id	sid	tid	token	lemma	pos
ejpam-5942	1	1	european	european	PROPN
ejpam-5942	1	2	journal	journal	PROPN
ejpam-5942	1	3	of	of	ADP
ejpam-5942	1	4	pure	pure	ADJ
ejpam-5942	1	5	and	and	CCONJ
ejpam-5942	1	6	applied	applied	ADJ
ejpam-5942	1	7	mathematics	mathematic	NOUN
ejpam-5942	1	8	2025	2025	NUM
ejpam-5942	1	9	,	,	PUNCT
ejpam-5942	1	10	vol	vol	NOUN
ejpam-5942	1	11	.	.	PROPN
ejpam-5942	1	12	18	18	NUM
ejpam-5942	1	13	,	,	PUNCT
ejpam-5942	1	14	issue	issue	NOUN
ejpam-5942	1	15	2	2	NUM
ejpam-5942	1	16	,	,	PUNCT
ejpam-5942	1	17	article	article	NOUN
ejpam-5942	1	18	number	number	NOUN
ejpam-5942	1	19	5942	5942	NUM
ejpam-5942	1	20	issn	issn	PROPN
ejpam-5942	1	21	1307	1307	NUM
ejpam-5942	1	22	-	-	SYM
ejpam-5942	1	23	5543	5543	NUM
ejpam-5942	1	24	–	–	PUNCT
ejpam-5942	1	25	ejpam.com	ejpam.com	X
ejpam-5942	1	26	published	publish	VERB
ejpam-5942	1	27	by	by	ADP
ejpam-5942	1	28	new	new	PROPN
ejpam-5942	1	29	york	york	PROPN
ejpam-5942	1	30	business	business	PROPN
ejpam-5942	1	31	global	global	PROPN
ejpam-5942	1	32	the	the	DET
ejpam-5942	1	33	total	total	ADJ
ejpam-5942	1	34	choosability	choosability	NOUN
ejpam-5942	1	35	with	with	ADP
ejpam-5942	1	36	neighbor	neighbor	NOUN
ejpam-5942	1	37	sum	sum	NOUN
ejpam-5942	1	38	distinguishing	distinguish	VERB
ejpam-5942	1	39	properties	property	NOUN
ejpam-5942	1	40	of	of	ADP
ejpam-5942	1	41	planar	planar	ADJ
ejpam-5942	1	42	graphs	graph	NOUN
ejpam-5942	1	43	that	that	PRON
ejpam-5942	1	44	are	be	AUX
ejpam-5942	1	45	devoid	devoid	ADJ
ejpam-5942	1	46	of	of	ADP
ejpam-5942	1	47	c5	c5	PROPN
ejpam-5942	1	48	adjacent	adjacent	ADJ
ejpam-5942	1	49	to	to	ADP
ejpam-5942	1	50	c3	c3	PROPN
ejpam-5942	1	51	pongpat	pongpat	PROPN
ejpam-5942	1	52	sittitrai1,4,kittikorn	sittitrai1,4,kittikorn	PROPN
ejpam-5942	1	53	nakprasit2,5	nakprasit2,5	PROPN
ejpam-5942	1	54	,	,	PUNCT
ejpam-5942	1	55	patcharapan	patcharapan	NOUN
ejpam-5942	1	56	jumnongnit3,∗	jumnongnit3,∗	NOUN
ejpam-5942	1	57	1	1	NUM
ejpam-5942	1	58	futuristic	futuristic	ADJ
ejpam-5942	1	59	science	science	NOUN
ejpam-5942	1	60	research	research	NOUN
ejpam-5942	1	61	center	center	NOUN
ejpam-5942	1	62	,	,	PUNCT
ejpam-5942	1	63	school	school	NOUN
ejpam-5942	1	64	of	of	ADP
ejpam-5942	1	65	science	science	NOUN
ejpam-5942	1	66	,	,	PUNCT
ejpam-5942	1	67	walailak	walailak	ADJ
ejpam-5942	1	68	university	university	NOUN
ejpam-5942	1	69	,	,	PUNCT
ejpam-5942	1	70	nakhonsithammarat	nakhonsithammarat	NOUN
ejpam-5942	1	71	,	,	PUNCT
ejpam-5942	1	72	80161	80161	NUM
ejpam-5942	1	73	,	,	PUNCT
ejpam-5942	1	74	thailand	thailand	PROPN
ejpam-5942	1	75	2	2	NUM
ejpam-5942	1	76	department	department	NOUN
ejpam-5942	1	77	of	of	ADP
ejpam-5942	1	78	mathematics	mathematic	NOUN
ejpam-5942	1	79	,	,	PUNCT
ejpam-5942	1	80	faculty	faculty	NOUN
ejpam-5942	1	81	of	of	ADP
ejpam-5942	1	82	science	science	NOUN
ejpam-5942	1	83	,	,	PUNCT
ejpam-5942	1	84	khon	khon	PROPN
ejpam-5942	1	85	kaen	kaen	PROPN
ejpam-5942	1	86	university	university	PROPN
ejpam-5942	1	87	,	,	PUNCT
ejpam-5942	1	88	40002	40002	NUM
ejpam-5942	1	89	,	,	PUNCT
ejpam-5942	1	90	khon	khon	PROPN
ejpam-5942	1	91	kaen	kaen	PROPN
ejpam-5942	1	92	,	,	PUNCT
ejpam-5942	1	93	thailand	thailand	PROPN
ejpam-5942	1	94	3	3	NUM
ejpam-5942	1	95	division	division	NOUN
ejpam-5942	1	96	of	of	ADP
ejpam-5942	1	97	mathematics	mathematic	NOUN
ejpam-5942	1	98	,	,	PUNCT
ejpam-5942	1	99	school	school	NOUN
ejpam-5942	1	100	of	of	ADP
ejpam-5942	1	101	science	science	NOUN
ejpam-5942	1	102	,	,	PUNCT
ejpam-5942	1	103	university	university	NOUN
ejpam-5942	1	104	of	of	ADP
ejpam-5942	1	105	phayao	phayao	NOUN
ejpam-5942	1	106	,	,	PUNCT
ejpam-5942	1	107	phayao	phayao	NOUN
ejpam-5942	1	108	,	,	PUNCT
ejpam-5942	1	109	56000	56000	NUM
ejpam-5942	1	110	,	,	PUNCT
ejpam-5942	1	111	thailand	thailand	PROPN
ejpam-5942	1	112	4	4	NUM
ejpam-5942	1	113	research	research	NOUN
ejpam-5942	1	114	center	center	NOUN
ejpam-5942	1	115	for	for	ADP
ejpam-5942	1	116	theoretical	theoretical	ADJ
ejpam-5942	1	117	simulation	simulation	NOUN
ejpam-5942	1	118	and	and	CCONJ
ejpam-5942	1	119	applied	apply	VERB
ejpam-5942	1	120	research	research	NOUN
ejpam-5942	1	121	in	in	ADP
ejpam-5942	1	122	bioscience	bioscience	NOUN
ejpam-5942	1	123	and	and	CCONJ
ejpam-5942	1	124	sensing	sense	VERB
ejpam-5942	1	125	,	,	PUNCT
ejpam-5942	1	126	walailak	walailak	ADJ
ejpam-5942	1	127	university	university	NOUN
ejpam-5942	1	128	,	,	PUNCT
ejpam-5942	1	129	nakhon	nakhon	PROPN
ejpam-5942	1	130	si	si	PROPN
ejpam-5942	1	131	thammarat	thammarat	PROPN
ejpam-5942	1	132	80160	80160	NUM
ejpam-5942	1	133	,	,	PUNCT
ejpam-5942	1	134	thailand	thailand	PROPN
ejpam-5942	1	135	5	5	NUM
ejpam-5942	1	136	centre	centre	NOUN
ejpam-5942	1	137	of	of	ADP
ejpam-5942	1	138	excellence	excellence	NOUN
ejpam-5942	1	139	in	in	ADP
ejpam-5942	1	140	mathematics	mathematics	PROPN
ejpam-5942	1	141	,	,	PUNCT
ejpam-5942	1	142	mhesi	mhesi	PROPN
ejpam-5942	1	143	,	,	PUNCT
ejpam-5942	1	144	bangkok	bangkok	PROPN
ejpam-5942	1	145	10400	10400	NUM
ejpam-5942	1	146	,	,	PUNCT
ejpam-5942	1	147	thailand	thailand	PROPN
ejpam-5942	1	148	abstract	abstract	PROPN
ejpam-5942	1	149	.	.	PUNCT
ejpam-5942	2	1	let	let	VERB
ejpam-5942	2	2	g	g	PRON
ejpam-5942	2	3	be	be	AUX
ejpam-5942	2	4	a	a	DET
ejpam-5942	2	5	graph	graph	NOUN
ejpam-5942	2	6	such	such	ADJ
ejpam-5942	2	7	that	that	SCONJ
ejpam-5942	2	8	a	a	DET
ejpam-5942	2	9	proper	proper	ADJ
ejpam-5942	2	10	total	total	ADJ
ejpam-5942	2	11	coloring	coloring	NOUN
ejpam-5942	2	12	ψ	ψ	X
ejpam-5942	2	13	:	:	PUNCT
ejpam-5942	2	14	v	v	X
ejpam-5942	2	15	(	(	PUNCT
ejpam-5942	2	16	g	g	NOUN
ejpam-5942	2	17	)	)	PUNCT
ejpam-5942	2	18	∪	∪	ADP
ejpam-5942	2	19	e(g	e(g	NOUN
ejpam-5942	2	20	)	)	PUNCT
ejpam-5942	2	21	−→	−→	PROPN
ejpam-5942	2	22	n.	n.	NOUN
ejpam-5942	2	23	let	let	VERB
ejpam-5942	2	24	s(x	s(x	NOUN
ejpam-5942	2	25	)	)	PUNCT
ejpam-5942	2	26	denote	denote	VERB
ejpam-5942	2	27	the	the	DET
ejpam-5942	2	28	sum	sum	NOUN
ejpam-5942	2	29	of	of	ADP
ejpam-5942	2	30	colors	color	NOUN
ejpam-5942	2	31	assigned	assign	VERB
ejpam-5942	2	32	to	to	ADP
ejpam-5942	2	33	x	x	PUNCT
ejpam-5942	2	34	and	and	CCONJ
ejpam-5942	2	35	those	those	DET
ejpam-5942	2	36	incident	incident	NOUN
ejpam-5942	2	37	edges	edge	NOUN
ejpam-5942	2	38	of	of	ADP
ejpam-5942	2	39	x.	x.	NOUN
ejpam-5942	2	40	a	a	DET
ejpam-5942	2	41	coloring	coloring	NOUN
ejpam-5942	2	42	ψ	ψ	X
ejpam-5942	2	43	is	be	AUX
ejpam-5942	2	44	a	a	DET
ejpam-5942	2	45	neighbor	neighbor	NOUN
ejpam-5942	2	46	sum	sum	NOUN
ejpam-5942	2	47	distinguishing	distinguish	VERB
ejpam-5942	2	48	total	total	ADJ
ejpam-5942	2	49	coloring	coloring	NOUN
ejpam-5942	2	50	if	if	SCONJ
ejpam-5942	2	51	s(x	s(x	NOUN
ejpam-5942	2	52	)	)	PUNCT
ejpam-5942	2	53	̸=	̸=	PROPN
ejpam-5942	2	54	s(y	s(y	PROPN
ejpam-5942	2	55	)	)	PUNCT
ejpam-5942	2	56	,	,	PUNCT
ejpam-5942	2	57	whenever	whenever	SCONJ
ejpam-5942	2	58	xy	xy	PROPN
ejpam-5942	2	59	is	be	AUX
ejpam-5942	2	60	an	an	DET
ejpam-5942	2	61	edge	edge	NOUN
ejpam-5942	2	62	in	in	ADP
ejpam-5942	2	63	g.	g.	PROPN
ejpam-5942	2	64	let	let	VERB
ejpam-5942	2	65	l	l	NOUN
ejpam-5942	2	66	be	be	AUX
ejpam-5942	2	67	a	a	DET
ejpam-5942	2	68	k	k	ADJ
ejpam-5942	2	69	-	-	PUNCT
ejpam-5942	2	70	list	list	NOUN
ejpam-5942	2	71	assignment	assignment	NOUN
ejpam-5942	2	72	of	of	ADP
ejpam-5942	2	73	a	a	DET
ejpam-5942	2	74	graph	graph	NOUN
ejpam-5942	2	75	g	g	NOUN
ejpam-5942	2	76	if	if	SCONJ
ejpam-5942	2	77	l	l	NOUN
ejpam-5942	2	78	is	be	AUX
ejpam-5942	2	79	a	a	DET
ejpam-5942	2	80	function	function	NOUN
ejpam-5942	2	81	,	,	PUNCT
ejpam-5942	2	82	say	say	VERB
ejpam-5942	2	83	l	l	NOUN
ejpam-5942	2	84	:	:	PUNCT
ejpam-5942	3	1	v	v	X
ejpam-5942	3	2	(	(	PUNCT
ejpam-5942	3	3	g	g	NOUN
ejpam-5942	3	4	)	)	PUNCT
ejpam-5942	3	5	∪	∪	ADP
ejpam-5942	3	6	e(g	e(g	PROPN
ejpam-5942	3	7	)	)	PUNCT
ejpam-5942	4	1	→	→	SYM
ejpam-5942	4	2	2n	2n	NUM
ejpam-5942	4	3	such	such	ADJ
ejpam-5942	4	4	that	that	SCONJ
ejpam-5942	4	5	|l(t)|	|l(t)|	PROPN
ejpam-5942	4	6	=	=	SYM
ejpam-5942	4	7	k	k	NOUN
ejpam-5942	4	8	for	for	ADP
ejpam-5942	4	9	all	all	DET
ejpam-5942	4	10	t	t	NOUN
ejpam-5942	4	11	in	in	ADP
ejpam-5942	4	12	the	the	DET
ejpam-5942	4	13	set	set	NOUN
ejpam-5942	4	14	v	v	NOUN
ejpam-5942	4	15	(	(	PUNCT
ejpam-5942	4	16	g	g	NOUN
ejpam-5942	4	17	)	)	PUNCT
ejpam-5942	4	18	∪	∪	ADP
ejpam-5942	4	19	e(g	e(g	PROPN
ejpam-5942	4	20	)	)	PUNCT
ejpam-5942	4	21	.	.	PUNCT
ejpam-5942	5	1	if	if	SCONJ
ejpam-5942	5	2	g	g	PROPN
ejpam-5942	5	3	has	have	AUX
ejpam-5942	5	4	a	a	DET
ejpam-5942	5	5	total	total	ADJ
ejpam-5942	5	6	coloring	coloring	NOUN
ejpam-5942	5	7	such	such	ADJ
ejpam-5942	5	8	that	that	DET
ejpam-5942	5	9	α(x	α(x	NOUN
ejpam-5942	5	10	)	)	PUNCT
ejpam-5942	5	11	is	be	AUX
ejpam-5942	5	12	the	the	DET
ejpam-5942	5	13	element	element	NOUN
ejpam-5942	5	14	of	of	ADP
ejpam-5942	5	15	l(x	l(x	PROPN
ejpam-5942	5	16	)	)	PUNCT
ejpam-5942	5	17	for	for	ADP
ejpam-5942	5	18	all	all	DET
ejpam-5942	5	19	x	x	NOUN
ejpam-5942	5	20	in	in	ADP
ejpam-5942	5	21	the	the	DET
ejpam-5942	5	22	set	set	NOUN
ejpam-5942	5	23	v	v	NOUN
ejpam-5942	5	24	(	(	PUNCT
ejpam-5942	5	25	g)∪e(g	g)∪e(g	NOUN
ejpam-5942	5	26	)	)	PUNCT
ejpam-5942	5	27	,	,	PUNCT
ejpam-5942	5	28	then	then	ADV
ejpam-5942	5	29	we	we	PRON
ejpam-5942	5	30	call	call	VERB
ejpam-5942	5	31	α	α	PRON
ejpam-5942	5	32	total	total	ADJ
ejpam-5942	5	33	-	-	PUNCT
ejpam-5942	5	34	l	l	NOUN
ejpam-5942	5	35	-	-	NOUN
ejpam-5942	5	36	coloring	coloring	NOUN
ejpam-5942	5	37	.	.	PUNCT
ejpam-5942	6	1	moreover	moreover	ADV
ejpam-5942	6	2	,	,	PUNCT
ejpam-5942	6	3	a	a	DET
ejpam-5942	6	4	total	total	ADJ
ejpam-5942	6	5	-	-	PUNCT
ejpam-5942	6	6	l	l	NOUN
ejpam-5942	6	7	-	-	ADJ
ejpam-5942	6	8	coloring	color	VERB
ejpam-5942	6	9	α	α	NOUN
ejpam-5942	6	10	is	be	AUX
ejpam-5942	6	11	called	call	VERB
ejpam-5942	6	12	a	a	DET
ejpam-5942	6	13	neighbor	neighbor	NOUN
ejpam-5942	6	14	sum	sum	NOUN
ejpam-5942	6	15	distinguishing	distinguish	VERB
ejpam-5942	6	16	total	total	ADJ
ejpam-5942	6	17	-	-	PUNCT
ejpam-5942	6	18	l	l	NOUN
ejpam-5942	6	19	-	-	ADJ
ejpam-5942	6	20	coloring	coloring	NOUN
ejpam-5942	6	21	if	if	SCONJ
ejpam-5942	6	22	s(x	s(x	NOUN
ejpam-5942	6	23	)	)	PUNCT
ejpam-5942	6	24	̸=	̸=	PROPN
ejpam-5942	6	25	s(y	s(y	PROPN
ejpam-5942	6	26	)	)	PUNCT
ejpam-5942	6	27	where	where	SCONJ
ejpam-5942	6	28	xy	xy	PROPN
ejpam-5942	6	29	is	be	AUX
ejpam-5942	6	30	an	an	DET
ejpam-5942	6	31	edge	edge	NOUN
ejpam-5942	6	32	in	in	ADP
ejpam-5942	6	33	g.	g.	PROPN
ejpam-5942	6	34	let	let	VERB
ejpam-5942	6	35	ch′′∑(g	ch′′∑(g	X
ejpam-5942	6	36	)	)	PUNCT
ejpam-5942	6	37	be	be	AUX
ejpam-5942	6	38	the	the	DET
ejpam-5942	6	39	minimum	minimum	ADJ
ejpam-5942	6	40	number	number	NOUN
ejpam-5942	6	41	k	k	NOUN
ejpam-5942	6	42	such	such	ADJ
ejpam-5942	6	43	that	that	SCONJ
ejpam-5942	6	44	g	g	PROPN
ejpam-5942	6	45	has	have	VERB
ejpam-5942	6	46	such	such	ADJ
ejpam-5942	6	47	coloring	coloring	NOUN
ejpam-5942	6	48	for	for	ADP
ejpam-5942	6	49	every	every	DET
ejpam-5942	6	50	k	k	ADJ
ejpam-5942	6	51	-	-	PUNCT
ejpam-5942	6	52	list	list	NOUN
ejpam-5942	6	53	assignment	assignment	NOUN
ejpam-5942	6	54	l.	l.	NOUN
ejpam-5942	6	55	in	in	ADP
ejpam-5942	6	56	this	this	DET
ejpam-5942	6	57	work	work	NOUN
ejpam-5942	6	58	,	,	PUNCT
ejpam-5942	6	59	we	we	PRON
ejpam-5942	6	60	present	present	VERB
ejpam-5942	6	61	that	that	SCONJ
ejpam-5942	6	62	for	for	SCONJ
ejpam-5942	6	63	a	a	DET
ejpam-5942	6	64	graph	graph	NOUN
ejpam-5942	6	65	g	g	PROPN
ejpam-5942	6	66	has	have	VERB
ejpam-5942	6	67	ch′′∑(g	ch′′∑(g	VERB
ejpam-5942	6	68	)	)	PUNCT
ejpam-5942	6	69	≤	≤	NOUN
ejpam-5942	6	70	max{10,∆(g	max{10,∆(g	NOUN
ejpam-5942	6	71	)	)	PUNCT
ejpam-5942	7	1	+	+	CCONJ
ejpam-5942	7	2	3	3	X
ejpam-5942	7	3	}	}	PUNCT
ejpam-5942	7	4	if	if	SCONJ
ejpam-5942	7	5	g	g	PROPN
ejpam-5942	7	6	is	be	AUX
ejpam-5942	7	7	a	a	DET
ejpam-5942	7	8	planar	planar	ADJ
ejpam-5942	7	9	graph	graph	NOUN
ejpam-5942	7	10	that	that	PRON
ejpam-5942	7	11	are	be	AUX
ejpam-5942	7	12	devoid	devoid	ADJ
ejpam-5942	7	13	of	of	ADP
ejpam-5942	7	14	c5	c5	PROPN
ejpam-5942	7	15	adjacent	adjacent	ADJ
ejpam-5942	7	16	to	to	ADP
ejpam-5942	7	17	c3	c3	PROPN
ejpam-5942	7	18	.	.	PROPN
ejpam-5942	8	1	2020	2020	NUM
ejpam-5942	8	2	mathematics	mathematics	PROPN
ejpam-5942	8	3	subject	subject	NOUN
ejpam-5942	8	4	classifications	classification	NOUN
ejpam-5942	8	5	:	:	PUNCT
ejpam-5942	8	6	05c10	05c10	NUM
ejpam-5942	8	7	key	key	ADJ
ejpam-5942	8	8	words	word	NOUN
ejpam-5942	8	9	and	and	CCONJ
ejpam-5942	8	10	phrases	phrase	NOUN
ejpam-5942	8	11	:	:	PUNCT
ejpam-5942	8	12	neighbor	neighbor	NOUN
ejpam-5942	8	13	sum	sum	NOUN
ejpam-5942	8	14	distinguishing	distinguish	VERB
ejpam-5942	8	15	total	total	ADJ
ejpam-5942	8	16	coloring	coloring	NOUN
ejpam-5942	8	17	,	,	PUNCT
ejpam-5942	8	18	coloring	coloring	NOUN
ejpam-5942	8	19	,	,	PUNCT
ejpam-5942	8	20	discharging	discharge	VERB
ejpam-5942	8	21	method	method	NOUN
ejpam-5942	8	22	1	1	NUM
ejpam-5942	8	23	.	.	PUNCT
ejpam-5942	9	1	introduction	introduction	NOUN
ejpam-5942	9	2	simple	simple	ADJ
ejpam-5942	9	3	,	,	PUNCT
ejpam-5942	9	4	undirected	undirected	ADJ
ejpam-5942	9	5	,	,	PUNCT
ejpam-5942	9	6	finite	finite	ADJ
ejpam-5942	9	7	graphs	graph	NOUN
ejpam-5942	9	8	are	be	AUX
ejpam-5942	9	9	considered	consider	VERB
ejpam-5942	9	10	in	in	ADP
ejpam-5942	9	11	all	all	DET
ejpam-5942	9	12	cases	case	NOUN
ejpam-5942	9	13	.	.	PUNCT
ejpam-5942	10	1	when	when	SCONJ
ejpam-5942	10	2	referring	refer	VERB
ejpam-5942	10	3	to	to	ADP
ejpam-5942	10	4	the	the	DET
ejpam-5942	10	5	maximum	maximum	ADJ
ejpam-5942	10	6	degree	degree	NOUN
ejpam-5942	10	7	,	,	PUNCT
ejpam-5942	10	8	face	face	NOUN
ejpam-5942	10	9	set	set	NOUN
ejpam-5942	10	10	,	,	PUNCT
ejpam-5942	10	11	edge	edge	NOUN
ejpam-5942	10	12	set	set	NOUN
ejpam-5942	10	13	,	,	PUNCT
ejpam-5942	10	14	and	and	CCONJ
ejpam-5942	10	15	vertex	vertex	NOUN
ejpam-5942	10	16	set	set	NOUN
ejpam-5942	10	17	of	of	ADP
ejpam-5942	10	18	a	a	DET
ejpam-5942	10	19	graph	graph	NOUN
ejpam-5942	10	20	g	g	NOUN
ejpam-5942	10	21	,	,	PUNCT
ejpam-5942	10	22	respectively	respectively	ADV
ejpam-5942	10	23	,	,	PUNCT
ejpam-5942	10	24	we	we	PRON
ejpam-5942	10	25	use	use	VERB
ejpam-5942	10	26	∗corresponding	∗corresponde	VERB
ejpam-5942	10	27	author	author	NOUN
ejpam-5942	10	28	.	.	PUNCT
ejpam-5942	11	1	doi	doi	NOUN
ejpam-5942	11	2	:	:	PUNCT
ejpam-5942	11	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5942	https://doi.org/10.29020/nybg.ejpam.v18i2.5942	ADJ
ejpam-5942	11	4	email	email	NOUN
ejpam-5942	11	5	addresses	address	NOUN
ejpam-5942	11	6	:	:	PUNCT
ejpam-5942	11	7	pongpat.sittitrai@gmail.com	pongpat.sittitrai@gmail.com	X
ejpam-5942	11	8	(	(	PUNCT
ejpam-5942	11	9	p.	p.	NOUN
ejpam-5942	11	10	sittitrai	sittitrai	NOUN
ejpam-5942	11	11	)	)	PUNCT
ejpam-5942	11	12	,	,	PUNCT
ejpam-5942	11	13	kitnak@hotmail.com	kitnak@hotmail.com	X
ejpam-5942	11	14	(	(	PUNCT
ejpam-5942	11	15	k.	k.	PROPN
ejpam-5942	11	16	nakprasit),patcharapan.ju@up.ac.th	nakprasit),patcharapan.ju@up.ac.th	PROPN
ejpam-5942	11	17	(	(	PUNCT
ejpam-5942	11	18	p.	p.	PROPN
ejpam-5942	11	19	jumnongnit	jumnongnit	PROPN
ejpam-5942	11	20	)	)	PUNCT
ejpam-5942	11	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5942	12	1	1	1	NUM
ejpam-5942	12	2	copyright	copyright	NOUN
ejpam-5942	12	3	:	:	PUNCT
ejpam-5942	12	4	©	©	PROPN
ejpam-5942	12	5	2025	2025	NUM
ejpam-5942	12	6	the	the	DET
ejpam-5942	12	7	author(s	author(s	NOUN
ejpam-5942	12	8	)	)	PUNCT
ejpam-5942	12	9	.	.	PUNCT
ejpam-5942	13	1	(	(	PUNCT
ejpam-5942	13	2	cc	cc	NOUN
ejpam-5942	13	3	by	by	ADP
ejpam-5942	13	4	-	-	PUNCT
ejpam-5942	13	5	nc	nc	PROPN
ejpam-5942	13	6	4.0	4.0	NUM
ejpam-5942	13	7	)	)	PUNCT
ejpam-5942	13	8	p.	p.	NOUN
ejpam-5942	13	9	sittitrai	sittitrai	NOUN
ejpam-5942	13	10	,	,	PUNCT
ejpam-5942	13	11	k.	k.	PROPN
ejpam-5942	13	12	nakprasit	nakprasit	PROPN
ejpam-5942	13	13	,	,	PUNCT
ejpam-5942	13	14	p.	p.	PROPN
ejpam-5942	13	15	jumnongnit	jumnongnit	PROPN
ejpam-5942	13	16	/	/	SYM
ejpam-5942	13	17	eur	eur	PROPN
ejpam-5942	13	18	.	.	PUNCT
ejpam-5942	14	1	j.	j.	PROPN
ejpam-5942	14	2	pure	pure	PROPN
ejpam-5942	14	3	appl	appl	PROPN
ejpam-5942	14	4	.	.	PROPN
ejpam-5942	14	5	math	math	PROPN
ejpam-5942	14	6	,	,	PUNCT
ejpam-5942	14	7	18	18	NUM
ejpam-5942	14	8	(	(	PUNCT
ejpam-5942	14	9	2	2	NUM
ejpam-5942	14	10	)	)	PUNCT
ejpam-5942	14	11	(	(	PUNCT
ejpam-5942	14	12	2025	2025	NUM
ejpam-5942	14	13	)	)	PUNCT
ejpam-5942	14	14	,	,	PUNCT
ejpam-5942	14	15	5942	5942	NUM
ejpam-5942	14	16	2	2	NUM
ejpam-5942	14	17	of	of	ADP
ejpam-5942	14	18	7	7	NUM
ejpam-5942	14	19	the	the	DET
ejpam-5942	14	20	notation	notation	NOUN
ejpam-5942	14	21	∆(g	∆(g	PROPN
ejpam-5942	14	22	)	)	PUNCT
ejpam-5942	14	23	,	,	PUNCT
ejpam-5942	14	24	f	f	PROPN
ejpam-5942	14	25	(	(	PUNCT
ejpam-5942	14	26	g	g	NOUN
ejpam-5942	14	27	)	)	PUNCT
ejpam-5942	14	28	,	,	PUNCT
ejpam-5942	14	29	e(g	e(g	PROPN
