id	sid	tid	token	lemma	pos
ejpam-4220	1	1	european	european	PROPN
ejpam-4220	1	2	journal	journal	PROPN
ejpam-4220	1	3	of	of	ADP
ejpam-4220	1	4	pure	pure	ADJ
ejpam-4220	1	5	and	and	CCONJ
ejpam-4220	1	6	applied	apply	VERB
ejpam-4220	1	7	mathematics	mathematic	NOUN
ejpam-4220	1	8	vol	vol	NOUN
ejpam-4220	1	9	.	.	PROPN
ejpam-4220	2	1	15	15	NUM
ejpam-4220	2	2	,	,	PUNCT
ejpam-4220	2	3	no	no	INTJ
ejpam-4220	2	4	.	.	NOUN
ejpam-4220	2	5	1	1	NUM
ejpam-4220	2	6	,	,	PUNCT
ejpam-4220	2	7	2022	2022	NUM
ejpam-4220	2	8	,	,	PUNCT
ejpam-4220	2	9	64	64	NUM
ejpam-4220	2	10	-	-	SYM
ejpam-4220	2	11	81	81	NUM
ejpam-4220	2	12	issn	issn	PROPN
ejpam-4220	2	13	1307	1307	NUM
ejpam-4220	2	14	-	-	SYM
ejpam-4220	2	15	5543	5543	NUM
ejpam-4220	2	16	–	–	PUNCT
ejpam-4220	3	1	ejpam.com	ejpam.com	X
ejpam-4220	3	2	published	publish	VERB
ejpam-4220	3	3	by	by	ADP
ejpam-4220	3	4	new	new	PROPN
ejpam-4220	3	5	york	york	PROPN
ejpam-4220	3	6	business	business	PROPN
ejpam-4220	3	7	global	global	PROPN
ejpam-4220	3	8	on	on	ADP
ejpam-4220	3	9	the	the	DET
ejpam-4220	3	10	independent	independent	ADJ
ejpam-4220	3	11	neighborhood	neighborhood	NOUN
ejpam-4220	3	12	polynomial	polynomial	NOUN
ejpam-4220	3	13	of	of	ADP
ejpam-4220	3	14	the	the	DET
ejpam-4220	3	15	rooted	rooted	ADJ
ejpam-4220	3	16	product	product	NOUN
ejpam-4220	3	17	of	of	ADP
ejpam-4220	3	18	two	two	NUM
ejpam-4220	3	19	trees	tree	NOUN
ejpam-4220	3	20	normalah	normalah	PROPN
ejpam-4220	3	21	s.	s.	PROPN
ejpam-4220	3	22	abdulcarim1,∗	abdulcarim1,∗	PROPN
ejpam-4220	3	23	,	,	PUNCT
ejpam-4220	3	24	susan	susan	PROPN
ejpam-4220	3	25	c.	c.	PROPN
ejpam-4220	3	26	dagondon2	dagondon2	PROPN
ejpam-4220	3	27	1	1	NUM
ejpam-4220	3	28	department	department	NOUN
ejpam-4220	3	29	of	of	ADP
ejpam-4220	3	30	mathematics	mathematic	NOUN
ejpam-4220	3	31	,	,	PUNCT
ejpam-4220	3	32	college	college	NOUN
ejpam-4220	3	33	of	of	ADP
ejpam-4220	3	34	natural	natural	ADJ
ejpam-4220	3	35	sciences	science	NOUN
ejpam-4220	3	36	and	and	CCONJ
ejpam-4220	3	37	mathematics	mathematic	NOUN
ejpam-4220	3	38	,	,	PUNCT
ejpam-4220	3	39	mindanao	mindanao	PROPN
ejpam-4220	3	40	state	state	PROPN
ejpam-4220	3	41	university	university	PROPN
ejpam-4220	3	42	main	main	ADJ
ejpam-4220	3	43	campus	campus	NOUN
ejpam-4220	3	44	,	,	PUNCT
ejpam-4220	3	45	9700	9700	NUM
ejpam-4220	3	46	marawi	marawi	PROPN
ejpam-4220	3	47	city	city	PROPN
ejpam-4220	3	48	,	,	PUNCT
ejpam-4220	3	49	philippines	philippines	PROPN
ejpam-4220	3	50	2	2	NUM
ejpam-4220	3	51	department	department	NOUN
ejpam-4220	3	52	of	of	ADP
ejpam-4220	3	53	mathematics	mathematic	NOUN
ejpam-4220	3	54	and	and	CCONJ
ejpam-4220	3	55	statistics	statistic	NOUN
ejpam-4220	3	56	,	,	PUNCT
ejpam-4220	3	57	college	college	NOUN
ejpam-4220	3	58	of	of	ADP
ejpam-4220	3	59	science	science	NOUN
ejpam-4220	3	60	and	and	CCONJ
ejpam-4220	3	61	mathematics	mathematic	NOUN
ejpam-4220	3	62	,	,	PUNCT
ejpam-4220	3	63	center	center	NOUN
ejpam-4220	3	64	of	of	ADP
ejpam-4220	3	65	graph	graph	NOUN
ejpam-4220	3	66	theory	theory	NOUN
ejpam-4220	3	67	,	,	PUNCT
ejpam-4220	3	68	algebra	algebra	NOUN
ejpam-4220	3	69	,	,	PUNCT
ejpam-4220	3	70	and	and	CCONJ
ejpam-4220	3	71	analysis	analysis	NOUN
ejpam-4220	3	72	-	-	PUNCT
ejpam-4220	3	73	premier	premier	NOUN
ejpam-4220	3	74	research	research	NOUN
ejpam-4220	3	75	institute	institute	PROPN
ejpam-4220	3	76	of	of	ADP
ejpam-4220	3	77	science	science	NOUN
ejpam-4220	3	78	and	and	CCONJ
ejpam-4220	3	79	mathematics	mathematic	NOUN
ejpam-4220	3	80	,	,	PUNCT
ejpam-4220	3	81	mindanao	mindanao	PROPN
ejpam-4220	3	82	state	state	PROPN
ejpam-4220	3	83	university	university	PROPN
ejpam-4220	3	84	-	-	PUNCT
ejpam-4220	3	85	iligan	iligan	PROPN
ejpam-4220	3	86	institute	institute	PROPN
ejpam-4220	3	87	of	of	ADP
ejpam-4220	3	88	technology	technology	PROPN
ejpam-4220	3	89	,	,	PUNCT
ejpam-4220	3	90	9200	9200	NUM
ejpam-4220	3	91	iligan	iligan	ADJ
ejpam-4220	3	92	city	city	NOUN
ejpam-4220	3	93	,	,	PUNCT
ejpam-4220	3	94	philippines	philippine	NOUN
ejpam-4220	3	95	abstract	abstract	ADJ
ejpam-4220	3	96	.	.	PUNCT
ejpam-4220	4	1	let	let	VERB
ejpam-4220	4	2	g	g	PRON
ejpam-4220	4	3	be	be	AUX
ejpam-4220	4	4	a	a	DET
ejpam-4220	4	5	connected	connected	ADJ
ejpam-4220	4	6	graph	graph	NOUN
ejpam-4220	4	7	.	.	PUNCT
ejpam-4220	5	1	we	we	PRON
ejpam-4220	5	2	say	say	VERB
ejpam-4220	5	3	that	that	SCONJ
ejpam-4220	5	4	a	a	DET
ejpam-4220	5	5	given	give	VERB
ejpam-4220	5	6	graph	graph	NOUN
ejpam-4220	5	7	is	be	AUX
ejpam-4220	5	8	a	a	DET
ejpam-4220	5	9	tree	tree	NOUN
ejpam-4220	5	10	if	if	SCONJ
ejpam-4220	5	11	every	every	DET
ejpam-4220	5	12	pair	pair	NOUN
ejpam-4220	5	13	of	of	ADP
ejpam-4220	5	14	vertices	vertex	NOUN
ejpam-4220	5	15	is	be	AUX
ejpam-4220	5	16	connected	connect	VERB
ejpam-4220	5	17	by	by	ADP
ejpam-4220	5	18	a	a	DET
ejpam-4220	5	19	unique	unique	ADJ
ejpam-4220	5	20	path	path	NOUN
ejpam-4220	5	21	.	.	PUNCT
ejpam-4220	6	1	the	the	DET
ejpam-4220	6	2	rooted	rooted	ADJ
ejpam-4220	6	3	product	product	NOUN
ejpam-4220	6	4	of	of	ADP
ejpam-4220	6	5	two	two	NUM
ejpam-4220	6	6	trees	tree	NOUN
ejpam-4220	6	7	is	be	AUX
ejpam-4220	6	8	relevant	relevant	ADJ
ejpam-4220	6	9	to	to	ADP
ejpam-4220	6	10	tree	tree	NOUN
ejpam-4220	6	11	,	,	PUNCT
ejpam-4220	6	12	as	as	SCONJ
ejpam-4220	6	13	the	the	DET
ejpam-4220	6	14	obtained	obtain	VERB
ejpam-4220	6	15	product	product	NOUN
ejpam-4220	6	16	is	be	AUX
ejpam-4220	6	17	another	another	DET
ejpam-4220	6	18	tree	tree	NOUN
ejpam-4220	6	19	.	.	PUNCT
ejpam-4220	7	1	in	in	ADP
ejpam-4220	7	2	this	this	DET
ejpam-4220	7	3	paper	paper	NOUN
ejpam-4220	7	4	,	,	PUNCT
ejpam-4220	7	5	we	we	PRON
ejpam-4220	7	6	establish	establish	VERB
ejpam-4220	7	7	the	the	DET
ejpam-4220	7	8	independent	independent	ADJ
ejpam-4220	7	9	neighborhood	neighborhood	NOUN
ejpam-4220	7	10	sets	set	NOUN
ejpam-4220	7	11	of	of	ADP
ejpam-4220	7	12	a	a	DET
ejpam-4220	7	13	tree	tree	NOUN
ejpam-4220	7	14	and	and	CCONJ
ejpam-4220	7	15	obtain	obtain	VERB
ejpam-4220	7	16	its	its	PRON
ejpam-4220	7	17	corresponding	corresponding	ADJ
ejpam-4220	7	18	independent	independent	ADJ
ejpam-4220	7	19	neighborhood	neighborhood	NOUN
ejpam-4220	7	20	polynomial	polynomial	NOUN
ejpam-4220	7	21	.	.	PUNCT
ejpam-4220	8	1	furthermore	furthermore	ADV
ejpam-4220	8	2	,	,	PUNCT
ejpam-4220	8	3	the	the	DET
ejpam-4220	8	4	independent	independent	ADJ
ejpam-4220	8	5	neighborhood	neighborhood	NOUN
ejpam-4220	8	6	polynomial	polynomial	NOUN
ejpam-4220	8	7	of	of	ADP
ejpam-4220	8	8	the	the	DET
ejpam-4220	8	9	rooted	rooted	ADJ
ejpam-4220	8	10	product	product	NOUN
ejpam-4220	8	11	of	of	ADP
ejpam-4220	8	12	two	two	NUM
ejpam-4220	8	13	trees	tree	NOUN
ejpam-4220	8	14	were	be	AUX
ejpam-4220	8	15	determine	determine	NOUN
ejpam-4220	8	16	using	use	VERB
ejpam-4220	8	17	their	their	PRON
ejpam-4220	8	18	independent	independent	ADJ
ejpam-4220	8	19	neighborhood	neighborhood	NOUN
ejpam-4220	8	20	sets	set	NOUN
ejpam-4220	8	21	.	.	PUNCT
ejpam-4220	9	1	2020	2020	NUM
ejpam-4220	9	2	mathematics	mathematic	NOUN
ejpam-4220	9	3	subject	subject	NOUN
ejpam-4220	9	4	classifications	classification	NOUN
ejpam-4220	9	5	:	:	PUNCT
ejpam-4220	9	6	05c05	05c05	NOUN
ejpam-4220	9	7	,	,	PUNCT
ejpam-4220	9	8	05c76	05c76	NUM
ejpam-4220	9	9	,	,	PUNCT
ejpam-4220	9	10	05c31	05c31	PRON
ejpam-4220	9	11	key	key	ADJ
ejpam-4220	9	12	words	word	NOUN
ejpam-4220	9	13	and	and	CCONJ
ejpam-4220	9	14	phrases	phrase	NOUN
ejpam-4220	9	15	:	:	PUNCT
ejpam-4220	9	16	rooted	rooted	ADJ
ejpam-4220	9	17	graph	graph	NOUN
ejpam-4220	9	18	,	,	PUNCT
ejpam-4220	9	19	rooted	rooted	ADJ
ejpam-4220	9	20	product	product	NOUN
ejpam-4220	9	21	of	of	ADP
ejpam-4220	9	22	graphs	graph	NOUN
ejpam-4220	9	23	,	,	PUNCT
ejpam-4220	9	24	independent	independent	ADJ
ejpam-4220	9	25	neighborhood	neighborhood	NOUN
ejpam-4220	9	26	polynomial	polynomial	ADJ
ejpam-4220	9	27	1	1	NUM
ejpam-4220	9	28	.	.	PUNCT
ejpam-4220	9	29	introduction	introduction	NOUN
ejpam-4220	9	30	a	a	DET
ejpam-4220	9	31	graph	graph	NOUN
ejpam-4220	9	32	g	g	NOUN
ejpam-4220	9	33	is	be	AUX
ejpam-4220	9	34	a	a	DET
ejpam-4220	9	35	pair	pair	NOUN
ejpam-4220	9	36	(	(	PUNCT
ejpam-4220	9	37	v	v	NOUN
ejpam-4220	9	38	(	(	PUNCT
ejpam-4220	9	39	g	g	NOUN
ejpam-4220	9	40	)	)	PUNCT
ejpam-4220	9	41	,	,	PUNCT
ejpam-4220	9	42	e(g	e(g	PROPN
ejpam-4220	9	43	)	)	PUNCT
ejpam-4220	9	44	)	)	PUNCT
ejpam-4220	10	1	consisting	consist	VERB
ejpam-4220	10	2	of	of	ADP
ejpam-4220	10	3	a	a	DET
ejpam-4220	10	4	nonempty	nonempty	ADJ
ejpam-4220	10	5	finite	finite	NOUN
ejpam-4220	10	6	set	set	NOUN
ejpam-4220	10	7	of	of	ADP
ejpam-4220	10	8	vertices	vertex	NOUN
ejpam-4220	10	9	v	v	X
ejpam-4220	10	10	(	(	PUNCT
ejpam-4220	10	11	g	g	NOUN
ejpam-4220	10	12	)	)	PUNCT
ejpam-4220	10	13	and	and	CCONJ
ejpam-4220	10	14	a	a	DET
ejpam-4220	10	15	set	set	NOUN
ejpam-4220	10	16	of	of	ADP
ejpam-4220	10	17	edges	edge	NOUN
ejpam-4220	10	18	e(g	e(g	PROPN
ejpam-4220	10	19	)	)	PUNCT
ejpam-4220	10	20	of	of	ADP
ejpam-4220	10	21	unordered	unordered	ADJ
ejpam-4220	10	22	pairs	pair	NOUN
ejpam-4220	10	23	of	of	ADP
ejpam-4220	10	24	elements	element	NOUN
ejpam-4220	10	25	of	of	ADP
ejpam-4220	10	26	v	v	NOUN
ejpam-4220	10	27	(	(	PUNCT
ejpam-4220	10	28	g	g	NOUN
ejpam-4220	10	29	)	)	PUNCT
ejpam-4220	10	30	.	.	PUNCT
ejpam-4220	11	1	the	the	DET
ejpam-4220	11	2	cardinalities	cardinality	NOUN
ejpam-4220	11	3	of	of	ADP
ejpam-4220	11	4	v	v	NOUN
ejpam-4220	11	5	(	(	PUNCT
ejpam-4220	11	6	g	g	NOUN
ejpam-4220	11	7	)	)	PUNCT
ejpam-4220	11	8	and	and	CCONJ
ejpam-4220	11	9	e(g	e(g	PROPN
ejpam-4220	11	10	)	)	PUNCT
ejpam-4220	11	11	are	be	AUX
ejpam-4220	11	12	called	call	VERB
ejpam-4220	11	13	the	the	DET
ejpam-4220	11	14	order	order	NOUN
ejpam-4220	11	15	and	and	CCONJ
ejpam-4220	11	16	size	size	NOUN
ejpam-4220	11	17	of	of	ADP
ejpam-4220	11	18	g	g	NOUN
ejpam-4220	11	19	,	,	PUNCT
ejpam-4220	11	20	respectively	respectively	ADV
ejpam-4220	11	21	.	.	PUNCT
ejpam-4220	12	1	we	we	PRON
ejpam-4220	12	2	write	write	VERB
ejpam-4220	12	3	x	x	PUNCT
ejpam-4220	12	4	=	=	PUNCT
ejpam-4220	12	5	uv	uv	NOUN
ejpam-4220	12	6	and	and	CCONJ
ejpam-4220	12	7	say	say	VERB
ejpam-4220	12	8	that	that	SCONJ
ejpam-4220	12	9	u	u	PROPN
ejpam-4220	12	10	and	and	CCONJ
ejpam-4220	12	11	v	v	NOUN
ejpam-4220	12	12	are	be	AUX
ejpam-4220	12	13	adjacent	adjacent	ADJ
ejpam-4220	12	14	vertices	vertex	NOUN
ejpam-4220	12	15	;	;	PUNCT
ejpam-4220	12	16	vertex	vertex	NOUN
ejpam-4220	12	17	u	u	NOUN
ejpam-4220	12	18	and	and	CCONJ
ejpam-4220	12	19	edge	edge	NOUN
ejpam-4220	12	20	x	x	VERB
ejpam-4220	12	21	are	be	AUX
ejpam-4220	12	22	incident	incident	NOUN
ejpam-4220	12	23	with	with	ADP
ejpam-4220	12	24	each	each	DET
ejpam-4220	12	25	other	other	ADJ
ejpam-4220	12	26	,	,	PUNCT
ejpam-4220	12	27	so	so	ADV
ejpam-4220	12	28	are	be	AUX
ejpam-4220	12	29	v	v	ADJ
ejpam-4220	12	30	and	and	CCONJ
ejpam-4220	12	31	x.	x.	NOUN
ejpam-4220	12	32	the	the	DET
ejpam-4220	12	33	two	two	NUM
ejpam-4220	12	34	vertices	vertex	NOUN
ejpam-4220	12	35	incident	incident	NOUN
ejpam-4220	12	36	with	with	ADP
ejpam-4220	12	37	an	an	DET
ejpam-4220	12	38	edge	edge	NOUN
ejpam-4220	12	39	are	be	AUX
ejpam-4220	12	40	its	its	PRON
ejpam-4220	12	41	end	end	NOUN
ejpam-4220	12	42	vertices	vertex	NOUN
ejpam-4220	12	43	or	or	CCONJ
ejpam-4220	12	44	ends	end	NOUN
ejpam-4220	12	45	,	,	PUNCT
ejpam-4220	12	46	and	and	CCONJ
ejpam-4220	12	47	an	an	DET
ejpam-4220	12	48	edge	edge	NOUN
ejpam-4220	12	49	joins	join	VERB
ejpam-4220	12	50	its	its	PRON
ejpam-4220	12	51	ends	end	NOUN
ejpam-4220	12	52	.	.	PUNCT
ejpam-4220	13	1	two	two	NUM
ejpam-4220	13	2	vertices	vertex	NOUN
ejpam-4220	13	3	of	of	ADP
ejpam-4220	13	4	a	a	DET
ejpam-4220	13	5	graph	graph	NOUN
ejpam-4220	13	6	g	g	NOUN
ejpam-4220	13	7	are	be	AUX
ejpam-4220	13	8	said	say	VERB
ejpam-4220	13	9	to	to	PART
ejpam-4220	13	10	be	be	AUX
ejpam-4220	13	11	neighbors	neighbor	NOUN
ejpam-4220	13	12	if	if	SCONJ
ejpam-4220	13	13	they	they	PRON
ejpam-4220	13	14	are	be	AUX
ejpam-4220	13	15	adjacent	adjacent	ADJ
ejpam-4220	13	16	in	in	ADP
ejpam-4220	13	17	g.	g.	PROPN
ejpam-4220	13	18	the	the	DET
ejpam-4220	13	19	neighborhood	neighborhood	NOUN
ejpam-4220	13	20	of	of	ADP
ejpam-4220	13	21	a	a	DET
ejpam-4220	13	22	vertex	vertex	NOUN
ejpam-4220	13	23	v	v	ADP
ejpam-4220	13	24	∈	∈	NOUN
ejpam-4220	13	25	v	v	NOUN
ejpam-4220	13	26	(	(	PUNCT
ejpam-4220	13	27	g	g	NOUN
ejpam-4220	13	28	)	)	PUNCT
ejpam-4220	13	29	is	be	AUX
ejpam-4220	13	30	the	the	DET
ejpam-4220	13	31	set	set	NOUN
ejpam-4220	13	32	n(v	n(v	PROPN
ejpam-4220	13	33	)	)	PUNCT
ejpam-4220	14	1	=	=	PRON
ejpam-4220	14	2	{	{	PUNCT
ejpam-4220	14	3	w	w	NOUN
ejpam-4220	14	4	:	:	PUNCT
ejpam-4220	14	5	w	w	PROPN
ejpam-4220	14	6	∈	∈	PROPN
ejpam-4220	14	7	v	v	ADP
ejpam-4220	14	8	(	(	PUNCT
ejpam-4220	14	9	g	g	NOUN
ejpam-4220	14	10	)	)	PUNCT
ejpam-4220	14	11	and	and	CCONJ
ejpam-4220	14	12	vw	vw	PROPN
ejpam-4220	14	13	∈	∈	PROPN
ejpam-4220	14	14	e(g	e(g	PROPN
ejpam-4220	14	15	)	)	PUNCT
ejpam-4220	14	16	}	}	PUNCT
ejpam-4220	14	17	.	.	PUNCT
ejpam-4220	15	1	a	a	DET
ejpam-4220	15	2	vertex	vertex	NOUN
ejpam-4220	15	3	v	v	NOUN
ejpam-4220	15	4	is	be	AUX
ejpam-4220	15	5	pendant	pendant	ADJ
ejpam-4220	15	6	if	if	SCONJ
ejpam-4220	15	7	its	its	PRON
ejpam-4220	15	8	neighborhood	neighborhood	NOUN
ejpam-4220	15	9	contains	contain	VERB
ejpam-4220	15	10	only	only	ADV
ejpam-4220	15	11	one	one	NUM
ejpam-4220	15	12	vertex	vertex	NOUN
ejpam-4220	15	13	;	;	PUNCT
ejpam-4220	15	14	and	and	CCONJ
ejpam-4220	15	15	edge	edge	NOUN
ejpam-4220	15	16	e	e	NOUN
ejpam-4220	15	17	=	=	NOUN
ejpam-4220	15	18	uv	uv	NOUN
ejpam-4220	15	19	is	be	AUX
ejpam-4220	15	20	pendant	pendant	ADJ
ejpam-4220	15	21	if	if	SCONJ
ejpam-4220	15	22	one	one	NUM
ejpam-4220	15	23	of	of	ADP
ejpam-4220	15	24	its	its	PRON
ejpam-4220	15	25	end	end	NOUN
ejpam-4220	15	26	vertices	vertex	NOUN
ejpam-4220	15	27	is	be	AUX
ejpam-4220	15	28	a	a	DET
ejpam-4220	15	29	pendant	pendant	ADJ
ejpam-4220	15	30	vertex	vertex	NOUN
ejpam-4220	15	31	.	.	PUNCT
ejpam-4220	16	1	∗corresponding	∗corresponde	VERB
ejpam-4220	16	2	author	author	NOUN
ejpam-4220	16	3	.	.	PUNCT
ejpam-4220	17	1	doi	doi	NOUN
ejpam-4220	17	2	:	:	PUNCT
ejpam-4220	17	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4220	https://doi.org/10.29020/nybg.ejpam.v15i1.4220	ADP
ejpam-4220	17	4	email	email	NOUN
ejpam-4220	17	5	addresses	address	NOUN
ejpam-4220	17	6	:	:	PUNCT
ejpam-4220	17	7	normalah.abdulcarim@msumain.edu.ph	normalah.abdulcarim@msumain.edu.ph	PROPN
ejpam-4220	17	8	(	(	PUNCT
ejpam-4220	17	9	n.	n.	PROPN
ejpam-4220	17	10	s.	s.	PROPN
ejpam-4220	17	11	abdulcarim	abdulcarim	PROPN
ejpam-4220	17	12	)	)	PUNCT
ejpam-4220	17	13	,	,	PUNCT
ejpam-4220	17	14	susan.dagondon@g.msuiit.edu.ph	susan.dagondon@g.msuiit.edu.ph	PROPN
ejpam-4220	17	15	(	(	PUNCT
ejpam-4220	17	16	s.	s.	PROPN
ejpam-4220	17	17	c.	c.	PROPN
ejpam-4220	17	18	dagondon	dagondon	PROPN
ejpam-4220	17	19	)	)	PUNCT
ejpam-4220	17	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4220	18	1	64	64	NUM
ejpam-4220	18	2	©	©	PROPN
ejpam-4220	18	3	2022	2022	NUM
ejpam-4220	18	4	ejpam	ejpam	VERB
ejpam-4220	18	5	all	all	DET
ejpam-4220	18	6	rights	right	NOUN
ejpam-4220	18	7	reserved	reserve	VERB
ejpam-4220	18	8	.	.	PUNCT
ejpam-4220	19	1	n.	n.	PROPN
ejpam-4220	19	2	s.	s.	PROPN
ejpam-4220	19	3	abdulcarim	abdulcarim	PROPN
ejpam-4220	19	4	,	,	PUNCT
ejpam-4220	19	5	s.	s.	PROPN
ejpam-4220	19	6	c.	c.	PROPN
ejpam-4220	19	7	dagondon	dagondon	PROPN
ejpam-4220	19	8	/	/	SYM
ejpam-4220	19	9	eur	eur	PROPN
ejpam-4220	19	10	.	.	PUNCT
ejpam-4220	20	1	j.	j.	PROPN
ejpam-4220	20	2	pure	pure	PROPN
ejpam-4220	20	3	appl	appl	PROPN
ejpam-4220	20	4	.	.	PROPN
ejpam-4220	20	5	math	math	PROPN
ejpam-4220	20	6	,	,	PUNCT
ejpam-4220	20	7	15	15	NUM
ejpam-4220	20	8	(	(	PUNCT
ejpam-4220	20	9	1	1	NUM
ejpam-4220	20	10	)	)	PUNCT
ejpam-4220	20	11	(	(	PUNCT
ejpam-4220	20	12	2022	2022	NUM
ejpam-4220	20	13	)	)	PUNCT
ejpam-4220	20	14	,	,	PUNCT
ejpam-4220	20	15	64	64	NUM
ejpam-4220	20	16	-	-	SYM
ejpam-4220	20	17	81	81	NUM
ejpam-4220	20	18	65	65	NUM
ejpam-4220	20	19	a	a	DET
ejpam-4220	20	20	path	path	NOUN
ejpam-4220	20	21	is	be	AUX
ejpam-4220	20	22	a	a	DET
ejpam-4220	20	23	nonempty	nonempty	ADJ
ejpam-4220	20	24	graph	graph	NOUN
ejpam-4220	20	25	p	p	NOUN
ejpam-4220	20	26	=	=	X
ejpam-4220	20	27	(	(	PUNCT
ejpam-4220	20	28	v	v	NOUN
ejpam-4220	20	29	(	(	PUNCT
ejpam-4220	20	30	p	p	NOUN
ejpam-4220	20	31	)	)	PUNCT
ejpam-4220	20	32	,	,	PUNCT
ejpam-4220	20	33	e(p	e(p	PROPN
ejpam-4220	20	34	)	)	PUNCT
ejpam-4220	20	35	)	)	PUNCT
ejpam-4220	20	36	of	of	ADP
ejpam-4220	20	37	the	the	DET
ejpam-4220	20	38	form	form	NOUN
ejpam-4220	20	39	v	v	NOUN
ejpam-4220	20	40	(	(	PUNCT
ejpam-4220	20	41	p	p	NOUN
ejpam-4220	20	42	)	)	PUNCT
ejpam-4220	20	43	=	=	SYM
ejpam-4220	20	44	{	{	PUNCT
ejpam-4220	20	45	v1	v1	PROPN
ejpam-4220	20	46	,	,	PUNCT
ejpam-4220	20	47	·	·	PUNCT
ejpam-4220	20	48	·	·	PUNCT
ejpam-4220	20	49	·	·	PUNCT
ejpam-4220	20	50	,	,	PUNCT
ejpam-4220	20	51	vm	vm	NOUN
ejpam-4220	20	52	}	}	PUNCT
ejpam-4220	20	53	,	,	PUNCT
ejpam-4220	20	54	e(p	e(p	NOUN
ejpam-4220	20	55	)	)	PUNCT
ejpam-4220	20	56	=	=	PRON
ejpam-4220	21	1	{	{	PUNCT
ejpam-4220	21	2	v1v2	v1v2	PROPN
ejpam-4220	21	3	,	,	PUNCT
ejpam-4220	21	4	v2v3	v2v3	PROPN
ejpam-4220	21	5	,	,	PUNCT
ejpam-4220	21	6	·	·	PUNCT
ejpam-4220	21	7	·	·	PUNCT
ejpam-4220	21	8	·	·	PUNCT
ejpam-4220	21	9	,	,	PUNCT
ejpam-4220	21	10	vm−1vm	vm−1vm	NOUN
ejpam-4220	21	11	}	}	PUNCT
ejpam-4220	21	12	,	,	PUNCT
ejpam-4220	21	13	where	where	SCONJ
ejpam-4220	21	14	the	the	DET
ejpam-4220	21	15	vi	vi	NOUN
ejpam-4220	21	16	are	be	AUX
ejpam-4220	21	17	all	all	ADV
ejpam-4220	21	18	distinct	distinct	ADJ
ejpam-4220	21	19	.	.	PUNCT
ejpam-4220	22	1	if	if	SCONJ
ejpam-4220	22	2	e	e	PROPN
ejpam-4220	22	3	=	=	PRON
ejpam-4220	22	4	{	{	PUNCT
ejpam-4220	22	5	v1v2	v1v2	PROPN
ejpam-4220	22	6	,	,	PUNCT
ejpam-4220	22	7	v2v3	v2v3	PROPN
ejpam-4220	22	8	,	,	PUNCT
ejpam-4220	22	9	·	·	PUNCT
ejpam-4220	22	10	·	·	PUNCT
ejpam-4220	22	11	·	·	PUNCT
ejpam-4220	22	12	,	,	PUNCT
ejpam-4220	22	13	vm−1vm	vm−1vm	PROPN
ejpam-4220	22	14	,	,	PUNCT
ejpam-4220	22	15	vmv1	vmv1	NOUN
ejpam-4220	22	16	}	}	PUNCT
ejpam-4220	22	17	,	,	PUNCT
ejpam-4220	22	18	then	then	ADV
ejpam-4220	22	19	the	the	DET
ejpam-4220	22	20	graph	graph	NOUN
ejpam-4220	22	21	is	be	AUX
ejpam-4220	22	22	called	call	VERB
ejpam-4220	22	23	a	a	DET
ejpam-4220	22	24	cycle	cycle	NOUN
ejpam-4220	22	25	.	.	PUNCT
ejpam-4220	23	1	in	in	ADP
ejpam-4220	23	2	this	this	DET
ejpam-4220	23	3	study	study	NOUN
ejpam-4220	23	4	,	,	PUNCT
ejpam-4220	23	5	we	we	PRON
ejpam-4220	23	6	consider	consider	VERB
ejpam-4220	23	7	the	the	DET
ejpam-4220	23	8	graph	graph	NOUN
ejpam-4220	23	9	polynomial	polynomial	ADJ
ejpam-4220	23	10	.	.	PUNCT
ejpam-4220	24	1	some	some	DET
ejpam-4220	24	2	familiar	familiar	ADJ
ejpam-4220	24	3	examples	example	NOUN
ejpam-4220	24	4	include	include	VERB
ejpam-4220	24	5	chromatic	chromatic	ADJ
ejpam-4220	24	6	polynomial	polynomial	NOUN
ejpam-4220	24	7	by	by	ADP
ejpam-4220	24	8	george	george	PROPN
ejpam-4220	24	9	david	david	PROPN
ejpam-4220	24	10	birkhoff	birkhoff	PROPN
ejpam-4220	25	1	[	[	X
ejpam-4220	25	2	1	1	NUM
ejpam-4220	25	3	]	]	PUNCT
ejpam-4220	25	4	,	,	PUNCT
ejpam-4220	25	5	matching	match	VERB
ejpam-4220	25	6	polynomial	polynomial	NOUN
ejpam-4220	25	7	by	by	ADP
ejpam-4220	25	8	farrel	farrel	NOUN
ejpam-4220	25	9	[	[	X
ejpam-4220	25	10	4	4	NUM
ejpam-4220	25	11	]	]	PUNCT
ejpam-4220	25	12	,	,	PUNCT
ejpam-4220	25	13	independence	independence	NOUN
ejpam-4220	25	14	polynomial	polynomial	NOUN
ejpam-4220	25	15	by	by	ADP
ejpam-4220	25	16	gutman	gutman	NOUN
ejpam-4220	25	17	and	and	CCONJ
ejpam-4220	25	18	harary	harary	NOUN
ejpam-4220	26	1	[	[	X
ejpam-4220	26	2	7	7	NUM
ejpam-4220	26	3	]	]	PUNCT
ejpam-4220	26	4	,	,	PUNCT
ejpam-4220	26	5	and	and	CCONJ
ejpam-4220	26	6	by	by	ADP
ejpam-4220	26	7	levit	levit	PROPN
ejpam-4220	26	8	and	and	CCONJ
ejpam-4220	26	9	mandrescu	mandrescu	NOUN
ejpam-4220	27	1	[	[	X
ejpam-4220	27	2	10	10	NUM
ejpam-4220	27	3	]	]	PUNCT
ejpam-4220	27	4	.	.	PUNCT
ejpam-4220	28	1	recently	recently	ADV
ejpam-4220	28	2	,	,	PUNCT
ejpam-4220	28	3	another	another	DET
ejpam-4220	28	4	type	type	NOUN
ejpam-4220	28	5	of	of	ADP
ejpam-4220	28	6	graph	graph	NOUN
ejpam-4220	28	7	polynomial	polynomial	ADJ
ejpam-4220	28	8	,	,	PUNCT
ejpam-4220	28	9	the	the	DET
ejpam-4220	28	10	neighborhood	neighborhood	NOUN
ejpam-4220	28	11	polynomial	polynomial	NOUN
ejpam-4220	28	12	were	be	AUX
ejpam-4220	28	13	studied	study	VERB
ejpam-4220	28	14	by	by	ADP
ejpam-4220	28	15	some	some	DET
ejpam-4220	28	16	researchers	researcher	NOUN
ejpam-4220	28	17	.	.	PUNCT
ejpam-4220	29	1	some	some	PRON
ejpam-4220	29	2	of	of	ADP
ejpam-4220	29	3	these	these	PRON
ejpam-4220	29	4	are	be	AUX
ejpam-4220	29	5	the	the	DET
ejpam-4220	29	6	articles	article	NOUN
ejpam-4220	29	7	“	"	PUNCT
ejpam-4220	29	8	neighborhood	neighborhood	NOUN
ejpam-4220	29	9	polynomial	polynomial	NOUN
ejpam-4220	29	10	of	of	ADP
ejpam-4220	29	11	graphs	graph	NOUN
ejpam-4220	29	12	”	"	PUNCT
ejpam-4220	29	13	by	by	ADP
ejpam-4220	29	14	j.	j.	PROPN
ejpam-4220	29	15	brown	brown	PROPN
ejpam-4220	29	16	and	and	CCONJ
ejpam-4220	29	17	r.	r.	PROPN
ejpam-4220	29	18	nowakowski	nowakowski	PROPN
ejpam-4220	30	1	[	[	X
ejpam-4220	30	2	9	9	NUM
ejpam-4220	30	3	]	]	PUNCT
ejpam-4220	30	4	and	and	CCONJ
ejpam-4220	30	5	“	"	PUNCT
ejpam-4220	30	6	on	on	ADP
ejpam-4220	30	7	the	the	DET
ejpam-4220	30	8	independent	independent	ADJ
ejpam-4220	30	9	neighborhood	neighborhood	NOUN
ejpam-4220	30	10	polynomial	polynomial	NOUN
ejpam-4220	30	11	of	of	ADP
ejpam-4220	30	12	graphs	graph	NOUN
ejpam-4220	30	13	”	"	PUNCT
ejpam-4220	30	14	by	by	ADP
ejpam-4220	30	15	k.b	k.b	PROPN
ejpam-4220	30	16	.	.	PROPN
ejpam-4220	30	17	murthy	murthy	PROPN
ejpam-4220	30	18	and	and	CCONJ
ejpam-4220	30	19	puttaswamy[11	puttaswamy[11	ADV
ejpam-4220	30	20	]	]	PUNCT
ejpam-4220	30	21	.	.	PUNCT
ejpam-4220	31	1	the	the	DET
ejpam-4220	31	2	main	main	ADJ
ejpam-4220	31	3	interest	interest	NOUN
ejpam-4220	31	4	of	of	ADP
ejpam-4220	31	5	this	this	DET
ejpam-4220	31	6	study	study	NOUN
ejpam-4220	31	7	is	be	AUX
ejpam-4220	31	8	to	to	PART
ejpam-4220	31	9	establish	establish	VERB
ejpam-4220	31	10	results	result	NOUN
ejpam-4220	31	11	on	on	ADP
ejpam-4220	31	12	the	the	DET
ejpam-4220	31	13	independent	independent	ADJ
ejpam-4220	31	14	neighborhood	neighborhood	NOUN
ejpam-4220	31	15	polynomial	polynomial	NOUN
ejpam-4220	31	16	of	of	ADP
ejpam-4220	31	17	tree	tree	NOUN
ejpam-4220	31	18	and	and	CCONJ
ejpam-4220	31	19	the	the	DET
ejpam-4220	31	20	rooted	rooted	ADJ
ejpam-4220	31	21	product	product	NOUN
ejpam-4220	31	22	of	of	ADP
ejpam-4220	31	23	two	two	NUM
ejpam-4220	31	24	trees	tree	NOUN
ejpam-4220	31	25	.	.	PUNCT
ejpam-4220	32	1	2	2	X
ejpam-4220	32	2	.	.	X
ejpam-4220	32	3	preliminaries	preliminary	NOUN
ejpam-4220	32	4	this	this	DET
ejpam-4220	32	5	section	section	NOUN
ejpam-4220	32	6	presents	present	VERB
ejpam-4220	32	7	some	some	DET
ejpam-4220	32	8	basic	basic	ADJ
ejpam-4220	32	9	concepts	concept	NOUN
ejpam-4220	32	10	in	in	ADP
ejpam-4220	32	11	graph	graph	NOUN
ejpam-4220	32	12	theory	theory	NOUN
ejpam-4220	32	13	and	and	CCONJ
ejpam-4220	32	14	known	know	VERB
ejpam-4220	32	15	results	result	NOUN
ejpam-4220	32	16	needed	need	VERB
ejpam-4220	32	17	in	in	ADP
ejpam-4220	32	18	this	this	DET
ejpam-4220	32	19	study	study	NOUN
ejpam-4220	32	20	.	.	PUNCT
ejpam-4220	33	1	definition	definition	NOUN
ejpam-4220	33	2	1	1	NUM
ejpam-4220	33	3	.	.	PUNCT
ejpam-4220	34	1	[	[	X
ejpam-4220	34	2	2	2	X
ejpam-4220	34	3	]	]	PUNCT
ejpam-4220	34	4	the	the	DET
ejpam-4220	34	5	open	open	ADJ
ejpam-4220	34	6	neighborhood	neighborhood	NOUN
ejpam-4220	34	7	of	of	ADP
ejpam-4220	34	8	a	a	DET
ejpam-4220	34	9	vertex	vertex	NOUN
ejpam-4220	34	10	x	x	NOUN
ejpam-4220	34	11	,	,	PUNCT
ejpam-4220	34	12	denoted	denote	VERB
ejpam-4220	34	13	byn(x	byn(x	PROPN
ejpam-4220	34	14	)	)	PUNCT
ejpam-4220	34	15	,	,	PUNCT
ejpam-4220	34	16	is	be	AUX
ejpam-4220	34	17	a	a	DET
ejpam-4220	34	18	set	set	NOUN
ejpam-4220	34	19	containing	contain	VERB
ejpam-4220	34	20	all	all	DET
ejpam-4220	34	21	vertices	vertex	NOUN
ejpam-4220	34	22	y	y	PRON
ejpam-4220	34	23	which	which	PRON
ejpam-4220	34	24	are	be	AUX
ejpam-4220	34	25	adjacent	adjacent	ADJ
ejpam-4220	34	26	to	to	ADP
ejpam-4220	34	27	x	x	PRON
ejpam-4220	34	28	,	,	PUNCT
ejpam-4220	34	29	that	that	ADV
ejpam-4220	34	30	is	is	ADV
ejpam-4220	34	31	,	,	PUNCT
ejpam-4220	34	32	n(x	n(x	X
ejpam-4220	34	33	)	)	PUNCT
ejpam-4220	34	34	=	=	SYM
ejpam-4220	34	35	{	{	PUNCT
ejpam-4220	34	36	y	y	PROPN
ejpam-4220	34	37	∈	∈	PROPN
ejpam-4220	34	38	v	v	NOUN
ejpam-4220	34	39	(	(	PUNCT
ejpam-4220	34	40	g	g	NOUN
ejpam-4220	34	41	)	)	PUNCT
ejpam-4220	34	42	:	:	PUNCT
ejpam-4220	34	43	xy	xy	PROPN
ejpam-4220	34	44	∈	∈	PROPN
ejpam-4220	34	45	e(g	e(g	PROPN
ejpam-4220	34	46	)	)	PUNCT
ejpam-4220	34	47	}	}	PUNCT
ejpam-4220	34	48	.	.	PUNCT
ejpam-4220	35	1	in	in	ADP
ejpam-4220	35	2	case	case	NOUN
ejpam-4220	35	3	n(x	n(x	PROPN
ejpam-4220	35	4	)	)	PUNCT
ejpam-4220	35	5	is	be	AUX
ejpam-4220	35	6	a	a	DET
ejpam-4220	35	7	singleton	singleton	NOUN
ejpam-4220	35	8	,	,	PUNCT
ejpam-4220	35	9	x	x	X
ejpam-4220	35	10	is	be	AUX
ejpam-4220	35	11	an	an	DET
ejpam-4220	35	12	end	end	NOUN
ejpam-4220	35	13	-	-	PUNCT
ejpam-4220	35	14	vertex	vertex	NOUN
ejpam-4220	35	15	.	.	PUNCT
ejpam-4220	36	1	the	the	DET
ejpam-4220	36	2	closed	closed	ADJ
ejpam-4220	36	3	neighborhood	neighborhood	NOUN
ejpam-4220	36	4	of	of	ADP
ejpam-4220	36	5	a	a	DET
ejpam-4220	36	6	vertex	vertex	NOUN
ejpam-4220	36	7	x	x	X
ejpam-4220	36	8	of	of	ADP
ejpam-4220	36	9	g	g	PROPN
ejpam-4220	36	10	is	be	AUX
ejpam-4220	36	11	the	the	DET
ejpam-4220	36	12	set	set	ADJ
ejpam-4220	36	13	n	n	NOUN
ejpam-4220	36	14	[	[	X
ejpam-4220	36	15	x	x	X
ejpam-4220	36	16	]	]	X
ejpam-4220	36	17	=	=	SYM
ejpam-4220	36	18	n(x	n(x	X
ejpam-4220	36	19	)	)	PUNCT
ejpam-4220	36	20	∪	∪	ADP
ejpam-4220	36	21	{	{	PUNCT
ejpam-4220	36	22	x	x	NOUN
ejpam-4220	36	23	}	}	PUNCT
ejpam-4220	36	24	.	.	PUNCT
ejpam-4220	37	1	definition	definition	NOUN
ejpam-4220	37	2	2	2	NUM
ejpam-4220	37	3	.	.	PUNCT
ejpam-4220	38	1	[	[	X
ejpam-4220	38	2	11	11	NUM
ejpam-4220	38	3	]	]	PUNCT
ejpam-4220	38	4	a	a	DET
ejpam-4220	38	5	set	set	NOUN
ejpam-4220	38	6	s	s	NOUN
ejpam-4220	38	7	of	of	ADP
ejpam-4220	38	8	vertices	vertex	NOUN
ejpam-4220	38	9	in	in	ADP
ejpam-4220	38	10	a	a	DET
ejpam-4220	38	11	graph	graph	NOUN
ejpam-4220	38	12	g	g	NOUN
ejpam-4220	38	13	is	be	AUX
ejpam-4220	38	14	a	a	DET
ejpam-4220	38	15	neighborhood	neighborhood	NOUN
ejpam-4220	38	16	set	set	VERB
ejpam-4220	38	17	if	if	SCONJ
ejpam-4220	38	18	g	g	NOUN
ejpam-4220	38	19	=	=	SYM
ejpam-4220	38	20	⋃	⋃	NOUN
ejpam-4220	38	21	u∈s	u∈s	NOUN
ejpam-4220	38	22	⟨n	⟨n	NUM
ejpam-4220	38	23	[	[	X
ejpam-4220	38	24	u]⟩	u]⟩	X
ejpam-4220	38	25	where	where	SCONJ
ejpam-4220	38	26	⟨n	⟨n	NUM
ejpam-4220	38	27	[	[	X
ejpam-4220	38	28	u]⟩	u]⟩	NOUN
ejpam-4220	38	29	is	be	AUX
ejpam-4220	38	30	the	the	DET
ejpam-4220	38	31	subgraph	subgraph	NOUN
ejpam-4220	38	32	of	of	ADP
ejpam-4220	38	33	g	g	PROPN
ejpam-4220	38	34	induced	induce	VERB
ejpam-4220	38	35	by	by	ADP
ejpam-4220	38	36	u	u	NOUN
ejpam-4220	38	37	and	and	CCONJ
ejpam-4220	38	38	all	all	DET
ejpam-4220	38	39	the	the	DET
ejpam-4220	38	40	vertices	vertex	NOUN
ejpam-4220	38	41	adjacent	adjacent	ADJ
ejpam-4220	38	42	to	to	PART
ejpam-4220	38	43	u.	u.	VERB
ejpam-4220	38	44	the	the	DET
ejpam-4220	38	45	neighborhood	neighborhood	NOUN
ejpam-4220	38	46	number	number	NOUN
ejpam-4220	38	47	of	of	ADP
ejpam-4220	38	48	g	g	PROPN
ejpam-4220	38	49	is	be	AUX
ejpam-4220	38	50	the	the	DET
ejpam-4220	38	51	minimum	minimum	ADJ
ejpam-4220	38	52	cardinality	cardinality	NOUN
ejpam-4220	38	53	of	of	ADP
ejpam-4220	38	54	neighborhood	neighborhood	NOUN
ejpam-4220	38	55	sets	set	NOUN
ejpam-4220	38	56	,	,	PUNCT
ejpam-4220	38	57	denoted	denote	VERB
ejpam-4220	38	58	by	by	ADP
ejpam-4220	38	59	ηi(g	ηi(g	NOUN
ejpam-4220	38	60	)	)	PUNCT
ejpam-4220	38	61	.	.	PUNCT
ejpam-4220	39	1	example	example	NOUN
ejpam-4220	40	1	1	1	X
ejpam-4220	40	2	.	.	X
ejpam-4220	40	3	consider	consider	VERB
ejpam-4220	40	4	the	the	DET
ejpam-4220	40	5	graph	graph	NOUN
ejpam-4220	40	6	h	h	NOUN
ejpam-4220	40	7	in	in	ADP
ejpam-4220	40	8	figure	figure	NOUN
ejpam-4220	40	9	1	1	NUM
ejpam-4220	40	10	.	.	PUNCT
ejpam-4220	40	11	v1	v1	PROPN
ejpam-4220	40	12	v2	v2	PROPN
ejpam-4220	40	13	v3	v3	PROPN
ejpam-4220	40	14	v4	v4	PROPN
ejpam-4220	40	15	figure	figure	NOUN
ejpam-4220	40	16	1	1	NUM
ejpam-4220	40	17	:	:	PUNCT
ejpam-4220	40	18	a	a	DET
ejpam-4220	40	19	graph	graph	NOUN
ejpam-4220	40	20	h	h	NOUN
ejpam-4220	40	21	n.	n.	PROPN
ejpam-4220	40	22	s.	s.	PROPN
ejpam-4220	40	23	abdulcarim	abdulcarim	PROPN
ejpam-4220	40	24	,	,	PUNCT
ejpam-4220	40	25	s.	s.	PROPN
ejpam-4220	40	26	c.	c.	PROPN
ejpam-4220	40	27	dagondon	dagondon	PROPN
ejpam-4220	40	28	/	/	SYM
ejpam-4220	40	29	eur	eur	PROPN
ejpam-4220	40	30	.	.	PUNCT
ejpam-4220	41	1	j.	j.	PROPN
ejpam-4220	41	2	pure	pure	PROPN
ejpam-4220	41	3	appl	appl	PROPN
ejpam-4220	41	4	.	.	PROPN
ejpam-4220	41	5	math	math	PROPN
ejpam-4220	41	6	,	,	PUNCT
ejpam-4220	41	7	15	15	NUM
ejpam-4220	41	8	(	(	PUNCT
ejpam-4220	41	9	1	1	NUM
ejpam-4220	41	10	)	)	PUNCT
ejpam-4220	41	11	(	(	PUNCT
ejpam-4220	41	12	2022	2022	NUM
ejpam-4220	41	13	)	)	PUNCT
ejpam-4220	41	14	,	,	PUNCT
ejpam-4220	41	15	64	64	NUM
ejpam-4220	41	16	-	-	SYM
ejpam-4220	41	17	81	81	NUM
ejpam-4220	41	18	66	66	NUM
ejpam-4220	41	19	the	the	DET
ejpam-4220	41	20	neighborhood	neighborhood	NOUN
ejpam-4220	41	21	sets	set	NOUN
ejpam-4220	41	22	of	of	ADP
ejpam-4220	41	23	h	h	NOUN
ejpam-4220	41	24	are	be	AUX
ejpam-4220	41	25	{	{	PUNCT
ejpam-4220	41	26	v1	v1	NOUN
ejpam-4220	41	27	,	,	PUNCT
ejpam-4220	41	28	v3	v3	PROPN
ejpam-4220	41	29	}	}	PUNCT
ejpam-4220	41	30	,	,	PUNCT
ejpam-4220	41	31	{	{	PUNCT
ejpam-4220	41	32	v2	v2	NOUN
ejpam-4220	41	33	}	}	PUNCT
ejpam-4220	41	34	,	,	PUNCT
ejpam-4220	41	35	{	{	PUNCT
ejpam-4220	41	36	v4	v4	NOUN
ejpam-4220	41	37	}	}	PUNCT
ejpam-4220	41	38	,	,	PUNCT
ejpam-4220	41	39	{	{	PUNCT
ejpam-4220	41	40	v1	v1	NOUN
ejpam-4220	41	41	,	,	PUNCT
ejpam-4220	41	42	v2	v2	PROPN
ejpam-4220	41	43	}	}	PUNCT
ejpam-4220	41	44	,	,	PUNCT
ejpam-4220	41	45	{	{	PUNCT
ejpam-4220	41	46	v2	v2	NOUN
ejpam-4220	41	47	,	,	PUNCT
ejpam-4220	41	48	v3	v3	PROPN
ejpam-4220	41	49	}	}	PUNCT
ejpam-4220	41	50	,	,	PUNCT
ejpam-4220	41	51	{	{	PUNCT
ejpam-4220	41	52	v2	v2	NOUN
ejpam-4220	41	53	,	,	PUNCT
ejpam-4220	41	54	v4}{v1	v4}{v1	PROPN
ejpam-4220	41	55	,	,	PUNCT
ejpam-4220	41	56	v4	v4	PROPN
ejpam-4220	41	57	}	}	PUNCT
ejpam-4220	41	58	,	,	PUNCT
ejpam-4220	41	59	{	{	PUNCT
ejpam-4220	41	60	v3	v3	PROPN
ejpam-4220	41	61	,	,	PUNCT
ejpam-4220	41	62	v4	v4	PROPN
ejpam-4220	41	63	}	}	PUNCT
ejpam-4220	41	64	,	,	PUNCT
ejpam-4220	41	65	{	{	PUNCT
ejpam-4220	41	66	v1	v1	NOUN
ejpam-4220	41	67	,	,	PUNCT
ejpam-4220	41	68	v2	v2	PROPN
ejpam-4220	41	69	,	,	PUNCT
ejpam-4220	41	70	v3	v3	PROPN
ejpam-4220	41	71	}	}	PUNCT
ejpam-4220	41	72	,	,	PUNCT
ejpam-4220	41	73	{	{	PUNCT
ejpam-4220	41	74	v1	v1	NOUN
ejpam-4220	41	75	,	,	PUNCT
ejpam-4220	41	76	v2	v2	PROPN
ejpam-4220	41	77	,	,	PUNCT
ejpam-4220	41	78	v4	v4	PROPN
ejpam-4220	41	79	}	}	PUNCT
ejpam-4220	41	80	,	,	PUNCT
ejpam-4220	41	81	{	{	PUNCT
ejpam-4220	41	82	v1	v1	NOUN
ejpam-4220	41	83	,	,	PUNCT
ejpam-4220	41	84	v3	v3	PROPN
ejpam-4220	41	85	,	,	PUNCT
ejpam-4220	41	86	v4	v4	PROPN
ejpam-4220	41	87	}	}	PUNCT
ejpam-4220	41	88	,	,	PUNCT
ejpam-4220	41	89	{	{	PUNCT
ejpam-4220	41	90	v2	v2	PROPN
ejpam-4220	41	91	,	,	PUNCT
ejpam-4220	41	92	v3	v3	PROPN
ejpam-4220	41	93	,	,	PUNCT
ejpam-4220	41	94	v4	v4	PROPN
ejpam-4220	41	95	}	}	PUNCT
ejpam-4220	41	96	and	and	CCONJ
ejpam-4220	41	97	{	{	PUNCT
ejpam-4220	41	98	v1	v1	NOUN
ejpam-4220	41	99	,	,	PUNCT
ejpam-4220	41	100	v2	v2	PROPN
ejpam-4220	41	101	,	,	PUNCT
ejpam-4220	41	102	v3	v3	PROPN
ejpam-4220	41	103	,	,	PUNCT
ejpam-4220	41	104	v4	v4	PROPN
ejpam-4220	41	105	}	}	PUNCT
ejpam-4220	41	106	.	.	PUNCT
ejpam-4220	42	1	here	here	ADV
ejpam-4220	42	2	,	,	PUNCT
ejpam-4220	42	3	ηi(h	ηi(h	NOUN
ejpam-4220	42	4	)	)	PUNCT
ejpam-4220	42	5	=	=	SYM
ejpam-4220	43	1	1	1	X
ejpam-4220	43	2	.	.	X
ejpam-4220	43	3	definition	definition	NOUN
ejpam-4220	43	4	3	3	NUM
ejpam-4220	43	5	.	.	PUNCT
ejpam-4220	44	1	[	[	X
ejpam-4220	44	2	11	11	NUM
ejpam-4220	44	3	]	]	PUNCT
ejpam-4220	44	4	a	a	DET
ejpam-4220	44	5	set	set	NOUN
ejpam-4220	44	6	s	s	NOUN
ejpam-4220	44	7	⊆	⊆	NUM
ejpam-4220	44	8	v	v	NOUN
ejpam-4220	44	9	(	(	PUNCT
ejpam-4220	44	10	g	g	NOUN
ejpam-4220	44	11	)	)	PUNCT
ejpam-4220	44	12	is	be	AUX
ejpam-4220	44	13	an	an	DET
ejpam-4220	44	14	independent	independent	ADJ
ejpam-4220	44	15	neighborhood	neighborhood	NOUN
ejpam-4220	44	16	set	set	NOUN
ejpam-4220	44	17	of	of	ADP
ejpam-4220	44	18	g	g	NOUN
ejpam-4220	44	19	,	,	PUNCT
ejpam-4220	44	20	if	if	SCONJ
ejpam-4220	44	21	s	s	VERB
ejpam-4220	44	22	is	be	AUX
ejpam-4220	44	23	a	a	DET
ejpam-4220	44	24	neighborhood	neighborhood	NOUN
ejpam-4220	44	25	set	set	VERB
ejpam-4220	44	26	and	and	CCONJ
ejpam-4220	44	27	no	no	DET
ejpam-4220	44	28	two	two	NUM
ejpam-4220	44	29	vertices	vertex	NOUN
ejpam-4220	44	30	in	in	ADP
ejpam-4220	44	31	s	s	NOUN
ejpam-4220	44	32	are	be	AUX
ejpam-4220	44	33	adjacent	adjacent	ADJ
ejpam-4220	44	34	.	.	PUNCT
ejpam-4220	45	1	definition	definition	NOUN
ejpam-4220	45	2	4	4	NUM
ejpam-4220	45	3	.	.	PUNCT
ejpam-4220	46	1	[	[	X
ejpam-4220	46	2	11	11	NUM
ejpam-4220	46	3	]	]	PUNCT
ejpam-4220	46	4	let	let	VERB
ejpam-4220	46	5	g	g	PROPN
ejpam-4220	46	6	=	=	SYM
ejpam-4220	46	7	(	(	PUNCT
ejpam-4220	46	8	v	v	NOUN
ejpam-4220	46	9	(	(	PUNCT
ejpam-4220	46	10	g	g	NOUN
ejpam-4220	46	11	)	)	PUNCT
ejpam-4220	46	12	,	,	PUNCT
ejpam-4220	46	13	e(g	e(g	PROPN
ejpam-4220	46	14	)	)	PUNCT
ejpam-4220	46	15	)	)	PUNCT
ejpam-4220	46	16	be	be	AUX
ejpam-4220	46	17	a	a	DET
ejpam-4220	46	18	graph	graph	NOUN
ejpam-4220	46	19	with	with	ADP
ejpam-4220	46	20	m	m	PROPN
ejpam-4220	46	21	vertices	vertex	NOUN
ejpam-4220	46	22	.	.	PUNCT
ejpam-4220	47	1	then	then	ADV
ejpam-4220	47	2	the	the	DET
ejpam-4220	47	3	independent	independent	ADJ
ejpam-4220	47	4	neighborhood	neighborhood	NOUN
ejpam-4220	47	5	polynomial	polynomial	NOUN
ejpam-4220	47	6	of	of	ADP
ejpam-4220	47	7	g	g	NOUN
ejpam-4220	47	8	of	of	ADP
ejpam-4220	47	9	order	order	NOUN
ejpam-4220	47	10	m	m	NOUN
ejpam-4220	47	11	is	be	AUX
ejpam-4220	47	12	ni(g	ni(g	NOUN
ejpam-4220	47	13	,	,	PUNCT
ejpam-4220	47	14	x	x	X
ejpam-4220	47	15	)	)	PUNCT
ejpam-4220	47	16	=	=	PUNCT
ejpam-4220	47	17	m∑	m∑	PRON
ejpam-4220	47	18	j	j	X
ejpam-4220	47	19	=	=	NOUN
ejpam-4220	47	20	ηi(g	ηi(g	NOUN
ejpam-4220	47	21	)	)	PUNCT
ejpam-4220	47	22	ni(g	ni(g	PUNCT
ejpam-4220	47	23	,	,	PUNCT
ejpam-4220	47	24	j)xj	j)xj	NOUN
ejpam-4220	47	25	,	,	PUNCT
ejpam-4220	47	26	where	where	SCONJ
ejpam-4220	47	27	ni(g	ni(g	NUM
ejpam-4220	47	28	,	,	PUNCT
ejpam-4220	47	29	j	j	NOUN
ejpam-4220	47	30	)	)	PUNCT
ejpam-4220	47	31	is	be	AUX
ejpam-4220	47	32	the	the	DET
ejpam-4220	47	33	number	number	NOUN
ejpam-4220	47	34	of	of	ADP
ejpam-4220	47	35	independent	independent	ADJ
ejpam-4220	47	36	neighborhood	neighborhood	NOUN
ejpam-4220	47	37	set	set	VERB
ejpam-4220	47	38	ofg	ofg	PROPN
ejpam-4220	47	39	of	of	ADP
ejpam-4220	47	40	size	size	NOUN
ejpam-4220	47	41	j	j	PROPN
ejpam-4220	47	42	and	and	CCONJ
ejpam-4220	47	43	ηi(g	ηi(g	NOUN
ejpam-4220	47	44	)	)	PUNCT
ejpam-4220	47	45	is	be	AUX
ejpam-4220	47	46	the	the	DET
ejpam-4220	47	47	minimum	minimum	ADJ
ejpam-4220	47	48	cardinality	cardinality	NOUN
ejpam-4220	47	49	of	of	ADP
ejpam-4220	47	50	an	an	DET
ejpam-4220	47	51	independent	independent	ADJ
ejpam-4220	47	52	neighborhood	neighborhood	NOUN
ejpam-4220	47	53	set	set	NOUN
ejpam-4220	47	54	which	which	PRON
ejpam-4220	47	55	is	be	AUX
ejpam-4220	47	56	called	call	VERB
ejpam-4220	47	57	the	the	DET
ejpam-4220	47	58	independent	independent	ADJ
ejpam-4220	47	59	neighborhood	neighborhood	NOUN
ejpam-4220	47	60	number	number	NOUN
ejpam-4220	47	61	of	of	ADP
ejpam-4220	47	62	g.	g.	PROPN
ejpam-4220	47	63	example	example	NOUN
ejpam-4220	48	1	2	2	NUM
ejpam-4220	48	2	.	.	X
ejpam-4220	48	3	in	in	ADP
ejpam-4220	48	4	figure	figure	NOUN
ejpam-4220	48	5	1	1	NUM
ejpam-4220	48	6	above	above	ADV
ejpam-4220	48	7	,	,	PUNCT
ejpam-4220	48	8	the	the	DET
ejpam-4220	48	9	only	only	ADJ
ejpam-4220	48	10	independent	independent	ADJ
ejpam-4220	48	11	neighborhood	neighborhood	NOUN
ejpam-4220	48	12	sets	set	VERB
ejpam-4220	48	13	ofh	ofh	PROPN
ejpam-4220	48	14	are	be	AUX
ejpam-4220	48	15	{	{	PUNCT
ejpam-4220	48	16	v2	v2	NOUN
ejpam-4220	48	17	}	}	PUNCT
ejpam-4220	48	18	,	,	PUNCT
ejpam-4220	48	19	{	{	PUNCT
ejpam-4220	48	20	v4	v4	NOUN
ejpam-4220	48	21	}	}	PUNCT
ejpam-4220	48	22	and	and	CCONJ
ejpam-4220	48	23	{	{	PUNCT
ejpam-4220	48	24	v1	v1	NOUN
ejpam-4220	48	25	,	,	PUNCT
ejpam-4220	48	26	v3	v3	PROPN
ejpam-4220	48	27	}	}	PUNCT
ejpam-4220	48	28	.	.	PUNCT
ejpam-4220	49	1	therefore	therefore	ADV
ejpam-4220	49	2	,	,	PUNCT
ejpam-4220	49	3	the	the	DET
ejpam-4220	49	4	independent	independent	ADJ
ejpam-4220	49	5	neighborhood	neighborhood	NOUN
ejpam-4220	49	6	polynomial	polynomial	NOUN
ejpam-4220	49	7	of	of	ADP
ejpam-4220	49	8	h	h	NOUN
ejpam-4220	49	9	is	be	AUX
ejpam-4220	49	10	ni(h	ni(h	VERB
