NOUN
ejpam-5342	237	10	,	,	PUNCT
ejpam-5342	237	11	coi	coi	NOUN
ejpam-5342	237	12	-	-	PUNCT
ejpam-5342	237	13	set	set	NOUN
ejpam-5342	237	14	of	of	ADP
ejpam-5342	237	15	gg	gg	PROPN
ejpam-5342	237	16	.	.	PUNCT
ejpam-5342	238	1	then	then	ADV
ejpam-5342	238	2	s	s	VERB
ejpam-5342	238	3	=	=	PUNCT
ejpam-5342	238	4	sg	sg	X
ejpam-5342	238	5	∪	∪	ADJ
ejpam-5342	238	6	sg	sg	PROPN
ejpam-5342	239	1	and	and	CCONJ
ejpam-5342	239	2	(	(	PUNCT
ejpam-5342	239	3	i	i	NOUN
ejpam-5342	239	4	)	)	PUNCT
ejpam-5342	239	5	and	and	CCONJ
ejpam-5342	239	6	(	(	PUNCT
ejpam-5342	239	7	ii	ii	NOUN
ejpam-5342	239	8	)	)	PUNCT
ejpam-5342	239	9	of	of	ADP
ejpam-5342	239	10	theorem	theorem	ADJ
ejpam-5342	239	11	4	4	NUM
ejpam-5342	239	12	hold	hold	VERB
ejpam-5342	239	13	.	.	PUNCT
ejpam-5342	240	1	if	if	SCONJ
ejpam-5342	240	2	(	(	PUNCT
ejpam-5342	240	3	i	i	NOUN
ejpam-5342	240	4	)	)	PUNCT
ejpam-5342	240	5	holds	hold	VERB
ejpam-5342	240	6	,	,	PUNCT
ejpam-5342	240	7	then	then	ADV
ejpam-5342	240	8	sg	sg	PROPN
ejpam-5342	240	9	=	=	SYM
ejpam-5342	240	10	v	v	PROPN
ejpam-5342	240	11	(	(	PUNCT
ejpam-5342	240	12	g	g	NOUN
ejpam-5342	240	13	)	)	PUNCT
ejpam-5342	240	14	and	and	CCONJ
ejpam-5342	240	15	sg	sg	ADP
ejpam-5342	240	16	⊆	⊆	NUM
ejpam-5342	240	17	v	v	NOUN
ejpam-5342	240	18	(	(	PUNCT
ejpam-5342	240	19	ḡ	ḡ	VERB
ejpam-5342	240	20	)	)	PUNCT
ejpam-5342	240	21	.	.	PUNCT
ejpam-5342	241	1	hence	hence	ADV
ejpam-5342	241	2	,	,	PUNCT
ejpam-5342	241	3	γch	γch	NOUN
ejpam-5342	241	4	,	,	PUNCT
ejpam-5342	241	5	coi(gg	coi(gg	NOUN
ejpam-5342	241	6	)	)	PUNCT
ejpam-5342	242	1	=	=	SYM
ejpam-5342	242	2	|s|	|s|	PROPN
ejpam-5342	242	3	=	=	PUNCT
ejpam-5342	242	4	|v	|v	PROPN
ejpam-5342	242	5	(	(	PUNCT
ejpam-5342	242	6	g)|	g)|	NOUN
ejpam-5342	242	7	+	+	CCONJ
ejpam-5342	242	8	|sg|	|sg|	PROPN
ejpam-5342	242	9	≥	≥	NOUN
ejpam-5342	242	10	n.	n.	NOUN
ejpam-5342	242	11	on	on	ADP
ejpam-5342	242	12	the	the	DET
ejpam-5342	242	13	other	other	ADJ
ejpam-5342	242	14	hand	hand	NOUN
ejpam-5342	242	15	,	,	PUNCT
ejpam-5342	242	16	if	if	SCONJ
ejpam-5342	242	17	(	(	PUNCT
ejpam-5342	242	18	ii	ii	NOUN
ejpam-5342	242	19	)	)	PUNCT
ejpam-5342	242	20	holds	hold	VERB
ejpam-5342	242	21	,	,	PUNCT
ejpam-5342	242	22	then	then	ADV
ejpam-5342	242	23	sg	sg	PROPN
ejpam-5342	242	24	=	=	SYM
ejpam-5342	242	25	v	v	PROPN
ejpam-5342	242	26	(	(	PUNCT
ejpam-5342	242	27	g	g	NOUN
ejpam-5342	242	28	)	)	PUNCT
ejpam-5342	242	29	and	and	CCONJ
ejpam-5342	242	30	sg	sg	X
ejpam-5342	242	31	=	=	SYM
ejpam-5342	242	32	v	v	PROPN
ejpam-5342	242	33	(	(	PUNCT
ejpam-5342	242	34	g	g	NOUN
ejpam-5342	242	35	)	)	PUNCT
ejpam-5342	242	36	.	.	PUNCT
ejpam-5342	243	1	hence	hence	ADV
ejpam-5342	243	2	,	,	PUNCT
ejpam-5342	243	3	γch	γch	NOUN
ejpam-5342	243	4	,	,	PUNCT
ejpam-5342	243	5	coi(gg	coi(gg	NOUN
ejpam-5342	243	6	)	)	PUNCT
ejpam-5342	244	1	=	=	SYM
ejpam-5342	244	2	|s|	|s|	PROPN
ejpam-5342	244	3	=	=	PUNCT
ejpam-5342	244	4	|v	|v	PROPN
ejpam-5342	244	5	(	(	PUNCT
ejpam-5342	244	6	g)|	g)|	NOUN
ejpam-5342	244	7	+	+	CCONJ
ejpam-5342	244	8	|sg|	|sg|	PROPN
ejpam-5342	244	9	≥	≥	NOUN
ejpam-5342	244	10	n.	n.	NOUN
ejpam-5342	244	11	now	now	ADV
ejpam-5342	244	12	,	,	PUNCT
ejpam-5342	244	13	let	let	VERB
ejpam-5342	244	14	sg	sg	VERB
ejpam-5342	244	15	=	=	VERB
ejpam-5342	244	16	∅	∅	NOUN
ejpam-5342	244	17	if	if	SCONJ
ejpam-5342	244	18	(	(	PUNCT
ejpam-5342	244	19	i	i	NOUN
ejpam-5342	244	20	)	)	PUNCT
ejpam-5342	244	21	holds	hold	VERB
ejpam-5342	244	22	.	.	PUNCT
ejpam-5342	245	1	thus	thus	ADV
ejpam-5342	245	2	,	,	PUNCT
ejpam-5342	245	3	s	s	VERB
ejpam-5342	245	4	=	=	SYM
ejpam-5342	245	5	v	v	X
ejpam-5342	245	6	(	(	PUNCT
ejpam-5342	245	7	g	g	NOUN
ejpam-5342	245	8	)	)	PUNCT
ejpam-5342	245	9	∪	∪	NOUN
ejpam-5342	245	10	sg	sg	PROPN
ejpam-5342	245	11	is	be	AUX
ejpam-5342	245	12	a	a	DET
ejpam-5342	245	13	connected	connected	ADJ
ejpam-5342	245	14	co	co	NOUN
ejpam-5342	245	15	-	-	ADJ
ejpam-5342	245	16	independent	independent	ADJ
ejpam-5342	245	17	hop	hop	NOUN
ejpam-5342	245	18	dominating	dominating	NOUN
ejpam-5342	245	19	set	set	NOUN
ejpam-5342	245	20	of	of	ADP
ejpam-5342	245	21	gg	gg	PROPN
ejpam-5342	245	22	by	by	ADP
ejpam-5342	245	23	theorem	theorem	NOUN
ejpam-5342	245	24	4	4	NUM
ejpam-5342	245	25	.	.	PUNCT
ejpam-5342	246	1	hence	hence	ADV
ejpam-5342	246	2	,	,	PUNCT
ejpam-5342	246	3	γch	γch	NOUN
ejpam-5342	246	4	,	,	PUNCT
ejpam-5342	246	5	coi(gg	coi(gg	NOUN
ejpam-5342	246	6	)	)	PUNCT
ejpam-5342	246	7	≤	≤	NUM
ejpam-5342	246	8	|s|	|s|	PROPN
ejpam-5342	246	9	=	=	SYM
ejpam-5342	246	10	|v	|v	X
ejpam-5342	246	11	(	(	PUNCT
ejpam-5342	246	12	g)|	g)|	NOUN
ejpam-5342	246	13	=	=	SYM
ejpam-5342	246	14	n.	n.	NOUN
ejpam-5342	246	15	if	if	SCONJ
ejpam-5342	246	16	(	(	PUNCT
ejpam-5342	246	17	ii	ii	NOUN
ejpam-5342	246	18	)	)	PUNCT
ejpam-5342	246	19	holds	hold	VERB
ejpam-5342	246	20	,	,	PUNCT
ejpam-5342	246	21	then	then	ADV
ejpam-5342	246	22	let	let	VERB
ejpam-5342	246	23	sg	sg	VERB
ejpam-5342	246	24	=	=	VERB
ejpam-5342	246	25	∅.	∅.	X
ejpam-5342	246	26	by	by	ADP
ejpam-5342	246	27	theorem	theorem	ADJ
ejpam-5342	246	28	4	4	NUM
ejpam-5342	246	29	,	,	PUNCT
ejpam-5342	246	30	s	s	PART
ejpam-5342	246	31	=	=	SYM
ejpam-5342	246	32	v	v	X
ejpam-5342	246	33	(	(	PUNCT
ejpam-5342	246	34	g	g	NOUN
ejpam-5342	246	35	)	)	PUNCT
ejpam-5342	246	36	∪	∪	ADP
ejpam-5342	246	37	sg	sg	PROPN
ejpam-5342	246	38	.	.	PUNCT
ejpam-5342	247	1	thus	thus	ADV
ejpam-5342	247	2	,	,	PUNCT
ejpam-5342	247	3	γch	γch	NOUN
ejpam-5342	247	4	,	,	PUNCT
ejpam-5342	247	5	coi(gg	coi(gg	NOUN
ejpam-5342	247	6	)	)	PUNCT
ejpam-5342	247	7	≤	≤	NUM
ejpam-5342	247	8	|s|	|s|	PROPN
ejpam-5342	247	9	=	=	SYM
ejpam-5342	247	10	|v	|v	X
ejpam-5342	247	11	(	(	PUNCT
ejpam-5342	247	12	g	g	NOUN
ejpam-5342	247	13	)	)	PUNCT
ejpam-5342	247	14	=	=	VERB
ejpam-5342	247	15	n.	n.	NOUN
ejpam-5342	247	16	therefore	therefore	ADV
ejpam-5342	247	17	,	,	PUNCT
ejpam-5342	247	18	in	in	ADP
ejpam-5342	247	19	any	any	DET
ejpam-5342	247	20	case	case	NOUN
ejpam-5342	247	21	,	,	PUNCT
ejpam-5342	247	22	γch	γch	NOUN
ejpam-5342	247	23	,	,	PUNCT
ejpam-5342	247	24	coi(gg	coi(gg	NOUN
ejpam-5342	247	25	)	)	PUNCT
ejpam-5342	247	26	=	=	SYM
ejpam-5342	247	27	n.	n.	NOUN
ejpam-5342	247	28	theorem	theorem	VERB
ejpam-5342	247	29	5	5	NUM
ejpam-5342	247	30	.	.	PUNCT
ejpam-5342	248	1	let	let	VERB
ejpam-5342	248	2	g	g	PRON
ejpam-5342	248	3	be	be	AUX
ejpam-5342	248	4	a	a	DET
ejpam-5342	248	5	nontrivial	nontrivial	ADJ
ejpam-5342	248	6	connected	connect	VERB
ejpam-5342	248	7	noncomplete	noncomplete	ADJ
ejpam-5342	248	8	graph	graph	NOUN
ejpam-5342	248	9	and	and	CCONJ
ejpam-5342	248	10	g	g	PROPN
ejpam-5342	248	11	be	be	AUX
ejpam-5342	248	12	the	the	DET
ejpam-5342	248	13	complement	complement	NOUN
ejpam-5342	248	14	of	of	ADP
ejpam-5342	248	15	g.	g.	PROPN
ejpam-5342	248	16	then	then	ADV
ejpam-5342	248	17	s	s	VERB
ejpam-5342	248	18	⊆	⊆	NUM
ejpam-5342	248	19	v	v	NOUN
ejpam-5342	248	20	(	(	PUNCT
ejpam-5342	248	21	gg	gg	NOUN
ejpam-5342	248	22	)	)	PUNCT
ejpam-5342	248	23	is	be	AUX
ejpam-5342	248	24	a	a	DET
ejpam-5342	248	25	connected	connected	ADJ
ejpam-5342	248	26	co	co	NOUN
ejpam-5342	248	27	-	-	ADJ
ejpam-5342	248	28	independent	independent	ADJ
ejpam-5342	248	29	hop	hop	NOUN
ejpam-5342	248	30	dominating	dominating	NOUN
ejpam-5342	248	31	set	set	NOUN
ejpam-5342	248	32	of	of	ADP
ejpam-5342	248	33	gg	gg	PROPN
ejpam-5342	248	34	if	if	SCONJ
ejpam-5342	249	1	and	and	CCONJ
ejpam-5342	249	2	only	only	ADV
ejpam-5342	249	3	if	if	SCONJ
ejpam-5342	249	4	s	s	VERB
ejpam-5342	249	5	=	=	PUNCT
ejpam-5342	249	6	sg	sg	X
ejpam-5342	249	7	∪	∪	ADJ
ejpam-5342	249	8	sg	sg	ADP
ejpam-5342	249	9	where	where	SCONJ
ejpam-5342	249	10	sg	sg	PROPN
ejpam-5342	249	11	⊆	⊆	NUM
ejpam-5342	249	12	v	v	NOUN
ejpam-5342	249	13	(	(	PUNCT
ejpam-5342	249	14	g	g	NOUN
ejpam-5342	249	15	)	)	PUNCT
ejpam-5342	249	16	and	and	CCONJ
ejpam-5342	249	17	sg	sg	ADP
