id	sid	tid	token	lemma	pos
ejpam-3716	1	1	compile	compile	NOUN
ejpam-3716	1	2	/	/	SYM
ejpam-3716	1	3	output.dvi	output.dvi	NOUN
ejpam-3716	1	4	european	european	ADJ
ejpam-3716	1	5	journal	journal	NOUN
ejpam-3716	1	6	of	of	ADP
ejpam-3716	1	7	pure	pure	ADJ
ejpam-3716	1	8	and	and	CCONJ
ejpam-3716	1	9	applied	apply	VERB
ejpam-3716	1	10	mathematics	mathematic	NOUN
ejpam-3716	1	11	vol	vol	NOUN
ejpam-3716	1	12	.	.	PROPN
ejpam-3716	2	1	13	13	NUM
ejpam-3716	2	2	,	,	PUNCT
ejpam-3716	2	3	no	no	INTJ
ejpam-3716	2	4	.	.	NOUN
ejpam-3716	2	5	5	5	NUM
ejpam-3716	2	6	,	,	PUNCT
ejpam-3716	2	7	2020	2020	NUM
ejpam-3716	2	8	,	,	PUNCT
ejpam-3716	2	9	1300	1300	NUM
ejpam-3716	2	10	-	-	SYM
ejpam-3716	2	11	1305	1305	NUM
ejpam-3716	2	12	issn	issn	VERB
ejpam-3716	2	13	1307	1307	NUM
ejpam-3716	2	14	-	-	SYM
ejpam-3716	2	15	5543	5543	NUM
ejpam-3716	2	16	–	–	PUNCT
ejpam-3716	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3716	2	18	published	publish	VERB
ejpam-3716	2	19	by	by	ADP
ejpam-3716	2	20	new	new	PROPN
ejpam-3716	2	21	york	york	PROPN
ejpam-3716	2	22	business	business	PROPN
ejpam-3716	2	23	global	global	ADJ
ejpam-3716	2	24	special	special	ADJ
ejpam-3716	2	25	issue	issue	NOUN
ejpam-3716	2	26	dedicated	dedicate	VERB
ejpam-3716	2	27	to	to	ADP
ejpam-3716	2	28	professor	professor	NOUN
ejpam-3716	2	29	hari	hari	PROPN
ejpam-3716	2	30	m.	m.	PROPN
ejpam-3716	2	31	srivastava	srivastava	PROPN
ejpam-3716	2	32	on	on	ADP
ejpam-3716	2	33	the	the	DET
ejpam-3716	2	34	occasion	occasion	NOUN
ejpam-3716	2	35	of	of	ADP
ejpam-3716	2	36	his	his	PRON
ejpam-3716	2	37	80th	80th	ADJ
ejpam-3716	2	38	birthday	birthday	NOUN
ejpam-3716	2	39	on	on	ADP
ejpam-3716	2	40	plick	plick	NOUN
ejpam-3716	2	41	graphs	graph	NOUN
ejpam-3716	2	42	with	with	ADP
ejpam-3716	2	43	point	point	NOUN
ejpam-3716	2	44	-	-	PUNCT
ejpam-3716	2	45	outercoarseness	outercoarseness	NOUN
ejpam-3716	2	46	number	number	NOUN
ejpam-3716	2	47	one	one	NUM
ejpam-3716	2	48	v.	v.	ADP
ejpam-3716	2	49	lokesha1	lokesha1	NOUN
ejpam-3716	2	50	,	,	PUNCT
ejpam-3716	2	51	sunilkumar	sunilkumar	NOUN
ejpam-3716	2	52	m.	m.	NOUN
ejpam-3716	2	53	hosamani2,∗	hosamani2,∗	NOUN
ejpam-3716	2	54	,	,	PUNCT
ejpam-3716	2	55	shobha	shobha	NOUN
ejpam-3716	2	56	v.	v.	ADP
ejpam-3716	2	57	patil3	patil3	PROPN
ejpam-3716	2	58	1	1	NUM
ejpam-3716	2	59	department	department	NOUN
ejpam-3716	2	60	of	of	ADP
ejpam-3716	2	61	studies	study	NOUN
ejpam-3716	2	62	in	in	ADP
ejpam-3716	2	63	mathematics	mathematics	PROPN
ejpam-3716	2	64	vsk	vsk	PROPN
ejpam-3716	2	65	university	university	PROPN
ejpam-3716	2	66	,	,	PUNCT
ejpam-3716	2	67	bellary	bellary	PROPN
ejpam-3716	2	68	,	,	PUNCT
ejpam-3716	2	69	karnataka	karnataka	PROPN
ejpam-3716	2	70	,	,	PUNCT
ejpam-3716	2	71	india	india	PROPN
ejpam-3716	2	72	2	2	NUM
ejpam-3716	2	73	department	department	NOUN
ejpam-3716	2	74	of	of	ADP
ejpam-3716	2	75	mathematics	mathematic	NOUN
ejpam-3716	2	76	,	,	PUNCT
ejpam-3716	2	77	rani	rani	PROPN
ejpam-3716	2	78	channamma	channamma	PROPN
ejpam-3716	2	79	university	university	PROPN
ejpam-3716	2	80	,	,	PUNCT
ejpam-3716	2	81	belagavi	belagavi	VERB
ejpam-3716	2	82	,	,	PUNCT
ejpam-3716	2	83	karnataka	karnataka	PROPN
ejpam-3716	2	84	,	,	PUNCT
ejpam-3716	2	85	india	india	PROPN
ejpam-3716	2	86	3	3	PROPN
ejpam-3716	2	87	department	department	PROPN
ejpam-3716	2	88	of	of	ADP
ejpam-3716	2	89	mathematics	mathematics	PROPN
ejpam-3716	2	90	,	,	PUNCT
ejpam-3716	2	91	kle	kle	PROPN
ejpam-3716	2	92	’s	’s	PROPN
ejpam-3716	2	93	dr	dr	PROPN
ejpam-3716	2	94	.	.	PROPN
ejpam-3716	2	95	m.	m.	PROPN
ejpam-3716	2	96	s.	s.	PROPN
ejpam-3716	2	97	sheshgiri	sheshgiri	PROPN
ejpam-3716	2	98	college	college	PROPN
ejpam-3716	2	99	of	of	ADP
ejpam-3716	2	100	engineering	engineering	NOUN
ejpam-3716	2	101	and	and	CCONJ
ejpam-3716	2	102	technology	technology	NOUN
ejpam-3716	2	103	belagavi	belagavi	NOUN
ejpam-3716	2	104	,	,	PUNCT
ejpam-3716	2	105	karnataka	karnataka	PROPN
ejpam-3716	2	106	,	,	PUNCT
ejpam-3716	2	107	india	india	PROPN
ejpam-3716	2	108	abstract	abstract	NOUN
ejpam-3716	2	109	.	.	PUNCT
ejpam-3716	3	1	the	the	DET
ejpam-3716	3	2	plick	plick	NOUN
ejpam-3716	3	3	graph	graph	NOUN
ejpam-3716	3	4	p	p	X
ejpam-3716	3	5	(	(	PUNCT
ejpam-3716	3	6	g	g	NOUN
ejpam-3716	3	7	)	)	PUNCT
ejpam-3716	3	8	of	of	ADP
ejpam-3716	3	9	a	a	DET
ejpam-3716	3	10	graph	graph	NOUN
ejpam-3716	3	11	g	g	NOUN
ejpam-3716	3	12	is	be	AUX
ejpam-3716	3	13	obtained	obtain	VERB
ejpam-3716	3	14	from	from	ADP
ejpam-3716	3	15	the	the	DET
ejpam-3716	3	16	line	line	NOUN
ejpam-3716	3	17	graph	graph	NOUN
ejpam-3716	3	18	by	by	ADP
ejpam-3716	3	19	adding	add	VERB
ejpam-3716	3	20	a	a	DET
ejpam-3716	3	21	new	new	ADJ
ejpam-3716	3	22	vertex	vertex	NOUN
ejpam-3716	3	23	corresponding	correspond	VERB
ejpam-3716	3	24	to	to	ADP
ejpam-3716	3	25	each	each	DET
ejpam-3716	3	26	block	block	NOUN
ejpam-3716	3	27	of	of	ADP
ejpam-3716	3	28	the	the	DET
ejpam-3716	3	29	original	original	ADJ
ejpam-3716	3	30	graph	graph	NOUN
ejpam-3716	3	31	and	and	CCONJ
ejpam-3716	3	32	joining	join	VERB
ejpam-3716	3	33	this	this	DET
ejpam-3716	3	34	vertex	vertex	NOUN
ejpam-3716	3	35	to	to	ADP
ejpam-3716	3	36	the	the	DET
ejpam-3716	3	37	vertices	vertex	NOUN
ejpam-3716	3	38	of	of	ADP
ejpam-3716	3	39	the	the	DET
ejpam-3716	3	40	line	line	NOUN
ejpam-3716	3	41	graph	graph	NOUN
ejpam-3716	3	42	which	which	PRON
ejpam-3716	3	43	correspond	correspond	VERB
ejpam-3716	3	44	to	to	ADP
ejpam-3716	3	45	the	the	DET
ejpam-3716	3	46	edges	edge	NOUN
ejpam-3716	3	47	of	of	ADP
ejpam-3716	3	48	the	the	DET
ejpam-3716	3	49	block	block	NOUN
ejpam-3716	3	50	of	of	ADP
ejpam-3716	3	51	the	the	DET
ejpam-3716	3	52	original	original	ADJ
ejpam-3716	3	53	graph	graph	NOUN
ejpam-3716	3	54	.	.	PUNCT
ejpam-3716	4	1	the	the	DET
ejpam-3716	4	2	point	point	NOUN
ejpam-3716	4	3	outer	outer	NOUN
ejpam-3716	4	4	-	-	PUNCT
ejpam-3716	4	5	coarseness	coarseness	NOUN
ejpam-3716	4	6	is	be	AUX
ejpam-3716	4	7	the	the	DET
ejpam-3716	4	8	maximum	maximum	ADJ
ejpam-3716	4	9	number	number	NOUN
ejpam-3716	4	10	of	of	ADP
ejpam-3716	4	11	vertex	vertex	NOUN
ejpam-3716	4	12	-	-	PUNCT
ejpam-3716	4	13	disjoint	disjoint	NOUN
ejpam-3716	4	14	nonouterplanar	nonouterplanar	NOUN
ejpam-3716	4	15	subgraphs	subgraph	NOUN
ejpam-3716	4	16	of	of	ADP
ejpam-3716	4	17	g.	g.	PROPN
ejpam-3716	4	18	in	in	ADP
ejpam-3716	4	19	this	this	DET
ejpam-3716	4	20	paper	paper	NOUN
ejpam-3716	4	21	,	,	PUNCT
ejpam-3716	4	22	we	we	PRON
ejpam-3716	4	23	obtain	obtain	VERB
ejpam-3716	4	24	a	a	DET
ejpam-3716	4	25	necessary	necessary	ADJ
ejpam-3716	4	26	and	and	CCONJ
ejpam-3716	4	27	sufficient	sufficient	ADJ
ejpam-3716	4	28	conditions	condition	NOUN
ejpam-3716	4	29	for	for	SCONJ
ejpam-3716	4	30	the	the	DET
ejpam-3716	4	31	plick	plick	NOUN
ejpam-3716	4	32	graph	graph	NOUN
ejpam-3716	4	33	p	p	X
ejpam-3716	4	34	(	(	PUNCT
ejpam-3716	4	35	g	g	NOUN
ejpam-3716	4	36	)	)	PUNCT
ejpam-3716	4	37	to	to	PART
ejpam-3716	4	38	have	have	VERB
ejpam-3716	4	39	pointoutercoarseness	pointoutercoarseness	ADJ
ejpam-3716	4	40	number	number	NOUN
ejpam-3716	4	41	one	one	NUM
ejpam-3716	4	42	.	.	PUNCT
ejpam-3716	5	1	2020	2020	NUM
ejpam-3716	5	2	mathematics	mathematic	NOUN
ejpam-3716	5	3	subject	subject	NOUN
ejpam-3716	5	4	classifications	classification	NOUN
ejpam-3716	5	5	:	:	PUNCT
ejpam-3716	5	6	05c99	05c99	NUM
ejpam-3716	5	7	key	key	ADJ
ejpam-3716	5	8	words	word	NOUN
ejpam-3716	5	9	and	and	CCONJ
ejpam-3716	5	10	phrases	phrase	NOUN
ejpam-3716	5	11	:	:	PUNCT
ejpam-3716	5	12	plick	plick	NOUN
ejpam-3716	5	13	graph	graph	NOUN
ejpam-3716	5	14	,	,	PUNCT
ejpam-3716	5	15	edge	edge	NOUN
ejpam-3716	5	16	-	-	PUNCT
ejpam-3716	5	17	disjoint	disjoint	NOUN
ejpam-3716	5	18	,	,	PUNCT
ejpam-3716	5	19	nonplanar	nonplanar	NOUN
ejpam-3716	5	20	,	,	PUNCT
ejpam-3716	5	21	coarseness	coarseness	NOUN
ejpam-3716	5	22	,	,	PUNCT
ejpam-3716	5	23	outercoarseness	outercoarseness	NOUN
ejpam-3716	5	24	1	1	NUM
ejpam-3716	5	25	.	.	PUNCT
ejpam-3716	6	1	introduction	introduction	NOUN
ejpam-3716	6	2	by	by	ADP
ejpam-3716	6	3	a	a	DET
ejpam-3716	6	4	graph	graph	NOUN
ejpam-3716	6	5	we	we	PRON
ejpam-3716	6	6	mean	mean	VERB
ejpam-3716	6	7	a	a	DET
ejpam-3716	6	8	finite	finite	ADJ
ejpam-3716	6	9	,	,	PUNCT
ejpam-3716	6	10	undirected	undirected	ADJ
ejpam-3716	6	11	graph	graph	NOUN
ejpam-3716	6	12	without	without	ADP
ejpam-3716	6	13	loops	loop	NOUN
ejpam-3716	6	14	or	or	CCONJ
ejpam-3716	6	15	multiple	multiple	ADJ
ejpam-3716	6	16	edges	edge	NOUN
ejpam-3716	6	17	.	.	PUNCT
ejpam-3716	7	1	let	let	VERB
ejpam-3716	7	2	v	v	X
ejpam-3716	7	3	(	(	PUNCT
ejpam-3716	7	4	g	g	NOUN
ejpam-3716	7	5	)	)	PUNCT
ejpam-3716	7	6	,	,	PUNCT
ejpam-3716	7	7	e(g	e(g	PROPN
ejpam-3716	7	8	)	)	PUNCT
ejpam-3716	7	9	and	and	CCONJ
ejpam-3716	7	10	l(g	l(g	PROPN
ejpam-3716	7	11	)	)	PUNCT
ejpam-3716	7	12	denote	denote	VERB
ejpam-3716	7	13	the	the	DET
ejpam-3716	7	14	vertex	vertex	NOUN
ejpam-3716	7	15	set	set	NOUN
ejpam-3716	7	16	,	,	PUNCT
ejpam-3716	7	17	edge	edge	NOUN
ejpam-3716	7	18	set	set	NOUN
ejpam-3716	7	19	and	and	CCONJ
ejpam-3716	7	20	line	line	NOUN
ejpam-3716	7	21	graph	graph	NOUN
ejpam-3716	7	22	of	of	ADP
ejpam-3716	7	23	a	a	DET
ejpam-3716	7	24	graph	graph	NOUN
ejpam-3716	7	25	respectively	respectively	ADV
ejpam-3716	7	26	.	.	PUNCT
ejpam-3716	8	1	the	the	DET
ejpam-3716	8	2	all	all	DET
ejpam-3716	8	3	undefined	undefined	ADJ
ejpam-3716	8	4	terminology	terminology	NOUN
ejpam-3716	8	5	will	will	AUX
ejpam-3716	8	6	conform	conform	VERB
ejpam-3716	8	7	with	with	ADP
ejpam-3716	8	8	that	that	PRON
ejpam-3716	8	9	in	in	ADP
ejpam-3716	8	10	harary	harary	NOUN
ejpam-3716	8	11	[	[	X
ejpam-3716	8	12	4	4	NUM
ejpam-3716	8	13	]	]	PUNCT
ejpam-3716	8	14	.	.	PUNCT
ejpam-3716	9	1	for	for	ADP
ejpam-3716	9	2	a	a	DET
ejpam-3716	9	3	real	real	ADJ
ejpam-3716	9	4	number	number	NOUN
ejpam-3716	9	5	x	x	NOUN
ejpam-3716	9	6	,	,	PUNCT
ejpam-3716	9	7	⌊x⌋	⌊x⌋	PUNCT
ejpam-3716	9	8	denotes	denote	VERB
ejpam-3716	9	9	the	the	DET
ejpam-3716	9	10	greatest	great	ADJ
ejpam-3716	9	11	integer	integer	NOUN
ejpam-3716	9	12	not	not	PART
ejpam-3716	9	13	exceeding	exceed	VERB
ejpam-3716	9	14	x	x	PUNCT
ejpam-3716	9	15	and	and	CCONJ
ejpam-3716	9	16	⌈x⌉	⌈x⌉	NOUN