ejpam-5942	14	30	)	)	PUNCT
ejpam-5942	14	31	,	,	PUNCT
ejpam-5942	14	32	and	and	CCONJ
ejpam-5942	14	33	v	v	X
ejpam-5942	14	34	(	(	PUNCT
ejpam-5942	14	35	g	g	NOUN
ejpam-5942	14	36	)	)	PUNCT
ejpam-5942	14	37	,	,	PUNCT
ejpam-5942	14	38	respectively	respectively	ADV
ejpam-5942	14	39	.	.	PUNCT
ejpam-5942	15	1	if	if	SCONJ
ejpam-5942	15	2	the	the	DET
ejpam-5942	15	3	boundary	boundary	NOUN
ejpam-5942	15	4	of	of	ADP
ejpam-5942	15	5	two	two	NUM
ejpam-5942	15	6	faces	face	NOUN
ejpam-5942	15	7	is	be	AUX
ejpam-5942	15	8	shared	share	VERB
ejpam-5942	15	9	,	,	PUNCT
ejpam-5942	15	10	then	then	ADV
ejpam-5942	15	11	two	two	NUM
ejpam-5942	15	12	faces	face	NOUN
ejpam-5942	15	13	are	be	AUX
ejpam-5942	15	14	said	say	VERB
ejpam-5942	15	15	to	to	PART
ejpam-5942	15	16	be	be	AUX
ejpam-5942	15	17	adjacent	adjacent	ADJ
ejpam-5942	15	18	.	.	PUNCT
ejpam-5942	16	1	let	let	VERB
ejpam-5942	16	2	a	a	DET
ejpam-5942	16	3	proper	proper	ADJ
ejpam-5942	16	4	total	total	ADJ
ejpam-5942	16	5	coloring	coloring	NOUN
ejpam-5942	16	6	ψ	ψ	X
ejpam-5942	16	7	:	:	PUNCT
ejpam-5942	16	8	v	v	X
ejpam-5942	16	9	(	(	PUNCT
ejpam-5942	16	10	g	g	NOUN
ejpam-5942	16	11	)	)	PUNCT
ejpam-5942	16	12	∪	∪	ADP
ejpam-5942	16	13	e(g	e(g	NOUN
ejpam-5942	16	14	)	)	PUNCT
ejpam-5942	16	15	−→	−→	NOUN
ejpam-5942	16	16	n	n	NOUN
ejpam-5942	16	17	and	and	CCONJ
ejpam-5942	16	18	s(x	s(x	PROPN
ejpam-5942	16	19	)	)	PUNCT
ejpam-5942	16	20	denote	denote	VERB
ejpam-5942	16	21	the	the	DET
ejpam-5942	16	22	sum	sum	NOUN
ejpam-5942	16	23	of	of	ADP
ejpam-5942	16	24	colors	color	NOUN
ejpam-5942	16	25	assigned	assign	VERB
ejpam-5942	16	26	to	to	ADP
ejpam-5942	16	27	x	x	PUNCT
ejpam-5942	16	28	and	and	CCONJ
ejpam-5942	16	29	those	those	DET
ejpam-5942	16	30	incident	incident	NOUN
ejpam-5942	16	31	edges	edge	NOUN
ejpam-5942	16	32	of	of	ADP
ejpam-5942	16	33	x.	x.	NOUN
ejpam-5942	16	34	a	a	DET
ejpam-5942	16	35	coloring	coloring	NOUN
ejpam-5942	16	36	ψ	ψ	X
ejpam-5942	16	37	is	be	AUX
ejpam-5942	16	38	a	a	DET
ejpam-5942	16	39	neighbor	neighbor	NOUN
ejpam-5942	16	40	sum	sum	NOUN
ejpam-5942	16	41	distinguishing	distinguish	VERB
ejpam-5942	16	42	total	total	ADJ
ejpam-5942	16	43	coloring	coloring	NOUN
ejpam-5942	16	44	(	(	PUNCT
ejpam-5942	16	45	abridged	abridge	VERB
ejpam-5942	16	46	as	as	ADP
ejpam-5942	16	47	nsdt	nsdt	NOUN
ejpam-5942	16	48	-	-	ADJ
ejpam-5942	16	49	coloring	coloring	NOUN
ejpam-5942	16	50	)	)	PUNCT
ejpam-5942	16	51	if	if	SCONJ
ejpam-5942	16	52	s(x	s(x	NOUN
ejpam-5942	16	53	)	)	PUNCT
ejpam-5942	16	54	̸=	̸=	PROPN
ejpam-5942	16	55	s(y	s(y	PROPN
ejpam-5942	16	56	)	)	PUNCT
ejpam-5942	16	57	,	,	PUNCT
ejpam-5942	16	58	whenever	whenever	SCONJ
ejpam-5942	16	59	xy	xy	PROPN
ejpam-5942	16	60	is	be	AUX
ejpam-5942	16	61	an	an	DET
ejpam-5942	16	62	edge	edge	NOUN
ejpam-5942	16	63	in	in	ADP
ejpam-5942	16	64	g.	g.	PROPN
ejpam-5942	16	65	the	the	DET
ejpam-5942	16	66	neighbor	neighbor	NOUN
ejpam-5942	16	67	sum	sum	NOUN
ejpam-5942	16	68	distinguishing	distinguish	VERB
ejpam-5942	16	69	total	total	ADJ
ejpam-5942	16	70	chromatic	chromatic	ADJ
ejpam-5942	16	71	number	number	NOUN
ejpam-5942	16	72	of	of	ADP
ejpam-5942	16	73	g	g	NOUN
ejpam-5942	16	74	,	,	PUNCT
ejpam-5942	16	75	say	say	VERB
ejpam-5942	16	76	tndi∑(g	tndi∑(g	NOUN
ejpam-5942	16	77	)	)	PUNCT
ejpam-5942	16	78	is	be	AUX
ejpam-5942	16	79	the	the	DET
ejpam-5942	16	80	minimum	minimum	ADJ
ejpam-5942	16	81	number	number	NOUN
ejpam-5942	16	82	such	such	ADJ
ejpam-5942	16	83	that	that	SCONJ
ejpam-5942	16	84	g	g	PROPN
ejpam-5942	16	85	has	have	VERB
ejpam-5942	16	86	a	a	DET
ejpam-5942	16	87	nsdt	nsdt	NOUN
ejpam-5942	16	88	-	-	ADJ
ejpam-5942	16	89	coloring	coloring	NOUN
ejpam-5942	16	90	.	.	PUNCT
ejpam-5942	17	1	piĺsniak	piĺsniak	PROPN
ejpam-5942	17	2	and	and	CCONJ
ejpam-5942	17	3	woźniak	woźniak	PROPN
ejpam-5942	18	1	[	[	X
ejpam-5942	18	2	1	1	NUM
ejpam-5942	18	3	]	]	PUNCT
ejpam-5942	18	4	introduced	introduce	VERB
ejpam-5942	18	5	neighbor	neighbor	NOUN
ejpam-5942	18	6	sum	sum	NOUN
ejpam-5942	18	7	distinguishing	distinguish	VERB
ejpam-5942	18	8	total	total	ADJ
ejpam-5942	18	9	coloring	coloring	NOUN
ejpam-5942	18	10	and	and	CCONJ
ejpam-5942	18	11	obtained	obtain	VERB
ejpam-5942	18	12	tndi∑(g	tndi∑(g	NOUN
ejpam-5942	18	13	)	)	PUNCT
ejpam-5942	18	14	for	for	ADP
ejpam-5942	18	15	cycles	cycle	NOUN
ejpam-5942	18	16	,	,	PUNCT
ejpam-5942	18	17	bipartite	bipartite	NOUN
ejpam-5942	18	18	graphs	graph	NOUN
ejpam-5942	18	19	,	,	PUNCT
ejpam-5942	18	20	cubic	cubic	ADJ
ejpam-5942	18	21	graphs	graph	NOUN
ejpam-5942	18	22	,	,	PUNCT
ejpam-5942	18	23	and	and	CCONJ
ejpam-5942	18	24	complete	complete	ADJ
ejpam-5942	18	25	graphs	graph	NOUN
ejpam-5942	18	26	.	.	PUNCT
ejpam-5942	19	1	additionally	additionally	ADV
ejpam-5942	19	2	,	,	PUNCT
ejpam-5942	19	3	the	the	DET
ejpam-5942	19	4	authors	author	NOUN
ejpam-5942	19	5	posed	pose	VERB
ejpam-5942	19	6	the	the	DET
ejpam-5942	19	7	following	follow	VERB
ejpam-5942	19	8	conjecture	conjecture	NOUN
ejpam-5942	19	9	.	.	PUNCT
ejpam-5942	20	1	[	[	X
ejpam-5942	20	2	1	1	X
ejpam-5942	20	3	]	]	X
ejpam-5942	20	4	if	if	SCONJ
ejpam-5942	20	5	|g|	|g|	PROPN
ejpam-5942	20	6	≥	≥	PROPN
ejpam-5942	20	7	2	2	NUM
ejpam-5942	20	8	,	,	PUNCT
ejpam-5942	20	9	then	then	ADV
ejpam-5942	20	10	tndi∑(g	tndi∑(g	NOUN
ejpam-5942	20	11	)	)	PUNCT
ejpam-5942	20	12	≤	≤	NOUN
ejpam-5942	20	13	∆(g	∆(g	NOUN
ejpam-5942	20	14	)	)	PUNCT
ejpam-5942	21	1	+	+	NOUN
ejpam-5942	22	1	3	3	X
ejpam-5942	22	2	.	.	PUNCT
ejpam-5942	22	3	the	the	DET
ejpam-5942	22	4	conjecture	conjecture	NOUN
ejpam-5942	22	5	is	be	AUX
ejpam-5942	22	6	verified	verify	VERB
ejpam-5942	22	7	for	for	ADP
ejpam-5942	22	8	k4	k4	ADJ
ejpam-5942	22	9	-	-	PUNCT
ejpam-5942	22	10	minor	minor	ADJ
ejpam-5942	22	11	free	free	ADJ
ejpam-5942	22	12	graphs	graph	NOUN
ejpam-5942	22	13	by	by	ADP
ejpam-5942	22	14	li	li	PROPN
ejpam-5942	22	15	,	,	PUNCT
ejpam-5942	22	16	liu	liu	PROPN
ejpam-5942	22	17	,	,	PUNCT
ejpam-5942	22	18	and	and	CCONJ
ejpam-5942	22	19	wang	wang	PROPN
ejpam-5942	23	1	[	[	X
ejpam-5942	23	2	2	2	NUM
ejpam-5942	23	3	]	]	PUNCT
ejpam-5942	23	4	and	and	CCONJ
ejpam-5942	23	5	planar	planar	ADJ
ejpam-5942	23	6	graphs	graph	NOUN
ejpam-5942	23	7	with	with	ADP
ejpam-5942	23	8	maximum	maximum	ADJ
ejpam-5942	23	9	degree	degree	NOUN
ejpam-5942	23	10	at	at	ADV
ejpam-5942	23	11	least	least	ADV
ejpam-5942	23	12	13	13	NUM
ejpam-5942	23	13	by	by	ADP
ejpam-5942	23	14	zhang	zhang	PROPN
ejpam-5942	23	15	and	and	CCONJ
ejpam-5942	23	16	li	li	PROPN
ejpam-5942	24	1	[	[	X
ejpam-5942	24	2	3	3	NUM
ejpam-5942	24	3	]	]	PUNCT
ejpam-5942	24	4	.	.	PUNCT
ejpam-5942	25	1	later	later	ADV
ejpam-5942	25	2	,	,	PUNCT
ejpam-5942	25	3	the	the	DET
ejpam-5942	25	4	result	result	NOUN
ejpam-5942	25	5	of	of	ADP
ejpam-5942	25	6	zhang	zhang	PROPN
ejpam-5942	25	7	and	and	CCONJ
ejpam-5942	25	8	li	li	PROPN
ejpam-5942	26	1	[	[	X
ejpam-5942	26	2	3	3	NUM
ejpam-5942	26	3	]	]	PUNCT
ejpam-5942	26	4	was	be	AUX
ejpam-5942	26	5	improved	improve	VERB
ejpam-5942	26	6	by	by	ADP
ejpam-5942	26	7	ic	ic	PROPN
ejpam-5942	26	8	-	-	PUNCT
ejpam-5942	26	9	planar	planar	ADJ
ejpam-5942	26	10	graphs	graph	NOUN
ejpam-5942	26	11	with	with	ADP
ejpam-5942	26	12	a	a	DET
ejpam-5942	26	13	maximum	maximum	ADJ
ejpam-5942	26	14	degree	degree	NOUN
ejpam-5942	26	15	of	of	ADP
ejpam-5942	26	16	13	13	NUM
ejpam-5942	26	17	by	by	ADP
ejpam-5942	26	18	song	song	NOUN
ejpam-5942	26	19	et	et	PROPN
ejpam-5942	26	20	al	al	PROPN
ejpam-5942	26	21	.	.	PUNCT
ejpam-5942	27	1	[	[	X
ejpam-5942	27	2	4	4	X
ejpam-5942	27	3	]	]	PUNCT
ejpam-5942	27	4	and	and	CCONJ
ejpam-5942	27	5	planar	planar	ADJ
ejpam-5942	27	6	graphs	graph	NOUN
ejpam-5942	27	7	with	with	ADP
ejpam-5942	27	8	a	a	DET
ejpam-5942	27	9	maximum	maximum	ADJ
ejpam-5942	27	10	degree	degree	NOUN
ejpam-5942	27	11	at	at	ADV
ejpam-5942	27	12	least	least	ADJ
ejpam-5942	27	13	11	11	NUM
ejpam-5942	27	14	by	by	ADP
ejpam-5942	27	15	qu	qu	PROPN
ejpam-5942	27	16	et	et	PROPN
ejpam-5942	27	17	al	al	PROPN
ejpam-5942	27	18	.	.	PUNCT
ejpam-5942	28	1	[	[	X
ejpam-5942	28	2	5	5	NUM
ejpam-5942	28	3	]	]	PUNCT
ejpam-5942	28	4	.	.	PUNCT
ejpam-5942	29	1	for	for	ADP
ejpam-5942	29	2	other	other	ADJ
ejpam-5942	29	3	classes	class	NOUN
ejpam-5942	29	4	,	,	PUNCT
ejpam-5942	29	5	wang	wang	PROPN
ejpam-5942	29	6	,	,	PUNCT
ejpam-5942	29	7	ma	ma	PROPN
ejpam-5942	29	8	,	,	PUNCT
ejpam-5942	29	9	and	and	CCONJ
ejpam-5942	29	10	han	han	PROPN
ejpam-5942	30	1	[	[	X
ejpam-5942	30	2	6	6	NUM
ejpam-5942	30	3	]	]	PUNCT
ejpam-5942	30	4	and	and	CCONJ
ejpam-5942	30	5	ge	ge	PROPN
ejpam-5942	30	6	,	,	PUNCT
ejpam-5942	30	7	li	li	PROPN
ejpam-5942	30	8	,	,	PUNCT
ejpam-5942	30	9	and	and	CCONJ
ejpam-5942	30	10	xu	xu	X
ejpam-5942	31	1	[	[	X
ejpam-5942	31	2	7	7	X
ejpam-5942	31	3	]	]	PUNCT
ejpam-5942	31	4	confirmed	confirm	VERB
ejpam-5942	31	5	the	the	DET
ejpam-5942	31	6	conjecture	conjecture	NOUN
ejpam-5942	31	7	by	by	ADP
ejpam-5942	31	8	planar	planar	ADJ
ejpam-5942	31	9	graphs	graph	NOUN
ejpam-5942	31	10	without	without	ADP
ejpam-5942	31	11	3	3	NOUN
ejpam-5942	31	12	-	-	PUNCT
ejpam-5942	31	13	cycles	cycle	NOUN
ejpam-5942	31	14	with	with	ADP
ejpam-5942	31	15	maximum	maximum	ADJ
ejpam-5942	31	16	degree	degree	NOUN
ejpam-5942	31	17	at	at	ADP
ejpam-5942	31	18	least	least	ADV
ejpam-5942	31	19	7	7	NUM
ejpam-5942	31	20	and	and	CCONJ
ejpam-5942	31	21	planar	planar	ADJ
ejpam-5942	31	22	graphs	graph	NOUN
ejpam-5942	31	23	without	without	ADP
ejpam-5942	31	24	5	5	NUM
ejpam-5942	31	25	-	-	PUNCT
ejpam-5942	31	26	cycles	cycle	NOUN
ejpam-5942	31	27	with	with	ADP
ejpam-5942	31	28	maximum	maximum	ADJ
ejpam-5942	31	29	degree	degree	NOUN
ejpam-5942	31	30	at	at	ADV
ejpam-5942	31	31	least	least	ADV
ejpam-5942	31	32	7	7	NUM
ejpam-5942	31	33	,	,	PUNCT
ejpam-5942	31	34	respectively	respectively	ADV
ejpam-5942	31	35	.	.	PUNCT
ejpam-5942	32	1	the	the	DET
ejpam-5942	32	2	conjecture	conjecture	NOUN
ejpam-5942	32	3	is	be	AUX
ejpam-5942	32	4	also	also	ADV
ejpam-5942	32	5	shown	show	VERB
ejpam-5942	32	6	to	to	PART
ejpam-5942	32	7	be	be	AUX
ejpam-5942	32	8	true	true	ADJ
ejpam-5942	32	9	for	for	ADP
ejpam-5942	32	10	planar	planar	ADJ
ejpam-5942	32	11	graphs	graph	NOUN
ejpam-5942	32	12	with	with	ADP
ejpam-5942	32	13	a	a	DET
ejpam-5942	32	14	better	well	ADV
ejpam-5942	32	15	bound	bind	VERB
ejpam-5942	32	16	,	,	PUNCT
ejpam-5942	32	17	tndi∑(g	tndi∑(g	NOUN
ejpam-5942	32	18	)	)	PUNCT
ejpam-5942	32	19	≤	≤	NOUN
ejpam-5942	32	20	∆(g	∆(g	NOUN
ejpam-5942	32	21	)	)	PUNCT
ejpam-5942	33	1	+	+	NUM
ejpam-5942	34	1	2	2	NUM
ejpam-5942	34	2	,	,	PUNCT
ejpam-5942	34	3	by	by	ADP
ejpam-5942	34	4	[	[	X
ejpam-5942	34	5	4	4	NUM
ejpam-5942	34	6	,	,	PUNCT
ejpam-5942	34	7	8	8	NUM
ejpam-5942	34	8	,	,	PUNCT
ejpam-5942	34	9	9	9	NUM
ejpam-5942	34	10	]	]	PUNCT
ejpam-5942	34	11	.	.	PUNCT
ejpam-5942	35	1	let	let	VERB
ejpam-5942	35	2	l	l	NOUN
ejpam-5942	35	3	be	be	AUX
ejpam-5942	35	4	a	a	DET
ejpam-5942	35	5	k	k	ADJ
ejpam-5942	35	6	-	-	PUNCT
ejpam-5942	35	7	list	list	NOUN
ejpam-5942	35	8	assignment	assignment	NOUN
ejpam-5942	35	9	of	of	ADP
ejpam-5942	35	10	a	a	DET
ejpam-5942	35	11	graph	graph	NOUN
ejpam-5942	35	12	g	g	NOUN
ejpam-5942	35	13	if	if	SCONJ
ejpam-5942	35	14	l	l	NOUN
ejpam-5942	35	15	is	be	AUX
ejpam-5942	35	16	a	a	DET
ejpam-5942	35	17	mapping	mapping	NOUN
ejpam-5942	35	18	,	,	PUNCT
ejpam-5942	35	19	say	say	VERB
ejpam-5942	35	20	l	l	NOUN
ejpam-5942	35	21	:	:	PUNCT
ejpam-5942	36	1	v	v	X
ejpam-5942	36	2	(	(	PUNCT
ejpam-5942	36	3	g)∪e(g	g)∪e(g	NOUN
ejpam-5942	36	4	)	)	PUNCT
ejpam-5942	36	5	→	→	SYM
ejpam-5942	36	6	2n	2n	NUM
ejpam-5942	36	7	where	where	SCONJ
ejpam-5942	36	8	|l(t)|	|l(t)|	PROPN
ejpam-5942	36	9	=	=	SYM
ejpam-5942	36	10	k	k	NOUN
ejpam-5942	36	11	for	for	ADP
ejpam-5942	36	12	each	each	DET
ejpam-5942	36	13	t	t	NOUN
ejpam-5942	36	14	∈	∈	PROPN
ejpam-5942	36	15	v	v	PROPN
ejpam-5942	36	16	(	(	PUNCT
ejpam-5942	36	17	g)∪e(g	g)∪e(g	NOUN
ejpam-5942	36	18	)	)	PUNCT
ejpam-5942	36	19	.	.	PUNCT
ejpam-5942	37	1	if	if	SCONJ
ejpam-5942	37	2	g	g	PROPN
ejpam-5942	37	3	has	have	VERB
ejpam-5942	37	4	a	a	DET
ejpam-5942	37	5	total	total	ADJ
ejpam-5942	37	6	coloring	coloring	NOUN
ejpam-5942	37	7	such	such	ADJ
ejpam-5942	37	8	that	that	DET
ejpam-5942	37	9	α(t	α(t	PROPN
ejpam-5942	37	10	)	)	PUNCT
ejpam-5942	37	11	∈	∈	PROPN
ejpam-5942	37	12	l(t	l(t	PROPN
ejpam-5942	37	13	)	)	PUNCT
ejpam-5942	37	14	for	for	ADP
ejpam-5942	37	15	all	all	DET
ejpam-5942	37	16	t	t	NOUN
ejpam-5942	37	17	in	in	ADP
ejpam-5942	37	18	the	the	DET
ejpam-5942	37	19	set	set	NOUN
ejpam-5942	37	20	v	v	NOUN
ejpam-5942	37	21	(	(	PUNCT
ejpam-5942	37	22	g	g	NOUN
ejpam-5942	37	23	)	)	PUNCT
ejpam-5942	37	24	∪	∪	ADP
ejpam-5942	37	25	e(g	e(g	PROPN
ejpam-5942	37	26	)	)	PUNCT
ejpam-5942	37	27	,	,	PUNCT
ejpam-5942	37	28	then	then	ADV
ejpam-5942	37	29	we	we	PRON
ejpam-5942	37	30	call	call	VERB
ejpam-5942	37	31	α	α	PRON
ejpam-5942	37	32	total	total	ADJ
ejpam-5942	37	33	-	-	PUNCT
ejpam-5942	37	34	l	l	NOUN
ejpam-5942	37	35	-	-	NOUN
ejpam-5942	37	36	coloring	coloring	NOUN
ejpam-5942	37	37	.	.	PUNCT
ejpam-5942	38	1	moreover	moreover	ADV
ejpam-5942	38	2	,	,	PUNCT
ejpam-5942	38	3	a	a	DET
ejpam-5942	38	4	total	total	NOUN
ejpam-5942	38	5	-	-	PUNCT
ejpam-5942	38	6	lcoloring	lcolore	VERB
ejpam-5942	38	7	α	α	NOUN
ejpam-5942	38	8	is	be	AUX
ejpam-5942	38	9	called	call	VERB
ejpam-5942	38	10	a	a	DET
ejpam-5942	38	11	neighbor	neighbor	NOUN
ejpam-5942	38	12	sum	sum	NOUN
ejpam-5942	38	13	distinguishing	distinguish	VERB
ejpam-5942	38	14	total	total	ADJ
ejpam-5942	38	15	-	-	PUNCT
ejpam-5942	38	16	l	l	NOUN
ejpam-5942	38	17	-	-	ADJ
ejpam-5942	38	18	coloring	coloring	NOUN
ejpam-5942	38	19	if	if	SCONJ
ejpam-5942	38	20	s(x	s(x	NOUN
ejpam-5942	38	21	)	)	PUNCT
ejpam-5942	38	22	̸=	̸=	PROPN
ejpam-5942	38	23	s(y	s(y	PROPN
ejpam-5942	38	24	)	)	PUNCT
ejpam-5942	38	25	where	where	SCONJ
ejpam-5942	38	26	xy	xy	PROPN
ejpam-5942	38	27	is	be	AUX
ejpam-5942	38	28	an	an	DET
ejpam-5942	38	29	edge	edge	NOUN
ejpam-5942	38	30	in	in	ADP
ejpam-5942	38	31	g.	g.	PROPN
ejpam-5942	38	32	let	let	VERB
ejpam-5942	38	33	ch′′∑(g	ch′′∑(g	X
ejpam-5942	38	34	)	)	PUNCT
ejpam-5942	38	35	be	be	AUX
ejpam-5942	38	36	the	the	DET
ejpam-5942	38	37	minimum	minimum	ADJ
ejpam-5942	38	38	number	number	NOUN
ejpam-5942	38	39	k	k	NOUN
ejpam-5942	38	40	such	such	ADJ
ejpam-5942	38	41	that	that	SCONJ
ejpam-5942	38	42	g	g	PROPN
ejpam-5942	38	43	has	have	VERB
ejpam-5942	38	44	such	such	ADJ
ejpam-5942	38	45	coloring	coloring	NOUN
ejpam-5942	38	46	for	for	ADP
ejpam-5942	38	47	every	every	DET
ejpam-5942	38	48	k	k	ADJ
ejpam-5942	38	49	-	-	PUNCT
ejpam-5942	38	50	list	list	NOUN
ejpam-5942	38	51	assignment	assignment	NOUN
ejpam-5942	38	52	l	l	NOUN
ejpam-5942	38	53	,	,	PUNCT
ejpam-5942	38	54	which	which	PRON
ejpam-5942	38	55	is	be	AUX
ejpam-5942	38	56	called	call	VERB
ejpam-5942	38	57	the	the	DET
ejpam-5942	38	58	neighbor	neighbor	NOUN
ejpam-5942	38	59	sum	sum	NOUN
ejpam-5942	38	60	distinguishing	distinguish	VERB
ejpam-5942	38	61	total	total	ADJ
ejpam-5942	38	62	choosability	choosability	NOUN
ejpam-5942	38	63	of	of	ADP
ejpam-5942	38	64	g.	g.	PROPN
ejpam-5942	38	65	qu	qu	PROPN
ejpam-5942	38	66	et	et	PROPN
ejpam-5942	38	67	al	al	PROPN
ejpam-5942	38	68	.	.	PUNCT
ejpam-5942	39	1	[	[	X
ejpam-5942	39	2	10	10	NUM
ejpam-5942	39	3	]	]	PUNCT
ejpam-5942	39	4	proved	prove	VERB
ejpam-5942	39	5	that	that	SCONJ
ejpam-5942	39	6	ch′′∑(g	ch′′∑(g	PROPN
ejpam-5942	39	7	)	)	PUNCT
ejpam-5942	39	8	≤	≤	NOUN
ejpam-5942	39	9	∆(g	∆(g	NOUN
ejpam-5942	39	10	)	)	PUNCT
ejpam-5942	40	1	+	+	CCONJ
ejpam-5942	40	2	3	3	NUM
ejpam-5942	40	3	for	for	ADP
ejpam-5942	40	4	every	every	DET
ejpam-5942	40	5	planar	planar	ADJ
ejpam-5942	40	6	graph	graph	NOUN
ejpam-5942	40	7	g	g	NOUN
ejpam-5942	40	8	with	with	ADP
ejpam-5942	40	9	∆(g	∆(g	PROPN
ejpam-5942	40	10	)	)	PUNCT
ejpam-5942	40	11	≥	≥	NOUN
ejpam-5942	40	12	13	13	NUM
ejpam-5942	40	13	.	.	PUNCT
ejpam-5942	41	1	yao	yao	PROPN
ejpam-5942	41	2	et	et	PROPN
ejpam-5942	41	3	al	al	PROPN
ejpam-5942	41	4	.	.	PUNCT
ejpam-5942	42	1	[	[	X
ejpam-5942	42	2	11	11	NUM
ejpam-5942	42	3	]	]	PUNCT
ejpam-5942	42	4	studied	study	VERB
ejpam-5942	42	5	ch′′∑(g	ch′′∑(g	PROPN
ejpam-5942	42	6	)	)	PUNCT
ejpam-5942	42	7	of	of	ADP
ejpam-5942	42	8	d	d	ADJ
ejpam-5942	42	9	-	-	ADJ
ejpam-5942	42	10	degenerate	degenerate	ADJ
ejpam-5942	42	11	graphs	graph	NOUN
ejpam-5942	42	12	.	.	PUNCT
ejpam-5942	43	1	conjecture	conjecture	NOUN
ejpam-5942	43	2	1	1	NUM
ejpam-5942	43	3	has	have	AUX
ejpam-5942	43	4	been	be	AUX
ejpam-5942	43	5	verified	verify	VERB
ejpam-5942	43	6	for	for	ADP
ejpam-5942	43	7	several	several	ADJ
ejpam-5942	43	8	classes	class	NOUN
ejpam-5942	43	9	of	of	ADP
ejpam-5942	43	10	planar	planar	ADJ
ejpam-5942	43	11	graphs	graph	NOUN
ejpam-5942	43	12	as	as	SCONJ
ejpam-5942	43	13	follows	follow	VERB
ejpam-5942	43	14	:	:	PUNCT
ejpam-5942	43	15	planar	planar	ADJ