ejpam-5342	249	18	⊆	⊆	NUM
ejpam-5342	249	19	v	v	NOUN
ejpam-5342	249	20	(	(	PUNCT
ejpam-5342	249	21	g	g	NOUN
ejpam-5342	249	22	)	)	PUNCT
ejpam-5342	249	23	and	and	CCONJ
ejpam-5342	249	24	the	the	DET
ejpam-5342	249	25	following	follow	VERB
ejpam-5342	249	26	hold	hold	NOUN
ejpam-5342	249	27	:	:	PUNCT
ejpam-5342	249	28	(	(	PUNCT
ejpam-5342	249	29	i	i	NOUN
ejpam-5342	249	30	)	)	PUNCT
ejpam-5342	249	31	sg	sg	ADP
ejpam-5342	249	32	̸=	̸=	PROPN
ejpam-5342	249	33	∅	∅	NOUN
ejpam-5342	249	34	and	and	CCONJ
ejpam-5342	249	35	sg	sg	ADP
ejpam-5342	249	36	̸=	̸=	PROPN
ejpam-5342	249	37	∅	∅	NOUN
ejpam-5342	249	38	(	(	PUNCT
ejpam-5342	249	39	ii	ii	NOUN
ejpam-5342	249	40	)	)	PUNCT
ejpam-5342	249	41	v	v	NOUN
ejpam-5342	249	42	(	(	PUNCT
ejpam-5342	249	43	g)\sg	g)\sg	PROPN
ejpam-5342	249	44	and	and	CCONJ
ejpam-5342	249	45	v	v	NOUN
ejpam-5342	249	46	(	(	PUNCT
ejpam-5342	249	47	g)\sg	g)\sg	PROPN
ejpam-5342	249	48	are	be	AUX
ejpam-5342	249	49	independent	independent	ADJ
ejpam-5342	249	50	sets	set	NOUN
ejpam-5342	249	51	in	in	ADP
ejpam-5342	249	52	g	g	PROPN
ejpam-5342	249	53	and	and	CCONJ
ejpam-5342	249	54	g	g	NOUN
ejpam-5342	249	55	,	,	PUNCT
ejpam-5342	249	56	respectively	respectively	ADV
ejpam-5342	249	57	.	.	PUNCT
ejpam-5342	250	1	(	(	PUNCT
ejpam-5342	250	2	iii	iii	X
ejpam-5342	250	3	)	)	PUNCT
ejpam-5342	250	4	for	for	ADP
ejpam-5342	250	5	every	every	DET
ejpam-5342	250	6	x	x	SYM
ejpam-5342	250	7	∈	∈	PROPN
ejpam-5342	250	8	v	v	NOUN
ejpam-5342	250	9	(	(	PUNCT
ejpam-5342	250	10	g)\sg	g)\sg	PROPN
ejpam-5342	250	11	,	,	PUNCT
ejpam-5342	250	12	x	x	SYM
ejpam-5342	250	13	∈	∈	PROPN
ejpam-5342	250	14	sg	sg	PROPN
ejpam-5342	250	15	.	.	PUNCT
ejpam-5342	251	1	(	(	PUNCT
ejpam-5342	251	2	iv	iv	X
ejpam-5342	251	3	)	)	PUNCT
ejpam-5342	251	4	either	either	CCONJ
ejpam-5342	251	5	⟨sg⟩	⟨sg⟩	PRON
ejpam-5342	251	6	is	be	AUX
ejpam-5342	251	7	connected	connect	VERB
ejpam-5342	251	8	or	or	CCONJ
ejpam-5342	251	9	for	for	ADP
ejpam-5342	251	10	every	every	DET
ejpam-5342	251	11	pair	pair	NOUN
ejpam-5342	251	12	of	of	ADP
ejpam-5342	251	13	distinct	distinct	ADJ
ejpam-5342	251	14	vertices	vertex	NOUN
ejpam-5342	251	15	x	x	X
ejpam-5342	251	16	,	,	PUNCT
ejpam-5342	251	17	y	y	PROPN
ejpam-5342	251	18	∈	∈	PROPN
ejpam-5342	251	19	sg	sg	X
ejpam-5342	251	20	with	with	ADP
ejpam-5342	251	21	xy	xy	PROPN
ejpam-5342	251	22	/∈	/∈	PUNCT
ejpam-5342	251	23	e(g	e(g	PROPN
ejpam-5342	251	24	)	)	PUNCT
ejpam-5342	251	25	,	,	PUNCT
ejpam-5342	251	26	x	x	X
ejpam-5342	251	27	,	,	PUNCT
ejpam-5342	251	28	y	y	PROPN
ejpam-5342	251	29	∈	∈	PROPN
ejpam-5342	251	30	sg	sg	PROPN
ejpam-5342	251	31	.	.	PUNCT
ejpam-5342	252	1	(	(	PUNCT
ejpam-5342	252	2	v	v	NOUN
ejpam-5342	252	3	)	)	PUNCT
ejpam-5342	252	4	either	either	CCONJ
ejpam-5342	252	5	〈	〈	PROPN
ejpam-5342	252	6	sg	sg	ADP
ejpam-5342	252	7	〉	〉	NOUN
ejpam-5342	252	8	is	be	AUX
ejpam-5342	252	9	connected	connect	VERB
ejpam-5342	252	10	or	or	CCONJ
ejpam-5342	252	11	for	for	ADP
ejpam-5342	252	12	every	every	DET
ejpam-5342	252	13	pair	pair	NOUN
ejpam-5342	252	14	of	of	ADP
ejpam-5342	252	15	distinct	distinct	ADJ
ejpam-5342	252	16	vertices	vertex	NOUN
ejpam-5342	252	17	p	p	NOUN
ejpam-5342	252	18	,	,	PUNCT
ejpam-5342	252	19	q	q	PROPN
ejpam-5342	252	20	∈	∈	PROPN
ejpam-5342	252	21	sg	sg	NOUN
ejpam-5342	252	22	with	with	ADP
ejpam-5342	252	23	pq	pq	PROPN
ejpam-5342	252	24	/∈	/∈	PUNCT
ejpam-5342	252	25	e(g	e(g	PROPN
ejpam-5342	252	26	)	)	PUNCT
ejpam-5342	252	27	,	,	PUNCT
ejpam-5342	253	1	p	p	X
ejpam-5342	253	2	,	,	PUNCT
ejpam-5342	253	3	q	q	PROPN
ejpam-5342	253	4	∈	∈	PROPN
ejpam-5342	253	5	sg	sg	PROPN
ejpam-5342	253	6	.	.	PUNCT
ejpam-5342	253	7	(	(	PUNCT
ejpam-5342	253	8	vi	vi	NOUN
ejpam-5342	253	9	)	)	PUNCT
ejpam-5342	253	10	for	for	ADP
ejpam-5342	253	11	every	every	DET
ejpam-5342	253	12	pair	pair	NOUN
ejpam-5342	253	13	of	of	ADP
ejpam-5342	253	14	vertices	vertex	NOUN
ejpam-5342	253	15	x	x	X
ejpam-5342	253	16	∈	∈	NOUN
ejpam-5342	253	17	sg	sg	NOUN
ejpam-5342	253	18	and	and	CCONJ
ejpam-5342	253	19	q	q	PROPN
ejpam-5342	253	20	∈	∈	PROPN
ejpam-5342	253	21	sg	sg	PROPN
ejpam-5342	253	22	,	,	PUNCT
ejpam-5342	253	23	q	q	PROPN
ejpam-5342	253	24	∈	∈	PROPN
ejpam-5342	253	25	sg	sg	ADP
ejpam-5342	253	26	if	if	SCONJ
ejpam-5342	253	27	xq	xq	PROPN
ejpam-5342	253	28	∈	∈	PROPN
ejpam-5342	253	29	e(g	e(g	PROPN
ejpam-5342	253	30	)	)	PUNCT
ejpam-5342	253	31	or	or	CCONJ
ejpam-5342	253	32	x	x	SYM
ejpam-5342	253	33	∈	∈	NOUN
ejpam-5342	253	34	sg	sg	X
ejpam-5342	253	35	if	if	SCONJ
ejpam-5342	253	36	xq	xq	PROPN
ejpam-5342	253	37	/∈	/∈	PUNCT
ejpam-5342	253	38	e(g	e(g	PROPN
ejpam-5342	253	39	)	)	PUNCT
ejpam-5342	253	40	.	.	PUNCT
ejpam-5342	254	1	s.	s.	PROPN
ejpam-5342	254	2	a.	a.	PROPN
ejpam-5342	254	3	nanding	nanding	PROPN
ejpam-5342	254	4	,	,	PUNCT
ejpam-5342	254	5	h.	h.	PROPN
ejpam-5342	254	6	m.	m.	PROPN
ejpam-5342	254	7	rara	rara	PROPN
ejpam-5342	254	8	,	,	PUNCT
ejpam-5342	254	9	i.	i.	PROPN
ejpam-5342	254	10	s.	s.	PROPN
ejpam-5342	254	11	aniversario	aniversario	PROPN
ejpam-5342	254	12	/	/	SYM
ejpam-5342	254	13	eur	eur	PROPN
ejpam-5342	254	14	.	.	PUNCT
ejpam-5342	255	1	j.	j.	PROPN
ejpam-5342	255	2	pure	pure	PROPN
ejpam-5342	255	3	appl	appl	PROPN
ejpam-5342	255	4	.	.	PROPN
ejpam-5342	255	5	math	math	PROPN
ejpam-5342	255	6	,	,	PUNCT
ejpam-5342	255	7	17	17	NUM
ejpam-5342	255	8	(	(	PUNCT
ejpam-5342	255	9	4	4	NUM
ejpam-5342	255	10	)	)	PUNCT
ejpam-5342	255	11	(	(	PUNCT
ejpam-5342	255	12	2024	2024	NUM
ejpam-5342	255	13	)	)	PUNCT
ejpam-5342	255	14	,	,	PUNCT
ejpam-5342	255	15	2505	2505	NUM
ejpam-5342	255	16	-	-	SYM
ejpam-5342	255	17	2515	2515	NUM
ejpam-5342	255	18	2513	2513	NUM
ejpam-5342	255	19	(	(	PUNCT
ejpam-5342	255	20	vii	vii	PROPN
ejpam-5342	255	21	)	)	PUNCT
ejpam-5342	255	22	for	for	ADP
ejpam-5342	255	23	every	every	DET
ejpam-5342	255	24	x	x	SYM
ejpam-5342	255	25	∈	∈	PROPN
ejpam-5342	255	26	v	v	NOUN
ejpam-5342	255	27	(	(	PUNCT
ejpam-5342	255	28	g)\sg	g)\sg	PROPN
ejpam-5342	255	29	such	such	ADJ
ejpam-5342	255	30	that	that	SCONJ
ejpam-5342	255	31	ng(x	ng(x	NUM
ejpam-5342	255	32	,	,	PUNCT
ejpam-5342	255	33	2	2	X
ejpam-5342	255	34	)	)	PUNCT
ejpam-5342	255	35	∩	∩	NOUN
ejpam-5342	255	36	sg	sg	ADP
ejpam-5342	255	37	=	=	SYM
ejpam-5342	255	38	∅	∅	NOUN
ejpam-5342	255	39	,	,	PUNCT
ejpam-5342	255	40	either	either	CCONJ
ejpam-5342	255	41	there	there	PRON
ejpam-5342	255	42	exists	exist	VERB
ejpam-5342	255	43	y	y	PROPN
ejpam-5342	255	44	∈	∈	PROPN
ejpam-5342	255	45	v	v	ADP
ejpam-5342	255	46	(	(	PUNCT
ejpam-5342	255	47	g	g	NOUN
ejpam-5342	255	48	)	)	PUNCT
ejpam-5342	255	49	∩ng(x	∩ng(x	NOUN
ejpam-5342	255	50	)	)	PUNCT
ejpam-5342	255	51	such	such	ADJ
ejpam-5342	255	52	that	that	SCONJ
ejpam-5342	255	53	y	y	PROPN
ejpam-5342	255	54	∈	∈	PROPN
ejpam-5342	255	55	sg	sg	ADV
ejpam-5342	255	56	or	or	CCONJ
ejpam-5342	255	57	there	there	ADV
ejpam-5342	255	58	exists	exist	VERB
ejpam-5342	255	59	p	p	PROPN
ejpam-5342	255	60	∈	∈	PROPN
ejpam-5342	255	61	sg	sg	X
ejpam-5342	255	62	∩ng(x	∩ng(x	PROPN
ejpam-5342	255	63	)	)	PUNCT
ejpam-5342	255	64	.	.	PUNCT
ejpam-5342	256	1	(	(	PUNCT
ejpam-5342	256	2	viii	viii	NOUN
ejpam-5342	256	3	)	)	PUNCT
ejpam-5342	256	4	for	for	ADP
ejpam-5342	256	5	every	every	DET
ejpam-5342	256	6	q	q	PROPN
ejpam-5342	256	7	∈	∈	PROPN
ejpam-5342	256	8	v	v	NOUN
ejpam-5342	256	9	(	(	PUNCT
ejpam-5342	256	10	g)\sg	g)\sg	PROPN
ejpam-5342	256	11	such	such	ADJ
ejpam-5342	256	12	that	that	DET
ejpam-5342	256	13	ng(q	ng(q	NOUN
ejpam-5342	256	14	,	,	PUNCT
ejpam-5342	256	15	2	2	NUM
ejpam-5342	256	16	)	)	PUNCT
ejpam-5342	256	17	∩	∩	NOUN
ejpam-5342	256	18	sg	sg	ADP
ejpam-5342	256	19	=	=	VERB
ejpam-5342	256	20	∅	∅	NOUN
ejpam-5342	256	21	,	,	PUNCT
ejpam-5342	256	22	there	there	PRON
ejpam-5342	256	23	exists	exist	VERB
ejpam-5342	256	24	z	z	PROPN
ejpam-5342	256	25	∈	∈	PROPN
ejpam-5342	256	26	v	v	ADP
