id	sid	tid	token	lemma	pos
ejpam-4492	1	1	european	european	PROPN
ejpam-4492	1	2	journal	journal	PROPN
ejpam-4492	1	3	of	of	ADP
ejpam-4492	1	4	pure	pure	ADJ
ejpam-4492	1	5	and	and	CCONJ
ejpam-4492	1	6	applied	apply	VERB
ejpam-4492	1	7	mathematics	mathematic	NOUN
ejpam-4492	1	8	vol	vol	NOUN
ejpam-4492	1	9	.	.	PROPN
ejpam-4492	2	1	15	15	NUM
ejpam-4492	2	2	,	,	PUNCT
ejpam-4492	2	3	no	no	INTJ
ejpam-4492	2	4	.	.	NOUN
ejpam-4492	2	5	3	3	NUM
ejpam-4492	2	6	,	,	PUNCT
ejpam-4492	2	7	2022	2022	NUM
ejpam-4492	2	8	,	,	PUNCT
ejpam-4492	2	9	1331	1331	NUM
ejpam-4492	2	10	-	-	SYM
ejpam-4492	2	11	1343	1343	NUM
ejpam-4492	2	12	issn	issn	PROPN
ejpam-4492	2	13	1307	1307	NUM
ejpam-4492	2	14	-	-	SYM
ejpam-4492	2	15	5543	5543	NUM
ejpam-4492	2	16	–	–	PUNCT
ejpam-4492	2	17	ejpam.com	ejpam.com	X
ejpam-4492	2	18	published	publish	VERB
ejpam-4492	2	19	by	by	ADP
ejpam-4492	2	20	new	new	PROPN
ejpam-4492	2	21	york	york	PROPN
ejpam-4492	2	22	business	business	PROPN
ejpam-4492	2	23	global	global	PROPN
ejpam-4492	2	24	on	on	ADP
ejpam-4492	2	25	the	the	DET
ejpam-4492	2	26	planarity	planarity	NOUN
ejpam-4492	2	27	of	of	ADP
ejpam-4492	2	28	a	a	DET
ejpam-4492	2	29	directed	direct	VERB
ejpam-4492	2	30	pathos	pathos	NOUN
ejpam-4492	2	31	total	total	NOUN
ejpam-4492	2	32	digraph	digraph	NOUN
ejpam-4492	2	33	of	of	ADP
ejpam-4492	2	34	some	some	DET
ejpam-4492	2	35	special	special	ADJ
ejpam-4492	2	36	arborescence	arborescence	NOUN
ejpam-4492	2	37	graphs	graph	NOUN
ejpam-4492	2	38	jill	jill	PROPN
ejpam-4492	2	39	maegan	maegan	PROPN
ejpam-4492	2	40	b.	b.	PROPN
ejpam-4492	2	41	pamplona1	pamplona1	PROPN
ejpam-4492	2	42	,	,	PUNCT
ejpam-4492	3	1	imelda	imelda	PROPN
ejpam-4492	3	2	s.	s.	PROPN
ejpam-4492	3	3	aniversario2	aniversario2	PROPN
ejpam-4492	4	1	1	1	NUM
ejpam-4492	4	2	mathematics	mathematics	PROPN
ejpam-4492	4	3	department	department	NOUN
ejpam-4492	4	4	,	,	PUNCT
ejpam-4492	4	5	northwestern	northwestern	ADJ
ejpam-4492	4	6	mindanao	mindanao	PROPN
ejpam-4492	4	7	state	state	PROPN
ejpam-4492	4	8	college	college	PROPN
ejpam-4492	4	9	of	of	ADP
ejpam-4492	4	10	science	science	NOUN
ejpam-4492	4	11	and	and	CCONJ
ejpam-4492	4	12	technology	technology	NOUN
ejpam-4492	4	13	,	,	PUNCT
ejpam-4492	4	14	tangub	tangub	NOUN
ejpam-4492	4	15	city	city	PROPN
ejpam-4492	4	16	,	,	PUNCT
ejpam-4492	4	17	misamis	misamis	PROPN
ejpam-4492	4	18	occidental	occidental	PROPN
ejpam-4492	4	19	2	2	NUM
ejpam-4492	4	20	department	department	NOUN
ejpam-4492	4	21	of	of	ADP
ejpam-4492	4	22	mathematics	mathematic	NOUN
ejpam-4492	4	23	and	and	CCONJ
ejpam-4492	4	24	statistics	statistic	NOUN
ejpam-4492	4	25	,	,	PUNCT
ejpam-4492	4	26	college	college	NOUN
ejpam-4492	4	27	of	of	ADP
ejpam-4492	4	28	science	science	NOUN
ejpam-4492	4	29	and	and	CCONJ
ejpam-4492	4	30	mathematics	mathematic	NOUN
ejpam-4492	4	31	,	,	PUNCT
ejpam-4492	4	32	mindanao	mindanao	PROPN
ejpam-4492	4	33	state	state	PROPN
ejpam-4492	4	34	university	university	PROPN
ejpam-4492	4	35	iligan	iligan	PROPN
ejpam-4492	4	36	institute	institute	PROPN
ejpam-4492	4	37	of	of	ADP
ejpam-4492	4	38	technology	technology	PROPN
ejpam-4492	4	39	,	,	PUNCT
ejpam-4492	4	40	9200	9200	NUM
ejpam-4492	4	41	iligan	iligan	ADJ
ejpam-4492	4	42	city	city	NOUN
ejpam-4492	4	43	,	,	PUNCT
ejpam-4492	4	44	philippines	philippine	NOUN
ejpam-4492	4	45	abstract	abstract	ADJ
ejpam-4492	4	46	.	.	PUNCT
ejpam-4492	5	1	an	an	DET
ejpam-4492	5	2	arborescence	arborescence	NOUN
ejpam-4492	5	3	graph	graph	NOUN
ejpam-4492	5	4	is	be	AUX
ejpam-4492	5	5	a	a	DET
ejpam-4492	5	6	directed	direct	VERB
ejpam-4492	5	7	graph	graph	NOUN
ejpam-4492	5	8	in	in	ADP
ejpam-4492	5	9	which	which	PRON
ejpam-4492	5	10	,	,	PUNCT
ejpam-4492	5	11	for	for	ADP
ejpam-4492	5	12	a	a	DET
ejpam-4492	5	13	vertex	vertex	NOUN
ejpam-4492	5	14	u	u	NOUN
ejpam-4492	5	15	called	call	VERB
ejpam-4492	5	16	the	the	DET
ejpam-4492	5	17	root	root	NOUN
ejpam-4492	5	18	,	,	PUNCT
ejpam-4492	5	19	and	and	CCONJ
ejpam-4492	5	20	any	any	DET
ejpam-4492	5	21	other	other	ADJ
ejpam-4492	5	22	vertex	vertex	NOUN
ejpam-4492	5	23	v	v	NOUN
ejpam-4492	5	24	,	,	PUNCT
ejpam-4492	5	25	there	there	PRON
ejpam-4492	5	26	is	be	VERB
ejpam-4492	5	27	exactly	exactly	ADV
ejpam-4492	5	28	one	one	NUM
ejpam-4492	5	29	directed	direct	VERB
ejpam-4492	5	30	path	path	NOUN
ejpam-4492	5	31	from	from	ADP
ejpam-4492	5	32	u	u	PRON
ejpam-4492	5	33	to	to	ADP
ejpam-4492	5	34	v.	v.	ADP
ejpam-4492	5	35	the	the	DET
ejpam-4492	5	36	directed	direct	VERB
ejpam-4492	5	37	pathos	pathos	NOUN
ejpam-4492	5	38	of	of	ADP
ejpam-4492	5	39	an	an	DET
ejpam-4492	5	40	arborescence	arborescence	NOUN
ejpam-4492	5	41	ar	ar	PROPN
ejpam-4492	5	42	is	be	AUX
ejpam-4492	5	43	defined	define	VERB
ejpam-4492	5	44	as	as	ADP
ejpam-4492	5	45	a	a	DET
ejpam-4492	5	46	collection	collection	NOUN
ejpam-4492	5	47	of	of	ADP
ejpam-4492	5	48	minimum	minimum	ADJ
ejpam-4492	5	49	number	number	NOUN
ejpam-4492	5	50	of	of	ADP
ejpam-4492	5	51	arc	arc	NOUN
ejpam-4492	5	52	disjoint	disjoint	VERB
ejpam-4492	5	53	open	open	ADJ
ejpam-4492	5	54	directed	direct	VERB
ejpam-4492	5	55	paths	path	NOUN
ejpam-4492	5	56	whose	whose	DET
ejpam-4492	5	57	union	union	NOUN
ejpam-4492	5	58	is	be	AUX
ejpam-4492	5	59	ar	ar	NOUN
ejpam-4492	5	60	.	.	PUNCT
ejpam-4492	5	61	in	in	ADP
ejpam-4492	5	62	[	[	X
ejpam-4492	5	63	6	6	NUM
ejpam-4492	5	64	]	]	PUNCT
ejpam-4492	5	65	,	,	PUNCT
ejpam-4492	5	66	for	for	ADP
ejpam-4492	5	67	an	an	DET
ejpam-4492	5	68	arborescence	arborescence	PROPN
ejpam-4492	5	69	ar	ar	PROPN
ejpam-4492	5	70	,	,	PUNCT
ejpam-4492	5	71	a	a	DET
ejpam-4492	5	72	directed	direct	VERB
ejpam-4492	5	73	pathos	pathos	NOUN
ejpam-4492	5	74	total	total	NOUN
ejpam-4492	5	75	digraph	digraph	NOUN
ejpam-4492	5	76	q	q	PROPN
ejpam-4492	5	77	=	=	SYM
ejpam-4492	5	78	dpt	dpt	PROPN
ejpam-4492	5	79	(	(	PUNCT
ejpam-4492	5	80	ar	ar	NOUN
ejpam-4492	5	81	)	)	PUNCT
ejpam-4492	5	82	has	have	AUX
ejpam-4492	5	83	vertex	vertex	NOUN
ejpam-4492	5	84	set	set	VERB
ejpam-4492	5	85	v	v	NOUN
ejpam-4492	5	86	(	(	PUNCT
ejpam-4492	5	87	q	q	NOUN
ejpam-4492	5	88	)	)	PUNCT
ejpam-4492	5	89	=	=	SYM
ejpam-4492	5	90	v	v	X
ejpam-4492	5	91	(	(	PUNCT
ejpam-4492	5	92	ar	ar	NOUN
ejpam-4492	5	93	)	)	PUNCT
ejpam-4492	5	94	∪	∪	ADP
ejpam-4492	5	95	a(ar	a(ar	NOUN
ejpam-4492	5	96	)	)	PUNCT
ejpam-4492	5	97	∪	∪	ADP
ejpam-4492	5	98	p	p	PROPN
ejpam-4492	5	99	(	(	PUNCT
ejpam-4492	5	100	ar	ar	NOUN
ejpam-4492	5	101	)	)	PUNCT
ejpam-4492	5	102	,	,	PUNCT
ejpam-4492	5	103	where	where	SCONJ
ejpam-4492	5	104	v	v	NOUN
ejpam-4492	5	105	(	(	PUNCT
ejpam-4492	5	106	ar	ar	NOUN
ejpam-4492	5	107	)	)	PUNCT
ejpam-4492	5	108	is	be	AUX
ejpam-4492	5	109	the	the	DET
ejpam-4492	5	110	vertex	vertex	NOUN
ejpam-4492	5	111	set	set	NOUN
ejpam-4492	5	112	,	,	PUNCT
ejpam-4492	5	113	a(ar	a(ar	NOUN
ejpam-4492	5	114	)	)	PUNCT
ejpam-4492	5	115	is	be	AUX
ejpam-4492	5	116	the	the	DET
ejpam-4492	5	117	arc	arc	NOUN
ejpam-4492	5	118	set	set	NOUN
ejpam-4492	5	119	,	,	PUNCT
ejpam-4492	5	120	and	and	CCONJ
ejpam-4492	5	121	p	p	NOUN
ejpam-4492	5	122	(	(	PUNCT
ejpam-4492	5	123	ar	ar	NOUN
ejpam-4492	5	124	)	)	PUNCT
ejpam-4492	5	125	is	be	AUX
ejpam-4492	5	126	a	a	DET
ejpam-4492	5	127	directed	direct	VERB
ejpam-4492	5	128	pathos	pathos	NOUN
ejpam-4492	5	129	set	set	NOUN
ejpam-4492	5	130	of	of	ADP
ejpam-4492	5	131	ar	ar	PROPN
ejpam-4492	5	132	.	.	PUNCT
ejpam-4492	6	1	the	the	DET
ejpam-4492	6	2	arc	arc	NOUN
ejpam-4492	6	3	set	set	VERB
ejpam-4492	6	4	a(q	a(q	NOUN
ejpam-4492	6	5	)	)	PUNCT
ejpam-4492	6	6	consists	consist	VERB
ejpam-4492	6	7	of	of	ADP
ejpam-4492	6	8	the	the	DET
ejpam-4492	6	9	following	following	ADJ
ejpam-4492	6	10	arcs	arc	NOUN
ejpam-4492	6	11	:	:	PUNCT
ejpam-4492	7	1	ab	ab	PROPN
ejpam-4492	7	2	such	such	ADJ
ejpam-4492	7	3	that	that	SCONJ
ejpam-4492	7	4	a	a	PRON
ejpam-4492	7	5	,	,	PUNCT
ejpam-4492	7	6	b	b	PROPN
ejpam-4492	7	7	∈	∈	PROPN
ejpam-4492	7	8	a(ar	a(ar	PROPN
ejpam-4492	7	9	)	)	PUNCT
ejpam-4492	7	10	and	and	CCONJ
ejpam-4492	7	11	the	the	DET
ejpam-4492	7	12	head	head	NOUN
ejpam-4492	7	13	of	of	ADP
ejpam-4492	7	14	a	a	DET
ejpam-4492	7	15	coincides	coincide	NOUN
ejpam-4492	7	16	with	with	ADP
ejpam-4492	7	17	the	the	DET
ejpam-4492	7	18	tail	tail	NOUN
ejpam-4492	7	19	of	of	ADP
ejpam-4492	7	20	b	b	NOUN
ejpam-4492	7	21	;	;	PUNCT
ejpam-4492	7	22	uv	uv	NOUN
ejpam-4492	7	23	such	such	ADJ
ejpam-4492	7	24	that	that	DET
ejpam-4492	7	25	u	u	NOUN
ejpam-4492	7	26	,	,	PUNCT
ejpam-4492	7	27	v	v	PROPN
ejpam-4492	7	28	∈	∈	PROPN
ejpam-4492	7	29	v	v	NOUN
ejpam-4492	7	30	(	(	PUNCT
ejpam-4492	7	31	ar	ar	NOUN
ejpam-4492	7	32	)	)	PUNCT
ejpam-4492	7	33	and	and	CCONJ
ejpam-4492	7	34	u	u	NOUN
ejpam-4492	7	35	is	be	AUX
ejpam-4492	7	36	adjacent	adjacent	ADJ
ejpam-4492	7	37	to	to	ADP
ejpam-4492	7	38	v	v	NOUN
ejpam-4492	7	39	;	;	PUNCT
ejpam-4492	7	40	au(ua	au(ua	PROPN
ejpam-4492	7	41	)	)	PUNCT
ejpam-4492	7	42	such	such	ADJ
ejpam-4492	7	43	that	that	SCONJ
ejpam-4492	7	44	a	a	DET
ejpam-4492	7	45	∈	∈	PROPN
ejpam-4492	7	46	a(ar	a(ar	NOUN
ejpam-4492	7	47	)	)	PUNCT
ejpam-4492	7	48	and	and	CCONJ
ejpam-4492	7	49	u	u	PROPN
ejpam-4492	7	50	∈	∈	PROPN
ejpam-4492	7	51	v	v	ADP
ejpam-4492	7	52	(	(	PUNCT
ejpam-4492	7	53	ar	ar	NOUN
ejpam-4492	7	54	)	)	PUNCT
ejpam-4492	7	55	and	and	CCONJ
ejpam-4492	7	56	the	the	DET
ejpam-4492	7	57	head	head	NOUN
ejpam-4492	7	58	(	(	PUNCT
ejpam-4492	7	59	tail	tail	NOUN
ejpam-4492	7	60	)	)	PUNCT
ejpam-4492	7	61	of	of	ADP
ejpam-4492	7	62	a	a	PRON
ejpam-4492	7	63	is	be	AUX
ejpam-4492	7	64	u	u	NOUN
ejpam-4492	7	65	;	;	PUNCT
ejpam-4492	7	66	pa	pa	PROPN
ejpam-4492	7	67	such	such	ADJ
ejpam-4492	7	68	that	that	SCONJ
ejpam-4492	7	69	a	a	DET
ejpam-4492	7	70	∈	∈	PROPN
ejpam-4492	7	71	a(ar	a(ar	NOUN
ejpam-4492	7	72	)	)	PUNCT
ejpam-4492	7	73	and	and	CCONJ
ejpam-4492	7	74	p	p	NOUN
ejpam-4492	7	75	∈	∈	PROPN
ejpam-4492	7	76	p	p	X
ejpam-4492	7	77	(	(	PUNCT
ejpam-4492	7	78	ar	ar	NOUN
ejpam-4492	7	79	)	)	PUNCT
ejpam-4492	7	80	and	and	CCONJ
ejpam-4492	7	81	the	the	DET
ejpam-4492	7	82	arc	arc	NOUN
ejpam-4492	7	83	a	a	DET
ejpam-4492	7	84	lies	lie	NOUN
ejpam-4492	7	85	on	on	ADP
ejpam-4492	7	86	the	the	DET
ejpam-4492	7	87	directed	direct	VERB
ejpam-4492	7	88	path	path	NOUN
ejpam-4492	7	89	p	p	NOUN
ejpam-4492	7	90	;	;	PUNCT
ejpam-4492	7	91	pipj	pipj	VERB
ejpam-4492	7	92	such	such	DET
ejpam-4492	7	93	that	that	DET
ejpam-4492	7	94	pi	pi	NOUN
ejpam-4492	7	95	,	,	PUNCT
ejpam-4492	7	96	pj	pj	PROPN
ejpam-4492	7	97	∈	∈	PROPN
ejpam-4492	7	98	p	p	PROPN
ejpam-4492	7	99	(	(	PUNCT
ejpam-4492	7	100	ar	ar	NOUN
ejpam-4492	7	101	)	)	PUNCT
ejpam-4492	7	102	and	and	CCONJ
ejpam-4492	7	103	it	it	PRON
ejpam-4492	7	104	is	be	AUX
ejpam-4492	7	105	possible	possible	ADJ
ejpam-4492	7	106	to	to	PART
ejpam-4492	7	107	reach	reach	VERB
ejpam-4492	7	108	the	the	DET
ejpam-4492	7	109	head	head	NOUN
ejpam-4492	7	110	of	of	ADP
ejpam-4492	7	111	pj	pj	PROPN
ejpam-4492	7	112	from	from	ADP
ejpam-4492	7	113	the	the	DET
ejpam-4492	7	114	tail	tail	NOUN
ejpam-4492	7	115	of	of	ADP
ejpam-4492	7	116	pi	pi	NOUN
ejpam-4492	7	117	through	through	ADP
ejpam-4492	7	118	a	a	DET
ejpam-4492	7	119	common	common	ADJ
ejpam-4492	7	120	vertex	vertex	NOUN
ejpam-4492	7	121	,	,	PUNCT
ejpam-4492	7	122	and	and	CCONJ
ejpam-4492	7	123	it	it	PRON
ejpam-4492	7	124	is	be	AUX
ejpam-4492	7	125	also	also	ADV
ejpam-4492	7	126	possible	possible	ADJ
ejpam-4492	7	127	to	to	PART
ejpam-4492	7	128	reach	reach	VERB
ejpam-4492	7	129	the	the	DET
ejpam-4492	7	130	head	head	NOUN
ejpam-4492	7	131	of	of	ADP
ejpam-4492	7	132	pi	pi	NOUN
ejpam-4492	7	133	from	from	ADP
ejpam-4492	7	134	the	the	DET
ejpam-4492	7	135	tail	tail	NOUN
ejpam-4492	7	136	of	of	ADP
ejpam-4492	7	137	pj	pj	PROPN
ejpam-4492	7	138	.	.	PUNCT
ejpam-4492	8	1	in	in	ADP
ejpam-4492	8	2	this	this	DET
ejpam-4492	8	3	paper	paper	NOUN
ejpam-4492	8	4	,	,	PUNCT
ejpam-4492	8	5	the	the	DET
ejpam-4492	8	6	concept	concept	NOUN
ejpam-4492	8	7	of	of	ADP
ejpam-4492	8	8	planarity	planarity	NOUN
ejpam-4492	8	9	of	of	ADP
ejpam-4492	8	10	the	the	DET
ejpam-4492	8	11	directed	direct	VERB
ejpam-4492	8	12	pathos	pathos	NOUN
ejpam-4492	8	13	total	total	NOUN
ejpam-4492	8	14	digraph	digraph	NOUN
ejpam-4492	8	15	(	(	PUNCT
ejpam-4492	8	16	that	that	PRON
ejpam-4492	8	17	is	is	ADV
ejpam-4492	8	18	,	,	PUNCT
ejpam-4492	8	19	as	as	ADP
ejpam-4492	8	20	an	an	DET
ejpam-4492	8	21	acyclic	acyclic	ADJ
ejpam-4492	8	22	directed	direct	VERB
ejpam-4492	8	23	graph	graph	NOUN
ejpam-4492	8	24	which	which	PRON
ejpam-4492	8	25	can	can	AUX
ejpam-4492	8	26	be	be	AUX
ejpam-4492	8	27	drawn	draw	VERB
ejpam-4492	8	28	with	with	ADP
ejpam-4492	8	29	non	non	ADJ
ejpam-4492	8	30	crossing	cross	VERB
ejpam-4492	8	31	arcs	arc	NOUN
ejpam-4492	8	32	oriented	orient	VERB
ejpam-4492	8	33	in	in	ADP
ejpam-4492	8	34	one	one	NUM
ejpam-4492	8	35	direction	direction	NOUN
ejpam-4492	8	36	)	)	PUNCT
ejpam-4492	8	37	is	be	AUX
ejpam-4492	8	38	being	be	AUX
ejpam-4492	8	39	discussed	discuss	VERB
ejpam-4492	8	40	and	and	CCONJ
ejpam-4492	8	41	applied	apply	VERB
ejpam-4492	8	42	to	to	ADP
ejpam-4492	8	43	a	a	DET
ejpam-4492	8	44	directed	direct	VERB
ejpam-4492	8	45	pathos	pathos	NOUN
ejpam-4492	8	46	total	total	NOUN
ejpam-4492	8	47	digraph	digraph	NOUN
ejpam-4492	8	48	of	of	ADP
ejpam-4492	8	49	an	an	DET
ejpam-4492	8	50	arborescence	arborescence	NOUN
ejpam-4492	8	51	ar	ar	PROPN
ejpam-4492	8	52	(	(	PUNCT
ejpam-4492	8	53	dpt	dpt	PROPN
ejpam-4492	8	54	(	(	PUNCT
ejpam-4492	8	55	ar	ar	NOUN
ejpam-4492	8	56	)	)	PUNCT
ejpam-4492	8	57	)	)	PUNCT
ejpam-4492	8	58	.	.	PUNCT
ejpam-4492	9	1	further	far	ADV
ejpam-4492	9	2	,	,	PUNCT
ejpam-4492	9	3	the	the	DET
ejpam-4492	9	4	internal	internal	ADJ
ejpam-4492	9	5	vertices	vertex	NOUN
ejpam-4492	9	6	of	of	ADP
ejpam-4492	9	7	these	these	DET
ejpam-4492	9	8	directed	direct	VERB
ejpam-4492	9	9	pathos	pathos	NOUN
ejpam-4492	9	10	total	total	NOUN
ejpam-4492	9	11	digraph	digraph	NOUN
ejpam-4492	9	12	of	of	ADP
ejpam-4492	9	13	ar	ar	NOUN
ejpam-4492	9	14	are	be	AUX
ejpam-4492	9	15	cconsidered	cconsidere	VERB
ejpam-4492	9	16	.	.	PUNCT
ejpam-4492	10	1	finally	finally	ADV
ejpam-4492	10	2	,	,	PUNCT
ejpam-4492	10	3	the	the	DET
ejpam-4492	10	4	planarity	planarity	NOUN
ejpam-4492	10	5	of	of	ADP
ejpam-4492	10	6	an	an	DET
ejpam-4492	10	7	arborescence	arborescence	NOUN
ejpam-4492	10	8	resulting	result	VERB
ejpam-4492	10	9	from	from	ADP
ejpam-4492	10	10	the	the	DET
ejpam-4492	10	11	vertex	vertex	NOUN
ejpam-4492	10	12	-	-	PUNCT
ejpam-4492	10	13	gluing	gluing	NOUN
ejpam-4492	10	14	of	of	ADP
ejpam-4492	10	15	two	two	NUM
ejpam-4492	10	16	directed	direct	VERB
ejpam-4492	10	17	paths	path	NOUN
ejpam-4492	10	18	is	be	AUX
ejpam-4492	10	19	presented	present	VERB
ejpam-4492	10	20	and	and	CCONJ
ejpam-4492	10	21	corresponding	correspond	VERB
ejpam-4492	10	22	internal	internal	ADJ
ejpam-4492	10	23	vertex	vertex	NOUN
ejpam-4492	10	24	number	number	NOUN
ejpam-4492	10	25	is	be	AUX
ejpam-4492	10	26	obtained	obtain	VERB
ejpam-4492	10	27	.	.	PUNCT
ejpam-4492	11	1	2020	2020	NUM
ejpam-4492	11	2	mathematics	mathematic	NOUN
ejpam-4492	11	3	subject	subject	NOUN
ejpam-4492	11	4	classifications	classification	NOUN
ejpam-4492	11	5	:	:	PUNCT
ejpam-4492	11	6	05c20	05c20	NUM
ejpam-4492	11	7	key	key	ADJ
ejpam-4492	11	8	words	word	NOUN
ejpam-4492	11	9	and	and	CCONJ
ejpam-4492	11	10	phrases	phrase	NOUN
ejpam-4492	11	11	:	:	PUNCT
ejpam-4492	11	12	directed	direct	VERB
ejpam-4492	11	13	path	path	NOUN
ejpam-4492	11	14	,	,	PUNCT
ejpam-4492	11	15	arborescence	arborescence	NOUN
ejpam-4492	11	16	graph	graph	NOUN
ejpam-4492	11	17	,	,	PUNCT
ejpam-4492	11	18	directed	direct	VERB
ejpam-4492	11	19	pathos	pathos	NOUN
ejpam-4492	11	20	total	total	ADJ
ejpam-4492	11	21	digraph	digraph	NOUN
ejpam-4492	11	22	of	of	ADP
ejpam-4492	11	23	an	an	DET
ejpam-4492	11	24	arborescence	arborescence	NOUN
ejpam-4492	11	25	,	,	PUNCT
ejpam-4492	11	26	internal	internal	ADJ
ejpam-4492	11	27	vertex	vertex	NOUN
ejpam-4492	11	28	number	number	NOUN
ejpam-4492	11	29	of	of	ADP
ejpam-4492	11	30	a	a	DET
ejpam-4492	11	31	directed	direct	VERB
ejpam-4492	11	32	pathos	pathos	NOUN
ejpam-4492	11	33	total	total	NOUN
ejpam-4492	11	34	digraph	digraph	NOUN
ejpam-4492	11	35	of	of	ADP
ejpam-4492	11	36	an	an	DET
ejpam-4492	11	37	arborescence	arborescence	NOUN
ejpam-4492	11	38	doi	doi	NOUN
ejpam-4492	11	39	:	:	PUNCT
ejpam-4492	11	40	https://doi.org/10.29020/nybg.ejpam.v15i3.4492	https://doi.org/10.29020/nybg.ejpam.v15i3.4492	NOUN
ejpam-4492	11	41	email	email	NOUN
ejpam-4492	11	42	addresses	address	NOUN
ejpam-4492	11	43	:	:	PUNCT
ejpam-4492	11	44	jillmaegan.pamplona@g.msuiit.edu.ph	jillmaegan.pamplona@g.msuiit.edu.ph	PROPN
ejpam-4492	11	45	(	(	PUNCT
ejpam-4492	11	46	j.m.e	j.m.e	PROPN
ejpam-4492	11	47	.	.	PUNCT
ejpam-4492	11	48	pamplona	pamplona	PROPN
ejpam-4492	11	49	)	)	PUNCT
ejpam-4492	11	50	,	,	PUNCT
ejpam-4492	11	51	imelda.aniverasrio@g.msuiit.edu.ph	imelda.aniverasrio@g.msuiit.edu.ph	PROPN
ejpam-4492	11	52	(	(	PUNCT
ejpam-4492	11	53	i.s	i.s	PROPN
ejpam-4492	11	54	.	.	PROPN
ejpam-4492	11	55	aniverasrio	aniverasrio	PROPN
ejpam-4492	11	56	)	)	PUNCT
ejpam-4492	11	57	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4492	11	58	1331	1331	NUM
ejpam-4492	12	1	©	©	ADP
ejpam-4492	12	2	2022	2022	NUM
ejpam-4492	12	3	ejpam	ejpam	VERB
ejpam-4492	12	4	all	all	DET
ejpam-4492	12	5	rights	right	NOUN
ejpam-4492	12	6	reserved	reserve	VERB
ejpam-4492	12	7	.	.	PUNCT
ejpam-4492	13	1	jill	jill	PROPN
ejpam-4492	13	2	maegan	maegan	PROPN
ejpam-4492	13	3	b.	b.	PROPN
ejpam-4492	13	4	pamplona	pamplona	PROPN
ejpam-4492	13	5	,	,	PUNCT
ejpam-4492	13	6	imelda	imelda	PROPN
ejpam-4492	13	7	s.	s.	PROPN
ejpam-4492	13	8	aniversario	aniversario	PROPN
ejpam-4492	13	9	/	/	SYM
ejpam-4492	13	10	eur	eur	PROPN
ejpam-4492	13	11	.	.	PUNCT
ejpam-4492	14	1	j.	j.	PROPN
ejpam-4492	14	2	pure	pure	PROPN
ejpam-4492	14	3	appl	appl	PROPN
ejpam-4492	14	4	.	.	PROPN
ejpam-4492	14	5	math	math	PROPN
ejpam-4492	14	6	,	,	PUNCT
ejpam-4492	14	7	15	15	NUM
ejpam-4492	14	8	(	(	PUNCT
ejpam-4492	14	9	3	3	NUM
ejpam-4492	14	10	)	)	PUNCT
ejpam-4492	14	11	(	(	PUNCT
ejpam-4492	14	12	2022	2022	NUM
ejpam-4492	14	13	)	)	PUNCT
ejpam-4492	14	14	,	,	PUNCT
ejpam-4492	14	15	1331	1331	NUM
ejpam-4492	14	16	-	-	SYM
ejpam-4492	14	17	1343	1343	NUM
ejpam-4492	14	18	1332	1332	NUM
ejpam-4492	14	19	1	1	NUM
ejpam-4492	14	20	.	.	PUNCT
ejpam-4492	15	1	introduction	introduction	NOUN
ejpam-4492	15	2	there	there	PRON
ejpam-4492	15	3	are	be	VERB
ejpam-4492	15	4	many	many	ADJ
ejpam-4492	15	5	graph	graph	NOUN
ejpam-4492	15	6	valued	value	VERB
ejpam-4492	15	7	functions	function	NOUN
ejpam-4492	15	8	(	(	PUNCT
ejpam-4492	15	9	or	or	CCONJ
ejpam-4492	15	10	graph	graph	NOUN
ejpam-4492	15	11	operators	operator	NOUN
ejpam-4492	15	12	)	)	PUNCT
ejpam-4492	15	13	for	for	ADP
ejpam-4492	15	14	which	which	PRON
ejpam-4492	15	15	one	one	PRON
ejpam-4492	15	16	can	can	AUX
ejpam-4492	15	17	construct	construct	VERB
ejpam-4492	15	18	a	a	DET
ejpam-4492	15	19	new	new	ADJ
ejpam-4492	15	20	graph	graph	NOUN
ejpam-4492	15	21	from	from	ADP
ejpam-4492	15	22	a	a	DET
ejpam-4492	15	23	given	give	VERB
ejpam-4492	15	24	graph	graph	NOUN
ejpam-4492	15	25	,	,	PUNCT
ejpam-4492	15	26	such	such	ADJ
ejpam-4492	15	27	as	as	ADP
ejpam-4492	15	28	the	the	DET
ejpam-4492	15	29	line	line	NOUN
ejpam-4492	15	30	graphs	graph	NOUN
ejpam-4492	15	31	,	,	PUNCT
ejpam-4492	15	32	the	the	DET
ejpam-4492	15	33	total	total	ADJ
ejpam-4492	15	34	graphs	graph	NOUN
ejpam-4492	15	35	,	,	PUNCT
ejpam-4492	15	36	and	and	CCONJ
ejpam-4492	15	37	their	their	PRON
ejpam-4492	15	38	generalizations	generalization	NOUN
ejpam-4492	15	39	.	.	PUNCT
ejpam-4492	16	1	the	the	DET
ejpam-4492	16	2	line	line	NOUN
ejpam-4492	16	3	graph	graph	NOUN
ejpam-4492	16	4	of	of	ADP
ejpam-4492	16	5	a	a	DET
ejpam-4492	16	6	graph	graph	NOUN
ejpam-4492	16	7	g	g	NOUN
ejpam-4492	16	8	,	,	PUNCT
ejpam-4492	16	9	written	write	VERB
ejpam-4492	16	10	l(g	l(g	NOUN
ejpam-4492	16	11	)	)	PUNCT
ejpam-4492	16	12	,	,	PUNCT
ejpam-4492	16	13	is	be	AUX
ejpam-4492	16	14	the	the	DET
ejpam-4492	16	15	graph	graph	NOUN
ejpam-4492	16	16	whose	whose	DET
ejpam-4492	16	17	vertices	vertex	NOUN
ejpam-4492	16	18	are	be	AUX
ejpam-4492	16	19	the	the	DET
ejpam-4492	16	20	edges	edge	NOUN
ejpam-4492	16	21	of	of	ADP
ejpam-4492	16	22	g	g	NOUN
ejpam-4492	16	23	,	,	PUNCT
ejpam-4492	16	24	with	with	ADP
ejpam-4492	16	25	two	two	NUM
ejpam-4492	16	26	vertices	vertex	NOUN
ejpam-4492	16	27	of	of	ADP
ejpam-4492	16	28	l(g	l(g	NOUN
ejpam-4492	16	29	)	)	PUNCT
ejpam-4492	16	30	adjacent	adjacent	ADJ
ejpam-4492	16	31	whenever	whenever	SCONJ
ejpam-4492	16	32	the	the	DET
ejpam-4492	16	33	corresponding	corresponding	ADJ
ejpam-4492	16	34	edges	edge	NOUN
ejpam-4492	16	35	of	of	ADP
ejpam-4492	16	36	g	g	PROPN
ejpam-4492	16	37	have	have	VERB
ejpam-4492	16	38	a	a	DET
ejpam-4492	16	39	common	common	ADJ
ejpam-4492	16	40	vertex	vertex	NOUN
ejpam-4492	16	41	[	[	X
ejpam-4492	16	42	8	8	NUM
ejpam-4492	16	43	]	]	PUNCT
ejpam-4492	16	44	.	.	PUNCT
ejpam-4492	17	1	harary	harary	PROPN
ejpam-4492	17	2	and	and	CCONJ
ejpam-4492	17	3	norman	norman	NOUN
ejpam-4492	18	1	[	[	X
ejpam-4492	18	2	5	5	X
ejpam-4492	18	3	]	]	PUNCT
ejpam-4492	18	4	extended	extend	VERB
ejpam-4492	18	5	the	the	DET
ejpam-4492	18	6	concept	concept	NOUN
ejpam-4492	18	7	of	of	ADP
ejpam-4492	18	8	line	line	NOUN
ejpam-4492	18	9	graph	graph	NOUN
ejpam-4492	18	10	of	of	ADP
ejpam-4492	18	11	a	a	DET
ejpam-4492	18	12	graph	graph	NOUN
ejpam-4492	18	13	and	and	CCONJ
ejpam-4492	18	14	introduced	introduce	VERB
ejpam-4492	18	15	the	the	DET
ejpam-4492	18	16	concept	concept	NOUN
ejpam-4492	18	17	of	of	ADP
ejpam-4492	18	18	line	line	NOUN
ejpam-4492	18	19	digraph	digraph	NOUN
ejpam-4492	18	20	of	of	ADP
ejpam-4492	18	21	a	a	DET
ejpam-4492	18	22	directed	direct	VERB
ejpam-4492	18	23	graph	graph	NOUN
ejpam-4492	18	24	.	.	PUNCT
ejpam-4492	19	1	the	the	DET
ejpam-4492	19	2	line	line	NOUN
ejpam-4492	19	3	digraph	digraph	NOUN
ejpam-4492	19	4	l(d	l(d	PROPN
ejpam-4492	19	5	)	)	PUNCT
ejpam-4492	19	6	of	of	ADP
ejpam-4492	19	7	a	a	DET
ejpam-4492	19	8	digraph	digraph	NOUN
ejpam-4492	19	9	d	d	NOUN
ejpam-4492	19	10	has	have	VERB
ejpam-4492	19	11	the	the	DET
ejpam-4492	19	12	arcs	arc	NOUN
ejpam-4492	19	13	of	of	ADP
ejpam-4492	19	14	d	d	PROPN
ejpam-4492	19	15	as	as	ADP
ejpam-4492	19	16	vertices	vertex	NOUN
ejpam-4492	19	17	.	.	PUNCT
ejpam-4492	20	1	there	there	PRON
ejpam-4492	20	2	is	be	VERB
ejpam-4492	20	3	an	an	DET
ejpam-4492	20	4	arc	arc	NOUN
ejpam-4492	20	5	from	from	ADP
ejpam-4492	20	6	d	d	ADJ
ejpam-4492	20	7	-	-	PUNCT
ejpam-4492	20	8	arc	arc	NOUN
ejpam-4492	20	9	pq	pq	NOUN
ejpam-4492	20	10	towards	towards	ADP
ejpam-4492	20	11	d	d	NOUN
ejpam-4492	20	12	-	-	NOUN
ejpam-4492	20	13	arc	arc	NOUN
ejpam-4492	20	14	uv	uv	NOUN
ejpam-4492	20	15	if	if	SCONJ
ejpam-4492	21	1	and	and	CCONJ
ejpam-4492	21	2	only	only	ADV
ejpam-4492	21	3	if	if	SCONJ
ejpam-4492	21	4	q	q	PROPN
ejpam-4492	21	5	=	=	VERB
ejpam-4492	21	6	u.	u.	PROPN
ejpam-4492	21	7	behzad	behzad	PROPN
ejpam-4492	22	1	[	[	X
ejpam-4492	22	2	1	1	X
ejpam-4492	22	3	]	]	PUNCT
ejpam-4492	22	4	introduced	introduce	VERB
ejpam-4492	22	5	the	the	DET
ejpam-4492	22	6	concept	concept	NOUN
ejpam-4492	22	7	of	of	ADP
ejpam-4492	22	8	total	total	ADJ
ejpam-4492	22	9	graph	graph	NOUN
ejpam-4492	22	10	of	of	ADP
ejpam-4492	22	11	a	a	DET
ejpam-4492	22	12	graph	graph	NOUN
ejpam-4492	22	13	.	.	PUNCT
ejpam-4492	23	1	the	the	DET
ejpam-4492	23	2	total	total	ADJ
ejpam-4492	23	3	graph	graph	NOUN
ejpam-4492	23	4	of	of	ADP
ejpam-4492	23	5	a	a	DET
ejpam-4492	23	6	graph	graph	NOUN
ejpam-4492	23	7	g	g	NOUN
ejpam-4492	23	8	,	,	PUNCT
ejpam-4492	23	9	written	write	VERB
ejpam-4492	23	10	t	t	PROPN
ejpam-4492	23	11	(	(	PUNCT
ejpam-4492	23	12	g	g	NOUN
ejpam-4492	23	13	)	)	PUNCT
ejpam-4492	23	14	,	,	PUNCT
ejpam-4492	23	15	is	be	AUX
ejpam-4492	23	16	the	the	DET
ejpam-4492	23	17	graph	graph	NOUN
ejpam-4492	23	18	whose	whose	DET
ejpam-4492	23	19	vertices	vertex	NOUN
ejpam-4492	23	20	can	can	AUX
ejpam-4492	23	21	be	be	AUX
ejpam-4492	23	22	put	put	VERB
ejpam-4492	23	23	in	in	ADP
ejpam-4492	23	24	one	one	NUM
ejpam-4492	23	25	-	-	PUNCT
ejpam-4492	23	26	to	to	ADP
ejpam-4492	23	27	-	-	PUNCT
ejpam-4492	23	28	one	one	NUM
ejpam-4492	23	29	correspondence	correspondence	NOUN
ejpam-4492	23	30	with	with	ADP
ejpam-4492	23	31	the	the	DET
ejpam-4492	23	32	vertices	vertex	NOUN
ejpam-4492	23	33	and	and	CCONJ
ejpam-4492	23	34	edges	edge	NOUN
ejpam-4492	23	35	of	of	ADP
ejpam-4492	23	36	g	g	NOUN
ejpam-4492	23	37	in	in	ADP
ejpam-4492	23	38	such	such	DET
ejpam-4492	23	39	a	a	DET
ejpam-4492	23	40	way	way	NOUN
ejpam-4492	23	41	that	that	PRON
ejpam-4492	23	42	two	two	NUM
ejpam-4492	23	43	vertices	vertex	NOUN
ejpam-4492	23	44	of	of	ADP
ejpam-4492	23	45	t	t	PROPN
ejpam-4492	23	46	(	(	PUNCT
ejpam-4492	23	47	g	g	NOUN
ejpam-4492	23	48	)	)	PUNCT
ejpam-4492	23	49	are	be	AUX
ejpam-4492	23	50	adjacent	adjacent	ADJ
ejpam-4492	23	51	if	if	SCONJ
ejpam-4492	23	52	and	and	CCONJ
ejpam-4492	23	53	only	only	ADV
ejpam-4492	23	54	if	if	SCONJ
ejpam-4492	23	55	the	the	DET
ejpam-4492	23	56	corresponding	correspond	VERB
ejpam-4492	23	57	elements	element	NOUN
ejpam-4492	23	58	of	of	ADP
ejpam-4492	23	59	g	g	NOUN
ejpam-4492	23	60	are	be	AUX
ejpam-4492	23	61	adjacent	adjacent	ADJ
ejpam-4492	23	62	,	,	PUNCT
ejpam-4492	23	63	where	where	SCONJ
ejpam-4492	23	64	the	the	DET
ejpam-4492	23	65	vertices	vertex	NOUN
ejpam-4492	23	66	and	and	CCONJ
ejpam-4492	23	67	edges	edge	NOUN
ejpam-4492	23	68	of	of	ADP
ejpam-4492	23	69	g	g	NOUN
ejpam-4492	23	70	are	be	AUX
ejpam-4492	23	71	called	call	VERB
ejpam-4492	23	72	its	its	PRON
ejpam-4492	23	73	members	member	NOUN
ejpam-4492	23	74	.	.	PUNCT
ejpam-4492	24	1	gary	gary	PROPN
ejpam-4492	24	2	chatrand	chatrand	PROPN
ejpam-4492	24	3	and	and	CCONJ
ejpam-4492	24	4	james	james	PROPN
ejpam-4492	24	5	stewart	stewart	PROPN
ejpam-4492	25	1	[	[	X
ejpam-4492	25	2	2	2	NUM
ejpam-4492	25	3	]	]	PUNCT
ejpam-4492	25	4	extended	extend	VERB
ejpam-4492	25	5	the	the	DET
ejpam-4492	25	6	concept	concept	NOUN
ejpam-4492	25	7	of	of	ADP
ejpam-4492	25	8	total	total	ADJ
ejpam-4492	25	9	graph	graph	NOUN
ejpam-4492	25	10	of	of	ADP
ejpam-4492	25	11	a	a	DET
ejpam-4492	25	12	graph	graph	NOUN
ejpam-4492	25	13	to	to	ADP
ejpam-4492	25	14	the	the	DET
ejpam-4492	25	15	directed	direct	VERB
ejpam-4492	25	16	case	case	NOUN
ejpam-4492	25	17	thereby	thereby	ADV
ejpam-4492	25	18	introducing	introduce	VERB
ejpam-4492	25	19	the	the	DET
ejpam-4492	25	20	total	total	ADJ
ejpam-4492	25	21	digraph	digraph	NOUN
ejpam-4492	25	22	.	.	PUNCT
ejpam-4492	26	1	the	the	DET
ejpam-4492	26	2	total	total	ADJ
ejpam-4492	26	3	digraph	digraph	NOUN
ejpam-4492	26	4	of	of	ADP
ejpam-4492	26	5	a	a	DET
ejpam-4492	26	6	directed	direct	VERB
ejpam-4492	26	7	graph	graph	NOUN
ejpam-4492	26	8	d	d	NOUN
ejpam-4492	26	9	,	,	PUNCT
ejpam-4492	26	10	written	write	VERB
ejpam-4492	26	11	t	t	PROPN
ejpam-4492	26	12	(	(	PUNCT
ejpam-4492	26	13	d	d	PROPN
ejpam-4492	26	14	)	)	PUNCT
ejpam-4492	26	15	,	,	PUNCT
ejpam-4492	26	16	is	be	AUX
ejpam-4492	26	17	the	the	DET
ejpam-4492	26	18	digraph	digraph	NOUN
ejpam-4492	26	19	whose	whose	DET
ejpam-4492	26	20	vertices	vertex	NOUN
ejpam-4492	26	21	are	be	AUX
ejpam-4492	26	22	in	in	ADP
ejpam-4492	26	23	one	one	NUM
ejpam-4492	26	24	-	-	PUNCT
ejpam-4492	26	25	to	to	ADP
ejpam-4492	26	26	-	-	PUNCT
ejpam-4492	26	27	one	one	NUM
ejpam-4492	26	28	correspondence	correspondence	NOUN
ejpam-4492	26	29	with	with	ADP
ejpam-4492	26	30	the	the	DET
ejpam-4492	26	31	vertices	vertex	NOUN
ejpam-4492	26	32	and	and	CCONJ
ejpam-4492	26	33	arcs	arc	NOUN
ejpam-4492	26	34	of	of	ADP
ejpam-4492	26	35	d	d	PROPN
ejpam-4492	26	36	and	and	CCONJ
ejpam-4492	26	37	such	such	ADJ
ejpam-4492	26	38	that	that	SCONJ
ejpam-4492	26	39	the	the	DET
ejpam-4492	26	40	vertex	vertex	NOUN
ejpam-4492	26	41	u	u	NOUN
ejpam-4492	26	42	is	be	AUX
ejpam-4492	26	43	adjacent	adjacent	ADJ
ejpam-4492	26	44	to	to	ADP
ejpam-4492	26	45	the	the	DET
ejpam-4492	26	46	vertex	vertex	NOUN
ejpam-4492	26	47	v	v	NOUN
ejpam-4492	26	48	in	in	ADP
ejpam-4492	26	49	t	t	PROPN
ejpam-4492	26	50	(	(	PUNCT
ejpam-4492	26	51	d	d	NOUN
ejpam-4492	26	52	)	)	PUNCT
ejpam-4492	26	53	if	if	SCONJ
ejpam-4492	27	1	and	and	CCONJ
ejpam-4492	27	2	only	only	ADV
ejpam-4492	27	3	if	if	SCONJ
ejpam-4492	27	4	the	the	DET
ejpam-4492	27	5	element	element	NOUN
ejpam-4492	27	6	corresponding	correspond	VERB
ejpam-4492	27	7	to	to	ADP
ejpam-4492	27	8	u	u	PRON
ejpam-4492	27	9	is	be	AUX
ejpam-4492	27	10	adjacent	adjacent	ADJ
ejpam-4492	27	11	to	to	ADP
ejpam-4492	27	12	the	the	DET
ejpam-4492	27	13	element	element	NOUN
ejpam-4492	27	14	corresponding	correspond	VERB
ejpam-4492	27	15	to	to	ADP
ejpam-4492	27	16	v	v	NOUN
ejpam-4492	27	17	in	in	ADP
ejpam-4492	27	18	d.	d.	PROPN
ejpam-4492	27	19	the	the	DET
ejpam-4492	27	20	concept	concept	NOUN
ejpam-4492	27	21	of	of	ADP
ejpam-4492	27	22	pathos	pathos	NOUN
ejpam-4492	27	23	of	of	ADP
ejpam-4492	27	24	a	a	DET
ejpam-4492	27	25	graph	graph	NOUN
ejpam-4492	27	26	g	g	NOUN
ejpam-4492	27	27	was	be	AUX
ejpam-4492	27	28	introduced	introduce	VERB
ejpam-4492	27	29	by	by	ADP
ejpam-4492	27	30	harary	harary	NOUN
ejpam-4492	27	31	[	[	X
ejpam-4492	27	32	4	4	NUM
ejpam-4492	27	33	]	]	PUNCT
ejpam-4492	27	34	as	as	ADP
ejpam-4492	27	35	a	a	DET
ejpam-4492	27	36	collection	collection	NOUN
ejpam-4492	27	37	of	of	ADP
