id	sid	tid	token	lemma	pos
ejpam-6611	1	1	european	european	PROPN
ejpam-6611	1	2	journal	journal	PROPN
ejpam-6611	1	3	of	of	ADP
ejpam-6611	1	4	pure	pure	ADJ
ejpam-6611	1	5	and	and	CCONJ
ejpam-6611	1	6	applied	applied	ADJ
ejpam-6611	1	7	mathematics	mathematic	NOUN
ejpam-6611	1	8	2025	2025	NUM
ejpam-6611	1	9	,	,	PUNCT
ejpam-6611	1	10	vol	vol	NOUN
ejpam-6611	1	11	.	.	PROPN
ejpam-6611	1	12	18	18	NUM
ejpam-6611	1	13	,	,	PUNCT
ejpam-6611	1	14	issue	issue	NOUN
ejpam-6611	1	15	3	3	NUM
ejpam-6611	1	16	,	,	PUNCT
ejpam-6611	1	17	article	article	NOUN
ejpam-6611	1	18	number	number	NOUN
ejpam-6611	1	19	6611	6611	NUM
ejpam-6611	1	20	issn	issn	PROPN
ejpam-6611	1	21	1307	1307	NUM
ejpam-6611	1	22	-	-	SYM
ejpam-6611	1	23	5543	5543	NUM
ejpam-6611	1	24	–	–	PUNCT
ejpam-6611	1	25	ejpam.com	ejpam.com	X
ejpam-6611	1	26	published	publish	VERB
ejpam-6611	1	27	by	by	ADP
ejpam-6611	1	28	new	new	PROPN
ejpam-6611	1	29	york	york	PROPN
ejpam-6611	1	30	business	business	PROPN
ejpam-6611	1	31	global	global	ADJ
ejpam-6611	1	32	folding	folding	NOUN
ejpam-6611	1	33	on	on	ADP
ejpam-6611	1	34	topological	topological	ADJ
ejpam-6611	1	35	graphs	graph	NOUN
ejpam-6611	1	36	and	and	CCONJ
ejpam-6611	1	37	their	their	PRON
ejpam-6611	1	38	fundamental	fundamental	ADJ
ejpam-6611	1	39	group	group	NOUN
ejpam-6611	1	40	mohammed	mohammed	PROPN
ejpam-6611	1	41	abu	abu	PROPN
ejpam-6611	1	42	-	-	PUNCT
ejpam-6611	1	43	saleem	saleem	PROPN
ejpam-6611	1	44	1	1	NUM
ejpam-6611	1	45	department	department	NOUN
ejpam-6611	1	46	of	of	ADP
ejpam-6611	1	47	mathematics	mathematic	NOUN
ejpam-6611	1	48	,	,	PUNCT
ejpam-6611	1	49	faculty	faculty	NOUN
ejpam-6611	1	50	of	of	ADP
ejpam-6611	1	51	science	science	NOUN
ejpam-6611	1	52	,	,	PUNCT
ejpam-6611	1	53	al	al	PROPN
ejpam-6611	1	54	-	-	PUNCT
ejpam-6611	1	55	balqa	balqa	NOUN
ejpam-6611	1	56	applied	apply	VERB
ejpam-6611	1	57	university	university	NOUN
ejpam-6611	1	58	,	,	PUNCT
ejpam-6611	1	59	salt	salt	NOUN
ejpam-6611	1	60	19117	19117	NUM
ejpam-6611	1	61	,	,	PUNCT
ejpam-6611	1	62	jordan	jordan	PROPN
ejpam-6611	1	63	abstract	abstract	PROPN
ejpam-6611	1	64	.	.	PUNCT
ejpam-6611	2	1	we	we	PRON
ejpam-6611	2	2	introduce	introduce	VERB
ejpam-6611	2	3	the	the	DET
ejpam-6611	2	4	effect	effect	NOUN
ejpam-6611	2	5	of	of	ADP
ejpam-6611	2	6	folding	fold	VERB
ejpam-6611	2	7	on	on	ADP
ejpam-6611	2	8	the	the	DET
ejpam-6611	2	9	fundamental	fundamental	ADJ
ejpam-6611	2	10	groups	group	NOUN
ejpam-6611	2	11	of	of	ADP
ejpam-6611	2	12	a	a	DET
ejpam-6611	2	13	connected	connected	ADJ
ejpam-6611	2	14	topological	topological	ADJ
ejpam-6611	2	15	graph	graph	NOUN
ejpam-6611	2	16	and	and	CCONJ
ejpam-6611	2	17	its	its	PRON
ejpam-6611	2	18	dual	dual	ADJ
ejpam-6611	2	19	graph	graph	NOUN
ejpam-6611	2	20	.	.	PUNCT
ejpam-6611	3	1	we	we	PRON
ejpam-6611	3	2	will	will	AUX
ejpam-6611	3	3	deduce	deduce	VERB
ejpam-6611	3	4	the	the	DET
ejpam-6611	3	5	limit	limit	NOUN
ejpam-6611	3	6	of	of	ADP
ejpam-6611	3	7	folding	fold	VERB
ejpam-6611	3	8	on	on	ADP
ejpam-6611	3	9	the	the	DET
ejpam-6611	3	10	fundamental	fundamental	ADJ
ejpam-6611	3	11	group	group	NOUN
ejpam-6611	3	12	of	of	ADP
ejpam-6611	3	13	a	a	DET
ejpam-6611	3	14	topological	topological	ADJ
ejpam-6611	3	15	graph	graph	NOUN
ejpam-6611	3	16	and	and	CCONJ
ejpam-6611	3	17	its	its	PRON
ejpam-6611	3	18	duality	duality	NOUN
ejpam-6611	3	19	.	.	PUNCT
ejpam-6611	4	1	we	we	PRON
ejpam-6611	4	2	obtain	obtain	VERB
ejpam-6611	4	3	the	the	DET
ejpam-6611	4	4	relations	relation	NOUN
ejpam-6611	4	5	between	between	ADP
ejpam-6611	4	6	the	the	DET
ejpam-6611	4	7	induced	induced	ADJ
ejpam-6611	4	8	folding	folding	NOUN
ejpam-6611	4	9	and	and	CCONJ
ejpam-6611	4	10	the	the	DET
ejpam-6611	4	11	induced	induced	ADJ
ejpam-6611	4	12	retraction	retraction	NOUN
ejpam-6611	4	13	on	on	ADP
ejpam-6611	4	14	the	the	DET
ejpam-6611	4	15	fundamental	fundamental	ADJ
ejpam-6611	4	16	group	group	NOUN
ejpam-6611	4	17	.	.	PUNCT
ejpam-6611	5	1	we	we	PRON
ejpam-6611	5	2	apply	apply	VERB
ejpam-6611	5	3	retraction	retraction	NOUN
ejpam-6611	5	4	and	and	CCONJ
ejpam-6611	5	5	folding	fold	VERB
ejpam-6611	5	6	operations	operation	NOUN
ejpam-6611	5	7	to	to	PART
ejpam-6611	5	8	reduce	reduce	VERB
ejpam-6611	5	9	the	the	DET
ejpam-6611	5	10	size	size	NOUN
ejpam-6611	5	11	of	of	ADP
ejpam-6611	5	12	the	the	DET
ejpam-6611	5	13	graph	graph	NOUN
ejpam-6611	5	14	while	while	SCONJ
ejpam-6611	5	15	preserving	preserve	VERB
ejpam-6611	5	16	its	its	PRON
ejpam-6611	5	17	essential	essential	ADJ
ejpam-6611	5	18	structural	structural	ADJ
ejpam-6611	5	19	properties	property	NOUN
ejpam-6611	5	20	,	,	PUNCT
ejpam-6611	5	21	which	which	PRON
ejpam-6611	5	22	can	can	AUX
ejpam-6611	5	23	assist	assist	VERB
ejpam-6611	5	24	us	we	PRON
ejpam-6611	5	25	in	in	ADP
ejpam-6611	5	26	developing	develop	VERB
ejpam-6611	5	27	mathematical	mathematical	ADJ
ejpam-6611	5	28	software	software	NOUN
ejpam-6611	5	29	.	.	PUNCT
ejpam-6611	6	1	2020	2020	NUM
ejpam-6611	6	2	mathematics	mathematic	NOUN
ejpam-6611	6	3	subject	subject	NOUN
ejpam-6611	6	4	classifications	classification	NOUN
ejpam-6611	6	5	:	:	PUNCT
ejpam-6611	6	6	05c10	05c10	ADJ
ejpam-6611	6	7	,	,	PUNCT
ejpam-6611	6	8	19d55	19d55	NUM
ejpam-6611	6	9	,	,	PUNCT
ejpam-6611	6	10	55n10	55n10	NUM
ejpam-6611	6	11	,	,	PUNCT
ejpam-6611	6	12	54	54	NUM
ejpam-6611	6	13	-	-	SYM
ejpam-6611	6	14	xx	xx	NUM
ejpam-6611	6	15	key	key	ADJ
ejpam-6611	6	16	words	word	NOUN
ejpam-6611	6	17	and	and	CCONJ
ejpam-6611	6	18	phrases	phrase	NOUN
ejpam-6611	6	19	:	:	PUNCT
ejpam-6611	6	20	topological	topological	ADJ
ejpam-6611	6	21	graph	graph	NOUN
ejpam-6611	6	22	,	,	PUNCT
ejpam-6611	6	23	dual	dual	ADJ
ejpam-6611	6	24	topological	topological	ADJ
ejpam-6611	6	25	graph	graph	NOUN
ejpam-6611	6	26	,	,	PUNCT
ejpam-6611	6	27	folding	folding	NOUN
ejpam-6611	6	28	,	,	PUNCT
ejpam-6611	6	29	fundamental	fundamental	ADJ
ejpam-6611	6	30	group	group	NOUN
ejpam-6611	6	31	1	1	NUM
ejpam-6611	6	32	.	.	PUNCT
ejpam-6611	7	1	introduction	introduction	NOUN
ejpam-6611	7	2	graph	graph	NOUN
ejpam-6611	7	3	theory	theory	NOUN
ejpam-6611	7	4	serves	serve	VERB
ejpam-6611	7	5	as	as	ADP
ejpam-6611	7	6	a	a	DET
ejpam-6611	7	7	mathematical	mathematical	ADJ
ejpam-6611	7	8	representation	representation	NOUN
ejpam-6611	7	9	that	that	PRON
ejpam-6611	7	10	effectively	effectively	ADV
ejpam-6611	7	11	investigates	investigate	VERB
ejpam-6611	7	12	several	several	ADJ
ejpam-6611	7	13	tangible	tangible	ADJ
ejpam-6611	7	14	,	,	PUNCT
ejpam-6611	7	15	real	real	ADJ
ejpam-6611	7	16	-	-	PUNCT
ejpam-6611	7	17	world	world	NOUN
ejpam-6611	7	18	problems	problem	NOUN
ejpam-6611	7	19	.	.	PUNCT
ejpam-6611	8	1	many	many	ADJ
ejpam-6611	8	2	different	different	ADJ
ejpam-6611	8	3	concerns	concern	NOUN
ejpam-6611	8	4	related	relate	VERB
ejpam-6611	8	5	to	to	ADP
ejpam-6611	8	6	the	the	DET
ejpam-6611	8	7	fields	field	NOUN
ejpam-6611	8	8	of	of	ADP
ejpam-6611	8	9	chemistry	chemistry	NOUN
ejpam-6611	8	10	,	,	PUNCT
ejpam-6611	8	11	physics	physics	NOUN
ejpam-6611	8	12	,	,	PUNCT
ejpam-6611	8	13	communication	communication	NOUN
ejpam-6611	8	14	,	,	PUNCT
ejpam-6611	8	15	computer	computer	NOUN
ejpam-6611	8	16	science	science	NOUN
ejpam-6611	8	17	,	,	PUNCT
ejpam-6611	8	18	the	the	DET
ejpam-6611	8	19	genetic	genetic	ADJ
ejpam-6611	8	20	code	code	NOUN
ejpam-6611	8	21	,	,	PUNCT
ejpam-6611	8	22	social	social	ADJ
ejpam-6611	8	23	science	science	NOUN
ejpam-6611	8	24	,	,	PUNCT
ejpam-6611	8	25	psychology	psychology	NOUN
ejpam-6611	8	26	,	,	PUNCT
ejpam-6611	8	27	and	and	CCONJ
ejpam-6611	8	28	linguistics	linguistic	NOUN
ejpam-6611	8	29	could	could	AUX
ejpam-6611	8	30	potentially	potentially	ADV
ejpam-6611	8	31	be	be	AUX
ejpam-6611	8	32	articulated	articulate	VERB
ejpam-6611	8	33	as	as	ADP
ejpam-6611	8	34	problems	problem	NOUN
ejpam-6611	8	35	related	relate	VERB
ejpam-6611	8	36	to	to	AUX
ejpam-6611	8	37	graph	graph	NOUN
ejpam-6611	8	38	theory	theory	NOUN
ejpam-6611	8	39	.	.	PUNCT
ejpam-6611	9	1	many	many	ADJ
ejpam-6611	9	2	different	different	ADJ
ejpam-6611	9	3	areas	area	NOUN
ejpam-6611	9	4	of	of	ADP
ejpam-6611	9	5	mathematics	mathematic	NOUN
ejpam-6611	9	6	,	,	PUNCT
ejpam-6611	9	7	including	include	VERB
ejpam-6611	9	8	matrix	matrix	NOUN
ejpam-6611	9	9	theory	theory	NOUN
ejpam-6611	9	10	,	,	PUNCT
ejpam-6611	9	11	group	group	NOUN
ejpam-6611	9	12	theory	theory	NOUN
ejpam-6611	9	13	,	,	PUNCT
ejpam-6611	9	14	and	and	CCONJ
ejpam-6611	9	15	topological	topological	ADJ
ejpam-6611	9	16	structures	structure	NOUN
ejpam-6611	9	17	,	,	PUNCT
ejpam-6611	9	18	have	have	VERB
ejpam-6611	9	19	strong	strong	ADJ
ejpam-6611	9	20	relationships	relationship	NOUN
ejpam-6611	9	21	with	with	ADP
ejpam-6611	9	22	graph	graph	NOUN
ejpam-6611	9	23	theory	theory	NOUN
ejpam-6611	9	24	[	[	X
ejpam-6611	9	25	1	1	NUM
ejpam-6611	9	26	]	]	PUNCT
ejpam-6611	9	27	.	.	PUNCT
ejpam-6611	10	1	any	any	DET
ejpam-6611	10	2	graph	graph	NOUN
ejpam-6611	10	3	g	g	PROPN
ejpam-6611	10	4	could	could	AUX
ejpam-6611	10	5	indicate	indicate	VERB
ejpam-6611	10	6	a	a	DET
ejpam-6611	10	7	topological	topological	ADJ
ejpam-6611	10	8	space	space	NOUN
ejpam-6611	10	9	such	such	ADJ
ejpam-6611	10	10	that	that	SCONJ
ejpam-6611	10	11	every	every	DET
ejpam-6611	10	12	vertex	vertex	NOUN
ejpam-6611	10	13	corresponds	correspond	VERB
ejpam-6611	10	14	to	to	ADP
ejpam-6611	10	15	only	only	ADV
ejpam-6611	10	16	one	one	NUM
ejpam-6611	10	17	point	point	NOUN
ejpam-6611	10	18	and	and	CCONJ
ejpam-6611	10	19	every	every	DET
ejpam-6611	10	20	edge	edge	NOUN
ejpam-6611	10	21	corresponds	correspond	VERB
ejpam-6611	10	22	to	to	ADP
ejpam-6611	10	23	a	a	DET
ejpam-6611	10	24	distinct	distinct	ADJ
ejpam-6611	10	25	arc	arc	NOUN
ejpam-6611	10	26	,	,	PUNCT
ejpam-6611	10	27	homeomorphic	homeomorphic	ADJ
ejpam-6611	10	28	to	to	ADP
ejpam-6611	10	29	the	the	DET
ejpam-6611	10	30	closed	closed	ADJ
ejpam-6611	10	31	interval	interval	NOUN
ejpam-6611	10	32	.	.	PUNCT
ejpam-6611	11	1	the	the	DET
ejpam-6611	11	2	boundary	boundary	ADJ
ejpam-6611	11	3	points	point	NOUN
ejpam-6611	11	4	of	of	ADP
ejpam-6611	11	5	an	an	DET
ejpam-6611	11	6	arc	arc	NOUN
ejpam-6611	11	7	denote	denote	VERB
ejpam-6611	11	8	the	the	DET
ejpam-6611	11	9	endpoints	endpoint	NOUN
ejpam-6611	11	10	of	of	ADP
ejpam-6611	11	11	the	the	DET
ejpam-6611	11	12	associated	associated	ADJ
ejpam-6611	11	13	edge	edge	NOUN
ejpam-6611	11	14	,	,	PUNCT
ejpam-6611	11	15	the	the	DET
ejpam-6611	11	16	interiors	interior	NOUN
ejpam-6611	11	17	of	of	ADP
ejpam-6611	11	18	the	the	DET
ejpam-6611	11	19	arcs	arc	NOUN
ejpam-6611	11	20	are	be	AUX
ejpam-6611	11	21	mutually	mutually	ADV
ejpam-6611	11	22	disjoint	disjoint	ADJ
ejpam-6611	11	23	and	and	CCONJ
ejpam-6611	11	24	do	do	AUX
ejpam-6611	11	25	not	not	PART
ejpam-6611	11	26	intersect	intersect	VERB
ejpam-6611	11	27	the	the	DET
ejpam-6611	11	28	points	point	NOUN
ejpam-6611	11	29	representing	represent	VERB
ejpam-6611	11	30	vertices	vertex	NOUN
ejpam-6611	11	31	,	,	PUNCT
ejpam-6611	11	32	and	and	CCONJ
ejpam-6611	11	33	this	this	DET
ejpam-6611	11	34	configuration	configuration	NOUN
ejpam-6611	11	35	is	be	AUX
ejpam-6611	11	36	referred	refer	VERB
ejpam-6611	11	37	to	to	ADP
ejpam-6611	11	38	as	as	ADP
ejpam-6611	11	39	a	a	DET
ejpam-6611	11	40	topological	topological	ADJ
ejpam-6611	11	41	representation	representation	NOUN
ejpam-6611	11	42	of	of	ADP
ejpam-6611	11	43	g	g	PROPN
ejpam-6611	11	44	[	[	X
ejpam-6611	11	45	2	2	NUM
ejpam-6611	11	46	,	,	PUNCT
ejpam-6611	11	47	3	3	NUM
ejpam-6611	11	48	]	]	PUNCT
ejpam-6611	11	49	.	.	PUNCT
ejpam-6611	12	1	a	a	DET
ejpam-6611	12	2	graph	graph	NOUN
ejpam-6611	12	3	is	be	AUX
ejpam-6611	12	4	defined	define	VERB
ejpam-6611	12	5	as	as	ADP
ejpam-6611	12	6	an	an	DET
ejpam-6611	12	7	ordered	order	VERB
ejpam-6611	12	8	pair	pair	NOUN
ejpam-6611	12	9	g	g	NOUN
ejpam-6611	12	10	=	=	PUNCT
ejpam-6611	12	11	(	(	PUNCT
ejpam-6611	12	12	v	v	NOUN
ejpam-6611	12	13	(	(	PUNCT
ejpam-6611	12	14	g	g	NOUN
ejpam-6611	12	15	)	)	PUNCT
ejpam-6611	12	16	,	,	PUNCT
ejpam-6611	12	17	e(g	e(g	PROPN
ejpam-6611	12	18	)	)	PUNCT
ejpam-6611	12	19	)	)	PUNCT
ejpam-6611	12	20	,	,	PUNCT
ejpam-6611	12	21	in	in	ADP
ejpam-6611	12	22	which	which	PRON
ejpam-6611	12	23	v	v	ADP
ejpam-6611	12	24	(	(	PUNCT
ejpam-6611	12	25	g	g	NOUN
ejpam-6611	12	26	)	)	PUNCT
ejpam-6611	12	27	̸=	̸=	PROPN
ejpam-6611	12	28	φ	φ	PROPN
ejpam-6611	12	29	is	be	AUX
ejpam-6611	12	30	a	a	DET
ejpam-6611	12	31	set	set	NOUN
ejpam-6611	12	32	and	and	CCONJ
ejpam-6611	12	33	e(g	e(g	NOUN
ejpam-6611	12	34	)	)	PUNCT
ejpam-6611	12	35	is	be	AUX
ejpam-6611	12	36	a	a	DET
ejpam-6611	12	37	set	set	NOUN
ejpam-6611	12	38	that	that	PRON
ejpam-6611	12	39	is	be	AUX
ejpam-6611	12	40	disjoint	disjoint	NOUN
ejpam-6611	12	41	from	from	ADP
ejpam-6611	12	42	v	v	NUM
ejpam-6611	12	43	(	(	PUNCT
ejpam-6611	12	44	g	g	NOUN
ejpam-6611	12	45	)	)	PUNCT
ejpam-6611	12	46	,	,	PUNCT
ejpam-6611	12	47	which	which	PRON
ejpam-6611	12	48	are	be	AUX
ejpam-6611	12	49	referred	refer	VERB
ejpam-6611	12	50	to	to	ADP
ejpam-6611	12	51	as	as	ADP
ejpam-6611	12	52	the	the	DET
ejpam-6611	12	53	vertices	vertex	NOUN
ejpam-6611	12	54	of	of	ADP
ejpam-6611	12	55	g.	g.	NOUN
ejpam-6611	12	56	the	the	DET
ejpam-6611	12	57	elements	element	NOUN
ejpam-6611	12	58	of	of	ADP
ejpam-6611	12	59	e(g	e(g	PROPN
ejpam-6611	12	60	)	)	PUNCT
ejpam-6611	12	61	are	be	AUX
ejpam-6611	12	62	referred	refer	VERB
ejpam-6611	12	63	to	to	ADP
ejpam-6611	12	64	as	as	ADP
ejpam-6611	12	65	the	the	DET
ejpam-6611	12	66	edges	edge	NOUN
ejpam-6611	12	67	of	of	ADP
ejpam-6611	12	68	g	g	PROPN
ejpam-6611	13	1	[	[	X
ejpam-6611	13	2	1	1	NUM
ejpam-6611	13	3	,	,	PUNCT
ejpam-6611	13	4	4	4	NUM
ejpam-6611	13	5	,	,	PUNCT
ejpam-6611	13	6	5	5	NUM
ejpam-6611	13	7	]	]	PUNCT
ejpam-6611	13	8	.	.	PUNCT
ejpam-6611	14	1	a	a	DET
ejpam-6611	14	2	graph	graph	NOUN
ejpam-6611	14	3	h	h	NOUN
ejpam-6611	14	4	is	be	AUX
ejpam-6611	14	5	called	call	VERB
ejpam-6611	14	6	a	a	DET
ejpam-6611	14	7	subgraph	subgraph	NOUN
ejpam-6611	14	8	of	of	ADP
ejpam-6611	14	9	a	a	DET
ejpam-6611	14	10	graph	graph	NOUN
ejpam-6611	14	11	g	g	NOUN
ejpam-6611	14	12	,	,	PUNCT
ejpam-6611	14	13	denoted	denote	VERB
ejpam-6611	14	14	h	h	NOUN