ejpam-5342	256	27	(	(	PUNCT
ejpam-5342	256	28	g	g	NOUN
ejpam-5342	256	29	)	)	PUNCT
ejpam-5342	256	30	∩ng	∩ng	NOUN
ejpam-5342	256	31	∩	∩	NOUN
ejpam-5342	256	32	ng(q	ng(q	NOUN
ejpam-5342	256	33	)	)	PUNCT
ejpam-5342	256	34	such	such	ADJ
ejpam-5342	256	35	that	that	SCONJ
ejpam-5342	256	36	z	z	PROPN
ejpam-5342	256	37	∈	∈	PROPN
ejpam-5342	256	38	sg	sg	PROPN
ejpam-5342	256	39	.	.	PUNCT
ejpam-5342	257	1	proof	proof	NOUN
ejpam-5342	257	2	:	:	PUNCT
ejpam-5342	257	3	suppose	suppose	VERB
ejpam-5342	257	4	that	that	SCONJ
ejpam-5342	257	5	s	s	VERB
ejpam-5342	257	6	is	be	AUX
ejpam-5342	257	7	a	a	DET
ejpam-5342	257	8	connected	connected	ADJ
ejpam-5342	257	9	co	co	NOUN
ejpam-5342	257	10	-	-	ADJ
ejpam-5342	257	11	independent	independent	ADJ
ejpam-5342	257	12	hop	hop	NOUN
ejpam-5342	257	13	dominating	dominating	NOUN
ejpam-5342	257	14	set	set	NOUN
ejpam-5342	257	15	of	of	ADP
ejpam-5342	257	16	gg	gg	PROPN
ejpam-5342	257	17	.	.	PUNCT
ejpam-5342	258	1	let	let	VERB
ejpam-5342	258	2	sg	sg	VERB
ejpam-5342	258	3	=	=	SYM
ejpam-5342	258	4	s	s	PART
ejpam-5342	258	5	∩	∩	ADJ
ejpam-5342	258	6	v	v	X
ejpam-5342	258	7	(	(	PUNCT
ejpam-5342	258	8	g	g	NOUN
ejpam-5342	258	9	)	)	PUNCT
ejpam-5342	258	10	and	and	CCONJ
ejpam-5342	258	11	sg	sg	X
ejpam-5342	258	12	=	=	SYM
ejpam-5342	258	13	s	s	PROPN
ejpam-5342	258	14	∩	∩	ADJ
ejpam-5342	258	15	v	v	X
ejpam-5342	258	16	(	(	PUNCT
ejpam-5342	258	17	g	g	NOUN
ejpam-5342	258	18	)	)	PUNCT
ejpam-5342	258	19	.	.	PUNCT
ejpam-5342	259	1	then	then	ADV
ejpam-5342	259	2	s	s	VERB
ejpam-5342	259	3	=	=	PUNCT
ejpam-5342	259	4	sg	sg	PART
ejpam-5342	259	5	∪sg	∪sg	PROPN
ejpam-5342	259	6	.	.	PUNCT
ejpam-5342	259	7	suppose	suppose	VERB
ejpam-5342	259	8	sg	sg	ADP
ejpam-5342	259	9	=	=	PUNCT
ejpam-5342	259	10	∅.	∅.	VERB
ejpam-5342	259	11	then	then	ADV
ejpam-5342	259	12	s	s	VERB
ejpam-5342	259	13	=	=	PUNCT
ejpam-5342	259	14	sg	sg	NOUN
ejpam-5342	259	15	and	and	CCONJ
ejpam-5342	259	16	v	v	NOUN
ejpam-5342	259	17	(	(	PUNCT
ejpam-5342	259	18	gg)\s	gg)\s	NOUN
ejpam-5342	259	19	=	=	SYM
ejpam-5342	259	20	v	v	NOUN
ejpam-5342	259	21	(	(	PUNCT
ejpam-5342	259	22	g	g	NOUN
ejpam-5342	259	23	)	)	PUNCT
ejpam-5342	259	24	∪	∪	ADP
ejpam-5342	260	1	[	[	X
ejpam-5342	260	2	v	v	X
ejpam-5342	260	3	(	(	PUNCT
ejpam-5342	260	4	g)\sg	g)\sg	PROPN
ejpam-5342	260	5	]	]	PUNCT
ejpam-5342	260	6	is	be	AUX
ejpam-5342	260	7	not	not	PART
ejpam-5342	260	8	independent	independent	ADJ
ejpam-5342	260	9	since	since	SCONJ
ejpam-5342	260	10	g	g	PROPN
ejpam-5342	260	11	is	be	AUX
ejpam-5342	260	12	connected	connect	VERB
ejpam-5342	260	13	.	.	PUNCT
ejpam-5342	261	1	this	this	PRON
ejpam-5342	261	2	is	be	AUX
ejpam-5342	261	3	a	a	DET
ejpam-5342	261	4	contradiction	contradiction	NOUN
ejpam-5342	261	5	to	to	ADP
ejpam-5342	261	6	the	the	DET
ejpam-5342	261	7	independence	independence	NOUN
ejpam-5342	261	8	of	of	ADP
ejpam-5342	261	9	v	v	NOUN
ejpam-5342	261	10	(	(	PUNCT
ejpam-5342	261	11	gg)\s	gg)\s	NOUN
ejpam-5342	261	12	.	.	PUNCT
ejpam-5342	262	1	thus	thus	ADV
ejpam-5342	262	2	,	,	PUNCT
ejpam-5342	262	3	sg	sg	ADP
ejpam-5342	262	4	̸=	̸=	PROPN
ejpam-5342	262	5	∅.	∅.	ADV
ejpam-5342	262	6	since	since	SCONJ
ejpam-5342	262	7	g	g	PROPN
ejpam-5342	262	8	is	be	AUX
ejpam-5342	262	9	a	a	DET
ejpam-5342	262	10	connected	connected	ADJ
ejpam-5342	262	11	noncomplete	noncomplete	ADJ
ejpam-5342	262	12	graph	graph	NOUN
ejpam-5342	262	13	,	,	PUNCT
ejpam-5342	262	14	there	there	PRON
ejpam-5342	262	15	exist	exist	VERB
ejpam-5342	262	16	x	x	NOUN
ejpam-5342	262	17	,	,	PUNCT
ejpam-5342	262	18	y	y	PROPN
ejpam-5342	262	19	∈	∈	PROPN
ejpam-5342	262	20	v	v	ADP
ejpam-5342	262	21	(	(	PUNCT
ejpam-5342	262	22	g	g	NOUN
ejpam-5342	262	23	)	)	PUNCT
ejpam-5342	262	24	such	such	ADJ
ejpam-5342	262	25	that	that	PRON
ejpam-5342	262	26	xy	xy	PROPN
ejpam-5342	262	27	/∈	/∈	PUNCT
ejpam-5342	262	28	e(g	e(g	PROPN
ejpam-5342	262	29	)	)	PUNCT
ejpam-5342	262	30	.	.	PUNCT
ejpam-5342	263	1	hence	hence	ADV
ejpam-5342	263	2	,	,	PUNCT
ejpam-5342	263	3	xy	xy	PROPN
ejpam-5342	263	4	∈	∈	PROPN
ejpam-5342	263	5	e(g	e(g	PROPN
ejpam-5342	263	6	)	)	PUNCT
ejpam-5342	263	7	.	.	PUNCT
ejpam-5342	264	1	this	this	PRON
ejpam-5342	264	2	implies	imply	VERB
ejpam-5342	264	3	that	that	SCONJ
ejpam-5342	264	4	x	x	SYM
ejpam-5342	264	5	∈	∈	NOUN
ejpam-5342	264	6	sg	sg	VERB
ejpam-5342	264	7	or	or	CCONJ
ejpam-5342	264	8	y	y	PROPN
ejpam-5342	264	9	∈	∈	PROPN
ejpam-5342	264	10	sg	sg	PROPN
ejpam-5342	264	11	,	,	PUNCT
ejpam-5342	264	12	showing	show	VERB
ejpam-5342	264	13	that	that	SCONJ
ejpam-5342	264	14	sg	sg	VERB
ejpam-5342	264	15	̸=	̸=	PROPN
ejpam-5342	264	16	∅.	∅.	PRON
ejpam-5342	264	17	hence	hence	ADV
ejpam-5342	264	18	,	,	PUNCT
ejpam-5342	264	19	(	(	PUNCT
ejpam-5342	264	20	i	i	NOUN
ejpam-5342	264	21	)	)	PUNCT
ejpam-5342	264	22	holds	hold	VERB
ejpam-5342	264	23	.	.	PUNCT
ejpam-5342	265	1	for	for	ADP
ejpam-5342	265	2	(	(	PUNCT
ejpam-5342	265	3	ii	ii	NOUN
ejpam-5342	265	4	)	)	PUNCT
ejpam-5342	265	5	,	,	PUNCT
ejpam-5342	265	6	since	since	SCONJ
ejpam-5342	265	7	v	v	NOUN
ejpam-5342	265	8	(	(	PUNCT
ejpam-5342	265	9	gg)\s	gg)\s	NOUN
ejpam-5342	265	10	=	=	SYM
ejpam-5342	265	11	(	(	PUNCT
ejpam-5342	265	12	v	v	NOUN
ejpam-5342	265	13	(	(	PUNCT
ejpam-5342	265	14	g)\sg)∪̇(v	g)\sg)∪̇(v	PROPN
ejpam-5342	265	15	(	(	PUNCT
ejpam-5342	265	16	g)\sg	g)\sg	PROPN
ejpam-5342	265	17	)	)	PUNCT
ejpam-5342	265	18	,	,	PUNCT
ejpam-5342	265	19	v	v	X
ejpam-5342	265	20	(	(	PUNCT
ejpam-5342	265	21	gg)\s	gg)\s	NOUN
ejpam-5342	265	22	is	be	AUX
ejpam-5342	265	23	independent	independent	ADJ
ejpam-5342	265	24	,	,	PUNCT
ejpam-5342	265	25	v	v	NOUN
ejpam-5342	265	26	(	(	PUNCT
ejpam-5342	265	27	g)\sg	g)\sg	PROPN
ejpam-5342	265	28	and	and	CCONJ
ejpam-5342	265	29	v	v	NOUN
ejpam-5342	265	30	(	(	PUNCT
ejpam-5342	265	31	g)\sg	g)\sg	PROPN
ejpam-5342	265	32	are	be	AUX
ejpam-5342	265	33	independent	independent	ADJ
ejpam-5342	265	34	sets	set	NOUN
ejpam-5342	265	35	of	of	ADP
ejpam-5342	265	36	g	g	NOUN
ejpam-5342	265	37	and	and	CCONJ
ejpam-5342	265	38	g	g	NOUN
ejpam-5342	265	39	,	,	PUNCT
ejpam-5342	265	40	respectively	respectively	ADV
ejpam-5342	265	41	.	.	PUNCT
ejpam-5342	266	1	now	now	ADV
ejpam-5342	266	2	,	,	PUNCT
ejpam-5342	266	3	let	let	VERB
ejpam-5342	266	4	x	x	PUNCT
ejpam-5342	266	5	∈	∈	PROPN
ejpam-5342	266	6	v	v	NOUN
ejpam-5342	266	7	(	(	PUNCT
ejpam-5342	266	8	g)\sg	g)\sg	PROPN
ejpam-5342	266	9	.	.	PUNCT
ejpam-5342	267	1	since	since	SCONJ
ejpam-5342	267	2	xx	xx	NUM
ejpam-5342	267	3	∈	∈	PROPN
ejpam-5342	267	4	e(gg	e(gg	PROPN
ejpam-5342	267	5	)	)	PUNCT
ejpam-5342	267	6	and	and	CCONJ
ejpam-5342	267	7	v	v	NOUN
ejpam-5342	267	8	(	(	PUNCT
ejpam-5342	267	9	gg)\s	gg)\s	NOUN
ejpam-5342	267	10	is	be	AUX
ejpam-5342	267	11	independent	independent	ADJ
ejpam-5342	267	12	,	,	PUNCT
ejpam-5342	267	13	x	x	SYM
ejpam-5342	267	14	∈	∈	PROPN
ejpam-5342	267	15	sg	sg	PROPN
ejpam-5342	267	16	.	.	PUNCT
ejpam-5342	268	1	hence	hence	ADV
ejpam-5342	268	2	,	,	PUNCT
ejpam-5342	268	3	(	(	PUNCT
ejpam-5342	268	4	iii	iii	NOUN
ejpam-5342	268	5	)	)	PUNCT
ejpam-5342	268	6	holds	hold	VERB
ejpam-5342	268	7	.	.	PUNCT
ejpam-5342	269	1	suppose	suppose	VERB
ejpam-5342	269	2	⟨sg⟩	⟨sg⟩	PRON
ejpam-5342	269	3	is	be	AUX
ejpam-5342	269	4	not	not	PART
ejpam-5342	269	5	connected	connect	VERB
ejpam-5342	269	6	.	.	PUNCT
ejpam-5342	270	1	let	let	VERB
ejpam-5342	270	2	x	x	PRON
ejpam-5342	270	3	,	,	PUNCT
ejpam-5342	270	4	y	y	PROPN
ejpam-5342	270	5	∈	∈	PROPN
ejpam-5342	270	6	sg	sg	X
ejpam-5342	270	7	with	with	ADP
ejpam-5342	270	8	x	x	X
ejpam-5342	270	9	̸=	̸=	PROPN
ejpam-5342	270	10	y	y	PROPN
ejpam-5342	270	11	and	and	CCONJ
ejpam-5342	270	12	xy	xy	PROPN
ejpam-5342	270	13	/∈	/∈	PUNCT
ejpam-5342	271	1	e(g	e(g	PROPN
ejpam-5342	271	2	)	)	PUNCT
ejpam-5342	271	3	.	.	PUNCT
ejpam-5342	272	1	since	since	SCONJ
ejpam-5342	272	2	⟨s⟩	⟨s⟩	PROPN
ejpam-5342	272	3	is	be	AUX
