id	sid	tid	token	lemma	pos
ejpam-3506	1	1	european	european	PROPN
ejpam-3506	1	2	journal	journal	PROPN
ejpam-3506	1	3	of	of	ADP
ejpam-3506	1	4	pure	pure	ADJ
ejpam-3506	1	5	and	and	CCONJ
ejpam-3506	1	6	applied	apply	VERB
ejpam-3506	1	7	mathematics	mathematic	NOUN
ejpam-3506	1	8	vol	vol	NOUN
ejpam-3506	1	9	.	.	PROPN
ejpam-3506	2	1	12	12	NUM
ejpam-3506	2	2	,	,	PUNCT
ejpam-3506	2	3	no	no	INTJ
ejpam-3506	2	4	.	.	NOUN
ejpam-3506	2	5	3	3	NUM
ejpam-3506	2	6	,	,	PUNCT
ejpam-3506	2	7	2019	2019	NUM
ejpam-3506	2	8	,	,	PUNCT
ejpam-3506	2	9	1337	1337	NUM
ejpam-3506	2	10	-	-	SYM
ejpam-3506	2	11	1349	1349	NUM
ejpam-3506	2	12	issn	issn	PROPN
ejpam-3506	2	13	1307	1307	NUM
ejpam-3506	2	14	-	-	SYM
ejpam-3506	2	15	5543	5543	NUM
ejpam-3506	2	16	–	–	PUNCT
ejpam-3506	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3506	2	18	published	publish	VERB
ejpam-3506	2	19	by	by	ADP
ejpam-3506	2	20	new	new	PROPN
ejpam-3506	2	21	york	york	PROPN
ejpam-3506	2	22	business	business	PROPN
ejpam-3506	2	23	global	global	ADJ
ejpam-3506	2	24	neighborhood	neighborhood	NOUN
ejpam-3506	2	25	connected	connect	VERB
ejpam-3506	2	26	k	k	ADJ
ejpam-3506	2	27	-	-	PUNCT
ejpam-3506	2	28	fair	fair	ADJ
ejpam-3506	2	29	domination	domination	NOUN
ejpam-3506	2	30	under	under	ADP
ejpam-3506	2	31	some	some	DET
ejpam-3506	2	32	binary	binary	ADJ
ejpam-3506	2	33	operations	operation	NOUN
ejpam-3506	2	34	wardah	wardah	PROPN
ejpam-3506	2	35	m.	m.	NOUN
ejpam-3506	2	36	bent	bent	NOUN
ejpam-3506	2	37	-	-	PUNCT
ejpam-3506	2	38	usman1,∗	usman1,∗	NOUN
ejpam-3506	2	39	,	,	PUNCT
ejpam-3506	2	40	rowena	rowena	PROPN
ejpam-3506	2	41	t.	t.	PROPN
ejpam-3506	2	42	isla2	isla2	PROPN
ejpam-3506	2	43	,	,	PUNCT
ejpam-3506	2	44	sergio	sergio	PROPN
ejpam-3506	2	45	r.	r.	PROPN
ejpam-3506	2	46	canoy	canoy	PROPN
ejpam-3506	2	47	,	,	PUNCT
ejpam-3506	2	48	jr.2	jr.2	PROPN
ejpam-3506	2	49	1	1	NUM
ejpam-3506	2	50	mathematics	mathematics	PROPN
ejpam-3506	2	51	department	department	NOUN
ejpam-3506	2	52	,	,	PUNCT
ejpam-3506	2	53	college	college	NOUN
ejpam-3506	2	54	of	of	ADP
ejpam-3506	2	55	natural	natural	ADJ
ejpam-3506	2	56	sciences	science	NOUN
ejpam-3506	2	57	and	and	CCONJ
ejpam-3506	2	58	mathematics	mathematic	NOUN
ejpam-3506	2	59	,	,	PUNCT
ejpam-3506	2	60	mindanao	mindanao	PROPN
ejpam-3506	2	61	state	state	PROPN
ejpam-3506	2	62	university	university	NOUN
ejpam-3506	2	63	-	-	PUNCT
ejpam-3506	2	64	main	main	ADJ
ejpam-3506	2	65	campus	campus	NOUN
ejpam-3506	2	66	,	,	PUNCT
ejpam-3506	2	67	9700	9700	NUM
ejpam-3506	2	68	marawi	marawi	PROPN
ejpam-3506	2	69	city	city	PROPN
ejpam-3506	2	70	,	,	PUNCT
ejpam-3506	2	71	philippines	philippines	PROPN
ejpam-3506	2	72	2	2	NUM
ejpam-3506	2	73	department	department	NOUN
ejpam-3506	2	74	of	of	ADP
ejpam-3506	2	75	mathematics	mathematic	NOUN
ejpam-3506	2	76	and	and	CCONJ
ejpam-3506	2	77	statistics	statistic	NOUN
ejpam-3506	2	78	,	,	PUNCT
ejpam-3506	2	79	college	college	NOUN
ejpam-3506	2	80	of	of	ADP
ejpam-3506	2	81	science	science	NOUN
ejpam-3506	2	82	and	and	CCONJ
ejpam-3506	2	83	mathematics	mathematic	NOUN
ejpam-3506	2	84	,	,	PUNCT
ejpam-3506	2	85	center	center	NOUN
ejpam-3506	2	86	for	for	ADP
ejpam-3506	2	87	graph	graph	NOUN
ejpam-3506	2	88	theory	theory	NOUN
ejpam-3506	2	89	,	,	PUNCT
ejpam-3506	2	90	algebra	algebra	NOUN
ejpam-3506	2	91	,	,	PUNCT
ejpam-3506	2	92	and	and	CCONJ
ejpam-3506	2	93	analysis	analysis	NOUN
ejpam-3506	2	94	,	,	PUNCT
ejpam-3506	2	95	premier	premier	PROPN
ejpam-3506	2	96	research	research	PROPN
ejpam-3506	2	97	institute	institute	PROPN
ejpam-3506	2	98	of	of	ADP
ejpam-3506	2	99	science	science	NOUN
ejpam-3506	2	100	and	and	CCONJ
ejpam-3506	2	101	mathematics	mathematic	NOUN
ejpam-3506	2	102	,	,	PUNCT
ejpam-3506	2	103	mindanao	mindanao	PROPN
ejpam-3506	2	104	state	state	PROPN
ejpam-3506	2	105	university	university	PROPN
ejpam-3506	2	106	-	-	PUNCT
ejpam-3506	2	107	iligan	iligan	PROPN
ejpam-3506	2	108	institute	institute	PROPN
ejpam-3506	2	109	of	of	ADP
ejpam-3506	2	110	technology	technology	PROPN
ejpam-3506	2	111	,	,	PUNCT
ejpam-3506	2	112	9200	9200	NUM
ejpam-3506	2	113	iligan	iligan	ADJ
ejpam-3506	2	114	city	city	NOUN
ejpam-3506	2	115	,	,	PUNCT
ejpam-3506	2	116	philippines	philippine	NOUN
ejpam-3506	2	117	abstract	abstract	ADJ
ejpam-3506	2	118	.	.	PUNCT
ejpam-3506	3	1	let	let	VERB
ejpam-3506	3	2	g	g	PROPN
ejpam-3506	3	3	=	=	SYM
ejpam-3506	3	4	(	(	PUNCT
ejpam-3506	3	5	v	v	NOUN
ejpam-3506	3	6	(	(	PUNCT
ejpam-3506	3	7	g	g	NOUN
ejpam-3506	3	8	)	)	PUNCT
ejpam-3506	3	9	,	,	PUNCT
ejpam-3506	3	10	e(g	e(g	PROPN
ejpam-3506	3	11	)	)	PUNCT
ejpam-3506	3	12	)	)	PUNCT
ejpam-3506	4	1	be	be	AUX
ejpam-3506	4	2	a	a	DET
ejpam-3506	4	3	simple	simple	ADJ
ejpam-3506	4	4	graph	graph	NOUN
ejpam-3506	4	5	.	.	PUNCT
ejpam-3506	5	1	a	a	DET
ejpam-3506	5	2	neighborhood	neighborhood	NOUN
ejpam-3506	5	3	connected	connect	VERB
ejpam-3506	5	4	k	k	ADJ
ejpam-3506	5	5	-	-	ADJ
ejpam-3506	5	6	fair	fair	ADJ
ejpam-3506	5	7	dominating	dominating	NOUN
ejpam-3506	5	8	set	set	NOUN
ejpam-3506	5	9	(	(	PUNCT
ejpam-3506	5	10	nckfd	nckfd	NOUN
ejpam-3506	5	11	-	-	PUNCT
ejpam-3506	5	12	set	set	NOUN
ejpam-3506	5	13	)	)	PUNCT
ejpam-3506	5	14	is	be	AUX
ejpam-3506	5	15	a	a	DET
ejpam-3506	5	16	dominating	dominating	NOUN
ejpam-3506	5	17	set	set	NOUN
ejpam-3506	5	18	s	s	PROPN
ejpam-3506	5	19	⊆	⊆	NUM
ejpam-3506	5	20	v	v	NOUN
ejpam-3506	5	21	(	(	PUNCT
ejpam-3506	5	22	g	g	NOUN
ejpam-3506	5	23	)	)	PUNCT
ejpam-3506	5	24	such	such	ADJ
ejpam-3506	5	25	that	that	SCONJ
ejpam-3506	5	26	the	the	DET
ejpam-3506	5	27	|n(u)∩	|n(u)∩	PROPN
ejpam-3506	5	28	s|	s|	PROPN
ejpam-3506	5	29	=	=	SYM
ejpam-3506	5	30	k	k	NOUN
ejpam-3506	5	31	for	for	ADP
ejpam-3506	5	32	every	every	DET
ejpam-3506	5	33	u	u	PROPN
ejpam-3506	5	34	∈	∈	PROPN
ejpam-3506	5	35	v	v	NOUN
ejpam-3506	5	36	(	(	PUNCT
ejpam-3506	5	37	g)\s	g)\s	NOUN
ejpam-3506	5	38	and	and	CCONJ
ejpam-3506	5	39	the	the	DET
ejpam-3506	5	40	induced	induced	ADJ
ejpam-3506	5	41	subgraph	subgraph	NOUN
ejpam-3506	5	42	〈	〈	PROPN
ejpam-3506	5	43	n(s	n(s	NOUN
ejpam-3506	5	44	)	)	PUNCT
ejpam-3506	5	45	〉	〉	NOUN
ejpam-3506	5	46	of	of	ADP
ejpam-3506	5	47	s	s	PRON
ejpam-3506	5	48	is	be	AUX
ejpam-3506	5	49	connected	connect	VERB
ejpam-3506	5	50	.	.	PUNCT
ejpam-3506	6	1	the	the	DET
ejpam-3506	6	2	neighborhood	neighborhood	NOUN
ejpam-3506	6	3	connected	connect	VERB
ejpam-3506	6	4	k	k	ADJ
ejpam-3506	6	5	-	-	PUNCT
ejpam-3506	6	6	fair	fair	ADJ
ejpam-3506	6	7	domination	domination	NOUN
ejpam-3506	6	8	number	number	NOUN
ejpam-3506	6	9	of	of	ADP
ejpam-3506	6	10	g	g	NOUN
ejpam-3506	6	11	,	,	PUNCT
ejpam-3506	6	12	denoted	denote	VERB
ejpam-3506	6	13	by	by	ADP
ejpam-3506	6	14	γnckfd(g	γnckfd(g	PROPN
ejpam-3506	6	15	)	)	PUNCT
ejpam-3506	6	16	,	,	PUNCT
ejpam-3506	6	17	is	be	AUX
ejpam-3506	6	18	the	the	DET
ejpam-3506	6	19	minimum	minimum	ADJ
ejpam-3506	6	20	cardinality	cardinality	NOUN
ejpam-3506	6	21	of	of	ADP
ejpam-3506	6	22	an	an	DET
ejpam-3506	6	23	nckfd	nckfd	NOUN
ejpam-3506	6	24	-	-	PUNCT
ejpam-3506	6	25	set	set	NOUN
ejpam-3506	6	26	.	.	PUNCT
ejpam-3506	7	1	in	in	ADP
ejpam-3506	7	2	this	this	DET
ejpam-3506	7	3	paper	paper	NOUN
ejpam-3506	7	4	,	,	PUNCT
ejpam-3506	7	5	we	we	PRON
ejpam-3506	7	6	introduce	introduce	VERB
ejpam-3506	7	7	and	and	CCONJ
ejpam-3506	7	8	investigate	investigate	VERB
ejpam-3506	7	9	the	the	DET
ejpam-3506	7	10	notion	notion	NOUN
ejpam-3506	7	11	of	of	ADP
ejpam-3506	7	12	neighborhood	neighborhood	NOUN
ejpam-3506	7	13	connected	connect	VERB
ejpam-3506	7	14	k	k	ADJ
ejpam-3506	7	15	-	-	PUNCT
ejpam-3506	7	16	fair	fair	ADJ
ejpam-3506	7	17	domination	domination	NOUN
ejpam-3506	7	18	in	in	ADP
ejpam-3506	7	19	graphs	graph	NOUN
ejpam-3506	7	20	.	.	PUNCT
ejpam-3506	8	1	we	we	PRON
ejpam-3506	8	2	also	also	ADV
ejpam-3506	8	3	characterize	characterize	VERB
ejpam-3506	8	4	such	such	ADJ
ejpam-3506	8	5	dominating	dominating	NOUN
ejpam-3506	8	6	sets	set	NOUN
ejpam-3506	8	7	in	in	ADP
ejpam-3506	8	8	the	the	DET
ejpam-3506	8	9	join	join	NOUN
ejpam-3506	8	10	,	,	PUNCT
ejpam-3506	8	11	corona	corona	PROPN
ejpam-3506	8	12	,	,	PUNCT
ejpam-3506	8	13	lexicographic	lexicographic	ADJ
ejpam-3506	8	14	and	and	CCONJ
ejpam-3506	8	15	cartesian	cartesian	ADJ
ejpam-3506	8	16	products	product	NOUN
ejpam-3506	8	17	of	of	ADP
ejpam-3506	8	18	graphs	graph	NOUN
ejpam-3506	8	19	and	and	CCONJ
ejpam-3506	8	20	determine	determine	VERB
ejpam-3506	8	21	the	the	DET
ejpam-3506	8	22	exact	exact	ADJ
ejpam-3506	8	23	values	value	NOUN
ejpam-3506	8	24	or	or	CCONJ
ejpam-3506	8	25	sharp	sharp	ADJ
ejpam-3506	8	26	bounds	bound	NOUN
ejpam-3506	8	27	of	of	ADP
ejpam-3506	8	28	their	their	PRON
ejpam-3506	8	29	corresponding	correspond	VERB
ejpam-3506	8	30	neighborhood	neighborhood	NOUN
ejpam-3506	8	31	connected	connect	VERB
ejpam-3506	8	32	k	k	ADJ
ejpam-3506	8	33	-	-	PUNCT
ejpam-3506	8	34	fair	fair	ADJ
ejpam-3506	8	35	domination	domination	NOUN
ejpam-3506	8	36	number	number	NOUN
ejpam-3506	8	37	.	.	PUNCT
ejpam-3506	9	1	2010	2010	NUM
ejpam-3506	9	2	mathematics	mathematic	NOUN
ejpam-3506	9	3	subject	subject	NOUN
ejpam-3506	9	4	classifications	classification	NOUN
ejpam-3506	9	5	:	:	PUNCT
ejpam-3506	9	6	05c69	05c69	NUM
ejpam-3506	9	7	,	,	PUNCT
ejpam-3506	9	8	05c76	05c76	DET
ejpam-3506	9	9	key	key	ADJ
ejpam-3506	9	10	words	word	NOUN
ejpam-3506	9	11	and	and	CCONJ
ejpam-3506	9	12	phrases	phrase	NOUN
ejpam-3506	9	13	:	:	PUNCT
ejpam-3506	9	14	k	k	ADJ
ejpam-3506	9	15	-	-	PUNCT
ejpam-3506	9	16	fair	fair	ADJ
ejpam-3506	9	17	domination	domination	NOUN
ejpam-3506	9	18	,	,	PUNCT
ejpam-3506	9	19	neighborhood	neighborhood	NOUN
ejpam-3506	9	20	connected	connect	VERB
ejpam-3506	9	21	k	k	ADJ
ejpam-3506	9	22	-	-	PUNCT
ejpam-3506	9	23	fair	fair	ADJ
ejpam-3506	9	24	domination	domination	NOUN
ejpam-3506	9	25	,	,	PUNCT
ejpam-3506	9	26	join	join	NOUN
ejpam-3506	9	27	,	,	PUNCT
ejpam-3506	9	28	corona	corona	PROPN
ejpam-3506	9	29	,	,	PUNCT
ejpam-3506	9	30	lexicographic	lexicographic	ADJ
ejpam-3506	9	31	product	product	NOUN
ejpam-3506	9	32	,	,	PUNCT
ejpam-3506	9	33	cartesian	cartesian	ADJ
ejpam-3506	9	34	product	product	NOUN
ejpam-3506	9	35	1	1	NUM
ejpam-3506	9	36	.	.	PUNCT
ejpam-3506	10	1	introduction	introduction	NOUN
ejpam-3506	10	2	let	let	VERB
ejpam-3506	10	3	g	g	NOUN
ejpam-3506	10	4	=	=	SYM
ejpam-3506	10	5	(	(	PUNCT
ejpam-3506	10	6	v	v	NOUN
ejpam-3506	10	7	(	(	PUNCT
ejpam-3506	10	8	g	g	NOUN
ejpam-3506	10	9	)	)	PUNCT
ejpam-3506	10	10	,	,	PUNCT
ejpam-3506	10	11	e(g	e(g	PROPN
ejpam-3506	10	12	)	)	PUNCT
ejpam-3506	10	13	)	)	PUNCT
ejpam-3506	10	14	be	be	AUX
ejpam-3506	10	15	a	a	DET
ejpam-3506	10	16	simple	simple	ADJ
ejpam-3506	10	17	graph	graph	NOUN
ejpam-3506	10	18	.	.	PUNCT
ejpam-3506	11	1	a	a	DET
ejpam-3506	11	2	set	set	NOUN
ejpam-3506	11	3	s	s	NOUN
ejpam-3506	11	4	⊆	⊆	NUM
ejpam-3506	11	5	v	v	NOUN
ejpam-3506	11	6	(	(	PUNCT
ejpam-3506	11	7	g	g	NOUN
ejpam-3506	11	8	)	)	PUNCT
ejpam-3506	11	9	is	be	AUX
ejpam-3506	11	10	a	a	DET
ejpam-3506	11	11	dominating	dominating	NOUN
ejpam-3506	11	12	set	set	VERB
ejpam-3506	11	13	in	in	ADP
ejpam-3506	11	14	g	g	PROPN
ejpam-3506	11	15	if	if	SCONJ
ejpam-3506	11	16	for	for	ADP
ejpam-3506	11	17	every	every	DET
ejpam-3506	11	18	v	v	NUM
ejpam-3506	11	19	∈	∈	NOUN
ejpam-3506	11	20	v	v	NOUN
ejpam-3506	11	21	(	(	PUNCT
ejpam-3506	11	22	g)\s	g)\s	NOUN
ejpam-3506	11	23	,	,	PUNCT
ejpam-3506	11	24	there	there	PRON
ejpam-3506	11	25	exists	exist	VERB
ejpam-3506	11	26	u	u	PROPN
ejpam-3506	11	27	∈	∈	PROPN
ejpam-3506	11	28	s	s	VERB
ejpam-3506	11	29	such	such	ADJ
ejpam-3506	11	30	that	that	DET
ejpam-3506	11	31	uv	uv	PROPN
ejpam-3506	11	32	∈	∈	PROPN
ejpam-3506	11	33	e(g	e(g	PROPN
ejpam-3506	11	34	)	)	PUNCT
ejpam-3506	11	35	.	.	PUNCT
ejpam-3506	12	1	the	the	DET
ejpam-3506	12	2	minimum	minimum	ADJ
ejpam-3506	12	3	cardinality	cardinality	NOUN
ejpam-3506	12	4	of	of	ADP
ejpam-3506	12	5	a	a	DET
ejpam-3506	12	6	dominating	dominating	NOUN
ejpam-3506	12	7	set	set	NOUN
ejpam-3506	12	8	in	in	ADP
ejpam-3506	12	9	g	g	NOUN
ejpam-3506	12	10	,	,	PUNCT
ejpam-3506	12	11	denoted	denote	VERB
ejpam-3506	12	12	by	by	ADP
ejpam-3506	12	13	γ(g	γ(g	PROPN
ejpam-3506	12	14	)	)	PUNCT
ejpam-3506	12	15	,	,	PUNCT
ejpam-3506	12	16	is	be	AUX
ejpam-3506	12	17	the	the	DET
ejpam-3506	12	18	domination	domination	NOUN
ejpam-3506	12	19	number	number	NOUN
ejpam-3506	12	20	of	of	ADP
ejpam-3506	12	21	g.	g.	PROPN
ejpam-3506	12	22	any	any	DET
ejpam-3506	12	23	dominating	dominating	NOUN
ejpam-3506	12	24	set	set	VERB
ejpam-3506	12	25	in	in	ADP
ejpam-3506	12	26	g	g	PROPN
ejpam-3506	12	27	of	of	ADP
ejpam-3506	12	28	cardinality	cardinality	PROPN
ejpam-3506	12	29	γ(g	γ(g	PROPN
ejpam-3506	12	30	)	)	PUNCT
ejpam-3506	12	31	is	be	AUX
ejpam-3506	12	32	referred	refer	VERB
ejpam-3506	12	33	to	to	ADP
ejpam-3506	12	34	as	as	ADP
ejpam-3506	12	35	a	a	DET
ejpam-3506	12	36	γ	γ	NOUN
ejpam-3506	12	37	-	-	PUNCT
ejpam-3506	12	38	set	set	NOUN
ejpam-3506	12	39	in	in	ADP
ejpam-3506	12	40	g.	g.	PROPN
ejpam-3506	12	41	arumugam	arumugam	PROPN
ejpam-3506	12	42	and	and	CCONJ
ejpam-3506	12	43	sivagnanam	sivagnanam	VERB
ejpam-3506	12	44	[	[	X
ejpam-3506	12	45	1	1	X
ejpam-3506	12	46	]	]	PUNCT
ejpam-3506	12	47	introduced	introduce	VERB
ejpam-3506	12	48	a	a	DET
ejpam-3506	12	49	variation	variation	NOUN
ejpam-3506	12	50	of	of	ADP
ejpam-3506	12	51	domination	domination	NOUN
ejpam-3506	12	52	called	call	VERB
ejpam-3506	12	53	the	the	DET
ejpam-3506	12	54	neighborhood	neighborhood	NOUN
ejpam-3506	12	55	connected	connect	VERB
ejpam-3506	12	56	domination	domination	NOUN
ejpam-3506	12	57	in	in	ADP
ejpam-3506	12	58	graphs	graph	NOUN
ejpam-3506	12	59	.	.	PUNCT
ejpam-3506	13	1	a	a	DET
ejpam-3506	13	2	dominating	dominating	NOUN
ejpam-3506	13	3	set	set	NOUN
ejpam-3506	13	4	s	s	PROPN
ejpam-3506	13	5	of	of	ADP
ejpam-3506	13	6	a	a	DET
ejpam-3506	13	7	connected	connected	ADJ
ejpam-3506	13	8	graph	graph	NOUN
ejpam-3506	13	9	g	g	NOUN
ejpam-3506	13	10	is	be	AUX
ejpam-3506	13	11	called	call	VERB
ejpam-3506	13	12	a	a	DET
ejpam-3506	13	13	neighborhood	neighborhood	NOUN
ejpam-3506	13	14	connected	connect	VERB
ejpam-3506	13	15	dominating	dominating	NOUN
ejpam-3506	13	16	set	set	NOUN
ejpam-3506	13	17	(	(	PUNCT
ejpam-3506	13	18	ncd	ncd	NOUN
ejpam-3506	13	19	-	-	PUNCT
ejpam-3506	13	20	set	set	NOUN
ejpam-3506	13	21	)	)	PUNCT
ejpam-3506	13	22	if	if	SCONJ
ejpam-3506	13	23	the	the	DET
ejpam-3506	13	24	induced	induced	ADJ
ejpam-3506	13	25	subgraph	subgraph	NOUN
ejpam-3506	13	26	〈	〈	PROPN
ejpam-3506	13	27	n(s	n(s	NOUN
ejpam-3506	13	28	)	)	PUNCT
ejpam-3506	13	29	〉	〉	NOUN
ejpam-3506	13	30	of	of	ADP
ejpam-3506	13	31	the	the	DET
ejpam-3506	13	32	open	open	ADJ
ejpam-3506	13	33	neighborhood	neighborhood	NOUN
ejpam-3506	13	34	n(s	n(s	NOUN
ejpam-3506	13	35	)	)	PUNCT
ejpam-3506	13	36	of	of	ADP
ejpam-3506	13	37	s	s	PROPN
ejpam-3506	13	38	is	be	AUX
ejpam-3506	13	39	connected	connect	VERB
ejpam-3506	13	40	.	.	PUNCT
ejpam-3506	14	1	the	the	DET
ejpam-3506	14	2	minimum	minimum	ADJ
ejpam-3506	14	3	cardinality	cardinality	NOUN
ejpam-3506	14	4	of	of	ADP
ejpam-3506	14	5	an	an	DET
ejpam-3506	14	6	ncd	ncd	NOUN
ejpam-3506	14	7	-	-	PUNCT
ejpam-3506	14	8	set	set	NOUN
ejpam-3506	14	9	of	of	ADP
ejpam-3506	14	10	g	g	PROPN
ejpam-3506	14	11	is	be	AUX
ejpam-3506	14	12	called	call	VERB
ejpam-3506	14	13	the	the	DET
ejpam-3506	14	14	neighborhood	neighborhood	NOUN
ejpam-3506	14	15	∗corresponding	∗corresponde	VERB
ejpam-3506	14	16	author	author	NOUN
ejpam-3506	14	17	.	.	PUNCT
ejpam-3506	15	1	doi	doi	NOUN
ejpam-3506	15	2	:	:	PUNCT
ejpam-3506	15	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3506	https://doi.org/10.29020/nybg.ejpam.v12i3.3506	PROPN
ejpam-3506	15	4	email	email	NOUN
ejpam-3506	15	5	addresses	address	VERB
ejpam-3506	15	6	:	:	PUNCT
ejpam-3506	15	7	wardah	wardah	PROPN
ejpam-3506	16	1	bentusman@yahoo.com	bentusman@yahoo.com	INTJ
ejpam-3506	16	2	(	(	PUNCT
ejpam-3506	16	3	w.	w.	PROPN
ejpam-3506	16	4	bent	bent	PROPN
ejpam-3506	16	5	-	-	PUNCT
ejpam-3506	16	6	usman	usman	PROPN
ejpam-3506	16	7	)	)	PUNCT
ejpam-3506	16	8	,	,	PUNCT
ejpam-3506	16	9	rowena.isla@g.msuiit.edu.ph	rowena.isla@g.msuiit.edu.ph	PROPN
ejpam-3506	16	10	(	(	PUNCT
ejpam-3506	16	11	r.	r.	PROPN
ejpam-3506	16	12	isla	isla	PROPN
ejpam-3506	16	13	)	)	PUNCT
ejpam-3506	16	14	,	,	PUNCT
ejpam-3506	16	15	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-3506	16	16	(	(	PUNCT
ejpam-3506	16	17	s.	s.	PROPN
ejpam-3506	16	18	canoy	canoy	PROPN
ejpam-3506	16	19	)	)	PUNCT
ejpam-3506	16	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3506	17	1	1337	1337	NUM
ejpam-3506	17	2	c	c	X
ejpam-3506	17	3	©	©	PROPN
ejpam-3506	17	4	2019	2019	NUM
ejpam-3506	17	5	ejpam	ejpam	NOUN
ejpam-3506	17	6	all	all	DET
ejpam-3506	17	7	rights	right	NOUN
ejpam-3506	17	8	reserved	reserve	VERB
ejpam-3506	17	9	.	.	PUNCT
ejpam-3506	18	1	w.	w.	PROPN
ejpam-3506	18	2	bent	bent	PROPN
ejpam-3506	18	3	-	-	PUNCT
ejpam-3506	18	4	usman	usman	PROPN
ejpam-3506	18	5	,	,	PUNCT
ejpam-3506	18	6	r.	r.	PROPN
ejpam-3506	18	7	isla	isla	PROPN
ejpam-3506	18	8	,	,	PUNCT
ejpam-3506	18	9	s.	s.	PROPN
ejpam-3506	18	10	canoy	canoy	PROPN
ejpam-3506	18	11	/	/	SYM
ejpam-3506	18	12	eur	eur	PROPN
ejpam-3506	18	13	.	.	PUNCT
ejpam-3506	19	1	j.	j.	PROPN
ejpam-3506	19	2	pure	pure	PROPN
ejpam-3506	19	3	appl	appl	PROPN
ejpam-3506	19	4	.	.	PROPN
ejpam-3506	19	5	math	math	PROPN
ejpam-3506	19	6	,	,	PUNCT
ejpam-3506	19	7	12	12	NUM
ejpam-3506	19	8	(	(	PUNCT
ejpam-3506	19	9	3	3	NUM
ejpam-3506	19	10	)	)	PUNCT
ejpam-3506	19	11	(	(	PUNCT
ejpam-3506	19	12	2019	2019	NUM
ejpam-3506	19	13	)	)	PUNCT
ejpam-3506	19	14	,	,	PUNCT
ejpam-3506	19	15	1337	1337	NUM
ejpam-3506	19	16	-	-	SYM
ejpam-3506	19	17	1349	1349	NUM
ejpam-3506	19	18	1338	1338	NUM
ejpam-3506	19	19	connected	connect	VERB
ejpam-3506	19	20	domination	domination	NOUN
ejpam-3506	19	21	number	number	NOUN
ejpam-3506	19	22	of	of	ADP
ejpam-3506	19	23	g	g	NOUN
ejpam-3506	19	24	and	and	CCONJ
ejpam-3506	19	25	is	be	AUX
ejpam-3506	19	26	denoted	denote	VERB
ejpam-3506	19	27	by	by	ADP
ejpam-3506	19	28	γnc(g	γnc(g	NOUN
ejpam-3506	19	29	)	)	PUNCT
ejpam-3506	19	30	.	.	PUNCT
ejpam-3506	20	1	we	we	PRON
ejpam-3506	20	2	refer	refer	VERB
ejpam-3506	20	3	to	to	ADP
ejpam-3506	20	4	a	a	DET
ejpam-3506	20	5	minimum	minimum	ADJ
ejpam-3506	20	6	ncd	ncd	X
ejpam-3506	20	7	-	-	PUNCT
ejpam-3506	20	8	set	set	NOUN
ejpam-3506	20	9	of	of	ADP
ejpam-3506	20	10	g	g	PROPN
ejpam-3506	20	11	as	as	ADP
ejpam-3506	20	12	a	a	DET
ejpam-3506	20	13	γnc	γnc	NOUN
ejpam-3506	20	14	-	-	PUNCT
ejpam-3506	20	15	set	set	NOUN
ejpam-3506	20	16	.	.	PUNCT
ejpam-3506	21	1	another	another	DET
ejpam-3506	21	2	domination	domination	NOUN
ejpam-3506	21	3	variant	variant	NOUN
ejpam-3506	21	4	is	be	AUX
ejpam-3506	21	5	fair	fair	ADJ
ejpam-3506	21	6	domination	domination	NOUN
ejpam-3506	21	7	,	,	PUNCT
ejpam-3506	21	8	introduced	introduce	VERB
ejpam-3506	21	9	by	by	ADP
ejpam-3506	21	10	caro	caro	PROPN
ejpam-3506	21	11	,	,	PUNCT
ejpam-3506	21	12	hansberg	hansberg	PROPN
ejpam-3506	21	13	and	and	CCONJ
ejpam-3506	21	14	henning	henne	VERB
ejpam-3506	22	1	[	[	X
ejpam-3506	22	2	3	3	X
ejpam-3506	22	3	]	]	PUNCT
ejpam-3506	22	4	in	in	ADP
ejpam-3506	22	5	2011	2011	NUM
ejpam-3506	22	6	.	.	PUNCT
ejpam-3506	23	1	for	for	ADP
ejpam-3506	23	2	an	an	DET
ejpam-3506	23	3	integer	integer	NOUN
ejpam-3506	23	4	k	k	PROPN
ejpam-3506	23	5	≥	≥	NUM
ejpam-3506	23	6	1	1	NUM
ejpam-3506	23	7	,	,	PUNCT
ejpam-3506	23	8	a	a	DET
ejpam-3506	23	9	k	k	ADJ
ejpam-3506	23	10	-	-	ADJ
ejpam-3506	23	11	fair	fair	ADJ
ejpam-3506	23	12	dominating	dominating	NOUN
ejpam-3506	23	13	set	set	NOUN
ejpam-3506	23	14	(	(	PUNCT
ejpam-3506	23	15	kfd	kfd	NOUN
ejpam-3506	23	16	-	-	PUNCT
ejpam-3506	23	17	set	set	NOUN
ejpam-3506	23	18	)	)	PUNCT
ejpam-3506	23	19	is	be	AUX
ejpam-3506	23	20	a	a	DET
ejpam-3506	23	21	dominating	dominating	NOUN
ejpam-3506	23	22	set	set	NOUN
ejpam-3506	23	23	s	s	PROPN
ejpam-3506	23	24	⊆	⊆	NUM
ejpam-3506	23	25	v	v	NOUN
ejpam-3506	23	26	(	(	PUNCT
ejpam-3506	23	27	g	g	NOUN
ejpam-3506	23	28	)	)	PUNCT
ejpam-3506	23	29	such	such	ADJ
ejpam-3506	23	30	that	that	SCONJ
ejpam-3506	23	31	|n(u	|n(u	NOUN
ejpam-3506	23	32	)	)	PUNCT
ejpam-3506	23	33	∩	∩	NOUN
ejpam-3506	23	34	s|	s|	VERB
ejpam-3506	23	35	=	=	SYM
ejpam-3506	23	36	k	k	NOUN
ejpam-3506	23	37	for	for	ADP
ejpam-3506	23	38	every	every	DET
ejpam-3506	23	39	u	u	PROPN
ejpam-3506	23	40	∈	∈	PROPN
ejpam-3506	23	41	v	v	NOUN
ejpam-3506	23	42	(	(	PUNCT
ejpam-3506	23	43	g)\s	g)\s	NOUN
ejpam-3506	23	44	.	.	PUNCT
ejpam-3506	24	1	the	the	DET
ejpam-3506	24	2	k	k	ADJ
ejpam-3506	24	3	-	-	PUNCT
ejpam-3506	24	4	fair	fair	ADJ
ejpam-3506	24	5	domination	domination	NOUN
ejpam-3506	24	6	number	number	NOUN
ejpam-3506	24	7	of	of	ADP
ejpam-3506	24	8	g	g	NOUN
ejpam-3506	24	9	,	,	PUNCT
ejpam-3506	24	10	denoted	denote	VERB
ejpam-3506	24	11	by	by	ADP
ejpam-3506	24	12	γkfd(g	γkfd(g	PROPN
ejpam-3506	24	13	)	)	PUNCT
ejpam-3506	24	14	,	,	PUNCT
ejpam-3506	24	15	is	be	AUX
ejpam-3506	24	16	the	the	DET
ejpam-3506	24	17	minimum	minimum	ADJ
ejpam-3506	24	18	cardinality	cardinality	NOUN
ejpam-3506	24	19	of	of	ADP
ejpam-3506	24	20	a	a	DET
ejpam-3506	24	21	kfd	kfd	NOUN
ejpam-3506	24	22	-	-	PUNCT
ejpam-3506	24	23	set	set	NOUN
ejpam-3506	24	24	.	.	PUNCT
ejpam-3506	25	1	maravilla	maravilla	PROPN
ejpam-3506	25	2	,	,	PUNCT
ejpam-3506	25	3	isla	isla	PROPN
ejpam-3506	25	4	,	,	PUNCT
ejpam-3506	25	5	and	and	CCONJ
ejpam-3506	25	6	canoy	canoy	ADJ
ejpam-3506	26	1	[	[	X
ejpam-3506	26	2	4–6	4–6	X
ejpam-3506	26	3	]	]	X
ejpam-3506	26	4	and	and	CCONJ
ejpam-3506	26	5	bent	bent	ADJ
ejpam-3506	26	6	-	-	PUNCT
ejpam-3506	26	7	usman	usman	ADJ
ejpam-3506	26	8	,	,	PUNCT
ejpam-3506	26	9	gomisong	gomisong	PROPN
ejpam-3506	26	10	,	,	PUNCT
ejpam-3506	26	11	and	and	CCONJ
ejpam-3506	26	12	isla	isla	PROPN
ejpam-3506	26	13	[	[	X
ejpam-3506	26	14	2	2	X
ejpam-3506	26	15	]	]	PUNCT
ejpam-3506	26	16	characterized	characterize	VERB
ejpam-3506	26	17	the	the	DET
ejpam-3506	26	18	fair	fair	ADJ
ejpam-3506	26	19	dominating	dominating	NOUN
ejpam-3506	26	20	,	,	PUNCT
ejpam-3506	26	21	k	k	ADJ
ejpam-3506	26	22	-	-	ADJ
ejpam-3506	26	23	fair	fair	ADJ
ejpam-3506	26	24	dominating	dominating	NOUN
ejpam-3506	26	25	,	,	PUNCT
ejpam-3506	26	26	fair	fair	ADJ
ejpam-3506	26	27	total	total	ADJ
ejpam-3506	26	28	dominating	dominating	NOUN
ejpam-3506	26	29	and	and	CCONJ
ejpam-3506	26	30	connected	connect	VERB
ejpam-3506	26	31	k	k	ADJ
ejpam-3506	26	32	-	-	ADJ
ejpam-3506	26	33	fair	fair	ADJ
ejpam-3506	26	34	dominating	dominating	NOUN
ejpam-3506	26	35	sets	set	NOUN
ejpam-3506	26	36	in	in	ADP
ejpam-3506	26	37	the	the	DET
ejpam-3506	26	38	join	join	NOUN
ejpam-3506	26	39	,	,	PUNCT
ejpam-3506	26	40	corona	corona	PROPN
ejpam-3506	26	41	,	,	PUNCT
ejpam-3506	26	42	lexicographic	lexicographic	ADJ
ejpam-3506	26	43	product	product	NOUN
ejpam-3506	26	44	,	,	PUNCT
ejpam-3506	26	45	and	and	CCONJ
ejpam-3506	26	46	cartesian	cartesian	ADJ
ejpam-3506	26	47	product	product	NOUN
ejpam-3506	26	48	of	of	ADP
ejpam-3506	26	49	graphs	graph	NOUN
ejpam-3506	26	50	and	and	CCONJ
ejpam-3506	26	51	determined	determine	VERB
ejpam-3506	26	52	the	the	DET
ejpam-3506	26	53	bounds	bound	NOUN
ejpam-3506	26	54	or	or	CCONJ
ejpam-3506	26	55	exact	exact	ADJ
ejpam-3506	26	56	values	value	NOUN
ejpam-3506	26	57	of	of	ADP
ejpam-3506	26	58	the	the	DET
ejpam-3506	26	59	fair	fair	ADJ
ejpam-3506	26	60	,	,	PUNCT
ejpam-3506	26	61	k	k	NOUN
ejpam-3506	26	62	-	-	ADJ
ejpam-3506	26	63	fair	fair	ADJ
ejpam-3506	26	64	,	,	PUNCT
ejpam-3506	26	65	fair	fair	ADJ
ejpam-3506	26	66	total	total	NOUN
ejpam-3506	26	67	,	,	PUNCT
ejpam-3506	26	68	and	and	CCONJ
ejpam-3506	26	69	connected	connect	VERB
ejpam-3506	26	70	k	k	ADJ
ejpam-3506	26	71	-	-	PUNCT
ejpam-3506	26	72	fair	fair	ADJ
ejpam-3506	26	73	domination	domination	NOUN
ejpam-3506	26	74	numbers	number	NOUN
ejpam-3506	26	75	,	,	PUNCT
ejpam-3506	26	76	respectively	respectively	ADV
ejpam-3506	26	77	,	,	PUNCT
ejpam-3506	26	78	of	of	ADP
ejpam-3506	26	79	these	these	DET
ejpam-3506	26	80	graphs	graph	NOUN
ejpam-3506	26	81	.	.	PUNCT
ejpam-3506	27	1	this	this	DET
ejpam-3506	27	2	study	study	NOUN
ejpam-3506	27	3	combines	combine	VERB
ejpam-3506	27	4	the	the	DET
ejpam-3506	27	5	concepts	concept	NOUN
ejpam-3506	27	6	of	of	ADP
ejpam-3506	27	7	neighborhood	neighborhood	NOUN
ejpam-3506	27	8	connected	connect	VERB
ejpam-3506	27	9	domination	domination	NOUN
ejpam-3506	27	10	in	in	ADP
ejpam-3506	27	11	graphs	graph	NOUN
ejpam-3506	27	12	and	and	CCONJ
ejpam-3506	27	13	of	of	ADP
ejpam-3506	27	14	k	k	ADJ
ejpam-3506	27	15	-	-	PUNCT
ejpam-3506	27	16	fair	fair	ADJ
ejpam-3506	27	17	domination	domination	NOUN
ejpam-3506	27	18	in	in	ADP
ejpam-3506	27	19	graphs	graph	NOUN
ejpam-3506	27	20	.	.	PUNCT
ejpam-3506	28	1	a	a	DET
ejpam-3506	28	2	neighborhood	neighborhood	NOUN
ejpam-3506	28	3	connected	connect	VERB
ejpam-3506	28	4	k	k	ADJ
ejpam-3506	28	5	-	-	ADJ
ejpam-3506	28	6	fair	fair	ADJ
ejpam-3506	28	7	dominating	dominating	NOUN
ejpam-3506	28	8	set	set	NOUN
ejpam-3506	28	9	(	(	PUNCT
ejpam-3506	28	10	nckfd	nckfd	NOUN
ejpam-3506	28	11	-	-	PUNCT
ejpam-3506	28	12	set	set	NOUN
ejpam-3506	28	13	)	)	PUNCT
ejpam-3506	28	14	is	be	AUX
ejpam-3506	28	15	a	a	DET
ejpam-3506	28	16	k	k	ADJ
ejpam-3506	28	17	-	-	ADJ
ejpam-3506	28	18	fair	fair	ADJ
ejpam-3506	28	19	dominating	dominating	NOUN
ejpam-3506	28	20	set	set	NOUN
ejpam-3506	28	21	s	s	PROPN
ejpam-3506	28	22	⊆	⊆	NUM
ejpam-3506	28	23	v	v	NOUN
ejpam-3506	28	24	(	(	PUNCT
ejpam-3506	28	25	g	g	NOUN
ejpam-3506	28	26	)	)	PUNCT
ejpam-3506	28	27	such	such	ADJ
ejpam-3506	28	28	that	that	SCONJ
ejpam-3506	28	29	the	the	DET
ejpam-3506	28	30	induced	induced	ADJ
ejpam-3506	28	31	subgraph	subgraph	NOUN
ejpam-3506	28	32	〈	〈	PROPN
ejpam-3506	28	33	n(s	n(s	NOUN
ejpam-3506	28	34	)	)	PUNCT
ejpam-3506	28	35	〉	〉	PROPN
ejpam-3506	28	36	is	be	AUX
ejpam-3506	28	37	connected	connect	VERB
ejpam-3506	28	38	.	.	PUNCT
ejpam-3506	29	1	the	the	DET
ejpam-3506	29	2	neighborhood	neighborhood	NOUN
ejpam-3506	29	3	connected	connect	VERB
ejpam-3506	29	4	k	k	ADJ
ejpam-3506	29	5	-	-	PUNCT
ejpam-3506	29	6	fair	fair	ADJ
ejpam-3506	29	7	domination	domination	NOUN
ejpam-3506	29	8	number	number	NOUN
ejpam-3506	29	9	of	of	ADP
ejpam-3506	29	10	g	g	NOUN
ejpam-3506	29	11	,	,	PUNCT
ejpam-3506	29	12	denoted	denote	VERB
ejpam-3506	29	13	by	by	ADP
ejpam-3506	29	14	γnckfd(g	γnckfd(g	PROPN
ejpam-3506	29	15	)	)	PUNCT
ejpam-3506	29	16	,	,	PUNCT
ejpam-3506	29	17	is	be	AUX
ejpam-3506	29	18	the	the	DET
ejpam-3506	29	19	minimum	minimum	ADJ
ejpam-3506	29	20	cardinality	cardinality	NOUN
ejpam-3506	29	21	of	of	ADP
ejpam-3506	29	22	an	an	DET
ejpam-3506	29	23	nckfd	nckfd	NOUN
ejpam-3506	29	24	-	-	PUNCT
ejpam-3506	29	25	set	set	NOUN
ejpam-3506	29	26	.	.	PUNCT
ejpam-3506	30	1	an	an	DET
ejpam-3506	30	2	nckfd	nckfd	NOUN
ejpam-3506	30	3	-	-	PUNCT
ejpam-3506	30	4	set	set	NOUN
ejpam-3506	30	5	in	in	ADP
ejpam-3506	30	6	g	g	NOUN
ejpam-3506	30	7	with	with	ADP
ejpam-3506	30	8	cardinality	cardinality	NOUN
ejpam-3506	30	9	γnckfd(g	γnckfd(g	PROPN
ejpam-3506	30	10	)	)	PUNCT
ejpam-3506	30	11	is	be	AUX
ejpam-3506	30	12	referred	refer	VERB
ejpam-3506	30	13	to	to	ADP
ejpam-3506	30	14	as	as	ADP
ejpam-3506	30	15	a	a	DET
ejpam-3506	30	16	γnckfd	γnckfd	NOUN
ejpam-3506	30	17	-	-	PUNCT
ejpam-3506	30	18	set	set	NOUN
ejpam-3506	30	19	.	.	PUNCT
ejpam-3506	31	1	2	2	X
ejpam-3506	31	2	.	.	X
ejpam-3506	31	3	preliminary	preliminary	ADJ
ejpam-3506	31	4	results	result	NOUN
ejpam-3506	31	5	remark	remark	VERB
ejpam-3506	31	6	1	1	NUM
ejpam-3506	31	7	.	.	PUNCT
ejpam-3506	32	1	every	every	DET
ejpam-3506	32	2	nckfd	nckfd	NOUN
ejpam-3506	32	3	-	-	PUNCT
ejpam-3506	32	4	set	set	NOUN
ejpam-3506	32	5	is	be	AUX
ejpam-3506	32	6	an	an	DET
ejpam-3506	32	7	ncd	ncd	NOUN
ejpam-3506	32	8	-	-	PUNCT
ejpam-3506	32	9	set	set	NOUN
ejpam-3506	32	10	,	,	PUNCT
ejpam-3506	32	11	where	where	SCONJ
ejpam-3506	32	12	k	k	PROPN
ejpam-3506	32	13	is	be	AUX
ejpam-3506	32	14	a	a	DET
ejpam-3506	32	15	positive	positive	ADJ
ejpam-3506	32	16	integer	integer	NOUN
ejpam-3506	32	17	.	.	PUNCT
ejpam-3506	33	1	remark	remark	NOUN
ejpam-3506	33	2	2	2	NUM
ejpam-3506	33	3	.	.	PUNCT
ejpam-3506	34	1	for	for	ADP
ejpam-3506	34	2	any	any	DET
ejpam-3506	34	3	connected	connected	ADJ
ejpam-3506	34	4	graph	graph	NOUN
ejpam-3506	34	5	g	g	NOUN
ejpam-3506	34	6	of	of	ADP
ejpam-3506	34	7	order	order	NOUN
ejpam-3506	34	8	m	m	VERB
ejpam-3506	34	9	≥	≥	NOUN
ejpam-3506	34	10	2	2	NUM
ejpam-3506	34	11	and	and	CCONJ
ejpam-3506	34	12	a	a	DET
ejpam-3506	34	13	positive	positive	ADJ
ejpam-3506	34	14	integer	integer	NOUN
ejpam-3506	34	15	k	k	PROPN
ejpam-3506	34	16	,	,	PUNCT
ejpam-3506	34	17	1	1	NUM
ejpam-3506	34	18	≤	≤	PROPN
ejpam-3506	34	19	γ(g	γ(g	PROPN
ejpam-3506	34	20	)	)	PUNCT
ejpam-3506	34	21	≤	≤	NUM
ejpam-3506	34	22	γkfd(g	γkfd(g	ADP
ejpam-3506	34	23	)	)	PUNCT
ejpam-3506	34	24	≤	≤	NUM
ejpam-3506	34	25	γnckfd(g	γnckfd(g	NOUN
ejpam-3506	34	26	)	)	PUNCT
ejpam-3506	34	27	≤	≤	NUM
ejpam-3506	34	28	m	m	PROPN
ejpam-3506	34	29	and	and	CCONJ
ejpam-3506	34	30	γ(g	γ(g	PROPN
ejpam-3506	34	31	)	)	PUNCT
ejpam-3506	35	1	≤	≤	NOUN
ejpam-3506	35	2	γnc(g	γnc(g	NUM
ejpam-3506	35	3	)	)	PUNCT
ejpam-3506	35	4	≤	≤	NUM
ejpam-3506	35	5	γnckfd(g	γnckfd(g	NOUN
ejpam-3506	35	6	)	)	PUNCT
ejpam-3506	35	7	.	.	PUNCT
ejpam-3506	36	1	the	the	DET
ejpam-3506	36	2	bounds	bound	NOUN
ejpam-3506	36	3	given	give	VERB
ejpam-3506	36	4	above	above	ADV
ejpam-3506	36	5	are	be	AUX
ejpam-3506	36	6	sharp	sharp	ADJ
ejpam-3506	36	7	.	.	PUNCT
ejpam-3506	37	1	however	however	ADV
ejpam-3506	37	2	,	,	PUNCT
ejpam-3506	37	3	the	the	DET
ejpam-3506	37	4	inequalities	inequality	NOUN
ejpam-3506	37	5	can	can	AUX
ejpam-3506	37	6	be	be	AUX
ejpam-3506	37	7	attained	attain	VERB
ejpam-3506	37	8	.	.	PUNCT
ejpam-3506	38	1	to	to	PART
ejpam-3506	38	2	see	see	VERB
ejpam-3506	38	3	this	this	PRON
ejpam-3506	38	4	,	,	PUNCT
ejpam-3506	38	5	consider	consider	VERB
ejpam-3506	38	6	g	g	NOUN
ejpam-3506	38	7	=	=	NOUN
ejpam-3506	38	8	k4	k4	NOUN
ejpam-3506	38	9	and	and	CCONJ
ejpam-3506	38	10	h	h	NOUN
ejpam-3506	38	11	=	=	PROPN
ejpam-3506	38	12	c6	c6	PROPN
ejpam-3506	38	13	.	.	PUNCT
ejpam-3506	39	1	clearly	clearly	ADV
ejpam-3506	39	2	,	,	PUNCT
ejpam-3506	39	3	1	1	NUM
ejpam-3506	39	4	=	=	SYM
ejpam-3506	39	5	γ(g	γ(g	PROPN
ejpam-3506	39	6	)	)	PUNCT
ejpam-3506	39	7	=	=	SYM
ejpam-3506	39	8	γ1fd(g	γ1fd(g	PROPN
ejpam-3506	39	9	)	)	PUNCT
ejpam-3506	39	10	=	=	SYM
ejpam-3506	39	11	γnc1fd(g	γnc1fd(g	PROPN
ejpam-3506	39	12	)	)	PUNCT
ejpam-3506	39	13	<	<	X
ejpam-3506	39	14	m.	m.	NOUN
ejpam-3506	39	15	moreover	moreover	ADV
ejpam-3506	39	16	,	,	PUNCT
ejpam-3506	39	17	γnc4fd(g	γnc4fd(g	ADJ
ejpam-3506	39	18	)	)	PUNCT
ejpam-3506	39	19	=	=	SYM
ejpam-3506	40	1	4	4	NUM
ejpam-3506	40	2	=	=	SYM
ejpam-3506	40	3	m	m	NOUN
ejpam-3506	40	4	while	while	SCONJ
ejpam-3506	40	5	γ(g	γ(g	PROPN
ejpam-3506	40	6	)	)	PUNCT
ejpam-3506	40	7	<	<	X
ejpam-3506	40	8	γ2fd(g	γ2fd(g	PROPN
ejpam-3506	40	9	)	)	PUNCT
ejpam-3506	40	10	=	=	SYM
ejpam-3506	40	11	γnc2fd(g	γnc2fd(g	PROPN
ejpam-3506	40	12	)	)	PUNCT
ejpam-3506	40	13	=	=	SYM
ejpam-3506	41	1	2	2	X
ejpam-3506	41	2	.	.	PUNCT
ejpam-3506	42	1	furthermore	furthermore	ADV
ejpam-3506	42	2	,	,	PUNCT
ejpam-3506	42	3	it	it	PRON
ejpam-3506	42	4	can	can	AUX
ejpam-3506	42	5	be	be	AUX
ejpam-3506	42	6	easily	easily	ADV
ejpam-3506	42	7	verified	verify	VERB
ejpam-3506	42	8	that	that	SCONJ
ejpam-3506	42	9	1	1	NUM
ejpam-3506	42	10	<	<	SYM
ejpam-3506	42	11	2	2	NUM
ejpam-3506	42	12	=	=	SYM
ejpam-3506	42	13	γ(h	γ(h	NOUN
ejpam-3506	42	14	)	)	PUNCT
ejpam-3506	42	15	=	=	SYM
ejpam-3506	42	16	γ1fd(h	γ1fd(h	PROPN
ejpam-3506	42	17	)	)	PUNCT
ejpam-3506	42	18	<	<	X
ejpam-3506	42	19	γnc1fd(h	γnc1fd(h	PROPN
ejpam-3506	42	20	)	)	PUNCT
ejpam-3506	43	1	=	=	SYM
ejpam-3506	43	2	4	4	X
ejpam-3506	43	3	.	.	X
ejpam-3506	43	4	proposition	proposition	NOUN
ejpam-3506	43	5	1	1	NUM
ejpam-3506	43	6	.	.	PUNCT
ejpam-3506	44	1	let	let	VERB
ejpam-3506	44	2	g	g	PRON
ejpam-3506	44	3	be	be	AUX
ejpam-3506	44	4	a	a	DET
ejpam-3506	44	5	connected	connected	ADJ
ejpam-3506	44	6	graph	graph	NOUN
ejpam-3506	44	7	of	of	ADP
ejpam-3506	44	8	order	order	NOUN
ejpam-3506	44	9	n	n	PRON
ejpam-3506	44	10	≥	≥	NOUN
ejpam-3506	44	11	2	2	NUM
ejpam-3506	44	12	and	and	CCONJ
ejpam-3506	44	13	k	k	PROPN
ejpam-3506	44	14	a	a	DET
ejpam-3506	44	15	positive	positive	ADJ
ejpam-3506	44	16	integer	integer	NOUN
ejpam-3506	44	17	such	such	ADJ
ejpam-3506	44	18	that	that	SCONJ
ejpam-3506	44	19	k	k	PROPN
ejpam-3506	44	20	≤	≤	PROPN
ejpam-3506	44	21	n.	n.	NOUN
ejpam-3506	44	22	then	then	ADV
ejpam-3506	44	23	the	the	DET
ejpam-3506	44	24	following	follow	VERB
ejpam-3506	44	25	hold	hold	NOUN
ejpam-3506	44	26	:	:	PUNCT
ejpam-3506	44	27	(	(	PUNCT
ejpam-3506	44	28	i	i	NOUN
ejpam-3506	44	29	)	)	PUNCT
ejpam-3506	44	30	γnckfd(g	γnckfd(g	PROPN
ejpam-3506	44	31	)	)	PUNCT
ejpam-3506	44	32	≥	≥	PROPN
ejpam-3506	44	33	k.	k.	PROPN
ejpam-3506	44	34	w.	w.	PROPN
ejpam-3506	44	35	bent	bent	PROPN
ejpam-3506	44	36	-	-	PUNCT
ejpam-3506	44	37	usman	usman	PROPN
ejpam-3506	44	38	,	,	PUNCT
ejpam-3506	44	39	r.	r.	PROPN
ejpam-3506	44	40	isla	isla	PROPN
ejpam-3506	44	41	,	,	PUNCT
ejpam-3506	44	42	s.	s.	PROPN
ejpam-3506	44	43	canoy	canoy	PROPN
ejpam-3506	44	44	/	/	SYM
ejpam-3506	44	45	eur	eur	PROPN
ejpam-3506	44	46	.	.	PUNCT
ejpam-3506	45	1	j.	j.	PROPN
ejpam-3506	45	2	pure	pure	PROPN
ejpam-3506	45	3	appl	appl	PROPN
ejpam-3506	45	4	.	.	PROPN
ejpam-3506	45	5	math	math	PROPN
ejpam-3506	45	6	,	,	PUNCT
ejpam-3506	45	7	12	12	NUM
ejpam-3506	45	8	(	(	PUNCT
ejpam-3506	45	9	3	3	NUM
ejpam-3506	45	10	)	)	PUNCT
ejpam-3506	45	11	(	(	PUNCT
ejpam-3506	45	12	2019	2019	NUM
ejpam-3506	45	13	)	)	PUNCT
ejpam-3506	45	14	,	,	PUNCT
ejpam-3506	45	15	1337	1337	NUM
ejpam-3506	45	16	-	-	SYM
ejpam-3506	45	17	1349	1349	NUM
ejpam-3506	45	18	1339	1339	NUM
ejpam-3506	45	19	(	(	PUNCT
ejpam-3506	45	20	ii	ii	NOUN
ejpam-3506	45	21	)	)	PUNCT
ejpam-3506	45	22	γnckfd(g	γnckfd(g	NOUN
ejpam-3506	45	23	)	)	PUNCT
ejpam-3506	45	24	=	=	SYM
ejpam-3506	46	1	k	k	NOUN
ejpam-3506	46	2	if	if	SCONJ
ejpam-3506	46	3	and	and	CCONJ
ejpam-3506	46	4	only	only	ADV
ejpam-3506	46	5	if	if	SCONJ
ejpam-3506	46	6	g	g	PROPN
ejpam-3506	46	7	has	have	VERB
ejpam-3506	46	8	an	an	DET
ejpam-3506	46	9	nckfd	nckfd	NOUN
ejpam-3506	46	10	-	-	PUNCT
ejpam-3506	46	11	set	set	NOUN
ejpam-3506	46	12	s	s	NOUN
ejpam-3506	46	13	with	with	ADP
ejpam-3506	46	14	|s|	|s|	PROPN
ejpam-3506	46	15	=	=	SYM
ejpam-3506	46	16	k.	k.	PROPN
ejpam-3506	46	17	(	(	PUNCT
ejpam-3506	46	18	iii	iii	X
ejpam-3506	46	19	)	)	PUNCT
ejpam-3506	46	20	γnckfd(kn	γnckfd(kn	NOUN
ejpam-3506	46	21	)	)	PUNCT
ejpam-3506	46	22	=	=	PUNCT
ejpam-3506	47	1	k.	k.	NOUN
ejpam-3506	47	2	proof	proof	NOUN
ejpam-3506	47	3	.	.	PUNCT
ejpam-3506	48	1	(	(	PUNCT
ejpam-3506	48	2	i	i	NOUN
ejpam-3506	48	3	)	)	PUNCT
ejpam-3506	48	4	let	let	VERB
ejpam-3506	48	5	s	s	PRON
ejpam-3506	48	6	be	be	AUX
ejpam-3506	48	7	a	a	DET
ejpam-3506	48	8	γnckfd	γnckfd	NOUN
ejpam-3506	48	9	-	-	PUNCT
ejpam-3506	48	10	set	set	NOUN
ejpam-3506	48	11	.	.	PUNCT
ejpam-3506	49	1	if	if	SCONJ
ejpam-3506	49	2	s	s	VERB
ejpam-3506	49	3	=	=	SYM
ejpam-3506	49	4	v	v	X
ejpam-3506	49	5	(	(	PUNCT
ejpam-3506	49	6	g	g	NOUN
ejpam-3506	49	7	)	)	PUNCT
ejpam-3506	49	8	,	,	PUNCT
ejpam-3506	49	9	then	then	ADV
ejpam-3506	49	10	γnckfd(g	γnckfd(g	NUM
ejpam-3506	49	11	)	)	PUNCT
ejpam-3506	49	12	=	=	PUNCT
ejpam-3506	49	13	|s|	|s|	PROPN
ejpam-3506	49	14	=	=	SYM
ejpam-3506	49	15	n	n	PRON
ejpam-3506	49	16	≥	≥	NOUN
ejpam-3506	49	17	k.	k.	PROPN
ejpam-3506	49	18	suppose	suppose	VERB
ejpam-3506	49	19	s	s	PROPN
ejpam-3506	49	20	6=	6=	NUM
ejpam-3506	49	21	v	v	ADP
ejpam-3506	49	22	(	(	PUNCT
ejpam-3506	49	23	g	g	NOUN
ejpam-3506	49	24	)	)	PUNCT
ejpam-3506	49	25	and	and	CCONJ
ejpam-3506	49	26	let	let	VERB
ejpam-3506	49	27	v	v	NUM
ejpam-3506	49	28	∈	∈	PROPN
ejpam-3506	49	29	v	v	NOUN
ejpam-3506	49	30	(	(	PUNCT
ejpam-3506	49	31	g)\s	g)\s	NOUN
ejpam-3506	49	32	.	.	PUNCT
ejpam-3506	50	1	then	then	ADV
ejpam-3506	50	2	|ng(v	|ng(v	NOUN
ejpam-3506	50	3	)	)	PUNCT
ejpam-3506	50	4	∩	∩	NOUN
ejpam-3506	50	5	s|	s|	NOUN
ejpam-3506	50	6	=	=	SYM
ejpam-3506	50	7	k	k	PROPN
ejpam-3506	50	8	≤	≤	PROPN
ejpam-3506	50	9	|s|	|s|	PROPN
ejpam-3506	50	10	=	=	PUNCT
ejpam-3506	50	11	γnckfd(g	γnckfd(g	PROPN
ejpam-3506	50	12	)	)	PUNCT
ejpam-3506	50	13	.	.	PUNCT
ejpam-3506	51	1	(	(	PUNCT
ejpam-3506	51	2	ii	ii	NOUN
ejpam-3506	51	3	)	)	PUNCT
ejpam-3506	51	4	next	next	ADV
ejpam-3506	51	5	,	,	PUNCT
ejpam-3506	51	6	suppose	suppose	VERB
ejpam-3506	51	7	that	that	SCONJ
ejpam-3506	51	8	γnckfd(g	γnckfd(g	NOUN
ejpam-3506	51	9	)	)	PUNCT
ejpam-3506	51	10	=	=	VERB
ejpam-3506	52	1	k.	k.	PROPN
ejpam-3506	52	2	then	then	ADV
ejpam-3506	52	3	g	g	PROPN
ejpam-3506	52	4	has	have	VERB
ejpam-3506	52	5	an	an	DET
ejpam-3506	52	6	nckfd	nckfd	NOUN
ejpam-3506	52	7	-	-	PUNCT
ejpam-3506	52	8	set	set	NOUN
ejpam-3506	52	9	s	s	NOUN
ejpam-3506	52	10	with	with	ADP
ejpam-3506	52	11	γnckfd(g	γnckfd(g	NOUN
ejpam-3506	52	12	)	)	PUNCT
ejpam-3506	52	13	=	=	SYM
ejpam-3506	52	14	|s|	|s|	PROPN
ejpam-3506	52	15	=	=	SYM
ejpam-3506	52	16	k.	k.	PROPN
ejpam-3506	52	17	for	for	ADP
ejpam-3506	52	18	the	the	DET
ejpam-3506	52	19	converse	converse	NOUN
ejpam-3506	52	20	,	,	PUNCT
ejpam-3506	52	21	suppose	suppose	VERB
ejpam-3506	52	22	that	that	SCONJ
ejpam-3506	52	23	g	g	PROPN
ejpam-3506	52	24	has	have	VERB
ejpam-3506	52	25	an	an	DET
ejpam-3506	52	26	nckfd	nckfd	NOUN
ejpam-3506	52	27	-	-	PUNCT
ejpam-3506	52	28	set	set	NOUN
ejpam-3506	52	29	s	s	NOUN
ejpam-3506	52	30	with	with	ADP
ejpam-3506	52	31	|s|	|s|	PROPN
ejpam-3506	52	32	=	=	SYM
ejpam-3506	52	33	k.	k.	PROPN
ejpam-3506	52	34	then	then	ADV
ejpam-3506	52	35	γnckfd(g	γnckfd(g	NUM
ejpam-3506	52	36	)	)	PUNCT
ejpam-3506	52	37	≤	≤	NUM
ejpam-3506	52	38	|s|	|s|	PROPN
ejpam-3506	52	39	=	=	SYM
ejpam-3506	52	40	k.	k.	PROPN
ejpam-3506	52	41	since	since	SCONJ
ejpam-3506	52	42	γnckfd(g	γnckfd(g	NUM
ejpam-3506	52	43	)	)	PUNCT
ejpam-3506	52	44	≥	≥	NOUN
ejpam-3506	53	1	k	k	NOUN
ejpam-3506	53	2	,	,	PUNCT
ejpam-3506	53	3	it	it	PRON
ejpam-3506	53	4	follows	follow	VERB
ejpam-3506	53	5	that	that	PRON
ejpam-3506	53	6	γnckfd(g	γnckfd(g	NOUN
ejpam-3506	53	7	)	)	PUNCT
ejpam-3506	53	8	=	=	PUNCT
ejpam-3506	53	9	k.	k.	PROPN
ejpam-3506	54	1	thus	thus	ADV
ejpam-3506	54	2	,	,	PUNCT
ejpam-3506	54	3	(	(	PUNCT
ejpam-3506	54	4	ii	ii	NOUN
ejpam-3506	54	5	)	)	PUNCT
ejpam-3506	54	6	holds	hold	VERB
ejpam-3506	54	7	.	.	PUNCT
ejpam-3506	55	1	(	(	PUNCT
ejpam-3506	55	2	iii	iii	X
ejpam-3506	55	3	)	)	PUNCT
ejpam-3506	55	4	let	let	VERB
ejpam-3506	55	5	g	g	PROPN
ejpam-3506	55	6	be	be	AUX
ejpam-3506	55	7	kn	kn	PROPN
ejpam-3506	55	8	.	.	PUNCT
ejpam-3506	56	1	clearly	clearly	ADV
ejpam-3506	56	2	,	,	PUNCT
ejpam-3506	56	3	s	s	NOUN
ejpam-3506	56	4	=	=	SYM
ejpam-3506	56	5	v	v	PROPN
ejpam-3506	56	6	(	(	PUNCT
ejpam-3506	56	7	kk	kk	PROPN
ejpam-3506	56	8	)	)	PUNCT
ejpam-3506	56	9	is	be	AUX
ejpam-3506	56	10	a	a	DET
ejpam-3506	56	11	kfd	kfd	NOUN
ejpam-3506	56	12	-	-	PUNCT
ejpam-3506	56	13	set	set	NOUN
ejpam-3506	56	14	of	of	ADP
ejpam-3506	56	15	kn	kn	PROPN
ejpam-3506	56	16	,	,	PUNCT
ejpam-3506	56	17	〈	〈	PROPN
ejpam-3506	56	18	n(s	n(s	NOUN
ejpam-3506	56	19	)	)	PUNCT
ejpam-3506	56	20	〉	〉	NOUN
ejpam-3506	56	21	=	=	SYM
ejpam-3506	56	22	kn−1	kn−1	PROPN
ejpam-3506	56	23	if	if	SCONJ
ejpam-3506	56	24	k	k	PROPN
ejpam-3506	56	25	=	=	SYM
ejpam-3506	56	26	1	1	NUM
ejpam-3506	56	27	and	and	CCONJ
ejpam-3506	56	28	〈	〈	PROPN
ejpam-3506	56	29	n(s	n(s	NOUN
ejpam-3506	56	30	)	)	PUNCT
ejpam-3506	56	31	〉	〉	NOUN
ejpam-3506	56	32	=	=	SYM
ejpam-3506	56	33	kn	kn	PROPN
ejpam-3506	56	34	if	if	SCONJ
ejpam-3506	56	35	k	k	PROPN
ejpam-3506	56	36	>	>	X
ejpam-3506	56	37	1	1	NUM
ejpam-3506	56	38	,	,	PUNCT
ejpam-3506	56	39	so	so	ADV
ejpam-3506	56	40	s	s	NOUN
ejpam-3506	56	41	is	be	AUX
ejpam-3506	56	42	an	an	DET
ejpam-3506	56	43	nckfd	nckfd	NOUN
ejpam-3506	56	44	-	-	PUNCT
ejpam-3506	56	45	set	set	NOUN
ejpam-3506	56	46	of	of	ADP
ejpam-3506	56	47	kn	kn	PROPN
ejpam-3506	56	48	.	.	PUNCT
ejpam-3506	57	1	the	the	DET
ejpam-3506	57	2	result	result	NOUN
ejpam-3506	57	3	now	now	ADV
ejpam-3506	57	4	follows	follow	VERB
ejpam-3506	57	5	by	by	ADP
ejpam-3506	57	6	(	(	PUNCT
ejpam-3506	57	7	ii	ii	NOUN
ejpam-3506	57	8	)	)	PUNCT
ejpam-3506	57	9	.	.	PUNCT
ejpam-3506	58	1	�	�	PROPN
ejpam-3506	58	2	remark	remark	VERB
ejpam-3506	58	3	3	3	NUM
ejpam-3506	58	4	.	.	PUNCT
ejpam-3506	59	1	[	[	X
ejpam-3506	59	2	1	1	NUM
ejpam-3506	59	3	]	]	PUNCT
ejpam-3506	59	4	(	(	PUNCT
