id	sid	tid	token	lemma	pos
ejpam-6048	1	1	european	european	PROPN
ejpam-6048	1	2	journal	journal	PROPN
ejpam-6048	1	3	of	of	ADP
ejpam-6048	1	4	pure	pure	ADJ
ejpam-6048	1	5	and	and	CCONJ
ejpam-6048	1	6	applied	applied	ADJ
ejpam-6048	1	7	mathematics	mathematic	NOUN
ejpam-6048	1	8	2025	2025	NUM
ejpam-6048	1	9	,	,	PUNCT
ejpam-6048	1	10	vol	vol	NOUN
ejpam-6048	1	11	.	.	PROPN
ejpam-6048	1	12	18	18	NUM
ejpam-6048	1	13	,	,	PUNCT
ejpam-6048	1	14	issue	issue	NOUN
ejpam-6048	1	15	3	3	NUM
ejpam-6048	1	16	,	,	PUNCT
ejpam-6048	1	17	article	article	NOUN
ejpam-6048	1	18	number	number	NOUN
ejpam-6048	1	19	6048	6048	NUM
ejpam-6048	1	20	issn	issn	VERB
ejpam-6048	1	21	1307	1307	NUM
ejpam-6048	1	22	-	-	SYM
ejpam-6048	1	23	5543	5543	NUM
ejpam-6048	1	24	–	–	PUNCT
ejpam-6048	1	25	ejpam.com	ejpam.com	X
ejpam-6048	1	26	published	publish	VERB
ejpam-6048	1	27	by	by	ADP
ejpam-6048	1	28	new	new	PROPN
ejpam-6048	1	29	york	york	PROPN
ejpam-6048	1	30	business	business	PROPN
ejpam-6048	1	31	global	global	ADJ
ejpam-6048	1	32	independent	independent	ADJ
ejpam-6048	1	33	neighborhood	neighborhood	NOUN
ejpam-6048	1	34	polynomial	polynomial	NOUN
ejpam-6048	1	35	of	of	ADP
ejpam-6048	1	36	the	the	DET
ejpam-6048	1	37	direct	direct	ADJ
ejpam-6048	1	38	and	and	CCONJ
ejpam-6048	1	39	corona	corona	NOUN
ejpam-6048	1	40	products	product	NOUN
ejpam-6048	1	41	of	of	ADP
ejpam-6048	1	42	trees	tree	NOUN
ejpam-6048	1	43	normalah	normalah	PROPN
ejpam-6048	1	44	s.	s.	PROPN
ejpam-6048	1	45	abdulcarim1,∗	abdulcarim1,∗	PROPN
ejpam-6048	1	46	,	,	PUNCT
ejpam-6048	1	47	susan	susan	PROPN
ejpam-6048	1	48	c.	c.	PROPN
ejpam-6048	1	49	dagondon2	dagondon2	PROPN
ejpam-6048	1	50	1	1	NUM
ejpam-6048	1	51	department	department	NOUN
ejpam-6048	1	52	of	of	ADP
ejpam-6048	1	53	mathematics	mathematic	NOUN
ejpam-6048	1	54	,	,	PUNCT
ejpam-6048	1	55	college	college	NOUN
ejpam-6048	1	56	of	of	ADP
ejpam-6048	1	57	natural	natural	ADJ
ejpam-6048	1	58	sciences	science	NOUN
ejpam-6048	1	59	and	and	CCONJ
ejpam-6048	1	60	mathematics	mathematic	NOUN
ejpam-6048	1	61	,	,	PUNCT
ejpam-6048	1	62	mindanao	mindanao	PROPN
ejpam-6048	1	63	state	state	PROPN
ejpam-6048	1	64	university	university	PROPN
ejpam-6048	1	65	main	main	ADJ
ejpam-6048	1	66	campus	campus	NOUN
ejpam-6048	1	67	,	,	PUNCT
ejpam-6048	1	68	9700	9700	NUM
ejpam-6048	1	69	marawi	marawi	PROPN
ejpam-6048	1	70	city	city	PROPN
ejpam-6048	1	71	,	,	PUNCT
ejpam-6048	1	72	philippines	philippines	PROPN
ejpam-6048	1	73	2	2	NUM
ejpam-6048	1	74	department	department	NOUN
ejpam-6048	1	75	of	of	ADP
ejpam-6048	1	76	mathematics	mathematic	NOUN
ejpam-6048	1	77	and	and	CCONJ
ejpam-6048	1	78	statistics	statistic	NOUN
ejpam-6048	1	79	,	,	PUNCT
ejpam-6048	1	80	college	college	NOUN
ejpam-6048	1	81	of	of	ADP
ejpam-6048	1	82	science	science	NOUN
ejpam-6048	1	83	and	and	CCONJ
ejpam-6048	1	84	mathematics	mathematic	NOUN
ejpam-6048	1	85	,	,	PUNCT
ejpam-6048	1	86	center	center	NOUN
ejpam-6048	1	87	of	of	ADP
ejpam-6048	1	88	graph	graph	NOUN
ejpam-6048	1	89	theory	theory	NOUN
ejpam-6048	1	90	,	,	PUNCT
ejpam-6048	1	91	algebra	algebra	NOUN
ejpam-6048	1	92	and	and	CCONJ
ejpam-6048	1	93	analysis	analysis	NOUN
ejpam-6048	1	94	-	-	PUNCT
ejpam-6048	1	95	premier	premier	NOUN
ejpam-6048	1	96	research	research	NOUN
ejpam-6048	1	97	institute	institute	PROPN
ejpam-6048	1	98	of	of	ADP
ejpam-6048	1	99	science	science	NOUN
ejpam-6048	1	100	and	and	CCONJ
ejpam-6048	1	101	mathematics	mathematic	NOUN
ejpam-6048	1	102	,	,	PUNCT
ejpam-6048	1	103	mindanao	mindanao	PROPN
ejpam-6048	1	104	state	state	PROPN
ejpam-6048	1	105	university	university	PROPN
ejpam-6048	1	106	-	-	PUNCT
ejpam-6048	1	107	iligan	iligan	PROPN
ejpam-6048	1	108	institute	institute	PROPN
ejpam-6048	1	109	of	of	ADP
ejpam-6048	1	110	technology	technology	PROPN
ejpam-6048	1	111	,	,	PUNCT
ejpam-6048	1	112	9200	9200	NUM
ejpam-6048	1	113	philippines	philippine	NOUN
ejpam-6048	1	114	abstract	abstract	ADJ
ejpam-6048	1	115	.	.	PUNCT
ejpam-6048	2	1	let	let	VERB
ejpam-6048	2	2	g	g	PRON
ejpam-6048	2	3	be	be	AUX
ejpam-6048	2	4	a	a	DET
ejpam-6048	2	5	connected	connected	ADJ
ejpam-6048	2	6	graph	graph	NOUN
ejpam-6048	2	7	.	.	PUNCT
ejpam-6048	3	1	we	we	PRON
ejpam-6048	3	2	say	say	VERB
ejpam-6048	3	3	that	that	SCONJ
ejpam-6048	3	4	a	a	DET
ejpam-6048	3	5	given	give	VERB
ejpam-6048	3	6	graph	graph	NOUN
ejpam-6048	3	7	is	be	AUX
ejpam-6048	3	8	a	a	DET
ejpam-6048	3	9	tree	tree	NOUN
ejpam-6048	3	10	if	if	SCONJ
ejpam-6048	3	11	every	every	DET
ejpam-6048	3	12	pair	pair	NOUN
ejpam-6048	3	13	of	of	ADP
ejpam-6048	3	14	vertices	vertex	NOUN
ejpam-6048	3	15	is	be	AUX
ejpam-6048	3	16	connected	connect	VERB
ejpam-6048	3	17	by	by	ADP
ejpam-6048	3	18	a	a	DET
ejpam-6048	3	19	unique	unique	ADJ
ejpam-6048	3	20	path	path	NOUN
ejpam-6048	3	21	.	.	PUNCT
ejpam-6048	4	1	the	the	DET
ejpam-6048	4	2	corona	corona	NOUN
ejpam-6048	4	3	product	product	NOUN
ejpam-6048	4	4	of	of	ADP
ejpam-6048	4	5	two	two	NUM
ejpam-6048	4	6	graphs	graph	NOUN
ejpam-6048	4	7	g	g	NOUN
ejpam-6048	4	8	and	and	CCONJ
ejpam-6048	4	9	h	h	NOUN
ejpam-6048	4	10	is	be	AUX
ejpam-6048	4	11	defined	define	VERB
ejpam-6048	4	12	as	as	ADP
ejpam-6048	4	13	the	the	DET
ejpam-6048	4	14	graph	graph	NOUN
ejpam-6048	4	15	obtained	obtain	VERB
ejpam-6048	4	16	by	by	ADP
ejpam-6048	4	17	taking	take	VERB
ejpam-6048	4	18	one	one	NUM
ejpam-6048	4	19	copy	copy	NOUN
ejpam-6048	4	20	of	of	ADP
ejpam-6048	4	21	g	g	PROPN
ejpam-6048	4	22	and	and	CCONJ
ejpam-6048	4	23	|v	|v	PROPN
ejpam-6048	4	24	(	(	PUNCT
ejpam-6048	4	25	g)|	g)|	NOUN
ejpam-6048	4	26	copies	copy	NOUN
ejpam-6048	4	27	of	of	ADP
ejpam-6048	4	28	h	h	NOUN
ejpam-6048	4	29	and	and	CCONJ
ejpam-6048	4	30	joining	join	VERB
ejpam-6048	4	31	the	the	DET
ejpam-6048	4	32	ith	ith	PROPN
ejpam-6048	4	33	vertex	vertex	NOUN
ejpam-6048	4	34	of	of	ADP
ejpam-6048	4	35	g	g	NOUN
ejpam-6048	4	36	to	to	ADP
ejpam-6048	4	37	every	every	DET
ejpam-6048	4	38	vertex	vertex	NOUN
ejpam-6048	4	39	in	in	ADP
ejpam-6048	4	40	the	the	DET
ejpam-6048	4	41	ith	ith	PROPN
ejpam-6048	4	42	copy	copy	NOUN
ejpam-6048	4	43	of	of	ADP
ejpam-6048	4	44	h.	h.	PROPN
ejpam-6048	4	45	on	on	ADP
ejpam-6048	4	46	the	the	DET
ejpam-6048	4	47	other	other	ADJ
ejpam-6048	4	48	hand	hand	NOUN
ejpam-6048	4	49	,	,	PUNCT
ejpam-6048	4	50	the	the	DET
ejpam-6048	4	51	direct	direct	ADJ
ejpam-6048	4	52	product	product	NOUN
ejpam-6048	4	53	g	g	PROPN
ejpam-6048	4	54	×	×	PROPN
ejpam-6048	4	55	h	h	NOUN
ejpam-6048	4	56	is	be	AUX
ejpam-6048	4	57	a	a	DET
ejpam-6048	4	58	graph	graph	NOUN
ejpam-6048	4	59	such	such	ADJ
ejpam-6048	4	60	that	that	SCONJ
ejpam-6048	4	61	the	the	DET
ejpam-6048	4	62	vertex	vertex	NOUN
ejpam-6048	4	63	set	set	NOUN
ejpam-6048	4	64	of	of	ADP
ejpam-6048	4	65	g×h	g×h	PROPN
ejpam-6048	4	66	is	be	AUX
ejpam-6048	4	67	the	the	DET
ejpam-6048	4	68	cartesian	cartesian	ADJ
ejpam-6048	4	69	product	product	NOUN
ejpam-6048	4	70	v	v	NOUN
ejpam-6048	4	71	(	(	PUNCT
ejpam-6048	4	72	g)×v	g)×v	PROPN
ejpam-6048	4	73	(	(	PUNCT
ejpam-6048	4	74	h	h	NOUN
ejpam-6048	4	75	)	)	PUNCT
ejpam-6048	4	76	;	;	PUNCT
ejpam-6048	4	77	and	and	CCONJ
ejpam-6048	4	78	vertices	vertex	NOUN
ejpam-6048	4	79	(	(	PUNCT
ejpam-6048	4	80	g	g	NOUN
ejpam-6048	4	81	,	,	PUNCT
ejpam-6048	4	82	h	h	NOUN
ejpam-6048	4	83	)	)	PUNCT
ejpam-6048	4	84	and	and	CCONJ
ejpam-6048	4	85	(	(	PUNCT
ejpam-6048	4	86	g′	g′	NOUN
ejpam-6048	4	87	,	,	PUNCT
ejpam-6048	4	88	h′	h′	PROPN
ejpam-6048	4	89	)	)	PUNCT
ejpam-6048	4	90	are	be	AUX
ejpam-6048	4	91	adjacent	adjacent	ADJ
ejpam-6048	4	92	in	in	ADP
ejpam-6048	4	93	g×h	g×h	PROPN
ejpam-6048	4	94	if	if	SCONJ
ejpam-6048	5	1	and	and	CCONJ
ejpam-6048	5	2	only	only	ADV
ejpam-6048	5	3	if	if	SCONJ
ejpam-6048	5	4	g	g	PROPN
ejpam-6048	5	5	is	be	AUX
ejpam-6048	5	6	adjacent	adjacent	ADJ
ejpam-6048	5	7	to	to	ADP
ejpam-6048	5	8	g′	g′	NOUN
ejpam-6048	5	9	in	in	ADP
ejpam-6048	5	10	g	g	NOUN
ejpam-6048	5	11	,	,	PUNCT
ejpam-6048	5	12	and	and	CCONJ
ejpam-6048	5	13	h	h	NOUN
ejpam-6048	5	14	is	be	AUX
ejpam-6048	5	15	adjacent	adjacent	ADJ
ejpam-6048	5	16	to	to	ADP
ejpam-6048	5	17	h′	h′	PROPN
ejpam-6048	5	18	in	in	ADP
ejpam-6048	5	19	h.	h.	PROPN
ejpam-6048	5	20	here	here	ADV
ejpam-6048	5	21	,	,	PUNCT
ejpam-6048	5	22	authors	author	NOUN
ejpam-6048	5	23	worked	work	VERB
ejpam-6048	5	24	on	on	ADP
ejpam-6048	5	25	the	the	DET
ejpam-6048	5	26	independent	independent	ADJ
ejpam-6048	5	27	neighborhood	neighborhood	NOUN
ejpam-6048	5	28	sets	set	NOUN
ejpam-6048	5	29	of	of	ADP
ejpam-6048	5	30	the	the	DET
ejpam-6048	5	31	direct	direct	ADJ
ejpam-6048	5	32	and	and	CCONJ
ejpam-6048	5	33	corona	corona	NOUN
ejpam-6048	5	34	products	product	NOUN
ejpam-6048	5	35	of	of	ADP
ejpam-6048	5	36	two	two	NUM
ejpam-6048	5	37	trees	tree	NOUN
ejpam-6048	5	38	are	be	AUX
ejpam-6048	5	39	obtained	obtain	VERB
ejpam-6048	5	40	.	.	PUNCT
ejpam-6048	6	1	also	also	ADV
ejpam-6048	6	2	,	,	PUNCT
ejpam-6048	6	3	corresponding	correspond	VERB
ejpam-6048	6	4	independent	independent	ADJ
ejpam-6048	6	5	neighborhood	neighborhood	NOUN
ejpam-6048	6	6	polynomialsare	polynomialsare	NOUN
ejpam-6048	6	7	found	find	VERB
ejpam-6048	6	8	.	.	PUNCT
ejpam-6048	7	1	2020	2020	NUM
ejpam-6048	7	2	mathematics	mathematics	PROPN
ejpam-6048	7	3	subject	subject	NOUN
ejpam-6048	7	4	classifications	classification	NOUN
ejpam-6048	7	5	:	:	PUNCT
ejpam-6048	7	6	05c05	05c05	NUM
ejpam-6048	7	7	,	,	PUNCT
ejpam-6048	7	8	05c31	05c31	NUM
ejpam-6048	7	9	,	,	PUNCT
ejpam-6048	7	10	05c76	05c76	PRON
ejpam-6048	7	11	key	key	ADJ
ejpam-6048	7	12	words	word	NOUN
ejpam-6048	7	13	and	and	CCONJ
ejpam-6048	7	14	phrases	phrase	NOUN
ejpam-6048	7	15	:	:	PUNCT
ejpam-6048	7	16	corona	corona	NOUN
ejpam-6048	7	17	product	product	NOUN
ejpam-6048	7	18	,	,	PUNCT
ejpam-6048	7	19	direct	direct	ADJ
ejpam-6048	7	20	product	product	NOUN
ejpam-6048	7	21	,	,	PUNCT
ejpam-6048	7	22	independent	independent	ADJ
ejpam-6048	7	23	neighborhood	neighborhood	NOUN
ejpam-6048	7	24	polynomial	polynomial	ADJ
ejpam-6048	7	25	1	1	NUM
ejpam-6048	7	26	.	.	PUNCT
ejpam-6048	7	27	introduction	introduction	NOUN
ejpam-6048	7	28	a	a	DET
ejpam-6048	7	29	graph	graph	NOUN
ejpam-6048	7	30	g	g	NOUN
ejpam-6048	7	31	is	be	AUX
ejpam-6048	7	32	a	a	DET
ejpam-6048	7	33	pair	pair	NOUN
ejpam-6048	7	34	(	(	PUNCT
ejpam-6048	7	35	v	v	NOUN
ejpam-6048	7	36	(	(	PUNCT
ejpam-6048	7	37	g	g	NOUN
ejpam-6048	7	38	)	)	PUNCT
ejpam-6048	7	39	,	,	PUNCT
ejpam-6048	7	40	e(g	e(g	PROPN
ejpam-6048	7	41	)	)	PUNCT
ejpam-6048	7	42	)	)	PUNCT
ejpam-6048	8	1	consisting	consist	VERB
ejpam-6048	8	2	of	of	ADP
ejpam-6048	8	3	a	a	DET
ejpam-6048	8	4	nonempty	nonempty	ADJ
ejpam-6048	8	5	finite	finite	NOUN
ejpam-6048	8	6	set	set	NOUN
ejpam-6048	8	7	of	of	ADP
ejpam-6048	8	8	vertices	vertex	NOUN
ejpam-6048	8	9	v	v	X
ejpam-6048	8	10	(	(	PUNCT
ejpam-6048	8	11	g	g	NOUN
ejpam-6048	8	12	)	)	PUNCT
ejpam-6048	8	13	and	and	CCONJ
ejpam-6048	8	14	a	a	DET
ejpam-6048	8	15	set	set	NOUN
ejpam-6048	8	16	of	of	ADP
ejpam-6048	8	17	edges	edge	NOUN
ejpam-6048	8	18	e(g	e(g	PROPN
ejpam-6048	8	19	)	)	PUNCT
ejpam-6048	8	20	of	of	ADP
ejpam-6048	8	21	unordered	unordered	ADJ
ejpam-6048	8	22	pairs	pair	NOUN
ejpam-6048	8	23	of	of	ADP
ejpam-6048	8	24	elements	element	NOUN
ejpam-6048	8	25	of	of	ADP
ejpam-6048	8	26	v	v	NOUN
ejpam-6048	8	27	(	(	PUNCT
ejpam-6048	8	28	g	g	NOUN
ejpam-6048	8	29	)	)	PUNCT
ejpam-6048	8	30	.	.	PUNCT
ejpam-6048	9	1	the	the	DET
ejpam-6048	9	2	cardinalities	cardinality	NOUN
ejpam-6048	9	3	of	of	ADP
ejpam-6048	9	4	v	v	NOUN
ejpam-6048	9	5	(	(	PUNCT
ejpam-6048	9	6	g	g	NOUN
ejpam-6048	9	7	)	)	PUNCT
ejpam-6048	9	8	and	and	CCONJ
ejpam-6048	9	9	e(g	e(g	PROPN
ejpam-6048	9	10	)	)	PUNCT
ejpam-6048	9	11	are	be	AUX
ejpam-6048	9	12	called	call	VERB
ejpam-6048	9	13	the	the	DET
ejpam-6048	9	14	order	order	NOUN
ejpam-6048	9	15	and	and	CCONJ
ejpam-6048	9	16	size	size	NOUN
ejpam-6048	9	17	of	of	ADP
ejpam-6048	9	18	g	g	NOUN
ejpam-6048	9	19	,	,	PUNCT
ejpam-6048	9	20	respectively	respectively	ADV
ejpam-6048	9	21	.	.	PUNCT
ejpam-6048	10	1	we	we	PRON
ejpam-6048	10	2	write	write	VERB
ejpam-6048	10	3	x	x	PUNCT
ejpam-6048	10	4	=	=	PUNCT
ejpam-6048	10	5	uv	uv	NOUN
ejpam-6048	10	6	and	and	CCONJ
ejpam-6048	10	7	say	say	VERB
ejpam-6048	10	8	that	that	SCONJ
ejpam-6048	10	9	u	u	PROPN
ejpam-6048	10	10	and	and	CCONJ
ejpam-6048	10	11	v	v	NOUN
ejpam-6048	10	12	are	be	AUX
ejpam-6048	10	13	adjacent	adjacent	ADJ
ejpam-6048	10	14	vertices	vertex	NOUN
ejpam-6048	10	15	;	;	PUNCT
ejpam-6048	10	16	vertex	vertex	NOUN
ejpam-6048	10	17	u	u	NOUN
ejpam-6048	10	18	and	and	CCONJ
ejpam-6048	10	19	edge	edge	NOUN
ejpam-6048	10	20	x	x	VERB
ejpam-6048	10	21	are	be	AUX
ejpam-6048	10	22	incident	incident	NOUN
ejpam-6048	10	23	with	with	ADP
ejpam-6048	10	24	each	each	DET
ejpam-6048	10	25	other	other	ADJ
ejpam-6048	10	26	,	,	PUNCT
ejpam-6048	10	27	so	so	ADV
ejpam-6048	10	28	are	be	AUX
ejpam-6048	10	29	v	v	ADJ
ejpam-6048	10	30	and	and	CCONJ
ejpam-6048	10	31	x.	x.	NOUN
ejpam-6048	10	32	the	the	DET
ejpam-6048	10	33	two	two	NUM
ejpam-6048	10	34	vertices	vertex	NOUN
ejpam-6048	10	35	incident	incident	NOUN
ejpam-6048	10	36	with	with	ADP
ejpam-6048	10	37	an	an	DET
ejpam-6048	10	38	edge	edge	NOUN
ejpam-6048	10	39	are	be	AUX
ejpam-6048	10	40	its	its	PRON
ejpam-6048	10	41	end	end	NOUN
ejpam-6048	10	42	vertices	vertex	NOUN
ejpam-6048	10	43	or	or	CCONJ
ejpam-6048	10	44	ends	end	NOUN
ejpam-6048	10	45	,	,	PUNCT
ejpam-6048	10	46	and	and	CCONJ
ejpam-6048	10	47	an	an	DET
ejpam-6048	10	48	edge	edge	NOUN
ejpam-6048	10	49	joins	join	VERB
ejpam-6048	10	50	its	its	PRON
ejpam-6048	10	51	ends	end	NOUN
ejpam-6048	10	52	.	.	PUNCT
ejpam-6048	11	1	two	two	NUM
ejpam-6048	11	2	vertices	vertex	NOUN
ejpam-6048	11	3	of	of	ADP
ejpam-6048	11	4	a	a	DET
ejpam-6048	11	5	graph	graph	NOUN
ejpam-6048	11	6	g	g	NOUN
ejpam-6048	11	7	are	be	AUX
ejpam-6048	11	8	said	say	VERB
ejpam-6048	11	9	to	to	PART
ejpam-6048	11	10	be	be	AUX
ejpam-6048	11	11	neighbors	neighbor	NOUN
ejpam-6048	11	12	if	if	SCONJ
ejpam-6048	11	13	they	they	PRON
ejpam-6048	11	14	are	be	AUX
ejpam-6048	11	15	adjacent	adjacent	ADJ
ejpam-6048	11	16	in	in	ADP
ejpam-6048	11	17	g.	g.	PROPN
ejpam-6048	11	18	the	the	DET
ejpam-6048	11	19	neighborhood	neighborhood	NOUN
ejpam-6048	11	20	of	of	ADP
ejpam-6048	11	21	a	a	DET
ejpam-6048	11	22	vertex	vertex	NOUN
ejpam-6048	11	23	v	v	ADP
ejpam-6048	11	24	∈	∈	NOUN
ejpam-6048	11	25	v	v	NOUN
ejpam-6048	11	26	(	(	PUNCT
ejpam-6048	11	27	g	g	NOUN
ejpam-6048	11	28	)	)	PUNCT
ejpam-6048	11	29	is	be	AUX
ejpam-6048	11	30	the	the	DET
ejpam-6048	11	31	set	set	NOUN
ejpam-6048	11	32	n(v	n(v	PROPN
ejpam-6048	11	33	)	)	PUNCT
ejpam-6048	12	1	=	=	PRON
ejpam-6048	12	2	{	{	PUNCT
ejpam-6048	12	3	w	w	NOUN
ejpam-6048	12	4	:	:	PUNCT
ejpam-6048	12	5	w	w	PROPN
ejpam-6048	12	6	∈	∈	PROPN
ejpam-6048	12	7	v	v	ADP
ejpam-6048	12	8	(	(	PUNCT
ejpam-6048	12	9	g	g	NOUN
ejpam-6048	12	10	)	)	PUNCT
ejpam-6048	12	11	and	and	CCONJ
ejpam-6048	12	12	vw	vw	PROPN
ejpam-6048	12	13	∈	∈	PROPN
ejpam-6048	12	14	e(g	e(g	PROPN
ejpam-6048	12	15	)	)	PUNCT
ejpam-6048	12	16	}	}	PUNCT
ejpam-6048	12	17	.	.	PUNCT
ejpam-6048	13	1	a	a	DET
ejpam-6048	13	2	vertex	vertex	NOUN
ejpam-6048	13	3	v	v	NOUN
ejpam-6048	13	4	is	be	AUX
ejpam-6048	13	5	pendant	pendant	ADJ
ejpam-6048	13	6	if	if	SCONJ
ejpam-6048	13	7	its	its	PRON
ejpam-6048	13	8	neighborhood	neighborhood	NOUN
ejpam-6048	13	9	contains	contain	VERB
ejpam-6048	13	10	only	only	ADV
ejpam-6048	13	11	one	one	NUM
ejpam-6048	13	12	vertex	vertex	NOUN
ejpam-6048	13	13	;	;	PUNCT
ejpam-6048	13	14	and	and	CCONJ
ejpam-6048	13	15	edge	edge	NOUN
ejpam-6048	13	16	e	e	NOUN
ejpam-6048	13	17	=	=	NOUN
ejpam-6048	13	18	uv	uv	NOUN
ejpam-6048	13	19	is	be	AUX
ejpam-6048	13	20	pendant	pendant	ADJ
ejpam-6048	13	21	if	if	SCONJ
ejpam-6048	13	22	one	one	NUM
ejpam-6048	13	23	of	of	ADP
ejpam-6048	13	24	its	its	PRON
ejpam-6048	13	25	end	end	NOUN
ejpam-6048	13	26	vertices	vertex	NOUN
ejpam-6048	13	27	is	be	AUX
ejpam-6048	13	28	a	a	DET
ejpam-6048	13	29	pendant	pendant	ADJ
ejpam-6048	13	30	vertex	vertex	NOUN
ejpam-6048	13	31	.	.	PUNCT
ejpam-6048	14	1	∗corresponding	∗corresponde	VERB
ejpam-6048	14	2	author	author	NOUN
ejpam-6048	14	3	.	.	PUNCT
ejpam-6048	15	1	doi	doi	NOUN
ejpam-6048	15	2	:	:	PUNCT
ejpam-6048	15	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6048	https://doi.org/10.29020/nybg.ejpam.v18i3.6048	ADJ
ejpam-6048	15	4	email	email	NOUN
ejpam-6048	15	5	addresses	address	VERB
ejpam-6048	15	6	:	:	PUNCT
ejpam-6048	15	7	normalah.abdulcarim@msumain.edu.ph	normalah.abdulcarim@msumain.edu.ph	PROPN
ejpam-6048	15	8	(	(	PUNCT
ejpam-6048	15	9	n.	n.	PROPN
ejpam-6048	15	10	abdulcarim	abdulcarim	PROPN
ejpam-6048	15	11	)	)	PUNCT
ejpam-6048	15	12	,	,	PUNCT
ejpam-6048	15	13	susan.dagondon@g.msuiit.edu.ph	susan.dagondon@g.msuiit.edu.ph	PROPN
ejpam-6048	15	14	(	(	PUNCT
ejpam-6048	15	15	s.	s.	PROPN
ejpam-6048	15	16	dagondon	dagondon	PROPN
ejpam-6048	15	17	)	)	PUNCT
ejpam-6048	15	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6048	16	1	1	1	NUM
ejpam-6048	16	2	copyright	copyright	NOUN
ejpam-6048	16	3	:	:	PUNCT
ejpam-6048	16	4	©	©	PROPN
ejpam-6048	16	5	2025	2025	NUM
ejpam-6048	16	6	the	the	DET
ejpam-6048	16	7	author(s	author(s	NOUN
ejpam-6048	16	8	)	)	PUNCT
ejpam-6048	16	9	.	.	PUNCT
ejpam-6048	17	1	(	(	PUNCT
ejpam-6048	17	2	cc	cc	NOUN
ejpam-6048	17	3	by	by	ADP
ejpam-6048	17	4	-	-	PUNCT
ejpam-6048	17	5	nc	nc	PROPN
ejpam-6048	17	6	4.0	4.0	NUM
ejpam-6048	17	7	)	)	PUNCT
ejpam-6048	17	8	n.	n.	NOUN
ejpam-6048	17	9	abdulcarim	abdulcarim	PROPN
ejpam-6048	17	10	,	,	PUNCT
ejpam-6048	17	11	s.	s.	PROPN
ejpam-6048	17	12	dagondon	dagondon	PROPN
ejpam-6048	17	13	/	/	SYM
ejpam-6048	17	14	eur	eur	PROPN
ejpam-6048	17	15	.	.	PUNCT
ejpam-6048	18	1	j.	j.	PROPN
ejpam-6048	18	2	pure	pure	PROPN
ejpam-6048	18	3	appl	appl	PROPN
ejpam-6048	18	4	.	.	PROPN
ejpam-6048	18	5	math	math	PROPN
ejpam-6048	18	6	,	,	PUNCT
ejpam-6048	18	7	18	18	NUM
ejpam-6048	18	8	(	(	PUNCT
ejpam-6048	18	9	3	3	NUM
ejpam-6048	18	10	)	)	PUNCT
ejpam-6048	18	11	(	(	PUNCT
ejpam-6048	18	12	2025	2025	NUM
ejpam-6048	18	13	)	)	PUNCT
ejpam-6048	18	14	,	,	PUNCT
ejpam-6048	18	15	6048	6048	NUM
ejpam-6048	18	16	2	2	NUM
ejpam-6048	18	17	of	of	ADP
ejpam-6048	18	18	14	14	NUM
ejpam-6048	18	19	a	a	DET
ejpam-6048	18	20	graph	graph	NOUN
ejpam-6048	18	21	is	be	AUX
ejpam-6048	18	22	acyclic	acyclic	ADJ
ejpam-6048	18	23	if	if	SCONJ
ejpam-6048	18	24	it	it	PRON
ejpam-6048	18	25	has	have	VERB
ejpam-6048	18	26	no	no	DET
ejpam-6048	18	27	cycles	cycle	NOUN
ejpam-6048	18	28	.	.	PUNCT
ejpam-6048	19	1	a	a	DET
ejpam-6048	19	2	graph	graph	NOUN
ejpam-6048	19	3	is	be	AUX
ejpam-6048	19	4	said	say	VERB
ejpam-6048	19	5	to	to	PART
ejpam-6048	19	6	be	be	AUX
ejpam-6048	19	7	connected	connect	VERB
ejpam-6048	19	8	if	if	SCONJ
ejpam-6048	19	9	every	every	DET
ejpam-6048	19	10	pair	pair	NOUN
ejpam-6048	19	11	of	of	ADP
ejpam-6048	19	12	vertices	vertex	NOUN
ejpam-6048	19	13	are	be	AUX
ejpam-6048	19	14	joined	join	VERB
ejpam-6048	19	15	by	by	ADP
ejpam-6048	19	16	a	a	DET
ejpam-6048	19	17	path	path	NOUN
ejpam-6048	19	18	.	.	PUNCT
ejpam-6048	20	1	a	a	DET
ejpam-6048	20	2	graph	graph	NOUN
ejpam-6048	20	3	that	that	PRON
ejpam-6048	20	4	is	be	AUX
ejpam-6048	20	5	not	not	PART
ejpam-6048	20	6	connected	connect	VERB
ejpam-6048	20	7	is	be	AUX
ejpam-6048	20	8	called	call	VERB
ejpam-6048	20	9	disconnected	disconnected	ADJ
ejpam-6048	20	10	.	.	PUNCT
ejpam-6048	21	1	a	a	DET
ejpam-6048	21	2	tree	tree	NOUN
ejpam-6048	21	3	is	be	AUX
ejpam-6048	21	4	a	a	DET
ejpam-6048	21	5	connected	connected	ADJ
ejpam-6048	21	6	acyclic	acyclic	ADJ
ejpam-6048	21	7	graph	graph	NOUN
ejpam-6048	21	8	.	.	PUNCT
ejpam-6048	22	1	in	in	ADP
ejpam-6048	22	2	2008	2008	NUM
ejpam-6048	22	3	,	,	PUNCT
ejpam-6048	22	4	brown	brown	PROPN
ejpam-6048	22	5	et	et	PROPN
ejpam-6048	22	6	al	al	PROPN
ejpam-6048	22	7	.	.	PUNCT
ejpam-6048	23	1	[	[	X
ejpam-6048	23	2	1	1	X
ejpam-6048	23	3	]	]	PUNCT
ejpam-6048	23	4	studied	study	VERB
ejpam-6048	23	5	the	the	DET
ejpam-6048	23	6	neighborhood	neighborhood	NOUN
ejpam-6048	23	7	polynomial	polynomial	NOUN
ejpam-6048	23	8	of	of	ADP
ejpam-6048	23	9	a	a	DET
ejpam-6048	23	10	graph	graph	NOUN
ejpam-6048	23	11	.	.	PUNCT
ejpam-6048	24	1	later	later	ADV
ejpam-6048	24	2	,	,	PUNCT
ejpam-6048	24	3	in	in	ADP
ejpam-6048	24	4	2014	2014	NUM
ejpam-6048	24	5	,	,	PUNCT
ejpam-6048	24	6	alwardi	alwardi	PROPN
ejpam-6048	24	7	et	et	PROPN
ejpam-6048	24	8	al	al	PROPN
ejpam-6048	24	9	.	.	PUNCT
ejpam-6048	25	1	[	[	X
ejpam-6048	25	2	2	2	NUM
ejpam-6048	25	3	]	]	PUNCT
ejpam-6048	25	4	also	also	ADV
ejpam-6048	25	5	investigated	investigate	VERB
ejpam-6048	25	6	the	the	DET
ejpam-6048	25	7	neighborhood	neighborhood	NOUN
ejpam-6048	25	8	polynomial	polynomial	NOUN
ejpam-6048	25	9	of	of	ADP
ejpam-6048	25	10	graphs	graph	NOUN
ejpam-6048	25	11	.	.	PUNCT
ejpam-6048	26	1	the	the	DET
ejpam-6048	26	2	following	following	ADJ
ejpam-6048	26	3	year	year	NOUN
ejpam-6048	26	4	,	,	PUNCT
ejpam-6048	26	5	in	in	ADP
ejpam-6048	26	6	2015	2015	NUM
ejpam-6048	26	7	,	,	PUNCT
ejpam-6048	26	8	kulli	kulli	VERB
ejpam-6048	27	1	[	[	X
ejpam-6048	27	2	3	3	NUM
ejpam-6048	27	3	]	]	PUNCT
ejpam-6048	27	4	focused	focus	VERB
ejpam-6048	27	5	on	on	ADP
ejpam-6048	27	6	the	the	DET
ejpam-6048	27	7	neighborhood	neighborhood	NOUN
ejpam-6048	27	8	graph	graph	NOUN
ejpam-6048	27	9	of	of	ADP
ejpam-6048	27	10	a	a	DET
ejpam-6048	27	11	graph	graph	NOUN
ejpam-6048	27	12	.	.	PUNCT
ejpam-6048	28	1	motivated	motivate	VERB
ejpam-6048	28	2	by	by	ADP
ejpam-6048	28	3	these	these	DET
ejpam-6048	28	4	studies	study	NOUN
ejpam-6048	28	5	,	,	PUNCT
ejpam-6048	28	6	the	the	DET
ejpam-6048	28	7	authors	author	NOUN
ejpam-6048	28	8	draw	draw	VERB
ejpam-6048	28	9	inspiration	inspiration	NOUN
ejpam-6048	28	10	from	from	ADP
ejpam-6048	28	11	murthy	murthy	PROPN
ejpam-6048	28	12	’s	’s	PART
ejpam-6048	28	13	paper	paper	NOUN
ejpam-6048	28	14	”	"	PUNCT
ejpam-6048	28	15	the	the	DET
ejpam-6048	28	16	independent	independent	ADJ
ejpam-6048	28	17	neighborhood	neighborhood	NOUN
ejpam-6048	28	18	polynomial	polynomial	NOUN
ejpam-6048	28	19	of	of	ADP
ejpam-6048	28	20	graphs	graph	NOUN
ejpam-6048	28	21	.	.	PUNCT
ejpam-6048	28	22	”	"	PUNCT
ejpam-6048	29	1	[	[	X
ejpam-6048	29	2	4	4	X
ejpam-6048	29	3	]	]	PUNCT
ejpam-6048	29	4	the	the	DET
ejpam-6048	29	5	main	main	ADJ
ejpam-6048	29	6	objective	objective	NOUN
ejpam-6048	29	7	of	of	ADP
ejpam-6048	29	8	the	the	DET
ejpam-6048	29	9	present	present	ADJ
ejpam-6048	29	10	paper	paper	NOUN
ejpam-6048	29	11	is	be	AUX
ejpam-6048	29	12	to	to	PART
ejpam-6048	29	13	establish	establish	VERB
ejpam-6048	29	14	results	result	NOUN
ejpam-6048	29	15	on	on	ADP
ejpam-6048	29	16	the	the	DET
ejpam-6048	29	17	independent	independent	ADJ
ejpam-6048	29	18	neighborhood	neighborhood	NOUN
ejpam-6048	29	19	polynomial	polynomial	NOUN
ejpam-6048	29	20	for	for	ADP
ejpam-6048	29	21	the	the	DET
ejpam-6048	29	22	direct	direct	ADJ
ejpam-6048	29	23	and	and	CCONJ
ejpam-6048	29	24	corona	corona	NOUN
ejpam-6048	29	25	products	product	NOUN
ejpam-6048	29	26	of	of	ADP
ejpam-6048	29	27	two	two	NUM
ejpam-6048	29	28	trees	tree	NOUN
ejpam-6048	29	29	.	.	PUNCT
ejpam-6048	30	1	2	2	X
ejpam-6048	30	2	.	.	X
ejpam-6048	30	3	preliminaries	preliminary	NOUN
ejpam-6048	30	4	this	this	DET
ejpam-6048	30	5	section	section	NOUN
ejpam-6048	30	6	presents	present	VERB
ejpam-6048	30	7	some	some	DET
ejpam-6048	30	8	basic	basic	ADJ
ejpam-6048	30	9	concepts	concept	NOUN
ejpam-6048	30	10	and	and	CCONJ
ejpam-6048	30	11	known	know	VERB
ejpam-6048	30	12	results	result	NOUN
ejpam-6048	30	13	needed	need	VERB
ejpam-6048	30	14	in	in	ADP
ejpam-6048	30	15	this	this	DET
ejpam-6048	30	16	study	study	NOUN
ejpam-6048	30	17	.	.	PUNCT
ejpam-6048	31	1	definition	definition	NOUN
ejpam-6048	31	2	1	1	NUM
ejpam-6048	31	3	.	.	PUNCT
ejpam-6048	32	1	[	[	X
ejpam-6048	32	2	5	5	NUM
ejpam-6048	32	3	]	]	PUNCT
ejpam-6048	32	4	a	a	DET
ejpam-6048	32	5	graph	graph	NOUN
ejpam-6048	32	6	is	be	AUX
ejpam-6048	32	7	acyclic	acyclic	ADJ
ejpam-6048	32	8	if	if	SCONJ
ejpam-6048	32	9	it	it	PRON
ejpam-6048	32	10	has	have	VERB
ejpam-6048	32	11	no	no	DET
ejpam-6048	32	12	cycles	cycle	NOUN
ejpam-6048	32	13	.	.	PUNCT
ejpam-6048	33	1	a	a	DET
ejpam-6048	33	2	graph	graph	NOUN
ejpam-6048	33	3	is	be	AUX
ejpam-6048	33	4	said	say	VERB
ejpam-6048	33	5	to	to	PART
ejpam-6048	33	6	be	be	AUX
ejpam-6048	33	7	connected	connect	VERB
ejpam-6048	33	8	if	if	SCONJ
ejpam-6048	33	9	every	every	DET
ejpam-6048	33	10	pair	pair	NOUN
ejpam-6048	33	11	of	of	ADP
ejpam-6048	33	12	vertices	vertex	NOUN
ejpam-6048	33	13	are	be	AUX
ejpam-6048	33	14	joined	join	VERB
ejpam-6048	33	15	by	by	ADP
ejpam-6048	33	16	a	a	DET
ejpam-6048	33	17	path	path	NOUN
ejpam-6048	33	18	.	.	PUNCT
ejpam-6048	34	1	a	a	DET
ejpam-6048	34	2	graph	graph	NOUN
ejpam-6048	34	3	that	that	PRON
ejpam-6048	34	4	is	be	AUX
ejpam-6048	34	5	not	not	PART
ejpam-6048	34	6	connected	connect	VERB
ejpam-6048	34	7	is	be	AUX
ejpam-6048	34	8	called	call	VERB
ejpam-6048	34	9	disconnected	disconnected	ADJ
ejpam-6048	34	10	.	.	PUNCT
ejpam-6048	35	1	a	a	DET
ejpam-6048	35	2	tree	tree	NOUN
ejpam-6048	35	3	is	be	AUX
ejpam-6048	35	4	a	a	DET
ejpam-6048	35	5	connected	connected	ADJ
ejpam-6048	35	6	acyclic	acyclic	ADJ
ejpam-6048	35	7	graph	graph	NOUN
ejpam-6048	35	8	.	.	PUNCT
ejpam-6048	36	1	definition	definition	NOUN
ejpam-6048	36	2	2	2	NUM
ejpam-6048	36	3	.	.	PUNCT
ejpam-6048	37	1	[	[	X
ejpam-6048	37	2	6	6	NUM
ejpam-6048	37	3	]	]	PUNCT
ejpam-6048	37	4	let	let	VERB
ejpam-6048	37	5	g	g	PRON
ejpam-6048	37	6	be	be	AUX
ejpam-6048	37	7	a	a	DET
ejpam-6048	37	8	graph	graph	NOUN
ejpam-6048	37	9	.	.	PUNCT
ejpam-6048	38	1	the	the	DET
ejpam-6048	38	2	distance	distance	NOUN
ejpam-6048	38	3	between	between	ADP
ejpam-6048	38	4	two	two	NUM
ejpam-6048	38	5	vertices	vertex	NOUN
ejpam-6048	38	6	x	x	PUNCT
ejpam-6048	38	7	and	and	CCONJ
ejpam-6048	38	8	y	y	PROPN
ejpam-6048	38	9	in	in	ADP
ejpam-6048	38	10	a	a	DET
ejpam-6048	38	11	graph	graph	NOUN
ejpam-6048	38	12	g	g	NOUN
ejpam-6048	38	13	,	,	PUNCT
ejpam-6048	38	14	denoted	denote	VERB
ejpam-6048	38	15	by	by	ADP
ejpam-6048	38	16	dg(x	dg(x	NUM
ejpam-6048	38	17	,	,	PUNCT
ejpam-6048	38	18	y	y	NOUN
ejpam-6048	38	19	)	)	PUNCT
ejpam-6048	38	20	or	or	CCONJ
ejpam-6048	38	21	simply	simply	ADV
ejpam-6048	38	22	d(x	d(x	PROPN
ejpam-6048	38	23	,	,	PUNCT
ejpam-6048	38	24	y	y	PROPN
ejpam-6048	38	25	)	)	PUNCT
ejpam-6048	38	26	,	,	PUNCT
ejpam-6048	38	27	is	be	AUX
ejpam-6048	38	28	the	the	DET
ejpam-6048	38	29	length	length	NOUN
ejpam-6048	38	30	of	of	ADP
ejpam-6048	38	31	the	the	DET
ejpam-6048	38	32	shortest	short	ADJ
ejpam-6048	38	33	path	path	NOUN
ejpam-6048	38	34	joining	join	VERB
ejpam-6048	38	35	them	they	PRON
ejpam-6048	38	36	,	,	PUNCT
ejpam-6048	38	37	otherwise	otherwise	ADV
ejpam-6048	38	38	,	,	PUNCT
ejpam-6048	38	39	d(x	d(x	PROPN
ejpam-6048	38	40	,	,	PUNCT
ejpam-6048	38	41	y	y	NOUN
ejpam-6048	38	42	)	)	PUNCT
ejpam-6048	38	43	=	=	SYM
ejpam-6048	38	44	∞.	∞.	PROPN
ejpam-6048	38	45	theorem	theorem	VERB
ejpam-6048	38	46	1	1	NUM
ejpam-6048	38	47	.	.	PUNCT
ejpam-6048	39	1	[	[	X
ejpam-6048	39	2	7	7	X
ejpam-6048	39	3	]	]	PUNCT
ejpam-6048	39	4	let	let	VERB
ejpam-6048	39	5	g	g	NOUN
ejpam-6048	39	6	be	be	AUX
ejpam-6048	39	7	any	any	DET
ejpam-6048	39	8	tree	tree	NOUN
