id	sid	tid	token	lemma	pos
ejpam-4704	1	1	european	european	PROPN
ejpam-4704	1	2	journal	journal	PROPN
ejpam-4704	1	3	of	of	ADP
ejpam-4704	1	4	pure	pure	ADJ
ejpam-4704	1	5	and	and	CCONJ
ejpam-4704	1	6	applied	apply	VERB
ejpam-4704	1	7	mathematics	mathematic	NOUN
ejpam-4704	1	8	vol	vol	NOUN
ejpam-4704	1	9	.	.	PUNCT
ejpam-4704	2	1	16	16	NUM
ejpam-4704	2	2	,	,	PUNCT
ejpam-4704	2	3	no	no	INTJ
ejpam-4704	2	4	.	.	NOUN
ejpam-4704	2	5	2	2	NUM
ejpam-4704	2	6	,	,	PUNCT
ejpam-4704	2	7	2023	2023	NUM
ejpam-4704	2	8	,	,	PUNCT
ejpam-4704	2	9	953	953	NUM
ejpam-4704	2	10	-	-	SYM
ejpam-4704	2	11	964	964	NUM
ejpam-4704	2	12	issn	issn	PROPN
ejpam-4704	2	13	1307	1307	NUM
ejpam-4704	2	14	-	-	SYM
ejpam-4704	2	15	5543	5543	NUM
ejpam-4704	2	16	–	–	PUNCT
ejpam-4704	2	17	ejpam.com	ejpam.com	X
ejpam-4704	2	18	published	publish	VERB
ejpam-4704	2	19	by	by	ADP
ejpam-4704	2	20	new	new	PROPN
ejpam-4704	2	21	york	york	PROPN
ejpam-4704	2	22	business	business	PROPN
ejpam-4704	2	23	global	global	PROPN
ejpam-4704	2	24	the	the	DET
ejpam-4704	2	25	basis	basis	NOUN
ejpam-4704	2	26	number	number	NOUN
ejpam-4704	2	27	of	of	ADP
ejpam-4704	2	28	mycielski	mycielski	NOUN
ejpam-4704	2	29	’s	’s	PART
ejpam-4704	2	30	graph	graph	NOUN
ejpam-4704	2	31	for	for	ADP
ejpam-4704	2	32	some	some	DET
ejpam-4704	2	33	cog	cog	NOUN
ejpam-4704	2	34	-	-	PUNCT
ejpam-4704	2	35	graphs	graphs	PROPN
ejpam-4704	2	36	barah	barah	PROPN
ejpam-4704	2	37	m.	m.	NOUN
ejpam-4704	2	38	sulaiman1	sulaiman1	PROPN
ejpam-4704	2	39	,	,	PUNCT
ejpam-4704	2	40	rasha	rasha	PROPN
ejpam-4704	2	41	s.	s.	PROPN
ejpam-4704	2	42	hasan1	hasan1	PROPN
ejpam-4704	2	43	,	,	PUNCT
ejpam-4704	2	44	raghad	raghad	ADJ
ejpam-4704	2	45	a.	a.	NOUN
ejpam-4704	2	46	mustafa1,∗	mustafa1,∗	NOUN
ejpam-4704	2	47	1	1	NUM
ejpam-4704	2	48	department	department	NOUN
ejpam-4704	2	49	of	of	ADP
ejpam-4704	2	50	mathematics	mathematic	NOUN
ejpam-4704	2	51	,	,	PUNCT
ejpam-4704	2	52	college	college	NOUN
ejpam-4704	2	53	of	of	ADP
ejpam-4704	2	54	computer	computer	NOUN
ejpam-4704	2	55	sciences	sciences	PROPN
ejpam-4704	2	56	and	and	CCONJ
ejpam-4704	2	57	mathematics	mathematic	NOUN
ejpam-4704	2	58	,	,	PUNCT
ejpam-4704	2	59	university	university	NOUN
ejpam-4704	2	60	of	of	ADP
ejpam-4704	2	61	mosul	mosul	PROPN
ejpam-4704	2	62	,	,	PUNCT
ejpam-4704	2	63	mosul	mosul	PROPN
ejpam-4704	2	64	,	,	PUNCT
ejpam-4704	2	65	iraq	iraq	PROPN
ejpam-4704	2	66	abstract	abstract	NOUN
ejpam-4704	2	67	.	.	PUNCT
ejpam-4704	3	1	let	let	VERB
ejpam-4704	3	2	g	g	PROPN
ejpam-4704	3	3	=	=	SYM
ejpam-4704	3	4	(	(	PUNCT
ejpam-4704	3	5	v	v	NOUN
ejpam-4704	3	6	,	,	PUNCT
ejpam-4704	3	7	e	e	NOUN
ejpam-4704	3	8	)	)	PUNCT
ejpam-4704	3	9	be	be	AUX
ejpam-4704	3	10	a	a	DET
ejpam-4704	3	11	simple	simple	ADJ
ejpam-4704	3	12	connected	connect	VERB
ejpam-4704	3	13	graph	graph	NOUN
ejpam-4704	3	14	,	,	PUNCT
ejpam-4704	3	15	then	then	ADV
ejpam-4704	3	16	the	the	DET
ejpam-4704	3	17	basis	basis	NOUN
ejpam-4704	3	18	number	number	NOUN
ejpam-4704	3	19	of	of	ADP
ejpam-4704	3	20	g	g	PROPN
ejpam-4704	3	21	is	be	AUX
ejpam-4704	3	22	denoted	denote	VERB
ejpam-4704	3	23	by	by	ADP
ejpam-4704	3	24	b(g	b(g	PROPN
ejpam-4704	3	25	)	)	PUNCT
ejpam-4704	3	26	and	and	CCONJ
ejpam-4704	3	27	is	be	AUX
ejpam-4704	3	28	defined	define	VERB
ejpam-4704	3	29	by	by	ADP
ejpam-4704	3	30	the	the	DET
ejpam-4704	3	31	least	least	ADV
ejpam-4704	3	32	positive	positive	ADJ
ejpam-4704	3	33	integer	integer	NOUN
ejpam-4704	3	34	k	k	PROPN
ejpam-4704	3	35	such	such	ADJ
ejpam-4704	3	36	that	that	SCONJ
ejpam-4704	3	37	the	the	DET
ejpam-4704	3	38	graph	graph	NOUN
ejpam-4704	3	39	g	g	PROPN
ejpam-4704	3	40	has	have	VERB
ejpam-4704	3	41	a	a	DET
ejpam-4704	3	42	k−	k−	PROPN
ejpam-4704	3	43	fold	fold	ADJ
ejpam-4704	3	44	basis	basis	NOUN
ejpam-4704	3	45	for	for	ADP
ejpam-4704	3	46	it	it	PRON
ejpam-4704	3	47	is	be	AUX
ejpam-4704	3	48	cycle	cycle	NOUN
ejpam-4704	3	49	space	space	NOUN
ejpam-4704	3	50	.	.	PUNCT
ejpam-4704	4	1	in	in	ADP
ejpam-4704	4	2	this	this	DET
ejpam-4704	4	3	paper	paper	NOUN
ejpam-4704	4	4	we	we	PRON
ejpam-4704	4	5	studied	study	VERB
ejpam-4704	4	6	the	the	DET
ejpam-4704	4	7	basis	basis	NOUN
ejpam-4704	4	8	number	number	NOUN
ejpam-4704	4	9	of	of	ADP
ejpam-4704	4	10	mycielski	mycielski	NOUN
ejpam-4704	4	11	’s	’s	PART
ejpam-4704	4	12	graph	graph	NOUN
ejpam-4704	4	13	for	for	ADP
ejpam-4704	4	14	some	some	DET
ejpam-4704	4	15	cog	cog	NOUN
ejpam-4704	4	16	-	-	PUNCT
ejpam-4704	4	17	special	special	ADJ
ejpam-4704	4	18	graphs	graph	NOUN
ejpam-4704	4	19	,	,	PUNCT
ejpam-4704	4	20	and	and	CCONJ
ejpam-4704	4	21	we	we	PRON
ejpam-4704	4	22	compute	compute	VERB
ejpam-4704	4	23	the	the	DET
ejpam-4704	4	24	basis	basis	NOUN
ejpam-4704	4	25	number	number	NOUN
ejpam-4704	4	26	of	of	ADP
ejpam-4704	4	27	mycielski	mycielski	NOUN
ejpam-4704	4	28	’s	’s	PART
ejpam-4704	4	29	graph	graph	NOUN
ejpam-4704	4	30	for	for	ADP
ejpam-4704	4	31	cog	cog	NOUN
ejpam-4704	4	32	-	-	PUNCT
ejpam-4704	4	33	path	path	NOUN
ejpam-4704	4	34	graph	graph	NOUN
ejpam-4704	4	35	,	,	PUNCT
ejpam-4704	4	36	cog	cog	NOUN
ejpam-4704	4	37	-	-	PUNCT
ejpam-4704	4	38	cycle	cycle	NOUN
ejpam-4704	4	39	graph	graph	NOUN
ejpam-4704	4	40	,	,	PUNCT
ejpam-4704	4	41	cog	cog	PROPN
ejpam-4704	4	42	-	-	PUNCT
ejpam-4704	4	43	star	star	NOUN
ejpam-4704	4	44	graph	graph	NOUN
ejpam-4704	4	45	,	,	PUNCT
ejpam-4704	4	46	and	and	CCONJ
ejpam-4704	4	47	cog	cog	NOUN
ejpam-4704	4	48	-	-	PUNCT
ejpam-4704	4	49	wheel	wheel	NOUN
ejpam-4704	4	50	graph	graph	NOUN
ejpam-4704	4	51	.	.	PUNCT
ejpam-4704	5	1	2020	2020	NUM
ejpam-4704	5	2	mathematics	mathematic	NOUN
ejpam-4704	5	3	subject	subject	NOUN
ejpam-4704	5	4	classifications	classification	NOUN
ejpam-4704	5	5	:	:	PUNCT
ejpam-4704	5	6	05c10	05c10	ADJ
ejpam-4704	5	7	,	,	PUNCT
ejpam-4704	5	8	05c25	05c25	NUM
ejpam-4704	5	9	,	,	PUNCT
ejpam-4704	5	10	05c35	05c35	NUM
ejpam-4704	5	11	key	key	ADJ
ejpam-4704	5	12	words	word	NOUN
ejpam-4704	5	13	and	and	CCONJ
ejpam-4704	5	14	phrases	phrase	NOUN
ejpam-4704	5	15	:	:	PUNCT
ejpam-4704	5	16	basis	basis	NOUN
ejpam-4704	5	17	number	number	NOUN
ejpam-4704	5	18	,	,	PUNCT
ejpam-4704	5	19	k	k	PROPN
ejpam-4704	5	20	−	−	PROPN
ejpam-4704	5	21	fold	fold	ADJ
ejpam-4704	5	22	,	,	PUNCT
ejpam-4704	5	23	mycielski	mycielski	NOUN
ejpam-4704	5	24	’s	’s	PART
ejpam-4704	5	25	graph	graph	NOUN
ejpam-4704	5	26	1	1	NUM
ejpam-4704	5	27	.	.	PUNCT
ejpam-4704	6	1	introduction	introduction	NOUN
ejpam-4704	6	2	let	let	VERB
ejpam-4704	6	3	g	g	NOUN
ejpam-4704	6	4	be	be	AUX
ejpam-4704	6	5	a	a	DET
ejpam-4704	6	6	connected	connected	ADJ
ejpam-4704	6	7	graph	graph	NOUN
ejpam-4704	6	8	with	with	ADP
ejpam-4704	6	9	edges	edge	NOUN
ejpam-4704	6	10	sets	set	NOUN
ejpam-4704	6	11	{	{	PUNCT
ejpam-4704	6	12	e1	e1	NOUN
ejpam-4704	6	13	,	,	PUNCT
ejpam-4704	6	14	e2	e2	PROPN
ejpam-4704	6	15	,	,	PUNCT
ejpam-4704	6	16	.	.	PUNCT
ejpam-4704	6	17	.	.	PUNCT
ejpam-4704	7	1	.	.	PUNCT
ejpam-4704	8	1	,	,	PUNCT
ejpam-4704	8	2	eq	eq	ADP
ejpam-4704	8	3	}	}	PUNCT
ejpam-4704	8	4	.	.	PUNCT
ejpam-4704	9	1	for	for	ADP
ejpam-4704	9	2	each	each	DET
ejpam-4704	9	3	subset	subset	NOUN
ejpam-4704	9	4	s	s	PROPN
ejpam-4704	9	5	of	of	ADP
ejpam-4704	9	6	edges	edge	NOUN
ejpam-4704	9	7	of	of	ADP
ejpam-4704	9	8	the	the	DET
ejpam-4704	9	9	graph	graph	NOUN
ejpam-4704	9	10	g	g	NOUN
ejpam-4704	9	11	,	,	PUNCT
ejpam-4704	9	12	there	there	PRON
ejpam-4704	9	13	is	be	VERB
ejpam-4704	9	14	a	a	DET
ejpam-4704	9	15	vector	vector	NOUN
ejpam-4704	9	16	(	(	PUNCT
ejpam-4704	9	17	a1	a1	PROPN
ejpam-4704	9	18	,	,	PUNCT
ejpam-4704	9	19	a2	a2	PROPN
ejpam-4704	9	20	,	,	PUNCT
ejpam-4704	9	21	a3	a3	NOUN
ejpam-4704	9	22	,	,	PUNCT
ejpam-4704	9	23	.	.	PUNCT
ejpam-4704	9	24	.	.	PUNCT
ejpam-4704	10	1	.	.	PUNCT
ejpam-4704	11	1	,	,	PUNCT
ejpam-4704	11	2	aq	aq	X
ejpam-4704	11	3	)	)	PUNCT
ejpam-4704	11	4	corresponding	correspond	VERB
ejpam-4704	11	5	to	to	ADP
ejpam-4704	11	6	s	s	PRON
ejpam-4704	11	7	such	such	ADJ
ejpam-4704	11	8	that	that	PRON
ejpam-4704	11	9	ai	ai	NOUN
ejpam-4704	11	10	=	=	ADJ
ejpam-4704	11	11	1	1	NUM
ejpam-4704	11	12	if	if	SCONJ
ejpam-4704	11	13	ei	ei	ADP
ejpam-4704	11	14	∈	∈	PROPN
ejpam-4704	11	15	s	s	PART
ejpam-4704	11	16	and	and	CCONJ
ejpam-4704	11	17	ai	ai	VERB
ejpam-4704	11	18	=	=	ADJ
ejpam-4704	11	19	0	0	PUNCT
ejpam-4704	12	1	if	if	SCONJ
ejpam-4704	12	2	ei	ei	X
ejpam-4704	12	3	/∈	/∈	PUNCT
ejpam-4704	12	4	s.	s.	PROPN
ejpam-4704	13	1	these	these	DET
ejpam-4704	13	2	vectors	vector	NOUN
ejpam-4704	13	3	form	form	VERB
ejpam-4704	13	4	a	a	DET
ejpam-4704	13	5	vector	vector	NOUN
ejpam-4704	13	6	space	space	NOUN
ejpam-4704	13	7	of	of	ADP
ejpam-4704	13	8	dimension	dimension	NOUN
ejpam-4704	13	9	q	q	PROPN
ejpam-4704	13	10	on	on	ADP
ejpam-4704	13	11	the	the	DET
ejpam-4704	13	12	field	field	NOUN
ejpam-4704	13	13	z2	z2	PROPN
ejpam-4704	13	14	,	,	PUNCT
ejpam-4704	13	15	called	call	VERB
ejpam-4704	13	16	the	the	DET
ejpam-4704	13	17	vector	vector	NOUN
ejpam-4704	13	18	space	space	NOUN
ejpam-4704	13	19	associated	associate	VERB
ejpam-4704	13	20	with	with	ADP
ejpam-4704	13	21	the	the	DET
ejpam-4704	13	22	graph	graph	NOUN
ejpam-4704	13	23	g	g	NOUN
ejpam-4704	13	24	and	and	CCONJ
ejpam-4704	13	25	denoted	denote	VERB
ejpam-4704	13	26	by	by	ADP
ejpam-4704	13	27	(	(	PUNCT
ejpam-4704	13	28	z2	z2	PROPN
ejpam-4704	13	29	)	)	PUNCT
ejpam-4704	13	30	q.	q.	NOUN
ejpam-4704	13	31	the	the	DET
ejpam-4704	13	32	vectors	vector	NOUN
ejpam-4704	13	33	of	of	ADP
ejpam-4704	13	34	(	(	PUNCT
ejpam-4704	13	35	z2	z2	PROPN
ejpam-4704	13	36	)	)	PUNCT
ejpam-4704	13	37	q	q	NOUN
ejpam-4704	13	38	that	that	PRON
ejpam-4704	13	39	correspond	correspond	VERB
ejpam-4704	13	40	to	to	ADP
ejpam-4704	13	41	the	the	DET
ejpam-4704	13	42	cycles	cycle	NOUN
ejpam-4704	13	43	of	of	ADP
ejpam-4704	13	44	g	g	PROPN
ejpam-4704	13	45	generate	generate	VERB
ejpam-4704	13	46	a	a	DET
ejpam-4704	13	47	vector	vector	NOUN
ejpam-4704	13	48	subspace	subspace	NOUN
ejpam-4704	13	49	called	call	VERB
ejpam-4704	13	50	the	the	DET
ejpam-4704	13	51	cycles	cycle	NOUN
ejpam-4704	13	52	space	space	NOUN
ejpam-4704	13	53	of	of	ADP
ejpam-4704	13	54	g	g	NOUN
ejpam-4704	13	55	and	and	CCONJ
ejpam-4704	13	56	denoted	denote	VERB
ejpam-4704	13	57	by	by	ADP
ejpam-4704	13	58	c(g	c(g	PROPN
ejpam-4704	13	59	)	)	PUNCT
ejpam-4704	13	60	.	.	PUNCT
ejpam-4704	14	1	each	each	DET
ejpam-4704	14	2	vector	vector	NOUN
ejpam-4704	14	3	in	in	ADP
ejpam-4704	14	4	c(g	c(g	PROPN
ejpam-4704	14	5	)	)	PUNCT
ejpam-4704	14	6	represents	represent	VERB
ejpam-4704	14	7	either	either	CCONJ
ejpam-4704	14	8	a	a	DET
ejpam-4704	14	9	cycle	cycle	NOUN
ejpam-4704	14	10	in	in	ADP
ejpam-4704	14	11	g	g	PROPN
ejpam-4704	14	12	or	or	CCONJ
ejpam-4704	14	13	the	the	DET
ejpam-4704	14	14	union	union	NOUN
ejpam-4704	14	15	of	of	ADP
ejpam-4704	14	16	separate	separate	ADJ
ejpam-4704	14	17	cycles	cycle	NOUN
ejpam-4704	14	18	with	with	ADP
ejpam-4704	14	19	respect	respect	NOUN
ejpam-4704	14	20	to	to	ADP
ejpam-4704	14	21	the	the	DET
ejpam-4704	14	22	edges	edge	NOUN
ejpam-4704	14	23	.	.	PUNCT
ejpam-4704	15	1	a	a	DET
ejpam-4704	15	2	known	know	VERB
ejpam-4704	15	3	corollary	corollary	NOUN
ejpam-4704	15	4	of	of	ADP
ejpam-4704	15	5	graph	graph	NOUN
ejpam-4704	15	6	theory	theory	NOUN
ejpam-4704	15	7	is	be	AUX
ejpam-4704	15	8	that	that	SCONJ
ejpam-4704	15	9	a	a	DET
ejpam-4704	15	10	dimension	dimension	NOUN
ejpam-4704	15	11	of	of	ADP
ejpam-4704	15	12	c(g	c(g	PROPN
ejpam-4704	15	13	)	)	PUNCT
ejpam-4704	15	14	is	be	AUX
ejpam-4704	15	15	q	q	NOUN
ejpam-4704	15	16	−	−	PROPN
ejpam-4704	15	17	p	p	NOUN
ejpam-4704	16	1	+	+	NOUN
ejpam-4704	16	2	1	1	NUM
ejpam-4704	16	3	where	where	SCONJ
ejpam-4704	16	4	p	p	NOUN
ejpam-4704	16	5	represents	represent	VERB
ejpam-4704	16	6	the	the	DET
ejpam-4704	16	7	number	number	NOUN
ejpam-4704	16	8	of	of	ADP
ejpam-4704	16	9	vertices	vertex	NOUN
ejpam-4704	16	10	of	of	ADP
ejpam-4704	16	11	graph	graph	NOUN
ejpam-4704	16	12	g	g	PROPN
ejpam-4704	16	13	and	and	CCONJ
ejpam-4704	16	14	q	q	DET
ejpam-4704	16	15	the	the	DET
ejpam-4704	16	16	number	number	NOUN
ejpam-4704	16	17	of	of	ADP
ejpam-4704	16	18	edges	edge	NOUN
ejpam-4704	16	19	.	.	PUNCT
ejpam-4704	17	1	the	the	DET
ejpam-4704	17	2	method	method	NOUN
ejpam-4704	17	3	for	for	ADP
ejpam-4704	17	4	finding	find	VERB
ejpam-4704	17	5	the	the	DET
ejpam-4704	17	6	base	base	NOUN
ejpam-4704	17	7	for	for	ADP
ejpam-4704	17	8	the	the	DET
ejpam-4704	17	9	cycles	cycle	NOUN
ejpam-4704	17	10	space	space	NOUN
ejpam-4704	17	11	of	of	ADP
ejpam-4704	17	12	c(g	c(g	PROPN
ejpam-4704	17	13	)	)	PUNCT
ejpam-4704	17	14	is	be	AUX
ejpam-4704	17	15	as	as	SCONJ
ejpam-4704	17	16	follows	follow	VERB
ejpam-4704	17	17	:	:	PUNCT
ejpam-4704	17	18	let	let	VERB
ejpam-4704	17	19	t	t	NOUN
ejpam-4704	17	20	be	be	AUX
ejpam-4704	17	21	a	a	DET
ejpam-4704	17	22	generating	generate	VERB
ejpam-4704	17	23	tree	tree	NOUN
ejpam-4704	17	24	for	for	ADP
ejpam-4704	17	25	the	the	DET
ejpam-4704	17	26	graph	graph	NOUN
ejpam-4704	17	27	g	g	NOUN
ejpam-4704	17	28	;	;	PUNCT
ejpam-4704	17	29	if	if	SCONJ
ejpam-4704	17	30	the	the	DET
ejpam-4704	17	31	edge	edge	NOUN
ejpam-4704	17	32	ei	ei	VERB
ejpam-4704	17	33	belongs	belong	VERB
ejpam-4704	17	34	to	to	PART
ejpam-4704	17	35	g−t	g−t	PROPN
ejpam-4704	17	36	then	then	ADV
ejpam-4704	17	37	t	t	PROPN
ejpam-4704	17	38	+	+	CCONJ
ejpam-4704	17	39	ei	ei	NOUN
ejpam-4704	17	40	contains	contain	VERB
ejpam-4704	17	41	only	only	ADV
ejpam-4704	17	42	one	one	NUM
ejpam-4704	17	43	cycle	cycle	NOUN
ejpam-4704	17	44	,	,	PUNCT
ejpam-4704	17	45	let	let	VERB
ejpam-4704	17	46	it	it	PRON
ejpam-4704	17	47	be	be	AUX
ejpam-4704	17	48	cei	cei	NOUN
ejpam-4704	17	49	.	.	PUNCT
ejpam-4704	18	1	clearly	clearly	ADV
ejpam-4704	18	2	,	,	PUNCT
ejpam-4704	18	3	q	q	PROPN
ejpam-4704	18	4	−	−	PROPN
ejpam-4704	19	1	p	p	X
ejpam-4704	20	1	+	+	NOUN
ejpam-4704	20	2	1	1	NUM
ejpam-4704	20	3	of	of	ADP
ejpam-4704	20	4	cycles	cycle	NOUN
ejpam-4704	20	5	cei	cei	NOUN
ejpam-4704	20	6	,	,	PUNCT
ejpam-4704	20	7	where	where	SCONJ
ejpam-4704	20	8	ei	ei	ADP
ejpam-4704	20	9	∈	∈	PROPN
ejpam-4704	20	10	g	g	PROPN
ejpam-4704	20	11	−	−	PROPN
ejpam-4704	20	12	t	t	PROPN
ejpam-4704	20	13	for	for	ADP
ejpam-4704	20	14	i	i	PRON
ejpam-4704	20	15	=	=	NOUN
ejpam-4704	20	16	1	1	NUM
ejpam-4704	20	17	,	,	PUNCT
ejpam-4704	20	18	2	2	NUM
ejpam-4704	20	19	,	,	PUNCT
ejpam-4704	20	20	.	.	PUNCT
ejpam-4704	20	21	.	.	PUNCT
ejpam-4704	21	1	.	.	PUNCT
ejpam-4704	22	1	,	,	PUNCT
ejpam-4704	22	2	q	q	PROPN
ejpam-4704	22	3	forms	form	VERB
ejpam-4704	22	4	the	the	DET
ejpam-4704	22	5	base	base	NOUN
ejpam-4704	22	6	of	of	ADP
ejpam-4704	22	7	the	the	DET
ejpam-4704	22	8	cycles	cycle	NOUN
ejpam-4704	22	9	space	space	NOUN
ejpam-4704	22	10	c(g	c(g	PROPN
ejpam-4704	22	11	)	)	PUNCT
ejpam-4704	22	12	.	.	PUNCT
ejpam-4704	23	1	the	the	DET
ejpam-4704	23	2	base	base	PROPN
ejpam-4704	23	3	b	b	PROPN
ejpam-4704	23	4	of	of	ADP
ejpam-4704	23	5	cycles	cycle	NOUN
ejpam-4704	23	6	space	space	NOUN
ejpam-4704	23	7	c(g	c(g	PROPN
ejpam-4704	23	8	)	)	PUNCT
ejpam-4704	23	9	is	be	AUX
ejpam-4704	23	10	said	say	VERB
ejpam-4704	23	11	to	to	PART
ejpam-4704	23	12	have	have	VERB
ejpam-4704	23	13	a	a	DET
ejpam-4704	23	14	k−	k−	NOUN
ejpam-4704	23	15	fold	fold	VERB
ejpam-4704	23	16	if	if	SCONJ
ejpam-4704	23	17	each	each	DET
ejpam-4704	23	18	edge	edge	NOUN
ejpam-4704	23	19	of	of	ADP
ejpam-4704	23	20	g	g	PROPN
ejpam-4704	23	21	shows	show	VERB
ejpam-4704	23	22	no	no	PRON
ejpam-4704	23	23	more	more	ADJ
ejpam-4704	23	24	than	than	ADP
ejpam-4704	23	25	k	k	PROPN
ejpam-4704	23	26	times	times	PROPN
ejpam-4704	23	27	(	(	PUNCT
ejpam-4704	23	28	iterations	iteration	NOUN
ejpam-4704	23	29	)	)	PUNCT
ejpam-4704	23	30	in	in	ADP
ejpam-4704	23	31	the	the	DET
ejpam-4704	23	32	cycles	cycle	NOUN
ejpam-4704	23	33	that	that	SCONJ
ejpam-4704	23	34	corresponding	correspond	VERB
ejpam-4704	23	35	to	to	ADP
ejpam-4704	23	36	the	the	DET
ejpam-4704	23	37	vectors	vector	NOUN
ejpam-4704	23	38	in	in	ADP
ejpam-4704	23	39	the	the	DET
ejpam-4704	23	40	base	base	PROPN
ejpam-4704	23	41	b.	b.	PROPN
ejpam-4704	23	42	∗corresponding	∗corresponde	VERB
ejpam-4704	23	43	author	author	NOUN
ejpam-4704	23	44	.	.	PUNCT
ejpam-4704	24	1	doi	doi	NOUN
ejpam-4704	24	2	:	:	PUNCT
ejpam-4704	24	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4704	https://doi.org/10.29020/nybg.ejpam.v16i2.4704	ADJ
ejpam-4704	24	4	email	email	NOUN
ejpam-4704	24	5	addresses	address	NOUN
ejpam-4704	24	6	:	:	PUNCT
ejpam-4704	24	7	barah	barah	PROPN
ejpam-4704	24	8	mahmood82@uomosul.edu.iq	mahmood82@uomosul.edu.iq	PROPN
ejpam-4704	24	9	(	(	PUNCT
ejpam-4704	24	10	b.	b.	PROPN
ejpam-4704	24	11	m.	m.	PROPN
ejpam-4704	24	12	sulaiman	sulaiman	PROPN
ejpam-4704	24	13	)	)	PUNCT
ejpam-4704	24	14	,	,	PUNCT
ejpam-4704	24	15	sallal-rasha@uomosul.edu.iq	sallal-rasha@uomosul.edu.iq	PROPN
ejpam-4704	24	16	(	(	PUNCT
ejpam-4704	24	17	r.	r.	PROPN
ejpam-4704	24	18	s.	s.	PROPN
ejpam-4704	24	19	hasan	hasan	PROPN
ejpam-4704	24	20	)	)	PUNCT
ejpam-4704	24	21	,	,	PUNCT
ejpam-4704	24	22	raghad.math@uomosul.edu.iq	raghad.math@uomosul.edu.iq	NOUN
ejpam-4704	24	23	(	(	PUNCT
ejpam-4704	24	24	r.	r.	PROPN
ejpam-4704	24	25	a.	a.	PROPN
ejpam-4704	24	26	mustafa	mustafa	PROPN
ejpam-4704	24	27	)	)	PUNCT
ejpam-4704	24	28	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4704	25	1	953	953	NUM
ejpam-4704	26	1	©	©	PROPN
ejpam-4704	26	2	2023	2023	NUM
ejpam-4704	26	3	ejpam	ejpam	NOUN
ejpam-4704	26	4	all	all	DET
ejpam-4704	26	5	rights	right	NOUN
ejpam-4704	26	6	reserved	reserve	VERB
ejpam-4704	26	7	.	.	PUNCT
ejpam-4704	27	1	b.	b.	PROPN
ejpam-4704	27	2	m.	m.	PROPN
ejpam-4704	27	3	sulaiman	sulaiman	PROPN
ejpam-4704	27	4	,	,	PUNCT
ejpam-4704	27	5	r.	r.	PROPN
ejpam-4704	27	6	s.	s.	PROPN
ejpam-4704	27	7	hasan	hasan	PROPN
ejpam-4704	27	8	,	,	PUNCT
ejpam-4704	27	9	r.	r.	PROPN
ejpam-4704	27	10	a.	a.	PROPN
ejpam-4704	27	11	mustafa	mustafa	PROPN
ejpam-4704	27	12	/	/	SYM
ejpam-4704	27	13	eur	eur	PROPN
ejpam-4704	27	14	.	.	PUNCT
ejpam-4704	28	1	j.	j.	PROPN
ejpam-4704	28	2	pure	pure	PROPN
ejpam-4704	28	3	appl	appl	PROPN
ejpam-4704	28	4	.	.	PROPN
ejpam-4704	28	5	math	math	PROPN
ejpam-4704	28	6	,	,	PUNCT
ejpam-4704	28	7	16	16	NUM
ejpam-4704	28	8	(	(	PUNCT
ejpam-4704	28	9	2	2	NUM
ejpam-4704	28	10	)	)	PUNCT
ejpam-4704	28	11	(	(	PUNCT
ejpam-4704	28	12	2023	2023	NUM
ejpam-4704	28	13	)	)	PUNCT
ejpam-4704	28	14	,	,	PUNCT
ejpam-4704	28	15	953	953	NUM
ejpam-4704	28	16	-	-	SYM
ejpam-4704	28	17	964	964	NUM
ejpam-4704	28	18	954	954	NUM
ejpam-4704	28	19	the	the	DET
ejpam-4704	28	20	basis	basis	NOUN
ejpam-4704	28	21	number	number	NOUN
ejpam-4704	28	22	of	of	ADP
ejpam-4704	28	23	the	the	DET
ejpam-4704	28	24	graph	graph	NOUN
ejpam-4704	28	25	g	g	NOUN
ejpam-4704	28	26	is	be	AUX
ejpam-4704	28	27	defined	define	VERB
ejpam-4704	28	28	as	as	ADP
ejpam-4704	28	29	the	the	DET
ejpam-4704	28	30	smallest	small	ADJ
ejpam-4704	28	31	integer	integer	NOUN
ejpam-4704	28	32	k	k	PROPN
ejpam-4704	28	33	,	,	PUNCT
ejpam-4704	28	34	such	such	ADJ
ejpam-4704	28	35	that	that	DET
ejpam-4704	28	36	c(g	c(g	PROPN
ejpam-4704	28	37	)	)	PUNCT
ejpam-4704	28	38	have	have	VERB
ejpam-4704	28	39	a	a	DET
ejpam-4704	28	40	k−	k−	PROPN
ejpam-4704	28	41	fold	fold	ADJ
ejpam-4704	28	42	base	base	NOUN
ejpam-4704	28	43	;	;	PUNCT
ejpam-4704	28	44	it	it	PRON
ejpam-4704	28	45	is	be	AUX
ejpam-4704	28	46	denoted	denote	VERB
ejpam-4704	28	47	by	by	ADP
ejpam-4704	28	48	b(g	b(g	PROPN
ejpam-4704	28	49	)	)	PUNCT
ejpam-4704	28	50	.	.	PUNCT
ejpam-4704	29	1	if	if	SCONJ
ejpam-4704	29	2	b	b	PROPN
ejpam-4704	29	3	is	be	AUX
ejpam-4704	29	4	the	the	DET
ejpam-4704	29	5	base	base	NOUN
ejpam-4704	29	6	of	of	ADP
ejpam-4704	29	7	the	the	DET
ejpam-4704	29	8	cycles	cycle	NOUN
ejpam-4704	29	9	space	space	NOUN
ejpam-4704	29	10	c(g	c(g	PROPN
ejpam-4704	29	11	)	)	PUNCT
ejpam-4704	29	12	and	and	CCONJ
ejpam-4704	29	13	e	e	NOUN
ejpam-4704	29	14	is	be	AUX
ejpam-4704	29	15	an	an	DET
ejpam-4704	29	16	edge	edge	NOUN
ejpam-4704	29	17	in	in	ADP
ejpam-4704	29	18	g	g	NOUN
ejpam-4704	29	19	,	,	PUNCT
ejpam-4704	29	20	then	then	ADV
ejpam-4704	29	21	the	the	DET
ejpam-4704	29	22	fold	fold	NOUN
ejpam-4704	29	23	of	of	ADP
ejpam-4704	29	24	the	the	DET
ejpam-4704	29	25	edge	edge	NOUN
ejpam-4704	29	26	e	e	NOUN
ejpam-4704	29	27	in	in	ADP
ejpam-4704	29	28	b	b	PROPN
ejpam-4704	29	29	is	be	AUX
ejpam-4704	29	30	defined	define	VERB
ejpam-4704	29	31	the	the	DET
ejpam-4704	29	32	number	number	NOUN
ejpam-4704	29	33	of	of	ADP
ejpam-4704	29	34	cycles	cycle	NOUN
ejpam-4704	29	35	that	that	PRON
ejpam-4704	29	36	exist	exist	VERB
ejpam-4704	29	37	in	in	ADP
ejpam-4704	29	38	b	b	PROPN
ejpam-4704	29	39	and	and	CCONJ
ejpam-4704	29	40	containing	contain	VERB
ejpam-4704	29	41	the	the	DET
ejpam-4704	29	42	edge	edge	NOUN
ejpam-4704	29	43	e	e	NOUN
ejpam-4704	29	44	,	,	PUNCT
ejpam-4704	29	45	and	and	CCONJ
ejpam-4704	29	46	is	be	AUX
ejpam-4704	29	47	denoted	denote	VERB
ejpam-4704	29	48	by	by	ADP
ejpam-4704	29	49	fb(e	fb(e	ADJ
ejpam-4704	29	50	)	)	PUNCT
ejpam-4704	29	51	.	.	PUNCT
ejpam-4704	30	1	in	in	ADP
ejpam-4704	30	2	recent	recent	ADJ
ejpam-4704	30	3	years	year	NOUN
ejpam-4704	30	4	,	,	PUNCT
ejpam-4704	30	5	interest	interest	NOUN
ejpam-4704	30	6	in	in	ADP
ejpam-4704	30	7	the	the	DET
ejpam-4704	30	8	basic	basic	ADJ
ejpam-4704	30	9	number	number	NOUN
ejpam-4704	30	10	has	have	AUX
ejpam-4704	30	11	increased	increase	VERB
ejpam-4704	30	12	,	,	PUNCT
ejpam-4704	30	13	we	we	PRON
ejpam-4704	30	14	refer	refer	VERB
ejpam-4704	30	15	the	the	DET
ejpam-4704	30	16	reader	reader	NOUN
ejpam-4704	30	17	to	to	ADP
ejpam-4704	30	18	references	reference	NOUN
ejpam-4704	30	19	[	[	X
ejpam-4704	30	20	3–6	3–6	NUM
ejpam-4704	30	21	,	,	PUNCT
ejpam-4704	30	22	9	9	NUM
ejpam-4704	30	23	,	,	PUNCT
ejpam-4704	30	24	10	10	NUM
ejpam-4704	30	25	,	,	PUNCT
ejpam-4704	30	26	13	13	NUM
ejpam-4704	30	27	]	]	PUNCT
ejpam-4704	30	28	for	for	ADP
ejpam-4704	30	29	more	more	ADJ
ejpam-4704	30	30	information	information	NOUN
ejpam-4704	30	31	.	.	PUNCT
ejpam-4704	31	1	in	in	ADP
ejpam-4704	31	2	this	this	DET
ejpam-4704	31	3	paper	paper	NOUN
ejpam-4704	31	4	,	,	PUNCT
ejpam-4704	31	5	we	we	PRON
ejpam-4704	31	6	will	will	AUX
ejpam-4704	31	7	assume	assume	VERB
ejpam-4704	31	8	that	that	SCONJ
ejpam-4704	31	9	all	all	DET
ejpam-4704	31	10	graphs	graph	NOUN
ejpam-4704	31	11	that	that	SCONJ
ejpam-4704	31	12	we	we	PRON
ejpam-4704	31	13	encounter	encounter	VERB
ejpam-4704	31	14	are	be	AUX
ejpam-4704	31	15	finite	finite	ADJ
ejpam-4704	31	16	,	,	PUNCT
ejpam-4704	31	17	unguided	unguided	ADJ
ejpam-4704	31	18	and	and	CCONJ
ejpam-4704	31	19	simple	simple	ADJ
ejpam-4704	31	20	;	;	PUNCT
ejpam-4704	31	21	for	for	ADP
ejpam-4704	31	22	undefined	undefined	ADJ
ejpam-4704	31	23	terms	term	NOUN
ejpam-4704	31	24	,	,	PUNCT
ejpam-4704	31	25	refer	refer	VERB
ejpam-4704	31	26	to	to	ADP
ejpam-4704	31	27	the	the	DET
ejpam-4704	31	28	references	reference	NOUN
ejpam-4704	31	29	[	[	X
ejpam-4704	31	30	7][8	7][8	X
ejpam-4704	31	31	]	]	X
ejpam-4704	31	32	.	.	PUNCT
ejpam-4704	32	1	there	there	PRON
ejpam-4704	32	2	are	be	VERB
ejpam-4704	32	3	other	other	ADJ
ejpam-4704	32	4	types	type	NOUN
ejpam-4704	32	5	of	of	ADP
ejpam-4704	32	6	numbers	number	NOUN
ejpam-4704	32	7	that	that	PRON
ejpam-4704	32	8	are	be	AUX
ejpam-4704	32	9	important	important	ADJ
ejpam-4704	32	10	in	in	ADP
ejpam-4704	32	11	graph	graph	NOUN
ejpam-4704	32	12	theory	theory	NOUN
ejpam-4704	32	13	such	such	ADJ
ejpam-4704	32	14	as	as	ADP
ejpam-4704	32	15	:	:	PUNCT
ejpam-4704	32	16	detour	detour	NOUN
ejpam-4704	32	17	number	number	NOUN
ejpam-4704	32	18	[	[	X
ejpam-4704	32	19	1	1	NUM
ejpam-4704	32	20	]	]	PUNCT
ejpam-4704	32	21	and	and	CCONJ
ejpam-4704	32	22	number	number	NOUN
ejpam-4704	32	23	of	of	ADP
ejpam-4704	32	24	domination	domination	NOUN
ejpam-4704	32	25	[	[	X
ejpam-4704	32	26	17	17	NUM
ejpam-4704	32	27	]	]	PUNCT
ejpam-4704	32	28	,	,	PUNCT
ejpam-4704	32	29	and	and	CCONJ
ejpam-4704	32	30	graph	graph	NOUN
ejpam-4704	32	31	theory	theory	NOUN
ejpam-4704	32	32	has	have	VERB
ejpam-4704	32	33	an	an	DET
ejpam-4704	32	34	important	important	ADJ
ejpam-4704	32	35	applications	application	NOUN
ejpam-4704	32	36	at	at	ADP
ejpam-4704	32	37	the	the	DET
ejpam-4704	32	38	present	present	ADJ
ejpam-4704	32	39	time	time	NOUN
ejpam-4704	32	40	,	,	PUNCT
ejpam-4704	32	41	see	see	VERB
ejpam-4704	32	42	[	[	X