ejpam-3506	59	5	i	i	NOUN
ejpam-3506	59	6	)	)	PUNCT
ejpam-3506	59	7	γnc	γnc	PROPN
ejpam-3506	59	8	≥	≥	NUM
ejpam-3506	59	9	γ	γ	X
ejpam-3506	59	10	.	.	PROPN
ejpam-3506	59	11	(	(	PUNCT
ejpam-3506	59	12	ii	ii	NOUN
ejpam-3506	59	13	)	)	PUNCT
ejpam-3506	59	14	for	for	ADP
ejpam-3506	59	15	any	any	DET
ejpam-3506	59	16	connected	connected	ADJ
ejpam-3506	59	17	graph	graph	NOUN
ejpam-3506	59	18	g	g	NOUN
ejpam-3506	59	19	,	,	PUNCT
ejpam-3506	59	20	γnc	γnc	NOUN
ejpam-3506	59	21	=	=	NOUN
ejpam-3506	59	22	1	1	NUM
ejpam-3506	59	23	if	if	SCONJ
ejpam-3506	59	24	and	and	CCONJ
ejpam-3506	59	25	only	only	ADV
ejpam-3506	59	26	if	if	SCONJ
ejpam-3506	59	27	there	there	PRON
ejpam-3506	59	28	exists	exist	VERB
ejpam-3506	59	29	a	a	DET
ejpam-3506	59	30	non	non	ADJ
ejpam-3506	59	31	-	-	ADJ
ejpam-3506	59	32	cut	cut	ADJ
ejpam-3506	59	33	vertex	vertex	NOUN
ejpam-3506	59	34	v	v	ADP
ejpam-3506	59	35	such	such	DET
ejpam-3506	59	36	that	that	DET
ejpam-3506	59	37	deg	deg	NOUN
ejpam-3506	59	38	v	v	NOUN
ejpam-3506	59	39	=	=	SYM
ejpam-3506	59	40	n	n	CCONJ
ejpam-3506	59	41	−	−	PROPN
ejpam-3506	59	42	1	1	NUM
ejpam-3506	59	43	.	.	PUNCT
ejpam-3506	60	1	thus	thus	ADV
ejpam-3506	60	2	,	,	PUNCT
ejpam-3506	60	3	γnc(g	γnc(g	X
ejpam-3506	60	4	)	)	PUNCT
ejpam-3506	60	5	=	=	SYM
ejpam-3506	60	6	1	1	NUM
ejpam-3506	60	7	if	if	SCONJ
ejpam-3506	60	8	and	and	CCONJ
ejpam-3506	60	9	only	only	ADV
ejpam-3506	60	10	if	if	SCONJ
ejpam-3506	60	11	g	g	NOUN
ejpam-3506	60	12	=	=	NOUN
ejpam-3506	60	13	h	h	PROPN
ejpam-3506	60	14	+	+	CCONJ
ejpam-3506	60	15	k1	k1	NOUN
ejpam-3506	60	16	for	for	ADP
ejpam-3506	60	17	some	some	DET
ejpam-3506	60	18	connected	connect	VERB
ejpam-3506	60	19	graph	graph	NOUN
ejpam-3506	60	20	h.	h.	PROPN
ejpam-3506	60	21	theorem	theorem	PROPN
ejpam-3506	60	22	1	1	NUM
ejpam-3506	60	23	.	.	PUNCT
ejpam-3506	61	1	[	[	X
ejpam-3506	61	2	1	1	X
ejpam-3506	61	3	]	]	PUNCT
ejpam-3506	61	4	for	for	ADP
ejpam-3506	61	5	any	any	DET
ejpam-3506	61	6	positive	positive	ADJ
ejpam-3506	61	7	integer	integer	NOUN
ejpam-3506	61	8	n	n	PRON
ejpam-3506	61	9	≥	≥	NUM
ejpam-3506	61	10	1	1	NUM
ejpam-3506	61	11	,	,	PUNCT
ejpam-3506	61	12	γnc(pn	γnc(pn	NOUN
ejpam-3506	61	13	)	)	PUNCT
ejpam-3506	61	14	=	=	VERB
ejpam-3506	61	15	dn2	dn2	PROPN
ejpam-3506	61	16	e.	e.	PROPN
ejpam-3506	61	17	theorem	theorem	PROPN
ejpam-3506	61	18	2	2	NUM
ejpam-3506	61	19	.	.	PUNCT
ejpam-3506	62	1	[	[	X
ejpam-3506	62	2	1	1	NUM
ejpam-3506	62	3	]	]	SYM
ejpam-3506	62	4	γnc(cn	γnc(cn	NOUN
ejpam-3506	62	5	)	)	PUNCT
ejpam-3506	62	6	=	=	PRON
ejpam-3506	62	7	{	{	PUNCT
ejpam-3506	62	8	dn2	dn2	NOUN
ejpam-3506	62	9	e	e	NOUN
ejpam-3506	62	10	,	,	PUNCT
ejpam-3506	62	11	if	if	SCONJ
ejpam-3506	62	12	n	n	X
ejpam-3506	62	13	�	�	PROPN
ejpam-3506	62	14	3(mod	3(mod	NUM
ejpam-3506	62	15	4	4	X
ejpam-3506	62	16	)	)	PUNCT
ejpam-3506	62	17	bn2	bn2	NOUN
ejpam-3506	63	1	c	c	X
ejpam-3506	63	2	,	,	PUNCT
ejpam-3506	63	3	if	if	SCONJ
ejpam-3506	63	4	n	n	PRON
ejpam-3506	63	5	≡	≡	PROPN
ejpam-3506	63	6	3(mod	3(mod	NUM
ejpam-3506	63	7	4	4	NUM
ejpam-3506	63	8	)	)	PUNCT
ejpam-3506	63	9	.	.	PUNCT
ejpam-3506	64	1	theorem	theorem	NOUN
ejpam-3506	64	2	3	3	NUM
ejpam-3506	64	3	.	.	X
ejpam-3506	65	1	for	for	ADP
ejpam-3506	65	2	any	any	DET
ejpam-3506	65	3	positive	positive	ADJ
ejpam-3506	65	4	integer	integer	NOUN
ejpam-3506	65	5	n	n	PRON
ejpam-3506	65	6	≥	≥	NOUN
ejpam-3506	65	7	1	1	NUM
ejpam-3506	65	8	,	,	PUNCT
ejpam-3506	65	9	γnc1fd(pn	γnc1fd(pn	NOUN
ejpam-3506	65	10	)	)	PUNCT
ejpam-3506	65	11	=	=	PUNCT
ejpam-3506	65	12	dn2	dn2	PROPN
ejpam-3506	65	13	e.	e.	PROPN
ejpam-3506	65	14	proof	proof	PROPN
ejpam-3506	65	15	.	.	PUNCT
ejpam-3506	66	1	let	let	VERB
ejpam-3506	66	2	pn	pn	VERB
ejpam-3506	66	3	=	=	PUNCT
ejpam-3506	67	1	[	[	X
ejpam-3506	67	2	v1	v1	NOUN
ejpam-3506	67	3	,	,	PUNCT
ejpam-3506	67	4	v2	v2	PROPN
ejpam-3506	67	5	,	,	PUNCT
ejpam-3506	67	6	...	...	PUNCT
ejpam-3506	67	7	,	,	PUNCT
ejpam-3506	67	8	vn	vn	X
ejpam-3506	67	9	]	]	PUNCT
ejpam-3506	67	10	.	.	PUNCT
ejpam-3506	68	1	clearly	clearly	ADV
ejpam-3506	68	2	,	,	PUNCT
ejpam-3506	68	3	the	the	DET
ejpam-3506	68	4	formula	formula	NOUN
ejpam-3506	68	5	holds	hold	VERB
ejpam-3506	68	6	for	for	ADP
ejpam-3506	68	7	n	n	NOUN
ejpam-3506	68	8	=	=	SYM
ejpam-3506	68	9	1	1	NUM
ejpam-3506	68	10	,	,	PUNCT
ejpam-3506	68	11	2	2	NUM
ejpam-3506	68	12	,	,	PUNCT
ejpam-3506	68	13	3	3	NUM
ejpam-3506	68	14	.	.	PUNCT
ejpam-3506	69	1	let	let	AUX
ejpam-3506	69	2	l	l	NOUN
ejpam-3506	69	3	be	be	AUX
ejpam-3506	69	4	a	a	DET
ejpam-3506	69	5	positive	positive	ADJ
ejpam-3506	69	6	integer	integer	NOUN
ejpam-3506	69	7	.	.	PUNCT
ejpam-3506	70	1	if	if	SCONJ
ejpam-3506	70	2	n	n	NOUN
ejpam-3506	70	3	=	=	SYM
ejpam-3506	70	4	4l	4l	NOUN
ejpam-3506	70	5	,	,	PUNCT
ejpam-3506	70	6	then	then	ADV
ejpam-3506	70	7	s	s	VERB
ejpam-3506	70	8	=	=	PUNCT
ejpam-3506	70	9	{	{	PUNCT
ejpam-3506	70	10	vi	vi	NOUN
ejpam-3506	70	11	:	:	PUNCT
ejpam-3506	71	1	i	i	PRON
ejpam-3506	71	2	=	=	SYM
ejpam-3506	71	3	2a	2a	NUM
ejpam-3506	71	4	,	,	PUNCT
ejpam-3506	71	5	2a+	2a+	NUM
ejpam-3506	71	6	1	1	NUM
ejpam-3506	71	7	,	,	PUNCT
ejpam-3506	71	8	a	a	PRON
ejpam-3506	71	9	is	be	AUX
ejpam-3506	71	10	odd	odd	ADJ
ejpam-3506	71	11	and	and	CCONJ
ejpam-3506	72	1	1	1	NUM
ejpam-3506	72	2	≤	≤	NOUN
ejpam-3506	72	3	a	a	DET
ejpam-3506	72	4	≤	≤	NUM
ejpam-3506	72	5	2l−	2l−	NUM
ejpam-3506	72	6	1	1	NUM
ejpam-3506	72	7	}	}	PUNCT
ejpam-3506	72	8	is	be	AUX
ejpam-3506	72	9	an	an	DET
ejpam-3506	72	10	nc1fd	nc1fd	NOUN
ejpam-3506	72	11	-	-	PUNCT
ejpam-3506	72	12	set	set	NOUN
ejpam-3506	72	13	of	of	ADP
ejpam-3506	72	14	pn	pn	NOUN
ejpam-3506	72	15	,	,	PUNCT
ejpam-3506	72	16	where	where	SCONJ
ejpam-3506	72	17	〈	〈	PROPN
ejpam-3506	72	18	n(s	n(s	NOUN
ejpam-3506	72	19	)	)	PUNCT
ejpam-3506	72	20	〉	〉	NOUN
ejpam-3506	72	21	=	=	SYM
ejpam-3506	72	22	pn	pn	PROPN
ejpam-3506	72	23	.	.	PUNCT
ejpam-3506	73	1	if	if	SCONJ
ejpam-3506	73	2	n	n	NUM
ejpam-3506	73	3	=	=	SYM
ejpam-3506	73	4	4l+	4l+	NUM
ejpam-3506	73	5	1	1	NUM
ejpam-3506	73	6	,	,	PUNCT
ejpam-3506	73	7	then	then	ADV
ejpam-3506	73	8	s1	s1	PROPN
ejpam-3506	73	9	=	=	X
ejpam-3506	73	10	s	s	X
ejpam-3506	73	11	∪	∪	X
ejpam-3506	73	12	{	{	PUNCT
ejpam-3506	73	13	vn−1	vn−1	PROPN
ejpam-3506	73	14	}	}	PUNCT
ejpam-3506	73	15	is	be	AUX
ejpam-3506	73	16	an	an	DET
ejpam-3506	73	17	nc1fd	nc1fd	NOUN
ejpam-3506	73	18	-	-	PUNCT
ejpam-3506	73	19	set	set	NOUN
ejpam-3506	73	20	of	of	ADP
ejpam-3506	73	21	pn	pn	NOUN
ejpam-3506	73	22	,	,	PUNCT
ejpam-3506	74	1	where	where	SCONJ
ejpam-3506	74	2	〈	〈	PROPN
ejpam-3506	74	3	n(s1	n(s1	ADJ
ejpam-3506	74	4	)	)	PUNCT
ejpam-3506	74	5	〉	〉	NOUN
ejpam-3506	74	6	=	=	SYM
ejpam-3506	74	7	pn	pn	PROPN
ejpam-3506	74	8	.	.	PUNCT
ejpam-3506	75	1	if	if	SCONJ
ejpam-3506	75	2	n	n	NOUN
ejpam-3506	75	3	=	=	NOUN
ejpam-3506	75	4	4l	4l	NOUN
ejpam-3506	75	5	+	+	X
ejpam-3506	75	6	2	2	NUM
ejpam-3506	75	7	,	,	PUNCT
ejpam-3506	75	8	then	then	ADV
ejpam-3506	75	9	s2	s2	VERB
ejpam-3506	75	10	=	=	SYM
ejpam-3506	75	11	s	s	PART
ejpam-3506	75	12	∪	∪	X
ejpam-3506	75	13	{	{	PUNCT
ejpam-3506	75	14	vn	vn	NOUN
ejpam-3506	75	15	}	}	PUNCT
ejpam-3506	75	16	is	be	AUX
ejpam-3506	75	17	an	an	DET
ejpam-3506	75	18	nc1fd	nc1fd	NOUN
ejpam-3506	75	19	-	-	PUNCT
ejpam-3506	75	20	set	set	NOUN
ejpam-3506	75	21	of	of	ADP
ejpam-3506	75	22	pn	pn	NOUN
ejpam-3506	75	23	,	,	PUNCT
ejpam-3506	76	1	where	where	SCONJ
ejpam-3506	76	2	〈	〈	PROPN
ejpam-3506	76	3	n(s2	n(s2	NOUN
ejpam-3506	76	4	)	)	PUNCT
ejpam-3506	76	5	〉	〉	NOUN
ejpam-3506	76	6	=	=	SYM
ejpam-3506	76	7	pn−1	pn−1	PROPN
ejpam-3506	76	8	.	.	PUNCT
ejpam-3506	77	1	finally	finally	ADV
ejpam-3506	77	2	,	,	PUNCT
ejpam-3506	77	3	if	if	SCONJ
ejpam-3506	77	4	n	n	NOUN
ejpam-3506	77	5	=	=	NOUN
ejpam-3506	77	6	4l	4l	NOUN
ejpam-3506	77	7	+	+	CCONJ
ejpam-3506	77	8	3	3	NUM
ejpam-3506	77	9	,	,	PUNCT
ejpam-3506	77	10	then	then	ADV
ejpam-3506	77	11	s3	s3	PROPN
ejpam-3506	77	12	=	=	PROPN
ejpam-3506	77	13	s	s	PART
ejpam-3506	77	14	∪	∪	X
ejpam-3506	77	15	{	{	PUNCT
ejpam-3506	77	16	vn−1	vn−1	ADJ
ejpam-3506	77	17	,	,	PUNCT
ejpam-3506	77	18	vn	vn	VERB
ejpam-3506	77	19	}	}	PUNCT
ejpam-3506	77	20	is	be	AUX
ejpam-3506	77	21	an	an	DET
ejpam-3506	77	22	nc1fd	nc1fd	NOUN
ejpam-3506	77	23	-	-	PUNCT
ejpam-3506	77	24	set	set	NOUN
ejpam-3506	77	25	of	of	ADP
ejpam-3506	77	26	pn	pn	NOUN
ejpam-3506	77	27	,	,	PUNCT
ejpam-3506	77	28	where	where	SCONJ
ejpam-3506	77	29	〈	〈	PROPN
ejpam-3506	77	30	n(s3	n(s3	NOUN
ejpam-3506	77	31	)	)	PUNCT
ejpam-3506	77	32	〉	〉	PROPN
ejpam-3506	77	33	=	=	SYM
ejpam-3506	77	34	pn	pn	PROPN
ejpam-3506	77	35	.	.	PROPN
ejpam-3506	77	36	hence	hence	ADV
ejpam-3506	77	37	,	,	PUNCT
ejpam-3506	77	38	γnc1fd(pn	γnc1fd(pn	NOUN
ejpam-3506	77	39	)	)	PUNCT
ejpam-3506	77	40	≤	≤	NUM
ejpam-3506	77	41	dn2	dn2	PROPN
ejpam-3506	77	42	e.	e.	PROPN
ejpam-3506	77	43	further	far	ADV
ejpam-3506	77	44	,	,	PUNCT
ejpam-3506	77	45	if	if	SCONJ
ejpam-3506	77	46	s	s	NOUN
ejpam-3506	77	47	is	be	AUX
ejpam-3506	77	48	any	any	DET
ejpam-3506	77	49	γnc1fd	γnc1fd	NOUN
ejpam-3506	77	50	-	-	PUNCT
ejpam-3506	77	51	set	set	NOUN
ejpam-3506	77	52	of	of	ADP
ejpam-3506	77	53	pn	pn	PROPN
ejpam-3506	77	54	,	,	PUNCT
ejpam-3506	77	55	then	then	ADV
ejpam-3506	77	56	s	s	VERB
ejpam-3506	77	57	is	be	AUX
ejpam-3506	77	58	an	an	DET
ejpam-3506	77	59	ncd	ncd	NOUN
ejpam-3506	77	60	-	-	PUNCT
ejpam-3506	77	61	set	set	NOUN
ejpam-3506	77	62	of	of	ADP
ejpam-3506	77	63	pn	pn	PROPN
ejpam-3506	77	64	.	.	PUNCT
ejpam-3506	77	65	by	by	ADP
ejpam-3506	77	66	remark	remark	NOUN
ejpam-3506	77	67	2	2	NUM
ejpam-3506	77	68	and	and	CCONJ
ejpam-3506	77	69	theorem	theorem	VERB
ejpam-3506	77	70	1	1	NUM
ejpam-3506	77	71	,	,	PUNCT
ejpam-3506	77	72	|s|	|s|	NOUN
ejpam-3506	77	73	≥	≥	PROPN
ejpam-3506	77	74	dn2	dn2	PROPN
ejpam-3506	77	75	e.	e.	PROPN
ejpam-3506	77	76	therefore	therefore	ADV
ejpam-3506	77	77	,	,	PUNCT
ejpam-3506	77	78	γnc1fd(pn	γnc1fd(pn	NOUN
ejpam-3506	77	79	)	)	PUNCT
ejpam-3506	77	80	=	=	VERB
ejpam-3506	77	81	dn2	dn2	PROPN
ejpam-3506	77	82	e.	e.	PROPN
ejpam-3506	77	83	�	�	PROPN
ejpam-3506	77	84	theorem	theorem	VERB
ejpam-3506	77	85	4	4	NUM
ejpam-3506	77	86	.	.	X
ejpam-3506	77	87	for	for	ADP
ejpam-3506	77	88	any	any	DET
ejpam-3506	77	89	positive	positive	ADJ
ejpam-3506	77	90	integer	integer	NOUN
ejpam-3506	77	91	n	n	PRON
ejpam-3506	77	92	≥	≥	NOUN
ejpam-3506	77	93	3	3	NUM
ejpam-3506	77	94	,	,	PUNCT
ejpam-3506	77	95	γnc1fd(cn	γnc1fd(cn	NOUN
ejpam-3506	77	96	)	)	PUNCT
ejpam-3506	78	1	=	=	PUNCT
ejpam-3506	79	1			PRON
ejpam-3506	79	2	dn2	dn2	VERB
ejpam-3506	79	3	e	e	NOUN
ejpam-3506	79	4	,	,	PUNCT
ejpam-3506	79	5	if	if	SCONJ
ejpam-3506	79	6	n	n	PRON
ejpam-3506	79	7	≡	≡	PROPN
ejpam-3506	79	8	0	0	NUM
ejpam-3506	79	9	or	or	CCONJ
ejpam-3506	79	10	1(mod	1(mod	NUM
ejpam-3506	79	11	4	4	NUM
ejpam-3506	79	12	)	)	PUNCT
ejpam-3506	79	13	dn2	dn2	NOUN
ejpam-3506	79	14	e+	e+	VERB
ejpam-3506	79	15	1	1	NUM
ejpam-3506	79	16	,	,	PUNCT
ejpam-3506	79	17	if	if	SCONJ
ejpam-3506	79	18	n	n	PRON
ejpam-3506	79	19	≡	≡	PROPN
ejpam-3506	79	20	2(mod	2(mod	NUM
ejpam-3506	79	21	4	4	X
ejpam-3506	79	22	)	)	PUNCT
ejpam-3506	79	23	bn2	bn2	NOUN
ejpam-3506	80	1	c	c	X
ejpam-3506	80	2	,	,	PUNCT
ejpam-3506	80	3	if	if	SCONJ
ejpam-3506	80	4	n	n	PRON
ejpam-3506	80	5	≡	≡	PROPN
ejpam-3506	80	6	3(mod	3(mod	NUM
ejpam-3506	80	7	4	4	NUM
ejpam-3506	80	8	)	)	PUNCT
ejpam-3506	80	9	.	.	PUNCT
ejpam-3506	81	1	w.	w.	PROPN
ejpam-3506	81	2	bent	bent	PROPN
ejpam-3506	81	3	-	-	PUNCT
ejpam-3506	81	4	usman	usman	PROPN
ejpam-3506	81	5	,	,	PUNCT
ejpam-3506	81	6	r.	r.	PROPN
ejpam-3506	81	7	isla	isla	PROPN
ejpam-3506	81	8	,	,	PUNCT
ejpam-3506	81	9	s.	s.	PROPN
ejpam-3506	81	10	canoy	canoy	PROPN
ejpam-3506	81	11	/	/	SYM
ejpam-3506	81	12	eur	eur	PROPN
ejpam-3506	81	13	.	.	PUNCT
ejpam-3506	82	1	j.	j.	PROPN
ejpam-3506	82	2	pure	pure	PROPN
ejpam-3506	82	3	appl	appl	PROPN
ejpam-3506	82	4	.	.	PROPN
ejpam-3506	82	5	math	math	PROPN
ejpam-3506	82	6	,	,	PUNCT
ejpam-3506	82	7	12	12	NUM
ejpam-3506	82	8	(	(	PUNCT
ejpam-3506	82	9	3	3	NUM
ejpam-3506	82	10	)	)	PUNCT
ejpam-3506	82	11	(	(	PUNCT
ejpam-3506	82	12	2019	2019	NUM
ejpam-3506	82	13	)	)	PUNCT
ejpam-3506	82	14	,	,	PUNCT
ejpam-3506	82	15	1337	1337	NUM
ejpam-3506	82	16	-	-	SYM
ejpam-3506	82	17	1349	1349	NUM
ejpam-3506	82	18	1340	1340	NUM
ejpam-3506	82	19	proof	proof	NOUN
ejpam-3506	82	20	.	.	PUNCT
ejpam-3506	83	1	let	let	VERB
ejpam-3506	83	2	cn	cn	PROPN
ejpam-3506	83	3	=	=	PUNCT
ejpam-3506	84	1	[	[	X
ejpam-3506	84	2	v1	v1	NOUN
ejpam-3506	84	3	,	,	PUNCT
ejpam-3506	84	4	v2	v2	PROPN
ejpam-3506	84	5	,	,	PUNCT
ejpam-3506	84	6	...	...	PUNCT
ejpam-3506	84	7	,	,	PUNCT
ejpam-3506	84	8	vn	vn	X
ejpam-3506	84	9	,	,	PUNCT
ejpam-3506	84	10	v1	v1	PROPN
ejpam-3506	84	11	]	]	PUNCT
ejpam-3506	84	12	.	.	PUNCT
ejpam-3506	85	1	clearly	clearly	ADV
ejpam-3506	85	2	,	,	PUNCT
ejpam-3506	85	3	γnc1fd(c3	γnc1fd(c3	NOUN
ejpam-3506	85	4	)	)	PUNCT
ejpam-3506	85	5	=	=	SYM
ejpam-3506	85	6	1	1	X
ejpam-3506	85	7	.	.	PUNCT
ejpam-3506	86	1	let	let	VERB
ejpam-3506	86	2	l	l	NOUN
ejpam-3506	86	3	be	be	AUX
ejpam-3506	86	4	a	a	DET
ejpam-3506	86	5	positive	positive	ADJ
ejpam-3506	86	6	integer	integer	NOUN
ejpam-3506	86	7	and	and	CCONJ
ejpam-3506	86	8	n	n	NOUN
ejpam-3506	86	9	=	=	NOUN
ejpam-3506	87	1	4l+	4l+	NUM
ejpam-3506	87	2	r	r	NOUN
ejpam-3506	87	3	,	,	PUNCT
ejpam-3506	87	4	where	where	SCONJ
ejpam-3506	87	5	0	0	NUM
ejpam-3506	87	6	≤	≤	NUM
ejpam-3506	87	7	r	r	NOUN
ejpam-3506	87	8	≤	≤	NUM
ejpam-3506	87	9	3	3	NUM
ejpam-3506	87	10	.	.	PUNCT
ejpam-3506	88	1	let	let	VERB
ejpam-3506	88	2	s	s	VERB
ejpam-3506	88	3	=	=	X
ejpam-3506	88	4	{	{	PUNCT
ejpam-3506	88	5	vi	vi	NOUN
ejpam-3506	88	6	:	:	PUNCT
ejpam-3506	88	7	i	i	NOUN
ejpam-3506	88	8	=	=	PUNCT
ejpam-3506	88	9	2j	2j	NUM
ejpam-3506	88	10	,	,	PUNCT
ejpam-3506	88	11	2j+	2j+	NUM
ejpam-3506	88	12	1	1	NUM
ejpam-3506	88	13	,	,	PUNCT
ejpam-3506	88	14	j	j	PROPN
ejpam-3506	88	15	is	be	AUX
ejpam-3506	88	16	odd	odd	ADJ
ejpam-3506	88	17	and	and	CCONJ
ejpam-3506	88	18	1	1	NUM
ejpam-3506	88	19	≤	≤	NUM
ejpam-3506	88	20	j	j	PROPN
ejpam-3506	88	21	≤	≤	PROPN
ejpam-3506	88	22	2l−	2l−	NUM
ejpam-3506	88	23	1	1	NUM
ejpam-3506	88	24	}	}	PUNCT
ejpam-3506	88	25	.	.	PUNCT
ejpam-3506	89	1	let	let	VERB
ejpam-3506	89	2	s1	s1	NOUN
ejpam-3506	89	3	=	=	PUNCT
ejpam-3506	89	4			VERB
ejpam-3506	89	5	s	s	PROPN
ejpam-3506	89	6	,	,	PUNCT
ejpam-3506	89	7	if	if	SCONJ
ejpam-3506	89	8	n	n	PRON
ejpam-3506	89	9	≡	≡	PROPN
ejpam-3506	89	10	0(mod	0(mod	NOUN
ejpam-3506	89	11	4	4	X
ejpam-3506	89	12	)	)	PUNCT
ejpam-3506	89	13	s	s	PART
ejpam-3506	89	14	∪	∪	X
ejpam-3506	89	15	{	{	PUNCT
ejpam-3506	89	16	v1	v1	NOUN
ejpam-3506	89	17	}	}	PUNCT
ejpam-3506	89	18	,	,	PUNCT
ejpam-3506	89	19	if	if	SCONJ
ejpam-3506	89	20	n	n	PRON
ejpam-3506	89	21	≡	≡	PROPN
ejpam-3506	89	22	1(mod	1(mod	NUM
ejpam-3506	89	23	4	4	X
ejpam-3506	89	24	)	)	PUNCT
ejpam-3506	89	25	s	s	PART
ejpam-3506	89	26	∪	∪	X
ejpam-3506	89	27	{	{	PUNCT
ejpam-3506	89	28	v1	v1	NOUN
ejpam-3506	89	29	,	,	PUNCT
ejpam-3506	89	30	vn	vn	NOUN
ejpam-3506	89	31	}	}	PUNCT
ejpam-3506	89	32	,	,	PUNCT
ejpam-3506	89	33	if	if	SCONJ
ejpam-3506	89	34	n	n	PRON
ejpam-3506	89	35	≡	≡	PROPN
ejpam-3506	89	36	2(mod	2(mod	NUM
ejpam-3506	89	37	4	4	X
ejpam-3506	89	38	)	)	PUNCT
ejpam-3506	89	39	s	s	VERB
ejpam-3506	89	40	∪	∪	X
ejpam-3506	89	41	{	{	PUNCT
ejpam-3506	89	42	vn−1	vn−1	PROPN
ejpam-3506	89	43	}	}	PUNCT
ejpam-3506	89	44	,	,	PUNCT
ejpam-3506	89	45	if	if	SCONJ
ejpam-3506	89	46	n	n	PRON
ejpam-3506	89	47	≡	≡	PROPN
ejpam-3506	89	48	3(mod	3(mod	NUM
ejpam-3506	89	49	4	4	NUM
ejpam-3506	89	50	)	)	PUNCT
ejpam-3506	89	51	.	.	PUNCT
ejpam-3506	90	1	clearly	clearly	ADV
ejpam-3506	90	2	,	,	PUNCT
ejpam-3506	90	3	s1	s1	PROPN
ejpam-3506	90	4	is	be	AUX
ejpam-3506	90	5	a	a	DET
ejpam-3506	90	6	1fd	1fd	NOUN
ejpam-3506	90	7	-	-	PUNCT
ejpam-3506	90	8	set	set	NOUN
ejpam-3506	90	9	of	of	ADP
ejpam-3506	90	10	cn	cn	PROPN
ejpam-3506	90	11	.	.	PUNCT
ejpam-3506	91	1	moreover	moreover	ADV
ejpam-3506	91	2	,	,	PUNCT
ejpam-3506	91	3	〈	〈	PROPN
ejpam-3506	91	4	n(s1	n(s1	ADJ
ejpam-3506	91	5	)	)	PUNCT
ejpam-3506	91	6	〉	〉	NOUN
ejpam-3506	91	7	=	=	SYM
ejpam-3506	91	8	{	{	PUNCT
ejpam-3506	91	9	cn	cn	INTJ
ejpam-3506	91	10	,	,	PUNCT
ejpam-3506	91	11	if	if	SCONJ
ejpam-3506	91	12	n	n	X
ejpam-3506	91	13	�	�	PROPN
ejpam-3506	91	14	3(mod	3(mod	NUM
ejpam-3506	91	15	4	4	X
ejpam-3506	91	16	)	)	PUNCT
ejpam-3506	91	17	pn−1	pn−1	PROPN
ejpam-3506	91	18	,	,	PUNCT
ejpam-3506	91	19	if	if	SCONJ
ejpam-3506	91	20	n	n	PRON
ejpam-3506	91	21	≡	≡	PROPN
ejpam-3506	91	22	3(mod	3(mod	NUM
ejpam-3506	91	23	4	4	NUM
ejpam-3506	91	24	)	)	PUNCT
ejpam-3506	91	25	,	,	PUNCT
ejpam-3506	91	26	thus	thus	ADV
ejpam-3506	91	27	,	,	PUNCT
ejpam-3506	91	28	s1	s1	PROPN
ejpam-3506	91	29	is	be	AUX
ejpam-3506	91	30	an	an	DET
ejpam-3506	91	31	nc1fd	nc1fd	NOUN
ejpam-3506	91	32	-	-	PUNCT
ejpam-3506	91	33	set	set	NOUN
ejpam-3506	91	34	of	of	ADP
ejpam-3506	91	35	cn	cn	PROPN
ejpam-3506	91	36	.	.	PUNCT
ejpam-3506	91	37	hence	hence	ADV
ejpam-3506	91	38	,	,	PUNCT
ejpam-3506	91	39	γnc1fd(cn	γnc1fd(cn	NOUN
ejpam-3506	91	40	)	)	PUNCT
ejpam-3506	91	41	≤	≤	NOUN
ejpam-3506	92	1			PROPN
ejpam-3506	92	2	dn2	dn2	VERB
ejpam-3506	92	3	e	e	NOUN
ejpam-3506	92	4	,	,	PUNCT
ejpam-3506	92	5	if	if	SCONJ
ejpam-3506	92	6	n	n	PRON
ejpam-3506	92	7	≡	≡	PROPN
ejpam-3506	92	8	0	0	NUM
ejpam-3506	92	9	or	or	CCONJ
ejpam-3506	92	10	1(mod	1(mod	NUM
ejpam-3506	92	11	4	4	NUM
ejpam-3506	92	12	)	)	PUNCT
ejpam-3506	92	13	dn2	dn2	NOUN
ejpam-3506	92	14	e+	e+	VERB
ejpam-3506	92	15	1	1	NUM
ejpam-3506	92	16	,	,	PUNCT
ejpam-3506	92	17	if	if	SCONJ
ejpam-3506	92	18	n	n	PRON
ejpam-3506	92	19	≡	≡	PROPN
ejpam-3506	92	20	2(mod	2(mod	NUM
ejpam-3506	92	21	4	4	X
ejpam-3506	92	22	)	)	PUNCT
ejpam-3506	92	23	bn2	bn2	NOUN
ejpam-3506	93	1	c	c	X
ejpam-3506	93	2	,	,	PUNCT
ejpam-3506	93	3	if	if	SCONJ
ejpam-3506	93	4	n	n	PRON
ejpam-3506	93	5	≡	≡	PROPN
ejpam-3506	93	6	3(mod	3(mod	NUM
ejpam-3506	93	7	4	4	NUM
ejpam-3506	93	8	)	)	PUNCT
ejpam-3506	93	9	.	.	PUNCT
ejpam-3506	94	1	now	now	ADV
ejpam-3506	94	2	,	,	PUNCT
ejpam-3506	94	3	let	let	VERB
ejpam-3506	94	4	s	s	PRON
ejpam-3506	94	5	be	be	AUX
ejpam-3506	94	6	any	any	DET
ejpam-3506	94	7	γnc1fd	γnc1fd	NOUN
ejpam-3506	94	8	-	-	PUNCT
ejpam-3506	94	9	set	set	NOUN
ejpam-3506	94	10	of	of	ADP
ejpam-3506	94	11	cn	cn	PROPN
ejpam-3506	94	12	.	.	PUNCT
ejpam-3506	94	13	by	by	ADP
ejpam-3506	94	14	remark	remark	NOUN
ejpam-3506	94	15	2	2	NUM
ejpam-3506	94	16	and	and	CCONJ
ejpam-3506	94	17	theorem	theorem	VERB
ejpam-3506	94	18	2	2	NUM
ejpam-3506	94	19	,	,	PUNCT
ejpam-3506	94	20	γnc1fd(cn	γnc1fd(cn	PROPN
ejpam-3506	94	21	)	)	PUNCT
ejpam-3506	94	22	≥	≥	NOUN
ejpam-3506	94	23	γnc(cn	γnc(cn	NOUN
ejpam-3506	94	24	)	)	PUNCT
ejpam-3506	94	25	=	=	PRON
ejpam-3506	94	26	{	{	PUNCT
ejpam-3506	94	27	dn2	dn2	NOUN
ejpam-3506	94	28	e	e	NOUN
ejpam-3506	94	29	,	,	PUNCT
ejpam-3506	94	30	if	if	SCONJ
ejpam-3506	94	31	n	n	X
ejpam-3506	94	32	�	�	PROPN
ejpam-3506	94	33	3(mod	3(mod	NUM
ejpam-3506	94	34	4	4	X
ejpam-3506	94	35	)	)	PUNCT
ejpam-3506	94	36	bn2	bn2	NOUN
ejpam-3506	95	1	c	c	X
ejpam-3506	95	2	,	,	PUNCT
ejpam-3506	95	3	if	if	SCONJ
ejpam-3506	95	4	n	n	PRON
ejpam-3506	95	5	≡	≡	PROPN
ejpam-3506	95	6	3(mod	3(mod	NUM
ejpam-3506	95	7	4	4	NUM
ejpam-3506	95	8	)	)	PUNCT
ejpam-3506	95	9	.	.	PUNCT
ejpam-3506	96	1	if	if	SCONJ
ejpam-3506	96	2	n	n	PRON
ejpam-3506	96	3	≡	≡	PROPN
ejpam-3506	96	4	0	0	NUM
ejpam-3506	96	5	or	or	CCONJ
ejpam-3506	96	6	1(mod	1(mod	NUM
ejpam-3506	96	7	4	4	NUM
ejpam-3506	96	8	)	)	PUNCT
ejpam-3506	96	9	,	,	PUNCT
ejpam-3506	96	10	then	then	ADV
ejpam-3506	96	11	γnc1fd(g	γnc1fd(g	PROPN
ejpam-3506	96	12	)	)	PUNCT
ejpam-3506	96	13	≥	≥	PROPN
ejpam-3506	96	14	dn2	dn2	PROPN
ejpam-3506	96	15	e.	e.	PROPN
ejpam-3506	96	16	if	if	SCONJ
ejpam-3506	96	17	n	n	PRON
ejpam-3506	96	18	≡	≡	PROPN
ejpam-3506	96	19	3(mod	3(mod	NUM
ejpam-3506	96	20	4	4	NUM
ejpam-3506	96	21	)	)	PUNCT
ejpam-3506	96	22	,	,	PUNCT
ejpam-3506	96	23	then	then	ADV
ejpam-3506	96	24	γnc1fd(g	γnc1fd(g	PROPN
ejpam-3506	96	25	)	)	PUNCT
ejpam-3506	96	26	≥	≥	NOUN
ejpam-3506	96	27	bn2	bn2	VERB
ejpam-3506	96	28	c.	c.	NOUN
ejpam-3506	96	29	moreover	moreover	ADV
ejpam-3506	96	30	,	,	PUNCT
ejpam-3506	96	31	when	when	SCONJ
ejpam-3506	96	32	n	n	PRON
ejpam-3506	96	33	≡	≡	PROPN
ejpam-3506	96	34	2(mod	2(mod	NUM
ejpam-3506	96	35	4	4	X
ejpam-3506	96	36	)	)	PUNCT
ejpam-3506	96	37	,	,	PUNCT
ejpam-3506	96	38	then	then	ADV
ejpam-3506	96	39	〈	〈	PROPN
ejpam-3506	96	40	s1	s1	PROPN
ejpam-3506	96	41	〉	〉	PROPN
ejpam-3506	96	42	contains	contain	VERB
ejpam-3506	96	43	two	two	NUM
ejpam-3506	96	44	vertices	vertex	NOUN
ejpam-3506	96	45	more	more	ADJ
ejpam-3506	96	46	than	than	ADP
ejpam-3506	96	47	when	when	SCONJ
ejpam-3506	96	48	n	n	X
ejpam-3506	96	49	≡	≡	PROPN
ejpam-3506	96	50	0(mod	0(mod	NOUN
ejpam-3506	96	51	4	4	NUM
ejpam-3506	96	52	)	)	PUNCT
ejpam-3506	96	53	and	and	CCONJ
ejpam-3506	96	54	one	one	NUM
ejpam-3506	96	55	vertex	vertex	NOUN
ejpam-3506	96	56	more	more	ADJ
ejpam-3506	96	57	than	than	ADP
ejpam-3506	96	58	when	when	SCONJ
ejpam-3506	96	59	n	n	X
ejpam-3506	96	60	≡	≡	PROPN
ejpam-3506	96	61	1(mod	1(mod	NUM
ejpam-3506	96	62	4	4	NUM
ejpam-3506	96	63	)	)	PUNCT
ejpam-3506	96	64	.	.	PUNCT
ejpam-3506	97	1	thus	thus	ADV
ejpam-3506	97	2	,	,	PUNCT
ejpam-3506	97	3	γnc1fd(cn	γnc1fd(cn	PROPN
ejpam-3506	97	4	)	)	PUNCT
ejpam-3506	97	5	≥	≥	NOUN
ejpam-3506	97	6	dn2	dn2	NOUN
ejpam-3506	97	7	e	e	NOUN
ejpam-3506	98	1	+	+	CCONJ
ejpam-3506	98	2	1	1	NUM
ejpam-3506	98	3	if	if	SCONJ
ejpam-3506	98	4	n	n	PRON
ejpam-3506	98	5	≡	≡	PROPN
ejpam-3506	98	6	2(mod	2(mod	NUM
ejpam-3506	98	7	4	4	NUM
ejpam-3506	98	8	)	)	PUNCT
ejpam-3506	98	9	.	.	PUNCT
ejpam-3506	99	1	the	the	DET
ejpam-3506	99	2	result	result	NOUN
ejpam-3506	99	3	now	now	ADV
ejpam-3506	99	4	follows	follow	VERB
ejpam-3506	99	5	.	.	PUNCT
ejpam-3506	100	1	�	�	PROPN
ejpam-3506	100	2	theorem	theorem	VERB
ejpam-3506	100	3	5	5	NUM
ejpam-3506	100	4	.	.	X
ejpam-3506	100	5	for	for	ADP
ejpam-3506	100	6	any	any	DET
ejpam-3506	100	7	nontrivial	nontrivial	ADJ
ejpam-3506	100	8	connected	connect	VERB
ejpam-3506	100	9	graph	graph	NOUN
ejpam-3506	100	10	g	g	NOUN
ejpam-3506	100	11	,	,	PUNCT
ejpam-3506	100	12	γnc1fd(g	γnc1fd(g	PROPN
ejpam-3506	100	13	)	)	PUNCT
ejpam-3506	101	1	=	=	SYM
ejpam-3506	101	2	1	1	NUM
ejpam-3506	101	3	if	if	SCONJ
ejpam-3506	101	4	and	and	CCONJ
ejpam-3506	101	5	only	only	ADV
ejpam-3506	101	6	if	if	SCONJ
ejpam-3506	101	7	g	g	NOUN
ejpam-3506	101	8	=	=	NOUN
ejpam-3506	101	9	h	h	PROPN
ejpam-3506	102	1	+	+	NOUN
ejpam-3506	102	2	k1	k1	NOUN
ejpam-3506	102	3	for	for	ADP
ejpam-3506	102	4	some	some	DET
ejpam-3506	102	5	connected	connect	VERB
ejpam-3506	102	6	graph	graph	NOUN
ejpam-3506	102	7	h.	h.	NOUN
ejpam-3506	102	8	proof	proof	NOUN
ejpam-3506	102	9	.	.	PUNCT
ejpam-3506	103	1	suppose	suppose	VERB
ejpam-3506	103	2	γnc1fd(g	γnc1fd(g	NOUN
ejpam-3506	103	3	)	)	PUNCT
ejpam-3506	104	1	=	=	SYM
ejpam-3506	105	1	1	1	X
ejpam-3506	105	2	.	.	PUNCT
ejpam-3506	105	3	then	then	ADV
ejpam-3506	105	4	by	by	ADP
ejpam-3506	105	5	remark	remark	NOUN
ejpam-3506	105	6	2	2	NUM
ejpam-3506	105	7	,	,	PUNCT
ejpam-3506	105	8	γnc(g	γnc(g	NUM
ejpam-3506	105	9	)	)	PUNCT
ejpam-3506	105	10	=	=	SYM
ejpam-3506	105	11	1	1	NUM
ejpam-3506	105	12	,	,	PUNCT
ejpam-3506	105	13	thus	thus	ADV
ejpam-3506	105	14	g	g	NOUN
ejpam-3506	105	15	=	=	SYM
ejpam-3506	105	16	h	h	PROPN
ejpam-3506	105	17	+	+	CCONJ
ejpam-3506	105	18	k1	k1	NOUN
ejpam-3506	105	19	for	for	ADP
ejpam-3506	105	20	some	some	DET
ejpam-3506	105	21	connected	connect	VERB
ejpam-3506	105	22	graph	graph	NOUN
ejpam-3506	105	23	h	h	NOUN
ejpam-3506	105	24	by	by	ADP
ejpam-3506	105	25	remark	remark	NOUN
ejpam-3506	105	26	3	3	NUM
ejpam-3506	105	27	.	.	PUNCT
ejpam-3506	106	1	conversely	conversely	ADV
ejpam-3506	106	2	,	,	PUNCT
ejpam-3506	106	3	suppose	suppose	VERB
ejpam-3506	106	4	g	g	PROPN
ejpam-3506	106	5	=	=	PROPN
ejpam-3506	106	6	h	h	PROPN
ejpam-3506	106	7	+	+	CCONJ
ejpam-3506	106	8	k1	k1	NOUN
ejpam-3506	106	9	for	for	ADP
ejpam-3506	106	10	some	some	DET
ejpam-3506	106	11	connected	connect	VERB
ejpam-3506	106	12	graph	graph	NOUN
ejpam-3506	106	13	h.	h.	PROPN
ejpam-3506	106	14	let	let	VERB
ejpam-3506	106	15	〈	〈	PROPN
ejpam-3506	106	16	s	s	PART
ejpam-3506	106	17	〉	〉	NOUN
ejpam-3506	106	18	=	=	SYM
ejpam-3506	106	19	k1	k1	NOUN
ejpam-3506	106	20	=	=	SYM
ejpam-3506	106	21	〈	〈	PROPN
ejpam-3506	106	22	{	{	PUNCT
ejpam-3506	106	23	v	v	NOUN
ejpam-3506	106	24	}	}	PUNCT
ejpam-3506	106	25	〉	〉	PROPN
ejpam-3506	106	26	.	.	PUNCT
ejpam-3506	107	1	then	then	ADV
ejpam-3506	107	2	〈	〈	PROPN
ejpam-3506	107	3	n(s	n(s	NOUN
ejpam-3506	107	4	)	)	PUNCT
ejpam-3506	107	5	〉	〉	NOUN
ejpam-3506	107	6	=	=	SYM
ejpam-3506	107	7	h	h	NOUN
ejpam-3506	107	8	and	and	CCONJ
ejpam-3506	107	9	clearly	clearly	ADV
ejpam-3506	107	10	s	s	VERB
ejpam-3506	107	11	is	be	AUX
ejpam-3506	107	12	a	a	DET
ejpam-3506	107	13	γnc1fd	γnc1fd	NOUN
ejpam-3506	107	14	-	-	PUNCT
ejpam-3506	107	15	set	set	NOUN
ejpam-3506	107	16	of	of	ADP
ejpam-3506	107	17	g.	g.	PROPN
ejpam-3506	107	18	hence	hence	ADV
ejpam-3506	107	19	,	,	PUNCT
ejpam-3506	107	20	γnc1fd(g	γnc1fd(g	PROPN
ejpam-3506	107	21	)	)	PUNCT
ejpam-3506	107	22	=	=	SYM
ejpam-3506	107	23	1	1	X
ejpam-3506	107	24	.	.	X
ejpam-3506	107	25	�	�	PROPN
ejpam-3506	107	26	corollary	corollary	NOUN
ejpam-3506	107	27	1	1	NUM
ejpam-3506	107	28	.	.	PUNCT
ejpam-3506	108	1	let	let	VERB
ejpam-3506	108	2	n	n	PRON
ejpam-3506	108	3	be	be	AUX
ejpam-3506	108	4	a	a	DET
ejpam-3506	108	5	positive	positive	ADJ
ejpam-3506	108	6	integer	integer	NOUN
ejpam-3506	108	7	.	.	PUNCT
ejpam-3506	109	1	then	then	ADV
ejpam-3506	109	2	γnc1fd(fn	γnc1fd(fn	NOUN
ejpam-3506	109	3	)	)	PUNCT
ejpam-3506	109	4	=	=	SYM
ejpam-3506	109	5	γnc1fd(k1,n	γnc1fd(k1,n	NOUN
ejpam-3506	109	6	)	)	PUNCT
ejpam-3506	109	7	=	=	SYM
ejpam-3506	109	8	1	1	NUM
ejpam-3506	109	9	for	for	ADP
ejpam-3506	109	10	n	n	X
ejpam-3506	109	11	≥	≥	NOUN
ejpam-3506	109	12	1	1	NUM
ejpam-3506	109	13	and	and	CCONJ
ejpam-3506	109	14	γnc1fd(wn	γnc1fd(wn	NOUN
ejpam-3506	109	15	)	)	PUNCT
ejpam-3506	110	1	=	=	SYM
ejpam-3506	110	2	1	1	NUM
ejpam-3506	110	3	for	for	ADP
ejpam-3506	110	4	n	n	X
ejpam-3506	110	5	≥	≥	NUM
ejpam-3506	110	6	3	3	NUM
ejpam-3506	110	7	.	.	PUNCT
ejpam-3506	110	8	theorem	theorem	NOUN
ejpam-3506	110	9	6	6	NUM
ejpam-3506	110	10	.	.	PUNCT
ejpam-3506	111	1	let	let	VERB
ejpam-3506	111	2	a	a	PRON
ejpam-3506	111	3	and	and	CCONJ
ejpam-3506	111	4	b	b	NOUN
ejpam-3506	111	5	be	be	AUX
ejpam-3506	111	6	positive	positive	ADJ
ejpam-3506	111	7	integers	integer	NOUN
ejpam-3506	111	8	such	such	ADJ
ejpam-3506	111	9	that	that	SCONJ
ejpam-3506	111	10	2	2	NUM
ejpam-3506	111	11	≤	≤	NUM
ejpam-3506	111	12	a	a	DET
ejpam-3506	111	13	≤	≤	PROPN
ejpam-3506	111	14	b.	b.	NOUN
ejpam-3506	112	1	then	then	ADV
ejpam-3506	112	2	there	there	PRON
ejpam-3506	112	3	exists	exist	VERB
ejpam-3506	112	4	a	a	DET
ejpam-3506	112	5	connected	connected	ADJ
ejpam-3506	112	6	graph	graph	NOUN
ejpam-3506	112	7	g	g	ADP
ejpam-3506	112	8	such	such	ADJ
ejpam-3506	112	9	that	that	DET
ejpam-3506	112	10	γ1fd(g	γ1fd(g	PROPN
ejpam-3506	112	11	)	)	PUNCT
ejpam-3506	112	12	=	=	SYM
ejpam-3506	112	13	a	a	PRON
ejpam-3506	112	14	and	and	CCONJ
ejpam-3506	112	15	γnc1fd(g	γnc1fd(g	NUM
ejpam-3506	112	16	)	)	PUNCT
ejpam-3506	113	1	=	=	SYM
ejpam-3506	113	2	b.	b.	PROPN
ejpam-3506	113	3	w.	w.	PROPN
ejpam-3506	113	4	bent	bent	PROPN
ejpam-3506	113	5	-	-	PUNCT
ejpam-3506	113	6	usman	usman	PROPN
ejpam-3506	113	7	,	,	PUNCT
ejpam-3506	113	8	r.	r.	PROPN
ejpam-3506	113	9	isla	isla	PROPN
ejpam-3506	113	10	,	,	PUNCT
ejpam-3506	113	11	s.	s.	PROPN
ejpam-3506	113	12	canoy	canoy	PROPN
ejpam-3506	113	13	/	/	SYM
ejpam-3506	113	14	eur	eur	PROPN
ejpam-3506	113	15	.	.	PUNCT
ejpam-3506	114	1	j.	j.	PROPN
ejpam-3506	114	2	pure	pure	PROPN
ejpam-3506	114	3	appl	appl	PROPN
ejpam-3506	114	4	.	.	PROPN
ejpam-3506	114	5	math	math	PROPN
ejpam-3506	114	6	,	,	PUNCT
ejpam-3506	114	7	12	12	NUM
ejpam-3506	114	8	(	(	PUNCT
ejpam-3506	114	9	3	3	NUM
ejpam-3506	114	10	)	)	PUNCT
ejpam-3506	114	11	(	(	PUNCT
ejpam-3506	114	12	2019	2019	NUM
ejpam-3506	114	13	)	)	PUNCT
ejpam-3506	114	14	,	,	PUNCT
ejpam-3506	114	15	1337	1337	NUM
ejpam-3506	114	16	-	-	SYM
ejpam-3506	114	17	1349	1349	NUM
ejpam-3506	114	18	1341	1341	NUM
ejpam-3506	114	19	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	114	20	................................................................................................................	................................................................................................................	PROPN
ejpam-3506	115	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	115	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	116	1	....................................	....................................	PUNCT
ejpam-3506	116	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	117	1	....................................	....................................	PUNCT
ejpam-3506	117	2	.........	.........	PUNCT
ejpam-3506	117	3	........	........	PUNCT
ejpam-3506	117	4	........	........	PUNCT
ejpam-3506	117	5	........	........	PUNCT
ejpam-3506	117	6	........	........	PUNCT
ejpam-3506	117	7	........	........	PUNCT
ejpam-3506	117	8	........	........	PUNCT
ejpam-3506	117	9	........	........	PUNCT
ejpam-3506	117	10	........	........	PUNCT
ejpam-3506	117	11	........	........	PUNCT
ejpam-3506	117	12	........	........	PUNCT
ejpam-3506	117	13	........	........	PUNCT
ejpam-3506	117	14	........	........	PUNCT
ejpam-3506	117	15	........	........	PUNCT
ejpam-3506	117	16	........	........	PUNCT
ejpam-3506	117	17	........	........	PUNCT
ejpam-3506	117	18	........	........	PUNCT
ejpam-3506	117	19	........	........	PUNCT
ejpam-3506	117	20	........	........	PUNCT
ejpam-3506	117	21	........	........	PUNCT
ejpam-3506	117	22	.	.	PUNCT
ejpam-3506	118	1	..	..	PUNCT
ejpam-3506	118	2	..................................	..................................	PUNCT
ejpam-3506	119	1	....................................	....................................	PUNCT
ejpam-3506	119	2	.........	.........	PUNCT
ejpam-3506	119	3	........	........	PUNCT
ejpam-3506	119	4	........	........	PUNCT
ejpam-3506	119	5	........	........	PUNCT
ejpam-3506	119	6	........	........	PUNCT
ejpam-3506	119	7	........	........	PUNCT
ejpam-3506	119	8	........	........	PUNCT
ejpam-3506	119	9	........	........	PUNCT
ejpam-3506	119	10	........	........	PUNCT
ejpam-3506	119	11	........	........	PUNCT
ejpam-3506	119	12	........	........	PUNCT
ejpam-3506	119	13	........	........	PUNCT
ejpam-3506	119	14	........	........	PUNCT
ejpam-3506	119	15	........	........	PUNCT
ejpam-3506	119	16	........	........	PUNCT
ejpam-3506	119	17	........	........	PUNCT
ejpam-3506	119	18	........	........	PUNCT
ejpam-3506	119	19	........	........	PUNCT
ejpam-3506	119	20	........	........	PUNCT
ejpam-3506	119	21	........	........	PUNCT
ejpam-3506	119	22	.	.	PUNCT
ejpam-3506	120	1	..	..	PUNCT
ejpam-3506	120	2	..................................	..................................	PUNCT
ejpam-3506	121	1	....................................	....................................	PUNCT
ejpam-3506	121	2	.........	.........	PUNCT
ejpam-3506	121	3	........	........	PUNCT
ejpam-3506	121	4	........	........	PUNCT
ejpam-3506	121	5	........	........	PUNCT
ejpam-3506	121	6	........	........	PUNCT
ejpam-3506	121	7	........	........	PUNCT
ejpam-3506	121	8	........	........	PUNCT
ejpam-3506	121	9	........	........	PUNCT
ejpam-3506	121	10	........	........	PUNCT
ejpam-3506	121	11	........	........	PUNCT
ejpam-3506	121	12	........	........	PUNCT
ejpam-3506	121	13	........	........	PUNCT
ejpam-3506	121	14	........	........	PUNCT
ejpam-3506	121	15	........	........	PUNCT
ejpam-3506	121	16	........	........	PUNCT
ejpam-3506	121	17	........	........	PUNCT
ejpam-3506	121	18	........	........	PUNCT
ejpam-3506	121	19	........	........	PUNCT
ejpam-3506	121	20	........	........	PUNCT
ejpam-3506	121	21	........	........	PUNCT
ejpam-3506	121	22	.	.	PUNCT
ejpam-3506	122	1	..	..	PUNCT
ejpam-3506	122	2	..................................	..................................	PUNCT
ejpam-3506	123	1	....................................	....................................	PUNCT
ejpam-3506	123	2	.........	.........	PUNCT
ejpam-3506	123	3	........	........	PUNCT
ejpam-3506	123	4	........	........	PUNCT
ejpam-3506	123	5	........	........	PUNCT
ejpam-3506	123	6	........	........	PUNCT
ejpam-3506	123	7	........	........	PUNCT
ejpam-3506	123	8	........	........	PUNCT
ejpam-3506	123	9	........	........	PUNCT
ejpam-3506	123	10	........	........	PUNCT
ejpam-3506	123	11	........	........	PUNCT
ejpam-3506	123	12	........	........	PUNCT
ejpam-3506	123	13	........	........	PUNCT
ejpam-3506	123	14	........	........	PUNCT
ejpam-3506	123	15	........	........	PUNCT
ejpam-3506	123	16	........	........	PUNCT
ejpam-3506	123	17	........	........	PUNCT
ejpam-3506	123	18	........	........	PUNCT
ejpam-3506	123	19	........	........	PUNCT
ejpam-3506	123	20	........	........	PUNCT
ejpam-3506	123	21	........	........	PUNCT
ejpam-3506	123	22	.	.	PUNCT
ejpam-3506	124	1	..	..	PUNCT
ejpam-3506	124	2	..................................	..................................	PUNCT
ejpam-3506	125	1	....................................	....................................	PUNCT
ejpam-3506	125	2	.........	.........	PUNCT
ejpam-3506	125	3	........	........	PUNCT
ejpam-3506	125	4	........	........	PUNCT
ejpam-3506	125	5	........	........	PUNCT
ejpam-3506	125	6	........	........	PUNCT
ejpam-3506	125	7	........	........	PUNCT
ejpam-3506	125	8	........	........	PUNCT
ejpam-3506	125	9	........	........	PUNCT
ejpam-3506	125	10	........	........	PUNCT
ejpam-3506	125	11	........	........	PUNCT
ejpam-3506	125	12	........	........	PUNCT
ejpam-3506	125	13	........	........	PUNCT
ejpam-3506	125	14	........	........	PUNCT
ejpam-3506	125	15	........	........	PUNCT
ejpam-3506	125	16	........	........	PUNCT
ejpam-3506	125	17	........	........	PUNCT
ejpam-3506	125	18	........	........	PUNCT
ejpam-3506	125	19	........	........	PUNCT
ejpam-3506	125	20	........	........	PUNCT
ejpam-3506	125	21	........	........	PUNCT
ejpam-3506	125	22	.	.	PUNCT
ejpam-3506	126	1	..	..	PUNCT
ejpam-3506	126	2	..................................	..................................	PUNCT
ejpam-3506	127	1	....................................	....................................	PUNCT
ejpam-3506	127	2	.........	.........	PUNCT
ejpam-3506	127	3	........	........	PUNCT
ejpam-3506	127	4	........	........	PUNCT
ejpam-3506	127	5	........	........	PUNCT
ejpam-3506	127	6	........	........	PUNCT
ejpam-3506	127	7	........	........	PUNCT
ejpam-3506	127	8	........	........	PUNCT
ejpam-3506	127	9	........	........	PUNCT
ejpam-3506	127	10	........	........	PUNCT
ejpam-3506	127	11	...	...	PUNCT
ejpam-3506	127	12	.........	.........	PUNCT
ejpam-3506	127	13	........	........	PUNCT
ejpam-3506	127	14	........	........	PUNCT
ejpam-3506	127	15	........	........	PUNCT
ejpam-3506	127	16	........	........	PUNCT
ejpam-3506	127	17	........	........	PUNCT
ejpam-3506	127	18	........	........	PUNCT
ejpam-3506	127	19	........	........	PUNCT
ejpam-3506	127	20	........	........	PUNCT
ejpam-3506	127	21	...	...	PUNCT
ejpam-3506	127	22	.........	.........	PUNCT
ejpam-3506	127	23	........	........	PUNCT
ejpam-3506	127	24	........	........	PUNCT
ejpam-3506	127	25	........	........	PUNCT
ejpam-3506	127	26	........	........	PUNCT
ejpam-3506	127	27	........	........	PUNCT
ejpam-3506	127	28	........	........	PUNCT
ejpam-3506	127	29	........	........	PUNCT
ejpam-3506	127	30	........	........	PUNCT
ejpam-3506	127	31	...	...	PUNCT
ejpam-3506	128	1	....................................	....................................	PUNCT
ejpam-3506	128	2	.........	.........	PUNCT
ejpam-3506	128	3	........	........	PUNCT
ejpam-3506	128	4	........	........	PUNCT
ejpam-3506	128	5	........	........	PUNCT
ejpam-3506	128	6	........	........	PUNCT
ejpam-3506	128	7	........	........	PUNCT
ejpam-3506	128	8	........	........	PUNCT
ejpam-3506	128	9	........	........	PUNCT
ejpam-3506	128	10	........	........	PUNCT
ejpam-3506	128	11	...	...	PUNCT
ejpam-3506	129	1	....................................	....................................	PUNCT
ejpam-3506	129	2	....................................	....................................	PUNCT
ejpam-3506	129	3	.........	.........	PUNCT
ejpam-3506	129	4	........	........	PUNCT
ejpam-3506	129	5	........	........	PUNCT
ejpam-3506	129	6	........	........	PUNCT
ejpam-3506	129	7	........	........	PUNCT
ejpam-3506	129	8	........	........	PUNCT
ejpam-3506	129	9	........	........	PUNCT
ejpam-3506	129	10	........	........	PUNCT
ejpam-3506	129	11	........	........	PUNCT
ejpam-3506	129	12	...	...	PUNCT
ejpam-3506	130	1	....................................	....................................	PUNCT
ejpam-3506	130	2	.........	.........	PUNCT
ejpam-3506	130	3	........	........	PUNCT
ejpam-3506	130	4	........	........	PUNCT
ejpam-3506	130	5	........	........	PUNCT
ejpam-3506	130	6	........	........	PUNCT
ejpam-3506	130	7	........	........	PUNCT
ejpam-3506	130	8	........	........	PUNCT
ejpam-3506	130	9	........	........	PUNCT
ejpam-3506	130	10	........	........	PUNCT
ejpam-3506	130	11	...	...	PUNCT
ejpam-3506	131	1	....................................	....................................	PUNCT
ejpam-3506	131	2	....................................	....................................	PUNCT
ejpam-3506	131	3	...........................	...........................	PUNCT
ejpam-3506	132	1	...........................	...........................	PUNCT
ejpam-3506	133	1	x1	x1	NUM
ejpam-3506	134	1	x2	x2	NOUN
ejpam-3506	134	2	x3	x3	PROPN
ejpam-3506	135	1	x4	x4	PROPN
ejpam-3506	135	2	x5	x5	PROPN
ejpam-3506	135	3	xa−1	xa−1	PROPN
ejpam-3506	135	4	xa	xa	PROPN
ejpam-3506	135	5	·	·	PUNCT
ejpam-3506	135	6	·	·	PUNCT
ejpam-3506	135	7	·	·	PUNCT
ejpam-3506	135	8	•	•	NUM
ejpam-3506	135	9	••	••	NOUN
ejpam-3506	135	10	•••	•••	PROPN
ejpam-3506	135	11	•	•	ADJ
ejpam-3506	135	12	y1	y1	NOUN
ejpam-3506	135	13	y2	y2	NOUN
ejpam-3506	135	14	y3	y3	NOUN
ejpam-3506	135	15	y4	y4	NOUN
ejpam-3506	135	16	y5	y5	PROPN
ejpam-3506	135	17	ya−1	ya−1	NOUN
ejpam-3506	135	18	ya	ya	PROPN
ejpam-3506	135	19	z1	z1	PROPN
ejpam-3506	135	20	z2	z2	PROPN
ejpam-3506	135	21	z3	z3	PROPN
ejpam-3506	135	22	z4	z4	PROPN
ejpam-3506	135	23	z5	z5	PROPN
ejpam-3506	135	24	za−1	za−1	PROPN
ejpam-3506	135	25	za	za	PROPN
ejpam-3506	135	26	figure	figure	NOUN
ejpam-3506	135	27	1	1	NUM
ejpam-3506	135	28	:	:	PUNCT
ejpam-3506	135	29	a	a	DET
ejpam-3506	135	30	graph	graph	NOUN
ejpam-3506	135	31	g	g	NOUN
ejpam-3506	135	32	with	with	ADP
ejpam-3506	135	33	γ1fd(g	γ1fd(g	PROPN
ejpam-3506	135	34	)	)	PUNCT
ejpam-3506	135	35	=	=	SYM
ejpam-3506	135	36	γnc1fd(g	γnc1fd(g	ADJ
ejpam-3506	135	37	)	)	PUNCT
ejpam-3506	135	38	=	=	SYM
ejpam-3506	136	1	a	a	DET
ejpam-3506	136	2	=	=	X
ejpam-3506	136	3	b.	b.	NOUN
ejpam-3506	136	4	proof	proof	NOUN
ejpam-3506	136	5	.	.	PUNCT
ejpam-3506	137	1	consider	consider	VERB
ejpam-3506	137	2	the	the	DET
ejpam-3506	137	3	following	follow	VERB
ejpam-3506	137	4	cases	case	NOUN
ejpam-3506	137	5	:	:	PUNCT
ejpam-3506	137	6	case	case	NOUN
ejpam-3506	137	7	1	1	NUM
ejpam-3506	137	8	.	.	PUNCT
ejpam-3506	138	1	a	a	DET
ejpam-3506	138	2	=	=	X
ejpam-3506	138	3	b	b	NOUN
ejpam-3506	138	4	let	let	VERB
ejpam-3506	138	5	g	g	PRON
ejpam-3506	138	6	be	be	AUX
ejpam-3506	138	7	the	the	DET
ejpam-3506	138	8	graph	graph	NOUN
ejpam-3506	138	9	shown	show	VERB
ejpam-3506	138	10	in	in	ADP
ejpam-3506	138	11	figure	figure	NOUN
ejpam-3506	138	12	1	1	NUM
ejpam-3506	138	13	.	.	PUNCT
ejpam-3506	139	1	it	it	PRON
ejpam-3506	139	2	is	be	AUX
ejpam-3506	139	3	clear	clear	ADJ
ejpam-3506	139	4	that	that	SCONJ
ejpam-3506	139	5	the	the	DET
ejpam-3506	139	6	set	set	NOUN
ejpam-3506	139	7	a	a	X
ejpam-3506	139	8	=	=	X
ejpam-3506	139	9	{	{	PUNCT
ejpam-3506	139	10	xi	xi	X
ejpam-3506	139	11	:	:	PUNCT
ejpam-3506	139	12	i	i	NOUN
ejpam-3506	139	13	=	=	NOUN
ejpam-3506	139	14	1	1	NUM
ejpam-3506	139	15	,	,	PUNCT
ejpam-3506	139	16	2	2	NUM
ejpam-3506	139	17	,	,	PUNCT
ejpam-3506	139	18	...	...	PUNCT
ejpam-3506	139	19	a	a	X
ejpam-3506	139	20	}	}	PUNCT
ejpam-3506	139	21	is	be	AUX
ejpam-3506	139	22	both	both	PRON
ejpam-3506	139	23	a	a	DET
ejpam-3506	139	24	γ1fd	γ1fd	NOUN
ejpam-3506	139	25	-	-	PUNCT
ejpam-3506	139	26	set	set	VERB