ejpam-4492	27	38	minimum	minimum	ADJ
ejpam-4492	27	39	number	number	NOUN
ejpam-4492	27	40	of	of	ADP
ejpam-4492	27	41	edge	edge	NOUN
ejpam-4492	27	42	disjoint	disjoint	X
ejpam-4492	27	43	open	open	ADJ
ejpam-4492	27	44	paths	path	NOUN
ejpam-4492	27	45	whose	whose	DET
ejpam-4492	27	46	union	union	NOUN
ejpam-4492	27	47	is	be	AUX
ejpam-4492	27	48	g.	g.	NOUN
ejpam-4492	27	49	the	the	DET
ejpam-4492	27	50	path	path	NOUN
ejpam-4492	27	51	number	number	NOUN
ejpam-4492	27	52	of	of	ADP
ejpam-4492	27	53	a	a	DET
ejpam-4492	27	54	graph	graph	NOUN
ejpam-4492	27	55	g	g	NOUN
ejpam-4492	27	56	is	be	AUX
ejpam-4492	27	57	the	the	DET
ejpam-4492	27	58	number	number	NOUN
ejpam-4492	27	59	of	of	ADP
ejpam-4492	27	60	paths	path	NOUN
ejpam-4492	27	61	in	in	ADP
ejpam-4492	27	62	any	any	DET
ejpam-4492	27	63	pathos	pathos	NOUN
ejpam-4492	27	64	.	.	PUNCT
ejpam-4492	28	1	the	the	DET
ejpam-4492	28	2	path	path	NOUN
ejpam-4492	28	3	number	number	NOUN
ejpam-4492	28	4	of	of	ADP
ejpam-4492	28	5	a	a	DET
ejpam-4492	28	6	tree	tree	NOUN
ejpam-4492	28	7	t	t	NOUN
ejpam-4492	28	8	equals	equal	VERB
ejpam-4492	28	9	k	k	PROPN
ejpam-4492	28	10	,	,	PUNCT
ejpam-4492	28	11	where	where	SCONJ
ejpam-4492	28	12	2k	2k	PROPN
ejpam-4492	28	13	is	be	AUX
ejpam-4492	28	14	the	the	DET
ejpam-4492	28	15	number	number	NOUN
ejpam-4492	28	16	of	of	ADP
ejpam-4492	28	17	odd	odd	ADJ
ejpam-4492	28	18	degree	degree	NOUN
ejpam-4492	28	19	vertices	vertex	NOUN
ejpam-4492	28	20	of	of	ADP
ejpam-4492	28	21	t	t	PROPN
ejpam-4492	28	22	.	.	PUNCT
ejpam-4492	29	1	stanton	stanton	PROPN
ejpam-4492	29	2	and	and	CCONJ
ejpam-4492	29	3	cowan	cowan	PROPN
ejpam-4492	29	4	[	[	X
ejpam-4492	29	5	7	7	X
ejpam-4492	29	6	]	]	PUNCT
ejpam-4492	29	7	calculated	calculate	VERB
ejpam-4492	29	8	the	the	DET
ejpam-4492	29	9	path	path	NOUN
ejpam-4492	29	10	number	number	NOUN
ejpam-4492	29	11	of	of	ADP
ejpam-4492	29	12	certain	certain	ADJ
ejpam-4492	29	13	classes	class	NOUN
ejpam-4492	29	14	of	of	ADP
ejpam-4492	29	15	graphs	graph	NOUN
ejpam-4492	29	16	like	like	ADP
ejpam-4492	29	17	trees	tree	NOUN
ejpam-4492	29	18	and	and	CCONJ
ejpam-4492	29	19	complete	complete	ADJ
ejpam-4492	29	20	graphs	graph	NOUN
ejpam-4492	29	21	.	.	PUNCT
ejpam-4492	30	1	gudagudi	gudagudi	PROPN
ejpam-4492	31	1	[	[	X
ejpam-4492	31	2	3	3	NUM
ejpam-4492	31	3	]	]	PUNCT
ejpam-4492	31	4	extended	extend	VERB
ejpam-4492	31	5	the	the	DET
ejpam-4492	31	6	concept	concept	NOUN
ejpam-4492	31	7	of	of	ADP
ejpam-4492	31	8	pathos	pathos	NOUN
ejpam-4492	31	9	of	of	ADP
ejpam-4492	31	10	graphs	graph	NOUN
ejpam-4492	31	11	to	to	ADP
ejpam-4492	31	12	trees	tree	NOUN
ejpam-4492	31	13	thereby	thereby	ADV
ejpam-4492	31	14	introducing	introduce	VERB
ejpam-4492	31	15	the	the	DET
ejpam-4492	31	16	concept	concept	NOUN
ejpam-4492	31	17	called	call	VERB
ejpam-4492	31	18	pathos	pathos	NOUN
ejpam-4492	31	19	line	line	NOUN
ejpam-4492	31	20	graph	graph	NOUN
ejpam-4492	31	21	of	of	ADP
ejpam-4492	31	22	a	a	DET
ejpam-4492	31	23	tree	tree	NOUN
ejpam-4492	31	24	.	.	PUNCT
ejpam-4492	32	1	a	a	DET
ejpam-4492	32	2	pathos	pathos	NOUN
ejpam-4492	32	3	line	line	NOUN
ejpam-4492	32	4	graph	graph	NOUN
ejpam-4492	32	5	of	of	ADP
ejpam-4492	32	6	a	a	DET
ejpam-4492	32	7	tree	tree	NOUN
ejpam-4492	32	8	t	t	NOUN
ejpam-4492	32	9	,	,	PUNCT
ejpam-4492	32	10	written	write	VERB
ejpam-4492	32	11	pl(t	pl(t	PUNCT
ejpam-4492	32	12	)	)	PUNCT
ejpam-4492	32	13	,	,	PUNCT
ejpam-4492	32	14	is	be	AUX
ejpam-4492	32	15	a	a	DET
ejpam-4492	32	16	graph	graph	NOUN
ejpam-4492	32	17	whose	whose	DET
ejpam-4492	32	18	vertices	vertex	NOUN
ejpam-4492	32	19	are	be	AUX
ejpam-4492	32	20	the	the	DET
ejpam-4492	32	21	edges	edge	NOUN
ejpam-4492	32	22	and	and	CCONJ
ejpam-4492	32	23	paths	path	NOUN
ejpam-4492	32	24	of	of	ADP
ejpam-4492	32	25	a	a	DET
ejpam-4492	32	26	pathos	pathos	NOUN
ejpam-4492	32	27	of	of	ADP
ejpam-4492	32	28	t	t	PROPN
ejpam-4492	32	29	,	,	PUNCT
ejpam-4492	32	30	with	with	ADP
ejpam-4492	32	31	two	two	NUM
ejpam-4492	32	32	vertices	vertex	NOUN
ejpam-4492	32	33	of	of	ADP
ejpam-4492	32	34	pl(t	pl(t	PUNCT
ejpam-4492	32	35	)	)	PUNCT
ejpam-4492	32	36	adjacent	adjacent	ADJ
ejpam-4492	32	37	whenever	whenever	SCONJ
ejpam-4492	32	38	the	the	DET
ejpam-4492	32	39	corresponding	corresponding	ADJ
ejpam-4492	32	40	edges	edge	NOUN
ejpam-4492	32	41	of	of	ADP
ejpam-4492	32	42	t	t	PROPN
ejpam-4492	32	43	are	be	AUX
ejpam-4492	32	44	adjacent	adjacent	ADJ
ejpam-4492	32	45	or	or	CCONJ
ejpam-4492	32	46	the	the	DET
ejpam-4492	32	47	edge	edge	NOUN
ejpam-4492	32	48	lies	lie	VERB
ejpam-4492	32	49	on	on	ADP
ejpam-4492	32	50	the	the	DET
ejpam-4492	32	51	corresponding	corresponding	ADJ
ejpam-4492	32	52	path	path	NOUN
ejpam-4492	32	53	of	of	ADP
ejpam-4492	32	54	the	the	DET
ejpam-4492	32	55	pathos	pathos	NOUN
ejpam-4492	32	56	.	.	PUNCT
ejpam-4492	33	1	since	since	SCONJ
ejpam-4492	33	2	the	the	DET
ejpam-4492	33	3	pattern	pattern	NOUN
ejpam-4492	33	4	of	of	ADP
ejpam-4492	33	5	pathos	pathos	NOUN
ejpam-4492	33	6	for	for	ADP
ejpam-4492	33	7	a	a	DET
ejpam-4492	33	8	tree	tree	NOUN
ejpam-4492	33	9	is	be	AUX
ejpam-4492	33	10	not	not	PART
ejpam-4492	33	11	unique	unique	ADJ
ejpam-4492	33	12	,	,	PUNCT
ejpam-4492	33	13	the	the	DET
ejpam-4492	33	14	corresponding	corresponding	ADJ
ejpam-4492	33	15	pathos	pathos	NOUN
ejpam-4492	33	16	line	line	NOUN
ejpam-4492	33	17	graph	graph	NOUN
ejpam-4492	33	18	is	be	AUX
ejpam-4492	33	19	also	also	ADV
ejpam-4492	33	20	not	not	PART
ejpam-4492	33	21	unique	unique	ADJ
ejpam-4492	33	22	.	.	PUNCT
ejpam-4492	34	1	the	the	DET
ejpam-4492	34	2	present	present	ADJ
ejpam-4492	34	3	study	study	NOUN
ejpam-4492	34	4	is	be	AUX
ejpam-4492	34	5	on	on	ADP
ejpam-4492	34	6	the	the	DET
ejpam-4492	34	7	directed	direct	VERB
ejpam-4492	34	8	pathos	pathos	NOUN
ejpam-4492	34	9	of	of	ADP
ejpam-4492	34	10	total	total	ADJ
ejpam-4492	34	11	arborescence	arborescence	NOUN
ejpam-4492	34	12	graphs	graph	NOUN
ejpam-4492	34	13	denoted	denote	VERB
ejpam-4492	34	14	by	by	ADP
ejpam-4492	34	15	dpt	dpt	PROPN
ejpam-4492	34	16	(	(	PUNCT
ejpam-4492	34	17	ar	ar	PROPN
ejpam-4492	34	18	)	)	PUNCT
ejpam-4492	34	19	,	,	PUNCT
ejpam-4492	34	20	where	where	SCONJ
ejpam-4492	34	21	an	an	DET
ejpam-4492	34	22	arborescence	arborescence	NOUN
ejpam-4492	34	23	graph	graph	NOUN
ejpam-4492	34	24	ar	ar	PROPN
ejpam-4492	34	25	is	be	AUX
ejpam-4492	34	26	a	a	DET
ejpam-4492	34	27	directed	direct	VERB
ejpam-4492	34	28	graph	graph	NOUN
ejpam-4492	34	29	for	for	ADP
ejpam-4492	34	30	which	which	PRON
ejpam-4492	34	31	from	from	ADP
ejpam-4492	34	32	an	an	DET
ejpam-4492	34	33	initial	initial	ADJ
ejpam-4492	34	34	vertex	vertex	NOUN
ejpam-4492	34	35	u	u	NOUN
ejpam-4492	34	36	there	there	PRON
ejpam-4492	34	37	is	be	VERB
ejpam-4492	34	38	only	only	ADV
ejpam-4492	34	39	one	one	NUM
ejpam-4492	34	40	directed	direct	VERB
ejpam-4492	34	41	path	path	NOUN
ejpam-4492	34	42	going	go	VERB
ejpam-4492	34	43	to	to	ADP
ejpam-4492	34	44	another	another	DET
ejpam-4492	34	45	vertex	vertex	NOUN
ejpam-4492	34	46	v.	v.	ADP
ejpam-4492	34	47	2	2	NUM
ejpam-4492	34	48	.	.	NOUN
ejpam-4492	34	49	preliminary	preliminary	ADJ
ejpam-4492	34	50	concepts	concept	NOUN
ejpam-4492	34	51	and	and	CCONJ
ejpam-4492	34	52	results	result	NOUN
ejpam-4492	34	53	in	in	ADP
ejpam-4492	34	54	this	this	DET
ejpam-4492	34	55	section	section	NOUN
ejpam-4492	34	56	,	,	PUNCT
ejpam-4492	34	57	some	some	DET
ejpam-4492	34	58	concepts	concept	NOUN
ejpam-4492	34	59	relating	relate	VERB
ejpam-4492	34	60	to	to	ADP
ejpam-4492	34	61	directed	direct	VERB
ejpam-4492	34	62	pathos	pathos	PROPN
ejpam-4492	34	63	total	total	ADJ
ejpam-4492	34	64	digraph	digraph	NOUN
ejpam-4492	34	65	of	of	ADP
ejpam-4492	34	66	an	an	DET
ejpam-4492	34	67	arborescence	arborescence	NOUN
ejpam-4492	34	68	are	be	AUX
ejpam-4492	34	69	defined	define	VERB
ejpam-4492	34	70	and	and	CCONJ
ejpam-4492	34	71	dpt	dpt	PROPN
ejpam-4492	34	72	(	(	PUNCT
ejpam-4492	34	73	ar	ar	NOUN
ejpam-4492	34	74	)	)	PUNCT
ejpam-4492	34	75	is	be	AUX
ejpam-4492	34	76	discussed	discuss	VERB
ejpam-4492	34	77	.	.	PUNCT
ejpam-4492	35	1	definition	definition	NOUN
ejpam-4492	35	2	2.1	2.1	NUM
ejpam-4492	35	3	.	.	PUNCT
ejpam-4492	36	1	a	a	DET
ejpam-4492	36	2	vertex	vertex	NOUN
ejpam-4492	36	3	u	u	NOUN
ejpam-4492	36	4	∈	∈	PROPN
ejpam-4492	36	5	v	v	NOUN
ejpam-4492	36	6	(	(	PUNCT
ejpam-4492	36	7	d	d	NOUN
ejpam-4492	36	8	)	)	PUNCT
ejpam-4492	36	9	of	of	ADP
ejpam-4492	36	10	a	a	DET
ejpam-4492	36	11	directed	direct	VERB
ejpam-4492	36	12	graph	graph	NOUN
ejpam-4492	36	13	d	d	NOUN
ejpam-4492	36	14	is	be	AUX
ejpam-4492	36	15	a	a	DET
ejpam-4492	36	16	root	root	NOUN
ejpam-4492	36	17	vertex	vertex	NOUN
ejpam-4492	36	18	if	if	SCONJ
ejpam-4492	36	19	u	u	NOUN
ejpam-4492	36	20	is	be	AUX
ejpam-4492	36	21	only	only	ADV
ejpam-4492	36	22	an	an	DET
ejpam-4492	36	23	initial	initial	ADJ
ejpam-4492	36	24	vertex	vertex	NOUN
ejpam-4492	36	25	,	,	PUNCT
ejpam-4492	36	26	that	that	ADV
ejpam-4492	36	27	is	is	ADV
ejpam-4492	36	28	,	,	PUNCT
ejpam-4492	36	29	d−(u	d−(u	NOUN
ejpam-4492	36	30	)	)	PUNCT
ejpam-4492	36	31	=	=	SYM
ejpam-4492	37	1	0	0	X
ejpam-4492	37	2	.	.	PUNCT
ejpam-4492	38	1	jill	jill	PROPN
ejpam-4492	38	2	maegan	maegan	PROPN
ejpam-4492	38	3	b.	b.	PROPN
ejpam-4492	38	4	pamplona	pamplona	PROPN
ejpam-4492	38	5	,	,	PUNCT
ejpam-4492	38	6	imelda	imelda	PROPN
ejpam-4492	38	7	s.	s.	PROPN
ejpam-4492	38	8	aniversario	aniversario	PROPN
ejpam-4492	38	9	/	/	SYM
ejpam-4492	38	10	eur	eur	PROPN
ejpam-4492	38	11	.	.	PUNCT
ejpam-4492	39	1	j.	j.	PROPN
ejpam-4492	39	2	pure	pure	PROPN
ejpam-4492	39	3	appl	appl	PROPN
ejpam-4492	39	4	.	.	PROPN
ejpam-4492	39	5	math	math	PROPN
ejpam-4492	39	6	,	,	PUNCT
ejpam-4492	39	7	15	15	NUM
ejpam-4492	39	8	(	(	PUNCT
ejpam-4492	39	9	3	3	NUM
ejpam-4492	39	10	)	)	PUNCT
ejpam-4492	39	11	(	(	PUNCT
ejpam-4492	39	12	2022	2022	NUM
ejpam-4492	39	13	)	)	PUNCT
ejpam-4492	39	14	,	,	PUNCT
ejpam-4492	39	15	1331	1331	NUM
ejpam-4492	39	16	-	-	SYM
ejpam-4492	39	17	1343	1343	NUM
ejpam-4492	39	18	1333	1333	NUM
ejpam-4492	39	19	definition	definition	NOUN
ejpam-4492	39	20	2.2	2.2	NUM
ejpam-4492	39	21	.	.	PUNCT
ejpam-4492	40	1	[	[	X
ejpam-4492	40	2	6	6	NUM
ejpam-4492	40	3	]	]	PUNCT
ejpam-4492	40	4	an	an	DET
ejpam-4492	40	5	arborescence	arborescence	NOUN
ejpam-4492	40	6	,	,	PUNCT
ejpam-4492	40	7	denoted	denote	VERB
ejpam-4492	40	8	by	by	ADP
ejpam-4492	40	9	ar	ar	NOUN
ejpam-4492	40	10	,	,	PUNCT
ejpam-4492	40	11	is	be	AUX
ejpam-4492	40	12	a	a	DET
ejpam-4492	40	13	directed	direct	VERB
ejpam-4492	40	14	graph	graph	NOUN
ejpam-4492	40	15	in	in	ADP
ejpam-4492	40	16	which	which	PRON
ejpam-4492	40	17	,	,	PUNCT
ejpam-4492	40	18	from	from	ADP
ejpam-4492	40	19	a	a	DET
ejpam-4492	40	20	root	root	NOUN
ejpam-4492	40	21	vertex	vertex	NOUN
ejpam-4492	40	22	u	u	NOUN
ejpam-4492	40	23	and	and	CCONJ
ejpam-4492	40	24	for	for	ADP
ejpam-4492	40	25	any	any	DET
ejpam-4492	40	26	other	other	ADJ
ejpam-4492	40	27	vertex	vertex	NOUN
ejpam-4492	40	28	v	v	NOUN
ejpam-4492	40	29	,	,	PUNCT
ejpam-4492	40	30	there	there	PRON
ejpam-4492	40	31	is	be	VERB
ejpam-4492	40	32	exactly	exactly	ADV
ejpam-4492	40	33	one	one	NUM
ejpam-4492	40	34	directed	direct	VERB
ejpam-4492	40	35	path	path	NOUN
ejpam-4492	40	36	from	from	ADP
ejpam-4492	40	37	u	u	PRON
ejpam-4492	40	38	to	to	ADP
ejpam-4492	40	39	v.	v.	ADP
ejpam-4492	40	40	example	example	NOUN
ejpam-4492	40	41	2.3	2.3	NUM
ejpam-4492	40	42	.	.	PUNCT
ejpam-4492	41	1	the	the	DET
ejpam-4492	41	2	graph	graph	NOUN
ejpam-4492	41	3	t	t	PROPN
ejpam-4492	41	4	in	in	ADP
ejpam-4492	41	5	figure	figure	NOUN
ejpam-4492	41	6	1	1	NUM
ejpam-4492	41	7	is	be	AUX
ejpam-4492	41	8	an	an	DET
ejpam-4492	41	9	example	example	NOUN
ejpam-4492	41	10	of	of	ADP
ejpam-4492	41	11	an	an	DET
ejpam-4492	41	12	arborescence	arborescence	NOUN
ejpam-4492	41	13	graph	graph	NOUN
ejpam-4492	41	14	where	where	SCONJ
ejpam-4492	41	15	vertex	vertex	NOUN
ejpam-4492	41	16	a	a	PRON
ejpam-4492	41	17	is	be	AUX
ejpam-4492	41	18	its	its	PRON
ejpam-4492	41	19	root	root	NOUN
ejpam-4492	41	20	,	,	PUNCT
ejpam-4492	41	21	that	that	ADV
ejpam-4492	41	22	is	is	ADV
ejpam-4492	41	23	,	,	PUNCT
ejpam-4492	41	24	d−(a	d−(a	NOUN
ejpam-4492	41	25	)	)	PUNCT
ejpam-4492	41	26	=	=	SYM
ejpam-4492	41	27	0	0	PUNCT
ejpam-4492	42	1	and	and	CCONJ
ejpam-4492	42	2	there	there	PRON
ejpam-4492	42	3	is	be	VERB
ejpam-4492	42	4	exactly	exactly	ADV
ejpam-4492	42	5	one	one	NUM
ejpam-4492	42	6	directed	direct	VERB
ejpam-4492	42	7	path	path	NOUN
ejpam-4492	42	8	from	from	ADP
ejpam-4492	42	9	a	a	PRON
ejpam-4492	42	10	to	to	ADP
ejpam-4492	42	11	other	other	ADJ
ejpam-4492	42	12	vertices	vertex	NOUN
ejpam-4492	42	13	b	b	NUM
ejpam-4492	42	14	,	,	PUNCT
ejpam-4492	42	15	c	c	NOUN
ejpam-4492	42	16	,	,	PUNCT
ejpam-4492	42	17	d	d	NOUN
ejpam-4492	42	18	,	,	PUNCT
ejpam-4492	42	19	e	e	NOUN
ejpam-4492	42	20	,	,	PUNCT
ejpam-4492	42	21	f	f	PROPN
ejpam-4492	42	22	,	,	PUNCT
ejpam-4492	42	23	g	g	PROPN
ejpam-4492	42	24	,	,	PUNCT
ejpam-4492	42	25	h	h	NOUN
ejpam-4492	42	26	,	,	PUNCT
ejpam-4492	42	27	i	i	PRON
ejpam-4492	42	28	,	,	PUNCT
ejpam-4492	42	29	j	j	PROPN
ejpam-4492	42	30	,	,	PUNCT
ejpam-4492	42	31	k	k	PROPN
ejpam-4492	42	32	,	,	PUNCT
ejpam-4492	42	33	l	l	NOUN
ejpam-4492	42	34	,	,	PUNCT
ejpam-4492	42	35	thus	thus	ADV
ejpam-4492	42	36	,	,	PUNCT
ejpam-4492	42	37	t	t	PROPN
ejpam-4492	42	38	=	=	SYM
ejpam-4492	42	39	ar	ar	PROPN
ejpam-4492	42	40	.	.	PROPN
ejpam-4492	42	41	figure	figure	NOUN
ejpam-4492	42	42	1	1	NUM
ejpam-4492	42	43	:	:	PUNCT
ejpam-4492	42	44	an	an	DET
ejpam-4492	42	45	arborescence	arborescence	NOUN
ejpam-4492	42	46	graph	graph	NOUN
ejpam-4492	42	47	t	t	PROPN
ejpam-4492	42	48	definition	definition	NOUN
ejpam-4492	42	49	2.4	2.4	NUM
ejpam-4492	42	50	.	.	PUNCT
ejpam-4492	43	1	[	[	X
ejpam-4492	43	2	4	4	X
ejpam-4492	43	3	]	]	PUNCT
ejpam-4492	43	4	the	the	DET
ejpam-4492	43	5	pathos	pathos	NOUN
ejpam-4492	43	6	of	of	ADP
ejpam-4492	43	7	a	a	DET
ejpam-4492	43	8	graph	graph	NOUN
ejpam-4492	43	9	g	g	NOUN
ejpam-4492	43	10	is	be	AUX
ejpam-4492	43	11	a	a	DET
ejpam-4492	43	12	collection	collection	NOUN
ejpam-4492	43	13	of	of	ADP
ejpam-4492	43	14	minimum	minimum	ADJ
ejpam-4492	43	15	number	number	NOUN
ejpam-4492	43	16	of	of	ADP
ejpam-4492	43	17	edge	edge	NOUN
ejpam-4492	43	18	disjoint	disjoint	X
ejpam-4492	43	19	open	open	ADJ
ejpam-4492	43	20	paths	path	NOUN
ejpam-4492	43	21	whose	whose	DET
ejpam-4492	43	22	union	union	NOUN
ejpam-4492	43	23	is	be	AUX
ejpam-4492	43	24	g.	g.	NOUN
ejpam-4492	43	25	the	the	DET
ejpam-4492	43	26	path	path	NOUN
ejpam-4492	43	27	number	number	NOUN
ejpam-4492	43	28	of	of	ADP
ejpam-4492	43	29	a	a	DET
ejpam-4492	43	30	graph	graph	NOUN
ejpam-4492	43	31	g	g	NOUN
ejpam-4492	43	32	is	be	AUX
ejpam-4492	43	33	the	the	DET
ejpam-4492	43	34	number	number	NOUN
ejpam-4492	43	35	of	of	ADP
ejpam-4492	43	36	paths	path	NOUN
ejpam-4492	43	37	in	in	ADP
ejpam-4492	43	38	a	a	DET
ejpam-4492	43	39	pathos	pathos	NOUN
ejpam-4492	43	40	.	.	PUNCT
ejpam-4492	44	1	definition	definition	NOUN
ejpam-4492	44	2	2.5	2.5	NUM
ejpam-4492	44	3	.	.	PUNCT
ejpam-4492	45	1	the	the	DET
ejpam-4492	45	2	directed	direct	VERB
ejpam-4492	45	3	pathos	pathos	NOUN
ejpam-4492	45	4	of	of	ADP
ejpam-4492	45	5	an	an	DET
ejpam-4492	45	6	arborescence	arborescence	NOUN
ejpam-4492	45	7	ar	ar	PROPN
ejpam-4492	45	8	is	be	AUX
ejpam-4492	45	9	defined	define	VERB
ejpam-4492	45	10	as	as	ADP
ejpam-4492	45	11	a	a	DET
ejpam-4492	45	12	collection	collection	NOUN
ejpam-4492	45	13	of	of	ADP
ejpam-4492	45	14	minimum	minimum	ADJ
ejpam-4492	45	15	number	number	NOUN
ejpam-4492	45	16	of	of	ADP
ejpam-4492	45	17	arc	arc	NOUN
ejpam-4492	45	18	disjoint	disjoint	VERB
ejpam-4492	45	19	open	open	ADJ
ejpam-4492	45	20	directed	direct	VERB
ejpam-4492	45	21	paths	path	NOUN
ejpam-4492	45	22	whose	whose	DET
ejpam-4492	45	23	union	union	NOUN
ejpam-4492	45	24	is	be	AUX
ejpam-4492	45	25	ar	ar	NOUN
ejpam-4492	45	26	.	.	PROPN
ejpam-4492	45	27	definition	definition	NOUN
ejpam-4492	45	28	2.6	2.6	NUM
ejpam-4492	45	29	.	.	PUNCT
ejpam-4492	46	1	[	[	X
ejpam-4492	46	2	6	6	NUM
ejpam-4492	46	3	]	]	PUNCT
ejpam-4492	46	4	for	for	ADP
ejpam-4492	46	5	an	an	DET
ejpam-4492	46	6	arborescence	arborescence	PROPN
ejpam-4492	46	7	ar	ar	PROPN
ejpam-4492	46	8	,	,	PUNCT
ejpam-4492	46	9	a	a	DET
ejpam-4492	46	10	directed	direct	VERB
ejpam-4492	46	11	pathos	pathos	NOUN
ejpam-4492	46	12	total	total	NOUN
ejpam-4492	46	13	digraph	digraph	NOUN
ejpam-4492	46	14	q	q	PROPN
ejpam-4492	46	15	=	=	SYM
ejpam-4492	46	16	dpt	dpt	PROPN
ejpam-4492	46	17	(	(	PUNCT
ejpam-4492	46	18	ar	ar	NOUN
ejpam-4492	46	19	)	)	PUNCT
ejpam-4492	46	20	has	have	AUX
ejpam-4492	46	21	vertex	vertex	NOUN
ejpam-4492	46	22	set	set	VERB
ejpam-4492	46	23	v	v	NOUN
ejpam-4492	46	24	(	(	PUNCT
ejpam-4492	46	25	q	q	NOUN
ejpam-4492	46	26	)	)	PUNCT
ejpam-4492	46	27	=	=	SYM
ejpam-4492	46	28	v	v	X
ejpam-4492	46	29	(	(	PUNCT
ejpam-4492	46	30	ar	ar	NOUN
ejpam-4492	46	31	)	)	PUNCT
ejpam-4492	46	32	∪	∪	ADP
ejpam-4492	46	33	a(ar	a(ar	NOUN
ejpam-4492	46	34	)	)	PUNCT
ejpam-4492	46	35	∪	∪	ADP
ejpam-4492	46	36	p	p	PROPN
ejpam-4492	46	37	(	(	PUNCT
ejpam-4492	46	38	ar	ar	NOUN
ejpam-4492	46	39	)	)	PUNCT
ejpam-4492	46	40	,	,	PUNCT
ejpam-4492	46	41	where	where	SCONJ
ejpam-4492	46	42	v	v	NOUN
ejpam-4492	46	43	(	(	PUNCT
ejpam-4492	46	44	ar	ar	NOUN
ejpam-4492	46	45	)	)	PUNCT
ejpam-4492	46	46	is	be	AUX
ejpam-4492	46	47	the	the	DET
ejpam-4492	46	48	vertex	vertex	NOUN
ejpam-4492	46	49	set	set	NOUN
ejpam-4492	46	50	,	,	PUNCT
ejpam-4492	46	51	a(ar	a(ar	NOUN
ejpam-4492	46	52	)	)	PUNCT
ejpam-4492	46	53	is	be	AUX
ejpam-4492	46	54	the	the	DET
ejpam-4492	46	55	arc	arc	NOUN
ejpam-4492	46	56	set	set	NOUN
ejpam-4492	46	57	,	,	PUNCT
ejpam-4492	46	58	and	and	CCONJ
ejpam-4492	46	59	p	p	NOUN
ejpam-4492	46	60	(	(	PUNCT
ejpam-4492	46	61	ar	ar	NOUN
ejpam-4492	46	62	)	)	PUNCT
ejpam-4492	46	63	is	be	AUX
ejpam-4492	46	64	a	a	DET
ejpam-4492	46	65	directed	direct	VERB
ejpam-4492	46	66	pathos	pathos	NOUN
ejpam-4492	46	67	set	set	NOUN
ejpam-4492	46	68	of	of	ADP
ejpam-4492	46	69	ar	ar	PROPN
ejpam-4492	46	70	.	.	PUNCT
ejpam-4492	47	1	the	the	DET
ejpam-4492	47	2	arc	arc	NOUN
ejpam-4492	47	3	set	set	VERB
ejpam-4492	47	4	a(q	a(q	NOUN
ejpam-4492	47	5	)	)	PUNCT
ejpam-4492	47	6	consists	consist	VERB
ejpam-4492	47	7	of	of	ADP
ejpam-4492	47	8	the	the	DET
ejpam-4492	47	9	following	follow	VERB
ejpam-4492	47	10	arcs	arc	NOUN
ejpam-4492	47	11	:	:	PUNCT
ejpam-4492	47	12	(	(	PUNCT
ejpam-4492	47	13	i	i	NOUN
ejpam-4492	47	14	)	)	PUNCT
ejpam-4492	47	15	ab	ab	PROPN
ejpam-4492	47	16	such	such	ADJ
ejpam-4492	47	17	that	that	SCONJ
ejpam-4492	47	18	a	a	PRON
ejpam-4492	47	19	,	,	PUNCT
ejpam-4492	47	20	b	b	PROPN
ejpam-4492	47	21	∈	∈	PROPN
ejpam-4492	47	22	a(ar	a(ar	PROPN
ejpam-4492	47	23	)	)	PUNCT
ejpam-4492	47	24	and	and	CCONJ
ejpam-4492	47	25	the	the	DET
ejpam-4492	47	26	head	head	NOUN
ejpam-4492	47	27	of	of	ADP
ejpam-4492	47	28	a	a	DET
ejpam-4492	47	29	coincides	coincide	NOUN
ejpam-4492	47	30	with	with	ADP
ejpam-4492	47	31	the	the	DET
ejpam-4492	47	32	tail	tail	NOUN
ejpam-4492	47	33	of	of	ADP
ejpam-4492	47	34	b	b	NOUN
ejpam-4492	47	35	;	;	PUNCT
ejpam-4492	47	36	(	(	PUNCT
ejpam-4492	47	37	ii	ii	NOUN
ejpam-4492	47	38	)	)	PUNCT
ejpam-4492	47	39	uv	uv	NOUN
ejpam-4492	47	40	such	such	ADJ
ejpam-4492	47	41	that	that	DET
ejpam-4492	47	42	u	u	NOUN
ejpam-4492	47	43	,	,	PUNCT
ejpam-4492	47	44	v	v	PROPN
ejpam-4492	47	45	∈	∈	PROPN
ejpam-4492	47	46	v	v	NOUN
ejpam-4492	47	47	(	(	PUNCT
ejpam-4492	47	48	ar	ar	NOUN
ejpam-4492	47	49	)	)	PUNCT
ejpam-4492	47	50	and	and	CCONJ
ejpam-4492	47	51	u	u	NOUN
ejpam-4492	47	52	is	be	AUX
ejpam-4492	47	53	adjacent	adjacent	ADJ
ejpam-4492	47	54	to	to	ADP
ejpam-4492	47	55	v	v	NOUN
ejpam-4492	47	56	or	or	CCONJ
ejpam-4492	47	57	an	an	DET
ejpam-4492	47	58	arc	arc	NOUN
ejpam-4492	47	59	from	from	ADP
ejpam-4492	47	60	u	u	PRON
ejpam-4492	47	61	to	to	ADP
ejpam-4492	47	62	v	v	NUM
ejpam-4492	47	63	exists	exist	VERB
ejpam-4492	47	64	;	;	PUNCT
ejpam-4492	47	65	(	(	PUNCT
ejpam-4492	47	66	iii	iii	X
ejpam-4492	47	67	)	)	PUNCT
ejpam-4492	47	68	au(ua	au(ua	PROPN
ejpam-4492	47	69	)	)	PUNCT
ejpam-4492	47	70	such	such	ADJ
ejpam-4492	47	71	that	that	SCONJ
ejpam-4492	47	72	a	a	DET
ejpam-4492	47	73	∈	∈	PROPN
ejpam-4492	47	74	a(ar	a(ar	NOUN
ejpam-4492	47	75	)	)	PUNCT
ejpam-4492	47	76	and	and	CCONJ
ejpam-4492	47	77	u	u	PROPN
ejpam-4492	47	78	∈	∈	PROPN
ejpam-4492	47	79	v	v	ADP
ejpam-4492	47	80	(	(	PUNCT
ejpam-4492	47	81	ar	ar	NOUN
ejpam-4492	47	82	)	)	PUNCT
ejpam-4492	47	83	and	and	CCONJ
ejpam-4492	47	84	the	the	DET
ejpam-4492	47	85	head	head	NOUN
ejpam-4492	47	86	(	(	PUNCT
ejpam-4492	47	87	tail	tail	NOUN
ejpam-4492	47	88	)	)	PUNCT
ejpam-4492	47	89	of	of	ADP
ejpam-4492	47	90	a	a	PRON
ejpam-4492	47	91	is	be	AUX
ejpam-4492	47	92	u	u	NOUN
ejpam-4492	47	93	;	;	PUNCT
ejpam-4492	47	94	(	(	PUNCT
ejpam-4492	47	95	iv	iv	X
ejpam-4492	47	96	)	)	PUNCT
ejpam-4492	47	97	pa	pa	NOUN
ejpam-4492	47	98	such	such	ADJ
ejpam-4492	47	99	that	that	SCONJ
ejpam-4492	47	100	a	a	DET
ejpam-4492	47	101	∈	∈	PROPN
ejpam-4492	47	102	a(ar	a(ar	NOUN
ejpam-4492	47	103	)	)	PUNCT
ejpam-4492	47	104	and	and	CCONJ
ejpam-4492	47	105	p	p	NOUN
ejpam-4492	47	106	∈	∈	PROPN
ejpam-4492	47	107	p	p	X
ejpam-4492	47	108	(	(	PUNCT
ejpam-4492	47	109	ar	ar	NOUN
ejpam-4492	47	110	)	)	PUNCT
ejpam-4492	47	111	and	and	CCONJ
ejpam-4492	47	112	the	the	DET
ejpam-4492	47	113	arc	arc	NOUN
ejpam-4492	47	114	a	a	DET
ejpam-4492	47	115	lies	lie	NOUN
ejpam-4492	47	116	on	on	ADP
ejpam-4492	47	117	the	the	DET
ejpam-4492	47	118	directed	direct	VERB
ejpam-4492	47	119	path	path	NOUN
ejpam-4492	47	120	p	p	NOUN
ejpam-4492	47	121	;	;	PUNCT
ejpam-4492	47	122	and	and	CCONJ
ejpam-4492	47	123	(	(	PUNCT
ejpam-4492	47	124	v	v	NOUN
ejpam-4492	47	125	)	)	PUNCT
ejpam-4492	47	126	pipj	pipj	NOUN
ejpam-4492	47	127	such	such	ADJ
ejpam-4492	47	128	that	that	DET
ejpam-4492	47	129	pi	pi	NOUN
ejpam-4492	47	130	,	,	PUNCT
ejpam-4492	47	131	pj	pj	PROPN
ejpam-4492	47	132	∈	∈	PROPN
ejpam-4492	47	133	p	p	PROPN
ejpam-4492	47	134	(	(	PUNCT
ejpam-4492	47	135	ar	ar	NOUN
ejpam-4492	47	136	)	)	PUNCT
ejpam-4492	47	137	and	and	CCONJ
ejpam-4492	47	138	it	it	PRON
ejpam-4492	47	139	is	be	AUX
ejpam-4492	47	140	possible	possible	ADJ
ejpam-4492	47	141	to	to	PART
ejpam-4492	47	142	reach	reach	VERB
ejpam-4492	47	143	the	the	DET
ejpam-4492	47	144	head	head	NOUN
ejpam-4492	47	145	of	of	ADP
ejpam-4492	47	146	pj	pj	PROPN
ejpam-4492	47	147	from	from	ADP
ejpam-4492	47	148	the	the	DET
ejpam-4492	47	149	tail	tail	NOUN
ejpam-4492	47	150	of	of	ADP
ejpam-4492	47	151	pi	pi	NOUN
ejpam-4492	47	152	through	through	ADP
ejpam-4492	47	153	a	a	DET
ejpam-4492	47	154	common	common	ADJ
ejpam-4492	47	155	vertex	vertex	NOUN
ejpam-4492	47	156	,	,	PUNCT
ejpam-4492	47	157	but	but	CCONJ
ejpam-4492	47	158	it	it	PRON
ejpam-4492	47	159	is	be	AUX
ejpam-4492	47	160	possible	possible	ADJ
ejpam-4492	47	161	to	to	PART
ejpam-4492	47	162	reach	reach	VERB
ejpam-4492	47	163	the	the	DET
ejpam-4492	47	164	head	head	NOUN
ejpam-4492	47	165	of	of	ADP
ejpam-4492	47	166	pi	pi	NOUN
ejpam-4492	47	167	from	from	ADP
ejpam-4492	47	168	the	the	DET
ejpam-4492	47	169	tail	tail	NOUN
ejpam-4492	47	170	of	of	ADP
ejpam-4492	47	171	pj	pj	PROPN
ejpam-4492	47	172	.	.	PUNCT
ejpam-4492	48	1	definition	definition	NOUN
ejpam-4492	48	2	2.7	2.7	NUM
ejpam-4492	48	3	.	.	PUNCT
ejpam-4492	49	1	a	a	DET
ejpam-4492	49	2	vertex	vertex	NOUN
ejpam-4492	49	3	v	v	ADP
ejpam-4492	49	4	∈	∈	PROPN
ejpam-4492	49	5	v	v	NOUN
ejpam-4492	49	6	(	(	PUNCT
ejpam-4492	49	7	g	g	NOUN
ejpam-4492	49	8	)	)	PUNCT
ejpam-4492	49	9	is	be	AUX
ejpam-4492	49	10	said	say	VERB
ejpam-4492	49	11	to	to	PART
ejpam-4492	49	12	be	be	AUX
ejpam-4492	49	13	an	an	DET
ejpam-4492	49	14	inner	inner	ADJ
ejpam-4492	49	15	vertex	vertex	NOUN
ejpam-4492	49	16	of	of	ADP
ejpam-4492	49	17	a	a	DET
ejpam-4492	49	18	planar	planar	ADJ
ejpam-4492	49	19	digraph	digraph	NOUN
ejpam-4492	49	20	g	g	PROPN
ejpam-4492	49	21	if	if	SCONJ
ejpam-4492	49	22	vertex	vertex	NOUN
ejpam-4492	49	23	v	v	NOUN
ejpam-4492	49	24	does	do	AUX
ejpam-4492	49	25	not	not	PART
ejpam-4492	49	26	belong	belong	VERB
ejpam-4492	49	27	to	to	ADP
ejpam-4492	49	28	the	the	DET
ejpam-4492	49	29	boundary	boundary	NOUN
ejpam-4492	49	30	of	of	ADP
ejpam-4492	49	31	the	the	DET
ejpam-4492	49	32	exterior	exterior	ADJ
ejpam-4492	49	33	region	region	NOUN
ejpam-4492	49	34	in	in	ADP
ejpam-4492	49	35	any	any	DET
ejpam-4492	49	36	embeddings	embedding	NOUN
ejpam-4492	49	37	of	of	ADP
ejpam-4492	49	38	g	g	NOUN
ejpam-4492	49	39	in	in	ADP
ejpam-4492	49	40	the	the	DET
ejpam-4492	49	41	plane	plane	NOUN
ejpam-4492	49	42	.	.	PUNCT
ejpam-4492	50	1	the	the	DET
ejpam-4492	50	2	inner	inner	ADJ
ejpam-4492	50	3	vertex	vertex	NOUN
ejpam-4492	50	4	number	number	NOUN
ejpam-4492	50	5	i(g	i(g	PROPN
ejpam-4492	50	6	)	)	PUNCT
ejpam-4492	50	7	is	be	AUX
ejpam-4492	50	8	the	the	DET
ejpam-4492	50	9	maximum	maximum	ADJ
ejpam-4492	50	10	number	number	NOUN
ejpam-4492	50	11	of	of	ADP
ejpam-4492	50	12	inner	inner	ADJ
ejpam-4492	50	13	vertices	vertex	NOUN
ejpam-4492	50	14	of	of	ADP
ejpam-4492	50	15	a	a	DET
ejpam-4492	50	16	planar	planar	ADJ
ejpam-4492	50	17	digraph	digraph	NOUN
ejpam-4492	50	18	g.	g.	PROPN
ejpam-4492	50	19	jill	jill	PROPN
ejpam-4492	50	20	maegan	maegan	PROPN
ejpam-4492	50	21	b.	b.	PROPN
ejpam-4492	50	22	pamplona	pamplona	PROPN
ejpam-4492	50	23	,	,	PUNCT
ejpam-4492	50	24	imelda	imelda	PROPN
ejpam-4492	50	25	s.	s.	PROPN
ejpam-4492	50	26	aniversario	aniversario	PROPN
ejpam-4492	50	27	/	/	SYM
ejpam-4492	50	28	eur	eur	PROPN
ejpam-4492	50	29	.	.	PUNCT
ejpam-4492	51	1	j.	j.	PROPN
ejpam-4492	51	2	pure	pure	PROPN
ejpam-4492	51	3	appl	appl	PROPN
ejpam-4492	51	4	.	.	PROPN
ejpam-4492	51	5	math	math	PROPN
ejpam-4492	51	6	,	,	PUNCT
ejpam-4492	51	7	15	15	NUM
ejpam-4492	51	8	(	(	PUNCT
ejpam-4492	51	9	3	3	NUM
ejpam-4492	51	10	)	)	PUNCT
ejpam-4492	51	11	(	(	PUNCT
ejpam-4492	51	12	2022	2022	NUM
ejpam-4492	51	13	)	)	PUNCT
ejpam-4492	51	14	,	,	PUNCT
ejpam-4492	51	15	1331	1331	NUM
ejpam-4492	51	16	-	-	SYM
ejpam-4492	51	17	1343	1343	NUM
ejpam-4492	51	18	1334	1334	NUM
ejpam-4492	51	19	example	example	NOUN
ejpam-4492	51	20	2.8	2.8	NUM
ejpam-4492	51	21	.	.	PUNCT
ejpam-4492	51	22	consider	consider	VERB
ejpam-4492	51	23	the	the	DET
ejpam-4492	51	24	graphs	graph	NOUN
ejpam-4492	51	25	in	in	ADP
ejpam-4492	51	26	figure	figure	NOUN
ejpam-4492	51	27	2	2	NUM
ejpam-4492	51	28	where	where	SCONJ
ejpam-4492	51	29	the	the	DET
ejpam-4492	51	30	directed	direct	VERB
ejpam-4492	51	31	pathos	pathos	NOUN
ejpam-4492	51	32	total	total	NOUN
ejpam-4492	51	33	digraph	digraph	NOUN
ejpam-4492	51	34	of	of	ADP
ejpam-4492	51	35	ar	ar	NOUN
ejpam-4492	51	36	is	be	AUX
ejpam-4492	51	37	shown	show	VERB
ejpam-4492	51	38	.	.	PUNCT
ejpam-4492	52	1	also	also	ADV
ejpam-4492	52	2	,	,	PUNCT
ejpam-4492	52	3	i(q	i(q	NOUN
ejpam-4492	52	4	)	)	PUNCT
ejpam-4492	52	5	=	=	SYM
ejpam-4492	52	6	2	2	X
ejpam-4492	52	7	.	.	X
ejpam-4492	52	8	figure	figure	NOUN
ejpam-4492	52	9	2	2	NUM
ejpam-4492	52	10	:	:	PUNCT
ejpam-4492	52	11	directed	direct	VERB
ejpam-4492	52	12	pathos	pathos	PROPN
ejpam-4492	52	13	total	total	ADJ
ejpam-4492	52	14	digraph	digraph	NOUN
ejpam-4492	52	15	of	of	ADP
ejpam-4492	52	16	ar	ar	NOUN
ejpam-4492	52	17	in	in	ADP
ejpam-4492	52	18	the	the	DET
ejpam-4492	52	19	context	context	NOUN
ejpam-4492	52	20	of	of	ADP
ejpam-4492	52	21	directed	direct	VERB
ejpam-4492	52	22	graphs	graph	NOUN
ejpam-4492	52	23	,	,	PUNCT
ejpam-4492	52	24	a	a	DET
ejpam-4492	52	25	digraph	digraph	NOUN
ejpam-4492	52	26	g	g	NOUN
ejpam-4492	52	27	is	be	AUX
ejpam-4492	52	28	outerplanar	outerplanar	PROPN
ejpam-4492	52	29	if	if	SCONJ
ejpam-4492	52	30	i(g	i(g	NOUN
ejpam-4492	52	31	)	)	PUNCT
ejpam-4492	53	1	=	=	SYM
ejpam-4492	53	2	0	0	PUNCT
ejpam-4492	54	1	and	and	CCONJ
ejpam-4492	54	2	it	it	PRON
ejpam-4492	54	3	is	be	AUX
ejpam-4492	54	4	minimally	minimally	ADV
ejpam-4492	54	5	non	non	X
ejpam-4492	54	6	outerplanar	outerplanar	NOUN
ejpam-4492	54	7	if	if	SCONJ
ejpam-4492	54	8	i(g	i(g	NOUN
ejpam-4492	54	9	)	)	PUNCT
ejpam-4492	55	1	=	=	PUNCT
ejpam-4492	56	1	1	1	X
ejpam-4492	56	2	.	.	X
ejpam-4492	56	3	we	we	PRON
ejpam-4492	56	4	now	now	ADV
ejpam-4492	56	5	enumerate	enumerate	VERB
ejpam-4492	56	6	some	some	PRON
ejpam-4492	56	7	of	of	ADP
ejpam-4492	56	8	the	the	DET
ejpam-4492	56	9	characterizations	characterization	NOUN
ejpam-4492	56	10	of	of	ADP
ejpam-4492	56	11	the	the	DET
ejpam-4492	56	12	planarity	planarity	NOUN
ejpam-4492	56	13	of	of	ADP
ejpam-4492	56	14	the	the	DET
ejpam-4492	56	15	dpt	dpt	PROPN
ejpam-4492	56	16	(	(	PUNCT
ejpam-4492	56	17	ar	ar	PROPN
ejpam-4492	56	18	)	)	PUNCT
ejpam-4492	57	1	[	[	X
ejpam-4492	57	2	6	6	NUM
ejpam-4492	57	3	]	]	PUNCT
ejpam-4492	57	4	.	.	PUNCT
ejpam-4492	58	1	theorem	theorem	VERB
ejpam-4492	58	2	2.9	2.9	NUM
ejpam-4492	58	3	.	.	PUNCT
ejpam-4492	59	1	every	every	DET
ejpam-4492	59	2	dpt	dpt	PROPN
ejpam-4492	59	3	(	(	PUNCT
ejpam-4492	59	4	ar	ar	NOUN
ejpam-4492	59	5	)	)	PUNCT
ejpam-4492	59	6	is	be	AUX
ejpam-4492	59	7	either	either	CCONJ
ejpam-4492	59	8	strictly	strictly	ADV
ejpam-4492	59	9	unilateral	unilateral	ADJ
ejpam-4492	59	10	or	or	CCONJ
ejpam-4492	59	11	strictly	strictly	ADV
ejpam-4492	59	12	weak	weak	ADJ
ejpam-4492	59	13	.	.	PUNCT
ejpam-4492	60	1	theorem	theorem	VERB
ejpam-4492	60	2	2.10	2.10	NUM
ejpam-4492	60	3	.	.	PUNCT
ejpam-4492	61	1	a	a	DET