ejpam-6048	39	9	.	.	PUNCT
ejpam-6048	40	1	then	then	ADV
ejpam-6048	40	2	for	for	ADP
ejpam-6048	40	3	any	any	PRON
ejpam-6048	40	4	u	u	PROPN
ejpam-6048	40	5	∈	∈	PROPN
ejpam-6048	40	6	v	v	NOUN
ejpam-6048	40	7	(	(	PUNCT
ejpam-6048	40	8	g	g	NOUN
ejpam-6048	40	9	)	)	PUNCT
ejpam-6048	40	10	,	,	PUNCT
ejpam-6048	40	11	the	the	DET
ejpam-6048	40	12	set	set	NOUN
ejpam-6048	40	13	ω	ω	PROPN
ejpam-6048	40	14	=	=	SYM
ejpam-6048	40	15	{	{	PUNCT
ejpam-6048	40	16	v	v	NUM
ejpam-6048	40	17	∈	∈	NOUN
ejpam-6048	40	18	v	v	NOUN
ejpam-6048	40	19	(	(	PUNCT
ejpam-6048	40	20	g	g	NOUN
ejpam-6048	40	21	)	)	PUNCT
ejpam-6048	40	22	:	:	PUNCT
ejpam-6048	41	1	d(u	d(u	PROPN
ejpam-6048	41	2	,	,	PUNCT
ejpam-6048	41	3	v	v	NOUN
ejpam-6048	41	4	)	)	PUNCT
ejpam-6048	41	5	=	=	SYM
ejpam-6048	41	6	2n	2n	NUM
ejpam-6048	41	7	,	,	PUNCT
ejpam-6048	41	8	n	n	PRON
ejpam-6048	41	9	∈	∈	PROPN
ejpam-6048	41	10	n∗	n∗	PROPN
ejpam-6048	41	11	}	}	PUNCT
ejpam-6048	41	12	is	be	AUX
ejpam-6048	41	13	an	an	DET
ejpam-6048	41	14	independent	independent	ADJ
ejpam-6048	41	15	neighborhood	neighborhood	NOUN
ejpam-6048	41	16	set	set	NOUN
ejpam-6048	41	17	of	of	ADP
ejpam-6048	41	18	g.	g.	PROPN
ejpam-6048	41	19	corollary	corollary	PROPN
ejpam-6048	41	20	1	1	NUM
ejpam-6048	41	21	.	.	PUNCT
ejpam-6048	42	1	[	[	X
ejpam-6048	42	2	7	7	X
ejpam-6048	42	3	]	]	PUNCT
ejpam-6048	42	4	let	let	VERB
ejpam-6048	42	5	f	f	PRON
ejpam-6048	42	6	be	be	AUX
ejpam-6048	42	7	the	the	DET
ejpam-6048	42	8	set	set	NOUN
ejpam-6048	42	9	of	of	ADP
ejpam-6048	42	10	nonpendant	nonpendant	ADJ
ejpam-6048	42	11	vertices	vertex	NOUN
ejpam-6048	42	12	in	in	ADP
ejpam-6048	42	13	a	a	DET
ejpam-6048	42	14	tree	tree	NOUN
ejpam-6048	42	15	g	g	NOUN
ejpam-6048	42	16	and	and	CCONJ
ejpam-6048	42	17	f	f	PROPN
ejpam-6048	42	18	∈	∈	PROPN
ejpam-6048	43	1	f	f	PROPN
ejpam-6048	43	2	.	.	PUNCT
ejpam-6048	44	1	let	let	VERB
ejpam-6048	44	2	a	a	PRON
ejpam-6048	44	3	=	=	X
ejpam-6048	44	4	{	{	PUNCT
ejpam-6048	44	5	a	a	DET
ejpam-6048	44	6	∈	∈	ADJ
ejpam-6048	44	7	f	f	X
ejpam-6048	44	8	:	:	PUNCT
ejpam-6048	44	9	dg(a	dg(a	X
ejpam-6048	44	10	,	,	PUNCT
ejpam-6048	44	11	f	f	X
ejpam-6048	44	12	)	)	PUNCT
ejpam-6048	44	13	=	=	SYM
ejpam-6048	44	14	2n	2n	NUM
ejpam-6048	44	15	,	,	PUNCT
ejpam-6048	44	16	n	n	PRON
ejpam-6048	44	17	∈	∈	PROPN
ejpam-6048	44	18	n∗	n∗	PROPN
ejpam-6048	44	19	}	}	PUNCT
ejpam-6048	44	20	and	and	CCONJ
ejpam-6048	44	21	b	b	X
ejpam-6048	44	22	=	=	SYM
ejpam-6048	44	23	f	f	PROPN
ejpam-6048	44	24	\a	\a	PROPN
ejpam-6048	44	25	.	.	PUNCT
ejpam-6048	45	1	then	then	ADV
ejpam-6048	45	2	the	the	DET
ejpam-6048	45	3	sets	set	NOUN
ejpam-6048	45	4	ω	ω	PUNCT
ejpam-6048	45	5	=	=	SYM
ejpam-6048	45	6	{	{	PUNCT
ejpam-6048	45	7	v	v	NOUN
ejpam-6048	45	8	:	:	PUNCT
ejpam-6048	45	9	v	v	NOUN
ejpam-6048	45	10	is	be	AUX
ejpam-6048	45	11	a	a	DET
ejpam-6048	45	12	pendant	pendant	ADJ
ejpam-6048	45	13	neighbor	neighbor	NOUN
ejpam-6048	45	14	of	of	ADP
ejpam-6048	45	15	a	a	PRON
ejpam-6048	45	16	,	,	PUNCT
ejpam-6048	45	17	for	for	SCONJ
ejpam-6048	45	18	some	some	DET
ejpam-6048	45	19	a	a	DET
ejpam-6048	45	20	∈	∈	PROPN
ejpam-6048	45	21	a	a	PRON
ejpam-6048	45	22	}	}	PUNCT
ejpam-6048	45	23	∪b	∪b	NOUN
ejpam-6048	45	24	and	and	CCONJ
ejpam-6048	45	25	∆	∆	X
ejpam-6048	45	26	=	=	PRON
ejpam-6048	45	27	{	{	PUNCT
ejpam-6048	45	28	u	u	NOUN
ejpam-6048	45	29	:	:	PUNCT
ejpam-6048	45	30	u	u	NOUN
ejpam-6048	45	31	is	be	AUX
ejpam-6048	45	32	a	a	DET
ejpam-6048	45	33	pendant	pendant	ADJ
ejpam-6048	45	34	neighbor	neighbor	NOUN
ejpam-6048	45	35	of	of	ADP
ejpam-6048	45	36	b	b	PROPN
ejpam-6048	45	37	,	,	PUNCT
ejpam-6048	45	38	for	for	SCONJ
ejpam-6048	45	39	some	some	DET
ejpam-6048	45	40	b	b	NOUN
ejpam-6048	45	41	∈	∈	PROPN
ejpam-6048	45	42	b	b	PROPN
ejpam-6048	45	43	}	}	PUNCT
ejpam-6048	45	44	∪a	∪a	NUM
ejpam-6048	45	45	are	be	AUX
ejpam-6048	45	46	the	the	DET
ejpam-6048	45	47	only	only	ADJ
ejpam-6048	45	48	independent	independent	ADJ
ejpam-6048	45	49	neighborhood	neighborhood	NOUN
ejpam-6048	45	50	sets	set	NOUN
ejpam-6048	45	51	of	of	ADP
ejpam-6048	45	52	g.	g.	PROPN
ejpam-6048	45	53	remark	remark	PROPN
ejpam-6048	45	54	1	1	NUM
ejpam-6048	45	55	.	.	PUNCT
ejpam-6048	46	1	[	[	X
ejpam-6048	46	2	7	7	X
ejpam-6048	46	3	]	]	PUNCT
ejpam-6048	46	4	for	for	ADP
ejpam-6048	46	5	any	any	DET
ejpam-6048	46	6	tree	tree	NOUN
ejpam-6048	46	7	t	t	NOUN
ejpam-6048	46	8	with	with	ADP
ejpam-6048	46	9	independent	independent	ADJ
ejpam-6048	46	10	neighborhood	neighborhood	NOUN
ejpam-6048	46	11	sets	set	VERB
ejpam-6048	46	12	ω	ω	NOUN
ejpam-6048	46	13	and	and	CCONJ
ejpam-6048	46	14	∆	∆	PROPN
ejpam-6048	46	15	,	,	PUNCT
ejpam-6048	46	16	ni(t	ni(t	ADV
ejpam-6048	46	17	,	,	PUNCT
ejpam-6048	46	18	x	x	X
ejpam-6048	46	19	)	)	PUNCT
ejpam-6048	46	20	=	=	PUNCT
ejpam-6048	46	21	x|ω|	x|ω|	PUNCT
ejpam-6048	47	1	+	+	CCONJ
ejpam-6048	47	2	x|∆|	x|∆|	X
ejpam-6048	47	3	.	.	PUNCT
ejpam-6048	48	1	n.	n.	PROPN
ejpam-6048	48	2	abdulcarim	abdulcarim	PROPN
ejpam-6048	48	3	,	,	PUNCT
ejpam-6048	48	4	s.	s.	PROPN
ejpam-6048	48	5	dagondon	dagondon	PROPN
ejpam-6048	48	6	/	/	SYM
ejpam-6048	48	7	eur	eur	PROPN
ejpam-6048	48	8	.	.	PUNCT
ejpam-6048	49	1	j.	j.	PROPN
ejpam-6048	49	2	pure	pure	PROPN
ejpam-6048	49	3	appl	appl	PROPN
ejpam-6048	49	4	.	.	PROPN
ejpam-6048	49	5	math	math	PROPN
ejpam-6048	49	6	,	,	PUNCT
ejpam-6048	49	7	18	18	NUM
ejpam-6048	49	8	(	(	PUNCT
ejpam-6048	49	9	3	3	NUM
ejpam-6048	49	10	)	)	PUNCT
ejpam-6048	49	11	(	(	PUNCT
ejpam-6048	49	12	2025	2025	NUM
ejpam-6048	49	13	)	)	PUNCT
ejpam-6048	49	14	,	,	PUNCT
ejpam-6048	49	15	6048	6048	NUM
ejpam-6048	49	16	3	3	NUM
ejpam-6048	49	17	of	of	ADP
ejpam-6048	49	18	14	14	NUM
ejpam-6048	49	19	corollary	corollary	ADJ
ejpam-6048	49	20	2	2	NUM
ejpam-6048	49	21	.	.	PUNCT
ejpam-6048	50	1	[	[	X
ejpam-6048	50	2	7	7	X
ejpam-6048	50	3	]	]	PUNCT
ejpam-6048	50	4	for	for	ADP
ejpam-6048	50	5	any	any	DET
ejpam-6048	50	6	tree	tree	NOUN
ejpam-6048	50	7	t	t	NOUN
ejpam-6048	50	8	with	with	ADP
ejpam-6048	50	9	independent	independent	ADJ
ejpam-6048	50	10	neighborhood	neighborhood	NOUN
ejpam-6048	50	11	sets	set	VERB
ejpam-6048	50	12	ω	ω	NOUN
ejpam-6048	50	13	and	and	CCONJ
ejpam-6048	50	14	∆	∆	NOUN
ejpam-6048	50	15	,	,	PUNCT
ejpam-6048	50	16	if	if	SCONJ
ejpam-6048	50	17	uv	uv	PROPN
ejpam-6048	50	18	∈	∈	PROPN
ejpam-6048	50	19	e(t	e(t	PROPN
ejpam-6048	50	20	)	)	PUNCT
ejpam-6048	50	21	,	,	PUNCT
ejpam-6048	50	22	then	then	ADV
ejpam-6048	50	23	u	u	PROPN
ejpam-6048	50	24	∈	∈	PROPN
ejpam-6048	50	25	ω	ω	PROPN
ejpam-6048	50	26	and	and	CCONJ
ejpam-6048	50	27	v	v	ADP
ejpam-6048	50	28	∈	∈	NOUN
ejpam-6048	50	29	∆.	∆.	NOUN
ejpam-6048	50	30	definition	definition	NOUN
ejpam-6048	50	31	3	3	NUM
ejpam-6048	50	32	.	.	PUNCT
ejpam-6048	51	1	[	[	X
ejpam-6048	51	2	8	8	NUM
ejpam-6048	51	3	]	]	PUNCT
ejpam-6048	51	4	the	the	DET
ejpam-6048	51	5	direct	direct	ADJ
ejpam-6048	51	6	product	product	NOUN
ejpam-6048	51	7	(	(	PUNCT
ejpam-6048	51	8	or	or	CCONJ
ejpam-6048	51	9	conjunction	conjunction	NOUN
ejpam-6048	51	10	)	)	PUNCT
ejpam-6048	51	11	of	of	ADP
ejpam-6048	51	12	two	two	NUM
ejpam-6048	51	13	graphs	graph	NOUN
ejpam-6048	51	14	g	g	NOUN
ejpam-6048	51	15	and	and	CCONJ
ejpam-6048	51	16	h	h	NOUN
ejpam-6048	51	17	,	,	PUNCT
ejpam-6048	51	18	denoted	denote	VERB
ejpam-6048	51	19	by	by	ADP
ejpam-6048	51	20	g	g	PROPN
ejpam-6048	51	21	·	·	PUNCT
ejpam-6048	51	22	h	h	NOUN
ejpam-6048	51	23	,	,	PUNCT
ejpam-6048	51	24	is	be	AUX
ejpam-6048	51	25	the	the	DET
ejpam-6048	51	26	graph	graph	NOUN
ejpam-6048	51	27	whose	whose	DET
ejpam-6048	51	28	vertex	vertex	NOUN
ejpam-6048	51	29	set	set	NOUN
ejpam-6048	51	30	is	be	AUX
ejpam-6048	51	31	v	v	NOUN
ejpam-6048	51	32	(	(	PUNCT
ejpam-6048	51	33	g	g	NOUN
ejpam-6048	51	34	)	)	PUNCT
ejpam-6048	51	35	×	×	NOUN
ejpam-6048	51	36	v	v	NOUN
ejpam-6048	51	37	(	(	PUNCT
ejpam-6048	51	38	h	h	NOUN
ejpam-6048	51	39	)	)	PUNCT
ejpam-6048	51	40	in	in	ADP
ejpam-6048	51	41	which	which	PRON
ejpam-6048	51	42	(	(	PUNCT
ejpam-6048	51	43	u	u	NOUN
ejpam-6048	51	44	,	,	PUNCT
ejpam-6048	51	45	v	v	NOUN
ejpam-6048	51	46	)	)	PUNCT
ejpam-6048	51	47	is	be	AUX
ejpam-6048	51	48	adjacent	adjacent	ADJ
ejpam-6048	51	49	to	to	PART
ejpam-6048	51	50	(	(	PUNCT
ejpam-6048	51	51	u′	u′	PROPN
ejpam-6048	51	52	,	,	PUNCT
ejpam-6048	51	53	v′	v′	PROPN
ejpam-6048	51	54	)	)	PUNCT
ejpam-6048	52	1	if	if	SCONJ
ejpam-6048	52	2	and	and	CCONJ
ejpam-6048	52	3	only	only	ADV
ejpam-6048	52	4	if	if	SCONJ
ejpam-6048	52	5	uu′	uu′	PROPN
ejpam-6048	52	6	∈	∈	PROPN
ejpam-6048	52	7	e(g	e(g	PROPN
ejpam-6048	52	8	)	)	PUNCT
ejpam-6048	52	9	and	and	CCONJ
ejpam-6048	52	10	vv′	vv′	PROPN
ejpam-6048	52	11	∈	∈	PROPN
ejpam-6048	52	12	e(h	e(h	PROPN
ejpam-6048	52	13	)	)	PUNCT
ejpam-6048	52	14	.	.	PUNCT
ejpam-6048	53	1	example	example	NOUN
ejpam-6048	54	1	1	1	NUM
ejpam-6048	54	2	.	.	PUNCT
ejpam-6048	54	3	figure	figure	NOUN
ejpam-6048	54	4	1	1	NUM
ejpam-6048	54	5	shows	show	VERB
ejpam-6048	54	6	two	two	NUM
ejpam-6048	54	7	graphs	graph	NOUN
ejpam-6048	54	8	g	g	NOUN
ejpam-6048	54	9	and	and	CCONJ
ejpam-6048	54	10	h	h	PROPN
ejpam-6048	54	11	and	and	CCONJ
ejpam-6048	54	12	their	their	PRON
ejpam-6048	54	13	direct	direct	ADJ
ejpam-6048	54	14	product	product	NOUN
ejpam-6048	54	15	.	.	PUNCT
ejpam-6048	55	1	a	a	DET
ejpam-6048	55	2	b	b	X
ejpam-6048	55	3	c	c	NOUN
ejpam-6048	55	4	d	d	X
ejpam-6048	55	5	e	e	X
ejpam-6048	55	6	g	g	NOUN
ejpam-6048	55	7	:	:	PUNCT
ejpam-6048	55	8	1	1	NUM
ejpam-6048	55	9	2	2	NUM
ejpam-6048	55	10	4	4	NUM
ejpam-6048	55	11	3	3	NUM
ejpam-6048	55	12	h	h	NOUN
ejpam-6048	55	13	:	:	PUNCT
ejpam-6048	55	14	(	(	PUNCT
ejpam-6048	55	15	a	a	DET
ejpam-6048	55	16	,	,	PUNCT
ejpam-6048	55	17	1	1	NUM
ejpam-6048	55	18	)	)	PUNCT
ejpam-6048	55	19	(	(	PUNCT
ejpam-6048	55	20	a	a	DET
ejpam-6048	55	21	,	,	PUNCT
ejpam-6048	55	22	4	4	NUM
ejpam-6048	55	23	)	)	PUNCT
ejpam-6048	55	24	(	(	PUNCT
ejpam-6048	55	25	a	a	DET
ejpam-6048	55	26	,	,	PUNCT
ejpam-6048	55	27	3	3	NUM
ejpam-6048	55	28	)	)	PUNCT
ejpam-6048	55	29	(	(	PUNCT
ejpam-6048	55	30	b	b	NOUN
ejpam-6048	55	31	,	,	PUNCT
ejpam-6048	55	32	2	2	NUM
ejpam-6048	55	33	)	)	PUNCT
ejpam-6048	55	34	(	(	PUNCT
ejpam-6048	55	35	c	c	X
ejpam-6048	55	36	,	,	PUNCT
ejpam-6048	55	37	2	2	NUM
ejpam-6048	55	38	)	)	PUNCT
ejpam-6048	55	39	(	(	PUNCT
ejpam-6048	55	40	d	d	NOUN
ejpam-6048	55	41	,	,	PUNCT
ejpam-6048	55	42	2	2	NUM
ejpam-6048	55	43	)	)	PUNCT
ejpam-6048	55	44	(	(	PUNCT
ejpam-6048	55	45	e	e	NOUN
ejpam-6048	55	46	,	,	PUNCT
ejpam-6048	55	47	1	1	NUM
ejpam-6048	55	48	)	)	PUNCT
ejpam-6048	55	49	(	(	PUNCT
ejpam-6048	55	50	e	e	NOUN
ejpam-6048	55	51	,	,	PUNCT
ejpam-6048	55	52	3	3	NUM
ejpam-6048	55	53	)	)	PUNCT
ejpam-6048	55	54	(	(	PUNCT
ejpam-6048	55	55	e	e	NOUN
ejpam-6048	55	56	,	,	PUNCT
ejpam-6048	55	57	4	4	NUM
ejpam-6048	55	58	)	)	PUNCT
ejpam-6048	55	59	g	g	NOUN
ejpam-6048	55	60	·	·	SYM
ejpam-6048	55	61	h	h	NOUN
ejpam-6048	55	62	:	:	PUNCT
ejpam-6048	55	63	(	(	PUNCT
ejpam-6048	55	64	b	b	X
ejpam-6048	55	65	,	,	PUNCT
ejpam-6048	55	66	1	1	NUM
ejpam-6048	55	67	)	)	PUNCT
ejpam-6048	55	68	(	(	PUNCT
ejpam-6048	55	69	b	b	NOUN
ejpam-6048	55	70	,	,	PUNCT
ejpam-6048	55	71	4	4	NUM
ejpam-6048	55	72	)	)	PUNCT
ejpam-6048	55	73	(	(	PUNCT
ejpam-6048	55	74	b	b	NOUN
ejpam-6048	55	75	,	,	PUNCT
ejpam-6048	55	76	3	3	NUM
ejpam-6048	55	77	)	)	PUNCT
ejpam-6048	55	78	(	(	PUNCT
ejpam-6048	55	79	c	c	X
ejpam-6048	55	80	,	,	PUNCT
ejpam-6048	55	81	1	1	NUM
ejpam-6048	55	82	)	)	PUNCT
ejpam-6048	55	83	(	(	PUNCT
ejpam-6048	55	84	c	c	X
ejpam-6048	55	85	,	,	PUNCT
ejpam-6048	55	86	3	3	NUM
ejpam-6048	55	87	)	)	PUNCT
ejpam-6048	55	88	(	(	PUNCT
ejpam-6048	55	89	c	c	X
ejpam-6048	55	90	,	,	PUNCT
ejpam-6048	55	91	4	4	NUM
ejpam-6048	55	92	)	)	PUNCT
ejpam-6048	55	93	(	(	PUNCT
ejpam-6048	55	94	d	d	NOUN
ejpam-6048	55	95	,	,	PUNCT
ejpam-6048	55	96	1	1	NUM
ejpam-6048	55	97	)	)	PUNCT
ejpam-6048	55	98	(	(	PUNCT
ejpam-6048	55	99	d	d	NOUN
ejpam-6048	55	100	,	,	PUNCT
ejpam-6048	55	101	3	3	NUM
ejpam-6048	55	102	)	)	PUNCT
ejpam-6048	55	103	(	(	PUNCT
ejpam-6048	55	104	d	d	NOUN
ejpam-6048	55	105	,	,	PUNCT
ejpam-6048	55	106	4	4	NUM
ejpam-6048	55	107	)	)	PUNCT
ejpam-6048	55	108	(	(	PUNCT
ejpam-6048	55	109	a	a	DET
ejpam-6048	55	110	,	,	PUNCT
ejpam-6048	55	111	2	2	NUM
ejpam-6048	55	112	)	)	PUNCT
ejpam-6048	55	113	(	(	PUNCT
ejpam-6048	55	114	e	e	NOUN
ejpam-6048	55	115	,	,	PUNCT
ejpam-6048	55	116	2	2	X
ejpam-6048	55	117	)	)	PUNCT
ejpam-6048	55	118	figure	figure	NOUN
ejpam-6048	55	119	1	1	NUM
ejpam-6048	55	120	:	:	PUNCT
ejpam-6048	55	121	graphs	graphs	VERB
ejpam-6048	55	122	g	g	NOUN
ejpam-6048	55	123	and	and	CCONJ
ejpam-6048	55	124	h	h	PROPN
ejpam-6048	55	125	and	and	CCONJ
ejpam-6048	55	126	their	their	PRON
ejpam-6048	55	127	direct	direct	ADJ
ejpam-6048	55	128	product	product	NOUN
ejpam-6048	55	129	definition	definition	NOUN
ejpam-6048	55	130	4	4	NUM
ejpam-6048	55	131	.	.	PUNCT
ejpam-6048	56	1	[	[	X
ejpam-6048	56	2	5	5	X
ejpam-6048	56	3	]	]	PUNCT
ejpam-6048	56	4	the	the	DET
ejpam-6048	56	5	corona	corona	NOUN
ejpam-6048	56	6	of	of	ADP
ejpam-6048	56	7	two	two	NUM
ejpam-6048	56	8	graphs	graph	NOUN
ejpam-6048	56	9	g	g	NOUN
ejpam-6048	56	10	and	and	CCONJ
ejpam-6048	56	11	h	h	NOUN
ejpam-6048	56	12	,	,	PUNCT
ejpam-6048	56	13	denoted	denote	VERB
ejpam-6048	56	14	g	g	PROPN
ejpam-6048	56	15	◦	◦	NOUN
ejpam-6048	56	16	h	h	NOUN
ejpam-6048	56	17	,	,	PUNCT
ejpam-6048	56	18	is	be	AUX
ejpam-6048	56	19	defined	define	VERB
ejpam-6048	56	20	as	as	ADP
ejpam-6048	56	21	the	the	DET
ejpam-6048	56	22	graph	graph	NOUN
ejpam-6048	56	23	obtained	obtain	VERB
ejpam-6048	56	24	by	by	ADP
ejpam-6048	56	25	taking	take	VERB
ejpam-6048	56	26	one	one	NUM
ejpam-6048	56	27	copy	copy	NOUN
ejpam-6048	56	28	of	of	ADP
ejpam-6048	56	29	g	g	PROPN
ejpam-6048	56	30	and	and	CCONJ
ejpam-6048	56	31	|v	|v	PROPN
ejpam-6048	56	32	(	(	PUNCT
ejpam-6048	56	33	g)|	g)|	NOUN
ejpam-6048	56	34	copies	copy	NOUN
ejpam-6048	56	35	of	of	ADP
ejpam-6048	56	36	h	h	NOUN
ejpam-6048	56	37	and	and	CCONJ
ejpam-6048	56	38	joining	join	VERB
ejpam-6048	56	39	the	the	DET
ejpam-6048	56	40	ith	ith	PROPN
ejpam-6048	56	41	vertex	vertex	NOUN
ejpam-6048	56	42	of	of	ADP
ejpam-6048	56	43	g	g	NOUN
ejpam-6048	56	44	to	to	ADP
ejpam-6048	56	45	every	every	DET
ejpam-6048	56	46	vertex	vertex	NOUN
ejpam-6048	56	47	in	in	ADP
ejpam-6048	56	48	the	the	DET
ejpam-6048	56	49	ith	ith	PROPN
ejpam-6048	56	50	copy	copy	NOUN
ejpam-6048	56	51	of	of	ADP
ejpam-6048	56	52	h.	h.	PROPN
ejpam-6048	56	53	it	it	PRON
ejpam-6048	56	54	is	be	AUX
ejpam-6048	56	55	customary	customary	ADJ
ejpam-6048	56	56	to	to	PART
ejpam-6048	56	57	denote	denote	VERB
ejpam-6048	56	58	by	by	ADP
ejpam-6048	56	59	hv	hv	PROPN
ejpam-6048	56	60	that	that	DET
ejpam-6048	56	61	copy	copy	NOUN
ejpam-6048	56	62	of	of	ADP
ejpam-6048	56	63	h	h	NOUN
ejpam-6048	56	64	whose	whose	DET
ejpam-6048	56	65	vertices	vertex	NOUN
ejpam-6048	56	66	are	be	AUX
ejpam-6048	56	67	adjoined	adjoin	VERB
ejpam-6048	56	68	with	with	ADP
ejpam-6048	56	69	the	the	DET
ejpam-6048	56	70	vertex	vertex	NOUN
ejpam-6048	56	71	v	v	NOUN
ejpam-6048	56	72	of	of	ADP
ejpam-6048	56	73	g.	g.	PROPN
ejpam-6048	56	74	in	in	ADP
ejpam-6048	56	75	effect	effect	NOUN
ejpam-6048	56	76	,	,	PUNCT
ejpam-6048	56	77	g	g	PROPN
ejpam-6048	56	78	◦	◦	NOUN
ejpam-6048	56	79	h	h	NOUN
ejpam-6048	56	80	is	be	AUX
ejpam-6048	56	81	composed	compose	VERB
ejpam-6048	56	82	of	of	ADP
ejpam-6048	56	83	the	the	DET
ejpam-6048	56	84	subgraphs	subgraph	NOUN
ejpam-6048	56	85	hv	hv	PROPN
ejpam-6048	56	86	+	+	NUM
ejpam-6048	56	87	v	v	NOUN
ejpam-6048	56	88	joined	join	VERB
ejpam-6048	56	89	together	together	ADV
ejpam-6048	56	90	by	by	ADP
ejpam-6048	56	91	the	the	DET
ejpam-6048	56	92	edges	edge	NOUN
ejpam-6048	56	93	of	of	ADP
ejpam-6048	56	94	g.	g.	PROPN
ejpam-6048	56	95	moreover	moreover	ADV
ejpam-6048	56	96	,	,	PUNCT
ejpam-6048	56	97	v	v	X
ejpam-6048	56	98	(	(	PUNCT
ejpam-6048	56	99	g	g	PROPN
ejpam-6048	56	100	◦	◦	NOUN
ejpam-6048	56	101	h	h	NOUN
ejpam-6048	56	102	)	)	PUNCT
ejpam-6048	57	1	=	=	SYM
ejpam-6048	57	2	⋃	⋃	NOUN
ejpam-6048	57	3	v∈v	v∈v	NOUN
ejpam-6048	57	4	(	(	PUNCT
ejpam-6048	57	5	g	g	NOUN
ejpam-6048	57	6	)	)	PUNCT
ejpam-6048	57	7	v	v	NOUN
ejpam-6048	57	8	(	(	PUNCT
ejpam-6048	57	9	hv	hv	PROPN
ejpam-6048	57	10	+	+	PROPN
ejpam-6048	57	11	v	v	NOUN
ejpam-6048	57	12	)	)	PUNCT
ejpam-6048	57	13	.	.	PUNCT
ejpam-6048	58	1	example	example	NOUN
ejpam-6048	59	1	2	2	NUM
ejpam-6048	59	2	.	.	X
ejpam-6048	59	3	figure	figure	NOUN
ejpam-6048	59	4	2	2	NUM
ejpam-6048	59	5	shows	show	VERB
ejpam-6048	59	6	two	two	NUM
ejpam-6048	59	7	graphs	graph	NOUN
ejpam-6048	59	8	g	g	NOUN
ejpam-6048	59	9	and	and	CCONJ
ejpam-6048	59	10	h	h	PROPN
ejpam-6048	59	11	and	and	CCONJ
ejpam-6048	59	12	their	their	PRON
ejpam-6048	59	13	corona	corona	NOUN
ejpam-6048	59	14	products	product	NOUN
ejpam-6048	59	15	g	g	ADP
ejpam-6048	59	16	◦	◦	NOUN
ejpam-6048	59	17	h	h	NOUN
ejpam-6048	59	18	and	and	CCONJ
ejpam-6048	59	19	h	h	PROPN
ejpam-6048	59	20	◦	◦	PROPN
ejpam-6048	59	21	g.	g.	PROPN
ejpam-6048	59	22	n.	n.	PROPN
ejpam-6048	59	23	abdulcarim	abdulcarim	PROPN
ejpam-6048	59	24	,	,	PUNCT
ejpam-6048	59	25	s.	s.	PROPN
ejpam-6048	59	26	dagondon	dagondon	PROPN
ejpam-6048	59	27	/	/	SYM
ejpam-6048	59	28	eur	eur	PROPN
ejpam-6048	59	29	.	.	PUNCT
ejpam-6048	60	1	j.	j.	PROPN
ejpam-6048	60	2	pure	pure	PROPN
ejpam-6048	60	3	appl	appl	PROPN
ejpam-6048	60	4	.	.	PROPN
ejpam-6048	60	5	math	math	PROPN
ejpam-6048	60	6	,	,	PUNCT
ejpam-6048	60	7	18	18	NUM
ejpam-6048	60	8	(	(	PUNCT
ejpam-6048	60	9	3	3	NUM
ejpam-6048	60	10	)	)	PUNCT
ejpam-6048	60	11	(	(	PUNCT
ejpam-6048	60	12	2025	2025	NUM
ejpam-6048	60	13	)	)	PUNCT
ejpam-6048	60	14	,	,	PUNCT
ejpam-6048	60	15	6048	6048	NUM
ejpam-6048	60	16	4	4	NUM
ejpam-6048	60	17	of	of	ADP
ejpam-6048	60	18	14	14	NUM
ejpam-6048	60	19	1	1	NUM
ejpam-6048	60	20	2	2	NUM
ejpam-6048	60	21	3	3	NUM
ejpam-6048	60	22	4	4	NUM
ejpam-6048	60	23	5	5	NUM
ejpam-6048	60	24	g	g	NOUN
ejpam-6048	60	25	a	a	DET
ejpam-6048	60	26	b	b	NOUN
ejpam-6048	60	27	c	c	NOUN
ejpam-6048	60	28	h	h	NOUN
ejpam-6048	60	29	4a	4a	NOUN
ejpam-6048	60	30	4b	4b	PROPN
ejpam-6048	60	31	4c	4c	PROPN
ejpam-6048	60	32	4	4	NUM
ejpam-6048	60	33	5a	5a	NUM
ejpam-6048	60	34	5b	5b	NUM
ejpam-6048	60	35	5c	5c	NUM
ejpam-6048	60	36	5	5	NUM
ejpam-6048	60	37	3a	3a	NUM
ejpam-6048	60	38	3b	3b	NUM
ejpam-6048	60	39	3c	3c	NUM
ejpam-6048	60	40	3	3	NUM
ejpam-6048	60	41	2a	2a	NUM
ejpam-6048	60	42	2b	2b	NUM
ejpam-6048	60	43	2c	2c	NUM
ejpam-6048	60	44	2	2	NUM
ejpam-6048	60	45	1a	1a	NOUN
ejpam-6048	60	46	1b	1b	NUM
ejpam-6048	60	47	1c	1c	NUM
ejpam-6048	60	48	1	1	NUM
ejpam-6048	60	49	g	g	NOUN
ejpam-6048	60	50	◦	◦	NOUN
ejpam-6048	60	51	h	h	NOUN
ejpam-6048	60	52	a	a	DET
ejpam-6048	60	53	a1	a1	NOUN
ejpam-6048	60	54	a2	a2	PROPN
ejpam-6048	60	55	a3	a3	NOUN
ejpam-6048	60	56	a4	a4	PROPN
ejpam-6048	60	57	a5	a5	PROPN
ejpam-6048	60	58	b	b	PROPN
ejpam-6048	60	59	b1	b1	PROPN
ejpam-6048	60	60	b2	b2	NOUN
ejpam-6048	60	61	b3	b3	PROPN
ejpam-6048	60	62	b4	b4	PROPN
ejpam-6048	60	63	b5	b5	PROPN
ejpam-6048	60	64	c	c	PROPN
ejpam-6048	60	65	c1	c1	PROPN
ejpam-6048	60	66	c2	c2	PROPN
ejpam-6048	60	67	c3	c3	PROPN
ejpam-6048	60	68	c4	c4	PROPN
ejpam-6048	60	69	c5	c5	PROPN
ejpam-6048	60	70	h	h	PROPN
ejpam-6048	60	71	◦	◦	PROPN
ejpam-6048	60	72	g	g	PROPN
ejpam-6048	60	73	figure	figure	NOUN
ejpam-6048	60	74	2	2	NUM
ejpam-6048	60	75	:	:	PUNCT
ejpam-6048	60	76	two	two	NUM
ejpam-6048	60	77	trees	tree	NOUN
ejpam-6048	60	78	and	and	CCONJ
ejpam-6048	60	79	their	their	PRON
ejpam-6048	60	80	two	two	NUM
ejpam-6048	60	81	coronas	corona	NOUN
ejpam-6048	60	82	definition	definition	NOUN
ejpam-6048	60	83	5	5	NUM
ejpam-6048	60	84	.	.	PUNCT
ejpam-6048	61	1	[	[	X
ejpam-6048	61	2	9	9	NUM
ejpam-6048	61	3	]	]	X
ejpam-6048	61	4	the	the	DET
ejpam-6048	61	5	open	open	ADJ
ejpam-6048	61	6	neighborhood	neighborhood	NOUN
ejpam-6048	61	7	of	of	ADP
ejpam-6048	61	8	a	a	DET
ejpam-6048	61	9	vertex	vertex	NOUN
ejpam-6048	61	10	x	x	NOUN
ejpam-6048	61	11	,	,	PUNCT
ejpam-6048	61	12	denoted	denote	VERB
ejpam-6048	61	13	byn(x	byn(x	PROPN
ejpam-6048	61	14	)	)	PUNCT
ejpam-6048	61	15	,	,	PUNCT
ejpam-6048	61	16	is	be	AUX
ejpam-6048	61	17	a	a	DET
ejpam-6048	61	18	set	set	NOUN
ejpam-6048	61	19	containing	contain	VERB
ejpam-6048	61	20	all	all	DET
ejpam-6048	61	21	vertices	vertex	NOUN
ejpam-6048	61	22	y	y	PRON
ejpam-6048	61	23	which	which	PRON
ejpam-6048	61	24	are	be	AUX
ejpam-6048	61	25	adjacent	adjacent	ADJ
ejpam-6048	61	26	to	to	ADP
ejpam-6048	61	27	x	x	PRON
ejpam-6048	61	28	,	,	PUNCT
ejpam-6048	61	29	that	that	ADV
ejpam-6048	61	30	is	is	ADV
ejpam-6048	61	31	,	,	PUNCT
ejpam-6048	61	32	n(x	n(x	X
ejpam-6048	61	33	)	)	PUNCT
ejpam-6048	61	34	=	=	SYM
ejpam-6048	61	35	{	{	PUNCT
ejpam-6048	61	36	y	y	PROPN
ejpam-6048	61	37	∈	∈	PROPN
ejpam-6048	61	38	v	v	NOUN
ejpam-6048	61	39	(	(	PUNCT
ejpam-6048	61	40	g	g	NOUN
ejpam-6048	61	41	)	)	PUNCT
ejpam-6048	61	42	:	:	PUNCT
ejpam-6048	61	43	xy	xy	PROPN
ejpam-6048	61	44	∈	∈	PROPN
ejpam-6048	61	45	e(g	e(g	PROPN
ejpam-6048	61	46	)	)	PUNCT
ejpam-6048	61	47	}	}	PUNCT
ejpam-6048	61	48	.	.	PUNCT
ejpam-6048	62	1	in	in	ADP
ejpam-6048	62	2	case	case	NOUN
ejpam-6048	62	3	n(x	n(x	PROPN
ejpam-6048	62	4	)	)	PUNCT
ejpam-6048	62	5	is	be	AUX
ejpam-6048	62	6	a	a	DET
ejpam-6048	62	7	singleton	singleton	NOUN
ejpam-6048	62	8	,	,	PUNCT
ejpam-6048	62	9	x	x	X
ejpam-6048	62	10	is	be	AUX
ejpam-6048	62	11	an	an	DET
ejpam-6048	62	12	end	end	NOUN
ejpam-6048	62	13	-	-	PUNCT
ejpam-6048	62	14	vertex	vertex	NOUN
ejpam-6048	62	15	.	.	PUNCT
ejpam-6048	63	1	the	the	DET
ejpam-6048	63	2	closed	closed	ADJ
ejpam-6048	63	3	neighborhood	neighborhood	NOUN
ejpam-6048	63	4	of	of	ADP
ejpam-6048	63	5	a	a	DET
ejpam-6048	63	6	vertex	vertex	NOUN
ejpam-6048	63	7	x	x	X
ejpam-6048	63	8	of	of	ADP
ejpam-6048	63	9	g	g	PROPN
ejpam-6048	63	10	is	be	AUX
ejpam-6048	63	11	the	the	DET
ejpam-6048	63	12	set	set	ADJ
ejpam-6048	63	13	n	n	NOUN
ejpam-6048	63	14	[	[	X
ejpam-6048	63	15	x	x	X
ejpam-6048	63	16	]	]	X
ejpam-6048	63	17	=	=	SYM
ejpam-6048	63	18	n(x	n(x	X
ejpam-6048	63	19	)	)	PUNCT
ejpam-6048	63	20	∪	∪	ADP
ejpam-6048	63	21	{	{	PUNCT
ejpam-6048	63	22	x	x	NOUN
ejpam-6048	63	23	}	}	PUNCT
ejpam-6048	63	24	.	.	PUNCT
ejpam-6048	64	1	definition	definition	NOUN
ejpam-6048	64	2	6	6	NUM
ejpam-6048	64	3	.	.	PUNCT
ejpam-6048	65	1	[	[	X
ejpam-6048	65	2	4	4	X
ejpam-6048	65	3	]	]	PUNCT
ejpam-6048	65	4	a	a	DET
ejpam-6048	65	5	set	set	NOUN
ejpam-6048	65	6	s	s	NOUN
ejpam-6048	65	7	of	of	ADP
ejpam-6048	65	8	vertices	vertex	NOUN
ejpam-6048	65	9	in	in	ADP
ejpam-6048	65	10	a	a	DET
ejpam-6048	65	11	graph	graph	NOUN
ejpam-6048	65	12	g	g	NOUN
ejpam-6048	65	13	is	be	AUX
ejpam-6048	65	14	a	a	DET
ejpam-6048	65	15	neighborhood	neighborhood	NOUN
ejpam-6048	65	16	set	set	VERB
ejpam-6048	65	17	if	if	SCONJ
ejpam-6048	65	18	g	g	NOUN
ejpam-6048	65	19	=	=	SYM
ejpam-6048	65	20	⋃	⋃	VERB
ejpam-6048	65	21	v∈s	v∈s	NOUN
ejpam-6048	65	22	⟨n	⟨n	NUM
ejpam-6048	65	23	[	[	X
ejpam-6048	65	24	v]⟩	v]⟩	X
ejpam-6048	66	1	where	where	SCONJ
ejpam-6048	66	2	⟨n	⟨n	NUM
ejpam-6048	67	1	[	[	X
ejpam-6048	67	2	v]⟩	v]⟩	NOUN
ejpam-6048	67	3	is	be	AUX
ejpam-6048	67	4	the	the	DET
ejpam-6048	67	5	subgraph	subgraph	NOUN
ejpam-6048	67	6	of	of	ADP
ejpam-6048	67	7	g	g	PROPN
ejpam-6048	67	8	induced	induce	VERB
ejpam-6048	67	9	by	by	ADP
ejpam-6048	67	10	v	v	NOUN
ejpam-6048	67	11	and	and	CCONJ
ejpam-6048	67	12	all	all	DET
ejpam-6048	67	13	the	the	DET
ejpam-6048	67	14	vertices	vertex	NOUN
ejpam-6048	67	15	adjacent	adjacent	ADJ
ejpam-6048	67	16	to	to	ADP
ejpam-6048	67	17	v.	v.	ADP
ejpam-6048	67	18	the	the	DET
ejpam-6048	67	19	neighborhood	neighborhood	NOUN
ejpam-6048	67	20	number	number	NOUN
ejpam-6048	67	21	of	of	ADP
ejpam-6048	67	22	g	g	PROPN
ejpam-6048	67	23	is	be	AUX
ejpam-6048	67	24	the	the	DET
ejpam-6048	67	25	minimum	minimum	ADJ
ejpam-6048	67	26	cardinality	cardinality	NOUN
ejpam-6048	67	27	of	of	ADP
ejpam-6048	67	28	neighborhood	neighborhood	NOUN
ejpam-6048	67	29	sets	set	NOUN
ejpam-6048	67	30	,	,	PUNCT
ejpam-6048	67	31	denoted	denote	VERB
ejpam-6048	67	32	by	by	ADP
ejpam-6048	67	33	ni(g	ni(g	NOUN
ejpam-6048	67	34	)	)	PUNCT
ejpam-6048	67	35	.	.	PUNCT
ejpam-6048	67	36	example	example	NOUN
ejpam-6048	68	1	3	3	X
ejpam-6048	68	2	.	.	X
ejpam-6048	68	3	consider	consider	VERB
ejpam-6048	68	4	the	the	DET
ejpam-6048	68	5	graph	graph	NOUN
ejpam-6048	68	6	h	h	NOUN
ejpam-6048	68	7	in	in	ADP
ejpam-6048	68	8	figure	figure	NOUN
ejpam-6048	68	9	3	3	NUM
ejpam-6048	68	10	.	.	PUNCT
ejpam-6048	68	11	v1	v1	PROPN
ejpam-6048	68	12	v2	v2	PROPN
ejpam-6048	68	13	v3	v3	PROPN
ejpam-6048	68	14	v4v5	v4v5	PROPN
ejpam-6048	68	15	h	h	NOUN
ejpam-6048	68	16	:	:	PUNCT
ejpam-6048	68	17	figure	figure	VERB
ejpam-6048	68	18	3	3	NUM
ejpam-6048	68	19	:	:	PUNCT
ejpam-6048	68	20	a	a	DET
ejpam-6048	68	21	graph	graph	NOUN
ejpam-6048	68	22	with	with	ADP
ejpam-6048	68	23	neighborhood	neighborhood	NOUN
ejpam-6048	68	24	number	number	NOUN
ejpam-6048	68	25	equals	equal	VERB
ejpam-6048	68	26	2	2	NUM
ejpam-6048	68	27	the	the	DET
ejpam-6048	68	28	neighborhood	neighborhood	NOUN
ejpam-6048	68	29	sets	set	VERB
ejpam-6048	68	30	ofh	ofh	PROPN
ejpam-6048	68	31	are	be	AUX
ejpam-6048	68	32	{	{	PUNCT
ejpam-6048	68	33	v2	v2	PROPN
ejpam-6048	68	34	,	,	PUNCT
ejpam-6048	68	35	v4	v4	PROPN
ejpam-6048	68	36	}	}	PUNCT
ejpam-6048	68	37	,	,	PUNCT
ejpam-6048	68	38	{	{	PUNCT
ejpam-6048	68	39	v1	v1	NOUN
ejpam-6048	68	40	,	,	PUNCT
ejpam-6048	68	41	v3	v3	PROPN
ejpam-6048	68	42	,	,	PUNCT
ejpam-6048	68	43	v5	v5	PROPN
ejpam-6048	68	44	}	}	PUNCT
ejpam-6048	68	45	,	,	PUNCT
ejpam-6048	68	46	{	{	PUNCT
ejpam-6048	68	47	v1	v1	NOUN
ejpam-6048	68	48	,	,	PUNCT
ejpam-6048	68	49	v2	v2	PROPN
ejpam-6048	68	50	,	,	PUNCT
ejpam-6048	68	51	v4	v4	PROPN
ejpam-6048	68	52	}	}	PUNCT
ejpam-6048	68	53	,	,	PUNCT
ejpam-6048	68	54	{	{	PUNCT
ejpam-6048	68	55	v1	v1	NOUN
ejpam-6048	68	56	,	,	PUNCT
ejpam-6048	68	57	v2	v2	PROPN
ejpam-6048	68	58	,	,	PUNCT
ejpam-6048	68	59	v3	v3	PROPN
ejpam-6048	68	60	,	,	PUNCT
ejpam-6048	68	61	v4	v4	PROPN
ejpam-6048	68	62	}	}	PUNCT
ejpam-6048	68	63	,	,	PUNCT
ejpam-6048	68	64	{	{	PUNCT
ejpam-6048	68	65	v1	v1	NOUN
ejpam-6048	68	66	,	,	PUNCT
ejpam-6048	68	67	v2	v2	PROPN
ejpam-6048	68	68	,	,	PUNCT
ejpam-6048	68	69	v3	v3	PROPN
ejpam-6048	68	70	,	,	PUNCT
ejpam-6048	68	71	v5	v5	PROPN
ejpam-6048	68	72	}	}	PUNCT
ejpam-6048	68	73	,	,	PUNCT
ejpam-6048	68	74	n.	n.	PROPN
ejpam-6048	68	75	abdulcarim	abdulcarim	PROPN
ejpam-6048	68	76	,	,	PUNCT
ejpam-6048	68	77	s.	s.	PROPN
ejpam-6048	68	78	dagondon	dagondon	PROPN
ejpam-6048	68	79	/	/	SYM
ejpam-6048	68	80	eur	eur	PROPN
ejpam-6048	68	81	.	.	PUNCT
ejpam-6048	69	1	j.	j.	PROPN
ejpam-6048	69	2	pure	pure	PROPN
ejpam-6048	69	3	appl	appl	PROPN
ejpam-6048	69	4	.	.	PROPN
ejpam-6048	69	5	math	math	PROPN
ejpam-6048	69	6	,	,	PUNCT
ejpam-6048	69	7	18	18	NUM
ejpam-6048	69	8	(	(	PUNCT
ejpam-6048	69	9	3	3	NUM
ejpam-6048	69	10	)	)	PUNCT
ejpam-6048	69	11	(	(	PUNCT
ejpam-6048	69	12	2025	2025	NUM
ejpam-6048	69	13	)	)	PUNCT
ejpam-6048	69	14	,	,	PUNCT
ejpam-6048	69	15	6048	6048	NUM
ejpam-6048	69	16	5	5	NUM
ejpam-6048	69	17	of	of	ADP
ejpam-6048	69	18	14	14	NUM
ejpam-6048	69	19	{	{	PUNCT
ejpam-6048	69	20	v1	v1	NOUN
ejpam-6048	69	21	,	,	PUNCT
ejpam-6048	69	22	v2	v2	PROPN
ejpam-6048	69	23	,	,	PUNCT
ejpam-6048	69	24	v4	v4	NOUN
ejpam-6048	69	25	,	,	PUNCT
