id	sid	tid	token	lemma	pos
ejpam-4354	1	1	european	european	PROPN
ejpam-4354	1	2	journal	journal	PROPN
ejpam-4354	1	3	of	of	ADP
ejpam-4354	1	4	pure	pure	ADJ
ejpam-4354	1	5	and	and	CCONJ
ejpam-4354	1	6	applied	apply	VERB
ejpam-4354	1	7	mathematics	mathematic	NOUN
ejpam-4354	1	8	vol	vol	NOUN
ejpam-4354	1	9	.	.	PROPN
ejpam-4354	2	1	15	15	NUM
ejpam-4354	2	2	,	,	PUNCT
ejpam-4354	2	3	no	no	INTJ
ejpam-4354	2	4	.	.	NOUN
ejpam-4354	2	5	2	2	NUM
ejpam-4354	2	6	,	,	PUNCT
ejpam-4354	2	7	2022	2022	NUM
ejpam-4354	2	8	,	,	PUNCT
ejpam-4354	2	9	635	635	NUM
ejpam-4354	2	10	-	-	SYM
ejpam-4354	2	11	645	645	NUM
ejpam-4354	2	12	issn	issn	PROPN
ejpam-4354	2	13	1307	1307	NUM
ejpam-4354	2	14	-	-	SYM
ejpam-4354	2	15	5543	5543	NUM
ejpam-4354	2	16	–	–	PUNCT
ejpam-4354	2	17	ejpam.com	ejpam.com	X
ejpam-4354	2	18	published	publish	VERB
ejpam-4354	2	19	by	by	ADP
ejpam-4354	2	20	new	new	PROPN
ejpam-4354	2	21	york	york	PROPN
ejpam-4354	2	22	business	business	PROPN
ejpam-4354	2	23	global	global	ADJ
ejpam-4354	2	24	monophonic	monophonic	ADJ
ejpam-4354	2	25	eccentric	eccentric	ADJ
ejpam-4354	2	26	domination	domination	NOUN
ejpam-4354	2	27	numbers	number	NOUN
ejpam-4354	2	28	of	of	ADP
ejpam-4354	2	29	graphs	graph	NOUN
ejpam-4354	2	30	sergio	sergio	PROPN
ejpam-4354	2	31	r.	r.	PROPN
ejpam-4354	2	32	canoy	canoy	PROPN
ejpam-4354	2	33	,	,	PUNCT
ejpam-4354	2	34	jr.1	jr.1	PROPN
ejpam-4354	2	35	,	,	PUNCT
ejpam-4354	2	36	anabel	anabel	PROPN
ejpam-4354	2	37	e.	e.	PROPN
ejpam-4354	2	38	gamorez2,∗	gamorez2,∗	VERB
ejpam-4354	2	39	1	1	NUM
ejpam-4354	2	40	department	department	NOUN
ejpam-4354	2	41	of	of	ADP
ejpam-4354	2	42	mathematics	mathematic	NOUN
ejpam-4354	2	43	and	and	CCONJ
ejpam-4354	2	44	statistics	statistic	NOUN
ejpam-4354	2	45	,	,	PUNCT
ejpam-4354	2	46	college	college	NOUN
ejpam-4354	2	47	of	of	ADP
ejpam-4354	2	48	science	science	NOUN
ejpam-4354	2	49	and	and	CCONJ
ejpam-4354	2	50	mathematics	mathematic	NOUN
ejpam-4354	2	51	,	,	PUNCT
ejpam-4354	2	52	center	center	NOUN
ejpam-4354	2	53	for	for	ADP
ejpam-4354	2	54	graph	graph	NOUN
ejpam-4354	2	55	theory	theory	NOUN
ejpam-4354	2	56	,	,	PUNCT
ejpam-4354	2	57	algebra	algebra	NOUN
ejpam-4354	2	58	and	and	CCONJ
ejpam-4354	2	59	analysis	analysis	NOUN
ejpam-4354	2	60	-	-	PUNCT
ejpam-4354	2	61	prism	prism	NOUN
ejpam-4354	2	62	,	,	PUNCT
ejpam-4354	2	63	msu	msu	PROPN
ejpam-4354	2	64	-	-	PUNCT
ejpam-4354	2	65	iligan	iligan	PROPN
ejpam-4354	2	66	institute	institute	PROPN
ejpam-4354	2	67	of	of	ADP
ejpam-4354	2	68	technology	technology	PROPN
ejpam-4354	2	69	,	,	PUNCT
ejpam-4354	2	70	iligan	iligan	ADJ
ejpam-4354	2	71	city	city	PROPN
ejpam-4354	2	72	9200	9200	NUM
ejpam-4354	2	73	,	,	PUNCT
ejpam-4354	2	74	philippines	philippine	NOUN
ejpam-4354	2	75	2	2	NUM
ejpam-4354	2	76	department	department	NOUN
ejpam-4354	2	77	of	of	ADP
ejpam-4354	2	78	mathematics	mathematic	NOUN
ejpam-4354	2	79	and	and	CCONJ
ejpam-4354	2	80	statistics	statistic	NOUN
ejpam-4354	2	81	,	,	PUNCT
ejpam-4354	2	82	college	college	NOUN
ejpam-4354	2	83	of	of	ADP
ejpam-4354	2	84	science	science	NOUN
ejpam-4354	2	85	and	and	CCONJ
ejpam-4354	2	86	mathematics	mathematic	NOUN
ejpam-4354	2	87	,	,	PUNCT
ejpam-4354	2	88	western	western	ADJ
ejpam-4354	2	89	mindanao	mindanao	PROPN
ejpam-4354	2	90	university	university	PROPN
ejpam-4354	2	91	,	,	PUNCT
ejpam-4354	2	92	baliwasan	baliwasan	VERB
ejpam-4354	2	93	,	,	PUNCT
ejpam-4354	2	94	zamboanga	zamboanga	PROPN
ejpam-4354	2	95	city	city	PROPN
ejpam-4354	2	96	7000	7000	NUM
ejpam-4354	2	97	,	,	PUNCT
ejpam-4354	2	98	philippines	philippine	NOUN
ejpam-4354	2	99	abstract	abstract	ADJ
ejpam-4354	2	100	.	.	PUNCT
ejpam-4354	3	1	let	let	VERB
ejpam-4354	3	2	g	g	PRON
ejpam-4354	3	3	be	be	AUX
ejpam-4354	3	4	a	a	DET
ejpam-4354	3	5	(	(	PUNCT
ejpam-4354	3	6	simple	simple	ADJ
ejpam-4354	3	7	)	)	PUNCT
ejpam-4354	3	8	undirected	undirected	ADJ
ejpam-4354	3	9	graph	graph	NOUN
ejpam-4354	3	10	with	with	ADP
ejpam-4354	3	11	vertex	vertex	NOUN
ejpam-4354	3	12	and	and	CCONJ
ejpam-4354	3	13	edge	edge	NOUN
ejpam-4354	3	14	sets	set	NOUN
ejpam-4354	3	15	v	v	ADP
ejpam-4354	3	16	(	(	PUNCT
ejpam-4354	3	17	g	g	NOUN
ejpam-4354	3	18	)	)	PUNCT
ejpam-4354	3	19	and	and	CCONJ
ejpam-4354	3	20	e(g	e(g	PROPN
ejpam-4354	3	21	)	)	PUNCT
ejpam-4354	3	22	,	,	PUNCT
ejpam-4354	3	23	respectively	respectively	ADV
ejpam-4354	3	24	.	.	PUNCT
ejpam-4354	4	1	a	a	DET
ejpam-4354	4	2	set	set	NOUN
ejpam-4354	4	3	s	s	NOUN
ejpam-4354	4	4	⊆	⊆	NUM
ejpam-4354	4	5	v	v	NOUN
ejpam-4354	4	6	(	(	PUNCT
ejpam-4354	4	7	g	g	NOUN
ejpam-4354	4	8	)	)	PUNCT
ejpam-4354	4	9	is	be	AUX
ejpam-4354	4	10	a	a	DET
ejpam-4354	4	11	monophonic	monophonic	ADJ
ejpam-4354	4	12	eccentric	eccentric	ADJ
ejpam-4354	4	13	dominating	dominating	NOUN
ejpam-4354	4	14	set	set	VERB
ejpam-4354	4	15	if	if	SCONJ
ejpam-4354	4	16	every	every	DET
ejpam-4354	4	17	vertex	vertex	NOUN
ejpam-4354	4	18	in	in	ADP
ejpam-4354	4	19	v	v	NOUN
ejpam-4354	4	20	(	(	PUNCT
ejpam-4354	4	21	g	g	NOUN
ejpam-4354	4	22	)	)	PUNCT
ejpam-4354	4	23	\s	\s	NOUN
ejpam-4354	4	24	has	have	VERB
ejpam-4354	4	25	a	a	DET
ejpam-4354	4	26	monophonic	monophonic	ADJ
ejpam-4354	4	27	eccentric	eccentric	ADJ
ejpam-4354	4	28	vertex	vertex	NOUN
ejpam-4354	4	29	in	in	ADP
ejpam-4354	4	30	s.	s.	PROPN
ejpam-4354	4	31	the	the	DET
ejpam-4354	4	32	minimum	minimum	ADJ
ejpam-4354	4	33	size	size	NOUN
ejpam-4354	4	34	of	of	ADP
ejpam-4354	4	35	a	a	DET
ejpam-4354	4	36	monophonic	monophonic	ADJ
ejpam-4354	4	37	eccentric	eccentric	ADJ
ejpam-4354	4	38	dominating	dominating	NOUN
ejpam-4354	4	39	set	set	VERB
ejpam-4354	4	40	in	in	ADP
ejpam-4354	4	41	g	g	PROPN
ejpam-4354	4	42	is	be	AUX
ejpam-4354	4	43	called	call	VERB
ejpam-4354	4	44	the	the	DET
ejpam-4354	4	45	monophonic	monophonic	ADJ
ejpam-4354	4	46	eccentric	eccentric	ADJ
ejpam-4354	4	47	domination	domination	NOUN
ejpam-4354	4	48	number	number	NOUN
ejpam-4354	4	49	of	of	ADP
ejpam-4354	4	50	g.	g.	PROPN
ejpam-4354	4	51	it	it	PRON
ejpam-4354	4	52	shown	show	VERB
ejpam-4354	4	53	that	that	SCONJ
ejpam-4354	4	54	the	the	DET
ejpam-4354	4	55	absolute	absolute	ADJ
ejpam-4354	4	56	difference	difference	NOUN
ejpam-4354	4	57	of	of	ADP
ejpam-4354	4	58	the	the	DET
ejpam-4354	4	59	domination	domination	NOUN
ejpam-4354	4	60	number	number	NOUN
ejpam-4354	4	61	and	and	CCONJ
ejpam-4354	4	62	monophonic	monophonic	ADJ
ejpam-4354	4	63	eccentric	eccentric	ADJ
ejpam-4354	4	64	domination	domination	NOUN
ejpam-4354	4	65	number	number	NOUN
ejpam-4354	4	66	of	of	ADP
ejpam-4354	4	67	a	a	DET
ejpam-4354	4	68	graph	graph	NOUN
ejpam-4354	4	69	can	can	AUX
ejpam-4354	4	70	be	be	AUX
ejpam-4354	4	71	made	make	VERB
ejpam-4354	4	72	arbitrarily	arbitrarily	ADV
ejpam-4354	4	73	large	large	ADJ
ejpam-4354	4	74	.	.	PUNCT
ejpam-4354	5	1	we	we	PRON
ejpam-4354	5	2	characterize	characterize	VERB
ejpam-4354	5	3	the	the	DET
ejpam-4354	5	4	monophonic	monophonic	ADJ
ejpam-4354	5	5	eccentric	eccentric	ADJ
ejpam-4354	5	6	dominating	dominating	NOUN
ejpam-4354	5	7	sets	set	NOUN
ejpam-4354	5	8	in	in	ADP
ejpam-4354	5	9	graphs	graph	NOUN
ejpam-4354	5	10	resulting	result	VERB
ejpam-4354	5	11	from	from	ADP
ejpam-4354	5	12	the	the	DET
ejpam-4354	5	13	join	join	NOUN
ejpam-4354	5	14	,	,	PUNCT
ejpam-4354	5	15	corona	corona	PROPN
ejpam-4354	5	16	,	,	PUNCT
ejpam-4354	5	17	and	and	CCONJ
ejpam-4354	5	18	lexicographic	lexicographic	ADJ
ejpam-4354	5	19	product	product	NOUN
ejpam-4354	5	20	of	of	ADP
ejpam-4354	5	21	two	two	NUM
ejpam-4354	5	22	graphs	graph	NOUN
ejpam-4354	5	23	and	and	CCONJ
ejpam-4354	5	24	determine	determine	VERB
ejpam-4354	5	25	bounds	bound	NOUN
ejpam-4354	5	26	on	on	ADP
ejpam-4354	5	27	their	their	PRON
ejpam-4354	5	28	monophonic	monophonic	ADJ
ejpam-4354	5	29	eccentric	eccentric	ADJ
ejpam-4354	5	30	domination	domination	NOUN
ejpam-4354	5	31	numbers	number	NOUN
ejpam-4354	5	32	.	.	PUNCT
ejpam-4354	6	1	2020	2020	NUM
ejpam-4354	6	2	mathematics	mathematic	NOUN
ejpam-4354	6	3	subject	subject	NOUN
ejpam-4354	6	4	classifications	classification	NOUN
ejpam-4354	6	5	:	:	PUNCT
ejpam-4354	6	6	05c69	05c69	X
ejpam-4354	6	7	key	key	ADJ
ejpam-4354	6	8	words	word	NOUN
ejpam-4354	6	9	and	and	CCONJ
ejpam-4354	6	10	phrases	phrase	NOUN
ejpam-4354	6	11	:	:	PUNCT
ejpam-4354	6	12	monophonic	monophonic	ADJ
ejpam-4354	6	13	,	,	PUNCT
ejpam-4354	6	14	eccentric	eccentric	ADJ
ejpam-4354	6	15	,	,	PUNCT
ejpam-4354	6	16	domination	domination	NOUN
ejpam-4354	6	17	,	,	PUNCT
ejpam-4354	6	18	join	join	NOUN
ejpam-4354	6	19	,	,	PUNCT
ejpam-4354	6	20	corona	corona	PROPN
ejpam-4354	6	21	,	,	PUNCT
ejpam-4354	6	22	lexicographic	lexicographic	ADJ
ejpam-4354	6	23	product	product	NOUN
ejpam-4354	6	24	1	1	NUM
ejpam-4354	6	25	.	.	PUNCT
ejpam-4354	6	26	introduction	introduction	NOUN
ejpam-4354	6	27	in	in	ADP
ejpam-4354	6	28	a	a	DET
ejpam-4354	6	29	recent	recent	ADJ
ejpam-4354	6	30	study	study	NOUN
ejpam-4354	6	31	,	,	PUNCT
ejpam-4354	6	32	santhakumaran	santhakumaran	PROPN
ejpam-4354	6	33	and	and	CCONJ
ejpam-4354	6	34	titus	titus	PROPN
ejpam-4354	6	35	in	in	ADP
ejpam-4354	6	36	[	[	X
ejpam-4354	6	37	3	3	NUM
ejpam-4354	6	38	]	]	PUNCT
ejpam-4354	6	39	and	and	CCONJ
ejpam-4354	6	40	[	[	X
ejpam-4354	6	41	4	4	X
ejpam-4354	6	42	]	]	ADV
ejpam-4354	6	43	defined	define	VERB
ejpam-4354	6	44	monophonic	monophonic	ADJ
ejpam-4354	6	45	distance	distance	NOUN
ejpam-4354	6	46	and	and	CCONJ
ejpam-4354	6	47	obtained	obtain	VERB
ejpam-4354	6	48	some	some	DET
ejpam-4354	6	49	results	result	NOUN
ejpam-4354	6	50	related	relate	VERB
ejpam-4354	6	51	to	to	ADP
ejpam-4354	6	52	the	the	DET
ejpam-4354	6	53	concept	concept	NOUN
ejpam-4354	6	54	.	.	PUNCT
ejpam-4354	7	1	using	use	VERB
ejpam-4354	7	2	monophonic	monophonic	ADJ
ejpam-4354	7	3	paths	path	NOUN
ejpam-4354	7	4	and	and	CCONJ
ejpam-4354	7	5	monophonic	monophonic	ADJ
ejpam-4354	7	6	distance	distance	NOUN
ejpam-4354	7	7	-	-	PUNCT
ejpam-4354	7	8	related	relate	VERB
ejpam-4354	7	9	concepts	concept	NOUN
ejpam-4354	7	10	,	,	PUNCT
ejpam-4354	7	11	titus	titus	PROPN
ejpam-4354	7	12	et	et	PROPN
ejpam-4354	7	13	al	al	PROPN
ejpam-4354	7	14	.	.	PUNCT
ejpam-4354	8	1	in	in	ADP
ejpam-4354	8	2	[	[	X
ejpam-4354	8	3	6	6	NUM
ejpam-4354	8	4	]	]	PUNCT
ejpam-4354	8	5	,	,	PUNCT
ejpam-4354	8	6	and	and	CCONJ
ejpam-4354	8	7	[	[	X
ejpam-4354	8	8	7	7	X
ejpam-4354	8	9	]	]	PUNCT
ejpam-4354	8	10	defined	define	VERB
ejpam-4354	8	11	and	and	CCONJ
ejpam-4354	8	12	studied	study	VERB
ejpam-4354	8	13	a	a	DET
ejpam-4354	8	14	variation	variation	NOUN
ejpam-4354	8	15	of	of	ADP
ejpam-4354	8	16	domination	domination	NOUN
ejpam-4354	8	17	called	call	VERB
ejpam-4354	8	18	monophonic	monophonic	ADJ
ejpam-4354	8	19	eccentric	eccentric	ADJ
ejpam-4354	8	20	domination	domination	NOUN
ejpam-4354	8	21	and	and	CCONJ
ejpam-4354	8	22	the	the	DET
ejpam-4354	8	23	corresponding	corresponding	ADJ
ejpam-4354	8	24	monophonic	monophonic	ADJ
ejpam-4354	8	25	eccentric	eccentric	ADJ
ejpam-4354	8	26	domination	domination	NOUN
ejpam-4354	8	27	number	number	NOUN
ejpam-4354	8	28	.	.	PUNCT
ejpam-4354	9	1	titus	titus	PROPN
ejpam-4354	9	2	and	and	CCONJ
ejpam-4354	9	3	fancy	fancy	ADJ
ejpam-4354	10	1	[	[	X
ejpam-4354	10	2	5	5	NUM
ejpam-4354	10	3	]	]	PUNCT
ejpam-4354	10	4	also	also	ADV
ejpam-4354	10	5	introduced	introduce	VERB
ejpam-4354	10	6	total	total	ADJ
ejpam-4354	10	7	monophonic	monophonic	ADJ
ejpam-4354	10	8	eccentric	eccentric	ADJ
ejpam-4354	10	9	dominating	dominating	NOUN
ejpam-4354	10	10	set	set	NOUN
ejpam-4354	10	11	.	.	PUNCT
ejpam-4354	11	1	the	the	DET
ejpam-4354	11	2	authors	author	NOUN
ejpam-4354	11	3	mentioned	mention	VERB
ejpam-4354	11	4	that	that	SCONJ
ejpam-4354	11	5	the	the	DET
ejpam-4354	11	6	monophonic	monophonic	ADJ
ejpam-4354	11	7	eccentric	eccentric	ADJ
ejpam-4354	11	8	domination	domination	NOUN
ejpam-4354	11	9	number	number	NOUN
ejpam-4354	11	10	and	and	CCONJ
ejpam-4354	11	11	total	total	ADJ
ejpam-4354	11	12	monophonic	monophonic	ADJ
ejpam-4354	11	13	eccentric	eccentric	ADJ
ejpam-4354	11	14	domination	domination	NOUN
ejpam-4354	11	15	number	number	NOUN
ejpam-4354	11	16	find	find	VERB
ejpam-4354	11	17	useful	useful	ADJ
ejpam-4354	11	18	applications	application	NOUN
ejpam-4354	11	19	in	in	ADP
ejpam-4354	11	20	channel	channel	NOUN
ejpam-4354	11	21	assignment	assignment	NOUN
ejpam-4354	11	22	problems	problem	NOUN
ejpam-4354	11	23	in	in	ADP
ejpam-4354	11	24	radio	radio	NOUN
ejpam-4354	11	25	technologies	technology	NOUN
ejpam-4354	11	26	and	and	CCONJ
ejpam-4354	11	27	in	in	ADP
ejpam-4354	11	28	molecular	molecular	ADJ
ejpam-4354	11	29	problems	problem	NOUN
ejpam-4354	11	30	in	in	ADP
ejpam-4354	11	31	theoretical	theoretical	ADJ
ejpam-4354	11	32	chemistry	chemistry	NOUN
ejpam-4354	11	33	.	.	PUNCT
ejpam-4354	12	1	recently	recently	ADV
ejpam-4354	12	2	,	,	PUNCT
ejpam-4354	12	3	gamorez	gamorez	NOUN
ejpam-4354	12	4	and	and	CCONJ
ejpam-4354	12	5	canoy	canoy	ADJ
ejpam-4354	12	6	in	in	ADP
ejpam-4354	12	7	[	[	X
ejpam-4354	12	8	1	1	NUM
ejpam-4354	12	9	]	]	PUNCT
ejpam-4354	12	10	and	and	CCONJ
ejpam-4354	12	11	[	[	X
ejpam-4354	12	12	2	2	NUM
ejpam-4354	12	13	]	]	PUNCT
ejpam-4354	12	14	also	also	ADV
ejpam-4354	12	15	made	make	VERB
ejpam-4354	12	16	use	use	NOUN
ejpam-4354	12	17	of	of	ADP
ejpam-4354	12	18	the	the	DET
ejpam-4354	12	19	monophonic	monophonic	ADJ
ejpam-4354	12	20	distance	distance	NOUN
ejpam-4354	12	21	and	and	CCONJ
ejpam-4354	12	22	related	related	ADJ
ejpam-4354	12	23	concepts	concept	NOUN
ejpam-4354	12	24	to	to	PART
ejpam-4354	12	25	construct	construct	VERB
ejpam-4354	12	26	a	a	DET
ejpam-4354	12	27	topology	topology	NOUN
ejpam-4354	12	28	on	on	ADP
ejpam-4354	12	29	a	a	DET
ejpam-4354	12	30	vertex	vertex	NOUN
ejpam-4354	12	31	set	set	NOUN
ejpam-4354	12	32	of	of	ADP
ejpam-4354	12	33	a	a	DET
ejpam-4354	12	34	given	give	VERB
ejpam-4354	12	35	undirected	undirected	ADJ
ejpam-4354	12	36	graph	graph	NOUN
ejpam-4354	12	37	.	.	PUNCT
ejpam-4354	13	1	some	some	DET
ejpam-4354	13	2	characterizations	characterization	NOUN
ejpam-4354	13	3	were	be	AUX
ejpam-4354	13	4	obtained	obtain	VERB
ejpam-4354	13	5	and	and	CCONJ
ejpam-4354	13	6	subbasic	subbasic	ADJ
ejpam-4354	13	7	open	open	ADJ
ejpam-4354	13	8	sets	set	NOUN
ejpam-4354	13	9	on	on	ADP
ejpam-4354	13	10	graphs	graph	NOUN
ejpam-4354	13	11	resulting	result	VERB
ejpam-4354	13	12	from	from	ADP
ejpam-4354	13	13	some	some	DET
ejpam-4354	13	14	binary	binary	ADJ
ejpam-4354	13	15	operations	operation	NOUN
ejpam-4354	13	16	were	be	AUX
ejpam-4354	13	17	determined	determine	VERB
ejpam-4354	13	18	.	.	PUNCT
ejpam-4354	14	1	∗corresponding	∗corresponde	VERB
ejpam-4354	14	2	author	author	NOUN
ejpam-4354	14	3	.	.	PUNCT
ejpam-4354	15	1	doi	doi	NOUN
ejpam-4354	15	2	:	:	PUNCT
ejpam-4354	15	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4354	https://doi.org/10.29020/nybg.ejpam.v15i2.4354	PROPN
ejpam-4354	15	4	email	email	NOUN
ejpam-4354	15	5	addresses	address	NOUN
ejpam-4354	15	6	:	:	PUNCT
ejpam-4354	15	7	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4354	15	8	(	(	PUNCT
ejpam-4354	15	9	s.	s.	PROPN
ejpam-4354	15	10	canoy	canoy	PROPN
ejpam-4354	15	11	,	,	PUNCT
ejpam-4354	15	12	jr	jr	PROPN
ejpam-4354	15	13	.	.	PUNCT
ejpam-4354	15	14	)	)	PUNCT
ejpam-4354	16	1	anabel.gamorez@wmsu.edu.ph	anabel.gamorez@wmsu.edu.ph	PROPN
ejpam-4354	16	2	(	(	PUNCT
ejpam-4354	16	3	a.	a.	NOUN
ejpam-4354	16	4	gamorez	gamorez	PROPN
ejpam-4354	16	5	)	)	PUNCT
ejpam-4354	16	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4354	17	1	635	635	NUM
ejpam-4354	18	1	©	©	ADP
ejpam-4354	18	2	2022	2022	NUM
ejpam-4354	18	3	ejpam	ejpam	VERB
ejpam-4354	18	4	all	all	DET
ejpam-4354	18	5	rights	right	NOUN
ejpam-4354	18	6	reserved	reserve	VERB
ejpam-4354	18	7	.	.	PUNCT
ejpam-4354	19	1	s.	s.	PROPN
ejpam-4354	19	2	canoy	canoy	PROPN
ejpam-4354	19	3	,	,	PUNCT
ejpam-4354	19	4	jr	jr	PROPN
ejpam-4354	19	5	.	.	PROPN
ejpam-4354	19	6	,	,	PUNCT
ejpam-4354	19	7	a.	a.	NOUN
ejpam-4354	19	8	gamorez	gamorez	PROPN
ejpam-4354	19	9	/	/	SYM
ejpam-4354	19	10	eur	eur	PROPN
ejpam-4354	19	11	.	.	PUNCT
ejpam-4354	20	1	j.	j.	PROPN
ejpam-4354	20	2	pure	pure	PROPN
ejpam-4354	20	3	appl	appl	PROPN
ejpam-4354	20	4	.	.	PROPN
ejpam-4354	20	5	math	math	PROPN
ejpam-4354	20	6	,	,	PUNCT
ejpam-4354	20	7	15	15	NUM
ejpam-4354	20	8	(	(	PUNCT
ejpam-4354	20	9	2	2	NUM
ejpam-4354	20	10	)	)	PUNCT
ejpam-4354	20	11	(	(	PUNCT
ejpam-4354	20	12	2022	2022	NUM
ejpam-4354	20	13	)	)	PUNCT
ejpam-4354	20	14	,	,	PUNCT
ejpam-4354	20	15	635	635	NUM
ejpam-4354	20	16	-	-	SYM
ejpam-4354	20	17	645	645	NUM
ejpam-4354	20	18	636	636	NUM
ejpam-4354	20	19	2	2	NUM
ejpam-4354	20	20	.	.	PUNCT
ejpam-4354	20	21	terminology	terminology	NOUN
ejpam-4354	20	22	and	and	CCONJ
ejpam-4354	20	23	notations	notation	NOUN
ejpam-4354	20	24	for	for	ADP
ejpam-4354	20	25	any	any	DET
ejpam-4354	20	26	two	two	NUM
ejpam-4354	20	27	vertices	vertex	NOUN
ejpam-4354	20	28	u	u	NOUN
ejpam-4354	20	29	and	and	CCONJ
ejpam-4354	20	30	v	v	NOUN
ejpam-4354	20	31	in	in	ADP
ejpam-4354	20	32	an	an	DET
ejpam-4354	20	33	undirected	undirected	ADJ
ejpam-4354	20	34	connected	connected	ADJ
ejpam-4354	20	35	graph	graph	NOUN
ejpam-4354	20	36	g	g	PROPN
ejpam-4354	20	37	,	,	PUNCT
ejpam-4354	20	38	the	the	DET
ejpam-4354	20	39	distance	distance	NOUN
ejpam-4354	20	40	dg(u	dg(u	X
ejpam-4354	20	41	,	,	PUNCT
ejpam-4354	20	42	v	v	NOUN
ejpam-4354	20	43	)	)	PUNCT
ejpam-4354	20	44	is	be	AUX
ejpam-4354	20	45	the	the	DET
ejpam-4354	20	46	length	length	NOUN
ejpam-4354	20	47	of	of	ADP
ejpam-4354	20	48	a	a	DET
ejpam-4354	20	49	shortest	short	ADJ
ejpam-4354	20	50	path	path	NOUN
ejpam-4354	20	51	joining	join	VERB
ejpam-4354	20	52	u	u	PROPN
ejpam-4354	20	53	and	and	CCONJ
ejpam-4354	20	54	v.	v.	ADP
ejpam-4354	20	55	the	the	DET
ejpam-4354	20	56	open	open	ADJ
ejpam-4354	20	57	neighborhood	neighborhood	NOUN
ejpam-4354	20	58	of	of	ADP
ejpam-4354	20	59	a	a	DET
ejpam-4354	20	60	point	point	NOUN
ejpam-4354	20	61	u	u	NOUN
ejpam-4354	20	62	is	be	AUX
ejpam-4354	20	63	the	the	DET
ejpam-4354	20	64	set	set	NOUN
ejpam-4354	20	65	ng(u	ng(u	NOUN
ejpam-4354	20	66	)	)	PUNCT
ejpam-4354	20	67	consisting	consist	VERB
ejpam-4354	20	68	of	of	ADP
ejpam-4354	20	69	all	all	DET
ejpam-4354	20	70	points	point	NOUN
ejpam-4354	20	71	v	v	NUM
ejpam-4354	20	72	which	which	PRON
ejpam-4354	20	73	are	be	AUX
ejpam-4354	20	74	adjacent	adjacent	ADJ
ejpam-4354	20	75	to	to	PART
ejpam-4354	20	76	u.	u.	VERB
ejpam-4354	20	77	the	the	DET
ejpam-4354	20	78	closed	closed	ADJ
ejpam-4354	20	79	neighborhood	neighborhood	NOUN
ejpam-4354	20	80	of	of	ADP
ejpam-4354	20	81	u	u	NOUN
ejpam-4354	20	82	is	be	AUX
ejpam-4354	20	83	ng[u	ng[u	PROPN
ejpam-4354	20	84	]	]	X
ejpam-4354	20	85	=	=	SYM
ejpam-4354	20	86	ng(u	ng(u	PROPN
ejpam-4354	20	87	)	)	PUNCT
ejpam-4354	20	88	∪	∪	NOUN
ejpam-4354	20	89	{	{	PUNCT
ejpam-4354	20	90	u	u	NOUN
ejpam-4354	20	91	}	}	PUNCT
ejpam-4354	20	92	.	.	PUNCT
ejpam-4354	21	1	a	a	DET
ejpam-4354	21	2	chord	chord	NOUN
ejpam-4354	21	3	of	of	ADP
ejpam-4354	21	4	a	a	DET
ejpam-4354	21	5	path	path	NOUN
ejpam-4354	21	6	p	p	NOUN
ejpam-4354	21	7	in	in	ADP
ejpam-4354	21	8	a	a	DET
ejpam-4354	21	9	graph	graph	NOUN
ejpam-4354	21	10	g	g	NOUN
ejpam-4354	21	11	is	be	AUX
ejpam-4354	21	12	an	an	DET
ejpam-4354	21	13	edge	edge	NOUN
ejpam-4354	21	14	joining	join	VERB
ejpam-4354	21	15	two	two	NUM
ejpam-4354	21	16	non	non	ADJ
ejpam-4354	21	17	-	-	ADJ
ejpam-4354	21	18	adjacent	adjacent	ADJ
ejpam-4354	21	19	vertices	vertex	NOUN
ejpam-4354	21	20	of	of	ADP
ejpam-4354	21	21	p	p	NOUN
ejpam-4354	21	22	.	.	PUNCT
ejpam-4354	22	1	a	a	DET
ejpam-4354	22	2	path	path	NOUN
ejpam-4354	22	3	p	p	NOUN
ejpam-4354	22	4	in	in	ADP
ejpam-4354	22	5	a	a	DET
ejpam-4354	22	6	graph	graph	NOUN
ejpam-4354	22	7	g	g	NOUN
ejpam-4354	22	8	is	be	AUX
ejpam-4354	22	9	called	call	VERB
ejpam-4354	22	10	a	a	DET
ejpam-4354	22	11	monophonic	monophonic	ADJ
ejpam-4354	22	12	path	path	NOUN
ejpam-4354	22	13	if	if	SCONJ
ejpam-4354	22	14	it	it	PRON
ejpam-4354	22	15	is	be	AUX
ejpam-4354	22	16	chordless	chordless	ADJ
ejpam-4354	22	17	.	.	PUNCT
ejpam-4354	23	1	for	for	ADP
ejpam-4354	23	2	any	any	DET
ejpam-4354	23	3	two	two	NUM
ejpam-4354	23	4	vertices	vertex	NOUN
ejpam-4354	23	5	u	u	NOUN
ejpam-4354	23	6	and	and	CCONJ
ejpam-4354	23	7	v	v	NOUN
ejpam-4354	23	8	in	in	ADP
ejpam-4354	23	9	a	a	DET
ejpam-4354	23	10	connected	connected	ADJ
ejpam-4354	23	11	graph	graph	NOUN
ejpam-4354	23	12	g	g	NOUN
ejpam-4354	23	13	,	,	PUNCT
ejpam-4354	23	14	the	the	DET
ejpam-4354	23	15	monophonic	monophonic	ADJ
ejpam-4354	23	16	distance	distance	NOUN
ejpam-4354	23	17	dmg	dmg	NOUN
ejpam-4354	23	18	(	(	PUNCT
ejpam-4354	23	19	u	u	NOUN
ejpam-4354	23	20	,	,	PUNCT
ejpam-4354	23	21	v	v	NOUN
ejpam-4354	23	22	)	)	PUNCT
ejpam-4354	23	23	from	from	ADP
ejpam-4354	23	24	u	u	PRON
ejpam-4354	23	25	to	to	ADP
ejpam-4354	23	26	v	v	NOUN
ejpam-4354	23	27	is	be	AUX
ejpam-4354	23	28	defined	define	VERB
ejpam-4354	23	29	as	as	ADP
ejpam-4354	23	30	the	the	DET
ejpam-4354	23	31	length	length	NOUN
ejpam-4354	23	32	of	of	ADP
ejpam-4354	23	33	a	a	DET
ejpam-4354	23	34	longest	long	ADJ
ejpam-4354	23	35	u	u	NOUN
ejpam-4354	23	36	-	-	ADJ
ejpam-4354	23	37	v	v	ADJ
ejpam-4354	23	38	monophonic	monophonic	ADJ
ejpam-4354	23	39	path	path	NOUN
ejpam-4354	23	40	in	in	ADP
ejpam-4354	23	41	g.	g.	PROPN
ejpam-4354	23	42	the	the	DET
ejpam-4354	23	43	monophonic	monophonic	ADJ
ejpam-4354	23	44	eccentricity	eccentricity	NOUN
ejpam-4354	23	45	emg	emg	NOUN
ejpam-4354	23	46	(	(	PUNCT
ejpam-4354	23	47	v	v	NOUN
ejpam-4354	23	48	)	)	PUNCT
ejpam-4354	23	49	of	of	ADP
ejpam-4354	23	50	a	a	DET
ejpam-4354	23	51	vertex	vertex	NOUN
ejpam-4354	23	52	v	v	NOUN
ejpam-4354	23	53	in	in	ADP
ejpam-4354	23	54	g	g	PROPN
ejpam-4354	23	55	is	be	AUX
ejpam-4354	23	56	the	the	DET
ejpam-4354	23	57	maximum	maximum	ADJ
ejpam-4354	23	58	monophonic	monophonic	ADJ
ejpam-4354	23	59	distance	distance	NOUN
ejpam-4354	23	60	from	from	ADP
ejpam-4354	23	61	v	v	NUM
ejpam-4354	23	62	to	to	ADP
ejpam-4354	23	63	a	a	DET
ejpam-4354	23	64	vertex	vertex	NOUN
ejpam-4354	23	65	of	of	ADP
ejpam-4354	23	66	g.	g.	PROPN
ejpam-4354	23	67	the	the	DET
ejpam-4354	23	68	monophonic	monophonic	ADJ
ejpam-4354	23	69	radius	radius	PROPN
ejpam-4354	23	70	radm(g	radm(g	PROPN
ejpam-4354	23	71	)	)	PUNCT
ejpam-4354	23	72	of	of	ADP
ejpam-4354	23	73	graph	graph	NOUN
ejpam-4354	23	74	g	g	PROPN
ejpam-4354	23	75	is	be	AUX
ejpam-4354	23	76	given	give	VERB
ejpam-4354	23	77	by	by	ADP
ejpam-4354	23	78	radm(g	radm(g	NOUN
ejpam-4354	23	79	)	)	PUNCT
ejpam-4354	24	1	=	=	VERB
ejpam-4354	24	2	min{emg	min{emg	NOUN
ejpam-4354	24	3	(	(	PUNCT
ejpam-4354	24	4	v	v	NOUN
ejpam-4354	24	5	)	)	PUNCT
ejpam-4354	24	6	:	:	PUNCT
ejpam-4354	24	7	v	v	X
ejpam-4354	24	8	∈	∈	PROPN
ejpam-4354	24	9	v	v	NOUN
ejpam-4354	24	10	(	(	PUNCT
ejpam-4354	24	11	g	g	NOUN
ejpam-4354	24	12	)	)	PUNCT
ejpam-4354	24	13	}	}	PUNCT
ejpam-4354	24	14	and	and	CCONJ
ejpam-4354	24	15	the	the	DET
ejpam-4354	24	16	monophonic	monophonic	ADJ
ejpam-4354	24	17	diameter	diameter	NOUN
ejpam-4354	24	18	diamm(g	diamm(g	PROPN
ejpam-4354	24	19	)	)	PUNCT
ejpam-4354	24	20	of	of	ADP
ejpam-4354	24	21	g	g	PROPN
ejpam-4354	24	22	is	be	AUX
ejpam-4354	24	23	given	give	VERB
ejpam-4354	24	24	by	by	ADP
ejpam-4354	24	25	diamm(g	diamm(g	PROPN
ejpam-4354	24	26	)	)	PUNCT
ejpam-4354	24	27	=	=	VERB
ejpam-4354	25	1	max{emg	max{emg	INTJ
ejpam-4354	25	2	(	(	PUNCT
ejpam-4354	25	3	v	v	NOUN
ejpam-4354	25	4	)	)	PUNCT
ejpam-4354	25	5	:	:	PUNCT
ejpam-4354	26	1	v	v	X
ejpam-4354	26	2	∈	∈	PROPN
ejpam-4354	26	3	v	v	NOUN
ejpam-4354	26	4	(	(	PUNCT
ejpam-4354	26	5	g	g	NOUN
ejpam-4354	26	6	)	)	PUNCT
