id	sid	tid	token	lemma	pos
asir-2054	1	1	applied	apply	VERB
asir-2054	1	2	science	science	NOUN
asir-2054	1	3	and	and	CCONJ
asir-2054	1	4	innovative	innovative	ADJ
asir-2054	1	5	research	research	NOUN
asir-2054	1	6	issn	issn	VERB
asir-2054	1	7	2474	2474	NUM
asir-2054	1	8	-	-	SYM
asir-2054	1	9	4972	4972	NUM
asir-2054	1	10	(	(	PUNCT
asir-2054	1	11	print	print	NOUN
asir-2054	1	12	)	)	PUNCT
asir-2054	1	13	issn	issn	VERB
asir-2054	1	14	2474	2474	NUM
asir-2054	1	15	-	-	SYM
asir-2054	1	16	4980	4980	NUM
asir-2054	1	17	(	(	PUNCT
asir-2054	1	18	online	online	ADJ
asir-2054	1	19	)	)	PUNCT
asir-2054	1	20	vol	vol	NOUN
asir-2054	1	21	.	.	PROPN
asir-2054	2	1	3	3	NUM
asir-2054	2	2	,	,	PUNCT
asir-2054	2	3	no	no	INTJ
asir-2054	2	4	.	.	NOUN
asir-2054	2	5	2	2	NUM
asir-2054	2	6	,	,	PUNCT
asir-2054	2	7	2019	2019	NUM
asir-2054	2	8	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2054	2	9	85	85	NUM
asir-2054	2	10	original	original	ADJ
asir-2054	2	11	paper	paper	NOUN
asir-2054	2	12	list	list	NOUN
asir-2054	2	13	edge	edge	NOUN
asir-2054	2	14	colorings	coloring	NOUN
asir-2054	2	15	of	of	ADP
asir-2054	2	16	planar	planar	ADJ
asir-2054	2	17	graphs	graph	NOUN
asir-2054	2	18	with	with	ADP
asir-2054	2	19	7	7	NUM
asir-2054	2	20	-	-	PUNCT
asir-2054	2	21	cycles	cycle	NOUN
asir-2054	2	22	containing	contain	VERB
asir-2054	2	23	at	at	ADP
asir-2054	2	24	most	most	ADV
asir-2054	2	25	two	two	NUM
asir-2054	2	26	chords	chord	NOUN
asir-2054	2	27	wenwen	wenwen	ADJ
asir-2054	2	28	zhang1	zhang1	PROPN
asir-2054	2	29	*	*	SYM
asir-2054	2	30	1	1	NUM
asir-2054	2	31	school	school	NOUN
asir-2054	2	32	of	of	ADP
asir-2054	2	33	date	date	NOUN
asir-2054	2	34	and	and	CCONJ
asir-2054	2	35	computer	computer	NOUN
asir-2054	2	36	science	science	NOUN
asir-2054	2	37	,	,	PUNCT
asir-2054	2	38	shandong	shandong	PROPN
asir-2054	2	39	women	women	PROPN
asir-2054	2	40	’s	’s	PART
asir-2054	2	41	university	university	PROPN
asir-2054	2	42	,	,	PUNCT
asir-2054	2	43	jinan	jinan	PROPN
asir-2054	2	44	,	,	PUNCT
asir-2054	2	45	250300	250300	NUM
asir-2054	2	46	,	,	PUNCT
asir-2054	2	47	china	china	PROPN
asir-2054	2	48	received	receive	VERB
asir-2054	2	49	:	:	PUNCT
asir-2054	2	50	may	may	AUX
asir-2054	2	51	5	5	NUM
asir-2054	2	52	,	,	PUNCT
asir-2054	2	53	2019	2019	NUM
asir-2054	2	54	accepted	accept	VERB
asir-2054	2	55	:	:	PUNCT
asir-2054	2	56	may	may	AUX
asir-2054	2	57	19	19	NUM
asir-2054	2	58	,	,	PUNCT
asir-2054	2	59	2019	2019	NUM
asir-2054	2	60	online	online	ADV
asir-2054	2	61	published	publish	VERB
asir-2054	2	62	:	:	PUNCT
asir-2054	2	63	may	may	AUX
asir-2054	2	64	27	27	NUM
asir-2054	2	65	,	,	PUNCT
asir-2054	2	66	2019	2019	NUM
asir-2054	2	67	doi:10.22158	doi:10.22158	NOUN
asir-2054	2	68	/	/	SYM
asir-2054	2	69	asir.v3n2p85	asir.v3n2p85	PROPN
asir-2054	2	70	url	url	PROPN
asir-2054	2	71	:	:	PUNCT
asir-2054	2	72	http://dx.doi.org/10.22158/asir.v3n2p85	http://dx.doi.org/10.22158/asir.v3n2p85	PROPN
asir-2054	2	73	abstract	abstract	NOUN
asir-2054	2	74	in	in	ADP
asir-2054	2	75	this	this	DET
asir-2054	2	76	paper	paper	NOUN
asir-2054	2	77	we	we	PRON
asir-2054	2	78	prove	prove	VERB
asir-2054	2	79	that	that	SCONJ
asir-2054	2	80	if	if	SCONJ
asir-2054	2	81	g	g	PROPN
asir-2054	2	82	is	be	AUX
asir-2054	2	83	a	a	DET
asir-2054	2	84	planar	planar	ADJ
asir-2054	2	85	graph	graph	NOUN
asir-2054	2	86	,	,	PUNCT
asir-2054	2	87	and	and	CCONJ
asir-2054	2	88	each	each	DET
asir-2054	2	89	7	7	NUM
asir-2054	2	90	-	-	PUNCT
asir-2054	2	91	cycle	cycle	NOUN
asir-2054	2	92	contains	contain	VERB
asir-2054	2	93	at	at	ADP
asir-2054	2	94	most	most	ADV
asir-2054	2	95	two	two	NUM
asir-2054	2	96	chords	chord	NOUN
asir-2054	2	97	,	,	PUNCT
asir-2054	2	98	then	then	ADV
asir-2054	2	99	g	g	PROPN
asir-2054	2	100	is	be	AUX
asir-2054	2	101	edge	edge	NOUN
asir-2054	2	102	-	-	PUNCT
asir-2054	2	103	k	k	NOUN
asir-2054	2	104	-	-	NOUN
asir-2054	2	105	choosable	choosable	NOUN
asir-2054	2	106	,	,	PUNCT
asir-2054	2	107	where	where	SCONJ
asir-2054	2	108	k	k	PROPN
asir-2054	2	109	=	=	SYM
asir-2054	2	110	max{8	max{8	PROPN
asir-2054	2	111	,	,	PUNCT
asir-2054	2	112	∆(g	∆(g	NOUN
asir-2054	2	113	)	)	PUNCT
asir-2054	3	1	+	+	NOUN
asir-2054	3	2	1	1	NUM
asir-2054	3	3	}	}	PUNCT
asir-2054	3	4	.	.	PUNCT
asir-2054	4	1	keywords	keyword	NOUN
asir-2054	4	2	list	list	VERB
asir-2054	4	3	edge	edge	NOUN
asir-2054	4	4	coloring	coloring	NOUN
asir-2054	4	5	,	,	PUNCT
asir-2054	4	6	planar	planar	ADJ
asir-2054	4	7	graph	graph	NOUN
asir-2054	4	8	,	,	PUNCT
asir-2054	4	9	cycle	cycle	NOUN
asir-2054	4	10	1	1	NUM
asir-2054	4	11	.	.	PUNCT
asir-2054	5	1	introduction	introduction	NOUN
asir-2054	5	2	all	all	DET
asir-2054	5	3	graphs	graph	NOUN
asir-2054	5	4	considered	consider	VERB
asir-2054	5	5	here	here	ADV
asir-2054	5	6	are	be	AUX
asir-2054	5	7	finite	finite	ADJ
asir-2054	5	8	,	,	PUNCT
asir-2054	5	9	simple	simple	ADJ
asir-2054	5	10	and	and	CCONJ
asir-2054	5	11	undirected	undirected	ADJ
asir-2054	5	12	.	.	PUNCT
asir-2054	6	1	let	let	VERB
asir-2054	6	2	g	g	PRON
asir-2054	6	3	be	be	AUX
asir-2054	6	4	a	a	DET
asir-2054	6	5	graph	graph	NOUN
asir-2054	6	6	with	with	ADP
asir-2054	6	7	vertex	vertex	NOUN
asir-2054	6	8	set	set	VERB
asir-2054	6	9	v	v	NOUN
asir-2054	6	10	(	(	PUNCT
asir-2054	6	11	g	g	NOUN
asir-2054	6	12	)	)	PUNCT
asir-2054	6	13	and	and	CCONJ
asir-2054	6	14	edge	edge	VERB
asir-2054	6	15	set	set	VERB
asir-2054	6	16	e(g	e(g	PROPN
asir-2054	6	17	)	)	PUNCT
asir-2054	6	18	.	.	PUNCT
asir-2054	7	1	for	for	ADP
asir-2054	7	2	vertex	vertex	NOUN
asir-2054	7	3	v	v	ADP
asir-2054	7	4	∈	∈	PROPN
asir-2054	7	5	v	v	NOUN
asir-2054	7	6	(	(	PUNCT
asir-2054	7	7	g	g	NOUN
asir-2054	7	8	)	)	PUNCT
asir-2054	7	9	,	,	PUNCT
asir-2054	7	10	let	let	VERB
asir-2054	7	11	e(v	e(v	NOUN
asir-2054	7	12	)	)	PUNCT
asir-2054	7	13	be	be	VERB
asir-2054	7	14	the	the	DET
asir-2054	7	15	set	set	NOUN
asir-2054	7	16	of	of	ADP
asir-2054	7	17	edges	edge	NOUN
asir-2054	7	18	incident	incident	NOUN
asir-2054	7	19	with	with	ADP
asir-2054	7	20	v.	v.	ADP
asir-2054	7	21	the	the	DET
asir-2054	7	22	degree	degree	NOUN
asir-2054	7	23	of	of	ADP
asir-2054	7	24	v	v	NOUN
asir-2054	7	25	in	in	ADP
asir-2054	7	26	g	g	NOUN
asir-2054	7	27	,	,	PUNCT
asir-2054	7	28	denoted	denote	VERB
asir-2054	7	29	d(v	d(v	PROPN
asir-2054	7	30	)	)	PUNCT
asir-2054	7	31	,	,	PUNCT
asir-2054	7	32	is	be	AUX
asir-2054	7	33	the	the	DET
asir-2054	7	34	cardinality	cardinality	NOUN
asir-2054	7	35	of	of	ADP
asir-2054	7	36	e(v	e(v	NOUN
asir-2054	7	37	)	)	PUNCT
asir-2054	7	38	.	.	PUNCT
asir-2054	8	1	a	a	DET
asir-2054	8	2	k	k	NOUN
asir-2054	8	3	-	-	NOUN
asir-2054	8	4	vertex	vertex	NOUN
asir-2054	8	5	,	,	PUNCT
asir-2054	8	6	k−-vertex	k−-vertex	NOUN
asir-2054	8	7	or	or	CCONJ
asir-2054	8	8	k+-vertex	k+-vertex	PROPN
asir-2054	8	9	is	be	AUX
asir-2054	8	10	a	a	DET
asir-2054	8	11	vertex	vertex	NOUN
asir-2054	8	12	of	of	ADP
asir-2054	8	13	degree	degree	NOUN
asir-2054	8	14	k	k	PROPN
asir-2054	8	15	,	,	PUNCT
asir-2054	8	16	at	at	ADP
asir-2054	8	17	most	most	ADJ
asir-2054	8	18	k	k	NOUN
asir-2054	8	19	or	or	CCONJ
asir-2054	8	20	at	at	ADP
asir-2054	8	21	least	least	ADJ
asir-2054	8	22	k	k	NOUN
asir-2054	8	23	,	,	PUNCT
asir-2054	8	24	respectively	respectively	ADV
asir-2054	8	25	.	.	PUNCT
asir-2054	9	1	we	we	PRON
asir-2054	9	2	denote	denote	VERB
asir-2054	9	3	the	the	DET
asir-2054	9	4	maximum	maximum	ADJ
asir-2054	9	5	degree	degree	NOUN
asir-2054	9	6	of	of	ADP
asir-2054	9	7	g	g	NOUN
asir-2054	9	8	by	by	ADP
asir-2054	9	9	∆(g	∆(g	PROPN
asir-2054	9	10	)	)	PUNCT
asir-2054	9	11	and	and	CCONJ
asir-2054	9	12	minimum	minimum	NOUN
asir-2054	9	13	degree	degree	NOUN
asir-2054	9	14	of	of	ADP
asir-2054	9	15	g	g	NOUN
asir-2054	9	16	by	by	ADP
asir-2054	9	17	δ(g	δ(g	NOUN
asir-2054	9	18	)	)	PUNCT
asir-2054	9	19	.	.	PUNCT
asir-2054	10	1	a	a	PRON
asir-2054	10	2	k	k	NOUN
asir-2054	10	3	(	(	PUNCT
asir-2054	10	4	or	or	CCONJ
asir-2054	10	5	k+)-vertex	k+)-vertex	NOUN
asir-2054	10	6	adjacent	adjacent	ADJ
asir-2054	10	7	to	to	ADP
asir-2054	10	8	a	a	DET
asir-2054	10	9	vertex	vertex	NOUN
asir-2054	10	10	x	x	PRON
asir-2054	10	11	is	be	AUX
asir-2054	10	12	called	call	VERB
asir-2054	10	13	a	a	DET
asir-2054	10	14	k	k	PROPN
asir-2054	10	15	(	(	PUNCT
asir-2054	10	16	or	or	CCONJ
asir-2054	10	17	k+)-neighbor	k+)-neighbor	PROPN
asir-2054	10	18	of	of	ADP
asir-2054	10	19	x.	x.	PROPN
asir-2054	10	20	a	a	DET
asir-2054	10	21	k	k	NOUN
asir-2054	10	22	-	-	NOUN
asir-2054	10	23	cycle	cycle	NOUN
asir-2054	10	24	is	be	AUX
asir-2054	10	25	a	a	DET
asir-2054	10	26	cycle	cycle	NOUN
asir-2054	10	27	of	of	ADP
asir-2054	10	28	length	length	NOUN
asir-2054	10	29	k.	k.	PROPN
asir-2054	11	1	given	give	VERB
asir-2054	11	2	a	a	DET
asir-2054	11	3	cycle	cycle	NOUN
asir-2054	11	4	c	c	NOUN
asir-2054	11	5	of	of	ADP
asir-2054	11	6	length	length	NOUN
asir-2054	11	7	k	k	PROPN
asir-2054	11	8	in	in	ADP
asir-2054	11	9	g	g	PROPN
asir-2054	11	10	,	,	PUNCT
asir-2054	11	11	an	an	DET
asir-2054	11	12	edge	edge	NOUN
asir-2054	11	13	xy	xy	PROPN
asir-2054	11	14	∈	∈	PROPN
asir-2054	11	15	e(g)\e(c	e(g)\e(c	PROPN
asir-2054	11	16	)	)	PUNCT
asir-2054	11	17	is	be	AUX
asir-2054	11	18	called	call	VERB
asir-2054	11	19	a	a	DET
asir-2054	11	20	chord	chord	NOUN
asir-2054	11	21	of	of	ADP
asir-2054	11	22	c	c	PROPN
asir-2054	11	23	if	if	SCONJ
asir-2054	11	24	x	x	PROPN
asir-2054	11	25	,	,	PUNCT
asir-2054	11	26	y	y	PROPN
asir-2054	11	27	∈	∈	PROPN
asir-2054	11	28	v	v	NOUN
asir-2054	11	29	(	(	PUNCT
asir-2054	11	30	c	c	NOUN
asir-2054	11	31	)	)	PUNCT
asir-2054	11	32	.	.	PUNCT
asir-2054	12	1	such	such	DET
asir-2054	12	2	a	a	DET
asir-2054	12	3	cycle	cycle	NOUN
asir-2054	12	4	c	c	NOUN
asir-2054	12	5	is	be	AUX
asir-2054	12	6	also	also	ADV
asir-2054	12	7	called	call	VERB
asir-2054	12	8	a	a	DET
asir-2054	12	9	chordal	chordal	NOUN
asir-2054	12	10	-	-	PUNCT
asir-2054	12	11	k	k	NOUN
asir-2054	12	12	-	-	NOUN
asir-2054	12	13	cycle	cycle	NOUN
asir-2054	12	14	.	.	PUNCT
asir-2054	13	1	let	let	VERB
asir-2054	13	2	g	g	PRON
asir-2054	13	3	be	be	AUX
asir-2054	13	4	a	a	DET
asir-2054	13	5	plane	plane	NOUN
asir-2054	13	6	graph	graph	NOUN
asir-2054	13	7	,	,	PUNCT
asir-2054	13	8	f	f	PROPN
asir-2054	13	9	(	(	PUNCT
asir-2054	13	10	g	g	NOUN
asir-2054	13	11	)	)	PUNCT
asir-2054	13	12	be	be	VERB
asir-2054	13	13	the	the	DET
asir-2054	13	14	face	face	NOUN
asir-2054	13	15	set	set	VERB
asir-2054	13	16	of	of	ADP
asir-2054	13	17	g.	g.	PROPN
asir-2054	13	18	the	the	DET
asir-2054	13	19	degree	degree	NOUN
asir-2054	13	20	of	of	ADP
asir-2054	13	21	a	a	DET
asir-2054	13	22	face	face	NOUN
asir-2054	13	23	f	f	NOUN
asir-2054	13	24	,	,	PUNCT
asir-2054	13	25	denoted	denote	VERB
asir-2054	13	26	by	by	ADP
asir-2054	13	27	dg(f	dg(f	NOUN
asir-2054	13	28	)	)	PUNCT
asir-2054	13	29	is	be	AUX
asir-2054	13	30	the	the	DET
asir-2054	13	31	number	number	NOUN
asir-2054	13	32	of	of	ADP
asir-2054	13	33	edges	edge	NOUN
asir-2054	13	34	incident	incident	NOUN
asir-2054	13	35	with	with	ADP
asir-2054	13	36	f	f	PROPN
asir-2054	13	37	where	where	SCONJ
asir-2054	13	38	each	each	DET
asir-2054	13	39	cut	cut	NOUN
asir-2054	13	40	edge	edge	NOUN
asir-2054	13	41	is	be	AUX
asir-2054	13	42	counted	count	VERB
asir-2054	13	43	twice	twice	ADV
asir-2054	13	44	.	.	PUNCT
asir-2054	14	1	a	a	DET
asir-2054	14	2	k-	k-	PROPN
asir-2054	14	3	,	,	PUNCT
asir-2054	14	4	k+-face	k+-face	NOUN
asir-2054	14	5	is	be	AUX
asir-2054	14	6	a	a	DET
asir-2054	14	7	face	face	NOUN
asir-2054	14	8	of	of	ADP
asir-2054	14	9	degree	degree	NOUN
asir-2054	14	10	k	k	NOUN
asir-2054	14	11	,	,	PUNCT
asir-2054	14	12	at	at	ADP
asir-2054	14	13	least	least	ADJ
asir-2054	14	14	k.	k.	NOUN
asir-2054	15	1	a	a	DET
asir-2054	15	2	k	k	NOUN
asir-2054	15	3	-	-	NOUN
asir-2054	15	4	face	face	NOUN
asir-2054	15	5	of	of	ADP
asir-2054	15	6	g	g	PROPN
asir-2054	15	7	is	be	AUX
asir-2054	15	8	called	call	VERB
asir-2054	15	9	an	an	DET
asir-2054	15	10	(	(	PUNCT
asir-2054	15	11	i	i	NOUN
asir-2054	15	12	1	1	NUM
asir-2054	15	13	,	,	PUNCT
asir-2054	15	14	i	i	PRON
asir-2054	15	15	2	2	NUM
asir-2054	15	16	,	,	PUNCT
asir-2054	15	17	…	…	PUNCT
asir-2054	15	18	,	,	PUNCT
asir-2054	15	19	i	i	PRON
asir-2054	15	20	k	k	NOUN
asir-2054	15	21	)	)	PUNCT
asir-2054	15	22	-face	-face	NOUN
asir-2054	15	23	if	if	SCONJ
asir-2054	15	24	the	the	DET
asir-2054	15	25	vertices	vertex	NOUN
asir-2054	15	26	in	in	ADP
asir-2054	15	27	its	its	PRON
asir-2054	15	28	boundary	boundary	NOUN
asir-2054	15	29	are	be	AUX
asir-2054	15	30	of	of	ADP
asir-2054	15	31	degrees	degree	NOUN
asir-2054	15	32	i	i	PRON
asir-2054	15	33	1	1	NUM
asir-2054	15	34	,	,	PUNCT
asir-2054	15	35	i	i	PRON
asir-2054	15	36	2	2	NUM
asir-2054	15	37	,	,	PUNCT
asir-2054	15	38	…	…	PUNCT
asir-2054	16	1	,	,	PUNCT
asir-2054	16	2	i	i	PRON
asir-2054	16	3	k	k	PROPN
asir-2054	16	4	respectively	respectively	ADV
asir-2054	16	5	.	.	PUNCT
asir-2054	17	1	for	for	ADP
asir-2054	17	2	a	a	DET
asir-2054	17	3	vertex	vertex	NOUN
asir-2054	17	4	v	v	ADP
asir-2054	17	5	∈	∈	NOUN
asir-2054	17	6	v	v	NOUN
asir-2054	17	7	(	(	PUNCT
asir-2054	17	8	g	g	NOUN
asir-2054	17	9	)	)	PUNCT
asir-2054	17	10	,	,	PUNCT
asir-2054	17	11	we	we	PRON
asir-2054	17	12	denote	denote	VERB
asir-2054	17	13	by	by	ADP
asir-2054	17	14	fk	fk	INTJ
asir-2054	17	15	(	(	PUNCT
asir-2054	17	16	v	v	NOUN
asir-2054	17	17	)	)	PUNCT
asir-2054	17	18	the	the	DET
asir-2054	17	19	number	number	NOUN
asir-2054	17	20	of	of	ADP
asir-2054	17	21	k	k	ADJ
asir-2054	17	22	-	-	PUNCT
asir-2054	17	23	faces	face	NOUN
asir-2054	17	24	incident	incident	NOUN
asir-2054	17	25	with	with	ADP
asir-2054	17	26	v.	v.	ADP
asir-2054	17	27	a	a	DET
asir-2054	17	28	graph	graph	NOUN
asir-2054	17	29	is	be	AUX
asir-2054	17	30	k	k	ADJ
asir-2054	17	31	-	-	PUNCT
asir-2054	17	32	edge	edge	NOUN
asir-2054	17	33	-	-	PUNCT
asir-2054	17	34	colorable	colorable	ADJ
asir-2054	17	35	,	,	PUNCT
asir-2054	17	36	if	if	SCONJ
asir-2054	17	37	its	its	PRON
asir-2054	17	38	edges	edge	NOUN
asir-2054	17	39	can	can	AUX
asir-2054	17	40	be	be	AUX
asir-2054	17	41	colored	color	VERB
asir-2054	17	42	with	with	ADP
asir-2054	17	43	k	k	PROPN
asir-2054	17	44	colors	color	NOUN
asir-2054	17	45	such	such	ADJ
asir-2054	17	46	that	that	SCONJ
asir-2054	17	47	adjacent	adjacent	ADJ
asir-2054	17	48	edges	edge	NOUN
asir-2054	17	49	receive	receive	VERB
asir-2054	17	50	different	different	ADJ
asir-2054	17	51	colors	color	NOUN
asir-2054	17	52	.	.	PUNCT
asir-2054	18	1	the	the	DET
asir-2054	18	2	edge	edge	NOUN
asir-2054	18	3	chromatic	chromatic	ADJ
asir-2054	18	4	number	number	NOUN
asir-2054	18	5	of	of	ADP
asir-2054	18	6	a	a	DET
asir-2054	18	7	graph	graph	NOUN
asir-2054	18	8	g	g	NOUN
asir-2054	18	9	,	,	PUNCT
asir-2054	18	10	denoted	denote	VERB
asir-2054	18	11	by	by	ADP
asir-2054	18	12	χ'(g	χ'(g	NOUN
asir-2054	18	13	)	)	PUNCT
asir-2054	18	14	,	,	PUNCT
asir-2054	18	15	is	be	AUX
asir-2054	18	16	the	the	DET
asir-2054	18	17	smallest	small	ADJ
asir-2054	18	18	integer	integer	NOUN
asir-2054	18	19	k	k	PROPN
asir-2054	18	20	such	such	ADJ
asir-2054	18	21	that	that	SCONJ
asir-2054	18	22	g	g	PROPN
asir-2054	18	23	is	be	AUX
asir-2054	18	24	k	k	ADJ
asir-2054	18	25	-	-	PUNCT
asir-2054	18	26	edge	edge	NOUN
asir-2054	18	27	-	-	PUNCT
asir-2054	18	28	colorable	colorable	ADJ
asir-2054	18	29	.	.	PUNCT
asir-2054	19	1	we	we	PRON
asir-2054	19	2	say	say	VERB
asir-2054	19	3	that	that	SCONJ
asir-2054	19	4	l	l	NOUN
asir-2054	19	5	is	be	AUX
asir-2054	19	6	an	an	DET
asir-2054	19	7	edge	edge	NOUN
asir-2054	19	8	assignment	assignment	NOUN
asir-2054	19	9	for	for	ADP
asir-2054	19	10	g	g	PROPN
asir-2054	19	11	if	if	SCONJ
asir-2054	19	12	it	it	PRON
asir-2054	19	13	assigns	assign	VERB
asir-2054	19	14	a	a	DET
asir-2054	19	15	list	list	NOUN
asir-2054	19	16	l(e	l(e	NOUN
asir-2054	19	17	)	)	PUNCT
asir-2054	19	18	of	of	ADP
asir-2054	19	19	colors	color	NOUN
asir-2054	19	20	to	to	ADP
asir-2054	19	21	each	each	DET
asir-2054	19	22	edge	edge	NOUN
asir-2054	19	23	e	e	PROPN
asir-2054	19	24	of	of	ADP
asir-2054	19	25	g.	g.	PROPN
asir-2054	19	26	if	if	SCONJ
asir-2054	19	27	g	g	PROPN
asir-2054	19	28	has	have	VERB
asir-2054	19	29	a	a	DET
asir-2054	19	30	proper	proper	ADJ
asir-2054	19	31	edge	edge	NOUN
asir-2054	19	32	-	-	PUNCT
asir-2054	19	33	coloring	color	VERB
asir-2054	19	34	φ	φ	NOUN
asir-2054	19	35	such	such	ADJ
asir-2054	19	36	that	that	SCONJ
asir-2054	19	37	φ(e	φ(e	NOUN
asir-2054	19	38	)	)	PUNCT
asir-2054	19	39	∈	∈	PROPN
asir-2054	19	40	l(e	l(e	NOUN
asir-2054	19	41	)	)	PUNCT
asir-2054	19	42	for	for	ADP
asir-2054	19	43	each	each	DET
asir-2054	19	44	edge	edge	NOUN
asir-2054	19	45	e	e	NOUN
asir-2054	19	46	of	of	ADP
asir-2054	19	47	g	g	PROPN
asir-2054	19	48	,	,	PUNCT
asir-2054	19	49	then	then	ADV
asir-2054	19	50	we	we	PRON
asir-2054	19	51	say	say	VERB
asir-2054	19	52	that	that	SCONJ
asir-2054	19	53	g	g	PROPN
asir-2054	19	54	is	be	AUX
asir-2054	19	55	edge	edge	NOUN
asir-2054	19	56	-	-	PUNCT