ejpam-6048	69	26	v5	v5	PROPN
ejpam-6048	69	27	}	}	PUNCT
ejpam-6048	69	28	,	,	PUNCT
ejpam-6048	69	29	{	{	PUNCT
ejpam-6048	69	30	v1	v1	NOUN
ejpam-6048	69	31	,	,	PUNCT
ejpam-6048	69	32	v3	v3	PROPN
ejpam-6048	69	33	,	,	PUNCT
ejpam-6048	69	34	v4	v4	PROPN
ejpam-6048	69	35	,	,	PUNCT
ejpam-6048	69	36	v5	v5	PROPN
ejpam-6048	69	37	}	}	PUNCT
ejpam-6048	69	38	,	,	PUNCT
ejpam-6048	69	39	{	{	PUNCT
ejpam-6048	69	40	v2	v2	PROPN
ejpam-6048	69	41	,	,	PUNCT
ejpam-6048	69	42	v3	v3	PROPN
ejpam-6048	69	43	,	,	PUNCT
ejpam-6048	69	44	v4	v4	PROPN
ejpam-6048	69	45	,	,	PUNCT
ejpam-6048	69	46	v5	v5	PROPN
ejpam-6048	69	47	}	}	PUNCT
ejpam-6048	69	48	and	and	CCONJ
ejpam-6048	69	49	{	{	PUNCT
ejpam-6048	69	50	v1	v1	NOUN
ejpam-6048	69	51	,	,	PUNCT
ejpam-6048	69	52	v2	v2	PROPN
ejpam-6048	69	53	,	,	PUNCT
ejpam-6048	69	54	v3	v3	PROPN
ejpam-6048	69	55	,	,	PUNCT
ejpam-6048	69	56	v4	v4	PROPN
ejpam-6048	69	57	,	,	PUNCT
ejpam-6048	69	58	v5	v5	PROPN
ejpam-6048	69	59	}	}	PUNCT
ejpam-6048	69	60	.	.	PUNCT
ejpam-6048	70	1	here	here	ADV
ejpam-6048	70	2	,	,	PUNCT
ejpam-6048	70	3	ni(h	ni(h	PUNCT
ejpam-6048	70	4	)	)	PUNCT
ejpam-6048	70	5	=	=	SYM
ejpam-6048	70	6	2	2	X
ejpam-6048	70	7	.	.	X
ejpam-6048	70	8	definition	definition	NOUN
ejpam-6048	70	9	7	7	NUM
ejpam-6048	70	10	.	.	PUNCT
ejpam-6048	71	1	[	[	X
ejpam-6048	71	2	4	4	X
ejpam-6048	71	3	]	]	PUNCT
ejpam-6048	71	4	a	a	DET
ejpam-6048	71	5	set	set	NOUN
ejpam-6048	71	6	s	s	NOUN
ejpam-6048	71	7	⊆	⊆	NUM
ejpam-6048	71	8	v	v	NOUN
ejpam-6048	71	9	(	(	PUNCT
ejpam-6048	71	10	g	g	NOUN
ejpam-6048	71	11	)	)	PUNCT
ejpam-6048	71	12	is	be	AUX
ejpam-6048	71	13	an	an	DET
ejpam-6048	71	14	independent	independent	ADJ
ejpam-6048	71	15	neighborhood	neighborhood	NOUN
ejpam-6048	71	16	set	set	NOUN
ejpam-6048	71	17	of	of	ADP
ejpam-6048	71	18	g	g	NOUN
ejpam-6048	71	19	,	,	PUNCT
ejpam-6048	71	20	if	if	SCONJ
ejpam-6048	71	21	s	s	VERB
ejpam-6048	71	22	is	be	AUX
ejpam-6048	71	23	a	a	DET
ejpam-6048	71	24	neighborhood	neighborhood	NOUN
ejpam-6048	71	25	set	set	VERB
ejpam-6048	71	26	and	and	CCONJ
ejpam-6048	71	27	no	no	DET
ejpam-6048	71	28	two	two	NUM
ejpam-6048	71	29	vertices	vertex	NOUN
ejpam-6048	71	30	in	in	ADP
ejpam-6048	71	31	s	s	NOUN
ejpam-6048	71	32	are	be	AUX
ejpam-6048	71	33	adjacent	adjacent	ADJ
ejpam-6048	71	34	.	.	PUNCT
ejpam-6048	72	1	remark	remark	PROPN
ejpam-6048	72	2	2	2	NUM
ejpam-6048	72	3	.	.	PUNCT
ejpam-6048	72	4	not	not	PART
ejpam-6048	72	5	all	all	DET
ejpam-6048	72	6	graphs	graph	NOUN
ejpam-6048	72	7	have	have	VERB
ejpam-6048	72	8	independent	independent	ADJ
ejpam-6048	72	9	neighborhood	neighborhood	NOUN
ejpam-6048	72	10	set	set	NOUN
ejpam-6048	72	11	.	.	PUNCT
ejpam-6048	73	1	if	if	SCONJ
ejpam-6048	73	2	it	it	PRON
ejpam-6048	73	3	has	have	VERB
ejpam-6048	73	4	an	an	DET
ejpam-6048	73	5	independent	independent	ADJ
ejpam-6048	73	6	neighborhood	neighborhood	NOUN
ejpam-6048	73	7	set	set	NOUN
ejpam-6048	73	8	,	,	PUNCT
ejpam-6048	73	9	then	then	ADV
ejpam-6048	73	10	it	it	PRON
ejpam-6048	73	11	is	be	AUX
ejpam-6048	73	12	called	call	VERB
ejpam-6048	73	13	an	an	DET
ejpam-6048	73	14	independent	independent	ADJ
ejpam-6048	73	15	neighborhood	neighborhood	NOUN
ejpam-6048	73	16	graph	graph	NOUN
ejpam-6048	73	17	or	or	CCONJ
ejpam-6048	73	18	an	an	PRON
ejpam-6048	73	19	in	in	ADP
ejpam-6048	73	20	-graph	-graph	NOUN
ejpam-6048	73	21	.	.	PUNCT
ejpam-6048	74	1	1	1	NUM
ejpam-6048	74	2	5	5	NUM
ejpam-6048	74	3	4	4	NUM
ejpam-6048	74	4	3	3	NUM
ejpam-6048	74	5	2	2	NUM
ejpam-6048	74	6	figure	figure	NOUN
ejpam-6048	74	7	4	4	NUM
ejpam-6048	74	8	:	:	PUNCT
ejpam-6048	74	9	a	a	DET
ejpam-6048	74	10	graph	graph	NOUN
ejpam-6048	74	11	that	that	PRON
ejpam-6048	74	12	is	be	AUX
ejpam-6048	74	13	not	not	PART
ejpam-6048	74	14	an	an	DET
ejpam-6048	74	15	in	in	ADP
ejpam-6048	74	16	-graph	-graph	NOUN
ejpam-6048	74	17	definition	definition	NOUN
ejpam-6048	74	18	8	8	NUM
ejpam-6048	74	19	.	.	PUNCT
ejpam-6048	75	1	[	[	X
ejpam-6048	75	2	4	4	X
ejpam-6048	75	3	]	]	PUNCT
ejpam-6048	75	4	let	let	AUX
ejpam-6048	75	5	g	g	NOUN
ejpam-6048	75	6	=	=	SYM
ejpam-6048	75	7	(	(	PUNCT
ejpam-6048	75	8	v	v	NOUN
ejpam-6048	75	9	,	,	PUNCT
ejpam-6048	75	10	e	e	NOUN
ejpam-6048	75	11	)	)	PUNCT
ejpam-6048	75	12	be	be	AUX
ejpam-6048	75	13	a	a	DET
ejpam-6048	75	14	graph	graph	NOUN
ejpam-6048	75	15	with	with	ADP
ejpam-6048	75	16	m	m	PROPN
ejpam-6048	75	17	vertices	vertex	NOUN
ejpam-6048	75	18	.	.	PUNCT
ejpam-6048	76	1	then	then	ADV
ejpam-6048	76	2	the	the	DET
ejpam-6048	76	3	independent	independent	ADJ
ejpam-6048	76	4	neighborhood	neighborhood	NOUN
ejpam-6048	76	5	polynomial	polynomial	NOUN
ejpam-6048	76	6	of	of	ADP
ejpam-6048	76	7	g	g	NOUN
ejpam-6048	76	8	of	of	ADP
ejpam-6048	76	9	order	order	NOUN
ejpam-6048	76	10	m	m	NOUN
ejpam-6048	76	11	is	be	AUX
ejpam-6048	76	12	ni(g	ni(g	NOUN
ejpam-6048	76	13	,	,	PUNCT
ejpam-6048	76	14	x	x	X
ejpam-6048	76	15	)	)	PUNCT
ejpam-6048	76	16	=	=	PUNCT
ejpam-6048	76	17	m∑	m∑	PRON
ejpam-6048	76	18	j	j	X
ejpam-6048	76	19	=	=	NOUN
ejpam-6048	76	20	ηi(g	ηi(g	NOUN
ejpam-6048	76	21	)	)	PUNCT
ejpam-6048	76	22	ni(g	ni(g	PUNCT
ejpam-6048	76	23	,	,	PUNCT
ejpam-6048	76	24	j)xj	j)xj	NOUN
ejpam-6048	76	25	,	,	PUNCT
ejpam-6048	76	26	where	where	SCONJ
ejpam-6048	76	27	ni(g	ni(g	NUM
ejpam-6048	76	28	,	,	PUNCT
ejpam-6048	76	29	j	j	NOUN
ejpam-6048	76	30	)	)	PUNCT
ejpam-6048	76	31	is	be	AUX
ejpam-6048	76	32	the	the	DET
ejpam-6048	76	33	number	number	NOUN
ejpam-6048	76	34	of	of	ADP
ejpam-6048	76	35	independent	independent	ADJ
ejpam-6048	76	36	neighborhood	neighborhood	NOUN
ejpam-6048	76	37	sets	set	NOUN
ejpam-6048	76	38	of	of	ADP
ejpam-6048	76	39	g	g	NOUN
ejpam-6048	76	40	of	of	ADP
ejpam-6048	76	41	cardinality	cardinality	PROPN
ejpam-6048	76	42	j	j	PROPN
ejpam-6048	76	43	and	and	CCONJ
ejpam-6048	76	44	ηi(g	ηi(g	NOUN
ejpam-6048	76	45	)	)	PUNCT
ejpam-6048	76	46	is	be	AUX
ejpam-6048	76	47	the	the	DET
ejpam-6048	76	48	minimum	minimum	ADJ
ejpam-6048	76	49	cardinality	cardinality	NOUN
ejpam-6048	76	50	of	of	ADP
ejpam-6048	76	51	an	an	DET
ejpam-6048	76	52	independent	independent	ADJ
ejpam-6048	76	53	neighborhood	neighborhood	NOUN
ejpam-6048	76	54	set	set	NOUN
ejpam-6048	76	55	which	which	PRON
ejpam-6048	76	56	is	be	AUX
ejpam-6048	76	57	called	call	VERB
ejpam-6048	76	58	the	the	DET
ejpam-6048	76	59	independent	independent	ADJ
ejpam-6048	76	60	neighborhood	neighborhood	NOUN
ejpam-6048	76	61	number	number	NOUN
ejpam-6048	76	62	of	of	ADP
ejpam-6048	76	63	g.	g.	PROPN
ejpam-6048	76	64	example	example	PROPN
ejpam-6048	76	65	4	4	NUM
ejpam-6048	76	66	.	.	X
ejpam-6048	77	1	in	in	ADP
ejpam-6048	77	2	figure	figure	NOUN
ejpam-6048	77	3	3	3	NUM
ejpam-6048	77	4	,	,	PUNCT
ejpam-6048	77	5	the	the	DET
ejpam-6048	77	6	only	only	ADJ
ejpam-6048	77	7	independent	independent	ADJ
ejpam-6048	77	8	neighborhood	neighborhood	NOUN
ejpam-6048	77	9	sets	set	NOUN
ejpam-6048	77	10	of	of	ADP
ejpam-6048	77	11	h	h	NOUN
ejpam-6048	77	12	are	be	AUX
ejpam-6048	77	13	{	{	PUNCT
ejpam-6048	77	14	v2	v2	PROPN
ejpam-6048	77	15	,	,	PUNCT
ejpam-6048	77	16	v4	v4	NOUN
ejpam-6048	77	17	}	}	PUNCT
ejpam-6048	77	18	and	and	CCONJ
ejpam-6048	77	19	{	{	PUNCT
ejpam-6048	77	20	v1	v1	PROPN
ejpam-6048	77	21	,	,	PUNCT
ejpam-6048	77	22	v3	v3	PROPN
ejpam-6048	77	23	,	,	PUNCT
ejpam-6048	77	24	v5	v5	PROPN
ejpam-6048	77	25	}	}	PUNCT
ejpam-6048	77	26	.	.	PUNCT
ejpam-6048	78	1	therefore	therefore	ADV
ejpam-6048	78	2	,	,	PUNCT
ejpam-6048	78	3	the	the	DET
ejpam-6048	78	4	independent	independent	ADJ
ejpam-6048	78	5	neighborhood	neighborhood	NOUN
ejpam-6048	78	6	polynomial	polynomial	NOUN
ejpam-6048	78	7	of	of	ADP
ejpam-6048	78	8	h	h	NOUN
ejpam-6048	78	9	is	be	AUX
ejpam-6048	78	10	ni(h	ni(h	VERB
ejpam-6048	78	11	,	,	PUNCT
ejpam-6048	78	12	x	x	X
ejpam-6048	78	13	)	)	PUNCT
ejpam-6048	79	1	=	=	SYM
ejpam-6048	79	2	x2	x2	PROPN
ejpam-6048	80	1	+	+	CCONJ
ejpam-6048	80	2	x3	x3	ADJ
ejpam-6048	80	3	.	.	PUNCT
ejpam-6048	81	1	proposition	proposition	NOUN
ejpam-6048	81	2	1	1	NUM
ejpam-6048	81	3	.	.	PUNCT
ejpam-6048	82	1	[	[	X
ejpam-6048	82	2	4	4	X
ejpam-6048	82	3	]	]	PUNCT
ejpam-6048	82	4	let	let	VERB
ejpam-6048	82	5	g	g	NOUN
ejpam-6048	82	6	=	=	VERB
ejpam-6048	82	7	g1∪g2	g1∪g2	X
ejpam-6048	82	8	where	where	SCONJ
ejpam-6048	82	9	g1	g1	NOUN
ejpam-6048	82	10	,	,	PUNCT
ejpam-6048	82	11	g2	g2	PROPN
ejpam-6048	82	12	be	be	VERB
ejpam-6048	82	13	any	any	DET
ejpam-6048	82	14	two	two	NUM
ejpam-6048	82	15	in	in	ADP
ejpam-6048	82	16	-graphs	-graph	NOUN
ejpam-6048	82	17	.	.	PUNCT
ejpam-6048	83	1	then	then	ADV
ejpam-6048	83	2	ni(g	ni(g	NOUN
ejpam-6048	83	3	,	,	PUNCT
ejpam-6048	83	4	x	x	X
ejpam-6048	83	5	)	)	PUNCT
ejpam-6048	83	6	=	=	SYM
ejpam-6048	83	7	ni(g1	ni(g1	NUM
ejpam-6048	83	8	,	,	PUNCT
ejpam-6048	83	9	x)ni(g2	x)ni(g2	PROPN
ejpam-6048	83	10	,	,	PUNCT
ejpam-6048	83	11	x	x	X
ejpam-6048	83	12	)	)	PUNCT
ejpam-6048	83	13	.	.	PUNCT
ejpam-6048	84	1	proposition	proposition	NOUN
ejpam-6048	84	2	2	2	NUM
ejpam-6048	84	3	.	.	PUNCT
ejpam-6048	85	1	[	[	X
ejpam-6048	85	2	4	4	X
ejpam-6048	85	3	]	]	PUNCT
ejpam-6048	85	4	let	let	VERB
ejpam-6048	85	5	g	g	PRON
ejpam-6048	85	6	be	be	AUX
ejpam-6048	85	7	an	an	PRON
ejpam-6048	85	8	in	in	ADP
ejpam-6048	85	9	-graph	-graph	NOUN
ejpam-6048	85	10	with	with	ADP
ejpam-6048	85	11	n+1	n+1	PROPN
ejpam-6048	85	12	vertices	vertex	NOUN
ejpam-6048	85	13	.	.	PUNCT
ejpam-6048	86	1	then	then	ADV
ejpam-6048	86	2	ni(g	ni(g	NUM
ejpam-6048	86	3	,	,	PUNCT
ejpam-6048	86	4	x	x	X
ejpam-6048	86	5	)	)	PUNCT
ejpam-6048	86	6	=	=	SYM
ejpam-6048	86	7	x(1+xn−1	x(1+xn−1	PROPN
ejpam-6048	86	8	)	)	PUNCT
ejpam-6048	87	1	if	if	SCONJ
ejpam-6048	87	2	and	and	CCONJ
ejpam-6048	87	3	only	only	ADV
ejpam-6048	87	4	if	if	SCONJ
ejpam-6048	87	5	g	g	PROPN
ejpam-6048	87	6	∼=	∼=	PROPN
ejpam-6048	87	7	k1,n	k1,n	PROPN
ejpam-6048	87	8	.	.	PROPN
ejpam-6048	88	1	3	3	NUM
ejpam-6048	88	2	.	.	X
ejpam-6048	88	3	main	main	ADJ
ejpam-6048	88	4	results	result	NOUN
ejpam-6048	88	5	3.1	3.1	NUM
ejpam-6048	88	6	.	.	PUNCT
ejpam-6048	89	1	independent	independent	ADJ
ejpam-6048	89	2	neighborhood	neighborhood	NOUN
ejpam-6048	89	3	polynomial	polynomial	NOUN
ejpam-6048	89	4	of	of	ADP
ejpam-6048	89	5	the	the	DET
ejpam-6048	89	6	direct	direct	ADJ
ejpam-6048	89	7	product	product	NOUN
ejpam-6048	89	8	of	of	ADP
ejpam-6048	89	9	trees	tree	NOUN
ejpam-6048	89	10	theorem	theorem	VERB
ejpam-6048	89	11	2	2	NUM
ejpam-6048	89	12	.	.	X
ejpam-6048	89	13	for	for	ADP
ejpam-6048	89	14	any	any	DET
ejpam-6048	89	15	trees	tree	NOUN
ejpam-6048	89	16	g	g	NOUN
ejpam-6048	89	17	and	and	CCONJ
ejpam-6048	89	18	h	h	NOUN
ejpam-6048	89	19	,	,	PUNCT
ejpam-6048	89	20	the	the	DET
ejpam-6048	89	21	direct	direct	ADJ
ejpam-6048	89	22	product	product	NOUN
ejpam-6048	89	23	of	of	ADP
ejpam-6048	89	24	g	g	PROPN
ejpam-6048	89	25	and	and	CCONJ
ejpam-6048	89	26	h	h	NOUN
ejpam-6048	89	27	,	,	PUNCT
ejpam-6048	89	28	g·h	g·h	NOUN
ejpam-6048	89	29	,	,	PUNCT
ejpam-6048	89	30	is	be	AUX
ejpam-6048	89	31	disconnected	disconnect	VERB
ejpam-6048	89	32	n.	n.	PROPN
ejpam-6048	89	33	abdulcarim	abdulcarim	PROPN
ejpam-6048	89	34	,	,	PUNCT
ejpam-6048	89	35	s.	s.	PROPN
ejpam-6048	89	36	dagondon	dagondon	PROPN
ejpam-6048	89	37	/	/	SYM
ejpam-6048	89	38	eur	eur	PROPN
ejpam-6048	89	39	.	.	PUNCT
ejpam-6048	90	1	j.	j.	PROPN
ejpam-6048	90	2	pure	pure	PROPN
ejpam-6048	90	3	appl	appl	PROPN
ejpam-6048	90	4	.	.	PROPN
ejpam-6048	90	5	math	math	PROPN
ejpam-6048	90	6	,	,	PUNCT
ejpam-6048	90	7	18	18	NUM
ejpam-6048	90	8	(	(	PUNCT
ejpam-6048	90	9	3	3	NUM
ejpam-6048	90	10	)	)	PUNCT
ejpam-6048	90	11	(	(	PUNCT
ejpam-6048	90	12	2025	2025	NUM
ejpam-6048	90	13	)	)	PUNCT
ejpam-6048	90	14	,	,	PUNCT
ejpam-6048	90	15	6048	6048	NUM
ejpam-6048	90	16	6	6	NUM
ejpam-6048	90	17	of	of	ADP
ejpam-6048	90	18	14	14	NUM
ejpam-6048	90	19	proof	proof	NOUN
ejpam-6048	90	20	.	.	PUNCT
ejpam-6048	91	1	label	label	VERB
ejpam-6048	91	2	the	the	DET
ejpam-6048	91	3	vertices	vertex	NOUN
ejpam-6048	91	4	of	of	ADP
ejpam-6048	91	5	g	g	NOUN
ejpam-6048	91	6	by	by	ADP
ejpam-6048	91	7	xi	xi	X
ejpam-6048	91	8	and	and	CCONJ
ejpam-6048	91	9	of	of	ADP
ejpam-6048	91	10	h	h	NOUN
ejpam-6048	91	11	by	by	ADP
ejpam-6048	91	12	yj	yj	PROPN
ejpam-6048	91	13	.	.	PUNCT
ejpam-6048	92	1	since	since	SCONJ
ejpam-6048	92	2	g	g	PROPN
ejpam-6048	92	3	and	and	CCONJ
ejpam-6048	92	4	h	h	NOUN
ejpam-6048	92	5	are	be	AUX
ejpam-6048	92	6	trees	tree	NOUN
ejpam-6048	92	7	,	,	PUNCT
ejpam-6048	92	8	by	by	ADP
ejpam-6048	92	9	corollary	corollary	ADJ
ejpam-6048	92	10	1	1	NUM
ejpam-6048	92	11	,	,	PUNCT
ejpam-6048	92	12	g	g	PROPN
ejpam-6048	92	13	and	and	CCONJ
ejpam-6048	92	14	h	h	NOUN
ejpam-6048	92	15	have	have	VERB
ejpam-6048	92	16	independent	independent	ADJ
ejpam-6048	92	17	neighborhood	neighborhood	NOUN
ejpam-6048	92	18	sets	set	NOUN
ejpam-6048	92	19	say	say	VERB
ejpam-6048	92	20	ω1,∆1	ω1,∆1	NOUN
ejpam-6048	92	21	and	and	CCONJ
ejpam-6048	92	22	ω2,∆2	ω2,∆2	PROPN
ejpam-6048	92	23	,	,	PUNCT
ejpam-6048	92	24	respectively	respectively	ADV
ejpam-6048	92	25	.	.	PUNCT
ejpam-6048	93	1	we	we	PRON
ejpam-6048	93	2	now	now	ADV
ejpam-6048	93	3	show	show	VERB
ejpam-6048	93	4	that	that	SCONJ
ejpam-6048	93	5	g	g	PROPN
ejpam-6048	93	6	·	·	PROPN
ejpam-6048	93	7	h	h	NOUN
ejpam-6048	93	8	is	be	AUX
ejpam-6048	93	9	disconnected	disconnect	VERB
ejpam-6048	93	10	,	,	PUNCT
ejpam-6048	93	11	that	that	ADV
ejpam-6048	93	12	is	is	ADV
ejpam-6048	93	13	,	,	PUNCT
ejpam-6048	93	14	there	there	PRON
ejpam-6048	93	15	exist	exist	VERB
ejpam-6048	93	16	(	(	PUNCT
ejpam-6048	93	17	xi1	xi1	PROPN
ejpam-6048	93	18	,	,	PUNCT
ejpam-6048	93	19	yj1	yj1	NOUN
ejpam-6048	93	20	)	)	PUNCT
ejpam-6048	93	21	,	,	PUNCT
ejpam-6048	93	22	(	(	PUNCT
ejpam-6048	93	23	xi2	xi2	PROPN
ejpam-6048	93	24	,	,	PUNCT
ejpam-6048	93	25	yj2	yj2	PROPN
ejpam-6048	93	26	)	)	PUNCT
ejpam-6048	93	27	∈	∈	PROPN
ejpam-6048	93	28	v	v	NOUN
ejpam-6048	93	29	(	(	PUNCT
ejpam-6048	93	30	g	g	PROPN
ejpam-6048	93	31	·	·	SYM
ejpam-6048	93	32	h	h	X
ejpam-6048	93	33	)	)	PUNCT
ejpam-6048	93	34	such	such	ADJ
ejpam-6048	93	35	that	that	PRON
ejpam-6048	93	36	(	(	PUNCT
ejpam-6048	93	37	xi1	xi1	PROPN
ejpam-6048	93	38	,	,	PUNCT
ejpam-6048	93	39	yj1	yj1	NOUN
ejpam-6048	93	40	)	)	PUNCT
ejpam-6048	93	41	and	and	CCONJ
ejpam-6048	93	42	(	(	PUNCT
ejpam-6048	93	43	xi2	xi2	PROPN
ejpam-6048	93	44	,	,	PUNCT
ejpam-6048	93	45	yj2	yj2	PROPN
ejpam-6048	93	46	)	)	PUNCT
ejpam-6048	93	47	are	be	AUX
ejpam-6048	93	48	not	not	PART
ejpam-6048	93	49	connected	connect	VERB
ejpam-6048	93	50	by	by	ADP
ejpam-6048	93	51	any	any	DET
ejpam-6048	93	52	path	path	NOUN
ejpam-6048	93	53	.	.	PUNCT
ejpam-6048	94	1	consider	consider	VERB
ejpam-6048	94	2	(	(	PUNCT
ejpam-6048	94	3	x1	x1	PROPN
ejpam-6048	94	4	,	,	PUNCT
ejpam-6048	94	5	y1	y1	PROPN
ejpam-6048	94	6	)	)	PUNCT
ejpam-6048	94	7	,	,	PUNCT
ejpam-6048	94	8	(	(	PUNCT
ejpam-6048	94	9	x2	x2	PROPN
ejpam-6048	94	10	,	,	PUNCT
ejpam-6048	94	11	y2	y2	PROPN
ejpam-6048	94	12	)	)	PUNCT
ejpam-6048	95	1	∈	∈	PROPN
ejpam-6048	95	2	v	v	NOUN
ejpam-6048	95	3	(	(	PUNCT
ejpam-6048	95	4	g	g	PROPN
ejpam-6048	95	5	·	·	SYM
ejpam-6048	95	6	h	h	X
ejpam-6048	95	7	)	)	PUNCT
ejpam-6048	95	8	such	such	ADJ
ejpam-6048	95	9	that	that	PRON
ejpam-6048	95	10	x1x2	x1x2	PUNCT
ejpam-6048	95	11	/∈	/∈	PUNCT
ejpam-6048	95	12	e(g	e(g	PROPN
ejpam-6048	95	13	)	)	PUNCT
ejpam-6048	95	14	or	or	CCONJ
ejpam-6048	95	15	y1y2	y1y2	PROPN
ejpam-6048	95	16	/∈	/∈	PUNCT
ejpam-6048	95	17	e(h	e(h	PROPN
ejpam-6048	95	18	)	)	PUNCT
ejpam-6048	95	19	.	.	PUNCT
ejpam-6048	96	1	without	without	ADP
ejpam-6048	96	2	loss	loss	NOUN
ejpam-6048	96	3	of	of	ADP
ejpam-6048	96	4	generality	generality	NOUN
ejpam-6048	96	5	,	,	PUNCT
ejpam-6048	96	6	let	let	VERB
ejpam-6048	96	7	xi1	xi1	PROPN
ejpam-6048	96	8	,	,	PUNCT
ejpam-6048	96	9	xi2	xi2	PROPN
ejpam-6048	96	10	∈	∈	PROPN
ejpam-6048	96	11	ω1	ω1	PROPN
ejpam-6048	96	12	,	,	PUNCT
ejpam-6048	96	13	yj1	yj1	NOUN
ejpam-6048	96	14	∈	∈	PROPN
ejpam-6048	96	15	ω2	ω2	NOUN
ejpam-6048	96	16	and	and	CCONJ
ejpam-6048	96	17	yj2	yj2	PROPN
ejpam-6048	96	18	∈	∈	PROPN
ejpam-6048	96	19	∆2	∆2	PROPN
ejpam-6048	96	20	.	.	PUNCT
ejpam-6048	97	1	clearly	clearly	ADV
ejpam-6048	97	2	,	,	PUNCT
ejpam-6048	97	3	(	(	PUNCT
ejpam-6048	97	4	xi1	xi1	PROPN
ejpam-6048	97	5	,	,	PUNCT
ejpam-6048	97	6	yj1)(xi2	yj1)(xi2	PROPN
ejpam-6048	97	7	,	,	PUNCT
ejpam-6048	97	8	yj2	yj2	PROPN
ejpam-6048	97	9	)	)	PUNCT
ejpam-6048	97	10	/∈	/∈	PUNCT
ejpam-6048	98	1	e(g	e(g	NOUN
ejpam-6048	98	2	·	·	PUNCT
ejpam-6048	98	3	h	h	NOUN
ejpam-6048	98	4	)	)	PUNCT
ejpam-6048	98	5	since	since	SCONJ
ejpam-6048	98	6	xi1	xi1	PROPN
ejpam-6048	98	7	,	,	PUNCT
ejpam-6048	98	8	xi2	xi2	PROPN
ejpam-6048	98	9	∈	∈	PROPN
ejpam-6048	98	10	ω2	ω2	PROPN
ejpam-6048	98	11	which	which	PRON
ejpam-6048	98	12	means	mean	VERB
ejpam-6048	98	13	xi1	xi1	PROPN
ejpam-6048	98	14	and	and	CCONJ
ejpam-6048	98	15	xi2	xi2	PROPN
ejpam-6048	98	16	are	be	AUX
ejpam-6048	98	17	nonadjacents	nonadjacent	NOUN
ejpam-6048	98	18	.	.	PUNCT
ejpam-6048	99	1	observe	observe	VERB
ejpam-6048	99	2	that	that	SCONJ
ejpam-6048	99	3	for	for	ADP
ejpam-6048	99	4	any	any	DET
ejpam-6048	99	5	(	(	PUNCT
ejpam-6048	99	6	xi	xi	PROPN
ejpam-6048	99	7	,	,	PUNCT
ejpam-6048	99	8	yi)(xn	yi)(xn	PROPN
ejpam-6048	99	9	,	,	PUNCT
ejpam-6048	99	10	yn	yn	NOUN
ejpam-6048	99	11	)	)	PUNCT
ejpam-6048	99	12	path	path	NOUN
ejpam-6048	99	13	in	in	ADP
ejpam-6048	99	14	g	g	PROPN
ejpam-6048	99	15	·	·	SYM
ejpam-6048	99	16	h	h	NOUN
ejpam-6048	99	17	,	,	PUNCT
ejpam-6048	99	18	if	if	SCONJ
ejpam-6048	99	19	xi	xi	PROPN
ejpam-6048	99	20	∈	∈	PROPN
ejpam-6048	99	21	ω1	ω1	PROPN
ejpam-6048	99	22	,	,	PUNCT
ejpam-6048	99	23	yi	yi	PROPN
ejpam-6048	99	24	∈	∈	PROPN
ejpam-6048	99	25	ω2	ω2	PROPN
ejpam-6048	99	26	,	,	PUNCT
ejpam-6048	99	27	then	then	ADV
ejpam-6048	99	28	xi+1	xi+1	PROPN
ejpam-6048	99	29	∈	∈	PROPN
ejpam-6048	99	30	∆1	∆1	PROPN
ejpam-6048	99	31	,	,	PUNCT
ejpam-6048	99	32	yi+1	yi+1	PROPN
ejpam-6048	99	33	∈	∈	PROPN
ejpam-6048	99	34	∆2	∆2	PROPN
ejpam-6048	99	35	while	while	SCONJ
ejpam-6048	99	36	if	if	SCONJ
ejpam-6048	99	37	xi	xi	PROPN
ejpam-6048	99	38	∈	∈	PROPN
ejpam-6048	99	39	ω1	ω1	PROPN
ejpam-6048	99	40	and	and	CCONJ
ejpam-6048	99	41	yi	yi	PROPN
ejpam-6048	99	42	∈	∈	PROPN
ejpam-6048	99	43	∆2	∆2	PROPN
ejpam-6048	99	44	,	,	PUNCT
ejpam-6048	99	45	then	then	ADV
ejpam-6048	99	46	xi+1	xi+1	PROPN
ejpam-6048	99	47	∈	∈	PROPN
ejpam-6048	99	48	∆1	∆1	PUNCT
ejpam-6048	99	49	and	and	CCONJ
ejpam-6048	99	50	yi+1	yi+1	PROPN
ejpam-6048	99	51	∈	∈	PROPN
ejpam-6048	99	52	ω2	ω2	PROPN
ejpam-6048	99	53	.	.	PUNCT
ejpam-6048	100	1	now	now	ADV
ejpam-6048	100	2	,	,	PUNCT
ejpam-6048	100	3	since	since	SCONJ
ejpam-6048	100	4	xi1	xi1	PROPN
ejpam-6048	100	5	∈	∈	PROPN
ejpam-6048	100	6	ω1	ω1	PROPN
ejpam-6048	100	7	,	,	PUNCT
ejpam-6048	100	8	yj1	yj1	NOUN
ejpam-6048	100	9	∈	∈	PROPN
ejpam-6048	100	10	ω2	ω2	NOUN
ejpam-6048	100	11	and	and	CCONJ
ejpam-6048	100	12	yj2	yj2	PROPN
ejpam-6048	100	13	∈	∈	PROPN
ejpam-6048	100	14	∆2	∆2	PROPN
ejpam-6048	100	15	but	but	CCONJ
ejpam-6048	100	16	xi2	xi2	PROPN
ejpam-6048	100	17	∈	∈	PROPN
ejpam-6048	100	18	∆1	∆1	PROPN
ejpam-6048	100	19	,	,	PUNCT
ejpam-6048	100	20	it	it	PRON
ejpam-6048	100	21	follows	follow	VERB
ejpam-6048	100	22	that	that	SCONJ
ejpam-6048	100	23	there	there	PRON
ejpam-6048	100	24	is	be	VERB
ejpam-6048	100	25	no	no	DET
ejpam-6048	100	26	path	path	NOUN
ejpam-6048	100	27	connecting	connect	VERB
ejpam-6048	100	28	the	the	DET
ejpam-6048	100	29	vertices	vertex	NOUN
ejpam-6048	100	30	(	(	PUNCT
ejpam-6048	100	31	xi1	xi1	PROPN
ejpam-6048	100	32	,	,	PUNCT
ejpam-6048	100	33	yj1	yj1	NOUN
ejpam-6048	100	34	)	)	PUNCT
ejpam-6048	100	35	and	and	CCONJ
ejpam-6048	100	36	(	(	PUNCT
ejpam-6048	100	37	xi2	xi2	PROPN
ejpam-6048	100	38	,	,	PUNCT
ejpam-6048	100	39	yj2	yj2	PROPN
ejpam-6048	100	40	)	)	PUNCT
ejpam-6048	100	41	in	in	ADP
ejpam-6048	100	42	g	g	PROPN
ejpam-6048	100	43	·	·	PUNCT
ejpam-6048	100	44	h.	h.	PROPN
ejpam-6048	100	45	therefore	therefore	ADV
ejpam-6048	100	46	,	,	PUNCT
ejpam-6048	100	47	g	g	PROPN
ejpam-6048	100	48	·	·	SYM
ejpam-6048	100	49	h	h	NOUN
ejpam-6048	100	50	is	be	AUX
ejpam-6048	100	51	disconnected	disconnect	VERB
ejpam-6048	100	52	.	.	PUNCT
ejpam-6048	101	1	theorem	theorem	NOUN
ejpam-6048	101	2	3	3	NUM
ejpam-6048	101	3	.	.	X
ejpam-6048	101	4	for	for	ADP
ejpam-6048	101	5	any	any	DET
ejpam-6048	101	6	trees	tree	NOUN
ejpam-6048	101	7	g	g	NOUN
ejpam-6048	101	8	and	and	CCONJ
ejpam-6048	101	9	h	h	NOUN
ejpam-6048	101	10	,	,	PUNCT
ejpam-6048	101	11	the	the	DET
ejpam-6048	101	12	direct	direct	ADJ
ejpam-6048	101	13	product	product	NOUN
ejpam-6048	101	14	of	of	ADP
ejpam-6048	101	15	g	g	PROPN
ejpam-6048	101	16	and	and	CCONJ
ejpam-6048	101	17	h	h	NOUN
ejpam-6048	101	18	has	have	VERB
ejpam-6048	101	19	2	2	NUM
ejpam-6048	101	20	components	component	NOUN
ejpam-6048	101	21	,	,	PUNCT
ejpam-6048	101	22	say	say	VERB
ejpam-6048	101	23	a	a	PRON
ejpam-6048	101	24	and	and	CCONJ
ejpam-6048	101	25	b	b	NOUN
ejpam-6048	101	26	,	,	PUNCT
ejpam-6048	101	27	that	that	ADV
ejpam-6048	101	28	is	is	ADV
ejpam-6048	101	29	,	,	PUNCT
ejpam-6048	101	30	g	g	NOUN
ejpam-6048	101	31	·	·	SYM
ejpam-6048	101	32	h	h	NOUN
ejpam-6048	101	33	=	=	NOUN
ejpam-6048	101	34	a	a	PRON
ejpam-6048	101	35	∪b	∪b	NOUN
ejpam-6048	101	36	.	.	PUNCT
ejpam-6048	102	1	proof	proof	NOUN
ejpam-6048	102	2	.	.	PUNCT
ejpam-6048	103	1	let	let	VERB
ejpam-6048	103	2	g	g	NOUN
ejpam-6048	103	3	and	and	CCONJ
ejpam-6048	103	4	h	h	NOUN
ejpam-6048	103	5	be	be	VERB
ejpam-6048	103	6	any	any	DET
ejpam-6048	103	7	trees	tree	NOUN
ejpam-6048	103	8	with	with	ADP
ejpam-6048	103	9	independent	independent	ADJ
ejpam-6048	103	10	neighborhood	neighborhood	NOUN
ejpam-6048	103	11	sets	set	VERB
ejpam-6048	103	12	ω1,∆1	ω1,∆1	NUM
ejpam-6048	103	13	and	and	CCONJ
ejpam-6048	103	14	ω2,∆2	ω2,∆2	PROPN
ejpam-6048	103	15	,	,	PUNCT
ejpam-6048	103	16	respectively	respectively	ADV
ejpam-6048	103	17	.	.	PUNCT
ejpam-6048	104	1	assume	assume	VERB
ejpam-6048	104	2	that	that	SCONJ
ejpam-6048	104	3	g	g	PROPN
ejpam-6048	104	4	·	·	PUNCT
ejpam-6048	104	5	h	h	PROPN
ejpam-6048	104	6	has	have	VERB
ejpam-6048	104	7	more	more	ADJ
ejpam-6048	104	8	than	than	ADP
ejpam-6048	104	9	2	2	NUM
ejpam-6048	104	10	components	component	NOUN
ejpam-6048	104	11	,	,	PUNCT
ejpam-6048	104	12	say	say	VERB
ejpam-6048	104	13	ar	ar	PROPN
ejpam-6048	104	14	,	,	PUNCT
ejpam-6048	104	15	r	r	NOUN
ejpam-6048	104	16	∈	∈	PROPN
ejpam-6048	104	17	z+	z+	PUNCT
ejpam-6048	104	18	.	.	PUNCT
ejpam-6048	105	1	this	this	PRON
ejpam-6048	105	2	means	mean	VERB
ejpam-6048	105	3	that	that	SCONJ
ejpam-6048	105	4	for	for	ADP
ejpam-6048	105	5	every	every	DET
ejpam-6048	105	6	(	(	PUNCT
ejpam-6048	105	7	ur	ur	INTJ
ejpam-6048	105	8	,	,	PUNCT
ejpam-6048	105	9	vr	vr	PROPN
ejpam-6048	105	10	)	)	PUNCT
ejpam-6048	105	11	∈	∈	PROPN
ejpam-6048	105	12	ar	ar	PROPN
ejpam-6048	105	13	,	,	PUNCT
ejpam-6048	105	14	(	(	PUNCT
ejpam-6048	105	15	ur	ur	INTJ
ejpam-6048	105	16	,	,	PUNCT
ejpam-6048	105	17	vr	vr	NOUN
ejpam-6048	105	18	)	)	PUNCT
ejpam-6048	105	19	are	be	AUX
ejpam-6048	105	20	disconnected	disconnect	VERB
ejpam-6048	105	21	∀r	∀r	NOUN
ejpam-6048	105	22	.	.	PUNCT
ejpam-6048	106	1	we	we	PRON
ejpam-6048	106	2	note	note	VERB
ejpam-6048	106	3	that	that	SCONJ
ejpam-6048	106	4	for	for	ADP
ejpam-6048	106	5	any	any	DET
ejpam-6048	106	6	(	(	PUNCT
ejpam-6048	106	7	u	u	NOUN
ejpam-6048	106	8	,	,	PUNCT
ejpam-6048	106	9	v	v	NOUN
ejpam-6048	106	10	)	)	PUNCT
ejpam-6048	106	11	∈	∈	NOUN
ejpam-6048	106	12	v	v	NOUN
ejpam-6048	106	13	(	(	PUNCT
ejpam-6048	106	14	g	g	PROPN
ejpam-6048	106	15	·	·	SYM
ejpam-6048	106	16	h	h	NOUN
ejpam-6048	106	17	)	)	PUNCT
ejpam-6048	106	18	,	,	PUNCT
ejpam-6048	106	19	either	either	CCONJ
ejpam-6048	106	20	u	u	PROPN
ejpam-6048	106	21	∈	∈	PROPN
ejpam-6048	106	22	ω1	ω1	PROPN
ejpam-6048	106	23	or	or	CCONJ
ejpam-6048	106	24	u	u	NOUN
ejpam-6048	106	25	∈	∈	PROPN
ejpam-6048	106	26	∆1	∆1	PUNCT
ejpam-6048	106	27	and	and	CCONJ
ejpam-6048	106	28	v	v	ADP
ejpam-6048	106	29	∈	∈	PROPN
ejpam-6048	106	30	ω2	ω2	ADJ
ejpam-6048	106	31	or	or	CCONJ
ejpam-6048	106	32	v	v	ADP
ejpam-6048	106	33	∈	∈	PROPN
ejpam-6048	106	34	∆2	∆2	PROPN
ejpam-6048	106	35	.	.	PUNCT
ejpam-6048	107	1	furthermore	furthermore	ADV
ejpam-6048	107	2	,	,	PUNCT
ejpam-6048	107	3	for	for	ADP
ejpam-6048	107	4	any	any	DET
ejpam-6048	107	5	(	(	PUNCT
ejpam-6048	107	6	ui	ui	PROPN
ejpam-6048	107	7	,	,	PUNCT
ejpam-6048	107	8	vi)-(un	vi)-(un	PROPN
ejpam-6048	107	9	,	,	PUNCT
ejpam-6048	107	10	vn	vn	PROPN
ejpam-6048	107	11	)	)	PUNCT
ejpam-6048	107	12	path	path	NOUN
ejpam-6048	107	13	in	in	ADP
ejpam-6048	107	14	g	g	PROPN
ejpam-6048	107	15	·	·	PUNCT
ejpam-6048	107	16	h	h	NOUN
ejpam-6048	107	17	,	,	PUNCT
ejpam-6048	107	18	uiui+1	uiui+1	PROPN
ejpam-6048	107	19	∈	∈	PROPN
ejpam-6048	107	20	e(g	e(g	PROPN
ejpam-6048	107	21	)	)	PUNCT
ejpam-6048	107	22	and	and	CCONJ
ejpam-6048	107	23	vivi+1	vivi+1	DET
ejpam-6048	107	24	∈	∈	PROPN
ejpam-6048	107	25	e(h	e(h	PROPN
ejpam-6048	107	26	)	)	PUNCT
ejpam-6048	107	27	.	.	PUNCT
ejpam-6048	108	1	by	by	ADP
ejpam-6048	108	2	corollary	corollary	ADJ
ejpam-6048	108	3	2	2	NUM
ejpam-6048	108	4	,	,	PUNCT
ejpam-6048	108	5	if	if	SCONJ
ejpam-6048	108	6	uiui+1	uiui+1	PROPN
ejpam-6048	108	7	∈	∈	PROPN
ejpam-6048	108	8	e(g	e(g	PROPN
ejpam-6048	108	9	)	)	PUNCT
ejpam-6048	108	10	and	and	CCONJ
ejpam-6048	108	11	vivi+1	vivi+1	DET
ejpam-6048	108	12	∈	∈	PROPN
ejpam-6048	108	13	e(h	e(h	PROPN
ejpam-6048	108	14	)	)	PUNCT
ejpam-6048	108	15	,	,	PUNCT
ejpam-6048	108	16	then	then	ADV
ejpam-6048	108	17	u1	u1	PROPN
ejpam-6048	108	18	∈	∈	PROPN
ejpam-6048	108	19	ω1	ω1	PROPN
ejpam-6048	108	20	,	,	PUNCT
ejpam-6048	108	21	ui+1	ui+1	PROPN
ejpam-6048	108	22	∈	∈	NOUN
ejpam-6048	108	23	∆1	∆1	PUNCT
ejpam-6048	108	24	and	and	CCONJ
ejpam-6048	108	25	v1	v1	PROPN
ejpam-6048	108	26	∈	∈	PROPN
ejpam-6048	108	27	ω2	ω2	ADJ
ejpam-6048	108	28	,	,	PUNCT
ejpam-6048	108	29	vi+1	vi+1	NOUN
ejpam-6048	108	30	∈	∈	PROPN
ejpam-6048	108	31	∆2	∆2	PROPN
ejpam-6048	108	32	.	.	PUNCT
ejpam-6048	109	1	it	it	PRON
ejpam-6048	109	2	follows	follow	VERB
ejpam-6048	109	3	that	that	SCONJ
ejpam-6048	109	4	for	for	ADP
ejpam-6048	109	5	(	(	PUNCT
ejpam-6048	109	6	ui	ui	PROPN
ejpam-6048	109	7	,	,	PUNCT
ejpam-6048	109	8	vi)-(un	vi)-(un	PROPN
ejpam-6048	109	9	,	,	PUNCT
ejpam-6048	109	10	vn	vn	PROPN
ejpam-6048	109	11	)	)	PUNCT
ejpam-6048	109	12	path	path	NOUN
ejpam-6048	109	13	in	in	ADP
ejpam-6048	109	14	g	g	PROPN
ejpam-6048	109	15	·	·	PUNCT
ejpam-6048	110	1	h	h	NOUN
ejpam-6048	110	2	,	,	PUNCT
ejpam-6048	110	3	if	if	SCONJ
ejpam-6048	110	4	ui	ui	PROPN
ejpam-6048	110	5	∈	∈	PROPN
ejpam-6048	110	6	ω1	ω1	PROPN
ejpam-6048	110	7	,	,	PUNCT
ejpam-6048	110	8	vi	vi	NOUN
ejpam-6048	110	9	∈	∈	PROPN
ejpam-6048	110	10	ω2	ω2	NOUN
ejpam-6048	110	11	for	for	SCONJ
ejpam-6048	110	12	i	i	PRON
ejpam-6048	110	13	odd	odd	ADJ
ejpam-6048	110	14	,	,	PUNCT
ejpam-6048	110	15	then	then	ADV
ejpam-6048	110	16	uj	uj	PROPN
ejpam-6048	110	17	∈	∈	PROPN
ejpam-6048	110	18	∆1	∆1	PROPN
ejpam-6048	110	19	,	,	PUNCT
ejpam-6048	110	20	vj	vj	PROPN
ejpam-6048	110	21	∈	∈	PROPN
ejpam-6048	110	22	∆2	∆2	PROPN
ejpam-6048	110	23	for	for	ADP
ejpam-6048	110	24	j	j	PROPN
ejpam-6048	110	25	even	even	ADV
ejpam-6048	110	26	while	while	SCONJ
ejpam-6048	110	27	if	if	SCONJ
ejpam-6048	110	28	ui	ui	PROPN