ejpam-4704	32	43	11	11	NUM
ejpam-4704	32	44	,	,	PUNCT
ejpam-4704	32	45	14	14	NUM
ejpam-4704	32	46	,	,	PUNCT
ejpam-4704	32	47	15	15	NUM
ejpam-4704	32	48	]	]	PUNCT
ejpam-4704	32	49	.	.	PUNCT
ejpam-4704	33	1	mycielski	mycielski	PROPN
ejpam-4704	33	2	’s	’s	PART
ejpam-4704	33	3	graph	graph	NOUN
ejpam-4704	33	4	[	[	X
ejpam-4704	33	5	16	16	NUM
ejpam-4704	33	6	]	]	X
ejpam-4704	33	7	:	:	PUNCT
ejpam-4704	33	8	let	let	VERB
ejpam-4704	33	9	g	g	NOUN
ejpam-4704	33	10	be	be	AUX
ejpam-4704	33	11	the	the	DET
ejpam-4704	33	12	graph	graph	NOUN
ejpam-4704	33	13	,	,	PUNCT
ejpam-4704	33	14	such	such	ADJ
ejpam-4704	33	15	that	that	SCONJ
ejpam-4704	33	16	the	the	DET
ejpam-4704	33	17	set	set	NOUN
ejpam-4704	33	18	of	of	ADP
ejpam-4704	33	19	its	its	PRON
ejpam-4704	33	20	vertices	vertex	NOUN
ejpam-4704	33	21	is	be	AUX
ejpam-4704	33	22	v	v	NOUN
ejpam-4704	33	23	=	=	PUNCT
ejpam-4704	33	24	{	{	PUNCT
ejpam-4704	33	25	u1	u1	NOUN
ejpam-4704	33	26	,	,	PUNCT
ejpam-4704	33	27	u2	u2	NOUN
ejpam-4704	33	28	,	,	PUNCT
ejpam-4704	33	29	u3	u3	NOUN
ejpam-4704	33	30	,	,	PUNCT
ejpam-4704	33	31	.	.	PUNCT
ejpam-4704	33	32	.	.	PUNCT
ejpam-4704	34	1	.	.	PUNCT
ejpam-4704	35	1	,	,	PUNCT
ejpam-4704	35	2	un	un	PROPN
ejpam-4704	35	3	}	}	PUNCT
ejpam-4704	35	4	,	,	PUNCT
ejpam-4704	35	5	then	then	ADV
ejpam-4704	35	6	the	the	DET
ejpam-4704	35	7	mycielski	mycielski	NOUN
ejpam-4704	35	8	’s	’s	PART
ejpam-4704	35	9	graph	graph	NOUN
ejpam-4704	35	10	for	for	ADP
ejpam-4704	35	11	g	g	NOUN
ejpam-4704	35	12	consists	consist	NOUN
ejpam-4704	35	13	of	of	ADP
ejpam-4704	35	14	g	g	PROPN
ejpam-4704	35	15	itself	itself	PRON
ejpam-4704	35	16	as	as	ADP
ejpam-4704	35	17	a	a	DET
ejpam-4704	35	18	sub	sub	NOUN
ejpam-4704	35	19	graph	graph	NOUN
ejpam-4704	35	20	isomorphic	isomorphic	ADJ
ejpam-4704	35	21	with	with	ADP
ejpam-4704	35	22	(	(	PUNCT
ejpam-4704	35	23	n	n	X
ejpam-4704	35	24	+	+	NOUN
ejpam-4704	35	25	1	1	NUM
ejpam-4704	35	26	)	)	PUNCT
ejpam-4704	35	27	additional	additional	ADJ
ejpam-4704	35	28	vertices	vertex	NOUN
ejpam-4704	35	29	,	,	PUNCT
ejpam-4704	35	30	the	the	DET
ejpam-4704	35	31	vertex	vertex	NOUN
ejpam-4704	35	32	vi	vi	NOUN
ejpam-4704	35	33	corresponding	correspond	VERB
ejpam-4704	35	34	to	to	ADP
ejpam-4704	35	35	ui	ui	NOUN
ejpam-4704	35	36	in	in	ADP
ejpam-4704	35	37	g	g	NOUN
ejpam-4704	35	38	,	,	PUNCT
ejpam-4704	35	39	for	for	ADP
ejpam-4704	35	40	i	i	PROPN
ejpam-4704	35	41	=	=	SYM
ejpam-4704	35	42	1	1	NUM
ejpam-4704	35	43	,	,	PUNCT
ejpam-4704	35	44	2	2	NUM
ejpam-4704	35	45	,	,	PUNCT
ejpam-4704	35	46	3	3	NUM
ejpam-4704	35	47	,	,	PUNCT
ejpam-4704	35	48	.	.	PUNCT
ejpam-4704	35	49	.	.	PUNCT
ejpam-4704	36	1	.	.	PUNCT
ejpam-4704	37	1	,	,	PUNCT
ejpam-4704	37	2	n	n	CCONJ
ejpam-4704	37	3	;	;	PUNCT
ejpam-4704	37	4	and	and	CCONJ
ejpam-4704	37	5	another	another	DET
ejpam-4704	37	6	vertex	vertex	NOUN
ejpam-4704	37	7	w	w	NOUN
ejpam-4704	37	8	which	which	PRON
ejpam-4704	37	9	is	be	AUX
ejpam-4704	37	10	adjacent	adjacent	ADJ
ejpam-4704	37	11	to	to	ADP
ejpam-4704	37	12	each	each	DET
ejpam-4704	37	13	vertex	vertex	NOUN
ejpam-4704	37	14	vi	vi	NOUN
ejpam-4704	38	1	such	such	ADJ
ejpam-4704	38	2	that	that	SCONJ
ejpam-4704	38	3	these	these	DET
ejpam-4704	38	4	vertices	vertex	NOUN
ejpam-4704	38	5	form	form	VERB
ejpam-4704	38	6	a	a	DET
ejpam-4704	38	7	sub	sub	NOUN
ejpam-4704	38	8	graph	graph	NOUN
ejpam-4704	38	9	isomorphic	isomorphic	ADJ
ejpam-4704	38	10	with	with	ADP
ejpam-4704	38	11	star	star	NOUN
ejpam-4704	38	12	k(1,n	k(1,n	PROPN
ejpam-4704	38	13	)	)	PUNCT
ejpam-4704	38	14	;	;	PUNCT
ejpam-4704	38	15	in	in	ADP
ejpam-4704	38	16	addition	addition	NOUN
ejpam-4704	38	17	,	,	PUNCT
ejpam-4704	38	18	for	for	ADP
ejpam-4704	38	19	each	each	DET
ejpam-4704	38	20	edge	edge	NOUN
ejpam-4704	38	21	ui	ui	PROPN
ejpam-4704	38	22	uj	uj	PROPN
ejpam-4704	38	23	in	in	ADP
ejpam-4704	38	24	g	g	PROPN
ejpam-4704	38	25	,	,	PUNCT
ejpam-4704	38	26	the	the	DET
ejpam-4704	38	27	mycielski	mycielski	NOUN
ejpam-4704	38	28	’s	’s	PART
ejpam-4704	38	29	graph	graph	NOUN
ejpam-4704	38	30	includes	include	VERB
ejpam-4704	38	31	two	two	NUM
ejpam-4704	38	32	edges	edge	NOUN
ejpam-4704	38	33	ui	ui	INTJ
ejpam-4704	38	34	vj	vj	PROPN
ejpam-4704	38	35	and	and	CCONJ
ejpam-4704	38	36	vi	vi	PROPN
ejpam-4704	38	37	uj	uj	PROPN
ejpam-4704	38	38	,	,	PUNCT
ejpam-4704	38	39	therefore	therefore	ADV
ejpam-4704	38	40	if	if	SCONJ
ejpam-4704	38	41	g	g	PROPN
ejpam-4704	38	42	is	be	AUX
ejpam-4704	38	43	a	a	DET
ejpam-4704	38	44	graph	graph	NOUN
ejpam-4704	38	45	of	of	ADP
ejpam-4704	38	46	n	n	NOUN
ejpam-4704	38	47	vertices	vertex	NOUN
ejpam-4704	38	48	and	and	CCONJ
ejpam-4704	38	49	m	m	PRON
ejpam-4704	38	50	edges	edge	NOUN
ejpam-4704	38	51	,	,	PUNCT
ejpam-4704	38	52	then	then	ADV
ejpam-4704	38	53	the	the	DET
ejpam-4704	38	54	mycielski	mycielski	NOUN
ejpam-4704	38	55	’s	’s	PART
ejpam-4704	38	56	graph	graph	NOUN
ejpam-4704	38	57	of	of	ADP
ejpam-4704	38	58	g	g	PROPN
ejpam-4704	38	59	has	have	VERB
ejpam-4704	38	60	2n	2n	NUM
ejpam-4704	38	61	+	+	CCONJ
ejpam-4704	38	62	1	1	NUM
ejpam-4704	38	63	vertices	vertex	NOUN
ejpam-4704	38	64	and	and	CCONJ
ejpam-4704	38	65	3	3	NUM
ejpam-4704	38	66	m	m	NOUN
ejpam-4704	38	67	+	+	NUM
ejpam-4704	38	68	n	n	CCONJ
ejpam-4704	38	69	edges	edge	NOUN
ejpam-4704	38	70	and	and	CCONJ
ejpam-4704	38	71	is	be	AUX
ejpam-4704	38	72	denoted	denote	VERB
ejpam-4704	38	73	by	by	ADP
ejpam-4704	38	74	µ(g	µ(g	PROPN
ejpam-4704	38	75	)	)	PUNCT
ejpam-4704	38	76	.	.	PUNCT
ejpam-4704	39	1	figure	figure	NOUN
ejpam-4704	39	2	(	(	PUNCT
ejpam-4704	39	3	1	1	NUM
ejpam-4704	39	4	)	)	PUNCT
ejpam-4704	39	5	represents	represent	VERB
ejpam-4704	39	6	mycielski	mycielski	ADJ
ejpam-4704	39	7	’s	’s	PART
ejpam-4704	39	8	graph	graph	NOUN
ejpam-4704	39	9	of	of	ADP
ejpam-4704	39	10	the	the	DET
ejpam-4704	39	11	cycle	cycle	NOUN
ejpam-4704	39	12	c3	c3	PROPN
ejpam-4704	39	13	.	.	PUNCT
ejpam-4704	40	1	figure	figure	NOUN
ejpam-4704	40	2	1	1	NUM
ejpam-4704	40	3	:	:	PUNCT
ejpam-4704	40	4	µ(c3	µ(c3	NOUN
ejpam-4704	40	5	)	)	PUNCT
ejpam-4704	40	6	2	2	NUM
ejpam-4704	40	7	.	.	X
ejpam-4704	40	8	main	main	ADJ
ejpam-4704	40	9	results	result	NOUN
ejpam-4704	40	10	2.1	2.1	NUM
ejpam-4704	40	11	.	.	PUNCT
ejpam-4704	41	1	cog	cog	NOUN
ejpam-4704	41	2	-	-	PUNCT
ejpam-4704	41	3	path	path	NOUN
ejpam-4704	41	4	graph	graph	NOUN
ejpam-4704	42	1	p	p	PROPN
ejpam-4704	42	2	c	c	NOUN
ejpam-4704	42	3	m	m	VERB
ejpam-4704	42	4	it	it	PRON
ejpam-4704	42	5	is	be	AUX
ejpam-4704	42	6	a	a	DET
ejpam-4704	42	7	graph	graph	NOUN
ejpam-4704	42	8	consists	consist	VERB
ejpam-4704	42	9	of	of	ADP
ejpam-4704	42	10	a	a	DET
ejpam-4704	42	11	path	path	NOUN
ejpam-4704	42	12	pm	pm	NOUN
ejpam-4704	42	13	:	:	PUNCT
ejpam-4704	42	14	u1	u1	NOUN
ejpam-4704	42	15	,	,	PUNCT
ejpam-4704	42	16	u2	u2	NOUN
ejpam-4704	42	17	,	,	PUNCT
ejpam-4704	42	18	.	.	PUNCT
ejpam-4704	42	19	.	.	PUNCT
ejpam-4704	43	1	.	.	PUNCT
ejpam-4704	44	1	,	,	PUNCT
ejpam-4704	44	2	um	um	INTJ
ejpam-4704	44	3	where	where	SCONJ
ejpam-4704	44	4	m	m	VERB
ejpam-4704	44	5	≥	≥	NOUN
ejpam-4704	44	6	3	3	NUM
ejpam-4704	44	7	,	,	PUNCT
ejpam-4704	44	8	with	with	ADP
ejpam-4704	44	9	m	m	PROPN
ejpam-4704	44	10	−	−	NUM
ejpam-4704	44	11	1	1	NUM
ejpam-4704	44	12	additional	additional	ADJ
ejpam-4704	44	13	vertices	vertex	NOUN
ejpam-4704	44	14	v1	v1	NOUN
ejpam-4704	44	15	,	,	PUNCT
ejpam-4704	44	16	v2	v2	NOUN
ejpam-4704	44	17	,	,	PUNCT
ejpam-4704	44	18	.	.	PUNCT
ejpam-4704	44	19	.	.	PUNCT
ejpam-4704	45	1	.	.	PUNCT
ejpam-4704	46	1	,	,	PUNCT
ejpam-4704	46	2	vm−1	vm−1	NOUN
ejpam-4704	46	3	and	and	CCONJ
ejpam-4704	46	4	additional	additional	ADJ
ejpam-4704	46	5	edges	edge	NOUN
ejpam-4704	46	6	{	{	PUNCT
ejpam-4704	46	7	uivi	uivi	NOUN
ejpam-4704	46	8	,	,	PUNCT
ejpam-4704	46	9	viui+1	viui+1	NOUN
ejpam-4704	46	10	,	,	PUNCT
ejpam-4704	46	11	i	i	PRON
ejpam-4704	46	12	=	=	NOUN
ejpam-4704	46	13	1	1	NUM
ejpam-4704	46	14	,	,	PUNCT
ejpam-4704	46	15	2	2	NUM
ejpam-4704	46	16	,	,	PUNCT
ejpam-4704	46	17	.	.	PUNCT
ejpam-4704	46	18	.	.	PUNCT
ejpam-4704	47	1	.	.	PUNCT
ejpam-4704	48	1	,	,	PUNCT
ejpam-4704	48	2	m−1	m−1	PROPN
ejpam-4704	48	3	}	}	PUNCT
ejpam-4704	48	4	.	.	PUNCT
ejpam-4704	49	1	the	the	DET
ejpam-4704	49	2	number	number	NOUN
ejpam-4704	49	3	of	of	ADP
ejpam-4704	49	4	vertices	vertex	NOUN
ejpam-4704	49	5	of	of	ADP
ejpam-4704	49	6	p	p	NOUN
ejpam-4704	49	7	c	c	PROPN
ejpam-4704	49	8	m	m	NOUN
ejpam-4704	49	9	is	be	AUX
ejpam-4704	49	10	2m−	2m−	PROPN
ejpam-4704	49	11	1	1	NUM
ejpam-4704	49	12	and	and	CCONJ
ejpam-4704	49	13	the	the	DET
ejpam-4704	49	14	number	number	NOUN
ejpam-4704	49	15	of	of	ADP
ejpam-4704	49	16	its	its	PRON
ejpam-4704	49	17	edges	edge	NOUN
ejpam-4704	49	18	is	be	AUX
ejpam-4704	49	19	3m−	3m−	NUM
ejpam-4704	49	20	3	3	NUM
ejpam-4704	50	1	[	[	X
ejpam-4704	50	2	2	2	NUM
ejpam-4704	50	3	]	]	PUNCT
ejpam-4704	50	4	.	.	PUNCT
ejpam-4704	50	5	b.	b.	PROPN
ejpam-4704	50	6	m.	m.	PROPN
ejpam-4704	50	7	sulaiman	sulaiman	PROPN
ejpam-4704	50	8	,	,	PUNCT
ejpam-4704	50	9	r.	r.	PROPN
ejpam-4704	50	10	s.	s.	PROPN
ejpam-4704	50	11	hasan	hasan	PROPN
ejpam-4704	50	12	,	,	PUNCT
ejpam-4704	50	13	r.	r.	PROPN
ejpam-4704	50	14	a.	a.	PROPN
ejpam-4704	50	15	mustafa	mustafa	PROPN
ejpam-4704	50	16	/	/	SYM
ejpam-4704	50	17	eur	eur	PROPN
ejpam-4704	50	18	.	.	PUNCT
ejpam-4704	51	1	j.	j.	PROPN
ejpam-4704	51	2	pure	pure	PROPN
ejpam-4704	51	3	appl	appl	PROPN
ejpam-4704	51	4	.	.	PROPN
ejpam-4704	51	5	math	math	PROPN
ejpam-4704	51	6	,	,	PUNCT
ejpam-4704	51	7	16	16	NUM
ejpam-4704	51	8	(	(	PUNCT
ejpam-4704	51	9	2	2	NUM
ejpam-4704	51	10	)	)	PUNCT
ejpam-4704	51	11	(	(	PUNCT
ejpam-4704	51	12	2023	2023	NUM
ejpam-4704	51	13	)	)	PUNCT
ejpam-4704	51	14	,	,	PUNCT
ejpam-4704	51	15	953	953	NUM
ejpam-4704	51	16	-	-	SYM
ejpam-4704	51	17	964	964	NUM
ejpam-4704	51	18	955	955	NUM
ejpam-4704	51	19	2.1.1	2.1.1	NUM
ejpam-4704	51	20	.	.	PUNCT
ejpam-4704	52	1	the	the	DET
ejpam-4704	52	2	basis	basis	NOUN
ejpam-4704	52	3	number	number	NOUN
ejpam-4704	52	4	for	for	ADP
ejpam-4704	52	5	mycielski	mycielski	NOUN
ejpam-4704	52	6	’s	’s	PART
ejpam-4704	52	7	graph	graph	NOUN
ejpam-4704	52	8	of	of	ADP
ejpam-4704	52	9	the	the	DET
ejpam-4704	52	10	cog	cog	NOUN
ejpam-4704	52	11	-	-	PUNCT
ejpam-4704	52	12	path	path	NOUN
ejpam-4704	52	13	µ(p	µ(p	PROPN
ejpam-4704	52	14	c	c	PROPN
ejpam-4704	52	15	m	m	VERB
ejpam-4704	52	16	)	)	PUNCT
ejpam-4704	52	17	let	let	VERB
ejpam-4704	52	18	the	the	DET
ejpam-4704	52	19	vertices	vertex	NOUN
ejpam-4704	52	20	of	of	ADP
ejpam-4704	52	21	the	the	DET
ejpam-4704	52	22	cog	cog	PROPN
ejpam-4704	52	23	path	path	NOUN
ejpam-4704	52	24	graph	graph	NOUN
ejpam-4704	52	25	p	p	PROPN
ejpam-4704	53	1	c	c	PROPN
ejpam-4704	53	2	m	m	NOUN
ejpam-4704	53	3	be	be	NOUN
ejpam-4704	53	4	u1	u1	NOUN
ejpam-4704	53	5	,	,	PUNCT
ejpam-4704	53	6	u2	u2	NOUN
ejpam-4704	53	7	,	,	PUNCT
ejpam-4704	53	8	u3	u3	NOUN
ejpam-4704	53	9	,	,	PUNCT
ejpam-4704	53	10	.	.	PUNCT
ejpam-4704	53	11	.	.	PUNCT
ejpam-4704	54	1	.	.	PUNCT
ejpam-4704	55	1	,	,	PUNCT
ejpam-4704	55	2	u2m−1	u2m−1	PROPN
ejpam-4704	55	3	and	and	CCONJ
ejpam-4704	55	4	the	the	DET
ejpam-4704	55	5	vertices	vertex	NOUN
ejpam-4704	55	6	opposite	opposite	ADJ
ejpam-4704	55	7	to	to	ADP
ejpam-4704	55	8	them	they	PRON
ejpam-4704	55	9	are	be	AUX
ejpam-4704	55	10	v1	v1	NOUN
ejpam-4704	55	11	,	,	PUNCT
ejpam-4704	55	12	v2	v2	PROPN
ejpam-4704	55	13	,	,	PUNCT
ejpam-4704	55	14	v3	v3	PROPN
ejpam-4704	55	15	,	,	PUNCT
ejpam-4704	55	16	.	.	PUNCT
ejpam-4704	55	17	.	.	PUNCT
ejpam-4704	56	1	.	.	PUNCT
ejpam-4704	57	1	,	,	PUNCT
ejpam-4704	57	2	v2m−1	v2m−1	PROPN
ejpam-4704	57	3	and	and	CCONJ
ejpam-4704	57	4	let	let	VERB
ejpam-4704	57	5	the	the	DET
ejpam-4704	57	6	other	other	ADJ
ejpam-4704	57	7	vertex	vertex	NOUN
ejpam-4704	57	8	be	be	AUX
ejpam-4704	57	9	w	w	PROPN
ejpam-4704	57	10	,	,	PUNCT
ejpam-4704	57	11	from	from	ADP
ejpam-4704	57	12	the	the	DET
ejpam-4704	57	13	definition	definition	NOUN
ejpam-4704	57	14	of	of	ADP
ejpam-4704	57	15	the	the	DET
ejpam-4704	57	16	mycielski	mycielski	NOUN
ejpam-4704	57	17	’s	’s	PART
ejpam-4704	57	18	graph	graph	NOUN
ejpam-4704	57	19	,	,	PUNCT
ejpam-4704	57	20	it	it	PRON
ejpam-4704	57	21	becomes	become	VERB
ejpam-4704	57	22	clear	clear	ADJ
ejpam-4704	57	23	that	that	SCONJ
ejpam-4704	57	24	the	the	DET
ejpam-4704	57	25	number	number	NOUN
ejpam-4704	57	26	of	of	ADP
ejpam-4704	57	27	vertices	vertex	NOUN
ejpam-4704	57	28	of	of	ADP
ejpam-4704	57	29	µ(p	µ(p	PROPN
ejpam-4704	57	30	c	c	PROPN
ejpam-4704	57	31	m	m	VERB
ejpam-4704	57	32	)	)	PUNCT
ejpam-4704	57	33	is	be	AUX
ejpam-4704	57	34	4	4	NUM
ejpam-4704	57	35	m	m	NOUN
ejpam-4704	57	36	−	−	NUM
ejpam-4704	57	37	1	1	NUM
ejpam-4704	57	38	and	and	CCONJ
ejpam-4704	57	39	the	the	DET
ejpam-4704	57	40	number	number	NOUN
ejpam-4704	57	41	of	of	ADP
ejpam-4704	57	42	its	its	PRON
ejpam-4704	57	43	edges	edge	NOUN
ejpam-4704	57	44	are	be	AUX
ejpam-4704	57	45	11m−	11m−	NUM
ejpam-4704	57	46	10	10	NUM
ejpam-4704	57	47	.	.	PUNCT
ejpam-4704	58	1	see	see	VERB
ejpam-4704	58	2	figure	figure	NOUN
ejpam-4704	58	3	(	(	PUNCT
ejpam-4704	58	4	2	2	NUM
ejpam-4704	58	5	)	)	PUNCT
ejpam-4704	58	6	.	.	PUNCT
ejpam-4704	59	1	figure	figure	NOUN
ejpam-4704	59	2	2	2	NUM
ejpam-4704	59	3	:	:	PUNCT
ejpam-4704	59	4	µ(p	µ(p	PROPN
ejpam-4704	59	5	c	c	PROPN
ejpam-4704	59	6	m	m	NOUN
ejpam-4704	59	7	)	)	PUNCT
ejpam-4704	59	8	theorem	theorem	NOUN
ejpam-4704	59	9	1	1	NUM
ejpam-4704	59	10	.	.	PUNCT
ejpam-4704	60	1	let	let	VERB
ejpam-4704	60	2	pm	pm	NOUN
ejpam-4704	60	3	be	be	AUX
ejpam-4704	60	4	a	a	DET
ejpam-4704	60	5	path	path	NOUN
ejpam-4704	60	6	of	of	ADP
ejpam-4704	60	7	order	order	NOUN
ejpam-4704	60	8	m	m	VERB
ejpam-4704	60	9	≥	≥	NUM
ejpam-4704	60	10	3	3	NUM
ejpam-4704	60	11	then	then	ADV
ejpam-4704	60	12	b	b	X
ejpam-4704	60	13	(	(	PUNCT
ejpam-4704	60	14	µ(p	µ(p	PROPN
ejpam-4704	60	15	c	c	PROPN
ejpam-4704	60	16	m	m	PROPN
ejpam-4704	60	17	)	)	PUNCT
ejpam-4704	60	18	)	)	PUNCT
ejpam-4704	61	1	=	=	SYM
ejpam-4704	62	1	3	3	NUM
ejpam-4704	62	2	proof	proof	NOUN
ejpam-4704	62	3	.	.	PUNCT
ejpam-4704	63	1	we	we	PRON
ejpam-4704	63	2	can	can	AUX
ejpam-4704	63	3	prove	prove	VERB
ejpam-4704	63	4	that	that	SCONJ
ejpam-4704	63	5	for	for	ADP
ejpam-4704	63	6	each	each	DET
ejpam-4704	63	7	m	m	PROPN
ejpam-4704	63	8	≥	≥	NOUN
ejpam-4704	63	9	3	3	NUM
ejpam-4704	63	10	,	,	PUNCT
ejpam-4704	63	11	there	there	PRON
ejpam-4704	63	12	is	be	VERB
ejpam-4704	63	13	a	a	DET
ejpam-4704	63	14	subgraph	subgraph	NOUN
ejpam-4704	63	15	of	of	ADP
ejpam-4704	63	16	µ(p	µ(p	PROPN
ejpam-4704	63	17	c	c	PROPN
ejpam-4704	63	18	m	m	PROPN
ejpam-4704	63	19	)	)	PUNCT
ejpam-4704	63	20	that	that	PRON
ejpam-4704	63	21	topologically	topologically	ADV
ejpam-4704	63	22	equivalent	equivalent	ADJ
ejpam-4704	63	23	k3,3	k3,3	PROPN
ejpam-4704	63	24	,	,	PUNCT
ejpam-4704	63	25	according	accord	VERB
ejpam-4704	63	26	to	to	ADP
ejpam-4704	63	27	kurtowski	kurtowski	PROPN
ejpam-4704	63	28	’s	’s	PART
ejpam-4704	63	29	theorem	theorem	NOUN
ejpam-4704	63	30	[	[	X
ejpam-4704	63	31	8	8	NUM
ejpam-4704	63	32	]	]	PUNCT
ejpam-4704	63	33	,	,	PUNCT
ejpam-4704	63	34	µ(p	µ(p	PROPN
ejpam-4704	63	35	c	c	PROPN
ejpam-4704	63	36	m	m	VERB
ejpam-4704	63	37	)	)	PUNCT
ejpam-4704	63	38	is	be	AUX
ejpam-4704	63	39	not	not	PART
ejpam-4704	63	40	planar	planar	ADJ
ejpam-4704	63	41	,	,	PUNCT
ejpam-4704	63	42	and	and	CCONJ
ejpam-4704	63	43	according	accord	VERB
ejpam-4704	63	44	to	to	ADP
ejpam-4704	63	45	mclean	mclean	PROPN
ejpam-4704	63	46	’s	’s	PART
ejpam-4704	63	47	theorem	theorem	NOUN
ejpam-4704	63	48	[	[	X
ejpam-4704	63	49	12	12	NUM
ejpam-4704	63	50	]	]	X
ejpam-4704	63	51	we	we	PRON
ejpam-4704	63	52	have	have	VERB
ejpam-4704	63	53	b	b	X
ejpam-4704	63	54	(	(	PUNCT
ejpam-4704	63	55	µ(p	µ(p	PROPN
ejpam-4704	63	56	c	c	PROPN
ejpam-4704	63	57	m	m	PROPN
ejpam-4704	63	58	)	)	PUNCT
ejpam-4704	63	59	)	)	PUNCT
ejpam-4704	63	60	≥	≥	NOUN
ejpam-4704	63	61	3	3	NUM
ejpam-4704	63	62	(	(	PUNCT
ejpam-4704	63	63	1	1	X
ejpam-4704	63	64	)	)	PUNCT
ejpam-4704	63	65	we	we	PRON
ejpam-4704	63	66	will	will	AUX
ejpam-4704	63	67	prove	prove	VERB
ejpam-4704	63	68	that	that	SCONJ
ejpam-4704	63	69	there	there	PRON
ejpam-4704	63	70	is	be	VERB
ejpam-4704	63	71	a	a	DET
ejpam-4704	63	72	base	base	NOUN
ejpam-4704	63	73	b	b	NOUN
ejpam-4704	63	74	for	for	ADP
ejpam-4704	63	75	the	the	DET
ejpam-4704	63	76	cycles	cycle	NOUN
ejpam-4704	63	77	space	space	NOUN
ejpam-4704	63	78	of	of	ADP
ejpam-4704	63	79	a	a	DET
ejpam-4704	63	80	graph	graph	NOUN
ejpam-4704	63	81	µ(p	µ(p	PROPN
ejpam-4704	63	82	c	c	NOUN
ejpam-4704	63	83	m	m	PROPN
ejpam-4704	63	84	)	)	PUNCT
ejpam-4704	63	85	with	with	ADP
ejpam-4704	63	86	3	3	NUM
ejpam-4704	63	87	-	-	NOUN
ejpam-4704	63	88	fold	fold	ADJ
ejpam-4704	63	89	.	.	PUNCT
ejpam-4704	64	1	let	let	VERB
ejpam-4704	64	2	b	b	X
ejpam-4704	64	3	be	be	AUX
ejpam-4704	64	4	a	a	DET
ejpam-4704	64	5	set	set	NOUN
ejpam-4704	64	6	of	of	ADP
ejpam-4704	64	7	cycles	cycle	NOUN
ejpam-4704	64	8	of	of	ADP
ejpam-4704	64	9	µ(p	µ(p	PROPN
ejpam-4704	64	10	c	c	PROPN
ejpam-4704	64	11	m	m	VERB
ejpam-4704	64	12	)	)	PUNCT
ejpam-4704	64	13	which	which	PRON
ejpam-4704	64	14	defined	define	VERB
ejpam-4704	64	15	by	by	ADP
ejpam-4704	64	16	the	the	DET
ejpam-4704	64	17	following	follow	VERB
ejpam-4704	64	18	formula	formula	NOUN
ejpam-4704	64	19	:	:	PUNCT
ejpam-4704	64	20	b	b	X
ejpam-4704	64	21	=	=	SYM
ejpam-4704	64	22	∪5	∪5	PROPN
ejpam-4704	64	23	j=1mj	j=1mj	PROPN
ejpam-4704	64	24	∪	∪	X
ejpam-4704	64	25	{	{	PUNCT
ejpam-4704	64	26	c	c	NOUN
ejpam-4704	64	27	}	}	PUNCT
ejpam-4704	64	28	,	,	PUNCT
ejpam-4704	64	29	where	where	SCONJ
ejpam-4704	64	30	m1	m1	PROPN
ejpam-4704	64	31	=	=	PRON
ejpam-4704	64	32	{	{	PUNCT
ejpam-4704	64	33	u2i−1u2i+1v2i−1u2iv2i+1u2i−1	u2i−1u2i+1v2i−1u2iv2i+1u2i−1	PROPN
ejpam-4704	64	34	:	:	PUNCT
ejpam-4704	64	35	i	i	NOUN
ejpam-4704	64	36	=	=	NOUN
ejpam-4704	64	37	1	1	NUM
ejpam-4704	64	38	,	,	PUNCT
ejpam-4704	64	39	2	2	NUM
ejpam-4704	64	40	,	,	PUNCT
ejpam-4704	64	41	3	3	NUM
ejpam-4704	64	42	,	,	PUNCT
ejpam-4704	64	43	.	.	PUNCT
ejpam-4704	64	44	.	.	PUNCT
ejpam-4704	65	1	.	.	PUNCT
ejpam-4704	66	1	,	,	PUNCT
ejpam-4704	66	2	m−	m−	PROPN
ejpam-4704	66	3	1	1	NUM
ejpam-4704	66	4	}	}	PUNCT
ejpam-4704	66	5	,	,	PUNCT
ejpam-4704	66	6	m2	m2	PROPN
ejpam-4704	66	7	=	=	PRON
ejpam-4704	66	8	{	{	PUNCT
ejpam-4704	66	9	wv2i−1u2i+1v2iw	wv2i−1u2i+1v2iw	NOUN
ejpam-4704	66	10	:	:	PUNCT
ejpam-4704	66	11	i	i	NOUN
ejpam-4704	66	12	=	=	NOUN
ejpam-4704	66	13	1	1	NUM
ejpam-4704	66	14	,	,	PUNCT
ejpam-4704	66	15	2	2	NUM
ejpam-4704	66	16	,	,	PUNCT
ejpam-4704	66	17	3	3	NUM
ejpam-4704	66	18	,	,	PUNCT
ejpam-4704	66	19	.	.	PUNCT
ejpam-4704	66	20	.	.	PUNCT
ejpam-4704	66	21	.	.	PUNCT
ejpam-4704	67	1	,	,	PUNCT
ejpam-4704	67	2	m−	m−	PROPN
ejpam-4704	67	3	1	1	NUM
ejpam-4704	67	4	}	}	PUNCT
ejpam-4704	67	5	,	,	PUNCT
ejpam-4704	67	6	m3	m3	PROPN
ejpam-4704	67	7	=	=	SYM
ejpam-4704	67	8	{	{	PUNCT
ejpam-4704	67	9	u2i−1u2iu2i+1u2i−1	u2i−1u2iu2i+1u2i−1	X
ejpam-4704	67	10	:	:	PUNCT
ejpam-4704	67	11	i	i	NOUN
ejpam-4704	67	12	=	=	NOUN
ejpam-4704	67	13	1	1	NUM
ejpam-4704	67	14	,	,	PUNCT
ejpam-4704	67	15	2	2	NUM
ejpam-4704	67	16	,	,	PUNCT
ejpam-4704	67	17	3	3	NUM
ejpam-4704	67	18	,	,	PUNCT
ejpam-4704	67	19	.	.	PUNCT
ejpam-4704	67	20	.	.	PUNCT
ejpam-4704	67	21	.	.	PUNCT
ejpam-4704	68	1	,	,	PUNCT
ejpam-4704	68	2	m−	m−	PROPN
ejpam-4704	68	3	1	1	NUM
ejpam-4704	68	4	}	}	PUNCT
ejpam-4704	68	5	,	,	PUNCT
ejpam-4704	68	6	m4	m4	PROPN
ejpam-4704	68	7	=	=	SYM
ejpam-4704	68	8	{	{	PUNCT
ejpam-4704	68	9	wviui+1vi+2w	wviui+1vi+2w	NOUN
ejpam-4704	68	10	:	:	PUNCT
ejpam-4704	68	11	i	i	NOUN
ejpam-4704	68	12	=	=	NOUN
ejpam-4704	68	13	1	1	NUM
ejpam-4704	68	14	,	,	PUNCT
ejpam-4704	68	15	2	2	NUM
ejpam-4704	68	16	,	,	PUNCT
ejpam-4704	68	17	3	3	NUM
ejpam-4704	68	18	,	,	PUNCT
ejpam-4704	68	19	.	.	PUNCT
ejpam-4704	68	20	.	.	PUNCT
ejpam-4704	68	21	.	.	PUNCT
ejpam-4704	69	1	,	,	PUNCT
ejpam-4704	69	2	2m−	2m−	PROPN
ejpam-4704	69	3	3	3	NUM
ejpam-4704	69	4	}	}	PUNCT
ejpam-4704	69	5	,	,	PUNCT
ejpam-4704	69	6	m5	m5	PROPN
ejpam-4704	69	7	=	=	PUNCT
ejpam-4704	69	8	{	{	PUNCT
ejpam-4704	69	9	uiui+1ui+2vi+1ui	uiui+1ui+2vi+1ui	PROPN
ejpam-4704	69	10	:	:	PUNCT
ejpam-4704	69	11	i	i	NOUN
ejpam-4704	69	12	=	=	NOUN
ejpam-4704	69	13	1	1	NUM
ejpam-4704	69	14	,	,	PUNCT
ejpam-4704	69	15	2	2	NUM
ejpam-4704	69	16	,	,	PUNCT
ejpam-4704	69	17	3	3	NUM
ejpam-4704	69	18	,	,	PUNCT
ejpam-4704	69	19	.	.	PUNCT
ejpam-4704	69	20	.	.	PUNCT
ejpam-4704	69	21	.	.	PUNCT
ejpam-4704	70	1	,	,	PUNCT
ejpam-4704	70	2	2m−	2m−	PROPN
ejpam-4704	70	3	3	3	NUM
ejpam-4704	70	4	}	}	PUNCT
ejpam-4704	70	5	,	,	PUNCT
ejpam-4704	70	6	c	c	X
ejpam-4704	70	7	=	=	PRON
ejpam-4704	70	8	{	{	PUNCT
ejpam-4704	70	9	wv1u2u1v2w	wv1u2u1v2w	NOUN
ejpam-4704	70	10	}	}	PUNCT
ejpam-4704	70	11	.	.	PUNCT
ejpam-4704	71	1	b.	b.	PROPN
ejpam-4704	71	2	m.	m.	PROPN
ejpam-4704	71	3	sulaiman	sulaiman	PROPN
ejpam-4704	71	4	,	,	PUNCT
ejpam-4704	71	5	r.	r.	PROPN
ejpam-4704	71	6	s.	s.	PROPN
ejpam-4704	71	7	hasan	hasan	PROPN
ejpam-4704	71	8	,	,	PUNCT
ejpam-4704	71	9	r.	r.	PROPN
ejpam-4704	71	10	a.	a.	PROPN
ejpam-4704	71	11	mustafa	mustafa	PROPN
ejpam-4704	71	12	/	/	SYM
ejpam-4704	71	13	eur	eur	PROPN
ejpam-4704	71	14	.	.	PUNCT
ejpam-4704	72	1	j.	j.	PROPN
ejpam-4704	72	2	pure	pure	PROPN
ejpam-4704	72	3	appl	appl	PROPN
ejpam-4704	72	4	.	.	PROPN
ejpam-4704	72	5	math	math	PROPN
ejpam-4704	72	6	,	,	PUNCT
ejpam-4704	72	7	16	16	NUM
ejpam-4704	72	8	(	(	PUNCT
ejpam-4704	72	9	2	2	NUM
ejpam-4704	72	10	)	)	PUNCT
ejpam-4704	72	11	(	(	PUNCT
ejpam-4704	72	12	2023	2023	NUM
ejpam-4704	72	13	)	)	PUNCT
ejpam-4704	72	14	,	,	PUNCT
ejpam-4704	72	15	953	953	NUM
ejpam-4704	72	16	-	-	SYM
ejpam-4704	72	17	964	964	NUM
ejpam-4704	72	18	956	956	NUM
ejpam-4704	72	19	in	in	ADP
ejpam-4704	72	20	order	order	NOUN
ejpam-4704	72	21	b	b	NOUN
ejpam-4704	72	22	to	to	PART
ejpam-4704	72	23	be	be	AUX
ejpam-4704	72	24	the	the	DET
ejpam-4704	72	25	base	base	NOUN
ejpam-4704	72	26	for	for	ADP
ejpam-4704	72	27	the	the	DET
ejpam-4704	72	28	cycles	cycle	NOUN
ejpam-4704	72	29	space	space	NOUN
ejpam-4704	72	30	of	of	ADP
ejpam-4704	72	31	the	the	DET
ejpam-4704	72	32	graph	graph	NOUN
ejpam-4704	72	33	µ(p	µ(p	PROPN
ejpam-4704	72	34	c	c	PROPN
ejpam-4704	72	35	m	m	PROPN
ejpam-4704	72	36	)	)	PUNCT
ejpam-4704	72	37	,	,	PUNCT
ejpam-4704	72	38	it	it	PRON
ejpam-4704	72	39	must	must	AUX
ejpam-4704	72	40	be	be	AUX
ejpam-4704	72	41	|b|	|b|	PROPN
ejpam-4704	72	42	=	=	PUNCT
ejpam-4704	72	43	dimc(µ(p	dimc(µ(p	PROPN
ejpam-4704	72	44	c	c	NOUN
ejpam-4704	72	45	m	m	NOUN
ejpam-4704	72	46	)	)	PUNCT
ejpam-4704	72	47	)	)	PUNCT
ejpam-4704	73	1	and	and	CCONJ
ejpam-4704	73	2	b	b	NOUN
ejpam-4704	73	3	must	must	AUX
ejpam-4704	73	4	be	be	AUX
ejpam-4704	73	5	a	a	DET
ejpam-4704	73	6	linearly	linearly	ADV
ejpam-4704	73	7	independent	independent	ADJ
ejpam-4704	73	8	set	set	NOUN
ejpam-4704	73	9	.	.	PUNCT
ejpam-4704	74	1	it	it	PRON
ejpam-4704	74	2	is	be	AUX
ejpam-4704	74	3	known	know	VERB
ejpam-4704	74	4	that	that	SCONJ
ejpam-4704	74	5	dimc(µ(p	dimc(µ(p	NOUN
ejpam-4704	74	6	c	c	PROPN
ejpam-4704	74	7	m	m	NOUN
ejpam-4704	74	8	)	)	PUNCT
ejpam-4704	74	9	)	)	PUNCT
ejpam-4704	75	1	=	=	PUNCT
ejpam-4704	76	1	7m−	7m−	NUM
ejpam-4704	76	2	8	8	NUM
ejpam-4704	76	3	|b|	|b|	PROPN
ejpam-4704	76	4	=	=	PUNCT
ejpam-4704	77	1	|	|	ADV
ejpam-4704	77	2	∪5	∪5	PROPN
ejpam-4704	77	3	j=1	j=1	PROPN
ejpam-4704	77	4	mj	mj	PROPN
ejpam-4704	77	5	|+	|+	NOUN
ejpam-4704	77	6	1	1	NUM
ejpam-4704	77	7	=	=	SYM
ejpam-4704	77	8	3(m−	3(m−	PROPN
ejpam-4704	77	9	1	1	NUM
ejpam-4704	77	10	)	)	PUNCT
ejpam-4704	77	11	+	+	CCONJ
ejpam-4704	78	1	2(2m−	2(2m−	NUM
ejpam-4704	78	2	3	3	NUM
ejpam-4704	78	3	)	)	PUNCT
ejpam-4704	78	4	+	+	CCONJ
ejpam-4704	78	5	1	1	NUM
ejpam-4704	78	6	=	=	SYM
ejpam-4704	78	7	7m−	7m−	NUM
ejpam-4704	78	8	8	8	NUM
ejpam-4704	78	9	.	.	PUNCT
ejpam-4704	79	1	it	it	PRON
ejpam-4704	79	2	remains	remain	VERB
ejpam-4704	79	3	to	to	PART
ejpam-4704	79	4	show	show	VERB
ejpam-4704	79	5	that	that	SCONJ
ejpam-4704	79	6	b	b	NOUN
ejpam-4704	79	7	is	be	AUX
ejpam-4704	79	8	linearly	linearly	ADV
ejpam-4704	79	9	independent	independent	ADJ
ejpam-4704	79	10	cycles	cycle	NOUN
ejpam-4704	79	11	.	.	PUNCT
ejpam-4704	80	1	clearly	clearly	ADV
ejpam-4704	80	2	that	that	SCONJ
ejpam-4704	80	3	the	the	DET
ejpam-4704	80	4	cycles	cycle	NOUN
ejpam-4704	80	5	of	of	ADP
ejpam-4704	80	6	each	each	DET
ejpam-4704	80	7	m1,m2	m1,m2	PROPN