ejpam-3716	9	17	is	be	AUX
ejpam-3716	9	18	the	the	DET
ejpam-3716	9	19	least	least	ADJ
ejpam-3716	9	20	integer	integer	NOUN
ejpam-3716	9	21	not	not	PART
ejpam-3716	9	22	less	less	ADJ
ejpam-3716	9	23	than	than	SCONJ
ejpam-3716	9	24	x.	x.	NOUN
ejpam-3716	9	25	two	two	NUM
ejpam-3716	9	26	graphs	graph	NOUN
ejpam-3716	9	27	are	be	AUX
ejpam-3716	9	28	said	say	VERB
ejpam-3716	9	29	to	to	PART
ejpam-3716	9	30	be	be	AUX
ejpam-3716	9	31	homeomorphic	homeomorphic	ADJ
ejpam-3716	9	32	if	if	SCONJ
ejpam-3716	9	33	both	both	PRON
ejpam-3716	9	34	can	can	AUX
ejpam-3716	9	35	be	be	AUX
ejpam-3716	9	36	obtained	obtain	VERB
ejpam-3716	9	37	from	from	ADP
ejpam-3716	9	38	the	the	DET
ejpam-3716	9	39	same	same	ADJ
ejpam-3716	9	40	graph	graph	NOUN
ejpam-3716	9	41	by	by	ADP
ejpam-3716	9	42	inserting	insert	VERB
ejpam-3716	9	43	new	new	ADJ
ejpam-3716	9	44	points	point	NOUN
ejpam-3716	9	45	of	of	ADP
ejpam-3716	9	46	degree	degree	NOUN
ejpam-3716	9	47	two	two	NUM
ejpam-3716	9	48	into	into	ADP
ejpam-3716	9	49	its	its	PRON
ejpam-3716	9	50	lines	line	NOUN
ejpam-3716	9	51	.	.	PUNCT
ejpam-3716	10	1	kuratowski	kuratowski	PROPN
ejpam-3716	11	1	[	[	X
ejpam-3716	11	2	8	8	NUM
ejpam-3716	11	3	]	]	PUNCT
ejpam-3716	11	4	has	have	AUX
ejpam-3716	11	5	characterized	characterize	VERB
ejpam-3716	11	6	planar	planar	ADJ
ejpam-3716	11	7	graphs	graph	NOUN
ejpam-3716	11	8	as	as	ADP
ejpam-3716	11	9	those	those	DET
ejpam-3716	11	10	graphs	graph	NOUN
ejpam-3716	11	11	which	which	PRON
ejpam-3716	11	12	contain	contain	VERB
ejpam-3716	11	13	no	no	DET
ejpam-3716	11	14	subgraphs	subgraphs	NOUN
ejpam-3716	11	15	homeomorphic	homeomorphic	ADJ
ejpam-3716	11	16	to	to	ADP
ejpam-3716	11	17	k5	k5	PROPN
ejpam-3716	11	18	or	or	CCONJ
ejpam-3716	11	19	k3,3	k3,3	PROPN
ejpam-3716	11	20	.	.	PUNCT
ejpam-3716	12	1	∗corresponding	∗corresponde	VERB
ejpam-3716	12	2	author	author	NOUN
ejpam-3716	12	3	.	.	PUNCT
ejpam-3716	13	1	doi	doi	NOUN
ejpam-3716	13	2	:	:	PUNCT
ejpam-3716	13	3	https://doi.org/10.29020/nybg.ejpam.v13i5.3716	https://doi.org/10.29020/nybg.ejpam.v13i5.3716	VERB
ejpam-3716	13	4	email	email	NOUN
ejpam-3716	13	5	addresses	address	NOUN
ejpam-3716	13	6	:	:	PUNCT
ejpam-3716	13	7	v.lokesha@gmail.com	v.lokesha@gmail.com	X
ejpam-3716	13	8	(	(	PUNCT
ejpam-3716	13	9	v.	v.	ADP
ejpam-3716	13	10	lokesha	lokesha	PROPN
ejpam-3716	13	11	)	)	PUNCT
ejpam-3716	13	12	,	,	PUNCT
ejpam-3716	13	13	sunilkumar.rcu@gmail.com	sunilkumar.rcu@gmail.com	PROPN
ejpam-3716	13	14	(	(	PUNCT
ejpam-3716	13	15	s.	s.	PROPN
ejpam-3716	13	16	m.	m.	PROPN
ejpam-3716	13	17	hosamani	hosamani	PROPN
ejpam-3716	13	18	)	)	PUNCT
ejpam-3716	13	19	,	,	PUNCT
ejpam-3716	13	20	shobhap49@gmail.com	shobhap49@gmail.com	PROPN
ejpam-3716	13	21	(	(	PUNCT
ejpam-3716	13	22	s.	s.	PROPN
ejpam-3716	13	23	v.	v.	PROPN
ejpam-3716	13	24	patil	patil	PROPN
ejpam-3716	13	25	)	)	PUNCT
ejpam-3716	13	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3716	13	27	1300	1300	NUM
ejpam-3716	14	1	c	c	NOUN
ejpam-3716	14	2	©	©	NOUN
ejpam-3716	14	3	2020	2020	NUM
ejpam-3716	14	4	ejpam	ejpam	VERB
ejpam-3716	14	5	all	all	DET
ejpam-3716	14	6	rights	right	NOUN
ejpam-3716	14	7	reserved	reserve	VERB
ejpam-3716	14	8	.	.	PUNCT
ejpam-3716	15	1	v.	v.	ADP
ejpam-3716	15	2	lokesha	lokesha	PROPN
ejpam-3716	15	3	,	,	PUNCT
ejpam-3716	15	4	s.	s.	PROPN
ejpam-3716	15	5	m.	m.	PROPN
ejpam-3716	15	6	hosamani	hosamani	PROPN
ejpam-3716	15	7	,	,	PUNCT
ejpam-3716	15	8	s.	s.	PROPN
ejpam-3716	15	9	v.	v.	PROPN
ejpam-3716	15	10	patil	patil	PROPN
ejpam-3716	15	11	/	/	SYM
ejpam-3716	15	12	eur	eur	PROPN
ejpam-3716	15	13	.	.	PUNCT
ejpam-3716	16	1	j.	j.	PROPN
ejpam-3716	16	2	pure	pure	PROPN
ejpam-3716	16	3	appl	appl	PROPN
ejpam-3716	16	4	.	.	PROPN
ejpam-3716	16	5	math	math	PROPN
ejpam-3716	16	6	,	,	PUNCT
ejpam-3716	16	7	13	13	NUM
ejpam-3716	16	8	(	(	PUNCT
ejpam-3716	16	9	5	5	NUM
ejpam-3716	16	10	)	)	PUNCT
ejpam-3716	16	11	(	(	PUNCT
ejpam-3716	16	12	2020	2020	NUM
ejpam-3716	16	13	)	)	PUNCT
ejpam-3716	16	14	,	,	PUNCT
ejpam-3716	16	15	1300	1300	NUM
ejpam-3716	16	16	-	-	SYM
ejpam-3716	16	17	1305	1305	NUM
ejpam-3716	16	18	1301	1301	NUM
ejpam-3716	16	19	chartrand	chartrand	NOUN
ejpam-3716	16	20	,	,	PUNCT
ejpam-3716	16	21	gellar	gellar	NOUN
ejpam-3716	16	22	and	and	CCONJ
ejpam-3716	16	23	hedetniemi	hedetniemi	ADV
ejpam-3716	17	1	[	[	X
ejpam-3716	17	2	2	2	X
ejpam-3716	17	3	]	]	PUNCT
ejpam-3716	17	4	introduced	introduce	VERB
ejpam-3716	17	5	the	the	DET
ejpam-3716	17	6	point	point	NOUN
ejpam-3716	17	7	-	-	PUNCT
ejpam-3716	17	8	partition	partition	NOUN
ejpam-3716	17	9	number	number	NOUN
ejpam-3716	17	10	denoted	denote	VERB
ejpam-3716	17	11	by	by	ADP
ejpam-3716	17	12	πn(g	πn(g	NOUN
ejpam-3716	17	13	)	)	PUNCT
ejpam-3716	17	14	for	for	ADP
ejpam-3716	17	15	each	each	DET
ejpam-3716	17	16	positive	positive	ADJ
ejpam-3716	17	17	integer	integer	NOUN
ejpam-3716	17	18	n.	n.	NOUN
ejpam-3716	17	19	the	the	DET
ejpam-3716	17	20	point	point	NOUN
ejpam-3716	17	21	-	-	PUNCT
ejpam-3716	17	22	partition	partition	NOUN
ejpam-3716	17	23	number	number	NOUN
ejpam-3716	17	24	πn(g	πn(g	PUNCT
ejpam-3716	17	25	)	)	PUNCT
ejpam-3716	17	26	is	be	AUX
ejpam-3716	17	27	defined	define	VERB
ejpam-3716	17	28	as	as	ADP
ejpam-3716	17	29	the	the	DET
ejpam-3716	17	30	maximum	maximum	ADJ
ejpam-3716	17	31	number	number	NOUN
ejpam-3716	17	32	of	of	ADP
ejpam-3716	17	33	subsets	subset	NOUN
ejpam-3716	17	34	into	into	ADP
ejpam-3716	17	35	which	which	PRON
ejpam-3716	17	36	the	the	DET
ejpam-3716	17	37	point	point	NOUN
ejpam-3716	17	38	set	set	NOUN
ejpam-3716	17	39	of	of	ADP
ejpam-3716	17	40	g	g	NOUN
ejpam-3716	17	41	can	can	AUX
ejpam-3716	17	42	be	be	AUX
ejpam-3716	17	43	partitioned	partition	VERB
ejpam-3716	17	44	so	so	SCONJ
ejpam-3716	17	45	that	that	SCONJ
ejpam-3716	17	46	each	each	DET
ejpam-3716	17	47	set	set	NOUN
ejpam-3716	17	48	induces	induce	VERB
ejpam-3716	17	49	a	a	DET
ejpam-3716	17	50	graph	graph	NOUN
ejpam-3716	17	51	which	which	PRON
ejpam-3716	17	52	contains	contain	VERB
ejpam-3716	17	53	a	a	DET
ejpam-3716	17	54	subgraph	subgraph	NOUN
ejpam-3716	17	55	homeomorphic	homeomorphic	NOUN
ejpam-3716	17	56	to	to	ADP
ejpam-3716	17	57	either	either	CCONJ
ejpam-3716	17	58	kn+1	kn+1	PROPN
ejpam-3716	17	59	or	or	CCONJ
ejpam-3716	17	60	k⌊n+2	k⌊n+2	PROPN
ejpam-3716	17	61	2	2	NUM
ejpam-3716	18	1	⌋,⌈n+2	⌋,⌈n+2	NOUN
ejpam-3716	18	2	2	2	NUM
ejpam-3716	18	3	⌉.	⌉.	ADV
ejpam-3716	18	4	this	this	DET
ejpam-3716	18	5	general	general	ADJ
ejpam-3716	18	6	parameter	parameter	NOUN
ejpam-3716	18	7	πn(g	πn(g	PUNCT
ejpam-3716	18	8	)	)	PUNCT
ejpam-3716	18	9	is	be	AUX
ejpam-3716	18	10	defined	define	VERB
ejpam-3716	18	11	for	for	ADP
ejpam-3716	18	12	n=1,2,3	n=1,2,3	NUM
ejpam-3716	18	13	and	and	CCONJ
ejpam-3716	18	14	4	4	NUM
ejpam-3716	18	15	.	.	X
ejpam-3716	19	1	π1(g	π1(g	NOUN
ejpam-3716	19	2	)	)	PUNCT
ejpam-3716	19	3	is	be	AUX
ejpam-3716	19	4	the	the	DET
ejpam-3716	19	5	line	line	NOUN
ejpam-3716	19	6	independence	independence	NOUN
ejpam-3716	19	7	number	number	NOUN
ejpam-3716	19	8	.	.	PUNCT
ejpam-3716	20	1	π2(g	π2(g	VERB
ejpam-3716	20	2	)	)	PUNCT
ejpam-3716	20	3	is	be	AUX
ejpam-3716	20	4	the	the	DET
ejpam-3716	20	5	maximum	maximum	ADJ
ejpam-3716	20	6	number	number	NOUN
ejpam-3716	20	7	of	of	ADP
ejpam-3716	20	8	point	point	NOUN
ejpam-3716	20	9	-	-	PUNCT
ejpam-3716	20	10	disjoint	disjoint	NOUN
ejpam-3716	20	11	subgraphs	subgraphs	NOUN
ejpam-3716	20	12	of	of	ADP
ejpam-3716	20	13	g	g	NOUN
ejpam-3716	20	14	,	,	PUNCT
ejpam-3716	20	15	such	such	ADJ
ejpam-3716	20	16	that	that	SCONJ
ejpam-3716	20	17	each	each	DET
ejpam-3716	20	18	subgraph	subgraph	NOUN
ejpam-3716	20	19	is	be	AUX
ejpam-3716	20	20	not	not	PART
ejpam-3716	20	21	a	a	DET
ejpam-3716	20	22	forest	forest	NOUN
ejpam-3716	20	23	.	.	PUNCT
ejpam-3716	21	1	this	this	PRON
ejpam-3716	21	2	is	be	AUX
ejpam-3716	21	3	also	also	ADV
ejpam-3716	21	4	the	the	DET
ejpam-3716	21	5	maximum	maximum	ADJ
ejpam-3716	21	6	number	number	NOUN
ejpam-3716	21	7	of	of	ADP
ejpam-3716	21	8	point	point	NOUN
ejpam-3716	21	9	-	-	PUNCT
ejpam-3716	21	10	disjoint	disjoint	NOUN
ejpam-3716	21	11	cycles	cycle	NOUN
ejpam-3716	21	12	contained	contain	VERB
ejpam-3716	21	13	in	in	ADP
ejpam-3716	21	14	g	g	PROPN
ejpam-3716	21	15	and	and	CCONJ
ejpam-3716	21	16	for	for	ADP
ejpam-3716	21	17	this	this	DET
ejpam-3716	21	18	reason	reason	NOUN
ejpam-3716	21	19	we	we	PRON
ejpam-3716	21	20	refer	refer	VERB
ejpam-3716	21	21	π2(g	π2(g	VERB
ejpam-3716	21	22	)	)	PUNCT
ejpam-3716	21	23	as	as	ADP
ejpam-3716	21	24	the	the	DET
ejpam-3716	21	25	point	point	NOUN
ejpam-3716	21	26	-	-	PUNCT
ejpam-3716	21	27	cycle	cycle	NOUN
ejpam-3716	21	28	multiplicity	multiplicity	NOUN
ejpam-3716	21	29	.	.	PUNCT
ejpam-3716	22	1	π3(g	π3(g	PUNCT
ejpam-3716	22	2	)	)	PUNCT
ejpam-3716	22	3	is	be	AUX
ejpam-3716	22	4	the	the	DET
ejpam-3716	22	5	maximum	maximum	ADJ
ejpam-3716	22	6	number	number	NOUN
ejpam-3716	22	7	of	of	ADP
ejpam-3716	22	8	point	point	NOUN
ejpam-3716	22	9	-	-	PUNCT
ejpam-3716	22	10	disjoint	disjoint	NOUN
ejpam-3716	22	11	nonouterplanar	nonouterplanar	NOUN
ejpam-3716	22	12	subgraphs	subgraph	NOUN
ejpam-3716	22	13	of	of	ADP
ejpam-3716	22	14	g	g	NOUN
ejpam-3716	22	15	and	and	CCONJ
ejpam-3716	22	16	is	be	AUX
ejpam-3716	22	17	called	call	VERB
ejpam-3716	22	18	point	point	NOUN
ejpam-3716	22	19	-	-	PUNCT
ejpam-3716	22	20	outercoarseness	outercoarseness	NOUN
ejpam-3716	22	21	number	number	NOUN
ejpam-3716	22	22	of	of	ADP
ejpam-3716	22	23	g.	g.	PROPN
ejpam-3716	22	24	π4(g	π4(g	PROPN
ejpam-3716	22	25	)	)	PUNCT
ejpam-3716	22	26	is	be	AUX
ejpam-3716	22	27	the	the	DET
ejpam-3716	22	28	maximum	maximum	ADJ
ejpam-3716	22	29	number	number	NOUN
ejpam-3716	22	30	of	of	ADP
ejpam-3716	22	31	point	point	NOUN
ejpam-3716	22	32	-	-	PUNCT
ejpam-3716	22	33	disjoint	disjoint	NOUN
ejpam-3716	22	34	nonplanar	nonplanar	NOUN
ejpam-3716	22	35	subgraphs	subgraph	NOUN
ejpam-3716	22	36	of	of	ADP
ejpam-3716	22	37	g	g	NOUN
ejpam-3716	22	38	and	and	CCONJ
ejpam-3716	22	39	is	be	AUX
ejpam-3716	22	40	called	call	VERB
ejpam-3716	22	41	the	the	DET
ejpam-3716	22	42	point	point	NOUN
ejpam-3716	22	43	coarseness	coarseness	NOUN
ejpam-3716	22	44	of	of	ADP
ejpam-3716	22	45	g	g	NOUN