ejpam-5342	272	4	connected	connect	VERB
ejpam-5342	272	5	,	,	PUNCT
ejpam-5342	272	6	an	an	DET
ejpam-5342	272	7	x	x	PROPN
ejpam-5342	272	8	-	-	PROPN
ejpam-5342	272	9	y	y	PROPN
ejpam-5342	272	10	path	path	NOUN
ejpam-5342	272	11	p	p	PROPN
ejpam-5342	273	1	[	[	X
ejpam-5342	273	2	x	x	X
ejpam-5342	273	3	,	,	PUNCT
ejpam-5342	273	4	y	y	X
ejpam-5342	273	5	]	]	X
ejpam-5342	273	6	in	in	ADP
ejpam-5342	273	7	s	s	NOUN
ejpam-5342	273	8	exists	exist	VERB
ejpam-5342	273	9	.	.	PUNCT
ejpam-5342	274	1	since	since	SCONJ
ejpam-5342	274	2	⟨sg⟩	⟨sg⟩	PRON
ejpam-5342	274	3	is	be	AUX
ejpam-5342	274	4	not	not	PART
ejpam-5342	274	5	connected	connect	VERB
ejpam-5342	274	6	and	and	CCONJ
ejpam-5342	274	7	xy	xy	PROPN
ejpam-5342	274	8	∈	∈	PROPN
ejpam-5342	274	9	e(g	e(g	PROPN
ejpam-5342	274	10	)	)	PUNCT
ejpam-5342	274	11	,	,	PUNCT
ejpam-5342	274	12	x	x	X
ejpam-5342	274	13	,	,	PUNCT
ejpam-5342	274	14	y	y	PROPN
ejpam-5342	274	15	∈	∈	PROPN
ejpam-5342	275	1	p	p	X
ejpam-5342	276	1	[	[	X
ejpam-5342	276	2	x	x	X
ejpam-5342	276	3	,	,	PUNCT
ejpam-5342	276	4	y	y	PROPN
ejpam-5342	276	5	]	]	PUNCT
ejpam-5342	276	6	.	.	PUNCT
ejpam-5342	277	1	hence	hence	ADV
ejpam-5342	277	2	,	,	PUNCT
ejpam-5342	277	3	x	x	PRON
ejpam-5342	277	4	,	,	PUNCT
ejpam-5342	277	5	y	y	PROPN
ejpam-5342	277	6	∈	∈	PROPN
ejpam-5342	277	7	sg	sg	VERB
ejpam-5342	277	8	and	and	CCONJ
ejpam-5342	277	9	(	(	PUNCT
ejpam-5342	277	10	iv	iv	X
ejpam-5342	277	11	)	)	PUNCT
ejpam-5342	277	12	holds	hold	NOUN
ejpam-5342	277	13	.	.	PUNCT
ejpam-5342	278	1	the	the	DET
ejpam-5342	278	2	proof	proof	NOUN
ejpam-5342	278	3	of	of	ADP
ejpam-5342	278	4	(	(	PUNCT
ejpam-5342	278	5	v	v	NOUN
ejpam-5342	278	6	)	)	PUNCT
ejpam-5342	278	7	is	be	AUX
ejpam-5342	278	8	similar	similar	ADJ
ejpam-5342	278	9	to	to	ADP
ejpam-5342	278	10	the	the	DET
ejpam-5342	278	11	proof	proof	NOUN
ejpam-5342	278	12	of	of	ADP
ejpam-5342	278	13	(	(	PUNCT
ejpam-5342	278	14	iv	iv	NOUN
ejpam-5342	278	15	)	)	PUNCT
ejpam-5342	278	16	.	.	PUNCT
ejpam-5342	279	1	next	next	ADV
ejpam-5342	279	2	,	,	PUNCT
ejpam-5342	279	3	let	let	VERB
ejpam-5342	279	4	x	x	PUNCT
ejpam-5342	279	5	∈	∈	PROPN
ejpam-5342	279	6	sg	sg	NOUN
ejpam-5342	279	7	and	and	CCONJ
ejpam-5342	279	8	q	q	PROPN
ejpam-5342	279	9	∈	∈	PROPN
ejpam-5342	279	10	sg	sg	PROPN
ejpam-5342	279	11	.	.	PUNCT
ejpam-5342	280	1	since	since	SCONJ
ejpam-5342	280	2	x	x	X
ejpam-5342	280	3	,	,	PUNCT
ejpam-5342	280	4	q	q	PROPN
ejpam-5342	280	5	∈	∈	PROPN
ejpam-5342	280	6	s	s	PART
ejpam-5342	280	7	and	and	CCONJ
ejpam-5342	280	8	x	x	SYM
ejpam-5342	280	9	̸=	̸=	PROPN
ejpam-5342	280	10	q	q	NOUN
ejpam-5342	280	11	,	,	PUNCT
ejpam-5342	280	12	by	by	ADP
ejpam-5342	280	13	connectedness	connectedness	NOUN
ejpam-5342	280	14	of	of	ADP
ejpam-5342	280	15	⟨s⟩	⟨s⟩	PROPN
ejpam-5342	280	16	,	,	PUNCT
ejpam-5342	280	17	there	there	PRON
ejpam-5342	280	18	exists	exist	VERB
ejpam-5342	280	19	an	an	DET
ejpam-5342	280	20	x	x	NOUN
ejpam-5342	280	21	-	-	ADJ
ejpam-5342	280	22	q	q	ADJ
ejpam-5342	280	23	path	path	NOUN
ejpam-5342	280	24	p	p	X
ejpam-5342	281	1	[	[	X
ejpam-5342	281	2	x	x	X
ejpam-5342	281	3	,	,	PUNCT
ejpam-5342	281	4	q	q	X
ejpam-5342	281	5	]	]	X
ejpam-5342	281	6	in	in	ADP
ejpam-5342	281	7	s.	s.	PROPN
ejpam-5342	281	8	if	if	SCONJ
ejpam-5342	281	9	xq	xq	PROPN
ejpam-5342	281	10	∈	∈	PROPN
ejpam-5342	281	11	e(g	e(g	PROPN
ejpam-5342	281	12	)	)	PUNCT
ejpam-5342	281	13	,	,	PUNCT
ejpam-5342	281	14	then	then	ADV
ejpam-5342	281	15	q	q	PROPN
ejpam-5342	281	16	∈	∈	PROPN
ejpam-5342	281	17	p	p	X
ejpam-5342	282	1	[	[	X
ejpam-5342	282	2	x	x	X
ejpam-5342	282	3	,	,	PUNCT
ejpam-5342	282	4	q	q	X
ejpam-5342	282	5	]	]	X
ejpam-5342	282	6	impyling	impyle	VERB
ejpam-5342	282	7	that	that	DET
ejpam-5342	282	8	q	q	PROPN
ejpam-5342	282	9	∈	∈	PROPN
ejpam-5342	282	10	sg	sg	PROPN
ejpam-5342	282	11	.	.	PUNCT
ejpam-5342	283	1	on	on	ADP
ejpam-5342	283	2	the	the	DET
ejpam-5342	283	3	other	other	ADJ
ejpam-5342	283	4	hand	hand	NOUN
ejpam-5342	283	5	,	,	PUNCT
ejpam-5342	283	6	if	if	SCONJ
ejpam-5342	283	7	xq	xq	PROPN
ejpam-5342	283	8	/∈	/∈	PROPN
ejpam-5342	283	9	e(g	e(g	PROPN
ejpam-5342	283	10	)	)	PUNCT
ejpam-5342	283	11	,	,	PUNCT
ejpam-5342	283	12	then	then	ADV
ejpam-5342	283	13	x	x	X
ejpam-5342	283	14	∈	∈	PROPN
ejpam-5342	283	15	p	p	X
ejpam-5342	284	1	[	[	X
ejpam-5342	284	2	x	x	X
ejpam-5342	284	3	,	,	PUNCT
ejpam-5342	284	4	q	q	X
ejpam-5342	284	5	]	]	X
ejpam-5342	284	6	,	,	PUNCT
ejpam-5342	284	7	showing	show	VERB
ejpam-5342	284	8	that	that	SCONJ
ejpam-5342	284	9	x	x	PROPN
ejpam-5342	284	10	∈	∈	PROPN
ejpam-5342	284	11	sg	sg	PROPN
ejpam-5342	284	12	.	.	PUNCT
ejpam-5342	285	1	hence	hence	ADV
ejpam-5342	285	2	,	,	PUNCT
ejpam-5342	285	3	(	(	PUNCT
ejpam-5342	285	4	vi	vi	NOUN
ejpam-5342	285	5	)	)	PUNCT
ejpam-5342	285	6	holds	hold	VERB
ejpam-5342	285	7	.	.	PUNCT
ejpam-5342	286	1	let	let	VERB
ejpam-5342	286	2	x	x	SYM
ejpam-5342	286	3	∈	∈	PROPN
ejpam-5342	286	4	v	v	NOUN
ejpam-5342	286	5	(	(	PUNCT
ejpam-5342	286	6	g)\sg	g)\sg	PROPN
ejpam-5342	286	7	such	such	ADJ
ejpam-5342	286	8	that	that	SCONJ
ejpam-5342	286	9	ng(x	ng(x	NUM
ejpam-5342	286	10	,	,	PUNCT
ejpam-5342	286	11	2	2	X
ejpam-5342	286	12	)	)	PUNCT
ejpam-5342	286	13	∩	∩	NOUN
ejpam-5342	286	14	sg	sg	ADP
ejpam-5342	286	15	=	=	PUNCT
ejpam-5342	286	16	∅.	∅.	NOUN
ejpam-5342	286	17	since	since	SCONJ
ejpam-5342	286	18	s	s	PRON
ejpam-5342	286	19	is	be	AUX
ejpam-5342	286	20	a	a	DET
ejpam-5342	286	21	hop	hop	NOUN
ejpam-5342	286	22	dominating	dominating	NOUN
ejpam-5342	286	23	set	set	NOUN
ejpam-5342	286	24	of	of	ADP
ejpam-5342	286	25	gg	gg	PROPN
ejpam-5342	286	26	and	and	CCONJ
ejpam-5342	286	27	x	x	SYM
ejpam-5342	286	28	/∈	/∈	PROPN
ejpam-5342	286	29	s	s	X
ejpam-5342	286	30	,	,	PUNCT
ejpam-5342	286	31	there	there	PRON
ejpam-5342	286	32	exist	exist	VERB
ejpam-5342	287	1	z	z	PROPN
ejpam-5342	287	2	∈	∈	PROPN
ejpam-5342	287	3	s	s	VERB
ejpam-5342	287	4	such	such	ADJ
ejpam-5342	287	5	that	that	SCONJ
ejpam-5342	287	6	dgg(x	dgg(x	PROPN
ejpam-5342	287	7	,	,	PUNCT
ejpam-5342	287	8	z	z	NOUN
ejpam-5342	287	9	)	)	PUNCT
ejpam-5342	287	10	=	=	SYM
ejpam-5342	288	1	2	2	X
ejpam-5342	288	2	.	.	X
ejpam-5342	289	1	sinceng(x	sinceng(x	ADV
ejpam-5342	289	2	,	,	PUNCT
ejpam-5342	289	3	2	2	X
ejpam-5342	289	4	)	)	PUNCT
ejpam-5342	289	5	∩	∩	NOUN
ejpam-5342	289	6	sg	sg	ADP
ejpam-5342	289	7	=	=	SYM
ejpam-5342	289	8	∅	∅	NOUN
ejpam-5342	289	9	,	,	PUNCT
ejpam-5342	289	10	either	either	CCONJ
ejpam-5342	289	11	z	z	X
ejpam-5342	289	12	=	=	PUNCT
ejpam-5342	289	13	p	p	NOUN
ejpam-5342	289	14	∈	∈	PROPN
ejpam-5342	289	15	sg	sg	NOUN
ejpam-5342	289	16	for	for	ADP
ejpam-5342	289	17	some	some	DET
ejpam-5342	289	18	p	p	NOUN
ejpam-5342	289	19	∈	∈	PROPN
ejpam-5342	289	20	v	v	ADP
ejpam-5342	289	21	(	(	PUNCT
ejpam-5342	289	22	g	g	NOUN
ejpam-5342	289	23	)	)	PUNCT
ejpam-5342	289	24	∩	∩	NOUN
ejpam-5342	289	25	ng(x	ng(x	NUM
ejpam-5342	289	26	)	)	PUNCT
ejpam-5342	289	27	or	or	CCONJ
ejpam-5342	289	28	p	p	NOUN
ejpam-5342	289	29	∈	∈	PROPN
ejpam-5342	289	30	v	v	ADP
ejpam-5342	289	31	(	(	PUNCT
ejpam-5342	289	32	g	g	NOUN
ejpam-5342	289	33	)	)	PUNCT
ejpam-5342	289	34	∩	∩	NOUN
ejpam-5342	289	35	ng(x	ng(x	NUM
ejpam-5342	289	36	)	)	PUNCT
ejpam-5342	289	37	.	.	PUNCT
ejpam-5342	290	1	hence	hence	ADV
ejpam-5342	290	2	,	,	PUNCT
ejpam-5342	290	3	(	(	PUNCT
ejpam-5342	290	4	vii	vii	PROPN
ejpam-5342	290	5	)	)	PUNCT
ejpam-5342	290	6	holds	hold	VERB
ejpam-5342	290	7	.	.	PUNCT
ejpam-5342	291	1	statement	statement	NOUN
ejpam-5342	291	2	(	(	PUNCT
ejpam-5342	291	3	viii	viii	NOUN
ejpam-5342	291	4	)	)	PUNCT
ejpam-5342	291	5	can	can	AUX
ejpam-5342	291	6	be	be	AUX
ejpam-5342	291	7	shown	show	VERB
ejpam-5342	291	8	similarly	similarly	ADV
ejpam-5342	291	9	with	with	ADP
ejpam-5342	291	10	(	(	PUNCT
ejpam-5342	291	11	vii	vii	PROPN
ejpam-5342	291	12	)	)	PUNCT
ejpam-5342	291	13	.	.	PUNCT
ejpam-5342	292	1	for	for	ADP