ejpam-4492	61	2	directed	direct	VERB
ejpam-4492	61	3	pathos	pathos	NOUN
ejpam-4492	61	4	total	total	NOUN
ejpam-4492	61	5	digraph	digraph	PROPN
ejpam-4492	61	6	dpt	dpt	PROPN
ejpam-4492	61	7	(	(	PUNCT
ejpam-4492	61	8	ar	ar	PROPN
ejpam-4492	61	9	)	)	PUNCT
ejpam-4492	61	10	of	of	ADP
ejpam-4492	61	11	an	an	DET
ejpam-4492	61	12	arborescence	arborescence	NOUN
ejpam-4492	61	13	ar	ar	NOUN
ejpam-4492	61	14	is	be	AUX
ejpam-4492	61	15	planar	planar	ADJ
ejpam-4492	61	16	if	if	SCONJ
ejpam-4492	61	17	and	and	CCONJ
ejpam-4492	61	18	only	only	ADV
ejpam-4492	61	19	if	if	SCONJ
ejpam-4492	61	20	the	the	DET
ejpam-4492	61	21	underlying	underlie	VERB
ejpam-4492	61	22	graph	graph	NOUN
ejpam-4492	61	23	of	of	ADP
ejpam-4492	61	24	ar	ar	NOUN
ejpam-4492	61	25	is	be	AUX
ejpam-4492	61	26	a	a	DET
ejpam-4492	61	27	star	star	NOUN
ejpam-4492	61	28	graph	graph	NOUN
ejpam-4492	61	29	k1,n	k1,n	PROPN
ejpam-4492	61	30	on	on	ADP
ejpam-4492	61	31	n	n	CCONJ
ejpam-4492	61	32	≤	≤	ADV
ejpam-4492	61	33	3	3	NUM
ejpam-4492	61	34	vertices	vertex	NOUN
ejpam-4492	61	35	.	.	PUNCT
ejpam-4492	62	1	theorem	theorem	VERB
ejpam-4492	62	2	2.11	2.11	NUM
ejpam-4492	62	3	.	.	PUNCT
ejpam-4492	63	1	a	a	DET
ejpam-4492	63	2	directed	direct	VERB
ejpam-4492	63	3	pathos	pathos	NOUN
ejpam-4492	63	4	total	total	NOUN
ejpam-4492	63	5	digraph	digraph	PROPN
ejpam-4492	63	6	dpt	dpt	PROPN
ejpam-4492	63	7	(	(	PUNCT
ejpam-4492	63	8	ar	ar	PROPN
ejpam-4492	63	9	)	)	PUNCT
ejpam-4492	63	10	of	of	ADP
ejpam-4492	63	11	an	an	DET
ejpam-4492	63	12	arborescence	arborescence	NOUN
ejpam-4492	63	13	ar	ar	PROPN
ejpam-4492	63	14	is	be	AUX
ejpam-4492	63	15	outerplanar	outerplanar	PROPN
ejpam-4492	63	16	if	if	SCONJ
ejpam-4492	63	17	and	and	CCONJ
ejpam-4492	63	18	only	only	ADV
ejpam-4492	63	19	if	if	SCONJ
ejpam-4492	63	20	ar	ar	NOUN
ejpam-4492	63	21	is	be	AUX
ejpam-4492	63	22	either	either	CCONJ
ejpam-4492	63	23	p⃗2	p⃗2	ADJ
ejpam-4492	63	24	or	or	CCONJ
ejpam-4492	63	25	p⃗3	p⃗3	NOUN
ejpam-4492	63	26	.	.	PUNCT
ejpam-4492	64	1	theorem	theorem	VERB
ejpam-4492	64	2	2.12	2.12	NUM
ejpam-4492	64	3	.	.	PUNCT
ejpam-4492	65	1	a	a	DET
ejpam-4492	65	2	directed	direct	VERB
ejpam-4492	65	3	pathos	pathos	NOUN
ejpam-4492	65	4	total	total	NOUN
ejpam-4492	65	5	digraph	digraph	PROPN
ejpam-4492	65	6	dpt	dpt	PROPN
ejpam-4492	65	7	(	(	PUNCT
ejpam-4492	65	8	ar	ar	PROPN
ejpam-4492	65	9	)	)	PUNCT
ejpam-4492	65	10	of	of	ADP
ejpam-4492	65	11	an	an	DET
ejpam-4492	65	12	arborescence	arborescence	NOUN
ejpam-4492	65	13	ar	ar	NOUN
ejpam-4492	65	14	is	be	AUX
ejpam-4492	65	15	maximal	maximal	ADJ
ejpam-4492	65	16	outerplanar	outerplanar	NOUN
ejpam-4492	65	17	if	if	SCONJ
ejpam-4492	65	18	and	and	CCONJ
ejpam-4492	65	19	only	only	ADV
ejpam-4492	65	20	if	if	SCONJ
ejpam-4492	65	21	ar	ar	NOUN
ejpam-4492	65	22	is	be	AUX
ejpam-4492	65	23	p⃗3	p⃗3	NOUN
ejpam-4492	65	24	.	.	PUNCT
ejpam-4492	66	1	theorem	theorem	VERB
ejpam-4492	66	2	2.13	2.13	NUM
ejpam-4492	66	3	.	.	PUNCT
ejpam-4492	67	1	a	a	DET
ejpam-4492	67	2	directed	direct	VERB
ejpam-4492	67	3	pathos	pathos	NOUN
ejpam-4492	67	4	total	total	NOUN
ejpam-4492	67	5	digraph	digraph	PROPN
ejpam-4492	67	6	dpt	dpt	PROPN
ejpam-4492	67	7	(	(	PUNCT
ejpam-4492	67	8	ar	ar	PROPN
ejpam-4492	67	9	)	)	PUNCT
ejpam-4492	67	10	of	of	ADP
ejpam-4492	67	11	an	an	DET
ejpam-4492	67	12	arborescence	arborescence	NOUN
ejpam-4492	67	13	ar	ar	PROPN
ejpam-4492	67	14	is	be	AUX
ejpam-4492	67	15	minimally	minimally	ADV
ejpam-4492	67	16	non	non	X
ejpam-4492	67	17	outerplanar	outerplanar	NOUN
ejpam-4492	67	18	if	if	SCONJ
ejpam-4492	67	19	and	and	CCONJ
ejpam-4492	67	20	only	only	ADV
ejpam-4492	67	21	if	if	SCONJ
ejpam-4492	67	22	ar	ar	PROPN
ejpam-4492	67	23	is	be	AUX
ejpam-4492	67	24	p⃗4	p⃗4	VERB
ejpam-4492	67	25	.	.	PUNCT
ejpam-4492	68	1	theorem	theorem	VERB
ejpam-4492	68	2	2.14	2.14	NUM
ejpam-4492	68	3	.	.	PUNCT
ejpam-4492	69	1	a	a	DET
ejpam-4492	69	2	directed	direct	VERB
ejpam-4492	69	3	pathos	pathos	NOUN
ejpam-4492	69	4	total	total	NOUN
ejpam-4492	69	5	digraph	digraph	PROPN
ejpam-4492	69	6	dpt	dpt	PROPN
ejpam-4492	69	7	(	(	PUNCT
ejpam-4492	69	8	ar	ar	PROPN
ejpam-4492	69	9	)	)	PUNCT
ejpam-4492	69	10	of	of	ADP
ejpam-4492	69	11	an	an	DET
ejpam-4492	69	12	arborescence	arborescence	NOUN
ejpam-4492	69	13	ar	ar	PROPN
ejpam-4492	69	14	has	have	AUX
ejpam-4492	69	15	crossing	cross	VERB
ejpam-4492	69	16	number	number	NOUN
ejpam-4492	69	17	one	one	NUM
ejpam-4492	69	18	if	if	SCONJ
ejpam-4492	69	19	and	and	CCONJ
ejpam-4492	69	20	only	only	ADV
ejpam-4492	69	21	if	if	SCONJ
ejpam-4492	69	22	the	the	DET
ejpam-4492	69	23	underlying	underlie	VERB
ejpam-4492	69	24	graph	graph	NOUN
ejpam-4492	69	25	of	of	ADP
ejpam-4492	69	26	ar	ar	NOUN
ejpam-4492	69	27	is	be	AUX
ejpam-4492	69	28	k1,4	k1,4	PRON
ejpam-4492	69	29	.	.	PUNCT
ejpam-4492	70	1	3	3	X
ejpam-4492	70	2	.	.	X
ejpam-4492	70	3	main	main	ADJ
ejpam-4492	70	4	results	result	NOUN
ejpam-4492	70	5	this	this	DET
ejpam-4492	70	6	section	section	NOUN
ejpam-4492	70	7	presents	present	VERB
ejpam-4492	70	8	some	some	DET
ejpam-4492	70	9	properties	property	NOUN
ejpam-4492	70	10	and	and	CCONJ
ejpam-4492	70	11	characterizations	characterization	NOUN
ejpam-4492	70	12	of	of	ADP
ejpam-4492	70	13	a	a	DET
ejpam-4492	70	14	directed	direct	VERB
ejpam-4492	70	15	pathos	pathos	NOUN
ejpam-4492	70	16	total	total	NOUN
ejpam-4492	70	17	digraph	digraph	NOUN
ejpam-4492	70	18	of	of	ADP
ejpam-4492	70	19	an	an	DET
ejpam-4492	70	20	arborescence	arborescence	NOUN
ejpam-4492	70	21	graph	graph	NOUN
ejpam-4492	70	22	.	.	PUNCT
ejpam-4492	71	1	the	the	DET
ejpam-4492	71	2	first	first	ADJ
ejpam-4492	71	3	result	result	NOUN
ejpam-4492	71	4	is	be	AUX
ejpam-4492	71	5	intended	intend	VERB
ejpam-4492	71	6	for	for	ADP
ejpam-4492	71	7	the	the	DET
ejpam-4492	71	8	arborescence	arborescence	NOUN
ejpam-4492	71	9	which	which	PRON
ejpam-4492	71	10	is	be	AUX
ejpam-4492	71	11	a	a	DET
ejpam-4492	71	12	directed	direct	VERB
ejpam-4492	71	13	path	path	NOUN
ejpam-4492	71	14	p⃗n	p⃗n	PROPN
ejpam-4492	71	15	.	.	PUNCT
ejpam-4492	72	1	jill	jill	PROPN
ejpam-4492	72	2	maegan	maegan	PROPN
ejpam-4492	72	3	b.	b.	PROPN
ejpam-4492	72	4	pamplona	pamplona	PROPN
ejpam-4492	72	5	,	,	PUNCT
ejpam-4492	72	6	imelda	imelda	PROPN
ejpam-4492	72	7	s.	s.	PROPN
ejpam-4492	72	8	aniversario	aniversario	PROPN
ejpam-4492	72	9	/	/	SYM
ejpam-4492	72	10	eur	eur	PROPN
ejpam-4492	72	11	.	.	PUNCT
ejpam-4492	73	1	j.	j.	PROPN
ejpam-4492	73	2	pure	pure	PROPN
ejpam-4492	73	3	appl	appl	PROPN
ejpam-4492	73	4	.	.	PROPN
ejpam-4492	73	5	math	math	PROPN
ejpam-4492	73	6	,	,	PUNCT
ejpam-4492	73	7	15	15	NUM
ejpam-4492	73	8	(	(	PUNCT
ejpam-4492	73	9	3	3	NUM
ejpam-4492	73	10	)	)	PUNCT
ejpam-4492	73	11	(	(	PUNCT
ejpam-4492	73	12	2022	2022	NUM
ejpam-4492	73	13	)	)	PUNCT
ejpam-4492	73	14	,	,	PUNCT
ejpam-4492	73	15	1331	1331	NUM
ejpam-4492	73	16	-	-	SYM
ejpam-4492	73	17	1343	1343	NUM
ejpam-4492	73	18	1335	1335	NUM
ejpam-4492	73	19	theorem	theorem	VERB
ejpam-4492	73	20	3.1	3.1	NUM
ejpam-4492	73	21	.	.	PUNCT
ejpam-4492	74	1	if	if	SCONJ
ejpam-4492	74	2	ar	ar	PROPN
ejpam-4492	74	3	=	=	PROPN
ejpam-4492	74	4	p⃗n	p⃗n	PROPN
ejpam-4492	74	5	,	,	PUNCT
ejpam-4492	74	6	then	then	ADV
ejpam-4492	74	7	the	the	DET
ejpam-4492	74	8	directed	direct	VERB
ejpam-4492	74	9	pathos	pathos	NOUN
ejpam-4492	74	10	total	total	NOUN
ejpam-4492	74	11	digraph	digraph	PROPN
ejpam-4492	74	12	dpt	dpt	PROPN
ejpam-4492	74	13	(	(	PUNCT
ejpam-4492	74	14	ar	ar	PROPN
ejpam-4492	74	15	)	)	PUNCT
ejpam-4492	74	16	of	of	ADP
ejpam-4492	74	17	ar	ar	PROPN
ejpam-4492	74	18	is	be	AUX
ejpam-4492	74	19	planar	planar	ADJ
ejpam-4492	74	20	.	.	PUNCT
ejpam-4492	75	1	proof	proof	NOUN
ejpam-4492	75	2	:	:	PUNCT
ejpam-4492	75	3	suppose	suppose	VERB
ejpam-4492	75	4	that	that	SCONJ
ejpam-4492	75	5	ar	ar	PROPN
ejpam-4492	75	6	=	=	PROPN
ejpam-4492	75	7	p⃗n	p⃗n	PROPN
ejpam-4492	75	8	.	.	PUNCT
ejpam-4492	76	1	let	let	VERB
ejpam-4492	76	2	v	v	NOUN
ejpam-4492	76	3	(	(	PUNCT
ejpam-4492	76	4	p⃗n	p⃗n	NOUN
ejpam-4492	76	5	)	)	PUNCT
ejpam-4492	76	6	=	=	SYM
ejpam-4492	76	7	{	{	PUNCT
ejpam-4492	76	8	v1	v1	PROPN
ejpam-4492	76	9	,	,	PUNCT
ejpam-4492	76	10	v2	v2	PROPN
ejpam-4492	76	11	,	,	PUNCT
ejpam-4492	76	12	v3	v3	PROPN
ejpam-4492	76	13	,	,	PUNCT
ejpam-4492	76	14	.	.	PUNCT
ejpam-4492	76	15	.	.	PUNCT
ejpam-4492	77	1	.	.	PUNCT
ejpam-4492	78	1	,	,	PUNCT
ejpam-4492	78	2	vn	vn	X
ejpam-4492	78	3	}	}	PUNCT
ejpam-4492	78	4	and	and	CCONJ
ejpam-4492	78	5	let	let	VERB
ejpam-4492	78	6	a(p⃗n	a(p⃗n	PRON
ejpam-4492	78	7	)	)	PUNCT
ejpam-4492	78	8	=	=	SYM
ejpam-4492	78	9	{	{	PUNCT
ejpam-4492	78	10	e1	e1	PROPN
ejpam-4492	78	11	,	,	PUNCT
ejpam-4492	78	12	e2	e2	PROPN
ejpam-4492	78	13	,	,	PUNCT
ejpam-4492	78	14	e3	e3	NOUN
ejpam-4492	78	15	,	,	PUNCT
ejpam-4492	78	16	.	.	PUNCT
ejpam-4492	78	17	.	.	PUNCT
ejpam-4492	79	1	.	.	PUNCT
ejpam-4492	80	1	,	,	PUNCT
ejpam-4492	80	2	en−1	en−1	PROPN
ejpam-4492	80	3	}	}	PUNCT
ejpam-4492	80	4	such	such	ADJ
ejpam-4492	80	5	that	that	DET
ejpam-4492	80	6	v1	v1	NOUN
ejpam-4492	80	7	and	and	CCONJ
ejpam-4492	80	8	e1	e1	NOUN
ejpam-4492	80	9	=	=	SYM
ejpam-4492	80	10	(	(	PUNCT
ejpam-4492	80	11	v1	v1	NOUN
ejpam-4492	80	12	,	,	PUNCT
ejpam-4492	80	13	v2	v2	PROPN
ejpam-4492	80	14	)	)	PUNCT
ejpam-4492	80	15	are	be	AUX
ejpam-4492	80	16	the	the	DET
ejpam-4492	80	17	root	root	NOUN
ejpam-4492	80	18	and	and	CCONJ
ejpam-4492	80	19	root	root	NOUN
ejpam-4492	80	20	arc	arc	NOUN
ejpam-4492	80	21	of	of	ADP
ejpam-4492	80	22	p⃗n	p⃗n	PROPN
ejpam-4492	80	23	,	,	PUNCT
ejpam-4492	80	24	respectively	respectively	ADV
ejpam-4492	80	25	and	and	CCONJ
ejpam-4492	80	26	ei	ei	X
ejpam-4492	80	27	=	=	SYM
ejpam-4492	80	28	(	(	PUNCT
ejpam-4492	80	29	vi	vi	PROPN
ejpam-4492	80	30	,	,	PUNCT
ejpam-4492	80	31	vi+1	vi+1	NOUN
ejpam-4492	80	32	)	)	PUNCT
ejpam-4492	80	33	for	for	ADP
ejpam-4492	80	34	2	2	NUM
ejpam-4492	80	35	≤	≤	NOUN
ejpam-4492	80	36	i	i	PRON
ejpam-4492	80	37	≤	≤	NOUN
ejpam-4492	81	1	n	n	CCONJ
ejpam-4492	81	2	−	−	PROPN
ejpam-4492	81	3	1	1	NUM
ejpam-4492	81	4	.	.	PUNCT
ejpam-4492	81	5	then	then	ADV
ejpam-4492	81	6	v1	v1	VERB
ejpam-4492	81	7	,	,	PUNCT
ejpam-4492	81	8	v2	v2	PROPN
ejpam-4492	81	9	,	,	PUNCT
ejpam-4492	81	10	.	.	PUNCT
ejpam-4492	81	11	.	.	PUNCT
ejpam-4492	81	12	.	.	PUNCT
ejpam-4492	82	1	,	,	PUNCT
ejpam-4492	82	2	vn	vn	PROPN
ejpam-4492	82	3	,	,	PUNCT
ejpam-4492	82	4	e1	e1	PROPN
ejpam-4492	82	5	,	,	PUNCT
ejpam-4492	82	6	e2	e2	PROPN
ejpam-4492	82	7	,	,	PUNCT
ejpam-4492	82	8	.	.	PUNCT
ejpam-4492	82	9	.	.	PUNCT
ejpam-4492	82	10	.	.	PUNCT
ejpam-4492	83	1	,	,	PUNCT
ejpam-4492	83	2	en−1	en−1	PROPN
ejpam-4492	83	3	are	be	AUX
ejpam-4492	83	4	the	the	DET
ejpam-4492	83	5	vertices	vertex	NOUN
ejpam-4492	83	6	of	of	ADP
ejpam-4492	83	7	t	t	PROPN
ejpam-4492	83	8	(	(	PUNCT
ejpam-4492	83	9	ar	ar	PROPN
ejpam-4492	83	10	)	)	PUNCT
ejpam-4492	83	11	.	.	PUNCT
ejpam-4492	84	1	also	also	ADV
ejpam-4492	84	2	,	,	PUNCT
ejpam-4492	84	3	(	(	PUNCT
ejpam-4492	84	4	vi	vi	NOUN
ejpam-4492	84	5	,	,	PUNCT
ejpam-4492	84	6	vi+1	vi+1	NOUN
ejpam-4492	84	7	)	)	PUNCT
ejpam-4492	84	8	,	,	PUNCT
ejpam-4492	84	9	(	(	PUNCT
ejpam-4492	84	10	vi	vi	NOUN
ejpam-4492	84	11	,	,	PUNCT
ejpam-4492	84	12	ei	ei	NOUN
ejpam-4492	84	13	)	)	PUNCT
ejpam-4492	84	14	,	,	PUNCT
ejpam-4492	84	15	(	(	PUNCT
ejpam-4492	84	16	ei	ei	NOUN
ejpam-4492	84	17	,	,	PUNCT
ejpam-4492	84	18	vi+1	vi+1	NOUN
ejpam-4492	84	19	)	)	PUNCT
ejpam-4492	84	20	,	,	PUNCT
ejpam-4492	84	21	(	(	PUNCT
ejpam-4492	84	22	ei	ei	X
ejpam-4492	84	23	,	,	PUNCT
ejpam-4492	84	24	ei+1	ei+1	PROPN
ejpam-4492	84	25	)	)	PUNCT
ejpam-4492	84	26	,	,	PUNCT
ejpam-4492	84	27	for	for	ADP
ejpam-4492	84	28	1	1	NUM
ejpam-4492	84	29	≤	≤	NUM
ejpam-4492	84	30	i	i	PRON
ejpam-4492	84	31	≤	≤	NOUN
ejpam-4492	84	32	n	n	CCONJ
ejpam-4492	84	33	−	−	PROPN
ejpam-4492	84	34	1	1	NUM
ejpam-4492	84	35	are	be	AUX
ejpam-4492	84	36	the	the	DET
ejpam-4492	84	37	arcs	arc	NOUN
ejpam-4492	84	38	of	of	ADP
ejpam-4492	84	39	t	t	PROPN
ejpam-4492	84	40	(	(	PUNCT
ejpam-4492	84	41	ar	ar	NOUN
ejpam-4492	84	42	)	)	PUNCT
ejpam-4492	84	43	.	.	PUNCT
ejpam-4492	85	1	let	let	VERB
ejpam-4492	85	2	p	p	PROPN
ejpam-4492	85	3	(	(	PUNCT
ejpam-4492	85	4	ar	ar	NOUN
ejpam-4492	85	5	)	)	PUNCT
ejpam-4492	85	6	=	=	SYM
ejpam-4492	85	7	{	{	PUNCT
ejpam-4492	85	8	p1	p1	PROPN
ejpam-4492	85	9	}	}	PUNCT
ejpam-4492	85	10	be	be	VERB
ejpam-4492	85	11	a	a	DET
ejpam-4492	85	12	directed	direct	VERB
ejpam-4492	85	13	pathos	pathos	NOUN
ejpam-4492	85	14	of	of	ADP
ejpam-4492	85	15	ar	ar	PROPN
ejpam-4492	85	16	such	such	ADJ
ejpam-4492	85	17	that	that	DET
ejpam-4492	85	18	p1	p1	PROPN
ejpam-4492	85	19	lies	lie	VERB
ejpam-4492	85	20	on	on	ADP
ejpam-4492	85	21	the	the	DET
ejpam-4492	85	22	arcs	arcs	NOUN
ejpam-4492	85	23	e1	e1	PROPN
ejpam-4492	85	24	=	=	SYM
ejpam-4492	85	25	(	(	PUNCT
ejpam-4492	85	26	v1	v1	NOUN
ejpam-4492	85	27	,	,	PUNCT
ejpam-4492	85	28	v2	v2	PROPN
ejpam-4492	85	29	)	)	PUNCT
ejpam-4492	85	30	,	,	PUNCT
ejpam-4492	85	31	e2	e2	PROPN
ejpam-4492	85	32	=	=	SYM
ejpam-4492	85	33	(	(	PUNCT
ejpam-4492	85	34	v2	v2	PROPN
ejpam-4492	85	35	,	,	PUNCT
ejpam-4492	85	36	v3	v3	PROPN
ejpam-4492	85	37	)	)	PUNCT
ejpam-4492	85	38	,	,	PUNCT
ejpam-4492	85	39	.	.	PUNCT
ejpam-4492	85	40	.	.	PUNCT
ejpam-4492	86	1	.	.	PUNCT
ejpam-4492	87	1	,	,	PUNCT
ejpam-4492	87	2	en−1	en−1	PROPN
ejpam-4492	87	3	=	=	SYM
ejpam-4492	87	4	(	(	PUNCT
ejpam-4492	87	5	vn−1	vn−1	PROPN
ejpam-4492	87	6	,	,	PUNCT
ejpam-4492	87	7	vn	vn	NOUN
ejpam-4492	87	8	)	)	PUNCT
ejpam-4492	87	9	.	.	PUNCT
ejpam-4492	88	1	the	the	DET
ejpam-4492	88	2	directed	direct	VERB
ejpam-4492	88	3	pathos	pathos	NOUN
ejpam-4492	88	4	vertex	vertex	NOUN
ejpam-4492	88	5	p	p	NOUN
ejpam-4492	88	6	is	be	AUX
ejpam-4492	88	7	a	a	DET
ejpam-4492	88	8	neighbor	neighbor	NOUN
ejpam-4492	88	9	of	of	ADP
ejpam-4492	88	10	the	the	DET
ejpam-4492	88	11	vertices	vertex	NOUN
ejpam-4492	88	12	e1	e1	PROPN
ejpam-4492	88	13	,	,	PUNCT
ejpam-4492	88	14	e2	e2	NOUN
ejpam-4492	88	15	,	,	PUNCT
ejpam-4492	88	16	.	.	PUNCT
ejpam-4492	88	17	.	.	PUNCT
ejpam-4492	89	1	.	.	PUNCT
ejpam-4492	90	1	,	,	PUNCT
ejpam-4492	90	2	en−1	en−1	PROPN
ejpam-4492	90	3	.	.	PUNCT
ejpam-4492	91	1	this	this	PRON
ejpam-4492	91	2	shows	show	VERB
ejpam-4492	91	3	that	that	SCONJ
ejpam-4492	91	4	the	the	DET
ejpam-4492	91	5	crossing	crossing	NOUN
ejpam-4492	91	6	number	number	NOUN
ejpam-4492	91	7	of	of	ADP
ejpam-4492	91	8	dpt	dpt	PROPN
ejpam-4492	91	9	(	(	PUNCT
ejpam-4492	91	10	p⃗n	p⃗n	PROPN
ejpam-4492	91	11	)	)	PUNCT
ejpam-4492	91	12	is	be	AUX
ejpam-4492	91	13	zero	zero	NUM
ejpam-4492	91	14	,	,	PUNCT
ejpam-4492	91	15	that	that	ADV
ejpam-4492	91	16	is	is	ADV
ejpam-4492	91	17	,	,	PUNCT
ejpam-4492	91	18	cr(dpt	cr(dpt	ADV
ejpam-4492	91	19	(	(	PUNCT
ejpam-4492	91	20	p⃗n	p⃗n	NOUN
ejpam-4492	91	21	)	)	PUNCT
ejpam-4492	91	22	)	)	PUNCT
ejpam-4492	92	1	=	=	SYM
ejpam-4492	92	2	0	0	PUNCT
ejpam-4492	92	3	(	(	PUNCT
ejpam-4492	92	4	see	see	VERB
ejpam-4492	92	5	figure	figure	NOUN
ejpam-4492	92	6	3	3	NUM
ejpam-4492	92	7	)	)	PUNCT
ejpam-4492	92	8	.	.	PUNCT
ejpam-4492	93	1	hence	hence	ADV
ejpam-4492	93	2	,	,	PUNCT
ejpam-4492	93	3	dpt	dpt	PROPN
ejpam-4492	93	4	(	(	PUNCT
ejpam-4492	93	5	p⃗n	p⃗n	PROPN
ejpam-4492	93	6	)	)	PUNCT
ejpam-4492	93	7	is	be	AUX
ejpam-4492	93	8	planar	planar	ADJ
ejpam-4492	93	9	.	.	PUNCT
ejpam-4492	94	1	figure	figure	VERB
ejpam-4492	94	2	3	3	NUM
ejpam-4492	94	3	:	:	PUNCT
ejpam-4492	94	4	directed	direct	VERB
ejpam-4492	94	5	pathos	pathos	PROPN
ejpam-4492	94	6	total	total	ADJ
ejpam-4492	94	7	digraph	digraph	NOUN
ejpam-4492	94	8	of	of	ADP
ejpam-4492	94	9	p⃗n	p⃗n	NOUN
ejpam-4492	94	10	theorem	theorem	NOUN
ejpam-4492	94	11	3.2	3.2	NUM
ejpam-4492	94	12	.	.	PUNCT
ejpam-4492	95	1	for	for	ADP
ejpam-4492	95	2	an	an	DET
ejpam-4492	95	3	arborescence	arborescence	NOUN
ejpam-4492	95	4	graph	graph	NOUN
ejpam-4492	95	5	p⃗n	p⃗n	NOUN
ejpam-4492	95	6	with	with	ADP
ejpam-4492	95	7	n	n	PRON
ejpam-4492	95	8	≥	≥	NUM
ejpam-4492	95	9	2	2	NUM
ejpam-4492	95	10	vertices	vertex	NOUN
ejpam-4492	95	11	and	and	CCONJ
ejpam-4492	95	12	n	n	CCONJ
ejpam-4492	95	13	−	−	PROPN
ejpam-4492	95	14	1	1	NUM
ejpam-4492	95	15	arcs,∣∣a(dpt	arcs,∣∣a(dpt	PUNCT
ejpam-4492	95	16	(	(	PUNCT
ejpam-4492	95	17	ar	ar	NOUN
ejpam-4492	95	18	)	)	PUNCT
ejpam-4492	95	19	)	)	PUNCT
ejpam-4492	95	20	∣∣	∣∣	X
ejpam-4492	96	1	=	=	SYM
ejpam-4492	96	2	5(n−	5(n−	NUM
ejpam-4492	96	3	1)−	1)−	NUM
ejpam-4492	96	4	1	1	NUM
ejpam-4492	96	5	=	=	SYM
ejpam-4492	96	6	5n−	5n−	NUM
ejpam-4492	96	7	6	6	NUM
ejpam-4492	96	8	.	.	PUNCT
ejpam-4492	97	1	proof	proof	NOUN
ejpam-4492	97	2	:	:	PUNCT
ejpam-4492	97	3	we	we	PRON
ejpam-4492	97	4	do	do	VERB
ejpam-4492	97	5	this	this	PRON
ejpam-4492	97	6	by	by	ADP
ejpam-4492	97	7	induction	induction	NOUN
ejpam-4492	97	8	.	.	PUNCT
ejpam-4492	98	1	for	for	ADP
ejpam-4492	98	2	n	n	NOUN
ejpam-4492	98	3	=	=	SYM
ejpam-4492	98	4	2	2	NUM
ejpam-4492	98	5	,	,	PUNCT
ejpam-4492	98	6	note	note	VERB
ejpam-4492	98	7	that	that	SCONJ
ejpam-4492	98	8	dpt	dpt	PROPN
ejpam-4492	98	9	(	(	PUNCT
ejpam-4492	98	10	p⃗2	p⃗2	NOUN
ejpam-4492	98	11	)	)	PUNCT
ejpam-4492	98	12	consists	consist	VERB
ejpam-4492	98	13	of	of	ADP
ejpam-4492	98	14	vertices	vertex	NOUN
ejpam-4492	98	15	v1	v1	NOUN
ejpam-4492	98	16	,	,	PUNCT
ejpam-4492	98	17	v2	v2	NOUN
ejpam-4492	98	18	,	,	PUNCT
ejpam-4492	98	19	e1	e1	NOUN
ejpam-4492	98	20	,	,	PUNCT
ejpam-4492	98	21	and	and	CCONJ
ejpam-4492	98	22	p	p	NOUN
ejpam-4492	98	23	and	and	CCONJ
ejpam-4492	98	24	arcs	arcs	PROPN
ejpam-4492	98	25	(	(	PUNCT
ejpam-4492	98	26	v1	v1	NOUN
ejpam-4492	98	27	,	,	PUNCT
ejpam-4492	98	28	v2	v2	PROPN
ejpam-4492	98	29	)	)	PUNCT
ejpam-4492	98	30	,	,	PUNCT
ejpam-4492	98	31	(	(	PUNCT
ejpam-4492	98	32	v1	v1	NOUN
ejpam-4492	98	33	,	,	PUNCT
ejpam-4492	98	34	e1	e1	PROPN
ejpam-4492	98	35	)	)	PUNCT
ejpam-4492	98	36	,	,	PUNCT
ejpam-4492	98	37	(	(	PUNCT
ejpam-4492	98	38	e1	e1	NOUN
ejpam-4492	98	39	,	,	PUNCT
ejpam-4492	98	40	v2	v2	NOUN
ejpam-4492	98	41	)	)	PUNCT
ejpam-4492	98	42	,	,	PUNCT
ejpam-4492	98	43	and	and	CCONJ
ejpam-4492	98	44	(	(	PUNCT
ejpam-4492	98	45	p	p	X
ejpam-4492	98	46	,	,	PUNCT
ejpam-4492	98	47	e1	e1	PROPN
ejpam-4492	98	48	)	)	PUNCT
ejpam-4492	98	49	.	.	PUNCT
ejpam-4492	99	1	(	(	PUNCT
ejpam-4492	99	2	see	see	VERB
ejpam-4492	99	3	figure	figure	NOUN
ejpam-4492	99	4	4	4	NUM
ejpam-4492	99	5	)	)	PUNCT
ejpam-4492	99	6	.	.	PUNCT
ejpam-4492	100	1	thus,∣∣a(dpt	thus,∣∣a(dpt	PUNCT
ejpam-4492	100	2	(	(	PUNCT
ejpam-4492	100	3	p⃗3	p⃗3	NOUN
ejpam-4492	100	4	)	)	PUNCT
ejpam-4492	100	5	)	)	PUNCT
ejpam-4492	101	1	∣∣	∣∣	X
ejpam-4492	102	1	=	=	SYM
ejpam-4492	102	2	4	4	NUM
ejpam-4492	102	3	=	=	SYM
ejpam-4492	102	4	5(2−	5(2−	PROPN
ejpam-4492	102	5	1)−	1)−	NUM
ejpam-4492	102	6	1	1	NUM
ejpam-4492	102	7	=	=	SYM
ejpam-4492	102	8	5(n−	5(n−	NUM
ejpam-4492	102	9	1)−	1)−	PROPN
ejpam-4492	102	10	1	1	NUM
ejpam-4492	102	11	.	.	PUNCT
ejpam-4492	102	12	figure	figure	VERB
ejpam-4492	102	13	4	4	NUM
ejpam-4492	102	14	:	:	PUNCT
ejpam-4492	102	15	digraph	digraph	VERB
ejpam-4492	102	16	p⃗2	p⃗2	NOUN
ejpam-4492	102	17	and	and	CCONJ
ejpam-4492	102	18	its	its	PRON
ejpam-4492	102	19	directed	direct	VERB
ejpam-4492	102	20	pathos	pathos	NOUN
ejpam-4492	102	21	total	total	NOUN
ejpam-4492	102	22	digraph	digraph	PROPN
ejpam-4492	102	23	jill	jill	PROPN
ejpam-4492	102	24	maegan	maegan	PROPN
ejpam-4492	102	25	b.	b.	PROPN
ejpam-4492	102	26	pamplona	pamplona	PROPN
ejpam-4492	102	27	,	,	PUNCT
ejpam-4492	102	28	imelda	imelda	PROPN
ejpam-4492	102	29	s.	s.	PROPN
ejpam-4492	102	30	aniversario	aniversario	PROPN
ejpam-4492	102	31	/	/	SYM
ejpam-4492	102	32	eur	eur	PROPN
ejpam-4492	102	33	.	.	PUNCT
ejpam-4492	103	1	j.	j.	PROPN
ejpam-4492	103	2	pure	pure	PROPN
ejpam-4492	103	3	appl	appl	PROPN
ejpam-4492	103	4	.	.	PROPN
ejpam-4492	103	5	math	math	PROPN
ejpam-4492	103	6	,	,	PUNCT
ejpam-4492	103	7	15	15	NUM
ejpam-4492	103	8	(	(	PUNCT
ejpam-4492	103	9	3	3	NUM
ejpam-4492	103	10	)	)	PUNCT
ejpam-4492	103	11	(	(	PUNCT
ejpam-4492	103	12	2022	2022	NUM
ejpam-4492	103	13	)	)	PUNCT
ejpam-4492	103	14	,	,	PUNCT
ejpam-4492	103	15	1331	1331	NUM
ejpam-4492	103	16	-	-	SYM
ejpam-4492	103	17	1343	1343	NUM
ejpam-4492	103	18	1336	1336	NUM
ejpam-4492	103	19	for	for	ADP
ejpam-4492	103	20	n	n	NOUN
ejpam-4492	103	21	=	=	SYM
ejpam-4492	103	22	3	3	NUM
ejpam-4492	103	23	,	,	PUNCT
ejpam-4492	103	24	dpt	dpt	PROPN
ejpam-4492	103	25	(	(	PUNCT
ejpam-4492	103	26	p⃗3	p⃗3	NOUN
ejpam-4492	103	27	)	)	PUNCT
ejpam-4492	103	28	consists	consist	VERB
ejpam-4492	103	29	of	of	ADP
ejpam-4492	103	30	vertices	vertex	NOUN
ejpam-4492	103	31	v1	v1	NOUN
ejpam-4492	103	32	,	,	PUNCT
ejpam-4492	103	33	v2	v2	PROPN
ejpam-4492	103	34	,	,	PUNCT
ejpam-4492	103	35	v3	v3	PROPN
ejpam-4492	103	36	,	,	PUNCT
ejpam-4492	103	37	e1	e1	PROPN
ejpam-4492	103	38	,	,	PUNCT
ejpam-4492	103	39	e2	e2	NOUN
ejpam-4492	103	40	,	,	PUNCT
ejpam-4492	103	41	and	and	CCONJ
ejpam-4492	103	42	p	p	NOUN
ejpam-4492	103	43	and	and	CCONJ
ejpam-4492	103	44	arcs	arcs	PROPN
ejpam-4492	103	45	(	(	PUNCT
ejpam-4492	103	46	v1	v1	NOUN
ejpam-4492	103	47	,	,	PUNCT
ejpam-4492	103	48	v2	v2	PROPN
ejpam-4492	103	49	)	)	PUNCT
ejpam-4492	103	50	,	,	PUNCT
ejpam-4492	103	51	(	(	PUNCT
ejpam-4492	103	52	v2	v2	PROPN
ejpam-4492	103	53	,	,	PUNCT
ejpam-4492	103	54	v3	v3	PROPN
ejpam-4492	103	55	)	)	PUNCT
ejpam-4492	103	56	,	,	PUNCT
ejpam-4492	103	57	(	(	PUNCT
ejpam-4492	103	58	v1	v1	NOUN
ejpam-4492	103	59	,	,	PUNCT
ejpam-4492	103	60	e1	e1	PROPN
ejpam-4492	103	61	)	)	PUNCT
ejpam-4492	103	62	,	,	PUNCT
ejpam-4492	103	63	(	(	PUNCT
ejpam-4492	103	64	v2	v2	PROPN
ejpam-4492	103	65	,	,	PUNCT
ejpam-4492	103	66	e2	e2	PROPN
ejpam-4492	103	67	)	)	PUNCT
ejpam-4492	103	68	,	,	PUNCT
ejpam-4492	103	69	(	(	PUNCT
ejpam-4492	103	70	e1	e1	NOUN
ejpam-4492	103	71	,	,	PUNCT
ejpam-4492	103	72	v2	v2	PROPN
ejpam-4492	103	73	)	)	PUNCT
ejpam-4492	103	74	,	,	PUNCT
ejpam-4492	103	75	(	(	PUNCT
ejpam-4492	103	76	e2	e2	PROPN
ejpam-4492	103	77	,	,	PUNCT
ejpam-4492	103	78	v3	v3	PROPN
ejpam-4492	103	79	)	)	PUNCT
ejpam-4492	103	80	,	,	PUNCT
ejpam-4492	103	81	(	(	PUNCT
ejpam-4492	103	82	e1	e1	PROPN
ejpam-4492	103	83	,	,	PUNCT
ejpam-4492	103	84	e2	e2	PROPN
ejpam-4492	103	85	)	)	PUNCT
ejpam-4492	103	86	,	,	PUNCT
ejpam-4492	103	87	(	(	PUNCT
ejpam-4492	103	88	p	p	X
ejpam-4492	103	89	,	,	PUNCT
ejpam-4492	103	90	e1	e1	NOUN
ejpam-4492	103	91	)	)	PUNCT
ejpam-4492	103	92	,	,	PUNCT
ejpam-4492	103	93	and	and	CCONJ
ejpam-4492	103	94	(	(	PUNCT
ejpam-4492	103	95	p	p	X
ejpam-4492	103	96	,	,	PUNCT
ejpam-4492	103	97	e2	e2	PROPN
ejpam-4492	103	98	)	)	PUNCT
ejpam-4492	103	99	.	.	PUNCT
ejpam-4492	104	1	(	(	PUNCT
ejpam-4492	104	2	see	see	VERB
ejpam-4492	104	3	figure	figure	NOUN
ejpam-4492	104	4	5	5	NUM
ejpam-4492	104	5	)	)	PUNCT
ejpam-4492	104	6	.	.	PUNCT
ejpam-4492	105	1	thus	thus	ADV
ejpam-4492	105	2	,	,	PUNCT
ejpam-4492	105	3	∣∣a(dpt	∣∣a(dpt	ADV
ejpam-4492	105	4	(	(	PUNCT
ejpam-4492	105	5	p⃗3	p⃗3	NOUN
ejpam-4492	105	6	)	)	PUNCT
ejpam-4492	105	7	)	)	PUNCT
ejpam-4492	105	8	∣∣	∣∣	X
ejpam-4492	106	1	=	=	SYM
ejpam-4492	106	2	9	9	NUM
ejpam-4492	106	3	=	=	SYM
ejpam-4492	106	4	5(3−	5(3−	PROPN
ejpam-4492	106	5	1)−	1)−	NUM
ejpam-4492	106	6	1	1	NUM
ejpam-4492	106	7	=	=	SYM
ejpam-4492	106	8	5(n−	5(n−	NUM
ejpam-4492	106	9	1)−	1)−	PROPN
ejpam-4492	106	10	1	1	NUM
ejpam-4492	106	11	.	.	PUNCT
ejpam-4492	106	12	figure	figure	VERB
ejpam-4492	106	13	5	5	NUM
ejpam-4492	106	14	:	:	PUNCT
ejpam-4492	106	15	digraph	digraph	NOUN
ejpam-4492	106	16	p⃗3	p⃗3	NOUN
ejpam-4492	106	17	and	and	CCONJ
ejpam-4492	106	18	its	its	PRON
ejpam-4492	106	19	directed	direct	VERB
ejpam-4492	106	20	pathos	pathos	NOUN
ejpam-4492	106	21	total	total	NOUN
ejpam-4492	106	22	digraph	digraph	NOUN
ejpam-4492	106	23	assume	assume	VERB
ejpam-4492	106	24	that	that	SCONJ
ejpam-4492	106	25	for	for	ADP
ejpam-4492	106	26	p⃗n−1	p⃗n−1	PROPN
ejpam-4492	106	27	with	with	ADP
ejpam-4492	106	28	n−	n−	NOUN
ejpam-4492	106	29	1	1	NUM
ejpam-4492	106	30	vertices	vertex	NOUN
ejpam-4492	106	31	,	,	PUNCT
ejpam-4492	106	32	∣∣a(dpt	∣∣a(dpt	X
ejpam-4492	106	33	(	(	PUNCT
ejpam-4492	106	34	p⃗n−1	p⃗n−1	ADJ
ejpam-4492	106	35	)	)	PUNCT
ejpam-4492	106	36	)	)	PUNCT
ejpam-4492	106	37	∣∣	∣∣	PUNCT
ejpam-4492	107	1	=	=	SYM
ejpam-4492	107	2	5	5	NUM
ejpam-4492	107	3	(	(	PUNCT
ejpam-4492	107	4	(	(	PUNCT
ejpam-4492	107	5	n−	n−	NOUN
ejpam-4492	107	6	1)−	1)−	PROPN
ejpam-4492	107	7	1	1	NUM
ejpam-4492	107	8	)	)	PUNCT
ejpam-4492	107	9	−	−	PROPN
ejpam-4492	108	1	1	1	X
ejpam-4492	108	2	.	.	PUNCT
ejpam-4492	109	1	that	that	DET
ejpam-4492	109	2	is,∣∣a(dpt	is,∣∣a(dpt	PROPN
ejpam-4492	109	3	(	(	PUNCT
ejpam-4492	109	4	p⃗n−1	p⃗n−1	ADJ
ejpam-4492	109	5	)	)	PUNCT
ejpam-4492	109	6	)	)	PUNCT
ejpam-4492	109	7	∣∣	∣∣	X
ejpam-4492	110	1	=	=	PUNCT
ejpam-4492	110	2	5((n−	5((n−	NUM
ejpam-4492	111	1	1)−	1)−	PROPN
ejpam-4492	111	2	1)−	1)−	PROPN
ejpam-4492	111	3	1	1	NUM
ejpam-4492	111	4	=	=	SYM
ejpam-4492	111	5	5(n−	5(n−	NUM
ejpam-4492	111	6	2)−	2)−	PROPN
ejpam-4492	111	7	1	1	NUM
ejpam-4492	111	8	=	=	SYM
ejpam-4492	111	9	5n−	5n−	NUM
ejpam-4492	111	10	10−	10−	ADJ
ejpam-4492	111	11	1	1	NUM
ejpam-4492	111	12	=	=	SYM
ejpam-4492	111	13	5(n−	5(n−	NUM
ejpam-4492	111	14	1)−	1)−	PROPN
ejpam-4492	111	15	6	6	NUM
ejpam-4492	111	16	=	=	SYM
ejpam-4492	111	17	5n−	5n−	NUM
ejpam-4492	111	18	11	11	NUM
ejpam-4492	111	19	.	.	PUNCT
ejpam-4492	112	1	that	that	PRON
ejpam-4492	112	2	is	is	ADV
ejpam-4492	112	3	,	,	PUNCT
ejpam-4492	112	4	a	a	DET
ejpam-4492	112	5	(	(	PUNCT
ejpam-4492	112	6	dpt	dpt	PROPN
ejpam-4492	112	7	(	(	PUNCT
ejpam-4492	112	8	p⃗n−1	p⃗n−1	PROPN
ejpam-4492	112	9	)	)	PUNCT
ejpam-4492	112	10	)	)	PUNCT
ejpam-4492	113	1	consists	consist	VERB
ejpam-4492	113	2	of	of	ADP
ejpam-4492	113	3	the	the	DET
ejpam-4492	113	4	arcs	arc	NOUN
ejpam-4492	113	5	(	(	PUNCT
ejpam-4492	113	6	v1	v1	NOUN
ejpam-4492	113	7	,	,	PUNCT
ejpam-4492	113	8	v2	v2	PROPN
ejpam-4492	113	9	)	)	PUNCT
ejpam-4492	113	10	,	,	PUNCT
ejpam-4492	113	11	(	(	PUNCT
ejpam-4492	113	12	v2	v2	PROPN
ejpam-4492	113	13	,	,	PUNCT
ejpam-4492	113	14	v3	v3	PROPN
ejpam-4492	113	15	)	)	PUNCT
ejpam-4492	113	16	,	,	PUNCT
ejpam-4492	113	17	.	.	PUNCT
ejpam-4492	113	18	.	.	PUNCT
ejpam-4492	114	1	.	.	PUNCT
ejpam-4492	115	1	,	,	PUNCT
ejpam-4492	115	2	(	(	PUNCT
ejpam-4492	115	3	vn−2	vn−2	PROPN
ejpam-4492	115	4	,	,	PUNCT
ejpam-4492	115	5	vn−1	vn−1	ADJ
ejpam-4492	115	6	)	)	PUNCT
ejpam-4492	115	7	,	,	PUNCT
ejpam-4492	115	8	(	(	PUNCT
ejpam-4492	115	9	v1	v1	NOUN
ejpam-4492	115	10	,	,	PUNCT
ejpam-4492	115	11	e1	e1	PROPN
ejpam-4492	115	12	)	)	PUNCT
ejpam-4492	115	13	,	,	PUNCT
ejpam-4492	115	14	(	(	PUNCT
ejpam-4492	115	15	v2	v2	PROPN
ejpam-4492	115	16	,	,	PUNCT
ejpam-4492	115	17	e2	e2	PROPN
ejpam-4492	115	18	)	)	PUNCT
ejpam-4492	115	19	,	,	PUNCT
ejpam-4492	115	20	.	.	PUNCT
ejpam-4492	115	21	.	.	PUNCT
ejpam-4492	115	22	.	.	PUNCT
ejpam-4492	116	1	,	,	PUNCT
ejpam-4492	116	2	(	(	PUNCT
ejpam-4492	116	3	vn−2	vn−2	PROPN
ejpam-4492	116	4	,	,	PUNCT
ejpam-4492	116	5	en−1	en−1	PROPN
ejpam-4492	116	6	)	)	PUNCT
ejpam-4492	116	7	,	,	PUNCT
ejpam-4492	116	8	(	(	PUNCT
ejpam-4492	116	9	e1	e1	NOUN
ejpam-4492	116	10	,	,	PUNCT
ejpam-4492	116	11	v2	v2	PROPN
ejpam-4492	116	12	)	)	PUNCT
ejpam-4492	116	13	,	,	PUNCT
ejpam-4492	116	14	(	(	PUNCT
ejpam-4492	116	15	e2	e2	PROPN
ejpam-4492	116	16	,	,	PUNCT
ejpam-4492	116	17	v3	v3	PROPN
ejpam-4492	116	18	)	)	PUNCT
ejpam-4492	116	19	,	,	PUNCT
ejpam-4492	116	20	.	.	PUNCT
ejpam-4492	116	21	.	.	PUNCT
ejpam-4492	116	22	.	.	PUNCT
ejpam-4492	117	1	,	,	PUNCT
ejpam-4492	117	2	(	(	PUNCT
ejpam-4492	117	3	en−2	en−2	PROPN
ejpam-4492	117	4	,	,	PUNCT
ejpam-4492	117	5	vn−1	vn−1	ADJ
ejpam-4492	117	6	)	)	PUNCT
ejpam-4492	117	7	,	,	PUNCT
ejpam-4492	117	8	(	(	PUNCT
ejpam-4492	117	9	e1	e1	PROPN
ejpam-4492	117	10	,	,	PUNCT
ejpam-4492	117	11	e2	e2	PROPN
ejpam-4492	117	12	)	)	PUNCT
ejpam-4492	117	13	,	,	PUNCT
ejpam-4492	117	14	(	(	PUNCT
ejpam-4492	117	15	e2	e2	PROPN
ejpam-4492	117	16	,	,	PUNCT
ejpam-4492	117	17	e3	e3	NOUN
ejpam-4492	117	18	)	)	PUNCT
ejpam-4492	117	19	,	,	PUNCT
ejpam-4492	117	20	.	.	PUNCT
ejpam-4492	117	21	.	.	PUNCT
ejpam-4492	117	22	.	.	PUNCT
ejpam-4492	118	1	,	,	PUNCT
ejpam-4492	118	2	(	(	PUNCT
ejpam-4492	118	3	en−3	en−3	PROPN
ejpam-4492	118	4	,	,	PUNCT
ejpam-4492	118	5	en−2	en−2	PROPN
ejpam-4492	118	6	)	)	PUNCT
ejpam-4492	118	7	,	,	PUNCT
ejpam-4492	118	8	(	(	PUNCT
ejpam-4492	118	9	p	p	X
ejpam-4492	118	10	,	,	PUNCT
ejpam-4492	118	11	e1	e1	PROPN
ejpam-4492	118	12	)	)	PUNCT
ejpam-4492	118	13	,	,	PUNCT
ejpam-4492	118	14	(	(	PUNCT
ejpam-4492	118	15	p	p	X
ejpam-4492	118	16	,	,	PUNCT
ejpam-4492	118	17	e2	e2	PROPN
ejpam-4492	118	18	)	)	PUNCT
ejpam-4492	118	19	,	,	PUNCT
ejpam-4492	118	20	.	.	PUNCT
ejpam-4492	118	21	.	.	PUNCT
ejpam-4492	118	22	.	.	PUNCT
ejpam-4492	119	1	,	,	PUNCT
ejpam-4492	119	2	(	(	PUNCT
ejpam-4492	119	3	p	p	X
ejpam-4492	119	4	,	,	PUNCT
ejpam-4492	119	5	en−2	en−2	PROPN
ejpam-4492	119	6	)	)	PUNCT
ejpam-4492	119	7	.	.	PUNCT
ejpam-4492	120	1	(	(	PUNCT
ejpam-4492	120	2	see	see	VERB
ejpam-4492	120	3	figure	figure	NOUN
ejpam-4492	120	4	6	6	NUM
ejpam-4492	120	5	)	)	PUNCT
ejpam-4492	120	6	.	.	PUNCT
ejpam-4492	121	1	figure	figure	VERB
ejpam-4492	121	2	6	6	NUM
ejpam-4492	121	3	:	:	PUNCT
ejpam-4492	121	4	digraph	digraph	VERB
ejpam-4492	121	5	p⃗n−1	p⃗n−1	ADV
ejpam-4492	121	6	and	and	CCONJ
ejpam-4492	121	7	its	its	PRON
ejpam-4492	121	8	directed	direct	VERB
ejpam-4492	121	9	pathos	pathos	NOUN
ejpam-4492	121	10	total	total	NOUN