ejpam-3716	22	46	and	and	CCONJ
ejpam-3716	22	47	denoted	denote	VERB
ejpam-3716	22	48	by	by	ADP
ejpam-3716	22	49	ξ	ξ	PROPN
ejpam-3716	22	50	′	′	NUM
ejpam-3716	22	51	(	(	PUNCT
ejpam-3716	22	52	g	g	NOUN
ejpam-3716	22	53	)	)	PUNCT
ejpam-3716	22	54	.	.	PUNCT
ejpam-3716	23	1	a	a	DET
ejpam-3716	23	2	point	point	NOUN
ejpam-3716	23	3	and	and	CCONJ
ejpam-3716	23	4	a	a	DET
ejpam-3716	23	5	line	line	NOUN
ejpam-3716	23	6	are	be	AUX
ejpam-3716	23	7	said	say	VERB
ejpam-3716	23	8	to	to	PART
ejpam-3716	23	9	cover	cover	VERB
ejpam-3716	23	10	each	each	DET
ejpam-3716	23	11	other	other	ADJ
ejpam-3716	23	12	if	if	SCONJ
ejpam-3716	23	13	they	they	PRON
ejpam-3716	23	14	are	be	AUX
ejpam-3716	23	15	incident	incident	NOUN
ejpam-3716	23	16	.	.	PUNCT
ejpam-3716	24	1	a	a	DET
ejpam-3716	24	2	set	set	NOUN
ejpam-3716	24	3	of	of	ADP
ejpam-3716	24	4	points	point	NOUN
ejpam-3716	24	5	which	which	PRON
ejpam-3716	24	6	cover	cover	VERB
ejpam-3716	24	7	all	all	DET
ejpam-3716	24	8	the	the	DET
ejpam-3716	24	9	lines	line	NOUN
ejpam-3716	24	10	is	be	AUX
ejpam-3716	24	11	a	a	DET
ejpam-3716	24	12	point	point	NOUN
ejpam-3716	24	13	cover	cover	NOUN
ejpam-3716	24	14	of	of	ADP
ejpam-3716	24	15	g	g	NOUN
ejpam-3716	24	16	while	while	SCONJ
ejpam-3716	24	17	a	a	DET
ejpam-3716	24	18	set	set	NOUN
ejpam-3716	24	19	of	of	ADP
ejpam-3716	24	20	lines	line	NOUN
ejpam-3716	24	21	which	which	PRON
ejpam-3716	24	22	cover	cover	VERB
ejpam-3716	24	23	all	all	DET
ejpam-3716	24	24	the	the	DET
ejpam-3716	24	25	points	point	NOUN
ejpam-3716	24	26	is	be	AUX
ejpam-3716	24	27	a	a	DET
ejpam-3716	24	28	line	line	NOUN
ejpam-3716	24	29	cover	cover	NOUN
ejpam-3716	24	30	.	.	PUNCT
ejpam-3716	25	1	the	the	DET
ejpam-3716	25	2	smallest	small	ADJ
ejpam-3716	25	3	number	number	NOUN
ejpam-3716	25	4	of	of	ADP
ejpam-3716	25	5	points	point	NOUN
ejpam-3716	25	6	in	in	ADP
ejpam-3716	25	7	any	any	DET
ejpam-3716	25	8	point	point	NOUN
ejpam-3716	25	9	cover	cover	NOUN
ejpam-3716	25	10	of	of	ADP
ejpam-3716	25	11	g	g	PROPN
ejpam-3716	25	12	is	be	AUX
ejpam-3716	25	13	called	call	VERB
ejpam-3716	25	14	its	its	PRON
ejpam-3716	25	15	point	point	NOUN
ejpam-3716	25	16	covering	cover	VERB
ejpam-3716	25	17	number	number	NOUN
ejpam-3716	25	18	and	and	CCONJ
ejpam-3716	25	19	is	be	AUX
ejpam-3716	25	20	denoted	denote	VERB
ejpam-3716	25	21	by	by	ADP
ejpam-3716	25	22	α0(g	α0(g	NOUN
ejpam-3716	25	23	)	)	PUNCT
ejpam-3716	25	24	or	or	CCONJ
ejpam-3716	25	25	α0	α0	ADJ
ejpam-3716	25	26	.	.	PUNCT
ejpam-3716	26	1	similarly	similarly	ADV
ejpam-3716	26	2	α1(g	α1(g	NUM
ejpam-3716	26	3	)	)	PUNCT
ejpam-3716	26	4	or	or	CCONJ
ejpam-3716	26	5	α1	α1	PROPN
ejpam-3716	26	6	is	be	AUX
ejpam-3716	26	7	the	the	DET
ejpam-3716	26	8	minimum	minimum	ADJ
ejpam-3716	26	9	number	number	NOUN
ejpam-3716	26	10	of	of	ADP
ejpam-3716	26	11	lines	line	NOUN
ejpam-3716	26	12	in	in	ADP
ejpam-3716	26	13	any	any	DET
ejpam-3716	26	14	line	line	NOUN
ejpam-3716	26	15	cover	cover	NOUN
ejpam-3716	26	16	of	of	ADP
ejpam-3716	26	17	g	g	NOUN
ejpam-3716	26	18	and	and	CCONJ
ejpam-3716	26	19	is	be	AUX
ejpam-3716	26	20	called	call	VERB
ejpam-3716	26	21	its	its	PRON
ejpam-3716	26	22	line	line	NOUN
ejpam-3716	26	23	covering	cover	VERB
ejpam-3716	26	24	number	number	NOUN
ejpam-3716	26	25	.	.	PUNCT
ejpam-3716	27	1	a	a	DET
ejpam-3716	27	2	point	point	NOUN
ejpam-3716	27	3	cover	cover	NOUN
ejpam-3716	27	4	(	(	PUNCT
ejpam-3716	27	5	line	line	NOUN
ejpam-3716	27	6	cover	cover	NOUN
ejpam-3716	27	7	)	)	PUNCT
ejpam-3716	27	8	is	be	AUX
ejpam-3716	27	9	called	call	VERB
ejpam-3716	27	10	minimum	minimum	NOUN
ejpam-3716	27	11	if	if	SCONJ
ejpam-3716	27	12	it	it	PRON
ejpam-3716	27	13	contains	contain	VERB
ejpam-3716	27	14	α0(α1	α0(α1	NUM
ejpam-3716	27	15	)	)	PUNCT
ejpam-3716	27	16	elements	element	NOUN
ejpam-3716	27	17	.	.	PUNCT
ejpam-3716	28	1	a	a	DET
ejpam-3716	28	2	graph	graph	NOUN
ejpam-3716	28	3	g+	g+	NOUN
ejpam-3716	28	4	is	be	AUX
ejpam-3716	28	5	the	the	DET
ejpam-3716	28	6	endedge	endedge	NOUN
ejpam-3716	28	7	graph	graph	NOUN
ejpam-3716	28	8	of	of	ADP
ejpam-3716	28	9	a	a	DET
ejpam-3716	28	10	graph	graph	NOUN
ejpam-3716	28	11	g	g	NOUN
ejpam-3716	28	12	if	if	SCONJ
ejpam-3716	28	13	g+	g+	NOUN
ejpam-3716	28	14	is	be	AUX
ejpam-3716	28	15	obtained	obtain	VERB
ejpam-3716	28	16	from	from	ADP
ejpam-3716	28	17	g	g	NOUN
ejpam-3716	28	18	by	by	ADP
ejpam-3716	28	19	adjoining	adjoin	VERB
ejpam-3716	28	20	an	an	DET
ejpam-3716	28	21	endedge	endedge	NOUN
ejpam-3716	28	22	uiu	uiu	NOUN
ejpam-3716	29	1	′	′	NUM
ejpam-3716	29	2	i	i	PRON
ejpam-3716	29	3	at	at	ADP
ejpam-3716	29	4	each	each	DET
ejpam-3716	29	5	point	point	NOUN
ejpam-3716	29	6	ui	ui	PROPN
ejpam-3716	29	7	of	of	ADP
ejpam-3716	29	8	g.	g.	PROPN
ejpam-3716	29	9	the	the	DET
ejpam-3716	29	10	plick	plick	NOUN
ejpam-3716	29	11	graph	graph	NOUN
ejpam-3716	29	12	p	p	X
ejpam-3716	29	13	(	(	PUNCT
ejpam-3716	29	14	g	g	NOUN
ejpam-3716	29	15	)	)	PUNCT
ejpam-3716	29	16	of	of	ADP
ejpam-3716	29	17	a	a	DET
ejpam-3716	29	18	graph	graph	NOUN
ejpam-3716	29	19	g	g	NOUN
ejpam-3716	29	20	is	be	AUX
ejpam-3716	29	21	obtained	obtain	VERB
ejpam-3716	29	22	from	from	ADP
ejpam-3716	29	23	the	the	DET
ejpam-3716	29	24	graph	graph	NOUN
ejpam-3716	29	25	by	by	ADP
ejpam-3716	29	26	adding	add	VERB
ejpam-3716	29	27	a	a	DET
ejpam-3716	29	28	new	new	ADJ
ejpam-3716	29	29	point	point	NOUN
ejpam-3716	29	30	corresponding	correspond	VERB
ejpam-3716	29	31	to	to	ADP
ejpam-3716	29	32	each	each	DET
ejpam-3716	29	33	block	block	NOUN
ejpam-3716	29	34	of	of	ADP
ejpam-3716	29	35	the	the	DET
ejpam-3716	29	36	original	original	ADJ
ejpam-3716	29	37	graph	graph	NOUN
ejpam-3716	29	38	and	and	CCONJ
ejpam-3716	29	39	joining	join	VERB
ejpam-3716	29	40	this	this	DET
ejpam-3716	29	41	point	point	NOUN
ejpam-3716	29	42	to	to	ADP
ejpam-3716	29	43	the	the	DET
ejpam-3716	29	44	points	point	NOUN
ejpam-3716	29	45	of	of	ADP
ejpam-3716	29	46	the	the	DET
ejpam-3716	29	47	line	line	NOUN
ejpam-3716	29	48	graph	graph	NOUN
ejpam-3716	29	49	which	which	PRON
ejpam-3716	29	50	correspond	correspond	VERB
ejpam-3716	29	51	to	to	ADP
ejpam-3716	29	52	the	the	DET
ejpam-3716	29	53	lines	line	NOUN
ejpam-3716	29	54	of	of	ADP
ejpam-3716	29	55	the	the	DET
ejpam-3716	29	56	block	block	NOUN
ejpam-3716	29	57	of	of	ADP
ejpam-3716	29	58	the	the	DET
ejpam-3716	29	59	original	original	ADJ
ejpam-3716	29	60	graph	graph	NOUN
ejpam-3716	29	61	.	.	PUNCT
ejpam-3716	30	1	for	for	ADP
ejpam-3716	30	2	n	n	X
ejpam-3716	30	3	≥	≥	NUM
ejpam-3716	30	4	2	2	NUM
ejpam-3716	30	5	,	,	PUNCT
ejpam-3716	30	6	pn(g)=p	pn(g)=p	VERB
ejpam-3716	30	7	(	(	PUNCT
ejpam-3716	30	8	pn−1(g	pn−1(g	NOUN
ejpam-3716	30	9	)	)	PUNCT
ejpam-3716	30	10	)	)	PUNCT
ejpam-3716	30	11	where	where	SCONJ
ejpam-3716	30	12	p	p	PRON
ejpam-3716	30	13	1(g)=p	1(g)=p	NUM
ejpam-3716	30	14	(	(	PUNCT
ejpam-3716	30	15	g	g	NOUN
ejpam-3716	30	16	)	)	PUNCT
ejpam-3716	30	17	is	be	AUX
ejpam-3716	30	18	the	the	DET
ejpam-3716	30	19	nth	nth	NOUN
ejpam-3716	30	20	iterated	iterated	ADJ
ejpam-3716	30	21	plick	plick	NOUN
ejpam-3716	30	22	graph	graph	NOUN
ejpam-3716	30	23	.	.	PUNCT
ejpam-3716	31	1	in	in	ADP
ejpam-3716	31	2	figure1	figure1	PROPN
ejpam-3716	31	3	,	,	PUNCT
ejpam-3716	31	4	a	a	DET
ejpam-3716	31	5	graph	graph	NOUN
ejpam-3716	31	6	and	and	CCONJ
ejpam-3716	31	7	its	its	PRON
ejpam-3716	31	8	plick	plick	NOUN
ejpam-3716	31	9	graph	graph	NOUN
ejpam-3716	31	10	p	p	X
ejpam-3716	31	11	(	(	PUNCT
ejpam-3716	31	12	g	g	NOUN
ejpam-3716	31	13	)	)	PUNCT
ejpam-3716	31	14	are	be	AUX
ejpam-3716	31	15	shown	show	VERB
ejpam-3716	31	16	.	.	PUNCT
ejpam-3716	32	1	b	b	X
ejpam-3716	32	2	b	b	X
ejpam-3716	32	3	b	b	PROPN
ejpam-3716	32	4	b	b	PROPN
ejpam-3716	32	5	b	b	PROPN
ejpam-3716	32	6	b	b	PROPN
ejpam-3716	32	7	bb	bb	INTJ
ejpam-3716	32	8	b	b	PROPN
ejpam-3716	32	9	b	b	PROPN
ejpam-3716	32	10	g	g	NOUN
ejpam-3716	32	11	:	:	PUNCT
ejpam-3716	32	12	p(g	p(g	NOUN
ejpam-3716	32	13	):	):	PUNCT
ejpam-3716	32	14	figure	figure	NOUN
ejpam-3716	32	15	1	1	NUM
ejpam-3716	32	16	.	.	PUNCT
ejpam-3716	33	1	if	if	SCONJ
ejpam-3716	33	2	g	g	PROPN
ejpam-3716	33	3	is	be	AUX
ejpam-3716	33	4	a	a	DET
ejpam-3716	33	5	planar	planar	ADJ
ejpam-3716	33	6	graph	graph	NOUN
ejpam-3716	33	7	,	,	PUNCT
ejpam-3716	33	8	then	then	ADV
ejpam-3716	33	9	the	the	DET
ejpam-3716	33	10	inner	inner	ADJ
ejpam-3716	33	11	vertex	vertex	NOUN
ejpam-3716	33	12	number	number	NOUN
ejpam-3716	33	13	i(g	i(g	PROPN
ejpam-3716	33	14	)	)	PUNCT
ejpam-3716	33	15	of	of	ADP
ejpam-3716	33	16	g	g	PROPN
ejpam-3716	33	17	is	be	AUX
ejpam-3716	33	18	the	the	DET
ejpam-3716	33	19	minimum	minimum	ADJ
ejpam-3716	33	20	number	number	NOUN
ejpam-3716	33	21	of	of	ADP
ejpam-3716	33	22	vertices	vertex	NOUN
ejpam-3716	33	23	not	not	PART
ejpam-3716	33	24	belonging	belong	VERB
ejpam-3716	33	25	to	to	ADP
ejpam-3716	33	26	the	the	DET
ejpam-3716	33	27	boundary	boundary	NOUN
ejpam-3716	33	28	of	of	ADP
ejpam-3716	33	29	the	the	DET
ejpam-3716	33	30	exterior	exterior	ADJ
ejpam-3716	33	31	region	region	NOUN
ejpam-3716	33	32	in	in	ADP
ejpam-3716	33	33	any	any	DET
ejpam-3716	33	34	embedding	embedding	NOUN
ejpam-3716	33	35	of	of	ADP
ejpam-3716	33	36	g	g	NOUN
ejpam-3716	33	37	in	in	ADP
ejpam-3716	33	38	v.	v.	ADP
ejpam-3716	33	39	lokesha	lokesha	PROPN
ejpam-3716	33	40	,	,	PUNCT
ejpam-3716	33	41	s.	s.	PROPN
ejpam-3716	33	42	m.	m.	PROPN
ejpam-3716	33	43	hosamani	hosamani	PROPN
ejpam-3716	33	44	,	,	PUNCT
ejpam-3716	33	45	s.	s.	PROPN
ejpam-3716	33	46	v.	v.	PROPN
ejpam-3716	33	47	patil	patil	PROPN
ejpam-3716	33	48	/	/	SYM
ejpam-3716	33	49	eur	eur	PROPN
ejpam-3716	33	50	.	.	PUNCT
ejpam-3716	34	1	j.	j.	PROPN
ejpam-3716	34	2	pure	pure	PROPN
ejpam-3716	34	3	appl	appl	PROPN
ejpam-3716	34	4	.	.	PROPN
ejpam-3716	34	5	math	math	PROPN
ejpam-3716	34	6	,	,	PUNCT
ejpam-3716	34	7	13	13	NUM
ejpam-3716	34	8	(	(	PUNCT
ejpam-3716	34	9	5	5	NUM
ejpam-3716	34	10	)	)	PUNCT
ejpam-3716	34	11	(	(	PUNCT
ejpam-3716	34	12	2020	2020	NUM
ejpam-3716	34	13	)	)	PUNCT
ejpam-3716	34	14	,	,	PUNCT
ejpam-3716	34	15	1300	1300	NUM
ejpam-3716	34	16	-	-	SYM
ejpam-3716	34	17	1305	1305	NUM
ejpam-3716	34	18	1302	1302	NUM
ejpam-3716	34	19	the	the	DET
ejpam-3716	34	20	plane[6	plane[6	NOUN
ejpam-3716	34	21	]	]	PUNCT