ejpam-4354	26	7	}	}	PUNCT
ejpam-4354	26	8	.	.	PUNCT
ejpam-4354	27	1	a	a	DET
ejpam-4354	27	2	vertex	vertex	NOUN
ejpam-4354	27	3	w	w	NOUN
ejpam-4354	27	4	in	in	ADP
ejpam-4354	27	5	g	g	PROPN
ejpam-4354	27	6	is	be	AUX
ejpam-4354	27	7	a	a	DET
ejpam-4354	27	8	monophonic	monophonic	ADJ
ejpam-4354	27	9	eccentric	eccentric	ADJ
ejpam-4354	27	10	vertex	vertex	NOUN
ejpam-4354	27	11	of	of	ADP
ejpam-4354	27	12	a	a	DET
ejpam-4354	27	13	vertex	vertex	NOUN
ejpam-4354	27	14	v	v	NOUN
ejpam-4354	27	15	in	in	ADP
ejpam-4354	27	16	g	g	PROPN
ejpam-4354	27	17	if	if	SCONJ
ejpam-4354	27	18	emg	emg	PROPN
ejpam-4354	27	19	(	(	PUNCT
ejpam-4354	27	20	v	v	NOUN
ejpam-4354	27	21	)	)	PUNCT
ejpam-4354	27	22	=	=	PUNCT
ejpam-4354	27	23	dmg	dmg	X
ejpam-4354	27	24	(	(	PUNCT
ejpam-4354	27	25	w	w	PROPN
ejpam-4354	27	26	,	,	PUNCT
ejpam-4354	27	27	v	v	NOUN
ejpam-4354	27	28	)	)	PUNCT
ejpam-4354	27	29	.	.	PUNCT
ejpam-4354	28	1	in	in	ADP
ejpam-4354	28	2	this	this	DET
ejpam-4354	28	3	case	case	NOUN
ejpam-4354	28	4	,	,	PUNCT
ejpam-4354	28	5	we	we	PRON
ejpam-4354	28	6	say	say	VERB
ejpam-4354	28	7	that	that	SCONJ
ejpam-4354	28	8	w	w	NOUN
ejpam-4354	28	9	is	be	AUX
ejpam-4354	28	10	a	a	DET
ejpam-4354	28	11	monophonic	monophonic	ADJ
ejpam-4354	28	12	eccentric	eccentric	ADJ
ejpam-4354	28	13	neighbor	neighbor	NOUN
ejpam-4354	28	14	of	of	ADP
ejpam-4354	28	15	v.	v.	ADP
ejpam-4354	28	16	the	the	DET
ejpam-4354	28	17	set	set	NOUN
ejpam-4354	28	18	consisting	consist	VERB
ejpam-4354	28	19	of	of	ADP
ejpam-4354	28	20	all	all	DET
ejpam-4354	28	21	the	the	DET
ejpam-4354	28	22	monophonic	monophonic	ADJ
ejpam-4354	28	23	eccentric	eccentric	ADJ
ejpam-4354	28	24	vertices	vertex	NOUN
ejpam-4354	28	25	of	of	ADP
ejpam-4354	28	26	v	v	NUM
ejpam-4354	28	27	∈	∈	NOUN
ejpam-4354	28	28	v	v	NOUN
ejpam-4354	28	29	(	(	PUNCT
ejpam-4354	28	30	g	g	NOUN
ejpam-4354	28	31	)	)	PUNCT
ejpam-4354	28	32	will	will	AUX
ejpam-4354	28	33	be	be	AUX
ejpam-4354	28	34	denoted	denote	VERB
ejpam-4354	28	35	by	by	ADP
ejpam-4354	28	36	nm	nm	ADV
ejpam-4354	28	37	g	g	PROPN
ejpam-4354	28	38	(	(	PUNCT
ejpam-4354	28	39	v	v	NOUN
ejpam-4354	28	40	)	)	PUNCT
ejpam-4354	28	41	,	,	PUNCT
ejpam-4354	29	1	i.e.	i.e.	X
ejpam-4354	29	2	,	,	PUNCT
ejpam-4354	29	3	nm	nm	ADV
ejpam-4354	29	4	g	g	NOUN
ejpam-4354	29	5	(	(	PUNCT
ejpam-4354	29	6	v	v	NOUN
ejpam-4354	29	7	)	)	PUNCT
ejpam-4354	29	8	=	=	PRON
ejpam-4354	29	9	{	{	PUNCT
ejpam-4354	29	10	w	w	NOUN
ejpam-4354	29	11	∈	∈	PROPN
ejpam-4354	29	12	v	v	ADP
ejpam-4354	29	13	(	(	PUNCT
ejpam-4354	29	14	g	g	NOUN
ejpam-4354	29	15	)	)	PUNCT
ejpam-4354	29	16	:	:	PUNCT
ejpam-4354	29	17	emg	emg	NOUN
ejpam-4354	29	18	(	(	PUNCT
ejpam-4354	29	19	v	v	NOUN
ejpam-4354	29	20	)	)	PUNCT
ejpam-4354	29	21	=	=	PUNCT
ejpam-4354	29	22	dmg	dmg	X
ejpam-4354	29	23	(	(	PUNCT
ejpam-4354	29	24	w	w	PROPN
ejpam-4354	29	25	,	,	PUNCT
ejpam-4354	29	26	v	v	NOUN
ejpam-4354	29	27	)	)	PUNCT
ejpam-4354	29	28	}	}	PUNCT
ejpam-4354	29	29	.	.	PUNCT
ejpam-4354	30	1	here	here	ADV
ejpam-4354	30	2	,	,	PUNCT
ejpam-4354	30	3	nm	nm	ADV
ejpam-4354	30	4	g	g	PROPN
ejpam-4354	31	1	[	[	X
ejpam-4354	31	2	v	v	X
ejpam-4354	31	3	]	]	X
ejpam-4354	31	4	=	=	SYM
ejpam-4354	31	5	nm	nm	PRON
ejpam-4354	31	6	g	g	PROPN
ejpam-4354	31	7	(	(	PUNCT
ejpam-4354	31	8	v	v	NOUN
ejpam-4354	31	9	)	)	PUNCT
ejpam-4354	31	10	∪	∪	NOUN
ejpam-4354	31	11	{	{	PUNCT
ejpam-4354	31	12	v	v	NOUN
ejpam-4354	31	13	}	}	PUNCT
ejpam-4354	31	14	.	.	PUNCT
ejpam-4354	32	1	a	a	DET
ejpam-4354	32	2	set	set	NOUN
ejpam-4354	32	3	s	s	NOUN
ejpam-4354	32	4	⊆	⊆	NUM
ejpam-4354	32	5	v	v	NOUN
ejpam-4354	32	6	(	(	PUNCT
ejpam-4354	32	7	g	g	NOUN
ejpam-4354	32	8	)	)	PUNCT
ejpam-4354	32	9	is	be	AUX
ejpam-4354	32	10	a	a	DET
ejpam-4354	32	11	monophonic	monophonic	ADJ
ejpam-4354	32	12	eccentric	eccentric	ADJ
ejpam-4354	32	13	dominating	dominating	NOUN
ejpam-4354	32	14	set	set	NOUN
ejpam-4354	32	15	(	(	PUNCT
ejpam-4354	32	16	total	total	ADJ
ejpam-4354	32	17	monophonic	monophonic	ADJ
ejpam-4354	32	18	eccentric	eccentric	ADJ
ejpam-4354	32	19	dominating	dominating	NOUN
ejpam-4354	32	20	set	set	NOUN
ejpam-4354	32	21	)	)	PUNCT
ejpam-4354	32	22	of	of	ADP
ejpam-4354	32	23	g	g	PROPN
ejpam-4354	32	24	if	if	SCONJ
ejpam-4354	32	25	each	each	PRON
ejpam-4354	32	26	w	w	PROPN
ejpam-4354	32	27	∈	∈	PROPN
ejpam-4354	32	28	v	v	ADP
ejpam-4354	32	29	(	(	PUNCT
ejpam-4354	32	30	g	g	NOUN
ejpam-4354	32	31	)	)	PUNCT
ejpam-4354	32	32	\	\	PROPN
ejpam-4354	33	1	s	s	PART
ejpam-4354	33	2	(	(	PUNCT
ejpam-4354	33	3	resp	resp	NOUN
ejpam-4354	33	4	.	.	PUNCT
ejpam-4354	34	1	w	w	PROPN
ejpam-4354	34	2	∈	∈	PROPN
ejpam-4354	34	3	v	v	ADP
ejpam-4354	34	4	(	(	PUNCT
ejpam-4354	34	5	g	g	NOUN
ejpam-4354	34	6	)	)	PUNCT
ejpam-4354	34	7	)	)	PUNCT
ejpam-4354	34	8	has	have	VERB
ejpam-4354	34	9	a	a	DET
ejpam-4354	34	10	monophonic	monophonic	ADJ
ejpam-4354	34	11	eccentric	eccentric	ADJ
ejpam-4354	34	12	vertex	vertex	NOUN
ejpam-4354	34	13	in	in	ADP
ejpam-4354	34	14	s.	s.	PROPN
ejpam-4354	34	15	the	the	DET
ejpam-4354	34	16	smallest	small	ADJ
ejpam-4354	34	17	size	size	NOUN
ejpam-4354	34	18	of	of	ADP
ejpam-4354	34	19	a	a	DET
ejpam-4354	34	20	monophonic	monophonic	ADJ
ejpam-4354	34	21	eccentric	eccentric	ADJ
ejpam-4354	34	22	dominating	dominating	NOUN
ejpam-4354	34	23	(	(	PUNCT
ejpam-4354	34	24	total	total	ADJ
ejpam-4354	34	25	monophonic	monophonic	ADJ
ejpam-4354	34	26	eccentric	eccentric	ADJ
ejpam-4354	34	27	dominating	dominating	NOUN
ejpam-4354	34	28	)	)	PUNCT
ejpam-4354	34	29	set	set	NOUN
ejpam-4354	34	30	of	of	ADP
ejpam-4354	34	31	g	g	NOUN
ejpam-4354	34	32	,	,	PUNCT
ejpam-4354	34	33	denoted	denote	VERB
ejpam-4354	34	34	by	by	ADP
ejpam-4354	34	35	γme(g	γme(g	PROPN
ejpam-4354	34	36	)	)	PUNCT
ejpam-4354	34	37	(	(	PUNCT
ejpam-4354	34	38	resp	resp	NOUN
ejpam-4354	34	39	.	.	PUNCT
ejpam-4354	35	1	γtme(g	γtme(g	NOUN
ejpam-4354	35	2	)	)	PUNCT
ejpam-4354	35	3	)	)	PUNCT
ejpam-4354	35	4	,	,	PUNCT
ejpam-4354	35	5	is	be	AUX
ejpam-4354	35	6	called	call	VERB
ejpam-4354	35	7	the	the	DET
ejpam-4354	35	8	monophonic	monophonic	ADJ
ejpam-4354	35	9	eccentric	eccentric	ADJ
ejpam-4354	35	10	domination	domination	NOUN
ejpam-4354	35	11	number	number	NOUN
ejpam-4354	35	12	(	(	PUNCT
ejpam-4354	35	13	resp	resp	NOUN
ejpam-4354	35	14	.	.	PUNCT
ejpam-4354	36	1	total	total	ADJ
ejpam-4354	36	2	monophonic	monophonic	ADJ
ejpam-4354	36	3	eccentric	eccentric	ADJ
ejpam-4354	36	4	domination	domination	NOUN
ejpam-4354	36	5	number	number	NOUN
ejpam-4354	36	6	)	)	PUNCT
ejpam-4354	36	7	of	of	ADP
ejpam-4354	36	8	g.	g.	PROPN
ejpam-4354	36	9	any	any	DET
ejpam-4354	36	10	monophonic	monophonic	ADJ
ejpam-4354	36	11	eccentric	eccentric	ADJ
ejpam-4354	36	12	dominating	dominating	NOUN
ejpam-4354	36	13	(	(	PUNCT
ejpam-4354	36	14	total	total	ADJ
ejpam-4354	36	15	monophonic	monophonic	ADJ
ejpam-4354	36	16	eccentric	eccentric	ADJ
ejpam-4354	36	17	dominating	dominating	NOUN
ejpam-4354	36	18	)	)	PUNCT
ejpam-4354	36	19	set	set	NOUN
ejpam-4354	36	20	of	of	ADP
ejpam-4354	36	21	g	g	NOUN
ejpam-4354	36	22	of	of	ADP
ejpam-4354	36	23	size	size	NOUN
ejpam-4354	36	24	γme(g	γme(g	PROPN
ejpam-4354	36	25	)	)	PUNCT
ejpam-4354	36	26	(	(	PUNCT
ejpam-4354	36	27	resp	resp	NOUN
ejpam-4354	36	28	.	.	PUNCT
ejpam-4354	37	1	γtme(g	γtme(g	NOUN
ejpam-4354	37	2	)	)	PUNCT
ejpam-4354	37	3	)	)	PUNCT
ejpam-4354	37	4	is	be	AUX
ejpam-4354	37	5	called	call	VERB
ejpam-4354	37	6	a	a	DET
ejpam-4354	37	7	minimum	minimum	ADJ
ejpam-4354	37	8	monophonic	monophonic	ADJ
ejpam-4354	37	9	eccentric	eccentric	ADJ
ejpam-4354	37	10	dominating	dominating	NOUN
ejpam-4354	37	11	set	set	NOUN
ejpam-4354	37	12	or	or	CCONJ
ejpam-4354	37	13	a	a	DET
ejpam-4354	37	14	γme	γme	NOUN
ejpam-4354	37	15	-	-	PUNCT
ejpam-4354	37	16	set	set	VERB
ejpam-4354	37	17	(	(	PUNCT
ejpam-4354	37	18	resp	resp	NOUN
ejpam-4354	37	19	.	.	PUNCT
ejpam-4354	38	1	minimum	minimum	ADJ
ejpam-4354	38	2	total	total	ADJ
ejpam-4354	38	3	monophonic	monophonic	ADJ
ejpam-4354	38	4	eccentric	eccentric	ADJ
ejpam-4354	38	5	dominating	dominating	NOUN
ejpam-4354	38	6	set	set	NOUN
ejpam-4354	38	7	or	or	CCONJ
ejpam-4354	38	8	γtme	γtme	NOUN
ejpam-4354	38	9	-	-	PUNCT
ejpam-4354	38	10	set	set	NOUN
ejpam-4354	38	11	)	)	PUNCT
ejpam-4354	38	12	of	of	ADP
ejpam-4354	38	13	g.	g.	PROPN
ejpam-4354	38	14	let	let	VERB
ejpam-4354	38	15	g	g	NOUN
ejpam-4354	38	16	be	be	AUX
ejpam-4354	38	17	a	a	DET
ejpam-4354	38	18	connected	connected	ADJ
ejpam-4354	38	19	graph	graph	NOUN
ejpam-4354	38	20	with	with	ADP
ejpam-4354	38	21	diamm(g	diamm(g	PROPN
ejpam-4354	38	22	)	)	PUNCT
ejpam-4354	38	23	≥	≥	NOUN
ejpam-4354	38	24	3	3	NUM
ejpam-4354	38	25	.	.	PUNCT
ejpam-4354	39	1	a	a	DET
ejpam-4354	39	2	set	set	NOUN
ejpam-4354	39	3	s	s	NOUN
ejpam-4354	39	4	⊆	⊆	NUM
ejpam-4354	39	5	v	v	NOUN
ejpam-4354	39	6	(	(	PUNCT
ejpam-4354	39	7	g	g	NOUN
ejpam-4354	39	8	)	)	PUNCT
ejpam-4354	39	9	is	be	AUX
ejpam-4354	39	10	a	a	DET
ejpam-4354	39	11	d3m	d3m	ADJ
ejpam-4354	39	12	-	-	PUNCT
ejpam-4354	39	13	monophonic	monophonic	ADJ
ejpam-4354	39	14	eccentric	eccentric	ADJ
ejpam-4354	39	15	set	set	NOUN
ejpam-4354	39	16	of	of	ADP
ejpam-4354	39	17	g	g	PROPN
ejpam-4354	39	18	if	if	SCONJ
ejpam-4354	39	19	for	for	ADP
ejpam-4354	39	20	each	each	DET
ejpam-4354	39	21	u	u	PROPN
ejpam-4354	39	22	∈	∈	PROPN
ejpam-4354	39	23	v	v	ADP
ejpam-4354	39	24	(	(	PUNCT
ejpam-4354	39	25	g	g	NOUN
ejpam-4354	39	26	)	)	PUNCT
ejpam-4354	39	27	\	\	PROPN
ejpam-4354	39	28	s	s	PART
ejpam-4354	39	29	with	with	ADP
ejpam-4354	39	30	emg	emg	PROPN
ejpam-4354	39	31	(	(	PUNCT
ejpam-4354	39	32	u	u	NOUN
ejpam-4354	39	33	)	)	PUNCT
ejpam-4354	39	34	≥	≥	NOUN
ejpam-4354	39	35	3	3	NUM
ejpam-4354	39	36	,	,	PUNCT
ejpam-4354	39	37	there	there	PRON
ejpam-4354	39	38	exists	exist	VERB
ejpam-4354	39	39	w	w	PROPN
ejpam-4354	39	40	∈	∈	PROPN
ejpam-4354	39	41	s	s	VERB
ejpam-4354	39	42	such	such	ADJ
ejpam-4354	39	43	that	that	DET
ejpam-4354	39	44	emg	emg	NOUN
ejpam-4354	39	45	(	(	PUNCT
ejpam-4354	39	46	u	u	NOUN
ejpam-4354	39	47	)	)	PUNCT
ejpam-4354	39	48	=	=	SYM
ejpam-4354	39	49	dmg	dmg	X
ejpam-4354	39	50	(	(	PUNCT
ejpam-4354	39	51	w	w	PROPN
ejpam-4354	39	52	,	,	PUNCT
ejpam-4354	39	53	u	u	NOUN
ejpam-4354	39	54	)	)	PUNCT
ejpam-4354	39	55	.	.	PUNCT
ejpam-4354	40	1	the	the	DET
ejpam-4354	40	2	minimum	minimum	ADJ
ejpam-4354	40	3	cardinality	cardinality	NOUN
ejpam-4354	40	4	of	of	ADP
ejpam-4354	40	5	a	a	DET
ejpam-4354	40	6	d3m	d3m	ADJ
ejpam-4354	40	7	-	-	PUNCT
ejpam-4354	40	8	monophonic	monophonic	ADJ
ejpam-4354	40	9	eccentric	eccentric	ADJ
ejpam-4354	40	10	set	set	NOUN
ejpam-4354	40	11	of	of	ADP
ejpam-4354	40	12	g	g	NOUN
ejpam-4354	40	13	,	,	PUNCT
ejpam-4354	40	14	denoted	denote	VERB
ejpam-4354	40	15	by	by	ADP
ejpam-4354	40	16	µ3	µ3	PROPN
ejpam-4354	40	17	me(g	me(g	NUM
ejpam-4354	40	18	)	)	PUNCT
ejpam-4354	40	19	,	,	PUNCT
ejpam-4354	40	20	is	be	AUX
ejpam-4354	40	21	called	call	VERB
ejpam-4354	40	22	the	the	DET
ejpam-4354	40	23	d3m	d3m	PROPN
ejpam-4354	40	24	-	-	PUNCT
ejpam-4354	40	25	monophonic	monophonic	ADJ
ejpam-4354	40	26	eccentric	eccentric	ADJ
ejpam-4354	40	27	number	number	NOUN
ejpam-4354	40	28	of	of	ADP
ejpam-4354	40	29	g.	g.	PROPN
ejpam-4354	40	30	the	the	DET
ejpam-4354	40	31	join	join	NOUN
ejpam-4354	40	32	of	of	ADP
ejpam-4354	40	33	two	two	NUM
ejpam-4354	40	34	graphs	graph	NOUN
ejpam-4354	40	35	g	g	NOUN
ejpam-4354	40	36	and	and	CCONJ
ejpam-4354	40	37	h	h	NOUN
ejpam-4354	40	38	,	,	PUNCT
ejpam-4354	40	39	denoted	denote	VERB
ejpam-4354	40	40	by	by	ADP
ejpam-4354	40	41	g	g	PROPN
ejpam-4354	41	1	+	+	CCONJ
ejpam-4354	41	2	h	h	NOUN
ejpam-4354	41	3	is	be	AUX
ejpam-4354	41	4	the	the	DET
ejpam-4354	41	5	graph	graph	NOUN
ejpam-4354	41	6	with	with	ADP
ejpam-4354	41	7	vertex	vertex	NOUN
ejpam-4354	41	8	set	set	VERB
ejpam-4354	41	9	v	v	NOUN
ejpam-4354	41	10	(	(	PUNCT
ejpam-4354	41	11	g+h	g+h	NOUN
ejpam-4354	41	12	)	)	PUNCT
ejpam-4354	41	13	=	=	SYM
ejpam-4354	41	14	v	v	NOUN
ejpam-4354	41	15	(	(	PUNCT
ejpam-4354	41	16	g)∪	g)∪	VERB
ejpam-4354	41	17	v	v	NUM
ejpam-4354	41	18	(	(	PUNCT
ejpam-4354	41	19	h	h	NOUN
ejpam-4354	41	20	)	)	PUNCT
ejpam-4354	41	21	and	and	CCONJ
ejpam-4354	41	22	edge	edge	NOUN
ejpam-4354	41	23	set	set	VERB
ejpam-4354	41	24	e(g+h	e(g+h	NUM
ejpam-4354	41	25	)	)	PUNCT
ejpam-4354	42	1	=	=	SYM
ejpam-4354	42	2	e(g)∪e(h)∪	e(g)∪e(h)∪	NOUN
ejpam-4354	42	3	{	{	PUNCT
ejpam-4354	42	4	uv	uv	NOUN
ejpam-4354	42	5	:	:	PUNCT
ejpam-4354	42	6	u	u	PROPN
ejpam-4354	42	7	∈	∈	PROPN
ejpam-4354	42	8	v	v	ADP
ejpam-4354	42	9	(	(	PUNCT
ejpam-4354	42	10	g	g	NOUN
ejpam-4354	42	11	)	)	PUNCT
ejpam-4354	42	12	,	,	PUNCT
ejpam-4354	42	13	v	v	X
ejpam-4354	42	14	∈	∈	PROPN
ejpam-4354	42	15	v	v	NOUN
ejpam-4354	42	16	(	(	PUNCT
ejpam-4354	42	17	h	h	NOUN
ejpam-4354	42	18	)	)	PUNCT
ejpam-4354	42	19	}	}	PUNCT
ejpam-4354	42	20	.	.	PUNCT
ejpam-4354	43	1	the	the	DET
ejpam-4354	43	2	corona	corona	NOUN
ejpam-4354	43	3	of	of	ADP
ejpam-4354	43	4	graphs	graph	NOUN
ejpam-4354	43	5	g	g	PROPN
ejpam-4354	43	6	and	and	CCONJ
ejpam-4354	43	7	h	h	NOUN
ejpam-4354	43	8	,	,	PUNCT
ejpam-4354	43	9	denoted	denote	VERB
ejpam-4354	43	10	by	by	ADP
ejpam-4354	43	11	g	g	PROPN
ejpam-4354	43	12	◦	◦	NOUN
ejpam-4354	43	13	h	h	NOUN
ejpam-4354	43	14	,	,	PUNCT
ejpam-4354	43	15	is	be	AUX
ejpam-4354	43	16	the	the	DET
ejpam-4354	43	17	graph	graph	NOUN
ejpam-4354	43	18	obtained	obtain	VERB
ejpam-4354	43	19	fromg	fromg	NOUN
ejpam-4354	43	20	by	by	ADP
ejpam-4354	43	21	taking	take	VERB
ejpam-4354	43	22	a	a	DET
ejpam-4354	43	23	copy	copy	NOUN
ejpam-4354	43	24	hv	hv	PROPN
ejpam-4354	43	25	of	of	ADP
ejpam-4354	43	26	h	h	PROPN
ejpam-4354	43	27	and	and	CCONJ
ejpam-4354	43	28	forming	form	VERB
ejpam-4354	43	29	the	the	DET
ejpam-4354	43	30	join	join	NOUN
ejpam-4354	43	31	〈	〈	PROPN
ejpam-4354	43	32	v	v	NOUN
ejpam-4354	43	33	〉	〉	NOUN
ejpam-4354	43	34	+	+	NUM
ejpam-4354	43	35	hv	hv	NOUN
ejpam-4354	43	36	=	=	SYM
ejpam-4354	43	37	v	v	PROPN
ejpam-4354	43	38	+	+	CCONJ
ejpam-4354	43	39	hv	hv	NOUN
ejpam-4354	43	40	for	for	ADP
ejpam-4354	43	41	each	each	DET
ejpam-4354	43	42	v	v	NUM
ejpam-4354	43	43	∈	∈	PROPN
ejpam-4354	43	44	v	v	NOUN
ejpam-4354	43	45	(	(	PUNCT
ejpam-4354	43	46	g	g	NOUN
ejpam-4354	43	47	)	)	PUNCT
ejpam-4354	43	48	.	.	PUNCT
ejpam-4354	44	1	the	the	DET
ejpam-4354	44	2	lexicographic	lexicographic	ADJ
ejpam-4354	44	3	product	product	NOUN
ejpam-4354	44	4	of	of	ADP
ejpam-4354	44	5	graphs	graph	NOUN
ejpam-4354	44	6	g	g	PROPN
ejpam-4354	44	7	and	and	CCONJ
ejpam-4354	44	8	h	h	NOUN
ejpam-4354	44	9	,	,	PUNCT
ejpam-4354	44	10	denoted	denote	VERB
ejpam-4354	44	11	by	by	ADP
ejpam-4354	44	12	g[h	g[h	NOUN
ejpam-4354	44	13	]	]	PUNCT
ejpam-4354	44	14	,	,	PUNCT
ejpam-4354	44	15	is	be	AUX
ejpam-4354	44	16	the	the	DET
ejpam-4354	44	17	graph	graph	NOUN
ejpam-4354	44	18	with	with	ADP
ejpam-4354	44	19	vertex	vertex	NOUN
ejpam-4354	44	20	set	set	VERB
ejpam-4354	44	21	v	v	NOUN
ejpam-4354	44	22	(	(	PUNCT
ejpam-4354	44	23	g[h	g[h	PROPN
ejpam-4354	44	24	]	]	PUNCT
ejpam-4354	44	25	)	)	PUNCT
ejpam-4354	44	26	=	=	SYM
ejpam-4354	44	27	v	v	X
ejpam-4354	44	28	(	(	PUNCT
ejpam-4354	44	29	g	g	NOUN
ejpam-4354	44	30	)	)	PUNCT
ejpam-4354	44	31	×	×	NOUN
ejpam-4354	44	32	v	v	NOUN
ejpam-4354	44	33	(	(	PUNCT
ejpam-4354	44	34	h	h	NOUN
ejpam-4354	44	35	)	)	PUNCT
ejpam-4354	44	36	and	and	CCONJ
ejpam-4354	44	37	(	(	PUNCT
ejpam-4354	44	38	v	v	NOUN
ejpam-4354	44	39	,	,	PUNCT
ejpam-4354	44	40	a)(u	a)(u	ADJ
ejpam-4354	44	41	,	,	PUNCT
ejpam-4354	44	42	b	b	X
ejpam-4354	44	43	)	)	PUNCT
ejpam-4354	44	44	∈	∈	NOUN
ejpam-4354	44	45	e(g[h	e(g[h	NOUN
ejpam-4354	44	46	]	]	PUNCT
ejpam-4354	44	47	)	)	PUNCT
ejpam-4354	45	1	if	if	SCONJ
ejpam-4354	45	2	and	and	CCONJ
ejpam-4354	45	3	only	only	ADV
ejpam-4354	45	4	if	if	SCONJ
ejpam-4354	45	5	either	either	DET
ejpam-4354	45	6	uv	uv	PROPN
ejpam-4354	45	7	∈	∈	PROPN
ejpam-4354	45	8	e(g	e(g	PROPN
ejpam-4354	45	9	)	)	PUNCT
ejpam-4354	45	10	or	or	CCONJ
ejpam-4354	45	11	u	u	X
ejpam-4354	45	12	=	=	PROPN
ejpam-4354	45	13	v	v	PROPN
ejpam-4354	45	14	and	and	CCONJ
ejpam-4354	45	15	ab	ab	PROPN
ejpam-4354	45	16	∈	∈	PROPN
ejpam-4354	45	17	e(h	e(h	PROPN
ejpam-4354	45	18	)	)	PUNCT
ejpam-4354	45	19	.	.	PUNCT
ejpam-4354	45	20	note	note	VERB
ejpam-4354	45	21	that	that	SCONJ
ejpam-4354	45	22	any	any	DET
ejpam-4354	45	23	non	non	ADJ
ejpam-4354	45	24	-	-	ADJ
ejpam-4354	45	25	empty	empty	ADJ
ejpam-4354	45	26	set	set	NOUN
ejpam-4354	45	27	c	c	NOUN
ejpam-4354	45	28	⊆	⊆	NUM
ejpam-4354	45	29	v	v	NOUN
ejpam-4354	45	30	(	(	PUNCT
ejpam-4354	45	31	g)×	g)×	NOUN
ejpam-4354	45	32	v	v	NOUN
ejpam-4354	45	33	(	(	PUNCT
ejpam-4354	45	34	h	h	NOUN
ejpam-4354	45	35	)	)	PUNCT
ejpam-4354	45	36	can	can	AUX
ejpam-4354	45	37	be	be	AUX
ejpam-4354	45	38	written	write	VERB
ejpam-4354	45	39	as	as	ADP
ejpam-4354	45	40	c	c	NOUN
ejpam-4354	45	41	=	=	PUNCT
ejpam-4354	45	42	⋃	⋃	PROPN
ejpam-4354	45	43	x∈s	x∈s	NOUN
ejpam-4354	46	1	[	[	X
ejpam-4354	46	2	{	{	PUNCT
ejpam-4354	46	3	x	x	NOUN
ejpam-4354	46	4	}	}	PUNCT
ejpam-4354	46	5	×	×	PROPN
ejpam-4354	46	6	tx	tx	PROPN
ejpam-4354	46	7	]	]	X
ejpam-4354	46	8	,	,	PUNCT
ejpam-4354	46	9	where	where	SCONJ
ejpam-4354	46	10	s	s	VERB
ejpam-4354	46	11	⊆	⊆	NUM
ejpam-4354	46	12	v	v	NOUN
ejpam-4354	46	13	(	(	PUNCT
ejpam-4354	46	14	g	g	NOUN
ejpam-4354	46	15	)	)	PUNCT
ejpam-4354	46	16	and	and	CCONJ
ejpam-4354	46	17	tx	tx	VERB
ejpam-4354	46	18	⊆	⊆	NUM
ejpam-4354	46	19	v	v	NOUN
ejpam-4354	46	20	(	(	PUNCT
ejpam-4354	46	21	h	h	NOUN
ejpam-4354	46	22	)	)	PUNCT
ejpam-4354	46	23	for	for	ADP
ejpam-4354	46	24	each	each	DET
ejpam-4354	46	25	x	x	PROPN
ejpam-4354	46	26	∈	∈	PROPN
ejpam-4354	46	27	s.	s.	PROPN
ejpam-4354	46	28	3	3	X
ejpam-4354	46	29	.	.	PUNCT
ejpam-4354	46	30	results	result	NOUN
ejpam-4354	46	31	theorem	theorem	VERB
ejpam-4354	46	32	1	1	X
ejpam-4354	46	33	.	.	PUNCT
ejpam-4354	47	1	let	let	VERB
ejpam-4354	47	2	g	g	PRON
ejpam-4354	47	3	be	be	AUX
ejpam-4354	47	4	a	a	DET
ejpam-4354	47	5	connected	connected	ADJ
ejpam-4354	47	6	graph	graph	NOUN
ejpam-4354	47	7	of	of	ADP
ejpam-4354	47	8	order	order	NOUN
ejpam-4354	47	9	n	n	PRON
ejpam-4354	47	10	≥	≥	NOUN
ejpam-4354	47	11	1	1	NUM
ejpam-4354	47	12	.	.	PUNCT
ejpam-4354	48	1	then	then	ADV
ejpam-4354	48	2	γme(g	γme(g	PROPN
ejpam-4354	48	3	)	)	PUNCT
ejpam-4354	48	4	=	=	PUNCT
ejpam-4354	48	5	1	1	NUM
ejpam-4354	48	6	if	if	SCONJ
ejpam-4354	48	7	and	and	CCONJ
ejpam-4354	48	8	only	only	ADV
ejpam-4354	48	9	if	if	SCONJ
ejpam-4354	48	10	g	g	PROPN
ejpam-4354	48	11	=	=	VERB
ejpam-4354	48	12	kn	kn	PROPN
ejpam-4354	48	13	or	or	CCONJ
ejpam-4354	48	14	there	there	ADV
ejpam-4354	48	15	exists	exist	VERB
ejpam-4354	48	16	v	v	ADP
ejpam-4354	48	17	∈	∈	PROPN
ejpam-4354	48	18	v	v	NOUN
ejpam-4354	48	19	(	(	PUNCT
ejpam-4354	48	20	g	g	NOUN
ejpam-4354	48	21	)	)	PUNCT
ejpam-4354	48	22	satisfying	satisfy	VERB
ejpam-4354	48	23	the	the	DET
ejpam-4354	48	24	following	follow	VERB
ejpam-4354	48	25	properties	property	NOUN
ejpam-4354	48	26	:	:	PUNCT
ejpam-4354	48	27	s.	s.	PROPN
ejpam-4354	48	28	canoy	canoy	PROPN
ejpam-4354	48	29	,	,	PUNCT
ejpam-4354	48	30	jr	jr	PROPN
ejpam-4354	48	31	.	.	PROPN
ejpam-4354	48	32	,	,	PUNCT
ejpam-4354	48	33	a.	a.	NOUN
ejpam-4354	48	34	gamorez	gamorez	PROPN
ejpam-4354	48	35	/	/	SYM
ejpam-4354	48	36	eur	eur	PROPN
ejpam-4354	48	37	.	.	PUNCT
ejpam-4354	49	1	j.	j.	PROPN
ejpam-4354	49	2	pure	pure	PROPN
ejpam-4354	49	3	appl	appl	PROPN
ejpam-4354	49	4	.	.	PROPN
ejpam-4354	49	5	math	math	PROPN
ejpam-4354	49	6	,	,	PUNCT
ejpam-4354	49	7	15	15	NUM
ejpam-4354	49	8	(	(	PUNCT
ejpam-4354	49	9	2	2	NUM
ejpam-4354	49	10	)	)	PUNCT
ejpam-4354	49	11	(	(	PUNCT
ejpam-4354	49	12	2022	2022	NUM
ejpam-4354	49	13	)	)	PUNCT
ejpam-4354	49	14	,	,	PUNCT
ejpam-4354	49	15	635	635	NUM
ejpam-4354	49	16	-	-	SYM
ejpam-4354	49	17	645	645	NUM
ejpam-4354	49	18	637	637	NUM
ejpam-4354	49	19	(	(	PUNCT
ejpam-4354	49	20	i	i	NOUN
ejpam-4354	49	21	)	)	PUNCT
ejpam-4354	49	22	v	v	PROPN
ejpam-4354	49	23	(	(	PUNCT
ejpam-4354	49	24	g	g	NOUN
ejpam-4354	49	25	)	)	PUNCT
ejpam-4354	49	26	\ng[v	\ng[v	NOUN
ejpam-4354	49	27	]	]	PUNCT
ejpam-4354	50	1	=	=	PRON
ejpam-4354	50	2	{	{	PUNCT
ejpam-4354	50	3	w	w	PROPN
ejpam-4354	50	4	∈	∈	PROPN
ejpam-4354	50	5	v	v	ADP
ejpam-4354	50	6	(	(	PUNCT
ejpam-4354	50	7	g	g	NOUN
ejpam-4354	50	8	)	)	PUNCT
ejpam-4354	50	9	:	:	PUNCT
ejpam-4354	50	10	dmg	dmg	X
ejpam-4354	50	11	(	(	PUNCT
ejpam-4354	50	12	v	v	NOUN
ejpam-4354	50	13	,	,	PUNCT
ejpam-4354	50	14	w	w	NOUN
ejpam-4354	50	15	)	)	PUNCT
ejpam-4354	50	16	=	=	SYM
ejpam-4354	50	17	2	2	NUM
ejpam-4354	50	18	}	}	PUNCT
ejpam-4354	50	19	6=	6=	NUM
ejpam-4354	50	20	∅	∅	NOUN
ejpam-4354	50	21	;	;	PUNCT
ejpam-4354	50	22	(	(	PUNCT
ejpam-4354	50	23	ii	ii	NOUN
ejpam-4354	50	24	)	)	PUNCT
ejpam-4354	50	25	ng(v	ng(v	PUNCT
ejpam-4354	50	26	)	)	PUNCT
ejpam-4354	50	27	⊆	⊆	NUM
ejpam-4354	50	28	ng(w	ng(w	NOUN
ejpam-4354	50	29	)	)	PUNCT
ejpam-4354	50	30	for	for	ADP
ejpam-4354	50	31	each	each	DET
ejpam-4354	50	32	w	w	PROPN
ejpam-4354	50	33	∈	∈	PROPN
ejpam-4354	50	34	v	v	ADP
ejpam-4354	50	35	(	(	PUNCT
ejpam-4354	50	36	g	g	NOUN
ejpam-4354	50	37	)	)	PUNCT
ejpam-4354	50	38	\ng[v	\ng[v	NOUN
ejpam-4354	50	39	]	]	PUNCT
ejpam-4354	50	40	;	;	PUNCT
ejpam-4354	50	41	and	and	CCONJ
ejpam-4354	50	42	(	(	PUNCT
ejpam-4354	50	43	iii	iii	NOUN
ejpam-4354	50	44	)	)	PUNCT
ejpam-4354	50	45	dmg	dmg	NOUN
ejpam-4354	50	46	(	(	PUNCT
ejpam-4354	50	47	x	x	NOUN
ejpam-4354	50	48	,	,	PUNCT
ejpam-4354	50	49	y	y	NOUN
ejpam-4354	50	50	)	)	PUNCT
ejpam-4354	50	51	≤	≤	NUM
ejpam-4354	50	52	2	2	NUM
ejpam-4354	50	53	for	for	ADP
ejpam-4354	50	54	all	all	DET
ejpam-4354	50	55	x	x	NOUN
ejpam-4354	50	56	,	,	PUNCT
ejpam-4354	50	57	y	y	PROPN
ejpam-4354	50	58	∈	∈	PROPN
ejpam-4354	50	59	v	v	ADP
ejpam-4354	50	60	(	(	PUNCT
ejpam-4354	50	61	g	g	NOUN
ejpam-4354	50	62	)	)	PUNCT
ejpam-4354	50	63	\ng[v	\ng[v	NOUN
ejpam-4354	50	64	]	]	PUNCT
ejpam-4354	50	65	.	.	PUNCT
ejpam-4354	51	1	proof	proof	NOUN
ejpam-4354	51	2	.	.	PUNCT
ejpam-4354	52	1	suppose	suppose	VERB
ejpam-4354	52	2	γme(g	γme(g	NOUN
ejpam-4354	52	3	)	)	PUNCT
ejpam-4354	52	4	=	=	SYM
ejpam-4354	52	5	1	1	NUM
ejpam-4354	52	6	and	and	CCONJ
ejpam-4354	52	7	let	let	VERB
ejpam-4354	52	8	s	s	PRON
ejpam-4354	52	9	=	=	NOUN
ejpam-4354	52	10	{	{	PUNCT
ejpam-4354	52	11	v	v	NOUN
ejpam-4354	52	12	}	}	PUNCT
ejpam-4354	52	13	be	be	AUX
ejpam-4354	52	14	a	a	DET
ejpam-4354	52	15	monophonic	monophonic	ADJ
ejpam-4354	52	16	eccentric	eccentric	ADJ
ejpam-4354	52	17	dominating	dominating	NOUN
ejpam-4354	52	18	set	set	NOUN
ejpam-4354	52	19	of	of	ADP
ejpam-4354	52	20	g.	g.	PROPN
ejpam-4354	52	21	if	if	SCONJ
ejpam-4354	52	22	g	g	PROPN
ejpam-4354	52	23	=	=	PROPN
ejpam-4354	52	24	kn	kn	PROPN
ejpam-4354	52	25	,	,	PUNCT
ejpam-4354	52	26	then	then	ADV
ejpam-4354	52	27	we	we	PRON
ejpam-4354	52	28	are	be	AUX
ejpam-4354	52	29	done	do	VERB
ejpam-4354	52	30	.	.	PUNCT
ejpam-4354	53	1	so	so	ADV
ejpam-4354	53	2	suppose	suppose	VERB
ejpam-4354	53	3	that	that	SCONJ
ejpam-4354	53	4	g	g	PROPN
ejpam-4354	53	5	6=	6=	PROPN
ejpam-4354	53	6	kn	kn	PROPN
ejpam-4354	53	7	.	.	PUNCT
ejpam-4354	53	8	suppose	suppose	VERB
ejpam-4354	53	9	ng[v	ng[v	NOUN
ejpam-4354	53	10	]	]	X
ejpam-4354	53	11	=	=	SYM
ejpam-4354	53	12	v	v	X
ejpam-4354	53	13	(	(	PUNCT
ejpam-4354	53	14	g	g	NOUN
ejpam-4354	53	15	)	)	PUNCT
ejpam-4354	53	16	.	.	PUNCT
ejpam-4354	54	1	since	since	SCONJ
ejpam-4354	54	2	g	g	PROPN
ejpam-4354	54	3	6=	6=	PROPN
ejpam-4354	54	4	kn	kn	PROPN
ejpam-4354	54	5	,	,	PUNCT
ejpam-4354	54	6	there	there	PRON
ejpam-4354	54	7	exist	exist	VERB
ejpam-4354	54	8	vertices	vertex	NOUN
ejpam-4354	54	9	a	a	PRON
ejpam-4354	54	10	,	,	PUNCT
ejpam-4354	54	11	b	b	PROPN
ejpam-4354	54	12	∈	∈	PROPN