asir-2054	19	57	l	l	NOUN
asir-2054	19	58	-	-	ADJ
asir-2054	19	59	colorable	colorable	ADJ
asir-2054	19	60	and	and	CCONJ
asir-2054	19	61	φ	φ	PROPN
asir-2054	19	62	is	be	AUX
asir-2054	19	63	an	an	DET
asir-2054	19	64	edge	edge	NOUN
asir-2054	19	65	-	-	PUNCT
asir-2054	19	66	l	l	NOUN
asir-2054	19	67	-	-	NOUN
asir-2054	19	68	coloring	coloring	NOUN
asir-2054	19	69	of	of	ADP
asir-2054	19	70	g.	g.	PROPN
asir-2054	19	71	the	the	DET
asir-2054	19	72	graph	graph	NOUN
asir-2054	19	73	g	g	PROPN
asir-2054	19	74	is	be	AUX
asir-2054	19	75	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2054	19	76	applied	apply	VERB
asir-2054	19	77	science	science	NOUN
asir-2054	19	78	and	and	CCONJ
asir-2054	19	79	innovative	innovative	ADJ
asir-2054	19	80	research	research	NOUN
asir-2054	19	81	vol	vol	NOUN
asir-2054	19	82	.	.	PUNCT
asir-2054	20	1	3	3	NUM
asir-2054	20	2	,	,	PUNCT
asir-2054	20	3	no	no	INTJ
asir-2054	20	4	.	.	NOUN
asir-2054	20	5	2	2	NUM
asir-2054	20	6	,	,	PUNCT
asir-2054	20	7	2019	2019	NUM
asir-2054	20	8	86	86	NUM
asir-2054	20	9	published	publish	VERB
asir-2054	20	10	by	by	ADP
asir-2054	20	11	scholink	scholink	PROPN
asir-2054	20	12	inc	inc	PROPN
asir-2054	20	13	.	.	PROPN
asir-2054	20	14	edge	edge	PROPN
asir-2054	20	15	-	-	PUNCT
asir-2054	20	16	k	k	NOUN
asir-2054	20	17	-	-	NOUN
asir-2054	20	18	choosable	choosable	ADJ
asir-2054	20	19	if	if	SCONJ
asir-2054	20	20	it	it	PRON
asir-2054	20	21	is	be	AUX
asir-2054	20	22	edge	edge	NOUN
asir-2054	20	23	-	-	PUNCT
asir-2054	20	24	l	l	NOUN
asir-2054	20	25	-	-	ADJ
asir-2054	20	26	colorable	colorable	ADJ
asir-2054	20	27	for	for	ADP
asir-2054	20	28	every	every	DET
asir-2054	20	29	edge	edge	NOUN
asir-2054	20	30	assignment	assignment	NOUN
asir-2054	20	31	l	l	NOUN
asir-2054	20	32	satisfying	satisfy	VERB
asir-2054	20	33	|l(e)|	|l(e)|	PROPN
asir-2054	20	34	≥	≥	NOUN
asir-2054	20	35	k	k	NOUN
asir-2054	20	36	for	for	ADP
asir-2054	20	37	each	each	DET
asir-2054	20	38	edge	edge	NOUN
asir-2054	20	39	e	e	PROPN
asir-2054	20	40	∈	∈	PROPN
asir-2054	20	41	e(g	e(g	PROPN
asir-2054	20	42	)	)	PUNCT
asir-2054	20	43	,	,	PUNCT
asir-2054	20	44	where	where	SCONJ
asir-2054	20	45	k	k	PROPN
asir-2054	20	46	is	be	AUX
asir-2054	20	47	a	a	DET
asir-2054	20	48	positive	positive	ADJ
asir-2054	20	49	integer	integer	NOUN
asir-2054	20	50	.	.	PUNCT
asir-2054	21	1	the	the	DET
asir-2054	21	2	list	list	NOUN
asir-2054	21	3	-	-	PUNCT
asir-2054	21	4	edge	edge	NOUN
asir-2054	21	5	-	-	PUNCT
asir-2054	21	6	chromatic	chromatic	ADJ
asir-2054	21	7	-	-	PUNCT
asir-2054	21	8	number	number	NOUN
asir-2054	21	9	χ'l	χ'l	NOUN
asir-2054	21	10	(	(	PUNCT
asir-2054	21	11	g	g	NOUN
asir-2054	21	12	)	)	PUNCT
asir-2054	21	13	of	of	ADP
asir-2054	21	14	g	g	PROPN
asir-2054	21	15	is	be	AUX
asir-2054	21	16	the	the	DET
asir-2054	21	17	smallest	small	ADJ
asir-2054	21	18	k	k	NOUN
asir-2054	21	19	such	such	ADJ
asir-2054	21	20	that	that	SCONJ
asir-2054	21	21	g	g	PROPN
asir-2054	21	22	is	be	AUX
asir-2054	21	23	edge	edge	NOUN
asir-2054	21	24	-	-	PUNCT
asir-2054	21	25	k	k	NOUN
asir-2054	21	26	-	-	NOUN
asir-2054	21	27	choosable	choosable	NOUN
asir-2054	21	28	.	.	PUNCT
asir-2054	22	1	list	list	NOUN
asir-2054	22	2	edge	edge	NOUN
asir-2054	22	3	coloring	coloring	NOUN
asir-2054	22	4	was	be	AUX
asir-2054	22	5	introduced	introduce	VERB
asir-2054	22	6	by	by	ADP
asir-2054	22	7	vizing	vize	VERB
asir-2054	22	8	(	(	PUNCT
asir-2054	22	9	haggkvist	haggkvist	NOUN
asir-2054	22	10	&	&	CCONJ
asir-2054	22	11	chetwynd	chetwynd	PROPN
asir-2054	22	12	,	,	PUNCT
asir-2054	22	13	1992	1992	NUM
asir-2054	22	14	)	)	PUNCT
asir-2054	22	15	,	,	PUNCT
asir-2054	22	16	later	later	ADV
asir-2054	22	17	bollobas	bollobas	PROPN
asir-2054	22	18	and	and	CCONJ
asir-2054	22	19	harris	harris	PROPN
asir-2054	22	20	(	(	PUNCT
asir-2054	22	21	1985	1985	NUM
asir-2054	22	22	)	)	PUNCT
asir-2054	22	23	.	.	PUNCT
asir-2054	23	1	they	they	PRON
asir-2054	23	2	posed	pose	VERB
asir-2054	23	3	the	the	DET
asir-2054	23	4	following	follow	VERB
asir-2054	23	5	conjecture	conjecture	NOUN
asir-2054	23	6	which	which	PRON
asir-2054	23	7	is	be	AUX
asir-2054	23	8	called	call	VERB
asir-2054	23	9	the	the	DET
asir-2054	23	10	list	list	NOUN
asir-2054	23	11	coloring	coloring	NOUN
asir-2054	23	12	conjecture	conjecture	NOUN
asir-2054	23	13	.	.	PUNCT
asir-2054	24	1	conjecture	conjecture	NOUN
asir-2054	24	2	1	1	NUM
asir-2054	24	3	.	.	PUNCT
asir-2054	25	1	for	for	ADP
asir-2054	25	2	any	any	DET
asir-2054	25	3	multigraph	multigraph	NOUN
asir-2054	25	4	g	g	NOUN
asir-2054	25	5	,	,	PUNCT
asir-2054	25	6	χ'l	χ'l	PROPN
asir-2054	25	7	(	(	PUNCT
asir-2054	25	8	g	g	NOUN
asir-2054	25	9	)	)	PUNCT
asir-2054	25	10	=	=	SYM
asir-2054	25	11	χ	χ	NOUN
asir-2054	25	12	'	'	PUNCT
asir-2054	25	13	(	(	PUNCT
asir-2054	25	14	g	g	NOUN
asir-2054	25	15	)	)	PUNCT
asir-2054	25	16	.	.	PUNCT
asir-2054	26	1	conjecture	conjecture	NOUN
asir-2054	26	2	1	1	NUM
asir-2054	26	3	was	be	AUX
asir-2054	26	4	verified	verify	VERB
asir-2054	26	5	for	for	ADP
asir-2054	26	6	some	some	DET
asir-2054	26	7	special	special	ADJ
asir-2054	26	8	classes	class	NOUN
asir-2054	26	9	of	of	ADP
asir-2054	26	10	graphs	graph	NOUN
asir-2054	26	11	,	,	PUNCT
asir-2054	26	12	including	include	VERB
asir-2054	26	13	bipartite	bipartite	PROPN
asir-2054	26	14	multigraphs	multigraph	NOUN
asir-2054	26	15	(	(	PUNCT
asir-2054	26	16	galvin	galvin	NOUN
asir-2054	26	17	,	,	PUNCT
asir-2054	26	18	1995	1995	NUM
asir-2054	26	19	)	)	PUNCT
asir-2054	26	20	,	,	PUNCT
asir-2054	26	21	complete	complete	ADJ
asir-2054	26	22	graphs	graph	NOUN
asir-2054	26	23	of	of	ADP
asir-2054	26	24	odd	odd	ADJ
asir-2054	26	25	order	order	NOUN
asir-2054	26	26	(	(	PUNCT
asir-2054	26	27	haggkvist	haggkvist	NOUN
asir-2054	26	28	&	&	CCONJ
asir-2054	26	29	janssen	janssen	PROPN
asir-2054	26	30	,	,	PUNCT
asir-2054	26	31	1997	1997	NUM
asir-2054	26	32	)	)	PUNCT
asir-2054	26	33	,	,	PUNCT
asir-2054	26	34	multicircuits	multicircuit	NOUN
asir-2054	26	35	(	(	PUNCT
asir-2054	26	36	woodall	woodall	PROPN
asir-2054	26	37	,	,	PUNCT
asir-2054	26	38	1999	1999	NUM
asir-2054	26	39	)	)	PUNCT
asir-2054	26	40	,	,	PUNCT
asir-2054	26	41	graphs	graph	NOUN
asir-2054	26	42	with	with	ADP
asir-2054	26	43	∆(g	∆(g	PROPN
asir-2054	26	44	)	)	PUNCT
asir-2054	26	45	≥	≥	NOUN
asir-2054	26	46	12	12	NUM
asir-2054	26	47	which	which	PRON
asir-2054	26	48	can	can	AUX
asir-2054	26	49	be	be	AUX
asir-2054	26	50	embedded	embed	VERB
asir-2054	26	51	in	in	ADP
asir-2054	26	52	a	a	DET
asir-2054	26	53	surface	surface	NOUN
asir-2054	26	54	of	of	ADP
asir-2054	26	55	non	non	ADJ
asir-2054	26	56	-	-	ADJ
asir-2054	26	57	negative	negative	ADJ
asir-2054	26	58	characteristic	characteristic	ADJ
asir-2054	26	59	(	(	PUNCT
asir-2054	26	60	borodin	borodin	NOUN
asir-2054	26	61	,	,	PUNCT
asir-2054	26	62	kostochka	kostochka	NOUN
asir-2054	26	63	,	,	PUNCT
asir-2054	26	64	&	&	CCONJ
asir-2054	26	65	woodall	woodall	PROPN
asir-2054	26	66	,	,	PUNCT
asir-2054	26	67	1997	1997	NUM
asir-2054	26	68	)	)	PUNCT
asir-2054	26	69	,	,	PUNCT
asir-2054	26	70	and	and	CCONJ
asir-2054	26	71	outer	outer	ADJ
asir-2054	26	72	planar	planar	ADJ
asir-2054	26	73	graphs	graph	NOUN
asir-2054	26	74	(	(	PUNCT
asir-2054	26	75	wang	wang	PROPN
asir-2054	26	76	&	&	CCONJ
asir-2054	26	77	lih	lih	PROPN
asir-2054	26	78	,	,	PUNCT
asir-2054	26	79	2001	2001	NUM
asir-2054	26	80	)	)	PUNCT
asir-2054	26	81	.	.	PUNCT
asir-2054	27	1	vizing	vizing	NOUN
asir-2054	27	2	(	(	PUNCT
asir-2054	27	3	see	see	VERB
asir-2054	27	4	kostochka	kostochka	NOUN
asir-2054	27	5	,	,	PUNCT
asir-2054	27	6	1992	1992	NUM
asir-2054	27	7	)	)	PUNCT
asir-2054	27	8	proposed	propose	VERB
asir-2054	27	9	a	a	DET
asir-2054	27	10	weaker	weak	ADJ
asir-2054	27	11	conjecture	conjecture	NOUN
asir-2054	27	12	as	as	SCONJ
asir-2054	27	13	follows	follow	VERB
asir-2054	27	14	.	.	PUNCT
asir-2054	28	1	conjecture	conjecture	NOUN
asir-2054	28	2	2	2	NUM
asir-2054	28	3	.	.	PUNCT
asir-2054	29	1	every	every	DET
asir-2054	29	2	graph	graph	NOUN
asir-2054	29	3	g	g	PROPN
asir-2054	29	4	is	be	AUX
asir-2054	29	5	edge-(∆(g	edge-(∆(g	PROPN
asir-2054	29	6	)	)	PUNCT
asir-2054	30	1	+	+	CCONJ
asir-2054	30	2	1)-choosable	1)-choosable	X
asir-2054	30	3	.	.	PUNCT
asir-2054	31	1	harris	harris	PROPN
asir-2054	31	2	(	(	PUNCT
asir-2054	31	3	n.d	n.d	PROPN
asir-2054	31	4	.	.	PROPN
asir-2054	31	5	)	)	PUNCT
asir-2054	31	6	proved	prove	VERB
asir-2054	31	7	that	that	SCONJ
asir-2054	32	1	χ'l	χ'l	NOUN
asir-2054	32	2	(	(	PUNCT
asir-2054	32	3	g	g	NOUN
asir-2054	32	4	)	)	PUNCT
asir-2054	32	5	≤	≤	NOUN
asir-2054	32	6	2∆(g	2∆(g	NOUN
asir-2054	32	7	)	)	PUNCT
asir-2054	33	1	−	−	PROPN
asir-2054	33	2	2	2	NUM
asir-2054	33	3	if	if	SCONJ
asir-2054	33	4	g	g	PROPN
asir-2054	33	5	is	be	AUX
asir-2054	33	6	a	a	DET
asir-2054	33	7	graph	graph	NOUN
asir-2054	33	8	with	with	ADP
asir-2054	33	9	∆(g	∆(g	PROPN
asir-2054	33	10	)	)	PUNCT
asir-2054	33	11	≥	≥	NOUN
asir-2054	33	12	3	3	NUM
asir-2054	33	13	.	.	PUNCT
asir-2054	34	1	this	this	PRON
asir-2054	34	2	implies	imply	VERB
asir-2054	34	3	conjecture	conjecture	NOUN
asir-2054	34	4	2	2	NUM
asir-2054	34	5	for	for	ADP
asir-2054	34	6	the	the	DET
asir-2054	34	7	case	case	NOUN
asir-2054	34	8	∆(g	∆(g	NOUN
asir-2054	34	9	)	)	PUNCT
asir-2054	34	10	=	=	SYM
asir-2054	35	1	3	3	X
asir-2054	35	2	.	.	X
asir-2054	35	3	juvan	juvan	NOUN
asir-2054	35	4	et	et	PROPN
asir-2054	35	5	al	al	PROPN
asir-2054	35	6	.	.	PROPN
asir-2054	36	1	(	(	PUNCT
asir-2054	36	2	1999	1999	NUM
asir-2054	36	3	)	)	PUNCT
asir-2054	36	4	settled	settle	VERB
asir-2054	36	5	the	the	DET
asir-2054	36	6	case	case	NOUN
asir-2054	36	7	for	for	ADP
asir-2054	36	8	∆(g	∆(g	NOUN
asir-2054	36	9	)	)	PUNCT
asir-2054	36	10	=	=	SYM
asir-2054	37	1	4	4	X
asir-2054	37	2	.	.	X
asir-2054	37	3	conjecture	conjecture	NOUN
asir-2054	37	4	2	2	NUM
asir-2054	37	5	was	be	AUX
asir-2054	37	6	verified	verify	VERB
asir-2054	37	7	for	for	ADP
asir-2054	37	8	some	some	DET
asir-2054	37	9	special	special	ADJ
asir-2054	37	10	classes	class	NOUN
asir-2054	37	11	of	of	ADP
asir-2054	37	12	graphs	graph	NOUN
asir-2054	37	13	,	,	PUNCT
asir-2054	37	14	including	include	VERB
asir-2054	37	15	complete	complete	ADJ
asir-2054	37	16	graphs	graph	NOUN
asir-2054	37	17	(	(	PUNCT
asir-2054	37	18	haggkvist	haggkvist	NOUN
asir-2054	37	19	&	&	CCONJ
asir-2054	37	20	janssen	janssen	PROPN
asir-2054	37	21	,	,	PUNCT
asir-2054	37	22	1997	1997	NUM
asir-2054	37	23	)	)	PUNCT
asir-2054	37	24	,	,	PUNCT
asir-2054	37	25	graphs	graph	VERB
asir-2054	37	26	with	with	ADP
asir-2054	37	27	girth	girth	NOUN
asir-2054	37	28	at	at	ADV
asir-2054	37	29	least	least	ADJ
asir-2054	37	30	8∆(ln	8∆(ln	NUM
asir-2054	37	31	∆	∆	NOUN
asir-2054	38	1	+	+	CCONJ
asir-2054	38	2	1.1	1.1	NUM
asir-2054	38	3	)	)	PUNCT
asir-2054	38	4	(	(	PUNCT
asir-2054	38	5	haggkvist	haggkvist	NOUN
asir-2054	38	6	&	&	CCONJ
asir-2054	38	7	chetwynd	chetwynd	PROPN
asir-2054	38	8	,	,	PUNCT
asir-2054	38	9	1992	1992	NUM
asir-2054	38	10	)	)	PUNCT
asir-2054	38	11	,	,	PUNCT
asir-2054	38	12	planar	planar	ADJ
asir-2054	38	13	graphs	graph	NOUN
asir-2054	38	14	with	with	ADP
asir-2054	38	15	∆	∆	PROPN
asir-2054	38	16	≥	≥	X
asir-2054	38	17	8	8	NUM
asir-2054	38	18	(	(	PUNCT
asir-2054	38	19	bonamy	bonamy	NOUN
asir-2054	38	20	,	,	PUNCT
asir-2054	38	21	2015	2015	NUM
asir-2054	38	22	)	)	PUNCT
asir-2054	38	23	.	.	PUNCT
asir-2054	39	1	for	for	ADP
asir-2054	39	2	planar	planar	ADJ
asir-2054	39	3	graphs	graph	NOUN
asir-2054	39	4	with	with	ADP
asir-2054	39	5	some	some	DET
asir-2054	39	6	local	local	ADJ
asir-2054	39	7	conditions	condition	NOUN
asir-2054	39	8	,	,	PUNCT
asir-2054	39	9	see	see	VERB
asir-2054	39	10	hou	hou	PROPN
asir-2054	39	11	,	,	PUNCT
asir-2054	39	12	liu	liu	PROPN
asir-2054	39	13	and	and	CCONJ
asir-2054	39	14	cai	cai	PROPN
asir-2054	39	15	(	(	PUNCT
asir-2054	39	16	2009	2009	NUM
asir-2054	39	17	)	)	PUNCT
asir-2054	39	18	,	,	PUNCT
asir-2054	39	19	ma	ma	PROPN
asir-2054	39	20	,	,	PUNCT
asir-2054	39	21	wang	wang	PROPN
asir-2054	39	22	,	,	PUNCT
asir-2054	39	23	cai	cai	PROPN
asir-2054	39	24	and	and	CCONJ
asir-2054	39	25	zhang	zhang	PROPN
asir-2054	39	26	(	(	PUNCT
asir-2054	39	27	2011	2011	NUM
asir-2054	39	28	)	)	PUNCT
asir-2054	39	29	,	,	PUNCT
asir-2054	39	30	wang	wang	PROPN
asir-2054	39	31	and	and	CCONJ
asir-2054	39	32	wu	wu	PROPN
asir-2054	39	33	(	(	PUNCT
asir-2054	39	34	2018	2018	NUM
asir-2054	39	35	)	)	PUNCT
asir-2054	39	36	.	.	PUNCT
asir-2054	40	1	ca	ca	PROPN
asir-2054	40	2	,	,	PUNCT
asir-2054	40	3	ge	ge	PROPN
asir-2054	40	4	,	,	PUNCT
asir-2054	40	5	zhang	zhang	PROPN
asir-2054	40	6	and	and	CCONJ
asir-2054	40	7	liu	liu	PROPN
asir-2054	40	8	(	(	PUNCT
asir-2054	40	9	2011	2011	NUM
asir-2054	40	10	)	)	PUNCT
asir-2054	40	11	proved	prove	VERB
asir-2054	40	12	that	that	SCONJ
asir-2054	40	13	if	if	SCONJ
asir-2054	40	14	g	g	PROPN
asir-2054	40	15	is	be	AUX
asir-2054	40	16	a	a	DET
asir-2054	40	17	planar	planar	ADJ
asir-2054	40	18	graph	graph	NOUN
asir-2054	40	19	without	without	ADP
asir-2054	40	20	chordal	chordal	ADJ
asir-2054	40	21	7	7	NUM
asir-2054	40	22	-	-	PUNCT
asir-2054	40	23	cycles	cycle	NOUN
asir-2054	40	24	,	,	PUNCT
asir-2054	40	25	then	then	ADV
asir-2054	40	26	g	g	PROPN
asir-2054	40	27	is	be	AUX
asir-2054	40	28	edge	edge	NOUN
asir-2054	40	29	-	-	PUNCT
asir-2054	40	30	k	k	NOUN
asir-2054	40	31	-	-	NOUN
asir-2054	40	32	choosable	choosable	NOUN
asir-2054	40	33	,	,	PUNCT
asir-2054	40	34	where	where	SCONJ
asir-2054	40	35	k	k	PROPN
asir-2054	40	36	=	=	SYM
asir-2054	40	37	max{8	max{8	PROPN
asir-2054	40	38	,	,	PUNCT
asir-2054	40	39	∆(g	∆(g	NOUN
asir-2054	40	40	)	)	PUNCT
asir-2054	41	1	+	+	NOUN
asir-2054	41	2	1	1	NUM
asir-2054	41	3	}	}	PUNCT
asir-2054	41	4	.	.	PUNCT
asir-2054	42	1	in	in	ADP
asir-2054	42	2	this	this	DET
asir-2054	42	3	paper	paper	NOUN
asir-2054	42	4	,	,	PUNCT
asir-2054	42	5	we	we	PRON
asir-2054	42	6	will	will	AUX
asir-2054	42	7	extend	extend	VERB
asir-2054	42	8	this	this	DET
asir-2054	42	9	result	result	NOUN
asir-2054	42	10	to	to	PART
asir-2054	42	11	planar	planar	ADJ
asir-2054	42	12	graphs	graph	NOUN
asir-2054	42	13	in	in	ADP
asir-2054	42	14	which	which	PRON
asir-2054	42	15	all	all	DET
asir-2054	42	16	7	7	NUM
asir-2054	42	17	-	-	PUNCT
asir-2054	42	18	cycles	cycle	NOUN
asir-2054	42	19	contain	contain	VERB
asir-2054	42	20	at	at	ADP
asir-2054	42	21	most	most	ADV
asir-2054	42	22	two	two	NUM
asir-2054	42	23	chords	chord	NOUN
asir-2054	42	24	and	and	CCONJ
asir-2054	42	25	get	get	VERB
asir-2054	42	26	the	the	DET
asir-2054	42	27	following	follow	VERB
asir-2054	42	28	theorem	theorem	VERB
asir-2054	42	29	.	.	PUNCT
asir-2054	42	30	theorem	theorem	NOUN
asir-2054	42	31	3	3	X
asir-2054	42	32	.	.	PUNCT
asir-2054	43	1	let	let	VERB
asir-2054	43	2	g	g	PRON
asir-2054	43	3	be	be	AUX
asir-2054	43	4	a	a	DET
asir-2054	43	5	planar	planar	ADJ
asir-2054	43	6	graph	graph	NOUN
asir-2054	43	7	in	in	ADP
asir-2054	43	8	which	which	PRON
asir-2054	43	9	each	each	DET
asir-2054	43	10	7	7	NUM
asir-2054	43	11	-	-	PUNCT
asir-2054	43	12	cycle	cycle	NOUN
asir-2054	43	13	contains	contain	VERB
asir-2054	43	14	at	at	ADP
asir-2054	43	15	most	most	ADJ
asir-2054	43	16	two	two	NUM
asir-2054	43	17	chords	chord	NOUN
asir-2054	43	18	.	.	PUNCT
asir-2054	44	1	then	then	ADV
asir-2054	44	2	g	g	PROPN
asir-2054	44	3	is	be	AUX
asir-2054	44	4	edge	edge	NOUN
asir-2054	44	5	-	-	PUNCT
asir-2054	44	6	k	k	NOUN
asir-2054	44	7	-	-	NOUN
asir-2054	44	8	choosable	choosable	NOUN
asir-2054	44	9	,	,	PUNCT
asir-2054	44	10	where	where	SCONJ
asir-2054	44	11	k	k	PROPN
asir-2054	44	12	=	=	SYM
asir-2054	44	13	max{8	max{8	PROPN
asir-2054	44	14	,	,	PUNCT
asir-2054	44	15	∆(g	∆(g	NOUN
asir-2054	44	16	)	)	PUNCT
asir-2054	44	17	+	+	NOUN
asir-2054	45	1	1	1	NUM
asir-2054	45	2	}	}	PUNCT
asir-2054	45	3	.	.	PUNCT
asir-2054	46	1	2	2	X
asir-2054	46	2	.	.	X
asir-2054	46	3	structural	structural	ADJ
asir-2054	46	4	properties	property	NOUN
asir-2054	46	5	of	of	ADP
asir-2054	46	6	planar	planar	ADJ
asir-2054	46	7	graphs	graph	NOUN
asir-2054	46	8	with	with	ADP
asir-2054	46	9	7	7	NUM
asir-2054	46	10	-	-	PUNCT
asir-2054	46	11	cycles	cycle	NOUN
asir-2054	46	12	containing	contain	VERB
asir-2054	46	13	at	at	ADP
asir-2054	46	14	most	most	ADV
asir-2054	46	15	two	two	NUM
asir-2054	46	16	chords	chord	NOUN
asir-2054	46	17	lemma	lemma	PROPN
asir-2054	46	18	4	4	X
asir-2054	46	19	.	.	PUNCT
asir-2054	47	1	let	let	VERB
asir-2054	47	2	g	g	PRON
asir-2054	47	3	be	be	AUX
asir-2054	47	4	a	a	DET
asir-2054	47	5	planar	planar	ADJ
asir-2054	47	6	graph	graph	NOUN
asir-2054	47	7	in	in	ADP
asir-2054	47	8	which	which	PRON
asir-2054	47	9	each	each	DET
asir-2054	47	10	7	7	NUM
asir-2054	47	11	-	-	PUNCT
asir-2054	47	12	cycle	cycle	NOUN
asir-2054	47	13	contains	contain	VERB
asir-2054	47	14	at	at	ADP
asir-2054	47	15	most	most	ADJ
asir-2054	47	16	two	two	NUM
asir-2054	47	17	chords	chord	NOUN
asir-2054	47	18	.	.	PUNCT