ejpam-6611	14	15	⊆	⊆	NUM
ejpam-6611	14	16	g	g	NOUN
ejpam-6611	14	17	,	,	PUNCT
ejpam-6611	14	18	if	if	SCONJ
ejpam-6611	14	19	v	v	X
ejpam-6611	14	20	(	(	PUNCT
ejpam-6611	14	21	h	h	NOUN
ejpam-6611	14	22	)	)	PUNCT
ejpam-6611	14	23	⊆	⊆	NUM
ejpam-6611	14	24	v	v	NOUN
ejpam-6611	14	25	(	(	PUNCT
ejpam-6611	14	26	g	g	NOUN
ejpam-6611	14	27	)	)	PUNCT
ejpam-6611	14	28	and	and	CCONJ
ejpam-6611	14	29	e(h	e(h	NOUN
ejpam-6611	14	30	)	)	PUNCT
ejpam-6611	14	31	⊆	⊆	NUM
ejpam-6611	14	32	e(g	e(g	NOUN
ejpam-6611	14	33	)	)	PUNCT
ejpam-6611	15	1	[	[	X
ejpam-6611	15	2	6	6	NUM
ejpam-6611	15	3	]	]	PUNCT
ejpam-6611	15	4	.	.	PUNCT
ejpam-6611	16	1	a	a	DET
ejpam-6611	16	2	graph	graph	NOUN
ejpam-6611	16	3	doi	doi	NOUN
ejpam-6611	16	4	:	:	PUNCT
ejpam-6611	16	5	https://doi.org/10.29020/nybg.ejpam.v18i3.6611	https://doi.org/10.29020/nybg.ejpam.v18i3.6611	ADJ
ejpam-6611	16	6	email	email	NOUN
ejpam-6611	16	7	address	address	NOUN
ejpam-6611	16	8	:	:	PUNCT
ejpam-6611	16	9	m	m	VERB
ejpam-6611	16	10	abusaleem@bau.edu.jo	abusaleem@bau.edu.jo	NOUN
ejpam-6611	16	11	(	(	PUNCT
ejpam-6611	16	12	m.	m.	NOUN
ejpam-6611	16	13	abu	abu	PROPN
ejpam-6611	16	14	-	-	PUNCT
ejpam-6611	16	15	saleem	saleem	PROPN
ejpam-6611	16	16	)	)	PUNCT
ejpam-6611	16	17	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6611	16	18	1	1	NUM
ejpam-6611	16	19	copyright	copyright	NOUN
ejpam-6611	16	20	:	:	PUNCT
ejpam-6611	16	21	©	©	PROPN
ejpam-6611	16	22	2025	2025	NUM
ejpam-6611	16	23	the	the	DET
ejpam-6611	16	24	author(s	author(s	NOUN
ejpam-6611	16	25	)	)	PUNCT
ejpam-6611	16	26	.	.	PUNCT
ejpam-6611	17	1	(	(	PUNCT
ejpam-6611	17	2	cc	cc	NOUN
ejpam-6611	17	3	by	by	ADP
ejpam-6611	17	4	-	-	PUNCT
ejpam-6611	17	5	nc	nc	PROPN
ejpam-6611	17	6	4.0	4.0	NUM
ejpam-6611	17	7	)	)	PUNCT
ejpam-6611	17	8	m.	m.	NOUN
ejpam-6611	17	9	abu	abu	PROPN
ejpam-6611	17	10	-	-	PUNCT
ejpam-6611	17	11	saleem	saleem	PROPN
ejpam-6611	17	12	/	/	SYM
ejpam-6611	17	13	eur	eur	PROPN
ejpam-6611	17	14	.	.	PUNCT
ejpam-6611	18	1	j.	j.	PROPN
ejpam-6611	18	2	pure	pure	PROPN
ejpam-6611	18	3	appl	appl	PROPN
ejpam-6611	18	4	.	.	PROPN
ejpam-6611	18	5	math	math	PROPN
ejpam-6611	18	6	,	,	PUNCT
ejpam-6611	18	7	18	18	NUM
ejpam-6611	18	8	(	(	PUNCT
ejpam-6611	18	9	3	3	NUM
ejpam-6611	18	10	)	)	PUNCT
ejpam-6611	18	11	(	(	PUNCT
ejpam-6611	18	12	2025	2025	NUM
ejpam-6611	18	13	)	)	PUNCT
ejpam-6611	18	14	,	,	PUNCT
ejpam-6611	18	15	6611	6611	NUM
ejpam-6611	18	16	2	2	NUM
ejpam-6611	18	17	of	of	ADP
ejpam-6611	18	18	7	7	NUM
ejpam-6611	18	19	g	g	NOUN
ejpam-6611	18	20	is	be	AUX
ejpam-6611	18	21	planar	planar	ADJ
ejpam-6611	18	22	if	if	SCONJ
ejpam-6611	18	23	its	its	PRON
ejpam-6611	18	24	edges	edge	NOUN
ejpam-6611	18	25	meet	meet	VERB
ejpam-6611	18	26	only	only	ADV
ejpam-6611	18	27	at	at	ADP
ejpam-6611	18	28	their	their	PRON
ejpam-6611	18	29	endpoints	endpoint	NOUN
ejpam-6611	18	30	in	in	ADP
ejpam-6611	18	31	the	the	DET
ejpam-6611	18	32	plane	plane	NOUN
ejpam-6611	18	33	.	.	PUNCT
ejpam-6611	19	1	we	we	PRON
ejpam-6611	19	2	refer	refer	VERB
ejpam-6611	19	3	to	to	ADP
ejpam-6611	19	4	a	a	DET
ejpam-6611	19	5	drawing	drawing	NOUN
ejpam-6611	19	6	of	of	ADP
ejpam-6611	19	7	this	this	DET
ejpam-6611	19	8	form	form	NOUN
ejpam-6611	19	9	as	as	ADP
ejpam-6611	19	10	a	a	DET
ejpam-6611	19	11	planar	planar	ADJ
ejpam-6611	19	12	embedding	embed	VERB
ejpam-6611	19	13	of	of	ADP
ejpam-6611	19	14	the	the	DET
ejpam-6611	19	15	graph	graph	NOUN
ejpam-6611	19	16	g	g	PROPN
ejpam-6611	20	1	[	[	X
ejpam-6611	20	2	7	7	NUM
ejpam-6611	20	3	]	]	PUNCT
ejpam-6611	20	4	.	.	PUNCT
ejpam-6611	21	1	let	let	VERB
ejpam-6611	21	2	g	g	PRON
ejpam-6611	21	3	be	be	AUX
ejpam-6611	21	4	a	a	DET
ejpam-6611	21	5	plane	plane	NOUN
ejpam-6611	21	6	graph	graph	NOUN
ejpam-6611	21	7	.	.	PUNCT
ejpam-6611	22	1	to	to	PART
ejpam-6611	22	2	construct	construct	VERB
ejpam-6611	22	3	a	a	DET
ejpam-6611	22	4	new	new	ADJ
ejpam-6611	22	5	graph	graph	NOUN
ejpam-6611	22	6	d(g	d(g	PROPN
ejpam-6611	22	7	)	)	PUNCT
ejpam-6611	22	8	of	of	ADP
ejpam-6611	22	9	g	g	NOUN
ejpam-6611	22	10	,	,	PUNCT
ejpam-6611	22	11	for	for	ADP
ejpam-6611	22	12	all	all	DET
ejpam-6611	22	13	faces	face	NOUN
ejpam-6611	22	14	f	f	PROPN
ejpam-6611	22	15	of	of	ADP
ejpam-6611	22	16	g	g	PROPN
ejpam-6611	22	17	,	,	PUNCT
ejpam-6611	22	18	select	select	VERB
ejpam-6611	22	19	a	a	DET
ejpam-6611	22	20	vertex	vertex	NOUN
ejpam-6611	22	21	f̂	f̂	NUM
ejpam-6611	22	22	,	,	PUNCT
ejpam-6611	22	23	with	with	ADP
ejpam-6611	22	24	respect	respect	NOUN
ejpam-6611	22	25	to	to	ADP
ejpam-6611	22	26	all	all	DET
ejpam-6611	22	27	edges	edge	NOUN
ejpam-6611	22	28	e	e	NOUN
ejpam-6611	22	29	of	of	ADP
ejpam-6611	22	30	g	g	PROPN
ejpam-6611	22	31	,	,	PUNCT
ejpam-6611	22	32	choose	choose	VERB
ejpam-6611	22	33	an	an	DET
ejpam-6611	22	34	edge	edge	NOUN
ejpam-6611	22	35	ê.	ê.	ADV
ejpam-6611	22	36	then	then	ADV
ejpam-6611	22	37	edge	edge	VERB
ejpam-6611	22	38	ê	ê	PROPN
ejpam-6611	22	39	joins	join	VERB
ejpam-6611	22	40	vertices	vertex	NOUN
ejpam-6611	22	41	f̂	f̂	NUM
ejpam-6611	22	42	and	and	CCONJ
ejpam-6611	22	43	ĝ	ĝ	X
ejpam-6611	22	44	in	in	ADP
ejpam-6611	22	45	d(g	d(g	PROPN
ejpam-6611	22	46	)	)	PUNCT
ejpam-6611	22	47	iff	iff	PROPN
ejpam-6611	22	48	edge	edge	NOUN
ejpam-6611	22	49	e	e	PROPN
ejpam-6611	22	50	is	be	AUX
ejpam-6611	22	51	common	common	ADJ
ejpam-6611	22	52	to	to	ADP
ejpam-6611	22	53	the	the	DET
ejpam-6611	22	54	boundaries	boundary	NOUN
ejpam-6611	22	55	of	of	ADP
ejpam-6611	22	56	faces	face	NOUN
ejpam-6611	22	57	f	f	PROPN
ejpam-6611	22	58	and	and	CCONJ
ejpam-6611	22	59	g	g	PROPN
ejpam-6611	22	60	in	in	ADP
ejpam-6611	22	61	g	g	PROPN
ejpam-6611	22	62	,	,	PUNCT
ejpam-6611	22	63	this	this	DET
ejpam-6611	22	64	graph	graph	NOUN
ejpam-6611	22	65	is	be	AUX
ejpam-6611	22	66	called	call	VERB
ejpam-6611	22	67	the	the	DET
ejpam-6611	22	68	dual	dual	ADJ
ejpam-6611	22	69	of	of	ADP
ejpam-6611	22	70	g	g	NOUN
ejpam-6611	22	71	[	[	X
ejpam-6611	22	72	1	1	NUM
ejpam-6611	22	73	]	]	PUNCT
ejpam-6611	22	74	.	.	PUNCT
ejpam-6611	23	1	we	we	PRON
ejpam-6611	23	2	refer	refer	VERB
ejpam-6611	23	3	to	to	ADP
ejpam-6611	23	4	an	an	DET
ejpam-6611	23	5	edge	edge	NOUN
ejpam-6611	23	6	with	with	ADP
ejpam-6611	23	7	coinciding	coincide	VERB
ejpam-6611	23	8	vertices	vertex	NOUN
ejpam-6611	23	9	as	as	ADP
ejpam-6611	23	10	a	a	DET
ejpam-6611	23	11	loop	loop	NOUN
ejpam-6611	23	12	,	,	PUNCT
ejpam-6611	23	13	while	while	SCONJ
ejpam-6611	23	14	we	we	PRON
ejpam-6611	23	15	refer	refer	VERB
ejpam-6611	23	16	to	to	ADP
ejpam-6611	23	17	two	two	NUM
ejpam-6611	23	18	vertices	vertex	NOUN
ejpam-6611	23	19	connected	connect	VERB
ejpam-6611	23	20	by	by	ADP
ejpam-6611	23	21	more	more	ADJ
ejpam-6611	23	22	than	than	ADP
ejpam-6611	23	23	one	one	NUM
ejpam-6611	23	24	edge	edge	NOUN
ejpam-6611	23	25	as	as	ADP
ejpam-6611	23	26	multiple	multiple	ADJ
ejpam-6611	23	27	edges	edge	NOUN
ejpam-6611	23	28	.	.	PUNCT
ejpam-6611	24	1	an	an	DET
ejpam-6611	24	2	infinite	infinite	ADJ
ejpam-6611	24	3	graph	graph	NOUN
ejpam-6611	24	4	is	be	AUX
ejpam-6611	24	5	defined	define	VERB
ejpam-6611	24	6	as	as	ADP
ejpam-6611	24	7	a	a	DET
ejpam-6611	24	8	graph	graph	NOUN
ejpam-6611	24	9	where	where	SCONJ
ejpam-6611	24	10	both	both	CCONJ
ejpam-6611	24	11	the	the	DET
ejpam-6611	24	12	edge	edge	NOUN
ejpam-6611	24	13	set	set	VERB
ejpam-6611	24	14	and	and	CCONJ
ejpam-6611	24	15	the	the	DET
ejpam-6611	24	16	vertex	vertex	NOUN
ejpam-6611	24	17	set	set	NOUN
ejpam-6611	24	18	have	have	VERB
ejpam-6611	24	19	infinite	infinite	ADJ
ejpam-6611	24	20	cardinality	cardinality	NOUN
ejpam-6611	24	21	.	.	PUNCT
ejpam-6611	25	1	a	a	DET
ejpam-6611	25	2	cycle	cycle	NOUN
ejpam-6611	25	3	graph	graph	NOUN
ejpam-6611	25	4	is	be	AUX
ejpam-6611	25	5	defined	define	VERB
ejpam-6611	25	6	by	by	ADP
ejpam-6611	25	7	the	the	DET
ejpam-6611	25	8	existence	existence	NOUN
ejpam-6611	25	9	of	of	ADP
ejpam-6611	25	10	a	a	DET
ejpam-6611	25	11	singular	singular	ADJ
ejpam-6611	25	12	cycle	cycle	NOUN
ejpam-6611	25	13	;	;	PUNCT
ejpam-6611	25	14	we	we	PRON
ejpam-6611	25	15	will	will	AUX
ejpam-6611	25	16	denote	denote	VERB
ejpam-6611	25	17	the	the	DET
ejpam-6611	25	18	cycle	cycle	NOUN
ejpam-6611	25	19	graph	graph	NOUN
ejpam-6611	25	20	with	with	ADP
ejpam-6611	25	21	one	one	NUM
ejpam-6611	25	22	vertex	vertex	NOUN
ejpam-6611	25	23	by	by	ADP
ejpam-6611	25	24	c	c	NOUN
ejpam-6611	25	25	,	,	PUNCT
ejpam-6611	25	26	and	and	CCONJ
ejpam-6611	25	27	the	the	DET
ejpam-6611	25	28	cycle	cycle	NOUN
ejpam-6611	25	29	graph	graph	NOUN
ejpam-6611	25	30	with	with	ADP
ejpam-6611	25	31	nvertices	nvertice	NOUN
ejpam-6611	25	32	is	be	AUX
ejpam-6611	25	33	represented	represent	VERB
ejpam-6611	25	34	as	as	ADP
ejpam-6611	25	35	cn	cn	PROPN
ejpam-6611	25	36	.	.	PUNCT
ejpam-6611	26	1	the	the	DET
ejpam-6611	26	2	path	path	NOUN
ejpam-6611	26	3	graph	graph	NOUN
ejpam-6611	26	4	is	be	AUX
ejpam-6611	26	5	a	a	DET
ejpam-6611	26	6	graph	graph	NOUN
ejpam-6611	26	7	that	that	PRON
ejpam-6611	26	8	consists	consist	VERB
ejpam-6611	26	9	of	of	ADP
ejpam-6611	26	10	a	a	DET
ejpam-6611	26	11	single	single	ADJ
ejpam-6611	26	12	path	path	NOUN
ejpam-6611	26	13	;	;	PUNCT
ejpam-6611	26	14	the	the	DET
ejpam-6611	26	15	path	path	NOUN
ejpam-6611	26	16	graph	graph	NOUN
ejpam-6611	26	17	with	with	ADP
ejpam-6611	26	18	n	n	NOUN
ejpam-6611	26	19	-	-	PUNCT
ejpam-6611	26	20	vertices	vertex	NOUN
ejpam-6611	26	21	is	be	AUX
ejpam-6611	26	22	represented	represent	VERB
ejpam-6611	26	23	as	as	ADP
ejpam-6611	26	24	pn	pn	PROPN
ejpam-6611	26	25	[	[	X
ejpam-6611	26	26	1	1	NUM
ejpam-6611	26	27	,	,	PUNCT
ejpam-6611	26	28	4	4	NUM
ejpam-6611	26	29	]	]	PUNCT
ejpam-6611	26	30	.	.	PUNCT
ejpam-6611	27	1	the	the	DET
ejpam-6611	27	2	cobblestone	cobblestone	PROPN
ejpam-6611	27	3	path	path	NOUN
ejpam-6611	27	4	jn	jn	PROPN
ejpam-6611	27	5	is	be	AUX
ejpam-6611	27	6	the	the	DET
ejpam-6611	27	7	graph	graph	NOUN
ejpam-6611	27	8	formed	form	VERB
ejpam-6611	27	9	by	by	ADP
ejpam-6611	27	10	duplicating	duplicate	VERB
ejpam-6611	27	11	each	each	DET
ejpam-6611	27	12	edge	edge	NOUN
ejpam-6611	27	13	of	of	ADP
ejpam-6611	27	14	the	the	DET
ejpam-6611	27	15	n	n	CCONJ
ejpam-6611	27	16	-	-	PUNCT
ejpam-6611	27	17	vertex	vertex	NOUN
ejpam-6611	27	18	path	path	NOUN
ejpam-6611	27	19	pn	pn	PROPN
ejpam-6611	27	20	.	.	PUNCT
ejpam-6611	28	1	a	a	DET
ejpam-6611	28	2	graph	graph	NOUN
ejpam-6611	28	3	with	with	ADP
ejpam-6611	28	4	one	one	NUM
ejpam-6611	28	5	vertex	vertex	NOUN
ejpam-6611	28	6	and	and	CCONJ
ejpam-6611	28	7	n	n	DET
ejpam-6611	28	8	self	self	NOUN
ejpam-6611	28	9	-	-	PUNCT
ejpam-6611	28	10	loops	loop	NOUN
ejpam-6611	28	11	is	be	AUX
ejpam-6611	28	12	called	call	VERB
ejpam-6611	28	13	an	an	DET
ejpam-6611	28	14	n	n	CCONJ
ejpam-6611	28	15	-	-	PUNCT
ejpam-6611	28	16	bouquet	bouquet	NOUN
ejpam-6611	28	17	bn	bn	NOUN
ejpam-6611	29	1	[	[	X
ejpam-6611	29	2	2	2	NUM
ejpam-6611	29	3	,	,	PUNCT
ejpam-6611	29	4	3	3	NUM
ejpam-6611	29	5	]	]	PUNCT
ejpam-6611	29	6	.	.	PUNCT
ejpam-6611	30	1	let	let	VERB
ejpam-6611	30	2	y	y	PRON
ejpam-6611	30	3	be	be	AUX
ejpam-6611	30	4	a	a	DET
ejpam-6611	30	5	space	space	NOUN
ejpam-6611	30	6	,	,	PUNCT
ejpam-6611	30	7	and	and	CCONJ
ejpam-6611	30	8	let	let	VERB
ejpam-6611	30	9	y0	y0	PRON
ejpam-6611	30	10	be	be	AUX
ejpam-6611	30	11	an	an	DET
ejpam-6611	30	12	element	element	NOUN
ejpam-6611	30	13	of	of	ADP
ejpam-6611	30	14	y	y	PROPN
ejpam-6611	30	15	.	.	PUNCT
ejpam-6611	31	1	the	the	DET
ejpam-6611	31	2	set	set	NOUN
ejpam-6611	31	3	π1(y	π1(y	PROPN
ejpam-6611	31	4	,	,	PUNCT
ejpam-6611	31	5	y0	y0	PROPN
ejpam-6611	31	6	)	)	PUNCT
ejpam-6611	31	7	consists	consist	VERB
ejpam-6611	31	8	of	of	ADP
ejpam-6611	31	9	the	the	DET
ejpam-6611	31	10	homotopy	homotopy	NOUN
ejpam-6611	31	11	classes	class	NOUN
ejpam-6611	31	12	of	of	ADP
ejpam-6611	31	13	loops	loop	NOUN
ejpam-6611	31	14	in	in	ADP
ejpam-6611	31	15	(	(	PUNCT
ejpam-6611	31	16	y	y	NOUN
ejpam-6611	31	17	,	,	PUNCT
ejpam-6611	31	18	y0	y0	NOUN
ejpam-6611	31	19	)	)	PUNCT
ejpam-6611	31	20	,	,	PUNCT
ejpam-6611	31	21	and	and	CCONJ
ejpam-6611	31	22	it	it	PRON
ejpam-6611	31	23	is	be	AUX
ejpam-6611	31	24	equipped	equip	VERB
ejpam-6611	31	25	with	with	ADP
ejpam-6611	31	26	the	the	DET
ejpam-6611	31	27	product	product	NOUN
ejpam-6611	31	28	operation	operation	NOUN
ejpam-6611	32	1	[	[	X
ejpam-6611	32	2	u][v	u][v	X
ejpam-6611	32	3	]	]	X
ejpam-6611	32	4	=	=	PUNCT
ejpam-6611	33	1	[	[	X
ejpam-6611	33	2	u.v	u.v	X
ejpam-6611	33	3	]	]	X
ejpam-6611	33	4	referred	refer	VERB
ejpam-6611	33	5	to	to	ADP
ejpam-6611	33	6	as	as	ADP
ejpam-6611	33	7	the	the	DET
ejpam-6611	33	8	fundamental	fundamental	ADJ
ejpam-6611	33	9	group	group	NOUN
ejpam-6611	33	10	[	[	X
ejpam-6611	33	11	8	8	NUM
ejpam-6611	33	12	,	,	PUNCT
ejpam-6611	33	13	9	9	NUM
ejpam-6611	33	14	]	]	PUNCT
ejpam-6611	33	15	.	.	PUNCT
ejpam-6611	34	1	the	the	DET
ejpam-6611	34	2	fundamental	fundamental	ADJ
ejpam-6611	34	3	groups	group	NOUN
ejpam-6611	34	4	with	with	ADP
ejpam-6611	34	5	particular	particular	ADJ
ejpam-6611	34	6	spaces	space	NOUN
ejpam-6611	34	7	were	be	AUX
ejpam-6611	34	8	looked	look	VERB
ejpam-6611	34	9	at	at	ADP
ejpam-6611	34	10	[	[	X
ejpam-6611	34	11	10	10	NUM
ejpam-6611	34	12	,	,	PUNCT
ejpam-6611	34	13	11	11	NUM
ejpam-6611	34	14	]	]	PUNCT
ejpam-6611	34	15	.	.	PUNCT
ejpam-6611	35	1	let	let	VERB
ejpam-6611	35	2	y1	y1	INTJ
ejpam-6611	35	3	and	and	CCONJ
ejpam-6611	35	4	y2	y2	PROPN
ejpam-6611	35	5	be	be	AUX
ejpam-6611	35	6	spaces	space	NOUN
ejpam-6611	35	7	such	such	ADJ
ejpam-6611	35	8	that	that	SCONJ
ejpam-6611	35	9	y1	y1	PROPN
ejpam-6611	35	10	∈	∈	PROPN
ejpam-6611	35	11	y1	y1	NOUN
ejpam-6611	35	12	and	and	CCONJ
ejpam-6611	35	13	y2	y2	NOUN
ejpam-6611	35	14	∈	∈	PROPN
ejpam-6611	35	15	y2	y2	PROPN
ejpam-6611	35	16	,	,	PUNCT
ejpam-6611	35	17	with	with	ADP
ejpam-6611	35	18	y1	y1	NOUN
ejpam-6611	35	19	∩	∩	ADJ
ejpam-6611	35	20	y2	y2	NOUN
ejpam-6611	35	21	.	.	PUNCT
ejpam-6611	36	1	the	the	DET
ejpam-6611	36	2	wedge	wedge	NOUN
ejpam-6611	36	3	sum	sum	NOUN
ejpam-6611	36	4	y1	y1	NOUN
ejpam-6611	36	5	⋎	⋎	NOUN
ejpam-6611	36	6	y2	y2	NOUN
ejpam-6611	36	7	is	be	AUX
ejpam-6611	36	8	defined	define	VERB
ejpam-6611	36	9	as	as	ADP
ejpam-6611	36	10	the	the	DET
ejpam-6611	36	11	quotient	quotient	NOUN