ejpam-6048	110	29	∈	∈	PROPN
ejpam-6048	110	30	ω1	ω1	PROPN
ejpam-6048	110	31	,	,	PUNCT
ejpam-6048	110	32	vi	vi	PROPN
ejpam-6048	110	33	∈	∈	PROPN
ejpam-6048	110	34	∆2	∆2	PROPN
ejpam-6048	110	35	,	,	PUNCT
ejpam-6048	110	36	then	then	ADV
ejpam-6048	110	37	uj	uj	PROPN
ejpam-6048	110	38	∈	∈	PROPN
ejpam-6048	110	39	∆1	∆1	PROPN
ejpam-6048	110	40	,	,	PUNCT
ejpam-6048	110	41	vj	vj	PROPN
ejpam-6048	110	42	∈	∈	PROPN
ejpam-6048	110	43	ω2	ω2	PROPN
ejpam-6048	110	44	.	.	PUNCT
ejpam-6048	111	1	now	now	ADV
ejpam-6048	111	2	,	,	PUNCT
ejpam-6048	111	3	consider	consider	VERB
ejpam-6048	111	4	(	(	PUNCT
ejpam-6048	111	5	u1	u1	NOUN
ejpam-6048	111	6	,	,	PUNCT
ejpam-6048	111	7	v1	v1	PROPN
ejpam-6048	111	8	)	)	PUNCT
ejpam-6048	111	9	∈a1	∈a1	NOUN
ejpam-6048	112	1	such	such	ADJ
ejpam-6048	112	2	that	that	DET
ejpam-6048	112	3	u1	u1	PROPN
ejpam-6048	112	4	∈	∈	PROPN
ejpam-6048	112	5	ω1	ω1	PROPN
ejpam-6048	112	6	,	,	PUNCT
ejpam-6048	112	7	v1	v1	PROPN
ejpam-6048	112	8	∈	∈	PROPN
ejpam-6048	112	9	ω2	ω2	NOUN
ejpam-6048	112	10	,	,	PUNCT
ejpam-6048	112	11	(	(	PUNCT
ejpam-6048	112	12	u2	u2	NOUN
ejpam-6048	112	13	,	,	PUNCT
ejpam-6048	112	14	v2	v2	PROPN
ejpam-6048	112	15	)	)	PUNCT
ejpam-6048	112	16	∈a2	∈a2	NOUN
ejpam-6048	112	17	such	such	ADJ
ejpam-6048	112	18	that	that	SCONJ
ejpam-6048	112	19	u2	u2	PROPN
ejpam-6048	112	20	∈	∈	PROPN
ejpam-6048	112	21	ω1	ω1	PROPN
ejpam-6048	112	22	,	,	PUNCT
ejpam-6048	112	23	v2	v2	PROPN
ejpam-6048	112	24	∈	∈	PROPN
ejpam-6048	112	25	∆2	∆2	PROPN
ejpam-6048	112	26	,	,	PUNCT
ejpam-6048	112	27	(	(	PUNCT
ejpam-6048	112	28	u3	u3	PROPN
ejpam-6048	112	29	,	,	PUNCT
ejpam-6048	112	30	v3	v3	PROPN
ejpam-6048	112	31	)	)	PUNCT
ejpam-6048	112	32	∈a3	∈a3	NOUN
ejpam-6048	112	33	such	such	ADJ
ejpam-6048	112	34	that	that	SCONJ
ejpam-6048	112	35	u3	u3	PROPN
ejpam-6048	112	36	∈	∈	PROPN
ejpam-6048	112	37	∆1	∆1	PROPN
ejpam-6048	112	38	,	,	PUNCT
ejpam-6048	112	39	v3	v3	PROPN
ejpam-6048	112	40	∈	∈	PROPN
ejpam-6048	112	41	ω2	ω2	PROPN
ejpam-6048	112	42	,	,	PUNCT
ejpam-6048	112	43	(	(	PUNCT
ejpam-6048	112	44	u4	u4	PROPN
ejpam-6048	112	45	,	,	PUNCT
ejpam-6048	112	46	v4	v4	PROPN
ejpam-6048	112	47	)	)	PUNCT
ejpam-6048	112	48	∈a4	∈a4	NOUN
ejpam-6048	112	49	such	such	ADJ
ejpam-6048	112	50	that	that	SCONJ
ejpam-6048	112	51	u4	u4	PROPN
ejpam-6048	112	52	∈	∈	PROPN
ejpam-6048	112	53	∆1	∆1	PROPN
ejpam-6048	112	54	,	,	PUNCT
ejpam-6048	112	55	v4	v4	PROPN
ejpam-6048	112	56	∈	∈	PROPN
ejpam-6048	112	57	∆2	∆2	PROPN
ejpam-6048	112	58	.	.	PUNCT
ejpam-6048	113	1	we	we	PRON
ejpam-6048	113	2	can	can	AUX
ejpam-6048	113	3	easily	easily	ADV
ejpam-6048	113	4	see	see	VERB
ejpam-6048	113	5	that	that	SCONJ
ejpam-6048	113	6	(	(	PUNCT
ejpam-6048	113	7	u1	u1	NOUN
ejpam-6048	113	8	,	,	PUNCT
ejpam-6048	113	9	v1	v1	NOUN
ejpam-6048	113	10	)	)	PUNCT
ejpam-6048	113	11	and	and	CCONJ
ejpam-6048	113	12	(	(	PUNCT
ejpam-6048	113	13	u3	u3	PROPN
ejpam-6048	113	14	,	,	PUNCT
ejpam-6048	113	15	v3	v3	PROPN
ejpam-6048	113	16	)	)	PUNCT
ejpam-6048	113	17	are	be	AUX
ejpam-6048	113	18	disconnected	disconnect	VERB
ejpam-6048	113	19	,	,	PUNCT
ejpam-6048	113	20	so	so	ADV
ejpam-6048	113	21	are	be	AUX
ejpam-6048	113	22	(	(	PUNCT
ejpam-6048	113	23	u1	u1	NOUN
ejpam-6048	113	24	,	,	PUNCT
ejpam-6048	113	25	v1	v1	NOUN
ejpam-6048	113	26	)	)	PUNCT
ejpam-6048	113	27	and	and	CCONJ
ejpam-6048	113	28	(	(	PUNCT
ejpam-6048	113	29	u2	u2	PROPN
ejpam-6048	113	30	,	,	PUNCT
ejpam-6048	113	31	v2	v2	PROPN
ejpam-6048	113	32	)	)	PUNCT
ejpam-6048	113	33	,	,	PUNCT
ejpam-6048	113	34	(	(	PUNCT
ejpam-6048	113	35	u2	u2	NOUN
ejpam-6048	113	36	,	,	PUNCT
ejpam-6048	113	37	v2	v2	PROPN
ejpam-6048	113	38	)	)	PUNCT
ejpam-6048	113	39	and	and	CCONJ
ejpam-6048	113	40	(	(	PUNCT
ejpam-6048	113	41	u4	u4	PROPN
ejpam-6048	113	42	,	,	PUNCT
ejpam-6048	113	43	v4	v4	NOUN
ejpam-6048	113	44	)	)	PUNCT
ejpam-6048	113	45	,	,	PUNCT
ejpam-6048	113	46	and	and	CCONJ
ejpam-6048	113	47	(	(	PUNCT
ejpam-6048	113	48	u3	u3	PROPN
ejpam-6048	113	49	,	,	PUNCT
ejpam-6048	113	50	v3	v3	PROPN
ejpam-6048	113	51	)	)	PUNCT
ejpam-6048	113	52	and	and	CCONJ
ejpam-6048	113	53	(	(	PUNCT
ejpam-6048	113	54	u4	u4	PROPN
ejpam-6048	113	55	,	,	PUNCT
ejpam-6048	113	56	v4	v4	PROPN
ejpam-6048	113	57	)	)	PUNCT
ejpam-6048	113	58	.	.	PUNCT
ejpam-6048	114	1	but	but	CCONJ
ejpam-6048	114	2	observe	observe	VERB
ejpam-6048	114	3	that	that	SCONJ
ejpam-6048	114	4	(	(	PUNCT
ejpam-6048	114	5	u1	u1	NOUN
ejpam-6048	114	6	,	,	PUNCT
ejpam-6048	114	7	v1)-(u4	v1)-(u4	NUM
ejpam-6048	114	8	,	,	PUNCT
ejpam-6048	114	9	v4	v4	NOUN
ejpam-6048	114	10	)	)	PUNCT
ejpam-6048	114	11	is	be	AUX
ejpam-6048	114	12	a	a	DET
ejpam-6048	114	13	path	path	NOUN
ejpam-6048	114	14	in	in	ADP
ejpam-6048	114	15	g	g	PROPN
ejpam-6048	114	16	·	·	PROPN
ejpam-6048	114	17	h.	h.	PROPN
ejpam-6048	114	18	this	this	PRON
ejpam-6048	114	19	implies	imply	VERB
ejpam-6048	114	20	(	(	PUNCT
ejpam-6048	114	21	u1	u1	NOUN
ejpam-6048	114	22	,	,	PUNCT
ejpam-6048	114	23	v1	v1	NOUN
ejpam-6048	114	24	)	)	PUNCT
ejpam-6048	114	25	and	and	CCONJ
ejpam-6048	114	26	(	(	PUNCT
ejpam-6048	114	27	u4	u4	PROPN
ejpam-6048	114	28	,	,	PUNCT
ejpam-6048	114	29	v4	v4	PROPN
ejpam-6048	114	30	)	)	PUNCT
ejpam-6048	114	31	belong	belong	VERB
ejpam-6048	114	32	to	to	ADP
ejpam-6048	114	33	1	1	NUM
ejpam-6048	114	34	component	component	NOUN
ejpam-6048	114	35	.	.	PUNCT
ejpam-6048	115	1	similarly	similarly	ADV
ejpam-6048	115	2	,	,	PUNCT
ejpam-6048	115	3	(	(	PUNCT
ejpam-6048	115	4	u2	u2	NOUN
ejpam-6048	115	5	,	,	PUNCT
ejpam-6048	115	6	v2	v2	PROPN
ejpam-6048	115	7	)	)	PUNCT
ejpam-6048	115	8	and	and	CCONJ
ejpam-6048	115	9	(	(	PUNCT
ejpam-6048	115	10	u3	u3	PROPN
ejpam-6048	115	11	,	,	PUNCT
ejpam-6048	115	12	v3	v3	PROPN
ejpam-6048	115	13	)	)	PUNCT
ejpam-6048	115	14	belong	belong	VERB
ejpam-6048	115	15	to	to	ADP
ejpam-6048	115	16	1	1	NUM
ejpam-6048	115	17	component	component	NOUN
ejpam-6048	115	18	.	.	PUNCT
ejpam-6048	116	1	this	this	PRON
ejpam-6048	116	2	is	be	AUX
ejpam-6048	116	3	a	a	DET
ejpam-6048	116	4	contradiction	contradiction	NOUN
ejpam-6048	116	5	.	.	PUNCT
ejpam-6048	117	1	thus	thus	ADV
ejpam-6048	117	2	,	,	PUNCT
ejpam-6048	117	3	g	g	PROPN
ejpam-6048	117	4	·	·	PUNCT
ejpam-6048	117	5	h	h	NOUN
ejpam-6048	117	6	can	can	AUX
ejpam-6048	117	7	not	not	PART
ejpam-6048	117	8	have	have	VERB
ejpam-6048	117	9	more	more	ADJ
ejpam-6048	117	10	than	than	ADP
ejpam-6048	117	11	2	2	NUM
ejpam-6048	117	12	components	component	NOUN
ejpam-6048	117	13	.	.	PUNCT
ejpam-6048	118	1	therefore	therefore	ADV
ejpam-6048	118	2	,	,	PUNCT
ejpam-6048	118	3	g	g	PROPN
ejpam-6048	118	4	·	·	PROPN
ejpam-6048	118	5	h	h	PROPN
ejpam-6048	118	6	has	have	VERB
ejpam-6048	118	7	exactly	exactly	ADV
ejpam-6048	118	8	2	2	NUM
ejpam-6048	118	9	components	component	NOUN
ejpam-6048	118	10	.	.	PUNCT
ejpam-6048	119	1	theorem	theorem	ADJ
ejpam-6048	119	2	4	4	NUM
ejpam-6048	119	3	.	.	PUNCT
ejpam-6048	120	1	suppose	suppose	VERB
ejpam-6048	120	2	g	g	PROPN
ejpam-6048	120	3	has	have	VERB
ejpam-6048	120	4	independent	independent	ADJ
ejpam-6048	120	5	neighborhood	neighborhood	NOUN
ejpam-6048	120	6	sets	set	NOUN
ejpam-6048	120	7	ω1,∆1	ω1,∆1	NOUN
ejpam-6048	120	8	and	and	CCONJ
ejpam-6048	120	9	h	h	NOUN
ejpam-6048	120	10	has	have	VERB
ejpam-6048	120	11	independent	independent	ADJ
ejpam-6048	120	12	neighborhood	neighborhood	NOUN
ejpam-6048	120	13	sets	set	NOUN
ejpam-6048	120	14	ω2,∆2	ω2,∆2	PROPN
ejpam-6048	120	15	.	.	PUNCT
ejpam-6048	121	1	if	if	SCONJ
ejpam-6048	121	2	a	a	PRON
ejpam-6048	121	3	and	and	CCONJ
ejpam-6048	121	4	b	b	NOUN
ejpam-6048	121	5	are	be	AUX
ejpam-6048	121	6	the	the	DET
ejpam-6048	121	7	components	component	NOUN
ejpam-6048	121	8	of	of	ADP
ejpam-6048	121	9	g	g	PROPN
ejpam-6048	121	10	·	·	SYM
ejpam-6048	121	11	h	h	NOUN
ejpam-6048	121	12	,	,	PUNCT
ejpam-6048	121	13	then	then	ADV
ejpam-6048	121	14	v	v	X
ejpam-6048	121	15	(	(	PUNCT
ejpam-6048	121	16	a	a	X
ejpam-6048	121	17	)	)	PUNCT
ejpam-6048	121	18	=	=	SYM
ejpam-6048	121	19	{	{	PUNCT
ejpam-6048	121	20	(	(	PUNCT
ejpam-6048	121	21	x	x	NOUN
ejpam-6048	121	22	,	,	PUNCT
ejpam-6048	121	23	y	y	PROPN
ejpam-6048	121	24	)	)	PUNCT
ejpam-6048	121	25	:	:	PUNCT
ejpam-6048	121	26	x	x	X
ejpam-6048	121	27	∈	∈	PROPN
ejpam-6048	121	28	ω1	ω1	PROPN
ejpam-6048	121	29	,	,	PUNCT
ejpam-6048	121	30	y	y	PROPN
ejpam-6048	121	31	∈	∈	PROPN
ejpam-6048	121	32	ω2	ω2	PROPN
ejpam-6048	121	33	}	}	PUNCT
ejpam-6048	121	34	∪	∪	X
ejpam-6048	121	35	{	{	PUNCT
ejpam-6048	121	36	(	(	PUNCT
ejpam-6048	121	37	w	w	PROPN
ejpam-6048	121	38	,	,	PUNCT
ejpam-6048	121	39	z	z	NOUN
ejpam-6048	121	40	)	)	PUNCT
ejpam-6048	121	41	:	:	PUNCT
ejpam-6048	121	42	w	w	X
ejpam-6048	121	43	∈	∈	PROPN
ejpam-6048	121	44	∆1	∆1	PROPN
ejpam-6048	121	45	,	,	PUNCT
ejpam-6048	121	46	z	z	PROPN
ejpam-6048	121	47	∈	∈	PROPN
ejpam-6048	121	48	∆2	∆2	PROPN
ejpam-6048	121	49	}	}	PUNCT
ejpam-6048	121	50	and	and	CCONJ
ejpam-6048	121	51	v	v	NOUN
ejpam-6048	121	52	(	(	PUNCT
ejpam-6048	121	53	b	b	NOUN
ejpam-6048	121	54	)	)	PUNCT
ejpam-6048	121	55	=	=	SYM
ejpam-6048	121	56	{	{	PUNCT
ejpam-6048	121	57	(	(	PUNCT
ejpam-6048	121	58	x	x	NOUN
ejpam-6048	121	59	,	,	PUNCT
ejpam-6048	121	60	y	y	PROPN
ejpam-6048	121	61	)	)	PUNCT
ejpam-6048	121	62	:	:	PUNCT
ejpam-6048	121	63	x	x	X
ejpam-6048	121	64	∈	∈	PROPN
ejpam-6048	121	65	ω1	ω1	PROPN
ejpam-6048	121	66	,	,	PUNCT
ejpam-6048	121	67	y	y	PROPN
ejpam-6048	121	68	∈	∈	PROPN
ejpam-6048	121	69	∆2	∆2	PROPN
ejpam-6048	121	70	}	}	PUNCT
ejpam-6048	121	71	∪	∪	X
ejpam-6048	121	72	{	{	PUNCT
ejpam-6048	121	73	(	(	PUNCT
ejpam-6048	121	74	w	w	PROPN
ejpam-6048	121	75	,	,	PUNCT
ejpam-6048	121	76	z	z	NOUN
ejpam-6048	121	77	)	)	PUNCT
ejpam-6048	121	78	:	:	PUNCT
ejpam-6048	121	79	w	w	X
ejpam-6048	121	80	∈	∈	PROPN
ejpam-6048	121	81	∆1	∆1	PROPN
ejpam-6048	121	82	,	,	PUNCT
ejpam-6048	121	83	z	z	PROPN
ejpam-6048	121	84	∈	∈	PROPN
ejpam-6048	121	85	ω2	ω2	NUM
ejpam-6048	121	86	}	}	PUNCT
ejpam-6048	121	87	.	.	PUNCT
ejpam-6048	122	1	n.	n.	PROPN
ejpam-6048	122	2	abdulcarim	abdulcarim	PROPN
ejpam-6048	122	3	,	,	PUNCT
ejpam-6048	122	4	s.	s.	PROPN
ejpam-6048	122	5	dagondon	dagondon	PROPN
ejpam-6048	122	6	/	/	SYM
ejpam-6048	122	7	eur	eur	PROPN
ejpam-6048	122	8	.	.	PUNCT
ejpam-6048	123	1	j.	j.	PROPN
ejpam-6048	123	2	pure	pure	PROPN
ejpam-6048	123	3	appl	appl	PROPN
ejpam-6048	123	4	.	.	PROPN
ejpam-6048	123	5	math	math	PROPN
ejpam-6048	123	6	,	,	PUNCT
ejpam-6048	123	7	18	18	NUM
ejpam-6048	123	8	(	(	PUNCT
ejpam-6048	123	9	3	3	NUM
ejpam-6048	123	10	)	)	PUNCT
ejpam-6048	123	11	(	(	PUNCT
ejpam-6048	123	12	2025	2025	NUM
ejpam-6048	123	13	)	)	PUNCT
ejpam-6048	123	14	,	,	PUNCT
ejpam-6048	123	15	6048	6048	NUM
ejpam-6048	123	16	7	7	NUM
ejpam-6048	123	17	of	of	ADP
ejpam-6048	123	18	14	14	NUM
ejpam-6048	123	19	proof	proof	NOUN
ejpam-6048	123	20	.	.	PUNCT
ejpam-6048	124	1	the	the	DET
ejpam-6048	124	2	proof	proof	NOUN
ejpam-6048	124	3	is	be	AUX
ejpam-6048	124	4	similar	similar	ADJ
ejpam-6048	124	5	to	to	ADP
ejpam-6048	124	6	the	the	DET
ejpam-6048	124	7	proof	proof	NOUN
ejpam-6048	124	8	of	of	ADP
ejpam-6048	124	9	theorem	theorem	ADJ
ejpam-6048	124	10	3	3	NUM
ejpam-6048	124	11	.	.	PUNCT
ejpam-6048	124	12	corollary	corollary	ADJ
ejpam-6048	124	13	3	3	X
ejpam-6048	124	14	.	.	PUNCT
ejpam-6048	125	1	let	let	VERB
ejpam-6048	125	2	a	a	PRON
ejpam-6048	125	3	and	and	CCONJ
ejpam-6048	125	4	b	b	NOUN
ejpam-6048	125	5	be	be	AUX
ejpam-6048	125	6	the	the	DET
ejpam-6048	125	7	components	component	NOUN
ejpam-6048	125	8	of	of	ADP
ejpam-6048	125	9	g	g	PROPN
ejpam-6048	125	10	·	·	PROPN
ejpam-6048	125	11	h	h	NOUN
ejpam-6048	125	12	such	such	ADJ
ejpam-6048	125	13	that	that	PRON
ejpam-6048	125	14	v	v	NOUN
ejpam-6048	125	15	(	(	PUNCT
ejpam-6048	125	16	a	a	NOUN
ejpam-6048	125	17	)	)	PUNCT
ejpam-6048	125	18	=	=	SYM
ejpam-6048	125	19	{	{	PUNCT
ejpam-6048	125	20	(	(	PUNCT
ejpam-6048	125	21	x	x	NOUN
ejpam-6048	125	22	,	,	PUNCT
ejpam-6048	125	23	y	y	PROPN
ejpam-6048	125	24	)	)	PUNCT
ejpam-6048	125	25	:	:	PUNCT
ejpam-6048	125	26	x	x	X
ejpam-6048	125	27	∈	∈	PROPN
ejpam-6048	125	28	ω1	ω1	PROPN
ejpam-6048	125	29	,	,	PUNCT
ejpam-6048	125	30	y	y	PROPN
ejpam-6048	125	31	∈	∈	PROPN
ejpam-6048	125	32	ω2	ω2	PROPN
ejpam-6048	125	33	}	}	PUNCT
ejpam-6048	125	34	∪	∪	X
ejpam-6048	125	35	{	{	PUNCT
ejpam-6048	125	36	(	(	PUNCT
ejpam-6048	125	37	w	w	PROPN
ejpam-6048	125	38	,	,	PUNCT
ejpam-6048	125	39	z	z	NOUN
ejpam-6048	125	40	)	)	PUNCT
ejpam-6048	125	41	:	:	PUNCT
ejpam-6048	125	42	w	w	X
ejpam-6048	125	43	∈	∈	PROPN
ejpam-6048	125	44	∆1	∆1	PROPN
ejpam-6048	125	45	,	,	PUNCT
ejpam-6048	125	46	z	z	PROPN
ejpam-6048	125	47	∈	∈	PROPN
ejpam-6048	125	48	∆2	∆2	PROPN
ejpam-6048	125	49	}	}	PUNCT
ejpam-6048	125	50	and	and	CCONJ
ejpam-6048	125	51	v	v	NOUN
ejpam-6048	125	52	(	(	PUNCT
ejpam-6048	125	53	b	b	NOUN
ejpam-6048	125	54	)	)	PUNCT
ejpam-6048	125	55	=	=	SYM
ejpam-6048	125	56	{	{	PUNCT
ejpam-6048	125	57	(	(	PUNCT
ejpam-6048	125	58	x	x	NOUN
ejpam-6048	125	59	,	,	PUNCT
ejpam-6048	125	60	y	y	PROPN
ejpam-6048	125	61	)	)	PUNCT
ejpam-6048	125	62	:	:	PUNCT
ejpam-6048	125	63	x	x	X
ejpam-6048	125	64	∈	∈	PROPN
ejpam-6048	125	65	ω1	ω1	PROPN
ejpam-6048	125	66	,	,	PUNCT
ejpam-6048	125	67	y	y	PROPN
ejpam-6048	125	68	∈	∈	PROPN
ejpam-6048	125	69	∆2	∆2	PROPN
ejpam-6048	125	70	}	}	PUNCT
ejpam-6048	125	71	∪	∪	X
ejpam-6048	125	72	{	{	PUNCT
ejpam-6048	125	73	(	(	PUNCT
ejpam-6048	125	74	w	w	PROPN
ejpam-6048	125	75	,	,	PUNCT
ejpam-6048	125	76	z	z	NOUN
ejpam-6048	125	77	)	)	PUNCT
ejpam-6048	125	78	:	:	PUNCT
ejpam-6048	125	79	w	w	X
ejpam-6048	125	80	∈	∈	PROPN
ejpam-6048	125	81	∆1	∆1	PROPN
ejpam-6048	125	82	,	,	PUNCT
ejpam-6048	125	83	z	z	PROPN
ejpam-6048	125	84	∈	∈	PROPN
ejpam-6048	125	85	ω2	ω2	ADJ
ejpam-6048	125	86	}	}	PUNCT
ejpam-6048	125	87	.	.	PUNCT
ejpam-6048	126	1	then	then	ADV
ejpam-6048	126	2	the	the	DET
ejpam-6048	126	3	independent	independent	ADJ
ejpam-6048	126	4	neighborhood	neighborhood	NOUN
ejpam-6048	126	5	sets	set	NOUN
ejpam-6048	126	6	of	of	ADP
ejpam-6048	126	7	a	a	PRON
ejpam-6048	126	8	are	be	AUX
ejpam-6048	126	9	the	the	DET
ejpam-6048	126	10	sets	set	NOUN
ejpam-6048	126	11	{	{	PUNCT
ejpam-6048	126	12	(	(	PUNCT
ejpam-6048	126	13	x	x	NOUN
ejpam-6048	126	14	,	,	PUNCT
ejpam-6048	126	15	y	y	PROPN
ejpam-6048	126	16	)	)	PUNCT
ejpam-6048	126	17	:	:	PUNCT
ejpam-6048	127	1	x	x	X
ejpam-6048	127	2	∈	∈	PROPN
ejpam-6048	127	3	ω1	ω1	PROPN
ejpam-6048	127	4	,	,	PUNCT
ejpam-6048	127	5	y	y	PROPN
ejpam-6048	127	6	∈	∈	PROPN
ejpam-6048	127	7	ω2	ω2	PROPN
ejpam-6048	127	8	}	}	PUNCT
ejpam-6048	127	9	and	and	CCONJ
ejpam-6048	127	10	{	{	PUNCT
ejpam-6048	127	11	(	(	PUNCT
ejpam-6048	127	12	w	w	PROPN
ejpam-6048	127	13	,	,	PUNCT
ejpam-6048	127	14	z	z	NOUN
ejpam-6048	127	15	)	)	PUNCT
ejpam-6048	127	16	:	:	PUNCT
ejpam-6048	127	17	w	w	X
ejpam-6048	127	18	∈	∈	PROPN
ejpam-6048	127	19	∆1	∆1	PROPN
ejpam-6048	127	20	,	,	PUNCT
ejpam-6048	127	21	z	z	PROPN
ejpam-6048	127	22	∈	∈	PROPN
ejpam-6048	127	23	∆2	∆2	NOUN
ejpam-6048	127	24	}	}	PUNCT
ejpam-6048	127	25	while	while	SCONJ
ejpam-6048	127	26	the	the	DET
ejpam-6048	127	27	independent	independent	ADJ
ejpam-6048	127	28	neighborhood	neighborhood	NOUN
ejpam-6048	127	29	sets	set	NOUN
ejpam-6048	127	30	of	of	ADP
ejpam-6048	127	31	b	b	NOUN
ejpam-6048	127	32	are	be	AUX
ejpam-6048	127	33	the	the	DET
ejpam-6048	127	34	sets	set	NOUN
ejpam-6048	127	35	{	{	PUNCT
ejpam-6048	127	36	(	(	PUNCT
ejpam-6048	127	37	x	x	NOUN
ejpam-6048	127	38	,	,	PUNCT
ejpam-6048	127	39	y	y	PROPN
ejpam-6048	127	40	)	)	PUNCT
ejpam-6048	127	41	:	:	PUNCT
ejpam-6048	127	42	x	x	X
ejpam-6048	127	43	∈	∈	PROPN
ejpam-6048	127	44	ω1	ω1	PROPN
ejpam-6048	127	45	,	,	PUNCT
ejpam-6048	127	46	y	y	PROPN
ejpam-6048	127	47	∈	∈	PROPN
ejpam-6048	127	48	∆2	∆2	PROPN
ejpam-6048	127	49	}	}	PUNCT
ejpam-6048	127	50	and	and	CCONJ
ejpam-6048	127	51	{	{	PUNCT
ejpam-6048	127	52	(	(	PUNCT
ejpam-6048	127	53	w	w	PROPN
ejpam-6048	127	54	,	,	PUNCT
ejpam-6048	127	55	z	z	NOUN
ejpam-6048	127	56	)	)	PUNCT
ejpam-6048	127	57	:	:	PUNCT
ejpam-6048	127	58	w	w	X
ejpam-6048	127	59	∈	∈	PROPN
ejpam-6048	127	60	∆1	∆1	PROPN
ejpam-6048	127	61	,	,	PUNCT
ejpam-6048	127	62	z	z	PROPN
ejpam-6048	127	63	∈	∈	PROPN
ejpam-6048	127	64	ω2	ω2	PROPN
ejpam-6048	127	65	}	}	PUNCT
ejpam-6048	127	66	where	where	SCONJ
ejpam-6048	127	67	ω1,∆1	ω1,∆1	NOUN
ejpam-6048	127	68	are	be	AUX
ejpam-6048	127	69	the	the	DET
ejpam-6048	127	70	independent	independent	ADJ
ejpam-6048	127	71	neighborhood	neighborhood	NOUN
ejpam-6048	127	72	sets	set	NOUN
ejpam-6048	127	73	of	of	ADP
ejpam-6048	127	74	g	g	PROPN
ejpam-6048	127	75	and	and	CCONJ
ejpam-6048	127	76	ω2,∆2	ω2,∆2	PROPN
ejpam-6048	127	77	are	be	AUX
ejpam-6048	127	78	the	the	DET
ejpam-6048	127	79	independent	independent	ADJ
ejpam-6048	127	80	neighborhood	neighborhood	NOUN
ejpam-6048	127	81	sets	set	NOUN
ejpam-6048	127	82	of	of	ADP
ejpam-6048	127	83	h.	h.	NOUN
ejpam-6048	127	84	proof	proof	NOUN
ejpam-6048	127	85	.	.	PUNCT
ejpam-6048	128	1	let	let	VERB
ejpam-6048	128	2	a	a	PRON
ejpam-6048	128	3	and	and	CCONJ
ejpam-6048	128	4	b	b	NOUN
ejpam-6048	128	5	be	be	AUX
ejpam-6048	128	6	the	the	DET
ejpam-6048	128	7	components	component	NOUN
ejpam-6048	128	8	of	of	ADP
ejpam-6048	128	9	g	g	PROPN
ejpam-6048	128	10	·	·	SYM
ejpam-6048	128	11	h	h	NOUN
ejpam-6048	128	12	with	with	ADP
ejpam-6048	128	13	v	v	PROPN
ejpam-6048	128	14	(	(	PUNCT
ejpam-6048	128	15	a	a	NOUN
ejpam-6048	128	16	)	)	PUNCT
ejpam-6048	128	17	=	=	SYM
ejpam-6048	128	18	{	{	PUNCT
ejpam-6048	128	19	(	(	PUNCT
ejpam-6048	128	20	x	x	NOUN
ejpam-6048	128	21	,	,	PUNCT
ejpam-6048	128	22	y	y	PROPN
ejpam-6048	128	23	)	)	PUNCT
ejpam-6048	128	24	:	:	PUNCT
ejpam-6048	128	25	x	x	X
ejpam-6048	128	26	∈	∈	PROPN
ejpam-6048	128	27	ω1	ω1	PROPN
ejpam-6048	128	28	,	,	PUNCT
ejpam-6048	128	29	y	y	PROPN
ejpam-6048	128	30	∈	∈	PROPN
ejpam-6048	128	31	ω2	ω2	PROPN
ejpam-6048	128	32	}	}	PUNCT
ejpam-6048	128	33	∪	∪	X
ejpam-6048	128	34	{	{	PUNCT
ejpam-6048	128	35	(	(	PUNCT
ejpam-6048	128	36	w	w	PROPN
ejpam-6048	128	37	,	,	PUNCT
ejpam-6048	128	38	z	z	NOUN
ejpam-6048	128	39	)	)	PUNCT
ejpam-6048	128	40	:	:	PUNCT
ejpam-6048	128	41	w	w	X
ejpam-6048	128	42	∈	∈	PROPN
ejpam-6048	128	43	∆1	∆1	PROPN
ejpam-6048	128	44	,	,	PUNCT
ejpam-6048	128	45	z	z	PROPN
ejpam-6048	128	46	∈	∈	PROPN
ejpam-6048	128	47	∆2	∆2	PROPN
ejpam-6048	128	48	}	}	PUNCT
ejpam-6048	128	49	and	and	CCONJ
ejpam-6048	128	50	v	v	NOUN
ejpam-6048	128	51	(	(	PUNCT
ejpam-6048	128	52	b	b	NOUN
ejpam-6048	128	53	)	)	PUNCT
ejpam-6048	128	54	=	=	SYM
ejpam-6048	128	55	{	{	PUNCT
ejpam-6048	128	56	(	(	PUNCT
ejpam-6048	128	57	x	x	NOUN
ejpam-6048	128	58	,	,	PUNCT
ejpam-6048	128	59	y	y	PROPN
ejpam-6048	128	60	)	)	PUNCT
ejpam-6048	128	61	:	:	PUNCT
ejpam-6048	128	62	x	x	X
ejpam-6048	128	63	∈	∈	PROPN
ejpam-6048	128	64	ω1	ω1	PROPN
ejpam-6048	128	65	,	,	PUNCT
ejpam-6048	128	66	y	y	PROPN
ejpam-6048	128	67	∈	∈	PROPN
ejpam-6048	128	68	∆2	∆2	PROPN
ejpam-6048	128	69	}	}	PUNCT
ejpam-6048	128	70	∪	∪	X
ejpam-6048	128	71	{	{	PUNCT
ejpam-6048	128	72	(	(	PUNCT
ejpam-6048	128	73	w	w	PROPN
ejpam-6048	128	74	,	,	PUNCT
ejpam-6048	128	75	z	z	NOUN
ejpam-6048	128	76	)	)	PUNCT
ejpam-6048	128	77	:	:	PUNCT
ejpam-6048	128	78	w	w	X
ejpam-6048	128	79	∈	∈	PROPN
ejpam-6048	128	80	∆1	∆1	PROPN
ejpam-6048	128	81	,	,	PUNCT
ejpam-6048	128	82	z	z	PROPN
ejpam-6048	128	83	∈	∈	PROPN
ejpam-6048	128	84	ω2	ω2	NUM
ejpam-6048	128	85	}	}	PUNCT
ejpam-6048	128	86	.	.	PUNCT
ejpam-6048	129	1	suppose	suppose	VERB
ejpam-6048	129	2	a1	a1	NOUN
ejpam-6048	129	3	=	=	SYM
ejpam-6048	129	4	{	{	PUNCT
ejpam-6048	129	5	(	(	PUNCT
ejpam-6048	129	6	x	x	NOUN
ejpam-6048	129	7	,	,	PUNCT
ejpam-6048	129	8	y	y	PROPN
ejpam-6048	129	9	)	)	PUNCT
ejpam-6048	129	10	:	:	PUNCT
ejpam-6048	129	11	x	x	X
ejpam-6048	129	12	∈	∈	PROPN
ejpam-6048	129	13	ω1	ω1	PROPN
ejpam-6048	129	14	,	,	PUNCT
ejpam-6048	129	15	y	y	PROPN
ejpam-6048	129	16	∈	∈	PROPN
ejpam-6048	129	17	ω2	ω2	PROPN
ejpam-6048	129	18	}	}	PUNCT
ejpam-6048	129	19	,	,	PUNCT
ejpam-6048	129	20	a2	a2	PROPN
ejpam-6048	129	21	=	=	PRON
ejpam-6048	129	22	{	{	PUNCT
ejpam-6048	129	23	(	(	PUNCT
ejpam-6048	129	24	w	w	PROPN
ejpam-6048	129	25	,	,	PUNCT
ejpam-6048	129	26	z	z	NOUN
ejpam-6048	129	27	)	)	PUNCT
ejpam-6048	129	28	:	:	PUNCT
ejpam-6048	129	29	w	w	X
ejpam-6048	129	30	∈	∈	PROPN
ejpam-6048	129	31	∆1	∆1	PROPN
ejpam-6048	129	32	,	,	PUNCT
ejpam-6048	129	33	z	z	PROPN
ejpam-6048	129	34	∈	∈	PROPN
ejpam-6048	129	35	∆2	∆2	PROPN
ejpam-6048	129	36	}	}	PUNCT
ejpam-6048	129	37	,	,	PUNCT
ejpam-6048	129	38	b1	b1	NOUN
ejpam-6048	129	39	=	=	SYM
ejpam-6048	129	40	{	{	PUNCT
ejpam-6048	129	41	(	(	PUNCT
ejpam-6048	129	42	x	x	NOUN
ejpam-6048	129	43	,	,	PUNCT
ejpam-6048	129	44	y	y	PROPN
ejpam-6048	129	45	)	)	PUNCT
ejpam-6048	129	46	:	:	PUNCT
ejpam-6048	129	47	x	x	X
ejpam-6048	129	48	∈	∈	PROPN
ejpam-6048	129	49	ω1	ω1	PROPN
ejpam-6048	129	50	,	,	PUNCT
ejpam-6048	129	51	y	y	PROPN
ejpam-6048	129	52	∈	∈	PROPN
ejpam-6048	129	53	∆2	∆2	PROPN
ejpam-6048	129	54	}	}	PUNCT
ejpam-6048	129	55	and	and	CCONJ
ejpam-6048	129	56	b2	b2	NOUN
ejpam-6048	129	57	=	=	SYM
ejpam-6048	129	58	{	{	PUNCT
ejpam-6048	129	59	(	(	PUNCT
ejpam-6048	129	60	w	w	PROPN
ejpam-6048	129	61	,	,	PUNCT
ejpam-6048	129	62	z	z	NOUN
ejpam-6048	129	63	)	)	PUNCT
ejpam-6048	129	64	:	:	PUNCT
ejpam-6048	129	65	w	w	X
ejpam-6048	129	66	∈	∈	PROPN
ejpam-6048	129	67	∆1	∆1	PROPN
ejpam-6048	129	68	,	,	PUNCT
ejpam-6048	129	69	z	z	PROPN
ejpam-6048	129	70	∈	∈	PROPN
ejpam-6048	129	71	ω2	ω2	NUM
ejpam-6048	129	72	}	}	PUNCT
ejpam-6048	129	73	.	.	PUNCT
ejpam-6048	130	1	we	we	PRON
ejpam-6048	130	2	will	will	AUX
ejpam-6048	130	3	show	show	VERB
ejpam-6048	130	4	that	that	SCONJ
ejpam-6048	130	5	a1	a1	NOUN
ejpam-6048	130	6	,	,	PUNCT
ejpam-6048	130	7	a2	a2	PROPN
ejpam-6048	130	8	are	be	AUX
ejpam-6048	130	9	the	the	DET
ejpam-6048	130	10	independent	independent	ADJ
ejpam-6048	130	11	neighborhood	neighborhood	NOUN
ejpam-6048	130	12	sets	set	NOUN
ejpam-6048	130	13	of	of	ADP
ejpam-6048	130	14	a	a	PRON
ejpam-6048	130	15	and	and	CCONJ
ejpam-6048	130	16	b1	b1	NOUN
ejpam-6048	130	17	,	,	PUNCT
ejpam-6048	130	18	b2	b2	NOUN
ejpam-6048	130	19	are	be	AUX
ejpam-6048	130	20	the	the	DET
ejpam-6048	130	21	independent	independent	ADJ
ejpam-6048	130	22	neighborhood	neighborhood	NOUN
ejpam-6048	130	23	sets	set	NOUN
ejpam-6048	130	24	of	of	ADP
ejpam-6048	130	25	b.	b.	PROPN
ejpam-6048	130	26	consider	consider	VERB
ejpam-6048	130	27	a1	a1	NOUN
ejpam-6048	130	28	.	.	PUNCT
ejpam-6048	131	1	let	let	VERB
ejpam-6048	131	2	(	(	PUNCT
ejpam-6048	131	3	x1	x1	PROPN
ejpam-6048	131	4	,	,	PUNCT
ejpam-6048	131	5	y1	y1	PROPN
ejpam-6048	131	6	)	)	PUNCT
ejpam-6048	131	7	,	,	PUNCT
ejpam-6048	131	8	(	(	PUNCT
ejpam-6048	131	9	x2	x2	PROPN
ejpam-6048	131	10	,	,	PUNCT
ejpam-6048	131	11	y2	y2	PROPN
ejpam-6048	131	12	)	)	PUNCT
ejpam-6048	131	13	∈	∈	PROPN
ejpam-6048	131	14	v	v	NOUN
ejpam-6048	131	15	(	(	PUNCT
ejpam-6048	131	16	a1	a1	NOUN
ejpam-6048	131	17	)	)	PUNCT
ejpam-6048	131	18	.	.	PUNCT
ejpam-6048	132	1	since	since	SCONJ
ejpam-6048	132	2	x1	x1	PROPN
ejpam-6048	132	3	,	,	PUNCT
ejpam-6048	132	4	x2	x2	PROPN
ejpam-6048	132	5	∈	∈	PROPN
ejpam-6048	132	6	ω1	ω1	PROPN
ejpam-6048	132	7	,	,	PUNCT
ejpam-6048	132	8	y1	y1	NOUN
ejpam-6048	132	9	,	,	PUNCT
ejpam-6048	132	10	y2	y2	PROPN
ejpam-6048	132	11	∈	∈	PROPN
ejpam-6048	132	12	ω2	ω2	ADJ
ejpam-6048	132	13	where	where	SCONJ
ejpam-6048	132	14	ω1	ω1	PROPN
ejpam-6048	132	15	and	and	CCONJ
ejpam-6048	132	16	ω2	ω2	NOUN
ejpam-6048	132	17	are	be	AUX
ejpam-6048	132	18	the	the	DET
ejpam-6048	132	19	independent	independent	ADJ
ejpam-6048	132	20	neighborhood	neighborhood	NOUN
ejpam-6048	132	21	sets	set	NOUN
ejpam-6048	132	22	of	of	ADP
ejpam-6048	132	23	g	g	PROPN
ejpam-6048	132	24	and	and	CCONJ
ejpam-6048	132	25	h	h	NOUN
ejpam-6048	132	26	,	,	PUNCT
ejpam-6048	132	27	respectively	respectively	ADV
ejpam-6048	132	28	,	,	PUNCT
ejpam-6048	132	29	implies	imply	VERB
ejpam-6048	132	30	x1	x1	PROPN
ejpam-6048	132	31	,	,	PUNCT
ejpam-6048	132	32	x2	x2	PRON
ejpam-6048	132	33	are	be	AUX
ejpam-6048	132	34	nonadjacent	nonadjacent	ADJ
ejpam-6048	132	35	vertices	vertex	NOUN
ejpam-6048	132	36	,	,	PUNCT
ejpam-6048	132	37	so	so	ADV
ejpam-6048	132	38	are	be	AUX
ejpam-6048	132	39	y1	y1	ADJ
ejpam-6048	132	40	,	,	PUNCT
ejpam-6048	132	41	y2	y2	PROPN
ejpam-6048	132	42	.	.	PUNCT
ejpam-6048	133	1	thus	thus	ADV
ejpam-6048	133	2	,	,	PUNCT
ejpam-6048	133	3	(	(	PUNCT
ejpam-6048	133	4	x1	x1	ADJ
ejpam-6048	133	5	,	,	PUNCT
ejpam-6048	133	6	y1)(x2	y1)(x2	NOUN
ejpam-6048	133	7	,	,	PUNCT
ejpam-6048	133	8	y2	y2	PROPN
ejpam-6048	133	9	)	)	PUNCT
ejpam-6048	133	10	/∈	/∈	PUNCT
ejpam-6048	134	1	e(a	e(a	PROPN
ejpam-6048	134	2	)	)	PUNCT
ejpam-6048	134	3	.	.	PUNCT
ejpam-6048	135	1	this	this	PRON
ejpam-6048	135	2	means	mean	VERB
ejpam-6048	135	3	(	(	PUNCT
ejpam-6048	135	4	x1	x1	PROPN
ejpam-6048	135	5	,	,	PUNCT
ejpam-6048	135	6	y1	y1	PROPN
ejpam-6048	135	7	)	)	PUNCT
ejpam-6048	135	8	and	and	CCONJ
ejpam-6048	135	9	(	(	PUNCT
ejpam-6048	135	10	x2	x2	PROPN
ejpam-6048	135	11	,	,	PUNCT
ejpam-6048	135	12	y2	y2	PROPN
ejpam-6048	135	13	)	)	PUNCT
ejpam-6048	135	14	are	be	AUX
ejpam-6048	135	15	nonadjacent	nonadjacent	ADJ
ejpam-6048	135	16	vertices	vertex	NOUN
ejpam-6048	135	17	.	.	PUNCT
ejpam-6048	136	1	next	next	ADV
ejpam-6048	136	2	,	,	PUNCT
ejpam-6048	136	3	we	we	PRON
ejpam-6048	136	4	will	will	AUX
ejpam-6048	136	5	show	show	VERB
ejpam-6048	136	6	that	that	SCONJ
ejpam-6048	136	7	⋃	⋃	PROPN
ejpam-6048	136	8	(	(	PUNCT
ejpam-6048	136	9	x	x	NOUN
ejpam-6048	136	10	,	,	PUNCT
ejpam-6048	136	11	y)∈a1	y)∈a1	NUM
ejpam-6048	136	12	⟨n	⟨n	NUM
ejpam-6048	137	1	[	[	X
ejpam-6048	137	2	(	(	PUNCT
ejpam-6048	137	3	x	x	NOUN
ejpam-6048	137	4	,	,	PUNCT
ejpam-6048	137	5	y)]⟩	y)]⟩	PROPN
ejpam-6048	137	6	=	=	NOUN
ejpam-6048	137	7	a.	a.	NOUN
ejpam-6048	137	8	assume	assume	VERB
ejpam-6048	137	9	to	to	ADP
ejpam-6048	137	10	the	the	DET
ejpam-6048	137	11	contrary	contrary	ADJ
ejpam-6048	137	12	that⋃	that⋃	PROPN
ejpam-6048	137	13	(	(	PUNCT
ejpam-6048	137	14	x	x	X
ejpam-6048	137	15	,	,	PUNCT
ejpam-6048	137	16	y)∈a1	y)∈a1	NUM
ejpam-6048	137	17	⟨n	⟨n	NUM
ejpam-6048	138	1	[	[	X
ejpam-6048	138	2	(	(	PUNCT
ejpam-6048	138	3	x	x	NOUN
ejpam-6048	138	4	,	,	PUNCT
ejpam-6048	138	5	y)]⟩	y)]⟩	PROPN
ejpam-6048	138	6	=	=	NOUN
ejpam-6048	138	7	̸	̸	PART
ejpam-6048	138	8	a.	a.	NOUN
ejpam-6048	139	1	then	then	ADV
ejpam-6048	139	2	there	there	PRON
ejpam-6048	139	3	exists	exist	VERB
ejpam-6048	139	4	(	(	PUNCT
ejpam-6048	139	5	x3	x3	ADJ
ejpam-6048	139	6	,	,	PUNCT
ejpam-6048	139	7	y3)(x4	y3)(x4	PROPN
ejpam-6048	139	8	,	,	PUNCT
ejpam-6048	139	9	y4	y4	NUM
ejpam-6048	139	10	)	)	PUNCT
ejpam-6048	139	11	∈	∈	PROPN
ejpam-6048	139	12	e(a	e(a	PROPN
ejpam-6048	139	13	)	)	PUNCT
ejpam-6048	139	14	such	such	ADJ
ejpam-6048	139	15	that	that	SCONJ
ejpam-6048	139	16	(	(	PUNCT
ejpam-6048	139	17	x3	x3	ADJ
ejpam-6048	139	18	,	,	PUNCT
ejpam-6048	139	19	y3)(x4	y3)(x4	PROPN
ejpam-6048	139	20	,	,	PUNCT
ejpam-6048	139	21	y4	y4	PROPN
ejpam-6048	139	22	)	)	PUNCT
ejpam-6048	139	23	/∈⋃	/∈⋃	PUNCT
ejpam-6048	140	1	(	(	PUNCT
ejpam-6048	140	2	x	x	X
ejpam-6048	140	3	,	,	PUNCT
ejpam-6048	140	4	y)∈a1	y)∈a1	NUM
ejpam-6048	140	5	⟨n	⟨n	NUM
ejpam-6048	141	1	[	[	X
ejpam-6048	141	2	(	(	PUNCT
ejpam-6048	141	3	x	x	X
ejpam-6048	141	4	,	,	PUNCT
ejpam-6048	141	5	y)]⟩.	y)]⟩.	ADJ
ejpam-6048	141	6	it	it	PRON