asir-2054	48	1	then	then	ADV
asir-2054	48	2	at	at	ADV
asir-2054	48	3	least	least	ADJ
asir-2054	48	4	one	one	NUM
asir-2054	48	5	of	of	ADP
asir-2054	48	6	the	the	DET
asir-2054	48	7	following	follow	VERB
asir-2054	48	8	holds	hold	NOUN
asir-2054	48	9	.	.	PUNCT
asir-2054	49	1	(	(	PUNCT
asir-2054	49	2	1	1	X
asir-2054	49	3	)	)	PUNCT
asir-2054	49	4	g	g	NOUN
asir-2054	49	5	has	have	VERB
asir-2054	49	6	an	an	DET
asir-2054	49	7	edge	edge	NOUN
asir-2054	49	8	uv	uv	NOUN
asir-2054	49	9	with	with	ADP
asir-2054	49	10	d(u	d(u	PROPN
asir-2054	49	11	)	)	PUNCT
asir-2054	50	1	+	+	CCONJ
asir-2054	50	2	d(v	d(v	PROPN
asir-2054	50	3	)	)	PUNCT
asir-2054	50	4	≤	≤	NUM
asir-2054	50	5	max{9	max{9	VERB
asir-2054	50	6	,	,	PUNCT
asir-2054	50	7	∆(g	∆(g	NOUN
asir-2054	50	8	)	)	PUNCT
asir-2054	51	1	+	+	CCONJ
asir-2054	51	2	2	2	NUM
asir-2054	51	3	}	}	PUNCT
asir-2054	51	4	;	;	PUNCT
asir-2054	51	5	(	(	PUNCT
asir-2054	51	6	2	2	X
asir-2054	51	7	)	)	PUNCT
asir-2054	51	8	g	g	NOUN
asir-2054	51	9	has	have	VERB
asir-2054	51	10	an	an	DET
asir-2054	51	11	even	even	ADJ
asir-2054	51	12	cycle	cycle	NOUN
asir-2054	51	13	c	c	NOUN
asir-2054	51	14	=	=	SYM
asir-2054	52	1	v1v2	v1v2	PROPN
asir-2054	52	2	...	...	PUNCT
asir-2054	52	3	v2nv1	v2nv1	NOUN
asir-2054	52	4	with	with	ADP
asir-2054	52	5	d(v1	d(v1	NOUN
asir-2054	52	6	)	)	PUNCT
asir-2054	52	7	=	=	SYM
asir-2054	52	8	d(v3	d(v3	NOUN
asir-2054	52	9	)	)	PUNCT
asir-2054	52	10	=	=	SYM
asir-2054	52	11	...	...	PUNCT
asir-2054	53	1	=	=	PUNCT
asir-2054	53	2	d(v2n−1	d(v2n−1	NOUN
asir-2054	53	3	)	)	PUNCT
asir-2054	53	4	=	=	SYM
asir-2054	54	1	3	3	X
asir-2054	54	2	.	.	X
asir-2054	54	3	proof	proof	NOUN
asir-2054	54	4	.	.	PUNCT
asir-2054	55	1	since	since	SCONJ
asir-2054	55	2	every	every	DET
asir-2054	55	3	planar	planar	ADJ
asir-2054	55	4	graph	graph	NOUN
asir-2054	55	5	with	with	ADP
asir-2054	55	6	maximum	maximum	ADJ
asir-2054	55	7	degree	degree	NOUN
asir-2054	55	8	∆(g	∆(g	NOUN
asir-2054	55	9	)	)	PUNCT
asir-2054	55	10	≥	≥	NOUN
asir-2054	55	11	8	8	NUM
asir-2054	55	12	has	have	VERB
asir-2054	55	13	chromatic	chromatic	ADJ
asir-2054	55	14	index	index	NOUN
asir-2054	55	15	∆(g)+1	∆(g)+1	NOUN
asir-2054	55	16	(	(	PUNCT
asir-2054	55	17	see	see	VERB
asir-2054	55	18	bonamy	bonamy	NOUN
asir-2054	55	19	,	,	PUNCT
asir-2054	55	20	2015	2015	NUM
asir-2054	55	21	)	)	PUNCT
asir-2054	55	22	,	,	PUNCT
asir-2054	55	23	we	we	PRON
asir-2054	55	24	assume	assume	VERB
asir-2054	55	25	that	that	SCONJ
asir-2054	55	26	∆(g	∆(g	NOUN
asir-2054	55	27	)	)	PUNCT
asir-2054	55	28	≤	≤	NOUN
asir-2054	55	29	7	7	NUM
asir-2054	55	30	in	in	ADP
asir-2054	55	31	the	the	DET
asir-2054	55	32	following	following	ADJ
asir-2054	55	33	proof	proof	NOUN
asir-2054	55	34	.	.	PUNCT
asir-2054	56	1	suppose	suppose	VERB
asir-2054	56	2	that	that	SCONJ
asir-2054	56	3	g	g	PROPN
asir-2054	56	4	is	be	AUX
asir-2054	56	5	a	a	DET
asir-2054	56	6	minimum	minimum	ADJ
asir-2054	56	7	counterexample	counterexample	NOUN
asir-2054	56	8	to	to	PART
asir-2054	56	9	lemma	lemma	PROPN
asir-2054	56	10	4	4	NUM
asir-2054	56	11	in	in	ADP
asir-2054	56	12	terms	term	NOUN
asir-2054	56	13	of	of	ADP
asir-2054	56	14	the	the	DET
asir-2054	56	15	sums	sum	NOUN
asir-2054	56	16	of	of	ADP
asir-2054	56	17	the	the	DET
asir-2054	56	18	number	number	NOUN
asir-2054	56	19	of	of	ADP
asir-2054	56	20	vertices	vertex	NOUN
asir-2054	56	21	and	and	CCONJ
asir-2054	56	22	edges	edge	NOUN
asir-2054	56	23	.	.	PUNCT
asir-2054	57	1	it	it	PRON
asir-2054	57	2	is	be	AUX
asir-2054	57	3	obvious	obvious	ADJ
asir-2054	57	4	that	that	SCONJ
asir-2054	57	5	g	g	PROPN
asir-2054	57	6	is	be	AUX
asir-2054	57	7	connected	connect	VERB
asir-2054	57	8	.	.	PUNCT
asir-2054	58	1	by	by	ADP
asir-2054	58	2	the	the	DET
asir-2054	58	3	choice	choice	NOUN
asir-2054	58	4	of	of	ADP
asir-2054	58	5	g	g	NOUN
asir-2054	58	6	,	,	PUNCT
asir-2054	58	7	we	we	PRON
asir-2054	58	8	have	have	VERB
asir-2054	58	9	there	there	PRON
asir-2054	58	10	observations	observation	NOUN
asir-2054	58	11	.	.	PUNCT
asir-2054	59	1	(	(	PUNCT
asir-2054	59	2	a	a	X
asir-2054	59	3	)	)	PUNCT
asir-2054	59	4	by	by	ADP
asir-2054	59	5	the	the	DET
asir-2054	59	6	assumption	assumption	NOUN
asir-2054	59	7	,	,	PUNCT
asir-2054	59	8	for	for	ADP
asir-2054	59	9	any	any	DET
asir-2054	59	10	edge	edge	NOUN
asir-2054	59	11	uv	uv	NOUN
asir-2054	59	12	,	,	PUNCT
asir-2054	59	13	d(u	d(u	PROPN
asir-2054	59	14	)	)	PUNCT
asir-2054	60	1	+	+	SYM
asir-2054	60	2	d(v	d(v	PROPN
asir-2054	60	3	)	)	PUNCT
asir-2054	60	4	≥	≥	NOUN
asir-2054	60	5	max{10	max{10	NOUN
asir-2054	60	6	,	,	PUNCT
asir-2054	60	7	∆(g	∆(g	NOUN
asir-2054	60	8	)	)	PUNCT
asir-2054	60	9	+	+	CCONJ
asir-2054	60	10	3	3	X
asir-2054	60	11	}	}	PUNCT
asir-2054	60	12	since	since	SCONJ
asir-2054	60	13	(	(	PUNCT
asir-2054	60	14	1	1	X
asir-2054	60	15	)	)	PUNCT
asir-2054	60	16	does	do	AUX
asir-2054	60	17	not	not	PART
asir-2054	60	18	hold	hold	VERB
asir-2054	60	19	.	.	PUNCT
asir-2054	61	1	so	so	ADV
asir-2054	61	2	δ(g	δ(g	PROPN
asir-2054	61	3	)	)	PUNCT
asir-2054	61	4	≥	≥	NOUN
asir-2054	61	5	3	3	NUM
asir-2054	61	6	and	and	CCONJ
asir-2054	61	7	all	all	DET
asir-2054	61	8	3	3	NUM
asir-2054	61	9	-	-	PUNCT
asir-2054	61	10	vertices	vertex	NOUN
asir-2054	61	11	must	must	AUX
asir-2054	61	12	be	be	AUX
asir-2054	61	13	adjacent	adjacent	ADJ
asir-2054	61	14	to	to	ADP
asir-2054	61	15	maximum	maximum	ADJ
asir-2054	61	16	degree	degree	NOUN
asir-2054	61	17	vertices	vertex	NOUN
asir-2054	61	18	.	.	PUNCT
asir-2054	62	1	besides	besides	SCONJ
asir-2054	62	2	,	,	PUNCT
asir-2054	62	3	any	any	DET
asir-2054	62	4	4	4	NUM
asir-2054	62	5	-	-	PUNCT
asir-2054	62	6	vertex	vertex	NOUN
asir-2054	62	7	is	be	AUX
asir-2054	62	8	only	only	ADV
asir-2054	62	9	adjacent	adjacent	ADJ
asir-2054	62	10	to	to	ADP
asir-2054	62	11	vertices	vertex	NOUN
asir-2054	62	12	of	of	ADP
asir-2054	62	13	degree	degree	NOUN
asir-2054	62	14	at	at	ADP
asir-2054	62	15	least	least	ADJ
asir-2054	62	16	∆(g	∆(g	NOUN
asir-2054	62	17	)	)	PUNCT
asir-2054	62	18	−	−	PROPN
asir-2054	63	1	1	1	X
asir-2054	63	2	.	.	PUNCT
asir-2054	63	3	(	(	PUNCT
asir-2054	63	4	b	b	X
asir-2054	63	5	)	)	PUNCT
asir-2054	63	6	since	since	SCONJ
asir-2054	63	7	g	g	PROPN
asir-2054	63	8	contains	contain	VERB
asir-2054	63	9	no	no	DET
asir-2054	63	10	7	7	NUM
asir-2054	63	11	-	-	PUNCT
asir-2054	63	12	cycles	cycle	NOUN
asir-2054	63	13	with	with	ADP
asir-2054	63	14	three	three	NUM
asir-2054	63	15	chords	chord	NOUN
asir-2054	63	16	,	,	PUNCT
asir-2054	63	17	so	so	SCONJ
asir-2054	63	18	for	for	ADP
asir-2054	63	19	any	any	DET
asir-2054	63	20	6	6	NUM
asir-2054	63	21	+	+	SYM
asir-2054	63	22	-vertex	-vertex	NOUN
asir-2054	63	23	v	v	ADP
asir-2054	63	24	∈	∈	NOUN
asir-2054	63	25	v	v	NOUN
asir-2054	63	26	(	(	PUNCT
asir-2054	63	27	g	g	NOUN
asir-2054	63	28	)	)	PUNCT
asir-2054	63	29	,	,	PUNCT
asir-2054	63	30	v	v	NOUN
asir-2054	63	31	is	be	AUX
asir-2054	63	32	not	not	PART
asir-2054	63	33	incident	incident	NOUN
asir-2054	63	34	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2054	63	35	applied	apply	VERB
asir-2054	63	36	science	science	NOUN
asir-2054	63	37	and	and	CCONJ
asir-2054	63	38	innovative	innovative	ADJ
asir-2054	63	39	research	research	NOUN
asir-2054	63	40	vol	vol	NOUN
asir-2054	63	41	.	.	PUNCT
asir-2054	64	1	3	3	NUM
asir-2054	64	2	,	,	PUNCT
asir-2054	64	3	no	no	INTJ
asir-2054	64	4	.	.	NOUN
asir-2054	64	5	2	2	NUM
asir-2054	64	6	,	,	PUNCT
asir-2054	64	7	2019	2019	NUM
asir-2054	64	8	87	87	NUM
asir-2054	64	9	published	publish	VERB
asir-2054	64	10	by	by	ADP
asir-2054	64	11	scholink	scholink	PROPN
asir-2054	64	12	inc	inc	PROPN
asir-2054	64	13	.	.	PROPN
asir-2054	64	14	with	with	ADP
asir-2054	64	15	five	five	NUM
asir-2054	64	16	3	3	NUM
asir-2054	64	17	-	-	PUNCT
asir-2054	64	18	faces	face	NOUN
asir-2054	64	19	f1	f1	NOUN
asir-2054	64	20	,	,	PUNCT
asir-2054	64	21	f2	f2	PROPN
asir-2054	64	22	,	,	PUNCT
asir-2054	64	23	f3	f3	ADJ
asir-2054	64	24	,	,	PUNCT
asir-2054	64	25	f4	f4	PROPN
asir-2054	64	26	,	,	PUNCT
asir-2054	64	27	f5	f5	VERB
asir-2054	64	28	such	such	ADJ
asir-2054	64	29	that	that	DET
asir-2054	64	30	fi	fi	NOUN
asir-2054	64	31	and	and	CCONJ
asir-2054	64	32	fi	fi	NOUN
asir-2054	65	1	+	+	CCONJ
asir-2054	65	2	1	1	NUM
asir-2054	65	3	are	be	AUX
asir-2054	65	4	adjacent	adjacent	ADJ
asir-2054	65	5	for	for	ADP
asir-2054	65	6	all	all	DET
asir-2054	65	7	i	i	PRON
asir-2054	65	8	=	=	NOUN
asir-2054	65	9	1	1	NUM
asir-2054	65	10	,	,	PUNCT
asir-2054	65	11	2	2	NUM
asir-2054	65	12	,	,	PUNCT
asir-2054	65	13	3	3	NUM
asir-2054	65	14	,	,	PUNCT
asir-2054	65	15	4	4	NUM
asir-2054	65	16	.	.	PUNCT
asir-2054	65	17	then	then	ADV
asir-2054	65	18	f3(v	f3(v	NOUN
asir-2054	65	19	)	)	PUNCT
asir-2054	65	20	≤	≤	NOUN
asir-2054	65	21	[	[	PUNCT
asir-2054	65	22	4	4	NUM
asir-2054	65	23	5	5	NUM
asir-2054	65	24	d(v	d(v	PROPN
asir-2054	65	25	)	)	PUNCT
asir-2054	65	26	]	]	PUNCT
asir-2054	65	27	.	.	PUNCT
asir-2054	66	1	(	(	PUNCT
asir-2054	66	2	c	c	X
asir-2054	66	3	)	)	PUNCT
asir-2054	66	4	let	let	VERB
asir-2054	66	5	g	g	PROPN
asir-2054	66	6	3	3	NUM
asir-2054	66	7	be	be	AUX
asir-2054	66	8	the	the	DET
asir-2054	66	9	subgraph	subgraph	NOUN
asir-2054	66	10	induced	induce	VERB
asir-2054	66	11	by	by	ADP
asir-2054	66	12	the	the	DET
asir-2054	66	13	edges	edge	NOUN
asir-2054	66	14	incident	incident	NOUN
asir-2054	66	15	with	with	ADP
asir-2054	66	16	all	all	DET
asir-2054	66	17	3	3	NUM
asir-2054	66	18	-	-	PUNCT
asir-2054	66	19	vertices	vertex	NOUN
asir-2054	66	20	of	of	ADP
asir-2054	66	21	g.	g.	PROPN
asir-2054	66	22	then	then	ADV
asir-2054	66	23	g	g	PROPN
asir-2054	66	24	3	3	NUM
asir-2054	66	25	is	be	AUX
asir-2054	66	26	a	a	DET
asir-2054	66	27	forest	forest	NOUN
asir-2054	67	1	and	and	CCONJ
asir-2054	67	2	it	it	PRON
asir-2054	67	3	contains	contain	VERB
asir-2054	67	4	a	a	DET
asir-2054	67	5	bipartite	bipartite	PROPN
asir-2054	67	6	subgraph	subgraph	NOUN
asir-2054	67	7	g	g	NOUN
asir-2054	67	8	'	'	PUNCT
asir-2054	67	9	=	=	SYM
asir-2054	67	10	(	(	PUNCT
asir-2054	67	11	v1	v1	NOUN
asir-2054	67	12	,	,	PUNCT
asir-2054	67	13	v2	v2	PROPN
asir-2054	67	14	)	)	PUNCT
asir-2054	67	15	with	with	ADP
asir-2054	67	16	two	two	NUM
asir-2054	67	17	partite	partite	ADJ
asir-2054	67	18	sets	set	NOUN
asir-2054	67	19	v1	v1	VERB
asir-2054	67	20	and	and	CCONJ
asir-2054	67	21	v2	v2	NOUN
asir-2054	67	22	,	,	PUNCT
asir-2054	67	23	such	such	ADJ
asir-2054	67	24	that	that	SCONJ
asir-2054	67	25	dg	dg	NOUN
asir-2054	67	26	'	'	PART
asir-2054	67	27	(	(	PUNCT
asir-2054	67	28	v	v	NOUN
asir-2054	67	29	)	)	PUNCT
asir-2054	67	30	=	=	SYM
asir-2054	67	31	2	2	NUM
asir-2054	67	32	for	for	ADP
asir-2054	67	33	each	each	DET
asir-2054	67	34	vertex	vertex	NOUN
asir-2054	67	35	v	v	ADP
asir-2054	67	36	∈	∈	NOUN
asir-2054	67	37	v1	v1	NOUN
asir-2054	67	38	and	and	CCONJ
asir-2054	67	39	dg	dg	NOUN
asir-2054	67	40	'	'	PART
asir-2054	67	41	(	(	PUNCT
asir-2054	67	42	v	v	NOUN
asir-2054	67	43	)	)	PUNCT
asir-2054	67	44	=	=	SYM
asir-2054	67	45	1	1	NUM
asir-2054	67	46	for	for	ADP
asir-2054	67	47	each	each	DET
asir-2054	67	48	vertex	vertex	NOUN
asir-2054	67	49	v	v	ADP
asir-2054	67	50	∈	∈	PROPN
asir-2054	67	51	v2	v2	NOUN
asir-2054	67	52	.	.	PUNCT
asir-2054	68	1	if	if	SCONJ
asir-2054	68	2	uv	uv	NOUN
asir-2054	68	3	∈	∈	PROPN
asir-2054	68	4	g	g	NOUN
asir-2054	68	5	'	'	PUNCT
asir-2054	68	6	and	and	CCONJ
asir-2054	68	7	dg(u	dg(u	X
asir-2054	68	8	)	)	PUNCT
asir-2054	68	9	=	=	SYM
asir-2054	68	10	3	3	NUM
asir-2054	68	11	,	,	PUNCT
asir-2054	68	12	then	then	ADV
asir-2054	68	13	v	v	NOUN
asir-2054	68	14	is	be	AUX
asir-2054	68	15	called	call	VERB
asir-2054	68	16	a	a	DET
asir-2054	68	17	3	3	NUM
asir-2054	68	18	-	-	PUNCT
asir-2054	68	19	master	master	NOUN
asir-2054	68	20	of	of	ADP
asir-2054	68	21	u	u	PROPN
asir-2054	68	22	and	and	CCONJ
asir-2054	68	23	u	u	NOUN
asir-2054	68	24	is	be	AUX
asir-2054	68	25	called	call	VERB
asir-2054	68	26	a	a	DET
asir-2054	68	27	dependent	dependent	NOUN
asir-2054	68	28	of	of	ADP
asir-2054	68	29	v.	v.	ADP
asir-2054	68	30	note	note	VERB
asir-2054	68	31	that	that	SCONJ
asir-2054	68	32	every	every	DET
asir-2054	68	33	3	3	NUM
asir-2054	68	34	-	-	PUNCT
asir-2054	68	35	vertex	vertex	NOUN
asir-2054	68	36	has	have	VERB
asir-2054	68	37	exactly	exactly	ADV
asir-2054	68	38	two	two	NUM
asir-2054	68	39	3	3	NUM
asir-2054	68	40	-	-	PUNCT
asir-2054	68	41	masters	master	NOUN
asir-2054	68	42	and	and	CCONJ
asir-2054	68	43	each	each	DET
asir-2054	68	44	7	7	NUM
asir-2054	68	45	+	+	SYM
asir-2054	68	46	-vertex	-vertex	NOUN
asir-2054	68	47	can	can	AUX
asir-2054	68	48	be	be	AUX
asir-2054	68	49	the	the	DET
asir-2054	68	50	3	3	NUM
asir-2054	68	51	-	-	PUNCT
asir-2054	68	52	master	master	NOUN
asir-2054	68	53	of	of	ADP
asir-2054	68	54	at	at	ADV
asir-2054	68	55	most	most	ADV
asir-2054	68	56	one	one	NUM
asir-2054	68	57	3	3	NUM
asir-2054	68	58	-	-	PUNCT
asir-2054	68	59	vertex	vertex	NOUN
asir-2054	68	60	.	.	PUNCT
asir-2054	69	1	next	next	ADV
asir-2054	69	2	we	we	PRON
asir-2054	69	3	show	show	VERB
asir-2054	69	4	that	that	SCONJ
asir-2054	69	5	(	(	PUNCT
asir-2054	69	6	c	c	X
asir-2054	69	7	)	)	PUNCT
asir-2054	69	8	is	be	AUX
asir-2054	69	9	true	true	ADJ
asir-2054	69	10	.	.	PUNCT
asir-2054	70	1	by	by	ADP
asir-2054	70	2	(	(	PUNCT
asir-2054	70	3	a	a	X
asir-2054	70	4	)	)	PUNCT
asir-2054	70	5	,	,	PUNCT
asir-2054	70	6	any	any	DET
asir-2054	70	7	two	two	NUM
asir-2054	70	8	3	3	NUM
asir-2054	70	9	-	-	PUNCT
asir-2054	70	10	vertices	vertex	NOUN
asir-2054	70	11	are	be	AUX
asir-2054	70	12	not	not	PART
asir-2054	70	13	adjacent	adjacent	ADJ
asir-2054	70	14	,	,	PUNCT
asir-2054	70	15	that	that	ADV
asir-2054	70	16	is	is	ADV
asir-2054	70	17	,	,	PUNCT
asir-2054	70	18	g3	g3	PROPN
asir-2054	70	19	does	do	AUX
asir-2054	70	20	not	not	PART
asir-2054	70	21	contain	contain	VERB
asir-2054	70	22	odd	odd	ADJ
asir-2054	70	23	cycles	cycle	NOUN
asir-2054	70	24	.	.	PUNCT
asir-2054	71	1	thus	thus	ADV
asir-2054	71	2	g	g	PROPN
asir-2054	71	3	3	3	NUM
asir-2054	71	4	is	be	AUX
asir-2054	71	5	a	a	DET
asir-2054	71	6	bipartite	bipartite	ADJ
asir-2054	71	7	graph	graph	NOUN
asir-2054	71	8	with	with	ADP
asir-2054	71	9	partite	partite	ADJ
asir-2054	71	10	sets	set	NOUN
asir-2054	71	11	v	v	ADP
asir-2054	71	12	1	1	NUM
asir-2054	71	13	,	,	PUNCT
asir-2054	71	14	v	v	NOUN
asir-2054	71	15	2	2	NUM
asir-2054	71	16	,	,	PUNCT
asir-2054	71	17	so	so	SCONJ
asir-2054	71	18	that	that	SCONJ
asir-2054	71	19	v	v	NOUN
asir-2054	71	20	(	(	PUNCT
asir-2054	71	21	g	g	NOUN
asir-2054	71	22	)	)	PUNCT
asir-2054	71	23	=	=	SYM
asir-2054	72	1	v1	v1	VERB
asir-2054	72	2	u	u	NOUN
asir-2054	72	3	v2	v2	NOUN
asir-2054	72	4	and	and	CCONJ
asir-2054	72	5	for	for	ADP
asir-2054	72	6	each	each	DET
asir-2054	72	7	vertex	vertex	NOUN
asir-2054	72	8	v	v	ADP
asir-2054	72	9	∈	∈	PROPN
asir-2054	72	10	v1	v1	NOUN
asir-2054	72	11	,	,	PUNCT
asir-2054	72	12	dg(v	dg(v	PUNCT
asir-2054	72	13	)	)	PUNCT
asir-2054	72	14	=	=	SYM
asir-2054	72	15	3	3	NUM
asir-2054	72	16	;	;	PUNCT
asir-2054	72	17	for	for	ADP
asir-2054	72	18	each	each	DET
asir-2054	72	19	vertex	vertex	NOUN
asir-2054	72	20	v	v	ADP
asir-2054	72	21	∈	∈	PROPN
asir-2054	72	22	v2	v2	NOUN
asir-2054	72	23	,	,	PUNCT
asir-2054	72	24	dg(v	dg(v	PUNCT
asir-2054	72	25	)	)	PUNCT
asir-2054	72	26	=	=	PUNCT
asir-2054	73	1	∆.	∆.	NOUN
asir-2054	73	2	since	since	SCONJ
asir-2054	73	3	g	g	PROPN
asir-2054	73	4	does	do	AUX
asir-2054	73	5	not	not	PART
asir-2054	73	6	satisfy	satisfy	VERB
asir-2054	73	7	(	(	PUNCT
asir-2054	73	8	2	2	NUM
asir-2054	73	9	)	)	PUNCT
asir-2054	73	10	,	,	PUNCT
asir-2054	73	11	g3	g3	PROPN
asir-2054	73	12	contains	contain	VERB
asir-2054	73	13	no	no	DET
asir-2054	73	14	even	even	ADV
asir-2054	73	15	cycles	cycle	NOUN
asir-2054	73	16	.	.	PUNCT
asir-2054	74	1	so	so	ADV
asir-2054	74	2	g3	g3	PROPN
asir-2054	74	3	is	be	AUX
asir-2054	74	4	a	a	DET
asir-2054	74	5	forest	forest	NOUN
asir-2054	74	6	.	.	PUNCT
asir-2054	75	1	for	for	ADP
asir-2054	75	2	any	any	DET
asir-2054	75	3	component	component	NOUN
asir-2054	75	4	of	of	ADP
asir-2054	75	5	g3	g3	NOUN
asir-2054	75	6	,	,	PUNCT
asir-2054	75	7	we	we	PRON
asir-2054	75	8	select	select	VERB
asir-2054	75	9	a	a	DET
asir-2054	75	10	vertex	vertex	NOUN
asir-2054	75	11	u	u	NOUN
asir-2054	75	12	with	with	ADP
asir-2054	75	13	dg(u	dg(u	NOUN
asir-2054	75	14	)	)	PUNCT
asir-2054	75	15	=	=	SYM
asir-2054	75	16	3	3	NUM
asir-2054	75	17	as	as	ADP
asir-2054	75	18	the	the	DET
asir-2054	75	19	root	root	NOUN
asir-2054	75	20	of	of	ADP
asir-2054	75	21	the	the	DET
asir-2054	75	22	tree	tree	NOUN
asir-2054	75	23	.	.	PUNCT
asir-2054	76	1	thus	thus	ADV
asir-2054	76	2	,	,	PUNCT
asir-2054	76	3	every	every	DET
asir-2054	76	4	3	3	NUM
asir-2054	76	5	-	-	PUNCT
asir-2054	76	6	vertex	vertex	NOUN
asir-2054	76	7	has	have	VERB
asir-2054	76	8	exactly	exactly	ADV
asir-2054	76	9	two	two	NUM
asir-2054	76	10	children	child	NOUN
asir-2054	76	11	.	.	PUNCT
asir-2054	77	1	we	we	PRON