ejpam-3716	34	22	.	.	PUNCT
ejpam-3716	35	1	note	note	NOUN
ejpam-3716	35	2	:	:	PUNCT
ejpam-3716	35	3	since	since	SCONJ
ejpam-3716	35	4	the	the	DET
ejpam-3716	35	5	definitions	definition	NOUN
ejpam-3716	35	6	of	of	ADP
ejpam-3716	35	7	point	point	NOUN
ejpam-3716	35	8	-	-	PUNCT
ejpam-3716	35	9	outercoarseness	outercoarseness	NOUN
ejpam-3716	35	10	number	number	NOUN
ejpam-3716	35	11	one	one	NUM
ejpam-3716	35	12	and	and	CCONJ
ejpam-3716	35	13	minimally	minimally	ADV
ejpam-3716	35	14	nonouterplanar	nonouterplanar	NOUN
ejpam-3716	35	15	are	be	AUX
ejpam-3716	35	16	isomorphic	isomorphic	ADJ
ejpam-3716	35	17	,	,	PUNCT
ejpam-3716	35	18	therefore	therefore	ADV
ejpam-3716	35	19	the	the	DET
ejpam-3716	35	20	aim	aim	NOUN
ejpam-3716	35	21	of	of	ADP
ejpam-3716	35	22	this	this	DET
ejpam-3716	35	23	paper	paper	NOUN
ejpam-3716	35	24	is	be	AUX
ejpam-3716	35	25	to	to	PART
ejpam-3716	35	26	characterize	characterize	VERB
ejpam-3716	35	27	all	all	DET
ejpam-3716	35	28	nth	nth	NOUN
ejpam-3716	35	29	plick	plick	NOUN
ejpam-3716	35	30	graphs	graph	NOUN
ejpam-3716	35	31	with	with	ADP
ejpam-3716	35	32	point	point	NOUN
ejpam-3716	35	33	-	-	PUNCT
ejpam-3716	35	34	outercoarseness	outercoarseness	NOUN
ejpam-3716	35	35	is	be	AUX
ejpam-3716	35	36	one	one	NUM
ejpam-3716	35	37	.	.	PUNCT
ejpam-3716	36	1	2	2	X
ejpam-3716	36	2	.	.	X
ejpam-3716	36	3	preliminary	preliminary	ADJ
ejpam-3716	36	4	results	result	NOUN
ejpam-3716	36	5	the	the	DET
ejpam-3716	36	6	following	following	NOUN
ejpam-3716	36	7	will	will	AUX
ejpam-3716	36	8	be	be	AUX
ejpam-3716	36	9	useful	useful	ADJ
ejpam-3716	36	10	in	in	ADP
ejpam-3716	36	11	the	the	DET
ejpam-3716	36	12	proof	proof	NOUN
ejpam-3716	36	13	of	of	ADP
ejpam-3716	36	14	our	our	PRON
ejpam-3716	36	15	results	result	NOUN
ejpam-3716	36	16	.	.	PUNCT
ejpam-3716	37	1	remark	remark	NOUN
ejpam-3716	37	2	1	1	NUM
ejpam-3716	37	3	.	.	PUNCT
ejpam-3716	38	1	for	for	ADP
ejpam-3716	38	2	any	any	DET
ejpam-3716	38	3	graph	graph	NOUN
ejpam-3716	38	4	g	g	NOUN
ejpam-3716	38	5	,	,	PUNCT
ejpam-3716	38	6	l(g	l(g	PROPN
ejpam-3716	38	7	)	)	PUNCT
ejpam-3716	38	8	is	be	AUX
ejpam-3716	38	9	a	a	DET
ejpam-3716	38	10	subgraph	subgraph	NOUN
ejpam-3716	38	11	of	of	ADP
ejpam-3716	38	12	p	p	NOUN
ejpam-3716	38	13	(	(	PUNCT
ejpam-3716	38	14	g	g	NOUN
ejpam-3716	38	15	)	)	PUNCT
ejpam-3716	38	16	.	.	PUNCT
ejpam-3716	39	1	theorem	theorem	NOUN
ejpam-3716	39	2	1	1	NUM
ejpam-3716	39	3	.	.	PUNCT
ejpam-3716	40	1	[	[	X
ejpam-3716	40	2	6	6	NUM
ejpam-3716	40	3	]	]	PUNCT
ejpam-3716	40	4	the	the	DET
ejpam-3716	40	5	plick	plick	NOUN
ejpam-3716	40	6	graph	graph	NOUN
ejpam-3716	40	7	p	p	X
ejpam-3716	40	8	(	(	PUNCT
ejpam-3716	40	9	g	g	NOUN
ejpam-3716	40	10	)	)	PUNCT
ejpam-3716	40	11	of	of	ADP
ejpam-3716	40	12	a	a	DET
ejpam-3716	40	13	graph	graph	NOUN
ejpam-3716	40	14	g	g	NOUN
ejpam-3716	40	15	is	be	AUX
ejpam-3716	40	16	planar	planar	ADJ
ejpam-3716	40	17	if	if	SCONJ
ejpam-3716	40	18	and	and	CCONJ
ejpam-3716	40	19	only	only	ADV
ejpam-3716	40	20	if	if	SCONJ
ejpam-3716	40	21	g	g	PROPN
ejpam-3716	40	22	satisfies	satisfy	VERB
ejpam-3716	40	23	the	the	DET
ejpam-3716	40	24	following	follow	VERB
ejpam-3716	40	25	conditions	condition	NOUN
ejpam-3716	40	26	:	:	PUNCT
ejpam-3716	40	27	(	(	PUNCT
ejpam-3716	40	28	i	i	NOUN
ejpam-3716	40	29	)	)	PUNCT
ejpam-3716	40	30	∆(g	∆(g	NOUN
ejpam-3716	40	31	)	)	PUNCT
ejpam-3716	40	32	≤	≤	NOUN
ejpam-3716	40	33	4	4	NUM
ejpam-3716	40	34	(	(	PUNCT
ejpam-3716	40	35	ii	ii	NOUN
ejpam-3716	40	36	)	)	PUNCT
ejpam-3716	40	37	every	every	DET
ejpam-3716	40	38	block	block	NOUN
ejpam-3716	40	39	of	of	ADP
ejpam-3716	40	40	g	g	PROPN
ejpam-3716	40	41	is	be	AUX
ejpam-3716	40	42	either	either	CCONJ
ejpam-3716	40	43	a	a	DET
ejpam-3716	40	44	cycle	cycle	NOUN
ejpam-3716	40	45	or	or	CCONJ
ejpam-3716	40	46	k2	k2	NOUN
ejpam-3716	40	47	.	.	PUNCT
ejpam-3716	41	1	theorem	theorem	NOUN
ejpam-3716	41	2	2	2	NUM
ejpam-3716	41	3	.	.	PUNCT
ejpam-3716	42	1	[	[	X
ejpam-3716	42	2	6	6	NUM
ejpam-3716	42	3	]	]	PUNCT
ejpam-3716	42	4	a	a	DET
ejpam-3716	42	5	graph	graph	NOUN
ejpam-3716	42	6	g	g	NOUN
ejpam-3716	42	7	has	have	VERB
ejpam-3716	42	8	a	a	DET
ejpam-3716	42	9	planar	planar	ADJ
ejpam-3716	42	10	plick	plick	NOUN
ejpam-3716	42	11	graph	graph	NOUN
ejpam-3716	42	12	if	if	SCONJ
ejpam-3716	42	13	and	and	CCONJ
ejpam-3716	42	14	only	only	ADV
ejpam-3716	42	15	if	if	SCONJ
ejpam-3716	42	16	it	it	PRON
ejpam-3716	42	17	has	have	VERB
ejpam-3716	42	18	no	no	DET
ejpam-3716	42	19	subgraph	subgraph	NOUN
ejpam-3716	42	20	homeomorphic	homeomorphic	NOUN
ejpam-3716	42	21	to	to	ADP
ejpam-3716	42	22	k1,5	k1,5	PROPN
ejpam-3716	42	23	or	or	CCONJ
ejpam-3716	42	24	k4	k4	VERB
ejpam-3716	42	25	−	−	PROPN
ejpam-3716	42	26	x	x	NOUN
ejpam-3716	42	27	,	,	PUNCT
ejpam-3716	42	28	where	where	SCONJ
ejpam-3716	42	29	x	x	PRON
ejpam-3716	42	30	is	be	AUX
ejpam-3716	42	31	any	any	DET
ejpam-3716	42	32	line	line	NOUN
ejpam-3716	42	33	of	of	ADP
ejpam-3716	42	34	k4	k4	PROPN
ejpam-3716	42	35	.	.	PUNCT
ejpam-3716	43	1	theorem	theorem	NOUN
ejpam-3716	43	2	3	3	NUM
ejpam-3716	43	3	.	.	PUNCT
ejpam-3716	44	1	[	[	X
ejpam-3716	44	2	6	6	NUM
ejpam-3716	44	3	]	]	PUNCT
ejpam-3716	44	4	a	a	DET
ejpam-3716	44	5	graph	graph	NOUN
ejpam-3716	44	6	g	g	NOUN
ejpam-3716	44	7	is	be	AUX
ejpam-3716	44	8	a	a	DET
ejpam-3716	44	9	cycle	cycle	NOUN
ejpam-3716	44	10	if	if	SCONJ
ejpam-3716	44	11	and	and	CCONJ
ejpam-3716	44	12	only	only	ADV
ejpam-3716	44	13	if	if	SCONJ
ejpam-3716	44	14	plick	plick	NOUN
ejpam-3716	44	15	graph	graph	NOUN
ejpam-3716	44	16	p	p	X
ejpam-3716	44	17	(	(	PUNCT
ejpam-3716	44	18	g	g	NOUN
ejpam-3716	44	19	)	)	PUNCT
ejpam-3716	44	20	is	be	AUX
ejpam-3716	44	21	a	a	DET
ejpam-3716	44	22	wheel	wheel	NOUN
ejpam-3716	44	23	.	.	PUNCT
ejpam-3716	45	1	theorem	theorem	ADJ
ejpam-3716	45	2	4	4	NUM
ejpam-3716	45	3	.	.	PUNCT
ejpam-3716	46	1	[	[	X
ejpam-3716	46	2	6	6	NUM
ejpam-3716	46	3	]	]	PUNCT
ejpam-3716	46	4	the	the	DET
ejpam-3716	46	5	plick	plick	NOUN
ejpam-3716	46	6	graph	graph	NOUN
ejpam-3716	46	7	p	p	X
ejpam-3716	46	8	(	(	PUNCT
ejpam-3716	46	9	g	g	NOUN
ejpam-3716	46	10	)	)	PUNCT
ejpam-3716	46	11	of	of	ADP
ejpam-3716	46	12	a	a	DET
ejpam-3716	46	13	graph	graph	NOUN
ejpam-3716	46	14	g	g	NOUN
ejpam-3716	46	15	is	be	AUX
ejpam-3716	46	16	minimally	minimally	ADV
ejpam-3716	46	17	nonouterplanar	nonouterplanar	ADJ
ejpam-3716	46	18	if	if	SCONJ
ejpam-3716	46	19	and	and	CCONJ
ejpam-3716	46	20	only	only	ADV
ejpam-3716	46	21	if	if	SCONJ
ejpam-3716	46	22	it	it	PRON
ejpam-3716	46	23	satisfies	satisfy	VERB
ejpam-3716	46	24	the	the	DET
ejpam-3716	46	25	following	follow	VERB
ejpam-3716	46	26	conditions	condition	NOUN
ejpam-3716	46	27	:	:	PUNCT
ejpam-3716	46	28	(	(	PUNCT
ejpam-3716	46	29	i	i	NOUN
ejpam-3716	46	30	)	)	PUNCT
ejpam-3716	46	31	∆(g	∆(g	NOUN
ejpam-3716	46	32	)	)	PUNCT
ejpam-3716	46	33	≤	≤	NOUN
ejpam-3716	46	34	3	3	NUM
ejpam-3716	46	35	and	and	CCONJ
ejpam-3716	46	36	(	(	PUNCT
ejpam-3716	46	37	ii	ii	NOUN
ejpam-3716	46	38	)	)	PUNCT
ejpam-3716	46	39	g	g	NOUN
ejpam-3716	46	40	is	be	AUX
ejpam-3716	46	41	unicyclic	unicyclic	ADJ
ejpam-3716	46	42	.	.	PUNCT
ejpam-3716	47	1	theorem	theorem	NOUN
ejpam-3716	47	2	5	5	NUM
ejpam-3716	47	3	.	.	PUNCT
ejpam-3716	48	1	let	let	VERB
ejpam-3716	48	2	g	g	NOUN
ejpam-3716	48	3	be	be	AUX
ejpam-3716	48	4	any	any	DET
ejpam-3716	48	5	connected	connected	ADJ
ejpam-3716	48	6	graph	graph	NOUN
ejpam-3716	48	7	.	.	PUNCT
ejpam-3716	49	1	π3(p	π3(p	PUNCT
ejpam-3716	49	2	(	(	PUNCT
ejpam-3716	49	3	g	g	NOUN
ejpam-3716	49	4	)	)	PUNCT
ejpam-3716	49	5	)	)	PUNCT
ejpam-3716	50	1	=	=	PUNCT
ejpam-3716	50	2	1	1	NUM
ejpam-3716	50	3	if	if	SCONJ
ejpam-3716	50	4	and	and	CCONJ
ejpam-3716	50	5	only	only	ADV
ejpam-3716	50	6	if	if	SCONJ
ejpam-3716	50	7	g	g	PROPN
ejpam-3716	50	8	has	have	VERB
ejpam-3716	50	9	one	one	NUM
ejpam-3716	50	10	of	of	ADP
ejpam-3716	50	11	the	the	DET
ejpam-3716	50	12	following	follow	VERB
ejpam-3716	50	13	properties	property	NOUN
ejpam-3716	50	14	:	:	PUNCT
ejpam-3716	50	15	(	(	PUNCT
ejpam-3716	50	16	i	i	NOUN
ejpam-3716	50	17	)	)	PUNCT
ejpam-3716	50	18	∆(g	∆(g	NOUN
ejpam-3716	50	19	)	)	PUNCT
ejpam-3716	50	20	≤	≤	NOUN
ejpam-3716	50	21	3	3	NUM
ejpam-3716	50	22	and	and	CCONJ
ejpam-3716	50	23	(	(	PUNCT
ejpam-3716	50	24	ii	ii	NOUN
ejpam-3716	50	25	)	)	PUNCT
ejpam-3716	50	26	g	g	NOUN
ejpam-3716	50	27	is	be	AUX
ejpam-3716	50	28	unicyclic	unicyclic	ADJ
ejpam-3716	50	29	.	.	PUNCT
ejpam-3716	51	1	proof	proof	NOUN
ejpam-3716	51	2	.	.	PUNCT
ejpam-3716	52	1	since	since	SCONJ
ejpam-3716	52	2	the	the	DET
ejpam-3716	52	3	definitions	definition	NOUN
ejpam-3716	52	4	of	of	ADP
ejpam-3716	52	5	point	point	NOUN
ejpam-3716	52	6	-	-	PUNCT
ejpam-3716	52	7	outercoarseness	outercoarseness	NOUN
ejpam-3716	52	8	number	number	NOUN
ejpam-3716	52	9	one	one	NUM
ejpam-3716	52	10	and	and	CCONJ
ejpam-3716	52	11	minimally	minimally	ADV
ejpam-3716	52	12	nonouterplanar	nonouterplanar	NOUN
ejpam-3716	52	13	are	be	AUX
ejpam-3716	52	14	isomorphic	isomorphic	ADJ
ejpam-3716	52	15	,	,	PUNCT
ejpam-3716	52	16	the	the	DET
ejpam-3716	52	17	proof	proof	NOUN
ejpam-3716	52	18	of	of	ADP
ejpam-3716	52	19	the	the	DET
ejpam-3716	52	20	theorem	theorem	NOUN
ejpam-3716	52	21	is	be	AUX
ejpam-3716	52	22	analogous	analogous	ADJ
ejpam-3716	52	23	to	to	ADP
ejpam-3716	52	24	the	the	DET
ejpam-3716	52	25	proof	proof	NOUN
ejpam-3716	52	26	of	of	ADP
ejpam-3716	52	27	the	the	DET
ejpam-3716	52	28	theorem	theorem	NOUN
ejpam-3716	52	29	4	4	NUM
ejpam-3716	52	30	.	.	NOUN
ejpam-3716	52	31	3	3	NUM
ejpam-3716	52	32	.	.	X
ejpam-3716	52	33	main	main	ADJ
ejpam-3716	52	34	results	result	NOUN
ejpam-3716	52	35	before	before	SCONJ
ejpam-3716	52	36	we	we	PRON
ejpam-3716	52	37	establish	establish	VERB
ejpam-3716	52	38	the	the	DET
ejpam-3716	52	39	first	first	ADJ
ejpam-3716	52	40	result	result	NOUN
ejpam-3716	52	41	,	,	PUNCT
ejpam-3716	52	42	we	we	PRON
ejpam-3716	52	43	prove	prove	VERB
ejpam-3716	52	44	the	the	DET
ejpam-3716	52	45	following	follow	VERB
ejpam-3716	52	46	lemma	lemma	PROPN
ejpam-3716	52	47	.	.	PUNCT
ejpam-3716	53	1	lemma	lemma	PROPN
ejpam-3716	53	2	1	1	NUM
ejpam-3716	53	3	.	.	PUNCT
ejpam-3716	54	1	p	p	X
ejpam-3716	54	2	(	(	PUNCT