ejpam-6611	36	12	of	of	ADP
ejpam-6611	36	13	y1	y1	NOUN
ejpam-6611	36	14	∪	∪	ADJ
ejpam-6611	36	15	y2	y2	NOUN
ejpam-6611	36	16	by	by	ADP
ejpam-6611	36	17	the	the	DET
ejpam-6611	36	18	identification	identification	NOUN
ejpam-6611	36	19	y1	y1	NOUN
ejpam-6611	36	20	∼	∼	NOUN
ejpam-6611	36	21	y2	y2	NOUN
ejpam-6611	36	22	.	.	PUNCT
ejpam-6611	37	1	[	[	X
ejpam-6611	37	2	8	8	NUM
ejpam-6611	37	3	]	]	PUNCT
ejpam-6611	37	4	.	.	PUNCT
ejpam-6611	38	1	a	a	DET
ejpam-6611	38	2	map	map	NOUN
ejpam-6611	38	3	φ	φ	X
ejpam-6611	38	4	:	:	PUNCT
ejpam-6611	38	5	v	v	X
ejpam-6611	38	6	(	(	PUNCT
ejpam-6611	38	7	g1	g1	PROPN
ejpam-6611	38	8	)	)	PUNCT
ejpam-6611	38	9	−→	−→	NOUN
ejpam-6611	38	10	v	v	NOUN
ejpam-6611	38	11	(	(	PUNCT
ejpam-6611	38	12	g2	g2	PROPN
ejpam-6611	38	13	)	)	PUNCT
ejpam-6611	38	14	constitutes	constitute	VERB
ejpam-6611	38	15	a	a	DET
ejpam-6611	38	16	homomorphism	homomorphism	NOUN
ejpam-6611	38	17	from	from	ADP
ejpam-6611	38	18	g1	g1	PROPN
ejpam-6611	38	19	to	to	ADP
ejpam-6611	38	20	g2	g2	PROPN
ejpam-6611	38	21	if	if	SCONJ
ejpam-6611	38	22	it	it	PRON
ejpam-6611	38	23	maintains	maintain	VERB
ejpam-6611	38	24	edge	edge	NOUN
ejpam-6611	38	25	preservation	preservation	NOUN
ejpam-6611	38	26	;	;	PUNCT
ejpam-6611	38	27	specifically	specifically	ADV
ejpam-6611	38	28	,	,	PUNCT
ejpam-6611	38	29	for	for	ADP
ejpam-6611	38	30	each	each	DET
ejpam-6611	38	31	edge	edge	NOUN
ejpam-6611	38	32	[	[	X
ejpam-6611	38	33	u1	u1	NOUN
ejpam-6611	38	34	,	,	PUNCT
ejpam-6611	38	35	u2	u2	PROPN
ejpam-6611	38	36	]	]	PUNCT
ejpam-6611	38	37	in	in	ADP
ejpam-6611	38	38	g1	g1	PROPN
ejpam-6611	38	39	,	,	PUNCT
ejpam-6611	38	40	[	[	X
ejpam-6611	38	41	φ(u1),φ(u2	φ(u1),φ(u2	NOUN
ejpam-6611	38	42	)	)	PUNCT
ejpam-6611	38	43	]	]	PUNCT
ejpam-6611	38	44	must	must	AUX
ejpam-6611	38	45	be	be	AUX
ejpam-6611	38	46	an	an	DET
ejpam-6611	38	47	edge	edge	NOUN
ejpam-6611	38	48	in	in	ADP
ejpam-6611	38	49	g1	g1	PROPN
ejpam-6611	39	1	[	[	X
ejpam-6611	39	2	3	3	NUM
ejpam-6611	39	3	]	]	PUNCT
ejpam-6611	39	4	.	.	PUNCT
ejpam-6611	40	1	a	a	DET
ejpam-6611	40	2	retract	retract	NOUN
ejpam-6611	40	3	of	of	ADP
ejpam-6611	40	4	a	a	DET
ejpam-6611	40	5	graph	graph	NOUN
ejpam-6611	40	6	g1	g1	NOUN
ejpam-6611	40	7	is	be	AUX
ejpam-6611	40	8	a	a	DET
ejpam-6611	40	9	subgraph	subgraph	NOUN
ejpam-6611	40	10	g2	g2	PROPN
ejpam-6611	40	11	of	of	ADP
ejpam-6611	40	12	g1	g1	PROPN
ejpam-6611	40	13	for	for	ADP
ejpam-6611	40	14	which	which	PRON
ejpam-6611	40	15	there	there	PRON
ejpam-6611	40	16	is	be	VERB
ejpam-6611	40	17	a	a	DET
ejpam-6611	40	18	homomorphism	homomorphism	NOUN
ejpam-6611	40	19	r	r	NOUN
ejpam-6611	40	20	:	:	PUNCT
ejpam-6611	40	21	g1	g1	PROPN
ejpam-6611	40	22	→	→	SYM
ejpam-6611	40	23	g2	g2	PROPN
ejpam-6611	40	24	,	,	PUNCT
ejpam-6611	40	25	denoted	denote	VERB
ejpam-6611	40	26	retraction	retraction	NOUN
ejpam-6611	40	27	,	,	PUNCT
ejpam-6611	40	28	providing	provide	VERB
ejpam-6611	40	29	r(u	r(u	NOUN
ejpam-6611	40	30	)	)	PUNCT
ejpam-6611	41	1	=	=	SYM
ejpam-6611	41	2	u	u	NOUN
ejpam-6611	41	3	for	for	ADP
ejpam-6611	41	4	every	every	DET
ejpam-6611	41	5	vertex	vertex	NOUN
ejpam-6611	41	6	u	u	NOUN
ejpam-6611	41	7	in	in	ADP
ejpam-6611	41	8	g2	g2	PROPN
ejpam-6611	42	1	[	[	X
ejpam-6611	42	2	8	8	NUM
ejpam-6611	42	3	]	]	PUNCT
ejpam-6611	42	4	.	.	PUNCT
ejpam-6611	43	1	the	the	DET
ejpam-6611	43	2	folding	folding	NOUN
ejpam-6611	43	3	is	be	AUX
ejpam-6611	43	4	a	a	DET
ejpam-6611	43	5	continuous	continuous	ADJ
ejpam-6611	43	6	map	map	NOUN
ejpam-6611	43	7	𭟋	𭟋	ADP
ejpam-6611	43	8	:	:	PUNCT
ejpam-6611	43	9	g1	g1	PROPN
ejpam-6611	43	10	→	→	PUNCT
ejpam-6611	43	11	g2	g2	PROPN
ejpam-6611	43	12	in	in	ADP
ejpam-6611	43	13	which	which	PRON
ejpam-6611	43	14	𭟋(υ	𭟋(υ	PROPN
ejpam-6611	43	15	)	)	PUNCT
ejpam-6611	43	16	∈	∈	PROPN
ejpam-6611	43	17	v	v	X
ejpam-6611	43	18	(	(	PUNCT
ejpam-6611	43	19	g2	g2	PROPN
ejpam-6611	43	20	)	)	PUNCT
ejpam-6611	43	21	for	for	ADP
ejpam-6611	43	22	every	every	DET
ejpam-6611	43	23	υ	υ	PROPN
ejpam-6611	43	24	∈	∈	PROPN
ejpam-6611	43	25	v	v	NOUN
ejpam-6611	43	26	(	(	PUNCT
ejpam-6611	43	27	g1	g1	PROPN
ejpam-6611	43	28	)	)	PUNCT
ejpam-6611	43	29	and	and	CCONJ
ejpam-6611	43	30	𭟋(e	𭟋(e	PROPN
ejpam-6611	43	31	)	)	PUNCT
ejpam-6611	43	32	∈	∈	PROPN
ejpam-6611	43	33	e(g2	e(g2	X
ejpam-6611	43	34	)	)	PUNCT
ejpam-6611	43	35	for	for	ADP
ejpam-6611	43	36	every	every	DET
ejpam-6611	43	37	e	e	PROPN
ejpam-6611	43	38	∈	∈	PROPN
ejpam-6611	43	39	e(g1	e(g1	ADV
ejpam-6611	43	40	)	)	PUNCT
ejpam-6611	44	1	[	[	X
ejpam-6611	44	2	12	12	NUM
ejpam-6611	44	3	,	,	PUNCT
ejpam-6611	44	4	13	13	NUM
ejpam-6611	44	5	]	]	PUNCT
ejpam-6611	44	6	.	.	PUNCT
ejpam-6611	45	1	the	the	DET
ejpam-6611	45	2	topological	topological	ADJ
ejpam-6611	45	3	and	and	CCONJ
ejpam-6611	45	4	banhatti	banhatti	ADJ
ejpam-6611	45	5	indices	index	NOUN
ejpam-6611	45	6	for	for	ADP
ejpam-6611	45	7	various	various	ADJ
ejpam-6611	45	8	silicate	silicate	NOUN
ejpam-6611	45	9	and	and	CCONJ
ejpam-6611	45	10	oxide	oxide	NOUN
ejpam-6611	45	11	networks	network	NOUN
ejpam-6611	45	12	,	,	PUNCT
ejpam-6611	45	13	using	use	VERB
ejpam-6611	45	14	fuzzy	fuzzy	ADJ
ejpam-6611	45	15	set	set	NOUN
ejpam-6611	45	16	extensions	extension	NOUN
ejpam-6611	45	17	,	,	PUNCT
ejpam-6611	45	18	were	be	AUX
ejpam-6611	45	19	presented	present	VERB
ejpam-6611	45	20	in	in	ADP
ejpam-6611	45	21	[	[	X
ejpam-6611	45	22	14	14	NUM
ejpam-6611	45	23	,	,	PUNCT
ejpam-6611	45	24	15	15	NUM
ejpam-6611	45	25	]	]	PUNCT
ejpam-6611	45	26	.	.	PUNCT
ejpam-6611	46	1	for	for	ADP
ejpam-6611	46	2	further	further	ADJ
ejpam-6611	46	3	information	information	NOUN
ejpam-6611	46	4	about	about	ADP
ejpam-6611	46	5	the	the	DET
ejpam-6611	46	6	folding	folding	NOUN
ejpam-6611	46	7	and	and	CCONJ
ejpam-6611	46	8	retraction	retraction	NOUN
ejpam-6611	46	9	on	on	ADP
ejpam-6611	46	10	manifolds	manifold	NOUN
ejpam-6611	46	11	and	and	CCONJ
ejpam-6611	46	12	graphs	graph	NOUN
ejpam-6611	46	13	,	,	PUNCT
ejpam-6611	46	14	see	see	VERB
ejpam-6611	46	15	[	[	X
ejpam-6611	46	16	12	12	NUM
ejpam-6611	46	17	,	,	PUNCT
ejpam-6611	46	18	16–19	16–19	NUM
ejpam-6611	46	19	]	]	PUNCT
ejpam-6611	46	20	.	.	PUNCT
ejpam-6611	47	1	the	the	DET
ejpam-6611	47	2	central	central	ADJ
ejpam-6611	47	3	problem	problem	NOUN
ejpam-6611	47	4	of	of	ADP
ejpam-6611	47	5	this	this	DET
ejpam-6611	47	6	paper	paper	NOUN
ejpam-6611	47	7	is	be	AUX
ejpam-6611	47	8	to	to	PART
ejpam-6611	47	9	investigate	investigate	VERB
ejpam-6611	47	10	the	the	DET
ejpam-6611	47	11	effects	effect	NOUN
ejpam-6611	47	12	of	of	ADP
ejpam-6611	47	13	folding	folding	NOUN
ejpam-6611	47	14	and	and	CCONJ
ejpam-6611	47	15	retraction	retraction	NOUN
ejpam-6611	47	16	on	on	ADP
ejpam-6611	47	17	various	various	ADJ
ejpam-6611	47	18	classes	class	NOUN
ejpam-6611	47	19	of	of	ADP
ejpam-6611	47	20	graphs	graph	NOUN
ejpam-6611	47	21	and	and	CCONJ
ejpam-6611	47	22	to	to	PART
ejpam-6611	47	23	characterize	characterize	VERB
ejpam-6611	47	24	how	how	SCONJ
ejpam-6611	47	25	retraction	retraction	NOUN
ejpam-6611	47	26	and	and	CCONJ
ejpam-6611	47	27	folding	fold	VERB
ejpam-6611	47	28	impact	impact	NOUN
ejpam-6611	47	29	key	key	ADJ
ejpam-6611	47	30	graph	graph	NOUN
ejpam-6611	47	31	invariants	invariant	NOUN
ejpam-6611	47	32	.	.	PUNCT
ejpam-6611	48	1	transformations	transformation	NOUN
ejpam-6611	48	2	mainly	mainly	ADV
ejpam-6611	48	3	consist	consist	VERB
ejpam-6611	48	4	of	of	ADP
ejpam-6611	48	5	folding	folding	NOUN
ejpam-6611	48	6	,	,	PUNCT
ejpam-6611	48	7	limit	limit	NOUN
ejpam-6611	48	8	folding	folding	NOUN
ejpam-6611	48	9	,	,	PUNCT
ejpam-6611	48	10	and	and	CCONJ
ejpam-6611	48	11	rewrite	rewrite	VERB
ejpam-6611	48	12	rules	rule	NOUN
ejpam-6611	48	13	that	that	PRON
ejpam-6611	48	14	help	help	VERB
ejpam-6611	48	15	sort	sort	VERB
ejpam-6611	48	16	graphs	graph	NOUN
ejpam-6611	48	17	,	,	PUNCT
ejpam-6611	48	18	find	find	VERB
ejpam-6611	48	19	unchanging	unchanging	ADJ
ejpam-6611	48	20	features	feature	NOUN
ejpam-6611	48	21	,	,	PUNCT
ejpam-6611	48	22	and	and	CCONJ
ejpam-6611	48	23	enhance	enhance	VERB
ejpam-6611	48	24	complex	complex	ADJ
ejpam-6611	48	25	networks	network	NOUN
ejpam-6611	48	26	while	while	SCONJ
ejpam-6611	48	27	keeping	keep	VERB
ejpam-6611	48	28	important	important	ADJ
ejpam-6611	48	29	information	information	NOUN
ejpam-6611	48	30	intact	intact	ADJ
ejpam-6611	48	31	.	.	PUNCT
ejpam-6611	49	1	folding	fold	VERB
ejpam-6611	49	2	theory	theory	NOUN
ejpam-6611	49	3	is	be	AUX
ejpam-6611	49	4	the	the	DET
ejpam-6611	49	5	important	important	ADJ
ejpam-6611	49	6	transformation	transformation	NOUN
ejpam-6611	49	7	used	use	VERB
ejpam-6611	49	8	in	in	ADP
ejpam-6611	49	9	structural	structural	ADJ
ejpam-6611	49	10	topology	topology	NOUN
ejpam-6611	49	11	.	.	PUNCT
ejpam-6611	50	1	its	its	PRON
ejpam-6611	50	2	simplest	simple	ADJ
ejpam-6611	50	3	form	form	NOUN
ejpam-6611	50	4	merges	merge	NOUN
ejpam-6611	50	5	and	and	CCONJ
ejpam-6611	50	6	eliminates	eliminate	VERB
ejpam-6611	50	7	edges	edge	NOUN
ejpam-6611	50	8	and	and	CCONJ
ejpam-6611	50	9	vertices	vertex	NOUN
ejpam-6611	50	10	.	.	PUNCT
ejpam-6611	51	1	this	this	DET
ejpam-6611	51	2	operation	operation	NOUN
ejpam-6611	51	3	may	may	AUX
ejpam-6611	51	4	remove	remove	VERB
ejpam-6611	51	5	multi	multi	ADJ
ejpam-6611	51	6	-	-	ADJ
ejpam-6611	51	7	edges	edge	NOUN
ejpam-6611	51	8	or	or	CCONJ
ejpam-6611	51	9	loops	loop	NOUN
ejpam-6611	51	10	by	by	ADP
ejpam-6611	51	11	using	use	VERB
ejpam-6611	51	12	folding	folding	NOUN
ejpam-6611	51	13	and	and	CCONJ
ejpam-6611	51	14	limit	limit	VERB
ejpam-6611	51	15	folding	fold	VERB
ejpam-6611	51	16	mapping	mapping	NOUN
ejpam-6611	51	17	in	in	ADP
ejpam-6611	51	18	a	a	DET
ejpam-6611	51	19	special	special	ADJ
ejpam-6611	51	20	family	family	NOUN
ejpam-6611	51	21	of	of	ADP
ejpam-6611	51	22	graph	graph	NOUN
ejpam-6611	51	23	theory	theory	NOUN
ejpam-6611	51	24	.	.	PUNCT
ejpam-6611	52	1	this	this	DET
ejpam-6611	52	2	study	study	NOUN
ejpam-6611	52	3	will	will	AUX
ejpam-6611	52	4	improve	improve	VERB
ejpam-6611	52	5	our	our	PRON
ejpam-6611	52	6	insight	insight	NOUN
ejpam-6611	52	7	into	into	ADP
ejpam-6611	52	8	graph	graph	NOUN
ejpam-6611	52	9	theory	theory	NOUN
ejpam-6611	52	10	by	by	ADP
ejpam-6611	52	11	looking	look	VERB
ejpam-6611	52	12	at	at	ADP
ejpam-6611	52	13	folding	fold	VERB
ejpam-6611	52	14	transformations	transformation	NOUN
ejpam-6611	52	15	,	,	PUNCT
ejpam-6611	52	16	which	which	PRON
ejpam-6611	52	17	will	will	AUX
ejpam-6611	52	18	help	help	VERB
ejpam-6611	52	19	us	we	PRON
ejpam-6611	52	20	better	well	ADV
ejpam-6611	52	21	understand	understand	VERB
ejpam-6611	52	22	graph	graph	NOUN
ejpam-6611	52	23	structure	structure	NOUN
ejpam-6611	52	24	and	and	CCONJ
ejpam-6611	52	25	classification	classification	NOUN
ejpam-6611	52	26	.	.	PUNCT
ejpam-6611	53	1	2	2	X
ejpam-6611	53	2	.	.	X
ejpam-6611	53	3	the	the	DET
ejpam-6611	53	4	main	main	ADJ
ejpam-6611	53	5	result	result	NOUN
ejpam-6611	53	6	theorem	theorem	VERB
ejpam-6611	53	7	1	1	NUM
ejpam-6611	53	8	.	.	PUNCT
ejpam-6611	53	9	given	give	VERB
ejpam-6611	53	10	a	a	DET
ejpam-6611	53	11	connected	connected	ADJ
ejpam-6611	53	12	graph	graph	NOUN
ejpam-6611	53	13	g	g	NOUN
ejpam-6611	53	14	,	,	PUNCT
ejpam-6611	53	15	then	then	ADV
ejpam-6611	53	16	(	(	PUNCT
ejpam-6611	53	17	i	i	NOUN
ejpam-6611	53	18	)	)	PUNCT
ejpam-6611	53	19	the	the	DET
ejpam-6611	53	20	folding	folding	NOUN
ejpam-6611	53	21	𭟋	𭟋	NOUN
ejpam-6611	53	22	:	:	PUNCT
ejpam-6611	53	23	g	g	ADP
ejpam-6611	53	24	−→	−→	NOUN
ejpam-6611	53	25	g	g	PROPN
ejpam-6611	53	26	,	,	PUNCT
ejpam-6611	53	27	induces	induce	VERB
ejpam-6611	53	28	�	�	PROPN
ejpam-6611	53	29	̂	̂	SYM
ejpam-6611	53	30	�	�	PROPN
ejpam-6611	53	31	:	:	PUNCT
ejpam-6611	53	32	π1(g	π1(g	NOUN
ejpam-6611	53	33	)	)	PUNCT
ejpam-6611	53	34	−→	−→	NOUN
ejpam-6611	53	35	π1(g	π1(g	NOUN
ejpam-6611	53	36	)	)	PUNCT
ejpam-6611	53	37	for	for	ADP
ejpam-6611	53	38	which	which	PRON
ejpam-6611	53	39	�	�	PROPN
ejpam-6611	53	40	̂	̂	SYM
ejpam-6611	53	41	�	�	NOUN
ejpam-6611	53	42	(π1(g	(π1(g	NOUN
ejpam-6611	53	43	)	)	PUNCT
ejpam-6611	53	44	)	)	PUNCT
ejpam-6611	54	1	=	=	SYM
ejpam-6611	54	2	π1(𭟋(g	π1(𭟋(g	X
ejpam-6611	54	3	)	)	PUNCT
ejpam-6611	54	4	)	)	PUNCT
ejpam-6611	54	5	.	.	PUNCT
ejpam-6611	55	1	(	(	PUNCT
ejpam-6611	55	2	ii	ii	X
ejpam-6611	55	3	)	)	PUNCT
ejpam-6611	55	4	there	there	PRON
ejpam-6611	55	5	exists	exist	VERB
ejpam-6611	55	6	a	a	DET
ejpam-6611	55	7	specific	specific	ADJ
ejpam-6611	55	8	type	type	NOUN
ejpam-6611	55	9	of	of	ADP
ejpam-6611	55	10	folding	fold	VERB
ejpam-6611	55	11	𭟋	𭟋	NOUN
ejpam-6611	55	12	:	:	PUNCT
ejpam-6611	55	13	g	g	ADP
ejpam-6611	55	14	−→	−→	PROPN
ejpam-6611	55	15	g̃	g̃	PROPN
ejpam-6611	55	16	that	that	PRON
ejpam-6611	55	17	induces	induce	VERB
ejpam-6611	55	18	�	�	PROPN
ejpam-6611	55	19	̂	̂	SYM
ejpam-6611	55	20	�	�	PROPN
ejpam-6611	55	21	:	:	PUNCT
ejpam-6611	55	22	π1(g	π1(g	NOUN
ejpam-6611	55	23	)	)	PUNCT
ejpam-6611	55	24	−→	−→	ADJ
ejpam-6611	55	25	π1(g̃	π1(g̃	PROPN
ejpam-6611	55	26	)	)	PUNCT
ejpam-6611	55	27	,	,	PUNCT
ejpam-6611	55	28	m.	m.	NOUN
ejpam-6611	55	29	abu	abu	PROPN
ejpam-6611	55	30	-	-	PUNCT
ejpam-6611	55	31	saleem	saleem	PROPN
ejpam-6611	55	32	/	/	SYM
ejpam-6611	55	33	eur	eur	PROPN
ejpam-6611	55	34	.	.	PUNCT
ejpam-6611	56	1	j.	j.	PROPN
ejpam-6611	56	2	pure	pure	PROPN
ejpam-6611	56	3	appl	appl	PROPN
ejpam-6611	56	4	.	.	PROPN
ejpam-6611	56	5	math	math	PROPN
ejpam-6611	56	6	,	,	PUNCT
ejpam-6611	56	7	18	18	NUM
ejpam-6611	56	8	(	(	PUNCT
ejpam-6611	56	9	3	3	NUM
ejpam-6611	56	10	)	)	PUNCT
ejpam-6611	56	11	(	(	PUNCT
ejpam-6611	56	12	2025	2025	NUM
ejpam-6611	56	13	)	)	PUNCT
ejpam-6611	56	14	,	,	PUNCT
ejpam-6611	56	15	6611	6611	NUM
ejpam-6611	56	16	3	3	NUM
ejpam-6611	56	17	of	of	ADP
ejpam-6611	56	18	7	7	NUM
ejpam-6611	56	19	and	and	CCONJ
ejpam-6611	56	20	for	for	ADP
ejpam-6611	56	21	this	this	DET
ejpam-6611	56	22	type	type	NOUN
ejpam-6611	56	23	,	,	PUNCT
ejpam-6611	56	24	rank	rank	NOUN
ejpam-6611	56	25	(	(	PUNCT
ejpam-6611	56	26	�	�	PROPN
ejpam-6611	56	27	̂	̂	SYM
ejpam-6611	56	28	�	�	NOUN
ejpam-6611	56	29	(π1(g	(π1(g	NOUN
ejpam-6611	56	30	)	)	PUNCT
ejpam-6611	56	31	)	)	PUNCT
ejpam-6611	56	32	)	)	PUNCT
ejpam-6611	56	33	≥	≥	PROPN