ejpam-6048	141	7	follows	follow	VERB
ejpam-6048	141	8	that	that	SCONJ
ejpam-6048	141	9	both	both	PRON
ejpam-6048	141	10	(	(	PUNCT
ejpam-6048	141	11	x3	x3	ADJ
ejpam-6048	141	12	,	,	PUNCT
ejpam-6048	141	13	y3	y3	NOUN
ejpam-6048	141	14	)	)	PUNCT
ejpam-6048	141	15	,	,	PUNCT
ejpam-6048	141	16	(	(	PUNCT
ejpam-6048	141	17	x4	x4	PROPN
ejpam-6048	141	18	,	,	PUNCT
ejpam-6048	141	19	y4	y4	NUM
ejpam-6048	141	20	)	)	PUNCT
ejpam-6048	141	21	/∈	/∈	PUNCT
ejpam-6048	142	1	v	v	NOUN
ejpam-6048	142	2	(	(	PUNCT
ejpam-6048	142	3	a1	a1	NOUN
ejpam-6048	142	4	)	)	PUNCT
ejpam-6048	142	5	.	.	PUNCT
ejpam-6048	143	1	hence	hence	ADV
ejpam-6048	143	2	,	,	PUNCT
ejpam-6048	143	3	x3	x3	ADJ
ejpam-6048	143	4	,	,	PUNCT
ejpam-6048	143	5	x4	x4	PROPN
ejpam-6048	143	6	∈	∈	PROPN
ejpam-6048	143	7	∆1	∆1	PUNCT
ejpam-6048	143	8	and	and	CCONJ
ejpam-6048	143	9	y3	y3	PROPN
ejpam-6048	143	10	,	,	PUNCT
ejpam-6048	143	11	y4	y4	PROPN
ejpam-6048	143	12	∈	∈	PROPN
ejpam-6048	143	13	∆2	∆2	PROPN
ejpam-6048	143	14	.	.	PUNCT
ejpam-6048	144	1	since	since	SCONJ
ejpam-6048	144	2	both	both	DET
ejpam-6048	144	3	∆1	∆1	PROPN
ejpam-6048	144	4	and	and	CCONJ
ejpam-6048	144	5	∆2	∆2	PROPN
ejpam-6048	144	6	are	be	AUX
ejpam-6048	144	7	independent	independent	ADJ
ejpam-6048	144	8	neighborhood	neighborhood	NOUN
ejpam-6048	144	9	sets	set	NOUN
ejpam-6048	144	10	,	,	PUNCT
ejpam-6048	144	11	x3	x3	ADJ
ejpam-6048	144	12	and	and	CCONJ
ejpam-6048	144	13	x4	x4	PROPN
ejpam-6048	144	14	are	be	AUX
ejpam-6048	144	15	nonadjacents	nonadjacent	NOUN
ejpam-6048	144	16	,	,	PUNCT
ejpam-6048	144	17	so	so	ADV
ejpam-6048	144	18	are	be	AUX
ejpam-6048	144	19	y3	y3	NOUN
ejpam-6048	144	20	and	and	CCONJ
ejpam-6048	144	21	y4	y4	NOUN
ejpam-6048	144	22	.	.	PUNCT
ejpam-6048	145	1	thus	thus	ADV
ejpam-6048	145	2	,	,	PUNCT
ejpam-6048	145	3	x3x4	x3x4	PROPN
ejpam-6048	145	4	/∈	/∈	PUNCT
ejpam-6048	145	5	e(g	e(g	PROPN
ejpam-6048	145	6	)	)	PUNCT
ejpam-6048	145	7	and	and	CCONJ
ejpam-6048	145	8	y3y4	y3y4	PROPN
ejpam-6048	145	9	/∈	/∈	PUNCT
ejpam-6048	145	10	e(h	e(h	PROPN
ejpam-6048	145	11	)	)	PUNCT
ejpam-6048	145	12	.	.	PUNCT
ejpam-6048	146	1	it	it	PRON
ejpam-6048	146	2	follows	follow	VERB
ejpam-6048	146	3	that	that	SCONJ
ejpam-6048	146	4	(	(	PUNCT
ejpam-6048	146	5	x3	x3	ADJ
ejpam-6048	146	6	,	,	PUNCT
ejpam-6048	146	7	y3)(x4	y3)(x4	PROPN
ejpam-6048	146	8	,	,	PUNCT
ejpam-6048	146	9	y4	y4	PROPN
ejpam-6048	146	10	)	)	PUNCT
ejpam-6048	146	11	/∈	/∈	PUNCT
ejpam-6048	146	12	e(g·h	e(g·h	NOUN
ejpam-6048	146	13	)	)	PUNCT
ejpam-6048	146	14	which	which	PRON
ejpam-6048	146	15	is	be	AUX
ejpam-6048	146	16	a	a	DET
ejpam-6048	146	17	contradiction	contradiction	NOUN
ejpam-6048	146	18	.	.	PUNCT
ejpam-6048	147	1	hence	hence	ADV
ejpam-6048	147	2	,	,	PUNCT
ejpam-6048	147	3	⋃	⋃	PROPN
ejpam-6048	147	4	(	(	PUNCT
ejpam-6048	147	5	x	x	X
ejpam-6048	147	6	,	,	PUNCT
ejpam-6048	147	7	y)∈a1	y)∈a1	NUM
ejpam-6048	147	8	⟨n	⟨n	NUM
ejpam-6048	147	9	[	[	X
ejpam-6048	147	10	(	(	PUNCT
ejpam-6048	147	11	x	x	NOUN
ejpam-6048	147	12	,	,	PUNCT
ejpam-6048	147	13	y)]⟩	y)]⟩	PROPN
ejpam-6048	147	14	=	=	PUNCT
ejpam-6048	147	15	a.	a.	NOUN
ejpam-6048	147	16	therefore	therefore	ADV
ejpam-6048	147	17	,	,	PUNCT
ejpam-6048	147	18	a1	a1	NOUN
ejpam-6048	147	19	is	be	AUX
ejpam-6048	147	20	an	an	DET
ejpam-6048	147	21	independent	independent	ADJ
ejpam-6048	147	22	neighborhood	neighborhood	NOUN
ejpam-6048	147	23	set	set	NOUN
ejpam-6048	147	24	of	of	ADP
ejpam-6048	147	25	a.	a.	NOUN
ejpam-6048	147	26	similarly	similarly	ADV
ejpam-6048	147	27	,	,	PUNCT
ejpam-6048	147	28	we	we	PRON
ejpam-6048	147	29	can	can	AUX
ejpam-6048	147	30	show	show	VERB
ejpam-6048	147	31	that	that	SCONJ
ejpam-6048	147	32	a2	a2	PROPN
ejpam-6048	147	33	is	be	AUX
ejpam-6048	147	34	also	also	ADV
ejpam-6048	147	35	an	an	DET
ejpam-6048	147	36	independent	independent	ADJ
ejpam-6048	147	37	neighborhood	neighborhood	NOUN
ejpam-6048	147	38	set	set	NOUN
ejpam-6048	147	39	of	of	ADP
ejpam-6048	147	40	a.	a.	NOUN
ejpam-6048	147	41	following	follow	VERB
ejpam-6048	147	42	the	the	DET
ejpam-6048	147	43	same	same	ADJ
ejpam-6048	147	44	argument	argument	NOUN
ejpam-6048	147	45	for	for	ADP
ejpam-6048	147	46	b1	b1	NOUN
ejpam-6048	147	47	and	and	CCONJ
ejpam-6048	147	48	b2	b2	NOUN
ejpam-6048	147	49	,	,	PUNCT
ejpam-6048	147	50	we	we	PRON
ejpam-6048	147	51	have	have	VERB
ejpam-6048	147	52	b1	b1	NOUN
ejpam-6048	147	53	and	and	CCONJ
ejpam-6048	147	54	b2	b2	NOUN
ejpam-6048	147	55	are	be	AUX
ejpam-6048	147	56	the	the	DET
ejpam-6048	147	57	independent	independent	ADJ
ejpam-6048	147	58	neighborhood	neighborhood	NOUN
ejpam-6048	147	59	sets	set	NOUN
ejpam-6048	147	60	of	of	ADP
ejpam-6048	147	61	b.	b.	PROPN
ejpam-6048	147	62	corollary	corollary	NOUN
ejpam-6048	147	63	4	4	NUM
ejpam-6048	147	64	.	.	PUNCT
ejpam-6048	148	1	let	let	VERB
ejpam-6048	148	2	g	g	NOUN
ejpam-6048	148	3	and	and	CCONJ
ejpam-6048	148	4	h	h	NOUN
ejpam-6048	148	5	be	be	VERB
ejpam-6048	148	6	trees	tree	NOUN
ejpam-6048	148	7	with	with	ADP
ejpam-6048	148	8	independent	independent	ADJ
ejpam-6048	148	9	neighborhood	neighborhood	NOUN
ejpam-6048	148	10	sets	set	VERB
ejpam-6048	148	11	ω1,∆1	ω1,∆1	NUM
ejpam-6048	148	12	and	and	CCONJ
ejpam-6048	148	13	ω2,∆2	ω2,∆2	PROPN
ejpam-6048	148	14	,	,	PUNCT
ejpam-6048	148	15	respectively	respectively	ADV
ejpam-6048	148	16	.	.	PUNCT
ejpam-6048	149	1	then	then	ADV
ejpam-6048	149	2	ni(g	ni(g	NOUN
ejpam-6048	149	3	·	·	PUNCT
ejpam-6048	149	4	h	h	NOUN
ejpam-6048	149	5	,	,	PUNCT
ejpam-6048	149	6	x	x	NOUN
ejpam-6048	149	7	)	)	PUNCT
ejpam-6048	149	8	=	=	SYM
ejpam-6048	149	9	x|ω1||ω2|+|ω1||∆2|	x|ω1||ω2|+|ω1||∆2|	NOUN
ejpam-6048	149	10	+	+	CCONJ
ejpam-6048	149	11	x|ω1||ω2|+|∆1||ω2|	x|ω1||ω2|+|∆1||ω2|	X
ejpam-6048	150	1	+	+	CCONJ
ejpam-6048	150	2	x|∆1||∆2|+|ω1||∆2|	x|∆1||∆2|+|ω1||∆2|	PROPN
ejpam-6048	150	3	+	+	CCONJ
ejpam-6048	150	4	x|∆1||∆2|+|∆1||ω2|	x|∆1||∆2|+|∆1||ω2|	PROPN
ejpam-6048	150	5	.	.	PUNCT
ejpam-6048	151	1	n.	n.	PROPN
ejpam-6048	151	2	abdulcarim	abdulcarim	PROPN
ejpam-6048	151	3	,	,	PUNCT
ejpam-6048	151	4	s.	s.	PROPN
ejpam-6048	151	5	dagondon	dagondon	PROPN
ejpam-6048	151	6	/	/	SYM
ejpam-6048	151	7	eur	eur	PROPN
ejpam-6048	151	8	.	.	PUNCT
ejpam-6048	152	1	j.	j.	PROPN
ejpam-6048	152	2	pure	pure	PROPN
ejpam-6048	152	3	appl	appl	PROPN
ejpam-6048	152	4	.	.	PROPN
ejpam-6048	152	5	math	math	PROPN
ejpam-6048	152	6	,	,	PUNCT
ejpam-6048	152	7	18	18	NUM
ejpam-6048	152	8	(	(	PUNCT
ejpam-6048	152	9	3	3	NUM
ejpam-6048	152	10	)	)	PUNCT
ejpam-6048	152	11	(	(	PUNCT
ejpam-6048	152	12	2025	2025	NUM
ejpam-6048	152	13	)	)	PUNCT
ejpam-6048	152	14	,	,	PUNCT
ejpam-6048	152	15	6048	6048	NUM
ejpam-6048	152	16	8	8	NUM
ejpam-6048	152	17	of	of	ADP
ejpam-6048	152	18	14	14	NUM
ejpam-6048	152	19	proof	proof	NOUN
ejpam-6048	152	20	.	.	PUNCT
ejpam-6048	153	1	suppose	suppose	VERB
ejpam-6048	153	2	g	g	PROPN
ejpam-6048	153	3	and	and	CCONJ
ejpam-6048	153	4	h	h	NOUN
ejpam-6048	153	5	are	be	AUX
ejpam-6048	153	6	trees	tree	NOUN
ejpam-6048	153	7	with	with	ADP
ejpam-6048	153	8	independent	independent	ADJ
ejpam-6048	153	9	neighborhood	neighborhood	NOUN
ejpam-6048	153	10	sets	set	VERB
ejpam-6048	153	11	ω1,∆1	ω1,∆1	NUM
ejpam-6048	153	12	and	and	CCONJ
ejpam-6048	153	13	ω2,∆2	ω2,∆2	PROPN
ejpam-6048	153	14	,	,	PUNCT
ejpam-6048	153	15	respectively	respectively	ADV
ejpam-6048	153	16	.	.	PUNCT
ejpam-6048	154	1	by	by	ADP
ejpam-6048	154	2	theorems	theorem	NOUN
ejpam-6048	154	3	3	3	NUM
ejpam-6048	154	4	and	and	CCONJ
ejpam-6048	154	5	4	4	NUM
ejpam-6048	154	6	,	,	PUNCT
ejpam-6048	154	7	g	g	NOUN
ejpam-6048	154	8	·	·	SYM
ejpam-6048	154	9	h	h	NOUN
ejpam-6048	154	10	=	=	PUNCT
ejpam-6048	154	11	a	a	PRON
ejpam-6048	154	12	∪b	∪b	X
ejpam-6048	154	13	where	where	SCONJ
ejpam-6048	154	14	v	v	X
ejpam-6048	154	15	(	(	PUNCT
ejpam-6048	154	16	a	a	NOUN
ejpam-6048	154	17	)	)	PUNCT
ejpam-6048	154	18	=	=	SYM
ejpam-6048	154	19	{	{	PUNCT
ejpam-6048	154	20	(	(	PUNCT
ejpam-6048	154	21	x	x	NOUN
ejpam-6048	154	22	,	,	PUNCT
ejpam-6048	154	23	y	y	PROPN
ejpam-6048	154	24	)	)	PUNCT
ejpam-6048	154	25	:	:	PUNCT
ejpam-6048	154	26	x	x	X
ejpam-6048	154	27	∈	∈	PROPN
ejpam-6048	154	28	ω1	ω1	PROPN
ejpam-6048	154	29	,	,	PUNCT
ejpam-6048	154	30	y	y	PROPN
ejpam-6048	154	31	∈	∈	PROPN
ejpam-6048	154	32	ω2	ω2	PROPN
ejpam-6048	154	33	}	}	PUNCT
ejpam-6048	154	34	∪	∪	X
ejpam-6048	154	35	{	{	PUNCT
ejpam-6048	154	36	(	(	PUNCT
ejpam-6048	154	37	w	w	PROPN
ejpam-6048	154	38	,	,	PUNCT
ejpam-6048	154	39	z	z	NOUN
ejpam-6048	154	40	)	)	PUNCT
ejpam-6048	154	41	:	:	PUNCT
ejpam-6048	154	42	w	w	X
ejpam-6048	154	43	∈	∈	PROPN
ejpam-6048	154	44	∆1	∆1	PROPN
ejpam-6048	154	45	,	,	PUNCT
ejpam-6048	154	46	z	z	PROPN
ejpam-6048	154	47	∈	∈	PROPN
ejpam-6048	154	48	∆2	∆2	PROPN
ejpam-6048	154	49	}	}	PUNCT
ejpam-6048	154	50	and	and	CCONJ
ejpam-6048	154	51	v	v	NOUN
ejpam-6048	154	52	(	(	PUNCT
ejpam-6048	154	53	b	b	NOUN
ejpam-6048	154	54	)	)	PUNCT
ejpam-6048	154	55	=	=	SYM
ejpam-6048	154	56	{	{	PUNCT
ejpam-6048	154	57	(	(	PUNCT
ejpam-6048	154	58	x	x	NOUN
ejpam-6048	154	59	,	,	PUNCT
ejpam-6048	154	60	y	y	PROPN
ejpam-6048	154	61	)	)	PUNCT
ejpam-6048	154	62	:	:	PUNCT
ejpam-6048	154	63	x	x	X
ejpam-6048	154	64	∈	∈	PROPN
ejpam-6048	154	65	ω1	ω1	PROPN
ejpam-6048	154	66	,	,	PUNCT
ejpam-6048	154	67	y	y	PROPN
ejpam-6048	154	68	∈	∈	PROPN
ejpam-6048	154	69	∆2	∆2	PROPN
ejpam-6048	154	70	}	}	PUNCT
ejpam-6048	154	71	∪	∪	X
ejpam-6048	154	72	{	{	PUNCT
ejpam-6048	154	73	(	(	PUNCT
ejpam-6048	154	74	w	w	PROPN
ejpam-6048	154	75	,	,	PUNCT
ejpam-6048	154	76	z	z	NOUN
ejpam-6048	154	77	)	)	PUNCT
ejpam-6048	154	78	:	:	PUNCT
ejpam-6048	154	79	w	w	X
ejpam-6048	154	80	∈	∈	PROPN
ejpam-6048	154	81	∆1	∆1	PROPN
ejpam-6048	154	82	,	,	PUNCT
ejpam-6048	154	83	z	z	PROPN
ejpam-6048	154	84	∈	∈	PROPN
ejpam-6048	154	85	ω2	ω2	ADJ
ejpam-6048	154	86	}	}	PUNCT
ejpam-6048	154	87	.	.	PUNCT
ejpam-6048	155	1	by	by	ADP
ejpam-6048	155	2	corollary	corollary	ADJ
ejpam-6048	155	3	3	3	NUM
ejpam-6048	155	4	,	,	PUNCT
ejpam-6048	155	5	the	the	DET
ejpam-6048	155	6	sets	set	NOUN
ejpam-6048	155	7	{	{	PUNCT
ejpam-6048	155	8	(	(	PUNCT
ejpam-6048	155	9	x	x	NOUN
ejpam-6048	155	10	,	,	PUNCT
ejpam-6048	155	11	y	y	PROPN
ejpam-6048	155	12	)	)	PUNCT
ejpam-6048	155	13	:	:	PUNCT
ejpam-6048	155	14	x	x	X
ejpam-6048	155	15	∈	∈	PROPN
ejpam-6048	155	16	ω1	ω1	PROPN
ejpam-6048	155	17	,	,	PUNCT
ejpam-6048	155	18	y	y	PROPN
ejpam-6048	155	19	∈	∈	PROPN
ejpam-6048	155	20	ω2	ω2	PROPN
ejpam-6048	155	21	}	}	PUNCT
ejpam-6048	155	22	and	and	CCONJ
ejpam-6048	155	23	{	{	PUNCT
ejpam-6048	155	24	(	(	PUNCT
ejpam-6048	155	25	w	w	PROPN
ejpam-6048	155	26	,	,	PUNCT
ejpam-6048	155	27	z	z	NOUN
ejpam-6048	155	28	)	)	PUNCT
ejpam-6048	155	29	:	:	PUNCT
ejpam-6048	155	30	w	w	X
ejpam-6048	155	31	∈	∈	PROPN
ejpam-6048	155	32	∆1	∆1	PROPN
ejpam-6048	155	33	,	,	PUNCT
ejpam-6048	155	34	z	z	PROPN
ejpam-6048	155	35	∈	∈	PROPN
ejpam-6048	155	36	∆2	∆2	PROPN
ejpam-6048	155	37	}	}	PUNCT
ejpam-6048	155	38	are	be	AUX
ejpam-6048	155	39	the	the	DET
ejpam-6048	155	40	independent	independent	ADJ
ejpam-6048	155	41	neighborhood	neighborhood	NOUN
ejpam-6048	155	42	sets	set	NOUN
ejpam-6048	155	43	of	of	ADP
ejpam-6048	155	44	a	a	DET
ejpam-6048	155	45	while	while	NOUN
ejpam-6048	155	46	the	the	DET
ejpam-6048	155	47	sets	set	NOUN
ejpam-6048	155	48	{	{	PUNCT
ejpam-6048	155	49	(	(	PUNCT
ejpam-6048	155	50	x	x	NOUN
ejpam-6048	155	51	,	,	PUNCT
ejpam-6048	155	52	y	y	PROPN
ejpam-6048	155	53	)	)	PUNCT
ejpam-6048	155	54	:	:	PUNCT
ejpam-6048	155	55	x	x	X
ejpam-6048	155	56	∈	∈	PROPN
ejpam-6048	155	57	ω1	ω1	PROPN
ejpam-6048	155	58	,	,	PUNCT
ejpam-6048	155	59	y	y	PROPN
ejpam-6048	155	60	∈	∈	PROPN
ejpam-6048	155	61	∆2	∆2	PROPN
ejpam-6048	155	62	}	}	PUNCT
ejpam-6048	155	63	and	and	CCONJ
ejpam-6048	155	64	{	{	PUNCT
ejpam-6048	155	65	(	(	PUNCT
ejpam-6048	155	66	w	w	PROPN
ejpam-6048	155	67	,	,	PUNCT
ejpam-6048	155	68	z	z	NOUN
ejpam-6048	155	69	)	)	PUNCT
ejpam-6048	155	70	:	:	PUNCT
ejpam-6048	155	71	w	w	X
ejpam-6048	155	72	∈	∈	PROPN
ejpam-6048	155	73	∆1	∆1	PROPN
ejpam-6048	155	74	,	,	PUNCT
ejpam-6048	155	75	z	z	PROPN
ejpam-6048	155	76	∈	∈	PROPN
ejpam-6048	155	77	ω2	ω2	ADJ
ejpam-6048	155	78	}	}	PUNCT
ejpam-6048	155	79	are	be	AUX
ejpam-6048	155	80	the	the	DET
ejpam-6048	155	81	independent	independent	ADJ
ejpam-6048	155	82	neighborhood	neighborhood	NOUN
ejpam-6048	155	83	sets	set	NOUN
ejpam-6048	155	84	of	of	ADP
ejpam-6048	155	85	b.	b.	NOUN
ejpam-6048	155	86	we	we	PRON
ejpam-6048	155	87	note	note	VERB
ejpam-6048	155	88	that	that	SCONJ
ejpam-6048	155	89	|{(x	|{(x	NOUN
ejpam-6048	155	90	,	,	PUNCT
ejpam-6048	155	91	y	y	NOUN
ejpam-6048	155	92	)	)	PUNCT
ejpam-6048	155	93	:	:	PUNCT
ejpam-6048	155	94	x	x	X
ejpam-6048	155	95	∈	∈	PROPN
ejpam-6048	155	96	ω1	ω1	PROPN
ejpam-6048	155	97	,	,	PUNCT
ejpam-6048	155	98	y	y	PROPN
ejpam-6048	155	99	∈	∈	PROPN
ejpam-6048	155	100	ω2}|	ω2}|	PROPN
ejpam-6048	156	1	=	=	NUM
ejpam-6048	156	2	|ω1||ω2|	|ω1||ω2|	NOUN
ejpam-6048	156	3	|{(w	|{(w	ADJ
ejpam-6048	156	4	,	,	PUNCT
ejpam-6048	156	5	z	z	NOUN
ejpam-6048	156	6	)	)	PUNCT
ejpam-6048	156	7	:	:	PUNCT
ejpam-6048	156	8	w	w	X
ejpam-6048	156	9	∈	∈	PROPN
ejpam-6048	156	10	∆1	∆1	PROPN
ejpam-6048	156	11	,	,	PUNCT
ejpam-6048	156	12	z	z	NOUN
ejpam-6048	156	13	∈	∈	PROPN
ejpam-6048	156	14	∆2}|	∆2}|	VERB
ejpam-6048	156	15	=	=	NOUN
ejpam-6048	156	16	|∆1||∆2|	|∆1||∆2|	NOUN
ejpam-6048	156	17	|{(x	|{(x	NOUN
ejpam-6048	156	18	,	,	PUNCT
ejpam-6048	156	19	y	y	NOUN
ejpam-6048	156	20	)	)	PUNCT
ejpam-6048	156	21	:	:	PUNCT
ejpam-6048	157	1	x	x	X
ejpam-6048	157	2	∈	∈	PROPN
ejpam-6048	157	3	ω1	ω1	PROPN
ejpam-6048	157	4	,	,	PUNCT
ejpam-6048	157	5	y	y	PROPN
ejpam-6048	157	6	∈	∈	PROPN
ejpam-6048	157	7	∆2}|	∆2}|	VERB
ejpam-6048	157	8	=	=	PUNCT
ejpam-6048	157	9	|ω1||∆2|	|ω1||∆2|	ADP
ejpam-6048	157	10	|{(w	|{(w	ADJ
ejpam-6048	157	11	,	,	PUNCT
ejpam-6048	157	12	z	z	NOUN
ejpam-6048	157	13	)	)	PUNCT
ejpam-6048	157	14	:	:	PUNCT
ejpam-6048	157	15	w	w	X
ejpam-6048	157	16	∈	∈	PROPN
ejpam-6048	157	17	∆1	∆1	PROPN
ejpam-6048	157	18	,	,	PUNCT
ejpam-6048	157	19	z	z	PROPN
ejpam-6048	157	20	∈	∈	PROPN
ejpam-6048	157	21	ω2}|	ω2}|	PROPN
ejpam-6048	157	22	=	=	NOUN
ejpam-6048	157	23	|∆1||ω2|	|∆1||ω2|	NOUN
ejpam-6048	157	24	.	.	PUNCT
ejpam-6048	158	1	thus	thus	ADV
ejpam-6048	158	2	,	,	PUNCT
ejpam-6048	158	3	ni(a	ni(a	X
ejpam-6048	158	4	,	,	PUNCT
ejpam-6048	158	5	x	x	NOUN
ejpam-6048	158	6	)	)	PUNCT
ejpam-6048	158	7	=	=	PUNCT
ejpam-6048	158	8	x|ω1||ω2|	x|ω1||ω2|	PROPN
ejpam-6048	159	1	+	+	CCONJ
ejpam-6048	159	2	x|∆1||∆2|	x|∆1||∆2|	PROPN
ejpam-6048	159	3	and	and	CCONJ
ejpam-6048	159	4	ni(b	ni(b	NUM
ejpam-6048	159	5	,	,	PUNCT
ejpam-6048	159	6	x	x	X
ejpam-6048	159	7	)	)	PUNCT
ejpam-6048	159	8	=	=	SYM
ejpam-6048	159	9	x|ω1||∆2|	x|ω1||∆2|	PROPN
ejpam-6048	160	1	+	+	NUM
ejpam-6048	160	2	x|∆1||ω2|	x|∆1||ω2|	PROPN
ejpam-6048	160	3	.	.	PUNCT
ejpam-6048	161	1	since	since	SCONJ
ejpam-6048	161	2	g	g	PROPN
ejpam-6048	161	3	·	·	SYM
ejpam-6048	161	4	h	h	NOUN
ejpam-6048	161	5	=	=	NOUN
ejpam-6048	161	6	a	a	PRON
ejpam-6048	161	7	∪b	∪b	NOUN
ejpam-6048	161	8	,	,	PUNCT
ejpam-6048	161	9	by	by	ADP
ejpam-6048	161	10	proposition	proposition	NOUN
ejpam-6048	161	11	1	1	NUM
ejpam-6048	161	12	,	,	PUNCT
ejpam-6048	161	13	ni(g	ni(g	NUM
ejpam-6048	161	14	·	·	PUNCT
ejpam-6048	161	15	h	h	NOUN
ejpam-6048	161	16	,	,	PUNCT
ejpam-6048	161	17	x	x	NOUN
ejpam-6048	161	18	)	)	PUNCT
ejpam-6048	161	19	=	=	SYM
ejpam-6048	161	20	ni(a	ni(a	NOUN
ejpam-6048	161	21	,	,	PUNCT
ejpam-6048	161	22	x)ni(b	x)ni(b	PROPN
ejpam-6048	161	23	,	,	PUNCT
ejpam-6048	161	24	x	x	NOUN
ejpam-6048	161	25	)	)	PUNCT
ejpam-6048	161	26	.	.	PUNCT
ejpam-6048	162	1	therefore	therefore	ADV
ejpam-6048	162	2	,	,	PUNCT
ejpam-6048	162	3	ni(g	ni(g	ADP
ejpam-6048	162	4	·	·	PUNCT
ejpam-6048	162	5	h	h	NOUN
ejpam-6048	162	6	,	,	PUNCT
ejpam-6048	162	7	x	x	NOUN
ejpam-6048	162	8	)	)	PUNCT
ejpam-6048	162	9	=	=	SYM
ejpam-6048	162	10	(	(	PUNCT
ejpam-6048	162	11	x|ω1||ω2|	x|ω1||ω2|	NOUN
ejpam-6048	163	1	+	+	CCONJ
ejpam-6048	163	2	x|∆1||∆2|	x|∆1||∆2|	PROPN
ejpam-6048	163	3	)	)	PUNCT
ejpam-6048	163	4	(	(	PUNCT
ejpam-6048	163	5	x|ω1||∆2|	x|ω1||∆2|	PUNCT
ejpam-6048	164	1	+	+	CCONJ
ejpam-6048	164	2	x|∆1||ω2|	x|∆1||ω2|	PUNCT
ejpam-6048	164	3	)	)	PUNCT
ejpam-6048	165	1	=	=	NOUN
ejpam-6048	165	2	x|ω1||ω2|x|ω1||∆2|	x|ω1||ω2|x|ω1||∆2|	PRON
ejpam-6048	165	3	+	+	NUM
ejpam-6048	165	4	x|ω1||ω2|x|∆1||ω2|	x|ω1||ω2|x|∆1||ω2|	PUNCT
ejpam-6048	166	1	+	+	CCONJ
ejpam-6048	166	2	x|∆1||∆2|x|ω1||∆2|	x|∆1||∆2|x|ω1||∆2|	PUNCT
ejpam-6048	167	1	+	+	PUNCT
ejpam-6048	167	2	x|∆1||∆2|x|∆1||ω2|	x|∆1||∆2|x|∆1||ω2|	NOUN
ejpam-6048	168	1	=	=	SYM
ejpam-6048	168	2	x|ω1||ω2|+|ω1||∆2|	x|ω1||ω2|+|ω1||∆2|	X
ejpam-6048	168	3	+	+	X
ejpam-6048	168	4	x|ω1||ω2|+|∆1||ω2|	x|ω1||ω2|+|∆1||ω2|	X
ejpam-6048	169	1	+	+	CCONJ
ejpam-6048	169	2	x|∆1||∆2|+|ω1||∆2|	x|∆1||∆2|+|ω1||∆2|	PROPN
ejpam-6048	169	3	+	+	CCONJ
ejpam-6048	169	4	x|∆1||∆2|+|∆1||ω2|	x|∆1||∆2|+|∆1||ω2|	PROPN
ejpam-6048	169	5	.	.	PUNCT
ejpam-6048	169	6	example	example	NOUN
ejpam-6048	170	1	5	5	NUM
ejpam-6048	170	2	.	.	PUNCT
ejpam-6048	170	3	given	give	VERB
ejpam-6048	170	4	the	the	DET
ejpam-6048	170	5	graphs	graph	NOUN
ejpam-6048	170	6	g	g	NOUN
ejpam-6048	170	7	and	and	CCONJ
ejpam-6048	170	8	h	h	PROPN
ejpam-6048	170	9	and	and	CCONJ
ejpam-6048	170	10	their	their	PRON
ejpam-6048	170	11	corresponding	corresponding	ADJ
ejpam-6048	170	12	direct	direct	ADJ
ejpam-6048	170	13	product	product	NOUN
ejpam-6048	170	14	in	in	ADP
ejpam-6048	170	15	figure	figure	NOUN
ejpam-6048	170	16	5	5	NUM
ejpam-6048	170	17	.	.	PUNCT
ejpam-6048	171	1	we	we	PRON
ejpam-6048	171	2	note	note	VERB
ejpam-6048	171	3	that	that	SCONJ
ejpam-6048	171	4	the	the	DET
ejpam-6048	171	5	independent	independent	ADJ
ejpam-6048	171	6	neighborhood	neighborhood	NOUN
ejpam-6048	171	7	sets	set	NOUN
ejpam-6048	171	8	of	of	ADP
ejpam-6048	171	9	g	g	NOUN
ejpam-6048	171	10	are	be	AUX
ejpam-6048	171	11	ω1	ω1	PROPN
ejpam-6048	171	12	=	=	PUNCT
ejpam-6048	171	13	{	{	PUNCT
ejpam-6048	171	14	a	a	X
ejpam-6048	171	15	,	,	PUNCT
ejpam-6048	171	16	c	c	NOUN
ejpam-6048	171	17	,	,	PUNCT
ejpam-6048	171	18	d	d	NOUN
ejpam-6048	171	19	}	}	PUNCT
ejpam-6048	171	20	and	and	CCONJ
ejpam-6048	171	21	∆1	∆1	PUNCT
ejpam-6048	171	22	=	=	SYM
ejpam-6048	171	23	{	{	PUNCT
ejpam-6048	171	24	b	b	NOUN
ejpam-6048	171	25	,	,	PUNCT
ejpam-6048	171	26	e	e	NOUN
ejpam-6048	171	27	,	,	PUNCT
ejpam-6048	171	28	f	f	X
ejpam-6048	171	29	}	}	PUNCT
ejpam-6048	171	30	while	while	SCONJ
ejpam-6048	171	31	the	the	DET
ejpam-6048	171	32	independent	independent	ADJ
ejpam-6048	171	33	neighborhood	neighborhood	NOUN
ejpam-6048	171	34	sets	set	NOUN
ejpam-6048	171	35	of	of	ADP
ejpam-6048	171	36	h	h	NOUN
ejpam-6048	171	37	are	be	AUX
ejpam-6048	171	38	ω2	ω2	ADJ
ejpam-6048	171	39	=	=	SYM
ejpam-6048	171	40	{	{	PUNCT
ejpam-6048	171	41	1	1	NUM
ejpam-6048	171	42	,	,	PUNCT
ejpam-6048	171	43	3	3	NUM
ejpam-6048	171	44	,	,	PUNCT
ejpam-6048	171	45	4	4	NUM
ejpam-6048	171	46	}	}	PUNCT
ejpam-6048	171	47	and	and	CCONJ
ejpam-6048	171	48	∆2	∆2	PROPN
ejpam-6048	171	49	=	=	SYM
ejpam-6048	171	50	n.	n.	PROPN
ejpam-6048	171	51	abdulcarim	abdulcarim	PROPN
ejpam-6048	171	52	,	,	PUNCT
ejpam-6048	171	53	s.	s.	PROPN
ejpam-6048	171	54	dagondon	dagondon	PROPN
ejpam-6048	171	55	/	/	SYM
ejpam-6048	171	56	eur	eur	PROPN
ejpam-6048	171	57	.	.	PUNCT
ejpam-6048	172	1	j.	j.	PROPN
ejpam-6048	172	2	pure	pure	PROPN
ejpam-6048	172	3	appl	appl	PROPN
ejpam-6048	172	4	.	.	PROPN
ejpam-6048	172	5	math	math	PROPN
ejpam-6048	172	6	,	,	PUNCT
ejpam-6048	172	7	18	18	NUM
ejpam-6048	172	8	(	(	PUNCT
ejpam-6048	172	9	3	3	NUM
ejpam-6048	172	10	)	)	PUNCT
ejpam-6048	172	11	(	(	PUNCT
ejpam-6048	172	12	2025	2025	NUM
ejpam-6048	172	13	)	)	PUNCT
ejpam-6048	172	14	,	,	PUNCT
ejpam-6048	172	15	6048	6048	NUM
ejpam-6048	172	16	9	9	NUM
ejpam-6048	172	17	of	of	ADP
ejpam-6048	172	18	14	14	NUM
ejpam-6048	173	1	a	a	DET
ejpam-6048	173	2	b	b	NOUN
ejpam-6048	173	3	c	c	NOUN
ejpam-6048	173	4	d	d	PROPN
ejpam-6048	173	5	e	e	X
ejpam-6048	173	6	f	f	PROPN
ejpam-6048	173	7	g	g	NOUN
ejpam-6048	173	8	:	:	PUNCT
ejpam-6048	173	9	1	1	NUM
ejpam-6048	173	10	2	2	NUM
ejpam-6048	173	11	3	3	NUM
ejpam-6048	173	12	4	4	NUM
ejpam-6048	173	13	5	5	NUM
ejpam-6048	173	14	6	6	NUM
ejpam-6048	173	15	7	7	NUM
ejpam-6048	173	16	h	h	NOUN
ejpam-6048	173	17	:	:	PUNCT
ejpam-6048	173	18	(	(	PUNCT
ejpam-6048	173	19	a	a	DET
ejpam-6048	173	20	,	,	PUNCT
ejpam-6048	173	21	1	1	NUM
ejpam-6048	173	22	)	)	PUNCT
ejpam-6048	173	23	(	(	PUNCT
ejpam-6048	173	24	a	a	DET
ejpam-6048	173	25	,	,	PUNCT
ejpam-6048	173	26	3	3	NUM
ejpam-6048	173	27	)	)	PUNCT
ejpam-6048	173	28	(	(	PUNCT
ejpam-6048	173	29	a	a	DET
ejpam-6048	173	30	,	,	PUNCT
ejpam-6048	173	31	4	4	NUM
ejpam-6048	173	32	)	)	PUNCT
ejpam-6048	173	33	(	(	PUNCT
ejpam-6048	173	34	b	b	NOUN
ejpam-6048	173	35	,	,	PUNCT
ejpam-6048	173	36	2	2	NUM
ejpam-6048	173	37	)	)	PUNCT
ejpam-6048	173	38	(	(	PUNCT
ejpam-6048	173	39	b	b	NOUN
ejpam-6048	173	40	,	,	PUNCT
ejpam-6048	173	41	5	5	NUM
ejpam-6048	173	42	)	)	PUNCT
ejpam-6048	173	43	(	(	PUNCT
ejpam-6048	173	44	b	b	NOUN
ejpam-6048	173	45	,	,	PUNCT
ejpam-6048	173	46	6	6	NUM
ejpam-6048	173	47	)	)	PUNCT
ejpam-6048	173	48	(	(	PUNCT
ejpam-6048	173	49	b	b	NOUN
ejpam-6048	173	50	,	,	PUNCT
ejpam-6048	173	51	7	7	NUM
ejpam-6048	173	52	)	)	PUNCT
ejpam-6048	173	53	(	(	PUNCT
ejpam-6048	173	54	c	c	X
ejpam-6048	173	55	,	,	PUNCT
ejpam-6048	173	56	1	1	NUM
ejpam-6048	173	57	)	)	PUNCT
ejpam-6048	173	58	(	(	PUNCT
ejpam-6048	173	59	c	c	X
ejpam-6048	173	60	,	,	PUNCT
ejpam-6048	173	61	3	3	NUM
ejpam-6048	173	62	)	)	PUNCT
ejpam-6048	173	63	(	(	PUNCT
ejpam-6048	173	64	c	c	X
ejpam-6048	173	65	,	,	PUNCT
ejpam-6048	173	66	4	4	NUM
ejpam-6048	173	67	)	)	PUNCT
ejpam-6048	173	68	(	(	PUNCT
ejpam-6048	173	69	d	d	NOUN
ejpam-6048	173	70	,	,	PUNCT
ejpam-6048	173	71	1	1	NUM
ejpam-6048	173	72	)	)	PUNCT
ejpam-6048	173	73	(	(	PUNCT
ejpam-6048	173	74	d	d	NOUN
ejpam-6048	173	75	,	,	PUNCT
ejpam-6048	173	76	3	3	NUM
ejpam-6048	173	77	)	)	PUNCT
ejpam-6048	173	78	(	(	PUNCT
ejpam-6048	173	79	d	d	NOUN
ejpam-6048	173	80	,	,	PUNCT
ejpam-6048	173	81	4	4	NUM
ejpam-6048	173	82	)	)	PUNCT
ejpam-6048	173	83	(	(	PUNCT
ejpam-6048	173	84	e	e	NOUN
ejpam-6048	173	85	,	,	PUNCT
ejpam-6048	173	86	2	2	NUM
ejpam-6048	173	87	)	)	PUNCT
ejpam-6048	173	88	(	(	PUNCT
ejpam-6048	173	89	e	e	NOUN
ejpam-6048	173	90	,	,	PUNCT
ejpam-6048	173	91	5	5	NUM
ejpam-6048	173	92	)	)	PUNCT
ejpam-6048	173	93	(	(	PUNCT
ejpam-6048	173	94	e	e	NOUN
ejpam-6048	173	95	,	,	PUNCT
ejpam-6048	173	96	6	6	NUM
ejpam-6048	173	97	)	)	PUNCT
ejpam-6048	173	98	(	(	PUNCT
ejpam-6048	173	99	e	e	NOUN
ejpam-6048	173	100	,	,	PUNCT
ejpam-6048	173	101	7	7	NUM
ejpam-6048	173	102	)	)	PUNCT
ejpam-6048	173	103	(	(	PUNCT
ejpam-6048	173	104	f	f	X
ejpam-6048	173	105	,	,	PUNCT
ejpam-6048	173	106	2	2	NUM
ejpam-6048	173	107	)	)	PUNCT
ejpam-6048	173	108	(	(	PUNCT
ejpam-6048	173	109	f	f	X
ejpam-6048	173	110	,	,	PUNCT
ejpam-6048	173	111	5	5	NUM
ejpam-6048	173	112	)	)	PUNCT
ejpam-6048	173	113	(	(	PUNCT
ejpam-6048	173	114	f	f	X
ejpam-6048	173	115	,	,	PUNCT
ejpam-6048	173	116	6	6	NUM
ejpam-6048	173	117	)	)	PUNCT
ejpam-6048	173	118	(	(	PUNCT
ejpam-6048	173	119	f	f	X
ejpam-6048	173	120	,	,	PUNCT
ejpam-6048	173	121	7	7	X
ejpam-6048	173	122	)	)	PUNCT
ejpam-6048	173	123	a	a	PRON
ejpam-6048	173	124	:	:	PUNCT
ejpam-6048	173	125	(	(	PUNCT
ejpam-6048	173	126	a	a	DET
ejpam-6048	173	127	,	,	PUNCT
ejpam-6048	173	128	2	2	NUM
ejpam-6048	173	129	)	)	PUNCT
ejpam-6048	173	130	(	(	PUNCT
ejpam-6048	173	131	a	a	DET
ejpam-6048	173	132	,	,	PUNCT
ejpam-6048	173	133	5	5	NUM
ejpam-6048	173	134	)	)	PUNCT
ejpam-6048	173	135	(	(	PUNCT
ejpam-6048	173	136	a	a	DET
ejpam-6048	173	137	,	,	PUNCT
ejpam-6048	173	138	6	6	NUM
ejpam-6048	173	139	)	)	PUNCT
ejpam-6048	173	140	(	(	PUNCT
ejpam-6048	173	141	a	a	DET
ejpam-6048	173	142	,	,	PUNCT
ejpam-6048	173	143	7	7	NUM
ejpam-6048	173	144	)	)	PUNCT
ejpam-6048	173	145	(	(	PUNCT
ejpam-6048	173	146	b	b	NOUN
ejpam-6048	173	147	,	,	PUNCT
ejpam-6048	173	148	1	1	NUM
ejpam-6048	173	149	)	)	PUNCT
ejpam-6048	173	150	(	(	PUNCT
ejpam-6048	173	151	b	b	NOUN
ejpam-6048	173	152	,	,	PUNCT
ejpam-6048	173	153	3	3	NUM
ejpam-6048	173	154	)	)	PUNCT
ejpam-6048	173	155	(	(	PUNCT
ejpam-6048	173	156	b	b	NOUN
ejpam-6048	173	157	,	,	PUNCT
ejpam-6048	173	158	4	4	NUM
ejpam-6048	173	159	)	)	PUNCT
ejpam-6048	173	160	(	(	PUNCT
ejpam-6048	173	161	c	c	X
ejpam-6048	173	162	,	,	PUNCT
ejpam-6048	173	163	2	2	NUM
ejpam-6048	173	164	)	)	PUNCT
ejpam-6048	173	165	(	(	PUNCT
ejpam-6048	173	166	c	c	X
ejpam-6048	173	167	,	,	PUNCT
ejpam-6048	173	168	5	5	NUM
ejpam-6048	173	169	)	)	PUNCT
ejpam-6048	173	170	(	(	PUNCT
ejpam-6048	173	171	c	c	X
ejpam-6048	173	172	,	,	PUNCT
ejpam-6048	173	173	6	6	NUM
ejpam-6048	173	174	)	)	PUNCT
ejpam-6048	173	175	(	(	PUNCT
ejpam-6048	173	176	c	c	X
ejpam-6048	173	177	,	,	PUNCT
ejpam-6048	173	178	7	7	NUM
ejpam-6048	173	179	)	)	PUNCT
ejpam-6048	173	180	(	(	PUNCT
ejpam-6048	173	181	d	d	NOUN
ejpam-6048	173	182	,	,	PUNCT
ejpam-6048	173	183	2	2	NUM
ejpam-6048	173	184	)	)	PUNCT
ejpam-6048	173	185	(	(	PUNCT
ejpam-6048	173	186	d	d	NOUN
ejpam-6048	173	187	,	,	PUNCT
ejpam-6048	173	188	5	5	NUM
ejpam-6048	173	189	)	)	PUNCT
ejpam-6048	173	190	(	(	PUNCT
ejpam-6048	173	191	d	d	NOUN
ejpam-6048	173	192	,	,	PUNCT
ejpam-6048	173	193	6	6	NUM
ejpam-6048	173	194	)	)	PUNCT
ejpam-6048	173	195	(	(	PUNCT
ejpam-6048	173	196	d	d	NOUN
ejpam-6048	173	197	,	,	PUNCT
ejpam-6048	173	198	7	7	NUM
ejpam-6048	173	199	)	)	PUNCT
ejpam-6048	173	200	(	(	PUNCT
ejpam-6048	173	201	e	e	NOUN
ejpam-6048	173	202	,	,	PUNCT
ejpam-6048	173	203	1	1	NUM
ejpam-6048	173	204	)	)	PUNCT
ejpam-6048	173	205	(	(	PUNCT
ejpam-6048	173	206	e	e	NOUN
ejpam-6048	173	207	,	,	PUNCT
ejpam-6048	173	208	3	3	NUM
ejpam-6048	173	209	)	)	PUNCT
ejpam-6048	173	210	(	(	PUNCT
ejpam-6048	173	211	e	e	NOUN
ejpam-6048	173	212	,	,	PUNCT
ejpam-6048	173	213	4	4	NUM
ejpam-6048	173	214	)	)	PUNCT
ejpam-6048	173	215	(	(	PUNCT
ejpam-6048	173	216	f	f	X
ejpam-6048	173	217	,	,	PUNCT
ejpam-6048	173	218	1	1	NUM
ejpam-6048	173	219	)	)	PUNCT
ejpam-6048	173	220	(	(	PUNCT
ejpam-6048	173	221	f	f	X
ejpam-6048	173	222	,	,	PUNCT
ejpam-6048	173	223	3	3	NUM
ejpam-6048	173	224	)	)	PUNCT
ejpam-6048	173	225	(	(	PUNCT
ejpam-6048	173	226	f	f	X
ejpam-6048	173	227	,	,	PUNCT
ejpam-6048	173	228	4	4	NUM
ejpam-6048	173	229	)	)	PUNCT
ejpam-6048	173	230	b	b	NOUN
ejpam-6048	173	231	:	:	PUNCT
ejpam-6048	173	232	g	g	PROPN
ejpam-6048	173	233	·	·	PUNCT
ejpam-6048	173	234	h	h	NOUN
ejpam-6048	173	235	figure	figure	NOUN
ejpam-6048	173	236	5	5	NUM
ejpam-6048	173	237	:	:	PUNCT
ejpam-6048	173	238	the	the	DET
ejpam-6048	173	239	graphs	graph	NOUN
ejpam-6048	173	240	g	g	NOUN
ejpam-6048	173	241	and	and	CCONJ
ejpam-6048	173	242	h	h	PROPN
ejpam-6048	173	243	and	and	CCONJ
ejpam-6048	173	244	their	their	PRON
ejpam-6048	173	245	direct	direct	ADJ
ejpam-6048	173	246	product	product	NOUN
ejpam-6048	173	247	g	g	PROPN
ejpam-6048	173	248	·	·	SYM
ejpam-6048	173	249	h	h	NOUN
ejpam-6048	173	250	{	{	PUNCT
ejpam-6048	173	251	2	2	NUM
ejpam-6048	173	252	,	,	PUNCT
ejpam-6048	173	253	5	5	NUM
ejpam-6048	173	254	,	,	PUNCT
ejpam-6048	173	255	6	6	NUM
ejpam-6048	173	256	,	,	PUNCT
ejpam-6048	173	257	7	7	NUM
ejpam-6048	173	258	}	}	PUNCT
ejpam-6048	173	259	.	.	PUNCT
ejpam-6048	174	1	by	by	ADP