ejpam-3716	54	3	g	g	NOUN
ejpam-3716	54	4	)	)	PUNCT
ejpam-3716	54	5	is	be	AUX
ejpam-3716	54	6	unicyclic	unicyclic	ADJ
ejpam-3716	54	7	if	if	SCONJ
ejpam-3716	55	1	and	and	CCONJ
ejpam-3716	55	2	only	only	ADV
ejpam-3716	55	3	if	if	SCONJ
ejpam-3716	55	4	there	there	PRON
ejpam-3716	55	5	exist	exist	VERB
ejpam-3716	55	6	a	a	DET
ejpam-3716	55	7	unique	unique	ADJ
ejpam-3716	55	8	vertex	vertex	NOUN
ejpam-3716	55	9	of	of	ADP
ejpam-3716	55	10	∆(g	∆(g	NOUN
ejpam-3716	55	11	)	)	PUNCT
ejpam-3716	55	12	=	=	SYM
ejpam-3716	55	13	3	3	NUM
ejpam-3716	55	14	in	in	ADP
ejpam-3716	55	15	g.	g.	PROPN
ejpam-3716	55	16	v.	v.	PROPN
ejpam-3716	55	17	lokesha	lokesha	PROPN
ejpam-3716	55	18	,	,	PUNCT
ejpam-3716	55	19	s.	s.	PROPN
ejpam-3716	55	20	m.	m.	PROPN
ejpam-3716	55	21	hosamani	hosamani	PROPN
ejpam-3716	55	22	,	,	PUNCT
ejpam-3716	55	23	s.	s.	PROPN
ejpam-3716	55	24	v.	v.	PROPN
ejpam-3716	55	25	patil	patil	PROPN
ejpam-3716	55	26	/	/	SYM
ejpam-3716	55	27	eur	eur	PROPN
ejpam-3716	55	28	.	.	PUNCT
ejpam-3716	56	1	j.	j.	PROPN
ejpam-3716	56	2	pure	pure	PROPN
ejpam-3716	56	3	appl	appl	PROPN
ejpam-3716	56	4	.	.	PROPN
ejpam-3716	56	5	math	math	PROPN
ejpam-3716	56	6	,	,	PUNCT
ejpam-3716	56	7	13	13	NUM
ejpam-3716	56	8	(	(	PUNCT
ejpam-3716	56	9	5	5	NUM
ejpam-3716	56	10	)	)	PUNCT
ejpam-3716	56	11	(	(	PUNCT
ejpam-3716	56	12	2020	2020	NUM
ejpam-3716	56	13	)	)	PUNCT
ejpam-3716	56	14	,	,	PUNCT
ejpam-3716	56	15	1300	1300	NUM
ejpam-3716	56	16	-	-	SYM
ejpam-3716	56	17	1305	1305	NUM
ejpam-3716	56	18	1303	1303	NUM
ejpam-3716	56	19	proof	proof	NOUN
ejpam-3716	56	20	.	.	PUNCT
ejpam-3716	57	1	suppose	suppose	VERB
ejpam-3716	57	2	p	p	X
ejpam-3716	57	3	(	(	PUNCT
ejpam-3716	57	4	g	g	NOUN
ejpam-3716	57	5	)	)	PUNCT
ejpam-3716	57	6	is	be	AUX
ejpam-3716	57	7	unicyclic	unicyclic	ADJ
ejpam-3716	57	8	.	.	PUNCT
ejpam-3716	58	1	we	we	PRON
ejpam-3716	58	2	consider	consider	VERB
ejpam-3716	58	3	the	the	DET
ejpam-3716	58	4	following	follow	VERB
ejpam-3716	58	5	cases	case	NOUN
ejpam-3716	58	6	.	.	PUNCT
ejpam-3716	59	1	case	case	NOUN
ejpam-3716	59	2	1	1	X
ejpam-3716	59	3	.	.	PUNCT
ejpam-3716	60	1	let	let	VERB
ejpam-3716	60	2	∆(g	∆(g	NOUN
ejpam-3716	60	3	)	)	PUNCT
ejpam-3716	60	4	≤	≤	NOUN
ejpam-3716	61	1	2	2	NUM
ejpam-3716	61	2	.	.	PUNCT
ejpam-3716	62	1	if	if	SCONJ
ejpam-3716	62	2	∆(g	∆(g	NOUN
ejpam-3716	62	3	)	)	PUNCT
ejpam-3716	62	4	=	=	SYM
ejpam-3716	62	5	1	1	NUM
ejpam-3716	62	6	,	,	PUNCT
ejpam-3716	62	7	then	then	ADV
ejpam-3716	62	8	g	g	PROPN
ejpam-3716	62	9	is	be	AUX
ejpam-3716	62	10	k2	k2	ADJ
ejpam-3716	62	11	.	.	PUNCT
ejpam-3716	63	1	consequently	consequently	ADV
ejpam-3716	63	2	p	p	X
ejpam-3716	63	3	(	(	PUNCT
ejpam-3716	63	4	g	g	NOUN
ejpam-3716	63	5	)	)	PUNCT
ejpam-3716	63	6	is	be	AUX
ejpam-3716	63	7	k2,a	k2,a	PROPN
ejpam-3716	63	8	contradiction	contradiction	NOUN
ejpam-3716	63	9	.	.	PUNCT
ejpam-3716	64	1	if	if	SCONJ
ejpam-3716	64	2	∆(g	∆(g	NOUN
ejpam-3716	64	3	)	)	PUNCT
ejpam-3716	64	4	=	=	SYM
ejpam-3716	64	5	2	2	NUM
ejpam-3716	64	6	then	then	ADV
ejpam-3716	64	7	g	g	PROPN
ejpam-3716	64	8	is	be	AUX
ejpam-3716	64	9	a	a	DET
ejpam-3716	64	10	path	path	NOUN
ejpam-3716	64	11	or	or	CCONJ
ejpam-3716	64	12	a	a	DET
ejpam-3716	64	13	cycle	cycle	NOUN
ejpam-3716	64	14	.	.	PUNCT
ejpam-3716	65	1	if	if	SCONJ
ejpam-3716	65	2	g	g	PROPN
ejpam-3716	65	3	is	be	AUX
ejpam-3716	65	4	a	a	DET
ejpam-3716	65	5	path	path	NOUN
ejpam-3716	65	6	,	,	PUNCT
ejpam-3716	65	7	then	then	ADV
ejpam-3716	65	8	clearly	clearly	ADV
ejpam-3716	65	9	p	p	X
ejpam-3716	65	10	(	(	PUNCT
ejpam-3716	65	11	g	g	NOUN
ejpam-3716	65	12	)	)	PUNCT
ejpam-3716	65	13	is	be	AUX
ejpam-3716	65	14	a	a	DET
ejpam-3716	65	15	tree	tree	NOUN
ejpam-3716	65	16	,	,	PUNCT
ejpam-3716	65	17	a	a	DET
ejpam-3716	65	18	contradiction.if	contradiction.if	NOUN
ejpam-3716	65	19	g	g	NOUN
ejpam-3716	65	20	is	be	AUX
ejpam-3716	65	21	a	a	DET
ejpam-3716	65	22	cycle	cycle	NOUN
ejpam-3716	65	23	cn	cn	NOUN
ejpam-3716	65	24	;	;	PUNCT
ejpam-3716	65	25	∀n	∀n	NUM
ejpam-3716	65	26	≥	≥	NOUN
ejpam-3716	65	27	3	3	NUM
ejpam-3716	65	28	,	,	PUNCT
ejpam-3716	65	29	then	then	ADV
ejpam-3716	65	30	by	by	ADP
ejpam-3716	65	31	theorem	theorem	NOUN
ejpam-3716	65	32	3	3	NUM
ejpam-3716	65	33	,	,	PUNCT
ejpam-3716	65	34	p	p	X
ejpam-3716	65	35	(	(	PUNCT
ejpam-3716	65	36	g	g	NOUN
ejpam-3716	65	37	)	)	PUNCT
ejpam-3716	65	38	is	be	AUX
ejpam-3716	65	39	a	a	DET
ejpam-3716	65	40	wheel	wheel	NOUN
ejpam-3716	65	41	,	,	PUNCT
ejpam-3716	65	42	a	a	DET
ejpam-3716	65	43	contradiction	contradiction	NOUN
ejpam-3716	65	44	.	.	PUNCT
ejpam-3716	66	1	case	case	NOUN
ejpam-3716	66	2	2	2	X
ejpam-3716	66	3	.	.	PUNCT
ejpam-3716	66	4	suppose	suppose	VERB
ejpam-3716	66	5	∆(g	∆(g	NOUN
ejpam-3716	66	6	)	)	PUNCT
ejpam-3716	66	7	=	=	SYM
ejpam-3716	67	1	4	4	X
ejpam-3716	67	2	.	.	X
ejpam-3716	67	3	clearly	clearly	ADV
ejpam-3716	67	4	k1,4	k1,4	ADV
ejpam-3716	67	5	is	be	AUX
ejpam-3716	67	6	a	a	DET
ejpam-3716	67	7	subgraph	subgraph	NOUN
ejpam-3716	67	8	of	of	ADP
ejpam-3716	67	9	g	g	NOUN
ejpam-3716	67	10	and	and	CCONJ
ejpam-3716	67	11	by	by	ADP
ejpam-3716	67	12	remark	remark	NOUN
ejpam-3716	67	13	1	1	NUM
ejpam-3716	67	14	,	,	PUNCT
ejpam-3716	67	15	p	p	X
ejpam-3716	67	16	(	(	PUNCT
ejpam-3716	67	17	g	g	NOUN
ejpam-3716	67	18	)	)	PUNCT
ejpam-3716	67	19	contains	contain	VERB
ejpam-3716	67	20	k4	k4	NOUN
ejpam-3716	67	21	as	as	ADP
ejpam-3716	67	22	an	an	DET
ejpam-3716	67	23	induced	induced	ADJ
ejpam-3716	67	24	subgraph	subgraph	NOUN
ejpam-3716	67	25	,	,	PUNCT
ejpam-3716	67	26	a	a	DET
ejpam-3716	67	27	contradiction	contradiction	NOUN
ejpam-3716	67	28	.	.	PUNCT
ejpam-3716	68	1	hence	hence	ADV
ejpam-3716	68	2	∆(g	∆(g	NOUN
ejpam-3716	68	3	)	)	PUNCT
ejpam-3716	68	4	≤	≤	NOUN
ejpam-3716	68	5	3	3	NUM
ejpam-3716	68	6	.	.	PUNCT
ejpam-3716	68	7	suppose	suppose	VERB
ejpam-3716	68	8	g	g	PROPN
ejpam-3716	68	9	has	have	VERB
ejpam-3716	68	10	two	two	NUM
ejpam-3716	68	11	or	or	CCONJ
ejpam-3716	68	12	more	more	ADJ
ejpam-3716	68	13	than	than	ADP
ejpam-3716	68	14	two	two	NUM
ejpam-3716	68	15	vertices	vertex	NOUN
ejpam-3716	68	16	of	of	ADP
ejpam-3716	68	17	degree	degree	NOUN
ejpam-3716	68	18	3	3	NUM
ejpam-3716	68	19	.	.	PUNCT
ejpam-3716	68	20	then	then	ADV
ejpam-3716	68	21	by	by	ADP
ejpam-3716	68	22	theorem	theorem	NOUN
ejpam-3716	68	23	1	1	NUM
ejpam-3716	68	24	,	,	PUNCT
ejpam-3716	68	25	p	p	X
ejpam-3716	68	26	(	(	PUNCT
ejpam-3716	68	27	g	g	NOUN
ejpam-3716	68	28	)	)	PUNCT
ejpam-3716	68	29	is	be	AUX
ejpam-3716	68	30	planar	planar	ADJ
ejpam-3716	68	31	and	and	CCONJ
ejpam-3716	68	32	there	there	PRON
ejpam-3716	68	33	exist	exist	VERB
ejpam-3716	68	34	at	at	ADV
ejpam-3716	68	35	least	least	ADV
ejpam-3716	68	36	two	two	NUM
ejpam-3716	68	37	blocks	block	NOUN
ejpam-3716	68	38	which	which	PRON
ejpam-3716	68	39	are	be	AUX
ejpam-3716	68	40	cycles	cycle	NOUN
ejpam-3716	68	41	c3	c3	PROPN
ejpam-3716	68	42	as	as	ADP
ejpam-3716	68	43	induced	induce	VERB
ejpam-3716	68	44	subgraphs	subgraph	NOUN
ejpam-3716	68	45	for	for	ADP
ejpam-3716	68	46	p	p	PROPN
ejpam-3716	68	47	(	(	PUNCT
ejpam-3716	68	48	g	g	NOUN
ejpam-3716	68	49	)	)	PUNCT
ejpam-3716	68	50	,	,	PUNCT
ejpam-3716	68	51	a	a	DET
ejpam-3716	68	52	contradiction	contradiction	NOUN
ejpam-3716	68	53	.	.	PUNCT
ejpam-3716	69	1	hence	hence	ADV
ejpam-3716	69	2	there	there	PRON
ejpam-3716	69	3	exists	exist	VERB
ejpam-3716	69	4	a	a	DET
ejpam-3716	69	5	unique	unique	ADJ
ejpam-3716	69	6	vertex	vertex	NOUN
ejpam-3716	69	7	of	of	ADP
ejpam-3716	69	8	∆(g	∆(g	NOUN
ejpam-3716	69	9	)	)	PUNCT
ejpam-3716	69	10	=	=	SYM
ejpam-3716	70	1	3	3	X
ejpam-3716	70	2	.	.	PUNCT
ejpam-3716	71	1	the	the	DET
ejpam-3716	71	2	converse	converse	NOUN
ejpam-3716	71	3	is	be	AUX
ejpam-3716	71	4	obvious	obvious	ADJ
ejpam-3716	71	5	.	.	PUNCT
ejpam-3716	72	1	corollary	corollary	ADJ
ejpam-3716	72	2	1	1	NUM
ejpam-3716	72	3	.	.	PUNCT
ejpam-3716	73	1	p	p	X
ejpam-3716	73	2	(	(	PUNCT
ejpam-3716	73	3	g	g	NOUN
ejpam-3716	73	4	)	)	PUNCT
ejpam-3716	73	5	is	be	AUX
ejpam-3716	73	6	a	a	DET
ejpam-3716	73	7	tree	tree	NOUN
ejpam-3716	73	8	if	if	SCONJ
ejpam-3716	74	1	and	and	CCONJ
ejpam-3716	74	2	only	only	ADV
ejpam-3716	74	3	if	if	SCONJ
ejpam-3716	74	4	g	g	PROPN
ejpam-3716	74	5	is	be	AUX
ejpam-3716	74	6	a	a	DET
ejpam-3716	74	7	path	path	NOUN
ejpam-3716	74	8	pn;n	pn;n	VERB
ejpam-3716	74	9	≥	≥	NOUN
ejpam-3716	74	10	2	2	NUM
ejpam-3716	74	11	.	.	PUNCT
ejpam-3716	74	12	theorem	theorem	VERB
ejpam-3716	74	13	6	6	NUM
ejpam-3716	74	14	.	.	PUNCT
ejpam-3716	75	1	for	for	ADP
ejpam-3716	75	2	any	any	DET
ejpam-3716	75	3	connected	connected	ADJ
ejpam-3716	75	4	graph	graph	NOUN
ejpam-3716	75	5	g	g	NOUN
ejpam-3716	75	6	,	,	PUNCT
ejpam-3716	75	7	π3(p	π3(p	NOUN
ejpam-3716	75	8	2(g	2(g	NUM
ejpam-3716	75	9	)	)	PUNCT
ejpam-3716	75	10	)	)	PUNCT
ejpam-3716	75	11	=	=	PUNCT
ejpam-3716	75	12	1	1	NUM
ejpam-3716	75	13	if	if	SCONJ
ejpam-3716	75	14	and	and	CCONJ
ejpam-3716	75	15	only	only	ADV
ejpam-3716	75	16	if	if	SCONJ
ejpam-3716	75	17	g	g	PROPN
ejpam-3716	75	18	is	be	AUX
ejpam-3716	75	19	a	a	DET
ejpam-3716	75	20	tree	tree	NOUN
ejpam-3716	75	21	with	with	ADP
ejpam-3716	75	22	∆(g	∆(g	PROPN
ejpam-3716	75	23	)	)	PUNCT
ejpam-3716	75	24	≤	≤	NOUN
ejpam-3716	75	25	3	3	NUM
ejpam-3716	75	26	and	and	CCONJ
ejpam-3716	75	27	contains	contain	VERB
ejpam-3716	75	28	a	a	DET
ejpam-3716	75	29	unique	unique	ADJ
ejpam-3716	75	30	vertex	vertex	NOUN
ejpam-3716	75	31	of	of	ADP
ejpam-3716	75	32	degree	degree	NOUN
ejpam-3716	75	33	3	3	NUM
ejpam-3716	75	34	.	.	PUNCT
ejpam-3716	75	35	proof	proof	NOUN
ejpam-3716	75	36	.	.	PUNCT
ejpam-3716	75	37	suppose	suppose	VERB
ejpam-3716	75	38	π3(p	π3(p	NUM
ejpam-3716	75	39	2(g	2(g	NUM
ejpam-3716	75	40	)	)	PUNCT
ejpam-3716	75	41	)	)	PUNCT
ejpam-3716	75	42	=	=	PUNCT
ejpam-3716	76	1	1	1	X
ejpam-3716	76	2	.	.	PUNCT
ejpam-3716	77	1	the	the	DET
ejpam-3716	77	2	plick	plick	NOUN
ejpam-3716	77	3	graph	graph	NOUN
ejpam-3716	77	4	p	p	X
ejpam-3716	77	5	(	(	PUNCT
ejpam-3716	77	6	g	g	NOUN
ejpam-3716	77	7	)	)	PUNCT
ejpam-3716	77	8	satisfies	satisfy	VERB
ejpam-3716	77	9	the	the	DET
ejpam-3716	77	10	hypothesis	hypothesis	NOUN
ejpam-3716	77	11	of	of	ADP
ejpam-3716	77	12	theorem	theorem	NOUN
ejpam-3716	77	13	5	5	NUM
ejpam-3716	77	14	.	.	PUNCT