ejpam-4220	49	11	,	,	PUNCT
ejpam-4220	49	12	x	x	X
ejpam-4220	49	13	)	)	PUNCT
ejpam-4220	50	1	=	=	SYM
ejpam-4220	50	2	2x+	2x+	NUM
ejpam-4220	50	3	x2	x2	NOUN
ejpam-4220	50	4	.	.	PUNCT
ejpam-4220	51	1	definition	definition	NOUN
ejpam-4220	51	2	5	5	NUM
ejpam-4220	51	3	.	.	PUNCT
ejpam-4220	52	1	[	[	X
ejpam-4220	52	2	6]a	6]a	NUM
ejpam-4220	52	3	graph	graph	NOUN
ejpam-4220	52	4	is	be	AUX
ejpam-4220	52	5	acyclic	acyclic	ADJ
ejpam-4220	52	6	if	if	SCONJ
ejpam-4220	52	7	it	it	PRON
ejpam-4220	52	8	has	have	VERB
ejpam-4220	52	9	no	no	DET
ejpam-4220	52	10	cycles	cycle	NOUN
ejpam-4220	52	11	.	.	PUNCT
ejpam-4220	53	1	a	a	DET
ejpam-4220	53	2	graph	graph	NOUN
ejpam-4220	53	3	is	be	AUX
ejpam-4220	53	4	said	say	VERB
ejpam-4220	53	5	to	to	PART
ejpam-4220	53	6	be	be	AUX
ejpam-4220	53	7	connected	connect	VERB
ejpam-4220	53	8	if	if	SCONJ
ejpam-4220	53	9	every	every	DET
ejpam-4220	53	10	pair	pair	NOUN
ejpam-4220	53	11	of	of	ADP
ejpam-4220	53	12	vertices	vertex	NOUN
ejpam-4220	53	13	are	be	AUX
ejpam-4220	53	14	joined	join	VERB
ejpam-4220	53	15	by	by	ADP
ejpam-4220	53	16	a	a	DET
ejpam-4220	53	17	path	path	NOUN
ejpam-4220	53	18	.	.	PUNCT
ejpam-4220	54	1	a	a	DET
ejpam-4220	54	2	graph	graph	NOUN
ejpam-4220	54	3	that	that	PRON
ejpam-4220	54	4	is	be	AUX
ejpam-4220	54	5	not	not	PART
ejpam-4220	54	6	connected	connect	VERB
ejpam-4220	54	7	is	be	AUX
ejpam-4220	54	8	called	call	VERB
ejpam-4220	54	9	disconnected	disconnected	ADJ
ejpam-4220	54	10	.	.	PUNCT
ejpam-4220	55	1	a	a	DET
ejpam-4220	55	2	tree	tree	NOUN
ejpam-4220	55	3	is	be	AUX
ejpam-4220	55	4	a	a	DET
ejpam-4220	55	5	connected	connected	ADJ
ejpam-4220	55	6	acyclic	acyclic	ADJ
ejpam-4220	55	7	graph	graph	NOUN
ejpam-4220	55	8	.	.	PUNCT
ejpam-4220	56	1	theorem	theorem	NOUN
ejpam-4220	56	2	1	1	NUM
ejpam-4220	56	3	.	.	PUNCT
ejpam-4220	57	1	[	[	X
ejpam-4220	57	2	8	8	NUM
ejpam-4220	57	3	]	]	PUNCT
ejpam-4220	57	4	for	for	ADP
ejpam-4220	57	5	a	a	DET
ejpam-4220	57	6	simple	simple	ADJ
ejpam-4220	57	7	graph	graph	NOUN
ejpam-4220	57	8	g	g	NOUN
ejpam-4220	57	9	(	(	PUNCT
ejpam-4220	57	10	with	with	ADP
ejpam-4220	57	11	n	n	ADP
ejpam-4220	57	12	vertices	vertex	NOUN
ejpam-4220	57	13	,	,	PUNCT
ejpam-4220	57	14	n	n	PRON
ejpam-4220	57	15	≥	≥	NOUN
ejpam-4220	57	16	1	1	NUM
ejpam-4220	57	17	)	)	PUNCT
ejpam-4220	57	18	,	,	PUNCT
ejpam-4220	57	19	the	the	DET
ejpam-4220	57	20	following	follow	VERB
ejpam-4220	57	21	statements	statement	NOUN
ejpam-4220	57	22	are	be	AUX
ejpam-4220	57	23	equivalent	equivalent	ADJ
ejpam-4220	57	24	(	(	PUNCT
ejpam-4220	57	25	i	i	NOUN
ejpam-4220	57	26	)	)	PUNCT
ejpam-4220	57	27	g	g	NOUN
ejpam-4220	57	28	is	be	AUX
ejpam-4220	57	29	a	a	DET
ejpam-4220	57	30	tree	tree	NOUN
ejpam-4220	57	31	(	(	PUNCT
ejpam-4220	57	32	ii	ii	NOUN
ejpam-4220	57	33	)	)	PUNCT
ejpam-4220	57	34	g	g	NOUN
ejpam-4220	57	35	is	be	AUX
ejpam-4220	57	36	connected	connect	VERB
ejpam-4220	57	37	and	and	CCONJ
ejpam-4220	57	38	has	have	VERB
ejpam-4220	57	39	no	no	DET
ejpam-4220	57	40	cycles	cycle	NOUN
ejpam-4220	57	41	(	(	PUNCT
ejpam-4220	57	42	iii	iii	X
ejpam-4220	57	43	)	)	PUNCT
ejpam-4220	57	44	g	g	NOUN
ejpam-4220	57	45	is	be	AUX
ejpam-4220	57	46	connected	connect	VERB
ejpam-4220	57	47	and	and	CCONJ
ejpam-4220	57	48	has	have	VERB
ejpam-4220	57	49	n−	n−	PROPN
ejpam-4220	57	50	1	1	NUM
ejpam-4220	57	51	edges	edge	NOUN
ejpam-4220	57	52	(	(	PUNCT
ejpam-4220	57	53	iv	iv	X
ejpam-4220	57	54	)	)	PUNCT
ejpam-4220	57	55	g	g	NOUN
ejpam-4220	57	56	has	have	VERB
ejpam-4220	57	57	n−	n−	PROPN
ejpam-4220	57	58	1	1	NUM
ejpam-4220	57	59	edges	edge	NOUN
ejpam-4220	57	60	and	and	CCONJ
ejpam-4220	57	61	has	have	VERB
ejpam-4220	57	62	no	no	DET
ejpam-4220	57	63	cycles	cycle	NOUN
ejpam-4220	57	64	(	(	PUNCT
ejpam-4220	57	65	v	v	NOUN
ejpam-4220	57	66	)	)	PUNCT
ejpam-4220	57	67	every	every	DET
ejpam-4220	57	68	two	two	NUM
ejpam-4220	57	69	vertices	vertex	NOUN
ejpam-4220	57	70	of	of	ADP
ejpam-4220	57	71	g	g	NOUN
ejpam-4220	57	72	are	be	AUX
ejpam-4220	57	73	joined	join	VERB
ejpam-4220	57	74	by	by	ADP
ejpam-4220	57	75	a	a	DET
ejpam-4220	57	76	unique	unique	ADJ
ejpam-4220	57	77	path	path	NOUN
ejpam-4220	57	78	corollary	corollary	ADJ
ejpam-4220	57	79	1	1	NUM
ejpam-4220	57	80	.	.	PUNCT
ejpam-4220	58	1	[	[	X
ejpam-4220	58	2	8	8	NUM
ejpam-4220	58	3	]	]	PUNCT
ejpam-4220	58	4	every	every	DET
ejpam-4220	58	5	nontrivial	nontrivial	ADJ
ejpam-4220	58	6	tree	tree	NOUN
ejpam-4220	58	7	has	have	VERB
ejpam-4220	58	8	at	at	ADV
ejpam-4220	58	9	least	least	ADV
ejpam-4220	58	10	two	two	NUM
ejpam-4220	58	11	end	end	NOUN
ejpam-4220	58	12	vertices	vertex	NOUN
ejpam-4220	58	13	.	.	PUNCT
ejpam-4220	59	1	definition	definition	NOUN
ejpam-4220	59	2	6	6	NUM
ejpam-4220	59	3	.	.	PUNCT
ejpam-4220	60	1	[	[	X
ejpam-4220	60	2	3	3	X
ejpam-4220	60	3	]	]	PUNCT
ejpam-4220	60	4	let	let	VERB
ejpam-4220	60	5	g	g	PRON
ejpam-4220	60	6	be	be	AUX
ejpam-4220	60	7	a	a	DET
ejpam-4220	60	8	graph	graph	NOUN
ejpam-4220	60	9	.	.	PUNCT
ejpam-4220	61	1	the	the	DET
ejpam-4220	61	2	distance	distance	NOUN
ejpam-4220	61	3	between	between	ADP
ejpam-4220	61	4	two	two	NUM
ejpam-4220	61	5	vertices	vertex	NOUN
ejpam-4220	61	6	x	x	PUNCT
ejpam-4220	61	7	and	and	CCONJ
ejpam-4220	61	8	y	y	PROPN
ejpam-4220	61	9	in	in	ADP
ejpam-4220	61	10	a	a	DET
ejpam-4220	61	11	graph	graph	NOUN
ejpam-4220	61	12	g	g	NOUN
ejpam-4220	61	13	,	,	PUNCT
ejpam-4220	61	14	denoted	denote	VERB
ejpam-4220	61	15	by	by	ADP
ejpam-4220	61	16	dg(x	dg(x	NUM
ejpam-4220	61	17	,	,	PUNCT
ejpam-4220	61	18	y	y	NOUN
ejpam-4220	61	19	)	)	PUNCT
ejpam-4220	61	20	or	or	CCONJ
ejpam-4220	61	21	simply	simply	ADV
ejpam-4220	61	22	d(x	d(x	PROPN
ejpam-4220	61	23	,	,	PUNCT
ejpam-4220	61	24	y	y	PROPN
ejpam-4220	61	25	)	)	PUNCT
ejpam-4220	61	26	,	,	PUNCT
ejpam-4220	61	27	is	be	AUX
ejpam-4220	61	28	the	the	DET
ejpam-4220	61	29	length	length	NOUN
ejpam-4220	61	30	of	of	ADP
ejpam-4220	61	31	the	the	DET
ejpam-4220	61	32	shortest	short	ADJ
ejpam-4220	61	33	path	path	NOUN
ejpam-4220	61	34	joining	join	VERB
ejpam-4220	61	35	them	they	PRON
ejpam-4220	61	36	,	,	PUNCT
ejpam-4220	61	37	otherwise	otherwise	ADV
ejpam-4220	61	38	,	,	PUNCT
ejpam-4220	61	39	d(x	d(x	PROPN
ejpam-4220	61	40	,	,	PUNCT
ejpam-4220	61	41	y	y	NOUN
ejpam-4220	61	42	)	)	PUNCT
ejpam-4220	61	43	=	=	SYM
ejpam-4220	61	44	∞.	∞.	PROPN
ejpam-4220	61	45	remark	remark	VERB
ejpam-4220	61	46	1	1	NUM
ejpam-4220	61	47	.	.	PUNCT
ejpam-4220	62	1	[	[	X
ejpam-4220	62	2	6	6	NUM
ejpam-4220	62	3	]	]	PUNCT
ejpam-4220	62	4	in	in	ADP
ejpam-4220	62	5	a	a	DET
ejpam-4220	62	6	connected	connected	ADJ
ejpam-4220	62	7	graph	graph	NOUN
ejpam-4220	62	8	g	g	PROPN
ejpam-4220	62	9	,	,	PUNCT
ejpam-4220	62	10	the	the	DET
ejpam-4220	62	11	distance	distance	NOUN
ejpam-4220	62	12	is	be	AUX
ejpam-4220	62	13	a	a	DET
ejpam-4220	62	14	metric	metric	NOUN
ejpam-4220	62	15	,	,	PUNCT
ejpam-4220	62	16	that	that	ADV
ejpam-4220	62	17	is	is	ADV
ejpam-4220	62	18	,	,	PUNCT
ejpam-4220	62	19	for	for	ADP
ejpam-4220	62	20	all	all	DET
ejpam-4220	62	21	x	x	NOUN
ejpam-4220	62	22	,	,	PUNCT
ejpam-4220	62	23	y	y	PROPN
ejpam-4220	62	24	,	,	PUNCT
ejpam-4220	62	25	z	z	PROPN
ejpam-4220	62	26	∈	∈	PROPN
ejpam-4220	62	27	v	v	NOUN
ejpam-4220	62	28	(	(	PUNCT
ejpam-4220	62	29	g	g	NOUN
ejpam-4220	62	30	)	)	PUNCT
ejpam-4220	62	31	,	,	PUNCT
ejpam-4220	62	32	n.	n.	PROPN
ejpam-4220	62	33	s.	s.	PROPN
ejpam-4220	62	34	abdulcarim	abdulcarim	PROPN
ejpam-4220	62	35	,	,	PUNCT
ejpam-4220	62	36	s.	s.	PROPN
ejpam-4220	62	37	c.	c.	PROPN
ejpam-4220	62	38	dagondon	dagondon	PROPN
ejpam-4220	62	39	/	/	SYM
ejpam-4220	62	40	eur	eur	PROPN
ejpam-4220	62	41	.	.	PUNCT
ejpam-4220	63	1	j.	j.	PROPN
ejpam-4220	63	2	pure	pure	PROPN
ejpam-4220	63	3	appl	appl	PROPN
ejpam-4220	63	4	.	.	PROPN
ejpam-4220	63	5	math	math	PROPN
ejpam-4220	63	6	,	,	PUNCT
ejpam-4220	63	7	15	15	NUM
ejpam-4220	63	8	(	(	PUNCT
ejpam-4220	63	9	1	1	NUM
ejpam-4220	63	10	)	)	PUNCT
ejpam-4220	63	11	(	(	PUNCT
ejpam-4220	63	12	2022	2022	NUM
ejpam-4220	63	13	)	)	PUNCT
ejpam-4220	63	14	,	,	PUNCT
ejpam-4220	63	15	64	64	NUM
ejpam-4220	63	16	-	-	SYM
ejpam-4220	63	17	81	81	NUM
ejpam-4220	63	18	67	67	NUM
ejpam-4220	63	19	(	(	PUNCT
ejpam-4220	63	20	i	i	NOUN
ejpam-4220	63	21	)	)	PUNCT
ejpam-4220	63	22	d(x	d(x	PROPN
ejpam-4220	63	23	,	,	PUNCT
ejpam-4220	63	24	y	y	NOUN
ejpam-4220	63	25	)	)	PUNCT
ejpam-4220	63	26	≥	≥	NOUN
ejpam-4220	63	27	0	0	NUM
ejpam-4220	63	28	,	,	PUNCT
ejpam-4220	63	29	with	with	ADP
ejpam-4220	63	30	d(x	d(x	PROPN
ejpam-4220	63	31	,	,	PUNCT
ejpam-4220	63	32	y	y	NOUN
ejpam-4220	63	33	)	)	PUNCT
ejpam-4220	63	34	=	=	SYM
ejpam-4220	63	35	0	0	PUNCT
ejpam-4220	64	1	if	if	SCONJ
ejpam-4220	64	2	and	and	CCONJ
ejpam-4220	64	3	only	only	ADV
ejpam-4220	64	4	if	if	SCONJ
ejpam-4220	64	5	x	x	X
ejpam-4220	64	6	=	=	SYM
ejpam-4220	64	7	y.	y.	PROPN
ejpam-4220	64	8	(	(	PUNCT
ejpam-4220	64	9	ii	ii	PROPN
ejpam-4220	64	10	)	)	PUNCT
ejpam-4220	64	11	d(x	d(x	PROPN
ejpam-4220	64	12	,	,	PUNCT
ejpam-4220	64	13	y	y	NOUN
ejpam-4220	64	14	)	)	PUNCT
ejpam-4220	64	15	=	=	SYM
ejpam-4220	64	16	d(y	d(y	NOUN
ejpam-4220	64	17	,	,	PUNCT
ejpam-4220	64	18	x	x	NOUN
ejpam-4220	64	19	)	)	PUNCT
ejpam-4220	64	20	(	(	PUNCT
ejpam-4220	64	21	iii	iii	NOUN
ejpam-4220	64	22	)	)	PUNCT
ejpam-4220	64	23	d(x	d(x	PROPN
ejpam-4220	64	24	,	,	PUNCT
ejpam-4220	64	25	y	y	NOUN
ejpam-4220	64	26	)	)	PUNCT
ejpam-4220	65	1	+	+	CCONJ
ejpam-4220	65	2	d(y	d(y	NOUN
ejpam-4220	65	3	,	,	PUNCT
ejpam-4220	65	4	z	z	NOUN
ejpam-4220	65	5	)	)	PUNCT
ejpam-4220	65	6	≥	≥	NOUN
ejpam-4220	65	7	d(x	d(x	PROPN
ejpam-4220	65	8	,	,	PUNCT
ejpam-4220	65	9	z	z	NOUN
ejpam-4220	65	10	)	)	PUNCT
ejpam-4220	65	11	.	.	PUNCT
ejpam-4220	66	1	remark	remark	PROPN
ejpam-4220	66	2	2	2	NUM
ejpam-4220	66	3	.	.	PUNCT
ejpam-4220	67	1	for	for	ADP
ejpam-4220	67	2	any	any	DET
ejpam-4220	67	3	tree	tree	NOUN
ejpam-4220	67	4	t	t	NOUN
ejpam-4220	67	5	,	,	PUNCT
ejpam-4220	67	6	d(x	d(x	PROPN
ejpam-4220	67	7	,	,	PUNCT
ejpam-4220	67	8	y	y	PROPN
ejpam-4220	67	9	)	)	PUNCT
ejpam-4220	68	1	+	+	CCONJ
ejpam-4220	68	2	d(y	d(y	NOUN
ejpam-4220	68	3	,	,	PUNCT
ejpam-4220	68	4	z	z	NOUN
ejpam-4220	68	5	)	)	PUNCT
ejpam-4220	69	1	=	=	SYM
ejpam-4220	69	2	d(x	d(x	PROPN
ejpam-4220	69	3	,	,	PUNCT
ejpam-4220	69	4	z	z	NOUN
ejpam-4220	69	5	)	)	PUNCT
ejpam-4220	69	6	.	.	PUNCT
ejpam-4220	70	1	example	example	NOUN
ejpam-4220	71	1	3	3	X
ejpam-4220	71	2	.	.	X
ejpam-4220	71	3	consider	consider	VERB
ejpam-4220	71	4	the	the	DET
ejpam-4220	71	5	tree	tree	NOUN
ejpam-4220	71	6	below	below	ADP
ejpam-4220	71	7	u	u	PROPN
ejpam-4220	71	8	a	a	DET
ejpam-4220	71	9	v	v	NOUN
ejpam-4220	71	10	b	b	NOUN
ejpam-4220	71	11	g	g	NOUN
ejpam-4220	71	12	figure	figure	NOUN
ejpam-4220	71	13	2	2	NUM
ejpam-4220	71	14	:	:	PUNCT
ejpam-4220	71	15	a	a	DET
ejpam-4220	71	16	tree	tree	NOUN
ejpam-4220	71	17	in	in	ADP
ejpam-4220	71	18	figure	figure	NOUN
ejpam-4220	71	19	2	2	NUM
ejpam-4220	71	20	,	,	PUNCT
ejpam-4220	71	21	the	the	DET
ejpam-4220	71	22	distance	distance	NOUN
ejpam-4220	71	23	between	between	ADP
ejpam-4220	71	24	vertices	vertex	NOUN
ejpam-4220	71	25	u	u	NOUN
ejpam-4220	71	26	and	and	CCONJ
ejpam-4220	71	27	v	v	NOUN
ejpam-4220	71	28	is	be	AUX
ejpam-4220	71	29	d(u	d(u	PROPN
ejpam-4220	71	30	,	,	PUNCT
ejpam-4220	71	31	v	v	NOUN
ejpam-4220	71	32	)	)	PUNCT
ejpam-4220	71	33	=	=	SYM
ejpam-4220	71	34	4	4	NUM
ejpam-4220	71	35	and	and	CCONJ
ejpam-4220	71	36	the	the	DET
ejpam-4220	71	37	distance	distance	NOUN
ejpam-4220	71	38	between	between	ADP
ejpam-4220	71	39	a	a	PRON
ejpam-4220	71	40	and	and	CCONJ
ejpam-4220	71	41	b	b	NOUN
ejpam-4220	71	42	is	be	AUX
ejpam-4220	71	43	d(a	d(a	PROPN
ejpam-4220	71	44	,	,	PUNCT
ejpam-4220	71	45	b	b	NOUN
ejpam-4220	71	46	)	)	PUNCT
ejpam-4220	71	47	=	=	SYM
ejpam-4220	71	48	3	3	X
ejpam-4220	71	49	.	.	X
ejpam-4220	71	50	definition	definition	NOUN
ejpam-4220	71	51	7	7	NUM
ejpam-4220	71	52	.	.	PUNCT
ejpam-4220	72	1	[	[	X
ejpam-4220	72	2	6	6	NUM
ejpam-4220	72	3	]	]	PUNCT
ejpam-4220	72	4	a	a	DET
ejpam-4220	72	5	graph	graph	NOUN
ejpam-4220	72	6	in	in	ADP
ejpam-4220	72	7	which	which	PRON
ejpam-4220	72	8	one	one	NUM
ejpam-4220	72	9	vertex	vertex	NOUN
ejpam-4220	72	10	is	be	AUX
ejpam-4220	72	11	fixed	fix	VERB
ejpam-4220	72	12	as	as	ADP
ejpam-4220	72	13	a	a	DET
ejpam-4220	72	14	root	root	NOUN
ejpam-4220	72	15	vertex	vertex	NOUN
ejpam-4220	72	16	to	to	PART
ejpam-4220	72	17	distinguish	distinguish	VERB
ejpam-4220	72	18	it	it	PRON
ejpam-4220	72	19	from	from	ADP
ejpam-4220	72	20	the	the	DET
ejpam-4220	72	21	other	other	ADJ
ejpam-4220	72	22	is	be	AUX
ejpam-4220	72	23	called	call	VERB
ejpam-4220	72	24	a	a	DET
ejpam-4220	72	25	rooted	rooted	ADJ
ejpam-4220	72	26	graph	graph	NOUN
ejpam-4220	72	27	.	.	PUNCT
ejpam-4220	73	1	the	the	DET
ejpam-4220	73	2	rooted	rooted	ADJ
ejpam-4220	73	3	product	product	NOUN
ejpam-4220	73	4	of	of	ADP
ejpam-4220	73	5	a	a	DET
ejpam-4220	73	6	graph	graph	NOUN
ejpam-4220	73	7	g	g	NOUN
ejpam-4220	73	8	and	and	CCONJ
ejpam-4220	73	9	a	a	DET
ejpam-4220	73	10	rooted	rooted	ADJ
ejpam-4220	73	11	graph	graph	NOUN
ejpam-4220	73	12	h	h	NOUN
ejpam-4220	73	13	is	be	AUX
ejpam-4220	73	14	defined	define	VERB
ejpam-4220	73	15	as	as	SCONJ
ejpam-4220	73	16	follows	follow	VERB
ejpam-4220	73	17	:	:	PUNCT
ejpam-4220	73	18	let	let	VERB
ejpam-4220	73	19	v	v	X
ejpam-4220	73	20	(	(	PUNCT
ejpam-4220	73	21	g	g	NOUN
ejpam-4220	73	22	)	)	PUNCT
ejpam-4220	73	23	=	=	PRON
ejpam-4220	73	24	{	{	PUNCT
ejpam-4220	73	25	g1	g1	PROPN
ejpam-4220	73	26	,	,	PUNCT
ejpam-4220	73	27	g2	g2	PROPN
ejpam-4220	73	28	,	,	PUNCT
ejpam-4220	73	29	·	·	PUNCT
ejpam-4220	73	30	·	·	PUNCT
ejpam-4220	73	31	·	·	PUNCT
ejpam-4220	73	32	,	,	PUNCT
ejpam-4220	73	33	gn	gn	PROPN
ejpam-4220	73	34	}	}	PUNCT
ejpam-4220	73	35	,	,	PUNCT
ejpam-4220	73	36	v	v	INTJ
ejpam-4220	73	37	(	(	PUNCT
ejpam-4220	73	38	h	h	NOUN
ejpam-4220	73	39	)	)	PUNCT
ejpam-4220	73	40	=	=	PRON
ejpam-4220	73	41	{	{	PUNCT
ejpam-4220	73	42	h1	h1	PROPN
ejpam-4220	73	43	,	,	PUNCT
ejpam-4220	73	44	h2	h2	PROPN
ejpam-4220	73	45	,	,	PUNCT
ejpam-4220	73	46	·	·	PUNCT
ejpam-4220	73	47	·	·	PUNCT
ejpam-4220	73	48	·	·	PUNCT
ejpam-4220	73	49	,	,	PUNCT
ejpam-4220	73	50	hm	hm	INTJ
ejpam-4220	73	51	}	}	PUNCT
ejpam-4220	73	52	and	and	CCONJ
ejpam-4220	73	53	that	that	DET
ejpam-4220	73	54	root	root	VERB
ejpam-4220	73	55	vertex	vertex	NOUN
ejpam-4220	73	56	of	of	ADP
ejpam-4220	73	57	h	h	NOUN
ejpam-4220	73	58	is	be	AUX
ejpam-4220	73	59	h1	h1	PROPN
ejpam-4220	73	60	,	,	PUNCT
ejpam-4220	73	61	we	we	PRON
ejpam-4220	73	62	define	define	VERB
ejpam-4220	73	63	g	g	PROPN
ejpam-4220	73	64	•	•	NUM
ejpam-4220	73	65	h	h	NOUN
ejpam-4220	73	66	=	=	SYM
ejpam-4220	73	67	(	(	PUNCT
ejpam-4220	73	68	v	v	NOUN
ejpam-4220	73	69	,	,	PUNCT
ejpam-4220	73	70	e	e	NOUN
ejpam-4220	73	71	)	)	PUNCT
ejpam-4220	73	72	where	where	SCONJ
ejpam-4220	73	73	v	v	NOUN
ejpam-4220	73	74	=	=	SYM
ejpam-4220	73	75	{	{	PUNCT
ejpam-4220	73	76	(	(	PUNCT
ejpam-4220	73	77	gi	gi	INTJ
ejpam-4220	73	78	,	,	PUNCT
ejpam-4220	73	79	hj	hj	PROPN
ejpam-4220	73	80	)	)	PUNCT
ejpam-4220	73	81	:	:	PUNCT
ejpam-4220	73	82	1	1	NUM
ejpam-4220	73	83	≤	≤	NUM
ejpam-4220	73	84	i	i	PRON
ejpam-4220	73	85	≤	≤	PROPN
ejpam-4220	73	86	n	n	CCONJ
ejpam-4220	73	87	,	,	PUNCT
ejpam-4220	73	88	1	1	NUM
ejpam-4220	73	89	≤	≤	NUM
ejpam-4220	73	90	j	j	PROPN
ejpam-4220	73	91	≤	≤	PROPN
ejpam-4220	73	92	m	m	PROPN
ejpam-4220	73	93	}	}	PUNCT
ejpam-4220	73	94	and	and	CCONJ
ejpam-4220	73	95	e	e	NOUN
ejpam-4220	73	96	=	=	PRON
ejpam-4220	73	97	{	{	PUNCT
ejpam-4220	73	98	(	(	PUNCT
ejpam-4220	73	99	gi	gi	INTJ
ejpam-4220	73	100	,	,	PUNCT
ejpam-4220	73	101	h1)(gk	h1)(gk	PROPN
ejpam-4220	73	102	,	,	PUNCT
ejpam-4220	73	103	h1	h1	PROPN
ejpam-4220	73	104	)	)	PUNCT
ejpam-4220	73	105	:	:	PUNCT
ejpam-4220	73	106	gigk	gigk	PROPN
ejpam-4220	73	107	∈	∈	PROPN
ejpam-4220	73	108	e(g	e(g	PROPN
ejpam-4220	73	109	)	)	PUNCT
ejpam-4220	73	110	}	}	PUNCT
ejpam-4220	73	111	∪	∪	ADP
ejpam-4220	73	112	n⋃	n⋃	VERB
ejpam-4220	73	113	i=1	i=1	PRON
ejpam-4220	73	114	{	{	PUNCT
ejpam-4220	73	115	(	(	PUNCT
ejpam-4220	73	116	gi	gi	INTJ
ejpam-4220	73	117	,	,	PUNCT
ejpam-4220	73	118	hj)(gi	hj)(gi	PROPN
ejpam-4220	73	119	,	,	PUNCT
ejpam-4220	73	120	hk	hk	PROPN
ejpam-4220	73	121	)	)	PUNCT
ejpam-4220	73	122	:	:	PUNCT
ejpam-4220	74	1	hjhk	hjhk	PROPN
ejpam-4220	74	2	∈	∈	PROPN
ejpam-4220	74	3	e(h	e(h	PROPN
ejpam-4220	74	4	)	)	PUNCT
ejpam-4220	74	5	}	}	PUNCT
ejpam-4220	74	6	.	.	PUNCT
ejpam-4220	75	1	example	example	NOUN
ejpam-4220	76	1	4	4	X
ejpam-4220	76	2	.	.	PUNCT
ejpam-4220	76	3	let	let	VERB
ejpam-4220	76	4	g	g	PRON
ejpam-4220	76	5	be	be	AUX
ejpam-4220	76	6	a	a	DET
ejpam-4220	76	7	graph	graph	NOUN
ejpam-4220	76	8	and	and	CCONJ
ejpam-4220	76	9	h	h	NOUN
ejpam-4220	76	10	be	be	AUX
ejpam-4220	76	11	a	a	DET
ejpam-4220	76	12	rooted	rooted	ADJ
ejpam-4220	76	13	graph	graph	NOUN
ejpam-4220	76	14	with	with	ADP
ejpam-4220	76	15	h1	h1	PROPN
ejpam-4220	76	16	as	as	ADP
ejpam-4220	76	17	its	its	PRON
ejpam-4220	76	18	root	root	NOUN
ejpam-4220	76	19	vertex	vertex	NOUN
ejpam-4220	76	20	.	.	PUNCT
ejpam-4220	77	1	then	then	ADV
ejpam-4220	77	2	the	the	DET
ejpam-4220	77	3	rooted	rooted	ADJ
ejpam-4220	77	4	product	product	NOUN
ejpam-4220	77	5	of	of	ADP
ejpam-4220	77	6	g	g	PROPN
ejpam-4220	77	7	and	and	CCONJ
ejpam-4220	77	8	h	h	NOUN
ejpam-4220	77	9	is	be	AUX
ejpam-4220	77	10	shown	show	VERB
ejpam-4220	77	11	in	in	ADP
ejpam-4220	77	12	figure	figure	NOUN
ejpam-4220	77	13	3	3	NUM
ejpam-4220	77	14	.	.	PUNCT
ejpam-4220	77	15	n.	n.	PROPN
ejpam-4220	77	16	s.	s.	PROPN
ejpam-4220	77	17	abdulcarim	abdulcarim	PROPN
ejpam-4220	77	18	,	,	PUNCT
ejpam-4220	77	19	s.	s.	PROPN
ejpam-4220	77	20	c.	c.	PROPN
ejpam-4220	77	21	dagondon	dagondon	PROPN
ejpam-4220	77	22	/	/	SYM
ejpam-4220	77	23	eur	eur	PROPN
ejpam-4220	77	24	.	.	PUNCT
ejpam-4220	78	1	j.	j.	PROPN
ejpam-4220	78	2	pure	pure	PROPN
ejpam-4220	78	3	appl	appl	PROPN
ejpam-4220	78	4	.	.	PROPN
ejpam-4220	78	5	math	math	PROPN
ejpam-4220	78	6	,	,	PUNCT
ejpam-4220	78	7	15	15	NUM
ejpam-4220	78	8	(	(	PUNCT
ejpam-4220	78	9	1	1	NUM
ejpam-4220	78	10	)	)	PUNCT
ejpam-4220	78	11	(	(	PUNCT
ejpam-4220	78	12	2022	2022	NUM
ejpam-4220	78	13	)	)	PUNCT
ejpam-4220	78	14	,	,	PUNCT
ejpam-4220	78	15	64	64	NUM
ejpam-4220	78	16	-	-	SYM
ejpam-4220	78	17	81	81	NUM
ejpam-4220	78	18	68	68	NUM
ejpam-4220	78	19	g1	g1	NOUN
ejpam-4220	78	20	g2	g2	PROPN
ejpam-4220	78	21	g4	g4	PROPN
ejpam-4220	78	22	g3	g3	PROPN
ejpam-4220	78	23	g	g	PROPN
ejpam-4220	78	24	h1	h1	PROPN
ejpam-4220	78	25	h2	h2	PROPN
ejpam-4220	78	26	h3	h3	NOUN
ejpam-4220	78	27	h4	h4	PROPN
ejpam-4220	78	28	h5	h5	PROPN
ejpam-4220	78	29	h	h	PROPN
ejpam-4220	78	30	(	(	PUNCT
ejpam-4220	78	31	g1	g1	PROPN
ejpam-4220	78	32	,	,	PUNCT
ejpam-4220	78	33	h1	h1	PROPN
ejpam-4220	78	34	)	)	PUNCT
ejpam-4220	78	35	(	(	PUNCT
ejpam-4220	78	36	g1	g1	PROPN
ejpam-4220	78	37	,	,	PUNCT
ejpam-4220	78	38	h2	h2	NOUN
ejpam-4220	78	39	)	)	PUNCT
ejpam-4220	78	40	(	(	PUNCT
ejpam-4220	78	41	g1	g1	NOUN
ejpam-4220	78	42	,	,	PUNCT
ejpam-4220	78	43	h3	h3	NOUN
ejpam-4220	78	44	)	)	PUNCT
ejpam-4220	78	45	(	(	PUNCT
ejpam-4220	78	46	g1	g1	PROPN
ejpam-4220	78	47	,	,	PUNCT
ejpam-4220	78	48	h4	h4	PROPN
ejpam-4220	78	49	)	)	PUNCT
ejpam-4220	78	50	(	(	PUNCT
ejpam-4220	78	51	g1	g1	PROPN
ejpam-4220	78	52	,	,	PUNCT
ejpam-4220	78	53	h5	h5	PROPN
ejpam-4220	78	54	)	)	PUNCT
ejpam-4220	78	55	(	(	PUNCT
ejpam-4220	78	56	g2	g2	PROPN
ejpam-4220	78	57	,	,	PUNCT
ejpam-4220	78	58	h1	h1	PROPN
ejpam-4220	78	59	)	)	PUNCT
ejpam-4220	78	60	(	(	PUNCT
ejpam-4220	78	61	g2	g2	PROPN
ejpam-4220	78	62	,	,	PUNCT
ejpam-4220	78	63	h2	h2	PROPN
ejpam-4220	78	64	)	)	PUNCT
ejpam-4220	78	65	(	(	PUNCT
ejpam-4220	78	66	g2	g2	PROPN
ejpam-4220	78	67	,	,	PUNCT
ejpam-4220	78	68	h3	h3	NOUN
ejpam-4220	78	69	)	)	PUNCT
ejpam-4220	78	70	(	(	PUNCT
ejpam-4220	78	71	g2	g2	PROPN
ejpam-4220	78	72	,	,	PUNCT
ejpam-4220	78	73	h4	h4	PROPN
ejpam-4220	78	74	)	)	PUNCT
ejpam-4220	78	75	(	(	PUNCT
ejpam-4220	78	76	g2	g2	PROPN
ejpam-4220	78	77	,	,	PUNCT
ejpam-4220	78	78	h5	h5	PROPN
ejpam-4220	78	79	)	)	PUNCT
ejpam-4220	78	80	(	(	PUNCT
ejpam-4220	78	81	g4	g4	NOUN
ejpam-4220	78	82	,	,	PUNCT
ejpam-4220	78	83	h1	h1	NOUN
ejpam-4220	78	84	)	)	PUNCT
ejpam-4220	78	85	(	(	PUNCT
ejpam-4220	78	86	g4	g4	NOUN
ejpam-4220	78	87	,	,	PUNCT
ejpam-4220	78	88	h2	h2	NOUN
ejpam-4220	78	89	)	)	PUNCT
ejpam-4220	78	90	(	(	PUNCT
ejpam-4220	78	91	g4	g4	NOUN
ejpam-4220	78	92	,	,	PUNCT
ejpam-4220	78	93	h3	h3	NOUN
ejpam-4220	78	94	)	)	PUNCT
ejpam-4220	78	95	(	(	PUNCT
ejpam-4220	78	96	g4	g4	NOUN
ejpam-4220	78	97	,	,	PUNCT
ejpam-4220	78	98	h4	h4	PROPN
ejpam-4220	78	99	)	)	PUNCT
ejpam-4220	78	100	(	(	PUNCT
ejpam-4220	78	101	g4	g4	NOUN
ejpam-4220	78	102	,	,	PUNCT
ejpam-4220	78	103	h5	h5	PROPN
ejpam-4220	78	104	)	)	PUNCT
ejpam-4220	78	105	(	(	PUNCT
ejpam-4220	78	106	g3	g3	PROPN
ejpam-4220	78	107	,	,	PUNCT
ejpam-4220	78	108	h1	h1	PROPN
ejpam-4220	78	109	)	)	PUNCT
ejpam-4220	78	110	(	(	PUNCT
ejpam-4220	78	111	g3	g3	PROPN
ejpam-4220	78	112	,	,	PUNCT
ejpam-4220	78	113	h2	h2	PROPN
ejpam-4220	78	114	)	)	PUNCT
ejpam-4220	78	115	(	(	PUNCT
ejpam-4220	78	116	g3	g3	PROPN
ejpam-4220	78	117	,	,	PUNCT
ejpam-4220	78	118	h3	h3	NOUN
ejpam-4220	78	119	)	)	PUNCT
ejpam-4220	78	120	(	(	PUNCT
ejpam-4220	78	121	g3	g3	PROPN
ejpam-4220	78	122	,	,	PUNCT
ejpam-4220	78	123	h4	h4	PROPN
ejpam-4220	78	124	)	)	PUNCT
ejpam-4220	78	125	(	(	PUNCT
ejpam-4220	78	126	g3	g3	PROPN
ejpam-4220	78	127	,	,	PUNCT
ejpam-4220	78	128	h5	h5	PROPN
ejpam-4220	78	129	)	)	PUNCT
ejpam-4220	78	130	g	g	PROPN
ejpam-4220	78	131	•h	•h	PROPN
ejpam-4220	78	132	figure	figure	NOUN
ejpam-4220	78	133	3	3	NUM
ejpam-4220	78	134	:	:	PUNCT
ejpam-4220	78	135	the	the	DET
ejpam-4220	78	136	rooted	rooted	ADJ
ejpam-4220	78	137	product	product	NOUN
ejpam-4220	78	138	g	g	PROPN
ejpam-4220	78	139	•h	•h	PROPN
ejpam-4220	78	140	of	of	ADP
ejpam-4220	78	141	graph	graph	NOUN
ejpam-4220	78	142	g	g	NOUN
ejpam-4220	78	143	and	and	CCONJ
ejpam-4220	78	144	rooted	rooted	ADJ
ejpam-4220	78	145	graph	graph	NOUN
ejpam-4220	78	146	h	h	NOUN
ejpam-4220	78	147	definition	definition	NOUN
ejpam-4220	78	148	8	8	NUM
ejpam-4220	78	149	.	.	PUNCT
ejpam-4220	79	1	[	[	X
ejpam-4220	79	2	5	5	X
ejpam-4220	79	3	]	]	PUNCT
ejpam-4220	79	4	let	let	VERB
ejpam-4220	79	5	s	s	PRON
ejpam-4220	79	6	and	and	CCONJ
ejpam-4220	79	7	t	t	PROPN
ejpam-4220	79	8	be	be	AUX
ejpam-4220	79	9	sets	set	NOUN
ejpam-4220	79	10	.	.	PUNCT
ejpam-4220	80	1	a	a	DET
ejpam-4220	80	2	function	function	NOUN
ejpam-4220	80	3	f	f	NOUN
ejpam-4220	80	4	:	:	PUNCT
ejpam-4220	80	5	s	s	AUX
ejpam-4220	80	6	−→	−→	NOUN
ejpam-4220	80	7	t	t	PROPN
ejpam-4220	80	8	is	be	AUX
ejpam-4220	80	9	one	one	NUM
ejpam-4220	80	10	-	-	PUNCT
ejpam-4220	80	11	to	to	ADP
ejpam-4220	80	12	-	-	PUNCT
ejpam-4220	80	13	one	one	NUM
ejpam-4220	80	14	(	(	PUNCT
ejpam-4220	80	15	injective	injective	ADJ
ejpam-4220	80	16	)	)	PUNCT
ejpam-4220	80	17	if	if	SCONJ
ejpam-4220	80	18	for	for	ADP
ejpam-4220	80	19	all	all	DET
ejpam-4220	80	20	s1	s1	NOUN
ejpam-4220	80	21	,	,	PUNCT
ejpam-4220	80	22	s2	s2	NOUN
ejpam-4220	80	23	∈	∈	PROPN
ejpam-4220	80	24	s	s	NOUN
ejpam-4220	80	25	,	,	PUNCT
ejpam-4220	80	26	f(s1	f(s1	NOUN
ejpam-4220	80	27	)	)	PUNCT
ejpam-4220	80	28	=	=	SYM
ejpam-4220	80	29	f(s2	f(s2	NOUN
ejpam-4220	80	30	)	)	PUNCT
ejpam-4220	80	31	⇐	⇐	ADJ
ejpam-4220	80	32	⇒	⇒	PROPN
ejpam-4220	80	33	s1	s1	NOUN
ejpam-4220	80	34	=	=	SYM
ejpam-4220	80	35	s2	s2	PROPN
ejpam-4220	80	36	.	.	PUNCT
ejpam-4220	81	1	definition	definition	NOUN
ejpam-4220	81	2	9	9	NUM
ejpam-4220	81	3	.	.	PUNCT
ejpam-4220	82	1	[	[	X
ejpam-4220	82	2	5	5	X
ejpam-4220	82	3	]	]	PUNCT
ejpam-4220	82	4	let	let	VERB
ejpam-4220	82	5	s	s	PRON
ejpam-4220	82	6	and	and	CCONJ
ejpam-4220	82	7	t	t	PROPN
ejpam-4220	82	8	be	be	AUX
ejpam-4220	82	9	sets	set	NOUN
ejpam-4220	82	10	.	.	PUNCT
ejpam-4220	83	1	a	a	DET
ejpam-4220	83	2	function	function	NOUN
ejpam-4220	83	3	f	f	NOUN
ejpam-4220	83	4	:	:	PUNCT
ejpam-4220	83	5	s	s	AUX
ejpam-4220	83	6	−→	−→	NOUN
ejpam-4220	83	7	t	t	PROPN
ejpam-4220	83	8	is	be	AUX
ejpam-4220	83	9	onto	onto	ADP
ejpam-4220	83	10	(	(	PUNCT
ejpam-4220	83	11	surjective	surjective	ADJ
ejpam-4220	83	12	)	)	PUNCT
ejpam-4220	83	13	if	if	SCONJ
ejpam-4220	83	14	for	for	ADP
ejpam-4220	83	15	all	all	DET
ejpam-4220	83	16	t	t	NOUN
ejpam-4220	83	17	∈	∈	PROPN
ejpam-4220	83	18	t	t	NOUN
ejpam-4220	83	19	,	,	PUNCT
ejpam-4220	83	20	there	there	PRON
ejpam-4220	83	21	exists	exist	VERB
ejpam-4220	83	22	s	s	PROPN
ejpam-4220	83	23	∈	∈	NOUN
ejpam-4220	83	24	s	s	VERB
ejpam-4220	83	25	such	such	ADJ
ejpam-4220	83	26	that	that	PRON
ejpam-4220	83	27	f(s	f(	NOUN
ejpam-4220	83	28	)	)	PUNCT
ejpam-4220	84	1	=	=	SYM
ejpam-4220	84	2	t.	t.	NOUN
ejpam-4220	84	3	definition	definition	NOUN
ejpam-4220	84	4	10	10	NUM
ejpam-4220	84	5	.	.	PUNCT
ejpam-4220	85	1	[	[	X
ejpam-4220	85	2	5	5	X
ejpam-4220	85	3	]	]	PUNCT
ejpam-4220	85	4	let	let	VERB
ejpam-4220	85	5	s	s	PRON
ejpam-4220	85	6	and	and	CCONJ
ejpam-4220	85	7	t	t	PROPN
ejpam-4220	85	8	be	be	AUX
ejpam-4220	85	9	sets	set	NOUN
ejpam-4220	85	10	.	.	PUNCT
ejpam-4220	86	1	a	a	DET
ejpam-4220	86	2	function	function	NOUN
ejpam-4220	86	3	f	f	NOUN
ejpam-4220	86	4	:	:	PUNCT
ejpam-4220	86	5	s	s	AUX
ejpam-4220	86	6	−→	−→	NOUN
ejpam-4220	86	7	t	t	PROPN
ejpam-4220	86	8	is	be	AUX
ejpam-4220	86	9	bijective	bijective	ADJ
ejpam-4220	86	10	if	if	SCONJ
ejpam-4220	86	11	f	f	PROPN
ejpam-4220	86	12	is	be	AUX
ejpam-4220	86	13	both	both	CCONJ
ejpam-4220	86	14	injective	injective	ADJ
ejpam-4220	86	15	and	and	CCONJ
ejpam-4220	86	16	surjective	surjective	ADJ
ejpam-4220	86	17	.	.	PUNCT
ejpam-4220	87	1	definition	definition	NOUN
ejpam-4220	87	2	11	11	NUM
ejpam-4220	87	3	.	.	PUNCT
ejpam-4220	88	1	[	[	X
ejpam-4220	88	2	5	5	X
ejpam-4220	88	3	]	]	PUNCT
ejpam-4220	88	4	graphs	graph	NOUN
ejpam-4220	88	5	g	g	NOUN
ejpam-4220	88	6	and	and	CCONJ
ejpam-4220	88	7	h	h	NOUN
ejpam-4220	88	8	are	be	AUX
ejpam-4220	88	9	isomorphic	isomorphic	ADJ
ejpam-4220	88	10	,	,	PUNCT
ejpam-4220	88	11	denoted	denote	VERB
ejpam-4220	88	12	by	by	ADP
ejpam-4220	88	13	g	g	PROPN
ejpam-4220	88	14	∼=	∼=	PROPN
ejpam-4220	88	15	h	h	NOUN
ejpam-4220	88	16	,	,	PUNCT
ejpam-4220	88	17	if	if	SCONJ
ejpam-4220	88	18	there	there	PRON
ejpam-4220	88	19	exists	exist	VERB
ejpam-4220	88	20	a	a	DET
ejpam-4220	88	21	bijective	bijective	ADJ
ejpam-4220	88	22	mapping	mapping	NOUN
ejpam-4220	89	1	f	f	NOUN
ejpam-4220	89	2	:	:	PUNCT
ejpam-4220	89	3	v	v	X
ejpam-4220	89	4	(	(	PUNCT
ejpam-4220	89	5	g	g	NOUN
ejpam-4220	89	6	)	)	PUNCT
ejpam-4220	89	7	−→	−→	NOUN
ejpam-4220	89	8	v	v	NOUN
ejpam-4220	89	9	(	(	PUNCT
ejpam-4220	89	10	h	h	NOUN
ejpam-4220	89	11	)	)	PUNCT
ejpam-4220	89	12	such	such	ADJ
ejpam-4220	89	13	that	that	SCONJ
ejpam-4220	89	14	uv	uv	PROPN
ejpam-4220	89	15	∈	∈	PROPN
ejpam-4220	89	16	e(g	e(g	PROPN
ejpam-4220	89	17	)	)	PUNCT
ejpam-4220	90	1	if	if	SCONJ
ejpam-4220	90	2	and	and	CCONJ
ejpam-4220	90	3	only	only	ADV
ejpam-4220	90	4	if	if	SCONJ
ejpam-4220	90	5	f(u)f(v	f(u)f(v	NUM
ejpam-4220	90	6	)	)	PUNCT
ejpam-4220	90	7	∈	∈	PROPN
ejpam-4220	90	8	e(h	e(h	PROPN
ejpam-4220	90	9	)	)	PUNCT
ejpam-4220	90	10	.	.	PUNCT
ejpam-4220	91	1	3	3	X
ejpam-4220	91	2	.	.	X
ejpam-4220	91	3	independent	independent	ADJ
ejpam-4220	91	4	neighborhood	neighborhood	NOUN
ejpam-4220	91	5	polynomial	polynomial	ADJ
ejpam-4220	91	6	trees	tree	NOUN
ejpam-4220	91	7	in	in	ADP
ejpam-4220	91	8	this	this	DET
ejpam-4220	91	9	section	section	NOUN
ejpam-4220	91	10	,	,	PUNCT
ejpam-4220	91	11	we	we	PRON
ejpam-4220	91	12	generalize	generalize	VERB
ejpam-4220	91	13	the	the	DET
ejpam-4220	91	14	independent	independent	ADJ
ejpam-4220	91	15	neighborhood	neighborhood	NOUN
ejpam-4220	91	16	set	set	NOUN
ejpam-4220	91	17	of	of	ADP
ejpam-4220	91	18	any	any	DET
ejpam-4220	91	19	tree	tree	NOUN
ejpam-4220	91	20	and	and	CCONJ
ejpam-4220	91	21	represent	represent	VERB
ejpam-4220	91	22	it	it	PRON
ejpam-4220	91	23	in	in	ADP
ejpam-4220	91	24	an	an	DET
ejpam-4220	91	25	independent	independent	ADJ
ejpam-4220	91	26	neighborhood	neighborhood	NOUN
ejpam-4220	91	27	polynomial	polynomial	NOUN
ejpam-4220	91	28	of	of	ADP
ejpam-4220	91	29	a	a	DET
ejpam-4220	91	30	graph	graph	NOUN
ejpam-4220	91	31	.	.	PUNCT
ejpam-4220	92	1	proposition	proposition	NOUN
ejpam-4220	92	2	1	1	NUM
ejpam-4220	92	3	.	.	PUNCT
ejpam-4220	93	1	let	let	VERB
ejpam-4220	93	2	g	g	PRON
ejpam-4220	93	3	be	be	AUX
ejpam-4220	93	4	a	a	DET
ejpam-4220	93	5	connected	connected	ADJ
ejpam-4220	93	6	graph	graph	NOUN
ejpam-4220	93	7	,	,	PUNCT
ejpam-4220	93	8	and	and	CCONJ
ejpam-4220	93	9	s	s	VERB
ejpam-4220	93	10	⊆	⊆	NUM
ejpam-4220	93	11	v	v	NOUN
ejpam-4220	93	12	(	(	PUNCT
ejpam-4220	93	13	g	g	NOUN
ejpam-4220	93	14	)	)	PUNCT
ejpam-4220	93	15	.	.	PUNCT
ejpam-4220	94	1	then	then	ADV
ejpam-4220	94	2	s	s	VERB
ejpam-4220	94	3	is	be	AUX
ejpam-4220	94	4	an	an	DET
ejpam-4220	94	5	independent	independent	ADJ
ejpam-4220	94	6	neighborhood	neighborhood	NOUN
ejpam-4220	94	7	set	set	NOUN
ejpam-4220	94	8	of	of	ADP
ejpam-4220	94	9	g	g	PROPN
ejpam-4220	94	10	if	if	SCONJ
ejpam-4220	95	1	and	and	CCONJ
ejpam-4220	95	2	only	only	ADV
ejpam-4220	95	3	if	if	SCONJ
ejpam-4220	95	4	the	the	DET
ejpam-4220	95	5	following	follow	VERB
ejpam-4220	95	6	hold	hold	NOUN
ejpam-4220	95	7	:	:	PUNCT
ejpam-4220	95	8	(	(	PUNCT
ejpam-4220	95	9	i	i	NOUN
ejpam-4220	95	10	)	)	PUNCT
ejpam-4220	95	11	s	s	VERB
ejpam-4220	95	12	is	be	AUX
ejpam-4220	95	13	an	an	DET
ejpam-4220	95	14	independent	independent	ADJ
ejpam-4220	95	15	set	set	NOUN
ejpam-4220	95	16	(	(	PUNCT
ejpam-4220	95	17	ii	ii	NOUN
ejpam-4220	95	18	)	)	PUNCT
ejpam-4220	95	19	for	for	ADP
ejpam-4220	95	20	each	each	DET
ejpam-4220	95	21	uv	uv	PROPN
ejpam-4220	95	22	∈	∈	PROPN
ejpam-4220	95	23	e(g	e(g	PROPN
ejpam-4220	95	24	)	)	PUNCT
ejpam-4220	95	25	,	,	PUNCT
ejpam-4220	95	26	there	there	PRON
ejpam-4220	95	27	exists	exist	VERB
ejpam-4220	95	28	w	w	PROPN
ejpam-4220	95	29	∈	∈	PROPN
ejpam-4220	95	30	s	s	VERB
ejpam-4220	95	31	such	such	ADJ
ejpam-4220	95	32	that	that	PRON
ejpam-4220	95	33	u	u	NOUN
ejpam-4220	95	34	,	,	PUNCT
ejpam-4220	95	35	v	v	PROPN
ejpam-4220	95	36	∈	∈	NOUN
ejpam-4220	95	37	n	n	CCONJ
ejpam-4220	95	38	[	[	X
ejpam-4220	95	39	w	w	X
ejpam-4220	95	40	]	]	X
ejpam-4220	95	41	.	.	PUNCT
ejpam-4220	96	1	n.	n.	PROPN
ejpam-4220	96	2	s.	s.	PROPN
ejpam-4220	96	3	abdulcarim	abdulcarim	PROPN
ejpam-4220	96	4	,	,	PUNCT
ejpam-4220	96	5	s.	s.	PROPN
ejpam-4220	96	6	c.	c.	PROPN
ejpam-4220	96	7	dagondon	dagondon	PROPN
ejpam-4220	96	8	/	/	SYM
ejpam-4220	96	9	eur	eur	PROPN
ejpam-4220	96	10	.	.	PUNCT
ejpam-4220	97	1	j.	j.	PROPN
ejpam-4220	97	2	pure	pure	PROPN
ejpam-4220	97	3	appl	appl	PROPN
ejpam-4220	97	4	.	.	PROPN
ejpam-4220	97	5	math	math	PROPN
ejpam-4220	97	6	,	,	PUNCT
ejpam-4220	97	7	15	15	NUM
ejpam-4220	97	8	(	(	PUNCT
ejpam-4220	97	9	1	1	NUM
ejpam-4220	97	10	)	)	PUNCT
ejpam-4220	97	11	(	(	PUNCT
ejpam-4220	97	12	2022	2022	NUM
ejpam-4220	97	13	)	)	PUNCT
ejpam-4220	97	14	,	,	PUNCT
ejpam-4220	97	15	64	64	NUM
ejpam-4220	97	16	-	-	SYM
ejpam-4220	97	17	81	81	NUM
ejpam-4220	97	18	69	69	NUM
ejpam-4220	97	19	proof	proof	NOUN
ejpam-4220	97	20	.	.	PUNCT
ejpam-4220	98	1	assume	assume	VERB
ejpam-4220	98	2	that	that	SCONJ
ejpam-4220	98	3	s	s	VERB
ejpam-4220	98	4	is	be	AUX
ejpam-4220	98	5	an	an	DET
ejpam-4220	98	6	independent	independent	ADJ
ejpam-4220	98	7	neighborhood	neighborhood	NOUN
ejpam-4220	98	8	set	set	NOUN
ejpam-4220	98	9	of	of	ADP
ejpam-4220	98	10	g.	g.	PROPN
ejpam-4220	98	11	then	then	ADV
ejpam-4220	98	12	s	s	VERB
ejpam-4220	98	13	is	be	AUX
ejpam-4220	98	14	an	an	DET
ejpam-4220	98	15	independent	independent	ADJ
ejpam-4220	98	16	set	set	NOUN
ejpam-4220	98	17	and	and	CCONJ
ejpam-4220	98	18	(	(	PUNCT
ejpam-4220	98	19	i	i	NOUN
ejpam-4220	98	20	)	)	PUNCT
ejpam-4220	98	21	holds	hold	VERB
ejpam-4220	98	22	.	.	PUNCT
ejpam-4220	99	1	let	let	VERB
ejpam-4220	99	2	uv	uv	PRON
ejpam-4220	99	3	∈	∈	PROPN
ejpam-4220	99	4	e(g	e(g	PROPN
ejpam-4220	99	5	)	)	PUNCT
ejpam-4220	99	6	.	.	PUNCT
ejpam-4220	100	1	since	since	SCONJ
ejpam-4220	100	2	g	g	PROPN
ejpam-4220	100	3	=	=	SYM
ejpam-4220	100	4	⋃	⋃	PROPN
ejpam-4220	100	5	w∈s	w∈	NOUN
ejpam-4220	100	6	⟨n	⟨n	NUM
ejpam-4220	100	7	[	[	PUNCT
ejpam-4220	100	8	w]⟩	w]⟩	NOUN
ejpam-4220	100	9	,	,	PUNCT
ejpam-4220	100	10	there	there	PRON
ejpam-4220	100	11	exists	exist	VERB
ejpam-4220	100	12	w	w	PROPN
ejpam-4220	100	13	∈	∈	PROPN
ejpam-4220	100	14	s	s	X
ejpam-4220	100	15	for	for	ADP
ejpam-4220	100	16	with	with	ADP
ejpam-4220	100	17	uv	uv	NOUN
ejpam-4220	100	18	∈	∈	NOUN
ejpam-4220	100	19	e(⟨n	e(⟨n	NOUN
ejpam-4220	100	20	[	[	X
ejpam-4220	100	21	w]⟩	w]⟩	NOUN
ejpam-4220	100	22	)	)	PUNCT
ejpam-4220	100	23	.	.	PUNCT
ejpam-4220	101	1	this	this	PRON
ejpam-4220	101	2	means	mean	VERB
ejpam-4220	101	3	that	that	SCONJ
ejpam-4220	101	4	u	u	NOUN
ejpam-4220	101	5	,	,	PUNCT
ejpam-4220	101	6	v	v	PROPN
ejpam-4220	101	7	∈	∈	NOUN
ejpam-4220	101	8	n	n	CCONJ
ejpam-4220	101	9	[	[	X
ejpam-4220	101	10	w	w	X
ejpam-4220	101	11	]	]	X
ejpam-4220	101	12	,	,	PUNCT
ejpam-4220	101	13	and	and	CCONJ
ejpam-4220	101	14	(	(	PUNCT
ejpam-4220	101	15	ii	ii	NOUN
ejpam-4220	101	16	)	)	PUNCT
ejpam-4220	101	17	holds	hold	VERB
ejpam-4220	101	18	.	.	PUNCT
ejpam-4220	101	19	suppose	suppose	VERB
ejpam-4220	101	20	that	that	SCONJ
ejpam-4220	101	21	(	(	PUNCT
ejpam-4220	101	22	i	i	NOUN
ejpam-4220	101	23	)	)	PUNCT
ejpam-4220	101	24	and	and	CCONJ
ejpam-4220	101	25	(	(	PUNCT
ejpam-4220	101	26	ii	ii	NOUN
ejpam-4220	101	27	)	)	PUNCT
ejpam-4220	101	28	hold	hold	VERB
ejpam-4220	101	29	for	for	ADP
ejpam-4220	101	30	s.	s.	PROPN
ejpam-4220	101	31	let	let	VERB
ejpam-4220	101	32	v	v	ADP
ejpam-4220	101	33	∈	∈	PROPN
ejpam-4220	101	34	v	v	NOUN
ejpam-4220	101	35	(	(	PUNCT
ejpam-4220	101	36	g	g	NOUN
ejpam-4220	101	37	)	)	PUNCT
ejpam-4220	101	38	and	and	CCONJ
ejpam-4220	101	39	let	let	VERB
ejpam-4220	101	40	u	u	PRON
ejpam-4220	101	41	∈	∈	PROPN
ejpam-4220	101	42	v	v	ADP
ejpam-4220	101	43	(	(	PUNCT
ejpam-4220	101	44	s	s	NOUN
ejpam-4220	101	45	)	)	PUNCT
ejpam-4220	101	46	\	\	NOUN
ejpam-4220	101	47	{	{	PUNCT
ejpam-4220	101	48	v	v	NOUN
ejpam-4220	101	49	}	}	PUNCT
ejpam-4220	101	50	for	for	ADP
ejpam-4220	101	51	which	which	PRON
ejpam-4220	101	52	uv	uv	NOUN
ejpam-4220	101	53	∈	∈	PROPN
ejpam-4220	101	54	e(g	e(g	PROPN
ejpam-4220	101	55	)	)	PUNCT
ejpam-4220	101	56	.	.	PUNCT
ejpam-4220	102	1	by	by	ADP
ejpam-4220	102	2	(	(	PUNCT
ejpam-4220	102	3	ii	ii	NOUN
ejpam-4220	102	4	)	)	PUNCT
ejpam-4220	102	5	,	,	PUNCT
ejpam-4220	102	6	there	there	PRON
ejpam-4220	102	7	exists	exist	VERB
ejpam-4220	102	8	w	w	PROPN
ejpam-4220	102	9	∈	∈	PROPN
ejpam-4220	102	10	s	s	VERB
ejpam-4220	102	11	such	such	ADJ
ejpam-4220	102	12	that	that	PRON
ejpam-4220	102	13	u	u	NOUN
ejpam-4220	102	14	,	,	PUNCT
ejpam-4220	102	15	v	v	PROPN
ejpam-4220	102	16	∈	∈	NOUN
ejpam-4220	102	17	n	n	CCONJ
ejpam-4220	102	18	[	[	X
ejpam-4220	102	19	w	w	X
ejpam-4220	102	20	]	]	X
ejpam-4220	102	21	.	.	PUNCT
ejpam-4220	103	1	thus	thus	ADV
ejpam-4220	103	2	,	,	PUNCT
ejpam-4220	103	3	v	v	PROPN
ejpam-4220	103	4	∈	∈	PROPN
ejpam-4220	103	5	v	v	NOUN
ejpam-4220	103	6	(	(	PUNCT
ejpam-4220	103	7	⟨n	⟨n	NUM
ejpam-4220	103	8	[	[	X
ejpam-4220	103	9	w]⟩	w]⟩	NOUN
ejpam-4220	103	10	)	)	PUNCT
ejpam-4220	103	11	.	.	PUNCT
ejpam-4220	104	1	since	since	SCONJ
ejpam-4220	104	2	v	v	NOUN
ejpam-4220	104	3	is	be	AUX
ejpam-4220	104	4	arbitrary	arbitrary	ADJ
ejpam-4220	104	5	,	,	PUNCT
ejpam-4220	104	6	v	v	ADJ
ejpam-4220	104	7	(	(	PUNCT
ejpam-4220	104	8	g	g	NOUN
ejpam-4220	104	9	)	)	PUNCT
ejpam-4220	104	10	=	=	SYM
ejpam-4220	104	11	v	v	NOUN
ejpam-4220	104	12	(	(	PUNCT
ejpam-4220	104	13	⋃	⋃	NOUN
ejpam-4220	104	14	w∈s	w∈s	NOUN
ejpam-4220	104	15	⟨n	⟨n	NUM
ejpam-4220	104	16	[	[	PUNCT
ejpam-4220	104	17	w]⟩	w]⟩	NOUN
ejpam-4220	104	18	)	)	PUNCT
ejpam-4220	104	19	.	.	PUNCT
ejpam-4220	105	1	let	let	VERB
ejpam-4220	105	2	uv	uv	PRON
ejpam-4220	105	3	∈	∈	PROPN
ejpam-4220	105	4	e(g	e(g	PROPN
ejpam-4220	105	5	)	)	PUNCT
ejpam-4220	105	6	.	.	PUNCT
ejpam-4220	106	1	by	by	ADP
ejpam-4220	106	2	(	(	PUNCT
ejpam-4220	106	3	ii	ii	NOUN
ejpam-4220	106	4	)	)	PUNCT
ejpam-4220	106	5	again	again	ADV
ejpam-4220	106	6	,	,	PUNCT
ejpam-4220	106	7	there	there	PRON
ejpam-4220	106	8	exists	exist	VERB
ejpam-4220	106	9	w	w	PROPN
ejpam-4220	106	10	∈	∈	PROPN
ejpam-4220	106	11	s	s	X
ejpam-4220	106	12	for	for	ADP
ejpam-4220	106	13	which	which	PRON
ejpam-4220	106	14	u	u	NOUN
ejpam-4220	106	15	,	,	PUNCT
ejpam-4220	106	16	v	v	PROPN
ejpam-4220	106	17	∈	∈	NOUN
ejpam-4220	106	18	n	n	CCONJ
ejpam-4220	106	19	[	[	X
ejpam-4220	106	20	w	w	X
ejpam-4220	106	21	]	]	X
ejpam-4220	106	22	.	.	PUNCT
ejpam-4220	107	1	hence	hence	ADV
ejpam-4220	107	2	,	,	PUNCT
ejpam-4220	107	3	uv	uv	PROPN
ejpam-4220	107	4	∈	∈	PROPN
ejpam-4220	107	5	e	e	X
ejpam-4220	107	6	(	(	PUNCT
ejpam-4220	107	7	⟨n	⟨n	NUM
ejpam-4220	107	8	[	[	X
ejpam-4220	107	9	w]⟩	w]⟩	NOUN
ejpam-4220	107	10	)	)	PUNCT
ejpam-4220	107	11	.	.	PUNCT
ejpam-4220	108	1	thus	thus	ADV
ejpam-4220	108	2	,	,	PUNCT
ejpam-4220	108	3	uv	uv	PROPN
ejpam-4220	108	4	∈	∈	PROPN
ejpam-4220	108	5	e	e	X
ejpam-4220	108	6	(	(	PUNCT
ejpam-4220	108	7	⋃	⋃	NOUN
ejpam-4220	108	8	w∈s	w∈s	VERB
ejpam-4220	108	9	⟨n	⟨n	NUM
ejpam-4220	108	10	[	[	PUNCT
ejpam-4220	108	11	w]⟩	w]⟩	NOUN
ejpam-4220	108	12	)	)	PUNCT
ejpam-4220	108	13	.	.	PUNCT
ejpam-4220	109	1	hence	hence	ADV
ejpam-4220	109	2	,	,	PUNCT