ejpam-4704	80	8	and	and	CCONJ
ejpam-4704	80	9	m3	m3	PROPN
ejpam-4704	80	10	are	be	AUX
ejpam-4704	80	11	independent	independent	ADJ
ejpam-4704	80	12	because	because	SCONJ
ejpam-4704	80	13	they	they	PRON
ejpam-4704	80	14	are	be	AUX
ejpam-4704	80	15	separate	separate	ADJ
ejpam-4704	80	16	cycles	cycle	NOUN
ejpam-4704	80	17	with	with	ADP
ejpam-4704	80	18	respect	respect	NOUN
ejpam-4704	80	19	to	to	ADP
ejpam-4704	80	20	edges	edge	NOUN
ejpam-4704	80	21	;	;	PUNCT
ejpam-4704	80	22	and	and	CCONJ
ejpam-4704	80	23	the	the	DET
ejpam-4704	80	24	cycles	cycle	NOUN
ejpam-4704	80	25	of	of	ADP
ejpam-4704	80	26	each	each	DET
ejpam-4704	80	27	m4	m4	PROPN
ejpam-4704	80	28	and	and	CCONJ
ejpam-4704	80	29	m5	m5	NOUN
ejpam-4704	80	30	are	be	AUX
ejpam-4704	80	31	independent	independent	ADJ
ejpam-4704	80	32	because	because	SCONJ
ejpam-4704	80	33	it	it	PRON
ejpam-4704	80	34	is	be	AUX
ejpam-4704	80	35	represent	represent	VERB
ejpam-4704	80	36	the	the	DET
ejpam-4704	80	37	boundaries	boundary	NOUN
ejpam-4704	80	38	of	of	ADP
ejpam-4704	80	39	the	the	DET
ejpam-4704	80	40	faces	face	NOUN
ejpam-4704	80	41	of	of	ADP
ejpam-4704	80	42	a	a	DET
ejpam-4704	80	43	planar	planar	ADJ
ejpam-4704	80	44	subgraph	subgraph	NOUN
ejpam-4704	80	45	.	.	PUNCT
ejpam-4704	81	1	now	now	ADV
ejpam-4704	81	2	;	;	PUNCT
ejpam-4704	81	3	the	the	DET
ejpam-4704	81	4	cycle	cycle	NOUN
ejpam-4704	81	5	c	c	PROPN
ejpam-4704	81	6	is	be	AUX
ejpam-4704	81	7	independent	independent	ADJ
ejpam-4704	81	8	of	of	ADP
ejpam-4704	81	9	m5	m5	NOUN
ejpam-4704	81	10	because	because	SCONJ
ejpam-4704	81	11	contains	contain	VERB
ejpam-4704	81	12	the	the	DET
ejpam-4704	81	13	edges	edge	NOUN
ejpam-4704	81	14	wv1	wv1	ADV
ejpam-4704	81	15	and	and	CCONJ
ejpam-4704	81	16	wv2	wv2	NOUN
ejpam-4704	82	1	but	but	CCONJ
ejpam-4704	82	2	these	these	DET
ejpam-4704	82	3	edges	edge	NOUN
ejpam-4704	82	4	are	be	AUX
ejpam-4704	82	5	not	not	PART
ejpam-4704	82	6	available	available	ADJ
ejpam-4704	82	7	in	in	ADP
ejpam-4704	82	8	any	any	DET
ejpam-4704	82	9	linear	linear	ADJ
ejpam-4704	82	10	combination	combination	NOUN
ejpam-4704	82	11	of	of	ADP
ejpam-4704	82	12	cycle	cycle	NOUN
ejpam-4704	82	13	m5	m5	NOUN
ejpam-4704	82	14	,	,	PUNCT
ejpam-4704	82	15	hence	hence	ADV
ejpam-4704	82	16	m5	m5	NOUN
ejpam-4704	82	17	∪	∪	ADJ
ejpam-4704	82	18	{	{	PUNCT
ejpam-4704	82	19	c	c	NOUN
ejpam-4704	82	20	}	}	PUNCT
ejpam-4704	82	21	is	be	AUX
ejpam-4704	82	22	linearly	linearly	ADV
ejpam-4704	82	23	independent	independent	ADJ
ejpam-4704	82	24	.	.	PUNCT
ejpam-4704	83	1	also	also	ADV
ejpam-4704	83	2	,	,	PUNCT
ejpam-4704	83	3	any	any	DET
ejpam-4704	83	4	linear	linear	ADJ
ejpam-4704	83	5	combination	combination	NOUN
ejpam-4704	83	6	of	of	ADP
ejpam-4704	83	7	m5∪{c	m5∪{c	PROPN
ejpam-4704	83	8	}	}	PUNCT
ejpam-4704	83	9	contains	contain	VERB
ejpam-4704	83	10	the	the	DET
ejpam-4704	83	11	edges	edge	NOUN
ejpam-4704	83	12	of	of	ADP
ejpam-4704	83	13	type	type	NOUN
ejpam-4704	83	14	ui	ui	PROPN
ejpam-4704	83	15	ui+1,i	ui+1,i	NOUN
ejpam-4704	83	16	=	=	SYM
ejpam-4704	83	17	1	1	NUM
ejpam-4704	83	18	,	,	PUNCT
ejpam-4704	83	19	2	2	NUM
ejpam-4704	83	20	,	,	PUNCT
ejpam-4704	83	21	.	.	PUNCT
ejpam-4704	83	22	.	.	PUNCT
ejpam-4704	84	1	.	.	PUNCT
ejpam-4704	85	1	,	,	PUNCT
ejpam-4704	85	2	2	2	NUM
ejpam-4704	85	3	m	m	NOUN
ejpam-4704	85	4	−	−	NUM
ejpam-4704	85	5	2	2	NUM
ejpam-4704	85	6	and	and	CCONJ
ejpam-4704	85	7	these	these	DET
ejpam-4704	85	8	edges	edge	NOUN
ejpam-4704	85	9	are	be	AUX
ejpam-4704	85	10	not	not	PART
ejpam-4704	85	11	available	available	ADJ
ejpam-4704	85	12	in	in	ADP
ejpam-4704	85	13	any	any	DET
ejpam-4704	85	14	linear	linear	ADJ
ejpam-4704	85	15	combination	combination	NOUN
ejpam-4704	85	16	of	of	ADP
ejpam-4704	85	17	cycle	cycle	NOUN
ejpam-4704	85	18	m4	m4	PROPN
ejpam-4704	85	19	,	,	PUNCT
ejpam-4704	85	20	therefore	therefore	ADV
ejpam-4704	85	21	m5	m5	NOUN
ejpam-4704	85	22	∪	∪	ADJ
ejpam-4704	85	23	{	{	PUNCT
ejpam-4704	85	24	c	c	NOUN
ejpam-4704	85	25	}	}	PUNCT
ejpam-4704	85	26	∪m4	∪m4	ADV
ejpam-4704	85	27	is	be	AUX
ejpam-4704	85	28	linearly	linearly	ADV
ejpam-4704	85	29	independent	independent	ADJ
ejpam-4704	85	30	.	.	PUNCT
ejpam-4704	86	1	further	far	ADV
ejpam-4704	86	2	more	more	ADV
ejpam-4704	86	3	m4	m4	PROPN
ejpam-4704	86	4	∪m5	∪m5	NOUN
ejpam-4704	86	5	∪	∪	X
ejpam-4704	86	6	{	{	PUNCT
ejpam-4704	86	7	c}∪m3	c}∪m3	NOUN
ejpam-4704	86	8	are	be	AUX
ejpam-4704	86	9	independent	independent	ADJ
ejpam-4704	86	10	set	set	NOUN
ejpam-4704	86	11	of	of	ADP
ejpam-4704	86	12	cycles	cycle	NOUN
ejpam-4704	86	13	since	since	SCONJ
ejpam-4704	86	14	any	any	DET
ejpam-4704	86	15	linear	linear	ADJ
ejpam-4704	86	16	combination	combination	NOUN
ejpam-4704	86	17	of	of	ADP
ejpam-4704	86	18	cycles	cycle	NOUN
ejpam-4704	86	19	m3	m3	PROPN
ejpam-4704	86	20	contains	contain	VERB
ejpam-4704	86	21	the	the	DET
ejpam-4704	86	22	edges	edge	NOUN
ejpam-4704	86	23	of	of	ADP
ejpam-4704	86	24	type	type	NOUN
ejpam-4704	86	25	u2i−1	u2i−1	PROPN
ejpam-4704	86	26	u2i+1	u2i+1	PROPN
ejpam-4704	86	27	,	,	PUNCT
ejpam-4704	86	28	i	i	PRON
ejpam-4704	86	29	=	=	NOUN
ejpam-4704	86	30	1	1	NUM
ejpam-4704	86	31	,	,	PUNCT
ejpam-4704	86	32	2	2	NUM
ejpam-4704	86	33	,	,	PUNCT
ejpam-4704	86	34	.	.	PUNCT
ejpam-4704	86	35	.	.	PUNCT
ejpam-4704	87	1	.	.	PUNCT
ejpam-4704	88	1	,	,	PUNCT
ejpam-4704	88	2	m	m	AUX
ejpam-4704	88	3	−	−	NOUN
ejpam-4704	88	4	1	1	NUM
ejpam-4704	88	5	and	and	CCONJ
ejpam-4704	88	6	these	these	DET
ejpam-4704	88	7	edges	edge	NOUN
ejpam-4704	88	8	are	be	AUX
ejpam-4704	88	9	not	not	PART
ejpam-4704	88	10	available	available	ADJ
ejpam-4704	88	11	in	in	ADP
ejpam-4704	88	12	m4	m4	PROPN
ejpam-4704	88	13	∪m5	∪m5	PROPN
ejpam-4704	88	14	∪{c}.also	∪{c}.also	PROPN
ejpam-4704	88	15	,	,	PUNCT
ejpam-4704	88	16	m3	m3	PROPN
ejpam-4704	88	17	∪m4	∪m4	PROPN
ejpam-4704	88	18	∪m5	∪m5	PROPN
ejpam-4704	88	19	∪{c}∪m2	∪{c}∪m2	PROPN
ejpam-4704	88	20	are	be	AUX
ejpam-4704	88	21	independent	independent	ADJ
ejpam-4704	88	22	set	set	NOUN
ejpam-4704	88	23	of	of	ADP
ejpam-4704	88	24	cycles	cycle	NOUN
ejpam-4704	88	25	because	because	SCONJ
ejpam-4704	88	26	m2	m2	PROPN
ejpam-4704	88	27	contains	contain	VERB
ejpam-4704	88	28	the	the	DET
ejpam-4704	88	29	edges	edge	NOUN
ejpam-4704	88	30	of	of	ADP
ejpam-4704	88	31	type	type	NOUN
ejpam-4704	88	32	v2i−1	v2i−1	PROPN
ejpam-4704	88	33	u2i+1	u2i+1	NOUN
ejpam-4704	88	34	,	,	PUNCT
ejpam-4704	88	35	i	i	PRON
ejpam-4704	88	36	=	=	NOUN
ejpam-4704	88	37	1	1	NUM
ejpam-4704	88	38	,	,	PUNCT
ejpam-4704	88	39	2	2	NUM
ejpam-4704	88	40	,	,	PUNCT
ejpam-4704	88	41	.	.	PUNCT
ejpam-4704	88	42	.	.	PUNCT
ejpam-4704	89	1	.	.	PUNCT
ejpam-4704	90	1	,	,	PUNCT
ejpam-4704	90	2	m−	m−	PROPN
ejpam-4704	90	3	1	1	NUM
ejpam-4704	90	4	but	but	CCONJ
ejpam-4704	90	5	these	these	DET
ejpam-4704	90	6	edges	edge	NOUN
ejpam-4704	90	7	are	be	AUX
ejpam-4704	90	8	not	not	PART
ejpam-4704	90	9	available	available	ADJ
ejpam-4704	90	10	in	in	ADP
ejpam-4704	90	11	m3	m3	PROPN
ejpam-4704	90	12	∪m4	∪m4	PROPN
ejpam-4704	90	13	∪m5	∪m5	PROPN
ejpam-4704	90	14	∪	∪	X
ejpam-4704	90	15	{	{	PUNCT
ejpam-4704	90	16	c	c	NOUN
ejpam-4704	90	17	}	}	PUNCT
ejpam-4704	90	18	.	.	PUNCT
ejpam-4704	91	1	finally	finally	ADV
ejpam-4704	91	2	;	;	PUNCT
ejpam-4704	91	3	the	the	DET
ejpam-4704	91	4	cycles	cycle	NOUN
ejpam-4704	91	5	of	of	ADP
ejpam-4704	91	6	the	the	DET
ejpam-4704	91	7	set	set	NOUN
ejpam-4704	91	8	b	b	PROPN
ejpam-4704	91	9	=	=	SYM
ejpam-4704	91	10	∪5	∪5	PROPN
ejpam-4704	91	11	j=1mj	j=1mj	PROPN
ejpam-4704	91	12	∪	∪	X
ejpam-4704	91	13	{	{	PUNCT
ejpam-4704	91	14	c	c	NOUN
ejpam-4704	91	15	}	}	PUNCT
ejpam-4704	91	16	are	be	AUX
ejpam-4704	91	17	independent	independent	ADJ
ejpam-4704	91	18	since	since	SCONJ
ejpam-4704	91	19	any	any	DET
ejpam-4704	91	20	linear	linear	ADJ
ejpam-4704	91	21	combination	combination	NOUN
ejpam-4704	91	22	of	of	ADP
ejpam-4704	91	23	cycles	cycle	NOUN
ejpam-4704	91	24	m1	m1	PROPN
ejpam-4704	91	25	contains	contain	VERB
ejpam-4704	91	26	the	the	DET
ejpam-4704	91	27	edges	edge	NOUN
ejpam-4704	91	28	of	of	ADP
ejpam-4704	91	29	type	type	NOUN
ejpam-4704	91	30	u2i−1v2i+1	u2i−1v2i+1	NOUN
ejpam-4704	91	31	,	,	PUNCT
ejpam-4704	91	32	i	i	PRON
ejpam-4704	91	33	=	=	NOUN
ejpam-4704	91	34	1	1	NUM
ejpam-4704	91	35	,	,	PUNCT
ejpam-4704	91	36	2	2	NUM
ejpam-4704	91	37	,	,	PUNCT
ejpam-4704	91	38	.	.	PUNCT
ejpam-4704	91	39	.	.	PUNCT
ejpam-4704	92	1	.	.	PUNCT
ejpam-4704	93	1	,	,	PUNCT
ejpam-4704	93	2	m	m	VERB
ejpam-4704	93	3	−	−	NOUN
ejpam-4704	93	4	1	1	NUM
ejpam-4704	93	5	while	while	SCONJ
ejpam-4704	93	6	these	these	DET
ejpam-4704	93	7	edges	edge	NOUN
ejpam-4704	93	8	are	be	AUX
ejpam-4704	93	9	not	not	PART
ejpam-4704	93	10	available	available	ADJ
ejpam-4704	93	11	in	in	ADP
ejpam-4704	93	12	any	any	DET
ejpam-4704	93	13	linear	linear	ADJ
ejpam-4704	93	14	combination	combination	NOUN
ejpam-4704	93	15	of	of	ADP
ejpam-4704	93	16	cycles	cycle	NOUN
ejpam-4704	93	17	m2∪m3∪m4∪m5∪{c	m2∪m3∪m4∪m5∪{c	NOUN
ejpam-4704	93	18	}	}	PUNCT
ejpam-4704	93	19	.	.	PUNCT
ejpam-4704	94	1	to	to	PART
ejpam-4704	94	2	find	find	VERB
ejpam-4704	94	3	the	the	DET
ejpam-4704	94	4	fold	fold	NOUN
ejpam-4704	94	5	for	for	ADP
ejpam-4704	94	6	base	base	NOUN
ejpam-4704	94	7	b	b	NOUN
ejpam-4704	94	8	,	,	PUNCT
ejpam-4704	94	9	we	we	PRON
ejpam-4704	94	10	divide	divide	VERB
ejpam-4704	94	11	the	the	DET
ejpam-4704	94	12	edges	edge	NOUN
ejpam-4704	94	13	of	of	ADP
ejpam-4704	94	14	the	the	DET
ejpam-4704	94	15	graph	graph	NOUN
ejpam-4704	94	16	µ(p	µ(p	PROPN
ejpam-4704	94	17	c	c	PROPN
ejpam-4704	94	18	m	m	PROPN
ejpam-4704	94	19	)	)	PUNCT
ejpam-4704	94	20	into	into	ADP
ejpam-4704	94	21	:	:	PUNCT
ejpam-4704	94	22	e1	e1	NOUN
ejpam-4704	94	23	=	=	SYM
ejpam-4704	94	24	{	{	PUNCT
ejpam-4704	94	25	uiui+1	uiui+1	NOUN
ejpam-4704	94	26	:	:	PUNCT
ejpam-4704	95	1	i	i	NOUN
ejpam-4704	95	2	=	=	NOUN
ejpam-4704	95	3	1	1	NUM
ejpam-4704	95	4	,	,	PUNCT
ejpam-4704	95	5	2	2	NUM
ejpam-4704	95	6	,	,	PUNCT
ejpam-4704	95	7	.	.	PUNCT
ejpam-4704	95	8	.	.	PUNCT
ejpam-4704	95	9	.	.	PUNCT
ejpam-4704	96	1	,	,	PUNCT
ejpam-4704	96	2	2m−	2m−	NOUN
ejpam-4704	96	3	2	2	NUM
ejpam-4704	96	4	}	}	PUNCT
ejpam-4704	96	5	e2	e2	NOUN
ejpam-4704	96	6	=	=	SYM
ejpam-4704	96	7	{	{	PUNCT
ejpam-4704	96	8	uivi+1	uivi+1	INTJ
ejpam-4704	96	9	:	:	PUNCT
ejpam-4704	96	10	i	i	NOUN
ejpam-4704	96	11	=	=	NOUN
ejpam-4704	96	12	1	1	NUM
ejpam-4704	96	13	,	,	PUNCT
ejpam-4704	96	14	2	2	NUM
ejpam-4704	96	15	,	,	PUNCT
ejpam-4704	96	16	.	.	PUNCT
ejpam-4704	96	17	.	.	PUNCT
ejpam-4704	96	18	.	.	PUNCT
ejpam-4704	97	1	,	,	PUNCT
ejpam-4704	97	2	2m−	2m−	PROPN
ejpam-4704	97	3	2	2	NUM
ejpam-4704	97	4	}	}	PUNCT
ejpam-4704	97	5	e3	e3	NOUN
ejpam-4704	97	6	=	=	SYM
ejpam-4704	97	7	{	{	PUNCT
ejpam-4704	97	8	v2i−1u2i	v2i−1u2i	NOUN
ejpam-4704	97	9	:	:	PUNCT
ejpam-4704	97	10	i	i	NOUN
ejpam-4704	97	11	=	=	NOUN
ejpam-4704	97	12	1	1	NUM
ejpam-4704	97	13	,	,	PUNCT
ejpam-4704	97	14	2	2	NUM
ejpam-4704	97	15	,	,	PUNCT
ejpam-4704	97	16	.	.	PUNCT
ejpam-4704	97	17	.	.	PUNCT
ejpam-4704	97	18	.	.	PUNCT
ejpam-4704	98	1	,	,	PUNCT
ejpam-4704	98	2	m−	m−	PROPN
ejpam-4704	98	3	1	1	NUM
ejpam-4704	98	4	}	}	PUNCT
ejpam-4704	98	5	e4	e4	PROPN
ejpam-4704	98	6	=	=	SYM
ejpam-4704	98	7	{	{	PUNCT
ejpam-4704	98	8	v2iu2i+1	v2iu2i+1	NOUN
ejpam-4704	98	9	:	:	PUNCT
ejpam-4704	98	10	i	i	NOUN
ejpam-4704	98	11	=	=	NOUN
ejpam-4704	98	12	1	1	NUM
ejpam-4704	98	13	,	,	PUNCT
ejpam-4704	98	14	2	2	NUM
ejpam-4704	98	15	,	,	PUNCT
ejpam-4704	98	16	.	.	PUNCT
ejpam-4704	98	17	.	.	PUNCT
ejpam-4704	98	18	.	.	PUNCT
ejpam-4704	99	1	,	,	PUNCT
ejpam-4704	99	2	m−	m−	PROPN
ejpam-4704	99	3	1	1	NUM
ejpam-4704	99	4	}	}	PUNCT
ejpam-4704	99	5	e5	e5	NOUN
ejpam-4704	99	6	=	=	PUNCT
ejpam-4704	99	7	{	{	PUNCT
ejpam-4704	99	8	wvi	wvi	NOUN
ejpam-4704	99	9	:	:	PUNCT
ejpam-4704	99	10	i	i	NOUN
ejpam-4704	99	11	=	=	NOUN
ejpam-4704	99	12	1	1	NUM
ejpam-4704	99	13	,	,	PUNCT
ejpam-4704	99	14	2	2	NUM
ejpam-4704	99	15	,	,	PUNCT
ejpam-4704	99	16	.	.	PUNCT
ejpam-4704	99	17	.	.	PUNCT
ejpam-4704	99	18	.	.	PUNCT
ejpam-4704	100	1	,	,	PUNCT
ejpam-4704	100	2	2m−	2m−	PROPN
ejpam-4704	100	3	1	1	NUM
ejpam-4704	100	4	}	}	PUNCT
ejpam-4704	100	5	e6	e6	NOUN
ejpam-4704	100	6	=	=	SYM
ejpam-4704	100	7	{	{	PUNCT
ejpam-4704	100	8	u2i−1u2i+1	u2i−1u2i+1	NOUN
ejpam-4704	100	9	:	:	PUNCT
ejpam-4704	101	1	i	i	NOUN
ejpam-4704	101	2	=	=	NOUN
ejpam-4704	101	3	1	1	NUM
ejpam-4704	101	4	,	,	PUNCT
ejpam-4704	101	5	2	2	NUM
ejpam-4704	101	6	,	,	PUNCT
ejpam-4704	101	7	.	.	PUNCT
ejpam-4704	101	8	.	.	PUNCT
ejpam-4704	101	9	.	.	PUNCT
ejpam-4704	102	1	,	,	PUNCT
ejpam-4704	102	2	m−	m−	PROPN
ejpam-4704	102	3	1	1	NUM
ejpam-4704	102	4	}	}	PUNCT
ejpam-4704	102	5	e7	e7	PROPN
ejpam-4704	102	6	=	=	PUNCT
ejpam-4704	102	7	{	{	PUNCT
ejpam-4704	102	8	u2i−1v2i+1	u2i−1v2i+1	NOUN
ejpam-4704	102	9	:	:	PUNCT
ejpam-4704	102	10	i	i	NOUN
ejpam-4704	102	11	=	=	NOUN
ejpam-4704	102	12	1	1	NUM
ejpam-4704	102	13	,	,	PUNCT
ejpam-4704	102	14	2	2	NUM
ejpam-4704	102	15	,	,	PUNCT
ejpam-4704	102	16	.	.	PUNCT
ejpam-4704	102	17	.	.	PUNCT
ejpam-4704	102	18	.	.	PUNCT
ejpam-4704	103	1	,	,	PUNCT
ejpam-4704	103	2	m−	m−	PROPN
ejpam-4704	103	3	1	1	NUM
ejpam-4704	103	4	}	}	PUNCT
ejpam-4704	103	5	e8	e8	PROPN
ejpam-4704	103	6	=	=	X
ejpam-4704	103	7	{	{	PUNCT
ejpam-4704	103	8	v2i−1u2i+1	v2i−1u2i+1	ADV
ejpam-4704	103	9	:	:	PUNCT
ejpam-4704	103	10	i	i	NOUN
ejpam-4704	103	11	=	=	NOUN
ejpam-4704	103	12	1	1	NUM
ejpam-4704	103	13	,	,	PUNCT
ejpam-4704	103	14	2	2	NUM
ejpam-4704	103	15	,	,	PUNCT
ejpam-4704	103	16	.	.	PUNCT
ejpam-4704	103	17	.	.	PUNCT
ejpam-4704	103	18	.	.	PUNCT
ejpam-4704	104	1	,	,	PUNCT
ejpam-4704	104	2	m−	m−	PROPN
ejpam-4704	104	3	1	1	NUM
ejpam-4704	104	4	}	}	PUNCT
ejpam-4704	104	5	now	now	ADV
ejpam-4704	104	6	,	,	PUNCT
ejpam-4704	104	7	we	we	PRON
ejpam-4704	104	8	calculate	calculate	VERB
ejpam-4704	104	9	the	the	DET
ejpam-4704	104	10	fold	fold	NOUN
ejpam-4704	104	11	for	for	ADP
ejpam-4704	104	12	a	a	DET
ejpam-4704	104	13	set	set	NOUN
ejpam-4704	104	14	of	of	ADP
ejpam-4704	104	15	the	the	DET
ejpam-4704	104	16	edges	edge	NOUN
ejpam-4704	104	17	of	of	ADP
ejpam-4704	104	18	the	the	DET
ejpam-4704	104	19	graph	graph	NOUN
ejpam-4704	104	20	µ(p	µ(p	PROPN
ejpam-4704	104	21	c	c	PROPN
ejpam-4704	104	22	m	m	PROPN
ejpam-4704	104	23	)	)	PUNCT
ejpam-4704	104	24	,	,	PUNCT
ejpam-4704	104	25	case	case	NOUN
ejpam-4704	105	1	i	i	PRON
ejpam-4704	105	2	:	:	PUNCT
ejpam-4704	105	3	fb(µ(p	fb(µ(p	PROPN
ejpam-4704	105	4	c	c	NOUN
ejpam-4704	105	5	m)(e	m)(e	NOUN
ejpam-4704	105	6	)	)	PUNCT
ejpam-4704	105	7	is	be	AUX
ejpam-4704	105	8	less	less	ADJ
ejpam-4704	105	9	than	than	ADP
ejpam-4704	105	10	or	or	CCONJ
ejpam-4704	105	11	equal	equal	ADJ
ejpam-4704	105	12	to	to	ADP
ejpam-4704	105	13	1	1	NUM
ejpam-4704	105	14	when	when	SCONJ
ejpam-4704	105	15	e	e	PROPN
ejpam-4704	105	16	∈	∈	PROPN
ejpam-4704	105	17	e7	e7	PROPN
ejpam-4704	105	18	.	.	PUNCT
ejpam-4704	106	1	case	case	NOUN
ejpam-4704	106	2	ii	ii	PROPN
ejpam-4704	106	3	:	:	PUNCT
ejpam-4704	106	4	fb(µ(p	fb(µ(p	PROPN
ejpam-4704	106	5	c	c	NOUN
ejpam-4704	106	6	m)(e	m)(e	NOUN
ejpam-4704	106	7	)	)	PUNCT
ejpam-4704	106	8	is	be	AUX
ejpam-4704	106	9	less	less	ADJ
ejpam-4704	106	10	than	than	ADP
ejpam-4704	106	11	or	or	CCONJ
ejpam-4704	106	12	equal	equal	ADJ
ejpam-4704	106	13	to	to	ADP
ejpam-4704	106	14	2	2	NUM
ejpam-4704	106	15	for	for	ADP
ejpam-4704	106	16	all	all	DET
ejpam-4704	106	17	e	e	PROPN
ejpam-4704	106	18	∈	∈	PROPN
ejpam-4704	106	19	ei	ei	X
ejpam-4704	106	20	,	,	PUNCT
ejpam-4704	106	21	i	i	PRON
ejpam-4704	106	22	=	=	NOUN
ejpam-4704	106	23	6	6	NUM
ejpam-4704	106	24	,	,	PUNCT
ejpam-4704	106	25	8	8	NUM
ejpam-4704	106	26	.	.	PUNCT
ejpam-4704	106	27	b.	b.	PROPN
ejpam-4704	106	28	m.	m.	PROPN
ejpam-4704	106	29	sulaiman	sulaiman	PROPN
ejpam-4704	106	30	,	,	PUNCT
ejpam-4704	106	31	r.	r.	PROPN
ejpam-4704	106	32	s.	s.	PROPN
ejpam-4704	106	33	hasan	hasan	PROPN
ejpam-4704	106	34	,	,	PUNCT
ejpam-4704	106	35	r.	r.	PROPN
ejpam-4704	106	36	a.	a.	PROPN
ejpam-4704	106	37	mustafa	mustafa	PROPN
ejpam-4704	106	38	/	/	SYM
ejpam-4704	106	39	eur	eur	PROPN
ejpam-4704	106	40	.	.	PUNCT
ejpam-4704	107	1	j.	j.	PROPN
ejpam-4704	107	2	pure	pure	PROPN
ejpam-4704	107	3	appl	appl	PROPN
ejpam-4704	107	4	.	.	PROPN
ejpam-4704	107	5	math	math	PROPN
ejpam-4704	107	6	,	,	PUNCT
ejpam-4704	107	7	16	16	NUM
ejpam-4704	107	8	(	(	PUNCT
ejpam-4704	107	9	2	2	NUM
ejpam-4704	107	10	)	)	PUNCT
ejpam-4704	107	11	(	(	PUNCT
ejpam-4704	107	12	2023	2023	NUM
ejpam-4704	107	13	)	)	PUNCT
ejpam-4704	107	14	,	,	PUNCT
ejpam-4704	107	15	953	953	NUM
ejpam-4704	107	16	-	-	SYM
ejpam-4704	107	17	964	964	NUM
ejpam-4704	107	18	957	957	NUM
ejpam-4704	107	19	case	case	NOUN
ejpam-4704	107	20	iii	iii	NOUN
ejpam-4704	107	21	:	:	PUNCT
ejpam-4704	107	22	fb(µ(p	fb(µ(p	PROPN
ejpam-4704	107	23	c	c	NOUN
ejpam-4704	107	24	m)(e	m)(e	NOUN
ejpam-4704	107	25	)	)	PUNCT
ejpam-4704	107	26	is	be	AUX
ejpam-4704	107	27	less	less	ADJ
ejpam-4704	107	28	than	than	ADP
ejpam-4704	107	29	or	or	CCONJ
ejpam-4704	107	30	equal	equal	ADJ
ejpam-4704	107	31	to	to	ADP
ejpam-4704	107	32	3	3	NUM
ejpam-4704	107	33	for	for	ADP
ejpam-4704	107	34	all	all	DET
ejpam-4704	107	35	e	e	PROPN
ejpam-4704	107	36	∈	∈	PROPN
ejpam-4704	107	37	ei	ei	X
ejpam-4704	107	38	,	,	PUNCT
ejpam-4704	107	39	i	i	PRON
ejpam-4704	107	40	=	=	NOUN
ejpam-4704	107	41	1	1	NUM
ejpam-4704	107	42	,	,	PUNCT
ejpam-4704	107	43	2	2	NUM
ejpam-4704	107	44	,	,	PUNCT
ejpam-4704	107	45	3	3	NUM
ejpam-4704	107	46	,	,	PUNCT
ejpam-4704	107	47	4	4	NUM
ejpam-4704	107	48	,	,	PUNCT
ejpam-4704	107	49	5	5	NUM
ejpam-4704	107	50	.	.	X
ejpam-4704	107	51	from	from	ADP
ejpam-4704	107	52	the	the	DET
ejpam-4704	107	53	above	above	ADJ
ejpam-4704	107	54	three	three	NUM
ejpam-4704	107	55	cases	case	NOUN
ejpam-4704	107	56	,	,	PUNCT
ejpam-4704	107	57	it	it	PRON
ejpam-4704	107	58	can	can	AUX
ejpam-4704	107	59	be	be	AUX
ejpam-4704	107	60	seen	see	VERB
ejpam-4704	107	61	that	that	SCONJ
ejpam-4704	107	62	the	the	DET
ejpam-4704	107	63	fold	fold	NOUN
ejpam-4704	107	64	for	for	ADP
ejpam-4704	107	65	each	each	DET
ejpam-4704	107	66	edge	edge	NOUN
ejpam-4704	107	67	in	in	ADP
ejpam-4704	107	68	the	the	DET
ejpam-4704	107	69	graph	graph	NOUN
ejpam-4704	107	70	µ(p	µ(p	PROPN
ejpam-4704	107	71	c	c	PROPN
ejpam-4704	107	72	m	m	VERB
ejpam-4704	107	73	)	)	PUNCT
ejpam-4704	107	74	is	be	AUX
ejpam-4704	107	75	not	not	PART
ejpam-4704	107	76	more	more	ADJ
ejpam-4704	107	77	than	than	ADP
ejpam-4704	107	78	3	3	NUM
ejpam-4704	107	79	in	in	ADP
ejpam-4704	107	80	the	the	DET
ejpam-4704	107	81	base	base	NOUN
ejpam-4704	107	82	b(µ(p	b(µ(p	NOUN
ejpam-4704	107	83	c	c	PROPN
ejpam-4704	107	84	m	m	PROPN
ejpam-4704	107	85	)	)	PUNCT
ejpam-4704	107	86	)	)	PUNCT
ejpam-4704	107	87	;	;	PUNCT
ejpam-4704	107	88	that	that	PRON
ejpam-4704	107	89	is	be	AUX
ejpam-4704	107	90	b	b	NOUN
ejpam-4704	107	91	(	(	PUNCT
ejpam-4704	107	92	µ(p	µ(p	PROPN
ejpam-4704	107	93	c	c	PROPN
ejpam-4704	107	94	m	m	PROPN
ejpam-4704	107	95	)	)	PUNCT
ejpam-4704	107	96	)	)	PUNCT
ejpam-4704	107	97	≤	≤	ADV
ejpam-4704	107	98	3	3	NUM
ejpam-4704	107	99	(	(	PUNCT
ejpam-4704	107	100	2	2	NUM
ejpam-4704	107	101	)	)	PUNCT
ejpam-4704	107	102	from	from	ADP
ejpam-4704	107	103	(	(	PUNCT
ejpam-4704	107	104	1	1	NUM
ejpam-4704	107	105	)	)	PUNCT
ejpam-4704	107	106	and	and	CCONJ
ejpam-4704	107	107	(	(	PUNCT
ejpam-4704	107	108	2	2	NUM
ejpam-4704	107	109	)	)	PUNCT
ejpam-4704	107	110	,	,	PUNCT
ejpam-4704	107	111	we	we	PRON
ejpam-4704	107	112	get	get	VERB
ejpam-4704	107	113	b(µ(p	b(µ(p	NOUN
ejpam-4704	107	114	c	c	PROPN
ejpam-4704	107	115	m	m	PROPN
ejpam-4704	107	116	)	)	PUNCT
ejpam-4704	107	117	)	)	PUNCT
ejpam-4704	108	1	=	=	PUNCT
ejpam-4704	108	2	3	3	X
ejpam-4704	108	3	.	.	X
ejpam-4704	108	4	2.2	2.2	NUM
ejpam-4704	108	5	.	.	PUNCT
ejpam-4704	109	1	cog	cog	NOUN
ejpam-4704	109	2	-	-	PUNCT
ejpam-4704	109	3	cycle	cycle	NOUN
ejpam-4704	109	4	graph	graph	NOUN
ejpam-4704	109	5	cc	cc	ADP
ejpam-4704	109	6	m	m	VERB
ejpam-4704	109	7	it	it	PRON
ejpam-4704	109	8	is	be	AUX
ejpam-4704	109	9	a	a	DET
ejpam-4704	109	10	graph	graph	NOUN
ejpam-4704	109	11	conclude	conclude	VERB
ejpam-4704	109	12	from	from	ADP
ejpam-4704	109	13	a	a	DET
ejpam-4704	109	14	cycle	cycle	NOUN
ejpam-4704	109	15	cm	cm	NOUN
ejpam-4704	109	16	:	:	PUNCT
ejpam-4704	109	17	u1	u1	NOUN
ejpam-4704	109	18	,	,	PUNCT
ejpam-4704	109	19	u2	u2	NOUN
ejpam-4704	109	20	,	,	PUNCT
ejpam-4704	109	21	.	.	PUNCT
ejpam-4704	109	22	.	.	PUNCT
ejpam-4704	109	23	.	.	PUNCT
ejpam-4704	110	1	,	,	PUNCT
ejpam-4704	110	2	um	um	INTJ
ejpam-4704	110	3	where	where	SCONJ
ejpam-4704	110	4	m	m	VERB
ejpam-4704	110	5	≥	≥	NOUN
ejpam-4704	110	6	3	3	NUM
ejpam-4704	110	7	,	,	PUNCT
ejpam-4704	110	8	by	by	ADP
ejpam-4704	110	9	adding	add	VERB
ejpam-4704	110	10	m	m	NOUN
ejpam-4704	110	11	vertices	vertex	NOUN
ejpam-4704	110	12	and	and	CCONJ
ejpam-4704	110	13	2	2	NUM
ejpam-4704	110	14	m	m	NOUN
ejpam-4704	110	15	edges	edge	NOUN
ejpam-4704	110	16	of	of	ADP
ejpam-4704	110	17	the	the	DET
ejpam-4704	110	18	form	form	NOUN
ejpam-4704	110	19	v1	v1	NOUN
ejpam-4704	110	20	,	,	PUNCT
ejpam-4704	110	21	v2	v2	NOUN
ejpam-4704	110	22	,	,	PUNCT
ejpam-4704	110	23	.	.	PUNCT
ejpam-4704	110	24	.	.	PUNCT
ejpam-4704	111	1	.	.	PUNCT
ejpam-4704	112	1	,	,	PUNCT
ejpam-4704	112	2	vm	vm	PROPN
ejpam-4704	112	3	and	and	CCONJ
ejpam-4704	112	4	{	{	PUNCT
ejpam-4704	112	5	uivi	uivi	NOUN
ejpam-4704	112	6	,	,	PUNCT
ejpam-4704	112	7	ui+1vi	ui+1vi	NOUN
ejpam-4704	112	8	:	:	PUNCT
ejpam-4704	112	9	i	i	PRON
ejpam-4704	112	10	=	=	NOUN
ejpam-4704	112	11	1	1	NUM
ejpam-4704	112	12	,	,	PUNCT
ejpam-4704	112	13	2	2	NUM
ejpam-4704	112	14	,	,	PUNCT
ejpam-4704	112	15	.	.	PUNCT
ejpam-4704	112	16	.	.	PUNCT
ejpam-4704	112	17	.	.	PUNCT
ejpam-4704	113	1	,	,	PUNCT
ejpam-4704	113	2	m	m	VERB
ejpam-4704	113	3	}	}	PUNCT
ejpam-4704	113	4	,	,	PUNCT
ejpam-4704	113	5	respectively	respectively	ADV
ejpam-4704	113	6	,	,	PUNCT
ejpam-4704	113	7	where	where	SCONJ
ejpam-4704	113	8	um+1	um+1	PROPN
ejpam-4704	113	9	≡	≡	PROPN
ejpam-4704	113	10	u1	u1	NOUN
ejpam-4704	113	11	.	.	PUNCT
ejpam-4704	114	1	it	it	PRON
ejpam-4704	114	2	is	be	AUX
ejpam-4704	114	3	clear	clear	ADJ
ejpam-4704	114	4	that	that	SCONJ
ejpam-4704	114	5	the	the	DET
ejpam-4704	114	6	number	number	NOUN
ejpam-4704	114	7	of	of	ADP
ejpam-4704	114	8	vertices	vertex	NOUN
ejpam-4704	114	9	of	of	ADP
ejpam-4704	114	10	a	a	DET
ejpam-4704	114	11	graph	graph	NOUN
ejpam-4704	114	12	cc	cc	ADP
ejpam-4704	114	13	m	m	VERB
ejpam-4704	114	14	is	be	AUX
ejpam-4704	114	15	2	2	NUM
ejpam-4704	114	16	m	m	NOUN
ejpam-4704	114	17	and	and	CCONJ
ejpam-4704	114	18	the	the	DET
ejpam-4704	114	19	number	number	NOUN
ejpam-4704	114	20	of	of	ADP
ejpam-4704	114	21	edges	edge	NOUN
ejpam-4704	114	22	is	be	AUX
ejpam-4704	114	23	3	3	NUM
ejpam-4704	114	24	m	m	NOUN
ejpam-4704	114	25	[	[	X
ejpam-4704	114	26	2	2	NUM
ejpam-4704	114	27	]	]	PUNCT
ejpam-4704	114	28	.	.	PUNCT
ejpam-4704	115	1	2.2.1	2.2.1	NUM
ejpam-4704	115	2	.	.	PUNCT
ejpam-4704	116	1	the	the	DET
ejpam-4704	116	2	basis	basis	NOUN
ejpam-4704	116	3	number	number	NOUN
ejpam-4704	116	4	for	for	ADP
ejpam-4704	116	5	mycielski	mycielski	NOUN
ejpam-4704	116	6	’s	’s	PART
ejpam-4704	116	7	graph	graph	NOUN
ejpam-4704	116	8	of	of	ADP
ejpam-4704	116	9	the	the	DET
ejpam-4704	116	10	cog	cog	NOUN
ejpam-4704	116	11	-	-	PUNCT
ejpam-4704	116	12	cycle	cycle	NOUN
ejpam-4704	116	13	µ(cc	µ(cc	NUM
ejpam-4704	116	14	m	m	NOUN
ejpam-4704	116	15	)	)	PUNCT
ejpam-4704	116	16	let	let	VERB
ejpam-4704	116	17	the	the	DET
ejpam-4704	116	18	vertices	vertex	NOUN
ejpam-4704	116	19	of	of	ADP
ejpam-4704	116	20	the	the	DET
ejpam-4704	116	21	cog	cog	NOUN
ejpam-4704	116	22	-	-	PUNCT
ejpam-4704	116	23	cycle	cycle	NOUN
ejpam-4704	116	24	graph	graph	NOUN
ejpam-4704	116	25	cc	cc	ADP
ejpam-4704	116	26	m	m	PROPN
ejpam-4704	116	27	are	be	AUX
ejpam-4704	116	28	u1	u1	NOUN
ejpam-4704	116	29	,	,	PUNCT
ejpam-4704	116	30	u2	u2	NOUN
ejpam-4704	116	31	,	,	PUNCT
ejpam-4704	116	32	.	.	PUNCT
ejpam-4704	116	33	.	.	PUNCT
ejpam-4704	117	1	.	.	PUNCT
ejpam-4704	118	1	,	,	PUNCT
ejpam-4704	118	2	u2	u2	NOUN
ejpam-4704	118	3	m	m	VERB
ejpam-4704	118	4	where	where	SCONJ
ejpam-4704	118	5	m	m	VERB
ejpam-4704	118	6	≥	≥	NOUN
ejpam-4704	118	7	3	3	NUM
ejpam-4704	118	8	,	,	PUNCT
ejpam-4704	118	9	and	and	CCONJ
ejpam-4704	118	10	the	the	DET
ejpam-4704	118	11	corresponding	corresponding	ADJ
ejpam-4704	118	12	vertices	vertex	NOUN