ejpam-3506	139	27	and	and	CCONJ
ejpam-3506	139	28	a	a	DET
ejpam-3506	139	29	γnc1fd	γnc1fd	NOUN
ejpam-3506	139	30	-	-	PUNCT
ejpam-3506	139	31	set	set	NOUN
ejpam-3506	139	32	in	in	ADP
ejpam-3506	139	33	g.	g.	PROPN
ejpam-3506	139	34	it	it	PRON
ejpam-3506	139	35	follows	follow	VERB
ejpam-3506	139	36	that	that	PRON
ejpam-3506	139	37	γ1fd(g	γ1fd(g	PROPN
ejpam-3506	139	38	)	)	PUNCT
ejpam-3506	140	1	=	=	SYM
ejpam-3506	140	2	γnc1fd(g	γnc1fd(g	PROPN
ejpam-3506	140	3	)	)	PUNCT
ejpam-3506	141	1	=	=	SYM
ejpam-3506	141	2	|a|	|a|	PROPN
ejpam-3506	141	3	=	=	NOUN
ejpam-3506	141	4	a	a	PROPN
ejpam-3506	141	5	=	=	X
ejpam-3506	141	6	b.	b.	NOUN
ejpam-3506	141	7	case	case	NOUN
ejpam-3506	141	8	2	2	NUM
ejpam-3506	141	9	.	.	PUNCT
ejpam-3506	142	1	a	a	DET
ejpam-3506	142	2	<	<	X
ejpam-3506	142	3	b	b	X
ejpam-3506	142	4	subcase	subcase	NOUN
ejpam-3506	142	5	1	1	NUM
ejpam-3506	142	6	.	.	X
ejpam-3506	142	7	b	b	X
ejpam-3506	143	1	=	=	PRON
ejpam-3506	143	2	a+	a+	PUNCT
ejpam-3506	143	3	1	1	NUM
ejpam-3506	143	4	let	let	VERB
ejpam-3506	143	5	g	g	NOUN
ejpam-3506	143	6	be	be	AUX
ejpam-3506	143	7	the	the	DET
ejpam-3506	143	8	graph	graph	NOUN
ejpam-3506	143	9	shown	show	VERB
ejpam-3506	143	10	in	in	ADP
ejpam-3506	143	11	figure	figure	NOUN
ejpam-3506	143	12	2	2	NUM
ejpam-3506	143	13	.	.	PUNCT
ejpam-3506	144	1	then	then	ADV
ejpam-3506	144	2	a	a	PRON
ejpam-3506	144	3	=	=	X
ejpam-3506	144	4	{	{	PUNCT
ejpam-3506	144	5	x1	x1	PROPN
ejpam-3506	144	6	,	,	PUNCT
ejpam-3506	144	7	x2	x2	PROPN
ejpam-3506	144	8	,	,	PUNCT
ejpam-3506	144	9	...	...	PUNCT
ejpam-3506	144	10	,	,	PUNCT
ejpam-3506	144	11	xa	xa	X
ejpam-3506	144	12	}	}	PUNCT
ejpam-3506	144	13	is	be	AUX
ejpam-3506	144	14	a	a	DET
ejpam-3506	144	15	γ1fd	γ1fd	NOUN
ejpam-3506	144	16	-	-	PUNCT
ejpam-3506	144	17	set	set	NOUN
ejpam-3506	144	18	of	of	ADP
ejpam-3506	144	19	g	g	NOUN
ejpam-3506	144	20	and	and	CCONJ
ejpam-3506	144	21	b1	b1	NOUN
ejpam-3506	144	22	=	=	PUNCT
ejpam-3506	144	23	a	a	PRON
ejpam-3506	144	24	∪	∪	ADJ
ejpam-3506	144	25	{	{	PUNCT
ejpam-3506	144	26	q	q	NOUN
ejpam-3506	144	27	}	}	PUNCT
ejpam-3506	144	28	and	and	CCONJ
ejpam-3506	144	29	b2	b2	NOUN
ejpam-3506	144	30	=	=	SYM
ejpam-3506	144	31	{	{	PUNCT
ejpam-3506	144	32	x1	x1	PROPN
ejpam-3506	144	33	,	,	PUNCT
ejpam-3506	144	34	x2	x2	PROPN
ejpam-3506	144	35	,	,	PUNCT
ejpam-3506	144	36	...	...	PUNCT
ejpam-3506	144	37	,	,	PUNCT
ejpam-3506	144	38	xa−1	xa−1	PROPN
ejpam-3506	144	39	,	,	PUNCT
ejpam-3506	144	40	w	w	PROPN
ejpam-3506	144	41	,	,	PUNCT
ejpam-3506	144	42	q	q	ADJ
ejpam-3506	144	43	}	}	PUNCT
ejpam-3506	144	44	are	be	AUX
ejpam-3506	144	45	the	the	DET
ejpam-3506	144	46	(	(	PUNCT
ejpam-3506	144	47	only	only	ADV
ejpam-3506	144	48	)	)	PUNCT
ejpam-3506	144	49	γnc1fd	γnc1fd	NOUN
ejpam-3506	144	50	-	-	PUNCT
ejpam-3506	144	51	sets	set	NOUN
ejpam-3506	144	52	of	of	ADP
ejpam-3506	144	53	g.	g.	PROPN
ejpam-3506	144	54	thus	thus	ADV
ejpam-3506	144	55	,	,	PUNCT
ejpam-3506	144	56	γ1fd(g	γ1fd(g	PROPN
ejpam-3506	144	57	)	)	PUNCT
ejpam-3506	144	58	=	=	SYM
ejpam-3506	144	59	a	a	PRON
ejpam-3506	144	60	and	and	CCONJ
ejpam-3506	144	61	γnc1fd(g	γnc1fd(g	NUM
ejpam-3506	144	62	)	)	PUNCT
ejpam-3506	145	1	=	=	SYM
ejpam-3506	145	2	b	b	X
ejpam-3506	145	3	=	=	PRON
ejpam-3506	145	4	a+	a+	PUNCT
ejpam-3506	145	5	1	1	X
ejpam-3506	145	6	.	.	PUNCT
ejpam-3506	145	7	................................................................................................................	................................................................................................................	PROPN
ejpam-3506	145	8	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	145	9	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	145	10	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	145	11	....................................	....................................	PUNCT
ejpam-3506	145	12	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	145	13	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	145	14	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	145	15	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	145	16	....................................	....................................	PUNCT
ejpam-3506	145	17	.........	.........	PUNCT
ejpam-3506	145	18	........	........	PUNCT
ejpam-3506	145	19	........	........	PUNCT
ejpam-3506	145	20	........	........	PUNCT
ejpam-3506	145	21	........	........	PUNCT
ejpam-3506	145	22	........	........	PUNCT
ejpam-3506	145	23	........	........	PUNCT
ejpam-3506	145	24	........	........	PUNCT
ejpam-3506	145	25	........	........	PUNCT
ejpam-3506	145	26	........	........	PUNCT
ejpam-3506	145	27	........	........	PUNCT
ejpam-3506	145	28	........	........	PUNCT
ejpam-3506	145	29	........	........	PUNCT
ejpam-3506	145	30	........	........	PUNCT
ejpam-3506	145	31	........	........	PUNCT
ejpam-3506	145	32	........	........	PUNCT
ejpam-3506	145	33	........	........	PUNCT
ejpam-3506	145	34	........	........	PUNCT
ejpam-3506	145	35	........	........	PUNCT
ejpam-3506	145	36	........	........	PUNCT
ejpam-3506	145	37	.	.	PUNCT
ejpam-3506	145	38	..	..	PUNCT
ejpam-3506	145	39	..................................	..................................	PUNCT
ejpam-3506	145	40	....................................	....................................	PUNCT
ejpam-3506	145	41	.........	.........	PUNCT
ejpam-3506	145	42	........	........	PUNCT
ejpam-3506	145	43	........	........	PUNCT
ejpam-3506	145	44	........	........	PUNCT
ejpam-3506	145	45	........	........	PUNCT
ejpam-3506	145	46	........	........	PUNCT
ejpam-3506	145	47	........	........	PUNCT
ejpam-3506	145	48	........	........	PUNCT
ejpam-3506	145	49	........	........	PUNCT
ejpam-3506	145	50	........	........	PUNCT
ejpam-3506	145	51	........	........	PUNCT
ejpam-3506	145	52	........	........	PUNCT
ejpam-3506	145	53	........	........	PUNCT
ejpam-3506	145	54	........	........	PUNCT
ejpam-3506	145	55	........	........	PUNCT
ejpam-3506	145	56	........	........	PUNCT
ejpam-3506	145	57	........	........	PUNCT
ejpam-3506	145	58	........	........	PUNCT
ejpam-3506	145	59	........	........	PUNCT
ejpam-3506	145	60	........	........	PUNCT
ejpam-3506	145	61	.	.	PUNCT
ejpam-3506	145	62	..	..	PUNCT
ejpam-3506	145	63	..................................	..................................	PUNCT
ejpam-3506	145	64	....................................	....................................	PUNCT
ejpam-3506	145	65	.........	.........	PUNCT
ejpam-3506	145	66	........	........	PUNCT
ejpam-3506	145	67	........	........	PUNCT
ejpam-3506	145	68	........	........	PUNCT
ejpam-3506	145	69	........	........	PUNCT
ejpam-3506	145	70	........	........	PUNCT
ejpam-3506	145	71	........	........	PUNCT
ejpam-3506	145	72	........	........	PUNCT
ejpam-3506	145	73	........	........	PUNCT
ejpam-3506	145	74	........	........	PUNCT
ejpam-3506	145	75	........	........	PUNCT
ejpam-3506	145	76	........	........	PUNCT
ejpam-3506	145	77	........	........	PUNCT
ejpam-3506	145	78	........	........	PUNCT
ejpam-3506	145	79	........	........	PUNCT
ejpam-3506	145	80	........	........	PUNCT
ejpam-3506	145	81	........	........	PUNCT
ejpam-3506	145	82	........	........	PUNCT
ejpam-3506	145	83	........	........	PUNCT
ejpam-3506	145	84	........	........	PUNCT
ejpam-3506	145	85	.	.	PUNCT
ejpam-3506	145	86	..	..	PUNCT
ejpam-3506	145	87	..................................	..................................	PUNCT
ejpam-3506	145	88	....................................	....................................	PUNCT
ejpam-3506	145	89	.........	.........	PUNCT
ejpam-3506	145	90	........	........	PUNCT
ejpam-3506	145	91	........	........	PUNCT
ejpam-3506	145	92	........	........	PUNCT
ejpam-3506	145	93	........	........	PUNCT
ejpam-3506	145	94	........	........	PUNCT
ejpam-3506	145	95	........	........	PUNCT
ejpam-3506	145	96	........	........	PUNCT
ejpam-3506	145	97	........	........	PUNCT
ejpam-3506	145	98	........	........	PUNCT
ejpam-3506	145	99	........	........	PUNCT
ejpam-3506	145	100	........	........	PUNCT
ejpam-3506	145	101	........	........	PUNCT
ejpam-3506	145	102	........	........	PUNCT
ejpam-3506	145	103	........	........	PUNCT
ejpam-3506	145	104	........	........	PUNCT
ejpam-3506	145	105	........	........	PUNCT
ejpam-3506	145	106	........	........	PUNCT
ejpam-3506	145	107	........	........	PUNCT
ejpam-3506	145	108	........	........	PUNCT
ejpam-3506	145	109	.	.	PUNCT
ejpam-3506	145	110	..	..	PUNCT
ejpam-3506	145	111	..................................	..................................	PUNCT
ejpam-3506	145	112	....................................	....................................	PUNCT
ejpam-3506	145	113	.........	.........	PUNCT
ejpam-3506	145	114	........	........	PUNCT
ejpam-3506	145	115	........	........	PUNCT
ejpam-3506	145	116	........	........	PUNCT
ejpam-3506	145	117	........	........	PUNCT
ejpam-3506	145	118	........	........	PUNCT
ejpam-3506	145	119	........	........	PUNCT
ejpam-3506	145	120	........	........	PUNCT
ejpam-3506	145	121	........	........	PUNCT
ejpam-3506	145	122	...	...	PUNCT
ejpam-3506	145	123	.........	.........	PUNCT
ejpam-3506	145	124	........	........	PUNCT
ejpam-3506	145	125	........	........	PUNCT
ejpam-3506	145	126	........	........	PUNCT
ejpam-3506	145	127	........	........	PUNCT
ejpam-3506	145	128	........	........	PUNCT
ejpam-3506	145	129	........	........	PUNCT
ejpam-3506	145	130	........	........	PUNCT
ejpam-3506	145	131	........	........	PUNCT
ejpam-3506	145	132	...	...	PUNCT
ejpam-3506	145	133	.........	.........	PUNCT
ejpam-3506	145	134	........	........	PUNCT
ejpam-3506	145	135	........	........	PUNCT
ejpam-3506	145	136	........	........	PUNCT
ejpam-3506	145	137	........	........	PUNCT
ejpam-3506	145	138	........	........	PUNCT
ejpam-3506	145	139	........	........	PUNCT
ejpam-3506	145	140	........	........	PUNCT
ejpam-3506	145	141	........	........	PUNCT
ejpam-3506	145	142	...	...	PUNCT
ejpam-3506	145	143	....................................	....................................	PUNCT
ejpam-3506	145	144	.........	.........	PUNCT
ejpam-3506	145	145	........	........	PUNCT
ejpam-3506	145	146	........	........	PUNCT
ejpam-3506	145	147	........	........	PUNCT
ejpam-3506	145	148	........	........	PUNCT
ejpam-3506	145	149	........	........	PUNCT
ejpam-3506	145	150	........	........	PUNCT
ejpam-3506	145	151	........	........	PUNCT
ejpam-3506	145	152	........	........	PUNCT
ejpam-3506	145	153	...	...	PUNCT
ejpam-3506	145	154	....................................	....................................	PUNCT
ejpam-3506	145	155	....................................	....................................	PUNCT
ejpam-3506	145	156	.........	.........	PUNCT
ejpam-3506	145	157	........	........	PUNCT
ejpam-3506	145	158	........	........	PUNCT
ejpam-3506	145	159	........	........	PUNCT
ejpam-3506	145	160	........	........	PUNCT
ejpam-3506	145	161	........	........	PUNCT
ejpam-3506	145	162	........	........	PUNCT
ejpam-3506	145	163	........	........	PUNCT
ejpam-3506	145	164	........	........	PUNCT
ejpam-3506	145	165	...	...	PUNCT
ejpam-3506	145	166	....................................	....................................	PUNCT
ejpam-3506	145	167	.........	.........	PUNCT
ejpam-3506	145	168	........	........	PUNCT
ejpam-3506	145	169	........	........	PUNCT
ejpam-3506	145	170	........	........	PUNCT
ejpam-3506	145	171	........	........	PUNCT
ejpam-3506	145	172	........	........	PUNCT
ejpam-3506	145	173	........	........	PUNCT
ejpam-3506	145	174	........	........	PUNCT
ejpam-3506	145	175	........	........	PUNCT
ejpam-3506	145	176	...	...	PUNCT
ejpam-3506	145	177	....................................	....................................	PUNCT
ejpam-3506	145	178	....................................	....................................	PUNCT
ejpam-3506	145	179	...........................	...........................	PUNCT
ejpam-3506	145	180	...........................	...........................	PUNCT
ejpam-3506	146	1	x1	x1	NUM
ejpam-3506	147	1	x2	x2	NOUN
ejpam-3506	147	2	x3	x3	PROPN
ejpam-3506	148	1	x4	x4	PROPN
ejpam-3506	148	2	x5	x5	PROPN
ejpam-3506	148	3	xa−1	xa−1	PROPN
ejpam-3506	148	4	w	w	PROPN
ejpam-3506	148	5	v	v	PROPN
ejpam-3506	148	6	xa	xa	PROPN
ejpam-3506	148	7	q	q	PROPN
ejpam-3506	148	8	·	·	PUNCT
ejpam-3506	148	9	·	·	PUNCT
ejpam-3506	148	10	·	·	PUNCT
ejpam-3506	148	11	•	•	NUM
ejpam-3506	148	12	••	••	NOUN
ejpam-3506	148	13	••	••	NOUN
ejpam-3506	148	14	•	•	NUM
ejpam-3506	148	15	•	•	NOUN
ejpam-3506	148	16	•	•	NOUN
ejpam-3506	148	17	y1	y1	NOUN
ejpam-3506	148	18	y2	y2	NOUN
ejpam-3506	148	19	y3	y3	NOUN
ejpam-3506	148	20	y4	y4	NOUN
ejpam-3506	148	21	y5	y5	PROPN
ejpam-3506	148	22	ya−1	ya−1	NOUN
ejpam-3506	148	23	z1	z1	ADJ
ejpam-3506	148	24	z2	z2	PROPN
ejpam-3506	148	25	z3	z3	PROPN
ejpam-3506	148	26	z4	z4	PROPN
ejpam-3506	148	27	z5	z5	PROPN
ejpam-3506	148	28	za−1	za−1	PROPN
ejpam-3506	148	29	figure	figure	NOUN
ejpam-3506	148	30	2	2	NUM
ejpam-3506	148	31	:	:	PUNCT
ejpam-3506	148	32	a	a	DET
ejpam-3506	148	33	graph	graph	NOUN
ejpam-3506	148	34	g	g	NOUN
ejpam-3506	148	35	with	with	ADP
ejpam-3506	148	36	γ1fd(g	γ1fd(g	PROPN
ejpam-3506	148	37	)	)	PUNCT
ejpam-3506	148	38	=	=	SYM
ejpam-3506	148	39	a	a	PRON
ejpam-3506	148	40	and	and	CCONJ
ejpam-3506	148	41	γnc1fd(g	γnc1fd(g	NUM
ejpam-3506	148	42	)	)	PUNCT
ejpam-3506	149	1	=	=	SYM
ejpam-3506	149	2	b	b	X
ejpam-3506	149	3	when	when	SCONJ
ejpam-3506	149	4	a	a	DET
ejpam-3506	149	5	<	<	X
ejpam-3506	149	6	b.	b.	PROPN
ejpam-3506	149	7	subcase	subcase	PROPN
ejpam-3506	149	8	2	2	NUM
ejpam-3506	149	9	.	.	X
ejpam-3506	149	10	b	b	NUM
ejpam-3506	149	11	≥	≥	X
ejpam-3506	149	12	a+	a+	SYM
ejpam-3506	149	13	2	2	NUM
ejpam-3506	149	14	let	let	VERB
ejpam-3506	149	15	r	r	NOUN
ejpam-3506	149	16	=	=	PUNCT
ejpam-3506	149	17	b−	b−	PROPN
ejpam-3506	149	18	a	a	DET
ejpam-3506	149	19	≥	≥	NUM
ejpam-3506	149	20	2	2	NUM
ejpam-3506	149	21	.	.	PUNCT
ejpam-3506	150	1	let	let	VERB
ejpam-3506	150	2	h1	h1	VERB
ejpam-3506	150	3	and	and	CCONJ
ejpam-3506	150	4	h2	h2	NOUN
ejpam-3506	150	5	be	be	AUX
ejpam-3506	150	6	graphs	graph	NOUN
ejpam-3506	150	7	such	such	ADJ
ejpam-3506	150	8	that	that	PRON
ejpam-3506	150	9	h1	h1	PROPN
ejpam-3506	150	10	∼=	∼=	PROPN
ejpam-3506	150	11	h2	h2	NOUN
ejpam-3506	150	12	∼=	∼=	PART
ejpam-3506	150	13	kr	kr	NOUN
ejpam-3506	150	14	.	.	PROPN
ejpam-3506	150	15	consider	consider	VERB
ejpam-3506	150	16	the	the	DET
ejpam-3506	150	17	graph	graph	NOUN
ejpam-3506	150	18	g	g	NOUN
ejpam-3506	150	19	in	in	ADP
ejpam-3506	150	20	figure	figure	NOUN
ejpam-3506	150	21	3	3	NUM
ejpam-3506	150	22	.	.	PUNCT
ejpam-3506	150	23	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	151	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	151	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	152	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	152	2	....................................	....................................	PUNCT
ejpam-3506	153	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	153	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	154	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	154	2	........................................	........................................	PUNCT
ejpam-3506	155	1	..........	..........	PUNCT
ejpam-3506	155	2	..........	..........	PUNCT
ejpam-3506	156	1	..........	..........	PUNCT
ejpam-3506	156	2	..........	..........	PUNCT
ejpam-3506	157	1	..........	..........	PUNCT
ejpam-3506	157	2	..........	..........	PUNCT
ejpam-3506	158	1	..........	..........	PUNCT
ejpam-3506	158	2	..........	..........	PUNCT
ejpam-3506	159	1	..........	..........	PUNCT
ejpam-3506	159	2	..........	..........	PUNCT
ejpam-3506	160	1	..........	..........	PUNCT
ejpam-3506	160	2	..........	..........	PUNCT
ejpam-3506	161	1	..........	..........	PUNCT
ejpam-3506	161	2	..........	..........	PUNCT
ejpam-3506	162	1	..........	..........	PUNCT
ejpam-3506	162	2	..........	..........	PUNCT
ejpam-3506	163	1	..........	..........	PUNCT
ejpam-3506	163	2	..........	..........	PUNCT
ejpam-3506	163	3	.	.	PUNCT
ejpam-3506	163	4	.........................................	.........................................	PUNCT
ejpam-3506	163	5	........................................	........................................	PUNCT
ejpam-3506	163	6	........................................	........................................	PUNCT
ejpam-3506	164	1	..........................	..........................	PUNCT
ejpam-3506	165	1	.........................................................................................................................................................................................	.........................................................................................................................................................................................	PUNCT
ejpam-3506	165	2	...................................................................................................................................................	...................................................................................................................................................	PUNCT
ejpam-3506	165	3	...........................................................................................................................	...........................................................................................................................	PUNCT
ejpam-3506	165	4	...........................................................................................................................	...........................................................................................................................	PUNCT
ejpam-3506	165	5	............	............	PUNCT
ejpam-3506	165	6	...........	...........	PUNCT
ejpam-3506	165	7	...........	...........	PUNCT
ejpam-3506	165	8	..........	..........	PUNCT
ejpam-3506	166	1	.........	.........	PUNCT
ejpam-3506	166	2	.........	.........	PUNCT
ejpam-3506	166	3	.........	.........	PUNCT
ejpam-3506	166	4	........	........	PUNCT
ejpam-3506	166	5	........	........	PUNCT
ejpam-3506	166	6	........	........	PUNCT
ejpam-3506	167	1	.........	.........	PUNCT
ejpam-3506	167	2	.........	.........	PUNCT
ejpam-3506	168	1	..........	..........	PUNCT
ejpam-3506	168	2	..........	..........	PUNCT
ejpam-3506	169	1	.........	.........	PUNCT
ejpam-3506	169	2	.........	.........	PUNCT
ejpam-3506	169	3	........	........	PUNCT
ejpam-3506	169	4	........	........	PUNCT
ejpam-3506	169	5	........	........	PUNCT
ejpam-3506	170	1	........	........	PUNCT
ejpam-3506	170	2	.........	.........	PUNCT
ejpam-3506	171	1	.........	.........	PUNCT
ejpam-3506	171	2	..........	..........	PUNCT
ejpam-3506	172	1	..........	..........	PUNCT
ejpam-3506	172	2	...........	...........	PUNCT
ejpam-3506	172	3	............	............	PUNCT
ejpam-3506	172	4	..	..	PUNCT
ejpam-3506	172	5	........................................................................................................................................................................................	........................................................................................................................................................................................	PUNCT
ejpam-3506	172	6	..................	..................	PUNCT
ejpam-3506	173	1	.................	.................	PUNCT
ejpam-3506	173	2	.................	.................	PUNCT
ejpam-3506	173	3	..............................	..............................	PUNCT
ejpam-3506	173	4	..................	..................	PUNCT
ejpam-3506	174	1	..................	..................	PUNCT
ejpam-3506	174	2	..............................	..............................	PUNCT
ejpam-3506	175	1	................	................	PUNCT
ejpam-3506	175	2	................	................	PUNCT
ejpam-3506	175	3	.........	.........	PUNCT
ejpam-3506	175	4	.........	.........	PUNCT
ejpam-3506	175	5	........	........	PUNCT
ejpam-3506	175	6	........	........	PUNCT
ejpam-3506	175	7	........	........	PUNCT
ejpam-3506	175	8	........	........	PUNCT
ejpam-3506	175	9	........	........	PUNCT
ejpam-3506	175	10	........	........	PUNCT
ejpam-3506	175	11	........	........	PUNCT
ejpam-3506	175	12	........	........	PUNCT
ejpam-3506	175	13	........	........	PUNCT
ejpam-3506	175	14	........	........	PUNCT
ejpam-3506	175	15	........	........	PUNCT
ejpam-3506	175	16	........	........	PUNCT
ejpam-3506	175	17	........	........	PUNCT
ejpam-3506	175	18	........	........	PUNCT
ejpam-3506	175	19	........	........	PUNCT
ejpam-3506	175	20	........	........	PUNCT
ejpam-3506	175	21	........	........	PUNCT
ejpam-3506	175	22	........	........	PUNCT
ejpam-3506	175	23	........	........	PUNCT
ejpam-3506	175	24	.	.	PUNCT
ejpam-3506	176	1	..	..	PUNCT
ejpam-3506	176	2	..................................	..................................	PUNCT
ejpam-3506	177	1	....................................	....................................	PUNCT
ejpam-3506	177	2	.........	.........	PUNCT
ejpam-3506	177	3	........	........	PUNCT
ejpam-3506	177	4	........	........	PUNCT
ejpam-3506	177	5	........	........	PUNCT
ejpam-3506	177	6	........	........	PUNCT
ejpam-3506	177	7	........	........	PUNCT
ejpam-3506	177	8	........	........	PUNCT
ejpam-3506	177	9	........	........	PUNCT
ejpam-3506	177	10	........	........	PUNCT
ejpam-3506	177	11	........	........	PUNCT
ejpam-3506	177	12	........	........	PUNCT
ejpam-3506	177	13	........	........	PUNCT
ejpam-3506	177	14	........	........	PUNCT
ejpam-3506	177	15	........	........	PUNCT
ejpam-3506	177	16	........	........	PUNCT
ejpam-3506	177	17	........	........	PUNCT
ejpam-3506	177	18	........	........	PUNCT
ejpam-3506	177	19	........	........	PUNCT
ejpam-3506	177	20	........	........	PUNCT
ejpam-3506	177	21	........	........	PUNCT
ejpam-3506	177	22	.	.	PUNCT
ejpam-3506	178	1	..	..	PUNCT
ejpam-3506	178	2	..................................	..................................	PUNCT
ejpam-3506	179	1	....................................	....................................	PUNCT
ejpam-3506	179	2	.........	.........	PUNCT
ejpam-3506	179	3	........	........	PUNCT
ejpam-3506	179	4	........	........	PUNCT
ejpam-3506	179	5	........	........	PUNCT
ejpam-3506	179	6	........	........	PUNCT
ejpam-3506	179	7	........	........	PUNCT
ejpam-3506	179	8	........	........	PUNCT
ejpam-3506	179	9	........	........	PUNCT
ejpam-3506	179	10	........	........	PUNCT
ejpam-3506	179	11	........	........	PUNCT
ejpam-3506	179	12	........	........	PUNCT
ejpam-3506	179	13	........	........	PUNCT
ejpam-3506	179	14	........	........	PUNCT
ejpam-3506	179	15	........	........	PUNCT
ejpam-3506	179	16	........	........	PUNCT
ejpam-3506	179	17	........	........	PUNCT
ejpam-3506	179	18	........	........	PUNCT
ejpam-3506	179	19	........	........	PUNCT
ejpam-3506	179	20	........	........	PUNCT
ejpam-3506	179	21	........	........	PUNCT
ejpam-3506	179	22	.	.	PUNCT
ejpam-3506	180	1	..	..	PUNCT
ejpam-3506	180	2	..................................	..................................	PUNCT
ejpam-3506	181	1	....................................	....................................	PUNCT
ejpam-3506	181	2	.........	.........	PUNCT
ejpam-3506	181	3	........	........	PUNCT
ejpam-3506	181	4	........	........	PUNCT
ejpam-3506	181	5	........	........	PUNCT
ejpam-3506	181	6	........	........	PUNCT
ejpam-3506	181	7	........	........	PUNCT
ejpam-3506	181	8	........	........	PUNCT
ejpam-3506	181	9	........	........	PUNCT
ejpam-3506	181	10	........	........	PUNCT
ejpam-3506	181	11	........	........	PUNCT
ejpam-3506	181	12	........	........	PUNCT
ejpam-3506	181	13	........	........	PUNCT
ejpam-3506	181	14	........	........	PUNCT
ejpam-3506	181	15	........	........	PUNCT
ejpam-3506	181	16	........	........	PUNCT
ejpam-3506	181	17	........	........	PUNCT
ejpam-3506	181	18	........	........	PUNCT
ejpam-3506	181	19	........	........	PUNCT
ejpam-3506	181	20	........	........	PUNCT
ejpam-3506	181	21	........	........	PUNCT
ejpam-3506	181	22	.	.	PUNCT
ejpam-3506	182	1	..	..	PUNCT
ejpam-3506	182	2	..................................	..................................	PUNCT
ejpam-3506	183	1	....................................	....................................	PUNCT
ejpam-3506	183	2	.........	.........	PUNCT
ejpam-3506	183	3	........	........	PUNCT
ejpam-3506	183	4	........	........	PUNCT
ejpam-3506	183	5	........	........	PUNCT
ejpam-3506	183	6	........	........	PUNCT
ejpam-3506	183	7	........	........	PUNCT
ejpam-3506	183	8	........	........	PUNCT
ejpam-3506	183	9	........	........	PUNCT
ejpam-3506	183	10	........	........	PUNCT
ejpam-3506	183	11	...	...	PUNCT
ejpam-3506	183	12	.........	.........	PUNCT
ejpam-3506	183	13	........	........	PUNCT
ejpam-3506	183	14	........	........	PUNCT
ejpam-3506	183	15	........	........	PUNCT
ejpam-3506	183	16	........	........	PUNCT
ejpam-3506	183	17	........	........	PUNCT
ejpam-3506	183	18	........	........	PUNCT
ejpam-3506	183	19	........	........	PUNCT
ejpam-3506	183	20	........	........	PUNCT
ejpam-3506	183	21	...	...	PUNCT
ejpam-3506	183	22	.........	.........	PUNCT
ejpam-3506	183	23	........	........	PUNCT
ejpam-3506	183	24	........	........	PUNCT
ejpam-3506	183	25	........	........	PUNCT
ejpam-3506	183	26	........	........	PUNCT
ejpam-3506	183	27	........	........	PUNCT
ejpam-3506	183	28	........	........	PUNCT
ejpam-3506	183	29	........	........	PUNCT
ejpam-3506	183	30	........	........	PUNCT
ejpam-3506	183	31	...	...	PUNCT
ejpam-3506	184	1	....................................	....................................	PUNCT
ejpam-3506	184	2	.........	.........	PUNCT
ejpam-3506	184	3	........	........	PUNCT
ejpam-3506	184	4	........	........	PUNCT
ejpam-3506	184	5	........	........	PUNCT
ejpam-3506	184	6	........	........	PUNCT
ejpam-3506	184	7	........	........	PUNCT
ejpam-3506	184	8	........	........	PUNCT
ejpam-3506	184	9	........	........	PUNCT
ejpam-3506	184	10	........	........	PUNCT
ejpam-3506	184	11	...	...	PUNCT
ejpam-3506	185	1	....................................	....................................	PUNCT
ejpam-3506	185	2	....................................	....................................	PUNCT
ejpam-3506	185	3	.........	.........	PUNCT
ejpam-3506	185	4	........	........	PUNCT
ejpam-3506	185	5	........	........	PUNCT
ejpam-3506	185	6	........	........	PUNCT
ejpam-3506	185	7	........	........	PUNCT
ejpam-3506	185	8	........	........	PUNCT
ejpam-3506	185	9	........	........	PUNCT
ejpam-3506	185	10	........	........	PUNCT
ejpam-3506	185	11	........	........	PUNCT
ejpam-3506	185	12	...	...	PUNCT
ejpam-3506	186	1	....................................	....................................	PUNCT
ejpam-3506	186	2	.........	.........	PUNCT
ejpam-3506	186	3	........	........	PUNCT
ejpam-3506	186	4	........	........	PUNCT
ejpam-3506	186	5	........	........	PUNCT
ejpam-3506	186	6	........	........	PUNCT
ejpam-3506	186	7	........	........	PUNCT
ejpam-3506	186	8	........	........	PUNCT
ejpam-3506	186	9	........	........	PUNCT
ejpam-3506	186	10	........	........	PUNCT
ejpam-3506	186	11	...	...	PUNCT
ejpam-3506	187	1	....................................	....................................	PUNCT
ejpam-3506	187	2	....................................	....................................	PUNCT
ejpam-3506	187	3	...........................	...........................	PUNCT
ejpam-3506	187	4	...........................	...........................	PUNCT
ejpam-3506	188	1	...................	...................	PUNCT
ejpam-3506	188	2	..................	..................	PUNCT
ejpam-3506	189	1	..................	..................	PUNCT
ejpam-3506	189	2	..................	..................	PUNCT
ejpam-3506	190	1	.............	.............	PUNCT
ejpam-3506	190	2	..........................................................................................................................	..........................................................................................................................	PUNCT
ejpam-3506	190	3	....................................	....................................	PUNCT
ejpam-3506	191	1	....................................	....................................	PUNCT
ejpam-3506	191	2	............	............	PUNCT
ejpam-3506	191	3	...........	...........	PUNCT
ejpam-3506	191	4	...........	...........	PUNCT
ejpam-3506	191	5	...........	...........	PUNCT
ejpam-3506	191	6	...........	...........	PUNCT
ejpam-3506	191	7	...........	...........	PUNCT
ejpam-3506	191	8	...........	...........	PUNCT
ejpam-3506	191	9	...........	...........	PUNCT
ejpam-3506	191	10	...........	...........	PUNCT
ejpam-3506	191	11	...........	...........	PUNCT
ejpam-3506	191	12	...................................................................................................................................................	...................................................................................................................................................	PUNCT
ejpam-3506	191	13	....................................	....................................	PUNCT
ejpam-3506	192	1	....................................	....................................	PUNCT
ejpam-3506	192	2	..........	..........	PUNCT
ejpam-3506	193	1	.........	.........	PUNCT
ejpam-3506	193	2	.........	.........	PUNCT
ejpam-3506	194	1	.........	.........	PUNCT
ejpam-3506	194	2	.........	.........	PUNCT
ejpam-3506	195	1	.........	.........	PUNCT
ejpam-3506	195	2	.........	.........	PUNCT
ejpam-3506	196	1	.........	.........	PUNCT
ejpam-3506	196	2	.........	.........	PUNCT
ejpam-3506	197	1	.........	.........	PUNCT
ejpam-3506	197	2	.........	.........	PUNCT
ejpam-3506	198	1	.........	.........	PUNCT
ejpam-3506	198	2	.........	.........	PUNCT
ejpam-3506	199	1	.........	.........	PUNCT
ejpam-3506	199	2	.........	.........	PUNCT
ejpam-3506	200	1	.........	.........	PUNCT
ejpam-3506	200	2	.........	.........	PUNCT
ejpam-3506	201	1	.........	.........	PUNCT
ejpam-3506	201	2	......	......	PUNCT
ejpam-3506	202	1	.............................................................................................................................................................................................................	.............................................................................................................................................................................................................	PUNCT
ejpam-3506	202	2	....................................	....................................	PUNCT
ejpam-3506	203	1	....................................	....................................	PUNCT
ejpam-3506	204	1	x1	x1	NUM
ejpam-3506	205	1	x2	x2	NOUN
ejpam-3506	205	2	x3	x3	PROPN
ejpam-3506	206	1	x4	x4	PROPN
ejpam-3506	206	2	x5	x5	PROPN
ejpam-3506	206	3	xa−1	xa−1	PROPN
ejpam-3506	206	4	w	w	PROPN
ejpam-3506	206	5	v	v	PROPN
ejpam-3506	206	6	xa	xa	PROPN
ejpam-3506	206	7	p1	p1	PROPN
ejpam-3506	206	8	p2	p2	X
ejpam-3506	206	9	pr	pr	NOUN
ejpam-3506	206	10	·	·	PUNCT
ejpam-3506	206	11	·	·	PUNCT
ejpam-3506	206	12	·	·	PUNCT
ejpam-3506	206	13	•	•	NUM
ejpam-3506	206	14	••	••	NOUN
ejpam-3506	206	15	••	••	NOUN
ejpam-3506	206	16	•	•	NUM
ejpam-3506	206	17	•	•	NOUN
ejpam-3506	206	18	h1	h1	PROPN
ejpam-3506	206	19	h2	h2	PROPN
ejpam-3506	206	20	·	·	PUNCT
ejpam-3506	206	21	·	·	PUNCT
ejpam-3506	206	22	·	·	PUNCT
ejpam-3506	206	23	y1	y1	INTJ
ejpam-3506	206	24	y2	y2	NOUN
ejpam-3506	206	25	y3	y3	PROPN
ejpam-3506	206	26	y4	y4	NOUN
ejpam-3506	206	27	y5	y5	PROPN
ejpam-3506	206	28	ya−1	ya−1	NOUN
ejpam-3506	206	29	z1	z1	ADJ
ejpam-3506	206	30	z2	z2	PROPN
ejpam-3506	206	31	z3	z3	PROPN
ejpam-3506	206	32	z4	z4	PROPN
ejpam-3506	206	33	z5	z5	PROPN
ejpam-3506	206	34	za−1	za−1	PROPN
ejpam-3506	206	35	figure	figure	NOUN
ejpam-3506	206	36	3	3	NUM
ejpam-3506	206	37	:	:	PUNCT
ejpam-3506	206	38	a	a	DET
ejpam-3506	206	39	graph	graph	NOUN
ejpam-3506	206	40	g	g	NOUN
ejpam-3506	206	41	with	with	ADP
ejpam-3506	206	42	γ1fd(g	γ1fd(g	PROPN
ejpam-3506	206	43	)	)	PUNCT
ejpam-3506	206	44	=	=	SYM
ejpam-3506	206	45	a	a	PRON
ejpam-3506	206	46	and	and	CCONJ
ejpam-3506	206	47	γnc1fd(g	γnc1fd(g	NUM
ejpam-3506	206	48	)	)	PUNCT
ejpam-3506	207	1	=	=	SYM
ejpam-3506	207	2	b	b	X
ejpam-3506	207	3	when	when	SCONJ
ejpam-3506	207	4	a	a	DET
ejpam-3506	207	5	<	<	X
ejpam-3506	207	6	b	b	NOUN
ejpam-3506	207	7	and	and	CCONJ
ejpam-3506	207	8	b−	b−	PROPN
ejpam-3506	207	9	a	a	DET
ejpam-3506	207	10	≥	≥	NUM
ejpam-3506	207	11	2	2	NUM
ejpam-3506	207	12	.	.	PUNCT
ejpam-3506	207	13	clearly	clearly	ADV
ejpam-3506	207	14	,	,	PUNCT
ejpam-3506	207	15	a1	a1	NOUN
ejpam-3506	207	16	=	=	SYM
ejpam-3506	207	17	{	{	PUNCT
ejpam-3506	207	18	x1	x1	PROPN
ejpam-3506	207	19	,	,	PUNCT
ejpam-3506	207	20	x2	x2	PROPN
ejpam-3506	207	21	...	...	PUNCT
ejpam-3506	207	22	,	,	PUNCT
ejpam-3506	207	23	xa	xa	PROPN
ejpam-3506	207	24	}	}	PUNCT
ejpam-3506	207	25	is	be	AUX
ejpam-3506	207	26	a	a	DET
ejpam-3506	207	27	γ1fd	γ1fd	NOUN
ejpam-3506	207	28	-	-	PUNCT
ejpam-3506	207	29	set	set	NOUN
ejpam-3506	207	30	of	of	ADP
ejpam-3506	207	31	g.	g.	PROPN
ejpam-3506	207	32	let	let	VERB
ejpam-3506	207	33	b	b	X
ejpam-3506	207	34	be	be	AUX
ejpam-3506	207	35	a	a	DET
ejpam-3506	207	36	γnc1fd	γnc1fd	NOUN
ejpam-3506	207	37	-	-	PUNCT
ejpam-3506	207	38	set	set	NOUN
ejpam-3506	207	39	of	of	ADP
ejpam-3506	207	40	g.	g.	PROPN
ejpam-3506	207	41	then	then	ADV
ejpam-3506	207	42	w.	w.	PROPN
ejpam-3506	207	43	bent	bent	PROPN
ejpam-3506	207	44	-	-	PUNCT
ejpam-3506	207	45	usman	usman	PROPN
ejpam-3506	207	46	,	,	PUNCT
ejpam-3506	207	47	r.	r.	PROPN
ejpam-3506	207	48	isla	isla	PROPN
ejpam-3506	207	49	,	,	PUNCT
ejpam-3506	207	50	s.	s.	PROPN
ejpam-3506	207	51	canoy	canoy	PROPN
ejpam-3506	207	52	/	/	SYM
ejpam-3506	207	53	eur	eur	PROPN
ejpam-3506	207	54	.	.	PUNCT
ejpam-3506	208	1	j.	j.	PROPN
ejpam-3506	208	2	pure	pure	PROPN
ejpam-3506	208	3	appl	appl	PROPN
ejpam-3506	208	4	.	.	PROPN
ejpam-3506	208	5	math	math	PROPN
ejpam-3506	208	6	,	,	PUNCT
ejpam-3506	208	7	12	12	NUM
ejpam-3506	208	8	(	(	PUNCT
ejpam-3506	208	9	3	3	NUM
ejpam-3506	208	10	)	)	PUNCT
ejpam-3506	208	11	(	(	PUNCT
ejpam-3506	208	12	2019	2019	NUM
ejpam-3506	208	13	)	)	PUNCT
ejpam-3506	208	14	,	,	PUNCT
ejpam-3506	208	15	1337	1337	NUM
ejpam-3506	208	16	-	-	SYM
ejpam-3506	208	17	1349	1349	NUM
ejpam-3506	208	18	1342	1342	NUM
ejpam-3506	208	19	clearly	clearly	ADV
ejpam-3506	208	20	,	,	PUNCT
ejpam-3506	208	21	{	{	PUNCT
ejpam-3506	208	22	x1	x1	PROPN
ejpam-3506	208	23	,	,	PUNCT
ejpam-3506	208	24	x2	x2	PROPN
ejpam-3506	208	25	,	,	PUNCT
ejpam-3506	208	26	...	...	PUNCT
ejpam-3506	208	27	,	,	PUNCT
ejpam-3506	208	28	xa−1	xa−1	PROPN
ejpam-3506	208	29	}	}	PUNCT
ejpam-3506	209	1	⊆	⊆	PROPN
ejpam-3506	209	2	b.	b.	PROPN
ejpam-3506	209	3	suppose	suppose	VERB
ejpam-3506	209	4	xa	xa	PROPN
ejpam-3506	209	5	/∈	/∈	PROPN
ejpam-3506	209	6	b.	b.	PROPN
ejpam-3506	210	1	then	then	ADV
ejpam-3506	210	2	v	v	INTJ
ejpam-3506	210	3	(	(	PUNCT
ejpam-3506	210	4	hj	hj	PROPN
ejpam-3506	210	5	)	)	PUNCT
ejpam-3506	210	6	∩	∩	PROPN
ejpam-3506	210	7	b	b	PROPN
ejpam-3506	210	8	6=	6=	PROPN
ejpam-3506	210	9	∅	∅	NOUN
ejpam-3506	210	10	for	for	ADP
ejpam-3506	210	11	j	j	PROPN
ejpam-3506	210	12	=	=	SYM
ejpam-3506	210	13	1	1	NUM
ejpam-3506	210	14	,	,	PUNCT
ejpam-3506	210	15	2	2	NUM
ejpam-3506	210	16	,	,	PUNCT
ejpam-3506	210	17	contrary	contrary	ADJ
ejpam-3506	210	18	to	to	ADP
ejpam-3506	210	19	the	the	DET
ejpam-3506	210	20	assumption	assumption	NOUN
ejpam-3506	210	21	that	that	SCONJ
ejpam-3506	210	22	b	b	PROPN
ejpam-3506	210	23	is	be	AUX
ejpam-3506	210	24	a	a	DET
ejpam-3506	210	25	1fd	1fd	NOUN
ejpam-3506	210	26	-	-	PUNCT
ejpam-3506	210	27	set	set	NOUN
ejpam-3506	210	28	.	.	PUNCT
ejpam-3506	211	1	therefore	therefore	ADV
ejpam-3506	211	2	,	,	PUNCT
ejpam-3506	211	3	xa	xa	PROPN
ejpam-3506	211	4	∈	∈	PROPN
ejpam-3506	211	5	b.	b.	PROPN
ejpam-3506	212	1	if	if	SCONJ
ejpam-3506	212	2	w	w	PROPN
ejpam-3506	212	3	/∈	/∈	PROPN
ejpam-3506	213	1	b	b	NOUN
ejpam-3506	213	2	,	,	PUNCT
ejpam-3506	213	3	then	then	ADV
ejpam-3506	213	4	v	v	NOUN
ejpam-3506	213	5	,	,	PUNCT
ejpam-3506	213	6	pi	pi	NOUN
ejpam-3506	213	7	/∈	/∈	PUNCT
ejpam-3506	214	1	b	b	X
ejpam-3506	214	2	for	for	ADP
ejpam-3506	214	3	all	all	PRON
ejpam-3506	214	4	i	i	PRON
ejpam-3506	214	5	∈	∈	PROPN
ejpam-3506	214	6	{	{	PUNCT
ejpam-3506	214	7	1	1	NUM
ejpam-3506	214	8	,	,	PUNCT
ejpam-3506	214	9	2	2	NUM
ejpam-3506	214	10	,	,	PUNCT
ejpam-3506	214	11	...	...	PUNCT
ejpam-3506	214	12	,	,	PUNCT
ejpam-3506	214	13	r	r	NOUN
ejpam-3506	214	14	}	}	PUNCT
ejpam-3506	214	15	.	.	PUNCT
ejpam-3506	215	1	since	since	SCONJ
ejpam-3506	215	2	b	b	PROPN
ejpam-3506	215	3	is	be	AUX
ejpam-3506	215	4	a	a	DET
ejpam-3506	215	5	γnc1fd	γnc1fd	NOUN
ejpam-3506	215	6	-	-	PUNCT
ejpam-3506	215	7	set	set	VERB
ejpam-3506	215	8	,	,	PUNCT
ejpam-3506	215	9	b	b	NOUN
ejpam-3506	215	10	=	=	PRON
ejpam-3506	215	11	{	{	PUNCT
ejpam-3506	215	12	x1	x1	PROPN
ejpam-3506	215	13	,	,	PUNCT
ejpam-3506	215	14	x2	x2	PROPN
ejpam-3506	215	15	,	,	PUNCT
ejpam-3506	215	16	...	...	PUNCT
ejpam-3506	215	17	,	,	PUNCT
ejpam-3506	215	18	xa	xa	PROPN
ejpam-3506	215	19	}	}	PUNCT
ejpam-3506	215	20	∪	∪	VERB
ejpam-3506	215	21	v	v	NOUN
ejpam-3506	215	22	(	(	PUNCT
ejpam-3506	215	23	h1	h1	PROPN
ejpam-3506	215	24	)	)	PUNCT
ejpam-3506	215	25	or	or	CCONJ
ejpam-3506	215	26	b	b	X
ejpam-3506	215	27	=	=	SYM
ejpam-3506	215	28	{	{	PUNCT
ejpam-3506	215	29	x1	x1	PROPN
ejpam-3506	215	30	,	,	PUNCT
ejpam-3506	215	31	x2	x2	PROPN
ejpam-3506	215	32	,	,	PUNCT
ejpam-3506	215	33	...	...	PUNCT
ejpam-3506	215	34	,	,	PUNCT
ejpam-3506	215	35	xa	xa	PROPN
ejpam-3506	215	36	}	}	PUNCT
ejpam-3506	215	37	∪	∪	VERB
ejpam-3506	215	38	v	v	NOUN
ejpam-3506	215	39	(	(	PUNCT
ejpam-3506	215	40	h2	h2	NOUN
ejpam-3506	215	41	)	)	PUNCT
ejpam-3506	215	42	,	,	PUNCT
ejpam-3506	215	43	where	where	SCONJ
ejpam-3506	215	44	∣∣b∣∣	∣∣b∣∣	ADP
ejpam-3506	215	45	=	=	SYM
ejpam-3506	215	46	a	a	PRON
ejpam-3506	215	47	+	+	NUM
ejpam-3506	215	48	r	r	NOUN
ejpam-3506	215	49	=	=	SYM
ejpam-3506	215	50	b.	b.	PROPN
ejpam-3506	215	51	suppose	suppose	VERB
ejpam-3506	215	52	that	that	SCONJ
ejpam-3506	215	53	w	w	PROPN
ejpam-3506	215	54	∈	∈	PROPN
ejpam-3506	215	55	b.	b.	PROPN
ejpam-3506	215	56	since	since	SCONJ
ejpam-3506	215	57	b	b	PROPN
ejpam-3506	215	58	is	be	AUX
ejpam-3506	215	59	a	a	DET
ejpam-3506	215	60	1fd	1fd	NOUN
ejpam-3506	215	61	-	-	PUNCT
ejpam-3506	215	62	set	set	NOUN
ejpam-3506	215	63	,	,	PUNCT
ejpam-3506	215	64	it	it	PRON
ejpam-3506	215	65	follows	follow	VERB
ejpam-3506	215	66	that	that	SCONJ
ejpam-3506	215	67	v	v	NOUN
ejpam-3506	215	68	,	,	PUNCT
ejpam-3506	215	69	pi	pi	NOUN
ejpam-3506	215	70	∈	∈	PROPN
ejpam-3506	215	71	b	b	PROPN
ejpam-3506	215	72	for	for	ADP
ejpam-3506	215	73	all	all	PRON
ejpam-3506	215	74	i	i	PRON
ejpam-3506	215	75	∈	∈	PROPN
ejpam-3506	215	76	{	{	PUNCT
ejpam-3506	215	77	1	1	NUM
ejpam-3506	215	78	,	,	PUNCT
ejpam-3506	215	79	2	2	NUM
ejpam-3506	215	80	,	,	PUNCT
ejpam-3506	215	81	...	...	PUNCT
ejpam-3506	215	82	,	,	PUNCT
ejpam-3506	215	83	r	r	NOUN
ejpam-3506	215	84	}	}	PUNCT
ejpam-3506	215	85	.	.	PUNCT
ejpam-3506	216	1	hence	hence	ADV
ejpam-3506	216	2	,	,	PUNCT
ejpam-3506	216	3	b	b	X
ejpam-3506	216	4	=	=	PRON
ejpam-3506	216	5	{	{	PUNCT
ejpam-3506	216	6	x1	x1	PROPN
ejpam-3506	216	7	,	,	PUNCT
ejpam-3506	216	8	x2	x2	PROPN
ejpam-3506	216	9	,	,	PUNCT
ejpam-3506	216	10	...	...	PUNCT
ejpam-3506	216	11	,	,	PUNCT
ejpam-3506	216	12	xa	xa	PROPN
ejpam-3506	216	13	,	,	PUNCT
ejpam-3506	216	14	w	w	PROPN
ejpam-3506	216	15	,	,	PUNCT
ejpam-3506	216	16	v	v	NOUN
ejpam-3506	216	17	}	}	PUNCT
ejpam-3506	216	18	∪	∪	ADJ
ejpam-3506	216	19	{	{	PUNCT
ejpam-3506	216	20	p1	p1	NOUN
ejpam-3506	216	21	,	,	PUNCT
ejpam-3506	216	22	p2	p2	NOUN
ejpam-3506	216	23	,	,	PUNCT
ejpam-3506	216	24	...	...	PUNCT
ejpam-3506	216	25	,	,	PUNCT
ejpam-3506	216	26	pr	pr	NOUN
ejpam-3506	216	27	}	}	PUNCT
ejpam-3506	216	28	and	and	CCONJ
ejpam-3506	216	29	∣∣b∣∣	∣∣b∣∣	ADP
ejpam-3506	216	30	=	=	NOUN
ejpam-3506	216	31	b+	b+	X
ejpam-3506	216	32	2	2	NUM