ejpam-4220	109	3	e(g	e(g	PROPN
ejpam-4220	109	4	)	)	PUNCT
ejpam-4220	110	1	=	=	SYM
ejpam-4220	110	2	e	e	X
ejpam-4220	110	3	(	(	PUNCT
ejpam-4220	110	4	⋃	⋃	NOUN
ejpam-4220	110	5	w∈s	w∈s	VERB
ejpam-4220	110	6	⟨n	⟨n	NUM
ejpam-4220	110	7	[	[	PUNCT
ejpam-4220	110	8	w]⟩	w]⟩	NOUN
ejpam-4220	110	9	)	)	PUNCT
ejpam-4220	110	10	.	.	PUNCT
ejpam-4220	111	1	therefore	therefore	ADV
ejpam-4220	111	2	,	,	PUNCT
ejpam-4220	111	3	s	s	VERB
ejpam-4220	111	4	is	be	AUX
ejpam-4220	111	5	an	an	DET
ejpam-4220	111	6	independent	independent	ADJ
ejpam-4220	111	7	neighborhood	neighborhood	NOUN
ejpam-4220	111	8	set	set	NOUN
ejpam-4220	111	9	of	of	ADP
ejpam-4220	111	10	g.	g.	PROPN
ejpam-4220	111	11	■	■	PUNCT
ejpam-4220	111	12	proposition	proposition	NOUN
ejpam-4220	111	13	2	2	NUM
ejpam-4220	111	14	.	.	PUNCT
ejpam-4220	112	1	let	let	VERB
ejpam-4220	112	2	g	g	NOUN
ejpam-4220	112	3	be	be	AUX
ejpam-4220	112	4	any	any	DET
ejpam-4220	112	5	in	in	ADP
ejpam-4220	112	6	-	-	PUNCT
ejpam-4220	112	7	graph	graph	NOUN
ejpam-4220	112	8	.	.	PUNCT
ejpam-4220	113	1	if	if	SCONJ
ejpam-4220	113	2	ω	ω	PROPN
ejpam-4220	113	3	is	be	AUX
ejpam-4220	113	4	an	an	DET
ejpam-4220	113	5	independent	independent	ADJ
ejpam-4220	113	6	neighborhood	neighborhood	NOUN
ejpam-4220	113	7	set	set	NOUN
ejpam-4220	113	8	of	of	ADP
ejpam-4220	113	9	g	g	NOUN
ejpam-4220	113	10	,	,	PUNCT
ejpam-4220	113	11	then	then	ADV
ejpam-4220	113	12	there	there	PRON
ejpam-4220	113	13	is	be	VERB
ejpam-4220	113	14	no	no	DET
ejpam-4220	113	15	proper	proper	ADJ
ejpam-4220	113	16	subset	subset	NOUN
ejpam-4220	113	17	of	of	ADP
ejpam-4220	113	18	ω	ω	PROPN
ejpam-4220	113	19	,	,	PUNCT
ejpam-4220	113	20	say	say	VERB
ejpam-4220	113	21	∆	∆	PROPN
ejpam-4220	113	22	,	,	PUNCT
ejpam-4220	113	23	such	such	ADJ
ejpam-4220	113	24	that	that	SCONJ
ejpam-4220	113	25	⋃	⋃	PROPN
ejpam-4220	113	26	v∈∆	v∈∆	X
ejpam-4220	113	27	⟨n	⟨n	NUM
ejpam-4220	113	28	[	[	X
ejpam-4220	113	29	v]⟩	v]⟩	X
ejpam-4220	113	30	=	=	PUNCT
ejpam-4220	113	31	g.	g.	NOUN
ejpam-4220	113	32	proof	proof	NOUN
ejpam-4220	113	33	.	.	PUNCT
ejpam-4220	114	1	let	let	VERB
ejpam-4220	114	2	g	g	NOUN
ejpam-4220	114	3	be	be	AUX
ejpam-4220	114	4	any	any	PRON
ejpam-4220	114	5	in	in	ADP
ejpam-4220	114	6	-graph	-graph	NOUN
ejpam-4220	114	7	.	.	PUNCT
ejpam-4220	115	1	let	let	VERB
ejpam-4220	115	2	ω	ω	PRON
ejpam-4220	115	3	be	be	AUX
ejpam-4220	115	4	an	an	DET
ejpam-4220	115	5	independent	independent	ADJ
ejpam-4220	115	6	neighborhood	neighborhood	NOUN
ejpam-4220	115	7	set	set	NOUN
ejpam-4220	115	8	of	of	ADP
ejpam-4220	115	9	g.	g.	PROPN
ejpam-4220	115	10	assume	assume	VERB
ejpam-4220	115	11	to	to	ADP
ejpam-4220	115	12	the	the	DET
ejpam-4220	115	13	contrary	contrary	NOUN
ejpam-4220	115	14	that	that	SCONJ
ejpam-4220	115	15	there	there	PRON
ejpam-4220	115	16	exists	exist	VERB
ejpam-4220	115	17	a	a	DET
ejpam-4220	115	18	proper	proper	ADJ
ejpam-4220	115	19	subset	subset	NOUN
ejpam-4220	115	20	∆	∆	PROPN
ejpam-4220	115	21	of	of	ADP
ejpam-4220	115	22	ω	ω	NUM
ejpam-4220	116	1	such	such	ADJ
ejpam-4220	116	2	that	that	SCONJ
ejpam-4220	116	3	⋃	⋃	PROPN
ejpam-4220	116	4	v∈∆	v∈∆	X
ejpam-4220	116	5	⟨n	⟨n	NUM
ejpam-4220	117	1	[	[	X
ejpam-4220	117	2	v]⟩	v]⟩	X
ejpam-4220	117	3	=	=	PUNCT
ejpam-4220	117	4	g.	g.	PROPN
ejpam-4220	117	5	let	let	VERB
ejpam-4220	117	6	u	u	PROPN
ejpam-4220	117	7	∈	∈	PROPN
ejpam-4220	117	8	ω\∆.	ω\∆.	PROPN
ejpam-4220	117	9	since	since	SCONJ
ejpam-4220	117	10	ω	ω	PROPN
ejpam-4220	117	11	is	be	AUX
ejpam-4220	117	12	an	an	DET
ejpam-4220	117	13	independent	independent	ADJ
ejpam-4220	117	14	neighborhood	neighborhood	NOUN
ejpam-4220	117	15	set	set	NOUN
ejpam-4220	117	16	,	,	PUNCT
ejpam-4220	117	17	every	every	DET
ejpam-4220	117	18	vertices	vertex	NOUN
ejpam-4220	117	19	in	in	ADP
ejpam-4220	117	20	ω	ω	NUM
ejpam-4220	117	21	are	be	AUX
ejpam-4220	117	22	not	not	PART
ejpam-4220	117	23	adjacent	adjacent	ADJ
ejpam-4220	117	24	.	.	PUNCT
ejpam-4220	118	1	this	this	PRON
ejpam-4220	118	2	implies	imply	VERB
ejpam-4220	118	3	u	u	PROPN
ejpam-4220	118	4	∈	∈	PROPN
ejpam-4220	118	5	ω\∆	ω\∆	NUM
ejpam-4220	118	6	is	be	AUX
ejpam-4220	118	7	not	not	PART
ejpam-4220	118	8	a	a	DET
ejpam-4220	118	9	neighborhood	neighborhood	NOUN
ejpam-4220	118	10	of	of	ADP
ejpam-4220	118	11	∆.	∆.	X
ejpam-4220	118	12	it	it	PRON
ejpam-4220	118	13	follows	follow	VERB
ejpam-4220	118	14	that	that	SCONJ
ejpam-4220	118	15	u	u	NOUN
ejpam-4220	118	16	is	be	AUX
ejpam-4220	118	17	not	not	PART
ejpam-4220	118	18	in⋃	in⋃	PROPN
ejpam-4220	118	19	v∈∆	v∈∆	X
ejpam-4220	118	20	⟨n	⟨n	NUM
ejpam-4220	119	1	[	[	X
ejpam-4220	119	2	v]⟩.	v]⟩.	VERB
ejpam-4220	119	3	this	this	PRON
ejpam-4220	119	4	is	be	AUX
ejpam-4220	119	5	a	a	DET
ejpam-4220	119	6	contradiction	contradiction	NOUN
ejpam-4220	119	7	for	for	ADP
ejpam-4220	119	8	⋃	⋃	PROPN
ejpam-4220	119	9	v∈∆	v∈∆	X
ejpam-4220	119	10	⟨n	⟨n	NUM
ejpam-4220	120	1	[	[	X
ejpam-4220	120	2	v]⟩	v]⟩	X
ejpam-4220	120	3	=	=	PUNCT
ejpam-4220	120	4	g.	g.	PROPN
ejpam-4220	120	5	hence	hence	ADV
ejpam-4220	120	6	,	,	PUNCT
ejpam-4220	120	7	there	there	PRON
ejpam-4220	120	8	is	be	VERB
ejpam-4220	120	9	no	no	DET
ejpam-4220	120	10	proper	proper	ADJ
ejpam-4220	120	11	subset	subset	NOUN
ejpam-4220	120	12	of	of	ADP
ejpam-4220	120	13	ω	ω	PROPN
ejpam-4220	120	14	that	that	PRON
ejpam-4220	120	15	is	be	AUX
ejpam-4220	120	16	also	also	ADV
ejpam-4220	120	17	an	an	DET
ejpam-4220	120	18	independent	independent	ADJ
ejpam-4220	120	19	neighborhood	neighborhood	NOUN
ejpam-4220	120	20	set	set	NOUN
ejpam-4220	120	21	of	of	ADP
ejpam-4220	120	22	g.	g.	PROPN
ejpam-4220	120	23	■	■	PUNCT
ejpam-4220	120	24	corollary	corollary	ADJ
ejpam-4220	120	25	2	2	NUM
ejpam-4220	120	26	.	.	PUNCT
ejpam-4220	121	1	let	let	VERB
ejpam-4220	121	2	g	g	PRON
ejpam-4220	121	3	be	be	AUX
ejpam-4220	121	4	an	an	DET
ejpam-4220	121	5	in	in	ADP
ejpam-4220	121	6	-	-	PUNCT
ejpam-4220	121	7	graph	graph	NOUN
ejpam-4220	121	8	.	.	PUNCT
ejpam-4220	122	1	if	if	SCONJ
ejpam-4220	122	2	ω	ω	PROPN
ejpam-4220	122	3	is	be	AUX
ejpam-4220	122	4	an	an	DET
ejpam-4220	122	5	independent	independent	ADJ
ejpam-4220	122	6	neighborhood	neighborhood	NOUN
ejpam-4220	122	7	set	set	NOUN
ejpam-4220	122	8	of	of	ADP
ejpam-4220	122	9	g	g	NOUN
ejpam-4220	122	10	,	,	PUNCT
ejpam-4220	122	11	then	then	ADV
ejpam-4220	122	12	there	there	PRON
ejpam-4220	122	13	is	be	VERB
ejpam-4220	122	14	no	no	DET
ejpam-4220	122	15	independent	independent	ADJ
ejpam-4220	122	16	neighborhood	neighborhood	NOUN
ejpam-4220	122	17	set	set	NOUN
ejpam-4220	122	18	of	of	ADP
ejpam-4220	122	19	g	g	PROPN
ejpam-4220	122	20	that	that	PRON
ejpam-4220	122	21	contains	contain	VERB
ejpam-4220	122	22	ω	ω	NOUN
ejpam-4220	122	23	.	.	PUNCT
ejpam-4220	123	1	proof	proof	NOUN
ejpam-4220	123	2	.	.	PUNCT
ejpam-4220	124	1	let	let	VERB
ejpam-4220	124	2	ω	ω	PRON
ejpam-4220	124	3	be	be	AUX
ejpam-4220	124	4	an	an	DET
ejpam-4220	124	5	independent	independent	ADJ
ejpam-4220	124	6	neighborhood	neighborhood	NOUN
ejpam-4220	124	7	set	set	NOUN
ejpam-4220	124	8	of	of	ADP
ejpam-4220	124	9	an	an	DET
ejpam-4220	124	10	in	in	ADP
ejpam-4220	124	11	-graph	-graph	PROPN
ejpam-4220	124	12	g.	g.	NOUN
ejpam-4220	124	13	assume	assume	VERB
ejpam-4220	124	14	that	that	SCONJ
ejpam-4220	124	15	there	there	PRON
ejpam-4220	124	16	exists	exist	VERB
ejpam-4220	124	17	an	an	DET
ejpam-4220	124	18	independent	independent	ADJ
ejpam-4220	124	19	neighborhood	neighborhood	NOUN
ejpam-4220	124	20	set	set	NOUN
ejpam-4220	124	21	of	of	ADP
ejpam-4220	124	22	g	g	PROPN
ejpam-4220	124	23	that	that	PRON
ejpam-4220	124	24	contains	contain	VERB
ejpam-4220	124	25	ω	ω	PROPN
ejpam-4220	124	26	,	,	PUNCT
ejpam-4220	124	27	say	say	VERB
ejpam-4220	124	28	∆.	∆.	NOUN
ejpam-4220	124	29	let	let	VERB
ejpam-4220	124	30	∆	∆	PROPN
ejpam-4220	124	31	=	=	SYM
ejpam-4220	124	32	ω	ω	X
ejpam-4220	124	33	∪	∪	X
ejpam-4220	124	34	{	{	PUNCT
ejpam-4220	124	35	x1	x1	PROPN
ejpam-4220	124	36	,	,	PUNCT
ejpam-4220	124	37	x2	x2	PROPN
ejpam-4220	124	38	,	,	PUNCT
ejpam-4220	124	39	·	·	PUNCT
ejpam-4220	124	40	·	·	PUNCT
ejpam-4220	124	41	·	·	PUNCT
ejpam-4220	124	42	,	,	PUNCT
ejpam-4220	124	43	xn	xn	X
ejpam-4220	124	44	}	}	PUNCT
ejpam-4220	124	45	for	for	ADP
ejpam-4220	124	46	some	some	DET
ejpam-4220	124	47	xi	xi	ADP
ejpam-4220	124	48	∈	∈	PROPN
ejpam-4220	124	49	v	v	ADP
ejpam-4220	124	50	(	(	PUNCT
ejpam-4220	124	51	g	g	NOUN
ejpam-4220	124	52	)	)	PUNCT
ejpam-4220	124	53	.	.	PUNCT
ejpam-4220	125	1	since	since	SCONJ
ejpam-4220	125	2	∆	∆	PROPN
ejpam-4220	125	3	is	be	AUX
ejpam-4220	125	4	an	an	DET
ejpam-4220	125	5	independent	independent	ADJ
ejpam-4220	125	6	neighborhood	neighborhood	NOUN
ejpam-4220	125	7	set	set	NOUN
ejpam-4220	125	8	of	of	ADP
ejpam-4220	125	9	g	g	NOUN
ejpam-4220	125	10	,	,	PUNCT
ejpam-4220	125	11	for	for	ADP
ejpam-4220	125	12	all	all	PRON
ejpam-4220	125	13	vj	vj	PRON
ejpam-4220	125	14	∈	∈	PROPN
ejpam-4220	125	15	ω	ω	PROPN
ejpam-4220	125	16	and	and	CCONJ
ejpam-4220	125	17	xi	xi	PROPN
ejpam-4220	125	18	,	,	PUNCT
ejpam-4220	125	19	vj′s	vj′s	PROPN
ejpam-4220	125	20	and	and	CCONJ
ejpam-4220	125	21	xi′s	xi′s	PROPN
ejpam-4220	125	22	are	be	AUX
ejpam-4220	125	23	non	non	X
ejpam-4220	125	24	adjacent	adjacent	ADJ
ejpam-4220	125	25	.	.	PUNCT
ejpam-4220	126	1	this	this	PRON
ejpam-4220	126	2	implies	imply	VERB
ejpam-4220	126	3	xi	xi	X
ejpam-4220	126	4	/∈	/∈	PUNCT
ejpam-4220	127	1	n	n	PROPN
ejpam-4220	128	1	[	[	X
ejpam-4220	128	2	vj	vj	X
ejpam-4220	128	3	]	]	PUNCT
ejpam-4220	128	4	for	for	ADP
ejpam-4220	128	5	all	all	PRON
ejpam-4220	128	6	vj	vj	PROPN
ejpam-4220	128	7	∈	∈	PROPN
ejpam-4220	128	8	ω	ω	PROPN
ejpam-4220	128	9	,	,	PUNCT
ejpam-4220	128	10	i	i	NOUN
ejpam-4220	128	11	=	=	NOUN
ejpam-4220	128	12	1	1	NUM
ejpam-4220	128	13	,	,	PUNCT
ejpam-4220	128	14	·	·	PUNCT
ejpam-4220	128	15	·	·	PUNCT
ejpam-4220	128	16	·	·	PUNCT
ejpam-4220	128	17	,	,	PUNCT
ejpam-4220	128	18	n.	n.	PROPN
ejpam-4220	128	19	it	it	PRON
ejpam-4220	128	20	follows	follow	VERB
ejpam-4220	128	21	that	that	SCONJ
ejpam-4220	128	22	xi	xi	PROPN
ejpam-4220	128	23	is	be	AUX
ejpam-4220	128	24	not	not	PART
ejpam-4220	128	25	in	in	ADP
ejpam-4220	128	26	⋃	⋃	NOUN
ejpam-4220	128	27	v∈ω	v∈ω	NOUN
ejpam-4220	128	28	⟨n	⟨n	NUM
ejpam-4220	128	29	[	[	X
ejpam-4220	128	30	v]⟩.	v]⟩.	VERB
ejpam-4220	128	31	hence	hence	ADV
ejpam-4220	128	32	,	,	PUNCT
ejpam-4220	128	33	⋃	⋃	NOUN
ejpam-4220	128	34	v∈ω	v∈ω	VERB
ejpam-4220	128	35	⟨n	⟨n	NUM
ejpam-4220	128	36	[	[	X
ejpam-4220	128	37	v]⟩	v]⟩	NOUN
ejpam-4220	128	38	=	=	NOUN
ejpam-4220	128	39	̸	̸	PUNCT
ejpam-4220	128	40	g.	g.	NOUN
ejpam-4220	128	41	this	this	PRON
ejpam-4220	128	42	is	be	AUX
ejpam-4220	128	43	a	a	DET
ejpam-4220	128	44	contradiction	contradiction	NOUN
ejpam-4220	128	45	to	to	ADP
ejpam-4220	128	46	our	our	PRON
ejpam-4220	128	47	assumption	assumption	NOUN
ejpam-4220	128	48	that	that	SCONJ
ejpam-4220	128	49	ω	ω	PROPN
ejpam-4220	128	50	is	be	AUX
ejpam-4220	128	51	an	an	DET
ejpam-4220	128	52	independent	independent	ADJ
ejpam-4220	128	53	neighborhood	neighborhood	NOUN
ejpam-4220	128	54	set	set	NOUN
ejpam-4220	128	55	of	of	ADP
ejpam-4220	128	56	g.	g.	PROPN
ejpam-4220	128	57	therefore	therefore	ADV
ejpam-4220	128	58	,	,	PUNCT
ejpam-4220	128	59	there	there	PRON
ejpam-4220	128	60	is	be	VERB
ejpam-4220	128	61	no	no	DET
ejpam-4220	128	62	independent	independent	ADJ
ejpam-4220	128	63	neighborhood	neighborhood	NOUN
ejpam-4220	128	64	set	set	NOUN
ejpam-4220	128	65	of	of	ADP
ejpam-4220	128	66	g	g	PROPN
ejpam-4220	128	67	that	that	PRON
ejpam-4220	128	68	contains	contain	VERB
ejpam-4220	128	69	ω	ω	NUM
ejpam-4220	128	70	.	.	PUNCT
ejpam-4220	129	1	■	■	PUNCT
ejpam-4220	129	2	for	for	ADP
ejpam-4220	129	3	the	the	DET
ejpam-4220	129	4	succeeding	succeed	VERB
ejpam-4220	129	5	results	result	NOUN
ejpam-4220	129	6	,	,	PUNCT
ejpam-4220	129	7	we	we	PRON
ejpam-4220	129	8	let	let	VERB
ejpam-4220	129	9	n∗	n∗	PROPN
ejpam-4220	129	10	=	=	SYM
ejpam-4220	129	11	n	n	NOUN
ejpam-4220	129	12	∪	∪	X
ejpam-4220	129	13	{	{	PUNCT
ejpam-4220	129	14	0	0	NUM
ejpam-4220	129	15	}	}	PUNCT
ejpam-4220	129	16	.	.	PUNCT
ejpam-4220	130	1	n.	n.	PROPN
ejpam-4220	130	2	s.	s.	PROPN
ejpam-4220	130	3	abdulcarim	abdulcarim	PROPN
ejpam-4220	130	4	,	,	PUNCT
ejpam-4220	130	5	s.	s.	PROPN
ejpam-4220	130	6	c.	c.	PROPN
ejpam-4220	130	7	dagondon	dagondon	PROPN
ejpam-4220	130	8	/	/	SYM
ejpam-4220	130	9	eur	eur	PROPN
ejpam-4220	130	10	.	.	PUNCT
ejpam-4220	131	1	j.	j.	PROPN
ejpam-4220	131	2	pure	pure	PROPN
ejpam-4220	131	3	appl	appl	PROPN
ejpam-4220	131	4	.	.	PROPN
ejpam-4220	131	5	math	math	PROPN
ejpam-4220	131	6	,	,	PUNCT
ejpam-4220	131	7	15	15	NUM
ejpam-4220	131	8	(	(	PUNCT
ejpam-4220	131	9	1	1	NUM
ejpam-4220	131	10	)	)	PUNCT
ejpam-4220	131	11	(	(	PUNCT
ejpam-4220	131	12	2022	2022	NUM
ejpam-4220	131	13	)	)	PUNCT
ejpam-4220	131	14	,	,	PUNCT
ejpam-4220	131	15	64	64	NUM
ejpam-4220	131	16	-	-	SYM
ejpam-4220	131	17	81	81	NUM
ejpam-4220	131	18	70	70	NUM
ejpam-4220	131	19	theorem	theorem	NOUN
ejpam-4220	131	20	2	2	NUM
ejpam-4220	131	21	.	.	PUNCT
ejpam-4220	132	1	let	let	VERB
ejpam-4220	132	2	g	g	NOUN
ejpam-4220	132	3	be	be	AUX
ejpam-4220	132	4	any	any	DET
ejpam-4220	132	5	tree	tree	NOUN
ejpam-4220	132	6	.	.	PUNCT
ejpam-4220	133	1	then	then	ADV
ejpam-4220	133	2	for	for	ADP
ejpam-4220	133	3	any	any	PRON
ejpam-4220	133	4	u	u	PROPN
ejpam-4220	133	5	∈	∈	PROPN
ejpam-4220	133	6	v	v	NOUN
ejpam-4220	133	7	(	(	PUNCT
ejpam-4220	133	8	g	g	NOUN
ejpam-4220	133	9	)	)	PUNCT
ejpam-4220	133	10	,	,	PUNCT
ejpam-4220	133	11	the	the	DET
ejpam-4220	133	12	set	set	NOUN
ejpam-4220	133	13	ω	ω	PROPN
ejpam-4220	133	14	=	=	SYM
ejpam-4220	133	15	{	{	PUNCT
ejpam-4220	133	16	v	v	NUM
ejpam-4220	133	17	∈	∈	NOUN
ejpam-4220	133	18	v	v	NOUN
ejpam-4220	133	19	(	(	PUNCT
ejpam-4220	133	20	g	g	NOUN
ejpam-4220	133	21	)	)	PUNCT
ejpam-4220	133	22	:	:	PUNCT
ejpam-4220	134	1	d(u	d(u	PROPN
ejpam-4220	134	2	,	,	PUNCT
ejpam-4220	134	3	v	v	NOUN
ejpam-4220	134	4	)	)	PUNCT
ejpam-4220	134	5	=	=	SYM
ejpam-4220	134	6	2n	2n	NUM
ejpam-4220	134	7	,	,	PUNCT
ejpam-4220	134	8	n	n	PRON
ejpam-4220	134	9	∈	∈	PROPN
ejpam-4220	134	10	n∗	n∗	PROPN
ejpam-4220	134	11	}	}	PUNCT
ejpam-4220	134	12	is	be	AUX
ejpam-4220	134	13	an	an	DET
ejpam-4220	134	14	independent	independent	ADJ
ejpam-4220	134	15	neighborhood	neighborhood	NOUN
ejpam-4220	134	16	set	set	NOUN
ejpam-4220	134	17	of	of	ADP
ejpam-4220	134	18	g.	g.	PROPN
ejpam-4220	134	19	proof	proof	PROPN
ejpam-4220	134	20	.	.	PUNCT
ejpam-4220	135	1	let	let	VERB
ejpam-4220	135	2	u	u	PRON
ejpam-4220	135	3	∈	∈	PROPN
ejpam-4220	135	4	v	v	ADP
ejpam-4220	135	5	(	(	PUNCT
ejpam-4220	135	6	g	g	NOUN
ejpam-4220	135	7	)	)	PUNCT
ejpam-4220	135	8	.	.	PUNCT
ejpam-4220	136	1	let	let	VERB
ejpam-4220	136	2	ω	ω	NOUN
ejpam-4220	136	3	=	=	PRON
ejpam-4220	136	4	{	{	PUNCT
ejpam-4220	136	5	v	v	NUM
ejpam-4220	136	6	∈	∈	NOUN
ejpam-4220	136	7	v	v	NOUN
ejpam-4220	136	8	(	(	PUNCT
ejpam-4220	136	9	g	g	NOUN
ejpam-4220	136	10	)	)	PUNCT
ejpam-4220	136	11	:	:	PUNCT
ejpam-4220	137	1	d(u	d(u	PROPN
ejpam-4220	137	2	,	,	PUNCT
ejpam-4220	137	3	v	v	NOUN
ejpam-4220	137	4	)	)	PUNCT
ejpam-4220	137	5	=	=	SYM
ejpam-4220	137	6	2n	2n	NUM
ejpam-4220	137	7	,	,	PUNCT
ejpam-4220	137	8	n	n	PRON
ejpam-4220	137	9	∈	∈	PROPN
ejpam-4220	137	10	n∗	n∗	PROPN
ejpam-4220	137	11	}	}	PUNCT
ejpam-4220	137	12	.	.	PUNCT
ejpam-4220	138	1	clearly	clearly	ADV
ejpam-4220	138	2	,	,	PUNCT
ejpam-4220	138	3	for	for	ADP
ejpam-4220	138	4	any	any	DET
ejpam-4220	138	5	v1	v1	NOUN
ejpam-4220	138	6	,	,	PUNCT
ejpam-4220	138	7	v2	v2	PROPN
ejpam-4220	138	8	∈	∈	PROPN
ejpam-4220	138	9	ω	ω	PROPN
ejpam-4220	138	10	,	,	PUNCT
ejpam-4220	138	11	v1	v1	NOUN
ejpam-4220	138	12	and	and	CCONJ
ejpam-4220	138	13	v2	v2	NOUN
ejpam-4220	138	14	are	be	AUX
ejpam-4220	138	15	not	not	PART
ejpam-4220	138	16	adjacent	adjacent	ADJ
ejpam-4220	138	17	.	.	PUNCT
ejpam-4220	139	1	we	we	PRON
ejpam-4220	139	2	are	be	AUX
ejpam-4220	139	3	left	leave	VERB
ejpam-4220	139	4	to	to	PART
ejpam-4220	139	5	show	show	VERB
ejpam-4220	139	6	that	that	SCONJ
ejpam-4220	139	7	⋃	⋃	SCONJ
ejpam-4220	139	8	ω∈ω	ω∈ω	ADJ
ejpam-4220	139	9	⟨n	⟨n	ADJ
ejpam-4220	139	10	[	[	X
ejpam-4220	139	11	ω]⟩	ω]⟩	NOUN
ejpam-4220	139	12	=	=	SYM
ejpam-4220	139	13	g.	g.	NOUN
ejpam-4220	139	14	assume	assume	VERB
ejpam-4220	139	15	to	to	ADP
ejpam-4220	139	16	the	the	DET
ejpam-4220	139	17	contrary	contrary	NOUN
ejpam-4220	139	18	that	that	SCONJ
ejpam-4220	139	19	⋃	⋃	PUNCT
ejpam-4220	139	20	ω∈ω	ω∈ω	ADJ
ejpam-4220	139	21	⟨n	⟨n	NUM
ejpam-4220	139	22	[	[	PUNCT
ejpam-4220	139	23	ω]⟩	ω]⟩	NOUN
ejpam-4220	139	24	̸=	̸=	PROPN
ejpam-4220	139	25	g.	g.	NOUN
ejpam-4220	139	26	then	then	ADV
ejpam-4220	139	27	there	there	PRON
ejpam-4220	139	28	exists	exist	VERB
ejpam-4220	139	29	xy	xy	PROPN
ejpam-4220	139	30	∈	∈	PROPN
ejpam-4220	139	31	e(g	e(g	PROPN
ejpam-4220	139	32	)	)	PUNCT
ejpam-4220	139	33	such	such	ADJ
ejpam-4220	139	34	that	that	PRON
ejpam-4220	139	35	xy	xy	PROPN
ejpam-4220	139	36	/∈	/∈	PUNCT
ejpam-4220	140	1	e	e	X
ejpam-4220	140	2	(	(	PUNCT
ejpam-4220	140	3	⋃	⋃	SCONJ
ejpam-4220	140	4	ω∈ω	ω∈ω	X
ejpam-4220	140	5	⟨n	⟨n	ADJ
ejpam-4220	140	6	[	[	X
ejpam-4220	140	7	ω]⟩	ω]⟩	NOUN
ejpam-4220	140	8	)	)	PUNCT
ejpam-4220	140	9	.	.	PUNCT
ejpam-4220	141	1	it	it	PRON
ejpam-4220	141	2	follows	follow	VERB
ejpam-4220	141	3	that	that	SCONJ
ejpam-4220	141	4	both	both	DET
ejpam-4220	141	5	x	x	NOUN
ejpam-4220	141	6	,	,	PUNCT
ejpam-4220	141	7	y	y	PROPN
ejpam-4220	141	8	/∈	/∈	PUNCT
ejpam-4220	142	1	ω	ω	X
ejpam-4220	142	2	.	.	PUNCT
ejpam-4220	142	3	observe	observe	VERB
ejpam-4220	142	4	that	that	SCONJ
ejpam-4220	142	5	for	for	ADP
ejpam-4220	142	6	any	any	DET
ejpam-4220	142	7	ω	ω	PROPN
ejpam-4220	142	8	∈	∈	PROPN
ejpam-4220	142	9	ω	ω	PROPN
ejpam-4220	142	10	,	,	PUNCT
ejpam-4220	142	11	d(ω	d(ω	PROPN
ejpam-4220	142	12	,	,	PUNCT
ejpam-4220	142	13	x	x	NOUN
ejpam-4220	142	14	)	)	PUNCT
ejpam-4220	142	15	=	=	SYM
ejpam-4220	142	16	2m+	2m+	NUM
ejpam-4220	142	17	1,m	1,m	PROPN
ejpam-4220	142	18	∈	∈	PROPN
ejpam-4220	142	19	n∗.	n∗.	PROPN
ejpam-4220	142	20	now	now	ADV
ejpam-4220	142	21	,	,	PUNCT
ejpam-4220	142	22	dg(ω	dg(ω	PROPN
ejpam-4220	142	23	,	,	PUNCT
ejpam-4220	142	24	y	y	NOUN
ejpam-4220	142	25	)	)	PUNCT
ejpam-4220	142	26	=	=	SYM
ejpam-4220	142	27	dg(ω	dg(ω	X
ejpam-4220	142	28	,	,	PUNCT
ejpam-4220	142	29	x	x	X
ejpam-4220	142	30	)	)	PUNCT
ejpam-4220	143	1	+	+	CCONJ
ejpam-4220	143	2	dg(x	dg(x	X
ejpam-4220	143	3	,	,	PUNCT
ejpam-4220	143	4	y	y	NOUN
ejpam-4220	143	5	)	)	PUNCT
ejpam-4220	143	6	=	=	PUNCT
ejpam-4220	143	7	(	(	PUNCT
ejpam-4220	143	8	2m+	2m+	NUM
ejpam-4220	143	9	1	1	NUM
ejpam-4220	143	10	)	)	PUNCT
ejpam-4220	143	11	+	+	CCONJ
ejpam-4220	143	12	1	1	NUM
ejpam-4220	143	13	=	=	SYM
ejpam-4220	143	14	2m+	2m+	NUM
ejpam-4220	143	15	2	2	NUM
ejpam-4220	143	16	=	=	SYM
ejpam-4220	143	17	2(m+	2(m+	NUM
ejpam-4220	143	18	1	1	NUM
ejpam-4220	143	19	)	)	PUNCT
ejpam-4220	143	20	.	.	PUNCT
ejpam-4220	144	1	let	let	VERB
ejpam-4220	144	2	n	n	NOUN
ejpam-4220	144	3	=	=	PUNCT
ejpam-4220	144	4	m+	m+	NUM
ejpam-4220	145	1	1	1	NUM
ejpam-4220	145	2	.	.	PUNCT
ejpam-4220	146	1	then	then	ADV
ejpam-4220	146	2	n	n	NUM
ejpam-4220	146	3	∈	∈	PROPN
ejpam-4220	146	4	n∗	n∗	NOUN
ejpam-4220	146	5	and	and	CCONJ
ejpam-4220	146	6	d(ω	d(ω	PROPN
ejpam-4220	146	7	,	,	PUNCT
ejpam-4220	146	8	y	y	NOUN
ejpam-4220	146	9	)	)	PUNCT
ejpam-4220	146	10	=	=	SYM
ejpam-4220	146	11	2n	2n	NUM
ejpam-4220	146	12	which	which	PRON
ejpam-4220	146	13	implies	imply	VERB
ejpam-4220	146	14	y	y	PROPN
ejpam-4220	146	15	∈	∈	PROPN
ejpam-4220	146	16	ω	ω	PROPN
ejpam-4220	146	17	,	,	PUNCT
ejpam-4220	146	18	a	a	DET
ejpam-4220	146	19	contradiction	contradiction	NOUN
ejpam-4220	146	20	since	since	SCONJ
ejpam-4220	146	21	y	y	PROPN
ejpam-4220	146	22	/∈	/∈	PUNCT
ejpam-4220	147	1	ω	ω	INTJ
ejpam-4220	147	2	.	.	PUNCT
ejpam-4220	148	1	hence	hence	ADV
ejpam-4220	148	2	,	,	PUNCT
ejpam-4220	148	3	⋃	⋃	SCONJ
ejpam-4220	148	4	ω∈ω	ω∈ω	NOUN
ejpam-4220	148	5	⟨n	⟨n	ADJ
ejpam-4220	148	6	[	[	X
ejpam-4220	148	7	ω]⟩	ω]⟩	NOUN
ejpam-4220	148	8	=	=	SYM
ejpam-4220	148	9	g.	g.	PROPN
ejpam-4220	148	10	therefore	therefore	ADV
ejpam-4220	148	11	,	,	PUNCT
ejpam-4220	148	12	ω	ω	PROPN
ejpam-4220	148	13	is	be	AUX
ejpam-4220	148	14	an	an	DET
ejpam-4220	148	15	independent	independent	ADJ
ejpam-4220	148	16	neighborhood	neighborhood	NOUN
ejpam-4220	148	17	set	set	NOUN
ejpam-4220	148	18	of	of	ADP
ejpam-4220	148	19	g.	g.	PROPN
ejpam-4220	148	20	■	■	PUNCT
ejpam-4220	148	21	corollary	corollary	ADJ
ejpam-4220	148	22	3	3	X
ejpam-4220	148	23	.	.	PUNCT
ejpam-4220	149	1	let	let	VERB
ejpam-4220	149	2	f	f	PRON
ejpam-4220	149	3	be	be	AUX
ejpam-4220	149	4	the	the	DET
ejpam-4220	149	5	set	set	NOUN
ejpam-4220	149	6	of	of	ADP
ejpam-4220	149	7	nonpendant	nonpendant	ADJ
ejpam-4220	149	8	vertices	vertex	NOUN
ejpam-4220	149	9	in	in	ADP
ejpam-4220	149	10	a	a	DET
ejpam-4220	149	11	tree	tree	NOUN
ejpam-4220	149	12	g	g	NOUN
ejpam-4220	149	13	and	and	CCONJ
ejpam-4220	149	14	f	f	PROPN
ejpam-4220	149	15	∈	∈	PROPN
ejpam-4220	150	1	f	f	PROPN
ejpam-4220	150	2	.	.	PUNCT
ejpam-4220	151	1	let	let	VERB
ejpam-4220	151	2	a	a	PRON
ejpam-4220	151	3	=	=	X
ejpam-4220	151	4	{	{	PUNCT
ejpam-4220	151	5	a	a	DET
ejpam-4220	151	6	∈	∈	ADJ
ejpam-4220	151	7	f	f	X
ejpam-4220	151	8	:	:	PUNCT
ejpam-4220	151	9	dg(a	dg(a	X
ejpam-4220	151	10	,	,	PUNCT
ejpam-4220	151	11	f	f	X
ejpam-4220	151	12	)	)	PUNCT
ejpam-4220	151	13	=	=	SYM
ejpam-4220	151	14	2n	2n	NUM
ejpam-4220	151	15	,	,	PUNCT
ejpam-4220	151	16	n	n	PRON
ejpam-4220	151	17	∈	∈	PROPN
ejpam-4220	151	18	n∗	n∗	PROPN
ejpam-4220	151	19	}	}	PUNCT
ejpam-4220	151	20	and	and	CCONJ
ejpam-4220	151	21	b	b	X
ejpam-4220	151	22	=	=	SYM
ejpam-4220	151	23	f	f	PROPN
ejpam-4220	151	24	\a	\a	PROPN
ejpam-4220	151	25	.	.	PUNCT
ejpam-4220	152	1	then	then	ADV
ejpam-4220	152	2	the	the	DET
ejpam-4220	152	3	sets	set	NOUN
ejpam-4220	152	4	ω	ω	PUNCT
ejpam-4220	152	5	=	=	SYM
ejpam-4220	152	6	{	{	PUNCT
ejpam-4220	152	7	v	v	NOUN
ejpam-4220	152	8	:	:	PUNCT
ejpam-4220	152	9	v	v	NOUN
ejpam-4220	152	10	is	be	AUX
ejpam-4220	152	11	a	a	DET
ejpam-4220	152	12	pendant	pendant	ADJ
ejpam-4220	152	13	neighbor	neighbor	NOUN
ejpam-4220	152	14	of	of	ADP
ejpam-4220	152	15	a	a	PRON
ejpam-4220	152	16	,	,	PUNCT
ejpam-4220	152	17	for	for	SCONJ
ejpam-4220	152	18	some	some	DET
ejpam-4220	152	19	a	a	DET
ejpam-4220	152	20	∈	∈	PROPN
ejpam-4220	152	21	a	a	PRON
ejpam-4220	152	22	}	}	PUNCT
ejpam-4220	152	23	∪b	∪b	NOUN
ejpam-4220	152	24	and	and	CCONJ
ejpam-4220	152	25	∆	∆	X
ejpam-4220	152	26	=	=	PRON
ejpam-4220	152	27	{	{	PUNCT
ejpam-4220	152	28	u	u	NOUN
ejpam-4220	152	29	:	:	PUNCT
ejpam-4220	152	30	u	u	NOUN
ejpam-4220	152	31	is	be	AUX
ejpam-4220	152	32	a	a	DET
ejpam-4220	152	33	pendant	pendant	ADJ
ejpam-4220	152	34	neighbor	neighbor	NOUN
ejpam-4220	152	35	of	of	ADP
ejpam-4220	152	36	b	b	PROPN
ejpam-4220	152	37	,	,	PUNCT
ejpam-4220	152	38	for	for	SCONJ
ejpam-4220	152	39	some	some	DET
ejpam-4220	152	40	b	b	NOUN
ejpam-4220	152	41	∈	∈	PROPN
ejpam-4220	152	42	b	b	PROPN
ejpam-4220	152	43	}	}	PUNCT
ejpam-4220	152	44	∪a	∪a	NUM
ejpam-4220	152	45	are	be	AUX
ejpam-4220	152	46	the	the	DET
ejpam-4220	152	47	only	only	ADJ
ejpam-4220	152	48	independent	independent	ADJ
ejpam-4220	152	49	neighborhood	neighborhood	NOUN
ejpam-4220	152	50	sets	set	NOUN
ejpam-4220	152	51	of	of	ADP
ejpam-4220	152	52	g.	g.	PROPN
ejpam-4220	152	53	proof	proof	NOUN
ejpam-4220	152	54	.	.	PUNCT
ejpam-4220	153	1	let	let	VERB
ejpam-4220	153	2	f	f	PRON
ejpam-4220	153	3	be	be	AUX
ejpam-4220	153	4	the	the	DET
ejpam-4220	153	5	set	set	NOUN
ejpam-4220	153	6	of	of	ADP
ejpam-4220	153	7	nonpendant	nonpendant	ADJ
ejpam-4220	153	8	vertices	vertex	NOUN
ejpam-4220	153	9	in	in	ADP
ejpam-4220	153	10	g	g	PROPN
ejpam-4220	153	11	and	and	CCONJ
ejpam-4220	153	12	f	f	PROPN
ejpam-4220	153	13	∈	∈	PROPN
ejpam-4220	153	14	f	f	PROPN
ejpam-4220	153	15	.	.	PUNCT
ejpam-4220	154	1	let	let	VERB
ejpam-4220	154	2	a	a	PRON
ejpam-4220	154	3	=	=	X
ejpam-4220	154	4	{	{	PUNCT
ejpam-4220	154	5	a	a	DET
ejpam-4220	154	6	∈	∈	ADJ
ejpam-4220	154	7	f	f	X
ejpam-4220	154	8	:	:	PUNCT
ejpam-4220	154	9	dg(a	dg(a	X
ejpam-4220	154	10	,	,	PUNCT
ejpam-4220	154	11	f	f	X
ejpam-4220	154	12	)	)	PUNCT
ejpam-4220	154	13	=	=	SYM
ejpam-4220	154	14	2n	2n	NUM
ejpam-4220	154	15	,	,	PUNCT
ejpam-4220	154	16	n	n	PRON
ejpam-4220	154	17	∈	∈	PROPN
ejpam-4220	154	18	n∗	n∗	PROPN
ejpam-4220	154	19	}	}	PUNCT
ejpam-4220	154	20	and	and	CCONJ
ejpam-4220	154	21	b	b	X
ejpam-4220	154	22	=	=	SYM
ejpam-4220	154	23	f	f	PROPN
ejpam-4220	154	24	\a	\a	ADJ
ejpam-4220	154	25	.	.	PUNCT
ejpam-4220	155	1	n.	n.	PROPN
ejpam-4220	155	2	s.	s.	PROPN
ejpam-4220	155	3	abdulcarim	abdulcarim	PROPN
ejpam-4220	155	4	,	,	PUNCT
ejpam-4220	155	5	s.	s.	PROPN
ejpam-4220	155	6	c.	c.	PROPN
ejpam-4220	155	7	dagondon	dagondon	PROPN
ejpam-4220	155	8	/	/	SYM
ejpam-4220	155	9	eur	eur	PROPN
ejpam-4220	155	10	.	.	PUNCT
ejpam-4220	156	1	j.	j.	PROPN
ejpam-4220	156	2	pure	pure	PROPN
ejpam-4220	156	3	appl	appl	PROPN
ejpam-4220	156	4	.	.	PROPN
ejpam-4220	156	5	math	math	PROPN
ejpam-4220	156	6	,	,	PUNCT
ejpam-4220	156	7	15	15	NUM
ejpam-4220	156	8	(	(	PUNCT
ejpam-4220	156	9	1	1	NUM
ejpam-4220	156	10	)	)	PUNCT
ejpam-4220	156	11	(	(	PUNCT
ejpam-4220	156	12	2022	2022	NUM
ejpam-4220	156	13	)	)	PUNCT
ejpam-4220	156	14	,	,	PUNCT
ejpam-4220	156	15	64	64	NUM
ejpam-4220	156	16	-	-	SYM
ejpam-4220	156	17	81	81	NUM
ejpam-4220	156	18	71	71	NUM
ejpam-4220	156	19	then	then	ADV
ejpam-4220	156	20	for	for	ADP
ejpam-4220	156	21	every	every	DET
ejpam-4220	156	22	a	a	DET
ejpam-4220	156	23	∈	∈	PROPN
ejpam-4220	156	24	a	a	PRON
ejpam-4220	156	25	and	and	CCONJ
ejpam-4220	156	26	b	b	PROPN
ejpam-4220	156	27	∈	∈	PROPN
ejpam-4220	156	28	b	b	PROPN
ejpam-4220	156	29	,	,	PUNCT
ejpam-4220	156	30	dg(a	dg(a	X
ejpam-4220	156	31	,	,	PUNCT
ejpam-4220	156	32	b	b	X
ejpam-4220	156	33	)	)	PUNCT
ejpam-4220	156	34	=	=	SYM
ejpam-4220	157	1	2	2	NUM
ejpam-4220	157	2	m	m	NOUN
ejpam-4220	157	3	+	+	NOUN
ejpam-4220	157	4	1,m	1,m	PROPN
ejpam-4220	157	5	∈	∈	PROPN
ejpam-4220	157	6	n∗.	n∗.	NOUN
ejpam-4220	157	7	we	we	PRON
ejpam-4220	157	8	note	note	VERB
ejpam-4220	157	9	that	that	SCONJ
ejpam-4220	157	10	for	for	ADP
ejpam-4220	157	11	any	any	DET
ejpam-4220	157	12	u	u	PROPN
ejpam-4220	157	13	∈	∈	PROPN
ejpam-4220	157	14	n(g	n(g	NUM
ejpam-4220	157	15	)	)	PUNCT
ejpam-4220	157	16	,	,	PUNCT
ejpam-4220	157	17	dg(u	dg(u	X
ejpam-4220	157	18	,	,	PUNCT
ejpam-4220	157	19	g	g	NOUN
ejpam-4220	157	20	)	)	PUNCT
ejpam-4220	157	21	=	=	SYM
ejpam-4220	157	22	1	1	NUM
ejpam-4220	157	23	for	for	ADP
ejpam-4220	157	24	every	every	DET
ejpam-4220	157	25	g	g	PROPN
ejpam-4220	157	26	∈	∈	PROPN
ejpam-4220	157	27	g.	g.	NOUN
ejpam-4220	157	28	let	let	VERB
ejpam-4220	157	29	v	v	PART
ejpam-4220	157	30	be	be	AUX
ejpam-4220	157	31	a	a	DET
ejpam-4220	157	32	pendant	pendant	ADJ
ejpam-4220	157	33	neighbor	neighbor	NOUN
ejpam-4220	157	34	of	of	ADP
ejpam-4220	157	35	a	a	DET
ejpam-4220	157	36	∈	∈	PROPN
ejpam-4220	157	37	a.	a.	NOUN
ejpam-4220	157	38	now	now	ADV
ejpam-4220	157	39	,	,	PUNCT
ejpam-4220	157	40	for	for	ADP
ejpam-4220	157	41	any	any	DET
ejpam-4220	157	42	b	b	PROPN
ejpam-4220	157	43	∈	∈	PROPN
ejpam-4220	157	44	b	b	NOUN
ejpam-4220	157	45	,	,	PUNCT
ejpam-4220	157	46	we	we	PRON
ejpam-4220	157	47	have	have	VERB
ejpam-4220	157	48	dg(v	dg(v	NOUN
ejpam-4220	157	49	,	,	PUNCT
ejpam-4220	157	50	b	b	X
ejpam-4220	157	51	)	)	PUNCT
ejpam-4220	157	52	=	=	NOUN
ejpam-4220	157	53	dg(v	dg(v	X
ejpam-4220	157	54	,	,	PUNCT
ejpam-4220	157	55	a	a	PRON
ejpam-4220	157	56	)	)	PUNCT
ejpam-4220	157	57	+	+	CCONJ
ejpam-4220	157	58	dg(a	dg(a	NUM
ejpam-4220	157	59	,	,	PUNCT
ejpam-4220	157	60	b	b	X
ejpam-4220	157	61	)	)	PUNCT
ejpam-4220	158	1	=	=	NOUN
ejpam-4220	158	2	1	1	NUM
ejpam-4220	158	3	+	+	NUM
ejpam-4220	158	4	2m+	2m+	NUM
ejpam-4220	158	5	1	1	NUM
ejpam-4220	158	6	=	=	SYM
ejpam-4220	158	7	2(m+	2(m+	NUM
ejpam-4220	158	8	1	1	NUM
ejpam-4220	158	9	)	)	PUNCT
ejpam-4220	158	10	.	.	PUNCT
ejpam-4220	159	1	let	let	VERB
ejpam-4220	159	2	n	n	NOUN
ejpam-4220	159	3	=	=	NOUN
ejpam-4220	159	4	m	m	VERB
ejpam-4220	159	5	+	+	ADJ
ejpam-4220	159	6	1	1	X
ejpam-4220	159	7	.	.	PUNCT
ejpam-4220	160	1	then	then	ADV
ejpam-4220	160	2	n	n	NUM
ejpam-4220	160	3	∈	∈	NOUN
ejpam-4220	160	4	n∗	n∗	NOUN
ejpam-4220	160	5	and	and	CCONJ
ejpam-4220	160	6	dg(v	dg(v	X
ejpam-4220	160	7	,	,	PUNCT
ejpam-4220	160	8	b	b	X
ejpam-4220	160	9	)	)	PUNCT
ejpam-4220	160	10	=	=	SYM
ejpam-4220	160	11	2n	2n	NUM
ejpam-4220	160	12	which	which	PRON
ejpam-4220	160	13	is	be	AUX
ejpam-4220	160	14	even	even	ADV
ejpam-4220	160	15	.	.	PUNCT
ejpam-4220	161	1	by	by	ADP
ejpam-4220	161	2	theorem	theorem	NOUN
ejpam-4220	161	3	2	2	NUM
ejpam-4220	161	4	,	,	PUNCT
ejpam-4220	161	5	ω	ω	PROPN
ejpam-4220	161	6	is	be	AUX
ejpam-4220	161	7	an	an	DET
ejpam-4220	161	8	independent	independent	ADJ
ejpam-4220	161	9	neighborhood	neighborhood	NOUN
ejpam-4220	161	10	set	set	NOUN
ejpam-4220	161	11	of	of	ADP
ejpam-4220	161	12	g.	g.	PROPN
ejpam-4220	161	13	similarly	similarly	ADV
ejpam-4220	161	14	,	,	PUNCT
ejpam-4220	161	15	we	we	PRON
ejpam-4220	161	16	can	can	AUX
ejpam-4220	161	17	show	show	VERB
ejpam-4220	161	18	that	that	SCONJ
ejpam-4220	161	19	∆	∆	PROPN
ejpam-4220	161	20	is	be	AUX
ejpam-4220	161	21	also	also	ADV
ejpam-4220	161	22	an	an	DET
ejpam-4220	161	23	independent	independent	ADJ
ejpam-4220	161	24	neighborhood	neighborhood	NOUN
ejpam-4220	161	25	set	set	NOUN
ejpam-4220	161	26	of	of	ADP
ejpam-4220	161	27	g.	g.	PROPN
ejpam-4220	161	28	we	we	PRON
ejpam-4220	161	29	are	be	AUX
ejpam-4220	161	30	left	leave	VERB
ejpam-4220	161	31	to	to	PART
ejpam-4220	161	32	show	show	VERB
ejpam-4220	161	33	that	that	SCONJ
ejpam-4220	161	34	ω	ω	PROPN
ejpam-4220	161	35	and	and	CCONJ
ejpam-4220	161	36	∆	∆	PROPN
ejpam-4220	161	37	are	be	AUX
ejpam-4220	161	38	the	the	DET
ejpam-4220	161	39	only	only	ADJ
ejpam-4220	161	40	independent	independent	ADJ
ejpam-4220	161	41	neighborhood	neighborhood	NOUN
ejpam-4220	161	42	sets	set	NOUN
ejpam-4220	161	43	of	of	ADP
ejpam-4220	161	44	g.	g.	PROPN
ejpam-4220	161	45	clearly	clearly	ADV
ejpam-4220	161	46	,	,	PUNCT
ejpam-4220	161	47	from	from	ADP
ejpam-4220	161	48	the	the	DET
ejpam-4220	161	49	definition	definition	NOUN
ejpam-4220	161	50	of	of	ADP
ejpam-4220	161	51	ω	ω	PROPN
ejpam-4220	161	52	and	and	CCONJ
ejpam-4220	161	53	∆	∆	NUM
ejpam-4220	161	54	,	,	PUNCT
ejpam-4220	161	55	ωc	ωc	PROPN
ejpam-4220	161	56	=	=	SYM
ejpam-4220	161	57	∆.	∆.	NOUN
ejpam-4220	161	58	assume	assume	VERB
ejpam-4220	161	59	that	that	SCONJ
ejpam-4220	161	60	there	there	PRON
ejpam-4220	161	61	is	be	VERB
ejpam-4220	161	62	another	another	DET
ejpam-4220	161	63	independent	independent	ADJ
ejpam-4220	161	64	neighborhood	neighborhood	NOUN
ejpam-4220	161	65	set	set	NOUN
ejpam-4220	161	66	of	of	ADP
ejpam-4220	161	67	g	g	NOUN
ejpam-4220	161	68	,	,	PUNCT
ejpam-4220	161	69	say	say	VERB
ejpam-4220	161	70	λ	λ	INTJ
ejpam-4220	161	71	.	.	NOUN
ejpam-4220	161	72	define	define	VERB
ejpam-4220	161	73	λ	λ	PROPN
ejpam-4220	161	74	=	=	SYM
ejpam-4220	161	75	ω1	ω1	PROPN
ejpam-4220	161	76	∪	∪	ADV
ejpam-4220	161	77	∆1	∆1	NUM
ejpam-4220	161	78	where	where	SCONJ
ejpam-4220	161	79	ω1	ω1	PROPN
ejpam-4220	161	80	⊂	⊂	PROPN
ejpam-4220	161	81	ω	ω	PROPN
ejpam-4220	161	82	and	and	CCONJ
ejpam-4220	161	83	∆1	∆1	NUM
ejpam-4220	161	84	⊂	⊂	PRON
ejpam-4220	162	1	∆.	∆.	X
ejpam-4220	162	2	let	let	VERB
ejpam-4220	162	3	x	x	X
ejpam-4220	162	4	∈	∈	NOUN
ejpam-4220	162	5	ω	ω	NUM
ejpam-4220	162	6	\ω1	\ω1	ADJ
ejpam-4220	162	7	and	and	CCONJ
ejpam-4220	162	8	y	y	PROPN
ejpam-4220	162	9	∈	∈	PROPN
ejpam-4220	162	10	∆	∆	X
ejpam-4220	162	11	\∆1	\∆1	PRON
ejpam-4220	162	12	.	.	PUNCT
ejpam-4220	162	13	suppose	suppose	VERB
ejpam-4220	162	14	that	that	SCONJ
ejpam-4220	162	15	xw	xw	PROPN
ejpam-4220	162	16	,	,	PUNCT
ejpam-4220	162	17	yz	yz	PROPN
ejpam-4220	162	18	∈	∈	PROPN
ejpam-4220	162	19	e(g	e(g	PROPN
ejpam-4220	162	20	)	)	PUNCT
ejpam-4220	162	21	for	for	ADP
ejpam-4220	162	22	some	some	DET
ejpam-4220	162	23	w	w	NOUN
ejpam-4220	162	24	,	,	PUNCT
ejpam-4220	162	25	z	z	PROPN
ejpam-4220	162	26	∈	∈	PROPN
ejpam-4220	162	27	λ	λ	PROPN
ejpam-4220	162	28	.	.	PUNCT
ejpam-4220	163	1	since	since	SCONJ
ejpam-4220	163	2	ω	ω	PROPN
ejpam-4220	163	3	and	and	CCONJ
ejpam-4220	163	4	∆	∆	PROPN
ejpam-4220	163	5	are	be	AUX
ejpam-4220	163	6	independent	independent	ADJ
ejpam-4220	163	7	neighborhood	neighborhood	NOUN
ejpam-4220	163	8	sets	set	NOUN
ejpam-4220	163	9	of	of	ADP
ejpam-4220	163	10	g	g	NOUN
ejpam-4220	163	11	,	,	PUNCT
ejpam-4220	163	12	w	w	PROPN
ejpam-4220	163	13	must	must	AUX
ejpam-4220	163	14	be	be	AUX
ejpam-4220	163	15	in	in	ADP
ejpam-4220	163	16	∆1	∆1	PROPN
ejpam-4220	163	17	and	and	CCONJ
ejpam-4220	163	18	z	z	NOUN
ejpam-4220	163	19	must	must	AUX
ejpam-4220	163	20	be	be	AUX
ejpam-4220	163	21	in	in	ADP
ejpam-4220	163	22	ω1	ω1	PROPN
ejpam-4220	163	23	.	.	PROPN
ejpam-4220	164	1	observe	observe	VERB
ejpam-4220	164	2	that	that	SCONJ
ejpam-4220	164	3	dg(w	dg(w	VERB
ejpam-4220	164	4	,	,	PUNCT
ejpam-4220	164	5	z	z	NOUN
ejpam-4220	164	6	)	)	PUNCT
ejpam-4220	164	7	=	=	SYM
ejpam-4220	164	8	2r	2r	NUM
ejpam-4220	164	9	for	for	ADP
ejpam-4220	164	10	some	some	DET
ejpam-4220	164	11	r	r	NOUN
ejpam-4220	164	12	∈	∈	PROPN
ejpam-4220	164	13	n∗	n∗	NOUN
ejpam-4220	164	14	and	and	CCONJ
ejpam-4220	164	15	dg(y	dg(y	ADJ
ejpam-4220	164	16	,	,	PUNCT
ejpam-4220	164	17	z	z	NOUN
ejpam-4220	164	18	)	)	PUNCT
ejpam-4220	164	19	=	=	SYM
ejpam-4220	164	20	1	1	NUM
ejpam-4220	164	21	since	since	SCONJ
ejpam-4220	164	22	λ	λ	PROPN
ejpam-4220	164	23	is	be	AUX
ejpam-4220	164	24	an	an	DET
ejpam-4220	164	25	independent	independent	ADJ
ejpam-4220	164	26	neighborhood	neighborhood	NOUN
ejpam-4220	164	27	set	set	NOUN
ejpam-4220	164	28	of	of	ADP
ejpam-4220	164	29	g	g	PROPN
ejpam-4220	164	30	and	and	CCONJ
ejpam-4220	164	31	yz	yz	PROPN
ejpam-4220	164	32	∈	∈	PROPN
ejpam-4220	164	33	e(g	e(g	PROPN
ejpam-4220	164	34	)	)	PUNCT
ejpam-4220	164	35	.	.	PUNCT
ejpam-4220	165	1	now	now	ADV
ejpam-4220	165	2	,	,	PUNCT
ejpam-4220	165	3	dg(w	dg(w	X
ejpam-4220	165	4	,	,	PUNCT
ejpam-4220	165	5	y	y	NOUN
ejpam-4220	165	6	)	)	PUNCT
ejpam-4220	165	7	=	=	NOUN
ejpam-4220	165	8	dg(w	dg(w	NOUN
ejpam-4220	165	9	,	,	PUNCT
ejpam-4220	165	10	z	z	NOUN
ejpam-4220	165	11	)	)	PUNCT
ejpam-4220	165	12	+	+	CCONJ
ejpam-4220	166	1	dg(y	dg(y	ADJ
ejpam-4220	166	2	,	,	PUNCT
ejpam-4220	166	3	z	z	NOUN
ejpam-4220	166	4	)	)	PUNCT
ejpam-4220	166	5	=	=	NOUN
ejpam-4220	166	6	2n+	2n+	NUM
ejpam-4220	166	7	1	1	NUM
ejpam-4220	166	8	.	.	PUNCT
ejpam-4220	167	1	this	this	PRON
ejpam-4220	167	2	means	mean	VERB
ejpam-4220	167	3	dg(w	dg(w	NOUN
ejpam-4220	167	4	,	,	PUNCT
ejpam-4220	167	5	y	y	NOUN
ejpam-4220	167	6	)	)	PUNCT
ejpam-4220	167	7	is	be	AUX
ejpam-4220	167	8	odd	odd	ADJ
ejpam-4220	167	9	which	which	PRON
ejpam-4220	167	10	is	be	AUX
ejpam-4220	167	11	a	a	DET
ejpam-4220	167	12	contradiction	contradiction	NOUN
ejpam-4220	167	13	since	since	SCONJ
ejpam-4220	167	14	∆	∆	PROPN
ejpam-4220	167	15	is	be	AUX
ejpam-4220	167	16	an	an	DET
ejpam-4220	167	17	independent	independent	ADJ
ejpam-4220	167	18	neighborhood	neighborhood	NOUN
ejpam-4220	167	19	set	set	NOUN
ejpam-4220	167	20	of	of	ADP
ejpam-4220	167	21	g.	g.	PROPN
ejpam-4220	167	22	hence	hence	ADV
ejpam-4220	167	23	,	,	PUNCT
ejpam-4220	167	24	λ	λ	PROPN
ejpam-4220	167	25	can	can	AUX
ejpam-4220	167	26	not	not	PART
ejpam-4220	167	27	be	be	AUX
ejpam-4220	167	28	an	an	DET
ejpam-4220	167	29	independent	independent	ADJ
ejpam-4220	167	30	neighborhood	neighborhood	NOUN
ejpam-4220	167	31	set	set	NOUN
ejpam-4220	167	32	of	of	ADP
ejpam-4220	167	33	g.	g.	PROPN
ejpam-4220	167	34	therefore	therefore	ADV
ejpam-4220	167	35	,	,	PUNCT
ejpam-4220	167	36	s	s	PART
ejpam-4220	167	37	and	and	CCONJ
ejpam-4220	167	38	t	t	PROPN
ejpam-4220	167	39	are	be	AUX
ejpam-4220	167	40	the	the	DET
ejpam-4220	167	41	only	only	ADJ
ejpam-4220	167	42	independent	independent	ADJ
ejpam-4220	167	43	neighborhood	neighborhood	NOUN
ejpam-4220	167	44	set	set	NOUN
ejpam-4220	167	45	of	of	ADP
ejpam-4220	167	46	g.	g.	PROPN
ejpam-4220	167	47	■	■	PUNCT
ejpam-4220	167	48	corollary	corollary	ADJ
ejpam-4220	167	49	4	4	NUM
ejpam-4220	167	50	.	.	PUNCT
ejpam-4220	168	1	let	let	VERB
ejpam-4220	168	2	f	f	PRON
ejpam-4220	168	3	be	be	AUX
ejpam-4220	168	4	the	the	DET
ejpam-4220	168	5	set	set	NOUN
ejpam-4220	168	6	of	of	ADP
ejpam-4220	168	7	nonpendant	nonpendant	ADJ
ejpam-4220	168	8	vertices	vertex	NOUN
ejpam-4220	168	9	in	in	ADP
ejpam-4220	168	10	a	a	DET
ejpam-4220	168	11	tree	tree	NOUN
ejpam-4220	168	12	g	g	NOUN
ejpam-4220	168	13	and	and	CCONJ
ejpam-4220	168	14	f	f	PROPN
ejpam-4220	168	15	∈	∈	PROPN
ejpam-4220	169	1	f	f	PROPN
ejpam-4220	169	2	.	.	PUNCT
ejpam-4220	170	1	let	let	VERB
ejpam-4220	170	2	a	a	PRON
ejpam-4220	170	3	=	=	X
ejpam-4220	170	4	{	{	PUNCT
ejpam-4220	170	5	a	a	DET
ejpam-4220	170	6	∈	∈	ADJ
ejpam-4220	170	7	f	f	X
ejpam-4220	170	8	:	:	PUNCT
ejpam-4220	170	9	d⟨f	d⟨f	NUM
ejpam-4220	170	10	⟩(a	⟩(a	NOUN
ejpam-4220	170	11	,	,	PUNCT
ejpam-4220	170	12	f	f	X
ejpam-4220	170	13	)	)	PUNCT
ejpam-4220	170	14	=	=	SYM
ejpam-4220	170	15	2n	2n	NUM
ejpam-4220	170	16	,	,	PUNCT
ejpam-4220	170	17	n	n	PRON
ejpam-4220	170	18	∈	∈	PROPN
ejpam-4220	170	19	n∗	n∗	PROPN
ejpam-4220	170	20	}	}	PUNCT