ejpam-4704	118	13	are	be	AUX
ejpam-4704	118	14	v1	v1	NOUN
ejpam-4704	118	15	,	,	PUNCT
ejpam-4704	118	16	v2	v2	NOUN
ejpam-4704	118	17	,	,	PUNCT
ejpam-4704	118	18	.	.	PUNCT
ejpam-4704	118	19	.	.	PUNCT
ejpam-4704	119	1	.	.	PUNCT
ejpam-4704	120	1	,	,	PUNCT
ejpam-4704	120	2	v2	v2	NOUN
ejpam-4704	120	3	m	m	NOUN
ejpam-4704	121	1	and	and	CCONJ
ejpam-4704	121	2	let	let	VERB
ejpam-4704	121	3	the	the	DET
ejpam-4704	121	4	other	other	ADJ
ejpam-4704	121	5	vertex	vertex	NOUN
ejpam-4704	121	6	be	be	AUX
ejpam-4704	121	7	w.	w.	NOUN
ejpam-4704	121	8	from	from	ADP
ejpam-4704	121	9	the	the	DET
ejpam-4704	121	10	definition	definition	NOUN
ejpam-4704	121	11	of	of	ADP
ejpam-4704	121	12	the	the	DET
ejpam-4704	121	13	mycielski	mycielski	NOUN
ejpam-4704	121	14	’s	’s	PART
ejpam-4704	121	15	graph	graph	NOUN
ejpam-4704	121	16	we	we	PRON
ejpam-4704	121	17	have	have	VERB
ejpam-4704	121	18	the	the	DET
ejpam-4704	121	19	number	number	NOUN
ejpam-4704	121	20	of	of	ADP
ejpam-4704	121	21	vertices	vertex	NOUN
ejpam-4704	121	22	of	of	ADP
ejpam-4704	121	23	the	the	DET
ejpam-4704	121	24	graph	graph	NOUN
ejpam-4704	121	25	µ(cc	µ(cc	NUM
ejpam-4704	121	26	m	m	NOUN
ejpam-4704	121	27	)	)	PUNCT
ejpam-4704	121	28	is	be	AUX
ejpam-4704	121	29	4m+1	4m+1	PROPN
ejpam-4704	121	30	and	and	CCONJ
ejpam-4704	122	1	the	the	DET
ejpam-4704	122	2	number	number	NOUN
ejpam-4704	122	3	of	of	ADP
ejpam-4704	122	4	its	its	PRON
ejpam-4704	122	5	edges	edge	NOUN
ejpam-4704	122	6	is	be	AUX
ejpam-4704	122	7	11	11	NUM
ejpam-4704	122	8	m.	m.	NOUN
ejpam-4704	122	9	theorem	theorem	NOUN
ejpam-4704	122	10	2	2	X
ejpam-4704	122	11	.	.	PUNCT
ejpam-4704	123	1	let	let	VERB
ejpam-4704	123	2	cm	cm	NOUN
ejpam-4704	123	3	be	be	AUX
ejpam-4704	123	4	a	a	DET
ejpam-4704	123	5	cycle	cycle	NOUN
ejpam-4704	123	6	of	of	ADP
ejpam-4704	123	7	order	order	NOUN
ejpam-4704	123	8	m	m	VERB
ejpam-4704	123	9	≥	≥	NOUN
ejpam-4704	123	10	3	3	NUM
ejpam-4704	123	11	then	then	ADV
ejpam-4704	123	12	b(µ(cc	b(µ(cc	INTJ
ejpam-4704	123	13	m	m	NOUN
ejpam-4704	123	14	)	)	PUNCT
ejpam-4704	123	15	)	)	PUNCT
ejpam-4704	124	1	=	=	SYM
ejpam-4704	125	1	3	3	NUM
ejpam-4704	125	2	proof	proof	NOUN
ejpam-4704	125	3	.	.	PUNCT
ejpam-4704	126	1	we	we	PRON
ejpam-4704	126	2	can	can	AUX
ejpam-4704	126	3	prove	prove	VERB
ejpam-4704	126	4	that	that	SCONJ
ejpam-4704	126	5	for	for	ADP
ejpam-4704	126	6	each	each	DET
ejpam-4704	126	7	m	m	PROPN
ejpam-4704	126	8	≥	≥	NOUN
ejpam-4704	126	9	3	3	NUM
ejpam-4704	126	10	,	,	PUNCT
ejpam-4704	126	11	there	there	PRON
ejpam-4704	126	12	is	be	VERB
ejpam-4704	126	13	a	a	DET
ejpam-4704	126	14	subgraph	subgraph	NOUN
ejpam-4704	126	15	of	of	ADP
ejpam-4704	126	16	µ(cc	µ(cc	NUM
ejpam-4704	126	17	m	m	NOUN
ejpam-4704	126	18	)	)	PUNCT
ejpam-4704	126	19	that	that	PRON
ejpam-4704	126	20	topologically	topologically	ADV
ejpam-4704	126	21	equivalent	equivalent	ADJ
ejpam-4704	126	22	k3,3	k3,3	PROPN
ejpam-4704	126	23	,	,	PUNCT
ejpam-4704	126	24	according	accord	VERB
ejpam-4704	126	25	to	to	ADP
ejpam-4704	126	26	kurtowski	kurtowski	PROPN
ejpam-4704	126	27	’s	’s	PART
ejpam-4704	126	28	theorem	theorem	NOUN
ejpam-4704	126	29	[	[	X
ejpam-4704	126	30	8	8	NUM
ejpam-4704	126	31	]	]	PUNCT
ejpam-4704	126	32	µ(cc	µ(cc	NUM
ejpam-4704	126	33	m	m	NOUN
ejpam-4704	126	34	)	)	PUNCT
ejpam-4704	126	35	is	be	AUX
ejpam-4704	126	36	not	not	PART
ejpam-4704	126	37	planar	planar	ADJ
ejpam-4704	126	38	,	,	PUNCT
ejpam-4704	126	39	and	and	CCONJ
ejpam-4704	126	40	according	accord	VERB
ejpam-4704	126	41	to	to	ADP
ejpam-4704	126	42	mclean	mclean	PROPN
ejpam-4704	126	43	’s	’s	PART
ejpam-4704	126	44	theorem	theorem	NOUN
ejpam-4704	126	45	[	[	X
ejpam-4704	126	46	12	12	NUM
ejpam-4704	126	47	]	]	X
ejpam-4704	126	48	we	we	PRON
ejpam-4704	126	49	have	have	VERB
ejpam-4704	126	50	b	b	NUM
ejpam-4704	126	51	(	(	PUNCT
ejpam-4704	126	52	µ(cc	µ(cc	NUM
ejpam-4704	126	53	m	m	NOUN
ejpam-4704	126	54	)	)	PUNCT
ejpam-4704	126	55	)	)	PUNCT
ejpam-4704	126	56	≥	≥	NOUN
ejpam-4704	126	57	3	3	NUM
ejpam-4704	126	58	(	(	PUNCT
ejpam-4704	126	59	3	3	X
ejpam-4704	126	60	)	)	PUNCT
ejpam-4704	126	61	we	we	PRON
ejpam-4704	126	62	will	will	AUX
ejpam-4704	126	63	prove	prove	VERB
ejpam-4704	126	64	that	that	SCONJ
ejpam-4704	126	65	there	there	PRON
ejpam-4704	126	66	is	be	VERB
ejpam-4704	126	67	a	a	DET
ejpam-4704	126	68	base	base	NOUN
ejpam-4704	126	69	b	b	NOUN
ejpam-4704	126	70	for	for	ADP
ejpam-4704	126	71	the	the	DET
ejpam-4704	126	72	cycles	cycle	NOUN
ejpam-4704	126	73	space	space	NOUN
ejpam-4704	126	74	of	of	ADP
ejpam-4704	126	75	the	the	DET
ejpam-4704	126	76	graph	graph	NOUN
ejpam-4704	126	77	µ(cc	µ(cc	NUM
ejpam-4704	126	78	m	m	NOUN
ejpam-4704	126	79	)	)	PUNCT
ejpam-4704	126	80	with	with	ADP
ejpam-4704	126	81	3	3	NUM
ejpam-4704	126	82	-	-	NOUN
ejpam-4704	126	83	fold	fold	ADJ
ejpam-4704	126	84	.	.	PUNCT
ejpam-4704	127	1	let	let	VERB
ejpam-4704	127	2	b	b	X
ejpam-4704	127	3	be	be	AUX
ejpam-4704	127	4	a	a	DET
ejpam-4704	127	5	set	set	NOUN
ejpam-4704	127	6	of	of	ADP
ejpam-4704	127	7	cycles	cycle	NOUN
ejpam-4704	127	8	of	of	ADP
ejpam-4704	127	9	µ(cc	µ(cc	NUM
ejpam-4704	127	10	m	m	NOUN
ejpam-4704	127	11	)	)	PUNCT
ejpam-4704	127	12	which	which	PRON
ejpam-4704	127	13	defined	define	VERB
ejpam-4704	127	14	by	by	ADP
ejpam-4704	127	15	the	the	DET
ejpam-4704	127	16	following	follow	VERB
ejpam-4704	127	17	formula	formula	NOUN
ejpam-4704	127	18	:	:	PUNCT
ejpam-4704	127	19	b	b	X
ejpam-4704	127	20	=	=	SYM
ejpam-4704	127	21	b(µ(p	b(µ(p	PROPN
ejpam-4704	127	22	c	c	PROPN
ejpam-4704	127	23	m	m	PROPN
ejpam-4704	127	24	)	)	PUNCT
ejpam-4704	127	25	)	)	PUNCT
ejpam-4704	127	26	∪m	∪m	NUM
ejpam-4704	127	27	,	,	PUNCT
ejpam-4704	127	28	where	where	SCONJ
ejpam-4704	127	29	m	m	VERB
ejpam-4704	127	30	=	=	X
ejpam-4704	127	31	{	{	PUNCT
ejpam-4704	127	32	m1,m2	m1,m2	PROPN
ejpam-4704	127	33	,	,	PUNCT
ejpam-4704	127	34	.	.	PUNCT
ejpam-4704	127	35	.	.	PUNCT
ejpam-4704	128	1	.	.	PUNCT
ejpam-4704	129	1	,	,	PUNCT
ejpam-4704	129	2	m8	m8	NOUN
ejpam-4704	129	3	}	}	PUNCT
ejpam-4704	129	4	where	where	SCONJ
ejpam-4704	129	5	b(µ(p	b(µ(p	PROPN
ejpam-4704	129	6	c	c	PROPN
ejpam-4704	129	7	m	m	PROPN
ejpam-4704	129	8	)	)	PUNCT
ejpam-4704	129	9	)	)	PUNCT
ejpam-4704	129	10	is	be	AUX
ejpam-4704	129	11	the	the	DET
ejpam-4704	129	12	base	base	NOUN
ejpam-4704	129	13	for	for	ADP
ejpam-4704	129	14	michelsky	michelsky	PROPN
ejpam-4704	129	15	’s	’s	PART
ejpam-4704	129	16	graph	graph	NOUN
ejpam-4704	129	17	of	of	ADP
ejpam-4704	129	18	the	the	DET
ejpam-4704	129	19	cog	cog	NOUN
ejpam-4704	129	20	-	-	PUNCT
ejpam-4704	129	21	path	path	NOUN
ejpam-4704	129	22	p	p	PROPN
ejpam-4704	129	23	c	c	NOUN
ejpam-4704	129	24	m	m	PROPN
ejpam-4704	129	25	,	,	PUNCT
ejpam-4704	129	26	which	which	PRON
ejpam-4704	129	27	defined	define	VERB
ejpam-4704	129	28	in	in	ADP
ejpam-4704	129	29	the	the	DET
ejpam-4704	129	30	previous	previous	ADJ
ejpam-4704	129	31	theorem	theorem	NOUN
ejpam-4704	129	32	,	,	PUNCT
ejpam-4704	129	33	also	also	ADV
ejpam-4704	130	1	m	m	VERB
ejpam-4704	130	2	is	be	AUX
ejpam-4704	130	3	a	a	DET
ejpam-4704	130	4	set	set	NOUN
ejpam-4704	130	5	of	of	ADP
ejpam-4704	130	6	cycles	cycle	NOUN
ejpam-4704	130	7	of	of	ADP
ejpam-4704	130	8	the	the	DET
ejpam-4704	130	9	graph	graph	NOUN
ejpam-4704	130	10	µ(cc	µ(cc	NUM
ejpam-4704	130	11	m	m	NOUN
ejpam-4704	130	12	)	)	PUNCT
ejpam-4704	130	13	defined	define	VERB
ejpam-4704	130	14	as	as	ADP
ejpam-4704	130	15	the	the	DET
ejpam-4704	130	16	following	follow	VERB
ejpam-4704	130	17	formula	formula	NOUN
ejpam-4704	130	18	:	:	PUNCT
ejpam-4704	130	19	m1	m1	PROPN
ejpam-4704	130	20	=	=	SYM
ejpam-4704	130	21	u1u2m−1u2mu1	u1u2m−1u2mu1	NOUN
ejpam-4704	130	22	,	,	PUNCT
ejpam-4704	130	23	m2	m2	PROPN
ejpam-4704	130	24	=	=	PROPN
ejpam-4704	130	25	u1u2m−1v2mu1	u1u2m−1v2mu1	PROPN
ejpam-4704	130	26	,	,	PUNCT
ejpam-4704	130	27	m3	m3	PROPN
ejpam-4704	130	28	=	=	PUNCT
ejpam-4704	130	29	u1u2m−1v2m−2wv2mu1	u1u2m−1v2m−2wv2mu1	PROPN
ejpam-4704	130	30	,	,	PUNCT
ejpam-4704	130	31	m4	m4	PROPN
ejpam-4704	130	32	=	=	SYM
ejpam-4704	130	33	u1u2mv2m−1u1	u1u2mv2m−1u1	PROPN
ejpam-4704	130	34	,	,	PUNCT
ejpam-4704	130	35	b.	b.	PROPN
ejpam-4704	130	36	m.	m.	PROPN
ejpam-4704	130	37	sulaiman	sulaiman	PROPN
ejpam-4704	130	38	,	,	PUNCT
ejpam-4704	130	39	r.	r.	PROPN
ejpam-4704	130	40	s.	s.	PROPN
ejpam-4704	130	41	hasan	hasan	PROPN
ejpam-4704	130	42	,	,	PUNCT
ejpam-4704	130	43	r.	r.	PROPN
ejpam-4704	130	44	a.	a.	PROPN
ejpam-4704	130	45	mustafa	mustafa	PROPN
ejpam-4704	130	46	/	/	SYM
ejpam-4704	130	47	eur	eur	PROPN
ejpam-4704	130	48	.	.	PUNCT
ejpam-4704	131	1	j.	j.	PROPN
ejpam-4704	131	2	pure	pure	PROPN
ejpam-4704	131	3	appl	appl	PROPN
ejpam-4704	131	4	.	.	PROPN
ejpam-4704	131	5	math	math	PROPN
ejpam-4704	131	6	,	,	PUNCT
ejpam-4704	131	7	16	16	NUM
ejpam-4704	131	8	(	(	PUNCT
ejpam-4704	131	9	2	2	NUM
ejpam-4704	131	10	)	)	PUNCT
ejpam-4704	131	11	(	(	PUNCT
ejpam-4704	131	12	2023	2023	NUM
ejpam-4704	131	13	)	)	PUNCT
ejpam-4704	131	14	,	,	PUNCT
ejpam-4704	131	15	953	953	NUM
ejpam-4704	131	16	-	-	SYM
ejpam-4704	131	17	964	964	NUM
ejpam-4704	131	18	958	958	NUM
ejpam-4704	131	19	m5	m5	NOUN
ejpam-4704	131	20	=	=	SYM
ejpam-4704	131	21	u1u2mv1u3u1	u1u2mv1u3u1	NOUN
ejpam-4704	131	22	,	,	PUNCT
ejpam-4704	131	23	m6	m6	PROPN
ejpam-4704	131	24	=	=	SYM
ejpam-4704	131	25	u2m−2u2m−1u2mv2m−1u2m−2	u2m−2u2m−1u2mv2m−1u2m−2	PROPN
ejpam-4704	131	26	,	,	PUNCT
ejpam-4704	131	27	m7	m7	NOUN
ejpam-4704	131	28	=	=	SYM
ejpam-4704	131	29	v1u2m−1u2mv1	v1u2m−1u2mv1	PROPN
ejpam-4704	131	30	,	,	PUNCT
ejpam-4704	131	31	m8	m8	NOUN
ejpam-4704	131	32	=	=	PUNCT
ejpam-4704	131	33	v2mu2m−1u2m−3v2m−1wv2	v2mu2m−1u2m−3v2m−1wv2	NOUN
ejpam-4704	131	34	m.	m.	NOUN
ejpam-4704	131	35	in	in	SCONJ
ejpam-4704	131	36	order	order	NOUN
ejpam-4704	131	37	b	b	ADP
ejpam-4704	131	38	to	to	PART
ejpam-4704	131	39	be	be	AUX
ejpam-4704	131	40	the	the	DET
ejpam-4704	131	41	base	base	NOUN
ejpam-4704	131	42	for	for	ADP
ejpam-4704	131	43	the	the	DET
ejpam-4704	131	44	cycles	cycle	NOUN
ejpam-4704	131	45	space	space	NOUN
ejpam-4704	131	46	of	of	ADP
ejpam-4704	131	47	graph	graph	NOUN
ejpam-4704	131	48	µ(cc	µ(cc	NUM
ejpam-4704	131	49	m	m	NOUN
ejpam-4704	131	50	)	)	PUNCT
ejpam-4704	131	51	must	must	AUX
ejpam-4704	131	52	be	be	AUX
ejpam-4704	131	53	|b|	|b|	PROPN
ejpam-4704	131	54	=	=	PUNCT
ejpam-4704	131	55	dimc(µ(cc	dimc(µ(cc	PROPN
ejpam-4704	131	56	m	m	PROPN
ejpam-4704	131	57	)	)	PUNCT
ejpam-4704	131	58	)	)	PUNCT
ejpam-4704	131	59	,	,	PUNCT
ejpam-4704	131	60	and	and	CCONJ
ejpam-4704	131	61	b	b	NOUN
ejpam-4704	131	62	must	must	AUX
ejpam-4704	131	63	be	be	AUX
ejpam-4704	131	64	a	a	DET
ejpam-4704	131	65	linearly	linearly	ADV
ejpam-4704	131	66	independent	independent	ADJ
ejpam-4704	131	67	set	set	NOUN
ejpam-4704	131	68	of	of	ADP
ejpam-4704	131	69	cycles	cycle	NOUN
ejpam-4704	131	70	.	.	PUNCT
ejpam-4704	132	1	it	it	PRON
ejpam-4704	132	2	is	be	AUX
ejpam-4704	132	3	known	know	VERB
ejpam-4704	132	4	that	that	SCONJ
ejpam-4704	132	5	dim	dim	VERB
ejpam-4704	132	6	c(µ(cc	c(µ(cc	NOUN
ejpam-4704	132	7	m	m	NOUN
ejpam-4704	132	8	)	)	PUNCT
ejpam-4704	132	9	)	)	PUNCT
ejpam-4704	133	1	=	=	SYM
ejpam-4704	133	2	11m−	11m−	NUM
ejpam-4704	133	3	(	(	PUNCT
ejpam-4704	133	4	2m+	2m+	NUM
ejpam-4704	133	5	1	1	NUM
ejpam-4704	133	6	)	)	PUNCT
ejpam-4704	133	7	+	+	CCONJ
ejpam-4704	133	8	1	1	NUM
ejpam-4704	133	9	=	=	SYM
ejpam-4704	133	10	7	7	NUM
ejpam-4704	133	11	m	m	NUM
ejpam-4704	133	12	,	,	PUNCT
ejpam-4704	133	13	and	and	CCONJ
ejpam-4704	133	14	|b|	|b|	PROPN
ejpam-4704	133	15	=	=	PUNCT
ejpam-4704	133	16	|b(µ(p	|b(µ(p	PROPN
ejpam-4704	133	17	c	c	PROPN
ejpam-4704	133	18	m))|+	m))|+	PRON
ejpam-4704	133	19	|m	|m	NOUN
ejpam-4704	133	20	|	|	ADV
ejpam-4704	133	21	=	=	SYM
ejpam-4704	133	22	(	(	PUNCT
ejpam-4704	133	23	7m−	7m−	NUM
ejpam-4704	133	24	8)	8)	NUM
ejpam-4704	133	25	+	+	CCONJ
ejpam-4704	133	26	8	8	NUM
ejpam-4704	133	27	=	=	SYM
ejpam-4704	133	28	7	7	NUM
ejpam-4704	133	29	m	m	NOUN
ejpam-4704	133	30	it	it	PRON
ejpam-4704	133	31	remains	remain	VERB
ejpam-4704	133	32	to	to	PART
ejpam-4704	133	33	show	show	VERB
ejpam-4704	133	34	that	that	SCONJ
ejpam-4704	133	35	b	b	NOUN
ejpam-4704	133	36	is	be	AUX
ejpam-4704	133	37	linearly	linearly	ADV
ejpam-4704	133	38	independent	independent	ADJ
ejpam-4704	133	39	.	.	PUNCT
ejpam-4704	134	1	it	it	PRON
ejpam-4704	134	2	is	be	AUX
ejpam-4704	134	3	known	know	VERB
ejpam-4704	134	4	that	that	SCONJ
ejpam-4704	134	5	b(µ(p	b(µ(p	NOUN
ejpam-4704	134	6	c	c	PROPN
ejpam-4704	134	7	m	m	PROPN
ejpam-4704	134	8	)	)	PUNCT
ejpam-4704	134	9	)	)	PUNCT
ejpam-4704	134	10	is	be	AUX
ejpam-4704	134	11	linearly	linearly	ADV
ejpam-4704	134	12	independent	independent	ADJ
ejpam-4704	134	13	because	because	SCONJ
ejpam-4704	134	14	it	it	PRON
ejpam-4704	134	15	is	be	AUX
ejpam-4704	134	16	represent	represent	VERB
ejpam-4704	134	17	the	the	DET
ejpam-4704	134	18	base	base	NOUN
ejpam-4704	134	19	of	of	ADP
ejpam-4704	134	20	the	the	DET
ejpam-4704	134	21	cycles	cycle	NOUN
ejpam-4704	134	22	space	space	NOUN
ejpam-4704	134	23	of	of	ADP
ejpam-4704	134	24	µ(p	µ(p	PROPN
ejpam-4704	134	25	c	c	PROPN
ejpam-4704	134	26	m	m	PROPN
ejpam-4704	134	27	)	)	PUNCT
ejpam-4704	134	28	.	.	PUNCT
ejpam-4704	135	1	in	in	ADP
ejpam-4704	135	2	addition	addition	NOUN
ejpam-4704	135	3	,	,	PUNCT
ejpam-4704	135	4	the	the	DET
ejpam-4704	135	5	cycles	cycle	NOUN
ejpam-4704	135	6	set	set	VERB
ejpam-4704	135	7	m	m	VERB
ejpam-4704	135	8	is	be	AUX
ejpam-4704	135	9	linearly	linearly	ADV
ejpam-4704	135	10	independent	independent	ADJ
ejpam-4704	135	11	because	because	SCONJ
ejpam-4704	135	12	one	one	NUM
ejpam-4704	135	13	of	of	ADP
ejpam-4704	135	14	them	they	PRON
ejpam-4704	135	15	can	can	AUX
ejpam-4704	135	16	not	not	PART
ejpam-4704	135	17	be	be	AUX
ejpam-4704	135	18	written	write	VERB
ejpam-4704	135	19	as	as	ADP
ejpam-4704	135	20	a	a	DET
ejpam-4704	135	21	linear	linear	ADJ
ejpam-4704	135	22	combination	combination	NOUN
ejpam-4704	135	23	of	of	ADP
ejpam-4704	135	24	the	the	DET
ejpam-4704	135	25	other	other	ADJ
ejpam-4704	135	26	cycles	cycle	NOUN
ejpam-4704	135	27	.	.	PUNCT
ejpam-4704	136	1	finally	finally	ADV
ejpam-4704	136	2	,	,	PUNCT
ejpam-4704	136	3	the	the	DET
ejpam-4704	136	4	set	set	NOUN
ejpam-4704	136	5	of	of	ADP
ejpam-4704	136	6	cycles	cycle	NOUN
ejpam-4704	136	7	b	b	PROPN
ejpam-4704	136	8	=	=	SYM
ejpam-4704	136	9	b(µ(p	b(µ(p	PROPN
ejpam-4704	136	10	c	c	PROPN
ejpam-4704	136	11	m	m	PROPN
ejpam-4704	136	12	)	)	PUNCT
ejpam-4704	136	13	)	)	PUNCT
ejpam-4704	136	14	∪	∪	ADP
ejpam-4704	136	15	{	{	PUNCT
ejpam-4704	136	16	m1,m2	m1,m2	PROPN
ejpam-4704	136	17	,	,	PUNCT
ejpam-4704	136	18	.	.	PUNCT
ejpam-4704	136	19	.	.	PUNCT
ejpam-4704	136	20	.	.	PUNCT
ejpam-4704	137	1	,	,	PUNCT
ejpam-4704	137	2	m8	m8	NOUN
ejpam-4704	137	3	}	}	PUNCT
ejpam-4704	137	4	is	be	AUX
ejpam-4704	137	5	independent	independent	ADJ
ejpam-4704	137	6	because	because	SCONJ
ejpam-4704	137	7	any	any	DET
ejpam-4704	137	8	linear	linear	ADJ
ejpam-4704	137	9	combination	combination	NOUN
ejpam-4704	137	10	of	of	ADP
ejpam-4704	137	11	mi	mi	PROPN
ejpam-4704	137	12	’s	’s	PART
ejpam-4704	137	13	cycles	cycle	NOUN
ejpam-4704	137	14	,	,	PUNCT
ejpam-4704	137	15	i	i	PRON
ejpam-4704	137	16	=	=	NOUN
ejpam-4704	137	17	1	1	NUM
ejpam-4704	137	18	,	,	PUNCT
ejpam-4704	137	19	2	2	NUM
ejpam-4704	137	20	,	,	PUNCT
ejpam-4704	137	21	.	.	PUNCT
ejpam-4704	137	22	.	.	PUNCT
ejpam-4704	138	1	.	.	PUNCT
ejpam-4704	139	1	,	,	PUNCT
ejpam-4704	139	2	8	8	NUM
ejpam-4704	139	3	contains	contain	VERB
ejpam-4704	139	4	at	at	ADP
ejpam-4704	139	5	least	least	ADV
ejpam-4704	139	6	one	one	NUM
ejpam-4704	139	7	new	new	ADJ
ejpam-4704	139	8	edge	edge	NOUN
ejpam-4704	139	9	of	of	ADP
ejpam-4704	139	10	type	type	NOUN
ejpam-4704	139	11	u1u2m−1	u1u2m−1	NOUN
ejpam-4704	139	12	,	,	PUNCT
ejpam-4704	139	13	u1u2	u1u2	NOUN
ejpam-4704	139	14	m	m	PROPN
ejpam-4704	139	15	,	,	PUNCT
ejpam-4704	139	16	u2m−1u2	u2m−1u2	PROPN
ejpam-4704	139	17	m	m	PROPN
ejpam-4704	139	18	,	,	PUNCT
ejpam-4704	139	19	u1v2m−1	u1v2m−1	PROPN
ejpam-4704	139	20	,	,	PUNCT
ejpam-4704	139	21	u1v2	u1v2	NOUN
ejpam-4704	139	22	m	m	X
ejpam-4704	139	23	,	,	PUNCT
ejpam-4704	139	24	v1u2m−1	v1u2m−1	PROPN
ejpam-4704	139	25	,	,	PUNCT
ejpam-4704	139	26	v1u2	v1u2	X
ejpam-4704	139	27	m	m	X
ejpam-4704	139	28	,	,	PUNCT
ejpam-4704	139	29	u2m−1v2	u2m−1v2	PROPN
ejpam-4704	139	30	m	m	PROPN
ejpam-4704	139	31	,	,	PUNCT
ejpam-4704	139	32	v2m−1u2	v2m−1u2	PROPN
ejpam-4704	139	33	m	m	PROPN
ejpam-4704	139	34	,	,	PUNCT
ejpam-4704	139	35	wv2	wv2	PROPN
ejpam-4704	139	36	m	m	PROPN
ejpam-4704	139	37	while	while	SCONJ
ejpam-4704	139	38	these	these	DET
ejpam-4704	139	39	edges	edge	NOUN
ejpam-4704	139	40	are	be	AUX
ejpam-4704	139	41	not	not	PART
ejpam-4704	139	42	exist	exist	ADJ
ejpam-4704	139	43	in	in	ADP
ejpam-4704	139	44	any	any	DET
ejpam-4704	139	45	linear	linear	ADJ
ejpam-4704	139	46	combination	combination	NOUN
ejpam-4704	139	47	for	for	ADP
ejpam-4704	139	48	cycles	cycle	NOUN
ejpam-4704	139	49	of	of	ADP
ejpam-4704	139	50	b(µ(p	b(µ(p	NOUN
ejpam-4704	139	51	c	c	PROPN
ejpam-4704	139	52	m	m	PROPN
ejpam-4704	139	53	)	)	PUNCT
ejpam-4704	139	54	)	)	PUNCT
ejpam-4704	139	55	.	.	PUNCT
ejpam-4704	140	1	to	to	PART
ejpam-4704	140	2	find	find	VERB
ejpam-4704	140	3	the	the	DET
ejpam-4704	140	4	fold	fold	NOUN
ejpam-4704	140	5	for	for	ADP
ejpam-4704	140	6	the	the	DET
ejpam-4704	140	7	base	base	NOUN
ejpam-4704	140	8	b	b	NOUN
ejpam-4704	140	9	we	we	PRON
ejpam-4704	140	10	divide	divide	VERB
ejpam-4704	140	11	the	the	DET
ejpam-4704	140	12	edges	edge	NOUN
ejpam-4704	140	13	of	of	ADP
ejpam-4704	140	14	the	the	DET
ejpam-4704	140	15	graph	graph	NOUN
ejpam-4704	140	16	µ(cc	µ(cc	NUM
ejpam-4704	140	17	m	m	NOUN
ejpam-4704	140	18	)	)	PUNCT
ejpam-4704	140	19	into	into	ADP
ejpam-4704	140	20	:	:	PUNCT
ejpam-4704	140	21	e1	e1	PROPN
ejpam-4704	140	22	=	=	SYM
ejpam-4704	140	23	e(µ(p	e(µ(p	PROPN
ejpam-4704	140	24	c	c	PROPN
ejpam-4704	140	25	m))−	m))−	PROPN
ejpam-4704	140	26	e2	e2	PROPN
ejpam-4704	140	27	e2	e2	PROPN
ejpam-4704	140	28	=	=	SYM
ejpam-4704	140	29	{	{	PUNCT
ejpam-4704	140	30	u1u3	u1u3	NOUN
ejpam-4704	140	31	,	,	PUNCT
ejpam-4704	140	32	v1u3	v1u3	X
ejpam-4704	140	33	,	,	PUNCT
ejpam-4704	140	34	u2m−3u2m−1	u2m−3u2m−1	NOUN
ejpam-4704	140	35	,	,	PUNCT
ejpam-4704	140	36	u2m−2u2m−1	u2m−2u2m−1	PROPN
ejpam-4704	140	37	,	,	PUNCT
ejpam-4704	140	38	u2m−2v2m−1	u2m−2v2m−1	NOUN
ejpam-4704	140	39	,	,	PUNCT
ejpam-4704	140	40	v2m−2u2m−1	v2m−2u2m−1	NOUN
ejpam-4704	140	41	,	,	PUNCT
ejpam-4704	140	42	wv2m−2	wv2m−2	NUM
ejpam-4704	140	43	,	,	PUNCT
ejpam-4704	140	44	wv2m−1	wv2m−1	NUM
ejpam-4704	140	45	}	}	PUNCT
ejpam-4704	140	46	e3	e3	VERB
ejpam-4704	140	47	=	=	SYM
ejpam-4704	140	48	{	{	PUNCT
ejpam-4704	140	49	u1u2m−1	u1u2m−1	X
ejpam-4704	140	50	,	,	PUNCT
ejpam-4704	140	51	u1u2	u1u2	NOUN
ejpam-4704	140	52	m	m	PROPN
ejpam-4704	140	53	,	,	PUNCT
ejpam-4704	140	54	u2m−1u2	u2m−1u2	PROPN
ejpam-4704	140	55	m	m	PROPN
ejpam-4704	140	56	,	,	PUNCT
ejpam-4704	140	57	u1v2m−1	u1v2m−1	PROPN
ejpam-4704	140	58	,	,	PUNCT
ejpam-4704	140	59	u1v2	u1v2	NOUN
ejpam-4704	140	60	m	m	X
ejpam-4704	140	61	,	,	PUNCT
ejpam-4704	140	62	v1u2m−1	v1u2m−1	PROPN
ejpam-4704	140	63	,	,	PUNCT
ejpam-4704	140	64	v1u2	v1u2	X
ejpam-4704	140	65	m	m	X
ejpam-4704	140	66	,	,	PUNCT
ejpam-4704	140	67	u2m−1v2	u2m−1v2	PROPN
ejpam-4704	140	68	m	m	PROPN
ejpam-4704	140	69	,	,	PUNCT
ejpam-4704	140	70	v2m−1u2	v2m−1u2	PROPN
ejpam-4704	140	71	m	m	PROPN
ejpam-4704	140	72	,	,	PUNCT
ejpam-4704	140	73	wv2	wv2	PROPN
ejpam-4704	140	74	m	m	ADJ
ejpam-4704	140	75	}	}	PUNCT
ejpam-4704	140	76	now	now	ADV
ejpam-4704	140	77	,	,	PUNCT
ejpam-4704	140	78	we	we	PRON
ejpam-4704	140	79	calculate	calculate	VERB
ejpam-4704	140	80	the	the	DET
ejpam-4704	140	81	fold	fold	NOUN
ejpam-4704	140	82	for	for	ADP
ejpam-4704	140	83	a	a	DET
ejpam-4704	140	84	set	set	NOUN
ejpam-4704	140	85	of	of	ADP
ejpam-4704	140	86	the	the	DET
ejpam-4704	140	87	edges	edge	NOUN
ejpam-4704	140	88	of	of	ADP
ejpam-4704	140	89	the	the	DET
ejpam-4704	140	90	graph	graph	NOUN
ejpam-4704	140	91	µ(cc	µ(cc	NUM
ejpam-4704	140	92	m	m	NOUN
ejpam-4704	140	93	)	)	PUNCT
ejpam-4704	140	94	,	,	PUNCT
ejpam-4704	140	95	we	we	PRON
ejpam-4704	140	96	note	note	VERB
ejpam-4704	140	97	that	that	SCONJ
ejpam-4704	140	98	fb(µ(cc	fb(µ(cc	NUM
ejpam-4704	140	99	m))(e	m))(e	PROPN
ejpam-4704	140	100	)	)	PUNCT
ejpam-4704	140	101	is	be	AUX
ejpam-4704	140	102	less	less	ADJ
ejpam-4704	140	103	than	than	ADP
ejpam-4704	140	104	or	or	CCONJ
ejpam-4704	140	105	equal	equal	ADJ
ejpam-4704	140	106	to	to	ADP
ejpam-4704	140	107	3	3	NUM
ejpam-4704	140	108	for	for	ADP
ejpam-4704	140	109	all	all	DET
ejpam-4704	140	110	e	e	PROPN
ejpam-4704	140	111	∈	∈	PROPN
ejpam-4704	140	112	ei	ei	X
ejpam-4704	140	113	,	,	PUNCT
ejpam-4704	140	114	i	i	PRON
ejpam-4704	140	115	=	=	NOUN
ejpam-4704	140	116	1	1	NUM
ejpam-4704	140	117	,	,	PUNCT
ejpam-4704	140	118	2	2	NUM
ejpam-4704	140	119	,	,	PUNCT
ejpam-4704	140	120	3	3	NUM
ejpam-4704	140	121	,	,	PUNCT
ejpam-4704	140	122	thus	thus	ADV
ejpam-4704	140	123	the	the	DET
ejpam-4704	140	124	fold	fold	NOUN
ejpam-4704	140	125	for	for	ADP
ejpam-4704	140	126	each	each	DET
ejpam-4704	140	127	edge	edge	NOUN
ejpam-4704	140	128	in	in	ADP
ejpam-4704	140	129	the	the	DET
ejpam-4704	140	130	graph	graph	NOUN
ejpam-4704	140	131	µ(cc	µ(cc	NUM
ejpam-4704	140	132	m	m	NOUN
ejpam-4704	140	133	)	)	PUNCT
ejpam-4704	140	134	is	be	AUX
ejpam-4704	140	135	not	not	PART
ejpam-4704	140	136	more	more	ADJ
ejpam-4704	140	137	than	than	ADP
ejpam-4704	140	138	3	3	NUM
ejpam-4704	140	139	in	in	ADP
ejpam-4704	140	140	the	the	DET
ejpam-4704	140	141	base	base	NOUN
ejpam-4704	140	142	b(µ(cc	b(µ(cc	X
ejpam-4704	140	143	m	m	NOUN
ejpam-4704	140	144	)	)	PUNCT
ejpam-4704	140	145	)	)	PUNCT
ejpam-4704	140	146	;	;	PUNCT
ejpam-4704	140	147	that	that	PRON
ejpam-4704	140	148	is	be	AUX
ejpam-4704	140	149	b	b	X
ejpam-4704	140	150	(	(	PUNCT
ejpam-4704	140	151	µ(cc	µ(cc	NUM
ejpam-4704	140	152	m	m	NOUN
ejpam-4704	140	153	)	)	PUNCT
ejpam-4704	140	154	)	)	PUNCT
ejpam-4704	140	155	≤	≤	ADV
ejpam-4704	140	156	3	3	NUM
ejpam-4704	140	157	(	(	PUNCT
ejpam-4704	140	158	4	4	NUM
ejpam-4704	140	159	)	)	PUNCT
ejpam-4704	140	160	from	from	ADP
ejpam-4704	140	161	(	(	PUNCT
ejpam-4704	140	162	3	3	NUM
ejpam-4704	140	163	)	)	PUNCT
ejpam-4704	140	164	and	and	CCONJ
ejpam-4704	140	165	(	(	PUNCT
ejpam-4704	140	166	4	4	NUM
ejpam-4704	140	167	)	)	PUNCT
ejpam-4704	140	168	,	,	PUNCT
ejpam-4704	140	169	we	we	PRON
ejpam-4704	140	170	get	get	VERB
ejpam-4704	140	171	b(µ(cc	b(µ(cc	NOUN
ejpam-4704	140	172	m	m	NOUN
ejpam-4704	140	173	)	)	PUNCT
ejpam-4704	140	174	)	)	PUNCT
ejpam-4704	141	1	=	=	PUNCT
ejpam-4704	142	1	3	3	X
ejpam-4704	142	2	.	.	NOUN
ejpam-4704	142	3	2.3	2.3	NUM
ejpam-4704	142	4	.	.	PUNCT
ejpam-4704	143	1	cog	cog	PROPN
ejpam-4704	143	2	-	-	PUNCT
ejpam-4704	143	3	star	star	PROPN
ejpam-4704	143	4	graph	graph	NOUN
ejpam-4704	143	5	sc	sc	PROPN
ejpam-4704	143	6	m	m	PRON
ejpam-4704	143	7	it	it	PRON
ejpam-4704	143	8	is	be	AUX
ejpam-4704	143	9	a	a	DET
ejpam-4704	143	10	graph	graph	NOUN
ejpam-4704	143	11	consisted	consist	VERB
ejpam-4704	143	12	of	of	ADP
ejpam-4704	143	13	a	a	DET
ejpam-4704	143	14	star	star	NOUN
ejpam-4704	143	15	graph	graph	NOUN
ejpam-4704	143	16	sm	sm	INTJ
ejpam-4704	143	17	:	:	PUNCT
ejpam-4704	143	18	u1	u1	NOUN
ejpam-4704	143	19	,	,	PUNCT
ejpam-4704	143	20	u2	u2	NOUN
ejpam-4704	143	21	,	,	PUNCT
ejpam-4704	143	22	.	.	PUNCT
ejpam-4704	143	23	.	.	PUNCT
ejpam-4704	144	1	.	.	PUNCT
ejpam-4704	145	1	,	,	PUNCT
ejpam-4704	145	2	um−1	um−1	PROPN
ejpam-4704	145	3	,	,	PUNCT
ejpam-4704	145	4	um	um	INTJ
ejpam-4704	145	5	,	,	PUNCT
ejpam-4704	145	6	where	where	SCONJ
ejpam-4704	145	7	m	m	PROPN
ejpam-4704	145	8	≥	≥	VERB
ejpam-4704	145	9	4	4	NUM
ejpam-4704	145	10	with	with	ADP
ejpam-4704	145	11	m−1	m−1	PROPN
ejpam-4704	145	12	of	of	ADP
ejpam-4704	145	13	additional	additional	ADJ
ejpam-4704	145	14	vertices	vertex	NOUN
ejpam-4704	145	15	v1	v1	NOUN
ejpam-4704	145	16	,	,	PUNCT
ejpam-4704	145	17	v2	v2	NOUN
ejpam-4704	145	18	,	,	PUNCT
ejpam-4704	145	19	.	.	PUNCT
ejpam-4704	145	20	.	.	PUNCT
ejpam-4704	145	21	.	.	PUNCT
ejpam-4704	146	1	,	,	PUNCT
ejpam-4704	146	2	vm−2	vm−2	PROPN
ejpam-4704	146	3	,	,	PUNCT
ejpam-4704	146	4	vm−1	vm−1	NOUN
ejpam-4704	146	5	and	and	CCONJ
ejpam-4704	146	6	additional	additional	ADJ