ejpam-5942	43	16	graphs	graph	NOUN
ejpam-5942	43	17	without	without	ADP
ejpam-5942	43	18	adjacent	adjacent	ADJ
ejpam-5942	43	19	3	3	NUM
ejpam-5942	43	20	-	-	PUNCT
ejpam-5942	43	21	cycles	cycle	NOUN
ejpam-5942	43	22	with	with	ADP
ejpam-5942	43	23	maximum	maximum	ADJ
ejpam-5942	43	24	degree	degree	NOUN
ejpam-5942	43	25	at	at	ADV
ejpam-5942	43	26	least	least	ADJ
ejpam-5942	43	27	8	8	NUM
ejpam-5942	43	28	by	by	ADP
ejpam-5942	43	29	[	[	X
ejpam-5942	43	30	12	12	NUM
ejpam-5942	43	31	]	]	PUNCT
ejpam-5942	43	32	,	,	PUNCT
ejpam-5942	43	33	planar	planar	ADJ
ejpam-5942	43	34	graphs	graph	NOUN
ejpam-5942	43	35	without	without	ADP
ejpam-5942	43	36	adjacent	adjacent	ADJ
ejpam-5942	43	37	6	6	NUM
ejpam-5942	43	38	-	-	PUNCT
ejpam-5942	43	39	cycles	cycle	NOUN
ejpam-5942	43	40	with	with	ADP
ejpam-5942	43	41	maximum	maximum	ADJ
ejpam-5942	43	42	degree	degree	NOUN
ejpam-5942	43	43	at	at	ADP
ejpam-5942	43	44	least	least	ADJ
ejpam-5942	43	45	7	7	NUM
ejpam-5942	44	1	[	[	SYM
ejpam-5942	44	2	13	13	NUM
ejpam-5942	44	3	]	]	PUNCT
ejpam-5942	44	4	,	,	PUNCT
ejpam-5942	44	5	and	and	CCONJ
ejpam-5942	44	6	planar	planar	ADJ
ejpam-5942	44	7	graphs	graph	NOUN
ejpam-5942	44	8	without	without	ADP
ejpam-5942	44	9	4	4	NUM
ejpam-5942	44	10	-	-	PUNCT
ejpam-5942	44	11	cycles	cycle	NOUN
ejpam-5942	44	12	adjacent	adjacent	ADJ
ejpam-5942	44	13	to	to	ADP
ejpam-5942	44	14	3	3	NUM
ejpam-5942	44	15	-	-	PUNCT
ejpam-5942	44	16	cycles	cycle	NOUN
ejpam-5942	44	17	with	with	ADP
ejpam-5942	44	18	maximum	maximum	ADJ
ejpam-5942	44	19	degree	degree	NOUN
ejpam-5942	44	20	at	at	ADV
ejpam-5942	44	21	least	least	ADV
ejpam-5942	44	22	7	7	NUM
ejpam-5942	44	23	by	by	ADP
ejpam-5942	44	24	[	[	X
ejpam-5942	44	25	14	14	NUM
ejpam-5942	44	26	]	]	PUNCT
ejpam-5942	44	27	.	.	PUNCT
ejpam-5942	45	1	more	more	ADJ
ejpam-5942	45	2	results	result	NOUN
ejpam-5942	45	3	about	about	ADP
ejpam-5942	45	4	the	the	DET
ejpam-5942	45	5	neighbor	neighbor	NOUN
ejpam-5942	45	6	sum	sum	NOUN
ejpam-5942	45	7	distinguishing	distinguish	VERB
ejpam-5942	45	8	total	total	ADJ
ejpam-5942	45	9	choosability	choosability	NOUN
ejpam-5942	45	10	for	for	ADP
ejpam-5942	45	11	planar	planar	ADJ
ejpam-5942	45	12	graphs	graph	NOUN
ejpam-5942	45	13	can	can	AUX
ejpam-5942	45	14	be	be	AUX
ejpam-5942	45	15	seen	see	VERB
ejpam-5942	45	16	in	in	ADP
ejpam-5942	45	17	[	[	X
ejpam-5942	45	18	3	3	NUM
ejpam-5942	45	19	,	,	PUNCT
ejpam-5942	45	20	15–19	15–19	PROPN
ejpam-5942	45	21	]	]	PUNCT
ejpam-5942	45	22	.	.	PUNCT
ejpam-5942	46	1	in	in	ADP
ejpam-5942	46	2	this	this	DET
ejpam-5942	46	3	paper	paper	NOUN
ejpam-5942	46	4	,	,	PUNCT
ejpam-5942	46	5	we	we	PRON
ejpam-5942	46	6	give	give	VERB
ejpam-5942	46	7	theorem	theorem	VERB
ejpam-5942	46	8	1	1	NUM
ejpam-5942	46	9	to	to	PART
ejpam-5942	46	10	confirm	confirm	VERB
ejpam-5942	46	11	the	the	DET
ejpam-5942	46	12	list	list	NOUN
ejpam-5942	46	13	version	version	NOUN
ejpam-5942	46	14	of	of	ADP
ejpam-5942	46	15	conjecture	conjecture	NOUN
ejpam-5942	46	16	1	1	NUM
ejpam-5942	46	17	on	on	ADP
ejpam-5942	46	18	planar	planar	ADJ
ejpam-5942	46	19	graphs	graph	NOUN
ejpam-5942	46	20	without	without	ADP
ejpam-5942	46	21	neighboring	neighbor	VERB
ejpam-5942	46	22	5	5	NUM
ejpam-5942	46	23	-	-	PUNCT
ejpam-5942	46	24	cycles	cycle	NOUN
ejpam-5942	46	25	and	and	CCONJ
ejpam-5942	46	26	3	3	NUM
ejpam-5942	46	27	-	-	PUNCT
ejpam-5942	46	28	cycles	cycle	NOUN
ejpam-5942	46	29	.	.	PUNCT
ejpam-5942	47	1	the	the	DET
ejpam-5942	47	2	theorem	theorem	NOUN
ejpam-5942	47	3	also	also	ADV
ejpam-5942	47	4	improves	improve	VERB
ejpam-5942	47	5	the	the	DET
ejpam-5942	47	6	results	result	NOUN
ejpam-5942	47	7	of	of	ADP
ejpam-5942	47	8	wang	wang	PROPN
ejpam-5942	47	9	,	,	PUNCT
ejpam-5942	47	10	ma	ma	PROPN
ejpam-5942	47	11	,	,	PUNCT
ejpam-5942	47	12	and	and	CCONJ
ejpam-5942	47	13	han	han	PROPN
ejpam-5942	48	1	[	[	X
ejpam-5942	48	2	6	6	NUM
ejpam-5942	48	3	]	]	PUNCT
ejpam-5942	48	4	(	(	PUNCT
ejpam-5942	48	5	on	on	ADP
ejpam-5942	48	6	planar	planar	ADJ
ejpam-5942	48	7	graphs	graph	NOUN
ejpam-5942	48	8	without	without	ADP
ejpam-5942	48	9	3	3	NUM
ejpam-5942	48	10	-	-	PUNCT
ejpam-5942	48	11	cycles	cycle	NOUN
ejpam-5942	48	12	)	)	PUNCT
ejpam-5942	48	13	and	and	CCONJ
ejpam-5942	48	14	ge	ge	PROPN
ejpam-5942	48	15	,	,	PUNCT
ejpam-5942	48	16	li	li	PROPN
ejpam-5942	48	17	,	,	PUNCT
ejpam-5942	48	18	and	and	CCONJ
ejpam-5942	48	19	xu	xu	X
ejpam-5942	49	1	[	[	X
ejpam-5942	49	2	7	7	X
ejpam-5942	49	3	]	]	PUNCT
ejpam-5942	49	4	(	(	PUNCT
ejpam-5942	49	5	on	on	ADP
ejpam-5942	49	6	planar	planar	ADJ
ejpam-5942	49	7	graphs	graph	NOUN
ejpam-5942	49	8	without	without	ADP
ejpam-5942	49	9	5	5	NUM
ejpam-5942	49	10	-	-	PUNCT
ejpam-5942	49	11	cycles	cycle	NOUN
ejpam-5942	49	12	)	)	PUNCT
ejpam-5942	49	13	.	.	PUNCT
ejpam-5942	50	1	2	2	X
ejpam-5942	50	2	.	.	X
ejpam-5942	50	3	notations	notation	NOUN
ejpam-5942	50	4	all	all	DET
ejpam-5942	50	5	subscripts	subscript	NOUN
ejpam-5942	50	6	are	be	AUX
ejpam-5942	50	7	modulo	modulo	NOUN
ejpam-5942	50	8	l	l	NOUN
ejpam-5942	50	9	unless	unless	SCONJ
ejpam-5942	50	10	stated	state	VERB
ejpam-5942	50	11	otherwise	otherwise	ADV
ejpam-5942	50	12	for	for	ADP
ejpam-5942	50	13	the	the	DET
ejpam-5942	50	14	remainder	remainder	NOUN
ejpam-5942	50	15	of	of	ADP
ejpam-5942	50	16	the	the	DET
ejpam-5942	50	17	paper	paper	NOUN
ejpam-5942	50	18	.	.	PUNCT
ejpam-5942	51	1	p.	p.	NOUN
ejpam-5942	51	2	sittitrai	sittitrai	NOUN
ejpam-5942	51	3	,	,	PUNCT
ejpam-5942	51	4	k.	k.	PROPN
ejpam-5942	51	5	nakprasit	nakprasit	PROPN
ejpam-5942	51	6	,	,	PUNCT
ejpam-5942	52	1	p.	p.	PROPN
ejpam-5942	52	2	jumnongnit	jumnongnit	PROPN
ejpam-5942	52	3	/	/	SYM
ejpam-5942	52	4	eur	eur	PROPN
ejpam-5942	52	5	.	.	PUNCT
ejpam-5942	53	1	j.	j.	PROPN
ejpam-5942	53	2	pure	pure	PROPN
ejpam-5942	53	3	appl	appl	PROPN
ejpam-5942	53	4	.	.	PROPN
ejpam-5942	53	5	math	math	PROPN
ejpam-5942	53	6	,	,	PUNCT
ejpam-5942	53	7	18	18	NUM
ejpam-5942	53	8	(	(	PUNCT
ejpam-5942	53	9	2	2	NUM
ejpam-5942	53	10	)	)	PUNCT
ejpam-5942	53	11	(	(	PUNCT
ejpam-5942	53	12	2025	2025	NUM
ejpam-5942	53	13	)	)	PUNCT
ejpam-5942	53	14	,	,	PUNCT
ejpam-5942	53	15	5942	5942	NUM
ejpam-5942	53	16	3	3	NUM
ejpam-5942	53	17	of	of	ADP
ejpam-5942	53	18	7	7	NUM
ejpam-5942	53	19	an	an	DET
ejpam-5942	53	20	l	l	NOUN
ejpam-5942	53	21	-	-	NOUN
ejpam-5942	53	22	vertex	vertex	NOUN
ejpam-5942	53	23	(	(	PUNCT
ejpam-5942	53	24	face	face	NOUN
ejpam-5942	53	25	)	)	PUNCT
ejpam-5942	53	26	,	,	PUNCT
ejpam-5942	53	27	an	an	DET
ejpam-5942	53	28	l+-vertex	l+-vertex	NOUN
ejpam-5942	53	29	(	(	PUNCT
ejpam-5942	53	30	face	face	NOUN
ejpam-5942	53	31	)	)	PUNCT
ejpam-5942	53	32	,	,	PUNCT
ejpam-5942	53	33	or	or	CCONJ
ejpam-5942	53	34	an	an	DET
ejpam-5942	53	35	l−-vertex	l−-vertex	X
ejpam-5942	53	36	(	(	PUNCT
ejpam-5942	53	37	face	face	NOUN
ejpam-5942	53	38	)	)	PUNCT
ejpam-5942	53	39	is	be	AUX
ejpam-5942	53	40	a	a	DET
ejpam-5942	53	41	vertex	vertex	NOUN
ejpam-5942	53	42	(	(	PUNCT
ejpam-5942	53	43	a	a	DET
ejpam-5942	53	44	face	face	NOUN
ejpam-5942	53	45	)	)	PUNCT
ejpam-5942	53	46	which	which	PRON
ejpam-5942	53	47	has	have	VERB
ejpam-5942	53	48	degree	degree	NOUN
ejpam-5942	53	49	l	l	NOUN
ejpam-5942	53	50	,	,	PUNCT
ejpam-5942	53	51	at	at	ADP
ejpam-5942	53	52	least	least	ADJ
ejpam-5942	53	53	l	l	NOUN
ejpam-5942	53	54	,	,	PUNCT
ejpam-5942	53	55	or	or	CCONJ
ejpam-5942	53	56	at	at	ADP
ejpam-5942	53	57	most	most	ADJ
ejpam-5942	53	58	l	l	NOUN
ejpam-5942	53	59	,	,	PUNCT
ejpam-5942	53	60	respectively	respectively	ADV
ejpam-5942	53	61	.	.	PUNCT
ejpam-5942	54	1	moreover	moreover	ADV
ejpam-5942	54	2	,	,	PUNCT
ejpam-5942	54	3	we	we	PRON
ejpam-5942	54	4	call	call	VERB
ejpam-5942	54	5	f	f	PROPN
ejpam-5942	54	6	a	a	DET
ejpam-5942	54	7	(	(	PUNCT
ejpam-5942	54	8	d1	d1	PROPN
ejpam-5942	54	9	,	,	PUNCT
ejpam-5942	54	10	d2	d2	PROPN
ejpam-5942	54	11	,	,	PUNCT
ejpam-5942	54	12	.	.	PUNCT
ejpam-5942	54	13	.	.	PUNCT
ejpam-5942	55	1	.	.	PUNCT
ejpam-5942	56	1	,	,	PUNCT
ejpam-5942	56	2	dl)-face	dl)-face	NOUN
ejpam-5942	56	3	if	if	SCONJ
ejpam-5942	56	4	f	f	PROPN
ejpam-5942	56	5	is	be	AUX
ejpam-5942	56	6	an	an	DET
ejpam-5942	56	7	l	l	NOUN
ejpam-5942	56	8	-	-	NOUN
ejpam-5942	56	9	face	face	NOUN
ejpam-5942	56	10	where	where	SCONJ
ejpam-5942	56	11	its	its	PRON
ejpam-5942	56	12	incident	incident	NOUN
ejpam-5942	56	13	vertices	vertex	NOUN
ejpam-5942	56	14	have	have	VERB
ejpam-5942	56	15	degree	degree	NOUN
ejpam-5942	56	16	d1	d1	NOUN
ejpam-5942	56	17	,	,	PUNCT
ejpam-5942	56	18	d2	d2	PROPN
ejpam-5942	56	19	,	,	PUNCT
ejpam-5942	56	20	.	.	PUNCT
ejpam-5942	56	21	.	.	PUNCT
ejpam-5942	57	1	.	.	PUNCT
ejpam-5942	58	1	,	,	PUNCT
ejpam-5942	58	2	dl	dl	PROPN
ejpam-5942	58	3	in	in	ADP
ejpam-5942	58	4	clockwise	clockwise	NOUN
ejpam-5942	58	5	order	order	NOUN
ejpam-5942	58	6	.	.	PUNCT
ejpam-5942	59	1	if	if	SCONJ
ejpam-5942	59	2	f1	f1	PROPN
ejpam-5942	59	3	and	and	CCONJ
ejpam-5942	59	4	f2	f2	PROPN
ejpam-5942	59	5	are	be	AUX
ejpam-5942	59	6	adjacent	adjacent	ADJ
ejpam-5942	59	7	3	3	NUM
ejpam-5942	59	8	-	-	PUNCT
ejpam-5942	59	9	faces	face	NOUN
ejpam-5942	59	10	with	with	ADP
ejpam-5942	59	11	a	a	DET
ejpam-5942	59	12	common	common	ADJ
ejpam-5942	59	13	incident	incident	NOUN
ejpam-5942	59	14	vertex	vertex	NOUN
ejpam-5942	59	15	v	v	NOUN
ejpam-5942	59	16	,	,	PUNCT
ejpam-5942	59	17	then	then	ADV
ejpam-5942	59	18	we	we	PRON
ejpam-5942	59	19	call	call	VERB
ejpam-5942	59	20	a	a	DET
ejpam-5942	59	21	vertex	vertex	NOUN
ejpam-5942	59	22	v	v	ADP
ejpam-5942	59	23	a	a	DET
ejpam-5942	59	24	rough	rough	ADJ
ejpam-5942	59	25	vertex	vertex	NOUN
ejpam-5942	59	26	of	of	ADP
ejpam-5942	59	27	f1	f1	NOUN
ejpam-5942	59	28	and	and	CCONJ
ejpam-5942	59	29	f2	f2	PROPN
ejpam-5942	59	30	.	.	PUNCT
ejpam-5942	60	1	for	for	ADP
ejpam-5942	60	2	an	an	DET
ejpam-5942	60	3	l	l	NOUN
ejpam-5942	60	4	-	-	NOUN
ejpam-5942	60	5	face	face	NOUN
ejpam-5942	60	6	f	f	NOUN
ejpam-5942	60	7	,	,	PUNCT
ejpam-5942	60	8	we	we	PRON
ejpam-5942	60	9	let	let	VERB
ejpam-5942	60	10	f1	f1	NOUN
ejpam-5942	60	11	,	,	PUNCT
ejpam-5942	60	12	.	.	PUNCT
ejpam-5942	60	13	.	.	PUNCT
ejpam-5942	61	1	.	.	PUNCT
ejpam-5942	62	1	,	,	PUNCT
ejpam-5942	62	2	fl	fl	NUM
ejpam-5942	62	3	adjacent	adjacent	ADJ
ejpam-5942	62	4	faces	face	NOUN
ejpam-5942	62	5	of	of	ADP
ejpam-5942	62	6	f	f	PROPN
ejpam-5942	62	7	in	in	ADP
ejpam-5942	62	8	clockwise	clockwise	NOUN
ejpam-5942	62	9	order	order	NOUN
ejpam-5942	62	10	.	.	PUNCT
ejpam-5942	63	1	an	an	DET
ejpam-5942	63	2	adjacent	adjacent	ADJ
ejpam-5942	63	3	k	k	ADJ
ejpam-5942	63	4	-	-	NOUN
ejpam-5942	63	5	face	face	NOUN
ejpam-5942	63	6	fi	fi	NOUN
ejpam-5942	63	7	of	of	ADP
ejpam-5942	63	8	f	f	PROPN
ejpam-5942	63	9	is	be	AUX
ejpam-5942	63	10	called	call	VERB
ejpam-5942	63	11	a	a	DET
ejpam-5942	63	12	thin	thin	ADJ
ejpam-5942	63	13	adjacent	adjacent	ADJ
ejpam-5942	63	14	k	k	NOUN
ejpam-5942	63	15	-	-	NOUN
ejpam-5942	63	16	face	face	NOUN
ejpam-5942	63	17	of	of	ADP
ejpam-5942	63	18	f	f	PROPN
ejpam-5942	63	19	if	if	SCONJ
ejpam-5942	63	20	fi−1	fi−1	PROPN
ejpam-5942	63	21	or	or	CCONJ
ejpam-5942	63	22	fi+1	fi+1	NOUN
ejpam-5942	63	23	is	be	AUX
ejpam-5942	63	24	a	a	DET
ejpam-5942	63	25	4	4	NUM
ejpam-5942	63	26	+	+	NOUN
ejpam-5942	63	27	-face	-face	NOUN
ejpam-5942	63	28	.	.	PUNCT
ejpam-5942	64	1	3	3	X
ejpam-5942	64	2	.	.	X
ejpam-5942	64	3	helpful	helpful	ADJ
ejpam-5942	64	4	tools	tool	NOUN
ejpam-5942	64	5	consider	consider	VERB
ejpam-5942	64	6	a	a	DET
ejpam-5942	64	7	minimal	minimal	ADJ
ejpam-5942	64	8	planar	planar	ADJ
ejpam-5942	64	9	graph	graph	NOUN
ejpam-5942	64	10	g	g	NOUN
ejpam-5942	64	11	with	with	ADP
ejpam-5942	64	12	ch′′∑(g	ch′′∑(g	PROPN
ejpam-5942	64	13	)	)	PUNCT
ejpam-5942	64	14	>	>	X
ejpam-5942	64	15	∆(g	∆(g	PROPN
ejpam-5942	64	16	)	)	PUNCT
ejpam-5942	65	1	+	+	NOUN
ejpam-5942	65	2	3	3	X
ejpam-5942	65	3	.	.	X
ejpam-5942	65	4	we	we	PRON
ejpam-5942	65	5	denote	denote	VERB
ejpam-5942	65	6	the	the	DET
ejpam-5942	65	7	plane	plane	NOUN
ejpam-5942	65	8	embedding	embed	VERB
ejpam-5942	65	9	of	of	ADP
ejpam-5942	65	10	the	the	DET
ejpam-5942	65	11	graph	graph	NOUN
ejpam-5942	65	12	obtained	obtain	VERB
ejpam-5942	65	13	by	by	ADP
ejpam-5942	65	14	removing	remove	VERB
ejpam-5942	65	15	all	all	DET
ejpam-5942	65	16	2−-vertices	2−-vertices	NUM
ejpam-5942	65	17	of	of	ADP
ejpam-5942	65	18	g	g	NOUN
ejpam-5942	65	19	by	by	ADP
ejpam-5942	65	20	h	h	NOUN
ejpam-5942	65	21	′	′	NOUN
ejpam-5942	65	22	.	.	PUNCT
ejpam-5942	66	1	lemma	lemma	PROPN
ejpam-5942	66	2	1	1	NUM
ejpam-5942	66	3	.	.	PUNCT
ejpam-5942	67	1	(	(	PUNCT
ejpam-5942	67	2	claim	claim	NOUN
ejpam-5942	67	3	1	1	NUM
ejpam-5942	67	4	,	,	PUNCT
ejpam-5942	67	5	observation	observation	NOUN
ejpam-5942	67	6	1	1	NUM
ejpam-5942	67	7	,	,	PUNCT
ejpam-5942	67	8	and	and	CCONJ
ejpam-5942	67	9	claim	claim	VERB
ejpam-5942	67	10	4	4	NUM
ejpam-5942	67	11	in	in	ADP
ejpam-5942	67	12	[	[	X
ejpam-5942	67	13	20	20	NUM
ejpam-5942	67	14	]	]	PUNCT
ejpam-5942	67	15	)	)	PUNCT
ejpam-5942	67	16	the	the	DET
ejpam-5942	67	17	graph	graph	NOUN
ejpam-5942	67	18	h	h	NOUN
ejpam-5942	67	19	′	′	NUM
ejpam-5942	67	20	satisfies	satisfy	VERB
ejpam-5942	67	21	the	the	DET
ejpam-5942	67	22	following	follow	VERB
ejpam-5942	67	23	properties	property	NOUN
ejpam-5942	67	24	:	:	PUNCT
ejpam-5942	67	25	(	(	PUNCT
ejpam-5942	67	26	i	i	NOUN
ejpam-5942	67	27	)	)	PUNCT
ejpam-5942	67	28	a	a	DET
ejpam-5942	67	29	graph	graph	NOUN
ejpam-5942	67	30	h	h	NOUN
ejpam-5942	67	31	′	′	NOUN
ejpam-5942	67	32	has	have	VERB
ejpam-5942	67	33	no	no	DET
ejpam-5942	67	34	2−-vertices	2−-vertices	NUM
ejpam-5942	67	35	.	.	PUNCT
ejpam-5942	68	1	(	(	PUNCT
ejpam-5942	68	2	ii	ii	NOUN
ejpam-5942	68	3	)	)	PUNCT
ejpam-5942	68	4	every	every	DET
ejpam-5942	68	5	3	3	NUM
ejpam-5942	68	6	-	-	PUNCT
ejpam-5942	68	7	vertex	vertex	NOUN
ejpam-5942	68	8	have	have	VERB
ejpam-5942	68	9	to	to	PART
ejpam-5942	68	10	be	be	AUX
ejpam-5942	68	11	adjacent	adjacent	ADJ
ejpam-5942	68	12	to	to	ADP
ejpam-5942	68	13	a	a	DET
ejpam-5942	68	14	5	5	NUM
ejpam-5942	68	15	+	+	SYM
ejpam-5942	68	16	-vertex	-vertex	NOUN
ejpam-5942	68	17	.	.	PUNCT
ejpam-5942	69	1	(	(	PUNCT
ejpam-5942	69	2	iii	iii	NOUN
ejpam-5942	69	3	)	)	PUNCT
ejpam-5942	69	4	only	only	ADV
ejpam-5942	69	5	a	a	DET
ejpam-5942	69	6	(	(	PUNCT
ejpam-5942	69	7	3	3	NUM
ejpam-5942	69	8	,	,	PUNCT
ejpam-5942	69	9	5	5	NUM
ejpam-5942	69	10	+	+	ADJ
ejpam-5942	69	11	,	,	PUNCT
ejpam-5942	69	12	5+)-face	5+)-face	NUM
ejpam-5942	69	13	or	or	CCONJ
ejpam-5942	69	14	a	a	DET
ejpam-5942	69	15	(	(	PUNCT
ejpam-5942	69	16	4	4	NUM
ejpam-5942	69	17	+	+	ADJ
ejpam-5942	69	18	,	,	PUNCT
ejpam-5942	69	19	4	4	NUM
ejpam-5942	69	20	+	+	ADJ
ejpam-5942	69	21	,	,	PUNCT
ejpam-5942	69	22	5+)-face	5+)-face	NUM
ejpam-5942	69	23	is	be	AUX
ejpam-5942	69	24	a	a	DET
ejpam-5942	69	25	3	3	NUM
ejpam-5942	69	26	-	-	PUNCT
ejpam-5942	69	27	face	face	NOUN
ejpam-5942	69	28	of	of	ADP
ejpam-5942	69	29	a	a	DET
ejpam-5942	69	30	graph	graph	NOUN
ejpam-5942	69	31	h	h	NOUN
ejpam-5942	69	32	′	′	NUM
ejpam-5942	69	33	.	.	PUNCT
ejpam-5942	70	1	lemma	lemma	PROPN
ejpam-5942	70	2	2	2	NUM
ejpam-5942	70	3	.	.	PUNCT
ejpam-5942	71	1	(	(	PUNCT
ejpam-5942	71	2	lemma	lemma	PROPN
ejpam-5942	71	3	7	7	NUM
ejpam-5942	71	4	in	in	ADP
ejpam-5942	71	5	[	[	X
ejpam-5942	71	6	14	14	NUM
ejpam-5942	71	7	]	]	PUNCT
ejpam-5942	71	8	)	)	PUNCT
ejpam-5942	71	9	the	the	DET
ejpam-5942	71	10	graph	graph	NOUN
ejpam-5942	71	11	h	h	NOUN
ejpam-5942	71	12	′	′	NUM
ejpam-5942	71	13	satisfies	satisfy	VERB
ejpam-5942	71	14	the	the	DET
ejpam-5942	71	15	following	follow	VERB
ejpam-5942	71	16	properties	property	NOUN
ejpam-5942	71	17	:	:	PUNCT
ejpam-5942	71	18	a	a	DET
ejpam-5942	71	19	5	5	NUM
ejpam-5942	71	20	-	-	PUNCT
ejpam-5942	71	21	vertex	vertex	NOUN
ejpam-5942	71	22	is	be	AUX
ejpam-5942	71	23	not	not	PART
ejpam-5942	71	24	adjacent	adjacent	ADJ
ejpam-5942	71	25	to	to	ADP
ejpam-5942	71	26	two	two	NUM
ejpam-5942	71	27	3	3	NUM
ejpam-5942	71	28	-	-	PUNCT
ejpam-5942	71	29	vertices	vertex	NOUN
ejpam-5942	71	30	.	.	PUNCT
ejpam-5942	72	1	from	from	ADP
ejpam-5942	72	2	now	now	ADV
ejpam-5942	72	3	on	on	ADV
ejpam-5942	72	4	,	,	PUNCT
ejpam-5942	72	5	we	we	PRON
ejpam-5942	72	6	impose	impose	VERB
ejpam-5942	72	7	an	an	DET
ejpam-5942	72	8	additional	additional	ADJ
ejpam-5942	72	9	condition	condition	NOUN
ejpam-5942	72	10	that	that	SCONJ
ejpam-5942	72	11	a	a	DET
ejpam-5942	72	12	planar	planar	ADJ
ejpam-5942	72	13	graph	graph	NOUN
ejpam-5942	72	14	g	g	NOUN
ejpam-5942	72	15	has	have	AUX
ejpam-5942	72	16	no	no	DET
ejpam-5942	72	17	the	the	DET
ejpam-5942	72	18	adjacency	adjacency	NOUN
ejpam-5942	72	19	of	of	ADP
ejpam-5942	72	20	3	3	NUM
ejpam-5942	72	21	-	-	PUNCT
ejpam-5942	72	22	cycles	cycle	NOUN
ejpam-5942	72	23	and	and	CCONJ
ejpam-5942	72	24	5	5	NUM
ejpam-5942	72	25	-	-	PUNCT
ejpam-5942	72	26	cycles	cycle	NOUN
ejpam-5942	72	27	.	.	PUNCT
ejpam-5942	73	1	the	the	DET