ejpam-4220	170	21	and	and	CCONJ
ejpam-4220	170	22	b	b	X
ejpam-4220	170	23	=	=	SYM
ejpam-4220	170	24	f	f	PROPN
ejpam-4220	170	25	\a	\a	ADJ
ejpam-4220	170	26	.	.	PUNCT
ejpam-4220	171	1	suppose	suppose	VERB
ejpam-4220	171	2	that	that	SCONJ
ejpam-4220	171	3	ω	ω	PROPN
ejpam-4220	171	4	=	=	PRON
ejpam-4220	171	5	{	{	PUNCT
ejpam-4220	171	6	v	v	NOUN
ejpam-4220	171	7	:	:	PUNCT
ejpam-4220	171	8	v	v	NOUN
ejpam-4220	171	9	is	be	AUX
ejpam-4220	171	10	a	a	DET
ejpam-4220	171	11	pendant	pendant	ADJ
ejpam-4220	171	12	neighbor	neighbor	NOUN
ejpam-4220	171	13	of	of	ADP
ejpam-4220	171	14	a	a	DET
ejpam-4220	171	15	∈	∈	PROPN
ejpam-4220	171	16	a	a	PRON
ejpam-4220	171	17	}	}	PUNCT
ejpam-4220	171	18	∪b	∪b	NOUN
ejpam-4220	171	19	and	and	CCONJ
ejpam-4220	171	20	∆	∆	X
ejpam-4220	171	21	=	=	PRON
ejpam-4220	171	22	{	{	PUNCT
ejpam-4220	171	23	u	u	NOUN
ejpam-4220	171	24	:	:	PUNCT
ejpam-4220	171	25	u	u	NOUN
ejpam-4220	171	26	is	be	AUX
ejpam-4220	171	27	a	a	DET
ejpam-4220	171	28	pendant	pendant	ADJ
ejpam-4220	171	29	neighbor	neighbor	NOUN
ejpam-4220	171	30	of	of	ADP
ejpam-4220	171	31	b	b	PROPN
ejpam-4220	171	32	∈	∈	PROPN
ejpam-4220	171	33	a	a	PRON
ejpam-4220	171	34	}	}	PUNCT
ejpam-4220	171	35	∪a	∪a	NUM
ejpam-4220	171	36	.	.	PUNCT
ejpam-4220	172	1	then	then	ADV
ejpam-4220	172	2	ni(g	ni(g	NOUN
ejpam-4220	172	3	,	,	PUNCT
ejpam-4220	172	4	x	x	X
ejpam-4220	172	5	)	)	PUNCT
ejpam-4220	172	6	=	=	PUNCT
ejpam-4220	172	7	x|ω|	x|ω|	PUNCT
ejpam-4220	173	1	+	+	CCONJ
ejpam-4220	173	2	x|∆|	x|∆|	X
ejpam-4220	173	3	.	.	PUNCT
ejpam-4220	173	4	example	example	NOUN
ejpam-4220	174	1	5	5	NUM
ejpam-4220	174	2	.	.	X
ejpam-4220	174	3	consider	consider	VERB
ejpam-4220	174	4	u	u	NOUN
ejpam-4220	174	5	=	=	SYM
ejpam-4220	174	6	5	5	NUM
ejpam-4220	174	7	∈	∈	NOUN
ejpam-4220	174	8	v	v	NOUN
ejpam-4220	174	9	(	(	PUNCT
ejpam-4220	174	10	g	g	NOUN
ejpam-4220	174	11	)	)	PUNCT
ejpam-4220	174	12	in	in	ADP
ejpam-4220	174	13	the	the	DET
ejpam-4220	174	14	graph	graph	NOUN
ejpam-4220	174	15	in	in	ADP
ejpam-4220	174	16	figure	figure	NOUN
ejpam-4220	174	17	4	4	NUM
ejpam-4220	174	18	.	.	PUNCT
ejpam-4220	174	19	n.	n.	PROPN
ejpam-4220	174	20	s.	s.	PROPN
ejpam-4220	174	21	abdulcarim	abdulcarim	PROPN
ejpam-4220	174	22	,	,	PUNCT
ejpam-4220	174	23	s.	s.	PROPN
ejpam-4220	174	24	c.	c.	PROPN
ejpam-4220	174	25	dagondon	dagondon	PROPN
ejpam-4220	174	26	/	/	SYM
ejpam-4220	174	27	eur	eur	PROPN
ejpam-4220	174	28	.	.	PUNCT
ejpam-4220	175	1	j.	j.	PROPN
ejpam-4220	175	2	pure	pure	PROPN
ejpam-4220	175	3	appl	appl	PROPN
ejpam-4220	175	4	.	.	PROPN
ejpam-4220	175	5	math	math	PROPN
ejpam-4220	175	6	,	,	PUNCT
ejpam-4220	175	7	15	15	NUM
ejpam-4220	175	8	(	(	PUNCT
ejpam-4220	175	9	1	1	NUM
ejpam-4220	175	10	)	)	PUNCT
ejpam-4220	175	11	(	(	PUNCT
ejpam-4220	175	12	2022	2022	NUM
ejpam-4220	175	13	)	)	PUNCT
ejpam-4220	175	14	,	,	PUNCT
ejpam-4220	175	15	64	64	NUM
ejpam-4220	175	16	-	-	SYM
ejpam-4220	175	17	81	81	NUM
ejpam-4220	175	18	72	72	NUM
ejpam-4220	175	19	1	1	NUM
ejpam-4220	175	20	2	2	NUM
ejpam-4220	175	21	3	3	NUM
ejpam-4220	175	22	45	45	NUM
ejpam-4220	175	23	6	6	NUM
ejpam-4220	175	24	7	7	NUM
ejpam-4220	175	25	8	8	NUM
ejpam-4220	175	26	9	9	NUM
ejpam-4220	175	27	10	10	NUM
ejpam-4220	175	28	11	11	NUM
ejpam-4220	175	29	12	12	NUM
ejpam-4220	175	30	13	13	NUM
ejpam-4220	175	31	14	14	NUM
ejpam-4220	175	32	15	15	NUM
ejpam-4220	175	33	16	16	NUM
ejpam-4220	175	34	17	17	NUM
ejpam-4220	175	35	18	18	NUM
ejpam-4220	175	36	1920	1920	NUM
ejpam-4220	175	37	g	g	NOUN
ejpam-4220	175	38	:	:	PUNCT
ejpam-4220	175	39	figure	figure	VERB
ejpam-4220	175	40	4	4	NUM
ejpam-4220	175	41	:	:	PUNCT
ejpam-4220	175	42	a	a	DET
ejpam-4220	175	43	tree	tree	NOUN
ejpam-4220	175	44	g	g	PROPN
ejpam-4220	175	45	observe	observe	VERB
ejpam-4220	175	46	that	that	SCONJ
ejpam-4220	175	47	for	for	ADP
ejpam-4220	175	48	every	every	DET
ejpam-4220	175	49	u	u	NOUN
ejpam-4220	175	50	in	in	ADP
ejpam-4220	175	51	the	the	DET
ejpam-4220	175	52	set	set	NOUN
ejpam-4220	175	53	ω	ω	PROPN
ejpam-4220	175	54	=	=	SYM
ejpam-4220	175	55	{	{	PUNCT
ejpam-4220	175	56	3	3	NUM
ejpam-4220	175	57	,	,	PUNCT
ejpam-4220	175	58	5	5	NUM
ejpam-4220	175	59	,	,	PUNCT
ejpam-4220	175	60	6	6	NUM
ejpam-4220	175	61	,	,	PUNCT
ejpam-4220	175	62	7	7	NUM
ejpam-4220	175	63	,	,	PUNCT
ejpam-4220	175	64	10	10	NUM
ejpam-4220	175	65	,	,	PUNCT
ejpam-4220	175	66	11	11	NUM
ejpam-4220	175	67	,	,	PUNCT
ejpam-4220	175	68	13	13	NUM
ejpam-4220	175	69	,	,	PUNCT
ejpam-4220	175	70	15	15	NUM
ejpam-4220	175	71	}	}	PUNCT
ejpam-4220	175	72	,	,	PUNCT
ejpam-4220	175	73	dg(u	dg(u	X
ejpam-4220	175	74	,	,	PUNCT
ejpam-4220	175	75	5	5	NUM
ejpam-4220	175	76	)	)	PUNCT
ejpam-4220	175	77	=	=	SYM
ejpam-4220	175	78	2n	2n	NUM
ejpam-4220	175	79	,	,	PUNCT
ejpam-4220	175	80	n	n	PROPN
ejpam-4220	175	81	∈	∈	PROPN
ejpam-4220	175	82	n∗.	n∗.	PROPN
ejpam-4220	175	83	by	by	ADP
ejpam-4220	175	84	theorem	theorem	NOUN
ejpam-4220	175	85	2	2	NUM
ejpam-4220	175	86	,	,	PUNCT
ejpam-4220	175	87	ω	ω	PROPN
ejpam-4220	175	88	is	be	AUX
ejpam-4220	175	89	an	an	DET
ejpam-4220	175	90	independent	independent	ADJ
ejpam-4220	175	91	neighborhood	neighborhood	NOUN
ejpam-4220	175	92	set	set	NOUN
ejpam-4220	175	93	of	of	ADP
ejpam-4220	175	94	g.	g.	PROPN
ejpam-4220	175	95	also	also	ADV
ejpam-4220	175	96	,	,	PUNCT
ejpam-4220	175	97	if	if	SCONJ
ejpam-4220	175	98	we	we	PRON
ejpam-4220	175	99	consider	consider	VERB
ejpam-4220	175	100	u	u	PRON
ejpam-4220	175	101	=	=	NOUN
ejpam-4220	175	102	1	1	NUM
ejpam-4220	175	103	∈	∈	NOUN
ejpam-4220	175	104	v	v	NOUN
ejpam-4220	175	105	(	(	PUNCT
ejpam-4220	175	106	g	g	NOUN
ejpam-4220	175	107	)	)	PUNCT
ejpam-4220	175	108	,	,	PUNCT
ejpam-4220	175	109	for	for	ADP
ejpam-4220	175	110	each	each	DET
ejpam-4220	175	111	v	v	NOUN
ejpam-4220	175	112	in	in	ADP
ejpam-4220	175	113	the	the	DET
ejpam-4220	175	114	set	set	NOUN
ejpam-4220	175	115	∆	∆	X
ejpam-4220	175	116	=	=	SYM
ejpam-4220	175	117	{	{	PUNCT
ejpam-4220	175	118	1	1	NUM
ejpam-4220	175	119	,	,	PUNCT
ejpam-4220	175	120	2	2	NUM
ejpam-4220	175	121	,	,	PUNCT
ejpam-4220	175	122	4	4	NUM
ejpam-4220	175	123	,	,	PUNCT
ejpam-4220	175	124	8	8	NUM
ejpam-4220	175	125	,	,	PUNCT
ejpam-4220	175	126	9	9	NUM
ejpam-4220	175	127	,	,	PUNCT
ejpam-4220	175	128	12	12	NUM
ejpam-4220	175	129	,	,	PUNCT
ejpam-4220	175	130	14	14	NUM
ejpam-4220	175	131	,	,	PUNCT
ejpam-4220	175	132	16	16	NUM
ejpam-4220	175	133	,	,	PUNCT
ejpam-4220	175	134	17	17	NUM
ejpam-4220	175	135	,	,	PUNCT
ejpam-4220	175	136	18	18	NUM
ejpam-4220	175	137	,	,	PUNCT
ejpam-4220	175	138	19	19	NUM
ejpam-4220	175	139	,	,	PUNCT
ejpam-4220	175	140	20	20	NUM
ejpam-4220	175	141	}	}	PUNCT
ejpam-4220	175	142	,	,	PUNCT
ejpam-4220	175	143	dg(v	dg(v	X
ejpam-4220	175	144	,	,	PUNCT
ejpam-4220	175	145	1	1	X
ejpam-4220	175	146	)	)	PUNCT
ejpam-4220	175	147	=	=	SYM
ejpam-4220	175	148	2m	2m	NUM
ejpam-4220	175	149	,	,	PUNCT
ejpam-4220	175	150	m	m	PROPN
ejpam-4220	175	151	∈	∈	NOUN
ejpam-4220	175	152	n∗.	n∗.	PROPN
ejpam-4220	175	153	by	by	ADP
ejpam-4220	175	154	theorem	theorem	NOUN
ejpam-4220	175	155	3.2.4	3.2.4	NUM
ejpam-4220	175	156	,	,	PUNCT
ejpam-4220	175	157	∆	∆	PROPN
ejpam-4220	175	158	is	be	AUX
ejpam-4220	175	159	also	also	ADV
ejpam-4220	175	160	an	an	DET
ejpam-4220	175	161	independent	independent	ADJ
ejpam-4220	175	162	neighborhood	neighborhood	NOUN
ejpam-4220	175	163	set	set	NOUN
ejpam-4220	175	164	of	of	ADP
ejpam-4220	175	165	g.	g.	PROPN
ejpam-4220	175	166	we	we	PRON
ejpam-4220	175	167	note	note	VERB
ejpam-4220	175	168	that	that	SCONJ
ejpam-4220	175	169	|ω|	|ω|	ADP
ejpam-4220	175	170	=	=	SYM
ejpam-4220	175	171	8	8	NUM
ejpam-4220	175	172	and	and	CCONJ
ejpam-4220	175	173	|∆|	|∆|	PROPN
ejpam-4220	175	174	=	=	SYM
ejpam-4220	175	175	12	12	NUM
ejpam-4220	175	176	.	.	PUNCT
ejpam-4220	176	1	therefore	therefore	ADV
ejpam-4220	176	2	,	,	PUNCT
ejpam-4220	176	3	ni(g	ni(g	ADP
ejpam-4220	176	4	,	,	PUNCT
ejpam-4220	176	5	x	x	X
ejpam-4220	176	6	)	)	PUNCT
ejpam-4220	176	7	=	=	SYM
ejpam-4220	176	8	x8	x8	PROPN
ejpam-4220	176	9	+	+	CCONJ
ejpam-4220	176	10	x12	x12	NUM
ejpam-4220	176	11	.	.	PUNCT
ejpam-4220	177	1	other	other	ADJ
ejpam-4220	177	2	solution	solution	NOUN
ejpam-4220	177	3	:	:	PUNCT
ejpam-4220	177	4	from	from	ADP
ejpam-4220	177	5	figure	figure	NOUN
ejpam-4220	177	6	4	4	NUM
ejpam-4220	177	7	,	,	PUNCT
ejpam-4220	177	8	we	we	PRON
ejpam-4220	177	9	can	can	AUX
ejpam-4220	177	10	see	see	VERB
ejpam-4220	177	11	that	that	SCONJ
ejpam-4220	177	12	the	the	DET
ejpam-4220	177	13	set	set	NOUN
ejpam-4220	177	14	of	of	ADP
ejpam-4220	177	15	nonpendant	nonpendant	ADJ
ejpam-4220	177	16	vertices	vertex	NOUN
ejpam-4220	177	17	in	in	ADP
ejpam-4220	177	18	g	g	PROPN
ejpam-4220	177	19	is	be	AUX
ejpam-4220	177	20	given	give	VERB
ejpam-4220	177	21	by	by	ADP
ejpam-4220	177	22	f	f	PROPN
ejpam-4220	177	23	=	=	PUNCT
ejpam-4220	177	24	{	{	PUNCT
ejpam-4220	177	25	3	3	NUM
ejpam-4220	177	26	,	,	PUNCT
ejpam-4220	177	27	4	4	NUM
ejpam-4220	177	28	,	,	PUNCT
ejpam-4220	177	29	7	7	NUM
ejpam-4220	177	30	,	,	PUNCT
ejpam-4220	177	31	9	9	NUM
ejpam-4220	177	32	,	,	PUNCT
ejpam-4220	177	33	11	11	NUM
ejpam-4220	177	34	,	,	PUNCT
ejpam-4220	177	35	13	13	NUM
ejpam-4220	177	36	,	,	PUNCT
ejpam-4220	177	37	14	14	NUM
ejpam-4220	177	38	,	,	PUNCT
ejpam-4220	177	39	15	15	NUM
ejpam-4220	177	40	}	}	PUNCT
ejpam-4220	177	41	.	.	PUNCT
ejpam-4220	178	1	consider	consider	VERB
ejpam-4220	178	2	f	f	NOUN
ejpam-4220	178	3	=	=	SYM
ejpam-4220	178	4	3	3	NUM
ejpam-4220	178	5	∈	∈	PROPN
ejpam-4220	178	6	f	f	NOUN
ejpam-4220	178	7	.	.	PUNCT
ejpam-4220	179	1	then	then	ADV
ejpam-4220	179	2	a	a	PRON
ejpam-4220	179	3	=	=	X
ejpam-4220	179	4	{	{	PUNCT
ejpam-4220	179	5	3	3	NUM
ejpam-4220	179	6	,	,	PUNCT
ejpam-4220	179	7	7	7	NUM
ejpam-4220	179	8	,	,	PUNCT
ejpam-4220	179	9	11	11	NUM
ejpam-4220	179	10	,	,	PUNCT
ejpam-4220	179	11	13	13	NUM
ejpam-4220	179	12	,	,	PUNCT
ejpam-4220	179	13	15	15	NUM
ejpam-4220	179	14	}	}	PUNCT
ejpam-4220	179	15	and	and	CCONJ
ejpam-4220	179	16	b	b	X
ejpam-4220	179	17	=	=	SYM
ejpam-4220	179	18	f	f	PROPN
ejpam-4220	179	19	\	\	PROPN
ejpam-4220	180	1	a	a	PRON
ejpam-4220	180	2	=	=	X
ejpam-4220	180	3	{	{	PUNCT
ejpam-4220	180	4	4	4	NUM
ejpam-4220	180	5	,	,	PUNCT
ejpam-4220	180	6	9	9	NUM
ejpam-4220	180	7	,	,	PUNCT
ejpam-4220	180	8	14	14	NUM
ejpam-4220	180	9	}	}	PUNCT
ejpam-4220	180	10	.	.	PUNCT
ejpam-4220	181	1	applying	apply	VERB
ejpam-4220	181	2	corollary	corollary	ADJ
ejpam-4220	181	3	3	3	NUM
ejpam-4220	181	4	,	,	PUNCT
ejpam-4220	181	5	the	the	DET
ejpam-4220	181	6	independent	independent	ADJ
ejpam-4220	181	7	neighborhood	neighborhood	NOUN
ejpam-4220	181	8	sets	set	NOUN
ejpam-4220	181	9	of	of	ADP
ejpam-4220	181	10	g	g	PROPN
ejpam-4220	181	11	are	be	AUX
ejpam-4220	181	12	ω	ω	NOUN
ejpam-4220	181	13	=	=	PRON
ejpam-4220	181	14	{	{	PUNCT
ejpam-4220	181	15	v	v	NOUN
ejpam-4220	181	16	:	:	PUNCT
ejpam-4220	181	17	v	v	NOUN
ejpam-4220	181	18	is	be	AUX
ejpam-4220	181	19	a	a	DET
ejpam-4220	181	20	pendant	pendant	ADJ
ejpam-4220	181	21	neighbor	neighbor	NOUN
ejpam-4220	181	22	of	of	ADP
ejpam-4220	181	23	a	a	PRON
ejpam-4220	181	24	,	,	PUNCT
ejpam-4220	181	25	for	for	ADP
ejpam-4220	181	26	some	some	DET
ejpam-4220	181	27	a	a	DET
ejpam-4220	181	28	∈	∈	PROPN
ejpam-4220	181	29	a	a	PRON
ejpam-4220	181	30	}	}	PUNCT
ejpam-4220	181	31	∪b	∪b	NOUN
ejpam-4220	181	32	=	=	PUNCT
ejpam-4220	181	33	{	{	PUNCT
ejpam-4220	181	34	1	1	NUM
ejpam-4220	181	35	,	,	PUNCT
ejpam-4220	181	36	2	2	NUM
ejpam-4220	181	37	,	,	PUNCT
ejpam-4220	181	38	8	8	NUM
ejpam-4220	181	39	,	,	PUNCT
ejpam-4220	181	40	12	12	NUM
ejpam-4220	181	41	,	,	PUNCT
ejpam-4220	181	42	16	16	NUM
ejpam-4220	181	43	,	,	PUNCT
ejpam-4220	181	44	17	17	NUM
ejpam-4220	181	45	,	,	PUNCT
ejpam-4220	181	46	18	18	NUM
ejpam-4220	181	47	,	,	PUNCT
ejpam-4220	181	48	19	19	NUM
ejpam-4220	181	49	,	,	PUNCT
ejpam-4220	181	50	20	20	NUM
ejpam-4220	181	51	}	}	PUNCT
ejpam-4220	181	52	∪	∪	X
ejpam-4220	181	53	{	{	PUNCT
ejpam-4220	181	54	4	4	NUM
ejpam-4220	181	55	,	,	PUNCT
ejpam-4220	181	56	9	9	NUM
ejpam-4220	181	57	,	,	PUNCT
ejpam-4220	181	58	14	14	NUM
ejpam-4220	181	59	}	}	PUNCT
ejpam-4220	181	60	=	=	SYM
ejpam-4220	181	61	{	{	PUNCT
ejpam-4220	181	62	1	1	NUM
ejpam-4220	181	63	,	,	PUNCT
ejpam-4220	181	64	2	2	NUM
ejpam-4220	181	65	,	,	PUNCT
ejpam-4220	181	66	4	4	NUM
ejpam-4220	181	67	,	,	PUNCT
ejpam-4220	181	68	8	8	NUM
ejpam-4220	181	69	,	,	PUNCT
ejpam-4220	181	70	9	9	NUM
ejpam-4220	181	71	,	,	PUNCT
ejpam-4220	181	72	12	12	NUM
ejpam-4220	181	73	,	,	PUNCT
ejpam-4220	181	74	14	14	NUM
ejpam-4220	181	75	,	,	PUNCT
ejpam-4220	181	76	16	16	NUM
ejpam-4220	181	77	,	,	PUNCT
ejpam-4220	181	78	17	17	NUM
ejpam-4220	181	79	,	,	PUNCT
ejpam-4220	181	80	18	18	NUM
ejpam-4220	181	81	,	,	PUNCT
ejpam-4220	181	82	19	19	NUM
ejpam-4220	181	83	,	,	PUNCT
ejpam-4220	181	84	20	20	NUM
ejpam-4220	181	85	}	}	PUNCT
ejpam-4220	181	86	and	and	CCONJ
ejpam-4220	181	87	∆	∆	X
ejpam-4220	182	1	=	=	PRON
ejpam-4220	182	2	{	{	PUNCT
ejpam-4220	182	3	v	v	NOUN
ejpam-4220	182	4	:	:	PUNCT
ejpam-4220	182	5	v	v	NOUN
ejpam-4220	182	6	is	be	AUX
ejpam-4220	182	7	a	a	DET
ejpam-4220	182	8	pendant	pendant	ADJ
ejpam-4220	182	9	neighbor	neighbor	NOUN
ejpam-4220	182	10	of	of	ADP
ejpam-4220	182	11	b	b	PROPN
ejpam-4220	182	12	,	,	PUNCT
ejpam-4220	182	13	for	for	ADP
ejpam-4220	182	14	some	some	DET
ejpam-4220	182	15	b	b	NOUN
ejpam-4220	182	16	∈	∈	PROPN
ejpam-4220	182	17	b	b	PROPN
ejpam-4220	182	18	}	}	PUNCT
ejpam-4220	182	19	∪a	∪a	NUM
ejpam-4220	182	20	=	=	SYM
ejpam-4220	182	21	{	{	PUNCT
ejpam-4220	182	22	5	5	NUM
ejpam-4220	182	23	,	,	PUNCT
ejpam-4220	182	24	6	6	NUM
ejpam-4220	182	25	,	,	PUNCT
ejpam-4220	182	26	10	10	NUM
ejpam-4220	182	27	}	}	PUNCT
ejpam-4220	182	28	∪	∪	X
ejpam-4220	182	29	{	{	PUNCT
ejpam-4220	182	30	3	3	NUM
ejpam-4220	182	31	,	,	PUNCT
ejpam-4220	182	32	7	7	NUM
ejpam-4220	182	33	,	,	PUNCT
ejpam-4220	182	34	11	11	NUM
ejpam-4220	182	35	,	,	PUNCT
ejpam-4220	182	36	13	13	NUM
ejpam-4220	182	37	,	,	PUNCT
ejpam-4220	182	38	15	15	NUM
ejpam-4220	182	39	}	}	PUNCT
ejpam-4220	182	40	=	=	SYM
ejpam-4220	182	41	{	{	PUNCT
ejpam-4220	182	42	3	3	NUM
ejpam-4220	182	43	,	,	PUNCT
ejpam-4220	182	44	5	5	NUM
ejpam-4220	182	45	,	,	PUNCT
ejpam-4220	182	46	6	6	NUM
ejpam-4220	182	47	,	,	PUNCT
ejpam-4220	182	48	7	7	NUM
ejpam-4220	182	49	,	,	PUNCT
ejpam-4220	182	50	10	10	NUM
ejpam-4220	182	51	,	,	PUNCT
ejpam-4220	182	52	11	11	NUM
ejpam-4220	182	53	,	,	PUNCT
ejpam-4220	182	54	13	13	NUM
ejpam-4220	182	55	,	,	PUNCT
ejpam-4220	182	56	15	15	NUM
ejpam-4220	182	57	}	}	PUNCT
ejpam-4220	182	58	.	.	PUNCT
ejpam-4220	183	1	therefore	therefore	ADV
ejpam-4220	183	2	,	,	PUNCT
ejpam-4220	183	3	by	by	ADP
ejpam-4220	183	4	corollary	corollary	ADJ
ejpam-4220	183	5	4	4	NUM
ejpam-4220	183	6	,	,	PUNCT
ejpam-4220	183	7	ni(g	ni(g	NUM
ejpam-4220	183	8	,	,	PUNCT
ejpam-4220	183	9	x	x	X
ejpam-4220	183	10	)	)	PUNCT
ejpam-4220	183	11	=	=	SYM
ejpam-4220	183	12	x8	x8	PROPN
ejpam-4220	183	13	+	+	CCONJ
ejpam-4220	183	14	x12	x12	NUM
ejpam-4220	183	15	.	.	PUNCT
ejpam-4220	183	16	corollary	corollary	ADJ
ejpam-4220	183	17	5	5	NUM
ejpam-4220	183	18	.	.	PUNCT
ejpam-4220	183	19	for	for	ADP
ejpam-4220	183	20	any	any	DET
ejpam-4220	183	21	tree	tree	NOUN
ejpam-4220	183	22	t	t	NOUN
ejpam-4220	183	23	,	,	PUNCT
ejpam-4220	183	24	if	if	SCONJ
ejpam-4220	183	25	ω	ω	PROPN
ejpam-4220	183	26	and	and	CCONJ
ejpam-4220	183	27	∆	∆	PROPN
ejpam-4220	183	28	are	be	AUX
ejpam-4220	183	29	the	the	DET
ejpam-4220	183	30	independent	independent	ADJ
ejpam-4220	183	31	neighborhood	neighborhood	NOUN
ejpam-4220	183	32	sets	set	NOUN
ejpam-4220	183	33	of	of	ADP
ejpam-4220	183	34	t	t	NOUN
ejpam-4220	183	35	,	,	PUNCT
ejpam-4220	183	36	then	then	ADV
ejpam-4220	183	37	ω	ω	NUM
ejpam-4220	183	38	∪∆	∪∆	NOUN
ejpam-4220	183	39	=	=	SYM
ejpam-4220	183	40	v	v	X
ejpam-4220	183	41	(	(	PUNCT
ejpam-4220	183	42	t	t	PROPN
ejpam-4220	183	43	)	)	PUNCT
ejpam-4220	183	44	.	.	PUNCT
ejpam-4220	184	1	proof	proof	NOUN
ejpam-4220	184	2	.	.	PUNCT
ejpam-4220	185	1	let	let	VERB
ejpam-4220	185	2	ω	ω	NOUN
ejpam-4220	185	3	and	and	CCONJ
ejpam-4220	185	4	∆	∆	PROPN
ejpam-4220	185	5	be	be	VERB
ejpam-4220	185	6	the	the	DET
ejpam-4220	185	7	independent	independent	ADJ
ejpam-4220	185	8	neighborhood	neighborhood	NOUN
ejpam-4220	185	9	sets	set	NOUN
ejpam-4220	185	10	of	of	ADP
ejpam-4220	185	11	a	a	DET
ejpam-4220	185	12	tree	tree	NOUN
ejpam-4220	185	13	t	t	NOUN
ejpam-4220	185	14	.	.	PUNCT
ejpam-4220	186	1	assume	assume	VERB
ejpam-4220	186	2	to	to	ADP
ejpam-4220	186	3	the	the	DET
ejpam-4220	186	4	contrary	contrary	NOUN
ejpam-4220	186	5	that	that	SCONJ
ejpam-4220	186	6	ω∪∆	ω∪∆	NOUN
ejpam-4220	186	7	̸=	̸=	PROPN
ejpam-4220	186	8	v	v	NOUN
ejpam-4220	186	9	(	(	PUNCT
ejpam-4220	186	10	t	t	PROPN
ejpam-4220	186	11	)	)	PUNCT
ejpam-4220	186	12	.	.	PUNCT
ejpam-4220	187	1	then	then	ADV
ejpam-4220	187	2	there	there	PRON
ejpam-4220	187	3	exists	exist	VERB
ejpam-4220	187	4	v	v	ADP
ejpam-4220	187	5	∈	∈	PROPN
ejpam-4220	187	6	v	v	NOUN
ejpam-4220	187	7	(	(	PUNCT
ejpam-4220	187	8	t	t	PROPN
ejpam-4220	187	9	)	)	PUNCT
ejpam-4220	187	10	such	such	ADJ
ejpam-4220	187	11	that	that	DET
ejpam-4220	187	12	v	v	NOUN
ejpam-4220	187	13	/∈	/∈	PUNCT
ejpam-4220	187	14	ω∪∆.	ω∪∆.	ADP
ejpam-4220	187	15	this	this	PRON
ejpam-4220	187	16	implies	imply	VERB
ejpam-4220	187	17	v	v	NUM
ejpam-4220	187	18	/∈	/∈	PUNCT
ejpam-4220	188	1	ω	ω	PROPN
ejpam-4220	189	1	and	and	CCONJ
ejpam-4220	189	2	v	v	NOUN
ejpam-4220	189	3	/∈	/∈	PUNCT
ejpam-4220	190	1	∆.	∆.	NOUN
ejpam-4220	190	2	since	since	SCONJ
ejpam-4220	190	3	ω	ω	PROPN
ejpam-4220	190	4	and	and	CCONJ
ejpam-4220	190	5	∆	∆	PROPN
ejpam-4220	190	6	are	be	AUX
ejpam-4220	190	7	both	both	PRON
ejpam-4220	190	8	independent	independent	ADJ
ejpam-4220	190	9	neighborhood	neighborhood	NOUN
ejpam-4220	190	10	sets	set	NOUN
ejpam-4220	190	11	of	of	ADP
ejpam-4220	190	12	t	t	NOUN
ejpam-4220	190	13	,	,	PUNCT
ejpam-4220	190	14	there	there	ADV
ejpam-4220	190	15	n.	n.	PROPN
ejpam-4220	190	16	s.	s.	PROPN
ejpam-4220	190	17	abdulcarim	abdulcarim	PROPN
ejpam-4220	190	18	,	,	PUNCT
ejpam-4220	190	19	s.	s.	PROPN
ejpam-4220	190	20	c.	c.	PROPN
ejpam-4220	190	21	dagondon	dagondon	PROPN
ejpam-4220	190	22	/	/	SYM
ejpam-4220	190	23	eur	eur	PROPN
ejpam-4220	190	24	.	.	PUNCT
ejpam-4220	191	1	j.	j.	PROPN
ejpam-4220	191	2	pure	pure	PROPN
ejpam-4220	191	3	appl	appl	PROPN
ejpam-4220	191	4	.	.	PROPN
ejpam-4220	191	5	math	math	PROPN
ejpam-4220	191	6	,	,	PUNCT
ejpam-4220	191	7	15	15	NUM
ejpam-4220	191	8	(	(	PUNCT
ejpam-4220	191	9	1	1	NUM
ejpam-4220	191	10	)	)	PUNCT
ejpam-4220	191	11	(	(	PUNCT
ejpam-4220	191	12	2022	2022	NUM
ejpam-4220	191	13	)	)	PUNCT
ejpam-4220	191	14	,	,	PUNCT
ejpam-4220	191	15	64	64	NUM
ejpam-4220	191	16	-	-	SYM
ejpam-4220	191	17	81	81	NUM
ejpam-4220	191	18	73	73	NUM
ejpam-4220	191	19	exists	exist	VERB
ejpam-4220	191	20	g	g	PROPN
ejpam-4220	191	21	∈	∈	PROPN
ejpam-4220	191	22	ω	ω	PROPN
ejpam-4220	191	23	and	and	CCONJ
ejpam-4220	191	24	h	h	NOUN
ejpam-4220	191	25	∈	∈	PROPN
ejpam-4220	191	26	∆	∆	PROPN
ejpam-4220	192	1	such	such	ADJ
ejpam-4220	192	2	that	that	SCONJ
ejpam-4220	192	3	v	v	NUM
ejpam-4220	192	4	∈	∈	PROPN
ejpam-4220	192	5	n	n	CCONJ
ejpam-4220	193	1	[	[	X
ejpam-4220	193	2	g	g	X
ejpam-4220	193	3	]	]	PUNCT
ejpam-4220	193	4	and	and	CCONJ
ejpam-4220	193	5	v	v	ADP
ejpam-4220	193	6	∈	∈	NOUN
ejpam-4220	193	7	n	n	CCONJ
ejpam-4220	194	1	[	[	X
ejpam-4220	194	2	h	h	X
ejpam-4220	194	3	]	]	X
ejpam-4220	194	4	.	.	PUNCT
ejpam-4220	195	1	this	this	PRON
ejpam-4220	195	2	shows	show	VERB
ejpam-4220	195	3	that	that	SCONJ
ejpam-4220	195	4	d(v	d(v	PROPN
ejpam-4220	195	5	,	,	PUNCT
ejpam-4220	195	6	g	g	NOUN
ejpam-4220	195	7	)	)	PUNCT
ejpam-4220	195	8	=	=	SYM
ejpam-4220	195	9	1	1	NUM
ejpam-4220	195	10	and	and	CCONJ
ejpam-4220	195	11	d(v	d(v	ADJ
ejpam-4220	195	12	,	,	PUNCT
ejpam-4220	195	13	h	h	NOUN
ejpam-4220	195	14	)	)	PUNCT
ejpam-4220	195	15	=	=	SYM
ejpam-4220	195	16	1	1	NUM
ejpam-4220	195	17	and	and	CCONJ
ejpam-4220	195	18	follows	follow	VERB
ejpam-4220	195	19	that	that	SCONJ
ejpam-4220	195	20	d(g	d(g	PROPN
ejpam-4220	195	21	,	,	PUNCT
ejpam-4220	195	22	h	h	NOUN
ejpam-4220	195	23	)	)	PUNCT
ejpam-4220	195	24	=	=	SYM
ejpam-4220	196	1	d(v	d(v	PROPN
ejpam-4220	196	2	,	,	PUNCT
ejpam-4220	196	3	g	g	NOUN
ejpam-4220	196	4	)	)	PUNCT
ejpam-4220	197	1	+	+	X
ejpam-4220	197	2	d(v	d(v	ADJ
ejpam-4220	197	3	,	,	PUNCT
ejpam-4220	197	4	h	h	NOUN
ejpam-4220	197	5	)	)	PUNCT
ejpam-4220	197	6	=	=	SYM
ejpam-4220	197	7	2	2	X
ejpam-4220	197	8	.	.	PUNCT
ejpam-4220	197	9	thus	thus	ADV
ejpam-4220	197	10	,	,	PUNCT
ejpam-4220	197	11	ω	ω	X
ejpam-4220	197	12	∪	∪	X
ejpam-4220	197	13	{	{	PUNCT
ejpam-4220	197	14	h	h	NOUN
ejpam-4220	197	15	}	}	PUNCT
ejpam-4220	197	16	and	and	CCONJ
ejpam-4220	197	17	∆	∆	PROPN
ejpam-4220	197	18	∪	∪	X
ejpam-4220	197	19	{	{	PUNCT
ejpam-4220	197	20	g	g	NOUN
ejpam-4220	197	21	}	}	PUNCT
ejpam-4220	197	22	are	be	AUX
ejpam-4220	197	23	independent	independent	ADJ
ejpam-4220	197	24	neighborhood	neighborhood	NOUN
ejpam-4220	197	25	sets	set	NOUN
ejpam-4220	197	26	of	of	ADP
ejpam-4220	197	27	t	t	NOUN
ejpam-4220	197	28	which	which	PRON
ejpam-4220	197	29	is	be	AUX
ejpam-4220	197	30	a	a	DET
ejpam-4220	197	31	contradiction	contradiction	NOUN
ejpam-4220	197	32	by	by	ADP
ejpam-4220	197	33	corollary	corollary	ADJ
ejpam-4220	197	34	3	3	NUM
ejpam-4220	197	35	.	.	PUNCT
ejpam-4220	198	1	hence	hence	ADV
ejpam-4220	198	2	,	,	PUNCT
ejpam-4220	198	3	ω	ω	NUM
ejpam-4220	198	4	∪∆	∪∆	NOUN
ejpam-4220	198	5	=	=	SYM
ejpam-4220	198	6	v	v	X
ejpam-4220	198	7	(	(	PUNCT
ejpam-4220	198	8	t	t	PROPN
ejpam-4220	198	9	)	)	PUNCT
ejpam-4220	198	10	.	.	PUNCT
ejpam-4220	199	1	■	■	PUNCT
ejpam-4220	199	2	corollary	corollary	ADJ
ejpam-4220	199	3	6	6	NUM
ejpam-4220	199	4	.	.	PUNCT
ejpam-4220	200	1	for	for	ADP
ejpam-4220	200	2	any	any	DET
ejpam-4220	200	3	tree	tree	NOUN
ejpam-4220	200	4	t	t	NOUN
ejpam-4220	200	5	,	,	PUNCT
ejpam-4220	200	6	if	if	SCONJ
ejpam-4220	200	7	ω	ω	PROPN
ejpam-4220	200	8	and	and	CCONJ
ejpam-4220	200	9	∆	∆	PROPN
ejpam-4220	200	10	are	be	AUX
ejpam-4220	200	11	the	the	DET
ejpam-4220	200	12	independent	independent	ADJ
ejpam-4220	200	13	neighborhood	neighborhood	NOUN
ejpam-4220	200	14	sets	set	NOUN
ejpam-4220	200	15	of	of	ADP
ejpam-4220	200	16	t	t	NOUN
ejpam-4220	200	17	,	,	PUNCT
ejpam-4220	200	18	then	then	ADV
ejpam-4220	200	19	ω	ω	NUM
ejpam-4220	200	20	∩∆	∩∆	X
ejpam-4220	200	21	=	=	PUNCT
ejpam-4220	200	22	∅.	∅.	NOUN
ejpam-4220	200	23	proof	proof	NOUN
ejpam-4220	200	24	.	.	PUNCT
ejpam-4220	201	1	let	let	VERB
ejpam-4220	201	2	ω	ω	NOUN
ejpam-4220	201	3	and	and	CCONJ
ejpam-4220	201	4	∆	∆	PROPN
ejpam-4220	201	5	be	be	VERB
ejpam-4220	201	6	the	the	DET
ejpam-4220	201	7	independent	independent	ADJ
ejpam-4220	201	8	neighborhood	neighborhood	NOUN
ejpam-4220	201	9	sets	set	NOUN
ejpam-4220	201	10	of	of	ADP
ejpam-4220	201	11	a	a	DET
ejpam-4220	201	12	tree	tree	NOUN
ejpam-4220	201	13	t	t	NOUN
ejpam-4220	201	14	.	.	PUNCT
ejpam-4220	202	1	assume	assume	VERB
ejpam-4220	202	2	to	to	ADP
ejpam-4220	202	3	the	the	DET
ejpam-4220	202	4	contrary	contrary	NOUN
ejpam-4220	202	5	that	that	SCONJ
ejpam-4220	202	6	ω	ω	NOUN
ejpam-4220	202	7	∩∆	∩∆	PUNCT
ejpam-4220	202	8	̸=	̸=	PROPN
ejpam-4220	202	9	∅.	∅.	ADP
ejpam-4220	202	10	this	this	DET
ejpam-4220	202	11	implies	imply	VERB
ejpam-4220	202	12	there	there	PRON
ejpam-4220	202	13	exists	exist	VERB
ejpam-4220	202	14	u	u	PROPN
ejpam-4220	202	15	∈	∈	PROPN
ejpam-4220	202	16	ω	ω	PROPN
ejpam-4220	202	17	∩∆.	∩∆.	NUM
ejpam-4220	202	18	it	it	PRON
ejpam-4220	202	19	follows	follow	VERB
ejpam-4220	202	20	that	that	SCONJ
ejpam-4220	202	21	u	u	PROPN
ejpam-4220	202	22	∈	∈	PROPN
ejpam-4220	202	23	ω	ω	NOUN
ejpam-4220	202	24	and	and	CCONJ
ejpam-4220	202	25	u	u	PROPN
ejpam-4220	202	26	∈	∈	PROPN
ejpam-4220	203	1	∆.	∆.	PROPN
ejpam-4220	203	2	since	since	SCONJ
ejpam-4220	203	3	ω	ω	PROPN
ejpam-4220	203	4	and	and	CCONJ
ejpam-4220	203	5	∆	∆	PROPN
ejpam-4220	203	6	are	be	AUX
ejpam-4220	203	7	both	both	PRON
ejpam-4220	203	8	independent	independent	ADJ
ejpam-4220	203	9	neighborhood	neighborhood	NOUN
ejpam-4220	203	10	sets	set	NOUN
ejpam-4220	203	11	of	of	ADP
ejpam-4220	203	12	t	t	PROPN
ejpam-4220	203	13	,	,	PUNCT
ejpam-4220	203	14	d(u	d(u	PROPN
ejpam-4220	203	15	,	,	PUNCT
ejpam-4220	203	16	g	g	NOUN
ejpam-4220	203	17	)	)	PUNCT
ejpam-4220	203	18	=	=	SYM
ejpam-4220	203	19	2n	2n	NUM
ejpam-4220	203	20	,	,	PUNCT
ejpam-4220	203	21	∀g	∀g	NOUN
ejpam-4220	203	22	∈	∈	PROPN
ejpam-4220	203	23	ω	ω	PROPN
ejpam-4220	203	24	and	and	CCONJ
ejpam-4220	203	25	d(u	d(u	PROPN
ejpam-4220	203	26	,	,	PUNCT
ejpam-4220	203	27	h	h	NOUN
ejpam-4220	203	28	)	)	PUNCT
ejpam-4220	203	29	=	=	SYM
ejpam-4220	203	30	2m,∀h	2m,∀h	NUM
ejpam-4220	203	31	∈	∈	PROPN
ejpam-4220	203	32	∆	∆	PROPN
ejpam-4220	203	33	for	for	ADP
ejpam-4220	203	34	some	some	DET
ejpam-4220	203	35	n	n	CCONJ
ejpam-4220	203	36	,	,	PUNCT
ejpam-4220	203	37	m	m	PROPN
ejpam-4220	203	38	∈	∈	NOUN
ejpam-4220	203	39	n∗.	n∗.	PROPN
ejpam-4220	203	40	consequently	consequently	ADV
ejpam-4220	203	41	,	,	PUNCT
ejpam-4220	203	42	d(g	d(g	PROPN
ejpam-4220	203	43	,	,	PUNCT
ejpam-4220	203	44	h	h	NOUN
ejpam-4220	203	45	)	)	PUNCT
ejpam-4220	203	46	=	=	SYM
ejpam-4220	203	47	d(g	d(g	PROPN
ejpam-4220	203	48	,	,	PUNCT
ejpam-4220	203	49	u	u	NOUN
ejpam-4220	203	50	)	)	PUNCT
ejpam-4220	203	51	+	+	CCONJ
ejpam-4220	203	52	d(u	d(u	PROPN
ejpam-4220	203	53	,	,	PUNCT
ejpam-4220	203	54	h	h	NOUN
ejpam-4220	203	55	)	)	PUNCT
ejpam-4220	203	56	=	=	SYM
ejpam-4220	203	57	2n+	2n+	NUM
ejpam-4220	203	58	2	2	NUM
ejpam-4220	203	59	m	m	NOUN
ejpam-4220	203	60	=	=	SYM
ejpam-4220	203	61	2(n+m	2(n+m	NUM
ejpam-4220	203	62	)	)	PUNCT
ejpam-4220	203	63	.	.	PUNCT
ejpam-4220	204	1	this	this	PRON
ejpam-4220	204	2	shows	show	VERB
ejpam-4220	204	3	that	that	SCONJ
ejpam-4220	204	4	ω∪∆	ω∪∆	NOUN
ejpam-4220	204	5	is	be	AUX
ejpam-4220	204	6	an	an	DET
ejpam-4220	204	7	independent	independent	ADJ
ejpam-4220	204	8	neighborhood	neighborhood	NOUN
ejpam-4220	204	9	set	set	NOUN
ejpam-4220	204	10	of	of	ADP
ejpam-4220	204	11	t	t	PROPN
ejpam-4220	204	12	.	.	PUNCT
ejpam-4220	205	1	but	but	CCONJ
ejpam-4220	205	2	ω∪∆	ω∪∆	NOUN
ejpam-4220	205	3	=	=	SYM
ejpam-4220	205	4	v	v	X
ejpam-4220	205	5	(	(	PUNCT
ejpam-4220	205	6	t	t	PROPN
ejpam-4220	205	7	)	)	PUNCT
ejpam-4220	205	8	which	which	PRON
ejpam-4220	205	9	is	be	AUX
ejpam-4220	205	10	clearly	clearly	ADV
ejpam-4220	205	11	not	not	PART
ejpam-4220	205	12	an	an	DET
ejpam-4220	205	13	independent	independent	ADJ
ejpam-4220	205	14	neighborhood	neighborhood	NOUN
ejpam-4220	205	15	set	set	NOUN
ejpam-4220	205	16	of	of	ADP
ejpam-4220	205	17	t	t	PROPN
ejpam-4220	205	18	.	.	PUNCT
ejpam-4220	206	1	hence	hence	ADV
ejpam-4220	206	2	,	,	PUNCT
ejpam-4220	206	3	ω	ω	X
ejpam-4220	206	4	∩∆	∩∆	X
ejpam-4220	206	5	=	=	PUNCT
ejpam-4220	206	6	∅.	∅.	ADP
ejpam-4220	206	7	■	■	PUNCT
ejpam-4220	206	8	corollary	corollary	ADJ
ejpam-4220	206	9	7	7	NUM
ejpam-4220	206	10	.	.	PUNCT
ejpam-4220	207	1	for	for	ADP
ejpam-4220	207	2	any	any	DET
ejpam-4220	207	3	tree	tree	NOUN
ejpam-4220	207	4	t	t	NOUN
ejpam-4220	207	5	with	with	ADP
ejpam-4220	207	6	independent	independent	ADJ
ejpam-4220	207	7	neighborhood	neighborhood	NOUN
ejpam-4220	207	8	sets	set	VERB
ejpam-4220	207	9	ω	ω	NOUN
ejpam-4220	207	10	and	and	CCONJ
ejpam-4220	207	11	∆	∆	NOUN
ejpam-4220	207	12	,	,	PUNCT
ejpam-4220	207	13	if	if	SCONJ
ejpam-4220	207	14	uv	uv	PROPN
ejpam-4220	207	15	∈	∈	PROPN
ejpam-4220	207	16	e(t	e(t	PROPN
ejpam-4220	207	17	)	)	PUNCT
ejpam-4220	207	18	,	,	PUNCT
ejpam-4220	207	19	then	then	ADV
ejpam-4220	207	20	u	u	PROPN
ejpam-4220	207	21	∈	∈	PROPN
ejpam-4220	207	22	ω	ω	PROPN
ejpam-4220	207	23	and	and	CCONJ
ejpam-4220	207	24	v	v	ADP
ejpam-4220	207	25	∈	∈	NOUN
ejpam-4220	207	26	∆.	∆.	NOUN
ejpam-4220	207	27	proof	proof	NOUN
ejpam-4220	207	28	.	.	PUNCT
ejpam-4220	208	1	let	let	VERB
ejpam-4220	208	2	t	t	NOUN
ejpam-4220	208	3	be	be	AUX
ejpam-4220	208	4	a	a	DET
ejpam-4220	208	5	tree	tree	NOUN
ejpam-4220	208	6	with	with	ADP
ejpam-4220	208	7	independent	independent	ADJ
ejpam-4220	208	8	neighborhood	neighborhood	NOUN
ejpam-4220	208	9	sets	set	VERB
ejpam-4220	208	10	ω	ω	NOUN
ejpam-4220	208	11	and	and	CCONJ
ejpam-4220	208	12	∆.	∆.	NOUN
ejpam-4220	208	13	let	let	VERB
ejpam-4220	208	14	uv	uv	PRON
ejpam-4220	208	15	∈	∈	PROPN
ejpam-4220	208	16	e(t	e(t	PROPN
ejpam-4220	208	17	)	)	PUNCT
ejpam-4220	208	18	.	.	PUNCT
ejpam-4220	209	1	suppose	suppose	VERB
ejpam-4220	209	2	that	that	SCONJ
ejpam-4220	209	3	u	u	PROPN
ejpam-4220	209	4	/∈	/∈	PROPN
ejpam-4220	209	5	ω	ω	PROPN
ejpam-4220	209	6	or	or	CCONJ
ejpam-4220	209	7	v	v	NOUN
ejpam-4220	209	8	/∈	/∈	PUNCT
ejpam-4220	210	1	∆.	∆.	NOUN
ejpam-4220	210	2	consider	consider	VERB
ejpam-4220	210	3	the	the	DET
ejpam-4220	210	4	following	follow	VERB
ejpam-4220	210	5	cases	case	NOUN
ejpam-4220	210	6	.	.	PUNCT
ejpam-4220	211	1	case	case	NOUN
ejpam-4220	211	2	1	1	NUM
ejpam-4220	211	3	:	:	PUNCT
ejpam-4220	211	4	u	u	PROPN
ejpam-4220	211	5	/∈	/∈	PROPN
ejpam-4220	212	1	ω	ω	PROPN
ejpam-4220	212	2	and	and	CCONJ
ejpam-4220	212	3	v	v	NOUN
ejpam-4220	212	4	∈	∈	NOUN
ejpam-4220	212	5	∆	∆	PROPN
ejpam-4220	212	6	since	since	SCONJ
ejpam-4220	212	7	uv	uv	PROPN
ejpam-4220	212	8	∈	∈	PROPN
ejpam-4220	212	9	e(t	e(t	PROPN
ejpam-4220	212	10	)	)	PUNCT
ejpam-4220	213	1	and	and	CCONJ
ejpam-4220	213	2	ω	ω	PROPN
ejpam-4220	213	3	is	be	AUX
ejpam-4220	213	4	an	an	DET
ejpam-4220	213	5	independent	independent	ADJ
ejpam-4220	213	6	neighborhood	neighborhood	NOUN
ejpam-4220	213	7	set	set	NOUN
ejpam-4220	213	8	of	of	ADP
ejpam-4220	213	9	t	t	PROPN
ejpam-4220	213	10	,	,	PUNCT
ejpam-4220	213	11	by	by	ADP
ejpam-4220	213	12	proposition	proposition	NOUN
ejpam-4220	213	13	1	1	NUM
ejpam-4220	213	14	,	,	PUNCT
ejpam-4220	213	15	there	there	PRON
ejpam-4220	213	16	exists	exist	VERB
ejpam-4220	213	17	w	w	PROPN
ejpam-4220	213	18	∈	∈	PROPN
ejpam-4220	213	19	ω	ω	NUM
ejpam-4220	213	20	such	such	ADJ
ejpam-4220	213	21	that	that	SCONJ
ejpam-4220	213	22	u	u	NOUN
ejpam-4220	213	23	,	,	PUNCT
ejpam-4220	213	24	v	v	PROPN
ejpam-4220	213	25	∈	∈	NOUN
ejpam-4220	213	26	n	n	CCONJ
ejpam-4220	213	27	[	[	X
ejpam-4220	213	28	w	w	X
ejpam-4220	213	29	]	]	X
ejpam-4220	213	30	.	.	PUNCT
ejpam-4220	214	1	but	but	CCONJ
ejpam-4220	214	2	the	the	DET
ejpam-4220	214	3	set	set	NOUN
ejpam-4220	214	4	of	of	ADP
ejpam-4220	214	5	edges	edge	NOUN
ejpam-4220	214	6	{	{	PUNCT
ejpam-4220	214	7	uw	uw	PROPN
ejpam-4220	214	8	,	,	PUNCT
ejpam-4220	214	9	vw	vw	PROPN
ejpam-4220	214	10	,	,	PUNCT
ejpam-4220	214	11	uv	uv	NOUN
ejpam-4220	214	12	}	}	PUNCT
ejpam-4220	214	13	forms	form	VERB
ejpam-4220	214	14	a	a	DET
ejpam-4220	214	15	cycle	cycle	NOUN
ejpam-4220	214	16	which	which	PRON
ejpam-4220	214	17	is	be	AUX
ejpam-4220	214	18	a	a	DET
ejpam-4220	214	19	contradiction	contradiction	NOUN
ejpam-4220	214	20	since	since	SCONJ
ejpam-4220	214	21	t	t	PROPN
ejpam-4220	214	22	is	be	AUX
ejpam-4220	214	23	a	a	DET
ejpam-4220	214	24	tree	tree	NOUN
ejpam-4220	214	25	.	.	PUNCT
ejpam-4220	215	1	case	case	NOUN
ejpam-4220	215	2	2	2	NUM
ejpam-4220	215	3	:	:	SYM
ejpam-4220	215	4	v	v	NOUN
ejpam-4220	215	5	/∈	/∈	PUNCT
ejpam-4220	215	6	∆	∆	PROPN
ejpam-4220	215	7	and	and	CCONJ
ejpam-4220	215	8	u	u	PROPN
ejpam-4220	215	9	∈	∈	PROPN
ejpam-4220	215	10	ω	ω	X
ejpam-4220	215	11	by	by	ADP
ejpam-4220	215	12	proposition	proposition	NOUN
ejpam-4220	215	13	1	1	NUM
ejpam-4220	215	14	,	,	PUNCT
ejpam-4220	215	15	being	be	AUX
ejpam-4220	215	16	∆	∆	PROPN
ejpam-4220	215	17	an	an	DET
ejpam-4220	215	18	independent	independent	ADJ
ejpam-4220	215	19	neighborhood	neighborhood	NOUN
ejpam-4220	215	20	set	set	NOUN
ejpam-4220	215	21	of	of	ADP
ejpam-4220	215	22	t	t	PROPN
ejpam-4220	215	23	implies	imply	VERB
ejpam-4220	215	24	there	there	PRON
ejpam-4220	215	25	exists	exist	VERB
ejpam-4220	215	26	z	z	PROPN
ejpam-4220	215	27	∈	∈	PROPN
ejpam-4220	215	28	∆	∆	PROPN
ejpam-4220	215	29	such	such	ADJ
ejpam-4220	215	30	that	that	SCONJ
ejpam-4220	215	31	u	u	NOUN
ejpam-4220	215	32	,	,	PUNCT
ejpam-4220	215	33	v	v	PROPN
ejpam-4220	215	34	∈	∈	NOUN
ejpam-4220	215	35	n	n	CCONJ
ejpam-4220	215	36	[	[	X
ejpam-4220	215	37	z	z	X
ejpam-4220	215	38	]	]	X
ejpam-4220	215	39	.	.	PUNCT
ejpam-4220	216	1	observe	observe	VERB
ejpam-4220	216	2	that	that	SCONJ
ejpam-4220	216	3	the	the	DET
ejpam-4220	216	4	edges	edge	NOUN
ejpam-4220	216	5	uz	uz	PROPN
ejpam-4220	216	6	,	,	PUNCT
ejpam-4220	216	7	vz	vz	NOUN
ejpam-4220	216	8	,	,	PUNCT
ejpam-4220	216	9	uv	uv	NOUN
ejpam-4220	216	10	form	form	NOUN
ejpam-4220	216	11	a	a	DET
ejpam-4220	216	12	cycle	cycle	NOUN
ejpam-4220	216	13	which	which	PRON
ejpam-4220	216	14	is	be	AUX
ejpam-4220	216	15	a	a	DET
ejpam-4220	216	16	contradiction	contradiction	NOUN
ejpam-4220	216	17	since	since	SCONJ
ejpam-4220	216	18	t	t	PROPN
ejpam-4220	216	19	is	be	AUX
ejpam-4220	216	20	acylic	acylic	ADJ
ejpam-4220	216	21	.	.	PUNCT
ejpam-4220	217	1	case	case	NOUN
ejpam-4220	217	2	3	3	NUM
ejpam-4220	217	3	:	:	PUNCT
ejpam-4220	217	4	u	u	PROPN
ejpam-4220	217	5	/∈	/∈	PROPN
ejpam-4220	218	1	ω	ω	PROPN
ejpam-4220	218	2	and	and	CCONJ
ejpam-4220	218	3	v	v	NOUN
ejpam-4220	218	4	/∈	/∈	PUNCT
ejpam-4220	218	5	∆	∆	PROPN
ejpam-4220	219	1	since	since	SCONJ
ejpam-4220	219	2	ω	ω	PROPN
ejpam-4220	219	3	and	and	CCONJ
ejpam-4220	219	4	∆	∆	PROPN
ejpam-4220	219	5	are	be	AUX
ejpam-4220	219	6	independent	independent	ADJ
ejpam-4220	219	7	neighborhood	neighborhood	NOUN
ejpam-4220	219	8	sets	set	NOUN
ejpam-4220	219	9	of	of	ADP
ejpam-4220	219	10	t	t	NOUN
ejpam-4220	219	11	,	,	PUNCT
ejpam-4220	219	12	there	there	PRON
ejpam-4220	219	13	exist	exist	VERB
ejpam-4220	219	14	x	x	X
ejpam-4220	219	15	∈	∈	PROPN
ejpam-4220	219	16	ω	ω	PROPN
ejpam-4220	219	17	and	and	CCONJ
ejpam-4220	219	18	y	y	PROPN
ejpam-4220	219	19	∈	∈	PROPN
ejpam-4220	219	20	∆	∆	PROPN
ejpam-4220	219	21	such	such	ADJ
ejpam-4220	219	22	that	that	SCONJ
ejpam-4220	219	23	u	u	NOUN
ejpam-4220	219	24	,	,	PUNCT
ejpam-4220	219	25	v	v	PROPN
ejpam-4220	219	26	∈	∈	NOUN
ejpam-4220	219	27	n	n	CCONJ
ejpam-4220	219	28	[	[	X
ejpam-4220	219	29	x	x	X
ejpam-4220	219	30	]	]	X
ejpam-4220	219	31	and	and	CCONJ
ejpam-4220	219	32	u	u	NOUN
ejpam-4220	219	33	,	,	PUNCT
ejpam-4220	219	34	v	v	NOUN
ejpam-4220	219	35	∈	∈	NOUN
ejpam-4220	219	36	n	n	CCONJ
ejpam-4220	219	37	[	[	X
ejpam-4220	219	38	y	y	X
ejpam-4220	219	39	]	]	PUNCT
ejpam-4220	219	40	by	by	ADP
ejpam-4220	219	41	proposition	proposition	NOUN
ejpam-4220	219	42	1	1	NUM
ejpam-4220	219	43	.	.	PUNCT
ejpam-4220	220	1	the	the	DET
ejpam-4220	220	2	set	set	NOUN
ejpam-4220	220	3	of	of	ADP
ejpam-4220	220	4	edges	edge	NOUN
ejpam-4220	220	5	{	{	PUNCT
ejpam-4220	220	6	ux	ux	PROPN
ejpam-4220	220	7	,	,	PUNCT
ejpam-4220	220	8	vx	vx	PROPN
ejpam-4220	220	9	,	,	PUNCT
ejpam-4220	220	10	uv	uv	NOUN
ejpam-4220	220	11	}	}	PUNCT
ejpam-4220	220	12	and	and	CCONJ
ejpam-4220	220	13	{	{	PUNCT
ejpam-4220	220	14	uy	uy	INTJ
ejpam-4220	220	15	,	,	PUNCT
ejpam-4220	220	16	vy	vy	NOUN
ejpam-4220	220	17	,	,	PUNCT
ejpam-4220	220	18	uv	uv	NOUN
ejpam-4220	220	19	}	}	PUNCT
ejpam-4220	220	20	are	be	AUX
ejpam-4220	220	21	all	all	ADV
ejpam-4220	220	22	cycle	cycle	NOUN
ejpam-4220	220	23	which	which	PRON
ejpam-4220	220	24	is	be	AUX
ejpam-4220	220	25	a	a	DET
ejpam-4220	220	26	contradiction	contradiction	NOUN
ejpam-4220	220	27	since	since	SCONJ
ejpam-4220	220	28	t	t	PROPN
ejpam-4220	220	29	is	be	AUX
ejpam-4220	220	30	acyclic	acyclic	ADJ
ejpam-4220	220	31	.	.	PUNCT
ejpam-4220	221	1	thus	thus	ADV
ejpam-4220	221	2	,	,	PUNCT
ejpam-4220	221	3	in	in	ADP
ejpam-4220	221	4	either	either	PRON
ejpam-4220	221	5	of	of	ADP
ejpam-4220	221	6	the	the	DET
ejpam-4220	221	7	cases	case	NOUN
ejpam-4220	221	8	,	,	PUNCT
ejpam-4220	221	9	we	we	PRON
ejpam-4220	221	10	arrived	arrive	VERB
ejpam-4220	221	11	at	at	ADP
ejpam-4220	221	12	a	a	DET
ejpam-4220	221	13	contradiction	contradiction	NOUN
ejpam-4220	221	14	.	.	PUNCT
ejpam-4220	222	1	therefore	therefore	ADV
ejpam-4220	222	2	,	,	PUNCT
ejpam-4220	222	3	u	u	PROPN
ejpam-4220	222	4	∈	∈	PROPN
ejpam-4220	222	5	ω	ω	PROPN
ejpam-4220	222	6	and	and	CCONJ
ejpam-4220	222	7	v	v	ADP
ejpam-4220	222	8	∈	∈	PROPN
ejpam-4220	222	9	∆.	∆.	X
ejpam-4220	222	10	■	■	PROPN
ejpam-4220	222	11	4	4	X
ejpam-4220	222	12	.	.	PUNCT
ejpam-4220	223	1	independent	independent	ADJ
ejpam-4220	223	2	neighborhood	neighborhood	NOUN
ejpam-4220	223	3	polynomial	polynomial	NOUN
ejpam-4220	223	4	of	of	ADP
ejpam-4220	223	5	the	the	DET
ejpam-4220	223	6	rooted	rooted	ADJ
ejpam-4220	223	7	product	product	NOUN
ejpam-4220	223	8	of	of	ADP
ejpam-4220	223	9	two	two	NUM
ejpam-4220	223	10	trees	tree	NOUN
ejpam-4220	223	11	in	in	ADP
ejpam-4220	223	12	this	this	DET
ejpam-4220	223	13	section	section	NOUN
ejpam-4220	223	14	,	,	PUNCT
ejpam-4220	223	15	we	we	PRON
ejpam-4220	223	16	establish	establish	VERB
ejpam-4220	223	17	the	the	DET
ejpam-4220	223	18	independent	independent	ADJ
ejpam-4220	223	19	neighborhood	neighborhood	NOUN
ejpam-4220	223	20	sets	set	NOUN
ejpam-4220	223	21	of	of	ADP
ejpam-4220	223	22	the	the	DET
ejpam-4220	223	23	rooted	rooted	ADJ
ejpam-4220	223	24	product	product	NOUN
ejpam-4220	223	25	of	of	ADP
ejpam-4220	223	26	a	a	DET
ejpam-4220	223	27	tree	tree	NOUN
ejpam-4220	223	28	and	and	CCONJ
ejpam-4220	223	29	a	a	DET
ejpam-4220	223	30	rooted	rooted	ADJ
ejpam-4220	223	31	tree	tree	NOUN