ejpam-6048	174	2	corollary	corollary	ADJ
ejpam-6048	174	3	3	3	NUM
ejpam-6048	174	4	,	,	PUNCT
ejpam-6048	174	5	the	the	DET
ejpam-6048	174	6	sets	set	NOUN
ejpam-6048	174	7	{	{	PUNCT
ejpam-6048	174	8	(	(	PUNCT
ejpam-6048	174	9	x	x	NOUN
ejpam-6048	174	10	,	,	PUNCT
ejpam-6048	174	11	y	y	PROPN
ejpam-6048	174	12	)	)	PUNCT
ejpam-6048	174	13	:	:	PUNCT
ejpam-6048	174	14	x	x	X
ejpam-6048	174	15	∈	∈	PROPN
ejpam-6048	174	16	ω1	ω1	PROPN
ejpam-6048	174	17	,	,	PUNCT
ejpam-6048	174	18	y	y	PROPN
ejpam-6048	174	19	∈	∈	PROPN
ejpam-6048	174	20	ω2	ω2	PROPN
ejpam-6048	174	21	}	}	PUNCT
ejpam-6048	174	22	=	=	SYM
ejpam-6048	174	23	{	{	PUNCT
ejpam-6048	174	24	(	(	PUNCT
ejpam-6048	174	25	a	a	PRON
ejpam-6048	174	26	,	,	PUNCT
ejpam-6048	174	27	1	1	NUM
ejpam-6048	174	28	)	)	PUNCT
ejpam-6048	174	29	,	,	PUNCT
ejpam-6048	174	30	(	(	PUNCT
ejpam-6048	174	31	a	a	PRON
ejpam-6048	174	32	,	,	PUNCT
ejpam-6048	174	33	3	3	NUM
ejpam-6048	174	34	)	)	PUNCT
ejpam-6048	174	35	,	,	PUNCT
ejpam-6048	174	36	(	(	PUNCT
ejpam-6048	174	37	a	a	PRON
ejpam-6048	174	38	,	,	PUNCT
ejpam-6048	174	39	4	4	NUM
ejpam-6048	174	40	)	)	PUNCT
ejpam-6048	174	41	,	,	PUNCT
ejpam-6048	174	42	(	(	PUNCT
ejpam-6048	174	43	c	c	X
ejpam-6048	174	44	,	,	PUNCT
ejpam-6048	174	45	1	1	NUM
ejpam-6048	174	46	)	)	PUNCT
ejpam-6048	174	47	,	,	PUNCT
ejpam-6048	174	48	(	(	PUNCT
ejpam-6048	174	49	c	c	X
ejpam-6048	174	50	,	,	PUNCT
ejpam-6048	174	51	3	3	NUM
ejpam-6048	174	52	)	)	PUNCT
ejpam-6048	174	53	,	,	PUNCT
ejpam-6048	174	54	(	(	PUNCT
ejpam-6048	174	55	c	c	X
ejpam-6048	174	56	,	,	PUNCT
ejpam-6048	174	57	4	4	NUM
ejpam-6048	174	58	)	)	PUNCT
ejpam-6048	174	59	,	,	PUNCT
ejpam-6048	174	60	(	(	PUNCT
ejpam-6048	174	61	d	d	X
ejpam-6048	174	62	,	,	PUNCT
ejpam-6048	174	63	1	1	NUM
ejpam-6048	174	64	)	)	PUNCT
ejpam-6048	174	65	,	,	PUNCT
ejpam-6048	174	66	(	(	PUNCT
ejpam-6048	174	67	d	d	X
ejpam-6048	174	68	,	,	PUNCT
ejpam-6048	174	69	3	3	NUM
ejpam-6048	174	70	)	)	PUNCT
ejpam-6048	174	71	,	,	PUNCT
ejpam-6048	174	72	(	(	PUNCT
ejpam-6048	174	73	d	d	X
ejpam-6048	174	74	,	,	PUNCT
ejpam-6048	174	75	4	4	NUM
ejpam-6048	174	76	)	)	PUNCT
ejpam-6048	174	77	}	}	PUNCT
ejpam-6048	174	78	and	and	CCONJ
ejpam-6048	174	79	{	{	PUNCT
ejpam-6048	174	80	(	(	PUNCT
ejpam-6048	174	81	w	w	PROPN
ejpam-6048	174	82	,	,	PUNCT
ejpam-6048	174	83	z	z	NOUN
ejpam-6048	174	84	)	)	PUNCT
ejpam-6048	174	85	:	:	PUNCT
ejpam-6048	174	86	w	w	X
ejpam-6048	174	87	∈	∈	PROPN
ejpam-6048	174	88	∆1	∆1	PROPN
ejpam-6048	174	89	,	,	PUNCT
ejpam-6048	174	90	z	z	PROPN
ejpam-6048	174	91	∈	∈	PROPN
ejpam-6048	174	92	∆2	∆2	PROPN
ejpam-6048	174	93	}	}	PUNCT
ejpam-6048	174	94	=	=	NOUN
ejpam-6048	174	95	{	{	PUNCT
ejpam-6048	174	96	(	(	PUNCT
ejpam-6048	174	97	b	b	NOUN
ejpam-6048	174	98	,	,	PUNCT
ejpam-6048	174	99	2	2	NUM
ejpam-6048	174	100	)	)	PUNCT
ejpam-6048	174	101	,	,	PUNCT
ejpam-6048	174	102	(	(	PUNCT
ejpam-6048	174	103	b	b	X
ejpam-6048	174	104	,	,	PUNCT
ejpam-6048	174	105	5	5	NUM
ejpam-6048	174	106	)	)	PUNCT
ejpam-6048	174	107	,	,	PUNCT
ejpam-6048	174	108	(	(	PUNCT
ejpam-6048	174	109	b	b	X
ejpam-6048	174	110	,	,	PUNCT
ejpam-6048	174	111	6	6	NUM
ejpam-6048	174	112	)	)	PUNCT
ejpam-6048	174	113	,	,	PUNCT
ejpam-6048	174	114	(	(	PUNCT
ejpam-6048	174	115	b	b	NOUN
ejpam-6048	174	116	,	,	PUNCT
ejpam-6048	174	117	7	7	NUM
ejpam-6048	174	118	)	)	PUNCT
ejpam-6048	174	119	,	,	PUNCT
ejpam-6048	174	120	(	(	PUNCT
ejpam-6048	174	121	e	e	NOUN
ejpam-6048	174	122	,	,	PUNCT
ejpam-6048	174	123	2	2	NUM
ejpam-6048	174	124	)	)	PUNCT
ejpam-6048	174	125	,	,	PUNCT
ejpam-6048	174	126	(	(	PUNCT
ejpam-6048	174	127	e	e	NOUN
ejpam-6048	174	128	,	,	PUNCT
ejpam-6048	174	129	5	5	NUM
ejpam-6048	174	130	)	)	PUNCT
ejpam-6048	174	131	,	,	PUNCT
ejpam-6048	174	132	(	(	PUNCT
ejpam-6048	174	133	e	e	NOUN
ejpam-6048	174	134	,	,	PUNCT
ejpam-6048	174	135	6	6	NUM
ejpam-6048	174	136	)	)	PUNCT
ejpam-6048	174	137	,	,	PUNCT
ejpam-6048	174	138	(	(	PUNCT
ejpam-6048	174	139	e	e	NOUN
ejpam-6048	174	140	,	,	PUNCT
ejpam-6048	174	141	7	7	NUM
ejpam-6048	174	142	)	)	PUNCT
ejpam-6048	174	143	,	,	PUNCT
ejpam-6048	174	144	(	(	PUNCT
ejpam-6048	174	145	f	f	X
ejpam-6048	174	146	,	,	PUNCT
ejpam-6048	174	147	2	2	NUM
ejpam-6048	174	148	)	)	PUNCT
ejpam-6048	174	149	,	,	PUNCT
ejpam-6048	174	150	(	(	PUNCT
ejpam-6048	174	151	f	f	X
ejpam-6048	174	152	,	,	PUNCT
ejpam-6048	174	153	5	5	NUM
ejpam-6048	174	154	)	)	PUNCT
ejpam-6048	174	155	,	,	PUNCT
ejpam-6048	174	156	(	(	PUNCT
ejpam-6048	174	157	f	f	X
ejpam-6048	174	158	,	,	PUNCT
ejpam-6048	174	159	6	6	NUM
ejpam-6048	174	160	)	)	PUNCT
ejpam-6048	174	161	,	,	PUNCT
ejpam-6048	174	162	(	(	PUNCT
ejpam-6048	174	163	f	f	X
ejpam-6048	174	164	,	,	PUNCT
ejpam-6048	174	165	7	7	NUM
ejpam-6048	174	166	)	)	PUNCT
ejpam-6048	174	167	}	}	PUNCT
ejpam-6048	174	168	are	be	AUX
ejpam-6048	174	169	the	the	DET
ejpam-6048	174	170	independent	independent	ADJ
ejpam-6048	174	171	neighborhood	neighborhood	NOUN
ejpam-6048	174	172	sets	set	NOUN
ejpam-6048	174	173	of	of	ADP
ejpam-6048	174	174	a	a	DET
ejpam-6048	174	175	while	while	NOUN
ejpam-6048	174	176	the	the	DET
ejpam-6048	174	177	sets	set	NOUN
ejpam-6048	174	178	{	{	PUNCT
ejpam-6048	174	179	(	(	PUNCT
ejpam-6048	174	180	x	x	NOUN
ejpam-6048	174	181	,	,	PUNCT
ejpam-6048	174	182	y	y	PROPN
ejpam-6048	174	183	)	)	PUNCT
ejpam-6048	174	184	:	:	PUNCT
ejpam-6048	174	185	x	x	X
ejpam-6048	174	186	∈	∈	PROPN
ejpam-6048	174	187	ω1	ω1	PROPN
ejpam-6048	174	188	,	,	PUNCT
ejpam-6048	174	189	y	y	PROPN
ejpam-6048	174	190	∈	∈	PROPN
ejpam-6048	174	191	∆2	∆2	PROPN
ejpam-6048	174	192	}	}	PUNCT
ejpam-6048	174	193	=	=	NOUN
ejpam-6048	174	194	{	{	PUNCT
ejpam-6048	174	195	(	(	PUNCT
ejpam-6048	174	196	a	a	PRON
ejpam-6048	174	197	,	,	PUNCT
ejpam-6048	174	198	2	2	NUM
ejpam-6048	174	199	)	)	PUNCT
ejpam-6048	174	200	,	,	PUNCT
ejpam-6048	174	201	(	(	PUNCT
ejpam-6048	174	202	a	a	PRON
ejpam-6048	174	203	,	,	PUNCT
ejpam-6048	174	204	5	5	NUM
ejpam-6048	174	205	)	)	PUNCT
ejpam-6048	174	206	,	,	PUNCT
ejpam-6048	174	207	(	(	PUNCT
ejpam-6048	174	208	a	a	PRON
ejpam-6048	174	209	,	,	PUNCT
ejpam-6048	174	210	6	6	NUM
ejpam-6048	174	211	)	)	PUNCT
ejpam-6048	174	212	,	,	PUNCT
ejpam-6048	174	213	(	(	PUNCT
ejpam-6048	174	214	a	a	PRON
ejpam-6048	174	215	,	,	PUNCT
ejpam-6048	174	216	7	7	NUM
ejpam-6048	174	217	)	)	PUNCT
ejpam-6048	174	218	,	,	PUNCT
ejpam-6048	174	219	(	(	PUNCT
ejpam-6048	174	220	c	c	X
ejpam-6048	174	221	,	,	PUNCT
ejpam-6048	174	222	2	2	NUM
ejpam-6048	174	223	)	)	PUNCT
ejpam-6048	174	224	,	,	PUNCT
ejpam-6048	174	225	(	(	PUNCT
ejpam-6048	174	226	c	c	X
ejpam-6048	174	227	,	,	PUNCT
ejpam-6048	174	228	5	5	NUM
ejpam-6048	174	229	)	)	PUNCT
ejpam-6048	174	230	,	,	PUNCT
ejpam-6048	174	231	(	(	PUNCT
ejpam-6048	174	232	c	c	X
ejpam-6048	174	233	,	,	PUNCT
ejpam-6048	174	234	6	6	NUM
ejpam-6048	174	235	)	)	PUNCT
ejpam-6048	174	236	,	,	PUNCT
ejpam-6048	174	237	(	(	PUNCT
ejpam-6048	174	238	c	c	X
ejpam-6048	174	239	,	,	PUNCT
ejpam-6048	174	240	7	7	NUM
ejpam-6048	174	241	)	)	PUNCT
ejpam-6048	174	242	,	,	PUNCT
ejpam-6048	174	243	(	(	PUNCT
ejpam-6048	174	244	d	d	X
ejpam-6048	174	245	,	,	PUNCT
ejpam-6048	174	246	2	2	NUM
ejpam-6048	174	247	)	)	PUNCT
ejpam-6048	174	248	,	,	PUNCT
ejpam-6048	174	249	(	(	PUNCT
ejpam-6048	174	250	d	d	X
ejpam-6048	174	251	,	,	PUNCT
ejpam-6048	174	252	5	5	NUM
ejpam-6048	174	253	)	)	PUNCT
ejpam-6048	174	254	,	,	PUNCT
ejpam-6048	174	255	(	(	PUNCT
ejpam-6048	174	256	d	d	X
ejpam-6048	174	257	,	,	PUNCT
ejpam-6048	174	258	6	6	NUM
ejpam-6048	174	259	)	)	PUNCT
ejpam-6048	174	260	,	,	PUNCT
ejpam-6048	174	261	(	(	PUNCT
ejpam-6048	174	262	d	d	X
ejpam-6048	174	263	,	,	PUNCT
ejpam-6048	174	264	7	7	NUM
ejpam-6048	174	265	)	)	PUNCT
ejpam-6048	174	266	}	}	PUNCT
ejpam-6048	174	267	and	and	CCONJ
ejpam-6048	174	268	{	{	PUNCT
ejpam-6048	174	269	(	(	PUNCT
ejpam-6048	174	270	w	w	PROPN
ejpam-6048	174	271	,	,	PUNCT
ejpam-6048	174	272	z	z	NOUN
ejpam-6048	174	273	)	)	PUNCT
ejpam-6048	174	274	:	:	PUNCT
ejpam-6048	174	275	w	w	X
ejpam-6048	174	276	∈	∈	PROPN
ejpam-6048	174	277	∆1	∆1	PROPN
ejpam-6048	174	278	,	,	PUNCT
ejpam-6048	174	279	z	z	PROPN
ejpam-6048	174	280	∈	∈	PROPN
ejpam-6048	174	281	ω2	ω2	ADJ
ejpam-6048	174	282	}	}	PUNCT
ejpam-6048	174	283	=	=	SYM
ejpam-6048	174	284	{	{	PUNCT
ejpam-6048	174	285	(	(	PUNCT
ejpam-6048	174	286	b	b	NOUN
ejpam-6048	174	287	,	,	PUNCT
ejpam-6048	174	288	1	1	NUM
ejpam-6048	174	289	)	)	PUNCT
ejpam-6048	174	290	,	,	PUNCT
ejpam-6048	174	291	(	(	PUNCT
ejpam-6048	174	292	b	b	X
ejpam-6048	174	293	,	,	PUNCT
ejpam-6048	174	294	3	3	NUM
ejpam-6048	174	295	)	)	PUNCT
ejpam-6048	174	296	,	,	PUNCT
ejpam-6048	174	297	(	(	PUNCT
ejpam-6048	174	298	b	b	NOUN
ejpam-6048	174	299	,	,	PUNCT
ejpam-6048	174	300	4	4	NUM
ejpam-6048	174	301	)	)	PUNCT
ejpam-6048	174	302	,	,	PUNCT
ejpam-6048	174	303	(	(	PUNCT
ejpam-6048	174	304	e	e	NOUN
ejpam-6048	174	305	,	,	PUNCT
ejpam-6048	174	306	1	1	NUM
ejpam-6048	174	307	)	)	PUNCT
ejpam-6048	174	308	,	,	PUNCT
ejpam-6048	174	309	(	(	PUNCT
ejpam-6048	174	310	e	e	NOUN
ejpam-6048	174	311	,	,	PUNCT
ejpam-6048	174	312	3	3	NUM
ejpam-6048	174	313	)	)	PUNCT
ejpam-6048	174	314	,	,	PUNCT
ejpam-6048	174	315	(	(	PUNCT
ejpam-6048	174	316	e	e	NOUN
ejpam-6048	174	317	,	,	PUNCT
ejpam-6048	174	318	4	4	NUM
ejpam-6048	174	319	)	)	PUNCT
ejpam-6048	174	320	,	,	PUNCT
ejpam-6048	174	321	(	(	PUNCT
ejpam-6048	174	322	f	f	X
ejpam-6048	174	323	,	,	PUNCT
ejpam-6048	174	324	1	1	NUM
ejpam-6048	174	325	)	)	PUNCT
ejpam-6048	174	326	,	,	PUNCT
ejpam-6048	174	327	(	(	PUNCT
ejpam-6048	174	328	f	f	X
ejpam-6048	174	329	,	,	PUNCT
ejpam-6048	174	330	3	3	NUM
ejpam-6048	174	331	)	)	PUNCT
ejpam-6048	174	332	,	,	PUNCT
ejpam-6048	174	333	(	(	PUNCT
ejpam-6048	174	334	f	f	X
ejpam-6048	174	335	,	,	PUNCT
ejpam-6048	174	336	4	4	NUM
ejpam-6048	174	337	)	)	PUNCT
ejpam-6048	174	338	}	}	PUNCT
ejpam-6048	174	339	n.	n.	PROPN
ejpam-6048	174	340	abdulcarim	abdulcarim	PROPN
ejpam-6048	174	341	,	,	PUNCT
ejpam-6048	174	342	s.	s.	PROPN
ejpam-6048	174	343	dagondon	dagondon	PROPN
ejpam-6048	174	344	/	/	SYM
ejpam-6048	174	345	eur	eur	PROPN
ejpam-6048	174	346	.	.	PUNCT
ejpam-6048	175	1	j.	j.	PROPN
ejpam-6048	175	2	pure	pure	PROPN
ejpam-6048	175	3	appl	appl	PROPN
ejpam-6048	175	4	.	.	PROPN
ejpam-6048	175	5	math	math	PROPN
ejpam-6048	175	6	,	,	PUNCT
ejpam-6048	175	7	18	18	NUM
ejpam-6048	175	8	(	(	PUNCT
ejpam-6048	175	9	3	3	NUM
ejpam-6048	175	10	)	)	PUNCT
ejpam-6048	175	11	(	(	PUNCT
ejpam-6048	175	12	2025	2025	NUM
ejpam-6048	175	13	)	)	PUNCT
ejpam-6048	175	14	,	,	PUNCT
ejpam-6048	175	15	6048	6048	NUM
ejpam-6048	175	16	10	10	NUM
ejpam-6048	175	17	of	of	ADP
ejpam-6048	175	18	14	14	NUM
ejpam-6048	175	19	are	be	AUX
ejpam-6048	175	20	the	the	DET
ejpam-6048	175	21	independent	independent	ADJ
ejpam-6048	175	22	neighborhood	neighborhood	NOUN
ejpam-6048	175	23	sets	set	NOUN
ejpam-6048	175	24	of	of	ADP
ejpam-6048	175	25	b.	b.	PROPN
ejpam-6048	175	26	furthermore	furthermore	ADV
ejpam-6048	175	27	,	,	PUNCT
ejpam-6048	175	28	|ω1|	|ω1|	NOUN
ejpam-6048	175	29	=	=	SYM
ejpam-6048	175	30	3	3	NUM
ejpam-6048	175	31	,	,	PUNCT
ejpam-6048	175	32	|∆1|	|∆1|	NOUN
ejpam-6048	175	33	=	=	SYM
ejpam-6048	175	34	3	3	NUM
ejpam-6048	175	35	,	,	PUNCT
ejpam-6048	175	36	|ω2|	|ω2|	NOUN
ejpam-6048	175	37	=	=	SYM
ejpam-6048	175	38	3	3	NUM
ejpam-6048	175	39	and	and	CCONJ
ejpam-6048	175	40	|∆2|	|∆2|	ADJ
ejpam-6048	175	41	=	=	SYM
ejpam-6048	175	42	4	4	X
ejpam-6048	175	43	.	.	PUNCT
ejpam-6048	175	44	therefore	therefore	ADV
ejpam-6048	175	45	,	,	PUNCT
ejpam-6048	175	46	by	by	ADP
ejpam-6048	175	47	corollary	corollary	ADJ
ejpam-6048	175	48	4	4	NUM
ejpam-6048	175	49	,	,	PUNCT
ejpam-6048	175	50	ni(g	ni(g	NUM
ejpam-6048	175	51	·	·	PUNCT
ejpam-6048	175	52	h	h	NOUN
ejpam-6048	175	53	,	,	PUNCT
ejpam-6048	175	54	x	x	NOUN
ejpam-6048	175	55	)	)	PUNCT
ejpam-6048	175	56	=	=	NOUN
ejpam-6048	175	57	x3(3)+3(4	x3(3)+3(4	NUM
ejpam-6048	175	58	)	)	PUNCT
ejpam-6048	175	59	+	+	CCONJ
ejpam-6048	175	60	x3(3)+3(3	x3(3)+3(3	NUM
ejpam-6048	175	61	)	)	PUNCT
ejpam-6048	175	62	+	+	NUM
ejpam-6048	175	63	x3(4)+3(4	x3(4)+3(4	NOUN
ejpam-6048	175	64	)	)	PUNCT
ejpam-6048	175	65	+	+	CCONJ
ejpam-6048	175	66	x3(4)+3(3	x3(4)+3(3	NUM
ejpam-6048	175	67	)	)	PUNCT
ejpam-6048	176	1	=	=	SYM
ejpam-6048	176	2	x21	x21	PROPN
ejpam-6048	176	3	+	+	NUM
ejpam-6048	176	4	x18	x18	NOUN
ejpam-6048	176	5	+	+	CCONJ
ejpam-6048	176	6	x24	x24	NOUN
ejpam-6048	177	1	+	+	CCONJ
ejpam-6048	177	2	x21	x21	NUM
ejpam-6048	177	3	=	=	NOUN
ejpam-6048	177	4	x18	x18	NOUN
ejpam-6048	177	5	+	+	CCONJ
ejpam-6048	177	6	2x21	2x21	NUM
ejpam-6048	177	7	+	+	CCONJ
ejpam-6048	177	8	x24	x24	NOUN
ejpam-6048	177	9	.	.	PUNCT
ejpam-6048	178	1	theorem	theorem	NOUN
ejpam-6048	178	2	5	5	NUM
ejpam-6048	178	3	.	.	X
ejpam-6048	178	4	for	for	ADP
ejpam-6048	178	5	any	any	DET
ejpam-6048	178	6	graphs	graph	NOUN
ejpam-6048	178	7	g	g	NOUN
ejpam-6048	178	8	and	and	CCONJ
ejpam-6048	178	9	h	h	NOUN
ejpam-6048	178	10	,	,	PUNCT
ejpam-6048	178	11	the	the	DET
ejpam-6048	178	12	direct	direct	ADJ
ejpam-6048	178	13	product	product	NOUN
ejpam-6048	178	14	of	of	ADP
ejpam-6048	178	15	g	g	PROPN
ejpam-6048	178	16	and	and	CCONJ
ejpam-6048	178	17	h	h	NOUN
ejpam-6048	178	18	is	be	AUX
ejpam-6048	178	19	commutative	commutative	ADJ
ejpam-6048	178	20	,	,	PUNCT
ejpam-6048	178	21	that	that	ADV
ejpam-6048	178	22	is	is	ADV
ejpam-6048	178	23	,	,	PUNCT
ejpam-6048	178	24	g	g	PROPN
ejpam-6048	178	25	·	·	SYM
ejpam-6048	178	26	h	h	NOUN
ejpam-6048	178	27	=	=	SYM
ejpam-6048	178	28	h	h	NOUN
ejpam-6048	178	29	·	·	PUNCT
ejpam-6048	178	30	g.	g.	PROPN
ejpam-6048	178	31	proof	proof	NOUN
ejpam-6048	178	32	.	.	PUNCT
ejpam-6048	179	1	let	let	VERB
ejpam-6048	179	2	g	g	NOUN
ejpam-6048	179	3	and	and	CCONJ
ejpam-6048	179	4	h	h	NOUN
ejpam-6048	179	5	be	be	VERB
ejpam-6048	179	6	any	any	DET
ejpam-6048	179	7	graphs	graph	NOUN
ejpam-6048	179	8	.	.	PUNCT
ejpam-6048	180	1	to	to	PART
ejpam-6048	180	2	show	show	VERB
ejpam-6048	180	3	that	that	SCONJ
ejpam-6048	180	4	the	the	DET
ejpam-6048	180	5	direct	direct	ADJ
ejpam-6048	180	6	product	product	NOUN
ejpam-6048	180	7	of	of	ADP
ejpam-6048	180	8	g	g	PROPN
ejpam-6048	180	9	and	and	CCONJ
ejpam-6048	180	10	h	h	NOUN
ejpam-6048	180	11	is	be	AUX
ejpam-6048	180	12	commutative	commutative	ADJ
ejpam-6048	180	13	,	,	PUNCT
ejpam-6048	180	14	we	we	PRON
ejpam-6048	180	15	will	will	AUX
ejpam-6048	180	16	show	show	VERB
ejpam-6048	180	17	that	that	SCONJ
ejpam-6048	180	18	g	g	PROPN
ejpam-6048	180	19	·	·	SYM
ejpam-6048	180	20	h	h	PROPN
ejpam-6048	180	21	and	and	CCONJ
ejpam-6048	180	22	h	h	NOUN
ejpam-6048	180	23	·	·	PUNCT
ejpam-6048	180	24	g	g	NOUN
ejpam-6048	180	25	are	be	AUX
ejpam-6048	180	26	isomorphic	isomorphic	ADJ
ejpam-6048	180	27	.	.	PUNCT
ejpam-6048	181	1	we	we	PRON
ejpam-6048	181	2	note	note	VERB
ejpam-6048	181	3	that	that	SCONJ
ejpam-6048	181	4	|v	|v	PROPN
ejpam-6048	181	5	(	(	PUNCT
ejpam-6048	181	6	g	g	NOUN
ejpam-6048	181	7	·	·	SYM
ejpam-6048	181	8	h)|	h)|	NOUN
ejpam-6048	181	9	=	=	PUNCT
ejpam-6048	181	10	|v	|v	PROPN
ejpam-6048	181	11	(	(	PUNCT
ejpam-6048	181	12	g)×v	g)×v	PROPN
ejpam-6048	181	13	(	(	PUNCT
ejpam-6048	181	14	h)|	h)|	NOUN
ejpam-6048	181	15	=	=	PUNCT
ejpam-6048	181	16	|v	|v	PROPN
ejpam-6048	181	17	(	(	PUNCT
ejpam-6048	181	18	h)×v	h)×v	NOUN
ejpam-6048	181	19	(	(	PUNCT
ejpam-6048	181	20	g)|	g)|	PROPN
ejpam-6048	181	21	=	=	PUNCT
ejpam-6048	181	22	|v	|v	X
ejpam-6048	181	23	(	(	PUNCT
ejpam-6048	181	24	h	h	NOUN
ejpam-6048	181	25	·	·	SYM
ejpam-6048	181	26	g)|	g)|	PROPN
ejpam-6048	181	27	.	.	PUNCT
ejpam-6048	181	28	define	define	VERB
ejpam-6048	181	29	the	the	DET
ejpam-6048	181	30	map	map	NOUN
ejpam-6048	182	1	β	β	X
ejpam-6048	182	2	:	:	PUNCT
ejpam-6048	182	3	v	v	NOUN
ejpam-6048	182	4	(	(	PUNCT
ejpam-6048	182	5	g	g	PROPN
ejpam-6048	182	6	·	·	SYM
ejpam-6048	182	7	h	h	NOUN
ejpam-6048	182	8	)	)	PUNCT
ejpam-6048	182	9	−→	−→	NOUN
ejpam-6048	182	10	v	v	NOUN
ejpam-6048	182	11	(	(	PUNCT
ejpam-6048	182	12	h	h	NOUN
ejpam-6048	182	13	·	·	SYM
ejpam-6048	182	14	g	g	NOUN
ejpam-6048	182	15	)	)	PUNCT
ejpam-6048	182	16	by	by	ADP
ejpam-6048	182	17	β((g	β((g	ADJ
ejpam-6048	182	18	,	,	PUNCT
ejpam-6048	182	19	h	h	NOUN
ejpam-6048	182	20	)	)	PUNCT
ejpam-6048	182	21	)	)	PUNCT
ejpam-6048	183	1	=	=	PRON
ejpam-6048	183	2	(	(	PUNCT
ejpam-6048	183	3	h	h	NOUN
ejpam-6048	183	4	,	,	PUNCT
ejpam-6048	183	5	g	g	NOUN
ejpam-6048	183	6	)	)	PUNCT
ejpam-6048	183	7	for	for	ADP
ejpam-6048	183	8	all	all	DET
ejpam-6048	183	9	(	(	PUNCT
ejpam-6048	183	10	g	g	NOUN
ejpam-6048	183	11	,	,	PUNCT
ejpam-6048	183	12	h	h	NOUN
ejpam-6048	183	13	)	)	PUNCT
ejpam-6048	183	14	∈	∈	NOUN
ejpam-6048	183	15	v	v	NOUN
ejpam-6048	183	16	(	(	PUNCT
ejpam-6048	183	17	g	g	PROPN
ejpam-6048	183	18	·	·	PROPN
ejpam-6048	183	19	h	h	NOUN
ejpam-6048	183	20	)	)	PUNCT
ejpam-6048	183	21	.	.	PUNCT
ejpam-6048	184	1	for	for	ADP
ejpam-6048	184	2	(	(	PUNCT
ejpam-6048	184	3	g1	g1	NOUN
ejpam-6048	184	4	,	,	PUNCT
ejpam-6048	184	5	h1	h1	PROPN
ejpam-6048	184	6	)	)	PUNCT
ejpam-6048	184	7	,	,	PUNCT
ejpam-6048	184	8	(	(	PUNCT
ejpam-6048	184	9	g2	g2	PROPN
ejpam-6048	184	10	,	,	PUNCT
ejpam-6048	184	11	h2	h2	PROPN
ejpam-6048	184	12	)	)	PUNCT
ejpam-6048	184	13	∈	∈	PROPN
ejpam-6048	184	14	v	v	ADP
ejpam-6048	184	15	(	(	PUNCT
ejpam-6048	184	16	g	g	PROPN
ejpam-6048	184	17	·	·	SYM
ejpam-6048	184	18	h	h	NOUN
ejpam-6048	184	19	)	)	PUNCT
ejpam-6048	184	20	such	such	ADJ
ejpam-6048	184	21	that	that	SCONJ
ejpam-6048	184	22	β((g1	β((g1	ADJ
ejpam-6048	184	23	,	,	PUNCT
ejpam-6048	184	24	h1	h1	PROPN
ejpam-6048	184	25	)	)	PUNCT
ejpam-6048	184	26	)	)	PUNCT
ejpam-6048	185	1	=	=	PUNCT
ejpam-6048	185	2	β((g2	β((g2	X
ejpam-6048	185	3	,	,	PUNCT
ejpam-6048	185	4	h2	h2	NOUN
ejpam-6048	185	5	)	)	PUNCT
ejpam-6048	185	6	)	)	PUNCT
ejpam-6048	185	7	,	,	PUNCT
ejpam-6048	185	8	we	we	PRON
ejpam-6048	185	9	have	have	VERB
ejpam-6048	185	10	(	(	PUNCT
ejpam-6048	185	11	h1	h1	PROPN
ejpam-6048	185	12	,	,	PUNCT
ejpam-6048	185	13	g1	g1	PROPN
ejpam-6048	185	14	)	)	PUNCT
ejpam-6048	185	15	=	=	SYM
ejpam-6048	185	16	β((g1	β((g1	X
ejpam-6048	185	17	,	,	PUNCT
ejpam-6048	185	18	h1	h1	PROPN
ejpam-6048	185	19	)	)	PUNCT
ejpam-6048	185	20	)	)	PUNCT
ejpam-6048	186	1	=	=	PUNCT
ejpam-6048	186	2	β((g2	β((g2	X
ejpam-6048	186	3	,	,	PUNCT
ejpam-6048	186	4	h2	h2	NOUN
ejpam-6048	186	5	)	)	PUNCT
ejpam-6048	186	6	)	)	PUNCT
ejpam-6048	187	1	=	=	PRON
ejpam-6048	187	2	(	(	PUNCT
ejpam-6048	187	3	h2	h2	PROPN
ejpam-6048	187	4	,	,	PUNCT
ejpam-6048	187	5	g2	g2	PROPN
ejpam-6048	187	6	)	)	PUNCT
ejpam-6048	188	1	=	=	VERB
ejpam-6048	188	2	⇒	⇒	NOUN
ejpam-6048	188	3	(	(	PUNCT
ejpam-6048	188	4	h1	h1	PROPN
ejpam-6048	188	5	,	,	PUNCT
ejpam-6048	188	6	g1	g1	PROPN
ejpam-6048	188	7	)	)	PUNCT
ejpam-6048	188	8	=	=	SYM
ejpam-6048	188	9	(	(	PUNCT
ejpam-6048	188	10	h2	h2	PROPN
ejpam-6048	188	11	,	,	PUNCT
ejpam-6048	188	12	g2	g2	PROPN
ejpam-6048	188	13	)	)	PUNCT
ejpam-6048	189	1	=	=	VERB
ejpam-6048	189	2	⇒	⇒	X
ejpam-6048	189	3	h1	h1	PROPN
ejpam-6048	189	4	=	=	PUNCT
ejpam-6048	189	5	h2	h2	PROPN
ejpam-6048	189	6	and	and	CCONJ
ejpam-6048	189	7	g1	g1	PROPN
ejpam-6048	189	8	=	=	PROPN
ejpam-6048	189	9	g2	g2	PROPN
ejpam-6048	189	10	.	.	PUNCT
ejpam-6048	190	1	thus	thus	ADV
ejpam-6048	190	2	,	,	PUNCT
ejpam-6048	190	3	(	(	PUNCT
ejpam-6048	190	4	g1	g1	PROPN
ejpam-6048	190	5	,	,	PUNCT
ejpam-6048	190	6	h1	h1	NOUN
ejpam-6048	190	7	)	)	PUNCT
ejpam-6048	190	8	=	=	SYM
ejpam-6048	190	9	(	(	PUNCT
ejpam-6048	190	10	g2	g2	PROPN
ejpam-6048	190	11	,	,	PUNCT
ejpam-6048	190	12	h2	h2	PROPN
ejpam-6048	190	13	)	)	PUNCT
ejpam-6048	190	14	which	which	PRON
ejpam-6048	190	15	shows	show	VERB
ejpam-6048	190	16	β	β	PROPN
ejpam-6048	190	17	is	be	AUX
ejpam-6048	190	18	one	one	NUM
ejpam-6048	190	19	-	-	PUNCT
ejpam-6048	190	20	to	to	ADP
ejpam-6048	190	21	-	-	PUNCT
ejpam-6048	190	22	one	one	NUM
ejpam-6048	190	23	.	.	PUNCT
ejpam-6048	191	1	now	now	ADV
ejpam-6048	191	2	,	,	PUNCT
ejpam-6048	191	3	observe	observe	VERB
ejpam-6048	191	4	that	that	SCONJ
ejpam-6048	191	5	for	for	ADP
ejpam-6048	191	6	every	every	DET
ejpam-6048	191	7	(	(	PUNCT
ejpam-6048	191	8	h	h	NOUN
ejpam-6048	191	9	,	,	PUNCT
ejpam-6048	191	10	g	g	NOUN
ejpam-6048	191	11	)	)	PUNCT
ejpam-6048	191	12	∈	∈	NOUN
ejpam-6048	191	13	v	v	NOUN
ejpam-6048	191	14	(	(	PUNCT
ejpam-6048	191	15	h	h	NOUN
ejpam-6048	191	16	·	·	SYM
ejpam-6048	191	17	g	g	NOUN
ejpam-6048	191	18	)	)	PUNCT
ejpam-6048	191	19	,	,	PUNCT
ejpam-6048	191	20	there	there	PRON
ejpam-6048	191	21	exists	exist	VERB
ejpam-6048	191	22	(	(	PUNCT
ejpam-6048	192	1	g	g	NOUN
ejpam-6048	192	2	,	,	PUNCT
ejpam-6048	192	3	h	h	NOUN
ejpam-6048	192	4	)	)	PUNCT
ejpam-6048	192	5	∈	∈	NOUN
ejpam-6048	192	6	v	v	NOUN
ejpam-6048	192	7	(	(	PUNCT
ejpam-6048	192	8	g·h	g·h	NOUN
ejpam-6048	192	9	)	)	PUNCT
ejpam-6048	192	10	such	such	ADJ
ejpam-6048	192	11	that	that	SCONJ
ejpam-6048	192	12	β((g	β((g	ADJ
ejpam-6048	192	13	,	,	PUNCT
ejpam-6048	192	14	h	h	NOUN
ejpam-6048	192	15	)	)	PUNCT
ejpam-6048	192	16	)	)	PUNCT
ejpam-6048	193	1	=	=	PRON
ejpam-6048	193	2	(	(	PUNCT
ejpam-6048	193	3	h	h	NOUN
ejpam-6048	193	4	,	,	PUNCT
ejpam-6048	193	5	g	g	NOUN
ejpam-6048	193	6	)	)	PUNCT
ejpam-6048	193	7	,	,	PUNCT
ejpam-6048	193	8	for	for	ADP
ejpam-6048	193	9	all	all	PRON
ejpam-6048	193	10	(	(	PUNCT
ejpam-6048	193	11	g	g	NOUN
ejpam-6048	193	12	,	,	PUNCT
ejpam-6048	193	13	h	h	NOUN
ejpam-6048	193	14	)	)	PUNCT
ejpam-6048	193	15	∈	∈	NOUN
ejpam-6048	193	16	v	v	NOUN
ejpam-6048	193	17	(	(	PUNCT
ejpam-6048	193	18	g·h	g·h	NOUN
ejpam-6048	193	19	)	)	PUNCT
ejpam-6048	193	20	.	.	PUNCT
ejpam-6048	194	1	this	this	PRON
ejpam-6048	194	2	implies	imply	VERB
ejpam-6048	194	3	β(v	β(v	PROPN
ejpam-6048	194	4	(	(	PUNCT
ejpam-6048	194	5	g	g	PROPN
ejpam-6048	194	6	·	·	SYM
ejpam-6048	194	7	h	h	NOUN
ejpam-6048	194	8	)	)	PUNCT
ejpam-6048	194	9	)	)	PUNCT
ejpam-6048	195	1	=	=	SYM
ejpam-6048	195	2	v	v	X
ejpam-6048	195	3	(	(	PUNCT
ejpam-6048	195	4	h	h	NOUN
ejpam-6048	195	5	·	·	PUNCT
ejpam-6048	195	6	g	g	NOUN
ejpam-6048	195	7	)	)	PUNCT
ejpam-6048	195	8	and	and	CCONJ
ejpam-6048	195	9	it	it	PRON
ejpam-6048	195	10	follows	follow	VERB
ejpam-6048	195	11	that	that	SCONJ
ejpam-6048	195	12	β	β	PROPN
ejpam-6048	195	13	is	be	AUX
ejpam-6048	195	14	onto	onto	ADP
ejpam-6048	195	15	.	.	PUNCT
ejpam-6048	196	1	finally	finally	ADV
ejpam-6048	196	2	,	,	PUNCT
ejpam-6048	196	3	we	we	PRON
ejpam-6048	196	4	let	let	VERB
ejpam-6048	196	5	(	(	PUNCT
ejpam-6048	196	6	g1	g1	X
ejpam-6048	196	7	,	,	PUNCT
ejpam-6048	196	8	h1	h1	PROPN
ejpam-6048	196	9	)	)	PUNCT
ejpam-6048	196	10	,	,	PUNCT
ejpam-6048	196	11	(	(	PUNCT
ejpam-6048	196	12	g2	g2	PROPN
ejpam-6048	196	13	,	,	PUNCT
ejpam-6048	196	14	h2	h2	PROPN
ejpam-6048	196	15	)	)	PUNCT
ejpam-6048	196	16	∈	∈	PROPN
ejpam-6048	196	17	v	v	NOUN
ejpam-6048	196	18	(	(	PUNCT
ejpam-6048	196	19	g	g	PROPN
ejpam-6048	196	20	·	·	PUNCT
ejpam-6048	196	21	h	h	NOUN
ejpam-6048	196	22	)	)	PUNCT
ejpam-6048	196	23	.	.	PUNCT
ejpam-6048	197	1	then	then	ADV
ejpam-6048	197	2	(	(	PUNCT
ejpam-6048	197	3	g1	g1	PROPN
ejpam-6048	197	4	,	,	PUNCT
ejpam-6048	197	5	h1)(g2	h1)(g2	PROPN
ejpam-6048	197	6	,	,	PUNCT
ejpam-6048	197	7	h2	h2	NOUN
ejpam-6048	197	8	)	)	PUNCT
ejpam-6048	197	9	∈	∈	PROPN
ejpam-6048	197	10	e(g	e(g	PROPN
ejpam-6048	197	11	·	·	PUNCT
ejpam-6048	197	12	h	h	X
ejpam-6048	197	13	)	)	PUNCT
ejpam-6048	197	14	⇔	⇔	PROPN
ejpam-6048	197	15	g1g2	g1g2	PROPN
ejpam-6048	197	16	∈	∈	PROPN
ejpam-6048	197	17	e(g	e(g	PROPN
ejpam-6048	197	18	)	)	PUNCT
ejpam-6048	197	19	and	and	CCONJ
ejpam-6048	197	20	h1h2	h1h2	NUM
ejpam-6048	197	21	∈	∈	PROPN
ejpam-6048	197	22	e(h	e(h	PROPN
ejpam-6048	197	23	)	)	PUNCT
ejpam-6048	197	24	⇔	⇔	NOUN
ejpam-6048	197	25	(	(	PUNCT
ejpam-6048	197	26	h1	h1	PROPN
ejpam-6048	197	27	,	,	PUNCT
ejpam-6048	197	28	g1)(h2	g1)(h2	NOUN
ejpam-6048	197	29	,	,	PUNCT
ejpam-6048	197	30	g2	g2	PROPN
ejpam-6048	197	31	)	)	PUNCT
ejpam-6048	197	32	∈	∈	PROPN
ejpam-6048	197	33	e(h	e(h	PROPN
ejpam-6048	197	34	·	·	SYM
ejpam-6048	197	35	g	g	NOUN
ejpam-6048	197	36	)	)	PUNCT
ejpam-6048	197	37	.	.	PUNCT
ejpam-6048	198	1	hence	hence	ADV
ejpam-6048	198	2	,	,	PUNCT
ejpam-6048	198	3	β	β	X
ejpam-6048	198	4	preserves	preserve	VERB
ejpam-6048	198	5	adjacency	adjacency	NOUN
ejpam-6048	198	6	.	.	PUNCT
ejpam-6048	199	1	consequently	consequently	ADV
ejpam-6048	199	2	,	,	PUNCT
ejpam-6048	199	3	g	g	NOUN
ejpam-6048	199	4	·	·	SYM
ejpam-6048	199	5	h	h	NOUN
ejpam-6048	199	6	∼=	∼=	PROPN
ejpam-6048	199	7	h	h	NOUN
ejpam-6048	199	8	·	·	PUNCT
ejpam-6048	199	9	g.	g.	PROPN
ejpam-6048	199	10	therefore	therefore	ADV
ejpam-6048	199	11	,	,	PUNCT
ejpam-6048	199	12	g	g	PROPN
ejpam-6048	199	13	·	·	SYM
ejpam-6048	199	14	h	h	NOUN
ejpam-6048	199	15	=	=	SYM
ejpam-6048	199	16	h	h	PROPN
ejpam-6048	199	17	·	·	PUNCT
ejpam-6048	199	18	g.	g.	PROPN
ejpam-6048	199	19	remark	remark	NOUN
ejpam-6048	199	20	3	3	NUM
ejpam-6048	199	21	.	.	PUNCT
ejpam-6048	200	1	for	for	ADP
ejpam-6048	200	2	any	any	DET
ejpam-6048	200	3	trees	tree	NOUN
ejpam-6048	200	4	g	g	NOUN
ejpam-6048	200	5	and	and	CCONJ
ejpam-6048	200	6	h	h	NOUN
ejpam-6048	200	7	,	,	PUNCT
ejpam-6048	200	8	the	the	DET
ejpam-6048	200	9	independent	independent	ADJ
ejpam-6048	200	10	neighborhood	neighborhood	NOUN
ejpam-6048	200	11	polynomial	polynomial	NOUN
ejpam-6048	200	12	of	of	ADP
ejpam-6048	200	13	g	g	PROPN
ejpam-6048	200	14	·	·	PROPN
ejpam-6048	200	15	h	h	PROPN
ejpam-6048	200	16	is	be	AUX
ejpam-6048	200	17	the	the	DET
ejpam-6048	200	18	same	same	ADJ
ejpam-6048	200	19	as	as	ADP
ejpam-6048	200	20	the	the	DET
ejpam-6048	200	21	independent	independent	ADJ
ejpam-6048	200	22	neighborhood	neighborhood	NOUN
ejpam-6048	200	23	polynomial	polynomial	NOUN
ejpam-6048	200	24	of	of	ADP
ejpam-6048	200	25	h	h	NOUN
ejpam-6048	200	26	·	·	SYM
ejpam-6048	200	27	g	g	NOUN
ejpam-6048	200	28	,	,	PUNCT
ejpam-6048	200	29	that	that	PRON
ejpam-6048	200	30	is	is	ADV
ejpam-6048	200	31	ni(g	ni(g	NOUN
ejpam-6048	200	32	·	·	PUNCT
ejpam-6048	200	33	h	h	NOUN
ejpam-6048	200	34	,	,	PUNCT
ejpam-6048	200	35	x	x	NOUN
ejpam-6048	200	36	)	)	PUNCT
ejpam-6048	200	37	=	=	PRON
ejpam-6048	200	38	ni(h	ni(h	NOUN
ejpam-6048	200	39	·	·	PUNCT
ejpam-6048	200	40	g	g	NOUN
ejpam-6048	200	41	,	,	PUNCT
ejpam-6048	200	42	x	x	NOUN
ejpam-6048	200	43	)	)	PUNCT
ejpam-6048	200	44	.	.	PUNCT
ejpam-6048	201	1	3.2	3.2	NUM
ejpam-6048	201	2	.	.	PUNCT
ejpam-6048	202	1	independent	independent	ADJ
ejpam-6048	202	2	neighborhood	neighborhood	NOUN
ejpam-6048	202	3	polynomial	polynomial	NOUN
ejpam-6048	202	4	of	of	ADP
ejpam-6048	202	5	the	the	DET
ejpam-6048	202	6	corona	corona	NOUN
ejpam-6048	202	7	product	product	NOUN
ejpam-6048	202	8	of	of	ADP
ejpam-6048	202	9	two	two	NUM
ejpam-6048	202	10	trees	tree	NOUN
ejpam-6048	202	11	theorem	theorem	VERB
ejpam-6048	202	12	6	6	NUM
ejpam-6048	202	13	.	.	PUNCT
ejpam-6048	203	1	let	let	VERB
ejpam-6048	203	2	g	g	NOUN
ejpam-6048	204	1	and	and	CCONJ
ejpam-6048	204	2	h	h	NOUN
ejpam-6048	204	3	be	be	VERB
ejpam-6048	204	4	any	any	DET
ejpam-6048	204	5	trees	tree	NOUN
ejpam-6048	204	6	.	.	PUNCT
ejpam-6048	205	1	suppose	suppose	VERB
ejpam-6048	205	2	g	g	PROPN
ejpam-6048	205	3	has	have	VERB
ejpam-6048	205	4	independent	independent	ADJ
ejpam-6048	205	5	neighborhood	neighborhood	NOUN
ejpam-6048	205	6	sets	set	NOUN
ejpam-6048	205	7	ω1,∆1	ω1,∆1	NOUN
ejpam-6048	205	8	and	and	CCONJ
ejpam-6048	205	9	h	h	NOUN