ejpam-6611	56	34	rank	rank	NOUN
ejpam-6611	56	35	(	(	PUNCT
ejpam-6611	56	36	π1(g	π1(g	NOUN
ejpam-6611	56	37	)	)	PUNCT
ejpam-6611	56	38	)	)	PUNCT
ejpam-6611	56	39	.	.	PUNCT
ejpam-6611	57	1	proof	proof	NOUN
ejpam-6611	57	2	.	.	PUNCT
ejpam-6611	58	1	(	(	PUNCT
ejpam-6611	58	2	i	i	NOUN
ejpam-6611	58	3	)	)	PUNCT
ejpam-6611	58	4	let	let	VERB
ejpam-6611	58	5	g	g	NOUN
ejpam-6611	58	6	be	be	AUX
ejpam-6611	58	7	a	a	DET
ejpam-6611	58	8	connected	connected	ADJ
ejpam-6611	58	9	graph	graph	NOUN
ejpam-6611	58	10	.	.	PUNCT
ejpam-6611	59	1	then	then	ADV
ejpam-6611	59	2	,	,	PUNCT
ejpam-6611	59	3	�	�	PROPN
ejpam-6611	59	4	̂	̂	NOUN
ejpam-6611	59	5	�	�	NOUN
ejpam-6611	59	6	(π1(g	(π1(g	NOUN
ejpam-6611	59	7	)	)	PUNCT
ejpam-6611	59	8	)	)	PUNCT
ejpam-6611	60	1	=	=	PUNCT
ejpam-6611	60	2	�	�	PROPN
ejpam-6611	60	3	̂	̂	NOUN
ejpam-6611	60	4	�	�	NOUN
ejpam-6611	60	5	{[c	{[c	NOUN
ejpam-6611	60	6	]	]	X
ejpam-6611	60	7	:	:	PUNCT
ejpam-6611	60	8	where	where	SCONJ
ejpam-6611	60	9	c	c	NOUN
ejpam-6611	60	10	is	be	AUX
ejpam-6611	60	11	a	a	DET
ejpam-6611	60	12	cycle	cycle	NOUN
ejpam-6611	60	13	based	base	VERB
ejpam-6611	60	14	at	at	ADP
ejpam-6611	60	15	one	one	NUM
ejpam-6611	60	16	vertex	vertex	NOUN
ejpam-6611	60	17	v0	v0	NOUN
ejpam-6611	60	18	∈	∈	NOUN
ejpam-6611	60	19	g	g	NOUN
ejpam-6611	60	20	}	}	PUNCT
ejpam-6611	60	21	=	=	SYM
ejpam-6611	60	22	{	{	PUNCT
ejpam-6611	60	23	[	[	X
ejpam-6611	60	24	𭟋(c	𭟋(c	NOUN
ejpam-6611	60	25	)	)	PUNCT
ejpam-6611	60	26	]	]	PUNCT
ejpam-6611	60	27	:	:	PUNCT
ejpam-6611	60	28	where	where	SCONJ
ejpam-6611	60	29	𭟋(c	𭟋(c	NOUN
ejpam-6611	60	30	)	)	PUNCT
ejpam-6611	60	31	is	be	AUX
ejpam-6611	60	32	a	a	DET
ejpam-6611	60	33	cycle	cycle	NOUN
ejpam-6611	60	34	based	base	VERB
ejpam-6611	60	35	at	at	ADP
ejpam-6611	60	36	𭟋(v0	𭟋(v0	NOUN
ejpam-6611	60	37	)	)	PUNCT
ejpam-6611	60	38	∈	∈	PROPN
ejpam-6611	60	39	𭟋(g	𭟋(g	NOUN
ejpam-6611	60	40	)	)	PUNCT
ejpam-6611	60	41	}	}	PUNCT
ejpam-6611	61	1	=	=	SYM
ejpam-6611	61	2	π1(𭟋(g	π1(𭟋(g	NOUN
ejpam-6611	61	3	)	)	PUNCT
ejpam-6611	61	4	)	)	PUNCT
ejpam-6611	61	5	.	.	PUNCT
ejpam-6611	62	1	(	(	PUNCT
ejpam-6611	62	2	ii	ii	NOUN
ejpam-6611	62	3	)	)	PUNCT
ejpam-6611	62	4	let	let	VERB
ejpam-6611	62	5	𭟋	𭟋	VERB
ejpam-6611	62	6	:	:	PUNCT
ejpam-6611	62	7	g	g	PROPN
ejpam-6611	62	8	−→	−→	PROPN
ejpam-6611	62	9	g̃	g̃	PROPN
ejpam-6611	62	10	be	be	VERB
ejpam-6611	62	11	a	a	DET
ejpam-6611	62	12	folding	fold	VERB
ejpam-6611	62	13	map	map	NOUN
ejpam-6611	62	14	in	in	ADP
ejpam-6611	62	15	such	such	DET
ejpam-6611	62	16	a	a	DET
ejpam-6611	62	17	way	way	NOUN
ejpam-6611	62	18	that	that	PRON
ejpam-6611	62	19	an	an	DET
ejpam-6611	62	20	edge	edge	NOUN
ejpam-6611	62	21	is	be	AUX
ejpam-6611	62	22	folded	fold	VERB
ejpam-6611	62	23	into	into	ADP
ejpam-6611	62	24	another	another	DET
ejpam-6611	62	25	edge	edge	NOUN
ejpam-6611	62	26	,	,	PUNCT
ejpam-6611	62	27	then	then	ADV
ejpam-6611	62	28	𭟋(g	𭟋(g	NOUN
ejpam-6611	62	29	)	)	PUNCT
ejpam-6611	62	30	contains	contain	VERB
ejpam-6611	62	31	a	a	DET
ejpam-6611	62	32	new	new	ADJ
ejpam-6611	62	33	multiple	multiple	ADJ
ejpam-6611	62	34	edge	edge	NOUN
ejpam-6611	62	35	that	that	PRON
ejpam-6611	62	36	induces	induce	VERB
ejpam-6611	62	37	�	�	PROPN
ejpam-6611	62	38	̂	̂	SYM
ejpam-6611	62	39	�	�	PROPN
ejpam-6611	62	40	:	:	PUNCT
ejpam-6611	62	41	π1(g	π1(g	NOUN
ejpam-6611	62	42	)	)	PUNCT
ejpam-6611	62	43	−→	−→	ADJ
ejpam-6611	62	44	π1(g̃	π1(g̃	PROPN
ejpam-6611	62	45	)	)	PUNCT
ejpam-6611	62	46	such	such	ADJ
ejpam-6611	62	47	that	that	SCONJ
ejpam-6611	62	48	�	�	PROPN
ejpam-6611	62	49	̂	̂	VERB
ejpam-6611	62	50	�	�	NOUN
ejpam-6611	62	51	(π1(g	(π1(g	NOUN
ejpam-6611	62	52	)	)	PUNCT
ejpam-6611	62	53	=	=	SYM
ejpam-6611	62	54	π1(𭟋(g	π1(𭟋(g	NOUN
ejpam-6611	62	55	)	)	PUNCT
ejpam-6611	62	56	)	)	PUNCT
ejpam-6611	62	57	.	.	PUNCT
ejpam-6611	63	1	since	since	SCONJ
ejpam-6611	63	2	rank	rank	NOUN
ejpam-6611	63	3	(	(	PUNCT
ejpam-6611	63	4	π1(𭟋(g	π1(𭟋(g	NOUN
ejpam-6611	63	5	)	)	PUNCT
ejpam-6611	63	6	)	)	PUNCT
ejpam-6611	63	7	)	)	PUNCT
ejpam-6611	63	8	≥rank	≥rank	NOUN
ejpam-6611	63	9	(	(	PUNCT
ejpam-6611	63	10	π1(g	π1(g	NOUN
ejpam-6611	63	11	)	)	PUNCT
ejpam-6611	63	12	)	)	PUNCT
ejpam-6611	63	13	,	,	PUNCT
ejpam-6611	63	14	it	it	PRON
ejpam-6611	63	15	follows	follow	VERB
ejpam-6611	63	16	that	that	DET
ejpam-6611	63	17	rank	rank	NOUN
ejpam-6611	63	18	(	(	PUNCT
ejpam-6611	63	19	�	�	PROPN
ejpam-6611	63	20	̂	̂	SYM
ejpam-6611	63	21	�	�	NOUN
ejpam-6611	63	22	(π1(g	(π1(g	NOUN
ejpam-6611	63	23	)	)	PUNCT
ejpam-6611	63	24	)	)	PUNCT
ejpam-6611	63	25	)	)	PUNCT
ejpam-6611	63	26	≥rank	≥rank	NOUN
ejpam-6611	63	27	(	(	PUNCT
ejpam-6611	63	28	π1(g	π1(g	NOUN
ejpam-6611	63	29	)	)	PUNCT
ejpam-6611	63	30	)	)	PUNCT
ejpam-6611	63	31	.	.	PUNCT
ejpam-6611	64	1	definition	definition	NOUN
ejpam-6611	64	2	1	1	NUM
ejpam-6611	64	3	.	.	PUNCT
ejpam-6611	65	1	let	let	VERB
ejpam-6611	65	2	{	{	PUNCT
ejpam-6611	65	3	𭟋i	𭟋i	NOUN
ejpam-6611	65	4	:	:	PUNCT
ejpam-6611	65	5	gi−1	gi−1	PROPN
ejpam-6611	65	6	→	→	PUNCT
ejpam-6611	65	7	gi	gi	INTJ
ejpam-6611	65	8	:	:	PUNCT
ejpam-6611	65	9	i	i	NOUN
ejpam-6611	65	10	=	=	NOUN
ejpam-6611	65	11	1	1	NUM
ejpam-6611	65	12	,	,	PUNCT
ejpam-6611	65	13	2	2	NUM
ejpam-6611	65	14	,	,	PUNCT
ejpam-6611	65	15	.	.	PUNCT
ejpam-6611	65	16	.	.	PUNCT
ejpam-6611	66	1	.m	.m	PROPN
ejpam-6611	66	2	}	}	PUNCT
ejpam-6611	66	3	be	be	AUX
ejpam-6611	66	4	a	a	DET
ejpam-6611	66	5	sequence	sequence	NOUN
ejpam-6611	66	6	of	of	ADP
ejpam-6611	66	7	folding	fold	VERB
ejpam-6611	66	8	maps	map	NOUN
ejpam-6611	66	9	on	on	ADP
ejpam-6611	66	10	a	a	DET
ejpam-6611	66	11	connected	connected	ADJ
ejpam-6611	66	12	graph	graph	NOUN
ejpam-6611	66	13	,	,	PUNCT
ejpam-6611	66	14	then	then	ADV
ejpam-6611	66	15	we	we	PRON
ejpam-6611	66	16	define	define	VERB
ejpam-6611	66	17	the	the	DET
ejpam-6611	66	18	limit	limit	NOUN
ejpam-6611	66	19	folding	folding	NOUN
ejpam-6611	66	20	map	map	NOUN
ejpam-6611	66	21	as	as	ADP
ejpam-6611	66	22	lim	lim	PROPN
ejpam-6611	66	23	m→∞	m→∞	NOUN
ejpam-6611	66	24	𭟋m(gm−1	𭟋m(gm−1	PROPN
ejpam-6611	66	25	)	)	PUNCT
ejpam-6611	67	1	=	=	SYM
ejpam-6611	67	2	lim	lim	PROPN
ejpam-6611	67	3	m→∞	m→∞	NOUN
ejpam-6611	67	4	𭟋m(𭟋m−1	𭟋m(𭟋m−1	PROPN
ejpam-6611	67	5	(	(	PUNCT
ejpam-6611	67	6	.	.	PUNCT
ejpam-6611	67	7	.	.	PUNCT
ejpam-6611	67	8	.	.	PUNCT
ejpam-6611	68	1	(	(	PUNCT
ejpam-6611	68	2	𭟋1(g0	𭟋1(g0	PROPN
ejpam-6611	68	3	)	)	PUNCT
ejpam-6611	68	4	.	.	PUNCT
ejpam-6611	68	5	.	.	PUNCT
ejpam-6611	68	6	.	.	PUNCT
ejpam-6611	68	7	)	)	PUNCT
ejpam-6611	68	8	.	.	PUNCT
ejpam-6611	69	1	theorem	theorem	NOUN
ejpam-6611	69	2	2	2	NUM
ejpam-6611	69	3	.	.	PUNCT
ejpam-6611	70	1	let	let	VERB
ejpam-6611	70	2	jn	jn	PROPN
ejpam-6611	70	3	be	be	AUX
ejpam-6611	70	4	a	a	DET
ejpam-6611	70	5	cobblestone	cobblestone	NOUN
ejpam-6611	70	6	path	path	NOUN
ejpam-6611	70	7	,	,	PUNCT
ejpam-6611	70	8	then	then	ADV
ejpam-6611	70	9	(	(	PUNCT
ejpam-6611	70	10	i	i	NOUN
ejpam-6611	70	11	)	)	PUNCT
ejpam-6611	70	12	there	there	PRON
ejpam-6611	70	13	is	be	VERB
ejpam-6611	70	14	folding	fold	VERB
ejpam-6611	70	15	𭟋	𭟋	ADP
ejpam-6611	70	16	:	:	PUNCT
ejpam-6611	70	17	jn	jn	PROPN
ejpam-6611	70	18	→	→	SYM
ejpam-6611	70	19	jn	jn	PROPN
ejpam-6611	70	20	which	which	PRON
ejpam-6611	70	21	induces	induce	VERB
ejpam-6611	70	22	�	�	PROPN
ejpam-6611	70	23	̂	̂	SYM
ejpam-6611	70	24	�	�	NOUN
ejpam-6611	70	25	:	:	PUNCT
ejpam-6611	70	26	π1(jn	π1(jn	PROPN
ejpam-6611	70	27	)	)	PUNCT
ejpam-6611	70	28	→	→	SYM
ejpam-6611	70	29	π1(jn	π1(jn	NUM
ejpam-6611	70	30	)	)	PUNCT
ejpam-6611	70	31	such	such	ADJ
ejpam-6611	70	32	that	that	DET
ejpam-6611	70	33	rank	rank	NOUN
ejpam-6611	70	34	(	(	PUNCT
ejpam-6611	70	35	�	�	PROPN
ejpam-6611	70	36	̂	̂	SYM
ejpam-6611	70	37	�	�	NOUN
ejpam-6611	70	38	(π1(jn	(π1(jn	NOUN
ejpam-6611	70	39	)	)	PUNCT
ejpam-6611	70	40	)	)	PUNCT
ejpam-6611	70	41	)	)	PUNCT
ejpam-6611	71	1	≤	≤	NUM
ejpam-6611	71	2	n−	n−	NOUN
ejpam-6611	71	3	1	1	NUM
ejpam-6611	71	4	.	.	PUNCT
ejpam-6611	72	1	(	(	PUNCT
ejpam-6611	72	2	ii	ii	NOUN
ejpam-6611	72	3	)	)	PUNCT
ejpam-6611	72	4	the	the	DET
ejpam-6611	72	5	folding	folding	NOUN
ejpam-6611	72	6	𭟋	𭟋	NOUN
ejpam-6611	72	7	:	:	PUNCT
ejpam-6611	72	8	dual(jn	dual(jn	PROPN
ejpam-6611	72	9	)	)	PUNCT
ejpam-6611	72	10	→	→	SYM
ejpam-6611	72	11	dual(jn	dual(jn	NOUN
ejpam-6611	72	12	)	)	PUNCT
ejpam-6611	72	13	induces	induce	VERB
ejpam-6611	72	14	�	�	PROPN
ejpam-6611	72	15	̂	̂	SYM
ejpam-6611	72	16	�	�	PROPN
ejpam-6611	72	17	:	:	PUNCT
ejpam-6611	72	18	π1(dual(jn	π1(dual(jn	NUM
ejpam-6611	72	19	)	)	PUNCT
ejpam-6611	72	20	)	)	PUNCT
ejpam-6611	73	1	→	→	SYM
ejpam-6611	73	2	π1(dual(jn	π1(dual(jn	NUM
ejpam-6611	73	3	)	)	PUNCT
ejpam-6611	73	4	)	)	PUNCT
ejpam-6611	73	5	for	for	ADP
ejpam-6611	73	6	which	which	DET
ejpam-6611	73	7	rank	rank	NOUN
ejpam-6611	73	8	(	(	PUNCT
ejpam-6611	73	9	�	�	PROPN
ejpam-6611	73	10	̂	̂	SYM
ejpam-6611	73	11	�	�	NOUN
ejpam-6611	73	12	(π1(jn	(π1(jn	NOUN
ejpam-6611	73	13	)	)	PUNCT
ejpam-6611	73	14	)	)	PUNCT
ejpam-6611	73	15	)	)	PUNCT
ejpam-6611	74	1	=	=	PUNCT
ejpam-6611	74	2	0	0	X
ejpam-6611	74	3	.	.	PUNCT
ejpam-6611	75	1	proof	proof	NOUN
ejpam-6611	75	2	.	.	PUNCT
ejpam-6611	76	1	(	(	PUNCT
ejpam-6611	76	2	i	i	NOUN
ejpam-6611	76	3	)	)	PUNCT
ejpam-6611	76	4	consider	consider	VERB
ejpam-6611	76	5	the	the	DET
ejpam-6611	76	6	folding𭟋	folding𭟋	NOUN
ejpam-6611	76	7	:	:	PUNCT
ejpam-6611	76	8	jn	jn	PROPN
ejpam-6611	76	9	→	→	SYM
ejpam-6611	76	10	jn	jn	PROPN
ejpam-6611	76	11	such	such	ADJ
ejpam-6611	76	12	that𭟋(jn	that𭟋(jn	PROPN
ejpam-6611	76	13	)	)	PUNCT
ejpam-6611	76	14	=	=	SYM
ejpam-6611	76	15	jm	jm	PROPN
ejpam-6611	76	16	,	,	PUNCT
ejpam-6611	76	17	m	m	VERB
ejpam-6611	76	18	≤	≤	ADJ
ejpam-6611	76	19	n−2	n−2	PROPN
ejpam-6611	76	20	,	,	PUNCT
ejpam-6611	76	21	n	n	PRON
ejpam-6611	76	22	≥	≥	NOUN
ejpam-6611	76	23	3	3	NUM
ejpam-6611	76	24	,	,	PUNCT
ejpam-6611	76	25	as	as	ADP
ejpam-6611	76	26	in	in	ADP
ejpam-6611	76	27	figure	figure	NOUN
ejpam-6611	76	28	1	1	NUM
ejpam-6611	76	29	,	,	PUNCT
ejpam-6611	76	30	for	for	ADP
ejpam-6611	76	31	n	n	NOUN
ejpam-6611	76	32	=	=	SYM
ejpam-6611	76	33	5	5	NUM
ejpam-6611	76	34	,	,	PUNCT
ejpam-6611	76	35	which	which	PRON
ejpam-6611	76	36	induces	induce	VERB
ejpam-6611	76	37	�	�	PROPN
ejpam-6611	76	38	̂	̂	SYM
ejpam-6611	76	39	�	�	NOUN
ejpam-6611	76	40	:	:	PUNCT
ejpam-6611	76	41	π1(jn	π1(jn	PROPN
ejpam-6611	76	42	)	)	PUNCT
ejpam-6611	76	43	→	→	SYM
ejpam-6611	76	44	π1(jn	π1(jn	NUM
ejpam-6611	76	45	)	)	PUNCT
ejpam-6611	76	46	for	for	ADP
ejpam-6611	76	47	which	which	DET
ejpam-6611	76	48	rank	rank	NOUN
ejpam-6611	76	49	(	(	PUNCT
ejpam-6611	76	50	�	�	PROPN
ejpam-6611	76	51	̂	̂	SYM
ejpam-6611	76	52	�	�	NOUN
ejpam-6611	76	53	(π1(jn	(π1(jn	NOUN
ejpam-6611	76	54	)	)	PUNCT
ejpam-6611	76	55	)	)	PUNCT
ejpam-6611	76	56	)	)	PUNCT
ejpam-6611	77	1	=	=	PUNCT
ejpam-6611	77	2	rank	rank	NOUN
ejpam-6611	77	3	(	(	PUNCT
ejpam-6611	77	4	π1(jn−2	π1(jn−2	NOUN
ejpam-6611	77	5	)	)	PUNCT
ejpam-6611	77	6	)	)	PUNCT
ejpam-6611	78	1	=	=	PUNCT
ejpam-6611	78	2	n−	n−	NOUN
ejpam-6611	78	3	1	1	NUM
ejpam-6611	78	4	.	.	PUNCT
ejpam-6611	78	5	figure	figure	VERB
ejpam-6611	78	6	1	1	NUM
ejpam-6611	78	7	:	:	PUNCT
ejpam-6611	78	8	(	(	PUNCT
ejpam-6611	78	9	ii	ii	NOUN
ejpam-6611	78	10	)	)	PUNCT
ejpam-6611	78	11	let	let	VERB
ejpam-6611	78	12	𭟋	𭟋	NOUN
ejpam-6611	78	13	:	:	PUNCT
ejpam-6611	78	14	dual(jn	dual(jn	PROPN
ejpam-6611	78	15	)	)	PUNCT
ejpam-6611	78	16	→	→	SYM
ejpam-6611	78	17	dual(jn	dual(jn	NOUN
ejpam-6611	78	18	)	)	PUNCT
ejpam-6611	78	19	be	be	AUX
ejpam-6611	78	20	a	a	DET
ejpam-6611	78	21	folding	folding	NOUN
ejpam-6611	78	22	such	such	ADJ
ejpam-6611	78	23	that	that	SCONJ
ejpam-6611	78	24	𭟋(dual(jn	𭟋(dual(jn	PROPN
ejpam-6611	78	25	)	)	PUNCT
ejpam-6611	78	26	)	)	PUNCT
ejpam-6611	79	1	=	=	SYM
ejpam-6611	79	2	𭟋	𭟋	X
ejpam-6611	79	3	(	(	PUNCT
ejpam-6611	79	4	pn+2	pn+2	NOUN
ejpam-6611	79	5	)	)	PUNCT
ejpam-6611	79	6	=	=	SYM
ejpam-6611	79	7	pm	pm	NOUN
ejpam-6611	79	8	and	and	CCONJ
ejpam-6611	79	9	m	m	VERB
ejpam-6611	79	10	≤	≤	NOUN
ejpam-6611	79	11	n	n	CCONJ
ejpam-6611	79	12	+	+	CCONJ
ejpam-6611	79	13	2	2	NUM
ejpam-6611	79	14	as	as	ADP
ejpam-6611	79	15	in	in	ADP
ejpam-6611	79	16	figure	figure	NOUN
ejpam-6611	79	17	2	2	NUM
ejpam-6611	79	18	,	,	PUNCT
ejpam-6611	79	19	for	for	ADP
ejpam-6611	79	20	n	n	NOUN
ejpam-6611	79	21	=	=	SYM
ejpam-6611	79	22	5	5	NUM
ejpam-6611	79	23	,	,	PUNCT
ejpam-6611	79	24	which	which	PRON
ejpam-6611	79	25	induces	induce	VERB
ejpam-6611	79	26	�	�	PROPN
ejpam-6611	79	27	̂	̂	SYM
ejpam-6611	79	28	�	�	PROPN
ejpam-6611	79	29	:	:	PUNCT
ejpam-6611	79	30	π1(dual(jn	π1(dual(jn	NUM
ejpam-6611	79	31	)	)	PUNCT
ejpam-6611	79	32	)	)	PUNCT
ejpam-6611	80	1	→	→	SYM
ejpam-6611	80	2	π1(dual(jn	π1(dual(jn	NUM
ejpam-6611	80	3	)	)	PUNCT
ejpam-6611	80	4	)	)	PUNCT
ejpam-6611	80	5	for	for	ADP
ejpam-6611	80	6	which	which	DET
ejpam-6611	80	7	rank	rank	NOUN
ejpam-6611	80	8	(	(	PUNCT
ejpam-6611	80	9	�	�	PROPN
ejpam-6611	80	10	̂	̂	SYM
ejpam-6611	80	11	�	�	NOUN
ejpam-6611	80	12	(π1(jn	(π1(jn	NOUN
ejpam-6611	80	13	)	)	PUNCT
ejpam-6611	80	14	)	)	PUNCT
ejpam-6611	80	15	)	)	PUNCT
ejpam-6611	81	1	=	=	SYM
ejpam-6611	81	2	0	0	X
ejpam-6611	81	3	.	.	PUNCT
ejpam-6611	81	4	theorem	theorem	NOUN
ejpam-6611	81	5	3	3	X
ejpam-6611	81	6	.	.	PUNCT
ejpam-6611	82	1	let	let	VERB
ejpam-6611	82	2	j∞	j∞	PROPN
ejpam-6611	82	3	be	be	AUX
ejpam-6611	82	4	an	an	DET
ejpam-6611	82	5	infinite	infinite	ADJ
ejpam-6611	82	6	cobblestone	cobblestone	NOUN
ejpam-6611	82	7	path	path	NOUN
ejpam-6611	82	8	.	.	PUNCT
ejpam-6611	83	1	then	then	ADV
ejpam-6611	83	2	,	,	PUNCT
ejpam-6611	83	3	there	there	PRON
ejpam-6611	83	4	are	be	VERB
ejpam-6611	83	5	two	two	NUM
ejpam-6611	83	6	types	type	NOUN
ejpam-6611	83	7	of	of	ADP
ejpam-6611	83	8	foldings	folding	NOUN
ejpam-6611	83	9	𭟋	𭟋	ADP
ejpam-6611	83	10	:	:	PUNCT
ejpam-6611	83	11	j∞	j∞	PROPN
ejpam-6611	83	12	→	→	PUNCT
ejpam-6611	83	13	j∞	j∞	PROPN
ejpam-6611	83	14	induce	induce	VERB
ejpam-6611	83	15	�	�	PROPN
ejpam-6611	83	16	̂	̂	SYM
ejpam-6611	83	17	�	�	NOUN
ejpam-6611	83	18	:	:	PUNCT
ejpam-6611	83	19	π1(j∞	π1(j∞	PROPN
ejpam-6611	83	20	)	)	PUNCT
ejpam-6611	83	21	→	→	PUNCT
ejpam-6611	83	22	π1(j∞	π1(j∞	NOUN
ejpam-6611	83	23	)	)	PUNCT
ejpam-6611	83	24	for	for	ADP