ejpam-4704	146	7	edges	edge	NOUN
ejpam-4704	146	8	{	{	PUNCT
ejpam-4704	146	9	uivi+1	uivi+1	PROPN
ejpam-4704	146	10	,	,	PUNCT
ejpam-4704	146	11	uivi+2	uivi+2	NOUN
ejpam-4704	146	12	,	,	PUNCT
ejpam-4704	146	13	i	i	PRON
ejpam-4704	146	14	=	=	NOUN
ejpam-4704	146	15	1	1	NUM
ejpam-4704	146	16	,	,	PUNCT
ejpam-4704	146	17	2	2	NUM
ejpam-4704	146	18	,	,	PUNCT
ejpam-4704	146	19	.	.	PUNCT
ejpam-4704	146	20	.	.	PUNCT
ejpam-4704	146	21	.	.	PUNCT
ejpam-4704	147	1	,	,	PUNCT
ejpam-4704	147	2	m−	m−	PROPN
ejpam-4704	147	3	1	1	NUM
ejpam-4704	147	4	}	}	PUNCT
ejpam-4704	147	5	,	,	PUNCT
ejpam-4704	147	6	where	where	SCONJ
ejpam-4704	147	7	vm+1	vm+1	NUM
ejpam-4704	147	8	≡	≡	PROPN
ejpam-4704	147	9	v2	v2	PROPN
ejpam-4704	148	1	[	[	X
ejpam-4704	148	2	2	2	NUM
ejpam-4704	148	3	]	]	PUNCT
ejpam-4704	148	4	.	.	PUNCT
ejpam-4704	149	1	it	it	PRON
ejpam-4704	149	2	is	be	AUX
ejpam-4704	149	3	clear	clear	ADJ
ejpam-4704	149	4	that	that	SCONJ
ejpam-4704	149	5	the	the	DET
ejpam-4704	149	6	number	number	NOUN
ejpam-4704	149	7	of	of	ADP
ejpam-4704	149	8	vertices	vertex	NOUN
ejpam-4704	149	9	of	of	ADP
ejpam-4704	149	10	a	a	DET
ejpam-4704	149	11	graph	graph	NOUN
ejpam-4704	149	12	sc	sc	PROPN
ejpam-4704	149	13	m	m	NOUN
ejpam-4704	149	14	is	be	AUX
ejpam-4704	149	15	2m−1	2m−1	NUM
ejpam-4704	149	16	and	and	CCONJ
ejpam-4704	149	17	the	the	DET
ejpam-4704	149	18	number	number	NOUN
ejpam-4704	149	19	of	of	ADP
ejpam-4704	149	20	edges	edge	NOUN
ejpam-4704	149	21	is	be	AUX
ejpam-4704	149	22	3m−	3m−	PROPN
ejpam-4704	149	23	3	3	NUM
ejpam-4704	149	24	.	.	PUNCT
ejpam-4704	149	25	b.	b.	PROPN
ejpam-4704	149	26	m.	m.	PROPN
ejpam-4704	149	27	sulaiman	sulaiman	PROPN
ejpam-4704	149	28	,	,	PUNCT
ejpam-4704	149	29	r.	r.	PROPN
ejpam-4704	149	30	s.	s.	PROPN
ejpam-4704	149	31	hasan	hasan	PROPN
ejpam-4704	149	32	,	,	PUNCT
ejpam-4704	149	33	r.	r.	PROPN
ejpam-4704	149	34	a.	a.	PROPN
ejpam-4704	149	35	mustafa	mustafa	PROPN
ejpam-4704	149	36	/	/	SYM
ejpam-4704	149	37	eur	eur	PROPN
ejpam-4704	149	38	.	.	PUNCT
ejpam-4704	150	1	j.	j.	PROPN
ejpam-4704	150	2	pure	pure	PROPN
ejpam-4704	150	3	appl	appl	PROPN
ejpam-4704	150	4	.	.	PROPN
ejpam-4704	150	5	math	math	PROPN
ejpam-4704	150	6	,	,	PUNCT
ejpam-4704	150	7	16	16	NUM
ejpam-4704	150	8	(	(	PUNCT
ejpam-4704	150	9	2	2	NUM
ejpam-4704	150	10	)	)	PUNCT
ejpam-4704	150	11	(	(	PUNCT
ejpam-4704	150	12	2023	2023	NUM
ejpam-4704	150	13	)	)	PUNCT
ejpam-4704	150	14	,	,	PUNCT
ejpam-4704	150	15	953	953	NUM
ejpam-4704	150	16	-	-	SYM
ejpam-4704	150	17	964	964	NUM
ejpam-4704	150	18	959	959	NUM
ejpam-4704	150	19	2.3.1	2.3.1	NUM
ejpam-4704	150	20	.	.	PUNCT
ejpam-4704	151	1	the	the	DET
ejpam-4704	151	2	basis	basis	NOUN
ejpam-4704	151	3	number	number	NOUN
ejpam-4704	151	4	for	for	ADP
ejpam-4704	151	5	mycielski	mycielski	NOUN
ejpam-4704	151	6	’s	’s	PART
ejpam-4704	151	7	graph	graph	NOUN
ejpam-4704	151	8	of	of	ADP
ejpam-4704	151	9	the	the	DET
ejpam-4704	151	10	cog	cog	NOUN
ejpam-4704	151	11	-	-	PUNCT
ejpam-4704	151	12	star	star	PROPN
ejpam-4704	151	13	µ(sc	µ(sc	PROPN
ejpam-4704	151	14	m	m	NOUN
ejpam-4704	151	15	)	)	PUNCT
ejpam-4704	151	16	let	let	VERB
ejpam-4704	151	17	the	the	DET
ejpam-4704	151	18	vertices	vertex	NOUN
ejpam-4704	151	19	of	of	ADP
ejpam-4704	151	20	the	the	DET
ejpam-4704	151	21	cog	cog	PROPN
ejpam-4704	151	22	-	-	PUNCT
ejpam-4704	151	23	star	star	PROPN
ejpam-4704	151	24	graph	graph	NOUN
ejpam-4704	151	25	sc	sc	PROPN
ejpam-4704	151	26	m	m	PROPN
ejpam-4704	151	27	are	be	AUX
ejpam-4704	151	28	u1	u1	NOUN
ejpam-4704	151	29	,	,	PUNCT
ejpam-4704	151	30	u2	u2	NOUN
ejpam-4704	151	31	,	,	PUNCT
ejpam-4704	151	32	.	.	PUNCT
ejpam-4704	151	33	.	.	PUNCT
ejpam-4704	152	1	.	.	PUNCT
ejpam-4704	153	1	,	,	PUNCT
ejpam-4704	153	2	u2m−1	u2m−1	PROPN
ejpam-4704	153	3	and	and	CCONJ
ejpam-4704	153	4	the	the	DET
ejpam-4704	153	5	corresponding	corresponding	ADJ
ejpam-4704	153	6	vertices	vertex	NOUN
ejpam-4704	153	7	are	be	AUX
ejpam-4704	153	8	v1	v1	NOUN
ejpam-4704	153	9	,	,	PUNCT
ejpam-4704	153	10	v2	v2	NOUN
ejpam-4704	153	11	,	,	PUNCT
ejpam-4704	153	12	.	.	PUNCT
ejpam-4704	153	13	.	.	PUNCT
ejpam-4704	154	1	.	.	PUNCT
ejpam-4704	155	1	,	,	PUNCT
ejpam-4704	155	2	v2m−1	v2m−1	PROPN
ejpam-4704	155	3	and	and	CCONJ
ejpam-4704	155	4	the	the	DET
ejpam-4704	155	5	other	other	ADJ
ejpam-4704	155	6	vertex	vertex	NOUN
ejpam-4704	155	7	is	be	AUX
ejpam-4704	155	8	w.	w.	NOUN
ejpam-4704	155	9	by	by	ADP
ejpam-4704	155	10	mycielski	mycielski	PROPN
ejpam-4704	155	11	’s	’s	PART
ejpam-4704	155	12	definition	definition	NOUN
ejpam-4704	155	13	,	,	PUNCT
ejpam-4704	155	14	it	it	PRON
ejpam-4704	155	15	turns	turn	VERB
ejpam-4704	155	16	out	out	ADP
ejpam-4704	155	17	that	that	SCONJ
ejpam-4704	155	18	the	the	DET
ejpam-4704	155	19	number	number	NOUN
ejpam-4704	155	20	of	of	ADP
ejpam-4704	155	21	vertices	vertex	NOUN
ejpam-4704	155	22	of	of	ADP
ejpam-4704	155	23	µ(sc	µ(sc	NUM
ejpam-4704	155	24	m	m	NOUN
ejpam-4704	155	25	)	)	PUNCT
ejpam-4704	155	26	is	be	AUX
ejpam-4704	155	27	4m−	4m−	PROPN
ejpam-4704	155	28	1	1	NUM
ejpam-4704	155	29	and	and	CCONJ
ejpam-4704	155	30	the	the	DET
ejpam-4704	155	31	number	number	NOUN
ejpam-4704	155	32	of	of	ADP
ejpam-4704	155	33	its	its	PRON
ejpam-4704	155	34	edges	edge	NOUN
ejpam-4704	155	35	is	be	AUX
ejpam-4704	155	36	11m−	11m−	NUM
ejpam-4704	155	37	10	10	NUM
ejpam-4704	155	38	.	.	PUNCT
ejpam-4704	156	1	theorem	theorem	NOUN
ejpam-4704	156	2	3	3	X
ejpam-4704	156	3	.	.	PUNCT
ejpam-4704	157	1	let	let	VERB
ejpam-4704	157	2	sm	sm	PRON
ejpam-4704	157	3	be	be	AUX
ejpam-4704	157	4	a	a	DET
ejpam-4704	157	5	star	star	NOUN
ejpam-4704	157	6	of	of	ADP
ejpam-4704	157	7	order	order	NOUN
ejpam-4704	157	8	m	m	VERB
ejpam-4704	157	9	≥	≥	NOUN
ejpam-4704	157	10	4	4	NUM
ejpam-4704	157	11	then	then	ADV
ejpam-4704	157	12	b(µ(sc	b(µ(sc	NOUN
ejpam-4704	157	13	m	m	NOUN
ejpam-4704	157	14	)	)	PUNCT
ejpam-4704	157	15	)	)	PUNCT
ejpam-4704	158	1	=	=	SYM
ejpam-4704	158	2	3	3	X
ejpam-4704	158	3	.	.	X
ejpam-4704	158	4	proof	proof	NOUN
ejpam-4704	158	5	.	.	PUNCT
ejpam-4704	159	1	we	we	PRON
ejpam-4704	159	2	can	can	AUX
ejpam-4704	159	3	prove	prove	VERB
ejpam-4704	159	4	that	that	SCONJ
ejpam-4704	159	5	for	for	ADP
ejpam-4704	159	6	each	each	DET
ejpam-4704	159	7	m	m	PROPN
ejpam-4704	159	8	≥	≥	NOUN
ejpam-4704	159	9	4	4	NUM
ejpam-4704	159	10	,	,	PUNCT
ejpam-4704	159	11	there	there	PRON
ejpam-4704	159	12	is	be	VERB
ejpam-4704	159	13	a	a	DET
ejpam-4704	159	14	subgraph	subgraph	NOUN
ejpam-4704	159	15	of	of	ADP
ejpam-4704	159	16	µ(sc	µ(sc	NUM
ejpam-4704	159	17	m	m	NOUN
ejpam-4704	159	18	)	)	PUNCT
ejpam-4704	159	19	that	that	PRON
ejpam-4704	159	20	topologically	topologically	ADV
ejpam-4704	159	21	equivalent	equivalent	ADJ
ejpam-4704	159	22	k3,3	k3,3	PROPN
ejpam-4704	159	23	,	,	PUNCT
ejpam-4704	159	24	according	accord	VERB
ejpam-4704	159	25	to	to	ADP
ejpam-4704	159	26	kurtowski	kurtowski	PROPN
ejpam-4704	159	27	’s	’s	PART
ejpam-4704	159	28	theorem	theorem	NOUN
ejpam-4704	159	29	[	[	X
ejpam-4704	159	30	8	8	NUM
ejpam-4704	159	31	]	]	PUNCT
ejpam-4704	159	32	,	,	PUNCT
ejpam-4704	159	33	µ(sc	µ(sc	NUM
ejpam-4704	159	34	m	m	NOUN
ejpam-4704	159	35	)	)	PUNCT
ejpam-4704	159	36	is	be	AUX
ejpam-4704	159	37	not	not	PART
ejpam-4704	159	38	planar	planar	ADJ
ejpam-4704	159	39	and	and	CCONJ
ejpam-4704	159	40	according	accord	VERB
ejpam-4704	159	41	to	to	ADP
ejpam-4704	159	42	mclean	mclean	PROPN
ejpam-4704	159	43	’s	’s	PART
ejpam-4704	159	44	theorem	theorem	NOUN
ejpam-4704	159	45	[	[	X
ejpam-4704	159	46	12	12	NUM
ejpam-4704	159	47	]	]	X
ejpam-4704	159	48	we	we	PRON
ejpam-4704	159	49	have	have	VERB
ejpam-4704	159	50	b	b	NUM
ejpam-4704	159	51	(	(	PUNCT
ejpam-4704	159	52	µ(sc	µ(sc	NUM
ejpam-4704	159	53	m	m	NOUN
ejpam-4704	159	54	)	)	PUNCT
ejpam-4704	159	55	)	)	PUNCT
ejpam-4704	159	56	≥	≥	NOUN
ejpam-4704	159	57	3	3	NUM
ejpam-4704	159	58	(	(	PUNCT
ejpam-4704	159	59	5	5	NUM
ejpam-4704	159	60	)	)	PUNCT
ejpam-4704	159	61	let	let	VERB
ejpam-4704	159	62	b	b	X
ejpam-4704	159	63	be	be	AUX
ejpam-4704	159	64	a	a	DET
ejpam-4704	159	65	set	set	NOUN
ejpam-4704	159	66	of	of	ADP
ejpam-4704	159	67	cycles	cycle	NOUN
ejpam-4704	159	68	of	of	ADP
ejpam-4704	159	69	µ(sc	µ(sc	NUM
ejpam-4704	159	70	m	m	NOUN
ejpam-4704	159	71	)	)	PUNCT
ejpam-4704	159	72	which	which	PRON
ejpam-4704	159	73	defined	define	VERB
ejpam-4704	159	74	by	by	ADP
ejpam-4704	159	75	the	the	DET
ejpam-4704	159	76	following	follow	VERB
ejpam-4704	159	77	formula	formula	NOUN
ejpam-4704	159	78	:	:	PUNCT
ejpam-4704	159	79	b	b	X
ejpam-4704	159	80	=	=	PUNCT
ejpam-4704	159	81	b(µ(sc	b(µ(sc	NOUN
ejpam-4704	159	82	m	m	PROPN
ejpam-4704	159	83	)	)	PUNCT
ejpam-4704	159	84	)	)	PUNCT
ejpam-4704	160	1	=	=	SYM
ejpam-4704	160	2	∪5	∪5	NOUN
ejpam-4704	160	3	i=1si	i=1si	X
ejpam-4704	160	4	∪	∪	X
ejpam-4704	160	5	{	{	PUNCT
ejpam-4704	160	6	c1	c1	NOUN
ejpam-4704	160	7	,	,	PUNCT
ejpam-4704	160	8	c2	c2	PROPN
ejpam-4704	160	9	,	,	PUNCT
ejpam-4704	160	10	c3	c3	PROPN
ejpam-4704	160	11	,	,	PUNCT
ejpam-4704	160	12	c4	c4	NOUN
ejpam-4704	160	13	,	,	PUNCT
ejpam-4704	160	14	c5	c5	PROPN
ejpam-4704	160	15	,	,	PUNCT
ejpam-4704	160	16	c6	c6	PROPN
ejpam-4704	160	17	}	}	PUNCT
ejpam-4704	160	18	where	where	SCONJ
ejpam-4704	160	19	s1	s1	NOUN
ejpam-4704	160	20	=	=	PUNCT
ejpam-4704	160	21	{	{	PUNCT
ejpam-4704	160	22	uiui+1ui+2vi+1ui	uiui+1ui+2vi+1ui	PROPN
ejpam-4704	160	23	:	:	PUNCT
ejpam-4704	160	24	i	i	NOUN
ejpam-4704	160	25	=	=	NOUN
ejpam-4704	160	26	1	1	NUM
ejpam-4704	160	27	,	,	PUNCT
ejpam-4704	160	28	2	2	NUM
ejpam-4704	160	29	,	,	PUNCT
ejpam-4704	160	30	3	3	NUM
ejpam-4704	160	31	,	,	PUNCT
ejpam-4704	160	32	.	.	PUNCT
ejpam-4704	160	33	.	.	PUNCT
ejpam-4704	160	34	.	.	PUNCT
ejpam-4704	161	1	,	,	PUNCT
ejpam-4704	161	2	2m−	2m−	PROPN
ejpam-4704	161	3	3	3	NUM
ejpam-4704	161	4	}	}	PUNCT
ejpam-4704	161	5	,	,	PUNCT
ejpam-4704	161	6	s2	s2	NOUN
ejpam-4704	161	7	=	=	SYM
ejpam-4704	161	8	{	{	PUNCT
ejpam-4704	161	9	wviui+1vi+2w	wviui+1vi+2w	NOUN
ejpam-4704	161	10	:	:	PUNCT
ejpam-4704	161	11	i	i	NOUN
ejpam-4704	161	12	=	=	NOUN
ejpam-4704	161	13	1	1	NUM
ejpam-4704	161	14	,	,	PUNCT
ejpam-4704	161	15	2	2	NUM
ejpam-4704	161	16	,	,	PUNCT
ejpam-4704	161	17	3	3	NUM
ejpam-4704	161	18	,	,	PUNCT
ejpam-4704	161	19	.	.	PUNCT
ejpam-4704	161	20	.	.	PUNCT
ejpam-4704	161	21	.	.	PUNCT
ejpam-4704	162	1	,	,	PUNCT
ejpam-4704	162	2	2m−	2m−	PROPN
ejpam-4704	162	3	3	3	NUM
ejpam-4704	162	4	}	}	PUNCT
ejpam-4704	162	5	,	,	PUNCT
ejpam-4704	162	6	s3	s3	PROPN
ejpam-4704	162	7	=	=	SYM
ejpam-4704	162	8	{	{	PUNCT
ejpam-4704	162	9	u2m−1viui+1vi+2u2m−1	u2m−1viui+1vi+2u2m−1	NOUN
ejpam-4704	162	10	,	,	PUNCT
ejpam-4704	162	11	i	i	PRON
ejpam-4704	162	12	=	=	NOUN
ejpam-4704	162	13	2	2	NUM
ejpam-4704	162	14	,	,	PUNCT
ejpam-4704	162	15	4	4	NUM
ejpam-4704	162	16	,	,	PUNCT
ejpam-4704	162	17	6	6	NUM
ejpam-4704	162	18	,	,	PUNCT
ejpam-4704	162	19	.	.	PUNCT
ejpam-4704	162	20	.	.	PUNCT
ejpam-4704	162	21	.	.	PUNCT
ejpam-4704	163	1	,	,	PUNCT
ejpam-4704	163	2	2m−	2m−	PROPN
ejpam-4704	163	3	4	4	NUM
ejpam-4704	163	4	}	}	PUNCT
ejpam-4704	163	5	,	,	PUNCT
ejpam-4704	163	6	s4	s4	PROPN
ejpam-4704	163	7	=	=	SYM
ejpam-4704	163	8	{	{	PUNCT
ejpam-4704	163	9	u2m−1uiv2m−1ui+2u2m−1	u2m−1uiv2m−1ui+2u2m−1	PROPN
ejpam-4704	163	10	,	,	PUNCT
ejpam-4704	163	11	i	i	NOUN
ejpam-4704	163	12	=	=	NOUN
ejpam-4704	163	13	2	2	NUM
ejpam-4704	163	14	,	,	PUNCT
ejpam-4704	163	15	4	4	NUM
ejpam-4704	163	16	,	,	PUNCT
ejpam-4704	163	17	6	6	NUM
ejpam-4704	163	18	,	,	PUNCT
ejpam-4704	163	19	.	.	PUNCT
ejpam-4704	163	20	.	.	PUNCT
ejpam-4704	163	21	.	.	PUNCT
ejpam-4704	164	1	,	,	PUNCT
ejpam-4704	164	2	2m−	2m−	PROPN
ejpam-4704	164	3	6	6	NUM
ejpam-4704	164	4	}	}	PUNCT
ejpam-4704	164	5	,	,	PUNCT
ejpam-4704	164	6	s5	s5	X
ejpam-4704	164	7	=	=	PUNCT
ejpam-4704	164	8	{	{	PUNCT
ejpam-4704	164	9	u2m−1viwvi+1ui+2u2m−1	u2m−1viwvi+1ui+2u2m−1	NOUN
ejpam-4704	164	10	,	,	PUNCT
ejpam-4704	164	11	i	i	PRON
ejpam-4704	164	12	=	=	NOUN
ejpam-4704	164	13	2	2	NUM
ejpam-4704	164	14	,	,	PUNCT
ejpam-4704	164	15	4	4	NUM
ejpam-4704	164	16	,	,	PUNCT
ejpam-4704	164	17	6	6	NUM
ejpam-4704	164	18	,	,	PUNCT
ejpam-4704	164	19	.	.	PUNCT
ejpam-4704	164	20	.	.	PUNCT
ejpam-4704	164	21	.	.	PUNCT
ejpam-4704	165	1	,	,	PUNCT
ejpam-4704	165	2	2m−	2m−	PROPN
ejpam-4704	165	3	6	6	NUM
ejpam-4704	165	4	}	}	PUNCT
ejpam-4704	165	5	,	,	PUNCT
ejpam-4704	165	6	c1	c1	PROPN
ejpam-4704	165	7	=	=	SYM
ejpam-4704	165	8	u2m−2u1u2u2m−1u2m−2	u2m−2u1u2u2m−1u2m−2	PROPN
ejpam-4704	165	9	,	,	PUNCT
ejpam-4704	165	10	c2	c2	PROPN
ejpam-4704	165	11	=	=	PUNCT
ejpam-4704	165	12	u2m−2v1wv2m−1u2m−2	u2m−2v1wv2m−1u2m−2	PROPN
ejpam-4704	165	13	,	,	PUNCT
ejpam-4704	165	14	c3	c3	PROPN
ejpam-4704	165	15	=	=	SYM
ejpam-4704	165	16	v2m−2u1u2m−2u2m−1v2m−2	v2m−2u1u2m−2u2m−1v2m−2	X
ejpam-4704	165	17	,	,	PUNCT
ejpam-4704	165	18	c4	c4	NOUN
ejpam-4704	165	19	=	=	SYM
ejpam-4704	165	20	v1u2m−2u1v2m−2wv1	v1u2m−2u1v2m−2wv1	PROPN
ejpam-4704	165	21	,	,	PUNCT
ejpam-4704	165	22	c5	c5	PROPN
ejpam-4704	165	23	=	=	SYM
ejpam-4704	165	24	v2m−2u1v2wv2m−2	v2m−2u1v2wv2m−2	PROPN
ejpam-4704	165	25	,	,	PUNCT
ejpam-4704	165	26	c6	c6	PROPN
ejpam-4704	165	27	=	=	PUNCT
ejpam-4704	165	28	u2m−1v2m−4wv2m−3u2m−4u2m−1	u2m−1v2m−4wv2m−3u2m−4u2m−1	PROPN
ejpam-4704	165	29	in	in	ADP
ejpam-4704	165	30	order	order	NOUN
ejpam-4704	165	31	b	b	NOUN
ejpam-4704	165	32	to	to	PART
ejpam-4704	165	33	be	be	AUX
ejpam-4704	165	34	the	the	DET
ejpam-4704	165	35	base	base	NOUN
ejpam-4704	165	36	for	for	ADP
ejpam-4704	165	37	the	the	DET
ejpam-4704	165	38	cycles	cycle	NOUN
ejpam-4704	165	39	space	space	NOUN
ejpam-4704	165	40	of	of	ADP
ejpam-4704	165	41	the	the	DET
ejpam-4704	165	42	graph	graph	NOUN
ejpam-4704	165	43	µ(sc	µ(sc	NUM
ejpam-4704	165	44	m	m	NOUN
ejpam-4704	165	45	)	)	PUNCT
ejpam-4704	165	46	,	,	PUNCT
ejpam-4704	165	47	it	it	PRON
ejpam-4704	165	48	must	must	AUX
ejpam-4704	165	49	be	be	AUX
ejpam-4704	165	50	|b|	|b|	VERB
ejpam-4704	165	51	=	=	PUNCT
ejpam-4704	165	52	dim	dim	VERB
ejpam-4704	165	53	c(µ(sc	c(µ(sc	NOUN
ejpam-4704	165	54	m	m	NOUN
ejpam-4704	165	55	)	)	PUNCT
ejpam-4704	165	56	)	)	PUNCT
ejpam-4704	165	57	,	,	PUNCT
ejpam-4704	165	58	and	and	CCONJ
ejpam-4704	165	59	b	b	NOUN
ejpam-4704	165	60	must	must	AUX
ejpam-4704	165	61	be	be	AUX
ejpam-4704	165	62	a	a	DET
ejpam-4704	165	63	linearly	linearly	ADV
ejpam-4704	165	64	independent	independent	ADJ
ejpam-4704	165	65	set	set	NOUN
ejpam-4704	165	66	of	of	ADP
ejpam-4704	165	67	cycles	cycle	NOUN
ejpam-4704	165	68	.	.	PUNCT
ejpam-4704	166	1	it	it	PRON
ejpam-4704	166	2	is	be	AUX
ejpam-4704	166	3	known	know	VERB
ejpam-4704	166	4	that	that	SCONJ
ejpam-4704	166	5	dim	dim	VERB
ejpam-4704	166	6	c(µ(sc	c(µ(sc	NOUN
ejpam-4704	166	7	m	m	NOUN
ejpam-4704	166	8	)	)	PUNCT
ejpam-4704	166	9	)	)	PUNCT
ejpam-4704	167	1	=	=	PUNCT
ejpam-4704	167	2	7m−	7m−	NUM
ejpam-4704	167	3	8	8	NUM
ejpam-4704	167	4	,	,	PUNCT
ejpam-4704	167	5	and	and	CCONJ
ejpam-4704	167	6	|b|	|b|	PROPN
ejpam-4704	167	7	=	=	NOUN
ejpam-4704	167	8	|b(µ(sc	|b(µ(sc	PROPN
ejpam-4704	168	1	m))|	m))|	PROPN
ejpam-4704	169	1	=	=	PUNCT
ejpam-4704	170	1	|	|	ADV
ejpam-4704	170	2	∪5	∪5	PROPN
ejpam-4704	170	3	i=1	i=1	PROPN
ejpam-4704	171	1	si|+	si|+	PROPN
ejpam-4704	171	2	|{c1	|{c1	PROPN
ejpam-4704	171	3	,	,	PUNCT
ejpam-4704	171	4	c2	c2	PROPN
ejpam-4704	171	5	,	,	PUNCT
ejpam-4704	171	6	c3	c3	PROPN
ejpam-4704	171	7	,	,	PUNCT
ejpam-4704	171	8	c4	c4	NOUN
ejpam-4704	171	9	,	,	PUNCT
ejpam-4704	171	10	c5	c5	PROPN
ejpam-4704	171	11	,	,	PUNCT
ejpam-4704	171	12	c6}|	c6}|	NOUN
ejpam-4704	171	13	=	=	SYM
ejpam-4704	171	14	(	(	PUNCT
ejpam-4704	171	15	7m−	7m−	NUM
ejpam-4704	171	16	14)+	14)+	NUM
ejpam-4704	171	17	6	6	NUM
ejpam-4704	171	18	=	=	SYM
ejpam-4704	171	19	7m−	7m−	NUM
ejpam-4704	171	20	8	8	NUM
ejpam-4704	171	21	,	,	PUNCT
ejpam-4704	171	22	since	since	SCONJ
ejpam-4704	171	23	|s1|	|s1|	NOUN
ejpam-4704	171	24	=	=	SYM
ejpam-4704	171	25	|s2|	|s2|	NOUN
ejpam-4704	172	1	=	=	SYM
ejpam-4704	172	2	2m−	2m−	PROPN
ejpam-4704	172	3	3	3	NUM
ejpam-4704	172	4	and	and	CCONJ
ejpam-4704	172	5	|s3|	|s3|	NOUN
ejpam-4704	172	6	=	=	SYM
ejpam-4704	172	7	m−	m−	PROPN
ejpam-4704	172	8	2	2	NUM
ejpam-4704	172	9	,	,	PUNCT
ejpam-4704	172	10	|s4|	|s4|	NOUN
ejpam-4704	172	11	=	=	SYM
ejpam-4704	172	12	|s5|	|s5|	PROPN
ejpam-4704	173	1	=	=	SYM
ejpam-4704	173	2	m−	m−	PROPN
ejpam-4704	173	3	3	3	NUM
ejpam-4704	173	4	.	.	PUNCT
ejpam-4704	174	1	it	it	PRON
ejpam-4704	174	2	remains	remain	VERB
ejpam-4704	174	3	to	to	PART
ejpam-4704	174	4	show	show	VERB
ejpam-4704	174	5	that	that	SCONJ
ejpam-4704	174	6	b	b	NOUN
ejpam-4704	174	7	is	be	AUX
ejpam-4704	174	8	linearly	linearly	ADV
ejpam-4704	174	9	independent	independent	ADJ
ejpam-4704	174	10	.	.	PUNCT
ejpam-4704	175	1	it	it	PRON
ejpam-4704	175	2	is	be	AUX
ejpam-4704	175	3	clear	clear	ADJ
ejpam-4704	175	4	that	that	SCONJ
ejpam-4704	175	5	each	each	PRON
ejpam-4704	175	6	of	of	ADP
ejpam-4704	175	7	s1	s1	PROPN
ejpam-4704	175	8	,	,	PUNCT
ejpam-4704	175	9	s2	s2	PROPN
ejpam-4704	175	10	,	,	PUNCT
ejpam-4704	175	11	s3	s3	PROPN
ejpam-4704	175	12	,	,	PUNCT
ejpam-4704	175	13	s4	s4	PROPN
ejpam-4704	175	14	and	and	CCONJ
ejpam-4704	175	15	s5	s5	PROPN
ejpam-4704	175	16	is	be	AUX
ejpam-4704	175	17	linearly	linearly	ADV
ejpam-4704	175	18	independent	independent	ADJ
ejpam-4704	175	19	because	because	SCONJ
ejpam-4704	175	20	it	it	PRON
ejpam-4704	175	21	is	be	AUX
ejpam-4704	175	22	represent	represent	VERB
ejpam-4704	175	23	the	the	DET
ejpam-4704	175	24	boundaries	boundary	NOUN
ejpam-4704	175	25	of	of	ADP
ejpam-4704	175	26	the	the	DET
ejpam-4704	175	27	faces	face	NOUN
ejpam-4704	175	28	of	of	ADP
ejpam-4704	175	29	a	a	DET
ejpam-4704	175	30	planar	planar	ADJ
ejpam-4704	175	31	subgraph	subgraph	NOUN
ejpam-4704	175	32	.	.	PUNCT
ejpam-4704	176	1	s1	s1	NOUN
ejpam-4704	176	2	∪	∪	NOUN
ejpam-4704	176	3	s2	s2	NOUN
ejpam-4704	176	4	is	be	AUX
ejpam-4704	176	5	linearly	linearly	ADV
ejpam-4704	176	6	independent	independent	ADJ
ejpam-4704	176	7	b.	b.	PROPN
ejpam-4704	176	8	m.	m.	PROPN
ejpam-4704	176	9	sulaiman	sulaiman	PROPN
ejpam-4704	176	10	,	,	PUNCT
ejpam-4704	176	11	r.	r.	PROPN
ejpam-4704	176	12	s.	s.	PROPN
ejpam-4704	176	13	hasan	hasan	PROPN
ejpam-4704	176	14	,	,	PUNCT
ejpam-4704	176	15	r.	r.	PROPN
ejpam-4704	176	16	a.	a.	PROPN
ejpam-4704	176	17	mustafa	mustafa	PROPN
ejpam-4704	176	18	/	/	SYM
ejpam-4704	176	19	eur	eur	PROPN
ejpam-4704	176	20	.	.	PUNCT
ejpam-4704	177	1	j.	j.	PROPN
ejpam-4704	177	2	pure	pure	PROPN
ejpam-4704	177	3	appl	appl	PROPN
ejpam-4704	177	4	.	.	PROPN
ejpam-4704	177	5	math	math	PROPN
ejpam-4704	177	6	,	,	PUNCT
ejpam-4704	177	7	16	16	NUM
ejpam-4704	177	8	(	(	PUNCT
ejpam-4704	177	9	2	2	NUM
ejpam-4704	177	10	)	)	PUNCT
ejpam-4704	177	11	(	(	PUNCT
ejpam-4704	177	12	2023	2023	NUM
ejpam-4704	177	13	)	)	PUNCT
ejpam-4704	177	14	,	,	PUNCT
ejpam-4704	177	15	953	953	NUM
ejpam-4704	177	16	-	-	SYM
ejpam-4704	177	17	964	964	NUM
ejpam-4704	177	18	960	960	NUM
ejpam-4704	177	19	because	because	SCONJ
ejpam-4704	177	20	any	any	DET
ejpam-4704	177	21	linear	linear	ADJ
ejpam-4704	177	22	combination	combination	NOUN
ejpam-4704	177	23	of	of	ADP
ejpam-4704	177	24	s2	s2	PROPN
ejpam-4704	177	25	contains	contain	VERB
ejpam-4704	177	26	edges	edge	NOUN
ejpam-4704	177	27	of	of	ADP
ejpam-4704	177	28	type	type	NOUN
ejpam-4704	177	29	wvi	wvi	NOUN
ejpam-4704	177	30	,	,	PUNCT
ejpam-4704	177	31	i	i	PRON
ejpam-4704	177	32	=	=	NOUN
ejpam-4704	177	33	1	1	NUM
ejpam-4704	177	34	,	,	PUNCT
ejpam-4704	177	35	2	2	NUM
ejpam-4704	177	36	,	,	PUNCT
ejpam-4704	177	37	.	.	PUNCT
ejpam-4704	177	38	.	.	PUNCT
ejpam-4704	177	39	.	.	PUNCT
ejpam-4704	178	1	,	,	PUNCT
ejpam-4704	178	2	2m−1	2m−1	NUM
ejpam-4704	178	3	,	,	PUNCT
ejpam-4704	178	4	which	which	PRON
ejpam-4704	178	5	are	be	AUX
ejpam-4704	178	6	not	not	PART
ejpam-4704	178	7	found	find	VERB
ejpam-4704	178	8	in	in	ADP
ejpam-4704	178	9	any	any	DET
ejpam-4704	178	10	linear	linear	ADJ
ejpam-4704	178	11	combination	combination	NOUN
ejpam-4704	178	12	of	of	ADP
ejpam-4704	178	13	s1	s1	NOUN
ejpam-4704	178	14	.	.	PUNCT
ejpam-4704	179	1	also	also	ADV
ejpam-4704	179	2	,	,	PUNCT
ejpam-4704	179	3	s3∪s4	s3∪s4	NOUN
ejpam-4704	179	4	is	be	AUX
ejpam-4704	179	5	linearly	linearly	ADV
ejpam-4704	179	6	independent	independent	ADJ
ejpam-4704	179	7	because	because	SCONJ
ejpam-4704	179	8	any	any	DET
ejpam-4704	179	9	linear	linear	ADJ
ejpam-4704	179	10	combination	combination	NOUN
ejpam-4704	179	11	of	of	ADP
ejpam-4704	179	12	s4	s4	PROPN
ejpam-4704	179	13	contains	contain	VERB
ejpam-4704	179	14	edges	edge	NOUN
ejpam-4704	179	15	of	of	ADP
ejpam-4704	179	16	type	type	NOUN
ejpam-4704	179	17	u2m−1ui	u2m−1ui	NOUN
ejpam-4704	179	18	,	,	PUNCT
ejpam-4704	179	19	i	i	PRON
ejpam-4704	179	20	=	=	NOUN
ejpam-4704	179	21	2	2	NUM
ejpam-4704	179	22	,	,	PUNCT
ejpam-4704	179	23	4	4	NUM
ejpam-4704	179	24	,	,	PUNCT
ejpam-4704	179	25	.	.	PUNCT
ejpam-4704	179	26	.	.	PUNCT
ejpam-4704	180	1	.	.	PUNCT
ejpam-4704	181	1	,	,	PUNCT
ejpam-4704	181	2	2m−4	2m−4	NUM
ejpam-4704	181	3	,	,	PUNCT
ejpam-4704	181	4	which	which	PRON
ejpam-4704	181	5	are	be	AUX
ejpam-4704	181	6	not	not	PART
ejpam-4704	181	7	found	find	VERB
ejpam-4704	181	8	in	in	ADP
ejpam-4704	181	9	any	any	DET
ejpam-4704	181	10	linear	linear	ADJ
ejpam-4704	181	11	combination	combination	NOUN
ejpam-4704	181	12	of	of	ADP
ejpam-4704	181	13	s3	s3	PROPN
ejpam-4704	181	14	.	.	PUNCT
ejpam-4704	182	1	in	in	ADP
ejpam-4704	182	2	addition	addition	NOUN
ejpam-4704	182	3	,	,	PUNCT
ejpam-4704	182	4	s3∪s4∪s5	s3∪s4∪s5	PROPN
ejpam-4704	182	5	is	be	AUX
ejpam-4704	182	6	linearly	linearly	ADV
ejpam-4704	182	7	independent	independent	ADJ
ejpam-4704	182	8	since	since	SCONJ
ejpam-4704	182	9	any	any	DET
ejpam-4704	182	10	linear	linear	ADJ
ejpam-4704	182	11	combination	combination	NOUN
ejpam-4704	182	12	of	of	ADP
ejpam-4704	182	13	s5	s5	PROPN
ejpam-4704	182	14	contains	contain	VERB
ejpam-4704	182	15	edges	edge	NOUN
ejpam-4704	182	16	of	of	ADP
ejpam-4704	182	17	type	type	NOUN
ejpam-4704	182	18	wvi	wvi	NOUN
ejpam-4704	182	19	,	,	PUNCT
ejpam-4704	182	20	i	i	PRON
ejpam-4704	182	21	=	=	NOUN
ejpam-4704	182	22	2	2	NUM
ejpam-4704	182	23	,	,	PUNCT
ejpam-4704	182	24	4	4	NUM
ejpam-4704	182	25	,	,	PUNCT
ejpam-4704	182	26	.	.	PUNCT
ejpam-4704	182	27	.	.	PUNCT
ejpam-4704	182	28	.	.	PUNCT
ejpam-4704	183	1	,	,	PUNCT
ejpam-4704	184	1	2m−	2m−	PROPN
ejpam-4704	184	2	1	1	NUM
ejpam-4704	184	3	,	,	PUNCT
ejpam-4704	184	4	which	which	PRON
ejpam-4704	184	5	are	be	AUX
ejpam-4704	184	6	not	not	PART
ejpam-4704	184	7	found	find	VERB
ejpam-4704	184	8	in	in	ADP
ejpam-4704	184	9	any	any	DET
ejpam-4704	184	10	linear	linear	ADJ
ejpam-4704	184	11	combination	combination	NOUN
ejpam-4704	184	12	of	of	ADP
ejpam-4704	184	13	s3∪s4	s3∪s4	NOUN
ejpam-4704	184	14	.	.	PUNCT
ejpam-4704	185	1	also	also	ADV
ejpam-4704	185	2	,	,	PUNCT
ejpam-4704	185	3	(	(	PUNCT
ejpam-4704	185	4	s1∪s2)∪(s3∪s4∪s5	s1∪s2)∪(s3∪s4∪s5	X
ejpam-4704	185	5	)	)	PUNCT
ejpam-4704	185	6	is	be	AUX
ejpam-4704	185	7	linearly	linearly	ADV
ejpam-4704	185	8	independent	independent	ADJ
ejpam-4704	185	9	because	because	SCONJ
ejpam-4704	185	10	s3	s3	PROPN
ejpam-4704	185	11	∪	∪	NOUN
ejpam-4704	185	12	s4	s4	PROPN
ejpam-4704	185	13	∪	∪	X
ejpam-4704	185	14	s5	s5	PROPN
ejpam-4704	185	15	contains	contain	VERB
ejpam-4704	185	16	edges	edge	NOUN
ejpam-4704	185	17	of	of	ADP
ejpam-4704	185	18	type	type	NOUN
ejpam-4704	185	19	u2m−1ui	u2m−1ui	NOUN
ejpam-4704	185	20	,	,	PUNCT
ejpam-4704	185	21	i	i	PRON
ejpam-4704	185	22	=	=	NOUN
ejpam-4704	185	23	2	2	NUM
ejpam-4704	185	24	,	,	PUNCT
ejpam-4704	185	25	4	4	NUM
ejpam-4704	185	26	,	,	PUNCT
ejpam-4704	185	27	.	.	PUNCT
ejpam-4704	185	28	.	.	PUNCT
ejpam-4704	186	1	.	.	PUNCT
ejpam-4704	187	1	,	,	PUNCT
ejpam-4704	187	2	2	2	NUM
ejpam-4704	187	3	m	m	NOUN
ejpam-4704	187	4	−	−	NOUN
ejpam-4704	187	5	4	4	NUM
ejpam-4704	187	6	,	,	PUNCT
ejpam-4704	187	7	which	which	PRON
ejpam-4704	187	8	are	be	AUX
ejpam-4704	187	9	not	not	PART
ejpam-4704	187	10	found	find	VERB
ejpam-4704	187	11	in	in	ADP
ejpam-4704	187	12	any	any	DET
ejpam-4704	187	13	linear	linear	ADJ
ejpam-4704	187	14	combination	combination	NOUN
ejpam-4704	187	15	of	of	ADP
ejpam-4704	187	16	s1	s1	PROPN
ejpam-4704	187	17	∪	∪	X
ejpam-4704	187	18	s2	s2	PROPN
ejpam-4704	187	19	.	.	PUNCT
ejpam-4704	188	1	finally	finally	ADV
ejpam-4704	188	2	,	,	PUNCT
ejpam-4704	188	3	(	(	PUNCT
ejpam-4704	188	4	∪5	∪5	PROPN