asir-2054	77	2	obtain	obtain	VERB
asir-2054	77	3	g	g	NOUN
asir-2054	77	4	'	'	PUNCT
asir-2054	77	5	by	by	ADP
asir-2054	77	6	letting	let	VERB
asir-2054	77	7	v	v	ADP
asir-2054	77	8	2	2	NUM
asir-2054	77	9	=	=	SYM
asir-2054	77	10	{	{	PUNCT
asir-2054	77	11	v	v	NOUN
asir-2054	77	12	:	:	PUNCT
asir-2054	77	13	v	v	NOUN
asir-2054	77	14	is	be	AUX
asir-2054	77	15	a	a	DET
asir-2054	77	16	child	child	NOUN
asir-2054	77	17	of	of	ADP
asir-2054	77	18	a	a	DET
asir-2054	77	19	3	3	NUM
asir-2054	77	20	-	-	PUNCT
asir-2054	77	21	vertex	vertex	NOUN
asir-2054	77	22	}	}	PUNCT
asir-2054	77	23	and	and	CCONJ
asir-2054	77	24	e(g	e(g	PROPN
asir-2054	77	25	'	'	PUNCT
asir-2054	77	26	)	)	PUNCT
asir-2054	78	1	=	=	PRON
asir-2054	78	2	{	{	PUNCT
asir-2054	78	3	uv	uv	NOUN
asir-2054	78	4	:	:	PUNCT
asir-2054	78	5	u	u	NOUN
asir-2054	78	6	is	be	AUX
asir-2054	78	7	3	3	NUM
asir-2054	78	8	-	-	PUNCT
asir-2054	78	9	vertex	vertex	NOUN
asir-2054	78	10	and	and	CCONJ
asir-2054	78	11	v	v	NOUN
asir-2054	78	12	is	be	AUX
asir-2054	78	13	a	a	DET
asir-2054	78	14	child	child	NOUN
asir-2054	78	15	of	of	ADP
asir-2054	78	16	u	u	NOUN
asir-2054	78	17	}	}	PUNCT
asir-2054	78	18	.	.	PUNCT
asir-2054	79	1	so	so	ADV
asir-2054	79	2	(	(	PUNCT
asir-2054	79	3	c	c	X
asir-2054	79	4	)	)	PUNCT
asir-2054	79	5	holds	hold	NOUN
asir-2054	79	6	.	.	PUNCT
asir-2054	80	1	since	since	SCONJ
asir-2054	80	2	g	g	PROPN
asir-2054	80	3	has	have	VERB
asir-2054	80	4	properties	property	NOUN
asir-2054	80	5	(	(	PUNCT
asir-2054	80	6	a	a	NOUN
asir-2054	80	7	)	)	PUNCT
asir-2054	80	8	,	,	PUNCT
asir-2054	80	9	and	and	CCONJ
asir-2054	80	10	g	g	NOUN
asir-2054	80	11	contains	contain	VERB
asir-2054	80	12	no	no	DET
asir-2054	80	13	7	7	NUM
asir-2054	80	14	-	-	PUNCT
asir-2054	80	15	cycles	cycle	NOUN
asir-2054	80	16	with	with	ADP
asir-2054	80	17	three	three	NUM
asir-2054	80	18	chords	chord	NOUN
asir-2054	80	19	.	.	PUNCT
asir-2054	80	20	suppose	suppose	VERB
asir-2054	80	21	that	that	SCONJ
asir-2054	80	22	v	v	NOUN
asir-2054	80	23	is	be	AUX
asir-2054	80	24	a	a	DET
asir-2054	80	25	5	5	NUM
asir-2054	80	26	-	-	PUNCT
asir-2054	80	27	vertex	vertex	NOUN
asir-2054	80	28	in	in	ADP
asir-2054	80	29	g.	g.	PROPN
asir-2054	80	30	then	then	ADV
asir-2054	80	31	we	we	PRON
asir-2054	80	32	can	can	AUX
asir-2054	80	33	get	get	VERB
asir-2054	80	34	the	the	DET
asir-2054	80	35	following	follow	VERB
asir-2054	80	36	observations	observation	NOUN
asir-2054	80	37	easily	easily	ADV
asir-2054	80	38	:	:	PUNCT
asir-2054	80	39	(	(	PUNCT
asir-2054	80	40	o1	o1	NOUN
asir-2054	80	41	)	)	PUNCT
asir-2054	80	42	if	if	SCONJ
asir-2054	80	43	f	f	PROPN
asir-2054	80	44	3	3	NUM
asir-2054	80	45	(	(	PUNCT
asir-2054	80	46	v	v	NOUN
asir-2054	80	47	)	)	PUNCT
asir-2054	80	48	=	=	SYM
asir-2054	80	49	4	4	NUM
asir-2054	80	50	and	and	CCONJ
asir-2054	80	51	f	f	PROPN
asir-2054	80	52	4	4	NUM
asir-2054	80	53	(	(	PUNCT
asir-2054	80	54	v	v	NOUN
asir-2054	80	55	)	)	PUNCT
asir-2054	80	56	=	=	SYM
asir-2054	80	57	1	1	NUM
asir-2054	80	58	(	(	PUNCT
asir-2054	80	59	as	as	ADP
asir-2054	80	60	in	in	ADP
asir-2054	80	61	figure	figure	NOUN
asir-2054	80	62	1	1	NUM
asir-2054	80	63	)	)	PUNCT
asir-2054	80	64	,	,	PUNCT
asir-2054	80	65	then	then	ADV
asir-2054	80	66	f	f	PROPN
asir-2054	80	67	5	5	NUM
asir-2054	80	68	+	+	CCONJ
asir-2054	80	69	(	(	PUNCT
asir-2054	80	70	v	v	NOUN
asir-2054	80	71	1	1	NUM
asir-2054	80	72	)	)	PUNCT
asir-2054	80	73	≥	≥	NOUN
asir-2054	80	74	2	2	NUM
asir-2054	80	75	;	;	PUNCT
asir-2054	80	76	(	(	PUNCT
asir-2054	80	77	o2	o2	PROPN
asir-2054	80	78	)	)	PUNCT
asir-2054	80	79	if	if	SCONJ
asir-2054	80	80	f	f	PROPN
asir-2054	80	81	3	3	NUM
asir-2054	80	82	(	(	PUNCT
asir-2054	80	83	v	v	NOUN
asir-2054	80	84	)	)	PUNCT
asir-2054	80	85	=	=	SYM
asir-2054	80	86	5	5	NUM
asir-2054	80	87	and	and	CCONJ
asir-2054	80	88	f	f	PROPN
asir-2054	80	89	4	4	NUM
asir-2054	80	90	(	(	PUNCT
asir-2054	80	91	v	v	NOUN
asir-2054	80	92	)	)	PUNCT
asir-2054	80	93	=	=	SYM
asir-2054	80	94	1	1	NUM
asir-2054	80	95	,	,	PUNCT
asir-2054	80	96	then	then	ADV
asir-2054	80	97	for	for	ADP
asir-2054	80	98	any	any	DET
asir-2054	80	99	neighbor	neighbor	NOUN
asir-2054	80	100	x	x	PROPN
asir-2054	80	101	of	of	ADP
asir-2054	80	102	v	v	NOUN
asir-2054	80	103	,	,	PUNCT
asir-2054	80	104	f	f	PROPN
asir-2054	80	105	5	5	NUM
asir-2054	80	106	+	+	CCONJ
asir-2054	80	107	(	(	PUNCT
asir-2054	80	108	x	x	X
asir-2054	80	109	)	)	PUNCT
asir-2054	80	110	≥	≥	NOUN
asir-2054	80	111	2	2	NUM
asir-2054	80	112	.	.	PUNCT
asir-2054	80	113	suppose	suppose	VERB
asir-2054	80	114	that	that	SCONJ
asir-2054	80	115	g	g	PROPN
asir-2054	80	116	is	be	AUX
asir-2054	80	117	embedded	embed	VERB
asir-2054	80	118	in	in	ADP
asir-2054	80	119	the	the	DET
asir-2054	80	120	plane	plane	NOUN
asir-2054	80	121	.	.	PUNCT
asir-2054	81	1	by	by	ADP
asir-2054	81	2	euler	euler	PROPN
asir-2054	81	3	’s	’s	PART
asir-2054	81	4	formula	formula	NOUN
asir-2054	81	5	|v	|v	X
asir-2054	81	6	(	(	PUNCT
asir-2054	81	7	g)|−|e(g)|+|f	g)|−|e(g)|+|f	X
asir-2054	81	8	(	(	PUNCT
asir-2054	81	9	g)|	g)|	NOUN
asir-2054	81	10	=	=	SYM
asir-2054	81	11	2	2	NUM
asir-2054	81	12	,	,	PUNCT
asir-2054	81	13	we	we	PRON
asir-2054	81	14	have	have	VERB
asir-2054	81	15	∑	∑	ADV
asir-2054	81	16	(	(	PUNCT
asir-2054	81	17	𝑑(𝑥	𝑑(𝑥	PROPN
asir-2054	81	18	)	)	PUNCT
asir-2054	81	19	−	−	ADP
asir-2054	82	1	4	4	X
asir-2054	82	2	)	)	PUNCT
asir-2054	82	3	+	+	CCONJ
asir-2054	82	4	∑	∑	PROPN
asir-2054	82	5	(	(	PUNCT
asir-2054	82	6	𝑑(𝑥	𝑑(𝑥	PROPN
asir-2054	82	7	)	)	PUNCT
asir-2054	82	8	−	−	ADP
asir-2054	82	9	4	4	X
asir-2054	82	10	)	)	PUNCT
asir-2054	82	11	=	=	PUNCT
asir-2054	83	1	−8	−8	X
asir-2054	83	2	<	<	X
asir-2054	83	3	0	0	NUM
asir-2054	83	4	𝑥∈𝐹(𝐺)𝑥∈𝑉(𝐺	𝑥∈𝐹(𝐺)𝑥∈𝑉(𝐺	NOUN
asir-2054	83	5	)	)	PUNCT
asir-2054	83	6	we	we	PRON
asir-2054	83	7	define	define	VERB
asir-2054	83	8	ch	ch	NOUN
asir-2054	83	9	to	to	PART
asir-2054	83	10	be	be	AUX
asir-2054	83	11	the	the	DET
asir-2054	83	12	initial	initial	ADJ
asir-2054	83	13	charge	charge	NOUN
asir-2054	83	14	.	.	PUNCT
asir-2054	84	1	let	let	VERB
asir-2054	84	2	ch(x	ch(x	PUNCT
asir-2054	84	3	)	)	PUNCT
asir-2054	84	4	=	=	SYM
asir-2054	84	5	d(x	d(x	NOUN
asir-2054	84	6	)	)	PUNCT
asir-2054	84	7	−	−	ADP
asir-2054	84	8	4	4	NUM
asir-2054	84	9	for	for	ADP
asir-2054	84	10	each	each	DET
asir-2054	84	11	x	x	SYM
asir-2054	84	12	∈	∈	PROPN
asir-2054	84	13	v	v	NOUN
asir-2054	84	14	∪	∪	VERB
asir-2054	84	15	f.	f.	PROPN
asir-2054	84	16	so	so	ADV
asir-2054	84	17	∑	∑	PUNCT
asir-2054	84	18	𝑐ℎ(𝑥	𝑐ℎ(𝑥	ADJ
asir-2054	84	19	)	)	PUNCT
asir-2054	84	20	<	<	X
asir-2054	84	21	𝑥∈𝑉∪𝐹	𝑥∈𝑉∪𝐹	PUNCT
asir-2054	84	22	0	0	NUM
asir-2054	84	23	.	.	PUNCT
asir-2054	85	1	then	then	ADV
asir-2054	85	2	we	we	PRON
asir-2054	85	3	apply	apply	VERB
asir-2054	85	4	the	the	DET
asir-2054	85	5	following	follow	VERB
asir-2054	85	6	rules	rule	NOUN
asir-2054	85	7	to	to	PART
asir-2054	85	8	redistribute	redistribute	VERB
asir-2054	85	9	the	the	DET
asir-2054	85	10	initial	initial	ADJ
asir-2054	85	11	charge	charge	NOUN
asir-2054	85	12	that	that	PRON
asir-2054	85	13	leads	lead	VERB
asir-2054	85	14	to	to	ADP
asir-2054	85	15	a	a	DET
asir-2054	85	16	new	new	ADJ
asir-2054	85	17	charge	charge	NOUN
asir-2054	85	18	ch	ch	NOUN
asir-2054	85	19	'	'	PUNCT
asir-2054	85	20	(	(	PUNCT
asir-2054	85	21	x	x	X
asir-2054	85	22	)	)	PUNCT
asir-2054	85	23	to	to	ADP
asir-2054	85	24	each	each	DET
asir-2054	85	25	x	x	SYM
asir-2054	85	26	∈	∈	PROPN
asir-2054	85	27	v	v	NOUN
asir-2054	85	28	∪	∪	VERB
asir-2054	85	29	f.	f.	PROPN
asir-2054	85	30	since	since	SCONJ
asir-2054	85	31	our	our	PRON
asir-2054	85	32	rules	rule	NOUN
asir-2054	85	33	only	only	ADV
asir-2054	85	34	move	move	VERB
asir-2054	85	35	charges	charge	NOUN
asir-2054	85	36	around	around	ADV
asir-2054	85	37	,	,	PUNCT
asir-2054	85	38	and	and	CCONJ
asir-2054	85	39	do	do	AUX
asir-2054	85	40	not	not	PART
asir-2054	85	41	affect	affect	VERB
asir-2054	85	42	the	the	DET
asir-2054	85	43	sum	sum	NOUN
asir-2054	85	44	.	.	PUNCT
asir-2054	86	1	if	if	SCONJ
asir-2054	86	2	we	we	PRON
asir-2054	86	3	can	can	AUX
asir-2054	86	4	show	show	VERB
asir-2054	86	5	that	that	DET
asir-2054	86	6	ch	ch	NOUN
asir-2054	86	7	'	'	PUNCT
asir-2054	86	8	(	(	PUNCT
asir-2054	86	9	x	x	X
asir-2054	86	10	)	)	PUNCT
asir-2054	86	11	≥	≥	NOUN
asir-2054	86	12	0	0	NUM
asir-2054	86	13	for	for	ADP
asir-2054	86	14	each	each	DET
asir-2054	86	15	x	x	NOUN
asir-2054	86	16	,	,	PUNCT
asir-2054	86	17	then	then	ADV
asir-2054	86	18	we	we	PRON
asir-2054	86	19	get	get	VERB
asir-2054	86	20	an	an	DET
asir-2054	86	21	obvious	obvious	ADJ
asir-2054	86	22	contradiction	contradiction	NOUN
asir-2054	86	23	,	,	PUNCT
asir-2054	86	24	0	0	NUM
asir-2054	86	25	≤	≤	NUM
asir-2054	86	26	∑	∑	PUNCT
asir-2054	86	27	𝑐ℎ′(𝑥	𝑐ℎ′(𝑥	PROPN
asir-2054	86	28	)	)	PUNCT
asir-2054	86	29	=	=	NOUN
asir-2054	86	30	𝑥∈𝑉∪𝐹	𝑥∈𝑉∪𝐹	PUNCT
asir-2054	86	31	∑	∑	INTJ
asir-2054	86	32	𝑐ℎ(𝑥	𝑐ℎ(𝑥	ADJ
asir-2054	86	33	)	)	PUNCT
asir-2054	86	34	<	<	X
asir-2054	86	35	0𝑥∈𝑉∪𝐹	0𝑥∈𝑉∪𝐹	NUM
asir-2054	86	36	.	.	PUNCT
asir-2054	87	1	which	which	PRON
asir-2054	87	2	completes	complete	VERB
asir-2054	87	3	our	our	PRON
asir-2054	87	4	proof	proof	NOUN
asir-2054	87	5	.	.	PUNCT
asir-2054	88	1	figure	figure	NOUN
asir-2054	88	2	1	1	NUM
asir-2054	88	3	.	.	PUNCT
asir-2054	89	1	black	black	ADJ
asir-2054	89	2	vertices	vertex	NOUN
asir-2054	89	3	do	do	AUX
asir-2054	89	4	not	not	PART
asir-2054	89	5	have	have	VERB
asir-2054	89	6	neighbors	neighbor	NOUN
asir-2054	89	7	other	other	ADJ
asir-2054	89	8	than	than	SCONJ
asir-2054	89	9	presented	present	VERB
asir-2054	89	10	in	in	ADP
asir-2054	89	11	the	the	DET
asir-2054	89	12	picture	picture	NOUN
asir-2054	89	13	,	,	PUNCT
asir-2054	89	14	white	white	ADJ
asir-2054	89	15	vertices	vertex	NOUN
asir-2054	89	16	can	can	AUX
asir-2054	89	17	be	be	AUX
asir-2054	89	18	adjacent	adjacent	ADJ
asir-2054	89	19	to	to	ADP
asir-2054	89	20	some	some	DET
asir-2054	89	21	other	other	ADJ
asir-2054	89	22	vertices	vertex	NOUN
asir-2054	89	23	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2054	89	24	applied	apply	VERB
asir-2054	89	25	science	science	NOUN
asir-2054	89	26	and	and	CCONJ
asir-2054	89	27	innovative	innovative	ADJ
asir-2054	89	28	research	research	NOUN
asir-2054	89	29	vol	vol	NOUN
asir-2054	89	30	.	.	PUNCT
asir-2054	90	1	3	3	NUM
asir-2054	90	2	,	,	PUNCT
asir-2054	90	3	no	no	INTJ
asir-2054	90	4	.	.	NOUN
asir-2054	90	5	2	2	NUM
asir-2054	90	6	,	,	PUNCT
asir-2054	90	7	2019	2019	NUM
asir-2054	90	8	88	88	NUM
asir-2054	90	9	published	publish	VERB
asir-2054	90	10	by	by	ADP
asir-2054	90	11	scholink	scholink	PROPN
asir-2054	90	12	inc	inc	PROPN
asir-2054	90	13	.	.	PUNCT
asir-2054	91	1	the	the	DET
asir-2054	91	2	discharging	discharge	VERB
asir-2054	91	3	rules	rule	NOUN
asir-2054	91	4	are	be	AUX
asir-2054	91	5	defined	define	VERB
asir-2054	91	6	as	as	ADP
asir-2054	91	7	follows	follow	VERB
asir-2054	91	8	.	.	PUNCT
asir-2054	92	1	r1	r1	PROPN
asir-2054	92	2	.	.	PUNCT
asir-2054	93	1	every	every	DET
asir-2054	93	2	3	3	NUM
asir-2054	93	3	-	-	PUNCT
asir-2054	93	4	vertex	vertex	NOUN
asir-2054	93	5	receives	receive	VERB
asir-2054	93	6	1	1	NUM
asir-2054	93	7	2	2	NUM
asir-2054	93	8	from	from	ADP
asir-2054	93	9	each	each	PRON
asir-2054	93	10	of	of	ADP
asir-2054	93	11	its	its	PRON
asir-2054	93	12	two	two	NUM
asir-2054	93	13	3	3	NUM
asir-2054	93	14	-	-	PUNCT
asir-2054	93	15	masters	master	NOUN
asir-2054	93	16	.	.	PUNCT
asir-2054	94	1	r2	r2	PROPN
asir-2054	94	2	.	.	PUNCT
asir-2054	95	1	let	let	VERB
asir-2054	95	2	f	f	PRON
asir-2054	95	3	be	be	AUX
asir-2054	95	4	a	a	DET
asir-2054	95	5	3	3	NUM
asir-2054	95	6	-	-	PUNCT
asir-2054	95	7	face	face	NOUN
asir-2054	95	8	uvw	uvw	NOUN
asir-2054	95	9	and	and	CCONJ
asir-2054	95	10	assume	assume	VERB
asir-2054	95	11	that	that	SCONJ
asir-2054	95	12	d(u	d(u	PROPN
asir-2054	95	13	)	)	PUNCT
asir-2054	95	14	≤	≤	NUM
asir-2054	95	15	d(v	d(v	PROPN
asir-2054	95	16	)	)	PUNCT
asir-2054	95	17	≤	≤	NUM
asir-2054	95	18	d(w	d(w	PROPN
asir-2054	95	19	)	)	PUNCT
asir-2054	95	20	.	.	PUNCT
asir-2054	96	1	r2.1	r2.1	VERB
asir-2054	96	2	if	if	SCONJ
asir-2054	96	3	d(u	d(u	PROPN
asir-2054	96	4	)	)	PUNCT
asir-2054	96	5	=	=	SYM
asir-2054	96	6	3	3	NUM
asir-2054	96	7	or	or	CCONJ
asir-2054	96	8	4	4	NUM
asir-2054	96	9	,	,	PUNCT
asir-2054	96	10	then	then	ADV
asir-2054	96	11	f	f	PROPN
asir-2054	96	12	receives	receive	VERB
asir-2054	96	13	1	1	NUM
asir-2054	96	14	2	2	NUM
asir-2054	96	15	from	from	ADP
asir-2054	96	16	v	v	NOUN
asir-2054	96	17	and	and	CCONJ
asir-2054	96	18	w	w	NOUN
asir-2054	96	19	respectively	respectively	ADV
asir-2054	96	20	;	;	PUNCT
asir-2054	96	21	r2.2	r2.2	PROPN
asir-2054	96	22	if	if	SCONJ
asir-2054	96	23	d(u	d(u	PROPN
asir-2054	96	24	)	)	PUNCT
asir-2054	96	25	≥	≥	NOUN
asir-2054	96	26	5	5	NUM
asir-2054	96	27	,	,	PUNCT
asir-2054	96	28	then	then	ADV
asir-2054	96	29	f	f	PROPN
asir-2054	96	30	receives	receive	VERB
asir-2054	96	31	1	1	NUM
asir-2054	96	32	3	3	NUM
asir-2054	96	33	from	from	ADP
asir-2054	96	34	u	u	PROPN
asir-2054	96	35	,	,	PUNCT
asir-2054	96	36	v	v	NOUN
asir-2054	96	37	and	and	CCONJ
asir-2054	96	38	w	w	NOUN
asir-2054	96	39	respectively	respectively	ADV
asir-2054	96	40	.	.	PUNCT
asir-2054	97	1	r3	r3	PROPN
asir-2054	97	2	.	.	PUNCT
asir-2054	98	1	let	let	VERB
asir-2054	98	2	f	f	PRON
asir-2054	98	3	be	be	AUX
asir-2054	98	4	a	a	DET
asir-2054	98	5	5	5	NUM
asir-2054	98	6	+	+	NOUN
asir-2054	98	7	-face	-face	NOUN
asir-2054	98	8	and	and	CCONJ
asir-2054	98	9	t	t	X
asir-2054	98	10	the	the	DET
asir-2054	98	11	number	number	NOUN
asir-2054	98	12	of	of	ADP
asir-2054	98	13	5	5	NUM
asir-2054	98	14	-	-	PUNCT
asir-2054	98	15	vertices	vertex	NOUN
asir-2054	98	16	satisfying	satisfy	VERB
asir-2054	98	17	f3(v	f3(v	NOUN
asir-2054	98	18	)	)	PUNCT
asir-2054	98	19	=	=	SYM
asir-2054	98	20	4	4	NUM
asir-2054	98	21	on	on	ADP
asir-2054	98	22	f.	f.	PROPN
asir-2054	98	23	r3.1	r3.1	PROPN
asir-2054	98	24	if	if	SCONJ
asir-2054	98	25	t	t	NOUN
asir-2054	98	26	=	=	SYM
asir-2054	98	27	0	0	NUM
asir-2054	98	28	,	,	PUNCT
asir-2054	98	29	then	then	ADV
asir-2054	98	30	every	every	PRON
asir-2054	98	31	of	of	ADP
asir-2054	98	32	vertices	vertex	NOUN
asir-2054	98	33	incident	incident	NOUN
asir-2054	98	34	with	with	ADP
asir-2054	98	35	f	f	PROPN
asir-2054	98	36	receives	receive	VERB
asir-2054	98	37	𝑑(𝑓)−4	𝑑(𝑓)−4	NOUN
asir-2054	98	38	𝑑(𝑓	𝑑(𝑓	PROPN
asir-2054	98	39	)	)	PUNCT
asir-2054	98	40	from	from	ADP
asir-2054	98	41	f	f	NOUN
asir-2054	98	42	;	;	PUNCT
asir-2054	98	43	r3.2	r3.2	PROPN
asir-2054	98	44	otherwise	otherwise	ADV
asir-2054	98	45	t	t	X
asir-2054	98	46	≥	≥	NUM
asir-2054	98	47	1	1	NUM
asir-2054	98	48	.	.	PUNCT
asir-2054	98	49	suppose	suppose	VERB
asir-2054	98	50	v	v	NOUN
asir-2054	98	51	is	be	AUX
asir-2054	98	52	such	such	DET
asir-2054	98	53	a	a	DET
asir-2054	98	54	vertex	vertex	NOUN
asir-2054	98	55	,	,	PUNCT
asir-2054	98	56	then	then	ADV
asir-2054	98	57	the	the	DET
asir-2054	98	58	every	every	PRON
asir-2054	98	59	of	of	ADP
asir-2054	98	60	remaining	remain	VERB
asir-2054	98	61	vertices	vertex	NOUN
asir-2054	98	62	incident	incident	NOUN
asir-2054	98	63	with	with	ADP
asir-2054	98	64	f	f	PROPN
asir-2054	98	65	receives	receive	VERB
asir-2054	98	66	𝑑(𝑓)−4	𝑑(𝑓)−4	NOUN
asir-2054	98	67	𝑑(𝑓)−2	𝑑(𝑓)−2	NOUN
asir-2054	98	68	from	from	ADP
asir-2054	98	69	f	f	PROPN
asir-2054	98	70	besides	besides	SCONJ
asir-2054	98	71	its	its	PRON
asir-2054	98	72	two	two	NUM
asir-2054	98	73	neighbors	neighbor	NOUN
asir-2054	98	74	on	on	ADP
asir-2054	98	75	f.	f.	PROPN
asir-2054	98	76	r4	r4	PROPN
asir-2054	98	77	.	.	PUNCT
asir-2054	99	1	let	let	VERB
asir-2054	99	2	v	v	PART
asir-2054	99	3	be	be	AUX
asir-2054	99	4	a	a	DET
asir-2054	99	5	5	5	NUM
asir-2054	99	6	-	-	PUNCT
asir-2054	99	7	vertex	vertex	NOUN
asir-2054	99	8	.	.	PUNCT
asir-2054	100	1	r4.1	r4.1	ADV
asir-2054	100	2	if	if	SCONJ
asir-2054	100	3	f3(v	f3(v	NOUN
asir-2054	100	4	)	)	PUNCT
asir-2054	100	5	=	=	SYM
asir-2054	100	6	4	4	NUM
asir-2054	100	7	and	and	CCONJ
asir-2054	100	8	f4(v	f4(v	NUM
asir-2054	100	9	)	)	PUNCT
asir-2054	101	1	=	=	SYM
asir-2054	101	2	1	1	NUM
asir-2054	101	3	(	(	PUNCT
asir-2054	101	4	as	as	ADP
asir-2054	101	5	in	in	ADP
asir-2054	101	6	figure	figure	NOUN
asir-2054	101	7	1	1	NUM
asir-2054	101	8	)	)	PUNCT
asir-2054	101	9	,	,	PUNCT
asir-2054	101	10	then	then	ADV
asir-2054	101	11	v	v	NOUN
asir-2054	101	12	receives	receive	VERB
asir-2054	101	13	at	at	ADV
asir-2054	101	14	least	least	ADJ
asir-2054	101	15	1	1	NUM
asir-2054	101	16	3	3	NUM
asir-2054	101	17	from	from	ADP
asir-2054	101	18	w	w	ADP
asir-2054	101	19	by	by	ADP
asir-2054	101	20	(	(	PUNCT
asir-2054	101	21	o1	o1	NOUN
asir-2054	101	22	)	)	PUNCT
asir-2054	101	23	;	;	PUNCT
asir-2054	101	24	r4.2	r4.2	NOUN
asir-2054	101	25	if	if	SCONJ
asir-2054	101	26	f3(v	f3(v	NOUN
asir-2054	101	27	)	)	PUNCT
asir-2054	101	28	=	=	SYM
asir-2054	101	29	5	5	NUM
asir-2054	101	30	,	,	PUNCT
asir-2054	101	31	then	then	ADV