ejpam-5342	292	2	the	the	DET
ejpam-5342	292	3	converse	converse	NOUN
ejpam-5342	292	4	,	,	PUNCT
ejpam-5342	292	5	let	let	VERB
ejpam-5342	292	6	s	s	PRON
ejpam-5342	292	7	=	=	VERB
ejpam-5342	292	8	sg	sg	X
ejpam-5342	292	9	∪	∪	ADJ
ejpam-5342	292	10	sg	sg	ADP
ejpam-5342	292	11	where	where	SCONJ
ejpam-5342	292	12	sg	sg	PROPN
ejpam-5342	292	13	⊆	⊆	NUM
ejpam-5342	292	14	v	v	NOUN
ejpam-5342	292	15	(	(	PUNCT
ejpam-5342	292	16	g	g	NOUN
ejpam-5342	292	17	)	)	PUNCT
ejpam-5342	292	18	and	and	CCONJ
ejpam-5342	292	19	sg	sg	ADP
ejpam-5342	292	20	⊆	⊆	NUM
ejpam-5342	292	21	v	v	NOUN
ejpam-5342	292	22	(	(	PUNCT
ejpam-5342	292	23	g	g	NOUN
ejpam-5342	292	24	)	)	PUNCT
ejpam-5342	292	25	and	and	CCONJ
ejpam-5342	292	26	conditions	condition	NOUN
ejpam-5342	292	27	(	(	PUNCT
ejpam-5342	292	28	i)-(viii	i)-(viii	X
ejpam-5342	292	29	)	)	PUNCT
ejpam-5342	292	30	are	be	AUX
ejpam-5342	292	31	satisfied	satisfied	ADJ
ejpam-5342	292	32	.	.	PUNCT
ejpam-5342	293	1	first	first	ADV
ejpam-5342	293	2	,	,	PUNCT
ejpam-5342	293	3	we	we	PRON
ejpam-5342	293	4	show	show	VERB
ejpam-5342	293	5	that	that	SCONJ
ejpam-5342	293	6	⟨s⟩	⟨s⟩	PROPN
ejpam-5342	293	7	is	be	AUX
ejpam-5342	293	8	connected	connect	VERB
ejpam-5342	293	9	.	.	PUNCT
ejpam-5342	294	1	let	let	VERB
ejpam-5342	294	2	x	x	PRON
ejpam-5342	294	3	,	,	PUNCT
ejpam-5342	294	4	y	y	PROPN
ejpam-5342	294	5	∈	∈	PROPN
ejpam-5342	294	6	s	s	PART
ejpam-5342	294	7	with	with	ADP
ejpam-5342	294	8	x	x	PART
ejpam-5342	294	9	̸=	̸=	PROPN
ejpam-5342	294	10	y.	y.	NOUN
ejpam-5342	294	11	if	if	SCONJ
ejpam-5342	294	12	xy	xy	PROPN
ejpam-5342	294	13	∈	∈	PROPN
ejpam-5342	294	14	e(gg	e(gg	PROPN
ejpam-5342	294	15	)	)	PUNCT
ejpam-5342	294	16	,	,	PUNCT
ejpam-5342	294	17	then	then	ADV
ejpam-5342	294	18	we	we	PRON
ejpam-5342	294	19	are	be	AUX
ejpam-5342	294	20	done	do	VERB
ejpam-5342	294	21	.	.	PUNCT
ejpam-5342	295	1	suppose	suppose	VERB
ejpam-5342	295	2	xy	xy	PROPN
ejpam-5342	295	3	/∈	/∈	PUNCT
ejpam-5342	295	4	e(gg	e(gg	NUM
ejpam-5342	295	5	)	)	PUNCT
ejpam-5342	295	6	.	.	PUNCT
ejpam-5342	296	1	consider	consider	VERB
ejpam-5342	296	2	the	the	DET
ejpam-5342	296	3	following	follow	VERB
ejpam-5342	296	4	cases	case	NOUN
ejpam-5342	296	5	.	.	PUNCT
ejpam-5342	297	1	case	case	NOUN
ejpam-5342	297	2	1	1	NUM
ejpam-5342	297	3	.	.	NUM
ejpam-5342	298	1	x	x	X
ejpam-5342	298	2	,	,	PUNCT
ejpam-5342	298	3	y	y	PROPN
ejpam-5342	298	4	∈	∈	PROPN
ejpam-5342	298	5	sg	sg	INTJ
ejpam-5342	298	6	if	if	SCONJ
ejpam-5342	298	7	⟨sg⟩	⟨sg⟩	PRON
ejpam-5342	298	8	is	be	AUX
ejpam-5342	298	9	connected	connect	VERB
ejpam-5342	298	10	,	,	PUNCT
ejpam-5342	298	11	then	then	ADV
ejpam-5342	298	12	an	an	DET
ejpam-5342	298	13	x	x	PROPN
ejpam-5342	298	14	-	-	ADJ
ejpam-5342	298	15	y	y	PROPN
ejpam-5342	298	16	path	path	NOUN
ejpam-5342	298	17	p	p	PROPN
ejpam-5342	299	1	[	[	X
ejpam-5342	299	2	x	x	X
ejpam-5342	299	3	,	,	PUNCT
ejpam-5342	299	4	y	y	PROPN
ejpam-5342	299	5	]	]	PUNCT
ejpam-5342	299	6	in	in	ADP
ejpam-5342	299	7	sg	sg	ADP
ejpam-5342	299	8	exists	exist	VERB
ejpam-5342	299	9	.	.	PUNCT
ejpam-5342	300	1	since	since	SCONJ
ejpam-5342	300	2	sg	sg	ADP
ejpam-5342	300	3	⊆	⊆	NUM
ejpam-5342	300	4	s	s	NOUN
ejpam-5342	300	5	,	,	PUNCT
ejpam-5342	300	6	p	p	X
ejpam-5342	300	7	[	[	X
ejpam-5342	300	8	x	x	X
ejpam-5342	300	9	,	,	PUNCT
ejpam-5342	300	10	y	y	PROPN
ejpam-5342	300	11	]	]	X
ejpam-5342	300	12	is	be	AUX
ejpam-5342	300	13	an	an	DET
ejpam-5342	300	14	x	x	ADJ
ejpam-5342	300	15	-	-	ADJ
ejpam-5342	300	16	y	y	ADJ
ejpam-5342	300	17	path	path	NOUN
ejpam-5342	300	18	in	in	ADP
ejpam-5342	300	19	s.	s.	PROPN
ejpam-5342	300	20	suppose	suppose	VERB
ejpam-5342	300	21	sg	sg	PROPN
ejpam-5342	300	22	is	be	AUX
ejpam-5342	300	23	not	not	PART
ejpam-5342	300	24	connected	connect	VERB
ejpam-5342	300	25	.	.	PUNCT
ejpam-5342	301	1	then	then	ADV
ejpam-5342	301	2	by	by	ADP
ejpam-5342	301	3	(	(	PUNCT
ejpam-5342	301	4	iv	iv	X
ejpam-5342	301	5	)	)	PUNCT
ejpam-5342	301	6	,	,	PUNCT
ejpam-5342	301	7	x	x	X
ejpam-5342	301	8	,	,	PUNCT
ejpam-5342	301	9	y	y	PROPN
ejpam-5342	301	10	∈	∈	PROPN
ejpam-5342	301	11	sg	sg	PROPN
ejpam-5342	301	12	.	.	PUNCT
ejpam-5342	302	1	thus	thus	ADV
ejpam-5342	302	2	,	,	PUNCT
ejpam-5342	302	3	[	[	X
ejpam-5342	302	4	x	x	X
ejpam-5342	302	5	,	,	PUNCT
ejpam-5342	302	6	x	x	PROPN
ejpam-5342	302	7	,	,	PUNCT
ejpam-5342	302	8	y	y	PROPN
ejpam-5342	302	9	,	,	PUNCT
ejpam-5342	302	10	y	y	PROPN
ejpam-5342	302	11	]	]	PUNCT
ejpam-5342	302	12	is	be	AUX
ejpam-5342	302	13	a	a	DET
ejpam-5342	302	14	path	path	NOUN
ejpam-5342	302	15	in	in	ADP
ejpam-5342	302	16	s.	s.	PROPN
ejpam-5342	302	17	case2	case2	PROPN
ejpam-5342	302	18	.	.	PUNCT
ejpam-5342	303	1	x	x	X
ejpam-5342	303	2	,	,	PUNCT
ejpam-5342	303	3	y	y	PROPN
ejpam-5342	303	4	∈	∈	PROPN
ejpam-5342	303	5	sg	sg	ADV
ejpam-5342	303	6	same	same	ADJ
ejpam-5342	303	7	with	with	ADP
ejpam-5342	303	8	case	case	NOUN
ejpam-5342	303	9	1	1	NUM
ejpam-5342	303	10	using	use	VERB
ejpam-5342	303	11	(	(	PUNCT
ejpam-5342	303	12	v	v	NOUN
ejpam-5342	303	13	)	)	PUNCT
ejpam-5342	303	14	.	.	PUNCT
ejpam-5342	304	1	case	case	NOUN
ejpam-5342	304	2	3.x	3.x	NUM
ejpam-5342	304	3	∈	∈	PROPN
ejpam-5342	304	4	sg	sg	PROPN
ejpam-5342	304	5	,	,	PUNCT
ejpam-5342	304	6	y	y	PROPN
ejpam-5342	304	7	∈	∈	PROPN
ejpam-5342	304	8	sg	sg	AUX
ejpam-5342	304	9	let	let	VERB
ejpam-5342	304	10	y	y	NOUN
ejpam-5342	304	11	=	=	PUNCT
ejpam-5342	304	12	p	p	PROPN
ejpam-5342	304	13	for	for	ADP
ejpam-5342	304	14	some	some	DET
ejpam-5342	304	15	p	p	NOUN
ejpam-5342	304	16	∈	∈	PROPN
ejpam-5342	304	17	v	v	NOUN
ejpam-5342	304	18	(	(	PUNCT
ejpam-5342	304	19	g	g	NOUN
ejpam-5342	304	20	)	)	PUNCT
ejpam-5342	304	21	.	.	PUNCT
ejpam-5342	305	1	then	then	ADV
ejpam-5342	305	2	by	by	ADP
ejpam-5342	305	3	(	(	PUNCT
ejpam-5342	305	4	vi	vi	NOUN
ejpam-5342	305	5	)	)	PUNCT
ejpam-5342	305	6	,	,	PUNCT
ejpam-5342	305	7	either	either	CCONJ
ejpam-5342	305	8	the	the	DET
ejpam-5342	305	9	path	path	NOUN
ejpam-5342	305	10	[	[	X
ejpam-5342	305	11	x	x	X
ejpam-5342	305	12	,	,	PUNCT
ejpam-5342	305	13	p	p	X
ejpam-5342	305	14	,	,	PUNCT
ejpam-5342	305	15	y	y	PROPN
ejpam-5342	305	16	]	]	PUNCT
ejpam-5342	305	17	or	or	CCONJ
ejpam-5342	305	18	[	[	X
ejpam-5342	305	19	x	x	X
ejpam-5342	305	20	,	,	PUNCT
ejpam-5342	305	21	x	x	X
ejpam-5342	305	22	,	,	PUNCT
ejpam-5342	305	23	y	y	PROPN
ejpam-5342	305	24	]	]	PUNCT
ejpam-5342	305	25	is	be	AUX
ejpam-5342	305	26	in	in	ADP
ejpam-5342	305	27	s.	s.	PROPN
ejpam-5342	305	28	therefore	therefore	ADV
ejpam-5342	305	29	,	,	PUNCT
ejpam-5342	305	30	in	in	ADP
ejpam-5342	305	31	any	any	DET
ejpam-5342	305	32	case	case	NOUN
ejpam-5342	305	33	,	,	PUNCT
ejpam-5342	305	34	⟨s⟩	⟨s⟩	PROPN
ejpam-5342	305	35	is	be	AUX
ejpam-5342	305	36	connected	connect	VERB
ejpam-5342	305	37	.	.	PUNCT
ejpam-5342	306	1	since	since	SCONJ
ejpam-5342	306	2	v	v	NOUN
ejpam-5342	306	3	(	(	PUNCT
ejpam-5342	306	4	g)\sg	g)\sg	PROPN
ejpam-5342	306	5	and	and	CCONJ
ejpam-5342	306	6	v	v	NOUN
ejpam-5342	306	7	(	(	PUNCT
ejpam-5342	306	8	g)\sg	g)\sg	PROPN
ejpam-5342	306	9	are	be	AUX
ejpam-5342	306	10	independent	independent	ADJ
ejpam-5342	306	11	in	in	ADP
ejpam-5342	306	12	g	g	PROPN
ejpam-5342	306	13	and	and	CCONJ
ejpam-5342	306	14	g	g	NOUN
ejpam-5342	306	15	,	,	PUNCT
ejpam-5342	306	16	respectively	respectively	ADV
ejpam-5342	306	17	by	by	ADP
ejpam-5342	306	18	(	(	PUNCT
ejpam-5342	306	19	ii	ii	NOUN
ejpam-5342	306	20	)	)	PUNCT
ejpam-5342	306	21	and	and	CCONJ
ejpam-5342	306	22	v	v	NOUN
ejpam-5342	306	23	(	(	PUNCT
ejpam-5342	306	24	gg)\s	gg)\s	NOUN
ejpam-5342	306	25	=	=	SYM
ejpam-5342	306	26	(	(	PUNCT
ejpam-5342	306	27	v	v	X
ejpam-5342	306	28	(	(	PUNCT
ejpam-5342	306	29	g)\sg	g)\sg	PROPN
ejpam-5342	306	30	)	)	PUNCT
ejpam-5342	306	31	∪	∪	NOUN
ejpam-5342	306	32	(	(	PUNCT
ejpam-5342	306	33	v	v	NOUN
ejpam-5342	306	34	(	(	PUNCT
ejpam-5342	306	35	g)\sg	g)\sg	PROPN