ejpam-6048	205	10	has	have	VERB
ejpam-6048	205	11	independent	independent	ADJ
ejpam-6048	205	12	neighborhood	neighborhood	NOUN
ejpam-6048	205	13	sets	set	NOUN
ejpam-6048	205	14	ω2,∆2	ω2,∆2	PROPN
ejpam-6048	205	15	.	.	PUNCT
ejpam-6048	206	1	then	then	ADV
ejpam-6048	206	2	ni(g	ni(g	PUNCT
ejpam-6048	206	3	◦	◦	NOUN
ejpam-6048	206	4	h	h	NOUN
ejpam-6048	206	5	,	,	PUNCT
ejpam-6048	206	6	x	x	NOUN
ejpam-6048	206	7	)	)	PUNCT
ejpam-6048	206	8	=	=	SYM
ejpam-6048	206	9	x|∆1|	x|∆1|	PROPN
ejpam-6048	206	10	(	(	PUNCT
ejpam-6048	206	11	x|ω2|	x|ω2|	PROPN
ejpam-6048	207	1	+	+	CCONJ
ejpam-6048	207	2	x|∆2|	x|∆2|	ADJ
ejpam-6048	207	3	)	)	PUNCT
ejpam-6048	207	4	|ω1|	|ω1|	NOUN
ejpam-6048	207	5	+	+	X
ejpam-6048	207	6	x|ω1|	x|ω1|	PUNCT
ejpam-6048	208	1	(	(	PUNCT
ejpam-6048	208	2	x|ω2|	x|ω2|	X
ejpam-6048	209	1	+	+	CCONJ
ejpam-6048	209	2	x|∆2|	x|∆2|	ADJ
ejpam-6048	209	3	)	)	PUNCT
ejpam-6048	209	4	|∆1|	|∆1|	NOUN
ejpam-6048	209	5	.	.	PUNCT
ejpam-6048	210	1	n.	n.	PROPN
ejpam-6048	210	2	abdulcarim	abdulcarim	PROPN
ejpam-6048	210	3	,	,	PUNCT
ejpam-6048	210	4	s.	s.	PROPN
ejpam-6048	210	5	dagondon	dagondon	PROPN
ejpam-6048	210	6	/	/	SYM
ejpam-6048	210	7	eur	eur	PROPN
ejpam-6048	210	8	.	.	PUNCT
ejpam-6048	211	1	j.	j.	PROPN
ejpam-6048	211	2	pure	pure	PROPN
ejpam-6048	211	3	appl	appl	PROPN
ejpam-6048	211	4	.	.	PROPN
ejpam-6048	211	5	math	math	PROPN
ejpam-6048	211	6	,	,	PUNCT
ejpam-6048	211	7	18	18	NUM
ejpam-6048	211	8	(	(	PUNCT
ejpam-6048	211	9	3	3	NUM
ejpam-6048	211	10	)	)	PUNCT
ejpam-6048	211	11	(	(	PUNCT
ejpam-6048	211	12	2025	2025	NUM
ejpam-6048	211	13	)	)	PUNCT
ejpam-6048	211	14	,	,	PUNCT
ejpam-6048	211	15	6048	6048	NUM
ejpam-6048	211	16	11	11	NUM
ejpam-6048	211	17	of	of	ADP
ejpam-6048	211	18	14	14	NUM
ejpam-6048	211	19	proof	proof	NOUN
ejpam-6048	211	20	.	.	PUNCT
ejpam-6048	212	1	let	let	VERB
ejpam-6048	212	2	g	g	NOUN
ejpam-6048	212	3	and	and	CCONJ
ejpam-6048	212	4	h	h	NOUN
ejpam-6048	212	5	be	be	VERB
ejpam-6048	212	6	any	any	DET
ejpam-6048	212	7	trees	tree	NOUN
ejpam-6048	212	8	.	.	PUNCT
ejpam-6048	213	1	suppose	suppose	VERB
ejpam-6048	213	2	g	g	PROPN
ejpam-6048	213	3	and	and	CCONJ
ejpam-6048	213	4	h	h	PROPN
ejpam-6048	213	5	has	have	VERB
ejpam-6048	213	6	independent	independent	ADJ
ejpam-6048	213	7	neighborhood	neighborhood	NOUN
ejpam-6048	213	8	sets	set	VERB
ejpam-6048	213	9	ω1,∆1	ω1,∆1	NUM
ejpam-6048	213	10	and	and	CCONJ
ejpam-6048	213	11	ω2,∆2	ω2,∆2	PROPN
ejpam-6048	213	12	,	,	PUNCT
ejpam-6048	213	13	respectively	respectively	ADV
ejpam-6048	213	14	.	.	PUNCT
ejpam-6048	214	1	then	then	ADV
ejpam-6048	214	2	by	by	ADP
ejpam-6048	214	3	remark	remark	NOUN
ejpam-6048	214	4	1	1	NUM
ejpam-6048	214	5	,	,	PUNCT
ejpam-6048	214	6	ni(g	ni(g	NUM
ejpam-6048	214	7	,	,	PUNCT
ejpam-6048	214	8	x	x	X
ejpam-6048	214	9	)	)	PUNCT
ejpam-6048	214	10	=	=	PUNCT
ejpam-6048	214	11	x|ω1|	x|ω1|	PUNCT
ejpam-6048	215	1	+	+	CCONJ
ejpam-6048	215	2	x|∆1|	x|∆1|	PROPN
ejpam-6048	215	3	and	and	CCONJ
ejpam-6048	215	4	ni(h	ni(h	NOUN
ejpam-6048	215	5	,	,	PUNCT
ejpam-6048	215	6	x	x	X
ejpam-6048	215	7	)	)	PUNCT
ejpam-6048	216	1	=	=	SYM
ejpam-6048	216	2	x|ω2|	x|ω2|	PROPN
ejpam-6048	217	1	+	+	CCONJ
ejpam-6048	217	2	x|∆2|	x|∆2|	PROPN
ejpam-6048	217	3	.	.	PUNCT
ejpam-6048	218	1	by	by	ADP
ejpam-6048	218	2	definition	definition	NOUN
ejpam-6048	218	3	of	of	ADP
ejpam-6048	218	4	corona	corona	NOUN
ejpam-6048	218	5	of	of	ADP
ejpam-6048	218	6	two	two	NUM
ejpam-6048	218	7	graphs	graph	NOUN
ejpam-6048	218	8	,	,	PUNCT
ejpam-6048	218	9	every	every	DET
ejpam-6048	218	10	ith	ith	ADJ
ejpam-6048	218	11	vertex	vertex	NOUN
ejpam-6048	218	12	of	of	ADP
ejpam-6048	218	13	g	g	PROPN
ejpam-6048	218	14	is	be	AUX
ejpam-6048	218	15	joined	join	VERB
ejpam-6048	218	16	to	to	ADP
ejpam-6048	218	17	every	every	DET
ejpam-6048	218	18	vertex	vertex	NOUN
ejpam-6048	218	19	in	in	ADP
ejpam-6048	218	20	the	the	DET
ejpam-6048	218	21	ith	ith	PROPN
ejpam-6048	218	22	copy	copy	NOUN
ejpam-6048	218	23	of	of	ADP
ejpam-6048	218	24	h.	h.	PROPN
ejpam-6048	218	25	observe	observe	VERB
ejpam-6048	218	26	that	that	SCONJ
ejpam-6048	218	27	the	the	DET
ejpam-6048	218	28	independent	independent	ADJ
ejpam-6048	218	29	neighborhood	neighborhood	NOUN
ejpam-6048	218	30	set	set	VERB
ejpam-6048	218	31	ω1	ω1	PROPN
ejpam-6048	218	32	of	of	ADP
ejpam-6048	218	33	g	g	PROPN
ejpam-6048	218	34	and	and	CCONJ
ejpam-6048	218	35	the	the	DET
ejpam-6048	218	36	independent	independent	ADJ
ejpam-6048	218	37	neighborhood	neighborhood	NOUN
ejpam-6048	218	38	sets	set	NOUN
ejpam-6048	218	39	in	in	ADP
ejpam-6048	218	40	each	each	DET
ejpam-6048	218	41	copy	copy	NOUN
ejpam-6048	218	42	of	of	ADP
ejpam-6048	218	43	h	h	NOUN
ejpam-6048	218	44	joined	join	VERB
ejpam-6048	218	45	to	to	ADP
ejpam-6048	218	46	every	every	DET
ejpam-6048	218	47	vertex	vertex	NOUN
ejpam-6048	218	48	in	in	ADP
ejpam-6048	218	49	∆1	∆1	PROPN
ejpam-6048	218	50	forms	form	VERB
ejpam-6048	218	51	an	an	DET
ejpam-6048	218	52	independent	independent	ADJ
ejpam-6048	218	53	neighborhood	neighborhood	NOUN
ejpam-6048	218	54	set	set	VERB
ejpam-6048	218	55	in	in	ADP
ejpam-6048	218	56	g	g	PROPN
ejpam-6048	218	57	◦	◦	NOUN
ejpam-6048	218	58	h.	h.	NOUN
ejpam-6048	218	59	similarly	similarly	ADV
ejpam-6048	218	60	,	,	PUNCT
ejpam-6048	218	61	the	the	DET
ejpam-6048	218	62	independent	independent	ADJ
ejpam-6048	218	63	neighborhood	neighborhood	NOUN
ejpam-6048	218	64	set	set	VERB
ejpam-6048	218	65	∆1	∆1	NOUN
ejpam-6048	218	66	of	of	ADP
ejpam-6048	218	67	g	g	PROPN
ejpam-6048	218	68	and	and	CCONJ
ejpam-6048	218	69	the	the	DET
ejpam-6048	218	70	independent	independent	ADJ
ejpam-6048	218	71	neighborhood	neighborhood	NOUN
ejpam-6048	218	72	sets	set	NOUN
ejpam-6048	218	73	in	in	ADP
ejpam-6048	218	74	each	each	DET
ejpam-6048	218	75	copy	copy	NOUN
ejpam-6048	218	76	of	of	ADP
ejpam-6048	218	77	h	h	NOUN
ejpam-6048	218	78	joined	join	VERB
ejpam-6048	218	79	to	to	ADP
ejpam-6048	218	80	every	every	DET
ejpam-6048	218	81	vertex	vertex	NOUN
ejpam-6048	218	82	in	in	ADP
ejpam-6048	218	83	ω1	ω1	PROPN
ejpam-6048	218	84	is	be	AUX
ejpam-6048	218	85	also	also	ADV
ejpam-6048	218	86	an	an	DET
ejpam-6048	218	87	independent	independent	ADJ
ejpam-6048	218	88	neighborhood	neighborhood	NOUN
ejpam-6048	218	89	set	set	VERB
ejpam-6048	218	90	in	in	ADP
ejpam-6048	218	91	g	g	PROPN
ejpam-6048	218	92	◦	◦	NOUN
ejpam-6048	218	93	h.	h.	NOUN
ejpam-6048	218	94	moreover	moreover	ADV
ejpam-6048	218	95	,	,	PUNCT
ejpam-6048	218	96	the	the	DET
ejpam-6048	218	97	number	number	NOUN
ejpam-6048	218	98	of	of	ADP
ejpam-6048	218	99	combinations	combination	NOUN
ejpam-6048	218	100	of	of	ADP
ejpam-6048	218	101	the	the	DET
ejpam-6048	218	102	indepedent	indepedent	ADJ
ejpam-6048	218	103	neighborhood	neighborhood	NOUN
ejpam-6048	218	104	sets	set	NOUN
ejpam-6048	218	105	of	of	ADP
ejpam-6048	218	106	each	each	DET
ejpam-6048	218	107	copy	copy	NOUN
ejpam-6048	218	108	ofh	ofh	PROPN
ejpam-6048	218	109	joined	join	VERB
ejpam-6048	218	110	to	to	ADP
ejpam-6048	218	111	every	every	DET
ejpam-6048	218	112	u	u	PROPN
ejpam-6048	218	113	∈	∈	PROPN
ejpam-6048	218	114	∆1	∆1	NOUN
ejpam-6048	218	115	is	be	AUX
ejpam-6048	218	116	|∆1|	|∆1|	ADJ
ejpam-6048	218	117	,	,	PUNCT
ejpam-6048	218	118	that	that	ADV
ejpam-6048	218	119	is	is	ADV
ejpam-6048	218	120	,	,	PUNCT
ejpam-6048	218	121	ni	ni	PROPN
ejpam-6048	218	122			PROPN
ejpam-6048	218	123	⋃	⋃	PROPN
ejpam-6048	218	124	j∈∆1	j∈∆1	PROPN
ejpam-6048	218	125	hj	hj	PROPN
ejpam-6048	218	126	,	,	PUNCT
ejpam-6048	218	127	x	x	X
ejpam-6048	218	128			PROPN
ejpam-6048	218	129	=	=	SYM
ejpam-6048	218	130	(	(	PUNCT
ejpam-6048	218	131	x|ω2|	x|ω2|	PROPN
ejpam-6048	219	1	+	+	CCONJ
ejpam-6048	219	2	x|∆2|	x|∆2|	ADJ
ejpam-6048	219	3	)	)	PUNCT
ejpam-6048	219	4	|∆1|	|∆1|	NOUN
ejpam-6048	219	5	.	.	PUNCT
ejpam-6048	220	1	also	also	ADV
ejpam-6048	220	2	,	,	PUNCT
ejpam-6048	220	3	there	there	PRON
ejpam-6048	220	4	are	be	VERB
ejpam-6048	220	5	|ω1|	|ω1|	NOUN
ejpam-6048	220	6	combinations	combination	NOUN
ejpam-6048	220	7	of	of	ADP
ejpam-6048	220	8	independent	independent	ADJ
ejpam-6048	220	9	neighborhood	neighborhood	NOUN
ejpam-6048	220	10	sets	set	NOUN
ejpam-6048	220	11	of	of	ADP
ejpam-6048	220	12	each	each	DET
ejpam-6048	220	13	copy	copy	NOUN
ejpam-6048	220	14	of	of	ADP
ejpam-6048	220	15	h	h	NOUN
ejpam-6048	220	16	joined	join	VERB
ejpam-6048	220	17	to	to	ADP
ejpam-6048	220	18	each	each	DET
ejpam-6048	220	19	v	v	ADP
ejpam-6048	220	20	∈	∈	PROPN
ejpam-6048	220	21	ω1	ω1	PROPN
ejpam-6048	220	22	,	,	PUNCT
ejpam-6048	220	23	that	that	ADV
ejpam-6048	220	24	is	is	ADV
ejpam-6048	220	25	,	,	PUNCT
ejpam-6048	220	26	ni	ni	PROPN
ejpam-6048	220	27			PROPN
ejpam-6048	220	28	⋃	⋃	PROPN
ejpam-6048	220	29	r∈ω1	r∈ω1	NOUN
ejpam-6048	220	30	hr	hr	NOUN
ejpam-6048	220	31	,	,	PUNCT
ejpam-6048	220	32	x	x	X
ejpam-6048	220	33			PROPN
ejpam-6048	220	34	=	=	SYM
ejpam-6048	220	35	(	(	PUNCT
ejpam-6048	220	36	x|ω2|	x|ω2|	PROPN
ejpam-6048	221	1	+	+	CCONJ
ejpam-6048	221	2	x|∆2|	x|∆2|	ADJ
ejpam-6048	221	3	)	)	PUNCT
ejpam-6048	221	4	|ω1|	|ω1|	NOUN
ejpam-6048	221	5	.	.	PUNCT
ejpam-6048	222	1	hence	hence	ADV
ejpam-6048	222	2	,	,	PUNCT
ejpam-6048	222	3	ni(g	ni(g	PUNCT
ejpam-6048	222	4	◦	◦	NOUN
ejpam-6048	222	5	h	h	NOUN
ejpam-6048	222	6	,	,	PUNCT
ejpam-6048	222	7	x	x	NOUN
ejpam-6048	222	8	)	)	PUNCT
ejpam-6048	222	9	=	=	SYM
ejpam-6048	222	10	x|∆1|	x|∆1|	PROPN
ejpam-6048	222	11	(	(	PUNCT
ejpam-6048	222	12	x|ω2|	x|ω2|	PROPN
ejpam-6048	223	1	+	+	CCONJ
ejpam-6048	223	2	x|∆2|	x|∆2|	ADJ
ejpam-6048	223	3	)	)	PUNCT
ejpam-6048	223	4	|ω1|	|ω1|	NOUN
ejpam-6048	223	5	+	+	X
ejpam-6048	223	6	x|ω1|	x|ω1|	PUNCT
ejpam-6048	224	1	(	(	PUNCT
ejpam-6048	224	2	x|ω2|	x|ω2|	X
ejpam-6048	225	1	+	+	CCONJ
ejpam-6048	225	2	x|∆2|	x|∆2|	ADJ
ejpam-6048	225	3	)	)	PUNCT
ejpam-6048	225	4	|∆1|	|∆1|	NOUN
ejpam-6048	225	5	.	.	PUNCT
ejpam-6048	226	1	example	example	NOUN
ejpam-6048	227	1	6	6	NUM
ejpam-6048	227	2	.	.	PUNCT
ejpam-6048	227	3	consider	consider	VERB
ejpam-6048	227	4	the	the	DET
ejpam-6048	227	5	corona	corona	NOUN
ejpam-6048	227	6	of	of	ADP
ejpam-6048	227	7	two	two	NUM
ejpam-6048	227	8	graphs	graph	NOUN
ejpam-6048	227	9	b(2	b(2	VERB
ejpam-6048	227	10	,	,	PUNCT
ejpam-6048	227	11	2	2	NUM
ejpam-6048	227	12	)	)	PUNCT
ejpam-6048	227	13	and	and	CCONJ
ejpam-6048	227	14	k1,3	k1,3	X
ejpam-6048	227	15	.	.	PROPN
ejpam-6048	227	16	1	1	NUM
ejpam-6048	227	17	2	2	NUM
ejpam-6048	227	18	3	3	NUM
ejpam-6048	227	19	4	4	NUM
ejpam-6048	227	20	5	5	NUM
ejpam-6048	227	21	6	6	NUM
ejpam-6048	227	22	b(2	b(2	PROPN
ejpam-6048	227	23	,	,	PUNCT
ejpam-6048	227	24	2	2	NUM
ejpam-6048	227	25	)	)	PUNCT
ejpam-6048	227	26	a	a	DET
ejpam-6048	227	27	b	b	NOUN
ejpam-6048	227	28	c	c	NOUN
ejpam-6048	228	1	d	d	NOUN
ejpam-6048	228	2	k1,3	k1,3	X
ejpam-6048	228	3	a1	a1	NOUN
ejpam-6048	228	4	b1	b1	NOUN
ejpam-6048	228	5	c1	c1	PROPN
ejpam-6048	228	6	d1	d1	PROPN
ejpam-6048	228	7	1	1	NUM
ejpam-6048	228	8	a2	a2	PROPN
ejpam-6048	228	9	b2	b2	NOUN
ejpam-6048	228	10	c2	c2	PROPN
ejpam-6048	228	11	d2	d2	PROPN
ejpam-6048	228	12	2	2	NUM
ejpam-6048	228	13	a3	a3	NOUN
ejpam-6048	228	14	b3	b3	PROPN
ejpam-6048	228	15	c3	c3	PROPN
ejpam-6048	228	16	d3	d3	PROPN
ejpam-6048	228	17	3	3	NUM
ejpam-6048	228	18	a4	a4	NOUN
ejpam-6048	228	19	b4	b4	NOUN
ejpam-6048	228	20	c4	c4	NOUN
ejpam-6048	228	21	d4	d4	PROPN
ejpam-6048	228	22	4	4	NUM
ejpam-6048	228	23	a5	a5	PROPN
ejpam-6048	228	24	b5	b5	PROPN
ejpam-6048	228	25	c5	c5	PROPN
ejpam-6048	228	26	d5	d5	PROPN
ejpam-6048	228	27	5	5	NUM
ejpam-6048	228	28	a6	a6	PROPN
ejpam-6048	228	29	b6	b6	PROPN
ejpam-6048	228	30	c6	c6	PROPN
ejpam-6048	228	31	d6	d6	VERB
ejpam-6048	228	32	6	6	NUM
ejpam-6048	229	1	b(2	b(2	PROPN
ejpam-6048	229	2	,	,	PUNCT
ejpam-6048	229	3	2	2	NUM
ejpam-6048	229	4	)	)	PUNCT
ejpam-6048	229	5	◦	◦	NOUN
ejpam-6048	229	6	k1,3	k1,3	NOUN
ejpam-6048	229	7	figure	figure	NOUN
ejpam-6048	229	8	6	6	NUM
ejpam-6048	229	9	:	:	PUNCT
ejpam-6048	229	10	the	the	DET
ejpam-6048	229	11	graph	graph	NOUN
ejpam-6048	229	12	b(2	b(2	PROPN
ejpam-6048	229	13	,	,	PUNCT
ejpam-6048	229	14	2),k1,3	2),k1,3	NUM
ejpam-6048	229	15	and	and	CCONJ
ejpam-6048	229	16	b(2	b(2	PROPN
ejpam-6048	229	17	,	,	PUNCT
ejpam-6048	229	18	2	2	NUM
ejpam-6048	229	19	)	)	PUNCT
ejpam-6048	229	20	◦	◦	NOUN
ejpam-6048	229	21	k1,3	k1,3	PROPN
ejpam-6048	229	22	n.	n.	NOUN
ejpam-6048	229	23	abdulcarim	abdulcarim	PROPN
ejpam-6048	229	24	,	,	PUNCT
ejpam-6048	229	25	s.	s.	PROPN
ejpam-6048	229	26	dagondon	dagondon	PROPN
ejpam-6048	229	27	/	/	SYM
ejpam-6048	229	28	eur	eur	PROPN
ejpam-6048	229	29	.	.	PUNCT
ejpam-6048	230	1	j.	j.	PROPN
ejpam-6048	230	2	pure	pure	PROPN
ejpam-6048	230	3	appl	appl	PROPN
ejpam-6048	230	4	.	.	PROPN
ejpam-6048	230	5	math	math	PROPN
ejpam-6048	230	6	,	,	PUNCT
ejpam-6048	230	7	18	18	NUM
ejpam-6048	230	8	(	(	PUNCT
ejpam-6048	230	9	3	3	NUM
ejpam-6048	230	10	)	)	PUNCT
ejpam-6048	230	11	(	(	PUNCT
ejpam-6048	230	12	2025	2025	NUM
ejpam-6048	230	13	)	)	PUNCT
ejpam-6048	230	14	,	,	PUNCT
ejpam-6048	230	15	6048	6048	NUM
ejpam-6048	230	16	12	12	NUM
ejpam-6048	230	17	of	of	ADP
ejpam-6048	230	18	14	14	NUM
ejpam-6048	230	19	note	note	NOUN
ejpam-6048	230	20	that	that	SCONJ
ejpam-6048	230	21	g	g	PROPN
ejpam-6048	230	22	has	have	AUX
ejpam-6048	230	23	independent	independent	ADJ
ejpam-6048	230	24	neighborhood	neighborhood	NOUN
ejpam-6048	230	25	sets	set	NOUN
ejpam-6048	230	26	ω1	ω1	PROPN
ejpam-6048	230	27	=	=	PUNCT
ejpam-6048	230	28	{	{	PUNCT
ejpam-6048	230	29	1	1	NUM
ejpam-6048	230	30	,	,	PUNCT
ejpam-6048	230	31	2	2	NUM
ejpam-6048	230	32	,	,	PUNCT
ejpam-6048	230	33	4},∆1	4},∆1	NOUN
ejpam-6048	230	34	=	=	SYM
ejpam-6048	230	35	{	{	PUNCT
ejpam-6048	230	36	3	3	NUM
ejpam-6048	230	37	,	,	PUNCT
ejpam-6048	230	38	5	5	NUM
ejpam-6048	230	39	,	,	PUNCT
ejpam-6048	230	40	6	6	NUM
ejpam-6048	230	41	}	}	PUNCT
ejpam-6048	230	42	and	and	CCONJ
ejpam-6048	230	43	h	h	NOUN
ejpam-6048	230	44	has	have	VERB
ejpam-6048	230	45	independent	independent	ADJ
ejpam-6048	230	46	neighborhood	neighborhood	NOUN
ejpam-6048	230	47	sets	set	NOUN
ejpam-6048	230	48	ω2	ω2	ADV
ejpam-6048	230	49	=	=	SYM
ejpam-6048	230	50	{	{	PUNCT
ejpam-6048	230	51	d	d	NOUN
ejpam-6048	230	52	}	}	PUNCT
ejpam-6048	230	53	,	,	PUNCT
ejpam-6048	230	54	∆2	∆2	X
ejpam-6048	231	1	=	=	PUNCT
ejpam-6048	231	2	{	{	PUNCT
ejpam-6048	231	3	a	a	PRON
ejpam-6048	231	4	,	,	PUNCT
ejpam-6048	231	5	b	b	NOUN
ejpam-6048	231	6	,	,	PUNCT
ejpam-6048	231	7	c	c	NOUN
ejpam-6048	231	8	}	}	PUNCT
ejpam-6048	231	9	.	.	PUNCT
ejpam-6048	232	1	we	we	PRON
ejpam-6048	232	2	can	can	AUX
ejpam-6048	232	3	see	see	VERB
ejpam-6048	232	4	that	that	SCONJ
ejpam-6048	232	5	the	the	DET
ejpam-6048	232	6	independent	independent	ADJ
ejpam-6048	232	7	neighborhood	neighborhood	NOUN
ejpam-6048	232	8	sets	set	NOUN
ejpam-6048	232	9	of	of	ADP
ejpam-6048	232	10	g	g	PROPN
ejpam-6048	232	11	◦	◦	NOUN
ejpam-6048	232	12	h	h	NOUN
ejpam-6048	232	13	are	be	AUX
ejpam-6048	232	14	{	{	PUNCT
ejpam-6048	232	15	1	1	NUM
ejpam-6048	232	16	,	,	PUNCT
ejpam-6048	232	17	2	2	NUM
ejpam-6048	232	18	,	,	PUNCT
ejpam-6048	232	19	4	4	NUM
ejpam-6048	232	20	,	,	PUNCT
ejpam-6048	232	21	a3	a3	NOUN
ejpam-6048	232	22	,	,	PUNCT
ejpam-6048	232	23	b3	b3	PROPN
ejpam-6048	232	24	,	,	PUNCT
ejpam-6048	232	25	c3	c3	PROPN
ejpam-6048	232	26	,	,	PUNCT
ejpam-6048	232	27	a5	a5	PROPN
ejpam-6048	232	28	,	,	PUNCT
ejpam-6048	232	29	b5	b5	PROPN
ejpam-6048	232	30	,	,	PUNCT
ejpam-6048	232	31	c5	c5	PROPN
ejpam-6048	232	32	,	,	PUNCT
ejpam-6048	232	33	a6	a6	NOUN
ejpam-6048	232	34	,	,	PUNCT
ejpam-6048	232	35	b6	b6	NOUN
ejpam-6048	232	36	,	,	PUNCT
ejpam-6048	232	37	c6	c6	PROPN
ejpam-6048	232	38	}	}	PUNCT
ejpam-6048	232	39	,	,	PUNCT
ejpam-6048	232	40	{	{	PUNCT
ejpam-6048	232	41	1	1	NUM
ejpam-6048	232	42	,	,	PUNCT
ejpam-6048	232	43	2	2	NUM
ejpam-6048	232	44	,	,	PUNCT
ejpam-6048	232	45	4	4	NUM
ejpam-6048	232	46	,	,	PUNCT
ejpam-6048	232	47	a3	a3	NOUN
ejpam-6048	232	48	,	,	PUNCT
ejpam-6048	232	49	b3	b3	PROPN
ejpam-6048	232	50	,	,	PUNCT
ejpam-6048	232	51	c3	c3	PROPN
ejpam-6048	232	52	,	,	PUNCT
ejpam-6048	232	53	a5	a5	PROPN
ejpam-6048	232	54	,	,	PUNCT
ejpam-6048	232	55	b5	b5	PROPN
ejpam-6048	232	56	,	,	PUNCT
ejpam-6048	232	57	c5	c5	PROPN
ejpam-6048	232	58	,	,	PUNCT
ejpam-6048	232	59	d6	d6	NOUN
ejpam-6048	232	60	}	}	PUNCT
ejpam-6048	232	61	,	,	PUNCT
ejpam-6048	232	62	{	{	PUNCT
ejpam-6048	232	63	1	1	NUM
ejpam-6048	232	64	,	,	PUNCT
ejpam-6048	232	65	2	2	NUM
ejpam-6048	232	66	,	,	PUNCT
ejpam-6048	232	67	4	4	NUM
ejpam-6048	232	68	,	,	PUNCT
ejpam-6048	232	69	a3	a3	NOUN
ejpam-6048	232	70	,	,	PUNCT
ejpam-6048	232	71	b3	b3	PROPN
ejpam-6048	232	72	,	,	PUNCT
ejpam-6048	232	73	c3	c3	PROPN
ejpam-6048	232	74	,	,	PUNCT
ejpam-6048	232	75	d5	d5	NOUN
ejpam-6048	232	76	,	,	PUNCT
ejpam-6048	232	77	a6	a6	NOUN
ejpam-6048	232	78	,	,	PUNCT
ejpam-6048	232	79	b6	b6	NOUN
ejpam-6048	232	80	,	,	PUNCT
ejpam-6048	232	81	c6	c6	PROPN
ejpam-6048	232	82	}	}	PUNCT
ejpam-6048	232	83	,	,	PUNCT
ejpam-6048	232	84	{	{	PUNCT
ejpam-6048	232	85	1	1	NUM
ejpam-6048	232	86	,	,	PUNCT
ejpam-6048	232	87	2	2	NUM
ejpam-6048	232	88	,	,	PUNCT
ejpam-6048	232	89	4	4	NUM
ejpam-6048	232	90	,	,	PUNCT
ejpam-6048	232	91	a3	a3	NOUN
ejpam-6048	232	92	,	,	PUNCT
ejpam-6048	232	93	b3	b3	PROPN
ejpam-6048	232	94	,	,	PUNCT
ejpam-6048	232	95	c3	c3	NOUN
ejpam-6048	232	96	,	,	PUNCT
ejpam-6048	232	97	d5	d5	NOUN
ejpam-6048	232	98	,	,	PUNCT
ejpam-6048	232	99	d6	d6	NOUN
ejpam-6048	232	100	}	}	PUNCT
ejpam-6048	232	101	,	,	PUNCT
ejpam-6048	232	102	{	{	PUNCT
ejpam-6048	232	103	1	1	NUM
ejpam-6048	232	104	,	,	PUNCT
ejpam-6048	232	105	2	2	NUM
ejpam-6048	232	106	,	,	PUNCT
ejpam-6048	232	107	4	4	NUM
ejpam-6048	232	108	,	,	PUNCT
ejpam-6048	232	109	d3	d3	PROPN
ejpam-6048	232	110	,	,	PUNCT
ejpam-6048	232	111	a5	a5	PROPN
ejpam-6048	232	112	,	,	PUNCT
ejpam-6048	232	113	b5	b5	PROPN
ejpam-6048	232	114	,	,	PUNCT
ejpam-6048	232	115	c5	c5	PROPN
ejpam-6048	232	116	,	,	PUNCT
ejpam-6048	232	117	a6	a6	NOUN
ejpam-6048	232	118	,	,	PUNCT
ejpam-6048	232	119	b6	b6	NOUN
ejpam-6048	232	120	,	,	PUNCT
ejpam-6048	232	121	c6	c6	PROPN
ejpam-6048	232	122	}	}	PUNCT
ejpam-6048	232	123	,	,	PUNCT
ejpam-6048	232	124	{	{	PUNCT
ejpam-6048	232	125	1	1	NUM
ejpam-6048	232	126	,	,	PUNCT
ejpam-6048	232	127	2	2	NUM
ejpam-6048	232	128	,	,	PUNCT
ejpam-6048	232	129	4	4	NUM
ejpam-6048	232	130	,	,	PUNCT
ejpam-6048	232	131	d3	d3	PROPN
ejpam-6048	232	132	,	,	PUNCT
ejpam-6048	232	133	a5	a5	PROPN
ejpam-6048	232	134	,	,	PUNCT
ejpam-6048	232	135	b5	b5	PROPN
ejpam-6048	232	136	,	,	PUNCT
ejpam-6048	232	137	c5	c5	PROPN
ejpam-6048	232	138	,	,	PUNCT
ejpam-6048	232	139	d6	d6	NOUN
ejpam-6048	232	140	}	}	PUNCT
ejpam-6048	232	141	,	,	PUNCT
ejpam-6048	232	142	{	{	PUNCT
ejpam-6048	232	143	1	1	NUM
ejpam-6048	232	144	,	,	PUNCT
ejpam-6048	232	145	2	2	NUM
ejpam-6048	232	146	,	,	PUNCT
ejpam-6048	232	147	4	4	NUM
ejpam-6048	232	148	,	,	PUNCT
ejpam-6048	232	149	d3	d3	PROPN
ejpam-6048	232	150	,	,	PUNCT
ejpam-6048	232	151	d5	d5	NOUN
ejpam-6048	232	152	,	,	PUNCT
ejpam-6048	232	153	a6	a6	NOUN
ejpam-6048	232	154	,	,	PUNCT
ejpam-6048	232	155	b6	b6	NOUN
ejpam-6048	232	156	,	,	PUNCT
ejpam-6048	232	157	c6	c6	PROPN
ejpam-6048	232	158	}	}	PUNCT
ejpam-6048	232	159	,	,	PUNCT
ejpam-6048	232	160	{	{	PUNCT
ejpam-6048	232	161	1	1	NUM
ejpam-6048	232	162	,	,	PUNCT
ejpam-6048	232	163	2	2	NUM
ejpam-6048	232	164	,	,	PUNCT
ejpam-6048	232	165	4	4	NUM
ejpam-6048	232	166	,	,	PUNCT
ejpam-6048	232	167	d3	d3	PROPN
ejpam-6048	232	168	,	,	PUNCT
ejpam-6048	232	169	d5	d5	NOUN
ejpam-6048	232	170	,	,	PUNCT
ejpam-6048	232	171	d6	d6	NOUN
ejpam-6048	232	172	}	}	PUNCT
ejpam-6048	232	173	,	,	PUNCT
ejpam-6048	232	174	{	{	PUNCT
ejpam-6048	232	175	3	3	NUM
ejpam-6048	232	176	,	,	PUNCT
ejpam-6048	232	177	5	5	NUM
ejpam-6048	232	178	,	,	PUNCT
ejpam-6048	232	179	6	6	NUM
ejpam-6048	232	180	,	,	PUNCT
ejpam-6048	232	181	a1	a1	NOUN
ejpam-6048	232	182	,	,	PUNCT
ejpam-6048	232	183	b1	b1	NOUN
ejpam-6048	232	184	,	,	PUNCT
ejpam-6048	232	185	c1	c1	NOUN
ejpam-6048	232	186	,	,	PUNCT
ejpam-6048	232	187	a2	a2	PROPN
ejpam-6048	232	188	,	,	PUNCT
ejpam-6048	232	189	b2	b2	NOUN
ejpam-6048	232	190	,	,	PUNCT
ejpam-6048	232	191	,	,	PUNCT
ejpam-6048	232	192	c2	c2	PROPN
ejpam-6048	232	193	,	,	PUNCT
ejpam-6048	232	194	a4	a4	PROPN
ejpam-6048	232	195	,	,	PUNCT
ejpam-6048	232	196	b4	b4	NOUN
ejpam-6048	232	197	,	,	PUNCT
ejpam-6048	232	198	c4	c4	NOUN
ejpam-6048	232	199	}	}	PUNCT
ejpam-6048	232	200	,	,	PUNCT
ejpam-6048	232	201	{	{	PUNCT
ejpam-6048	232	202	3	3	NUM
ejpam-6048	232	203	,	,	PUNCT
ejpam-6048	232	204	5	5	NUM
ejpam-6048	232	205	,	,	PUNCT
ejpam-6048	232	206	6	6	NUM
ejpam-6048	232	207	,	,	PUNCT
ejpam-6048	232	208	a1	a1	NOUN
ejpam-6048	232	209	,	,	PUNCT
ejpam-6048	232	210	b1	b1	NOUN
ejpam-6048	232	211	,	,	PUNCT
ejpam-6048	232	212	c1	c1	NOUN
ejpam-6048	232	213	,	,	PUNCT
ejpam-6048	232	214	a2	a2	PROPN
ejpam-6048	232	215	,	,	PUNCT
ejpam-6048	232	216	b2	b2	NOUN
ejpam-6048	232	217	,	,	PUNCT
ejpam-6048	232	218	,	,	PUNCT
ejpam-6048	232	219	c2	c2	PROPN
ejpam-6048	232	220	,	,	PUNCT
ejpam-6048	232	221	d4	d4	PROPN
ejpam-6048	232	222	}	}	PUNCT
ejpam-6048	232	223	,	,	PUNCT
ejpam-6048	232	224	{	{	PUNCT
ejpam-6048	232	225	3	3	NUM
ejpam-6048	232	226	,	,	PUNCT
ejpam-6048	232	227	5	5	NUM
ejpam-6048	232	228	,	,	PUNCT
ejpam-6048	232	229	6	6	NUM
ejpam-6048	232	230	,	,	PUNCT
ejpam-6048	232	231	a1	a1	NOUN
ejpam-6048	232	232	,	,	PUNCT
ejpam-6048	232	233	b1	b1	NOUN
ejpam-6048	232	234	,	,	PUNCT
ejpam-6048	232	235	c1	c1	PROPN
ejpam-6048	232	236	,	,	PUNCT
ejpam-6048	232	237	d2	d2	PROPN
ejpam-6048	232	238	,	,	PUNCT
ejpam-6048	232	239	a4	a4	NOUN
ejpam-6048	232	240	,	,	PUNCT
ejpam-6048	232	241	b4	b4	NOUN
ejpam-6048	232	242	,	,	PUNCT
ejpam-6048	232	243	c4	c4	NOUN
ejpam-6048	232	244	}	}	PUNCT
ejpam-6048	232	245	,	,	PUNCT
ejpam-6048	232	246	{	{	PUNCT
ejpam-6048	232	247	3	3	NUM
ejpam-6048	232	248	,	,	PUNCT
ejpam-6048	232	249	5	5	NUM
ejpam-6048	232	250	,	,	PUNCT
ejpam-6048	232	251	6	6	NUM
ejpam-6048	232	252	,	,	PUNCT
ejpam-6048	232	253	a1	a1	NOUN
ejpam-6048	232	254	,	,	PUNCT
ejpam-6048	232	255	b1	b1	NOUN
ejpam-6048	232	256	,	,	PUNCT
ejpam-6048	232	257	c1	c1	PROPN
ejpam-6048	232	258	,	,	PUNCT
ejpam-6048	232	259	d2	d2	PROPN
ejpam-6048	232	260	,	,	PUNCT
ejpam-6048	232	261	d4	d4	PROPN
ejpam-6048	232	262	}	}	PUNCT
ejpam-6048	232	263	,	,	PUNCT
ejpam-6048	232	264	{	{	PUNCT
ejpam-6048	232	265	3	3	NUM
ejpam-6048	232	266	,	,	PUNCT
ejpam-6048	232	267	5	5	NUM
ejpam-6048	232	268	,	,	PUNCT
ejpam-6048	232	269	6	6	NUM
ejpam-6048	232	270	,	,	PUNCT
ejpam-6048	232	271	d1	d1	NOUN
ejpam-6048	232	272	,	,	PUNCT
ejpam-6048	232	273	a2	a2	PROPN
ejpam-6048	232	274	,	,	PUNCT
ejpam-6048	232	275	b2	b2	NOUN
ejpam-6048	232	276	,	,	PUNCT
ejpam-6048	232	277	,	,	PUNCT
ejpam-6048	232	278	c2	c2	PROPN
ejpam-6048	232	279	,	,	PUNCT
ejpam-6048	232	280	a4	a4	PROPN
ejpam-6048	232	281	,	,	PUNCT
ejpam-6048	232	282	b4	b4	NOUN
ejpam-6048	232	283	,	,	PUNCT
ejpam-6048	232	284	c4	c4	NOUN
ejpam-6048	232	285	}	}	PUNCT
ejpam-6048	232	286	,	,	PUNCT
ejpam-6048	232	287	{	{	PUNCT
ejpam-6048	232	288	3	3	NUM
ejpam-6048	232	289	,	,	PUNCT
ejpam-6048	232	290	5	5	NUM
ejpam-6048	232	291	,	,	PUNCT
ejpam-6048	232	292	6	6	NUM
ejpam-6048	232	293	,	,	PUNCT
ejpam-6048	232	294	d1	d1	PROPN
ejpam-6048	232	295	,	,	PUNCT
ejpam-6048	232	296	d2	d2	PROPN
ejpam-6048	232	297	,	,	PUNCT
ejpam-6048	232	298	a4	a4	NOUN
ejpam-6048	232	299	,	,	PUNCT
ejpam-6048	232	300	b4	b4	NOUN
ejpam-6048	232	301	,	,	PUNCT
ejpam-6048	232	302	c4	c4	NOUN
ejpam-6048	232	303	}	}	PUNCT
ejpam-6048	232	304	,	,	PUNCT
ejpam-6048	232	305	{	{	PUNCT
ejpam-6048	232	306	3	3	NUM
ejpam-6048	232	307	,	,	PUNCT
ejpam-6048	232	308	5	5	NUM
ejpam-6048	232	309	,	,	PUNCT
ejpam-6048	232	310	6	6	NUM
ejpam-6048	232	311	,	,	PUNCT
ejpam-6048	232	312	d1	d1	NOUN
ejpam-6048	232	313	,	,	PUNCT
ejpam-6048	232	314	a2	a2	PROPN
ejpam-6048	232	315	,	,	PUNCT
ejpam-6048	232	316	b2	b2	NOUN
ejpam-6048	232	317	,	,	PUNCT
ejpam-6048	232	318	,	,	PUNCT
ejpam-6048	232	319	c2	c2	PROPN
ejpam-6048	232	320	,	,	PUNCT
ejpam-6048	232	321	d4	d4	PROPN
ejpam-6048	232	322	}	}	PUNCT
ejpam-6048	232	323	,	,	PUNCT
ejpam-6048	232	324	{	{	PUNCT
ejpam-6048	232	325	3	3	NUM
ejpam-6048	232	326	,	,	PUNCT
ejpam-6048	232	327	5	5	NUM
ejpam-6048	232	328	,	,	PUNCT
ejpam-6048	232	329	6	6	NUM
ejpam-6048	232	330	,	,	PUNCT
ejpam-6048	232	331	d1	d1	PROPN
ejpam-6048	232	332	,	,	PUNCT
ejpam-6048	232	333	d2	d2	PROPN
ejpam-6048	232	334	,	,	PUNCT
ejpam-6048	232	335	d4	d4	PROPN
ejpam-6048	232	336	}	}	PUNCT
ejpam-6048	232	337	.	.	PUNCT
ejpam-6048	233	1	moreover	moreover	ADV
ejpam-6048	233	2	,	,	PUNCT
ejpam-6048	233	3	by	by	ADP
ejpam-6048	233	4	theorem	theorem	NOUN
ejpam-6048	233	5	6	6	NUM
ejpam-6048	233	6	,	,	PUNCT
ejpam-6048	233	7	ni(g	ni(g	PUNCT
ejpam-6048	233	8	◦	◦	NOUN
ejpam-6048	233	9	h	h	NOUN
ejpam-6048	233	10	,	,	PUNCT
ejpam-6048	233	11	x	x	NOUN
ejpam-6048	233	12	)	)	PUNCT
ejpam-6048	233	13	=	=	SYM
ejpam-6048	233	14	x|∆1|	x|∆1|	PROPN
ejpam-6048	233	15	(	(	PUNCT
ejpam-6048	233	16	x|ω2|	x|ω2|	PROPN
ejpam-6048	234	1	+	+	CCONJ
ejpam-6048	234	2	x|∆2|	x|∆2|	ADJ
ejpam-6048	234	3	)	)	PUNCT
ejpam-6048	234	4	|ω1|	|ω1|	NOUN
ejpam-6048	234	5	+	+	X
ejpam-6048	234	6	x|ω1|	x|ω1|	PUNCT
ejpam-6048	235	1	(	(	PUNCT
ejpam-6048	235	2	x|ω2|	x|ω2|	X
ejpam-6048	236	1	+	+	CCONJ
ejpam-6048	236	2	x|∆2|	x|∆2|	ADJ
ejpam-6048	236	3	)	)	PUNCT
ejpam-6048	236	4	|∆1|	|∆1|	NOUN
ejpam-6048	236	5	=	=	SYM
ejpam-6048	236	6	x3(x+	x3(x+	PROPN
ejpam-6048	236	7	x3)3	x3)3	PROPN
ejpam-6048	237	1	+	+	PROPN
ejpam-6048	238	1	x3(x+	x3(x+	PROPN
ejpam-6048	238	2	x3)3	x3)3	PUNCT
ejpam-6048	238	3	=	=	SYM
ejpam-6048	238	4	2x3(x+	2x3(x+	NUM
ejpam-6048	238	5	x3)3	x3)3	X
ejpam-6048	238	6	=	=	SYM
ejpam-6048	238	7	2x3(x3	2x3(x3	NUM
ejpam-6048	238	8	+	+	CCONJ
ejpam-6048	238	9	3x5	3x5	NUM
ejpam-6048	238	10	+	+	CCONJ
ejpam-6048	238	11	3x7	3x7	NUM
ejpam-6048	238	12	+	+	NUM
ejpam-6048	238	13	x9	x9	NOUN
ejpam-6048	238	14	)	)	PUNCT
ejpam-6048	238	15	=	=	SYM
ejpam-6048	238	16	2x6	2x6	NUM
ejpam-6048	239	1	+	+	CCONJ
ejpam-6048	239	2	6x8	6x8	NUM
ejpam-6048	239	3	+	+	CCONJ
ejpam-6048	239	4	6x10	6x10	NUM
ejpam-6048	239	5	+	+	CCONJ
ejpam-6048	239	6	2x12	2x12	NOUN
ejpam-6048	239	7	.	.	PUNCT
ejpam-6048	240	1	on	on	ADP
ejpam-6048	240	2	the	the	DET
ejpam-6048	240	3	other	other	ADJ
ejpam-6048	240	4	hand	hand	NOUN
ejpam-6048	240	5	,	,	PUNCT
ejpam-6048	240	6	the	the	DET
ejpam-6048	240	7	corona	corona	NOUN
ejpam-6048	240	8	h	h	NOUN
ejpam-6048	240	9	◦	◦	NOUN
ejpam-6048	240	10	g	g	PROPN
ejpam-6048	240	11	is	be	AUX
ejpam-6048	240	12	given	give	VERB
ejpam-6048	240	13	in	in	ADP
ejpam-6048	240	14	figure	figure	NOUN
ejpam-6048	240	15	7	7	NUM
ejpam-6048	240	16	.	.	PUNCT
ejpam-6048	241	1	1a	1a	PROPN
ejpam-6048	241	2	2a	2a	NUM
ejpam-6048	241	3	3a	3a	NUM
ejpam-6048	241	4	4a	4a	NUM
ejpam-6048	241	5	5a	5a	NUM
ejpam-6048	241	6	6a	6a	NOUN
ejpam-6048	241	7	a	a	DET
ejpam-6048	241	8	1b	1b	NUM
ejpam-6048	241	9	2b	2b	NUM
ejpam-6048	241	10	3b	3b	NUM
ejpam-6048	241	11	4b	4b	PROPN
ejpam-6048	241	12	5b	5b	NUM
ejpam-6048	241	13	6b	6b	NUM
ejpam-6048	241	14	b	b	NUM
ejpam-6048	241	15	1c	1c	NUM
ejpam-6048	241	16	2c	2c	NUM
ejpam-6048	241	17	3c	3c	NUM
ejpam-6048	241	18	4c	4c	NOUN
ejpam-6048	241	19	5c	5c	NUM
ejpam-6048	241	20	6c	6c	NOUN
ejpam-6048	241	21	c	c	NOUN
ejpam-6048	241	22	1d	1d	NUM