ejpam-5942	73	2	additional	additional	ADJ
ejpam-5942	73	3	condition	condition	NOUN
ejpam-5942	73	4	implies	imply	VERB
ejpam-5942	73	5	the	the	DET
ejpam-5942	73	6	following	follow	VERB
ejpam-5942	73	7	lemma	lemma	PROPN
ejpam-5942	73	8	.	.	PUNCT
ejpam-5942	74	1	lemma	lemma	PROPN
ejpam-5942	74	2	3	3	NUM
ejpam-5942	74	3	.	.	PROPN
ejpam-5942	74	4	faces	face	NOUN
ejpam-5942	74	5	and	and	CCONJ
ejpam-5942	74	6	vertices	vertice	VERB
ejpam-5942	74	7	in	in	ADP
ejpam-5942	74	8	h	h	NOUN
ejpam-5942	74	9	′	′	NUM
ejpam-5942	74	10	satisfy	satisfy	VERB
ejpam-5942	74	11	the	the	DET
ejpam-5942	74	12	following	follow	VERB
ejpam-5942	74	13	properties	property	NOUN
ejpam-5942	74	14	.	.	PUNCT
ejpam-5942	75	1	(	(	PUNCT
ejpam-5942	75	2	i	i	NOUN
ejpam-5942	75	3	)	)	PUNCT
ejpam-5942	75	4	for	for	ADP
ejpam-5942	75	5	l	l	PROPN
ejpam-5942	75	6	∈	∈	PROPN
ejpam-5942	75	7	{	{	PUNCT
ejpam-5942	75	8	4	4	NUM
ejpam-5942	75	9	,	,	PUNCT
ejpam-5942	75	10	5	5	NUM
ejpam-5942	75	11	}	}	PUNCT
ejpam-5942	75	12	,	,	PUNCT
ejpam-5942	75	13	an	an	DET
ejpam-5942	75	14	l	l	NOUN
ejpam-5942	75	15	-	-	NOUN
ejpam-5942	75	16	face	face	NOUN
ejpam-5942	75	17	is	be	AUX
ejpam-5942	75	18	not	not	PART
ejpam-5942	75	19	adjacent	adjacent	ADJ
ejpam-5942	75	20	to	to	ADP
ejpam-5942	75	21	any	any	DET
ejpam-5942	75	22	3	3	NUM
ejpam-5942	75	23	-	-	PUNCT
ejpam-5942	75	24	faces	face	NOUN
ejpam-5942	75	25	.	.	PUNCT
ejpam-5942	76	1	if	if	SCONJ
ejpam-5942	76	2	f	f	PROPN
ejpam-5942	76	3	is	be	AUX
ejpam-5942	76	4	a	a	DET
ejpam-5942	76	5	3	3	NUM
ejpam-5942	76	6	-	-	PUNCT
ejpam-5942	76	7	face	face	NOUN
ejpam-5942	76	8	,	,	PUNCT
ejpam-5942	76	9	then	then	ADV
ejpam-5942	76	10	f	f	PROPN
ejpam-5942	76	11	is	be	AUX
ejpam-5942	76	12	not	not	PART
ejpam-5942	76	13	adjacent	adjacent	ADJ
ejpam-5942	76	14	to	to	ADP
ejpam-5942	76	15	l	l	NOUN
ejpam-5942	76	16	-	-	NOUN
ejpam-5942	76	17	face	face	NOUN
ejpam-5942	76	18	for	for	ADP
ejpam-5942	76	19	l	l	NOUN
ejpam-5942	76	20	∈	∈	PROPN
ejpam-5942	76	21	{	{	PUNCT
ejpam-5942	76	22	4	4	NUM
ejpam-5942	76	23	,	,	PUNCT
ejpam-5942	76	24	5	5	NUM
ejpam-5942	76	25	}	}	PUNCT
ejpam-5942	76	26	.	.	PUNCT
ejpam-5942	77	1	(	(	PUNCT
ejpam-5942	77	2	ii	ii	NOUN
ejpam-5942	77	3	)	)	PUNCT
ejpam-5942	77	4	let	let	VERB
ejpam-5942	77	5	fi	fi	NOUN
ejpam-5942	77	6	,	,	PUNCT
ejpam-5942	77	7	fi+1	fi+1	NOUN
ejpam-5942	77	8	,	,	PUNCT
ejpam-5942	77	9	and	and	CCONJ
ejpam-5942	77	10	fi+2	fi+2	PROPN
ejpam-5942	77	11	be	be	AUX
ejpam-5942	77	12	three	three	NUM
ejpam-5942	77	13	consecutive	consecutive	ADJ
ejpam-5942	77	14	incident	incident	NOUN
ejpam-5942	77	15	faces	face	NOUN
ejpam-5942	77	16	of	of	ADP
ejpam-5942	77	17	an	an	DET
ejpam-5942	77	18	l	l	NOUN
ejpam-5942	77	19	-	-	NOUN
ejpam-5942	77	20	vertex	vertex	NOUN
ejpam-5942	78	1	v.	v.	INTJ
ejpam-5942	78	2	if	if	SCONJ
ejpam-5942	78	3	l	l	PROPN
ejpam-5942	78	4	≥	≥	NOUN
ejpam-5942	78	5	4	4	NUM
ejpam-5942	78	6	,	,	PUNCT
ejpam-5942	78	7	then	then	ADV
ejpam-5942	78	8	one	one	NUM
ejpam-5942	78	9	of	of	ADP
ejpam-5942	78	10	fi	fi	NOUN
ejpam-5942	78	11	,	,	PUNCT
ejpam-5942	78	12	fi+1	fi+1	NOUN
ejpam-5942	78	13	,	,	PUNCT
ejpam-5942	78	14	and	and	CCONJ
ejpam-5942	78	15	fi+2	fi+2	PROPN
ejpam-5942	78	16	is	be	AUX
ejpam-5942	78	17	a	a	DET
ejpam-5942	78	18	4	4	NUM
ejpam-5942	78	19	+	+	NOUN
ejpam-5942	78	20	-face	-face	NOUN
ejpam-5942	78	21	.	.	PUNCT
ejpam-5942	79	1	(	(	PUNCT
ejpam-5942	79	2	iii	iii	X
ejpam-5942	79	3	)	)	PUNCT
ejpam-5942	79	4	any	any	DET
ejpam-5942	79	5	3	3	NUM
ejpam-5942	79	6	-	-	PUNCT
ejpam-5942	79	7	face	face	NOUN
ejpam-5942	79	8	is	be	AUX
ejpam-5942	79	9	not	not	PART
ejpam-5942	79	10	adjacent	adjacent	ADJ
ejpam-5942	79	11	to	to	ADP
ejpam-5942	79	12	three	three	NUM
ejpam-5942	79	13	3	3	NUM
ejpam-5942	79	14	-	-	PUNCT
ejpam-5942	79	15	faces	face	NOUN
ejpam-5942	79	16	.	.	PUNCT
ejpam-5942	80	1	proof	proof	NOUN
ejpam-5942	80	2	.	.	PUNCT
ejpam-5942	81	1	let	let	VERB
ejpam-5942	81	2	b(f	b(f	PROPN
ejpam-5942	81	3	)	)	PUNCT
ejpam-5942	81	4	be	be	AUX
ejpam-5942	81	5	the	the	DET
ejpam-5942	81	6	boundary	boundary	NOUN
ejpam-5942	81	7	of	of	ADP
ejpam-5942	81	8	a	a	DET
ejpam-5942	81	9	face	face	NOUN
ejpam-5942	81	10	f	f	NOUN
ejpam-5942	81	11	.	.	PUNCT
ejpam-5942	82	1	(	(	PUNCT
ejpam-5942	82	2	i	i	NOUN
ejpam-5942	82	3	)	)	PUNCT
ejpam-5942	82	4	let	let	VERB
ejpam-5942	82	5	f	f	PRON
ejpam-5942	82	6	be	be	AUX
ejpam-5942	82	7	a	a	DET
ejpam-5942	82	8	3	3	NUM
ejpam-5942	82	9	-	-	PUNCT
ejpam-5942	82	10	face	face	NOUN
ejpam-5942	82	11	and	and	CCONJ
ejpam-5942	82	12	g	g	NOUN
ejpam-5942	82	13	be	be	AUX
ejpam-5942	82	14	an	an	DET
ejpam-5942	82	15	l	l	NOUN
ejpam-5942	82	16	-	-	NOUN
ejpam-5942	82	17	face	face	NOUN
ejpam-5942	82	18	where	where	SCONJ
ejpam-5942	82	19	l	l	PROPN
ejpam-5942	82	20	∈	∈	PROPN
ejpam-5942	82	21	{	{	PUNCT
ejpam-5942	82	22	4	4	NUM
ejpam-5942	82	23	,	,	PUNCT
ejpam-5942	82	24	5	5	NUM
ejpam-5942	82	25	}	}	PUNCT
ejpam-5942	82	26	.	.	PUNCT
ejpam-5942	83	1	suppose	suppose	VERB
ejpam-5942	83	2	that	that	SCONJ
ejpam-5942	83	3	f	f	PROPN
ejpam-5942	83	4	is	be	AUX
ejpam-5942	83	5	adjacent	adjacent	ADJ
ejpam-5942	83	6	to	to	PART
ejpam-5942	83	7	g.	g.	PROPN
ejpam-5942	83	8	give	give	VERB
ejpam-5942	83	9	b(f	b(f	PROPN
ejpam-5942	83	10	)	)	PUNCT
ejpam-5942	84	1	=	=	NOUN
ejpam-5942	84	2	v1v2v3	v1v2v3	NOUN
ejpam-5942	84	3	and	and	CCONJ
ejpam-5942	84	4	b(g	b(g	NUM
ejpam-5942	84	5	)	)	PUNCT
ejpam-5942	85	1	=	=	PUNCT
ejpam-5942	85	2	v1v2u1	v1v2u1	PROPN
ejpam-5942	85	3	.	.	PUNCT
ejpam-5942	85	4	.	.	PUNCT
ejpam-5942	85	5	.	.	PUNCT
ejpam-5942	86	1	ul−2	ul−2	NOUN
ejpam-5942	86	2	.	.	PUNCT
ejpam-5942	87	1	consider	consider	VERB
ejpam-5942	87	2	l	l	NOUN
ejpam-5942	87	3	=	=	NOUN
ejpam-5942	87	4	4	4	X
ejpam-5942	87	5	.	.	X
ejpam-5942	87	6	one	one	PRON
ejpam-5942	87	7	can	can	AUX
ejpam-5942	87	8	see	see	VERB
ejpam-5942	87	9	that	that	DET
ejpam-5942	87	10	b(f	b(f	PROPN
ejpam-5942	87	11	)	)	PUNCT
ejpam-5942	87	12	and	and	CCONJ
ejpam-5942	87	13	b(g	b(g	NUM
ejpam-5942	87	14	)	)	PUNCT
ejpam-5942	87	15	share	share	VERB
ejpam-5942	87	16	three	three	NUM
ejpam-5942	87	17	vertices	vertex	NOUN
ejpam-5942	87	18	;	;	PUNCT
ejpam-5942	87	19	otherwise	otherwise	ADV
ejpam-5942	87	20	,	,	PUNCT
ejpam-5942	87	21	a	a	DET
ejpam-5942	87	22	5	5	NUM
ejpam-5942	87	23	-	-	PUNCT
ejpam-5942	87	24	cycle	cycle	NOUN
ejpam-5942	87	25	v2u1u2v1v3	v2u1u2v1v3	NOUN
ejpam-5942	87	26	is	be	AUX
ejpam-5942	87	27	adjacent	adjacent	ADJ
ejpam-5942	87	28	to	to	ADP
ejpam-5942	87	29	a	a	DET
ejpam-5942	87	30	3	3	NUM
ejpam-5942	87	31	-	-	PUNCT
ejpam-5942	87	32	cycle	cycle	NOUN
ejpam-5942	87	33	v1v2v3	v1v2v3	NOUN
ejpam-5942	87	34	,	,	PUNCT
ejpam-5942	87	35	a	a	DET
ejpam-5942	87	36	contradiction	contradiction	NOUN
ejpam-5942	87	37	.	.	PUNCT
ejpam-5942	88	1	if	if	SCONJ
ejpam-5942	88	2	v3	v3	PROPN
ejpam-5942	88	3	=	=	SYM
ejpam-5942	88	4	u1	u1	PROPN
ejpam-5942	88	5	or	or	CCONJ
ejpam-5942	88	6	v3	v3	PROPN
ejpam-5942	88	7	=	=	PROPN
ejpam-5942	88	8	u2	u2	PROPN
ejpam-5942	88	9	,	,	PUNCT
ejpam-5942	88	10	then	then	ADV
ejpam-5942	88	11	there	there	PRON
ejpam-5942	88	12	is	be	VERB
ejpam-5942	88	13	a	a	DET
ejpam-5942	88	14	2	2	NUM
ejpam-5942	88	15	-	-	PUNCT
ejpam-5942	88	16	vertex	vertex	NOUN
ejpam-5942	88	17	or	or	CCONJ
ejpam-5942	88	18	parallel	parallel	ADJ
ejpam-5942	88	19	edges	edge	NOUN
ejpam-5942	88	20	,	,	PUNCT
ejpam-5942	88	21	a	a	DET
ejpam-5942	88	22	contradiction	contradiction	NOUN
ejpam-5942	88	23	by	by	ADP
ejpam-5942	88	24	lemma	lemma	PROPN
ejpam-5942	88	25	1	1	NUM
ejpam-5942	88	26	(	(	PUNCT
ejpam-5942	88	27	1	1	NUM
ejpam-5942	88	28	)	)	PUNCT
ejpam-5942	88	29	or	or	CCONJ
ejpam-5942	88	30	property	property	NOUN
ejpam-5942	88	31	of	of	ADP
ejpam-5942	88	32	a	a	DET
ejpam-5942	88	33	graph	graph	NOUN
ejpam-5942	88	34	h	h	NOUN
ejpam-5942	88	35	′.	′.	NOUN
ejpam-5942	88	36	consider	consider	VERB
ejpam-5942	88	37	l	l	NOUN
ejpam-5942	88	38	=	=	SYM
ejpam-5942	88	39	5	5	X
ejpam-5942	88	40	.	.	X
ejpam-5942	88	41	one	one	PRON
ejpam-5942	88	42	can	can	AUX
ejpam-5942	88	43	see	see	VERB
ejpam-5942	88	44	that	that	SCONJ
ejpam-5942	88	45	a	a	DET
ejpam-5942	88	46	5	5	NUM
ejpam-5942	88	47	-	-	PUNCT
ejpam-5942	88	48	cycle	cycle	NOUN
ejpam-5942	88	49	b(g	b(g	NOUN
ejpam-5942	88	50	)	)	PUNCT
ejpam-5942	88	51	is	be	AUX
ejpam-5942	88	52	adjacent	adjacent	ADJ
ejpam-5942	88	53	to	to	ADP
ejpam-5942	88	54	a	a	DET
ejpam-5942	88	55	3	3	NUM
ejpam-5942	88	56	-	-	PUNCT
ejpam-5942	88	57	cycle	cycle	NOUN
ejpam-5942	88	58	b(f	b(f	PROPN
ejpam-5942	88	59	)	)	PUNCT
ejpam-5942	88	60	,	,	PUNCT
ejpam-5942	88	61	a	a	DET
ejpam-5942	88	62	contradiction	contradiction	NOUN
ejpam-5942	88	63	.	.	PUNCT
ejpam-5942	89	1	(	(	PUNCT
ejpam-5942	89	2	ii	ii	NOUN
ejpam-5942	89	3	)	)	PUNCT
ejpam-5942	89	4	let	let	VERB
ejpam-5942	89	5	v	v	PART
ejpam-5942	89	6	be	be	AUX
ejpam-5942	89	7	an	an	DET
ejpam-5942	89	8	4	4	NUM
ejpam-5942	89	9	+	+	SYM
ejpam-5942	89	10	-vertex	-vertex	NOUN
ejpam-5942	89	11	.	.	PUNCT
ejpam-5942	90	1	let	let	VERB
ejpam-5942	90	2	fi	fi	NOUN
ejpam-5942	90	3	,	,	PUNCT
ejpam-5942	90	4	fi+1	fi+1	NOUN
ejpam-5942	90	5	,	,	PUNCT
ejpam-5942	90	6	and	and	CCONJ
ejpam-5942	90	7	fi+2	fi+2	PROPN
ejpam-5942	90	8	be	be	AUX
ejpam-5942	90	9	three	three	NUM
ejpam-5942	90	10	consecutive	consecutive	ADJ
ejpam-5942	90	11	incident	incident	NOUN
ejpam-5942	90	12	faces	face	NOUN
ejpam-5942	90	13	of	of	ADP
ejpam-5942	90	14	v.	v.	INTJ
ejpam-5942	90	15	suppose	suppose	VERB
ejpam-5942	90	16	that	that	SCONJ
ejpam-5942	90	17	fi	fi	NOUN
ejpam-5942	90	18	,	,	PUNCT
ejpam-5942	90	19	fi+1	fi+1	NOUN
ejpam-5942	90	20	,	,	PUNCT
ejpam-5942	90	21	and	and	CCONJ
ejpam-5942	90	22	fi+2	fi+2	PROPN
ejpam-5942	90	23	are	be	AUX
ejpam-5942	90	24	3	3	NUM
ejpam-5942	90	25	-	-	PUNCT
ejpam-5942	90	26	faces	face	NOUN
ejpam-5942	90	27	.	.	PUNCT
ejpam-5942	91	1	give	give	VERB
ejpam-5942	91	2	b(fi	b(fi	NUM
ejpam-5942	91	3	)	)	PUNCT
ejpam-5942	91	4	=	=	SYM
ejpam-5942	91	5	vvivi+1	vvivi+1	PROPN
ejpam-5942	91	6	,	,	PUNCT
ejpam-5942	91	7	b(fi+1	b(fi+1	NOUN
ejpam-5942	91	8	)	)	PUNCT
ejpam-5942	91	9	=	=	SYM
ejpam-5942	91	10	vvi+1vi+2	vvi+1vi+2	PROPN
ejpam-5942	91	11	,	,	PUNCT
ejpam-5942	91	12	and	and	CCONJ
ejpam-5942	91	13	b(fi+2	b(fi+2	PROPN
ejpam-5942	91	14	)	)	PUNCT
ejpam-5942	92	1	=	=	SYM
ejpam-5942	92	2	vvi+2vi+3	vvi+2vi+3	NOUN
ejpam-5942	92	3	.	.	PUNCT
ejpam-5942	93	1	since	since	SCONJ
ejpam-5942	93	2	each	each	DET
ejpam-5942	93	3	vertex	vertex	NOUN
ejpam-5942	93	4	is	be	AUX
ejpam-5942	93	5	not	not	PART
ejpam-5942	93	6	a	a	DET
ejpam-5942	93	7	4	4	NUM
ejpam-5942	93	8	+	+	NOUN
ejpam-5942	93	9	-vertex	-vertex	NOUN
ejpam-5942	93	10	by	by	ADP
ejpam-5942	93	11	lemma	lemma	PROPN
ejpam-5942	93	12	1	1	NUM
ejpam-5942	93	13	(	(	PUNCT
ejpam-5942	93	14	i	i	NOUN
ejpam-5942	93	15	)	)	PUNCT
ejpam-5942	93	16	,	,	PUNCT
ejpam-5942	93	17	five	five	NUM
ejpam-5942	93	18	vertices	vertex	NOUN
ejpam-5942	93	19	p.	p.	NOUN
ejpam-5942	93	20	sittitrai	sittitrai	NOUN
ejpam-5942	93	21	,	,	PUNCT
ejpam-5942	93	22	k.	k.	PROPN
ejpam-5942	93	23	nakprasit	nakprasit	PROPN
ejpam-5942	93	24	,	,	PUNCT
ejpam-5942	93	25	p.	p.	PROPN
ejpam-5942	93	26	jumnongnit	jumnongnit	PROPN
ejpam-5942	93	27	/	/	SYM
ejpam-5942	93	28	eur	eur	PROPN
ejpam-5942	93	29	.	.	PUNCT
ejpam-5942	94	1	j.	j.	PROPN
ejpam-5942	94	2	pure	pure	PROPN
ejpam-5942	94	3	appl	appl	PROPN
ejpam-5942	94	4	.	.	PROPN
ejpam-5942	94	5	math	math	PROPN
ejpam-5942	94	6	,	,	PUNCT
ejpam-5942	94	7	18	18	NUM
ejpam-5942	94	8	(	(	PUNCT
ejpam-5942	94	9	2	2	NUM
ejpam-5942	94	10	)	)	PUNCT
ejpam-5942	94	11	(	(	PUNCT
ejpam-5942	94	12	2025	2025	NUM
ejpam-5942	94	13	)	)	PUNCT
ejpam-5942	94	14	,	,	PUNCT
ejpam-5942	94	15	5942	5942	NUM
ejpam-5942	94	16	4	4	NUM
ejpam-5942	94	17	of	of	ADP
ejpam-5942	94	18	7	7	NUM
ejpam-5942	94	19	v	v	NOUN
ejpam-5942	94	20	,	,	PUNCT
ejpam-5942	94	21	vi	vi	NOUN
ejpam-5942	94	22	,	,	PUNCT
ejpam-5942	94	23	vi+1	vi+1	ADJ
ejpam-5942	94	24	,	,	PUNCT
ejpam-5942	94	25	vi+2	vi+2	NUM
ejpam-5942	94	26	,	,	PUNCT
ejpam-5942	94	27	vi+3	vi+3	NUM
ejpam-5942	94	28	should	should	AUX
ejpam-5942	94	29	be	be	AUX
ejpam-5942	94	30	distinct	distinct	ADJ
ejpam-5942	94	31	;	;	PUNCT
ejpam-5942	94	32	otherwise	otherwise	ADV
ejpam-5942	94	33	,	,	PUNCT
ejpam-5942	94	34	parallel	parallel	ADJ
ejpam-5942	94	35	edges	edge	NOUN
ejpam-5942	94	36	exist	exist	VERB
ejpam-5942	94	37	,	,	PUNCT
ejpam-5942	94	38	a	a	DET
ejpam-5942	94	39	contradiction	contradiction	NOUN
ejpam-5942	94	40	.	.	PUNCT
ejpam-5942	95	1	then	then	ADV
ejpam-5942	95	2	a	a	DET
ejpam-5942	95	3	5	5	NUM
ejpam-5942	95	4	-	-	PUNCT
ejpam-5942	95	5	cycle	cycle	NOUN
ejpam-5942	95	6	vvivi+1vi+2vi+3	vvivi+1vi+2vi+3	NOUN
ejpam-5942	95	7	is	be	AUX
ejpam-5942	95	8	adjacent	adjacent	ADJ
ejpam-5942	95	9	to	to	ADP
ejpam-5942	95	10	a	a	DET
ejpam-5942	95	11	3	3	NUM
ejpam-5942	95	12	-	-	PUNCT
ejpam-5942	95	13	cycle	cycle	NOUN
ejpam-5942	95	14	vvivi+1	vvivi+1	NOUN
ejpam-5942	95	15	,	,	PUNCT
ejpam-5942	95	16	a	a	DET
ejpam-5942	95	17	contradiction	contradiction	NOUN
ejpam-5942	95	18	.	.	PUNCT
ejpam-5942	96	1	(	(	PUNCT
ejpam-5942	96	2	iii	iii	X
ejpam-5942	96	3	)	)	PUNCT
ejpam-5942	96	4	let	let	VERB
ejpam-5942	96	5	f	f	PRON
ejpam-5942	96	6	be	be	AUX
ejpam-5942	96	7	a	a	DET
ejpam-5942	96	8	3	3	NUM
ejpam-5942	96	9	-	-	PUNCT
ejpam-5942	96	10	face	face	NOUN
ejpam-5942	96	11	adjacent	adjacent	ADJ
ejpam-5942	96	12	to	to	ADP
ejpam-5942	96	13	faces	face	NOUN
ejpam-5942	96	14	f1	f1	NOUN
ejpam-5942	96	15	,	,	PUNCT
ejpam-5942	96	16	f2	f2	PROPN
ejpam-5942	96	17	,	,	PUNCT
ejpam-5942	96	18	and	and	CCONJ
ejpam-5942	96	19	f3	f3	PROPN
ejpam-5942	96	20	.	.	PUNCT
ejpam-5942	96	21	suppose	suppose	VERB
ejpam-5942	96	22	that	that	SCONJ
ejpam-5942	96	23	f1	f1	PROPN
ejpam-5942	96	24	,	,	PUNCT
ejpam-5942	96	25	f2	f2	PROPN
ejpam-5942	96	26	,	,	PUNCT
ejpam-5942	96	27	and	and	CCONJ
ejpam-5942	96	28	f3	f3	PROPN
ejpam-5942	96	29	are	be	AUX
ejpam-5942	96	30	3	3	NUM
ejpam-5942	96	31	-	-	NOUN
ejpam-5942	96	32	face	face	NOUN
ejpam-5942	96	33	.	.	PUNCT
ejpam-5942	97	1	by	by	ADP
ejpam-5942	97	2	lemma	lemma	PROPN
ejpam-5942	97	3	3	3	NUM
ejpam-5942	97	4	(	(	PUNCT
ejpam-5942	97	5	ii	ii	NOUN
ejpam-5942	97	6	)	)	PUNCT
ejpam-5942	97	7	,	,	PUNCT
ejpam-5942	97	8	each	each	DET
ejpam-5942	97	9	incident	incident	NOUN
ejpam-5942	97	10	vertex	vertex	NOUN
ejpam-5942	97	11	of	of	ADP
ejpam-5942	97	12	f	f	PROPN
ejpam-5942	97	13	is	be	AUX
ejpam-5942	97	14	a	a	DET
ejpam-5942	97	15	3	3	NUM
ejpam-5942	97	16	-	-	PUNCT
ejpam-5942	97	17	vertex	vertex	NOUN
ejpam-5942	97	18	.	.	PUNCT
ejpam-5942	98	1	this	this	PRON
ejpam-5942	98	2	contradicts	contradict	VERB
ejpam-5942	98	3	lemma	lemma	PROPN
ejpam-5942	98	4	1	1	NUM
ejpam-5942	98	5	(	(	PUNCT
ejpam-5942	98	6	iii	iii	NOUN
ejpam-5942	98	7	)	)	PUNCT
ejpam-5942	98	8	.	.	PUNCT
ejpam-5942	99	1	4	4	X
ejpam-5942	99	2	.	.	X
ejpam-5942	99	3	main	main	ADJ
ejpam-5942	99	4	theorem	theorem	NOUN
ejpam-5942	99	5	theorem	theorem	NOUN
ejpam-5942	99	6	1	1	NUM
ejpam-5942	99	7	.	.	PUNCT
ejpam-5942	100	1	a	a	DET
ejpam-5942	100	2	graph	graph	NOUN
ejpam-5942	100	3	g	g	PROPN
ejpam-5942	100	4	has	have	VERB
ejpam-5942	100	5	ch′′∑(g	ch′′∑(g	VERB
ejpam-5942	100	6	)	)	PUNCT
ejpam-5942	100	7	≤	≤	NUM
ejpam-5942	100	8	max{10,∆(g)+3	max{10,∆(g)+3	NOUN
ejpam-5942	100	9	}	}	PUNCT
ejpam-5942	100	10	if	if	SCONJ
ejpam-5942	100	11	g	g	PROPN
ejpam-5942	100	12	is	be	AUX
ejpam-5942	100	13	a	a	DET
ejpam-5942	100	14	planar	planar	ADJ
ejpam-5942	100	15	graph	graph	NOUN
ejpam-5942	100	16	without	without	ADP
ejpam-5942	100	17	c5	c5	PROPN
ejpam-5942	100	18	adjacent	adjacent	ADJ
ejpam-5942	100	19	to	to	ADP
ejpam-5942	100	20	c3	c3	PROPN
ejpam-5942	100	21	.	.	PUNCT
ejpam-5942	101	1	proof	proof	NOUN
ejpam-5942	101	2	.	.	PUNCT
ejpam-5942	102	1	suppose	suppose	VERB
ejpam-5942	102	2	theorem	theorem	ADJ
ejpam-5942	102	3	1	1	NUM
ejpam-5942	102	4	to	to	ADP
ejpam-5942	102	5	the	the	DET
ejpam-5942	102	6	contrary	contrary	NOUN
ejpam-5942	102	7	.	.	PUNCT
ejpam-5942	103	1	consider	consider	VERB
ejpam-5942	103	2	a	a	DET
ejpam-5942	103	3	minimal	minimal	ADJ
ejpam-5942	103	4	counterexample	counterexample	NOUN
ejpam-5942	103	5	g.	g.	PROPN
ejpam-5942	103	6	recall	recall	VERB
ejpam-5942	103	7	that	that	PRON
ejpam-5942	103	8	h	h	NOUN
ejpam-5942	104	1	′	′	NOUN
ejpam-5942	104	2	is	be	AUX
ejpam-5942	104	3	defined	define	VERB
ejpam-5942	104	4	as	as	ADP
ejpam-5942	104	5	in	in	ADP
ejpam-5942	104	6	the	the	DET
ejpam-5942	104	7	previous	previous	ADJ
ejpam-5942	104	8	section	section	NOUN
ejpam-5942	104	9	.	.	PUNCT
ejpam-5942	105	1	discharging	discharge	VERB
ejpam-5942	105	2	method	method	NOUN
ejpam-5942	105	3	is	be	AUX
ejpam-5942	105	4	used	use	VERB
ejpam-5942	105	5	to	to	PART
ejpam-5942	105	6	show	show	VERB
ejpam-5942	105	7	that	that	SCONJ
ejpam-5942	105	8	h	h	NOUN
ejpam-5942	105	9	′	′	NOUN
ejpam-5942	105	10	does	do	AUX
ejpam-5942	105	11	not	not	PART