ejpam-4704	188	5	i=1si)∪	i=1si)∪	X
ejpam-4704	188	6	(	(	PUNCT
ejpam-4704	188	7	{	{	PUNCT
ejpam-4704	188	8	c1	c1	NOUN
ejpam-4704	188	9	,	,	PUNCT
ejpam-4704	188	10	c2	c2	PROPN
ejpam-4704	188	11	,	,	PUNCT
ejpam-4704	188	12	c3	c3	PROPN
ejpam-4704	188	13	,	,	PUNCT
ejpam-4704	188	14	c4	c4	NOUN
ejpam-4704	188	15	,	,	PUNCT
ejpam-4704	188	16	c5	c5	PROPN
ejpam-4704	188	17	,	,	PUNCT
ejpam-4704	188	18	c6	c6	PROPN
ejpam-4704	188	19	}	}	PUNCT
ejpam-4704	188	20	)	)	PUNCT
ejpam-4704	188	21	is	be	AUX
ejpam-4704	188	22	linearly	linearly	ADV
ejpam-4704	188	23	independent	independent	ADJ
ejpam-4704	188	24	because	because	SCONJ
ejpam-4704	188	25	any	any	DET
ejpam-4704	188	26	linear	linear	ADJ
ejpam-4704	188	27	combination	combination	NOUN
ejpam-4704	188	28	of	of	ADP
ejpam-4704	188	29	{	{	PUNCT
ejpam-4704	188	30	c1	c1	PROPN
ejpam-4704	188	31	,	,	PUNCT
ejpam-4704	188	32	c2	c2	PROPN
ejpam-4704	188	33	,	,	PUNCT
ejpam-4704	188	34	c3	c3	PROPN
ejpam-4704	188	35	,	,	PUNCT
ejpam-4704	188	36	c4	c4	NOUN
ejpam-4704	188	37	,	,	PUNCT
ejpam-4704	188	38	c5	c5	PROPN
ejpam-4704	188	39	,	,	PUNCT
ejpam-4704	188	40	c6	c6	PROPN
ejpam-4704	188	41	}	}	PUNCT
ejpam-4704	188	42	contains	contain	VERB
ejpam-4704	188	43	edges	edge	NOUN
ejpam-4704	188	44	of	of	ADP
ejpam-4704	188	45	type	type	NOUN
ejpam-4704	188	46	u2m−2u1	u2m−2u1	PROPN
ejpam-4704	188	47	,	,	PUNCT
ejpam-4704	188	48	v2m−2v1	v2m−2v1	PROPN
ejpam-4704	188	49	,	,	PUNCT
ejpam-4704	188	50	which	which	PRON
ejpam-4704	188	51	are	be	AUX
ejpam-4704	188	52	not	not	PART
ejpam-4704	188	53	found	find	VERB
ejpam-4704	188	54	in	in	ADP
ejpam-4704	188	55	any	any	DET
ejpam-4704	188	56	linear	linear	ADJ
ejpam-4704	188	57	combination	combination	NOUN
ejpam-4704	188	58	of	of	ADP
ejpam-4704	188	59	∪5	∪5	PROPN
ejpam-4704	188	60	i=1si	i=1si	NUM
ejpam-4704	188	61	.	.	PUNCT
ejpam-4704	188	62	to	to	PART
ejpam-4704	188	63	find	find	VERB
ejpam-4704	188	64	the	the	DET
ejpam-4704	188	65	fold	fold	NOUN
ejpam-4704	188	66	for	for	ADP
ejpam-4704	188	67	the	the	DET
ejpam-4704	188	68	base	base	NOUN
ejpam-4704	188	69	b	b	NOUN
ejpam-4704	188	70	we	we	PRON
ejpam-4704	188	71	divide	divide	VERB
ejpam-4704	188	72	the	the	DET
ejpam-4704	188	73	edges	edge	NOUN
ejpam-4704	188	74	of	of	ADP
ejpam-4704	188	75	the	the	DET
ejpam-4704	188	76	graph	graph	NOUN
ejpam-4704	188	77	µ(sc	µ(sc	NUM
ejpam-4704	188	78	m	m	NOUN
ejpam-4704	188	79	)	)	PUNCT
ejpam-4704	188	80	into	into	ADP
ejpam-4704	188	81	:	:	PUNCT
ejpam-4704	188	82	e1	e1	NOUN
ejpam-4704	188	83	=	=	SYM
ejpam-4704	188	84	{	{	PUNCT
ejpam-4704	188	85	uiui+1	uiui+1	PROPN
ejpam-4704	188	86	,	,	PUNCT
ejpam-4704	188	87	i	i	PRON
ejpam-4704	188	88	=	=	NOUN
ejpam-4704	188	89	2	2	NUM
ejpam-4704	188	90	,	,	PUNCT
ejpam-4704	188	91	3	3	NUM
ejpam-4704	188	92	,	,	PUNCT
ejpam-4704	188	93	.	.	PUNCT
ejpam-4704	188	94	.	.	PUNCT
ejpam-4704	188	95	.	.	PUNCT
ejpam-4704	189	1	,	,	PUNCT
ejpam-4704	189	2	2m−	2m−	PROPN
ejpam-4704	189	3	3	3	NUM
ejpam-4704	189	4	}	}	PUNCT
ejpam-4704	189	5	,	,	PUNCT
ejpam-4704	189	6	e2	e2	PROPN
ejpam-4704	189	7	=	=	SYM
ejpam-4704	189	8	{	{	PUNCT
ejpam-4704	189	9	uivi+1	uivi+1	PROPN
ejpam-4704	189	10	,	,	PUNCT
ejpam-4704	189	11	i	i	NOUN
ejpam-4704	189	12	=	=	NOUN
ejpam-4704	189	13	2	2	NUM
ejpam-4704	189	14	,	,	PUNCT
ejpam-4704	189	15	3	3	NUM
ejpam-4704	189	16	,	,	PUNCT
ejpam-4704	189	17	.	.	PUNCT
ejpam-4704	189	18	.	.	PUNCT
ejpam-4704	189	19	.	.	PUNCT
ejpam-4704	190	1	,	,	PUNCT
ejpam-4704	190	2	2m−	2m−	PROPN
ejpam-4704	190	3	5	5	NUM
ejpam-4704	190	4	}	}	PUNCT
ejpam-4704	190	5	∪	∪	ADJ
ejpam-4704	190	6	{	{	PUNCT
ejpam-4704	190	7	u2m−3v2m−2	u2m−3v2m−2	PROPN
ejpam-4704	190	8	}	}	PUNCT
ejpam-4704	190	9	e3	e3	NOUN
ejpam-4704	190	10	=	=	SYM
ejpam-4704	190	11	{	{	PUNCT
ejpam-4704	190	12	viui+1	viui+1	NOUN
ejpam-4704	190	13	,	,	PUNCT
ejpam-4704	190	14	i	i	PRON
ejpam-4704	190	15	=	=	NOUN
ejpam-4704	190	16	1	1	NUM
ejpam-4704	190	17	,	,	PUNCT
ejpam-4704	190	18	2	2	NUM
ejpam-4704	190	19	,	,	PUNCT
ejpam-4704	190	20	.	.	PUNCT
ejpam-4704	190	21	.	.	PUNCT
ejpam-4704	190	22	.	.	PUNCT
ejpam-4704	191	1	,	,	PUNCT
ejpam-4704	191	2	2m−	2m−	NOUN
ejpam-4704	191	3	3	3	NUM
ejpam-4704	191	4	}	}	PUNCT
ejpam-4704	191	5	∪	∪	ADJ
ejpam-4704	191	6	{	{	PUNCT
ejpam-4704	191	7	u2m−1vj	u2m−1vj	NOUN
ejpam-4704	191	8	,	,	PUNCT
ejpam-4704	191	9	j	j	PROPN
ejpam-4704	191	10	=	=	SYM
ejpam-4704	191	11	2	2	NUM
ejpam-4704	191	12	,	,	PUNCT
ejpam-4704	191	13	4	4	NUM
ejpam-4704	191	14	,	,	PUNCT
ejpam-4704	191	15	.	.	PUNCT
ejpam-4704	191	16	.	.	PUNCT
ejpam-4704	191	17	.	.	PUNCT
ejpam-4704	192	1	,	,	PUNCT
ejpam-4704	193	1	2m−	2m−	PROPN
ejpam-4704	193	2	6	6	NUM
ejpam-4704	193	3	}	}	PUNCT
ejpam-4704	193	4	e4	e4	PROPN
ejpam-4704	193	5	=	=	SYM
ejpam-4704	193	6	{	{	PUNCT
ejpam-4704	193	7	wvi	wvi	PROPN
ejpam-4704	193	8	,	,	PUNCT
ejpam-4704	193	9	i	i	PRON
ejpam-4704	193	10	=	=	NOUN
ejpam-4704	193	11	3	3	NUM
ejpam-4704	193	12	,	,	PUNCT
ejpam-4704	193	13	4	4	NUM
ejpam-4704	193	14	,	,	PUNCT
ejpam-4704	193	15	.	.	PUNCT
ejpam-4704	193	16	.	.	PUNCT
ejpam-4704	193	17	.	.	PUNCT
ejpam-4704	194	1	,	,	PUNCT
ejpam-4704	195	1	2m−	2m−	PROPN
ejpam-4704	195	2	5	5	NUM
ejpam-4704	195	3	}	}	PUNCT
ejpam-4704	195	4	e5	e5	NOUN
ejpam-4704	195	5	=	=	PUNCT
ejpam-4704	195	6	{	{	PUNCT
ejpam-4704	195	7	u2m−1ui	u2m−1ui	PROPN
ejpam-4704	195	8	,	,	PUNCT
ejpam-4704	195	9	i	i	PRON
ejpam-4704	195	10	=	=	NOUN
ejpam-4704	195	11	4	4	NUM
ejpam-4704	195	12	,	,	PUNCT
ejpam-4704	195	13	6	6	NUM
ejpam-4704	195	14	,	,	PUNCT
ejpam-4704	195	15	.	.	PUNCT
ejpam-4704	195	16	.	.	PUNCT
ejpam-4704	195	17	.	.	PUNCT
ejpam-4704	196	1	,	,	PUNCT
ejpam-4704	196	2	2m−	2m−	PROPN
ejpam-4704	196	3	6	6	NUM
ejpam-4704	196	4	}	}	PUNCT
ejpam-4704	196	5	∪	∪	ADJ
ejpam-4704	196	6	{	{	PUNCT
ejpam-4704	196	7	v2m−1uj	v2m−1uj	NOUN
ejpam-4704	196	8	,	,	PUNCT
ejpam-4704	196	9	j	j	PROPN
ejpam-4704	196	10	=	=	SYM
ejpam-4704	196	11	2	2	NUM
ejpam-4704	196	12	,	,	PUNCT
ejpam-4704	196	13	4	4	NUM
ejpam-4704	196	14	,	,	PUNCT
ejpam-4704	196	15	.	.	PUNCT
ejpam-4704	196	16	.	.	PUNCT
ejpam-4704	196	17	.	.	PUNCT
ejpam-4704	197	1	,	,	PUNCT
ejpam-4704	197	2	2m−	2m−	PROPN
ejpam-4704	197	3	4	4	NUM
ejpam-4704	197	4	}	}	PUNCT
ejpam-4704	197	5	e6	e6	NOUN
ejpam-4704	197	6	=	=	SYM
ejpam-4704	197	7	{	{	PUNCT
ejpam-4704	197	8	v2m−2u1	v2m−2u1	PROPN
ejpam-4704	197	9	,	,	PUNCT
ejpam-4704	197	10	u2m−2u1	u2m−2u1	PROPN
ejpam-4704	197	11	,	,	PUNCT
ejpam-4704	197	12	u2m−2v1	u2m−2v1	PROPN
ejpam-4704	197	13	}	}	PUNCT
ejpam-4704	197	14	e7	e7	PROPN
ejpam-4704	197	15	=	=	PUNCT
ejpam-4704	197	16	{	{	PUNCT
ejpam-4704	197	17	u2m−2v2m−1	u2m−2v2m−1	PROPN
ejpam-4704	197	18	,	,	PUNCT
ejpam-4704	197	19	u1u2	u1u2	NOUN
ejpam-4704	197	20	,	,	PUNCT
ejpam-4704	197	21	wv2m−1	wv2m−1	NOUN
ejpam-4704	197	22	,	,	PUNCT
ejpam-4704	197	23	u2m−1u2	u2m−1u2	PROPN
ejpam-4704	197	24	,	,	PUNCT
ejpam-4704	197	25	u1v2	u1v2	ADJ
ejpam-4704	197	26	}	}	PUNCT
ejpam-4704	197	27	e8	e8	PROPN
ejpam-4704	197	28	=	=	SYM
ejpam-4704	197	29	{	{	PUNCT
ejpam-4704	197	30	wv1	wv1	PROPN
ejpam-4704	197	31	,	,	PUNCT
ejpam-4704	197	32	wv2m−2	wv2m−2	NUM
ejpam-4704	197	33	,	,	PUNCT
ejpam-4704	197	34	u2m−2u2m−1	u2m−2u2m−1	NOUN
ejpam-4704	197	35	}	}	PUNCT
ejpam-4704	197	36	e9	e9	PROPN
ejpam-4704	197	37	=	=	SYM
ejpam-4704	197	38	{	{	PUNCT
ejpam-4704	197	39	wv2	wv2	PROPN
ejpam-4704	197	40	,	,	PUNCT
ejpam-4704	197	41	wv2m−4	wv2m−4	NUM
ejpam-4704	197	42	,	,	PUNCT
ejpam-4704	197	43	wv2m−3	wv2m−3	X
ejpam-4704	197	44	,	,	PUNCT
ejpam-4704	197	45	u2m−4v2m−3	u2m−4v2m−3	PROPN
ejpam-4704	197	46	,	,	PUNCT
ejpam-4704	197	47	u2m−1u2m−4	u2m−1u2m−4	PROPN
ejpam-4704	197	48	,	,	PUNCT
ejpam-4704	197	49	u2m−1v2m−2	u2m−1v2m−2	INTJ
ejpam-4704	197	50	,	,	PUNCT
ejpam-4704	197	51	u2m−1v2m−4	u2m−1v2m−4	PROPN
ejpam-4704	197	52	}	}	PUNCT
ejpam-4704	197	53	now	now	ADV
ejpam-4704	197	54	,	,	PUNCT
ejpam-4704	197	55	we	we	PRON
ejpam-4704	197	56	calculate	calculate	VERB
ejpam-4704	197	57	the	the	DET
ejpam-4704	197	58	fold	fold	NOUN
ejpam-4704	197	59	for	for	ADP
ejpam-4704	197	60	a	a	DET
ejpam-4704	197	61	set	set	NOUN
ejpam-4704	197	62	of	of	ADP
ejpam-4704	197	63	the	the	DET
ejpam-4704	197	64	edges	edge	NOUN
ejpam-4704	197	65	of	of	ADP
ejpam-4704	197	66	the	the	DET
ejpam-4704	197	67	graph	graph	NOUN
ejpam-4704	197	68	µ(sc	µ(sc	NUM
ejpam-4704	197	69	m	m	NOUN
ejpam-4704	197	70	)	)	PUNCT
ejpam-4704	197	71	,	,	PUNCT
ejpam-4704	197	72	case	case	NOUN
ejpam-4704	198	1	i	i	PRON
ejpam-4704	198	2	:	:	PUNCT
ejpam-4704	198	3	fb(µ(sc	fb(µ(sc	ADJ
ejpam-4704	198	4	m))(e	m))(e	PROPN
ejpam-4704	198	5	)	)	PUNCT
ejpam-4704	198	6	is	be	AUX
ejpam-4704	198	7	equal	equal	ADJ
ejpam-4704	198	8	to	to	ADP
ejpam-4704	198	9	2	2	NUM
ejpam-4704	198	10	for	for	ADP
ejpam-4704	198	11	all	all	DET
ejpam-4704	198	12	e	e	PROPN
ejpam-4704	198	13	∈	∈	PROPN
ejpam-4704	198	14	ei	ei	X
ejpam-4704	198	15	,	,	PUNCT
ejpam-4704	198	16	i	i	PRON
ejpam-4704	198	17	=	=	NOUN
ejpam-4704	198	18	1	1	NUM
ejpam-4704	198	19	,	,	PUNCT
ejpam-4704	198	20	7	7	NUM
ejpam-4704	198	21	.	.	PUNCT
ejpam-4704	198	22	case	case	NOUN
ejpam-4704	198	23	ii	ii	PROPN
ejpam-4704	198	24	:	:	PUNCT
ejpam-4704	198	25	fb(µ(sc	fb(µ(sc	PROPN
ejpam-4704	198	26	m))(e	m))(e	PROPN
ejpam-4704	198	27	)	)	PUNCT
ejpam-4704	198	28	is	be	AUX
ejpam-4704	198	29	less	less	ADJ
ejpam-4704	198	30	than	than	ADP
ejpam-4704	198	31	or	or	CCONJ
ejpam-4704	198	32	equal	equal	ADJ
ejpam-4704	198	33	to	to	ADP
ejpam-4704	198	34	3	3	NUM
ejpam-4704	198	35	for	for	ADP
ejpam-4704	198	36	all	all	DET
ejpam-4704	198	37	e	e	PROPN
ejpam-4704	198	38	∈	∈	PROPN
ejpam-4704	198	39	ei	ei	X
ejpam-4704	198	40	,	,	PUNCT
ejpam-4704	198	41	i	i	PRON
ejpam-4704	198	42	=	=	NOUN
ejpam-4704	198	43	2	2	NUM
ejpam-4704	198	44	,	,	PUNCT
ejpam-4704	198	45	3	3	NUM
ejpam-4704	198	46	,	,	PUNCT
ejpam-4704	198	47	4	4	NUM
ejpam-4704	198	48	,	,	PUNCT
ejpam-4704	198	49	5	5	NUM
ejpam-4704	198	50	,	,	PUNCT
ejpam-4704	198	51	6	6	NUM
ejpam-4704	198	52	,	,	PUNCT
ejpam-4704	198	53	8	8	NUM
ejpam-4704	198	54	,	,	PUNCT
ejpam-4704	198	55	9	9	NUM
ejpam-4704	198	56	.	.	X
ejpam-4704	198	57	from	from	ADP
ejpam-4704	198	58	the	the	DET
ejpam-4704	198	59	above	above	ADJ
ejpam-4704	198	60	two	two	NUM
ejpam-4704	198	61	cases	case	NOUN
ejpam-4704	198	62	,	,	PUNCT
ejpam-4704	198	63	it	it	PRON
ejpam-4704	198	64	can	can	AUX
ejpam-4704	198	65	be	be	AUX
ejpam-4704	198	66	seen	see	VERB
ejpam-4704	198	67	that	that	SCONJ
ejpam-4704	198	68	the	the	DET
ejpam-4704	198	69	fold	fold	NOUN
ejpam-4704	198	70	for	for	ADP
ejpam-4704	198	71	each	each	DET
ejpam-4704	198	72	edge	edge	NOUN
ejpam-4704	198	73	in	in	ADP
ejpam-4704	198	74	the	the	DET
ejpam-4704	198	75	graph	graph	NOUN
ejpam-4704	198	76	µ(sc	µ(sc	NUM
ejpam-4704	198	77	m	m	NOUN
ejpam-4704	198	78	)	)	PUNCT
ejpam-4704	198	79	is	be	AUX
ejpam-4704	198	80	not	not	PART
ejpam-4704	198	81	more	more	ADJ
ejpam-4704	198	82	than	than	ADP
ejpam-4704	198	83	3	3	NUM
ejpam-4704	198	84	in	in	ADP
ejpam-4704	198	85	the	the	DET
ejpam-4704	198	86	base	base	NOUN
ejpam-4704	198	87	b(µ(sc	b(µ(sc	NOUN
ejpam-4704	198	88	m	m	PROPN
ejpam-4704	198	89	)	)	PUNCT
ejpam-4704	198	90	)	)	PUNCT
ejpam-4704	198	91	;	;	PUNCT
ejpam-4704	198	92	that	that	PRON
ejpam-4704	198	93	is	be	AUX
ejpam-4704	198	94	b	b	X
ejpam-4704	198	95	(	(	PUNCT
ejpam-4704	198	96	µ(sc	µ(sc	NUM
ejpam-4704	198	97	m	m	NOUN
ejpam-4704	198	98	)	)	PUNCT
ejpam-4704	198	99	)	)	PUNCT
ejpam-4704	198	100	≤	≤	ADV
ejpam-4704	198	101	3	3	NUM
ejpam-4704	198	102	(	(	PUNCT
ejpam-4704	198	103	6	6	NUM
ejpam-4704	198	104	)	)	PUNCT
ejpam-4704	198	105	from	from	ADP
ejpam-4704	198	106	(	(	PUNCT
ejpam-4704	198	107	5	5	NUM
ejpam-4704	198	108	)	)	PUNCT
ejpam-4704	198	109	and	and	CCONJ
ejpam-4704	198	110	(	(	PUNCT
ejpam-4704	198	111	6	6	NUM
ejpam-4704	198	112	)	)	PUNCT
ejpam-4704	198	113	,	,	PUNCT
ejpam-4704	198	114	we	we	PRON
ejpam-4704	198	115	get	get	VERB
ejpam-4704	198	116	b(µ(sc	b(µ(sc	NOUN
ejpam-4704	198	117	m	m	NOUN
ejpam-4704	198	118	)	)	PUNCT
ejpam-4704	198	119	)	)	PUNCT
ejpam-4704	199	1	=	=	PUNCT
ejpam-4704	199	2	3	3	X
ejpam-4704	199	3	.	.	X
ejpam-4704	199	4	2.4	2.4	NUM
ejpam-4704	199	5	.	.	PUNCT
ejpam-4704	200	1	cog	cog	NOUN
ejpam-4704	200	2	-	-	PUNCT
ejpam-4704	200	3	wheel	wheel	NOUN
ejpam-4704	200	4	graph	graph	NOUN
ejpam-4704	200	5	w	w	PROPN
ejpam-4704	200	6	c	c	NOUN
ejpam-4704	200	7	m	m	PRON
ejpam-4704	200	8	it	it	PRON
ejpam-4704	200	9	is	be	AUX
ejpam-4704	200	10	a	a	DET
ejpam-4704	200	11	graph	graph	NOUN
ejpam-4704	200	12	consisted	consist	VERB
ejpam-4704	200	13	of	of	ADP
ejpam-4704	200	14	a	a	DET
ejpam-4704	200	15	wheel	wheel	NOUN
ejpam-4704	200	16	wm	wm	PROPN
ejpam-4704	200	17	:	:	PUNCT
ejpam-4704	200	18	u1	u1	PROPN
ejpam-4704	200	19	,	,	PUNCT
ejpam-4704	200	20	u2	u2	NOUN
ejpam-4704	200	21	,	,	PUNCT
ejpam-4704	200	22	.	.	PUNCT
ejpam-4704	200	23	.	.	PUNCT
ejpam-4704	200	24	.	.	PUNCT
ejpam-4704	201	1	,	,	PUNCT
ejpam-4704	201	2	um	um	INTJ
ejpam-4704	201	3	where	where	SCONJ
ejpam-4704	201	4	m	m	PROPN
ejpam-4704	201	5	≥	≥	NOUN
ejpam-4704	201	6	4	4	NUM
ejpam-4704	201	7	,	,	PUNCT
ejpam-4704	201	8	by	by	ADP
ejpam-4704	201	9	adding	add	VERB
ejpam-4704	201	10	m−	m−	PROPN
ejpam-4704	201	11	1	1	NUM
ejpam-4704	201	12	vertices	vertex	NOUN
ejpam-4704	201	13	and	and	CCONJ
ejpam-4704	201	14	2m−2	2m−2	NUM
ejpam-4704	201	15	edges	edge	NOUN
ejpam-4704	201	16	of	of	ADP
ejpam-4704	201	17	the	the	DET
ejpam-4704	201	18	form	form	NOUN
ejpam-4704	201	19	v1	v1	NOUN
ejpam-4704	201	20	,	,	PUNCT
ejpam-4704	201	21	v2	v2	NOUN
ejpam-4704	201	22	,	,	PUNCT
ejpam-4704	201	23	.	.	PUNCT
ejpam-4704	201	24	.	.	PUNCT
ejpam-4704	202	1	.	.	PUNCT
ejpam-4704	203	1	,	,	PUNCT
ejpam-4704	203	2	vm−1	vm−1	NOUN
ejpam-4704	203	3	and	and	CCONJ
ejpam-4704	203	4	{	{	PUNCT
ejpam-4704	203	5	viui	viui	NOUN
ejpam-4704	203	6	,	,	PUNCT
ejpam-4704	203	7	viui+1	viui+1	NOUN
ejpam-4704	203	8	:	:	PUNCT
ejpam-4704	204	1	i	i	NOUN
ejpam-4704	204	2	=	=	NOUN
ejpam-4704	204	3	1	1	NUM
ejpam-4704	204	4	,	,	PUNCT
ejpam-4704	204	5	2	2	NUM
ejpam-4704	204	6	,	,	PUNCT
ejpam-4704	204	7	.	.	PUNCT
ejpam-4704	204	8	.	.	PUNCT
ejpam-4704	204	9	.	.	PUNCT
ejpam-4704	205	1	,	,	PUNCT
ejpam-4704	205	2	m−1	m−1	PROPN
ejpam-4704	205	3	}	}	PUNCT
ejpam-4704	205	4	respectively	respectively	ADV
ejpam-4704	205	5	,	,	PUNCT
ejpam-4704	205	6	where	where	SCONJ
ejpam-4704	205	7	um	um	INTJ
ejpam-4704	205	8	≡	≡	PROPN
ejpam-4704	205	9	u1	u1	NOUN
ejpam-4704	205	10	.	.	PUNCT
ejpam-4704	206	1	it	it	PRON
ejpam-4704	206	2	is	be	AUX
ejpam-4704	206	3	clear	clear	ADJ
ejpam-4704	206	4	that	that	SCONJ
ejpam-4704	206	5	the	the	DET
ejpam-4704	206	6	number	number	NOUN
ejpam-4704	206	7	of	of	ADP
ejpam-4704	206	8	vertices	vertex	NOUN
ejpam-4704	206	9	of	of	ADP
ejpam-4704	206	10	a	a	DET
ejpam-4704	206	11	graphw	graphw	NOUN
ejpam-4704	206	12	c	c	PROPN
ejpam-4704	206	13	m	m	PROPN
ejpam-4704	206	14	is	be	AUX
ejpam-4704	206	15	2m−1	2m−1	NUM
ejpam-4704	206	16	and	and	CCONJ
ejpam-4704	206	17	the	the	DET
ejpam-4704	206	18	number	number	NOUN
ejpam-4704	206	19	of	of	ADP
ejpam-4704	206	20	edges	edge	NOUN
ejpam-4704	206	21	is	be	AUX
ejpam-4704	206	22	4m−	4m−	PROPN
ejpam-4704	206	23	4	4	NUM
ejpam-4704	207	1	[	[	X
ejpam-4704	207	2	2	2	NUM
ejpam-4704	207	3	]	]	PUNCT
ejpam-4704	207	4	.	.	PUNCT
ejpam-4704	208	1	b.	b.	PROPN
ejpam-4704	208	2	m.	m.	PROPN
ejpam-4704	208	3	sulaiman	sulaiman	PROPN
ejpam-4704	208	4	,	,	PUNCT
ejpam-4704	208	5	r.	r.	PROPN
ejpam-4704	208	6	s.	s.	PROPN
ejpam-4704	208	7	hasan	hasan	PROPN
ejpam-4704	208	8	,	,	PUNCT
ejpam-4704	208	9	r.	r.	PROPN
ejpam-4704	208	10	a.	a.	PROPN
ejpam-4704	208	11	mustafa	mustafa	PROPN
ejpam-4704	208	12	/	/	SYM
ejpam-4704	208	13	eur	eur	PROPN
ejpam-4704	208	14	.	.	PUNCT
ejpam-4704	209	1	j.	j.	PROPN
ejpam-4704	209	2	pure	pure	PROPN
ejpam-4704	209	3	appl	appl	PROPN
ejpam-4704	209	4	.	.	PROPN
ejpam-4704	209	5	math	math	PROPN
ejpam-4704	209	6	,	,	PUNCT
ejpam-4704	209	7	16	16	NUM
ejpam-4704	209	8	(	(	PUNCT
ejpam-4704	209	9	2	2	NUM
ejpam-4704	209	10	)	)	PUNCT
ejpam-4704	209	11	(	(	PUNCT
ejpam-4704	209	12	2023	2023	NUM
ejpam-4704	209	13	)	)	PUNCT
ejpam-4704	209	14	,	,	PUNCT
ejpam-4704	209	15	953	953	NUM
ejpam-4704	209	16	-	-	SYM
ejpam-4704	209	17	964	964	NUM
ejpam-4704	209	18	961	961	NUM
ejpam-4704	209	19	2.4.1	2.4.1	NUM
ejpam-4704	209	20	.	.	PUNCT
ejpam-4704	210	1	the	the	DET
ejpam-4704	210	2	basis	basis	NOUN
ejpam-4704	210	3	number	number	NOUN
ejpam-4704	210	4	for	for	ADP
ejpam-4704	210	5	mycielski	mycielski	NOUN
ejpam-4704	210	6	’s	’s	PART
ejpam-4704	210	7	graph	graph	NOUN
ejpam-4704	210	8	of	of	ADP
ejpam-4704	210	9	the	the	DET
ejpam-4704	210	10	cog	cog	NOUN
ejpam-4704	210	11	-	-	PUNCT
ejpam-4704	210	12	wheel	wheel	NOUN
ejpam-4704	210	13	µ(w	µ(w	X
ejpam-4704	210	14	c	c	X
ejpam-4704	210	15	m	m	VERB
ejpam-4704	210	16	)	)	PUNCT
ejpam-4704	210	17	let	let	VERB
ejpam-4704	210	18	the	the	DET
ejpam-4704	210	19	vertices	vertex	NOUN
ejpam-4704	210	20	of	of	ADP
ejpam-4704	210	21	the	the	DET
ejpam-4704	210	22	cog	cog	NOUN
ejpam-4704	210	23	-	-	PUNCT
ejpam-4704	210	24	wheel	wheel	NOUN
ejpam-4704	210	25	graph	graph	NOUN
ejpam-4704	210	26	wc	wc	PROPN
ejpam-4704	210	27	m	m	PROPN
ejpam-4704	210	28	are	be	AUX
ejpam-4704	210	29	u1	u1	NOUN
ejpam-4704	210	30	,	,	PUNCT
ejpam-4704	210	31	u2	u2	NOUN
ejpam-4704	210	32	,	,	PUNCT
ejpam-4704	210	33	.	.	PUNCT
ejpam-4704	210	34	.	.	PUNCT
ejpam-4704	211	1	.	.	PUNCT
ejpam-4704	212	1	,	,	PUNCT
ejpam-4704	212	2	u2m−1	u2m−1	PROPN
ejpam-4704	212	3	and	and	CCONJ
ejpam-4704	212	4	the	the	DET
ejpam-4704	212	5	corresponding	corresponding	ADJ
ejpam-4704	212	6	vertices	vertex	NOUN
ejpam-4704	212	7	are	be	AUX
ejpam-4704	212	8	v1	v1	NOUN
ejpam-4704	212	9	,	,	PUNCT
ejpam-4704	212	10	v2	v2	NOUN
ejpam-4704	212	11	,	,	PUNCT
ejpam-4704	212	12	.	.	PUNCT
ejpam-4704	212	13	.	.	PUNCT
ejpam-4704	213	1	.	.	PUNCT
ejpam-4704	214	1	,	,	PUNCT
ejpam-4704	214	2	v2m−1	v2m−1	PROPN
ejpam-4704	214	3	and	and	CCONJ
ejpam-4704	214	4	the	the	DET
ejpam-4704	214	5	other	other	ADJ
ejpam-4704	214	6	vertex	vertex	NOUN
ejpam-4704	214	7	is	be	AUX
ejpam-4704	214	8	w	w	NOUN
ejpam-4704	214	9	,	,	PUNCT
ejpam-4704	214	10	since	since	SCONJ
ejpam-4704	214	11	the	the	DET
ejpam-4704	214	12	number	number	NOUN
ejpam-4704	214	13	of	of	ADP
ejpam-4704	214	14	vertices	vertex	NOUN
ejpam-4704	214	15	of	of	ADP
ejpam-4704	214	16	cog	cog	NOUN
ejpam-4704	214	17	-	-	PUNCT
ejpam-4704	214	18	wheel	wheel	NOUN
ejpam-4704	214	19	is	be	AUX
ejpam-4704	214	20	2m−1	2m−1	NUM
ejpam-4704	214	21	and	and	CCONJ
ejpam-4704	214	22	the	the	DET
ejpam-4704	214	23	number	number	NOUN
ejpam-4704	214	24	of	of	ADP
ejpam-4704	214	25	its	its	PRON
ejpam-4704	214	26	edges	edge	NOUN
ejpam-4704	214	27	is	be	AUX
ejpam-4704	214	28	4(m−1	4(m−1	NOUN
ejpam-4704	214	29	)	)	PUNCT
ejpam-4704	214	30	,	,	PUNCT
ejpam-4704	214	31	then	then	ADV
ejpam-4704	214	32	by	by	ADP
ejpam-4704	214	33	mycielski	mycielski	PROPN
ejpam-4704	214	34	’s	’s	PART
ejpam-4704	214	35	definition	definition	NOUN
ejpam-4704	214	36	,	,	PUNCT
ejpam-4704	214	37	it	it	PRON
ejpam-4704	214	38	turns	turn	VERB
ejpam-4704	214	39	out	out	ADP
ejpam-4704	214	40	that	that	SCONJ
ejpam-4704	214	41	the	the	DET
ejpam-4704	214	42	number	number	NOUN
ejpam-4704	214	43	of	of	ADP
ejpam-4704	214	44	vertices	vertex	NOUN
ejpam-4704	214	45	of	of	ADP
ejpam-4704	214	46	µ(wc	µ(wc	PROPN
ejpam-4704	214	47	m	m	VERB
ejpam-4704	214	48	)	)	PUNCT
ejpam-4704	214	49	is	be	AUX
ejpam-4704	214	50	4	4	NUM
ejpam-4704	214	51	m	m	NOUN
ejpam-4704	214	52	−	−	NUM
ejpam-4704	214	53	1	1	NUM
ejpam-4704	214	54	and	and	CCONJ
ejpam-4704	214	55	the	the	DET
ejpam-4704	214	56	number	number	NOUN
ejpam-4704	214	57	of	of	ADP
ejpam-4704	214	58	its	its	PRON
ejpam-4704	214	59	edges	edge	NOUN
ejpam-4704	214	60	is	be	AUX
ejpam-4704	214	61	14m−	14m−	NUM
ejpam-4704	214	62	13	13	NUM
ejpam-4704	214	63	.	.	PUNCT
ejpam-4704	215	1	theorem	theorem	VERB
ejpam-4704	215	2	4	4	NUM
ejpam-4704	215	3	.	.	PUNCT
ejpam-4704	216	1	let	let	VERB
ejpam-4704	216	2	wm	wm	PART
ejpam-4704	216	3	be	be	AUX
ejpam-4704	216	4	a	a	DET
ejpam-4704	216	5	wheel	wheel	NOUN
ejpam-4704	216	6	of	of	ADP
ejpam-4704	216	7	order	order	NOUN
ejpam-4704	216	8	m	m	VERB
ejpam-4704	216	9	≥	≥	NOUN
ejpam-4704	216	10	5	5	NUM
ejpam-4704	216	11	then	then	ADV
ejpam-4704	216	12	b(µ(w	b(µ(w	VERB
ejpam-4704	216	13	c	c	PROPN
ejpam-4704	216	14	m	m	PROPN
ejpam-4704	216	15	)	)	PUNCT
ejpam-4704	216	16	)	)	PUNCT
ejpam-4704	217	1	=	=	SYM
ejpam-4704	217	2	3	3	X
ejpam-4704	217	3	.	.	X
ejpam-4704	217	4	proof	proof	NOUN
ejpam-4704	217	5	.	.	PUNCT
ejpam-4704	218	1	we	we	PRON
ejpam-4704	218	2	can	can	AUX
ejpam-4704	218	3	prove	prove	VERB
ejpam-4704	218	4	that	that	SCONJ
ejpam-4704	218	5	for	for	ADP
ejpam-4704	218	6	each	each	DET
ejpam-4704	218	7	m	m	PROPN
ejpam-4704	218	8	≥	≥	NOUN
ejpam-4704	218	9	5	5	NUM
ejpam-4704	218	10	,	,	PUNCT
ejpam-4704	218	11	there	there	PRON
ejpam-4704	218	12	is	be	VERB
ejpam-4704	218	13	a	a	DET
ejpam-4704	218	14	subgraph	subgraph	NOUN
ejpam-4704	218	15	of	of	ADP
ejpam-4704	218	16	µ(w	µ(w	X
ejpam-4704	218	17	c	c	X
ejpam-4704	218	18	m	m	PROPN
ejpam-4704	218	19	)	)	PUNCT
ejpam-4704	218	20	that	that	PRON
ejpam-4704	218	21	topologically	topologically	ADV
ejpam-4704	218	22	equivalent	equivalent	ADJ
ejpam-4704	218	23	k3,3	k3,3	PROPN
ejpam-4704	218	24	,	,	PUNCT
ejpam-4704	218	25	according	accord	VERB
ejpam-4704	218	26	to	to	ADP
ejpam-4704	218	27	kurtowski	kurtowski	PROPN
ejpam-4704	218	28	’s	’s	PART
ejpam-4704	218	29	theorem	theorem	NOUN
ejpam-4704	218	30	[	[	X
ejpam-4704	218	31	8	8	NUM
ejpam-4704	218	32	]	]	PUNCT
ejpam-4704	218	33	µ(w	µ(w	X
ejpam-4704	218	34	c	c	X
ejpam-4704	218	35	m	m	VERB
ejpam-4704	218	36	)	)	PUNCT
ejpam-4704	218	37	is	be	AUX
ejpam-4704	218	38	not	not	PART
ejpam-4704	218	39	planar	planar	ADJ
ejpam-4704	218	40	and	and	CCONJ
ejpam-4704	218	41	according	accord	VERB
ejpam-4704	218	42	to	to	ADP
ejpam-4704	218	43	mclean	mclean	PROPN
ejpam-4704	218	44	’s	’s	PART
ejpam-4704	218	45	theorem	theorem	NOUN
ejpam-4704	218	46	[	[	X
ejpam-4704	218	47	12	12	NUM
ejpam-4704	218	48	]	]	X
ejpam-4704	218	49	we	we	PRON
ejpam-4704	218	50	have	have	VERB
ejpam-4704	218	51	b	b	NUM
ejpam-4704	218	52	(	(	PUNCT
ejpam-4704	218	53	µ(w	µ(w	NOUN
ejpam-4704	218	54	c	c	X
ejpam-4704	218	55	m	m	PROPN
ejpam-4704	218	56	)	)	PUNCT
ejpam-4704	218	57	)	)	PUNCT
ejpam-4704	218	58	≥	≥	NOUN
ejpam-4704	218	59	3	3	NUM
ejpam-4704	218	60	(	(	PUNCT
ejpam-4704	218	61	7	7	X
ejpam-4704	218	62	)	)	PUNCT
ejpam-4704	218	63	we	we	PRON
ejpam-4704	218	64	will	will	AUX
ejpam-4704	218	65	prove	prove	VERB
ejpam-4704	218	66	that	that	SCONJ
ejpam-4704	218	67	there	there	PRON
ejpam-4704	218	68	is	be	VERB
ejpam-4704	218	69	a	a	DET
ejpam-4704	218	70	base	base	NOUN
ejpam-4704	218	71	b	b	NOUN
ejpam-4704	218	72	for	for	ADP
ejpam-4704	218	73	the	the	DET
ejpam-4704	218	74	cycles	cycle	NOUN
ejpam-4704	218	75	space	space	NOUN
ejpam-4704	218	76	of	of	ADP
ejpam-4704	218	77	the	the	DET
ejpam-4704	218	78	graph	graph	NOUN
ejpam-4704	218	79	µ(w	µ(w	X
ejpam-4704	218	80	c	c	X
ejpam-4704	218	81	m	m	PROPN
ejpam-4704	218	82	)	)	PUNCT
ejpam-4704	218	83	of	of	ADP
ejpam-4704	218	84	3	3	NUM
ejpam-4704	218	85	-	-	NOUN
ejpam-4704	218	86	fold	fold	ADJ
ejpam-4704	218	87	.	.	PUNCT
ejpam-4704	219	1	let	let	VERB
ejpam-4704	219	2	b	b	X
ejpam-4704	219	3	be	be	AUX
ejpam-4704	219	4	a	a	DET
ejpam-4704	219	5	set	set	NOUN
ejpam-4704	219	6	of	of	ADP
ejpam-4704	219	7	cycles	cycle	NOUN
ejpam-4704	219	8	of	of	ADP
ejpam-4704	219	9	µ(w	µ(w	X
ejpam-4704	219	10	c	c	X
ejpam-4704	219	11	m	m	PROPN
ejpam-4704	219	12	)	)	PUNCT
ejpam-4704	219	13	which	which	PRON
ejpam-4704	219	14	defined	define	VERB
ejpam-4704	219	15	by	by	ADP
ejpam-4704	219	16	the	the	DET
ejpam-4704	219	17	following	follow	VERB
ejpam-4704	219	18	formula	formula	NOUN
ejpam-4704	219	19	:	:	PUNCT
ejpam-4704	219	20	b	b	X
ejpam-4704	219	21	=	=	SYM
ejpam-4704	219	22	b(µ(p	b(µ(p	PROPN
ejpam-4704	219	23	c	c	PROPN
ejpam-4704	219	24	m	m	PROPN
ejpam-4704	219	25	)	)	PUNCT
ejpam-4704	219	26	)	)	PUNCT
ejpam-4704	219	27	∪	∪	ADP
ejpam-4704	219	28	(	(	PUNCT
ejpam-4704	219	29	∪3	∪3	NUM
ejpam-4704	219	30	i=1si	i=1si	NUM
ejpam-4704	219	31	)	)	PUNCT
ejpam-4704	219	32	∪	∪	ADP
ejpam-4704	219	33	{	{	PUNCT
ejpam-4704	219	34	c1	c1	NOUN
ejpam-4704	219	35	,	,	PUNCT
ejpam-4704	219	36	c2	c2	PROPN
ejpam-4704	219	37	,	,	PUNCT
ejpam-4704	219	38	c3	c3	PROPN
ejpam-4704	219	39	}	}	PUNCT