ejpam-5342	306	36	)	)	PUNCT
ejpam-5342	306	37	,	,	PUNCT
ejpam-5342	306	38	we	we	PRON
ejpam-5342	306	39	have	have	VERB
ejpam-5342	306	40	v	v	NOUN
ejpam-5342	306	41	(	(	PUNCT
ejpam-5342	306	42	gg)\s	gg)\s	NOUN
ejpam-5342	306	43	is	be	AUX
ejpam-5342	306	44	independent	independent	ADJ
ejpam-5342	306	45	.	.	PUNCT
ejpam-5342	307	1	finally	finally	ADV
ejpam-5342	307	2	,	,	PUNCT
ejpam-5342	307	3	let	let	VERB
ejpam-5342	307	4	x	x	PUNCT
ejpam-5342	307	5	∈	∈	PROPN
ejpam-5342	307	6	v	v	NOUN
ejpam-5342	307	7	(	(	PUNCT
ejpam-5342	307	8	gg)\s	gg)\s	NOUN
ejpam-5342	307	9	.	.	PUNCT
ejpam-5342	308	1	consider	consider	VERB
ejpam-5342	308	2	the	the	DET
ejpam-5342	308	3	following	follow	VERB
ejpam-5342	308	4	cases	case	NOUN
ejpam-5342	308	5	.	.	PUNCT
ejpam-5342	309	1	case	case	NOUN
ejpam-5342	309	2	1	1	NUM
ejpam-5342	309	3	.	.	PUNCT
ejpam-5342	309	4	x	x	SYM
ejpam-5342	310	1	∈	∈	NOUN
ejpam-5342	310	2	v	v	X
ejpam-5342	310	3	(	(	PUNCT
ejpam-5342	310	4	g)\sg	g)\sg	PROPN
ejpam-5342	310	5	if	if	SCONJ
ejpam-5342	310	6	ng(x	ng(x	NUM
ejpam-5342	310	7	,	,	PUNCT
ejpam-5342	310	8	2)∩sg	2)∩sg	NUM
ejpam-5342	310	9	̸=	̸=	NOUN
ejpam-5342	310	10	∅	∅	NOUN
ejpam-5342	310	11	,	,	PUNCT
ejpam-5342	310	12	then	then	ADV
ejpam-5342	310	13	dgg(x	dgg(x	PRON
ejpam-5342	310	14	,	,	PUNCT
ejpam-5342	310	15	y	y	NOUN
ejpam-5342	310	16	)	)	PUNCT
ejpam-5342	310	17	=	=	SYM
ejpam-5342	310	18	2	2	NUM
ejpam-5342	310	19	for	for	ADP
ejpam-5342	310	20	some	some	DET
ejpam-5342	310	21	y	y	PROPN
ejpam-5342	310	22	∈	∈	PROPN
ejpam-5342	310	23	ng(x	ng(x	NUM
ejpam-5342	310	24	,	,	PUNCT
ejpam-5342	310	25	2)∩sg	2)∩sg	NUM
ejpam-5342	310	26	.	.	PUNCT
ejpam-5342	311	1	suppose	suppose	VERB
ejpam-5342	311	2	ng(x	ng(x	NOUN
ejpam-5342	311	3	,	,	PUNCT
ejpam-5342	311	4	2)∩	2)∩	NOUN
ejpam-5342	311	5	sg	sg	ADP
ejpam-5342	311	6	=	=	PUNCT
ejpam-5342	311	7	∅.	∅.	NOUN
ejpam-5342	311	8	then	then	ADV
ejpam-5342	311	9	by	by	ADP
ejpam-5342	311	10	(	(	PUNCT
ejpam-5342	311	11	vii	vii	PROPN
ejpam-5342	311	12	)	)	PUNCT
ejpam-5342	311	13	,	,	PUNCT
ejpam-5342	311	14	there	there	PRON
ejpam-5342	311	15	exists	exist	VERB
ejpam-5342	311	16	w	w	PROPN
ejpam-5342	311	17	∈	∈	PROPN
ejpam-5342	311	18	v	v	ADP
ejpam-5342	311	19	(	(	PUNCT
ejpam-5342	311	20	g	g	NOUN
ejpam-5342	311	21	)	)	PUNCT
ejpam-5342	311	22	∩	∩	NOUN
ejpam-5342	311	23	ng(x	ng(x	NUM
ejpam-5342	311	24	)	)	PUNCT
ejpam-5342	311	25	such	such	ADJ
ejpam-5342	311	26	that	that	SCONJ
ejpam-5342	311	27	w	w	PROPN
ejpam-5342	311	28	∈	∈	PROPN
ejpam-5342	311	29	sg	sg	PROPN
ejpam-5342	311	30	.	.	PUNCT
ejpam-5342	312	1	thus	thus	ADV
ejpam-5342	312	2	,	,	PUNCT
ejpam-5342	312	3	dgg(x	dgg(x	PRON
ejpam-5342	312	4	,	,	PUNCT
ejpam-5342	312	5	w	w	NOUN
ejpam-5342	312	6	)	)	PUNCT
ejpam-5342	312	7	=	=	SYM
ejpam-5342	312	8	2	2	X
ejpam-5342	312	9	.	.	NUM
ejpam-5342	312	10	references	reference	NOUN
ejpam-5342	312	11	2514	2514	NUM
ejpam-5342	312	12	case2	case2	NOUN
ejpam-5342	312	13	.	.	PUNCT
ejpam-5342	313	1	x	x	X
ejpam-5342	313	2	∈	∈	NOUN
ejpam-5342	313	3	v	v	X
ejpam-5342	313	4	(	(	PUNCT
ejpam-5342	313	5	g)\sg	g)\sg	PROPN
ejpam-5342	313	6	same	same	ADJ
ejpam-5342	313	7	with	with	ADP
ejpam-5342	313	8	case	case	NOUN
ejpam-5342	313	9	1	1	NUM
ejpam-5342	313	10	using	use	VERB
ejpam-5342	313	11	(	(	PUNCT
ejpam-5342	313	12	viii	viii	NOUN
ejpam-5342	313	13	)	)	PUNCT
ejpam-5342	313	14	.	.	PUNCT
ejpam-5342	314	1	hence	hence	ADV
ejpam-5342	314	2	,	,	PUNCT
ejpam-5342	314	3	in	in	ADP
ejpam-5342	314	4	any	any	DET
ejpam-5342	314	5	case	case	NOUN
ejpam-5342	314	6	,	,	PUNCT
ejpam-5342	314	7	s	s	VERB
ejpam-5342	314	8	is	be	AUX
ejpam-5342	314	9	a	a	DET
ejpam-5342	314	10	hop	hop	NOUN
ejpam-5342	314	11	dominating	dominating	NOUN
ejpam-5342	314	12	set	set	NOUN
ejpam-5342	314	13	of	of	ADP
ejpam-5342	314	14	gg	gg	PROPN
ejpam-5342	314	15	.	.	PUNCT
ejpam-5342	315	1	accordingly	accordingly	ADV
ejpam-5342	315	2	,	,	PUNCT
ejpam-5342	315	3	s	s	VERB
ejpam-5342	315	4	is	be	AUX
ejpam-5342	315	5	a	a	DET
ejpam-5342	315	6	connected	connected	ADJ
ejpam-5342	315	7	co	co	NOUN
ejpam-5342	315	8	-	-	ADJ
ejpam-5342	315	9	independent	independent	ADJ
ejpam-5342	315	10	hop	hop	NOUN
ejpam-5342	315	11	dominating	dominating	NOUN
ejpam-5342	315	12	set	set	NOUN
ejpam-5342	315	13	of	of	ADP
ejpam-5342	315	14	gg	gg	PROPN
ejpam-5342	315	15	.	.	PUNCT
ejpam-5342	316	1	the	the	DET
ejpam-5342	316	2	following	following	ADJ
ejpam-5342	316	3	result	result	NOUN
ejpam-5342	316	4	follows	follow	VERB
ejpam-5342	316	5	from	from	ADP
ejpam-5342	316	6	theorem	theorem	ADJ
ejpam-5342	316	7	5	5	NUM
ejpam-5342	316	8	.	.	PUNCT
ejpam-5342	316	9	corollary	corollary	ADJ
ejpam-5342	316	10	3	3	X
ejpam-5342	316	11	.	.	PUNCT
ejpam-5342	317	1	let	let	VERB
ejpam-5342	317	2	g	g	PRON
ejpam-5342	317	3	be	be	AUX
ejpam-5342	317	4	a	a	DET
ejpam-5342	317	5	nontrivial	nontrivial	ADJ
ejpam-5342	317	6	connected	connect	VERB
ejpam-5342	317	7	noncomplete	noncomplete	ADJ
ejpam-5342	317	8	graph	graph	NOUN
ejpam-5342	317	9	.	.	PUNCT
ejpam-5342	318	1	then	then	ADV
ejpam-5342	318	2	2	2	NUM
ejpam-5342	318	3	≤	≤	NOUN
ejpam-5342	318	4	γch	γch	NOUN
ejpam-5342	318	5	,	,	PUNCT
ejpam-5342	318	6	coi(gg	coi(gg	NOUN
ejpam-5342	318	7	)	)	PUNCT
ejpam-5342	318	8	≤	≤	NOUN
ejpam-5342	318	9	2|v	2|v	PROPN
ejpam-5342	318	10	(	(	PUNCT
ejpam-5342	318	11	g)|	g)|	NOUN
ejpam-5342	318	12	−	−	PROPN
ejpam-5342	318	13	β(g	β(g	PROPN
ejpam-5342	318	14	)	)	PUNCT
ejpam-5342	318	15	.	.	PUNCT
ejpam-5342	319	1	remark	remark	PROPN
ejpam-5342	319	2	5	5	NUM
ejpam-5342	319	3	.	.	PUNCT
ejpam-5342	320	1	the	the	DET
ejpam-5342	320	2	strictly	strictly	ADV
ejpam-5342	320	3	inequality	inequality	NOUN
ejpam-5342	320	4	in	in	ADP
ejpam-5342	320	5	γch	γch	NOUN
ejpam-5342	320	6	,	,	PUNCT
ejpam-5342	320	7	coi(gg	coi(gg	NOUN
ejpam-5342	320	8	)	)	PUNCT
ejpam-5342	320	9	≤	≤	NOUN
ejpam-5342	320	10	2|v	2|v	NUM
ejpam-5342	320	11	(	(	PUNCT
ejpam-5342	320	12	g)|−β(g	g)|−β(g	PROPN
ejpam-5342	320	13	)	)	PUNCT
ejpam-5342	320	14	presented	present	VERB
ejpam-5342	320	15	in	in	ADP
ejpam-5342	320	16	corollary	corollary	ADJ
ejpam-5342	320	17	3	3	NUM
ejpam-5342	320	18	can	can	AUX
ejpam-5342	320	19	be	be	AUX
ejpam-5342	320	20	attained	attain	VERB
ejpam-5342	320	21	.	.	PUNCT
ejpam-5342	321	1	however	however	ADV
ejpam-5342	321	2	the	the	DET
ejpam-5342	321	3	given	give	VERB
ejpam-5342	321	4	upper	upper	ADJ
ejpam-5342	321	5	bound	bind	VERB
ejpam-5342	321	6	is	be	AUX
ejpam-5342	321	7	sharp	sharp	ADJ
ejpam-5342	321	8	.	.	PUNCT
ejpam-5342	321	9	example	example	NOUN
ejpam-5342	322	1	7	7	NUM
ejpam-5342	322	2	.	.	PUNCT
ejpam-5342	322	3	to	to	PART
ejpam-5342	322	4	illustrate	illustrate	VERB
ejpam-5342	322	5	remark	remark	NOUN
ejpam-5342	322	6	5	5	NUM
ejpam-5342	322	7	,	,	PUNCT
ejpam-5342	322	8	consider	consider	VERB
ejpam-5342	322	9	the	the	DET
ejpam-5342	322	10	path	path	NOUN
ejpam-5342	322	11	p6	p6	NOUN
ejpam-5342	322	12	=	=	PUNCT
ejpam-5342	323	1	[	[	X
ejpam-5342	323	2	v1	v1	NOUN
ejpam-5342	323	3	,	,	PUNCT
ejpam-5342	323	4	v2	v2	PROPN
ejpam-5342	323	5	,	,	PUNCT
ejpam-5342	323	6	v3	v3	PROPN
ejpam-5342	323	7	,	,	PUNCT
ejpam-5342	323	8	v4	v4	PROPN
ejpam-5342	323	9	,	,	PUNCT
ejpam-5342	323	10	v5	v5	PROPN
ejpam-5342	323	11	,	,	PUNCT
ejpam-5342	323	12	v6	v6	NOUN
ejpam-5342	323	13	]	]	PUNCT
ejpam-5342	323	14	.	.	PUNCT
ejpam-5342	324	1	it	it	PRON
ejpam-5342	324	2	can	can	AUX
ejpam-5342	324	3	be	be	AUX
ejpam-5342	324	4	verified	verify	VERB
ejpam-5342	324	5	that	that	SCONJ
ejpam-5342	324	6	the	the	DET
ejpam-5342	324	7	set	set	NOUN
ejpam-5342	324	8	{	{	PUNCT
ejpam-5342	324	9	v2	v2	PROPN
ejpam-5342	324	10	,	,	PUNCT
ejpam-5342	324	11	v3	v3	PROPN
ejpam-5342	324	12	,	,	PUNCT
ejpam-5342	324	13	v4	v4	PROPN
ejpam-5342	324	14	,	,	PUNCT
ejpam-5342	324	15	v5	v5	NOUN
ejpam-5342	324	16	,	,	PUNCT
ejpam-5342	324	17	v1	v1	NOUN
ejpam-5342	324	18	,	,	PUNCT