ejpam-5942	105	12	exist	exist	VERB
ejpam-5942	105	13	.	.	PUNCT
ejpam-5942	106	1	for	for	ADP
ejpam-5942	106	2	each	each	DET
ejpam-5942	106	3	z	z	PROPN
ejpam-5942	106	4	∈	∈	PROPN
ejpam-5942	106	5	v	v	ADP
ejpam-5942	106	6	(	(	PUNCT
ejpam-5942	106	7	h	h	NOUN
ejpam-5942	106	8	′	′	NOUN
ejpam-5942	106	9	)	)	PUNCT
ejpam-5942	106	10	∪	∪	PROPN
ejpam-5942	106	11	f	f	PROPN
ejpam-5942	106	12	(	(	PUNCT
ejpam-5942	106	13	h	h	NOUN
ejpam-5942	106	14	′	′	NUM
ejpam-5942	106	15	)	)	PUNCT
ejpam-5942	106	16	,	,	PUNCT
ejpam-5942	106	17	we	we	PRON
ejpam-5942	106	18	let	let	VERB
ejpam-5942	106	19	µ(z	µ(z	NOUN
ejpam-5942	106	20	)	)	PUNCT
ejpam-5942	106	21	=	=	SYM
ejpam-5942	106	22	d(z	d(z	PROPN
ejpam-5942	106	23	)	)	PUNCT
ejpam-5942	106	24	−	−	PROPN
ejpam-5942	107	1	4	4	X
ejpam-5942	107	2	.	.	X
ejpam-5942	107	3	one	one	PRON
ejpam-5942	107	4	can	can	AUX
ejpam-5942	107	5	observe	observe	VERB
ejpam-5942	107	6	that	that	SCONJ
ejpam-5942	107	7	∑	∑	PROPN
ejpam-5942	107	8	z∈v	z∈v	NOUN
ejpam-5942	107	9	(	(	PUNCT
ejpam-5942	107	10	h′)∪f	h′)∪f	X
ejpam-5942	107	11	(	(	PUNCT
ejpam-5942	107	12	h′	h′	PROPN
ejpam-5942	107	13	)	)	PUNCT
ejpam-5942	107	14	µ(z	µ(z	PROPN
ejpam-5942	107	15	)	)	PUNCT
ejpam-5942	107	16	=	=	SYM
ejpam-5942	108	1	−8	−8	VERB
ejpam-5942	108	2	by	by	ADP
ejpam-5942	108	3	handshaking	handshake	VERB
ejpam-5942	108	4	lemma	lemma	PROPN
ejpam-5942	108	5	and	and	CCONJ
ejpam-5942	108	6	euler	euler	PROPN
ejpam-5942	108	7	’s	’s	PART
ejpam-5942	108	8	formula	formula	NOUN
ejpam-5942	108	9	.	.	PUNCT
ejpam-5942	109	1	next	next	ADV
ejpam-5942	109	2	,	,	PUNCT
ejpam-5942	109	3	we	we	PRON
ejpam-5942	109	4	desire	desire	VERB
ejpam-5942	109	5	some	some	DET
ejpam-5942	109	6	discharging	discharge	VERB
ejpam-5942	109	7	rules	rule	NOUN
ejpam-5942	109	8	to	to	PART
ejpam-5942	109	9	transfer	transfer	VERB
ejpam-5942	109	10	charge	charge	NOUN
ejpam-5942	109	11	w(x→	w(x→	NOUN
ejpam-5942	109	12	y	y	PROPN
ejpam-5942	109	13	)	)	PUNCT
ejpam-5942	109	14	from	from	ADP
ejpam-5942	109	15	x	x	PUNCT
ejpam-5942	109	16	to	to	ADP
ejpam-5942	109	17	y	y	PROPN
ejpam-5942	109	18	for	for	ADP
ejpam-5942	109	19	some	some	DET
ejpam-5942	109	20	x	x	NOUN
ejpam-5942	109	21	,	,	PUNCT
ejpam-5942	109	22	y	y	PROPN
ejpam-5942	109	23	∈	∈	PROPN
ejpam-5942	109	24	v	v	X
ejpam-5942	109	25	(	(	PUNCT
ejpam-5942	109	26	h	h	NOUN
ejpam-5942	109	27	′)∪f	′)∪f	PROPN
ejpam-5942	109	28	(	(	PUNCT
ejpam-5942	109	29	h	h	NOUN
ejpam-5942	109	30	′	′	NUM
ejpam-5942	109	31	)	)	PUNCT
ejpam-5942	109	32	.	.	PUNCT
ejpam-5942	110	1	in	in	ADP
ejpam-5942	110	2	additional	additional	ADJ
ejpam-5942	110	3	,	,	PUNCT
ejpam-5942	110	4	we	we	PRON
ejpam-5942	110	5	have	have	VERB
ejpam-5942	110	6	a	a	DET
ejpam-5942	110	7	new	new	ADJ
ejpam-5942	110	8	charge	charge	NOUN
ejpam-5942	110	9	µ∗(z	µ∗(z	NOUN
ejpam-5942	110	10	)	)	PUNCT
ejpam-5942	110	11	for	for	ADP
ejpam-5942	110	12	each	each	DET
ejpam-5942	110	13	z	z	PROPN
ejpam-5942	110	14	∈	∈	PROPN
ejpam-5942	110	15	v	v	NOUN
ejpam-5942	110	16	(	(	PUNCT
ejpam-5942	110	17	h	h	NOUN
ejpam-5942	110	18	′)∪f	′)∪f	PROPN
ejpam-5942	110	19	(	(	PUNCT
ejpam-5942	110	20	h	h	NOUN
ejpam-5942	110	21	′	′	NOUN
ejpam-5942	110	22	)	)	PUNCT
ejpam-5942	110	23	after	after	ADP
ejpam-5942	110	24	the	the	DET
ejpam-5942	110	25	transfer	transfer	NOUN
ejpam-5942	110	26	.	.	PUNCT
ejpam-5942	111	1	moreover	moreover	ADV
ejpam-5942	111	2	,	,	PUNCT
ejpam-5942	111	3	∑	∑	ADP
ejpam-5942	111	4	z∈v	z∈v	NOUN
ejpam-5942	111	5	(	(	PUNCT
ejpam-5942	111	6	h′)∪f	h′)∪f	X
ejpam-5942	111	7	(	(	PUNCT
ejpam-5942	111	8	h′	h′	PROPN
ejpam-5942	111	9	)	)	PUNCT
ejpam-5942	111	10	µ	µ	PRON
ejpam-5942	111	11	∗(z	∗(z	PROPN
ejpam-5942	111	12	)	)	PUNCT
ejpam-5942	111	13	=	=	PUNCT
ejpam-5942	111	14	∑	∑	PUNCT
ejpam-5942	111	15	z∈v	z∈v	NOUN
ejpam-5942	111	16	(	(	PUNCT
ejpam-5942	111	17	h′)∪f	h′)∪f	X
ejpam-5942	111	18	(	(	PUNCT
ejpam-5942	111	19	h′	h′	PROPN
ejpam-5942	111	20	)	)	PUNCT
ejpam-5942	111	21	µ(z	µ(z	PROPN
ejpam-5942	111	22	)	)	PUNCT
ejpam-5942	111	23	=	=	PUNCT
ejpam-5942	112	1	−8	−8	X
ejpam-5942	112	2	.	.	PUNCT
ejpam-5942	113	1	our	our	PRON
ejpam-5942	113	2	goal	goal	NOUN
ejpam-5942	113	3	is	be	AUX
ejpam-5942	113	4	to	to	PART
ejpam-5942	113	5	find	find	VERB
ejpam-5942	113	6	the	the	DET
ejpam-5942	113	7	discharging	discharge	VERB
ejpam-5942	113	8	rules	rule	NOUN
ejpam-5942	113	9	that	that	PRON
ejpam-5942	113	10	make	make	VERB
ejpam-5942	113	11	µ∗(z	µ∗(z	NOUN
ejpam-5942	113	12	)	)	PUNCT
ejpam-5942	113	13	≥	≥	NOUN
ejpam-5942	113	14	0	0	NUM
ejpam-5942	113	15	for	for	ADP
ejpam-5942	113	16	each	each	DET
ejpam-5942	113	17	z	z	NOUN
ejpam-5942	113	18	∈	∈	PROPN
ejpam-5942	113	19	v	v	ADP
ejpam-5942	113	20	(	(	PUNCT
ejpam-5942	113	21	h	h	NOUN
ejpam-5942	113	22	′	′	NOUN
ejpam-5942	113	23	)	)	PUNCT
ejpam-5942	113	24	∪	∪	PROPN
ejpam-5942	113	25	f	f	PROPN
ejpam-5942	113	26	(	(	PUNCT
ejpam-5942	113	27	h	h	NOUN
ejpam-5942	113	28	′	′	NUM
ejpam-5942	113	29	)	)	PUNCT
ejpam-5942	113	30	.	.	PUNCT
ejpam-5942	114	1	the	the	DET
ejpam-5942	114	2	following	follow	VERB
ejpam-5942	114	3	are	be	AUX
ejpam-5942	114	4	discharging	discharge	VERB
ejpam-5942	114	5	rules	rule	NOUN
ejpam-5942	114	6	.	.	PUNCT
ejpam-5942	115	1	(	(	PUNCT
ejpam-5942	115	2	r1	r1	PROPN
ejpam-5942	115	3	)	)	PUNCT
ejpam-5942	115	4	for	for	ADP
ejpam-5942	115	5	a	a	DET
ejpam-5942	115	6	3	3	NUM
ejpam-5942	115	7	-	-	PUNCT
ejpam-5942	115	8	face	face	NOUN
ejpam-5942	115	9	f	f	NOUN
ejpam-5942	115	10	,	,	PUNCT
ejpam-5942	115	11	let	let	VERB
ejpam-5942	115	12	g	g	PRON
ejpam-5942	115	13	be	be	AUX
ejpam-5942	115	14	an	an	DET
ejpam-5942	115	15	adjacent	adjacent	ADJ
ejpam-5942	115	16	to	to	ADP
ejpam-5942	115	17	a	a	DET
ejpam-5942	115	18	l	l	NOUN
ejpam-5942	115	19	-	-	NOUN
ejpam-5942	115	20	face	face	NOUN
ejpam-5942	115	21	g	g	NOUN
ejpam-5942	115	22	where	where	SCONJ
ejpam-5942	115	23	u	u	NOUN
ejpam-5942	115	24	is	be	AUX
ejpam-5942	115	25	a	a	DET
ejpam-5942	115	26	rough	rough	ADJ
ejpam-5942	115	27	5	5	NUM
ejpam-5942	115	28	+	+	SYM
ejpam-5942	115	29	-vertex	-vertex	NOUN
ejpam-5942	115	30	of	of	ADP
ejpam-5942	115	31	f	f	PROPN
ejpam-5942	115	32	and	and	CCONJ
ejpam-5942	115	33	g.	g.	PROPN
ejpam-5942	115	34	(	(	PUNCT
ejpam-5942	115	35	r1.1	r1.1	PROPN
ejpam-5942	115	36	)	)	PUNCT
ejpam-5942	115	37	let	let	VERB
ejpam-5942	115	38	l	l	NOUN
ejpam-5942	115	39	=	=	SYM
ejpam-5942	115	40	3	3	NUM
ejpam-5942	115	41	,	,	PUNCT
ejpam-5942	115	42	w(u	w(u	PROPN
ejpam-5942	115	43	→	→	SYM
ejpam-5942	115	44	f	f	X
ejpam-5942	115	45	)	)	PUNCT
ejpam-5942	115	46	=	=	SYM
ejpam-5942	115	47	1	1	NUM
ejpam-5942	115	48	3	3	NUM
ejpam-5942	115	49	when	when	SCONJ
ejpam-5942	115	50	the	the	DET
ejpam-5942	115	51	incident	incident	NOUN
ejpam-5942	115	52	vertex	vertex	NOUN
ejpam-5942	115	53	of	of	ADP
ejpam-5942	115	54	f	f	PROPN
ejpam-5942	115	55	not	not	PART
ejpam-5942	115	56	incident	incident	VERB
ejpam-5942	115	57	to	to	ADP
ejpam-5942	115	58	g	g	PROPN
ejpam-5942	115	59	is	be	AUX
ejpam-5942	115	60	a	a	DET
ejpam-5942	115	61	4	4	NUM
ejpam-5942	115	62	+	+	SYM
ejpam-5942	115	63	-vertex	-vertex	NOUN
ejpam-5942	115	64	.	.	PUNCT
ejpam-5942	116	1	(	(	PUNCT
ejpam-5942	116	2	r1.2	r1.2	NOUN
ejpam-5942	116	3	)	)	PUNCT
ejpam-5942	116	4	let	let	VERB
ejpam-5942	116	5	l	l	NOUN
ejpam-5942	116	6	≥	≥	NUM
ejpam-5942	116	7	6	6	NUM
ejpam-5942	116	8	,	,	PUNCT
ejpam-5942	116	9	w(g	w(g	PROPN
ejpam-5942	116	10	→	→	SYM
ejpam-5942	116	11	f	f	X
ejpam-5942	116	12	)	)	PUNCT
ejpam-5942	116	13	=	=	SYM
ejpam-5942	116	14	1	1	NUM
ejpam-5942	116	15	2	2	NUM
ejpam-5942	116	16	if	if	SCONJ
ejpam-5942	116	17	g	g	PROPN
ejpam-5942	116	18	is	be	AUX
ejpam-5942	116	19	a	a	DET
ejpam-5942	116	20	thin	thin	ADJ
ejpam-5942	116	21	adjacent	adjacent	ADJ
ejpam-5942	116	22	face	face	NOUN
ejpam-5942	116	23	of	of	ADP
ejpam-5942	116	24	f	f	PROPN
ejpam-5942	116	25	,	,	PUNCT
ejpam-5942	116	26	otherwise	otherwise	ADV
ejpam-5942	116	27	w(g	w(g	PROPN
ejpam-5942	116	28	→	→	SYM
ejpam-5942	116	29	f	f	X
ejpam-5942	116	30	)	)	PUNCT
ejpam-5942	116	31	=	=	SYM
ejpam-5942	116	32	1	1	NUM
ejpam-5942	116	33	3	3	NUM
ejpam-5942	116	34	.	.	PUNCT
ejpam-5942	117	1	(	(	PUNCT
ejpam-5942	117	2	r2	r2	PROPN
ejpam-5942	117	3	)	)	PUNCT
ejpam-5942	117	4	for	for	ADP
ejpam-5942	117	5	a	a	DET
ejpam-5942	117	6	5	5	NUM
ejpam-5942	117	7	+	+	SYM
ejpam-5942	117	8	-vertex	-vertex	NOUN
ejpam-5942	117	9	u	u	NOUN
ejpam-5942	117	10	,	,	PUNCT
ejpam-5942	117	11	w(u→	w(u→	NOUN
ejpam-5942	117	12	v	v	NOUN
ejpam-5942	117	13	)	)	PUNCT
ejpam-5942	117	14	=	=	SYM
ejpam-5942	117	15	1	1	NUM
ejpam-5942	117	16	3	3	NUM
ejpam-5942	117	17	for	for	ADP
ejpam-5942	117	18	each	each	DET
ejpam-5942	117	19	its	its	PRON
ejpam-5942	117	20	adjacent	adjacent	ADJ
ejpam-5942	117	21	3	3	NUM
ejpam-5942	117	22	-	-	PUNCT
ejpam-5942	117	23	vertex	vertex	NOUN
ejpam-5942	117	24	v.	v.	ADP
ejpam-5942	117	25	now	now	ADV
ejpam-5942	117	26	,	,	PUNCT
ejpam-5942	117	27	it	it	PRON
ejpam-5942	117	28	is	be	AUX
ejpam-5942	117	29	necessary	necessary	ADJ
ejpam-5942	117	30	to	to	PART
ejpam-5942	117	31	claim	claim	VERB
ejpam-5942	117	32	that	that	SCONJ
ejpam-5942	117	33	µ	µ	X
ejpam-5942	117	34	∗	∗	NOUN
ejpam-5942	117	35	(	(	PUNCT
ejpam-5942	117	36	z	z	NOUN
ejpam-5942	117	37	)	)	PUNCT
ejpam-5942	117	38	≥	≥	X
ejpam-5942	117	39	0	0	NUM
ejpam-5942	117	40	follows	follow	VERB
ejpam-5942	117	41	discharge	discharge	NOUN
ejpam-5942	117	42	for	for	ADP
ejpam-5942	117	43	each	each	DET
ejpam-5942	117	44	z	z	NOUN
ejpam-5942	117	45	∈	∈	PROPN
ejpam-5942	117	46	v	v	ADP
ejpam-5942	117	47	(	(	PUNCT
ejpam-5942	117	48	h	h	NOUN
ejpam-5942	117	49	′	′	NOUN
ejpam-5942	117	50	)	)	PUNCT
ejpam-5942	117	51	∪	∪	PROPN
ejpam-5942	117	52	f	f	PROPN
ejpam-5942	117	53	(	(	PUNCT
ejpam-5942	117	54	h	h	NOUN
ejpam-5942	117	55	′	′	NUM
ejpam-5942	117	56	)	)	PUNCT
ejpam-5942	117	57	.	.	PUNCT
ejpam-5942	118	1	it	it	PRON
ejpam-5942	118	2	is	be	AUX
ejpam-5942	118	3	clear	clear	ADJ
ejpam-5942	118	4	that	that	SCONJ
ejpam-5942	118	5	if	if	SCONJ
ejpam-5942	118	6	f	f	PROPN
ejpam-5942	118	7	is	be	AUX
ejpam-5942	118	8	a	a	DET
ejpam-5942	118	9	4	4	NUM
ejpam-5942	118	10	-	-	PUNCT
ejpam-5942	118	11	face	face	NOUN
ejpam-5942	118	12	or	or	CCONJ
ejpam-5942	118	13	5	5	NUM
ejpam-5942	118	14	-	-	PUNCT
ejpam-5942	118	15	face	face	NOUN
ejpam-5942	118	16	,	,	PUNCT
ejpam-5942	118	17	then	then	ADV
ejpam-5942	118	18	µ∗(f	µ∗(f	NUM
ejpam-5942	118	19	)	)	PUNCT
ejpam-5942	118	20	=	=	SYM
ejpam-5942	118	21	0	0	NUM
ejpam-5942	118	22	or	or	CCONJ
ejpam-5942	118	23	1	1	NUM
ejpam-5942	118	24	respectively	respectively	ADV
ejpam-5942	118	25	.	.	PUNCT
ejpam-5942	119	1	case	case	NOUN
ejpam-5942	119	2	1	1	NUM
ejpam-5942	119	3	:	:	PUNCT
ejpam-5942	119	4	consider	consider	VERB
ejpam-5942	119	5	a	a	DET
ejpam-5942	119	6	3	3	NUM
ejpam-5942	119	7	-	-	PUNCT
ejpam-5942	119	8	face	face	NOUN
ejpam-5942	119	9	f	f	NOUN
ejpam-5942	119	10	.	.	PUNCT
ejpam-5942	120	1	let	let	VERB
ejpam-5942	120	2	f1	f1	NOUN
ejpam-5942	120	3	,	,	PUNCT
ejpam-5942	120	4	f2	f2	PROPN
ejpam-5942	120	5	,	,	PUNCT
ejpam-5942	120	6	and	and	CCONJ
ejpam-5942	120	7	f3	f3	PROPN
ejpam-5942	120	8	be	be	AUX
ejpam-5942	120	9	adjacent	adjacent	ADJ
ejpam-5942	120	10	faces	face	NOUN
ejpam-5942	120	11	of	of	ADP
ejpam-5942	120	12	f	f	PRON
ejpam-5942	120	13	where	where	SCONJ
ejpam-5942	120	14	fi	fi	NOUN
ejpam-5942	120	15	is	be	AUX
ejpam-5942	120	16	incident	incident	NOUN
ejpam-5942	120	17	to	to	ADP
ejpam-5942	120	18	vi	vi	PROPN
ejpam-5942	120	19	and	and	CCONJ
ejpam-5942	120	20	vi+1	vi+1	ADV
ejpam-5942	120	21	.	.	PUNCT
ejpam-5942	121	1	we	we	PRON
ejpam-5942	121	2	consider	consider	VERB
ejpam-5942	121	3	three	three	NUM
ejpam-5942	121	4	cases	case	NOUN
ejpam-5942	121	5	by	by	ADP
ejpam-5942	121	6	lemma	lemma	PROPN
ejpam-5942	121	7	3	3	NUM
ejpam-5942	121	8	(	(	PUNCT
ejpam-5942	121	9	iii	iii	NOUN
ejpam-5942	121	10	)	)	PUNCT
ejpam-5942	121	11	.	.	PUNCT
ejpam-5942	122	1	a	a	DET
ejpam-5942	122	2	face	face	NOUN
ejpam-5942	122	3	f	f	NOUN
ejpam-5942	122	4	is	be	AUX
ejpam-5942	122	5	not	not	PART
ejpam-5942	122	6	incident	incident	NOUN
ejpam-5942	122	7	to	to	ADP
ejpam-5942	122	8	a	a	DET
ejpam-5942	122	9	3	3	NUM
ejpam-5942	122	10	-	-	PUNCT
ejpam-5942	122	11	face	face	NOUN
ejpam-5942	122	12	.	.	PUNCT
ejpam-5942	123	1	it	it	PRON
ejpam-5942	123	2	follows	follow	VERB
ejpam-5942	123	3	that	that	SCONJ
ejpam-5942	123	4	µ∗(f	µ∗(f	PROPN
ejpam-5942	123	5	)	)	PUNCT
ejpam-5942	123	6	≥	≥	NOUN
ejpam-5942	123	7	µ(f	µ(f	PROPN
ejpam-5942	123	8	)	)	PUNCT
ejpam-5942	124	1	+	+	PUNCT
ejpam-5942	125	1	3×	3×	NUM
ejpam-5942	125	2	1	1	NUM
ejpam-5942	125	3	3	3	NUM
ejpam-5942	125	4	=	=	SYM
ejpam-5942	125	5	0	0	NUM
ejpam-5942	125	6	by	by	ADP
ejpam-5942	125	7	(	(	PUNCT
ejpam-5942	125	8	r1.2	r1.2	NOUN
ejpam-5942	125	9	)	)	PUNCT
ejpam-5942	125	10	.	.	PUNCT
ejpam-5942	126	1	a	a	DET
ejpam-5942	126	2	face	face	NOUN
ejpam-5942	126	3	f	f	NOUN
ejpam-5942	126	4	is	be	AUX
ejpam-5942	126	5	incident	incident	NOUN
ejpam-5942	126	6	to	to	ADP
ejpam-5942	126	7	exactly	exactly	ADV
ejpam-5942	126	8	one	one	NUM
ejpam-5942	126	9	3	3	NUM
ejpam-5942	126	10	-	-	PUNCT
ejpam-5942	126	11	face	face	NOUN
ejpam-5942	126	12	,	,	PUNCT
ejpam-5942	126	13	say	say	VERB
ejpam-5942	126	14	f1	f1	NOUN
ejpam-5942	126	15	.	.	PUNCT
ejpam-5942	127	1	it	it	PRON
ejpam-5942	127	2	follows	follow	VERB
ejpam-5942	127	3	that	that	SCONJ
ejpam-5942	127	4	v1	v1	NOUN
ejpam-5942	127	5	and	and	CCONJ
ejpam-5942	127	6	v2	v2	NOUN
ejpam-5942	127	7	are	be	AUX
ejpam-5942	127	8	rough	rough	ADJ
ejpam-5942	127	9	vertices	vertex	NOUN
ejpam-5942	127	10	of	of	ADP
ejpam-5942	127	11	f	f	PROPN
ejpam-5942	127	12	and	and	CCONJ
ejpam-5942	127	13	f1	f1	NOUN
ejpam-5942	127	14	.	.	PUNCT
ejpam-5942	128	1	if	if	SCONJ
ejpam-5942	128	2	v1	v1	NOUN
ejpam-5942	128	3	and	and	CCONJ
ejpam-5942	128	4	v2	v2	NOUN
ejpam-5942	128	5	are	be	AUX
ejpam-5942	128	6	4	4	NUM
ejpam-5942	128	7	-	-	PUNCT
ejpam-5942	128	8	vertices	vertex	NOUN
ejpam-5942	128	9	or	or	CCONJ
ejpam-5942	128	10	v3	v3	PROPN
ejpam-5942	128	11	is	be	AUX
ejpam-5942	128	12	a	a	DET
ejpam-5942	128	13	3	3	NUM
ejpam-5942	128	14	-	-	PUNCT
ejpam-5942	128	15	vertex	vertex	NOUN
ejpam-5942	128	16	,	,	PUNCT
ejpam-5942	128	17	then	then	ADV
ejpam-5942	128	18	f2	f2	PROPN
ejpam-5942	128	19	and	and	CCONJ
ejpam-5942	128	20	f3	f3	PROPN
ejpam-5942	128	21	are	be	AUX
ejpam-5942	128	22	thin	thin	ADJ
ejpam-5942	128	23	adjacent	adjacent	ADJ
ejpam-5942	128	24	6	6	NUM
ejpam-5942	128	25	+	+	SYM
ejpam-5942	128	26	-faces	-face	NOUN
ejpam-5942	128	27	of	of	ADP
ejpam-5942	128	28	f	f	NOUN
ejpam-5942	128	29	by	by	ADP
ejpam-5942	128	30	lemma	lemma	PROPN
ejpam-5942	128	31	3	3	NUM
ejpam-5942	128	32	(	(	PUNCT
ejpam-5942	128	33	i	i	NOUN
ejpam-5942	128	34	)	)	PUNCT
ejpam-5942	128	35	or	or	CCONJ
ejpam-5942	128	36	lemma	lemma	PROPN
ejpam-5942	128	37	3	3	NUM
ejpam-5942	128	38	(	(	PUNCT
ejpam-5942	128	39	ii	ii	NOUN
ejpam-5942	128	40	)	)	PUNCT
ejpam-5942	128	41	,	,	PUNCT
ejpam-5942	128	42	respectively	respectively	ADV
ejpam-5942	128	43	.	.	PUNCT
ejpam-5942	129	1	then	then	ADV
ejpam-5942	129	2	µ∗(f	µ∗(f	PROPN
ejpam-5942	129	3	)	)	PUNCT
ejpam-5942	129	4	≥	≥	NOUN
ejpam-5942	129	5	µ(f	µ(f	PROPN
ejpam-5942	129	6	)	)	PUNCT
ejpam-5942	130	1	+	+	CCONJ
ejpam-5942	130	2	2	2	NUM
ejpam-5942	130	3	×	×	NOUN
ejpam-5942	130	4	1	1	NUM
ejpam-5942	130	5	2	2	NUM
ejpam-5942	130	6	=	=	SYM
ejpam-5942	130	7	0	0	NUM
ejpam-5942	130	8	by	by	ADP
ejpam-5942	130	9	(	(	PUNCT
ejpam-5942	130	10	r1.2	r1.2	NOUN
ejpam-5942	130	11	)	)	PUNCT
ejpam-5942	130	12	.	.	PUNCT
ejpam-5942	131	1	p.	p.	NOUN
ejpam-5942	131	2	sittitrai	sittitrai	NOUN
ejpam-5942	131	3	,	,	PUNCT
ejpam-5942	131	4	k.	k.	PROPN
ejpam-5942	131	5	nakprasit	nakprasit	PROPN
ejpam-5942	131	6	,	,	PUNCT
ejpam-5942	131	7	p.	p.	PROPN
ejpam-5942	131	8	jumnongnit	jumnongnit	PROPN
ejpam-5942	131	9	/	/	SYM
ejpam-5942	131	10	eur	eur	PROPN
ejpam-5942	131	11	.	.	PUNCT
ejpam-5942	132	1	j.	j.	PROPN
ejpam-5942	132	2	pure	pure	PROPN
ejpam-5942	132	3	appl	appl	PROPN
ejpam-5942	132	4	.	.	PROPN
ejpam-5942	132	5	math	math	PROPN
ejpam-5942	132	6	,	,	PUNCT
ejpam-5942	132	7	18	18	NUM
ejpam-5942	132	8	(	(	PUNCT
ejpam-5942	132	9	2	2	NUM
ejpam-5942	132	10	)	)	PUNCT
ejpam-5942	132	11	(	(	PUNCT
ejpam-5942	132	12	2025	2025	NUM
ejpam-5942	132	13	)	)	PUNCT
ejpam-5942	132	14	,	,	PUNCT
ejpam-5942	132	15	5942	5942	NUM
ejpam-5942	132	16	5	5	NUM
ejpam-5942	132	17	of	of	ADP
ejpam-5942	132	18	7	7	NUM
ejpam-5942	132	19	if	if	SCONJ
ejpam-5942	132	20	v1	v1	NOUN
ejpam-5942	132	21	or	or	CCONJ
ejpam-5942	132	22	v2	v2	NOUN
ejpam-5942	132	23	is	be	AUX
ejpam-5942	132	24	a	a	DET
ejpam-5942	132	25	5	5	NUM
ejpam-5942	132	26	+	+	SYM
ejpam-5942	132	27	-vertex	-vertex	NOUN
ejpam-5942	132	28	or	or	CCONJ
ejpam-5942	132	29	v3	v3	PROPN
ejpam-5942	132	30	is	be	AUX
ejpam-5942	132	31	a	a	DET
ejpam-5942	132	32	4	4	NUM
ejpam-5942	132	33	+	+	SYM