ejpam-6611	83	25	which	which	DET
ejpam-6611	83	26	rank	rank	NOUN
ejpam-6611	83	27	(	(	PUNCT
ejpam-6611	83	28	�	�	PROPN
ejpam-6611	83	29	̂	̂	NOUN
ejpam-6611	83	30	�	�	NOUN
ejpam-6611	83	31	(π1(j∞	(π1(j∞	NOUN
ejpam-6611	83	32	)	)	PUNCT
ejpam-6611	83	33	)	)	PUNCT
ejpam-6611	83	34	)	)	PUNCT
ejpam-6611	84	1	≤	≤	NUM
ejpam-6611	84	2	1	1	NUM
ejpam-6611	84	3	.	.	PUNCT
ejpam-6611	84	4	m.	m.	NOUN
ejpam-6611	84	5	abu	abu	PROPN
ejpam-6611	84	6	-	-	PUNCT
ejpam-6611	84	7	saleem	saleem	PROPN
ejpam-6611	84	8	/	/	SYM
ejpam-6611	84	9	eur	eur	PROPN
ejpam-6611	84	10	.	.	PUNCT
ejpam-6611	85	1	j.	j.	PROPN
ejpam-6611	85	2	pure	pure	PROPN
ejpam-6611	85	3	appl	appl	PROPN
ejpam-6611	85	4	.	.	PROPN
ejpam-6611	85	5	math	math	PROPN
ejpam-6611	85	6	,	,	PUNCT
ejpam-6611	85	7	18	18	NUM
ejpam-6611	85	8	(	(	PUNCT
ejpam-6611	85	9	3	3	NUM
ejpam-6611	85	10	)	)	PUNCT
ejpam-6611	85	11	(	(	PUNCT
ejpam-6611	85	12	2025	2025	NUM
ejpam-6611	85	13	)	)	PUNCT
ejpam-6611	85	14	,	,	PUNCT
ejpam-6611	85	15	6611	6611	NUM
ejpam-6611	85	16	4	4	NUM
ejpam-6611	85	17	of	of	ADP
ejpam-6611	85	18	7	7	NUM
ejpam-6611	85	19	figure	figure	NOUN
ejpam-6611	85	20	2	2	NUM
ejpam-6611	85	21	:	:	PUNCT
ejpam-6611	85	22	proof	proof	NOUN
ejpam-6611	85	23	.	.	PUNCT
ejpam-6611	86	1	let	let	VERB
ejpam-6611	86	2	j∞	j∞	PROPN
ejpam-6611	86	3	be	be	AUX
ejpam-6611	86	4	an	an	DET
ejpam-6611	86	5	infinite	infinite	ADJ
ejpam-6611	86	6	cobblestone	cobblestone	NOUN
ejpam-6611	86	7	path	path	NOUN
ejpam-6611	86	8	,	,	PUNCT
ejpam-6611	86	9	and	and	CCONJ
ejpam-6611	86	10	consider	consider	VERB
ejpam-6611	86	11	𭟋	𭟋	NOUN
ejpam-6611	86	12	:	:	PUNCT
ejpam-6611	86	13	j∞	j∞	PROPN
ejpam-6611	86	14	→	→	PUNCT
ejpam-6611	86	15	j∞	j∞	PROPN
ejpam-6611	86	16	to	to	PART
ejpam-6611	86	17	be	be	AUX
ejpam-6611	86	18	a	a	DET
ejpam-6611	86	19	folding	folding	NOUN
ejpam-6611	86	20	such	such	ADJ
ejpam-6611	86	21	that	that	DET
ejpam-6611	86	22	𭟋(j∞	𭟋(j∞	NOUN
ejpam-6611	86	23	)	)	PUNCT
ejpam-6611	87	1	=	=	SYM
ejpam-6611	87	2	c2	c2	PROPN
ejpam-6611	87	3	as	as	ADP
ejpam-6611	87	4	in	in	ADP
ejpam-6611	87	5	figure	figure	NOUN
ejpam-6611	87	6	3(a	3(a	NUM
ejpam-6611	87	7	)	)	PUNCT
ejpam-6611	87	8	,	,	PUNCT
ejpam-6611	87	9	which	which	PRON
ejpam-6611	87	10	induces	induce	VERB
ejpam-6611	87	11	�	�	PROPN
ejpam-6611	87	12	̂	̂	SYM
ejpam-6611	87	13	�	�	NOUN
ejpam-6611	87	14	:	:	PUNCT
ejpam-6611	87	15	π1(j∞	π1(j∞	PROPN
ejpam-6611	87	16	)	)	PUNCT
ejpam-6611	88	1	→	→	PUNCT
ejpam-6611	88	2	π1(j∞	π1(j∞	NOUN
ejpam-6611	88	3	)	)	PUNCT
ejpam-6611	88	4	in	in	ADP
ejpam-6611	88	5	which	which	PRON
ejpam-6611	88	6	rank	rank	NOUN
ejpam-6611	88	7	(	(	PUNCT
ejpam-6611	88	8	�	�	PROPN
ejpam-6611	88	9	̂	̂	NOUN
ejpam-6611	88	10	�	�	NOUN
ejpam-6611	88	11	(π1(j∞	(π1(j∞	NOUN
ejpam-6611	88	12	)	)	PUNCT
ejpam-6611	88	13	)	)	PUNCT
ejpam-6611	88	14	)	)	PUNCT
ejpam-6611	89	1	=	=	PUNCT
ejpam-6611	89	2	1	1	X
ejpam-6611	89	3	.	.	PUNCT
ejpam-6611	90	1	furthermore	furthermore	ADV
ejpam-6611	90	2	,	,	PUNCT
ejpam-6611	90	3	let	let	VERB
ejpam-6611	90	4	𭟋	𭟋	VERB
ejpam-6611	90	5	:	:	PUNCT
ejpam-6611	90	6	j∞	j∞	PROPN
ejpam-6611	90	7	→	→	PUNCT
ejpam-6611	90	8	j∞	j∞	PROPN
ejpam-6611	90	9	be	be	AUX
ejpam-6611	90	10	a	a	DET
ejpam-6611	90	11	folding	folding	NOUN
ejpam-6611	90	12	such	such	ADJ
ejpam-6611	90	13	that	that	DET
ejpam-6611	90	14	𭟋(j∞	𭟋(j∞	NOUN
ejpam-6611	90	15	)	)	PUNCT
ejpam-6611	90	16	=	=	PROPN
ejpam-6611	90	17	i1	i1	PROPN
ejpam-6611	90	18	⋎	⋎	PROPN
ejpam-6611	90	19	p∞	p∞	PROPN
ejpam-6611	90	20	⋎	⋎	PROPN
ejpam-6611	90	21	i2	i2	PROPN
ejpam-6611	90	22	,	,	PUNCT
ejpam-6611	90	23	where	where	SCONJ
ejpam-6611	90	24	i1	i1	PROPN
ejpam-6611	90	25	and	and	CCONJ
ejpam-6611	90	26	i2	i2	PROPN
ejpam-6611	90	27	are	be	AUX
ejpam-6611	90	28	arcs	arcs	X
ejpam-6611	90	29	homeomorphic	homeomorphic	ADJ
ejpam-6611	90	30	to	to	ADP
ejpam-6611	90	31	the	the	DET
ejpam-6611	90	32	closed	closed	ADJ
ejpam-6611	90	33	interval	interval	NOUN
ejpam-6611	90	34	[	[	X
ejpam-6611	90	35	a	a	X
ejpam-6611	90	36	,	,	PUNCT
ejpam-6611	90	37	b	b	NOUN
ejpam-6611	90	38	]	]	PUNCT
ejpam-6611	90	39	,	,	PUNCT
ejpam-6611	90	40	as	as	SCONJ
ejpam-6611	90	41	shown	show	VERB
ejpam-6611	90	42	in	in	ADP
ejpam-6611	90	43	figure	figure	NOUN
ejpam-6611	90	44	3(b	3(b	NUM
ejpam-6611	90	45	)	)	PUNCT
ejpam-6611	90	46	,	,	PUNCT
ejpam-6611	90	47	which	which	PRON
ejpam-6611	90	48	induces	induce	VERB
ejpam-6611	90	49	�	�	PROPN
ejpam-6611	90	50	̂	̂	SYM
ejpam-6611	90	51	�	�	NOUN
ejpam-6611	90	52	:	:	PUNCT
ejpam-6611	90	53	π1(j∞	π1(j∞	PROPN
ejpam-6611	90	54	)	)	PUNCT
ejpam-6611	91	1	→	→	PUNCT
ejpam-6611	91	2	π1(j∞	π1(j∞	NOUN
ejpam-6611	91	3	)	)	PUNCT
ejpam-6611	91	4	for	for	ADP
ejpam-6611	91	5	which	which	DET
ejpam-6611	91	6	rank	rank	NOUN
ejpam-6611	91	7	(	(	PUNCT
ejpam-6611	91	8	�	�	PROPN
ejpam-6611	91	9	̂	̂	NOUN
ejpam-6611	91	10	�	�	NOUN
ejpam-6611	91	11	(π1(j∞	(π1(j∞	NOUN
ejpam-6611	91	12	)	)	PUNCT
ejpam-6611	91	13	)	)	PUNCT
ejpam-6611	91	14	)	)	PUNCT
ejpam-6611	92	1	=	=	PUNCT
ejpam-6611	92	2	0	0	X
ejpam-6611	92	3	.	.	X
ejpam-6611	92	4	figure	figure	VERB
ejpam-6611	92	5	3	3	NUM
ejpam-6611	92	6	:	:	PUNCT
ejpam-6611	92	7	m.	m.	PROPN
ejpam-6611	92	8	abu	abu	PROPN
ejpam-6611	92	9	-	-	PUNCT
ejpam-6611	92	10	saleem	saleem	PROPN
ejpam-6611	92	11	/	/	SYM
ejpam-6611	92	12	eur	eur	PROPN
ejpam-6611	92	13	.	.	PUNCT
ejpam-6611	93	1	j.	j.	PROPN
ejpam-6611	93	2	pure	pure	PROPN
ejpam-6611	93	3	appl	appl	PROPN
ejpam-6611	93	4	.	.	PROPN
ejpam-6611	93	5	math	math	PROPN
ejpam-6611	93	6	,	,	PUNCT
ejpam-6611	93	7	18	18	NUM
ejpam-6611	93	8	(	(	PUNCT
ejpam-6611	93	9	3	3	NUM
ejpam-6611	93	10	)	)	PUNCT
ejpam-6611	93	11	(	(	PUNCT
ejpam-6611	93	12	2025	2025	NUM
ejpam-6611	93	13	)	)	PUNCT
ejpam-6611	93	14	,	,	PUNCT
ejpam-6611	93	15	6611	6611	NUM
ejpam-6611	93	16	5	5	NUM
ejpam-6611	93	17	of	of	ADP
ejpam-6611	93	18	7	7	NUM
ejpam-6611	93	19	theorem	theorem	ADJ
ejpam-6611	93	20	4	4	NUM
ejpam-6611	93	21	.	.	PUNCT
ejpam-6611	93	22	given	give	VERB
ejpam-6611	93	23	an	an	DET
ejpam-6611	93	24	m	m	NOUN
ejpam-6611	93	25	-	-	PUNCT
ejpam-6611	93	26	bouquet	bouquet	NOUN
ejpam-6611	93	27	graph	graph	NOUN
ejpam-6611	93	28	bm	bm	PROPN
ejpam-6611	93	29	,	,	PUNCT
ejpam-6611	93	30	then	then	ADV
ejpam-6611	93	31	the	the	DET
ejpam-6611	93	32	sequence	sequence	NOUN
ejpam-6611	93	33	of	of	ADP
ejpam-6611	93	34	folding	fold	VERB
ejpam-6611	93	35	maps	map	NOUN
ejpam-6611	93	36	{	{	PUNCT
ejpam-6611	93	37	𭟋i	𭟋i	NOUN
ejpam-6611	93	38	:	:	PUNCT
ejpam-6611	93	39	bmi−1	bmi−1	NOUN
ejpam-6611	93	40	→	→	SYM
ejpam-6611	93	41	bmi	bmi	X
ejpam-6611	93	42	:	:	PUNCT
ejpam-6611	94	1	i	i	NOUN
ejpam-6611	94	2	=	=	NOUN
ejpam-6611	94	3	1	1	NUM
ejpam-6611	94	4	,	,	PUNCT
ejpam-6611	94	5	2	2	NUM
ejpam-6611	94	6	,	,	PUNCT
ejpam-6611	94	7	.	.	PUNCT
ejpam-6611	94	8	.	.	PUNCT
ejpam-6611	94	9	.	.	PUNCT
ejpam-6611	95	1	n	n	CCONJ
ejpam-6611	95	2	}	}	PUNCT
ejpam-6611	95	3	induces	induce	VERB
ejpam-6611	95	4	{	{	PUNCT
ejpam-6611	95	5	�	�	NOUN
ejpam-6611	95	6	̂	̂	NOUN
ejpam-6611	95	7	�	�	NOUN
ejpam-6611	95	8	i	i	PRON
ejpam-6611	95	9	:	:	PUNCT
ejpam-6611	95	10	π1	π1	NOUN
ejpam-6611	95	11	(	(	PUNCT
ejpam-6611	95	12	bmi−1	bmi−1	NOUN
ejpam-6611	95	13	)	)	PUNCT
ejpam-6611	95	14	→	→	SYM
ejpam-6611	95	15	π1(bmi	π1(bmi	PROPN
ejpam-6611	95	16	)	)	PUNCT
ejpam-6611	95	17	:	:	PUNCT
ejpam-6611	96	1	i	i	NOUN
ejpam-6611	96	2	=	=	NOUN
ejpam-6611	96	3	1	1	NUM
ejpam-6611	96	4	,	,	PUNCT
ejpam-6611	96	5	2	2	NUM
ejpam-6611	96	6	,	,	PUNCT
ejpam-6611	96	7	.	.	PUNCT
ejpam-6611	96	8	.	.	PUNCT
ejpam-6611	96	9	.	.	PUNCT
ejpam-6611	97	1	n	n	CCONJ
ejpam-6611	97	2	}	}	PUNCT
ejpam-6611	97	3	such	such	ADJ
ejpam-6611	97	4	that	that	DET
ejpam-6611	97	5	rank	rank	NOUN
ejpam-6611	97	6	(	(	PUNCT
ejpam-6611	97	7	lim	lim	PROPN
ejpam-6611	97	8	n→∞	n→∞	X
ejpam-6611	97	9	(	(	PUNCT
ejpam-6611	97	10	�	�	NOUN
ejpam-6611	97	11	̂	̂	SYM
ejpam-6611	97	12	�	�	NOUN
ejpam-6611	97	13	n(π1	n(π1	PRON
ejpam-6611	97	14	(	(	PUNCT
ejpam-6611	97	15	bmn−1	bmn−1	PROPN
ejpam-6611	97	16	)	)	PUNCT
ejpam-6611	97	17	)	)	PUNCT
ejpam-6611	97	18	)	)	PUNCT
ejpam-6611	97	19	)	)	PUNCT
ejpam-6611	98	1	=	=	PUNCT
ejpam-6611	98	2	0	0	X
ejpam-6611	98	3	.	.	PUNCT
ejpam-6611	99	1	proof	proof	NOUN
ejpam-6611	99	2	.	.	PUNCT
ejpam-6611	100	1	given	give	VERB
ejpam-6611	100	2	an	an	DET
ejpam-6611	100	3	m	m	NOUN
ejpam-6611	100	4	-	-	PUNCT
ejpam-6611	100	5	bouquet	bouquet	NOUN
ejpam-6611	100	6	graph	graph	NOUN
ejpam-6611	100	7	bm	bm	PROPN
ejpam-6611	100	8	.	.	PUNCT
ejpam-6611	101	1	now	now	ADV
ejpam-6611	101	2	,	,	PUNCT
ejpam-6611	101	3	consider	consider	VERB
ejpam-6611	101	4	the	the	DET
ejpam-6611	101	5	following	follow	VERB
ejpam-6611	101	6	sequence	sequence	NOUN
ejpam-6611	101	7	of	of	ADP
ejpam-6611	101	8	folding	fold	VERB
ejpam-6611	101	9	maps	map	NOUN
ejpam-6611	101	10	:	:	PUNCT
ejpam-6611	101	11	𭟋1	𭟋1	NOUN
ejpam-6611	101	12	:	:	PUNCT
ejpam-6611	101	13	bm0	bm0	PROPN
ejpam-6611	101	14	→	→	SYM
ejpam-6611	101	15	bm1	bm1	X
ejpam-6611	101	16	,	,	PUNCT
ejpam-6611	101	17	𭟋2	𭟋2	PROPN
ejpam-6611	101	18	:	:	PUNCT
ejpam-6611	101	19	bm1	bm1	PROPN
ejpam-6611	101	20	→	→	SYM
ejpam-6611	101	21	bm2	bm2	NOUN
ejpam-6611	101	22	,	,	PUNCT
ejpam-6611	101	23	.	.	PUNCT
ejpam-6611	101	24	.	.	PUNCT
ejpam-6611	101	25	.	.	PUNCT
ejpam-6611	102	1	,	,	PUNCT
ejpam-6611	102	2	𭟋n	𭟋n	PROPN
ejpam-6611	102	3	:	:	PUNCT
ejpam-6611	102	4	bmn−1	bmn−1	PROPN
ejpam-6611	102	5	→	→	SYM
ejpam-6611	102	6	bmn	bmn	NOUN
ejpam-6611	102	7	,	,	PUNCT
ejpam-6611	102	8	for	for	ADP
ejpam-6611	102	9	which	which	PRON
ejpam-6611	102	10	lim	lim	PROPN
ejpam-6611	102	11	n→∞	n→∞	NUM
ejpam-6611	102	12	𭟋n(bmn−1	𭟋n(bmn−1	PROPN
ejpam-6611	102	13	)	)	PUNCT
ejpam-6611	103	1	=	=	SYM
ejpam-6611	103	2	v	v	NOUN
ejpam-6611	103	3	(	(	PUNCT
ejpam-6611	103	4	one	one	NUM
ejpam-6611	103	5	vertex	vertex	NOUN
ejpam-6611	103	6	)	)	PUNCT
ejpam-6611	103	7	as	as	ADP
ejpam-6611	103	8	in	in	ADP
ejpam-6611	103	9	figure	figure	NOUN
ejpam-6611	103	10	4	4	NUM
ejpam-6611	103	11	,	,	PUNCT
ejpam-6611	103	12	which	which	PRON
ejpam-6611	103	13	induces	induce	VERB
ejpam-6611	103	14	�	�	PROPN
ejpam-6611	103	15	̂	̂	NOUN
ejpam-6611	103	16	�	�	NOUN
ejpam-6611	103	17	1	1	NUM
ejpam-6611	103	18	:	:	PUNCT
ejpam-6611	103	19	π1	π1	NOUN
ejpam-6611	103	20	(	(	PUNCT
ejpam-6611	103	21	bm0	bm0	NOUN
ejpam-6611	103	22	)	)	PUNCT
ejpam-6611	103	23	→	→	SYM
ejpam-6611	103	24	π1	π1	NOUN
ejpam-6611	103	25	(	(	PUNCT
ejpam-6611	103	26	bm1	bm1	PROPN
ejpam-6611	103	27	)	)	PUNCT
ejpam-6611	103	28	,	,	PUNCT
ejpam-6611	103	29	�	�	PROPN
ejpam-6611	103	30	̂	̂	VERB
ejpam-6611	103	31	�	�	NOUN
ejpam-6611	103	32	2	2	NUM
ejpam-6611	103	33	:	:	PUNCT
ejpam-6611	103	34	π1	π1	NOUN
ejpam-6611	103	35	(	(	PUNCT
ejpam-6611	103	36	b1	b1	NOUN
ejpam-6611	103	37	)	)	PUNCT
ejpam-6611	103	38	→	→	SYM
ejpam-6611	103	39	π1	π1	NOUN
ejpam-6611	103	40	(	(	PUNCT
ejpam-6611	103	41	b2	b2	NOUN
ejpam-6611	103	42	)	)	PUNCT
ejpam-6611	103	43	,	,	PUNCT
ejpam-6611	103	44	.	.	PUNCT
ejpam-6611	103	45	.	.	PUNCT
ejpam-6611	103	46	.	.	PUNCT
ejpam-6611	103	47	,	,	PUNCT
ejpam-6611	103	48	�	�	PROPN
ejpam-6611	103	49	̂	̂	NOUN
ejpam-6611	103	50	�	�	NOUN
ejpam-6611	103	51	n	n	PART
ejpam-6611	103	52	:	:	PUNCT
ejpam-6611	103	53	π1	π1	NOUN
ejpam-6611	103	54	(	(	PUNCT
ejpam-6611	103	55	bmn−1	bmn−1	PROPN
ejpam-6611	103	56	)	)	PUNCT
ejpam-6611	103	57	→	→	SYM
ejpam-6611	103	58	π1(bmn	π1(bmn	NUM
ejpam-6611	103	59	)	)	PUNCT
ejpam-6611	103	60	,	,	PUNCT
ejpam-6611	103	61	for	for	ADP
ejpam-6611	103	62	which	which	PRON
ejpam-6611	103	63	lim	lim	PROPN
ejpam-6611	103	64	n→∞	n→∞	X
ejpam-6611	103	65	(	(	PUNCT
ejpam-6611	103	66	�	�	NOUN
ejpam-6611	103	67	̂	̂	SYM
ejpam-6611	103	68	�	�	NOUN
ejpam-6611	103	69	n(π1	n(π1	PRON
ejpam-6611	103	70	(	(	PUNCT
ejpam-6611	103	71	bmn−1	bmn−1	PROPN
ejpam-6611	103	72	)	)	PUNCT
ejpam-6611	103	73	)	)	PUNCT
ejpam-6611	103	74	)	)	PUNCT
ejpam-6611	104	1	=	=	SYM
ejpam-6611	104	2	π1	π1	NOUN
ejpam-6611	104	3	(	(	PUNCT
ejpam-6611	104	4	lim	lim	PROPN
ejpam-6611	104	5	n→∞	n→∞	X
ejpam-6611	104	6	(	(	PUNCT
ejpam-6611	104	7	𭟋n	𭟋n	PROPN
ejpam-6611	104	8	(	(	PUNCT
ejpam-6611	104	9	bmn−1	bmn−1	PROPN
ejpam-6611	104	10	)	)	PUNCT
ejpam-6611	104	11	)	)	PUNCT
ejpam-6611	104	12	)	)	PUNCT
ejpam-6611	105	1	=	=	SYM
ejpam-6611	105	2	π1	π1	NOUN
ejpam-6611	105	3	(	(	PUNCT
ejpam-6611	105	4	v	v	NOUN
ejpam-6611	105	5	)	)	PUNCT
ejpam-6611	105	6	.	.	PUNCT
ejpam-6611	106	1	hence	hence	ADV
ejpam-6611	106	2	,	,	PUNCT
ejpam-6611	106	3	rank	rank	PROPN
ejpam-6611	106	4	(	(	PUNCT
ejpam-6611	106	5	lim	lim	PROPN
ejpam-6611	106	6	n→∞	n→∞	X
ejpam-6611	106	7	(	(	PUNCT
ejpam-6611	106	8	�	�	NOUN
ejpam-6611	106	9	̂	̂	SYM
ejpam-6611	106	10	�	�	NOUN
ejpam-6611	106	11	n(π1	n(π1	PRON
ejpam-6611	106	12	(	(	PUNCT
ejpam-6611	106	13	bmn−1	bmn−1	PROPN
ejpam-6611	106	14	)	)	PUNCT
ejpam-6611	106	15	)	)	PUNCT
ejpam-6611	106	16	)	)	PUNCT
ejpam-6611	106	17	)	)	PUNCT
ejpam-6611	107	1	=	=	PUNCT
ejpam-6611	107	2	0	0	X
ejpam-6611	107	3	.	.	X
ejpam-6611	107	4	figure	figure	VERB
ejpam-6611	107	5	4	4	NUM
ejpam-6611	107	6	:	:	PUNCT
ejpam-6611	107	7	theorem	theorem	NOUN
ejpam-6611	107	8	5	5	NUM
ejpam-6611	107	9	.	.	PUNCT
ejpam-6611	107	10	given	give	VERB
ejpam-6611	107	11	a	a	DET
ejpam-6611	107	12	connected	connected	ADJ
ejpam-6611	107	13	graph	graph	NOUN
ejpam-6611	107	14	gk	gk	NOUN
ejpam-6611	107	15	that	that	PRON
ejpam-6611	107	16	is	be	AUX
ejpam-6611	107	17	homeomorphic	homeomorphic	ADJ
ejpam-6611	107	18	to	to	ADP
ejpam-6611	107	19	k	k	ADJ
ejpam-6611	107	20	-	-	PUNCT
ejpam-6611	107	21	bouquet	bouquet	NOUN
ejpam-6611	107	22	graph	graph	NOUN
ejpam-6611	107	23	bk	bk	NOUN
ejpam-6611	107	24	for	for	ADP
ejpam-6611	107	25	k	k	X
ejpam-6611	107	26	=	=	SYM
ejpam-6611	107	27	1	1	NUM
ejpam-6611	107	28	,	,	PUNCT
ejpam-6611	107	29	2	2	NUM
ejpam-6611	107	30	,	,	PUNCT
ejpam-6611	107	31	.	.	PUNCT
ejpam-6611	107	32	.	.	PUNCT
ejpam-6611	108	1	.	.	PUNCT
ejpam-6611	109	1	,	,	PUNCT
ejpam-6611	109	2	n	n	CCONJ
ejpam-6611	109	3	,	,	PUNCT
ejpam-6611	109	4	then	then	ADV
ejpam-6611	109	5	for	for	ADP
ejpam-6611	109	6	any	any	DET
ejpam-6611	109	7	h	h	NOUN
ejpam-6611	109	8	,	,	PUNCT
ejpam-6611	109	9	there	there	PRON
ejpam-6611	109	10	is	be	VERB
ejpam-6611	109	11	a	a	DET