ejpam-4354	54	13	v	v	NOUN
ejpam-4354	54	14	(	(	PUNCT
ejpam-4354	54	15	g	g	NOUN
ejpam-4354	54	16	)	)	PUNCT
ejpam-4354	54	17	such	such	ADJ
ejpam-4354	54	18	that	that	SCONJ
ejpam-4354	54	19	dg(a	dg(a	PROPN
ejpam-4354	54	20	,	,	PUNCT
ejpam-4354	54	21	b	b	X
ejpam-4354	54	22	)	)	PUNCT
ejpam-4354	54	23	=	=	SYM
ejpam-4354	54	24	2	2	NUM
ejpam-4354	54	25	≤	≤	NUM
ejpam-4354	54	26	dmg	dmg	NOUN
ejpam-4354	54	27	(	(	PUNCT
ejpam-4354	54	28	a	a	DET
ejpam-4354	54	29	,	,	PUNCT
ejpam-4354	54	30	b	b	NOUN
ejpam-4354	54	31	)	)	PUNCT
ejpam-4354	54	32	.	.	PUNCT
ejpam-4354	55	1	it	it	PRON
ejpam-4354	55	2	follows	follow	VERB
ejpam-4354	55	3	that	that	SCONJ
ejpam-4354	55	4	v	v	NOUN
ejpam-4354	55	5	is	be	AUX
ejpam-4354	55	6	not	not	PART
ejpam-4354	55	7	a	a	DET
ejpam-4354	55	8	monophonic	monophonic	ADJ
ejpam-4354	55	9	eccentric	eccentric	ADJ
ejpam-4354	55	10	vertex	vertex	NOUN
ejpam-4354	55	11	of	of	ADP
ejpam-4354	55	12	a	a	PRON
ejpam-4354	55	13	,	,	PUNCT
ejpam-4354	55	14	contrary	contrary	ADJ
ejpam-4354	55	15	to	to	ADP
ejpam-4354	55	16	our	our	PRON
ejpam-4354	55	17	assumption	assumption	NOUN
ejpam-4354	55	18	of	of	ADP
ejpam-4354	55	19	s.	s.	PROPN
ejpam-4354	55	20	thus	thus	ADV
ejpam-4354	55	21	,	,	PUNCT
ejpam-4354	55	22	v	v	INTJ
ejpam-4354	55	23	(	(	PUNCT
ejpam-4354	55	24	g)\ng[v	g)\ng[v	PROPN
ejpam-4354	55	25	]	]	PUNCT
ejpam-4354	55	26	6=	6=	ADP
ejpam-4354	55	27	∅.	∅.	PROPN
ejpam-4354	55	28	now	now	ADV
ejpam-4354	55	29	let	let	VERB
ejpam-4354	55	30	w	w	PROPN
ejpam-4354	55	31	∈	∈	PROPN
ejpam-4354	55	32	v	v	NOUN
ejpam-4354	55	33	(	(	PUNCT
ejpam-4354	55	34	g)\ng[v	g)\ng[v	PROPN
ejpam-4354	55	35	]	]	PUNCT
ejpam-4354	55	36	.	.	PUNCT
ejpam-4354	56	1	since	since	SCONJ
ejpam-4354	56	2	v	v	NOUN
ejpam-4354	56	3	is	be	AUX
ejpam-4354	56	4	a	a	DET
ejpam-4354	56	5	monophonic	monophonic	ADJ
ejpam-4354	56	6	eccentric	eccentric	ADJ
ejpam-4354	56	7	vertex	vertex	NOUN
ejpam-4354	56	8	of	of	ADP
ejpam-4354	56	9	w	w	PROPN
ejpam-4354	56	10	,	,	PUNCT
ejpam-4354	56	11	we	we	PRON
ejpam-4354	56	12	have	have	VERB
ejpam-4354	56	13	em(w	em(w	NOUN
ejpam-4354	56	14	)	)	PUNCT
ejpam-4354	57	1	=	=	SYM
ejpam-4354	57	2	dmg	dmg	X
ejpam-4354	57	3	(	(	PUNCT
ejpam-4354	57	4	v	v	NOUN
ejpam-4354	57	5	,	,	PUNCT
ejpam-4354	57	6	w	w	NOUN
ejpam-4354	57	7	)	)	PUNCT
ejpam-4354	57	8	≥	≥	NOUN
ejpam-4354	57	9	2	2	NUM
ejpam-4354	57	10	.	.	PUNCT
ejpam-4354	57	11	suppose	suppose	VERB
ejpam-4354	57	12	dmg	dmg	PROPN
ejpam-4354	57	13	(	(	PUNCT
ejpam-4354	57	14	v	v	NOUN
ejpam-4354	57	15	,	,	PUNCT
ejpam-4354	57	16	w	w	NOUN
ejpam-4354	57	17	)	)	PUNCT
ejpam-4354	57	18	6=	6=	ADP
ejpam-4354	57	19	2	2	NUM
ejpam-4354	57	20	,	,	PUNCT
ejpam-4354	57	21	say	say	VERB
ejpam-4354	57	22	[	[	X
ejpam-4354	57	23	v1	v1	NOUN
ejpam-4354	57	24	,	,	PUNCT
ejpam-4354	57	25	v2	v2	PROPN
ejpam-4354	57	26	,	,	PUNCT
ejpam-4354	57	27	...	...	PUNCT
ejpam-4354	57	28	,	,	PUNCT
ejpam-4354	57	29	vk	vk	ADP
ejpam-4354	57	30	]	]	PUNCT
ejpam-4354	57	31	,	,	PUNCT
ejpam-4354	57	32	where	where	SCONJ
ejpam-4354	57	33	v1	v1	NOUN
ejpam-4354	57	34	=	=	SYM
ejpam-4354	57	35	v	v	NOUN
ejpam-4354	57	36	,	,	PUNCT
ejpam-4354	57	37	vk	vk	ADP
ejpam-4354	57	38	=	=	SYM
ejpam-4354	57	39	w	w	PROPN
ejpam-4354	57	40	and	and	CCONJ
ejpam-4354	57	41	k	k	PROPN
ejpam-4354	57	42	≥	≥	NUM
ejpam-4354	57	43	4	4	NUM
ejpam-4354	57	44	,	,	PUNCT
ejpam-4354	57	45	is	be	AUX
ejpam-4354	57	46	a	a	DET
ejpam-4354	57	47	v	v	NOUN
ejpam-4354	57	48	-	-	PUNCT
ejpam-4354	57	49	w	w	NOUN
ejpam-4354	57	50	monophonic	monophonic	ADJ
ejpam-4354	57	51	path	path	NOUN
ejpam-4354	57	52	.	.	PUNCT
ejpam-4354	58	1	since	since	SCONJ
ejpam-4354	58	2	dg(v2	dg(v2	NOUN
ejpam-4354	58	3	,	,	PUNCT
ejpam-4354	58	4	w	w	PROPN
ejpam-4354	58	5	)	)	PUNCT
ejpam-4354	58	6	≥	≥	NOUN
ejpam-4354	58	7	2	2	NUM
ejpam-4354	58	8	,	,	PUNCT
ejpam-4354	58	9	this	this	PRON
ejpam-4354	58	10	would	would	AUX
ejpam-4354	58	11	imply	imply	VERB
ejpam-4354	58	12	that	that	SCONJ
ejpam-4354	58	13	v	v	NOUN
ejpam-4354	58	14	is	be	AUX
ejpam-4354	58	15	not	not	PART
ejpam-4354	58	16	a	a	DET
ejpam-4354	58	17	monophonic	monophonic	ADJ
ejpam-4354	58	18	eccentric	eccentric	ADJ
ejpam-4354	58	19	vertex	vertex	NOUN
ejpam-4354	58	20	of	of	ADP
ejpam-4354	58	21	v2	v2	NOUN
ejpam-4354	58	22	,	,	PUNCT
ejpam-4354	58	23	a	a	DET
ejpam-4354	58	24	contradiction	contradiction	NOUN
ejpam-4354	58	25	.	.	PUNCT
ejpam-4354	59	1	thus	thus	ADV
ejpam-4354	59	2	,	,	PUNCT
ejpam-4354	59	3	dmg	dmg	X
ejpam-4354	59	4	(	(	PUNCT
ejpam-4354	59	5	v	v	NOUN
ejpam-4354	59	6	,	,	PUNCT
ejpam-4354	59	7	w	w	NOUN
ejpam-4354	59	8	)	)	PUNCT
ejpam-4354	59	9	=	=	SYM
ejpam-4354	59	10	2	2	X
ejpam-4354	59	11	.	.	PUNCT
ejpam-4354	59	12	this	this	PRON
ejpam-4354	59	13	shows	show	VERB
ejpam-4354	59	14	that	that	SCONJ
ejpam-4354	59	15	(	(	PUNCT
ejpam-4354	59	16	i	i	NOUN
ejpam-4354	59	17	)	)	PUNCT
ejpam-4354	59	18	holds	hold	VERB
ejpam-4354	59	19	.	.	PUNCT
ejpam-4354	60	1	next	next	ADV
ejpam-4354	60	2	,	,	PUNCT
ejpam-4354	60	3	let	let	VERB
ejpam-4354	60	4	z	z	NOUN
ejpam-4354	60	5	∈	∈	PROPN
ejpam-4354	60	6	ng(v	ng(v	PUNCT
ejpam-4354	60	7	)	)	PUNCT
ejpam-4354	60	8	and	and	CCONJ
ejpam-4354	60	9	let	let	VERB
ejpam-4354	60	10	w	w	PROPN
ejpam-4354	60	11	∈	∈	PROPN
ejpam-4354	60	12	v	v	ADP
ejpam-4354	60	13	(	(	PUNCT
ejpam-4354	60	14	g	g	NOUN
ejpam-4354	60	15	)	)	PUNCT
ejpam-4354	60	16	\	\	PUNCT
ejpam-4354	61	1	ng[v	ng[v	ADV
ejpam-4354	61	2	]	]	PUNCT
ejpam-4354	61	3	.	.	PUNCT
ejpam-4354	62	1	since	since	SCONJ
ejpam-4354	62	2	v	v	NOUN
ejpam-4354	62	3	is	be	AUX
ejpam-4354	62	4	a	a	DET
ejpam-4354	62	5	monophonic	monophonic	ADJ
ejpam-4354	62	6	eccentric	eccentric	ADJ
ejpam-4354	62	7	vertex	vertex	NOUN
ejpam-4354	62	8	of	of	ADP
ejpam-4354	62	9	z	z	PROPN
ejpam-4354	62	10	,	,	PUNCT
ejpam-4354	62	11	it	it	PRON
ejpam-4354	62	12	follows	follow	VERB
ejpam-4354	62	13	that	that	SCONJ
ejpam-4354	62	14	dg(z	dg(z	NOUN
ejpam-4354	62	15	,	,	PUNCT
ejpam-4354	62	16	w	w	NOUN
ejpam-4354	62	17	)	)	PUNCT
ejpam-4354	62	18	=	=	SYM
ejpam-4354	62	19	1	1	NUM
ejpam-4354	62	20	,	,	PUNCT
ejpam-4354	62	21	that	that	ADV
ejpam-4354	62	22	is	is	ADV
ejpam-4354	62	23	,	,	PUNCT
ejpam-4354	62	24	z	z	PROPN
ejpam-4354	62	25	∈	∈	PROPN
ejpam-4354	62	26	ng(w	ng(w	NOUN
ejpam-4354	62	27	)	)	PUNCT
ejpam-4354	62	28	.	.	PUNCT
ejpam-4354	63	1	this	this	PRON
ejpam-4354	63	2	shows	show	VERB
ejpam-4354	63	3	that	that	SCONJ
ejpam-4354	63	4	(	(	PUNCT
ejpam-4354	63	5	ii	ii	NOUN
ejpam-4354	63	6	)	)	PUNCT
ejpam-4354	63	7	holds	hold	VERB
ejpam-4354	63	8	.	.	PUNCT
ejpam-4354	64	1	finally	finally	ADV
ejpam-4354	64	2	,	,	PUNCT
ejpam-4354	64	3	let	let	VERB
ejpam-4354	64	4	x	x	PRON
ejpam-4354	64	5	,	,	PUNCT
ejpam-4354	64	6	y	y	PROPN
ejpam-4354	64	7	∈	∈	PROPN
ejpam-4354	64	8	v	v	ADP
ejpam-4354	64	9	(	(	PUNCT
ejpam-4354	64	10	g	g	NOUN
ejpam-4354	64	11	)	)	PUNCT
ejpam-4354	64	12	\	\	PUNCT
ejpam-4354	65	1	ng[v	ng[v	ADV
ejpam-4354	65	2	]	]	PUNCT
ejpam-4354	65	3	.	.	PUNCT
ejpam-4354	66	1	if	if	SCONJ
ejpam-4354	66	2	dmg	dmg	X
ejpam-4354	66	3	(	(	PUNCT
ejpam-4354	66	4	x	x	NOUN
ejpam-4354	66	5	,	,	PUNCT
ejpam-4354	66	6	y	y	PROPN
ejpam-4354	66	7	)	)	PUNCT
ejpam-4354	66	8	≥	≥	NOUN
ejpam-4354	66	9	3	3	NUM
ejpam-4354	66	10	,	,	PUNCT
ejpam-4354	66	11	then	then	ADV
ejpam-4354	66	12	v	v	NOUN
ejpam-4354	66	13	is	be	AUX
ejpam-4354	66	14	not	not	PART
ejpam-4354	66	15	a	a	DET
ejpam-4354	66	16	monophonic	monophonic	ADJ
ejpam-4354	66	17	eccentric	eccentric	ADJ
ejpam-4354	66	18	vertex	vertex	NOUN
ejpam-4354	66	19	of	of	ADP
ejpam-4354	66	20	x	x	PROPN
ejpam-4354	66	21	,	,	PUNCT
ejpam-4354	66	22	a	a	DET
ejpam-4354	66	23	contradiction	contradiction	NOUN
ejpam-4354	66	24	.	.	PUNCT
ejpam-4354	67	1	thus	thus	ADV
ejpam-4354	67	2	,	,	PUNCT
ejpam-4354	67	3	dmg	dmg	INTJ
ejpam-4354	67	4	(	(	PUNCT
ejpam-4354	67	5	x	x	NOUN
ejpam-4354	67	6	,	,	PUNCT
ejpam-4354	67	7	y	y	NOUN
ejpam-4354	67	8	)	)	PUNCT
ejpam-4354	67	9	≤	≤	NOUN
ejpam-4354	67	10	2	2	NUM
ejpam-4354	67	11	,	,	PUNCT
ejpam-4354	67	12	showing	show	VERB
ejpam-4354	67	13	that	that	SCONJ
ejpam-4354	67	14	(	(	PUNCT
ejpam-4354	67	15	iii	iii	NOUN
ejpam-4354	67	16	)	)	PUNCT
ejpam-4354	67	17	holds	hold	VERB
ejpam-4354	67	18	.	.	PUNCT
ejpam-4354	68	1	for	for	ADP
ejpam-4354	68	2	the	the	DET
ejpam-4354	68	3	converse	converse	NOUN
ejpam-4354	68	4	,	,	PUNCT
ejpam-4354	68	5	suppose	suppose	VERB
ejpam-4354	68	6	first	first	ADV
ejpam-4354	68	7	that	that	SCONJ
ejpam-4354	68	8	g	g	PROPN
ejpam-4354	68	9	=	=	PROPN
ejpam-4354	68	10	kn	kn	PROPN
ejpam-4354	68	11	.	.	PUNCT
ejpam-4354	69	1	then	then	ADV
ejpam-4354	69	2	,	,	PUNCT
ejpam-4354	69	3	clearly	clearly	ADV
ejpam-4354	69	4	,	,	PUNCT
ejpam-4354	69	5	γme(g	γme(g	PROPN
ejpam-4354	69	6	)	)	PUNCT
ejpam-4354	69	7	=	=	PUNCT
ejpam-4354	70	1	1	1	X
ejpam-4354	70	2	.	.	PUNCT
ejpam-4354	71	1	next	next	ADV
ejpam-4354	71	2	,	,	PUNCT
ejpam-4354	71	3	suppose	suppose	VERB
ejpam-4354	71	4	that	that	SCONJ
ejpam-4354	71	5	there	there	PRON
ejpam-4354	71	6	exists	exist	VERB
ejpam-4354	71	7	v	v	ADP
ejpam-4354	71	8	∈	∈	PROPN
ejpam-4354	71	9	v	v	NOUN
ejpam-4354	71	10	(	(	PUNCT
ejpam-4354	71	11	g	g	NOUN
ejpam-4354	71	12	)	)	PUNCT
ejpam-4354	71	13	satisfying	satisfy	VERB
ejpam-4354	71	14	conditions	condition	NOUN
ejpam-4354	71	15	(	(	PUNCT
ejpam-4354	71	16	i	i	NOUN
ejpam-4354	71	17	)	)	PUNCT
ejpam-4354	71	18	,	,	PUNCT
ejpam-4354	71	19	(	(	PUNCT
ejpam-4354	71	20	ii	ii	NOUN
ejpam-4354	71	21	)	)	PUNCT
ejpam-4354	71	22	,	,	PUNCT
ejpam-4354	71	23	and	and	CCONJ
ejpam-4354	71	24	(	(	PUNCT
ejpam-4354	71	25	iii	iii	NOUN
ejpam-4354	71	26	)	)	PUNCT
ejpam-4354	71	27	.	.	PUNCT
ejpam-4354	72	1	let	let	VERB
ejpam-4354	72	2	s0	s0	PROPN
ejpam-4354	72	3	=	=	PUNCT
ejpam-4354	72	4	{	{	PUNCT
ejpam-4354	72	5	v	v	NOUN
ejpam-4354	72	6	}	}	PUNCT
ejpam-4354	72	7	.	.	PUNCT
ejpam-4354	73	1	by	by	ADP
ejpam-4354	73	2	(	(	PUNCT
ejpam-4354	73	3	ii	ii	NOUN
ejpam-4354	73	4	)	)	PUNCT
ejpam-4354	73	5	,	,	PUNCT
ejpam-4354	73	6	v	v	NOUN
ejpam-4354	73	7	is	be	AUX
ejpam-4354	73	8	a	a	DET
ejpam-4354	73	9	monophonic	monophonic	ADJ
ejpam-4354	73	10	eccentric	eccentric	ADJ
ejpam-4354	73	11	vertex	vertex	NOUN
ejpam-4354	73	12	of	of	ADP
ejpam-4354	73	13	every	every	DET
ejpam-4354	73	14	element	element	NOUN
ejpam-4354	73	15	of	of	ADP
ejpam-4354	73	16	ng(v	ng(v	NOUN
ejpam-4354	73	17	)	)	PUNCT
ejpam-4354	73	18	.	.	PUNCT
ejpam-4354	74	1	let	let	VERB
ejpam-4354	74	2	w	w	NOUN
ejpam-4354	74	3	∈	∈	PROPN
ejpam-4354	74	4	v	v	ADP
ejpam-4354	74	5	(	(	PUNCT
ejpam-4354	74	6	g	g	NOUN
ejpam-4354	74	7	)	)	PUNCT
ejpam-4354	74	8	\	\	PUNCT
ejpam-4354	75	1	ng[v	ng[v	ADV
ejpam-4354	75	2	]	]	PUNCT
ejpam-4354	75	3	.	.	PUNCT
ejpam-4354	76	1	then	then	ADV
ejpam-4354	76	2	dmg	dmg	VERB
ejpam-4354	76	3	(	(	PUNCT
ejpam-4354	76	4	v	v	NOUN
ejpam-4354	76	5	,	,	PUNCT
ejpam-4354	76	6	w	w	NOUN
ejpam-4354	76	7	)	)	PUNCT
ejpam-4354	76	8	=	=	SYM
ejpam-4354	76	9	2	2	NUM
ejpam-4354	76	10	by	by	ADP
ejpam-4354	76	11	(	(	PUNCT
ejpam-4354	76	12	i	i	NOUN
ejpam-4354	76	13	)	)	PUNCT
ejpam-4354	76	14	.	.	PUNCT
ejpam-4354	77	1	further	far	ADV
ejpam-4354	77	2	,	,	PUNCT
ejpam-4354	77	3	by	by	ADP
ejpam-4354	77	4	(	(	PUNCT
ejpam-4354	77	5	iii	iii	NOUN
ejpam-4354	77	6	)	)	PUNCT
ejpam-4354	77	7	,	,	PUNCT
ejpam-4354	77	8	it	it	PRON
ejpam-4354	77	9	follows	follow	VERB
ejpam-4354	77	10	that	that	SCONJ
ejpam-4354	77	11	v	v	NOUN
ejpam-4354	77	12	is	be	AUX
ejpam-4354	77	13	a	a	DET
ejpam-4354	77	14	monophonic	monophonic	ADJ
ejpam-4354	77	15	eccentric	eccentric	ADJ
ejpam-4354	77	16	vertex	vertex	NOUN
ejpam-4354	77	17	of	of	ADP
ejpam-4354	77	18	w.	w.	PROPN
ejpam-4354	77	19	therefore	therefore	ADV
ejpam-4354	77	20	,	,	PUNCT
ejpam-4354	77	21	γme(g	γme(g	NOUN
ejpam-4354	77	22	)	)	PUNCT
ejpam-4354	78	1	=	=	SYM
ejpam-4354	78	2	|s0|	|s0|	NOUN
ejpam-4354	78	3	=	=	SYM
ejpam-4354	78	4	1	1	X
ejpam-4354	78	5	.	.	PUNCT
ejpam-4354	78	6	theorem	theorem	NOUN
ejpam-4354	78	7	2	2	NUM
ejpam-4354	78	8	.	.	PUNCT
ejpam-4354	79	1	let	let	VERB
ejpam-4354	79	2	g1	g1	PROPN
ejpam-4354	79	3	,	,	PUNCT
ejpam-4354	79	4	g2	g2	PROPN
ejpam-4354	79	5	,	,	PUNCT
ejpam-4354	79	6	...	...	PUNCT
ejpam-4354	79	7	,	,	PUNCT
ejpam-4354	79	8	gk	gk	PROPN
ejpam-4354	79	9	be	be	AUX
ejpam-4354	79	10	the	the	DET
ejpam-4354	79	11	distinct	distinct	ADJ
ejpam-4354	79	12	components	component	NOUN
ejpam-4354	79	13	of	of	ADP
ejpam-4354	79	14	g	g	PROPN
ejpam-4354	79	15	with	with	ADP
ejpam-4354	79	16	k	k	PROPN
ejpam-4354	79	17	≥	≥	NUM
ejpam-4354	79	18	2	2	NUM
ejpam-4354	79	19	and	and	CCONJ
ejpam-4354	79	20	let	let	VERB
ejpam-4354	79	21	h	h	NOUN
ejpam-4354	79	22	=	=	PUNCT
ejpam-4354	79	23	k1	k1	PROPN
ejpam-4354	80	1	+	+	NOUN
ejpam-4354	80	2	g	g	NOUN
ejpam-4354	80	3	=	=	SYM
ejpam-4354	80	4	〈	〈	PROPN
ejpam-4354	80	5	v〉+g	v〉+g	NOUN
ejpam-4354	80	6	.	.	PUNCT
ejpam-4354	81	1	(	(	PUNCT
ejpam-4354	81	2	i	i	NOUN
ejpam-4354	81	3	)	)	PUNCT
ejpam-4354	81	4	if	if	SCONJ
ejpam-4354	81	5	diamm(gi	diamm(gi	ADJ
ejpam-4354	81	6	)	)	PUNCT
ejpam-4354	81	7	≤	≤	NOUN
ejpam-4354	81	8	2	2	NUM
ejpam-4354	81	9	for	for	ADP
ejpam-4354	81	10	each	each	DET
ejpam-4354	81	11	i	i	PRON
ejpam-4354	81	12	∈	∈	PROPN
ejpam-4354	81	13	{	{	PUNCT
ejpam-4354	81	14	1	1	NUM
ejpam-4354	81	15	,	,	PUNCT
ejpam-4354	81	16	2	2	NUM
ejpam-4354	81	17	,	,	PUNCT
ejpam-4354	81	18	...	...	PUNCT
ejpam-4354	81	19	,	,	PUNCT
ejpam-4354	81	20	k	k	NOUN
ejpam-4354	81	21	}	}	PUNCT
ejpam-4354	81	22	and	and	CCONJ
ejpam-4354	81	23	one	one	NUM
ejpam-4354	81	24	of	of	ADP
ejpam-4354	81	25	the	the	DET
ejpam-4354	81	26	components	component	NOUN
ejpam-4354	81	27	is	be	AUX
ejpam-4354	81	28	trivial	trivial	ADJ
ejpam-4354	81	29	,	,	PUNCT
ejpam-4354	81	30	then	then	ADV
ejpam-4354	81	31	γme(h	γme(h	PROPN
ejpam-4354	81	32	)	)	PUNCT
ejpam-4354	81	33	=	=	SYM
ejpam-4354	81	34	1	1	X
ejpam-4354	81	35	.	.	PUNCT
ejpam-4354	81	36	(	(	PUNCT
ejpam-4354	81	37	ii	ii	NOUN
ejpam-4354	81	38	)	)	PUNCT
ejpam-4354	81	39	if	if	SCONJ
ejpam-4354	81	40	diamm(gi	diamm(gi	NOUN
ejpam-4354	81	41	)	)	PUNCT
ejpam-4354	81	42	≤	≤	NOUN
ejpam-4354	81	43	2	2	NUM
ejpam-4354	81	44	for	for	ADP
ejpam-4354	81	45	each	each	DET
ejpam-4354	81	46	i	i	PRON
ejpam-4354	81	47	∈	∈	PROPN
ejpam-4354	81	48	{	{	PUNCT
ejpam-4354	81	49	1	1	NUM
ejpam-4354	81	50	,	,	PUNCT
ejpam-4354	81	51	2	2	NUM
ejpam-4354	81	52	,	,	PUNCT
ejpam-4354	81	53	...	...	PUNCT
ejpam-4354	81	54	,	,	PUNCT
ejpam-4354	81	55	k	k	NOUN
ejpam-4354	81	56	}	}	PUNCT
ejpam-4354	81	57	and	and	CCONJ
ejpam-4354	81	58	none	none	NOUN
ejpam-4354	81	59	of	of	ADP
ejpam-4354	81	60	the	the	DET
ejpam-4354	81	61	components	component	NOUN
ejpam-4354	81	62	is	be	AUX
ejpam-4354	81	63	trivial	trivial	ADJ
ejpam-4354	81	64	,	,	PUNCT
ejpam-4354	81	65	then	then	ADV
ejpam-4354	81	66	γme(h	γme(h	PROPN
ejpam-4354	81	67	)	)	PUNCT
ejpam-4354	82	1	=	=	SYM
ejpam-4354	82	2	2	2	X
ejpam-4354	82	3	.	.	PUNCT
ejpam-4354	82	4	proof	proof	NOUN
ejpam-4354	82	5	.	.	PUNCT
ejpam-4354	83	1	(	(	PUNCT
ejpam-4354	83	2	i	i	NOUN
ejpam-4354	83	3	)	)	PUNCT
ejpam-4354	83	4	let	let	VERB
ejpam-4354	83	5	gj	gj	NOUN
ejpam-4354	83	6	be	be	AUX
ejpam-4354	83	7	a	a	DET
ejpam-4354	83	8	trivial	trivial	ADJ
ejpam-4354	83	9	component	component	NOUN
ejpam-4354	83	10	of	of	ADP
ejpam-4354	83	11	g.	g.	PROPN
ejpam-4354	83	12	set	set	PROPN
ejpam-4354	83	13	s	s	PART
ejpam-4354	83	14	=	=	X
ejpam-4354	83	15	v	v	PROPN
ejpam-4354	83	16	(	(	PUNCT
ejpam-4354	83	17	gj	gj	NOUN
ejpam-4354	83	18	)	)	PUNCT
ejpam-4354	83	19	=	=	PRON
ejpam-4354	83	20	{	{	PUNCT
ejpam-4354	83	21	w	w	NOUN
ejpam-4354	83	22	}	}	PUNCT
ejpam-4354	83	23	.	.	PUNCT
ejpam-4354	84	1	clearly	clearly	ADV
ejpam-4354	84	2	,	,	PUNCT
ejpam-4354	84	3	nh(w	nh(w	PUNCT
ejpam-4354	84	4	)	)	PUNCT
ejpam-4354	84	5	=	=	SYM
ejpam-4354	84	6	{	{	PUNCT
ejpam-4354	84	7	v	v	NOUN
ejpam-4354	84	8	}	}	PUNCT
ejpam-4354	84	9	.	.	PUNCT
ejpam-4354	85	1	since	since	SCONJ
ejpam-4354	85	2	diamm(gi	diamm(gi	NOUN
ejpam-4354	85	3	)	)	PUNCT
ejpam-4354	85	4	≤	≤	NOUN
ejpam-4354	85	5	2	2	NUM
ejpam-4354	85	6	for	for	ADP
ejpam-4354	85	7	each	each	DET
ejpam-4354	85	8	i	i	PRON
ejpam-4354	85	9	∈	∈	PROPN
ejpam-4354	85	10	{	{	PUNCT
ejpam-4354	85	11	1	1	NUM
ejpam-4354	85	12	,	,	PUNCT
ejpam-4354	85	13	2	2	NUM
ejpam-4354	85	14	,	,	PUNCT
ejpam-4354	85	15	...	...	PUNCT
ejpam-4354	85	16	,	,	PUNCT
ejpam-4354	85	17	k	k	X
ejpam-4354	85	18	}	}	PUNCT
ejpam-4354	85	19	,	,	PUNCT
ejpam-4354	85	20	the	the	DET
ejpam-4354	85	21	conditions	condition	NOUN
ejpam-4354	85	22	given	give	VERB
ejpam-4354	85	23	in	in	ADP
ejpam-4354	85	24	theorem	theorem	ADJ
ejpam-4354	85	25	1	1	NUM
ejpam-4354	85	26	are	be	AUX
ejpam-4354	85	27	satisfied	satisfied	ADJ
ejpam-4354	85	28	.	.	PUNCT
ejpam-4354	86	1	therefore	therefore	ADV
ejpam-4354	86	2	,	,	PUNCT
ejpam-4354	86	3	γme(h	γme(h	PROPN
ejpam-4354	86	4	)	)	PUNCT
ejpam-4354	86	5	=	=	SYM
ejpam-4354	86	6	1	1	X
ejpam-4354	86	7	.	.	PUNCT
ejpam-4354	86	8	(	(	PUNCT
ejpam-4354	86	9	ii	ii	NOUN
ejpam-4354	86	10	)	)	PUNCT
ejpam-4354	86	11	since	since	SCONJ
ejpam-4354	86	12	none	none	NOUN
ejpam-4354	86	13	of	of	ADP
ejpam-4354	86	14	the	the	DET
ejpam-4354	86	15	components	component	NOUN
ejpam-4354	86	16	is	be	AUX
ejpam-4354	86	17	trivial	trivial	ADJ
ejpam-4354	86	18	,	,	PUNCT
ejpam-4354	86	19	none	none	NOUN
ejpam-4354	86	20	of	of	ADP
ejpam-4354	86	21	the	the	DET
ejpam-4354	86	22	vertices	vertex	NOUN
ejpam-4354	86	23	of	of	ADP
ejpam-4354	86	24	h	h	NOUN
ejpam-4354	86	25	satisfies	satisfie	NOUN
ejpam-4354	86	26	the	the	DET
ejpam-4354	86	27	conditions	condition	NOUN
ejpam-4354	86	28	in	in	ADP
ejpam-4354	86	29	theorem	theorem	NOUN
ejpam-4354	86	30	1	1	NUM
ejpam-4354	86	31	.	.	PUNCT
ejpam-4354	87	1	it	it	PRON
ejpam-4354	87	2	follows	follow	VERB
ejpam-4354	87	3	that	that	SCONJ
ejpam-4354	87	4	γme(h	γme(h	PROPN
ejpam-4354	87	5	)	)	PUNCT
ejpam-4354	87	6	≥	≥	NOUN
ejpam-4354	87	7	2	2	NUM
ejpam-4354	87	8	.	.	PUNCT
ejpam-4354	87	9	pick	pick	VERB
ejpam-4354	87	10	wi	wi	PROPN
ejpam-4354	87	11	∈	∈	PROPN
ejpam-4354	87	12	v	v	PROPN
ejpam-4354	87	13	(	(	PUNCT
ejpam-4354	87	14	gi	gi	INTJ
ejpam-4354	87	15	)	)	PUNCT
ejpam-4354	87	16	for	for	ADP
ejpam-4354	87	17	i	i	PROPN
ejpam-4354	87	18	=	=	SYM
ejpam-4354	87	19	1	1	NUM
ejpam-4354	87	20	,	,	PUNCT
ejpam-4354	87	21	2	2	NUM
ejpam-4354	87	22	and	and	CCONJ
ejpam-4354	87	23	let	let	VERB
ejpam-4354	87	24	s	s	PRON
ejpam-4354	87	25	=	=	NOUN
ejpam-4354	87	26	{	{	PUNCT
ejpam-4354	87	27	w1	w1	NOUN
ejpam-4354	87	28	,	,	PUNCT
ejpam-4354	87	29	w2	w2	NOUN
ejpam-4354	87	30	}	}	PUNCT
ejpam-4354	87	31	.	.	PUNCT
ejpam-4354	88	1	clearly	clearly	ADV
ejpam-4354	88	2	,	,	PUNCT
ejpam-4354	88	3	w1	w1	NOUN
ejpam-4354	88	4	is	be	AUX
ejpam-4354	88	5	a	a	DET
ejpam-4354	88	6	monophonic	monophonic	ADJ
ejpam-4354	88	7	eccentric	eccentric	ADJ
ejpam-4354	88	8	vertex	vertex	NOUN
ejpam-4354	88	9	of	of	ADP
ejpam-4354	88	10	v.	v.	INTJ
ejpam-4354	88	11	let	let	VERB
ejpam-4354	88	12	z	z	PROPN
ejpam-4354	88	13	∈	∈	PROPN
ejpam-4354	88	14	v	v	ADP
ejpam-4354	88	15	(	(	PUNCT
ejpam-4354	88	16	g	g	NOUN
ejpam-4354	88	17	)	)	PUNCT
ejpam-4354	88	18	\	\	PUNCT
ejpam-4354	89	1	s.	s.	PROPN
ejpam-4354	89	2	suppose	suppose	VERB
ejpam-4354	89	3	z	z	X
ejpam-4354	89	4	/∈	/∈	PUNCT
ejpam-4354	90	1	v	v	INTJ
ejpam-4354	90	2	(	(	PUNCT
ejpam-4354	90	3	g1	g1	PROPN
ejpam-4354	90	4	)	)	PUNCT
ejpam-4354	90	5	∪	∪	NOUN
ejpam-4354	90	6	v	v	PROPN
ejpam-4354	90	7	(	(	PUNCT
ejpam-4354	90	8	g2	g2	PROPN
ejpam-4354	90	9	)	)	PUNCT
ejpam-4354	90	10	.	.	PUNCT
ejpam-4354	91	1	since	since	SCONJ
ejpam-4354	91	2	diamm(gi	diamm(gi	NOUN
ejpam-4354	91	3	)	)	PUNCT
ejpam-4354	91	4	≤	≤	NOUN
ejpam-4354	91	5	2	2	NUM
ejpam-4354	91	6	for	for	ADP
ejpam-4354	91	7	each	each	DET
ejpam-4354	91	8	i	i	PRON
ejpam-4354	91	9	∈	∈	PROPN
ejpam-4354	91	10	{	{	PUNCT
ejpam-4354	91	11	1	1	NUM
ejpam-4354	91	12	,	,	PUNCT
ejpam-4354	91	13	2	2	NUM
ejpam-4354	91	14	,	,	PUNCT
ejpam-4354	91	15	...	...	PUNCT
ejpam-4354	91	16	,	,	PUNCT
ejpam-4354	91	17	k	k	X
ejpam-4354	91	18	}	}	PUNCT
ejpam-4354	91	19	,	,	PUNCT
ejpam-4354	91	20	it	it	PRON
ejpam-4354	91	21	follows	follow	VERB
ejpam-4354	91	22	that	that	SCONJ
ejpam-4354	91	23	w1	w1	NOUN
ejpam-4354	91	24	and	and	CCONJ
ejpam-4354	91	25	w2	w2	NOUN
ejpam-4354	91	26	are	be	AUX
ejpam-4354	91	27	monophonic	monophonic	ADJ
ejpam-4354	91	28	eccentric	eccentric	ADJ
ejpam-4354	91	29	vertices	vertex	NOUN
ejpam-4354	91	30	of	of	ADP
ejpam-4354	91	31	z	z	PROPN
ejpam-4354	91	32	in	in	ADP
ejpam-4354	91	33	h.	h.	PROPN
ejpam-4354	91	34	suppose	suppose	VERB
ejpam-4354	91	35	z	z	PROPN
ejpam-4354	91	36	∈	∈	PROPN
ejpam-4354	91	37	v	v	PROPN
ejpam-4354	91	38	(	(	PUNCT
ejpam-4354	91	39	g1	g1	PROPN
ejpam-4354	91	40	)	)	PUNCT
ejpam-4354	91	41	.	.	PUNCT
ejpam-4354	92	1	by	by	ADP
ejpam-4354	92	2	assumption	assumption	NOUN
ejpam-4354	92	3	,	,	PUNCT
ejpam-4354	92	4	dmgi	dmgi	NOUN
ejpam-4354	92	5	(	(	PUNCT
ejpam-4354	92	6	z	z	NOUN
ejpam-4354	92	7	,	,	PUNCT
ejpam-4354	92	8	w1	w1	NOUN
ejpam-4354	92	9	)	)	PUNCT
ejpam-4354	92	10	≤	≤	NOUN
ejpam-4354	92	11	2	2	NUM
ejpam-4354	92	12	.	.	PUNCT
ejpam-4354	93	1	hence	hence	ADV
ejpam-4354	93	2	,	,	PUNCT
ejpam-4354	93	3	emh(z	emh(z	PROPN
ejpam-4354	93	4	)	)	PUNCT
ejpam-4354	93	5	=	=	SYM
ejpam-4354	93	6	dmh(z	dmh(z	PROPN
ejpam-4354	93	7	,	,	PUNCT
ejpam-4354	93	8	w2	w2	NOUN
ejpam-4354	93	9	)	)	PUNCT
ejpam-4354	93	10	=	=	SYM
ejpam-4354	93	11	2	2	NUM
ejpam-4354	93	12	,	,	PUNCT
ejpam-4354	93	13	that	that	ADV
ejpam-4354	93	14	is	is	ADV
ejpam-4354	93	15	,	,	PUNCT
ejpam-4354	93	16	w2	w2	NOUN
ejpam-4354	93	17	is	be	AUX
ejpam-4354	93	18	a	a	DET
ejpam-4354	93	19	monophonic	monophonic	ADJ
ejpam-4354	93	20	eccentric	eccentric	ADJ
ejpam-4354	93	21	vertex	vertex	NOUN
ejpam-4354	93	22	of	of	ADP
ejpam-4354	93	23	z	z	PROPN
ejpam-4354	93	24	in	in	ADP
ejpam-4354	93	25	h.	h.	PROPN
ejpam-4354	93	26	similarly	similarly	ADV
ejpam-4354	93	27	,	,	PUNCT
ejpam-4354	93	28	w1	w1	NOUN
ejpam-4354	93	29	is	be	AUX
ejpam-4354	93	30	a	a	DET
ejpam-4354	93	31	monophonic	monophonic	ADJ
ejpam-4354	93	32	eccentric	eccentric	ADJ
ejpam-4354	93	33	vertex	vertex	NOUN
ejpam-4354	93	34	of	of	ADP
ejpam-4354	93	35	z	z	PROPN
ejpam-4354	93	36	in	in	ADP
ejpam-4354	93	37	h	h	NOUN
ejpam-4354	93	38	if	if	SCONJ
ejpam-4354	93	39	z	z	PROPN
ejpam-4354	93	40	∈	∈	PROPN
ejpam-4354	93	41	v	v	X
ejpam-4354	93	42	(	(	PUNCT
ejpam-4354	93	43	g2	g2	PROPN
ejpam-4354	93	44	)	)	PUNCT
ejpam-4354	93	45	.	.	PUNCT
ejpam-4354	94	1	this	this	PRON
ejpam-4354	94	2	shows	show	VERB
ejpam-4354	94	3	that	that	SCONJ
ejpam-4354	94	4	s	s	VERB
ejpam-4354	94	5	is	be	AUX
ejpam-4354	94	6	a	a	DET
ejpam-4354	94	7	monophonic	monophonic	ADJ
ejpam-4354	94	8	eccentric	eccentric	ADJ
ejpam-4354	94	9	dominating	dominating	NOUN
ejpam-4354	94	10	set	set	NOUN
ejpam-4354	94	11	of	of	ADP
ejpam-4354	94	12	h.	h.	PROPN
ejpam-4354	94	13	therefore	therefore	ADV
ejpam-4354	94	14	,	,	PUNCT
ejpam-4354	94	15	γme(h	γme(h	PROPN
ejpam-4354	94	16	)	)	PUNCT
ejpam-4354	94	17	=	=	SYM
ejpam-4354	94	18	|s|	|s|	NOUN
ejpam-4354	94	19	=	=	SYM
ejpam-4354	94	20	2	2	PROPN
ejpam-4354	94	21	.	.	PUNCT
ejpam-4354	94	22	s.	s.	PROPN
ejpam-4354	94	23	canoy	canoy	PROPN
ejpam-4354	94	24	,	,	PUNCT
ejpam-4354	94	25	jr	jr	PROPN
ejpam-4354	94	26	.	.	PROPN
ejpam-4354	94	27	,	,	PUNCT
ejpam-4354	94	28	a.	a.	NOUN
ejpam-4354	94	29	gamorez	gamorez	PROPN
ejpam-4354	94	30	/	/	SYM
ejpam-4354	94	31	eur	eur	PROPN
ejpam-4354	94	32	.	.	PUNCT
ejpam-4354	95	1	j.	j.	PROPN
ejpam-4354	95	2	pure	pure	PROPN
ejpam-4354	95	3	appl	appl	PROPN
ejpam-4354	95	4	.	.	PROPN
ejpam-4354	95	5	math	math	PROPN
ejpam-4354	95	6	,	,	PUNCT
ejpam-4354	95	7	15	15	NUM
ejpam-4354	95	8	(	(	PUNCT
ejpam-4354	95	9	2	2	NUM
ejpam-4354	95	10	)	)	PUNCT
ejpam-4354	95	11	(	(	PUNCT