ejpam-4492	121	11	digraph	digraph	PROPN
ejpam-4492	121	12	jill	jill	PROPN
ejpam-4492	121	13	maegan	maegan	PROPN
ejpam-4492	121	14	b.	b.	PROPN
ejpam-4492	121	15	pamplona	pamplona	PROPN
ejpam-4492	121	16	,	,	PUNCT
ejpam-4492	121	17	imelda	imelda	PROPN
ejpam-4492	121	18	s.	s.	PROPN
ejpam-4492	121	19	aniversario	aniversario	PROPN
ejpam-4492	121	20	/	/	SYM
ejpam-4492	121	21	eur	eur	PROPN
ejpam-4492	121	22	.	.	PUNCT
ejpam-4492	122	1	j.	j.	PROPN
ejpam-4492	122	2	pure	pure	PROPN
ejpam-4492	122	3	appl	appl	PROPN
ejpam-4492	122	4	.	.	PROPN
ejpam-4492	122	5	math	math	PROPN
ejpam-4492	122	6	,	,	PUNCT
ejpam-4492	122	7	15	15	NUM
ejpam-4492	122	8	(	(	PUNCT
ejpam-4492	122	9	3	3	NUM
ejpam-4492	122	10	)	)	PUNCT
ejpam-4492	122	11	(	(	PUNCT
ejpam-4492	122	12	2022	2022	NUM
ejpam-4492	122	13	)	)	PUNCT
ejpam-4492	122	14	,	,	PUNCT
ejpam-4492	122	15	1331	1331	NUM
ejpam-4492	122	16	-	-	SYM
ejpam-4492	122	17	1343	1343	NUM
ejpam-4492	122	18	1337	1337	NUM
ejpam-4492	122	19	adding	add	VERB
ejpam-4492	122	20	one	one	NUM
ejpam-4492	122	21	vertex	vertex	NOUN
ejpam-4492	122	22	to	to	PART
ejpam-4492	122	23	p⃗n−1	p⃗n−1	VERB
ejpam-4492	122	24	results	result	NOUN
ejpam-4492	122	25	into	into	ADP
ejpam-4492	122	26	a	a	DET
ejpam-4492	122	27	directed	direct	VERB
ejpam-4492	122	28	path	path	NOUN
ejpam-4492	122	29	p⃗n	p⃗n	NOUN
ejpam-4492	122	30	,	,	PUNCT
ejpam-4492	122	31	with	with	ADP
ejpam-4492	122	32	the	the	DET
ejpam-4492	122	33	additional	additional	ADJ
ejpam-4492	122	34	arc	arc	NOUN
ejpam-4492	122	35	(	(	PUNCT
ejpam-4492	122	36	vn−1	vn−1	PROPN
ejpam-4492	122	37	,	,	PUNCT
ejpam-4492	122	38	vn	vn	NOUN
ejpam-4492	122	39	)	)	PUNCT
ejpam-4492	122	40	.	.	PUNCT
ejpam-4492	123	1	(	(	PUNCT
ejpam-4492	123	2	see	see	VERB
ejpam-4492	123	3	figure	figure	NOUN
ejpam-4492	123	4	7	7	NUM
ejpam-4492	123	5	)	)	PUNCT
ejpam-4492	123	6	.	.	PUNCT
ejpam-4492	124	1	figure	figure	VERB
ejpam-4492	124	2	7	7	NUM
ejpam-4492	124	3	:	:	PUNCT
ejpam-4492	124	4	digraph	digraph	NOUN
ejpam-4492	124	5	p⃗n	p⃗n	NOUN
ejpam-4492	124	6	and	and	CCONJ
ejpam-4492	124	7	its	its	PRON
ejpam-4492	124	8	directed	direct	VERB
ejpam-4492	124	9	pathos	pathos	NOUN
ejpam-4492	124	10	total	total	NOUN
ejpam-4492	124	11	digraph	digraph	NOUN
ejpam-4492	124	12	hence	hence	ADV
ejpam-4492	124	13	,	,	PUNCT
ejpam-4492	124	14	dpt	dpt	PROPN
ejpam-4492	124	15	(	(	PUNCT
ejpam-4492	124	16	p⃗n	p⃗n	PROPN
ejpam-4492	124	17	)	)	PUNCT
ejpam-4492	124	18	contains	contain	VERB
ejpam-4492	124	19	the	the	DET
ejpam-4492	124	20	arcs	arc	NOUN
ejpam-4492	124	21	in	in	ADP
ejpam-4492	124	22	dpt	dpt	PROPN
ejpam-4492	124	23	(	(	PUNCT
ejpam-4492	124	24	p⃗n−1	p⃗n−1	PROPN
ejpam-4492	124	25	)	)	PUNCT
ejpam-4492	124	26	and	and	CCONJ
ejpam-4492	124	27	the	the	DET
ejpam-4492	124	28	arcs	arc	NOUN
ejpam-4492	124	29	(	(	PUNCT
ejpam-4492	124	30	vn−1	vn−1	PROPN
ejpam-4492	124	31	,	,	PUNCT
ejpam-4492	124	32	vn	vn	NOUN
ejpam-4492	124	33	)	)	PUNCT
ejpam-4492	124	34	,	,	PUNCT
ejpam-4492	124	35	(	(	PUNCT
ejpam-4492	124	36	en−1	en−1	PROPN
ejpam-4492	124	37	,	,	PUNCT
ejpam-4492	124	38	vn	vn	NOUN
ejpam-4492	124	39	)	)	PUNCT
ejpam-4492	124	40	,	,	PUNCT
ejpam-4492	124	41	(	(	PUNCT
ejpam-4492	124	42	vn−1	vn−1	PROPN
ejpam-4492	124	43	,	,	PUNCT
ejpam-4492	124	44	en−1	en−1	PROPN
ejpam-4492	124	45	)	)	PUNCT
ejpam-4492	124	46	,	,	PUNCT
ejpam-4492	124	47	(	(	PUNCT
ejpam-4492	124	48	en−2	en−2	PROPN
ejpam-4492	124	49	,	,	PUNCT
ejpam-4492	124	50	en−1	en−1	PROPN
ejpam-4492	124	51	)	)	PUNCT
ejpam-4492	124	52	,	,	PUNCT
ejpam-4492	124	53	and	and	CCONJ
ejpam-4492	124	54	(	(	PUNCT
ejpam-4492	124	55	p	p	X
ejpam-4492	124	56	,	,	PUNCT
ejpam-4492	124	57	en−1	en−1	PROPN
ejpam-4492	124	58	)	)	PUNCT
ejpam-4492	124	59	.	.	PUNCT
ejpam-4492	125	1	therefore	therefore	ADV
ejpam-4492	125	2	,	,	PUNCT
ejpam-4492	125	3	|a(dpt	|a(dpt	X
ejpam-4492	125	4	(	(	PUNCT
ejpam-4492	125	5	p⃗n))|	p⃗n))|	PROPN
ejpam-4492	125	6	=	=	PUNCT
ejpam-4492	125	7	5n−	5n−	NUM
ejpam-4492	125	8	11	11	NUM
ejpam-4492	125	9	+	+	CCONJ
ejpam-4492	125	10	5	5	NUM
ejpam-4492	125	11	=	=	SYM
ejpam-4492	125	12	5n−	5n−	NUM
ejpam-4492	125	13	6	6	NUM
ejpam-4492	125	14	=	=	SYM
ejpam-4492	125	15	5n−	5n−	NUM
ejpam-4492	125	16	5−	5−	NUM
ejpam-4492	125	17	1	1	NUM
ejpam-4492	125	18	=	=	SYM
ejpam-4492	125	19	5(n−	5(n−	PROPN
ejpam-4492	125	20	1)−	1)−	PROPN
ejpam-4492	125	21	1	1	NUM
ejpam-4492	125	22	.	.	PUNCT
ejpam-4492	126	1	we	we	PRON
ejpam-4492	126	2	present	present	VERB
ejpam-4492	126	3	a	a	DET
ejpam-4492	126	4	closely	closely	ADV
ejpam-4492	126	5	similar	similar	ADJ
ejpam-4492	126	6	result	result	NOUN
ejpam-4492	126	7	from	from	ADP
ejpam-4492	126	8	[	[	X
ejpam-4492	126	9	6	6	NUM
ejpam-4492	126	10	]	]	PUNCT
ejpam-4492	126	11	in	in	ADP
ejpam-4492	126	12	the	the	DET
ejpam-4492	126	13	next	next	ADJ
ejpam-4492	126	14	theorem	theorem	NOUN
ejpam-4492	126	15	using	use	VERB
ejpam-4492	126	16	the	the	DET
ejpam-4492	126	17	usual	usual	ADJ
ejpam-4492	126	18	notation	notation	NOUN
ejpam-4492	126	19	of	of	ADP
ejpam-4492	126	20	a	a	DET
ejpam-4492	126	21	path	path	NOUN
ejpam-4492	126	22	and	and	CCONJ
ejpam-4492	126	23	taking	take	VERB
ejpam-4492	126	24	into	into	ADP
ejpam-4492	126	25	consideration	consideration	NOUN
ejpam-4492	126	26	a	a	DET
ejpam-4492	126	27	directed	direct	VERB
ejpam-4492	126	28	path	path	NOUN
ejpam-4492	126	29	as	as	ADP
ejpam-4492	126	30	an	an	DET
ejpam-4492	126	31	arborescence	arborescence	NOUN
ejpam-4492	126	32	.	.	PUNCT
ejpam-4492	127	1	theorem	theorem	VERB
ejpam-4492	127	2	3.3	3.3	NUM
ejpam-4492	127	3	.	.	PUNCT
ejpam-4492	128	1	the	the	DET
ejpam-4492	128	2	i(dpt	i(dpt	PROPN
ejpam-4492	128	3	(	(	PUNCT
ejpam-4492	128	4	p⃗n	p⃗n	NOUN
ejpam-4492	128	5	)	)	PUNCT
ejpam-4492	128	6	)	)	PUNCT
ejpam-4492	129	1	=	=	PUNCT
ejpam-4492	129	2	n−	n−	NOUN
ejpam-4492	129	3	3	3	NUM
ejpam-4492	129	4	if	if	SCONJ
ejpam-4492	129	5	and	and	CCONJ
ejpam-4492	129	6	only	only	ADV
ejpam-4492	129	7	if	if	SCONJ
ejpam-4492	129	8	n	n	PRON
ejpam-4492	129	9	≥	≥	NOUN
ejpam-4492	129	10	4	4	NUM
ejpam-4492	129	11	.	.	PUNCT
ejpam-4492	130	1	proof	proof	NOUN
ejpam-4492	130	2	:	:	PUNCT
ejpam-4492	130	3	suppose	suppose	VERB
ejpam-4492	130	4	that	that	SCONJ
ejpam-4492	130	5	i(dpt	i(dpt	PROPN
ejpam-4492	130	6	(	(	PUNCT
ejpam-4492	130	7	p⃗n	p⃗n	NOUN
ejpam-4492	130	8	)	)	PUNCT
ejpam-4492	130	9	)	)	PUNCT
ejpam-4492	131	1	=	=	SYM
ejpam-4492	131	2	n	n	CCONJ
ejpam-4492	131	3	−	−	PROPN
ejpam-4492	131	4	3	3	NUM
ejpam-4492	131	5	,	,	PUNCT
ejpam-4492	131	6	where	where	SCONJ
ejpam-4492	131	7	n	n	X
ejpam-4492	131	8	<	<	X
ejpam-4492	131	9	4	4	X
ejpam-4492	131	10	.	.	PUNCT
ejpam-4492	131	11	suppose	suppose	VERB
ejpam-4492	131	12	n	n	PROPN
ejpam-4492	131	13	=	=	SYM
ejpam-4492	131	14	3	3	NUM
ejpam-4492	131	15	and	and	CCONJ
ejpam-4492	131	16	ar	ar	NOUN
ejpam-4492	131	17	=	=	NOUN
ejpam-4492	131	18	p⃗3	p⃗3	NOUN
ejpam-4492	131	19	.	.	PUNCT
ejpam-4492	132	1	thus	thus	ADV
ejpam-4492	132	2	we	we	PRON
ejpam-4492	132	3	have	have	VERB
ejpam-4492	132	4	v1	v1	NOUN
ejpam-4492	132	5	,	,	PUNCT
ejpam-4492	132	6	v2	v2	PROPN
ejpam-4492	132	7	,	,	PUNCT
ejpam-4492	132	8	v3	v3	PROPN
ejpam-4492	132	9	as	as	ADP
ejpam-4492	132	10	the	the	DET
ejpam-4492	132	11	vertices	vertex	NOUN
ejpam-4492	132	12	of	of	ADP
ejpam-4492	132	13	ar	ar	NOUN
ejpam-4492	132	14	and	and	CCONJ
ejpam-4492	132	15	e1	e1	PROPN
ejpam-4492	132	16	=	=	SYM
ejpam-4492	132	17	(	(	PUNCT
ejpam-4492	132	18	v1	v1	NOUN
ejpam-4492	132	19	,	,	PUNCT
ejpam-4492	132	20	v2	v2	PROPN
ejpam-4492	132	21	)	)	PUNCT
ejpam-4492	132	22	and	and	CCONJ
ejpam-4492	132	23	e2	e2	PROPN
ejpam-4492	132	24	=	=	SYM
ejpam-4492	132	25	v2	v2	PROPN
ejpam-4492	132	26	,	,	PUNCT
ejpam-4492	132	27	v3	v3	PROPN
ejpam-4492	132	28	as	as	ADP
ejpam-4492	132	29	the	the	DET
ejpam-4492	132	30	arcs	arcs	NOUN
ejpam-4492	132	31	of	of	ADP
ejpam-4492	132	32	ar	ar	PROPN
ejpam-4492	132	33	.	.	PROPN
ejpam-4492	132	34	then	then	ADV
ejpam-4492	132	35	the	the	DET
ejpam-4492	132	36	vertices	vertex	NOUN
ejpam-4492	132	37	of	of	ADP
ejpam-4492	132	38	t	t	PROPN
ejpam-4492	132	39	(	(	PUNCT
ejpam-4492	132	40	ar	ar	NOUN
ejpam-4492	132	41	)	)	PUNCT
ejpam-4492	132	42	are	be	AUX
ejpam-4492	132	43	{	{	PUNCT
ejpam-4492	132	44	v1	v1	NOUN
ejpam-4492	132	45	,	,	PUNCT
ejpam-4492	132	46	v2	v2	PROPN
ejpam-4492	132	47	,	,	PUNCT
ejpam-4492	132	48	v3	v3	PROPN
ejpam-4492	132	49	,	,	PUNCT
ejpam-4492	132	50	e1	e1	PROPN
ejpam-4492	132	51	,	,	PUNCT
ejpam-4492	132	52	e2	e2	PROPN
ejpam-4492	132	53	}	}	PUNCT
ejpam-4492	132	54	and	and	CCONJ
ejpam-4492	132	55	the	the	DET
ejpam-4492	132	56	arcs	arc	NOUN
ejpam-4492	132	57	are	be	AUX
ejpam-4492	132	58	(	(	PUNCT
ejpam-4492	132	59	v1	v1	NOUN
ejpam-4492	132	60	,	,	PUNCT
ejpam-4492	132	61	v2	v2	PROPN
ejpam-4492	132	62	)	)	PUNCT
ejpam-4492	132	63	,	,	PUNCT
ejpam-4492	132	64	(	(	PUNCT
ejpam-4492	132	65	v2	v2	PROPN
ejpam-4492	132	66	,	,	PUNCT
ejpam-4492	132	67	v3	v3	PROPN
ejpam-4492	132	68	)	)	PUNCT
ejpam-4492	132	69	,	,	PUNCT
ejpam-4492	132	70	(	(	PUNCT
ejpam-4492	132	71	v1	v1	NOUN
ejpam-4492	132	72	,	,	PUNCT
ejpam-4492	132	73	e1	e1	PROPN
ejpam-4492	132	74	)	)	PUNCT
ejpam-4492	132	75	,	,	PUNCT
ejpam-4492	132	76	(	(	PUNCT
ejpam-4492	132	77	e1	e1	NOUN
ejpam-4492	132	78	,	,	PUNCT
ejpam-4492	132	79	v2	v2	PROPN
ejpam-4492	132	80	)	)	PUNCT
ejpam-4492	132	81	,	,	PUNCT
ejpam-4492	132	82	(	(	PUNCT
ejpam-4492	132	83	v2	v2	PROPN
ejpam-4492	132	84	,	,	PUNCT
ejpam-4492	132	85	e2	e2	PROPN
ejpam-4492	132	86	)	)	PUNCT
ejpam-4492	132	87	,	,	PUNCT
ejpam-4492	132	88	(	(	PUNCT
ejpam-4492	132	89	e2	e2	PROPN
ejpam-4492	132	90	,	,	PUNCT
ejpam-4492	132	91	v3	v3	PROPN
ejpam-4492	132	92	)	)	PUNCT
ejpam-4492	132	93	,	,	PUNCT
ejpam-4492	132	94	(	(	PUNCT
ejpam-4492	132	95	e1	e1	PROPN
ejpam-4492	132	96	,	,	PUNCT
ejpam-4492	132	97	e2	e2	PROPN
ejpam-4492	132	98	)	)	PUNCT
ejpam-4492	132	99	.	.	PUNCT
ejpam-4492	133	1	let	let	VERB
ejpam-4492	133	2	p	p	PROPN
ejpam-4492	133	3	(	(	PUNCT
ejpam-4492	133	4	ar	ar	NOUN
ejpam-4492	133	5	)	)	PUNCT
ejpam-4492	133	6	=	=	SYM
ejpam-4492	133	7	{	{	PUNCT
ejpam-4492	133	8	p2	p2	NOUN
ejpam-4492	133	9	}	}	PUNCT
ejpam-4492	133	10	where	where	SCONJ
ejpam-4492	133	11	p2	p2	X
ejpam-4492	133	12	=	=	PUNCT
ejpam-4492	134	1	[	[	X
ejpam-4492	134	2	v1v2	v1v2	NOUN
ejpam-4492	134	3	,	,	PUNCT
ejpam-4492	134	4	v2v3	v2v3	PROPN
ejpam-4492	134	5	]	]	X
ejpam-4492	134	6	.	.	PUNCT
ejpam-4492	135	1	therefore	therefore	ADV
ejpam-4492	135	2	,	,	PUNCT
ejpam-4492	135	3	dpt	dpt	PROPN
ejpam-4492	135	4	(	(	PUNCT
ejpam-4492	135	5	ar	ar	PROPN
ejpam-4492	135	6	)	)	PUNCT
ejpam-4492	135	7	is	be	AUX
ejpam-4492	135	8	an	an	DET
ejpam-4492	135	9	outerplanar	outerplanar	NOUN
ejpam-4492	135	10	.	.	PUNCT
ejpam-4492	136	1	a	a	DET
ejpam-4492	136	2	contradiction	contradiction	NOUN
ejpam-4492	136	3	since	since	SCONJ
ejpam-4492	136	4	dpt	dpt	PROPN
ejpam-4492	136	5	(	(	PUNCT
ejpam-4492	136	6	ar	ar	NOUN
ejpam-4492	136	7	)	)	PUNCT
ejpam-4492	136	8	should	should	AUX
ejpam-4492	136	9	contain	contain	VERB
ejpam-4492	136	10	an	an	DET
ejpam-4492	136	11	internal	internal	ADJ
ejpam-4492	136	12	vertex	vertex	NOUN
ejpam-4492	136	13	.	.	PUNCT
ejpam-4492	137	1	(	(	PUNCT
ejpam-4492	137	2	see	see	VERB
ejpam-4492	137	3	figure	figure	NOUN
ejpam-4492	137	4	5	5	NUM
ejpam-4492	137	5	)	)	PUNCT
ejpam-4492	137	6	.	.	PUNCT
ejpam-4492	138	1	conversely	conversely	ADV
ejpam-4492	138	2	,	,	PUNCT
ejpam-4492	138	3	suppose	suppose	VERB
ejpam-4492	138	4	that	that	SCONJ
ejpam-4492	138	5	ar	ar	PROPN
ejpam-4492	138	6	=	=	PROPN
ejpam-4492	138	7	p⃗n	p⃗n	PROPN
ejpam-4492	138	8	for	for	ADP
ejpam-4492	138	9	n	n	X
ejpam-4492	138	10	≥	≥	NUM
ejpam-4492	138	11	4	4	NUM
ejpam-4492	138	12	.	.	PUNCT
ejpam-4492	139	1	we	we	PRON
ejpam-4492	139	2	will	will	AUX
ejpam-4492	139	3	show	show	VERB
ejpam-4492	139	4	i(dpt	i(dpt	ADP
ejpam-4492	139	5	(	(	PUNCT
ejpam-4492	139	6	p⃗n	p⃗n	NOUN
ejpam-4492	139	7	)	)	PUNCT
ejpam-4492	139	8	)	)	PUNCT
ejpam-4492	140	1	=	=	SYM
ejpam-4492	140	2	n	n	CCONJ
ejpam-4492	140	3	−	−	NOUN
ejpam-4492	140	4	3	3	NUM
ejpam-4492	140	5	by	by	ADP
ejpam-4492	140	6	induction	induction	NOUN
ejpam-4492	140	7	.	.	PUNCT
ejpam-4492	141	1	let	let	VERB
ejpam-4492	141	2	ar	ar	PROPN
ejpam-4492	141	3	=	=	VERB
ejpam-4492	141	4	p⃗4	p⃗4	VERB
ejpam-4492	141	5	and	and	CCONJ
ejpam-4492	141	6	let	let	VERB
ejpam-4492	141	7	v	v	NOUN
ejpam-4492	141	8	(	(	PUNCT
ejpam-4492	141	9	p⃗4	p⃗4	VERB
ejpam-4492	141	10	)	)	PUNCT
ejpam-4492	141	11	=	=	NOUN
ejpam-4492	141	12	{	{	PUNCT
ejpam-4492	141	13	v1	v1	PROPN
ejpam-4492	141	14	,	,	PUNCT
ejpam-4492	141	15	v2	v2	PROPN
ejpam-4492	141	16	,	,	PUNCT
ejpam-4492	141	17	v3	v3	PROPN
ejpam-4492	141	18	,	,	PUNCT
ejpam-4492	141	19	v4	v4	PROPN
ejpam-4492	141	20	}	}	PUNCT
ejpam-4492	141	21	.	.	PUNCT
ejpam-4492	142	1	thus	thus	ADV
ejpam-4492	142	2	,	,	PUNCT
ejpam-4492	142	3	v	v	X
ejpam-4492	142	4	(	(	PUNCT
ejpam-4492	142	5	dpt	dpt	PROPN
ejpam-4492	142	6	(	(	PUNCT
ejpam-4492	142	7	p⃗4	p⃗4	VERB
ejpam-4492	142	8	)	)	PUNCT
ejpam-4492	142	9	)	)	PUNCT
ejpam-4492	142	10	=	=	PRON
ejpam-4492	142	11	{	{	PUNCT
ejpam-4492	142	12	v1	v1	PROPN
ejpam-4492	142	13	,	,	PUNCT
ejpam-4492	142	14	v2	v2	PROPN
ejpam-4492	142	15	,	,	PUNCT
ejpam-4492	142	16	v3	v3	PROPN
ejpam-4492	142	17	,	,	PUNCT
ejpam-4492	142	18	v4	v4	PROPN
ejpam-4492	142	19	,	,	PUNCT
ejpam-4492	142	20	e1	e1	PROPN
ejpam-4492	142	21	,	,	PUNCT
ejpam-4492	142	22	e2	e2	PROPN
ejpam-4492	142	23	,	,	PUNCT
ejpam-4492	142	24	e3	e3	NOUN
ejpam-4492	142	25	,	,	PUNCT
ejpam-4492	142	26	p	p	X
ejpam-4492	142	27	}	}	PUNCT
ejpam-4492	142	28	where	where	SCONJ
ejpam-4492	142	29	e1	e1	NOUN
ejpam-4492	142	30	=	=	SYM
ejpam-4492	142	31	(	(	PUNCT
ejpam-4492	142	32	v1	v1	NOUN
ejpam-4492	142	33	,	,	PUNCT
ejpam-4492	142	34	v2	v2	PROPN
ejpam-4492	142	35	)	)	PUNCT
ejpam-4492	142	36	,	,	PUNCT
ejpam-4492	142	37	e2	e2	PROPN
ejpam-4492	142	38	=	=	SYM
ejpam-4492	142	39	(	(	PUNCT
ejpam-4492	142	40	v2	v2	PROPN
ejpam-4492	142	41	,	,	PUNCT
ejpam-4492	142	42	v3	v3	PROPN
ejpam-4492	142	43	)	)	PUNCT
ejpam-4492	142	44	,	,	PUNCT
ejpam-4492	142	45	and	and	CCONJ
ejpam-4492	142	46	e3	e3	NOUN
ejpam-4492	142	47	=	=	SYM
ejpam-4492	142	48	(	(	PUNCT
ejpam-4492	142	49	v3	v3	PROPN
ejpam-4492	142	50	,	,	PUNCT
ejpam-4492	142	51	v4	v4	PROPN
ejpam-4492	142	52	)	)	PUNCT
ejpam-4492	142	53	as	as	ADP
ejpam-4492	142	54	the	the	DET
ejpam-4492	142	55	arcs	arc	NOUN
ejpam-4492	142	56	of	of	ADP
ejpam-4492	142	57	p⃗4	p⃗4	PROPN
ejpam-4492	142	58	,	,	PUNCT
ejpam-4492	142	59	and	and	CCONJ
ejpam-4492	142	60	p	p	NOUN
ejpam-4492	142	61	is	be	AUX
ejpam-4492	142	62	the	the	DET
ejpam-4492	142	63	pathos	pathos	NOUN
ejpam-4492	142	64	of	of	ADP
ejpam-4492	142	65	p⃗4	p⃗4	PROPN
ejpam-4492	142	66	.	.	PUNCT
ejpam-4492	143	1	hence	hence	ADV
ejpam-4492	143	2	,	,	PUNCT
ejpam-4492	143	3	a(dpt	a(dpt	PROPN
ejpam-4492	143	4	(	(	PUNCT
ejpam-4492	143	5	p⃗4	p⃗4	VERB
ejpam-4492	143	6	)	)	PUNCT
ejpam-4492	143	7	)	)	PUNCT
ejpam-4492	144	1	=	=	PRON
ejpam-4492	144	2	{	{	PUNCT
ejpam-4492	144	3	(	(	PUNCT
ejpam-4492	144	4	v1	v1	NOUN
ejpam-4492	144	5	,	,	PUNCT
ejpam-4492	144	6	v2	v2	PROPN
ejpam-4492	144	7	)	)	PUNCT
ejpam-4492	144	8	,	,	PUNCT
ejpam-4492	144	9	(	(	PUNCT
ejpam-4492	144	10	v2	v2	PROPN
ejpam-4492	144	11	,	,	PUNCT
ejpam-4492	144	12	v3	v3	PROPN
ejpam-4492	144	13	)	)	PUNCT
ejpam-4492	144	14	,	,	PUNCT
ejpam-4492	144	15	(	(	PUNCT
ejpam-4492	144	16	v3	v3	PROPN
ejpam-4492	144	17	,	,	PUNCT
ejpam-4492	144	18	v4	v4	PROPN
ejpam-4492	144	19	)	)	PUNCT
ejpam-4492	144	20	,	,	PUNCT
ejpam-4492	144	21	(	(	PUNCT
ejpam-4492	144	22	v1	v1	NOUN
ejpam-4492	144	23	,	,	PUNCT
ejpam-4492	144	24	e1	e1	PROPN
ejpam-4492	144	25	)	)	PUNCT
ejpam-4492	144	26	,	,	PUNCT
ejpam-4492	144	27	(	(	PUNCT
ejpam-4492	144	28	e1	e1	NOUN
ejpam-4492	144	29	,	,	PUNCT
ejpam-4492	144	30	v2	v2	PROPN
ejpam-4492	144	31	)	)	PUNCT
ejpam-4492	144	32	,	,	PUNCT
ejpam-4492	144	33	(	(	PUNCT
ejpam-4492	144	34	v2	v2	PROPN
ejpam-4492	144	35	,	,	PUNCT
ejpam-4492	144	36	e2	e2	PROPN
ejpam-4492	144	37	)	)	PUNCT
ejpam-4492	144	38	,	,	PUNCT
ejpam-4492	144	39	(	(	PUNCT
ejpam-4492	144	40	e2	e2	PROPN
ejpam-4492	144	41	,	,	PUNCT
ejpam-4492	144	42	v3	v3	PROPN
ejpam-4492	144	43	)	)	PUNCT
ejpam-4492	144	44	,	,	PUNCT
ejpam-4492	144	45	(	(	PUNCT
ejpam-4492	144	46	v3	v3	PROPN
ejpam-4492	144	47	,	,	PUNCT
ejpam-4492	144	48	e3	e3	NOUN
ejpam-4492	144	49	)	)	PUNCT
ejpam-4492	144	50	,	,	PUNCT
ejpam-4492	144	51	(	(	PUNCT
ejpam-4492	144	52	e3	e3	NOUN
ejpam-4492	144	53	,	,	PUNCT
ejpam-4492	144	54	v4	v4	NOUN
ejpam-4492	144	55	)	)	PUNCT
ejpam-4492	144	56	,	,	PUNCT
ejpam-4492	144	57	(	(	PUNCT
ejpam-4492	144	58	e1	e1	PROPN
ejpam-4492	144	59	,	,	PUNCT
ejpam-4492	144	60	e2	e2	PROPN
ejpam-4492	144	61	)	)	PUNCT
ejpam-4492	144	62	,	,	PUNCT
ejpam-4492	144	63	(	(	PUNCT
ejpam-4492	144	64	e2	e2	PROPN
ejpam-4492	144	65	,	,	PUNCT
ejpam-4492	144	66	e3	e3	NOUN
ejpam-4492	144	67	)	)	PUNCT
ejpam-4492	144	68	,	,	PUNCT
ejpam-4492	144	69	(	(	PUNCT
ejpam-4492	144	70	p	p	X
ejpam-4492	144	71	,	,	PUNCT
ejpam-4492	144	72	e1	e1	PROPN
ejpam-4492	144	73	)	)	PUNCT
ejpam-4492	144	74	,	,	PUNCT
ejpam-4492	144	75	(	(	PUNCT
ejpam-4492	144	76	p	p	X
ejpam-4492	144	77	,	,	PUNCT
ejpam-4492	144	78	e2	e2	PROPN
ejpam-4492	144	79	)	)	PUNCT
ejpam-4492	144	80	,	,	PUNCT
ejpam-4492	144	81	(	(	PUNCT
ejpam-4492	144	82	p	p	X
ejpam-4492	144	83	,	,	PUNCT
ejpam-4492	144	84	e3	e3	NOUN
ejpam-4492	144	85	)	)	PUNCT
ejpam-4492	144	86	}	}	PUNCT
ejpam-4492	144	87	.	.	PUNCT
ejpam-4492	145	1	(	(	PUNCT
ejpam-4492	145	2	see	see	VERB
ejpam-4492	145	3	figure	figure	NOUN
ejpam-4492	145	4	8)	8)	NUM
ejpam-4492	145	5	.	.	PUNCT
ejpam-4492	146	1	jill	jill	PROPN
ejpam-4492	146	2	maegan	maegan	PROPN
ejpam-4492	146	3	b.	b.	PROPN
ejpam-4492	146	4	pamplona	pamplona	PROPN
ejpam-4492	146	5	,	,	PUNCT
ejpam-4492	146	6	imelda	imelda	PROPN
ejpam-4492	146	7	s.	s.	PROPN
ejpam-4492	146	8	aniversario	aniversario	PROPN
ejpam-4492	146	9	/	/	SYM
ejpam-4492	146	10	eur	eur	PROPN
ejpam-4492	146	11	.	.	PUNCT
ejpam-4492	147	1	j.	j.	PROPN
ejpam-4492	147	2	pure	pure	PROPN
ejpam-4492	147	3	appl	appl	PROPN
ejpam-4492	147	4	.	.	PROPN
ejpam-4492	147	5	math	math	PROPN
ejpam-4492	147	6	,	,	PUNCT
ejpam-4492	147	7	15	15	NUM
ejpam-4492	147	8	(	(	PUNCT
ejpam-4492	147	9	3	3	NUM
ejpam-4492	147	10	)	)	PUNCT
ejpam-4492	147	11	(	(	PUNCT
ejpam-4492	147	12	2022	2022	NUM
ejpam-4492	147	13	)	)	PUNCT
ejpam-4492	147	14	,	,	PUNCT
ejpam-4492	147	15	1331	1331	NUM
ejpam-4492	147	16	-	-	SYM
ejpam-4492	147	17	1343	1343	NUM
ejpam-4492	147	18	1338	1338	NUM
ejpam-4492	147	19	figure	figure	NOUN
ejpam-4492	147	20	8	8	NUM
ejpam-4492	147	21	:	:	PUNCT
ejpam-4492	147	22	dpt	dpt	PROPN
ejpam-4492	147	23	(	(	PUNCT
ejpam-4492	147	24	p⃗4	p⃗4	PROPN
ejpam-4492	147	25	)	)	PUNCT
ejpam-4492	147	26	of	of	ADP
ejpam-4492	147	27	p⃗4	p⃗4	PROPN
ejpam-4492	147	28	so	so	SCONJ
ejpam-4492	147	29	e2	e2	PROPN
ejpam-4492	147	30	is	be	AUX
ejpam-4492	147	31	the	the	DET
ejpam-4492	147	32	only	only	ADJ
ejpam-4492	147	33	internal	internal	ADJ
ejpam-4492	147	34	vertex	vertex	NOUN
ejpam-4492	147	35	of	of	ADP
ejpam-4492	147	36	dpt	dpt	PROPN
ejpam-4492	147	37	(	(	PUNCT
ejpam-4492	147	38	p⃗4	p⃗4	PROPN
ejpam-4492	147	39	)	)	PUNCT
ejpam-4492	147	40	.	.	PUNCT
ejpam-4492	148	1	that	that	PRON
ejpam-4492	148	2	is	is	ADV
ejpam-4492	148	3	,	,	PUNCT
ejpam-4492	148	4	i(dpt	i(dpt	X
ejpam-4492	148	5	(	(	PUNCT
ejpam-4492	148	6	p⃗4	p⃗4	VERB
ejpam-4492	148	7	)	)	PUNCT
ejpam-4492	148	8	)	)	PUNCT
ejpam-4492	149	1	=	=	SYM
ejpam-4492	149	2	1	1	NUM
ejpam-4492	149	3	=	=	SYM
ejpam-4492	149	4	4−	4−	NOUN
ejpam-4492	149	5	3	3	NUM
ejpam-4492	149	6	=	=	SYM
ejpam-4492	149	7	n−	n−	NOUN
ejpam-4492	149	8	3	3	NUM
ejpam-4492	149	9	.	.	PUNCT
ejpam-4492	149	10	assume	assume	VERB
ejpam-4492	149	11	that	that	SCONJ
ejpam-4492	149	12	for	for	ADP
ejpam-4492	149	13	n	n	X
ejpam-4492	149	14	>	>	X
ejpam-4492	149	15	4	4	NUM
ejpam-4492	149	16	,	,	PUNCT
ejpam-4492	149	17	i(dpt	i(dpt	X
ejpam-4492	149	18	(	(	PUNCT
ejpam-4492	149	19	p⃗n−1	p⃗n−1	ADJ
ejpam-4492	149	20	)	)	PUNCT
ejpam-4492	149	21	)	)	PUNCT
ejpam-4492	150	1	=	=	SYM
ejpam-4492	150	2	n	n	CCONJ
ejpam-4492	150	3	−	−	NUM
ejpam-4492	150	4	1	1	NUM
ejpam-4492	150	5	−	−	PROPN
ejpam-4492	150	6	3	3	NUM
ejpam-4492	150	7	=	=	SYM
ejpam-4492	150	8	n	n	CCONJ
ejpam-4492	150	9	−	−	NOUN
ejpam-4492	150	10	4	4	NUM
ejpam-4492	150	11	.	.	PUNCT
ejpam-4492	151	1	that	that	PRON
ejpam-4492	151	2	is	is	ADV
ejpam-4492	151	3	,	,	PUNCT
ejpam-4492	151	4	v	v	PROPN
ejpam-4492	151	5	(	(	PUNCT
ejpam-4492	151	6	dpt	dpt	PROPN
ejpam-4492	151	7	(	(	PUNCT
ejpam-4492	151	8	p⃗n−1	p⃗n−1	PROPN
ejpam-4492	151	9	)	)	PUNCT
ejpam-4492	151	10	)	)	PUNCT
ejpam-4492	152	1	=	=	PRON
ejpam-4492	152	2	{	{	PUNCT
ejpam-4492	152	3	v1	v1	PROPN
ejpam-4492	152	4	,	,	PUNCT
ejpam-4492	152	5	v2	v2	PROPN
ejpam-4492	152	6	,	,	PUNCT
ejpam-4492	152	7	.	.	PUNCT
ejpam-4492	152	8	.	.	PUNCT
ejpam-4492	153	1	.	.	PUNCT
ejpam-4492	154	1	,	,	PUNCT
ejpam-4492	154	2	vn−1	vn−1	PROPN
ejpam-4492	154	3	,	,	PUNCT
ejpam-4492	154	4	e1	e1	PROPN
ejpam-4492	154	5	,	,	PUNCT
ejpam-4492	154	6	e2	e2	PROPN
ejpam-4492	154	7	,	,	PUNCT
ejpam-4492	154	8	.	.	PUNCT
ejpam-4492	154	9	.	.	PUNCT
ejpam-4492	155	1	.	.	PUNCT
ejpam-4492	156	1	,	,	PUNCT
ejpam-4492	156	2	en−2	en−2	PROPN
ejpam-4492	156	3	,	,	PUNCT
ejpam-4492	156	4	p	p	X
ejpam-4492	156	5	}	}	PUNCT
ejpam-4492	156	6	where	where	SCONJ
ejpam-4492	156	7	e1	e1	NOUN
ejpam-4492	156	8	=	=	SYM
ejpam-4492	156	9	(	(	PUNCT
ejpam-4492	156	10	v1	v1	NOUN
ejpam-4492	156	11	,	,	PUNCT
ejpam-4492	156	12	v2	v2	PROPN
ejpam-4492	156	13	)	)	PUNCT
ejpam-4492	156	14	,	,	PUNCT
ejpam-4492	156	15	e2	e2	PROPN
ejpam-4492	156	16	=	=	SYM
ejpam-4492	156	17	(	(	PUNCT
ejpam-4492	156	18	v2	v2	PROPN
ejpam-4492	156	19	,	,	PUNCT
ejpam-4492	156	20	v3	v3	PROPN
ejpam-4492	156	21	)	)	PUNCT
ejpam-4492	156	22	,	,	PUNCT
ejpam-4492	156	23	.	.	PUNCT
ejpam-4492	156	24	.	.	PUNCT
ejpam-4492	157	1	.	.	PUNCT
ejpam-4492	158	1	,	,	PUNCT
ejpam-4492	158	2	en−2	en−2	PROPN
ejpam-4492	158	3	=	=	SYM
ejpam-4492	158	4	(	(	PUNCT
ejpam-4492	158	5	vn−2	vn−2	PROPN
ejpam-4492	158	6	,	,	PUNCT
ejpam-4492	158	7	vn−1	vn−1	ADJ
ejpam-4492	158	8	)	)	PUNCT
ejpam-4492	158	9	and	and	CCONJ
ejpam-4492	158	10	p	p	NOUN
ejpam-4492	158	11	is	be	AUX
ejpam-4492	158	12	the	the	DET
ejpam-4492	158	13	pathos	pathos	NOUN
ejpam-4492	158	14	of	of	ADP
ejpam-4492	158	15	p⃗n−1	p⃗n−1	PROPN
ejpam-4492	158	16	.	.	PUNCT
ejpam-4492	159	1	also	also	ADV
ejpam-4492	159	2	,	,	PUNCT
ejpam-4492	159	3	a(dpt	a(dpt	PROPN
ejpam-4492	159	4	(	(	PUNCT
ejpam-4492	159	5	p⃗n−1	p⃗n−1	ADJ
ejpam-4492	159	6	)	)	PUNCT
ejpam-4492	159	7	)	)	PUNCT
ejpam-4492	159	8	=	=	PRON
ejpam-4492	159	9	{	{	PUNCT
ejpam-4492	159	10	(	(	PUNCT
ejpam-4492	159	11	v1	v1	NOUN
ejpam-4492	159	12	,	,	PUNCT
ejpam-4492	159	13	v2	v2	PROPN
ejpam-4492	159	14	)	)	PUNCT
ejpam-4492	159	15	,	,	PUNCT
ejpam-4492	159	16	(	(	PUNCT
ejpam-4492	159	17	v2	v2	PROPN
ejpam-4492	159	18	,	,	PUNCT
ejpam-4492	159	19	v3	v3	PROPN
ejpam-4492	159	20	)	)	PUNCT
ejpam-4492	159	21	,	,	PUNCT
ejpam-4492	159	22	.	.	PUNCT
ejpam-4492	159	23	.	.	PUNCT
ejpam-4492	159	24	.	.	PUNCT
ejpam-4492	160	1	,	,	PUNCT
ejpam-4492	160	2	(	(	PUNCT
ejpam-4492	160	3	vn−2	vn−2	PROPN
ejpam-4492	160	4	,	,	PUNCT
ejpam-4492	160	5	vn−1	vn−1	ADJ
ejpam-4492	160	6	)	)	PUNCT
ejpam-4492	160	7	,	,	PUNCT
ejpam-4492	160	8	(	(	PUNCT
ejpam-4492	160	9	v1	v1	NOUN
ejpam-4492	160	10	,	,	PUNCT
ejpam-4492	160	11	e1	e1	PROPN
ejpam-4492	160	12	)	)	PUNCT
ejpam-4492	160	13	,	,	PUNCT
ejpam-4492	160	14	(	(	PUNCT
ejpam-4492	160	15	e1	e1	NOUN
ejpam-4492	160	16	,	,	PUNCT
ejpam-4492	160	17	v2	v2	PROPN
ejpam-4492	160	18	)	)	PUNCT
ejpam-4492	160	19	,	,	PUNCT
ejpam-4492	160	20	(	(	PUNCT
ejpam-4492	160	21	v2	v2	PROPN
ejpam-4492	160	22	,	,	PUNCT
ejpam-4492	160	23	e2	e2	PROPN
ejpam-4492	160	24	)	)	PUNCT
ejpam-4492	160	25	,	,	PUNCT
ejpam-4492	160	26	(	(	PUNCT
ejpam-4492	160	27	e2	e2	PROPN
ejpam-4492	160	28	,	,	PUNCT
ejpam-4492	160	29	v3	v3	PROPN
ejpam-4492	160	30	)	)	PUNCT
ejpam-4492	160	31	,	,	PUNCT
ejpam-4492	160	32	.	.	PUNCT
ejpam-4492	160	33	.	.	PUNCT
ejpam-4492	160	34	.	.	PUNCT
ejpam-4492	161	1	,	,	PUNCT
ejpam-4492	161	2	(	(	PUNCT
ejpam-4492	161	3	vn−2	vn−2	PROPN
ejpam-4492	161	4	,	,	PUNCT
ejpam-4492	161	5	en−2	en−2	PROPN
ejpam-4492	161	6	)	)	PUNCT
ejpam-4492	161	7	,	,	PUNCT
ejpam-4492	161	8	(	(	PUNCT
ejpam-4492	161	9	en−2	en−2	PROPN
ejpam-4492	161	10	,	,	PUNCT
ejpam-4492	161	11	vn−1	vn−1	ADJ
ejpam-4492	161	12	)	)	PUNCT
ejpam-4492	161	13	,	,	PUNCT
ejpam-4492	161	14	(	(	PUNCT
ejpam-4492	161	15	e1	e1	PROPN
ejpam-4492	161	16	,	,	PUNCT
ejpam-4492	161	17	e2	e2	PROPN
ejpam-4492	161	18	)	)	PUNCT
ejpam-4492	161	19	,	,	PUNCT
ejpam-4492	161	20	(	(	PUNCT
ejpam-4492	161	21	e2	e2	PROPN
ejpam-4492	161	22	,	,	PUNCT
ejpam-4492	161	23	e3	e3	NOUN
ejpam-4492	161	24	)	)	PUNCT
ejpam-4492	161	25	,	,	PUNCT
ejpam-4492	161	26	.	.	PUNCT
ejpam-4492	161	27	.	.	PUNCT
ejpam-4492	161	28	.	.	PUNCT
ejpam-4492	162	1	,	,	PUNCT
ejpam-4492	162	2	(	(	PUNCT
ejpam-4492	162	3	e1	e1	PROPN
ejpam-4492	162	4	,	,	PUNCT
ejpam-4492	162	5	e2	e2	PROPN
ejpam-4492	162	6	)	)	PUNCT
ejpam-4492	162	7	,	,	PUNCT
ejpam-4492	162	8	(	(	PUNCT
ejpam-4492	162	9	e2	e2	PROPN
ejpam-4492	162	10	,	,	PUNCT
ejpam-4492	162	11	e3	e3	NOUN
ejpam-4492	162	12	)	)	PUNCT
ejpam-4492	162	13	,	,	PUNCT
ejpam-4492	162	14	.	.	PUNCT
ejpam-4492	162	15	.	.	PUNCT
ejpam-4492	162	16	.	.	PUNCT
ejpam-4492	163	1	,	,	PUNCT
ejpam-4492	163	2	(	(	PUNCT
ejpam-4492	163	3	en−3	en−3	PROPN
ejpam-4492	163	4	,	,	PUNCT
ejpam-4492	163	5	en−2	en−2	PROPN
ejpam-4492	163	6	)	)	PUNCT
ejpam-4492	163	7	,	,	PUNCT
ejpam-4492	163	8	(	(	PUNCT
ejpam-4492	163	9	p	p	X
ejpam-4492	163	10	,	,	PUNCT
ejpam-4492	163	11	e1	e1	PROPN
ejpam-4492	163	12	)	)	PUNCT
ejpam-4492	163	13	,	,	PUNCT
ejpam-4492	163	14	(	(	PUNCT
ejpam-4492	163	15	p	p	X
ejpam-4492	163	16	,	,	PUNCT
ejpam-4492	163	17	e2	e2	PROPN
ejpam-4492	163	18	)	)	PUNCT
ejpam-4492	163	19	,	,	PUNCT
ejpam-4492	163	20	.	.	PUNCT
ejpam-4492	163	21	.	.	PUNCT
ejpam-4492	163	22	.	.	PUNCT
ejpam-4492	164	1	,	,	PUNCT
ejpam-4492	164	2	(	(	PUNCT
ejpam-4492	164	3	p	p	X
ejpam-4492	164	4	,	,	PUNCT
ejpam-4492	164	5	en−2	en−2	PROPN
ejpam-4492	164	6	)	)	PUNCT
ejpam-4492	164	7	}	}	PUNCT
ejpam-4492	164	8	.	.	PUNCT
ejpam-4492	165	1	(	(	PUNCT
ejpam-4492	165	2	see	see	VERB
ejpam-4492	165	3	figure	figure	NOUN
ejpam-4492	165	4	9	9	NUM
ejpam-4492	165	5	)	)	PUNCT
ejpam-4492	165	6	.	.	PUNCT
ejpam-4492	166	1	figure	figure	VERB
ejpam-4492	166	2	9	9	NUM
ejpam-4492	166	3	:	:	PUNCT
ejpam-4492	166	4	dpt	dpt	PROPN
ejpam-4492	166	5	(	(	PUNCT
ejpam-4492	166	6	p⃗n−1	p⃗n−1	PROPN
ejpam-4492	166	7	)	)	PUNCT
ejpam-4492	166	8	of	of	ADP
ejpam-4492	166	9	p⃗n−1	p⃗n−1	INTJ
ejpam-4492	166	10	it	it	PRON
ejpam-4492	166	11	follows	follow	VERB
ejpam-4492	166	12	that	that	SCONJ
ejpam-4492	166	13	e2	e2	PROPN
ejpam-4492	166	14	,	,	PUNCT
ejpam-4492	166	15	e3	e3	NOUN
ejpam-4492	166	16	,	,	PUNCT
ejpam-4492	166	17	.	.	PUNCT
ejpam-4492	166	18	.	.	PUNCT
ejpam-4492	167	1	.	.	PUNCT
ejpam-4492	168	1	,	,	PUNCT
ejpam-4492	168	2	en−3	en−3	PROPN
ejpam-4492	168	3	are	be	AUX
ejpam-4492	168	4	the	the	DET
ejpam-4492	168	5	internal	internal	ADJ
ejpam-4492	168	6	vertices	vertex	NOUN
ejpam-4492	168	7	of	of	ADP
ejpam-4492	168	8	dpt	dpt	PROPN
ejpam-4492	168	9	(	(	PUNCT
ejpam-4492	168	10	p⃗n−1	p⃗n−1	PROPN
ejpam-4492	168	11	)	)	PUNCT
ejpam-4492	168	12	.	.	PUNCT
ejpam-4492	169	1	that	that	PRON
ejpam-4492	169	2	is	be	AUX
ejpam-4492	169	3	,	,	PUNCT
ejpam-4492	169	4	i(dpt	i(dpt	X
ejpam-4492	169	5	(	(	PUNCT
ejpam-4492	169	6	p⃗n−1	p⃗n−1	ADJ
ejpam-4492	169	7	)	)	PUNCT
ejpam-4492	169	8	)	)	PUNCT
ejpam-4492	170	1	=	=	SYM
ejpam-4492	170	2	n	n	CCONJ
ejpam-4492	170	3	−	−	NOUN
ejpam-4492	170	4	3	3	NUM
ejpam-4492	170	5	−	−	PROPN
ejpam-4492	170	6	2	2	NUM
ejpam-4492	170	7	+	+	CCONJ
ejpam-4492	170	8	1	1	NUM
ejpam-4492	170	9	=	=	SYM
ejpam-4492	170	10	n	n	PRON
ejpam-4492	170	11	−	−	NOUN
ejpam-4492	170	12	4	4	NUM
ejpam-4492	170	13	.	.	PUNCT
ejpam-4492	171	1	now	now	ADV
ejpam-4492	171	2	,	,	PUNCT
ejpam-4492	171	3	adding	add	VERB
ejpam-4492	171	4	one	one	NUM
ejpam-4492	171	5	vertex	vertex	NOUN
ejpam-4492	171	6	to	to	ADP
ejpam-4492	171	7	the	the	DET
ejpam-4492	171	8	right	right	ADJ
ejpam-4492	171	9	side	side	NOUN
ejpam-4492	171	10	of	of	ADP
ejpam-4492	171	11	vn−1	vn−1	ADJ
ejpam-4492	171	12	of	of	ADP
ejpam-4492	171	13	p⃗n−1	p⃗n−1	ADP
ejpam-4492	171	14	to	to	PART
ejpam-4492	171	15	obtain	obtain	VERB
ejpam-4492	171	16	p⃗n	p⃗n	NOUN
ejpam-4492	171	17	,	,	PUNCT
ejpam-4492	171	18	we	we	PRON
ejpam-4492	171	19	will	will	AUX
ejpam-4492	171	20	have	have	VERB
ejpam-4492	171	21	v	v	NUM
ejpam-4492	171	22	(	(	PUNCT
ejpam-4492	171	23	p⃗n	p⃗n	NOUN
ejpam-4492	171	24	)	)	PUNCT
ejpam-4492	171	25	=	=	SYM
ejpam-4492	171	26	{	{	PUNCT
ejpam-4492	171	27	v1	v1	PROPN
ejpam-4492	171	28	,	,	PUNCT
ejpam-4492	171	29	v2	v2	PROPN
ejpam-4492	171	30	,	,	PUNCT
ejpam-4492	171	31	.	.	PUNCT
ejpam-4492	171	32	.	.	PUNCT
ejpam-4492	172	1	.	.	PUNCT
ejpam-4492	173	1	,	,	PUNCT
ejpam-4492	173	2	vn	vn	NOUN
ejpam-4492	173	3	}	}	PUNCT
ejpam-4492	173	4	and	and	CCONJ
ejpam-4492	173	5	a(p⃗n	a(p⃗n	NOUN
ejpam-4492	173	6	)	)	PUNCT
ejpam-4492	173	7	=	=	SYM
ejpam-4492	173	8	{	{	PUNCT
ejpam-4492	173	9	e1	e1	PROPN
ejpam-4492	173	10	,	,	PUNCT
ejpam-4492	173	11	e2	e2	PROPN
ejpam-4492	173	12	,	,	PUNCT
ejpam-4492	173	13	.	.	PUNCT
ejpam-4492	173	14	.	.	PUNCT
ejpam-4492	174	1	.	.	PUNCT
ejpam-4492	175	1	,	,	PUNCT
ejpam-4492	175	2	en−1	en−1	PROPN