ejpam-4704	219	40	where	where	SCONJ
ejpam-4704	219	41	b(µ(p	b(µ(p	PROPN
ejpam-4704	219	42	c	c	PROPN
ejpam-4704	219	43	m	m	PROPN
ejpam-4704	219	44	)	)	PUNCT
ejpam-4704	219	45	)	)	PUNCT
ejpam-4704	219	46	is	be	AUX
ejpam-4704	219	47	the	the	DET
ejpam-4704	219	48	base	base	NOUN
ejpam-4704	219	49	for	for	ADP
ejpam-4704	219	50	michelsky	michelsky	PROPN
ejpam-4704	219	51	’s	’s	PART
ejpam-4704	219	52	graph	graph	NOUN
ejpam-4704	219	53	of	of	ADP
ejpam-4704	219	54	the	the	DET
ejpam-4704	219	55	cog	cog	NOUN
ejpam-4704	219	56	-	-	PUNCT
ejpam-4704	219	57	path	path	NOUN
ejpam-4704	219	58	,	,	PUNCT
ejpam-4704	219	59	m	m	VERB
ejpam-4704	219	60	≥	≥	NOUN
ejpam-4704	219	61	5	5	NUM
ejpam-4704	219	62	and	and	CCONJ
ejpam-4704	219	63	s1	s1	PROPN
ejpam-4704	219	64	=	=	SYM
ejpam-4704	219	65	{	{	PUNCT
ejpam-4704	219	66	u2m−1viui+2u2m−1	u2m−1viui+2u2m−1	NOUN
ejpam-4704	219	67	:	:	PUNCT
ejpam-4704	219	68	i	i	NOUN
ejpam-4704	219	69	=	=	NOUN
ejpam-4704	219	70	1	1	NUM
ejpam-4704	219	71	,	,	PUNCT
ejpam-4704	219	72	3	3	NUM
ejpam-4704	219	73	,	,	PUNCT
ejpam-4704	219	74	5	5	NUM
ejpam-4704	219	75	,	,	PUNCT
ejpam-4704	219	76	.	.	PUNCT
ejpam-4704	219	77	.	.	PUNCT
ejpam-4704	220	1	.	.	PUNCT
ejpam-4704	221	1	,	,	PUNCT
ejpam-4704	222	1	2m−	2m−	PROPN
ejpam-4704	222	2	5	5	NUM
ejpam-4704	222	3	}	}	PUNCT
ejpam-4704	222	4	,	,	PUNCT
ejpam-4704	222	5	s2	s2	NOUN
ejpam-4704	222	6	=	=	SYM
ejpam-4704	222	7	{	{	PUNCT
ejpam-4704	222	8	v2m−1uiui+2v2m−1	v2m−1uiui+2v2m−1	NOUN
ejpam-4704	222	9	:	:	PUNCT
ejpam-4704	223	1	i	i	NOUN
ejpam-4704	223	2	=	=	NOUN
ejpam-4704	223	3	1	1	NUM
ejpam-4704	223	4	,	,	PUNCT
ejpam-4704	223	5	3	3	NUM
ejpam-4704	223	6	,	,	PUNCT
ejpam-4704	223	7	5	5	NUM
ejpam-4704	223	8	,	,	PUNCT
ejpam-4704	223	9	.	.	PUNCT
ejpam-4704	223	10	.	.	PUNCT
ejpam-4704	223	11	.	.	PUNCT
ejpam-4704	224	1	,	,	PUNCT
ejpam-4704	224	2	2m−	2m−	PROPN
ejpam-4704	224	3	5	5	NUM
ejpam-4704	224	4	}	}	PUNCT
ejpam-4704	224	5	,	,	PUNCT
ejpam-4704	224	6	s3	s3	PROPN
ejpam-4704	224	7	=	=	SYM
ejpam-4704	224	8	{	{	PUNCT
ejpam-4704	224	9	u2m−1uivi+2u2m−1	u2m−1uivi+2u2m−1	NOUN
ejpam-4704	224	10	:	:	PUNCT
ejpam-4704	224	11	i	i	NOUN
ejpam-4704	224	12	=	=	NOUN
ejpam-4704	224	13	1	1	NUM
ejpam-4704	224	14	,	,	PUNCT
ejpam-4704	224	15	3	3	NUM
ejpam-4704	224	16	,	,	PUNCT
ejpam-4704	224	17	5	5	NUM
ejpam-4704	224	18	,	,	PUNCT
ejpam-4704	224	19	.	.	PUNCT
ejpam-4704	224	20	.	.	PUNCT
ejpam-4704	224	21	.	.	PUNCT
ejpam-4704	225	1	,	,	PUNCT
ejpam-4704	226	1	2m−	2m−	PROPN
ejpam-4704	226	2	5	5	NUM
ejpam-4704	226	3	}	}	PUNCT
ejpam-4704	226	4	,	,	PUNCT
ejpam-4704	226	5	c1	c1	PROPN
ejpam-4704	226	6	=	=	PROPN
ejpam-4704	226	7	v2m−1u1u2m−3v2m−1	v2m−1u1u2m−3v2m−1	PROPN
ejpam-4704	226	8	,	,	PUNCT
ejpam-4704	226	9	c2	c2	PROPN
ejpam-4704	226	10	=	=	PUNCT
ejpam-4704	226	11	u1v2m−3u2m−5u2m−1u1	u1v2m−3u2m−5u2m−1u1	PROPN
ejpam-4704	227	1	c3	c3	NOUN
ejpam-4704	227	2	=	=	SYM
ejpam-4704	227	3	u2m−3v1u2m−1u1u2m−3	u2m−3v1u2m−1u1u2m−3	PROPN
ejpam-4704	227	4	,	,	PUNCT
ejpam-4704	227	5	in	in	ADP
ejpam-4704	227	6	order	order	NOUN
ejpam-4704	227	7	b	b	NOUN
ejpam-4704	227	8	to	to	PART
ejpam-4704	227	9	be	be	AUX
ejpam-4704	227	10	the	the	DET
ejpam-4704	227	11	base	base	NOUN
ejpam-4704	227	12	for	for	ADP
ejpam-4704	227	13	the	the	DET
ejpam-4704	227	14	cycles	cycle	NOUN
ejpam-4704	227	15	space	space	NOUN
ejpam-4704	227	16	of	of	ADP
ejpam-4704	227	17	the	the	DET
ejpam-4704	227	18	graph	graph	NOUN
ejpam-4704	227	19	µ(w	µ(w	X
ejpam-4704	227	20	c	c	X
ejpam-4704	227	21	m	m	PROPN
ejpam-4704	227	22	)	)	PUNCT
ejpam-4704	227	23	,	,	PUNCT
ejpam-4704	227	24	it	it	PRON
ejpam-4704	227	25	must	must	AUX
ejpam-4704	227	26	be	be	AUX
ejpam-4704	227	27	|b|	|b|	VERB
ejpam-4704	227	28	=	=	PUNCT
ejpam-4704	227	29	dim	dim	ADJ
ejpam-4704	227	30	c(µ(w	c(µ(w	NOUN
ejpam-4704	227	31	c	c	NOUN
ejpam-4704	227	32	m	m	NOUN
ejpam-4704	227	33	)	)	PUNCT
ejpam-4704	227	34	)	)	PUNCT
ejpam-4704	227	35	,	,	PUNCT
ejpam-4704	227	36	and	and	CCONJ
ejpam-4704	227	37	b	b	NOUN
ejpam-4704	227	38	must	must	AUX
ejpam-4704	227	39	be	be	AUX
ejpam-4704	227	40	a	a	DET
ejpam-4704	227	41	linearly	linearly	ADV
ejpam-4704	227	42	independent	independent	ADJ
ejpam-4704	227	43	set	set	NOUN
ejpam-4704	227	44	of	of	ADP
ejpam-4704	227	45	cycles	cycle	NOUN
ejpam-4704	227	46	.	.	PUNCT
ejpam-4704	228	1	clearly	clearly	ADV
ejpam-4704	228	2	,	,	PUNCT
ejpam-4704	228	3	dim	dim	ADJ
ejpam-4704	228	4	c(µ(w	c(µ(w	NOUN
ejpam-4704	228	5	c	c	NOUN
ejpam-4704	228	6	m	m	NOUN
ejpam-4704	228	7	)	)	PUNCT
ejpam-4704	228	8	)	)	PUNCT
ejpam-4704	229	1	=	=	PUNCT
ejpam-4704	229	2	10m−	10m−	NUM
ejpam-4704	229	3	11	11	NUM
ejpam-4704	229	4	,	,	PUNCT
ejpam-4704	229	5	and	and	CCONJ
ejpam-4704	229	6	since	since	SCONJ
ejpam-4704	229	7	|b|	|b|	PROPN
ejpam-4704	229	8	=	=	PUNCT
ejpam-4704	229	9	|b(µ(p	|b(µ(p	PROPN
ejpam-4704	229	10	c	c	NOUN
ejpam-4704	229	11	m))|+	m))|+	NOUN
ejpam-4704	230	1	|	|	ADV
ejpam-4704	230	2	∪3	∪3	X
ejpam-4704	230	3	i=1	i=1	PROPN
ejpam-4704	231	1	si|+	si|+	PROPN
ejpam-4704	231	2	|{c1	|{c1	PROPN
ejpam-4704	231	3	,	,	PUNCT
ejpam-4704	231	4	c2	c2	PROPN
ejpam-4704	231	5	,	,	PUNCT
ejpam-4704	231	6	c3}|	c3}|	NOUN
ejpam-4704	231	7	=	=	SYM
ejpam-4704	231	8	7m−	7m−	NUM
ejpam-4704	231	9	8	8	NUM
ejpam-4704	232	1	+	+	NUM
ejpam-4704	232	2	3m−	3m−	NUM
ejpam-4704	232	3	6	6	NUM
ejpam-4704	232	4	+	+	CCONJ
ejpam-4704	232	5	3	3	NUM
ejpam-4704	232	6	=	=	SYM
ejpam-4704	232	7	10m−	10m−	NUM
ejpam-4704	232	8	11	11	NUM
ejpam-4704	232	9	now	now	ADV
ejpam-4704	232	10	,	,	PUNCT
ejpam-4704	232	11	it	it	PRON
ejpam-4704	232	12	remains	remain	VERB
ejpam-4704	232	13	to	to	PART
ejpam-4704	232	14	show	show	VERB
ejpam-4704	232	15	that	that	SCONJ
ejpam-4704	232	16	b	b	NOUN
ejpam-4704	232	17	is	be	AUX
ejpam-4704	232	18	linearly	linearly	ADV
ejpam-4704	232	19	independent	independent	ADJ
ejpam-4704	232	20	.	.	PUNCT
ejpam-4704	233	1	it	it	PRON
ejpam-4704	233	2	is	be	AUX
ejpam-4704	233	3	known	know	VERB
ejpam-4704	233	4	that	that	SCONJ
ejpam-4704	233	5	b(µ(p	b(µ(p	NOUN
ejpam-4704	233	6	c	c	PROPN
ejpam-4704	233	7	m	m	PROPN
ejpam-4704	233	8	)	)	PUNCT
ejpam-4704	233	9	)	)	PUNCT
ejpam-4704	233	10	is	be	AUX
ejpam-4704	233	11	linearly	linearly	ADV
ejpam-4704	233	12	independent	independent	ADJ
ejpam-4704	233	13	because	because	SCONJ
ejpam-4704	233	14	it	it	PRON
ejpam-4704	233	15	is	be	AUX
ejpam-4704	233	16	represent	represent	VERB
ejpam-4704	233	17	the	the	DET
ejpam-4704	233	18	base	base	NOUN
ejpam-4704	233	19	of	of	ADP
ejpam-4704	233	20	the	the	DET
ejpam-4704	233	21	cycles	cycle	NOUN
ejpam-4704	233	22	space	space	NOUN
ejpam-4704	233	23	of	of	ADP
ejpam-4704	233	24	µ(p	µ(p	PROPN
ejpam-4704	233	25	c	c	PROPN
ejpam-4704	233	26	m	m	PROPN
ejpam-4704	233	27	)	)	PUNCT
ejpam-4704	233	28	.	.	PUNCT
ejpam-4704	234	1	note	note	VERB
ejpam-4704	234	2	that	that	SCONJ
ejpam-4704	234	3	each	each	PRON
ejpam-4704	234	4	of	of	ADP
ejpam-4704	234	5	s1	s1	NOUN
ejpam-4704	234	6	,	,	PUNCT
ejpam-4704	234	7	s2ands3	s2ands3	ADV
ejpam-4704	234	8	is	be	AUX
ejpam-4704	234	9	linearly	linearly	ADV
ejpam-4704	234	10	independent	independent	ADJ
ejpam-4704	234	11	because	because	SCONJ
ejpam-4704	234	12	it	it	PRON
ejpam-4704	234	13	is	be	AUX
ejpam-4704	234	14	represent	represent	VERB
ejpam-4704	234	15	the	the	DET
ejpam-4704	234	16	boundaries	boundary	NOUN
ejpam-4704	234	17	of	of	ADP
ejpam-4704	234	18	the	the	DET
ejpam-4704	234	19	faces	face	NOUN
ejpam-4704	234	20	of	of	ADP
ejpam-4704	234	21	a	a	DET
ejpam-4704	234	22	planar	planar	ADJ
ejpam-4704	234	23	subgraph	subgraph	NOUN
ejpam-4704	234	24	.	.	PUNCT
ejpam-4704	235	1	now	now	ADV
ejpam-4704	235	2	,	,	PUNCT
ejpam-4704	235	3	s1	s1	PROPN
ejpam-4704	235	4	∪	∪	NOUN
ejpam-4704	235	5	s2	s2	NOUN
ejpam-4704	235	6	is	be	AUX
ejpam-4704	235	7	linearly	linearly	ADV
ejpam-4704	235	8	independent	independent	ADJ
ejpam-4704	235	9	because	because	SCONJ
ejpam-4704	235	10	any	any	DET
ejpam-4704	235	11	linear	linear	ADJ
ejpam-4704	235	12	combination	combination	NOUN
ejpam-4704	235	13	of	of	ADP
ejpam-4704	235	14	s2	s2	PROPN
ejpam-4704	235	15	contains	contain	VERB
ejpam-4704	235	16	edges	edge	NOUN
ejpam-4704	235	17	of	of	ADP
ejpam-4704	235	18	type	type	NOUN
ejpam-4704	235	19	b.	b.	PROPN
ejpam-4704	235	20	m.	m.	PROPN
ejpam-4704	235	21	sulaiman	sulaiman	PROPN
ejpam-4704	235	22	,	,	PUNCT
ejpam-4704	235	23	r.	r.	PROPN
ejpam-4704	235	24	s.	s.	PROPN
ejpam-4704	235	25	hasan	hasan	PROPN
ejpam-4704	235	26	,	,	PUNCT
ejpam-4704	235	27	r.	r.	PROPN
ejpam-4704	235	28	a.	a.	PROPN
ejpam-4704	235	29	mustafa	mustafa	PROPN
ejpam-4704	235	30	/	/	SYM
ejpam-4704	235	31	eur	eur	PROPN
ejpam-4704	235	32	.	.	PUNCT
ejpam-4704	236	1	j.	j.	PROPN
ejpam-4704	236	2	pure	pure	PROPN
ejpam-4704	236	3	appl	appl	PROPN
ejpam-4704	236	4	.	.	PROPN
ejpam-4704	236	5	math	math	PROPN
ejpam-4704	236	6	,	,	PUNCT
ejpam-4704	236	7	16	16	NUM
ejpam-4704	236	8	(	(	PUNCT
ejpam-4704	236	9	2	2	NUM
ejpam-4704	236	10	)	)	PUNCT
ejpam-4704	236	11	(	(	PUNCT
ejpam-4704	236	12	2023	2023	NUM
ejpam-4704	236	13	)	)	PUNCT
ejpam-4704	236	14	,	,	PUNCT
ejpam-4704	236	15	953	953	NUM
ejpam-4704	236	16	-	-	SYM
ejpam-4704	236	17	964	964	NUM
ejpam-4704	236	18	962	962	NUM
ejpam-4704	236	19	uiui+2	uiui+2	NOUN
ejpam-4704	236	20	,	,	PUNCT
ejpam-4704	236	21	i	i	PRON
ejpam-4704	236	22	=	=	NOUN
ejpam-4704	236	23	1	1	NUM
ejpam-4704	236	24	,	,	PUNCT
ejpam-4704	236	25	3	3	NUM
ejpam-4704	236	26	,	,	PUNCT
ejpam-4704	236	27	5	5	NUM
ejpam-4704	236	28	,	,	PUNCT
ejpam-4704	236	29	.	.	PUNCT
ejpam-4704	236	30	.	.	PUNCT
ejpam-4704	236	31	.	.	PUNCT
ejpam-4704	237	1	,	,	PUNCT
ejpam-4704	237	2	2m−	2m−	PROPN
ejpam-4704	237	3	3	3	NUM
ejpam-4704	237	4	,	,	PUNCT
ejpam-4704	237	5	which	which	PRON
ejpam-4704	237	6	are	be	AUX
ejpam-4704	237	7	not	not	PART
ejpam-4704	237	8	found	find	VERB
ejpam-4704	237	9	in	in	ADP
ejpam-4704	237	10	any	any	DET
ejpam-4704	237	11	linear	linear	ADJ
ejpam-4704	237	12	combination	combination	NOUN
ejpam-4704	237	13	of	of	ADP
ejpam-4704	237	14	s1	s1	NOUN
ejpam-4704	237	15	.	.	PUNCT
ejpam-4704	238	1	now	now	ADV
ejpam-4704	238	2	,	,	PUNCT
ejpam-4704	238	3	s1	s1	PROPN
ejpam-4704	238	4	∪	∪	ADP
ejpam-4704	238	5	s2	s2	PROPN
ejpam-4704	238	6	∪	∪	ADP
ejpam-4704	238	7	s3	s3	PROPN
ejpam-4704	238	8	is	be	AUX
ejpam-4704	238	9	linearly	linearly	ADV
ejpam-4704	238	10	independent	independent	ADJ
ejpam-4704	238	11	because	because	SCONJ
ejpam-4704	238	12	any	any	DET
ejpam-4704	238	13	linear	linear	ADJ
ejpam-4704	238	14	combination	combination	NOUN
ejpam-4704	238	15	of	of	ADP
ejpam-4704	238	16	s3	s3	PROPN
ejpam-4704	238	17	contains	contain	VERB
ejpam-4704	238	18	edges	edge	NOUN
ejpam-4704	238	19	of	of	ADP
ejpam-4704	238	20	type	type	NOUN
ejpam-4704	238	21	uivi+2	uivi+2	NOUN
ejpam-4704	238	22	,	,	PUNCT
ejpam-4704	238	23	i	i	PRON
ejpam-4704	238	24	=	=	NOUN
ejpam-4704	238	25	1	1	NUM
ejpam-4704	238	26	,	,	PUNCT
ejpam-4704	238	27	3	3	NUM
ejpam-4704	238	28	,	,	PUNCT
ejpam-4704	238	29	.	.	PUNCT
ejpam-4704	238	30	.	.	PUNCT
ejpam-4704	239	1	.	.	PUNCT
ejpam-4704	240	1	,	,	PUNCT
ejpam-4704	240	2	2	2	NUM
ejpam-4704	240	3	m	m	NOUN
ejpam-4704	240	4	−	−	NOUN
ejpam-4704	240	5	5	5	NUM
ejpam-4704	240	6	,	,	PUNCT
ejpam-4704	240	7	which	which	PRON
ejpam-4704	240	8	are	be	AUX
ejpam-4704	240	9	not	not	PART
ejpam-4704	240	10	found	find	VERB
ejpam-4704	240	11	in	in	ADP
ejpam-4704	240	12	any	any	DET
ejpam-4704	240	13	linear	linear	ADJ
ejpam-4704	240	14	combination	combination	NOUN
ejpam-4704	240	15	of	of	ADP
ejpam-4704	240	16	s1	s1	PROPN
ejpam-4704	240	17	∪	∪	X
ejpam-4704	240	18	s2	s2	PROPN
ejpam-4704	240	19	.	.	PUNCT
ejpam-4704	241	1	in	in	ADP
ejpam-4704	241	2	addition	addition	NOUN
ejpam-4704	241	3	,	,	PUNCT
ejpam-4704	241	4	{	{	PUNCT
ejpam-4704	241	5	c1	c1	NOUN
ejpam-4704	241	6	,	,	PUNCT
ejpam-4704	241	7	c2	c2	PROPN
ejpam-4704	241	8	,	,	PUNCT
ejpam-4704	241	9	c3	c3	PROPN
ejpam-4704	241	10	}	}	PUNCT
ejpam-4704	241	11	is	be	AUX
ejpam-4704	241	12	linearly	linearly	ADV
ejpam-4704	241	13	independent	independent	ADJ
ejpam-4704	241	14	because	because	SCONJ
ejpam-4704	241	15	we	we	PRON
ejpam-4704	241	16	can	can	AUX
ejpam-4704	241	17	not	not	PART
ejpam-4704	241	18	write	write	VERB
ejpam-4704	241	19	any	any	DET
ejpam-4704	241	20	one	one	NUM
ejpam-4704	241	21	of	of	ADP
ejpam-4704	241	22	them	they	PRON
ejpam-4704	241	23	as	as	ADP
ejpam-4704	241	24	a	a	DET
ejpam-4704	241	25	linear	linear	ADJ
ejpam-4704	241	26	combination	combination	NOUN
ejpam-4704	241	27	of	of	ADP
ejpam-4704	241	28	the	the	DET
ejpam-4704	241	29	others	other	NOUN
ejpam-4704	241	30	cycles	cycle	NOUN
ejpam-4704	241	31	.	.	PUNCT
ejpam-4704	242	1	now	now	ADV
ejpam-4704	242	2	,	,	PUNCT
ejpam-4704	242	3	(	(	PUNCT
ejpam-4704	242	4	∪3	∪3	X
ejpam-4704	242	5	i=1si)∪	i=1si)∪	X
ejpam-4704	242	6	(	(	PUNCT
ejpam-4704	242	7	{	{	PUNCT
ejpam-4704	242	8	c1	c1	NOUN
ejpam-4704	242	9	,	,	PUNCT
ejpam-4704	242	10	c2	c2	PROPN
ejpam-4704	242	11	,	,	PUNCT
ejpam-4704	242	12	c3	c3	PROPN
ejpam-4704	242	13	}	}	PUNCT
ejpam-4704	242	14	)	)	PUNCT
ejpam-4704	242	15	is	be	AUX
ejpam-4704	242	16	linearly	linearly	ADV
ejpam-4704	242	17	independent	independent	ADJ
ejpam-4704	242	18	because	because	SCONJ
ejpam-4704	242	19	any	any	DET
ejpam-4704	242	20	linear	linear	ADJ
ejpam-4704	242	21	combination	combination	NOUN
ejpam-4704	242	22	of	of	ADP
ejpam-4704	242	23	{	{	PUNCT
ejpam-4704	242	24	c1	c1	PROPN
ejpam-4704	242	25	,	,	PUNCT
ejpam-4704	242	26	c2	c2	PROPN
ejpam-4704	242	27	,	,	PUNCT
ejpam-4704	242	28	c3	c3	PROPN
ejpam-4704	242	29	}	}	PUNCT
ejpam-4704	242	30	contains	contain	VERB
ejpam-4704	242	31	at	at	ADP
ejpam-4704	242	32	least	least	ADJ
ejpam-4704	242	33	one	one	NUM
ejpam-4704	242	34	of	of	ADP
ejpam-4704	242	35	the	the	DET
ejpam-4704	242	36	edges	edge	NOUN
ejpam-4704	242	37	u1u2m−3	u1u2m−3	NOUN
ejpam-4704	242	38	,	,	PUNCT
ejpam-4704	242	39	u1v2m−3	u1v2m−3	PROPN
ejpam-4704	242	40	,	,	PUNCT
ejpam-4704	242	41	v1u2m−3	v1u2m−3	PROPN
ejpam-4704	242	42	,	,	PUNCT
ejpam-4704	242	43	which	which	PRON
ejpam-4704	242	44	are	be	AUX
ejpam-4704	242	45	not	not	PART
ejpam-4704	242	46	found	find	VERB
ejpam-4704	242	47	in	in	ADP
ejpam-4704	242	48	any	any	DET
ejpam-4704	242	49	linear	linear	ADJ
ejpam-4704	242	50	combination	combination	NOUN
ejpam-4704	242	51	of	of	ADP
ejpam-4704	242	52	∪3	∪3	NOUN
ejpam-4704	242	53	i=1si	i=1si	NUM
ejpam-4704	242	54	.	.	PUNCT
ejpam-4704	243	1	finally	finally	ADV
ejpam-4704	243	2	,	,	PUNCT
ejpam-4704	243	3	the	the	DET
ejpam-4704	243	4	set	set	NOUN
ejpam-4704	243	5	of	of	ADP
ejpam-4704	243	6	cycles	cycle	NOUN
ejpam-4704	243	7	b	b	PROPN
ejpam-4704	243	8	=	=	SYM
ejpam-4704	243	9	b(µ(p	b(µ(p	NOUN
ejpam-4704	243	10	c	c	NOUN
ejpam-4704	243	11	m))∪	m))∪	NOUN
ejpam-4704	243	12	(	(	PUNCT
ejpam-4704	243	13	∪3	∪3	X
ejpam-4704	243	14	i=1si)∪	i=1si)∪	X
ejpam-4704	243	15	(	(	PUNCT
ejpam-4704	243	16	{	{	PUNCT
ejpam-4704	243	17	c1	c1	NOUN
ejpam-4704	243	18	,	,	PUNCT
ejpam-4704	243	19	c2	c2	PROPN
ejpam-4704	243	20	,	,	PUNCT
ejpam-4704	243	21	c3	c3	PROPN
ejpam-4704	243	22	}	}	PUNCT
ejpam-4704	243	23	)	)	PUNCT
ejpam-4704	243	24	is	be	AUX
ejpam-4704	243	25	linearly	linearly	ADV
ejpam-4704	243	26	independent	independent	ADJ
ejpam-4704	243	27	because	because	SCONJ
ejpam-4704	243	28	any	any	DET
ejpam-4704	243	29	linear	linear	ADJ
ejpam-4704	243	30	combination	combination	NOUN
ejpam-4704	243	31	of	of	ADP
ejpam-4704	243	32	cycles	cycle	NOUN
ejpam-4704	243	33	in	in	ADP
ejpam-4704	243	34	(	(	PUNCT
ejpam-4704	243	35	∪3	∪3	NUM
ejpam-4704	243	36	i=1si	i=1si	NUM
ejpam-4704	243	37	)	)	PUNCT
ejpam-4704	243	38	∪	∪	X
ejpam-4704	243	39	(	(	PUNCT
ejpam-4704	243	40	{	{	PUNCT
ejpam-4704	243	41	c1	c1	NOUN
ejpam-4704	243	42	,	,	PUNCT
ejpam-4704	243	43	c2	c2	PROPN
ejpam-4704	243	44	,	,	PUNCT
ejpam-4704	243	45	c3	c3	PROPN
ejpam-4704	243	46	}	}	PUNCT
ejpam-4704	243	47	)	)	PUNCT
ejpam-4704	243	48	contains	contain	VERB
ejpam-4704	243	49	edges	edge	NOUN
ejpam-4704	243	50	of	of	ADP
ejpam-4704	243	51	type	type	NOUN
ejpam-4704	243	52	u2m−1ui	u2m−1ui	NOUN
ejpam-4704	243	53	,	,	PUNCT
ejpam-4704	243	54	i	i	PRON
ejpam-4704	243	55	=	=	NOUN
ejpam-4704	243	56	1	1	NUM
ejpam-4704	243	57	,	,	PUNCT
ejpam-4704	243	58	3	3	NUM
ejpam-4704	243	59	,	,	PUNCT
ejpam-4704	243	60	.	.	PUNCT
ejpam-4704	243	61	.	.	PUNCT
ejpam-4704	243	62	.	.	PUNCT
ejpam-4704	244	1	,	,	PUNCT
ejpam-4704	244	2	2	2	NUM
ejpam-4704	244	3	m	m	NOUN
ejpam-4704	244	4	−	−	NOUN
ejpam-4704	244	5	5	5	NUM
ejpam-4704	244	6	,	,	PUNCT
ejpam-4704	244	7	which	which	PRON
ejpam-4704	244	8	are	be	AUX
ejpam-4704	244	9	not	not	PART
ejpam-4704	244	10	found	find	VERB
ejpam-4704	244	11	in	in	ADP
ejpam-4704	244	12	any	any	DET
ejpam-4704	244	13	linear	linear	ADJ
ejpam-4704	244	14	combination	combination	NOUN
ejpam-4704	244	15	in	in	ADP
ejpam-4704	244	16	b(µ(p	b(µ(p	PROPN
ejpam-4704	244	17	c	c	PROPN
ejpam-4704	244	18	m	m	PROPN
ejpam-4704	244	19	)	)	PUNCT
ejpam-4704	244	20	)	)	PUNCT
ejpam-4704	244	21	,	,	PUNCT
ejpam-4704	244	22	therefore	therefore	ADV
ejpam-4704	244	23	b(µ(w	b(µ(w	VERB
ejpam-4704	244	24	c	c	PROPN
ejpam-4704	244	25	m	m	PROPN
ejpam-4704	244	26	)	)	PUNCT
ejpam-4704	244	27	)	)	PUNCT
ejpam-4704	245	1	is	be	AUX
ejpam-4704	245	2	linearly	linearly	ADV
ejpam-4704	245	3	independent	independent	ADJ
ejpam-4704	245	4	.	.	PUNCT
ejpam-4704	246	1	to	to	PART
ejpam-4704	246	2	find	find	VERB
ejpam-4704	246	3	the	the	DET
ejpam-4704	246	4	fold	fold	NOUN
ejpam-4704	246	5	for	for	ADP
ejpam-4704	246	6	the	the	DET
ejpam-4704	246	7	base	base	NOUN
ejpam-4704	246	8	b	b	NOUN
ejpam-4704	246	9	we	we	PRON
ejpam-4704	246	10	divide	divide	VERB
ejpam-4704	246	11	the	the	DET
ejpam-4704	246	12	edges	edge	NOUN
ejpam-4704	246	13	of	of	ADP
ejpam-4704	246	14	the	the	DET
ejpam-4704	246	15	graph	graph	NOUN
ejpam-4704	246	16	µ(w	µ(w	X
ejpam-4704	246	17	c	c	X
ejpam-4704	246	18	m	m	PROPN
ejpam-4704	246	19	)	)	PUNCT
ejpam-4704	246	20	into	into	ADP
ejpam-4704	246	21	:	:	PUNCT
ejpam-4704	246	22	e1	e1	NOUN
ejpam-4704	246	23	=	=	SYM
ejpam-4704	246	24	{	{	PUNCT
ejpam-4704	246	25	uiui+1	uiui+1	PROPN
ejpam-4704	246	26	,	,	PUNCT
ejpam-4704	246	27	i	i	PRON
ejpam-4704	246	28	=	=	NOUN
ejpam-4704	246	29	1	1	NUM
ejpam-4704	246	30	,	,	PUNCT
ejpam-4704	246	31	2	2	NUM
ejpam-4704	246	32	,	,	PUNCT
ejpam-4704	246	33	.	.	PUNCT
ejpam-4704	246	34	.	.	PUNCT
ejpam-4704	247	1	.	.	PUNCT
ejpam-4704	248	1	,	,	PUNCT
ejpam-4704	249	1	2m−	2m−	NOUN
ejpam-4704	249	2	2	2	NUM
ejpam-4704	249	3	}	}	PUNCT
ejpam-4704	249	4	e2	e2	NOUN
ejpam-4704	249	5	=	=	SYM
ejpam-4704	249	6	{	{	PUNCT
ejpam-4704	249	7	uivi+1	uivi+1	PROPN
ejpam-4704	249	8	,	,	PUNCT
ejpam-4704	249	9	viui+1	viui+1	NOUN
ejpam-4704	249	10	,	,	PUNCT
ejpam-4704	249	11	i	i	PRON
ejpam-4704	249	12	=	=	NOUN
ejpam-4704	249	13	1	1	NUM
ejpam-4704	249	14	,	,	PUNCT
ejpam-4704	249	15	2	2	NUM
ejpam-4704	249	16	,	,	PUNCT
ejpam-4704	249	17	.	.	PUNCT
ejpam-4704	249	18	.	.	PUNCT
ejpam-4704	249	19	.	.	PUNCT
ejpam-4704	250	1	,	,	PUNCT
ejpam-4704	250	2	2m−	2m−	PROPN
ejpam-4704	250	3	2	2	NUM
ejpam-4704	250	4	}	}	PUNCT
ejpam-4704	250	5	e3	e3	NOUN
ejpam-4704	250	6	=	=	SYM
ejpam-4704	250	7	{	{	PUNCT
ejpam-4704	250	8	wvi	wvi	PROPN
ejpam-4704	250	9	,	,	PUNCT
ejpam-4704	250	10	i	i	PRON
ejpam-4704	250	11	=	=	NOUN
ejpam-4704	250	12	1	1	NUM
ejpam-4704	250	13	,	,	PUNCT
ejpam-4704	250	14	2	2	NUM
ejpam-4704	250	15	,	,	PUNCT
ejpam-4704	250	16	.	.	PUNCT
ejpam-4704	250	17	.	.	PUNCT
ejpam-4704	250	18	.	.	PUNCT
ejpam-4704	251	1	,	,	PUNCT
ejpam-4704	252	1	2m−	2m−	PROPN
ejpam-4704	252	2	1	1	NUM
ejpam-4704	252	3	}	}	PUNCT
ejpam-4704	252	4	e4	e4	PROPN
ejpam-4704	252	5	=	=	SYM
ejpam-4704	252	6	{	{	PUNCT
ejpam-4704	252	7	uivi+2	uivi+2	PROPN
ejpam-4704	252	8	,	,	PUNCT
ejpam-4704	252	9	i	i	PRON
ejpam-4704	252	10	=	=	NOUN
ejpam-4704	252	11	1	1	NUM
ejpam-4704	252	12	,	,	PUNCT
ejpam-4704	252	13	3	3	NUM
ejpam-4704	252	14	,	,	PUNCT
ejpam-4704	252	15	.	.	PUNCT
ejpam-4704	252	16	.	.	PUNCT
ejpam-4704	252	17	.	.	PUNCT
ejpam-4704	253	1	,	,	PUNCT
ejpam-4704	253	2	2m−	2m−	PROPN
ejpam-4704	253	3	3	3	NUM
ejpam-4704	253	4	}	}	PUNCT
ejpam-4704	253	5	e5	e5	NOUN
ejpam-4704	253	6	=	=	PUNCT
ejpam-4704	253	7	{	{	PUNCT
ejpam-4704	253	8	viui+2	viui+2	NOUN
ejpam-4704	253	9	,	,	PUNCT
ejpam-4704	253	10	i	i	PRON
ejpam-4704	253	11	=	=	NOUN
ejpam-4704	253	12	1	1	NUM
ejpam-4704	253	13	,	,	PUNCT
ejpam-4704	253	14	3	3	NUM
ejpam-4704	253	15	,	,	PUNCT
ejpam-4704	253	16	.	.	PUNCT
ejpam-4704	253	17	.	.	PUNCT
ejpam-4704	253	18	.	.	PUNCT
ejpam-4704	254	1	,	,	PUNCT
ejpam-4704	255	1	2m−	2m−	PROPN
ejpam-4704	255	2	3	3	NUM
ejpam-4704	255	3	}	}	PUNCT
ejpam-4704	255	4	e6	e6	NOUN
ejpam-4704	255	5	=	=	SYM
ejpam-4704	255	6	{	{	PUNCT
ejpam-4704	255	7	uiui+2	uiui+2	PROPN
ejpam-4704	255	8	,	,	PUNCT
ejpam-4704	255	9	i	i	PRON
ejpam-4704	255	10	=	=	NOUN
ejpam-4704	255	11	1	1	NUM
ejpam-4704	255	12	,	,	PUNCT
ejpam-4704	255	13	3	3	NUM
ejpam-4704	255	14	,	,	PUNCT
ejpam-4704	255	15	.	.	PUNCT
ejpam-4704	255	16	.	.	PUNCT
ejpam-4704	255	17	.	.	PUNCT
ejpam-4704	256	1	,	,	PUNCT
ejpam-4704	256	2	2m−	2m−	PROPN
ejpam-4704	256	3	3	3	NUM
ejpam-4704	256	4	}	}	PUNCT
ejpam-4704	256	5	e7	e7	PROPN
ejpam-4704	256	6	=	=	PUNCT
ejpam-4704	256	7	{	{	PUNCT
ejpam-4704	256	8	u2m−1ui	u2m−1ui	PROPN
ejpam-4704	256	9	,	,	PUNCT
ejpam-4704	256	10	i	i	PRON
ejpam-4704	256	11	=	=	NOUN
ejpam-4704	256	12	1	1	NUM
ejpam-4704	256	13	,	,	PUNCT
ejpam-4704	256	14	3	3	NUM
ejpam-4704	256	15	,	,	PUNCT
ejpam-4704	256	16	.	.	PUNCT
ejpam-4704	256	17	.	.	PUNCT
ejpam-4704	256	18	.	.	PUNCT
ejpam-4704	257	1	,	,	PUNCT
ejpam-4704	258	1	2m−	2m−	PROPN
ejpam-4704	258	2	5	5	NUM
ejpam-4704	258	3	}	}	PUNCT
ejpam-4704	258	4	e8	e8	PROPN
ejpam-4704	258	5	=	=	SYM
ejpam-4704	258	6	{	{	PUNCT
ejpam-4704	258	7	v2m−1ui	v2m−1ui	NOUN
ejpam-4704	258	8	,	,	PUNCT
ejpam-4704	258	9	u2m−1vi	u2m−1vi	PROPN
ejpam-4704	258	10	,	,	PUNCT
ejpam-4704	258	11	i	i	PRON
ejpam-4704	258	12	=	=	NOUN
ejpam-4704	258	13	1	1	NUM
ejpam-4704	258	14	,	,	PUNCT
ejpam-4704	258	15	3	3	NUM
ejpam-4704	258	16	,	,	PUNCT
ejpam-4704	258	17	.	.	PUNCT
ejpam-4704	258	18	.	.	PUNCT
ejpam-4704	258	19	.	.	PUNCT
ejpam-4704	259	1	,	,	PUNCT
ejpam-4704	259	2	2m−	2m−	PROPN
ejpam-4704	259	3	5	5	NUM
ejpam-4704	259	4	}	}	PUNCT
ejpam-4704	259	5	e9	e9	PROPN
ejpam-4704	259	6	=	=	SYM
ejpam-4704	259	7	{	{	PUNCT
ejpam-4704	259	8	u1v2m−3	u1v2m−3	NOUN
ejpam-4704	259	9	,	,	PUNCT
ejpam-4704	259	10	v1u2m−3	v1u2m−3	PROPN
ejpam-4704	259	11	,	,	PUNCT
ejpam-4704	259	12	u1u2m−3	u1u2m−3	NOUN
ejpam-4704	259	13	}	}	PUNCT
ejpam-4704	259	14	now	now	ADV
ejpam-4704	259	15	,	,	PUNCT
ejpam-4704	259	16	we	we	PRON
ejpam-4704	259	17	calculate	calculate	VERB
ejpam-4704	259	18	the	the	DET
ejpam-4704	259	19	fold	fold	NOUN
ejpam-4704	259	20	for	for	ADP
ejpam-4704	259	21	a	a	DET
ejpam-4704	259	22	set	set	NOUN
ejpam-4704	259	23	of	of	ADP
ejpam-4704	259	24	the	the	DET
ejpam-4704	259	25	edges	edge	NOUN
ejpam-4704	259	26	of	of	ADP
ejpam-4704	259	27	the	the	DET
ejpam-4704	259	28	graph	graph	NOUN
ejpam-4704	259	29	µ(w	µ(w	X
ejpam-4704	259	30	c	c	X
ejpam-4704	259	31	m	m	PROPN
ejpam-4704	259	32	)	)	PUNCT
ejpam-4704	259	33	,	,	PUNCT
ejpam-4704	259	34	case	case	NOUN
ejpam-4704	260	1	i	i	PRON
ejpam-4704	260	2	:	:	PUNCT
ejpam-4704	260	3	fb(µ(w	fb(µ(w	PUNCT
ejpam-4704	260	4	c	c	NOUN
ejpam-4704	260	5	m))(e	m))(e	PROPN
ejpam-4704	260	6	)	)	PUNCT
ejpam-4704	260	7	is	be	AUX
ejpam-4704	260	8	less	less	ADJ
ejpam-4704	260	9	than	than	ADP
ejpam-4704	260	10	or	or	CCONJ
ejpam-4704	260	11	equal	equal	ADJ
ejpam-4704	260	12	to	to	ADP
ejpam-4704	260	13	2	2	NUM
ejpam-4704	260	14	for	for	ADP
ejpam-4704	260	15	all	all	DET
ejpam-4704	260	16	e	e	PROPN
ejpam-4704	260	17	∈	∈	PROPN
ejpam-4704	260	18	ei	ei	X
ejpam-4704	260	19	,	,	PUNCT
ejpam-4704	260	20	i	i	PRON
ejpam-4704	260	21	=	=	NOUN
ejpam-4704	260	22	8	8	NUM
ejpam-4704	260	23	,	,	PUNCT
ejpam-4704	260	24	9	9	NUM
ejpam-4704	260	25	.	.	PUNCT
ejpam-4704	260	26	case	case	NOUN
ejpam-4704	260	27	ii	ii	PROPN
ejpam-4704	260	28	:	:	PUNCT
ejpam-4704	260	29	fb(µ(w	fb(µ(w	NUM
ejpam-4704	260	30	c	c	NOUN
ejpam-4704	260	31	m))(e	m))(e	PROPN
ejpam-4704	260	32	)	)	PUNCT
ejpam-4704	260	33	is	be	AUX
ejpam-4704	260	34	less	less	ADJ
ejpam-4704	260	35	than	than	ADP
ejpam-4704	260	36	or	or	CCONJ
ejpam-4704	260	37	equal	equal	ADJ
ejpam-4704	260	38	to	to	ADP
ejpam-4704	260	39	3	3	NUM
ejpam-4704	260	40	for	for	ADP
ejpam-4704	260	41	all	all	DET
ejpam-4704	260	42	e	e	PROPN