ejpam-3716	77	15	clearly	clearly	ADV
ejpam-3716	77	16	∆(g	∆(g	NOUN
ejpam-3716	77	17	)	)	PUNCT
ejpam-3716	77	18	≤	≤	NOUN
ejpam-3716	77	19	3	3	NUM
ejpam-3716	77	20	and	and	CCONJ
ejpam-3716	77	21	unicyclic.if	unicyclic.if	NUM
ejpam-3716	77	22	∆(g	∆(g	NOUN
ejpam-3716	77	23	)	)	PUNCT
ejpam-3716	77	24	=	=	SYM
ejpam-3716	77	25	3	3	NUM
ejpam-3716	77	26	and	and	CCONJ
ejpam-3716	77	27	is	be	AUX
ejpam-3716	77	28	unicyclic	unicyclic	ADJ
ejpam-3716	77	29	,	,	PUNCT
ejpam-3716	77	30	then	then	ADV
ejpam-3716	77	31	there	there	PRON
ejpam-3716	77	32	exist	exist	VERB
ejpam-3716	77	33	exactly	exactly	ADV
ejpam-3716	77	34	one	one	NUM
ejpam-3716	77	35	vertex	vertex	NOUN
ejpam-3716	77	36	of	of	ADP
ejpam-3716	77	37	degree	degree	NOUN
ejpam-3716	77	38	3	3	NUM
ejpam-3716	77	39	in	in	ADP
ejpam-3716	77	40	g	g	PROPN
ejpam-3716	77	41	and	and	CCONJ
ejpam-3716	77	42	g	g	PROPN
ejpam-3716	77	43	does	do	AUX
ejpam-3716	77	44	not	not	PART
ejpam-3716	77	45	contain	contain	VERB
ejpam-3716	77	46	any	any	DET
ejpam-3716	77	47	cycle	cycle	NOUN
ejpam-3716	77	48	as	as	ADP
ejpam-3716	77	49	an	an	DET
ejpam-3716	77	50	induced	induced	ADJ
ejpam-3716	77	51	subgraph	subgraph	NOUN
ejpam-3716	77	52	.	.	PUNCT
ejpam-3716	78	1	suppose	suppose	VERB
ejpam-3716	78	2	g	g	PROPN
ejpam-3716	78	3	contains	contain	VERB
ejpam-3716	78	4	a	a	DET
ejpam-3716	78	5	cycle	cycle	NOUN
ejpam-3716	78	6	,	,	PUNCT
ejpam-3716	78	7	then	then	ADV
ejpam-3716	78	8	by	by	ADP
ejpam-3716	78	9	theorem	theorem	NOUN
ejpam-3716	78	10	3	3	NUM
ejpam-3716	78	11	,	,	PUNCT
ejpam-3716	78	12	p	p	X
ejpam-3716	78	13	(	(	PUNCT
ejpam-3716	78	14	g	g	NOUN
ejpam-3716	78	15	)	)	PUNCT
ejpam-3716	78	16	contains	contain	VERB
ejpam-3716	78	17	a	a	DET
ejpam-3716	78	18	wheel	wheel	NOUN
ejpam-3716	78	19	,	,	PUNCT
ejpam-3716	78	20	a	a	DET
ejpam-3716	78	21	contradiction	contradiction	NOUN
ejpam-3716	78	22	to	to	ADP
ejpam-3716	78	23	the	the	DET
ejpam-3716	78	24	hypothesis	hypothesis	NOUN
ejpam-3716	78	25	.	.	PUNCT
ejpam-3716	79	1	therefore	therefore	ADV
ejpam-3716	79	2	g	g	PROPN
ejpam-3716	79	3	must	must	AUX
ejpam-3716	79	4	be	be	AUX
ejpam-3716	79	5	a	a	DET
ejpam-3716	79	6	tree	tree	NOUN
ejpam-3716	79	7	.	.	PUNCT
ejpam-3716	80	1	by	by	ADP
ejpam-3716	80	2	lemma	lemma	PROPN
ejpam-3716	80	3	1	1	NUM
ejpam-3716	80	4	,	,	PUNCT
ejpam-3716	80	5	there	there	PRON
ejpam-3716	80	6	exists	exist	VERB
ejpam-3716	80	7	a	a	DET
ejpam-3716	80	8	unique	unique	ADJ
ejpam-3716	80	9	vertex	vertex	NOUN
ejpam-3716	80	10	of	of	ADP
ejpam-3716	80	11	∆(g	∆(g	NOUN
ejpam-3716	80	12	)	)	PUNCT
ejpam-3716	80	13	=	=	SYM
ejpam-3716	81	1	3	3	X
ejpam-3716	81	2	.	.	PUNCT
ejpam-3716	81	3	conversely	conversely	ADV
ejpam-3716	81	4	,	,	PUNCT
ejpam-3716	81	5	suppose	suppose	VERB
ejpam-3716	81	6	g	g	PROPN
ejpam-3716	81	7	is	be	AUX
ejpam-3716	81	8	a	a	DET
ejpam-3716	81	9	tree	tree	NOUN
ejpam-3716	81	10	.	.	PUNCT
ejpam-3716	82	1	we	we	PRON
ejpam-3716	82	2	consider	consider	VERB
ejpam-3716	82	3	the	the	DET
ejpam-3716	82	4	following	follow	VERB
ejpam-3716	82	5	cases	case	NOUN
ejpam-3716	82	6	depending	depend	VERB
ejpam-3716	82	7	on	on	ADP
ejpam-3716	82	8	∆(g	∆(g	NOUN
ejpam-3716	82	9	)	)	PUNCT
ejpam-3716	82	10	.	.	PUNCT
ejpam-3716	83	1	case	case	NOUN
ejpam-3716	83	2	1	1	X
ejpam-3716	83	3	.	.	PUNCT
ejpam-3716	84	1	if	if	SCONJ
ejpam-3716	84	2	∆(g	∆(g	NOUN
ejpam-3716	84	3	)	)	PUNCT
ejpam-3716	84	4	=	=	SYM
ejpam-3716	84	5	1	1	NUM
ejpam-3716	84	6	,	,	PUNCT
ejpam-3716	84	7	then	then	ADV
ejpam-3716	84	8	g	g	PROPN
ejpam-3716	84	9	=	=	SYM
ejpam-3716	84	10	k2	k2	PROPN
ejpam-3716	84	11	.	.	PUNCT
ejpam-3716	85	1	consequently	consequently	ADV
ejpam-3716	85	2	p	p	X
ejpam-3716	85	3	(	(	PUNCT
ejpam-3716	85	4	g	g	NOUN
ejpam-3716	85	5	)	)	PUNCT
ejpam-3716	85	6	=	=	SYM
ejpam-3716	85	7	k2	k2	NOUN
ejpam-3716	85	8	and	and	CCONJ
ejpam-3716	85	9	p	p	NOUN
ejpam-3716	85	10	2(g	2(g	NUM
ejpam-3716	85	11	)	)	PUNCT
ejpam-3716	86	1	=	=	SYM
ejpam-3716	86	2	k2	k2	PROPN
ejpam-3716	86	3	,	,	PUNCT
ejpam-3716	86	4	a	a	DET
ejpam-3716	86	5	contradiction	contradiction	NOUN
ejpam-3716	86	6	to	to	ADP
ejpam-3716	86	7	our	our	PRON
ejpam-3716	86	8	assumption	assumption	NOUN
ejpam-3716	86	9	.	.	PUNCT
ejpam-3716	87	1	case	case	NOUN
ejpam-3716	87	2	2	2	X
ejpam-3716	87	3	.	.	X
ejpam-3716	88	1	if	if	SCONJ
ejpam-3716	88	2	∆(g	∆(g	NOUN
ejpam-3716	88	3	)	)	PUNCT
ejpam-3716	88	4	=	=	SYM
ejpam-3716	88	5	2	2	NUM
ejpam-3716	88	6	,	,	PUNCT
ejpam-3716	88	7	then	then	ADV
ejpam-3716	88	8	g	g	PROPN
ejpam-3716	88	9	is	be	AUX
ejpam-3716	88	10	either	either	CCONJ
ejpam-3716	88	11	a	a	DET
ejpam-3716	88	12	cycle	cycle	NOUN
ejpam-3716	88	13	or	or	CCONJ
ejpam-3716	88	14	a	a	DET
ejpam-3716	88	15	path	path	NOUN
ejpam-3716	88	16	.	.	PUNCT
ejpam-3716	89	1	if	if	SCONJ
ejpam-3716	89	2	g	g	PROPN
ejpam-3716	89	3	is	be	AUX
ejpam-3716	89	4	a	a	DET
ejpam-3716	89	5	cycle	cycle	NOUN
ejpam-3716	89	6	,	,	PUNCT
ejpam-3716	89	7	then	then	ADV
ejpam-3716	89	8	by	by	ADP
ejpam-3716	89	9	theorem	theorem	NOUN
ejpam-3716	89	10	3	3	NUM
ejpam-3716	89	11	,	,	PUNCT
ejpam-3716	89	12	p	p	X
ejpam-3716	89	13	(	(	PUNCT
ejpam-3716	89	14	g	g	NOUN
ejpam-3716	89	15	)	)	PUNCT
ejpam-3716	89	16	is	be	AUX
ejpam-3716	89	17	a	a	DET
ejpam-3716	89	18	wheel	wheel	NOUN
ejpam-3716	89	19	,	,	PUNCT
ejpam-3716	89	20	a	a	DET
ejpam-3716	89	21	contradiction	contradiction	NOUN
ejpam-3716	89	22	.	.	PUNCT
ejpam-3716	90	1	if	if	SCONJ
ejpam-3716	90	2	g	g	PROPN
ejpam-3716	90	3	is	be	AUX
ejpam-3716	90	4	a	a	DET
ejpam-3716	90	5	path	path	NOUN
ejpam-3716	90	6	,	,	PUNCT
ejpam-3716	90	7	then	then	ADV
ejpam-3716	90	8	by	by	ADP
ejpam-3716	90	9	corollary	corollary	ADJ
ejpam-3716	90	10	1	1	NUM
ejpam-3716	90	11	,	,	PUNCT
ejpam-3716	90	12	p	p	X
ejpam-3716	90	13	(	(	PUNCT
ejpam-3716	90	14	g	g	NOUN
ejpam-3716	90	15	)	)	PUNCT
ejpam-3716	90	16	is	be	AUX
ejpam-3716	90	17	a	a	DET
ejpam-3716	90	18	tree	tree	NOUN
ejpam-3716	90	19	with	with	ADP
ejpam-3716	90	20	∆(g	∆(g	PROPN
ejpam-3716	90	21	)	)	PUNCT
ejpam-3716	90	22	=	=	SYM
ejpam-3716	90	23	3	3	NUM
ejpam-3716	90	24	and	and	CCONJ
ejpam-3716	90	25	every	every	DET
ejpam-3716	90	26	block	block	NOUN
ejpam-3716	90	27	of	of	ADP
ejpam-3716	90	28	p	p	NOUN
ejpam-3716	90	29	(	(	PUNCT
ejpam-3716	90	30	g	g	NOUN
ejpam-3716	90	31	)	)	PUNCT
ejpam-3716	90	32	is	be	AUX
ejpam-3716	90	33	k2	k2	ADJ
ejpam-3716	90	34	.	.	PUNCT
ejpam-3716	91	1	by	by	ADP
ejpam-3716	91	2	theorem	theorem	NOUN
ejpam-3716	91	3	1	1	NUM
ejpam-3716	91	4	,	,	PUNCT
ejpam-3716	91	5	p	p	NOUN
ejpam-3716	91	6	2(g	2(g	NUM
ejpam-3716	91	7	)	)	PUNCT
ejpam-3716	91	8	is	be	AUX
ejpam-3716	91	9	planar	planar	ADJ
ejpam-3716	91	10	with	with	ADP
ejpam-3716	91	11	an	an	DET
ejpam-3716	91	12	induced	induced	ADJ
ejpam-3716	91	13	subgraph	subgraph	NOUN
ejpam-3716	91	14	of	of	ADP
ejpam-3716	91	15	c3	c3	PROPN
ejpam-3716	91	16	,	,	PUNCT
ejpam-3716	91	17	a	a	DET
ejpam-3716	91	18	contradiction	contradiction	NOUN
ejpam-3716	91	19	.	.	PUNCT
ejpam-3716	92	1	case	case	NOUN
ejpam-3716	92	2	3	3	X
ejpam-3716	92	3	.	.	PUNCT
ejpam-3716	92	4	suppose	suppose	VERB
ejpam-3716	92	5	g	g	PROPN
ejpam-3716	92	6	has	have	VERB
ejpam-3716	92	7	exactly	exactly	ADV
ejpam-3716	92	8	two	two	NUM
ejpam-3716	92	9	vertices	vertex	NOUN
ejpam-3716	92	10	of	of	ADP
ejpam-3716	92	11	degree	degree	NOUN
ejpam-3716	92	12	3	3	NUM
ejpam-3716	92	13	.	.	PUNCT
ejpam-3716	92	14	then	then	ADV
ejpam-3716	92	15	by	by	ADP
ejpam-3716	92	16	theorem	theorem	NOUN
ejpam-3716	92	17	1	1	NUM
ejpam-3716	92	18	,	,	PUNCT
ejpam-3716	92	19	p	p	X
ejpam-3716	92	20	(	(	PUNCT
ejpam-3716	92	21	g	g	NOUN
ejpam-3716	92	22	)	)	PUNCT
ejpam-3716	92	23	is	be	AUX
ejpam-3716	92	24	planar	planar	ADJ
ejpam-3716	92	25	and	and	CCONJ
ejpam-3716	92	26	there	there	PRON
ejpam-3716	92	27	exist	exist	VERB
ejpam-3716	92	28	exactly	exactly	ADV
ejpam-3716	92	29	two	two	NUM
ejpam-3716	92	30	cycles	cycle	NOUN
ejpam-3716	92	31	c3	c3	NOUN
ejpam-3716	92	32	as	as	SCONJ
ejpam-3716	92	33	induced	induce	VERB
ejpam-3716	92	34	subgraphs	subgraph	NOUN
ejpam-3716	92	35	of	of	ADP
ejpam-3716	92	36	p	p	NOUN
ejpam-3716	92	37	(	(	PUNCT
ejpam-3716	92	38	g	g	NOUN
ejpam-3716	92	39	)	)	PUNCT
ejpam-3716	92	40	.	.	PUNCT
ejpam-3716	93	1	by	by	ADP
ejpam-3716	93	2	theorem	theorem	NOUN
ejpam-3716	93	3	3	3	NUM
ejpam-3716	93	4	,	,	PUNCT
ejpam-3716	93	5	in	in	ADP
ejpam-3716	93	6	p	p	NOUN
ejpam-3716	93	7	2(g	2(g	NUM
ejpam-3716	93	8	)	)	PUNCT
ejpam-3716	93	9	there	there	PRON
ejpam-3716	93	10	exist	exist	VERB
ejpam-3716	93	11	exactly	exactly	ADV
ejpam-3716	93	12	two	two	NUM
ejpam-3716	93	13	wheels	wheel	NOUN
ejpam-3716	93	14	of	of	ADP
ejpam-3716	93	15	length	length	NOUN
ejpam-3716	93	16	four	four	NUM
ejpam-3716	93	17	w4	w4	NOUN
ejpam-3716	93	18	that	that	PRON
ejpam-3716	93	19	is	be	AUX
ejpam-3716	93	20	k4	k4	ADJ
ejpam-3716	93	21	as	as	ADP
ejpam-3716	93	22	an	an	DET
ejpam-3716	93	23	induced	induced	ADJ
ejpam-3716	93	24	subgraph	subgraph	NOUN
ejpam-3716	93	25	,	,	PUNCT
ejpam-3716	93	26	a	a	DET
ejpam-3716	93	27	contradiction	contradiction	NOUN
ejpam-3716	93	28	.	.	PUNCT
ejpam-3716	94	1	hence	hence	ADV
ejpam-3716	94	2	,	,	PUNCT
ejpam-3716	94	3	there	there	PRON
ejpam-3716	94	4	exist	exist	VERB
ejpam-3716	94	5	exactly	exactly	ADV
ejpam-3716	94	6	one	one	NUM
ejpam-3716	94	7	vertex	vertex	NOUN
ejpam-3716	94	8	one	one	NUM
ejpam-3716	94	9	vertex	vertex	NOUN
ejpam-3716	94	10	of	of	ADP
ejpam-3716	94	11	degree	degree	NOUN
ejpam-3716	94	12	3	3	NUM
ejpam-3716	94	13	in	in	ADP
ejpam-3716	94	14	g.	g.	PROPN
ejpam-3716	94	15	theorem	theorem	VERB
ejpam-3716	94	16	7	7	NUM
ejpam-3716	94	17	.	.	X
ejpam-3716	95	1	there	there	PRON
ejpam-3716	95	2	is	be	VERB
ejpam-3716	95	3	only	only	ADV
ejpam-3716	95	4	one	one	NUM
ejpam-3716	95	5	graph	graph	NOUN
ejpam-3716	95	6	p4	p4	ADJ
ejpam-3716	95	7	whose	whose	DET
ejpam-3716	95	8	third	third	ADJ
ejpam-3716	95	9	plick	plick	NOUN
ejpam-3716	95	10	graph	graph	NOUN
ejpam-3716	95	11	p	p	PROPN
ejpam-3716	95	12	3(g	3(g	NUM
ejpam-3716	95	13	)	)	PUNCT
ejpam-3716	95	14	has	have	VERB
ejpam-3716	95	15	pointoutercoarseness	pointoutercoarseness	ADJ
ejpam-3716	95	16	number	number	NOUN
ejpam-3716	95	17	1	1	NUM
ejpam-3716	95	18	.	.	PUNCT
ejpam-3716	96	1	v.	v.	ADP
ejpam-3716	96	2	lokesha	lokesha	PROPN