ejpam-4220	223	32	using	use	VERB
ejpam-4220	223	33	the	the	DET
ejpam-4220	223	34	independent	independent	ADJ
ejpam-4220	223	35	neighborhood	neighborhood	NOUN
ejpam-4220	223	36	sets	set	NOUN
ejpam-4220	223	37	of	of	ADP
ejpam-4220	223	38	each	each	DET
ejpam-4220	223	39	tree	tree	NOUN
ejpam-4220	223	40	and	and	CCONJ
ejpam-4220	223	41	represent	represent	VERB
ejpam-4220	223	42	it	it	PRON
ejpam-4220	223	43	in	in	ADP
ejpam-4220	223	44	an	an	DET
ejpam-4220	223	45	independent	independent	ADJ
ejpam-4220	223	46	neighborhood	neighborhood	NOUN
ejpam-4220	223	47	polynomial	polynomial	NOUN
ejpam-4220	223	48	of	of	ADP
ejpam-4220	223	49	a	a	DET
ejpam-4220	223	50	graph	graph	NOUN
ejpam-4220	223	51	.	.	PUNCT
ejpam-4220	224	1	n.	n.	PROPN
ejpam-4220	224	2	s.	s.	PROPN
ejpam-4220	224	3	abdulcarim	abdulcarim	PROPN
ejpam-4220	224	4	,	,	PUNCT
ejpam-4220	224	5	s.	s.	PROPN
ejpam-4220	224	6	c.	c.	PROPN
ejpam-4220	224	7	dagondon	dagondon	PROPN
ejpam-4220	224	8	/	/	SYM
ejpam-4220	224	9	eur	eur	PROPN
ejpam-4220	224	10	.	.	PUNCT
ejpam-4220	225	1	j.	j.	PROPN
ejpam-4220	225	2	pure	pure	PROPN
ejpam-4220	225	3	appl	appl	PROPN
ejpam-4220	225	4	.	.	PROPN
ejpam-4220	225	5	math	math	PROPN
ejpam-4220	225	6	,	,	PUNCT
ejpam-4220	225	7	15	15	NUM
ejpam-4220	225	8	(	(	PUNCT
ejpam-4220	225	9	1	1	NUM
ejpam-4220	225	10	)	)	PUNCT
ejpam-4220	225	11	(	(	PUNCT
ejpam-4220	225	12	2022	2022	NUM
ejpam-4220	225	13	)	)	PUNCT
ejpam-4220	225	14	,	,	PUNCT
ejpam-4220	225	15	64	64	NUM
ejpam-4220	225	16	-	-	SYM
ejpam-4220	225	17	81	81	NUM
ejpam-4220	225	18	74	74	NUM
ejpam-4220	225	19	theorem	theorem	NOUN
ejpam-4220	225	20	3	3	X
ejpam-4220	225	21	.	.	PUNCT
ejpam-4220	226	1	let	let	VERB
ejpam-4220	226	2	g	g	NOUN
ejpam-4220	226	3	be	be	AUX
ejpam-4220	226	4	any	any	DET
ejpam-4220	226	5	tree	tree	NOUN
ejpam-4220	227	1	and	and	CCONJ
ejpam-4220	227	2	h	h	NOUN
ejpam-4220	227	3	be	be	AUX
ejpam-4220	227	4	a	a	DET
ejpam-4220	227	5	rooted	rooted	ADJ
ejpam-4220	227	6	tree	tree	NOUN
ejpam-4220	227	7	with	with	ADP
ejpam-4220	227	8	root	root	NOUN
ejpam-4220	227	9	vertex	vertex	NOUN
ejpam-4220	227	10	u.	u.	PROPN
ejpam-4220	228	1	then	then	ADV
ejpam-4220	228	2	the	the	DET
ejpam-4220	228	3	distance	distance	NOUN
ejpam-4220	228	4	d((x	d((x	PROPN
ejpam-4220	228	5	,	,	PUNCT
ejpam-4220	228	6	y	y	PROPN
ejpam-4220	228	7	)	)	PUNCT
ejpam-4220	228	8	,	,	PUNCT
ejpam-4220	228	9	(	(	PUNCT
ejpam-4220	228	10	w	w	PROPN
ejpam-4220	228	11	,	,	PUNCT
ejpam-4220	228	12	z	z	NOUN
ejpam-4220	228	13	)	)	PUNCT
ejpam-4220	228	14	)	)	PUNCT
ejpam-4220	228	15	between	between	ADP
ejpam-4220	228	16	two	two	NUM
ejpam-4220	228	17	vertices	vertex	NOUN
ejpam-4220	228	18	(	(	PUNCT
ejpam-4220	228	19	x	x	NOUN
ejpam-4220	228	20	,	,	PUNCT
ejpam-4220	228	21	y	y	PROPN
ejpam-4220	228	22	)	)	PUNCT
ejpam-4220	228	23	,	,	PUNCT
ejpam-4220	228	24	(	(	PUNCT
ejpam-4220	228	25	w	w	PROPN
ejpam-4220	228	26	,	,	PUNCT
ejpam-4220	228	27	z	z	NOUN
ejpam-4220	228	28	)	)	PUNCT
ejpam-4220	228	29	of	of	ADP
ejpam-4220	228	30	the	the	DET
ejpam-4220	228	31	rooted	rooted	ADJ
ejpam-4220	228	32	product	product	NOUN
ejpam-4220	228	33	graph	graph	NOUN
ejpam-4220	228	34	g•h	g•h	PROPN
ejpam-4220	228	35	is	be	AUX
ejpam-4220	228	36	given	give	VERB
ejpam-4220	228	37	by	by	ADP
ejpam-4220	228	38	:	:	PUNCT
ejpam-4220	228	39	1	1	X
ejpam-4220	228	40	.	.	X
ejpam-4220	229	1	d((x	d((x	ADJ
ejpam-4220	229	2	,	,	PUNCT
ejpam-4220	229	3	y	y	PROPN
ejpam-4220	229	4	)	)	PUNCT
ejpam-4220	229	5	,	,	PUNCT
ejpam-4220	229	6	(	(	PUNCT
ejpam-4220	229	7	w	w	PROPN
ejpam-4220	229	8	,	,	PUNCT
ejpam-4220	229	9	z	z	NOUN
ejpam-4220	229	10	)	)	PUNCT
ejpam-4220	229	11	)	)	PUNCT
ejpam-4220	230	1	=	=	SYM
ejpam-4220	230	2	d(y	d(y	NOUN
ejpam-4220	230	3	,	,	PUNCT
ejpam-4220	230	4	z	z	NOUN
ejpam-4220	230	5	)	)	PUNCT
ejpam-4220	230	6	if	if	SCONJ
ejpam-4220	230	7	x	x	X
ejpam-4220	230	8	=	=	SYM
ejpam-4220	230	9	w	w	NOUN
ejpam-4220	230	10	,	,	PUNCT
ejpam-4220	230	11	2	2	X
ejpam-4220	230	12	.	.	PUNCT
ejpam-4220	231	1	d((x	d((x	PROPN
ejpam-4220	231	2	,	,	PUNCT
ejpam-4220	231	3	y	y	PROPN
ejpam-4220	231	4	)	)	PUNCT
ejpam-4220	231	5	,	,	PUNCT
ejpam-4220	231	6	(	(	PUNCT
ejpam-4220	231	7	w	w	PROPN
ejpam-4220	231	8	,	,	PUNCT
ejpam-4220	231	9	z	z	NOUN
ejpam-4220	231	10	)	)	PUNCT
ejpam-4220	231	11	)	)	PUNCT
ejpam-4220	232	1	=	=	SYM
ejpam-4220	232	2	d(x	d(x	PROPN
ejpam-4220	232	3	,	,	PUNCT
ejpam-4220	232	4	w	w	NOUN
ejpam-4220	232	5	)	)	PUNCT
ejpam-4220	232	6	if	if	SCONJ
ejpam-4220	232	7	y	y	PROPN
ejpam-4220	232	8	=	=	SYM
ejpam-4220	232	9	u	u	PROPN
ejpam-4220	232	10	=	=	PROPN
ejpam-4220	232	11	z	z	PROPN
ejpam-4220	232	12	,	,	PUNCT
ejpam-4220	232	13	otherwise	otherwise	ADV
ejpam-4220	232	14	,	,	PUNCT
ejpam-4220	232	15	3	3	X
ejpam-4220	232	16	.	.	PUNCT
ejpam-4220	233	1	d((x	d((x	PROPN
ejpam-4220	233	2	,	,	PUNCT
ejpam-4220	233	3	y	y	PROPN
ejpam-4220	233	4	)	)	PUNCT
ejpam-4220	233	5	,	,	PUNCT
ejpam-4220	233	6	(	(	PUNCT
ejpam-4220	233	7	w	w	PROPN
ejpam-4220	233	8	,	,	PUNCT
ejpam-4220	233	9	z	z	NOUN
ejpam-4220	233	10	)	)	PUNCT
ejpam-4220	233	11	)	)	PUNCT
ejpam-4220	234	1	=	=	PUNCT
ejpam-4220	234	2	d((x	d((x	ADJ
ejpam-4220	234	3	,	,	PUNCT
ejpam-4220	234	4	y	y	PROPN
ejpam-4220	234	5	)	)	PUNCT
ejpam-4220	234	6	,	,	PUNCT
ejpam-4220	234	7	(	(	PUNCT
ejpam-4220	234	8	x	x	NOUN
ejpam-4220	234	9	,	,	PUNCT
ejpam-4220	234	10	u	u	NOUN
ejpam-4220	234	11	)	)	PUNCT
ejpam-4220	234	12	)	)	PUNCT
ejpam-4220	235	1	+	+	CCONJ
ejpam-4220	235	2	d((x	d((x	ADJ
ejpam-4220	235	3	,	,	PUNCT
ejpam-4220	235	4	u	u	NOUN
ejpam-4220	235	5	)	)	PUNCT
ejpam-4220	235	6	,	,	PUNCT
ejpam-4220	235	7	(	(	PUNCT
ejpam-4220	235	8	w	w	PROPN
ejpam-4220	235	9	,	,	PUNCT
ejpam-4220	235	10	u	u	NOUN
ejpam-4220	235	11	)	)	PUNCT
ejpam-4220	235	12	)	)	PUNCT
ejpam-4220	236	1	+	+	CCONJ
ejpam-4220	236	2	d((w	d((w	NOUN
ejpam-4220	236	3	,	,	PUNCT
ejpam-4220	236	4	u	u	NOUN
ejpam-4220	236	5	)	)	PUNCT
ejpam-4220	236	6	,	,	PUNCT
ejpam-4220	236	7	(	(	PUNCT
ejpam-4220	236	8	w	w	PROPN
ejpam-4220	236	9	,	,	PUNCT
ejpam-4220	236	10	z	z	NOUN
ejpam-4220	236	11	)	)	PUNCT
ejpam-4220	236	12	)	)	PUNCT
ejpam-4220	236	13	.	.	PUNCT
ejpam-4220	237	1	proof	proof	NOUN
ejpam-4220	237	2	.	.	PUNCT
ejpam-4220	238	1	1	1	X
ejpam-4220	238	2	.	.	X
ejpam-4220	238	3	let	let	VERB
ejpam-4220	238	4	s	s	PRON
ejpam-4220	238	5	=	=	VERB
ejpam-4220	238	6	{	{	PUNCT
ejpam-4220	238	7	(	(	PUNCT
ejpam-4220	238	8	x	x	NOUN
ejpam-4220	238	9	,	,	PUNCT
ejpam-4220	238	10	y	y	PROPN
ejpam-4220	238	11	)	)	PUNCT
ejpam-4220	238	12	,	,	PUNCT
ejpam-4220	238	13	(	(	PUNCT
ejpam-4220	238	14	w	w	PROPN
ejpam-4220	238	15	,	,	PUNCT
ejpam-4220	238	16	z	z	NOUN
ejpam-4220	238	17	)	)	PUNCT
ejpam-4220	238	18	∈	∈	NOUN
ejpam-4220	238	19	v	v	NOUN
ejpam-4220	238	20	(	(	PUNCT
ejpam-4220	238	21	g	g	PROPN
ejpam-4220	238	22	•	•	NUM
ejpam-4220	238	23	h	h	NOUN
ejpam-4220	238	24	)	)	PUNCT
ejpam-4220	238	25	:	:	PUNCT
ejpam-4220	239	1	x	x	X
ejpam-4220	239	2	=	=	PUNCT
ejpam-4220	239	3	w	w	NOUN
ejpam-4220	239	4	}	}	PUNCT
ejpam-4220	239	5	.	.	PUNCT
ejpam-4220	240	1	we	we	PRON
ejpam-4220	240	2	claim	claim	VERB
ejpam-4220	240	3	that	that	SCONJ
ejpam-4220	240	4	⟨s⟩	⟨s⟩	PROPN
ejpam-4220	240	5	∼=	∼=	PROPN
ejpam-4220	240	6	h.	h.	NOUN
ejpam-4220	240	7	first	first	ADV
ejpam-4220	240	8	,	,	PUNCT
ejpam-4220	240	9	we	we	PRON
ejpam-4220	240	10	define	define	VERB
ejpam-4220	240	11	the	the	DET
ejpam-4220	240	12	map	map	NOUN
ejpam-4220	240	13	function	function	VERB
ejpam-4220	240	14	β	β	NOUN
ejpam-4220	240	15	:	:	PUNCT
ejpam-4220	240	16	s	s	X
ejpam-4220	240	17	→	→	SYM
ejpam-4220	240	18	v	v	ADJ
ejpam-4220	240	19	(	(	PUNCT
ejpam-4220	240	20	h	h	NOUN
ejpam-4220	240	21	)	)	PUNCT
ejpam-4220	240	22	given	give	VERB
ejpam-4220	240	23	by	by	ADP
ejpam-4220	240	24	(	(	PUNCT
ejpam-4220	240	25	x	x	NOUN
ejpam-4220	240	26	,	,	PUNCT
ejpam-4220	240	27	y	y	NOUN
ejpam-4220	240	28	)	)	PUNCT
ejpam-4220	240	29	7→	7→	NUM
ejpam-4220	240	30	y	y	NOUN
ejpam-4220	240	31	for	for	ADP
ejpam-4220	240	32	y	y	PROPN
ejpam-4220	240	33	∈	∈	PROPN
ejpam-4220	240	34	h.	h.	PROPN
ejpam-4220	240	35	for	for	ADP
ejpam-4220	240	36	(	(	PUNCT
ejpam-4220	240	37	x	x	NOUN
ejpam-4220	240	38	,	,	PUNCT
ejpam-4220	240	39	y1	y1	NOUN
ejpam-4220	240	40	)	)	PUNCT
ejpam-4220	240	41	,	,	PUNCT
ejpam-4220	240	42	(	(	PUNCT
ejpam-4220	240	43	x	x	X
ejpam-4220	240	44	,	,	PUNCT
ejpam-4220	240	45	y2	y2	PROPN
ejpam-4220	240	46	)	)	PUNCT
ejpam-4220	240	47	∈	∈	PROPN
ejpam-4220	240	48	s	s	VERB
ejpam-4220	240	49	such	such	ADJ
ejpam-4220	240	50	that	that	DET
ejpam-4220	240	51	β((x	β((x	ADJ
ejpam-4220	240	52	,	,	PUNCT
ejpam-4220	240	53	y1	y1	NOUN
ejpam-4220	240	54	)	)	PUNCT
ejpam-4220	240	55	)	)	PUNCT
ejpam-4220	241	1	=	=	SYM
ejpam-4220	241	2	β((x	β((x	ADJ
ejpam-4220	241	3	,	,	PUNCT
ejpam-4220	241	4	y2	y2	PROPN
ejpam-4220	241	5	)	)	PUNCT
ejpam-4220	241	6	)	)	PUNCT
ejpam-4220	241	7	,	,	PUNCT
ejpam-4220	241	8	we	we	PRON
ejpam-4220	241	9	have	have	VERB
ejpam-4220	241	10	y1	y1	NOUN
ejpam-4220	241	11	=	=	SYM
ejpam-4220	241	12	β((x	β((x	ADJ
ejpam-4220	241	13	,	,	PUNCT
ejpam-4220	241	14	y1	y1	NOUN
ejpam-4220	241	15	)	)	PUNCT
ejpam-4220	241	16	)	)	PUNCT
ejpam-4220	242	1	=	=	SYM
ejpam-4220	242	2	β((x	β((x	ADJ
ejpam-4220	242	3	,	,	PUNCT
ejpam-4220	242	4	y2	y2	PROPN
ejpam-4220	242	5	)	)	PUNCT
ejpam-4220	242	6	)	)	PUNCT
ejpam-4220	243	1	=	=	PUNCT
ejpam-4220	243	2	y2	y2	PROPN
ejpam-4220	243	3	.	.	PUNCT
ejpam-4220	244	1	this	this	PRON
ejpam-4220	244	2	shows	show	VERB
ejpam-4220	244	3	that	that	SCONJ
ejpam-4220	244	4	β	β	PROPN
ejpam-4220	244	5	is	be	AUX
ejpam-4220	244	6	one	one	NUM
ejpam-4220	244	7	-	-	PUNCT
ejpam-4220	244	8	to	to	ADP
ejpam-4220	244	9	-	-	PUNCT
ejpam-4220	244	10	one	one	NUM
ejpam-4220	244	11	.	.	PUNCT
ejpam-4220	245	1	since	since	SCONJ
ejpam-4220	245	2	s	s	PART
ejpam-4220	245	3	=	=	PUNCT
ejpam-4220	245	4	{	{	PUNCT
ejpam-4220	245	5	(	(	PUNCT
ejpam-4220	245	6	x	x	NOUN
ejpam-4220	245	7	,	,	PUNCT
ejpam-4220	245	8	y	y	NOUN
ejpam-4220	245	9	)	)	PUNCT
ejpam-4220	245	10	∈	∈	PROPN
ejpam-4220	245	11	v	v	NOUN
ejpam-4220	245	12	(	(	PUNCT
ejpam-4220	245	13	g•h	g•h	PROPN
ejpam-4220	245	14	)	)	PUNCT
ejpam-4220	245	15	:	:	PUNCT
ejpam-4220	246	1	x	x	X
ejpam-4220	246	2	∈	∈	NOUN
ejpam-4220	246	3	v	v	ADP
ejpam-4220	246	4	(	(	PUNCT
ejpam-4220	246	5	g	g	NOUN
ejpam-4220	246	6	)	)	PUNCT
ejpam-4220	246	7	,	,	PUNCT
ejpam-4220	246	8	y	y	PROPN
ejpam-4220	246	9	∈	∈	PROPN
ejpam-4220	246	10	v	v	ADP
ejpam-4220	246	11	(	(	PUNCT
ejpam-4220	246	12	h	h	NOUN
ejpam-4220	246	13	)	)	PUNCT
ejpam-4220	246	14	}	}	PUNCT
ejpam-4220	246	15	,	,	PUNCT
ejpam-4220	246	16	for	for	ADP
ejpam-4220	246	17	every	every	DET
ejpam-4220	246	18	h	h	NOUN
ejpam-4220	246	19	∈	∈	PROPN
ejpam-4220	246	20	v	v	ADP
ejpam-4220	246	21	(	(	PUNCT
ejpam-4220	246	22	h	h	NOUN
ejpam-4220	246	23	)	)	PUNCT
ejpam-4220	246	24	,	,	PUNCT
ejpam-4220	246	25	there	there	PRON
ejpam-4220	246	26	exists	exist	VERB
ejpam-4220	246	27	g	g	PROPN
ejpam-4220	246	28	∈	∈	PROPN
ejpam-4220	246	29	v	v	ADP
ejpam-4220	246	30	(	(	PUNCT
ejpam-4220	246	31	g	g	NOUN
ejpam-4220	246	32	)	)	PUNCT
ejpam-4220	246	33	such	such	ADJ
ejpam-4220	246	34	that	that	SCONJ
ejpam-4220	246	35	(	(	PUNCT
ejpam-4220	246	36	g	g	NOUN
ejpam-4220	246	37	,	,	PUNCT
ejpam-4220	246	38	h	h	NOUN
ejpam-4220	246	39	)	)	PUNCT
ejpam-4220	246	40	∈	∈	NOUN
ejpam-4220	246	41	v	v	NOUN
ejpam-4220	246	42	(	(	PUNCT
ejpam-4220	246	43	g	g	PROPN
ejpam-4220	246	44	•	•	NUM
ejpam-4220	246	45	h	h	NOUN
ejpam-4220	246	46	)	)	PUNCT
ejpam-4220	246	47	.	.	PUNCT
ejpam-4220	247	1	observe	observe	VERB
ejpam-4220	247	2	that	that	SCONJ
ejpam-4220	247	3	h	h	NOUN
ejpam-4220	247	4	=	=	PUNCT
ejpam-4220	247	5	β((g	β((g	ADJ
ejpam-4220	247	6	,	,	PUNCT
ejpam-4220	247	7	h	h	NOUN
ejpam-4220	247	8	)	)	PUNCT
ejpam-4220	247	9	)	)	PUNCT
ejpam-4220	247	10	.	.	PUNCT
ejpam-4220	248	1	hence	hence	ADV
ejpam-4220	248	2	,	,	PUNCT
ejpam-4220	248	3	β	β	X
ejpam-4220	248	4	is	be	AUX
ejpam-4220	248	5	onto	onto	ADP
ejpam-4220	248	6	.	.	PUNCT
ejpam-4220	249	1	lastly	lastly	ADV
ejpam-4220	249	2	,	,	PUNCT
ejpam-4220	249	3	we	we	PRON
ejpam-4220	249	4	show	show	VERB
ejpam-4220	249	5	that	that	SCONJ
ejpam-4220	249	6	β	β	PROPN
ejpam-4220	249	7	preserves	preserve	VERB
ejpam-4220	249	8	adjacency	adjacency	PROPN
ejpam-4220	249	9	.	.	PUNCT
ejpam-4220	250	1	let	let	VERB
ejpam-4220	250	2	(	(	PUNCT
ejpam-4220	250	3	g	g	NOUN
ejpam-4220	250	4	,	,	PUNCT
ejpam-4220	250	5	h1	h1	PROPN
ejpam-4220	250	6	)	)	PUNCT
ejpam-4220	250	7	,	,	PUNCT
ejpam-4220	250	8	(	(	PUNCT
ejpam-4220	250	9	g	g	NOUN
ejpam-4220	250	10	,	,	PUNCT
ejpam-4220	250	11	h2	h2	NOUN
ejpam-4220	250	12	)	)	PUNCT
ejpam-4220	250	13	∈	∈	PROPN
ejpam-4220	250	14	s	s	VERB
ejpam-4220	250	15	⊆	⊆	NUM
ejpam-4220	250	16	v	v	NOUN
ejpam-4220	250	17	(	(	PUNCT
ejpam-4220	250	18	g	g	PROPN
ejpam-4220	250	19	•	•	NUM
ejpam-4220	250	20	h	h	NOUN
ejpam-4220	250	21	)	)	PUNCT
ejpam-4220	250	22	such	such	ADJ
ejpam-4220	250	23	that	that	SCONJ
ejpam-4220	250	24	(	(	PUNCT
ejpam-4220	250	25	g	g	NOUN
ejpam-4220	250	26	,	,	PUNCT
ejpam-4220	250	27	h1)(g	h1)(g	PROPN
ejpam-4220	250	28	,	,	PUNCT
ejpam-4220	250	29	h2	h2	NOUN
ejpam-4220	250	30	)	)	PUNCT
ejpam-4220	250	31	∈	∈	PROPN
ejpam-4220	250	32	e(g	e(g	PROPN
ejpam-4220	250	33	•	•	NUM
ejpam-4220	250	34	h	h	NOUN
ejpam-4220	250	35	)	)	PUNCT
ejpam-4220	250	36	.	.	PUNCT
ejpam-4220	251	1	by	by	ADP
ejpam-4220	251	2	definition	definition	NOUN
ejpam-4220	251	3	7	7	NUM
ejpam-4220	251	4	,	,	PUNCT
ejpam-4220	251	5	h1h2	h1h2	NUM
ejpam-4220	251	6	∈	∈	PROPN
ejpam-4220	251	7	e(h	e(h	PROPN
ejpam-4220	251	8	)	)	PUNCT
ejpam-4220	251	9	.	.	PUNCT
ejpam-4220	252	1	thus	thus	ADV
ejpam-4220	252	2	,	,	PUNCT
ejpam-4220	252	3	(	(	PUNCT
ejpam-4220	252	4	g	g	NOUN
ejpam-4220	252	5	,	,	PUNCT
ejpam-4220	252	6	h1)(g	h1)(g	PROPN
ejpam-4220	252	7	,	,	PUNCT
ejpam-4220	252	8	h2	h2	NOUN
ejpam-4220	252	9	)	)	PUNCT
ejpam-4220	252	10	∈	∈	PROPN
ejpam-4220	252	11	e(g	e(g	PROPN
ejpam-4220	252	12	•	•	PROPN
ejpam-4220	252	13	h	h	PROPN
ejpam-4220	252	14	)	)	PUNCT
ejpam-4220	252	15	⇔	⇔	X
ejpam-4220	252	16	β((g	β((g	PROPN
ejpam-4220	252	17	,	,	PUNCT
ejpam-4220	252	18	h1))β((g	h1))β((g	NOUN
ejpam-4220	252	19	,	,	PUNCT
ejpam-4220	252	20	h2	h2	NOUN
ejpam-4220	252	21	)	)	PUNCT
ejpam-4220	252	22	)	)	PUNCT
ejpam-4220	253	1	=	=	PUNCT
ejpam-4220	254	1	h1h2	h1h2	X
ejpam-4220	254	2	∈	∈	PROPN
ejpam-4220	254	3	e(h	e(h	PROPN
ejpam-4220	254	4	)	)	PUNCT
ejpam-4220	254	5	.	.	PUNCT
ejpam-4220	255	1	hence	hence	ADV
ejpam-4220	255	2	,	,	PUNCT
ejpam-4220	255	3	β	β	X
ejpam-4220	255	4	preserves	preserve	VERB
ejpam-4220	255	5	adjacency	adjacency	PROPN
ejpam-4220	255	6	.	.	PUNCT
ejpam-4220	256	1	therefore	therefore	ADV
ejpam-4220	256	2	,	,	PUNCT
ejpam-4220	256	3	⟨s⟩	⟨s⟩	PROPN
ejpam-4220	256	4	∼=	∼=	PROPN
ejpam-4220	256	5	h.	h.	NOUN
ejpam-4220	256	6	consequently	consequently	ADV
ejpam-4220	256	7	,	,	PUNCT
ejpam-4220	256	8	d((x	d((x	PROPN
ejpam-4220	256	9	,	,	PUNCT
ejpam-4220	256	10	y	y	PROPN
ejpam-4220	256	11	)	)	PUNCT
ejpam-4220	256	12	,	,	PUNCT
ejpam-4220	256	13	(	(	PUNCT
ejpam-4220	256	14	w	w	PROPN
ejpam-4220	256	15	,	,	PUNCT
ejpam-4220	256	16	z	z	NOUN
ejpam-4220	256	17	)	)	PUNCT
ejpam-4220	256	18	)	)	PUNCT
ejpam-4220	257	1	=	=	SYM
ejpam-4220	257	2	d(y	d(y	NOUN
ejpam-4220	257	3	,	,	PUNCT
ejpam-4220	257	4	z	z	NOUN
ejpam-4220	257	5	)	)	PUNCT
ejpam-4220	257	6	for	for	ADP
ejpam-4220	257	7	x	x	X
ejpam-4220	257	8	=	=	SYM
ejpam-4220	257	9	w.	w.	PROPN
ejpam-4220	257	10	2	2	NUM
ejpam-4220	257	11	.	.	PUNCT
ejpam-4220	258	1	let	let	VERB
ejpam-4220	258	2	t	t	NOUN
ejpam-4220	258	3	=	=	SYM
ejpam-4220	258	4	{	{	PUNCT
ejpam-4220	258	5	(	(	PUNCT
ejpam-4220	258	6	x	x	NOUN
ejpam-4220	258	7	,	,	PUNCT
ejpam-4220	258	8	y	y	PROPN
ejpam-4220	258	9	)	)	PUNCT
ejpam-4220	258	10	,	,	PUNCT
ejpam-4220	258	11	(	(	PUNCT
ejpam-4220	258	12	w	w	PROPN
ejpam-4220	258	13	,	,	PUNCT
ejpam-4220	258	14	z	z	NOUN
ejpam-4220	258	15	)	)	PUNCT
ejpam-4220	258	16	∈	∈	NOUN
ejpam-4220	258	17	v	v	NOUN
ejpam-4220	258	18	(	(	PUNCT
ejpam-4220	258	19	g	g	PROPN
ejpam-4220	258	20	•	•	NUM
ejpam-4220	258	21	h	h	NOUN
ejpam-4220	258	22	)	)	PUNCT
ejpam-4220	258	23	:	:	PUNCT
ejpam-4220	259	1	y	y	NOUN
ejpam-4220	259	2	=	=	SYM
ejpam-4220	259	3	u	u	PROPN
ejpam-4220	259	4	=	=	PROPN
ejpam-4220	259	5	z	z	NOUN
ejpam-4220	259	6	}	}	PUNCT
ejpam-4220	259	7	.	.	PUNCT
ejpam-4220	260	1	we	we	PRON
ejpam-4220	260	2	claim	claim	VERB
ejpam-4220	260	3	that	that	SCONJ
ejpam-4220	260	4	⟨t	⟨t	VERB
ejpam-4220	260	5	⟩	⟩	NOUN
ejpam-4220	260	6	∼=	∼=	PROPN
ejpam-4220	260	7	g.	g.	NOUN
ejpam-4220	260	8	first	first	ADV
ejpam-4220	260	9	,	,	PUNCT
ejpam-4220	260	10	we	we	PRON
ejpam-4220	260	11	define	define	VERB
ejpam-4220	260	12	the	the	DET
ejpam-4220	260	13	map	map	NOUN
ejpam-4220	260	14	function	function	VERB
ejpam-4220	260	15	γ	γ	X
ejpam-4220	260	16	:	:	PUNCT
ejpam-4220	260	17	t	t	PROPN
ejpam-4220	260	18	→	→	SYM
ejpam-4220	260	19	v	v	PROPN
ejpam-4220	260	20	(	(	PUNCT
ejpam-4220	260	21	g	g	NOUN
ejpam-4220	260	22	)	)	PUNCT
ejpam-4220	260	23	given	give	VERB
ejpam-4220	260	24	by	by	ADP
ejpam-4220	260	25	(	(	PUNCT
ejpam-4220	260	26	x	x	NOUN
ejpam-4220	260	27	,	,	PUNCT
ejpam-4220	260	28	y	y	NOUN
ejpam-4220	260	29	)	)	PUNCT
ejpam-4220	260	30	7→	7→	NUM
ejpam-4220	260	31	x.	x.	NOUN
ejpam-4220	261	1	let	let	VERB
ejpam-4220	261	2	(	(	PUNCT
ejpam-4220	261	3	x1	x1	PROPN
ejpam-4220	261	4	,	,	PUNCT
ejpam-4220	261	5	u	u	NOUN
ejpam-4220	261	6	)	)	PUNCT
ejpam-4220	261	7	,	,	PUNCT
ejpam-4220	261	8	(	(	PUNCT
ejpam-4220	261	9	x2	x2	PROPN
ejpam-4220	261	10	,	,	PUNCT
ejpam-4220	261	11	u	u	NOUN
ejpam-4220	261	12	)	)	PUNCT
ejpam-4220	261	13	∈	∈	PROPN
ejpam-4220	261	14	t	t	NOUN
ejpam-4220	261	15	.	.	PUNCT
ejpam-4220	262	1	if	if	SCONJ
ejpam-4220	262	2	γ((x1	γ((x1	NOUN
ejpam-4220	262	3	,	,	PUNCT
ejpam-4220	262	4	u	u	NOUN
ejpam-4220	262	5	)	)	PUNCT
ejpam-4220	262	6	)	)	PUNCT
ejpam-4220	263	1	=	=	SYM
ejpam-4220	263	2	γ((x2	γ((x2	NOUN
ejpam-4220	263	3	,	,	PUNCT
ejpam-4220	263	4	u	u	NOUN
ejpam-4220	263	5	)	)	PUNCT
ejpam-4220	263	6	)	)	PUNCT
ejpam-4220	263	7	,	,	PUNCT
ejpam-4220	263	8	then	then	ADV
ejpam-4220	263	9	x1	x1	PROPN
ejpam-4220	263	10	=	=	SYM
ejpam-4220	263	11	γ((x1	γ((x1	PROPN
ejpam-4220	263	12	,	,	PUNCT
ejpam-4220	263	13	u	u	NOUN
ejpam-4220	263	14	)	)	PUNCT
ejpam-4220	263	15	)	)	PUNCT
ejpam-4220	264	1	=	=	SYM
ejpam-4220	264	2	γ((x2	γ((x2	NOUN
ejpam-4220	264	3	,	,	PUNCT
ejpam-4220	264	4	u	u	NOUN
ejpam-4220	264	5	)	)	PUNCT
ejpam-4220	264	6	)	)	PUNCT
ejpam-4220	265	1	=	=	SYM
ejpam-4220	265	2	x2	x2	PROPN
ejpam-4220	265	3	.	.	PUNCT
ejpam-4220	266	1	this	this	PRON
ejpam-4220	266	2	implies	imply	VERB
ejpam-4220	266	3	γ	γ	PROPN
ejpam-4220	266	4	is	be	AUX
ejpam-4220	266	5	oneto	oneto	NOUN
ejpam-4220	266	6	-	-	PUNCT
ejpam-4220	266	7	one	one	NUM
ejpam-4220	266	8	.	.	PUNCT
ejpam-4220	267	1	since	since	SCONJ
ejpam-4220	267	2	for	for	ADP
ejpam-4220	267	3	every	every	PRON
ejpam-4220	267	4	g1	g1	PROPN
ejpam-4220	267	5	∈	∈	PROPN
ejpam-4220	267	6	v	v	NOUN
ejpam-4220	267	7	(	(	PUNCT
ejpam-4220	267	8	g	g	NOUN
ejpam-4220	267	9	)	)	PUNCT
ejpam-4220	267	10	,	,	PUNCT
ejpam-4220	267	11	γ((g	γ((g	NOUN
ejpam-4220	267	12	,	,	PUNCT
ejpam-4220	267	13	u	u	NOUN
ejpam-4220	267	14	)	)	PUNCT
ejpam-4220	267	15	)	)	PUNCT
ejpam-4220	268	1	=	=	SYM
ejpam-4220	268	2	g	g	PROPN
ejpam-4220	268	3	,	,	PUNCT
ejpam-4220	268	4	γ	γ	PROPN
ejpam-4220	268	5	is	be	AUX
ejpam-4220	268	6	onto	onto	ADP
ejpam-4220	268	7	.	.	PUNCT
ejpam-4220	269	1	lastly	lastly	ADV
ejpam-4220	269	2	,	,	PUNCT
ejpam-4220	269	3	let	let	VERB
ejpam-4220	269	4	(	(	PUNCT
ejpam-4220	269	5	g1	g1	X
ejpam-4220	269	6	,	,	PUNCT
ejpam-4220	269	7	u	u	NOUN
ejpam-4220	269	8	)	)	PUNCT
ejpam-4220	269	9	,	,	PUNCT
ejpam-4220	269	10	(	(	PUNCT
ejpam-4220	269	11	g2	g2	PROPN
ejpam-4220	269	12	,	,	PUNCT
ejpam-4220	269	13	u	u	NOUN
ejpam-4220	269	14	)	)	PUNCT
ejpam-4220	269	15	∈	∈	NOUN
ejpam-4220	269	16	v	v	NOUN
ejpam-4220	269	17	(	(	PUNCT
ejpam-4220	269	18	g	g	PROPN
ejpam-4220	269	19	•	•	NUM
ejpam-4220	269	20	h	h	NOUN
ejpam-4220	269	21	)	)	PUNCT
ejpam-4220	269	22	such	such	ADJ
ejpam-4220	269	23	that	that	SCONJ
ejpam-4220	269	24	(	(	PUNCT
ejpam-4220	269	25	g1	g1	PROPN
ejpam-4220	269	26	,	,	PUNCT
ejpam-4220	269	27	u)(g2	u)(g2	NUM
ejpam-4220	269	28	,	,	PUNCT
ejpam-4220	269	29	u	u	NOUN
ejpam-4220	269	30	)	)	PUNCT
ejpam-4220	269	31	∈	∈	PROPN
ejpam-4220	269	32	e(g	e(g	PROPN
ejpam-4220	269	33	•	•	NUM
ejpam-4220	269	34	h	h	NOUN
ejpam-4220	269	35	)	)	PUNCT
ejpam-4220	269	36	.	.	PUNCT
ejpam-4220	270	1	by	by	ADP
ejpam-4220	270	2	definition	definition	NOUN
ejpam-4220	270	3	7	7	NUM
ejpam-4220	270	4	,	,	PUNCT
ejpam-4220	270	5	g1g2	g1g2	PROPN
ejpam-4220	270	6	∈	∈	PROPN
ejpam-4220	270	7	e(g	e(g	PROPN
ejpam-4220	270	8	)	)	PUNCT
ejpam-4220	270	9	.	.	PUNCT
ejpam-4220	271	1	now	now	ADV
ejpam-4220	271	2	,	,	PUNCT
ejpam-4220	271	3	(	(	PUNCT
ejpam-4220	271	4	g1	g1	X
ejpam-4220	271	5	,	,	PUNCT
ejpam-4220	271	6	u)(g2	u)(g2	NUM
ejpam-4220	271	7	,	,	PUNCT
ejpam-4220	271	8	u	u	NOUN
ejpam-4220	271	9	)	)	PUNCT
ejpam-4220	271	10	∈	∈	PROPN
ejpam-4220	271	11	e(g	e(g	PROPN
ejpam-4220	271	12	•h	•h	PROPN
ejpam-4220	271	13	)	)	PUNCT
ejpam-4220	271	14	⇔	⇔	X
ejpam-4220	271	15	γ((g1	γ((g1	PROPN
ejpam-4220	271	16	,	,	PUNCT
ejpam-4220	271	17	u))γ((g2	u))γ((g2	ADJ
ejpam-4220	271	18	,	,	PUNCT
ejpam-4220	271	19	u	u	NOUN
ejpam-4220	271	20	)	)	PUNCT
ejpam-4220	271	21	)	)	PUNCT
ejpam-4220	272	1	=	=	PUNCT
ejpam-4220	272	2	g1g2	g1g2	PROPN
ejpam-4220	272	3	∈	∈	PROPN
ejpam-4220	272	4	e(g	e(g	PROPN
ejpam-4220	272	5	)	)	PUNCT
ejpam-4220	272	6	.	.	PUNCT
ejpam-4220	273	1	hence	hence	ADV
ejpam-4220	273	2	,	,	PUNCT
ejpam-4220	273	3	γ	γ	PROPN
ejpam-4220	273	4	preserves	preserve	VERB
ejpam-4220	273	5	adjacency	adjacency	NOUN
ejpam-4220	273	6	.	.	PUNCT
ejpam-4220	274	1	thus	thus	ADV
ejpam-4220	274	2	,	,	PUNCT
ejpam-4220	274	3	⟨t	⟨t	VERB
ejpam-4220	274	4	⟩	⟩	NOUN
ejpam-4220	274	5	∼=	∼=	PROPN
ejpam-4220	274	6	g.	g.	NOUN
ejpam-4220	274	7	therefore	therefore	ADV
ejpam-4220	274	8	,	,	PUNCT
ejpam-4220	274	9	d((x	d((x	PROPN
ejpam-4220	274	10	,	,	PUNCT
ejpam-4220	274	11	y	y	PROPN
ejpam-4220	274	12	)	)	PUNCT
ejpam-4220	274	13	,	,	PUNCT
ejpam-4220	274	14	(	(	PUNCT
ejpam-4220	274	15	w	w	PROPN
ejpam-4220	274	16	,	,	PUNCT
ejpam-4220	274	17	z	z	NOUN
ejpam-4220	274	18	)	)	PUNCT
ejpam-4220	274	19	)	)	PUNCT
ejpam-4220	275	1	=	=	SYM
ejpam-4220	275	2	d(x	d(x	PROPN
ejpam-4220	275	3	,	,	PUNCT
ejpam-4220	275	4	w	w	NOUN
ejpam-4220	275	5	)	)	PUNCT
ejpam-4220	275	6	for	for	ADP
ejpam-4220	275	7	y	y	PROPN
ejpam-4220	275	8	=	=	SYM
ejpam-4220	275	9	u	u	PROPN
ejpam-4220	275	10	=	=	PROPN
ejpam-4220	275	11	z.	z.	PROPN
ejpam-4220	275	12	3	3	NUM
ejpam-4220	275	13	.	.	PUNCT
ejpam-4220	276	1	since	since	SCONJ
ejpam-4220	276	2	g	g	PROPN
ejpam-4220	276	3	•	•	PROPN
ejpam-4220	276	4	h	h	NOUN
ejpam-4220	276	5	is	be	AUX
ejpam-4220	276	6	a	a	DET
ejpam-4220	276	7	tree	tree	NOUN
ejpam-4220	276	8	,	,	PUNCT
ejpam-4220	276	9	every	every	DET
ejpam-4220	276	10	vertices	vertex	NOUN
ejpam-4220	276	11	of	of	ADP
ejpam-4220	276	12	g	g	NOUN
ejpam-4220	276	13	•	•	NUM
ejpam-4220	276	14	h	h	NOUN
ejpam-4220	276	15	is	be	AUX
ejpam-4220	276	16	connected	connect	VERB
ejpam-4220	276	17	by	by	ADP
ejpam-4220	276	18	a	a	DET
ejpam-4220	276	19	unique	unique	ADJ
ejpam-4220	276	20	path	path	NOUN
ejpam-4220	276	21	.	.	PUNCT
ejpam-4220	277	1	by	by	ADP
ejpam-4220	277	2	definition	definition	NOUN
ejpam-4220	277	3	of	of	ADP
ejpam-4220	277	4	rooted	rooted	ADJ
ejpam-4220	277	5	product	product	NOUN
ejpam-4220	277	6	,	,	PUNCT
ejpam-4220	277	7	for	for	ADP
ejpam-4220	277	8	vertices	vertex	NOUN
ejpam-4220	277	9	(	(	PUNCT
ejpam-4220	277	10	x	x	X
ejpam-4220	277	11	,	,	PUNCT
ejpam-4220	277	12	y	y	PROPN
ejpam-4220	277	13	)	)	PUNCT
ejpam-4220	277	14	,	,	PUNCT
ejpam-4220	277	15	(	(	PUNCT
ejpam-4220	277	16	w	w	PROPN
ejpam-4220	277	17	,	,	PUNCT
ejpam-4220	277	18	z	z	NOUN
ejpam-4220	277	19	)	)	PUNCT
ejpam-4220	277	20	where	where	SCONJ
ejpam-4220	277	21	x	x	X
ejpam-4220	277	22	̸=	̸=	PROPN
ejpam-4220	277	23	w	w	PROPN
ejpam-4220	277	24	and	and	CCONJ
ejpam-4220	277	25	y	y	PROPN
ejpam-4220	277	26	̸=	̸=	PROPN
ejpam-4220	277	27	z	z	PROPN
ejpam-4220	277	28	,	,	PUNCT
ejpam-4220	277	29	the	the	DET
ejpam-4220	277	30	vertices	vertex	NOUN
ejpam-4220	277	31	(	(	PUNCT
ejpam-4220	277	32	x	x	NOUN
ejpam-4220	277	33	,	,	PUNCT
ejpam-4220	277	34	y	y	PROPN
ejpam-4220	277	35	)	)	PUNCT
ejpam-4220	277	36	and	and	CCONJ
ejpam-4220	277	37	(	(	PUNCT
ejpam-4220	277	38	w	w	PROPN
ejpam-4220	277	39	,	,	PUNCT
ejpam-4220	277	40	z	z	NOUN
ejpam-4220	277	41	)	)	PUNCT
ejpam-4220	277	42	is	be	AUX
ejpam-4220	277	43	connected	connect	VERB
ejpam-4220	277	44	by	by	ADP
ejpam-4220	277	45	the	the	DET
ejpam-4220	277	46	paths	path	NOUN
ejpam-4220	277	47	(	(	PUNCT
ejpam-4220	277	48	x	x	X
ejpam-4220	277	49	,	,	PUNCT
ejpam-4220	277	50	y)-(x	y)-(x	PROPN
ejpam-4220	277	51	,	,	PUNCT
ejpam-4220	277	52	u	u	NOUN
ejpam-4220	277	53	)	)	PUNCT
ejpam-4220	277	54	path	path	NOUN
ejpam-4220	277	55	,	,	PUNCT
ejpam-4220	277	56	(	(	PUNCT
ejpam-4220	277	57	x	x	NOUN
ejpam-4220	277	58	,	,	PUNCT
ejpam-4220	277	59	u)-(w	u)-(w	ADJ
ejpam-4220	277	60	,	,	PUNCT
ejpam-4220	277	61	u	u	NOUN
ejpam-4220	277	62	)	)	PUNCT
ejpam-4220	277	63	path	path	NOUN
ejpam-4220	277	64	and	and	CCONJ
ejpam-4220	277	65	(	(	PUNCT
ejpam-4220	277	66	w	w	NOUN
ejpam-4220	277	67	,	,	PUNCT
ejpam-4220	277	68	u)-(w	u)-(w	ADJ
ejpam-4220	277	69	,	,	PUNCT
ejpam-4220	277	70	z	z	NOUN
ejpam-4220	277	71	)	)	PUNCT
ejpam-4220	277	72	path	path	NOUN
ejpam-4220	277	73	where	where	SCONJ
ejpam-4220	277	74	u	u	NOUN
ejpam-4220	277	75	is	be	AUX
ejpam-4220	277	76	the	the	DET
ejpam-4220	277	77	root	root	NOUN
ejpam-4220	277	78	vertex	vertex	NOUN
ejpam-4220	277	79	of	of	ADP
ejpam-4220	277	80	graph	graph	NOUN
ejpam-4220	277	81	h.	h.	PROPN
ejpam-4220	277	82	hence	hence	ADV
ejpam-4220	277	83	,	,	PUNCT
ejpam-4220	277	84	by	by	ADP
ejpam-4220	277	85	remark	remark	NOUN
ejpam-4220	277	86	2	2	NUM
ejpam-4220	277	87	,	,	PUNCT
ejpam-4220	277	88	d((x	d((x	ADJ
ejpam-4220	277	89	,	,	PUNCT
ejpam-4220	277	90	y	y	PROPN
ejpam-4220	277	91	)	)	PUNCT
ejpam-4220	277	92	,	,	PUNCT
ejpam-4220	277	93	(	(	PUNCT
ejpam-4220	277	94	w	w	PROPN
ejpam-4220	277	95	,	,	PUNCT
ejpam-4220	277	96	z	z	NOUN
ejpam-4220	277	97	)	)	PUNCT
ejpam-4220	277	98	)	)	PUNCT
ejpam-4220	278	1	=	=	PUNCT
ejpam-4220	278	2	d((x	d((x	ADJ
ejpam-4220	278	3	,	,	PUNCT
ejpam-4220	278	4	y	y	PROPN
ejpam-4220	278	5	)	)	PUNCT
ejpam-4220	278	6	,	,	PUNCT
ejpam-4220	278	7	(	(	PUNCT
ejpam-4220	278	8	x	x	NOUN
ejpam-4220	278	9	,	,	PUNCT
ejpam-4220	278	10	u	u	NOUN
ejpam-4220	278	11	)	)	PUNCT
ejpam-4220	278	12	)	)	PUNCT
ejpam-4220	279	1	+	+	CCONJ
ejpam-4220	279	2	d((x	d((x	ADJ
ejpam-4220	279	3	,	,	PUNCT
ejpam-4220	279	4	u	u	NOUN
ejpam-4220	279	5	)	)	PUNCT
ejpam-4220	279	6	,	,	PUNCT
ejpam-4220	279	7	(	(	PUNCT
ejpam-4220	279	8	w	w	PROPN
ejpam-4220	279	9	,	,	PUNCT
ejpam-4220	279	10	u	u	NOUN
ejpam-4220	279	11	)	)	PUNCT
ejpam-4220	279	12	)	)	PUNCT
ejpam-4220	280	1	+	+	CCONJ
ejpam-4220	280	2	d((w	d((w	NOUN
ejpam-4220	280	3	,	,	PUNCT
ejpam-4220	280	4	u	u	NOUN
ejpam-4220	280	5	)	)	PUNCT
ejpam-4220	280	6	,	,	PUNCT
ejpam-4220	280	7	(	(	PUNCT
ejpam-4220	280	8	w	w	PROPN
ejpam-4220	280	9	,	,	PUNCT
ejpam-4220	280	10	z	z	NOUN
ejpam-4220	280	11	)	)	PUNCT
ejpam-4220	280	12	)	)	PUNCT
ejpam-4220	280	13	.	.	PUNCT
ejpam-4220	281	1	■	■	PUNCT
ejpam-4220	281	2	remark	remark	NOUN
ejpam-4220	281	3	3	3	NUM
ejpam-4220	281	4	.	.	PUNCT
ejpam-4220	282	1	let	let	VERB
ejpam-4220	282	2	g	g	PRON
ejpam-4220	282	3	be	be	AUX
ejpam-4220	282	4	a	a	DET
ejpam-4220	282	5	tree	tree	NOUN
ejpam-4220	282	6	graph	graph	NOUN
ejpam-4220	282	7	,	,	PUNCT
ejpam-4220	282	8	h	h	PRON
ejpam-4220	282	9	be	be	VERB
ejpam-4220	282	10	a	a	DET
ejpam-4220	282	11	rooted	rooted	ADJ
ejpam-4220	282	12	tree	tree	NOUN
ejpam-4220	282	13	and	and	CCONJ
ejpam-4220	282	14	u	u	NOUN
ejpam-4220	282	15	be	be	VERB
ejpam-4220	282	16	its	its	PRON
ejpam-4220	282	17	rooted	rooted	ADJ
ejpam-4220	282	18	vertex	vertex	NOUN
ejpam-4220	282	19	.	.	PUNCT
ejpam-4220	283	1	if	if	SCONJ
ejpam-4220	283	2	y	y	PROPN
ejpam-4220	283	3	=	=	SYM
ejpam-4220	283	4	u	u	PROPN
ejpam-4220	283	5	and	and	CCONJ
ejpam-4220	283	6	z	z	PROPN
ejpam-4220	283	7	̸=	̸=	PROPN
ejpam-4220	283	8	u	u	NOUN
ejpam-4220	283	9	,	,	PUNCT
ejpam-4220	283	10	then	then	ADV
ejpam-4220	283	11	d((x	d((x	PROPN
ejpam-4220	283	12	,	,	PUNCT
ejpam-4220	283	13	y	y	PROPN
ejpam-4220	283	14	)	)	PUNCT
ejpam-4220	283	15	,	,	PUNCT
ejpam-4220	283	16	(	(	PUNCT
ejpam-4220	283	17	w	w	PROPN
ejpam-4220	283	18	,	,	PUNCT
ejpam-4220	283	19	z	z	NOUN
ejpam-4220	283	20	)	)	PUNCT
ejpam-4220	283	21	)	)	PUNCT
ejpam-4220	284	1	=	=	PUNCT
ejpam-4220	284	2	d((x	d((x	ADJ
ejpam-4220	284	3	,	,	PUNCT
ejpam-4220	284	4	y	y	PROPN
ejpam-4220	284	5	)	)	PUNCT
ejpam-4220	284	6	,	,	PUNCT
ejpam-4220	284	7	(	(	PUNCT
ejpam-4220	284	8	x	x	NOUN
ejpam-4220	284	9	,	,	PUNCT
ejpam-4220	284	10	u	u	NOUN
ejpam-4220	284	11	)	)	PUNCT
ejpam-4220	284	12	)	)	PUNCT
ejpam-4220	285	1	+	+	CCONJ
ejpam-4220	285	2	d((x	d((x	ADJ
ejpam-4220	285	3	,	,	PUNCT
ejpam-4220	285	4	u	u	NOUN
ejpam-4220	285	5	)	)	PUNCT
ejpam-4220	285	6	,	,	PUNCT
ejpam-4220	285	7	(	(	PUNCT
ejpam-4220	285	8	w	w	PROPN
ejpam-4220	285	9	,	,	PUNCT
ejpam-4220	285	10	u	u	NOUN
ejpam-4220	285	11	)	)	PUNCT
ejpam-4220	285	12	)	)	PUNCT
ejpam-4220	286	1	+	+	CCONJ
ejpam-4220	286	2	d((w	d((w	NOUN
ejpam-4220	286	3	,	,	PUNCT
ejpam-4220	286	4	u	u	NOUN
ejpam-4220	286	5	)	)	PUNCT
ejpam-4220	286	6	,	,	PUNCT
ejpam-4220	286	7	(	(	PUNCT
ejpam-4220	286	8	w	w	PROPN
ejpam-4220	286	9	,	,	PUNCT
ejpam-4220	286	10	z	z	NOUN
ejpam-4220	286	11	)	)	PUNCT
ejpam-4220	286	12	)	)	PUNCT
ejpam-4220	286	13	=	=	SYM
ejpam-4220	286	14	0	0	PUNCT
ejpam-4220	287	1	+	+	CCONJ
ejpam-4220	287	2	d((x	d((x	ADJ
ejpam-4220	287	3	,	,	PUNCT
ejpam-4220	287	4	u	u	NOUN
ejpam-4220	287	5	)	)	PUNCT
ejpam-4220	287	6	,	,	PUNCT
ejpam-4220	287	7	(	(	PUNCT
ejpam-4220	287	8	w	w	PROPN
ejpam-4220	287	9	,	,	PUNCT
ejpam-4220	287	10	u	u	NOUN
ejpam-4220	287	11	)	)	PUNCT
ejpam-4220	287	12	)	)	PUNCT
ejpam-4220	288	1	+	+	CCONJ
ejpam-4220	288	2	d((w	d((w	NOUN
ejpam-4220	288	3	,	,	PUNCT
ejpam-4220	288	4	u	u	NOUN
ejpam-4220	288	5	)	)	PUNCT
ejpam-4220	288	6	,	,	PUNCT
ejpam-4220	288	7	(	(	PUNCT
ejpam-4220	288	8	w	w	PROPN
ejpam-4220	288	9	,	,	PUNCT
ejpam-4220	288	10	z	z	NOUN
ejpam-4220	288	11	)	)	PUNCT
ejpam-4220	288	12	)	)	PUNCT
ejpam-4220	289	1	=	=	PUNCT
ejpam-4220	289	2	d((x	d((x	ADJ
ejpam-4220	289	3	,	,	PUNCT
ejpam-4220	289	4	u	u	NOUN
ejpam-4220	289	5	)	)	PUNCT
ejpam-4220	289	6	,	,	PUNCT
ejpam-4220	289	7	(	(	PUNCT
ejpam-4220	289	8	w	w	PROPN
ejpam-4220	289	9	,	,	PUNCT
ejpam-4220	289	10	u	u	NOUN
ejpam-4220	289	11	)	)	PUNCT
ejpam-4220	289	12	)	)	PUNCT
ejpam-4220	290	1	+	+	CCONJ
ejpam-4220	290	2	d((w	d((w	NOUN
ejpam-4220	290	3	,	,	PUNCT
ejpam-4220	290	4	u	u	NOUN
ejpam-4220	290	5	)	)	PUNCT
ejpam-4220	290	6	,	,	PUNCT
ejpam-4220	290	7	(	(	PUNCT
ejpam-4220	290	8	w	w	PROPN
ejpam-4220	290	9	,	,	PUNCT
ejpam-4220	290	10	z	z	NOUN
ejpam-4220	290	11	)	)	PUNCT
ejpam-4220	290	12	)	)	PUNCT
ejpam-4220	291	1	=	=	SYM
ejpam-4220	291	2	d(x	d(x	PROPN
ejpam-4220	291	3	,	,	PUNCT
ejpam-4220	291	4	w	w	NOUN
ejpam-4220	291	5	)	)	PUNCT
ejpam-4220	292	1	+	+	CCONJ
ejpam-4220	292	2	d(u	d(u	PROPN
ejpam-4220	292	3	,	,	PUNCT
ejpam-4220	292	4	z	z	NOUN
ejpam-4220	292	5	)	)	PUNCT
ejpam-4220	292	6	.	.	PUNCT
ejpam-4220	293	1	n.	n.	PROPN
ejpam-4220	293	2	s.	s.	PROPN
ejpam-4220	293	3	abdulcarim	abdulcarim	PROPN
ejpam-4220	293	4	,	,	PUNCT
ejpam-4220	293	5	s.	s.	PROPN
ejpam-4220	293	6	c.	c.	PROPN
ejpam-4220	293	7	dagondon	dagondon	PROPN
ejpam-4220	293	8	/	/	SYM
ejpam-4220	293	9	eur	eur	PROPN
ejpam-4220	293	10	.	.	PUNCT
ejpam-4220	294	1	j.	j.	PROPN
ejpam-4220	294	2	pure	pure	PROPN
ejpam-4220	294	3	appl	appl	PROPN
ejpam-4220	294	4	.	.	PROPN
ejpam-4220	294	5	math	math	PROPN
ejpam-4220	294	6	,	,	PUNCT
ejpam-4220	294	7	15	15	NUM
ejpam-4220	294	8	(	(	PUNCT
ejpam-4220	294	9	1	1	NUM
ejpam-4220	294	10	)	)	PUNCT
ejpam-4220	294	11	(	(	PUNCT
ejpam-4220	294	12	2022	2022	NUM
ejpam-4220	294	13	)	)	PUNCT
ejpam-4220	294	14	,	,	PUNCT
ejpam-4220	294	15	64	64	NUM
ejpam-4220	294	16	-	-	SYM
ejpam-4220	294	17	81	81	NUM
ejpam-4220	294	18	75	75	NUM
ejpam-4220	294	19	theorem	theorem	NOUN
ejpam-4220	294	20	4	4	NUM
ejpam-4220	294	21	.	.	PUNCT
ejpam-4220	295	1	let	let	VERB
ejpam-4220	295	2	g	g	NOUN
ejpam-4220	295	3	and	and	CCONJ
ejpam-4220	295	4	rooted	rooted	ADJ
ejpam-4220	295	5	h	h	NOUN
ejpam-4220	295	6	be	be	VERB
ejpam-4220	295	7	trees	tree	NOUN
ejpam-4220	295	8	with	with	ADP
ejpam-4220	295	9	independent	independent	ADJ
ejpam-4220	295	10	neighborhood	neighborhood	NOUN
ejpam-4220	295	11	sets	set	VERB
ejpam-4220	295	12	ω1,∆1	ω1,∆1	NUM
ejpam-4220	295	13	and	and	CCONJ
ejpam-4220	295	14	ω2,∆2	ω2,∆2	PROPN
ejpam-4220	295	15	,	,	PUNCT
ejpam-4220	295	16	respectively	respectively	ADV
ejpam-4220	295	17	.	.	PUNCT
ejpam-4220	296	1	then	then	ADV
ejpam-4220	296	2	the	the	DET
ejpam-4220	296	3	independent	independent	ADJ
ejpam-4220	296	4	neighborhood	neighborhood	NOUN
ejpam-4220	296	5	sets	set	NOUN
ejpam-4220	296	6	of	of	ADP
ejpam-4220	296	7	g	g	PROPN
ejpam-4220	296	8	•h	•h	VERB
ejpam-4220	296	9	are	be	AUX
ejpam-4220	296	10	{	{	PUNCT
ejpam-4220	296	11	(	(	PUNCT
ejpam-4220	296	12	x	x	NOUN
ejpam-4220	296	13	,	,	PUNCT
ejpam-4220	296	14	y	y	PROPN
ejpam-4220	296	15	)	)	PUNCT
ejpam-4220	296	16	:	:	PUNCT
ejpam-4220	296	17	x	x	X
ejpam-4220	296	18	∈	∈	PROPN
ejpam-4220	296	19	ω1	ω1	PROPN
ejpam-4220	296	20	,	,	PUNCT
ejpam-4220	296	21	y	y	PROPN
ejpam-4220	296	22	∈	∈	PROPN
ejpam-4220	296	23	ω2	ω2	PROPN
ejpam-4220	296	24	}	}	PUNCT
ejpam-4220	296	25	∪	∪	X
ejpam-4220	296	26	{	{	PUNCT
ejpam-4220	296	27	(	(	PUNCT
ejpam-4220	296	28	w	w	PROPN
ejpam-4220	296	29	,	,	PUNCT
ejpam-4220	296	30	z	z	NOUN
ejpam-4220	296	31	)	)	PUNCT
ejpam-4220	296	32	:	:	PUNCT
ejpam-4220	296	33	w	w	X
ejpam-4220	296	34	∈	∈	PROPN
ejpam-4220	296	35	∆1	∆1	PROPN
ejpam-4220	296	36	,	,	PUNCT
ejpam-4220	296	37	z	z	PROPN
ejpam-4220	296	38	∈	∈	PROPN
ejpam-4220	296	39	∆2	∆2	PROPN
ejpam-4220	296	40	}	}	PUNCT
ejpam-4220	296	41	and	and	CCONJ
ejpam-4220	296	42	{	{	PUNCT
ejpam-4220	296	43	(	(	PUNCT
ejpam-4220	296	44	w	w	PROPN
ejpam-4220	296	45	,	,	PUNCT
ejpam-4220	296	46	y	y	PROPN
ejpam-4220	296	47	)	)	PUNCT
ejpam-4220	296	48	:	:	PUNCT
ejpam-4220	296	49	w	w	X
ejpam-4220	296	50	∈	∈	PROPN
ejpam-4220	296	51	∆1	∆1	PROPN
ejpam-4220	296	52	,	,	PUNCT
ejpam-4220	296	53	y	y	PROPN
ejpam-4220	296	54	∈	∈	PROPN
ejpam-4220	296	55	ω2	ω2	PROPN
ejpam-4220	296	56	}	}	PUNCT
ejpam-4220	296	57	∪	∪	X
ejpam-4220	296	58	{	{	PUNCT
ejpam-4220	296	59	(	(	PUNCT
ejpam-4220	296	60	x	x	NOUN
ejpam-4220	296	61	,	,	PUNCT
ejpam-4220	296	62	z	z	NOUN
ejpam-4220	296	63	)	)	PUNCT
ejpam-4220	296	64	:	:	PUNCT
ejpam-4220	296	65	x	x	X
ejpam-4220	296	66	∈	∈	PROPN
ejpam-4220	296	67	ω1	ω1	PROPN
ejpam-4220	296	68	,	,	PUNCT
ejpam-4220	296	69	z	z	PROPN
ejpam-4220	296	70	∈	∈	PROPN
ejpam-4220	296	71	∆2	∆2	PROPN
ejpam-4220	296	72	}	}	PUNCT
ejpam-4220	296	73	.	.	PUNCT
ejpam-4220	297	1	proof	proof	NOUN
ejpam-4220	297	2	.	.	PUNCT
ejpam-4220	298	1	let	let	VERB
ejpam-4220	298	2	g	g	NOUN
ejpam-4220	298	3	and	and	CCONJ
ejpam-4220	298	4	rooted	rooted	ADJ
ejpam-4220	298	5	h	h	NOUN
ejpam-4220	298	6	be	be	VERB
ejpam-4220	298	7	trees	tree	NOUN
ejpam-4220	298	8	with	with	ADP
ejpam-4220	298	9	independent	independent	ADJ
ejpam-4220	298	10	neighborhood	neighborhood	NOUN
ejpam-4220	298	11	sets	set	VERB
ejpam-4220	298	12	ω1,∆1	ω1,∆1	NUM
ejpam-4220	298	13	and	and	CCONJ
ejpam-4220	298	14	ω2,∆2	ω2,∆2	PROPN
ejpam-4220	298	15	,	,	PUNCT
ejpam-4220	298	16	respectively	respectively	ADV
ejpam-4220	298	17	.	.	PUNCT
ejpam-4220	299	1	let	let	VERB
ejpam-4220	299	2	u	u	PRON
ejpam-4220	299	3	be	be	AUX
ejpam-4220	299	4	the	the	DET
ejpam-4220	299	5	root	root	NOUN
ejpam-4220	299	6	vertex	vertex	NOUN
ejpam-4220	299	7	of	of	ADP
ejpam-4220	299	8	h	h	NOUN
ejpam-4220	299	9	and	and	CCONJ
ejpam-4220	299	10	that	that	SCONJ
ejpam-4220	299	11	without	without	ADP
ejpam-4220	299	12	loss	loss	NOUN
ejpam-4220	299	13	of	of	ADP
ejpam-4220	299	14	generality	generality	NOUN
ejpam-4220	299	15	,	,	PUNCT
ejpam-4220	299	16	let	let	VERB
ejpam-4220	299	17	u	u	PRON
ejpam-4220	299	18	∈	∈	PROPN
ejpam-4220	299	19	ω2	ω2	PROPN
ejpam-4220	299	20	.	.	PUNCT
ejpam-4220	300	1	we	we	PRON
ejpam-4220	300	2	will	will	AUX
ejpam-4220	300	3	show	show	VERB
ejpam-4220	300	4	that	that	SCONJ
ejpam-4220	300	5	the	the	DET
ejpam-4220	300	6	sets	set	NOUN
ejpam-4220	300	7	{	{	PUNCT
ejpam-4220	300	8	(	(	PUNCT
ejpam-4220	300	9	x	x	NOUN
ejpam-4220	300	10	,	,	PUNCT
ejpam-4220	300	11	y	y	PROPN
ejpam-4220	300	12	)	)	PUNCT
ejpam-4220	300	13	:	:	PUNCT
ejpam-4220	300	14	x	x	X
ejpam-4220	300	15	∈	∈	PROPN
ejpam-4220	300	16	ω1	ω1	PROPN
ejpam-4220	300	17	,	,	PUNCT
ejpam-4220	300	18	y	y	PROPN
ejpam-4220	300	19	∈	∈	PROPN
ejpam-4220	300	20	ω2	ω2	PROPN
ejpam-4220	300	21	}	}	PUNCT
ejpam-4220	300	22	∪	∪	X
ejpam-4220	300	23	{	{	PUNCT
ejpam-4220	300	24	(	(	PUNCT
ejpam-4220	300	25	w	w	PROPN
ejpam-4220	300	26	,	,	PUNCT
ejpam-4220	300	27	z	z	NOUN
ejpam-4220	300	28	)	)	PUNCT
ejpam-4220	300	29	:	:	PUNCT
ejpam-4220	300	30	w	w	X
ejpam-4220	300	31	∈	∈	PROPN
ejpam-4220	300	32	∆1	∆1	PROPN
ejpam-4220	300	33	,	,	PUNCT
ejpam-4220	300	34	z	z	PROPN
ejpam-4220	300	35	∈	∈	PROPN