ejpam-4492	175	3	}	}	PUNCT
ejpam-4492	175	4	where	where	SCONJ
ejpam-4492	175	5	e1	e1	NOUN
ejpam-4492	175	6	=	=	SYM
ejpam-4492	175	7	(	(	PUNCT
ejpam-4492	175	8	v1	v1	NOUN
ejpam-4492	175	9	,	,	PUNCT
ejpam-4492	175	10	v2	v2	PROPN
ejpam-4492	175	11	)	)	PUNCT
ejpam-4492	175	12	,	,	PUNCT
ejpam-4492	175	13	e2	e2	PROPN
ejpam-4492	175	14	=	=	SYM
ejpam-4492	175	15	(	(	PUNCT
ejpam-4492	175	16	v2	v2	PROPN
ejpam-4492	175	17	,	,	PUNCT
ejpam-4492	175	18	v3	v3	PROPN
ejpam-4492	175	19	)	)	PUNCT
ejpam-4492	175	20	,	,	PUNCT
ejpam-4492	175	21	.	.	PUNCT
ejpam-4492	175	22	.	.	PUNCT
ejpam-4492	176	1	.	.	PUNCT
ejpam-4492	177	1	,	,	PUNCT
ejpam-4492	177	2	en−2	en−2	PROPN
ejpam-4492	177	3	=	=	SYM
ejpam-4492	177	4	(	(	PUNCT
ejpam-4492	177	5	vn−2	vn−2	PROPN
ejpam-4492	177	6	,	,	PUNCT
ejpam-4492	177	7	vn−1	vn−1	ADJ
ejpam-4492	177	8	)	)	PUNCT
ejpam-4492	177	9	,	,	PUNCT
ejpam-4492	177	10	en−1	en−1	PROPN
ejpam-4492	177	11	=	=	SYM
ejpam-4492	177	12	(	(	PUNCT
ejpam-4492	177	13	vn−1	vn−1	PROPN
ejpam-4492	177	14	,	,	PUNCT
ejpam-4492	177	15	vn	vn	NOUN
ejpam-4492	177	16	)	)	PUNCT
ejpam-4492	177	17	.	.	PUNCT
ejpam-4492	178	1	thus	thus	ADV
ejpam-4492	178	2	,	,	PUNCT
ejpam-4492	178	3	an	an	DET
ejpam-4492	178	4	addition	addition	NOUN
ejpam-4492	178	5	of	of	ADP
ejpam-4492	178	6	the	the	DET
ejpam-4492	178	7	vertices	vertex	NOUN
ejpam-4492	178	8	vn	vn	NOUN
ejpam-4492	178	9	and	and	CCONJ
ejpam-4492	178	10	en−1	en−1	PROPN
ejpam-4492	178	11	to	to	ADP
ejpam-4492	178	12	the	the	DET
ejpam-4492	178	13	v	v	NOUN
ejpam-4492	178	14	(	(	PUNCT
ejpam-4492	178	15	p⃗n	p⃗n	NOUN
ejpam-4492	178	16	)	)	PUNCT
ejpam-4492	178	17	results	result	NOUN
ejpam-4492	178	18	in	in	ADP
ejpam-4492	178	19	additional	additional	ADJ
ejpam-4492	178	20	arcs	arc	NOUN
ejpam-4492	178	21	(	(	PUNCT
ejpam-4492	178	22	vn−1	vn−1	PROPN
ejpam-4492	178	23	,	,	PUNCT
ejpam-4492	178	24	vn	vn	NOUN
ejpam-4492	178	25	)	)	PUNCT
ejpam-4492	178	26	,	,	PUNCT
ejpam-4492	178	27	(	(	PUNCT
ejpam-4492	178	28	vn−1	vn−1	PROPN
ejpam-4492	178	29	,	,	PUNCT
ejpam-4492	178	30	en−1	en−1	PROPN
ejpam-4492	178	31	)	)	PUNCT
ejpam-4492	178	32	,	,	PUNCT
ejpam-4492	178	33	(	(	PUNCT
ejpam-4492	178	34	en−1	en−1	PROPN
ejpam-4492	178	35	,	,	PUNCT
ejpam-4492	178	36	vn	vn	NOUN
ejpam-4492	178	37	)	)	PUNCT
ejpam-4492	178	38	,	,	PUNCT
ejpam-4492	178	39	(	(	PUNCT
ejpam-4492	178	40	en−2	en−2	PROPN
ejpam-4492	178	41	,	,	PUNCT
ejpam-4492	178	42	en−1	en−1	PROPN
ejpam-4492	178	43	)	)	PUNCT
ejpam-4492	178	44	,	,	PUNCT
ejpam-4492	178	45	and	and	CCONJ
ejpam-4492	178	46	(	(	PUNCT
ejpam-4492	178	47	p	p	X
ejpam-4492	178	48	,	,	PUNCT
ejpam-4492	178	49	en−1	en−1	PROPN
ejpam-4492	178	50	)	)	PUNCT
ejpam-4492	178	51	.	.	PUNCT
ejpam-4492	179	1	(	(	PUNCT
ejpam-4492	179	2	see	see	VERB
ejpam-4492	179	3	figure	figure	NOUN
ejpam-4492	179	4	10	10	NUM
ejpam-4492	179	5	)	)	PUNCT
ejpam-4492	179	6	.	.	PUNCT
ejpam-4492	180	1	jill	jill	PROPN
ejpam-4492	180	2	maegan	maegan	PROPN
ejpam-4492	180	3	b.	b.	PROPN
ejpam-4492	180	4	pamplona	pamplona	PROPN
ejpam-4492	180	5	,	,	PUNCT
ejpam-4492	180	6	imelda	imelda	PROPN
ejpam-4492	180	7	s.	s.	PROPN
ejpam-4492	180	8	aniversario	aniversario	PROPN
ejpam-4492	180	9	/	/	SYM
ejpam-4492	180	10	eur	eur	PROPN
ejpam-4492	180	11	.	.	PUNCT
ejpam-4492	181	1	j.	j.	PROPN
ejpam-4492	181	2	pure	pure	PROPN
ejpam-4492	181	3	appl	appl	PROPN
ejpam-4492	181	4	.	.	PROPN
ejpam-4492	181	5	math	math	PROPN
ejpam-4492	181	6	,	,	PUNCT
ejpam-4492	181	7	15	15	NUM
ejpam-4492	181	8	(	(	PUNCT
ejpam-4492	181	9	3	3	NUM
ejpam-4492	181	10	)	)	PUNCT
ejpam-4492	181	11	(	(	PUNCT
ejpam-4492	181	12	2022	2022	NUM
ejpam-4492	181	13	)	)	PUNCT
ejpam-4492	181	14	,	,	PUNCT
ejpam-4492	181	15	1331	1331	NUM
ejpam-4492	181	16	-	-	SYM
ejpam-4492	181	17	1343	1343	NUM
ejpam-4492	181	18	1339	1339	NUM
ejpam-4492	181	19	figure	figure	NOUN
ejpam-4492	181	20	10	10	NUM
ejpam-4492	181	21	:	:	PUNCT
ejpam-4492	181	22	dpt	dpt	PROPN
ejpam-4492	181	23	(	(	PUNCT
ejpam-4492	181	24	p⃗n	p⃗n	PROPN
ejpam-4492	181	25	)	)	PUNCT
ejpam-4492	181	26	of	of	ADP
ejpam-4492	181	27	p⃗n	p⃗n	NOUN
ejpam-4492	181	28	therefore	therefore	ADV
ejpam-4492	181	29	,	,	PUNCT
ejpam-4492	181	30	the	the	DET
ejpam-4492	181	31	vertices	vertex	NOUN
ejpam-4492	181	32	e2	e2	PROPN
ejpam-4492	181	33	,	,	PUNCT
ejpam-4492	181	34	e3	e3	NOUN
ejpam-4492	181	35	,	,	PUNCT
ejpam-4492	181	36	.	.	PUNCT
ejpam-4492	181	37	.	.	PUNCT
ejpam-4492	182	1	.	.	PUNCT
ejpam-4492	183	1	,	,	PUNCT
ejpam-4492	183	2	en−2	en−2	PROPN
ejpam-4492	183	3	are	be	AUX
ejpam-4492	183	4	the	the	DET
ejpam-4492	183	5	internal	internal	ADJ
ejpam-4492	183	6	vertices	vertex	NOUN
ejpam-4492	183	7	of	of	ADP
ejpam-4492	183	8	dpt	dpt	PROPN
ejpam-4492	183	9	(	(	PUNCT
ejpam-4492	183	10	p⃗n	p⃗n	PROPN
ejpam-4492	183	11	)	)	PUNCT
ejpam-4492	183	12	.	.	PUNCT
ejpam-4492	184	1	that	that	PRON
ejpam-4492	184	2	is	be	AUX
ejpam-4492	184	3	,	,	PUNCT
ejpam-4492	184	4	i(dpt	i(dpt	X
ejpam-4492	184	5	(	(	PUNCT
ejpam-4492	184	6	p⃗n	p⃗n	NOUN
ejpam-4492	184	7	)	)	PUNCT
ejpam-4492	184	8	)	)	PUNCT
ejpam-4492	185	1	=	=	PUNCT
ejpam-4492	185	2	n−	n−	NOUN
ejpam-4492	185	3	2−	2−	NUM
ejpam-4492	185	4	2	2	NUM
ejpam-4492	185	5	+	+	CCONJ
ejpam-4492	185	6	1	1	NUM
ejpam-4492	185	7	=	=	SYM
ejpam-4492	185	8	n−	n−	NOUN
ejpam-4492	185	9	3	3	NUM
ejpam-4492	185	10	.	.	PUNCT
ejpam-4492	186	1	in	in	ADP
ejpam-4492	186	2	view	view	NOUN
ejpam-4492	186	3	of	of	ADP
ejpam-4492	186	4	theorem	theorem	ADJ
ejpam-4492	186	5	3.3	3.3	NUM
ejpam-4492	186	6	,	,	PUNCT
ejpam-4492	186	7	a	a	DET
ejpam-4492	186	8	directed	direct	VERB
ejpam-4492	186	9	pathos	pathos	NOUN
ejpam-4492	186	10	total	total	NOUN
ejpam-4492	186	11	digraph	digraph	PROPN
ejpam-4492	186	12	dpt	dpt	PROPN
ejpam-4492	186	13	(	(	PUNCT
ejpam-4492	186	14	p⃗n	p⃗n	PROPN
ejpam-4492	186	15	)	)	PUNCT
ejpam-4492	186	16	is	be	AUX
ejpam-4492	186	17	outerplanar	outerplanar	NOUN
ejpam-4492	186	18	for	for	ADP
ejpam-4492	186	19	n	n	NOUN
ejpam-4492	186	20	=	=	SYM
ejpam-4492	186	21	3	3	NUM
ejpam-4492	186	22	and	and	CCONJ
ejpam-4492	186	23	minimally	minimally	ADV
ejpam-4492	186	24	non	non	ADJ
ejpam-4492	186	25	outerplanar	outerplanar	NOUN
ejpam-4492	186	26	for	for	ADP
ejpam-4492	186	27	n	n	NOUN
ejpam-4492	186	28	=	=	SYM
ejpam-4492	186	29	4	4	NUM
ejpam-4492	186	30	.	.	PUNCT
ejpam-4492	186	31	theorem	theorem	VERB
ejpam-4492	186	32	3.4	3.4	NUM
ejpam-4492	186	33	.	.	PUNCT
ejpam-4492	187	1	for	for	ADP
ejpam-4492	187	2	an	an	DET
ejpam-4492	187	3	arborescence	arborescence	PROPN
ejpam-4492	187	4	p⃗n	p⃗n	PROPN
ejpam-4492	187	5	,	,	PUNCT
ejpam-4492	187	6	dpt	dpt	PROPN
ejpam-4492	187	7	(	(	PUNCT
ejpam-4492	187	8	p⃗n	p⃗n	PROPN
ejpam-4492	187	9	)	)	PUNCT
ejpam-4492	187	10	is	be	AUX
ejpam-4492	187	11	strictly	strictly	ADV
ejpam-4492	187	12	weak	weak	ADJ
ejpam-4492	187	13	.	.	PUNCT
ejpam-4492	188	1	proof	proof	NOUN
ejpam-4492	188	2	:	:	PUNCT
ejpam-4492	188	3	suppose	suppose	VERB
ejpam-4492	188	4	that	that	SCONJ
ejpam-4492	188	5	ar	ar	PROPN
ejpam-4492	188	6	=	=	PROPN
ejpam-4492	188	7	p⃗n	p⃗n	PROPN
ejpam-4492	188	8	.	.	PUNCT
ejpam-4492	189	1	let	let	VERB
ejpam-4492	189	2	v	v	NOUN
ejpam-4492	189	3	(	(	PUNCT
ejpam-4492	189	4	p⃗n	p⃗n	NOUN
ejpam-4492	189	5	)	)	PUNCT
ejpam-4492	189	6	=	=	SYM
ejpam-4492	189	7	{	{	PUNCT
ejpam-4492	189	8	v1	v1	PROPN
ejpam-4492	189	9	,	,	PUNCT
ejpam-4492	189	10	v2	v2	PROPN
ejpam-4492	189	11	,	,	PUNCT
ejpam-4492	189	12	v3	v3	PROPN
ejpam-4492	189	13	,	,	PUNCT
ejpam-4492	189	14	.	.	PUNCT
ejpam-4492	189	15	.	.	PUNCT
ejpam-4492	190	1	.	.	PUNCT
ejpam-4492	191	1	,	,	PUNCT
ejpam-4492	191	2	vn	vn	AUX
ejpam-4492	191	3	}	}	PUNCT
ejpam-4492	191	4	be	be	AUX
ejpam-4492	191	5	the	the	DET
ejpam-4492	191	6	vertex	vertex	NOUN
ejpam-4492	191	7	set	set	NOUN
ejpam-4492	191	8	and	and	CCONJ
ejpam-4492	191	9	let	let	VERB
ejpam-4492	191	10	a(p⃗n	a(p⃗n	PRON
ejpam-4492	191	11	)	)	PUNCT
ejpam-4492	191	12	=	=	SYM
ejpam-4492	191	13	{	{	PUNCT
ejpam-4492	191	14	e1	e1	PROPN
ejpam-4492	191	15	,	,	PUNCT
ejpam-4492	191	16	e2	e2	PROPN
ejpam-4492	191	17	,	,	PUNCT
ejpam-4492	191	18	e3	e3	NOUN
ejpam-4492	191	19	,	,	PUNCT
ejpam-4492	191	20	.	.	PUNCT
ejpam-4492	191	21	.	.	PUNCT
ejpam-4492	192	1	.	.	PUNCT
ejpam-4492	193	1	,	,	PUNCT
ejpam-4492	193	2	en−1	en−1	PROPN
ejpam-4492	193	3	}	}	PUNCT
ejpam-4492	193	4	be	be	VERB
ejpam-4492	193	5	the	the	DET
ejpam-4492	193	6	arc	arc	NOUN
ejpam-4492	193	7	set	set	NOUN
ejpam-4492	193	8	of	of	ADP
ejpam-4492	193	9	p⃗n	p⃗n	NOUN
ejpam-4492	193	10	such	such	ADJ
ejpam-4492	193	11	that	that	DET
ejpam-4492	193	12	v1	v1	NOUN
ejpam-4492	193	13	and	and	CCONJ
ejpam-4492	193	14	e1	e1	NOUN
ejpam-4492	193	15	=	=	SYM
ejpam-4492	193	16	(	(	PUNCT
ejpam-4492	193	17	v1	v1	NOUN
ejpam-4492	193	18	,	,	PUNCT
ejpam-4492	193	19	v2	v2	PROPN
ejpam-4492	193	20	)	)	PUNCT
ejpam-4492	193	21	are	be	AUX
ejpam-4492	193	22	the	the	DET
ejpam-4492	193	23	root	root	NOUN
ejpam-4492	193	24	and	and	CCONJ
ejpam-4492	193	25	root	root	NOUN
ejpam-4492	193	26	arc	arc	NOUN
ejpam-4492	193	27	of	of	ADP
ejpam-4492	193	28	p⃗n	p⃗n	PROPN
ejpam-4492	193	29	,	,	PUNCT
ejpam-4492	193	30	respectively	respectively	ADV
ejpam-4492	193	31	,	,	PUNCT
ejpam-4492	193	32	and	and	CCONJ
ejpam-4492	193	33	ei	ei	X
ejpam-4492	193	34	=	=	SYM
ejpam-4492	193	35	(	(	PUNCT
ejpam-4492	193	36	vi	vi	PROPN
ejpam-4492	193	37	,	,	PUNCT
ejpam-4492	193	38	vi+1	vi+1	NOUN
ejpam-4492	193	39	)	)	PUNCT
ejpam-4492	193	40	for	for	ADP
ejpam-4492	193	41	2	2	NUM
ejpam-4492	193	42	≤	≤	NOUN
ejpam-4492	194	1	i	i	PRON
ejpam-4492	194	2	≤	≤	NOUN
ejpam-4492	194	3	n	n	CCONJ
ejpam-4492	194	4	−	−	PROPN
ejpam-4492	194	5	1	1	NUM
ejpam-4492	194	6	.	.	PUNCT
ejpam-4492	194	7	then	then	ADV
ejpam-4492	194	8	v1	v1	VERB
ejpam-4492	194	9	,	,	PUNCT
ejpam-4492	194	10	v2	v2	PROPN
ejpam-4492	194	11	,	,	PUNCT
ejpam-4492	194	12	.	.	PUNCT
ejpam-4492	194	13	.	.	PUNCT
ejpam-4492	194	14	.	.	PUNCT
ejpam-4492	195	1	,	,	PUNCT
ejpam-4492	195	2	vn	vn	PROPN
ejpam-4492	195	3	,	,	PUNCT
ejpam-4492	195	4	e1	e1	PROPN
ejpam-4492	195	5	,	,	PUNCT
ejpam-4492	195	6	e2	e2	PROPN
ejpam-4492	195	7	,	,	PUNCT
ejpam-4492	195	8	.	.	PUNCT
ejpam-4492	195	9	.	.	PUNCT
ejpam-4492	196	1	.	.	PUNCT
ejpam-4492	197	1	,	,	PUNCT
ejpam-4492	197	2	en−1	en−1	PROPN
ejpam-4492	197	3	,	,	PUNCT
ejpam-4492	197	4	p	p	NOUN
ejpam-4492	197	5	are	be	AUX
ejpam-4492	197	6	the	the	DET
ejpam-4492	197	7	vertices	vertex	NOUN
ejpam-4492	197	8	of	of	ADP
ejpam-4492	197	9	t	t	PROPN
ejpam-4492	197	10	(	(	PUNCT
ejpam-4492	197	11	ar	ar	PROPN
ejpam-4492	197	12	)	)	PUNCT
ejpam-4492	197	13	where	where	SCONJ
ejpam-4492	197	14	p	p	PROPN
ejpam-4492	197	15	(	(	PUNCT
ejpam-4492	197	16	ar	ar	NOUN
ejpam-4492	197	17	)	)	PUNCT
ejpam-4492	197	18	=	=	SYM
ejpam-4492	198	1	p	p	NOUN
ejpam-4492	198	2	is	be	AUX
ejpam-4492	198	3	the	the	DET
ejpam-4492	198	4	directed	direct	VERB
ejpam-4492	198	5	pathos	pathos	NOUN
ejpam-4492	198	6	of	of	ADP
ejpam-4492	198	7	ar	ar	PROPN
ejpam-4492	198	8	such	such	ADJ
ejpam-4492	198	9	that	that	SCONJ
ejpam-4492	198	10	p	p	PROPN
ejpam-4492	198	11	lies	lie	VERB
ejpam-4492	198	12	on	on	ADP
ejpam-4492	198	13	the	the	DET
ejpam-4492	198	14	arcs	arcs	NOUN
ejpam-4492	199	1	x1	x1	PROPN
ejpam-4492	199	2	=	=	SYM
ejpam-4492	199	3	(	(	PUNCT
ejpam-4492	199	4	v1	v1	PROPN
ejpam-4492	199	5	,	,	PUNCT
ejpam-4492	199	6	v2	v2	PROPN
ejpam-4492	199	7	)	)	PUNCT
ejpam-4492	199	8	,	,	PUNCT
ejpam-4492	199	9	x2	x2	NOUN
ejpam-4492	199	10	=	=	PRON
ejpam-4492	199	11	(	(	PUNCT
ejpam-4492	199	12	v2	v2	PROPN
ejpam-4492	199	13	,	,	PUNCT
ejpam-4492	199	14	v3	v3	PROPN
ejpam-4492	199	15	)	)	PUNCT
ejpam-4492	199	16	,	,	PUNCT
ejpam-4492	199	17	.	.	PUNCT
ejpam-4492	199	18	.	.	PUNCT
ejpam-4492	199	19	.	.	PUNCT
ejpam-4492	200	1	,	,	PUNCT
ejpam-4492	200	2	xn−1	xn−1	PROPN
ejpam-4492	200	3	=	=	PRON
ejpam-4492	200	4	(	(	PUNCT
ejpam-4492	200	5	vn−1	vn−1	PROPN
ejpam-4492	200	6	,	,	PUNCT
ejpam-4492	200	7	vn	vn	NOUN
ejpam-4492	200	8	)	)	PUNCT
ejpam-4492	200	9	.	.	PUNCT
ejpam-4492	201	1	also	also	ADV
ejpam-4492	201	2	,	,	PUNCT
ejpam-4492	201	3	(	(	PUNCT
ejpam-4492	201	4	vi	vi	NOUN
ejpam-4492	201	5	,	,	PUNCT
ejpam-4492	201	6	vi+1	vi+1	NOUN
ejpam-4492	201	7	)	)	PUNCT
ejpam-4492	201	8	,	,	PUNCT
ejpam-4492	201	9	(	(	PUNCT
ejpam-4492	201	10	vi	vi	NOUN
ejpam-4492	201	11	,	,	PUNCT
ejpam-4492	201	12	ei	ei	NOUN
ejpam-4492	201	13	)	)	PUNCT
ejpam-4492	201	14	,	,	PUNCT
ejpam-4492	201	15	(	(	PUNCT
ejpam-4492	201	16	ei	ei	NOUN
ejpam-4492	201	17	,	,	PUNCT
ejpam-4492	201	18	vi+1	vi+1	NOUN
ejpam-4492	201	19	)	)	PUNCT
ejpam-4492	201	20	,	,	PUNCT
ejpam-4492	201	21	(	(	PUNCT
ejpam-4492	201	22	ei	ei	X
ejpam-4492	201	23	,	,	PUNCT
ejpam-4492	201	24	ei+1	ei+1	PROPN
ejpam-4492	201	25	)	)	PUNCT
ejpam-4492	201	26	,	,	PUNCT
ejpam-4492	201	27	for	for	ADP
ejpam-4492	201	28	1	1	NUM
ejpam-4492	201	29	≤	≤	NUM
ejpam-4492	201	30	i	i	PRON
ejpam-4492	201	31	≤	≤	NOUN
ejpam-4492	201	32	n	n	CCONJ
ejpam-4492	201	33	−	−	PROPN
ejpam-4492	201	34	1	1	NUM
ejpam-4492	201	35	are	be	AUX
ejpam-4492	201	36	the	the	DET
ejpam-4492	201	37	arcs	arc	NOUN
ejpam-4492	201	38	of	of	ADP
ejpam-4492	201	39	t	t	PROPN
ejpam-4492	201	40	(	(	PUNCT
ejpam-4492	201	41	ar	ar	NOUN
ejpam-4492	201	42	)	)	PUNCT
ejpam-4492	201	43	and	and	CCONJ
ejpam-4492	201	44	since	since	SCONJ
ejpam-4492	201	45	p	p	PRON
ejpam-4492	201	46	lies	lie	VERB
ejpam-4492	201	47	on	on	ADP
ejpam-4492	201	48	the	the	DET
ejpam-4492	201	49	arcs	arcs	X
ejpam-4492	201	50	x1	x1	PROPN
ejpam-4492	201	51	,	,	PUNCT
ejpam-4492	201	52	x2	x2	PROPN
ejpam-4492	201	53	,	,	PUNCT
ejpam-4492	201	54	.	.	PUNCT
ejpam-4492	201	55	.	.	PUNCT
ejpam-4492	202	1	.	.	PUNCT
ejpam-4492	203	1	,	,	PUNCT
ejpam-4492	203	2	xn−1	xn−1	PROPN
ejpam-4492	203	3	,	,	PUNCT
ejpam-4492	203	4	the	the	DET
ejpam-4492	203	5	directed	direct	VERB
ejpam-4492	203	6	pathos	pathos	NOUN
ejpam-4492	203	7	vertex	vertex	NOUN
ejpam-4492	203	8	p	p	NOUN
ejpam-4492	203	9	is	be	AUX
ejpam-4492	203	10	a	a	DET
ejpam-4492	203	11	neighbor	neighbor	NOUN
ejpam-4492	203	12	of	of	ADP
ejpam-4492	203	13	the	the	DET
ejpam-4492	203	14	vertices	vertex	NOUN
ejpam-4492	203	15	x1	x1	PROPN
ejpam-4492	203	16	,	,	PUNCT
ejpam-4492	203	17	x2	x2	PROPN
ejpam-4492	203	18	,	,	PUNCT
ejpam-4492	203	19	.	.	PUNCT
ejpam-4492	203	20	.	.	PUNCT
ejpam-4492	204	1	.	.	PUNCT
ejpam-4492	205	1	,	,	PUNCT
ejpam-4492	205	2	xn−1	xn−1	PROPN
ejpam-4492	205	3	.	.	PUNCT
ejpam-4492	205	4	note	note	VERB
ejpam-4492	205	5	that	that	SCONJ
ejpam-4492	205	6	from	from	ADP
ejpam-4492	205	7	v1	v1	NOUN
ejpam-4492	205	8	,	,	PUNCT
ejpam-4492	205	9	there	there	PRON
ejpam-4492	205	10	is	be	VERB
ejpam-4492	205	11	a	a	DET
ejpam-4492	205	12	semi	semi	ADJ
ejpam-4492	205	13	-	-	ADJ
ejpam-4492	205	14	directed	directed	ADJ
ejpam-4492	205	15	path	path	NOUN
ejpam-4492	205	16	to	to	PART
ejpam-4492	205	17	vertices	vertice	VERB
ejpam-4492	205	18	v2	v2	PROPN
ejpam-4492	205	19	,	,	PUNCT
ejpam-4492	205	20	v3	v3	PROPN
ejpam-4492	205	21	,	,	PUNCT
ejpam-4492	205	22	.	.	PUNCT
ejpam-4492	205	23	.	.	PUNCT
ejpam-4492	206	1	.	.	PUNCT
ejpam-4492	207	1	,	,	PUNCT
ejpam-4492	207	2	vn	vn	INTJ
ejpam-4492	207	3	and	and	CCONJ
ejpam-4492	207	4	from	from	ADP
ejpam-4492	207	5	v1	v1	NOUN
ejpam-4492	207	6	,	,	PUNCT
ejpam-4492	207	7	also	also	ADV
ejpam-4492	207	8	there	there	PRON
ejpam-4492	207	9	is	be	VERB
ejpam-4492	207	10	a	a	DET
ejpam-4492	207	11	semi	semi	ADJ
ejpam-4492	207	12	-	-	ADJ
ejpam-4492	207	13	directed	directed	ADJ
ejpam-4492	207	14	path	path	NOUN
ejpam-4492	207	15	to	to	PART
ejpam-4492	207	16	vertices	vertice	VERB
ejpam-4492	207	17	e1	e1	PROPN
ejpam-4492	207	18	,	,	PUNCT
ejpam-4492	207	19	e2	e2	NOUN
ejpam-4492	207	20	,	,	PUNCT
ejpam-4492	207	21	.	.	PUNCT
ejpam-4492	207	22	.	.	PUNCT
ejpam-4492	208	1	.	.	PUNCT
ejpam-4492	209	1	,	,	PUNCT
ejpam-4492	209	2	en−1	en−1	PROPN
ejpam-4492	209	3	.	.	PUNCT
ejpam-4492	209	4	however	however	ADV
ejpam-4492	209	5	,	,	PUNCT
ejpam-4492	209	6	there	there	PRON
ejpam-4492	209	7	is	be	VERB
ejpam-4492	209	8	no	no	DET
ejpam-4492	209	9	semi	semi	ADJ
ejpam-4492	209	10	-	-	ADJ
ejpam-4492	209	11	directed	directed	ADJ
ejpam-4492	209	12	path	path	NOUN
ejpam-4492	209	13	from	from	ADP
ejpam-4492	209	14	v1	v1	NOUN
ejpam-4492	209	15	to	to	ADP
ejpam-4492	209	16	p	p	NOUN
ejpam-4492	209	17	.	.	PUNCT
ejpam-4492	210	1	from	from	ADP
ejpam-4492	210	2	theorem	theorem	ADJ
ejpam-4492	210	3	2.9	2.9	NUM
ejpam-4492	210	4	,	,	PUNCT
ejpam-4492	210	5	a	a	DET
ejpam-4492	210	6	directed	direct	VERB
ejpam-4492	210	7	pathos	pathos	NOUN
ejpam-4492	210	8	total	total	NOUN
ejpam-4492	210	9	digraph	digraph	NOUN
ejpam-4492	210	10	of	of	ADP
ejpam-4492	210	11	an	an	DET
ejpam-4492	210	12	arborescence	arborescence	NOUN
ejpam-4492	210	13	is	be	AUX
ejpam-4492	210	14	either	either	CCONJ
ejpam-4492	210	15	strictly	strictly	ADV
ejpam-4492	210	16	unilateral	unilateral	ADJ
ejpam-4492	210	17	or	or	CCONJ
ejpam-4492	210	18	strictly	strictly	ADV
ejpam-4492	210	19	weak	weak	ADJ
ejpam-4492	210	20	.	.	PUNCT
ejpam-4492	211	1	thus	thus	ADV
ejpam-4492	211	2	,	,	PUNCT
ejpam-4492	211	3	for	for	ADP
ejpam-4492	211	4	any	any	DET
ejpam-4492	211	5	arborescence	arborescence	NOUN
ejpam-4492	211	6	directed	direct	VERB
ejpam-4492	211	7	planar	planar	ADJ
ejpam-4492	211	8	graph	graph	NOUN
ejpam-4492	211	9	,	,	PUNCT
ejpam-4492	211	10	its	its	PRON
ejpam-4492	211	11	dpt	dpt	PROPN
ejpam-4492	211	12	(	(	PUNCT
ejpam-4492	211	13	ar	ar	NOUN
ejpam-4492	211	14	)	)	PUNCT
ejpam-4492	211	15	is	be	AUX
ejpam-4492	211	16	strictly	strictly	ADV
ejpam-4492	211	17	weak	weak	ADJ
ejpam-4492	211	18	.	.	PUNCT
ejpam-4492	212	1	corollary	corollary	ADJ
ejpam-4492	212	2	3.5	3.5	NUM
ejpam-4492	212	3	.	.	PUNCT
ejpam-4492	213	1	for	for	ADP
ejpam-4492	213	2	any	any	DET
ejpam-4492	213	3	arborescence	arborescence	NOUN
ejpam-4492	213	4	graph	graph	NOUN
ejpam-4492	213	5	ar	ar	NOUN
ejpam-4492	213	6	containing	contain	VERB
ejpam-4492	213	7	k1,4	k1,4	PROPN
ejpam-4492	213	8	,	,	PUNCT
ejpam-4492	213	9	its	its	PRON
ejpam-4492	213	10	dpt	dpt	PROPN
ejpam-4492	213	11	(	(	PUNCT
ejpam-4492	213	12	ar	ar	NOUN
ejpam-4492	213	13	)	)	PUNCT
ejpam-4492	213	14	is	be	AUX
ejpam-4492	213	15	nonplanar	nonplanar	ADJ
ejpam-4492	213	16	.	.	PUNCT
ejpam-4492	214	1	proof	proof	NOUN
ejpam-4492	214	2	:	:	PUNCT
ejpam-4492	214	3	this	this	PRON
ejpam-4492	214	4	follows	follow	VERB
ejpam-4492	214	5	from	from	ADP
ejpam-4492	214	6	theorem	theorem	ADJ
ejpam-4492	214	7	2.14	2.14	NUM
ejpam-4492	214	8	.	.	PUNCT
ejpam-4492	215	1	jill	jill	PROPN
ejpam-4492	215	2	maegan	maegan	PROPN
ejpam-4492	215	3	b.	b.	PROPN
ejpam-4492	215	4	pamplona	pamplona	PROPN
ejpam-4492	215	5	,	,	PUNCT
ejpam-4492	215	6	imelda	imelda	PROPN
ejpam-4492	215	7	s.	s.	PROPN
ejpam-4492	215	8	aniversario	aniversario	PROPN
ejpam-4492	215	9	/	/	SYM
ejpam-4492	215	10	eur	eur	PROPN
ejpam-4492	215	11	.	.	PUNCT
ejpam-4492	216	1	j.	j.	PROPN
ejpam-4492	216	2	pure	pure	PROPN
ejpam-4492	216	3	appl	appl	PROPN
ejpam-4492	216	4	.	.	PROPN
ejpam-4492	216	5	math	math	PROPN
ejpam-4492	216	6	,	,	PUNCT
ejpam-4492	216	7	15	15	NUM
ejpam-4492	216	8	(	(	PUNCT
ejpam-4492	216	9	3	3	NUM
ejpam-4492	216	10	)	)	PUNCT
ejpam-4492	216	11	(	(	PUNCT
ejpam-4492	216	12	2022	2022	NUM
ejpam-4492	216	13	)	)	PUNCT
ejpam-4492	216	14	,	,	PUNCT
ejpam-4492	216	15	1331	1331	NUM
ejpam-4492	216	16	-	-	SYM
ejpam-4492	216	17	1343	1343	NUM
ejpam-4492	216	18	1340	1340	NUM
ejpam-4492	216	19	theorem	theorem	VERB
ejpam-4492	216	20	3.6	3.6	NUM
ejpam-4492	216	21	.	.	PUNCT
ejpam-4492	217	1	for	for	ADP
ejpam-4492	217	2	an	an	DET
ejpam-4492	217	3	arborescence	arborescence	NOUN
ejpam-4492	217	4	graph	graph	NOUN
ejpam-4492	217	5	ar	ar	PROPN
ejpam-4492	217	6	=	=	PUNCT
ejpam-4492	217	7	s⃗1,2(n	s⃗1,2(n	PROPN
ejpam-4492	217	8	)	)	PUNCT
ejpam-4492	217	9	,	,	PUNCT
ejpam-4492	217	10	the	the	DET
ejpam-4492	217	11	directed	direct	VERB
ejpam-4492	217	12	pathos	pathos	NOUN
ejpam-4492	217	13	total	total	NOUN
ejpam-4492	217	14	digraph	digraph	PROPN
ejpam-4492	217	15	dpt	dpt	PROPN
ejpam-4492	217	16	(	(	PUNCT
ejpam-4492	217	17	ar	ar	NOUN
ejpam-4492	217	18	)	)	PUNCT
ejpam-4492	217	19	is	be	AUX
ejpam-4492	217	20	nonplanar	nonplanar	ADJ
ejpam-4492	217	21	if	if	SCONJ
ejpam-4492	217	22	and	and	CCONJ
ejpam-4492	217	23	only	only	ADV
ejpam-4492	217	24	if	if	SCONJ
ejpam-4492	217	25	n	n	PRON
ejpam-4492	217	26	≥	≥	NOUN
ejpam-4492	217	27	3	3	NUM
ejpam-4492	217	28	.	.	PUNCT
ejpam-4492	218	1	proof	proof	NOUN
ejpam-4492	218	2	:	:	PUNCT
ejpam-4492	218	3	suppose	suppose	VERB
ejpam-4492	218	4	ar	ar	PROPN
ejpam-4492	218	5	=	=	PUNCT
ejpam-4492	218	6	s⃗1,2(n	s⃗1,2(n	PROPN
ejpam-4492	218	7	)	)	PUNCT
ejpam-4492	218	8	,	,	PUNCT
ejpam-4492	218	9	where	where	SCONJ
ejpam-4492	218	10	n	n	PRON
ejpam-4492	218	11	≤	≤	ADV
ejpam-4492	218	12	2	2	NUM
ejpam-4492	218	13	.	.	PUNCT
ejpam-4492	219	1	then	then	ADV
ejpam-4492	219	2	ar	ar	PROPN
ejpam-4492	219	3	is	be	AUX
ejpam-4492	219	4	just	just	ADV
ejpam-4492	219	5	a	a	DET
ejpam-4492	219	6	path	path	NOUN
ejpam-4492	219	7	.	.	PUNCT
ejpam-4492	220	1	by	by	ADP
ejpam-4492	220	2	theorem	theorem	ADJ
ejpam-4492	220	3	3.1	3.1	NUM
ejpam-4492	220	4	,	,	PUNCT
ejpam-4492	220	5	dpt	dpt	PROPN
ejpam-4492	220	6	(	(	PUNCT
ejpam-4492	220	7	ar	ar	NOUN
ejpam-4492	220	8	)	)	PUNCT
ejpam-4492	220	9	is	be	AUX
ejpam-4492	220	10	planar	planar	ADJ
ejpam-4492	220	11	.	.	PUNCT
ejpam-4492	221	1	conversely	conversely	ADV
ejpam-4492	221	2	,	,	PUNCT
ejpam-4492	221	3	suppose	suppose	VERB
ejpam-4492	221	4	that	that	SCONJ
ejpam-4492	221	5	ar	ar	PROPN
ejpam-4492	221	6	=	=	PUNCT
ejpam-4492	221	7	s⃗1,2(n	s⃗1,2(n	NOUN
ejpam-4492	221	8	)	)	PUNCT
ejpam-4492	221	9	,	,	PUNCT
ejpam-4492	221	10	where	where	SCONJ
ejpam-4492	221	11	n	n	PRON
ejpam-4492	221	12	≥	≥	NOUN
ejpam-4492	221	13	3	3	NUM
ejpam-4492	221	14	.	.	PUNCT
ejpam-4492	221	15	for	for	ADP
ejpam-4492	221	16	n	n	NOUN
ejpam-4492	221	17	=	=	SYM
ejpam-4492	221	18	3	3	NUM
ejpam-4492	221	19	,	,	PUNCT
ejpam-4492	221	20	let	let	VERB
ejpam-4492	221	21	v	v	NOUN
ejpam-4492	221	22	(	(	PUNCT
ejpam-4492	221	23	ar	ar	NOUN
ejpam-4492	221	24	)	)	PUNCT
ejpam-4492	221	25	=	=	SYM
ejpam-4492	221	26	{	{	PUNCT
ejpam-4492	221	27	v1	v1	PROPN
ejpam-4492	221	28	,	,	PUNCT
ejpam-4492	221	29	v2	v2	PROPN
ejpam-4492	221	30	,	,	PUNCT
ejpam-4492	221	31	v3	v3	PROPN
ejpam-4492	221	32	,	,	PUNCT
ejpam-4492	221	33	v4	v4	PROPN
ejpam-4492	221	34	,	,	PUNCT
ejpam-4492	221	35	v5	v5	PROPN
ejpam-4492	221	36	,	,	PUNCT
ejpam-4492	221	37	v6	v6	NOUN
ejpam-4492	221	38	,	,	PUNCT
ejpam-4492	221	39	v7	v7	VERB
ejpam-4492	221	40	}	}	PUNCT
ejpam-4492	221	41	be	be	AUX
ejpam-4492	221	42	the	the	DET
ejpam-4492	221	43	vertex	vertex	NOUN
ejpam-4492	221	44	set	set	NOUN
ejpam-4492	221	45	and	and	CCONJ
ejpam-4492	221	46	a(ar	a(ar	NOUN
ejpam-4492	221	47	)	)	PUNCT
ejpam-4492	221	48	=	=	PRON
ejpam-4492	221	49	{	{	PUNCT
ejpam-4492	221	50	e1	e1	NOUN
ejpam-4492	221	51	=	=	SYM
ejpam-4492	221	52	(	(	PUNCT
ejpam-4492	221	53	v1v2	v1v2	NOUN
ejpam-4492	221	54	)	)	PUNCT
ejpam-4492	221	55	,	,	PUNCT
ejpam-4492	221	56	e2	e2	PROPN
ejpam-4492	221	57	=	=	SYM
ejpam-4492	221	58	(	(	PUNCT
ejpam-4492	221	59	v2v3	v2v3	NOUN
ejpam-4492	221	60	)	)	PUNCT
ejpam-4492	221	61	,	,	PUNCT
ejpam-4492	221	62	e3	e3	NOUN
ejpam-4492	221	63	=	=	SYM
ejpam-4492	221	64	(	(	PUNCT
ejpam-4492	221	65	v3v4	v3v4	NOUN
ejpam-4492	221	66	)	)	PUNCT
ejpam-4492	221	67	,	,	PUNCT
ejpam-4492	221	68	e4	e4	PROPN
ejpam-4492	221	69	=	=	SYM
ejpam-4492	221	70	(	(	PUNCT
ejpam-4492	221	71	v4v5	v4v5	NOUN
ejpam-4492	221	72	)	)	PUNCT
ejpam-4492	221	73	,	,	PUNCT
ejpam-4492	221	74	e5	e5	PROPN
ejpam-4492	221	75	=	=	PUNCT
ejpam-4492	221	76	(	(	PUNCT
ejpam-4492	221	77	v3v6	v3v6	NOUN
ejpam-4492	221	78	)	)	PUNCT
ejpam-4492	221	79	,	,	PUNCT
ejpam-4492	221	80	e6	e6	PROPN
ejpam-4492	221	81	=	=	SYM
ejpam-4492	221	82	(	(	PUNCT
ejpam-4492	221	83	v6v7	v6v7	NOUN
ejpam-4492	221	84	)	)	PUNCT
ejpam-4492	221	85	}	}	PUNCT
ejpam-4492	221	86	be	be	AUX
ejpam-4492	221	87	the	the	DET
ejpam-4492	221	88	arc	arc	NOUN
ejpam-4492	221	89	set	set	NOUN
ejpam-4492	221	90	of	of	ADP
ejpam-4492	221	91	ar	ar	NOUN
ejpam-4492	221	92	such	such	ADJ
ejpam-4492	221	93	that	that	DET
ejpam-4492	221	94	v1	v1	NOUN
ejpam-4492	221	95	and	and	CCONJ
ejpam-4492	221	96	e1	e1	NOUN
ejpam-4492	221	97	=	=	SYM
ejpam-4492	221	98	(	(	PUNCT
ejpam-4492	221	99	v1	v1	NOUN
ejpam-4492	221	100	,	,	PUNCT
ejpam-4492	221	101	v2	v2	PROPN
ejpam-4492	221	102	)	)	PUNCT
ejpam-4492	221	103	are	be	AUX
ejpam-4492	221	104	the	the	DET
ejpam-4492	221	105	root	root	NOUN
ejpam-4492	221	106	and	and	CCONJ
ejpam-4492	221	107	root	root	NOUN
ejpam-4492	221	108	arc	arc	NOUN
ejpam-4492	221	109	of	of	ADP
ejpam-4492	221	110	ar	ar	NOUN
ejpam-4492	221	111	,	,	PUNCT
ejpam-4492	221	112	respectively	respectively	ADV
ejpam-4492	221	113	.	.	PUNCT
ejpam-4492	222	1	then	then	ADV
ejpam-4492	222	2	we	we	PRON
ejpam-4492	222	3	have	have	VERB
ejpam-4492	222	4	the	the	DET
ejpam-4492	222	5	following	follow	VERB
ejpam-4492	222	6	vertices	vertex	NOUN
ejpam-4492	222	7	for	for	ADP
ejpam-4492	222	8	t	t	PROPN
ejpam-4492	222	9	(	(	PUNCT
ejpam-4492	222	10	ar	ar	PROPN
ejpam-4492	222	11	)	)	PUNCT
ejpam-4492	222	12	,	,	PUNCT
ejpam-4492	222	13	that	that	PRON
ejpam-4492	222	14	is	be	AUX
ejpam-4492	222	15	v	v	NOUN
ejpam-4492	222	16	(	(	PUNCT
ejpam-4492	222	17	t	t	PROPN
ejpam-4492	222	18	(	(	PUNCT
ejpam-4492	222	19	ar	ar	NOUN
ejpam-4492	222	20	)	)	PUNCT
ejpam-4492	222	21	)	)	PUNCT
ejpam-4492	223	1	=	=	PRON
ejpam-4492	223	2	{	{	PUNCT
ejpam-4492	223	3	v1	v1	PROPN
ejpam-4492	223	4	,	,	PUNCT
ejpam-4492	223	5	v2	v2	PROPN
ejpam-4492	223	6	,	,	PUNCT
ejpam-4492	223	7	.	.	PUNCT
ejpam-4492	223	8	.	.	PUNCT
ejpam-4492	224	1	.	.	PUNCT
ejpam-4492	225	1	,	,	PUNCT
ejpam-4492	225	2	v7	v7	NUM
ejpam-4492	225	3	,	,	PUNCT
ejpam-4492	225	4	e1	e1	PROPN
ejpam-4492	225	5	,	,	PUNCT
ejpam-4492	225	6	e2	e2	PROPN
ejpam-4492	225	7	,	,	PUNCT
ejpam-4492	225	8	e3	e3	NOUN
ejpam-4492	225	9	,	,	PUNCT
ejpam-4492	225	10	.	.	PUNCT
ejpam-4492	225	11	.	.	PUNCT
ejpam-4492	225	12	.	.	PUNCT
ejpam-4492	226	1	,	,	PUNCT
ejpam-4492	226	2	e6	e6	PROPN
ejpam-4492	226	3	}	}	PUNCT
ejpam-4492	226	4	and	and	CCONJ
ejpam-4492	226	5	arcs	arcs	PROPN
ejpam-4492	226	6	(	(	PUNCT
ejpam-4492	226	7	vi	vi	NOUN
ejpam-4492	226	8	,	,	PUNCT
ejpam-4492	226	9	ei	ei	NOUN
ejpam-4492	226	10	)	)	PUNCT
ejpam-4492	226	11	for	for	ADP
ejpam-4492	226	12	1	1	NUM
ejpam-4492	226	13	≤	≤	NUM
ejpam-4492	226	14	i	i	PRON
ejpam-4492	226	15	≤	≤	NOUN
ejpam-4492	226	16	4	4	NUM
ejpam-4492	226	17	,	,	PUNCT
ejpam-4492	226	18	6	6	NUM
ejpam-4492	226	19	,	,	PUNCT
ejpam-4492	226	20	(	(	PUNCT
ejpam-4492	226	21	v3	v3	PROPN
ejpam-4492	226	22	,	,	PUNCT
ejpam-4492	226	23	e5	e5	PROPN
ejpam-4492	226	24	)	)	PUNCT
ejpam-4492	226	25	,	,	PUNCT
ejpam-4492	226	26	(	(	PUNCT
ejpam-4492	226	27	ei	ei	NOUN
ejpam-4492	226	28	,	,	PUNCT
ejpam-4492	226	29	vi+1	vi+1	NOUN
ejpam-4492	226	30	)	)	PUNCT
ejpam-4492	226	31	for	for	ADP
ejpam-4492	226	32	1	1	NUM
ejpam-4492	226	33	≤	≤	NUM
ejpam-4492	226	34	i	i	PRON
ejpam-4492	226	35	≤	≤	NOUN
ejpam-4492	226	36	6	6	NUM
ejpam-4492	226	37	,	,	PUNCT
ejpam-4492	226	38	(	(	PUNCT
ejpam-4492	226	39	vi	vi	NOUN
ejpam-4492	226	40	,	,	PUNCT
ejpam-4492	226	41	vi+1	vi+1	NOUN
ejpam-4492	226	42	)	)	PUNCT
ejpam-4492	226	43	for	for	ADP
ejpam-4492	226	44	1	1	NUM
ejpam-4492	226	45	≤	≤	NUM
ejpam-4492	226	46	i	i	PRON
ejpam-4492	226	47	≤	≤	NOUN
ejpam-4492	226	48	4	4	NUM
ejpam-4492	226	49	,	,	PUNCT
ejpam-4492	226	50	6	6	NUM
ejpam-4492	226	51	,	,	PUNCT
ejpam-4492	226	52	(	(	PUNCT
ejpam-4492	226	53	v3	v3	PROPN
ejpam-4492	226	54	,	,	PUNCT
ejpam-4492	226	55	v6	v6	PROPN
ejpam-4492	226	56	)	)	PUNCT
ejpam-4492	226	57	,	,	PUNCT
ejpam-4492	226	58	(	(	PUNCT
ejpam-4492	226	59	e1	e1	PROPN
ejpam-4492	226	60	,	,	PUNCT
ejpam-4492	226	61	e2	e2	PROPN
ejpam-4492	226	62	)	)	PUNCT
ejpam-4492	226	63	,	,	PUNCT
ejpam-4492	226	64	(	(	PUNCT
ejpam-4492	226	65	e2	e2	PROPN
ejpam-4492	226	66	,	,	PUNCT
ejpam-4492	226	67	e3	e3	NOUN
ejpam-4492	226	68	)	)	PUNCT
ejpam-4492	226	69	,	,	PUNCT
ejpam-4492	226	70	(	(	PUNCT
ejpam-4492	226	71	e3	e3	NOUN
ejpam-4492	226	72	,	,	PUNCT
ejpam-4492	226	73	e4	e4	PROPN
ejpam-4492	226	74	)	)	PUNCT
ejpam-4492	226	75	,	,	PUNCT
ejpam-4492	226	76	(	(	PUNCT
ejpam-4492	226	77	e5	e5	INTJ
ejpam-4492	226	78	,	,	PUNCT
ejpam-4492	226	79	e6	e6	PROPN
ejpam-4492	226	80	)	)	PUNCT
ejpam-4492	226	81	,	,	PUNCT
ejpam-4492	226	82	(	(	PUNCT
ejpam-4492	226	83	e2	e2	PROPN
ejpam-4492	226	84	,	,	PUNCT
ejpam-4492	226	85	e5	e5	PROPN
ejpam-4492	226	86	)	)	PUNCT
ejpam-4492	226	87	.	.	PUNCT
ejpam-4492	227	1	let	let	VERB
ejpam-4492	227	2	p	p	PROPN
ejpam-4492	227	3	(	(	PUNCT
ejpam-4492	227	4	ar	ar	NOUN
ejpam-4492	227	5	)	)	PUNCT
ejpam-4492	227	6	=	=	SYM
ejpam-4492	227	7	{	{	PUNCT
ejpam-4492	227	8	p1	p1	NOUN
ejpam-4492	227	9	,	,	PUNCT
ejpam-4492	227	10	p2	p2	PROPN
ejpam-4492	227	11	}	}	PUNCT
ejpam-4492	227	12	be	be	VERB
ejpam-4492	227	13	a	a	DET
ejpam-4492	227	14	directed	direct	VERB
ejpam-4492	227	15	pathos	pathos	NOUN
ejpam-4492	227	16	set	set	NOUN
ejpam-4492	227	17	of	of	ADP
ejpam-4492	227	18	ar	ar	NOUN
ejpam-4492	227	19	such	such	ADJ
ejpam-4492	227	20	that	that	DET
ejpam-4492	227	21	p1	p1	PROPN
ejpam-4492	227	22	lies	lie	VERB
ejpam-4492	227	23	on	on	ADP
ejpam-4492	227	24	the	the	DET
ejpam-4492	227	25	arcs	arcs	NOUN
ejpam-4492	227	26	(	(	PUNCT
ejpam-4492	227	27	v1	v1	NOUN
ejpam-4492	227	28	,	,	PUNCT
ejpam-4492	227	29	v2	v2	PROPN
ejpam-4492	227	30	)	)	PUNCT
ejpam-4492	227	31	,	,	PUNCT
ejpam-4492	227	32	(	(	PUNCT