ejpam-5942	132	34	-vertex	-vertex	NOUN
ejpam-5942	132	35	,	,	PUNCT
ejpam-5942	132	36	then	then	ADV
ejpam-5942	132	37	v1	v1	VERB
ejpam-5942	132	38	or	or	CCONJ
ejpam-5942	132	39	v2	v2	NOUN
ejpam-5942	132	40	gives	give	VERB
ejpam-5942	132	41	charge	charge	VERB
ejpam-5942	132	42	1	1	NUM
ejpam-5942	132	43	3	3	NUM
ejpam-5942	132	44	to	to	ADP
ejpam-5942	132	45	f	f	PROPN
ejpam-5942	132	46	by	by	ADP
ejpam-5942	132	47	(	(	PUNCT
ejpam-5942	132	48	r1.1	r1.1	NOUN
ejpam-5942	132	49	)	)	PUNCT
ejpam-5942	132	50	.	.	PUNCT
ejpam-5942	133	1	combining	combine	VERB
ejpam-5942	133	2	with	with	ADP
ejpam-5942	133	3	(	(	PUNCT
ejpam-5942	133	4	r1.2	r1.2	NOUN
ejpam-5942	133	5	)	)	PUNCT
ejpam-5942	133	6	,	,	PUNCT
ejpam-5942	133	7	we	we	PRON
ejpam-5942	133	8	have	have	VERB
ejpam-5942	133	9	µ∗(f	µ∗(f	NUM
ejpam-5942	133	10	)	)	PUNCT
ejpam-5942	133	11	≥	≥	NOUN
ejpam-5942	133	12	µ(f	µ(f	PROPN
ejpam-5942	133	13	)	)	PUNCT
ejpam-5942	134	1	+	+	PUNCT
ejpam-5942	135	1	3×	3×	NUM
ejpam-5942	135	2	1	1	NUM
ejpam-5942	135	3	3	3	NUM
ejpam-5942	135	4	=	=	SYM
ejpam-5942	135	5	0	0	NUM
ejpam-5942	135	6	.	.	PUNCT
ejpam-5942	136	1	a	a	DET
ejpam-5942	136	2	face	face	NOUN
ejpam-5942	136	3	f	f	NOUN
ejpam-5942	136	4	is	be	AUX
ejpam-5942	136	5	incident	incident	NOUN
ejpam-5942	136	6	to	to	ADP
ejpam-5942	136	7	two	two	NUM
ejpam-5942	136	8	3	3	NUM
ejpam-5942	136	9	-	-	PUNCT
ejpam-5942	136	10	faces	face	NOUN
ejpam-5942	136	11	,	,	PUNCT
ejpam-5942	136	12	say	say	VERB
ejpam-5942	136	13	f1	f1	NOUN
ejpam-5942	136	14	and	and	CCONJ
ejpam-5942	136	15	f2	f2	PROPN
ejpam-5942	136	16	.	.	PUNCT
ejpam-5942	137	1	note	note	VERB
ejpam-5942	137	2	that	that	SCONJ
ejpam-5942	137	3	v2	v2	PROPN
ejpam-5942	137	4	is	be	AUX
ejpam-5942	137	5	incident	incident	NOUN
ejpam-5942	137	6	to	to	ADP
ejpam-5942	137	7	three	three	NUM
ejpam-5942	137	8	consecutive	consecutive	ADJ
ejpam-5942	137	9	3	3	NUM
ejpam-5942	137	10	-	-	PUNCT
ejpam-5942	137	11	faces	face	NOUN
ejpam-5942	137	12	.	.	PUNCT
ejpam-5942	138	1	then	then	ADV
ejpam-5942	138	2	v2	v2	PROPN
ejpam-5942	138	3	is	be	AUX
ejpam-5942	138	4	a	a	DET
ejpam-5942	138	5	3	3	NUM
ejpam-5942	138	6	-	-	PUNCT
ejpam-5942	138	7	vertex	vertex	NOUN
ejpam-5942	138	8	by	by	ADP
ejpam-5942	138	9	lemma	lemma	PROPN
ejpam-5942	138	10	3	3	NUM
ejpam-5942	138	11	(	(	PUNCT
ejpam-5942	138	12	ii	ii	NOUN
ejpam-5942	138	13	)	)	PUNCT
ejpam-5942	138	14	.	.	PUNCT
ejpam-5942	139	1	moreover	moreover	ADV
ejpam-5942	139	2	,	,	PUNCT
ejpam-5942	139	3	v1	v1	PROPN
ejpam-5942	139	4	and	and	CCONJ
ejpam-5942	139	5	v3	v3	PROPN
ejpam-5942	139	6	are	be	AUX
ejpam-5942	139	7	5	5	NUM
ejpam-5942	139	8	+	+	SYM
ejpam-5942	139	9	-vertices	-vertice	NOUN
ejpam-5942	139	10	by	by	ADP
ejpam-5942	139	11	lemma	lemma	PROPN
ejpam-5942	139	12	1	1	NUM
ejpam-5942	139	13	(	(	PUNCT
ejpam-5942	139	14	iii	iii	NOUN
ejpam-5942	139	15	)	)	PUNCT
ejpam-5942	139	16	.	.	PUNCT
ejpam-5942	140	1	similarly	similarly	ADV
ejpam-5942	140	2	,	,	PUNCT
ejpam-5942	140	3	a	a	DET
ejpam-5942	140	4	vertex	vertex	NOUN
ejpam-5942	140	5	incident	incident	NOUN
ejpam-5942	140	6	to	to	ADP
ejpam-5942	140	7	f1	f1	NOUN
ejpam-5942	140	8	or	or	CCONJ
ejpam-5942	140	9	f2	f2	NOUN
ejpam-5942	140	10	but	but	CCONJ
ejpam-5942	140	11	not	not	PART
ejpam-5942	140	12	incident	incident	NOUN
ejpam-5942	140	13	to	to	ADP
ejpam-5942	140	14	f	f	PROPN
ejpam-5942	140	15	is	be	AUX
ejpam-5942	140	16	a	a	DET
ejpam-5942	140	17	5	5	NUM
ejpam-5942	140	18	+	+	SYM
ejpam-5942	140	19	-vertex	-vertex	NOUN
ejpam-5942	140	20	.	.	PUNCT
ejpam-5942	141	1	then	then	ADV
ejpam-5942	141	2	each	each	PRON
ejpam-5942	141	3	of	of	ADP
ejpam-5942	141	4	v1	v1	NOUN
ejpam-5942	141	5	,	,	PUNCT
ejpam-5942	141	6	v2	v2	NOUN
ejpam-5942	141	7	,	,	PUNCT
ejpam-5942	141	8	and	and	CCONJ
ejpam-5942	141	9	f3	f3	PROPN
ejpam-5942	141	10	gives	gives	AUX
ejpam-5942	141	11	charge	charge	VERB
ejpam-5942	141	12	1	1	NUM
ejpam-5942	141	13	3	3	NUM
ejpam-5942	141	14	to	to	ADP
ejpam-5942	141	15	f	f	PROPN
ejpam-5942	141	16	by	by	ADP
ejpam-5942	141	17	(	(	PUNCT
ejpam-5942	141	18	r1	r1	PROPN
ejpam-5942	141	19	)	)	PUNCT
ejpam-5942	141	20	.	.	PUNCT
ejpam-5942	142	1	thus	thus	ADV
ejpam-5942	142	2	µ∗(f	µ∗(f	NUM
ejpam-5942	142	3	)	)	PUNCT
ejpam-5942	142	4	≥	≥	NOUN
ejpam-5942	142	5	µ(f	µ(f	PROPN
ejpam-5942	142	6	)	)	PUNCT
ejpam-5942	143	1	+	+	PUNCT
ejpam-5942	143	2	3×	3×	NUM
ejpam-5942	143	3	1	1	NUM
ejpam-5942	143	4	3	3	NUM
ejpam-5942	143	5	=	=	SYM
ejpam-5942	143	6	0	0	NUM
ejpam-5942	143	7	.	.	PUNCT
ejpam-5942	143	8	case	case	NOUN
ejpam-5942	143	9	2	2	NUM
ejpam-5942	143	10	:	:	PUNCT
ejpam-5942	143	11	consider	consider	VERB
ejpam-5942	143	12	a	a	DET
ejpam-5942	143	13	6	6	NUM
ejpam-5942	143	14	+	+	NOUN
ejpam-5942	143	15	-face	-face	NOUN
ejpam-5942	143	16	.	.	PUNCT
ejpam-5942	144	1	let	let	VERB
ejpam-5942	144	2	f	f	PRON
ejpam-5942	144	3	be	be	AUX
ejpam-5942	144	4	an	an	DET
ejpam-5942	144	5	l	l	NOUN
ejpam-5942	144	6	-	-	NOUN
ejpam-5942	144	7	face	face	NOUN
ejpam-5942	144	8	where	where	SCONJ
ejpam-5942	144	9	l	l	NOUN
ejpam-5942	144	10	≥	≥	NUM
ejpam-5942	144	11	6	6	NUM
ejpam-5942	144	12	.	.	PUNCT
ejpam-5942	145	1	we	we	PRON
ejpam-5942	145	2	let	let	VERB
ejpam-5942	145	3	f1	f1	NOUN
ejpam-5942	145	4	,	,	PUNCT
ejpam-5942	145	5	.	.	PUNCT
ejpam-5942	145	6	.	.	PUNCT
ejpam-5942	146	1	.	.	PUNCT
ejpam-5942	147	1	,	,	PUNCT
ejpam-5942	147	2	fl	fl	NUM
ejpam-5942	147	3	adjacent	adjacent	ADJ
ejpam-5942	147	4	faces	face	NOUN
ejpam-5942	147	5	of	of	ADP
ejpam-5942	147	6	f	f	PROPN
ejpam-5942	147	7	in	in	ADP
ejpam-5942	147	8	clockwise	clockwise	NOUN
ejpam-5942	147	9	order	order	NOUN
ejpam-5942	147	10	.	.	PUNCT
ejpam-5942	148	1	for	for	ADP
ejpam-5942	148	2	the	the	DET
ejpam-5942	148	3	convenience	convenience	NOUN
ejpam-5942	148	4	of	of	ADP
ejpam-5942	148	5	calculating	calculate	VERB
ejpam-5942	148	6	µ∗(f	µ∗(f	PROPN
ejpam-5942	148	7	)	)	PUNCT
ejpam-5942	148	8	,	,	PUNCT
ejpam-5942	148	9	we	we	PRON
ejpam-5942	148	10	redistribute	redistribute	VERB
ejpam-5942	148	11	the	the	DET
ejpam-5942	148	12	charge	charge	NOUN
ejpam-5942	148	13	that	that	PRON
ejpam-5942	148	14	was	be	AUX
ejpam-5942	148	15	transferred	transfer	VERB
ejpam-5942	148	16	from	from	ADP
ejpam-5942	148	17	f	f	PROPN
ejpam-5942	148	18	as	as	SCONJ
ejpam-5942	148	19	follows	follow	VERB
ejpam-5942	148	20	.	.	PUNCT
ejpam-5942	149	1	first	first	ADV
ejpam-5942	149	2	,	,	PUNCT
ejpam-5942	149	3	we	we	PRON
ejpam-5942	149	4	give	give	VERB
ejpam-5942	149	5	w(f	w(f	PROPN
ejpam-5942	149	6	→	→	SYM
ejpam-5942	149	7	fi	fi	NOUN
ejpam-5942	149	8	)	)	PUNCT
ejpam-5942	149	9	=	=	SYM
ejpam-5942	149	10	1	1	NUM
ejpam-5942	149	11	3	3	NUM
ejpam-5942	149	12	for	for	ADP
ejpam-5942	149	13	each	each	DET
ejpam-5942	149	14	fi	fi	NOUN
ejpam-5942	149	15	where	where	SCONJ
ejpam-5942	149	16	fi	fi	NOUN
ejpam-5942	149	17	transfer	transfer	VERB
ejpam-5942	149	18	its	its	PRON
ejpam-5942	149	19	charge	charge	NOUN
ejpam-5942	149	20	1	1	NUM
ejpam-5942	149	21	6	6	NUM
ejpam-5942	149	22	revived	revive	VERB
ejpam-5942	149	23	form	form	NOUN
ejpam-5942	149	24	f	f	X
ejpam-5942	149	25	to	to	ADP
ejpam-5942	149	26	fi−1	fi−1	PROPN
ejpam-5942	149	27	and	and	CCONJ
ejpam-5942	149	28	fi+1	fi+1	NOUN
ejpam-5942	149	29	.	.	PUNCT
ejpam-5942	150	1	one	one	PRON
ejpam-5942	150	2	can	can	AUX
ejpam-5942	150	3	see	see	VERB
ejpam-5942	150	4	that	that	SCONJ
ejpam-5942	150	5	the	the	DET
ejpam-5942	150	6	process	process	NOUN
ejpam-5942	150	7	is	be	AUX
ejpam-5942	150	8	as	as	SCONJ
ejpam-5942	150	9	described	describe	VERB
ejpam-5942	150	10	in	in	ADP
ejpam-5942	150	11	(	(	PUNCT
ejpam-5942	150	12	r1.2	r1.2	NOUN
ejpam-5942	150	13	)	)	PUNCT
ejpam-5942	150	14	.	.	PUNCT
ejpam-5942	151	1	if	if	SCONJ
ejpam-5942	151	2	fi	fi	NOUN
ejpam-5942	151	3	is	be	AUX
ejpam-5942	151	4	a	a	DET
ejpam-5942	151	5	3	3	NUM
ejpam-5942	151	6	-	-	PUNCT
ejpam-5942	151	7	face	face	NOUN
ejpam-5942	151	8	being	be	AUX
ejpam-5942	151	9	not	not	PART
ejpam-5942	151	10	a	a	DET
ejpam-5942	151	11	thin	thin	ADJ
ejpam-5942	151	12	adjacent	adjacent	ADJ
ejpam-5942	151	13	face	face	NOUN
ejpam-5942	151	14	of	of	ADP
ejpam-5942	151	15	f	f	PROPN
ejpam-5942	151	16	,	,	PUNCT
ejpam-5942	151	17	then	then	ADV
ejpam-5942	151	18	w(f	w(f	PROPN
ejpam-5942	151	19	→	→	SYM
ejpam-5942	151	20	fi	fi	NOUN
ejpam-5942	151	21	)	)	PUNCT
ejpam-5942	151	22	≥	≥	NOUN
ejpam-5942	151	23	1	1	NUM
ejpam-5942	151	24	3	3	NUM
ejpam-5942	151	25	.	.	PUNCT
ejpam-5942	152	1	if	if	SCONJ
ejpam-5942	152	2	fi	fi	NOUN
ejpam-5942	152	3	is	be	AUX
ejpam-5942	152	4	a	a	DET
ejpam-5942	152	5	thin	thin	ADJ
ejpam-5942	152	6	adjacent	adjacent	ADJ
ejpam-5942	152	7	3	3	NUM
ejpam-5942	152	8	-	-	PUNCT
ejpam-5942	152	9	face	face	NOUN
ejpam-5942	152	10	of	of	ADP
ejpam-5942	152	11	f	f	PROPN
ejpam-5942	152	12	,	,	PUNCT
ejpam-5942	152	13	then	then	ADV
ejpam-5942	152	14	w(f	w(f	PROPN
ejpam-5942	152	15	→	→	SYM
ejpam-5942	152	16	fi	fi	NOUN
ejpam-5942	152	17	)	)	PUNCT
ejpam-5942	152	18	≥	≥	NOUN
ejpam-5942	152	19	1	1	NUM
ejpam-5942	152	20	3	3	NUM
ejpam-5942	152	21	+	+	CCONJ
ejpam-5942	152	22	1	1	NUM
ejpam-5942	152	23	6	6	NUM
ejpam-5942	152	24	=	=	SYM
ejpam-5942	152	25	1	1	NUM
ejpam-5942	152	26	2	2	NUM
ejpam-5942	152	27	.	.	PUNCT
ejpam-5942	153	1	if	if	SCONJ
ejpam-5942	153	2	fi	fi	NOUN
ejpam-5942	153	3	is	be	AUX
ejpam-5942	153	4	a	a	DET
ejpam-5942	153	5	4	4	NUM
ejpam-5942	153	6	+	+	NOUN
ejpam-5942	153	7	-face	-face	NOUN
ejpam-5942	153	8	,	,	PUNCT
ejpam-5942	153	9	then	then	ADV
ejpam-5942	153	10	w(f	w(f	PROPN
ejpam-5942	153	11	→	→	SYM
ejpam-5942	153	12	fi	fi	NOUN
ejpam-5942	153	13	)	)	PUNCT
ejpam-5942	153	14	≥	≥	NOUN
ejpam-5942	153	15	1	1	NUM
ejpam-5942	153	16	3	3	NUM
ejpam-5942	153	17	−	−	NUM
ejpam-5942	153	18	2×	2×	NUM
ejpam-5942	153	19	1	1	NUM
ejpam-5942	153	20	3	3	NUM
ejpam-5942	153	21	=	=	SYM
ejpam-5942	153	22	0	0	NUM
ejpam-5942	153	23	.	.	PUNCT
ejpam-5942	154	1	hence	hence	ADV
ejpam-5942	154	2	,	,	PUNCT
ejpam-5942	154	3	µ∗(f	µ∗(f	PROPN
ejpam-5942	154	4	)	)	PUNCT
ejpam-5942	154	5	≥	≥	NOUN
ejpam-5942	154	6	µ(f)−	µ(f)−	PROPN
ejpam-5942	154	7	l	l	NOUN
ejpam-5942	154	8	×	×	NOUN
ejpam-5942	154	9	1	1	NUM
ejpam-5942	154	10	3	3	NUM
ejpam-5942	154	11	=	=	SYM
ejpam-5942	154	12	l	l	NOUN
ejpam-5942	154	13	−	−	PROPN
ejpam-5942	155	1	4−	4−	NOUN
ejpam-5942	155	2	l	l	NOUN
ejpam-5942	155	3	×	×	NOUN
ejpam-5942	155	4	1	1	NUM
ejpam-5942	155	5	3	3	NUM
ejpam-5942	155	6	=	=	SYM
ejpam-5942	155	7	l	l	NOUN
ejpam-5942	155	8	×	×	NOUN
ejpam-5942	155	9	2	2	NUM
ejpam-5942	155	10	3	3	NUM
ejpam-5942	155	11	−	−	PROPN
ejpam-5942	155	12	4	4	NUM
ejpam-5942	155	13	≥	≥	NOUN
ejpam-5942	155	14	0	0	NUM
ejpam-5942	155	15	as	as	SCONJ
ejpam-5942	155	16	desired	desire	VERB
ejpam-5942	155	17	.	.	PUNCT
ejpam-5942	156	1	case	case	NOUN
ejpam-5942	156	2	3	3	NUM
ejpam-5942	156	3	:	:	PUNCT
ejpam-5942	156	4	consider	consider	VERB
ejpam-5942	156	5	a	a	DET
ejpam-5942	156	6	3	3	NUM
ejpam-5942	156	7	-	-	PUNCT
ejpam-5942	156	8	vertex	vertex	NOUN
ejpam-5942	156	9	v.	v.	NOUN
ejpam-5942	156	10	by	by	ADP
ejpam-5942	156	11	lemma	lemma	PROPN
ejpam-5942	156	12	1(ii	1(ii	NUM
ejpam-5942	156	13	)	)	PUNCT
ejpam-5942	156	14	,	,	PUNCT
ejpam-5942	156	15	v	v	NOUN
ejpam-5942	156	16	is	be	AUX
ejpam-5942	156	17	not	not	PART
ejpam-5942	156	18	adjacent	adjacent	ADJ
ejpam-5942	156	19	to	to	ADP
ejpam-5942	156	20	any	any	DET
ejpam-5942	156	21	4−-vertices	4−-vertices	NUM
ejpam-5942	156	22	.	.	PUNCT
ejpam-5942	157	1	thus	thus	ADV
ejpam-5942	157	2	µ∗(v	µ∗(v	PRON
ejpam-5942	157	3	)	)	PUNCT
ejpam-5942	157	4	≥	≥	NOUN
ejpam-5942	157	5	µ(v	µ(v	PROPN
ejpam-5942	157	6	)	)	PUNCT
ejpam-5942	158	1	+	+	CCONJ
ejpam-5942	158	2	3×	3×	NUM
ejpam-5942	158	3	1	1	NUM
ejpam-5942	158	4	3	3	NUM
ejpam-5942	158	5	=	=	SYM
ejpam-5942	158	6	0	0	NUM
ejpam-5942	158	7	by	by	ADP
ejpam-5942	158	8	(	(	PUNCT
ejpam-5942	158	9	r2	r2	PROPN
ejpam-5942	158	10	)	)	PUNCT
ejpam-5942	158	11	case	case	NOUN
ejpam-5942	158	12	4	4	NUM
ejpam-5942	158	13	:	:	PUNCT
ejpam-5942	158	14	consider	consider	VERB
ejpam-5942	158	15	a	a	DET
ejpam-5942	158	16	5	5	NUM
ejpam-5942	158	17	-	-	PUNCT
ejpam-5942	158	18	vertex	vertex	NOUN
ejpam-5942	158	19	v.	v.	NOUN
ejpam-5942	158	20	by	by	ADP
ejpam-5942	158	21	lemma	lemma	PROPN
ejpam-5942	158	22	3	3	NUM
ejpam-5942	158	23	(	(	PUNCT
ejpam-5942	158	24	ii	ii	NOUN
ejpam-5942	158	25	)	)	PUNCT
ejpam-5942	158	26	,	,	PUNCT
ejpam-5942	158	27	a	a	DET
ejpam-5942	158	28	vertex	vertex	NOUN
ejpam-5942	158	29	v	v	NOUN
ejpam-5942	158	30	is	be	AUX
ejpam-5942	158	31	a	a	DET
ejpam-5942	158	32	rough	rough	ADJ
ejpam-5942	158	33	vertex	vertex	NOUN
ejpam-5942	158	34	of	of	ADP
ejpam-5942	158	35	at	at	ADV
ejpam-5942	158	36	most	most	ADV
ejpam-5942	158	37	two	two	NUM
ejpam-5942	158	38	of	of	ADP
ejpam-5942	158	39	its	its	PRON
ejpam-5942	158	40	incident	incident	NOUN
ejpam-5942	158	41	faces	face	VERB
ejpam-5942	158	42	.	.	PUNCT
ejpam-5942	159	1	it	it	PRON
ejpam-5942	159	2	follows	follow	VERB
ejpam-5942	159	3	from	from	ADP
ejpam-5942	159	4	lemma	lemma	PROPN
ejpam-5942	159	5	2	2	NUM
ejpam-5942	159	6	that	that	SCONJ
ejpam-5942	159	7	a	a	DET
ejpam-5942	159	8	vertex	vertex	NOUN
ejpam-5942	159	9	v	v	NOUN
ejpam-5942	159	10	is	be	AUX
ejpam-5942	159	11	adjacent	adjacent	ADJ
ejpam-5942	159	12	to	to	ADP
ejpam-5942	159	13	at	at	ADP
ejpam-5942	159	14	most	most	ADV
ejpam-5942	159	15	one	one	NUM
ejpam-5942	159	16	3	3	NUM
ejpam-5942	159	17	-	-	PUNCT
ejpam-5942	159	18	vertex	vertex	NOUN
ejpam-5942	159	19	.	.	PUNCT
ejpam-5942	160	1	hence	hence	ADV
ejpam-5942	160	2	,	,	PUNCT
ejpam-5942	160	3	µ∗(v	µ∗(v	PRON
ejpam-5942	160	4	)	)	PUNCT
ejpam-5942	160	5	≥	≥	NOUN
ejpam-5942	160	6	µ(v)−	µ(v)−	PROPN
ejpam-5942	160	7	3×	3×	NUM
ejpam-5942	160	8	1	1	NUM
ejpam-5942	160	9	3	3	NUM
ejpam-5942	160	10	=	=	SYM
ejpam-5942	160	11	0	0	NUM
ejpam-5942	160	12	by	by	ADP
ejpam-5942	160	13	(	(	PUNCT
ejpam-5942	160	14	r1.1	r1.1	NOUN
ejpam-5942	160	15	)	)	PUNCT
ejpam-5942	160	16	and	and	CCONJ
ejpam-5942	160	17	(	(	PUNCT
ejpam-5942	160	18	r2	r2	PROPN
ejpam-5942	160	19	)	)	PUNCT
ejpam-5942	160	20	.	.	PUNCT
ejpam-5942	161	1	case	case	NOUN
ejpam-5942	161	2	5	5	NUM
ejpam-5942	161	3	:	:	PUNCT
ejpam-5942	161	4	consider	consider	VERB
ejpam-5942	161	5	a	a	DET
ejpam-5942	161	6	6	6	NUM
ejpam-5942	161	7	+	+	SYM
ejpam-5942	161	8	-vertex	-vertex	NOUN
ejpam-5942	161	9	v.	v.	ADP
ejpam-5942	161	10	let	let	VERB
ejpam-5942	161	11	v	v	PART
ejpam-5942	161	12	be	be	AUX
ejpam-5942	161	13	a	a	DET
ejpam-5942	161	14	l	l	NOUN
ejpam-5942	161	15	-	-	NOUN
ejpam-5942	161	16	vertex	vertex	NOUN
ejpam-5942	161	17	where	where	SCONJ
ejpam-5942	161	18	k	k	PROPN
ejpam-5942	161	19	≥	≥	NUM
ejpam-5942	161	20	6	6	NUM
ejpam-5942	161	21	.	.	PUNCT
ejpam-5942	162	1	we	we	PRON
ejpam-5942	162	2	let	let	VERB
ejpam-5942	162	3	v1	v1	VERB
ejpam-5942	162	4	,	,	PUNCT
ejpam-5942	162	5	.	.	PUNCT
ejpam-5942	162	6	.	.	PUNCT
ejpam-5942	163	1	.	.	PUNCT
ejpam-5942	164	1	,	,	PUNCT
ejpam-5942	164	2	vl	vl	PROPN
ejpam-5942	164	3	adjacent	adjacent	ADJ
ejpam-5942	164	4	vertices	vertex	NOUN
ejpam-5942	164	5	of	of	ADP
ejpam-5942	164	6	v	v	NOUN
ejpam-5942	164	7	in	in	ADP
ejpam-5942	164	8	clockwise	clockwise	NOUN
ejpam-5942	164	9	order	order	NOUN
ejpam-5942	164	10	.	.	PUNCT
ejpam-5942	165	1	for	for	ADP
ejpam-5942	165	2	the	the	DET
ejpam-5942	165	3	convenience	convenience	NOUN
ejpam-5942	165	4	of	of	ADP
ejpam-5942	165	5	calculating	calculate	VERB
ejpam-5942	165	6	µ∗(v	µ∗(v	NOUN
ejpam-5942	165	7	)	)	PUNCT
ejpam-5942	165	8	,	,	PUNCT
ejpam-5942	165	9	we	we	PRON
ejpam-5942	165	10	redistribute	redistribute	VERB
ejpam-5942	165	11	the	the	DET
ejpam-5942	165	12	charge	charge	NOUN
ejpam-5942	165	13	that	that	PRON
ejpam-5942	165	14	was	be	AUX
ejpam-5942	165	15	transferred	transfer	VERB
ejpam-5942	165	16	from	from	ADP
ejpam-5942	165	17	v	v	NUM
ejpam-5942	165	18	as	as	SCONJ
ejpam-5942	165	19	follows	follow	VERB
ejpam-5942	165	20	.	.	PUNCT
ejpam-5942	166	1	first	first	ADV
ejpam-5942	166	2	,	,	PUNCT
ejpam-5942	166	3	we	we	PRON
ejpam-5942	166	4	give	give	VERB
ejpam-5942	166	5	w(v	w(v	PROPN
ejpam-5942	166	6	→	→	SYM
ejpam-5942	166	7	vi	vi	NOUN
ejpam-5942	166	8	)	)	PUNCT
ejpam-5942	166	9	=	=	SYM
ejpam-5942	166	10	1	1	NUM
ejpam-5942	166	11	3	3	NUM
ejpam-5942	166	12	for	for	ADP
ejpam-5942	166	13	each	each	DET
ejpam-5942	166	14	vi	vi	NOUN
ejpam-5942	166	15	.	.	PUNCT
ejpam-5942	167	1	now	now	ADV
ejpam-5942	167	2	,	,	PUNCT
ejpam-5942	167	3	we	we	PRON
ejpam-5942	167	4	consider	consider	VERB
ejpam-5942	167	5	a	a	DET
ejpam-5942	167	6	3	3	NUM
ejpam-5942	167	7	-	-	PUNCT
ejpam-5942	167	8	face	face	NOUN
ejpam-5942	167	9	f	f	NOUN
ejpam-5942	167	10	bounded	bound	VERB
ejpam-5942	167	11	by	by	ADP
ejpam-5942	167	12	vi	vi	PROPN
ejpam-5942	167	13	,	,	PUNCT
ejpam-5942	167	14	vi+1	vi+1	NOUN
ejpam-5942	167	15	,	,	PUNCT
ejpam-5942	167	16	and	and	CCONJ
ejpam-5942	167	17	v	v	NOUN
ejpam-5942	167	18	in	in	ADP