ejpam-4220	300	36	∆2	∆2	PROPN
ejpam-4220	300	37	}	}	PUNCT
ejpam-4220	300	38	and	and	CCONJ
ejpam-4220	300	39	{	{	PUNCT
ejpam-4220	300	40	(	(	PUNCT
ejpam-4220	300	41	w	w	PROPN
ejpam-4220	300	42	,	,	PUNCT
ejpam-4220	300	43	y	y	PROPN
ejpam-4220	300	44	)	)	PUNCT
ejpam-4220	300	45	:	:	PUNCT
ejpam-4220	300	46	w	w	X
ejpam-4220	300	47	∈	∈	PROPN
ejpam-4220	300	48	∆1	∆1	PROPN
ejpam-4220	300	49	,	,	PUNCT
ejpam-4220	300	50	y	y	PROPN
ejpam-4220	300	51	∈	∈	PROPN
ejpam-4220	300	52	ω2	ω2	PROPN
ejpam-4220	300	53	}	}	PUNCT
ejpam-4220	300	54	∪	∪	X
ejpam-4220	300	55	{	{	PUNCT
ejpam-4220	300	56	(	(	PUNCT
ejpam-4220	300	57	x	x	NOUN
ejpam-4220	300	58	,	,	PUNCT
ejpam-4220	300	59	z	z	NOUN
ejpam-4220	300	60	)	)	PUNCT
ejpam-4220	300	61	:	:	PUNCT
ejpam-4220	300	62	x	x	X
ejpam-4220	300	63	∈	∈	PROPN
ejpam-4220	300	64	ω1	ω1	PROPN
ejpam-4220	300	65	,	,	PUNCT
ejpam-4220	300	66	z	z	PROPN
ejpam-4220	300	67	∈	∈	PROPN
ejpam-4220	300	68	∆2	∆2	PROPN
ejpam-4220	300	69	}	}	PUNCT
ejpam-4220	300	70	are	be	AUX
ejpam-4220	300	71	the	the	DET
ejpam-4220	300	72	independent	independent	ADJ
ejpam-4220	300	73	neighborhood	neighborhood	NOUN
ejpam-4220	300	74	sets	set	NOUN
ejpam-4220	300	75	of	of	ADP
ejpam-4220	300	76	g	g	PROPN
ejpam-4220	300	77	•h	•h	PROPN
ejpam-4220	300	78	.	.	PUNCT
ejpam-4220	301	1	now	now	ADV
ejpam-4220	301	2	,	,	PUNCT
ejpam-4220	301	3	for	for	ADP
ejpam-4220	301	4	any	any	DET
ejpam-4220	301	5	x	x	PROPN
ejpam-4220	301	6	∈	∈	PROPN
ejpam-4220	301	7	ω1	ω1	PROPN
ejpam-4220	301	8	,	,	PUNCT
ejpam-4220	301	9	y	y	PROPN
ejpam-4220	301	10	∈	∈	PROPN
ejpam-4220	301	11	ω2	ω2	PROPN
ejpam-4220	301	12	,	,	PUNCT
ejpam-4220	301	13	w	w	PROPN
ejpam-4220	301	14	∈	∈	PROPN
ejpam-4220	301	15	∆1	∆1	PUNCT
ejpam-4220	301	16	and	and	CCONJ
ejpam-4220	301	17	z	z	PROPN
ejpam-4220	301	18	∈	∈	PROPN
ejpam-4220	301	19	∆2	∆2	PROPN
ejpam-4220	301	20	,	,	PUNCT
ejpam-4220	301	21	d((x	d((x	PROPN
ejpam-4220	301	22	,	,	PUNCT
ejpam-4220	301	23	y	y	PROPN
ejpam-4220	301	24	)	)	PUNCT
ejpam-4220	301	25	,	,	PUNCT
ejpam-4220	301	26	(	(	PUNCT
ejpam-4220	301	27	w	w	PROPN
ejpam-4220	301	28	,	,	PUNCT
ejpam-4220	301	29	z	z	NOUN
ejpam-4220	301	30	)	)	PUNCT
ejpam-4220	301	31	)	)	PUNCT
ejpam-4220	302	1	=	=	PUNCT
ejpam-4220	302	2	d((x	d((x	ADJ
ejpam-4220	302	3	,	,	PUNCT
ejpam-4220	302	4	y	y	PROPN
ejpam-4220	302	5	)	)	PUNCT
ejpam-4220	302	6	,	,	PUNCT
ejpam-4220	302	7	(	(	PUNCT
ejpam-4220	302	8	x	x	NOUN
ejpam-4220	302	9	,	,	PUNCT
ejpam-4220	302	10	u	u	NOUN
ejpam-4220	302	11	)	)	PUNCT
ejpam-4220	302	12	)	)	PUNCT
ejpam-4220	303	1	+	+	CCONJ
ejpam-4220	303	2	d((x	d((x	ADJ
ejpam-4220	303	3	,	,	PUNCT
ejpam-4220	303	4	u	u	NOUN
ejpam-4220	303	5	)	)	PUNCT
ejpam-4220	303	6	,	,	PUNCT
ejpam-4220	303	7	(	(	PUNCT
ejpam-4220	303	8	w	w	PROPN
ejpam-4220	303	9	,	,	PUNCT
ejpam-4220	303	10	u	u	NOUN
ejpam-4220	303	11	)	)	PUNCT
ejpam-4220	303	12	)	)	PUNCT
ejpam-4220	304	1	+	+	CCONJ
ejpam-4220	304	2	d((w	d((w	NOUN
ejpam-4220	304	3	,	,	PUNCT
ejpam-4220	304	4	u	u	NOUN
ejpam-4220	304	5	)	)	PUNCT
ejpam-4220	304	6	,	,	PUNCT
ejpam-4220	304	7	(	(	PUNCT
ejpam-4220	304	8	w	w	PROPN
ejpam-4220	304	9	,	,	PUNCT
ejpam-4220	304	10	z	z	NOUN
ejpam-4220	304	11	)	)	PUNCT
ejpam-4220	304	12	)	)	PUNCT
ejpam-4220	304	13	.	.	PUNCT
ejpam-4220	305	1	since	since	SCONJ
ejpam-4220	305	2	ω2	ω2	NOUN
ejpam-4220	305	3	is	be	AUX
ejpam-4220	305	4	an	an	DET
ejpam-4220	305	5	independent	independent	ADJ
ejpam-4220	305	6	neighborhood	neighborhood	NOUN
ejpam-4220	305	7	set	set	NOUN
ejpam-4220	305	8	of	of	ADP
ejpam-4220	305	9	h	h	NOUN
ejpam-4220	305	10	,	,	PUNCT
ejpam-4220	305	11	by	by	ADP
ejpam-4220	305	12	theorem	theorem	NOUN
ejpam-4220	305	13	2	2	NUM
ejpam-4220	305	14	,	,	PUNCT
ejpam-4220	305	15	d((x	d((x	ADJ
ejpam-4220	305	16	,	,	PUNCT
ejpam-4220	305	17	y	y	PROPN
ejpam-4220	305	18	)	)	PUNCT
ejpam-4220	305	19	,	,	PUNCT
ejpam-4220	305	20	(	(	PUNCT
ejpam-4220	305	21	x	x	NOUN
ejpam-4220	305	22	,	,	PUNCT
ejpam-4220	305	23	u	u	NOUN
ejpam-4220	305	24	)	)	PUNCT
ejpam-4220	305	25	)	)	PUNCT
ejpam-4220	306	1	=	=	SYM
ejpam-4220	306	2	d(y	d(y	NOUN
ejpam-4220	306	3	,	,	PUNCT
ejpam-4220	306	4	u	u	NOUN
ejpam-4220	306	5	)	)	PUNCT
ejpam-4220	306	6	=	=	SYM
ejpam-4220	306	7	2m	2m	NUM
ejpam-4220	306	8	,	,	PUNCT
ejpam-4220	306	9	m	m	PROPN
ejpam-4220	306	10	∈	∈	NOUN
ejpam-4220	306	11	n∗.	n∗.	PROPN
ejpam-4220	306	12	observe	observe	VERB
ejpam-4220	306	13	that	that	SCONJ
ejpam-4220	306	14	d((x	d((x	NOUN
ejpam-4220	306	15	,	,	PUNCT
ejpam-4220	306	16	u	u	NOUN
ejpam-4220	306	17	)	)	PUNCT
ejpam-4220	306	18	,	,	PUNCT
ejpam-4220	306	19	(	(	PUNCT
ejpam-4220	306	20	w	w	PROPN
ejpam-4220	306	21	,	,	PUNCT
ejpam-4220	306	22	u	u	NOUN
ejpam-4220	306	23	)	)	PUNCT
ejpam-4220	306	24	)	)	PUNCT
ejpam-4220	307	1	=	=	SYM
ejpam-4220	307	2	d(x	d(x	PROPN
ejpam-4220	307	3	,	,	PUNCT
ejpam-4220	307	4	w	w	NOUN
ejpam-4220	307	5	)	)	PUNCT
ejpam-4220	307	6	=	=	SYM
ejpam-4220	307	7	2n	2n	NUM
ejpam-4220	308	1	+	+	CCONJ
ejpam-4220	308	2	1	1	NUM
ejpam-4220	308	3	,	,	PUNCT
ejpam-4220	308	4	n	n	PRON
ejpam-4220	308	5	∈	∈	NOUN
ejpam-4220	308	6	n∗	n∗	NOUN
ejpam-4220	308	7	for	for	ADP
ejpam-4220	308	8	x	x	PROPN
ejpam-4220	308	9	∈	∈	PROPN
ejpam-4220	308	10	ω1	ω1	PROPN
ejpam-4220	308	11	,	,	PUNCT
ejpam-4220	308	12	w	w	PROPN
ejpam-4220	308	13	∈	∈	PROPN
ejpam-4220	308	14	∆1	∆1	PUNCT
ejpam-4220	308	15	and	and	CCONJ
ejpam-4220	308	16	d((w	d((w	NOUN
ejpam-4220	308	17	,	,	PUNCT
ejpam-4220	308	18	u	u	NOUN
ejpam-4220	308	19	)	)	PUNCT
ejpam-4220	308	20	,	,	PUNCT
ejpam-4220	308	21	(	(	PUNCT
ejpam-4220	308	22	w	w	PROPN
ejpam-4220	308	23	,	,	PUNCT
ejpam-4220	308	24	z	z	NOUN
ejpam-4220	308	25	)	)	PUNCT
ejpam-4220	308	26	)	)	PUNCT
ejpam-4220	309	1	=	=	SYM
ejpam-4220	309	2	d(u	d(u	PROPN
ejpam-4220	309	3	,	,	PUNCT
ejpam-4220	309	4	z	z	NOUN
ejpam-4220	309	5	)	)	PUNCT
ejpam-4220	309	6	=	=	SYM
ejpam-4220	310	1	2r	2r	NUM
ejpam-4220	311	1	+	+	CCONJ
ejpam-4220	311	2	1	1	NUM
ejpam-4220	311	3	,	,	PUNCT
ejpam-4220	311	4	r	r	NOUN
ejpam-4220	311	5	∈	∈	PROPN
ejpam-4220	311	6	n∗	n∗	NOUN
ejpam-4220	311	7	for	for	ADP
ejpam-4220	311	8	u	u	PROPN
ejpam-4220	311	9	∈	∈	PROPN
ejpam-4220	311	10	ω2	ω2	PROPN
ejpam-4220	311	11	,	,	PUNCT
ejpam-4220	311	12	z	z	PROPN
ejpam-4220	311	13	∈	∈	PROPN
ejpam-4220	311	14	∆2	∆2	PROPN
ejpam-4220	311	15	.	.	PUNCT
ejpam-4220	312	1	it	it	PRON
ejpam-4220	312	2	follows	follow	VERB
ejpam-4220	312	3	that	that	SCONJ
ejpam-4220	312	4	d((x	d((x	PROPN
ejpam-4220	312	5	,	,	PUNCT
ejpam-4220	312	6	y	y	PROPN
ejpam-4220	312	7	)	)	PUNCT
ejpam-4220	312	8	,	,	PUNCT
ejpam-4220	312	9	(	(	PUNCT
ejpam-4220	312	10	w	w	PROPN
ejpam-4220	312	11	,	,	PUNCT
ejpam-4220	312	12	z	z	NOUN
ejpam-4220	312	13	)	)	PUNCT
ejpam-4220	312	14	)	)	PUNCT
ejpam-4220	313	1	=	=	SYM
ejpam-4220	314	1	2m+(2n+1)+	2m+(2n+1)+	NUM
ejpam-4220	314	2	(	(	PUNCT
ejpam-4220	314	3	2r+1	2r+1	NUM
ejpam-4220	314	4	)	)	PUNCT
ejpam-4220	314	5	=	=	SYM
ejpam-4220	314	6	2(m+n+1	2(m+n+1	NOUN
ejpam-4220	314	7	)	)	PUNCT
ejpam-4220	314	8	,	,	PUNCT
ejpam-4220	314	9	which	which	PRON
ejpam-4220	314	10	is	be	AUX
ejpam-4220	314	11	even	even	ADV
ejpam-4220	314	12	and	and	CCONJ
ejpam-4220	314	13	by	by	ADP
ejpam-4220	314	14	theorem	theorem	NOUN
ejpam-4220	314	15	2	2	NUM
ejpam-4220	314	16	,	,	PUNCT
ejpam-4220	314	17	the	the	DET
ejpam-4220	314	18	set	set	NOUN
ejpam-4220	314	19	{	{	PUNCT
ejpam-4220	314	20	(	(	PUNCT
ejpam-4220	314	21	x	x	NOUN
ejpam-4220	314	22	,	,	PUNCT
ejpam-4220	314	23	y	y	PROPN
ejpam-4220	314	24	)	)	PUNCT
ejpam-4220	314	25	:	:	PUNCT
ejpam-4220	314	26	x	x	X
ejpam-4220	314	27	∈	∈	PROPN
ejpam-4220	314	28	ω1	ω1	PROPN
ejpam-4220	314	29	,	,	PUNCT
ejpam-4220	314	30	y	y	PROPN
ejpam-4220	314	31	∈	∈	PROPN
ejpam-4220	314	32	ω2	ω2	PROPN
ejpam-4220	314	33	}	}	PUNCT
ejpam-4220	314	34	∪	∪	X
ejpam-4220	314	35	{	{	PUNCT
ejpam-4220	314	36	(	(	PUNCT
ejpam-4220	314	37	w	w	PROPN
ejpam-4220	314	38	,	,	PUNCT
ejpam-4220	314	39	z	z	NOUN
ejpam-4220	314	40	)	)	PUNCT
ejpam-4220	314	41	:	:	PUNCT
ejpam-4220	314	42	w	w	X
ejpam-4220	314	43	∈	∈	PROPN
ejpam-4220	314	44	∆1	∆1	PROPN
ejpam-4220	314	45	,	,	PUNCT
ejpam-4220	314	46	z	z	PROPN
ejpam-4220	314	47	∈	∈	PROPN
ejpam-4220	314	48	∆2	∆2	PROPN
ejpam-4220	314	49	}	}	PUNCT
ejpam-4220	314	50	is	be	AUX
ejpam-4220	314	51	an	an	DET
ejpam-4220	314	52	independent	independent	ADJ
ejpam-4220	314	53	neighborhood	neighborhood	NOUN
ejpam-4220	314	54	set	set	NOUN
ejpam-4220	314	55	of	of	ADP
ejpam-4220	314	56	g	g	PROPN
ejpam-4220	314	57	•h	•h	PROPN
ejpam-4220	314	58	.	.	PUNCT
ejpam-4220	315	1	following	follow	VERB
ejpam-4220	315	2	same	same	ADJ
ejpam-4220	315	3	argument	argument	NOUN
ejpam-4220	315	4	for	for	ADP
ejpam-4220	315	5	the	the	DET
ejpam-4220	315	6	set	set	NOUN
ejpam-4220	315	7	{	{	PUNCT
ejpam-4220	315	8	(	(	PUNCT
ejpam-4220	315	9	w	w	PROPN
ejpam-4220	315	10	,	,	PUNCT
ejpam-4220	315	11	y	y	PROPN
ejpam-4220	315	12	)	)	PUNCT
ejpam-4220	315	13	:	:	PUNCT
ejpam-4220	315	14	w	w	X
ejpam-4220	315	15	∈	∈	PROPN
ejpam-4220	315	16	∆1	∆1	PROPN
ejpam-4220	315	17	,	,	PUNCT
ejpam-4220	315	18	y	y	PROPN
ejpam-4220	315	19	∈	∈	PROPN
ejpam-4220	315	20	ω2	ω2	PROPN
ejpam-4220	315	21	}	}	PUNCT
ejpam-4220	315	22	∪	∪	X
ejpam-4220	315	23	{	{	PUNCT
ejpam-4220	315	24	(	(	PUNCT
ejpam-4220	315	25	x	x	NOUN
ejpam-4220	315	26	,	,	PUNCT
ejpam-4220	315	27	z	z	NOUN
ejpam-4220	315	28	)	)	PUNCT
ejpam-4220	315	29	:	:	PUNCT
ejpam-4220	315	30	x	x	X
ejpam-4220	315	31	∈	∈	PROPN
ejpam-4220	315	32	ω1	ω1	PROPN
ejpam-4220	315	33	,	,	PUNCT
ejpam-4220	315	34	z	z	PROPN
ejpam-4220	315	35	∈	∈	PROPN
ejpam-4220	315	36	∆2	∆2	PROPN
ejpam-4220	315	37	}	}	PUNCT
ejpam-4220	315	38	shows	show	VERB
ejpam-4220	315	39	that	that	SCONJ
ejpam-4220	315	40	it	it	PRON
ejpam-4220	315	41	is	be	AUX
ejpam-4220	315	42	also	also	ADV
ejpam-4220	315	43	an	an	DET
ejpam-4220	315	44	independent	independent	ADJ
ejpam-4220	315	45	neighborhood	neighborhood	NOUN
ejpam-4220	315	46	set	set	NOUN
ejpam-4220	315	47	of	of	ADP
ejpam-4220	315	48	g	g	PROPN
ejpam-4220	315	49	•h	•h	PROPN
ejpam-4220	315	50	.	.	PUNCT
ejpam-4220	316	1	■	■	PUNCT
ejpam-4220	316	2	corollary	corollary	ADJ
ejpam-4220	316	3	8	8	NUM
ejpam-4220	316	4	.	.	PUNCT
ejpam-4220	317	1	let	let	VERB
ejpam-4220	317	2	ω1,∆1	ω1,∆1	NOUN
ejpam-4220	317	3	and	and	CCONJ
ejpam-4220	317	4	ω2,∆2	ω2,∆2	NUM
ejpam-4220	317	5	be	be	VERB
ejpam-4220	317	6	the	the	DET
ejpam-4220	317	7	independent	independent	ADJ
ejpam-4220	317	8	neighborhood	neighborhood	NOUN
ejpam-4220	317	9	sets	set	NOUN
ejpam-4220	317	10	of	of	ADP
ejpam-4220	317	11	trees	tree	NOUN
ejpam-4220	317	12	g	g	NOUN
ejpam-4220	317	13	and	and	CCONJ
ejpam-4220	317	14	h	h	NOUN
ejpam-4220	317	15	,	,	PUNCT
ejpam-4220	317	16	respectively	respectively	ADV
ejpam-4220	317	17	.	.	PUNCT
ejpam-4220	318	1	then	then	ADV
ejpam-4220	318	2	ni(g	ni(g	PUNCT
ejpam-4220	318	3	•h	•h	PROPN
ejpam-4220	318	4	,	,	PUNCT
ejpam-4220	318	5	x	x	X
ejpam-4220	318	6	)	)	PUNCT
ejpam-4220	319	1	=	=	SYM
ejpam-4220	319	2	x|ω1||ω2|+|∆1||∆2|	x|ω1||ω2|+|∆1||∆2|	PROPN
ejpam-4220	319	3	+	+	NUM
ejpam-4220	319	4	x|∆1||ω2|+|ω1||∆2|	x|∆1||ω2|+|ω1||∆2|	PROPN
ejpam-4220	319	5	.	.	PUNCT
ejpam-4220	320	1	n.	n.	PROPN
ejpam-4220	320	2	s.	s.	PROPN
ejpam-4220	320	3	abdulcarim	abdulcarim	PROPN
ejpam-4220	320	4	,	,	PUNCT
ejpam-4220	320	5	s.	s.	PROPN
ejpam-4220	320	6	c.	c.	PROPN
ejpam-4220	320	7	dagondon	dagondon	PROPN
ejpam-4220	320	8	/	/	SYM
ejpam-4220	320	9	eur	eur	PROPN
ejpam-4220	320	10	.	.	PUNCT
ejpam-4220	321	1	j.	j.	PROPN
ejpam-4220	321	2	pure	pure	PROPN
ejpam-4220	321	3	appl	appl	PROPN
ejpam-4220	321	4	.	.	PROPN
ejpam-4220	321	5	math	math	PROPN
ejpam-4220	321	6	,	,	PUNCT
ejpam-4220	321	7	15	15	NUM
ejpam-4220	321	8	(	(	PUNCT
ejpam-4220	321	9	1	1	NUM
ejpam-4220	321	10	)	)	PUNCT
ejpam-4220	321	11	(	(	PUNCT
ejpam-4220	321	12	2022	2022	NUM
ejpam-4220	321	13	)	)	PUNCT
ejpam-4220	321	14	,	,	PUNCT
ejpam-4220	321	15	64	64	NUM
ejpam-4220	321	16	-	-	SYM
ejpam-4220	321	17	81	81	NUM
ejpam-4220	321	18	76	76	NUM
ejpam-4220	321	19	example	example	NOUN
ejpam-4220	321	20	6	6	NUM
ejpam-4220	321	21	.	.	PUNCT
ejpam-4220	321	22	consider	consider	VERB
ejpam-4220	321	23	the	the	DET
ejpam-4220	321	24	graph	graph	NOUN
ejpam-4220	321	25	g	g	NOUN
ejpam-4220	321	26	and	and	CCONJ
ejpam-4220	321	27	graph	graph	NOUN
ejpam-4220	321	28	h	h	NOUN
ejpam-4220	321	29	in	in	ADP
ejpam-4220	321	30	figure	figure	NOUN
ejpam-4220	321	31	5	5	NUM
ejpam-4220	321	32	.	.	PUNCT
ejpam-4220	322	1	a	a	DET
ejpam-4220	322	2	b	b	NOUN
ejpam-4220	322	3	c	c	NOUN
ejpam-4220	322	4	d	d	X
ejpam-4220	322	5	e	e	X
ejpam-4220	322	6	g	g	NOUN
ejpam-4220	322	7	:	:	PUNCT
ejpam-4220	322	8	1	1	NUM
ejpam-4220	322	9	2	2	NUM
ejpam-4220	322	10	3	3	NUM
ejpam-4220	322	11	45	45	NUM
ejpam-4220	322	12	6	6	NUM
ejpam-4220	322	13	78	78	NUM
ejpam-4220	322	14	h	h	NOUN
ejpam-4220	322	15	:	:	PUNCT
ejpam-4220	322	16	figure	figure	VERB
ejpam-4220	322	17	5	5	NUM
ejpam-4220	322	18	:	:	PUNCT
ejpam-4220	322	19	trees	tree	NOUN
ejpam-4220	322	20	g	g	PROPN
ejpam-4220	323	1	and	and	CCONJ
ejpam-4220	323	2	h	h	NOUN
ejpam-4220	323	3	let	let	VERB
ejpam-4220	323	4	the	the	DET
ejpam-4220	323	5	vertex	vertex	NOUN
ejpam-4220	323	6	2	2	NUM
ejpam-4220	323	7	be	be	AUX
ejpam-4220	323	8	a	a	DET
ejpam-4220	323	9	rooted	rooted	ADJ
ejpam-4220	323	10	vertex	vertex	NOUN
ejpam-4220	323	11	and	and	CCONJ
ejpam-4220	323	12	label	label	VERB
ejpam-4220	323	13	the	the	DET
ejpam-4220	323	14	rooted	rooted	ADJ
ejpam-4220	323	15	tree	tree	NOUN
ejpam-4220	323	16	as	as	ADP
ejpam-4220	323	17	h1	h1	PROPN
ejpam-4220	323	18	.	.	PUNCT
ejpam-4220	324	1	then	then	ADV
ejpam-4220	324	2	the	the	DET
ejpam-4220	324	3	rooted	rooted	ADJ
ejpam-4220	324	4	product	product	NOUN
ejpam-4220	324	5	of	of	ADP
ejpam-4220	324	6	g	g	PROPN
ejpam-4220	324	7	and	and	CCONJ
ejpam-4220	324	8	h1	h1	PROPN
ejpam-4220	324	9	is	be	AUX
ejpam-4220	324	10	given	give	VERB
ejpam-4220	324	11	in	in	ADP
ejpam-4220	324	12	figure	figure	NOUN
ejpam-4220	324	13	6	6	NUM
ejpam-4220	324	14	.	.	PUNCT
ejpam-4220	325	1	(	(	PUNCT
ejpam-4220	325	2	a	a	DET
ejpam-4220	325	3	,	,	PUNCT
ejpam-4220	325	4	1	1	NUM
ejpam-4220	325	5	)	)	PUNCT
ejpam-4220	325	6	(	(	PUNCT
ejpam-4220	325	7	a	a	DET
ejpam-4220	325	8	,	,	PUNCT
ejpam-4220	325	9	2	2	NUM
ejpam-4220	325	10	)	)	PUNCT
ejpam-4220	325	11	(	(	PUNCT
ejpam-4220	325	12	a	a	DET
ejpam-4220	325	13	,	,	PUNCT
ejpam-4220	325	14	3	3	NUM
ejpam-4220	325	15	)	)	PUNCT
ejpam-4220	325	16	(	(	PUNCT
ejpam-4220	325	17	a	a	PRON
ejpam-4220	325	18	,	,	PUNCT
ejpam-4220	325	19	4)(a	4)(a	NOUN
ejpam-4220	325	20	,	,	PUNCT
ejpam-4220	325	21	5	5	NUM
ejpam-4220	325	22	)	)	PUNCT
ejpam-4220	325	23	(	(	PUNCT
ejpam-4220	325	24	a	a	DET
ejpam-4220	325	25	,	,	PUNCT
ejpam-4220	325	26	6	6	NUM
ejpam-4220	325	27	)	)	PUNCT
ejpam-4220	325	28	(	(	PUNCT
ejpam-4220	325	29	a	a	DET
ejpam-4220	325	30	,	,	PUNCT
ejpam-4220	325	31	7)(a	7)(a	NUM
ejpam-4220	325	32	,	,	PUNCT
ejpam-4220	325	33	8)	8)	NUM
ejpam-4220	325	34	(	(	PUNCT
ejpam-4220	325	35	b	b	NOUN
ejpam-4220	325	36	,	,	PUNCT
ejpam-4220	325	37	1	1	NUM
ejpam-4220	325	38	)	)	PUNCT
ejpam-4220	325	39	(	(	PUNCT
ejpam-4220	325	40	b	b	NOUN
ejpam-4220	325	41	,	,	PUNCT
ejpam-4220	325	42	2	2	NUM
ejpam-4220	325	43	)	)	PUNCT
ejpam-4220	325	44	(	(	PUNCT
ejpam-4220	325	45	b	b	NOUN
ejpam-4220	325	46	,	,	PUNCT
ejpam-4220	325	47	3	3	NUM
ejpam-4220	325	48	)	)	PUNCT
ejpam-4220	325	49	(	(	PUNCT
ejpam-4220	325	50	b	b	NOUN
ejpam-4220	325	51	,	,	PUNCT
ejpam-4220	325	52	4)(b	4)(b	NUM
ejpam-4220	325	53	,	,	PUNCT
ejpam-4220	325	54	5	5	NUM
ejpam-4220	325	55	)	)	PUNCT
ejpam-4220	325	56	(	(	PUNCT
ejpam-4220	325	57	b	b	NOUN
ejpam-4220	325	58	,	,	PUNCT
ejpam-4220	325	59	6	6	NUM
ejpam-4220	325	60	)	)	PUNCT
ejpam-4220	325	61	(	(	PUNCT
ejpam-4220	325	62	b	b	NOUN
ejpam-4220	325	63	,	,	PUNCT
ejpam-4220	325	64	7)(b	7)(b	NUM
ejpam-4220	325	65	,	,	PUNCT
ejpam-4220	325	66	8)	8)	NUM
ejpam-4220	325	67	(	(	PUNCT
ejpam-4220	325	68	d	d	PROPN
ejpam-4220	325	69	,	,	PUNCT
ejpam-4220	325	70	1	1	NUM
ejpam-4220	325	71	)	)	PUNCT
ejpam-4220	325	72	(	(	PUNCT
ejpam-4220	325	73	d	d	NOUN
ejpam-4220	325	74	,	,	PUNCT
ejpam-4220	325	75	2	2	NUM
ejpam-4220	325	76	)	)	PUNCT
ejpam-4220	325	77	(	(	PUNCT
ejpam-4220	325	78	d	d	NOUN
ejpam-4220	325	79	,	,	PUNCT
ejpam-4220	325	80	3	3	NUM
ejpam-4220	325	81	)	)	PUNCT
ejpam-4220	325	82	(	(	PUNCT
ejpam-4220	325	83	d	d	X
ejpam-4220	325	84	,	,	PUNCT
ejpam-4220	325	85	4)(d	4)(d	NUM
ejpam-4220	325	86	,	,	PUNCT
ejpam-4220	325	87	5	5	NUM
ejpam-4220	325	88	)	)	PUNCT
ejpam-4220	325	89	(	(	PUNCT
ejpam-4220	325	90	d	d	NOUN
ejpam-4220	325	91	,	,	PUNCT
ejpam-4220	325	92	6	6	NUM
ejpam-4220	325	93	)	)	PUNCT
ejpam-4220	325	94	(	(	PUNCT
ejpam-4220	325	95	d	d	NOUN
ejpam-4220	325	96	,	,	PUNCT
ejpam-4220	325	97	7)(d	7)(d	NUM
ejpam-4220	325	98	,	,	PUNCT
ejpam-4220	325	99	8)	8)	NUM
ejpam-4220	325	100	(	(	PUNCT
ejpam-4220	325	101	c	c	NOUN
ejpam-4220	325	102	,	,	PUNCT
ejpam-4220	325	103	1	1	NUM
ejpam-4220	325	104	)	)	PUNCT
ejpam-4220	325	105	(	(	PUNCT
ejpam-4220	325	106	c	c	X
ejpam-4220	325	107	,	,	PUNCT
ejpam-4220	325	108	2	2	NUM
ejpam-4220	325	109	)	)	PUNCT
ejpam-4220	325	110	(	(	PUNCT
ejpam-4220	325	111	c	c	X
ejpam-4220	325	112	,	,	PUNCT
ejpam-4220	325	113	3	3	NUM
ejpam-4220	325	114	)	)	PUNCT
ejpam-4220	325	115	(	(	PUNCT
ejpam-4220	325	116	c	c	X
ejpam-4220	325	117	,	,	PUNCT
ejpam-4220	325	118	4)(c	4)(c	NUM
ejpam-4220	325	119	,	,	PUNCT
ejpam-4220	325	120	5	5	NUM
ejpam-4220	325	121	)	)	PUNCT
ejpam-4220	325	122	(	(	PUNCT
ejpam-4220	325	123	c	c	X
ejpam-4220	325	124	,	,	PUNCT
ejpam-4220	325	125	6	6	NUM
ejpam-4220	325	126	)	)	PUNCT
ejpam-4220	325	127	(	(	PUNCT
ejpam-4220	325	128	c	c	X
ejpam-4220	325	129	,	,	PUNCT
ejpam-4220	325	130	7)(c	7)(c	NUM
ejpam-4220	325	131	,	,	PUNCT
ejpam-4220	325	132	8)	8)	NUM
ejpam-4220	325	133	(	(	PUNCT
ejpam-4220	325	134	e	e	NOUN
ejpam-4220	325	135	,	,	PUNCT
ejpam-4220	325	136	1	1	NUM
ejpam-4220	325	137	)	)	PUNCT
ejpam-4220	325	138	(	(	PUNCT
ejpam-4220	325	139	e	e	NOUN
ejpam-4220	325	140	,	,	PUNCT
ejpam-4220	325	141	2	2	NUM
ejpam-4220	325	142	)	)	PUNCT
ejpam-4220	325	143	(	(	PUNCT
ejpam-4220	325	144	e	e	NOUN
ejpam-4220	325	145	,	,	PUNCT
ejpam-4220	325	146	3	3	NUM
ejpam-4220	325	147	)	)	PUNCT
ejpam-4220	325	148	(	(	PUNCT
ejpam-4220	325	149	e	e	NOUN
ejpam-4220	325	150	,	,	PUNCT
ejpam-4220	325	151	4)(e	4)(e	NUM
ejpam-4220	325	152	,	,	PUNCT
ejpam-4220	325	153	5	5	NUM
ejpam-4220	325	154	)	)	PUNCT
ejpam-4220	325	155	(	(	PUNCT
ejpam-4220	325	156	e	e	NOUN
ejpam-4220	325	157	,	,	PUNCT
ejpam-4220	325	158	6	6	NUM
ejpam-4220	325	159	)	)	PUNCT
ejpam-4220	325	160	(	(	PUNCT
ejpam-4220	325	161	e	e	NOUN
ejpam-4220	325	162	,	,	PUNCT
ejpam-4220	325	163	7)(e	7)(e	NUM
ejpam-4220	325	164	,	,	PUNCT
ejpam-4220	325	165	8)	8)	NUM
ejpam-4220	325	166	figure	figure	NOUN
ejpam-4220	325	167	6	6	NUM
ejpam-4220	325	168	:	:	PUNCT
ejpam-4220	325	169	rooted	rooted	ADJ
ejpam-4220	325	170	product	product	NOUN
ejpam-4220	325	171	of	of	ADP
ejpam-4220	325	172	graph	graph	NOUN
ejpam-4220	325	173	g	g	NOUN
ejpam-4220	325	174	and	and	CCONJ
ejpam-4220	325	175	rooted	rooted	ADJ
ejpam-4220	325	176	graph	graph	NOUN
ejpam-4220	325	177	h1	h1	PROPN
ejpam-4220	326	1	we	we	PRON
ejpam-4220	326	2	note	note	VERB
ejpam-4220	326	3	that	that	SCONJ
ejpam-4220	326	4	the	the	DET
ejpam-4220	326	5	independent	independent	ADJ
ejpam-4220	326	6	neighborhood	neighborhood	NOUN
ejpam-4220	326	7	sets	set	NOUN
ejpam-4220	326	8	of	of	ADP
ejpam-4220	326	9	g	g	NOUN
ejpam-4220	326	10	are	be	AUX
ejpam-4220	326	11	ω1	ω1	PROPN
ejpam-4220	326	12	=	=	PUNCT
ejpam-4220	326	13	{	{	PUNCT
ejpam-4220	326	14	a	a	X
ejpam-4220	326	15	,	,	PUNCT
ejpam-4220	326	16	d	d	NOUN
ejpam-4220	326	17	,	,	PUNCT
ejpam-4220	326	18	c	c	NOUN
ejpam-4220	326	19	}	}	PUNCT
ejpam-4220	326	20	,	,	PUNCT
ejpam-4220	326	21	∆1	∆1	PUNCT
ejpam-4220	326	22	=	=	SYM
ejpam-4220	326	23	{	{	PUNCT
ejpam-4220	326	24	b	b	NOUN
ejpam-4220	326	25	,	,	PUNCT
ejpam-4220	326	26	e	e	NOUN
ejpam-4220	326	27	}	}	PUNCT
ejpam-4220	326	28	and	and	CCONJ
ejpam-4220	326	29	the	the	DET
ejpam-4220	326	30	independent	independent	ADJ
ejpam-4220	326	31	neighborhood	neighborhood	NOUN
ejpam-4220	326	32	sets	set	NOUN
ejpam-4220	326	33	of	of	ADP
ejpam-4220	326	34	h1	h1	NOUN
ejpam-4220	326	35	are	be	AUX
ejpam-4220	326	36	ω2	ω2	ADJ
ejpam-4220	326	37	=	=	PUNCT
ejpam-4220	326	38	{	{	PUNCT
ejpam-4220	326	39	2	2	NUM
ejpam-4220	326	40	,	,	PUNCT
ejpam-4220	326	41	4	4	NUM
ejpam-4220	326	42	,	,	PUNCT
ejpam-4220	326	43	5	5	NUM
ejpam-4220	326	44	,	,	PUNCT
ejpam-4220	326	45	7	7	NUM
ejpam-4220	326	46	,	,	PUNCT
ejpam-4220	326	47	8	8	NUM
ejpam-4220	326	48	}	}	PUNCT
ejpam-4220	326	49	,	,	PUNCT
ejpam-4220	326	50	∆2	∆2	X
ejpam-4220	326	51	=	=	PUNCT
ejpam-4220	326	52	{	{	PUNCT
ejpam-4220	326	53	1	1	NUM
ejpam-4220	326	54	,	,	PUNCT
ejpam-4220	326	55	3	3	NUM
ejpam-4220	326	56	,	,	PUNCT
ejpam-4220	326	57	6	6	NUM
ejpam-4220	326	58	}	}	PUNCT
ejpam-4220	326	59	.	.	PUNCT
ejpam-4220	327	1	by	by	ADP
ejpam-4220	327	2	theorem	theorem	NOUN
ejpam-4220	327	3	4	4	NUM
ejpam-4220	327	4	,	,	PUNCT
ejpam-4220	327	5	the	the	DET
ejpam-4220	327	6	independent	independent	ADJ
ejpam-4220	327	7	neighborhood	neighborhood	NOUN
ejpam-4220	327	8	sets	set	NOUN
ejpam-4220	327	9	of	of	ADP
ejpam-4220	327	10	g	g	PROPN
ejpam-4220	327	11	•h1	•h1	NUM
ejpam-4220	327	12	are	be	AUX
ejpam-4220	327	13	{	{	PUNCT
ejpam-4220	327	14	(	(	PUNCT
ejpam-4220	327	15	x	x	NOUN
ejpam-4220	327	16	,	,	PUNCT
ejpam-4220	327	17	y	y	PROPN
ejpam-4220	327	18	)	)	PUNCT
ejpam-4220	327	19	:	:	PUNCT
ejpam-4220	328	1	x	x	X
ejpam-4220	328	2	∈	∈	PROPN
ejpam-4220	328	3	ω1	ω1	PROPN
ejpam-4220	328	4	,	,	PUNCT
ejpam-4220	328	5	y	y	PROPN
ejpam-4220	328	6	∈	∈	PROPN
ejpam-4220	328	7	ω2	ω2	PROPN
ejpam-4220	328	8	}	}	PUNCT
ejpam-4220	328	9	∪	∪	X
ejpam-4220	328	10	{	{	PUNCT
ejpam-4220	328	11	(	(	PUNCT
ejpam-4220	328	12	w	w	PROPN
ejpam-4220	328	13	,	,	PUNCT
ejpam-4220	328	14	z	z	NOUN
ejpam-4220	328	15	)	)	PUNCT
ejpam-4220	328	16	:	:	PUNCT
ejpam-4220	328	17	w	w	X
ejpam-4220	328	18	∈	∈	PROPN
ejpam-4220	328	19	∆1	∆1	PROPN
ejpam-4220	328	20	,	,	PUNCT
ejpam-4220	328	21	z	z	PROPN
ejpam-4220	328	22	∈	∈	PROPN
ejpam-4220	328	23	∆2	∆2	PROPN
ejpam-4220	328	24	}	}	PUNCT
ejpam-4220	328	25	=	=	SYM
ejpam-4220	328	26	{	{	PUNCT
ejpam-4220	328	27	(	(	PUNCT
ejpam-4220	328	28	a	a	PRON
ejpam-4220	328	29	,	,	PUNCT
ejpam-4220	328	30	2	2	NUM
ejpam-4220	328	31	)	)	PUNCT
ejpam-4220	328	32	,	,	PUNCT
ejpam-4220	328	33	(	(	PUNCT
ejpam-4220	328	34	a	a	PRON
ejpam-4220	328	35	,	,	PUNCT
ejpam-4220	328	36	4	4	NUM
ejpam-4220	328	37	)	)	PUNCT
ejpam-4220	328	38	,	,	PUNCT
ejpam-4220	328	39	(	(	PUNCT
ejpam-4220	328	40	a	a	PRON
ejpam-4220	328	41	,	,	PUNCT
ejpam-4220	328	42	5	5	NUM
ejpam-4220	328	43	)	)	PUNCT
ejpam-4220	328	44	,	,	PUNCT
ejpam-4220	328	45	(	(	PUNCT
ejpam-4220	328	46	a	a	PRON
ejpam-4220	328	47	,	,	PUNCT
ejpam-4220	328	48	7	7	NUM
ejpam-4220	328	49	)	)	PUNCT
ejpam-4220	328	50	,	,	PUNCT
ejpam-4220	328	51	(	(	PUNCT
ejpam-4220	328	52	a	a	DET
ejpam-4220	328	53	,	,	PUNCT
ejpam-4220	328	54	8)	8)	NUM
ejpam-4220	328	55	,	,	PUNCT
ejpam-4220	328	56	(	(	PUNCT
ejpam-4220	328	57	d	d	NOUN
ejpam-4220	328	58	,	,	PUNCT
ejpam-4220	328	59	2	2	NUM
ejpam-4220	328	60	)	)	PUNCT
ejpam-4220	328	61	,	,	PUNCT
ejpam-4220	328	62	(	(	PUNCT
ejpam-4220	328	63	d	d	X
ejpam-4220	328	64	,	,	PUNCT
ejpam-4220	328	65	4	4	NUM
ejpam-4220	328	66	)	)	PUNCT
ejpam-4220	328	67	,	,	PUNCT
ejpam-4220	328	68	(	(	PUNCT
ejpam-4220	328	69	d	d	X
ejpam-4220	328	70	,	,	PUNCT
ejpam-4220	328	71	5	5	NUM
ejpam-4220	328	72	)	)	PUNCT
ejpam-4220	328	73	,	,	PUNCT
ejpam-4220	328	74	(	(	PUNCT
ejpam-4220	328	75	d	d	X
ejpam-4220	328	76	,	,	PUNCT
ejpam-4220	328	77	7	7	NUM
ejpam-4220	328	78	)	)	PUNCT
ejpam-4220	328	79	,	,	PUNCT
ejpam-4220	328	80	(	(	PUNCT
ejpam-4220	328	81	d	d	NOUN
ejpam-4220	328	82	,	,	PUNCT
ejpam-4220	328	83	8)	8)	NUM
ejpam-4220	328	84	,	,	PUNCT
ejpam-4220	328	85	(	(	PUNCT
ejpam-4220	328	86	c	c	X
ejpam-4220	328	87	,	,	PUNCT
ejpam-4220	328	88	2	2	NUM
ejpam-4220	328	89	)	)	PUNCT
ejpam-4220	328	90	,	,	PUNCT
ejpam-4220	328	91	(	(	PUNCT
ejpam-4220	328	92	c	c	X
ejpam-4220	328	93	,	,	PUNCT
ejpam-4220	328	94	4	4	NUM
ejpam-4220	328	95	)	)	PUNCT
ejpam-4220	328	96	,	,	PUNCT
ejpam-4220	328	97	(	(	PUNCT
ejpam-4220	328	98	c	c	X
ejpam-4220	328	99	,	,	PUNCT
ejpam-4220	328	100	5	5	NUM
ejpam-4220	328	101	)	)	PUNCT
ejpam-4220	328	102	,	,	PUNCT
ejpam-4220	328	103	(	(	PUNCT
ejpam-4220	328	104	c	c	X
ejpam-4220	328	105	,	,	PUNCT
ejpam-4220	328	106	7	7	NUM
ejpam-4220	328	107	)	)	PUNCT
ejpam-4220	328	108	,	,	PUNCT
ejpam-4220	328	109	(	(	PUNCT
ejpam-4220	328	110	c	c	X
ejpam-4220	328	111	,	,	PUNCT
ejpam-4220	328	112	8)	8)	NUM
ejpam-4220	328	113	}	}	PUNCT
ejpam-4220	328	114	∪	∪	X
ejpam-4220	328	115	{	{	PUNCT
ejpam-4220	328	116	(	(	PUNCT
ejpam-4220	328	117	b	b	NOUN
ejpam-4220	328	118	,	,	PUNCT
ejpam-4220	328	119	1	1	NUM
ejpam-4220	328	120	)	)	PUNCT
ejpam-4220	328	121	,	,	PUNCT
ejpam-4220	328	122	(	(	PUNCT
ejpam-4220	328	123	b	b	X
ejpam-4220	328	124	,	,	PUNCT
ejpam-4220	328	125	3	3	NUM
ejpam-4220	328	126	)	)	PUNCT
ejpam-4220	328	127	,	,	PUNCT
ejpam-4220	328	128	(	(	PUNCT
ejpam-4220	328	129	b	b	X
ejpam-4220	328	130	,	,	PUNCT
ejpam-4220	328	131	6	6	NUM
ejpam-4220	328	132	)	)	PUNCT
ejpam-4220	328	133	,	,	PUNCT
ejpam-4220	328	134	(	(	PUNCT
ejpam-4220	328	135	e	e	NOUN
ejpam-4220	328	136	,	,	PUNCT
ejpam-4220	328	137	1	1	NUM
ejpam-4220	328	138	)	)	PUNCT
ejpam-4220	328	139	,	,	PUNCT
ejpam-4220	328	140	(	(	PUNCT
ejpam-4220	328	141	e	e	NOUN
ejpam-4220	328	142	,	,	PUNCT
ejpam-4220	328	143	3	3	NUM
ejpam-4220	328	144	)	)	PUNCT
ejpam-4220	328	145	,	,	PUNCT
ejpam-4220	328	146	(	(	PUNCT
ejpam-4220	328	147	e	e	NOUN
ejpam-4220	328	148	,	,	PUNCT
ejpam-4220	328	149	6	6	NUM
ejpam-4220	328	150	)	)	PUNCT
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ejpam-4220	328	152	=	=	SYM
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ejpam-4220	328	154	(	(	PUNCT
ejpam-4220	328	155	a	a	PRON
ejpam-4220	328	156	,	,	PUNCT
ejpam-4220	328	157	2	2	NUM
ejpam-4220	328	158	)	)	PUNCT
ejpam-4220	328	159	,	,	PUNCT
ejpam-4220	328	160	(	(	PUNCT
ejpam-4220	328	161	a	a	PRON
ejpam-4220	328	162	,	,	PUNCT
ejpam-4220	328	163	4	4	NUM
ejpam-4220	328	164	)	)	PUNCT
ejpam-4220	328	165	,	,	PUNCT
ejpam-4220	328	166	(	(	PUNCT
ejpam-4220	328	167	a	a	PRON
ejpam-4220	328	168	,	,	PUNCT
ejpam-4220	328	169	5	5	NUM
ejpam-4220	328	170	)	)	PUNCT
ejpam-4220	328	171	,	,	PUNCT
ejpam-4220	328	172	(	(	PUNCT
ejpam-4220	328	173	a	a	PRON
ejpam-4220	328	174	,	,	PUNCT
ejpam-4220	328	175	7	7	NUM
ejpam-4220	328	176	)	)	PUNCT
ejpam-4220	328	177	,	,	PUNCT
ejpam-4220	328	178	(	(	PUNCT
ejpam-4220	328	179	a	a	PRON
ejpam-4220	328	180	,	,	PUNCT
ejpam-4220	328	181	8)	8)	NUM
ejpam-4220	328	182	,	,	PUNCT
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ejpam-4220	328	184	d	d	NOUN
ejpam-4220	328	185	,	,	PUNCT
ejpam-4220	328	186	2	2	NUM
ejpam-4220	328	187	)	)	PUNCT
ejpam-4220	328	188	,	,	PUNCT
ejpam-4220	328	189	(	(	PUNCT
ejpam-4220	328	190	d	d	X
ejpam-4220	328	191	,	,	PUNCT
ejpam-4220	328	192	4	4	NUM
ejpam-4220	328	193	)	)	PUNCT
ejpam-4220	328	194	,	,	PUNCT
ejpam-4220	328	195	(	(	PUNCT
ejpam-4220	328	196	d	d	X
ejpam-4220	328	197	,	,	PUNCT
ejpam-4220	328	198	5	5	NUM
ejpam-4220	328	199	)	)	PUNCT
ejpam-4220	328	200	,	,	PUNCT
ejpam-4220	328	201	(	(	PUNCT
ejpam-4220	328	202	d	d	X
ejpam-4220	328	203	,	,	PUNCT
ejpam-4220	328	204	7	7	NUM
ejpam-4220	328	205	)	)	PUNCT
ejpam-4220	328	206	,	,	PUNCT
ejpam-4220	328	207	(	(	PUNCT
ejpam-4220	328	208	d	d	NOUN
ejpam-4220	328	209	,	,	PUNCT
ejpam-4220	328	210	8)	8)	NUM
ejpam-4220	328	211	,	,	PUNCT
ejpam-4220	328	212	(	(	PUNCT
ejpam-4220	328	213	c	c	X
ejpam-4220	328	214	,	,	PUNCT
ejpam-4220	328	215	2	2	NUM
ejpam-4220	328	216	)	)	PUNCT
ejpam-4220	328	217	,	,	PUNCT
ejpam-4220	328	218	(	(	PUNCT
ejpam-4220	328	219	c	c	X
ejpam-4220	328	220	,	,	PUNCT
ejpam-4220	328	221	4	4	NUM
ejpam-4220	328	222	)	)	PUNCT
ejpam-4220	328	223	,	,	PUNCT
ejpam-4220	328	224	(	(	PUNCT
ejpam-4220	328	225	c	c	X
ejpam-4220	328	226	,	,	PUNCT
ejpam-4220	328	227	5	5	NUM
ejpam-4220	328	228	)	)	PUNCT
ejpam-4220	328	229	,	,	PUNCT
ejpam-4220	328	230	(	(	PUNCT
ejpam-4220	328	231	c	c	X
ejpam-4220	328	232	,	,	PUNCT
ejpam-4220	328	233	7	7	NUM
ejpam-4220	328	234	)	)	PUNCT
ejpam-4220	328	235	,	,	PUNCT
ejpam-4220	328	236	(	(	PUNCT
ejpam-4220	328	237	c	c	X
ejpam-4220	328	238	,	,	PUNCT
ejpam-4220	328	239	8)	8)	NUM
ejpam-4220	328	240	,	,	PUNCT
ejpam-4220	328	241	(	(	PUNCT
ejpam-4220	328	242	b	b	NOUN
ejpam-4220	328	243	,	,	PUNCT
ejpam-4220	328	244	1	1	NUM
ejpam-4220	328	245	)	)	PUNCT
ejpam-4220	328	246	,	,	PUNCT
ejpam-4220	328	247	(	(	PUNCT
ejpam-4220	328	248	b	b	X
ejpam-4220	328	249	,	,	PUNCT
ejpam-4220	328	250	3	3	NUM
ejpam-4220	328	251	)	)	PUNCT
ejpam-4220	328	252	,	,	PUNCT
ejpam-4220	328	253	(	(	PUNCT
ejpam-4220	328	254	b	b	X
ejpam-4220	328	255	,	,	PUNCT
ejpam-4220	328	256	6	6	NUM
ejpam-4220	328	257	)	)	PUNCT
ejpam-4220	328	258	,	,	PUNCT
ejpam-4220	328	259	(	(	PUNCT
ejpam-4220	328	260	e	e	NOUN
ejpam-4220	328	261	,	,	PUNCT
ejpam-4220	328	262	1	1	NUM
ejpam-4220	328	263	)	)	PUNCT
ejpam-4220	328	264	,	,	PUNCT
ejpam-4220	328	265	(	(	PUNCT
ejpam-4220	328	266	e	e	NOUN
ejpam-4220	328	267	,	,	PUNCT
ejpam-4220	328	268	3	3	NUM
ejpam-4220	328	269	)	)	PUNCT
ejpam-4220	328	270	,	,	PUNCT
ejpam-4220	328	271	(	(	PUNCT
ejpam-4220	328	272	e	e	NOUN
ejpam-4220	328	273	,	,	PUNCT
ejpam-4220	328	274	6	6	NUM
ejpam-4220	328	275	)	)	PUNCT
ejpam-4220	328	276	}	}	PUNCT
ejpam-4220	328	277	n.	n.	PROPN
ejpam-4220	328	278	s.	s.	PROPN
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ejpam-4220	328	280	,	,	PUNCT
ejpam-4220	328	281	s.	s.	PROPN
ejpam-4220	328	282	c.	c.	PROPN
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ejpam-4220	328	284	/	/	SYM
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ejpam-4220	328	286	.	.	PUNCT
ejpam-4220	329	1	j.	j.	PROPN
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ejpam-4220	329	4	.	.	PROPN
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ejpam-4220	329	6	,	,	PUNCT
ejpam-4220	329	7	15	15	NUM
ejpam-4220	329	8	(	(	PUNCT
ejpam-4220	329	9	1	1	NUM
ejpam-4220	329	10	)	)	PUNCT
ejpam-4220	329	11	(	(	PUNCT
ejpam-4220	329	12	2022	2022	NUM
ejpam-4220	329	13	)	)	PUNCT
ejpam-4220	329	14	,	,	PUNCT
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ejpam-4220	329	16	-	-	SYM
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ejpam-4220	329	19	and	and	CCONJ
ejpam-4220	329	20	{	{	PUNCT
ejpam-4220	329	21	(	(	PUNCT
ejpam-4220	329	22	w	w	PROPN
ejpam-4220	329	23	,	,	PUNCT
ejpam-4220	329	24	y	y	PROPN
ejpam-4220	329	25	)	)	PUNCT
ejpam-4220	329	26	:	:	PUNCT
ejpam-4220	329	27	w	w	X
ejpam-4220	329	28	∈	∈	PROPN
ejpam-4220	329	29	∆1	∆1	PROPN
ejpam-4220	329	30	,	,	PUNCT
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ejpam-4220	329	32	∈	∈	PROPN
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ejpam-4220	329	35	∪	∪	X
ejpam-4220	329	36	{	{	PUNCT
ejpam-4220	329	37	(	(	PUNCT
ejpam-4220	329	38	x	x	NOUN
ejpam-4220	329	39	,	,	PUNCT
ejpam-4220	329	40	z	z	NOUN
ejpam-4220	329	41	)	)	PUNCT
ejpam-4220	329	42	:	:	PUNCT
ejpam-4220	329	43	x	x	X
ejpam-4220	329	44	∈	∈	PROPN
ejpam-4220	329	45	ω1	ω1	PROPN
ejpam-4220	329	46	,	,	PUNCT
ejpam-4220	329	47	z	z	PROPN
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ejpam-4220	329	51	=	=	SYM
ejpam-4220	329	52	{	{	PUNCT
ejpam-4220	329	53	(	(	PUNCT
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ejpam-4220	329	55	,	,	PUNCT
ejpam-4220	329	56	2	2	NUM
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ejpam-4220	329	58	,	,	PUNCT
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ejpam-4220	329	61	,	,	PUNCT
ejpam-4220	329	62	4	4	NUM
ejpam-4220	329	63	)	)	PUNCT
ejpam-4220	329	64	,	,	PUNCT
ejpam-4220	329	65	(	(	PUNCT
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ejpam-4220	329	67	,	,	PUNCT
ejpam-4220	329	68	5	5	NUM
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ejpam-4220	329	70	,	,	PUNCT
ejpam-4220	329	71	(	(	PUNCT
ejpam-4220	329	72	b	b	NOUN
ejpam-4220	329	73	,	,	PUNCT
ejpam-4220	329	74	7	7	NUM
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ejpam-4220	329	76	,	,	PUNCT
ejpam-4220	329	77	(	(	PUNCT
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ejpam-4220	329	79	,	,	PUNCT
ejpam-4220	329	80	8)	8)	NUM
ejpam-4220	329	81	,	,	PUNCT
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ejpam-4220	329	83	e	e	NOUN
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ejpam-4220	329	85	2	2	NUM
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ejpam-4220	329	87	,	,	PUNCT
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ejpam-4220	329	89	e	e	NOUN
ejpam-4220	329	90	,	,	PUNCT
ejpam-4220	329	91	4	4	NUM
ejpam-4220	329	92	)	)	PUNCT
ejpam-4220	329	93	,	,	PUNCT
ejpam-4220	329	94	(	(	PUNCT
ejpam-4220	329	95	e	e	NOUN
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ejpam-4220	329	97	5	5	NUM
ejpam-4220	329	98	)	)	PUNCT
ejpam-4220	329	99	,	,	PUNCT
ejpam-4220	329	100	(	(	PUNCT
ejpam-4220	329	101	e	e	NOUN
ejpam-4220	329	102	,	,	PUNCT
ejpam-4220	329	103	7	7	NUM
ejpam-4220	329	104	)	)	PUNCT
ejpam-4220	329	105	,	,	PUNCT
ejpam-4220	329	106	(	(	PUNCT
ejpam-4220	329	107	e	e	NOUN
ejpam-4220	329	108	,	,	PUNCT
ejpam-4220	329	109	8)	8)	NUM
ejpam-4220	329	110	}	}	PUNCT
ejpam-4220	329	111	∪	∪	X
ejpam-4220	329	112	{	{	PUNCT
ejpam-4220	329	113	(	(	PUNCT
ejpam-4220	329	114	a	a	PRON
ejpam-4220	329	115	,	,	PUNCT
ejpam-4220	329	116	1	1	NUM
ejpam-4220	329	117	)	)	PUNCT
ejpam-4220	329	118	,	,	PUNCT
ejpam-4220	329	119	(	(	PUNCT
ejpam-4220	329	120	a	a	DET
ejpam-4220	329	121	,	,	PUNCT
ejpam-4220	329	122	3	3	NUM
ejpam-4220	329	123	)	)	PUNCT
ejpam-4220	329	124	,	,	PUNCT
ejpam-4220	329	125	(	(	PUNCT
ejpam-4220	329	126	a	a	DET
ejpam-4220	329	127	,	,	PUNCT
ejpam-4220	329	128	6	6	NUM
ejpam-4220	329	129	)	)	PUNCT
ejpam-4220	329	130	,	,	PUNCT
ejpam-4220	329	131	(	(	PUNCT
ejpam-4220	329	132	d	d	X
ejpam-4220	329	133	,	,	PUNCT
ejpam-4220	329	134	1	1	NUM
ejpam-4220	329	135	)	)	PUNCT
ejpam-4220	329	136	,	,	PUNCT
ejpam-4220	329	137	(	(	PUNCT
ejpam-4220	329	138	d	d	X
ejpam-4220	329	139	,	,	PUNCT
ejpam-4220	329	140	3	3	NUM
ejpam-4220	329	141	)	)	PUNCT
ejpam-4220	329	142	,	,	PUNCT
ejpam-4220	329	143	(	(	PUNCT
ejpam-4220	329	144	d	d	X
ejpam-4220	329	145	,	,	PUNCT
ejpam-4220	329	146	6	6	NUM
ejpam-4220	329	147	)	)	PUNCT
ejpam-4220	329	148	,	,	PUNCT
ejpam-4220	329	149	(	(	PUNCT
ejpam-4220	329	150	c	c	X
ejpam-4220	329	151	,	,	PUNCT
ejpam-4220	329	152	1	1	NUM
ejpam-4220	329	153	)	)	PUNCT
ejpam-4220	329	154	,	,	PUNCT
ejpam-4220	329	155	(	(	PUNCT
ejpam-4220	329	156	c	c	X
ejpam-4220	329	157	,	,	PUNCT
ejpam-4220	329	158	3	3	NUM
ejpam-4220	329	159	)	)	PUNCT
ejpam-4220	329	160	,	,	PUNCT
ejpam-4220	329	161	(	(	PUNCT
ejpam-4220	329	162	c	c	X
ejpam-4220	329	163	,	,	PUNCT
ejpam-4220	329	164	6	6	NUM
ejpam-4220	329	165	)	)	PUNCT
ejpam-4220	329	166	}	}	PUNCT
ejpam-4220	329	167	=	=	SYM
ejpam-4220	329	168	{	{	PUNCT
ejpam-4220	329	169	(	(	PUNCT
ejpam-4220	329	170	b	b	NOUN
ejpam-4220	329	171	,	,	PUNCT
ejpam-4220	329	172	2	2	NUM
ejpam-4220	329	173	)	)	PUNCT
ejpam-4220	329	174	,	,	PUNCT
ejpam-4220	329	175	(	(	PUNCT
ejpam-4220	329	176	b	b	NOUN
ejpam-4220	329	177	,	,	PUNCT
ejpam-4220	329	178	4	4	NUM
ejpam-4220	329	179	)	)	PUNCT
ejpam-4220	329	180	,	,	PUNCT
ejpam-4220	329	181	(	(	PUNCT
ejpam-4220	329	182	b	b	X
ejpam-4220	329	183	,	,	PUNCT
ejpam-4220	329	184	5	5	NUM
ejpam-4220	329	185	)	)	PUNCT
ejpam-4220	329	186	,	,	PUNCT
ejpam-4220	329	187	(	(	PUNCT
ejpam-4220	329	188	b	b	NOUN
ejpam-4220	329	189	,	,	PUNCT
ejpam-4220	329	190	7	7	NUM
ejpam-4220	329	191	)	)	PUNCT
ejpam-4220	329	192	,	,	PUNCT
ejpam-4220	329	193	(	(	PUNCT
ejpam-4220	329	194	b	b	NOUN
ejpam-4220	329	195	,	,	PUNCT
ejpam-4220	329	196	8)	8)	NUM
ejpam-4220	329	197	,	,	PUNCT
ejpam-4220	329	198	(	(	PUNCT
ejpam-4220	329	199	e	e	NOUN
ejpam-4220	329	200	,	,	PUNCT
ejpam-4220	329	201	2	2	NUM
ejpam-4220	329	202	)	)	PUNCT
ejpam-4220	329	203	,	,	PUNCT
ejpam-4220	329	204	(	(	PUNCT
ejpam-4220	329	205	e	e	NOUN
ejpam-4220	329	206	,	,	PUNCT
ejpam-4220	329	207	4	4	NUM
ejpam-4220	329	208	)	)	PUNCT
ejpam-4220	329	209	,	,	PUNCT
ejpam-4220	329	210	(	(	PUNCT
ejpam-4220	329	211	e	e	NOUN
ejpam-4220	329	212	,	,	PUNCT
ejpam-4220	329	213	5	5	NUM
ejpam-4220	329	214	)	)	PUNCT
ejpam-4220	329	215	,	,	PUNCT
ejpam-4220	329	216	(	(	PUNCT
ejpam-4220	329	217	e	e	NOUN
ejpam-4220	329	218	,	,	PUNCT
ejpam-4220	329	219	7	7	NUM
ejpam-4220	329	220	)	)	PUNCT
ejpam-4220	329	221	,	,	PUNCT
ejpam-4220	329	222	(	(	PUNCT
ejpam-4220	329	223	e	e	NOUN
ejpam-4220	329	224	,	,	PUNCT
ejpam-4220	329	225	8)	8)	NUM
ejpam-4220	329	226	,	,	PUNCT
ejpam-4220	329	227	(	(	PUNCT
ejpam-4220	329	228	a	a	DET
ejpam-4220	329	229	,	,	PUNCT
ejpam-4220	329	230	1	1	NUM
ejpam-4220	329	231	)	)	PUNCT
ejpam-4220	329	232	,	,	PUNCT
ejpam-4220	329	233	(	(	PUNCT
ejpam-4220	329	234	a	a	PRON
ejpam-4220	329	235	,	,	PUNCT
ejpam-4220	329	236	3	3	NUM
ejpam-4220	329	237	)	)	PUNCT
ejpam-4220	329	238	,	,	PUNCT
ejpam-4220	329	239	(	(	PUNCT
ejpam-4220	329	240	a	a	PRON
ejpam-4220	329	241	,	,	PUNCT
ejpam-4220	329	242	6	6	NUM
ejpam-4220	329	243	)	)	PUNCT
ejpam-4220	329	244	,	,	PUNCT
ejpam-4220	329	245	(	(	PUNCT
ejpam-4220	329	246	d	d	X
ejpam-4220	329	247	,	,	PUNCT
ejpam-4220	329	248	1	1	NUM