ejpam-4492	227	33	v2	v2	PROPN
ejpam-4492	227	34	,	,	PUNCT
ejpam-4492	227	35	v3	v3	PROPN
ejpam-4492	227	36	)	)	PUNCT
ejpam-4492	227	37	,	,	PUNCT
ejpam-4492	227	38	(	(	PUNCT
ejpam-4492	227	39	v3	v3	PROPN
ejpam-4492	227	40	,	,	PUNCT
ejpam-4492	227	41	v4	v4	PROPN
ejpam-4492	227	42	)	)	PUNCT
ejpam-4492	227	43	,	,	PUNCT
ejpam-4492	227	44	(	(	PUNCT
ejpam-4492	227	45	v4	v4	NOUN
ejpam-4492	227	46	,	,	PUNCT
ejpam-4492	227	47	v5	v5	PROPN
ejpam-4492	227	48	)	)	PUNCT
ejpam-4492	227	49	;	;	PUNCT
ejpam-4492	227	50	p2	p2	X
ejpam-4492	227	51	lies	lie	VERB
ejpam-4492	227	52	on	on	ADP
ejpam-4492	227	53	(	(	PUNCT
ejpam-4492	227	54	v3	v3	PROPN
ejpam-4492	227	55	,	,	PUNCT
ejpam-4492	227	56	v6	v6	PROPN
ejpam-4492	227	57	)	)	PUNCT
ejpam-4492	227	58	,	,	PUNCT
ejpam-4492	227	59	(	(	PUNCT
ejpam-4492	227	60	v6	v6	NOUN
ejpam-4492	227	61	,	,	PUNCT
ejpam-4492	227	62	v7	v7	NUM
ejpam-4492	227	63	)	)	PUNCT
ejpam-4492	227	64	.	.	PUNCT
ejpam-4492	228	1	thus	thus	ADV
ejpam-4492	228	2	the	the	DET
ejpam-4492	228	3	directed	direct	VERB
ejpam-4492	228	4	pathos	pathos	NOUN
ejpam-4492	228	5	vertex	vertex	NOUN
ejpam-4492	228	6	p1	p1	NOUN
ejpam-4492	228	7	is	be	AUX
ejpam-4492	228	8	a	a	DET
ejpam-4492	228	9	neighbor	neighbor	NOUN
ejpam-4492	228	10	of	of	ADP
ejpam-4492	228	11	the	the	DET
ejpam-4492	228	12	vertices	vertex	NOUN
ejpam-4492	228	13	v1v2	v1v2	X
ejpam-4492	228	14	,	,	PUNCT
ejpam-4492	228	15	v2v3	v2v3	NUM
ejpam-4492	228	16	,	,	PUNCT
ejpam-4492	228	17	v3v4	v3v4	NOUN
ejpam-4492	228	18	,	,	PUNCT
ejpam-4492	228	19	v4v5	v4v5	NOUN
ejpam-4492	228	20	;	;	PUNCT
ejpam-4492	228	21	p2	p2	PROPN
ejpam-4492	228	22	is	be	AUX
ejpam-4492	228	23	a	a	DET
ejpam-4492	228	24	neighbor	neighbor	NOUN
ejpam-4492	228	25	of	of	ADP
ejpam-4492	228	26	v3v6	v3v6	PROPN
ejpam-4492	228	27	,	,	PUNCT
ejpam-4492	228	28	v6v7	v6v7	X
ejpam-4492	228	29	.	.	PUNCT
ejpam-4492	229	1	this	this	PRON
ejpam-4492	229	2	shows	show	VERB
ejpam-4492	229	3	that	that	SCONJ
ejpam-4492	229	4	cr(dpt	cr(dpt	ADV
ejpam-4492	229	5	(	(	PUNCT
ejpam-4492	229	6	ar	ar	NOUN
ejpam-4492	229	7	)	)	PUNCT
ejpam-4492	229	8	)	)	PUNCT
ejpam-4492	230	1	=	=	SYM
ejpam-4492	230	2	1	1	NUM
ejpam-4492	230	3	,	,	PUNCT
ejpam-4492	230	4	a	a	DET
ejpam-4492	230	5	nonplanar	nonplanar	NOUN
ejpam-4492	230	6	.	.	PUNCT
ejpam-4492	231	1	for	for	ADP
ejpam-4492	231	2	n	n	X
ejpam-4492	231	3	≥	≥	NOUN
ejpam-4492	231	4	4	4	NUM
ejpam-4492	231	5	,	,	PUNCT
ejpam-4492	231	6	it	it	PRON
ejpam-4492	231	7	is	be	AUX
ejpam-4492	231	8	nonplanar	nonplanar	ADJ
ejpam-4492	231	9	since	since	SCONJ
ejpam-4492	231	10	k1,4	k1,4	PROPN
ejpam-4492	231	11	is	be	AUX
ejpam-4492	231	12	its	its	PRON
ejpam-4492	231	13	subdigraph	subdigraph	NOUN
ejpam-4492	231	14	.	.	PUNCT
ejpam-4492	232	1	this	this	PRON
ejpam-4492	232	2	shows	show	VERB
ejpam-4492	232	3	that	that	SCONJ
ejpam-4492	232	4	cr(dpt	cr(dpt	ADV
ejpam-4492	232	5	(	(	PUNCT
ejpam-4492	232	6	ar	ar	NOUN
ejpam-4492	232	7	)	)	PUNCT
ejpam-4492	232	8	)	)	PUNCT
ejpam-4492	233	1	̸=	̸=	PROPN
ejpam-4492	233	2	0	0	NUM
ejpam-4492	233	3	by	by	ADP
ejpam-4492	233	4	theorem	theorem	NOUN
ejpam-4492	233	5	2.14	2.14	NUM
ejpam-4492	233	6	.	.	PUNCT
ejpam-4492	234	1	hence	hence	ADV
ejpam-4492	234	2	,	,	PUNCT
ejpam-4492	234	3	dpt	dpt	PROPN
ejpam-4492	234	4	(	(	PUNCT
ejpam-4492	234	5	ar	ar	NOUN
ejpam-4492	234	6	)	)	PUNCT
ejpam-4492	234	7	is	be	AUX
ejpam-4492	234	8	nonplanar	nonplanar	ADJ
ejpam-4492	234	9	.	.	PUNCT
ejpam-4492	235	1	theorem	theorem	VERB
ejpam-4492	235	2	3.7	3.7	NUM
ejpam-4492	235	3	.	.	PUNCT
ejpam-4492	236	1	for	for	ADP
ejpam-4492	236	2	an	an	DET
ejpam-4492	236	3	arborescence	arborescence	PROPN
ejpam-4492	236	4	p⃗n	p⃗n	PROPN
ejpam-4492	236	5	,	,	PUNCT
ejpam-4492	236	6	dpt	dpt	PROPN
ejpam-4492	236	7	(	(	PUNCT
ejpam-4492	236	8	p⃗n	p⃗n	PROPN
ejpam-4492	236	9	)	)	PUNCT
ejpam-4492	236	10	contains	contain	VERB
ejpam-4492	236	11	a	a	DET
ejpam-4492	236	12	k1,n−1	k1,n−1	ADJ
ejpam-4492	236	13	graph	graph	NOUN
ejpam-4492	236	14	.	.	PUNCT
ejpam-4492	237	1	proof	proof	NOUN
ejpam-4492	237	2	:	:	PUNCT
ejpam-4492	237	3	from	from	ADP
ejpam-4492	237	4	theorem	theorem	ADJ
ejpam-4492	237	5	3.1	3.1	NUM
ejpam-4492	237	6	,	,	PUNCT
ejpam-4492	237	7	note	note	VERB
ejpam-4492	237	8	that	that	SCONJ
ejpam-4492	237	9	p	p	NOUN
ejpam-4492	237	10	lies	lie	VERB
ejpam-4492	237	11	on	on	ADP
ejpam-4492	237	12	the	the	DET
ejpam-4492	237	13	arcs	arc	NOUN
ejpam-4492	237	14	e1e2	e1e2	NOUN
ejpam-4492	237	15	,	,	PUNCT
ejpam-4492	237	16	e2e3	e2e3	CCONJ
ejpam-4492	237	17	,	,	PUNCT
ejpam-4492	237	18	.	.	PUNCT
ejpam-4492	237	19	.	.	PUNCT
ejpam-4492	238	1	.	.	PUNCT
ejpam-4492	239	1	,	,	PUNCT
ejpam-4492	239	2	en−2en−1	en−2en−1	PROPN
ejpam-4492	239	3	.	.	PUNCT
ejpam-4492	240	1	thus	thus	ADV
ejpam-4492	240	2	,	,	PUNCT
ejpam-4492	240	3	p	p	PROPN
ejpam-4492	240	4	is	be	AUX
ejpam-4492	240	5	a	a	DET
ejpam-4492	240	6	neighbor	neighbor	NOUN
ejpam-4492	240	7	of	of	ADP
ejpam-4492	240	8	e1e2	e1e2	NOUN
ejpam-4492	240	9	,	,	PUNCT
ejpam-4492	240	10	e2e3	e2e3	CCONJ
ejpam-4492	240	11	,	,	PUNCT
ejpam-4492	240	12	.	.	PUNCT
ejpam-4492	240	13	.	.	PUNCT
ejpam-4492	241	1	.	.	PUNCT
ejpam-4492	242	1	,	,	PUNCT
ejpam-4492	242	2	en−2en−1	en−2en−1	PROPN
ejpam-4492	242	3	.	.	PUNCT
ejpam-4492	242	4	therefore	therefore	ADV
ejpam-4492	242	5	,	,	PUNCT
ejpam-4492	242	6	k1,n−1	k1,n−1	ADJ
ejpam-4492	242	7	is	be	AUX
ejpam-4492	242	8	a	a	DET
ejpam-4492	242	9	subdigraph	subdigraph	NOUN
ejpam-4492	242	10	of	of	ADP
ejpam-4492	242	11	dpt	dpt	PROPN
ejpam-4492	242	12	(	(	PUNCT
ejpam-4492	242	13	p⃗n	p⃗n	PROPN
ejpam-4492	242	14	)	)	PUNCT
ejpam-4492	242	15	.	.	PUNCT
ejpam-4492	243	1	theorem	theorem	VERB
ejpam-4492	243	2	3.8	3.8	NUM
ejpam-4492	243	3	.	.	PUNCT
ejpam-4492	244	1	for	for	ADP
ejpam-4492	244	2	an	an	DET
ejpam-4492	244	3	arborescence	arborescence	NOUN
ejpam-4492	244	4	graph	graph	NOUN
ejpam-4492	244	5	ar	ar	PROPN
ejpam-4492	244	6	which	which	PRON
ejpam-4492	244	7	is	be	AUX
ejpam-4492	244	8	an	an	DET
ejpam-4492	244	9	n	n	CCONJ
ejpam-4492	244	10	-	-	PUNCT
ejpam-4492	244	11	pan	pan	NOUN
ejpam-4492	244	12	,	,	PUNCT
ejpam-4492	244	13	the	the	DET
ejpam-4492	244	14	directed	direct	VERB
ejpam-4492	244	15	pathos	pathos	NOUN
ejpam-4492	244	16	total	total	NOUN
ejpam-4492	244	17	digraph	digraph	PROPN
ejpam-4492	244	18	dpt	dpt	PROPN
ejpam-4492	244	19	(	(	PUNCT
ejpam-4492	244	20	ar	ar	NOUN
ejpam-4492	244	21	)	)	PUNCT
ejpam-4492	244	22	has	have	VERB
ejpam-4492	244	23	cr(n	cr(n	NOUN
ejpam-4492	244	24	-	-	PUNCT
ejpam-4492	244	25	pan	pan	NOUN
ejpam-4492	244	26	)	)	PUNCT
ejpam-4492	244	27	=	=	SYM
ejpam-4492	244	28	1	1	NUM
ejpam-4492	245	1	if	if	SCONJ
ejpam-4492	245	2	and	and	CCONJ
ejpam-4492	245	3	only	only	ADV
ejpam-4492	245	4	if	if	SCONJ
ejpam-4492	245	5	n	n	PRON
ejpam-4492	245	6	≥	≥	NOUN
ejpam-4492	245	7	3	3	NUM
ejpam-4492	245	8	.	.	PUNCT
ejpam-4492	245	9	proof	proof	NOUN
ejpam-4492	245	10	:	:	PUNCT
ejpam-4492	245	11	suppose	suppose	VERB
ejpam-4492	245	12	that	that	SCONJ
ejpam-4492	245	13	ar	ar	PROPN
ejpam-4492	245	14	is	be	AUX
ejpam-4492	245	15	an	an	DET
ejpam-4492	245	16	n	n	NOUN
ejpam-4492	245	17	-	-	PUNCT
ejpam-4492	245	18	pan	pan	NOUN
ejpam-4492	245	19	with	with	ADP
ejpam-4492	245	20	n	n	CCONJ
ejpam-4492	245	21	<	<	X
ejpam-4492	245	22	2	2	NUM
ejpam-4492	245	23	and	and	CCONJ
ejpam-4492	245	24	cr(ar	cr(ar	NOUN
ejpam-4492	245	25	)	)	PUNCT
ejpam-4492	245	26	=	=	SYM
ejpam-4492	245	27	1	1	X
ejpam-4492	245	28	.	.	PUNCT
ejpam-4492	245	29	let	let	VERB
ejpam-4492	245	30	v	v	NOUN
ejpam-4492	245	31	(	(	PUNCT
ejpam-4492	245	32	ar	ar	NOUN
ejpam-4492	245	33	)	)	PUNCT
ejpam-4492	245	34	=	=	SYM
ejpam-4492	245	35	{	{	PUNCT
ejpam-4492	245	36	v1	v1	PROPN
ejpam-4492	245	37	,	,	PUNCT
ejpam-4492	245	38	v2	v2	PROPN
ejpam-4492	245	39	,	,	PUNCT
ejpam-4492	245	40	v3	v3	PROPN
ejpam-4492	245	41	}	}	PUNCT
ejpam-4492	245	42	be	be	VERB
ejpam-4492	245	43	the	the	DET
ejpam-4492	245	44	vertex	vertex	NOUN
ejpam-4492	245	45	set	set	NOUN
ejpam-4492	245	46	and	and	CCONJ
ejpam-4492	245	47	a(ar	a(ar	NOUN
ejpam-4492	245	48	)	)	PUNCT
ejpam-4492	245	49	=	=	SYM
ejpam-4492	245	50	{	{	PUNCT
ejpam-4492	245	51	e1	e1	PROPN
ejpam-4492	245	52	,	,	PUNCT
ejpam-4492	245	53	e2	e2	PROPN
ejpam-4492	245	54	}	}	PUNCT
ejpam-4492	245	55	be	be	VERB
ejpam-4492	245	56	the	the	DET
ejpam-4492	245	57	arc	arc	NOUN
ejpam-4492	245	58	set	set	NOUN
ejpam-4492	245	59	of	of	ADP
ejpam-4492	245	60	ar	ar	NOUN
ejpam-4492	245	61	such	such	ADJ
ejpam-4492	245	62	that	that	DET
ejpam-4492	245	63	v1	v1	NOUN
ejpam-4492	245	64	and	and	CCONJ
ejpam-4492	245	65	e1	e1	NOUN
ejpam-4492	245	66	=	=	SYM
ejpam-4492	245	67	(	(	PUNCT
ejpam-4492	245	68	v1	v1	NOUN
ejpam-4492	245	69	,	,	PUNCT
ejpam-4492	245	70	v2	v2	PROPN
ejpam-4492	245	71	)	)	PUNCT
ejpam-4492	245	72	are	be	AUX
ejpam-4492	245	73	the	the	DET
ejpam-4492	245	74	root	root	NOUN
ejpam-4492	245	75	and	and	CCONJ
ejpam-4492	245	76	root	root	NOUN
ejpam-4492	245	77	arc	arc	NOUN
ejpam-4492	245	78	of	of	ADP
ejpam-4492	245	79	ar	ar	NOUN
ejpam-4492	245	80	,	,	PUNCT
ejpam-4492	245	81	respectively	respectively	ADV
ejpam-4492	245	82	.	.	PUNCT
ejpam-4492	246	1	thus	thus	ADV
ejpam-4492	246	2	,	,	PUNCT
ejpam-4492	246	3	ar	ar	NOUN
ejpam-4492	246	4	∼=	∼=	PART
ejpam-4492	246	5	p⃗3	p⃗3	NOUN
ejpam-4492	246	6	.	.	PUNCT
ejpam-4492	247	1	by	by	ADP
ejpam-4492	247	2	theorem	theorem	NOUN
ejpam-4492	247	3	3.1	3.1	NUM
ejpam-4492	247	4	,	,	PUNCT
ejpam-4492	247	5	all	all	DET
ejpam-4492	247	6	path	path	NOUN
ejpam-4492	247	7	graphs	graph	NOUN
ejpam-4492	247	8	are	be	AUX
ejpam-4492	247	9	planar	planar	ADJ
ejpam-4492	247	10	,	,	PUNCT
ejpam-4492	247	11	thus	thus	ADV
ejpam-4492	247	12	cr(ar	cr(ar	NOUN
ejpam-4492	247	13	)	)	PUNCT
ejpam-4492	247	14	=	=	SYM
ejpam-4492	247	15	0	0	NUM
ejpam-4492	247	16	,	,	PUNCT
ejpam-4492	247	17	a	a	DET
ejpam-4492	247	18	contradiction	contradiction	NOUN
ejpam-4492	247	19	.	.	PUNCT
ejpam-4492	248	1	conversely	conversely	ADV
ejpam-4492	248	2	,	,	PUNCT
ejpam-4492	248	3	suppose	suppose	VERB
ejpam-4492	248	4	that	that	SCONJ
ejpam-4492	248	5	ar	ar	PROPN
ejpam-4492	248	6	is	be	AUX
ejpam-4492	248	7	an	an	DET
ejpam-4492	248	8	n	n	CCONJ
ejpam-4492	248	9	-	-	PUNCT
ejpam-4492	248	10	pan	pan	NOUN
ejpam-4492	248	11	graph	graph	NOUN
ejpam-4492	248	12	with	with	ADP
ejpam-4492	248	13	n	n	NUM
ejpam-4492	248	14	≥	≥	NUM
ejpam-4492	248	15	3	3	NUM
ejpam-4492	248	16	vertices	vertex	NOUN
ejpam-4492	248	17	.	.	PUNCT
ejpam-4492	249	1	we	we	PRON
ejpam-4492	249	2	consider	consider	VERB
ejpam-4492	249	3	the	the	DET
ejpam-4492	249	4	following	follow	VERB
ejpam-4492	249	5	cases	case	NOUN
ejpam-4492	249	6	.	.	PUNCT
ejpam-4492	250	1	case	case	NOUN
ejpam-4492	250	2	1	1	NUM
ejpam-4492	250	3	:	:	PUNCT
ejpam-4492	250	4	suppose	suppose	VERB
ejpam-4492	250	5	that	that	SCONJ
ejpam-4492	250	6	ar	ar	PROPN
ejpam-4492	250	7	is	be	AUX
ejpam-4492	250	8	an	an	DET
ejpam-4492	250	9	n	n	CCONJ
ejpam-4492	250	10	-	-	PUNCT
ejpam-4492	250	11	pan	pan	NOUN
ejpam-4492	250	12	graph	graph	NOUN
ejpam-4492	250	13	with	with	ADP
ejpam-4492	250	14	n	n	NOUN
ejpam-4492	250	15	=	=	SYM
ejpam-4492	250	16	3	3	X
ejpam-4492	250	17	.	.	PUNCT
ejpam-4492	250	18	then	then	ADV
ejpam-4492	250	19	v	v	INTJ
ejpam-4492	250	20	(	(	PUNCT
ejpam-4492	250	21	t	t	PROPN
ejpam-4492	250	22	(	(	PUNCT
ejpam-4492	250	23	ar	ar	NOUN
ejpam-4492	250	24	)	)	PUNCT
ejpam-4492	250	25	)	)	PUNCT
ejpam-4492	251	1	=	=	PRON
ejpam-4492	251	2	{	{	PUNCT
ejpam-4492	251	3	v1	v1	PROPN
ejpam-4492	251	4	,	,	PUNCT
ejpam-4492	251	5	v2	v2	PROPN
ejpam-4492	251	6	,	,	PUNCT
ejpam-4492	251	7	v3	v3	PROPN
ejpam-4492	251	8	,	,	PUNCT
ejpam-4492	251	9	v4	v4	PROPN
ejpam-4492	251	10	,	,	PUNCT
ejpam-4492	251	11	e1	e1	PROPN
ejpam-4492	251	12	,	,	PUNCT
ejpam-4492	251	13	e2	e2	PROPN
ejpam-4492	251	14	,	,	PUNCT
ejpam-4492	251	15	e3	e3	NOUN
ejpam-4492	251	16	,	,	PUNCT
ejpam-4492	251	17	e4	e4	PROPN
ejpam-4492	251	18	}	}	PUNCT
ejpam-4492	251	19	is	be	AUX
ejpam-4492	251	20	the	the	DET
ejpam-4492	251	21	vertex	vertex	NOUN
ejpam-4492	251	22	set	set	NOUN
ejpam-4492	251	23	of	of	ADP
ejpam-4492	251	24	t	t	PROPN
ejpam-4492	251	25	(	(	PUNCT
ejpam-4492	251	26	ar	ar	NOUN
ejpam-4492	251	27	)	)	PUNCT
ejpam-4492	251	28	and	and	CCONJ
ejpam-4492	251	29	its	its	PRON
ejpam-4492	251	30	arcs	arc	NOUN
ejpam-4492	251	31	are	be	AUX
ejpam-4492	251	32	(	(	PUNCT
ejpam-4492	251	33	vi	vi	ADJ
ejpam-4492	251	34	,	,	PUNCT
ejpam-4492	251	35	vi+1	vi+1	NOUN
ejpam-4492	251	36	)	)	PUNCT
ejpam-4492	251	37	,	,	PUNCT
ejpam-4492	251	38	(	(	PUNCT
ejpam-4492	251	39	ei	ei	X
ejpam-4492	251	40	,	,	PUNCT
ejpam-4492	251	41	ei+1	ei+1	PROPN
ejpam-4492	251	42	)	)	PUNCT
ejpam-4492	251	43	,	,	PUNCT
ejpam-4492	251	44	(	(	PUNCT
ejpam-4492	251	45	ei	ei	NOUN
ejpam-4492	251	46	,	,	PUNCT
ejpam-4492	251	47	vi+1	vi+1	NOUN
ejpam-4492	251	48	)	)	PUNCT
ejpam-4492	251	49	for	for	ADP
ejpam-4492	251	50	1	1	NUM
ejpam-4492	251	51	≤	≤	NUM
ejpam-4492	251	52	i	i	PRON
ejpam-4492	251	53	≤	≤	NOUN
ejpam-4492	251	54	3	3	NUM
ejpam-4492	251	55	,	,	PUNCT
ejpam-4492	251	56	(	(	PUNCT
ejpam-4492	251	57	vi	vi	NOUN
ejpam-4492	251	58	,	,	PUNCT
ejpam-4492	251	59	ei	ei	NOUN
ejpam-4492	251	60	)	)	PUNCT
ejpam-4492	251	61	for	for	ADP
ejpam-4492	251	62	1	1	NUM
ejpam-4492	251	63	≤	≤	NUM
ejpam-4492	251	64	i	i	PRON
ejpam-4492	251	65	≤	≤	NOUN
ejpam-4492	251	66	4	4	NUM
ejpam-4492	251	67	,	,	PUNCT
ejpam-4492	251	68	(	(	PUNCT
ejpam-4492	251	69	v4	v4	NOUN
ejpam-4492	251	70	,	,	PUNCT
ejpam-4492	251	71	v2	v2	PROPN
ejpam-4492	251	72	)	)	PUNCT
ejpam-4492	251	73	,	,	PUNCT
ejpam-4492	251	74	and	and	CCONJ
ejpam-4492	251	75	(	(	PUNCT
ejpam-4492	251	76	e4	e4	PROPN
ejpam-4492	251	77	,	,	PUNCT
ejpam-4492	251	78	e2	e2	PROPN
ejpam-4492	251	79	)	)	PUNCT
ejpam-4492	251	80	.	.	PUNCT
ejpam-4492	252	1	let	let	VERB
ejpam-4492	252	2	p	p	PROPN
ejpam-4492	252	3	(	(	PUNCT
ejpam-4492	252	4	ar	ar	NOUN
ejpam-4492	252	5	)	)	PUNCT
ejpam-4492	252	6	=	=	SYM
ejpam-4492	252	7	{	{	PUNCT
ejpam-4492	252	8	p1	p1	PROPN
ejpam-4492	252	9	}	}	PUNCT
ejpam-4492	252	10	be	be	VERB
ejpam-4492	252	11	a	a	DET
ejpam-4492	252	12	directed	direct	VERB
ejpam-4492	252	13	pathos	pathos	NOUN
ejpam-4492	252	14	set	set	NOUN
ejpam-4492	252	15	of	of	ADP
ejpam-4492	252	16	ar	ar	NOUN
ejpam-4492	252	17	such	such	ADJ
ejpam-4492	252	18	that	that	DET
ejpam-4492	252	19	p1	p1	PROPN
ejpam-4492	252	20	lies	lie	VERB
ejpam-4492	252	21	on	on	ADP
ejpam-4492	252	22	the	the	DET
ejpam-4492	252	23	arcs	arcs	NOUN
ejpam-4492	252	24	(	(	PUNCT
ejpam-4492	252	25	v1	v1	NOUN
ejpam-4492	252	26	,	,	PUNCT
ejpam-4492	252	27	v2	v2	PROPN
ejpam-4492	252	28	)	)	PUNCT
ejpam-4492	252	29	,	,	PUNCT
ejpam-4492	252	30	(	(	PUNCT
ejpam-4492	252	31	v2	v2	PROPN
ejpam-4492	252	32	,	,	PUNCT
ejpam-4492	252	33	v3	v3	PROPN
ejpam-4492	252	34	)	)	PUNCT
ejpam-4492	252	35	,	,	PUNCT
ejpam-4492	252	36	(	(	PUNCT
ejpam-4492	252	37	v3	v3	PROPN
ejpam-4492	252	38	,	,	PUNCT
ejpam-4492	252	39	v4	v4	PROPN
ejpam-4492	252	40	)	)	PUNCT
ejpam-4492	252	41	,	,	PUNCT
ejpam-4492	252	42	(	(	PUNCT
ejpam-4492	252	43	v4	v4	NOUN
ejpam-4492	252	44	,	,	PUNCT
ejpam-4492	252	45	v2	v2	PROPN
ejpam-4492	252	46	)	)	PUNCT
ejpam-4492	252	47	.	.	PUNCT
ejpam-4492	253	1	then	then	ADV
ejpam-4492	253	2	the	the	DET
ejpam-4492	253	3	directed	direct	VERB
ejpam-4492	253	4	pathos	pathos	NOUN
ejpam-4492	253	5	vertex	vertex	NOUN
ejpam-4492	253	6	p1	p1	NOUN
ejpam-4492	253	7	is	be	AUX
ejpam-4492	253	8	a	a	DET
ejpam-4492	253	9	neighbor	neighbor	NOUN
ejpam-4492	253	10	of	of	ADP
ejpam-4492	253	11	the	the	DET
ejpam-4492	253	12	vertices	vertex	NOUN
ejpam-4492	253	13	v1v2	v1v2	X
ejpam-4492	253	14	,	,	PUNCT
ejpam-4492	253	15	v2v3	v2v3	NUM
ejpam-4492	253	16	,	,	PUNCT
ejpam-4492	253	17	v3v4	v3v4	NOUN
ejpam-4492	253	18	,	,	PUNCT
ejpam-4492	253	19	v4v2	v4v2	PROPN
ejpam-4492	253	20	.	.	PUNCT
ejpam-4492	254	1	this	this	PRON
ejpam-4492	254	2	shows	show	VERB
ejpam-4492	254	3	that	that	SCONJ
ejpam-4492	254	4	the	the	DET
ejpam-4492	254	5	crossing	crossing	NOUN
ejpam-4492	254	6	number	number	NOUN
ejpam-4492	254	7	of	of	ADP
ejpam-4492	254	8	dpt	dpt	PROPN
ejpam-4492	254	9	(	(	PUNCT
ejpam-4492	254	10	ar	ar	NOUN
ejpam-4492	254	11	)	)	PUNCT
ejpam-4492	254	12	is	be	AUX
ejpam-4492	254	13	one	one	NUM
ejpam-4492	254	14	,	,	PUNCT
ejpam-4492	254	15	that	that	ADV
ejpam-4492	254	16	is	is	ADV
ejpam-4492	254	17	,	,	PUNCT
ejpam-4492	254	18	cr(dpt	cr(dpt	ADV
ejpam-4492	254	19	(	(	PUNCT
ejpam-4492	254	20	ar	ar	NOUN
ejpam-4492	254	21	)	)	PUNCT
ejpam-4492	254	22	)	)	PUNCT
ejpam-4492	255	1	=	=	PUNCT
ejpam-4492	255	2	1	1	NUM
ejpam-4492	255	3	where	where	SCONJ
ejpam-4492	255	4	(	(	PUNCT
ejpam-4492	255	5	e4	e4	PROPN
ejpam-4492	255	6	,	,	PUNCT
ejpam-4492	255	7	e2	e2	PROPN
ejpam-4492	255	8	)	)	PUNCT
ejpam-4492	255	9	crosses	crosse	NOUN
ejpam-4492	255	10	(	(	PUNCT
ejpam-4492	255	11	p1	p1	NOUN
ejpam-4492	255	12	,	,	PUNCT
ejpam-4492	255	13	e1	e1	PROPN
ejpam-4492	255	14	)	)	PUNCT
ejpam-4492	255	15	.	.	PUNCT
ejpam-4492	256	1	case	case	NOUN
ejpam-4492	256	2	2	2	NUM
ejpam-4492	256	3	:	:	PUNCT
ejpam-4492	256	4	suppose	suppose	VERB
ejpam-4492	256	5	that	that	SCONJ
ejpam-4492	256	6	the	the	DET
ejpam-4492	256	7	underlying	underlie	VERB
ejpam-4492	256	8	graph	graph	NOUN
ejpam-4492	256	9	of	of	ADP
ejpam-4492	256	10	ar	ar	NOUN
ejpam-4492	256	11	is	be	AUX
ejpam-4492	256	12	an	an	DET
ejpam-4492	256	13	n	n	CCONJ
ejpam-4492	256	14	-	-	PUNCT
ejpam-4492	256	15	pan	pan	NOUN
ejpam-4492	256	16	graph	graph	NOUN
ejpam-4492	256	17	with	with	ADP
ejpam-4492	256	18	n	n	NOUN
ejpam-4492	256	19	=	=	SYM
ejpam-4492	256	20	4	4	NUM
ejpam-4492	256	21	.	.	PUNCT
ejpam-4492	256	22	then	then	ADV
ejpam-4492	256	23	v	v	INTJ
ejpam-4492	256	24	(	(	PUNCT
ejpam-4492	256	25	t	t	PROPN
ejpam-4492	256	26	(	(	PUNCT
ejpam-4492	256	27	ar	ar	NOUN
ejpam-4492	256	28	)	)	PUNCT
ejpam-4492	256	29	)	)	PUNCT
ejpam-4492	257	1	=	=	PRON
ejpam-4492	257	2	{	{	PUNCT
ejpam-4492	257	3	v1	v1	NOUN
ejpam-4492	257	4	,	,	PUNCT
ejpam-4492	257	5	v2	v2	PROPN
ejpam-4492	257	6	,	,	PUNCT
ejpam-4492	257	7	.	.	PUNCT
ejpam-4492	257	8	.	.	PUNCT
ejpam-4492	258	1	.	.	PUNCT
ejpam-4492	259	1	,	,	PUNCT
ejpam-4492	259	2	vn	vn	PROPN
ejpam-4492	259	3	,	,	PUNCT
ejpam-4492	259	4	e1	e1	PROPN
ejpam-4492	259	5	,	,	PUNCT
ejpam-4492	259	6	e2	e2	PROPN
ejpam-4492	259	7	,	,	PUNCT
ejpam-4492	259	8	.	.	PUNCT
ejpam-4492	259	9	.	.	PUNCT
ejpam-4492	259	10	.	.	PUNCT
ejpam-4492	260	1	,	,	PUNCT
ejpam-4492	260	2	en	en	ADP
ejpam-4492	260	3	}	}	PUNCT
ejpam-4492	260	4	is	be	AUX
ejpam-4492	260	5	the	the	DET
ejpam-4492	260	6	vertex	vertex	NOUN
ejpam-4492	260	7	set	set	NOUN
ejpam-4492	260	8	of	of	ADP
ejpam-4492	260	9	t	t	PROPN
ejpam-4492	260	10	(	(	PUNCT
ejpam-4492	260	11	ar	ar	PROPN
ejpam-4492	260	12	)	)	PUNCT
ejpam-4492	260	13	and	and	CCONJ
ejpam-4492	260	14	(	(	PUNCT
ejpam-4492	260	15	vi	vi	PROPN
ejpam-4492	260	16	,	,	PUNCT
ejpam-4492	260	17	vi+1	vi+1	NOUN
ejpam-4492	260	18	)	)	PUNCT
ejpam-4492	260	19	,	,	PUNCT
ejpam-4492	260	20	(	(	PUNCT
ejpam-4492	260	21	ei	ei	X
ejpam-4492	260	22	,	,	PUNCT
ejpam-4492	260	23	ei+1	ei+1	PROPN
ejpam-4492	260	24	)	)	PUNCT
ejpam-4492	260	25	,	,	PUNCT
ejpam-4492	260	26	(	(	PUNCT
ejpam-4492	260	27	ei	ei	NOUN
ejpam-4492	260	28	,	,	PUNCT
ejpam-4492	260	29	vi+1	vi+1	NOUN
ejpam-4492	260	30	)	)	PUNCT
ejpam-4492	260	31	,	,	PUNCT
ejpam-4492	260	32	(	(	PUNCT
ejpam-4492	260	33	vi	vi	NOUN
ejpam-4492	260	34	,	,	PUNCT
ejpam-4492	260	35	ei	ei	NOUN
ejpam-4492	260	36	)	)	PUNCT
ejpam-4492	260	37	,	,	PUNCT
ejpam-4492	260	38	(	(	PUNCT
ejpam-4492	260	39	v4	v4	NOUN
ejpam-4492	260	40	,	,	PUNCT
ejpam-4492	260	41	v2	v2	PROPN
ejpam-4492	260	42	)	)	PUNCT
ejpam-4492	260	43	,	,	PUNCT
ejpam-4492	260	44	and	and	CCONJ
ejpam-4492	260	45	(	(	PUNCT
ejpam-4492	260	46	e4	e4	PROPN
ejpam-4492	260	47	,	,	PUNCT
ejpam-4492	260	48	e2	e2	PROPN
ejpam-4492	260	49	)	)	PUNCT
ejpam-4492	260	50	are	be	AUX
ejpam-4492	260	51	the	the	DET
ejpam-4492	260	52	arcs	arc	NOUN
ejpam-4492	260	53	.	.	PUNCT
ejpam-4492	261	1	let	let	VERB
ejpam-4492	261	2	p	p	PROPN
ejpam-4492	261	3	(	(	PUNCT
ejpam-4492	261	4	ar	ar	NOUN
ejpam-4492	261	5	)	)	PUNCT
ejpam-4492	261	6	=	=	SYM
ejpam-4492	261	7	{	{	PUNCT
ejpam-4492	261	8	p1	p1	PROPN
ejpam-4492	261	9	}	}	PUNCT
ejpam-4492	261	10	be	be	VERB
ejpam-4492	261	11	a	a	DET
ejpam-4492	261	12	directed	direct	VERB
ejpam-4492	261	13	pathos	pathos	NOUN
ejpam-4492	261	14	set	set	NOUN
ejpam-4492	261	15	of	of	ADP
ejpam-4492	261	16	ar	ar	NOUN
ejpam-4492	261	17	such	such	ADJ
ejpam-4492	261	18	that	that	DET
ejpam-4492	261	19	p1	p1	PROPN
ejpam-4492	261	20	lies	lie	VERB
ejpam-4492	261	21	on	on	ADP
ejpam-4492	261	22	the	the	DET
ejpam-4492	261	23	arcs	arcs	NOUN
ejpam-4492	261	24	(	(	PUNCT
ejpam-4492	261	25	v1	v1	NOUN
ejpam-4492	261	26	,	,	PUNCT
ejpam-4492	261	27	v2	v2	PROPN
ejpam-4492	261	28	)	)	PUNCT
ejpam-4492	261	29	,	,	PUNCT
ejpam-4492	261	30	(	(	PUNCT
ejpam-4492	261	31	v2	v2	PROPN
ejpam-4492	261	32	,	,	PUNCT
ejpam-4492	261	33	v3	v3	PROPN
ejpam-4492	261	34	)	)	PUNCT
ejpam-4492	261	35	,	,	PUNCT
ejpam-4492	261	36	(	(	PUNCT
ejpam-4492	261	37	v3	v3	PROPN
ejpam-4492	261	38	,	,	PUNCT
ejpam-4492	261	39	v4	v4	NOUN
ejpam-4492	261	40	)	)	PUNCT
ejpam-4492	261	41	,	,	PUNCT
ejpam-4492	261	42	.	.	PUNCT
ejpam-4492	261	43	.	.	PUNCT
ejpam-4492	262	1	.	.	PUNCT
ejpam-4492	263	1	,	,	PUNCT
ejpam-4492	263	2	(	(	PUNCT
ejpam-4492	263	3	vi	vi	NOUN
ejpam-4492	263	4	,	,	PUNCT
ejpam-4492	263	5	vi+1	vi+1	NOUN
ejpam-4492	263	6	)	)	PUNCT
ejpam-4492	263	7	,	,	PUNCT
ejpam-4492	264	1	jill	jill	PROPN
ejpam-4492	264	2	maegan	maegan	PROPN
ejpam-4492	264	3	b.	b.	PROPN
ejpam-4492	264	4	pamplona	pamplona	PROPN
ejpam-4492	264	5	,	,	PUNCT
ejpam-4492	264	6	imelda	imelda	PROPN
ejpam-4492	264	7	s.	s.	PROPN
ejpam-4492	264	8	aniversario	aniversario	PROPN
ejpam-4492	264	9	/	/	SYM
ejpam-4492	264	10	eur	eur	PROPN
ejpam-4492	264	11	.	.	PUNCT
ejpam-4492	265	1	j.	j.	PROPN
ejpam-4492	265	2	pure	pure	PROPN
ejpam-4492	265	3	appl	appl	PROPN
ejpam-4492	265	4	.	.	PROPN
ejpam-4492	265	5	math	math	PROPN
ejpam-4492	265	6	,	,	PUNCT
ejpam-4492	265	7	15	15	NUM
ejpam-4492	265	8	(	(	PUNCT
ejpam-4492	265	9	3	3	NUM
ejpam-4492	265	10	)	)	PUNCT
ejpam-4492	265	11	(	(	PUNCT
ejpam-4492	265	12	2022	2022	NUM
ejpam-4492	265	13	)	)	PUNCT
ejpam-4492	265	14	,	,	PUNCT
ejpam-4492	265	15	1331	1331	NUM
ejpam-4492	265	16	-	-	SYM
ejpam-4492	265	17	1343	1343	NUM
ejpam-4492	265	18	1341	1341	NUM
ejpam-4492	265	19	(	(	PUNCT
ejpam-4492	265	20	v4	v4	NOUN
ejpam-4492	265	21	,	,	PUNCT
ejpam-4492	265	22	v2	v2	PROPN
ejpam-4492	265	23	)	)	PUNCT
ejpam-4492	265	24	for	for	ADP
ejpam-4492	265	25	1	1	NUM
ejpam-4492	265	26	≤	≤	NUM
ejpam-4492	265	27	i	i	PRON
ejpam-4492	265	28	≤	≤	ADJ
ejpam-4492	265	29	n−	n−	PROPN
ejpam-4492	265	30	1	1	NUM
ejpam-4492	265	31	.	.	PUNCT
ejpam-4492	266	1	then	then	ADV
ejpam-4492	266	2	the	the	DET
ejpam-4492	266	3	directed	direct	VERB
ejpam-4492	266	4	pathos	pathos	NOUN
ejpam-4492	266	5	vertex	vertex	NOUN
ejpam-4492	266	6	p1	p1	NOUN
ejpam-4492	266	7	is	be	AUX
ejpam-4492	266	8	a	a	DET
ejpam-4492	266	9	neighbor	neighbor	NOUN
ejpam-4492	266	10	of	of	ADP
ejpam-4492	266	11	the	the	DET
ejpam-4492	266	12	vertices	vertex	NOUN
ejpam-4492	266	13	v1v2	v1v2	X
ejpam-4492	266	14	,	,	PUNCT
ejpam-4492	266	15	v2v3	v2v3	PROPN
ejpam-4492	266	16	,	,	PUNCT
ejpam-4492	266	17	v3v4	v3v4	NOUN
ejpam-4492	266	18	,	,	PUNCT
ejpam-4492	266	19	.	.	PUNCT
ejpam-4492	266	20	.	.	PUNCT
ejpam-4492	267	1	.	.	PUNCT
ejpam-4492	268	1	,	,	PUNCT
ejpam-4492	268	2	vivi+1	vivi+1	ADJ
ejpam-4492	268	3	,	,	PUNCT
ejpam-4492	268	4	v4v2	v4v2	PUNCT
ejpam-4492	268	5	for	for	ADP
ejpam-4492	268	6	1	1	NUM
ejpam-4492	268	7	≤	≤	NUM
ejpam-4492	268	8	i	i	PRON
ejpam-4492	268	9	≤	≤	ADJ
ejpam-4492	268	10	n−	n−	NOUN
ejpam-4492	268	11	1	1	NUM
ejpam-4492	268	12	.	.	PUNCT
ejpam-4492	269	1	this	this	PRON
ejpam-4492	269	2	shows	show	VERB
ejpam-4492	269	3	that	that	SCONJ
ejpam-4492	269	4	the	the	DET
ejpam-4492	269	5	crossing	crossing	NOUN
ejpam-4492	269	6	number	number	NOUN
ejpam-4492	269	7	of	of	ADP
ejpam-4492	269	8	dpt	dpt	PROPN
ejpam-4492	269	9	(	(	PUNCT
ejpam-4492	269	10	ar	ar	NOUN
ejpam-4492	269	11	)	)	PUNCT
ejpam-4492	269	12	is	be	AUX
ejpam-4492	269	13	one	one	NUM
ejpam-4492	269	14	,	,	PUNCT
ejpam-4492	269	15	that	that	ADV
ejpam-4492	269	16	is	is	ADV
ejpam-4492	269	17	,	,	PUNCT
ejpam-4492	269	18	cr(dpt	cr(dpt	ADV
ejpam-4492	269	19	(	(	PUNCT
ejpam-4492	269	20	ar	ar	NOUN
ejpam-4492	269	21	)	)	PUNCT
ejpam-4492	269	22	)	)	PUNCT
ejpam-4492	270	1	=	=	PUNCT
ejpam-4492	270	2	1	1	X
ejpam-4492	270	3	.	.	X
ejpam-4492	270	4	for	for	ADP
ejpam-4492	270	5	all	all	DET
ejpam-4492	270	6	n	n	CCONJ
ejpam-4492	270	7	,	,	PUNCT
ejpam-4492	270	8	(	(	PUNCT
ejpam-4492	270	9	e4	e4	PROPN
ejpam-4492	270	10	,	,	PUNCT
ejpam-4492	270	11	e2	e2	PROPN
ejpam-4492	270	12	)	)	PUNCT
ejpam-4492	270	13	crosses	crosse	NOUN
ejpam-4492	270	14	(	(	PUNCT
ejpam-4492	270	15	p1	p1	NOUN
ejpam-4492	270	16	,	,	PUNCT
ejpam-4492	270	17	e1	e1	PROPN
ejpam-4492	270	18	)	)	PUNCT
ejpam-4492	270	19	.	.	PUNCT
ejpam-4492	271	1	theorem	theorem	VERB
ejpam-4492	271	2	3.9	3.9	NUM
ejpam-4492	271	3	.	.	PUNCT
ejpam-4492	272	1	if	if	SCONJ
ejpam-4492	272	2	ar	ar	NOUN
ejpam-4492	272	3	=	=	NOUN
ejpam-4492	272	4	p⃗m(x1	p⃗m(x1	PROPN
ejpam-4492	272	5	)	)	PUNCT
ejpam-4492	272	6	•	•	NOUN
ejpam-4492	272	7	p⃗n(y1	p⃗n(y1	NOUN
ejpam-4492	272	8	)	)	PUNCT
ejpam-4492	272	9	then	then	ADV
ejpam-4492	272	10	the	the	DET
ejpam-4492	272	11	directed	direct	VERB
ejpam-4492	272	12	pathos	pathos	NOUN
ejpam-4492	272	13	total	total	NOUN
ejpam-4492	272	14	digraph	digraph	PROPN
ejpam-4492	272	15	dpt	dpt	PROPN
ejpam-4492	272	16	(	(	PUNCT
ejpam-4492	272	17	ar	ar	PROPN
ejpam-4492	272	18	)	)	PUNCT
ejpam-4492	272	19	of	of	ADP
ejpam-4492	272	20	ar	ar	NOUN
ejpam-4492	272	21	is	be	AUX
ejpam-4492	272	22	planar	planar	ADJ
ejpam-4492	272	23	where	where	SCONJ
ejpam-4492	272	24	x1	x1	PROPN
ejpam-4492	272	25	and	and	CCONJ
ejpam-4492	272	26	y1	y1	NOUN
ejpam-4492	272	27	are	be	AUX
ejpam-4492	272	28	the	the	DET
ejpam-4492	272	29	initial	initial	ADJ
ejpam-4492	272	30	vertices	vertex	NOUN
ejpam-4492	272	31	of	of	ADP
ejpam-4492	272	32	p⃗m(x1	p⃗m(x1	NOUN
ejpam-4492	272	33	)	)	PUNCT
ejpam-4492	272	34	and	and	CCONJ
ejpam-4492	272	35	p⃗n(y1	p⃗n(y1	NOUN
ejpam-4492	272	36	)	)	PUNCT
ejpam-4492	272	37	,	,	PUNCT
ejpam-4492	272	38	respectively	respectively	ADV
ejpam-4492	272	39	.	.	PUNCT
ejpam-4492	273	1	proof	proof	NOUN
ejpam-4492	273	2	:	:	PUNCT
ejpam-4492	273	3	suppose	suppose	VERB
ejpam-4492	273	4	that	that	SCONJ
ejpam-4492	273	5	ar	ar	PROPN
ejpam-4492	273	6	=	=	PROPN
ejpam-4492	273	7	p⃗m	p⃗m	PROPN
ejpam-4492	273	8	•	•	NUM
ejpam-4492	273	9	p⃗n	p⃗n	PROPN
ejpam-4492	273	10	.	.	PUNCT
ejpam-4492	274	1	let	let	VERB
ejpam-4492	274	2	v	v	X
ejpam-4492	274	3	(	(	PUNCT
ejpam-4492	274	4	p⃗m	p⃗m	PROPN
ejpam-4492	274	5	)	)	PUNCT
ejpam-4492	274	6	=	=	PUNCT
ejpam-4492	274	7	{	{	PUNCT
ejpam-4492	274	8	x1	x1	PROPN
ejpam-4492	274	9	,	,	PUNCT
ejpam-4492	274	10	x2	x2	PROPN
ejpam-4492	274	11	,	,	PUNCT
ejpam-4492	274	12	x3	x3	ADJ
ejpam-4492	274	13	,	,	PUNCT
ejpam-4492	274	14	.	.	PUNCT
ejpam-4492	274	15	.	.	PUNCT
ejpam-4492	275	1	.	.	PUNCT
ejpam-4492	276	1	,	,	PUNCT
ejpam-4492	276	2	xm	xm	PROPN
ejpam-4492	276	3	}	}	PUNCT
ejpam-4492	276	4	and	and	CCONJ
ejpam-4492	276	5	let	let	VERB
ejpam-4492	276	6	a(p⃗m	a(p⃗m	NOUN
ejpam-4492	276	7	)	)	PUNCT
ejpam-4492	276	8	=	=	PRON
ejpam-4492	276	9	{	{	PUNCT
ejpam-4492	276	10	a1	a1	PROPN
ejpam-4492	276	11	,	,	PUNCT
ejpam-4492	276	12	a2	a2	PROPN
ejpam-4492	276	13	,	,	PUNCT
ejpam-4492	276	14	a3	a3	NOUN
ejpam-4492	276	15	,	,	PUNCT
ejpam-4492	276	16	.	.	PUNCT
ejpam-4492	276	17	.	.	PUNCT
ejpam-4492	277	1	.	.	PUNCT
ejpam-4492	278	1	,	,	PUNCT
ejpam-4492	278	2	am−1	am−1	PROPN
ejpam-4492	278	3	}	}	PUNCT
ejpam-4492	278	4	such	such	ADJ
ejpam-4492	278	5	that	that	SCONJ
ejpam-4492	278	6	x1	x1	PROPN
ejpam-4492	278	7	and	and	CCONJ
ejpam-4492	278	8	a1	a1	NOUN
ejpam-4492	278	9	=	=	SYM
ejpam-4492	278	10	(	(	PUNCT
ejpam-4492	278	11	x1	x1	PROPN
ejpam-4492	278	12	,	,	PUNCT
ejpam-4492	278	13	x2	x2	PROPN
ejpam-4492	278	14	)	)	PUNCT
ejpam-4492	278	15	are	be	AUX
ejpam-4492	278	16	the	the	DET
ejpam-4492	278	17	root	root	NOUN
ejpam-4492	278	18	and	and	CCONJ
ejpam-4492	278	19	root	root	NOUN
ejpam-4492	278	20	arc	arc	NOUN
ejpam-4492	278	21	of	of	ADP
ejpam-4492	278	22	p⃗m	p⃗m	NOUN
ejpam-4492	278	23	,	,	PUNCT
ejpam-4492	278	24	respectively	respectively	ADV
ejpam-4492	278	25	and	and	CCONJ
ejpam-4492	278	26	ai	ai	VERB
ejpam-4492	278	27	=	=	PUNCT
ejpam-4492	278	28	(	(	PUNCT
ejpam-4492	278	29	xi	xi	PROPN
ejpam-4492	278	30	,	,	PUNCT
ejpam-4492	278	31	xi+1	xi+1	PROPN
ejpam-4492	278	32	)	)	PUNCT
ejpam-4492	278	33	for	for	ADP
ejpam-4492	278	34	2	2	NUM
ejpam-4492	278	35	≤	≤	NOUN
ejpam-4492	278	36	i	i	PRON
ejpam-4492	278	37	≤	≤	NOUN
ejpam-4492	278	38	m	m	VERB
ejpam-4492	278	39	−	−	PROPN
ejpam-4492	278	40	1	1	NUM
ejpam-4492	278	41	.	.	PUNCT
ejpam-4492	279	1	then	then	ADV
ejpam-4492	279	2	x1	x1	NUM
ejpam-4492	279	3	,	,	PUNCT
ejpam-4492	279	4	x2	x2	PROPN
ejpam-4492	279	5	,	,	PUNCT
ejpam-4492	279	6	.	.	PUNCT
ejpam-4492	279	7	.	.	PUNCT
ejpam-4492	279	8	.	.	PUNCT
ejpam-4492	280	1	,	,	PUNCT
ejpam-4492	280	2	xm	xm	PROPN
ejpam-4492	280	3	,	,	PUNCT
ejpam-4492	280	4	a1	a1	PROPN
ejpam-4492	280	5	,	,	PUNCT
ejpam-4492	280	6	a2	a2	PROPN
ejpam-4492	280	7	,	,	PUNCT
ejpam-4492	280	8	.	.	PUNCT
ejpam-4492	280	9	.	.	PUNCT
ejpam-4492	280	10	.	.	PUNCT
ejpam-4492	281	1	,	,	PUNCT
ejpam-4492	281	2	am−1	am−1	PROPN