ejpam-6611	109	12	folding	fold	VERB
ejpam-6611	109	13	𭟋h	𭟋h	NOUN
ejpam-6611	109	14	:	:	PUNCT
ejpam-6611	109	15	n	n	CCONJ
ejpam-6611	109	16	⋎	⋎	NOUN
ejpam-6611	109	17	k=1	k=1	INTJ
ejpam-6611	110	1	gk	gk	INTJ
ejpam-6611	110	2	−→	−→	NOUN
ejpam-6611	110	3	n	n	ADV
ejpam-6611	110	4	⋎	⋎	NOUN
ejpam-6611	111	1	k=1	k=1	X
ejpam-6611	111	2	gk	gk	NOUN
ejpam-6611	111	3	which	which	PRON
ejpam-6611	111	4	induces	induce	VERB
ejpam-6611	111	5	a	a	DET
ejpam-6611	111	6	folding	fold	VERB
ejpam-6611	111	7	�	�	NOUN
ejpam-6611	111	8	̂	̂	NOUN
ejpam-6611	111	9	�	�	NOUN
ejpam-6611	111	10	h	h	NOUN
ejpam-6611	111	11	:	:	PUNCT
ejpam-6611	111	12	n∗	n∗	PROPN
ejpam-6611	111	13	k=1	k=1	X
ejpam-6611	111	14	π1(gk	π1(gk	NUM
ejpam-6611	111	15	)	)	PUNCT
ejpam-6611	111	16	→	→	SYM
ejpam-6611	111	17	n∗	n∗	PROPN
ejpam-6611	111	18	k=1	k=1	X
ejpam-6611	111	19	π1(gk	π1(gk	NOUN
ejpam-6611	111	20	)	)	PUNCT
ejpam-6611	111	21	such	such	ADJ
ejpam-6611	111	22	that	that	PRON
ejpam-6611	111	23	�	�	PROPN
ejpam-6611	111	24	̂	̂	SYM
ejpam-6611	111	25	�	�	NOUN
ejpam-6611	111	26	h	h	NOUN
ejpam-6611	111	27	(	(	PUNCT
ejpam-6611	111	28	n∗	n∗	PROPN
ejpam-6611	111	29	k=1	k=1	PUNCT
ejpam-6611	111	30	π1(gk	π1(gk	NOUN
ejpam-6611	111	31	)	)	PUNCT
ejpam-6611	111	32	)	)	PUNCT
ejpam-6611	111	33	is	be	AUX
ejpam-6611	111	34	a	a	DET
ejpam-6611	111	35	free	free	ADJ
ejpam-6611	111	36	group	group	NOUN
ejpam-6611	111	37	of	of	ADP
ejpam-6611	111	38	rank	rank	NOUN
ejpam-6611	111	39	m−	m−	PROPN
ejpam-6611	111	40	h	h	PROPN
ejpam-6611	111	41	,	,	PUNCT
ejpam-6611	111	42	for	for	ADP
ejpam-6611	111	43	h	h	NOUN
ejpam-6611	111	44	=	=	SYM
ejpam-6611	111	45	1	1	NUM
ejpam-6611	111	46	,	,	PUNCT
ejpam-6611	111	47	2	2	NUM
ejpam-6611	111	48	,	,	PUNCT
ejpam-6611	111	49	.	.	PUNCT
ejpam-6611	111	50	.	.	PUNCT
ejpam-6611	112	1	.	.	PUNCT
ejpam-6611	113	1	,	,	PUNCT
ejpam-6611	113	2	n	n	CCONJ
ejpam-6611	113	3	where	where	SCONJ
ejpam-6611	113	4	,	,	PUNCT
ejpam-6611	113	5	m	m	PROPN
ejpam-6611	113	6	=	=	SYM
ejpam-6611	113	7	n(n+1	n(n+1	PROPN
ejpam-6611	113	8	)	)	PUNCT
ejpam-6611	113	9	2	2	NUM
ejpam-6611	113	10	.	.	PUNCT
ejpam-6611	114	1	proof	proof	NOUN
ejpam-6611	114	2	.	.	PUNCT
ejpam-6611	115	1	let	let	VERB
ejpam-6611	115	2	𭟋1	𭟋1	NOUN
ejpam-6611	115	3	:	:	PUNCT
ejpam-6611	115	4	n	n	X
ejpam-6611	115	5	⋎	⋎	NOUN
ejpam-6611	115	6	k=1	k=1	INTJ
ejpam-6611	116	1	gk	gk	INTJ
ejpam-6611	116	2	−→	−→	NOUN
ejpam-6611	116	3	n	n	PRON
ejpam-6611	116	4	⋎	⋎	NOUN
ejpam-6611	117	1	k=1	k=1	PUNCT
ejpam-6611	117	2	gk	gk	INTJ
ejpam-6611	117	3	be	be	AUX
ejpam-6611	117	4	a	a	DET
ejpam-6611	117	5	folding	folding	NOUN
ejpam-6611	117	6	such	such	ADJ
ejpam-6611	117	7	that	that	DET
ejpam-6611	117	8	𭟋1	𭟋1	NOUN
ejpam-6611	117	9	(	(	PUNCT
ejpam-6611	117	10	n	n	NUM
ejpam-6611	117	11	⋎	⋎	NOUN
ejpam-6611	117	12	k=1	k=1	X
ejpam-6611	117	13	gk	gk	PROPN
ejpam-6611	117	14	)	)	PUNCT
ejpam-6611	117	15	=	=	PUNCT
ejpam-6611	117	16	g1	g1	PROPN
ejpam-6611	117	17	⋎	⋎	PROPN
ejpam-6611	117	18	g2	g2	PROPN
ejpam-6611	117	19	⋎	⋎	PROPN
ejpam-6611	117	20	.	.	PUNCT
ejpam-6611	117	21	.	.	PUNCT
ejpam-6611	117	22	.	.	PUNCT
ejpam-6611	118	1	⋎	⋎	NOUN
ejpam-6611	118	2	𭟋1(gr1	𭟋1(gr1	NUM
ejpam-6611	118	3	)	)	PUNCT
ejpam-6611	118	4	⋎	⋎	NOUN
ejpam-6611	118	5	.	.	PUNCT
ejpam-6611	118	6	.	.	PUNCT
ejpam-6611	118	7	.	.	PUNCT
ejpam-6611	119	1	⋎	⋎	PROPN
ejpam-6611	119	2	gn	gn	PROPN
ejpam-6611	119	3	for	for	ADP
ejpam-6611	119	4	r1	r1	PROPN
ejpam-6611	119	5	=	=	SYM
ejpam-6611	119	6	1	1	NUM
ejpam-6611	119	7	,	,	PUNCT
ejpam-6611	119	8	2	2	NUM
ejpam-6611	119	9	,	,	PUNCT
ejpam-6611	119	10	.	.	PUNCT
ejpam-6611	119	11	.	.	PUNCT
ejpam-6611	119	12	.	.	PUNCT
ejpam-6611	120	1	,	,	PUNCT
ejpam-6611	120	2	n	n	PRON
ejpam-6611	120	3	where	where	SCONJ
ejpam-6611	120	4	𭟋1(gt	𭟋1(gt	PROPN
ejpam-6611	120	5	)	)	PUNCT
ejpam-6611	120	6	=	=	SYM
ejpam-6611	120	7	𭟋1(bt	𭟋1(bt	NUM
ejpam-6611	120	8	)	)	PUNCT
ejpam-6611	120	9	=	=	SYM
ejpam-6611	120	10	bt−1	bt−1	PROPN
ejpam-6611	120	11	,	,	PUNCT
ejpam-6611	120	12	folding	fold	VERB
ejpam-6611	120	13	one	one	NUM
ejpam-6611	120	14	loop	loop	NOUN
ejpam-6611	120	15	into	into	ADP
ejpam-6611	120	16	another	another	PRON
ejpam-6611	120	17	,	,	PUNCT
ejpam-6611	120	18	then	then	ADV
ejpam-6611	120	19	we	we	PRON
ejpam-6611	120	20	obtain	obtain	VERB
ejpam-6611	120	21	the	the	DET
ejpam-6611	120	22	induced	induced	ADJ
ejpam-6611	120	23	folding	fold	VERB
ejpam-6611	120	24	�	�	PROPN
ejpam-6611	120	25	̂	̂	NOUN
ejpam-6611	120	26	�	�	NOUN
ejpam-6611	120	27	1	1	NUM
ejpam-6611	120	28	:	:	PUNCT
ejpam-6611	120	29	n∗	n∗	PROPN
ejpam-6611	120	30	k=1	k=1	PUNCT
ejpam-6611	120	31	π1(gk	π1(gk	NUM
ejpam-6611	120	32	)	)	PUNCT
ejpam-6611	120	33	−→	−→	NOUN
ejpam-6611	120	34	n∗	n∗	VERB
ejpam-6611	120	35	k=1	k=1	PUNCT
ejpam-6611	120	36	π1(gk	π1(gk	NOUN
ejpam-6611	120	37	)	)	PUNCT
ejpam-6611	120	38	such	such	ADJ
ejpam-6611	120	39	that	that	SCONJ
ejpam-6611	120	40	�	�	PROPN
ejpam-6611	120	41	̂	̂	VERB
ejpam-6611	120	42	�	�	NOUN
ejpam-6611	120	43	1	1	NUM
ejpam-6611	120	44	(	(	PUNCT
ejpam-6611	120	45	n∗	n∗	NOUN
ejpam-6611	120	46	k=1	k=1	PUNCT
ejpam-6611	120	47	π1(gk	π1(gk	NOUN
ejpam-6611	120	48	)	)	PUNCT
ejpam-6611	120	49	)	)	PUNCT
ejpam-6611	121	1	=	=	SYM
ejpam-6611	121	2	π1(𭟋1	π1(𭟋1	PROPN
ejpam-6611	121	3	(	(	PUNCT
ejpam-6611	121	4	n	n	PRON
ejpam-6611	121	5	⋎	⋎	NOUN
ejpam-6611	121	6	i=1	i=1	PROPN
ejpam-6611	121	7	gk	gk	PROPN
ejpam-6611	121	8	)	)	PUNCT
ejpam-6611	121	9	)	)	PUNCT
ejpam-6611	121	10	and	and	CCONJ
ejpam-6611	121	11	so	so	ADV
ejpam-6611	121	12	�	�	PROPN
ejpam-6611	121	13	̂	̂	VERB
ejpam-6611	121	14	�	�	NOUN
ejpam-6611	121	15	1	1	NUM
ejpam-6611	121	16	(	(	PUNCT
ejpam-6611	121	17	n∗	n∗	X
ejpam-6611	121	18	k=1	k=1	PROPN
ejpam-6611	121	19	π1(gi	π1(gi	PROPN
ejpam-6611	121	20	)	)	PUNCT
ejpam-6611	121	21	)	)	PUNCT
ejpam-6611	122	1	≈	≈	PROPN
ejpam-6611	122	2	π1(g1	π1(g1	PROPN
ejpam-6611	122	3	)	)	PUNCT
ejpam-6611	122	4	∗	∗	NOUN
ejpam-6611	122	5	π1(g2	π1(g2	PROPN
ejpam-6611	122	6	)	)	PUNCT
ejpam-6611	122	7	∗	∗	NOUN
ejpam-6611	122	8	·	·	PUNCT
ejpam-6611	122	9	·	·	PUNCT
ejpam-6611	122	10	·	·	PUNCT
ejpam-6611	123	1	∗	∗	NOUN
ejpam-6611	123	2	π1(𭟋1(gr1	π1(𭟋1(gr1	NOUN
ejpam-6611	123	3	)	)	PUNCT
ejpam-6611	123	4	)	)	PUNCT
ejpam-6611	123	5	∗	∗	NOUN
ejpam-6611	123	6	·	·	PUNCT
ejpam-6611	123	7	·	·	PUNCT
ejpam-6611	123	8	·	·	PUNCT
ejpam-6611	123	9	∗π1(gn	∗π1(gn	NOUN
ejpam-6611	123	10	)	)	PUNCT
ejpam-6611	123	11	.	.	PUNCT
ejpam-6611	124	1	since	since	SCONJ
ejpam-6611	124	2	π1(𭟋1(gr1	π1(𭟋1(gr1	PROPN
ejpam-6611	124	3	)	)	PUNCT
ejpam-6611	124	4	)	)	PUNCT
ejpam-6611	125	1	=	=	SYM
ejpam-6611	125	2	π1(br1−1	π1(br1−1	PROPN
ejpam-6611	125	3	)	)	PUNCT
ejpam-6611	125	4	,	,	PUNCT
ejpam-6611	125	5	it	it	PRON
ejpam-6611	125	6	follows	follow	VERB
ejpam-6611	125	7	that	that	DET
ejpam-6611	125	8	rank	rank	NOUN
ejpam-6611	125	9	(	(	PUNCT
ejpam-6611	125	10	π1(𭟋1(gr1	π1(𭟋1(gr1	NOUN
ejpam-6611	125	11	)	)	PUNCT
ejpam-6611	125	12	)	)	PUNCT
ejpam-6611	125	13	)	)	PUNCT
ejpam-6611	126	1	=	=	X
ejpam-6611	126	2	rank	rank	NOUN
ejpam-6611	126	3	(	(	PUNCT
ejpam-6611	126	4	π1(gr1	π1(gr1	X
ejpam-6611	126	5	)	)	PUNCT
ejpam-6611	126	6	)	)	PUNCT
ejpam-6611	126	7	−	−	PROPN
ejpam-6611	127	1	1	1	X
ejpam-6611	127	2	.	.	PUNCT
ejpam-6611	128	1	hence	hence	ADV
ejpam-6611	128	2	,	,	PUNCT
ejpam-6611	128	3	rank	rank	PROPN
ejpam-6611	128	4	(	(	PUNCT
ejpam-6611	128	5	�	�	PROPN
ejpam-6611	128	6	̂	̂	VERB
ejpam-6611	128	7	�	�	NOUN
ejpam-6611	128	8	1	1	NUM
ejpam-6611	128	9	(	(	PUNCT
ejpam-6611	128	10	n∗	n∗	PROPN
ejpam-6611	128	11	i=1	i=1	PROPN
ejpam-6611	128	12	π1(gi	π1(gi	PROPN
ejpam-6611	128	13	)	)	PUNCT
ejpam-6611	128	14	)	)	PUNCT
ejpam-6611	128	15	)	)	PUNCT
ejpam-6611	129	1	=	=	PUNCT
ejpam-6611	129	2	n−	n−	NOUN
ejpam-6611	129	3	1	1	NUM
ejpam-6611	129	4	.	.	PUNCT
ejpam-6611	130	1	moreover	moreover	ADV
ejpam-6611	130	2	,	,	PUNCT
ejpam-6611	130	3	let	let	VERB
ejpam-6611	130	4	𭟋2	𭟋2	VERB
ejpam-6611	130	5	:	:	PUNCT
ejpam-6611	130	6	n	n	NUM
ejpam-6611	130	7	⋎	⋎	NOUN
ejpam-6611	131	1	k=1	k=1	INTJ
ejpam-6611	131	2	gi	gi	VERB
ejpam-6611	131	3	−→	−→	NOUN
ejpam-6611	131	4	n	n	ADV
ejpam-6611	131	5	⋎	⋎	NOUN
ejpam-6611	132	1	k=1	k=1	AUX
ejpam-6611	132	2	gi	gi	INTJ
ejpam-6611	132	3	be	be	AUX
ejpam-6611	132	4	folding	fold	VERB
ejpam-6611	132	5	such	such	ADJ
ejpam-6611	132	6	that	that	DET
ejpam-6611	132	7	𭟋2	𭟋2	NOUN
ejpam-6611	132	8	(	(	PUNCT
ejpam-6611	132	9	n	n	NUM
ejpam-6611	133	1	⋎	⋎	NOUN
ejpam-6611	133	2	k=1	k=1	X
ejpam-6611	133	3	gk	gk	PROPN
ejpam-6611	133	4	)	)	PUNCT
ejpam-6611	133	5	=	=	SYM
ejpam-6611	133	6	g1⋎g2⋎	g1⋎g2⋎	PROPN
ejpam-6611	133	7	.	.	PUNCT
ejpam-6611	133	8	.	.	PUNCT
ejpam-6611	134	1	.⋎𭟋2(gr1	.⋎𭟋2(gr1	PROPN
ejpam-6611	134	2	)	)	PUNCT
ejpam-6611	135	1	⋎	⋎	NOUN
ejpam-6611	135	2	.	.	PUNCT
ejpam-6611	135	3	.	.	PUNCT
ejpam-6611	136	1	.⋎𭟋2(gr2	.⋎𭟋2(gr2	PUNCT
ejpam-6611	136	2	)	)	PUNCT
ejpam-6611	137	1	⋎	⋎	NOUN
ejpam-6611	137	2	.	.	PUNCT
ejpam-6611	137	3	.	.	PUNCT
ejpam-6611	138	1	.⋎gn	.⋎gn	PROPN
ejpam-6611	139	1	for	for	ADP
ejpam-6611	139	2	r1	r1	NOUN
ejpam-6611	139	3	,	,	PUNCT
ejpam-6611	139	4	r2	r2	PROPN
ejpam-6611	139	5	=	=	SYM
ejpam-6611	139	6	1	1	NUM
ejpam-6611	139	7	,	,	PUNCT
ejpam-6611	139	8	2	2	NUM
ejpam-6611	139	9	,	,	PUNCT
ejpam-6611	139	10	.	.	PUNCT
ejpam-6611	139	11	.	.	PUNCT
ejpam-6611	139	12	.	.	PUNCT
ejpam-6611	140	1	,	,	PUNCT
ejpam-6611	140	2	n	n	CCONJ
ejpam-6611	140	3	,	,	PUNCT
ejpam-6611	140	4	r1	r1	NOUN
ejpam-6611	140	5	≺	≺	NOUN
ejpam-6611	140	6	r2	r2	NOUN
ejpam-6611	140	7	,	,	PUNCT
ejpam-6611	140	8	and	and	CCONJ
ejpam-6611	140	9	𭟋2(gr1	𭟋2(gr1	NOUN
ejpam-6611	140	10	)	)	PUNCT
ejpam-6611	140	11	=	=	SYM
ejpam-6611	140	12	𭟋2(br1	𭟋2(br1	X
ejpam-6611	140	13	)	)	PUNCT
ejpam-6611	140	14	=	=	SYM
ejpam-6611	140	15	br1−1	br1−1	ADJ
ejpam-6611	140	16	,	,	PUNCT
ejpam-6611	140	17	𭟋2(gr2	𭟋2(gr2	NOUN
ejpam-6611	140	18	)	)	PUNCT
ejpam-6611	140	19	=	=	SYM
ejpam-6611	140	20	𭟋2(br2	𭟋2(br2	NOUN
ejpam-6611	140	21	)	)	PUNCT
ejpam-6611	140	22	=	=	NOUN
ejpam-6611	140	23	br2−1	br2−1	NOUN
ejpam-6611	140	24	,	,	PUNCT
ejpam-6611	140	25	then	then	ADV
ejpam-6611	140	26	m.	m.	PROPN
ejpam-6611	140	27	abu	abu	PROPN
ejpam-6611	140	28	-	-	PUNCT
ejpam-6611	140	29	saleem	saleem	PROPN
ejpam-6611	140	30	/	/	SYM
ejpam-6611	140	31	eur	eur	PROPN
ejpam-6611	140	32	.	.	PUNCT
ejpam-6611	141	1	j.	j.	PROPN
ejpam-6611	141	2	pure	pure	PROPN
ejpam-6611	141	3	appl	appl	PROPN
ejpam-6611	141	4	.	.	PROPN
ejpam-6611	141	5	math	math	PROPN
ejpam-6611	141	6	,	,	PUNCT
ejpam-6611	141	7	18	18	NUM
ejpam-6611	141	8	(	(	PUNCT
ejpam-6611	141	9	3	3	NUM
ejpam-6611	141	10	)	)	PUNCT
ejpam-6611	141	11	(	(	PUNCT
ejpam-6611	141	12	2025	2025	NUM
ejpam-6611	141	13	)	)	PUNCT
ejpam-6611	141	14	,	,	PUNCT
ejpam-6611	141	15	6611	6611	NUM
ejpam-6611	141	16	6	6	NUM
ejpam-6611	141	17	of	of	ADP
ejpam-6611	141	18	7	7	NUM
ejpam-6611	141	19	we	we	PRON
ejpam-6611	141	20	get	get	VERB
ejpam-6611	141	21	the	the	DET
ejpam-6611	141	22	induced	induced	ADJ
ejpam-6611	141	23	folding	fold	VERB
ejpam-6611	141	24	�	�	PROPN
ejpam-6611	141	25	̂	̂	NOUN
ejpam-6611	141	26	�	�	NOUN
ejpam-6611	141	27	2	2	NUM
ejpam-6611	141	28	:	:	PUNCT
ejpam-6611	141	29	n∗	n∗	PROPN
ejpam-6611	141	30	k=1	k=1	PUNCT
ejpam-6611	141	31	π1(gk	π1(gk	NUM
ejpam-6611	141	32	)	)	PUNCT
ejpam-6611	141	33	−→	−→	NOUN
ejpam-6611	141	34	n∗	n∗	VERB
ejpam-6611	141	35	k=1	k=1	PUNCT
ejpam-6611	141	36	π1(gk	π1(gk	NOUN
ejpam-6611	141	37	)	)	PUNCT
ejpam-6611	141	38	such	such	ADJ
ejpam-6611	141	39	that	that	DET
ejpam-6611	141	40	rank	rank	NOUN
ejpam-6611	141	41	(	(	PUNCT
ejpam-6611	141	42	�	�	PROPN
ejpam-6611	141	43	̂	̂	VERB
ejpam-6611	141	44	�	�	NOUN
ejpam-6611	141	45	2	2	NUM
ejpam-6611	141	46	(	(	PUNCT
ejpam-6611	141	47	n∗	n∗	NOUN
ejpam-6611	141	48	k=1	k=1	PUNCT
ejpam-6611	141	49	π1(gk	π1(gk	NOUN
ejpam-6611	141	50	)	)	PUNCT
ejpam-6611	141	51	)	)	PUNCT
ejpam-6611	142	1	=	=	PUNCT
ejpam-6611	142	2	n−	n−	NOUN
ejpam-6611	142	3	2	2	X
ejpam-6611	142	4	.	.	PUNCT
ejpam-6611	143	1	we	we	PRON
ejpam-6611	143	2	follow	follow	VERB
ejpam-6611	143	3	this	this	DET
ejpam-6611	143	4	approach	approach	NOUN
ejpam-6611	143	5	,	,	PUNCT
ejpam-6611	143	6	we	we	PRON
ejpam-6611	143	7	have	have	VERB
ejpam-6611	143	8	𭟋n	𭟋n	X
ejpam-6611	143	9	:	:	PUNCT
ejpam-6611	143	10	n	n	CCONJ
ejpam-6611	143	11	⋎	⋎	NOUN
ejpam-6611	143	12	k=1	k=1	INTJ
ejpam-6611	144	1	gk	gk	INTJ
ejpam-6611	144	2	−→	−→	NOUN
ejpam-6611	144	3	n	n	ADV
ejpam-6611	144	4	⋎	⋎	NOUN
ejpam-6611	145	1	k=1	k=1	X
ejpam-6611	145	2	gk	gk	PROPN
ejpam-6611	145	3	such	such	ADJ
ejpam-6611	145	4	that	that	SCONJ
ejpam-6611	145	5	𭟋n	𭟋n	PROPN
ejpam-6611	145	6	(	(	PUNCT
ejpam-6611	145	7	n	n	PRON
ejpam-6611	145	8	⋎	⋎	NOUN
ejpam-6611	145	9	k=1	k=1	X
ejpam-6611	145	10	gk	gk	PROPN
ejpam-6611	145	11	)	)	PUNCT
ejpam-6611	145	12	=	=	SYM
ejpam-6611	145	13	n	n	NUM
ejpam-6611	145	14	⋎	⋎	NOUN
ejpam-6611	145	15	k=1	k=1	X
ejpam-6611	145	16	𭟋n(gk	𭟋n(gk	PROPN
ejpam-6611	145	17	)	)	PUNCT
ejpam-6611	145	18	and	and	CCONJ
ejpam-6611	145	19	𭟋n(gk	𭟋n(gk	PROPN
ejpam-6611	145	20	)	)	PUNCT
ejpam-6611	145	21	=	=	PUNCT
ejpam-6611	145	22	𭟋n(bk	𭟋n(bk	PROPN
ejpam-6611	145	23	)	)	PUNCT
ejpam-6611	145	24	=	=	PUNCT
ejpam-6611	145	25	bk−1	bk−1	ADJ
ejpam-6611	145	26	,	,	PUNCT
ejpam-6611	145	27	∀k	∀k	NOUN
ejpam-6611	145	28	=	=	SYM
ejpam-6611	145	29	1	1	NUM
ejpam-6611	145	30	,	,	PUNCT
ejpam-6611	145	31	2	2	NUM
ejpam-6611	145	32	,	,	PUNCT
ejpam-6611	145	33	.	.	PUNCT
ejpam-6611	145	34	.	.	PUNCT
ejpam-6611	145	35	.	.	PUNCT
ejpam-6611	145	36	,	,	PUNCT
ejpam-6611	145	37	n	n	CCONJ
ejpam-6611	145	38	,	,	PUNCT
ejpam-6611	145	39	which	which	PRON
ejpam-6611	145	40	induces	induce	VERB
ejpam-6611	145	41	a	a	DET
ejpam-6611	145	42	folding	fold	VERB
ejpam-6611	145	43	�	�	NOUN
ejpam-6611	145	44	̂	̂	NOUN
ejpam-6611	145	45	�	�	NOUN
ejpam-6611	145	46	n	n	NUM
ejpam-6611	145	47	:	:	PUNCT
ejpam-6611	145	48	n∗	n∗	PROPN
ejpam-6611	145	49	k=1	k=1	PUNCT
ejpam-6611	145	50	π1(gk	π1(gk	NUM
ejpam-6611	145	51	)	)	PUNCT
ejpam-6611	145	52	−→	−→	NOUN
ejpam-6611	145	53	n∗	n∗	VERB
ejpam-6611	145	54	k=1	k=1	PUNCT
ejpam-6611	145	55	π1(gk	π1(gk	NOUN
ejpam-6611	145	56	)	)	PUNCT
ejpam-6611	145	57	such	such	ADJ
ejpam-6611	145	58	that	that	SCONJ
ejpam-6611	145	59	�	�	PROPN
ejpam-6611	145	60	̂	̂	VERB