ejpam-4220	329	249	)	)	PUNCT
ejpam-4220	329	250	,	,	PUNCT
ejpam-4220	329	251	(	(	PUNCT
ejpam-4220	329	252	d	d	X
ejpam-4220	329	253	,	,	PUNCT
ejpam-4220	329	254	3	3	NUM
ejpam-4220	329	255	)	)	PUNCT
ejpam-4220	329	256	,	,	PUNCT
ejpam-4220	329	257	(	(	PUNCT
ejpam-4220	329	258	d	d	X
ejpam-4220	329	259	,	,	PUNCT
ejpam-4220	329	260	6	6	NUM
ejpam-4220	329	261	)	)	PUNCT
ejpam-4220	329	262	,	,	PUNCT
ejpam-4220	329	263	(	(	PUNCT
ejpam-4220	329	264	c	c	X
ejpam-4220	329	265	,	,	PUNCT
ejpam-4220	329	266	1	1	NUM
ejpam-4220	329	267	)	)	PUNCT
ejpam-4220	329	268	,	,	PUNCT
ejpam-4220	329	269	(	(	PUNCT
ejpam-4220	329	270	c	c	X
ejpam-4220	329	271	,	,	PUNCT
ejpam-4220	329	272	3	3	NUM
ejpam-4220	329	273	)	)	PUNCT
ejpam-4220	329	274	,	,	PUNCT
ejpam-4220	329	275	(	(	PUNCT
ejpam-4220	329	276	c	c	X
ejpam-4220	329	277	,	,	PUNCT
ejpam-4220	329	278	6	6	NUM
ejpam-4220	329	279	)	)	PUNCT
ejpam-4220	329	280	}	}	PUNCT
ejpam-4220	329	281	.	.	PUNCT
ejpam-4220	330	1	furthermore	furthermore	ADV
ejpam-4220	330	2	,	,	PUNCT
ejpam-4220	330	3	|ω1|	|ω1|	NOUN
ejpam-4220	330	4	=	=	SYM
ejpam-4220	330	5	3	3	NUM
ejpam-4220	330	6	,	,	PUNCT
ejpam-4220	330	7	|∆1|	|∆1|	NOUN
ejpam-4220	330	8	=	=	SYM
ejpam-4220	330	9	2	2	NUM
ejpam-4220	330	10	,	,	PUNCT
ejpam-4220	330	11	|ω2|	|ω2|	NOUN
ejpam-4220	330	12	=	=	SYM
ejpam-4220	330	13	5	5	NUM
ejpam-4220	330	14	and	and	CCONJ
ejpam-4220	330	15	|∆2|	|∆2|	ADJ
ejpam-4220	330	16	=	=	SYM
ejpam-4220	330	17	3	3	X
ejpam-4220	330	18	.	.	PUNCT
ejpam-4220	330	19	therefore	therefore	ADV
ejpam-4220	330	20	,	,	PUNCT
ejpam-4220	330	21	by	by	ADP
ejpam-4220	330	22	corollary	corollary	ADJ
ejpam-4220	330	23	8	8	NUM
ejpam-4220	330	24	,	,	PUNCT
ejpam-4220	330	25	ni(g	ni(g	NUM
ejpam-4220	330	26	•h1	•h1	NUM
ejpam-4220	330	27	,	,	PUNCT
ejpam-4220	330	28	x	x	X
ejpam-4220	330	29	)	)	PUNCT
ejpam-4220	330	30	=	=	SYM
ejpam-4220	330	31	x3(5)+2(3	x3(5)+2(3	PROPN
ejpam-4220	330	32	)	)	PUNCT
ejpam-4220	330	33	+	+	NUM
ejpam-4220	330	34	x2(5)+3(3	x2(5)+3(3	X
ejpam-4220	330	35	)	)	PUNCT
ejpam-4220	330	36	=	=	SYM
ejpam-4220	330	37	x21	x21	PROPN
ejpam-4220	330	38	+	+	NUM
ejpam-4220	330	39	x19	x19	NOUN
ejpam-4220	330	40	.	.	PUNCT
ejpam-4220	331	1	theorem	theorem	NOUN
ejpam-4220	331	2	5	5	NUM
ejpam-4220	331	3	.	.	PUNCT
ejpam-4220	332	1	let	let	VERB
ejpam-4220	332	2	g	g	NOUN
ejpam-4220	332	3	be	be	AUX
ejpam-4220	332	4	any	any	DET
ejpam-4220	332	5	tree	tree	NOUN
ejpam-4220	333	1	and	and	CCONJ
ejpam-4220	333	2	h	h	NOUN
ejpam-4220	333	3	be	be	AUX
ejpam-4220	333	4	another	another	DET
ejpam-4220	333	5	tree	tree	NOUN
ejpam-4220	333	6	.	.	PUNCT
ejpam-4220	334	1	suppose	suppose	VERB
ejpam-4220	334	2	h1	h1	PROPN
ejpam-4220	334	3	is	be	AUX
ejpam-4220	334	4	a	a	DET
ejpam-4220	334	5	rooted	rooted	ADJ
ejpam-4220	334	6	tree	tree	NOUN
ejpam-4220	334	7	from	from	ADP
ejpam-4220	334	8	h	h	NOUN
ejpam-4220	334	9	with	with	ADP
ejpam-4220	334	10	rooted	rooted	ADJ
ejpam-4220	334	11	vertex	vertex	NOUN
ejpam-4220	334	12	u1	u1	NOUN
ejpam-4220	334	13	and	and	CCONJ
ejpam-4220	334	14	h2	h2	NOUN
ejpam-4220	334	15	is	be	AUX
ejpam-4220	334	16	also	also	ADV
ejpam-4220	334	17	a	a	DET
ejpam-4220	334	18	rooted	rooted	ADJ
ejpam-4220	334	19	tree	tree	NOUN
ejpam-4220	334	20	from	from	ADP
ejpam-4220	334	21	h	h	NOUN
ejpam-4220	334	22	with	with	ADP
ejpam-4220	334	23	rooted	rooted	ADJ
ejpam-4220	334	24	vertex	vertex	NOUN
ejpam-4220	334	25	u2	u2	NOUN
ejpam-4220	334	26	where	where	SCONJ
ejpam-4220	334	27	h1	h1	VERB
ejpam-4220	334	28	∼=	∼=	PROPN
ejpam-4220	334	29	h2	h2	NOUN
ejpam-4220	334	30	.	.	PUNCT
ejpam-4220	335	1	then	then	ADV
ejpam-4220	335	2	the	the	DET
ejpam-4220	335	3	independent	independent	ADJ
ejpam-4220	335	4	neighborhood	neighborhood	NOUN
ejpam-4220	335	5	polynomial	polynomial	NOUN
ejpam-4220	335	6	of	of	ADP
ejpam-4220	335	7	the	the	DET
ejpam-4220	335	8	rooted	rooted	ADJ
ejpam-4220	335	9	product	product	NOUN
ejpam-4220	335	10	of	of	ADP
ejpam-4220	335	11	g	g	PROPN
ejpam-4220	335	12	and	and	CCONJ
ejpam-4220	335	13	h2	h2	PROPN
ejpam-4220	335	14	is	be	AUX
ejpam-4220	335	15	the	the	DET
ejpam-4220	335	16	same	same	ADJ
ejpam-4220	335	17	as	as	ADP
ejpam-4220	335	18	the	the	DET
ejpam-4220	335	19	independent	independent	ADJ
ejpam-4220	335	20	neighborhood	neighborhood	NOUN
ejpam-4220	335	21	polynomial	polynomial	NOUN
ejpam-4220	335	22	of	of	ADP
ejpam-4220	335	23	the	the	DET
ejpam-4220	335	24	rooted	rooted	ADJ
ejpam-4220	335	25	product	product	NOUN
ejpam-4220	335	26	of	of	ADP
ejpam-4220	335	27	g	g	PROPN
ejpam-4220	335	28	and	and	CCONJ
ejpam-4220	335	29	h1	h1	PROPN
ejpam-4220	335	30	,	,	PUNCT
ejpam-4220	335	31	that	that	ADV
ejpam-4220	335	32	is	is	ADV
ejpam-4220	335	33	,	,	PUNCT
ejpam-4220	335	34	ni(g	ni(g	NUM
ejpam-4220	335	35	•h2	•h2	PROPN
ejpam-4220	335	36	,	,	PUNCT
ejpam-4220	335	37	x	x	NOUN
ejpam-4220	335	38	)	)	PUNCT
ejpam-4220	335	39	=	=	NOUN
ejpam-4220	335	40	ni(g	ni(g	NUM
ejpam-4220	335	41	•h1	•h1	NUM
ejpam-4220	335	42	,	,	PUNCT
ejpam-4220	335	43	x	x	NOUN
ejpam-4220	335	44	)	)	PUNCT
ejpam-4220	335	45	.	.	PUNCT
ejpam-4220	336	1	proof	proof	NOUN
ejpam-4220	336	2	.	.	PUNCT
ejpam-4220	337	1	let	let	VERB
ejpam-4220	337	2	g	g	NOUN
ejpam-4220	337	3	and	and	CCONJ
ejpam-4220	337	4	h	h	NOUN
ejpam-4220	337	5	be	be	VERB
ejpam-4220	337	6	trees	tree	NOUN
ejpam-4220	337	7	with	with	ADP
ejpam-4220	337	8	independent	independent	ADJ
ejpam-4220	337	9	neighborhood	neighborhood	NOUN
ejpam-4220	337	10	sets	set	VERB
ejpam-4220	337	11	ω1,∆1	ω1,∆1	NUM
ejpam-4220	337	12	and	and	CCONJ
ejpam-4220	337	13	ω2,∆2	ω2,∆2	PROPN
ejpam-4220	337	14	,	,	PUNCT
ejpam-4220	337	15	respectively	respectively	ADV
ejpam-4220	337	16	.	.	PUNCT
ejpam-4220	338	1	suppose	suppose	VERB
ejpam-4220	338	2	h1	h1	PROPN
ejpam-4220	338	3	is	be	AUX
ejpam-4220	338	4	a	a	DET
ejpam-4220	338	5	rooted	rooted	ADJ
ejpam-4220	338	6	tree	tree	NOUN
ejpam-4220	338	7	from	from	ADP
ejpam-4220	338	8	h	h	NOUN
ejpam-4220	338	9	with	with	ADP
ejpam-4220	338	10	rooted	rooted	ADJ
ejpam-4220	338	11	vertex	vertex	NOUN
ejpam-4220	338	12	u1	u1	NOUN
ejpam-4220	338	13	and	and	CCONJ
ejpam-4220	338	14	that	that	SCONJ
ejpam-4220	338	15	u1	u1	PROPN
ejpam-4220	338	16	∈	∈	PROPN
ejpam-4220	338	17	ω2	ω2	PROPN
ejpam-4220	338	18	.	.	PUNCT
ejpam-4220	339	1	by	by	ADP
ejpam-4220	339	2	theorem	theorem	NOUN
ejpam-4220	339	3	4	4	NUM
ejpam-4220	339	4	,	,	PUNCT
ejpam-4220	339	5	the	the	DET
ejpam-4220	339	6	sets	set	NOUN
ejpam-4220	339	7	{	{	PUNCT
ejpam-4220	339	8	(	(	PUNCT
ejpam-4220	339	9	x	x	NOUN
ejpam-4220	339	10	,	,	PUNCT
ejpam-4220	339	11	y	y	PROPN
ejpam-4220	339	12	)	)	PUNCT
ejpam-4220	339	13	:	:	PUNCT
ejpam-4220	339	14	x	x	X
ejpam-4220	339	15	∈	∈	PROPN
ejpam-4220	339	16	ω1	ω1	PROPN
ejpam-4220	339	17	,	,	PUNCT
ejpam-4220	339	18	y	y	PROPN
ejpam-4220	339	19	∈	∈	PROPN
ejpam-4220	339	20	ω2	ω2	PROPN
ejpam-4220	339	21	}	}	PUNCT
ejpam-4220	339	22	∪	∪	X
ejpam-4220	339	23	{	{	PUNCT
ejpam-4220	339	24	(	(	PUNCT
ejpam-4220	339	25	w	w	PROPN
ejpam-4220	339	26	,	,	PUNCT
ejpam-4220	339	27	z	z	NOUN
ejpam-4220	339	28	)	)	PUNCT
ejpam-4220	339	29	:	:	PUNCT
ejpam-4220	339	30	w	w	X
ejpam-4220	339	31	∈	∈	PROPN
ejpam-4220	339	32	∆1	∆1	PROPN
ejpam-4220	339	33	,	,	PUNCT
ejpam-4220	339	34	z	z	PROPN
ejpam-4220	339	35	∈	∈	PROPN
ejpam-4220	339	36	∆2	∆2	PROPN
ejpam-4220	339	37	}	}	PUNCT
ejpam-4220	339	38	and	and	CCONJ
ejpam-4220	339	39	{	{	PUNCT
ejpam-4220	339	40	(	(	PUNCT
ejpam-4220	339	41	w	w	PROPN
ejpam-4220	339	42	,	,	PUNCT
ejpam-4220	339	43	y	y	PROPN
ejpam-4220	339	44	)	)	PUNCT
ejpam-4220	339	45	:	:	PUNCT
ejpam-4220	339	46	w	w	X
ejpam-4220	339	47	∈	∈	PROPN
ejpam-4220	339	48	∆1	∆1	PROPN
ejpam-4220	339	49	,	,	PUNCT
ejpam-4220	339	50	y	y	PROPN
ejpam-4220	339	51	∈	∈	PROPN
ejpam-4220	339	52	ω2	ω2	PROPN
ejpam-4220	339	53	}	}	PUNCT
ejpam-4220	339	54	∪	∪	X
ejpam-4220	339	55	{	{	PUNCT
ejpam-4220	339	56	(	(	PUNCT
ejpam-4220	339	57	x	x	NOUN
ejpam-4220	339	58	,	,	PUNCT
ejpam-4220	339	59	z	z	NOUN
ejpam-4220	339	60	)	)	PUNCT
ejpam-4220	339	61	:	:	PUNCT
ejpam-4220	339	62	x	x	X
ejpam-4220	339	63	∈	∈	PROPN
ejpam-4220	339	64	ω1	ω1	PROPN
ejpam-4220	339	65	,	,	PUNCT
ejpam-4220	339	66	z	z	PROPN
ejpam-4220	339	67	∈	∈	PROPN
ejpam-4220	339	68	∆2	∆2	PROPN
ejpam-4220	339	69	}	}	PUNCT
ejpam-4220	339	70	are	be	AUX
ejpam-4220	339	71	the	the	DET
ejpam-4220	339	72	independent	independent	ADJ
ejpam-4220	339	73	neighborhood	neighborhood	NOUN
ejpam-4220	339	74	sets	set	NOUN
ejpam-4220	339	75	of	of	ADP
ejpam-4220	339	76	g	g	PROPN
ejpam-4220	339	77	•h1	•h1	PROPN
ejpam-4220	339	78	.	.	PUNCT
ejpam-4220	340	1	suppose	suppose	VERB
ejpam-4220	340	2	h2	h2	NOUN
ejpam-4220	340	3	is	be	AUX
ejpam-4220	340	4	another	another	DET
ejpam-4220	340	5	rooted	rooted	ADJ
ejpam-4220	340	6	tree	tree	NOUN
ejpam-4220	340	7	with	with	ADP
ejpam-4220	340	8	rooted	rooted	ADJ
ejpam-4220	340	9	vertex	vertex	NOUN
ejpam-4220	340	10	u2	u2	NOUN
ejpam-4220	340	11	different	different	ADJ
ejpam-4220	340	12	from	from	ADP
ejpam-4220	340	13	u1	u1	NOUN
ejpam-4220	340	14	whose	whose	DET
ejpam-4220	340	15	graph	graph	NOUN
ejpam-4220	340	16	is	be	AUX
ejpam-4220	340	17	the	the	DET
ejpam-4220	340	18	same	same	ADJ
ejpam-4220	340	19	with	with	ADP
ejpam-4220	340	20	h1	h1	PROPN
ejpam-4220	340	21	.	.	PUNCT
ejpam-4220	341	1	without	without	ADP
ejpam-4220	341	2	loss	loss	NOUN
ejpam-4220	341	3	of	of	ADP
ejpam-4220	341	4	generality	generality	NOUN
ejpam-4220	341	5	,	,	PUNCT
ejpam-4220	341	6	let	let	VERB
ejpam-4220	341	7	u2	u2	PROPN
ejpam-4220	341	8	∈	∈	PROPN
ejpam-4220	341	9	∆2	∆2	PROPN
ejpam-4220	341	10	.	.	PUNCT
ejpam-4220	342	1	we	we	PRON
ejpam-4220	342	2	can	can	AUX
ejpam-4220	342	3	see	see	VERB
ejpam-4220	342	4	that	that	SCONJ
ejpam-4220	342	5	the	the	DET
ejpam-4220	342	6	sets	set	NOUN
ejpam-4220	342	7	{	{	PUNCT
ejpam-4220	342	8	(	(	PUNCT
ejpam-4220	342	9	x	x	NOUN
ejpam-4220	342	10	,	,	PUNCT
ejpam-4220	342	11	y	y	PROPN
ejpam-4220	342	12	)	)	PUNCT
ejpam-4220	342	13	:	:	PUNCT
ejpam-4220	342	14	x	x	X
ejpam-4220	342	15	∈	∈	PROPN
ejpam-4220	342	16	ω1	ω1	PROPN
ejpam-4220	342	17	,	,	PUNCT
ejpam-4220	342	18	y	y	PROPN
ejpam-4220	342	19	∈	∈	PROPN
ejpam-4220	342	20	ω2	ω2	PROPN
ejpam-4220	342	21	}	}	PUNCT
ejpam-4220	342	22	∪	∪	X
ejpam-4220	342	23	{	{	PUNCT
ejpam-4220	342	24	(	(	PUNCT
ejpam-4220	342	25	w	w	PROPN
ejpam-4220	342	26	,	,	PUNCT
ejpam-4220	342	27	z	z	NOUN
ejpam-4220	342	28	)	)	PUNCT
ejpam-4220	342	29	:	:	PUNCT
ejpam-4220	342	30	w	w	X
ejpam-4220	342	31	∈	∈	PROPN
ejpam-4220	342	32	∆1	∆1	PROPN
ejpam-4220	342	33	,	,	PUNCT
ejpam-4220	342	34	z	z	PROPN
ejpam-4220	342	35	∈	∈	PROPN
ejpam-4220	342	36	∆2	∆2	PROPN
ejpam-4220	342	37	}	}	PUNCT
ejpam-4220	342	38	and	and	CCONJ
ejpam-4220	342	39	{	{	PUNCT
ejpam-4220	342	40	(	(	PUNCT
ejpam-4220	342	41	w	w	PROPN
ejpam-4220	342	42	,	,	PUNCT
ejpam-4220	342	43	y	y	PROPN
ejpam-4220	342	44	)	)	PUNCT
ejpam-4220	342	45	:	:	PUNCT
ejpam-4220	342	46	w	w	X
ejpam-4220	342	47	∈	∈	PROPN
ejpam-4220	342	48	∆1	∆1	PROPN
ejpam-4220	342	49	,	,	PUNCT
ejpam-4220	342	50	y	y	PROPN
ejpam-4220	342	51	∈	∈	PROPN
ejpam-4220	342	52	ω2	ω2	PROPN
ejpam-4220	342	53	}	}	PUNCT
ejpam-4220	342	54	∪	∪	X
ejpam-4220	342	55	{	{	PUNCT
ejpam-4220	342	56	(	(	PUNCT
ejpam-4220	342	57	x	x	NOUN
ejpam-4220	342	58	,	,	PUNCT
ejpam-4220	342	59	z	z	NOUN
ejpam-4220	342	60	)	)	PUNCT
ejpam-4220	342	61	:	:	PUNCT
ejpam-4220	342	62	x	x	X
ejpam-4220	342	63	∈	∈	PROPN
ejpam-4220	342	64	ω1	ω1	PROPN
ejpam-4220	342	65	,	,	PUNCT
ejpam-4220	342	66	z	z	PROPN
ejpam-4220	342	67	∈	∈	PROPN
ejpam-4220	342	68	∆2	∆2	PROPN
ejpam-4220	342	69	}	}	PUNCT
ejpam-4220	342	70	are	be	AUX
ejpam-4220	342	71	also	also	ADV
ejpam-4220	342	72	the	the	DET
ejpam-4220	342	73	independent	independent	ADJ
ejpam-4220	342	74	neighborhood	neighborhood	NOUN
ejpam-4220	342	75	sets	set	NOUN
ejpam-4220	342	76	of	of	ADP
ejpam-4220	342	77	g	g	PROPN
ejpam-4220	342	78	•h2	•h2	PROPN
ejpam-4220	342	79	.	.	PUNCT
ejpam-4220	343	1	thus	thus	ADV
ejpam-4220	343	2	,	,	PUNCT
ejpam-4220	343	3	ni(g	ni(g	NUM
ejpam-4220	343	4	•h2	•h2	PROPN
ejpam-4220	343	5	,	,	PUNCT
ejpam-4220	343	6	x	x	X
ejpam-4220	343	7	)	)	PUNCT
ejpam-4220	344	1	=	=	SYM
ejpam-4220	344	2	x|ω1||ω2|+|∆1||∆2|	x|ω1||ω2|+|∆1||∆2|	PROPN
ejpam-4220	344	3	+	+	NUM
ejpam-4220	344	4	x|∆1||ω2|+|ω1||∆2|	x|∆1||ω2|+|ω1||∆2|	PROPN
ejpam-4220	344	5	.	.	PUNCT
ejpam-4220	345	1	therefore	therefore	ADV
ejpam-4220	345	2	,	,	PUNCT
ejpam-4220	345	3	ni(g	ni(g	NUM
ejpam-4220	345	4	•h2	•h2	PROPN
ejpam-4220	345	5	,	,	PUNCT
ejpam-4220	345	6	x	x	NOUN
ejpam-4220	345	7	)	)	PUNCT
ejpam-4220	345	8	=	=	NOUN
ejpam-4220	345	9	ni(g	ni(g	NUM
ejpam-4220	345	10	•h1	•h1	NUM
ejpam-4220	345	11	,	,	PUNCT
ejpam-4220	345	12	x	x	NOUN
ejpam-4220	345	13	)	)	PUNCT
ejpam-4220	345	14	.	.	PUNCT
ejpam-4220	346	1	■	■	PUNCT
ejpam-4220	346	2	n.	n.	PROPN
ejpam-4220	346	3	s.	s.	PROPN
ejpam-4220	346	4	abdulcarim	abdulcarim	PROPN
ejpam-4220	346	5	,	,	PUNCT
ejpam-4220	346	6	s.	s.	PROPN
ejpam-4220	346	7	c.	c.	PROPN
ejpam-4220	346	8	dagondon	dagondon	PROPN
ejpam-4220	346	9	/	/	SYM
ejpam-4220	346	10	eur	eur	PROPN
ejpam-4220	346	11	.	.	PUNCT
ejpam-4220	347	1	j.	j.	PROPN
ejpam-4220	347	2	pure	pure	PROPN
ejpam-4220	347	3	appl	appl	PROPN
ejpam-4220	347	4	.	.	PROPN
ejpam-4220	347	5	math	math	PROPN
ejpam-4220	347	6	,	,	PUNCT
ejpam-4220	347	7	15	15	NUM
ejpam-4220	347	8	(	(	PUNCT
ejpam-4220	347	9	1	1	NUM
ejpam-4220	347	10	)	)	PUNCT
ejpam-4220	347	11	(	(	PUNCT
ejpam-4220	347	12	2022	2022	NUM
ejpam-4220	347	13	)	)	PUNCT
ejpam-4220	347	14	,	,	PUNCT
ejpam-4220	347	15	64	64	NUM
ejpam-4220	347	16	-	-	SYM
ejpam-4220	347	17	81	81	NUM
ejpam-4220	347	18	78	78	NUM
ejpam-4220	347	19	example	example	NOUN
ejpam-4220	347	20	7	7	NUM
ejpam-4220	347	21	.	.	X
ejpam-4220	347	22	consider	consider	VERB
ejpam-4220	347	23	the	the	DET
ejpam-4220	347	24	graphs	graph	NOUN
ejpam-4220	347	25	g	g	NOUN
ejpam-4220	347	26	and	and	CCONJ
ejpam-4220	347	27	h	h	NOUN
ejpam-4220	347	28	in	in	ADP
ejpam-4220	347	29	figure	figure	NOUN
ejpam-4220	347	30	5	5	NUM
ejpam-4220	347	31	.	.	PUNCT
ejpam-4220	348	1	let	let	VERB
ejpam-4220	348	2	h2	h2	NOUN
ejpam-4220	348	3	be	be	AUX
ejpam-4220	348	4	a	a	DET
ejpam-4220	348	5	rooted	rooted	ADJ
ejpam-4220	348	6	graph	graph	NOUN
ejpam-4220	348	7	with	with	ADP
ejpam-4220	348	8	rooted	rooted	ADJ
ejpam-4220	348	9	vertex	vertex	NOUN
ejpam-4220	348	10	1	1	NUM
ejpam-4220	348	11	whose	whose	DET
ejpam-4220	348	12	graph	graph	NOUN
ejpam-4220	348	13	is	be	AUX
ejpam-4220	348	14	the	the	DET
ejpam-4220	348	15	same	same	ADJ
ejpam-4220	348	16	with	with	ADP
ejpam-4220	348	17	h.	h.	PROPN
ejpam-4220	348	18	(	(	PUNCT
ejpam-4220	348	19	a	a	DET
ejpam-4220	348	20	,	,	PUNCT
ejpam-4220	348	21	1	1	NUM
ejpam-4220	348	22	)	)	PUNCT
ejpam-4220	348	23	(	(	PUNCT
ejpam-4220	348	24	a	a	DET
ejpam-4220	348	25	,	,	PUNCT
ejpam-4220	348	26	2	2	NUM
ejpam-4220	348	27	)	)	PUNCT
ejpam-4220	348	28	(	(	PUNCT
ejpam-4220	348	29	a	a	DET
ejpam-4220	348	30	,	,	PUNCT
ejpam-4220	348	31	3	3	NUM
ejpam-4220	348	32	)	)	PUNCT
ejpam-4220	348	33	(	(	PUNCT
ejpam-4220	348	34	a	a	PRON
ejpam-4220	348	35	,	,	PUNCT
ejpam-4220	348	36	4)(a	4)(a	NOUN
ejpam-4220	348	37	,	,	PUNCT
ejpam-4220	348	38	5	5	NUM
ejpam-4220	348	39	)	)	PUNCT
ejpam-4220	348	40	(	(	PUNCT
ejpam-4220	348	41	a	a	DET
ejpam-4220	348	42	,	,	PUNCT
ejpam-4220	348	43	6	6	NUM
ejpam-4220	348	44	)	)	PUNCT
ejpam-4220	348	45	(	(	PUNCT
ejpam-4220	348	46	a	a	PRON
ejpam-4220	348	47	,	,	PUNCT
ejpam-4220	348	48	7)(a	7)(a	NUM
ejpam-4220	348	49	,	,	PUNCT
ejpam-4220	348	50	8)	8)	NUM
ejpam-4220	348	51	(	(	PUNCT
ejpam-4220	348	52	b	b	NOUN
ejpam-4220	348	53	,	,	PUNCT
ejpam-4220	348	54	1	1	NUM
ejpam-4220	348	55	)	)	PUNCT
ejpam-4220	348	56	(	(	PUNCT
ejpam-4220	348	57	b	b	NOUN
ejpam-4220	348	58	,	,	PUNCT
ejpam-4220	348	59	2	2	NUM
ejpam-4220	348	60	)	)	PUNCT
ejpam-4220	348	61	(	(	PUNCT
ejpam-4220	348	62	b	b	NOUN
ejpam-4220	348	63	,	,	PUNCT
ejpam-4220	348	64	3	3	NUM
ejpam-4220	348	65	)	)	PUNCT
ejpam-4220	348	66	(	(	PUNCT
ejpam-4220	348	67	b	b	NOUN
ejpam-4220	348	68	,	,	PUNCT
ejpam-4220	348	69	4)(b	4)(b	NUM
ejpam-4220	348	70	,	,	PUNCT
ejpam-4220	348	71	5	5	NUM
ejpam-4220	348	72	)	)	PUNCT
ejpam-4220	348	73	(	(	PUNCT
ejpam-4220	348	74	b	b	NOUN
ejpam-4220	348	75	,	,	PUNCT
ejpam-4220	348	76	6	6	NUM
ejpam-4220	348	77	)	)	PUNCT
ejpam-4220	348	78	(	(	PUNCT
ejpam-4220	348	79	b	b	NOUN
ejpam-4220	348	80	,	,	PUNCT
ejpam-4220	348	81	7)(b	7)(b	NUM
ejpam-4220	348	82	,	,	PUNCT
ejpam-4220	348	83	8)	8)	NUM
ejpam-4220	348	84	(	(	PUNCT
ejpam-4220	348	85	c	c	NOUN
ejpam-4220	348	86	,	,	PUNCT
ejpam-4220	348	87	1	1	NUM
ejpam-4220	348	88	)	)	PUNCT
ejpam-4220	348	89	(	(	PUNCT
ejpam-4220	348	90	c	c	X
ejpam-4220	348	91	,	,	PUNCT
ejpam-4220	348	92	2	2	NUM
ejpam-4220	348	93	)	)	PUNCT
ejpam-4220	348	94	(	(	PUNCT
ejpam-4220	348	95	c	c	X
ejpam-4220	348	96	,	,	PUNCT
ejpam-4220	348	97	3	3	NUM
ejpam-4220	348	98	)	)	PUNCT
ejpam-4220	348	99	(	(	PUNCT
ejpam-4220	348	100	c	c	X
ejpam-4220	348	101	,	,	PUNCT
ejpam-4220	348	102	4)(c	4)(c	NUM
ejpam-4220	348	103	,	,	PUNCT
ejpam-4220	348	104	5	5	NUM
ejpam-4220	348	105	)	)	PUNCT
ejpam-4220	348	106	(	(	PUNCT
ejpam-4220	348	107	c	c	X
ejpam-4220	348	108	,	,	PUNCT
ejpam-4220	348	109	6	6	NUM
ejpam-4220	348	110	)	)	PUNCT
ejpam-4220	348	111	(	(	PUNCT
ejpam-4220	348	112	c	c	X
ejpam-4220	348	113	,	,	PUNCT
ejpam-4220	348	114	7)(c	7)(c	NUM
ejpam-4220	348	115	,	,	PUNCT
ejpam-4220	348	116	8)	8)	NUM
ejpam-4220	348	117	(	(	PUNCT
ejpam-4220	348	118	d	d	PROPN
ejpam-4220	348	119	,	,	PUNCT
ejpam-4220	348	120	1	1	NUM
ejpam-4220	348	121	)	)	PUNCT
ejpam-4220	348	122	(	(	PUNCT
ejpam-4220	348	123	d	d	NOUN
ejpam-4220	348	124	,	,	PUNCT
ejpam-4220	348	125	2	2	NUM
ejpam-4220	348	126	)	)	PUNCT
ejpam-4220	348	127	(	(	PUNCT
ejpam-4220	348	128	d	d	NOUN
ejpam-4220	348	129	,	,	PUNCT
ejpam-4220	348	130	3	3	NUM
ejpam-4220	348	131	)	)	PUNCT
ejpam-4220	348	132	(	(	PUNCT
ejpam-4220	348	133	d	d	X
ejpam-4220	348	134	,	,	PUNCT
ejpam-4220	348	135	4)(d	4)(d	NUM
ejpam-4220	348	136	,	,	PUNCT
ejpam-4220	348	137	5	5	NUM
ejpam-4220	348	138	)	)	PUNCT
ejpam-4220	348	139	(	(	PUNCT
ejpam-4220	348	140	d	d	NOUN
ejpam-4220	348	141	,	,	PUNCT
ejpam-4220	348	142	6	6	NUM
ejpam-4220	348	143	)	)	PUNCT
ejpam-4220	348	144	(	(	PUNCT
ejpam-4220	348	145	d	d	NOUN
ejpam-4220	348	146	,	,	PUNCT
ejpam-4220	348	147	7)(d	7)(d	NUM
ejpam-4220	348	148	,	,	PUNCT
ejpam-4220	348	149	8)	8)	NUM
ejpam-4220	348	150	(	(	PUNCT
ejpam-4220	348	151	e	e	NOUN
ejpam-4220	348	152	,	,	PUNCT
ejpam-4220	348	153	1	1	NUM
ejpam-4220	348	154	)	)	PUNCT
ejpam-4220	348	155	(	(	PUNCT
ejpam-4220	348	156	e	e	NOUN
ejpam-4220	348	157	,	,	PUNCT
ejpam-4220	348	158	2	2	NUM
ejpam-4220	348	159	)	)	PUNCT
ejpam-4220	348	160	(	(	PUNCT
ejpam-4220	348	161	e	e	NOUN
ejpam-4220	348	162	,	,	PUNCT
ejpam-4220	348	163	3	3	NUM
ejpam-4220	348	164	)	)	PUNCT
ejpam-4220	348	165	(	(	PUNCT
ejpam-4220	348	166	e	e	NOUN
ejpam-4220	348	167	,	,	PUNCT
ejpam-4220	348	168	4)(e	4)(e	NUM
ejpam-4220	348	169	,	,	PUNCT
ejpam-4220	348	170	5	5	NUM
ejpam-4220	348	171	)	)	PUNCT
ejpam-4220	348	172	(	(	PUNCT
ejpam-4220	348	173	e	e	NOUN
ejpam-4220	348	174	,	,	PUNCT
ejpam-4220	348	175	6	6	NUM
ejpam-4220	348	176	)	)	PUNCT
ejpam-4220	348	177	(	(	PUNCT
ejpam-4220	348	178	e	e	NOUN
ejpam-4220	348	179	,	,	PUNCT
ejpam-4220	348	180	7)(e	7)(e	NUM
ejpam-4220	348	181	,	,	PUNCT
ejpam-4220	348	182	8)	8)	NUM
ejpam-4220	348	183	figure	figure	NOUN
ejpam-4220	348	184	7	7	NUM
ejpam-4220	348	185	:	:	PUNCT
ejpam-4220	348	186	rooted	rooted	ADJ
ejpam-4220	348	187	product	product	NOUN
ejpam-4220	348	188	of	of	ADP
ejpam-4220	348	189	tree	tree	NOUN
ejpam-4220	348	190	g	g	PROPN
ejpam-4220	348	191	and	and	CCONJ
ejpam-4220	348	192	rooted	root	VERB
ejpam-4220	348	193	tree	tree	NOUN
ejpam-4220	348	194	h2	h2	NOUN
ejpam-4220	348	195	we	we	PRON
ejpam-4220	348	196	can	can	AUX
ejpam-4220	348	197	verify	verify	VERB
ejpam-4220	348	198	that	that	SCONJ
ejpam-4220	348	199	the	the	DET
ejpam-4220	348	200	independent	independent	ADJ
ejpam-4220	348	201	neighborhood	neighborhood	NOUN
ejpam-4220	348	202	sets	set	NOUN
ejpam-4220	348	203	of	of	ADP
ejpam-4220	348	204	g	g	PROPN
ejpam-4220	348	205	•h2	•h2	PROPN
ejpam-4220	348	206	are	be	AUX
ejpam-4220	348	207	{	{	PUNCT
ejpam-4220	348	208	(	(	PUNCT
ejpam-4220	348	209	a	a	DET
ejpam-4220	348	210	,	,	PUNCT
ejpam-4220	348	211	2	2	NUM
ejpam-4220	348	212	)	)	PUNCT
ejpam-4220	348	213	,	,	PUNCT
ejpam-4220	348	214	(	(	PUNCT
ejpam-4220	348	215	a	a	DET
ejpam-4220	348	216	,	,	PUNCT
ejpam-4220	348	217	4	4	NUM
ejpam-4220	348	218	)	)	PUNCT
ejpam-4220	348	219	,	,	PUNCT
ejpam-4220	348	220	(	(	PUNCT
ejpam-4220	348	221	a	a	DET
ejpam-4220	348	222	,	,	PUNCT
ejpam-4220	348	223	5	5	NUM
ejpam-4220	348	224	)	)	PUNCT
ejpam-4220	348	225	,	,	PUNCT
ejpam-4220	348	226	(	(	PUNCT
ejpam-4220	348	227	a	a	PRON
ejpam-4220	348	228	,	,	PUNCT
ejpam-4220	348	229	7	7	NUM
ejpam-4220	348	230	)	)	PUNCT
ejpam-4220	348	231	,	,	PUNCT
ejpam-4220	348	232	(	(	PUNCT
ejpam-4220	348	233	a	a	DET
ejpam-4220	348	234	,	,	PUNCT
ejpam-4220	348	235	8)	8)	NUM
ejpam-4220	348	236	,	,	PUNCT
ejpam-4220	348	237	(	(	PUNCT
ejpam-4220	348	238	d	d	NOUN
ejpam-4220	348	239	,	,	PUNCT
ejpam-4220	348	240	2	2	NUM
ejpam-4220	348	241	)	)	PUNCT
ejpam-4220	348	242	,	,	PUNCT
ejpam-4220	348	243	(	(	PUNCT
ejpam-4220	348	244	d	d	X
ejpam-4220	348	245	,	,	PUNCT
ejpam-4220	348	246	4	4	NUM
ejpam-4220	348	247	)	)	PUNCT
ejpam-4220	348	248	,	,	PUNCT
ejpam-4220	348	249	(	(	PUNCT
ejpam-4220	348	250	d	d	X
ejpam-4220	348	251	,	,	PUNCT
ejpam-4220	348	252	5	5	NUM
ejpam-4220	348	253	)	)	PUNCT
ejpam-4220	348	254	,	,	PUNCT
ejpam-4220	348	255	(	(	PUNCT
ejpam-4220	348	256	d	d	X
ejpam-4220	348	257	,	,	PUNCT
ejpam-4220	348	258	7	7	NUM
ejpam-4220	348	259	)	)	PUNCT
ejpam-4220	348	260	,	,	PUNCT
ejpam-4220	348	261	(	(	PUNCT
ejpam-4220	348	262	d	d	NOUN
ejpam-4220	348	263	,	,	PUNCT
ejpam-4220	348	264	8)	8)	NUM
ejpam-4220	348	265	,	,	PUNCT
ejpam-4220	348	266	(	(	PUNCT
ejpam-4220	348	267	c	c	X
ejpam-4220	348	268	,	,	PUNCT
ejpam-4220	348	269	2	2	NUM
ejpam-4220	348	270	)	)	PUNCT
ejpam-4220	348	271	,	,	PUNCT
ejpam-4220	348	272	(	(	PUNCT
ejpam-4220	348	273	c	c	X
ejpam-4220	348	274	,	,	PUNCT
ejpam-4220	348	275	4	4	NUM
ejpam-4220	348	276	)	)	PUNCT
ejpam-4220	348	277	,	,	PUNCT
ejpam-4220	348	278	(	(	PUNCT
ejpam-4220	348	279	c	c	X
ejpam-4220	348	280	,	,	PUNCT
ejpam-4220	348	281	5	5	NUM
ejpam-4220	348	282	)	)	PUNCT
ejpam-4220	348	283	,	,	PUNCT
ejpam-4220	348	284	(	(	PUNCT
ejpam-4220	348	285	c	c	X
ejpam-4220	348	286	,	,	PUNCT
ejpam-4220	348	287	7	7	NUM
ejpam-4220	348	288	)	)	PUNCT
ejpam-4220	348	289	,	,	PUNCT
ejpam-4220	348	290	(	(	PUNCT
ejpam-4220	348	291	c	c	X
ejpam-4220	348	292	,	,	PUNCT
ejpam-4220	348	293	8)	8)	NUM
ejpam-4220	348	294	,	,	PUNCT
ejpam-4220	348	295	(	(	PUNCT
ejpam-4220	348	296	b	b	NOUN
ejpam-4220	348	297	,	,	PUNCT
ejpam-4220	348	298	1	1	NUM
ejpam-4220	348	299	)	)	PUNCT
ejpam-4220	348	300	,	,	PUNCT
ejpam-4220	348	301	(	(	PUNCT
ejpam-4220	348	302	b	b	X
ejpam-4220	348	303	,	,	PUNCT
ejpam-4220	348	304	3	3	NUM
ejpam-4220	348	305	)	)	PUNCT
ejpam-4220	348	306	,	,	PUNCT
ejpam-4220	348	307	(	(	PUNCT
ejpam-4220	348	308	b	b	X
ejpam-4220	348	309	,	,	PUNCT
ejpam-4220	348	310	6	6	NUM
ejpam-4220	348	311	)	)	PUNCT
ejpam-4220	348	312	,	,	PUNCT
ejpam-4220	348	313	(	(	PUNCT
ejpam-4220	348	314	e	e	NOUN
ejpam-4220	348	315	,	,	PUNCT
ejpam-4220	348	316	1	1	NUM
ejpam-4220	348	317	)	)	PUNCT
ejpam-4220	348	318	,	,	PUNCT
ejpam-4220	348	319	(	(	PUNCT
ejpam-4220	348	320	e	e	NOUN
ejpam-4220	348	321	,	,	PUNCT
ejpam-4220	348	322	3	3	NUM
ejpam-4220	348	323	)	)	PUNCT
ejpam-4220	348	324	,	,	PUNCT
ejpam-4220	348	325	(	(	PUNCT
ejpam-4220	348	326	e	e	NOUN
ejpam-4220	348	327	,	,	PUNCT
ejpam-4220	348	328	6	6	NUM
ejpam-4220	348	329	)	)	PUNCT
ejpam-4220	348	330	}	}	PUNCT
ejpam-4220	348	331	and	and	CCONJ
ejpam-4220	348	332	{	{	PUNCT
ejpam-4220	348	333	(	(	PUNCT
ejpam-4220	348	334	b	b	NOUN
ejpam-4220	348	335	,	,	PUNCT
ejpam-4220	348	336	2	2	NUM
ejpam-4220	348	337	)	)	PUNCT
ejpam-4220	348	338	,	,	PUNCT
ejpam-4220	348	339	(	(	PUNCT
ejpam-4220	348	340	b	b	NOUN
ejpam-4220	348	341	,	,	PUNCT
ejpam-4220	348	342	4	4	NUM
ejpam-4220	348	343	)	)	PUNCT
ejpam-4220	348	344	,	,	PUNCT
ejpam-4220	348	345	(	(	PUNCT
ejpam-4220	348	346	b	b	X
ejpam-4220	348	347	,	,	PUNCT
ejpam-4220	348	348	5	5	NUM
ejpam-4220	348	349	)	)	PUNCT
ejpam-4220	348	350	,	,	PUNCT
ejpam-4220	348	351	(	(	PUNCT
ejpam-4220	348	352	b	b	NOUN
ejpam-4220	348	353	,	,	PUNCT
ejpam-4220	348	354	7	7	NUM
ejpam-4220	348	355	)	)	PUNCT
ejpam-4220	348	356	,	,	PUNCT
ejpam-4220	348	357	(	(	PUNCT
ejpam-4220	348	358	b	b	NOUN
ejpam-4220	348	359	,	,	PUNCT
ejpam-4220	348	360	8)	8)	NUM
ejpam-4220	348	361	,	,	PUNCT
ejpam-4220	348	362	(	(	PUNCT
ejpam-4220	348	363	e	e	NOUN
ejpam-4220	348	364	,	,	PUNCT
ejpam-4220	348	365	2	2	NUM
ejpam-4220	348	366	)	)	PUNCT
ejpam-4220	348	367	,	,	PUNCT
ejpam-4220	348	368	(	(	PUNCT
ejpam-4220	348	369	e	e	NOUN
ejpam-4220	348	370	,	,	PUNCT
ejpam-4220	348	371	4	4	NUM
ejpam-4220	348	372	)	)	PUNCT
ejpam-4220	348	373	,	,	PUNCT
ejpam-4220	348	374	(	(	PUNCT
ejpam-4220	348	375	e	e	NOUN
ejpam-4220	348	376	,	,	PUNCT
ejpam-4220	348	377	5	5	NUM
ejpam-4220	348	378	)	)	PUNCT
ejpam-4220	348	379	,	,	PUNCT
ejpam-4220	348	380	(	(	PUNCT
ejpam-4220	348	381	e	e	NOUN
ejpam-4220	348	382	,	,	PUNCT
ejpam-4220	348	383	7	7	NUM
ejpam-4220	348	384	)	)	PUNCT
ejpam-4220	348	385	,	,	PUNCT
ejpam-4220	348	386	(	(	PUNCT
ejpam-4220	348	387	e	e	NOUN
ejpam-4220	348	388	,	,	PUNCT
ejpam-4220	348	389	8)	8)	NUM
ejpam-4220	348	390	,	,	PUNCT
ejpam-4220	348	391	(	(	PUNCT
ejpam-4220	348	392	a	a	DET
ejpam-4220	348	393	,	,	PUNCT
ejpam-4220	348	394	1	1	NUM
ejpam-4220	348	395	)	)	PUNCT
ejpam-4220	348	396	,	,	PUNCT
ejpam-4220	348	397	(	(	PUNCT
ejpam-4220	348	398	a	a	DET
ejpam-4220	348	399	,	,	PUNCT
ejpam-4220	348	400	3)(a	3)(a	NUM
ejpam-4220	348	401	,	,	PUNCT
ejpam-4220	348	402	6	6	NUM
ejpam-4220	348	403	)	)	PUNCT
ejpam-4220	348	404	,	,	PUNCT
ejpam-4220	348	405	(	(	PUNCT
ejpam-4220	348	406	d	d	X
ejpam-4220	348	407	,	,	PUNCT
ejpam-4220	348	408	1	1	NUM
ejpam-4220	348	409	)	)	PUNCT
ejpam-4220	348	410	,	,	PUNCT
ejpam-4220	348	411	(	(	PUNCT
ejpam-4220	348	412	d	d	X
ejpam-4220	348	413	,	,	PUNCT
ejpam-4220	348	414	3	3	NUM
ejpam-4220	348	415	)	)	PUNCT
ejpam-4220	348	416	,	,	PUNCT
ejpam-4220	348	417	(	(	PUNCT
ejpam-4220	348	418	d	d	X
ejpam-4220	348	419	,	,	PUNCT
ejpam-4220	348	420	6	6	NUM
ejpam-4220	348	421	)	)	PUNCT
ejpam-4220	348	422	,	,	PUNCT
ejpam-4220	348	423	(	(	PUNCT
ejpam-4220	348	424	c	c	X
ejpam-4220	348	425	,	,	PUNCT
ejpam-4220	348	426	1	1	NUM
ejpam-4220	348	427	)	)	PUNCT
ejpam-4220	348	428	,	,	PUNCT
ejpam-4220	348	429	(	(	PUNCT
ejpam-4220	348	430	c	c	X
ejpam-4220	348	431	,	,	PUNCT
ejpam-4220	348	432	3	3	NUM
ejpam-4220	348	433	)	)	PUNCT
ejpam-4220	348	434	,	,	PUNCT
ejpam-4220	348	435	(	(	PUNCT
ejpam-4220	348	436	c	c	X
ejpam-4220	348	437	,	,	PUNCT
ejpam-4220	348	438	6	6	NUM
ejpam-4220	348	439	)	)	PUNCT
ejpam-4220	348	440	}	}	PUNCT
ejpam-4220	348	441	.	.	PUNCT
ejpam-4220	349	1	therefore	therefore	ADV
ejpam-4220	349	2	,	,	PUNCT
ejpam-4220	349	3	ni(g	ni(g	NUM
ejpam-4220	349	4	•h2	•h2	PROPN
ejpam-4220	349	5	,	,	PUNCT
ejpam-4220	349	6	x	x	NOUN
ejpam-4220	349	7	)	)	PUNCT
ejpam-4220	349	8	=	=	NOUN
ejpam-4220	349	9	ni(g	ni(g	NUM
ejpam-4220	349	10	•h1	•h1	NUM
ejpam-4220	349	11	,	,	PUNCT
ejpam-4220	349	12	x	x	NOUN
ejpam-4220	349	13	)	)	PUNCT
ejpam-4220	349	14	.	.	PUNCT
ejpam-4220	350	1	theorem	theorem	NOUN
ejpam-4220	350	2	6	6	NUM
ejpam-4220	350	3	.	.	PUNCT
ejpam-4220	351	1	suppose	suppose	VERB
ejpam-4220	351	2	g	g	PROPN
ejpam-4220	351	3	is	be	AUX
ejpam-4220	351	4	the	the	DET
ejpam-4220	351	5	rooted	rooted	ADJ
ejpam-4220	351	6	tree	tree	NOUN
ejpam-4220	351	7	with	with	ADP
ejpam-4220	351	8	independent	independent	ADJ
ejpam-4220	351	9	neighborhood	neighborhood	NOUN
ejpam-4220	351	10	sets	set	VERB
ejpam-4220	351	11	ω1,∆1	ω1,∆1	NOUN
ejpam-4220	351	12	and	and	CCONJ
ejpam-4220	351	13	h	h	NOUN
ejpam-4220	351	14	be	be	VERB
ejpam-4220	351	15	any	any	DET
ejpam-4220	351	16	tree	tree	NOUN
ejpam-4220	351	17	with	with	ADP
ejpam-4220	351	18	independent	independent	ADJ
ejpam-4220	351	19	neighborhood	neighborhood	NOUN
ejpam-4220	351	20	sets	set	VERB
ejpam-4220	351	21	ω2,∆2	ω2,∆2	PROPN
ejpam-4220	351	22	.	.	PUNCT
ejpam-4220	352	1	then	then	ADV
ejpam-4220	352	2	the	the	DET
ejpam-4220	352	3	independent	independent	ADJ
ejpam-4220	352	4	neighborhood	neighborhood	NOUN
ejpam-4220	352	5	sets	set	NOUN
ejpam-4220	352	6	of	of	ADP
ejpam-4220	352	7	h	h	PROPN
ejpam-4220	352	8	•g	•g	PROPN
ejpam-4220	352	9	are	be	AUX
ejpam-4220	352	10	{	{	PUNCT
ejpam-4220	352	11	(	(	PUNCT
ejpam-4220	352	12	x	x	NOUN
ejpam-4220	352	13	,	,	PUNCT
ejpam-4220	352	14	y	y	PROPN
ejpam-4220	352	15	)	)	PUNCT
ejpam-4220	352	16	:	:	PUNCT
ejpam-4220	353	1	x	x	PUNCT
ejpam-4220	353	2	∈	∈	PROPN
ejpam-4220	353	3	ω2	ω2	PROPN
ejpam-4220	353	4	,	,	PUNCT
ejpam-4220	353	5	y	y	PROPN
ejpam-4220	353	6	∈	∈	PROPN
ejpam-4220	353	7	ω1	ω1	PROPN
ejpam-4220	353	8	}	}	PUNCT
ejpam-4220	353	9	∪	∪	NOUN
ejpam-4220	353	10	{	{	PUNCT
ejpam-4220	353	11	(	(	PUNCT
ejpam-4220	353	12	w	w	PROPN
ejpam-4220	353	13	,	,	PUNCT
ejpam-4220	353	14	z	z	NOUN
ejpam-4220	353	15	)	)	PUNCT
ejpam-4220	353	16	:	:	PUNCT
ejpam-4220	353	17	w	w	PROPN
ejpam-4220	353	18	∈	∈	PROPN
ejpam-4220	353	19	∆2	∆2	PROPN
ejpam-4220	353	20	,	,	PUNCT
ejpam-4220	353	21	z	z	PROPN
ejpam-4220	353	22	∈	∈	PROPN
ejpam-4220	353	23	∆1	∆1	PROPN
ejpam-4220	353	24	}	}	PUNCT
ejpam-4220	353	25	and	and	CCONJ
ejpam-4220	353	26	{	{	PUNCT
ejpam-4220	353	27	(	(	PUNCT
ejpam-4220	353	28	w	w	PROPN
ejpam-4220	353	29	,	,	PUNCT
ejpam-4220	353	30	y	y	PROPN
ejpam-4220	353	31	)	)	PUNCT
ejpam-4220	353	32	:	:	PUNCT
ejpam-4220	353	33	w	w	PROPN
ejpam-4220	353	34	∈	∈	PROPN
ejpam-4220	353	35	∆2	∆2	PROPN
ejpam-4220	353	36	,	,	PUNCT
ejpam-4220	353	37	y	y	PROPN
ejpam-4220	353	38	∈	∈	PROPN
ejpam-4220	353	39	ω1	ω1	PROPN
ejpam-4220	353	40	}	}	PUNCT
ejpam-4220	353	41	∪	∪	NOUN
ejpam-4220	353	42	{	{	PUNCT
ejpam-4220	353	43	(	(	PUNCT
ejpam-4220	353	44	x	x	NOUN
ejpam-4220	353	45	,	,	PUNCT
ejpam-4220	353	46	z	z	NOUN
ejpam-4220	353	47	)	)	PUNCT
ejpam-4220	353	48	:	:	PUNCT
ejpam-4220	353	49	x	x	PUNCT
ejpam-4220	353	50	∈	∈	PROPN
ejpam-4220	353	51	ω2	ω2	PROPN
ejpam-4220	353	52	,	,	PUNCT
ejpam-4220	353	53	z	z	NOUN
ejpam-4220	353	54	∈	∈	PROPN
ejpam-4220	353	55	∆1	∆1	NOUN
ejpam-4220	353	56	}	}	PUNCT
ejpam-4220	353	57	.	.	PUNCT
ejpam-4220	354	1	proof	proof	NOUN
ejpam-4220	354	2	.	.	PUNCT
ejpam-4220	355	1	the	the	DET
ejpam-4220	355	2	proof	proof	NOUN
ejpam-4220	355	3	can	can	AUX
ejpam-4220	355	4	be	be	AUX
ejpam-4220	355	5	shown	show	VERB
ejpam-4220	355	6	similar	similar	ADJ
ejpam-4220	355	7	to	to	ADP
ejpam-4220	355	8	theorem	theorem	NOUN
ejpam-4220	355	9	4	4	NUM
ejpam-4220	355	10	by	by	ADP
ejpam-4220	355	11	just	just	ADV
ejpam-4220	355	12	interchanging	interchange	VERB
ejpam-4220	355	13	the	the	DET
ejpam-4220	355	14	first	first	ADJ
ejpam-4220	355	15	and	and	CCONJ
ejpam-4220	355	16	second	second	ADJ
ejpam-4220	355	17	coordinates	coordinate	NOUN
ejpam-4220	355	18	of	of	ADP
ejpam-4220	355	19	the	the	DET
ejpam-4220	355	20	ordered	order	VERB
ejpam-4220	355	21	pairs	pair	NOUN
ejpam-4220	355	22	of	of	ADP
ejpam-4220	355	23	vertices	vertex	NOUN
ejpam-4220	355	24	.	.	PUNCT
ejpam-4220	356	1	■	■	PUNCT
ejpam-4220	356	2	theorem	theorem	ADJ
ejpam-4220	356	3	7	7	NUM
ejpam-4220	356	4	.	.	PUNCT
ejpam-4220	356	5	let	let	VERB
ejpam-4220	356	6	ω1,∆1	ω1,∆1	NOUN
ejpam-4220	356	7	and	and	CCONJ
ejpam-4220	356	8	ω2,∆2	ω2,∆2	NUM
ejpam-4220	356	9	be	be	VERB
ejpam-4220	356	10	the	the	DET
ejpam-4220	356	11	independent	independent	ADJ
ejpam-4220	356	12	neighborhood	neighborhood	NOUN
ejpam-4220	356	13	sets	set	NOUN
ejpam-4220	356	14	of	of	ADP
ejpam-4220	356	15	trees	tree	NOUN
ejpam-4220	356	16	g	g	NOUN
ejpam-4220	356	17	and	and	CCONJ
ejpam-4220	356	18	h	h	NOUN
ejpam-4220	356	19	,	,	PUNCT
ejpam-4220	356	20	respectively	respectively	ADV
ejpam-4220	356	21	.	.	PUNCT
ejpam-4220	357	1	then	then	ADV
ejpam-4220	357	2	ni(h	ni(h	VERB
ejpam-4220	357	3	•g	•g	PROPN
ejpam-4220	357	4	,	,	PUNCT
ejpam-4220	357	5	x	x	NOUN
ejpam-4220	357	6	)	)	PUNCT
ejpam-4220	357	7	=	=	SYM
ejpam-4220	357	8	ni(g	ni(g	NOUN
ejpam-4220	357	9	•h	•h	PROPN
ejpam-4220	357	10	,	,	PUNCT
ejpam-4220	357	11	x	x	NOUN
ejpam-4220	357	12	)	)	PUNCT
ejpam-4220	357	13	.	.	PUNCT
ejpam-4220	358	1	proof	proof	NOUN
ejpam-4220	358	2	.	.	PUNCT
ejpam-4220	359	1	let	let	VERB
ejpam-4220	359	2	g	g	NOUN
ejpam-4220	359	3	and	and	CCONJ
ejpam-4220	359	4	h	h	NOUN
ejpam-4220	359	5	be	be	VERB
ejpam-4220	359	6	trees	tree	NOUN
ejpam-4220	359	7	with	with	ADP
ejpam-4220	359	8	independent	independent	ADJ
ejpam-4220	359	9	neighborhood	neighborhood	NOUN
ejpam-4220	359	10	sets	set	VERB
ejpam-4220	359	11	ω1,∆1	ω1,∆1	NUM
ejpam-4220	359	12	and	and	CCONJ
ejpam-4220	359	13	ω2,∆2	ω2,∆2	PROPN
ejpam-4220	359	14	,	,	PUNCT
ejpam-4220	359	15	respectively	respectively	ADV
ejpam-4220	359	16	.	.	PUNCT
ejpam-4220	360	1	notice	notice	VERB
ejpam-4220	360	2	that	that	SCONJ
ejpam-4220	360	3	|{(x1	|{(x1	PROPN
ejpam-4220	360	4	,	,	PUNCT
ejpam-4220	360	5	y1	y1	NOUN
ejpam-4220	360	6	)	)	PUNCT
ejpam-4220	360	7	:	:	PUNCT
ejpam-4220	360	8	x1	x1	PROPN
ejpam-4220	360	9	∈	∈	PROPN
ejpam-4220	360	10	ω1	ω1	PROPN
ejpam-4220	360	11	,	,	PUNCT
ejpam-4220	360	12	y1	y1	PROPN
ejpam-4220	360	13	∈	∈	PROPN
ejpam-4220	360	14	ω2}|	ω2}|	PROPN
ejpam-4220	360	15	=	=	SYM
ejpam-4220	360	16	|{(x2	|{(x2	PROPN
ejpam-4220	360	17	,	,	PUNCT
ejpam-4220	360	18	y2	y2	PROPN
ejpam-4220	360	19	)	)	PUNCT
ejpam-4220	360	20	:	:	PUNCT
ejpam-4220	361	1	x2	x2	PROPN
ejpam-4220	361	2	∈	∈	PROPN
ejpam-4220	361	3	ω2	ω2	PROPN
ejpam-4220	361	4	,	,	PUNCT
ejpam-4220	361	5	y2	y2	PROPN
ejpam-4220	361	6	∈	∈	PROPN
ejpam-4220	361	7	ω1}|	ω1}|	PROPN
ejpam-4220	361	8	n.	n.	PROPN
ejpam-4220	361	9	s.	s.	PROPN
ejpam-4220	361	10	abdulcarim	abdulcarim	PROPN
ejpam-4220	361	11	,	,	PUNCT
ejpam-4220	361	12	s.	s.	PROPN
ejpam-4220	361	13	c.	c.	PROPN
ejpam-4220	361	14	dagondon	dagondon	PROPN
ejpam-4220	361	15	/	/	SYM
ejpam-4220	361	16	eur	eur	PROPN
ejpam-4220	361	17	.	.	PUNCT
ejpam-4220	362	1	j.	j.	PROPN
ejpam-4220	362	2	pure	pure	PROPN
ejpam-4220	362	3	appl	appl	PROPN
ejpam-4220	362	4	.	.	PROPN
ejpam-4220	362	5	math	math	PROPN
ejpam-4220	362	6	,	,	PUNCT
ejpam-4220	362	7	15	15	NUM
ejpam-4220	362	8	(	(	PUNCT
ejpam-4220	362	9	1	1	NUM
ejpam-4220	362	10	)	)	PUNCT
ejpam-4220	362	11	(	(	PUNCT
ejpam-4220	362	12	2022	2022	NUM
ejpam-4220	362	13	)	)	PUNCT
ejpam-4220	362	14	,	,	PUNCT
ejpam-4220	362	15	64	64	NUM
ejpam-4220	362	16	-	-	SYM
ejpam-4220	362	17	81	81	NUM
ejpam-4220	362	18	79	79	NUM
ejpam-4220	362	19	|{(x3	|{(x3	NOUN
ejpam-4220	362	20	,	,	PUNCT
ejpam-4220	362	21	y3	y3	PROPN
ejpam-4220	362	22	)	)	PUNCT
ejpam-4220	362	23	:	:	PUNCT
ejpam-4220	363	1	x3	x3	PROPN
ejpam-4220	363	2	∈	∈	PROPN
ejpam-4220	363	3	∆1	∆1	NOUN
ejpam-4220	363	4	,	,	PUNCT
ejpam-4220	363	5	y3	y3	PROPN
ejpam-4220	363	6	∈	∈	NOUN
ejpam-4220	363	7	∆2}|	∆2}|	VERB
ejpam-4220	363	8	=	=	SYM
ejpam-4220	363	9	|{(x4	|{(x4	X
ejpam-4220	363	10	,	,	PUNCT
ejpam-4220	363	11	y4	y4	NUM
ejpam-4220	363	12	)	)	PUNCT
ejpam-4220	363	13	:	:	PUNCT
ejpam-4220	363	14	x4	x4	PROPN
ejpam-4220	363	15	∈	∈	PROPN
ejpam-4220	363	16	∆2	∆2	PROPN
ejpam-4220	363	17	,	,	PUNCT
ejpam-4220	363	18	y4	y4	PROPN
ejpam-4220	363	19	∈	∈	PROPN
ejpam-4220	363	20	∆1}|	∆1}|	PROPN
ejpam-4220	363	21	|{(x5	|{(x5	PROPN
ejpam-4220	363	22	,	,	PUNCT
ejpam-4220	363	23	y5	y5	NOUN
ejpam-4220	363	24	)	)	PUNCT
ejpam-4220	363	25	:	:	PUNCT
ejpam-4220	363	26	x5	x5	PROPN
ejpam-4220	363	27	∈	∈	PROPN
ejpam-4220	363	28	∆1	∆1	NOUN
ejpam-4220	363	29	,	,	PUNCT
ejpam-4220	363	30	y5	y5	PROPN
ejpam-4220	363	31	∈	∈	NOUN
ejpam-4220	363	32	ω2}|	ω2}|	PROPN
ejpam-4220	363	33	=	=	SYM
ejpam-4220	363	34	|{(x6	|{(x6	NOUN
ejpam-4220	363	35	,	,	PUNCT
ejpam-4220	363	36	y6	y6	PROPN
ejpam-4220	363	37	)	)	PUNCT
ejpam-4220	363	38	:	:	PUNCT
ejpam-4220	363	39	x5	x5	PROPN
ejpam-4220	363	40	∈	∈	PROPN
ejpam-4220	363	41	ω2	ω2	PROPN
ejpam-4220	363	42	,	,	PUNCT
ejpam-4220	363	43	y6	y6	PROPN
ejpam-4220	363	44	∈	∈	PROPN
ejpam-4220	363	45	∆1}|	∆1}|	PROPN
ejpam-4220	363	46	|{(x7	|{(x7	PROPN
ejpam-4220	363	47	,	,	PUNCT
ejpam-4220	363	48	y7	y7	PROPN
ejpam-4220	363	49	)	)	PUNCT
ejpam-4220	363	50	:	:	PUNCT
ejpam-4220	364	1	x7	x7	X
ejpam-4220	364	2	∈	∈	PROPN
ejpam-4220	364	3	ω1	ω1	PROPN
ejpam-4220	364	4	,	,	PUNCT
ejpam-4220	364	5	y7	y7	PROPN
ejpam-4220	364	6	∈	∈	NOUN
ejpam-4220	364	7	∆2}|	∆2}|	PROPN
ejpam-4220	364	8	=	=	SYM
ejpam-4220	364	9	|{(x8	|{(x8	PROPN
ejpam-4220	364	10	,	,	PUNCT
ejpam-4220	364	11	y8	y8	PROPN
ejpam-4220	364	12	)	)	PUNCT
ejpam-4220	364	13	:	:	PUNCT
ejpam-4220	364	14	x8	x8	PROPN
ejpam-4220	364	15	∈	∈	PROPN
ejpam-4220	364	16	∆2	∆2	PROPN
ejpam-4220	364	17	,	,	PUNCT
ejpam-4220	364	18	y8	y8	PROPN
ejpam-4220	364	19	∈	∈	PROPN
ejpam-4220	364	20	ω1}|	ω1}|	PROPN
ejpam-4220	364	21	.	.	PUNCT
ejpam-4220	365	1	therefore	therefore	ADV
ejpam-4220	365	2	,	,	PUNCT
ejpam-4220	365	3	ni(h	ni(h	PUNCT
ejpam-4220	365	4	•g	•g	PROPN
ejpam-4220	365	5	,	,	PUNCT
ejpam-4220	365	6	x	x	NOUN
ejpam-4220	365	7	)	)	PUNCT
ejpam-4220	365	8	=	=	SYM
ejpam-4220	365	9	ni(g	ni(g	NOUN
ejpam-4220	365	10	•h	•h	PROPN
ejpam-4220	365	11	,	,	PUNCT
ejpam-4220	365	12	x	x	NOUN