ejpam-3506	216	33	.	.	PUNCT
ejpam-3506	217	1	this	this	PRON
ejpam-3506	217	2	is	be	AUX
ejpam-3506	217	3	not	not	PART
ejpam-3506	217	4	possible	possible	ADJ
ejpam-3506	217	5	because	because	SCONJ
ejpam-3506	217	6	{	{	PUNCT
ejpam-3506	217	7	x1	x1	ADJ
ejpam-3506	217	8	,	,	PUNCT
ejpam-3506	217	9	x2	x2	PROPN
ejpam-3506	217	10	,	,	PUNCT
ejpam-3506	217	11	...	...	PUNCT
ejpam-3506	217	12	,	,	PUNCT
ejpam-3506	217	13	xa	xa	PROPN
ejpam-3506	217	14	}	}	PUNCT
ejpam-3506	217	15	∪	∪	VERB
ejpam-3506	217	16	v	v	NOUN
ejpam-3506	217	17	(	(	PUNCT
ejpam-3506	217	18	h1	h1	PROPN
ejpam-3506	217	19	)	)	PUNCT
ejpam-3506	217	20	is	be	AUX
ejpam-3506	217	21	an	an	DET
ejpam-3506	217	22	nc1fd	nc1fd	NOUN
ejpam-3506	217	23	-	-	PUNCT
ejpam-3506	217	24	set	set	VERB
ejpam-3506	217	25	having	have	VERB
ejpam-3506	217	26	exactly	exactly	ADV
ejpam-3506	217	27	b	b	NOUN
ejpam-3506	217	28	elements	element	NOUN
ejpam-3506	217	29	.	.	PUNCT
ejpam-3506	218	1	therefore	therefore	ADV
ejpam-3506	218	2	,	,	PUNCT
ejpam-3506	218	3	w	w	PROPN
ejpam-3506	218	4	/∈	/∈	PROPN
ejpam-3506	218	5	b	b	NOUN
ejpam-3506	218	6	and	and	CCONJ
ejpam-3506	218	7	b	b	X
ejpam-3506	218	8	=	=	SYM
ejpam-3506	218	9	{	{	PUNCT
ejpam-3506	218	10	x1	x1	PROPN
ejpam-3506	218	11	,	,	PUNCT
ejpam-3506	218	12	x2	x2	PROPN
ejpam-3506	218	13	,	,	PUNCT
ejpam-3506	218	14	...	...	PUNCT
ejpam-3506	218	15	,	,	PUNCT
ejpam-3506	218	16	xa	xa	PROPN
ejpam-3506	218	17	}	}	PUNCT
ejpam-3506	218	18	∪	∪	VERB
ejpam-3506	218	19	v	v	NOUN
ejpam-3506	218	20	(	(	PUNCT
ejpam-3506	218	21	h1	h1	PROPN
ejpam-3506	218	22	)	)	PUNCT
ejpam-3506	218	23	or	or	CCONJ
ejpam-3506	218	24	b	b	X
ejpam-3506	218	25	=	=	SYM
ejpam-3506	218	26	{	{	PUNCT
ejpam-3506	218	27	x1	x1	PROPN
ejpam-3506	218	28	,	,	PUNCT
ejpam-3506	218	29	x2	x2	PROPN
ejpam-3506	218	30	,	,	PUNCT
ejpam-3506	218	31	...	...	PUNCT
ejpam-3506	218	32	,	,	PUNCT
ejpam-3506	218	33	xa	xa	PROPN
ejpam-3506	218	34	}	}	PUNCT
ejpam-3506	218	35	∪	∪	VERB
ejpam-3506	218	36	v	v	NOUN
ejpam-3506	218	37	(	(	PUNCT
ejpam-3506	218	38	h2	h2	NOUN
ejpam-3506	218	39	)	)	PUNCT
ejpam-3506	218	40	.	.	PUNCT
ejpam-3506	219	1	accordingly	accordingly	ADV
ejpam-3506	219	2	,	,	PUNCT
ejpam-3506	219	3	γ1fd(g	γ1fd(g	PROPN
ejpam-3506	219	4	)	)	PUNCT
ejpam-3506	219	5	=	=	SYM
ejpam-3506	220	1	a	a	PRON
ejpam-3506	220	2	and	and	CCONJ
ejpam-3506	220	3	γnc1fd(g	γnc1fd(g	NUM
ejpam-3506	220	4	)	)	PUNCT
ejpam-3506	221	1	=	=	SYM
ejpam-3506	221	2	b.	b.	PROPN
ejpam-3506	221	3	�	�	PROPN
ejpam-3506	221	4	corollary	corollary	NOUN
ejpam-3506	221	5	2	2	PROPN
ejpam-3506	221	6	.	.	PUNCT
ejpam-3506	221	7	γnc1fd	γnc1fd	PROPN
ejpam-3506	222	1	−	−	NOUN
ejpam-3506	222	2	γ1fd	γ1fd	PUNCT
ejpam-3506	222	3	can	can	AUX
ejpam-3506	222	4	be	be	AUX
ejpam-3506	222	5	made	make	VERB
ejpam-3506	222	6	arbitrarily	arbitrarily	ADV
ejpam-3506	222	7	large	large	ADJ
ejpam-3506	222	8	.	.	PUNCT
ejpam-3506	223	1	theorem	theorem	ADJ
ejpam-3506	223	2	7	7	NUM
ejpam-3506	223	3	.	.	PUNCT
ejpam-3506	224	1	let	let	VERB
ejpam-3506	224	2	a	a	PRON
ejpam-3506	224	3	and	and	CCONJ
ejpam-3506	224	4	b	b	NOUN
ejpam-3506	224	5	be	be	AUX
ejpam-3506	224	6	positive	positive	ADJ
ejpam-3506	224	7	integers	integer	NOUN
ejpam-3506	224	8	such	such	ADJ
ejpam-3506	224	9	that	that	SCONJ
ejpam-3506	224	10	4	4	NUM
ejpam-3506	224	11	≤	≤	NUM
ejpam-3506	224	12	a	a	DET
ejpam-3506	224	13	≤	≤	PROPN
ejpam-3506	224	14	b.	b.	NOUN
ejpam-3506	225	1	then	then	ADV
ejpam-3506	225	2	there	there	PRON
ejpam-3506	225	3	exists	exist	VERB
ejpam-3506	225	4	a	a	DET
ejpam-3506	225	5	connected	connected	ADJ
ejpam-3506	225	6	graph	graph	NOUN
ejpam-3506	225	7	g	g	ADP
ejpam-3506	225	8	such	such	ADJ
ejpam-3506	225	9	that	that	DET
ejpam-3506	225	10	γ2fd(g	γ2fd(g	PROPN
ejpam-3506	225	11	)	)	PUNCT
ejpam-3506	225	12	=	=	SYM
ejpam-3506	225	13	a	a	PRON
ejpam-3506	225	14	and	and	CCONJ
ejpam-3506	225	15	γnc2fd(g	γnc2fd(g	NUM
ejpam-3506	225	16	)	)	PUNCT
ejpam-3506	225	17	=	=	SYM
ejpam-3506	225	18	b.	b.	PROPN
ejpam-3506	225	19	proof	proof	NOUN
ejpam-3506	225	20	.	.	PUNCT
ejpam-3506	226	1	consider	consider	VERB
ejpam-3506	226	2	the	the	DET
ejpam-3506	226	3	following	follow	VERB
ejpam-3506	226	4	cases	case	NOUN
ejpam-3506	226	5	:	:	PUNCT
ejpam-3506	226	6	case	case	NOUN
ejpam-3506	226	7	1	1	NUM
ejpam-3506	226	8	.	.	PUNCT
ejpam-3506	227	1	a	a	DET
ejpam-3506	227	2	=	=	X
ejpam-3506	227	3	b	b	NOUN
ejpam-3506	227	4	let	let	VERB
ejpam-3506	227	5	g	g	PRON
ejpam-3506	227	6	be	be	AUX
ejpam-3506	227	7	the	the	DET
ejpam-3506	227	8	graph	graph	NOUN
ejpam-3506	227	9	shown	show	VERB
ejpam-3506	227	10	in	in	ADP
ejpam-3506	227	11	figure	figure	NOUN
ejpam-3506	227	12	4	4	NUM
ejpam-3506	227	13	.	.	PUNCT
ejpam-3506	228	1	clearly	clearly	ADV
ejpam-3506	228	2	,	,	PUNCT
ejpam-3506	228	3	the	the	DET
ejpam-3506	228	4	set	set	NOUN
ejpam-3506	228	5	b	b	NOUN
ejpam-3506	228	6	=	=	PRON
ejpam-3506	228	7	{	{	PUNCT
ejpam-3506	228	8	xi	xi	X
ejpam-3506	228	9	:	:	PUNCT
ejpam-3506	228	10	i	i	NOUN
ejpam-3506	228	11	=	=	NOUN
ejpam-3506	228	12	1	1	NUM
ejpam-3506	228	13	,	,	PUNCT
ejpam-3506	228	14	2	2	NUM
ejpam-3506	228	15	,	,	PUNCT
ejpam-3506	228	16	...	...	PUNCT
ejpam-3506	228	17	a	a	X
ejpam-3506	228	18	}	}	PUNCT
ejpam-3506	228	19	is	be	AUX
ejpam-3506	228	20	both	both	CCONJ
ejpam-3506	228	21	a	a	DET
ejpam-3506	228	22	γ2fd	γ2fd	NOUN
ejpam-3506	228	23	-	-	PUNCT
ejpam-3506	228	24	set	set	NOUN
ejpam-3506	228	25	and	and	CCONJ
ejpam-3506	228	26	a	a	DET
ejpam-3506	228	27	γnc2fd	γnc2fd	PROPN
ejpam-3506	228	28	-	-	PUNCT
ejpam-3506	228	29	set	set	NOUN
ejpam-3506	228	30	in	in	ADP
ejpam-3506	228	31	g.	g.	PROPN
ejpam-3506	228	32	it	it	PRON
ejpam-3506	228	33	follows	follow	VERB
ejpam-3506	228	34	that	that	PRON
ejpam-3506	228	35	γ2fd(g	γ2fd(g	PROPN
ejpam-3506	228	36	)	)	PUNCT
ejpam-3506	229	1	=	=	SYM
ejpam-3506	229	2	γnc2fd(g	γnc2fd(g	PROPN
ejpam-3506	229	3	)	)	PUNCT
ejpam-3506	230	1	=	=	PRON
ejpam-3506	230	2	|b|	|b|	X
ejpam-3506	230	3	=	=	PUNCT
ejpam-3506	230	4	a	a	DET
ejpam-3506	230	5	=	=	X
ejpam-3506	230	6	b.	b.	PROPN
ejpam-3506	230	7	................................................................................................................	................................................................................................................	PROPN
ejpam-3506	230	8	................................................................................................................	................................................................................................................	PROPN
ejpam-3506	231	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	231	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	232	1	....................................	....................................	PUNCT
ejpam-3506	232	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	233	1	....................................	....................................	PUNCT
ejpam-3506	233	2	.........	.........	PUNCT
ejpam-3506	233	3	........	........	PUNCT
ejpam-3506	233	4	........	........	PUNCT
ejpam-3506	233	5	........	........	PUNCT
ejpam-3506	233	6	........	........	PUNCT
ejpam-3506	233	7	........	........	PUNCT
ejpam-3506	233	8	........	........	PUNCT
ejpam-3506	233	9	........	........	PUNCT
ejpam-3506	233	10	........	........	PUNCT
ejpam-3506	233	11	........	........	PUNCT
ejpam-3506	233	12	........	........	PUNCT
ejpam-3506	233	13	........	........	PUNCT
ejpam-3506	233	14	........	........	PUNCT
ejpam-3506	233	15	........	........	PUNCT
ejpam-3506	233	16	........	........	PUNCT
ejpam-3506	233	17	........	........	PUNCT
ejpam-3506	233	18	........	........	PUNCT
ejpam-3506	233	19	........	........	PUNCT
ejpam-3506	233	20	........	........	PUNCT
ejpam-3506	233	21	........	........	PUNCT
ejpam-3506	233	22	.	.	PUNCT
ejpam-3506	234	1	..	..	PUNCT
ejpam-3506	234	2	..................................	..................................	PUNCT
ejpam-3506	235	1	....................................	....................................	PUNCT
ejpam-3506	235	2	.........	.........	PUNCT
ejpam-3506	235	3	........	........	PUNCT
ejpam-3506	235	4	........	........	PUNCT
ejpam-3506	235	5	........	........	PUNCT
ejpam-3506	235	6	........	........	PUNCT
ejpam-3506	235	7	........	........	PUNCT
ejpam-3506	235	8	........	........	PUNCT
ejpam-3506	235	9	........	........	PUNCT
ejpam-3506	235	10	........	........	PUNCT
ejpam-3506	235	11	........	........	PUNCT
ejpam-3506	235	12	........	........	PUNCT
ejpam-3506	235	13	........	........	PUNCT
ejpam-3506	235	14	........	........	PUNCT
ejpam-3506	235	15	........	........	PUNCT
ejpam-3506	235	16	........	........	PUNCT
ejpam-3506	235	17	........	........	PUNCT
ejpam-3506	235	18	........	........	PUNCT
ejpam-3506	235	19	........	........	PUNCT
ejpam-3506	235	20	........	........	PUNCT
ejpam-3506	235	21	........	........	PUNCT
ejpam-3506	235	22	.	.	PUNCT
ejpam-3506	236	1	..	..	PUNCT
ejpam-3506	236	2	..................................	..................................	PUNCT
ejpam-3506	237	1	....................................	....................................	PUNCT
ejpam-3506	237	2	.........	.........	PUNCT
ejpam-3506	237	3	........	........	PUNCT
ejpam-3506	237	4	........	........	PUNCT
ejpam-3506	237	5	........	........	PUNCT
ejpam-3506	237	6	........	........	PUNCT
ejpam-3506	237	7	........	........	PUNCT
ejpam-3506	237	8	........	........	PUNCT
ejpam-3506	237	9	........	........	PUNCT
ejpam-3506	237	10	........	........	PUNCT
ejpam-3506	237	11	........	........	PUNCT
ejpam-3506	237	12	........	........	PUNCT
ejpam-3506	237	13	........	........	PUNCT
ejpam-3506	237	14	........	........	PUNCT
ejpam-3506	237	15	........	........	PUNCT
ejpam-3506	237	16	........	........	PUNCT
ejpam-3506	237	17	........	........	PUNCT
ejpam-3506	237	18	........	........	PUNCT
ejpam-3506	237	19	........	........	PUNCT
ejpam-3506	237	20	........	........	PUNCT
ejpam-3506	237	21	........	........	PUNCT
ejpam-3506	237	22	.	.	PUNCT
ejpam-3506	238	1	..	..	PUNCT
ejpam-3506	238	2	..................................	..................................	PUNCT
ejpam-3506	239	1	....................................	....................................	PUNCT
ejpam-3506	239	2	.........	.........	PUNCT
ejpam-3506	239	3	........	........	PUNCT
ejpam-3506	239	4	........	........	PUNCT
ejpam-3506	239	5	........	........	PUNCT
ejpam-3506	239	6	........	........	PUNCT
ejpam-3506	239	7	........	........	PUNCT
ejpam-3506	239	8	........	........	PUNCT
ejpam-3506	239	9	........	........	PUNCT
ejpam-3506	239	10	........	........	PUNCT
ejpam-3506	239	11	........	........	PUNCT
ejpam-3506	239	12	........	........	PUNCT
ejpam-3506	239	13	........	........	PUNCT
ejpam-3506	239	14	........	........	PUNCT
ejpam-3506	239	15	........	........	PUNCT
ejpam-3506	239	16	........	........	PUNCT
ejpam-3506	239	17	........	........	PUNCT
ejpam-3506	239	18	........	........	PUNCT
ejpam-3506	239	19	........	........	PUNCT
ejpam-3506	239	20	........	........	PUNCT
ejpam-3506	239	21	........	........	PUNCT
ejpam-3506	239	22	.	.	PUNCT
ejpam-3506	240	1	..	..	PUNCT
ejpam-3506	240	2	..................................	..................................	PUNCT
ejpam-3506	241	1	....................................	....................................	PUNCT
ejpam-3506	241	2	.........	.........	PUNCT
ejpam-3506	241	3	........	........	PUNCT
ejpam-3506	241	4	........	........	PUNCT
ejpam-3506	241	5	........	........	PUNCT
ejpam-3506	241	6	........	........	PUNCT
ejpam-3506	241	7	........	........	PUNCT
ejpam-3506	241	8	........	........	PUNCT
ejpam-3506	241	9	........	........	PUNCT
ejpam-3506	241	10	........	........	PUNCT
ejpam-3506	241	11	...	...	PUNCT
ejpam-3506	241	12	.........	.........	PUNCT
ejpam-3506	241	13	........	........	PUNCT
ejpam-3506	241	14	........	........	PUNCT
ejpam-3506	241	15	........	........	PUNCT
ejpam-3506	241	16	........	........	PUNCT
ejpam-3506	241	17	........	........	PUNCT
ejpam-3506	241	18	........	........	PUNCT
ejpam-3506	241	19	........	........	PUNCT
ejpam-3506	241	20	........	........	PUNCT
ejpam-3506	241	21	...	...	PUNCT
ejpam-3506	241	22	.........	.........	PUNCT
ejpam-3506	241	23	........	........	PUNCT
ejpam-3506	241	24	........	........	PUNCT
ejpam-3506	241	25	........	........	PUNCT
ejpam-3506	241	26	........	........	PUNCT
ejpam-3506	241	27	........	........	PUNCT
ejpam-3506	241	28	........	........	PUNCT
ejpam-3506	241	29	........	........	PUNCT
ejpam-3506	241	30	........	........	PUNCT
ejpam-3506	241	31	...	...	PUNCT
ejpam-3506	242	1	....................................	....................................	PUNCT
ejpam-3506	242	2	.........	.........	PUNCT
ejpam-3506	242	3	........	........	PUNCT
ejpam-3506	242	4	........	........	PUNCT
ejpam-3506	242	5	........	........	PUNCT
ejpam-3506	242	6	........	........	PUNCT
ejpam-3506	242	7	........	........	PUNCT
ejpam-3506	242	8	........	........	PUNCT
ejpam-3506	242	9	........	........	PUNCT
ejpam-3506	242	10	........	........	PUNCT
ejpam-3506	242	11	...	...	PUNCT
ejpam-3506	243	1	....................................	....................................	PUNCT
ejpam-3506	243	2	....................................	....................................	PUNCT
ejpam-3506	243	3	.........	.........	PUNCT
ejpam-3506	243	4	........	........	PUNCT
ejpam-3506	243	5	........	........	PUNCT
ejpam-3506	243	6	........	........	PUNCT
ejpam-3506	243	7	........	........	PUNCT
ejpam-3506	243	8	........	........	PUNCT
ejpam-3506	243	9	........	........	PUNCT
ejpam-3506	243	10	........	........	PUNCT
ejpam-3506	243	11	........	........	PUNCT
ejpam-3506	243	12	...	...	PUNCT
ejpam-3506	244	1	....................................	....................................	PUNCT
ejpam-3506	244	2	.........	.........	PUNCT
ejpam-3506	244	3	........	........	PUNCT
ejpam-3506	244	4	........	........	PUNCT
ejpam-3506	244	5	........	........	PUNCT
ejpam-3506	244	6	........	........	PUNCT
ejpam-3506	244	7	........	........	PUNCT
ejpam-3506	244	8	........	........	PUNCT
ejpam-3506	244	9	........	........	PUNCT
ejpam-3506	244	10	........	........	PUNCT
ejpam-3506	244	11	...	...	PUNCT
ejpam-3506	245	1	....................................	....................................	PUNCT
ejpam-3506	245	2	....................................	....................................	PUNCT
ejpam-3506	246	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3506	246	2	....................................	....................................	PUNCT
ejpam-3506	247	1	....................................	....................................	PUNCT
ejpam-3506	247	2	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3506	248	1	....................................	....................................	PUNCT
ejpam-3506	248	2	....................................	....................................	PUNCT
ejpam-3506	249	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3506	249	2	....................................	....................................	PUNCT
ejpam-3506	250	1	....................................	....................................	PUNCT
ejpam-3506	250	2	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3506	251	1	....................................	....................................	PUNCT
ejpam-3506	251	2	....................................	....................................	PUNCT
ejpam-3506	252	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3506	252	2	....................................	....................................	PUNCT
ejpam-3506	253	1	....................................	....................................	PUNCT
ejpam-3506	253	2	............	............	PUNCT
ejpam-3506	253	3	...........	...........	PUNCT
ejpam-3506	253	4	...........	...........	PUNCT
ejpam-3506	253	5	...........	...........	PUNCT
ejpam-3506	253	6	...........	...........	PUNCT
ejpam-3506	253	7	...........	...........	PUNCT
ejpam-3506	253	8	...........	...........	PUNCT
ejpam-3506	253	9	...........	...........	PUNCT
ejpam-3506	253	10	...........	...........	PUNCT
ejpam-3506	253	11	...........	...........	PUNCT
ejpam-3506	253	12	....................................	....................................	PUNCT
ejpam-3506	253	13	....................................	....................................	PUNCT
ejpam-3506	253	14	............	............	PUNCT
ejpam-3506	253	15	...........	...........	PUNCT
ejpam-3506	253	16	...........	...........	PUNCT
ejpam-3506	253	17	...........	...........	PUNCT
ejpam-3506	253	18	...........	...........	PUNCT
ejpam-3506	253	19	...........	...........	PUNCT
ejpam-3506	253	20	...........	...........	PUNCT
ejpam-3506	253	21	...........	...........	PUNCT
ejpam-3506	253	22	...........	...........	PUNCT
ejpam-3506	253	23	...........	...........	PUNCT
ejpam-3506	253	24	....................................	....................................	PUNCT
ejpam-3506	253	25	....................................	....................................	PUNCT
ejpam-3506	253	26	............	............	PUNCT
ejpam-3506	253	27	...........	...........	PUNCT
ejpam-3506	253	28	...........	...........	PUNCT
ejpam-3506	253	29	...........	...........	PUNCT
ejpam-3506	253	30	...........	...........	PUNCT
ejpam-3506	253	31	...........	...........	PUNCT
ejpam-3506	253	32	...........	...........	PUNCT
ejpam-3506	253	33	...........	...........	PUNCT
ejpam-3506	253	34	...........	...........	PUNCT
ejpam-3506	253	35	...........	...........	PUNCT
ejpam-3506	253	36	....................................	....................................	PUNCT
ejpam-3506	253	37	....................................	....................................	PUNCT
ejpam-3506	253	38	............	............	PUNCT
ejpam-3506	253	39	...........	...........	PUNCT
ejpam-3506	253	40	...........	...........	PUNCT
ejpam-3506	253	41	...........	...........	PUNCT
ejpam-3506	253	42	...........	...........	PUNCT
ejpam-3506	253	43	...........	...........	PUNCT
ejpam-3506	253	44	...........	...........	PUNCT
ejpam-3506	253	45	...........	...........	PUNCT
ejpam-3506	253	46	...........	...........	PUNCT
ejpam-3506	253	47	...........	...........	PUNCT
ejpam-3506	253	48	....................................	....................................	PUNCT
ejpam-3506	253	49	....................................	....................................	PUNCT
ejpam-3506	253	50	............	............	PUNCT
ejpam-3506	253	51	...........	...........	PUNCT
ejpam-3506	253	52	...........	...........	PUNCT
ejpam-3506	253	53	...........	...........	PUNCT
ejpam-3506	253	54	...........	...........	PUNCT
ejpam-3506	253	55	...........	...........	PUNCT
ejpam-3506	253	56	...........	...........	PUNCT
ejpam-3506	253	57	...........	...........	PUNCT
ejpam-3506	253	58	...........	...........	PUNCT
ejpam-3506	253	59	...........	...........	PUNCT
ejpam-3506	253	60	....................................	....................................	PUNCT
ejpam-3506	253	61	...............................................................	...............................................................	PUNCT
ejpam-3506	254	1	...........................	...........................	PUNCT
ejpam-3506	255	1	x1	x1	NUM
ejpam-3506	256	1	x2	x2	NOUN
ejpam-3506	256	2	x3	x3	PROPN
ejpam-3506	257	1	x4	x4	PROPN
ejpam-3506	257	2	x5	x5	PROPN
ejpam-3506	257	3	xa−1	xa−1	PROPN
ejpam-3506	257	4	xa	xa	PROPN
ejpam-3506	257	5	·	·	PUNCT
ejpam-3506	257	6	·	·	PUNCT
ejpam-3506	257	7	·	·	PUNCT
ejpam-3506	257	8	•	•	NUM
ejpam-3506	257	9	••	••	NOUN
ejpam-3506	257	10	•••	•••	PROPN
ejpam-3506	257	11	•	•	ADJ
ejpam-3506	257	12	y1	y1	NOUN
ejpam-3506	257	13	y2	y2	NOUN
ejpam-3506	257	14	y3	y3	NOUN
ejpam-3506	257	15	y4	y4	NOUN
ejpam-3506	257	16	y5	y5	PROPN
ejpam-3506	257	17	ya−1	ya−1	NOUN
ejpam-3506	257	18	z1	z1	ADJ
ejpam-3506	257	19	z2	z2	PROPN
ejpam-3506	257	20	z3	z3	PROPN
ejpam-3506	257	21	z4	z4	PROPN
ejpam-3506	257	22	z5	z5	PROPN
ejpam-3506	257	23	za−1	za−1	PROPN
ejpam-3506	257	24	figure	figure	NOUN
ejpam-3506	257	25	4	4	NUM
ejpam-3506	257	26	:	:	PUNCT
ejpam-3506	257	27	a	a	DET
ejpam-3506	257	28	graph	graph	NOUN
ejpam-3506	257	29	g	g	NOUN
ejpam-3506	257	30	with	with	ADP
ejpam-3506	257	31	γ2fd(g	γ2fd(g	PROPN
ejpam-3506	257	32	)	)	PUNCT
ejpam-3506	257	33	=	=	SYM
ejpam-3506	257	34	γnc2fd(g	γnc2fd(g	PROPN
ejpam-3506	257	35	)	)	PUNCT
ejpam-3506	257	36	=	=	SYM
ejpam-3506	258	1	a	a	DET
ejpam-3506	258	2	=	=	PROPN
ejpam-3506	258	3	b.	b.	NOUN
ejpam-3506	258	4	case	case	NOUN
ejpam-3506	258	5	2	2	NUM
ejpam-3506	258	6	.	.	PUNCT
ejpam-3506	259	1	a	a	DET
ejpam-3506	259	2	<	<	X
ejpam-3506	259	3	b	b	X
ejpam-3506	259	4	let	let	VERB
ejpam-3506	259	5	m	m	VERB
ejpam-3506	259	6	=	=	VERB
ejpam-3506	259	7	b−	b−	PROPN
ejpam-3506	259	8	a	a	PROPN
ejpam-3506	259	9	and	and	CCONJ
ejpam-3506	259	10	let	let	VERB
ejpam-3506	259	11	h1	h1	PROPN
ejpam-3506	259	12	,	,	PUNCT
ejpam-3506	259	13	h2	h2	NOUN
ejpam-3506	259	14	,	,	PUNCT
ejpam-3506	259	15	h3	h3	NOUN
ejpam-3506	259	16	and	and	CCONJ
ejpam-3506	259	17	h4	h4	PROPN
ejpam-3506	259	18	be	be	AUX
ejpam-3506	259	19	graphs	graph	NOUN
ejpam-3506	259	20	such	such	ADJ
ejpam-3506	259	21	that	that	PRON
ejpam-3506	259	22	h1	h1	PROPN
ejpam-3506	259	23	∼=	∼=	PROPN
ejpam-3506	259	24	h2	h2	NOUN
ejpam-3506	259	25	∼=	∼=	NOUN
ejpam-3506	259	26	h3	h3	NOUN
ejpam-3506	259	27	∼=	∼=	PART
ejpam-3506	259	28	h4	h4	NOUN
ejpam-3506	259	29	∼=	∼=	PART
ejpam-3506	259	30	km	km	NOUN
ejpam-3506	259	31	.	.	PUNCT
ejpam-3506	260	1	consider	consider	VERB
ejpam-3506	260	2	the	the	DET
ejpam-3506	260	3	graph	graph	NOUN
ejpam-3506	260	4	g	g	NOUN
ejpam-3506	260	5	in	in	ADP
ejpam-3506	260	6	figure	figure	NOUN
ejpam-3506	260	7	5	5	NUM
ejpam-3506	260	8	.	.	PUNCT
ejpam-3506	261	1	clearly	clearly	ADV
ejpam-3506	261	2	,	,	PUNCT
ejpam-3506	261	3	a1	a1	NOUN
ejpam-3506	261	4	=	=	SYM
ejpam-3506	261	5	{	{	PUNCT
ejpam-3506	261	6	x1	x1	PROPN
ejpam-3506	261	7	,	,	PUNCT
ejpam-3506	261	8	x2	x2	PROPN
ejpam-3506	261	9	,	,	PUNCT
ejpam-3506	261	10	...	...	PUNCT
ejpam-3506	261	11	,	,	PUNCT
ejpam-3506	261	12	xa	xa	X
ejpam-3506	261	13	}	}	PUNCT
ejpam-3506	261	14	is	be	AUX
ejpam-3506	261	15	a	a	DET
ejpam-3506	261	16	γ2fd	γ2fd	PUNCT
ejpam-3506	261	17	-	-	PUNCT
ejpam-3506	261	18	set	set	NOUN
ejpam-3506	261	19	of	of	ADP
ejpam-3506	261	20	g.	g.	PROPN
ejpam-3506	261	21	suppose	suppose	VERB
ejpam-3506	261	22	a	a	PRON
ejpam-3506	261	23	is	be	AUX
ejpam-3506	261	24	a	a	DET
ejpam-3506	261	25	γnc2fd	γnc2fd	PROPN
ejpam-3506	261	26	-	-	PUNCT
ejpam-3506	261	27	set	set	NOUN
ejpam-3506	261	28	of	of	ADP
ejpam-3506	261	29	g.	g.	PROPN
ejpam-3506	261	30	it	it	PRON
ejpam-3506	261	31	is	be	AUX
ejpam-3506	261	32	easy	easy	ADJ
ejpam-3506	261	33	to	to	PART
ejpam-3506	261	34	show	show	VERB
ejpam-3506	261	35	that	that	SCONJ
ejpam-3506	261	36	{	{	PUNCT
ejpam-3506	261	37	x1	x1	ADJ
ejpam-3506	261	38	,	,	PUNCT
ejpam-3506	261	39	x2	x2	PROPN
ejpam-3506	261	40	,	,	PUNCT
ejpam-3506	261	41	...	...	PUNCT
ejpam-3506	261	42	,	,	PUNCT
ejpam-3506	261	43	xa−2	xa−2	PROPN
ejpam-3506	261	44	}	}	PUNCT
ejpam-3506	261	45	⊆	⊆	NUM
ejpam-3506	261	46	a.	a.	NOUN
ejpam-3506	261	47	suppose	suppose	VERB
ejpam-3506	261	48	that	that	SCONJ
ejpam-3506	261	49	xa−1	xa−1	PROPN
ejpam-3506	261	50	/∈	/∈	PUNCT
ejpam-3506	261	51	a.	a.	PROPN
ejpam-3506	261	52	then	then	ADV
ejpam-3506	261	53	ya−2	ya−2	PROPN
ejpam-3506	261	54	,	,	PUNCT
ejpam-3506	261	55	za−2	za−2	PROPN
ejpam-3506	261	56	∈	∈	PROPN
ejpam-3506	261	57	a.	a.	NOUN
ejpam-3506	261	58	this	this	PRON
ejpam-3506	261	59	implies	imply	VERB
ejpam-3506	261	60	that	that	SCONJ
ejpam-3506	261	61	ya−1	ya−1	PROPN
ejpam-3506	261	62	/∈	/∈	PUNCT
ejpam-3506	261	63	a	a	PRON
ejpam-3506	261	64	and	and	CCONJ
ejpam-3506	261	65	v	v	NOUN
ejpam-3506	261	66	(	(	PUNCT
ejpam-3506	261	67	h1	h1	PROPN
ejpam-3506	261	68	)	)	PUNCT
ejpam-3506	261	69	∩	∩	NOUN
ejpam-3506	261	70	a	a	DET
ejpam-3506	261	71	=	=	PUNCT
ejpam-3506	261	72	∅.	∅.	X
ejpam-3506	261	73	hence	hence	ADV
ejpam-3506	261	74	,	,	PUNCT
ejpam-3506	261	75	∣∣ng(ya−1	∣∣ng(ya−1	NOUN
ejpam-3506	261	76	)	)	PUNCT
ejpam-3506	261	77	∩	∩	NOUN
ejpam-3506	261	78	a	a	PRON
ejpam-3506	261	79	∣∣	∣∣	NUM
ejpam-3506	261	80	≤	≤	NUM
ejpam-3506	261	81	1	1	NUM
ejpam-3506	261	82	,	,	PUNCT
ejpam-3506	261	83	a	a	DET
ejpam-3506	261	84	contradiction	contradiction	NOUN
ejpam-3506	261	85	.	.	PUNCT
ejpam-3506	262	1	thus	thus	ADV
ejpam-3506	262	2	,	,	PUNCT
ejpam-3506	262	3	xa−1	xa−1	PROPN
ejpam-3506	262	4	∈	∈	PROPN
ejpam-3506	262	5	a.	a.	NOUN
ejpam-3506	262	6	suppose	suppose	VERB
ejpam-3506	262	7	that	that	SCONJ
ejpam-3506	262	8	xa	xa	PROPN
ejpam-3506	262	9	/∈	/∈	PUNCT
ejpam-3506	262	10	a.	a.	NOUN
ejpam-3506	262	11	then	then	ADV
ejpam-3506	262	12	∣∣v	∣∣v	NOUN
ejpam-3506	262	13	(	(	PUNCT
ejpam-3506	262	14	h3	h3	NOUN
ejpam-3506	262	15	)	)	PUNCT
ejpam-3506	262	16	∩	∩	NOUN
ejpam-3506	262	17	a	a	DET
ejpam-3506	262	18	∣∣	∣∣	NUM
ejpam-3506	262	19	=	=	SYM
ejpam-3506	262	20	1	1	NUM
ejpam-3506	262	21	and∣∣v	and∣∣v	PROPN
ejpam-3506	262	22	(	(	PUNCT
ejpam-3506	262	23	h4	h4	PROPN
ejpam-3506	262	24	)	)	PUNCT
ejpam-3506	262	25	∩	∩	NOUN
ejpam-3506	262	26	a	a	PRON
ejpam-3506	262	27	∣∣	∣∣	NUM
ejpam-3506	262	28	=	=	SYM
ejpam-3506	262	29	1	1	X
ejpam-3506	262	30	.	.	PUNCT
ejpam-3506	263	1	it	it	PRON
ejpam-3506	263	2	follows	follow	VERB
ejpam-3506	263	3	that	that	SCONJ
ejpam-3506	263	4	v	v	X
ejpam-3506	263	5	(	(	PUNCT
ejpam-3506	263	6	h1	h1	PROPN
ejpam-3506	263	7	)	)	PUNCT
ejpam-3506	263	8	∩	∩	NOUN
ejpam-3506	263	9	a	a	DET
ejpam-3506	263	10	=	=	SYM
ejpam-3506	263	11	∅	∅	NOUN
ejpam-3506	263	12	and	and	CCONJ
ejpam-3506	263	13	ya−1	ya−1	NOUN
ejpam-3506	263	14	/∈	/∈	PUNCT
ejpam-3506	264	1	a.	a.	NOUN
ejpam-3506	264	2	this	this	PRON
ejpam-3506	264	3	,	,	PUNCT
ejpam-3506	264	4	however	however	ADV
ejpam-3506	264	5	,	,	PUNCT
ejpam-3506	264	6	implies	imply	VERB
ejpam-3506	264	7	that	that	SCONJ
ejpam-3506	264	8	ng(ya−1	ng(ya−1	PROPN
ejpam-3506	264	9	)	)	PUNCT
ejpam-3506	264	10	∩	∩	NOUN
ejpam-3506	264	11	a	a	PRON
ejpam-3506	264	12	=	=	X
ejpam-3506	264	13	{	{	PUNCT
ejpam-3506	264	14	xa−1	xa−1	PROPN
ejpam-3506	264	15	}	}	PUNCT
ejpam-3506	264	16	,	,	PUNCT
ejpam-3506	264	17	a	a	DET
ejpam-3506	264	18	contradiction	contradiction	NOUN
ejpam-3506	264	19	.	.	PUNCT
ejpam-3506	265	1	therefore	therefore	ADV
ejpam-3506	265	2	,	,	PUNCT
ejpam-3506	265	3	a1	a1	VERB
ejpam-3506	265	4	⊆	⊆	NUM
ejpam-3506	265	5	a.	a.	NOUN
ejpam-3506	265	6	since	since	SCONJ
ejpam-3506	265	7	〈	〈	PROPN
ejpam-3506	265	8	ng(a1	ng(a1	PART
ejpam-3506	265	9	)	)	PUNCT
ejpam-3506	265	10	〉	〉	NOUN
ejpam-3506	265	11	is	be	AUX
ejpam-3506	265	12	not	not	PART
ejpam-3506	265	13	connected	connect	VERB
ejpam-3506	265	14	,	,	PUNCT
ejpam-3506	265	15	|a1|	|a1|	X
ejpam-3506	265	16	=	=	PUNCT
ejpam-3506	265	17	a	a	DET
ejpam-3506	265	18	<	<	X
ejpam-3506	265	19	|a|	|a|	NOUN
ejpam-3506	265	20	,	,	PUNCT
ejpam-3506	265	21	that	that	ADV
ejpam-3506	265	22	is	is	ADV
ejpam-3506	265	23	,	,	PUNCT
ejpam-3506	265	24	a1	a1	PROPN
ejpam-3506	265	25	6=	6=	ADP
ejpam-3506	265	26	a.	a.	NOUN
ejpam-3506	265	27	let	let	VERB
ejpam-3506	265	28	v	v	ADP
ejpam-3506	265	29	∈	∈	PROPN
ejpam-3506	265	30	a\a1	a\a1	NOUN
ejpam-3506	265	31	.	.	PUNCT
ejpam-3506	266	1	if	if	SCONJ
ejpam-3506	266	2	v	v	NOUN
ejpam-3506	266	3	=	=	SYM
ejpam-3506	266	4	ya−1	ya−1	NOUN
ejpam-3506	266	5	or	or	CCONJ
ejpam-3506	266	6	v	v	ADP
ejpam-3506	266	7	∈	∈	PROPN
ejpam-3506	266	8	v	v	NOUN
ejpam-3506	266	9	(	(	PUNCT
ejpam-3506	266	10	h1	h1	PROPN
ejpam-3506	266	11	)	)	PUNCT
ejpam-3506	266	12	,	,	PUNCT
ejpam-3506	266	13	then	then	ADV
ejpam-3506	266	14	{	{	PUNCT
ejpam-3506	266	15	ya−1	ya−1	NOUN
ejpam-3506	266	16	}	}	PUNCT
ejpam-3506	266	17	∪	∪	NOUN
ejpam-3506	266	18	v	v	NOUN
ejpam-3506	266	19	(	(	PUNCT
ejpam-3506	266	20	h1	h1	PROPN
ejpam-3506	266	21	)	)	PUNCT
ejpam-3506	266	22	⊆	⊆	NUM
ejpam-3506	266	23	a.	a.	NOUN
ejpam-3506	266	24	if	if	SCONJ
ejpam-3506	266	25	v	v	NUM
ejpam-3506	266	26	=	=	SYM
ejpam-3506	266	27	za−1	za−1	PROPN
ejpam-3506	266	28	or	or	CCONJ
ejpam-3506	266	29	v	v	ADP
ejpam-3506	266	30	∈	∈	PROPN
ejpam-3506	266	31	v	v	NOUN
ejpam-3506	266	32	(	(	PUNCT
ejpam-3506	266	33	h2	h2	NOUN
ejpam-3506	266	34	)	)	PUNCT
ejpam-3506	266	35	,	,	PUNCT
ejpam-3506	266	36	then	then	ADV
ejpam-3506	266	37	{	{	PUNCT
ejpam-3506	266	38	za−1	za−1	NOUN
ejpam-3506	266	39	}	}	PUNCT
ejpam-3506	266	40	∪	∪	NOUN
ejpam-3506	266	41	v	v	NOUN
ejpam-3506	266	42	(	(	PUNCT
ejpam-3506	266	43	h2	h2	NOUN
ejpam-3506	266	44	)	)	PUNCT
ejpam-3506	267	1	⊆	⊆	NUM
ejpam-3506	267	2	a.	a.	NOUN
ejpam-3506	267	3	let	let	VERB
ejpam-3506	267	4	b	b	NOUN
ejpam-3506	267	5	=	=	NOUN
ejpam-3506	267	6	a1	a1	NOUN
ejpam-3506	267	7	∪	∪	X
ejpam-3506	267	8	{	{	PUNCT
ejpam-3506	267	9	ya−1	ya−1	NOUN
ejpam-3506	267	10	}	}	PUNCT
ejpam-3506	267	11	∪	∪	NOUN
ejpam-3506	267	12	v	v	NOUN
ejpam-3506	267	13	(	(	PUNCT
ejpam-3506	267	14	h1	h1	PROPN
ejpam-3506	267	15	)	)	PUNCT
ejpam-3506	267	16	or	or	CCONJ
ejpam-3506	267	17	b	b	X
ejpam-3506	267	18	=	=	NOUN
ejpam-3506	267	19	a1	a1	NOUN
ejpam-3506	267	20	∪	∪	X
ejpam-3506	267	21	{	{	PUNCT
ejpam-3506	267	22	za−1	za−1	NOUN
ejpam-3506	267	23	}	}	PUNCT
ejpam-3506	267	24	∪	∪	NOUN
ejpam-3506	267	25	v	v	NOUN
ejpam-3506	267	26	(	(	PUNCT
ejpam-3506	267	27	h2	h2	NOUN
ejpam-3506	267	28	)	)	PUNCT
ejpam-3506	267	29	.	.	PUNCT
ejpam-3506	268	1	then	then	ADV
ejpam-3506	268	2	b	b	PROPN
ejpam-3506	268	3	is	be	AUX
ejpam-3506	268	4	an	an	DET
ejpam-3506	268	5	nc2fd	nc2fd	NOUN
ejpam-3506	268	6	-	-	PUNCT
ejpam-3506	268	7	set	set	NOUN
ejpam-3506	268	8	of	of	ADP
ejpam-3506	268	9	g.	g.	PROPN
ejpam-3506	268	10	hence	hence	ADV
ejpam-3506	268	11	,	,	PUNCT
ejpam-3506	268	12	|a|	|a|	PROPN
ejpam-3506	268	13	≤	≤	ADV
ejpam-3506	268	14	|b|	|b|	X
ejpam-3506	268	15	=	=	PUNCT
ejpam-3506	268	16	b	b	PROPN
ejpam-3506	269	1	+	+	CCONJ
ejpam-3506	269	2	1	1	NUM
ejpam-3506	269	3	.	.	PUNCT
ejpam-3506	270	1	now	now	ADV
ejpam-3506	270	2	,	,	PUNCT
ejpam-3506	270	3	if	if	SCONJ
ejpam-3506	270	4	v	v	NUM
ejpam-3506	270	5	∈	∈	PROPN
ejpam-3506	270	6	v	v	NOUN
ejpam-3506	270	7	(	(	PUNCT
ejpam-3506	270	8	h3	h3	NOUN
ejpam-3506	270	9	)	)	PUNCT
ejpam-3506	270	10	,	,	PUNCT
ejpam-3506	270	11	then	then	ADV
ejpam-3506	270	12	v	v	X
ejpam-3506	270	13	(	(	PUNCT
ejpam-3506	270	14	h3	h3	NOUN
ejpam-3506	270	15	)	)	PUNCT
ejpam-3506	270	16	⊆	⊆	NUM
ejpam-3506	270	17	a.	a.	NOUN
ejpam-3506	270	18	similarly	similarly	ADV
ejpam-3506	270	19	,	,	PUNCT
ejpam-3506	270	20	if	if	SCONJ
ejpam-3506	270	21	v	v	NUM
ejpam-3506	270	22	∈	∈	PROPN
ejpam-3506	270	23	v	v	NOUN
ejpam-3506	270	24	(	(	PUNCT
ejpam-3506	270	25	h4	h4	PROPN
ejpam-3506	270	26	)	)	PUNCT
ejpam-3506	270	27	,	,	PUNCT
ejpam-3506	270	28	then	then	ADV
ejpam-3506	270	29	v	v	X
ejpam-3506	270	30	(	(	PUNCT
ejpam-3506	270	31	h4	h4	PROPN
ejpam-3506	270	32	)	)	PUNCT
ejpam-3506	270	33	⊆	⊆	NUM
ejpam-3506	270	34	a.	a.	NOUN
ejpam-3506	270	35	let	let	VERB
ejpam-3506	270	36	a∗	a∗	NOUN
ejpam-3506	270	37	=	=	SYM
ejpam-3506	270	38	a1	a1	NOUN
ejpam-3506	270	39	∪	∪	ADJ
ejpam-3506	270	40	v	v	NOUN
ejpam-3506	270	41	(	(	PUNCT
ejpam-3506	270	42	h3	h3	NOUN
ejpam-3506	270	43	)	)	PUNCT
ejpam-3506	270	44	or	or	CCONJ
ejpam-3506	270	45	a∗	a∗	NOUN
ejpam-3506	270	46	=	=	SYM
ejpam-3506	270	47	a1	a1	NOUN
ejpam-3506	270	48	∪	∪	ADJ
ejpam-3506	270	49	v	v	NOUN
ejpam-3506	270	50	(	(	PUNCT
ejpam-3506	270	51	h4	h4	PROPN
ejpam-3506	270	52	)	)	PUNCT
ejpam-3506	270	53	.	.	PUNCT
ejpam-3506	271	1	then	then	ADV
ejpam-3506	271	2	a∗	a∗	PROPN
ejpam-3506	271	3	is	be	AUX
ejpam-3506	271	4	an	an	DET
ejpam-3506	271	5	nc2fd	nc2fd	NOUN
ejpam-3506	271	6	-	-	PUNCT
ejpam-3506	271	7	set	set	NOUN
ejpam-3506	271	8	of	of	ADP
ejpam-3506	271	9	g	g	NOUN
ejpam-3506	271	10	and	and	CCONJ
ejpam-3506	271	11	|a∗|	|a∗|	PUNCT
ejpam-3506	271	12	=	=	SYM
ejpam-3506	271	13	b	b	PROPN
ejpam-3506	271	14	<	<	X
ejpam-3506	271	15	|b|	|b|	PROPN
ejpam-3506	271	16	.	.	PROPN
ejpam-3506	271	17	since	since	SCONJ
ejpam-3506	271	18	such	such	ADJ
ejpam-3506	271	19	v	v	NOUN
ejpam-3506	271	20	exists	exist	VERB
ejpam-3506	271	21	,	,	PUNCT
ejpam-3506	271	22	a	a	DET
ejpam-3506	271	23	=	=	X
ejpam-3506	271	24	a1∪v	a1∪v	PRON
ejpam-3506	271	25	(	(	PUNCT
ejpam-3506	271	26	h3	h3	NOUN
ejpam-3506	271	27	)	)	PUNCT
ejpam-3506	271	28	or	or	CCONJ
ejpam-3506	271	29	a	a	PRON
ejpam-3506	271	30	=	=	X
ejpam-3506	271	31	a1∪v	a1∪v	PRON
ejpam-3506	271	32	(	(	PUNCT
ejpam-3506	271	33	h4	h4	PROPN
ejpam-3506	271	34	)	)	PUNCT
ejpam-3506	271	35	.	.	PUNCT
ejpam-3506	272	1	therefore	therefore	ADV
ejpam-3506	272	2	,	,	PUNCT
ejpam-3506	272	3	γ2fd(g	γ2fd(g	PROPN
ejpam-3506	272	4	)	)	PUNCT
ejpam-3506	272	5	=	=	SYM
ejpam-3506	272	6	|a1|	|a1|	NOUN
ejpam-3506	272	7	=	=	SYM
ejpam-3506	272	8	a	a	PRON
ejpam-3506	272	9	and	and	CCONJ
ejpam-3506	272	10	γnc2fd(g	γnc2fd(g	NUM
ejpam-3506	272	11	)	)	PUNCT
ejpam-3506	273	1	=	=	SYM
ejpam-3506	273	2	|a|	|a|	PROPN
ejpam-3506	273	3	=	=	PROPN
ejpam-3506	273	4	b.	b.	PROPN
ejpam-3506	273	5	�	�	PROPN
ejpam-3506	273	6	w.	w.	PROPN
ejpam-3506	273	7	bent	bent	PROPN
ejpam-3506	273	8	-	-	PUNCT
ejpam-3506	273	9	usman	usman	PROPN
ejpam-3506	273	10	,	,	PUNCT
ejpam-3506	273	11	r.	r.	PROPN
ejpam-3506	273	12	isla	isla	PROPN
ejpam-3506	273	13	,	,	PUNCT
ejpam-3506	273	14	s.	s.	PROPN
ejpam-3506	273	15	canoy	canoy	PROPN
ejpam-3506	273	16	/	/	SYM
ejpam-3506	273	17	eur	eur	PROPN
ejpam-3506	273	18	.	.	PUNCT
ejpam-3506	274	1	j.	j.	PROPN
ejpam-3506	274	2	pure	pure	PROPN
ejpam-3506	274	3	appl	appl	PROPN
ejpam-3506	274	4	.	.	PROPN
ejpam-3506	274	5	math	math	PROPN
ejpam-3506	274	6	,	,	PUNCT
ejpam-3506	274	7	12	12	NUM
ejpam-3506	274	8	(	(	PUNCT
ejpam-3506	274	9	3	3	NUM
ejpam-3506	274	10	)	)	PUNCT
ejpam-3506	274	11	(	(	PUNCT
ejpam-3506	274	12	2019	2019	NUM
ejpam-3506	274	13	)	)	PUNCT
ejpam-3506	274	14	,	,	PUNCT
ejpam-3506	274	15	1337	1337	NUM
ejpam-3506	274	16	-	-	SYM
ejpam-3506	274	17	1349	1349	NUM
ejpam-3506	274	18	1343	1343	NUM
ejpam-3506	274	19	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	274	20	................................................................................................................	................................................................................................................	PUNCT
ejpam-3506	274	21	....................................	....................................	PUNCT
ejpam-3506	274	22	.......................................................................................	.......................................................................................	PUNCT
ejpam-3506	274	23	.........	.........	PUNCT
ejpam-3506	274	24	........	........	PUNCT
ejpam-3506	274	25	........	........	PUNCT
ejpam-3506	274	26	........	........	PUNCT
ejpam-3506	274	27	........	........	PUNCT
ejpam-3506	274	28	........	........	PUNCT
ejpam-3506	274	29	........	........	PUNCT
ejpam-3506	274	30	........	........	PUNCT
ejpam-3506	274	31	........	........	PUNCT
ejpam-3506	274	32	........	........	PUNCT
ejpam-3506	274	33	........	........	PUNCT
ejpam-3506	274	34	........	........	PUNCT
ejpam-3506	274	35	........	........	PUNCT
ejpam-3506	274	36	........	........	PUNCT
ejpam-3506	274	37	........	........	PUNCT
ejpam-3506	274	38	........	........	PUNCT
ejpam-3506	274	39	........	........	PUNCT
ejpam-3506	274	40	........	........	PUNCT
ejpam-3506	274	41	........	........	PUNCT
ejpam-3506	274	42	........	........	PUNCT
ejpam-3506	274	43	.	.	PUNCT
ejpam-3506	275	1	..	..	PUNCT
ejpam-3506	275	2	..................................	..................................	PUNCT
ejpam-3506	276	1	....................................	....................................	PUNCT
ejpam-3506	276	2	.........	.........	PUNCT
ejpam-3506	276	3	........	........	PUNCT
ejpam-3506	276	4	........	........	PUNCT
ejpam-3506	276	5	........	........	PUNCT
ejpam-3506	276	6	........	........	PUNCT
ejpam-3506	276	7	........	........	PUNCT
ejpam-3506	276	8	........	........	PUNCT
ejpam-3506	276	9	........	........	PUNCT
ejpam-3506	276	10	........	........	PUNCT
ejpam-3506	276	11	........	........	PUNCT
ejpam-3506	276	12	........	........	PUNCT
ejpam-3506	276	13	........	........	PUNCT
ejpam-3506	276	14	........	........	PUNCT
ejpam-3506	276	15	........	........	PUNCT
ejpam-3506	276	16	........	........	PUNCT
ejpam-3506	276	17	........	........	PUNCT
ejpam-3506	276	18	........	........	PUNCT
ejpam-3506	276	19	........	........	PUNCT
ejpam-3506	276	20	........	........	PUNCT
ejpam-3506	276	21	........	........	PUNCT
ejpam-3506	276	22	.	.	PUNCT
ejpam-3506	277	1	..	..	PUNCT
ejpam-3506	277	2	..................................	..................................	PUNCT
ejpam-3506	278	1	....................................	....................................	PUNCT
ejpam-3506	278	2	.........	.........	PUNCT
ejpam-3506	278	3	........	........	PUNCT
ejpam-3506	278	4	........	........	PUNCT
ejpam-3506	278	5	........	........	PUNCT
ejpam-3506	278	6	........	........	PUNCT
ejpam-3506	278	7	........	........	PUNCT
ejpam-3506	278	8	........	........	PUNCT
ejpam-3506	278	9	........	........	PUNCT
ejpam-3506	278	10	........	........	PUNCT
ejpam-3506	278	11	........	........	PUNCT
ejpam-3506	278	12	........	........	PUNCT
ejpam-3506	278	13	........	........	PUNCT
ejpam-3506	278	14	........	........	PUNCT
ejpam-3506	278	15	........	........	PUNCT
ejpam-3506	278	16	........	........	PUNCT
ejpam-3506	278	17	........	........	PUNCT
ejpam-3506	278	18	........	........	PUNCT
ejpam-3506	278	19	........	........	PUNCT
ejpam-3506	278	20	........	........	PUNCT
ejpam-3506	278	21	........	........	PUNCT
ejpam-3506	278	22	.	.	PUNCT
ejpam-3506	279	1	..	..	PUNCT
ejpam-3506	279	2	..................................	..................................	PUNCT
ejpam-3506	280	1	....................................	....................................	PUNCT
ejpam-3506	280	2	.........	.........	PUNCT
ejpam-3506	280	3	........	........	PUNCT
ejpam-3506	280	4	........	........	PUNCT
ejpam-3506	280	5	........	........	PUNCT
ejpam-3506	280	6	........	........	PUNCT
ejpam-3506	280	7	........	........	PUNCT
ejpam-3506	280	8	........	........	PUNCT
ejpam-3506	280	9	........	........	PUNCT
ejpam-3506	280	10	........	........	PUNCT
ejpam-3506	280	11	........	........	PUNCT
ejpam-3506	280	12	........	........	PUNCT
ejpam-3506	280	13	........	........	PUNCT
ejpam-3506	280	14	........	........	PUNCT
ejpam-3506	280	15	........	........	PUNCT
ejpam-3506	280	16	........	........	PUNCT
ejpam-3506	280	17	........	........	PUNCT
ejpam-3506	280	18	........	........	PUNCT
ejpam-3506	280	19	........	........	PUNCT
ejpam-3506	280	20	........	........	PUNCT
ejpam-3506	280	21	........	........	PUNCT
ejpam-3506	280	22	.	.	PUNCT
ejpam-3506	281	1	..	..	PUNCT
ejpam-3506	281	2	..................................	..................................	PUNCT
ejpam-3506	282	1	....................................	....................................	PUNCT
ejpam-3506	282	2	.........	.........	PUNCT
ejpam-3506	282	3	........	........	PUNCT
ejpam-3506	282	4	........	........	PUNCT
ejpam-3506	282	5	........	........	PUNCT
ejpam-3506	282	6	........	........	PUNCT
ejpam-3506	282	7	........	........	PUNCT
ejpam-3506	282	8	........	........	PUNCT
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ejpam-3506	282	10	........	........	PUNCT
ejpam-3506	282	11	...	...	PUNCT
ejpam-3506	282	12	.........	.........	PUNCT
ejpam-3506	282	13	........	........	PUNCT
ejpam-3506	282	14	........	........	PUNCT
ejpam-3506	282	15	........	........	PUNCT
ejpam-3506	282	16	........	........	PUNCT
ejpam-3506	282	17	........	........	PUNCT
ejpam-3506	282	18	........	........	PUNCT
ejpam-3506	282	19	........	........	PUNCT
ejpam-3506	282	20	........	........	PUNCT
ejpam-3506	282	21	...	...	PUNCT
ejpam-3506	282	22	.........	.........	PUNCT
ejpam-3506	282	23	........	........	PUNCT
ejpam-3506	282	24	........	........	PUNCT
ejpam-3506	282	25	........	........	PUNCT
ejpam-3506	282	26	........	........	PUNCT
ejpam-3506	282	27	........	........	PUNCT
ejpam-3506	282	28	........	........	PUNCT
ejpam-3506	282	29	........	........	PUNCT
ejpam-3506	282	30	........	........	PUNCT
ejpam-3506	282	31	...	...	PUNCT
ejpam-3506	283	1	....................................	....................................	PUNCT