ejpam-5942	167	19	two	two	NUM
ejpam-5942	167	20	situations	situation	NOUN
ejpam-5942	167	21	.	.	PUNCT
ejpam-5942	168	1	if	if	SCONJ
ejpam-5942	168	2	(	(	PUNCT
ejpam-5942	168	3	1	1	X
ejpam-5942	168	4	)	)	PUNCT
ejpam-5942	168	5	vi	vi	NOUN
ejpam-5942	168	6	is	be	AUX
ejpam-5942	168	7	not	not	PART
ejpam-5942	168	8	a	a	DET
ejpam-5942	168	9	3	3	NUM
ejpam-5942	168	10	-	-	PUNCT
ejpam-5942	168	11	vertex	vertex	NOUN
ejpam-5942	168	12	,	,	PUNCT
ejpam-5942	168	13	and	and	CCONJ
ejpam-5942	168	14	(	(	PUNCT
ejpam-5942	168	15	2	2	NUM
ejpam-5942	168	16	)	)	PUNCT
ejpam-5942	168	17	vi+1	vi+1	NOUN
ejpam-5942	168	18	,	,	PUNCT
ejpam-5942	168	19	vi+2	vi+2	PROPN
ejpam-5942	168	20	,	,	PUNCT
ejpam-5942	168	21	and	and	CCONJ
ejpam-5942	168	22	v	v	X
ejpam-5942	168	23	bound	bind	VERB
ejpam-5942	168	24	the	the	DET
ejpam-5942	168	25	same	same	ADJ
ejpam-5942	168	26	3	3	NUM
ejpam-5942	168	27	-	-	PUNCT
ejpam-5942	168	28	face	face	NOUN
ejpam-5942	168	29	then	then	ADV
ejpam-5942	168	30	reduce	reduce	VERB
ejpam-5942	168	31	w(v	w(v	PROPN
ejpam-5942	168	32	→	→	SYM
ejpam-5942	168	33	vi	vi	NOUN
ejpam-5942	168	34	)	)	PUNCT
ejpam-5942	168	35	to	to	ADP
ejpam-5942	168	36	0	0	NUM
ejpam-5942	168	37	and	and	CCONJ
ejpam-5942	168	38	transfer	transfer	VERB
ejpam-5942	168	39	charge	charge	NOUN
ejpam-5942	168	40	1	1	NUM
ejpam-5942	168	41	3	3	NUM
ejpam-5942	168	42	to	to	ADP
ejpam-5942	168	43	a	a	DET
ejpam-5942	168	44	3	3	NUM
ejpam-5942	168	45	-	-	PUNCT
ejpam-5942	168	46	face	face	NOUN
ejpam-5942	168	47	f	f	NOUN
ejpam-5942	168	48	instead	instead	ADV
ejpam-5942	168	49	.	.	PUNCT
ejpam-5942	169	1	if	if	SCONJ
ejpam-5942	169	2	(	(	PUNCT
ejpam-5942	169	3	1	1	X
ejpam-5942	169	4	)	)	PUNCT
ejpam-5942	169	5	vi+1	vi+1	PRON
ejpam-5942	169	6	is	be	AUX
ejpam-5942	169	7	a	a	DET
ejpam-5942	169	8	4	4	NUM
ejpam-5942	169	9	+	+	NOUN
ejpam-5942	169	10	-vertex	-vertex	NOUN
ejpam-5942	169	11	and	and	CCONJ
ejpam-5942	169	12	(	(	PUNCT
ejpam-5942	169	13	2	2	NUM
ejpam-5942	169	14	)	)	PUNCT
ejpam-5942	169	15	or	or	CCONJ
ejpam-5942	169	16	vi−1	vi−1	PROPN
ejpam-5942	169	17	,	,	PUNCT
ejpam-5942	169	18	vi	vi	PROPN
ejpam-5942	169	19	,	,	PUNCT
ejpam-5942	169	20	and	and	CCONJ
ejpam-5942	169	21	v	v	ADP
ejpam-5942	169	22	bound	bind	VERB
ejpam-5942	169	23	the	the	DET
ejpam-5942	169	24	same	same	ADJ
ejpam-5942	169	25	3	3	NUM
ejpam-5942	169	26	-	-	PUNCT
ejpam-5942	169	27	face	face	NOUN
ejpam-5942	169	28	,	,	PUNCT
ejpam-5942	169	29	then	then	ADV
ejpam-5942	169	30	adjust	adjust	VERB
ejpam-5942	169	31	w(v	w(v	PROPN
ejpam-5942	169	32	→	→	SYM
ejpam-5942	169	33	vi+1	vi+1	NOUN
ejpam-5942	169	34	)	)	PUNCT
ejpam-5942	169	35	to	to	ADP
ejpam-5942	169	36	0	0	NUM
ejpam-5942	169	37	and	and	CCONJ
ejpam-5942	169	38	carry	carry	VERB
ejpam-5942	169	39	charge	charge	NOUN
ejpam-5942	169	40	1	1	NUM
ejpam-5942	169	41	3	3	NUM
ejpam-5942	169	42	from	from	ADP
ejpam-5942	169	43	v	v	NUM
ejpam-5942	169	44	to	to	ADP
ejpam-5942	169	45	f	f	PROPN
ejpam-5942	169	46	instead	instead	ADV
ejpam-5942	169	47	.	.	PUNCT
ejpam-5942	170	1	note	note	VERB
ejpam-5942	170	2	that	that	SCONJ
ejpam-5942	170	3	lemma	lemma	PROPN
ejpam-5942	170	4	3	3	NUM
ejpam-5942	170	5	(	(	PUNCT
ejpam-5942	170	6	ii	ii	NOUN
ejpam-5942	170	7	)	)	PUNCT
ejpam-5942	170	8	implies	imply	VERB
ejpam-5942	170	9	two	two	NUM
ejpam-5942	170	10	previously	previously	ADV
ejpam-5942	170	11	mentioned	mention	VERB
ejpam-5942	170	12	situations	situation	NOUN
ejpam-5942	170	13	can	can	AUX
ejpam-5942	170	14	not	not	PART
ejpam-5942	170	15	happen	happen	VERB
ejpam-5942	170	16	simultaneously	simultaneously	ADV
ejpam-5942	170	17	.	.	PUNCT
ejpam-5942	171	1	consequently	consequently	ADV
ejpam-5942	171	2	,	,	PUNCT
ejpam-5942	171	3	each	each	PRON
ejpam-5942	171	4	of	of	ADP
ejpam-5942	171	5	a	a	DET
ejpam-5942	171	6	3	3	NUM
ejpam-5942	171	7	-	-	PUNCT
ejpam-5942	171	8	vertex	vertex	NOUN
ejpam-5942	171	9	vi	vi	NOUN
ejpam-5942	171	10	receives	receive	VERB
ejpam-5942	171	11	1	1	NUM
ejpam-5942	171	12	3	3	NUM
ejpam-5942	171	13	from	from	ADP
ejpam-5942	171	14	v	v	NUM
ejpam-5942	171	15	as	as	ADP
ejpam-5942	171	16	by	by	ADP
ejpam-5942	171	17	(	(	PUNCT
ejpam-5942	171	18	r2	r2	PROPN
ejpam-5942	171	19	)	)	PUNCT
ejpam-5942	171	20	and	and	CCONJ
ejpam-5942	171	21	each	each	PRON
ejpam-5942	171	22	of	of	ADP
ejpam-5942	171	23	a	a	DET
ejpam-5942	171	24	3	3	NUM
ejpam-5942	171	25	-	-	PUNCT
ejpam-5942	171	26	face	face	NOUN
ejpam-5942	171	27	that	that	PRON
ejpam-5942	171	28	v	v	NOUN
ejpam-5942	171	29	is	be	AUX
ejpam-5942	171	30	a	a	DET
ejpam-5942	171	31	rough	rough	ADJ
ejpam-5942	171	32	vertex	vertex	NOUN
ejpam-5942	171	33	as	as	ADP
ejpam-5942	171	34	in	in	ADP
ejpam-5942	171	35	(	(	PUNCT
ejpam-5942	171	36	r1.1	r1.1	NOUN
ejpam-5942	171	37	)	)	PUNCT
ejpam-5942	171	38	receive	receive	VERB
ejpam-5942	171	39	1	1	NUM
ejpam-5942	171	40	3	3	NUM
ejpam-5942	171	41	from	from	ADP
ejpam-5942	171	42	v.	v.	ADP
ejpam-5942	171	43	additionally	additionally	ADV
ejpam-5942	171	44	,	,	PUNCT
ejpam-5942	171	45	we	we	PRON
ejpam-5942	171	46	get	get	VERB
ejpam-5942	171	47	µ∗(v	µ∗(v	PRON
ejpam-5942	171	48	)	)	PUNCT
ejpam-5942	171	49	≥	≥	NOUN
ejpam-5942	171	50	µ(v)−	µ(v)−	PROPN
ejpam-5942	171	51	l×	l×	PROPN
ejpam-5942	171	52	1	1	NUM
ejpam-5942	171	53	3	3	NUM
ejpam-5942	171	54	=	=	SYM
ejpam-5942	171	55	l−	l−	NOUN
ejpam-5942	171	56	4−	4−	NOUN
ejpam-5942	171	57	l×	l×	NOUN
ejpam-5942	171	58	1	1	NUM
ejpam-5942	171	59	3	3	NUM
ejpam-5942	171	60	=	=	SYM
ejpam-5942	171	61	l×	l×	NUM
ejpam-5942	171	62	2	2	NUM
ejpam-5942	171	63	3	3	NUM
ejpam-5942	171	64	−	−	PROPN
ejpam-5942	171	65	4	4	NUM
ejpam-5942	171	66	≥	≥	NOUN
ejpam-5942	171	67	0	0	NUM
ejpam-5942	171	68	as	as	SCONJ
ejpam-5942	171	69	desired	desire	VERB
ejpam-5942	171	70	.	.	PUNCT
ejpam-5942	172	1	this	this	PRON
ejpam-5942	172	2	completes	complete	VERB
ejpam-5942	172	3	the	the	DET
ejpam-5942	172	4	proof	proof	NOUN
ejpam-5942	172	5	.	.	PUNCT
ejpam-5942	173	1	p.	p.	NOUN
ejpam-5942	173	2	sittitrai	sittitrai	NOUN
ejpam-5942	173	3	,	,	PUNCT
ejpam-5942	173	4	k.	k.	PROPN
ejpam-5942	173	5	nakprasit	nakprasit	PROPN
ejpam-5942	173	6	,	,	PUNCT
ejpam-5942	173	7	p.	p.	PROPN
ejpam-5942	173	8	jumnongnit	jumnongnit	PROPN
ejpam-5942	173	9	/	/	SYM
ejpam-5942	173	10	eur	eur	PROPN
ejpam-5942	173	11	.	.	PUNCT
ejpam-5942	174	1	j.	j.	PROPN
ejpam-5942	174	2	pure	pure	PROPN
ejpam-5942	174	3	appl	appl	PROPN
ejpam-5942	174	4	.	.	PROPN
ejpam-5942	174	5	math	math	PROPN
ejpam-5942	174	6	,	,	PUNCT
ejpam-5942	174	7	18	18	NUM
ejpam-5942	174	8	(	(	PUNCT
ejpam-5942	174	9	2	2	NUM
ejpam-5942	174	10	)	)	PUNCT
ejpam-5942	174	11	(	(	PUNCT
ejpam-5942	174	12	2025	2025	NUM
ejpam-5942	174	13	)	)	PUNCT
ejpam-5942	174	14	,	,	PUNCT
ejpam-5942	174	15	5942	5942	NUM
ejpam-5942	174	16	6	6	NUM
ejpam-5942	174	17	of	of	ADP
ejpam-5942	174	18	7	7	NUM
ejpam-5942	174	19	acknowledgements	acknowledgement	NOUN
ejpam-5942	174	20	this	this	DET
ejpam-5942	174	21	work	work	NOUN
ejpam-5942	174	22	was	be	AUX
ejpam-5942	174	23	supported	support	VERB
ejpam-5942	174	24	by	by	ADP
ejpam-5942	174	25	walailak	walailak	ADJ
ejpam-5942	174	26	university	university	NOUN
ejpam-5942	174	27	under	under	ADP
ejpam-5942	174	28	the	the	DET
ejpam-5942	174	29	new	new	ADJ
ejpam-5942	174	30	researcher	researcher	NOUN
ejpam-5942	174	31	development	development	NOUN
ejpam-5942	174	32	scheme	scheme	NOUN
ejpam-5942	174	33	(	(	PUNCT
ejpam-5942	174	34	contract	contract	NOUN
ejpam-5942	174	35	number	number	NOUN
ejpam-5942	174	36	wu67234	wu67234	NOUN
ejpam-5942	174	37	)	)	PUNCT
ejpam-5942	174	38	the	the	DET
ejpam-5942	174	39	second	second	ADJ
ejpam-5942	174	40	author	author	NOUN
ejpam-5942	174	41	is	be	AUX
ejpam-5942	174	42	(	(	PUNCT
ejpam-5942	174	43	partially	partially	ADV
ejpam-5942	174	44	)	)	PUNCT
ejpam-5942	174	45	supported	support	VERB
ejpam-5942	174	46	by	by	ADP
ejpam-5942	174	47	the	the	DET
ejpam-5942	174	48	centre	centre	NOUN
ejpam-5942	174	49	of	of	ADP
ejpam-5942	174	50	excellence	excellence	PROPN
ejpam-5942	174	51	in	in	ADP
ejpam-5942	174	52	mathematics	mathematics	PROPN
ejpam-5942	174	53	,	,	PUNCT
ejpam-5942	174	54	ministry	ministry	NOUN
ejpam-5942	174	55	of	of	ADP
ejpam-5942	174	56	higher	high	ADJ
ejpam-5942	174	57	education	education	NOUN
ejpam-5942	174	58	,	,	PUNCT
ejpam-5942	174	59	science	science	NOUN
ejpam-5942	174	60	,	,	PUNCT
ejpam-5942	174	61	research	research	NOUN
ejpam-5942	174	62	,	,	PUNCT
ejpam-5942	174	63	and	and	CCONJ
ejpam-5942	174	64	innovation	innovation	NOUN
ejpam-5942	174	65	,	,	PUNCT
ejpam-5942	174	66	thailand	thailand	PROPN
ejpam-5942	174	67	.	.	PUNCT
ejpam-5942	175	1	references	reference	NOUN
ejpam-5942	175	2	[	[	X
ejpam-5942	175	3	1	1	NUM
ejpam-5942	175	4	]	]	PUNCT
ejpam-5942	175	5	m.	m.	PROPN
ejpam-5942	175	6	piĺsniak	piĺsniak	PROPN
ejpam-5942	175	7	and	and	CCONJ
ejpam-5942	175	8	m.	m.	PROPN
ejpam-5942	175	9	woźniak	woźniak	PROPN
ejpam-5942	175	10	.	.	PROPN
ejpam-5942	176	1	on	on	ADP
ejpam-5942	176	2	the	the	DET
ejpam-5942	176	3	total	total	ADJ
ejpam-5942	176	4	-	-	PUNCT
ejpam-5942	176	5	neighbor	neighbor	NOUN
ejpam-5942	176	6	-	-	PUNCT
ejpam-5942	176	7	distinguishing	distinguish	VERB
ejpam-5942	176	8	index	index	NOUN
ejpam-5942	176	9	by	by	ADP
ejpam-5942	176	10	sums	sum	NOUN
ejpam-5942	176	11	.	.	PUNCT
ejpam-5942	177	1	graphs	graph	NOUN
ejpam-5942	177	2	and	and	CCONJ
ejpam-5942	177	3	combinatorics	combinatoric	NOUN
ejpam-5942	177	4	,	,	PUNCT
ejpam-5942	177	5	31(3):771–782	31(3):771–782	PROPN
ejpam-5942	177	6	,	,	PUNCT
ejpam-5942	177	7	2015	2015	NUM
ejpam-5942	177	8	.	.	PUNCT
ejpam-5942	178	1	[	[	X
ejpam-5942	178	2	2	2	X
ejpam-5942	178	3	]	]	X
ejpam-5942	178	4	h.	h.	PROPN
ejpam-5942	178	5	li	li	PROPN
ejpam-5942	178	6	,	,	PUNCT
ejpam-5942	178	7	b.	b.	PROPN
ejpam-5942	178	8	liu	liu	PROPN
ejpam-5942	178	9	,	,	PUNCT
ejpam-5942	178	10	and	and	CCONJ
ejpam-5942	178	11	g.	g.	PROPN
ejpam-5942	178	12	wang	wang	PROPN
ejpam-5942	178	13	.	.	PUNCT
ejpam-5942	179	1	neighbor	neighbor	PROPN
ejpam-5942	179	2	sum	sum	NOUN
ejpam-5942	179	3	distinguishing	distinguish	VERB
ejpam-5942	179	4	total	total	ADJ
ejpam-5942	179	5	colorings	coloring	NOUN
ejpam-5942	179	6	of	of	ADP
ejpam-5942	179	7	k4	k4	ADJ
ejpam-5942	179	8	-	-	PUNCT
ejpam-5942	179	9	minor	minor	ADJ
ejpam-5942	179	10	free	free	ADJ
ejpam-5942	179	11	graphs	graph	NOUN
ejpam-5942	179	12	.	.	PUNCT
ejpam-5942	180	1	frontiers	frontier	NOUN
ejpam-5942	180	2	of	of	ADP
ejpam-5942	180	3	mathematics	mathematics	PROPN
ejpam-5942	180	4	in	in	ADP
ejpam-5942	180	5	china	china	PROPN
ejpam-5942	180	6	,	,	PUNCT
ejpam-5942	180	7	8(6):1351–1366	8(6):1351–1366	PROPN
ejpam-5942	180	8	,	,	PUNCT
ejpam-5942	180	9	2013	2013	NUM
ejpam-5942	180	10	.	.	PUNCT
ejpam-5942	181	1	[	[	X
ejpam-5942	181	2	3	3	X
ejpam-5942	181	3	]	]	X
ejpam-5942	181	4	w.	w.	PROPN
ejpam-5942	181	5	zhang	zhang	PROPN
ejpam-5942	181	6	and	and	CCONJ
ejpam-5942	181	7	y.	y.	PROPN
ejpam-5942	181	8	li	li	PROPN
ejpam-5942	181	9	.	.	PROPN
ejpam-5942	181	10	list	list	NOUN
ejpam-5942	181	11	edge	edge	NOUN
ejpam-5942	181	12	and	and	CCONJ
ejpam-5942	181	13	list	list	VERB
ejpam-5942	181	14	total	total	ADJ
ejpam-5942	181	15	coloring	coloring	NOUN
ejpam-5942	181	16	of	of	ADP
ejpam-5942	181	17	planar	planar	ADJ
ejpam-5942	181	18	graphs	graph	NOUN
ejpam-5942	181	19	without	without	ADP
ejpam-5942	181	20	intersecting	intersect	VERB
ejpam-5942	181	21	8	8	NUM
ejpam-5942	181	22	-	-	PUNCT
ejpam-5942	181	23	cycles	cycle	NOUN
ejpam-5942	181	24	.	.	PUNCT
ejpam-5942	182	1	journal	journal	NOUN
ejpam-5942	182	2	of	of	ADP
ejpam-5942	182	3	discrete	discrete	ADJ
ejpam-5942	182	4	mathematical	mathematical	ADJ
ejpam-5942	182	5	sciences	science	NOUN
ejpam-5942	182	6	and	and	CCONJ
ejpam-5942	182	7	cryptography	cryptography	NOUN
ejpam-5942	182	8	,	,	PUNCT
ejpam-5942	182	9	23(4):925–934	23(4):925–934	NOUN
ejpam-5942	182	10	,	,	PUNCT
ejpam-5942	182	11	2020	2020	NUM
ejpam-5942	182	12	.	.	PUNCT
ejpam-5942	183	1	[	[	X
ejpam-5942	183	2	4	4	X
ejpam-5942	183	3	]	]	PUNCT
ejpam-5942	183	4	h.	h.	PROPN
ejpam-5942	183	5	j.	j.	PROPN
ejpam-5942	183	6	song	song	PROPN
ejpam-5942	183	7	,	,	PUNCT
ejpam-5942	183	8	w.	w.	PROPN
ejpam-5942	183	9	h.	h.	PROPN
ejpam-5942	183	10	pan	pan	PROPN
ejpam-5942	183	11	,	,	PUNCT
ejpam-5942	183	12	x.	x.	PROPN
ejpam-5942	183	13	n.	n.	PROPN
ejpam-5942	183	14	gong	gong	PROPN
ejpam-5942	183	15	,	,	PUNCT
ejpam-5942	183	16	and	and	CCONJ
ejpam-5942	183	17	c.	c.	PROPN
ejpam-5942	183	18	q.	q.	PROPN
ejpam-5942	183	19	xu	xu	PROPN
ejpam-5942	183	20	.	.	PUNCT
ejpam-5942	184	1	a	a	DET
ejpam-5942	184	2	note	note	NOUN
ejpam-5942	184	3	on	on	ADP
ejpam-5942	184	4	the	the	DET
ejpam-5942	184	5	neighbor	neighbor	NOUN
ejpam-5942	184	6	sum	sum	NOUN
ejpam-5942	184	7	distinguishing	distinguish	VERB
ejpam-5942	184	8	total	total	ADJ
ejpam-5942	184	9	coloring	coloring	NOUN
ejpam-5942	184	10	of	of	ADP
ejpam-5942	184	11	planar	planar	ADJ
ejpam-5942	184	12	graphs	graph	NOUN
ejpam-5942	184	13	.	.	PUNCT
ejpam-5942	185	1	theoretical	theoretical	ADJ
ejpam-5942	185	2	computer	computer	NOUN
ejpam-5942	185	3	science	science	NOUN
ejpam-5942	185	4	,	,	PUNCT
ejpam-5942	185	5	640:125	640:125	NUM
ejpam-5942	185	6	–	–	PUNCT
ejpam-5942	185	7	129	129	NUM
ejpam-5942	185	8	,	,	PUNCT
ejpam-5942	185	9	2016	2016	NUM
ejpam-5942	185	10	.	.	PUNCT
ejpam-5942	186	1	[	[	X
ejpam-5942	186	2	5	5	X
ejpam-5942	186	3	]	]	X
ejpam-5942	186	4	c.	c.	PROPN
ejpam-5942	186	5	qu	qu	PROPN
ejpam-5942	186	6	,	,	PUNCT
ejpam-5942	186	7	g.	g.	PROPN
ejpam-5942	186	8	wang	wang	PROPN
ejpam-5942	186	9	,	,	PUNCT
ejpam-5942	186	10	j.	j.	PROPN
ejpam-5942	186	11	wu	wu	PROPN
ejpam-5942	186	12	,	,	PUNCT
ejpam-5942	186	13	and	and	CCONJ
ejpam-5942	186	14	x.	x.	NOUN
ejpam-5942	186	15	yu	yu	PROPN
ejpam-5942	186	16	.	.	PROPN
ejpam-5942	187	1	on	on	ADP
ejpam-5942	187	2	the	the	DET
ejpam-5942	187	3	neighbor	neighbor	NOUN
ejpam-5942	187	4	sum	sum	NOUN
ejpam-5942	187	5	distinguishing	distinguish	VERB
ejpam-5942	187	6	total	total	ADJ
ejpam-5942	187	7	coloring	coloring	NOUN
ejpam-5942	187	8	of	of	ADP
ejpam-5942	187	9	planar	planar	ADJ
ejpam-5942	187	10	graphs	graph	NOUN
ejpam-5942	187	11	.	.	PUNCT
ejpam-5942	188	1	theoretical	theoretical	ADJ
ejpam-5942	188	2	computer	computer	NOUN
ejpam-5942	188	3	science	science	NOUN
ejpam-5942	188	4	,	,	PUNCT
ejpam-5942	188	5	609(1):162–170	609(1):162–170	PROPN
ejpam-5942	188	6	,	,	PUNCT
ejpam-5942	188	7	2016	2016	NUM
ejpam-5942	188	8	.	.	PUNCT
ejpam-5942	189	1	[	[	X
ejpam-5942	189	2	6	6	NUM
ejpam-5942	189	3	]	]	PUNCT
ejpam-5942	189	4	j.	j.	PROPN
ejpam-5942	189	5	wang	wang	PROPN
ejpam-5942	189	6	,	,	PUNCT
ejpam-5942	189	7	q.	q.	PROPN
ejpam-5942	189	8	ma	ma	PROPN
ejpam-5942	189	9	,	,	PUNCT
ejpam-5942	189	10	and	and	CCONJ
ejpam-5942	189	11	x.	x.	PROPN
ejpam-5942	189	12	han	han	PROPN
ejpam-5942	189	13	.	.	PROPN
ejpam-5942	189	14	neighbor	neighbor	PROPN
ejpam-5942	189	15	sum	sum	NOUN
ejpam-5942	189	16	distinguishing	distinguish	VERB
ejpam-5942	189	17	total	total	ADJ
ejpam-5942	189	18	colorings	coloring	NOUN
ejpam-5942	189	19	of	of	ADP
ejpam-5942	189	20	triangle	triangle	NOUN
ejpam-5942	189	21	free	free	ADJ
ejpam-5942	189	22	planar	planar	ADJ
ejpam-5942	189	23	graphs	graph	NOUN
ejpam-5942	189	24	.	.	PUNCT
ejpam-5942	190	1	acta	acta	PROPN
ejpam-5942	190	2	mathematica	mathematica	PROPN
ejpam-5942	190	3	sinica	sinica	PROPN
ejpam-5942	190	4	,	,	PUNCT
ejpam-5942	190	5	english	english	ADJ
ejpam-5942	190	6	series	series	NOUN
ejpam-5942	190	7	,	,	PUNCT
ejpam-5942	190	8	31(2):216–224	31(2):216–224	PROPN
ejpam-5942	190	9	,	,	PUNCT
ejpam-5942	190	10	2015	2015	NUM
ejpam-5942	190	11	.	.	PUNCT
ejpam-5942	191	1	[	[	X
ejpam-5942	191	2	7	7	X
ejpam-5942	191	3	]	]	X
ejpam-5942	191	4	s.	s.	PROPN
ejpam-5942	191	5	ge	ge	PROPN
ejpam-5942	191	6	,	,	PUNCT
ejpam-5942	191	7	j.	j.	PROPN
ejpam-5942	191	8	li	li	PROPN
ejpam-5942	191	9	,	,	PUNCT
ejpam-5942	191	10	and	and	CCONJ
ejpam-5942	191	11	c.	c.	PROPN
ejpam-5942	191	12	xu	xu	PROPN
ejpam-5942	191	13	.	.	PUNCT
ejpam-5942	192	1	neighbor	neighbor	PROPN
ejpam-5942	192	2	sum	sum	NOUN
ejpam-5942	192	3	distinguishing	distinguish	VERB
ejpam-5942	192	4	total	total	ADJ
ejpam-5942	192	5	coloring	coloring	NOUN
ejpam-5942	192	6	of	of	ADP
ejpam-5942	192	7	planar	planar	ADJ
ejpam-5942	192	8	graphs	graph	NOUN
ejpam-5942	192	9	without	without	ADP
ejpam-5942	192	10	5	5	NUM
ejpam-5942	192	11	-	-	PUNCT
ejpam-5942	192	12	cycles	cycle	NOUN
ejpam-5942	192	13	.	.	PUNCT
ejpam-5942	193	1	theoretical	theoretical	ADJ
ejpam-5942	193	2	computer	computer	NOUN
ejpam-5942	193	3	science	science	NOUN
ejpam-5942	193	4	,	,	PUNCT
ejpam-5942	193	5	689:169–175	689:169–175	NUM
ejpam-5942	193	6	,	,	PUNCT
ejpam-5942	193	7	2017	2017	NUM
ejpam-5942	193	8	.	.	PUNCT
ejpam-5942	194	1	[	[	X
ejpam-5942	194	2	8	8	NUM
ejpam-5942	194	3	]	]	PUNCT
ejpam-5942	194	4	x.	x.	NOUN