ejpam-6611	145	61	�	�	NOUN
ejpam-6611	145	62	n	n	CCONJ
ejpam-6611	145	63	(	(	PUNCT
ejpam-6611	145	64	n∗	n∗	PROPN
ejpam-6611	145	65	k=1	k=1	PUNCT
ejpam-6611	145	66	π1(gk	π1(gk	NOUN
ejpam-6611	145	67	)	)	PUNCT
ejpam-6611	145	68	)	)	PUNCT
ejpam-6611	145	69	is	be	AUX
ejpam-6611	145	70	a	a	DET
ejpam-6611	145	71	free	free	ADJ
ejpam-6611	145	72	group	group	NOUN
ejpam-6611	145	73	of	of	ADP
ejpam-6611	145	74	rank	rank	NOUN
ejpam-6611	145	75	m−	m−	PROPN
ejpam-6611	145	76	n.	n.	PROPN
ejpam-6611	145	77	consequently	consequently	ADV
ejpam-6611	145	78	,	,	PUNCT
ejpam-6611	145	79	rank	rank	PROPN
ejpam-6611	145	80	(	(	PUNCT
ejpam-6611	145	81	�	�	PROPN
ejpam-6611	145	82	̂	̂	NOUN
ejpam-6611	145	83	�	�	NOUN
ejpam-6611	145	84	h	h	NOUN
ejpam-6611	145	85	(	(	PUNCT
ejpam-6611	145	86	n∗	n∗	PROPN
ejpam-6611	145	87	k=1	k=1	PUNCT
ejpam-6611	145	88	π1(gk	π1(gk	NUM
ejpam-6611	145	89	)	)	PUNCT
ejpam-6611	145	90	)	)	PUNCT
ejpam-6611	145	91	)	)	PUNCT
ejpam-6611	146	1	=	=	PRON
ejpam-6611	146	2	m−	m−	PROPN
ejpam-6611	146	3	h	h	NOUN
ejpam-6611	146	4	,	,	PUNCT
ejpam-6611	146	5	for	for	ADP
ejpam-6611	146	6	h	h	NOUN
ejpam-6611	146	7	=	=	SYM
ejpam-6611	146	8	1	1	NUM
ejpam-6611	146	9	,	,	PUNCT
ejpam-6611	146	10	2	2	NUM
ejpam-6611	146	11	,	,	PUNCT
ejpam-6611	146	12	.	.	PUNCT
ejpam-6611	146	13	.	.	PUNCT
ejpam-6611	147	1	.	.	PUNCT
ejpam-6611	148	1	,	,	PUNCT
ejpam-6611	148	2	n.	n.	PROPN
ejpam-6611	148	3	theorem	theorem	VERB
ejpam-6611	148	4	6	6	NUM
ejpam-6611	148	5	.	.	PUNCT
ejpam-6611	148	6	assume	assume	VERB
ejpam-6611	148	7	that	that	SCONJ
ejpam-6611	148	8	g	g	PROPN
ejpam-6611	148	9	is	be	AUX
ejpam-6611	148	10	a	a	DET
ejpam-6611	148	11	graph	graph	NOUN
ejpam-6611	148	12	and	and	CCONJ
ejpam-6611	148	13	h	h	NOUN
ejpam-6611	148	14	is	be	AUX
ejpam-6611	148	15	a	a	DET
ejpam-6611	148	16	subgraph	subgraph	NOUN
ejpam-6611	148	17	of	of	ADP
ejpam-6611	148	18	it	it	PRON
ejpam-6611	148	19	.	.	PUNCT
ejpam-6611	149	1	for	for	ADP
ejpam-6611	149	2	i	i	PRON
ejpam-6611	149	3	=	=	SYM
ejpam-6611	149	4	1	1	NUM
ejpam-6611	149	5	,	,	PUNCT
ejpam-6611	149	6	2	2	NUM
ejpam-6611	149	7	,	,	PUNCT
ejpam-6611	149	8	.	.	PUNCT
ejpam-6611	149	9	.	.	PUNCT
ejpam-6611	149	10	.	.	PUNCT
ejpam-6611	150	1	n	n	CCONJ
ejpam-6611	150	2	,	,	PUNCT
ejpam-6611	150	3	let	let	VERB
ejpam-6611	150	4	𭟋i	𭟋i	NOUN
ejpam-6611	150	5	and	and	CCONJ
ejpam-6611	150	6	ri	ri	PROPN
ejpam-6611	150	7	be	be	AUX
ejpam-6611	150	8	chains	chain	NOUN
ejpam-6611	150	9	of	of	ADP
ejpam-6611	150	10	folding	folding	NOUN
ejpam-6611	150	11	and	and	CCONJ
ejpam-6611	150	12	retraction	retraction	NOUN
ejpam-6611	150	13	functions	function	NOUN
ejpam-6611	150	14	,	,	PUNCT
ejpam-6611	150	15	respectively	respectively	ADV
ejpam-6611	150	16	.	.	PUNCT
ejpam-6611	151	1	then	then	ADV
ejpam-6611	151	2	,	,	PUNCT
ejpam-6611	151	3	there	there	PRON
ejpam-6611	151	4	is	be	VERB
ejpam-6611	151	5	a	a	DET
ejpam-6611	151	6	chain	chain	NOUN
ejpam-6611	151	7	of	of	ADP
ejpam-6611	151	8	a	a	DET
ejpam-6611	151	9	commutative	commutative	ADJ
ejpam-6611	151	10	diagram	diagram	NOUN
ejpam-6611	151	11	of	of	ADP
ejpam-6611	151	12	a	a	DET
ejpam-6611	151	13	graph	graph	NOUN
ejpam-6611	151	14	that	that	PRON
ejpam-6611	151	15	induces	induce	VERB
ejpam-6611	151	16	a	a	DET
ejpam-6611	151	17	chain	chain	NOUN
ejpam-6611	151	18	of	of	ADP
ejpam-6611	151	19	a	a	DET
ejpam-6611	151	20	commutative	commutative	ADJ
ejpam-6611	151	21	diagram	diagram	NOUN
ejpam-6611	151	22	of	of	ADP
ejpam-6611	151	23	fundamental	fundamental	ADJ
ejpam-6611	151	24	groups	group	NOUN
ejpam-6611	151	25	.	.	PUNCT
ejpam-6611	152	1	proof	proof	NOUN
ejpam-6611	152	2	.	.	PUNCT
ejpam-6611	153	1	given	give	VERB
ejpam-6611	153	2	a	a	DET
ejpam-6611	153	3	commutative	commutative	ADJ
ejpam-6611	153	4	diagram	diagram	NOUN
ejpam-6611	153	5	:	:	PUNCT
ejpam-6611	153	6	g	g	PROPN
ejpam-6611	153	7	𭟋1−−−→	𭟋1−−−→	PROPN
ejpam-6611	153	8	g1	g1	PROPN
ejpam-6611	153	9	𭟋2−−−−−→	𭟋2−−−−−→	PROPN
ejpam-6611	153	10	g2	g2	PROPN
ejpam-6611	153	11	−−−	−−−	PUNCT
ejpam-6611	154	1	lim	lim	PROPN
ejpam-6611	154	2	m→∞	m→∞	NUM
ejpam-6611	154	3	𭟋m	𭟋m	NOUN
ejpam-6611	154	4	−−−−−−−−→	−−−−−−−−→	NOUN
ejpam-6611	154	5	only	only	ADV
ejpam-6611	154	6	one	one	NUM
ejpam-6611	154	7	vertex	vertex	NOUN
ejpam-6611	154	8	or	or	CCONJ
ejpam-6611	154	9	one	one	NUM
ejpam-6611	154	10	edge	edge	NOUN
ejpam-6611	154	11	↓	↓	PROPN
ejpam-6611	154	12	r1	r1	PROPN
ejpam-6611	154	13	↓	↓	PROPN
ejpam-6611	154	14	r2	r2	PROPN
ejpam-6611	154	15	↓	↓	PROPN
ejpam-6611	154	16	r3	r3	PROPN
ejpam-6611	154	17	↓	↓	PROPN
ejpam-6611	154	18	lim	lim	PROPN
ejpam-6611	154	19	m→∞	m→∞	PROPN
ejpam-6611	154	20	rm	rm	PROPN
ejpam-6611	154	21	h	h	PROPN
ejpam-6611	154	22	𭟋1−−−−−→	𭟋1−−−−−→	PROPN
ejpam-6611	154	23	h	h	PROPN
ejpam-6611	154	24	1	1	NUM
ejpam-6611	154	25	𭟋2−−−−→	𭟋2−−−−→	PROPN
ejpam-6611	154	26	h2	h2	PROPN
ejpam-6611	154	27	−−−	−−−	PUNCT
ejpam-6611	155	1	lim	lim	PROPN
ejpam-6611	155	2	m→∞	m→∞	NUM
ejpam-6611	155	3	𭟋m	𭟋m	ADP
ejpam-6611	155	4	−−−−−−−−−→	−−−−−−−−−→	NOUN
ejpam-6611	155	5	only	only	ADV
ejpam-6611	155	6	one	one	NUM
ejpam-6611	155	7	vertex	vertex	NOUN
ejpam-6611	155	8	or	or	CCONJ
ejpam-6611	155	9	one	one	NUM
ejpam-6611	155	10	edge	edge	NOUN
ejpam-6611	155	11	.	.	PUNCT
ejpam-6611	156	1	as	as	SCONJ
ejpam-6611	156	2	the	the	DET
ejpam-6611	156	3	fundamental	fundamental	ADJ
ejpam-6611	156	4	group	group	NOUN
ejpam-6611	156	5	constitutes	constitute	VERB
ejpam-6611	156	6	a	a	DET
ejpam-6611	156	7	functor	functor	NOUN
ejpam-6611	156	8	,	,	PUNCT
ejpam-6611	156	9	we	we	PRON
ejpam-6611	156	10	get	get	VERB
ejpam-6611	156	11	the	the	DET
ejpam-6611	156	12	following	follow	VERB
ejpam-6611	156	13	chain	chain	NOUN
ejpam-6611	156	14	of	of	ADP
ejpam-6611	156	15	a	a	DET
ejpam-6611	156	16	commutative	commutative	ADJ
ejpam-6611	156	17	diagram	diagram	NOUN
ejpam-6611	156	18	of	of	ADP
ejpam-6611	156	19	fundamental	fundamental	ADJ
ejpam-6611	156	20	groups	group	NOUN
ejpam-6611	156	21	:	:	PUNCT
ejpam-6611	156	22	π1	π1	NOUN
ejpam-6611	156	23	(	(	PUNCT
ejpam-6611	156	24	g	g	NOUN
ejpam-6611	156	25	)	)	PUNCT
ejpam-6611	156	26	�	�	PROPN
ejpam-6611	156	27	̂	̂	SYM
ejpam-6611	156	28	�	�	PROPN
ejpam-6611	156	29	1−−−−−→	1−−−−−→	NUM
ejpam-6611	156	30	π1	π1	NOUN
ejpam-6611	156	31	(	(	PUNCT
ejpam-6611	156	32	g1	g1	PROPN
ejpam-6611	156	33	)	)	PUNCT
ejpam-6611	156	34	�	�	PROPN
ejpam-6611	156	35	̂	̂	SYM
ejpam-6611	156	36	�	�	NOUN
ejpam-6611	156	37	1−−−−−−→	1−−−−−−→	NUM
ejpam-6611	156	38	π1	π1	NOUN
ejpam-6611	156	39	(	(	PUNCT
ejpam-6611	156	40	g2	g2	PROPN
ejpam-6611	156	41	)	)	PUNCT
ejpam-6611	156	42	−−−	−−−	PROPN
ejpam-6611	157	1	lim	lim	PROPN
ejpam-6611	157	2	m→∞	m→∞	NUM
ejpam-6611	157	3	�	�	PROPN
ejpam-6611	157	4	̂	̂	NOUN
ejpam-6611	157	5	�	�	NOUN
ejpam-6611	157	6	m	m	NOUN
ejpam-6611	157	7	−−−−−−−−→	−−−−−−−−→	NOUN
ejpam-6611	157	8	{	{	PUNCT
ejpam-6611	157	9	0	0	NUM
ejpam-6611	157	10	}	}	PUNCT
ejpam-6611	157	11	↓	↓	NOUN
ejpam-6611	157	12	r̂1	r̂1	PROPN
ejpam-6611	157	13	↓	↓	PROPN
ejpam-6611	157	14	r̂2	r̂2	PROPN
ejpam-6611	157	15	↓	↓	PROPN
ejpam-6611	158	1	r̂3	r̂3	PROPN
ejpam-6611	158	2	↓	↓	PROPN
ejpam-6611	158	3	lim	lim	PROPN
ejpam-6611	158	4	m→∞	m→∞	NOUN
ejpam-6611	158	5	r̂m	r̂m	PROPN
ejpam-6611	158	6	π1	π1	NOUN
ejpam-6611	158	7	(	(	PUNCT
ejpam-6611	158	8	h	h	NOUN
ejpam-6611	158	9	)	)	PUNCT
ejpam-6611	158	10	�	�	PROPN
ejpam-6611	158	11	̂	̂	SYM
ejpam-6611	158	12	�	�	PROPN
ejpam-6611	158	13	1−−−−−→	1−−−−−→	NUM
ejpam-6611	158	14	π1	π1	NOUN
ejpam-6611	158	15	(	(	PUNCT
ejpam-6611	158	16	h1	h1	PROPN
ejpam-6611	158	17	)	)	PUNCT
ejpam-6611	158	18	�	�	PROPN
ejpam-6611	158	19	̂	̂	SYM
ejpam-6611	158	20	�	�	NOUN
ejpam-6611	158	21	2−−−−−−→	2−−−−−−→	NUM
ejpam-6611	158	22	π1	π1	NOUN
ejpam-6611	158	23	(	(	PUNCT
ejpam-6611	158	24	h2	h2	NOUN
ejpam-6611	158	25	)	)	PUNCT
ejpam-6611	158	26	−−−	−−−	NOUN
ejpam-6611	159	1	lim	lim	PROPN
ejpam-6611	159	2	m→∞	m→∞	NUM
ejpam-6611	159	3	�	�	PROPN
ejpam-6611	159	4	̂	̂	NOUN
ejpam-6611	159	5	�	�	NOUN
ejpam-6611	159	6	m	m	NOUN
ejpam-6611	159	7	−−−−−−−−→	−−−−−−−−→	NOUN
ejpam-6611	159	8	{	{	PUNCT
ejpam-6611	159	9	0	0	NUM
ejpam-6611	159	10	}	}	PUNCT
ejpam-6611	159	11	.	.	PUNCT
ejpam-6611	160	1	3	3	X
ejpam-6611	160	2	.	.	X
ejpam-6611	160	3	conclusion	conclusion	NOUN
ejpam-6611	160	4	in	in	ADP
ejpam-6611	160	5	topological	topological	ADJ
ejpam-6611	160	6	graph	graph	NOUN
ejpam-6611	160	7	theory	theory	NOUN
ejpam-6611	160	8	,	,	PUNCT
ejpam-6611	160	9	the	the	DET
ejpam-6611	160	10	effect	effect	NOUN
ejpam-6611	160	11	of	of	ADP
ejpam-6611	160	12	folding	fold	VERB
ejpam-6611	160	13	on	on	ADP
ejpam-6611	160	14	special	special	ADJ
ejpam-6611	160	15	types	type	NOUN
ejpam-6611	160	16	of	of	ADP
ejpam-6611	160	17	graphs	graph	NOUN
ejpam-6611	160	18	and	and	CCONJ
ejpam-6611	160	19	their	their	PRON
ejpam-6611	160	20	duals	dual	NOUN
ejpam-6611	160	21	is	be	AUX
ejpam-6611	160	22	introduced	introduce	VERB
ejpam-6611	160	23	.	.	PUNCT
ejpam-6611	161	1	also	also	ADV
ejpam-6611	161	2	,	,	PUNCT
ejpam-6611	161	3	the	the	DET
ejpam-6611	161	4	folding	folding	NOUN
ejpam-6611	161	5	induced	induce	VERB
ejpam-6611	161	6	by	by	ADP
ejpam-6611	161	7	the	the	DET
ejpam-6611	161	8	fundamental	fundamental	ADJ
ejpam-6611	161	9	groups	group	NOUN
ejpam-6611	161	10	is	be	AUX
ejpam-6611	161	11	obtained	obtain	VERB
ejpam-6611	161	12	.	.	PUNCT
ejpam-6611	162	1	the	the	DET
ejpam-6611	162	2	limits	limit	NOUN
ejpam-6611	162	3	of	of	ADP
ejpam-6611	162	4	folding	fold	VERB
ejpam-6611	162	5	on	on	ADP
ejpam-6611	162	6	the	the	DET
ejpam-6611	162	7	induced	induced	ADJ
ejpam-6611	162	8	fundamental	fundamental	ADJ
ejpam-6611	162	9	group	group	NOUN
ejpam-6611	162	10	are	be	AUX
ejpam-6611	162	11	presented	present	VERB
ejpam-6611	162	12	.	.	PUNCT
ejpam-6611	163	1	the	the	DET
ejpam-6611	163	2	relations	relation	NOUN
ejpam-6611	163	3	between	between	ADP
ejpam-6611	163	4	the	the	DET
ejpam-6611	163	5	induced	induced	ADJ
ejpam-6611	163	6	folding	folding	NOUN
ejpam-6611	163	7	and	and	CCONJ
ejpam-6611	163	8	the	the	DET
ejpam-6611	163	9	induced	induced	ADJ
ejpam-6611	163	10	retraction	retraction	NOUN
ejpam-6611	163	11	on	on	ADP
ejpam-6611	163	12	the	the	DET
ejpam-6611	163	13	fundamental	fundamental	ADJ
ejpam-6611	163	14	group	group	NOUN
ejpam-6611	163	15	are	be	AUX
ejpam-6611	163	16	deduced	deduce	VERB
ejpam-6611	163	17	.	.	PUNCT
ejpam-6611	164	1	references	reference	NOUN
ejpam-6611	164	2	[	[	X
ejpam-6611	164	3	1	1	NUM
ejpam-6611	164	4	]	]	PUNCT
ejpam-6611	164	5	r.	r.	PROPN
ejpam-6611	164	6	balakrishnan	balakrishnan	PROPN
ejpam-6611	164	7	and	and	CCONJ
ejpam-6611	164	8	k.	k.	PROPN
ejpam-6611	164	9	ranganathan	ranganathan	PROPN
ejpam-6611	164	10	.	.	PUNCT
ejpam-6611	165	1	a	a	DET
ejpam-6611	165	2	textbook	textbook	NOUN
ejpam-6611	165	3	of	of	ADP
ejpam-6611	165	4	graph	graph	NOUN
ejpam-6611	165	5	theory	theory	NOUN
ejpam-6611	165	6	.	.	PUNCT
ejpam-6611	166	1	springer	springer	NOUN
ejpam-6611	166	2	,	,	PUNCT
ejpam-6611	166	3	new	new	PROPN
ejpam-6611	166	4	york	york	PROPN
ejpam-6611	166	5	,	,	PUNCT
ejpam-6611	166	6	heidelberg	heidelberg	PROPN
ejpam-6611	166	7	,	,	PUNCT
ejpam-6611	166	8	dordrecht	dordrecht	PROPN
ejpam-6611	166	9	,	,	PUNCT
ejpam-6611	166	10	london	london	PROPN
ejpam-6611	166	11	,	,	PUNCT
ejpam-6611	166	12	2012	2012	NUM
ejpam-6611	166	13	.	.	PUNCT
ejpam-6611	167	1	[	[	X
ejpam-6611	167	2	2	2	X
ejpam-6611	167	3	]	]	PUNCT
ejpam-6611	167	4	l.	l.	PROPN
ejpam-6611	167	5	w.	w.	PROPN
ejpam-6611	167	6	beineke	beineke	PROPN
ejpam-6611	167	7	,	,	PUNCT
ejpam-6611	167	8	r.	r.	PROPN
ejpam-6611	167	9	j.	j.	PROPN
ejpam-6611	167	10	wilson	wilson	PROPN
ejpam-6611	167	11	,	,	PUNCT
ejpam-6611	167	12	j.	j.	PROPN
ejpam-6611	167	13	l.	l.	PROPN
ejpam-6611	167	14	gross	gross	PROPN
ejpam-6611	167	15	,	,	PUNCT
ejpam-6611	167	16	and	and	CCONJ
ejpam-6611	167	17	t.	t.	PROPN
ejpam-6611	167	18	w.	w.	PROPN
ejpam-6611	167	19	tucker	tucker	PROPN
ejpam-6611	167	20	.	.	PUNCT
ejpam-6611	168	1	topics	topic	NOUN
ejpam-6611	168	2	in	in	ADP
ejpam-6611	168	3	topological	topological	ADJ
ejpam-6611	168	4	graph	graph	NOUN
ejpam-6611	168	5	theory	theory	NOUN
ejpam-6611	168	6	.	.	PUNCT
ejpam-6611	169	1	cambridge	cambridge	PROPN
ejpam-6611	169	2	university	university	PROPN
ejpam-6611	169	3	press	press	PROPN
ejpam-6611	169	4	,	,	PUNCT
ejpam-6611	169	5	new	new	PROPN
ejpam-6611	169	6	york	york	PROPN
ejpam-6611	169	7	,	,	PUNCT
ejpam-6611	169	8	2009	2009	NUM
ejpam-6611	169	9	.	.	PUNCT
ejpam-6611	170	1	[	[	X
ejpam-6611	170	2	3	3	X
ejpam-6611	170	3	]	]	X
ejpam-6611	170	4	j.	j.	PROPN
ejpam-6611	170	5	l.	l.	PROPN
ejpam-6611	170	6	gross	gross	PROPN
ejpam-6611	170	7	and	and	CCONJ
ejpam-6611	170	8	t.	t.	PROPN
ejpam-6611	170	9	w.	w.	PROPN
ejpam-6611	170	10	tucker	tucker	PROPN
ejpam-6611	170	11	.	.	PUNCT
ejpam-6611	171	1	topological	topological	ADJ
ejpam-6611	171	2	graph	graph	NOUN
ejpam-6611	171	3	theory	theory	NOUN
ejpam-6611	171	4	.	.	PUNCT
ejpam-6611	172	1	courier	courier	NOUN
ejpam-6611	172	2	corporation	corporation	NOUN
ejpam-6611	172	3	,	,	PUNCT
ejpam-6611	172	4	2001	2001	NUM
ejpam-6611	172	5	.	.	PUNCT
ejpam-6611	173	1	[	[	X
ejpam-6611	173	2	4	4	NUM
ejpam-6611	173	3	]	]	PUNCT
ejpam-6611	173	4	a.	a.	NOUN
ejpam-6611	173	5	t.	t.	PROPN
ejpam-6611	173	6	white	white	PROPN
ejpam-6611	173	7	.	.	PUNCT
ejpam-6611	173	8	graphs	graph	NOUN
ejpam-6611	173	9	,	,	PUNCT
ejpam-6611	173	10	groups	group	NOUN
ejpam-6611	173	11	and	and	CCONJ
ejpam-6611	173	12	surfaces	surface	NOUN
ejpam-6611	173	13	,	,	PUNCT
ejpam-6611	173	14	volume	volume	NOUN
ejpam-6611	173	15	8	8	NUM
ejpam-6611	173	16	.	.	PUNCT
ejpam-6611	174	1	elsevier	elsevier	NOUN
ejpam-6611	174	2	,	,	PUNCT
ejpam-6611	174	3	1985	1985	NUM
ejpam-6611	174	4	.	.	PUNCT
ejpam-6611	175	1	m.	m.	NOUN
ejpam-6611	175	2	abu	abu	PROPN
ejpam-6611	175	3	-	-	PUNCT
ejpam-6611	175	4	saleem	saleem	PROPN
ejpam-6611	175	5	/	/	SYM
ejpam-6611	175	6	eur	eur	PROPN
ejpam-6611	175	7	.	.	PUNCT
ejpam-6611	176	1	j.	j.	PROPN
ejpam-6611	176	2	pure	pure	PROPN
ejpam-6611	176	3	appl	appl	PROPN
ejpam-6611	176	4	.	.	PROPN
ejpam-6611	176	5	math	math	PROPN
ejpam-6611	176	6	,	,	PUNCT
ejpam-6611	176	7	18	18	NUM
ejpam-6611	176	8	(	(	PUNCT