ejpam-4220	365	13	)	)	PUNCT
ejpam-4220	365	14	.	.	PUNCT
ejpam-4220	366	1	■	■	PUNCT
ejpam-4220	366	2	example	example	NOUN
ejpam-4220	366	3	8	8	NUM
ejpam-4220	366	4	.	.	PUNCT
ejpam-4220	367	1	consider	consider	VERB
ejpam-4220	367	2	the	the	DET
ejpam-4220	367	3	graphs	graph	NOUN
ejpam-4220	367	4	g	g	NOUN
ejpam-4220	367	5	and	and	CCONJ
ejpam-4220	367	6	h	h	NOUN
ejpam-4220	367	7	in	in	ADP
ejpam-4220	367	8	figure	figure	NOUN
ejpam-4220	367	9	5	5	NUM
ejpam-4220	367	10	.	.	PUNCT
ejpam-4220	367	11	suppose	suppose	VERB
ejpam-4220	367	12	that	that	SCONJ
ejpam-4220	367	13	g	g	PROPN
ejpam-4220	367	14	is	be	AUX
ejpam-4220	367	15	the	the	DET
ejpam-4220	367	16	rooted	rooted	ADJ
ejpam-4220	367	17	graph	graph	NOUN
ejpam-4220	367	18	and	and	CCONJ
ejpam-4220	367	19	wihtout	wihtout	VERB
ejpam-4220	367	20	loss	loss	NOUN
ejpam-4220	367	21	of	of	ADP
ejpam-4220	367	22	generality	generality	NOUN
ejpam-4220	367	23	,	,	PUNCT
ejpam-4220	367	24	let	let	VERB
ejpam-4220	367	25	a	a	PRON
ejpam-4220	367	26	be	be	AUX
ejpam-4220	367	27	its	its	PRON
ejpam-4220	367	28	rooted	rooted	ADJ
ejpam-4220	367	29	vertex	vertex	NOUN
ejpam-4220	367	30	shown	show	VERB
ejpam-4220	367	31	in	in	ADP
ejpam-4220	367	32	figure	figure	NOUN
ejpam-4220	367	33	8	8	NUM
ejpam-4220	367	34	.	.	PUNCT
ejpam-4220	368	1	(	(	PUNCT
ejpam-4220	368	2	1	1	NUM
ejpam-4220	368	3	,	,	PUNCT
ejpam-4220	368	4	a	a	NOUN
ejpam-4220	368	5	)	)	PUNCT
ejpam-4220	368	6	(	(	PUNCT
ejpam-4220	368	7	1	1	NUM
ejpam-4220	368	8	,	,	PUNCT
ejpam-4220	368	9	b	b	NOUN
ejpam-4220	368	10	)	)	PUNCT
ejpam-4220	368	11	(	(	PUNCT
ejpam-4220	368	12	1	1	NUM
ejpam-4220	368	13	,	,	PUNCT
ejpam-4220	368	14	c	c	NOUN
ejpam-4220	368	15	)	)	PUNCT
ejpam-4220	368	16	(	(	PUNCT
ejpam-4220	368	17	1	1	NUM
ejpam-4220	368	18	,	,	PUNCT
ejpam-4220	368	19	d	d	NOUN
ejpam-4220	368	20	)	)	PUNCT
ejpam-4220	368	21	(	(	PUNCT
ejpam-4220	368	22	1	1	NUM
ejpam-4220	368	23	,	,	PUNCT
ejpam-4220	368	24	e	e	NOUN
ejpam-4220	368	25	)	)	PUNCT
ejpam-4220	368	26	(	(	PUNCT
ejpam-4220	368	27	2	2	NUM
ejpam-4220	368	28	,	,	PUNCT
ejpam-4220	368	29	a	a	NOUN
ejpam-4220	368	30	)	)	PUNCT
ejpam-4220	368	31	(	(	PUNCT
ejpam-4220	368	32	2	2	NUM
ejpam-4220	368	33	,	,	PUNCT
ejpam-4220	368	34	b	b	NOUN
ejpam-4220	368	35	)	)	PUNCT
ejpam-4220	368	36	(	(	PUNCT
ejpam-4220	368	37	2	2	NUM
ejpam-4220	368	38	,	,	PUNCT
ejpam-4220	368	39	c	c	NOUN
ejpam-4220	368	40	)	)	PUNCT
ejpam-4220	368	41	(	(	PUNCT
ejpam-4220	368	42	2	2	NUM
ejpam-4220	368	43	,	,	PUNCT
ejpam-4220	368	44	d	d	NOUN
ejpam-4220	368	45	)	)	PUNCT
ejpam-4220	368	46	(	(	PUNCT
ejpam-4220	368	47	2	2	NUM
ejpam-4220	368	48	,	,	PUNCT
ejpam-4220	368	49	e	e	NOUN
ejpam-4220	368	50	)	)	PUNCT
ejpam-4220	368	51	(	(	PUNCT
ejpam-4220	368	52	3	3	NUM
ejpam-4220	368	53	,	,	PUNCT
ejpam-4220	368	54	a	a	NOUN
ejpam-4220	368	55	)	)	PUNCT
ejpam-4220	368	56	(	(	PUNCT
ejpam-4220	368	57	3	3	NUM
ejpam-4220	368	58	,	,	PUNCT
ejpam-4220	368	59	b	b	NOUN
ejpam-4220	368	60	)	)	PUNCT
ejpam-4220	368	61	(	(	PUNCT
ejpam-4220	368	62	3	3	NUM
ejpam-4220	368	63	,	,	PUNCT
ejpam-4220	368	64	c	c	NOUN
ejpam-4220	368	65	)	)	PUNCT
ejpam-4220	368	66	(	(	PUNCT
ejpam-4220	368	67	3	3	NUM
ejpam-4220	368	68	,	,	PUNCT
ejpam-4220	368	69	d	d	NOUN
ejpam-4220	368	70	)	)	PUNCT
ejpam-4220	368	71	(	(	PUNCT
ejpam-4220	368	72	3	3	NUM
ejpam-4220	368	73	,	,	PUNCT
ejpam-4220	368	74	e	e	NOUN
ejpam-4220	368	75	)	)	PUNCT
ejpam-4220	368	76	(	(	PUNCT
ejpam-4220	368	77	4	4	NUM
ejpam-4220	368	78	,	,	PUNCT
ejpam-4220	368	79	a	a	NOUN
ejpam-4220	368	80	)	)	PUNCT
ejpam-4220	368	81	(	(	PUNCT
ejpam-4220	368	82	4	4	NUM
ejpam-4220	368	83	,	,	PUNCT
ejpam-4220	368	84	b	b	NOUN
ejpam-4220	368	85	)	)	PUNCT
ejpam-4220	368	86	(	(	PUNCT
ejpam-4220	368	87	4	4	NUM
ejpam-4220	368	88	,	,	PUNCT
ejpam-4220	368	89	c	c	NOUN
ejpam-4220	368	90	)	)	PUNCT
ejpam-4220	368	91	(	(	PUNCT
ejpam-4220	368	92	4	4	NUM
ejpam-4220	368	93	,	,	PUNCT
ejpam-4220	368	94	d	d	NOUN
ejpam-4220	368	95	)	)	PUNCT
ejpam-4220	368	96	(	(	PUNCT
ejpam-4220	368	97	4	4	NUM
ejpam-4220	368	98	,	,	PUNCT
ejpam-4220	368	99	e	e	NOUN
ejpam-4220	368	100	)	)	PUNCT
ejpam-4220	368	101	(	(	PUNCT
ejpam-4220	368	102	5	5	NUM
ejpam-4220	368	103	,	,	PUNCT
ejpam-4220	368	104	a	a	NOUN
ejpam-4220	368	105	)	)	PUNCT
ejpam-4220	368	106	(	(	PUNCT
ejpam-4220	368	107	5	5	NUM
ejpam-4220	368	108	,	,	PUNCT
ejpam-4220	368	109	b	b	NOUN
ejpam-4220	368	110	)	)	PUNCT
ejpam-4220	368	111	(	(	PUNCT
ejpam-4220	368	112	5	5	NUM
ejpam-4220	368	113	,	,	PUNCT
ejpam-4220	368	114	c	c	NOUN
ejpam-4220	368	115	)	)	PUNCT
ejpam-4220	368	116	(	(	PUNCT
ejpam-4220	368	117	5	5	NUM
ejpam-4220	368	118	,	,	PUNCT
ejpam-4220	368	119	d	d	NOUN
ejpam-4220	368	120	)	)	PUNCT
ejpam-4220	368	121	(	(	PUNCT
ejpam-4220	368	122	5	5	NUM
ejpam-4220	368	123	,	,	PUNCT
ejpam-4220	368	124	e	e	NOUN
ejpam-4220	368	125	)	)	PUNCT
ejpam-4220	368	126	(	(	PUNCT
ejpam-4220	368	127	6	6	NUM
ejpam-4220	368	128	,	,	PUNCT
ejpam-4220	368	129	a	a	NOUN
ejpam-4220	368	130	)	)	PUNCT
ejpam-4220	368	131	(	(	PUNCT
ejpam-4220	368	132	6	6	NUM
ejpam-4220	368	133	,	,	PUNCT
ejpam-4220	368	134	b	b	NOUN
ejpam-4220	368	135	)	)	PUNCT
ejpam-4220	368	136	(	(	PUNCT
ejpam-4220	368	137	6	6	NUM
ejpam-4220	368	138	,	,	PUNCT
ejpam-4220	368	139	c	c	NOUN
ejpam-4220	368	140	)	)	PUNCT
ejpam-4220	368	141	(	(	PUNCT
ejpam-4220	368	142	6	6	NUM
ejpam-4220	368	143	,	,	PUNCT
ejpam-4220	368	144	d	d	NOUN
ejpam-4220	368	145	)	)	PUNCT
ejpam-4220	368	146	(	(	PUNCT
ejpam-4220	368	147	6	6	NUM
ejpam-4220	368	148	,	,	PUNCT
ejpam-4220	368	149	e	e	NOUN
ejpam-4220	368	150	)	)	PUNCT
ejpam-4220	368	151	(	(	PUNCT
ejpam-4220	368	152	7	7	NUM
ejpam-4220	368	153	,	,	PUNCT
ejpam-4220	368	154	a	a	NOUN
ejpam-4220	368	155	)	)	PUNCT
ejpam-4220	368	156	(	(	PUNCT
ejpam-4220	368	157	7	7	NUM
ejpam-4220	368	158	,	,	PUNCT
ejpam-4220	368	159	b	b	NOUN
ejpam-4220	368	160	)	)	PUNCT
ejpam-4220	368	161	(	(	PUNCT
ejpam-4220	368	162	7	7	NUM
ejpam-4220	368	163	,	,	PUNCT
ejpam-4220	368	164	c	c	NOUN
ejpam-4220	368	165	)	)	PUNCT
ejpam-4220	368	166	(	(	PUNCT
ejpam-4220	368	167	7	7	NUM
ejpam-4220	368	168	,	,	PUNCT
ejpam-4220	368	169	d	d	NOUN
ejpam-4220	368	170	)	)	PUNCT
ejpam-4220	368	171	(	(	PUNCT
ejpam-4220	368	172	7	7	NUM
ejpam-4220	368	173	,	,	PUNCT
ejpam-4220	368	174	e	e	NOUN
ejpam-4220	368	175	)	)	PUNCT
ejpam-4220	368	176	(	(	PUNCT
ejpam-4220	368	177	8	8	NUM
ejpam-4220	368	178	,	,	PUNCT
ejpam-4220	368	179	a	a	NOUN
ejpam-4220	368	180	)	)	PUNCT
ejpam-4220	368	181	(	(	PUNCT
ejpam-4220	368	182	8	8	NUM
ejpam-4220	368	183	,	,	PUNCT
ejpam-4220	368	184	b	b	NOUN
ejpam-4220	368	185	)	)	PUNCT
ejpam-4220	368	186	(	(	PUNCT
ejpam-4220	368	187	8	8	NUM
ejpam-4220	368	188	,	,	PUNCT
ejpam-4220	368	189	c	c	NOUN
ejpam-4220	368	190	)	)	PUNCT
ejpam-4220	368	191	(	(	PUNCT
ejpam-4220	368	192	8	8	NUM
ejpam-4220	368	193	,	,	PUNCT
ejpam-4220	368	194	d	d	NOUN
ejpam-4220	368	195	)	)	PUNCT
ejpam-4220	368	196	(	(	PUNCT
ejpam-4220	368	197	8	8	NUM
ejpam-4220	368	198	,	,	PUNCT
ejpam-4220	368	199	e	e	NOUN
ejpam-4220	368	200	)	)	PUNCT
ejpam-4220	368	201	figure	figure	NOUN
ejpam-4220	368	202	8	8	NUM
ejpam-4220	368	203	:	:	PUNCT
ejpam-4220	368	204	rooted	rooted	ADJ
ejpam-4220	368	205	product	product	NOUN
ejpam-4220	368	206	of	of	ADP
ejpam-4220	368	207	tree	tree	NOUN
ejpam-4220	368	208	h	h	NOUN
ejpam-4220	368	209	and	and	CCONJ
ejpam-4220	368	210	rooted	root	VERB
ejpam-4220	368	211	tree	tree	NOUN
ejpam-4220	368	212	g	g	NOUN
ejpam-4220	368	213	by	by	ADP
ejpam-4220	368	214	theorem	theorem	NOUN
ejpam-4220	368	215	6	6	NUM
ejpam-4220	368	216	,	,	PUNCT
ejpam-4220	368	217	the	the	DET
ejpam-4220	368	218	independent	independent	ADJ
ejpam-4220	368	219	neighborhood	neighborhood	NOUN
ejpam-4220	368	220	sets	set	NOUN
ejpam-4220	368	221	of	of	ADP
ejpam-4220	368	222	h	h	PROPN
ejpam-4220	368	223	•g	•g	PROPN
ejpam-4220	368	224	are	be	AUX
ejpam-4220	368	225	{	{	PUNCT
ejpam-4220	368	226	(	(	PUNCT
ejpam-4220	368	227	x	x	NOUN
ejpam-4220	368	228	,	,	PUNCT
ejpam-4220	368	229	y	y	PROPN
ejpam-4220	368	230	)	)	PUNCT
ejpam-4220	368	231	:	:	PUNCT
ejpam-4220	369	1	x	x	PUNCT
ejpam-4220	369	2	∈	∈	PROPN
ejpam-4220	369	3	ω2	ω2	PROPN
ejpam-4220	369	4	,	,	PUNCT
ejpam-4220	369	5	y	y	PROPN
ejpam-4220	369	6	∈	∈	PROPN
ejpam-4220	369	7	ω1	ω1	PROPN
ejpam-4220	369	8	}	}	PUNCT
ejpam-4220	369	9	∪	∪	NOUN
ejpam-4220	369	10	{	{	PUNCT
ejpam-4220	369	11	(	(	PUNCT
ejpam-4220	369	12	w	w	PROPN
ejpam-4220	369	13	,	,	PUNCT
ejpam-4220	369	14	z	z	NOUN
ejpam-4220	369	15	)	)	PUNCT
ejpam-4220	369	16	:	:	PUNCT
ejpam-4220	369	17	w	w	PROPN
ejpam-4220	369	18	∈	∈	PROPN
ejpam-4220	369	19	∆2	∆2	PROPN
ejpam-4220	369	20	,	,	PUNCT
ejpam-4220	369	21	z	z	PROPN
ejpam-4220	369	22	∈	∈	PROPN
ejpam-4220	369	23	∆1	∆1	PROPN
ejpam-4220	369	24	}	}	PUNCT
ejpam-4220	369	25	=	=	SYM
ejpam-4220	369	26	{	{	PUNCT
ejpam-4220	369	27	(	(	PUNCT
ejpam-4220	369	28	2	2	NUM
ejpam-4220	369	29	,	,	PUNCT
ejpam-4220	369	30	a	a	NOUN
ejpam-4220	369	31	)	)	PUNCT
ejpam-4220	369	32	,	,	PUNCT
ejpam-4220	369	33	(	(	PUNCT
ejpam-4220	369	34	2	2	NUM
ejpam-4220	369	35	,	,	PUNCT
ejpam-4220	369	36	d	d	NOUN
ejpam-4220	369	37	)	)	PUNCT
ejpam-4220	369	38	,	,	PUNCT
ejpam-4220	369	39	(	(	PUNCT
ejpam-4220	369	40	2	2	NUM
ejpam-4220	369	41	,	,	PUNCT
ejpam-4220	369	42	c	c	NOUN
ejpam-4220	369	43	)	)	PUNCT
ejpam-4220	369	44	,	,	PUNCT
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ejpam-4220	369	46	4	4	NUM
ejpam-4220	369	47	,	,	PUNCT
ejpam-4220	369	48	a	a	NOUN
ejpam-4220	369	49	)	)	PUNCT
ejpam-4220	369	50	,	,	PUNCT
ejpam-4220	369	51	(	(	PUNCT
ejpam-4220	369	52	4	4	NUM
ejpam-4220	369	53	,	,	PUNCT
ejpam-4220	369	54	d	d	NOUN
ejpam-4220	369	55	)	)	PUNCT
ejpam-4220	369	56	,	,	PUNCT
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ejpam-4220	369	58	4	4	NUM
ejpam-4220	369	59	,	,	PUNCT
ejpam-4220	369	60	c	c	NOUN
ejpam-4220	369	61	)	)	PUNCT
ejpam-4220	369	62	,	,	PUNCT
ejpam-4220	369	63	(	(	PUNCT
ejpam-4220	369	64	5	5	NUM
ejpam-4220	369	65	,	,	PUNCT
ejpam-4220	369	66	a	a	PRON
ejpam-4220	369	67	)	)	PUNCT
ejpam-4220	369	68	,	,	PUNCT
ejpam-4220	369	69	(	(	PUNCT
ejpam-4220	369	70	5	5	NUM
ejpam-4220	369	71	,	,	PUNCT
ejpam-4220	369	72	d	d	NOUN
ejpam-4220	369	73	)	)	PUNCT
ejpam-4220	369	74	,	,	PUNCT
ejpam-4220	369	75	(	(	PUNCT
ejpam-4220	369	76	5	5	NUM
ejpam-4220	369	77	,	,	PUNCT
ejpam-4220	369	78	c	c	NOUN
ejpam-4220	369	79	)	)	PUNCT
ejpam-4220	369	80	,	,	PUNCT
ejpam-4220	369	81	(	(	PUNCT
ejpam-4220	369	82	7	7	NUM
ejpam-4220	369	83	,	,	PUNCT
ejpam-4220	369	84	a	a	PRON
ejpam-4220	369	85	)	)	PUNCT
ejpam-4220	369	86	,	,	PUNCT
ejpam-4220	369	87	(	(	PUNCT
ejpam-4220	369	88	7	7	NUM
ejpam-4220	369	89	,	,	PUNCT
ejpam-4220	369	90	d	d	NOUN
ejpam-4220	369	91	)	)	PUNCT
ejpam-4220	369	92	,	,	PUNCT
ejpam-4220	369	93	(	(	PUNCT
ejpam-4220	369	94	7	7	NUM
ejpam-4220	369	95	,	,	PUNCT
ejpam-4220	369	96	c	c	NOUN
ejpam-4220	369	97	)	)	PUNCT
ejpam-4220	369	98	,	,	PUNCT
ejpam-4220	369	99	(	(	PUNCT
ejpam-4220	369	100	8	8	NUM
ejpam-4220	369	101	,	,	PUNCT
ejpam-4220	369	102	a	a	PRON
ejpam-4220	369	103	)	)	PUNCT
ejpam-4220	369	104	,	,	PUNCT
ejpam-4220	369	105	(	(	PUNCT
ejpam-4220	369	106	8	8	NUM
ejpam-4220	369	107	,	,	PUNCT
ejpam-4220	369	108	d	d	NOUN
ejpam-4220	369	109	)	)	PUNCT
ejpam-4220	369	110	,	,	PUNCT
ejpam-4220	369	111	(	(	PUNCT
ejpam-4220	369	112	8	8	NUM
ejpam-4220	369	113	,	,	PUNCT
ejpam-4220	369	114	c	c	NOUN
ejpam-4220	369	115	)	)	PUNCT
ejpam-4220	369	116	}	}	PUNCT
ejpam-4220	369	117	∪	∪	X
ejpam-4220	369	118	{	{	PUNCT
ejpam-4220	369	119	(	(	PUNCT
ejpam-4220	369	120	1	1	NUM
ejpam-4220	369	121	,	,	PUNCT
ejpam-4220	369	122	b	b	NOUN
ejpam-4220	369	123	)	)	PUNCT
ejpam-4220	369	124	,	,	PUNCT
ejpam-4220	369	125	(	(	PUNCT
ejpam-4220	369	126	1	1	NUM
ejpam-4220	369	127	,	,	PUNCT
ejpam-4220	369	128	e	e	NOUN
ejpam-4220	369	129	)	)	PUNCT
ejpam-4220	369	130	,	,	PUNCT
ejpam-4220	369	131	(	(	PUNCT
ejpam-4220	369	132	3	3	NUM
ejpam-4220	369	133	,	,	PUNCT
ejpam-4220	369	134	b	b	NOUN
ejpam-4220	369	135	)	)	PUNCT
ejpam-4220	369	136	,	,	PUNCT
ejpam-4220	369	137	(	(	PUNCT
ejpam-4220	369	138	3	3	NUM
ejpam-4220	369	139	,	,	PUNCT
ejpam-4220	369	140	e	e	NOUN
ejpam-4220	369	141	)	)	PUNCT
ejpam-4220	369	142	,	,	PUNCT
ejpam-4220	369	143	(	(	PUNCT
ejpam-4220	369	144	6	6	NUM
ejpam-4220	369	145	,	,	PUNCT
ejpam-4220	369	146	b	b	NOUN
ejpam-4220	369	147	)	)	PUNCT
ejpam-4220	369	148	,	,	PUNCT
ejpam-4220	369	149	(	(	PUNCT
ejpam-4220	369	150	6	6	NUM
ejpam-4220	369	151	,	,	PUNCT
ejpam-4220	369	152	e	e	NOUN
ejpam-4220	369	153	)	)	PUNCT
ejpam-4220	369	154	}	}	PUNCT
ejpam-4220	369	155	=	=	SYM
ejpam-4220	369	156	{	{	PUNCT
ejpam-4220	369	157	(	(	PUNCT
ejpam-4220	369	158	2	2	NUM
ejpam-4220	369	159	,	,	PUNCT
ejpam-4220	369	160	a	a	NOUN
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ejpam-4220	369	162	,	,	PUNCT
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ejpam-4220	369	164	2	2	NUM
ejpam-4220	369	165	,	,	PUNCT
ejpam-4220	369	166	d	d	NOUN
ejpam-4220	369	167	)	)	PUNCT
ejpam-4220	369	168	,	,	PUNCT
ejpam-4220	369	169	(	(	PUNCT
ejpam-4220	369	170	2	2	NUM
ejpam-4220	369	171	,	,	PUNCT
ejpam-4220	369	172	c	c	NOUN
ejpam-4220	369	173	)	)	PUNCT
ejpam-4220	369	174	,	,	PUNCT
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ejpam-4220	369	176	4	4	NUM
ejpam-4220	369	177	,	,	PUNCT
ejpam-4220	369	178	a	a	NOUN
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ejpam-4220	369	180	,	,	PUNCT
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ejpam-4220	369	182	4	4	NUM
ejpam-4220	369	183	,	,	PUNCT
ejpam-4220	369	184	d	d	NOUN
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ejpam-4220	369	186	,	,	PUNCT
ejpam-4220	369	187	(	(	PUNCT
ejpam-4220	369	188	4	4	NUM
ejpam-4220	369	189	,	,	PUNCT
ejpam-4220	369	190	c	c	NOUN
ejpam-4220	369	191	)	)	PUNCT
ejpam-4220	369	192	,	,	PUNCT
ejpam-4220	369	193	(	(	PUNCT
ejpam-4220	369	194	5	5	NUM
ejpam-4220	369	195	,	,	PUNCT
ejpam-4220	369	196	a	a	PRON
ejpam-4220	369	197	)	)	PUNCT
ejpam-4220	369	198	,	,	PUNCT
ejpam-4220	369	199	(	(	PUNCT
ejpam-4220	369	200	5	5	NUM
ejpam-4220	369	201	,	,	PUNCT
ejpam-4220	369	202	d	d	NOUN
ejpam-4220	369	203	)	)	PUNCT
ejpam-4220	369	204	,	,	PUNCT
ejpam-4220	369	205	(	(	PUNCT
ejpam-4220	369	206	5	5	NUM
ejpam-4220	369	207	,	,	PUNCT
ejpam-4220	369	208	c	c	NOUN
ejpam-4220	369	209	)	)	PUNCT
ejpam-4220	369	210	,	,	PUNCT
ejpam-4220	369	211	(	(	PUNCT
ejpam-4220	369	212	7	7	NUM
ejpam-4220	369	213	,	,	PUNCT
ejpam-4220	369	214	a	a	PRON
ejpam-4220	369	215	)	)	PUNCT
ejpam-4220	369	216	,	,	PUNCT
ejpam-4220	369	217	(	(	PUNCT
ejpam-4220	369	218	7	7	NUM
ejpam-4220	369	219	,	,	PUNCT
ejpam-4220	369	220	d	d	NOUN
ejpam-4220	369	221	)	)	PUNCT
ejpam-4220	369	222	,	,	PUNCT
ejpam-4220	369	223	(	(	PUNCT
ejpam-4220	369	224	7	7	NUM
ejpam-4220	369	225	,	,	PUNCT
ejpam-4220	369	226	c	c	NOUN
ejpam-4220	369	227	)	)	PUNCT
ejpam-4220	369	228	,	,	PUNCT
ejpam-4220	369	229	(	(	PUNCT
ejpam-4220	369	230	8	8	NUM
ejpam-4220	369	231	,	,	PUNCT
ejpam-4220	369	232	a	a	PRON
ejpam-4220	369	233	)	)	PUNCT
ejpam-4220	369	234	,	,	PUNCT
ejpam-4220	369	235	(	(	PUNCT
ejpam-4220	369	236	8	8	NUM
ejpam-4220	369	237	,	,	PUNCT
ejpam-4220	369	238	d	d	NOUN
ejpam-4220	369	239	)	)	PUNCT
ejpam-4220	369	240	,	,	PUNCT
ejpam-4220	369	241	(	(	PUNCT
ejpam-4220	369	242	8	8	NUM
ejpam-4220	369	243	,	,	PUNCT
ejpam-4220	369	244	c	c	NOUN
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ejpam-4220	369	246	,	,	PUNCT
ejpam-4220	369	247	(	(	PUNCT
ejpam-4220	369	248	1	1	NUM
ejpam-4220	369	249	,	,	PUNCT
ejpam-4220	369	250	b	b	NOUN
ejpam-4220	369	251	)	)	PUNCT
ejpam-4220	369	252	,	,	PUNCT
ejpam-4220	369	253	(	(	PUNCT
ejpam-4220	369	254	1	1	NUM
ejpam-4220	369	255	,	,	PUNCT
ejpam-4220	369	256	e	e	NOUN
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ejpam-4220	369	258	,	,	PUNCT
ejpam-4220	369	259	(	(	PUNCT
ejpam-4220	369	260	3	3	NUM
ejpam-4220	369	261	,	,	PUNCT
ejpam-4220	369	262	b	b	NOUN
ejpam-4220	369	263	)	)	PUNCT
ejpam-4220	369	264	,	,	PUNCT
ejpam-4220	369	265	(	(	PUNCT
ejpam-4220	369	266	3	3	NUM
ejpam-4220	369	267	,	,	PUNCT
ejpam-4220	369	268	e	e	NOUN
ejpam-4220	369	269	)	)	PUNCT
ejpam-4220	369	270	,	,	PUNCT
ejpam-4220	369	271	(	(	PUNCT
ejpam-4220	369	272	6	6	NUM
ejpam-4220	369	273	,	,	PUNCT
ejpam-4220	369	274	b	b	NOUN
ejpam-4220	369	275	)	)	PUNCT
ejpam-4220	369	276	,	,	PUNCT
ejpam-4220	369	277	(	(	PUNCT
ejpam-4220	369	278	6	6	NUM
ejpam-4220	369	279	,	,	PUNCT
ejpam-4220	369	280	e	e	NOUN
ejpam-4220	369	281	)	)	PUNCT
ejpam-4220	369	282	}	}	PUNCT
ejpam-4220	369	283	and	and	CCONJ
ejpam-4220	369	284	{	{	PUNCT
ejpam-4220	369	285	(	(	PUNCT
ejpam-4220	369	286	x	x	NOUN
ejpam-4220	369	287	,	,	PUNCT
ejpam-4220	369	288	y	y	PROPN
ejpam-4220	369	289	)	)	PUNCT
ejpam-4220	369	290	:	:	PUNCT
ejpam-4220	369	291	x	x	X
ejpam-4220	369	292	∈	∈	PROPN
ejpam-4220	369	293	∆2	∆2	PROPN
ejpam-4220	369	294	,	,	PUNCT
ejpam-4220	369	295	y	y	PROPN
ejpam-4220	369	296	∈	∈	PROPN
ejpam-4220	369	297	ω1	ω1	PROPN
ejpam-4220	369	298	}	}	PUNCT
ejpam-4220	369	299	∪	∪	NOUN
ejpam-4220	369	300	{	{	PUNCT
ejpam-4220	369	301	(	(	PUNCT
ejpam-4220	369	302	w	w	PROPN
ejpam-4220	369	303	,	,	PUNCT
ejpam-4220	369	304	z	z	NOUN
ejpam-4220	369	305	)	)	PUNCT
ejpam-4220	369	306	:	:	PUNCT
ejpam-4220	369	307	w	w	PROPN
ejpam-4220	369	308	∈	∈	PROPN
ejpam-4220	369	309	ω2	ω2	PROPN
ejpam-4220	369	310	,	,	PUNCT
ejpam-4220	369	311	z	z	PROPN
ejpam-4220	369	312	∈	∈	PROPN
ejpam-4220	369	313	∆1	∆1	PROPN
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ejpam-4220	369	315	=	=	SYM
ejpam-4220	369	316	{	{	PUNCT
ejpam-4220	369	317	(	(	PUNCT
ejpam-4220	369	318	1	1	NUM
ejpam-4220	369	319	,	,	PUNCT
ejpam-4220	369	320	a	a	NOUN
ejpam-4220	369	321	)	)	PUNCT
ejpam-4220	369	322	,	,	PUNCT
ejpam-4220	369	323	(	(	PUNCT
ejpam-4220	369	324	1	1	NUM
ejpam-4220	369	325	,	,	PUNCT
ejpam-4220	369	326	d	d	NOUN
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ejpam-4220	369	328	,	,	PUNCT
ejpam-4220	369	329	(	(	PUNCT
ejpam-4220	369	330	1	1	NUM
ejpam-4220	369	331	,	,	PUNCT
ejpam-4220	369	332	c	c	NOUN
ejpam-4220	369	333	)	)	PUNCT
ejpam-4220	369	334	,	,	PUNCT
ejpam-4220	369	335	(	(	PUNCT
ejpam-4220	369	336	3	3	NUM
ejpam-4220	369	337	,	,	PUNCT
ejpam-4220	369	338	a	a	NOUN
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ejpam-4220	369	340	,	,	PUNCT
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ejpam-4220	369	342	3	3	NUM
ejpam-4220	369	343	,	,	PUNCT
ejpam-4220	369	344	d	d	NOUN
ejpam-4220	369	345	)	)	PUNCT
ejpam-4220	369	346	,	,	PUNCT
ejpam-4220	369	347	(	(	PUNCT
ejpam-4220	369	348	3	3	NUM
ejpam-4220	369	349	,	,	PUNCT
ejpam-4220	369	350	c	c	NOUN
ejpam-4220	369	351	)	)	PUNCT
ejpam-4220	369	352	,	,	PUNCT
ejpam-4220	369	353	(	(	PUNCT
ejpam-4220	369	354	6	6	NUM
ejpam-4220	369	355	,	,	PUNCT
ejpam-4220	369	356	a	a	NOUN
ejpam-4220	369	357	)	)	PUNCT
ejpam-4220	369	358	,	,	PUNCT
ejpam-4220	369	359	(	(	PUNCT
ejpam-4220	369	360	6	6	NUM
ejpam-4220	369	361	,	,	PUNCT
ejpam-4220	369	362	d	d	NOUN
ejpam-4220	369	363	)	)	PUNCT
ejpam-4220	369	364	,	,	PUNCT
ejpam-4220	369	365	(	(	PUNCT
ejpam-4220	369	366	6	6	NUM
ejpam-4220	369	367	,	,	PUNCT
ejpam-4220	369	368	c	c	NOUN
ejpam-4220	369	369	)	)	PUNCT
ejpam-4220	369	370	}	}	PUNCT
ejpam-4220	369	371	∪	∪	X
ejpam-4220	369	372	{	{	PUNCT
ejpam-4220	369	373	(	(	PUNCT
ejpam-4220	369	374	2	2	NUM
ejpam-4220	369	375	,	,	PUNCT
ejpam-4220	369	376	b	b	NOUN
ejpam-4220	369	377	)	)	PUNCT
ejpam-4220	369	378	,	,	PUNCT
ejpam-4220	369	379	(	(	PUNCT
ejpam-4220	369	380	2	2	NUM
ejpam-4220	369	381	,	,	PUNCT
ejpam-4220	369	382	e	e	NOUN
ejpam-4220	369	383	)	)	PUNCT
ejpam-4220	369	384	,	,	PUNCT
ejpam-4220	369	385	(	(	PUNCT
ejpam-4220	369	386	4	4	NUM
ejpam-4220	369	387	,	,	PUNCT
ejpam-4220	369	388	b	b	NOUN
ejpam-4220	369	389	)	)	PUNCT
ejpam-4220	369	390	,	,	PUNCT
ejpam-4220	369	391	(	(	PUNCT
ejpam-4220	369	392	4	4	NUM
ejpam-4220	369	393	,	,	PUNCT
ejpam-4220	369	394	e	e	NOUN
ejpam-4220	369	395	)	)	PUNCT
ejpam-4220	369	396	,	,	PUNCT
ejpam-4220	369	397	(	(	PUNCT
ejpam-4220	369	398	5	5	NUM
ejpam-4220	369	399	,	,	PUNCT
ejpam-4220	369	400	b	b	NOUN
ejpam-4220	369	401	)	)	PUNCT
ejpam-4220	369	402	,	,	PUNCT
ejpam-4220	369	403	(	(	PUNCT
ejpam-4220	369	404	5	5	NUM
ejpam-4220	369	405	,	,	PUNCT
ejpam-4220	369	406	e	e	NOUN
ejpam-4220	369	407	)	)	PUNCT
ejpam-4220	369	408	,	,	PUNCT
ejpam-4220	369	409	(	(	PUNCT
ejpam-4220	369	410	7	7	NUM
ejpam-4220	369	411	,	,	PUNCT
ejpam-4220	369	412	b	b	NOUN
ejpam-4220	369	413	)	)	PUNCT
ejpam-4220	369	414	,	,	PUNCT
ejpam-4220	369	415	(	(	PUNCT
ejpam-4220	369	416	7	7	NUM
ejpam-4220	369	417	,	,	PUNCT
ejpam-4220	369	418	e	e	NOUN
ejpam-4220	369	419	)	)	PUNCT
ejpam-4220	369	420	,	,	PUNCT
ejpam-4220	369	421	(	(	PUNCT
ejpam-4220	369	422	8	8	NUM
ejpam-4220	369	423	,	,	PUNCT
ejpam-4220	369	424	b	b	NOUN
ejpam-4220	369	425	)	)	PUNCT
ejpam-4220	369	426	,	,	PUNCT
ejpam-4220	369	427	(	(	PUNCT
ejpam-4220	369	428	8	8	NUM
ejpam-4220	369	429	,	,	PUNCT
ejpam-4220	369	430	e	e	NOUN
ejpam-4220	369	431	)	)	PUNCT
ejpam-4220	369	432	}	}	PUNCT
ejpam-4220	369	433	references	reference	VERB
ejpam-4220	369	434	80	80	NUM
ejpam-4220	369	435	=	=	SYM
ejpam-4220	369	436	{	{	PUNCT
ejpam-4220	369	437	(	(	PUNCT
ejpam-4220	369	438	1	1	NUM
ejpam-4220	369	439	,	,	PUNCT
ejpam-4220	369	440	a	a	NOUN
ejpam-4220	369	441	)	)	PUNCT
ejpam-4220	369	442	,	,	PUNCT
ejpam-4220	369	443	(	(	PUNCT
ejpam-4220	369	444	1	1	NUM
ejpam-4220	369	445	,	,	PUNCT
ejpam-4220	369	446	d	d	NOUN
ejpam-4220	369	447	)	)	PUNCT
ejpam-4220	369	448	,	,	PUNCT
ejpam-4220	369	449	(	(	PUNCT
ejpam-4220	369	450	1	1	NUM
ejpam-4220	369	451	,	,	PUNCT
ejpam-4220	369	452	c	c	NOUN
ejpam-4220	369	453	)	)	PUNCT
ejpam-4220	369	454	,	,	PUNCT
ejpam-4220	369	455	(	(	PUNCT
ejpam-4220	369	456	3	3	NUM
ejpam-4220	369	457	,	,	PUNCT
ejpam-4220	369	458	a	a	NOUN
ejpam-4220	369	459	)	)	PUNCT
ejpam-4220	369	460	,	,	PUNCT
ejpam-4220	369	461	(	(	PUNCT
ejpam-4220	369	462	3	3	NUM
ejpam-4220	369	463	,	,	PUNCT
ejpam-4220	369	464	d	d	NOUN
ejpam-4220	369	465	)	)	PUNCT
ejpam-4220	369	466	,	,	PUNCT
ejpam-4220	369	467	(	(	PUNCT
ejpam-4220	369	468	3	3	NUM
ejpam-4220	369	469	,	,	PUNCT
ejpam-4220	369	470	c	c	NOUN
ejpam-4220	369	471	)	)	PUNCT
ejpam-4220	369	472	,	,	PUNCT
ejpam-4220	369	473	(	(	PUNCT
ejpam-4220	369	474	6	6	NUM
ejpam-4220	369	475	,	,	PUNCT
ejpam-4220	369	476	a	a	NOUN
ejpam-4220	369	477	)	)	PUNCT
ejpam-4220	369	478	,	,	PUNCT
ejpam-4220	369	479	(	(	PUNCT
ejpam-4220	369	480	6	6	NUM
ejpam-4220	369	481	,	,	PUNCT
ejpam-4220	369	482	d	d	NOUN
ejpam-4220	369	483	)	)	PUNCT
ejpam-4220	369	484	,	,	PUNCT
ejpam-4220	369	485	(	(	PUNCT
ejpam-4220	369	486	6	6	NUM
ejpam-4220	369	487	,	,	PUNCT
ejpam-4220	369	488	c	c	NOUN
ejpam-4220	369	489	)	)	PUNCT
ejpam-4220	369	490	,	,	PUNCT
ejpam-4220	369	491	(	(	PUNCT
ejpam-4220	369	492	2	2	NUM
ejpam-4220	369	493	,	,	PUNCT
ejpam-4220	369	494	b	b	NOUN
ejpam-4220	369	495	)	)	PUNCT
ejpam-4220	369	496	,	,	PUNCT
ejpam-4220	369	497	(	(	PUNCT
ejpam-4220	369	498	2	2	NUM
ejpam-4220	369	499	,	,	PUNCT
ejpam-4220	369	500	e	e	NOUN
ejpam-4220	369	501	)	)	PUNCT
ejpam-4220	369	502	,	,	PUNCT
ejpam-4220	369	503	(	(	PUNCT
ejpam-4220	369	504	4	4	NUM
ejpam-4220	369	505	,	,	PUNCT
ejpam-4220	369	506	b	b	NOUN
ejpam-4220	369	507	)	)	PUNCT
ejpam-4220	369	508	,	,	PUNCT
ejpam-4220	369	509	(	(	PUNCT
ejpam-4220	369	510	4	4	NUM
ejpam-4220	369	511	,	,	PUNCT
ejpam-4220	369	512	e	e	NOUN
ejpam-4220	369	513	)	)	PUNCT
ejpam-4220	369	514	,	,	PUNCT
ejpam-4220	369	515	(	(	PUNCT
ejpam-4220	369	516	5	5	NUM
ejpam-4220	369	517	,	,	PUNCT
ejpam-4220	369	518	b	b	NOUN
ejpam-4220	369	519	)	)	PUNCT
ejpam-4220	369	520	,	,	PUNCT
ejpam-4220	369	521	(	(	PUNCT
ejpam-4220	369	522	5	5	NUM
ejpam-4220	369	523	,	,	PUNCT
ejpam-4220	369	524	e	e	NOUN
ejpam-4220	369	525	)	)	PUNCT
ejpam-4220	369	526	,	,	PUNCT
ejpam-4220	369	527	(	(	PUNCT
ejpam-4220	369	528	7	7	NUM
ejpam-4220	369	529	,	,	PUNCT
ejpam-4220	369	530	b	b	NOUN
ejpam-4220	369	531	)	)	PUNCT
ejpam-4220	369	532	,	,	PUNCT
ejpam-4220	369	533	(	(	PUNCT
ejpam-4220	369	534	7	7	NUM
ejpam-4220	369	535	,	,	PUNCT
ejpam-4220	369	536	e	e	NOUN
ejpam-4220	369	537	)	)	PUNCT
ejpam-4220	369	538	,	,	PUNCT
ejpam-4220	369	539	(	(	PUNCT
ejpam-4220	369	540	8	8	NUM
ejpam-4220	369	541	,	,	PUNCT
ejpam-4220	369	542	b	b	NOUN
ejpam-4220	369	543	)	)	PUNCT
ejpam-4220	369	544	,	,	PUNCT
ejpam-4220	369	545	(	(	PUNCT
ejpam-4220	369	546	8	8	NUM
ejpam-4220	369	547	,	,	PUNCT
ejpam-4220	369	548	e	e	NOUN
ejpam-4220	369	549	)	)	PUNCT
ejpam-4220	369	550	}	}	PUNCT
ejpam-4220	369	551	.	.	PUNCT
ejpam-4220	370	1	furthermore	furthermore	ADV
ejpam-4220	370	2	,	,	PUNCT
ejpam-4220	370	3	|{(x	|{(x	NOUN
ejpam-4220	370	4	,	,	PUNCT
ejpam-4220	370	5	y	y	NOUN
ejpam-4220	370	6	)	)	PUNCT
ejpam-4220	370	7	:	:	PUNCT
ejpam-4220	371	1	x	x	PUNCT
ejpam-4220	371	2	∈	∈	PROPN
ejpam-4220	371	3	ω2	ω2	PROPN
ejpam-4220	371	4	,	,	PUNCT
ejpam-4220	371	5	y	y	PROPN
ejpam-4220	371	6	∈	∈	PROPN
ejpam-4220	371	7	ω1	ω1	PROPN
ejpam-4220	371	8	}	}	PUNCT
ejpam-4220	371	9	∪	∪	NOUN
ejpam-4220	371	10	{	{	PUNCT
ejpam-4220	371	11	(	(	PUNCT
ejpam-4220	371	12	w	w	PROPN
ejpam-4220	371	13	,	,	PUNCT
ejpam-4220	371	14	z	z	NOUN
ejpam-4220	371	15	)	)	PUNCT
ejpam-4220	371	16	:	:	PUNCT
ejpam-4220	371	17	w	w	PROPN
ejpam-4220	371	18	∈	∈	PROPN
ejpam-4220	371	19	∆2	∆2	PROPN
ejpam-4220	371	20	,	,	PUNCT
ejpam-4220	371	21	z	z	PROPN
ejpam-4220	371	22	∈	∈	PROPN
ejpam-4220	371	23	∆1}|	∆1}|	PROPN
ejpam-4220	371	24	=	=	SYM
ejpam-4220	371	25	21	21	NUM
ejpam-4220	371	26	and	and	CCONJ
ejpam-4220	371	27	|{(x	|{(x	NOUN
ejpam-4220	371	28	,	,	PUNCT
ejpam-4220	371	29	y	y	NOUN
ejpam-4220	371	30	)	)	PUNCT
ejpam-4220	371	31	:	:	PUNCT
ejpam-4220	371	32	x	x	X
ejpam-4220	371	33	∈	∈	PROPN
ejpam-4220	371	34	∆2	∆2	PROPN
ejpam-4220	371	35	,	,	PUNCT
ejpam-4220	371	36	y	y	PROPN
ejpam-4220	371	37	∈	∈	PROPN
ejpam-4220	371	38	ω1	ω1	PROPN
ejpam-4220	371	39	}	}	PUNCT
ejpam-4220	371	40	∪	∪	NOUN
ejpam-4220	371	41	{	{	PUNCT
ejpam-4220	371	42	(	(	PUNCT
ejpam-4220	371	43	w	w	PROPN
ejpam-4220	371	44	,	,	PUNCT
ejpam-4220	371	45	z	z	NOUN
ejpam-4220	371	46	)	)	PUNCT
ejpam-4220	371	47	:	:	PUNCT
ejpam-4220	371	48	w	w	PROPN
ejpam-4220	371	49	∈	∈	PROPN
ejpam-4220	371	50	ω2	ω2	PROPN
ejpam-4220	371	51	,	,	PUNCT
ejpam-4220	371	52	z	z	PROPN
ejpam-4220	371	53	∈	∈	PROPN
ejpam-4220	371	54	∆1}|	∆1}|	PROPN
ejpam-4220	371	55	=	=	SYM
ejpam-4220	371	56	19	19	NUM
ejpam-4220	371	57	.	.	PUNCT
ejpam-4220	372	1	therefore	therefore	ADV
ejpam-4220	372	2	,	,	PUNCT
ejpam-4220	372	3	ni(h	ni(h	PUNCT
ejpam-4220	372	4	•g	•g	PROPN
ejpam-4220	372	5	,	,	PUNCT
ejpam-4220	372	6	x	x	NOUN
ejpam-4220	372	7	)	)	PUNCT
ejpam-4220	372	8	=	=	SYM
ejpam-4220	373	1	x19	x19	NOUN
ejpam-4220	374	1	+	+	CCONJ
ejpam-4220	374	2	x21	x21	NUM
ejpam-4220	374	3	=	=	SYM
ejpam-4220	374	4	ni(g	ni(g	NOUN
ejpam-4220	374	5	•h	•h	PROPN
ejpam-4220	374	6	,	,	PUNCT
ejpam-4220	374	7	x	x	NOUN
ejpam-4220	374	8	)	)	PUNCT
ejpam-4220	374	9	.	.	PUNCT
ejpam-4220	375	1	acknowledgements	acknowledgement	NOUN
ejpam-4220	375	2	this	this	DET
ejpam-4220	375	3	research	research	NOUN
ejpam-4220	375	4	is	be	AUX
ejpam-4220	375	5	funded	fund	VERB
ejpam-4220	375	6	by	by	ADP
ejpam-4220	375	7	the	the	DET
ejpam-4220	375	8	department	department	PROPN
ejpam-4220	375	9	of	of	ADP
ejpam-4220	375	10	science	science	NOUN
ejpam-4220	375	11	and	and	CCONJ
ejpam-4220	375	12	technology	technology	NOUN
ejpam-4220	375	13	(	(	PUNCT
ejpam-4220	375	14	dost	dost	NOUN
ejpam-4220	375	15	)	)	PUNCT
ejpam-4220	375	16	,	,	PUNCT
ejpam-4220	375	17	mindanao	mindanao	PROPN
ejpam-4220	375	18	state	state	PROPN
ejpam-4220	375	19	university	university	PROPN
ejpam-4220	375	20	iit	iit	PROPN
ejpam-4220	375	21	,	,	PUNCT
ejpam-4220	375	22	department	department	NOUN
ejpam-4220	375	23	of	of	ADP
ejpam-4220	375	24	research	research	NOUN
ejpam-4220	375	25	,	,	PUNCT
ejpam-4220	375	26	office	office	NOUN
ejpam-4220	375	27	of	of	ADP
ejpam-4220	375	28	the	the	DET
ejpam-4220	375	29	vice	vice	NOUN
ejpam-4220	375	30	chancellor	chancellor	NOUN
ejpam-4220	375	31	for	for	ADP
ejpam-4220	375	32	research	research	NOUN
ejpam-4220	375	33	and	and	CCONJ
ejpam-4220	375	34	extension(ovcre	extension(ovcre	PROPN
ejpam-4220	375	35	)	)	PUNCT
ejpam-4220	375	36	,	,	PUNCT
ejpam-4220	375	37	and	and	CCONJ
ejpam-4220	375	38	mindanao	mindanao	PROPN
ejpam-4220	375	39	state	state	PROPN
ejpam-4220	375	40	university	university	PROPN
ejpam-4220	375	41	main	main	ADJ
ejpam-4220	375	42	campus	campus	NOUN
ejpam-4220	375	43	(	(	PUNCT
ejpam-4220	375	44	msu	msu	NOUN
ejpam-4220	375	45	main	main	ADJ
ejpam-4220	375	46	)	)	PUNCT
ejpam-4220	375	47	.	.	PUNCT
ejpam-4220	376	1	references	reference	NOUN
ejpam-4220	376	2	[	[	X
ejpam-4220	376	3	1	1	NUM
ejpam-4220	376	4	]	]	PUNCT
ejpam-4220	376	5	g.d	g.d	NOUN
ejpam-4220	376	6	birkhoff	birkhoff	NOUN
ejpam-4220	376	7	.	.	PUNCT
ejpam-4220	377	1	a	a	DET
ejpam-4220	377	2	determinant	determinant	ADJ
ejpam-4220	377	3	formula	formula	NOUN
ejpam-4220	377	4	for	for	ADP
ejpam-4220	377	5	the	the	DET
ejpam-4220	377	6	number	number	NOUN
ejpam-4220	377	7	of	of	ADP
ejpam-4220	377	8	ways	way	NOUN
ejpam-4220	377	9	of	of	ADP
ejpam-4220	377	10	coloring	color	VERB
ejpam-4220	377	11	a	a	DET
ejpam-4220	377	12	map	map	NOUN
ejpam-4220	377	13	.	.	PUNCT
ejpam-4220	378	1	ann	ann	PROPN
ejpam-4220	378	2	.	.	PROPN
ejpam-4220	378	3	of	of	ADP
ejpam-4220	378	4	math	math	NOUN
ejpam-4220	378	5	.	.	PUNCT
ejpam-4220	379	1	(	(	PUNCT
ejpam-4220	379	2	2	2	NUM
ejpam-4220	379	3	)	)	PUNCT
ejpam-4220	379	4	,	,	PUNCT
ejpam-4220	379	5	14:42–46	14:42–46	NUM
ejpam-4220	379	6	,	,	PUNCT
ejpam-4220	379	7	1912	1912	NUM
ejpam-4220	379	8	.	.	PUNCT
ejpam-4220	380	1	[	[	X
ejpam-4220	380	2	2	2	NUM
ejpam-4220	380	3	]	]	X
ejpam-4220	380	4	f.	f.	PROPN
ejpam-4220	380	5	buckley	buckley	PROPN
ejpam-4220	380	6	and	and	CCONJ
ejpam-4220	380	7	f.	f.	PROPN
ejpam-4220	380	8	harary	harary	PROPN
ejpam-4220	380	9	.	.	PUNCT
ejpam-4220	381	1	distance	distance	NOUN
ejpam-4220	381	2	in	in	ADP
ejpam-4220	381	3	graphs	graph	NOUN
ejpam-4220	381	4	.	.	PUNCT
ejpam-4220	382	1	addison	addison	PROPN
ejpam-4220	382	2	-	-	PUNCT
ejpam-4220	382	3	wesley	wesley	PROPN
ejpam-4220	382	4	series	series	PROPN
ejpam-4220	382	5	in	in	ADP
ejpam-4220	382	6	mathematics	mathematic	NOUN
ejpam-4220	382	7	,	,	PUNCT
ejpam-4220	382	8	1990	1990	NUM
ejpam-4220	382	9	.	.	PUNCT
ejpam-4220	383	1	[	[	X
ejpam-4220	383	2	3	3	X
ejpam-4220	383	3	]	]	X
ejpam-4220	383	4	r.	r.	PROPN
ejpam-4220	383	5	diestel	diestel	PROPN
ejpam-4220	383	6	.	.	PUNCT
ejpam-4220	384	1	graph	graph	NOUN
ejpam-4220	384	2	theory	theory	NOUN
ejpam-4220	384	3	.	.	PUNCT
ejpam-4220	385	1	springer	springer	NOUN
ejpam-4220	385	2	nature	nature	NOUN
ejpam-4220	385	3	,	,	PUNCT
ejpam-4220	385	4	2017	2017	NUM
ejpam-4220	385	5	.	.	PUNCT
ejpam-4220	386	1	[	[	X
ejpam-4220	386	2	4	4	NUM
ejpam-4220	386	3	]	]	X
ejpam-4220	386	4	e.j	e.j	PROPN
ejpam-4220	386	5	.	.	PROPN
ejpam-4220	386	6	farrel	farrel	PROPN
ejpam-4220	386	7	.	.	PUNCT
ejpam-4220	387	1	introduction	introduction	NOUN
ejpam-4220	387	2	to	to	ADP
ejpam-4220	387	3	matching	matching	NOUN
ejpam-4220	387	4	polynomials	polynomial	NOUN
ejpam-4220	387	5	.	.	PUNCT
ejpam-4220	388	1	j.	j.	PROPN
ejpam-4220	388	2	combinatorial	combinatorial	PROPN
ejpam-4220	388	3	thoery	thoery	PROPN
ejpam-4220	388	4	b	b	PROPN
ejpam-4220	388	5	,	,	PUNCT
ejpam-4220	388	6	27:75–86	27:75–86	NUM
ejpam-4220	388	7	,	,	PUNCT
ejpam-4220	388	8	1979	1979	NUM
ejpam-4220	388	9	.	.	PUNCT
ejpam-4220	389	1	[	[	X
ejpam-4220	389	2	5	5	X
ejpam-4220	389	3	]	]	PUNCT
ejpam-4220	389	4	p.	p.	NOUN
ejpam-4220	389	5	zhang	zhang	PROPN
ejpam-4220	390	1	g.	g.	PROPN
ejpam-4220	390	2	chartrand	chartrand	PROPN
ejpam-4220	390	3	.	.	PUNCT
ejpam-4220	391	1	a	a	DET
ejpam-4220	391	2	first	first	ADJ
ejpam-4220	391	3	course	course	NOUN
ejpam-4220	391	4	in	in	ADP
ejpam-4220	391	5	graph	graph	NOUN
ejpam-4220	391	6	theory	theory	NOUN
ejpam-4220	391	7	.	.	PUNCT
ejpam-4220	392	1	dover	dover	PROPN
ejpam-4220	392	2	publications	publications	PROPN
ejpam-4220	392	3	,	,	PUNCT
ejpam-4220	392	4	inc	inc	PROPN
ejpam-4220	392	5	,	,	PUNCT
ejpam-4220	392	6	mineola	mineola	PROPN
ejpam-4220	392	7	,	,	PUNCT
ejpam-4220	392	8	new	new	PROPN
ejpam-4220	392	9	york	york	PROPN
ejpam-4220	392	10	,	,	PUNCT
ejpam-4220	392	11	2012	2012	NUM
ejpam-4220	392	12	.	.	PUNCT
ejpam-4220	393	1	[	[	X
ejpam-4220	393	2	6	6	NUM
ejpam-4220	393	3	]	]	PUNCT
ejpam-4220	393	4	f.	f.	PROPN
ejpam-4220	393	5	harary	harary	PROPN
ejpam-4220	393	6	.	.	PUNCT
ejpam-4220	394	1	graph	graph	NOUN
ejpam-4220	394	2	theory	theory	NOUN
ejpam-4220	394	3	.	.	PUNCT
ejpam-4220	395	1	addison	addison	PROPN
ejpam-4220	395	2	-	-	PUNCT
ejpam-4220	395	3	wesley	wesley	PROPN
ejpam-4220	395	4	publishing	publishing	PROPN
ejpam-4220	395	5	company	company	NOUN
ejpam-4220	395	6	,	,	PUNCT
ejpam-4220	395	7	1969	1969	NUM
ejpam-4220	395	8	.	.	PUNCT
ejpam-4220	396	1	[	[	X
ejpam-4220	396	2	7	7	X
ejpam-4220	396	3	]	]	X
ejpam-4220	396	4	f.	f.	PROPN
ejpam-4220	396	5	harary	harary	PROPN
ejpam-4220	396	6	i.	i.	PROPN
ejpam-4220	396	7	gutman	gutman	PROPN
ejpam-4220	396	8	.	.	PUNCT
ejpam-4220	397	1	generalizations	generalization	NOUN
ejpam-4220	397	2	of	of	ADP
ejpam-4220	397	3	the	the	DET
ejpam-4220	397	4	matching	matching	ADJ
ejpam-4220	397	5	polynomial	polynomial	NOUN
ejpam-4220	397	6	.	.	PUNCT
ejpam-4220	398	1	util	util	PROPN
ejpam-4220	398	2	.	.	PUNCT
ejpam-4220	399	1	math	math	NOUN
ejpam-4220	399	2	,	,	PUNCT
ejpam-4220	399	3	24:97	24:97	NUM
ejpam-4220	399	4	–	–	PUNCT
ejpam-4220	399	5	106	106	NUM
ejpam-4220	399	6	,	,	PUNCT
ejpam-4220	399	7	1983	1983	NUM
ejpam-4220	399	8	.	.	PUNCT
ejpam-4220	400	1	[	[	X
ejpam-4220	400	2	8	8	NUM
ejpam-4220	400	3	]	]	SYM
ejpam-4220	400	4	u.s.r	u.s.r	NOUN
ejpam-4220	400	5	.	.	PROPN
ejpam-4220	400	6	murthy	murthy	PROPN
ejpam-4220	400	7	j.a	j.a	PROPN
ejpam-4220	400	8	.	.	PROPN
ejpam-4220	400	9	bondy	bondy	PROPN
ejpam-4220	400	10	.	.	PUNCT
ejpam-4220	401	1	graph	graph	NOUN
ejpam-4220	401	2	theory	theory	NOUN
ejpam-4220	401	3	,	,	PUNCT
ejpam-4220	401	4	graduate	graduate	NOUN
ejpam-4220	401	5	texts	text	NOUN
ejpam-4220	401	6	in	in	ADP
ejpam-4220	401	7	mathematics	mathematic	NOUN
ejpam-4220	401	8	.	.	PUNCT
ejpam-4220	401	9	springer	springer	NOUN
ejpam-4220	401	10	,	,	PUNCT
ejpam-4220	401	11	2007	2007	NUM
ejpam-4220	401	12	.	.	PUNCT
ejpam-4220	402	1	[	[	X
ejpam-4220	402	2	9	9	NUM
ejpam-4220	402	3	]	]	X
ejpam-4220	402	4	r.j	r.j	PROPN
ejpam-4220	402	5	.	.	PROPN
ejpam-4220	402	6	nowakowski	nowakowski	PROPN
ejpam-4220	402	7	j.i	j.i	PROPN
ejpam-4220	402	8	.	.	PROPN
ejpam-4220	402	9	brown	brown	PROPN
ejpam-4220	402	10	.	.	PUNCT
ejpam-4220	403	1	the	the	DET
ejpam-4220	403	2	neighbourhood	neighbourhood	NOUN
ejpam-4220	403	3	polynomial	polynomial	NOUN
ejpam-4220	403	4	of	of	ADP
ejpam-4220	403	5	a	a	DET
ejpam-4220	403	6	graph	graph	NOUN
ejpam-4220	403	7	.	.	PUNCT
ejpam-4220	404	1	astralasian	astralasian	PROPN
ejpam-4220	404	2	journal	journal	PROPN
ejpam-4220	404	3	of	of	ADP
ejpam-4220	404	4	combinatorics	combinatoric	NOUN
ejpam-4220	404	5	,	,	PUNCT
ejpam-4220	404	6	42:55–68	42:55–68	PROPN
ejpam-4220	404	7	,	,	PUNCT
ejpam-4220	404	8	2008	2008	NUM
ejpam-4220	404	9	.	.	PUNCT
ejpam-4220	405	1	references	reference	NOUN
ejpam-4220	405	2	81	81	NUM
ejpam-4220	406	1	[	[	X
ejpam-4220	406	2	10	10	NUM
ejpam-4220	406	3	]	]	X
ejpam-4220	406	4	v.	v.	PROPN
ejpam-4220	406	5	e.	e.	PROPN
ejpam-4220	406	6	levit	levit	PROPN
ejpam-4220	406	7	and	and	CCONJ
ejpam-4220	406	8	e.	e.	PROPN
ejpam-4220	406	9	mandrescu	mandrescu	PROPN
ejpam-4220	406	10	.	.	PUNCT
ejpam-4220	407	1	the	the	DET
ejpam-4220	407	2	independence	independence	NOUN
ejpam-4220	407	3	polynomial	polynomial	NOUN
ejpam-4220	407	4	of	of	ADP
ejpam-4220	407	5	a	a	DET
ejpam-4220	407	6	graph	graph	NOUN
ejpam-4220	407	7	-	-	PUNCT
ejpam-4220	407	8	a	a	DET
ejpam-4220	407	9	survey	survey	NOUN
ejpam-4220	407	10	.	.	PUNCT
ejpam-4220	408	1	in	in	ADP
ejpam-4220	408	2	proceedings	proceeding	NOUN
ejpam-4220	408	3	of	of	ADP
ejpam-4220	408	4	the	the	DET
ejpam-4220	408	5	1st	1st	ADJ
ejpam-4220	408	6	international	international	ADJ
ejpam-4220	408	7	conference	conference	NOUN
ejpam-4220	408	8	on	on	ADP
ejpam-4220	408	9	algebraic	algebraic	PROPN
ejpam-4220	408	10	informatics	informatic	NOUN
ejpam-4220	408	11	,	,	PUNCT
ejpam-4220	408	12	pages	page	NOUN
ejpam-4220	408	13	233–254	233–254	NUM
ejpam-4220	408	14	,	,	PUNCT
ejpam-4220	408	15	2005	2005	NUM
ejpam-4220	408	16	.	.	PUNCT
ejpam-4220	409	1	[	[	X
ejpam-4220	409	2	11	11	NUM
ejpam-4220	409	3	]	]	X
ejpam-4220	409	4	k.b	k.b	PROPN
ejpam-4220	409	5	.	.	PROPN
ejpam-4220	409	6	murthy	murthy	PROPN
ejpam-4220	409	7	and	and	CCONJ
ejpam-4220	409	8	puttaswamy	puttaswamy	ADJ
ejpam-4220	409	9	.	.	PUNCT
ejpam-4220	410	1	on	on	ADP
ejpam-4220	410	2	the	the	DET
ejpam-4220	410	3	independent	independent	ADJ
ejpam-4220	410	4	neighbourhood	neighbourhood	NOUN
ejpam-4220	410	5	polynomial	polynomial	NOUN
ejpam-4220	410	6	of	of	ADP
ejpam-4220	410	7	graphs	graph	NOUN
ejpam-4220	410	8	.	.	PUNCT
ejpam-4220	411	1	indian	indian	ADJ
ejpam-4220	411	2	streams	streams	PROPN
ejpam-4220	411	3	research	research	NOUN
ejpam-4220	411	4	journal	journal	NOUN
ejpam-4220	411	5	,	,	PUNCT
ejpam-4220	411	6	5(12):1–7	5(12):1–7	NUM
ejpam-4220	411	7	,	,	PUNCT
ejpam-4220	411	8	2015	2015	NUM
ejpam-4220	411	9	.	.	PUNCT