ejpam-3506	283	2	.........	.........	PUNCT
ejpam-3506	283	3	........	........	PUNCT
ejpam-3506	283	4	........	........	PUNCT
ejpam-3506	283	5	........	........	PUNCT
ejpam-3506	283	6	........	........	PUNCT
ejpam-3506	283	7	........	........	PUNCT
ejpam-3506	283	8	........	........	PUNCT
ejpam-3506	283	9	........	........	PUNCT
ejpam-3506	283	10	........	........	PUNCT
ejpam-3506	283	11	...	...	PUNCT
ejpam-3506	284	1	....................................	....................................	PUNCT
ejpam-3506	284	2	....................................	....................................	PUNCT
ejpam-3506	284	3	.........	.........	PUNCT
ejpam-3506	284	4	........	........	PUNCT
ejpam-3506	284	5	........	........	PUNCT
ejpam-3506	284	6	........	........	PUNCT
ejpam-3506	284	7	........	........	PUNCT
ejpam-3506	284	8	........	........	PUNCT
ejpam-3506	284	9	........	........	PUNCT
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ejpam-3506	284	12	...	...	PUNCT
ejpam-3506	285	1	....................................	....................................	PUNCT
ejpam-3506	285	2	.........	.........	PUNCT
ejpam-3506	285	3	........	........	PUNCT
ejpam-3506	285	4	........	........	PUNCT
ejpam-3506	285	5	........	........	PUNCT
ejpam-3506	285	6	........	........	PUNCT
ejpam-3506	285	7	........	........	PUNCT
ejpam-3506	285	8	........	........	PUNCT
ejpam-3506	285	9	........	........	PUNCT
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ejpam-3506	285	11	...	...	PUNCT
ejpam-3506	286	1	....................................	....................................	PUNCT
ejpam-3506	286	2	....................................	....................................	PUNCT
ejpam-3506	287	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3506	287	2	....................................	....................................	PUNCT
ejpam-3506	288	1	....................................	....................................	PUNCT
ejpam-3506	288	2	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3506	289	1	....................................	....................................	PUNCT
ejpam-3506	289	2	....................................	....................................	PUNCT
ejpam-3506	290	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-3506	290	2	....................................	....................................	PUNCT
ejpam-3506	291	1	....................................	....................................	PUNCT
ejpam-3506	291	2	............	............	PUNCT
ejpam-3506	291	3	...........	...........	PUNCT
ejpam-3506	291	4	...........	...........	PUNCT
ejpam-3506	291	5	...........	...........	PUNCT
ejpam-3506	291	6	...........	...........	PUNCT
ejpam-3506	291	7	...........	...........	PUNCT
ejpam-3506	291	8	...........	...........	PUNCT
ejpam-3506	291	9	...........	...........	PUNCT
ejpam-3506	291	10	...........	...........	PUNCT
ejpam-3506	291	11	...........	...........	PUNCT
ejpam-3506	291	12	....................................	....................................	PUNCT
ejpam-3506	292	1	....................................	....................................	PUNCT
ejpam-3506	292	2	......................................................................................................................................................................................	......................................................................................................................................................................................	PUNCT
ejpam-3506	292	3	....................................	....................................	PUNCT
ejpam-3506	293	1	....................................	....................................	PUNCT
ejpam-3506	293	2	...................	...................	PUNCT
ejpam-3506	294	1	..................	..................	PUNCT
ejpam-3506	294	2	..................	..................	PUNCT
ejpam-3506	295	1	..................	..................	PUNCT
ejpam-3506	295	2	..................	..................	PUNCT
ejpam-3506	296	1	..................	..................	PUNCT
ejpam-3506	296	2	..................	..................	PUNCT
ejpam-3506	297	1	..................	..................	PUNCT
ejpam-3506	297	2	..................	..................	PUNCT
ejpam-3506	297	3	..................	..................	PUNCT
ejpam-3506	297	4	.	.	PUNCT
ejpam-3506	298	1	....................................	....................................	PUNCT
ejpam-3506	298	2	....................................	....................................	PUNCT
ejpam-3506	299	1	......................................................................................................................................................................................	......................................................................................................................................................................................	PUNCT
ejpam-3506	299	2	....................................	....................................	PUNCT
ejpam-3506	300	1	....................................	....................................	PUNCT
ejpam-3506	300	2	...................	...................	PUNCT
ejpam-3506	301	1	..................	..................	PUNCT
ejpam-3506	301	2	..................	..................	PUNCT
ejpam-3506	302	1	..................	..................	PUNCT
ejpam-3506	302	2	..................	..................	PUNCT
ejpam-3506	303	1	..................	..................	PUNCT
ejpam-3506	303	2	..................	..................	PUNCT
ejpam-3506	304	1	..................	..................	PUNCT
ejpam-3506	304	2	..................	..................	PUNCT
ejpam-3506	304	3	..................	..................	PUNCT
ejpam-3506	304	4	.	.	PUNCT
ejpam-3506	305	1	....................................	....................................	PUNCT
ejpam-3506	305	2	....................................	....................................	PUNCT
ejpam-3506	305	3	............	............	PUNCT
ejpam-3506	305	4	...........	...........	PUNCT
ejpam-3506	305	5	...........	...........	PUNCT
ejpam-3506	305	6	...........	...........	PUNCT
ejpam-3506	305	7	...........	...........	PUNCT
ejpam-3506	305	8	...........	...........	PUNCT
ejpam-3506	305	9	...........	...........	PUNCT
ejpam-3506	305	10	...........	...........	PUNCT
ejpam-3506	305	11	...........	...........	PUNCT
ejpam-3506	305	12	...........	...........	PUNCT
ejpam-3506	305	13	....................................	....................................	PUNCT
ejpam-3506	306	1	....................................	....................................	PUNCT
ejpam-3506	306	2	............	............	PUNCT
ejpam-3506	306	3	...........	...........	PUNCT
ejpam-3506	306	4	...........	...........	PUNCT
ejpam-3506	306	5	...........	...........	PUNCT
ejpam-3506	306	6	...........	...........	PUNCT
ejpam-3506	306	7	...........	...........	PUNCT
ejpam-3506	306	8	...........	...........	PUNCT
ejpam-3506	306	9	...........	...........	PUNCT
ejpam-3506	306	10	...........	...........	PUNCT
ejpam-3506	306	11	...........	...........	PUNCT
ejpam-3506	306	12	....................................	....................................	PUNCT
ejpam-3506	306	13	....................................	....................................	PUNCT
ejpam-3506	306	14	............	............	PUNCT
ejpam-3506	306	15	...........	...........	PUNCT
ejpam-3506	306	16	...........	...........	PUNCT
ejpam-3506	306	17	...........	...........	PUNCT
ejpam-3506	306	18	...........	...........	PUNCT
ejpam-3506	306	19	...........	...........	PUNCT
ejpam-3506	306	20	...........	...........	PUNCT
ejpam-3506	306	21	...........	...........	PUNCT
ejpam-3506	306	22	...........	...........	PUNCT
ejpam-3506	306	23	...........	...........	PUNCT
ejpam-3506	306	24	...........	...........	PUNCT
ejpam-3506	306	25	...........	...........	PUNCT
ejpam-3506	306	26	...........	...........	PUNCT
ejpam-3506	306	27	...........	...........	PUNCT
ejpam-3506	306	28	...........	...........	PUNCT
ejpam-3506	306	29	...........	...........	PUNCT
ejpam-3506	306	30	...........	...........	PUNCT
ejpam-3506	306	31	...........	...........	PUNCT
ejpam-3506	306	32	...........	...........	PUNCT
ejpam-3506	306	33	...........	...........	PUNCT
ejpam-3506	306	34	...........	...........	PUNCT
ejpam-3506	306	35	...........	...........	PUNCT
ejpam-3506	306	36	.	.	PUNCT
ejpam-3506	307	1	..........................	..........................	PUNCT
ejpam-3506	307	2	.........................	.........................	PUNCT
ejpam-3506	308	1	.........................	.........................	PUNCT
ejpam-3506	308	2	.........................	.........................	PUNCT
ejpam-3506	308	3	.........................	.........................	PUNCT
ejpam-3506	308	4	.........................	.........................	PUNCT
ejpam-3506	308	5	.........................	.........................	PUNCT
ejpam-3506	308	6	.......	.......	PUNCT
ejpam-3506	309	1	.................	.................	PUNCT
ejpam-3506	309	2	................	................	PUNCT
ejpam-3506	310	1	................	................	PUNCT
ejpam-3506	310	2	...........	...........	PUNCT
ejpam-3506	310	3	...................	...................	PUNCT
ejpam-3506	310	4	..................	..................	PUNCT
ejpam-3506	310	5	..................	..................	PUNCT
ejpam-3506	311	1	....	....	PUNCT
ejpam-3506	311	2	.................	.................	PUNCT
ejpam-3506	312	1	................	................	PUNCT
ejpam-3506	312	2	................	................	PUNCT
ejpam-3506	312	3	..	..	PUNCT
ejpam-3506	312	4	........................................................................................................................	........................................................................................................................	PUNCT
ejpam-3506	313	1	........................................................................................................................	........................................................................................................................	PUNCT
ejpam-3506	313	2	..................	..................	PUNCT
ejpam-3506	314	1	..................	..................	PUNCT
ejpam-3506	314	2	..................	..................	PUNCT
ejpam-3506	315	1	..................	..................	PUNCT
ejpam-3506	315	2	..................	..................	PUNCT
ejpam-3506	316	1	..................	..................	PUNCT
ejpam-3506	316	2	..................	..................	PUNCT
ejpam-3506	317	1	..................	..................	PUNCT
ejpam-3506	317	2	..................	..................	PUNCT
ejpam-3506	318	1	..................	..................	PUNCT
ejpam-3506	318	2	..................	..................	PUNCT
ejpam-3506	319	1	..................	..................	PUNCT
ejpam-3506	319	2	..................	..................	PUNCT
ejpam-3506	320	1	..................	..................	PUNCT
ejpam-3506	320	2	..................	..................	PUNCT
ejpam-3506	321	1	..................	..................	PUNCT
ejpam-3506	321	2	..................	..................	PUNCT
ejpam-3506	322	1	..................	..................	PUNCT
ejpam-3506	322	2	..................	..................	PUNCT
ejpam-3506	323	1	..................	..................	PUNCT
ejpam-3506	323	2	.............	.............	PUNCT
ejpam-3506	324	1	................................................	................................................	PUNCT
ejpam-3506	324	2	................................................	................................................	PUNCT
ejpam-3506	324	3	................................................	................................................	PUNCT
ejpam-3506	324	4	................................................	................................................	PUNCT
ejpam-3506	324	5	................................................	................................................	PUNCT
ejpam-3506	324	6	................................................	................................................	PUNCT
ejpam-3506	324	7	................................................	................................................	PUNCT
ejpam-3506	324	8	..	..	PUNCT
ejpam-3506	324	9	..........	..........	PUNCT
ejpam-3506	325	1	.........	.........	PUNCT
ejpam-3506	325	2	.........	.........	PUNCT
ejpam-3506	326	1	.........	.........	PUNCT
ejpam-3506	326	2	.........	.........	PUNCT
ejpam-3506	327	1	.........	.........	PUNCT
ejpam-3506	327	2	.........	.........	PUNCT
ejpam-3506	328	1	.........	.........	PUNCT
ejpam-3506	328	2	.........	.........	PUNCT
ejpam-3506	329	1	.........	.........	PUNCT
ejpam-3506	329	2	.........	.........	PUNCT
ejpam-3506	330	1	.........	.........	PUNCT
ejpam-3506	330	2	.........	.........	PUNCT
ejpam-3506	331	1	.........	.........	PUNCT
ejpam-3506	331	2	.........	.........	PUNCT
ejpam-3506	332	1	.........	.........	PUNCT
ejpam-3506	332	2	.........	.........	PUNCT
ejpam-3506	333	1	.........	.........	PUNCT
ejpam-3506	333	2	.........	.........	PUNCT
ejpam-3506	334	1	.........	.........	PUNCT
ejpam-3506	334	2	.........	.........	PUNCT
ejpam-3506	335	1	...................................................................................................................................................................................	...................................................................................................................................................................................	PUNCT
ejpam-3506	335	2	...........	...........	PUNCT
ejpam-3506	336	1	..........	..........	PUNCT
ejpam-3506	336	2	..........	..........	PUNCT
ejpam-3506	337	1	..........	..........	PUNCT
ejpam-3506	337	2	..........	..........	PUNCT
ejpam-3506	338	1	..	..	PUNCT
ejpam-3506	338	2	..........	..........	PUNCT
ejpam-3506	339	1	.........	.........	PUNCT
ejpam-3506	339	2	.........	.........	PUNCT
ejpam-3506	340	1	.........	.........	PUNCT
ejpam-3506	340	2	.........	.........	PUNCT
ejpam-3506	341	1	.........	.........	PUNCT
ejpam-3506	341	2	.....	.....	PUNCT
ejpam-3506	342	1	..........	..........	PUNCT
ejpam-3506	342	2	.........	.........	PUNCT
ejpam-3506	343	1	.........	.........	PUNCT
ejpam-3506	343	2	.........	.........	PUNCT
ejpam-3506	344	1	.........	.........	PUNCT
ejpam-3506	344	2	.........	.........	PUNCT
ejpam-3506	344	3	............	............	PUNCT
ejpam-3506	344	4	...............	...............	PUNCT
ejpam-3506	344	5	........................	........................	PUNCT
ejpam-3506	344	6	.....................................................................	.....................................................................	PUNCT
ejpam-3506	344	7	...........................................................................................	...........................................................................................	PUNCT
ejpam-3506	344	8	...............	...............	PUNCT
ejpam-3506	344	9	.............	.............	PUNCT
ejpam-3506	344	10	.	.	PUNCT
ejpam-3506	345	1	...................	...................	PUNCT
ejpam-3506	345	2	..................	..................	PUNCT
ejpam-3506	346	1	.................	.................	PUNCT
ejpam-3506	346	2	.................	.................	PUNCT
ejpam-3506	347	1	................	................	PUNCT
ejpam-3506	347	2	................	................	PUNCT
ejpam-3506	347	3	...............	...............	PUNCT
ejpam-3506	347	4	...............	...............	PUNCT
ejpam-3506	347	5	...............	...............	PUNCT
ejpam-3506	347	6	..............	..............	PUNCT
ejpam-3506	348	1	..............	..............	PUNCT
ejpam-3506	348	2	..............	..............	PUNCT
ejpam-3506	348	3	.............	.............	PUNCT
ejpam-3506	348	4	.............	.............	PUNCT
ejpam-3506	348	5	.............	.............	PUNCT
ejpam-3506	348	6	.............	.............	PUNCT
ejpam-3506	348	7	.............	.............	PUNCT
ejpam-3506	348	8	.............	.............	PUNCT
ejpam-3506	348	9	............	............	PUNCT
ejpam-3506	348	10	............	............	PUNCT
ejpam-3506	348	11	.........	.........	PUNCT
ejpam-3506	348	12	...........	...........	PUNCT
ejpam-3506	348	13	...........	...........	PUNCT
ejpam-3506	348	14	...........	...........	PUNCT
ejpam-3506	348	15	...........	...........	PUNCT
ejpam-3506	348	16	...........	...........	PUNCT
ejpam-3506	348	17	...........	...........	PUNCT
ejpam-3506	348	18	...........	...........	PUNCT
ejpam-3506	348	19	...........	...........	PUNCT
ejpam-3506	348	20	...........	...........	PUNCT
ejpam-3506	348	21	...........	...........	PUNCT
ejpam-3506	348	22	...........	...........	PUNCT
ejpam-3506	348	23	...........	...........	PUNCT
ejpam-3506	348	24	...........	...........	PUNCT
ejpam-3506	348	25	...........	...........	PUNCT
ejpam-3506	348	26	...........	...........	PUNCT
ejpam-3506	348	27	...........	...........	PUNCT
ejpam-3506	348	28	...........	...........	PUNCT
ejpam-3506	348	29	...........	...........	PUNCT
ejpam-3506	348	30	...........	...........	PUNCT
ejpam-3506	348	31	....	....	PUNCT
ejpam-3506	348	32	...............................................................................................	...............................................................................................	PUNCT
ejpam-3506	348	33	.............................	.............................	PUNCT
ejpam-3506	349	1	.......................	.......................	PUNCT
ejpam-3506	349	2	....................	....................	PUNCT
ejpam-3506	349	3	..................	..................	PUNCT
ejpam-3506	350	1	.................	.................	PUNCT
ejpam-3506	350	2	................	................	PUNCT
ejpam-3506	350	3	...............	...............	PUNCT
ejpam-3506	350	4	..............	..............	PUNCT
ejpam-3506	351	1	..............	..............	PUNCT
ejpam-3506	351	2	.......	.......	PUNCT
ejpam-3506	352	1	................	................	PUNCT
ejpam-3506	352	2	................	................	PUNCT
ejpam-3506	353	1	................	................	PUNCT
ejpam-3506	353	2	................	................	PUNCT
ejpam-3506	354	1	................	................	PUNCT
ejpam-3506	354	2	................	................	PUNCT
ejpam-3506	355	1	................	................	PUNCT
ejpam-3506	355	2	................	................	PUNCT
ejpam-3506	356	1	................	................	PUNCT
ejpam-3506	356	2	............	............	PUNCT
ejpam-3506	356	3	...........................................................................................................................................................................................................	...........................................................................................................................................................................................................	PUNCT
ejpam-3506	356	4	........	........	PUNCT
ejpam-3506	356	5	........	........	PUNCT
ejpam-3506	356	6	........	........	PUNCT
ejpam-3506	356	7	........	........	PUNCT
ejpam-3506	356	8	........	........	PUNCT
ejpam-3506	356	9	........	........	PUNCT
ejpam-3506	356	10	........	........	PUNCT
ejpam-3506	356	11	........	........	PUNCT
ejpam-3506	356	12	........	........	PUNCT
ejpam-3506	356	13	........	........	PUNCT
ejpam-3506	356	14	........	........	PUNCT
ejpam-3506	356	15	........	........	PUNCT
ejpam-3506	356	16	........	........	PUNCT
ejpam-3506	356	17	........	........	PUNCT
ejpam-3506	356	18	........	........	PUNCT
ejpam-3506	356	19	........	........	PUNCT
ejpam-3506	356	20	........	........	PUNCT
ejpam-3506	356	21	........	........	PUNCT
ejpam-3506	356	22	........	........	PUNCT
ejpam-3506	356	23	........	........	PUNCT
ejpam-3506	357	1	......	......	PUNCT
ejpam-3506	357	2	...................................................	...................................................	PUNCT
ejpam-3506	357	3	..............................................................	..............................................................	PUNCT
ejpam-3506	357	4	........................................................	........................................................	PUNCT
ejpam-3506	357	5	...........................................................................................	...........................................................................................	PUNCT
ejpam-3506	357	6	...............	...............	PUNCT
ejpam-3506	357	7	.............	.............	PUNCT
ejpam-3506	357	8	.	.	PUNCT
ejpam-3506	357	9	............	............	PUNCT
ejpam-3506	357	10	...............	...............	PUNCT
ejpam-3506	357	11	........................	........................	PUNCT
ejpam-3506	357	12	.....................................................................	.....................................................................	PUNCT
ejpam-3506	358	1	.............................................................................................................................................................................................................................................................................................................	.............................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-3506	358	2	.....................................................................................................................................................................................................................	.....................................................................................................................................................................................................................	PUNCT
ejpam-3506	359	1	............................................................................................................................................................................................................................................................................	............................................................................................................................................................................................................................................................................	PUNCT
ejpam-3506	359	2	............................................................................................................................................................	............................................................................................................................................................	PUNCT
ejpam-3506	360	1	....................................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................................	PUNCT
ejpam-3506	360	2	.......................................................................................................................................................................................	.......................................................................................................................................................................................	PUNCT
ejpam-3506	361	1	............................................................	............................................................	PUNCT
ejpam-3506	361	2	...........................................................	...........................................................	PUNCT
ejpam-3506	362	1	...................................................	...................................................	PUNCT
ejpam-3506	362	2	...........	...........	PUNCT
ejpam-3506	362	3	..........	..........	PUNCT
ejpam-3506	363	1	.........	.........	PUNCT
ejpam-3506	363	2	.........	.........	PUNCT
ejpam-3506	363	3	.........	.........	PUNCT
ejpam-3506	363	4	........	........	PUNCT
ejpam-3506	363	5	........	........	PUNCT
ejpam-3506	363	6	........	........	PUNCT
ejpam-3506	364	1	.........	.........	PUNCT
ejpam-3506	364	2	.........	.........	PUNCT
ejpam-3506	365	1	.........	.........	PUNCT
ejpam-3506	365	2	..........	..........	PUNCT
ejpam-3506	365	3	...........	...........	PUNCT
ejpam-3506	365	4	...........	...........	PUNCT
ejpam-3506	366	1	..........	..........	PUNCT
ejpam-3506	366	2	.........	.........	PUNCT
ejpam-3506	367	1	.........	.........	PUNCT
ejpam-3506	367	2	.........	.........	PUNCT
ejpam-3506	367	3	........	........	PUNCT
ejpam-3506	367	4	........	........	PUNCT
ejpam-3506	367	5	........	........	PUNCT
ejpam-3506	368	1	.........	.........	PUNCT
ejpam-3506	368	2	.........	.........	PUNCT
ejpam-3506	369	1	.........	.........	PUNCT
ejpam-3506	369	2	..........	..........	PUNCT
ejpam-3506	369	3	...........	...........	PUNCT
ejpam-3506	369	4	.....................................................................................................................................................................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-3506	369	5	..................................................................................................................................................................................................................................................................................................................................................	..................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-3506	370	1	h4	h4	PROPN
ejpam-3506	370	2	h3	h3	NOUN
ejpam-3506	370	3	h1	h1	PROPN
ejpam-3506	370	4	h2	h2	NOUN
ejpam-3506	370	5	·	·	PUNCT
ejpam-3506	370	6	·	·	PUNCT
ejpam-3506	370	7	·	·	PUNCT
ejpam-3506	371	1	x1	x1	PUNCT
ejpam-3506	372	1	x2	x2	NOUN
ejpam-3506	372	2	x3	x3	PROPN
ejpam-3506	373	1	xa−3	xa−3	PROPN
ejpam-3506	373	2	xa−2	xa−2	PROPN
ejpam-3506	373	3	xa−1	xa−1	PROPN
ejpam-3506	374	1	xa	xa	PROPN
ejpam-3506	375	1	ya−3	ya−3	PROPN
ejpam-3506	375	2	ya−2	ya−2	PROPN
ejpam-3506	375	3	ya−1	ya−1	PROPN
ejpam-3506	375	4	za−3	za−3	PROPN
ejpam-3506	375	5	za−2	za−2	PROPN
ejpam-3506	375	6	za−1	za−1	PROPN
ejpam-3506	375	7	•	•	NUM
ejpam-3506	375	8	••	••	NOUN
ejpam-3506	375	9	•••	•••	PROPN
ejpam-3506	375	10	•	•	ADJ
ejpam-3506	375	11	y1	y1	NOUN
ejpam-3506	375	12	y2	y2	NOUN
ejpam-3506	375	13	y3	y3	NOUN
ejpam-3506	375	14	z1	z1	ADJ
ejpam-3506	375	15	z2	z2	PROPN
ejpam-3506	375	16	z3	z3	PROPN
ejpam-3506	375	17	figure	figure	NOUN
ejpam-3506	375	18	5	5	NUM
ejpam-3506	375	19	:	:	PUNCT
ejpam-3506	375	20	a	a	DET
ejpam-3506	375	21	graph	graph	NOUN
ejpam-3506	375	22	g	g	NOUN
ejpam-3506	375	23	with	with	ADP
ejpam-3506	375	24	γ2fd(g	γ2fd(g	PROPN
ejpam-3506	375	25	)	)	PUNCT
ejpam-3506	375	26	=	=	SYM
ejpam-3506	375	27	a	a	PRON
ejpam-3506	375	28	and	and	CCONJ
ejpam-3506	375	29	γnc2fd(g	γnc2fd(g	NUM
ejpam-3506	375	30	)	)	PUNCT
ejpam-3506	376	1	=	=	SYM
ejpam-3506	376	2	b	b	X
ejpam-3506	376	3	when	when	SCONJ
ejpam-3506	376	4	a	a	DET
ejpam-3506	376	5	<	<	X
ejpam-3506	376	6	b.	b.	PROPN
ejpam-3506	376	7	corollary	corollary	NOUN
ejpam-3506	376	8	3	3	PROPN
ejpam-3506	376	9	.	.	PUNCT
ejpam-3506	377	1	γnc2fd	γnc2fd	PROPN
ejpam-3506	377	2	−	−	PROPN
ejpam-3506	377	3	γ2fd	γ2fd	PUNCT
ejpam-3506	377	4	can	can	AUX
ejpam-3506	377	5	be	be	AUX
ejpam-3506	377	6	made	make	VERB
ejpam-3506	377	7	arbitrarily	arbitrarily	ADV
ejpam-3506	377	8	large	large	ADJ
ejpam-3506	377	9	.	.	PUNCT
ejpam-3506	378	1	theorem	theorem	ADJ
ejpam-3506	378	2	8	8	NUM
ejpam-3506	378	3	.	.	PUNCT
ejpam-3506	379	1	[	[	X
ejpam-3506	379	2	6	6	NUM
ejpam-3506	379	3	]	]	PUNCT
ejpam-3506	379	4	let	let	VERB
ejpam-3506	379	5	g	g	NOUN
ejpam-3506	379	6	and	and	CCONJ
ejpam-3506	379	7	h	h	NOUN
ejpam-3506	379	8	be	be	AUX
ejpam-3506	379	9	nontrivial	nontrivial	ADJ
ejpam-3506	379	10	connected	connect	VERB
ejpam-3506	379	11	graphs	graph	NOUN
ejpam-3506	379	12	of	of	ADP
ejpam-3506	379	13	orders	order	NOUN
ejpam-3506	379	14	m	m	VERB
ejpam-3506	379	15	and	and	CCONJ
ejpam-3506	379	16	n	n	CCONJ
ejpam-3506	379	17	,	,	PUNCT
ejpam-3506	379	18	respectively	respectively	ADV
ejpam-3506	379	19	,	,	PUNCT
ejpam-3506	379	20	and	and	CCONJ
ejpam-3506	379	21	k	k	X
ejpam-3506	379	22	a	a	DET
ejpam-3506	379	23	positive	positive	ADJ
ejpam-3506	379	24	integer	integer	NOUN
ejpam-3506	379	25	with	with	ADP
ejpam-3506	379	26	1	1	NUM
ejpam-3506	379	27	≤	≤	NUM
ejpam-3506	379	28	k	k	NOUN
ejpam-3506	379	29	≤	≤	ADJ
ejpam-3506	379	30	max{m	max{m	NOUN
ejpam-3506	379	31	,	,	PUNCT
ejpam-3506	379	32	n	n	CCONJ
ejpam-3506	379	33	}	}	PUNCT
ejpam-3506	379	34	.	.	PUNCT
ejpam-3506	380	1	then	then	ADV
ejpam-3506	380	2	s	s	VERB
ejpam-3506	380	3	⊆	⊆	NUM
ejpam-3506	380	4	v	v	NOUN
ejpam-3506	380	5	(	(	PUNCT
ejpam-3506	380	6	g+h	g+h	PROPN
ejpam-3506	380	7	)	)	PUNCT
ejpam-3506	380	8	is	be	AUX
ejpam-3506	380	9	a	a	DET
ejpam-3506	380	10	kfd	kfd	NOUN
ejpam-3506	380	11	-	-	PUNCT
ejpam-3506	380	12	set	set	NOUN
ejpam-3506	380	13	of	of	ADP
ejpam-3506	380	14	g+h	g+h	PROPN
ejpam-3506	380	15	if	if	SCONJ
ejpam-3506	380	16	and	and	CCONJ
ejpam-3506	380	17	only	only	ADV
ejpam-3506	380	18	if	if	SCONJ
ejpam-3506	380	19	one	one	NUM
ejpam-3506	380	20	of	of	ADP
ejpam-3506	380	21	the	the	DET
ejpam-3506	380	22	following	following	NOUN
ejpam-3506	380	23	holds	hold	VERB
ejpam-3506	380	24	:	:	PUNCT
ejpam-3506	380	25	(	(	PUNCT
ejpam-3506	380	26	a	a	X
ejpam-3506	380	27	)	)	PUNCT
ejpam-3506	380	28	s	s	PART
ejpam-3506	380	29	=	=	SYM
ejpam-3506	380	30	v	v	PROPN
ejpam-3506	380	31	(	(	PUNCT
ejpam-3506	380	32	g+h	g+h	PROPN
ejpam-3506	380	33	)	)	PUNCT
ejpam-3506	380	34	.	.	PUNCT
ejpam-3506	381	1	(	(	PUNCT
ejpam-3506	381	2	b	b	X
ejpam-3506	381	3	)	)	PUNCT
ejpam-3506	381	4	s	s	PART
ejpam-3506	381	5	⊆	⊆	NUM
ejpam-3506	381	6	v	v	NOUN
ejpam-3506	381	7	(	(	PUNCT
ejpam-3506	381	8	g	g	NOUN
ejpam-3506	381	9	)	)	PUNCT
ejpam-3506	381	10	,	,	PUNCT
ejpam-3506	381	11	|s|	|s|	PROPN
ejpam-3506	381	12	=	=	SYM
ejpam-3506	381	13	k	k	PROPN
ejpam-3506	381	14	and	and	CCONJ
ejpam-3506	381	15	s	s	PROPN
ejpam-3506	381	16	is	be	AUX
ejpam-3506	381	17	a	a	DET
ejpam-3506	381	18	kfd	kfd	NOUN
ejpam-3506	381	19	-	-	PUNCT
ejpam-3506	381	20	set	set	NOUN
ejpam-3506	381	21	in	in	ADP
ejpam-3506	381	22	g.	g.	PROPN
ejpam-3506	381	23	(	(	PUNCT
ejpam-3506	381	24	c	c	X
ejpam-3506	381	25	)	)	PUNCT
ejpam-3506	381	26	s	s	PART
ejpam-3506	381	27	⊆	⊆	NUM
ejpam-3506	381	28	v	v	NOUN
ejpam-3506	381	29	(	(	PUNCT
ejpam-3506	381	30	h	h	NOUN
ejpam-3506	381	31	)	)	PUNCT
ejpam-3506	381	32	,	,	PUNCT
ejpam-3506	381	33	|s|	|s|	PROPN
ejpam-3506	381	34	=	=	SYM
ejpam-3506	381	35	k	k	PROPN
ejpam-3506	381	36	and	and	CCONJ
ejpam-3506	381	37	s	s	PROPN
ejpam-3506	381	38	is	be	AUX
ejpam-3506	381	39	a	a	DET
ejpam-3506	381	40	kfd	kfd	NOUN
ejpam-3506	381	41	-	-	PUNCT
ejpam-3506	381	42	set	set	NOUN
ejpam-3506	381	43	in	in	ADP
ejpam-3506	381	44	h.	h.	PROPN
ejpam-3506	381	45	(	(	PUNCT
ejpam-3506	381	46	d	d	X
ejpam-3506	381	47	)	)	PUNCT
ejpam-3506	381	48	s	s	PART
ejpam-3506	381	49	=	=	PUNCT
ejpam-3506	381	50	sg	sg	X
ejpam-3506	381	51	∪	∪	ADJ
ejpam-3506	381	52	sh	sh	PROPN
ejpam-3506	381	53	,	,	PUNCT
ejpam-3506	381	54	where	where	SCONJ
ejpam-3506	381	55	sg	sg	PROPN
ejpam-3506	381	56	is	be	AUX
ejpam-3506	381	57	a	a	DET
ejpam-3506	381	58	(	(	PUNCT
ejpam-3506	381	59	k	k	PROPN
ejpam-3506	381	60	−	−	PROPN
ejpam-3506	381	61	|sh	|sh	ADP
ejpam-3506	381	62	|)fd	|)fd	PROPN
ejpam-3506	381	63	-	-	PUNCT
ejpam-3506	381	64	set	set	NOUN
ejpam-3506	381	65	of	of	ADP
ejpam-3506	381	66	g	g	PROPN
ejpam-3506	381	67	and	and	CCONJ
ejpam-3506	381	68	sh	sh	PROPN
ejpam-3506	381	69	is	be	AUX
ejpam-3506	381	70	a	a	DET
ejpam-3506	381	71	(	(	PUNCT
ejpam-3506	381	72	k	k	PROPN
ejpam-3506	381	73	−	−	PROPN
ejpam-3506	381	74	|sg|)fd	|sg|)fd	NOUN
ejpam-3506	381	75	-	-	PUNCT
ejpam-3506	381	76	set	set	NOUN
ejpam-3506	381	77	in	in	ADP
ejpam-3506	381	78	h.	h.	PROPN
ejpam-3506	382	1	(	(	PUNCT
ejpam-3506	382	2	e	e	X
ejpam-3506	382	3	)	)	PUNCT
ejpam-3506	382	4	s	s	PART
ejpam-3506	382	5	=	=	SYM
ejpam-3506	382	6	v	v	X
ejpam-3506	382	7	(	(	PUNCT
ejpam-3506	382	8	g	g	NOUN
ejpam-3506	382	9	)	)	PUNCT
ejpam-3506	382	10	∪	∪	ADP
ejpam-3506	382	11	t	t	PROPN
ejpam-3506	382	12	,	,	PUNCT
ejpam-3506	382	13	where	where	SCONJ
ejpam-3506	382	14	|v	|v	PROPN
ejpam-3506	382	15	(	(	PUNCT
ejpam-3506	382	16	g)|	g)|	NOUN
ejpam-3506	382	17	=	=	NOUN
ejpam-3506	382	18	m	m	PROPN
ejpam-3506	382	19	<	<	X
ejpam-3506	382	20	k	k	X
ejpam-3506	382	21	and	and	CCONJ
ejpam-3506	382	22	t	t	PROPN
ejpam-3506	382	23	is	be	AUX
ejpam-3506	382	24	a	a	DET
ejpam-3506	382	25	(	(	PUNCT
ejpam-3506	382	26	k	k	X
ejpam-3506	382	27	−m)fd	−m)fd	X
ejpam-3506	382	28	-	-	PUNCT
ejpam-3506	382	29	set	set	NOUN
ejpam-3506	382	30	in	in	ADP
ejpam-3506	382	31	h.	h.	PROPN
ejpam-3506	382	32	(	(	PUNCT
ejpam-3506	382	33	f	f	X
ejpam-3506	382	34	)	)	PUNCT
ejpam-3506	382	35	s	s	PART
ejpam-3506	383	1	=	=	X
ejpam-3506	383	2	d	d	X
ejpam-3506	383	3	∪	∪	X
ejpam-3506	383	4	v	v	NOUN
ejpam-3506	383	5	(	(	PUNCT
ejpam-3506	383	6	h	h	NOUN
ejpam-3506	383	7	)	)	PUNCT
ejpam-3506	383	8	,	,	PUNCT
ejpam-3506	384	1	where	where	SCONJ
ejpam-3506	384	2	|v	|v	PROPN
ejpam-3506	384	3	(	(	PUNCT
ejpam-3506	384	4	h)|	h)|	NOUN
ejpam-3506	384	5	=	=	SYM
ejpam-3506	384	6	n	n	CCONJ
ejpam-3506	384	7	<	<	X
ejpam-3506	384	8	k	k	PROPN
ejpam-3506	384	9	and	and	CCONJ
ejpam-3506	384	10	d	d	PROPN
ejpam-3506	384	11	is	be	AUX
ejpam-3506	384	12	a	a	DET
ejpam-3506	384	13	(	(	PUNCT
ejpam-3506	384	14	k	k	PROPN
ejpam-3506	384	15	−	−	PROPN
ejpam-3506	384	16	n)fd	n)fd	PROPN
ejpam-3506	384	17	-	-	PUNCT
ejpam-3506	384	18	set	set	NOUN
ejpam-3506	384	19	in	in	ADP
ejpam-3506	384	20	g.	g.	PROPN
ejpam-3506	384	21	theorem	theorem	VERB
ejpam-3506	384	22	9	9	NUM
ejpam-3506	384	23	.	.	PUNCT
ejpam-3506	385	1	[	[	X
ejpam-3506	385	2	6	6	NUM
ejpam-3506	385	3	]	]	PUNCT
ejpam-3506	385	4	let	let	VERB
ejpam-3506	385	5	g	g	NOUN
ejpam-3506	385	6	and	and	CCONJ
ejpam-3506	385	7	h	h	NOUN
ejpam-3506	385	8	be	be	AUX
ejpam-3506	385	9	nontrivial	nontrivial	ADJ
ejpam-3506	385	10	connected	connect	VERB
ejpam-3506	385	11	graphs	graph	NOUN
ejpam-3506	385	12	and	and	CCONJ
ejpam-3506	385	13	let	let	VERB
ejpam-3506	385	14	k	k	PRON
ejpam-3506	385	15	be	be	AUX
ejpam-3506	385	16	a	a	DET
ejpam-3506	385	17	positive	positive	ADJ
ejpam-3506	385	18	integer	integer	NOUN
ejpam-3506	385	19	with	with	ADP
ejpam-3506	385	20	k	k	PROPN
ejpam-3506	385	21	≤	≤	PROPN
ejpam-3506	385	22	|v	|v	PROPN
ejpam-3506	385	23	(	(	PUNCT
ejpam-3506	385	24	h)|	h)|	PROPN
ejpam-3506	385	25	.	.	PUNCT
ejpam-3506	386	1	then	then	ADV
ejpam-3506	386	2	c	c	PROPN
ejpam-3506	386	3	⊆	⊆	NUM
ejpam-3506	386	4	v	v	NOUN
ejpam-3506	386	5	(	(	PUNCT
ejpam-3506	386	6	g	g	PROPN
ejpam-3506	386	7	◦	◦	NOUN
ejpam-3506	386	8	h	h	NOUN
ejpam-3506	386	9	)	)	PUNCT
ejpam-3506	386	10	is	be	AUX
ejpam-3506	386	11	a	a	DET
ejpam-3506	386	12	kfd	kfd	NOUN
ejpam-3506	386	13	-	-	PUNCT
ejpam-3506	386	14	set	set	NOUN
ejpam-3506	386	15	in	in	ADP
ejpam-3506	386	16	g	g	PROPN
ejpam-3506	386	17	◦	◦	NOUN
ejpam-3506	386	18	h	h	NOUN
ejpam-3506	387	1	if	if	SCONJ
ejpam-3506	388	1	and	and	CCONJ
ejpam-3506	388	2	only	only	ADV
ejpam-3506	388	3	if	if	SCONJ
ejpam-3506	388	4	one	one	NUM
ejpam-3506	388	5	of	of	ADP
ejpam-3506	388	6	the	the	DET
ejpam-3506	388	7	following	following	NOUN
ejpam-3506	388	8	holds	hold	VERB
ejpam-3506	388	9	:	:	PUNCT
ejpam-3506	388	10	(	(	PUNCT
ejpam-3506	388	11	a	a	X
ejpam-3506	388	12	)	)	PUNCT
ejpam-3506	388	13	c	c	NOUN
ejpam-3506	388	14	=	=	SYM
ejpam-3506	388	15	v	v	PROPN
ejpam-3506	388	16	(	(	PUNCT
ejpam-3506	388	17	g	g	NOUN
ejpam-3506	388	18	)	)	PUNCT
ejpam-3506	388	19	∪	∪	ADP
ejpam-3506	388	20	b	b	NOUN
ejpam-3506	388	21	,	,	PUNCT
ejpam-3506	388	22	where	where	SCONJ
ejpam-3506	388	23	b	b	NOUN
ejpam-3506	388	24	=	=	NOUN
ejpam-3506	388	25	∅	∅	NOUN
ejpam-3506	388	26	(	(	PUNCT
ejpam-3506	388	27	k	k	NOUN
ejpam-3506	388	28	=	=	SYM
ejpam-3506	388	29	1	1	NUM
ejpam-3506	388	30	)	)	PUNCT
ejpam-3506	388	31	or	or	CCONJ
ejpam-3506	388	32	b	b	NOUN
ejpam-3506	388	33	=	=	SYM
ejpam-3506	388	34	⋃	⋃	NOUN
ejpam-3506	388	35	v∈v	v∈v	NOUN
ejpam-3506	388	36	(	(	PUNCT
ejpam-3506	388	37	g	g	NOUN
ejpam-3506	388	38	)	)	PUNCT
ejpam-3506	388	39	sv	sv	NOUN
ejpam-3506	388	40	,	,	PUNCT
ejpam-3506	388	41	where	where	SCONJ
ejpam-3506	388	42	each	each	PRON
ejpam-3506	388	43	sv	sv	PROPN
ejpam-3506	388	44	is	be	AUX
ejpam-3506	388	45	a	a	DET
ejpam-3506	388	46	(	(	PUNCT
ejpam-3506	388	47	k	k	PROPN
ejpam-3506	388	48	−	−	PROPN
ejpam-3506	388	49	1)fd	1)fd	PROPN
ejpam-3506	388	50	-	-	PUNCT
ejpam-3506	388	51	set	set	NOUN
ejpam-3506	388	52	of	of	ADP
ejpam-3506	388	53	hv	hv	PROPN
ejpam-3506	388	54	(	(	PUNCT
ejpam-3506	388	55	k	k	X
ejpam-3506	388	56	≥	≥	NUM
ejpam-3506	388	57	2	2	NUM
ejpam-3506	388	58	)	)	PUNCT
ejpam-3506	388	59	.	.	PUNCT
ejpam-3506	389	1	(	(	PUNCT
ejpam-3506	389	2	b	b	X
ejpam-3506	389	3	)	)	PUNCT
ejpam-3506	389	4	c	c	NOUN
ejpam-3506	390	1	=	=	PUNCT
ejpam-3506	390	2	⋃	⋃	NOUN
ejpam-3506	390	3	v∈v	v∈v	NOUN
ejpam-3506	390	4	(	(	PUNCT
ejpam-3506	390	5	g	g	NOUN
ejpam-3506	390	6	)	)	PUNCT
ejpam-3506	390	7	sv	sv	NOUN
ejpam-3506	390	8	,	,	PUNCT
ejpam-3506	390	9	where	where	SCONJ
ejpam-3506	390	10	each	each	PRON
ejpam-3506	390	11	sv	sv	PROPN
ejpam-3506	390	12	is	be	AUX
ejpam-3506	390	13	a	a	DET
ejpam-3506	390	14	kfd	kfd	NOUN
ejpam-3506	390	15	-	-	PUNCT
ejpam-3506	390	16	set	set	NOUN
ejpam-3506	390	17	of	of	ADP
ejpam-3506	390	18	hv	hv	PROPN
ejpam-3506	390	19	and	and	CCONJ
ejpam-3506	390	20	|sv|	|sv|	PROPN
ejpam-3506	390	21	=	=	SYM
ejpam-3506	390	22	k.	k.	PROPN
ejpam-3506	390	23	theorem	theorem	VERB
ejpam-3506	390	24	10	10	NUM
ejpam-3506	390	25	.	.	PUNCT
ejpam-3506	391	1	[	[	X
ejpam-3506	391	2	6	6	NUM
ejpam-3506	391	3	]	]	PUNCT
ejpam-3506	391	4	let	let	VERB
ejpam-3506	391	5	g	g	NOUN
ejpam-3506	391	6	and	and	CCONJ
ejpam-3506	391	7	h	h	NOUN
ejpam-3506	391	8	be	be	AUX
ejpam-3506	391	9	nontrivial	nontrivial	ADJ
ejpam-3506	391	10	connected	connected	ADJ
ejpam-3506	391	11	graphs	graph	NOUN
ejpam-3506	391	12	.	.	PUNCT
ejpam-3506	392	1	then	then	ADV
ejpam-3506	392	2	c	c	X
ejpam-3506	392	3	=	=	PUNCT
ejpam-3506	392	4	⋃	⋃	PROPN
ejpam-3506	392	5	x∈s	x∈s	NOUN
ejpam-3506	392	6	(	(	PUNCT
ejpam-3506	392	7	{	{	PUNCT
ejpam-3506	392	8	x}×tx	x}×tx	NUM
ejpam-3506	392	9	)	)	PUNCT
ejpam-3506	392	10	⊆	⊆	NUM
ejpam-3506	392	11	v	v	NOUN
ejpam-3506	392	12	(	(	PUNCT
ejpam-3506	392	13	g[h	g[h	PROPN
ejpam-3506	392	14	]	]	PUNCT
ejpam-3506	392	15	)	)	PUNCT
ejpam-3506	392	16	is	be	AUX
ejpam-3506	392	17	a	a	DET
ejpam-3506	392	18	kfd	kfd	NOUN
ejpam-3506	392	19	-	-	PUNCT
ejpam-3506	392	20	set	set	NOUN
ejpam-3506	392	21	in	in	ADP
ejpam-3506	392	22	g[h	g[h	PROPN
ejpam-3506	392	23	]	]	PUNCT
ejpam-3506	392	24	if	if	SCONJ
ejpam-3506	393	1	and	and	CCONJ
ejpam-3506	393	2	only	only	ADV
ejpam-3506	393	3	if	if	SCONJ
ejpam-3506	393	4	the	the	DET
ejpam-3506	393	5	following	follow	VERB
ejpam-3506	393	6	hold	hold	NOUN
ejpam-3506	393	7	:	:	PUNCT
ejpam-3506	393	8	w.	w.	PROPN
ejpam-3506	393	9	bent	bent	PROPN
ejpam-3506	393	10	-	-	PUNCT
ejpam-3506	393	11	usman	usman	PROPN
ejpam-3506	393	12	,	,	PUNCT
ejpam-3506	393	13	r.	r.	PROPN
ejpam-3506	393	14	isla	isla	PROPN
ejpam-3506	393	15	,	,	PUNCT
ejpam-3506	393	16	s.	s.	PROPN
ejpam-3506	393	17	canoy	canoy	PROPN
ejpam-3506	393	18	/	/	SYM
ejpam-3506	393	19	eur	eur	PROPN
ejpam-3506	393	20	.	.	PUNCT
ejpam-3506	394	1	j.	j.	PROPN
ejpam-3506	394	2	pure	pure	PROPN
ejpam-3506	394	3	appl	appl	PROPN
ejpam-3506	394	4	.	.	PROPN
ejpam-3506	394	5	math	math	PROPN
ejpam-3506	394	6	,	,	PUNCT
ejpam-3506	394	7	12	12	NUM
ejpam-3506	394	8	(	(	PUNCT
ejpam-3506	394	9	3	3	NUM
ejpam-3506	394	10	)	)	PUNCT
ejpam-3506	394	11	(	(	PUNCT
ejpam-3506	394	12	2019	2019	NUM
ejpam-3506	394	13	)	)	PUNCT
ejpam-3506	394	14	,	,	PUNCT
ejpam-3506	394	15	1337	1337	NUM
ejpam-3506	394	16	-	-	SYM
ejpam-3506	394	17	1349	1349	NUM
ejpam-3506	394	18	1344	1344	NUM
ejpam-3506	394	19	(	(	PUNCT
ejpam-3506	394	20	i	i	NOUN