ejpam-4354	95	12	2022	2022	NUM
ejpam-4354	95	13	)	)	PUNCT
ejpam-4354	95	14	,	,	PUNCT
ejpam-4354	95	15	635	635	NUM
ejpam-4354	95	16	-	-	SYM
ejpam-4354	95	17	645	645	NUM
ejpam-4354	95	18	638	638	NUM
ejpam-4354	95	19	theorem	theorem	NOUN
ejpam-4354	95	20	3	3	X
ejpam-4354	95	21	.	.	PUNCT
ejpam-4354	96	1	let	let	VERB
ejpam-4354	96	2	g	g	PRON
ejpam-4354	96	3	be	be	AUX
ejpam-4354	96	4	a	a	DET
ejpam-4354	96	5	connected	connected	ADJ
ejpam-4354	96	6	non	non	ADJ
ejpam-4354	96	7	-	-	ADJ
ejpam-4354	96	8	complete	complete	ADJ
ejpam-4354	96	9	graph	graph	NOUN
ejpam-4354	96	10	and	and	CCONJ
ejpam-4354	96	11	let	let	VERB
ejpam-4354	96	12	k1	k1	NOUN
ejpam-4354	96	13	=	=	PUNCT
ejpam-4354	96	14	〈	〈	PROPN
ejpam-4354	96	15	v	v	NOUN
ejpam-4354	96	16	〉	〉	PROPN
ejpam-4354	96	17	.	.	PUNCT
ejpam-4354	97	1	then	then	ADV
ejpam-4354	97	2	s	s	VERB
ejpam-4354	97	3	is	be	AUX
ejpam-4354	97	4	a	a	DET
ejpam-4354	97	5	monophonic	monophonic	ADJ
ejpam-4354	97	6	eccentric	eccentric	ADJ
ejpam-4354	97	7	dominating	dominating	NOUN
ejpam-4354	97	8	set	set	NOUN
ejpam-4354	97	9	of	of	ADP
ejpam-4354	97	10	k1	k1	NOUN
ejpam-4354	98	1	+	+	ADP
ejpam-4354	98	2	g	g	PROPN
ejpam-4354	98	3	if	if	SCONJ
ejpam-4354	98	4	and	and	CCONJ
ejpam-4354	98	5	only	only	ADV
ejpam-4354	98	6	if	if	SCONJ
ejpam-4354	98	7	s	s	X
ejpam-4354	98	8	∩	∩	ADJ
ejpam-4354	98	9	v	v	ADJ
ejpam-4354	98	10	(	(	PUNCT
ejpam-4354	98	11	g	g	NOUN
ejpam-4354	98	12	)	)	PUNCT
ejpam-4354	98	13	is	be	AUX
ejpam-4354	98	14	a	a	DET
ejpam-4354	98	15	monophonic	monophonic	ADJ
ejpam-4354	98	16	eccentric	eccentric	ADJ
ejpam-4354	98	17	dominating	dominating	NOUN
ejpam-4354	98	18	set	set	NOUN
ejpam-4354	98	19	of	of	ADP
ejpam-4354	98	20	g.	g.	PROPN
ejpam-4354	98	21	proof	proof	PROPN
ejpam-4354	98	22	.	.	PUNCT
ejpam-4354	99	1	suppose	suppose	VERB
ejpam-4354	99	2	s	s	NOUN
ejpam-4354	99	3	is	be	AUX
ejpam-4354	99	4	a	a	DET
ejpam-4354	99	5	monophonic	monophonic	ADJ
ejpam-4354	99	6	eccentric	eccentric	ADJ
ejpam-4354	99	7	dominating	dominating	NOUN
ejpam-4354	99	8	set	set	NOUN
ejpam-4354	99	9	of	of	ADP
ejpam-4354	99	10	k1	k1	PROPN
ejpam-4354	99	11	+	+	CCONJ
ejpam-4354	99	12	g.	g.	NOUN
ejpam-4354	99	13	since	since	SCONJ
ejpam-4354	99	14	g	g	PROPN
ejpam-4354	99	15	is	be	AUX
ejpam-4354	99	16	non	non	ADJ
ejpam-4354	99	17	-	-	ADJ
ejpam-4354	99	18	complete	complete	ADJ
ejpam-4354	99	19	,	,	PUNCT
ejpam-4354	99	20	sg	sg	ADP
ejpam-4354	99	21	=	=	SYM
ejpam-4354	99	22	s	s	PROPN
ejpam-4354	99	23	∩	∩	ADJ
ejpam-4354	99	24	v	v	X
ejpam-4354	99	25	(	(	PUNCT
ejpam-4354	99	26	g	g	NOUN
ejpam-4354	99	27	)	)	PUNCT
ejpam-4354	99	28	6=	6=	ADP
ejpam-4354	99	29	∅.	∅.	AUX
ejpam-4354	99	30	let	let	VERB
ejpam-4354	99	31	w	w	PROPN
ejpam-4354	99	32	∈	∈	PROPN
ejpam-4354	99	33	v	v	ADP
ejpam-4354	99	34	(	(	PUNCT
ejpam-4354	99	35	g	g	NOUN
ejpam-4354	99	36	)	)	PUNCT
ejpam-4354	99	37	\	\	PROPN
ejpam-4354	100	1	sg	sg	PROPN
ejpam-4354	100	2	.	.	PUNCT
ejpam-4354	101	1	if	if	SCONJ
ejpam-4354	101	2	dg(w	dg(w	NOUN
ejpam-4354	101	3	,	,	PUNCT
ejpam-4354	101	4	x	x	X
ejpam-4354	101	5	)	)	PUNCT
ejpam-4354	101	6	=	=	SYM
ejpam-4354	101	7	1	1	NUM
ejpam-4354	101	8	for	for	ADP
ejpam-4354	101	9	every	every	DET
ejpam-4354	101	10	x	x	SYM
ejpam-4354	101	11	∈	∈	PROPN
ejpam-4354	101	12	s	s	NOUN
ejpam-4354	101	13	,	,	PUNCT
ejpam-4354	101	14	then	then	ADV
ejpam-4354	101	15	every	every	DET
ejpam-4354	101	16	element	element	NOUN
ejpam-4354	101	17	of	of	ADP
ejpam-4354	101	18	sg	sg	PROPN
ejpam-4354	101	19	is	be	AUX
ejpam-4354	101	20	a	a	DET
ejpam-4354	101	21	monophonic	monophonic	ADJ
ejpam-4354	101	22	eccentric	eccentric	ADJ
ejpam-4354	101	23	vertex	vertex	NOUN
ejpam-4354	101	24	of	of	ADP
ejpam-4354	101	25	w.	w.	PROPN
ejpam-4354	101	26	suppose	suppose	VERB
ejpam-4354	101	27	dg(w	dg(w	NOUN
ejpam-4354	101	28	,	,	PUNCT
ejpam-4354	101	29	y	y	PROPN
ejpam-4354	101	30	)	)	PUNCT
ejpam-4354	101	31	6=	6=	ADP
ejpam-4354	101	32	1	1	NUM
ejpam-4354	101	33	for	for	ADP
ejpam-4354	101	34	some	some	DET
ejpam-4354	101	35	y	y	PROPN
ejpam-4354	101	36	∈	∈	PROPN
ejpam-4354	101	37	s.	s.	PROPN
ejpam-4354	101	38	then	then	ADV
ejpam-4354	101	39	emk1+g(w	emk1+g(w	PROPN
ejpam-4354	101	40	)	)	PUNCT
ejpam-4354	102	1	=	=	SYM
ejpam-4354	102	2	emg	emg	NOUN
ejpam-4354	102	3	(	(	PUNCT
ejpam-4354	102	4	w	w	PROPN
ejpam-4354	102	5	)	)	PUNCT
ejpam-4354	102	6	≥	≥	NOUN
ejpam-4354	102	7	dmg	dmg	NOUN
ejpam-4354	102	8	(	(	PUNCT
ejpam-4354	102	9	w	w	PROPN
ejpam-4354	102	10	,	,	PUNCT
ejpam-4354	102	11	y	y	PROPN
ejpam-4354	102	12	)	)	PUNCT
ejpam-4354	102	13	≥	≥	NOUN
ejpam-4354	102	14	2	2	NUM
ejpam-4354	102	15	.	.	PUNCT
ejpam-4354	103	1	since	since	SCONJ
ejpam-4354	103	2	s	s	PROPN
ejpam-4354	103	3	is	be	AUX
ejpam-4354	103	4	a	a	DET
ejpam-4354	103	5	monophonic	monophonic	ADJ
ejpam-4354	103	6	eccentric	eccentric	ADJ
ejpam-4354	103	7	dominating	dominating	NOUN
ejpam-4354	103	8	set	set	NOUN
ejpam-4354	103	9	of	of	ADP
ejpam-4354	103	10	k1	k1	NOUN
ejpam-4354	103	11	+	+	CCONJ
ejpam-4354	103	12	g	g	NOUN
ejpam-4354	103	13	,	,	PUNCT
ejpam-4354	103	14	there	there	PRON
ejpam-4354	103	15	exists	exist	VERB
ejpam-4354	103	16	a	a	DET
ejpam-4354	103	17	monophonic	monophonic	ADJ
ejpam-4354	103	18	eccentric	eccentric	ADJ
ejpam-4354	103	19	vertex	vertex	NOUN
ejpam-4354	103	20	z	z	PROPN
ejpam-4354	103	21	∈	∈	PROPN
ejpam-4354	103	22	s	s	X
ejpam-4354	103	23	of	of	ADP
ejpam-4354	103	24	w.	w.	NOUN
ejpam-4354	103	25	since	since	SCONJ
ejpam-4354	103	26	dmk1+g(w	dmk1+g(w	PROPN
ejpam-4354	103	27	,	,	PUNCT
ejpam-4354	103	28	v	v	NOUN
ejpam-4354	103	29	)	)	PUNCT
ejpam-4354	103	30	=	=	SYM
ejpam-4354	103	31	1	1	NUM
ejpam-4354	103	32	,	,	PUNCT
ejpam-4354	103	33	z	z	NOUN
ejpam-4354	103	34	6=	6=	PROPN
ejpam-4354	103	35	v.	v.	ADP
ejpam-4354	103	36	thus	thus	ADV
ejpam-4354	103	37	,	,	PUNCT
ejpam-4354	103	38	z	z	PROPN
ejpam-4354	103	39	∈	∈	PROPN
ejpam-4354	103	40	sg	sg	PROPN
ejpam-4354	103	41	and	and	CCONJ
ejpam-4354	103	42	emg	emg	PROPN
ejpam-4354	103	43	(	(	PUNCT
ejpam-4354	103	44	w	w	NOUN
ejpam-4354	103	45	)	)	PUNCT
ejpam-4354	103	46	=	=	SYM
ejpam-4354	103	47	dmg	dmg	X
ejpam-4354	103	48	(	(	PUNCT
ejpam-4354	103	49	z	z	NOUN
ejpam-4354	103	50	,	,	PUNCT
ejpam-4354	103	51	w	w	NOUN
ejpam-4354	103	52	)	)	PUNCT
ejpam-4354	103	53	.	.	PUNCT
ejpam-4354	104	1	hence	hence	ADV
ejpam-4354	104	2	,	,	PUNCT
ejpam-4354	104	3	s	s	VERB
ejpam-4354	104	4	∩	∩	ADJ
ejpam-4354	104	5	v	v	ADJ
ejpam-4354	104	6	(	(	PUNCT
ejpam-4354	104	7	g	g	NOUN
ejpam-4354	104	8	)	)	PUNCT
ejpam-4354	104	9	is	be	AUX
ejpam-4354	104	10	a	a	DET
ejpam-4354	104	11	monophonic	monophonic	ADJ
ejpam-4354	104	12	eccentric	eccentric	ADJ
ejpam-4354	104	13	dominating	dominating	NOUN
ejpam-4354	104	14	set	set	NOUN
ejpam-4354	104	15	of	of	ADP
ejpam-4354	104	16	g.	g.	PROPN
ejpam-4354	104	17	for	for	ADP
ejpam-4354	104	18	the	the	DET
ejpam-4354	104	19	converse	converse	NOUN
ejpam-4354	104	20	,	,	PUNCT
ejpam-4354	104	21	suppose	suppose	VERB
ejpam-4354	104	22	that	that	SCONJ
ejpam-4354	104	23	sg	sg	VERB
ejpam-4354	104	24	=	=	SYM
ejpam-4354	104	25	s	s	PROPN
ejpam-4354	104	26	∩	∩	ADJ
ejpam-4354	104	27	v	v	X
ejpam-4354	104	28	(	(	PUNCT
ejpam-4354	104	29	g	g	NOUN
ejpam-4354	104	30	)	)	PUNCT
ejpam-4354	104	31	is	be	AUX
ejpam-4354	104	32	a	a	DET
ejpam-4354	104	33	monophonic	monophonic	ADJ
ejpam-4354	104	34	eccentric	eccentric	ADJ
ejpam-4354	104	35	dominating	dominating	NOUN
ejpam-4354	104	36	set	set	NOUN
ejpam-4354	104	37	of	of	ADP
ejpam-4354	104	38	g.	g.	PROPN
ejpam-4354	104	39	let	let	VERB
ejpam-4354	104	40	u	u	PRON
ejpam-4354	104	41	∈	∈	PROPN
ejpam-4354	104	42	v	v	NOUN
ejpam-4354	104	43	(	(	PUNCT
ejpam-4354	104	44	k1	k1	NOUN
ejpam-4354	104	45	+	+	CCONJ
ejpam-4354	104	46	g	g	NOUN
ejpam-4354	104	47	)	)	PUNCT
ejpam-4354	104	48	\	\	PUNCT
ejpam-4354	105	1	s.	s.	PROPN
ejpam-4354	105	2	if	if	SCONJ
ejpam-4354	105	3	u	u	PROPN
ejpam-4354	105	4	=	=	PROPN
ejpam-4354	105	5	v	v	NOUN
ejpam-4354	105	6	,	,	PUNCT
ejpam-4354	105	7	then	then	ADV
ejpam-4354	105	8	every	every	DET
ejpam-4354	105	9	element	element	NOUN
ejpam-4354	105	10	of	of	ADP
ejpam-4354	105	11	s	s	PROPN
ejpam-4354	105	12	is	be	AUX
ejpam-4354	105	13	a	a	DET
ejpam-4354	105	14	monophonic	monophonic	ADJ
ejpam-4354	105	15	eccentric	eccentric	ADJ
ejpam-4354	105	16	vertex	vertex	NOUN
ejpam-4354	105	17	of	of	ADP
ejpam-4354	105	18	u	u	NOUN
ejpam-4354	105	19	in	in	ADP
ejpam-4354	105	20	k1	k1	PROPN
ejpam-4354	105	21	+	+	CCONJ
ejpam-4354	105	22	g.	g.	PROPN
ejpam-4354	105	23	suppose	suppose	VERB
ejpam-4354	105	24	u	u	PROPN
ejpam-4354	105	25	6=	6=	PROPN
ejpam-4354	105	26	v.	v.	ADP
ejpam-4354	105	27	since	since	SCONJ
ejpam-4354	105	28	sg	sg	PROPN
ejpam-4354	105	29	is	be	AUX
ejpam-4354	105	30	a	a	DET
ejpam-4354	105	31	monophonic	monophonic	ADJ
ejpam-4354	105	32	eccentric	eccentric	ADJ
ejpam-4354	105	33	dominating	dominating	NOUN
ejpam-4354	105	34	set	set	NOUN
ejpam-4354	105	35	of	of	ADP
ejpam-4354	105	36	g	g	PROPN
ejpam-4354	105	37	and	and	CCONJ
ejpam-4354	106	1	u	u	PROPN
ejpam-4354	106	2	∈	∈	PROPN
ejpam-4354	106	3	v	v	ADP
ejpam-4354	106	4	(	(	PUNCT
ejpam-4354	106	5	g	g	NOUN
ejpam-4354	106	6	)	)	PUNCT
ejpam-4354	106	7	\	\	PROPN
ejpam-4354	106	8	sg	sg	PROPN
ejpam-4354	106	9	,	,	PUNCT
ejpam-4354	106	10	there	there	PRON
ejpam-4354	106	11	exists	exist	VERB
ejpam-4354	106	12	p	p	PROPN
ejpam-4354	106	13	∈	∈	PROPN
ejpam-4354	106	14	sg	sg	ADP
ejpam-4354	106	15	such	such	ADJ
ejpam-4354	106	16	that	that	DET
ejpam-4354	106	17	emg	emg	NOUN
ejpam-4354	106	18	(	(	PUNCT
ejpam-4354	106	19	u	u	NOUN
ejpam-4354	106	20	)	)	PUNCT
ejpam-4354	106	21	=	=	SYM
ejpam-4354	106	22	dmg	dmg	NOUN
ejpam-4354	106	23	(	(	PUNCT
ejpam-4354	106	24	p	p	NOUN
ejpam-4354	106	25	,	,	PUNCT
ejpam-4354	106	26	u	u	NOUN
ejpam-4354	106	27	)	)	PUNCT
ejpam-4354	106	28	.	.	PUNCT
ejpam-4354	107	1	hence	hence	ADV
ejpam-4354	107	2	,	,	PUNCT
ejpam-4354	107	3	emk1+g(u	emk1+g(u	PROPN
ejpam-4354	107	4	)	)	PUNCT
ejpam-4354	107	5	=	=	PUNCT
ejpam-4354	108	1	dmk1+g(p	dmk1+g(p	X
ejpam-4354	108	2	,	,	PUNCT
ejpam-4354	108	3	u	u	NOUN
ejpam-4354	108	4	)	)	PUNCT
ejpam-4354	108	5	.	.	PUNCT
ejpam-4354	109	1	this	this	PRON
ejpam-4354	109	2	proves	prove	VERB
ejpam-4354	109	3	that	that	SCONJ
ejpam-4354	109	4	s	s	VERB
ejpam-4354	109	5	is	be	AUX
ejpam-4354	109	6	a	a	DET
ejpam-4354	109	7	monophonic	monophonic	ADJ
ejpam-4354	109	8	eccentric	eccentric	ADJ
ejpam-4354	109	9	dominating	dominating	NOUN
ejpam-4354	109	10	set	set	NOUN
ejpam-4354	109	11	of	of	ADP
ejpam-4354	109	12	k1	k1	PROPN
ejpam-4354	110	1	+	+	CCONJ
ejpam-4354	110	2	g.	g.	NOUN
ejpam-4354	110	3	the	the	DET
ejpam-4354	110	4	next	next	ADJ
ejpam-4354	110	5	result	result	NOUN
ejpam-4354	110	6	is	be	AUX
ejpam-4354	110	7	a	a	DET
ejpam-4354	110	8	consequence	consequence	NOUN
ejpam-4354	110	9	of	of	ADP
ejpam-4354	110	10	theorem	theorem	NOUN
ejpam-4354	110	11	3	3	NUM
ejpam-4354	110	12	and	and	CCONJ
ejpam-4354	110	13	the	the	DET
ejpam-4354	110	14	fact	fact	NOUN
ejpam-4354	110	15	that	that	SCONJ
ejpam-4354	110	16	γme(h	γme(h	PROPN
ejpam-4354	110	17	)	)	PUNCT
ejpam-4354	110	18	=	=	SYM
ejpam-4354	110	19	1	1	NUM
ejpam-4354	110	20	for	for	ADP
ejpam-4354	110	21	every	every	DET
ejpam-4354	110	22	complete	complete	ADJ
ejpam-4354	110	23	graph	graph	NOUN
ejpam-4354	110	24	h.	h.	PROPN
ejpam-4354	110	25	corollary	corollary	NOUN
ejpam-4354	110	26	1	1	PROPN
ejpam-4354	110	27	.	.	PUNCT
ejpam-4354	111	1	let	let	VERB
ejpam-4354	111	2	g	g	PRON
ejpam-4354	111	3	be	be	AUX
ejpam-4354	111	4	a	a	DET
ejpam-4354	111	5	connected	connected	ADJ
ejpam-4354	111	6	graph	graph	NOUN
ejpam-4354	111	7	.	.	PUNCT
ejpam-4354	112	1	then	then	ADV
ejpam-4354	112	2	γme(k1	γme(k1	PROPN
ejpam-4354	113	1	+	+	PROPN
ejpam-4354	113	2	g	g	NOUN
ejpam-4354	113	3	)	)	PUNCT
ejpam-4354	113	4	=	=	SYM
ejpam-4354	113	5	γme(g	γme(g	PROPN
ejpam-4354	113	6	)	)	PUNCT
ejpam-4354	113	7	.	.	PUNCT
ejpam-4354	114	1	theorem	theorem	ADJ
ejpam-4354	114	2	4	4	NUM
ejpam-4354	114	3	.	.	PUNCT
ejpam-4354	115	1	let	let	VERB
ejpam-4354	115	2	g1	g1	PROPN
ejpam-4354	115	3	,	,	PUNCT
ejpam-4354	115	4	g2	g2	PROPN
ejpam-4354	115	5	,	,	PUNCT
ejpam-4354	115	6	...	...	PUNCT
ejpam-4354	115	7	,	,	PUNCT
ejpam-4354	115	8	gk	gk	PROPN
ejpam-4354	115	9	be	be	AUX
ejpam-4354	115	10	the	the	DET
ejpam-4354	115	11	distinct	distinct	ADJ
ejpam-4354	115	12	components	component	NOUN
ejpam-4354	115	13	of	of	ADP
ejpam-4354	115	14	g	g	PROPN
ejpam-4354	115	15	with	with	ADP
ejpam-4354	115	16	k	k	PROPN
ejpam-4354	115	17	≥	≥	NUM
ejpam-4354	115	18	2	2	NUM
ejpam-4354	115	19	and	and	CCONJ
ejpam-4354	115	20	let	let	VERB
ejpam-4354	115	21	h	h	NOUN
ejpam-4354	115	22	=	=	PUNCT
ejpam-4354	115	23	k1	k1	PROPN
ejpam-4354	115	24	+	+	CCONJ
ejpam-4354	115	25	g	g	NOUN
ejpam-4354	115	26	=	=	SYM
ejpam-4354	115	27	〈	〈	PROPN
ejpam-4354	115	28	v	v	NOUN
ejpam-4354	115	29	〉	〉	NOUN
ejpam-4354	115	30	+	+	CCONJ
ejpam-4354	115	31	g.	g.	PROPN
ejpam-4354	115	32	suppose	suppose	VERB
ejpam-4354	115	33	rg	rg	X
ejpam-4354	115	34	=	=	PRON
ejpam-4354	115	35	{	{	PUNCT
ejpam-4354	115	36	j	j	PROPN
ejpam-4354	115	37	∈	∈	PROPN
ejpam-4354	115	38	{	{	PUNCT
ejpam-4354	115	39	1	1	NUM
ejpam-4354	115	40	,	,	PUNCT
ejpam-4354	115	41	2	2	NUM
ejpam-4354	115	42	,	,	PUNCT
ejpam-4354	115	43	...	...	PUNCT
ejpam-4354	115	44	,	,	PUNCT
ejpam-4354	115	45	k	k	NOUN
ejpam-4354	115	46	}	}	PUNCT
ejpam-4354	115	47	:	:	PUNCT
ejpam-4354	115	48	diamm(gj	diamm(gj	PROPN
ejpam-4354	115	49	)	)	PUNCT
ejpam-4354	115	50	≥	≥	NOUN
ejpam-4354	115	51	3	3	NUM
ejpam-4354	115	52	}	}	PUNCT
ejpam-4354	115	53	6=	6=	ADP
ejpam-4354	115	54	∅.	∅.	NOUN
ejpam-4354	115	55	then	then	ADV
ejpam-4354	115	56	s	s	VERB
ejpam-4354	115	57	is	be	AUX
ejpam-4354	115	58	a	a	DET
ejpam-4354	115	59	monophonic	monophonic	ADJ
ejpam-4354	115	60	eccentric	eccentric	ADJ
ejpam-4354	115	61	dominating	dominating	NOUN
ejpam-4354	115	62	set	set	NOUN
ejpam-4354	115	63	of	of	ADP
ejpam-4354	115	64	h	h	NOUN
ejpam-4354	116	1	if	if	SCONJ
ejpam-4354	117	1	and	and	CCONJ
ejpam-4354	117	2	only	only	ADV
ejpam-4354	117	3	if	if	SCONJ
ejpam-4354	117	4	sj	sj	ADP
ejpam-4354	117	5	=	=	NOUN
ejpam-4354	117	6	s	s	PART
ejpam-4354	117	7	∩	∩	ADJ
ejpam-4354	117	8	v	v	NOUN
ejpam-4354	117	9	(	(	PUNCT
ejpam-4354	117	10	gj	gj	NOUN
ejpam-4354	117	11	)	)	PUNCT
ejpam-4354	117	12	is	be	AUX
ejpam-4354	117	13	a	a	DET
ejpam-4354	117	14	d3m	d3m	ADJ
ejpam-4354	117	15	-	-	PUNCT
ejpam-4354	117	16	monophonic	monophonic	ADJ
ejpam-4354	117	17	eccentric	eccentric	ADJ
ejpam-4354	117	18	set	set	NOUN
ejpam-4354	117	19	of	of	ADP
ejpam-4354	117	20	gj	gj	NOUN
ejpam-4354	117	21	for	for	ADP
ejpam-4354	117	22	each	each	DET
ejpam-4354	117	23	j	j	PROPN
ejpam-4354	117	24	∈	∈	PROPN
ejpam-4354	117	25	rg	rg	NOUN
ejpam-4354	117	26	and	and	CCONJ
ejpam-4354	117	27	,	,	PUNCT
ejpam-4354	117	28	in	in	ADP
ejpam-4354	117	29	addition	addition	NOUN
ejpam-4354	117	30	,	,	PUNCT
ejpam-4354	117	31	s	s	NOUN
ejpam-4354	117	32	∩	∩	ADJ
ejpam-4354	117	33	v	v	X
ejpam-4354	117	34	(	(	PUNCT
ejpam-4354	117	35	gt	gt	PROPN
ejpam-4354	117	36	)	)	PUNCT
ejpam-4354	117	37	6=	6=	NOUN
ejpam-4354	117	38	∅	∅	NOUN
ejpam-4354	117	39	for	for	ADP
ejpam-4354	117	40	some	some	DET
ejpam-4354	117	41	t	t	NOUN
ejpam-4354	117	42	∈	∈	PROPN
ejpam-4354	117	43	{	{	PUNCT
ejpam-4354	117	44	1	1	NUM
ejpam-4354	117	45	,	,	PUNCT
ejpam-4354	117	46	2	2	NUM
ejpam-4354	117	47	,	,	PUNCT
ejpam-4354	117	48	...	...	PUNCT
ejpam-4354	117	49	,	,	PUNCT
ejpam-4354	117	50	k	k	NOUN
ejpam-4354	117	51	}	}	PUNCT
ejpam-4354	117	52	\	\	NOUN
ejpam-4354	118	1	rg	rg	X
ejpam-4354	118	2	whenever	whenever	SCONJ
ejpam-4354	118	3	|rg|	|rg|	PROPN
ejpam-4354	118	4	=	=	SYM
ejpam-4354	118	5	1	1	NUM
ejpam-4354	118	6	and	and	CCONJ
ejpam-4354	118	7	there	there	PRON
ejpam-4354	118	8	exists	exist	VERB
ejpam-4354	118	9	p	p	PROPN
ejpam-4354	118	10	∈	∈	PROPN
ejpam-4354	118	11	v	v	ADP
ejpam-4354	118	12	(	(	PUNCT
ejpam-4354	118	13	gr	gr	NOUN
ejpam-4354	118	14	)	)	PUNCT
ejpam-4354	118	15	\	\	PROPN
ejpam-4354	118	16	sr	sr	PROPN
ejpam-4354	118	17	such	such	ADJ
ejpam-4354	118	18	that	that	DET
ejpam-4354	118	19	emgr	emgr	NOUN
ejpam-4354	118	20	(	(	PUNCT
ejpam-4354	118	21	p	p	X
ejpam-4354	118	22	)	)	PUNCT
ejpam-4354	118	23	=	=	SYM
ejpam-4354	118	24	1	1	NUM
ejpam-4354	118	25	or	or	CCONJ
ejpam-4354	118	26	emgr	emgr	NOUN
ejpam-4354	118	27	(	(	PUNCT
ejpam-4354	118	28	p	p	X
ejpam-4354	118	29	)	)	PUNCT
ejpam-4354	118	30	=	=	SYM
ejpam-4354	118	31	2	2	NUM
ejpam-4354	118	32	and	and	CCONJ
ejpam-4354	118	33	dmgr	dmgr	NOUN
ejpam-4354	118	34	(	(	PUNCT
ejpam-4354	118	35	p	p	X
ejpam-4354	118	36	,	,	PUNCT
ejpam-4354	118	37	w	w	NOUN
ejpam-4354	118	38	)	)	PUNCT
ejpam-4354	118	39	=	=	SYM
ejpam-4354	118	40	1	1	NUM
ejpam-4354	118	41	for	for	ADP
ejpam-4354	118	42	all	all	DET
ejpam-4354	118	43	w	w	PROPN
ejpam-4354	118	44	∈	∈	PROPN
ejpam-4354	118	45	sr	sr	PROPN
ejpam-4354	118	46	,	,	PUNCT
ejpam-4354	118	47	where	where	SCONJ
ejpam-4354	118	48	rg	rg	PROPN
ejpam-4354	118	49	=	=	PUNCT
ejpam-4354	118	50	{	{	PUNCT
ejpam-4354	118	51	r	r	NOUN
ejpam-4354	118	52	}	}	PUNCT
ejpam-4354	118	53	.	.	PUNCT
ejpam-4354	119	1	proof	proof	NOUN
ejpam-4354	119	2	.	.	PUNCT
ejpam-4354	120	1	suppose	suppose	VERB
ejpam-4354	120	2	s	s	NOUN
ejpam-4354	120	3	is	be	AUX
ejpam-4354	120	4	a	a	DET
ejpam-4354	120	5	monophonic	monophonic	ADJ
ejpam-4354	120	6	eccentric	eccentric	ADJ
ejpam-4354	120	7	dominating	dominating	NOUN
ejpam-4354	120	8	set	set	NOUN
ejpam-4354	120	9	of	of	ADP
ejpam-4354	120	10	h	h	NOUN
ejpam-4354	120	11	and	and	CCONJ
ejpam-4354	120	12	let	let	VERB
ejpam-4354	120	13	j	j	PROPN
ejpam-4354	120	14	∈	∈	PROPN
ejpam-4354	120	15	rg	rg	PROPN
ejpam-4354	120	16	.	.	PUNCT
ejpam-4354	120	17	let	let	VERB
ejpam-4354	120	18	u	u	PRON
ejpam-4354	120	19	∈	∈	PROPN
ejpam-4354	120	20	v	v	ADP
ejpam-4354	120	21	(	(	PUNCT
ejpam-4354	120	22	gj	gj	NOUN
ejpam-4354	120	23	)	)	PUNCT
ejpam-4354	120	24	\	\	PUNCT
ejpam-4354	121	1	sj	sj	INTJ
ejpam-4354	121	2	with	with	ADP
ejpam-4354	121	3	emgj	emgj	PROPN
ejpam-4354	121	4	(	(	PUNCT
ejpam-4354	121	5	u	u	NOUN
ejpam-4354	121	6	)	)	PUNCT
ejpam-4354	121	7	≥	≥	NOUN
ejpam-4354	121	8	3	3	NUM
ejpam-4354	121	9	.	.	PUNCT
ejpam-4354	121	10	then	then	ADV
ejpam-4354	121	11	by	by	ADP
ejpam-4354	121	12	assumption	assumption	NOUN
ejpam-4354	121	13	,	,	PUNCT
ejpam-4354	121	14	there	there	PRON
ejpam-4354	121	15	exists	exist	VERB
ejpam-4354	121	16	w	w	PROPN
ejpam-4354	121	17	∈	∈	PROPN
ejpam-4354	121	18	s	s	VERB
ejpam-4354	121	19	such	such	ADJ
ejpam-4354	121	20	that	that	DET
ejpam-4354	121	21	emh(u	emh(u	NOUN
ejpam-4354	121	22	)	)	PUNCT
ejpam-4354	121	23	=	=	SYM
ejpam-4354	121	24	dmh(w	dmh(w	PROPN
ejpam-4354	121	25	,	,	PUNCT
ejpam-4354	121	26	u	u	NOUN
ejpam-4354	121	27	)	)	PUNCT
ejpam-4354	121	28	.	.	PUNCT
ejpam-4354	122	1	since	since	SCONJ
ejpam-4354	122	2	emh(u	emh(u	X
ejpam-4354	122	3	)	)	PUNCT
ejpam-4354	122	4	=	=	SYM
ejpam-4354	122	5	emgj	emgj	PROPN
ejpam-4354	122	6	(	(	PUNCT
ejpam-4354	122	7	u	u	NOUN
ejpam-4354	122	8	)	)	PUNCT
ejpam-4354	122	9	≥	≥	NOUN
ejpam-4354	122	10	3	3	NUM
ejpam-4354	122	11	,	,	PUNCT
ejpam-4354	122	12	it	it	PRON
ejpam-4354	122	13	follows	follow	VERB
ejpam-4354	122	14	that	that	SCONJ
ejpam-4354	122	15	w	w	PROPN
ejpam-4354	122	16	∈	∈	PROPN
ejpam-4354	122	17	sj	sj	INTJ
ejpam-4354	122	18	and	and	CCONJ
ejpam-4354	122	19	that	that	SCONJ
ejpam-4354	122	20	emgj	emgj	PROPN
ejpam-4354	122	21	(	(	PUNCT
ejpam-4354	122	22	v	v	NOUN
ejpam-4354	122	23	)	)	PUNCT
ejpam-4354	122	24	=	=	VERB
ejpam-4354	122	25	dmgj	dmgj	NOUN
ejpam-4354	122	26	(	(	PUNCT
ejpam-4354	122	27	w	w	PROPN
ejpam-4354	122	28	,	,	PUNCT
ejpam-4354	122	29	u	u	NOUN
ejpam-4354	122	30	)	)	PUNCT
ejpam-4354	122	31	.	.	PUNCT
ejpam-4354	123	1	this	this	PRON
ejpam-4354	123	2	shows	show	VERB
ejpam-4354	123	3	that	that	SCONJ
ejpam-4354	123	4	sj	sj	PROPN
ejpam-4354	123	5	is	be	AUX
ejpam-4354	123	6	a	a	DET
ejpam-4354	123	7	a	a	DET
ejpam-4354	123	8	d3m	d3m	ADJ
ejpam-4354	123	9	-	-	PUNCT
ejpam-4354	123	10	monophonic	monophonic	ADJ
ejpam-4354	123	11	eccentric	eccentric	ADJ
ejpam-4354	123	12	set	set	NOUN
ejpam-4354	123	13	of	of	ADP
ejpam-4354	123	14	gj	gj	NOUN
ejpam-4354	123	15	for	for	ADP
ejpam-4354	123	16	each	each	DET
ejpam-4354	123	17	j	j	PROPN
ejpam-4354	123	18	∈	∈	PROPN
ejpam-4354	123	19	rg	rg	AUX
ejpam-4354	123	20	.	.	PROPN
ejpam-4354	123	21	suppose	suppose	VERB
ejpam-4354	123	22	now	now	ADV
ejpam-4354	123	23	that	that	SCONJ
ejpam-4354	123	24	|rg|	|rg|	NUM
ejpam-4354	123	25	=	=	SYM
ejpam-4354	123	26	1	1	NUM
ejpam-4354	123	27	,	,	PUNCT
ejpam-4354	123	28	say	say	VERB
ejpam-4354	123	29	rg	rg	X
ejpam-4354	123	30	=	=	PUNCT
ejpam-4354	123	31	{	{	PUNCT
ejpam-4354	123	32	r	r	NOUN
ejpam-4354	123	33	}	}	PUNCT
ejpam-4354	123	34	.	.	PUNCT
ejpam-4354	124	1	suppose	suppose	VERB
ejpam-4354	124	2	there	there	PRON
ejpam-4354	124	3	exists	exist	VERB
ejpam-4354	124	4	p	p	PROPN
ejpam-4354	124	5	∈	∈	PROPN
ejpam-4354	124	6	v	v	ADP
ejpam-4354	124	7	(	(	PUNCT
ejpam-4354	124	8	gr	gr	NOUN
ejpam-4354	124	9	)	)	PUNCT
ejpam-4354	124	10	\	\	PROPN
ejpam-4354	124	11	sr	sr	PROPN
ejpam-4354	124	12	such	such	ADJ
ejpam-4354	124	13	that	that	DET
ejpam-4354	124	14	emgr	emgr	NOUN
ejpam-4354	124	15	(	(	PUNCT
ejpam-4354	124	16	p	p	X
ejpam-4354	124	17	)	)	PUNCT
ejpam-4354	124	18	=	=	SYM
ejpam-4354	124	19	1	1	NUM
ejpam-4354	124	20	or	or	CCONJ
ejpam-4354	124	21	emgr	emgr	NOUN
ejpam-4354	124	22	(	(	PUNCT
ejpam-4354	124	23	p	p	X
ejpam-4354	124	24	)	)	PUNCT
ejpam-4354	124	25	=	=	SYM
ejpam-4354	124	26	2	2	NUM
ejpam-4354	124	27	and	and	CCONJ
ejpam-4354	124	28	dmgr	dmgr	NOUN
ejpam-4354	124	29	(	(	PUNCT
ejpam-4354	124	30	p	p	X
ejpam-4354	124	31	,	,	PUNCT
ejpam-4354	124	32	w	w	NOUN
ejpam-4354	124	33	)	)	PUNCT
ejpam-4354	124	34	=	=	SYM
ejpam-4354	124	35	1	1	NUM
ejpam-4354	124	36	for	for	ADP
ejpam-4354	124	37	all	all	DET
ejpam-4354	124	38	w	w	PROPN
ejpam-4354	124	39	∈	∈	PROPN
ejpam-4354	124	40	sr	sr	PROPN
ejpam-4354	124	41	,	,	PUNCT
ejpam-4354	124	42	where	where	SCONJ
ejpam-4354	124	43	rg	rg	PROPN
ejpam-4354	124	44	=	=	PUNCT
ejpam-4354	124	45	{	{	PUNCT
ejpam-4354	124	46	r	r	NOUN
ejpam-4354	124	47	}	}	PUNCT
ejpam-4354	124	48	.	.	PUNCT
ejpam-4354	125	1	since	since	SCONJ
ejpam-4354	125	2	emh(p	emh(p	PROPN
ejpam-4354	125	3	)	)	PUNCT
ejpam-4354	125	4	=	=	SYM
ejpam-4354	125	5	2	2	NUM
ejpam-4354	125	6	and	and	CCONJ
ejpam-4354	125	7	s	s	NOUN
ejpam-4354	125	8	is	be	AUX
ejpam-4354	125	9	a	a	DET
ejpam-4354	125	10	monophonic	monophonic	ADJ
ejpam-4354	125	11	eccentric	eccentric	ADJ
ejpam-4354	125	12	dominating	dominating	NOUN
ejpam-4354	125	13	set	set	NOUN
ejpam-4354	125	14	of	of	ADP
ejpam-4354	125	15	h	h	NOUN
ejpam-4354	125	16	,	,	PUNCT
ejpam-4354	125	17	there	there	PRON
ejpam-4354	125	18	exist	exist	VERB
ejpam-4354	125	19	t	t	PROPN
ejpam-4354	125	20	∈	∈	PROPN
ejpam-4354	125	21	{	{	PUNCT
ejpam-4354	125	22	1	1	NUM
ejpam-4354	125	23	,	,	PUNCT
ejpam-4354	125	24	2	2	NUM
ejpam-4354	125	25	,	,	PUNCT
ejpam-4354	125	26	...	...	PUNCT
ejpam-4354	125	27	,	,	PUNCT
ejpam-4354	125	28	k	k	X
ejpam-4354	125	29	}	}	PUNCT
ejpam-4354	125	30	\rg	\rg	NOUN
ejpam-4354	125	31	and	and	CCONJ
ejpam-4354	125	32	x	x	SYM
ejpam-4354	125	33	∈	∈	PROPN
ejpam-4354	125	34	s	s	PART
ejpam-4354	125	35	∩	∩	ADJ
ejpam-4354	125	36	v	v	X
ejpam-4354	125	37	(	(	PUNCT
ejpam-4354	125	38	gt	gt	INTJ
ejpam-4354	125	39	)	)	PUNCT
ejpam-4354	125	40	such	such	ADJ
ejpam-4354	125	41	that	that	SCONJ
ejpam-4354	125	42	emh(p	emh(p	PROPN
ejpam-4354	125	43	)	)	PUNCT
ejpam-4354	125	44	=	=	SYM
ejpam-4354	125	45	dmh(p	dmh(p	PROPN
ejpam-4354	125	46	,	,	PUNCT
ejpam-4354	125	47	x	x	NOUN
ejpam-4354	125	48	)	)	PUNCT