asir-2054	101	32	v	v	NOUN
asir-2054	101	33	receives	receive	VERB
asir-2054	101	34	1	1	NUM
asir-2054	101	35	5	5	NUM
asir-2054	101	36	from	from	ADP
asir-2054	101	37	each	each	PRON
asir-2054	101	38	of	of	ADP
asir-2054	101	39	the	the	DET
asir-2054	101	40	neighbors	neighbor	NOUN
asir-2054	101	41	by	by	ADP
asir-2054	101	42	(	(	PUNCT
asir-2054	101	43	o2	o2	PROPN
asir-2054	101	44	)	)	PUNCT
asir-2054	101	45	.	.	PUNCT
asir-2054	102	1	now	now	ADV
asir-2054	102	2	,	,	PUNCT
asir-2054	102	3	let	let	VERB
asir-2054	102	4	’s	’s	PRON
asir-2054	102	5	begin	begin	VERB
asir-2054	102	6	to	to	PART
asir-2054	102	7	check	check	VERB
asir-2054	102	8	ch'(x	ch'(x	ADP
asir-2054	102	9	)	)	PUNCT
asir-2054	102	10	≥	≥	NOUN
asir-2054	102	11	0	0	NUM
asir-2054	102	12	for	for	ADP
asir-2054	102	13	all	all	DET
asir-2054	102	14	x	x	SYM
asir-2054	102	15	∈	∈	NOUN
asir-2054	102	16	v	v	NOUN
asir-2054	102	17	∪	∪	PROPN
asir-2054	102	18	f.	f.	PROPN
asir-2054	102	19	let	let	VERB
asir-2054	102	20	f	f	PROPN
asir-2054	102	21	∈	∈	PROPN
asir-2054	102	22	f	f	PROPN
asir-2054	102	23	(	(	PUNCT
asir-2054	102	24	g	g	NOUN
asir-2054	102	25	)	)	PUNCT
asir-2054	102	26	.	.	PUNCT
asir-2054	103	1	then	then	ADV
asir-2054	103	2	d(f	d(f	NOUN
asir-2054	103	3	)	)	PUNCT
asir-2054	103	4	≥	≥	NOUN
asir-2054	103	5	3	3	NUM
asir-2054	103	6	.	.	PUNCT
asir-2054	104	1	if	if	SCONJ
asir-2054	104	2	d(f	d(f	NOUN
asir-2054	104	3	)	)	PUNCT
asir-2054	104	4	=	=	SYM
asir-2054	104	5	3	3	NUM
asir-2054	104	6	,	,	PUNCT
asir-2054	104	7	then	then	ADV
asir-2054	104	8	ch'(f	ch'(f	NUM
asir-2054	104	9	)	)	PUNCT
asir-2054	104	10	=	=	PUNCT
asir-2054	104	11	ch(f)+min{2×	ch(f)+min{2×	NOUN
asir-2054	104	12	1	1	NUM
asir-2054	104	13	2	2	NUM
asir-2054	104	14	,	,	PUNCT
asir-2054	104	15	3×	3×	NUM
asir-2054	104	16	1	1	NUM
asir-2054	104	17	3	3	NUM
asir-2054	104	18	}	}	PUNCT
asir-2054	104	19	=	=	SYM
asir-2054	104	20	0	0	NUM
asir-2054	104	21	by	by	ADP
asir-2054	104	22	r2	r2	PROPN
asir-2054	104	23	.	.	PUNCT
asir-2054	105	1	if	if	SCONJ
asir-2054	105	2	d(f	d(f	NOUN
asir-2054	105	3	)	)	PUNCT
asir-2054	105	4	=	=	SYM
asir-2054	105	5	4	4	NUM
asir-2054	105	6	,	,	PUNCT
asir-2054	105	7	then	then	ADV
asir-2054	105	8	ch'(f	ch'(f	NUM
asir-2054	105	9	)	)	PUNCT
asir-2054	105	10	=	=	SYM
asir-2054	105	11	ch(f	ch(f	NOUN
asir-2054	105	12	)	)	PUNCT
asir-2054	106	1	=	=	NOUN
asir-2054	106	2	0	0	X
asir-2054	106	3	.	.	PUNCT
asir-2054	107	1	if	if	SCONJ
asir-2054	107	2	d(f	d(f	NOUN
asir-2054	107	3	)	)	PUNCT
asir-2054	107	4	≥	≥	NOUN
asir-2054	107	5	5	5	NUM
asir-2054	107	6	,	,	PUNCT
asir-2054	107	7	then	then	ADV
asir-2054	107	8	ch'(f	ch'(f	NUM
asir-2054	107	9	)	)	PUNCT
asir-2054	107	10	≥	≥	NOUN
asir-2054	107	11	ch(f	ch(f	ADV
asir-2054	107	12	)	)	PUNCT
asir-2054	108	1	−	−	PROPN
asir-2054	108	2	𝑑(𝑓)−4	𝑑(𝑓)−4	NOUN
asir-2054	108	3	𝑑(𝑓	𝑑(𝑓	PROPN
asir-2054	108	4	)	)	PUNCT
asir-2054	108	5	×d(f	×d(f	NOUN
asir-2054	108	6	)	)	PUNCT
asir-2054	108	7	=	=	SYM
asir-2054	108	8	0	0	NUM
asir-2054	108	9	or	or	CCONJ
asir-2054	108	10	ch'(f	ch'(f	NUM
asir-2054	108	11	)	)	PUNCT
asir-2054	108	12	≥	≥	NOUN
asir-2054	108	13	ch(f	ch(f	ADV
asir-2054	108	14	)	)	PUNCT
asir-2054	109	1	−	−	PROPN
asir-2054	109	2	𝑑(𝑓)−4	𝑑(𝑓)−4	NOUN
asir-2054	109	3	𝑑(𝑓)−2	𝑑(𝑓)−2	NOUN
asir-2054	109	4	×(d(f	×(d(f	NOUN
asir-2054	109	5	)	)	PUNCT
asir-2054	109	6	−2	−2	NOUN
asir-2054	109	7	)	)	PUNCT
asir-2054	109	8	=	=	SYM
asir-2054	109	9	0	0	NUM
asir-2054	109	10	by	by	ADP
asir-2054	109	11	r3	r3	PROPN
asir-2054	109	12	.	.	PUNCT
asir-2054	110	1	let	let	VERB
asir-2054	110	2	v	v	NUM
asir-2054	110	3	∈	∈	PROPN
asir-2054	110	4	v	v	NOUN
asir-2054	110	5	(	(	PUNCT
asir-2054	110	6	g	g	NOUN
asir-2054	110	7	)	)	PUNCT
asir-2054	110	8	.	.	PUNCT
asir-2054	111	1	then	then	ADV
asir-2054	111	2	d(v	d(v	PROPN
asir-2054	111	3	)	)	PUNCT
asir-2054	111	4	≥	≥	NOUN
asir-2054	112	1	3	3	NUM
asir-2054	112	2	.	.	PUNCT
asir-2054	113	1	if	if	SCONJ
asir-2054	113	2	d(v	d(v	PROPN
asir-2054	113	3	)	)	PUNCT
asir-2054	113	4	=	=	SYM
asir-2054	114	1	3	3	NUM
asir-2054	114	2	,	,	PUNCT
asir-2054	114	3	then	then	ADV
asir-2054	114	4	v	v	NOUN
asir-2054	114	5	is	be	AUX
asir-2054	114	6	exactly	exactly	ADV
asir-2054	114	7	adjacent	adjacent	ADJ
asir-2054	114	8	to	to	ADP
asir-2054	114	9	two	two	NUM
asir-2054	114	10	3	3	NUM
asir-2054	114	11	-	-	PUNCT
asir-2054	114	12	masters	master	NOUN
asir-2054	114	13	,	,	PUNCT
asir-2054	114	14	so	so	ADV
asir-2054	114	15	ch'(v	ch'(v	NOUN
asir-2054	114	16	)	)	PUNCT
asir-2054	114	17	=	=	SYM
asir-2054	114	18	ch(v	ch(v	NOUN
asir-2054	114	19	)	)	PUNCT
asir-2054	115	1	+	+	CCONJ
asir-2054	115	2	2	2	NUM
asir-2054	115	3	×	×	NOUN
asir-2054	115	4	1	1	NUM
asir-2054	115	5	2	2	NUM
asir-2054	115	6	=	=	SYM
asir-2054	115	7	0	0	NUM
asir-2054	115	8	by	by	ADP
asir-2054	115	9	r1	r1	PROPN
asir-2054	115	10	.	.	PUNCT
asir-2054	116	1	if	if	SCONJ
asir-2054	116	2	d(v	d(v	PROPN
asir-2054	116	3	)	)	PUNCT
asir-2054	116	4	=	=	SYM
asir-2054	116	5	4	4	NUM
asir-2054	116	6	,	,	PUNCT
asir-2054	116	7	then	then	ADV
asir-2054	116	8	ch'(v	ch'(v	NOUN
asir-2054	116	9	)	)	PUNCT
asir-2054	116	10	≥	≥	NOUN
asir-2054	116	11	0	0	NUM
asir-2054	117	1	+	+	CCONJ
asir-2054	117	2	min{0	min{0	PROPN
asir-2054	117	3	,	,	PUNCT
asir-2054	117	4	𝑑(𝑓)−4	𝑑(𝑓)−4	PROPN
asir-2054	117	5	𝑑(𝑓)−2	𝑑(𝑓)−2	PROPN
asir-2054	117	6	,	,	PUNCT
asir-2054	117	7	𝑑(𝑓)−4	𝑑(𝑓)−4	PROPN
asir-2054	117	8	𝑑(𝑓	𝑑(𝑓	PROPN
asir-2054	117	9	)	)	PUNCT
asir-2054	117	10	}	}	PUNCT
asir-2054	118	1	=	=	SYM
asir-2054	118	2	0	0	NUM
asir-2054	118	3	by	by	ADP
asir-2054	118	4	r3	r3	PROPN
asir-2054	118	5	.	.	PUNCT
asir-2054	119	1	in	in	ADP
asir-2054	119	2	the	the	DET
asir-2054	119	3	following	following	NOUN
asir-2054	119	4	we	we	PRON
asir-2054	119	5	check	check	VERB
asir-2054	119	6	the	the	DET
asir-2054	119	7	cases	case	NOUN
asir-2054	119	8	that	that	SCONJ
asir-2054	119	9	d(v	d(v	ADJ
asir-2054	119	10	)	)	PUNCT
asir-2054	119	11	=	=	SYM
asir-2054	119	12	5	5	NUM
asir-2054	119	13	,	,	PUNCT
asir-2054	119	14	6	6	NUM
asir-2054	119	15	,	,	PUNCT
asir-2054	119	16	7	7	NUM
asir-2054	119	17	.	.	PUNCT
asir-2054	119	18	case	case	NOUN
asir-2054	119	19	1	1	X
asir-2054	119	20	.	.	PUNCT
asir-2054	120	1	let	let	VERB
asir-2054	120	2	v	v	PART
asir-2054	120	3	be	be	AUX
asir-2054	120	4	a	a	DET
asir-2054	120	5	5	5	NUM
asir-2054	120	6	-	-	PUNCT
asir-2054	120	7	vertex	vertex	NOUN
asir-2054	120	8	.	.	PUNCT
asir-2054	121	1	then	then	ADV
asir-2054	121	2	ch(v	ch(v	VERB
asir-2054	121	3	)	)	PUNCT
asir-2054	121	4	=	=	SYM
asir-2054	121	5	1	1	NUM
asir-2054	121	6	and	and	CCONJ
asir-2054	121	7	all	all	DET
asir-2054	121	8	neighbors	neighbor	NOUN
asir-2054	121	9	of	of	ADP
asir-2054	121	10	5	5	NUM
asir-2054	121	11	-	-	PUNCT
asir-2054	121	12	vertex	vertex	NOUN
asir-2054	121	13	should	should	AUX
asir-2054	121	14	be	be	AUX
asir-2054	121	15	5	5	NUM
asir-2054	121	16	+	+	SYM
asir-2054	121	17	-vertices	-vertice	NOUN
asir-2054	121	18	by	by	ADP
asir-2054	121	19	(	(	PUNCT
asir-2054	121	20	a	a	NOUN
asir-2054	121	21	)	)	PUNCT
asir-2054	121	22	.	.	PUNCT
asir-2054	122	1	if	if	SCONJ
asir-2054	122	2	f3(v	f3(v	NOUN
asir-2054	122	3	)	)	PUNCT
asir-2054	122	4	=	=	SYM
asir-2054	122	5	5	5	NUM
asir-2054	122	6	,	,	PUNCT
asir-2054	122	7	then	then	ADV
asir-2054	122	8	v	v	NOUN
asir-2054	122	9	receives	receive	VERB
asir-2054	122	10	1	1	NUM
asir-2054	122	11	5	5	NUM
asir-2054	122	12	by	by	ADP
asir-2054	122	13	r4.2	r4.2	NOUN
asir-2054	122	14	.	.	PUNCT
asir-2054	123	1	so	so	ADV
asir-2054	123	2	ch'(v	ch'(v	NOUN
asir-2054	123	3	)	)	PUNCT
asir-2054	123	4	≥	≥	NOUN
asir-2054	124	1	1	1	NUM
asir-2054	124	2	+	+	NOUN
asir-2054	124	3	5×	5×	PROPN
asir-2054	124	4	1	1	NUM
asir-2054	124	5	5	5	NUM
asir-2054	124	6	−5×	−5×	SYM
asir-2054	124	7	1	1	NUM
asir-2054	124	8	3	3	NUM
asir-2054	124	9	=	=	SYM
asir-2054	124	10	1	1	NUM
asir-2054	124	11	3	3	NUM
asir-2054	124	12	>	>	SYM
asir-2054	124	13	0	0	NUM
asir-2054	124	14	by	by	ADP
asir-2054	124	15	r2	r2	PROPN
asir-2054	124	16	.	.	PUNCT
asir-2054	124	17	suppose	suppose	VERB
asir-2054	124	18	that	that	SCONJ
asir-2054	124	19	f3(v	f3(v	NOUN
asir-2054	124	20	)	)	PUNCT
asir-2054	125	1	=	=	SYM
asir-2054	125	2	4	4	X
asir-2054	125	3	.	.	X
asir-2054	126	1	if	if	SCONJ
asir-2054	126	2	the	the	DET
asir-2054	126	3	remaining	remain	VERB
asir-2054	126	4	face	face	NOUN
asir-2054	126	5	is	be	AUX
asir-2054	126	6	a	a	DET
asir-2054	126	7	4	4	NUM
asir-2054	126	8	-	-	PUNCT
asir-2054	126	9	face	face	NOUN
asir-2054	126	10	(	(	PUNCT
asir-2054	126	11	as	as	ADP
asir-2054	126	12	figure	figure	NOUN
asir-2054	126	13	1	1	NUM
asir-2054	126	14	)	)	PUNCT
asir-2054	126	15	,	,	PUNCT
asir-2054	126	16	then	then	ADV
asir-2054	126	17	ch'(v	ch'(v	NOUN
asir-2054	126	18	)	)	PUNCT
asir-2054	126	19	≥	≥	NOUN
asir-2054	126	20	1	1	NUM
asir-2054	126	21	−	−	NOUN
asir-2054	126	22	4	4	NUM
asir-2054	126	23	×	×	NOUN
asir-2054	126	24	1	1	NUM
asir-2054	126	25	3	3	NUM
asir-2054	126	26	+	+	CCONJ
asir-2054	126	27	1	1	NUM
asir-2054	126	28	3	3	NUM
asir-2054	126	29	=	=	SYM
asir-2054	126	30	0	0	NUM
asir-2054	126	31	by	by	ADP
asir-2054	126	32	r2	r2	PROPN
asir-2054	126	33	and	and	CCONJ
asir-2054	126	34	r4.1	r4.1	NOUN
asir-2054	126	35	;	;	PUNCT
asir-2054	126	36	otherwise	otherwise	ADV
asir-2054	126	37	the	the	DET
asir-2054	126	38	remaining	remain	VERB
asir-2054	126	39	face	face	NOUN
asir-2054	126	40	is	be	AUX
asir-2054	126	41	a	a	DET
asir-2054	126	42	5	5	NUM
asir-2054	126	43	+	+	NOUN
asir-2054	126	44	-face	-face	NOUN
asir-2054	126	45	.	.	PUNCT
asir-2054	127	1	then	then	ADV
asir-2054	127	2	v	v	NOUN
asir-2054	127	3	receives	receive	VERB
asir-2054	127	4	𝑑(𝑓)−4	𝑑(𝑓)−4	PROPN
asir-2054	127	5	𝑑(𝑓)−2	𝑑(𝑓)−2	PROPN
asir-2054	127	6	≥	≥	NUM
asir-2054	127	7	1	1	NUM
asir-2054	127	8	3	3	NUM
asir-2054	127	9	from	from	ADP
asir-2054	127	10	the	the	DET
asir-2054	127	11	5	5	NUM
asir-2054	127	12	+	+	NOUN
asir-2054	127	13	-face	-face	NOUN
asir-2054	127	14	by	by	ADP
asir-2054	127	15	r3.2	r3.2	NOUN
asir-2054	127	16	.	.	PUNCT
asir-2054	128	1	so	so	ADV
asir-2054	128	2	ch'(v	ch'(v	NOUN
asir-2054	128	3	)	)	PUNCT
asir-2054	128	4	≥	≥	NOUN
asir-2054	128	5	1	1	NUM
asir-2054	129	1	−	−	NOUN
asir-2054	129	2	4	4	NUM
asir-2054	129	3	×	×	NOUN
asir-2054	129	4	1	1	NUM
asir-2054	129	5	3	3	NUM
asir-2054	129	6	+	+	CCONJ
asir-2054	129	7	𝑑(𝑓)−4	𝑑(𝑓)−4	PROPN
asir-2054	129	8	𝑑(𝑓)−2	𝑑(𝑓)−2	PROPN
asir-2054	129	9	≥	≥	NOUN
asir-2054	129	10	0	0	NUM
asir-2054	129	11	by	by	ADP
asir-2054	129	12	r2	r2	PROPN
asir-2054	129	13	and	and	CCONJ
asir-2054	129	14	r3.2	r3.2	NOUN
asir-2054	129	15	.	.	PUNCT
asir-2054	130	1	if	if	SCONJ
asir-2054	130	2	f3(v	f3(v	NOUN
asir-2054	130	3	)	)	PUNCT
asir-2054	130	4	≤	≤	NUM
asir-2054	130	5	3	3	NUM
asir-2054	130	6	,	,	PUNCT
asir-2054	130	7	then	then	ADV
asir-2054	130	8	v	v	NOUN
asir-2054	130	9	may	may	AUX
asir-2054	130	10	send	send	VERB
asir-2054	130	11	some	some	DET
asir-2054	130	12	charge	charge	NOUN
asir-2054	130	13	to	to	ADP
asir-2054	130	14	its	its	PRON
asir-2054	130	15	5	5	NUM
asir-2054	130	16	-	-	NOUN
asir-2054	130	17	neighbors	neighbor	NOUN
asir-2054	130	18	.	.	PUNCT
asir-2054	131	1	so	so	ADV
asir-2054	131	2	there	there	PRON
asir-2054	131	3	are	be	VERB
asir-2054	131	4	two	two	NUM
asir-2054	131	5	subcases	subcase	NOUN
asir-2054	131	6	.	.	PUNCT
asir-2054	132	1	subcase	subcase	PROPN
asir-2054	132	2	2.1	2.1	NUM
asir-2054	132	3	v	v	NOUN
asir-2054	132	4	sends	send	VERB
asir-2054	132	5	no	no	DET
asir-2054	132	6	charge	charge	NOUN
asir-2054	132	7	to	to	ADP
asir-2054	132	8	some	some	DET
asir-2054	132	9	5	5	NUM
asir-2054	132	10	-	-	NOUN
asir-2054	132	11	neighbor	neighbor	NOUN
asir-2054	132	12	.	.	PUNCT
asir-2054	133	1	then	then	ADV
asir-2054	133	2	ch'(v	ch'(v	NOUN
asir-2054	133	3	)	)	PUNCT
asir-2054	133	4	≥	≥	NOUN
asir-2054	134	1	1	1	NUM
asir-2054	134	2	−	−	NOUN
asir-2054	134	3	3	3	NUM
asir-2054	134	4	×	×	NOUN
asir-2054	134	5	1	1	NUM
asir-2054	134	6	3	3	NUM
asir-2054	134	7	=	=	SYM
asir-2054	134	8	0	0	NUM
asir-2054	134	9	by	by	ADP
asir-2054	134	10	r2	r2	PROPN
asir-2054	134	11	.	.	PUNCT
asir-2054	135	1	subcase	subcase	PROPN
asir-2054	135	2	2.2	2.2	NUM
asir-2054	135	3	v	v	NOUN
asir-2054	135	4	sends	send	VERB
asir-2054	135	5	some	some	DET
asir-2054	135	6	charge	charge	NOUN
asir-2054	135	7	to	to	ADP
asir-2054	135	8	some	some	DET
asir-2054	135	9	5	5	NUM
asir-2054	135	10	-	-	NOUN
asir-2054	135	11	neighbor	neighbor	NOUN
asir-2054	135	12	.	.	PUNCT
asir-2054	136	1	suppose	suppose	VERB
asir-2054	136	2	that	that	SCONJ
asir-2054	136	3	v	v	NOUN
asir-2054	136	4	is	be	AUX
asir-2054	136	5	adjacent	adjacent	ADJ
asir-2054	136	6	to	to	ADP
asir-2054	136	7	a	a	DET
asir-2054	136	8	5	5	NUM
asir-2054	136	9	-	-	PUNCT
asir-2054	136	10	vertex	vertex	NOUN
asir-2054	136	11	w	w	NOUN
asir-2054	136	12	such	such	ADJ
asir-2054	136	13	that	that	SCONJ
asir-2054	136	14	f3(w	f3(w	PROPN
asir-2054	136	15	)	)	PUNCT
asir-2054	136	16	=	=	SYM
asir-2054	136	17	4	4	NUM
asir-2054	136	18	and	and	CCONJ
asir-2054	136	19	f4(w	f4(w	PROPN
asir-2054	136	20	)	)	PUNCT
asir-2054	136	21	=	=	SYM
asir-2054	136	22	1	1	NUM
asir-2054	136	23	(	(	PUNCT
asir-2054	136	24	as	as	ADP
asir-2054	136	25	in	in	ADP
asir-2054	136	26	figure	figure	NOUN
asir-2054	136	27	1	1	NUM
asir-2054	136	28	)	)	PUNCT
asir-2054	136	29	,	,	PUNCT
asir-2054	136	30	then	then	ADV
asir-2054	136	31	f3(v	f3(v	NOUN
asir-2054	136	32	)	)	PUNCT
asir-2054	136	33	≤	≤	NUM
asir-2054	136	34	2	2	NUM
asir-2054	136	35	,	,	PUNCT
asir-2054	136	36	f4(v	f4(v	NOUN
asir-2054	136	37	)	)	PUNCT
asir-2054	136	38	=	=	SYM
asir-2054	136	39	1	1	NUM
asir-2054	136	40	and	and	CCONJ
asir-2054	136	41	f5	f5	PROPN
asir-2054	136	42	+	+	CCONJ
asir-2054	136	43	(	(	PUNCT
asir-2054	136	44	v	v	NOUN
asir-2054	136	45	)	)	PUNCT
asir-2054	136	46	=	=	SYM
asir-2054	137	1	2	2	X
asir-2054	137	2	.	.	PUNCT
asir-2054	138	1	so	so	ADV
asir-2054	138	2	ch'(v	ch'(v	NOUN
asir-2054	138	3	)	)	PUNCT
asir-2054	138	4	≥	≥	NOUN
asir-2054	139	1	1	1	NUM
asir-2054	139	2	−	−	NUM
asir-2054	139	3	2	2	NUM
asir-2054	139	4	×	×	NOUN
asir-2054	139	5	1	1	NUM
asir-2054	139	6	3	3	NUM
asir-2054	139	7	−	−	NOUN
asir-2054	139	8	1	1	NUM
asir-2054	139	9	3	3	NUM
asir-2054	139	10	=	=	SYM
asir-2054	139	11	0	0	NUM
asir-2054	139	12	by	by	ADP
asir-2054	139	13	r2	r2	PROPN
asir-2054	139	14	and	and	CCONJ
asir-2054	139	15	r4.1	r4.1	PROPN
asir-2054	139	16	.	.	PROPN
asir-2054	139	17	suppose	suppose	VERB
asir-2054	139	18	that	that	SCONJ
asir-2054	139	19	v	v	NOUN
asir-2054	139	20	is	be	AUX
asir-2054	139	21	adjacent	adjacent	ADJ
asir-2054	139	22	to	to	ADP
asir-2054	139	23	a	a	DET
asir-2054	139	24	5	5	NUM
asir-2054	139	25	-	-	PUNCT
asir-2054	139	26	vertex	vertex	NOUN
asir-2054	139	27	w	w	NOUN
asir-2054	139	28	such	such	ADJ
asir-2054	139	29	that	that	SCONJ
asir-2054	139	30	f3(w	f3(w	PROPN
asir-2054	139	31	)	)	PUNCT
asir-2054	139	32	=	=	SYM
asir-2054	139	33	5	5	X
asir-2054	139	34	.	.	PUNCT
asir-2054	139	35	then	then	ADV
asir-2054	139	36	f3(v	f3(v	NOUN
asir-2054	139	37	)	)	PUNCT
asir-2054	139	38	≤	≤	NUM
asir-2054	139	39	3	3	NUM
asir-2054	139	40	,	,	PUNCT
asir-2054	139	41	f5	f5	PROPN
asir-2054	139	42	+	+	CCONJ
asir-2054	139	43	(	(	PUNCT
asir-2054	139	44	v	v	NOUN
asir-2054	139	45	)	)	PUNCT
asir-2054	139	46	≥	≥	NOUN
asir-2054	139	47	2	2	NUM
asir-2054	139	48	and	and	CCONJ
asir-2054	139	49	each	each	DET
asir-2054	139	50	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2054	139	51	applied	apply	VERB
asir-2054	139	52	science	science	NOUN
asir-2054	139	53	and	and	CCONJ
asir-2054	139	54	innovative	innovative	ADJ
asir-2054	139	55	research	research	NOUN
asir-2054	139	56	vol	vol	NOUN
asir-2054	139	57	.	.	PUNCT
asir-2054	140	1	3	3	NUM
asir-2054	140	2	,	,	PUNCT
asir-2054	140	3	no	no	INTJ
asir-2054	140	4	.	.	NOUN
asir-2054	140	5	2	2	NUM
asir-2054	140	6	,	,	PUNCT
asir-2054	140	7	2019	2019	NUM
asir-2054	140	8	89	89	NUM
asir-2054	140	9	published	publish	VERB
asir-2054	140	10	by	by	ADP
asir-2054	140	11	scholink	scholink	PROPN
asir-2054	140	12	inc	inc	PROPN
asir-2054	140	13	.	.	PROPN
asir-2054	141	1	5	5	NUM
asir-2054	141	2	5	5	NUM
asir-2054	141	3	+	+	NUM
asir-2054	141	4	-face	-face	NOUN
asir-2054	141	5	sends	send	VERB
asir-2054	141	6	at	at	ADV
asir-2054	141	7	least	least	ADJ
asir-2054	141	8	1	1	NUM
asir-2054	141	9	5	5	NUM
asir-2054	141	10	to	to	PART
asir-2054	141	11	v	v	NOUN
asir-2054	141	12	by	by	ADP
asir-2054	141	13	r3	r3	PROPN
asir-2054	141	14	.	.	PUNCT
asir-2054	142	1	so	so	ADV
asir-2054	142	2	ch'(v	ch'(v	NOUN
asir-2054	142	3	)	)	PUNCT
asir-2054	142	4	≥	≥	NOUN
asir-2054	142	5	1	1	NUM
asir-2054	143	1	+	+	CCONJ
asir-2054	143	2	2	2	NUM
asir-2054	143	3	×	×	NOUN
asir-2054	143	4	1	1	NUM
asir-2054	143	5	5	5	NUM
asir-2054	143	6	−	−	NUM
asir-2054	143	7	3	3	NUM
asir-2054	143	8	×	×	NOUN
asir-2054	143	9	1	1	NUM
asir-2054	143	10	3	3	NUM
asir-2054	143	11	−	−	NOUN
asir-2054	143	12	1	1	NUM
asir-2054	143	13	5	5	NUM
asir-2054	143	14	=	=	SYM
asir-2054	143	15	1	1	NUM