ejpam-4704	260	43	∈	∈	PROPN
ejpam-4704	260	44	ei	ei	X
ejpam-4704	260	45	,	,	PUNCT
ejpam-4704	260	46	i	i	PRON
ejpam-4704	260	47	=	=	NOUN
ejpam-4704	260	48	1	1	NUM
ejpam-4704	260	49	,	,	PUNCT
ejpam-4704	260	50	2	2	NUM
ejpam-4704	260	51	,	,	PUNCT
ejpam-4704	260	52	.	.	PUNCT
ejpam-4704	260	53	.	.	PUNCT
ejpam-4704	260	54	.	.	PUNCT
ejpam-4704	261	1	,	,	PUNCT
ejpam-4704	261	2	7	7	X
ejpam-4704	261	3	.	.	X
ejpam-4704	261	4	from	from	ADP
ejpam-4704	261	5	the	the	DET
ejpam-4704	261	6	above	above	ADJ
ejpam-4704	261	7	two	two	NUM
ejpam-4704	261	8	cases	case	NOUN
ejpam-4704	261	9	,	,	PUNCT
ejpam-4704	261	10	it	it	PRON
ejpam-4704	261	11	can	can	AUX
ejpam-4704	261	12	be	be	AUX
ejpam-4704	261	13	seen	see	VERB
ejpam-4704	261	14	that	that	SCONJ
ejpam-4704	261	15	the	the	DET
ejpam-4704	261	16	fold	fold	NOUN
ejpam-4704	261	17	for	for	ADP
ejpam-4704	261	18	each	each	DET
ejpam-4704	261	19	edge	edge	NOUN
ejpam-4704	261	20	in	in	ADP
ejpam-4704	261	21	the	the	DET
ejpam-4704	261	22	graph	graph	NOUN
ejpam-4704	261	23	µ(w	µ(w	X
ejpam-4704	261	24	c	c	X
ejpam-4704	261	25	m	m	VERB
ejpam-4704	261	26	)	)	PUNCT
ejpam-4704	261	27	is	be	AUX
ejpam-4704	261	28	not	not	PART
ejpam-4704	261	29	more	more	ADJ
ejpam-4704	261	30	than	than	ADP
ejpam-4704	261	31	3	3	NUM
ejpam-4704	261	32	in	in	ADP
ejpam-4704	261	33	the	the	DET
ejpam-4704	261	34	base	base	NOUN
ejpam-4704	262	1	b(µ(w	b(µ(w	NOUN
ejpam-4704	262	2	c	c	NOUN
ejpam-4704	262	3	m	m	PROPN
ejpam-4704	262	4	)	)	PUNCT
ejpam-4704	262	5	)	)	PUNCT
ejpam-4704	263	1	;	;	PUNCT
ejpam-4704	263	2	that	that	PRON
ejpam-4704	263	3	is	be	AUX
ejpam-4704	263	4	b(µ(w	b(µ(w	PROPN
ejpam-4704	263	5	c	c	PROPN
ejpam-4704	263	6	m	m	PROPN
ejpam-4704	263	7	)	)	PUNCT
ejpam-4704	263	8	)	)	PUNCT
ejpam-4704	263	9	≤	≤	ADV
ejpam-4704	263	10	3	3	NUM
ejpam-4704	263	11	(	(	PUNCT
ejpam-4704	263	12	8)	8)	NUM
ejpam-4704	263	13	from	from	ADP
ejpam-4704	263	14	(	(	PUNCT
ejpam-4704	263	15	7	7	NUM
ejpam-4704	263	16	)	)	PUNCT
ejpam-4704	263	17	and	and	CCONJ
ejpam-4704	263	18	(	(	PUNCT
ejpam-4704	263	19	8)	8)	NUM
ejpam-4704	263	20	,	,	PUNCT
ejpam-4704	263	21	we	we	PRON
ejpam-4704	263	22	get	get	VERB
ejpam-4704	263	23	b(µ(w	b(µ(w	PROPN
ejpam-4704	263	24	c	c	NOUN
ejpam-4704	263	25	m	m	PROPN
ejpam-4704	263	26	)	)	PUNCT
ejpam-4704	263	27	)	)	PUNCT
ejpam-4704	264	1	=	=	PUNCT
ejpam-4704	265	1	3	3	X
ejpam-4704	265	2	.	.	NOUN
ejpam-4704	265	3	3	3	NUM
ejpam-4704	265	4	.	.	X
ejpam-4704	265	5	conclusion	conclusion	NOUN
ejpam-4704	265	6	after	after	ADP
ejpam-4704	265	7	studying	study	VERB
ejpam-4704	265	8	the	the	DET
ejpam-4704	265	9	basis	basis	NOUN
ejpam-4704	265	10	number	number	NOUN
ejpam-4704	265	11	of	of	ADP
ejpam-4704	265	12	mycielski	mycielski	PROPN
ejpam-4704	265	13	’s	’s	PART
ejpam-4704	265	14	graph	graph	NOUN
ejpam-4704	265	15	for	for	ADP
ejpam-4704	265	16	some	some	DET
ejpam-4704	265	17	cog	cog	NOUN
ejpam-4704	265	18	-	-	PUNCT
ejpam-4704	265	19	graphs	graph	NOUN
ejpam-4704	265	20	,	,	PUNCT
ejpam-4704	265	21	we	we	PRON
ejpam-4704	265	22	concluded	conclude	VERB
ejpam-4704	265	23	that	that	SCONJ
ejpam-4704	265	24	b(µ(g	b(µ(g	PROPN
ejpam-4704	265	25	)	)	PUNCT
ejpam-4704	265	26	)	)	PUNCT
ejpam-4704	266	1	=	=	SYM
ejpam-4704	266	2	3	3	X
ejpam-4704	266	3	,	,	PUNCT
ejpam-4704	266	4	where	where	SCONJ
ejpam-4704	266	5	g	g	PROPN
ejpam-4704	266	6	are	be	AUX
ejpam-4704	266	7	cog	cog	NOUN
ejpam-4704	266	8	-	-	PUNCT
ejpam-4704	266	9	path	path	NOUN
ejpam-4704	266	10	graph	graph	NOUN
ejpam-4704	266	11	,	,	PUNCT
ejpam-4704	266	12	cog	cog	NOUN
ejpam-4704	266	13	-	-	PUNCT
ejpam-4704	266	14	cycle	cycle	NOUN
ejpam-4704	266	15	graph	graph	NOUN
ejpam-4704	266	16	,	,	PUNCT
ejpam-4704	266	17	cog	cog	PROPN
ejpam-4704	266	18	-	-	PUNCT
ejpam-4704	266	19	star	star	NOUN
ejpam-4704	266	20	graph	graph	NOUN
ejpam-4704	266	21	and	and	CCONJ
ejpam-4704	266	22	cog	cog	NOUN
ejpam-4704	266	23	-	-	PUNCT
ejpam-4704	266	24	wheel	wheel	NOUN
ejpam-4704	266	25	graph	graph	NOUN
ejpam-4704	266	26	.	.	PUNCT
ejpam-4704	267	1	references	reference	NOUN
ejpam-4704	267	2	963	963	NUM
ejpam-4704	267	3	acknowledgements	acknowledgement	NOUN
ejpam-4704	267	4	authors	author	NOUN
ejpam-4704	267	5	sincerely	sincerely	ADV
ejpam-4704	267	6	thank	thank	VERB
ejpam-4704	267	7	ministry	ministry	PROPN
ejpam-4704	267	8	of	of	ADP
ejpam-4704	267	9	higher	high	ADJ
ejpam-4704	267	10	education	education	NOUN
ejpam-4704	267	11	and	and	CCONJ
ejpam-4704	267	12	scientific	scientific	ADJ
ejpam-4704	267	13	research	research	NOUN
ejpam-4704	267	14	ministry	ministry	PROPN
ejpam-4704	267	15	,	,	PUNCT
ejpam-4704	267	16	university	university	PROPN
ejpam-4704	267	17	of	of	ADP
ejpam-4704	267	18	mosul	mosul	PROPN
ejpam-4704	267	19	,	,	PUNCT
ejpam-4704	267	20	college	college	NOUN
ejpam-4704	267	21	computer	computer	NOUN
ejpam-4704	267	22	sciences	sciences	PROPN
ejpam-4704	267	23	and	and	CCONJ
ejpam-4704	267	24	mathematics	mathematic	NOUN
ejpam-4704	267	25	for	for	ADP
ejpam-4704	267	26	their	their	PRON
ejpam-4704	267	27	continued	continue	VERB
ejpam-4704	267	28	support	support	NOUN
ejpam-4704	267	29	to	to	PART
ejpam-4704	267	30	make	make	VERB
ejpam-4704	267	31	this	this	DET
ejpam-4704	267	32	study	study	NOUN
ejpam-4704	267	33	as	as	ADV
ejpam-4704	267	34	successful	successful	ADJ
ejpam-4704	267	35	as	as	SCONJ
ejpam-4704	267	36	it	it	PRON
ejpam-4704	267	37	is	be	AUX
ejpam-4704	267	38	.	.	PUNCT
ejpam-4704	268	1	references	reference	NOUN
ejpam-4704	268	2	[	[	X
ejpam-4704	268	3	1	1	X
ejpam-4704	268	4	]	]	X
ejpam-4704	268	5	ahmed	ahmed	PROPN
ejpam-4704	268	6	m	m	PROPN
ejpam-4704	268	7	ali	ali	PROPN
ejpam-4704	268	8	and	and	CCONJ
ejpam-4704	268	9	ali	ali	PROPN
ejpam-4704	268	10	a	a	PROPN
ejpam-4704	268	11	ali	ali	PROPN
ejpam-4704	268	12	.	.	PUNCT
ejpam-4704	269	1	the	the	DET
ejpam-4704	269	2	connected	connect	VERB
ejpam-4704	269	3	detour	detour	NOUN
ejpam-4704	269	4	numbers	number	NOUN
ejpam-4704	269	5	of	of	ADP
ejpam-4704	269	6	special	special	ADJ
ejpam-4704	269	7	classes	class	NOUN
ejpam-4704	269	8	of	of	ADP
ejpam-4704	269	9	connected	connected	ADJ
ejpam-4704	269	10	graphs	graph	NOUN
ejpam-4704	269	11	.	.	PUNCT
ejpam-4704	270	1	journal	journal	NOUN
ejpam-4704	270	2	of	of	ADP
ejpam-4704	270	3	mathematics	mathematic	NOUN
ejpam-4704	270	4	,	,	PUNCT
ejpam-4704	270	5	2019:1–9	2019:1–9	PROPN
ejpam-4704	270	6	,	,	PUNCT
ejpam-4704	270	7	2019	2019	NUM
ejpam-4704	270	8	.	.	PUNCT
ejpam-4704	271	1	[	[	X
ejpam-4704	271	2	2	2	NUM
ejpam-4704	271	3	]	]	PUNCT
ejpam-4704	271	4	am	be	AUX
ejpam-4704	271	5	ali	ali	PROPN
ejpam-4704	271	6	,	,	PUNCT
ejpam-4704	271	7	aa	aa	PROPN
ejpam-4704	271	8	ali	ali	PROPN
ejpam-4704	271	9	,	,	PUNCT
ejpam-4704	271	10	and	and	CCONJ
ejpam-4704	271	11	th	th	X
ejpam-4704	271	12	ismail	ismail	NOUN
ejpam-4704	271	13	.	.	PUNCT
ejpam-4704	272	1	hosoya	hosoya	PROPN
ejpam-4704	272	2	polynomial	polynomial	ADJ
ejpam-4704	272	3	and	and	CCONJ
ejpam-4704	272	4	wiener	wiener	NOUN
ejpam-4704	272	5	indices	index	NOUN
ejpam-4704	272	6	of	of	ADP
ejpam-4704	272	7	distances	distance	NOUN
ejpam-4704	272	8	in	in	ADP
ejpam-4704	272	9	graphs	graph	NOUN
ejpam-4704	272	10	.	.	PUNCT
ejpam-4704	273	1	lap	lap	NOUN
ejpam-4704	273	2	lampart	lampart	PROPN
ejpam-4704	273	3	academic	academic	PROPN
ejpam-4704	273	4	publishing	publishing	PROPN
ejpam-4704	273	5	gmbh	gmbh	PROPN
ejpam-4704	273	6	&	&	CCONJ
ejpam-4704	273	7	co	co	PROPN
ejpam-4704	273	8	,	,	PUNCT
ejpam-4704	273	9	2011	2011	NUM
ejpam-4704	273	10	.	.	PUNCT
ejpam-4704	274	1	[	[	X
ejpam-4704	274	2	3	3	X
ejpam-4704	274	3	]	]	X
ejpam-4704	274	4	salar	salar	NOUN
ejpam-4704	274	5	y	y	PROPN
ejpam-4704	274	6	alsardary	alsardary	PROPN
ejpam-4704	274	7	and	and	CCONJ
ejpam-4704	274	8	ali	ali	PROPN
ejpam-4704	274	9	a	a	DET
ejpam-4704	274	10	ali	ali	PROPN
ejpam-4704	274	11	.	.	PUNCT
ejpam-4704	275	1	the	the	DET
ejpam-4704	275	2	basis	basis	NOUN
ejpam-4704	275	3	number	number	NOUN
ejpam-4704	275	4	of	of	ADP
ejpam-4704	275	5	some	some	DET
ejpam-4704	275	6	special	special	ADJ
ejpam-4704	275	7	non	non	ADJ
ejpam-4704	275	8	-	-	ADJ
ejpam-4704	275	9	planar	planar	ADJ
ejpam-4704	275	10	graphs	graph	NOUN
ejpam-4704	275	11	.	.	PUNCT
ejpam-4704	276	1	czechoslovak	czechoslovak	ADJ
ejpam-4704	276	2	mathematical	mathematical	PROPN
ejpam-4704	276	3	journal	journal	PROPN
ejpam-4704	276	4	,	,	PUNCT
ejpam-4704	276	5	53(2):225–240	53(2):225–240	NOUN
ejpam-4704	276	6	,	,	PUNCT
ejpam-4704	276	7	2003	2003	NUM
ejpam-4704	276	8	.	.	PUNCT
ejpam-4704	277	1	[	[	X
ejpam-4704	277	2	4	4	X
ejpam-4704	277	3	]	]	PUNCT
ejpam-4704	277	4	maref	maref	PROPN
ejpam-4704	277	5	y	y	PROPN
ejpam-4704	277	6	alzoubi	alzoubi	PROPN
ejpam-4704	277	7	and	and	CCONJ
ejpam-4704	277	8	mohammed	mohammed	PROPN
ejpam-4704	277	9	mm	mm	PROPN
ejpam-4704	277	10	jaradat	jaradat	PROPN
ejpam-4704	277	11	.	.	PUNCT
ejpam-4704	278	1	on	on	ADP
ejpam-4704	278	2	the	the	DET
ejpam-4704	278	3	basis	basis	NOUN
ejpam-4704	278	4	number	number	NOUN
ejpam-4704	278	5	of	of	ADP
ejpam-4704	278	6	the	the	DET
ejpam-4704	278	7	composition	composition	NOUN
ejpam-4704	278	8	of	of	ADP
ejpam-4704	278	9	different	different	ADJ
ejpam-4704	278	10	ladders	ladder	NOUN
ejpam-4704	278	11	with	with	ADP
ejpam-4704	278	12	some	some	DET
ejpam-4704	278	13	graphs	graph	NOUN
ejpam-4704	278	14	.	.	PUNCT
ejpam-4704	279	1	international	international	ADJ
ejpam-4704	279	2	journal	journal	NOUN
ejpam-4704	279	3	of	of	ADP
ejpam-4704	279	4	mathematics	mathematics	PROPN
ejpam-4704	279	5	and	and	CCONJ
ejpam-4704	279	6	mathematical	mathematical	ADJ
ejpam-4704	279	7	sciences	science	NOUN
ejpam-4704	279	8	,	,	PUNCT
ejpam-4704	279	9	2005(12):1861–1868	2005(12):1861–1868	NUM
ejpam-4704	279	10	,	,	PUNCT
ejpam-4704	279	11	2005	2005	NUM
ejpam-4704	279	12	.	.	PUNCT
ejpam-4704	280	1	[	[	X
ejpam-4704	280	2	5	5	X
ejpam-4704	280	3	]	]	PUNCT
ejpam-4704	280	4	maref	maref	PROPN
ejpam-4704	280	5	y	y	PROPN
ejpam-4704	280	6	alzoubi	alzoubi	PROPN
ejpam-4704	280	7	and	and	CCONJ
ejpam-4704	280	8	mohammed	mohammed	PROPN
ejpam-4704	280	9	mm	mm	PROPN
ejpam-4704	280	10	jaradat	jaradat	PROPN
ejpam-4704	280	11	.	.	PUNCT
ejpam-4704	281	1	the	the	DET
ejpam-4704	281	2	basis	basis	NOUN
ejpam-4704	281	3	number	number	NOUN
ejpam-4704	281	4	of	of	ADP
ejpam-4704	281	5	the	the	DET
ejpam-4704	281	6	cartesian	cartesian	ADJ
ejpam-4704	281	7	product	product	NOUN
ejpam-4704	281	8	of	of	ADP
ejpam-4704	281	9	a	a	DET
ejpam-4704	281	10	path	path	NOUN
ejpam-4704	281	11	with	with	ADP
ejpam-4704	281	12	a	a	DET
ejpam-4704	281	13	circular	circular	ADJ
ejpam-4704	281	14	ladder	ladder	NOUN
ejpam-4704	281	15	,	,	PUNCT
ejpam-4704	281	16	a	a	DET
ejpam-4704	281	17	möbius	möbius	NOUN
ejpam-4704	281	18	ladder	ladder	NOUN
ejpam-4704	281	19	and	and	CCONJ
ejpam-4704	281	20	a	a	DET
ejpam-4704	281	21	net	net	NOUN
ejpam-4704	281	22	.	.	PUNCT
ejpam-4704	282	1	kyungpook	kyungpook	PROPN
ejpam-4704	282	2	mathematical	mathematical	PROPN
ejpam-4704	282	3	journal	journal	PROPN
ejpam-4704	282	4	,	,	PUNCT
ejpam-4704	282	5	47(2):165–174	47(2):165–174	PROPN
ejpam-4704	282	6	,	,	PUNCT
ejpam-4704	282	7	2007	2007	NUM
ejpam-4704	282	8	.	.	PUNCT
ejpam-4704	283	1	[	[	X
ejpam-4704	283	2	6	6	NUM
ejpam-4704	283	3	]	]	PUNCT
ejpam-4704	283	4	maref	maref	PROPN
ejpam-4704	283	5	ym	ym	PROPN
ejpam-4704	283	6	alzoubi	alzoubi	PROPN
ejpam-4704	283	7	and	and	CCONJ
ejpam-4704	283	8	mmm	mmm	PROPN
ejpam-4704	283	9	jaradat	jaradat	NOUN
ejpam-4704	283	10	.	.	PUNCT
ejpam-4704	284	1	the	the	DET
ejpam-4704	284	2	basis	basis	NOUN
ejpam-4704	284	3	number	number	NOUN
ejpam-4704	284	4	of	of	ADP
ejpam-4704	284	5	the	the	DET
ejpam-4704	284	6	composition	composition	NOUN
ejpam-4704	284	7	of	of	ADP
ejpam-4704	284	8	theta	theta	NOUN
ejpam-4704	284	9	graphs	graph	NOUN
ejpam-4704	284	10	with	with	ADP
ejpam-4704	284	11	some	some	DET
ejpam-4704	284	12	graphs	graph	NOUN
ejpam-4704	284	13	.	.	PUNCT
ejpam-4704	285	1	ars	ar	NOUN
ejpam-4704	285	2	combinatoria	combinatoria	NOUN
ejpam-4704	285	3	,	,	PUNCT
ejpam-4704	285	4	79:107–114	79:107–114	NUM
ejpam-4704	285	5	,	,	PUNCT
ejpam-4704	285	6	2006	2006	NUM
ejpam-4704	285	7	.	.	PUNCT
ejpam-4704	286	1	[	[	X
ejpam-4704	286	2	7	7	X
ejpam-4704	286	3	]	]	X
ejpam-4704	286	4	gary	gary	PROPN
ejpam-4704	286	5	chartrand	chartrand	PROPN
ejpam-4704	286	6	and	and	CCONJ
ejpam-4704	286	7	linda	linda	PROPN
ejpam-4704	286	8	lesniak	lesniak	PROPN
ejpam-4704	286	9	.	.	PUNCT
ejpam-4704	286	10	graphs	graph	NOUN
ejpam-4704	286	11	&	&	CCONJ
ejpam-4704	286	12	digraphs	digraph	NOUN
ejpam-4704	286	13	.	.	PUNCT
ejpam-4704	287	1	chapman	chapman	PROPN
ejpam-4704	287	2	&	&	CCONJ
ejpam-4704	287	3	hall	hall	PROPN
ejpam-4704	287	4	crc	crc	PROPN
ejpam-4704	287	5	press	press	PROPN
ejpam-4704	287	6	,	,	PUNCT
ejpam-4704	287	7	3rd	3rd	ADJ
ejpam-4704	287	8	edition	edition	NOUN
ejpam-4704	287	9	,	,	PUNCT
ejpam-4704	287	10	1996	1996	NUM
ejpam-4704	287	11	.	.	PUNCT
ejpam-4704	288	1	[	[	X
ejpam-4704	288	2	8	8	NUM
ejpam-4704	288	3	]	]	SYM
ejpam-4704	288	4	f	f	PROPN
ejpam-4704	288	5	harary	harary	NOUN
ejpam-4704	288	6	.	.	PUNCT
ejpam-4704	289	1	graph	graph	NOUN
ejpam-4704	289	2	theory	theory	NOUN
ejpam-4704	289	3	,	,	PUNCT
ejpam-4704	289	4	3rd	3rd	ADJ
ejpam-4704	289	5	printing	printing	NOUN
ejpam-4704	289	6	.	.	PUNCT
ejpam-4704	290	1	addison	addison	PROPN
ejpam-4704	290	2	-	-	PUNCT
ejpam-4704	290	3	wesley	wesley	PROPN
ejpam-4704	290	4	,	,	PUNCT
ejpam-4704	290	5	reading	reading	NOUN
ejpam-4704	290	6	,	,	PUNCT
ejpam-4704	290	7	ma	ma	PROPN
ejpam-4704	290	8	,	,	PUNCT
ejpam-4704	290	9	1971	1971	NUM
ejpam-4704	290	10	.	.	PUNCT
ejpam-4704	291	1	[	[	X
ejpam-4704	291	2	9	9	NUM
ejpam-4704	291	3	]	]	SYM
ejpam-4704	291	4	mmm	mmm	NOUN
ejpam-4704	291	5	jaradat	jaradat	PROPN
ejpam-4704	291	6	,	,	PUNCT
ejpam-4704	291	7	my	my	PRON
ejpam-4704	291	8	alzoubi	alzoubi	ADJ
ejpam-4704	291	9	,	,	PUNCT
ejpam-4704	291	10	ea	ea	NUM
ejpam-4704	291	11	rawashdeh	rawashdeh	NOUN
ejpam-4704	291	12	,	,	PUNCT
ejpam-4704	291	13	et	et	PROPN
ejpam-4704	291	14	al	al	PROPN
ejpam-4704	291	15	.	.	PUNCT
ejpam-4704	292	1	the	the	DET
ejpam-4704	292	2	basis	basis	NOUN
ejpam-4704	292	3	number	number	NOUN
ejpam-4704	292	4	of	of	ADP
ejpam-4704	292	5	the	the	DET
ejpam-4704	292	6	lexicographic	lexicographic	ADJ
ejpam-4704	292	7	product	product	NOUN
ejpam-4704	292	8	of	of	ADP
ejpam-4704	292	9	different	different	ADJ
ejpam-4704	292	10	ladders	ladder	NOUN
ejpam-4704	292	11	.	.	PUNCT
ejpam-4704	293	1	sut	sut	PROPN
ejpam-4704	293	2	journal	journal	PROPN
ejpam-4704	293	3	of	of	ADP
ejpam-4704	293	4	mathematics	mathematics	PROPN
ejpam-4704	293	5	,	,	PUNCT
ejpam-4704	293	6	40(2):91–101	40(2):91–101	NUM
ejpam-4704	293	7	,	,	PUNCT
ejpam-4704	293	8	2004	2004	NUM
ejpam-4704	293	9	.	.	PUNCT
ejpam-4704	294	1	[	[	X
ejpam-4704	294	2	10	10	NUM
ejpam-4704	294	3	]	]	X
ejpam-4704	294	4	mohammed	mohammed	PROPN
ejpam-4704	294	5	mm	mm	PROPN
ejpam-4704	294	6	jaradat	jaradat	PROPN
ejpam-4704	294	7	and	and	CCONJ
ejpam-4704	294	8	maref	maref	PROPN
ejpam-4704	294	9	y	y	PROPN
ejpam-4704	294	10	alzoubi	alzoubi	PROPN
ejpam-4704	294	11	.	.	PUNCT
ejpam-4704	295	1	an	an	DET
ejpam-4704	295	2	upper	upper	ADJ
ejpam-4704	295	3	bound	bound	NOUN
ejpam-4704	295	4	of	of	ADP
ejpam-4704	295	5	the	the	DET
ejpam-4704	295	6	basis	basis	NOUN
ejpam-4704	295	7	number	number	NOUN
ejpam-4704	295	8	of	of	ADP
ejpam-4704	295	9	the	the	DET
ejpam-4704	295	10	lexicographic	lexicographic	ADJ
ejpam-4704	295	11	product	product	NOUN
ejpam-4704	295	12	of	of	ADP
ejpam-4704	295	13	graphs	graph	NOUN
ejpam-4704	295	14	.	.	PUNCT
ejpam-4704	296	1	australasian	australasian	ADJ
ejpam-4704	296	2	journal	journal	NOUN
ejpam-4704	296	3	of	of	ADP
ejpam-4704	296	4	combinatorics	combinatoric	NOUN
ejpam-4704	296	5	,	,	PUNCT
ejpam-4704	296	6	32:305–312	32:305–312	NUM
ejpam-4704	296	7	,	,	PUNCT
ejpam-4704	296	8	2005	2005	NUM
ejpam-4704	296	9	.	.	PUNCT
ejpam-4704	297	1	[	[	X
ejpam-4704	297	2	11	11	NUM
ejpam-4704	297	3	]	]	SYM
ejpam-4704	297	4	abdulsattar	abdulsattar	PROPN
ejpam-4704	297	5	m	m	PROPN
ejpam-4704	297	6	khidhir	khidhir	NOUN
ejpam-4704	297	7	,	,	PUNCT
ejpam-4704	297	8	ahmed	ahmed	PROPN
ejpam-4704	297	9	m	m	PROPN
ejpam-4704	297	10	ali	ali	PROPN
ejpam-4704	297	11	,	,	PUNCT
ejpam-4704	297	12	and	and	CCONJ
ejpam-4704	297	13	shuaa’m	shuaa’m	VERB
ejpam-4704	297	14	aziz	aziz	PROPN
ejpam-4704	297	15	.	.	PUNCT
ejpam-4704	298	1	application	application	NOUN
ejpam-4704	298	2	of	of	ADP
ejpam-4704	298	3	width	width	ADJ
ejpam-4704	298	4	distance	distance	NOUN
ejpam-4704	298	5	on	on	ADP
ejpam-4704	298	6	semi	semi	ADJ
ejpam-4704	298	7	–	–	PUNCT
ejpam-4704	298	8	star	star	ADJ
ejpam-4704	298	9	link	link	NOUN
ejpam-4704	298	10	satellite	satellite	NOUN
ejpam-4704	298	11	constellation	constellation	PROPN
ejpam-4704	298	12	.	.	PUNCT
ejpam-4704	299	1	journal	journal	NOUN
ejpam-4704	299	2	of	of	ADP
ejpam-4704	299	3	discrete	discrete	ADJ
ejpam-4704	299	4	mathematical	mathematical	ADJ
ejpam-4704	299	5	sciences	science	NOUN
ejpam-4704	299	6	and	and	CCONJ
ejpam-4704	299	7	cryptography	cryptography	NOUN
ejpam-4704	299	8	,	,	PUNCT
ejpam-4704	299	9	24(3):797–807	24(3):797–807	NUM
ejpam-4704	299	10	,	,	PUNCT
ejpam-4704	299	11	2021	2021	NUM
ejpam-4704	299	12	.	.	PUNCT
ejpam-4704	300	1	[	[	X
ejpam-4704	300	2	12	12	NUM
ejpam-4704	300	3	]	]	X
ejpam-4704	300	4	saunders	saunders	PROPN
ejpam-4704	300	5	mac	mac	PROPN
ejpam-4704	300	6	lane	lane	PROPN
ejpam-4704	300	7	.	.	PUNCT
ejpam-4704	301	1	a	a	DET
ejpam-4704	301	2	combinatorial	combinatorial	ADJ
ejpam-4704	301	3	condition	condition	NOUN
ejpam-4704	301	4	for	for	ADP
ejpam-4704	301	5	planar	planar	ADJ
ejpam-4704	301	6	graphs	graph	NOUN
ejpam-4704	301	7	.	.	PUNCT
ejpam-4704	302	1	fundamenta	fundamenta	PROPN
ejpam-4704	302	2	mathematicae	mathematicae	PROPN
ejpam-4704	302	3	,	,	PUNCT
ejpam-4704	302	4	28(1):22–32	28(1):22–32	NUM
ejpam-4704	302	5	,	,	PUNCT
ejpam-4704	302	6	1937	1937	NUM
ejpam-4704	302	7	.	.	PUNCT
ejpam-4704	303	1	references	reference	NOUN
ejpam-4704	303	2	964	964	NUM
ejpam-4704	303	3	[	[	SYM
ejpam-4704	303	4	13	13	NUM
ejpam-4704	303	5	]	]	X
ejpam-4704	303	6	ghassan	ghassan	PROPN
ejpam-4704	303	7	t	t	PROPN
ejpam-4704	303	8	marougi	marougi	NOUN
ejpam-4704	303	9	.	.	PUNCT
ejpam-4704	304	1	on	on	ADP
ejpam-4704	304	2	the	the	DET
ejpam-4704	304	3	basis	basis	NOUN
ejpam-4704	304	4	number	number	NOUN
ejpam-4704	304	5	of	of	ADP
ejpam-4704	304	6	semi	semi	ADJ
ejpam-4704	304	7	-	-	ADJ
ejpam-4704	304	8	strong	strong	ADJ
ejpam-4704	304	9	product	product	NOUN
ejpam-4704	304	10	of	of	ADP
ejpam-4704	304	11	with	with	ADP
ejpam-4704	304	12	some	some	DET
ejpam-4704	304	13	special	special	ADJ
ejpam-4704	304	14	graphs	graph	NOUN
ejpam-4704	304	15	.	.	PUNCT
ejpam-4704	305	1	al	al	PROPN
ejpam-4704	305	2	-	-	PUNCT
ejpam-4704	305	3	rafidain	rafidain	PROPN
ejpam-4704	305	4	journal	journal	NOUN
ejpam-4704	305	5	of	of	ADP
ejpam-4704	305	6	computer	computer	NOUN
ejpam-4704	305	7	sciences	science	NOUN
ejpam-4704	305	8	and	and	CCONJ
ejpam-4704	305	9	mathematics	mathematic	NOUN
ejpam-4704	305	10	,	,	PUNCT
ejpam-4704	305	11	6(3):173–181	6(3):173–181	NUM
ejpam-4704	305	12	,	,	PUNCT
ejpam-4704	305	13	2009	2009	NUM
ejpam-4704	305	14	.	.	PUNCT
ejpam-4704	306	1	[	[	X
ejpam-4704	306	2	14	14	NUM
ejpam-4704	306	3	]	]	PUNCT
ejpam-4704	306	4	raghad	raghad	VERB
ejpam-4704	306	5	a	a	DET
ejpam-4704	306	6	mustafa	mustafa	PROPN
ejpam-4704	306	7	,	,	PUNCT
ejpam-4704	306	8	ahmed	ahmed	PROPN
ejpam-4704	306	9	m	m	PROPN
ejpam-4704	306	10	ali	ali	PROPN
ejpam-4704	306	11	,	,	PUNCT
ejpam-4704	306	12	and	and	CCONJ
ejpam-4704	306	13	abdul	abdul	PROPN
ejpam-4704	306	14	sattar	sattar	PROPN
ejpam-4704	306	15	m	m	PROPN
ejpam-4704	306	16	khidhir	khidhir	PROPN
ejpam-4704	306	17	.	.	PUNCT
ejpam-4704	307	1	mn	mn	PROPN
ejpam-4704	307	2	–	–	PUNCT
ejpam-4704	307	3	polynomials	polynomial	NOUN
ejpam-4704	307	4	of	of	ADP
ejpam-4704	307	5	general	general	ADJ
ejpam-4704	307	6	thorn	thorn	NOUN
ejpam-4704	307	7	path	path	NOUN
ejpam-4704	307	8	graph	graph	NOUN
ejpam-4704	307	9	.	.	PUNCT
ejpam-4704	308	1	in	in	ADP
ejpam-4704	308	2	journal	journal	PROPN
ejpam-4704	308	3	of	of	ADP
ejpam-4704	308	4	physics	physics	PROPN
ejpam-4704	308	5	:	:	PUNCT
ejpam-4704	308	6	conference	conference	NOUN
ejpam-4704	308	7	series	series	NOUN
ejpam-4704	308	8	,	,	PUNCT
ejpam-4704	308	9	volume	volume	NOUN
ejpam-4704	308	10	1897	1897	NUM
ejpam-4704	308	11	,	,	PUNCT
ejpam-4704	308	12	pages	page	NOUN
ejpam-4704	308	13	1–10	1–10	NOUN
ejpam-4704	308	14	.	.	PUNCT
ejpam-4704	309	1	iop	iop	PROPN
ejpam-4704	309	2	publishing	publishing	NOUN
ejpam-4704	309	3	,	,	PUNCT
ejpam-4704	309	4	2021	2021	NUM
ejpam-4704	309	5	.	.	PUNCT
ejpam-4704	310	1	[	[	X
ejpam-4704	310	2	15	15	NUM
ejpam-4704	310	3	]	]	X
ejpam-4704	310	4	raghad	raghad	VERB
ejpam-4704	310	5	a	a	DET
ejpam-4704	310	6	mustafa	mustafa	PROPN
ejpam-4704	310	7	,	,	PUNCT
ejpam-4704	310	8	ahmed	ahmed	PROPN
ejpam-4704	310	9	m	m	PROPN
ejpam-4704	310	10	ali	ali	PROPN
ejpam-4704	310	11	,	,	PUNCT
ejpam-4704	310	12	and	and	CCONJ
ejpam-4704	310	13	abdul	abdul	PROPN
ejpam-4704	310	14	sattar	sattar	PROPN
ejpam-4704	310	15	m	m	PROPN
ejpam-4704	310	16	khidhir	khidhir	PROPN
ejpam-4704	310	17	.	.	PUNCT
ejpam-4704	311	1	mn	mn	PROPN
ejpam-4704	311	2	–	–	PUNCT
ejpam-4704	311	3	polynomials	polynomial	NOUN
ejpam-4704	311	4	of	of	ADP
ejpam-4704	311	5	some	some	DET
ejpam-4704	311	6	special	special	ADJ
ejpam-4704	311	7	graphs	graph	NOUN
ejpam-4704	311	8	.	.	PUNCT
ejpam-4704	312	1	iraqi	iraqi	ADJ
ejpam-4704	312	2	journal	journal	PROPN
ejpam-4704	312	3	of	of	ADP
ejpam-4704	312	4	science	science	NOUN
ejpam-4704	312	5	,	,	PUNCT
ejpam-4704	312	6	62(6):1986–1993	62(6):1986–1993	NUM
ejpam-4704	312	7	,	,	PUNCT
ejpam-4704	312	8	2021	2021	NUM
ejpam-4704	312	9	.	.	PUNCT
ejpam-4704	313	1	[	[	X
ejpam-4704	313	2	16	16	NUM
ejpam-4704	313	3	]	]	X
ejpam-4704	313	4	nk	nk	PROPN
ejpam-4704	313	5	sudev	sudev	PROPN
ejpam-4704	313	6	,	,	PUNCT
ejpam-4704	313	7	kp	kp	PROPN
ejpam-4704	313	8	chithra	chithra	PROPN
ejpam-4704	313	9	,	,	PUNCT
ejpam-4704	313	10	k	k	PROPN
ejpam-4704	313	11	augustine	augustine	PROPN
ejpam-4704	313	12	germina	germina	PROPN
ejpam-4704	313	13	,	,	PUNCT
ejpam-4704	313	14	s	s	PART
ejpam-4704	313	15	satheesh	satheesh	NOUN
ejpam-4704	313	16	,	,	PUNCT
ejpam-4704	313	17	and	and	CCONJ
ejpam-4704	313	18	johan	johan	PROPN
ejpam-4704	313	19	kok	kok	PROPN
ejpam-4704	313	20	.	.	PUNCT
ejpam-4704	314	1	on	on	ADP
ejpam-4704	314	2	certain	certain	ADJ
ejpam-4704	314	3	coloring	color	VERB
ejpam-4704	314	4	parameters	parameter	NOUN
ejpam-4704	314	5	of	of	ADP
ejpam-4704	314	6	mycielski	mycielski	ADJ
ejpam-4704	314	7	graphs	graph	NOUN
ejpam-4704	314	8	of	of	ADP
ejpam-4704	314	9	some	some	DET
ejpam-4704	314	10	graphs	graph	NOUN
ejpam-4704	314	11	.	.	PUNCT
ejpam-4704	315	1	discrete	discrete	ADJ
ejpam-4704	315	2	mathematics	mathematic	NOUN
ejpam-4704	315	3	,	,	PUNCT
ejpam-4704	315	4	algorithms	algorithm	NOUN
ejpam-4704	315	5	and	and	CCONJ
ejpam-4704	315	6	applications	application	NOUN
ejpam-4704	315	7	,	,	PUNCT
ejpam-4704	315	8	10(03):1850030	10(03):1850030	NUM
ejpam-4704	315	9	,	,	PUNCT
ejpam-4704	315	10	2018	2018	NUM
ejpam-4704	315	11	.	.	PUNCT
ejpam-4704	316	1	[	[	X
ejpam-4704	316	2	17	17	NUM
ejpam-4704	316	3	]	]	X
ejpam-4704	316	4	e	e	X
ejpam-4704	316	5	yi	yi	PROPN
ejpam-4704	316	6	,	,	PUNCT
ejpam-4704	316	7	ja	ja	PROPN
ejpam-4704	316	8	rodŕıguez	rodŕıguez	PROPN
ejpam-4704	316	9	-	-	NOUN
ejpam-4704	316	10	velázquez	velázquez	NOUN
ejpam-4704	316	11	,	,	PUNCT
ejpam-4704	316	12	and	and	CCONJ
ejpam-4704	316	13	dj	dj	X
ejpam-4704	316	14	klein	klein	PROPN
ejpam-4704	316	15	.	.	PUNCT
ejpam-4704	317	1	on	on	ADP
ejpam-4704	317	2	the	the	DET
ejpam-4704	317	3	super	super	ADJ
ejpam-4704	317	4	domination	domination	NOUN
ejpam-4704	317	5	number	number	NOUN
ejpam-4704	317	6	of	of	ADP
ejpam-4704	317	7	graphs	graph	NOUN
ejpam-4704	317	8	.	.	PUNCT
ejpam-4704	318	1	communication	communication	NOUN
ejpam-4704	318	2	in	in	ADP
ejpam-4704	318	3	combinatorics	combinatoric	NOUN
ejpam-4704	318	4	and	and	CCONJ
ejpam-4704	318	5	optimization	optimization	NOUN
ejpam-4704	318	6	,	,	PUNCT
ejpam-4704	318	7	5(2):83–96	5(2):83–96	NUM
ejpam-4704	318	8	,	,	PUNCT
ejpam-4704	318	9	2020	2020	NUM
ejpam-4704	318	10	.	.	PUNCT