ejpam-4354	125	49	=	=	SYM
ejpam-4354	125	50	2	2	X
ejpam-4354	125	51	.	.	PUNCT
ejpam-4354	126	1	this	this	PRON
ejpam-4354	126	2	shows	show	VERB
ejpam-4354	126	3	that	that	SCONJ
ejpam-4354	126	4	s	s	VERB
ejpam-4354	126	5	∩	∩	ADJ
ejpam-4354	126	6	v	v	X
ejpam-4354	126	7	(	(	PUNCT
ejpam-4354	126	8	gt	gt	PROPN
ejpam-4354	126	9	)	)	PUNCT
ejpam-4354	126	10	6=	6=	NOUN
ejpam-4354	126	11	∅	∅	NOUN
ejpam-4354	126	12	for	for	ADP
ejpam-4354	126	13	some	some	DET
ejpam-4354	126	14	t	t	NOUN
ejpam-4354	126	15	∈	∈	PROPN
ejpam-4354	126	16	{	{	PUNCT
ejpam-4354	126	17	1	1	NUM
ejpam-4354	126	18	,	,	PUNCT
ejpam-4354	126	19	2	2	NUM
ejpam-4354	126	20	,	,	PUNCT
ejpam-4354	126	21	...	...	PUNCT
ejpam-4354	126	22	,	,	PUNCT
ejpam-4354	126	23	k	k	X
ejpam-4354	126	24	}	}	PUNCT
ejpam-4354	126	25	\rg	\rg	NOUN
ejpam-4354	126	26	.	.	PUNCT
ejpam-4354	127	1	for	for	ADP
ejpam-4354	127	2	the	the	DET
ejpam-4354	127	3	converse	converse	NOUN
ejpam-4354	127	4	,	,	PUNCT
ejpam-4354	127	5	suppose	suppose	VERB
ejpam-4354	127	6	that	that	SCONJ
ejpam-4354	127	7	sj	sj	VERB
ejpam-4354	127	8	=	=	SYM
ejpam-4354	127	9	s	s	PROPN
ejpam-4354	127	10	∩	∩	ADJ
ejpam-4354	127	11	v	v	NOUN
ejpam-4354	127	12	(	(	PUNCT
ejpam-4354	127	13	gj	gj	NOUN
ejpam-4354	127	14	)	)	PUNCT
ejpam-4354	127	15	is	be	AUX
ejpam-4354	127	16	a	a	DET
ejpam-4354	127	17	d3m	d3m	ADJ
ejpam-4354	127	18	-	-	PUNCT
ejpam-4354	127	19	monophonic	monophonic	ADJ
ejpam-4354	127	20	eccentric	eccentric	ADJ
ejpam-4354	127	21	set	set	NOUN
ejpam-4354	127	22	of	of	ADP
ejpam-4354	127	23	gj	gj	NOUN
ejpam-4354	127	24	for	for	ADP
ejpam-4354	127	25	each	each	DET
ejpam-4354	127	26	j	j	PROPN
ejpam-4354	127	27	∈	∈	PROPN
ejpam-4354	127	28	rg	rg	NOUN
ejpam-4354	127	29	and	and	CCONJ
ejpam-4354	127	30	,	,	PUNCT
ejpam-4354	127	31	in	in	ADP
ejpam-4354	127	32	addition	addition	NOUN
ejpam-4354	127	33	,	,	PUNCT
ejpam-4354	127	34	s	s	NOUN
ejpam-4354	127	35	∩	∩	ADJ
ejpam-4354	127	36	v	v	X
ejpam-4354	127	37	(	(	PUNCT
ejpam-4354	127	38	gt	gt	PROPN
ejpam-4354	127	39	)	)	PUNCT
ejpam-4354	127	40	6=	6=	NOUN
ejpam-4354	127	41	∅	∅	NOUN
ejpam-4354	127	42	for	for	ADP
ejpam-4354	127	43	some	some	DET
ejpam-4354	127	44	t	t	NOUN
ejpam-4354	127	45	∈	∈	PROPN
ejpam-4354	127	46	{	{	PUNCT
ejpam-4354	127	47	1	1	NUM
ejpam-4354	127	48	,	,	PUNCT
ejpam-4354	127	49	2	2	NUM
ejpam-4354	127	50	,	,	PUNCT
ejpam-4354	127	51	...	...	PUNCT
ejpam-4354	127	52	,	,	PUNCT
ejpam-4354	128	1	k	k	NOUN
ejpam-4354	128	2	}	}	PUNCT
ejpam-4354	128	3	\	\	NOUN
ejpam-4354	128	4	rg	rg	X
ejpam-4354	128	5	whenever	whenever	SCONJ
ejpam-4354	128	6	|rg|	|rg|	PROPN
ejpam-4354	128	7	=	=	SYM
ejpam-4354	128	8	1	1	NUM
ejpam-4354	128	9	and	and	CCONJ
ejpam-4354	128	10	there	there	PRON
ejpam-4354	128	11	exists	exist	VERB
ejpam-4354	128	12	p	p	PROPN
ejpam-4354	128	13	∈	∈	PROPN
ejpam-4354	128	14	v	v	NOUN
ejpam-4354	128	15	(	(	PUNCT
ejpam-4354	128	16	gr)\sr	gr)\sr	PROPN
ejpam-4354	128	17	such	such	ADJ
ejpam-4354	128	18	that	that	DET
ejpam-4354	128	19	emgr	emgr	NOUN
ejpam-4354	128	20	(	(	PUNCT
ejpam-4354	128	21	p	p	X
ejpam-4354	128	22	)	)	PUNCT
ejpam-4354	128	23	=	=	SYM
ejpam-4354	128	24	1	1	NUM
ejpam-4354	128	25	or	or	CCONJ
ejpam-4354	128	26	emgr	emgr	NOUN
ejpam-4354	128	27	(	(	PUNCT
ejpam-4354	128	28	p	p	X
ejpam-4354	128	29	)	)	PUNCT
ejpam-4354	128	30	=	=	SYM
ejpam-4354	128	31	2	2	NUM
ejpam-4354	128	32	and	and	CCONJ
ejpam-4354	128	33	dmgr	dmgr	NOUN
ejpam-4354	128	34	(	(	PUNCT
ejpam-4354	128	35	p	p	X
ejpam-4354	128	36	,	,	PUNCT
ejpam-4354	128	37	w	w	NOUN
ejpam-4354	128	38	)	)	PUNCT
ejpam-4354	128	39	=	=	SYM
ejpam-4354	128	40	1	1	NUM
ejpam-4354	128	41	for	for	ADP
ejpam-4354	128	42	all	all	DET
ejpam-4354	128	43	w	w	PROPN
ejpam-4354	128	44	∈	∈	PROPN
ejpam-4354	128	45	sr	sr	PROPN
ejpam-4354	128	46	,	,	PUNCT
ejpam-4354	128	47	where	where	SCONJ
ejpam-4354	128	48	rg	rg	PROPN
ejpam-4354	128	49	=	=	PUNCT
ejpam-4354	128	50	{	{	PUNCT
ejpam-4354	128	51	r	r	NOUN
ejpam-4354	128	52	}	}	PUNCT
ejpam-4354	128	53	.	.	PUNCT
ejpam-4354	129	1	let	let	VERB
ejpam-4354	129	2	z	z	NOUN
ejpam-4354	129	3	∈	∈	PROPN
ejpam-4354	129	4	v	v	NOUN
ejpam-4354	129	5	(	(	PUNCT
ejpam-4354	129	6	h)\s	h)\s	NOUN
ejpam-4354	129	7	.	.	PUNCT
ejpam-4354	130	1	if	if	SCONJ
ejpam-4354	130	2	v	v	NUM
ejpam-4354	130	3	/∈	/∈	PUNCT
ejpam-4354	130	4	s	s	NOUN
ejpam-4354	130	5	and	and	CCONJ
ejpam-4354	130	6	z	z	NOUN
ejpam-4354	130	7	=	=	SYM
ejpam-4354	130	8	v	v	NOUN
ejpam-4354	130	9	,	,	PUNCT
ejpam-4354	130	10	then	then	ADV
ejpam-4354	130	11	every	every	DET
ejpam-4354	130	12	element	element	NOUN
ejpam-4354	130	13	of	of	ADP
ejpam-4354	130	14	s	s	PROPN
ejpam-4354	130	15	is	be	AUX
ejpam-4354	130	16	a	a	DET
ejpam-4354	130	17	monophonic	monophonic	ADJ
ejpam-4354	130	18	eccentric	eccentric	ADJ
ejpam-4354	130	19	vertex	vertex	NOUN
ejpam-4354	130	20	of	of	ADP
ejpam-4354	130	21	z	z	PROPN
ejpam-4354	130	22	in	in	ADP
ejpam-4354	130	23	h.	h.	PROPN
ejpam-4354	130	24	suppose	suppose	VERB
ejpam-4354	130	25	that	that	SCONJ
ejpam-4354	130	26	z	z	PROPN
ejpam-4354	130	27	∈	∈	PROPN
ejpam-4354	130	28	v	v	ADP
ejpam-4354	130	29	(	(	PUNCT
ejpam-4354	130	30	g	g	NOUN
ejpam-4354	130	31	)	)	PUNCT
ejpam-4354	130	32	.	.	PUNCT
ejpam-4354	131	1	s.	s.	PROPN
ejpam-4354	131	2	canoy	canoy	PROPN
ejpam-4354	131	3	,	,	PUNCT
ejpam-4354	131	4	jr	jr	PROPN
ejpam-4354	131	5	.	.	PROPN
ejpam-4354	131	6	,	,	PUNCT
ejpam-4354	131	7	a.	a.	NOUN
ejpam-4354	131	8	gamorez	gamorez	PROPN
ejpam-4354	131	9	/	/	SYM
ejpam-4354	131	10	eur	eur	PROPN
ejpam-4354	131	11	.	.	PUNCT
ejpam-4354	132	1	j.	j.	PROPN
ejpam-4354	132	2	pure	pure	PROPN
ejpam-4354	132	3	appl	appl	PROPN
ejpam-4354	132	4	.	.	PROPN
ejpam-4354	132	5	math	math	PROPN
ejpam-4354	132	6	,	,	PUNCT
ejpam-4354	132	7	15	15	NUM
ejpam-4354	132	8	(	(	PUNCT
ejpam-4354	132	9	2	2	NUM
ejpam-4354	132	10	)	)	PUNCT
ejpam-4354	132	11	(	(	PUNCT
ejpam-4354	132	12	2022	2022	NUM
ejpam-4354	132	13	)	)	PUNCT
ejpam-4354	132	14	,	,	PUNCT
ejpam-4354	132	15	635	635	NUM
ejpam-4354	132	16	-	-	SYM
ejpam-4354	132	17	645	645	NUM
ejpam-4354	132	18	639	639	NUM
ejpam-4354	132	19	if	if	SCONJ
ejpam-4354	132	20	|rg|	|rg|	PRON
ejpam-4354	132	21	≥	≥	NOUN
ejpam-4354	132	22	2	2	NUM
ejpam-4354	132	23	,	,	PUNCT
ejpam-4354	132	24	then	then	ADV
ejpam-4354	132	25	by	by	ADP
ejpam-4354	132	26	assumption	assumption	NOUN
ejpam-4354	132	27	,	,	PUNCT
ejpam-4354	132	28	there	there	PRON
ejpam-4354	132	29	exists	exist	VERB
ejpam-4354	132	30	q	q	PROPN
ejpam-4354	132	31	∈	∈	PROPN
ejpam-4354	132	32	s	s	X
ejpam-4354	132	33	(	(	PUNCT
ejpam-4354	132	34	q	q	NOUN
ejpam-4354	132	35	∈	∈	PROPN
ejpam-4354	132	36	si	si	NOUN
ejpam-4354	132	37	or	or	CCONJ
ejpam-4354	132	38	q	q	PROPN
ejpam-4354	132	39	∈	∈	PROPN
ejpam-4354	132	40	sj	sj	INTJ
ejpam-4354	132	41	,	,	PUNCT
ejpam-4354	132	42	where	where	SCONJ
ejpam-4354	132	43	i	i	PRON
ejpam-4354	132	44	,	,	PUNCT
ejpam-4354	132	45	j	j	PROPN
ejpam-4354	132	46	∈	∈	PROPN
ejpam-4354	132	47	rg	rg	PROPN
ejpam-4354	132	48	and	and	CCONJ
ejpam-4354	132	49	i	i	PROPN
ejpam-4354	132	50	6=	6=	PROPN
ejpam-4354	132	51	j	j	NOUN
ejpam-4354	132	52	)	)	PUNCT
ejpam-4354	132	53	such	such	ADJ
ejpam-4354	132	54	that	that	SCONJ
ejpam-4354	132	55	emh(z	emh(z	PROPN
ejpam-4354	132	56	)	)	PUNCT
ejpam-4354	132	57	=	=	SYM
ejpam-4354	132	58	dmh(z	dmh(z	PROPN
ejpam-4354	132	59	,	,	PUNCT
ejpam-4354	132	60	q	q	NOUN
ejpam-4354	132	61	)	)	PUNCT
ejpam-4354	132	62	.	.	PUNCT
ejpam-4354	133	1	suppose	suppose	VERB
ejpam-4354	133	2	|rg|	|rg|	NUM
ejpam-4354	133	3	=	=	SYM
ejpam-4354	133	4	1	1	NUM
ejpam-4354	133	5	,	,	PUNCT
ejpam-4354	133	6	say	say	VERB
ejpam-4354	133	7	rg	rg	X
ejpam-4354	133	8	=	=	PUNCT
ejpam-4354	133	9	{	{	PUNCT
ejpam-4354	133	10	r	r	NOUN
ejpam-4354	133	11	}	}	PUNCT
ejpam-4354	133	12	.	.	PUNCT
ejpam-4354	134	1	assume	assume	VERB
ejpam-4354	134	2	first	first	ADV
ejpam-4354	134	3	that	that	SCONJ
ejpam-4354	134	4	z	z	PROPN
ejpam-4354	134	5	∈	∈	PROPN
ejpam-4354	134	6	v	v	ADP
ejpam-4354	134	7	(	(	PUNCT
ejpam-4354	134	8	gr	gr	NOUN
ejpam-4354	134	9	)	)	PUNCT
ejpam-4354	134	10	.	.	PUNCT
ejpam-4354	135	1	if	if	SCONJ
ejpam-4354	135	2	emgr	emgr	NOUN
ejpam-4354	135	3	(	(	PUNCT
ejpam-4354	135	4	z	z	NOUN
ejpam-4354	135	5	)	)	PUNCT
ejpam-4354	135	6	≥	≥	NOUN
ejpam-4354	135	7	3	3	NUM
ejpam-4354	135	8	,	,	PUNCT
ejpam-4354	135	9	then	then	ADV
ejpam-4354	135	10	emgr	emgr	NOUN
ejpam-4354	135	11	(	(	PUNCT
ejpam-4354	135	12	z	z	X
ejpam-4354	135	13	)	)	PUNCT
ejpam-4354	135	14	=	=	SYM
ejpam-4354	135	15	emh(z	emh(z	PROPN
ejpam-4354	135	16	)	)	PUNCT
ejpam-4354	135	17	and	and	CCONJ
ejpam-4354	135	18	so	so	ADV
ejpam-4354	135	19	z	z	PROPN
ejpam-4354	135	20	has	have	VERB
ejpam-4354	135	21	a	a	DET
ejpam-4354	135	22	monophonic	monophonic	ADJ
ejpam-4354	135	23	eccentric	eccentric	ADJ
ejpam-4354	135	24	vertex	vertex	NOUN
ejpam-4354	135	25	in	in	ADP
ejpam-4354	135	26	h	h	NOUN
ejpam-4354	135	27	(	(	PUNCT
ejpam-4354	135	28	in	in	ADP
ejpam-4354	135	29	gr	gr	NOUN
ejpam-4354	135	30	)	)	PUNCT
ejpam-4354	135	31	by	by	ADP
ejpam-4354	135	32	assumption	assumption	NOUN
ejpam-4354	135	33	.	.	PUNCT
ejpam-4354	136	1	suppose	suppose	VERB
ejpam-4354	136	2	emgr	emgr	NOUN
ejpam-4354	136	3	(	(	PUNCT
ejpam-4354	136	4	z	z	NOUN
ejpam-4354	136	5	)	)	PUNCT
ejpam-4354	136	6	=	=	SYM
ejpam-4354	137	1	2	2	X
ejpam-4354	137	2	.	.	X
ejpam-4354	137	3	if	if	SCONJ
ejpam-4354	137	4	dmgr	dmgr	NOUN
ejpam-4354	137	5	(	(	PUNCT
ejpam-4354	137	6	p	p	X
ejpam-4354	137	7	,	,	PUNCT
ejpam-4354	137	8	w	w	NOUN
ejpam-4354	137	9	)	)	PUNCT
ejpam-4354	137	10	=	=	SYM
ejpam-4354	137	11	2	2	NUM
ejpam-4354	137	12	for	for	ADP
ejpam-4354	137	13	some	some	DET
ejpam-4354	137	14	w	w	PROPN
ejpam-4354	137	15	∈	∈	PROPN
ejpam-4354	137	16	sr	sr	PROPN
ejpam-4354	137	17	,	,	PUNCT
ejpam-4354	137	18	then	then	ADV
ejpam-4354	137	19	w	w	PROPN
ejpam-4354	137	20	is	be	AUX
ejpam-4354	137	21	a	a	DET
ejpam-4354	137	22	monophonic	monophonic	ADJ
ejpam-4354	137	23	eccentric	eccentric	ADJ
ejpam-4354	137	24	vertex	vertex	NOUN
ejpam-4354	137	25	of	of	ADP
ejpam-4354	137	26	z	z	PROPN
ejpam-4354	137	27	in	in	ADP
ejpam-4354	137	28	h.	h.	PROPN
ejpam-4354	137	29	suppose	suppose	VERB
ejpam-4354	137	30	dmgr	dmgr	PROPN
ejpam-4354	137	31	(	(	PUNCT
ejpam-4354	137	32	p	p	X
ejpam-4354	137	33	,	,	PUNCT
ejpam-4354	137	34	w	w	NOUN
ejpam-4354	137	35	)	)	PUNCT
ejpam-4354	137	36	=	=	SYM
ejpam-4354	137	37	1	1	NUM
ejpam-4354	137	38	for	for	ADP
ejpam-4354	137	39	all	all	DET
ejpam-4354	137	40	w	w	PROPN
ejpam-4354	137	41	∈	∈	PROPN
ejpam-4354	137	42	sr	sr	PROPN
ejpam-4354	137	43	.	.	PUNCT
ejpam-4354	138	1	by	by	ADP
ejpam-4354	138	2	assumption	assumption	NOUN
ejpam-4354	138	3	,	,	PUNCT
ejpam-4354	138	4	s∩v	s∩v	PROPN
ejpam-4354	138	5	(	(	PUNCT
ejpam-4354	138	6	gt	gt	PROPN
ejpam-4354	138	7	)	)	PUNCT
ejpam-4354	138	8	6=	6=	NOUN
ejpam-4354	138	9	∅	∅	NOUN
ejpam-4354	138	10	for	for	ADP
ejpam-4354	138	11	some	some	DET
ejpam-4354	138	12	t	t	NOUN
ejpam-4354	138	13	∈	∈	PROPN
ejpam-4354	138	14	{	{	PUNCT
ejpam-4354	138	15	1	1	NUM
ejpam-4354	138	16	,	,	PUNCT
ejpam-4354	138	17	2	2	NUM
ejpam-4354	138	18	,	,	PUNCT
ejpam-4354	138	19	...	...	PUNCT
ejpam-4354	138	20	,	,	PUNCT
ejpam-4354	138	21	k}\rg	k}\rg	PROPN
ejpam-4354	138	22	.	.	PUNCT
ejpam-4354	139	1	then	then	ADV
ejpam-4354	139	2	every	every	DET
ejpam-4354	139	3	element	element	NOUN
ejpam-4354	139	4	of	of	ADP
ejpam-4354	139	5	s∩v	s∩v	PROPN
ejpam-4354	139	6	(	(	PUNCT
ejpam-4354	139	7	gt	gt	PROPN
ejpam-4354	139	8	)	)	PUNCT
ejpam-4354	139	9	is	be	AUX
ejpam-4354	139	10	a	a	DET
ejpam-4354	139	11	monophonic	monophonic	ADJ
ejpam-4354	139	12	eccentric	eccentric	ADJ
ejpam-4354	139	13	vertex	vertex	NOUN
ejpam-4354	139	14	of	of	ADP
ejpam-4354	139	15	z	z	PROPN
ejpam-4354	139	16	in	in	ADP
ejpam-4354	139	17	h.	h.	PROPN
ejpam-4354	139	18	if	if	SCONJ
ejpam-4354	139	19	emgr	emgr	NOUN
ejpam-4354	139	20	(	(	PUNCT
ejpam-4354	139	21	z	z	NOUN
ejpam-4354	139	22	)	)	PUNCT
ejpam-4354	139	23	=	=	SYM
ejpam-4354	139	24	1	1	NUM
ejpam-4354	139	25	,	,	PUNCT
ejpam-4354	139	26	then	then	ADV
ejpam-4354	139	27	every	every	DET
ejpam-4354	139	28	element	element	NOUN
ejpam-4354	139	29	of	of	ADP
ejpam-4354	139	30	s∩v	s∩v	PROPN
ejpam-4354	139	31	(	(	PUNCT
ejpam-4354	139	32	gt	gt	PROPN
ejpam-4354	139	33	)	)	PUNCT
ejpam-4354	139	34	is	be	AUX
ejpam-4354	139	35	a	a	DET
ejpam-4354	139	36	monophonic	monophonic	ADJ
ejpam-4354	139	37	eccentric	eccentric	ADJ
ejpam-4354	139	38	vertex	vertex	NOUN
ejpam-4354	139	39	of	of	ADP
ejpam-4354	139	40	z	z	NOUN
ejpam-4354	139	41	in	in	ADP
ejpam-4354	139	42	h	h	NOUN
ejpam-4354	139	43	because	because	SCONJ
ejpam-4354	139	44	emh(z	emh(z	PROPN
ejpam-4354	139	45	)	)	PUNCT
ejpam-4354	139	46	=	=	SYM
ejpam-4354	140	1	2	2	X
ejpam-4354	140	2	.	.	PUNCT
ejpam-4354	141	1	next	next	ADV
ejpam-4354	141	2	,	,	PUNCT
ejpam-4354	141	3	suppose	suppose	VERB
ejpam-4354	141	4	that	that	SCONJ
ejpam-4354	141	5	z	z	PROPN
ejpam-4354	141	6	∈	∈	NOUN
ejpam-4354	141	7	gi	gi	NOUN
ejpam-4354	141	8	for	for	ADP
ejpam-4354	141	9	i	i	PROPN
ejpam-4354	141	10	6=	6=	PROPN
ejpam-4354	141	11	r.	r.	PROPN
ejpam-4354	141	12	then	then	ADV
ejpam-4354	141	13	emh(z	emh(z	PROPN
ejpam-4354	141	14	)	)	PUNCT
ejpam-4354	141	15	=	=	SYM
ejpam-4354	142	1	2	2	X
ejpam-4354	142	2	.	.	X
ejpam-4354	143	1	hence	hence	ADV
ejpam-4354	143	2	,	,	PUNCT
ejpam-4354	143	3	every	every	DET
ejpam-4354	143	4	element	element	NOUN
ejpam-4354	143	5	of	of	ADP
ejpam-4354	143	6	sr	sr	PROPN
ejpam-4354	143	7	is	be	AUX
ejpam-4354	143	8	a	a	DET
ejpam-4354	143	9	monophonic	monophonic	ADJ
ejpam-4354	143	10	eccentric	eccentric	ADJ
ejpam-4354	143	11	vertex	vertex	NOUN
ejpam-4354	143	12	of	of	ADP
ejpam-4354	143	13	z	z	PROPN
ejpam-4354	143	14	in	in	ADP
ejpam-4354	143	15	h.	h.	PROPN
ejpam-4354	143	16	therefore	therefore	ADV
ejpam-4354	143	17	,	,	PUNCT
ejpam-4354	143	18	s	s	VERB
ejpam-4354	143	19	is	be	AUX
ejpam-4354	143	20	a	a	DET
ejpam-4354	143	21	monophonic	monophonic	ADJ
ejpam-4354	143	22	eccentric	eccentric	ADJ
ejpam-4354	143	23	dominating	dominating	NOUN
ejpam-4354	143	24	set	set	NOUN
ejpam-4354	143	25	of	of	ADP
ejpam-4354	143	26	h.	h.	PROPN
ejpam-4354	143	27	corollary	corollary	PROPN
ejpam-4354	143	28	2	2	PROPN
ejpam-4354	143	29	.	.	PUNCT
ejpam-4354	144	1	let	let	VERB
ejpam-4354	144	2	g1	g1	PROPN
ejpam-4354	144	3	,	,	PUNCT
ejpam-4354	144	4	g2	g2	PROPN
ejpam-4354	144	5	,	,	PUNCT
ejpam-4354	144	6	...	...	PUNCT
ejpam-4354	144	7	,	,	PUNCT
ejpam-4354	144	8	gk	gk	PROPN
ejpam-4354	144	9	be	be	AUX
ejpam-4354	144	10	the	the	DET
ejpam-4354	144	11	distinct	distinct	ADJ
ejpam-4354	144	12	components	component	NOUN
ejpam-4354	144	13	of	of	ADP
ejpam-4354	144	14	g	g	PROPN
ejpam-4354	144	15	with	with	ADP
ejpam-4354	144	16	k	k	PROPN
ejpam-4354	144	17	≥	≥	NUM
ejpam-4354	144	18	2	2	NUM
ejpam-4354	144	19	and	and	CCONJ
ejpam-4354	144	20	let	let	VERB
ejpam-4354	144	21	h	h	NOUN
ejpam-4354	144	22	=	=	PUNCT
ejpam-4354	144	23	k1	k1	PROPN
ejpam-4354	145	1	+	+	NOUN
ejpam-4354	145	2	g	g	NOUN
ejpam-4354	145	3	=	=	SYM
ejpam-4354	145	4	〈	〈	PROPN
ejpam-4354	145	5	v〉+g	v〉+g	NOUN
ejpam-4354	145	6	.	.	PUNCT
ejpam-4354	145	7	suppose	suppose	VERB
ejpam-4354	145	8	rg	rg	PROPN
ejpam-4354	145	9	=	=	SYM
ejpam-4354	145	10	{	{	PUNCT
ejpam-4354	145	11	j	j	PROPN
ejpam-4354	145	12	∈	∈	PROPN
ejpam-4354	145	13	{	{	PUNCT
ejpam-4354	145	14	1	1	NUM
ejpam-4354	145	15	,	,	PUNCT
ejpam-4354	145	16	2	2	NUM
ejpam-4354	145	17	,	,	PUNCT
ejpam-4354	145	18	...	...	PUNCT
ejpam-4354	145	19	,	,	PUNCT
ejpam-4354	145	20	k	k	NOUN
ejpam-4354	145	21	}	}	PUNCT
ejpam-4354	145	22	:	:	PUNCT
ejpam-4354	145	23	diamm(gj	diamm(gj	PROPN
ejpam-4354	145	24	)	)	PUNCT
ejpam-4354	145	25	≥	≥	NOUN
ejpam-4354	145	26	3	3	NUM
ejpam-4354	145	27	}	}	PUNCT
ejpam-4354	145	28	6=	6=	ADP
ejpam-4354	145	29	∅.	∅.	PROPN
ejpam-4354	145	30	(	(	PUNCT
ejpam-4354	145	31	i	i	NOUN
ejpam-4354	145	32	)	)	PUNCT
ejpam-4354	145	33	if	if	SCONJ
ejpam-4354	145	34	|rg|	|rg|	PRON
ejpam-4354	145	35	≥	≥	NOUN
ejpam-4354	145	36	2	2	NUM
ejpam-4354	145	37	,	,	PUNCT
ejpam-4354	145	38	then	then	ADV
ejpam-4354	145	39	γme(h	γme(h	PROPN
ejpam-4354	145	40	)	)	PUNCT
ejpam-4354	145	41	=	=	SYM
ejpam-4354	145	42	∑	∑	PUNCT
ejpam-4354	145	43	j∈rg	j∈rg	NOUN
ejpam-4354	145	44	µ3	µ3	NOUN
ejpam-4354	145	45	m(gj	m(gj	NOUN
ejpam-4354	145	46	)	)	PUNCT
ejpam-4354	145	47	.	.	PUNCT
ejpam-4354	146	1	(	(	PUNCT
ejpam-4354	146	2	ii	ii	X
ejpam-4354	146	3	)	)	PUNCT
ejpam-4354	146	4	if	if	SCONJ
ejpam-4354	146	5	rg	rg	PROPN
ejpam-4354	146	6	=	=	SYM
ejpam-4354	146	7	{	{	PUNCT
ejpam-4354	146	8	r	r	NOUN
ejpam-4354	146	9	}	}	PUNCT
ejpam-4354	146	10	and	and	CCONJ
ejpam-4354	146	11	γme(h	γme(h	PROPN
ejpam-4354	146	12	)	)	PUNCT
ejpam-4354	146	13	6=	6=	NUM
ejpam-4354	147	1	µ3	µ3	PROPN
ejpam-4354	147	2	m(gr	m(gr	PROPN
ejpam-4354	147	3	)	)	PUNCT
ejpam-4354	147	4	,	,	PUNCT
ejpam-4354	147	5	then	then	ADV
ejpam-4354	147	6	γme(h	γme(h	PROPN
ejpam-4354	147	7	)	)	PUNCT
ejpam-4354	147	8	=	=	SYM
ejpam-4354	147	9	µ3	µ3	NOUN
ejpam-4354	147	10	m(gr	m(gr	PROPN
ejpam-4354	147	11	)	)	PUNCT
ejpam-4354	148	1	+	+	NOUN
ejpam-4354	148	2	1	1	X
ejpam-4354	148	3	.	.	X
ejpam-4354	148	4	proof	proof	NOUN
ejpam-4354	148	5	.	.	PUNCT
ejpam-4354	149	1	(	(	PUNCT
ejpam-4354	149	2	i	i	NOUN
ejpam-4354	149	3	)	)	PUNCT
ejpam-4354	149	4	suppose	suppose	VERB
ejpam-4354	149	5	|rg|	|rg|	X
ejpam-4354	149	6	≥	≥	NOUN
ejpam-4354	149	7	2	2	NUM
ejpam-4354	149	8	.	.	PUNCT
ejpam-4354	150	1	let	let	VERB
ejpam-4354	150	2	sj	sj	INTJ
ejpam-4354	150	3	be	be	AUX
ejpam-4354	150	4	a	a	DET
ejpam-4354	150	5	d3m	d3m	ADJ
ejpam-4354	150	6	-	-	PUNCT
ejpam-4354	150	7	monophonic	monophonic	ADJ
ejpam-4354	150	8	eccentric	eccentric	ADJ
ejpam-4354	150	9	set	set	NOUN
ejpam-4354	150	10	of	of	ADP
ejpam-4354	150	11	gj	gj	NOUN
ejpam-4354	150	12	such	such	ADJ
ejpam-4354	150	13	that	that	DET
ejpam-4354	150	14	µ3	µ3	NOUN
ejpam-4354	150	15	m(gj	m(gj	X
ejpam-4354	150	16	)	)	PUNCT
ejpam-4354	150	17	=	=	SYM
ejpam-4354	150	18	|sj	|sj	ADP
ejpam-4354	150	19	|	|	ADV
ejpam-4354	150	20	for	for	ADP
ejpam-4354	150	21	each	each	DET
ejpam-4354	150	22	j	j	PROPN
ejpam-4354	150	23	∈	∈	PROPN
ejpam-4354	150	24	rg	rg	PROPN
ejpam-4354	150	25	and	and	CCONJ
ejpam-4354	150	26	set	set	VERB
ejpam-4354	150	27	s	s	PART
ejpam-4354	150	28	=	=	PUNCT
ejpam-4354	150	29	∪j∈rg	∪j∈rg	NOUN
ejpam-4354	150	30	sj	sj	INTJ
ejpam-4354	150	31	.	.	PUNCT
ejpam-4354	151	1	then	then	ADV
ejpam-4354	151	2	s	s	VERB
ejpam-4354	151	3	is	be	AUX
ejpam-4354	151	4	a	a	DET
ejpam-4354	151	5	monophonic	monophonic	ADJ
ejpam-4354	151	6	eccentric	eccentric	ADJ
ejpam-4354	151	7	dominating	dominating	NOUN
ejpam-4354	151	8	set	set	NOUN
ejpam-4354	151	9	of	of	ADP
ejpam-4354	151	10	h	h	NOUN
ejpam-4354	151	11	by	by	ADP
ejpam-4354	151	12	theorem	theorem	NOUN
ejpam-4354	151	13	4	4	NUM
ejpam-4354	151	14	.	.	PUNCT
ejpam-4354	152	1	hence	hence	ADV
ejpam-4354	152	2	,	,	PUNCT
ejpam-4354	152	3	γme(h	γme(h	PROPN
ejpam-4354	152	4	)	)	PUNCT
ejpam-4354	152	5	≤	≤	NUM
ejpam-4354	152	6	|s|	|s|	PROPN
ejpam-4354	152	7	=	=	PUNCT
ejpam-4354	152	8	∑	∑	PUNCT
ejpam-4354	152	9	j∈rg	j∈rg	NOUN
ejpam-4354	152	10	µ3	µ3	NOUN
ejpam-4354	152	11	m(gj	m(gj	NOUN
ejpam-4354	152	12	)	)	PUNCT
ejpam-4354	152	13	.	.	PUNCT
ejpam-4354	153	1	next	next	ADV
ejpam-4354	153	2	,	,	PUNCT
ejpam-4354	153	3	suppose	suppose	VERB
ejpam-4354	153	4	that	that	SCONJ
ejpam-4354	153	5	s0	s0	PROPN
ejpam-4354	153	6	is	be	AUX
ejpam-4354	153	7	a	a	DET
ejpam-4354	153	8	minimum	minimum	ADJ
ejpam-4354	153	9	monophonic	monophonic	ADJ
ejpam-4354	153	10	eccentric	eccentric	ADJ
ejpam-4354	153	11	dominating	dominating	NOUN
ejpam-4354	153	12	set	set	NOUN
ejpam-4354	153	13	of	of	ADP
ejpam-4354	153	14	h.	h.	PROPN
ejpam-4354	153	15	let	let	VERB
ejpam-4354	153	16	s′	s′	ADJ
ejpam-4354	153	17	j	j	PROPN
ejpam-4354	153	18	=	=	SYM
ejpam-4354	153	19	s0∩v	s0∩v	PROPN
ejpam-4354	153	20	(	(	PUNCT
ejpam-4354	153	21	gj	gj	NOUN
ejpam-4354	153	22	)	)	PUNCT
ejpam-4354	153	23	for	for	ADP
ejpam-4354	153	24	each	each	DET
ejpam-4354	153	25	j	j	PROPN
ejpam-4354	153	26	∈	∈	PROPN
ejpam-4354	153	27	rg	rg	PROPN
ejpam-4354	153	28	.	.	PUNCT
ejpam-4354	153	29	by	by	ADP
ejpam-4354	153	30	theorem	theorem	NOUN
ejpam-4354	153	31	4	4	NUM
ejpam-4354	153	32	,	,	PUNCT
ejpam-4354	153	33	s′	s′	ADJ
ejpam-4354	153	34	j	j	PROPN
ejpam-4354	153	35	is	be	AUX
ejpam-4354	153	36	a	a	DET
ejpam-4354	153	37	d3m	d3m	ADJ
ejpam-4354	153	38	-	-	PUNCT
ejpam-4354	153	39	monophonic	monophonic	ADJ
ejpam-4354	153	40	eccentric	eccentric	ADJ
ejpam-4354	153	41	set	set	NOUN
ejpam-4354	153	42	of	of	ADP
ejpam-4354	153	43	gj	gj	NOUN
ejpam-4354	153	44	for	for	ADP
ejpam-4354	153	45	each	each	DET
ejpam-4354	153	46	j	j	PROPN
ejpam-4354	153	47	∈	∈	PROPN
ejpam-4354	154	1	rg	rg	PROPN
ejpam-4354	154	2	.	.	PUNCT
ejpam-4354	155	1	since	since	SCONJ
ejpam-4354	155	2	|s′	|s′	PROPN
ejpam-4354	155	3	j	j	PROPN
ejpam-4354	155	4	|	|	CCONJ
ejpam-4354	155	5	≥	≥	NOUN
ejpam-4354	155	6	µ3	µ3	NOUN
ejpam-4354	155	7	m(gj	m(gj	PROPN
ejpam-4354	155	8	)	)	PUNCT
ejpam-4354	155	9	for	for	ADP
ejpam-4354	155	10	each	each	DET
ejpam-4354	155	11	j	j	PROPN
ejpam-4354	155	12	∈	∈	PROPN
ejpam-4354	155	13	rg	rg	PROPN
ejpam-4354	155	14	,	,	PUNCT
ejpam-4354	155	15	γme(h	γme(h	PROPN
ejpam-4354	155	16	)	)	PUNCT
ejpam-4354	155	17	=	=	SYM
ejpam-4354	155	18	|s0|	|s0|	NOUN
ejpam-4354	155	19	≥	≥	PROPN
ejpam-4354	155	20	∑	∑	ADV
ejpam-4354	155	21	j∈rg	j∈rg	NOUN
ejpam-4354	155	22	µ3	µ3	NOUN
ejpam-4354	155	23	m(gj	m(gj	NOUN
ejpam-4354	155	24	)	)	PUNCT
ejpam-4354	155	25	.	.	PUNCT
ejpam-4354	156	1	this	this	PRON
ejpam-4354	156	2	proves	prove	VERB
ejpam-4354	156	3	the	the	DET
ejpam-4354	156	4	assertion	assertion	NOUN
ejpam-4354	156	5	.	.	PUNCT
ejpam-4354	157	1	(	(	PUNCT
ejpam-4354	157	2	ii	ii	NOUN
ejpam-4354	157	3	)	)	PUNCT
ejpam-4354	157	4	suppose	suppose	VERB
ejpam-4354	157	5	rg	rg	X
ejpam-4354	157	6	=	=	SYM
ejpam-4354	157	7	{	{	PUNCT
ejpam-4354	157	8	r	r	NOUN
ejpam-4354	157	9	}	}	PUNCT
ejpam-4354	157	10	and	and	CCONJ
ejpam-4354	157	11	γme(h	γme(h	PROPN
ejpam-4354	157	12	)	)	PUNCT
ejpam-4354	157	13	6=	6=	NUM
ejpam-4354	157	14	µ3	µ3	PROPN
ejpam-4354	157	15	m(gr	m(gr	PROPN
ejpam-4354	157	16	)	)	PUNCT
ejpam-4354	157	17	.	.	PUNCT
ejpam-4354	158	1	let	let	VERB
ejpam-4354	158	2	s	s	PRON
ejpam-4354	158	3	be	be	AUX
ejpam-4354	158	4	a	a	DET
ejpam-4354	158	5	minimum	minimum	ADJ
ejpam-4354	158	6	monophonic	monophonic	ADJ
ejpam-4354	158	7	eccentric	eccentric	ADJ
ejpam-4354	158	8	dominating	dominating	NOUN
ejpam-4354	158	9	set	set	NOUN
ejpam-4354	158	10	of	of	ADP
ejpam-4354	158	11	h.	h.	PROPN
ejpam-4354	158	12	then	then	ADV
ejpam-4354	158	13	s	s	VERB
ejpam-4354	158	14	∩	∩	ADJ
ejpam-4354	158	15	v	v	X
ejpam-4354	158	16	(	(	PUNCT
ejpam-4354	158	17	gr	gr	NOUN
ejpam-4354	158	18	)	)	PUNCT
ejpam-4354	158	19	is	be	AUX
ejpam-4354	158	20	a	a	DET
ejpam-4354	158	21	d3m	d3m	ADJ
ejpam-4354	158	22	-	-	PUNCT
ejpam-4354	158	23	monophonic	monophonic	ADJ
ejpam-4354	158	24	eccentric	eccentric	ADJ
ejpam-4354	158	25	set	set	NOUN
ejpam-4354	158	26	of	of	ADP
ejpam-4354	158	27	gr	gr	NUM
ejpam-4354	158	28	by	by	ADP
ejpam-4354	158	29	theorem	theorem	NOUN
ejpam-4354	158	30	4	4	NUM
ejpam-4354	158	31	.	.	PUNCT
ejpam-4354	159	1	if	if	SCONJ
ejpam-4354	159	2	s	s	ADP
ejpam-4354	159	3	∩	∩	ADJ
ejpam-4354	159	4	v	v	X
ejpam-4354	159	5	(	(	PUNCT
ejpam-4354	159	6	gr	gr	NOUN
ejpam-4354	159	7	)	)	PUNCT
ejpam-4354	159	8	=	=	SYM
ejpam-4354	159	9	s	s	X
ejpam-4354	159	10	,	,	PUNCT
ejpam-4354	159	11	then	then	ADV
ejpam-4354	159	12	µ3	µ3	PROPN
ejpam-4354	159	13	m(gr	m(gr	PROPN
ejpam-4354	159	14	)	)	PUNCT
ejpam-4354	159	15	<	<	X
ejpam-4354	159	16	|s|	|s|	PROPN