ejpam-4492	281	3	are	be	AUX
ejpam-4492	281	4	the	the	DET
ejpam-4492	281	5	vertices	vertex	NOUN
ejpam-4492	281	6	of	of	ADP
ejpam-4492	281	7	t	t	PROPN
ejpam-4492	281	8	(	(	PUNCT
ejpam-4492	281	9	p⃗m	p⃗m	PROPN
ejpam-4492	281	10	)	)	PUNCT
ejpam-4492	281	11	.	.	PUNCT
ejpam-4492	282	1	also	also	ADV
ejpam-4492	282	2	,	,	PUNCT
ejpam-4492	282	3	(	(	PUNCT
ejpam-4492	282	4	xi	xi	PROPN
ejpam-4492	282	5	,	,	PUNCT
ejpam-4492	282	6	xi+1	xi+1	PROPN
ejpam-4492	282	7	)	)	PUNCT
ejpam-4492	282	8	,	,	PUNCT
ejpam-4492	282	9	(	(	PUNCT
ejpam-4492	282	10	xi	xi	X
ejpam-4492	282	11	,	,	PUNCT
ejpam-4492	282	12	ai	ai	NOUN
ejpam-4492	282	13	)	)	PUNCT
ejpam-4492	282	14	,	,	PUNCT
ejpam-4492	282	15	(	(	PUNCT
ejpam-4492	282	16	ai	ai	PROPN
ejpam-4492	282	17	,	,	PUNCT
ejpam-4492	282	18	xi+1	xi+1	PROPN
ejpam-4492	282	19	)	)	PUNCT
ejpam-4492	282	20	,	,	PUNCT
ejpam-4492	282	21	(	(	PUNCT
ejpam-4492	282	22	ai	ai	PROPN
ejpam-4492	282	23	,	,	PUNCT
ejpam-4492	282	24	ai+1	ai+1	NOUN
ejpam-4492	282	25	)	)	PUNCT
ejpam-4492	282	26	,	,	PUNCT
ejpam-4492	282	27	are	be	AUX
ejpam-4492	282	28	the	the	DET
ejpam-4492	282	29	arcs	arc	NOUN
ejpam-4492	282	30	of	of	ADP
ejpam-4492	282	31	t	t	PROPN
ejpam-4492	282	32	(	(	PUNCT
ejpam-4492	282	33	p⃗m	p⃗m	PROPN
ejpam-4492	282	34	)	)	PUNCT
ejpam-4492	282	35	.	.	PUNCT
ejpam-4492	283	1	let	let	VERB
ejpam-4492	283	2	v	v	NOUN
ejpam-4492	283	3	(	(	PUNCT
ejpam-4492	283	4	p⃗n	p⃗n	NOUN
ejpam-4492	283	5	)	)	PUNCT
ejpam-4492	283	6	=	=	PRON
ejpam-4492	283	7	{	{	PUNCT
ejpam-4492	283	8	y1	y1	PROPN
ejpam-4492	283	9	,	,	PUNCT
ejpam-4492	283	10	y2	y2	PROPN
ejpam-4492	283	11	,	,	PUNCT
ejpam-4492	283	12	y3	y3	PROPN
ejpam-4492	283	13	,	,	PUNCT
ejpam-4492	283	14	.	.	PUNCT
ejpam-4492	283	15	.	.	PUNCT
ejpam-4492	284	1	.	.	PUNCT
ejpam-4492	285	1	,	,	PUNCT
ejpam-4492	285	2	yn	yn	PROPN
ejpam-4492	285	3	}	}	PUNCT
ejpam-4492	285	4	and	and	CCONJ
ejpam-4492	285	5	let	let	VERB
ejpam-4492	285	6	a(p⃗n	a(p⃗n	PRON
ejpam-4492	285	7	)	)	PUNCT
ejpam-4492	285	8	=	=	SYM
ejpam-4492	285	9	{	{	PUNCT
ejpam-4492	285	10	b1	b1	NOUN
ejpam-4492	285	11	,	,	PUNCT
ejpam-4492	285	12	b2	b2	NOUN
ejpam-4492	285	13	,	,	PUNCT
ejpam-4492	285	14	b3	b3	PROPN
ejpam-4492	285	15	,	,	PUNCT
ejpam-4492	285	16	.	.	PUNCT
ejpam-4492	285	17	.	.	PUNCT
ejpam-4492	286	1	.	.	PUNCT
ejpam-4492	287	1	,	,	PUNCT
ejpam-4492	287	2	bn−1	bn−1	PRON
ejpam-4492	287	3	}	}	PUNCT
ejpam-4492	287	4	such	such	ADJ
ejpam-4492	287	5	that	that	SCONJ
ejpam-4492	287	6	y1	y1	NOUN
ejpam-4492	287	7	and	and	CCONJ
ejpam-4492	287	8	b1	b1	NOUN
ejpam-4492	287	9	=	=	SYM
ejpam-4492	287	10	(	(	PUNCT
ejpam-4492	287	11	y1	y1	PROPN
ejpam-4492	287	12	,	,	PUNCT
ejpam-4492	287	13	y2	y2	PROPN
ejpam-4492	287	14	)	)	PUNCT
ejpam-4492	287	15	are	be	AUX
ejpam-4492	287	16	the	the	DET
ejpam-4492	287	17	root	root	NOUN
ejpam-4492	287	18	and	and	CCONJ
ejpam-4492	287	19	root	root	NOUN
ejpam-4492	287	20	arc	arc	NOUN
ejpam-4492	287	21	of	of	ADP
ejpam-4492	287	22	p⃗n	p⃗n	PROPN
ejpam-4492	287	23	,	,	PUNCT
ejpam-4492	287	24	respectively	respectively	ADV
ejpam-4492	287	25	and	and	CCONJ
ejpam-4492	287	26	bj	bj	VERB
ejpam-4492	287	27	=	=	SYM
ejpam-4492	287	28	(	(	PUNCT
ejpam-4492	287	29	yj	yj	PROPN
ejpam-4492	287	30	,	,	PUNCT
ejpam-4492	287	31	yj+1	yj+1	PROPN
ejpam-4492	287	32	)	)	PUNCT
ejpam-4492	287	33	for	for	ADP
ejpam-4492	287	34	2	2	NUM
ejpam-4492	287	35	≤	≤	NUM
ejpam-4492	287	36	j	j	PROPN
ejpam-4492	287	37	≤	≤	PROPN
ejpam-4492	287	38	n	n	CCONJ
ejpam-4492	287	39	−	−	PROPN
ejpam-4492	287	40	1	1	NUM
ejpam-4492	287	41	.	.	PUNCT
ejpam-4492	288	1	then	then	ADV
ejpam-4492	288	2	y1	y1	PROPN
ejpam-4492	288	3	,	,	PUNCT
ejpam-4492	288	4	y2	y2	PROPN
ejpam-4492	288	5	,	,	PUNCT
ejpam-4492	288	6	.	.	PUNCT
ejpam-4492	288	7	.	.	PUNCT
ejpam-4492	288	8	.	.	PUNCT
ejpam-4492	289	1	,	,	PUNCT
ejpam-4492	289	2	yn	yn	PROPN
ejpam-4492	289	3	,	,	PUNCT
ejpam-4492	289	4	b1	b1	NOUN
ejpam-4492	289	5	,	,	PUNCT
ejpam-4492	289	6	b2	b2	NOUN
ejpam-4492	289	7	,	,	PUNCT
ejpam-4492	289	8	.	.	PUNCT
ejpam-4492	289	9	.	.	PUNCT
ejpam-4492	289	10	.	.	PUNCT
ejpam-4492	290	1	,	,	PUNCT
ejpam-4492	290	2	bn−1	bn−1	PRON
ejpam-4492	290	3	are	be	AUX
ejpam-4492	290	4	the	the	DET
ejpam-4492	290	5	vertices	vertex	NOUN
ejpam-4492	290	6	of	of	ADP
ejpam-4492	290	7	t	t	PROPN
ejpam-4492	290	8	(	(	PUNCT
ejpam-4492	290	9	p⃗n	p⃗n	PROPN
ejpam-4492	290	10	)	)	PUNCT
ejpam-4492	290	11	.	.	PUNCT
ejpam-4492	291	1	also	also	ADV
ejpam-4492	291	2	,	,	PUNCT
ejpam-4492	291	3	(	(	PUNCT
ejpam-4492	291	4	yj	yj	PROPN
ejpam-4492	291	5	,	,	PUNCT
ejpam-4492	291	6	yj+1	yj+1	PROPN
ejpam-4492	291	7	)	)	PUNCT
ejpam-4492	291	8	,	,	PUNCT
ejpam-4492	291	9	(	(	PUNCT
ejpam-4492	291	10	yj	yj	NOUN
ejpam-4492	291	11	,	,	PUNCT
ejpam-4492	291	12	bj	bj	NOUN
ejpam-4492	291	13	)	)	PUNCT
ejpam-4492	291	14	,	,	PUNCT
ejpam-4492	291	15	(	(	PUNCT
ejpam-4492	291	16	bj	bj	NOUN
ejpam-4492	291	17	,	,	PUNCT
ejpam-4492	291	18	yj+1	yj+1	NUM
ejpam-4492	291	19	)	)	PUNCT
ejpam-4492	291	20	,	,	PUNCT
ejpam-4492	291	21	(	(	PUNCT
ejpam-4492	291	22	bj	bj	NOUN
ejpam-4492	291	23	,	,	PUNCT
ejpam-4492	291	24	bj+1	bj+1	PROPN
ejpam-4492	291	25	)	)	PUNCT
ejpam-4492	291	26	,	,	PUNCT
ejpam-4492	291	27	are	be	AUX
ejpam-4492	291	28	the	the	DET
ejpam-4492	291	29	arcs	arc	NOUN
ejpam-4492	291	30	of	of	ADP
ejpam-4492	291	31	t	t	PROPN
ejpam-4492	291	32	(	(	PUNCT
ejpam-4492	291	33	p⃗n	p⃗n	PROPN
ejpam-4492	291	34	)	)	PUNCT
ejpam-4492	291	35	.	.	PUNCT
ejpam-4492	292	1	let	let	VERB
ejpam-4492	292	2	p	p	PROPN
ejpam-4492	292	3	(	(	PUNCT
ejpam-4492	292	4	ar	ar	NOUN
ejpam-4492	292	5	)	)	PUNCT
ejpam-4492	292	6	=	=	SYM
ejpam-4492	292	7	{	{	PUNCT
ejpam-4492	292	8	p1	p1	NOUN
ejpam-4492	292	9	,	,	PUNCT
ejpam-4492	292	10	p2	p2	PROPN
ejpam-4492	292	11	}	}	PUNCT
ejpam-4492	292	12	such	such	ADJ
ejpam-4492	292	13	that	that	SCONJ
ejpam-4492	292	14	p1	p1	PROPN
ejpam-4492	292	15	lies	lie	VERB
ejpam-4492	292	16	on	on	ADP
ejpam-4492	292	17	the	the	DET
ejpam-4492	292	18	arcs	arcs	NOUN
ejpam-4492	292	19	a1	a1	NOUN
ejpam-4492	292	20	=	=	SYM
ejpam-4492	292	21	(	(	PUNCT
ejpam-4492	292	22	x1	x1	PROPN
ejpam-4492	292	23	,	,	PUNCT
ejpam-4492	292	24	x2	x2	PROPN
ejpam-4492	292	25	)	)	PUNCT
ejpam-4492	292	26	,	,	PUNCT
ejpam-4492	292	27	a2	a2	PROPN
ejpam-4492	292	28	=	=	SYM
ejpam-4492	292	29	(	(	PUNCT
ejpam-4492	292	30	x2	x2	PROPN
ejpam-4492	292	31	,	,	PUNCT
ejpam-4492	292	32	x3	x3	ADJ
ejpam-4492	292	33	)	)	PUNCT
ejpam-4492	292	34	,	,	PUNCT
ejpam-4492	292	35	.	.	PUNCT
ejpam-4492	292	36	.	.	PUNCT
ejpam-4492	293	1	.	.	PUNCT
ejpam-4492	294	1	,	,	PUNCT
ejpam-4492	294	2	am−1	am−1	PROPN
ejpam-4492	294	3	=	=	SYM
ejpam-4492	294	4	(	(	PUNCT
ejpam-4492	294	5	xm−1	xm−1	PROPN
ejpam-4492	294	6	,	,	PUNCT
ejpam-4492	294	7	xm	xm	PROPN
ejpam-4492	294	8	)	)	PUNCT
ejpam-4492	294	9	and	and	CCONJ
ejpam-4492	294	10	p2	p2	PROPN
ejpam-4492	294	11	lies	lie	VERB
ejpam-4492	294	12	on	on	ADP
ejpam-4492	294	13	the	the	DET
ejpam-4492	294	14	arcs	arcs	NOUN
ejpam-4492	294	15	b1	b1	NOUN
ejpam-4492	294	16	=	=	SYM
ejpam-4492	294	17	(	(	PUNCT
ejpam-4492	294	18	y1	y1	PROPN
ejpam-4492	294	19	,	,	PUNCT
ejpam-4492	294	20	y2	y2	PROPN
ejpam-4492	294	21	)	)	PUNCT
ejpam-4492	294	22	,	,	PUNCT
ejpam-4492	294	23	b2	b2	NOUN
ejpam-4492	294	24	=	=	SYM
ejpam-4492	294	25	(	(	PUNCT
ejpam-4492	294	26	y2	y2	PROPN
ejpam-4492	294	27	,	,	PUNCT
ejpam-4492	294	28	y3	y3	PROPN
ejpam-4492	294	29	)	)	PUNCT
ejpam-4492	294	30	,	,	PUNCT
ejpam-4492	294	31	.	.	PUNCT
ejpam-4492	294	32	.	.	PUNCT
ejpam-4492	295	1	.	.	PUNCT
ejpam-4492	296	1	,	,	PUNCT
ejpam-4492	296	2	bn−1	bn−1	PRON
ejpam-4492	296	3	=	=	SYM
ejpam-4492	296	4	(	(	PUNCT
ejpam-4492	296	5	yn−1	yn−1	PROPN
ejpam-4492	296	6	,	,	PUNCT
ejpam-4492	296	7	yn	yn	PROPN
ejpam-4492	296	8	)	)	PUNCT
ejpam-4492	296	9	.	.	PUNCT
ejpam-4492	297	1	the	the	DET
ejpam-4492	297	2	directed	direct	VERB
ejpam-4492	297	3	pathos	pathos	NOUN
ejpam-4492	297	4	vertex	vertex	NOUN
ejpam-4492	297	5	p2	p2	PROPN
ejpam-4492	297	6	is	be	AUX
ejpam-4492	297	7	a	a	DET
ejpam-4492	297	8	neighbor	neighbor	NOUN
ejpam-4492	297	9	of	of	ADP
ejpam-4492	297	10	the	the	DET
ejpam-4492	297	11	vertices	vertex	NOUN
ejpam-4492	297	12	b1	b1	NOUN
ejpam-4492	297	13	,	,	PUNCT
ejpam-4492	297	14	b2	b2	NOUN
ejpam-4492	297	15	,	,	PUNCT
ejpam-4492	297	16	.	.	PUNCT
ejpam-4492	297	17	.	.	PUNCT
ejpam-4492	298	1	.	.	PUNCT
ejpam-4492	299	1	,	,	PUNCT
ejpam-4492	299	2	bn−1	bn−1	X
ejpam-4492	299	3	.	.	PUNCT
ejpam-4492	300	1	note	note	VERB
ejpam-4492	300	2	that	that	SCONJ
ejpam-4492	300	3	x1	x1	PROPN
ejpam-4492	300	4	and	and	CCONJ
ejpam-4492	300	5	y1	y1	NOUN
ejpam-4492	300	6	are	be	AUX
ejpam-4492	300	7	the	the	DET
ejpam-4492	300	8	initial	initial	ADJ
ejpam-4492	300	9	vertices	vertex	NOUN
ejpam-4492	300	10	of	of	ADP
ejpam-4492	300	11	graphs	graph	NOUN
ejpam-4492	300	12	p⃗m	p⃗m	PROPN
ejpam-4492	300	13	and	and	CCONJ
ejpam-4492	300	14	p⃗n	p⃗n	PROPN
ejpam-4492	300	15	,	,	PUNCT
ejpam-4492	300	16	respectively	respectively	ADV
ejpam-4492	300	17	,	,	PUNCT
ejpam-4492	300	18	so	so	CCONJ
ejpam-4492	301	1	x1	x1	PROPN
ejpam-4492	301	2	=	=	NOUN
ejpam-4492	301	3	y1	y1	PROPN
ejpam-4492	301	4	in	in	ADP
ejpam-4492	301	5	p⃗m	p⃗m	PROPN
ejpam-4492	301	6	•	•	NUM
ejpam-4492	301	7	p⃗n	p⃗n	PROPN
ejpam-4492	301	8	.	.	PUNCT
ejpam-4492	302	1	this	this	PRON
ejpam-4492	302	2	shows	show	VERB
ejpam-4492	302	3	that	that	SCONJ
ejpam-4492	302	4	the	the	DET
ejpam-4492	302	5	cr(dpt	cr(dpt	NOUN
ejpam-4492	302	6	(	(	PUNCT
ejpam-4492	302	7	p⃗n	p⃗n	NOUN
ejpam-4492	302	8	)	)	PUNCT
ejpam-4492	302	9	)	)	PUNCT
ejpam-4492	303	1	=	=	SYM
ejpam-4492	303	2	0	0	PUNCT
ejpam-4492	303	3	(	(	PUNCT
ejpam-4492	303	4	see	see	VERB
ejpam-4492	303	5	figure	figure	NOUN
ejpam-4492	303	6	11	11	NUM
ejpam-4492	303	7	)	)	PUNCT
ejpam-4492	303	8	.	.	PUNCT
ejpam-4492	304	1	hence	hence	ADV
ejpam-4492	304	2	,	,	PUNCT
ejpam-4492	304	3	dpt	dpt	PROPN
ejpam-4492	304	4	(	(	PUNCT
ejpam-4492	304	5	p⃗n	p⃗n	PROPN
ejpam-4492	304	6	)	)	PUNCT
ejpam-4492	304	7	is	be	AUX
ejpam-4492	304	8	planar	planar	ADJ
ejpam-4492	304	9	.	.	PUNCT
ejpam-4492	305	1	figure	figure	NOUN
ejpam-4492	305	2	11	11	NUM
ejpam-4492	305	3	:	:	PUNCT
ejpam-4492	305	4	directed	direct	VERB
ejpam-4492	305	5	pathos	pathos	PROPN
ejpam-4492	305	6	total	total	ADJ
ejpam-4492	305	7	digraph	digraph	NOUN
ejpam-4492	305	8	of	of	ADP
ejpam-4492	305	9	p⃗m(x1	p⃗m(x1	ADJ
ejpam-4492	305	10	)	)	PUNCT
ejpam-4492	305	11	•	•	NUM
ejpam-4492	305	12	p⃗n(y1	p⃗n(y1	NOUN
ejpam-4492	305	13	)	)	PUNCT
ejpam-4492	305	14	theorem	theorem	VERB
ejpam-4492	305	15	3.10	3.10	NUM
ejpam-4492	305	16	.	.	PUNCT
ejpam-4492	306	1	for	for	ADP
ejpam-4492	306	2	an	an	DET
ejpam-4492	306	3	ar	ar	NOUN
ejpam-4492	306	4	=	=	NOUN
ejpam-4492	306	5	p⃗m(x1	p⃗m(x1	PROPN
ejpam-4492	306	6	)	)	PUNCT
ejpam-4492	306	7	•	•	NOUN
ejpam-4492	306	8	p⃗n(y1	p⃗n(y1	NOUN
ejpam-4492	306	9	)	)	PUNCT
ejpam-4492	306	10	,	,	PUNCT
ejpam-4492	306	11	i(dpt	i(dpt	PROPN
ejpam-4492	306	12	(	(	PUNCT
ejpam-4492	306	13	ar	ar	NOUN
ejpam-4492	306	14	)	)	PUNCT
ejpam-4492	306	15	)	)	PUNCT
ejpam-4492	307	1	=	=	PUNCT
ejpam-4492	307	2	(	(	PUNCT
ejpam-4492	307	3	m	m	VERB
ejpam-4492	307	4	+	+	NUM
ejpam-4492	307	5	n	n	CCONJ
ejpam-4492	307	6	)	)	PUNCT
ejpam-4492	307	7	−	−	PROPN
ejpam-4492	307	8	6	6	NUM
ejpam-4492	308	1	if	if	SCONJ
ejpam-4492	308	2	and	and	CCONJ
ejpam-4492	308	3	only	only	ADV
ejpam-4492	308	4	if	if	SCONJ
ejpam-4492	308	5	m	m	PROPN
ejpam-4492	308	6	,	,	PUNCT
ejpam-4492	308	7	n	n	PRON
ejpam-4492	308	8	≥	≥	NOUN
ejpam-4492	308	9	4	4	NUM
ejpam-4492	308	10	.	.	PUNCT
ejpam-4492	309	1	proof	proof	NOUN
ejpam-4492	309	2	:	:	PUNCT
ejpam-4492	309	3	suppose	suppose	VERB
ejpam-4492	309	4	that	that	SCONJ
ejpam-4492	309	5	i(dpt	i(dpt	ADP
ejpam-4492	309	6	(	(	PUNCT
ejpam-4492	309	7	ar	ar	NOUN
ejpam-4492	309	8	)	)	PUNCT
ejpam-4492	309	9	)	)	PUNCT
ejpam-4492	309	10	=	=	PUNCT
ejpam-4492	310	1	(	(	PUNCT
ejpam-4492	310	2	m+	m+	NOUN
ejpam-4492	310	3	n)−	n)−	PROPN
ejpam-4492	310	4	6	6	NUM
ejpam-4492	310	5	,	,	PUNCT
ejpam-4492	310	6	where	where	SCONJ
ejpam-4492	310	7	m	m	NOUN
ejpam-4492	310	8	,	,	PUNCT
ejpam-4492	310	9	n	n	CCONJ
ejpam-4492	310	10	<	<	X
ejpam-4492	310	11	4	4	X
ejpam-4492	310	12	.	.	PUNCT
ejpam-4492	311	1	let	let	VERB
ejpam-4492	311	2	m	m	PRON
ejpam-4492	311	3	,	,	PUNCT
ejpam-4492	311	4	n	n	PROPN
ejpam-4492	311	5	=	=	SYM
ejpam-4492	311	6	3	3	NUM
ejpam-4492	311	7	.	.	PUNCT
ejpam-4492	312	1	thus	thus	ADV
ejpam-4492	312	2	,	,	PUNCT
ejpam-4492	312	3	we	we	PRON
ejpam-4492	312	4	have	have	VERB
ejpam-4492	312	5	v1	v1	NOUN
ejpam-4492	312	6	,	,	PUNCT
ejpam-4492	312	7	v2	v2	PROPN
ejpam-4492	312	8	,	,	PUNCT
ejpam-4492	312	9	v3	v3	PROPN
ejpam-4492	312	10	,	,	PUNCT
ejpam-4492	312	11	v4	v4	PROPN
ejpam-4492	312	12	,	,	PUNCT
ejpam-4492	312	13	v5	v5	PROPN
ejpam-4492	312	14	,	,	PUNCT
ejpam-4492	312	15	v6	v6	NOUN
ejpam-4492	312	16	as	as	ADP
ejpam-4492	312	17	the	the	DET
ejpam-4492	312	18	vertices	vertex	NOUN
ejpam-4492	312	19	of	of	ADP
ejpam-4492	312	20	ar	ar	NOUN
ejpam-4492	312	21	and	and	CCONJ
ejpam-4492	312	22	e1	e1	PROPN
ejpam-4492	312	23	=	=	SYM
ejpam-4492	312	24	(	(	PUNCT
ejpam-4492	312	25	v1	v1	NOUN
ejpam-4492	312	26	,	,	PUNCT
ejpam-4492	312	27	v2	v2	PROPN
ejpam-4492	312	28	)	)	PUNCT
ejpam-4492	312	29	,	,	PUNCT
ejpam-4492	312	30	e2	e2	PROPN
ejpam-4492	312	31	=	=	SYM
ejpam-4492	312	32	(	(	PUNCT
ejpam-4492	312	33	v2	v2	PROPN
ejpam-4492	312	34	,	,	PUNCT
ejpam-4492	312	35	v3	v3	PROPN
ejpam-4492	312	36	)	)	PUNCT
ejpam-4492	312	37	,	,	PUNCT
ejpam-4492	312	38	e3	e3	NOUN
ejpam-4492	312	39	=	=	SYM
ejpam-4492	312	40	(	(	PUNCT
ejpam-4492	312	41	v1	v1	PROPN
ejpam-4492	312	42	,	,	PUNCT
ejpam-4492	312	43	v4	v4	NOUN
ejpam-4492	312	44	)	)	PUNCT
ejpam-4492	312	45	e4	e4	PROPN
ejpam-4492	312	46	=	=	SYM
ejpam-4492	312	47	(	(	PUNCT
ejpam-4492	312	48	v4	v4	NOUN
ejpam-4492	312	49	,	,	PUNCT
ejpam-4492	312	50	v5	v5	PROPN
ejpam-4492	312	51	)	)	PUNCT
ejpam-4492	312	52	as	as	ADP
ejpam-4492	312	53	the	the	DET
ejpam-4492	312	54	arcs	arcs	NOUN
ejpam-4492	312	55	of	of	ADP
ejpam-4492	312	56	ar	ar	PROPN
ejpam-4492	312	57	.	.	PROPN
ejpam-4492	313	1	then	then	ADV
ejpam-4492	313	2	the	the	DET
ejpam-4492	313	3	vertices	vertex	NOUN
ejpam-4492	313	4	of	of	ADP
ejpam-4492	313	5	t	t	PROPN
ejpam-4492	313	6	(	(	PUNCT
ejpam-4492	313	7	ar	ar	NOUN
ejpam-4492	313	8	)	)	PUNCT
ejpam-4492	313	9	are	be	AUX
ejpam-4492	313	10	{	{	PUNCT
ejpam-4492	313	11	v1	v1	NOUN
ejpam-4492	313	12	,	,	PUNCT
ejpam-4492	313	13	v2	v2	PROPN
ejpam-4492	313	14	,	,	PUNCT
ejpam-4492	313	15	v3	v3	PROPN
ejpam-4492	313	16	,	,	PUNCT
ejpam-4492	313	17	v4	v4	PROPN
ejpam-4492	313	18	,	,	PUNCT
ejpam-4492	313	19	v5	v5	NOUN
ejpam-4492	313	20	,	,	PUNCT
ejpam-4492	313	21	e1	e1	PROPN
ejpam-4492	313	22	,	,	PUNCT
ejpam-4492	313	23	e2	e2	PROPN
ejpam-4492	313	24	,	,	PUNCT
ejpam-4492	313	25	e3	e3	NOUN
ejpam-4492	313	26	,	,	PUNCT
ejpam-4492	313	27	e4	e4	PROPN
ejpam-4492	313	28	}	}	PUNCT
ejpam-4492	313	29	jill	jill	PROPN
ejpam-4492	313	30	maegan	maegan	PROPN
ejpam-4492	313	31	b.	b.	PROPN
ejpam-4492	313	32	pamplona	pamplona	PROPN
ejpam-4492	313	33	,	,	PUNCT
ejpam-4492	313	34	imelda	imelda	PROPN
ejpam-4492	313	35	s.	s.	PROPN
ejpam-4492	313	36	aniversario	aniversario	PROPN
ejpam-4492	313	37	/	/	SYM
ejpam-4492	313	38	eur	eur	PROPN
ejpam-4492	313	39	.	.	PUNCT
ejpam-4492	314	1	j.	j.	PROPN
ejpam-4492	314	2	pure	pure	PROPN
ejpam-4492	314	3	appl	appl	PROPN
ejpam-4492	314	4	.	.	PROPN
ejpam-4492	314	5	math	math	PROPN
ejpam-4492	314	6	,	,	PUNCT
ejpam-4492	314	7	15	15	NUM
ejpam-4492	314	8	(	(	PUNCT
ejpam-4492	314	9	3	3	NUM
ejpam-4492	314	10	)	)	PUNCT
ejpam-4492	314	11	(	(	PUNCT
ejpam-4492	314	12	2022	2022	NUM
ejpam-4492	314	13	)	)	PUNCT
ejpam-4492	314	14	,	,	PUNCT
ejpam-4492	314	15	1331	1331	NUM
ejpam-4492	314	16	-	-	SYM
ejpam-4492	314	17	1343	1343	NUM
ejpam-4492	314	18	1342	1342	NUM
ejpam-4492	314	19	and	and	CCONJ
ejpam-4492	314	20	the	the	DET
ejpam-4492	314	21	arcs	arc	NOUN
ejpam-4492	314	22	are	be	AUX
ejpam-4492	314	23	(	(	PUNCT
ejpam-4492	314	24	v1	v1	NOUN
ejpam-4492	314	25	,	,	PUNCT
ejpam-4492	314	26	v2	v2	PROPN
ejpam-4492	314	27	)	)	PUNCT
ejpam-4492	314	28	,	,	PUNCT
ejpam-4492	314	29	(	(	PUNCT
ejpam-4492	314	30	v2	v2	PROPN
ejpam-4492	314	31	,	,	PUNCT
ejpam-4492	314	32	v3	v3	PROPN
ejpam-4492	314	33	)	)	PUNCT
ejpam-4492	314	34	,	,	PUNCT
ejpam-4492	314	35	(	(	PUNCT
ejpam-4492	314	36	v1	v1	NOUN
ejpam-4492	314	37	,	,	PUNCT
ejpam-4492	314	38	v4	v4	NOUN
ejpam-4492	314	39	)	)	PUNCT
ejpam-4492	314	40	,	,	PUNCT
ejpam-4492	314	41	(	(	PUNCT
ejpam-4492	314	42	v4	v4	NOUN
ejpam-4492	314	43	,	,	PUNCT
ejpam-4492	314	44	v5	v5	PROPN
ejpam-4492	314	45	)	)	PUNCT
ejpam-4492	314	46	,	,	PUNCT
ejpam-4492	314	47	(	(	PUNCT
ejpam-4492	314	48	v1	v1	NOUN
ejpam-4492	314	49	,	,	PUNCT
ejpam-4492	314	50	e1	e1	PROPN
ejpam-4492	314	51	)	)	PUNCT
ejpam-4492	314	52	,	,	PUNCT
ejpam-4492	314	53	(	(	PUNCT
ejpam-4492	314	54	e1	e1	NOUN
ejpam-4492	314	55	,	,	PUNCT
ejpam-4492	314	56	v2	v2	PROPN
ejpam-4492	314	57	)	)	PUNCT
ejpam-4492	314	58	,	,	PUNCT
ejpam-4492	314	59	(	(	PUNCT
ejpam-4492	314	60	v2	v2	PROPN
ejpam-4492	314	61	,	,	PUNCT
ejpam-4492	314	62	e2	e2	PROPN
ejpam-4492	314	63	)	)	PUNCT
ejpam-4492	314	64	,	,	PUNCT
ejpam-4492	314	65	(	(	PUNCT
ejpam-4492	314	66	e2	e2	PROPN
ejpam-4492	314	67	,	,	PUNCT
ejpam-4492	314	68	v3	v3	PROPN
ejpam-4492	314	69	)	)	PUNCT
ejpam-4492	314	70	,	,	PUNCT
ejpam-4492	314	71	(	(	PUNCT
ejpam-4492	314	72	v1	v1	NOUN
ejpam-4492	314	73	,	,	PUNCT
ejpam-4492	314	74	e3	e3	NOUN
ejpam-4492	314	75	)	)	PUNCT
ejpam-4492	314	76	,	,	PUNCT
ejpam-4492	314	77	(	(	PUNCT
ejpam-4492	314	78	e3	e3	NOUN
ejpam-4492	314	79	,	,	PUNCT
ejpam-4492	314	80	v4	v4	NOUN
ejpam-4492	314	81	)	)	PUNCT
ejpam-4492	314	82	,	,	PUNCT
ejpam-4492	314	83	(	(	PUNCT
ejpam-4492	314	84	v4	v4	NOUN
ejpam-4492	314	85	,	,	PUNCT
ejpam-4492	314	86	e4	e4	PROPN
ejpam-4492	314	87	)	)	PUNCT
ejpam-4492	314	88	,	,	PUNCT
ejpam-4492	314	89	(	(	PUNCT
ejpam-4492	314	90	e4	e4	PROPN
ejpam-4492	314	91	,	,	PUNCT
ejpam-4492	314	92	v5	v5	PROPN
ejpam-4492	314	93	)	)	PUNCT
ejpam-4492	314	94	.	.	PUNCT
ejpam-4492	315	1	let	let	VERB
ejpam-4492	315	2	p	p	PROPN
ejpam-4492	315	3	(	(	PUNCT
ejpam-4492	315	4	ar	ar	NOUN
ejpam-4492	315	5	)	)	PUNCT
ejpam-4492	315	6	=	=	SYM
ejpam-4492	315	7	{	{	PUNCT
ejpam-4492	315	8	p1	p1	NOUN
ejpam-4492	315	9	,	,	PUNCT
ejpam-4492	315	10	p2	p2	NOUN
ejpam-4492	315	11	}	}	PUNCT
ejpam-4492	315	12	where	where	SCONJ
ejpam-4492	315	13	p1	p1	NOUN
ejpam-4492	315	14	=	=	PUNCT
ejpam-4492	316	1	[	[	X
ejpam-4492	316	2	v1v2	v1v2	X
ejpam-4492	316	3	,	,	PUNCT
ejpam-4492	316	4	v2v3	v2v3	NOUN
ejpam-4492	316	5	]	]	PUNCT
ejpam-4492	316	6	and	and	CCONJ
ejpam-4492	316	7	p2	p2	PROPN
ejpam-4492	316	8	=	=	PUNCT
ejpam-4492	317	1	[	[	X
ejpam-4492	317	2	v1v4	v1v4	X
ejpam-4492	317	3	,	,	PUNCT
ejpam-4492	317	4	v4v5	v4v5	NOUN
ejpam-4492	317	5	]	]	PUNCT
ejpam-4492	317	6	.	.	PUNCT
ejpam-4492	318	1	therefore	therefore	ADV
ejpam-4492	318	2	,	,	PUNCT
ejpam-4492	318	3	dpt	dpt	PROPN
ejpam-4492	318	4	(	(	PUNCT
ejpam-4492	318	5	ar	ar	PROPN
ejpam-4492	318	6	)	)	PUNCT
ejpam-4492	318	7	is	be	AUX
ejpam-4492	318	8	an	an	DET
ejpam-4492	318	9	outerplanar	outerplanar	NOUN
ejpam-4492	318	10	.	.	PUNCT
ejpam-4492	319	1	a	a	DET
ejpam-4492	319	2	contradiction	contradiction	NOUN
ejpam-4492	319	3	since	since	SCONJ
ejpam-4492	319	4	dpt	dpt	PROPN
ejpam-4492	319	5	(	(	PUNCT
ejpam-4492	319	6	ar	ar	NOUN
ejpam-4492	319	7	)	)	PUNCT
ejpam-4492	319	8	should	should	AUX
ejpam-4492	319	9	contain	contain	VERB
ejpam-4492	319	10	an	an	DET
ejpam-4492	319	11	internal	internal	ADJ
ejpam-4492	319	12	vertex	vertex	NOUN
ejpam-4492	319	13	.	.	PUNCT
ejpam-4492	320	1	conversely	conversely	ADV
ejpam-4492	320	2	,	,	PUNCT
ejpam-4492	320	3	suppose	suppose	VERB
ejpam-4492	320	4	thatar	thatar	NOUN
ejpam-4492	320	5	=	=	SYM
ejpam-4492	320	6	p⃗m(x1	p⃗m(x1	ADJ
ejpam-4492	320	7	)	)	PUNCT
ejpam-4492	320	8	•p⃗n(y1	•p⃗n(y1	NOUN
ejpam-4492	320	9	)	)	PUNCT
ejpam-4492	320	10	form	form	NOUN
ejpam-4492	320	11	,	,	PUNCT
ejpam-4492	320	12	n	n	PRON
ejpam-4492	320	13	≥	≥	NOUN
ejpam-4492	320	14	4	4	NUM
ejpam-4492	320	15	.	.	PUNCT
ejpam-4492	321	1	we	we	PRON
ejpam-4492	321	2	will	will	AUX
ejpam-4492	321	3	show	show	VERB
ejpam-4492	321	4	i(dpt	i(dpt	ADP
ejpam-4492	321	5	(	(	PUNCT
ejpam-4492	321	6	p⃗m(x1	p⃗m(x1	ADJ
ejpam-4492	321	7	)	)	PUNCT
ejpam-4492	321	8	•	•	NOUN
ejpam-4492	321	9	p⃗n(y1	p⃗n(y1	NOUN
ejpam-4492	321	10	)	)	PUNCT
ejpam-4492	321	11	)	)	PUNCT
ejpam-4492	321	12	)	)	PUNCT
ejpam-4492	322	1	=	=	PUNCT
ejpam-4492	322	2	(	(	PUNCT
ejpam-4492	322	3	m	m	VERB
ejpam-4492	322	4	+	+	NUM
ejpam-4492	322	5	n	n	CCONJ
ejpam-4492	322	6	)	)	PUNCT
ejpam-4492	322	7	−	−	ADP
ejpam-4492	322	8	6	6	NUM
ejpam-4492	322	9	by	by	ADP
ejpam-4492	322	10	induction	induction	NOUN
ejpam-4492	322	11	.	.	PUNCT
ejpam-4492	323	1	let	let	VERB
ejpam-4492	323	2	ar	ar	NOUN
ejpam-4492	323	3	=	=	SYM
ejpam-4492	323	4	p⃗4(x1	p⃗4(x1	ADJ
ejpam-4492	323	5	)	)	PUNCT
ejpam-4492	323	6	•	•	NUM
ejpam-4492	323	7	p⃗4(y1	p⃗4(y1	NUM
ejpam-4492	323	8	)	)	PUNCT
ejpam-4492	323	9	and	and	CCONJ
ejpam-4492	323	10	let	let	VERB
ejpam-4492	323	11	v	v	NOUN
ejpam-4492	323	12	(	(	PUNCT
ejpam-4492	323	13	p⃗4(x1	p⃗4(x1	ADJ
ejpam-4492	323	14	)	)	PUNCT
ejpam-4492	323	15	•	•	NUM
ejpam-4492	323	16	p⃗4(y1	p⃗4(y1	NOUN
ejpam-4492	323	17	)	)	PUNCT
ejpam-4492	323	18	)	)	PUNCT
ejpam-4492	324	1	=	=	PRON
ejpam-4492	324	2	{	{	PUNCT
ejpam-4492	324	3	v1	v1	PROPN
ejpam-4492	324	4	,	,	PUNCT
ejpam-4492	324	5	v2	v2	PROPN
ejpam-4492	324	6	,	,	PUNCT
ejpam-4492	324	7	v3	v3	PROPN
ejpam-4492	324	8	,	,	PUNCT
ejpam-4492	324	9	v4	v4	PROPN
ejpam-4492	324	10	,	,	PUNCT
ejpam-4492	324	11	v5	v5	PROPN
ejpam-4492	324	12	,	,	PUNCT
ejpam-4492	324	13	v6	v6	NOUN
ejpam-4492	324	14	,	,	PUNCT
ejpam-4492	324	15	v7	v7	NOUN
ejpam-4492	324	16	}	}	PUNCT
ejpam-4492	324	17	.	.	PUNCT
ejpam-4492	325	1	thus	thus	ADV
ejpam-4492	325	2	,	,	PUNCT
ejpam-4492	325	3	v	v	X
ejpam-4492	325	4	(	(	PUNCT
ejpam-4492	325	5	dpt	dpt	PROPN
ejpam-4492	325	6	(	(	PUNCT
ejpam-4492	325	7	p⃗4(x1	p⃗4(x1	ADJ
ejpam-4492	325	8	)	)	PUNCT
ejpam-4492	325	9	•p⃗4(y1	•p⃗4(y1	NOUN
ejpam-4492	325	10	)	)	PUNCT
ejpam-4492	325	11	)	)	PUNCT
ejpam-4492	325	12	)	)	PUNCT
ejpam-4492	326	1	=	=	PRON
ejpam-4492	326	2	{	{	PUNCT
ejpam-4492	326	3	v1	v1	PROPN
ejpam-4492	326	4	,	,	PUNCT
ejpam-4492	326	5	v2	v2	PROPN
ejpam-4492	326	6	,	,	PUNCT
ejpam-4492	326	7	v3	v3	PROPN
ejpam-4492	326	8	,	,	PUNCT
ejpam-4492	326	9	v4	v4	PROPN
ejpam-4492	326	10	,	,	PUNCT
ejpam-4492	326	11	v5	v5	PROPN
ejpam-4492	326	12	,	,	PUNCT
ejpam-4492	326	13	v6	v6	NOUN
ejpam-4492	326	14	,	,	PUNCT
ejpam-4492	326	15	v7	v7	NUM
ejpam-4492	326	16	,	,	PUNCT
ejpam-4492	326	17	e1	e1	PROPN
ejpam-4492	326	18	,	,	PUNCT
ejpam-4492	326	19	e2	e2	PROPN
ejpam-4492	326	20	,	,	PUNCT
ejpam-4492	326	21	e3	e3	NOUN
ejpam-4492	326	22	,	,	PUNCT
ejpam-4492	326	23	e4	e4	PROPN
ejpam-4492	326	24	,	,	PUNCT
ejpam-4492	326	25	e5	e5	PROPN
ejpam-4492	326	26	,	,	PUNCT
ejpam-4492	326	27	e6	e6	PROPN
ejpam-4492	326	28	,	,	PUNCT
ejpam-4492	326	29	p1	p1	NOUN
ejpam-4492	326	30	,	,	PUNCT
ejpam-4492	326	31	p2	p2	NOUN
ejpam-4492	326	32	}	}	PUNCT
ejpam-4492	326	33	where	where	SCONJ
ejpam-4492	326	34	e1	e1	NOUN
ejpam-4492	326	35	=	=	SYM
ejpam-4492	326	36	(	(	PUNCT
ejpam-4492	326	37	v1	v1	NOUN
ejpam-4492	326	38	,	,	PUNCT
ejpam-4492	326	39	v2	v2	PROPN
ejpam-4492	326	40	)	)	PUNCT
ejpam-4492	326	41	,	,	PUNCT
ejpam-4492	326	42	e2	e2	PROPN
ejpam-4492	326	43	=	=	SYM
ejpam-4492	326	44	(	(	PUNCT
ejpam-4492	326	45	v2	v2	PROPN
ejpam-4492	326	46	,	,	PUNCT
ejpam-4492	326	47	v3	v3	PROPN
ejpam-4492	326	48	)	)	PUNCT
ejpam-4492	326	49	,	,	PUNCT
ejpam-4492	326	50	e3	e3	NOUN
ejpam-4492	326	51	=	=	SYM
ejpam-4492	326	52	(	(	PUNCT
ejpam-4492	326	53	v3	v3	PROPN
ejpam-4492	326	54	,	,	PUNCT
ejpam-4492	326	55	v4	v4	PROPN
ejpam-4492	326	56	)	)	PUNCT
ejpam-4492	326	57	,	,	PUNCT
ejpam-4492	326	58	e4	e4	PROPN
ejpam-4492	326	59	=	=	SYM
ejpam-4492	326	60	(	(	PUNCT
ejpam-4492	326	61	v1	v1	PROPN
ejpam-4492	326	62	,	,	PUNCT
ejpam-4492	326	63	v5	v5	PROPN
ejpam-4492	326	64	)	)	PUNCT
ejpam-4492	326	65	,	,	PUNCT
ejpam-4492	326	66	e5	e5	PROPN
ejpam-4492	326	67	=	=	PUNCT
ejpam-4492	326	68	(	(	PUNCT
ejpam-4492	326	69	v5	v5	PROPN
ejpam-4492	326	70	,	,	PUNCT
ejpam-4492	326	71	v6	v6	NOUN
ejpam-4492	326	72	)	)	PUNCT
ejpam-4492	326	73	,	,	PUNCT
ejpam-4492	326	74	and	and	CCONJ
ejpam-4492	326	75	e6	e6	PROPN
ejpam-4492	326	76	=	=	SYM
ejpam-4492	326	77	(	(	PUNCT
ejpam-4492	326	78	v6	v6	NOUN
ejpam-4492	326	79	,	,	PUNCT
ejpam-4492	326	80	v7	v7	NUM
ejpam-4492	326	81	)	)	PUNCT
ejpam-4492	326	82	as	as	ADP
ejpam-4492	326	83	the	the	DET
ejpam-4492	326	84	arcs	arcs	NOUN
ejpam-4492	326	85	of	of	ADP
ejpam-4492	326	86	p⃗4(x1	p⃗4(x1	ADJ
ejpam-4492	326	87	)	)	PUNCT
ejpam-4492	326	88	•	•	NUM
ejpam-4492	326	89	p⃗4(y1	p⃗4(y1	NOUN
ejpam-4492	326	90	)	)	PUNCT
ejpam-4492	326	91	,	,	PUNCT
ejpam-4492	326	92	and	and	CCONJ
ejpam-4492	326	93	{	{	PUNCT
ejpam-4492	326	94	p1	p1	NOUN
ejpam-4492	326	95	,	,	PUNCT
ejpam-4492	326	96	p2	p2	PROPN
ejpam-4492	326	97	}	}	PUNCT
ejpam-4492	326	98	is	be	AUX
ejpam-4492	326	99	the	the	DET
ejpam-4492	326	100	pathos	pathos	NOUN
ejpam-4492	326	101	set	set	NOUN
ejpam-4492	326	102	of	of	ADP
ejpam-4492	326	103	p⃗4(x1	p⃗4(x1	ADJ
ejpam-4492	326	104	)	)	PUNCT
ejpam-4492	326	105	•	•	NUM
ejpam-4492	326	106	p⃗4(y1	p⃗4(y1	NOUN
ejpam-4492	326	107	)	)	PUNCT
ejpam-4492	326	108	.	.	PUNCT
ejpam-4492	327	1	hence	hence	ADV
ejpam-4492	327	2	,	,	PUNCT
ejpam-4492	327	3	a(dpt	a(dpt	PROPN
ejpam-4492	327	4	(	(	PUNCT
ejpam-4492	327	5	p⃗4(x1	p⃗4(x1	ADJ
ejpam-4492	327	6	)	)	PUNCT
ejpam-4492	327	7	•	•	NUM
ejpam-4492	327	8	p⃗4(y1	p⃗4(y1	NOUN
ejpam-4492	327	9	)	)	PUNCT
ejpam-4492	327	10	)	)	PUNCT
ejpam-4492	327	11	)	)	PUNCT
ejpam-4492	328	1	=	=	PRON
ejpam-4492	328	2	{	{	PUNCT
ejpam-4492	328	3	(	(	PUNCT
ejpam-4492	328	4	v1	v1	NOUN
ejpam-4492	328	5	,	,	PUNCT
ejpam-4492	328	6	v2	v2	PROPN
ejpam-4492	328	7	)	)	PUNCT
ejpam-4492	328	8	,	,	PUNCT
ejpam-4492	328	9	(	(	PUNCT
ejpam-4492	328	10	v2	v2	PROPN
ejpam-4492	328	11	,	,	PUNCT
ejpam-4492	328	12	v3	v3	PROPN
ejpam-4492	328	13	)	)	PUNCT
ejpam-4492	328	14	,	,	PUNCT
ejpam-4492	328	15	(	(	PUNCT
ejpam-4492	328	16	v3	v3	PROPN
ejpam-4492	328	17	,	,	PUNCT
ejpam-4492	328	18	v4	v4	PROPN
ejpam-4492	328	19	)	)	PUNCT
ejpam-4492	328	20	,	,	PUNCT
ejpam-4492	328	21	(	(	PUNCT
ejpam-4492	328	22	v1	v1	NOUN
ejpam-4492	328	23	,	,	PUNCT
ejpam-4492	328	24	v5	v5	PROPN
ejpam-4492	328	25	)	)	PUNCT
ejpam-4492	328	26	,	,	PUNCT
ejpam-4492	328	27	(	(	PUNCT
ejpam-4492	328	28	v5	v5	PROPN
ejpam-4492	328	29	,	,	PUNCT
ejpam-4492	328	30	v6	v6	NOUN
ejpam-4492	328	31	)	)	PUNCT
ejpam-4492	328	32	,	,	PUNCT
ejpam-4492	328	33	(	(	PUNCT
ejpam-4492	328	34	v6	v6	NOUN
ejpam-4492	328	35	,	,	PUNCT
ejpam-4492	328	36	v7	v7	NUM
ejpam-4492	328	37	)	)	PUNCT
ejpam-4492	328	38	,	,	PUNCT
ejpam-4492	328	39	(	(	PUNCT
ejpam-4492	328	40	v1	v1	NOUN
ejpam-4492	328	41	,	,	PUNCT
ejpam-4492	328	42	e1	e1	PROPN
ejpam-4492	328	43	)	)	PUNCT
ejpam-4492	328	44	,	,	PUNCT
ejpam-4492	328	45	(	(	PUNCT
ejpam-4492	328	46	e1	e1	NOUN
ejpam-4492	328	47	,	,	PUNCT
ejpam-4492	328	48	v2	v2	PROPN
ejpam-4492	328	49	)	)	PUNCT
ejpam-4492	328	50	,	,	PUNCT
ejpam-4492	328	51	(	(	PUNCT
ejpam-4492	328	52	v2	v2	PROPN
ejpam-4492	328	53	,	,	PUNCT
ejpam-4492	328	54	e2	e2	PROPN
ejpam-4492	328	55	)	)	PUNCT
ejpam-4492	328	56	,	,	PUNCT
ejpam-4492	328	57	(	(	PUNCT
ejpam-4492	328	58	e2	e2	PROPN
ejpam-4492	328	59	,	,	PUNCT
ejpam-4492	328	60	v3	v3	PROPN
ejpam-4492	328	61	)	)	PUNCT
ejpam-4492	328	62	,	,	PUNCT
ejpam-4492	328	63	(	(	PUNCT
ejpam-4492	328	64	v3	v3	PROPN
ejpam-4492	328	65	,	,	PUNCT
ejpam-4492	328	66	e3	e3	NOUN
ejpam-4492	328	67	)	)	PUNCT
ejpam-4492	328	68	,	,	PUNCT
ejpam-4492	328	69	(	(	PUNCT
ejpam-4492	328	70	e3	e3	NOUN
ejpam-4492	328	71	,	,	PUNCT
ejpam-4492	328	72	v4	v4	NOUN
ejpam-4492	328	73	)	)	PUNCT
ejpam-4492	328	74	,	,	PUNCT
ejpam-4492	328	75	(	(	PUNCT
ejpam-4492	328	76	v1	v1	NOUN
ejpam-4492	328	77	,	,	PUNCT
ejpam-4492	328	78	e4	e4	PROPN
ejpam-4492	328	79	)	)	PUNCT
ejpam-4492	328	80	,	,	PUNCT
ejpam-4492	328	81	(	(	PUNCT
ejpam-4492	328	82	e4	e4	PROPN
ejpam-4492	328	83	,	,	PUNCT
ejpam-4492	328	84	v5	v5	PROPN
ejpam-4492	328	85	)	)	PUNCT
ejpam-4492	328	86	,	,	PUNCT
ejpam-4492	328	87	(	(	PUNCT
ejpam-4492	328	88	v5	v5	PROPN
ejpam-4492	328	89	,	,	PUNCT
ejpam-4492	328	90	e6	e6	NOUN
ejpam-4492	328	91	)	)	PUNCT
ejpam-4492	328	92	,	,	PUNCT
ejpam-4492	328	93	(	(	PUNCT
ejpam-4492	328	94	e6	e6	PROPN
ejpam-4492	328	95	,	,	PUNCT
ejpam-4492	328	96	v7	v7	NUM
ejpam-4492	328	97	)	)	PUNCT
ejpam-4492	328	98	,	,	PUNCT
ejpam-4492	328	99	(	(	PUNCT
ejpam-4492	328	100	e1	e1	PROPN
ejpam-4492	328	101	,	,	PUNCT
ejpam-4492	328	102	e2	e2	PROPN
ejpam-4492	328	103	)	)	PUNCT
ejpam-4492	328	104	,	,	PUNCT
ejpam-4492	328	105	(	(	PUNCT
ejpam-4492	328	106	e2	e2	PROPN
ejpam-4492	328	107	,	,	PUNCT
ejpam-4492	328	108	e3	e3	NOUN
ejpam-4492	328	109	)	)	PUNCT
ejpam-4492	328	110	,	,	PUNCT
ejpam-4492	328	111	(	(	PUNCT
ejpam-4492	328	112	e4	e4	PROPN
ejpam-4492	328	113	,	,	PUNCT
ejpam-4492	328	114	e5	e5	PROPN
ejpam-4492	328	115	)	)	PUNCT
ejpam-4492	328	116	,	,	PUNCT
ejpam-4492	328	117	(	(	PUNCT
ejpam-4492	328	118	e5	e5	INTJ
ejpam-4492	328	119	,	,	PUNCT
ejpam-4492	328	120	e6	e6	PROPN
ejpam-4492	328	121	)	)	PUNCT
ejpam-4492	328	122	,	,	PUNCT
ejpam-4492	328	123	(	(	PUNCT
ejpam-4492	328	124	p1	p1	NOUN
ejpam-4492	328	125	,	,	PUNCT
ejpam-4492	328	126	e1	e1	PROPN