ejpam-5342	324	19	v2	v2	PROPN
ejpam-5342	324	20	,	,	PUNCT
ejpam-5342	324	21	v5	v5	PROPN
ejpam-5342	324	22	,	,	PUNCT
ejpam-5342	324	23	v6	v6	NOUN
ejpam-5342	324	24	}	}	PUNCT
ejpam-5342	324	25	is	be	AUX
ejpam-5342	324	26	a	a	DET
ejpam-5342	324	27	γch	γch	NOUN
ejpam-5342	324	28	,	,	PUNCT
ejpam-5342	324	29	coi	coi	NOUN
ejpam-5342	324	30	-	-	PUNCT
ejpam-5342	324	31	set	set	NOUN
ejpam-5342	324	32	of	of	ADP
ejpam-5342	324	33	p6p	p6p	PROPN
ejpam-5342	324	34	6	6	NUM
ejpam-5342	324	35	,	,	PUNCT
ejpam-5342	324	36	that	that	ADV
ejpam-5342	324	37	is	is	ADV
ejpam-5342	324	38	,	,	PUNCT
ejpam-5342	324	39	γch	γch	X
ejpam-5342	324	40	,	,	PUNCT
ejpam-5342	324	41	coi(p6p	coi(p6p	PROPN
ejpam-5342	324	42	6	6	NUM
ejpam-5342	324	43	)	)	PUNCT
ejpam-5342	324	44	=	=	SYM
ejpam-5342	324	45	8	8	X
ejpam-5342	324	46	.	.	PUNCT
ejpam-5342	325	1	however	however	ADV
ejpam-5342	325	2	,	,	PUNCT
ejpam-5342	325	3	2|v	2|v	PROPN
ejpam-5342	325	4	(	(	PUNCT
ejpam-5342	325	5	p6)|	p6)|	X
ejpam-5342	325	6	−	−	PROPN
ejpam-5342	325	7	β(p6	β(p6	NOUN
ejpam-5342	325	8	)	)	PUNCT
ejpam-5342	325	9	=	=	SYM
ejpam-5342	325	10	2(6	2(6	NUM
ejpam-5342	325	11	)	)	PUNCT
ejpam-5342	325	12	−	−	NOUN
ejpam-5342	325	13	3	3	NUM
ejpam-5342	325	14	=	=	SYM
ejpam-5342	325	15	9	9	NUM
ejpam-5342	325	16	.	.	PUNCT
ejpam-5342	326	1	hence	hence	ADV
ejpam-5342	326	2	,	,	PUNCT
ejpam-5342	326	3	strict	strict	ADJ
ejpam-5342	326	4	inequality	inequality	NOUN
ejpam-5342	326	5	is	be	AUX
ejpam-5342	326	6	attained	attain	VERB
ejpam-5342	326	7	.	.	PUNCT
ejpam-5342	327	1	on	on	ADP
ejpam-5342	327	2	the	the	DET
ejpam-5342	327	3	other	other	ADJ
ejpam-5342	327	4	hand	hand	NOUN
ejpam-5342	327	5	,	,	PUNCT
ejpam-5342	327	6	equality	equality	NOUN
ejpam-5342	327	7	is	be	AUX
ejpam-5342	327	8	attained	attain	VERB
ejpam-5342	327	9	for	for	ADP
ejpam-5342	327	10	c4	c4	NOUN
ejpam-5342	327	11	=	=	PUNCT
ejpam-5342	328	1	[	[	X
ejpam-5342	328	2	u1	u1	NOUN
ejpam-5342	328	3	,	,	PUNCT
ejpam-5342	328	4	u2	u2	NOUN
ejpam-5342	328	5	,	,	PUNCT
ejpam-5342	328	6	u3	u3	PROPN
ejpam-5342	328	7	,	,	PUNCT
ejpam-5342	328	8	u4	u4	PROPN
ejpam-5342	328	9	]	]	X
ejpam-5342	328	10	,	,	PUNCT
ejpam-5342	328	11	since	since	SCONJ
ejpam-5342	328	12	{	{	PUNCT
ejpam-5342	328	13	u1	u1	PROPN
ejpam-5342	328	14	,	,	PUNCT
ejpam-5342	328	15	u2	u2	NOUN
ejpam-5342	328	16	,	,	PUNCT
ejpam-5342	328	17	u3	u3	NOUN
ejpam-5342	328	18	,	,	PUNCT
ejpam-5342	328	19	u2	u2	NOUN
ejpam-5342	328	20	,	,	PUNCT
ejpam-5342	328	21	u3	u3	PROPN
ejpam-5342	328	22	,	,	PUNCT
ejpam-5342	328	23	u4	u4	PROPN
ejpam-5342	328	24	}	}	PUNCT
ejpam-5342	328	25	is	be	AUX
ejpam-5342	328	26	a	a	DET
ejpam-5342	328	27	γch	γch	NOUN
ejpam-5342	328	28	,	,	PUNCT
ejpam-5342	328	29	coi	coi	NOUN
ejpam-5342	328	30	-	-	PUNCT
ejpam-5342	328	31	set	set	NOUN
ejpam-5342	328	32	of	of	ADP
ejpam-5342	328	33	c4c4	c4c4	PROPN
ejpam-5342	328	34	,	,	PUNCT
ejpam-5342	328	35	that	that	ADV
ejpam-5342	328	36	is	is	ADV
ejpam-5342	328	37	,	,	PUNCT
ejpam-5342	328	38	γch	γch	NOUN
ejpam-5342	328	39	,	,	PUNCT
ejpam-5342	328	40	coi(c4c4	coi(c4c4	NOUN
ejpam-5342	328	41	)	)	PUNCT
ejpam-5342	328	42	=	=	SYM
ejpam-5342	328	43	6	6	NUM
ejpam-5342	328	44	=	=	SYM
ejpam-5342	328	45	2|v	2|v	PROPN
ejpam-5342	328	46	(	(	PUNCT
ejpam-5342	328	47	c4)|−β(c4	c4)|−β(c4	NOUN
ejpam-5342	328	48	)	)	PUNCT
ejpam-5342	328	49	.	.	PUNCT
ejpam-5342	329	1	figure	figure	VERB
ejpam-5342	329	2	4	4	NUM
ejpam-5342	329	3	:	:	PUNCT
ejpam-5342	329	4	connected	connected	ADJ
ejpam-5342	329	5	co	co	ADJ
ejpam-5342	329	6	-	-	ADJ
ejpam-5342	329	7	independent	independent	ADJ
ejpam-5342	329	8	hop	hop	NOUN
ejpam-5342	329	9	dominating	dominating	NOUN
ejpam-5342	329	10	set	set	NOUN
ejpam-5342	329	11	of	of	ADP
ejpam-5342	329	12	p6p	p6p	PROPN
ejpam-5342	329	13	6	6	NUM
ejpam-5342	329	14	and	and	CCONJ
ejpam-5342	329	15	c4c4	c4c4	VERB
ejpam-5342	329	16	acknowledgements	acknowledgement	NOUN
ejpam-5342	329	17	the	the	DET
ejpam-5342	329	18	authors	author	NOUN
ejpam-5342	329	19	would	would	AUX
ejpam-5342	329	20	like	like	VERB
ejpam-5342	329	21	to	to	PART
ejpam-5342	329	22	express	express	VERB
ejpam-5342	329	23	their	their	PRON
ejpam-5342	329	24	gratitude	gratitude	NOUN
ejpam-5342	329	25	to	to	ADP
ejpam-5342	329	26	the	the	DET
ejpam-5342	329	27	anonymous	anonymous	ADJ
ejpam-5342	329	28	reviewers	reviewer	NOUN
ejpam-5342	329	29	of	of	ADP
ejpam-5342	329	30	this	this	DET
ejpam-5342	329	31	study	study	NOUN
ejpam-5342	329	32	and	and	CCONJ
ejpam-5342	329	33	the	the	DET
ejpam-5342	329	34	editors	editor	NOUN
ejpam-5342	329	35	of	of	ADP
ejpam-5342	329	36	this	this	DET
ejpam-5342	329	37	journal	journal	NOUN
ejpam-5342	329	38	,	,	PUNCT
ejpam-5342	329	39	for	for	ADP
ejpam-5342	329	40	their	their	PRON
ejpam-5342	329	41	efforts	effort	NOUN
ejpam-5342	329	42	in	in	ADP
ejpam-5342	329	43	reviewing	review	VERB
ejpam-5342	329	44	this	this	DET
ejpam-5342	329	45	publication	publication	NOUN
ejpam-5342	329	46	.	.	PUNCT
ejpam-5342	330	1	references	reference	NOUN
ejpam-5342	330	2	[	[	X
ejpam-5342	330	3	1	1	NUM
ejpam-5342	330	4	]	]	PUNCT
ejpam-5342	330	5	m.	m.	NOUN
ejpam-5342	330	6	bonsocan	bonsocan	PROPN
ejpam-5342	330	7	,	,	PUNCT
ejpam-5342	330	8	i.	i.	PROPN
ejpam-5342	330	9	aniversario	aniversario	PROPN
ejpam-5342	330	10	.	.	PUNCT
ejpam-5342	331	1	on	on	ADP
ejpam-5342	331	2	connected	connected	ADJ
ejpam-5342	331	3	co	co	ADJ
ejpam-5342	331	4	-	-	ADJ
ejpam-5342	331	5	independent	independent	ADJ
ejpam-5342	331	6	domination	domination	NOUN
ejpam-5342	331	7	of	of	ADP
ejpam-5342	331	8	some	some	DET
ejpam-5342	331	9	graphs	graph	NOUN
ejpam-5342	331	10	.	.	PUNCT
ejpam-5342	332	1	undergraduate	undergraduate	ADJ
ejpam-5342	332	2	thesis	thesis	NOUN
ejpam-5342	332	3	,	,	PUNCT
ejpam-5342	332	4	2018	2018	NUM
ejpam-5342	332	5	.	.	PUNCT
ejpam-5342	333	1	[	[	X
ejpam-5342	333	2	2	2	NUM
ejpam-5342	333	3	]	]	PUNCT
ejpam-5342	333	4	c.	c.	PROPN
ejpam-5342	333	5	berge	berge	PROPN
ejpam-5342	333	6	.	.	PUNCT
ejpam-5342	334	1	theorie	theorie	PROPN
ejpam-5342	334	2	des	des	PROPN
ejpam-5342	334	3	graphes	graphes	PROPN
ejpam-5342	334	4	et	et	PROPN
ejpam-5342	334	5	ses	ses	PROPN
ejpam-5342	334	6	applications	application	NOUN
ejpam-5342	334	7	.	.	PUNCT
ejpam-5342	335	1	metheun	metheun	NOUN
ejpam-5342	335	2	and	and	CCONJ
ejpam-5342	335	3	wiley	wiley	PROPN
ejpam-5342	335	4	,	,	PUNCT
ejpam-5342	335	5	london	london	PROPN
ejpam-5342	335	6	and	and	CCONJ
ejpam-5342	335	7	new	new	PROPN
ejpam-5342	335	8	york	york	PROPN
ejpam-5342	335	9	,	,	PUNCT
ejpam-5342	335	10	1962	1962	NUM
ejpam-5342	335	11	.	.	PUNCT
ejpam-5342	336	1	[	[	X
ejpam-5342	336	2	3	3	X
ejpam-5342	336	3	]	]	X
ejpam-5342	336	4	b.	b.	PROPN
ejpam-5342	336	5	gayathri	gayathri	PROPN
ejpam-5342	336	6	and	and	CCONJ
ejpam-5342	336	7	s.	s.	PROPN
ejpam-5342	336	8	kaspar	kaspar	PROPN
ejpam-5342	336	9	.	.	PUNCT
ejpam-5342	337	1	connected	connect	VERB
ejpam-5342	337	2	co	co	ADJ
ejpam-5342	337	3	-	-	ADJ
ejpam-5342	337	4	independent	independent	ADJ
ejpam-5342	337	5	domination	domination	NOUN
ejpam-5342	337	6	of	of	ADP
ejpam-5342	337	7	a	a	DET
ejpam-5342	337	8	graph	graph	NOUN
ejpam-5342	337	9	.	.	PUNCT
ejpam-5342	338	1	international	international	ADJ
ejpam-5342	338	2	journal	journal	PROPN
ejpam-5342	338	3	contemp	contemp	NOUN
ejpam-5342	338	4	.	.	PUNCT
ejpam-5342	339	1	mathematics	mathematic	NOUN
ejpam-5342	339	2	and	and	CCONJ
ejpam-5342	339	3	sciences	science	NOUN
ejpam-5342	339	4	,	,	PUNCT
ejpam-5342	339	5	6:423–429	6:423–429	PROPN
ejpam-5342	339	6	,	,	PUNCT
ejpam-5342	339	7	2011	2011	NUM
ejpam-5342	339	8	.	.	PUNCT
ejpam-5342	340	1	references	reference	NOUN
ejpam-5342	340	2	2515	2515	NUM
ejpam-5342	340	3	[	[	X
ejpam-5342	340	4	4	4	NUM
ejpam-5342	340	5	]	]	PUNCT
ejpam-5342	340	6	f.	f.	PROPN
ejpam-5342	340	7	harary	harary	PROPN
ejpam-5342	340	8	.	.	PUNCT
ejpam-5342	341	1	graph	graph	NOUN