ejpam-4354	159	17	=	=	SYM
ejpam-4354	159	18	γme(h	γme(h	PROPN
ejpam-4354	159	19	)	)	PUNCT
ejpam-4354	159	20	by	by	ADP
ejpam-4354	159	21	assumption	assumption	NOUN
ejpam-4354	159	22	.	.	PUNCT
ejpam-4354	160	1	if	if	SCONJ
ejpam-4354	160	2	s	s	ADP
ejpam-4354	160	3	∩	∩	ADJ
ejpam-4354	160	4	v	v	X
ejpam-4354	160	5	(	(	PUNCT
ejpam-4354	160	6	gr	gr	PROPN
ejpam-4354	160	7	)	)	PUNCT
ejpam-4354	160	8	6=	6=	NUM
ejpam-4354	161	1	s	s	X
ejpam-4354	161	2	,	,	PUNCT
ejpam-4354	161	3	again	again	ADV
ejpam-4354	161	4	,	,	PUNCT
ejpam-4354	161	5	µ3	µ3	PROPN
ejpam-4354	161	6	m(gr	m(gr	PROPN
ejpam-4354	161	7	)	)	PUNCT
ejpam-4354	161	8	≤	≤	PROPN
ejpam-4354	161	9	|s	|s	PROPN
ejpam-4354	161	10	∩	∩	ADJ
ejpam-4354	161	11	v	v	NOUN
ejpam-4354	161	12	(	(	PUNCT
ejpam-4354	161	13	gr)|	gr)|	PROPN
ejpam-4354	161	14	<	<	X
ejpam-4354	161	15	|s|	|s|	PROPN
ejpam-4354	161	16	=	=	SYM
ejpam-4354	161	17	γme(h	γme(h	PROPN
ejpam-4354	161	18	)	)	PUNCT
ejpam-4354	161	19	by	by	ADP
ejpam-4354	161	20	assumption	assumption	NOUN
ejpam-4354	161	21	.	.	PUNCT
ejpam-4354	162	1	thus	thus	ADV
ejpam-4354	162	2	,	,	PUNCT
ejpam-4354	162	3	µ3	µ3	PROPN
ejpam-4354	162	4	m(gr	m(gr	PROPN
ejpam-4354	162	5	)	)	PUNCT
ejpam-4354	162	6	+	+	CCONJ
ejpam-4354	162	7	1	1	NUM
ejpam-4354	162	8	≤	≤	NUM
ejpam-4354	162	9	γme(h	γme(h	PROPN
ejpam-4354	162	10	)	)	PUNCT
ejpam-4354	162	11	.	.	PUNCT
ejpam-4354	163	1	next	next	ADV
ejpam-4354	163	2	,	,	PUNCT
ejpam-4354	163	3	let	let	VERB
ejpam-4354	163	4	sg	sg	PART
ejpam-4354	163	5	be	be	AUX
ejpam-4354	163	6	a	a	DET
ejpam-4354	163	7	minimum	minimum	ADJ
ejpam-4354	163	8	d3m	d3m	ADJ
ejpam-4354	163	9	-	-	PUNCT
ejpam-4354	163	10	monophonic	monophonic	ADJ
ejpam-4354	163	11	eccentric	eccentric	ADJ
ejpam-4354	163	12	set	set	NOUN
ejpam-4354	163	13	of	of	ADP
ejpam-4354	163	14	gr	gr	PROPN
ejpam-4354	163	15	.	.	PUNCT
ejpam-4354	164	1	let	let	VERB
ejpam-4354	164	2	t	t	PROPN
ejpam-4354	164	3	∈	∈	PROPN
ejpam-4354	164	4	{	{	PUNCT
ejpam-4354	164	5	1	1	NUM
ejpam-4354	164	6	,	,	PUNCT
ejpam-4354	164	7	2	2	NUM
ejpam-4354	164	8	,	,	PUNCT
ejpam-4354	164	9	...	...	PUNCT
ejpam-4354	164	10	,	,	PUNCT
ejpam-4354	164	11	k	k	NOUN
ejpam-4354	164	12	}	}	PUNCT
ejpam-4354	164	13	\	\	NOUN
ejpam-4354	164	14	{	{	PUNCT
ejpam-4354	164	15	r	r	NOUN
ejpam-4354	164	16	}	}	PUNCT
ejpam-4354	164	17	and	and	CCONJ
ejpam-4354	164	18	choose	choose	VERB
ejpam-4354	164	19	any	any	DET
ejpam-4354	164	20	q	q	PROPN
ejpam-4354	164	21	∈	∈	PROPN
ejpam-4354	164	22	v	v	NOUN
ejpam-4354	164	23	(	(	PUNCT
ejpam-4354	164	24	gt	gt	PROPN
ejpam-4354	164	25	)	)	PUNCT
ejpam-4354	164	26	.	.	PUNCT
ejpam-4354	165	1	let	let	VERB
ejpam-4354	165	2	s0	s0	PROPN
ejpam-4354	165	3	=	=	PUNCT
ejpam-4354	165	4	sg	sg	ADP
ejpam-4354	165	5	∪	∪	X
ejpam-4354	165	6	{	{	PUNCT
ejpam-4354	165	7	q	q	NOUN
ejpam-4354	165	8	}	}	PUNCT
ejpam-4354	165	9	.	.	PUNCT
ejpam-4354	166	1	then	then	ADV
ejpam-4354	166	2	s0	s0	PROPN
ejpam-4354	166	3	is	be	AUX
ejpam-4354	166	4	a	a	DET
ejpam-4354	166	5	monophonic	monophonic	ADJ
ejpam-4354	166	6	eccentric	eccentric	ADJ
ejpam-4354	166	7	dominating	dominating	NOUN
ejpam-4354	166	8	set	set	NOUN
ejpam-4354	166	9	of	of	ADP
ejpam-4354	166	10	h	h	NOUN
ejpam-4354	166	11	by	by	ADP
ejpam-4354	166	12	theorem	theorem	NOUN
ejpam-4354	166	13	4	4	NUM
ejpam-4354	166	14	.	.	PUNCT
ejpam-4354	167	1	this	this	PRON
ejpam-4354	167	2	implies	imply	VERB
ejpam-4354	167	3	that	that	SCONJ
ejpam-4354	167	4	γme(h	γme(h	PROPN
ejpam-4354	167	5	)	)	PUNCT
ejpam-4354	167	6	≤	≤	NUM
ejpam-4354	167	7	|s0|	|s0|	NOUN
ejpam-4354	167	8	=	=	SYM
ejpam-4354	167	9	µ3	µ3	PROPN
ejpam-4354	167	10	m(gr	m(gr	PROPN
ejpam-4354	167	11	)	)	PUNCT
ejpam-4354	168	1	+	+	CCONJ
ejpam-4354	168	2	1	1	X
ejpam-4354	168	3	.	.	X
ejpam-4354	168	4	therefore	therefore	ADV
ejpam-4354	168	5	,	,	PUNCT
ejpam-4354	168	6	γme(h	γme(h	PROPN
ejpam-4354	168	7	)	)	PUNCT
ejpam-4354	168	8	=	=	SYM
ejpam-4354	168	9	µ3	µ3	NOUN
ejpam-4354	168	10	m(gr	m(gr	PROPN
ejpam-4354	168	11	)	)	PUNCT
ejpam-4354	169	1	+	+	NUM
ejpam-4354	169	2	1	1	X
ejpam-4354	169	3	.	.	X
ejpam-4354	169	4	theorem	theorem	NOUN
ejpam-4354	169	5	5	5	NUM
ejpam-4354	169	6	.	.	PUNCT
ejpam-4354	170	1	let	let	VERB
ejpam-4354	170	2	g	g	NOUN
ejpam-4354	170	3	and	and	CCONJ
ejpam-4354	170	4	h	h	NOUN
ejpam-4354	170	5	be	be	AUX
ejpam-4354	170	6	connected	connect	VERB
ejpam-4354	170	7	non	non	ADJ
ejpam-4354	170	8	-	-	ADJ
ejpam-4354	170	9	complete	complete	ADJ
ejpam-4354	170	10	graphs	graph	NOUN
ejpam-4354	170	11	.	.	PUNCT
ejpam-4354	171	1	then	then	ADV
ejpam-4354	171	2	s	s	VERB
ejpam-4354	171	3	is	be	AUX
ejpam-4354	171	4	a	a	DET
ejpam-4354	171	5	monophonic	monophonic	ADJ
ejpam-4354	171	6	eccentric	eccentric	ADJ
ejpam-4354	171	7	dominating	dominating	NOUN
ejpam-4354	171	8	set	set	NOUN
ejpam-4354	171	9	of	of	ADP
ejpam-4354	171	10	g	g	PROPN
ejpam-4354	172	1	+	+	CCONJ
ejpam-4354	172	2	h	h	NOUN
ejpam-4354	172	3	if	if	SCONJ
ejpam-4354	172	4	and	and	CCONJ
ejpam-4354	172	5	only	only	ADV
ejpam-4354	172	6	if	if	SCONJ
ejpam-4354	172	7	s	s	VERB
ejpam-4354	172	8	=	=	PUNCT
ejpam-4354	172	9	sg	sg	X
ejpam-4354	172	10	∪	∪	ADJ
ejpam-4354	172	11	sh	sh	PROPN
ejpam-4354	172	12	,	,	PUNCT
ejpam-4354	172	13	where	where	SCONJ
ejpam-4354	172	14	sg	sg	PROPN
ejpam-4354	172	15	and	and	CCONJ
ejpam-4354	172	16	sh	sh	PROPN
ejpam-4354	172	17	are	be	AUX
ejpam-4354	172	18	monophonic	monophonic	ADJ
ejpam-4354	172	19	eccentric	eccentric	ADJ
ejpam-4354	172	20	dominating	dominating	NOUN
ejpam-4354	172	21	sets	set	NOUN
ejpam-4354	172	22	of	of	ADP
ejpam-4354	172	23	g	g	PROPN
ejpam-4354	172	24	and	and	CCONJ
ejpam-4354	172	25	h	h	NOUN
ejpam-4354	172	26	,	,	PUNCT
ejpam-4354	172	27	respectively	respectively	ADV
ejpam-4354	172	28	.	.	PUNCT
ejpam-4354	173	1	proof	proof	NOUN
ejpam-4354	173	2	.	.	PUNCT
ejpam-4354	174	1	suppose	suppose	VERB
ejpam-4354	174	2	s	s	NOUN
ejpam-4354	174	3	is	be	AUX
ejpam-4354	174	4	a	a	DET
ejpam-4354	174	5	monophonic	monophonic	ADJ
ejpam-4354	174	6	eccentric	eccentric	ADJ
ejpam-4354	174	7	dominating	dominating	NOUN
ejpam-4354	174	8	set	set	NOUN
ejpam-4354	174	9	of	of	ADP
ejpam-4354	174	10	g	g	PROPN
ejpam-4354	174	11	+	+	CCONJ
ejpam-4354	174	12	h.	h.	PROPN
ejpam-4354	174	13	let	let	VERB
ejpam-4354	174	14	sg	sg	VERB
ejpam-4354	174	15	=	=	SYM
ejpam-4354	174	16	s	s	PART
ejpam-4354	174	17	∩	∩	ADJ
ejpam-4354	174	18	v	v	X
ejpam-4354	174	19	(	(	PUNCT
ejpam-4354	174	20	g	g	NOUN
ejpam-4354	174	21	)	)	PUNCT
ejpam-4354	174	22	and	and	CCONJ
ejpam-4354	174	23	sh	sh	INTJ
ejpam-4354	174	24	=	=	SYM
ejpam-4354	174	25	s	s	PROPN
ejpam-4354	174	26	∩	∩	ADJ
ejpam-4354	174	27	v	v	ADJ
ejpam-4354	174	28	(	(	PUNCT
ejpam-4354	174	29	h	h	NOUN
ejpam-4354	174	30	)	)	PUNCT
ejpam-4354	174	31	.	.	PUNCT
ejpam-4354	175	1	since	since	SCONJ
ejpam-4354	175	2	g	g	PROPN
ejpam-4354	175	3	and	and	CCONJ
ejpam-4354	175	4	h	h	NOUN
ejpam-4354	175	5	are	be	AUX
ejpam-4354	175	6	non	non	ADJ
ejpam-4354	175	7	-	-	ADJ
ejpam-4354	175	8	complete	complete	ADJ
ejpam-4354	175	9	graphs	graph	NOUN
ejpam-4354	175	10	,	,	PUNCT
ejpam-4354	175	11	sg	sg	ADP
ejpam-4354	175	12	6=	6=	NOUN
ejpam-4354	175	13	∅	∅	NOUN
ejpam-4354	175	14	and	and	CCONJ
ejpam-4354	175	15	sh	sh	PROPN
ejpam-4354	175	16	6=	6=	NOUN
ejpam-4354	175	17	∅.	∅.	ADV
ejpam-4354	175	18	let	let	VERB
ejpam-4354	175	19	v	v	ADP
ejpam-4354	175	20	∈	∈	PROPN
ejpam-4354	175	21	v	v	NOUN
ejpam-4354	175	22	(	(	PUNCT
ejpam-4354	175	23	g	g	NOUN
ejpam-4354	175	24	)	)	PUNCT
ejpam-4354	175	25	\	\	PROPN
ejpam-4354	175	26	sg	sg	PROPN
ejpam-4354	175	27	.	.	PUNCT
ejpam-4354	176	1	if	if	SCONJ
ejpam-4354	176	2	dmg	dmg	X
ejpam-4354	176	3	(	(	PUNCT
ejpam-4354	176	4	v	v	NOUN
ejpam-4354	176	5	,	,	PUNCT
ejpam-4354	176	6	x	x	NOUN
ejpam-4354	176	7	)	)	PUNCT
ejpam-4354	176	8	=	=	SYM
ejpam-4354	176	9	1	1	NUM
ejpam-4354	176	10	for	for	ADP
ejpam-4354	176	11	all	all	PRON
ejpam-4354	176	12	x	x	SYM
ejpam-4354	176	13	∈	∈	NOUN
ejpam-4354	176	14	v	v	NOUN
ejpam-4354	176	15	(	(	PUNCT
ejpam-4354	176	16	g	g	NOUN
ejpam-4354	176	17	)	)	PUNCT
ejpam-4354	176	18	\	\	NOUN
ejpam-4354	176	19	{	{	PUNCT
ejpam-4354	176	20	v	v	NOUN
ejpam-4354	176	21	}	}	PUNCT
ejpam-4354	176	22	,	,	PUNCT
ejpam-4354	176	23	then	then	ADV
ejpam-4354	176	24	every	every	DET
ejpam-4354	176	25	element	element	NOUN
ejpam-4354	176	26	of	of	ADP
ejpam-4354	176	27	sg	sg	PROPN
ejpam-4354	176	28	is	be	AUX
ejpam-4354	176	29	a	a	DET
ejpam-4354	176	30	monophonic	monophonic	ADJ
ejpam-4354	176	31	eccentic	eccentic	ADJ
ejpam-4354	176	32	vertex	vertex	NOUN
ejpam-4354	176	33	of	of	ADP
ejpam-4354	176	34	v	v	NOUN
ejpam-4354	176	35	in	in	ADP
ejpam-4354	176	36	g.	g.	PROPN
ejpam-4354	176	37	suppose	suppose	VERB
ejpam-4354	176	38	dmg	dmg	PROPN
ejpam-4354	176	39	(	(	PUNCT
ejpam-4354	176	40	v	v	NOUN
ejpam-4354	176	41	,	,	PUNCT
ejpam-4354	176	42	y	y	PROPN
ejpam-4354	176	43	)	)	PUNCT
ejpam-4354	176	44	6=	6=	ADP
ejpam-4354	176	45	1	1	NUM
ejpam-4354	176	46	for	for	ADP
ejpam-4354	176	47	some	some	DET
ejpam-4354	176	48	y	y	PROPN
ejpam-4354	176	49	∈	∈	PROPN
ejpam-4354	176	50	v	v	ADP
ejpam-4354	176	51	(	(	PUNCT
ejpam-4354	176	52	g	g	NOUN
ejpam-4354	176	53	)	)	PUNCT
ejpam-4354	176	54	\	\	NOUN
ejpam-4354	176	55	{	{	PUNCT
ejpam-4354	176	56	v	v	NOUN
ejpam-4354	176	57	}	}	PUNCT
ejpam-4354	176	58	.	.	PUNCT
ejpam-4354	177	1	since	since	SCONJ
ejpam-4354	177	2	s	s	PROPN
ejpam-4354	177	3	is	be	AUX
ejpam-4354	177	4	a	a	DET
ejpam-4354	177	5	monophonic	monophonic	ADJ
ejpam-4354	177	6	eccentric	eccentric	ADJ
ejpam-4354	177	7	dominating	dominating	NOUN
ejpam-4354	177	8	set	set	NOUN
ejpam-4354	177	9	of	of	ADP
ejpam-4354	177	10	g+h	g+h	PROPN
ejpam-4354	177	11	,	,	PUNCT
ejpam-4354	177	12	there	there	PRON
ejpam-4354	177	13	exists	exist	VERB
ejpam-4354	177	14	q	q	PROPN
ejpam-4354	177	15	∈	∈	PROPN
ejpam-4354	177	16	s	s	VERB
ejpam-4354	177	17	such	such	ADJ
ejpam-4354	177	18	that	that	SCONJ
ejpam-4354	177	19	emg+h(v	emg+h(v	NOUN
ejpam-4354	177	20	)	)	PUNCT
ejpam-4354	177	21	=	=	SYM
ejpam-4354	178	1	dmg+h(v	dmg+h(v	PROPN
ejpam-4354	178	2	,	,	PUNCT
ejpam-4354	178	3	q	q	NOUN
ejpam-4354	178	4	)	)	PUNCT
ejpam-4354	178	5	.	.	PUNCT
ejpam-4354	179	1	since	since	SCONJ
ejpam-4354	179	2	dmg+h(v	dmg+h(v	PROPN
ejpam-4354	179	3	,	,	PUNCT
ejpam-4354	179	4	h	h	NOUN
ejpam-4354	179	5	)	)	PUNCT
ejpam-4354	179	6	=	=	SYM
ejpam-4354	179	7	1	1	NUM
ejpam-4354	179	8	for	for	ADP
ejpam-4354	179	9	all	all	DET
ejpam-4354	179	10	h	h	NOUN
ejpam-4354	179	11	∈	∈	NOUN
ejpam-4354	179	12	sh	sh	INTJ
ejpam-4354	179	13	,	,	PUNCT
ejpam-4354	179	14	it	it	PRON
ejpam-4354	179	15	s.	s.	PROPN
ejpam-4354	179	16	canoy	canoy	PROPN
ejpam-4354	179	17	,	,	PUNCT
ejpam-4354	179	18	jr	jr	PROPN
ejpam-4354	179	19	.	.	PROPN
ejpam-4354	179	20	,	,	PUNCT
ejpam-4354	179	21	a.	a.	NOUN
ejpam-4354	179	22	gamorez	gamorez	PROPN
ejpam-4354	179	23	/	/	SYM
ejpam-4354	179	24	eur	eur	PROPN
ejpam-4354	179	25	.	.	PUNCT
ejpam-4354	180	1	j.	j.	PROPN
ejpam-4354	180	2	pure	pure	PROPN
ejpam-4354	180	3	appl	appl	PROPN
ejpam-4354	180	4	.	.	PROPN
ejpam-4354	180	5	math	math	PROPN
ejpam-4354	180	6	,	,	PUNCT
ejpam-4354	180	7	15	15	NUM
ejpam-4354	180	8	(	(	PUNCT
ejpam-4354	180	9	2	2	NUM
ejpam-4354	180	10	)	)	PUNCT
ejpam-4354	180	11	(	(	PUNCT
ejpam-4354	180	12	2022	2022	NUM
ejpam-4354	180	13	)	)	PUNCT
ejpam-4354	180	14	,	,	PUNCT
ejpam-4354	180	15	635	635	NUM
ejpam-4354	180	16	-	-	SYM
ejpam-4354	180	17	645	645	NUM
ejpam-4354	180	18	640	640	NUM
ejpam-4354	180	19	follows	follow	VERB
ejpam-4354	180	20	that	that	SCONJ
ejpam-4354	180	21	q	q	PROPN
ejpam-4354	180	22	∈	∈	PROPN
ejpam-4354	180	23	sg	sg	PROPN
ejpam-4354	180	24	and	and	CCONJ
ejpam-4354	180	25	emg	emg	PROPN
ejpam-4354	180	26	(	(	PUNCT
ejpam-4354	180	27	v	v	NOUN
ejpam-4354	180	28	)	)	PUNCT
ejpam-4354	180	29	=	=	PUNCT
ejpam-4354	180	30	dmg	dmg	X
ejpam-4354	180	31	(	(	PUNCT
ejpam-4354	180	32	v	v	NOUN
ejpam-4354	180	33	,	,	PUNCT
ejpam-4354	180	34	q	q	NOUN
ejpam-4354	180	35	)	)	PUNCT
ejpam-4354	180	36	.	.	PUNCT
ejpam-4354	181	1	this	this	PRON
ejpam-4354	181	2	implies	imply	VERB
ejpam-4354	181	3	that	that	SCONJ
ejpam-4354	181	4	sg	sg	PROPN
ejpam-4354	181	5	is	be	AUX
ejpam-4354	181	6	a	a	DET
ejpam-4354	181	7	monophonic	monophonic	ADJ
ejpam-4354	181	8	eccentric	eccentric	ADJ
ejpam-4354	181	9	dominating	dominating	NOUN
ejpam-4354	181	10	set	set	NOUN
ejpam-4354	181	11	of	of	ADP
ejpam-4354	181	12	g.	g.	PROPN
ejpam-4354	181	13	similarly	similarly	ADV
ejpam-4354	181	14	,	,	PUNCT
ejpam-4354	181	15	sh	sh	PROPN
ejpam-4354	181	16	is	be	AUX
ejpam-4354	181	17	a	a	DET
ejpam-4354	181	18	monophonic	monophonic	ADJ
ejpam-4354	181	19	eccentric	eccentric	ADJ
ejpam-4354	181	20	dominating	dominating	NOUN
ejpam-4354	181	21	set	set	NOUN
ejpam-4354	181	22	of	of	ADP
ejpam-4354	181	23	h.	h.	PROPN
ejpam-4354	181	24	for	for	ADP
ejpam-4354	181	25	the	the	DET
ejpam-4354	181	26	converse	converse	NOUN
ejpam-4354	181	27	,	,	PUNCT
ejpam-4354	181	28	suppose	suppose	VERB
ejpam-4354	181	29	that	that	SCONJ
ejpam-4354	181	30	s	s	VERB
ejpam-4354	181	31	=	=	PUNCT
ejpam-4354	181	32	sg	sg	X
ejpam-4354	181	33	∪	∪	ADJ
ejpam-4354	181	34	sh	sh	PROPN
ejpam-4354	181	35	,	,	PUNCT
ejpam-4354	181	36	where	where	SCONJ
ejpam-4354	181	37	sg	sg	PROPN
ejpam-4354	181	38	and	and	CCONJ
ejpam-4354	181	39	sh	sh	PROPN
ejpam-4354	181	40	are	be	AUX
ejpam-4354	181	41	monophonic	monophonic	ADJ
ejpam-4354	181	42	eccentric	eccentric	ADJ
ejpam-4354	181	43	dominating	dominating	NOUN
ejpam-4354	181	44	sets	set	NOUN
ejpam-4354	181	45	of	of	ADP
ejpam-4354	181	46	g	g	PROPN
ejpam-4354	181	47	and	and	CCONJ
ejpam-4354	181	48	h	h	NOUN
ejpam-4354	181	49	,	,	PUNCT
ejpam-4354	181	50	respectively	respectively	ADV
ejpam-4354	181	51	.	.	PUNCT
ejpam-4354	182	1	let	let	VERB
ejpam-4354	182	2	x	x	SYM
ejpam-4354	182	3	∈	∈	PROPN
ejpam-4354	182	4	v	v	X
ejpam-4354	182	5	(	(	PUNCT
ejpam-4354	182	6	g	g	PROPN
ejpam-4354	182	7	+	+	NOUN
ejpam-4354	182	8	h	h	NOUN
ejpam-4354	182	9	)	)	PUNCT
ejpam-4354	182	10	\	\	PUNCT
ejpam-4354	183	1	s.	s.	PROPN
ejpam-4354	183	2	suppose	suppose	VERB
ejpam-4354	183	3	x	x	X
ejpam-4354	183	4	∈	∈	PROPN
ejpam-4354	183	5	v	v	X
ejpam-4354	183	6	(	(	PUNCT
ejpam-4354	183	7	g	g	NOUN
ejpam-4354	183	8	)	)	PUNCT
ejpam-4354	183	9	.	.	PUNCT
ejpam-4354	184	1	then	then	ADV
ejpam-4354	184	2	x	x	SYM
ejpam-4354	184	3	∈	∈	PROPN
ejpam-4354	184	4	v	v	ADP
ejpam-4354	184	5	(	(	PUNCT
ejpam-4354	184	6	g	g	NOUN
ejpam-4354	184	7	)	)	PUNCT
ejpam-4354	184	8	\	\	PROPN
ejpam-4354	184	9	sg	sg	PROPN
ejpam-4354	184	10	.	.	PUNCT
ejpam-4354	185	1	by	by	ADP
ejpam-4354	185	2	assumption	assumption	NOUN
ejpam-4354	185	3	,	,	PUNCT
ejpam-4354	185	4	there	there	PRON
ejpam-4354	185	5	exists	exist	VERB
ejpam-4354	185	6	w	w	PROPN
ejpam-4354	185	7	∈	∈	PROPN
ejpam-4354	185	8	sg	sg	ADP
ejpam-4354	185	9	such	such	ADJ
ejpam-4354	185	10	that	that	DET
ejpam-4354	185	11	emg	emg	NOUN
ejpam-4354	185	12	(	(	PUNCT
ejpam-4354	185	13	x	x	X
ejpam-4354	185	14	)	)	PUNCT
ejpam-4354	185	15	=	=	SYM
ejpam-4354	185	16	dmg	dmg	X
ejpam-4354	185	17	(	(	PUNCT
ejpam-4354	185	18	x	x	NOUN
ejpam-4354	185	19	,	,	PUNCT
ejpam-4354	185	20	w	w	NOUN
ejpam-4354	185	21	)	)	PUNCT
ejpam-4354	185	22	.	.	PUNCT
ejpam-4354	186	1	it	it	PRON
ejpam-4354	186	2	follows	follow	VERB
ejpam-4354	186	3	that	that	SCONJ
ejpam-4354	186	4	emg+h(x	emg+h(x	PROPN
ejpam-4354	186	5	)	)	PUNCT
ejpam-4354	187	1	=	=	SYM
ejpam-4354	187	2	dmg+h(x	dmg+h(x	PROPN
ejpam-4354	187	3	,	,	PUNCT
ejpam-4354	187	4	w	w	NOUN
ejpam-4354	187	5	)	)	PUNCT
ejpam-4354	187	6	.	.	PUNCT
ejpam-4354	188	1	similarly	similarly	ADV
ejpam-4354	188	2	,	,	PUNCT
ejpam-4354	188	3	if	if	SCONJ
ejpam-4354	188	4	x	x	PROPN
ejpam-4354	188	5	∈	∈	PROPN
ejpam-4354	188	6	v	v	ADP
ejpam-4354	188	7	(	(	PUNCT
ejpam-4354	188	8	h	h	NOUN
ejpam-4354	188	9	)	)	PUNCT
ejpam-4354	188	10	,	,	PUNCT
ejpam-4354	188	11	then	then	ADV
ejpam-4354	188	12	there	there	PRON
ejpam-4354	188	13	exists	exist	VERB
ejpam-4354	188	14	u	u	PROPN
ejpam-4354	188	15	∈	∈	PROPN
ejpam-4354	188	16	sh	sh	ADP
ejpam-4354	188	17	⊆	⊆	NUM
ejpam-4354	188	18	s	s	VERB
ejpam-4354	188	19	such	such	ADJ
ejpam-4354	188	20	that	that	SCONJ
ejpam-4354	188	21	emg+h(x	emg+h(x	NOUN
ejpam-4354	188	22	)	)	PUNCT
ejpam-4354	189	1	=	=	SYM
ejpam-4354	189	2	dmg+h(x	dmg+h(x	PROPN
ejpam-4354	189	3	,	,	PUNCT
ejpam-4354	189	4	u	u	NOUN
ejpam-4354	189	5	)	)	PUNCT
ejpam-4354	189	6	.	.	PUNCT
ejpam-4354	190	1	therefore	therefore	ADV
ejpam-4354	190	2	,	,	PUNCT
ejpam-4354	190	3	s	s	VERB
ejpam-4354	190	4	is	be	AUX
ejpam-4354	190	5	a	a	DET
ejpam-4354	190	6	monophonic	monophonic	ADJ
ejpam-4354	190	7	eccentric	eccentric	ADJ
ejpam-4354	190	8	dominating	dominating	NOUN
ejpam-4354	190	9	set	set	NOUN
ejpam-4354	190	10	of	of	ADP
ejpam-4354	190	11	g+h	g+h	PROPN
ejpam-4354	190	12	.	.	PUNCT
ejpam-4354	191	1	corollary	corollary	ADJ
ejpam-4354	191	2	3	3	X
ejpam-4354	191	3	.	.	PUNCT
ejpam-4354	192	1	let	let	VERB
ejpam-4354	192	2	g	g	NOUN
ejpam-4354	192	3	and	and	CCONJ
ejpam-4354	192	4	h	h	NOUN
ejpam-4354	192	5	be	be	AUX
ejpam-4354	192	6	connected	connect	VERB
ejpam-4354	192	7	non	non	ADJ
ejpam-4354	192	8	-	-	ADJ
ejpam-4354	192	9	complete	complete	ADJ
ejpam-4354	192	10	graphs	graph	NOUN
ejpam-4354	192	11	.	.	PUNCT
ejpam-4354	193	1	then	then	ADV
ejpam-4354	193	2	γme(g+h	γme(g+h	PROPN
ejpam-4354	193	3	)	)	PUNCT
ejpam-4354	193	4	=	=	SYM
ejpam-4354	193	5	γme(g	γme(g	PROPN
ejpam-4354	193	6	)	)	PUNCT
ejpam-4354	194	1	+	+	CCONJ
ejpam-4354	194	2	γme(h	γme(h	PROPN
ejpam-4354	194	3	)	)	PUNCT
ejpam-4354	194	4	.	.	PUNCT
ejpam-4354	195	1	the	the	DET
ejpam-4354	195	2	next	next	ADJ
ejpam-4354	195	3	result	result	NOUN
ejpam-4354	195	4	shows	show	VERB
ejpam-4354	195	5	that	that	SCONJ
ejpam-4354	195	6	the	the	DET
ejpam-4354	195	7	absolute	absolute	ADJ
ejpam-4354	195	8	difference	difference	NOUN
ejpam-4354	195	9	of	of	ADP
ejpam-4354	195	10	the	the	DET
ejpam-4354	195	11	domination	domination	NOUN
ejpam-4354	195	12	number	number	NOUN
ejpam-4354	195	13	the	the	DET
ejpam-4354	195	14	monophonic	monophonic	ADJ
ejpam-4354	195	15	eccentric	eccentric	ADJ
ejpam-4354	195	16	domination	domination	NOUN
ejpam-4354	195	17	number	number	NOUN
ejpam-4354	195	18	can	can	AUX
ejpam-4354	195	19	be	be	AUX
ejpam-4354	195	20	made	make	VERB
ejpam-4354	195	21	arbitrarily	arbitrarily	ADV
ejpam-4354	195	22	large	large	ADJ
ejpam-4354	195	23	.	.	PUNCT
ejpam-4354	196	1	theorem	theorem	NOUN
ejpam-4354	196	2	6	6	NUM
ejpam-4354	196	3	.	.	PUNCT
ejpam-4354	197	1	let	let	VERB
ejpam-4354	197	2	n	n	PRON
ejpam-4354	197	3	be	be	AUX
ejpam-4354	197	4	a	a	DET
ejpam-4354	197	5	positive	positive	ADJ
ejpam-4354	197	6	integer	integer	NOUN
ejpam-4354	197	7	.	.	PUNCT
ejpam-4354	198	1	then	then	ADV
ejpam-4354	198	2	the	the	DET
ejpam-4354	198	3	following	following	ADJ
ejpam-4354	198	4	statements	statement	NOUN
ejpam-4354	198	5	hold	hold	VERB
ejpam-4354	198	6	:	:	PUNCT
ejpam-4354	198	7	(	(	PUNCT
ejpam-4354	198	8	i	i	NOUN
ejpam-4354	198	9	)	)	PUNCT
ejpam-4354	198	10	there	there	PRON
ejpam-4354	198	11	exists	exist	VERB
ejpam-4354	198	12	a	a	DET
ejpam-4354	198	13	connected	connected	ADJ
ejpam-4354	198	14	graph	graph	NOUN
ejpam-4354	198	15	g1	g1	NOUN
ejpam-4354	198	16	such	such	ADJ
ejpam-4354	198	17	that	that	SCONJ
ejpam-4354	198	18	γ(g1)−	γ(g1)−	PROPN
ejpam-4354	198	19	γme(g1	γme(g1	NOUN
ejpam-4354	198	20	)	)	PUNCT
ejpam-4354	198	21	=	=	SYM
ejpam-4354	198	22	n.	n.	NOUN
ejpam-4354	198	23	(	(	PUNCT
ejpam-4354	198	24	ii	ii	NOUN
ejpam-4354	198	25	)	)	PUNCT
ejpam-4354	198	26	there	there	PRON
ejpam-4354	198	27	exists	exist	VERB
ejpam-4354	198	28	a	a	DET
ejpam-4354	198	29	connected	connected	ADJ
ejpam-4354	198	30	graph	graph	NOUN
ejpam-4354	198	31	g2	g2	PROPN
ejpam-4354	198	32	such	such	ADJ
ejpam-4354	198	33	that	that	DET
ejpam-4354	198	34	γme(g2)−	γme(g2)−	NUM
ejpam-4354	198	35	γ(g2	γ(g2	NUM
ejpam-4354	198	36	)	)	PUNCT
ejpam-4354	198	37	=	=	SYM
ejpam-4354	198	38	n.	n.	NOUN
ejpam-4354	198	39	proof	proof	NOUN
ejpam-4354	198	40	.	.	PUNCT
ejpam-4354	199	1	(	(	PUNCT
ejpam-4354	199	2	i	i	NOUN
ejpam-4354	199	3	)	)	PUNCT
ejpam-4354	199	4	consider	consider	VERB
ejpam-4354	199	5	the	the	DET
ejpam-4354	199	6	corona	corona	NOUN
ejpam-4354	199	7	g1	g1	NOUN
ejpam-4354	199	8	=	=	SYM
ejpam-4354	199	9	pn+2	pn+2	NOUN
ejpam-4354	199	10	◦	◦	NOUN
ejpam-4354	199	11	k1	k1	NOUN
ejpam-4354	199	12	of	of	ADP
ejpam-4354	199	13	pn+2	pn+2	NOUN
ejpam-4354	199	14	=	=	PUNCT
ejpam-4354	200	1	[	[	X
ejpam-4354	200	2	x1	x1	PROPN
ejpam-4354	200	3	,	,	PUNCT
ejpam-4354	200	4	x2	x2	PROPN
ejpam-4354	200	5	,	,	PUNCT
ejpam-4354	200	6	...	...	PUNCT
ejpam-4354	200	7	,	,	PUNCT
ejpam-4354	200	8	xn+2	xn+2	X
ejpam-4354	200	9	]	]	PUNCT
ejpam-4354	200	10	and	and	CCONJ
ejpam-4354	200	11	k1	k1	NOUN
ejpam-4354	200	12	in	in	ADP
ejpam-4354	200	13	figure	figure	NOUN
ejpam-4354	200	14	1	1	NUM
ejpam-4354	200	15	.	.	PUNCT
ejpam-4354	200	16	clearly	clearly	ADV
ejpam-4354	200	17	,	,	PUNCT
ejpam-4354	200	18	s1	s1	PROPN
ejpam-4354	200	19	=	=	PUNCT
ejpam-4354	200	20	{	{	PUNCT
ejpam-4354	200	21	x1	x1	PROPN
ejpam-4354	200	22	,	,	PUNCT
ejpam-4354	200	23	x2	x2	PROPN
ejpam-4354	200	24	,	,	PUNCT
ejpam-4354	200	25	...	...	PUNCT
ejpam-4354	200	26	,	,	PUNCT
ejpam-4354	200	27	xn+1	xn+1	PROPN
ejpam-4354	200	28	,	,	PUNCT
ejpam-4354	200	29	xn+2	xn+2	PRON
ejpam-4354	200	30	}	}	PUNCT
ejpam-4354	200	31	is	be	AUX
ejpam-4354	200	32	a	a	DET
ejpam-4354	200	33	minimum	minimum	ADJ
ejpam-4354	200	34	dominating	dominating	NOUN
ejpam-4354	200	35	set	set	NOUN
ejpam-4354	200	36	and	and	CCONJ
ejpam-4354	200	37	s2	s2	PROPN
ejpam-4354	200	38	=	=	PUNCT
ejpam-4354	200	39	{	{	PUNCT
ejpam-4354	200	40	a	a	DET
ejpam-4354	200	41	,	,	PUNCT
ejpam-4354	200	42	b	b	NOUN
ejpam-4354	200	43	}	}	PUNCT
ejpam-4354	200	44	is	be	AUX
ejpam-4354	200	45	a	a	DET
ejpam-4354	200	46	minimum	minimum	ADJ
ejpam-4354	200	47	monophonic	monophonic	ADJ
ejpam-4354	200	48	eccentric	eccentric	ADJ
ejpam-4354	200	49	dominating	dominating	NOUN
ejpam-4354	200	50	set	set	NOUN
ejpam-4354	200	51	of	of	ADP
ejpam-4354	200	52	g1	g1	PROPN
ejpam-4354	200	53	.	.	PUNCT
ejpam-4354	201	1	thus	thus	ADV
ejpam-4354	201	2	,	,	PUNCT
ejpam-4354	201	3	γ(g1)−	γ(g1)−	PROPN
ejpam-4354	201	4	γme(g1	γme(g1	NOUN
ejpam-4354	201	5	)	)	PUNCT
ejpam-4354	201	6	=	=	VERB
ejpam-4354	201	7	n.	n.	NOUN
ejpam-4354	201	8	....................................	....................................	PUNCT
ejpam-4354	201	9	....................................	....................................	PUNCT
ejpam-4354	201	10	....................................	....................................	PUNCT
ejpam-4354	201	11	....................................	....................................	PUNCT
ejpam-4354	201	12	....................................	....................................	PUNCT
ejpam-4354	201	13	....................................	....................................	PUNCT
ejpam-4354	201	14	....................................	....................................	PUNCT
ejpam-4354	201	15	....................................	....................................	PUNCT
ejpam-4354	201	16	....................................	....................................	PUNCT
ejpam-4354	201	17	....................................	....................................	PUNCT
ejpam-4354	201	18	....................................	....................................	PUNCT
ejpam-4354	201	19	....................................	....................................	PUNCT
ejpam-4354	201	20	....................................	....................................	PUNCT
ejpam-4354	201	21	....................................	....................................	PUNCT