asir-2054	143	16	5	5	NUM
asir-2054	143	17	>	>	SYM
asir-2054	143	18	0	0	NUM
asir-2054	143	19	by	by	ADP
asir-2054	143	20	r2	r2	PROPN
asir-2054	143	21	and	and	CCONJ
asir-2054	143	22	r4.2	r4.2	NOUN
asir-2054	143	23	.	.	PUNCT
asir-2054	143	24	case	case	NOUN
asir-2054	143	25	2	2	X
asir-2054	143	26	.	.	PUNCT
asir-2054	144	1	let	let	VERB
asir-2054	144	2	v	v	PART
asir-2054	144	3	be	be	AUX
asir-2054	144	4	a	a	DET
asir-2054	144	5	6	6	NUM
asir-2054	144	6	-	-	PUNCT
asir-2054	144	7	vertex	vertex	NOUN
asir-2054	144	8	.	.	PUNCT
asir-2054	145	1	then	then	ADV
asir-2054	145	2	ch(v	ch(v	VERB
asir-2054	145	3	)	)	PUNCT
asir-2054	146	1	=	=	SYM
asir-2054	146	2	2	2	NUM
asir-2054	146	3	,	,	PUNCT
asir-2054	146	4	f3(v	f3(v	NOUN
asir-2054	146	5	)	)	PUNCT
asir-2054	146	6	≤	≤	NUM
asir-2054	146	7	4	4	NUM
asir-2054	146	8	by	by	ADP
asir-2054	146	9	(	(	PUNCT
asir-2054	146	10	b	b	NOUN
asir-2054	146	11	)	)	PUNCT
asir-2054	146	12	.	.	PUNCT
asir-2054	147	1	if	if	SCONJ
asir-2054	147	2	v	v	NOUN
asir-2054	147	3	is	be	AUX
asir-2054	147	4	not	not	PART
asir-2054	147	5	adjacent	adjacent	ADJ
asir-2054	147	6	to	to	ADP
asir-2054	147	7	a	a	DET
asir-2054	147	8	5	5	NUM
asir-2054	147	9	-	-	PUNCT
asir-2054	147	10	vertex	vertex	NOUN
asir-2054	147	11	w	w	NOUN
asir-2054	147	12	such	such	ADJ
asir-2054	147	13	that	that	SCONJ
asir-2054	147	14	f3(w	f3(w	PROPN
asir-2054	147	15	)	)	PUNCT
asir-2054	147	16	=	=	SYM
asir-2054	147	17	4	4	NUM
asir-2054	147	18	and	and	CCONJ
asir-2054	147	19	f4(w	f4(w	PROPN
asir-2054	147	20	)	)	PUNCT
asir-2054	147	21	=	=	SYM
asir-2054	147	22	1	1	NUM
asir-2054	147	23	or	or	CCONJ
asir-2054	147	24	f3(w	f3(w	NUM
asir-2054	147	25	)	)	PUNCT
asir-2054	147	26	=	=	SYM
asir-2054	147	27	5	5	NUM
asir-2054	147	28	,	,	PUNCT
asir-2054	147	29	then	then	ADV
asir-2054	147	30	v	v	NOUN
asir-2054	147	31	sends	send	VERB
asir-2054	147	32	no	no	DET
asir-2054	147	33	charge	charge	NOUN
asir-2054	147	34	to	to	ADP
asir-2054	147	35	its	its	PRON
asir-2054	147	36	5	5	NUM
asir-2054	147	37	-	-	NOUN
asir-2054	147	38	neighbors	neighbor	NOUN
asir-2054	147	39	,	,	PUNCT
asir-2054	147	40	so	so	ADV
asir-2054	147	41	ch'(v	ch'(v	NOUN
asir-2054	147	42	)	)	PUNCT
asir-2054	147	43	≥	≥	NOUN
asir-2054	147	44	2	2	NUM
asir-2054	147	45	−	−	NOUN
asir-2054	147	46	4	4	NUM
asir-2054	147	47	×	×	PROPN
asir-2054	147	48	max	max	PROPN
asir-2054	147	49	{	{	PUNCT
asir-2054	147	50	1	1	NUM
asir-2054	147	51	3	3	NUM
asir-2054	147	52	,	,	PUNCT
asir-2054	147	53	1	1	NUM
asir-2054	147	54	2	2	NUM
asir-2054	147	55	}	}	PUNCT
asir-2054	147	56	=	=	SYM
asir-2054	147	57	0	0	NUM
asir-2054	147	58	by	by	ADP
asir-2054	147	59	r3	r3	PROPN
asir-2054	147	60	.	.	PUNCT
asir-2054	148	1	suppose	suppose	VERB
asir-2054	148	2	that	that	SCONJ
asir-2054	148	3	v	v	NOUN
asir-2054	148	4	is	be	AUX
asir-2054	148	5	adjacent	adjacent	ADJ
asir-2054	148	6	to	to	ADP
asir-2054	148	7	a	a	DET
asir-2054	148	8	5	5	NUM
asir-2054	148	9	-	-	PUNCT
asir-2054	148	10	vertex	vertex	NOUN
asir-2054	148	11	w	w	NOUN
asir-2054	148	12	such	such	ADJ
asir-2054	148	13	that	that	SCONJ
asir-2054	148	14	f3(w	f3(w	PROPN
asir-2054	148	15	)	)	PUNCT
asir-2054	148	16	=	=	SYM
asir-2054	148	17	4	4	NUM
asir-2054	148	18	and	and	CCONJ
asir-2054	148	19	f4(w	f4(w	PROPN
asir-2054	148	20	)	)	PUNCT
asir-2054	148	21	=	=	SYM
asir-2054	148	22	1	1	NUM
asir-2054	148	23	(	(	PUNCT
asir-2054	148	24	as	as	ADP
asir-2054	148	25	in	in	ADP
asir-2054	148	26	figure	figure	NOUN
asir-2054	148	27	1	1	NUM
asir-2054	148	28	)	)	PUNCT
asir-2054	148	29	.	.	PUNCT
asir-2054	149	1	note	note	VERB
asir-2054	149	2	that	that	SCONJ
asir-2054	149	3	v	v	NOUN
asir-2054	149	4	is	be	AUX
asir-2054	149	5	adjacent	adjacent	ADJ
asir-2054	149	6	to	to	ADP
asir-2054	149	7	only	only	ADV
asir-2054	149	8	one	one	NUM
asir-2054	149	9	such	such	ADJ
asir-2054	149	10	vertex	vertex	NOUN
asir-2054	149	11	w	w	NOUN
asir-2054	149	12	because	because	SCONJ
asir-2054	149	13	each	each	DET
asir-2054	149	14	7	7	NUM
asir-2054	149	15	-	-	PUNCT
asir-2054	149	16	cycle	cycle	NOUN
asir-2054	149	17	contains	contain	VERB
asir-2054	149	18	at	at	ADP
asir-2054	149	19	most	most	ADV
asir-2054	149	20	two	two	NUM
asir-2054	149	21	chords	chord	NOUN
asir-2054	149	22	in	in	ADP
asir-2054	149	23	g.	g.	PROPN
asir-2054	149	24	then	then	ADV
asir-2054	149	25	f3(v	f3(v	NOUN
asir-2054	149	26	)	)	PUNCT
asir-2054	149	27	≤	≤	NUM
asir-2054	149	28	3	3	NUM
asir-2054	149	29	,	,	PUNCT
asir-2054	149	30	f4(v	f4(v	PROPN
asir-2054	149	31	)	)	PUNCT
asir-2054	149	32	=	=	SYM
asir-2054	149	33	1	1	NUM
asir-2054	149	34	and	and	CCONJ
asir-2054	149	35	f5	f5	PROPN
asir-2054	149	36	+	+	CCONJ
asir-2054	149	37	(	(	PUNCT
asir-2054	149	38	v	v	NOUN
asir-2054	149	39	)	)	PUNCT
asir-2054	149	40	=	=	SYM
asir-2054	150	1	2	2	X
asir-2054	150	2	.	.	PUNCT
asir-2054	150	3	so	so	ADV
asir-2054	150	4	ch'(v	ch'(v	NOUN
asir-2054	150	5	)	)	PUNCT
asir-2054	150	6	≥	≥	NOUN
asir-2054	150	7	2	2	NUM
asir-2054	150	8	−	−	NOUN
asir-2054	150	9	3	3	NUM
asir-2054	150	10	×	×	NOUN
asir-2054	150	11	1	1	NUM
asir-2054	150	12	2	2	NUM
asir-2054	150	13	−	−	NOUN
asir-2054	150	14	1	1	NUM
asir-2054	150	15	3	3	NUM
asir-2054	150	16	=	=	SYM
asir-2054	150	17	1	1	NUM
asir-2054	150	18	6	6	NUM
asir-2054	150	19	>	>	SYM
asir-2054	150	20	0	0	NUM
asir-2054	150	21	by	by	ADP
asir-2054	150	22	r2	r2	PROPN
asir-2054	150	23	and	and	CCONJ
asir-2054	150	24	r4.1	r4.1	PROPN
asir-2054	150	25	.	.	PROPN
asir-2054	150	26	suppose	suppose	VERB
asir-2054	150	27	that	that	SCONJ
asir-2054	150	28	v	v	NOUN
asir-2054	150	29	is	be	AUX
asir-2054	150	30	adjacent	adjacent	ADJ
asir-2054	150	31	to	to	ADP
asir-2054	150	32	a	a	DET
asir-2054	150	33	5	5	NUM
asir-2054	150	34	-	-	PUNCT
asir-2054	150	35	vertex	vertex	NOUN
asir-2054	150	36	w	w	NOUN
asir-2054	150	37	such	such	ADJ
asir-2054	150	38	that	that	SCONJ
asir-2054	150	39	f3(w	f3(w	PROPN
asir-2054	150	40	)	)	PUNCT
asir-2054	150	41	=	=	SYM
asir-2054	150	42	5	5	X
asir-2054	150	43	.	.	X
asir-2054	150	44	note	note	VERB
asir-2054	150	45	that	that	SCONJ
asir-2054	150	46	v	v	NOUN
asir-2054	150	47	may	may	AUX
asir-2054	150	48	be	be	AUX
asir-2054	150	49	adjacent	adjacent	ADJ
asir-2054	150	50	to	to	ADP
asir-2054	150	51	two	two	NUM
asir-2054	150	52	such	such	ADJ
asir-2054	150	53	vertices	vertex	NOUN
asir-2054	150	54	.	.	PUNCT
asir-2054	151	1	then	then	ADV
asir-2054	151	2	f3(v	f3(v	NOUN
asir-2054	151	3	)	)	PUNCT
asir-2054	151	4	≤	≤	NUM
asir-2054	151	5	4	4	NUM
asir-2054	151	6	and	and	CCONJ
asir-2054	151	7	f5	f5	NOUN
asir-2054	151	8	+	+	CCONJ
asir-2054	151	9	(	(	PUNCT
asir-2054	151	10	v	v	NOUN
asir-2054	151	11	)	)	PUNCT
asir-2054	151	12	≥	≥	NOUN
asir-2054	151	13	2	2	NUM
asir-2054	151	14	.	.	PUNCT
asir-2054	152	1	so	so	ADV
asir-2054	152	2	ch'(v	ch'(v	NOUN
asir-2054	152	3	)	)	PUNCT
asir-2054	152	4	≥	≥	NOUN
asir-2054	152	5	2	2	NUM
asir-2054	152	6	+	+	NUM
asir-2054	152	7	2×	2×	NUM
asir-2054	152	8	1	1	NUM
asir-2054	152	9	5	5	NUM
asir-2054	152	10	−2×	−2×	NOUN
asir-2054	152	11	1	1	NUM
asir-2054	152	12	3	3	NUM
asir-2054	152	13	−2×	−2×	NOUN
asir-2054	152	14	1	1	NUM
asir-2054	152	15	2	2	NUM
asir-2054	152	16	−2×	−2×	NOUN
asir-2054	152	17	1	1	NUM
asir-2054	152	18	3	3	NUM
asir-2054	152	19	=	=	SYM
asir-2054	152	20	1	1	NUM
asir-2054	152	21	15	15	NUM
asir-2054	152	22	>	>	SYM
asir-2054	152	23	0	0	NUM
asir-2054	152	24	by	by	ADP
asir-2054	152	25	r2	r2	PROPN
asir-2054	152	26	,	,	PUNCT
asir-2054	152	27	r3.1	r3.1	NOUN
asir-2054	152	28	and	and	CCONJ
asir-2054	152	29	r4.2	r4.2	NOUN
asir-2054	152	30	.	.	PUNCT
asir-2054	153	1	case	case	NOUN
asir-2054	153	2	3	3	X
asir-2054	153	3	.	.	PUNCT
asir-2054	154	1	let	let	VERB
asir-2054	154	2	v	v	PART
asir-2054	154	3	be	be	AUX
asir-2054	154	4	a	a	DET
asir-2054	154	5	7	7	NUM
asir-2054	154	6	-	-	PUNCT
asir-2054	154	7	vertex	vertex	NOUN
asir-2054	154	8	.	.	PUNCT
asir-2054	155	1	then	then	ADV
asir-2054	155	2	ch(v	ch(v	VERB
asir-2054	155	3	)	)	PUNCT
asir-2054	156	1	=	=	SYM
asir-2054	156	2	3	3	X
asir-2054	156	3	,	,	PUNCT
asir-2054	156	4	f	f	PROPN
asir-2054	156	5	3	3	NUM
asir-2054	156	6	(	(	PUNCT
asir-2054	156	7	v	v	NOUN
asir-2054	156	8	)	)	PUNCT
asir-2054	156	9	≤	≤	NOUN
asir-2054	156	10	5	5	NUM
asir-2054	156	11	by	by	ADP
asir-2054	156	12	(	(	PUNCT
asir-2054	156	13	b	b	NOUN
asir-2054	156	14	)	)	PUNCT
asir-2054	156	15	.	.	PUNCT
asir-2054	157	1	if	if	SCONJ
asir-2054	157	2	v	v	NOUN
asir-2054	157	3	is	be	AUX
asir-2054	157	4	not	not	PART
asir-2054	157	5	adjacent	adjacent	ADJ
asir-2054	157	6	to	to	ADP
asir-2054	157	7	a	a	DET
asir-2054	157	8	5	5	NUM
asir-2054	157	9	-	-	PUNCT
asir-2054	157	10	vertex	vertex	NOUN
asir-2054	157	11	w	w	NOUN
asir-2054	157	12	such	such	ADJ
asir-2054	157	13	that	that	SCONJ
asir-2054	157	14	f3(w	f3(w	PROPN
asir-2054	157	15	)	)	PUNCT
asir-2054	157	16	=	=	SYM
asir-2054	157	17	4	4	NUM
asir-2054	157	18	and	and	CCONJ
asir-2054	157	19	f4(w	f4(w	PROPN
asir-2054	157	20	)	)	PUNCT
asir-2054	157	21	=	=	SYM
asir-2054	157	22	1	1	NUM
asir-2054	157	23	or	or	CCONJ
asir-2054	157	24	f3(w	f3(w	NUM
asir-2054	157	25	)	)	PUNCT
asir-2054	157	26	=	=	SYM
asir-2054	157	27	5	5	NUM
asir-2054	157	28	,	,	PUNCT
asir-2054	157	29	then	then	ADV
asir-2054	157	30	v	v	NOUN
asir-2054	157	31	sends	send	VERB
asir-2054	157	32	no	no	DET
asir-2054	157	33	charge	charge	NOUN
asir-2054	157	34	to	to	ADP
asir-2054	157	35	its	its	PRON
asir-2054	157	36	5	5	NUM
asir-2054	157	37	-	-	NOUN
asir-2054	157	38	neighbors	neighbor	NOUN
asir-2054	157	39	,	,	PUNCT
asir-2054	157	40	so	so	ADV
asir-2054	157	41	ch'(v	ch'(v	NOUN
asir-2054	157	42	)	)	PUNCT
asir-2054	157	43	≥	≥	NOUN
asir-2054	157	44	3	3	NUM
asir-2054	157	45	−	−	PROPN
asir-2054	157	46	5	5	NUM
asir-2054	157	47	×	×	PROPN
asir-2054	157	48	max	max	PROPN
asir-2054	157	49	{	{	PUNCT
asir-2054	157	50	1	1	NUM
asir-2054	157	51	3	3	NUM
asir-2054	157	52	,	,	PUNCT
asir-2054	157	53	1	1	NUM
asir-2054	157	54	2	2	NUM
asir-2054	157	55	}	}	PUNCT
asir-2054	157	56	−	−	PROPN
asir-2054	157	57	1	1	NUM
asir-2054	157	58	2	2	NUM
asir-2054	157	59	=	=	SYM
asir-2054	157	60	0	0	NUM
asir-2054	157	61	by	by	ADP
asir-2054	157	62	r1	r1	NOUN
asir-2054	157	63	and	and	CCONJ
asir-2054	157	64	r2	r2	PROPN
asir-2054	157	65	.	.	PUNCT
asir-2054	158	1	suppose	suppose	VERB
asir-2054	158	2	that	that	SCONJ
asir-2054	158	3	v	v	NOUN
asir-2054	158	4	is	be	AUX
asir-2054	158	5	adjacent	adjacent	ADJ
asir-2054	158	6	to	to	ADP
asir-2054	158	7	a	a	DET
asir-2054	158	8	5	5	NUM
asir-2054	158	9	-	-	PUNCT
asir-2054	158	10	vertex	vertex	NOUN
asir-2054	158	11	w	w	NOUN
asir-2054	158	12	such	such	ADJ
asir-2054	158	13	that	that	SCONJ
asir-2054	158	14	f3(w	f3(w	PROPN
asir-2054	158	15	)	)	PUNCT
asir-2054	158	16	=	=	SYM
asir-2054	158	17	4	4	NUM
asir-2054	158	18	and	and	CCONJ
asir-2054	158	19	f4(w	f4(w	PROPN
asir-2054	158	20	)	)	PUNCT
asir-2054	158	21	=	=	SYM
asir-2054	158	22	1	1	NUM
asir-2054	158	23	(	(	PUNCT
asir-2054	158	24	as	as	ADP
asir-2054	158	25	in	in	ADP
asir-2054	158	26	figure	figure	NOUN
asir-2054	158	27	1	1	NUM
asir-2054	158	28	)	)	PUNCT
asir-2054	158	29	.	.	PUNCT
asir-2054	159	1	now	now	ADV
asir-2054	159	2	f3(v	f3(v	NOUN
asir-2054	159	3	)	)	PUNCT
asir-2054	159	4	≤	≤	NUM
asir-2054	159	5	4	4	NUM
asir-2054	159	6	and	and	CCONJ
asir-2054	159	7	v	v	NOUN
asir-2054	159	8	is	be	AUX
asir-2054	159	9	adjacent	adjacent	ADJ
asir-2054	159	10	to	to	ADP
asir-2054	159	11	at	at	ADP
asir-2054	159	12	most	most	ADV
asir-2054	159	13	two	two	NUM
asir-2054	159	14	such	such	ADJ
asir-2054	159	15	vertices	vertex	NOUN
asir-2054	159	16	because	because	SCONJ
asir-2054	159	17	each	each	DET
asir-2054	159	18	7	7	NUM
asir-2054	159	19	-	-	PUNCT
asir-2054	159	20	cycle	cycle	NOUN
asir-2054	159	21	contains	contain	VERB
asir-2054	159	22	at	at	ADP
asir-2054	159	23	most	most	ADV
asir-2054	159	24	two	two	NUM
asir-2054	159	25	chords	chord	NOUN
asir-2054	159	26	in	in	ADP
asir-2054	159	27	g.	g.	PROPN
asir-2054	159	28	so	so	ADV
asir-2054	159	29	ch'(v	ch'(v	NOUN
asir-2054	159	30	)	)	PUNCT
asir-2054	159	31	≥	≥	NOUN
asir-2054	160	1	3	3	NUM
asir-2054	160	2	−	−	NOUN
asir-2054	160	3	2	2	NUM
asir-2054	160	4	×	×	NOUN
asir-2054	160	5	1	1	NUM
asir-2054	160	6	2	2	NUM
asir-2054	160	7	−	−	NUM
asir-2054	160	8	2	2	NUM
asir-2054	160	9	×	×	NOUN
asir-2054	160	10	1	1	NUM
asir-2054	160	11	3	3	NUM
asir-2054	160	12	−	−	NOUN
asir-2054	160	13	1	1	NUM
asir-2054	160	14	2	2	NUM
asir-2054	160	15	−	−	NUM
asir-2054	160	16	2	2	NUM
asir-2054	160	17	×	×	NOUN
asir-2054	160	18	1	1	NUM
asir-2054	160	19	3	3	NUM
asir-2054	160	20	=	=	SYM
asir-2054	160	21	1	1	NUM
asir-2054	160	22	6	6	NUM
asir-2054	160	23	>	>	SYM
asir-2054	160	24	0	0	NUM
asir-2054	160	25	by	by	ADP
asir-2054	160	26	r1	r1	PROPN
asir-2054	160	27	,	,	PUNCT
asir-2054	160	28	r2	r2	PROPN
asir-2054	160	29	and	and	CCONJ
asir-2054	160	30	r4.1	r4.1	PROPN
asir-2054	160	31	.	.	PROPN
asir-2054	160	32	suppose	suppose	VERB
asir-2054	160	33	that	that	SCONJ
asir-2054	160	34	v	v	NOUN
asir-2054	160	35	is	be	AUX
asir-2054	160	36	adjacent	adjacent	ADJ
asir-2054	160	37	to	to	ADP
asir-2054	160	38	a	a	DET
asir-2054	160	39	5	5	NUM
asir-2054	160	40	-	-	PUNCT
asir-2054	160	41	vertex	vertex	NOUN
asir-2054	160	42	w	w	NOUN
asir-2054	160	43	such	such	ADJ
asir-2054	160	44	that	that	SCONJ
asir-2054	160	45	f3(w	f3(w	PROPN
asir-2054	160	46	)	)	PUNCT
asir-2054	160	47	=	=	SYM
asir-2054	160	48	5	5	X
asir-2054	160	49	.	.	X
asir-2054	160	50	note	note	VERB
asir-2054	160	51	that	that	SCONJ
asir-2054	160	52	v	v	NOUN
asir-2054	160	53	may	may	AUX
asir-2054	160	54	be	be	AUX
asir-2054	160	55	adjacent	adjacent	ADJ
asir-2054	160	56	to	to	ADP
asir-2054	160	57	two	two	NUM
asir-2054	160	58	such	such	ADJ
asir-2054	160	59	vertices	vertex	NOUN
asir-2054	160	60	.	.	PUNCT
asir-2054	161	1	then	then	ADV
asir-2054	161	2	f3(v	f3(v	NOUN
asir-2054	161	3	)	)	PUNCT
asir-2054	161	4	≤	≤	NUM
asir-2054	161	5	5	5	NUM
asir-2054	161	6	and	and	CCONJ
asir-2054	161	7	f5	f5	NOUN
asir-2054	161	8	+	+	CCONJ
asir-2054	161	9	(	(	PUNCT
asir-2054	161	10	v	v	NOUN
asir-2054	161	11	)	)	PUNCT
asir-2054	161	12	≥	≥	NOUN
asir-2054	161	13	2	2	NUM
asir-2054	161	14	.	.	PUNCT
asir-2054	162	1	so	so	ADV
asir-2054	162	2	ch'(v	ch'(v	NOUN
asir-2054	162	3	)	)	PUNCT
asir-2054	162	4	≥	≥	NOUN
asir-2054	162	5	3	3	NUM
asir-2054	163	1	+	+	CCONJ
asir-2054	163	2	2	2	NUM
asir-2054	163	3	×	×	NOUN
asir-2054	163	4	1	1	NUM
asir-2054	163	5	5	5	NUM
asir-2054	163	6	−	−	NUM
asir-2054	163	7	2	2	NUM
asir-2054	163	8	×	×	NOUN
asir-2054	163	9	1	1	NUM
asir-2054	163	10	3	3	NUM
asir-2054	163	11	−	−	NUM
asir-2054	163	12	3	3	NUM
asir-2054	163	13	×	×	NOUN
asir-2054	163	14	1	1	NUM
asir-2054	163	15	2	2	NUM
asir-2054	163	16	−	−	NOUN
asir-2054	163	17	1	1	NUM
asir-2054	163	18	2	2	NUM
asir-2054	163	19	−	−	NUM
asir-2054	163	20	2	2	NUM
asir-2054	163	21	×	×	NOUN
asir-2054	163	22	1	1	NUM
asir-2054	163	23	3	3	NUM
asir-2054	163	24	=	=	SYM
asir-2054	163	25	1	1	NUM
asir-2054	163	26	15	15	NUM
asir-2054	163	27	>	>	SYM
asir-2054	163	28	0	0	PUNCT
asir-2054	163	29	by	by	ADP
asir-2054	163	30	r1	r1	PROPN
asir-2054	163	31	,	,	PUNCT
asir-2054	163	32	r2	r2	PROPN
asir-2054	163	33	,	,	PUNCT
asir-2054	163	34	r3.1	r3.1	NOUN
asir-2054	163	35	and	and	CCONJ
asir-2054	163	36	r4.2	r4.2	NOUN
asir-2054	163	37	.	.	PUNCT
asir-2054	164	1	3	3	X
asir-2054	164	2	.	.	X
asir-2054	164	3	proof	proof	NOUN
asir-2054	164	4	of	of	ADP
asir-2054	164	5	theorem	theorem	ADJ
asir-2054	164	6	3	3	NUM
asir-2054	164	7	proof	proof	NOUN
asir-2054	164	8	.	.	PUNCT
asir-2054	165	1	the	the	DET
asir-2054	165	2	proof	proof	NOUN
asir-2054	165	3	is	be	AUX
asir-2054	165	4	carried	carry	VERB
asir-2054	165	5	out	out	ADP
asir-2054	165	6	by	by	ADP
asir-2054	165	7	contradiction	contradiction	NOUN
asir-2054	165	8	.	.	PUNCT
asir-2054	166	1	suppose	suppose	VERB
asir-2054	166	2	that	that	SCONJ
asir-2054	166	3	g	g	PROPN
asir-2054	166	4	is	be	AUX
asir-2054	166	5	a	a	DET
asir-2054	166	6	counterexample	counterexample	NOUN
asir-2054	166	7	to	to	ADP
asir-2054	166	8	our	our	PRON
asir-2054	166	9	theorem	theorem	NOUN
asir-2054	166	10	with	with	ADP
asir-2054	166	11	the	the	DET
asir-2054	166	12	minimum	minimum	ADJ
asir-2054	166	13	number	number	NOUN
asir-2054	166	14	of	of	ADP
asir-2054	166	15	edges	edge	NOUN
asir-2054	166	16	and	and	CCONJ
asir-2054	166	17	g	g	NOUN
asir-2054	166	18	is	be	AUX
asir-2054	166	19	any	any	DET
asir-2054	166	20	planar	planar	ADJ
asir-2054	166	21	graph	graph	NOUN
asir-2054	166	22	in	in	ADP
asir-2054	166	23	which	which	PRON
asir-2054	166	24	every	every	DET
asir-2054	166	25	7	7	NUM
asir-2054	166	26	-	-	PUNCT
asir-2054	166	27	cycle	cycle	NOUN
asir-2054	166	28	contains	contain	VERB
asir-2054	166	29	at	at	ADP
asir-2054	166	30	most	most	ADJ
asir-2054	166	31	two	two	NUM
asir-2054	166	32	chords	chord	NOUN
asir-2054	166	33	.	.	PUNCT
asir-2054	167	1	then	then	ADV
asir-2054	167	2	there	there	PRON
asir-2054	167	3	is	be	VERB
asir-2054	167	4	an	an	DET