ejpam-5342	341	2	theory	theory	NOUN
ejpam-5342	341	3	.	.	PUNCT
ejpam-5342	342	1	addison	addison	PROPN
ejpam-5342	342	2	-	-	PUNCT
ejpam-5342	342	3	wesley	wesley	PROPN
ejpam-5342	342	4	publishing	publishing	PROPN
ejpam-5342	342	5	company	company	NOUN
ejpam-5342	342	6	,	,	PUNCT
ejpam-5342	342	7	usa	usa	PROPN
ejpam-5342	342	8	,	,	PUNCT
ejpam-5342	342	9	1969	1969	NUM
ejpam-5342	342	10	.	.	PUNCT
ejpam-5342	343	1	[	[	X
ejpam-5342	343	2	5	5	X
ejpam-5342	343	3	]	]	PUNCT
ejpam-5342	343	4	s.	s.	PROPN
ejpam-5342	343	5	canoy	canoy	PROPN
ejpam-5342	343	6	,	,	PUNCT
ejpam-5342	343	7	r.	r.	NOUN
ejpam-5342	343	8	mollejon	mollejon	NOUN
ejpam-5342	343	9	and	and	CCONJ
ejpam-5342	343	10	j.	j.	PROPN
ejpam-5342	343	11	canoy	canoy	PROPN
ejpam-5342	343	12	.	.	PUNCT
ejpam-5342	344	1	hop	hop	PROPN
ejpam-5342	344	2	dominating	dominating	NOUN
ejpam-5342	344	3	sets	set	NOUN
ejpam-5342	344	4	in	in	ADP
ejpam-5342	344	5	graphs	graph	NOUN
ejpam-5342	344	6	under	under	ADP
ejpam-5342	344	7	binary	binary	ADJ
ejpam-5342	344	8	operations	operation	NOUN
ejpam-5342	344	9	.	.	PUNCT
ejpam-5342	345	1	european	european	ADJ
ejpam-5342	345	2	journal	journal	PROPN
ejpam-5342	345	3	of	of	ADP
ejpam-5342	345	4	pure	pure	ADJ
ejpam-5342	345	5	and	and	CCONJ
ejpam-5342	345	6	applied	applied	ADJ
ejpam-5342	345	7	mathematics	mathematic	NOUN
ejpam-5342	345	8	,	,	PUNCT
ejpam-5342	345	9	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-5342	345	10	,	,	PUNCT
ejpam-5342	345	11	2019	2019	NUM
ejpam-5342	345	12	.	.	PUNCT
ejpam-5342	346	1	[	[	X
ejpam-5342	346	2	6	6	NUM
ejpam-5342	346	3	]	]	PUNCT
ejpam-5342	346	4	s.	s.	PROPN
ejpam-5342	346	5	nanding	nanding	PROPN
ejpam-5342	346	6	and	and	CCONJ
ejpam-5342	346	7	h.	h.	PROPN
ejpam-5342	346	8	rara	rara	PROPN
ejpam-5342	346	9	.	.	PUNCT
ejpam-5342	347	1	on	on	ADP
ejpam-5342	347	2	connected	connected	ADJ
ejpam-5342	347	3	co	co	ADJ
ejpam-5342	347	4	-	-	ADJ
ejpam-5342	347	5	independent	independent	ADJ
ejpam-5342	347	6	hop	hop	NOUN
ejpam-5342	347	7	domination	domination	NOUN
ejpam-5342	347	8	in	in	ADP
ejpam-5342	347	9	graphs	graph	NOUN
ejpam-5342	347	10	.	.	PUNCT
ejpam-5342	348	1	european	european	ADJ
ejpam-5342	348	2	journal	journal	PROPN
ejpam-5342	348	3	of	of	ADP
ejpam-5342	348	4	pure	pure	ADJ
ejpam-5342	348	5	and	and	CCONJ
ejpam-5342	348	6	applied	applied	ADJ
ejpam-5342	348	7	mathematics	mathematic	NOUN
ejpam-5342	348	8	,	,	PUNCT
ejpam-5342	348	9	14(4):1226–1236	14(4):1226–1236	NUM
ejpam-5342	348	10	,	,	PUNCT
ejpam-5342	348	11	2021	2021	NUM
ejpam-5342	348	12	.	.	PUNCT
ejpam-5342	349	1	[	[	X
ejpam-5342	349	2	7	7	X
ejpam-5342	349	3	]	]	X
ejpam-5342	349	4	c.	c.	PROPN
ejpam-5342	349	5	natarajan	natarajan	PROPN
ejpam-5342	349	6	and	and	CCONJ
ejpam-5342	349	7	s.	s.	PROPN
ejpam-5342	349	8	ayyaswamy	ayyaswamy	PROPN
ejpam-5342	349	9	.	.	PUNCT
ejpam-5342	350	1	hop	hop	PROPN
ejpam-5342	350	2	domination	domination	NOUN
ejpam-5342	350	3	in	in	ADP
ejpam-5342	350	4	graphs	graph	NOUN
ejpam-5342	350	5	-	-	PUNCT
ejpam-5342	350	6	ii	ii	NOUN
ejpam-5342	350	7	.	.	PUNCT
ejpam-5342	350	8	versita	versita	PROPN
ejpam-5342	350	9	,	,	PUNCT
ejpam-5342	350	10	23(2):187	23(2):187	NUM
ejpam-5342	350	11	–	–	PUNCT
ejpam-5342	350	12	199	199	NUM
ejpam-5342	350	13	,	,	PUNCT
ejpam-5342	350	14	2015	2015	NUM
ejpam-5342	350	15	.	.	PUNCT
ejpam-5342	351	1	[	[	X
ejpam-5342	351	2	8	8	NUM
ejpam-5342	351	3	]	]	PUNCT
ejpam-5342	351	4	s.	s.	PROPN
ejpam-5342	351	5	ayyaswamy	ayyaswamy	PROPN
ejpam-5342	351	6	,	,	PUNCT
ejpam-5342	351	7	c.	c.	PROPN
ejpam-5342	351	8	natarajan	natarajan	PROPN
ejpam-5342	351	9	and	and	CCONJ
ejpam-5342	351	10	g.	g.	PROPN
ejpam-5342	351	11	sathiamoorphy	sathiamoorphy	PROPN
ejpam-5342	351	12	.	.	PUNCT
ejpam-5342	352	1	a	a	DET
ejpam-5342	352	2	note	note	NOUN
ejpam-5342	352	3	on	on	ADP
ejpam-5342	352	4	hop	hop	NOUN
ejpam-5342	352	5	domination	domination	NOUN
ejpam-5342	352	6	number	number	NOUN
ejpam-5342	352	7	of	of	ADP
ejpam-5342	352	8	some	some	DET
ejpam-5342	352	9	special	special	ADJ
ejpam-5342	352	10	families	family	NOUN
ejpam-5342	352	11	of	of	ADP
ejpam-5342	352	12	graphs	graph	NOUN
ejpam-5342	352	13	.	.	PUNCT
ejpam-5342	353	1	international	international	ADJ
ejpam-5342	353	2	journal	journal	NOUN
ejpam-5342	353	3	of	of	ADP
ejpam-5342	353	4	pure	pure	ADJ
ejpam-5342	353	5	and	and	CCONJ
ejpam-5342	353	6	applied	applied	ADJ
ejpam-5342	353	7	mathematics	mathematic	NOUN
ejpam-5342	353	8	,	,	PUNCT
ejpam-5342	353	9	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-5342	353	10	,	,	PUNCT
ejpam-5342	353	11	2018	2018	NUM
ejpam-5342	353	12	.	.	PUNCT
ejpam-5342	354	1	[	[	X
ejpam-5342	354	2	9	9	NUM
ejpam-5342	354	3	]	]	X
ejpam-5342	354	4	y.	y.	NOUN
ejpam-5342	354	5	pabilona	pabilona	PROPN
ejpam-5342	354	6	and	and	CCONJ
ejpam-5342	354	7	h.	h.	PROPN
ejpam-5342	354	8	rara	rara	PROPN
ejpam-5342	354	9	.	.	PUNCT
ejpam-5342	355	1	connected	connect	VERB
ejpam-5342	355	2	hop	hop	NOUN
ejpam-5342	355	3	domination	domination	NOUN
ejpam-5342	355	4	in	in	ADP
ejpam-5342	355	5	graphs	graph	NOUN
ejpam-5342	355	6	under	under	ADP
ejpam-5342	355	7	some	some	DET
ejpam-5342	355	8	binary	binary	ADJ
ejpam-5342	355	9	operations	operation	NOUN
ejpam-5342	355	10	.	.	PUNCT
ejpam-5342	356	1	asian	asian	ADJ
ejpam-5342	356	2	-	-	PUNCT
ejpam-5342	356	3	european	european	ADJ
ejpam-5342	356	4	journal	journal	NOUN
ejpam-5342	356	5	of	of	ADP
ejpam-5342	356	6	mathematics	mathematic	NOUN
ejpam-5342	356	7	,	,	PUNCT
ejpam-5342	356	8	2018	2018	NUM
ejpam-5342	356	9	.	.	PUNCT
ejpam-5342	357	1	[	[	X
ejpam-5342	357	2	10	10	NUM
ejpam-5342	357	3	]	]	X
ejpam-5342	357	4	r.	r.	NOUN
ejpam-5342	357	5	detalla	detalla	PROPN
ejpam-5342	357	6	,	,	PUNCT
ejpam-5342	357	7	m.	m.	NOUN
ejpam-5342	357	8	perocho	perocho	PROPN
ejpam-5342	357	9	,	,	PUNCT
ejpam-5342	357	10	h.	h.	PROPN
ejpam-5342	357	11	rara	rara	PROPN
ejpam-5342	357	12	and	and	CCONJ
ejpam-5342	357	13	s.	s.	PROPN
ejpam-5342	357	14	canoy	canoy	PROPN
ejpam-5342	357	15	.	.	PUNCT
ejpam-5342	358	1	on	on	ADP
ejpam-5342	358	2	connected	connected	ADJ
ejpam-5342	358	3	co	co	ADJ
ejpam-5342	358	4	-	-	ADJ
ejpam-5342	358	5	independent	independent	ADJ
ejpam-5342	358	6	domination	domination	NOUN
ejpam-5342	358	7	in	in	ADP
ejpam-5342	358	8	the	the	DET
ejpam-5342	358	9	join	join	NOUN
ejpam-5342	358	10	,	,	PUNCT
ejpam-5342	358	11	corona	corona	NOUN
ejpam-5342	358	12	and	and	CCONJ
ejpam-5342	358	13	lexicographic	lexicographic	ADJ
ejpam-5342	358	14	product	product	NOUN
ejpam-5342	358	15	of	of	ADP
ejpam-5342	358	16	graphs	graph	NOUN
ejpam-5342	358	17	.	.	PUNCT
ejpam-5342	359	1	discrete	discrete	ADJ
ejpam-5342	359	2	mathematics	mathematic	NOUN
ejpam-5342	359	3	,	,	PUNCT
ejpam-5342	359	4	algorithms	algorithm	NOUN
ejpam-5342	359	5	and	and	CCONJ
ejpam-5342	359	6	applications	application	NOUN
ejpam-5342	359	7	,	,	PUNCT
ejpam-5342	359	8	2023	2023	NUM
ejpam-5342	359	9	.	.	PUNCT
ejpam-5342	360	1	[	[	X
ejpam-5342	360	2	11	11	NUM
ejpam-5342	360	3	]	]	X
ejpam-5342	360	4	g.	g.	NOUN
ejpam-5342	360	5	salasalan	salasalan	NOUN
ejpam-5342	360	6	and	and	CCONJ
ejpam-5342	360	7	s.	s.	PROPN
ejpam-5342	360	8	canoy	canoy	PROPN
ejpam-5342	360	9	.	.	PUNCT
ejpam-5342	361	1	global	global	ADJ
ejpam-5342	361	2	hop	hop	PROPN
ejpam-5342	361	3	domination	domination	NOUN
ejpam-5342	361	4	number	number	NOUN
ejpam-5342	361	5	of	of	ADP
ejpam-5342	361	6	graphs	graph	NOUN
ejpam-5342	361	7	.	.	PUNCT
ejpam-5342	362	1	european	european	ADJ
ejpam-5342	362	2	journal	journal	PROPN
ejpam-5342	362	3	of	of	ADP
ejpam-5342	362	4	pure	pure	ADJ
ejpam-5342	362	5	and	and	CCONJ
ejpam-5342	362	6	applied	applied	ADJ
ejpam-5342	362	7	mathematics	mathematic	NOUN
ejpam-5342	362	8	,	,	PUNCT
ejpam-5342	362	9	14(1):112–125	14(1):112–125	NUM
ejpam-5342	362	10	,	,	PUNCT
ejpam-5342	362	11	2021	2021	NUM
ejpam-5342	362	12	.	.	PUNCT