ejpam-4492	328	127	)	)	PUNCT
ejpam-4492	328	128	,	,	PUNCT
ejpam-4492	328	129	(	(	PUNCT
ejpam-4492	328	130	p1	p1	PROPN
ejpam-4492	328	131	,	,	PUNCT
ejpam-4492	328	132	e2	e2	PROPN
ejpam-4492	328	133	)	)	PUNCT
ejpam-4492	328	134	,	,	PUNCT
ejpam-4492	328	135	(	(	PUNCT
ejpam-4492	328	136	p1	p1	NOUN
ejpam-4492	328	137	,	,	PUNCT
ejpam-4492	328	138	e3	e3	NOUN
ejpam-4492	328	139	)	)	PUNCT
ejpam-4492	328	140	,	,	PUNCT
ejpam-4492	328	141	(	(	PUNCT
ejpam-4492	328	142	p2	p2	X
ejpam-4492	328	143	,	,	PUNCT
ejpam-4492	328	144	e4	e4	PROPN
ejpam-4492	328	145	)	)	PUNCT
ejpam-4492	328	146	,	,	PUNCT
ejpam-4492	328	147	(	(	PUNCT
ejpam-4492	328	148	p2	p2	X
ejpam-4492	328	149	,	,	PUNCT
ejpam-4492	328	150	e5	e5	PROPN
ejpam-4492	328	151	)	)	PUNCT
ejpam-4492	328	152	,	,	PUNCT
ejpam-4492	328	153	(	(	PUNCT
ejpam-4492	328	154	p2	p2	PROPN
ejpam-4492	328	155	,	,	PUNCT
ejpam-4492	328	156	e6	e6	NOUN
ejpam-4492	328	157	)	)	PUNCT
ejpam-4492	328	158	}	}	PUNCT
ejpam-4492	328	159	.	.	PUNCT
ejpam-4492	329	1	so	so	ADV
ejpam-4492	329	2	e2	e2	PROPN
ejpam-4492	329	3	and	and	CCONJ
ejpam-4492	329	4	e5	e5	PROPN
ejpam-4492	329	5	are	be	AUX
ejpam-4492	329	6	the	the	DET
ejpam-4492	329	7	only	only	ADJ
ejpam-4492	329	8	internal	internal	ADJ
ejpam-4492	329	9	vertices	vertex	NOUN
ejpam-4492	329	10	of	of	ADP
ejpam-4492	329	11	dpt	dpt	PROPN
ejpam-4492	329	12	(	(	PUNCT
ejpam-4492	329	13	p⃗4(x1	p⃗4(x1	ADJ
ejpam-4492	329	14	)	)	PUNCT
ejpam-4492	329	15	•	•	NUM
ejpam-4492	329	16	p⃗4(y1	p⃗4(y1	NOUN
ejpam-4492	329	17	)	)	PUNCT
ejpam-4492	329	18	)	)	PUNCT
ejpam-4492	329	19	.	.	PUNCT
ejpam-4492	330	1	that	that	PRON
ejpam-4492	330	2	is	be	AUX
ejpam-4492	330	3	,	,	PUNCT
ejpam-4492	330	4	i(dpt	i(dpt	PRON
ejpam-4492	330	5	(	(	PUNCT
ejpam-4492	330	6	ar	ar	NOUN
ejpam-4492	330	7	)	)	PUNCT
ejpam-4492	330	8	)	)	PUNCT
ejpam-4492	331	1	=	=	SYM
ejpam-4492	331	2	2	2	NUM
ejpam-4492	331	3	=	=	SYM
ejpam-4492	331	4	4	4	NUM
ejpam-4492	331	5	+	+	NUM
ejpam-4492	331	6	4−	4−	NUM
ejpam-4492	331	7	6	6	NUM
ejpam-4492	331	8	=	=	SYM
ejpam-4492	331	9	m+	m+	NUM
ejpam-4492	331	10	n−	n−	NOUN
ejpam-4492	331	11	6	6	NUM
ejpam-4492	331	12	.	.	PUNCT
ejpam-4492	331	13	assume	assume	VERB
ejpam-4492	331	14	that	that	SCONJ
ejpam-4492	331	15	form	form	NOUN
ejpam-4492	331	16	,	,	PUNCT
ejpam-4492	331	17	n	n	CCONJ
ejpam-4492	331	18	>	>	X
ejpam-4492	331	19	4	4	NUM
ejpam-4492	331	20	,	,	PUNCT
ejpam-4492	331	21	i(dpt	i(dpt	PRON
ejpam-4492	331	22	(	(	PUNCT
ejpam-4492	331	23	ar	ar	NOUN
ejpam-4492	331	24	)	)	PUNCT
ejpam-4492	331	25	)	)	PUNCT
ejpam-4492	332	1	=	=	SYM
ejpam-4492	332	2	(	(	PUNCT
ejpam-4492	332	3	m−1)+(n−1)−6	m−1)+(n−1)−6	NOUN
ejpam-4492	332	4	.	.	NOUN
ejpam-4492	332	5	that	that	PRON
ejpam-4492	332	6	is	be	AUX
ejpam-4492	332	7	,	,	PUNCT
ejpam-4492	332	8	v	v	PROPN
ejpam-4492	332	9	(	(	PUNCT
ejpam-4492	332	10	dpt	dpt	PROPN
ejpam-4492	332	11	(	(	PUNCT
ejpam-4492	332	12	ar	ar	NOUN
ejpam-4492	332	13	)	)	PUNCT
ejpam-4492	332	14	)	)	PUNCT
ejpam-4492	333	1	=	=	PRON
ejpam-4492	333	2	{	{	PUNCT
ejpam-4492	333	3	x1	x1	PROPN
ejpam-4492	333	4	,	,	PUNCT
ejpam-4492	333	5	x2	x2	PROPN
ejpam-4492	333	6	,	,	PUNCT
ejpam-4492	333	7	x3	x3	ADJ
ejpam-4492	333	8	,	,	PUNCT
ejpam-4492	333	9	.	.	PUNCT
ejpam-4492	333	10	.	.	PUNCT
ejpam-4492	333	11	.	.	PUNCT
ejpam-4492	334	1	,	,	PUNCT
ejpam-4492	334	2	xm−1	xm−1	PROPN
ejpam-4492	334	3	,	,	PUNCT
ejpam-4492	334	4	y1	y1	PROPN
ejpam-4492	334	5	,	,	PUNCT
ejpam-4492	334	6	y2	y2	PROPN
ejpam-4492	334	7	,	,	PUNCT
ejpam-4492	334	8	y3	y3	PROPN
ejpam-4492	334	9	,	,	PUNCT
ejpam-4492	334	10	.	.	PUNCT
ejpam-4492	334	11	.	.	PUNCT
ejpam-4492	335	1	.	.	PUNCT
ejpam-4492	336	1	,	,	PUNCT
ejpam-4492	336	2	yn−1	yn−1	PROPN
ejpam-4492	336	3	,	,	PUNCT
ejpam-4492	336	4	a1	a1	NOUN
ejpam-4492	336	5	,	,	PUNCT
ejpam-4492	336	6	a2	a2	PROPN
ejpam-4492	336	7	,	,	PUNCT
ejpam-4492	336	8	a3	a3	NOUN
ejpam-4492	336	9	,	,	PUNCT
ejpam-4492	336	10	.	.	PUNCT
ejpam-4492	336	11	.	.	PUNCT
ejpam-4492	337	1	.	.	PUNCT
ejpam-4492	338	1	,	,	PUNCT
ejpam-4492	338	2	am−2	am−2	PROPN
ejpam-4492	338	3	,	,	PUNCT
ejpam-4492	338	4	b1	b1	NOUN
ejpam-4492	338	5	,	,	PUNCT
ejpam-4492	338	6	b2	b2	NOUN
ejpam-4492	338	7	,	,	PUNCT
ejpam-4492	338	8	b3	b3	PROPN
ejpam-4492	338	9	,	,	PUNCT
ejpam-4492	338	10	.	.	PUNCT
ejpam-4492	338	11	.	.	PUNCT
ejpam-4492	339	1	.	.	PUNCT
ejpam-4492	340	1	,	,	PUNCT
ejpam-4492	340	2	bn−2	bn−2	PROPN
ejpam-4492	340	3	,	,	PUNCT
ejpam-4492	340	4	p1	p1	NOUN
ejpam-4492	340	5	,	,	PUNCT
ejpam-4492	340	6	p2	p2	PROPN
ejpam-4492	340	7	}	}	PUNCT
ejpam-4492	340	8	.	.	PUNCT
ejpam-4492	341	1	also	also	ADV
ejpam-4492	341	2	,	,	PUNCT
ejpam-4492	341	3	a(dpt	a(dpt	PROPN
ejpam-4492	341	4	(	(	PUNCT
ejpam-4492	341	5	ar	ar	NOUN
ejpam-4492	341	6	)	)	PUNCT
ejpam-4492	341	7	)	)	PUNCT
ejpam-4492	342	1	=	=	PRON
ejpam-4492	342	2	{	{	PUNCT
ejpam-4492	342	3	(	(	PUNCT
ejpam-4492	342	4	x1	x1	PROPN
ejpam-4492	342	5	,	,	PUNCT
ejpam-4492	342	6	x2	x2	PROPN
ejpam-4492	342	7	)	)	PUNCT
ejpam-4492	342	8	,	,	PUNCT
ejpam-4492	342	9	(	(	PUNCT
ejpam-4492	342	10	x2	x2	PROPN
ejpam-4492	342	11	,	,	PUNCT
ejpam-4492	342	12	x3	x3	ADJ
ejpam-4492	342	13	)	)	PUNCT
ejpam-4492	342	14	,	,	PUNCT
ejpam-4492	342	15	.	.	PUNCT
ejpam-4492	342	16	.	.	PUNCT
ejpam-4492	342	17	.	.	PUNCT
ejpam-4492	343	1	,	,	PUNCT
ejpam-4492	343	2	(	(	PUNCT
ejpam-4492	343	3	xm−2	xm−2	PROPN
ejpam-4492	343	4	,	,	PUNCT
ejpam-4492	343	5	xm−1	xm−1	PROPN
ejpam-4492	343	6	)	)	PUNCT
ejpam-4492	343	7	,	,	PUNCT
ejpam-4492	343	8	(	(	PUNCT
ejpam-4492	343	9	y1	y1	INTJ
ejpam-4492	343	10	,	,	PUNCT
ejpam-4492	343	11	y2	y2	PROPN
ejpam-4492	343	12	)	)	PUNCT
ejpam-4492	343	13	,	,	PUNCT
ejpam-4492	343	14	(	(	PUNCT
ejpam-4492	343	15	y2	y2	PROPN
ejpam-4492	343	16	,	,	PUNCT
ejpam-4492	343	17	y3	y3	PROPN
ejpam-4492	343	18	)	)	PUNCT
ejpam-4492	343	19	,	,	PUNCT
ejpam-4492	343	20	.	.	PUNCT
ejpam-4492	343	21	.	.	PUNCT
ejpam-4492	343	22	.	.	PUNCT
ejpam-4492	344	1	,	,	PUNCT
ejpam-4492	344	2	(	(	PUNCT
ejpam-4492	344	3	yn−2	yn−2	PROPN
ejpam-4492	344	4	,	,	PUNCT
ejpam-4492	344	5	yn−1	yn−1	NOUN
ejpam-4492	344	6	)	)	PUNCT
ejpam-4492	344	7	,	,	PUNCT
ejpam-4492	344	8	(	(	PUNCT
ejpam-4492	344	9	x1	x1	ADJ
ejpam-4492	344	10	,	,	PUNCT
ejpam-4492	344	11	a1	a1	NOUN
ejpam-4492	344	12	)	)	PUNCT
ejpam-4492	344	13	,	,	PUNCT
ejpam-4492	344	14	(	(	PUNCT
ejpam-4492	344	15	a1	a1	NOUN
ejpam-4492	344	16	,	,	PUNCT
ejpam-4492	344	17	x2	x2	PROPN
ejpam-4492	344	18	)	)	PUNCT
ejpam-4492	344	19	,	,	PUNCT
ejpam-4492	344	20	.	.	PUNCT
ejpam-4492	344	21	.	.	PUNCT
ejpam-4492	344	22	.	.	PUNCT
ejpam-4492	345	1	,	,	PUNCT
ejpam-4492	345	2	(	(	PUNCT
ejpam-4492	345	3	xm−2	xm−2	PROPN
ejpam-4492	345	4	,	,	PUNCT
ejpam-4492	345	5	am−2	am−2	PROPN
ejpam-4492	345	6	)	)	PUNCT
ejpam-4492	345	7	,	,	PUNCT
ejpam-4492	345	8	(	(	PUNCT
ejpam-4492	345	9	am−2	am−2	PROPN
ejpam-4492	345	10	,	,	PUNCT
ejpam-4492	345	11	xm−1	xm−1	PROPN
ejpam-4492	345	12	)	)	PUNCT
ejpam-4492	345	13	,	,	PUNCT
ejpam-4492	345	14	(	(	PUNCT
ejpam-4492	345	15	y1	y1	INTJ
ejpam-4492	345	16	,	,	PUNCT
ejpam-4492	345	17	b1	b1	NOUN
ejpam-4492	345	18	)	)	PUNCT
ejpam-4492	345	19	,	,	PUNCT
ejpam-4492	345	20	(	(	PUNCT
ejpam-4492	345	21	b1	b1	NOUN
ejpam-4492	345	22	,	,	PUNCT
ejpam-4492	345	23	y2	y2	PROPN
ejpam-4492	345	24	)	)	PUNCT
ejpam-4492	345	25	,	,	PUNCT
ejpam-4492	345	26	.	.	PUNCT
ejpam-4492	345	27	.	.	PUNCT
ejpam-4492	345	28	.	.	PUNCT
ejpam-4492	346	1	,	,	PUNCT
ejpam-4492	346	2	(	(	PUNCT
ejpam-4492	346	3	yn−2	yn−2	PROPN
ejpam-4492	346	4	,	,	PUNCT
ejpam-4492	346	5	bn−2	bn−2	PROPN
ejpam-4492	346	6	)	)	PUNCT
ejpam-4492	346	7	,	,	PUNCT
ejpam-4492	346	8	(	(	PUNCT
ejpam-4492	346	9	bn−2	bn−2	PROPN
ejpam-4492	346	10	,	,	PUNCT
ejpam-4492	346	11	yn−1	yn−1	NOUN
ejpam-4492	346	12	)	)	PUNCT
ejpam-4492	346	13	,	,	PUNCT
ejpam-4492	346	14	(	(	PUNCT
ejpam-4492	346	15	a1	a1	NOUN
ejpam-4492	346	16	,	,	PUNCT
ejpam-4492	346	17	a2	a2	PROPN
ejpam-4492	346	18	)	)	PUNCT
ejpam-4492	346	19	,	,	PUNCT
ejpam-4492	346	20	.	.	PUNCT
ejpam-4492	346	21	.	.	PUNCT
ejpam-4492	346	22	.	.	PUNCT
ejpam-4492	347	1	,	,	PUNCT
ejpam-4492	347	2	(	(	PUNCT
ejpam-4492	347	3	am−3	am−3	PROPN
ejpam-4492	347	4	,	,	PUNCT
ejpam-4492	347	5	am−2	am−2	PROPN
ejpam-4492	347	6	)	)	PUNCT
ejpam-4492	347	7	,	,	PUNCT
ejpam-4492	347	8	(	(	PUNCT
ejpam-4492	347	9	b1	b1	NOUN
ejpam-4492	347	10	,	,	PUNCT
ejpam-4492	347	11	b2	b2	NOUN
ejpam-4492	347	12	)	)	PUNCT
ejpam-4492	347	13	,	,	PUNCT
ejpam-4492	347	14	.	.	PUNCT
ejpam-4492	347	15	.	.	PUNCT
ejpam-4492	347	16	.	.	PUNCT
ejpam-4492	348	1	,	,	PUNCT
ejpam-4492	348	2	(	(	PUNCT
ejpam-4492	348	3	bn−3	bn−3	PROPN
ejpam-4492	348	4	,	,	PUNCT
ejpam-4492	348	5	bn−2	bn−2	PROPN
ejpam-4492	348	6	)	)	PUNCT
ejpam-4492	348	7	,	,	PUNCT
ejpam-4492	348	8	(	(	PUNCT
ejpam-4492	348	9	p1	p1	NOUN
ejpam-4492	348	10	,	,	PUNCT
ejpam-4492	348	11	a1	a1	NOUN
ejpam-4492	348	12	)	)	PUNCT
ejpam-4492	348	13	,	,	PUNCT
ejpam-4492	348	14	.	.	PUNCT
ejpam-4492	348	15	.	.	PUNCT
ejpam-4492	348	16	.	.	PUNCT
ejpam-4492	349	1	,	,	PUNCT
ejpam-4492	349	2	(	(	PUNCT
ejpam-4492	349	3	p1	p1	NOUN
ejpam-4492	349	4	,	,	PUNCT
ejpam-4492	349	5	am−2	am−2	PROPN
ejpam-4492	349	6	)	)	PUNCT
ejpam-4492	349	7	,	,	PUNCT
ejpam-4492	349	8	(	(	PUNCT
ejpam-4492	349	9	p2	p2	X
ejpam-4492	349	10	,	,	PUNCT
ejpam-4492	349	11	b1	b1	NOUN
ejpam-4492	349	12	)	)	PUNCT
ejpam-4492	349	13	,	,	PUNCT
ejpam-4492	349	14	.	.	PUNCT
ejpam-4492	349	15	.	.	PUNCT
ejpam-4492	349	16	.	.	PUNCT
ejpam-4492	350	1	,	,	PUNCT
ejpam-4492	350	2	(	(	PUNCT
ejpam-4492	350	3	p2	p2	PROPN
ejpam-4492	350	4	,	,	PUNCT
ejpam-4492	350	5	bn−2	bn−2	PROPN
ejpam-4492	350	6	)	)	PUNCT
ejpam-4492	350	7	}	}	PUNCT
ejpam-4492	350	8	.	.	PUNCT
ejpam-4492	351	1	it	it	PRON
ejpam-4492	351	2	follows	follow	VERB
ejpam-4492	351	3	that	that	SCONJ
ejpam-4492	351	4	a2	a2	PROPN
ejpam-4492	351	5	,	,	PUNCT
ejpam-4492	351	6	a3	a3	NOUN
ejpam-4492	351	7	,	,	PUNCT
ejpam-4492	351	8	.	.	PUNCT
ejpam-4492	351	9	.	.	PUNCT
ejpam-4492	352	1	.	.	PUNCT
ejpam-4492	353	1	,	,	PUNCT
ejpam-4492	353	2	am−3	am−3	PROPN
ejpam-4492	353	3	and	and	CCONJ
ejpam-4492	353	4	b2	b2	NOUN
ejpam-4492	353	5	,	,	PUNCT
ejpam-4492	353	6	b3	b3	PROPN
ejpam-4492	353	7	,	,	PUNCT
ejpam-4492	353	8	.	.	PUNCT
ejpam-4492	353	9	.	.	PUNCT
ejpam-4492	354	1	.	.	PUNCT
ejpam-4492	355	1	,	,	PUNCT
ejpam-4492	355	2	bn−3	bn−3	PROPN
ejpam-4492	355	3	are	be	AUX
ejpam-4492	355	4	the	the	DET
ejpam-4492	355	5	internal	internal	ADJ
ejpam-4492	355	6	vertices	vertex	NOUN
ejpam-4492	355	7	of	of	ADP
ejpam-4492	355	8	dpt	dpt	PROPN
ejpam-4492	355	9	(	(	PUNCT
ejpam-4492	355	10	ar	ar	PROPN
ejpam-4492	355	11	)	)	PUNCT
ejpam-4492	355	12	.	.	PUNCT
ejpam-4492	356	1	that	that	PRON
ejpam-4492	356	2	is	be	AUX
ejpam-4492	356	3	i(dpt	i(dpt	PRON
ejpam-4492	356	4	(	(	PUNCT
ejpam-4492	356	5	p⃗m−1(x1	p⃗m−1(x1	NOUN
ejpam-4492	356	6	)	)	PUNCT
ejpam-4492	356	7	•	•	X
ejpam-4492	356	8	p⃗n−1(y1	p⃗n−1(y1	NOUN
ejpam-4492	356	9	)	)	PUNCT
ejpam-4492	356	10	)	)	PUNCT
ejpam-4492	356	11	)	)	PUNCT
ejpam-4492	357	1	=	=	PUNCT
ejpam-4492	357	2	m−3−1+n−3−1	m−3−1+n−3−1	NOUN
ejpam-4492	357	3	=	=	PUNCT
ejpam-4492	357	4	m+n−4	m+n−4	NOUN
ejpam-4492	357	5	.	.	PUNCT
ejpam-4492	358	1	now	now	ADV
ejpam-4492	358	2	,	,	PUNCT
ejpam-4492	358	3	adding	add	VERB
ejpam-4492	358	4	one	one	NUM
ejpam-4492	358	5	vertex	vertex	NOUN
ejpam-4492	358	6	to	to	ADP
ejpam-4492	358	7	the	the	DET
ejpam-4492	358	8	right	right	ADJ
ejpam-4492	358	9	sides	side	NOUN
ejpam-4492	358	10	of	of	ADP
ejpam-4492	358	11	xm−1	xm−1	PROPN
ejpam-4492	358	12	and	and	CCONJ
ejpam-4492	358	13	yn−1	yn−1	NOUN
ejpam-4492	358	14	of	of	ADP
ejpam-4492	358	15	p⃗m−1	p⃗m−1	NOUN
ejpam-4492	358	16	and	and	CCONJ
ejpam-4492	358	17	pn−1	pn−1	PROPN
ejpam-4492	358	18	to	to	PART
ejpam-4492	358	19	obtain	obtain	VERB
ejpam-4492	358	20	p⃗m•p⃗n	p⃗m•p⃗n	NOUN
ejpam-4492	358	21	,	,	PUNCT
ejpam-4492	358	22	we	we	PRON
ejpam-4492	358	23	will	will	AUX
ejpam-4492	358	24	have	have	VERB
ejpam-4492	358	25	v	v	X
ejpam-4492	358	26	(	(	PUNCT
ejpam-4492	358	27	dpt	dpt	PROPN
ejpam-4492	358	28	(	(	PUNCT
ejpam-4492	358	29	p⃗m(x1	p⃗m(x1	PROPN
ejpam-4492	358	30	)	)	PUNCT
ejpam-4492	358	31	•p⃗n(y1	•p⃗n(y1	NOUN
ejpam-4492	358	32	)	)	PUNCT
ejpam-4492	358	33	)	)	PUNCT
ejpam-4492	358	34	)	)	PUNCT
ejpam-4492	359	1	=	=	PRON
ejpam-4492	359	2	{	{	PUNCT
ejpam-4492	359	3	x1	x1	PROPN
ejpam-4492	359	4	,	,	PUNCT
ejpam-4492	359	5	x2	x2	PROPN
ejpam-4492	359	6	,	,	PUNCT
ejpam-4492	359	7	x3	x3	ADJ
ejpam-4492	359	8	,	,	PUNCT
ejpam-4492	359	9	.	.	PUNCT
ejpam-4492	359	10	.	.	PUNCT
ejpam-4492	359	11	.	.	PUNCT
ejpam-4492	360	1	,	,	PUNCT
ejpam-4492	360	2	xm−1	xm−1	PROPN
ejpam-4492	360	3	,	,	PUNCT
ejpam-4492	360	4	xm	xm	PROPN
ejpam-4492	360	5	,	,	PUNCT
ejpam-4492	360	6	y1	y1	PROPN
ejpam-4492	360	7	,	,	PUNCT
ejpam-4492	360	8	y2	y2	PROPN
ejpam-4492	360	9	,	,	PUNCT
ejpam-4492	360	10	y3	y3	PROPN
ejpam-4492	360	11	,	,	PUNCT
ejpam-4492	360	12	.	.	PUNCT
ejpam-4492	360	13	.	.	PUNCT
ejpam-4492	361	1	.	.	PUNCT
ejpam-4492	362	1	,	,	PUNCT
ejpam-4492	362	2	yn−1	yn−1	PROPN
ejpam-4492	362	3	,	,	PUNCT
ejpam-4492	362	4	yn	yn	PROPN
ejpam-4492	362	5	,	,	PUNCT
ejpam-4492	362	6	a1	a1	PROPN
ejpam-4492	362	7	,	,	PUNCT
ejpam-4492	362	8	a2	a2	PROPN
ejpam-4492	362	9	,	,	PUNCT
ejpam-4492	362	10	a3	a3	NOUN
ejpam-4492	362	11	,	,	PUNCT
ejpam-4492	362	12	.	.	PUNCT
ejpam-4492	362	13	.	.	PUNCT
ejpam-4492	363	1	.	.	PUNCT
ejpam-4492	364	1	,	,	PUNCT
ejpam-4492	364	2	am−2	am−2	PROPN
ejpam-4492	364	3	,	,	PUNCT
ejpam-4492	364	4	am−1	am−1	PROPN
ejpam-4492	364	5	,	,	PUNCT
ejpam-4492	364	6	b1	b1	PROPN
ejpam-4492	364	7	,	,	PUNCT
ejpam-4492	364	8	b2	b2	NOUN
ejpam-4492	364	9	,	,	PUNCT
ejpam-4492	364	10	b3	b3	PROPN
ejpam-4492	364	11	,	,	PUNCT
ejpam-4492	364	12	.	.	PUNCT
ejpam-4492	364	13	.	.	PUNCT
ejpam-4492	365	1	.	.	PUNCT
ejpam-4492	366	1	,	,	PUNCT
ejpam-4492	366	2	bn−2	bn−2	PROPN
ejpam-4492	366	3	,	,	PUNCT
ejpam-4492	366	4	bn−1	bn−1	ADJ
ejpam-4492	366	5	,	,	PUNCT
ejpam-4492	366	6	p1	p1	NOUN
ejpam-4492	366	7	,	,	PUNCT
ejpam-4492	366	8	p2	p2	PROPN
ejpam-4492	366	9	}	}	PUNCT
ejpam-4492	366	10	.	.	PUNCT
ejpam-4492	367	1	also	also	ADV
ejpam-4492	367	2	,	,	PUNCT
ejpam-4492	367	3	a(dpt	a(dpt	PROPN
ejpam-4492	367	4	(	(	PUNCT
ejpam-4492	367	5	ar	ar	NOUN
ejpam-4492	367	6	)	)	PUNCT
ejpam-4492	367	7	)	)	PUNCT
ejpam-4492	368	1	=	=	PRON
ejpam-4492	368	2	{	{	PUNCT
ejpam-4492	368	3	(	(	PUNCT
ejpam-4492	368	4	x1	x1	PROPN
ejpam-4492	368	5	,	,	PUNCT
ejpam-4492	368	6	x2	x2	PROPN
ejpam-4492	368	7	)	)	PUNCT
ejpam-4492	368	8	,	,	PUNCT
ejpam-4492	368	9	(	(	PUNCT
ejpam-4492	368	10	x2	x2	PROPN
ejpam-4492	368	11	,	,	PUNCT
ejpam-4492	368	12	x3	x3	ADJ
ejpam-4492	368	13	)	)	PUNCT
ejpam-4492	368	14	,	,	PUNCT
ejpam-4492	368	15	.	.	PUNCT
ejpam-4492	368	16	.	.	PUNCT
ejpam-4492	368	17	.	.	PUNCT
ejpam-4492	369	1	,	,	PUNCT
ejpam-4492	369	2	(	(	PUNCT
ejpam-4492	369	3	xm−2	xm−2	PROPN
ejpam-4492	369	4	,	,	PUNCT
ejpam-4492	369	5	xm−1	xm−1	PROPN
ejpam-4492	369	6	)	)	PUNCT
ejpam-4492	369	7	,	,	PUNCT
ejpam-4492	369	8	(	(	PUNCT
ejpam-4492	369	9	xm−1	xm−1	PROPN
ejpam-4492	369	10	,	,	PUNCT
ejpam-4492	369	11	xm	xm	PROPN
ejpam-4492	369	12	)	)	PUNCT
ejpam-4492	369	13	,	,	PUNCT
ejpam-4492	369	14	(	(	PUNCT
ejpam-4492	369	15	y1	y1	INTJ
ejpam-4492	369	16	,	,	PUNCT
ejpam-4492	369	17	y2	y2	PROPN
ejpam-4492	369	18	)	)	PUNCT
ejpam-4492	369	19	,	,	PUNCT
ejpam-4492	369	20	(	(	PUNCT
ejpam-4492	369	21	y2	y2	PROPN
ejpam-4492	369	22	,	,	PUNCT
ejpam-4492	369	23	y3	y3	PROPN
ejpam-4492	369	24	)	)	PUNCT
ejpam-4492	369	25	,	,	PUNCT
ejpam-4492	369	26	.	.	PUNCT
ejpam-4492	369	27	.	.	PUNCT
ejpam-4492	369	28	.	.	PUNCT
ejpam-4492	370	1	,	,	PUNCT
ejpam-4492	370	2	(	(	PUNCT
ejpam-4492	370	3	yn−2	yn−2	PROPN
ejpam-4492	370	4	,	,	PUNCT
ejpam-4492	370	5	yn−1	yn−1	NOUN
ejpam-4492	370	6	)	)	PUNCT
ejpam-4492	370	7	,	,	PUNCT
ejpam-4492	370	8	(	(	PUNCT
ejpam-4492	370	9	yn−1	yn−1	PROPN
ejpam-4492	370	10	,	,	PUNCT
ejpam-4492	370	11	yn	yn	PROPN
ejpam-4492	370	12	)	)	PUNCT
ejpam-4492	370	13	,	,	PUNCT
ejpam-4492	370	14	(	(	PUNCT
ejpam-4492	370	15	x1	x1	ADJ
ejpam-4492	370	16	,	,	PUNCT
ejpam-4492	370	17	a1	a1	NOUN
ejpam-4492	370	18	)	)	PUNCT
ejpam-4492	370	19	,	,	PUNCT
ejpam-4492	370	20	(	(	PUNCT
ejpam-4492	370	21	a1	a1	NOUN
ejpam-4492	370	22	,	,	PUNCT
ejpam-4492	370	23	x2	x2	PROPN
ejpam-4492	370	24	)	)	PUNCT
ejpam-4492	370	25	,	,	PUNCT
ejpam-4492	370	26	.	.	PUNCT
ejpam-4492	370	27	.	.	PUNCT
ejpam-4492	370	28	.	.	PUNCT
ejpam-4492	371	1	,	,	PUNCT
ejpam-4492	371	2	(	(	PUNCT
ejpam-4492	371	3	xm−2	xm−2	PROPN
ejpam-4492	371	4	,	,	PUNCT
ejpam-4492	371	5	am−2	am−2	PROPN
ejpam-4492	371	6	)	)	PUNCT
ejpam-4492	371	7	,	,	PUNCT
ejpam-4492	371	8	(	(	PUNCT
ejpam-4492	371	9	am−2	am−2	PROPN
ejpam-4492	371	10	,	,	PUNCT
ejpam-4492	371	11	xm−1	xm−1	PROPN
ejpam-4492	371	12	)	)	PUNCT
ejpam-4492	371	13	,	,	PUNCT
ejpam-4492	371	14	(	(	PUNCT
ejpam-4492	371	15	y1	y1	INTJ
ejpam-4492	371	16	,	,	PUNCT
ejpam-4492	371	17	b1	b1	NOUN
ejpam-4492	371	18	)	)	PUNCT
ejpam-4492	371	19	,	,	PUNCT
ejpam-4492	371	20	(	(	PUNCT
ejpam-4492	371	21	b1	b1	NOUN
ejpam-4492	371	22	,	,	PUNCT
ejpam-4492	371	23	y2	y2	PROPN
ejpam-4492	371	24	)	)	PUNCT
ejpam-4492	371	25	,	,	PUNCT
ejpam-4492	371	26	.	.	PUNCT
ejpam-4492	371	27	.	.	PUNCT
ejpam-4492	371	28	.	.	PUNCT
ejpam-4492	372	1	,	,	PUNCT
ejpam-4492	372	2	(	(	PUNCT
ejpam-4492	372	3	yn−2	yn−2	PROPN
ejpam-4492	372	4	,	,	PUNCT
ejpam-4492	372	5	bn−2	bn−2	PROPN
ejpam-4492	372	6	)	)	PUNCT
ejpam-4492	372	7	,	,	PUNCT
ejpam-4492	372	8	(	(	PUNCT
ejpam-4492	372	9	bn−2	bn−2	PROPN
ejpam-4492	372	10	,	,	PUNCT
ejpam-4492	372	11	yn−1	yn−1	NOUN
ejpam-4492	372	12	)	)	PUNCT
ejpam-4492	372	13	,	,	PUNCT
ejpam-4492	372	14	(	(	PUNCT
ejpam-4492	372	15	a1	a1	NOUN
ejpam-4492	372	16	,	,	PUNCT
ejpam-4492	372	17	a2	a2	PROPN
ejpam-4492	372	18	)	)	PUNCT
ejpam-4492	372	19	,	,	PUNCT
ejpam-4492	372	20	.	.	PUNCT
ejpam-4492	372	21	.	.	PUNCT
ejpam-4492	372	22	.	.	PUNCT
ejpam-4492	373	1	,	,	PUNCT
ejpam-4492	373	2	(	(	PUNCT
ejpam-4492	373	3	am−3	am−3	PROPN
ejpam-4492	373	4	,	,	PUNCT
ejpam-4492	373	5	am−2	am−2	PROPN
ejpam-4492	373	6	)	)	PUNCT
ejpam-4492	373	7	,	,	PUNCT
ejpam-4492	373	8	(	(	PUNCT
ejpam-4492	373	9	am−2	am−2	PROPN
ejpam-4492	373	10	,	,	PUNCT
ejpam-4492	373	11	am−1	am−1	PROPN
ejpam-4492	373	12	)	)	PUNCT
ejpam-4492	373	13	,	,	PUNCT
ejpam-4492	373	14	(	(	PUNCT
ejpam-4492	373	15	b1	b1	NOUN
ejpam-4492	373	16	,	,	PUNCT
ejpam-4492	373	17	b2	b2	NOUN
ejpam-4492	373	18	)	)	PUNCT
ejpam-4492	373	19	,	,	PUNCT
ejpam-4492	373	20	.	.	PUNCT
ejpam-4492	373	21	.	.	PUNCT
ejpam-4492	373	22	.	.	PUNCT
ejpam-4492	374	1	,	,	PUNCT
ejpam-4492	374	2	(	(	PUNCT
ejpam-4492	374	3	bn−3	bn−3	PROPN
ejpam-4492	374	4	,	,	PUNCT
ejpam-4492	374	5	bn−2	bn−2	PROPN
ejpam-4492	374	6	)	)	PUNCT
ejpam-4492	374	7	,	,	PUNCT
ejpam-4492	374	8	(	(	PUNCT
ejpam-4492	374	9	bn−2	bn−2	PROPN
ejpam-4492	374	10	,	,	PUNCT
ejpam-4492	374	11	bn−1	bn−1	NOUN
ejpam-4492	374	12	)	)	PUNCT
ejpam-4492	374	13	,	,	PUNCT
ejpam-4492	374	14	(	(	PUNCT
ejpam-4492	374	15	p1	p1	NOUN
ejpam-4492	374	16	,	,	PUNCT
ejpam-4492	374	17	a1	a1	NOUN
ejpam-4492	374	18	)	)	PUNCT
ejpam-4492	374	19	,	,	PUNCT
ejpam-4492	374	20	.	.	PUNCT
ejpam-4492	374	21	.	.	PUNCT
ejpam-4492	374	22	.	.	PUNCT
ejpam-4492	375	1	,	,	PUNCT
ejpam-4492	375	2	(	(	PUNCT
ejpam-4492	375	3	p1	p1	NOUN
ejpam-4492	375	4	,	,	PUNCT
ejpam-4492	375	5	am−2	am−2	PROPN
ejpam-4492	375	6	)	)	PUNCT
ejpam-4492	375	7	,	,	PUNCT
ejpam-4492	375	8	(	(	PUNCT
ejpam-4492	375	9	p1	p1	PROPN
ejpam-4492	375	10	,	,	PUNCT
ejpam-4492	375	11	am−1	am−1	PROPN
ejpam-4492	375	12	)	)	PUNCT
ejpam-4492	375	13	,	,	PUNCT
ejpam-4492	375	14	(	(	PUNCT
ejpam-4492	375	15	p2	p2	X
ejpam-4492	375	16	,	,	PUNCT
ejpam-4492	375	17	b1	b1	NOUN
ejpam-4492	375	18	)	)	PUNCT
ejpam-4492	375	19	,	,	PUNCT
ejpam-4492	375	20	.	.	PUNCT
ejpam-4492	375	21	.	.	PUNCT
ejpam-4492	375	22	.	.	PUNCT
ejpam-4492	376	1	,	,	PUNCT
ejpam-4492	376	2	(	(	PUNCT
ejpam-4492	376	3	p2	p2	PROPN
ejpam-4492	376	4	,	,	PUNCT
ejpam-4492	376	5	bn−2	bn−2	PROPN
ejpam-4492	376	6	)	)	PUNCT
ejpam-4492	376	7	,	,	PUNCT
ejpam-4492	376	8	(	(	PUNCT
ejpam-4492	376	9	p2	p2	X
ejpam-4492	376	10	,	,	PUNCT
ejpam-4492	376	11	bn−1	bn−1	NOUN
ejpam-4492	376	12	)	)	PUNCT
ejpam-4492	376	13	}	}	PUNCT
ejpam-4492	376	14	.	.	PUNCT
ejpam-4492	377	1	therefore	therefore	ADV
ejpam-4492	377	2	,	,	PUNCT
ejpam-4492	377	3	the	the	DET
ejpam-4492	377	4	vertices	vertex	NOUN
ejpam-4492	377	5	a2	a2	PROPN
ejpam-4492	377	6	,	,	PUNCT
ejpam-4492	377	7	a3	a3	NOUN
ejpam-4492	377	8	,	,	PUNCT
ejpam-4492	377	9	.	.	PUNCT
ejpam-4492	377	10	.	.	PUNCT
ejpam-4492	377	11	.	.	PUNCT
ejpam-4492	378	1	,	,	PUNCT
ejpam-4492	378	2	am−2	am−2	PROPN
ejpam-4492	378	3	and	and	CCONJ
ejpam-4492	378	4	b2	b2	NOUN
ejpam-4492	378	5	,	,	PUNCT
ejpam-4492	378	6	b3	b3	PROPN
ejpam-4492	378	7	,	,	PUNCT
ejpam-4492	378	8	.	.	PUNCT
ejpam-4492	378	9	.	.	PUNCT
ejpam-4492	379	1	.	.	PUNCT
ejpam-4492	380	1	,	,	PUNCT
ejpam-4492	380	2	bn−2	bn−2	PROPN
ejpam-4492	380	3	are	be	AUX
ejpam-4492	380	4	the	the	DET
ejpam-4492	380	5	internal	internal	ADJ
ejpam-4492	380	6	vertices	vertex	NOUN
ejpam-4492	380	7	of	of	ADP
ejpam-4492	380	8	dpt	dpt	PROPN
ejpam-4492	380	9	(	(	PUNCT
ejpam-4492	380	10	ar	ar	PROPN
ejpam-4492	380	11	)	)	PUNCT
ejpam-4492	380	12	.	.	PUNCT
ejpam-4492	381	1	that	that	PRON
ejpam-4492	381	2	is	be	AUX
ejpam-4492	381	3	,	,	PUNCT
ejpam-4492	381	4	i(dpt	i(dpt	ADV
ejpam-4492	381	5	(	(	PUNCT
ejpam-4492	381	6	p⃗m(x1	p⃗m(x1	ADJ
ejpam-4492	381	7	)	)	PUNCT
ejpam-4492	381	8	•	•	NOUN
ejpam-4492	381	9	p⃗n(y1	p⃗n(y1	NOUN
ejpam-4492	381	10	)	)	PUNCT
ejpam-4492	381	11	)	)	PUNCT
ejpam-4492	381	12	)	)	PUNCT
ejpam-4492	382	1	=	=	PUNCT
ejpam-4492	383	1	m	m	VERB
ejpam-4492	383	2	−	−	NOUN
ejpam-4492	383	3	3	3	NUM
ejpam-4492	383	4	+	+	CCONJ
ejpam-4492	383	5	n	n	CCONJ
ejpam-4492	383	6	−	−	NUM
ejpam-4492	383	7	3	3	NUM
ejpam-4492	383	8	=	=	SYM
ejpam-4492	383	9	m+	m+	NUM
ejpam-4492	383	10	n−	n−	NOUN
ejpam-4492	383	11	6	6	NUM
ejpam-4492	383	12	.	.	PUNCT
ejpam-4492	384	1	acknowledgements	acknowledgement	NOUN
ejpam-4492	384	2	this	this	DET
ejpam-4492	384	3	research	research	NOUN
ejpam-4492	384	4	is	be	AUX
ejpam-4492	384	5	funded	fund	VERB
ejpam-4492	384	6	by	by	ADP
ejpam-4492	384	7	the	the	DET
ejpam-4492	384	8	department	department	PROPN
ejpam-4492	384	9	of	of	ADP
ejpam-4492	384	10	science	science	NOUN
ejpam-4492	384	11	and	and	CCONJ
ejpam-4492	384	12	technology	technology	NOUN
ejpam-4492	384	13	accelerated	accelerate	VERB
ejpam-4492	384	14	science	science	NOUN
ejpam-4492	384	15	and	and	CCONJ
ejpam-4492	384	16	technology	technology	NOUN
ejpam-4492	384	17	human	human	ADJ
ejpam-4492	384	18	resource	resource	NOUN
ejpam-4492	384	19	development	development	NOUN
ejpam-4492	384	20	program	program	NOUN
ejpam-4492	384	21	(	(	PUNCT
ejpam-4492	384	22	dost	dost	NOUN
ejpam-4492	384	23	-	-	PUNCT
ejpam-4492	384	24	asthrdp	asthrdp	NOUN
ejpam-4492	384	25	)	)	PUNCT
ejpam-4492	384	26	,	,	PUNCT
ejpam-4492	384	27	philippines	philippine	NOUN
ejpam-4492	384	28	.	.	PUNCT
ejpam-4492	385	1	references	reference	NOUN
ejpam-4492	385	2	1343	1343	NUM
ejpam-4492	385	3	references	reference	NOUN
ejpam-4492	385	4	[	[	X
ejpam-4492	385	5	1	1	NUM
ejpam-4492	385	6	]	]	X
ejpam-4492	385	7	m	m	VERB
ejpam-4492	385	8	behzad	behzad	PROPN
ejpam-4492	385	9	.	.	PUNCT
ejpam-4492	386	1	graphs	graph	NOUN
ejpam-4492	386	2	and	and	CCONJ
ejpam-4492	386	3	their	their	PRON
ejpam-4492	386	4	chromatic	chromatic	ADJ
ejpam-4492	386	5	numbers	number	NOUN
ejpam-4492	386	6	.	.	PUNCT
ejpam-4492	387	1	doctoral	doctoral	ADJ
ejpam-4492	387	2	thesis	thesis	NOUN
ejpam-4492	387	3	,	,	PUNCT
ejpam-4492	387	4	michigan	michigan	PROPN
ejpam-4492	387	5	state	state	PROPN
ejpam-4492	387	6	university	university	PROPN
ejpam-4492	387	7	,	,	PUNCT
ejpam-4492	387	8	1967	1967	NUM
ejpam-4492	387	9	.	.	PUNCT
ejpam-4492	388	1	[	[	X
ejpam-4492	388	2	2	2	X
ejpam-4492	388	3	]	]	PUNCT
ejpam-4492	388	4	g	g	NOUN
ejpam-4492	388	5	chartrand	chartrand	NOUN
ejpam-4492	388	6	and	and	CCONJ
ejpam-4492	388	7	mj	mj	PROPN
ejpam-4492	388	8	stewart	stewart	PROPN
ejpam-4492	388	9	.	.	PUNCT
ejpam-4492	389	1	total	total	ADJ
ejpam-4492	389	2	digraph	digraph	NOUN
ejpam-4492	389	3	.	.	PUNCT
ejpam-4492	390	1	canadian	canadian	ADJ
ejpam-4492	390	2	math	math	NOUN
ejpam-4492	390	3	.	.	PUNCT
ejpam-4492	391	1	bull	bull	PROPN
ejpam-4492	391	2	.	.	PUNCT
ejpam-4492	391	3	,	,	PUNCT
ejpam-4492	391	4	9:171–176	9:171–176	NOUN
ejpam-4492	391	5	,	,	PUNCT
ejpam-4492	391	6	1966	1966	NUM
ejpam-4492	391	7	.	.	PUNCT
ejpam-4492	392	1	[	[	X
ejpam-4492	392	2	3	3	X
ejpam-4492	392	3	]	]	X
ejpam-4492	392	4	br	br	X
ejpam-4492	392	5	gudagudi	gudagudi	PROPN
ejpam-4492	392	6	.	.	PUNCT
ejpam-4492	393	1	some	some	DET
ejpam-4492	393	2	topics	topic	NOUN
ejpam-4492	393	3	in	in	ADP
ejpam-4492	393	4	graph	graph	NOUN
ejpam-4492	393	5	theory	theory	NOUN
ejpam-4492	393	6	.	.	PUNCT
ejpam-4492	394	1	doctoral	doctoral	ADJ
ejpam-4492	394	2	thesis	thesis	NOUN
ejpam-4492	394	3	,	,	PUNCT
ejpam-4492	394	4	karnatak	karnatak	PROPN
ejpam-4492	394	5	university	university	PROPN
ejpam-4492	394	6	,	,	PUNCT
ejpam-4492	394	7	dharwado	dharwado	PROPN
ejpam-4492	394	8	,	,	PUNCT
ejpam-4492	394	9	9(2):161–168	9(2):161–168	NOUN
ejpam-4492	394	10	,	,	PUNCT
ejpam-4492	394	11	1975	1975	NUM
ejpam-4492	394	12	.	.	PUNCT
ejpam-4492	395	1	[	[	X
ejpam-4492	395	2	4	4	NUM
ejpam-4492	395	3	]	]	SYM
ejpam-4492	395	4	f	f	PROPN
ejpam-4492	395	5	harary	harary	NOUN
ejpam-4492	395	6	.	.	PUNCT
ejpam-4492	396	1	converging	converge	VERB
ejpam-4492	396	2	and	and	CCONJ
ejpam-4492	396	3	packing	pack	VERB
ejpam-4492	396	4	in	in	ADP
ejpam-4492	396	5	graphs	graph	NOUN
ejpam-4492	396	6	-	-	PUNCT
ejpam-4492	396	7	i.	i.	NOUN
ejpam-4492	396	8	annals	annals	NOUN
ejpam-4492	396	9	of	of	ADP
ejpam-4492	396	10	new	new	PROPN
ejpam-4492	396	11	york	york	PROPN
ejpam-4492	396	12	academy	academy	PROPN
ejpam-4492	396	13	of	of	ADP
ejpam-4492	396	14	science	science	PROPN
ejpam-4492	396	15	,	,	PUNCT
ejpam-4492	396	16	1969	1969	NUM
ejpam-4492	396	17	.	.	PUNCT
ejpam-4492	397	1	[	[	X
ejpam-4492	397	2	5	5	NUM
ejpam-4492	397	3	]	]	SYM
ejpam-4492	397	4	f	f	PROPN
ejpam-4492	397	5	harary	harary	PROPN
ejpam-4492	397	6	and	and	CCONJ
ejpam-4492	397	7	rz	rz	PROPN
ejpam-4492	397	8	norman	norman	PROPN
ejpam-4492	397	9	.	.	PUNCT
ejpam-4492	398	1	some	some	DET
ejpam-4492	398	2	properties	property	NOUN
ejpam-4492	398	3	of	of	ADP
ejpam-4492	398	4	line	line	NOUN
ejpam-4492	398	5	digraphs	digraph	VERB
ejpam-4492	398	6	.	.	PUNCT
ejpam-4492	399	1	rendiconti	rendiconti	ADJ
ejpam-4492	399	2	del	del	PROPN
ejpam-4492	399	3	circolo	circolo	PROPN
ejpam-4492	399	4	matematico	matematico	NOUN
ejpam-4492	399	5	di	di	NOUN
ejpam-4492	399	6	palermo	palermo	NOUN
ejpam-4492	399	7	,	,	PUNCT
ejpam-4492	399	8	9(2):161–168	9(2):161–168	NOUN
ejpam-4492	399	9	,	,	PUNCT
ejpam-4492	399	10	1960	1960	NUM
ejpam-4492	399	11	.	.	PUNCT
ejpam-4492	400	1	[	[	X
ejpam-4492	400	2	6	6	NUM
ejpam-4492	400	3	]	]	PUNCT
ejpam-4492	400	4	mc	mc	PROPN
ejpam-4492	400	5	mahesh	mahesh	PROPN
ejpam-4492	400	6	kumar	kumar	PROPN
ejpam-4492	400	7	and	and	CCONJ
ejpam-4492	400	8	hm	hm	INTJ
ejpam-4492	400	9	nagesh	nagesh	PROPN
ejpam-4492	400	10	.	.	PUNCT
ejpam-4492	401	1	directed	direct	VERB
ejpam-4492	401	2	pathos	pathos	PROPN
ejpam-4492	401	3	total	total	ADJ
ejpam-4492	401	4	digraph	digraph	NOUN
ejpam-4492	401	5	of	of	ADP
ejpam-4492	401	6	an	an	DET
ejpam-4492	401	7	arborescence	arborescence	NOUN
ejpam-4492	401	8	.	.	PUNCT
ejpam-4492	402	1	engineering	engineering	NOUN
ejpam-4492	402	2	applied	apply	VERB
ejpam-4492	402	3	science	science	NOUN
ejpam-4492	402	4	letters	letter	NOUN
ejpam-4492	402	5	,	,	PUNCT
ejpam-4492	402	6	1:29–42	1:29–42	PROPN
ejpam-4492	402	7	,	,	PUNCT
ejpam-4492	402	8	2018	2018	NUM
ejpam-4492	402	9	.	.	PUNCT
ejpam-4492	403	1	[	[	X
ejpam-4492	403	2	7	7	X
ejpam-4492	403	3	]	]	X
ejpam-4492	403	4	dd	dd	NOUN
ejpam-4492	403	5	cowan	cowan	PROPN
ejpam-4492	403	6	rg	rg	PROPN
ejpam-4492	403	7	stanton	stanton	PROPN
ejpam-4492	403	8	and	and	CCONJ
ejpam-4492	403	9	lo	lo	PROPN
ejpam-4492	403	10	james	james	PROPN
ejpam-4492	403	11	.	.	PUNCT
ejpam-4492	404	1	some	some	DET
ejpam-4492	404	2	results	result	NOUN
ejpam-4492	404	3	on	on	ADP
ejpam-4492	404	4	path	path	NOUN
ejpam-4492	404	5	numbers	number	NOUN
ejpam-4492	404	6	.	.	PUNCT
ejpam-4492	405	1	in	in	ADP
ejpam-4492	405	2	proc	proc	PROPN
ejpam-4492	405	3	.	.	PUNCT
ejpam-4492	406	1	louisiana	louisiana	PROPN
ejpam-4492	406	2	conf	conf	PROPN
ejpam-4492	406	3	.	.	PUNCT
ejpam-4492	407	1	on	on	ADP
ejpam-4492	407	2	combinatorics	combinatoric	NOUN
ejpam-4492	407	3	,	,	PUNCT
ejpam-4492	407	4	graph	graph	NOUN
ejpam-4492	407	5	theory	theory	NOUN
ejpam-4492	407	6	and	and	CCONJ
ejpam-4492	407	7	computing	computing	NOUN
ejpam-4492	407	8	,	,	PUNCT
ejpam-4492	407	9	pages	page	NOUN
ejpam-4492	407	10	112–135	112–135	NUM
ejpam-4492	407	11	,	,	PUNCT
ejpam-4492	407	12	1970	1970	NUM
ejpam-4492	407	13	.	.	PUNCT
ejpam-4492	408	1	[	[	X
ejpam-4492	408	2	8	8	NUM
ejpam-4492	408	3	]	]	X
ejpam-4492	408	4	h	h	PROPN
ejpam-4492	408	5	whitney	whitney	PROPN
ejpam-4492	408	6	.	.	PUNCT
ejpam-4492	409	1	congruent	congruent	ADJ
ejpam-4492	409	2	graphs	graph	NOUN
ejpam-4492	409	3	and	and	CCONJ
ejpam-4492	409	4	the	the	DET
ejpam-4492	409	5	connectivity	connectivity	NOUN
ejpam-4492	409	6	of	of	ADP
ejpam-4492	409	7	graphs	graph	NOUN
ejpam-4492	409	8	.	.	PUNCT
ejpam-4492	410	1	1992	1992	NUM
ejpam-4492	410	2	.	.	PUNCT