ejpam-3506	394	21	)	)	PUNCT
ejpam-3506	394	22	s	s	VERB
ejpam-3506	394	23	is	be	AUX
ejpam-3506	394	24	a	a	DET
ejpam-3506	394	25	dominating	dominating	NOUN
ejpam-3506	394	26	set	set	VERB
ejpam-3506	394	27	in	in	ADP
ejpam-3506	394	28	g.	g.	PROPN
ejpam-3506	394	29	(	(	PUNCT
ejpam-3506	394	30	ii	ii	PROPN
ejpam-3506	394	31	)	)	PUNCT
ejpam-3506	394	32	for	for	ADP
ejpam-3506	394	33	each	each	DET
ejpam-3506	394	34	x	x	SYM
ejpam-3506	394	35	∈	∈	PROPN
ejpam-3506	394	36	s	s	NOUN
ejpam-3506	394	37	∩ng(s	∩ng(s	NOUN
ejpam-3506	394	38	)	)	PUNCT
ejpam-3506	394	39	,	,	PUNCT
ejpam-3506	394	40	tx	tx	PROPN
ejpam-3506	394	41	=	=	SYM
ejpam-3506	394	42	v	v	PROPN
ejpam-3506	394	43	(	(	PUNCT
ejpam-3506	394	44	h	h	NOUN
ejpam-3506	394	45	)	)	PUNCT
ejpam-3506	394	46	and	and	CCONJ
ejpam-3506	394	47	|v	|v	PROPN
ejpam-3506	394	48	(	(	PUNCT
ejpam-3506	394	49	h)|	h)|	NOUN
ejpam-3506	394	50	=	=	NOUN
ejpam-3506	394	51	r	r	NOUN
ejpam-3506	394	52	≤	≤	NOUN
ejpam-3506	395	1	k	k	NOUN
ejpam-3506	395	2	whenever	whenever	SCONJ
ejpam-3506	395	3	c	c	PROPN
ejpam-3506	395	4	6=	6=	PROPN
ejpam-3506	395	5	v	v	PROPN
ejpam-3506	395	6	(	(	PUNCT
ejpam-3506	395	7	g[h	g[h	PROPN
ejpam-3506	395	8	]	]	PUNCT
ejpam-3506	395	9	)	)	PUNCT
ejpam-3506	395	10	or	or	CCONJ
ejpam-3506	395	11	tx	tx	PROPN
ejpam-3506	395	12	is	be	AUX
ejpam-3506	395	13	an	an	DET
ejpam-3506	395	14	rfd	rfd	NOUN
ejpam-3506	395	15	-	-	PUNCT
ejpam-3506	395	16	set	set	VERB
ejpam-3506	395	17	and	and	CCONJ
ejpam-3506	395	18	∑	∑	ADP
ejpam-3506	395	19	z∈ng(x)∩s	z∈ng(x)∩s	NUM
ejpam-3506	395	20	|tz|	|tz|	NOUN
ejpam-3506	396	1	=	=	SYM
ejpam-3506	396	2	k	k	PROPN
ejpam-3506	396	3	−	−	PROPN
ejpam-3506	396	4	r.	r.	PROPN
ejpam-3506	396	5	(	(	PUNCT
ejpam-3506	396	6	iii	iii	NOUN
ejpam-3506	396	7	)	)	PUNCT
ejpam-3506	396	8	for	for	ADP
ejpam-3506	396	9	each	each	DET
ejpam-3506	396	10	x	x	SYM
ejpam-3506	396	11	∈	∈	PROPN
ejpam-3506	396	12	s\ng(s	s\ng(s	NOUN
ejpam-3506	396	13	)	)	PUNCT
ejpam-3506	396	14	,	,	PUNCT
ejpam-3506	396	15	tx	tx	PROPN
ejpam-3506	396	16	=	=	SYM
ejpam-3506	396	17	v	v	PROPN
ejpam-3506	396	18	(	(	PUNCT
ejpam-3506	396	19	h	h	NOUN
ejpam-3506	396	20	)	)	PUNCT
ejpam-3506	396	21	and	and	CCONJ
ejpam-3506	396	22	|v	|v	PROPN
ejpam-3506	396	23	(	(	PUNCT
ejpam-3506	396	24	h)|	h)|	NOUN
ejpam-3506	396	25	≤	≤	PROPN
ejpam-3506	396	26	k	k	NOUN
ejpam-3506	396	27	or	or	CCONJ
ejpam-3506	396	28	|tx|	|tx|	NUM
ejpam-3506	396	29	=	=	SYM
ejpam-3506	396	30	k	k	PROPN
ejpam-3506	396	31	and	and	CCONJ
ejpam-3506	396	32	tx	tx	PROPN
ejpam-3506	396	33	is	be	AUX
ejpam-3506	396	34	a	a	DET
ejpam-3506	396	35	kfd	kfd	NOUN
ejpam-3506	396	36	-	-	PUNCT
ejpam-3506	396	37	set	set	NOUN
ejpam-3506	396	38	in	in	ADP
ejpam-3506	396	39	h.	h.	PROPN
ejpam-3506	396	40	(	(	PUNCT
ejpam-3506	396	41	iv	iv	X
ejpam-3506	396	42	)	)	PUNCT
ejpam-3506	396	43	for	for	ADP
ejpam-3506	396	44	each	each	DET
ejpam-3506	396	45	y	y	PROPN
ejpam-3506	396	46	∈	∈	PROPN
ejpam-3506	396	47	v	v	NOUN
ejpam-3506	396	48	(	(	PUNCT
ejpam-3506	396	49	g)\s	g)\s	NOUN
ejpam-3506	396	50	,	,	PUNCT
ejpam-3506	396	51	∑	∑	PUNCT
ejpam-3506	396	52	v∈ng(y)∩s	v∈ng(y)∩s	ADJ
ejpam-3506	396	53	|tv|	|tv|	PROPN
ejpam-3506	396	54	=	=	SYM
ejpam-3506	396	55	k.	k.	PROPN
ejpam-3506	396	56	corollary	corollary	NOUN
ejpam-3506	396	57	4	4	NUM
ejpam-3506	396	58	.	.	PUNCT
ejpam-3506	397	1	[	[	X
ejpam-3506	397	2	6	6	NUM
ejpam-3506	397	3	]	]	PUNCT
ejpam-3506	397	4	let	let	VERB
ejpam-3506	397	5	g	g	NOUN
ejpam-3506	397	6	and	and	CCONJ
ejpam-3506	397	7	h	h	NOUN
ejpam-3506	397	8	be	be	AUX
ejpam-3506	397	9	nontrivial	nontrivial	ADJ
ejpam-3506	397	10	connected	connect	VERB
ejpam-3506	397	11	graphs	graph	NOUN
ejpam-3506	397	12	of	of	ADP
ejpam-3506	397	13	orders	order	NOUN
ejpam-3506	397	14	m	m	VERB
ejpam-3506	397	15	and	and	CCONJ
ejpam-3506	397	16	n	n	CCONJ
ejpam-3506	397	17	,	,	PUNCT
ejpam-3506	397	18	respectively	respectively	ADV
ejpam-3506	397	19	,	,	PUNCT
ejpam-3506	397	20	and	and	CCONJ
ejpam-3506	397	21	k	k	X
ejpam-3506	397	22	a	a	DET
ejpam-3506	397	23	positive	positive	ADJ
ejpam-3506	397	24	integer	integer	NOUN
ejpam-3506	397	25	with	with	ADP
ejpam-3506	397	26	1	1	NUM
ejpam-3506	397	27	≤	≤	NUM
ejpam-3506	397	28	k	k	PROPN
ejpam-3506	397	29	≤	≤	ADJ
ejpam-3506	397	30	min{m	min{m	PROPN
ejpam-3506	397	31	,	,	PUNCT
ejpam-3506	397	32	n	n	CCONJ
ejpam-3506	397	33	}	}	PUNCT
ejpam-3506	397	34	.	.	PUNCT
ejpam-3506	398	1	if	if	SCONJ
ejpam-3506	398	2	d	d	PROPN
ejpam-3506	398	3	is	be	AUX
ejpam-3506	398	4	a	a	DET
ejpam-3506	398	5	kfd	kfd	NOUN
ejpam-3506	398	6	-	-	PUNCT
ejpam-3506	398	7	set	set	NOUN
ejpam-3506	398	8	in	in	ADP
ejpam-3506	398	9	h	h	NOUN
ejpam-3506	398	10	,	,	PUNCT
ejpam-3506	398	11	then	then	ADV
ejpam-3506	398	12	v	v	INTJ
ejpam-3506	398	13	(	(	PUNCT
ejpam-3506	398	14	g)×d	g)×d	PROPN
ejpam-3506	398	15	is	be	AUX
ejpam-3506	398	16	a	a	DET
ejpam-3506	398	17	kfd	kfd	NOUN
ejpam-3506	398	18	-	-	PUNCT
ejpam-3506	398	19	set	set	NOUN
ejpam-3506	398	20	in	in	ADP
ejpam-3506	398	21	g	g	PROPN
ejpam-3506	398	22	�	�	PROPN
ejpam-3506	398	23	h.	h.	PROPN
ejpam-3506	398	24	3	3	NUM
ejpam-3506	398	25	.	.	X
ejpam-3506	398	26	neighborhood	neighborhood	NOUN
ejpam-3506	398	27	connected	connect	VERB
ejpam-3506	398	28	k	k	ADJ
ejpam-3506	398	29	-	-	PUNCT
ejpam-3506	398	30	fair	fair	ADJ
ejpam-3506	398	31	domination	domination	NOUN
ejpam-3506	398	32	in	in	ADP
ejpam-3506	398	33	the	the	DET
ejpam-3506	398	34	join	join	NOUN
ejpam-3506	398	35	of	of	ADP
ejpam-3506	398	36	graphs	graph	NOUN
ejpam-3506	398	37	the	the	DET
ejpam-3506	398	38	join	join	NOUN
ejpam-3506	398	39	g	g	PROPN
ejpam-3506	398	40	+	+	CCONJ
ejpam-3506	398	41	h	h	NOUN
ejpam-3506	398	42	of	of	ADP
ejpam-3506	398	43	two	two	NUM
ejpam-3506	398	44	graphs	graph	NOUN
ejpam-3506	398	45	g	g	NOUN
ejpam-3506	398	46	and	and	CCONJ
ejpam-3506	398	47	h	h	NOUN
ejpam-3506	398	48	is	be	AUX
ejpam-3506	398	49	the	the	DET
ejpam-3506	398	50	graph	graph	NOUN
ejpam-3506	398	51	with	with	ADP
ejpam-3506	398	52	vertex	vertex	NOUN
ejpam-3506	398	53	set	set	VERB
ejpam-3506	398	54	v	v	NOUN
ejpam-3506	398	55	(	(	PUNCT
ejpam-3506	398	56	g	g	PROPN
ejpam-3506	398	57	+	+	NOUN
ejpam-3506	398	58	h	h	NOUN
ejpam-3506	398	59	)	)	PUNCT
ejpam-3506	399	1	=	=	NOUN
ejpam-3506	399	2	v	v	X
ejpam-3506	399	3	(	(	PUNCT
ejpam-3506	399	4	g	g	NOUN
ejpam-3506	399	5	)	)	PUNCT
ejpam-3506	399	6	∪	∪	NOUN
ejpam-3506	399	7	v	v	NOUN
ejpam-3506	399	8	(	(	PUNCT
ejpam-3506	399	9	h	h	NOUN
ejpam-3506	399	10	)	)	PUNCT
ejpam-3506	399	11	and	and	CCONJ
ejpam-3506	399	12	edge	edge	NOUN
ejpam-3506	399	13	set	set	VERB
ejpam-3506	399	14	e(g+h	e(g+h	NUM
ejpam-3506	399	15	)	)	PUNCT
ejpam-3506	399	16	=	=	SYM
ejpam-3506	399	17	e(g	e(g	NOUN
ejpam-3506	399	18	)	)	PUNCT
ejpam-3506	399	19	∪	∪	ADP
ejpam-3506	399	20	e(h	e(h	PROPN
ejpam-3506	399	21	)	)	PUNCT
ejpam-3506	399	22	∪	∪	NOUN
ejpam-3506	399	23	{	{	PUNCT
ejpam-3506	399	24	uv	uv	NOUN
ejpam-3506	399	25	:	:	PUNCT
ejpam-3506	399	26	u	u	PROPN
ejpam-3506	399	27	∈	∈	PROPN
ejpam-3506	399	28	v	v	ADP
ejpam-3506	399	29	(	(	PUNCT
ejpam-3506	399	30	g	g	NOUN
ejpam-3506	399	31	)	)	PUNCT
ejpam-3506	399	32	,	,	PUNCT
ejpam-3506	399	33	v	v	X
ejpam-3506	399	34	∈	∈	PROPN
ejpam-3506	399	35	v	v	NOUN
ejpam-3506	399	36	(	(	PUNCT
ejpam-3506	399	37	h	h	NOUN
ejpam-3506	399	38	)	)	PUNCT
ejpam-3506	399	39	}	}	PUNCT
ejpam-3506	399	40	.	.	PUNCT
ejpam-3506	400	1	theorem	theorem	VERB
ejpam-3506	400	2	11	11	NUM
ejpam-3506	400	3	.	.	PUNCT
ejpam-3506	401	1	let	let	VERB
ejpam-3506	401	2	g	g	NOUN
ejpam-3506	401	3	and	and	CCONJ
ejpam-3506	401	4	h	h	NOUN
ejpam-3506	401	5	be	be	AUX
ejpam-3506	401	6	nontrivial	nontrivial	ADJ
ejpam-3506	401	7	connected	connect	VERB
ejpam-3506	401	8	graphs	graph	NOUN
ejpam-3506	401	9	of	of	ADP
ejpam-3506	401	10	orders	order	NOUN
ejpam-3506	401	11	m	m	VERB
ejpam-3506	401	12	and	and	CCONJ
ejpam-3506	401	13	n	n	CCONJ
ejpam-3506	401	14	,	,	PUNCT
ejpam-3506	401	15	respectively	respectively	ADV
ejpam-3506	401	16	,	,	PUNCT
ejpam-3506	401	17	and	and	CCONJ
ejpam-3506	401	18	k	k	X
ejpam-3506	401	19	a	a	DET
ejpam-3506	401	20	positive	positive	ADJ
ejpam-3506	401	21	integer	integer	NOUN
ejpam-3506	401	22	with	with	ADP
ejpam-3506	401	23	1	1	NUM
ejpam-3506	401	24	≤	≤	NUM
ejpam-3506	401	25	k	k	NOUN
ejpam-3506	401	26	≤	≤	ADJ
ejpam-3506	401	27	max{m	max{m	NOUN
ejpam-3506	401	28	,	,	PUNCT
ejpam-3506	401	29	n	n	CCONJ
ejpam-3506	401	30	}	}	PUNCT
ejpam-3506	401	31	.	.	PUNCT
ejpam-3506	402	1	then	then	ADV
ejpam-3506	402	2	s	s	VERB
ejpam-3506	402	3	⊆	⊆	NUM
ejpam-3506	402	4	v	v	NOUN
ejpam-3506	402	5	(	(	PUNCT
ejpam-3506	402	6	g	g	PROPN
ejpam-3506	402	7	+	+	NOUN
ejpam-3506	402	8	h	h	NOUN
ejpam-3506	402	9	)	)	PUNCT
ejpam-3506	402	10	is	be	AUX
ejpam-3506	402	11	an	an	DET
ejpam-3506	402	12	nckfd	nckfd	NOUN
ejpam-3506	402	13	-	-	PUNCT
ejpam-3506	402	14	set	set	NOUN
ejpam-3506	402	15	in	in	ADP
ejpam-3506	402	16	g+h	g+h	PROPN
ejpam-3506	403	1	if	if	SCONJ
ejpam-3506	403	2	and	and	CCONJ
ejpam-3506	403	3	only	only	ADV
ejpam-3506	403	4	if	if	SCONJ
ejpam-3506	403	5	s	s	NOUN
ejpam-3506	403	6	is	be	AUX
ejpam-3506	403	7	a	a	DET
ejpam-3506	403	8	kfd	kfd	NOUN
ejpam-3506	403	9	-	-	PUNCT
ejpam-3506	403	10	set	set	NOUN
ejpam-3506	403	11	in	in	ADP
ejpam-3506	403	12	g+h	g+h	PROPN
ejpam-3506	403	13	.	.	PUNCT
ejpam-3506	404	1	proof	proof	NOUN
ejpam-3506	404	2	.	.	PUNCT
ejpam-3506	405	1	let	let	VERB
ejpam-3506	405	2	s	s	PRON
ejpam-3506	405	3	⊆	⊆	NUM
ejpam-3506	405	4	v	v	NOUN
ejpam-3506	405	5	(	(	PUNCT
ejpam-3506	405	6	g+h	g+h	NOUN
ejpam-3506	405	7	)	)	PUNCT
ejpam-3506	405	8	be	be	AUX
ejpam-3506	405	9	an	an	DET
ejpam-3506	405	10	nckfd	nckfd	NOUN
ejpam-3506	405	11	-	-	PUNCT
ejpam-3506	405	12	set	set	NOUN
ejpam-3506	405	13	in	in	ADP
ejpam-3506	405	14	g+h	g+h	PROPN
ejpam-3506	405	15	.	.	PUNCT
ejpam-3506	406	1	then	then	ADV
ejpam-3506	406	2	by	by	ADP
ejpam-3506	406	3	definition	definition	NOUN
ejpam-3506	406	4	,	,	PUNCT
ejpam-3506	406	5	s	s	PART
ejpam-3506	406	6	is	be	AUX
ejpam-3506	406	7	a	a	DET
ejpam-3506	406	8	kfd	kfd	NOUN
ejpam-3506	406	9	-	-	PUNCT
ejpam-3506	406	10	set	set	NOUN
ejpam-3506	406	11	in	in	ADP
ejpam-3506	406	12	g+h	g+h	PROPN
ejpam-3506	406	13	.	.	PUNCT
ejpam-3506	407	1	for	for	ADP
ejpam-3506	407	2	the	the	DET
ejpam-3506	407	3	converse	converse	NOUN
ejpam-3506	407	4	,	,	PUNCT
ejpam-3506	407	5	suppose	suppose	VERB
ejpam-3506	407	6	s	s	VERB
ejpam-3506	407	7	⊆	⊆	NUM
ejpam-3506	407	8	v	v	NOUN
ejpam-3506	407	9	(	(	PUNCT
ejpam-3506	407	10	g+h	g+h	PROPN
ejpam-3506	407	11	)	)	PUNCT
ejpam-3506	407	12	is	be	AUX
ejpam-3506	407	13	a	a	DET
ejpam-3506	407	14	kfd	kfd	NOUN
ejpam-3506	407	15	-	-	PUNCT
ejpam-3506	407	16	set	set	NOUN
ejpam-3506	407	17	in	in	ADP
ejpam-3506	407	18	g+h	g+h	PROPN
ejpam-3506	407	19	.	.	PUNCT
ejpam-3506	408	1	then	then	ADV
ejpam-3506	408	2	at	at	ADV
ejpam-3506	408	3	least	least	ADJ
ejpam-3506	408	4	one	one	NUM
ejpam-3506	408	5	of	of	ADP
ejpam-3506	408	6	statements	statement	NOUN
ejpam-3506	408	7	(	(	PUNCT
ejpam-3506	408	8	a	a	NOUN
ejpam-3506	408	9	)	)	PUNCT
ejpam-3506	408	10	to	to	ADP
ejpam-3506	408	11	(	(	PUNCT
ejpam-3506	408	12	f	f	X
ejpam-3506	408	13	)	)	PUNCT
ejpam-3506	408	14	of	of	ADP
ejpam-3506	408	15	theorem	theorem	ADJ
ejpam-3506	408	16	8	8	NUM
ejpam-3506	408	17	holds	hold	NOUN
ejpam-3506	408	18	.	.	PUNCT
ejpam-3506	409	1	we	we	PRON
ejpam-3506	409	2	claim	claim	VERB
ejpam-3506	409	3	that	that	SCONJ
ejpam-3506	409	4	〈	〈	PROPN
ejpam-3506	409	5	n(s	n(s	NOUN
ejpam-3506	409	6	)	)	PUNCT
ejpam-3506	409	7	〉	〉	PROPN
ejpam-3506	409	8	is	be	AUX
ejpam-3506	409	9	connected	connect	VERB
ejpam-3506	409	10	.	.	PUNCT
ejpam-3506	410	1	if	if	SCONJ
ejpam-3506	410	2	statement	statement	NOUN
ejpam-3506	410	3	(	(	PUNCT
ejpam-3506	410	4	a	a	NOUN
ejpam-3506	410	5	)	)	PUNCT
ejpam-3506	410	6	holds	hold	NOUN
ejpam-3506	410	7	,	,	PUNCT
ejpam-3506	410	8	that	that	ADV
ejpam-3506	410	9	is	be	AUX
ejpam-3506	410	10	,	,	PUNCT
ejpam-3506	410	11	s	s	PART
ejpam-3506	410	12	=	=	SYM
ejpam-3506	410	13	v	v	NOUN
ejpam-3506	410	14	(	(	PUNCT
ejpam-3506	410	15	g	g	PROPN
ejpam-3506	410	16	+	+	NOUN
ejpam-3506	410	17	h	h	NOUN
ejpam-3506	410	18	)	)	PUNCT
ejpam-3506	410	19	,	,	PUNCT
ejpam-3506	410	20	then	then	ADV
ejpam-3506	410	21	we	we	PRON
ejpam-3506	410	22	are	be	AUX
ejpam-3506	410	23	done	do	VERB
ejpam-3506	410	24	.	.	PUNCT
ejpam-3506	411	1	suppose	suppose	VERB
ejpam-3506	411	2	statement	statement	NOUN
ejpam-3506	411	3	(	(	PUNCT
ejpam-3506	411	4	b	b	NOUN
ejpam-3506	411	5	)	)	PUNCT
ejpam-3506	411	6	holds	hold	VERB
ejpam-3506	411	7	;	;	PUNCT
ejpam-3506	412	1	that	that	PRON
ejpam-3506	412	2	is	be	AUX
ejpam-3506	412	3	,	,	PUNCT
ejpam-3506	412	4	s	s	VERB
ejpam-3506	412	5	⊆	⊆	NUM
ejpam-3506	412	6	v	v	NOUN
ejpam-3506	412	7	(	(	PUNCT
ejpam-3506	412	8	g	g	NOUN
ejpam-3506	412	9	)	)	PUNCT
ejpam-3506	412	10	,	,	PUNCT
ejpam-3506	412	11	|s|	|s|	PROPN
ejpam-3506	412	12	=	=	SYM
ejpam-3506	412	13	k	k	PROPN
ejpam-3506	412	14	and	and	CCONJ
ejpam-3506	412	15	s	s	PROPN
ejpam-3506	412	16	is	be	AUX
ejpam-3506	412	17	a	a	DET
ejpam-3506	412	18	kfd	kfd	NOUN
ejpam-3506	412	19	-	-	PUNCT
ejpam-3506	412	20	set	set	NOUN
ejpam-3506	412	21	of	of	ADP
ejpam-3506	412	22	g.	g.	PROPN
ejpam-3506	412	23	then	then	ADV
ejpam-3506	412	24	〈	〈	PROPN
ejpam-3506	412	25	ng+h(s	ng+h(s	PROPN
ejpam-3506	412	26	)	)	PUNCT
ejpam-3506	412	27	〉	〉	NOUN
ejpam-3506	412	28	=	=	SYM
ejpam-3506	412	29	〈	〈	PROPN
ejpam-3506	412	30	ng(s	ng(s	NUM
ejpam-3506	412	31	)	)	PUNCT
ejpam-3506	412	32	〉	〉	PROPN
ejpam-3506	413	1	+	+	CCONJ
ejpam-3506	413	2	h	h	NOUN
ejpam-3506	413	3	,	,	PUNCT
ejpam-3506	413	4	which	which	PRON
ejpam-3506	413	5	is	be	AUX
ejpam-3506	413	6	connected	connect	VERB
ejpam-3506	413	7	.	.	PUNCT
ejpam-3506	414	1	similarly	similarly	ADV
ejpam-3506	414	2	,	,	PUNCT
ejpam-3506	414	3	if	if	SCONJ
ejpam-3506	414	4	statement	statement	NOUN
ejpam-3506	414	5	(	(	PUNCT
ejpam-3506	414	6	c	c	NOUN
ejpam-3506	414	7	)	)	PUNCT
ejpam-3506	414	8	holds	hold	NOUN
ejpam-3506	414	9	,	,	PUNCT
ejpam-3506	414	10	then	then	ADV
ejpam-3506	414	11	〈	〈	PROPN
ejpam-3506	414	12	ng+h(s	ng+h(s	PROPN
ejpam-3506	414	13	)	)	PUNCT
ejpam-3506	414	14	〉	〉	NOUN
ejpam-3506	414	15	=	=	SYM
ejpam-3506	414	16	g+	g+	X
ejpam-3506	414	17	〈	〈	NOUN
ejpam-3506	414	18	nh(s	nh(	NOUN
ejpam-3506	414	19	)	)	PUNCT
ejpam-3506	414	20	〉	〉	PROPN
ejpam-3506	414	21	is	be	AUX
ejpam-3506	414	22	connected	connect	VERB
ejpam-3506	414	23	.	.	PUNCT
ejpam-3506	415	1	suppose	suppose	VERB
ejpam-3506	415	2	statement	statement	NOUN
ejpam-3506	415	3	(	(	PUNCT
ejpam-3506	415	4	d	d	NOUN
ejpam-3506	415	5	)	)	PUNCT
ejpam-3506	415	6	holds	hold	VERB
ejpam-3506	415	7	;	;	PUNCT
ejpam-3506	415	8	that	that	PRON
ejpam-3506	415	9	is	be	AUX
ejpam-3506	415	10	,	,	PUNCT
ejpam-3506	415	11	s	s	PART
ejpam-3506	415	12	=	=	PUNCT
ejpam-3506	415	13	sg∪sh	sg∪sh	PROPN
ejpam-3506	415	14	,	,	PUNCT
ejpam-3506	415	15	where	where	SCONJ
ejpam-3506	415	16	sg	sg	PROPN
ejpam-3506	415	17	is	be	AUX
ejpam-3506	415	18	a	a	DET
ejpam-3506	415	19	(	(	PUNCT
ejpam-3506	415	20	k−|sh	k−|sh	VERB
ejpam-3506	415	21	|)fdset	|)fdset	VERB
ejpam-3506	415	22	in	in	ADP
ejpam-3506	415	23	g	g	PROPN
ejpam-3506	415	24	and	and	CCONJ
ejpam-3506	415	25	sh	sh	PROPN
ejpam-3506	415	26	is	be	AUX
ejpam-3506	415	27	a	a	DET
ejpam-3506	415	28	(	(	PUNCT
ejpam-3506	415	29	k−	k−	NOUN
ejpam-3506	415	30	|sg|)fd	|sg|)fd	PROPN
ejpam-3506	415	31	-	-	PUNCT
ejpam-3506	415	32	set	set	NOUN
ejpam-3506	415	33	in	in	ADP
ejpam-3506	415	34	h.	h.	PROPN
ejpam-3506	415	35	then	then	ADV
ejpam-3506	415	36	ng+h(s	ng+h(s	NUM
ejpam-3506	415	37	)	)	PUNCT
ejpam-3506	415	38	=	=	SYM
ejpam-3506	415	39	ng+h(sg)∪ng+h(sh	ng+h(sg)∪ng+h(sh	ADV
ejpam-3506	415	40	)	)	PUNCT
ejpam-3506	415	41	=	=	PUNCT
ejpam-3506	416	1	[	[	X
ejpam-3506	416	2	ng(sg	ng(sg	PROPN
ejpam-3506	416	3	)	)	PUNCT
ejpam-3506	416	4	∪	∪	ADP
ejpam-3506	416	5	v	v	NOUN
ejpam-3506	416	6	(	(	PUNCT
ejpam-3506	416	7	h)]∪	h)]∪	PROPN
ejpam-3506	416	8	[	[	X
ejpam-3506	416	9	nh(sh	nh(sh	PROPN
ejpam-3506	416	10	)	)	PUNCT
ejpam-3506	416	11	∪	∪	ADP
ejpam-3506	416	12	v	v	NOUN
ejpam-3506	416	13	(	(	PUNCT
ejpam-3506	416	14	g	g	NOUN
ejpam-3506	416	15	)	)	PUNCT
ejpam-3506	416	16	]	]	PUNCT
ejpam-3506	416	17	=	=	SYM
ejpam-3506	416	18	v	v	X
ejpam-3506	416	19	(	(	PUNCT
ejpam-3506	416	20	g	g	PROPN
ejpam-3506	416	21	+	+	NOUN
ejpam-3506	416	22	h	h	NOUN
ejpam-3506	416	23	)	)	PUNCT
ejpam-3506	416	24	.	.	PUNCT
ejpam-3506	417	1	hence	hence	ADV
ejpam-3506	417	2	,	,	PUNCT
ejpam-3506	417	3	〈	〈	PROPN
ejpam-3506	417	4	ng+h(s	ng+h(s	PROPN
ejpam-3506	417	5	)	)	PUNCT
ejpam-3506	417	6	〉	〉	NOUN
ejpam-3506	417	7	=	=	SYM
ejpam-3506	417	8	g	g	PROPN
ejpam-3506	417	9	+	+	NOUN
ejpam-3506	417	10	h	h	NOUN
ejpam-3506	417	11	is	be	AUX
ejpam-3506	417	12	connected	connect	VERB
ejpam-3506	417	13	.	.	PUNCT
ejpam-3506	418	1	suppose	suppose	VERB
ejpam-3506	418	2	statement	statement	NOUN
ejpam-3506	418	3	(	(	PUNCT
ejpam-3506	418	4	e	e	NOUN
ejpam-3506	418	5	)	)	PUNCT
ejpam-3506	418	6	holds	hold	VERB
ejpam-3506	418	7	;	;	PUNCT
ejpam-3506	418	8	that	that	PRON
ejpam-3506	418	9	is	be	AUX
ejpam-3506	418	10	,	,	PUNCT
ejpam-3506	418	11	s	s	PART
ejpam-3506	418	12	=	=	SYM
ejpam-3506	418	13	v	v	X
ejpam-3506	418	14	(	(	PUNCT
ejpam-3506	418	15	g	g	NOUN
ejpam-3506	418	16	)	)	PUNCT
ejpam-3506	418	17	∪	∪	ADP
ejpam-3506	418	18	t	t	PROPN
ejpam-3506	418	19	,	,	PUNCT
ejpam-3506	418	20	where	where	SCONJ
ejpam-3506	418	21	|v	|v	PROPN
ejpam-3506	418	22	(	(	PUNCT
ejpam-3506	418	23	g)|	g)|	NOUN
ejpam-3506	418	24	=	=	NOUN
ejpam-3506	418	25	m	m	PROPN
ejpam-3506	418	26	<	<	X
ejpam-3506	418	27	k	k	X
ejpam-3506	418	28	and	and	CCONJ
ejpam-3506	418	29	t	t	PROPN
ejpam-3506	418	30	is	be	AUX
ejpam-3506	418	31	a	a	DET
ejpam-3506	418	32	(	(	PUNCT
ejpam-3506	418	33	k−m)fd	k−m)fd	PROPN
ejpam-3506	418	34	-	-	PUNCT
ejpam-3506	418	35	set	set	NOUN
ejpam-3506	418	36	in	in	ADP
ejpam-3506	418	37	h.	h.	PROPN
ejpam-3506	418	38	then	then	ADV
ejpam-3506	418	39	ng+h(s	ng+h(s	NUM
ejpam-3506	418	40	)	)	PUNCT
ejpam-3506	419	1	=	=	SYM
ejpam-3506	419	2	ng+h(v	ng+h(v	ADV
ejpam-3506	419	3	(	(	PUNCT
ejpam-3506	419	4	g))∪ng+h(t	g))∪ng+h(t	VERB
ejpam-3506	419	5	)	)	PUNCT
ejpam-3506	419	6	=	=	SYM
ejpam-3506	419	7	v	v	X
ejpam-3506	419	8	(	(	PUNCT
ejpam-3506	419	9	h)∪	h)∪	NOUN
ejpam-3506	420	1	[	[	X
ejpam-3506	420	2	v	v	X
ejpam-3506	420	3	(	(	PUNCT
ejpam-3506	420	4	g)∪	g)∪	VERB
ejpam-3506	420	5	nh(t	nh(t	NUM
ejpam-3506	420	6	)	)	PUNCT
ejpam-3506	420	7	]	]	PUNCT
ejpam-3506	421	1	=	=	SYM
ejpam-3506	421	2	v	v	X
ejpam-3506	421	3	(	(	PUNCT
ejpam-3506	421	4	g)∪v	g)∪v	NOUN
ejpam-3506	421	5	(	(	PUNCT
ejpam-3506	421	6	h	h	NOUN
ejpam-3506	421	7	)	)	PUNCT
ejpam-3506	421	8	.	.	PUNCT
ejpam-3506	422	1	thus	thus	ADV
ejpam-3506	422	2	,	,	PUNCT
ejpam-3506	422	3	〈	〈	PROPN
ejpam-3506	422	4	ng+h(s	ng+h(s	PROPN
ejpam-3506	422	5	)	)	PUNCT
ejpam-3506	422	6	〉	〉	PROPN
ejpam-3506	422	7	=	=	SYM
ejpam-3506	422	8	g+h	g+h	PROPN
ejpam-3506	422	9	is	be	AUX
ejpam-3506	422	10	connected	connect	VERB
ejpam-3506	422	11	.	.	PUNCT
ejpam-3506	423	1	similarly	similarly	ADV
ejpam-3506	423	2	,	,	PUNCT
ejpam-3506	423	3	if	if	SCONJ
ejpam-3506	423	4	statement	statement	NOUN
ejpam-3506	423	5	(	(	PUNCT
ejpam-3506	423	6	f	f	X
ejpam-3506	423	7	)	)	PUNCT
ejpam-3506	423	8	holds	hold	VERB
ejpam-3506	423	9	,	,	PUNCT
ejpam-3506	423	10	that	that	ADV
ejpam-3506	423	11	is	be	AUX
ejpam-3506	423	12	,	,	PUNCT
ejpam-3506	423	13	s	s	PART
ejpam-3506	423	14	=	=	X
ejpam-3506	423	15	d	d	X
ejpam-3506	423	16	∪	∪	X
ejpam-3506	423	17	v	v	NOUN
ejpam-3506	423	18	(	(	PUNCT
ejpam-3506	423	19	h	h	NOUN
ejpam-3506	423	20	)	)	PUNCT
ejpam-3506	423	21	,	,	PUNCT
ejpam-3506	423	22	where	where	SCONJ
ejpam-3506	423	23	|v	|v	PROPN
ejpam-3506	423	24	(	(	PUNCT
ejpam-3506	423	25	h)|	h)|	NOUN
ejpam-3506	423	26	=	=	SYM
ejpam-3506	423	27	n	n	CCONJ
ejpam-3506	423	28	<	<	X
ejpam-3506	423	29	k	k	PROPN
ejpam-3506	423	30	and	and	CCONJ
ejpam-3506	423	31	d	d	PROPN
ejpam-3506	423	32	is	be	AUX
ejpam-3506	423	33	a	a	DET
ejpam-3506	423	34	(	(	PUNCT
ejpam-3506	423	35	k	k	PROPN
ejpam-3506	423	36	−	−	PROPN
ejpam-3506	423	37	n)fd	n)fd	PROPN
ejpam-3506	423	38	-	-	PUNCT
ejpam-3506	423	39	set	set	NOUN
ejpam-3506	423	40	in	in	ADP
ejpam-3506	423	41	g	g	NOUN
ejpam-3506	423	42	,	,	PUNCT
ejpam-3506	423	43	then	then	ADV
ejpam-3506	423	44	〈	〈	PROPN
ejpam-3506	423	45	ng+h(s	ng+h(s	PROPN
ejpam-3506	423	46	)	)	PUNCT
ejpam-3506	423	47	〉	〉	PROPN
ejpam-3506	423	48	=	=	SYM
ejpam-3506	423	49	g+h	g+h	PROPN
ejpam-3506	423	50	is	be	AUX
ejpam-3506	423	51	connected	connect	VERB
ejpam-3506	423	52	.	.	PUNCT
ejpam-3506	424	1	therefore	therefore	ADV
ejpam-3506	424	2	,	,	PUNCT
ejpam-3506	424	3	s	s	VERB
ejpam-3506	424	4	is	be	AUX
ejpam-3506	424	5	an	an	DET
ejpam-3506	424	6	nckfd	nckfd	NOUN
ejpam-3506	424	7	-	-	PUNCT
ejpam-3506	424	8	set	set	NOUN
ejpam-3506	424	9	in	in	ADP
ejpam-3506	424	10	g+h	g+h	PROPN
ejpam-3506	424	11	.	.	PUNCT
ejpam-3506	425	1	�	�	PROPN
ejpam-3506	425	2	the	the	DET
ejpam-3506	425	3	next	next	ADJ
ejpam-3506	425	4	result	result	NOUN
ejpam-3506	425	5	immediately	immediately	ADV
ejpam-3506	425	6	follows	follow	VERB
ejpam-3506	425	7	from	from	ADP
ejpam-3506	425	8	theorem	theorem	ADJ
ejpam-3506	425	9	11	11	NUM
ejpam-3506	425	10	.	.	PUNCT
ejpam-3506	426	1	corollary	corollary	ADJ
ejpam-3506	426	2	5	5	NUM
ejpam-3506	426	3	.	.	PUNCT
ejpam-3506	427	1	let	let	VERB
ejpam-3506	427	2	g	g	NOUN
ejpam-3506	427	3	and	and	CCONJ
ejpam-3506	427	4	h	h	NOUN
ejpam-3506	427	5	be	be	AUX
ejpam-3506	427	6	nontrivial	nontrivial	ADJ
ejpam-3506	427	7	connected	connect	VERB
ejpam-3506	427	8	graphs	graph	NOUN
ejpam-3506	427	9	of	of	ADP
ejpam-3506	427	10	orders	order	NOUN
ejpam-3506	427	11	m	m	VERB
ejpam-3506	427	12	and	and	CCONJ
ejpam-3506	427	13	n	n	CCONJ
ejpam-3506	427	14	,	,	PUNCT
ejpam-3506	427	15	respectively	respectively	ADV
ejpam-3506	427	16	,	,	PUNCT
ejpam-3506	427	17	and	and	CCONJ
ejpam-3506	427	18	k	k	X
ejpam-3506	427	19	a	a	DET
ejpam-3506	427	20	positive	positive	ADJ
ejpam-3506	427	21	integer	integer	NOUN
ejpam-3506	427	22	with	with	ADP
ejpam-3506	427	23	1	1	NUM
ejpam-3506	427	24	≤	≤	NUM
ejpam-3506	427	25	k	k	NOUN
ejpam-3506	427	26	≤	≤	ADJ
ejpam-3506	427	27	max{m	max{m	NOUN
ejpam-3506	427	28	,	,	PUNCT
ejpam-3506	427	29	n	n	CCONJ
ejpam-3506	427	30	}	}	PUNCT
ejpam-3506	427	31	.	.	PUNCT
ejpam-3506	428	1	then	then	ADV
ejpam-3506	428	2	,	,	PUNCT
ejpam-3506	428	3	γnckfd(g	γnckfd(g	NOUN
ejpam-3506	428	4	+	+	CCONJ
ejpam-3506	428	5	h	h	NOUN
ejpam-3506	428	6	)	)	PUNCT
ejpam-3506	428	7	=	=	PUNCT
ejpam-3506	428	8	γkfd(g	γkfd(g	ADP
ejpam-3506	428	9	+	+	NUM
ejpam-3506	428	10	h	h	NOUN
ejpam-3506	428	11	)	)	PUNCT
ejpam-3506	428	12	.	.	PUNCT
ejpam-3506	429	1	in	in	ADP
ejpam-3506	429	2	particular	particular	ADJ
ejpam-3506	429	3	,	,	PUNCT
ejpam-3506	429	4	if	if	SCONJ
ejpam-3506	429	5	g	g	PROPN
ejpam-3506	429	6	or	or	CCONJ
ejpam-3506	429	7	h	h	NOUN
ejpam-3506	429	8	has	have	VERB
ejpam-3506	429	9	a	a	DET
ejpam-3506	429	10	kfd	kfd	NOUN
ejpam-3506	429	11	-	-	PUNCT
ejpam-3506	429	12	set	set	NOUN
ejpam-3506	429	13	s	s	NOUN
ejpam-3506	429	14	with	with	ADP
ejpam-3506	429	15	|s|	|s|	PROPN
ejpam-3506	429	16	=	=	SYM
ejpam-3506	429	17	k	k	PROPN
ejpam-3506	429	18	,	,	PUNCT
ejpam-3506	429	19	then	then	ADV
ejpam-3506	429	20	γnckfd(g+h	γnckfd(g+h	NOUN
ejpam-3506	429	21	)	)	PUNCT
ejpam-3506	430	1	=	=	PUNCT
ejpam-3506	430	2	k.	k.	PROPN
ejpam-3506	430	3	w.	w.	PROPN
ejpam-3506	430	4	bent	bent	PROPN
ejpam-3506	430	5	-	-	PUNCT
ejpam-3506	430	6	usman	usman	PROPN
ejpam-3506	430	7	,	,	PUNCT
ejpam-3506	430	8	r.	r.	PROPN
ejpam-3506	430	9	isla	isla	PROPN
ejpam-3506	430	10	,	,	PUNCT
ejpam-3506	430	11	s.	s.	PROPN
ejpam-3506	430	12	canoy	canoy	PROPN
ejpam-3506	430	13	/	/	SYM
ejpam-3506	430	14	eur	eur	PROPN
ejpam-3506	430	15	.	.	PUNCT
ejpam-3506	431	1	j.	j.	PROPN
ejpam-3506	431	2	pure	pure	PROPN
ejpam-3506	431	3	appl	appl	PROPN
ejpam-3506	431	4	.	.	PROPN
ejpam-3506	431	5	math	math	PROPN
ejpam-3506	431	6	,	,	PUNCT
ejpam-3506	431	7	12	12	NUM
ejpam-3506	431	8	(	(	PUNCT
ejpam-3506	431	9	3	3	NUM
ejpam-3506	431	10	)	)	PUNCT
ejpam-3506	431	11	(	(	PUNCT
ejpam-3506	431	12	2019	2019	NUM
ejpam-3506	431	13	)	)	PUNCT
ejpam-3506	431	14	,	,	PUNCT
ejpam-3506	431	15	1337	1337	NUM
ejpam-3506	431	16	-	-	SYM
ejpam-3506	431	17	1349	1349	NUM
ejpam-3506	431	18	1345	1345	NUM
ejpam-3506	431	19	4	4	NUM
ejpam-3506	431	20	.	.	PUNCT
ejpam-3506	432	1	neighborhood	neighborhood	NOUN
ejpam-3506	432	2	connected	connect	VERB
ejpam-3506	432	3	k	k	ADJ
ejpam-3506	432	4	-	-	PUNCT
ejpam-3506	432	5	fair	fair	ADJ
ejpam-3506	432	6	domination	domination	NOUN
ejpam-3506	432	7	in	in	ADP
ejpam-3506	432	8	the	the	DET
ejpam-3506	432	9	corona	corona	NOUN
ejpam-3506	432	10	of	of	ADP
ejpam-3506	432	11	graphs	graph	NOUN
ejpam-3506	432	12	the	the	DET
ejpam-3506	432	13	corona	corona	NOUN
ejpam-3506	432	14	of	of	ADP
ejpam-3506	432	15	two	two	NUM
ejpam-3506	432	16	graphs	graph	NOUN
ejpam-3506	432	17	g	g	NOUN
ejpam-3506	432	18	and	and	CCONJ
ejpam-3506	432	19	h	h	NOUN
ejpam-3506	432	20	,	,	PUNCT
ejpam-3506	432	21	denoted	denote	VERB
ejpam-3506	432	22	by	by	ADP
ejpam-3506	432	23	g	g	PROPN
ejpam-3506	432	24	◦	◦	NOUN
ejpam-3506	432	25	h	h	NOUN
ejpam-3506	432	26	,	,	PUNCT
ejpam-3506	432	27	is	be	AUX
ejpam-3506	432	28	the	the	DET
ejpam-3506	432	29	graph	graph	NOUN
ejpam-3506	432	30	obtained	obtain	VERB
ejpam-3506	432	31	by	by	ADP
ejpam-3506	432	32	taking	take	VERB
ejpam-3506	432	33	one	one	NUM
ejpam-3506	432	34	copy	copy	NOUN
ejpam-3506	432	35	of	of	ADP
ejpam-3506	432	36	g	g	NOUN
ejpam-3506	432	37	of	of	ADP
ejpam-3506	432	38	order	order	NOUN
ejpam-3506	432	39	n	n	NOUN
ejpam-3506	432	40	and	and	CCONJ
ejpam-3506	432	41	n	n	PRON
ejpam-3506	432	42	copies	copy	NOUN
ejpam-3506	432	43	of	of	ADP
ejpam-3506	432	44	h	h	NOUN
ejpam-3506	432	45	,	,	PUNCT
ejpam-3506	432	46	and	and	CCONJ
ejpam-3506	432	47	then	then	ADV
ejpam-3506	432	48	joining	join	VERB
ejpam-3506	432	49	the	the	DET
ejpam-3506	432	50	i	i	PROPN
ejpam-3506	432	51	-	-	PUNCT
ejpam-3506	432	52	th	th	X
ejpam-3506	432	53	vertex	vertex	NOUN
ejpam-3506	432	54	of	of	ADP
ejpam-3506	432	55	g	g	NOUN
ejpam-3506	432	56	to	to	ADP
ejpam-3506	432	57	every	every	DET
ejpam-3506	432	58	vertex	vertex	NOUN
ejpam-3506	432	59	in	in	ADP
ejpam-3506	432	60	the	the	DET
ejpam-3506	432	61	i	i	PROPN
ejpam-3506	432	62	-	-	PUNCT
ejpam-3506	432	63	th	th	PROPN
ejpam-3506	432	64	copy	copy	NOUN
ejpam-3506	432	65	of	of	ADP
ejpam-3506	432	66	h.	h.	PROPN
ejpam-3506	432	67	for	for	ADP
ejpam-3506	432	68	every	every	DET
ejpam-3506	432	69	v	v	NUM
ejpam-3506	432	70	∈	∈	PROPN
ejpam-3506	432	71	v	v	NOUN
ejpam-3506	432	72	(	(	PUNCT
ejpam-3506	432	73	g	g	NOUN
ejpam-3506	432	74	)	)	PUNCT
ejpam-3506	432	75	,	,	PUNCT
ejpam-3506	432	76	we	we	PRON
ejpam-3506	432	77	denote	denote	VERB
ejpam-3506	432	78	by	by	ADP
ejpam-3506	432	79	hv	hv	PROPN
ejpam-3506	432	80	the	the	DET
ejpam-3506	432	81	copy	copy	NOUN
ejpam-3506	432	82	of	of	ADP
ejpam-3506	432	83	h	h	NOUN
ejpam-3506	432	84	whose	whose	DET
ejpam-3506	432	85	vertices	vertex	NOUN
ejpam-3506	432	86	are	be	AUX
ejpam-3506	432	87	joined	join	VERB
ejpam-3506	432	88	or	or	CCONJ
ejpam-3506	432	89	attached	attach	VERB
ejpam-3506	432	90	to	to	ADP
ejpam-3506	432	91	the	the	DET
ejpam-3506	432	92	vertex	vertex	NOUN
ejpam-3506	432	93	v.	v.	CCONJ
ejpam-3506	432	94	for	for	ADP
ejpam-3506	432	95	each	each	DET
ejpam-3506	432	96	v	v	NUM
ejpam-3506	432	97	∈	∈	PROPN
ejpam-3506	432	98	v	v	NOUN
ejpam-3506	432	99	(	(	PUNCT
ejpam-3506	432	100	g	g	NOUN
ejpam-3506	432	101	)	)	PUNCT
ejpam-3506	432	102	,	,	PUNCT
ejpam-3506	432	103	the	the	DET
ejpam-3506	432	104	subgraph	subgraph	PROPN
ejpam-3506	432	105	〈	〈	PROPN
ejpam-3506	432	106	v〉+hv	v〉+hv	NOUN
ejpam-3506	432	107	of	of	ADP
ejpam-3506	432	108	g	g	PROPN
ejpam-3506	432	109	◦	◦	NOUN
ejpam-3506	432	110	h	h	NOUN
ejpam-3506	432	111	will	will	AUX
ejpam-3506	432	112	be	be	AUX
ejpam-3506	432	113	denoted	denote	VERB
ejpam-3506	432	114	by	by	ADP
ejpam-3506	432	115	v	v	DET
ejpam-3506	432	116	+	+	PROPN
ejpam-3506	432	117	hv	hv	PROPN
ejpam-3506	432	118	.	.	PUNCT
ejpam-3506	432	119	theorem	theorem	PROPN
ejpam-3506	432	120	12	12	NUM
ejpam-3506	432	121	.	.	PUNCT
ejpam-3506	433	1	let	let	VERB
ejpam-3506	433	2	g	g	NOUN
ejpam-3506	433	3	and	and	CCONJ
ejpam-3506	433	4	h	h	NOUN
ejpam-3506	433	5	be	be	AUX
ejpam-3506	433	6	nontrivial	nontrivial	ADJ
ejpam-3506	433	7	connected	connected	ADJ
ejpam-3506	433	8	graphs	graph	NOUN
ejpam-3506	433	9	,	,	PUNCT
ejpam-3506	433	10	and	and	CCONJ
ejpam-3506	433	11	let	let	VERB
ejpam-3506	433	12	k	k	PRON
ejpam-3506	433	13	be	be	AUX
ejpam-3506	433	14	a	a	DET
ejpam-3506	433	15	positive	positive	ADJ
ejpam-3506	433	16	integer	integer	NOUN
ejpam-3506	433	17	with	with	ADP
ejpam-3506	433	18	2	2	NUM
ejpam-3506	433	19	≤	≤	NOUN
ejpam-3506	433	20	k	k	PROPN
ejpam-3506	433	21	≤	≤	PROPN
ejpam-3506	433	22	|v	|v	X
ejpam-3506	433	23	(	(	PUNCT
ejpam-3506	433	24	h)|	h)|	PROPN
ejpam-3506	433	25	.	.	PUNCT
ejpam-3506	434	1	then	then	ADV
ejpam-3506	434	2	c	c	PROPN
ejpam-3506	434	3	⊆	⊆	NUM
ejpam-3506	434	4	v	v	NOUN
ejpam-3506	434	5	(	(	PUNCT
ejpam-3506	434	6	g	g	PROPN
ejpam-3506	434	7	◦	◦	NOUN
ejpam-3506	434	8	h	h	NOUN
ejpam-3506	434	9	)	)	PUNCT
ejpam-3506	434	10	is	be	AUX
ejpam-3506	434	11	an	an	DET
ejpam-3506	434	12	nckfd	nckfd	NOUN
ejpam-3506	434	13	-	-	PUNCT
ejpam-3506	434	14	set	set	NOUN
ejpam-3506	434	15	in	in	ADP
ejpam-3506	434	16	g	g	PROPN
ejpam-3506	434	17	◦	◦	NOUN
ejpam-3506	434	18	h	h	NOUN
ejpam-3506	434	19	if	if	SCONJ
ejpam-3506	435	1	and	and	CCONJ
ejpam-3506	435	2	only	only	ADV
ejpam-3506	435	3	if	if	SCONJ
ejpam-3506	435	4	c	c	PROPN
ejpam-3506	435	5	is	be	AUX
ejpam-3506	435	6	a	a	DET
ejpam-3506	435	7	kfd	kfd	NOUN
ejpam-3506	435	8	-	-	PUNCT
ejpam-3506	435	9	set	set	NOUN
ejpam-3506	435	10	in	in	ADP
ejpam-3506	435	11	g	g	PROPN
ejpam-3506	435	12	◦	◦	NOUN
ejpam-3506	435	13	h.	h.	NOUN
ejpam-3506	435	14	proof	proof	NOUN
ejpam-3506	435	15	.	.	PUNCT
ejpam-3506	436	1	if	if	SCONJ
ejpam-3506	436	2	c	c	PROPN
ejpam-3506	436	3	is	be	AUX
ejpam-3506	436	4	an	an	DET
ejpam-3506	436	5	nckfd	nckfd	NOUN
ejpam-3506	436	6	-	-	PUNCT
ejpam-3506	436	7	set	set	NOUN
ejpam-3506	436	8	in	in	ADP
ejpam-3506	436	9	g	g	PROPN
ejpam-3506	436	10	◦	◦	NOUN
ejpam-3506	436	11	h	h	NOUN
ejpam-3506	436	12	,	,	PUNCT
ejpam-3506	436	13	then	then	ADV
ejpam-3506	436	14	c	c	PROPN
ejpam-3506	436	15	is	be	AUX
ejpam-3506	436	16	a	a	DET
ejpam-3506	436	17	kfd	kfd	NOUN
ejpam-3506	436	18	-	-	PUNCT
ejpam-3506	436	19	set	set	NOUN
ejpam-3506	436	20	in	in	ADP
ejpam-3506	436	21	g	g	PROPN
ejpam-3506	436	22	◦	◦	NOUN
ejpam-3506	436	23	h.	h.	NOUN
ejpam-3506	436	24	conversely	conversely	ADV
ejpam-3506	436	25	,	,	PUNCT
ejpam-3506	436	26	let	let	VERB
ejpam-3506	436	27	c	c	PRON
ejpam-3506	436	28	be	be	AUX
ejpam-3506	436	29	a	a	DET
ejpam-3506	436	30	kfd	kfd	NOUN
ejpam-3506	436	31	-	-	PUNCT
ejpam-3506	436	32	set	set	NOUN
ejpam-3506	436	33	in	in	ADP
ejpam-3506	436	34	g	g	PROPN
ejpam-3506	436	35	◦	◦	NOUN
ejpam-3506	436	36	h.	h.	NOUN
ejpam-3506	436	37	then	then	ADV
ejpam-3506	436	38	by	by	ADP
ejpam-3506	436	39	theorem	theorem	NOUN
ejpam-3506	436	40	9	9	NUM
ejpam-3506	436	41	,	,	PUNCT
ejpam-3506	436	42	(	(	PUNCT
ejpam-3506	436	43	a	a	X
ejpam-3506	436	44	)	)	PUNCT
ejpam-3506	437	1	c	c	NOUN
ejpam-3506	437	2	=	=	SYM
ejpam-3506	437	3	v	v	PROPN
ejpam-3506	437	4	(	(	PUNCT
ejpam-3506	437	5	g	g	NOUN
ejpam-3506	437	6	)	)	PUNCT
ejpam-3506	437	7	∪	∪	ADP
ejpam-3506	437	8	b	b	NOUN
ejpam-3506	437	9	,	,	PUNCT
ejpam-3506	437	10	where	where	SCONJ
ejpam-3506	437	11	b	b	NOUN
ejpam-3506	437	12	=	=	NOUN
ejpam-3506	437	13	∅	∅	NOUN
ejpam-3506	437	14	when	when	SCONJ
ejpam-3506	437	15	k	k	PROPN
ejpam-3506	437	16	=	=	SYM
ejpam-3506	437	17	1	1	NUM
ejpam-3506	437	18	and	and	CCONJ
ejpam-3506	437	19	b	b	NOUN
ejpam-3506	437	20	=	=	PUNCT
ejpam-3506	437	21	⋃	⋃	NOUN
ejpam-3506	437	22	v∈v	v∈v	NOUN
ejpam-3506	437	23	(	(	PUNCT
ejpam-3506	437	24	g	g	NOUN
ejpam-3506	437	25	)	)	PUNCT
ejpam-3506	437	26	sv	sv	NOUN
ejpam-3506	437	27	,	,	PUNCT
ejpam-3506	437	28	where	where	SCONJ
ejpam-3506	437	29	each	each	PRON
ejpam-3506	437	30	sv	sv	PROPN
ejpam-3506	437	31	is	be	AUX
ejpam-3506	437	32	a	a	DET
ejpam-3506	437	33	(	(	PUNCT
ejpam-3506	437	34	k	k	PROPN
ejpam-3506	437	35	−	−	PROPN
ejpam-3506	437	36	1)fd	1)fd	PROPN
ejpam-3506	437	37	-	-	PUNCT
ejpam-3506	437	38	set	set	NOUN
ejpam-3506	437	39	of	of	ADP
ejpam-3506	437	40	hv	hv	PROPN
ejpam-3506	437	41	when	when	SCONJ
ejpam-3506	437	42	k	k	PROPN
ejpam-3506	437	43	≥	≥	PROPN
ejpam-3506	437	44	2	2	NUM
ejpam-3506	437	45	,	,	PUNCT
ejpam-3506	437	46	or	or	CCONJ
ejpam-3506	437	47	(	(	PUNCT
ejpam-3506	437	48	b	b	NOUN
ejpam-3506	437	49	)	)	PUNCT
ejpam-3506	437	50	c	c	NOUN
ejpam-3506	437	51	=	=	PUNCT
ejpam-3506	437	52	⋃	⋃	NOUN
ejpam-3506	437	53	v∈v	v∈v	NOUN
ejpam-3506	437	54	(	(	PUNCT
ejpam-3506	437	55	g	g	NOUN
ejpam-3506	437	56	)	)	PUNCT
ejpam-3506	437	57	sv	sv	NOUN
ejpam-3506	437	58	,	,	PUNCT
ejpam-3506	437	59	where	where	SCONJ
ejpam-3506	437	60	each	each	PRON
ejpam-3506	437	61	sv	sv	PROPN
ejpam-3506	437	62	is	be	AUX
ejpam-3506	437	63	a	a	DET
ejpam-3506	437	64	kfd	kfd	NOUN
ejpam-3506	437	65	-	-	PUNCT
ejpam-3506	437	66	set	set	NOUN
ejpam-3506	437	67	of	of	ADP
ejpam-3506	437	68	hv	hv	PROPN
ejpam-3506	437	69	and	and	CCONJ
ejpam-3506	437	70	|sv|	|sv|	PROPN
ejpam-3506	437	71	=	=	PUNCT
ejpam-3506	438	1	k.	k.	NOUN
ejpam-3506	438	2	we	we	PRON
ejpam-3506	438	3	claim	claim	VERB
ejpam-3506	438	4	that	that	SCONJ
ejpam-3506	438	5	〈	〈	PROPN
ejpam-3506	438	6	n(c	n(c	NOUN
ejpam-3506	438	7	)	)	PUNCT
ejpam-3506	438	8	〉	〉	PROPN
ejpam-3506	438	9	is	be	AUX
ejpam-3506	438	10	connected	connect	VERB
ejpam-3506	438	11	.	.	PUNCT
ejpam-3506	439	1	suppose	suppose	VERB
ejpam-3506	439	2	condition	condition	NOUN
ejpam-3506	439	3	(	(	PUNCT
ejpam-3506	439	4	a	a	NOUN
ejpam-3506	439	5	)	)	PUNCT
ejpam-3506	439	6	holds	hold	NOUN
ejpam-3506	439	7	.	.	PUNCT
ejpam-3506	440	1	suppose	suppose	VERB
ejpam-3506	440	2	further	far	ADV
ejpam-3506	440	3	that	that	PRON
ejpam-3506	440	4	b	b	X
ejpam-3506	440	5	=	=	PUNCT
ejpam-3506	440	6	∅.	∅.	PROPN
ejpam-3506	440	7	then	then	ADV
ejpam-3506	440	8	c	c	PROPN
ejpam-3506	440	9	is	be	AUX
ejpam-3506	440	10	a	a	DET
ejpam-3506	440	11	1fd	1fd	ADV
ejpam-3506	440	12	-	-	PUNCT
ejpam-3506	440	13	set	set	VERB
ejpam-3506	440	14	and	and	CCONJ
ejpam-3506	440	15	〈	〈	NOUN
ejpam-3506	440	16	n(c	n(c	NOUN
ejpam-3506	440	17	)	)	PUNCT
ejpam-3506	440	18	〉	〉	NOUN
ejpam-3506	440	19	=	=	SYM
ejpam-3506	441	1	g	g	ADP
ejpam-3506	441	2	◦	◦	NOUN
ejpam-3506	441	3	h	h	NOUN
ejpam-3506	441	4	,	,	PUNCT
ejpam-3506	441	5	which	which	PRON
ejpam-3506	441	6	is	be	AUX
ejpam-3506	441	7	connected	connect	VERB
ejpam-3506	441	8	.	.	PUNCT
ejpam-3506	442	1	we	we	PRON
ejpam-3506	442	2	next	next	ADV
ejpam-3506	442	3	assume	assume	VERB
ejpam-3506	442	4	that	that	SCONJ
ejpam-3506	442	5	b	b	X
ejpam-3506	442	6	=	=	PUNCT
ejpam-3506	442	7	⋃	⋃	NOUN
ejpam-3506	442	8	v∈v	v∈v	NOUN
ejpam-3506	442	9	(	(	PUNCT
ejpam-3506	442	10	g	g	NOUN
ejpam-3506	442	11	)	)	PUNCT
ejpam-3506	442	12	sv	sv	NOUN
ejpam-3506	442	13	,	,	PUNCT
ejpam-3506	442	14	where	where	SCONJ
ejpam-3506	442	15	each	each	PRON
ejpam-3506	442	16	sv	sv	PROPN
ejpam-3506	442	17	is	be	AUX
ejpam-3506	442	18	a	a	DET
ejpam-3506	442	19	(	(	PUNCT
ejpam-3506	442	20	k−1)fd	k−1)fd	NOUN
ejpam-3506	442	21	-	-	PUNCT
ejpam-3506	442	22	set	set	NOUN
ejpam-3506	442	23	in	in	ADP
ejpam-3506	442	24	hv	hv	PROPN
ejpam-3506	442	25	.	.	PUNCT
ejpam-3506	443	1	then	then	ADV
ejpam-3506	443	2	〈	〈	PROPN
ejpam-3506	443	3	n(c	n(c	NOUN
ejpam-3506	443	4	)	)	PUNCT
ejpam-3506	443	5	〉	〉	NOUN
ejpam-3506	443	6	=	=	SYM
ejpam-3506	443	7	〈	〈	PROPN
ejpam-3506	443	8	⋃	⋃	ADJ
ejpam-3506	443	9	v∈v	v∈v	NOUN
ejpam-3506	443	10	(	(	PUNCT
ejpam-3506	443	11	g	g	NOUN
ejpam-3506	443	12	)	)	PUNCT
ejpam-3506	443	13	(	(	PUNCT
ejpam-3506	443	14	v+hv	v+hv	NOUN
ejpam-3506	443	15	)	)	PUNCT
ejpam-3506	443	16	〉	〉	NOUN
ejpam-3506	443	17	=	=	SYM
ejpam-3506	443	18	g	g	NOUN
ejpam-3506	443	19	◦	◦	NOUN
ejpam-3506	443	20	h	h	NOUN
ejpam-3506	443	21	is	be	AUX
ejpam-3506	443	22	connected	connect	VERB
ejpam-3506	443	23	.	.	PUNCT
ejpam-3506	444	1	suppose	suppose	VERB
ejpam-3506	444	2	condition	condition	NOUN
ejpam-3506	444	3	(	(	PUNCT
ejpam-3506	444	4	b	b	NOUN
ejpam-3506	444	5	)	)	PUNCT
ejpam-3506	444	6	holds	hold	NOUN
ejpam-3506	444	7	.	.	PUNCT
ejpam-3506	445	1	then	then	ADV
ejpam-3506	445	2	〈	〈	PROPN
ejpam-3506	445	3	n(c	n(c	NOUN
ejpam-3506	445	4	)	)	PUNCT
ejpam-3506	445	5	〉	〉	NOUN
ejpam-3506	445	6	=	=	SYM
ejpam-3506	445	7	〈	〈	PROPN
ejpam-3506	445	8	⋃	⋃	ADJ
ejpam-3506	445	9	v∈v	v∈v	NOUN
ejpam-3506	445	10	(	(	PUNCT
ejpam-3506	445	11	g	g	NOUN
ejpam-3506	445	12	)	)	PUNCT
ejpam-3506	445	13	(	(	PUNCT
ejpam-3506	445	14	{	{	PUNCT
ejpam-3506	445	15	v}∪nhv(sv	v}∪nhv(sv	NOUN
ejpam-3506	445	16	)	)	PUNCT
ejpam-3506	445	17	)	)	PUNCT
ejpam-3506	445	18	〉	〉	NOUN
ejpam-3506	445	19	which	which	PRON
ejpam-3506	445	20	is	be	AUX
ejpam-3506	445	21	connected	connect	VERB
ejpam-3506	445	22	.	.	PUNCT
ejpam-3506	446	1	therefore	therefore	ADV
ejpam-3506	446	2	,	,	PUNCT
ejpam-3506	446	3	c	c	PROPN
ejpam-3506	446	4	is	be	AUX
ejpam-3506	446	5	an	an	DET
ejpam-3506	446	6	nckfd	nckfd	NOUN
ejpam-3506	446	7	-	-	PUNCT
ejpam-3506	446	8	set	set	NOUN
ejpam-3506	446	9	in	in	ADP
ejpam-3506	446	10	g	g	PROPN
ejpam-3506	446	11	◦	◦	PROPN
ejpam-3506	446	12	h.	h.	PROPN
ejpam-3506	446	13	�	�	PROPN
ejpam-3506	446	14	corollary	corollary	NOUN
ejpam-3506	446	15	6	6	NUM
ejpam-3506	446	16	.	.	PUNCT
ejpam-3506	447	1	let	let	VERB
ejpam-3506	447	2	g	g	NOUN
ejpam-3506	447	3	and	and	CCONJ
ejpam-3506	447	4	h	h	NOUN
ejpam-3506	447	5	be	be	AUX
ejpam-3506	447	6	nontrivial	nontrivial	ADJ
ejpam-3506	447	7	connected	connect	VERB
ejpam-3506	447	8	graphs	graph	NOUN
ejpam-3506	447	9	of	of	ADP
ejpam-3506	447	10	orders	order	NOUN
ejpam-3506	447	11	m	m	VERB
ejpam-3506	447	12	and	and	CCONJ
ejpam-3506	447	13	n	n	CCONJ
ejpam-3506	447	14	,	,	PUNCT
ejpam-3506	447	15	respectively	respectively	ADV
ejpam-3506	447	16	,	,	PUNCT
ejpam-3506	447	17	and	and	CCONJ
ejpam-3506	447	18	let	let	VERB
ejpam-3506	447	19	k	k	PRON
ejpam-3506	447	20	be	be	AUX
ejpam-3506	447	21	a	a	DET
ejpam-3506	447	22	positive	positive	ADJ
ejpam-3506	447	23	integer	integer	NOUN
ejpam-3506	447	24	with	with	ADP
ejpam-3506	447	25	1	1	NUM
ejpam-3506	447	26	≤	≤	NUM
ejpam-3506	447	27	k	k	PROPN
ejpam-3506	447	28	≤	≤	PROPN
ejpam-3506	447	29	n.	n.	NOUN
ejpam-3506	447	30	then	then	ADV
ejpam-3506	447	31	γnc1fd(g	γnc1fd(g	PROPN
ejpam-3506	447	32	◦	◦	PROPN
ejpam-3506	447	33	h	h	NOUN
ejpam-3506	447	34	)	)	PUNCT
ejpam-3506	448	1	=	=	NOUN
ejpam-3506	448	2	m.	m.	NOUN
ejpam-3506	448	3	for	for	ADP
ejpam-3506	448	4	k	k	PROPN
ejpam-3506	448	5	≥	≥	PROPN
ejpam-3506	448	6	2	2	NUM
ejpam-3506	448	7	,	,	PUNCT
ejpam-3506	448	8	γnckfd(g	γnckfd(g	PRON
ejpam-3506	448	9	◦	◦	NOUN
ejpam-3506	448	10	h	h	NOUN
ejpam-3506	448	11	)	)	PUNCT
ejpam-3506	448	12	=	=	PRON
ejpam-3506	448	13	{	{	PUNCT
ejpam-3506	448	14	mk	mk	NOUN
ejpam-3506	448	15	,	,	PUNCT
ejpam-3506	448	16	if	if	SCONJ
ejpam-3506	448	17	h	h	NOUN
ejpam-3506	448	18	has	have	VERB
ejpam-3506	448	19	a	a	DET
ejpam-3506	448	20	kfd	kfd	NOUN
ejpam-3506	448	21	-	-	PUNCT
ejpam-3506	448	22	set	set	NOUN
ejpam-3506	448	23	with	with	ADP
ejpam-3506	448	24	|s|=k	|s|=k	PROPN
ejpam-3506	448	25	m(1	m(1	PROPN
ejpam-3506	448	26	+	+	NOUN
ejpam-3506	448	27	γ(k−1)fd(h	γ(k−1)fd(h	NOUN
ejpam-3506	448	28	)	)	PUNCT
ejpam-3506	448	29	,	,	PUNCT
ejpam-3506	448	30	if	if	SCONJ
ejpam-3506	448	31	h	h	NOUN
ejpam-3506	448	32	has	have	VERB
ejpam-3506	448	33	no	no	DET
ejpam-3506	448	34	kfd	kfd	NOUN
ejpam-3506	448	35	-	-	PUNCT
ejpam-3506	448	36	set	set	NOUN
ejpam-3506	448	37	with	with	ADP
ejpam-3506	448	38	|s|=k	|s|=k	PROPN
ejpam-3506	448	39	.	.	PUNCT
ejpam-3506	449	1	proof	proof	NOUN
ejpam-3506	449	2	.	.	PUNCT
ejpam-3506	450	1	this	this	PRON
ejpam-3506	450	2	immediately	immediately	ADV
ejpam-3506	450	3	follows	follow	VERB
ejpam-3506	450	4	from	from	ADP
ejpam-3506	450	5	theorem	theorem	ADJ
ejpam-3506	450	6	12	12	NUM
ejpam-3506	450	7	(	(	PUNCT
ejpam-3506	450	8	and	and	CCONJ
ejpam-3506	450	9	its	its	PRON
ejpam-3506	450	10	proof	proof	NOUN
ejpam-3506	450	11	)	)	PUNCT
ejpam-3506	450	12	.	.	PUNCT
ejpam-3506	451	1	�	�	PROPN
ejpam-3506	451	2	5	5	NUM
ejpam-3506	451	3	.	.	PUNCT
ejpam-3506	451	4	neighborhood	neighborhood	NOUN
ejpam-3506	451	5	connected	connect	VERB
ejpam-3506	451	6	k	k	ADJ
ejpam-3506	451	7	-	-	PUNCT
ejpam-3506	451	8	fair	fair	ADJ