ejpam-3716	96	3	,	,	PUNCT
ejpam-3716	96	4	s.	s.	PROPN
ejpam-3716	96	5	m.	m.	PROPN
ejpam-3716	96	6	hosamani	hosamani	PROPN
ejpam-3716	96	7	,	,	PUNCT
ejpam-3716	96	8	s.	s.	PROPN
ejpam-3716	96	9	v.	v.	PROPN
ejpam-3716	96	10	patil	patil	PROPN
ejpam-3716	96	11	/	/	SYM
ejpam-3716	96	12	eur	eur	PROPN
ejpam-3716	96	13	.	.	PUNCT
ejpam-3716	97	1	j.	j.	PROPN
ejpam-3716	97	2	pure	pure	PROPN
ejpam-3716	97	3	appl	appl	PROPN
ejpam-3716	97	4	.	.	PROPN
ejpam-3716	97	5	math	math	PROPN
ejpam-3716	97	6	,	,	PUNCT
ejpam-3716	97	7	13	13	NUM
ejpam-3716	97	8	(	(	PUNCT
ejpam-3716	97	9	5	5	NUM
ejpam-3716	97	10	)	)	PUNCT
ejpam-3716	97	11	(	(	PUNCT
ejpam-3716	97	12	2020	2020	NUM
ejpam-3716	97	13	)	)	PUNCT
ejpam-3716	97	14	,	,	PUNCT
ejpam-3716	97	15	1300	1300	NUM
ejpam-3716	97	16	-	-	SYM
ejpam-3716	97	17	1305	1305	NUM
ejpam-3716	97	18	1304	1304	NUM
ejpam-3716	97	19	proof	proof	NOUN
ejpam-3716	97	20	.	.	PUNCT
ejpam-3716	98	1	suppose	suppose	VERB
ejpam-3716	99	1	π3(p	π3(p	NUM
ejpam-3716	99	2	3(g	3(g	NUM
ejpam-3716	99	3	)	)	PUNCT
ejpam-3716	99	4	)	)	PUNCT
ejpam-3716	100	1	=	=	SYM
ejpam-3716	100	2	1	1	NUM
ejpam-3716	100	3	for	for	ADP
ejpam-3716	100	4	a	a	DET
ejpam-3716	100	5	connected	connected	ADJ
ejpam-3716	100	6	graph	graph	NOUN
ejpam-3716	100	7	g.	g.	NOUN
ejpam-3716	100	8	then	then	ADV
ejpam-3716	100	9	p	p	NOUN
ejpam-3716	100	10	2	2	NUM
ejpam-3716	100	11	is	be	AUX
ejpam-3716	100	12	planar	planar	ADJ
ejpam-3716	100	13	and	and	CCONJ
ejpam-3716	100	14	satisfies	satisfy	VERB
ejpam-3716	100	15	the	the	DET
ejpam-3716	100	16	hypothesis	hypothesis	NOUN
ejpam-3716	100	17	of	of	ADP
ejpam-3716	100	18	theorem	theorem	NOUN
ejpam-3716	100	19	5	5	NUM
ejpam-3716	100	20	.	.	PUNCT
ejpam-3716	100	21	clearly	clearly	ADV
ejpam-3716	100	22	∆(p	∆(p	NOUN
ejpam-3716	100	23	2(g	2(g	NUM
ejpam-3716	100	24	)	)	PUNCT
ejpam-3716	100	25	)	)	PUNCT
ejpam-3716	101	1	≤	≤	ADV
ejpam-3716	101	2	3	3	NUM
ejpam-3716	101	3	and	and	CCONJ
ejpam-3716	101	4	p	p	NOUN
ejpam-3716	101	5	2(g	2(g	NUM
ejpam-3716	101	6	)	)	PUNCT
ejpam-3716	101	7	is	be	AUX
ejpam-3716	101	8	unicyclic	unicyclic	ADJ
ejpam-3716	101	9	.	.	PUNCT
ejpam-3716	102	1	by	by	ADP
ejpam-3716	102	2	lemma	lemma	PROPN
ejpam-3716	102	3	1	1	NUM
ejpam-3716	102	4	,	,	PUNCT
ejpam-3716	102	5	p	p	X
ejpam-3716	102	6	(	(	PUNCT
ejpam-3716	102	7	g	g	NOUN
ejpam-3716	102	8	)	)	PUNCT
ejpam-3716	102	9	has	have	VERB
ejpam-3716	102	10	a	a	DET
ejpam-3716	102	11	unique	unique	ADJ
ejpam-3716	102	12	vertex	vertex	NOUN
ejpam-3716	102	13	of	of	ADP
ejpam-3716	102	14	∆(p	∆(p	PROPN
ejpam-3716	102	15	(	(	PUNCT
ejpam-3716	102	16	g	g	NOUN
ejpam-3716	102	17	)	)	PUNCT
ejpam-3716	102	18	)	)	PUNCT
ejpam-3716	103	1	=	=	SYM
ejpam-3716	103	2	3	3	X
ejpam-3716	103	3	.	.	X
ejpam-3716	103	4	hence	hence	ADV
ejpam-3716	103	5	p	p	X
ejpam-3716	103	6	(	(	PUNCT
ejpam-3716	103	7	g	g	NOUN
ejpam-3716	103	8	)	)	PUNCT
ejpam-3716	103	9	is	be	AUX
ejpam-3716	103	10	a	a	DET
ejpam-3716	103	11	tree	tree	NOUN
ejpam-3716	103	12	.	.	PUNCT
ejpam-3716	104	1	by	by	ADP
ejpam-3716	104	2	corollary	corollary	ADJ
ejpam-3716	104	3	1	1	NUM
ejpam-3716	104	4	,	,	PUNCT
ejpam-3716	104	5	g	g	PROPN
ejpam-3716	104	6	is	be	AUX
ejpam-3716	104	7	a	a	DET
ejpam-3716	104	8	path	path	NOUN
ejpam-3716	104	9	.	.	PUNCT
ejpam-3716	105	1	assume	assume	VERB
ejpam-3716	105	2	g	g	PROPN
ejpam-3716	105	3	6=	6=	SYM
ejpam-3716	105	4	p4	p4	ADJ
ejpam-3716	105	5	.	.	PUNCT
ejpam-3716	106	1	then	then	ADV
ejpam-3716	106	2	immediately	immediately	ADV
ejpam-3716	106	3	g	g	PROPN
ejpam-3716	106	4	is	be	AUX
ejpam-3716	106	5	either	either	CCONJ
ejpam-3716	106	6	pn;n	pn;n	ADJ
ejpam-3716	106	7	≤	≤	NUM
ejpam-3716	106	8	3	3	NUM
ejpam-3716	106	9	or	or	CCONJ
ejpam-3716	106	10	pn;n	pn;n	ADJ
ejpam-3716	106	11	≥	≥	NOUN
ejpam-3716	106	12	5	5	NUM
ejpam-3716	106	13	.	.	PUNCT
ejpam-3716	107	1	if	if	SCONJ
ejpam-3716	107	2	g	g	NOUN
ejpam-3716	107	3	=	=	SYM
ejpam-3716	107	4	pn;n	pn;n	X
ejpam-3716	107	5	≤	≤	NUM
ejpam-3716	107	6	3	3	NUM
ejpam-3716	107	7	then	then	ADV
ejpam-3716	107	8	π3(p	π3(p	NUM
ejpam-3716	107	9	3(g	3(g	NUM
ejpam-3716	107	10	)	)	PUNCT
ejpam-3716	107	11	)	)	PUNCT
ejpam-3716	108	1	=	=	SYM
ejpam-3716	108	2	0	0	NUM
ejpam-3716	108	3	,	,	PUNCT
ejpam-3716	108	4	a	a	DET
ejpam-3716	108	5	contradiction	contradiction	NOUN
ejpam-3716	108	6	.	.	PUNCT
ejpam-3716	109	1	if	if	SCONJ
ejpam-3716	109	2	g	g	PROPN
ejpam-3716	109	3	=	=	SYM
ejpam-3716	109	4	pn;n	pn;n	X
ejpam-3716	109	5	≥	≥	NUM
ejpam-3716	109	6	5	5	NUM
ejpam-3716	109	7	,	,	PUNCT
ejpam-3716	109	8	then	then	ADV
ejpam-3716	109	9	p	p	NOUN
ejpam-3716	109	10	2(g	2(g	NUM
ejpam-3716	109	11	)	)	PUNCT
ejpam-3716	109	12	contains	contain	VERB
ejpam-3716	109	13	at	at	ADP
ejpam-3716	109	14	least	least	ADV
ejpam-3716	109	15	two	two	NUM
ejpam-3716	109	16	edge	edge	NOUN
ejpam-3716	109	17	disjoint	disjoint	NOUN
ejpam-3716	109	18	induced	induce	VERB
ejpam-3716	109	19	subgraphs	subgraph	NOUN
ejpam-3716	109	20	of	of	ADP
ejpam-3716	109	21	c3	c3	PROPN
ejpam-3716	109	22	.	.	PUNCT
ejpam-3716	110	1	by	by	ADP
ejpam-3716	110	2	theorem	theorem	NOUN
ejpam-3716	110	3	3	3	NUM
ejpam-3716	110	4	,	,	PUNCT
ejpam-3716	110	5	p	p	NOUN
ejpam-3716	110	6	3(g	3(g	NUM
ejpam-3716	110	7	)	)	PUNCT
ejpam-3716	110	8	will	will	AUX
ejpam-3716	110	9	contain	contain	VERB
ejpam-3716	110	10	two	two	NUM
ejpam-3716	110	11	copies	copy	NOUN
ejpam-3716	110	12	of	of	ADP
ejpam-3716	110	13	complete	complete	ADJ
ejpam-3716	110	14	graph	graph	NOUN
ejpam-3716	110	15	k4	k4	NOUN
ejpam-3716	110	16	,	,	PUNCT
ejpam-3716	110	17	a	a	DET
ejpam-3716	110	18	contradiction	contradiction	NOUN
ejpam-3716	110	19	.	.	PUNCT
ejpam-3716	111	1	if	if	SCONJ
ejpam-3716	111	2	g	g	NOUN
ejpam-3716	111	3	=	=	SYM
ejpam-3716	111	4	p4	p4	ADJ
ejpam-3716	111	5	,	,	PUNCT
ejpam-3716	111	6	then	then	ADV
ejpam-3716	111	7	p	p	X
ejpam-3716	111	8	(	(	PUNCT
ejpam-3716	111	9	g	g	NOUN
ejpam-3716	111	10	)	)	PUNCT
ejpam-3716	111	11	is	be	AUX
ejpam-3716	111	12	p+	p+	PROPN
ejpam-3716	111	13	3	3	NUM
ejpam-3716	111	14	with	with	ADP
ejpam-3716	111	15	∆(p+	∆(p+	PROPN
ejpam-3716	111	16	3	3	NUM
ejpam-3716	111	17	)	)	PUNCT
ejpam-3716	111	18	=	=	SYM
ejpam-3716	112	1	3	3	X
ejpam-3716	112	2	.	.	X
ejpam-3716	112	3	therefore	therefore	ADV
ejpam-3716	112	4	by	by	ADP
ejpam-3716	112	5	lemma	lemma	PROPN
ejpam-3716	112	6	1	1	NUM
ejpam-3716	112	7	,	,	PUNCT
ejpam-3716	112	8	p	p	NOUN
ejpam-3716	112	9	2(g	2(g	NUM
ejpam-3716	112	10	)	)	PUNCT
ejpam-3716	112	11	will	will	AUX
ejpam-3716	112	12	be	be	AUX
ejpam-3716	112	13	unicyclic	unicyclic	ADJ
ejpam-3716	112	14	.	.	PUNCT
ejpam-3716	113	1	by	by	ADP
ejpam-3716	113	2	theorem	theorem	NOUN
ejpam-3716	113	3	3	3	NUM
ejpam-3716	113	4	,	,	PUNCT
ejpam-3716	113	5	p	p	NOUN
ejpam-3716	113	6	3(g	3(g	NUM
ejpam-3716	113	7	)	)	PUNCT
ejpam-3716	113	8	will	will	AUX
ejpam-3716	113	9	contain	contain	VERB
ejpam-3716	113	10	k4	k4	NOUN
ejpam-3716	113	11	.	.	PUNCT
ejpam-3716	114	1	hence	hence	ADV
ejpam-3716	114	2	π3(p	π3(p	NUM
ejpam-3716	114	3	3(g	3(g	NUM
ejpam-3716	114	4	)	)	PUNCT
ejpam-3716	114	5	)	)	PUNCT
ejpam-3716	115	1	=	=	SYM
ejpam-3716	115	2	1	1	X
ejpam-3716	115	3	.	.	X
ejpam-3716	115	4	theorem	theorem	VERB
ejpam-3716	115	5	8	8	NUM
ejpam-3716	115	6	.	.	PUNCT
ejpam-3716	116	1	there	there	PRON
ejpam-3716	116	2	is	be	VERB
ejpam-3716	116	3	only	only	ADV
ejpam-3716	116	4	one	one	NUM
ejpam-3716	116	5	graph	graph	NOUN
ejpam-3716	116	6	p3	p3	NOUN
ejpam-3716	116	7	whose	whose	DET
ejpam-3716	116	8	fourth	fourth	ADJ
ejpam-3716	116	9	plick	plick	NOUN
ejpam-3716	116	10	graph	graph	NOUN
ejpam-3716	116	11	p	p	PROPN
ejpam-3716	116	12	4(g	4(g	NUM
ejpam-3716	116	13	)	)	PUNCT
ejpam-3716	116	14	has	have	VERB
ejpam-3716	116	15	pointoutercoarseness	pointoutercoarseness	ADJ
ejpam-3716	116	16	number	number	NOUN
ejpam-3716	116	17	1	1	NUM
ejpam-3716	116	18	.	.	PUNCT
ejpam-3716	117	1	proof	proof	NOUN
ejpam-3716	117	2	.	.	PUNCT
ejpam-3716	118	1	the	the	DET
ejpam-3716	118	2	proof	proof	NOUN
ejpam-3716	118	3	is	be	AUX
ejpam-3716	118	4	similar	similar	ADJ
ejpam-3716	118	5	to	to	AUX
ejpam-3716	118	6	theorem	theorem	VERB
ejpam-3716	118	7	7	7	NUM
ejpam-3716	118	8	.	.	PUNCT
ejpam-3716	118	9	theorem	theorem	VERB
ejpam-3716	118	10	9	9	NUM
ejpam-3716	118	11	.	.	PUNCT
ejpam-3716	118	12	for	for	ADP
ejpam-3716	118	13	n	n	X
ejpam-3716	118	14	≥	≥	NUM
ejpam-3716	118	15	5	5	NUM
ejpam-3716	118	16	,	,	PUNCT
ejpam-3716	118	17	there	there	PRON
ejpam-3716	118	18	is	be	VERB
ejpam-3716	118	19	no	no	DET
ejpam-3716	118	20	graph	graph	NOUN
ejpam-3716	118	21	whose	whose	DET
ejpam-3716	118	22	nth	nth	NOUN
ejpam-3716	118	23	plick	plick	NOUN
ejpam-3716	118	24	graph	graph	NOUN
ejpam-3716	118	25	pn(g	pn(g	NOUN
ejpam-3716	118	26	)	)	PUNCT
ejpam-3716	118	27	has	have	VERB
ejpam-3716	118	28	pointoutercoarseness	pointoutercoarseness	ADJ
ejpam-3716	118	29	number	number	NOUN
ejpam-3716	118	30	1	1	NUM
ejpam-3716	118	31	.	.	PUNCT
ejpam-3716	119	1	proof	proof	NOUN
ejpam-3716	119	2	.	.	PUNCT
ejpam-3716	120	1	assume	assume	VERB
ejpam-3716	120	2	π3(p	π3(p	NUM
ejpam-3716	120	3	4(g	4(g	NUM
ejpam-3716	120	4	)	)	PUNCT
ejpam-3716	120	5	)	)	PUNCT
ejpam-3716	121	1	=	=	PUNCT
ejpam-3716	121	2	1	1	X
ejpam-3716	121	3	.	.	PUNCT
ejpam-3716	121	4	then	then	ADV
ejpam-3716	121	5	p	p	NOUN
ejpam-3716	121	6	3(g	3(g	NUM
ejpam-3716	121	7	)	)	PUNCT
ejpam-3716	121	8	must	must	AUX
ejpam-3716	121	9	satisfy	satisfy	VERB
ejpam-3716	121	10	the	the	DET
ejpam-3716	121	11	hypothesis	hypothesis	NOUN
ejpam-3716	121	12	of	of	ADP
ejpam-3716	121	13	theorem	theorem	NOUN
ejpam-3716	121	14	5	5	NUM
ejpam-3716	121	15	.	.	PUNCT
ejpam-3716	121	16	clearly	clearly	ADV
ejpam-3716	121	17	∆(p	∆(p	NOUN
ejpam-3716	121	18	3(g	3(g	NUM
ejpam-3716	121	19	)	)	PUNCT
ejpam-3716	121	20	)	)	PUNCT
ejpam-3716	121	21	≤	≤	ADV
ejpam-3716	121	22	3	3	NUM
ejpam-3716	121	23	and	and	CCONJ
ejpam-3716	121	24	is	be	AUX
ejpam-3716	121	25	unicyclic	unicyclic	ADJ
ejpam-3716	121	26	or	or	CCONJ
ejpam-3716	121	27	a	a	DET
ejpam-3716	121	28	tree	tree	NOUN
ejpam-3716	121	29	or	or	CCONJ
ejpam-3716	121	30	a	a	DET
ejpam-3716	121	31	path	path	NOUN
ejpam-3716	121	32	.	.	PUNCT
ejpam-3716	122	1	thus	thus	ADV
ejpam-3716	122	2	there	there	PRON
ejpam-3716	122	3	does	do	AUX