ejpam-4354	201	22	....................................	....................................	PUNCT
ejpam-4354	201	23	....................................	....................................	PUNCT
ejpam-4354	201	24	............................................................................	............................................................................	PUNCT
ejpam-4354	201	25	............................................................................	............................................................................	PUNCT
ejpam-4354	201	26	............................................................................	............................................................................	PUNCT
ejpam-4354	201	27	............................................................................	............................................................................	PUNCT
ejpam-4354	201	28	............................................................................	............................................................................	PUNCT
ejpam-4354	201	29	...............................................................................................	...............................................................................................	PUNCT
ejpam-4354	201	30	............................	............................	PUNCT
ejpam-4354	201	31	........	........	PUNCT
ejpam-4354	201	32	........	........	PUNCT
ejpam-4354	201	33	........	........	PUNCT
ejpam-4354	201	34	........	........	PUNCT
ejpam-4354	201	35	........	........	PUNCT
ejpam-4354	201	36	........	........	PUNCT
ejpam-4354	201	37	........	........	PUNCT
ejpam-4354	201	38	........	........	PUNCT
ejpam-4354	201	39	...	...	PUNCT
ejpam-4354	201	40	.........	.........	PUNCT
ejpam-4354	201	41	........	........	PUNCT
ejpam-4354	201	42	........	........	PUNCT
ejpam-4354	201	43	........	........	PUNCT
ejpam-4354	201	44	........	........	PUNCT
ejpam-4354	201	45	........	........	PUNCT
ejpam-4354	201	46	........	........	PUNCT
ejpam-4354	201	47	........	........	PUNCT
ejpam-4354	201	48	........	........	PUNCT
ejpam-4354	201	49	...	...	PUNCT
ejpam-4354	201	50	.........	.........	PUNCT
ejpam-4354	201	51	........	........	PUNCT
ejpam-4354	201	52	........	........	PUNCT
ejpam-4354	201	53	........	........	PUNCT
ejpam-4354	201	54	........	........	PUNCT
ejpam-4354	201	55	........	........	PUNCT
ejpam-4354	201	56	........	........	PUNCT
ejpam-4354	201	57	........	........	PUNCT
ejpam-4354	201	58	........	........	PUNCT
ejpam-4354	201	59	...	...	PUNCT
ejpam-4354	201	60	.........	.........	PUNCT
ejpam-4354	201	61	........	........	PUNCT
ejpam-4354	201	62	........	........	PUNCT
ejpam-4354	201	63	........	........	PUNCT
ejpam-4354	201	64	........	........	PUNCT
ejpam-4354	201	65	........	........	PUNCT
ejpam-4354	201	66	........	........	PUNCT
ejpam-4354	201	67	........	........	PUNCT
ejpam-4354	201	68	........	........	PUNCT
ejpam-4354	201	69	...	...	PUNCT
ejpam-4354	201	70	.........	.........	PUNCT
ejpam-4354	201	71	........	........	PUNCT
ejpam-4354	201	72	........	........	PUNCT
ejpam-4354	201	73	........	........	PUNCT
ejpam-4354	201	74	........	........	PUNCT
ejpam-4354	201	75	........	........	PUNCT
ejpam-4354	201	76	........	........	PUNCT
ejpam-4354	201	77	........	........	PUNCT
ejpam-4354	201	78	........	........	PUNCT
ejpam-4354	201	79	...	...	PUNCT
ejpam-4354	201	80	.........	.........	PUNCT
ejpam-4354	201	81	........	........	PUNCT
ejpam-4354	201	82	........	........	PUNCT
ejpam-4354	201	83	........	........	PUNCT
ejpam-4354	201	84	........	........	PUNCT
ejpam-4354	201	85	........	........	PUNCT
ejpam-4354	201	86	........	........	PUNCT
ejpam-4354	201	87	........	........	PUNCT
ejpam-4354	201	88	........	........	PUNCT
ejpam-4354	201	89	...	...	PUNCT
ejpam-4354	201	90	.........	.........	PUNCT
ejpam-4354	201	91	........	........	PUNCT
ejpam-4354	201	92	........	........	PUNCT
ejpam-4354	201	93	........	........	PUNCT
ejpam-4354	201	94	........	........	PUNCT
ejpam-4354	201	95	........	........	PUNCT
ejpam-4354	201	96	........	........	PUNCT
ejpam-4354	201	97	........	........	PUNCT
ejpam-4354	201	98	........	........	PUNCT
ejpam-4354	201	99	...	...	PUNCT
ejpam-4354	201	100	.........	.........	PUNCT
ejpam-4354	201	101	........	........	PUNCT
ejpam-4354	201	102	........	........	PUNCT
ejpam-4354	201	103	........	........	PUNCT
ejpam-4354	201	104	........	........	PUNCT
ejpam-4354	201	105	........	........	PUNCT
ejpam-4354	201	106	........	........	PUNCT
ejpam-4354	201	107	........	........	PUNCT
ejpam-4354	201	108	........	........	PUNCT
ejpam-4354	201	109	....	....	PUNCT
ejpam-4354	201	110	.	.	PUNCT
ejpam-4354	202	1	.	.	PUNCT
ejpam-4354	203	1	•	•	NUM
ejpam-4354	204	1	•	•	NOUN
ejpam-4354	204	2	x1	x1	NOUN
ejpam-4354	205	1	x2	x2	NOUN
ejpam-4354	205	2	x3	x3	PROPN
ejpam-4354	205	3	x4	x4	PROPN
ejpam-4354	205	4	x5	x5	PROPN
ejpam-4354	205	5	x6	x6	PROPN
ejpam-4354	205	6	xn+1	xn+1	PROPN
ejpam-4354	205	7	xn+2	xn+2	PROPN
ejpam-4354	206	1	b	b	X
ejpam-4354	206	2	a	a	DET
ejpam-4354	206	3	figure	figure	NOUN
ejpam-4354	206	4	1	1	NUM
ejpam-4354	206	5	:	:	PUNCT
ejpam-4354	206	6	a	a	DET
ejpam-4354	206	7	graph	graph	NOUN
ejpam-4354	206	8	g1	g1	NOUN
ejpam-4354	206	9	with	with	ADP
ejpam-4354	206	10	γ(g1	γ(g1	NOUN
ejpam-4354	206	11	)	)	PUNCT
ejpam-4354	206	12	=	=	SYM
ejpam-4354	206	13	n+	n+	ADP
ejpam-4354	206	14	2	2	NUM
ejpam-4354	206	15	and	and	CCONJ
ejpam-4354	206	16	γme(g1	γme(g1	NOUN
ejpam-4354	206	17	)	)	PUNCT
ejpam-4354	206	18	=	=	SYM
ejpam-4354	206	19	2	2	NUM
ejpam-4354	206	20	(	(	PUNCT
ejpam-4354	206	21	ii	ii	NOUN
ejpam-4354	206	22	)	)	PUNCT
ejpam-4354	206	23	consider	consider	VERB
ejpam-4354	206	24	the	the	DET
ejpam-4354	206	25	graph	graph	NOUN
ejpam-4354	206	26	g2	g2	PROPN
ejpam-4354	206	27	=	=	PUNCT
ejpam-4354	206	28	k1+(∪n+2	k1+(∪n+2	PROPN
ejpam-4354	206	29	j=1hj	j=1hj	PROPN
ejpam-4354	206	30	)	)	PUNCT
ejpam-4354	206	31	,	,	PUNCT
ejpam-4354	206	32	where	where	SCONJ
ejpam-4354	206	33	hj	hj	PROPN
ejpam-4354	206	34	=	=	PUNCT
ejpam-4354	206	35	p4	p4	PROPN
ejpam-4354	206	36	for	for	ADP
ejpam-4354	206	37	each	each	DET
ejpam-4354	206	38	j	j	PROPN
ejpam-4354	206	39	∈	∈	PROPN
ejpam-4354	206	40	{	{	PUNCT
ejpam-4354	206	41	1	1	NUM
ejpam-4354	206	42	,	,	PUNCT
ejpam-4354	206	43	.	.	PUNCT
ejpam-4354	206	44	.	.	PUNCT
ejpam-4354	207	1	.	.	PUNCT
ejpam-4354	208	1	,	,	PUNCT
ejpam-4354	208	2	n+1	n+1	ADV
ejpam-4354	208	3	}	}	PUNCT
ejpam-4354	208	4	.	.	PUNCT
ejpam-4354	209	1	clearly	clearly	ADV
ejpam-4354	209	2	,	,	PUNCT
ejpam-4354	209	3	γ(g2	γ(g2	NUM
ejpam-4354	209	4	)	)	PUNCT
ejpam-4354	209	5	=	=	SYM
ejpam-4354	209	6	1	1	X
ejpam-4354	209	7	.	.	PUNCT
ejpam-4354	209	8	now	now	ADV
ejpam-4354	209	9	rg2	rg2	VERB
ejpam-4354	210	1	=	=	SYM
ejpam-4354	211	1	{	{	PUNCT
ejpam-4354	211	2	1	1	NUM
ejpam-4354	211	3	,	,	PUNCT
ejpam-4354	211	4	2	2	NUM
ejpam-4354	211	5	,	,	PUNCT
ejpam-4354	211	6	...	...	PUNCT
ejpam-4354	211	7	,	,	PUNCT
ejpam-4354	212	1	n	n	PROPN
ejpam-4354	212	2	+	+	CCONJ
ejpam-4354	212	3	1	1	NUM
ejpam-4354	212	4	}	}	PUNCT
ejpam-4354	212	5	(	(	PUNCT
ejpam-4354	212	6	see	see	VERB
ejpam-4354	212	7	theorem	theorem	NOUN
ejpam-4354	212	8	4	4	NUM
ejpam-4354	212	9	)	)	PUNCT
ejpam-4354	212	10	and	and	CCONJ
ejpam-4354	212	11	µ3	µ3	PROPN
ejpam-4354	212	12	m(hj	m(hj	NOUN
ejpam-4354	212	13	)	)	PUNCT
ejpam-4354	212	14	=	=	SYM
ejpam-4354	212	15	µ3	µ3	NUM
ejpam-4354	212	16	m(p4	m(p4	NOUN
ejpam-4354	212	17	)	)	PUNCT
ejpam-4354	212	18	=	=	SYM
ejpam-4354	212	19	1	1	NUM
ejpam-4354	212	20	for	for	ADP
ejpam-4354	212	21	each	each	DET
ejpam-4354	212	22	j	j	PROPN
ejpam-4354	212	23	∈	∈	PROPN
ejpam-4354	212	24	rg2	rg2	NOUN
ejpam-4354	212	25	.	.	PUNCT
ejpam-4354	213	1	hence	hence	ADV
ejpam-4354	213	2	,	,	PUNCT
ejpam-4354	213	3	γme(g2	γme(g2	ADV
ejpam-4354	213	4	)	)	PUNCT
ejpam-4354	213	5	=	=	SYM
ejpam-4354	213	6	∑	∑	PUNCT
ejpam-4354	213	7	j∈rg	j∈rg	NOUN
ejpam-4354	213	8	µ3	µ3	NOUN
ejpam-4354	213	9	m(hj	m(hj	NOUN
ejpam-4354	213	10	)	)	PUNCT
ejpam-4354	213	11	=	=	SYM
ejpam-4354	214	1	n	n	PROPN
ejpam-4354	214	2	+	+	CCONJ
ejpam-4354	214	3	1	1	NUM
ejpam-4354	214	4	by	by	ADP
ejpam-4354	214	5	corollary	corollary	ADJ
ejpam-4354	214	6	2	2	NUM
ejpam-4354	214	7	.	.	PUNCT
ejpam-4354	215	1	thus	thus	ADV
ejpam-4354	215	2	,	,	PUNCT
ejpam-4354	215	3	γme(g2)−	γme(g2)−	NUM
ejpam-4354	215	4	γ(g2	γ(g2	NUM
ejpam-4354	215	5	)	)	PUNCT
ejpam-4354	216	1	=	=	VERB
ejpam-4354	216	2	n.	n.	NOUN
ejpam-4354	216	3	this	this	PRON
ejpam-4354	216	4	proves	prove	VERB
ejpam-4354	216	5	the	the	DET
ejpam-4354	216	6	assertion	assertion	NOUN
ejpam-4354	216	7	.	.	PUNCT
ejpam-4354	217	1	theorem	theorem	ADJ
ejpam-4354	217	2	7	7	NUM
ejpam-4354	217	3	.	.	PUNCT
ejpam-4354	218	1	let	let	VERB
ejpam-4354	218	2	g	g	NOUN
ejpam-4354	219	1	and	and	CCONJ
ejpam-4354	219	2	h	h	NOUN
ejpam-4354	219	3	be	be	VERB
ejpam-4354	219	4	any	any	DET
ejpam-4354	219	5	connected	connected	ADJ
ejpam-4354	219	6	non	non	ADJ
ejpam-4354	219	7	-	-	ADJ
ejpam-4354	219	8	trivial	trivial	ADJ
ejpam-4354	219	9	graphs	graph	NOUN
ejpam-4354	219	10	.	.	PUNCT
ejpam-4354	220	1	then	then	ADV
ejpam-4354	220	2	s	s	VERB
ejpam-4354	220	3	is	be	AUX
ejpam-4354	220	4	a	a	DET
ejpam-4354	220	5	monophonic	monophonic	ADJ
ejpam-4354	220	6	eccentric	eccentric	ADJ
ejpam-4354	220	7	dominating	dominating	NOUN
ejpam-4354	220	8	set	set	NOUN
ejpam-4354	220	9	of	of	ADP
ejpam-4354	220	10	g	g	PROPN
ejpam-4354	220	11	◦	◦	NOUN
ejpam-4354	220	12	h	h	NOUN
ejpam-4354	220	13	if	if	SCONJ
ejpam-4354	221	1	and	and	CCONJ
ejpam-4354	221	2	only	only	ADV
ejpam-4354	221	3	if	if	SCONJ
ejpam-4354	221	4	s	s	VERB
ejpam-4354	221	5	=	=	NOUN
ejpam-4354	221	6	a	a	DET
ejpam-4354	221	7	∪	∪	X
ejpam-4354	221	8	(	(	PUNCT
ejpam-4354	221	9	∪v∈v	∪v∈v	X
ejpam-4354	221	10	(	(	PUNCT
ejpam-4354	221	11	g)sv	g)sv	PROPN
ejpam-4354	221	12	)	)	PUNCT
ejpam-4354	221	13	,	,	PUNCT
ejpam-4354	221	14	where	where	SCONJ
ejpam-4354	221	15	a	a	DET
ejpam-4354	221	16	⊆	⊆	NUM
ejpam-4354	221	17	v	v	NOUN
ejpam-4354	221	18	(	(	PUNCT
ejpam-4354	221	19	g	g	NOUN
ejpam-4354	221	20	)	)	PUNCT
ejpam-4354	221	21	and	and	CCONJ
ejpam-4354	221	22	sv	sv	X
ejpam-4354	221	23	⊆	⊆	NUM
ejpam-4354	221	24	v	v	X
ejpam-4354	221	25	(	(	PUNCT
ejpam-4354	221	26	hv	hv	PROPN
ejpam-4354	221	27	)	)	PUNCT
ejpam-4354	221	28	for	for	ADP
ejpam-4354	221	29	each	each	DET
ejpam-4354	221	30	v	v	NUM
ejpam-4354	221	31	∈	∈	PROPN
ejpam-4354	221	32	v	v	NOUN
ejpam-4354	221	33	(	(	PUNCT
ejpam-4354	221	34	g	g	NOUN
ejpam-4354	221	35	)	)	PUNCT
ejpam-4354	221	36	,	,	PUNCT
ejpam-4354	221	37	and	and	CCONJ
ejpam-4354	221	38	satisfies	satisfy	VERB
ejpam-4354	221	39	the	the	DET
ejpam-4354	221	40	following	follow	VERB
ejpam-4354	221	41	conditions	condition	NOUN
ejpam-4354	221	42	:	:	PUNCT
ejpam-4354	221	43	(	(	PUNCT
ejpam-4354	221	44	i	i	NOUN
ejpam-4354	221	45	)	)	PUNCT
ejpam-4354	221	46	if	if	SCONJ
ejpam-4354	221	47	v	v	NUM
ejpam-4354	221	48	∈	∈	PROPN
ejpam-4354	221	49	v	v	NOUN
ejpam-4354	221	50	(	(	PUNCT
ejpam-4354	221	51	g	g	NOUN
ejpam-4354	221	52	)	)	PUNCT
ejpam-4354	221	53	\a	\a	ADJ
ejpam-4354	221	54	,	,	PUNCT
ejpam-4354	221	55	then	then	ADV
ejpam-4354	221	56	sw	sw	PROPN
ejpam-4354	221	57	6=	6=	PROPN
ejpam-4354	221	58	∅	∅	NOUN
ejpam-4354	221	59	for	for	ADP
ejpam-4354	221	60	some	some	DET
ejpam-4354	221	61	w	w	PROPN
ejpam-4354	221	62	∈	∈	PROPN
ejpam-4354	221	63	v	v	ADP
ejpam-4354	221	64	(	(	PUNCT
ejpam-4354	221	65	g	g	NOUN
ejpam-4354	221	66	)	)	PUNCT
ejpam-4354	221	67	with	with	ADP
ejpam-4354	221	68	emg	emg	NOUN
ejpam-4354	221	69	(	(	PUNCT
ejpam-4354	221	70	v	v	NOUN
ejpam-4354	221	71	)	)	PUNCT
ejpam-4354	221	72	=	=	PUNCT
ejpam-4354	221	73	dmg	dmg	X
ejpam-4354	221	74	(	(	PUNCT
ejpam-4354	221	75	v	v	NOUN
ejpam-4354	221	76	,	,	PUNCT
ejpam-4354	221	77	w	w	NOUN
ejpam-4354	221	78	)	)	PUNCT
ejpam-4354	221	79	.	.	PUNCT
ejpam-4354	222	1	s.	s.	PROPN
ejpam-4354	222	2	canoy	canoy	PROPN
ejpam-4354	222	3	,	,	PUNCT
ejpam-4354	222	4	jr	jr	PROPN
ejpam-4354	222	5	.	.	PROPN
ejpam-4354	222	6	,	,	PUNCT
ejpam-4354	222	7	a.	a.	NOUN
ejpam-4354	222	8	gamorez	gamorez	PROPN
ejpam-4354	222	9	/	/	SYM
ejpam-4354	222	10	eur	eur	PROPN
ejpam-4354	222	11	.	.	PUNCT
ejpam-4354	223	1	j.	j.	PROPN
ejpam-4354	223	2	pure	pure	PROPN
ejpam-4354	223	3	appl	appl	PROPN
ejpam-4354	223	4	.	.	PROPN
ejpam-4354	223	5	math	math	PROPN
ejpam-4354	223	6	,	,	PUNCT
ejpam-4354	223	7	15	15	NUM
ejpam-4354	223	8	(	(	PUNCT
ejpam-4354	223	9	2	2	NUM
ejpam-4354	223	10	)	)	PUNCT
ejpam-4354	223	11	(	(	PUNCT
ejpam-4354	223	12	2022	2022	NUM
ejpam-4354	223	13	)	)	PUNCT
ejpam-4354	223	14	,	,	PUNCT
ejpam-4354	223	15	635	635	NUM
ejpam-4354	223	16	-	-	SYM
ejpam-4354	223	17	645	645	NUM
ejpam-4354	223	18	641	641	NUM
ejpam-4354	223	19	(	(	PUNCT
ejpam-4354	223	20	ii	ii	NOUN
ejpam-4354	223	21	)	)	PUNCT
ejpam-4354	223	22	if	if	SCONJ
ejpam-4354	223	23	x	x	SYM
ejpam-4354	223	24	∈	∈	PROPN
ejpam-4354	223	25	v	v	ADP
ejpam-4354	223	26	(	(	PUNCT
ejpam-4354	223	27	h	h	NOUN
ejpam-4354	223	28	)	)	PUNCT
ejpam-4354	223	29	\	\	PROPN
ejpam-4354	223	30	sv	sv	NOUN
ejpam-4354	223	31	and	and	CCONJ
ejpam-4354	223	32	emhv(x	emhv(x	NUM
ejpam-4354	223	33	)	)	PUNCT
ejpam-4354	223	34	<	<	X
ejpam-4354	223	35	emg	emg	PROPN
ejpam-4354	223	36	(	(	PUNCT
ejpam-4354	223	37	v	v	NOUN
ejpam-4354	223	38	)	)	PUNCT
ejpam-4354	223	39	+	+	NOUN
ejpam-4354	223	40	2	2	NUM
ejpam-4354	223	41	,	,	PUNCT
ejpam-4354	223	42	then	then	ADV
ejpam-4354	223	43	sw	sw	PROPN
ejpam-4354	223	44	6=	6=	PROPN
ejpam-4354	223	45	∅	∅	NOUN
ejpam-4354	223	46	for	for	ADP
ejpam-4354	223	47	some	some	DET
ejpam-4354	223	48	w	w	PROPN
ejpam-4354	223	49	∈	∈	PROPN
ejpam-4354	223	50	v	v	ADP
ejpam-4354	223	51	(	(	PUNCT
ejpam-4354	223	52	g	g	NOUN
ejpam-4354	223	53	)	)	PUNCT
ejpam-4354	223	54	with	with	ADP
ejpam-4354	223	55	emg	emg	NOUN
ejpam-4354	223	56	(	(	PUNCT
ejpam-4354	223	57	v	v	NOUN
ejpam-4354	223	58	)	)	PUNCT
ejpam-4354	223	59	=	=	PUNCT
ejpam-4354	223	60	dmg	dmg	X
ejpam-4354	223	61	(	(	PUNCT
ejpam-4354	223	62	v	v	NOUN
ejpam-4354	223	63	,	,	PUNCT
ejpam-4354	223	64	w	w	NOUN
ejpam-4354	223	65	)	)	PUNCT
ejpam-4354	223	66	.	.	PUNCT
ejpam-4354	224	1	(	(	PUNCT
ejpam-4354	224	2	iii	iii	X
ejpam-4354	224	3	)	)	PUNCT
ejpam-4354	224	4	if	if	SCONJ
ejpam-4354	224	5	x	x	SYM
ejpam-4354	224	6	∈	∈	PROPN
ejpam-4354	224	7	v	v	ADP
ejpam-4354	224	8	(	(	PUNCT
ejpam-4354	224	9	h	h	NOUN
ejpam-4354	224	10	)	)	PUNCT
ejpam-4354	224	11	\	\	PROPN
ejpam-4354	224	12	sv	sv	NOUN
ejpam-4354	224	13	and	and	CCONJ
ejpam-4354	224	14	emhv(x	emhv(x	NUM
ejpam-4354	224	15	)	)	PUNCT
ejpam-4354	224	16	=	=	SYM
ejpam-4354	224	17	emg	emg	NOUN
ejpam-4354	224	18	(	(	PUNCT
ejpam-4354	224	19	v	v	NOUN
ejpam-4354	224	20	)	)	PUNCT
ejpam-4354	224	21	+	+	NOUN
ejpam-4354	224	22	2	2	NUM
ejpam-4354	224	23	,	,	PUNCT
ejpam-4354	224	24	then	then	ADV
ejpam-4354	224	25	there	there	PRON
ejpam-4354	224	26	exists	exist	VERB
ejpam-4354	224	27	y	y	PROPN
ejpam-4354	224	28	∈	∈	PROPN
ejpam-4354	224	29	sv	sv	INTJ
ejpam-4354	225	1	such	such	ADJ
ejpam-4354	225	2	that	that	DET
ejpam-4354	225	3	emhv(x	emhv(x	NOUN
ejpam-4354	225	4	)	)	PUNCT
ejpam-4354	225	5	=	=	SYM
ejpam-4354	226	1	dmhv(x	dmhv(x	PROPN
ejpam-4354	226	2	,	,	PUNCT
ejpam-4354	226	3	y	y	NOUN
ejpam-4354	226	4	)	)	PUNCT
ejpam-4354	226	5	or	or	CCONJ
ejpam-4354	226	6	sw	sw	PROPN
ejpam-4354	226	7	6=	6=	NOUN
ejpam-4354	226	8	∅	∅	NOUN
ejpam-4354	226	9	for	for	ADP
ejpam-4354	226	10	some	some	PRON
ejpam-4354	226	11	w	w	PROPN
ejpam-4354	226	12	∈	∈	PROPN
ejpam-4354	226	13	v	v	ADP
ejpam-4354	226	14	(	(	PUNCT
ejpam-4354	226	15	g	g	NOUN
ejpam-4354	226	16	)	)	PUNCT
ejpam-4354	226	17	with	with	ADP
ejpam-4354	226	18	emg	emg	NOUN
ejpam-4354	226	19	(	(	PUNCT
ejpam-4354	226	20	v	v	NOUN
ejpam-4354	226	21	)	)	PUNCT
ejpam-4354	226	22	=	=	PUNCT
ejpam-4354	226	23	dmg	dmg	X
ejpam-4354	226	24	(	(	PUNCT
ejpam-4354	226	25	v	v	NOUN
ejpam-4354	226	26	,	,	PUNCT
ejpam-4354	226	27	w	w	NOUN
ejpam-4354	226	28	)	)	PUNCT
ejpam-4354	226	29	.	.	PUNCT
ejpam-4354	227	1	(	(	PUNCT
ejpam-4354	227	2	iv	iv	X
ejpam-4354	227	3	)	)	PUNCT
ejpam-4354	227	4	if	if	SCONJ
ejpam-4354	227	5	x	x	SYM
ejpam-4354	227	6	∈	∈	PROPN
ejpam-4354	227	7	v	v	ADP
ejpam-4354	227	8	(	(	PUNCT
ejpam-4354	227	9	h	h	NOUN
ejpam-4354	227	10	)	)	PUNCT
ejpam-4354	227	11	\	\	PROPN
ejpam-4354	227	12	sv	sv	PROPN
ejpam-4354	227	13	and	and	CCONJ
ejpam-4354	227	14	emhv(x	emhv(x	PROPN
ejpam-4354	227	15	)	)	PUNCT
ejpam-4354	227	16	>	>	X
ejpam-4354	227	17	emg	emg	PROPN
ejpam-4354	227	18	(	(	PUNCT
ejpam-4354	227	19	v	v	NOUN
ejpam-4354	227	20	)	)	PUNCT
ejpam-4354	227	21	+	+	NOUN
ejpam-4354	227	22	2	2	NUM
ejpam-4354	227	23	,	,	PUNCT
ejpam-4354	227	24	then	then	ADV
ejpam-4354	227	25	there	there	PRON
ejpam-4354	227	26	exists	exist	VERB
ejpam-4354	227	27	y	y	PROPN
ejpam-4354	227	28	∈	∈	PROPN
ejpam-4354	227	29	sv	sv	INTJ
ejpam-4354	227	30	such	such	ADJ
ejpam-4354	227	31	that	that	DET
ejpam-4354	227	32	emhv(x	emhv(x	NOUN
ejpam-4354	227	33	)	)	PUNCT
ejpam-4354	227	34	=	=	SYM
ejpam-4354	227	35	dmhv(x	dmhv(x	PROPN
ejpam-4354	227	36	,	,	PUNCT
ejpam-4354	227	37	y	y	NOUN
ejpam-4354	227	38	)	)	PUNCT
ejpam-4354	227	39	.	.	PUNCT
ejpam-4354	228	1	proof	proof	NOUN
ejpam-4354	228	2	.	.	PUNCT
ejpam-4354	229	1	suppose	suppose	VERB
ejpam-4354	229	2	s	s	NOUN
ejpam-4354	229	3	is	be	AUX
ejpam-4354	229	4	a	a	DET
ejpam-4354	229	5	monophonic	monophonic	ADJ
ejpam-4354	229	6	eccentric	eccentric	ADJ
ejpam-4354	229	7	dominating	dominating	NOUN
ejpam-4354	229	8	set	set	NOUN
ejpam-4354	229	9	of	of	ADP
ejpam-4354	229	10	g	g	PROPN
ejpam-4354	229	11	◦	◦	PROPN
ejpam-4354	229	12	h.	h.	PROPN
ejpam-4354	229	13	let	let	VERB
ejpam-4354	229	14	a	a	DET
ejpam-4354	229	15	=	=	PUNCT
ejpam-4354	229	16	s∩v	s∩v	NOUN
ejpam-4354	229	17	(	(	PUNCT
ejpam-4354	229	18	g	g	NOUN
ejpam-4354	229	19	)	)	PUNCT
ejpam-4354	229	20	and	and	CCONJ
ejpam-4354	229	21	sv	sv	X
ejpam-4354	229	22	=	=	SYM
ejpam-4354	229	23	s∩v	s∩v	PROPN
ejpam-4354	229	24	(	(	PUNCT
ejpam-4354	229	25	hv	hv	PROPN
ejpam-4354	229	26	)	)	PUNCT
ejpam-4354	229	27	for	for	ADP
ejpam-4354	229	28	each	each	DET
ejpam-4354	229	29	v	v	NUM
ejpam-4354	229	30	∈	∈	PROPN
ejpam-4354	229	31	v	v	NOUN
ejpam-4354	229	32	(	(	PUNCT
ejpam-4354	229	33	g	g	NOUN
ejpam-4354	229	34	)	)	PUNCT
ejpam-4354	229	35	.	.	PUNCT
ejpam-4354	230	1	let	let	VERB
ejpam-4354	230	2	v	v	NUM
ejpam-4354	230	3	∈	∈	PROPN
ejpam-4354	230	4	v	v	NOUN
ejpam-4354	230	5	(	(	PUNCT
ejpam-4354	230	6	g	g	NOUN
ejpam-4354	230	7	)	)	PUNCT
ejpam-4354	230	8	.	.	PUNCT
ejpam-4354	231	1	if	if	SCONJ
ejpam-4354	231	2	v	v	NUM
ejpam-4354	231	3	∈	∈	PROPN
ejpam-4354	231	4	v	v	NOUN
ejpam-4354	231	5	(	(	PUNCT
ejpam-4354	231	6	g)\a	g)\a	NOUN
ejpam-4354	231	7	,	,	PUNCT
ejpam-4354	231	8	then	then	ADV
ejpam-4354	231	9	emg	emg	NOUN
ejpam-4354	231	10	◦	◦	PROPN
ejpam-4354	231	11	h(v	h(v	NOUN
ejpam-4354	231	12	)	)	PUNCT
ejpam-4354	231	13	=	=	SYM
ejpam-4354	231	14	emg	emg	NOUN
ejpam-4354	231	15	(	(	PUNCT
ejpam-4354	231	16	v)+1	v)+1	PROPN
ejpam-4354	231	17	.	.	PUNCT
ejpam-4354	232	1	hence	hence	ADV
ejpam-4354	232	2	,	,	PUNCT
ejpam-4354	232	3	by	by	ADP
ejpam-4354	232	4	assumption	assumption	NOUN
ejpam-4354	232	5	,	,	PUNCT
ejpam-4354	232	6	there	there	PRON
ejpam-4354	232	7	exist	exist	VERB
ejpam-4354	232	8	w	w	PROPN
ejpam-4354	232	9	∈	∈	PROPN
ejpam-4354	232	10	v	v	ADP
ejpam-4354	232	11	(	(	PUNCT
ejpam-4354	232	12	g	g	NOUN
ejpam-4354	232	13	)	)	PUNCT
ejpam-4354	232	14	with	with	ADP
ejpam-4354	232	15	emg	emg	NOUN
ejpam-4354	232	16	(	(	PUNCT
ejpam-4354	232	17	v	v	NOUN
ejpam-4354	232	18	)	)	PUNCT
ejpam-4354	232	19	=	=	PUNCT
ejpam-4354	232	20	dmg	dmg	X
ejpam-4354	232	21	(	(	PUNCT
ejpam-4354	232	22	v	v	NOUN
ejpam-4354	232	23	,	,	PUNCT
ejpam-4354	232	24	w	w	NOUN
ejpam-4354	232	25	)	)	PUNCT
ejpam-4354	232	26	and	and	CCONJ
ejpam-4354	232	27	q	q	PROPN
ejpam-4354	232	28	∈	∈	PROPN
ejpam-4354	232	29	sw	sw	NOUN
ejpam-4354	232	30	such	such	ADJ
ejpam-4354	232	31	that	that	PRON
ejpam-4354	232	32	emg	emg	NOUN
ejpam-4354	232	33	◦	◦	PROPN
ejpam-4354	232	34	h(v	h(v	PROPN
ejpam-4354	232	35	)	)	PUNCT
ejpam-4354	232	36	=	=	SYM
ejpam-4354	232	37	dmg	dmg	VERB
ejpam-4354	232	38	◦	◦	NOUN
ejpam-4354	232	39	h(v	h(v	NOUN
ejpam-4354	232	40	,	,	PUNCT
ejpam-4354	232	41	q	q	NOUN
ejpam-4354	232	42	)	)	PUNCT
ejpam-4354	232	43	.	.	PUNCT
ejpam-4354	233	1	this	this	PRON
ejpam-4354	233	2	shows	show	VERB
ejpam-4354	233	3	that	that	SCONJ
ejpam-4354	233	4	(	(	PUNCT
ejpam-4354	233	5	i	i	NOUN
ejpam-4354	233	6	)	)	PUNCT
ejpam-4354	233	7	holds	hold	VERB
ejpam-4354	233	8	.	.	PUNCT
ejpam-4354	234	1	again	again	ADV
ejpam-4354	234	2	,	,	PUNCT
ejpam-4354	234	3	since	since	SCONJ
ejpam-4354	234	4	s	s	NOUN
ejpam-4354	234	5	is	be	AUX
ejpam-4354	234	6	a	a	DET
ejpam-4354	234	7	monophonic	monophonic	ADJ
ejpam-4354	234	8	eccentric	eccentric	ADJ
ejpam-4354	234	9	dominating	dominating	NOUN
ejpam-4354	234	10	set	set	NOUN
ejpam-4354	234	11	of	of	ADP
ejpam-4354	234	12	g	g	PROPN
ejpam-4354	234	13	◦	◦	NOUN
ejpam-4354	234	14	h	h	NOUN
ejpam-4354	234	15	,	,	PUNCT
ejpam-4354	234	16	it	it	PRON
ejpam-4354	234	17	is	be	AUX
ejpam-4354	234	18	routine	routine	ADJ
ejpam-4354	234	19	to	to	PART
ejpam-4354	234	20	show	show	VERB
ejpam-4354	234	21	that	that	SCONJ
ejpam-4354	234	22	(	(	PUNCT
ejpam-4354	234	23	ii	ii	NOUN
ejpam-4354	234	24	)	)	PUNCT
ejpam-4354	234	25	,	,	PUNCT
ejpam-4354	234	26	(	(	PUNCT
ejpam-4354	234	27	iii	iii	NOUN
ejpam-4354	234	28	)	)	PUNCT
ejpam-4354	234	29	and	and	CCONJ
ejpam-4354	234	30	(	(	PUNCT
ejpam-4354	234	31	iv	iv	X
ejpam-4354	234	32	)	)	PUNCT
ejpam-4354	234	33	hold	hold	NOUN
ejpam-4354	234	34	.	.	PUNCT
ejpam-4354	235	1	for	for	ADP
ejpam-4354	235	2	the	the	DET
ejpam-4354	235	3	converse	converse	NOUN
ejpam-4354	235	4	,	,	PUNCT
ejpam-4354	235	5	suppose	suppose	VERB
ejpam-4354	235	6	that	that	SCONJ
ejpam-4354	235	7	s	s	VERB
ejpam-4354	235	8	is	be	AUX
ejpam-4354	235	9	the	the	DET
ejpam-4354	235	10	given	give	VERB
ejpam-4354	235	11	set	set	NOUN
ejpam-4354	235	12	and	and	CCONJ
ejpam-4354	235	13	satisfies	satisfy	VERB
ejpam-4354	235	14	the	the	DET
ejpam-4354	235	15	given	give	VERB
ejpam-4354	235	16	conditions	condition	NOUN
ejpam-4354	235	17	.	.	PUNCT
ejpam-4354	236	1	let	let	VERB
ejpam-4354	236	2	x	x	SYM
ejpam-4354	236	3	∈	∈	PROPN
ejpam-4354	236	4	v	v	X
ejpam-4354	236	5	(	(	PUNCT
ejpam-4354	236	6	g	g	PROPN
ejpam-4354	236	7	◦	◦	NOUN
ejpam-4354	236	8	h	h	NOUN
ejpam-4354	236	9	)	)	PUNCT
ejpam-4354	236	10	\	\	PROPN
ejpam-4354	236	11	s	s	PART
ejpam-4354	236	12	and	and	CCONJ
ejpam-4354	236	13	let	let	VERB
ejpam-4354	236	14	v	v	NUM
ejpam-4354	236	15	∈	∈	PROPN
ejpam-4354	236	16	v	v	NOUN
ejpam-4354	236	17	(	(	PUNCT
ejpam-4354	236	18	g	g	NOUN
ejpam-4354	236	19	)	)	PUNCT
ejpam-4354	236	20	such	such	ADJ
ejpam-4354	236	21	that	that	SCONJ
ejpam-4354	236	22	x	x	SYM
ejpam-4354	236	23	∈	∈	NOUN
ejpam-4354	236	24	v	v	ADP
ejpam-4354	236	25	+	+	X
ejpam-4354	236	26	hv	hv	NOUN
ejpam-4354	236	27	.	.	PUNCT
ejpam-4354	237	1	if	if	SCONJ
ejpam-4354	237	2	x	x	X
ejpam-4354	237	3	=	=	SYM
ejpam-4354	237	4	v	v	NOUN
ejpam-4354	237	5	,	,	PUNCT
ejpam-4354	237	6	then	then	ADV
ejpam-4354	237	7	sw	sw	PROPN
ejpam-4354	237	8	6=	6=	PROPN
ejpam-4354	237	9	∅	∅	NOUN
ejpam-4354	237	10	for	for	ADP
ejpam-4354	237	11	some	some	DET
ejpam-4354	237	12	w	w	PROPN
ejpam-4354	237	13	∈	∈	PROPN
ejpam-4354	237	14	v	v	ADP
ejpam-4354	237	15	(	(	PUNCT
ejpam-4354	237	16	g	g	NOUN
ejpam-4354	237	17	)	)	PUNCT