ejpam-6611	176	9	3	3	NUM
ejpam-6611	176	10	)	)	PUNCT
ejpam-6611	176	11	(	(	PUNCT
ejpam-6611	176	12	2025	2025	NUM
ejpam-6611	176	13	)	)	PUNCT
ejpam-6611	176	14	,	,	PUNCT
ejpam-6611	176	15	6611	6611	NUM
ejpam-6611	176	16	7	7	NUM
ejpam-6611	176	17	of	of	ADP
ejpam-6611	176	18	7	7	NUM
ejpam-6611	176	19	[	[	SYM
ejpam-6611	176	20	5	5	NUM
ejpam-6611	176	21	]	]	PUNCT
ejpam-6611	176	22	r.	r.	PROPN
ejpam-6611	176	23	j.	j.	PROPN
ejpam-6611	176	24	wilson	wilson	PROPN
ejpam-6611	176	25	and	and	CCONJ
ejpam-6611	176	26	j.	j.	PROPN
ejpam-6611	176	27	j.	j.	PROPN
ejpam-6611	176	28	watkins	watkins	PROPN
ejpam-6611	176	29	.	.	PUNCT
ejpam-6611	177	1	graphs	graph	NOUN
ejpam-6611	177	2	:	:	PUNCT
ejpam-6611	177	3	an	an	DET
ejpam-6611	177	4	introductory	introductory	ADJ
ejpam-6611	177	5	approach	approach	NOUN
ejpam-6611	177	6	.	.	PUNCT
ejpam-6611	178	1	a	a	DET
ejpam-6611	178	2	first	first	ADJ
ejpam-6611	178	3	course	course	NOUN
ejpam-6611	178	4	in	in	ADP
ejpam-6611	178	5	discrete	discrete	ADJ
ejpam-6611	178	6	mathematics	mathematic	NOUN
ejpam-6611	178	7	.	.	PUNCT
ejpam-6611	179	1	john	john	PROPN
ejpam-6611	179	2	wiley	wiley	PROPN
ejpam-6611	179	3	&	&	CCONJ
ejpam-6611	179	4	sons	sons	PROPN
ejpam-6611	179	5	,	,	PUNCT
ejpam-6611	179	6	inc	inc	PROPN
ejpam-6611	179	7	.	.	PROPN
ejpam-6611	179	8	,	,	PUNCT
ejpam-6611	179	9	canada	canada	PROPN
ejpam-6611	179	10	,	,	PUNCT
ejpam-6611	179	11	1990	1990	NUM
ejpam-6611	179	12	.	.	PUNCT
ejpam-6611	180	1	[	[	X
ejpam-6611	180	2	6	6	NUM
ejpam-6611	180	3	]	]	PUNCT
ejpam-6611	180	4	g.	g.	PROPN
ejpam-6611	180	5	chartrand	chartrand	PROPN
ejpam-6611	180	6	and	and	CCONJ
ejpam-6611	180	7	p.	p.	PROPN
ejpam-6611	180	8	zhang	zhang	PROPN
ejpam-6611	180	9	.	.	PUNCT
ejpam-6611	181	1	a	a	DET
ejpam-6611	181	2	first	first	ADJ
ejpam-6611	181	3	course	course	NOUN
ejpam-6611	181	4	in	in	ADP
ejpam-6611	181	5	graph	graph	NOUN
ejpam-6611	181	6	theory	theory	NOUN
ejpam-6611	181	7	.	.	PUNCT
ejpam-6611	182	1	dover	dover	PROPN
ejpam-6611	182	2	publications	publication	NOUN
ejpam-6611	182	3	,	,	PUNCT
ejpam-6611	182	4	new	new	PROPN
ejpam-6611	182	5	york	york	PROPN
ejpam-6611	182	6	,	,	PUNCT
ejpam-6611	182	7	2012	2012	NUM
ejpam-6611	182	8	.	.	PUNCT
ejpam-6611	183	1	[	[	X
ejpam-6611	183	2	7	7	X
ejpam-6611	183	3	]	]	PUNCT
ejpam-6611	183	4	j.	j.	PROPN
ejpam-6611	183	5	a.	a.	PROPN
ejpam-6611	183	6	bondy	bondy	PROPN
ejpam-6611	183	7	and	and	CCONJ
ejpam-6611	183	8	u.	u.	PROPN
ejpam-6611	183	9	s.	s.	PROPN
ejpam-6611	183	10	r.	r.	PROPN
ejpam-6611	183	11	murty	murty	PROPN
ejpam-6611	183	12	.	.	PUNCT
ejpam-6611	184	1	graph	graph	NOUN
ejpam-6611	184	2	theory	theory	NOUN
ejpam-6611	184	3	.	.	PUNCT
ejpam-6611	185	1	springer	springer	NOUN
ejpam-6611	185	2	,	,	PUNCT
ejpam-6611	185	3	2008	2008	NUM
ejpam-6611	185	4	.	.	PUNCT
ejpam-6611	186	1	[	[	X
ejpam-6611	186	2	8	8	NUM
ejpam-6611	186	3	]	]	PUNCT
ejpam-6611	186	4	a.	a.	NOUN
ejpam-6611	186	5	hatcher	hatcher	PROPN
ejpam-6611	186	6	.	.	PUNCT
ejpam-6611	187	1	algebraic	algebraic	ADJ
ejpam-6611	187	2	topology	topology	PROPN
ejpam-6611	187	3	.	.	PUNCT
ejpam-6611	188	1	cambridge	cambridge	PROPN
ejpam-6611	188	2	university	university	PROPN
ejpam-6611	188	3	press	press	PROPN
ejpam-6611	188	4	,	,	PUNCT
ejpam-6611	188	5	cambridge	cambridge	PROPN
ejpam-6611	188	6	,	,	PUNCT
ejpam-6611	188	7	2002	2002	NUM
ejpam-6611	188	8	.	.	PUNCT
ejpam-6611	189	1	[	[	X
ejpam-6611	189	2	9	9	NUM
ejpam-6611	189	3	]	]	PUNCT
ejpam-6611	189	4	w.	w.	PROPN
ejpam-6611	189	5	s.	s.	PROPN
ejpam-6611	189	6	massey	massey	PROPN
ejpam-6611	189	7	.	.	PUNCT
ejpam-6611	190	1	algebraic	algebraic	ADJ
ejpam-6611	190	2	topology	topology	NOUN
ejpam-6611	190	3	:	:	PUNCT
ejpam-6611	190	4	an	an	DET
ejpam-6611	190	5	introduction	introduction	NOUN
ejpam-6611	190	6	.	.	PUNCT
ejpam-6611	191	1	harcourt	harcourt	PROPN
ejpam-6611	191	2	brace	brace	PROPN
ejpam-6611	191	3	and	and	CCONJ
ejpam-6611	191	4	world	world	NOUN
ejpam-6611	191	5	,	,	PUNCT
ejpam-6611	191	6	new	new	PROPN
ejpam-6611	191	7	york	york	PROPN
ejpam-6611	191	8	,	,	PUNCT
ejpam-6611	191	9	1967	1967	NUM
ejpam-6611	191	10	.	.	PUNCT
ejpam-6611	192	1	[	[	X
ejpam-6611	192	2	10	10	NUM
ejpam-6611	192	3	]	]	X
ejpam-6611	192	4	j.	j.	PROPN
ejpam-6611	192	5	brazas	brazas	PROPN
ejpam-6611	192	6	.	.	PUNCT
ejpam-6611	193	1	the	the	DET
ejpam-6611	193	2	fundamental	fundamental	ADJ
ejpam-6611	193	3	group	group	NOUN
ejpam-6611	193	4	as	as	ADP
ejpam-6611	193	5	a	a	DET
ejpam-6611	193	6	topological	topological	ADJ
ejpam-6611	193	7	group	group	NOUN
ejpam-6611	193	8	.	.	PUNCT
ejpam-6611	194	1	topology	topology	NOUN
ejpam-6611	194	2	and	and	CCONJ
ejpam-6611	194	3	its	its	PRON
ejpam-6611	194	4	applications	application	NOUN
ejpam-6611	194	5	,	,	PUNCT
ejpam-6611	194	6	160:70–188	160:70–188	NUM
ejpam-6611	194	7	,	,	PUNCT
ejpam-6611	194	8	2013	2013	NUM
ejpam-6611	194	9	.	.	PUNCT
ejpam-6611	195	1	[	[	X
ejpam-6611	195	2	11	11	NUM
ejpam-6611	195	3	]	]	X
ejpam-6611	195	4	o.	o.	PROPN
ejpam-6611	195	5	neto	neto	PROPN
ejpam-6611	195	6	and	and	CCONJ
ejpam-6611	195	7	p.	p.	PROPN
ejpam-6611	195	8	c.	c.	PROPN
ejpam-6611	195	9	silva	silva	PROPN
ejpam-6611	195	10	.	.	PUNCT
ejpam-6611	196	1	the	the	DET
ejpam-6611	196	2	fundamental	fundamental	ADJ
ejpam-6611	196	3	group	group	NOUN
ejpam-6611	196	4	of	of	ADP
ejpam-6611	196	5	an	an	DET
ejpam-6611	196	6	algebraic	algebraic	ADJ
ejpam-6611	196	7	link	link	NOUN
ejpam-6611	196	8	.	.	PUNCT
ejpam-6611	197	1	comptes	compte	VERB
ejpam-6611	197	2	rendus	rendus	PROPN
ejpam-6611	197	3	mathematique	mathematique	PROPN
ejpam-6611	197	4	,	,	PUNCT
ejpam-6611	197	5	340(2):141–146	340(2):141–146	NUM
ejpam-6611	197	6	,	,	PUNCT
ejpam-6611	197	7	2005	2005	NUM
ejpam-6611	197	8	.	.	PUNCT
ejpam-6611	198	1	[	[	X
ejpam-6611	198	2	12	12	NUM
ejpam-6611	198	3	]	]	PUNCT
ejpam-6611	198	4	p.	p.	NOUN
ejpam-6611	198	5	hell	hell	PROPN
ejpam-6611	198	6	and	and	CCONJ
ejpam-6611	198	7	j.	j.	PROPN
ejpam-6611	198	8	nešetřil	nešetřil	PROPN
ejpam-6611	198	9	.	.	PUNCT
ejpam-6611	199	1	graphs	graph	NOUN
ejpam-6611	199	2	and	and	CCONJ
ejpam-6611	199	3	homomorphisms	homomorphism	NOUN
ejpam-6611	199	4	,	,	PUNCT
ejpam-6611	199	5	volume	volume	NOUN
ejpam-6611	199	6	28	28	NUM
ejpam-6611	199	7	of	of	ADP
ejpam-6611	199	8	oxford	oxford	PROPN
ejpam-6611	199	9	lecture	lecture	NOUN
ejpam-6611	199	10	series	series	NOUN
ejpam-6611	199	11	in	in	ADP
ejpam-6611	199	12	mathematics	mathematics	PROPN
ejpam-6611	199	13	and	and	CCONJ
ejpam-6611	199	14	its	its	PRON
ejpam-6611	199	15	applications	application	NOUN
ejpam-6611	199	16	.	.	PUNCT
ejpam-6611	200	1	oxford	oxford	PROPN
ejpam-6611	200	2	university	university	PROPN
ejpam-6611	200	3	press	press	NOUN
ejpam-6611	200	4	,	,	PUNCT
ejpam-6611	200	5	2004	2004	NUM
ejpam-6611	200	6	.	.	PUNCT
ejpam-6611	201	1	[	[	X
ejpam-6611	201	2	13	13	NUM
ejpam-6611	201	3	]	]	PUNCT
ejpam-6611	201	4	s.	s.	PROPN
ejpam-6611	201	5	i.	i.	PROPN
ejpam-6611	201	6	nada	nada	PROPN
ejpam-6611	201	7	and	and	CCONJ
ejpam-6611	201	8	e.	e.	PROPN
ejpam-6611	201	9	hamouda	hamouda	PROPN
ejpam-6611	201	10	.	.	PUNCT
ejpam-6611	202	1	on	on	ADP
ejpam-6611	202	2	the	the	DET
ejpam-6611	202	3	folding	folding	NOUN
ejpam-6611	202	4	of	of	ADP
ejpam-6611	202	5	graphs	graph	NOUN
ejpam-6611	202	6	-	-	PUNCT
ejpam-6611	202	7	theory	theory	NOUN
ejpam-6611	202	8	and	and	CCONJ
ejpam-6611	202	9	application	application	NOUN
ejpam-6611	202	10	.	.	PUNCT
ejpam-6611	203	1	chaos	chaos	NOUN
ejpam-6611	203	2	,	,	PUNCT
ejpam-6611	203	3	solitons	soliton	NOUN
ejpam-6611	203	4	&	&	CCONJ
ejpam-6611	203	5	fractals	fractal	NOUN
ejpam-6611	203	6	,	,	PUNCT
ejpam-6611	203	7	42(2):669–675	42(2):669–675	NOUN
ejpam-6611	203	8	,	,	PUNCT
ejpam-6611	203	9	2009	2009	NUM
ejpam-6611	203	10	.	.	PUNCT
ejpam-6611	204	1	[	[	X
ejpam-6611	204	2	14	14	NUM
ejpam-6611	204	3	]	]	X
ejpam-6611	204	4	f.	f.	PROPN
ejpam-6611	204	5	dayan	dayan	PROPN
ejpam-6611	204	6	,	,	PUNCT
ejpam-6611	204	7	m.	m.	PROPN
ejpam-6611	204	8	javaid	javaid	PROPN
ejpam-6611	204	9	,	,	PUNCT
ejpam-6611	204	10	m.	m.	NOUN
ejpam-6611	204	11	zulqarnain	zulqarnain	PROPN
ejpam-6611	204	12	,	,	PUNCT
ejpam-6611	204	13	m.	m.	NOUN
ejpam-6611	204	14	t.	t.	PROPN
ejpam-6611	204	15	ali	ali	PROPN
ejpam-6611	204	16	,	,	PUNCT
ejpam-6611	204	17	and	and	CCONJ
ejpam-6611	204	18	b.	b.	PROPN
ejpam-6611	204	19	ahmad	ahmad	PROPN
ejpam-6611	204	20	.	.	PUNCT
ejpam-6611	205	1	computing	compute	VERB
ejpam-6611	205	2	banhatti	banhatti	ADJ
ejpam-6611	205	3	indices	index	NOUN
ejpam-6611	205	4	of	of	ADP
ejpam-6611	205	5	hexagonal	hexagonal	ADJ
ejpam-6611	205	6	,	,	PUNCT
ejpam-6611	205	7	honeycomb	honeycomb	NOUN
ejpam-6611	205	8	and	and	CCONJ
ejpam-6611	205	9	derived	derive	VERB
ejpam-6611	205	10	networks	network	NOUN
ejpam-6611	205	11	.	.	PUNCT
ejpam-6611	206	1	american	american	PROPN
ejpam-6611	206	2	journal	journal	PROPN
ejpam-6611	206	3	of	of	ADP
ejpam-6611	206	4	mathematical	mathematical	ADJ
ejpam-6611	206	5	and	and	CCONJ
ejpam-6611	206	6	computer	computer	NOUN
ejpam-6611	206	7	modelling	modelling	NOUN
ejpam-6611	206	8	,	,	PUNCT
ejpam-6611	206	9	3(2):38–45	3(2):38–45	NUM
ejpam-6611	206	10	,	,	PUNCT
ejpam-6611	206	11	2018	2018	NUM
ejpam-6611	206	12	.	.	PUNCT
ejpam-6611	207	1	[	[	X
ejpam-6611	207	2	15	15	NUM
ejpam-6611	207	3	]	]	X
ejpam-6611	207	4	r.	r.	PROPN
ejpam-6611	207	5	m.	m.	PROPN
ejpam-6611	207	6	zulqarnain	zulqarnain	PROPN
ejpam-6611	207	7	,	,	PUNCT
ejpam-6611	207	8	x.	x.	PROPN
ejpam-6611	207	9	l.	l.	PROPN
ejpam-6611	207	10	xin	xin	PROPN
ejpam-6611	207	11	,	,	PUNCT
ejpam-6611	207	12	and	and	CCONJ
ejpam-6611	208	1	y.	y.	PROPN
ejpam-6611	208	2	b.	b.	PROPN
ejpam-6611	208	3	jun	jun	PROPN
ejpam-6611	208	4	.	.	PROPN
ejpam-6611	208	5	fuzzy	fuzzy	ADJ
ejpam-6611	208	6	axiom	axiom	NOUN
ejpam-6611	208	7	of	of	ADP
ejpam-6611	208	8	choice	choice	NOUN
ejpam-6611	208	9	,	,	PUNCT
ejpam-6611	208	10	fuzzy	fuzzy	ADJ
ejpam-6611	208	11	zorn	zorn	PROPN
ejpam-6611	208	12	’s	’s	PART
ejpam-6611	208	13	lemma	lemma	PROPN
ejpam-6611	208	14	and	and	CCONJ
ejpam-6611	208	15	fuzzy	fuzzy	ADJ
ejpam-6611	208	16	hausdorff	hausdorff	NOUN
ejpam-6611	208	17	maximal	maximal	ADJ
ejpam-6611	208	18	principle	principle	NOUN
ejpam-6611	208	19	.	.	PUNCT
ejpam-6611	209	1	soft	soft	ADJ
ejpam-6611	209	2	computing	computing	NOUN
ejpam-6611	209	3	,	,	PUNCT
ejpam-6611	209	4	25(25):11421–11428	25(25):11421–11428	NUM
ejpam-6611	209	5	,	,	PUNCT
ejpam-6611	209	6	2021	2021	NUM
ejpam-6611	209	7	.	.	PUNCT
ejpam-6611	210	1	[	[	X
ejpam-6611	210	2	16	16	NUM
ejpam-6611	210	3	]	]	PUNCT
ejpam-6611	210	4	m.	m.	NOUN
ejpam-6611	210	5	abu	abu	PROPN
ejpam-6611	210	6	-	-	PUNCT
ejpam-6611	210	7	saleem	saleem	PROPN
ejpam-6611	210	8	.	.	PUNCT
ejpam-6611	211	1	the	the	DET
ejpam-6611	211	2	folded	fold	VERB
ejpam-6611	211	3	map	map	NOUN
ejpam-6611	211	4	on	on	ADP
ejpam-6611	211	5	an	an	DET
ejpam-6611	211	6	identification	identification	NOUN
ejpam-6611	211	7	graph	graph	NOUN
ejpam-6611	211	8	and	and	CCONJ
ejpam-6611	211	9	its	its	PRON
ejpam-6611	211	10	application	application	NOUN
ejpam-6611	211	11	.	.	PUNCT
ejpam-6611	212	1	afrika	afrika	PROPN
ejpam-6611	212	2	matematika	matematika	PROPN
ejpam-6611	212	3	,	,	PUNCT
ejpam-6611	212	4	36(1):23	36(1):23	NUM
ejpam-6611	212	5	,	,	PUNCT
ejpam-6611	212	6	2025	2025	NUM
ejpam-6611	212	7	.	.	PUNCT
ejpam-6611	213	1	[	[	X
ejpam-6611	213	2	17	17	NUM
ejpam-6611	213	3	]	]	PUNCT
ejpam-6611	213	4	m.	m.	NOUN
ejpam-6611	213	5	abu	abu	PROPN
ejpam-6611	213	6	-	-	PUNCT
ejpam-6611	213	7	saleem	saleem	PROPN
ejpam-6611	213	8	.	.	PUNCT
ejpam-6611	214	1	retractions	retraction	NOUN
ejpam-6611	214	2	and	and	CCONJ
ejpam-6611	214	3	homomorphisms	homomorphism	NOUN
ejpam-6611	214	4	on	on	ADP
ejpam-6611	214	5	some	some	DET
ejpam-6611	214	6	operations	operation	NOUN
ejpam-6611	214	7	of	of	ADP
ejpam-6611	214	8	graphs	graph	NOUN
ejpam-6611	214	9	.	.	PUNCT
ejpam-6611	215	1	journal	journal	NOUN
ejpam-6611	215	2	of	of	ADP
ejpam-6611	215	3	mathematics	mathematic	NOUN
ejpam-6611	215	4	,	,	PUNCT
ejpam-6611	215	5	2018(1):7328065	2018(1):7328065	NOUN
ejpam-6611	215	6	,	,	PUNCT
ejpam-6611	215	7	2018	2018	NUM
ejpam-6611	215	8	.	.	PUNCT
ejpam-6611	216	1	[	[	X
ejpam-6611	216	2	18	18	NUM
ejpam-6611	216	3	]	]	PUNCT
ejpam-6611	216	4	m.	m.	NOUN
ejpam-6611	216	5	abu	abu	PROPN
ejpam-6611	216	6	-	-	PUNCT
ejpam-6611	216	7	saleem	saleem	PROPN
ejpam-6611	216	8	.	.	PUNCT
ejpam-6611	217	1	a	a	DET
ejpam-6611	217	2	neutrosophic	neutrosophic	ADJ
ejpam-6611	217	3	folding	folding	NOUN
ejpam-6611	217	4	and	and	CCONJ
ejpam-6611	217	5	retraction	retraction	NOUN
ejpam-6611	217	6	on	on	ADP
ejpam-6611	217	7	a	a	DET
ejpam-6611	217	8	single	single	ADV
ejpam-6611	217	9	-	-	PUNCT
ejpam-6611	217	10	valued	value	VERB
ejpam-6611	217	11	neutrosophic	neutrosophic	ADJ
ejpam-6611	217	12	graph	graph	NOUN
ejpam-6611	217	13	.	.	PUNCT
ejpam-6611	217	14	journal	journal	NOUN
ejpam-6611	217	15	of	of	ADP
ejpam-6611	217	16	intelligent	intelligent	ADJ
ejpam-6611	217	17	&	&	CCONJ
ejpam-6611	217	18	fuzzy	fuzzy	ADJ
ejpam-6611	217	19	systems	system	NOUN
ejpam-6611	217	20	,	,	PUNCT
ejpam-6611	217	21	40(3):5207–5213	40(3):5207–5213	NUM
ejpam-6611	217	22	,	,	PUNCT
ejpam-6611	217	23	2021	2021	NUM
ejpam-6611	217	24	.	.	PUNCT
ejpam-6611	218	1	[	[	X
ejpam-6611	218	2	19	19	NUM
ejpam-6611	218	3	]	]	PUNCT
ejpam-6611	218	4	m.	m.	NOUN
ejpam-6611	218	5	abu	abu	PROPN
ejpam-6611	218	6	-	-	PUNCT
ejpam-6611	218	7	saleem	saleem	PROPN
ejpam-6611	218	8	.	.	PUNCT
ejpam-6611	219	1	folding	fold	VERB
ejpam-6611	219	2	on	on	ADP
ejpam-6611	219	3	the	the	DET
ejpam-6611	219	4	wedge	wedge	NOUN
ejpam-6611	219	5	sum	sum	NOUN
ejpam-6611	219	6	of	of	ADP
ejpam-6611	219	7	graphs	graph	NOUN
ejpam-6611	219	8	and	and	CCONJ
ejpam-6611	219	9	their	their	PRON
ejpam-6611	219	10	fundamental	fundamental	ADJ
ejpam-6611	219	11	group	group	NOUN
ejpam-6611	219	12	.	.	PUNCT
ejpam-6611	220	1	apps	app	NOUN
ejpam-6611	220	2	.	.	PUNCT
ejpam-6611	221	1	applied	apply	VERB
ejpam-6611	221	2	sciences	science	NOUN
ejpam-6611	221	3	,	,	PUNCT
ejpam-6611	221	4	12:14–19	12:14–19	NUM
ejpam-6611	221	5	,	,	PUNCT
ejpam-6611	221	6	2010	2010	NUM
ejpam-6611	221	7	.	.	PUNCT