asir-2054	167	5	edge	edge	NOUN
asir-2054	167	6	assignment	assignment	NOUN
asir-2054	167	7	l	l	NOUN
asir-2054	167	8	with	with	ADP
asir-2054	167	9	|l(e)|	|l(e)|	PROPN
asir-2054	167	10	≥	≥	NOUN
asir-2054	167	11	k	k	NOUN
asir-2054	167	12	for	for	ADP
asir-2054	167	13	all	all	DET
asir-2054	167	14	e	e	PROPN
asir-2054	167	15	∈	∈	PROPN
asir-2054	167	16	e(g	e(g	PROPN
asir-2054	167	17	)	)	PUNCT
asir-2054	167	18	,	,	PUNCT
asir-2054	167	19	where	where	SCONJ
asir-2054	167	20	k	k	PROPN
asir-2054	167	21	=	=	SYM
asir-2054	167	22	max{8	max{8	PROPN
asir-2054	167	23	,	,	PUNCT
asir-2054	167	24	∆(g	∆(g	NOUN
asir-2054	167	25	)	)	PUNCT
asir-2054	167	26	+	+	CCONJ
asir-2054	167	27	1	1	NUM
asir-2054	167	28	}	}	PUNCT
asir-2054	167	29	,	,	PUNCT
asir-2054	167	30	such	such	ADJ
asir-2054	167	31	that	that	SCONJ
asir-2054	167	32	g	g	PROPN
asir-2054	167	33	is	be	AUX
asir-2054	167	34	not	not	PART
asir-2054	167	35	edge	edge	NOUN
asir-2054	167	36	-	-	PUNCT
asir-2054	167	37	l	l	NOUN
asir-2054	167	38	-	-	NOUN
asir-2054	167	39	colorable	colorable	ADJ
asir-2054	167	40	.	.	PUNCT
asir-2054	168	1	by	by	ADP
asir-2054	168	2	lemma	lemma	PROPN
asir-2054	168	3	4	4	NUM
asir-2054	168	4	,	,	PUNCT
asir-2054	168	5	we	we	PRON
asir-2054	168	6	consider	consider	VERB
asir-2054	168	7	two	two	NUM
asir-2054	168	8	cases	case	NOUN
asir-2054	168	9	as	as	SCONJ
asir-2054	168	10	follows	follow	VERB
asir-2054	168	11	.	.	PUNCT
asir-2054	169	1	case	case	NOUN
asir-2054	169	2	1	1	NUM
asir-2054	169	3	.	.	PUNCT
asir-2054	170	1	g	g	PROPN
asir-2054	170	2	contains	contain	VERB
asir-2054	170	3	an	an	DET
asir-2054	170	4	edge	edge	NOUN
asir-2054	170	5	uv	uv	NOUN
asir-2054	170	6	with	with	ADP
asir-2054	170	7	d(u	d(u	PROPN
asir-2054	170	8	)	)	PUNCT
asir-2054	171	1	+	+	CCONJ
asir-2054	171	2	d(v	d(v	PROPN
asir-2054	171	3	)	)	PUNCT
asir-2054	171	4	≤	≤	NUM
asir-2054	171	5	max{9	max{9	VERB
asir-2054	171	6	,	,	PUNCT
asir-2054	171	7	∆(g	∆(g	NOUN
asir-2054	171	8	)	)	PUNCT
asir-2054	171	9	+	+	NOUN
asir-2054	171	10	2	2	NUM
asir-2054	171	11	}	}	PUNCT
asir-2054	171	12	.	.	PUNCT
asir-2054	172	1	consider	consider	VERB
asir-2054	172	2	the	the	DET
asir-2054	172	3	graph	graph	NOUN
asir-2054	172	4	g	g	NOUN
asir-2054	172	5	'	'	PUNCT
asir-2054	172	6	=	=	NOUN
asir-2054	172	7	g	g	NOUN
asir-2054	172	8	−	−	PROPN
asir-2054	173	1	uv	uv	NOUN
asir-2054	173	2	.	.	PUNCT
asir-2054	174	1	by	by	ADP
asir-2054	174	2	inductive	inductive	ADJ
asir-2054	174	3	hypothesis	hypothesis	NOUN
asir-2054	174	4	,	,	PUNCT
asir-2054	174	5	g	g	PROPN
asir-2054	174	6	has	have	VERB
asir-2054	174	7	an	an	DET
asir-2054	174	8	edge	edge	NOUN
asir-2054	174	9	-	-	PUNCT
asir-2054	174	10	lcoloring	lcolore	VERB
asir-2054	174	11	φ	φ	NOUN
asir-2054	174	12	,	,	PUNCT
asir-2054	174	13	where	where	SCONJ
asir-2054	174	14	l	l	NOUN
asir-2054	174	15	is	be	AUX
asir-2054	174	16	an	an	DET
asir-2054	174	17	edge	edge	NOUN
asir-2054	174	18	assignment	assignment	NOUN
asir-2054	174	19	with	with	ADP
asir-2054	174	20	|l(e)|	|l(e)|	PROPN
asir-2054	174	21	≥	≥	NOUN
asir-2054	174	22	k	k	NOUN
asir-2054	174	23	for	for	ADP
asir-2054	174	24	all	all	DET
asir-2054	174	25	e	e	PROPN
asir-2054	174	26	∈	∈	PROPN
asir-2054	174	27	e(g	e(g	PROPN
asir-2054	174	28	'	'	PUNCT
asir-2054	174	29	)	)	PUNCT
asir-2054	174	30	and	and	CCONJ
asir-2054	174	31	k	k	PROPN
asir-2054	174	32	=	=	SYM
asir-2054	174	33	max{8	max{8	PROPN
asir-2054	174	34	,	,	PUNCT
asir-2054	174	35	∆(g	∆(g	NOUN
asir-2054	174	36	'	'	PUNCT
asir-2054	174	37	)	)	PUNCT
asir-2054	175	1	+	+	CCONJ
asir-2054	175	2	1	1	NUM
asir-2054	175	3	}	}	PUNCT
asir-2054	175	4	.	.	PUNCT
asir-2054	176	1	since	since	SCONJ
asir-2054	176	2	there	there	PRON
asir-2054	176	3	exist	exist	VERB
asir-2054	176	4	at	at	ADP
asir-2054	176	5	most	most	ADV
asir-2054	176	6	max{7	max{7	ADJ
asir-2054	176	7	,	,	PUNCT
asir-2054	176	8	∆(g	∆(g	NOUN
asir-2054	176	9	)	)	PUNCT
asir-2054	176	10	}	}	PUNCT
asir-2054	176	11	edges	edge	VERB
asir-2054	176	12	adjacent	adjacent	ADJ
asir-2054	176	13	in	in	ADP
asir-2054	176	14	g	g	PROPN
asir-2054	176	15	to	to	ADP
asir-2054	176	16	uv	uv	NOUN
asir-2054	176	17	and	and	CCONJ
asir-2054	176	18	|l(uv)|	|l(uv)|	NOUN
asir-2054	176	19	≥	≥	NOUN
asir-2054	176	20	max{8	max{8	PROPN
asir-2054	176	21	,	,	PUNCT
asir-2054	176	22	∆(g	∆(g	NOUN
asir-2054	176	23	)	)	PUNCT
asir-2054	176	24	+	+	NOUN
asir-2054	176	25	1	1	NUM
asir-2054	176	26	}	}	PUNCT
asir-2054	176	27	,	,	PUNCT
asir-2054	176	28	we	we	PRON
asir-2054	176	29	can	can	AUX
asir-2054	176	30	color	color	VERB
asir-2054	176	31	uv	uv	NOUN
asir-2054	176	32	with	with	ADP
asir-2054	176	33	some	some	DET
asir-2054	176	34	color	color	NOUN
asir-2054	176	35	from	from	ADP
asir-2054	176	36	l(uv	l(uv	PROPN
asir-2054	176	37	)	)	PUNCT
asir-2054	176	38	that	that	PRON
asir-2054	176	39	was	be	AUX
asir-2054	176	40	not	not	PART
asir-2054	176	41	used	use	VERB
asir-2054	176	42	by	by	ADP
asir-2054	176	43	φ	φ	PROPN
asir-2054	176	44	on	on	ADP
asir-2054	176	45	the	the	DET
asir-2054	176	46	edges	edge	NOUN
asir-2054	176	47	adjacent	adjacent	ADJ
asir-2054	176	48	to	to	ADP
asir-2054	176	49	uv	uv	VERB
asir-2054	176	50	.	.	PUNCT
asir-2054	177	1	it	it	PRON
asir-2054	177	2	is	be	AUX
asir-2054	177	3	easy	easy	ADJ
asir-2054	177	4	to	to	PART
asir-2054	177	5	see	see	VERB
asir-2054	177	6	that	that	SCONJ
asir-2054	177	7	the	the	DET
asir-2054	177	8	resulting	result	VERB
asir-2054	177	9	coloring	coloring	NOUN
asir-2054	177	10	is	be	AUX
asir-2054	177	11	an	an	DET
asir-2054	177	12	edge	edge	NOUN
asir-2054	177	13	-	-	PUNCT
asir-2054	177	14	l	l	NOUN
asir-2054	177	15	-	-	NOUN
asir-2054	177	16	coloring	coloring	NOUN
asir-2054	177	17	of	of	ADP
asir-2054	177	18	g.	g.	PROPN
asir-2054	177	19	case	case	NOUN
asir-2054	177	20	2	2	X
asir-2054	177	21	.	.	PUNCT
asir-2054	178	1	g	g	PROPN
asir-2054	178	2	contains	contain	VERB
asir-2054	178	3	an	an	DET
asir-2054	178	4	even	even	ADJ
asir-2054	178	5	cycle	cycle	NOUN
asir-2054	178	6	c	c	NOUN
asir-2054	178	7	=	=	SYM
asir-2054	178	8	v1v2	v1v2	PROPN
asir-2054	178	9	...	...	PUNCT
asir-2054	178	10	v2nv1	v2nv1	NOUN
asir-2054	178	11	with	with	ADP
asir-2054	178	12	d(v1	d(v1	NOUN
asir-2054	178	13	)	)	PUNCT
asir-2054	178	14	=	=	SYM
asir-2054	178	15	d(v3	d(v3	NOUN
asir-2054	178	16	)	)	PUNCT
asir-2054	178	17	=	=	SYM
asir-2054	178	18	...	...	PUNCT
asir-2054	179	1	=	=	PUNCT
asir-2054	179	2	d(v2n−1	d(v2n−1	NOUN
asir-2054	179	3	)	)	PUNCT
asir-2054	179	4	=	=	SYM
asir-2054	180	1	3	3	X
asir-2054	180	2	.	.	X
asir-2054	180	3	let	let	VERB
asir-2054	180	4	g	g	PRON
asir-2054	180	5	'	'	PUNCT
asir-2054	180	6	be	be	AUX
asir-2054	180	7	the	the	DET
asir-2054	180	8	subgraph	subgraph	NOUN
asir-2054	180	9	of	of	ADP
asir-2054	180	10	g	g	PROPN
asir-2054	180	11	obtained	obtain	VERB
asir-2054	180	12	by	by	ADP
asir-2054	180	13	deleting	delete	VERB
asir-2054	180	14	the	the	DET
asir-2054	180	15	edges	edge	NOUN
asir-2054	180	16	of	of	ADP
asir-2054	180	17	c.	c.	NOUN
asir-2054	180	18	by	by	ADP
asir-2054	180	19	inductive	inductive	ADJ
asir-2054	180	20	hypothesis	hypothesis	NOUN
asir-2054	180	21	,	,	PUNCT
asir-2054	180	22	g	g	NOUN
asir-2054	180	23	'	'	PUNCT
asir-2054	180	24	has	have	VERB
asir-2054	180	25	an	an	DET
asir-2054	180	26	edge	edge	NOUN
asir-2054	180	27	-	-	PUNCT
asir-2054	180	28	l	l	NOUN
asir-2054	180	29	-	-	ADJ
asir-2054	180	30	coloring	color	VERB
asir-2054	180	31	φ	φ	NOUN
asir-2054	180	32	,	,	PUNCT
asir-2054	180	33	where	where	SCONJ
asir-2054	180	34	l	l	NOUN
asir-2054	180	35	is	be	AUX
asir-2054	180	36	an	an	DET
asir-2054	180	37	edge	edge	NOUN
asir-2054	180	38	assignment	assignment	NOUN
asir-2054	180	39	with	with	ADP
asir-2054	180	40	|l(e)|	|l(e)|	PROPN
asir-2054	180	41	≥	≥	NOUN
asir-2054	180	42	k	k	NOUN
asir-2054	180	43	for	for	ADP
asir-2054	180	44	all	all	DET
asir-2054	180	45	e	e	PROPN
asir-2054	180	46	∈	∈	PROPN
asir-2054	180	47	e(g	e(g	PROPN
asir-2054	180	48	)	)	PUNCT
asir-2054	180	49	and	and	CCONJ
asir-2054	180	50	k	k	PROPN
asir-2054	180	51	=	=	SYM
asir-2054	180	52	max{8	max{8	PROPN
asir-2054	180	53	,	,	PUNCT
asir-2054	180	54	∆(g	∆(g	NOUN
asir-2054	180	55	)	)	PUNCT
asir-2054	181	1	+	+	NOUN
asir-2054	181	2	1	1	NUM
asir-2054	181	3	}	}	PUNCT
asir-2054	181	4	.	.	PUNCT
asir-2054	182	1	define	define	VERB
asir-2054	182	2	a	a	DET
asir-2054	182	3	new	new	ADJ
asir-2054	182	4	edge	edge	NOUN
asir-2054	182	5	assignment	assignment	NOUN
asir-2054	182	6	l	l	NOUN
asir-2054	182	7	'	'	PUNCT
asir-2054	182	8	(	(	PUNCT
asir-2054	182	9	e	e	NOUN
asir-2054	182	10	)	)	PUNCT
asir-2054	182	11	of	of	ADP
asir-2054	182	12	c	c	NOUN
asir-2054	182	13	such	such	ADJ
asir-2054	182	14	that	that	DET
asir-2054	182	15	l	l	NOUN
asir-2054	182	16	'	'	PUNCT
asir-2054	182	17	(	(	PUNCT
asir-2054	182	18	e	e	NOUN
asir-2054	182	19	)	)	PUNCT
asir-2054	182	20	=	=	SYM
asir-2054	182	21	l(e	l(e	NOUN
asir-2054	182	22	)	)	PUNCT
asir-2054	182	23	\	\	NOUN
asir-2054	182	24	{	{	PUNCT
asir-2054	182	25	φ(e	φ(e	NOUN
asir-2054	182	26	'	'	PUNCT
asir-2054	182	27	)	)	PUNCT
asir-2054	183	1	|e'∈	|e'∈	PROPN
asir-2054	183	2	e(g	e(g	NOUN
asir-2054	183	3	'	'	PUNCT
asir-2054	183	4	)	)	PUNCT
asir-2054	183	5	is	be	AUX
asir-2054	183	6	adjacent	adjacent	ADJ
asir-2054	183	7	to	to	ADP
asir-2054	183	8	e	e	VERB
asir-2054	183	9	in	in	ADP
asir-2054	183	10	g	g	NOUN
asir-2054	183	11	}	}	PUNCT
asir-2054	183	12	for	for	ADP
asir-2054	183	13	each	each	DET
asir-2054	183	14	e	e	PROPN
asir-2054	183	15	∈	∈	PROPN
asir-2054	183	16	e(c	e(c	NUM
asir-2054	183	17	)	)	PUNCT
asir-2054	183	18	.	.	PUNCT
asir-2054	184	1	it	it	PRON
asir-2054	184	2	is	be	AUX
asir-2054	184	3	easy	easy	ADJ
asir-2054	184	4	to	to	PART
asir-2054	184	5	see	see	VERB
asir-2054	184	6	that	that	DET
asir-2054	184	7	|l	|l	PROPN
asir-2054	184	8	'	'	PUNCT
asir-2054	184	9	(	(	PUNCT
asir-2054	184	10	e)|	e)|	INTJ
asir-2054	184	11	≥	≥	NOUN
asir-2054	184	12	2	2	NUM
asir-2054	184	13	for	for	ADP
asir-2054	184	14	each	each	DET
asir-2054	184	15	e	e	PROPN
asir-2054	184	16	∈	∈	PROPN
asir-2054	184	17	e(c	e(c	NUM
asir-2054	184	18	)	)	PUNCT
asir-2054	184	19	.	.	PUNCT
asir-2054	185	1	it	it	PRON
asir-2054	185	2	follows	follow	VERB
asir-2054	185	3	from	from	ADP
asir-2054	185	4	erdős	erdős	PROPN
asir-2054	185	5	et	et	PROPN
asir-2054	185	6	al	al	PROPN
asir-2054	185	7	.	.	PROPN
asir-2054	186	1	(	(	PUNCT
asir-2054	186	2	1979	1979	NUM
asir-2054	186	3	)	)	PUNCT
asir-2054	186	4	that	that	SCONJ
asir-2054	186	5	an	an	DET
asir-2054	186	6	even	even	ADJ
asir-2054	186	7	cycle	cycle	NOUN
asir-2054	186	8	is	be	AUX
asir-2054	186	9	edge-2	edge-2	NOUN
asir-2054	186	10	-	-	PUNCT
asir-2054	186	11	choosable	choosable	NOUN
asir-2054	186	12	(	(	PUNCT
asir-2054	186	13	since	since	SCONJ
asir-2054	186	14	an	an	DET
asir-2054	186	15	even	even	ADJ
asir-2054	186	16	cycle	cycle	NOUN
asir-2054	186	17	is	be	AUX
asir-2054	186	18	also	also	ADV
asir-2054	186	19	a	a	DET
asir-2054	186	20	bipartite	bipartite	ADJ
asir-2054	186	21	graph	graph	NOUN
asir-2054	186	22	)	)	PUNCT
asir-2054	186	23	.	.	PUNCT
asir-2054	187	1	so	so	ADV
asir-2054	187	2	c	c	PROPN
asir-2054	187	3	is	be	AUX
asir-2054	187	4	edge	edge	NOUN
asir-2054	187	5	-	-	PUNCT
asir-2054	187	6	l	l	NOUN
asir-2054	187	7	-	-	ADJ
asir-2054	187	8	colorable	colorable	ADJ
asir-2054	187	9	and	and	CCONJ
asir-2054	187	10	it	it	PRON
asir-2054	187	11	follows	follow	VERB
asir-2054	187	12	that	that	SCONJ
asir-2054	187	13	g	g	PROPN
asir-2054	187	14	is	be	AUX
asir-2054	187	15	edge	edge	NOUN
asir-2054	187	16	-	-	PUNCT
asir-2054	187	17	l	l	NOUN
asir-2054	187	18	-	-	NOUN
asir-2054	187	19	colorable	colorable	ADJ
asir-2054	187	20	.	.	PUNCT
asir-2054	188	1	this	this	PRON
asir-2054	188	2	completes	complete	VERB
asir-2054	188	3	the	the	DET
asir-2054	188	4	proof	proof	NOUN
asir-2054	188	5	of	of	ADP
asir-2054	188	6	theorem	theorem	ADJ
asir-2054	188	7	3	3	NUM
asir-2054	188	8	.	.	NOUN
asir-2054	188	9	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2054	188	10	applied	apply	VERB
asir-2054	188	11	science	science	NOUN
asir-2054	188	12	and	and	CCONJ
asir-2054	188	13	innovative	innovative	ADJ
asir-2054	188	14	research	research	NOUN
asir-2054	188	15	vol	vol	NOUN
asir-2054	188	16	.	.	PUNCT
asir-2054	189	1	3	3	NUM
asir-2054	189	2	,	,	PUNCT
asir-2054	189	3	no	no	INTJ
asir-2054	189	4	.	.	NOUN
asir-2054	189	5	2	2	NUM
asir-2054	189	6	,	,	PUNCT
asir-2054	189	7	2019	2019	NUM
asir-2054	189	8	90	90	NUM
asir-2054	189	9	published	publish	VERB
asir-2054	189	10	by	by	ADP
asir-2054	189	11	scholink	scholink	PROPN
asir-2054	189	12	inc	inc	PROPN
asir-2054	189	13	.	.	PROPN
asir-2054	189	14	acknowledgements	acknowledgement	NOUN
asir-2054	189	15	this	this	DET
asir-2054	189	16	work	work	NOUN
asir-2054	189	17	was	be	AUX
asir-2054	189	18	partially	partially	ADV
asir-2054	189	19	supported	support	VERB
asir-2054	189	20	by	by	ADP
asir-2054	189	21	shandong	shandong	PROPN
asir-2054	189	22	provincial	provincial	ADJ
asir-2054	189	23	natural	natural	ADJ
asir-2054	189	24	science	science	PROPN
asir-2054	189	25	foundation	foundation	PROPN
asir-2054	189	26	,	,	PUNCT
asir-2054	189	27	china	china	PROPN
asir-2054	189	28	(	(	PUNCT
asir-2054	189	29	no.zr2017ba009	no.zr2017ba009	NOUN
asir-2054	189	30	)	)	PUNCT
asir-2054	189	31	,	,	PUNCT
asir-2054	189	32	a	a	DET
asir-2054	189	33	project	project	NOUN
asir-2054	189	34	of	of	ADP
asir-2054	189	35	shandong	shandong	PROPN
asir-2054	189	36	province	province	PROPN
asir-2054	189	37	higher	high	ADJ
asir-2054	189	38	educational	educational	ADJ
asir-2054	189	39	science	science	NOUN
asir-2054	189	40	and	and	CCONJ
asir-2054	189	41	technology	technology	NOUN
asir-2054	189	42	program	program	NOUN
asir-2054	189	43	(	(	PUNCT
asir-2054	189	44	no.j17ka168	no.j17ka168	PROPN
asir-2054	189	45	)	)	PUNCT
asir-2054	189	46	and	and	CCONJ
asir-2054	189	47	talent	talent	NOUN
asir-2054	189	48	introduction	introduction	NOUN
asir-2054	189	49	research	research	NOUN
asir-2054	189	50	project	project	NOUN
asir-2054	189	51	of	of	ADP
asir-2054	189	52	shangdong	shangdong	ADJ
asir-2054	189	53	woman	woman	NOUN
asir-2054	189	54	’s	’s	PART
asir-2054	189	55	university	university	PROPN
asir-2054	189	56	(	(	PUNCT
asir-2054	189	57	no.2016yjrc12	no.2016yjrc12	NOUN
asir-2054	189	58	)	)	PUNCT
asir-2054	189	59	.	.	PUNCT
asir-2054	190	1	references	reference	NOUN
asir-2054	190	2	bollobas	bollobas	PROPN
asir-2054	190	3	,	,	PUNCT
asir-2054	190	4	b.	b.	PROPN
asir-2054	190	5	,	,	PUNCT
asir-2054	190	6	&	&	CCONJ
asir-2054	190	7	harris	harris	PROPN
asir-2054	190	8	,	,	PUNCT
asir-2054	190	9	a.	a.	PROPN
asir-2054	190	10	j.	j.	PROPN
asir-2054	190	11	(	(	PUNCT
asir-2054	190	12	1985	1985	NUM
asir-2054	190	13	)	)	PUNCT
asir-2054	190	14	.	.	PUNCT
asir-2054	191	1	list	list	NOUN
asir-2054	191	2	-	-	PUNCT
asir-2054	191	3	colourings	colouring	NOUN
asir-2054	191	4	of	of	ADP
asir-2054	191	5	graphs	graph	NOUN
asir-2054	191	6	.	.	PUNCT
asir-2054	192	1	graph	graph	NOUN
asir-2054	192	2	comb	comb	NOUN
asir-2054	192	3	.	.	PUNCT
asir-2054	193	1	,	,	PUNCT
asir-2054	193	2	1	1	NUM
asir-2054	193	3	,	,	PUNCT
asir-2054	193	4	115	115	NUM
asir-2054	193	5	-	-	SYM
asir-2054	193	6	127	127	NUM
asir-2054	193	7	.	.	PUNCT
asir-2054	194	1	https://doi.org/10.1007/bf02582936	https://doi.org/10.1007/bf02582936	NOUN
asir-2054	194	2	bonamy	bonamy	NOUN
asir-2054	194	3	,	,	PUNCT
asir-2054	194	4	m.	m.	NOUN
asir-2054	194	5	(	(	PUNCT
asir-2054	194	6	2015	2015	NUM
asir-2054	194	7	)	)	PUNCT
asir-2054	194	8	.	.	PUNCT
asir-2054	195	1	planar	planar	ADJ
asir-2054	195	2	graphs	graph	NOUN
asir-2054	195	3	with	with	ADP
asir-2054	195	4	∆	∆	PROPN
asir-2054	195	5	≥	≥	X
asir-2054	195	6	8	8	NUM
asir-2054	195	7	are(∆	are(∆	PUNCT
asir-2054	195	8	+	+	CCONJ
asir-2054	195	9	1)-edge	1)-edge	NUM
asir-2054	195	10	-	-	PUNCT
asir-2054	195	11	choosable	choosable	NOUN
asir-2054	195	12	.	.	PUNCT
asir-2054	196	1	siam	siam	PROPN
asir-2054	196	2	j	j	PROPN
asir-2054	196	3	discrete	discrete	ADJ
asir-2054	196	4	math	math	NOUN
asir-2054	196	5	,	,	PUNCT
asir-2054	196	6	29	29	NUM
asir-2054	196	7	,	,	PUNCT
asir-2054	196	8	1735	1735	NUM
asir-2054	196	9	-	-	SYM
asir-2054	196	10	1763	1763	NUM
asir-2054	196	11	.	.	PUNCT
asir-2054	197	1	https://doi.org/10.1137/130927449	https://doi.org/10.1137/130927449	PROPN
asir-2054	197	2	borodin	borodin	PROPN
asir-2054	197	3	,	,	PUNCT
asir-2054	197	4	o.	o.	PROPN
asir-2054	197	5	v.	v.	PROPN
asir-2054	197	6	,	,	PUNCT
asir-2054	197	7	kostochka	kostochka	PROPN
asir-2054	197	8	,	,	PUNCT
asir-2054	197	9	a.	a.	NOUN
asir-2054	197	10	v.	v.	PROPN
asir-2054	197	11	,	,	PUNCT
asir-2054	197	12	&	&	CCONJ
asir-2054	197	13	woodall	woodall	PROPN
asir-2054	197	14	.	.	PUNCT
asir-2054	198	1	d.	d.	PROPN
asir-2054	198	2	r.	r.	PROPN
asir-2054	198	3	(	(	PUNCT
asir-2054	198	4	1997	1997	NUM
asir-2054	198	5	)	)	PUNCT
asir-2054	198	6	.	.	PUNCT
asir-2054	199	1	list	list	NOUN
asir-2054	199	2	edge	edge	NOUN
asir-2054	199	3	and	and	CCONJ