ejpam-6048	241	23	2d	2d	NOUN
ejpam-6048	241	24	3d	3d	NUM
ejpam-6048	241	25	4d	4d	NUM
ejpam-6048	241	26	5d	5d	NUM
ejpam-6048	241	27	6d	6d	NUM
ejpam-6048	242	1	d	d	X
ejpam-6048	242	2	k1,3	k1,3	X
ejpam-6048	242	3	◦	◦	NOUN
ejpam-6048	242	4	b(2	b(2	PROPN
ejpam-6048	242	5	,	,	PUNCT
ejpam-6048	242	6	2	2	X
ejpam-6048	242	7	)	)	PUNCT
ejpam-6048	242	8	figure	figure	NOUN
ejpam-6048	242	9	7	7	NUM
ejpam-6048	242	10	:	:	PUNCT
ejpam-6048	242	11	the	the	DET
ejpam-6048	242	12	graph	graph	NOUN
ejpam-6048	242	13	k1,3	k1,3	VERB
ejpam-6048	242	14	◦	◦	NOUN
ejpam-6048	242	15	b(2	b(2	PROPN
ejpam-6048	242	16	,	,	PUNCT
ejpam-6048	242	17	2	2	NUM
ejpam-6048	242	18	)	)	PUNCT
ejpam-6048	242	19	we	we	PRON
ejpam-6048	242	20	can	can	AUX
ejpam-6048	242	21	see	see	VERB
ejpam-6048	242	22	that	that	SCONJ
ejpam-6048	242	23	the	the	DET
ejpam-6048	242	24	independent	independent	ADJ
ejpam-6048	242	25	neighborhhood	neighborhhood	PROPN
ejpam-6048	242	26	sets	set	VERB
ejpam-6048	242	27	ofk1,3	ofk1,3	NOUN
ejpam-6048	242	28	◦	◦	NOUN
ejpam-6048	242	29	b(2	b(2	PROPN
ejpam-6048	242	30	,	,	PUNCT
ejpam-6048	242	31	2	2	NUM
ejpam-6048	242	32	)	)	PUNCT
ejpam-6048	242	33	are	be	AUX
ejpam-6048	242	34	{	{	PUNCT
ejpam-6048	242	35	a	a	DET
ejpam-6048	242	36	,	,	PUNCT
ejpam-6048	242	37	b	b	NOUN
ejpam-6048	242	38	,	,	PUNCT
ejpam-6048	242	39	c	c	NOUN
ejpam-6048	242	40	,	,	PUNCT
ejpam-6048	242	41	1d	1d	NUM
ejpam-6048	242	42	,	,	PUNCT
ejpam-6048	242	43	2d	2d	NOUN
ejpam-6048	242	44	,	,	PUNCT
ejpam-6048	242	45	4d	4d	NUM
ejpam-6048	242	46	}	}	PUNCT
ejpam-6048	242	47	,	,	PUNCT
ejpam-6048	242	48	{	{	PUNCT
ejpam-6048	242	49	a	a	PRON
ejpam-6048	242	50	,	,	PUNCT
ejpam-6048	242	51	b	b	NOUN
ejpam-6048	242	52	,	,	PUNCT
ejpam-6048	242	53	c	c	NOUN
ejpam-6048	242	54	,	,	PUNCT
ejpam-6048	242	55	3d	3d	NUM
ejpam-6048	242	56	,	,	PUNCT
ejpam-6048	242	57	5d	5d	NUM
ejpam-6048	242	58	,	,	PUNCT
ejpam-6048	242	59	6d	6d	NUM
ejpam-6048	242	60	}	}	PUNCT
ejpam-6048	242	61	,	,	PUNCT
ejpam-6048	242	62	{	{	PUNCT
ejpam-6048	242	63	d	d	NOUN
ejpam-6048	242	64	,	,	PUNCT
ejpam-6048	242	65	1a	1a	NUM
ejpam-6048	242	66	,	,	PUNCT
ejpam-6048	242	67	2a	2a	NUM
ejpam-6048	242	68	,	,	PUNCT
ejpam-6048	242	69	4a	4a	NUM
ejpam-6048	242	70	,	,	PUNCT
ejpam-6048	242	71	1b	1b	NUM
ejpam-6048	242	72	,	,	PUNCT
ejpam-6048	242	73	2b	2b	NUM
ejpam-6048	242	74	,	,	PUNCT
ejpam-6048	242	75	4b	4b	NOUN
ejpam-6048	242	76	,	,	PUNCT
ejpam-6048	242	77	1c	1c	NOUN
ejpam-6048	242	78	,	,	PUNCT
ejpam-6048	242	79	2c	2c	NUM
ejpam-6048	242	80	,	,	PUNCT
ejpam-6048	242	81	4c	4c	NOUN
ejpam-6048	242	82	}	}	PUNCT
ejpam-6048	242	83	,	,	PUNCT
ejpam-6048	242	84	{	{	PUNCT
ejpam-6048	242	85	d	d	NOUN
ejpam-6048	242	86	,	,	PUNCT
ejpam-6048	242	87	1a	1a	NUM
ejpam-6048	242	88	,	,	PUNCT
ejpam-6048	242	89	2a	2a	NUM
ejpam-6048	242	90	,	,	PUNCT
ejpam-6048	242	91	4a	4a	NUM
ejpam-6048	242	92	,	,	PUNCT
ejpam-6048	242	93	1b	1b	NUM
ejpam-6048	242	94	,	,	PUNCT
ejpam-6048	242	95	2b	2b	NUM
ejpam-6048	242	96	,	,	PUNCT
ejpam-6048	242	97	4b	4b	X
ejpam-6048	242	98	,	,	PUNCT
ejpam-6048	242	99	3c	3c	NUM
ejpam-6048	242	100	,	,	PUNCT
ejpam-6048	242	101	5c	5c	NUM
ejpam-6048	242	102	,	,	PUNCT
ejpam-6048	242	103	6c	6c	NOUN
ejpam-6048	242	104	}	}	PUNCT
ejpam-6048	242	105	,	,	PUNCT
ejpam-6048	242	106	{	{	PUNCT
ejpam-6048	242	107	d	d	NOUN
ejpam-6048	242	108	,	,	PUNCT
ejpam-6048	242	109	1a	1a	NUM
ejpam-6048	242	110	,	,	PUNCT
ejpam-6048	242	111	2a	2a	NUM
ejpam-6048	242	112	,	,	PUNCT
ejpam-6048	242	113	4a	4a	NUM
ejpam-6048	242	114	,	,	PUNCT
ejpam-6048	242	115	3b	3b	NUM
ejpam-6048	242	116	,	,	PUNCT
ejpam-6048	242	117	5b	5b	NUM
ejpam-6048	242	118	,	,	PUNCT
ejpam-6048	242	119	6b	6b	NOUN
ejpam-6048	242	120	,	,	PUNCT
ejpam-6048	242	121	1c	1c	NOUN
ejpam-6048	242	122	,	,	PUNCT
ejpam-6048	242	123	2c	2c	NUM
ejpam-6048	242	124	,	,	PUNCT
ejpam-6048	242	125	4c	4c	NOUN
ejpam-6048	242	126	}	}	PUNCT
ejpam-6048	242	127	,	,	PUNCT
ejpam-6048	242	128	{	{	PUNCT
ejpam-6048	242	129	d	d	NOUN
ejpam-6048	242	130	,	,	PUNCT
ejpam-6048	242	131	1a	1a	NUM
ejpam-6048	242	132	,	,	PUNCT
ejpam-6048	242	133	2a	2a	NUM
ejpam-6048	242	134	,	,	PUNCT
ejpam-6048	242	135	4a	4a	NUM
ejpam-6048	242	136	,	,	PUNCT
ejpam-6048	242	137	3b	3b	NUM
ejpam-6048	242	138	,	,	PUNCT
ejpam-6048	242	139	5b	5b	NUM
ejpam-6048	242	140	,	,	PUNCT
ejpam-6048	242	141	6b	6b	NUM
ejpam-6048	242	142	,	,	PUNCT
ejpam-6048	242	143	3c	3c	NUM
ejpam-6048	242	144	,	,	PUNCT
ejpam-6048	242	145	5c	5c	NUM
ejpam-6048	242	146	,	,	PUNCT
ejpam-6048	242	147	6c	6c	NOUN
ejpam-6048	242	148	}	}	PUNCT
ejpam-6048	242	149	,	,	PUNCT
ejpam-6048	242	150	{	{	PUNCT
ejpam-6048	242	151	d	d	NOUN
ejpam-6048	242	152	,	,	PUNCT
ejpam-6048	242	153	3a	3a	NUM
ejpam-6048	242	154	,	,	PUNCT
ejpam-6048	242	155	5a	5a	NUM
ejpam-6048	242	156	,	,	PUNCT
ejpam-6048	242	157	6a	6a	NOUN
ejpam-6048	242	158	,	,	PUNCT
ejpam-6048	242	159	1b	1b	NUM
ejpam-6048	242	160	,	,	PUNCT
ejpam-6048	242	161	2b	2b	NUM
ejpam-6048	242	162	,	,	PUNCT
ejpam-6048	242	163	4b	4b	NOUN
ejpam-6048	242	164	,	,	PUNCT
ejpam-6048	242	165	1c	1c	NOUN
ejpam-6048	242	166	,	,	PUNCT
ejpam-6048	242	167	2c	2c	NUM
ejpam-6048	242	168	,	,	PUNCT
ejpam-6048	242	169	4c	4c	NOUN
ejpam-6048	242	170	}	}	PUNCT
ejpam-6048	242	171	,	,	PUNCT
ejpam-6048	242	172	{	{	PUNCT
ejpam-6048	242	173	d	d	NOUN
ejpam-6048	242	174	,	,	PUNCT
ejpam-6048	242	175	3a	3a	NUM
ejpam-6048	242	176	,	,	PUNCT
ejpam-6048	242	177	5a	5a	NUM
ejpam-6048	242	178	,	,	PUNCT
ejpam-6048	242	179	6a	6a	NOUN
ejpam-6048	242	180	,	,	PUNCT
ejpam-6048	242	181	1b	1b	NUM
ejpam-6048	242	182	,	,	PUNCT
ejpam-6048	242	183	2b	2b	NUM
ejpam-6048	242	184	,	,	PUNCT
ejpam-6048	242	185	4b	4b	X
ejpam-6048	242	186	,	,	PUNCT
ejpam-6048	242	187	3c	3c	NUM
ejpam-6048	242	188	,	,	PUNCT
ejpam-6048	242	189	5c	5c	NUM
ejpam-6048	242	190	,	,	PUNCT
ejpam-6048	242	191	6c	6c	NOUN
ejpam-6048	242	192	}	}	PUNCT
ejpam-6048	242	193	,	,	PUNCT
ejpam-6048	242	194	{	{	PUNCT
ejpam-6048	242	195	d	d	NOUN
ejpam-6048	242	196	,	,	PUNCT
ejpam-6048	242	197	3a	3a	NUM
ejpam-6048	242	198	,	,	PUNCT
ejpam-6048	242	199	5a	5a	NUM
ejpam-6048	242	200	,	,	PUNCT
ejpam-6048	242	201	6a	6a	NOUN
ejpam-6048	242	202	,	,	PUNCT
ejpam-6048	242	203	3b	3b	NUM
ejpam-6048	242	204	,	,	PUNCT
ejpam-6048	242	205	5b	5b	NUM
ejpam-6048	242	206	,	,	PUNCT
ejpam-6048	242	207	6b	6b	NOUN
ejpam-6048	242	208	,	,	PUNCT
ejpam-6048	242	209	1c	1c	NOUN
ejpam-6048	242	210	,	,	PUNCT
ejpam-6048	242	211	2c	2c	NUM
ejpam-6048	242	212	,	,	PUNCT
ejpam-6048	242	213	4c	4c	NOUN
ejpam-6048	242	214	}	}	PUNCT
ejpam-6048	242	215	,	,	PUNCT
ejpam-6048	242	216	{	{	PUNCT
ejpam-6048	242	217	d	d	NOUN
ejpam-6048	242	218	,	,	PUNCT
ejpam-6048	242	219	3a	3a	NUM
ejpam-6048	242	220	,	,	PUNCT
ejpam-6048	242	221	5a	5a	NUM
ejpam-6048	242	222	,	,	PUNCT
ejpam-6048	242	223	6a	6a	NOUN
ejpam-6048	242	224	,	,	PUNCT
ejpam-6048	242	225	3b	3b	NUM
ejpam-6048	242	226	,	,	PUNCT
ejpam-6048	242	227	5b	5b	NUM
ejpam-6048	242	228	,	,	PUNCT
ejpam-6048	242	229	6b	6b	NUM
ejpam-6048	242	230	,	,	PUNCT
ejpam-6048	242	231	3c	3c	NUM
ejpam-6048	242	232	,	,	PUNCT
ejpam-6048	242	233	5c	5c	NUM
ejpam-6048	242	234	,	,	PUNCT
ejpam-6048	242	235	6c	6c	NUM
ejpam-6048	242	236	}	}	PUNCT
ejpam-6048	242	237	.	.	PUNCT
ejpam-6048	243	1	by	by	ADP
ejpam-6048	243	2	theorem	theorem	NOUN
ejpam-6048	243	3	6	6	NUM
ejpam-6048	243	4	,	,	PUNCT
ejpam-6048	243	5	ni(k1,3	ni(k1,3	PROPN
ejpam-6048	243	6	◦	◦	PROPN
ejpam-6048	243	7	b(2	b(2	PROPN
ejpam-6048	243	8	,	,	PUNCT
ejpam-6048	243	9	2	2	NUM
ejpam-6048	243	10	)	)	PUNCT
ejpam-6048	243	11	)	)	PUNCT
ejpam-6048	244	1	=	=	PUNCT
ejpam-6048	245	1	x3(x3	x3(x3	PROPN
ejpam-6048	245	2	+	+	CCONJ
ejpam-6048	245	3	x3	x3	ADJ
ejpam-6048	245	4	)	)	PUNCT
ejpam-6048	246	1	+	+	CCONJ
ejpam-6048	246	2	x(x3	x(x3	PUNCT
ejpam-6048	247	1	+	+	CCONJ
ejpam-6048	247	2	x3)3	x3)3	PROPN
ejpam-6048	247	3	n.	n.	PROPN
ejpam-6048	247	4	abdulcarim	abdulcarim	PROPN
ejpam-6048	247	5	,	,	PUNCT
ejpam-6048	247	6	s.	s.	PROPN
ejpam-6048	247	7	dagondon	dagondon	PROPN
ejpam-6048	247	8	/	/	SYM
ejpam-6048	247	9	eur	eur	PROPN
ejpam-6048	247	10	.	.	PUNCT
ejpam-6048	248	1	j.	j.	PROPN
ejpam-6048	248	2	pure	pure	PROPN
ejpam-6048	248	3	appl	appl	PROPN
ejpam-6048	248	4	.	.	PROPN
ejpam-6048	248	5	math	math	PROPN
ejpam-6048	248	6	,	,	PUNCT
ejpam-6048	248	7	18	18	NUM
ejpam-6048	248	8	(	(	PUNCT
ejpam-6048	248	9	3	3	NUM
ejpam-6048	248	10	)	)	PUNCT
ejpam-6048	248	11	(	(	PUNCT
ejpam-6048	248	12	2025	2025	NUM
ejpam-6048	248	13	)	)	PUNCT
ejpam-6048	248	14	,	,	PUNCT
ejpam-6048	248	15	6048	6048	NUM
ejpam-6048	248	16	13	13	NUM
ejpam-6048	248	17	of	of	ADP
ejpam-6048	248	18	14	14	NUM
ejpam-6048	248	19	=	=	SYM
ejpam-6048	248	20	x3(2x3	x3(2x3	NUM
ejpam-6048	248	21	)	)	PUNCT
ejpam-6048	249	1	+	+	CCONJ
ejpam-6048	249	2	x(2x3)3	x(2x3)3	PROPN
ejpam-6048	249	3	=	=	SYM
ejpam-6048	249	4	2x6	2x6	PUNCT
ejpam-6048	250	1	+	+	NUM
ejpam-6048	250	2	8x10	8x10	NUM
ejpam-6048	250	3	.	.	PUNCT
ejpam-6048	251	1	theorem	theorem	VERB
ejpam-6048	251	2	7	7	NUM
ejpam-6048	251	3	.	.	X
ejpam-6048	251	4	for	for	ADP
ejpam-6048	251	5	any	any	DET
ejpam-6048	251	6	trees	tree	NOUN
ejpam-6048	251	7	g	g	NOUN
ejpam-6048	251	8	and	and	CCONJ
ejpam-6048	251	9	h	h	NOUN
ejpam-6048	251	10	,	,	PUNCT
ejpam-6048	251	11	if	if	SCONJ
ejpam-6048	251	12	g	g	PROPN
ejpam-6048	251	13	∼=	∼=	PROPN
ejpam-6048	251	14	h	h	NOUN
ejpam-6048	251	15	,	,	PUNCT
ejpam-6048	251	16	then	then	ADV
ejpam-6048	251	17	ni(g	ni(g	PUNCT
ejpam-6048	251	18	◦	◦	NOUN
ejpam-6048	251	19	h	h	NOUN
ejpam-6048	251	20	,	,	PUNCT
ejpam-6048	251	21	x	x	NOUN
ejpam-6048	251	22	)	)	PUNCT
ejpam-6048	251	23	=	=	PRON
ejpam-6048	251	24	ni(h	ni(h	VERB
ejpam-6048	251	25	◦	◦	NOUN
ejpam-6048	251	26	g	g	NOUN
ejpam-6048	251	27	,	,	PUNCT
ejpam-6048	251	28	x	x	NOUN
ejpam-6048	251	29	)	)	PUNCT
ejpam-6048	251	30	.	.	PUNCT
ejpam-6048	252	1	proof	proof	NOUN
ejpam-6048	252	2	.	.	PUNCT
ejpam-6048	253	1	let	let	VERB
ejpam-6048	253	2	g	g	NOUN
ejpam-6048	253	3	and	and	CCONJ
ejpam-6048	253	4	h	h	NOUN
ejpam-6048	253	5	be	be	VERB
ejpam-6048	253	6	any	any	DET
ejpam-6048	253	7	trees	tree	NOUN
ejpam-6048	253	8	.	.	PUNCT
ejpam-6048	254	1	suppose	suppose	VERB
ejpam-6048	254	2	g	g	PROPN
ejpam-6048	254	3	∼=	∼=	PROPN
ejpam-6048	254	4	h.	h.	NOUN
ejpam-6048	254	5	then	then	ADV
ejpam-6048	254	6	g	g	PROPN
ejpam-6048	254	7	and	and	CCONJ
ejpam-6048	254	8	h	h	NOUN
ejpam-6048	254	9	has	have	AUX
ejpam-6048	254	10	indepedent	indepedent	ADJ
ejpam-6048	254	11	neighborhood	neighborhood	NOUN
ejpam-6048	254	12	sets	set	VERB
ejpam-6048	254	13	ω1,∆1	ω1,∆1	NUM
ejpam-6048	254	14	and	and	CCONJ
ejpam-6048	254	15	ω2,∆2	ω2,∆2	PROPN
ejpam-6048	254	16	,	,	PUNCT
ejpam-6048	254	17	respectively	respectively	ADV
ejpam-6048	254	18	.	.	PUNCT
ejpam-6048	255	1	since	since	SCONJ
ejpam-6048	255	2	g	g	PROPN
ejpam-6048	255	3	∼=	∼=	PROPN
ejpam-6048	255	4	h	h	NOUN
ejpam-6048	255	5	,	,	PUNCT
ejpam-6048	255	6	either	either	CCONJ
ejpam-6048	255	7	|ω1|	|ω1|	NOUN
ejpam-6048	255	8	=	=	SYM
ejpam-6048	255	9	|ω2|	|ω2|	NOUN
ejpam-6048	255	10	and	and	CCONJ
ejpam-6048	255	11	|∆1|	|∆1|	NOUN
ejpam-6048	255	12	=	=	SYM
ejpam-6048	255	13	|∆2|	|∆2|	NOUN
ejpam-6048	255	14	or	or	CCONJ
ejpam-6048	255	15	|ω1|	|ω1|	NOUN
ejpam-6048	255	16	=	=	SYM
ejpam-6048	255	17	|∆2|	|∆2|	NOUN
ejpam-6048	255	18	and	and	CCONJ
ejpam-6048	255	19	|∆1|	|∆1|	NOUN
ejpam-6048	255	20	=	=	NOUN
ejpam-6048	255	21	|ω2|	|ω2|	NOUN
ejpam-6048	255	22	.	.	PUNCT
ejpam-6048	256	1	without	without	ADP
ejpam-6048	256	2	loss	loss	NOUN
ejpam-6048	256	3	of	of	ADP
ejpam-6048	256	4	generality	generality	NOUN
ejpam-6048	256	5	,	,	PUNCT
ejpam-6048	256	6	assume	assume	VERB
ejpam-6048	256	7	|ω1|	|ω1|	NOUN
ejpam-6048	256	8	=	=	SYM
ejpam-6048	256	9	|ω2|	|ω2|	NOUN
ejpam-6048	256	10	and	and	CCONJ
ejpam-6048	256	11	|∆1|	|∆1|	NOUN
ejpam-6048	256	12	=	=	NOUN
ejpam-6048	256	13	|∆2|	|∆2|	ADJ
ejpam-6048	256	14	.	.	PUNCT
ejpam-6048	257	1	thus	thus	ADV
ejpam-6048	257	2	,	,	PUNCT
ejpam-6048	257	3	ni(g	ni(g	PUNCT
ejpam-6048	257	4	◦	◦	NOUN
ejpam-6048	257	5	h	h	NOUN
ejpam-6048	257	6	,	,	PUNCT
ejpam-6048	257	7	x	x	NOUN
ejpam-6048	257	8	)	)	PUNCT
ejpam-6048	257	9	=	=	SYM
ejpam-6048	257	10	x|∆1|	x|∆1|	PROPN
ejpam-6048	257	11	(	(	PUNCT
ejpam-6048	257	12	x|ω2|	x|ω2|	PROPN
ejpam-6048	258	1	+	+	CCONJ
ejpam-6048	258	2	x|∆2|	x|∆2|	ADJ
ejpam-6048	258	3	)	)	PUNCT
ejpam-6048	258	4	|ω1|	|ω1|	NOUN
ejpam-6048	258	5	+	+	X
ejpam-6048	258	6	x|ω1|	x|ω1|	PUNCT
ejpam-6048	259	1	(	(	PUNCT
ejpam-6048	259	2	x|ω2|	x|ω2|	X
ejpam-6048	260	1	+	+	CCONJ
ejpam-6048	260	2	x|∆2|	x|∆2|	ADJ
ejpam-6048	260	3	)	)	PUNCT
ejpam-6048	260	4	|∆1|	|∆1|	NOUN
ejpam-6048	260	5	=	=	SYM
ejpam-6048	260	6	x|∆2|	x|∆2|	PROPN
ejpam-6048	260	7	(	(	PUNCT
ejpam-6048	260	8	x|ω1|	x|ω1|	PROPN
ejpam-6048	261	1	+	+	CCONJ
ejpam-6048	261	2	x|∆1|	x|∆1|	PROPN
ejpam-6048	261	3	)	)	PUNCT
ejpam-6048	261	4	|ω2|	|ω2|	PROPN
ejpam-6048	261	5	+	+	X
ejpam-6048	261	6	x|ω2|	x|ω2|	PROPN
ejpam-6048	261	7	(	(	PUNCT
ejpam-6048	261	8	x|ω1|	x|ω1|	PROPN
ejpam-6048	262	1	+	+	CCONJ
ejpam-6048	262	2	x|∆1|	x|∆1|	PROPN
ejpam-6048	262	3	)	)	PUNCT
ejpam-6048	262	4	|∆2|	|∆2|	PROPN
ejpam-6048	262	5	=	=	PUNCT
ejpam-6048	262	6	ni(h	ni(h	X
ejpam-6048	262	7	◦	◦	NOUN
ejpam-6048	262	8	g	g	NOUN
ejpam-6048	262	9	,	,	PUNCT
ejpam-6048	262	10	x	x	NOUN
ejpam-6048	262	11	)	)	PUNCT
ejpam-6048	262	12	.	.	PUNCT
ejpam-6048	263	1	example	example	NOUN
ejpam-6048	264	1	7	7	X
ejpam-6048	264	2	.	.	X
ejpam-6048	265	1	consider	consider	VERB
ejpam-6048	265	2	the	the	DET
ejpam-6048	265	3	corona	corona	NOUN
ejpam-6048	265	4	of	of	ADP
ejpam-6048	265	5	k1,4	k1,4	PROPN
ejpam-6048	265	6	to	to	ADP
ejpam-6048	265	7	itself	itself	PRON
ejpam-6048	265	8	as	as	SCONJ
ejpam-6048	265	9	shown	show	VERB
ejpam-6048	265	10	in	in	ADP
ejpam-6048	265	11	figure	figure	NOUN
ejpam-6048	265	12	8	8	NUM
ejpam-6048	265	13	.	.	NOUN
ejpam-6048	265	14	1	1	NUM
ejpam-6048	265	15	2	2	NUM
ejpam-6048	265	16	3	3	NUM
ejpam-6048	265	17	4	4	NUM
ejpam-6048	265	18	0	0	NUM
ejpam-6048	265	19	k1,4	k1,4	NOUN
ejpam-6048	265	20	:	:	PUNCT
ejpam-6048	265	21	b	b	X
ejpam-6048	265	22	c	c	X
ejpam-6048	265	23	d	d	X
ejpam-6048	265	24	e	e	PROPN
ejpam-6048	265	25	a	a	DET
ejpam-6048	265	26	k1,4	k1,4	PROPN
ejpam-6048	265	27	:	:	PUNCT
ejpam-6048	265	28	b1	b1	PROPN
ejpam-6048	265	29	c1	c1	PROPN
ejpam-6048	265	30	d1	d1	PROPN
ejpam-6048	265	31	e1	e1	PROPN
ejpam-6048	265	32	a1	a1	NOUN
ejpam-6048	265	33	1	1	NUM
ejpam-6048	265	34	b2	b2	NOUN
ejpam-6048	265	35	c2	c2	PROPN
ejpam-6048	265	36	d2	d2	PROPN
ejpam-6048	265	37	e2	e2	PROPN
ejpam-6048	265	38	a2	a2	PROPN
ejpam-6048	265	39	2	2	NUM
ejpam-6048	265	40	b3	b3	PROPN
ejpam-6048	265	41	c3	c3	PROPN
ejpam-6048	265	42	d3	d3	PROPN
ejpam-6048	265	43	e3	e3	PROPN
ejpam-6048	265	44	a3	a3	NOUN
ejpam-6048	265	45	3	3	NUM
ejpam-6048	265	46	b4	b4	NOUN
ejpam-6048	265	47	c4	c4	NOUN
ejpam-6048	265	48	d4	d4	PROPN
ejpam-6048	265	49	e4	e4	PROPN
ejpam-6048	265	50	a4	a4	PROPN
ejpam-6048	265	51	4	4	NUM
ejpam-6048	265	52	b0	b0	NOUN
ejpam-6048	265	53	c0	c0	PROPN
ejpam-6048	265	54	d0	d0	PROPN
ejpam-6048	265	55	e0	e0	PROPN
ejpam-6048	265	56	a0	a0	PROPN
ejpam-6048	265	57	0	0	NUM
ejpam-6048	266	1	k1,4	k1,4	PROPN
ejpam-6048	266	2	◦	◦	PROPN
ejpam-6048	266	3	k1,4	k1,4	PROPN
ejpam-6048	266	4	figure	figure	NOUN
ejpam-6048	266	5	8	8	NUM
ejpam-6048	266	6	:	:	PUNCT
ejpam-6048	266	7	the	the	DET
ejpam-6048	266	8	graph	graph	NOUN
ejpam-6048	266	9	k1,4	k1,4	PROPN
ejpam-6048	266	10	◦	◦	NOUN
ejpam-6048	266	11	k1,4	k1,4	NOUN
ejpam-6048	266	12	by	by	ADP
ejpam-6048	266	13	proposition	proposition	NOUN
ejpam-6048	266	14	2	2	NUM
ejpam-6048	266	15	,	,	PUNCT
ejpam-6048	266	16	k1,4	k1,4	PROPN
ejpam-6048	266	17	has	have	VERB
ejpam-6048	266	18	independent	independent	ADJ
ejpam-6048	266	19	neighborhood	neighborhood	NOUN
ejpam-6048	266	20	sets	set	NOUN
ejpam-6048	266	21	of	of	ADP
ejpam-6048	266	22	cardinalities	cardinality	NOUN
ejpam-6048	266	23	1	1	NUM
ejpam-6048	266	24	and	and	CCONJ
ejpam-6048	266	25	4	4	NUM
ejpam-6048	266	26	,	,	PUNCT
ejpam-6048	266	27	n.	n.	PROPN
ejpam-6048	266	28	abdulcarim	abdulcarim	PROPN
ejpam-6048	266	29	,	,	PUNCT
ejpam-6048	266	30	s.	s.	PROPN
ejpam-6048	266	31	dagondon	dagondon	PROPN
ejpam-6048	266	32	/	/	SYM
ejpam-6048	266	33	eur	eur	PROPN
ejpam-6048	266	34	.	.	PUNCT
ejpam-6048	267	1	j.	j.	PROPN
ejpam-6048	267	2	pure	pure	PROPN
ejpam-6048	267	3	appl	appl	PROPN
ejpam-6048	267	4	.	.	PROPN
ejpam-6048	267	5	math	math	PROPN
ejpam-6048	267	6	,	,	PUNCT
ejpam-6048	267	7	18	18	NUM
ejpam-6048	267	8	(	(	PUNCT
ejpam-6048	267	9	3	3	NUM
ejpam-6048	267	10	)	)	PUNCT
ejpam-6048	267	11	(	(	PUNCT
ejpam-6048	267	12	2025	2025	NUM
ejpam-6048	267	13	)	)	PUNCT
ejpam-6048	267	14	,	,	PUNCT
ejpam-6048	267	15	6048	6048	NUM
ejpam-6048	267	16	14	14	NUM
ejpam-6048	267	17	of	of	ADP
ejpam-6048	267	18	14	14	NUM
ejpam-6048	267	19	respectively	respectively	ADV
ejpam-6048	267	20	.	.	PUNCT
ejpam-6048	268	1	this	this	PRON
ejpam-6048	268	2	implies	imply	VERB
ejpam-6048	268	3	|ω1|	|ω1|	NOUN
ejpam-6048	268	4	=	=	SYM
ejpam-6048	268	5	1	1	NUM
ejpam-6048	268	6	,	,	PUNCT
ejpam-6048	268	7	|∆1|	|∆1|	NOUN
ejpam-6048	268	8	=	=	SYM
ejpam-6048	268	9	4	4	NUM
ejpam-6048	268	10	,	,	PUNCT
ejpam-6048	268	11	|ω2|	|ω2|	NOUN
ejpam-6048	268	12	=	=	SYM
ejpam-6048	268	13	1	1	NUM
ejpam-6048	268	14	,	,	PUNCT
ejpam-6048	268	15	and	and	CCONJ
ejpam-6048	268	16	|∆2|	|∆2|	ADJ
ejpam-6048	268	17	=	=	SYM
ejpam-6048	268	18	4	4	X
ejpam-6048	268	19	.	.	PUNCT
ejpam-6048	268	20	therefore	therefore	ADV
ejpam-6048	268	21	,	,	PUNCT
ejpam-6048	268	22	ni(k1,4	ni(k1,4	ADV
ejpam-6048	268	23	◦	◦	VERB
ejpam-6048	268	24	k1,4	k1,4	PROPN
ejpam-6048	268	25	,	,	PUNCT
ejpam-6048	268	26	x	x	X
ejpam-6048	268	27	)	)	PUNCT
ejpam-6048	268	28	=	=	PUNCT
ejpam-6048	269	1	x1(x+	x1(x+	PUNCT
ejpam-6048	269	2	x4)4	x4)4	X
ejpam-6048	270	1	+	+	CCONJ
ejpam-6048	271	1	x4(x+	x4(x+	PROPN
ejpam-6048	271	2	x4)1	x4)1	PUNCT
ejpam-6048	272	1	=	=	NOUN
ejpam-6048	272	2	x(x4	x(x4	X
ejpam-6048	272	3	+	+	SYM
ejpam-6048	272	4	4x3	4x3	NUM
ejpam-6048	272	5	·	·	PUNCT
ejpam-6048	272	6	x4	x4	X
ejpam-6048	273	1	+	+	CCONJ
ejpam-6048	273	2	6x2	6x2	NUM
ejpam-6048	273	3	·	·	PUNCT
ejpam-6048	273	4	x8	x8	NOUN
ejpam-6048	273	5	+	+	CCONJ
ejpam-6048	273	6	4x	4x	NOUN
ejpam-6048	273	7	·	·	PUNCT
ejpam-6048	273	8	x12	x12	NUM
ejpam-6048	274	1	+	+	CCONJ
ejpam-6048	274	2	x16	x16	NOUN
ejpam-6048	274	3	)	)	PUNCT
ejpam-6048	275	1	+	+	NUM
ejpam-6048	275	2	x5	x5	NOUN
ejpam-6048	275	3	+	+	NUM
ejpam-6048	275	4	x8	x8	NOUN
ejpam-6048	275	5	=	=	SYM
ejpam-6048	275	6	2x5	2x5	NUM
ejpam-6048	275	7	+	+	CCONJ
ejpam-6048	275	8	5x8	5x8	NUM
ejpam-6048	276	1	+	+	CCONJ
ejpam-6048	276	2	6x11	6x11	NUM
ejpam-6048	276	3	+	+	CCONJ
ejpam-6048	276	4	4x14	4x14	PROPN
ejpam-6048	277	1	+	+	CCONJ
ejpam-6048	277	2	x17	x17	ADJ
ejpam-6048	277	3	.	.	PUNCT
ejpam-6048	278	1	acknowledgements	acknowledgement	NOUN
ejpam-6048	278	2	this	this	DET
ejpam-6048	278	3	research	research	NOUN
ejpam-6048	278	4	is	be	AUX
ejpam-6048	278	5	funded	fund	VERB
ejpam-6048	278	6	by	by	ADP
ejpam-6048	278	7	the	the	DET
ejpam-6048	278	8	department	department	PROPN
ejpam-6048	278	9	of	of	ADP
ejpam-6048	278	10	science	science	NOUN
ejpam-6048	278	11	and	and	CCONJ
ejpam-6048	278	12	technology	technology	NOUN
ejpam-6048	278	13	(	(	PUNCT
ejpam-6048	278	14	dost	dost	NOUN
ejpam-6048	278	15	)	)	PUNCT
ejpam-6048	278	16	,	,	PUNCT
ejpam-6048	278	17	mindanao	mindanao	PROPN
ejpam-6048	278	18	state	state	PROPN
ejpam-6048	278	19	university	university	PROPN
ejpam-6048	278	20	iligan	iligan	PROPN
ejpam-6048	278	21	institute	institute	PROPN
ejpam-6048	278	22	of	of	ADP
ejpam-6048	278	23	technology	technology	PROPN
ejpam-6048	278	24	,	,	PUNCT
ejpam-6048	278	25	and	and	CCONJ
ejpam-6048	278	26	the	the	DET
ejpam-6048	278	27	mindanao	mindanao	PROPN
ejpam-6048	278	28	state	state	PROPN
ejpam-6048	278	29	university	university	PROPN
ejpam-6048	278	30	main	main	ADJ
ejpam-6048	278	31	campus	campus	NOUN
ejpam-6048	278	32	,	,	PUNCT
ejpam-6048	278	33	marawi	marawi	PROPN
ejpam-6048	278	34	city	city	PROPN
ejpam-6048	278	35	.	.	PUNCT
ejpam-6048	279	1	references	reference	NOUN
ejpam-6048	279	2	[	[	X
ejpam-6048	279	3	1	1	NUM
ejpam-6048	279	4	]	]	X
ejpam-6048	279	5	j.i	j.i	PROPN
ejpam-6048	279	6	.	.	PROPN
ejpam-6048	279	7	brown	brown	PROPN
ejpam-6048	279	8	and	and	CCONJ
ejpam-6048	279	9	r.j	r.j	PROPN
ejpam-6048	279	10	.	.	PROPN
ejpam-6048	279	11	nowakowski	nowakowski	PROPN
ejpam-6048	279	12	.	.	PUNCT
ejpam-6048	280	1	the	the	DET
ejpam-6048	280	2	neighbourhood	neighbourhood	NOUN
ejpam-6048	280	3	polynomial	polynomial	NOUN
ejpam-6048	280	4	of	of	ADP
ejpam-6048	280	5	a	a	DET
ejpam-6048	280	6	graph	graph	NOUN
ejpam-6048	280	7	.	.	PUNCT
ejpam-6048	281	1	astralasian	astralasian	PROPN
ejpam-6048	281	2	journal	journal	PROPN
ejpam-6048	281	3	of	of	ADP
ejpam-6048	281	4	combinatorics	combinatoric	NOUN
ejpam-6048	281	5	,	,	PUNCT
ejpam-6048	281	6	42:55–68	42:55–68	PROPN
ejpam-6048	281	7	,	,	PUNCT
ejpam-6048	281	8	2008	2008	NUM
ejpam-6048	281	9	.	.	PUNCT
ejpam-6048	282	1	[	[	X
ejpam-6048	282	2	2	2	NUM
ejpam-6048	282	3	]	]	PUNCT
ejpam-6048	282	4	a.	a.	NOUN
ejpam-6048	282	5	alwardi	alwardi	PROPN
ejpam-6048	282	6	and	and	CCONJ
ejpam-6048	282	7	p.m.	p.m.	NOUN
ejpam-6048	282	8	shivaswamy	shivaswamy	ADJ
ejpam-6048	282	9	.	.	PUNCT
ejpam-6048	283	1	on	on	ADP
ejpam-6048	283	2	the	the	DET
ejpam-6048	283	3	neighbourhood	neighbourhood	NOUN
ejpam-6048	283	4	polynomial	polynomial	NOUN
ejpam-6048	283	5	of	of	ADP
ejpam-6048	283	6	graphs	graph	NOUN
ejpam-6048	283	7	.	.	PUNCT
ejpam-6048	284	1	european	european	ADJ
ejpam-6048	284	2	journal	journal	PROPN
ejpam-6048	284	3	of	of	ADP
ejpam-6048	284	4	pure	pure	ADJ
ejpam-6048	284	5	and	and	CCONJ
ejpam-6048	284	6	applied	applied	ADJ
ejpam-6048	284	7	mathematics	mathematic	NOUN
ejpam-6048	284	8	,	,	PUNCT
ejpam-6048	284	9	6:13–24	6:13–24	NOUN
ejpam-6048	284	10	,	,	PUNCT
ejpam-6048	284	11	2016	2016	NUM
ejpam-6048	284	12	.	.	PUNCT
ejpam-6048	285	1	[	[	X
ejpam-6048	285	2	3	3	NUM
ejpam-6048	285	3	]	]	X
ejpam-6048	285	4	v.r	v.r	PROPN
ejpam-6048	285	5	.	.	PROPN
ejpam-6048	285	6	kulli	kulli	PROPN
ejpam-6048	285	7	.	.	PUNCT
ejpam-6048	286	1	the	the	DET
ejpam-6048	286	2	neighborhood	neighborhood	NOUN
ejpam-6048	286	3	graph	graph	NOUN
ejpam-6048	286	4	of	of	ADP
ejpam-6048	286	5	a	a	DET
ejpam-6048	286	6	graph	graph	NOUN
ejpam-6048	286	7	.	.	PUNCT
ejpam-6048	287	1	international	international	ADJ
ejpam-6048	287	2	journal	journal	NOUN
ejpam-6048	287	3	of	of	ADP
ejpam-6048	287	4	fuzzy	fuzzy	ADJ
ejpam-6048	287	5	mathematical	mathematical	ADJ
ejpam-6048	287	6	archive	archive	NOUN
ejpam-6048	287	7	,	,	PUNCT
ejpam-6048	287	8	8:93–99	8:93–99	NUM
ejpam-6048	287	9	,	,	PUNCT
ejpam-6048	287	10	2015	2015	NUM
ejpam-6048	287	11	.	.	PUNCT
ejpam-6048	288	1	[	[	X
ejpam-6048	288	2	4	4	X
ejpam-6048	288	3	]	]	PUNCT
ejpam-6048	288	4	puttaswamy	puttaswamy	PROPN
ejpam-6048	288	5	k.b	k.b	PROPN
ejpam-6048	288	6	.	.	PROPN
ejpam-6048	288	7	murthy	murthy	PROPN
ejpam-6048	288	8	.	.	PUNCT
ejpam-6048	289	1	on	on	ADP
ejpam-6048	289	2	the	the	DET
ejpam-6048	289	3	independent	independent	ADJ
ejpam-6048	289	4	neighbourhood	neighbourhood	NOUN
ejpam-6048	289	5	polynomial	polynomial	NOUN
ejpam-6048	289	6	of	of	ADP
ejpam-6048	289	7	graphs	graph	NOUN
ejpam-6048	289	8	.	.	PUNCT
ejpam-6048	290	1	indian	indian	ADJ
ejpam-6048	290	2	streams	streams	PROPN
ejpam-6048	290	3	research	research	NOUN
ejpam-6048	290	4	journal	journal	NOUN
ejpam-6048	290	5	,	,	PUNCT
ejpam-6048	290	6	,	,	PUNCT
ejpam-6048	290	7	pages	page	NOUN
ejpam-6048	290	8	vol.5	vol.5	ADV
ejpam-6048	290	9	,	,	PUNCT
ejpam-6048	290	10	1–7	1–7	NUM
ejpam-6048	290	11	,	,	PUNCT
ejpam-6048	290	12	2014	2014	NUM
ejpam-6048	290	13	.	.	PUNCT
ejpam-6048	291	1	[	[	X
ejpam-6048	291	2	5	5	X
ejpam-6048	291	3	]	]	PUNCT
ejpam-6048	291	4	f.	f.	PROPN
ejpam-6048	291	5	harary	harary	PROPN
ejpam-6048	291	6	.	.	PUNCT
ejpam-6048	292	1	graph	graph	NOUN
ejpam-6048	292	2	theory	theory	NOUN
ejpam-6048	292	3	.	.	PUNCT
ejpam-6048	293	1	addison	addison	PROPN
ejpam-6048	293	2	-	-	PUNCT
ejpam-6048	293	3	wesley	wesley	PROPN
ejpam-6048	293	4	publishing	publishing	PROPN
ejpam-6048	293	5	company	company	NOUN
ejpam-6048	293	6	,	,	PUNCT
ejpam-6048	293	7	1969	1969	NUM
ejpam-6048	293	8	.	.	PUNCT
ejpam-6048	294	1	[	[	X
ejpam-6048	294	2	6	6	NUM
ejpam-6048	294	3	]	]	PUNCT
ejpam-6048	294	4	r.	r.	PROPN
ejpam-6048	294	5	diestel	diestel	PROPN
ejpam-6048	294	6	.	.	PUNCT
ejpam-6048	295	1	graph	graph	NOUN
ejpam-6048	295	2	theory	theory	NOUN
ejpam-6048	295	3	,	,	PUNCT
ejpam-6048	295	4	fifth	fifth	ADJ
ejpam-6048	295	5	edition	edition	NOUN
ejpam-6048	295	6	.	.	PUNCT
ejpam-6048	296	1	springer	springer	PROPN
ejpam-6048	296	2	nature	nature	NOUN
ejpam-6048	296	3	,	,	PUNCT
ejpam-6048	296	4	2017	2017	NUM
ejpam-6048	296	5	.	.	PUNCT
ejpam-6048	297	1	[	[	X
ejpam-6048	297	2	7	7	X
ejpam-6048	297	3	]	]	X
ejpam-6048	297	4	n.	n.	NOUN
ejpam-6048	297	5	abdulcarim	abdulcarim	PROPN
ejpam-6048	297	6	and	and	CCONJ
ejpam-6048	297	7	s.	s.	PROPN
ejpam-6048	297	8	dagondon	dagondon	PROPN
ejpam-6048	297	9	.	.	PUNCT
ejpam-6048	298	1	on	on	ADP
ejpam-6048	298	2	the	the	DET
ejpam-6048	298	3	independent	independent	ADJ
ejpam-6048	298	4	neighborhood	neighborhood	NOUN
ejpam-6048	298	5	polynomial	polynomial	NOUN
ejpam-6048	298	6	of	of	ADP
ejpam-6048	298	7	the	the	DET
ejpam-6048	298	8	rooted	rooted	ADJ
ejpam-6048	298	9	product	product	NOUN
ejpam-6048	298	10	of	of	ADP
ejpam-6048	298	11	two	two	NUM
ejpam-6048	298	12	trees	tree	NOUN
ejpam-6048	298	13	.	.	PUNCT
ejpam-6048	299	1	european	european	ADJ
ejpam-6048	299	2	journal	journal	PROPN
ejpam-6048	299	3	of	of	ADP
ejpam-6048	299	4	pure	pure	ADJ
ejpam-6048	299	5	and	and	CCONJ
ejpam-6048	299	6	applied	applied	ADJ
ejpam-6048	299	7	mathematics	mathematic	NOUN
ejpam-6048	299	8	,	,	PUNCT
ejpam-6048	299	9	1:64–81	1:64–81	NUM
ejpam-6048	299	10	,	,	PUNCT
ejpam-6048	299	11	2022	2022	NUM
ejpam-6048	299	12	.	.	PUNCT
ejpam-6048	300	1	[	[	X
ejpam-6048	300	2	8	8	NUM
ejpam-6048	300	3	]	]	X
ejpam-6048	300	4	j.a	j.a	PROPN
ejpam-6048	300	5	.	.	PROPN
ejpam-6048	300	6	bondy	bondy	PROPN
ejpam-6048	300	7	and	and	CCONJ
ejpam-6048	300	8	u.s.r	u.s.r	ADJ
ejpam-6048	300	9	.	.	PUNCT
ejpam-6048	300	10	murthy	murthy	PROPN
ejpam-6048	300	11	.	.	PUNCT
ejpam-6048	301	1	graph	graph	NOUN
ejpam-6048	301	2	theory	theory	NOUN
ejpam-6048	301	3	.	.	PUNCT
ejpam-6048	302	1	springer	springer	NOUN
ejpam-6048	302	2	,	,	PUNCT
ejpam-6048	302	3	2007	2007	NUM
ejpam-6048	302	4	.	.	PUNCT
ejpam-6048	303	1	[	[	X
ejpam-6048	303	2	9	9	NUM
ejpam-6048	303	3	]	]	X
ejpam-6048	303	4	f.	f.	PROPN
ejpam-6048	303	5	buckley	buckley	PROPN
ejpam-6048	303	6	and	and	CCONJ
ejpam-6048	303	7	f.	f.	PROPN
ejpam-6048	303	8	harary	harary	PROPN
ejpam-6048	303	9	.	.	PUNCT
ejpam-6048	304	1	distance	distance	NOUN
ejpam-6048	304	2	in	in	ADP
ejpam-6048	304	3	graphs	graph	NOUN
ejpam-6048	304	4	.	.	PUNCT
ejpam-6048	305	1	addison	addison	PROPN
ejpam-6048	305	2	-	-	PUNCT
ejpam-6048	305	3	wesley	wesley	PROPN
ejpam-6048	305	4	series	series	PROPN
ejpam-6048	305	5	in	in	ADP
ejpam-6048	305	6	mathematics	mathematic	NOUN
ejpam-6048	305	7	,	,	PUNCT
ejpam-6048	305	8	reedwood	reedwood	ADJ
ejpam-6048	305	9	city	city	NOUN
ejpam-6048	305	10	,	,	PUNCT
ejpam-6048	305	11	1990	1990	NUM
ejpam-6048	305	12	.	.	PUNCT