ejpam-3506	451	9	domination	domination	NOUN
ejpam-3506	451	10	in	in	ADP
ejpam-3506	451	11	the	the	DET
ejpam-3506	451	12	lexicographic	lexicographic	ADJ
ejpam-3506	451	13	product	product	NOUN
ejpam-3506	451	14	of	of	ADP
ejpam-3506	451	15	graphs	graph	NOUN
ejpam-3506	451	16	the	the	DET
ejpam-3506	451	17	lexicographic	lexicographic	ADJ
ejpam-3506	451	18	product	product	NOUN
ejpam-3506	451	19	of	of	ADP
ejpam-3506	451	20	two	two	NUM
ejpam-3506	451	21	graphs	graph	NOUN
ejpam-3506	451	22	g	g	NOUN
ejpam-3506	451	23	and	and	CCONJ
ejpam-3506	451	24	h	h	NOUN
ejpam-3506	451	25	,	,	PUNCT
ejpam-3506	451	26	denoted	denote	VERB
ejpam-3506	451	27	by	by	ADP
ejpam-3506	451	28	g[h	g[h	NOUN
ejpam-3506	451	29	]	]	PUNCT
ejpam-3506	451	30	,	,	PUNCT
ejpam-3506	451	31	is	be	AUX
ejpam-3506	451	32	the	the	DET
ejpam-3506	451	33	graph	graph	NOUN
ejpam-3506	451	34	with	with	ADP
ejpam-3506	451	35	vertex	vertex	NOUN
ejpam-3506	451	36	set	set	VERB
ejpam-3506	451	37	v	v	NOUN
ejpam-3506	451	38	(	(	PUNCT
ejpam-3506	451	39	g[h	g[h	PROPN
ejpam-3506	451	40	]	]	PUNCT
ejpam-3506	451	41	)	)	PUNCT
ejpam-3506	451	42	=	=	SYM
ejpam-3506	451	43	v	v	X
ejpam-3506	451	44	(	(	PUNCT
ejpam-3506	451	45	g	g	NOUN
ejpam-3506	451	46	)	)	PUNCT
ejpam-3506	451	47	×	×	NOUN
ejpam-3506	451	48	v	v	NOUN
ejpam-3506	451	49	(	(	PUNCT
ejpam-3506	451	50	h	h	NOUN
ejpam-3506	451	51	)	)	PUNCT
ejpam-3506	451	52	and	and	CCONJ
ejpam-3506	451	53	edge	edge	VERB
ejpam-3506	451	54	set	set	VERB
ejpam-3506	451	55	e(g[h	e(g[h	NOUN
ejpam-3506	451	56	]	]	PUNCT
ejpam-3506	451	57	)	)	PUNCT
ejpam-3506	451	58	satisfying	satisfy	VERB
ejpam-3506	451	59	the	the	DET
ejpam-3506	451	60	following	follow	VERB
ejpam-3506	451	61	conditions	condition	NOUN
ejpam-3506	451	62	:	:	PUNCT
ejpam-3506	451	63	(	(	PUNCT
ejpam-3506	451	64	u1	u1	PROPN
ejpam-3506	451	65	,	,	PUNCT
ejpam-3506	451	66	v1)(u2	v1)(u2	PROPN
ejpam-3506	451	67	,	,	PUNCT
ejpam-3506	451	68	v2	v2	PROPN
ejpam-3506	451	69	)	)	PUNCT
ejpam-3506	451	70	∈	∈	NOUN
ejpam-3506	451	71	e(g[h	e(g[h	NOUN
ejpam-3506	451	72	]	]	PUNCT
ejpam-3506	451	73	)	)	PUNCT
ejpam-3506	451	74	if	if	SCONJ
ejpam-3506	451	75	and	and	CCONJ
ejpam-3506	451	76	only	only	ADV
ejpam-3506	451	77	if	if	SCONJ
ejpam-3506	451	78	either	either	PRON
ejpam-3506	451	79	u1u2	u1u2	PROPN
ejpam-3506	451	80	∈	∈	PROPN
ejpam-3506	451	81	e(g	e(g	PROPN
ejpam-3506	451	82	)	)	PUNCT
ejpam-3506	451	83	or	or	CCONJ
ejpam-3506	451	84	u1	u1	NOUN
ejpam-3506	451	85	=	=	SYM
ejpam-3506	451	86	u2	u2	PROPN
ejpam-3506	451	87	and	and	CCONJ
ejpam-3506	451	88	v1v2	v1v2	PUNCT
ejpam-3506	451	89	∈	∈	PROPN
ejpam-3506	451	90	e(h	e(h	PROPN
ejpam-3506	451	91	)	)	PUNCT
ejpam-3506	451	92	.	.	PUNCT
ejpam-3506	452	1	w.	w.	PROPN
ejpam-3506	452	2	bent	bent	PROPN
ejpam-3506	452	3	-	-	PUNCT
ejpam-3506	452	4	usman	usman	PROPN
ejpam-3506	452	5	,	,	PUNCT
ejpam-3506	452	6	r.	r.	PROPN
ejpam-3506	452	7	isla	isla	PROPN
ejpam-3506	452	8	,	,	PUNCT
ejpam-3506	452	9	s.	s.	PROPN
ejpam-3506	452	10	canoy	canoy	PROPN
ejpam-3506	452	11	/	/	SYM
ejpam-3506	452	12	eur	eur	PROPN
ejpam-3506	452	13	.	.	PUNCT
ejpam-3506	453	1	j.	j.	PROPN
ejpam-3506	453	2	pure	pure	PROPN
ejpam-3506	453	3	appl	appl	PROPN
ejpam-3506	453	4	.	.	PROPN
ejpam-3506	453	5	math	math	PROPN
ejpam-3506	453	6	,	,	PUNCT
ejpam-3506	453	7	12	12	NUM
ejpam-3506	453	8	(	(	PUNCT
ejpam-3506	453	9	3	3	NUM
ejpam-3506	453	10	)	)	PUNCT
ejpam-3506	453	11	(	(	PUNCT
ejpam-3506	453	12	2019	2019	NUM
ejpam-3506	453	13	)	)	PUNCT
ejpam-3506	453	14	,	,	PUNCT
ejpam-3506	453	15	1337	1337	NUM
ejpam-3506	453	16	-	-	SYM
ejpam-3506	453	17	1349	1349	NUM
ejpam-3506	453	18	1346	1346	NUM
ejpam-3506	453	19	theorem	theorem	NOUN
ejpam-3506	453	20	13	13	NUM
ejpam-3506	453	21	.	.	PUNCT
ejpam-3506	454	1	let	let	VERB
ejpam-3506	454	2	g	g	NOUN
ejpam-3506	454	3	and	and	CCONJ
ejpam-3506	454	4	h	h	NOUN
ejpam-3506	454	5	be	be	AUX
ejpam-3506	454	6	nontrivial	nontrivial	ADJ
ejpam-3506	454	7	connected	connect	VERB
ejpam-3506	454	8	graphs	graph	NOUN
ejpam-3506	454	9	of	of	ADP
ejpam-3506	454	10	orders	order	NOUN
ejpam-3506	454	11	m	m	VERB
ejpam-3506	454	12	and	and	CCONJ
ejpam-3506	454	13	n	n	CCONJ
ejpam-3506	454	14	,	,	PUNCT
ejpam-3506	454	15	respectively	respectively	ADV
ejpam-3506	454	16	,	,	PUNCT
ejpam-3506	454	17	and	and	CCONJ
ejpam-3506	454	18	k	k	X
ejpam-3506	454	19	a	a	DET
ejpam-3506	454	20	positive	positive	ADJ
ejpam-3506	454	21	integer	integer	NOUN
ejpam-3506	454	22	with	with	ADP
ejpam-3506	454	23	1	1	NUM
ejpam-3506	454	24	≤	≤	NUM
ejpam-3506	454	25	k	k	NOUN
ejpam-3506	454	26	≤	≤	ADJ
ejpam-3506	454	27	max{m	max{m	NOUN
ejpam-3506	454	28	,	,	PUNCT
ejpam-3506	454	29	n	n	CCONJ
ejpam-3506	454	30	}	}	PUNCT
ejpam-3506	454	31	.	.	PUNCT
ejpam-3506	455	1	then	then	ADV
ejpam-3506	455	2	c	c	X
ejpam-3506	455	3	=	=	PUNCT
ejpam-3506	455	4	⋃	⋃	PROPN
ejpam-3506	455	5	x∈s	x∈s	NOUN
ejpam-3506	455	6	(	(	PUNCT
ejpam-3506	455	7	{	{	PUNCT
ejpam-3506	455	8	x}×tx	x}×tx	PROPN
ejpam-3506	455	9	)	)	PUNCT
ejpam-3506	456	1	⊆	⊆	NUM
ejpam-3506	456	2	v	v	NOUN
ejpam-3506	456	3	(	(	PUNCT
ejpam-3506	456	4	g[h	g[h	PROPN
ejpam-3506	456	5	]	]	PUNCT
ejpam-3506	456	6	)	)	PUNCT
ejpam-3506	456	7	is	be	AUX
ejpam-3506	456	8	an	an	DET
ejpam-3506	456	9	nckfd	nckfd	NOUN
ejpam-3506	456	10	-	-	PUNCT
ejpam-3506	456	11	set	set	NOUN
ejpam-3506	456	12	in	in	ADP
ejpam-3506	456	13	g[h	g[h	PROPN
ejpam-3506	456	14	]	]	PUNCT
ejpam-3506	456	15	if	if	SCONJ
ejpam-3506	456	16	and	and	CCONJ
ejpam-3506	456	17	only	only	ADV
ejpam-3506	456	18	if	if	SCONJ
ejpam-3506	456	19	the	the	DET
ejpam-3506	456	20	following	follow	VERB
ejpam-3506	456	21	conditions	condition	NOUN
ejpam-3506	456	22	hold	hold	VERB
ejpam-3506	456	23	:	:	PUNCT
ejpam-3506	456	24	(	(	PUNCT
ejpam-3506	456	25	i	i	NOUN
ejpam-3506	456	26	)	)	PUNCT
ejpam-3506	456	27	s	s	VERB
ejpam-3506	456	28	is	be	AUX
ejpam-3506	456	29	a	a	DET
ejpam-3506	456	30	dominating	dominating	NOUN
ejpam-3506	456	31	set	set	VERB
ejpam-3506	456	32	in	in	ADP
ejpam-3506	456	33	g.	g.	PROPN
ejpam-3506	456	34	(	(	PUNCT
ejpam-3506	456	35	ii	ii	PROPN
ejpam-3506	456	36	)	)	PUNCT
ejpam-3506	456	37	for	for	ADP
ejpam-3506	456	38	each	each	DET
ejpam-3506	456	39	x	x	PROPN
ejpam-3506	456	40	∈	∈	PROPN
ejpam-3506	456	41	s∩ng(s	s∩ng(s	NOUN
ejpam-3506	456	42	)	)	PUNCT
ejpam-3506	456	43	with	with	ADP
ejpam-3506	456	44	tx	tx	PROPN
ejpam-3506	456	45	6=	6=	PROPN
ejpam-3506	456	46	v	v	ADP
ejpam-3506	456	47	(	(	PUNCT
ejpam-3506	456	48	h	h	NOUN
ejpam-3506	456	49	)	)	PUNCT
ejpam-3506	456	50	,	,	PUNCT
ejpam-3506	456	51	tx	tx	PROPN
ejpam-3506	456	52	is	be	AUX
ejpam-3506	456	53	an	an	DET
ejpam-3506	456	54	rfd	rfd	NOUN
ejpam-3506	456	55	-	-	PUNCT
ejpam-3506	456	56	set	set	VERB
ejpam-3506	456	57	and	and	CCONJ
ejpam-3506	456	58	∑	∑	ADP
ejpam-3506	456	59	z∈ng(x)∩s	z∈ng(x)∩s	ADJ
ejpam-3506	456	60	|tz|	|tz|	NOUN
ejpam-3506	456	61	=	=	SYM
ejpam-3506	456	62	k−r	k−r	PROPN
ejpam-3506	456	63	for	for	ADP
ejpam-3506	456	64	some	some	DET
ejpam-3506	456	65	r	r	NOUN
ejpam-3506	456	66	<	<	X
ejpam-3506	456	67	k.	k.	PROPN
ejpam-3506	456	68	(	(	PUNCT
ejpam-3506	456	69	iii	iii	NOUN
ejpam-3506	456	70	)	)	PUNCT
ejpam-3506	456	71	for	for	ADP
ejpam-3506	456	72	each	each	DET
ejpam-3506	456	73	x	x	SYM
ejpam-3506	456	74	∈	∈	PROPN
ejpam-3506	456	75	s\ng(s	s\ng(s	NOUN
ejpam-3506	456	76	)	)	PUNCT
ejpam-3506	456	77	with	with	ADP
ejpam-3506	456	78	tx	tx	PROPN
ejpam-3506	456	79	6=	6=	PROPN
ejpam-3506	456	80	v	v	ADP
ejpam-3506	456	81	(	(	PUNCT
ejpam-3506	456	82	h	h	NOUN
ejpam-3506	456	83	)	)	PUNCT
ejpam-3506	456	84	,	,	PUNCT
ejpam-3506	456	85	|tx|	|tx|	X
ejpam-3506	456	86	=	=	SYM
ejpam-3506	457	1	k	k	PROPN
ejpam-3506	457	2	and	and	CCONJ
ejpam-3506	457	3	tx	tx	PROPN
ejpam-3506	457	4	is	be	AUX
ejpam-3506	457	5	a	a	DET
ejpam-3506	457	6	kfd	kfd	NOUN
ejpam-3506	457	7	-	-	PUNCT
ejpam-3506	457	8	set	set	NOUN
ejpam-3506	457	9	in	in	ADP
ejpam-3506	457	10	h.	h.	PROPN
ejpam-3506	457	11	(	(	PUNCT
ejpam-3506	457	12	iv	iv	X
ejpam-3506	457	13	)	)	PUNCT
ejpam-3506	457	14	for	for	ADP
ejpam-3506	457	15	each	each	DET
ejpam-3506	457	16	y	y	PROPN
ejpam-3506	457	17	∈	∈	PROPN
ejpam-3506	457	18	v	v	NOUN
ejpam-3506	457	19	(	(	PUNCT
ejpam-3506	457	20	g)\s	g)\s	NOUN
ejpam-3506	457	21	,	,	PUNCT
ejpam-3506	457	22	∑	∑	PUNCT
ejpam-3506	457	23	v∈ng(y)∩s	v∈ng(y)∩s	ADJ
ejpam-3506	457	24	|tv|	|tv|	PROPN
ejpam-3506	457	25	=	=	SYM
ejpam-3506	457	26	k.	k.	PROPN
ejpam-3506	457	27	proof	proof	NOUN
ejpam-3506	457	28	.	.	PUNCT
ejpam-3506	458	1	suppose	suppose	VERB
ejpam-3506	458	2	c	c	NOUN
ejpam-3506	458	3	=	=	SYM
ejpam-3506	458	4	⋃	⋃	PROPN
ejpam-3506	458	5	x∈s	x∈s	NOUN
ejpam-3506	458	6	(	(	PUNCT
ejpam-3506	458	7	{	{	PUNCT
ejpam-3506	458	8	x}×tx	x}×tx	X
ejpam-3506	458	9	)	)	PUNCT
ejpam-3506	458	10	is	be	AUX
ejpam-3506	458	11	an	an	DET
ejpam-3506	458	12	nckfd	nckfd	NOUN
ejpam-3506	458	13	-	-	PUNCT
ejpam-3506	458	14	set	set	NOUN
ejpam-3506	458	15	in	in	ADP
ejpam-3506	458	16	g[h	g[h	NOUN
ejpam-3506	458	17	]	]	PUNCT
ejpam-3506	458	18	.	.	PUNCT
ejpam-3506	459	1	then	then	ADV
ejpam-3506	459	2	c	c	PROPN
ejpam-3506	459	3	is	be	AUX
ejpam-3506	459	4	a	a	DET
ejpam-3506	459	5	kfd	kfd	NOUN
ejpam-3506	459	6	-	-	PUNCT
ejpam-3506	459	7	set	set	NOUN
ejpam-3506	459	8	in	in	ADP
ejpam-3506	459	9	g[h	g[h	PROPN
ejpam-3506	459	10	]	]	PUNCT
ejpam-3506	459	11	,	,	PUNCT
ejpam-3506	459	12	hence	hence	ADV
ejpam-3506	459	13	statements	statement	NOUN
ejpam-3506	459	14	(	(	PUNCT
ejpam-3506	459	15	i	i	NOUN
ejpam-3506	459	16	)	)	PUNCT
ejpam-3506	459	17	to	to	PART
ejpam-3506	459	18	(	(	PUNCT
ejpam-3506	459	19	iv	iv	X
ejpam-3506	459	20	)	)	PUNCT
ejpam-3506	459	21	hold	hold	NOUN
ejpam-3506	459	22	by	by	ADP
ejpam-3506	459	23	theorem	theorem	NOUN
ejpam-3506	459	24	10	10	NUM
ejpam-3506	459	25	.	.	PUNCT
ejpam-3506	460	1	for	for	ADP
ejpam-3506	460	2	the	the	DET
ejpam-3506	460	3	converse	converse	NOUN
ejpam-3506	460	4	,	,	PUNCT
ejpam-3506	460	5	suppose	suppose	VERB
ejpam-3506	460	6	statements	statement	NOUN
ejpam-3506	460	7	(	(	PUNCT
ejpam-3506	460	8	i	i	NOUN
ejpam-3506	460	9	)	)	PUNCT
ejpam-3506	460	10	to	to	PART
ejpam-3506	460	11	(	(	PUNCT
ejpam-3506	460	12	iv	iv	X
ejpam-3506	460	13	)	)	PUNCT
ejpam-3506	460	14	hold	hold	NOUN
ejpam-3506	460	15	.	.	PUNCT
ejpam-3506	461	1	we	we	PRON
ejpam-3506	461	2	claim	claim	VERB
ejpam-3506	461	3	that	that	SCONJ
ejpam-3506	461	4	〈	〈	PROPN
ejpam-3506	461	5	ng[h](c	ng[h](c	NUM
ejpam-3506	461	6	)	)	PUNCT
ejpam-3506	461	7	〉	〉	PROPN
ejpam-3506	461	8	is	be	AUX
ejpam-3506	461	9	connected	connect	VERB
ejpam-3506	461	10	.	.	PUNCT
ejpam-3506	462	1	suppose	suppose	VERB
ejpam-3506	462	2	c	c	PROPN
ejpam-3506	462	3	6=	6=	ADP
ejpam-3506	462	4	v	v	PROPN
ejpam-3506	462	5	(	(	PUNCT
ejpam-3506	462	6	g[h	g[h	PROPN
ejpam-3506	462	7	]	]	PUNCT
ejpam-3506	462	8	)	)	PUNCT
ejpam-3506	462	9	.	.	PUNCT
ejpam-3506	463	1	let	let	VERB
ejpam-3506	463	2	(	(	PUNCT
ejpam-3506	463	3	x	x	X
ejpam-3506	463	4	,	,	PUNCT
ejpam-3506	463	5	a	a	PRON
ejpam-3506	463	6	)	)	PUNCT
ejpam-3506	463	7	,	,	PUNCT
ejpam-3506	463	8	(	(	PUNCT
ejpam-3506	463	9	y	y	PROPN
ejpam-3506	463	10	,	,	PUNCT
ejpam-3506	463	11	b	b	NOUN
ejpam-3506	463	12	)	)	PUNCT
ejpam-3506	463	13	∈	∈	PROPN
ejpam-3506	463	14	ng[h](c	ng[h](c	PROPN
ejpam-3506	463	15	)	)	PUNCT
ejpam-3506	463	16	such	such	ADJ
ejpam-3506	463	17	that	that	SCONJ
ejpam-3506	463	18	(	(	PUNCT
ejpam-3506	463	19	x	x	NOUN
ejpam-3506	463	20	,	,	PUNCT
ejpam-3506	463	21	a	a	PRON
ejpam-3506	463	22	)	)	PUNCT
ejpam-3506	463	23	6=	6=	ADP
ejpam-3506	463	24	(	(	PUNCT
ejpam-3506	463	25	y	y	PROPN
ejpam-3506	463	26	,	,	PUNCT
ejpam-3506	463	27	b	b	NOUN
ejpam-3506	463	28	)	)	PUNCT
ejpam-3506	463	29	and	and	CCONJ
ejpam-3506	463	30	(	(	PUNCT
ejpam-3506	463	31	x	x	X
ejpam-3506	463	32	,	,	PUNCT
ejpam-3506	463	33	a)(y	a)(y	PROPN
ejpam-3506	463	34	,	,	PUNCT
ejpam-3506	463	35	b	b	NOUN
ejpam-3506	463	36	)	)	PUNCT
ejpam-3506	463	37	/∈	/∈	PUNCT
ejpam-3506	464	1	e(〈ng[h](c	e(〈ng[h](c	NOUN
ejpam-3506	464	2	)	)	PUNCT
ejpam-3506	464	3	〉	〉	NOUN
ejpam-3506	464	4	)	)	PUNCT
ejpam-3506	464	5	.	.	PUNCT
ejpam-3506	465	1	consider	consider	VERB
ejpam-3506	465	2	the	the	DET
ejpam-3506	465	3	following	follow	VERB
ejpam-3506	465	4	cases	case	NOUN
ejpam-3506	465	5	:	:	PUNCT
ejpam-3506	465	6	case	case	NOUN
ejpam-3506	465	7	1	1	NUM
ejpam-3506	465	8	.	.	PUNCT
ejpam-3506	465	9	x	x	NOUN
ejpam-3506	466	1	=	=	PUNCT
ejpam-3506	466	2	y	y	PROPN
ejpam-3506	466	3	let	let	VERB
ejpam-3506	466	4	z	z	NOUN
ejpam-3506	466	5	∈	∈	PROPN
ejpam-3506	466	6	v	v	ADP
ejpam-3506	466	7	(	(	PUNCT
ejpam-3506	466	8	g	g	NOUN
ejpam-3506	466	9	)	)	PUNCT
ejpam-3506	466	10	∩	∩	NOUN
ejpam-3506	466	11	ng(x	ng(x	NUM
ejpam-3506	466	12	)	)	PUNCT
ejpam-3506	466	13	.	.	PUNCT
ejpam-3506	467	1	if	if	SCONJ
ejpam-3506	467	2	z	z	PROPN
ejpam-3506	467	3	∈	∈	PROPN
ejpam-3506	467	4	s	s	PART
ejpam-3506	467	5	,	,	PUNCT
ejpam-3506	467	6	pick	pick	VERB
ejpam-3506	467	7	any	any	DET
ejpam-3506	467	8	c	c	PROPN
ejpam-3506	467	9	∈	∈	PROPN
ejpam-3506	467	10	tz	tz	NOUN
ejpam-3506	467	11	and	and	CCONJ
ejpam-3506	467	12	let	let	VERB
ejpam-3506	467	13	d	d	X
ejpam-3506	467	14	∈	∈	PROPN
ejpam-3506	467	15	nh(c	nh(c	NOUN
ejpam-3506	467	16	)	)	PUNCT
ejpam-3506	467	17	.	.	PUNCT
ejpam-3506	468	1	then	then	ADV
ejpam-3506	468	2	(	(	PUNCT
ejpam-3506	468	3	z	z	NOUN
ejpam-3506	468	4	,	,	PUNCT
ejpam-3506	468	5	d	d	NOUN
ejpam-3506	468	6	)	)	PUNCT
ejpam-3506	468	7	∈	∈	PROPN
ejpam-3506	468	8	ng[h](z	ng[h](z	NOUN
ejpam-3506	468	9	,	,	PUNCT
ejpam-3506	468	10	c	c	NOUN
ejpam-3506	468	11	)	)	PUNCT
ejpam-3506	468	12	⊆	⊆	NUM
ejpam-3506	468	13	ng[h](c	ng[h](c	NUM
ejpam-3506	468	14	)	)	PUNCT
ejpam-3506	468	15	and	and	CCONJ
ejpam-3506	468	16	[	[	X
ejpam-3506	468	17	(	(	PUNCT
ejpam-3506	468	18	x	x	X
ejpam-3506	468	19	,	,	PUNCT
ejpam-3506	468	20	a	a	PRON
ejpam-3506	468	21	)	)	PUNCT
ejpam-3506	468	22	,	,	PUNCT
ejpam-3506	468	23	(	(	PUNCT
ejpam-3506	468	24	z	z	X
ejpam-3506	468	25	,	,	PUNCT
ejpam-3506	468	26	d	d	NOUN
ejpam-3506	468	27	)	)	PUNCT
ejpam-3506	468	28	,	,	PUNCT
ejpam-3506	468	29	(	(	PUNCT
ejpam-3506	468	30	y	y	PROPN
ejpam-3506	468	31	,	,	PUNCT
ejpam-3506	468	32	b	b	NOUN
ejpam-3506	468	33	)	)	PUNCT
ejpam-3506	468	34	]	]	PUNCT
ejpam-3506	468	35	is	be	AUX
ejpam-3506	468	36	an	an	DET
ejpam-3506	468	37	(	(	PUNCT
ejpam-3506	468	38	x	x	NOUN
ejpam-3506	468	39	,	,	PUNCT
ejpam-3506	468	40	a)-(y	a)-(y	PROPN
ejpam-3506	468	41	,	,	PUNCT
ejpam-3506	468	42	b	b	NOUN
ejpam-3506	468	43	)	)	PUNCT
ejpam-3506	468	44	geodesic	geodesic	NOUN
ejpam-3506	468	45	in	in	ADP
ejpam-3506	468	46	ng[h](c	ng[h](c	PROPN
ejpam-3506	468	47	)	)	PUNCT
ejpam-3506	468	48	.	.	PUNCT
ejpam-3506	469	1	if	if	SCONJ
ejpam-3506	469	2	z	z	NOUN
ejpam-3506	469	3	/∈	/∈	PUNCT
ejpam-3506	470	1	s	s	X
ejpam-3506	470	2	,	,	PUNCT
ejpam-3506	470	3	then	then	ADV
ejpam-3506	470	4	{	{	PUNCT
ejpam-3506	470	5	z	z	NOUN
ejpam-3506	470	6	}	}	PUNCT
ejpam-3506	470	7	×	×	NOUN
ejpam-3506	470	8	tz	tz	PROPN
ejpam-3506	470	9	⊆	⊆	NUM
ejpam-3506	470	10	ng[h](c	ng[h](c	NUM
ejpam-3506	470	11	)	)	PUNCT
ejpam-3506	470	12	since	since	SCONJ
ejpam-3506	470	13	s	s	NOUN
ejpam-3506	470	14	is	be	AUX
ejpam-3506	470	15	a	a	DET
ejpam-3506	470	16	dominating	dominating	NOUN
ejpam-3506	470	17	set	set	NOUN
ejpam-3506	470	18	of	of	ADP
ejpam-3506	470	19	g.	g.	PROPN
ejpam-3506	471	1	thus	thus	ADV
ejpam-3506	471	2	,	,	PUNCT
ejpam-3506	471	3	[	[	X
ejpam-3506	471	4	(	(	PUNCT
ejpam-3506	471	5	x	x	NOUN
ejpam-3506	471	6	,	,	PUNCT
ejpam-3506	471	7	a	a	PRON
ejpam-3506	471	8	)	)	PUNCT
ejpam-3506	471	9	,	,	PUNCT
ejpam-3506	471	10	(	(	PUNCT
ejpam-3506	471	11	z	z	X
ejpam-3506	471	12	,	,	PUNCT
ejpam-3506	471	13	d	d	NOUN
ejpam-3506	471	14	)	)	PUNCT
ejpam-3506	471	15	,	,	PUNCT
ejpam-3506	471	16	(	(	PUNCT
ejpam-3506	471	17	y	y	PROPN
ejpam-3506	471	18	,	,	PUNCT
ejpam-3506	471	19	b	b	NOUN
ejpam-3506	471	20	)	)	PUNCT
ejpam-3506	471	21	]	]	PUNCT
ejpam-3506	471	22	is	be	AUX
ejpam-3506	471	23	an	an	DET
ejpam-3506	471	24	(	(	PUNCT
ejpam-3506	471	25	x	x	NOUN
ejpam-3506	471	26	,	,	PUNCT
ejpam-3506	471	27	a)-(y	a)-(y	PROPN
ejpam-3506	471	28	,	,	PUNCT
ejpam-3506	471	29	b	b	NOUN
ejpam-3506	471	30	)	)	PUNCT
ejpam-3506	471	31	geodesic	geodesic	NOUN
ejpam-3506	471	32	in	in	ADP
ejpam-3506	471	33	ng[h](c	ng[h](c	PROPN
ejpam-3506	471	34	)	)	PUNCT
ejpam-3506	471	35	for	for	ADP
ejpam-3506	471	36	all	all	DET
ejpam-3506	471	37	d	d	PROPN
ejpam-3506	471	38	∈	∈	PROPN
ejpam-3506	471	39	tz	tz	PROPN
ejpam-3506	471	40	.	.	PUNCT
ejpam-3506	471	41	case	case	NOUN
ejpam-3506	471	42	2	2	NUM
ejpam-3506	471	43	.	.	NUM
ejpam-3506	471	44	x	x	SYM
ejpam-3506	472	1	6=	6=	NUM
ejpam-3506	472	2	y	y	PRON
ejpam-3506	472	3	let	let	VERB
ejpam-3506	472	4	[	[	X
ejpam-3506	472	5	x1	x1	ADJ
ejpam-3506	472	6	,	,	PUNCT
ejpam-3506	472	7	x2	x2	PROPN
ejpam-3506	472	8	,	,	PUNCT
ejpam-3506	472	9	...	...	PUNCT
ejpam-3506	472	10	,	,	PUNCT
ejpam-3506	472	11	xk	xk	PROPN
ejpam-3506	472	12	]	]	X
ejpam-3506	472	13	,	,	PUNCT
ejpam-3506	472	14	where	where	SCONJ
ejpam-3506	472	15	x1	x1	ADJ
ejpam-3506	472	16	=	=	PUNCT
ejpam-3506	472	17	x	x	X
ejpam-3506	472	18	and	and	CCONJ
ejpam-3506	472	19	xk	xk	PROPN
ejpam-3506	472	20	=	=	SYM
ejpam-3506	472	21	y	y	PROPN
ejpam-3506	472	22	,	,	PUNCT
ejpam-3506	472	23	be	be	AUX
ejpam-3506	472	24	an	an	DET
ejpam-3506	472	25	x	x	ADJ
ejpam-3506	472	26	-	-	NOUN
ejpam-3506	472	27	y	y	ADJ
ejpam-3506	472	28	geodesic	geodesic	NOUN
ejpam-3506	472	29	.	.	PUNCT
ejpam-3506	473	1	since	since	SCONJ
ejpam-3506	473	2	s	s	PROPN
ejpam-3506	473	3	is	be	AUX
ejpam-3506	473	4	a	a	DET
ejpam-3506	473	5	dominating	dominating	NOUN
ejpam-3506	473	6	set	set	NOUN
ejpam-3506	473	7	of	of	ADP
ejpam-3506	473	8	g	g	NOUN
ejpam-3506	473	9	,	,	PUNCT
ejpam-3506	473	10	(	(	PUNCT
ejpam-3506	473	11	{	{	PUNCT
ejpam-3506	473	12	xj}×	xj}×	X
ejpam-3506	473	13	txj	txj	NOUN
ejpam-3506	473	14	)	)	PUNCT
ejpam-3506	473	15	∩ng[h](c	∩ng[h](c	PROPN
ejpam-3506	473	16	)	)	PUNCT
ejpam-3506	473	17	6=	6=	ADP
ejpam-3506	473	18	∅	∅	NOUN
ejpam-3506	473	19	for	for	ADP
ejpam-3506	473	20	each	each	DET
ejpam-3506	473	21	j	j	PROPN
ejpam-3506	473	22	∈	∈	PROPN
ejpam-3506	473	23	{	{	PUNCT
ejpam-3506	473	24	2	2	NUM
ejpam-3506	473	25	,	,	PUNCT
ejpam-3506	473	26	3	3	NUM
ejpam-3506	473	27	,	,	PUNCT
ejpam-3506	473	28	...	...	PUNCT
ejpam-3506	473	29	,	,	PUNCT
ejpam-3506	473	30	k−	k−	PROPN
ejpam-3506	473	31	1	1	NUM
ejpam-3506	473	32	}	}	PUNCT
ejpam-3506	473	33	.	.	PUNCT
ejpam-3506	474	1	pick	pick	PROPN
ejpam-3506	474	2	(	(	PUNCT
ejpam-3506	474	3	xj	xj	PROPN
ejpam-3506	474	4	,	,	PUNCT
ejpam-3506	474	5	aj	aj	PROPN
ejpam-3506	474	6	)	)	PUNCT
ejpam-3506	474	7	∈	∈	PROPN
ejpam-3506	474	8	ng[h](c	ng[h](c	PROPN
ejpam-3506	474	9	)	)	PUNCT
ejpam-3506	474	10	for	for	ADP
ejpam-3506	474	11	each	each	DET
ejpam-3506	474	12	j	j	PROPN
ejpam-3506	474	13	∈	∈	PROPN
ejpam-3506	474	14	{	{	PUNCT
ejpam-3506	474	15	2	2	NUM
ejpam-3506	474	16	,	,	PUNCT
ejpam-3506	474	17	3	3	NUM
ejpam-3506	474	18	,	,	PUNCT
ejpam-3506	474	19	...	...	PUNCT
ejpam-3506	474	20	,	,	PUNCT
ejpam-3506	474	21	k	k	PROPN
ejpam-3506	474	22	−	−	PROPN
ejpam-3506	474	23	1	1	NUM
ejpam-3506	474	24	}	}	PUNCT
ejpam-3506	474	25	.	.	PUNCT
ejpam-3506	475	1	then	then	ADV
ejpam-3506	476	1	[	[	X
ejpam-3506	476	2	(	(	PUNCT
ejpam-3506	476	3	x1	x1	ADJ
ejpam-3506	476	4	,	,	PUNCT
ejpam-3506	476	5	a1	a1	NOUN
ejpam-3506	476	6	)	)	PUNCT
ejpam-3506	476	7	,	,	PUNCT
ejpam-3506	476	8	(	(	PUNCT
ejpam-3506	476	9	x2	x2	PROPN
ejpam-3506	476	10	,	,	PUNCT
ejpam-3506	476	11	a2	a2	PROPN
ejpam-3506	476	12	)	)	PUNCT
ejpam-3506	476	13	,	,	PUNCT
ejpam-3506	476	14	...	...	PUNCT
ejpam-3506	476	15	,	,	PUNCT
ejpam-3506	476	16	(	(	PUNCT
ejpam-3506	476	17	xk−1	xk−1	PROPN
ejpam-3506	476	18	,	,	PUNCT
ejpam-3506	476	19	ak−1	ak−1	PROPN
ejpam-3506	476	20	)	)	PUNCT
ejpam-3506	476	21	,	,	PUNCT
ejpam-3506	476	22	(	(	PUNCT
ejpam-3506	476	23	xk	xk	PROPN
ejpam-3506	476	24	,	,	PUNCT
ejpam-3506	476	25	ak	ak	PROPN
ejpam-3506	476	26	)	)	PUNCT
ejpam-3506	476	27	]	]	PUNCT
ejpam-3506	476	28	,	,	PUNCT
ejpam-3506	476	29	where	where	SCONJ
ejpam-3506	476	30	a1	a1	NOUN
ejpam-3506	476	31	=	=	PUNCT
ejpam-3506	476	32	a	a	NOUN
ejpam-3506	476	33	and	and	CCONJ
ejpam-3506	476	34	ak	ak	PROPN
ejpam-3506	476	35	=	=	SYM
ejpam-3506	476	36	b	b	PROPN
ejpam-3506	476	37	,	,	PUNCT
ejpam-3506	476	38	is	be	AUX
ejpam-3506	476	39	an	an	DET
ejpam-3506	476	40	(	(	PUNCT
ejpam-3506	476	41	x	x	NOUN
ejpam-3506	476	42	,	,	PUNCT
ejpam-3506	476	43	a)-(y	a)-(y	PROPN
ejpam-3506	476	44	,	,	PUNCT
ejpam-3506	476	45	b	b	NOUN
ejpam-3506	476	46	)	)	PUNCT
ejpam-3506	476	47	path	path	NOUN
ejpam-3506	476	48	in	in	ADP
ejpam-3506	476	49	ng[h](c	ng[h](c	PROPN
ejpam-3506	476	50	)	)	PUNCT
ejpam-3506	476	51	.	.	PUNCT
ejpam-3506	477	1	therefore	therefore	ADV
ejpam-3506	477	2	,	,	PUNCT
ejpam-3506	477	3	〈	〈	PROPN
ejpam-3506	477	4	ng[h](c	ng[h](c	NUM
ejpam-3506	477	5	)	)	PUNCT
ejpam-3506	477	6	〉	〉	PROPN
ejpam-3506	477	7	is	be	AUX
ejpam-3506	477	8	connected	connect	VERB
ejpam-3506	477	9	.	.	PUNCT
ejpam-3506	478	1	hence	hence	ADV
ejpam-3506	478	2	,	,	PUNCT
ejpam-3506	478	3	c	c	PROPN
ejpam-3506	478	4	is	be	AUX
ejpam-3506	478	5	an	an	DET
ejpam-3506	478	6	nckfd	nckfd	NOUN
ejpam-3506	478	7	-	-	PUNCT
ejpam-3506	478	8	set	set	NOUN
ejpam-3506	478	9	in	in	ADP
ejpam-3506	478	10	g[h	g[h	NOUN
ejpam-3506	478	11	]	]	PUNCT
ejpam-3506	478	12	.	.	PUNCT
ejpam-3506	479	1	�	�	PROPN
ejpam-3506	479	2	the	the	DET
ejpam-3506	479	3	next	next	ADJ
ejpam-3506	479	4	result	result	NOUN
ejpam-3506	479	5	immediately	immediately	ADV
ejpam-3506	479	6	follows	follow	VERB
ejpam-3506	479	7	from	from	ADP
ejpam-3506	479	8	theorem	theorem	ADJ
ejpam-3506	479	9	13	13	NUM
ejpam-3506	479	10	and	and	CCONJ
ejpam-3506	479	11	theorem	theorem	VERB
ejpam-3506	479	12	10	10	NUM
ejpam-3506	479	13	.	.	PUNCT
ejpam-3506	480	1	corollary	corollary	ADJ
ejpam-3506	480	2	7	7	NUM
ejpam-3506	480	3	.	.	PUNCT
ejpam-3506	481	1	let	let	VERB
ejpam-3506	481	2	g	g	NOUN
ejpam-3506	481	3	and	and	CCONJ
ejpam-3506	481	4	h	h	NOUN
ejpam-3506	481	5	be	be	AUX
ejpam-3506	481	6	nontrivial	nontrivial	ADJ
ejpam-3506	481	7	connected	connect	VERB
ejpam-3506	481	8	graphs	graph	NOUN
ejpam-3506	481	9	of	of	ADP
ejpam-3506	481	10	orders	order	NOUN
ejpam-3506	481	11	m	m	VERB
ejpam-3506	481	12	and	and	CCONJ
ejpam-3506	481	13	n	n	CCONJ
ejpam-3506	481	14	,	,	PUNCT
ejpam-3506	481	15	respectively	respectively	ADV
ejpam-3506	481	16	,	,	PUNCT
ejpam-3506	481	17	and	and	CCONJ
ejpam-3506	481	18	k	k	X
ejpam-3506	481	19	a	a	DET
ejpam-3506	481	20	positive	positive	ADJ
ejpam-3506	481	21	integer	integer	NOUN
ejpam-3506	481	22	with	with	ADP
ejpam-3506	481	23	1	1	NUM
ejpam-3506	481	24	≤	≤	NUM
ejpam-3506	481	25	k	k	NOUN
ejpam-3506	481	26	≤	≤	ADJ
ejpam-3506	481	27	max{m	max{m	NOUN
ejpam-3506	481	28	,	,	PUNCT
ejpam-3506	481	29	n	n	CCONJ
ejpam-3506	481	30	}	}	PUNCT
ejpam-3506	481	31	.	.	PUNCT
ejpam-3506	482	1	then	then	ADV
ejpam-3506	482	2	c	c	X
ejpam-3506	482	3	=	=	PUNCT
ejpam-3506	482	4	⋃	⋃	PROPN
ejpam-3506	482	5	x∈s	x∈s	NOUN
ejpam-3506	482	6	(	(	PUNCT
ejpam-3506	482	7	{	{	PUNCT
ejpam-3506	482	8	x	x	NOUN
ejpam-3506	482	9	}	}	PUNCT
ejpam-3506	482	10	×	×	PROPN
ejpam-3506	482	11	tx	tx	PROPN
ejpam-3506	482	12	)	)	PUNCT
ejpam-3506	482	13	⊆	⊆	NUM
ejpam-3506	482	14	v	v	NOUN
ejpam-3506	482	15	(	(	PUNCT
ejpam-3506	482	16	g[h	g[h	PROPN
ejpam-3506	482	17	]	]	PUNCT
ejpam-3506	482	18	)	)	PUNCT
ejpam-3506	482	19	is	be	AUX
ejpam-3506	482	20	an	an	DET
ejpam-3506	482	21	nckfd	nckfd	NOUN
ejpam-3506	482	22	-	-	PUNCT
ejpam-3506	482	23	set	set	NOUN
ejpam-3506	482	24	in	in	ADP
ejpam-3506	482	25	g[h	g[h	PROPN
ejpam-3506	482	26	]	]	PUNCT
ejpam-3506	482	27	if	if	SCONJ
ejpam-3506	483	1	and	and	CCONJ
ejpam-3506	483	2	only	only	ADV
ejpam-3506	483	3	if	if	SCONJ
ejpam-3506	483	4	c	c	PROPN
ejpam-3506	483	5	is	be	AUX
ejpam-3506	483	6	a	a	DET
ejpam-3506	483	7	kfd	kfd	NOUN
ejpam-3506	483	8	-	-	PUNCT
ejpam-3506	483	9	set	set	NOUN
ejpam-3506	483	10	in	in	ADP
ejpam-3506	483	11	g[h	g[h	NOUN
ejpam-3506	483	12	]	]	PUNCT
ejpam-3506	483	13	.	.	PUNCT
ejpam-3506	484	1	in	in	ADP
ejpam-3506	484	2	particular	particular	ADJ
ejpam-3506	484	3	,	,	PUNCT
ejpam-3506	484	4	γnckfd(g[h	γnckfd(g[h	ADJ
ejpam-3506	484	5	]	]	X
ejpam-3506	484	6	)	)	PUNCT
ejpam-3506	484	7	=	=	SYM
ejpam-3506	484	8	γkfd(g[h	γkfd(g[h	ADJ
ejpam-3506	484	9	]	]	PUNCT
ejpam-3506	484	10	)	)	PUNCT
ejpam-3506	484	11	.	.	PUNCT
ejpam-3506	485	1	6	6	X
ejpam-3506	485	2	.	.	X
ejpam-3506	485	3	neighborhood	neighborhood	NOUN
ejpam-3506	485	4	connected	connect	VERB
ejpam-3506	485	5	k	k	ADJ
ejpam-3506	485	6	-	-	PUNCT
ejpam-3506	485	7	fair	fair	ADJ
ejpam-3506	485	8	domination	domination	NOUN
ejpam-3506	485	9	in	in	ADP
ejpam-3506	485	10	the	the	DET
ejpam-3506	485	11	cartesian	cartesian	ADJ
ejpam-3506	485	12	product	product	NOUN
ejpam-3506	485	13	of	of	ADP
ejpam-3506	485	14	graphs	graph	NOUN
ejpam-3506	485	15	the	the	DET
ejpam-3506	485	16	cartesian	cartesian	ADJ
ejpam-3506	485	17	product	product	NOUN
ejpam-3506	485	18	of	of	ADP
ejpam-3506	485	19	two	two	NUM
ejpam-3506	485	20	graphs	graph	NOUN
ejpam-3506	485	21	g	g	NOUN
ejpam-3506	485	22	and	and	CCONJ
ejpam-3506	485	23	h	h	NOUN
ejpam-3506	485	24	,	,	PUNCT
ejpam-3506	485	25	denoted	denote	VERB
ejpam-3506	485	26	by	by	ADP
ejpam-3506	485	27	g	g	PROPN
ejpam-3506	485	28	�	�	PROPN
ejpam-3506	485	29	h	h	NOUN
ejpam-3506	485	30	,	,	PUNCT
ejpam-3506	485	31	is	be	AUX
ejpam-3506	485	32	the	the	DET
ejpam-3506	485	33	graph	graph	NOUN
ejpam-3506	485	34	with	with	ADP
ejpam-3506	485	35	vertex	vertex	NOUN
ejpam-3506	485	36	-	-	PUNCT
ejpam-3506	485	37	set	set	VERB
ejpam-3506	485	38	v	v	NOUN
ejpam-3506	485	39	(	(	PUNCT
ejpam-3506	485	40	g	g	PROPN
ejpam-3506	485	41	�	�	NOUN
ejpam-3506	485	42	h	h	NOUN
ejpam-3506	485	43	)	)	PUNCT
ejpam-3506	485	44	=	=	NOUN
ejpam-3506	485	45	v	v	X
ejpam-3506	485	46	(	(	PUNCT
ejpam-3506	485	47	g)×v	g)×v	PROPN
ejpam-3506	485	48	(	(	PUNCT
ejpam-3506	485	49	h	h	NOUN
ejpam-3506	485	50	)	)	PUNCT
ejpam-3506	485	51	and	and	CCONJ
ejpam-3506	485	52	edge	edge	NOUN
ejpam-3506	485	53	-	-	PUNCT
ejpam-3506	485	54	set	set	VERB
ejpam-3506	485	55	e(g	e(g	PROPN
ejpam-3506	485	56	�	�	PROPN
ejpam-3506	485	57	h	h	NOUN
ejpam-3506	485	58	)	)	PUNCT
ejpam-3506	485	59	satisfying	satisfy	VERB
ejpam-3506	485	60	the	the	DET
ejpam-3506	485	61	following	follow	VERB
ejpam-3506	485	62	conditions	condition	NOUN
ejpam-3506	485	63	:	:	PUNCT
ejpam-3506	485	64	(	(	PUNCT
ejpam-3506	485	65	u1	u1	PROPN
ejpam-3506	485	66	,	,	PUNCT
ejpam-3506	485	67	v1)(u2	v1)(u2	PROPN
ejpam-3506	485	68	,	,	PUNCT
ejpam-3506	485	69	v2	v2	PROPN
ejpam-3506	485	70	)	)	PUNCT
ejpam-3506	485	71	∈	∈	PROPN
ejpam-3506	485	72	e(g	e(g	PROPN
ejpam-3506	485	73	�	�	PROPN
ejpam-3506	485	74	h	h	PROPN
ejpam-3506	485	75	)	)	PUNCT
ejpam-3506	485	76	if	if	SCONJ
ejpam-3506	485	77	and	and	CCONJ
ejpam-3506	485	78	only	only	ADV
ejpam-3506	485	79	if	if	SCONJ
ejpam-3506	485	80	either	either	DET
ejpam-3506	485	81	u1u2	u1u2	PROPN
ejpam-3506	485	82	∈	∈	PROPN
ejpam-3506	485	83	e(g	e(g	PROPN
ejpam-3506	485	84	)	)	PUNCT
ejpam-3506	485	85	and	and	CCONJ
ejpam-3506	485	86	v1	v1	NOUN
ejpam-3506	485	87	=	=	SYM
ejpam-3506	485	88	v2	v2	NOUN
ejpam-3506	485	89	or	or	CCONJ
ejpam-3506	485	90	u1	u1	NOUN
ejpam-3506	485	91	=	=	SYM
ejpam-3506	485	92	u2	u2	PROPN
ejpam-3506	485	93	and	and	CCONJ
ejpam-3506	485	94	v1v2	v1v2	PUNCT
ejpam-3506	485	95	∈	∈	PROPN
ejpam-3506	485	96	e(h	e(h	PROPN
ejpam-3506	485	97	)	)	PUNCT
ejpam-3506	485	98	.	.	PUNCT
ejpam-3506	486	1	w.	w.	PROPN
ejpam-3506	486	2	bent	bent	PROPN
ejpam-3506	486	3	-	-	PUNCT
ejpam-3506	486	4	usman	usman	PROPN
ejpam-3506	486	5	,	,	PUNCT
ejpam-3506	486	6	r.	r.	PROPN
ejpam-3506	486	7	isla	isla	PROPN
ejpam-3506	486	8	,	,	PUNCT
ejpam-3506	486	9	s.	s.	PROPN
ejpam-3506	486	10	canoy	canoy	PROPN
ejpam-3506	486	11	/	/	SYM
ejpam-3506	486	12	eur	eur	PROPN
ejpam-3506	486	13	.	.	PUNCT
ejpam-3506	487	1	j.	j.	PROPN
ejpam-3506	487	2	pure	pure	PROPN
ejpam-3506	487	3	appl	appl	PROPN
ejpam-3506	487	4	.	.	PROPN
ejpam-3506	487	5	math	math	PROPN
ejpam-3506	487	6	,	,	PUNCT
ejpam-3506	487	7	12	12	NUM
ejpam-3506	487	8	(	(	PUNCT
ejpam-3506	487	9	3	3	NUM
ejpam-3506	487	10	)	)	PUNCT
ejpam-3506	487	11	(	(	PUNCT
ejpam-3506	487	12	2019	2019	NUM
ejpam-3506	487	13	)	)	PUNCT
ejpam-3506	487	14	,	,	PUNCT
ejpam-3506	487	15	1337	1337	NUM
ejpam-3506	487	16	-	-	SYM
ejpam-3506	487	17	1349	1349	NUM
ejpam-3506	487	18	1347	1347	NUM
ejpam-3506	487	19	theorem	theorem	NOUN
ejpam-3506	487	20	14	14	NUM
ejpam-3506	487	21	.	.	PUNCT
ejpam-3506	488	1	let	let	VERB
ejpam-3506	488	2	g	g	NOUN
ejpam-3506	488	3	and	and	CCONJ
ejpam-3506	488	4	h	h	NOUN
ejpam-3506	488	5	be	be	AUX
ejpam-3506	488	6	nontrivial	nontrivial	ADJ
ejpam-3506	488	7	connected	connected	ADJ
ejpam-3506	488	8	graphs	graph	NOUN
ejpam-3506	488	9	.	.	PUNCT
ejpam-3506	489	1	if	if	SCONJ
ejpam-3506	489	2	s1	s1	PROPN
ejpam-3506	489	3	and	and	CCONJ
ejpam-3506	489	4	s2	s2	PROPN
ejpam-3506	489	5	are	be	AUX
ejpam-3506	489	6	kfd	kfd	ADJ
ejpam-3506	489	7	-	-	PUNCT
ejpam-3506	489	8	sets	set	NOUN
ejpam-3506	489	9	in	in	ADP
ejpam-3506	489	10	g	g	PROPN
ejpam-3506	489	11	and	and	CCONJ
ejpam-3506	489	12	h	h	NOUN
ejpam-3506	489	13	,	,	PUNCT
ejpam-3506	489	14	respectively	respectively	ADV
ejpam-3506	489	15	,	,	PUNCT
ejpam-3506	489	16	then	then	ADV
ejpam-3506	489	17	c1	c1	PROPN
ejpam-3506	489	18	=	=	PROPN
ejpam-3506	490	1	s1	s1	PROPN
ejpam-3506	490	2	×	×	PROPN
ejpam-3506	490	3	v	v	NOUN
ejpam-3506	490	4	(	(	PUNCT
ejpam-3506	490	5	h	h	NOUN
ejpam-3506	490	6	)	)	PUNCT
ejpam-3506	490	7	and	and	CCONJ
ejpam-3506	490	8	c2	c2	PROPN
ejpam-3506	490	9	=	=	SYM
ejpam-3506	490	10	v	v	PROPN
ejpam-3506	490	11	(	(	PUNCT
ejpam-3506	490	12	g	g	NOUN
ejpam-3506	490	13	)	)	PUNCT
ejpam-3506	490	14	×	×	NOUN
ejpam-3506	490	15	s2	s2	NOUN
ejpam-3506	490	16	are	be	AUX
ejpam-3506	490	17	nckfd	nckfd	ADJ
ejpam-3506	490	18	-	-	PUNCT
ejpam-3506	490	19	sets	set	NOUN
ejpam-3506	490	20	in	in	ADP
ejpam-3506	490	21	g	g	PROPN
ejpam-3506	490	22	�	�	PROPN
ejpam-3506	490	23	h.	h.	NOUN
ejpam-3506	490	24	proof	proof	NOUN
ejpam-3506	490	25	.	.	PUNCT
ejpam-3506	491	1	let	let	VERB
ejpam-3506	491	2	s1	s1	NOUN
ejpam-3506	491	3	be	be	AUX
ejpam-3506	491	4	a	a	DET
ejpam-3506	491	5	kfd	kfd	NOUN
ejpam-3506	491	6	-	-	PUNCT
ejpam-3506	491	7	set	set	NOUN
ejpam-3506	491	8	in	in	ADP
ejpam-3506	491	9	g.	g.	NOUN
ejpam-3506	491	10	by	by	ADP
ejpam-3506	491	11	corollary	corollary	ADJ
ejpam-3506	491	12	4	4	NUM
ejpam-3506	491	13	,	,	PUNCT
ejpam-3506	491	14	c1	c1	NOUN
ejpam-3506	491	15	=	=	PROPN
ejpam-3506	491	16	s1	s1	PROPN
ejpam-3506	491	17	×	×	PROPN
ejpam-3506	491	18	v	v	NOUN
ejpam-3506	491	19	(	(	PUNCT
ejpam-3506	491	20	h	h	NOUN
ejpam-3506	491	21	)	)	PUNCT
ejpam-3506	491	22	is	be	AUX
ejpam-3506	491	23	a	a	DET
ejpam-3506	491	24	kfd	kfd	NOUN
ejpam-3506	491	25	-	-	PUNCT
ejpam-3506	491	26	set	set	NOUN
ejpam-3506	491	27	of	of	ADP
ejpam-3506	491	28	g	g	PROPN
ejpam-3506	491	29	�	�	PROPN
ejpam-3506	491	30	h.	h.	PROPN
ejpam-3506	491	31	next	next	ADV
ejpam-3506	491	32	,	,	PUNCT
ejpam-3506	491	33	let	let	VERB
ejpam-3506	491	34	(	(	PUNCT
ejpam-3506	491	35	x	x	NOUN
ejpam-3506	491	36	,	,	PUNCT
ejpam-3506	491	37	a	a	PRON
ejpam-3506	491	38	)	)	PUNCT
ejpam-3506	491	39	and	and	CCONJ
ejpam-3506	491	40	(	(	PUNCT
ejpam-3506	491	41	y	y	PROPN
ejpam-3506	491	42	,	,	PUNCT
ejpam-3506	491	43	b	b	NOUN
ejpam-3506	491	44	)	)	PUNCT
ejpam-3506	491	45	be	be	AUX
ejpam-3506	491	46	distinct	distinct	ADJ
ejpam-3506	491	47	non	non	ADJ
ejpam-3506	491	48	-	-	ADJ
ejpam-3506	491	49	adjacent	adjacent	ADJ
ejpam-3506	491	50	vertices	vertex	NOUN
ejpam-3506	491	51	of	of	ADP
ejpam-3506	491	52	〈	〈	PROPN
ejpam-3506	491	53	ng(c1	ng(c1	NOUN
ejpam-3506	491	54	)	)	PUNCT
ejpam-3506	491	55	〉	〉	PROPN
ejpam-3506	491	56	.	.	PUNCT
ejpam-3506	492	1	consider	consider	VERB
ejpam-3506	492	2	the	the	DET
ejpam-3506	492	3	following	follow	VERB
ejpam-3506	492	4	cases	case	NOUN
ejpam-3506	492	5	:	:	PUNCT
ejpam-3506	492	6	case	case	NOUN
ejpam-3506	492	7	1	1	NUM
ejpam-3506	492	8	.	.	PUNCT
ejpam-3506	492	9	x	x	NOUN
ejpam-3506	493	1	=	=	SYM
ejpam-3506	493	2	y	y	NOUN
ejpam-3506	493	3	let	let	VERB
ejpam-3506	493	4	[	[	X
ejpam-3506	493	5	a1	a1	NOUN
ejpam-3506	493	6	,	,	PUNCT
ejpam-3506	493	7	a2	a2	PROPN
ejpam-3506	493	8	,	,	PUNCT
ejpam-3506	493	9	...	...	PUNCT
ejpam-3506	493	10	,	,	PUNCT
ejpam-3506	493	11	ak	ak	PROPN
ejpam-3506	493	12	]	]	X
ejpam-3506	493	13	,	,	PUNCT
ejpam-3506	493	14	where	where	SCONJ
ejpam-3506	493	15	a1	a1	NOUN
ejpam-3506	493	16	=	=	PUNCT
ejpam-3506	493	17	a	a	NOUN
ejpam-3506	493	18	and	and	CCONJ
ejpam-3506	493	19	ak	ak	PROPN
ejpam-3506	493	20	=	=	SYM
ejpam-3506	493	21	b	b	PROPN
ejpam-3506	493	22	,	,	PUNCT
ejpam-3506	493	23	be	be	AUX
ejpam-3506	493	24	an	an	DET
ejpam-3506	493	25	a	a	DET
ejpam-3506	493	26	-	-	PUNCT
ejpam-3506	493	27	b	b	NOUN
ejpam-3506	493	28	geodesic	geodesic	NOUN
ejpam-3506	493	29	.	.	PUNCT
ejpam-3506	494	1	if	if	SCONJ
ejpam-3506	494	2	x	x	SYM
ejpam-3506	494	3	∈	∈	PROPN
ejpam-3506	494	4	s1	s1	NOUN
ejpam-3506	494	5	,	,	PUNCT
ejpam-3506	494	6	then	then	ADV
ejpam-3506	494	7	{	{	PUNCT
ejpam-3506	494	8	x	x	NOUN
ejpam-3506	494	9	}	}	PUNCT
ejpam-3506	494	10	×	×	NOUN
ejpam-3506	494	11	v	v	NOUN
ejpam-3506	494	12	(	(	PUNCT
ejpam-3506	494	13	h	h	NOUN
ejpam-3506	494	14	)	)	PUNCT
ejpam-3506	494	15	⊆	⊆	NUM
ejpam-3506	494	16	ng	ng	PROPN
ejpam-3506	494	17	�	�	PROPN
ejpam-3506	494	18	h(c1	h(c1	PROPN
ejpam-3506	494	19	)	)	PUNCT
ejpam-3506	494	20	.	.	PUNCT
ejpam-3506	495	1	it	it	PRON
ejpam-3506	495	2	follows	follow	VERB
ejpam-3506	495	3	that	that	SCONJ
ejpam-3506	495	4	[	[	X
ejpam-3506	495	5	(	(	PUNCT
ejpam-3506	495	6	x	x	NOUN
ejpam-3506	495	7	,	,	PUNCT
ejpam-3506	495	8	a1	a1	NOUN
ejpam-3506	495	9	)	)	PUNCT
ejpam-3506	495	10	,	,	PUNCT
ejpam-3506	495	11	(	(	PUNCT
ejpam-3506	495	12	x	x	NOUN
ejpam-3506	495	13	,	,	PUNCT
ejpam-3506	495	14	a2	a2	PROPN
ejpam-3506	495	15	)	)	PUNCT
ejpam-3506	495	16	...	...	PUNCT
ejpam-3506	495	17	,	,	PUNCT
ejpam-3506	495	18	(	(	PUNCT
ejpam-3506	495	19	x	x	NOUN
ejpam-3506	495	20	,	,	PUNCT
ejpam-3506	495	21	ak	ak	PROPN
ejpam-3506	495	22	)	)	PUNCT
ejpam-3506	495	23	]	]	PUNCT
ejpam-3506	495	24	is	be	AUX
ejpam-3506	495	25	an	an	DET
ejpam-3506	495	26	(	(	PUNCT
ejpam-3506	495	27	x	x	NOUN
ejpam-3506	495	28	,	,	PUNCT
ejpam-3506	495	29	a)-(y	a)-(y	PROPN
ejpam-3506	495	30	,	,	PUNCT
ejpam-3506	495	31	b	b	NOUN
ejpam-3506	495	32	)	)	PUNCT
ejpam-3506	495	33	path	path	NOUN
ejpam-3506	495	34	in	in	ADP
ejpam-3506	495	35	〈	〈	PROPN
ejpam-3506	495	36	ng	ng	PROPN
ejpam-3506	495	37	�	�	PROPN
ejpam-3506	495	38	h(c1	h(c1	PROPN
ejpam-3506	495	39	)	)	PUNCT
ejpam-3506	495	40	〉	〉	PROPN
ejpam-3506	495	41	.	.	PUNCT
ejpam-3506	496	1	if	if	SCONJ
ejpam-3506	496	2	x	x	X
ejpam-3506	496	3	/∈	/∈	PUNCT
ejpam-3506	496	4	s1	s1	NOUN
ejpam-3506	496	5	,	,	PUNCT
ejpam-3506	496	6	then	then	ADV
ejpam-3506	496	7	there	there	PRON
ejpam-3506	496	8	exists	exist	VERB
ejpam-3506	496	9	z	z	NOUN
ejpam-3506	496	10	∈	∈	PROPN
ejpam-3506	496	11	s1	s1	PROPN
ejpam-3506	496	12	∩ng(x	∩ng(x	PROPN
ejpam-3506	496	13	)	)	PUNCT
ejpam-3506	496	14	since	since	SCONJ
ejpam-3506	496	15	s1	s1	NOUN
ejpam-3506	496	16	is	be	AUX
ejpam-3506	496	17	a	a	DET
ejpam-3506	496	18	dominating	dominating	NOUN
ejpam-3506	496	19	set	set	NOUN
ejpam-3506	496	20	of	of	ADP
ejpam-3506	496	21	g.	g.	PROPN
ejpam-3506	496	22	since	since	SCONJ
ejpam-3506	496	23	{	{	PUNCT
ejpam-3506	496	24	z}×v	z}×v	X
ejpam-3506	496	25	(	(	PUNCT
ejpam-3506	496	26	h	h	NOUN
ejpam-3506	496	27	)	)	PUNCT
ejpam-3506	496	28	⊆	⊆	NUM
ejpam-3506	496	29	c1	c1	NOUN
ejpam-3506	496	30	,	,	PUNCT
ejpam-3506	496	31	{	{	PUNCT
ejpam-3506	496	32	x}×v	x}×v	PROPN
ejpam-3506	496	33	(	(	PUNCT
ejpam-3506	496	34	h	h	NOUN
ejpam-3506	496	35	)	)	PUNCT
ejpam-3506	496	36	⊆	⊆	NUM
ejpam-3506	496	37	ng	ng	PROPN
ejpam-3506	496	38	�	�	PROPN
ejpam-3506	496	39	h(c1	h(c1	PROPN
ejpam-3506	496	40	)	)	PUNCT
ejpam-3506	496	41	.	.	PUNCT
ejpam-3506	497	1	hence	hence	ADV
ejpam-3506	497	2	,	,	PUNCT
ejpam-3506	497	3	[	[	X
ejpam-3506	497	4	(	(	PUNCT
ejpam-3506	497	5	x	x	NOUN
ejpam-3506	497	6	,	,	PUNCT
ejpam-3506	497	7	a1	a1	NOUN
ejpam-3506	497	8	)	)	PUNCT
ejpam-3506	497	9	,	,	PUNCT
ejpam-3506	497	10	(	(	PUNCT
ejpam-3506	497	11	x	x	NOUN
ejpam-3506	497	12	,	,	PUNCT
ejpam-3506	497	13	a2	a2	PROPN
ejpam-3506	497	14	)	)	PUNCT
ejpam-3506	497	15	...	...	PUNCT
ejpam-3506	497	16	,	,	PUNCT
ejpam-3506	497	17	(	(	PUNCT
ejpam-3506	497	18	x	x	NOUN
ejpam-3506	497	19	,	,	PUNCT
ejpam-3506	497	20	ak	ak	PROPN
ejpam-3506	497	21	)	)	PUNCT
ejpam-3506	497	22	]	]	PUNCT
ejpam-3506	497	23	is	be	AUX
ejpam-3506	497	24	an	an	DET
ejpam-3506	497	25	(	(	PUNCT
ejpam-3506	497	26	x	x	NOUN
ejpam-3506	497	27	,	,	PUNCT
ejpam-3506	497	28	a)-(y	a)-(y	PROPN
ejpam-3506	497	29	,	,	PUNCT
ejpam-3506	497	30	b	b	NOUN
ejpam-3506	497	31	)	)	PUNCT
ejpam-3506	497	32	path	path	NOUN
ejpam-3506	497	33	in	in	ADP
ejpam-3506	497	34	〈	〈	PROPN
ejpam-3506	497	35	ng	ng	PROPN
ejpam-3506	497	36	�	�	PROPN
ejpam-3506	497	37	h(c1	h(c1	PROPN
ejpam-3506	497	38	)	)	PUNCT
ejpam-3506	497	39	〉	〉	PROPN
ejpam-3506	497	40	.	.	PUNCT
ejpam-3506	497	41	case	case	NOUN
ejpam-3506	497	42	2	2	NUM
ejpam-3506	497	43	.	.	NUM
ejpam-3506	497	44	x	x	SYM
ejpam-3506	498	1	6=	6=	NUM
ejpam-3506	498	2	y	y	PRON
ejpam-3506	498	3	let	let	VERB
ejpam-3506	498	4	[	[	X
ejpam-3506	498	5	x1	x1	ADJ
ejpam-3506	498	6	,	,	PUNCT
ejpam-3506	498	7	x2	x2	PROPN
ejpam-3506	498	8	,	,	PUNCT
ejpam-3506	498	9	...	...	PUNCT
ejpam-3506	498	10	,	,	PUNCT
ejpam-3506	498	11	xk	xk	PROPN
ejpam-3506	498	12	]	]	X
ejpam-3506	498	13	,	,	PUNCT
ejpam-3506	498	14	where	where	SCONJ
ejpam-3506	498	15	x1	x1	ADJ
ejpam-3506	498	16	=	=	PUNCT
ejpam-3506	498	17	x	x	X
ejpam-3506	498	18	and	and	CCONJ
ejpam-3506	498	19	xk	xk	PROPN
ejpam-3506	498	20	=	=	SYM
ejpam-3506	498	21	y	y	PROPN
ejpam-3506	498	22	,	,	PUNCT
ejpam-3506	498	23	be	be	AUX
ejpam-3506	498	24	an	an	DET
ejpam-3506	498	25	x	x	ADJ
ejpam-3506	498	26	-	-	NOUN
ejpam-3506	498	27	y	y	ADJ
ejpam-3506	498	28	geodesic	geodesic	NOUN
ejpam-3506	498	29	.	.	PUNCT
ejpam-3506	499	1	let	let	VERB
ejpam-3506	499	2	j	j	PROPN
ejpam-3506	499	3	∈	∈	PROPN
ejpam-3506	499	4	{	{	PUNCT
ejpam-3506	499	5	1	1	NUM
ejpam-3506	499	6	,	,	PUNCT
ejpam-3506	499	7	2	2	NUM
ejpam-3506	499	8	,	,	PUNCT
ejpam-3506	499	9	...	...	PUNCT
ejpam-3506	499	10	,	,	PUNCT
ejpam-3506	499	11	k	k	NOUN
ejpam-3506	499	12	}	}	PUNCT
ejpam-3506	499	13	.	.	PUNCT
ejpam-3506	500	1	if	if	SCONJ
ejpam-3506	500	2	xj	xj	PROPN
ejpam-3506	500	3	∈	∈	PROPN
ejpam-3506	500	4	s1	s1	NOUN
ejpam-3506	500	5	,	,	PUNCT
ejpam-3506	500	6	then	then	ADV
ejpam-3506	500	7	{	{	PUNCT
ejpam-3506	500	8	xj	xj	PROPN
ejpam-3506	500	9	}	}	PUNCT
ejpam-3506	500	10	×	×	NOUN
ejpam-3506	500	11	v	v	NOUN
ejpam-3506	500	12	(	(	PUNCT
ejpam-3506	500	13	h	h	NOUN
ejpam-3506	500	14	)	)	PUNCT
ejpam-3506	500	15	⊆	⊆	NUM
ejpam-3506	500	16	c1	c1	NOUN
ejpam-3506	500	17	;	;	PUNCT
ejpam-3506	500	18	hence	hence	ADV
ejpam-3506	500	19	,	,	PUNCT
ejpam-3506	500	20	{	{	PUNCT
ejpam-3506	500	21	xj	xj	ADJ
ejpam-3506	500	22	}	}	PUNCT
ejpam-3506	500	23	×	×	NOUN
ejpam-3506	500	24	v	v	NOUN
ejpam-3506	500	25	(	(	PUNCT
ejpam-3506	500	26	h	h	NOUN
ejpam-3506	500	27	)	)	PUNCT
ejpam-3506	500	28	⊆	⊆	NUM
ejpam-3506	500	29	ng	ng	PROPN
ejpam-3506	500	30	�	�	PROPN
ejpam-3506	500	31	h(c1	h(c1	PROPN
ejpam-3506	500	32	)	)	PUNCT
ejpam-3506	500	33	(	(	PUNCT
ejpam-3506	500	34	since	since	SCONJ
ejpam-3506	500	35	h	h	NOUN
ejpam-3506	500	36	is	be	AUX
ejpam-3506	500	37	connected	connect	VERB
ejpam-3506	500	38	)	)	PUNCT
ejpam-3506	500	39	.	.	PUNCT
ejpam-3506	501	1	if	if	SCONJ
ejpam-3506	501	2	xj	xj	PROPN
ejpam-3506	501	3	∈	∈	PROPN
ejpam-3506	501	4	s1	s1	NOUN
ejpam-3506	501	5	,	,	PUNCT
ejpam-3506	501	6	then	then	ADV
ejpam-3506	501	7	there	there	PRON
ejpam-3506	501	8	exists	exist	VERB
ejpam-3506	501	9	zj	zj	PROPN
ejpam-3506	501	10	∈	∈	PROPN
ejpam-3506	501	11	s1	s1	PROPN
ejpam-3506	501	12	∩	∩	NOUN
ejpam-3506	501	13	ng(xj	ng(xj	ADV
ejpam-3506	501	14	)	)	PUNCT
ejpam-3506	501	15	because	because	SCONJ
ejpam-3506	501	16	s1	s1	NOUN
ejpam-3506	501	17	is	be	AUX
ejpam-3506	501	18	a	a	DET
ejpam-3506	501	19	dominating	dominating	NOUN
ejpam-3506	501	20	set	set	NOUN
ejpam-3506	501	21	.	.	PUNCT
ejpam-3506	502	1	since	since	SCONJ
ejpam-3506	502	2	{	{	PUNCT
ejpam-3506	502	3	zj	zj	NOUN
ejpam-3506	502	4	}	}	PUNCT
ejpam-3506	502	5	×	×	PROPN
ejpam-3506	502	6	v	v	NOUN
ejpam-3506	502	7	(	(	PUNCT
ejpam-3506	502	8	h	h	NOUN
ejpam-3506	502	9	)	)	PUNCT
ejpam-3506	502	10	⊆	⊆	NUM
ejpam-3506	502	11	c1	c1	NOUN