ejpam-5942	194	5	cheng	cheng	PROPN
ejpam-5942	194	6	,	,	PUNCT
ejpam-5942	194	7	d.	d.	PROPN
ejpam-5942	194	8	huang	huang	PROPN
ejpam-5942	194	9	,	,	PUNCT
ejpam-5942	194	10	g.	g.	PROPN
ejpam-5942	194	11	wang	wang	PROPN
ejpam-5942	194	12	,	,	PUNCT
ejpam-5942	194	13	and	and	CCONJ
ejpam-5942	194	14	j.	j.	PROPN
ejpam-5942	194	15	wu	wu	PROPN
ejpam-5942	194	16	.	.	PUNCT
ejpam-5942	195	1	neighbor	neighbor	PROPN
ejpam-5942	195	2	sum	sum	NOUN
ejpam-5942	195	3	distinguishing	distinguish	VERB
ejpam-5942	195	4	total	total	ADJ
ejpam-5942	195	5	colorings	coloring	NOUN
ejpam-5942	195	6	of	of	ADP
ejpam-5942	195	7	planar	planar	ADJ
ejpam-5942	195	8	graphs	graph	NOUN
ejpam-5942	195	9	with	with	ADP
ejpam-5942	195	10	maximum	maximum	ADJ
ejpam-5942	195	11	degree	degree	NOUN
ejpam-5942	195	12	∆.	∆.	X
ejpam-5942	195	13	discrete	discrete	ADJ
ejpam-5942	195	14	applied	apply	VERB
ejpam-5942	195	15	mathematics	mathematic	NOUN
ejpam-5942	195	16	,	,	PUNCT
ejpam-5942	195	17	190	190	NUM
ejpam-5942	195	18	-	-	PUNCT
ejpam-5942	195	19	191:34–41	191:34–41	NUM
ejpam-5942	195	20	,	,	PUNCT
ejpam-5942	195	21	2015	2015	NUM
ejpam-5942	195	22	.	.	PUNCT
ejpam-5942	196	1	[	[	X
ejpam-5942	196	2	9	9	NUM
ejpam-5942	196	3	]	]	PUNCT
ejpam-5942	196	4	a.	a.	NOUN
ejpam-5942	196	5	j.	j.	PROPN
ejpam-5942	196	6	dong	dong	PROPN
ejpam-5942	196	7	and	and	CCONJ
ejpam-5942	196	8	g.	g.	PROPN
ejpam-5942	196	9	h.	h.	PROPN
ejpam-5942	196	10	wang	wang	PROPN
ejpam-5942	196	11	.	.	PUNCT
ejpam-5942	197	1	neighbor	neighbor	PROPN
ejpam-5942	197	2	sum	sum	NOUN
ejpam-5942	197	3	distinguishing	distinguish	VERB
ejpam-5942	197	4	total	total	ADJ
ejpam-5942	197	5	colorings	coloring	NOUN
ejpam-5942	197	6	of	of	ADP
ejpam-5942	197	7	graphs	graph	NOUN
ejpam-5942	197	8	with	with	ADP
ejpam-5942	197	9	bounded	bounded	ADJ
ejpam-5942	197	10	maximum	maximum	ADJ
ejpam-5942	197	11	average	average	ADJ
ejpam-5942	197	12	degree	degree	NOUN
ejpam-5942	197	13	.	.	PUNCT
ejpam-5942	198	1	acta	acta	PROPN
ejpam-5942	198	2	mathematica	mathematica	PROPN
ejpam-5942	198	3	sinica	sinica	PROPN
ejpam-5942	198	4	,	,	PUNCT
ejpam-5942	198	5	english	english	ADJ
ejpam-5942	198	6	series	series	NOUN
ejpam-5942	198	7	,	,	PUNCT
ejpam-5942	198	8	30(4):703–709	30(4):703–709	NUM
ejpam-5942	198	9	,	,	PUNCT
ejpam-5942	198	10	2014	2014	NUM
ejpam-5942	198	11	.	.	PUNCT
ejpam-5942	199	1	[	[	X
ejpam-5942	199	2	10	10	NUM
ejpam-5942	199	3	]	]	X
ejpam-5942	199	4	c.	c.	PROPN
ejpam-5942	199	5	qu	qu	PROPN
ejpam-5942	199	6	,	,	PUNCT
ejpam-5942	199	7	g.	g.	PROPN
ejpam-5942	199	8	wang	wang	PROPN
ejpam-5942	199	9	,	,	PUNCT
ejpam-5942	199	10	g.	g.	PROPN
ejpam-5942	199	11	yan	yan	PROPN
ejpam-5942	199	12	,	,	PUNCT
ejpam-5942	199	13	and	and	CCONJ
ejpam-5942	199	14	x.	x.	PROPN
ejpam-5942	199	15	yu	yu	PROPN
ejpam-5942	199	16	.	.	PROPN
ejpam-5942	199	17	neighbor	neighbor	PROPN
ejpam-5942	199	18	sum	sum	NOUN
ejpam-5942	199	19	distinguishing	distinguish	VERB
ejpam-5942	199	20	total	total	ADJ
ejpam-5942	199	21	choosability	choosability	NOUN
ejpam-5942	199	22	of	of	ADP
ejpam-5942	199	23	planar	planar	ADJ
ejpam-5942	199	24	graphs	graph	NOUN
ejpam-5942	199	25	.	.	PUNCT
ejpam-5942	200	1	journal	journal	NOUN
ejpam-5942	200	2	of	of	ADP
ejpam-5942	200	3	combinatorial	combinatorial	ADJ
ejpam-5942	200	4	optimization	optimization	NOUN
ejpam-5942	200	5	,	,	PUNCT
ejpam-5942	200	6	32(3):906–916	32(3):906–916	NUM
ejpam-5942	200	7	,	,	PUNCT
ejpam-5942	200	8	2016	2016	NUM
ejpam-5942	200	9	.	.	PUNCT
ejpam-5942	201	1	[	[	X
ejpam-5942	201	2	11	11	NUM
ejpam-5942	201	3	]	]	PUNCT
ejpam-5942	201	4	j.	j.	PROPN
ejpam-5942	201	5	yao	yao	PROPN
ejpam-5942	201	6	,	,	PUNCT
ejpam-5942	201	7	x.	x.	PROPN
ejpam-5942	201	8	yu	yu	PROPN
ejpam-5942	201	9	,	,	PUNCT
ejpam-5942	201	10	g.	g.	PROPN
ejpam-5942	201	11	wang	wang	PROPN
ejpam-5942	201	12	,	,	PUNCT
ejpam-5942	201	13	and	and	CCONJ
ejpam-5942	201	14	c.	c.	PROPN
ejpam-5942	201	15	xu	xu	PROPN
ejpam-5942	201	16	.	.	PUNCT
ejpam-5942	202	1	neighbor	neighbor	PROPN
ejpam-5942	202	2	sum	sum	PROPN
ejpam-5942	202	3	(	(	PUNCT
ejpam-5942	202	4	set	set	NOUN
ejpam-5942	202	5	)	)	PUNCT
ejpam-5942	202	6	distinguishing	distinguish	VERB
ejpam-5942	202	7	total	total	ADJ
ejpam-5942	202	8	choosability	choosability	NOUN
ejpam-5942	202	9	of	of	ADP
ejpam-5942	202	10	d	d	ADJ
ejpam-5942	202	11	-	-	ADJ
ejpam-5942	202	12	degenerate	degenerate	ADJ
ejpam-5942	202	13	graphs	graph	NOUN
ejpam-5942	202	14	.	.	PUNCT
ejpam-5942	203	1	graphs	graph	NOUN
ejpam-5942	203	2	and	and	CCONJ
ejpam-5942	203	3	combinatorics	combinatoric	NOUN
ejpam-5942	203	4	,	,	PUNCT
ejpam-5942	203	5	32:1611–1620	32:1611–1620	NUM
ejpam-5942	203	6	,	,	PUNCT
ejpam-5942	203	7	2016	2016	NUM
ejpam-5942	203	8	.	.	PUNCT
ejpam-5942	204	1	[	[	X
ejpam-5942	204	2	12	12	NUM
ejpam-5942	204	3	]	]	PUNCT
ejpam-5942	204	4	j.	j.	PROPN
ejpam-5942	204	5	wang	wang	PROPN
ejpam-5942	204	6	,	,	PUNCT
ejpam-5942	204	7	j.	j.	PROPN
ejpam-5942	204	8	cai	cai	PROPN
ejpam-5942	204	9	,	,	PUNCT
ejpam-5942	204	10	and	and	CCONJ
ejpam-5942	204	11	b.	b.	PROPN
ejpam-5942	204	12	qiu	qiu	PROPN
ejpam-5942	204	13	.	.	PROPN
ejpam-5942	205	1	neighbor	neighbor	PROPN
ejpam-5942	205	2	sum	sum	NOUN
ejpam-5942	205	3	distinguishing	distinguish	VERB
ejpam-5942	205	4	total	total	ADJ
ejpam-5942	205	5	choosability	choosability	NOUN
ejpam-5942	205	6	of	of	ADP
ejpam-5942	205	7	planar	planar	ADJ
ejpam-5942	205	8	graphs	graph	NOUN
ejpam-5942	205	9	without	without	ADP
ejpam-5942	205	10	adjacent	adjacent	ADJ
ejpam-5942	205	11	triangles	triangle	NOUN
ejpam-5942	205	12	.	.	PUNCT
ejpam-5942	206	1	theoretical	theoretical	ADJ
ejpam-5942	206	2	computer	computer	NOUN
ejpam-5942	206	3	science	science	NOUN
ejpam-5942	206	4	,	,	PUNCT
ejpam-5942	206	5	661:1–7	661:1–7	NUM
ejpam-5942	206	6	,	,	PUNCT
ejpam-5942	206	7	2017	2017	NUM
ejpam-5942	206	8	.	.	PUNCT
ejpam-5942	207	1	[	[	X
ejpam-5942	207	2	13	13	NUM
ejpam-5942	207	3	]	]	X
ejpam-5942	207	4	d.	d.	PROPN
ejpam-5942	207	5	h.	h.	PROPN
ejpam-5942	207	6	zhang	zhang	PROPN
ejpam-5942	207	7	,	,	PUNCT
ejpam-5942	207	8	y.	y.	PROPN
ejpam-5942	207	9	lu	lu	PROPN
ejpam-5942	207	10	,	,	PUNCT
ejpam-5942	207	11	and	and	CCONJ
ejpam-5942	207	12	s.	s.	PROPN
ejpam-5942	207	13	g.	g.	PROPN
ejpam-5942	207	14	zhang	zhang	PROPN
ejpam-5942	207	15	.	.	PROPN
ejpam-5942	208	1	neighbor	neighbor	PROPN
ejpam-5942	208	2	sum	sum	NOUN
ejpam-5942	208	3	distinguishing	distinguish	VERB
ejpam-5942	208	4	total	total	ADJ
ejpam-5942	208	5	choice	choice	NOUN
ejpam-5942	208	6	number	number	NOUN
ejpam-5942	208	7	of	of	ADP
ejpam-5942	208	8	planar	planar	ADJ
ejpam-5942	208	9	graphs	graph	NOUN
ejpam-5942	208	10	without	without	ADP
ejpam-5942	208	11	6	6	NUM
ejpam-5942	208	12	-	-	PUNCT
ejpam-5942	208	13	cycles	cycle	NOUN
ejpam-5942	208	14	.	.	PUNCT
ejpam-5942	209	1	acta	acta	PROPN
ejpam-5942	209	2	mathematica	mathematica	PROPN
ejpam-5942	209	3	sinica	sinica	PROPN
ejpam-5942	209	4	,	,	PUNCT
ejpam-5942	209	5	english	english	ADJ
ejpam-5942	209	6	series	series	NOUN
ejpam-5942	209	7	,	,	PUNCT
ejpam-5942	209	8	36(12):1417–1428	36(12):1417–1428	NUM
ejpam-5942	209	9	,	,	PUNCT
ejpam-5942	209	10	2020	2020	NUM
ejpam-5942	209	11	.	.	PUNCT
ejpam-5942	210	1	[	[	X
ejpam-5942	210	2	14	14	NUM
ejpam-5942	210	3	]	]	PUNCT
ejpam-5942	210	4	k.	k.	PROPN
ejpam-5942	210	5	nakprasit	nakprasit	PROPN
ejpam-5942	210	6	and	and	CCONJ
ejpam-5942	210	7	p.	p.	PROPN
ejpam-5942	210	8	jumnongnit	jumnongnit	PROPN
ejpam-5942	210	9	.	.	PUNCT
ejpam-5942	211	1	neighbor	neighbor	PROPN
ejpam-5942	211	2	sum	sum	NOUN
ejpam-5942	211	3	distinguishing	distinguish	VERB
ejpam-5942	211	4	total	total	ADJ
ejpam-5942	211	5	choosability	choosability	NOUN
ejpam-5942	211	6	of	of	ADP
ejpam-5942	211	7	planar	planar	ADJ
ejpam-5942	211	8	graphs	graph	NOUN
ejpam-5942	211	9	without	without	ADP
ejpam-5942	211	10	4	4	NUM
ejpam-5942	211	11	-	-	PUNCT
ejpam-5942	211	12	cycles	cycle	NOUN
ejpam-5942	211	13	adjacent	adjacent	ADJ
ejpam-5942	211	14	to	to	ADP
ejpam-5942	211	15	3	3	NUM
ejpam-5942	211	16	-	-	PUNCT
ejpam-5942	211	17	cycles	cycle	NOUN
ejpam-5942	211	18	.	.	PUNCT
ejpam-5942	212	1	journal	journal	PROPN
ejpam-5942	212	2	of	of	ADP
ejpam-5942	212	3	mathematical	mathematical	ADJ
ejpam-5942	212	4	and	and	CCONJ
ejpam-5942	212	5	computational	computational	ADJ
ejpam-5942	212	6	science	science	NOUN
ejpam-5942	212	7	,	,	PUNCT
ejpam-5942	212	8	12	12	NUM
ejpam-5942	212	9	,	,	PUNCT
ejpam-5942	212	10	2022	2022	NUM
ejpam-5942	212	11	.	.	PUNCT
ejpam-5942	213	1	article	article	NOUN
ejpam-5942	213	2	i	i	PRON
ejpam-5942	213	3	d.	d.	PROPN
ejpam-5942	213	4	111	111	NUM
ejpam-5942	213	5	.	.	PUNCT
ejpam-5942	214	1	p.	p.	NOUN
ejpam-5942	214	2	sittitrai	sittitrai	NOUN
ejpam-5942	214	3	,	,	PUNCT
ejpam-5942	214	4	k.	k.	PROPN
ejpam-5942	214	5	nakprasit	nakprasit	PROPN
ejpam-5942	214	6	,	,	PUNCT
ejpam-5942	214	7	p.	p.	PROPN
ejpam-5942	214	8	jumnongnit	jumnongnit	PROPN
ejpam-5942	214	9	/	/	SYM
ejpam-5942	214	10	eur	eur	PROPN
ejpam-5942	214	11	.	.	PUNCT
ejpam-5942	215	1	j.	j.	PROPN
ejpam-5942	215	2	pure	pure	PROPN
ejpam-5942	215	3	appl	appl	PROPN
ejpam-5942	215	4	.	.	PROPN
ejpam-5942	215	5	math	math	PROPN
ejpam-5942	215	6	,	,	PUNCT
ejpam-5942	215	7	18	18	NUM
ejpam-5942	215	8	(	(	PUNCT
ejpam-5942	215	9	2	2	NUM
ejpam-5942	215	10	)	)	PUNCT
ejpam-5942	215	11	(	(	PUNCT
ejpam-5942	215	12	2025	2025	NUM
ejpam-5942	215	13	)	)	PUNCT
ejpam-5942	215	14	,	,	PUNCT
ejpam-5942	215	15	5942	5942	NUM
ejpam-5942	215	16	7	7	NUM
ejpam-5942	215	17	of	of	ADP
ejpam-5942	215	18	7	7	NUM
ejpam-5942	215	19	[	[	SYM
ejpam-5942	215	20	15	15	NUM
ejpam-5942	215	21	]	]	X
ejpam-5942	215	22	c.	c.	NOUN
ejpam-5942	215	23	song	song	PROPN
ejpam-5942	215	24	,	,	PUNCT
ejpam-5942	215	25	x.	x.	NOUN
ejpam-5942	215	26	jin	jin	PROPN
ejpam-5942	215	27	,	,	PUNCT
ejpam-5942	215	28	and	and	CCONJ
ejpam-5942	215	29	c.	c.	PROPN
ejpam-5942	215	30	q.	q.	PROPN
ejpam-5942	216	1	xu	xu	PROPN
ejpam-5942	216	2	.	.	PUNCT
ejpam-5942	217	1	neighbor	neighbor	PROPN
ejpam-5942	217	2	sum	sum	NOUN
ejpam-5942	217	3	distinguishing	distinguish	VERB
ejpam-5942	217	4	total	total	ADJ
ejpam-5942	217	5	coloring	coloring	NOUN
ejpam-5942	217	6	of	of	ADP
ejpam-5942	217	7	icplanar	icplanar	ADJ
ejpam-5942	217	8	graphs	graph	NOUN
ejpam-5942	217	9	with	with	ADP
ejpam-5942	217	10	short	short	ADJ
ejpam-5942	217	11	cycle	cycle	NOUN
ejpam-5942	217	12	restrictions	restriction	NOUN
ejpam-5942	217	13	.	.	PUNCT
ejpam-5942	218	1	discrete	discrete	ADJ
ejpam-5942	218	2	applied	applied	ADJ
ejpam-5942	218	3	mathematics	mathematic	NOUN
ejpam-5942	218	4	,	,	PUNCT
ejpam-5942	218	5	279:202	279:202	NOUN
ejpam-5942	218	6	–	–	PUNCT
ejpam-5942	218	7	209	209	NUM
ejpam-5942	218	8	,	,	PUNCT
ejpam-5942	218	9	2020	2020	NUM
ejpam-5942	218	10	.	.	PUNCT
ejpam-5942	219	1	[	[	X
ejpam-5942	219	2	16	16	NUM
ejpam-5942	219	3	]	]	PUNCT
ejpam-5942	219	4	w.-y	w.-y	NOUN
ejpam-5942	219	5	.	.	PUNCT
ejpam-5942	220	1	song	song	NOUN
ejpam-5942	220	2	,	,	PUNCT
ejpam-5942	220	3	l.-y	l.-y	PROPN
ejpam-5942	220	4	.	.	PUNCT
ejpam-5942	221	1	miao	miao	NOUN
ejpam-5942	221	2	,	,	PUNCT
ejpam-5942	221	3	and	and	CCONJ
ejpam-5942	221	4	y.-y	y.-y	PROPN
ejpam-5942	221	5	.	.	PUNCT
ejpam-5942	222	1	duan	duan	PROPN
ejpam-5942	222	2	.	.	PROPN
ejpam-5942	222	3	neighbor	neighbor	PROPN
ejpam-5942	222	4	sum	sum	NOUN
ejpam-5942	222	5	distinguishing	distinguish	VERB
ejpam-5942	222	6	total	total	ADJ
ejpam-5942	222	7	choosability	choosability	NOUN
ejpam-5942	222	8	of	of	ADP
ejpam-5942	222	9	ic	ic	PROPN
ejpam-5942	222	10	-	-	PUNCT
ejpam-5942	222	11	planar	planar	ADJ
ejpam-5942	222	12	graphs	graph	NOUN
ejpam-5942	222	13	.	.	PUNCT
ejpam-5942	223	1	discussiones	discussione	NOUN
ejpam-5942	223	2	mathematicae	mathematicae	PROPN
ejpam-5942	223	3	graph	graph	NOUN
ejpam-5942	223	4	theory	theory	NOUN
ejpam-5942	223	5	,	,	PUNCT
ejpam-5942	223	6	40(1):331–344	40(1):331–344	NOUN
ejpam-5942	223	7	,	,	PUNCT
ejpam-5942	223	8	2020	2020	NUM
ejpam-5942	223	9	.	.	PUNCT
ejpam-5942	224	1	[	[	X
ejpam-5942	224	2	17	17	NUM
ejpam-5942	224	3	]	]	PUNCT
ejpam-5942	224	4	w.-y	w.-y	NOUN
ejpam-5942	224	5	.	.	PUNCT
ejpam-5942	225	1	song	song	NOUN
ejpam-5942	225	2	,	,	PUNCT
ejpam-5942	225	3	l.-y	l.-y	PROPN
ejpam-5942	225	4	.	.	PUNCT
ejpam-5942	226	1	miao	miao	NOUN
ejpam-5942	226	2	,	,	PUNCT
ejpam-5942	226	3	j.-b	j.-b	PROPN
ejpam-5942	226	4	.	.	PUNCT
ejpam-5942	227	1	li	li	PROPN
ejpam-5942	227	2	,	,	PUNCT
ejpam-5942	227	3	y.-y	y.-y	PROPN
ejpam-5942	227	4	.	.	PUNCT
ejpam-5942	228	1	zhao	zhao	PROPN
ejpam-5942	228	2	,	,	PUNCT
ejpam-5942	228	3	and	and	CCONJ
ejpam-5942	228	4	j.-p	j.-p	PROPN
ejpam-5942	228	5	.	.	PUNCT
ejpam-5942	229	1	pang	pang	NOUN
ejpam-5942	229	2	.	.	PUNCT
ejpam-5942	230	1	neighbor	neighbor	NOUN
ejpam-5942	230	2	sum	sum	NOUN
ejpam-5942	230	3	distinguishing	distinguish	VERB
ejpam-5942	230	4	total	total	ADJ
ejpam-5942	230	5	coloring	coloring	NOUN
ejpam-5942	230	6	of	of	ADP
ejpam-5942	230	7	sparse	sparse	ADJ
ejpam-5942	230	8	ic	ic	ADJ
ejpam-5942	230	9	-	-	PUNCT
ejpam-5942	230	10	planar	planar	ADJ
ejpam-5942	230	11	graphs	graph	NOUN
ejpam-5942	230	12	.	.	PUNCT
ejpam-5942	231	1	discrete	discrete	ADJ
ejpam-5942	231	2	applied	apply	VERB
ejpam-5942	231	3	mathematics	mathematic	NOUN
ejpam-5942	231	4	,	,	PUNCT
ejpam-5942	231	5	239:183–192	239:183–192	NUM
ejpam-5942	231	6	,	,	PUNCT
ejpam-5942	231	7	2018	2018	NUM
ejpam-5942	231	8	.	.	PUNCT
ejpam-5942	232	1	[	[	X
ejpam-5942	232	2	18	18	NUM
ejpam-5942	232	3	]	]	PUNCT
ejpam-5942	232	4	c.	c.	NOUN
ejpam-5942	232	5	song	song	NOUN
ejpam-5942	232	6	and	and	CCONJ
ejpam-5942	232	7	c.	c.	PROPN
ejpam-5942	232	8	xu	xu	PROPN
ejpam-5942	232	9	.	.	PUNCT
ejpam-5942	233	1	neighbor	neighbor	PROPN
ejpam-5942	233	2	sum	sum	NOUN
ejpam-5942	233	3	distinguishing	distinguish	VERB
ejpam-5942	233	4	total	total	ADJ
ejpam-5942	233	5	colorings	coloring	NOUN
ejpam-5942	233	6	of	of	ADP
ejpam-5942	233	7	ic	ic	PROPN
ejpam-5942	233	8	-	-	PUNCT
ejpam-5942	233	9	planar	planar	ADJ
ejpam-5942	233	10	graphs	graph	NOUN
ejpam-5942	233	11	with	with	ADP
ejpam-5942	233	12	maximum	maximum	ADJ
ejpam-5942	233	13	degree	degree	NOUN
ejpam-5942	233	14	13	13	NUM
ejpam-5942	233	15	.	.	PUNCT
ejpam-5942	233	16	journal	journal	NOUN
ejpam-5942	233	17	of	of	ADP
ejpam-5942	233	18	combinatorial	combinatorial	ADJ
ejpam-5942	233	19	optimization	optimization	NOUN
ejpam-5942	233	20	,	,	PUNCT
ejpam-5942	233	21	39(1):293–303	39(1):293–303	NUM
ejpam-5942	233	22	,	,	PUNCT
ejpam-5942	233	23	2020	2020	NUM
ejpam-5942	233	24	.	.	PUNCT
ejpam-5942	234	1	[	[	X
ejpam-5942	234	2	19	19	NUM
ejpam-5942	234	3	]	]	X
ejpam-5942	234	4	d.	d.	PROPN
ejpam-5942	234	5	zhang	zhang	PROPN
ejpam-5942	234	6	.	.	PROPN
ejpam-5942	234	7	neighbor	neighbor	PROPN
ejpam-5942	234	8	sum	sum	NOUN
ejpam-5942	234	9	distinguishing	distinguish	VERB
ejpam-5942	234	10	total	total	ADJ
ejpam-5942	234	11	choice	choice	NOUN
ejpam-5942	234	12	number	number	NOUN
ejpam-5942	234	13	of	of	ADP
ejpam-5942	234	14	nic	nic	NOUN
ejpam-5942	234	15	-	-	PUNCT
ejpam-5942	234	16	planar	planar	ADJ
ejpam-5942	234	17	graphs	graph	NOUN
ejpam-5942	234	18	with	with	ADP
ejpam-5942	234	19	restricted	restricted	ADJ
ejpam-5942	234	20	conditions	condition	NOUN
ejpam-5942	234	21	.	.	PUNCT
ejpam-5942	235	1	journal	journal	NOUN
ejpam-5942	235	2	of	of	ADP
ejpam-5942	235	3	discrete	discrete	ADJ
ejpam-5942	235	4	mathematical	mathematical	ADJ
ejpam-5942	235	5	sciences	science	NOUN
ejpam-5942	235	6	and	and	CCONJ
ejpam-5942	235	7	cryptography	cryptography	NOUN
ejpam-5942	235	8	,	,	PUNCT
ejpam-5942	235	9	24(6):1845–1856	24(6):1845–1856	NUM
ejpam-5942	235	10	,	,	PUNCT
ejpam-5942	235	11	2021	2021	NUM
ejpam-5942	235	12	.	.	PUNCT
ejpam-5942	236	1	[	[	X
ejpam-5942	236	2	20	20	NUM
ejpam-5942	236	3	]	]	PUNCT
ejpam-5942	236	4	j.	j.	PROPN
ejpam-5942	236	5	wang	wang	PROPN
ejpam-5942	236	6	,	,	PUNCT
ejpam-5942	236	7	j.	j.	PROPN
ejpam-5942	236	8	cai	cai	PROPN
ejpam-5942	236	9	,	,	PUNCT
ejpam-5942	236	10	and	and	CCONJ
ejpam-5942	236	11	q.	q.	PROPN
ejpam-5942	236	12	ma	ma	PROPN
ejpam-5942	236	13	.	.	PROPN
ejpam-5942	236	14	neighbor	neighbor	PROPN
ejpam-5942	236	15	sum	sum	NOUN
ejpam-5942	236	16	distinguishing	distinguish	VERB
ejpam-5942	236	17	total	total	ADJ
ejpam-5942	236	18	choosability	choosability	NOUN
ejpam-5942	236	19	of	of	ADP
ejpam-5942	236	20	planar	planar	ADJ
ejpam-5942	236	21	graphs	graph	NOUN
ejpam-5942	236	22	without	without	ADP
ejpam-5942	236	23	4	4	NOUN
ejpam-5942	236	24	-	-	PUNCT
ejpam-5942	236	25	cycles	cycle	NOUN
ejpam-5942	236	26	.	.	PUNCT
ejpam-5942	237	1	discrete	discrete	ADJ
ejpam-5942	237	2	applied	apply	VERB
ejpam-5942	237	3	mathematics	mathematic	NOUN
ejpam-5942	237	4	,	,	PUNCT
ejpam-5942	237	5	206:215–219	206:215–219	NUM
ejpam-5942	237	6	,	,	PUNCT
ejpam-5942	237	7	2016	2016	NUM
ejpam-5942	237	8	.	.	PUNCT