ejpam-3716	122	4	not	not	PART
ejpam-3716	122	5	exist	exist	VERB
ejpam-3716	122	6	any	any	DET
ejpam-3716	122	7	graph	graph	NOUN
ejpam-3716	122	8	whose	whose	DET
ejpam-3716	122	9	nth;n	nth;n	ADJ
ejpam-3716	122	10	≥	≥	NOUN
ejpam-3716	122	11	5	5	NUM
ejpam-3716	122	12	plick	plick	NOUN
ejpam-3716	122	13	graph	graph	NOUN
ejpam-3716	122	14	have	have	VERB
ejpam-3716	122	15	point	point	NOUN
ejpam-3716	122	16	-	-	PUNCT
ejpam-3716	122	17	outercoarseness	outercoarseness	NOUN
ejpam-3716	122	18	one	one	NUM
ejpam-3716	122	19	.	.	PUNCT
ejpam-3716	123	1	acknowledgements	acknowledgement	NOUN
ejpam-3716	123	2	the	the	DET
ejpam-3716	123	3	authors	author	NOUN
ejpam-3716	123	4	are	be	AUX
ejpam-3716	123	5	thankful	thankful	ADJ
ejpam-3716	123	6	to	to	ADP
ejpam-3716	123	7	anonymous	anonymous	ADJ
ejpam-3716	123	8	referees	referee	NOUN
ejpam-3716	123	9	for	for	ADP
ejpam-3716	123	10	their	their	PRON
ejpam-3716	123	11	useful	useful	ADJ
ejpam-3716	123	12	suggestions	suggestion	NOUN
ejpam-3716	123	13	to	to	ADP
ejpam-3716	123	14	the	the	DET
ejpam-3716	123	15	improvement	improvement	NOUN
ejpam-3716	123	16	of	of	ADP
ejpam-3716	123	17	the	the	DET
ejpam-3716	123	18	paper	paper	NOUN
ejpam-3716	123	19	.	.	PUNCT
ejpam-3716	124	1	references	reference	NOUN
ejpam-3716	124	2	[	[	X
ejpam-3716	124	3	1	1	NUM
ejpam-3716	124	4	]	]	PUNCT
ejpam-3716	124	5	.	.	PUNCT
ejpam-3716	125	1	b	b	X
ejpam-3716	125	2	basavanagoud	basavanagoud	NOUN
ejpam-3716	125	3	,	,	PUNCT
ejpam-3716	125	4	k	k	PROPN
ejpam-3716	125	5	mirajakar	mirajakar	NOUN
ejpam-3716	125	6	.	.	PUNCT
ejpam-3716	126	1	on	on	ADP
ejpam-3716	126	2	plick	plick	NOUN
ejpam-3716	126	3	graphs	graph	NOUN
ejpam-3716	126	4	with	with	ADP
ejpam-3716	126	5	coarseness	coarseness	NOUN
ejpam-3716	126	6	number	number	NOUN
ejpam-3716	126	7	one	one	NUM
ejpam-3716	126	8	.	.	PUNCT
ejpam-3716	127	1	math	math	PROPN
ejpam-3716	127	2	comput	comput	PROPN
ejpam-3716	127	3	sci	sci	PROPN
ejpam-3716	127	4	,	,	PUNCT
ejpam-3716	127	5	5:7	5:7	NUM
ejpam-3716	127	6	-	-	SYM
ejpam-3716	127	7	10	10	NUM
ejpam-3716	127	8	,	,	PUNCT
ejpam-3716	127	9	2011	2011	NUM
ejpam-3716	127	10	.	.	PUNCT
ejpam-3716	128	1	[	[	X
ejpam-3716	128	2	2	2	NUM
ejpam-3716	128	3	]	]	PUNCT
ejpam-3716	128	4	.	.	PUNCT
ejpam-3716	129	1	g	g	PROPN
ejpam-3716	129	2	chartrand	chartrand	NOUN
ejpam-3716	129	3	,	,	PUNCT
ejpam-3716	129	4	d	d	X
ejpam-3716	129	5	geller	geller	PROPN
ejpam-3716	129	6	,	,	PUNCT
ejpam-3716	129	7	s	s	VERB
ejpam-3716	129	8	hedetniemi	hedetniemi	NOUN
ejpam-3716	129	9	.	.	PUNCT
ejpam-3716	130	1	graphs	graph	NOUN
ejpam-3716	130	2	with	with	ADP
ejpam-3716	130	3	forbidden	forbid	VERB
ejpam-3716	130	4	subgraphs	subgraph	NOUN
ejpam-3716	130	5	.	.	PUNCT
ejpam-3716	131	1	j	j	PROPN
ejpam-3716	131	2	comb	comb	NOUN
ejpam-3716	131	3	theory	theory	NOUN
ejpam-3716	131	4	,	,	PUNCT
ejpam-3716	131	5	10:12	10:12	NUM
ejpam-3716	131	6	-	-	SYM
ejpam-3716	131	7	41	41	NUM
ejpam-3716	131	8	,	,	PUNCT
ejpam-3716	131	9	1971	1971	NUM
ejpam-3716	131	10	.	.	PUNCT
ejpam-3716	132	1	[	[	X
ejpam-3716	132	2	3	3	NUM
ejpam-3716	132	3	]	]	PUNCT
ejpam-3716	132	4	.	.	PUNCT
ejpam-3716	133	1	g	g	PROPN
ejpam-3716	133	2	chartrand	chartrand	PROPN
ejpam-3716	133	3	,	,	PUNCT
ejpam-3716	133	4	h	h	PROPN
ejpam-3716	133	5	kronk	kronk	ADV
ejpam-3716	133	6	,	,	PUNCT
ejpam-3716	133	7	c	c	PROPN
ejpam-3716	133	8	e	e	NOUN
ejpam-3716	133	9	wall	wall	NOUN
ejpam-3716	133	10	.	.	PUNCT
ejpam-3716	134	1	the	the	DET
ejpam-3716	134	2	point	point	NOUN
ejpam-3716	134	3	-	-	PUNCT
ejpam-3716	134	4	arboricity	arboricity	NOUN
ejpam-3716	134	5	of	of	ADP
ejpam-3716	134	6	graphs	graph	NOUN
ejpam-3716	134	7	.	.	PUNCT
ejpam-3716	135	1	israel	israel	PROPN
ejpam-3716	135	2	j	j	PROPN
ejpam-3716	135	3	math	math	PROPN
ejpam-3716	135	4	,	,	PUNCT
ejpam-3716	135	5	6:168	6:168	NOUN
ejpam-3716	135	6	-	-	SYM
ejpam-3716	135	7	175	175	NUM
ejpam-3716	135	8	,	,	PUNCT
ejpam-3716	135	9	1968	1968	NUM
ejpam-3716	135	10	.	.	PUNCT
ejpam-3716	136	1	[	[	X
ejpam-3716	136	2	4	4	NUM
ejpam-3716	136	3	]	]	PUNCT
ejpam-3716	136	4	.	.	PUNCT
ejpam-3716	137	1	f	f	PROPN
ejpam-3716	137	2	harary	harary	PROPN
ejpam-3716	137	3	.	.	PUNCT
ejpam-3716	138	1	graph	graph	NOUN
ejpam-3716	138	2	theory	theory	NOUN
ejpam-3716	138	3	.	.	PUNCT
ejpam-3716	139	1	addison	addison	PROPN
ejpam-3716	139	2	-	-	PUNCT
ejpam-3716	139	3	wesely	wesely	ADV
ejpam-3716	139	4	reading	read	VERB
ejpam-3716	139	5	mass	mass	NOUN
ejpam-3716	139	6	1969	1969	NUM
ejpam-3716	139	7	.	.	PUNCT
ejpam-3716	140	1	[	[	X
ejpam-3716	140	2	5	5	NUM
ejpam-3716	140	3	]	]	PUNCT
ejpam-3716	140	4	.	.	PUNCT
ejpam-3716	141	1	j	j	PROPN
ejpam-3716	141	2	mitchem	mitchem	PROPN
ejpam-3716	141	3	.	.	PUNCT
ejpam-3716	142	1	the	the	DET
ejpam-3716	142	2	point	point	NOUN
ejpam-3716	142	3	-	-	PUNCT
ejpam-3716	142	4	outercoarseness	outercoarseness	NOUN
ejpam-3716	142	5	of	of	ADP
ejpam-3716	142	6	n	n	CCONJ
ejpam-3716	142	7	-	-	PUNCT
ejpam-3716	142	8	partite	partite	ADJ
ejpam-3716	142	9	graphs	graph	NOUN
ejpam-3716	142	10	.	.	PUNCT
ejpam-3716	143	1	compositio	compositio	PROPN
ejpam-3716	143	2	mathematica	mathematica	PROPN
ejpam-3716	143	3	26:101	26:101	PROPN
ejpam-3716	143	4	-	-	PUNCT
ejpam-3716	143	5	110	110	NUM
ejpam-3716	143	6	,	,	PUNCT
ejpam-3716	143	7	1973	1973	NUM
ejpam-3716	143	8	.	.	PUNCT
ejpam-3716	144	1	[	[	X
ejpam-3716	144	2	6	6	NUM
ejpam-3716	144	3	]	]	PUNCT
ejpam-3716	144	4	.	.	PUNCT
ejpam-3716	145	1	v	v	X
ejpam-3716	145	2	r	r	NOUN
ejpam-3716	145	3	kulli	kulli	PROPN
ejpam-3716	145	4	,	,	PUNCT
ejpam-3716	145	5	b	b	PROPN
ejpam-3716	145	6	basavanagoud	basavanagoud	NOUN
ejpam-3716	145	7	.	.	PUNCT
ejpam-3716	146	1	characterization	characterization	NOUN
ejpam-3716	146	2	of	of	ADP
ejpam-3716	146	3	planar	planar	ADJ
ejpam-3716	146	4	plick	plick	NOUN
ejpam-3716	146	5	graphs	graph	NOUN
ejpam-3716	146	6	.	.	PUNCT
ejpam-3716	147	1	discussiones	discussione	NOUN
ejpam-3716	147	2	mathematicae	mathematicae	VERB
ejpam-3716	147	3	graph	graph	NOUN
ejpam-3716	147	4	theory	theory	NOUN
ejpam-3716	147	5	24:41	24:41	NUM
ejpam-3716	147	6	-	-	SYM
ejpam-3716	147	7	45	45	NUM
ejpam-3716	147	8	,	,	PUNCT
ejpam-3716	147	9	2004	2004	NUM
ejpam-3716	147	10	.	.	PUNCT
ejpam-3716	148	1	[	[	X
ejpam-3716	148	2	7	7	NUM
ejpam-3716	148	3	]	]	PUNCT
ejpam-3716	148	4	.	.	PUNCT
ejpam-3716	149	1	v	v	X
ejpam-3716	149	2	r	r	NOUN
ejpam-3716	149	3	kulli	kulli	PROPN
ejpam-3716	149	4	.	.	PUNCT
ejpam-3716	150	1	on	on	ADP
ejpam-3716	150	2	minimally	minimally	ADV
ejpam-3716	150	3	nonouterplanar	nonouterplanar	NOUN
ejpam-3716	150	4	graphs	graph	NOUN
ejpam-3716	150	5	.	.	PUNCT
ejpam-3716	151	1	proceedings	proceeding	NOUN
ejpam-3716	151	2	of	of	ADP
ejpam-3716	151	3	the	the	DET
ejpam-3716	151	4	indian	indian	ADJ
ejpam-3716	151	5	national	national	PROPN
ejpam-3716	151	6	science	science	PROPN
ejpam-3716	151	7	academy	academy	PROPN
ejpam-3716	151	8	41a:275	41a:275	PROPN
ejpam-3716	151	9	-	-	SYM
ejpam-3716	151	10	280	280	NUM
ejpam-3716	151	11	,	,	PUNCT
ejpam-3716	151	12	1975	1975	NUM
ejpam-3716	151	13	.	.	PUNCT
ejpam-3716	152	1	v.	v.	ADP
ejpam-3716	152	2	lokesha	lokesha	PROPN
ejpam-3716	152	3	,	,	PUNCT
ejpam-3716	152	4	s.	s.	PROPN
ejpam-3716	152	5	m.	m.	PROPN
ejpam-3716	152	6	hosamani	hosamani	PROPN
ejpam-3716	152	7	,	,	PUNCT
ejpam-3716	152	8	s.	s.	PROPN
ejpam-3716	152	9	v.	v.	PROPN
ejpam-3716	152	10	patil	patil	PROPN
ejpam-3716	152	11	/	/	SYM
ejpam-3716	152	12	eur	eur	PROPN
ejpam-3716	152	13	.	.	PUNCT
ejpam-3716	153	1	j.	j.	PROPN
ejpam-3716	153	2	pure	pure	PROPN
ejpam-3716	153	3	appl	appl	PROPN
ejpam-3716	153	4	.	.	PROPN
ejpam-3716	153	5	math	math	PROPN
ejpam-3716	153	6	,	,	PUNCT
ejpam-3716	153	7	13	13	NUM
ejpam-3716	153	8	(	(	PUNCT
ejpam-3716	153	9	5	5	NUM
ejpam-3716	153	10	)	)	PUNCT
ejpam-3716	153	11	(	(	PUNCT
ejpam-3716	153	12	2020	2020	NUM
ejpam-3716	153	13	)	)	PUNCT
ejpam-3716	153	14	,	,	PUNCT
ejpam-3716	153	15	1300	1300	NUM
ejpam-3716	153	16	-	-	SYM
ejpam-3716	153	17	1305	1305	NUM
ejpam-3716	153	18	1305	1305	NUM
ejpam-3716	154	1	[	[	X
ejpam-3716	154	2	8	8	NUM
ejpam-3716	154	3	]	]	PUNCT
ejpam-3716	154	4	.	.	PUNCT
ejpam-3716	155	1	k.kuratowski	k.kuratowski	PROPN
ejpam-3716	155	2	.	.	PUNCT
ejpam-3716	156	1	sur	sur	PROPN
ejpam-3716	156	2	le	le	X
ejpam-3716	156	3	probleme	probleme	PROPN
ejpam-3716	156	4	des	des	X
ejpam-3716	156	5	courbes	courbes	PROPN
ejpam-3716	156	6	gauches	gauche	NOUN
ejpam-3716	156	7	en	en	ADP
ejpam-3716	156	8	topologie	topologie	NOUN
ejpam-3716	156	9	.	.	PUNCT
ejpam-3716	157	1	fund.math	fund.math	NUM
ejpam-3716	157	2	,	,	PUNCT
ejpam-3716	157	3	15:271283,1930	15:271283,1930	NOUN
ejpam-3716	157	4	.	.	PUNCT
ejpam-3716	158	1	[	[	X
ejpam-3716	158	2	9	9	NUM
ejpam-3716	158	3	]	]	PUNCT
ejpam-3716	158	4	.	.	PUNCT
ejpam-3716	159	1	h	h	PROPN
ejpam-3716	160	1	p	p	PROPN
ejpam-3716	160	2	patil	patil	PROPN
ejpam-3716	160	3	,	,	PUNCT
ejpam-3716	160	4	u	u	NOUN
ejpam-3716	160	5	rengarasu	rengarasu	NOUN
ejpam-3716	160	6	.	.	PUNCT
ejpam-3716	161	1	the	the	DET
ejpam-3716	161	2	vertex	vertex	NOUN
ejpam-3716	161	3	-	-	PUNCT
ejpam-3716	161	4	coarseness	coarseness	NOUN
ejpam-3716	161	5	of	of	ADP
ejpam-3716	161	6	iterated	iterated	ADJ
ejpam-3716	161	7	line	line	NOUN
ejpam-3716	161	8	graphs	graph	NOUN
ejpam-3716	161	9	.	.	PUNCT
ejpam-3716	162	1	graph	graph	NOUN
ejpam-3716	162	2	theory	theory	NOUN
ejpam-3716	162	3	and	and	CCONJ
ejpam-3716	162	4	its	its	PRON
ejpam-3716	162	5	applications(eds	applications(ed	NOUN
ejpam-3716	162	6	)	)	PUNCT
ejpam-3716	162	7	s	s	VERB
ejpam-3716	162	8	arumugam	arumugam	NOUN
ejpam-3716	162	9	et	et	PROPN
ejpam-3716	162	10	al	al	PROPN
ejpam-3716	162	11	.	.	PROPN
ejpam-3716	162	12	,	,	PUNCT
ejpam-3716	162	13	tata	tata	PROPN
ejpam-3716	162	14	mcgraw	mcgraw	PROPN
ejpam-3716	162	15	-	-	PUNCT
ejpam-3716	162	16	hill	hill	NOUN
ejpam-3716	162	17	publishing	publish	VERB
ejpam-3716	162	18	company	company	NOUN
ejpam-3716	162	19	limited	limit	VERB
ejpam-3716	162	20	new	new	ADJ
ejpam-3716	162	21	-	-	PUNCT
ejpam-3716	162	22	delhi	delhi	ADJ
ejpam-3716	162	23	109	109	NUM
ejpam-3716	162	24	-	-	SYM
ejpam-3716	162	25	120	120	NUM
ejpam-3716	162	26	,	,	PUNCT
ejpam-3716	162	27	1996	1996	NUM
ejpam-3716	162	28	.	.	PUNCT