ejpam-3506	502	12	,	,	PUNCT
ejpam-3506	502	13	it	it	PRON
ejpam-3506	502	14	follows	follow	VERB
ejpam-3506	502	15	that	that	SCONJ
ejpam-3506	502	16	{	{	PUNCT
ejpam-3506	502	17	xj	xj	PROPN
ejpam-3506	502	18	}	}	PUNCT
ejpam-3506	502	19	×	×	NOUN
ejpam-3506	502	20	v	v	NOUN
ejpam-3506	502	21	(	(	PUNCT
ejpam-3506	502	22	h	h	NOUN
ejpam-3506	502	23	)	)	PUNCT
ejpam-3506	502	24	⊆	⊆	NUM
ejpam-3506	502	25	ng	ng	PROPN
ejpam-3506	502	26	�	�	PROPN
ejpam-3506	502	27	h(c1	h(c1	PROPN
ejpam-3506	502	28	)	)	PUNCT
ejpam-3506	502	29	.	.	PUNCT
ejpam-3506	503	1	hence	hence	ADV
ejpam-3506	503	2	,	,	PUNCT
ejpam-3506	503	3	if	if	SCONJ
ejpam-3506	503	4	a	a	DET
ejpam-3506	503	5	=	=	SYM
ejpam-3506	503	6	b	b	NOUN
ejpam-3506	503	7	,	,	PUNCT
ejpam-3506	503	8	then	then	ADV
ejpam-3506	503	9	[	[	X
ejpam-3506	503	10	(	(	PUNCT
ejpam-3506	503	11	x1	x1	PROPN
ejpam-3506	503	12	,	,	PUNCT
ejpam-3506	503	13	a	a	NOUN
ejpam-3506	503	14	)	)	PUNCT
ejpam-3506	503	15	,	,	PUNCT
ejpam-3506	503	16	(	(	PUNCT
ejpam-3506	503	17	x2	x2	PROPN
ejpam-3506	503	18	,	,	PUNCT
ejpam-3506	503	19	a	a	NOUN
ejpam-3506	503	20	)	)	PUNCT
ejpam-3506	503	21	...	...	PUNCT
ejpam-3506	503	22	,	,	PUNCT
ejpam-3506	503	23	(	(	PUNCT
ejpam-3506	503	24	xk	xk	PROPN
ejpam-3506	503	25	,	,	PUNCT
ejpam-3506	503	26	a	a	NOUN
ejpam-3506	503	27	)	)	PUNCT
ejpam-3506	503	28	]	]	PUNCT
ejpam-3506	503	29	is	be	AUX
ejpam-3506	503	30	an	an	DET
ejpam-3506	503	31	(	(	PUNCT
ejpam-3506	503	32	x	x	NOUN
ejpam-3506	503	33	,	,	PUNCT
ejpam-3506	503	34	a)-(y	a)-(y	PROPN
ejpam-3506	503	35	,	,	PUNCT
ejpam-3506	503	36	b	b	NOUN
ejpam-3506	503	37	)	)	PUNCT
ejpam-3506	503	38	path	path	NOUN
ejpam-3506	503	39	in	in	ADP
ejpam-3506	503	40	〈	〈	PROPN
ejpam-3506	503	41	ng	ng	PROPN
ejpam-3506	503	42	�	�	PROPN
ejpam-3506	503	43	h(c1	h(c1	PROPN
ejpam-3506	503	44	)	)	PUNCT
ejpam-3506	503	45	〉	〉	PROPN
ejpam-3506	503	46	.	.	PUNCT
ejpam-3506	504	1	suppose	suppose	VERB
ejpam-3506	505	1	a	a	DET
ejpam-3506	505	2	6=	6=	PROPN
ejpam-3506	505	3	b.	b.	PROPN
ejpam-3506	505	4	let	let	VERB
ejpam-3506	505	5	[	[	X
ejpam-3506	505	6	a1	a1	NOUN
ejpam-3506	505	7	,	,	PUNCT
ejpam-3506	505	8	a2	a2	PROPN
ejpam-3506	505	9	,	,	PUNCT
ejpam-3506	505	10	...	...	PUNCT
ejpam-3506	505	11	,	,	PUNCT
ejpam-3506	505	12	ar	ar	PROPN
ejpam-3506	505	13	]	]	X
ejpam-3506	505	14	,	,	PUNCT
ejpam-3506	505	15	where	where	SCONJ
ejpam-3506	505	16	a1	a1	NOUN
ejpam-3506	505	17	=	=	PUNCT
ejpam-3506	505	18	a	a	PRON
ejpam-3506	505	19	and	and	CCONJ
ejpam-3506	505	20	ar	ar	PROPN
ejpam-3506	505	21	=	=	SYM
ejpam-3506	505	22	b	b	PROPN
ejpam-3506	505	23	,	,	PUNCT
ejpam-3506	505	24	be	be	AUX
ejpam-3506	505	25	an	an	DET
ejpam-3506	505	26	a	a	DET
ejpam-3506	505	27	-	-	PUNCT
ejpam-3506	505	28	b	b	NOUN
ejpam-3506	505	29	geodesic	geodesic	NOUN
ejpam-3506	505	30	.	.	PUNCT
ejpam-3506	506	1	then	then	ADV
ejpam-3506	506	2	[	[	X
ejpam-3506	506	3	(	(	PUNCT
ejpam-3506	506	4	x1	x1	ADJ
ejpam-3506	506	5	,	,	PUNCT
ejpam-3506	506	6	a1	a1	NOUN
ejpam-3506	506	7	)	)	PUNCT
ejpam-3506	506	8	,	,	PUNCT
ejpam-3506	506	9	(	(	PUNCT
ejpam-3506	506	10	x2	x2	NOUN
ejpam-3506	506	11	,	,	PUNCT
ejpam-3506	506	12	a1	a1	PROPN
ejpam-3506	506	13	)	)	PUNCT
ejpam-3506	506	14	...	...	PUNCT
ejpam-3506	506	15	,	,	PUNCT
ejpam-3506	506	16	(	(	PUNCT
ejpam-3506	506	17	xk	xk	NOUN
ejpam-3506	506	18	,	,	PUNCT
ejpam-3506	506	19	a1	a1	PROPN
ejpam-3506	506	20	)	)	PUNCT
ejpam-3506	506	21	,	,	PUNCT
ejpam-3506	506	22	(	(	PUNCT
ejpam-3506	506	23	xk	xk	PROPN
ejpam-3506	506	24	,	,	PUNCT
ejpam-3506	506	25	a2	a2	PROPN
ejpam-3506	506	26	)	)	PUNCT
ejpam-3506	506	27	,	,	PUNCT
ejpam-3506	506	28	...	...	PUNCT
ejpam-3506	506	29	,	,	PUNCT
ejpam-3506	506	30	(	(	PUNCT
ejpam-3506	506	31	xk	xk	PROPN
ejpam-3506	506	32	,	,	PUNCT
ejpam-3506	506	33	ar	ar	PROPN
ejpam-3506	506	34	)	)	PUNCT
ejpam-3506	506	35	]	]	PUNCT
ejpam-3506	506	36	is	be	AUX
ejpam-3506	506	37	an	an	DET
ejpam-3506	506	38	(	(	PUNCT
ejpam-3506	506	39	x	x	NOUN
ejpam-3506	506	40	,	,	PUNCT
ejpam-3506	506	41	a)-(y	a)-(y	PROPN
ejpam-3506	506	42	,	,	PUNCT
ejpam-3506	506	43	b	b	NOUN
ejpam-3506	506	44	)	)	PUNCT
ejpam-3506	506	45	path	path	NOUN
ejpam-3506	506	46	in	in	ADP
ejpam-3506	506	47	〈	〈	PROPN
ejpam-3506	506	48	ng	ng	PROPN
ejpam-3506	506	49	�	�	PROPN
ejpam-3506	506	50	h(c1	h(c1	PROPN
ejpam-3506	506	51	)	)	PUNCT
ejpam-3506	506	52	〉	〉	PROPN
ejpam-3506	506	53	.	.	PUNCT
ejpam-3506	507	1	therefore	therefore	ADV
ejpam-3506	507	2	,	,	PUNCT
ejpam-3506	507	3	c1	c1	PROPN
ejpam-3506	507	4	is	be	AUX
ejpam-3506	507	5	an	an	DET
ejpam-3506	507	6	nckfd	nckfd	NOUN
ejpam-3506	507	7	-	-	PUNCT
ejpam-3506	507	8	set	set	NOUN
ejpam-3506	507	9	in	in	ADP
ejpam-3506	507	10	g	g	PROPN
ejpam-3506	507	11	�	�	PROPN
ejpam-3506	507	12	h.	h.	PROPN
ejpam-3506	507	13	similarly	similarly	ADV
ejpam-3506	507	14	,	,	PUNCT
ejpam-3506	507	15	if	if	SCONJ
ejpam-3506	507	16	s2	s2	NOUN
ejpam-3506	507	17	is	be	AUX
ejpam-3506	507	18	a	a	DET
ejpam-3506	507	19	kfd	kfd	NOUN
ejpam-3506	507	20	-	-	PUNCT
ejpam-3506	507	21	set	set	NOUN
ejpam-3506	507	22	in	in	ADP
ejpam-3506	507	23	h	h	NOUN
ejpam-3506	507	24	,	,	PUNCT
ejpam-3506	507	25	then	then	ADV
ejpam-3506	507	26	c2	c2	PROPN
ejpam-3506	507	27	=	=	SYM
ejpam-3506	507	28	v	v	PROPN
ejpam-3506	507	29	(	(	PUNCT
ejpam-3506	507	30	g)×	g)×	NOUN
ejpam-3506	507	31	s2	s2	NOUN
ejpam-3506	507	32	is	be	AUX
ejpam-3506	507	33	an	an	DET
ejpam-3506	507	34	nckfd	nckfd	NOUN
ejpam-3506	507	35	-	-	PUNCT
ejpam-3506	507	36	set	set	NOUN
ejpam-3506	507	37	in	in	ADP
ejpam-3506	507	38	g	g	PROPN
ejpam-3506	507	39	�	�	PROPN
ejpam-3506	507	40	h.	h.	PROPN
ejpam-3506	507	41	�	�	PROPN
ejpam-3506	507	42	corollary	corollary	ADJ
ejpam-3506	507	43	8	8	NUM
ejpam-3506	507	44	.	.	PUNCT
ejpam-3506	508	1	let	let	VERB
ejpam-3506	508	2	g	g	NOUN
ejpam-3506	508	3	and	and	CCONJ
ejpam-3506	508	4	h	h	NOUN
ejpam-3506	508	5	be	be	AUX
ejpam-3506	508	6	nontrivial	nontrivial	ADJ
ejpam-3506	508	7	connected	connect	VERB
ejpam-3506	508	8	graphs	graph	NOUN
ejpam-3506	508	9	and	and	CCONJ
ejpam-3506	508	10	∅	∅	NOUN
ejpam-3506	508	11	6=	6=	ADP
ejpam-3506	508	12	s1	s1	PROPN
ejpam-3506	508	13	⊆	⊆	NUM
ejpam-3506	508	14	v	v	NOUN
ejpam-3506	508	15	(	(	PUNCT
ejpam-3506	508	16	g	g	NOUN
ejpam-3506	508	17	)	)	PUNCT
ejpam-3506	508	18	.	.	PUNCT
ejpam-3506	509	1	the	the	DET
ejpam-3506	509	2	following	follow	VERB
ejpam-3506	509	3	are	be	AUX
ejpam-3506	509	4	equivalent	equivalent	ADJ
ejpam-3506	509	5	:	:	PUNCT
ejpam-3506	509	6	(	(	PUNCT
ejpam-3506	509	7	i	i	NOUN
ejpam-3506	509	8	)	)	PUNCT
ejpam-3506	509	9	s1	s1	PROPN
ejpam-3506	509	10	is	be	AUX
ejpam-3506	509	11	a	a	DET
ejpam-3506	509	12	kfd	kfd	NOUN
ejpam-3506	509	13	-	-	PUNCT
ejpam-3506	509	14	set	set	NOUN
ejpam-3506	509	15	of	of	ADP
ejpam-3506	509	16	g.	g.	PROPN
ejpam-3506	509	17	(	(	PUNCT
ejpam-3506	509	18	ii	ii	PROPN
ejpam-3506	509	19	)	)	PUNCT
ejpam-3506	509	20	c1	c1	NOUN
ejpam-3506	509	21	=	=	PROPN
ejpam-3506	510	1	s1	s1	PROPN
ejpam-3506	510	2	×	×	PROPN
ejpam-3506	510	3	v	v	NOUN
ejpam-3506	510	4	(	(	PUNCT
ejpam-3506	510	5	h	h	NOUN
ejpam-3506	510	6	)	)	PUNCT
ejpam-3506	510	7	is	be	AUX
ejpam-3506	510	8	a	a	DET
ejpam-3506	510	9	kfd	kfd	NOUN
ejpam-3506	510	10	-	-	PUNCT
ejpam-3506	510	11	set	set	NOUN
ejpam-3506	510	12	of	of	ADP
ejpam-3506	510	13	g	g	PROPN
ejpam-3506	510	14	�	�	PROPN
ejpam-3506	510	15	h.	h.	PROPN
ejpam-3506	510	16	(	(	PUNCT
ejpam-3506	510	17	iii	iii	NOUN
ejpam-3506	510	18	)	)	PUNCT
ejpam-3506	510	19	c1	c1	NOUN
ejpam-3506	510	20	=	=	PROPN
ejpam-3506	511	1	s1	s1	PROPN
ejpam-3506	511	2	×	×	PROPN
ejpam-3506	511	3	v	v	NOUN
ejpam-3506	511	4	(	(	PUNCT
ejpam-3506	511	5	h	h	NOUN
ejpam-3506	511	6	)	)	PUNCT
ejpam-3506	511	7	is	be	AUX
ejpam-3506	511	8	an	an	DET
ejpam-3506	511	9	nckfd	nckfd	NOUN
ejpam-3506	511	10	-	-	PUNCT
ejpam-3506	511	11	set	set	NOUN
ejpam-3506	511	12	of	of	ADP
ejpam-3506	511	13	g	g	PROPN
ejpam-3506	511	14	�	�	PROPN
ejpam-3506	511	15	h.	h.	NOUN
ejpam-3506	511	16	proof	proof	NOUN
ejpam-3506	511	17	.	.	PUNCT
ejpam-3506	512	1	by	by	ADP
ejpam-3506	512	2	corollary	corollary	ADJ
ejpam-3506	512	3	4	4	NUM
ejpam-3506	512	4	,	,	PUNCT
ejpam-3506	512	5	(	(	PUNCT
ejpam-3506	512	6	i	i	NOUN
ejpam-3506	512	7	)	)	PUNCT
ejpam-3506	512	8	implies	imply	VERB
ejpam-3506	512	9	(	(	PUNCT
ejpam-3506	512	10	ii	ii	NOUN
ejpam-3506	512	11	)	)	PUNCT
ejpam-3506	512	12	.	.	PUNCT
ejpam-3506	513	1	suppose	suppose	VERB
ejpam-3506	513	2	c1	c1	PROPN
ejpam-3506	513	3	is	be	AUX
ejpam-3506	513	4	a	a	DET
ejpam-3506	513	5	kfd	kfd	NOUN
ejpam-3506	513	6	-	-	PUNCT
ejpam-3506	513	7	set	set	NOUN
ejpam-3506	513	8	of	of	ADP
ejpam-3506	513	9	g	g	PROPN
ejpam-3506	513	10	�	�	PROPN
ejpam-3506	513	11	h.	h.	PROPN
ejpam-3506	513	12	let	let	VERB
ejpam-3506	513	13	v	v	ADP
ejpam-3506	513	14	∈	∈	PROPN
ejpam-3506	513	15	v	v	NOUN
ejpam-3506	513	16	(	(	PUNCT
ejpam-3506	513	17	g)\s1	g)\s1	NOUN
ejpam-3506	513	18	and	and	CCONJ
ejpam-3506	513	19	let	let	VERB
ejpam-3506	513	20	a	a	DET
ejpam-3506	513	21	∈	∈	PROPN
ejpam-3506	513	22	v	v	NOUN
ejpam-3506	513	23	(	(	PUNCT
ejpam-3506	513	24	h	h	NOUN
ejpam-3506	513	25	)	)	PUNCT
ejpam-3506	513	26	.	.	PUNCT
ejpam-3506	514	1	then	then	ADV
ejpam-3506	514	2	(	(	PUNCT
ejpam-3506	514	3	v	v	NOUN
ejpam-3506	514	4	,	,	PUNCT
ejpam-3506	514	5	a	a	PRON
ejpam-3506	514	6	)	)	PUNCT
ejpam-3506	514	7	/∈	/∈	PUNCT
ejpam-3506	515	1	c1	c1	PROPN
ejpam-3506	515	2	and	and	CCONJ
ejpam-3506	515	3	|ng	|ng	NOUN
ejpam-3506	515	4	�	�	NOUN
ejpam-3506	515	5	h((v	h((v	NOUN
ejpam-3506	515	6	,	,	PUNCT
ejpam-3506	515	7	a))∩c1|	a))∩c1|	PUNCT
ejpam-3506	515	8	=	=	SYM
ejpam-3506	515	9	|ng(v)∩s1|	|ng(v)∩s1|	PUNCT
ejpam-3506	515	10	=	=	SYM
ejpam-3506	515	11	k	k	PROPN
ejpam-3506	515	12	since	since	SCONJ
ejpam-3506	515	13	c1	c1	PROPN
ejpam-3506	515	14	is	be	AUX
ejpam-3506	515	15	a	a	DET
ejpam-3506	515	16	kfd	kfd	NOUN
ejpam-3506	515	17	-	-	PUNCT
ejpam-3506	515	18	set	set	NOUN
ejpam-3506	515	19	.	.	PUNCT
ejpam-3506	516	1	thus	thus	ADV
ejpam-3506	516	2	,	,	PUNCT
ejpam-3506	516	3	s1	s1	PROPN
ejpam-3506	516	4	is	be	AUX
ejpam-3506	516	5	a	a	DET
ejpam-3506	516	6	kfd	kfd	NOUN
ejpam-3506	516	7	-	-	PUNCT
ejpam-3506	516	8	set	set	NOUN
ejpam-3506	516	9	of	of	ADP
ejpam-3506	516	10	g	g	PROPN
ejpam-3506	516	11	and	and	CCONJ
ejpam-3506	516	12	(	(	PUNCT
ejpam-3506	516	13	ii	ii	NOUN
ejpam-3506	516	14	)	)	PUNCT
ejpam-3506	516	15	implies	imply	VERB
ejpam-3506	516	16	(	(	PUNCT
ejpam-3506	516	17	i	i	NOUN
ejpam-3506	516	18	)	)	PUNCT
ejpam-3506	516	19	.	.	PUNCT
ejpam-3506	517	1	by	by	ADP
ejpam-3506	517	2	theorem	theorem	NOUN
ejpam-3506	517	3	14	14	NUM
ejpam-3506	517	4	,	,	PUNCT
ejpam-3506	517	5	(	(	PUNCT
ejpam-3506	517	6	i	i	NOUN
ejpam-3506	517	7	)	)	PUNCT
ejpam-3506	517	8	implies	imply	VERB
ejpam-3506	517	9	(	(	PUNCT
ejpam-3506	517	10	iii	iii	NOUN
ejpam-3506	517	11	)	)	PUNCT
ejpam-3506	517	12	.	.	PUNCT
ejpam-3506	518	1	by	by	ADP
ejpam-3506	518	2	definitions	definition	NOUN
ejpam-3506	518	3	of	of	ADP
ejpam-3506	518	4	kfd	kfd	NOUN
ejpam-3506	518	5	-	-	PUNCT
ejpam-3506	518	6	set	set	VERB
ejpam-3506	518	7	and	and	CCONJ
ejpam-3506	518	8	nckfd	nckfd	NOUN
ejpam-3506	518	9	-	-	PUNCT
ejpam-3506	518	10	set	set	NOUN
ejpam-3506	518	11	,	,	PUNCT
ejpam-3506	518	12	(	(	PUNCT
ejpam-3506	518	13	iii	iii	NOUN
ejpam-3506	518	14	)	)	PUNCT
ejpam-3506	518	15	implies	imply	VERB
ejpam-3506	518	16	(	(	PUNCT
ejpam-3506	518	17	ii	ii	NOUN
ejpam-3506	518	18	)	)	PUNCT
ejpam-3506	518	19	.	.	PUNCT
ejpam-3506	519	1	therefore	therefore	ADV
ejpam-3506	519	2	,	,	PUNCT
ejpam-3506	519	3	statements	statement	NOUN
ejpam-3506	519	4	(	(	PUNCT
ejpam-3506	519	5	i	i	NOUN
ejpam-3506	519	6	)	)	PUNCT
ejpam-3506	519	7	,	,	PUNCT
ejpam-3506	519	8	(	(	PUNCT
ejpam-3506	519	9	ii	ii	NOUN
ejpam-3506	519	10	)	)	PUNCT
ejpam-3506	519	11	,	,	PUNCT
ejpam-3506	519	12	and	and	CCONJ
ejpam-3506	519	13	(	(	PUNCT
ejpam-3506	519	14	iii	iii	X
ejpam-3506	519	15	)	)	PUNCT
ejpam-3506	519	16	are	be	AUX
ejpam-3506	519	17	equivalent	equivalent	ADJ
ejpam-3506	519	18	.	.	PUNCT
ejpam-3506	520	1	�	�	PROPN
ejpam-3506	520	2	corollary	corollary	ADJ
ejpam-3506	520	3	9	9	NUM
ejpam-3506	520	4	.	.	PUNCT
ejpam-3506	521	1	let	let	VERB
ejpam-3506	521	2	g	g	NOUN
ejpam-3506	521	3	and	and	CCONJ
ejpam-3506	521	4	h	h	NOUN
ejpam-3506	521	5	be	be	AUX
ejpam-3506	521	6	nontrivial	nontrivial	ADJ
ejpam-3506	521	7	connected	connect	VERB
ejpam-3506	521	8	graphs	graph	NOUN
ejpam-3506	521	9	of	of	ADP
ejpam-3506	521	10	orders	order	NOUN
ejpam-3506	521	11	m	m	VERB
ejpam-3506	521	12	and	and	CCONJ
ejpam-3506	521	13	n	n	CCONJ
ejpam-3506	521	14	,	,	PUNCT
ejpam-3506	521	15	respectively	respectively	ADV
ejpam-3506	521	16	,	,	PUNCT
ejpam-3506	521	17	and	and	CCONJ
ejpam-3506	521	18	k	k	X
ejpam-3506	521	19	a	a	DET
ejpam-3506	521	20	positive	positive	ADJ
ejpam-3506	521	21	integer	integer	NOUN
ejpam-3506	521	22	with	with	ADP
ejpam-3506	521	23	k	k	PROPN
ejpam-3506	521	24	≤	≤	X
ejpam-3506	521	25	min{m	min{m	PROPN
ejpam-3506	521	26	,	,	PUNCT
ejpam-3506	521	27	n	n	CCONJ
ejpam-3506	521	28	}	}	PUNCT
ejpam-3506	521	29	.	.	PUNCT
ejpam-3506	522	1	then	then	ADV
ejpam-3506	522	2	γnckfd(g	γnckfd(g	NUM
ejpam-3506	522	3	�	�	NOUN
ejpam-3506	522	4	h	h	NOUN
ejpam-3506	522	5	)	)	PUNCT
ejpam-3506	522	6	≤	≤	NOUN
ejpam-3506	522	7	min{n	min{n	NOUN
ejpam-3506	522	8	·	·	PUNCT
ejpam-3506	522	9	γkfd(g),m	γkfd(g),m	PROPN
ejpam-3506	522	10	·	·	PUNCT
ejpam-3506	522	11	γkfd(h	γkfd(h	NOUN
ejpam-3506	522	12	)	)	PUNCT
ejpam-3506	522	13	}	}	PUNCT
ejpam-3506	522	14	.	.	PUNCT
ejpam-3506	523	1	in	in	ADP
ejpam-3506	523	2	particular	particular	ADJ
ejpam-3506	523	3	,	,	PUNCT
ejpam-3506	523	4	γnckfd(g	γnckfd(g	PROPN
ejpam-3506	523	5	�	�	PROPN
ejpam-3506	523	6	kn	kn	NOUN
ejpam-3506	523	7	)	)	PUNCT
ejpam-3506	523	8	≤	≤	NOUN
ejpam-3506	523	9	min{n	min{n	NOUN
ejpam-3506	523	10	·	·	PUNCT
ejpam-3506	523	11	γkfd(g),mk	γkfd(g),mk	ADJ
ejpam-3506	523	12	}	}	PUNCT
ejpam-3506	523	13	.	.	PUNCT
ejpam-3506	524	1	references	reference	NOUN
ejpam-3506	524	2	1348	1348	NUM
ejpam-3506	524	3	remark	remark	NOUN
ejpam-3506	524	4	4	4	NUM
ejpam-3506	524	5	.	.	PUNCT
ejpam-3506	525	1	the	the	DET
ejpam-3506	525	2	bound	bind	VERB
ejpam-3506	525	3	given	give	VERB
ejpam-3506	525	4	in	in	ADP
ejpam-3506	525	5	corollary	corollary	ADJ
ejpam-3506	525	6	9	9	NUM
ejpam-3506	525	7	is	be	AUX
ejpam-3506	525	8	sharp	sharp	ADJ
ejpam-3506	525	9	.	.	PUNCT
ejpam-3506	526	1	however	however	ADV
ejpam-3506	526	2	,	,	PUNCT
ejpam-3506	526	3	the	the	DET
ejpam-3506	526	4	strict	strict	ADJ
ejpam-3506	526	5	inequality	inequality	NOUN
ejpam-3506	526	6	can	can	AUX
ejpam-3506	526	7	be	be	AUX
ejpam-3506	526	8	attained	attain	VERB
ejpam-3506	526	9	.	.	PUNCT
ejpam-3506	527	1	to	to	PART
ejpam-3506	527	2	see	see	VERB
ejpam-3506	527	3	this	this	PRON
ejpam-3506	527	4	,	,	PUNCT
ejpam-3506	527	5	consider	consider	VERB
ejpam-3506	527	6	the	the	DET
ejpam-3506	527	7	graphs	graph	NOUN
ejpam-3506	527	8	shown	show	VERB
ejpam-3506	527	9	in	in	ADP
ejpam-3506	527	10	figure	figure	NOUN
ejpam-3506	527	11	6	6	NUM
ejpam-3506	527	12	.	.	PUNCT
ejpam-3506	528	1	the	the	DET
ejpam-3506	528	2	shaded	shade	VERB
ejpam-3506	528	3	vertices	vertex	NOUN
ejpam-3506	528	4	in	in	ADP
ejpam-3506	528	5	each	each	DET
ejpam-3506	528	6	graph	graph	NOUN
ejpam-3506	528	7	form	form	VERB
ejpam-3506	528	8	a	a	DET
ejpam-3506	528	9	γnckfd	γnckfd	NOUN
ejpam-3506	528	10	-	-	PUNCT
ejpam-3506	528	11	set	set	NOUN
ejpam-3506	528	12	.	.	PUNCT
ejpam-3506	529	1	thus	thus	ADV
ejpam-3506	529	2	,	,	PUNCT
ejpam-3506	529	3	(	(	PUNCT
ejpam-3506	529	4	a	a	X
ejpam-3506	529	5	)	)	PUNCT
ejpam-3506	529	6	γnc1fd(k3	γnc1fd(k3	PROPN
ejpam-3506	529	7	�	�	NOUN
ejpam-3506	529	8	p2	p2	NOUN
ejpam-3506	529	9	)	)	PUNCT
ejpam-3506	529	10	=	=	SYM
ejpam-3506	530	1	2	2	NUM
ejpam-3506	530	2	=	=	SYM
ejpam-3506	530	3	min{2	min{2	NOUN
ejpam-3506	530	4	·	·	SYM
ejpam-3506	530	5	1	1	NUM
ejpam-3506	530	6	,	,	PUNCT
ejpam-3506	530	7	3	3	NUM
ejpam-3506	530	8	·	·	SYM
ejpam-3506	530	9	1	1	NUM
ejpam-3506	530	10	}	}	PUNCT
ejpam-3506	530	11	=	=	SYM
ejpam-3506	530	12	min{|v	min{|v	PROPN
ejpam-3506	530	13	(	(	PUNCT
ejpam-3506	530	14	p2)|	p2)|	PROPN
ejpam-3506	530	15	·	·	SYM
ejpam-3506	530	16	γ1fd(k3	γ1fd(k3	NUM
ejpam-3506	530	17	)	)	PUNCT
ejpam-3506	530	18	,	,	PUNCT
ejpam-3506	530	19	|v	|v	PROPN
ejpam-3506	530	20	(	(	PUNCT
ejpam-3506	530	21	k3)|	k3)|	PROPN
ejpam-3506	530	22	·	·	SYM
ejpam-3506	530	23	γ1fd(p2	γ1fd(p2	PROPN
ejpam-3506	530	24	)	)	PUNCT
ejpam-3506	530	25	}	}	PUNCT
ejpam-3506	530	26	,	,	PUNCT
ejpam-3506	530	27	(	(	PUNCT
ejpam-3506	530	28	b	b	X
ejpam-3506	530	29	)	)	PUNCT
ejpam-3506	530	30	γnc2fd(p3	γnc2fd(p3	PROPN
ejpam-3506	530	31	�	�	PROPN
ejpam-3506	530	32	c4	c4	NOUN
ejpam-3506	530	33	)	)	PUNCT
ejpam-3506	530	34	=	=	PUNCT
ejpam-3506	531	1	6	6	NUM
ejpam-3506	531	2	=	=	SYM
ejpam-3506	531	3	min{4	min{4	PART
ejpam-3506	531	4	·	·	PUNCT
ejpam-3506	531	5	2	2	NUM
ejpam-3506	531	6	,	,	PUNCT
ejpam-3506	531	7	3	3	NUM
ejpam-3506	531	8	·	·	SYM
ejpam-3506	531	9	2	2	NUM
ejpam-3506	531	10	}	}	PUNCT
ejpam-3506	531	11	=	=	SYM
ejpam-3506	531	12	min{|v	min{|v	PROPN
ejpam-3506	531	13	(	(	PUNCT
ejpam-3506	531	14	c4)|	c4)|	PROPN
ejpam-3506	531	15	·	·	PUNCT
ejpam-3506	531	16	γ2fd(p3	γ2fd(p3	PROPN
ejpam-3506	531	17	)	)	PUNCT
ejpam-3506	531	18	,	,	PUNCT
ejpam-3506	531	19	|v	|v	PROPN
ejpam-3506	531	20	(	(	PUNCT
ejpam-3506	531	21	p3)|	p3)|	NOUN
ejpam-3506	531	22	·	·	PUNCT
ejpam-3506	531	23	γ2fd(c4	γ2fd(c4	NUM
ejpam-3506	531	24	)	)	PUNCT
ejpam-3506	531	25	}	}	PUNCT
ejpam-3506	531	26	,	,	PUNCT
ejpam-3506	531	27	and	and	CCONJ
ejpam-3506	531	28	(	(	PUNCT
ejpam-3506	531	29	c	c	X
ejpam-3506	531	30	)	)	PUNCT
ejpam-3506	531	31	γnc2fd(p3	γnc2fd(p3	PROPN
ejpam-3506	531	32	�	�	NOUN
ejpam-3506	531	33	p4	p4	ADJ
ejpam-3506	531	34	)	)	PUNCT
ejpam-3506	531	35	=	=	SYM
ejpam-3506	531	36	7	7	NUM
ejpam-3506	531	37	<	<	X
ejpam-3506	531	38	min{4	min{4	X
ejpam-3506	531	39	·	·	PUNCT
ejpam-3506	531	40	2	2	NUM
ejpam-3506	531	41	,	,	PUNCT
ejpam-3506	531	42	3	3	NUM
ejpam-3506	531	43	·	·	SYM
ejpam-3506	531	44	3	3	NUM
ejpam-3506	531	45	}	}	PUNCT
ejpam-3506	531	46	=	=	SYM
ejpam-3506	531	47	min{|v	min{|v	PROPN
ejpam-3506	531	48	(	(	PUNCT
ejpam-3506	531	49	p4)|	p4)|	PROPN
ejpam-3506	531	50	·	·	PUNCT
ejpam-3506	531	51	γ2fd(p3	γ2fd(p3	PROPN
ejpam-3506	531	52	)	)	PUNCT
ejpam-3506	531	53	,	,	PUNCT
ejpam-3506	531	54	|v	|v	PROPN
ejpam-3506	531	55	(	(	PUNCT
ejpam-3506	531	56	p3)|	p3)|	PROPN
ejpam-3506	531	57	·	·	SYM
ejpam-3506	531	58	γ2fd(p4	γ2fd(p4	NUM
ejpam-3506	531	59	)	)	PUNCT
ejpam-3506	531	60	}	}	PUNCT
ejpam-3506	531	61	.	.	PUNCT
ejpam-3506	531	62	...................................................................................	...................................................................................	PUNCT
ejpam-3506	531	63	....................................	....................................	PUNCT
ejpam-3506	531	64	...................................................................................	...................................................................................	PUNCT
ejpam-3506	531	65	....................................	....................................	PUNCT
ejpam-3506	531	66	...................................................................................	...................................................................................	PUNCT
ejpam-3506	532	1	....................................	....................................	PUNCT
ejpam-3506	532	2	.........	.........	PUNCT
ejpam-3506	532	3	........	........	PUNCT
ejpam-3506	532	4	........	........	PUNCT
ejpam-3506	532	5	........	........	PUNCT
ejpam-3506	532	6	........	........	PUNCT
ejpam-3506	533	1	......	......	PUNCT
ejpam-3506	533	2	.........	.........	PUNCT
ejpam-3506	533	3	........	........	PUNCT
ejpam-3506	533	4	........	........	PUNCT
ejpam-3506	533	5	........	........	PUNCT
ejpam-3506	533	6	........	........	PUNCT
ejpam-3506	534	1	......	......	PUNCT
ejpam-3506	534	2	.........	.........	PUNCT
ejpam-3506	534	3	........	........	PUNCT
ejpam-3506	534	4	........	........	PUNCT
ejpam-3506	534	5	........	........	PUNCT
ejpam-3506	534	6	........	........	PUNCT
ejpam-3506	535	1	......	......	PUNCT
ejpam-3506	535	2	.........	.........	PUNCT
ejpam-3506	535	3	........	........	PUNCT
ejpam-3506	535	4	........	........	PUNCT
ejpam-3506	535	5	........	........	PUNCT
ejpam-3506	535	6	........	........	PUNCT
ejpam-3506	536	1	......	......	PUNCT
ejpam-3506	536	2	.........	.........	PUNCT
ejpam-3506	537	1	.........	.........	PUNCT
ejpam-3506	537	2	.........	.........	PUNCT
ejpam-3506	537	3	........	........	PUNCT
ejpam-3506	537	4	........	........	PUNCT
ejpam-3506	537	5	........	........	PUNCT
ejpam-3506	537	6	........	........	PUNCT
ejpam-3506	537	7	........	........	PUNCT
ejpam-3506	537	8	........	........	PUNCT
ejpam-3506	537	9	........	........	PUNCT
ejpam-3506	538	1	.........	.........	PUNCT
ejpam-3506	538	2	.........	.........	PUNCT
ejpam-3506	539	1	.......	.......	PUNCT
ejpam-3506	539	2	.........	.........	PUNCT
ejpam-3506	540	1	.........	.........	PUNCT
ejpam-3506	540	2	.........	.........	PUNCT
ejpam-3506	540	3	........	........	PUNCT
ejpam-3506	540	4	........	........	PUNCT
ejpam-3506	540	5	........	........	PUNCT
ejpam-3506	540	6	........	........	PUNCT
ejpam-3506	540	7	........	........	PUNCT
ejpam-3506	540	8	........	........	PUNCT
ejpam-3506	540	9	........	........	PUNCT
ejpam-3506	541	1	.........	.........	PUNCT
ejpam-3506	541	2	.........	.........	PUNCT
ejpam-3506	542	1	.......	.......	PUNCT
ejpam-3506	543	1	•	•	NUM
ejpam-3506	543	2	•	•	X
ejpam-3506	543	3	(	(	PUNCT
ejpam-3506	543	4	a	a	NOUN
ejpam-3506	543	5	)	)	PUNCT
ejpam-3506	543	6	...................................................................................	...................................................................................	PUNCT
ejpam-3506	543	7	...................................................................................	...................................................................................	PUNCT
ejpam-3506	543	8	...................................................................................	...................................................................................	PUNCT
ejpam-3506	543	9	....................................	....................................	PUNCT
ejpam-3506	543	10	...................................................................................	...................................................................................	PUNCT
ejpam-3506	543	11	...................................................................................	...................................................................................	PUNCT
ejpam-3506	543	12	...................................................................................	...................................................................................	PUNCT
ejpam-3506	543	13	....................................	....................................	PUNCT
ejpam-3506	543	14	...................................................................................	...................................................................................	PUNCT
ejpam-3506	543	15	...................................................................................	...................................................................................	PUNCT
ejpam-3506	543	16	...................................................................................	...................................................................................	PUNCT
ejpam-3506	543	17	....................................	....................................	PUNCT
ejpam-3506	543	18	.........	.........	PUNCT
ejpam-3506	543	19	........	........	PUNCT
ejpam-3506	543	20	........	........	PUNCT
ejpam-3506	543	21	........	........	PUNCT
ejpam-3506	543	22	........	........	PUNCT
ejpam-3506	543	23	......	......	PUNCT
ejpam-3506	543	24	.........	.........	PUNCT
ejpam-3506	543	25	........	........	PUNCT
ejpam-3506	543	26	........	........	PUNCT
ejpam-3506	543	27	........	........	PUNCT
ejpam-3506	543	28	........	........	PUNCT
ejpam-3506	543	29	......	......	PUNCT
ejpam-3506	543	30	.........	.........	PUNCT
ejpam-3506	543	31	........	........	PUNCT
ejpam-3506	543	32	........	........	PUNCT
ejpam-3506	543	33	........	........	PUNCT
ejpam-3506	543	34	........	........	PUNCT
ejpam-3506	543	35	......	......	PUNCT
ejpam-3506	543	36	.........	.........	PUNCT
ejpam-3506	543	37	........	........	PUNCT
ejpam-3506	543	38	........	........	PUNCT
ejpam-3506	543	39	........	........	PUNCT
ejpam-3506	543	40	........	........	PUNCT
ejpam-3506	543	41	......	......	PUNCT
ejpam-3506	543	42	.........	.........	PUNCT
ejpam-3506	543	43	........	........	PUNCT
ejpam-3506	543	44	........	........	PUNCT
ejpam-3506	543	45	........	........	PUNCT
ejpam-3506	543	46	........	........	PUNCT
ejpam-3506	543	47	......	......	PUNCT
ejpam-3506	543	48	.........	.........	PUNCT
ejpam-3506	543	49	........	........	PUNCT
ejpam-3506	543	50	........	........	PUNCT
ejpam-3506	543	51	........	........	PUNCT
ejpam-3506	543	52	........	........	PUNCT
ejpam-3506	543	53	......	......	PUNCT
ejpam-3506	543	54	.........	.........	PUNCT
ejpam-3506	543	55	........	........	PUNCT
ejpam-3506	543	56	........	........	PUNCT
ejpam-3506	543	57	........	........	PUNCT
ejpam-3506	543	58	........	........	PUNCT
ejpam-3506	543	59	......	......	PUNCT
ejpam-3506	543	60	.........	.........	PUNCT
ejpam-3506	543	61	........	........	PUNCT
ejpam-3506	543	62	........	........	PUNCT
ejpam-3506	543	63	........	........	PUNCT
ejpam-3506	543	64	........	........	PUNCT
ejpam-3506	543	65	......	......	PUNCT
ejpam-3506	543	66	................	................	PUNCT
ejpam-3506	543	67	...................	...................	PUNCT
ejpam-3506	543	68	.............................	.............................	PUNCT
ejpam-3506	543	69	.............................................................................................................	.............................................................................................................	PUNCT
ejpam-3506	543	70	................	................	PUNCT
ejpam-3506	543	71	...................	...................	PUNCT
ejpam-3506	543	72	.............................	.............................	PUNCT
ejpam-3506	543	73	.............................................................................................................	.............................................................................................................	PUNCT
ejpam-3506	543	74	................	................	PUNCT
ejpam-3506	543	75	...................	...................	PUNCT
ejpam-3506	543	76	.............................	.............................	PUNCT
ejpam-3506	543	77	.............................................................................................................	.............................................................................................................	PUNCT
ejpam-3506	544	1	•	•	NUM
ejpam-3506	545	1	•	•	NUM
ejpam-3506	545	2	•	•	NUM
ejpam-3506	545	3	•	•	NUM
ejpam-3506	545	4	•	•	NOUN
ejpam-3506	545	5	•	•	NOUN
ejpam-3506	545	6	(	(	PUNCT
ejpam-3506	545	7	b	b	NOUN
ejpam-3506	545	8	)	)	PUNCT
ejpam-3506	545	9	...................................................................................	...................................................................................	PUNCT
ejpam-3506	545	10	...................................................................................	...................................................................................	PUNCT
ejpam-3506	545	11	...................................................................................	...................................................................................	PUNCT
ejpam-3506	545	12	....................................	....................................	PUNCT
ejpam-3506	545	13	...................................................................................	...................................................................................	PUNCT
ejpam-3506	545	14	...................................................................................	...................................................................................	PUNCT
ejpam-3506	545	15	...................................................................................	...................................................................................	PUNCT
ejpam-3506	545	16	....................................	....................................	PUNCT
ejpam-3506	545	17	...................................................................................	...................................................................................	PUNCT
ejpam-3506	545	18	...................................................................................	...................................................................................	PUNCT
ejpam-3506	545	19	...................................................................................	...................................................................................	PUNCT
ejpam-3506	546	1	....................................	....................................	PUNCT
ejpam-3506	546	2	.........	.........	PUNCT
ejpam-3506	546	3	........	........	PUNCT
ejpam-3506	546	4	........	........	PUNCT
ejpam-3506	546	5	........	........	PUNCT
ejpam-3506	546	6	........	........	PUNCT
ejpam-3506	547	1	......	......	PUNCT
ejpam-3506	547	2	.........	.........	PUNCT
ejpam-3506	547	3	........	........	PUNCT
ejpam-3506	547	4	........	........	PUNCT
ejpam-3506	547	5	........	........	PUNCT
ejpam-3506	547	6	........	........	PUNCT
ejpam-3506	548	1	......	......	PUNCT
ejpam-3506	548	2	.........	.........	PUNCT
ejpam-3506	548	3	........	........	PUNCT
ejpam-3506	548	4	........	........	PUNCT
ejpam-3506	548	5	........	........	PUNCT
ejpam-3506	548	6	........	........	PUNCT
ejpam-3506	549	1	......	......	PUNCT
ejpam-3506	549	2	.........	.........	PUNCT
ejpam-3506	549	3	........	........	PUNCT
ejpam-3506	549	4	........	........	PUNCT
ejpam-3506	549	5	........	........	PUNCT
ejpam-3506	549	6	........	........	PUNCT
ejpam-3506	550	1	......	......	PUNCT
ejpam-3506	550	2	.........	.........	PUNCT
ejpam-3506	550	3	........	........	PUNCT
ejpam-3506	550	4	........	........	PUNCT
ejpam-3506	550	5	........	........	PUNCT
ejpam-3506	550	6	........	........	PUNCT
ejpam-3506	551	1	......	......	PUNCT
ejpam-3506	551	2	.........	.........	PUNCT
ejpam-3506	551	3	........	........	PUNCT
ejpam-3506	551	4	........	........	PUNCT
ejpam-3506	551	5	........	........	PUNCT
ejpam-3506	551	6	........	........	PUNCT
ejpam-3506	552	1	......	......	PUNCT
ejpam-3506	552	2	.........	.........	PUNCT
ejpam-3506	552	3	........	........	PUNCT
ejpam-3506	552	4	........	........	PUNCT
ejpam-3506	552	5	........	........	PUNCT
ejpam-3506	552	6	........	........	PUNCT
ejpam-3506	553	1	......	......	PUNCT
ejpam-3506	553	2	.........	.........	PUNCT
ejpam-3506	553	3	........	........	PUNCT
ejpam-3506	553	4	........	........	PUNCT
ejpam-3506	553	5	........	........	PUNCT
ejpam-3506	554	1	........	........	PUNCT
ejpam-3506	555	1	......	......	PUNCT
ejpam-3506	556	1	•	•	NUM
ejpam-3506	557	1	•	•	NUM
ejpam-3506	557	2	•	•	NUM
ejpam-3506	557	3	•	•	NUM
ejpam-3506	557	4	•	•	NUM
ejpam-3506	557	5	•	•	NOUN
ejpam-3506	557	6	•	•	NOUN
ejpam-3506	557	7	(	(	PUNCT
ejpam-3506	557	8	c	c	NOUN
ejpam-3506	557	9	)	)	PUNCT
ejpam-3506	557	10	figure	figure	NOUN
ejpam-3506	557	11	6	6	NUM
ejpam-3506	557	12	:	:	PUNCT
ejpam-3506	557	13	the	the	DET
ejpam-3506	557	14	graphs	graph	NOUN
ejpam-3506	557	15	k3	k3	VERB
ejpam-3506	557	16	�	�	NOUN
ejpam-3506	557	17	p2	p2	NOUN
ejpam-3506	557	18	,	,	PUNCT
ejpam-3506	557	19	p3	p3	PROPN
ejpam-3506	557	20	�	�	PROPN
ejpam-3506	557	21	c4	c4	NOUN
ejpam-3506	557	22	and	and	CCONJ
ejpam-3506	557	23	p3	p3	PROPN
ejpam-3506	557	24	�	�	PROPN
ejpam-3506	557	25	p4	p4	ADJ
ejpam-3506	557	26	.	.	PUNCT
ejpam-3506	558	1	acknowledgements	acknowledgement	NOUN
ejpam-3506	558	2	this	this	DET
ejpam-3506	558	3	research	research	NOUN
ejpam-3506	558	4	is	be	AUX
ejpam-3506	558	5	funded	fund	VERB
ejpam-3506	558	6	by	by	ADP
ejpam-3506	558	7	the	the	DET
ejpam-3506	558	8	the	the	DET
ejpam-3506	558	9	philippine	philippine	ADJ
ejpam-3506	558	10	commission	commission	NOUN
ejpam-3506	558	11	on	on	ADP
ejpam-3506	558	12	higher	high	ADJ
ejpam-3506	558	13	education	education	NOUN
ejpam-3506	558	14	-	-	PUNCT
ejpam-3506	558	15	faculty	faculty	NOUN
ejpam-3506	558	16	development	development	NOUN
ejpam-3506	558	17	program	program	NOUN
ejpam-3506	558	18	phase	phase	NOUN
ejpam-3506	558	19	ii	ii	PROPN
ejpam-3506	558	20	(	(	PUNCT
ejpam-3506	558	21	ched	che	VERB
ejpam-3506	558	22	-	-	PUNCT
ejpam-3506	558	23	fdp	fdp	NUM
ejpam-3506	558	24	ii	ii	PROPN
ejpam-3506	558	25	)	)	PUNCT
ejpam-3506	558	26	and	and	CCONJ
ejpam-3506	558	27	the	the	DET
ejpam-3506	558	28	mindanao	mindanao	PROPN
ejpam-3506	558	29	state	state	PROPN
ejpam-3506	558	30	university	university	PROPN
ejpam-3506	558	31	-	-	PUNCT
ejpam-3506	558	32	iligan	iligan	PROPN
ejpam-3506	558	33	institute	institute	PROPN
ejpam-3506	558	34	of	of	ADP
ejpam-3506	558	35	technology	technology	PROPN
ejpam-3506	558	36	.	.	PUNCT
ejpam-3506	559	1	references	reference	NOUN
ejpam-3506	559	2	[	[	X
ejpam-3506	559	3	1	1	X
ejpam-3506	559	4	]	]	PUNCT
ejpam-3506	559	5	s.	s.	PROPN
ejpam-3506	559	6	arumugam	arumugam	PROPN
ejpam-3506	559	7	and	and	CCONJ
ejpam-3506	559	8	c.	c.	PROPN
ejpam-3506	559	9	sivagnanam	sivagnanam	PROPN
ejpam-3506	559	10	.	.	PUNCT
ejpam-3506	560	1	neighborhood	neighborhood	NOUN
ejpam-3506	560	2	connected	connect	VERB
ejpam-3506	560	3	domination	domination	NOUN
ejpam-3506	560	4	in	in	ADP
ejpam-3506	560	5	graphs	graph	NOUN
ejpam-3506	560	6	.	.	PUNCT
ejpam-3506	561	1	journal	journal	NOUN
ejpam-3506	561	2	of	of	ADP
ejpam-3506	561	3	combinatorial	combinatorial	ADJ
ejpam-3506	561	4	mathematics	mathematic	NOUN
ejpam-3506	561	5	and	and	CCONJ
ejpam-3506	561	6	combinatorial	combinatorial	ADJ
ejpam-3506	561	7	computing	computing	NOUN
ejpam-3506	561	8	,	,	PUNCT
ejpam-3506	561	9	73:55–64	73:55–64	PROPN
ejpam-3506	561	10	,	,	PUNCT
ejpam-3506	561	11	2010	2010	NUM
ejpam-3506	561	12	.	.	PUNCT
ejpam-3506	562	1	[	[	X
ejpam-3506	562	2	2	2	X
ejpam-3506	562	3	]	]	PUNCT
ejpam-3506	562	4	w.	w.	PROPN
ejpam-3506	562	5	m.	m.	PROPN
ejpam-3506	562	6	bent	bent	PROPN
ejpam-3506	562	7	-	-	PUNCT
ejpam-3506	562	8	usman	usman	PROPN
ejpam-3506	562	9	d.	d.	PROPN
ejpam-3506	562	10	p.	p.	PROPN
ejpam-3506	562	11	gomisong	gomisong	PROPN
ejpam-3506	562	12	and	and	CCONJ
ejpam-3506	562	13	r.	r.	PROPN
ejpam-3506	562	14	t.	t.	PROPN
ejpam-3506	562	15	isla	isla	PROPN
ejpam-3506	562	16	.	.	PUNCT
ejpam-3506	563	1	connected	connect	VERB
ejpam-3506	563	2	k	k	ADJ
ejpam-3506	563	3	-	-	PUNCT
ejpam-3506	563	4	fair	fair	ADJ
ejpam-3506	563	5	domination	domination	NOUN
ejpam-3506	563	6	in	in	ADP
ejpam-3506	563	7	the	the	DET
ejpam-3506	563	8	join	join	NOUN
ejpam-3506	563	9	,	,	PUNCT
ejpam-3506	563	10	corona	corona	PROPN
ejpam-3506	563	11	,	,	PUNCT
ejpam-3506	563	12	lexicographic	lexicographic	ADJ
ejpam-3506	563	13	and	and	CCONJ
ejpam-3506	563	14	cartesian	cartesian	ADJ
ejpam-3506	563	15	products	product	NOUN
ejpam-3506	563	16	of	of	ADP
ejpam-3506	563	17	graphs	graph	NOUN
ejpam-3506	563	18	.	.	PUNCT
ejpam-3506	564	1	applied	apply	VERB
ejpam-3506	564	2	mathematical	mathematical	ADJ
ejpam-3506	564	3	sciences	science	NOUN
ejpam-3506	564	4	,	,	PUNCT
ejpam-3506	564	5	12:1341–1355	12:1341–1355	NUM
ejpam-3506	564	6	,	,	PUNCT
ejpam-3506	564	7	2018	2018	NUM
ejpam-3506	564	8	.	.	PUNCT
ejpam-3506	565	1	[	[	X
ejpam-3506	565	2	3	3	X
ejpam-3506	565	3	]	]	X
ejpam-3506	565	4	y.	y.	PROPN
ejpam-3506	565	5	caro	caro	PROPN
ejpam-3506	565	6	a.	a.	PROPN
ejpam-3506	565	7	hansberg	hansberg	PROPN
ejpam-3506	565	8	and	and	CCONJ
ejpam-3506	565	9	m.	m.	PROPN
ejpam-3506	565	10	a.	a.	PROPN
ejpam-3506	565	11	henning	henning	PROPN
ejpam-3506	565	12	.	.	PUNCT
ejpam-3506	566	1	fair	fair	ADJ
ejpam-3506	566	2	domination	domination	NOUN
ejpam-3506	566	3	in	in	ADP
ejpam-3506	566	4	graphs	graph	NOUN
ejpam-3506	566	5	.	.	PUNCT
ejpam-3506	567	1	discrete	discrete	ADJ
ejpam-3506	567	2	mathematics	mathematic	NOUN
ejpam-3506	567	3	,	,	PUNCT
ejpam-3506	567	4	19:1–18	19:1–18	NUM
ejpam-3506	567	5	,	,	PUNCT
ejpam-3506	567	6	2011	2011	NUM
ejpam-3506	567	7	.	.	PUNCT
ejpam-3506	568	1	[	[	X
ejpam-3506	568	2	4	4	X
ejpam-3506	568	3	]	]	PUNCT
ejpam-3506	568	4	e.	e.	PROPN
ejpam-3506	568	5	maravilla	maravilla	PROPN
ejpam-3506	568	6	r.	r.	PROPN
ejpam-3506	568	7	isla	isla	PROPN
ejpam-3506	568	8	and	and	CCONJ
ejpam-3506	568	9	s.	s.	PROPN
ejpam-3506	568	10	r.	r.	PROPN
ejpam-3506	568	11	canoy	canoy	PROPN
ejpam-3506	568	12	jr	jr	PROPN
ejpam-3506	568	13	.	.	PROPN
ejpam-3506	568	14	fair	fair	ADJ
ejpam-3506	568	15	domination	domination	NOUN
ejpam-3506	568	16	in	in	ADP
ejpam-3506	568	17	the	the	DET
ejpam-3506	568	18	join	join	NOUN
ejpam-3506	568	19	,	,	PUNCT
ejpam-3506	568	20	corona	corona	NOUN
ejpam-3506	568	21	and	and	CCONJ
ejpam-3506	568	22	composition	composition	NOUN
ejpam-3506	568	23	of	of	ADP
ejpam-3506	568	24	graphs	graph	NOUN
ejpam-3506	568	25	.	.	PUNCT
ejpam-3506	569	1	applied	apply	VERB
ejpam-3506	569	2	mathematical	mathematical	ADJ
ejpam-3506	569	3	sciences	sciences	PROPN
ejpam-3506	569	4	,	,	PUNCT
ejpam-3506	569	5	93:4609–4620	93:4609–4620	NUM
ejpam-3506	569	6	,	,	PUNCT
ejpam-3506	569	7	2014	2014	NUM
ejpam-3506	569	8	.	.	PUNCT
ejpam-3506	570	1	references	reference	NOUN
ejpam-3506	570	2	1349	1349	NUM
ejpam-3506	571	1	[	[	X
ejpam-3506	571	2	5	5	NUM
ejpam-3506	571	3	]	]	PUNCT
ejpam-3506	571	4	e.	e.	PROPN
ejpam-3506	571	5	maravilla	maravilla	PROPN
ejpam-3506	571	6	r.	r.	PROPN
ejpam-3506	571	7	isla	isla	PROPN
ejpam-3506	571	8	and	and	CCONJ
ejpam-3506	571	9	s.	s.	PROPN
ejpam-3506	571	10	r.	r.	PROPN
ejpam-3506	571	11	canoy	canoy	PROPN
ejpam-3506	571	12	jr	jr	PROPN
ejpam-3506	571	13	.	.	PROPN
ejpam-3506	571	14	fair	fair	ADJ
ejpam-3506	571	15	total	total	ADJ
ejpam-3506	571	16	domination	domination	NOUN
ejpam-3506	571	17	in	in	ADP
ejpam-3506	571	18	the	the	DET
ejpam-3506	571	19	join	join	NOUN
ejpam-3506	571	20	,	,	PUNCT
ejpam-3506	571	21	corona	corona	NOUN
ejpam-3506	571	22	and	and	CCONJ
ejpam-3506	571	23	composition	composition	NOUN
ejpam-3506	571	24	of	of	ADP
ejpam-3506	571	25	graphs	graph	NOUN
ejpam-3506	571	26	.	.	PUNCT
ejpam-3506	572	1	international	international	ADJ
ejpam-3506	572	2	journal	journal	PROPN
ejpam-3506	572	3	of	of	ADP
ejpam-3506	572	4	mathematical	mathematical	ADJ
ejpam-3506	572	5	analysis	analysis	NOUN
ejpam-3506	572	6	,	,	PUNCT
ejpam-3506	572	7	54:2677	54:2677	NUM
ejpam-3506	572	8	–	–	PUNCT
ejpam-3506	572	9	2685	2685	NUM
ejpam-3506	572	10	,	,	PUNCT
ejpam-3506	572	11	2014	2014	NUM
ejpam-3506	572	12	.	.	PUNCT
ejpam-3506	573	1	[	[	X
ejpam-3506	573	2	6	6	NUM
ejpam-3506	573	3	]	]	PUNCT
ejpam-3506	573	4	e.	e.	PROPN
ejpam-3506	573	5	maravilla	maravilla	PROPN
ejpam-3506	573	6	r.	r.	PROPN
ejpam-3506	573	7	isla	isla	PROPN
ejpam-3506	573	8	and	and	CCONJ
ejpam-3506	573	9	s.	s.	PROPN
ejpam-3506	573	10	r.	r.	PROPN
ejpam-3506	573	11	canoy	canoy	PROPN
ejpam-3506	573	12	jr	jr	PROPN
ejpam-3506	573	13	.	.	PUNCT
ejpam-3506	574	1	k	k	ADJ
ejpam-3506	574	2	-	-	PUNCT
ejpam-3506	574	3	fair	fair	ADJ
ejpam-3506	574	4	domination	domination	NOUN
ejpam-3506	574	5	in	in	ADP
ejpam-3506	574	6	the	the	DET
ejpam-3506	574	7	join	join	NOUN
ejpam-3506	574	8	,	,	PUNCT
ejpam-3506	574	9	corona	corona	NOUN
ejpam-3506	574	10	,	,	PUNCT
ejpam-3506	574	11	composition	composition	NOUN
ejpam-3506	574	12	and	and	CCONJ
ejpam-3506	574	13	cartesian	cartesian	ADJ
ejpam-3506	574	14	product	product	NOUN
ejpam-3506	574	15	of	of	ADP
ejpam-3506	574	16	graphs	graph	NOUN
ejpam-3506	574	17	.	.	PUNCT
ejpam-3506	575	1	applied	apply	VERB
ejpam-3506	575	2	mathematical	mathematical	ADJ
ejpam-3506	575	3	sciences	science	NOUN
ejpam-3506	575	4	,	,	PUNCT
ejpam-3506	575	5	178:8863	178:8863	NUM
ejpam-3506	575	6	–	–	PUNCT
ejpam-3506	575	7	8874	8874	NUM
ejpam-3506	575	8	,	,	PUNCT
ejpam-3506	575	9	2014	2014	NUM
ejpam-3506	575	10	.	.	PUNCT