asir-2054	199	4	list	list	VERB
asir-2054	199	5	total	total	ADJ
asir-2054	199	6	colourings	colouring	NOUN
asir-2054	199	7	of	of	ADP
asir-2054	199	8	multi	multi	ADJ
asir-2054	199	9	graphs	graph	NOUN
asir-2054	199	10	.	.	PUNCT
asir-2054	200	1	j.	j.	PROPN
asir-2054	200	2	comb	comb	PROPN
asir-2054	200	3	.	.	PUNCT
asir-2054	201	1	theory	theory	NOUN
asir-2054	201	2	ser	ser	PROPN
asir-2054	201	3	.	.	PUNCT
asir-2054	202	1	b.	b.	PROPN
asir-2054	202	2	,	,	PUNCT
asir-2054	202	3	71	71	NUM
asir-2054	202	4	,	,	PUNCT
asir-2054	202	5	184	184	NUM
asir-2054	202	6	-	-	SYM
asir-2054	202	7	204	204	NUM
asir-2054	202	8	.	.	PUNCT
asir-2054	203	1	https://doi.org/10.1006/jctb.1997.1780	https://doi.org/10.1006/jctb.1997.1780	PROPN
asir-2054	203	2	ca	ca	NOUN
asir-2054	203	3	,	,	PUNCT
asir-2054	203	4	j.	j.	PROPN
asir-2054	203	5	s.	s.	PROPN
asir-2054	203	6	,	,	PUNCT
asir-2054	203	7	ge	ge	PROPN
asir-2054	203	8	,	,	PUNCT
asir-2054	203	9	l.	l.	PROPN
asir-2054	203	10	s.	s.	PROPN
asir-2054	203	11	,	,	PUNCT
asir-2054	203	12	zhang	zhang	PROPN
asir-2054	203	13	,	,	PUNCT
asir-2054	203	14	x.	x.	PROPN
asir-2054	203	15	,	,	PUNCT
asir-2054	203	16	&	&	CCONJ
asir-2054	203	17	liu	liu	PROPN
asir-2054	203	18	,	,	PUNCT
asir-2054	203	19	g.	g.	PROPN
asir-2054	203	20	z.	z.	PROPN
asir-2054	203	21	(	(	PUNCT
asir-2054	203	22	2011	2011	NUM
asir-2054	203	23	)	)	PUNCT
asir-2054	203	24	.	.	PUNCT
asir-2054	204	1	edge	edge	NOUN
asir-2054	204	2	-	-	PUNCT
asir-2054	204	3	choosability	choosability	NOUN
asir-2054	204	4	of	of	ADP
asir-2054	204	5	planar	planar	ADJ
asir-2054	204	6	graphs	graph	NOUN
asir-2054	204	7	without	without	ADP
asir-2054	204	8	chordal	chordal	ADJ
asir-2054	204	9	7	7	NUM
asir-2054	204	10	-	-	PUNCT
asir-2054	204	11	cycles	cycle	NOUN
asir-2054	204	12	.	.	PUNCT
asir-2054	205	1	ars	ars	PROPN
asir-2054	205	2	combinatoria	combinatoria	PROPN
asir-2054	205	3	,	,	PUNCT
asir-2054	205	4	100	100	NUM
asir-2054	205	5	,	,	PUNCT
asir-2054	205	6	169	169	NUM
asir-2054	205	7	-	-	SYM
asir-2054	205	8	176	176	NUM
asir-2054	205	9	.	.	PUNCT
asir-2054	206	1	erdős	erdős	PROPN
asir-2054	206	2	,	,	PUNCT
asir-2054	206	3	p.	p.	PROPN
asir-2054	206	4	,	,	PUNCT
asir-2054	206	5	rubin	rubin	PROPN
asir-2054	206	6	,	,	PUNCT
asir-2054	206	7	a.	a.	PROPN
asir-2054	206	8	l.	l.	PROPN
asir-2054	206	9	,	,	PUNCT
asir-2054	206	10	&	&	CCONJ
asir-2054	206	11	taylor	taylor	PROPN
asir-2054	206	12	,	,	PUNCT
asir-2054	206	13	h.	h.	PROPN
asir-2054	206	14	(	(	PUNCT
asir-2054	206	15	1979	1979	NUM
asir-2054	206	16	)	)	PUNCT
asir-2054	206	17	.	.	PUNCT
asir-2054	207	1	choosability	choosability	NOUN
asir-2054	207	2	in	in	ADP
asir-2054	207	3	graphs	graph	NOUN
asir-2054	207	4	.	.	PUNCT
asir-2054	208	1	congr	congr	PROPN
asir-2054	208	2	numer	numer	PROPN
asir-2054	208	3	,	,	PUNCT
asir-2054	208	4	26	26	NUM
asir-2054	208	5	,	,	PUNCT
asir-2054	208	6	125	125	NUM
asir-2054	208	7	-	-	SYM
asir-2054	208	8	157	157	NUM
asir-2054	208	9	.	.	PUNCT
asir-2054	209	1	galvin	galvin	PROPN
asir-2054	209	2	,	,	PUNCT
asir-2054	209	3	f.	f.	PROPN
asir-2054	209	4	(	(	PUNCT
asir-2054	209	5	1995	1995	NUM
asir-2054	209	6	)	)	PUNCT
asir-2054	209	7	.	.	PUNCT
asir-2054	210	1	the	the	DET
asir-2054	210	2	list	list	NOUN
asir-2054	210	3	chromatic	chromatic	ADJ
asir-2054	210	4	index	index	NOUN
asir-2054	210	5	of	of	ADP
asir-2054	210	6	a	a	DET
asir-2054	210	7	bipartite	bipartite	PROPN
asir-2054	210	8	multigraph	multigraph	NOUN
asir-2054	210	9	.	.	PUNCT
asir-2054	211	1	j.	j.	PROPN
asir-2054	211	2	comb	comb	PROPN
asir-2054	211	3	.	.	PUNCT
asir-2054	212	1	theory	theory	NOUN
asir-2054	212	2	ser	ser	PROPN
asir-2054	212	3	.	.	PUNCT
asir-2054	213	1	b.	b.	PROPN
asir-2054	213	2	,	,	PUNCT
asir-2054	213	3	63	63	NUM
asir-2054	213	4	,	,	PUNCT
asir-2054	213	5	153	153	NUM
asir-2054	213	6	-	-	SYM
asir-2054	213	7	158	158	NUM
asir-2054	213	8	.	.	PUNCT
asir-2054	214	1	https://doi.org/10.1006/jctb.1995.1011	https://doi.org/10.1006/jctb.1995.1011	PROPN
asir-2054	214	2	haggkvist	haggkvist	NOUN
asir-2054	214	3	,	,	PUNCT
asir-2054	214	4	r.	r.	PROPN
asir-2054	214	5	,	,	PUNCT
asir-2054	214	6	&	&	CCONJ
asir-2054	214	7	chetwynd	chetwynd	PROPN
asir-2054	214	8	a.	a.	PROPN
asir-2054	214	9	(	(	PUNCT
asir-2054	214	10	1992	1992	NUM
asir-2054	214	11	)	)	PUNCT
asir-2054	214	12	.	.	PUNCT
asir-2054	215	1	some	some	DET
asir-2054	215	2	upper	upper	ADJ
asir-2054	215	3	bounds	bound	NOUN
asir-2054	215	4	on	on	ADP
asir-2054	215	5	the	the	DET
asir-2054	215	6	total	total	ADJ
asir-2054	215	7	and	and	CCONJ
asir-2054	215	8	list	list	VERB
asir-2054	215	9	chromatic	chromatic	ADJ
asir-2054	215	10	numbers	number	NOUN
asir-2054	215	11	of	of	ADP
asir-2054	215	12	multi	multi	NOUN
asir-2054	215	13	graphs	graph	NOUN
asir-2054	215	14	.	.	PUNCT
asir-2054	216	1	j.	j.	PROPN
asir-2054	216	2	graph	graph	PROPN
asir-2054	216	3	theory	theory	NOUN
asir-2054	216	4	,	,	PUNCT
asir-2054	216	5	16	16	NUM
asir-2054	216	6	,	,	PUNCT
asir-2054	216	7	503	503	NUM
asir-2054	216	8	-	-	SYM
asir-2054	216	9	516	516	NUM
asir-2054	216	10	.	.	PUNCT
asir-2054	217	1	https://doi.org/10.1002/jgt.3190160510	https://doi.org/10.1002/jgt.3190160510	ADJ
asir-2054	217	2	haggkvist	haggkvist	NOUN
asir-2054	217	3	,	,	PUNCT
asir-2054	217	4	r.	r.	PROPN
asir-2054	217	5	,	,	PUNCT
asir-2054	217	6	&	&	CCONJ
asir-2054	217	7	janssen	janssen	PROPN
asir-2054	217	8	,	,	PUNCT
asir-2054	217	9	j.	j.	PROPN
asir-2054	217	10	(	(	PUNCT
asir-2054	217	11	1997	1997	NUM
asir-2054	217	12	)	)	PUNCT
asir-2054	217	13	.	.	PUNCT
asir-2054	218	1	new	new	ADJ
asir-2054	218	2	bounds	bound	NOUN
asir-2054	218	3	on	on	ADP
asir-2054	218	4	the	the	DET
asir-2054	218	5	list	list	NOUN
asir-2054	218	6	-	-	PUNCT
asir-2054	218	7	chromatic	chromatic	ADJ
asir-2054	218	8	index	index	NOUN
asir-2054	218	9	of	of	ADP
asir-2054	218	10	the	the	DET
asir-2054	218	11	complete	complete	ADJ
asir-2054	218	12	graph	graph	NOUN
asir-2054	218	13	and	and	CCONJ
asir-2054	218	14	other	other	ADJ
asir-2054	218	15	simple	simple	ADJ
asir-2054	218	16	graphs	graph	NOUN
asir-2054	218	17	.	.	PUNCT
asir-2054	219	1	comb	comb	NOUN
asir-2054	219	2	.	.	PUNCT
asir-2054	220	1	probab	probab	PROPN
asir-2054	220	2	.	.	PUNCT
asir-2054	221	1	comput	comput	PROPN
asir-2054	221	2	.	.	PUNCT
asir-2054	221	3	,	,	PUNCT
asir-2054	221	4	6	6	NUM
asir-2054	221	5	,	,	PUNCT
asir-2054	221	6	295	295	NUM
asir-2054	221	7	-	-	SYM
asir-2054	221	8	313	313	NUM
asir-2054	221	9	.	.	PUNCT
asir-2054	222	1	https://doi.org/10.1017/s0963548397002927	https://doi.org/10.1017/s0963548397002927	NUM
asir-2054	222	2	harris	harris	PROPN
asir-2054	222	3	,	,	PUNCT
asir-2054	222	4	a.	a.	PROPN
asir-2054	222	5	j.	j.	PROPN
asir-2054	222	6	(	(	PUNCT
asir-2054	222	7	n.d	n.d	PROPN
asir-2054	222	8	.	.	PROPN
asir-2054	222	9	)	)	PUNCT
asir-2054	222	10	.	.	PUNCT
asir-2054	223	1	problems	problem	NOUN
asir-2054	223	2	and	and	CCONJ
asir-2054	223	3	conjectures	conjecture	VERB
asir-2054	223	4	in	in	ADP
asir-2054	223	5	extremal	extremal	ADJ
asir-2054	223	6	graph	graph	NOUN
asir-2054	223	7	theory	theory	NOUN
asir-2054	223	8	(	(	PUNCT
asir-2054	223	9	ph.d	ph.d	PROPN
asir-2054	223	10	.	.	PUNCT
asir-2054	224	1	dissertation	dissertation	NOUN
asir-2054	224	2	)	)	PUNCT
asir-2054	224	3	.	.	PUNCT
asir-2054	225	1	cambridge	cambridge	PROPN
asir-2054	225	2	university	university	PROPN
asir-2054	225	3	,	,	PUNCT
asir-2054	225	4	uk	uk	PROPN
asir-2054	225	5	.	.	PROPN
asir-2054	225	6	hou	hou	PROPN
asir-2054	225	7	,	,	PUNCT
asir-2054	225	8	j.	j.	PROPN
asir-2054	225	9	f.	f.	PROPN
asir-2054	225	10	,	,	PUNCT
asir-2054	225	11	liu	liu	PROPN
asir-2054	225	12	,	,	PUNCT
asir-2054	225	13	g.	g.	PROPN
asir-2054	225	14	z.	z.	PROPN
asir-2054	225	15	,	,	PUNCT
asir-2054	225	16	&	&	CCONJ
asir-2054	225	17	cai	cai	PROPN
asir-2054	225	18	,	,	PUNCT
asir-2054	225	19	j.	j.	PROPN
asir-2054	225	20	s.	s.	PROPN
asir-2054	225	21	(	(	PUNCT
asir-2054	225	22	2009	2009	NUM
asir-2054	225	23	)	)	PUNCT
asir-2054	225	24	.	.	PUNCT
asir-2054	226	1	edge	edge	NOUN
asir-2054	226	2	-	-	PUNCT
asir-2054	226	3	choosability	choosability	NOUN
asir-2054	226	4	of	of	ADP
asir-2054	226	5	planar	planar	ADJ
asir-2054	226	6	graphs	graph	NOUN
asir-2054	226	7	without	without	ADP
asir-2054	226	8	adjacent	adjacent	ADJ
asir-2054	226	9	triangles	triangle	NOUN
asir-2054	226	10	or	or	CCONJ
asir-2054	226	11	without	without	ADP
asir-2054	226	12	7	7	NOUN
asir-2054	226	13	-	-	PUNCT
asir-2054	226	14	cycles	cycle	NOUN
asir-2054	226	15	.	.	PUNCT
asir-2054	227	1	discrete	discrete	ADJ
asir-2054	227	2	math	math	NOUN
asir-2054	227	3	,	,	PUNCT
asir-2054	227	4	309	309	NUM
asir-2054	227	5	,	,	PUNCT
asir-2054	227	6	77	77	NUM
asir-2054	227	7	-	-	SYM
asir-2054	227	8	84	84	NUM
asir-2054	227	9	.	.	PUNCT
asir-2054	228	1	https://doi.org/10.1016/j.disc.2007.12.046	https://doi.org/10.1016/j.disc.2007.12.046	PROPN
asir-2054	228	2	juvan	juvan	NOUN
asir-2054	228	3	,	,	PUNCT
asir-2054	228	4	m.	m.	NOUN
asir-2054	228	5	,	,	PUNCT
asir-2054	228	6	mohar	mohar	PROPN
asir-2054	228	7	,	,	PUNCT
asir-2054	228	8	b.	b.	PROPN
asir-2054	228	9	,	,	PUNCT
asir-2054	228	10	&	&	CCONJ
asir-2054	228	11	srekovski	srekovski	PROPN
asir-2054	228	12	,	,	PUNCT
asir-2054	228	13	r.	r.	PROPN
asir-2054	228	14	(	(	PUNCT
asir-2054	228	15	1999	1999	NUM
asir-2054	228	16	)	)	PUNCT
asir-2054	228	17	.	.	PUNCT
asir-2054	229	1	graphs	graph	NOUN
asir-2054	229	2	of	of	ADP
asir-2054	229	3	degree	degree	NOUN
asir-2054	229	4	4	4	NUM
asir-2054	229	5	are	be	AUX
asir-2054	229	6	5	5	NUM
asir-2054	229	7	-	-	NOUN
asir-2054	229	8	choosable	choosable	NOUN
asir-2054	229	9	.	.	PUNCT
asir-2054	230	1	j	j	PROPN
asir-2054	230	2	graph	graph	NOUN
asir-2054	230	3	theory	theory	NOUN
asir-2054	230	4	,	,	PUNCT
asir-2054	230	5	32	32	NUM
asir-2054	230	6	,	,	PUNCT
asir-2054	230	7	250	250	NUM
asir-2054	230	8	-	-	SYM
asir-2054	230	9	262	262	NUM
asir-2054	230	10	.	.	PUNCT
asir-2054	231	1	https://doi.org/10.1002/(sici)1097-0118(199911)32:3%3c250::aid-jgt5%3e3.0.co	https://doi.org/10.1002/(sici)1097-0118(199911)32:3%3c250::aid-jgt5%3e3.0.co	NUM
asir-2054	231	2	;	;	PUNCT
asir-2054	231	3	2	2	NUM
asir-2054	231	4	-	-	PUNCT
asir-2054	231	5	r	r	NOUN
asir-2054	231	6	kostochka	kostochka	NOUN
asir-2054	231	7	,	,	PUNCT
asir-2054	231	8	a.	a.	NOUN
asir-2054	231	9	v.	v.	PROPN
asir-2054	231	10	(	(	PUNCT
asir-2054	231	11	1992	1992	NUM
asir-2054	231	12	)	)	PUNCT
asir-2054	231	13	.	.	PUNCT
asir-2054	232	1	list	list	NOUN
asir-2054	232	2	edge	edge	VERB
asir-2054	232	3	chromatic	chromatic	ADJ
asir-2054	232	4	number	number	NOUN
asir-2054	232	5	of	of	ADP
asir-2054	232	6	graphs	graph	NOUN
asir-2054	232	7	with	with	ADP
asir-2054	232	8	large	large	ADJ
asir-2054	232	9	girth	girth	NOUN
asir-2054	232	10	.	.	PUNCT
asir-2054	233	1	discrete	discrete	ADJ
asir-2054	233	2	math	math	NOUN
asir-2054	233	3	,	,	PUNCT
asir-2054	233	4	101	101	NUM
asir-2054	233	5	,	,	PUNCT
asir-2054	233	6	189	189	NUM
asir-2054	233	7	-	-	PUNCT
asir-2054	233	8	201	201	NUM
asir-2054	233	9	.	.	PUNCT
asir-2054	234	1	https://doi.org/10.1016/0012-365x(92)90602-c	https://doi.org/10.1016/0012-365x(92)90602-c	PROPN
asir-2054	234	2	ma	ma	PROPN
asir-2054	234	3	,	,	PUNCT
asir-2054	234	4	q.	q.	PROPN
asir-2054	234	5	l.	l.	PROPN
asir-2054	234	6	,	,	PUNCT
asir-2054	234	7	wang	wang	PROPN
asir-2054	234	8	,	,	PUNCT
asir-2054	234	9	j.	j.	PROPN
asir-2054	234	10	h.	h.	PROPN
asir-2054	234	11	,	,	PUNCT
asir-2054	234	12	cai	cai	PROPN
asir-2054	234	13	,	,	PUNCT
asir-2054	234	14	j.	j.	PROPN
asir-2054	234	15	s.	s.	PROPN
asir-2054	234	16	,	,	PUNCT
asir-2054	234	17	&	&	CCONJ
asir-2054	234	18	zhang	zhang	PROPN
asir-2054	234	19	,	,	PUNCT
asir-2054	234	20	s.	s.	PROPN
asir-2054	234	21	m.	m.	PROPN
asir-2054	234	22	(	(	PUNCT
asir-2054	234	23	2011	2011	NUM
asir-2054	234	24	)	)	PUNCT
asir-2054	234	25	.	.	PUNCT
asir-2054	235	1	a	a	DET
asir-2054	235	2	note	note	NOUN
asir-2054	235	3	on	on	ADP
asir-2054	235	4	edge	edge	NOUN
asir-2054	235	5	-	-	PUNCT
asir-2054	235	6	choosability	choosability	NOUN
asir-2054	235	7	of	of	ADP
asir-2054	235	8	planar	planar	ADJ
asir-2054	235	9	graphs	graph	NOUN
asir-2054	235	10	without	without	ADP
asir-2054	235	11	intersecting	intersect	VERB
asir-2054	235	12	4	4	NUM
asir-2054	235	13	-	-	PUNCT
asir-2054	235	14	cycles	cycle	NOUN
asir-2054	235	15	.	.	PUNCT
asir-2054	236	1	j	j	PROPN
asir-2054	236	2	appl	appl	PROPN
asir-2054	236	3	math	math	PROPN
asir-2054	236	4	comput	comput	PROPN
asir-2054	236	5	,	,	PUNCT
asir-2054	236	6	36	36	NUM
asir-2054	236	7	,	,	PUNCT
asir-2054	236	8	367	367	NUM
asir-2054	236	9	-	-	SYM
asir-2054	236	10	372	372	NUM
asir-2054	236	11	.	.	PUNCT
asir-2054	237	1	https://doi.org/10.1007/s12190-010-0408-5	https://doi.org/10.1007/s12190-010-0408-5	PROPN
asir-2054	237	2	wang	wang	PROPN
asir-2054	237	3	,	,	PUNCT
asir-2054	237	4	h.	h.	PROPN
asir-2054	237	5	y.	y.	PROPN
asir-2054	237	6	,	,	PUNCT
asir-2054	237	7	&	&	CCONJ
asir-2054	237	8	wu	wu	PROPN
asir-2054	237	9	,	,	PUNCT
asir-2054	237	10	j.	j.	PROPN
asir-2054	237	11	l.	l.	PROPN
asir-2054	237	12	(	(	PUNCT
asir-2054	237	13	2018	2018	NUM
asir-2054	237	14	)	)	PUNCT
asir-2054	237	15	.	.	PUNCT
asir-2054	238	1	list	list	NOUN
asir-2054	238	2	-	-	PUNCT
asir-2054	238	3	edge	edge	NOUN
asir-2054	238	4	-	-	PUNCT
asir-2054	238	5	coloring	coloring	NOUN
asir-2054	238	6	of	of	ADP
asir-2054	238	7	planar	planar	ADJ
asir-2054	238	8	graphs	graph	NOUN
asir-2054	238	9	without	without	ADP
asir-2054	238	10	6	6	NUM
asir-2054	238	11	-	-	PUNCT
asir-2054	238	12	cycles	cycle	NOUN
asir-2054	238	13	with	with	ADP
asir-2054	238	14	three	three	NUM
asir-2054	238	15	chords	chord	NOUN
asir-2054	238	16	,	,	PUNCT
asir-2054	238	17	j	j	PROPN
asir-2054	238	18	comb	comb	NOUN
asir-2054	238	19	optim	optim	VERB
asir-2054	238	20	,	,	PUNCT
asir-2054	238	21	35	35	NUM
asir-2054	238	22	,	,	PUNCT
asir-2054	238	23	555	555	NUM
asir-2054	238	24	-	-	SYM
asir-2054	238	25	562	562	NUM
asir-2054	238	26	.	.	PUNCT
asir-2054	239	1	https://doi.org/10.1007/s10878-017-0193-2	https://doi.org/10.1007/s10878-017-0193-2	NUM
asir-2054	239	2	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-2054	239	3	applied	apply	VERB
asir-2054	239	4	science	science	NOUN
asir-2054	239	5	and	and	CCONJ
asir-2054	239	6	innovative	innovative	ADJ
asir-2054	239	7	research	research	NOUN
asir-2054	239	8	vol	vol	NOUN
asir-2054	239	9	.	.	PUNCT
asir-2054	240	1	3	3	NUM
asir-2054	240	2	,	,	PUNCT
asir-2054	240	3	no	no	INTJ
asir-2054	240	4	.	.	NOUN
asir-2054	240	5	2	2	NUM
asir-2054	240	6	,	,	PUNCT
asir-2054	240	7	2019	2019	NUM
asir-2054	240	8	91	91	NUM
asir-2054	240	9	published	publish	VERB
asir-2054	240	10	by	by	ADP
asir-2054	240	11	scholink	scholink	PROPN
asir-2054	240	12	inc	inc	PROPN
asir-2054	240	13	.	.	PROPN
asir-2054	240	14	wang	wang	PROPN
asir-2054	240	15	,	,	PUNCT
asir-2054	240	16	w.	w.	PROPN
asir-2054	240	17	f.	f.	PROPN
asir-2054	240	18	,	,	PUNCT
asir-2054	240	19	&	&	CCONJ
asir-2054	240	20	lih	lih	PROPN
asir-2054	240	21	,	,	PUNCT
asir-2054	240	22	k.	k.	PROPN
asir-2054	240	23	w.	w.	PROPN
asir-2054	240	24	(	(	PUNCT
asir-2054	240	25	2001	2001	NUM
asir-2054	240	26	)	)	PUNCT
asir-2054	240	27	.	.	PUNCT
asir-2054	241	1	choosability	choosability	NOUN
asir-2054	241	2	,	,	PUNCT
asir-2054	241	3	edge	edge	NOUN
asir-2054	241	4	choosability	choosability	NOUN
asir-2054	241	5	and	and	CCONJ
asir-2054	241	6	total	total	ADJ
asir-2054	241	7	choosability	choosability	NOUN
asir-2054	241	8	of	of	ADP
asir-2054	241	9	outerpla	outerpla	NOUN
asir-2054	241	10	-	-	PUNCT
asir-2054	241	11	nar	nar	NOUN
asir-2054	241	12	graphs	graph	NOUN
asir-2054	241	13	.	.	PUNCT
asir-2054	242	1	eur	eur	PROPN
asir-2054	242	2	.	.	PUNCT
asir-2054	243	1	j.	j.	PROPN
asir-2054	243	2	comb	comb	PROPN
asir-2054	243	3	.	.	PUNCT
asir-2054	243	4	,	,	PUNCT
asir-2054	243	5	22	22	NUM
asir-2054	243	6	,	,	PUNCT
asir-2054	243	7	71	71	NUM
asir-2054	243	8	-	-	SYM
asir-2054	243	9	78	78	NUM
asir-2054	243	10	.	.	PUNCT
asir-2054	244	1	https://doi.org/10.1006/eujc.2000.0430	https://doi.org/10.1006/eujc.2000.0430	PROPN
asir-2054	244	2	woodall	woodall	PROPN
asir-2054	244	3	,	,	PUNCT
asir-2054	244	4	d.	d.	PROPN
asir-2054	244	5	r.	r.	PROPN
asir-2054	244	6	(	(	PUNCT
asir-2054	244	7	1999	1999	NUM
asir-2054	244	8	)	)	PUNCT
asir-2054	244	9	.	.	PUNCT
asir-2054	245	1	edge	edge	NOUN
asir-2054	245	2	-	-	PUNCT
asir-2054	245	3	choosability	choosability	NOUN
asir-2054	245	4	of	of	ADP
asir-2054	245	5	multicircuits	multicircuit	NOUN
asir-2054	245	6	.	.	PUNCT
asir-2054	246	1	discrete	discrete	ADJ
asir-2054	246	2	math	math	NOUN
asir-2054	246	3	,	,	PUNCT
asir-2054	246	4	202	202	NUM
asir-2054	246	5	,	,	PUNCT
asir-2054	246	6	271	271	NUM
asir-2054	246	7	-	-	SYM
asir-2054	246	8	277	277	NUM
asir-2054	246	9	.	.	PUNCT
asir-2054	247	1	https://doi.org/10.1016/s0012-365x(98)00297-0	https://doi.org/10.1016/s0012-365x(98)00297-0	VERB