ejpam-4354	237	18	with	with	ADP
ejpam-4354	237	19	emg	emg	NOUN
ejpam-4354	237	20	(	(	PUNCT
ejpam-4354	237	21	v	v	NOUN
ejpam-4354	237	22	)	)	PUNCT
ejpam-4354	237	23	=	=	PUNCT
ejpam-4354	237	24	dmg	dmg	X
ejpam-4354	237	25	(	(	PUNCT
ejpam-4354	237	26	v	v	NOUN
ejpam-4354	237	27	,	,	PUNCT
ejpam-4354	237	28	w	w	NOUN
ejpam-4354	237	29	)	)	PUNCT
ejpam-4354	237	30	by	by	ADP
ejpam-4354	237	31	(	(	PUNCT
ejpam-4354	237	32	i	i	NOUN
ejpam-4354	237	33	)	)	PUNCT
ejpam-4354	237	34	.	.	PUNCT
ejpam-4354	238	1	it	it	PRON
ejpam-4354	238	2	follows	follow	VERB
ejpam-4354	238	3	that	that	SCONJ
ejpam-4354	238	4	every	every	DET
ejpam-4354	238	5	element	element	NOUN
ejpam-4354	238	6	of	of	ADP
ejpam-4354	238	7	sw	sw	PROPN
ejpam-4354	238	8	is	be	AUX
ejpam-4354	238	9	a	a	DET
ejpam-4354	238	10	monophonic	monophonic	ADJ
ejpam-4354	238	11	eccentric	eccentric	ADJ
ejpam-4354	238	12	vertex	vertex	NOUN
ejpam-4354	238	13	of	of	ADP
ejpam-4354	238	14	x	x	PUNCT
ejpam-4354	238	15	in	in	ADP
ejpam-4354	238	16	g	g	PROPN
ejpam-4354	238	17	◦	◦	NOUN
ejpam-4354	238	18	h.	h.	NOUN
ejpam-4354	238	19	suppose	suppose	VERB
ejpam-4354	238	20	x	x	SYM
ejpam-4354	238	21	∈	∈	PROPN
ejpam-4354	238	22	v	v	NOUN
ejpam-4354	238	23	(	(	PUNCT
ejpam-4354	238	24	hv)\sv	hv)\sv	PROPN
ejpam-4354	238	25	.	.	PUNCT
ejpam-4354	239	1	if	if	SCONJ
ejpam-4354	239	2	emhv(x	emhv(x	NUM
ejpam-4354	239	3	)	)	PUNCT
ejpam-4354	239	4	>	>	X
ejpam-4354	240	1	emg	emg	PROPN
ejpam-4354	240	2	(	(	PUNCT
ejpam-4354	240	3	v)+2	v)+2	PROPN
ejpam-4354	240	4	,	,	PUNCT
ejpam-4354	240	5	then	then	ADV
ejpam-4354	240	6	sv	sv	PROPN
ejpam-4354	240	7	contains	contain	VERB
ejpam-4354	240	8	a	a	DET
ejpam-4354	240	9	monophonic	monophonic	ADJ
ejpam-4354	240	10	eccentric	eccentric	ADJ
ejpam-4354	240	11	vertex	vertex	NOUN
ejpam-4354	240	12	of	of	ADP
ejpam-4354	240	13	x	x	PUNCT
ejpam-4354	240	14	in	in	ADP
ejpam-4354	240	15	g	g	NOUN
ejpam-4354	240	16	◦	◦	NOUN
ejpam-4354	240	17	h	h	NOUN
ejpam-4354	240	18	by	by	ADP
ejpam-4354	240	19	(	(	PUNCT
ejpam-4354	240	20	iv	iv	NOUN
ejpam-4354	240	21	)	)	PUNCT
ejpam-4354	240	22	.	.	PUNCT
ejpam-4354	241	1	if	if	SCONJ
ejpam-4354	241	2	emhv(x	emhv(x	NUM
ejpam-4354	241	3	)	)	PUNCT
ejpam-4354	241	4	≤	≤	NOUN
ejpam-4354	241	5	emg	emg	NOUN
ejpam-4354	241	6	(	(	PUNCT
ejpam-4354	241	7	v)+2	v)+2	PROPN
ejpam-4354	241	8	,	,	PUNCT
ejpam-4354	241	9	then	then	ADV
ejpam-4354	241	10	x	x	PUNCT
ejpam-4354	241	11	has	have	VERB
ejpam-4354	241	12	a	a	DET
ejpam-4354	241	13	monophonic	monophonic	ADJ
ejpam-4354	241	14	eccentric	eccentric	ADJ
ejpam-4354	241	15	vertex	vertex	NOUN
ejpam-4354	241	16	in	in	ADP
ejpam-4354	241	17	g	g	PROPN
ejpam-4354	241	18	◦	◦	NOUN
ejpam-4354	241	19	h	h	NOUN
ejpam-4354	241	20	by	by	ADP
ejpam-4354	241	21	(	(	PUNCT
ejpam-4354	241	22	ii	ii	NOUN
ejpam-4354	241	23	)	)	PUNCT
ejpam-4354	241	24	and	and	CCONJ
ejpam-4354	241	25	(	(	PUNCT
ejpam-4354	241	26	iii	iii	NOUN
ejpam-4354	241	27	)	)	PUNCT
ejpam-4354	241	28	.	.	PUNCT
ejpam-4354	242	1	therefore	therefore	ADV
ejpam-4354	242	2	,	,	PUNCT
ejpam-4354	242	3	s	s	VERB
ejpam-4354	242	4	is	be	AUX
ejpam-4354	242	5	a	a	DET
ejpam-4354	242	6	monophonic	monophonic	ADJ
ejpam-4354	242	7	eccentric	eccentric	ADJ
ejpam-4354	242	8	dominating	dominating	NOUN
ejpam-4354	242	9	set	set	NOUN
ejpam-4354	242	10	of	of	ADP
ejpam-4354	242	11	g	g	PROPN
ejpam-4354	242	12	◦	◦	PROPN
ejpam-4354	242	13	h.	h.	NOUN
ejpam-4354	242	14	theorem	theorem	ADJ
ejpam-4354	242	15	8	8	NUM
ejpam-4354	242	16	.	.	PUNCT
ejpam-4354	243	1	let	let	VERB
ejpam-4354	243	2	g	g	NOUN
ejpam-4354	244	1	and	and	CCONJ
ejpam-4354	244	2	h	h	NOUN
ejpam-4354	244	3	be	be	VERB
ejpam-4354	244	4	any	any	DET
ejpam-4354	244	5	connected	connected	ADJ
ejpam-4354	244	6	non	non	ADJ
ejpam-4354	244	7	-	-	ADJ
ejpam-4354	244	8	trivial	trivial	ADJ
ejpam-4354	244	9	graphs	graph	NOUN
ejpam-4354	244	10	such	such	ADJ
ejpam-4354	244	11	that	that	DET
ejpam-4354	244	12	radm(h	radm(h	NOUN
ejpam-4354	244	13	)	)	PUNCT
ejpam-4354	244	14	>	>	X
ejpam-4354	245	1	diamm(g	diamm(g	PROPN
ejpam-4354	245	2	)	)	PUNCT
ejpam-4354	245	3	+	+	CCONJ
ejpam-4354	245	4	2	2	X
ejpam-4354	245	5	.	.	X
ejpam-4354	245	6	then	then	ADV
ejpam-4354	245	7	s	s	VERB
ejpam-4354	245	8	is	be	AUX
ejpam-4354	245	9	a	a	DET
ejpam-4354	245	10	monophonic	monophonic	ADJ
ejpam-4354	245	11	eccentric	eccentric	ADJ
ejpam-4354	245	12	dominating	dominating	NOUN
ejpam-4354	245	13	set	set	NOUN
ejpam-4354	245	14	of	of	ADP
ejpam-4354	245	15	g	g	PROPN
ejpam-4354	245	16	◦	◦	NOUN
ejpam-4354	245	17	h	h	NOUN
ejpam-4354	245	18	if	if	SCONJ
ejpam-4354	246	1	and	and	CCONJ
ejpam-4354	246	2	only	only	ADV
ejpam-4354	246	3	if	if	SCONJ
ejpam-4354	246	4	sv	sv	PROPN
ejpam-4354	246	5	=	=	SYM
ejpam-4354	246	6	s	s	PROPN
ejpam-4354	246	7	∩	∩	ADJ
ejpam-4354	246	8	v	v	X
ejpam-4354	246	9	(	(	PUNCT
ejpam-4354	246	10	hv	hv	X
ejpam-4354	246	11	)	)	PUNCT
ejpam-4354	246	12	is	be	AUX
ejpam-4354	246	13	a	a	DET
ejpam-4354	246	14	monophonic	monophonic	ADJ
ejpam-4354	246	15	eccentric	eccentric	ADJ
ejpam-4354	246	16	dominating	dominating	NOUN
ejpam-4354	246	17	set	set	NOUN
ejpam-4354	246	18	of	of	ADP
ejpam-4354	246	19	hv	hv	PROPN
ejpam-4354	246	20	for	for	ADP
ejpam-4354	246	21	each	each	DET
ejpam-4354	246	22	v	v	NUM
ejpam-4354	246	23	∈	∈	PROPN
ejpam-4354	246	24	v	v	NOUN
ejpam-4354	246	25	(	(	PUNCT
ejpam-4354	246	26	g	g	NOUN
ejpam-4354	246	27	)	)	PUNCT
ejpam-4354	246	28	.	.	PUNCT
ejpam-4354	247	1	moreover	moreover	ADV
ejpam-4354	247	2	,	,	PUNCT
ejpam-4354	247	3	γme(g	γme(g	PROPN
ejpam-4354	247	4	◦	◦	NOUN
ejpam-4354	247	5	h	h	NOUN
ejpam-4354	247	6	)	)	PUNCT
ejpam-4354	247	7	=	=	SYM
ejpam-4354	247	8	|v	|v	PROPN
ejpam-4354	247	9	(	(	PUNCT
ejpam-4354	247	10	g)|γme(h	g)|γme(h	NOUN
ejpam-4354	247	11	)	)	PUNCT
ejpam-4354	247	12	.	.	PUNCT
ejpam-4354	248	1	proof	proof	NOUN
ejpam-4354	248	2	.	.	PUNCT
ejpam-4354	249	1	let	let	VERB
ejpam-4354	249	2	v	v	NUM
ejpam-4354	249	3	∈	∈	PROPN
ejpam-4354	249	4	v	v	NOUN
ejpam-4354	249	5	(	(	PUNCT
ejpam-4354	249	6	g	g	NOUN
ejpam-4354	249	7	)	)	PUNCT
ejpam-4354	249	8	and	and	CCONJ
ejpam-4354	249	9	let	let	VERB
ejpam-4354	249	10	sv	sv	VERB
ejpam-4354	249	11	=	=	SYM
ejpam-4354	249	12	s	s	PROPN
ejpam-4354	249	13	∩	∩	ADJ
ejpam-4354	249	14	v	v	X
ejpam-4354	249	15	(	(	PUNCT
ejpam-4354	249	16	hv	hv	PROPN
ejpam-4354	249	17	)	)	PUNCT
ejpam-4354	249	18	.	.	PUNCT
ejpam-4354	250	1	let	let	VERB
ejpam-4354	250	2	x	x	SYM
ejpam-4354	250	3	∈	∈	PROPN
ejpam-4354	250	4	v	v	ADP
ejpam-4354	250	5	(	(	PUNCT
ejpam-4354	250	6	hv	hv	PROPN
ejpam-4354	250	7	)	)	PUNCT
ejpam-4354	250	8	\	\	PROPN
ejpam-4354	251	1	sv	sv	PROPN
ejpam-4354	251	2	.	.	PUNCT
ejpam-4354	252	1	since	since	SCONJ
ejpam-4354	252	2	radm(h	radm(h	NOUN
ejpam-4354	252	3	)	)	PUNCT
ejpam-4354	252	4	>	>	X
ejpam-4354	253	1	diamm(g	diamm(g	PROPN
ejpam-4354	253	2	)	)	PUNCT
ejpam-4354	253	3	+	+	CCONJ
ejpam-4354	253	4	2	2	NUM
ejpam-4354	253	5	,	,	PUNCT
ejpam-4354	253	6	emhv(x	emhv(x	NOUN
ejpam-4354	253	7	)	)	PUNCT
ejpam-4354	253	8	>	>	X
ejpam-4354	254	1	emg	emg	PROPN
ejpam-4354	255	1	(	(	PUNCT
ejpam-4354	256	1	v	v	NOUN
ejpam-4354	256	2	)	)	PUNCT
ejpam-4354	256	3	+	+	NOUN
ejpam-4354	256	4	2	2	X
ejpam-4354	256	5	.	.	PUNCT
ejpam-4354	256	6	by	by	ADP
ejpam-4354	256	7	theorem	theorem	ADJ
ejpam-4354	256	8	7(iv	7(iv	NUM
ejpam-4354	256	9	)	)	PUNCT
ejpam-4354	256	10	,	,	PUNCT
ejpam-4354	256	11	there	there	PRON
ejpam-4354	256	12	exists	exist	VERB
ejpam-4354	256	13	y	y	PROPN
ejpam-4354	256	14	∈	∈	PROPN
ejpam-4354	256	15	sv	sv	INTJ
ejpam-4354	257	1	such	such	ADJ
ejpam-4354	257	2	that	that	DET
ejpam-4354	257	3	emhv(x	emhv(x	NOUN
ejpam-4354	257	4	)	)	PUNCT
ejpam-4354	257	5	=	=	SYM
ejpam-4354	258	1	dmhv(x	dmhv(x	PROPN
ejpam-4354	258	2	,	,	PUNCT
ejpam-4354	258	3	y	y	NOUN
ejpam-4354	258	4	)	)	PUNCT
ejpam-4354	258	5	=	=	SYM
ejpam-4354	258	6	dmg	dmg	PROPN
ejpam-4354	258	7	◦	◦	NOUN
ejpam-4354	258	8	h(x	h(x	PROPN
ejpam-4354	258	9	,	,	PUNCT
ejpam-4354	258	10	y	y	PROPN
ejpam-4354	258	11	)	)	PUNCT
ejpam-4354	258	12	.	.	PUNCT
ejpam-4354	259	1	this	this	PRON
ejpam-4354	259	2	shows	show	VERB
ejpam-4354	259	3	that	that	SCONJ
ejpam-4354	259	4	sv	sv	PROPN
ejpam-4354	259	5	is	be	AUX
ejpam-4354	259	6	a	a	DET
ejpam-4354	259	7	monophonic	monophonic	ADJ
ejpam-4354	259	8	eccentric	eccentric	ADJ
ejpam-4354	259	9	dominating	dominating	NOUN
ejpam-4354	259	10	set	set	NOUN
ejpam-4354	259	11	of	of	ADP
ejpam-4354	259	12	hv	hv	PROPN
ejpam-4354	259	13	.	.	PROPN
ejpam-4354	260	1	for	for	ADP
ejpam-4354	260	2	the	the	DET
ejpam-4354	260	3	converse	converse	NOUN
ejpam-4354	260	4	,	,	PUNCT
ejpam-4354	260	5	suppose	suppose	VERB
ejpam-4354	260	6	that	that	SCONJ
ejpam-4354	260	7	sv	sv	PROPN
ejpam-4354	260	8	is	be	AUX
ejpam-4354	260	9	a	a	DET
ejpam-4354	260	10	monophonic	monophonic	ADJ
ejpam-4354	260	11	eccentric	eccentric	ADJ
ejpam-4354	260	12	dominating	dominating	NOUN
ejpam-4354	260	13	set	set	NOUN
ejpam-4354	260	14	of	of	ADP
ejpam-4354	260	15	hv	hv	PROPN
ejpam-4354	260	16	for	for	ADP
ejpam-4354	260	17	each	each	DET
ejpam-4354	260	18	v	v	NUM
ejpam-4354	260	19	∈	∈	PROPN
ejpam-4354	260	20	v	v	NOUN
ejpam-4354	260	21	(	(	PUNCT
ejpam-4354	260	22	g	g	NOUN
ejpam-4354	260	23	)	)	PUNCT
ejpam-4354	260	24	.	.	PUNCT
ejpam-4354	261	1	let	let	VERB
ejpam-4354	261	2	z	z	NOUN
ejpam-4354	261	3	∈	∈	PROPN
ejpam-4354	261	4	v	v	NOUN
ejpam-4354	261	5	(	(	PUNCT
ejpam-4354	261	6	g	g	PROPN
ejpam-4354	261	7	◦	◦	NOUN
ejpam-4354	261	8	h	h	NOUN
ejpam-4354	261	9	)	)	PUNCT
ejpam-4354	261	10	\	\	PROPN
ejpam-4354	261	11	s	s	PART
ejpam-4354	261	12	and	and	CCONJ
ejpam-4354	261	13	let	let	VERB
ejpam-4354	261	14	w	w	PROPN
ejpam-4354	261	15	∈	∈	PROPN
ejpam-4354	261	16	v	v	ADP
ejpam-4354	261	17	(	(	PUNCT
ejpam-4354	261	18	g	g	NOUN
ejpam-4354	261	19	)	)	PUNCT
ejpam-4354	261	20	such	such	ADJ
ejpam-4354	261	21	that	that	SCONJ
ejpam-4354	261	22	z	z	PROPN
ejpam-4354	261	23	∈	∈	PROPN
ejpam-4354	261	24	w	w	PROPN
ejpam-4354	262	1	+	+	NUM
ejpam-4354	262	2	v	v	PROPN
ejpam-4354	262	3	(	(	PUNCT
ejpam-4354	262	4	hw	hw	NOUN
ejpam-4354	262	5	)	)	PUNCT
ejpam-4354	262	6	.	.	PUNCT
ejpam-4354	263	1	since	since	SCONJ
ejpam-4354	263	2	radm(h	radm(h	NOUN
ejpam-4354	263	3	)	)	PUNCT
ejpam-4354	263	4	>	>	X
ejpam-4354	264	1	diamm(g	diamm(g	PROPN
ejpam-4354	264	2	)	)	PUNCT
ejpam-4354	264	3	+	+	CCONJ
ejpam-4354	264	4	2	2	NUM
ejpam-4354	264	5	,	,	PUNCT
ejpam-4354	264	6	the	the	DET
ejpam-4354	264	7	conditions	condition	NOUN
ejpam-4354	264	8	in	in	ADP
ejpam-4354	264	9	theorem	theorem	ADJ
ejpam-4354	264	10	7	7	NUM
ejpam-4354	264	11	are	be	AUX
ejpam-4354	264	12	satisfied	satisfied	ADJ
ejpam-4354	264	13	by	by	ADP
ejpam-4354	264	14	s.	s.	PROPN
ejpam-4354	264	15	therefore	therefore	ADV
ejpam-4354	264	16	,	,	PUNCT
ejpam-4354	264	17	s	s	VERB
ejpam-4354	264	18	is	be	AUX
ejpam-4354	264	19	a	a	DET
ejpam-4354	264	20	monophonic	monophonic	ADJ
ejpam-4354	264	21	eccentric	eccentric	ADJ
ejpam-4354	264	22	dominating	dominating	NOUN
ejpam-4354	264	23	set	set	NOUN
ejpam-4354	264	24	of	of	ADP
ejpam-4354	264	25	g	g	PROPN
ejpam-4354	264	26	◦	◦	NOUN
ejpam-4354	264	27	h.	h.	PROPN
ejpam-4354	264	28	next	next	ADV
ejpam-4354	264	29	,	,	PUNCT
ejpam-4354	264	30	let	let	VERB
ejpam-4354	264	31	dv	dv	PROPN
ejpam-4354	264	32	be	be	AUX
ejpam-4354	264	33	a	a	DET
ejpam-4354	264	34	minimum	minimum	ADJ
ejpam-4354	264	35	monophonic	monophonic	ADJ
ejpam-4354	264	36	eccentric	eccentric	ADJ
ejpam-4354	264	37	dominating	dominating	NOUN
ejpam-4354	264	38	set	set	NOUN
ejpam-4354	264	39	of	of	ADP
ejpam-4354	264	40	hv	hv	PROPN
ejpam-4354	264	41	for	for	ADP
ejpam-4354	264	42	each	each	DET
ejpam-4354	264	43	v	v	NUM
ejpam-4354	264	44	∈	∈	PROPN
ejpam-4354	264	45	v	v	NOUN
ejpam-4354	264	46	(	(	PUNCT
ejpam-4354	264	47	g	g	NOUN
ejpam-4354	264	48	)	)	PUNCT
ejpam-4354	264	49	.	.	PUNCT
ejpam-4354	265	1	then	then	ADV
ejpam-4354	265	2	s0	s0	PROPN
ejpam-4354	265	3	=	=	PUNCT
ejpam-4354	266	1	∪v∈v	∪v∈v	X
ejpam-4354	266	2	(	(	PUNCT
ejpam-4354	266	3	g)dv	g)dv	PROPN
ejpam-4354	266	4	is	be	AUX
ejpam-4354	266	5	a	a	DET
ejpam-4354	266	6	minimum	minimum	ADJ
ejpam-4354	266	7	monophonic	monophonic	ADJ
ejpam-4354	266	8	eccentric	eccentric	ADJ
ejpam-4354	266	9	dominating	dominating	NOUN
ejpam-4354	266	10	set	set	NOUN
ejpam-4354	266	11	of	of	ADP
ejpam-4354	266	12	g	g	PROPN
ejpam-4354	266	13	◦	◦	NOUN
ejpam-4354	266	14	h.	h.	PROPN
ejpam-4354	266	15	thus	thus	ADV
ejpam-4354	266	16	,	,	PUNCT
ejpam-4354	266	17	γme(g	γme(g	PROPN
ejpam-4354	266	18	◦	◦	NOUN
ejpam-4354	266	19	h	h	NOUN
ejpam-4354	266	20	)	)	PUNCT
ejpam-4354	266	21	=	=	SYM
ejpam-4354	266	22	|s0|	|s0|	NOUN
ejpam-4354	266	23	=	=	SYM
ejpam-4354	266	24	|v	|v	PROPN
ejpam-4354	266	25	(	(	PUNCT
ejpam-4354	266	26	g)|γme(h	g)|γme(h	NOUN
ejpam-4354	266	27	)	)	PUNCT
ejpam-4354	266	28	.	.	PUNCT
ejpam-4354	267	1	for	for	ADP
ejpam-4354	267	2	vertex	vertex	NOUN
ejpam-4354	267	3	v	v	ADP
ejpam-4354	267	4	∈	∈	PROPN
ejpam-4354	267	5	v	v	NOUN
ejpam-4354	267	6	(	(	PUNCT
ejpam-4354	267	7	g	g	NOUN
ejpam-4354	267	8	)	)	PUNCT
ejpam-4354	267	9	,	,	PUNCT
ejpam-4354	267	10	we	we	PRON
ejpam-4354	267	11	denote	denote	VERB
ejpam-4354	267	12	by	by	ADP
ejpam-4354	267	13	nm	nm	PRON
ejpam-4354	267	14	g	g	PROPN
ejpam-4354	267	15	(	(	PUNCT
ejpam-4354	267	16	v	v	NOUN
ejpam-4354	267	17	)	)	PUNCT
ejpam-4354	267	18	the	the	DET
ejpam-4354	267	19	set	set	NOUN
ejpam-4354	267	20	of	of	ADP
ejpam-4354	267	21	all	all	DET
ejpam-4354	267	22	monophonic	monophonic	ADJ
ejpam-4354	267	23	eccentric	eccentric	ADJ
ejpam-4354	267	24	vertices	vertex	NOUN
ejpam-4354	267	25	of	of	ADP
ejpam-4354	267	26	v	v	NOUN
ejpam-4354	267	27	,	,	PUNCT
ejpam-4354	267	28	i.e.	i.e.	X
ejpam-4354	267	29	,	,	PUNCT
ejpam-4354	267	30	nm	nm	ADV
ejpam-4354	267	31	g	g	NOUN
ejpam-4354	267	32	(	(	PUNCT
ejpam-4354	267	33	v	v	NOUN
ejpam-4354	267	34	)	)	PUNCT
ejpam-4354	267	35	=	=	PRON
ejpam-4354	267	36	{	{	PUNCT
ejpam-4354	267	37	w	w	NOUN
ejpam-4354	267	38	∈	∈	PROPN
ejpam-4354	267	39	v	v	ADP
ejpam-4354	267	40	(	(	PUNCT
ejpam-4354	267	41	g	g	NOUN
ejpam-4354	267	42	)	)	PUNCT
ejpam-4354	267	43	:	:	PUNCT
ejpam-4354	267	44	emg	emg	NOUN
ejpam-4354	267	45	(	(	PUNCT
ejpam-4354	267	46	v	v	NOUN
ejpam-4354	267	47	)	)	PUNCT
ejpam-4354	267	48	=	=	PUNCT
ejpam-4354	267	49	dmg	dmg	X
ejpam-4354	267	50	(	(	PUNCT
ejpam-4354	267	51	v	v	NOUN
ejpam-4354	267	52	,	,	PUNCT
ejpam-4354	267	53	w	w	NOUN
ejpam-4354	267	54	)	)	PUNCT
ejpam-4354	267	55	}	}	PUNCT
ejpam-4354	267	56	.	.	PUNCT
ejpam-4354	268	1	let	let	VERB
ejpam-4354	268	2	g	g	PRON
ejpam-4354	268	3	be	be	AUX
ejpam-4354	268	4	a	a	DET
ejpam-4354	268	5	connected	connected	ADJ
ejpam-4354	268	6	graph	graph	NOUN
ejpam-4354	268	7	.	.	PUNCT
ejpam-4354	269	1	denote	denote	VERB
ejpam-4354	269	2	by	by	ADP
ejpam-4354	269	3	vm(g	vm(g	NOUN
ejpam-4354	269	4	)	)	PUNCT
ejpam-4354	269	5	a	a	DET
ejpam-4354	269	6	smallest	small	ADJ
ejpam-4354	269	7	set	set	NOUN
ejpam-4354	269	8	of	of	ADP
ejpam-4354	269	9	vertices	vertex	NOUN
ejpam-4354	269	10	of	of	ADP
ejpam-4354	269	11	g	g	NOUN
ejpam-4354	269	12	satisfying	satisfy	VERB
ejpam-4354	269	13	the	the	DET
ejpam-4354	269	14	properties	property	NOUN
ejpam-4354	269	15	:	:	PUNCT
ejpam-4354	269	16	s.	s.	PROPN
ejpam-4354	269	17	canoy	canoy	PROPN
ejpam-4354	269	18	,	,	PUNCT
ejpam-4354	269	19	jr	jr	PROPN
ejpam-4354	269	20	.	.	PROPN
ejpam-4354	269	21	,	,	PUNCT
ejpam-4354	269	22	a.	a.	NOUN
ejpam-4354	269	23	gamorez	gamorez	PROPN
ejpam-4354	269	24	/	/	SYM
ejpam-4354	269	25	eur	eur	PROPN
ejpam-4354	269	26	.	.	PUNCT
ejpam-4354	270	1	j.	j.	PROPN
ejpam-4354	270	2	pure	pure	PROPN
ejpam-4354	270	3	appl	appl	PROPN
ejpam-4354	270	4	.	.	PROPN
ejpam-4354	270	5	math	math	PROPN
ejpam-4354	270	6	,	,	PUNCT
ejpam-4354	270	7	15	15	NUM
ejpam-4354	270	8	(	(	PUNCT
ejpam-4354	270	9	2	2	NUM
ejpam-4354	270	10	)	)	PUNCT
ejpam-4354	270	11	(	(	PUNCT
ejpam-4354	270	12	2022	2022	NUM
ejpam-4354	270	13	)	)	PUNCT
ejpam-4354	270	14	,	,	PUNCT
ejpam-4354	270	15	635	635	NUM
ejpam-4354	270	16	-	-	SYM
ejpam-4354	270	17	645	645	NUM
ejpam-4354	270	18	642	642	NUM
ejpam-4354	270	19	(	(	PUNCT
ejpam-4354	270	20	a	a	NOUN
ejpam-4354	270	21	)	)	PUNCT
ejpam-4354	270	22	for	for	ADP
ejpam-4354	270	23	each	each	DET
ejpam-4354	270	24	v	v	NOUN
ejpam-4354	270	25	∈	∈	PROPN
ejpam-4354	270	26	vm(g	vm(g	PUNCT
ejpam-4354	270	27	)	)	PUNCT
ejpam-4354	270	28	there	there	PRON
ejpam-4354	270	29	exists	exist	VERB
ejpam-4354	270	30	w	w	PROPN
ejpam-4354	270	31	∈	∈	PROPN
ejpam-4354	270	32	v	v	ADP
ejpam-4354	270	33	(	(	PUNCT
ejpam-4354	270	34	g	g	NOUN
ejpam-4354	270	35	)	)	PUNCT
ejpam-4354	270	36	such	such	ADJ
ejpam-4354	270	37	that	that	PRON
ejpam-4354	270	38	v	v	NUM
ejpam-4354	270	39	∈	∈	PROPN
ejpam-4354	270	40	nm	nm	INTJ
ejpam-4354	270	41	g	g	NOUN
ejpam-4354	270	42	(	(	PUNCT
ejpam-4354	270	43	w	w	NOUN
ejpam-4354	270	44	)	)	PUNCT
ejpam-4354	270	45	,	,	PUNCT
ejpam-4354	270	46	and	and	CCONJ
ejpam-4354	270	47	(	(	PUNCT
ejpam-4354	270	48	b	b	NOUN
ejpam-4354	270	49	)	)	PUNCT
ejpam-4354	270	50	|vm(g	|vm(g	NUM
ejpam-4354	270	51	)	)	PUNCT
ejpam-4354	270	52	∩nm	∩nm	NOUN
ejpam-4354	270	53	g	g	NOUN
ejpam-4354	270	54	(	(	PUNCT
ejpam-4354	270	55	u)|	u)|	NOUN
ejpam-4354	270	56	=	=	NOUN
ejpam-4354	270	57	1	1	NUM
ejpam-4354	270	58	for	for	ADP
ejpam-4354	270	59	each	each	DET
ejpam-4354	270	60	u	u	PROPN
ejpam-4354	270	61	∈	∈	PROPN
ejpam-4354	270	62	v	v	NOUN
ejpam-4354	270	63	(	(	PUNCT
ejpam-4354	270	64	g	g	NOUN
ejpam-4354	270	65	)	)	PUNCT
ejpam-4354	270	66	.	.	PUNCT
ejpam-4354	271	1	as	as	ADP
ejpam-4354	271	2	an	an	DET
ejpam-4354	271	3	example	example	NOUN
ejpam-4354	271	4	,	,	PUNCT
ejpam-4354	271	5	consider	consider	VERB
ejpam-4354	271	6	the	the	DET
ejpam-4354	271	7	graph	graph	NOUN
ejpam-4354	271	8	g	g	PROPN
ejpam-4354	271	9	obtained	obtain	VERB
ejpam-4354	271	10	from	from	ADP
ejpam-4354	271	11	c4	c4	NOUN
ejpam-4354	271	12	=	=	PUNCT
ejpam-4354	272	1	[	[	X
ejpam-4354	272	2	a	a	PRON
ejpam-4354	272	3	,	,	PUNCT
ejpam-4354	272	4	b	b	NOUN
ejpam-4354	272	5	,	,	PUNCT
ejpam-4354	272	6	c	c	NOUN
ejpam-4354	272	7	,	,	PUNCT
ejpam-4354	272	8	d	d	NOUN
ejpam-4354	272	9	,	,	PUNCT
ejpam-4354	272	10	a	a	PRON
ejpam-4354	272	11	]	]	X
ejpam-4354	272	12	by	by	ADP
ejpam-4354	272	13	adding	add	VERB
ejpam-4354	272	14	the	the	DET
ejpam-4354	272	15	pendant	pendant	ADJ
ejpam-4354	272	16	edge	edge	NOUN
ejpam-4354	272	17	ae	ae	PROPN
ejpam-4354	272	18	.	.	PUNCT
ejpam-4354	273	1	the	the	DET
ejpam-4354	273	2	set	set	NOUN
ejpam-4354	273	3	{	{	PUNCT
ejpam-4354	273	4	c	c	NOUN
ejpam-4354	273	5	,	,	PUNCT
ejpam-4354	273	6	e	e	NOUN
ejpam-4354	273	7	}	}	PUNCT
ejpam-4354	273	8	is	be	AUX
ejpam-4354	273	9	the	the	DET
ejpam-4354	273	10	smallest	small	ADJ
ejpam-4354	273	11	subset	subset	NOUN
ejpam-4354	273	12	of	of	ADP
ejpam-4354	273	13	g	g	NOUN
ejpam-4354	273	14	satisfying	satisfy	VERB
ejpam-4354	273	15	properties	property	NOUN
ejpam-4354	273	16	(	(	PUNCT
ejpam-4354	273	17	a	a	X
ejpam-4354	273	18	)	)	PUNCT
ejpam-4354	273	19	and	and	CCONJ
ejpam-4354	273	20	(	(	PUNCT
ejpam-4354	273	21	b	b	NOUN
ejpam-4354	273	22	)	)	PUNCT
ejpam-4354	273	23	.	.	PUNCT
ejpam-4354	274	1	thus	thus	ADV
ejpam-4354	274	2	,	,	PUNCT
ejpam-4354	274	3	vm(g	vm(g	NOUN
ejpam-4354	274	4	)	)	PUNCT
ejpam-4354	274	5	=	=	PRON
ejpam-4354	275	1	{	{	PUNCT
ejpam-4354	275	2	c	c	NOUN
ejpam-4354	275	3	,	,	PUNCT
ejpam-4354	275	4	e	e	NOUN
ejpam-4354	275	5	}	}	PUNCT
ejpam-4354	275	6	.	.	PUNCT
ejpam-4354	276	1	theorem	theorem	NOUN
ejpam-4354	276	2	9	9	NUM
ejpam-4354	276	3	.	.	PUNCT
ejpam-4354	277	1	let	let	VERB
ejpam-4354	277	2	g	g	NOUN
ejpam-4354	278	1	and	and	CCONJ
ejpam-4354	278	2	h	h	NOUN
ejpam-4354	278	3	be	be	VERB
ejpam-4354	278	4	any	any	DET
ejpam-4354	278	5	connected	connected	ADJ
ejpam-4354	278	6	non	non	ADJ
ejpam-4354	278	7	-	-	ADJ
ejpam-4354	278	8	trivial	trivial	ADJ
ejpam-4354	278	9	graphs	graph	NOUN
ejpam-4354	278	10	such	such	ADJ
ejpam-4354	278	11	that	that	PRON
ejpam-4354	278	12	diamm(h	diamm(h	NOUN
ejpam-4354	278	13	)	)	PUNCT
ejpam-4354	278	14	<	<	X
ejpam-4354	279	1	radm(g	radm(g	NOUN
ejpam-4354	279	2	)	)	PUNCT
ejpam-4354	279	3	+	+	CCONJ
ejpam-4354	280	1	2	2	X
ejpam-4354	280	2	.	.	X
ejpam-4354	280	3	then	then	ADV
ejpam-4354	280	4	s	s	VERB
ejpam-4354	280	5	is	be	AUX
ejpam-4354	280	6	a	a	DET
ejpam-4354	280	7	monophonic	monophonic	ADJ
ejpam-4354	280	8	eccentric	eccentric	ADJ
ejpam-4354	280	9	dominating	dominating	NOUN
ejpam-4354	280	10	set	set	NOUN
ejpam-4354	280	11	of	of	ADP
ejpam-4354	280	12	g	g	PROPN
ejpam-4354	280	13	◦	◦	NOUN
ejpam-4354	280	14	h	h	NOUN
ejpam-4354	280	15	if	if	SCONJ
ejpam-4354	281	1	and	and	CCONJ
ejpam-4354	281	2	only	only	ADV
ejpam-4354	281	3	if	if	SCONJ
ejpam-4354	281	4	sv	sv	PROPN
ejpam-4354	281	5	6=	6=	NOUN
ejpam-4354	281	6	∅	∅	NOUN
ejpam-4354	281	7	for	for	ADP
ejpam-4354	281	8	each	each	DET
ejpam-4354	281	9	v	v	NOUN
ejpam-4354	281	10	∈	∈	PROPN
ejpam-4354	281	11	vm(g	vm(g	PRON
ejpam-4354	281	12	)	)	PUNCT
ejpam-4354	281	13	having	have	VERB
ejpam-4354	281	14	sw	sw	PROPN
ejpam-4354	281	15	6=	6=	ADP
ejpam-4354	281	16	v	v	PROPN
ejpam-4354	281	17	(	(	PUNCT
ejpam-4354	281	18	hw	hw	NOUN
ejpam-4354	281	19	)	)	PUNCT
ejpam-4354	281	20	for	for	ADP
ejpam-4354	281	21	some	some	DET
ejpam-4354	281	22	w	w	PROPN
ejpam-4354	281	23	∈	∈	PROPN
ejpam-4354	281	24	v	v	ADP
ejpam-4354	281	25	(	(	PUNCT
ejpam-4354	281	26	g	g	NOUN
ejpam-4354	281	27	)	)	PUNCT
ejpam-4354	281	28	with	with	ADP
ejpam-4354	281	29	v	v	NUM
ejpam-4354	281	30	∈	∈	PROPN
ejpam-4354	281	31	nm	nm	INTJ
ejpam-4354	281	32	g	g	NOUN
ejpam-4354	281	33	(	(	PUNCT
ejpam-4354	281	34	w	w	PROPN
ejpam-4354	281	35	)	)	PUNCT
ejpam-4354	281	36	,	,	PUNCT
ejpam-4354	281	37	where	where	SCONJ
ejpam-4354	281	38	su	su	PROPN
ejpam-4354	281	39	=	=	NOUN
ejpam-4354	281	40	s∩v	s∩v	PROPN
ejpam-4354	281	41	(	(	PUNCT
ejpam-4354	281	42	hu	hu	PROPN
ejpam-4354	281	43	)	)	PUNCT
ejpam-4354	281	44	for	for	ADP
ejpam-4354	281	45	each	each	DET
ejpam-4354	281	46	u	u	PROPN
ejpam-4354	281	47	∈	∈	PROPN
ejpam-4354	281	48	v	v	NOUN
ejpam-4354	281	49	(	(	PUNCT
ejpam-4354	281	50	g	g	NOUN
ejpam-4354	281	51	)	)	PUNCT
ejpam-4354	281	52	.	.	PUNCT
ejpam-4354	282	1	moreover	moreover	ADV
ejpam-4354	282	2	,	,	PUNCT
ejpam-4354	282	3	γme(g	γme(g	PROPN
ejpam-4354	282	4	◦	◦	NOUN
ejpam-4354	282	5	h	h	NOUN
ejpam-4354	282	6	)	)	PUNCT
ejpam-4354	282	7	=	=	NOUN
ejpam-4354	282	8	|vm(g)|	|vm(g)|	NOUN
ejpam-4354	282	9	.	.	PUNCT
ejpam-4354	283	1	proof	proof	NOUN
ejpam-4354	283	2	.	.	PUNCT
ejpam-4354	284	1	suppose	suppose	VERB
ejpam-4354	284	2	s	s	NOUN
ejpam-4354	284	3	is	be	AUX
ejpam-4354	284	4	a	a	DET
ejpam-4354	284	5	monophonic	monophonic	ADJ
ejpam-4354	284	6	eccentric	eccentric	ADJ
ejpam-4354	284	7	dominating	dominating	NOUN
ejpam-4354	284	8	set	set	NOUN
ejpam-4354	284	9	of	of	ADP
ejpam-4354	284	10	g	g	PROPN
ejpam-4354	284	11	◦	◦	PROPN
ejpam-4354	284	12	h.	h.	PROPN
ejpam-4354	284	13	let	let	VERB
ejpam-4354	284	14	v	v	ADP
ejpam-4354	284	15	∈	∈	NOUN
ejpam-4354	284	16	vm(g	vm(g	NOUN
ejpam-4354	284	17	)	)	PUNCT
ejpam-4354	284	18	and	and	CCONJ
ejpam-4354	284	19	sv	sv	X
ejpam-4354	284	20	=	=	SYM
ejpam-4354	284	21	s∩v	s∩v	PROPN
ejpam-4354	284	22	(	(	PUNCT
ejpam-4354	284	23	hv	hv	PROPN
ejpam-4354	284	24	)	)	PUNCT
ejpam-4354	284	25	.	.	PUNCT
ejpam-4354	285	1	then	then	ADV
ejpam-4354	285	2	qv	qv	ADV
ejpam-4354	285	3	=	=	SYM
ejpam-4354	285	4	{	{	PUNCT
ejpam-4354	285	5	y	y	PROPN
ejpam-4354	285	6	∈	∈	PROPN
ejpam-4354	285	7	v	v	NOUN
ejpam-4354	285	8	(	(	PUNCT
ejpam-4354	285	9	g	g	NOUN
ejpam-4354	285	10	)	)	PUNCT
ejpam-4354	285	11	:	:	PUNCT
ejpam-4354	286	1	v	v	X
ejpam-4354	286	2	∈	∈	PROPN
ejpam-4354	286	3	nm	nm	INTJ
ejpam-4354	286	4	g	g	PROPN
ejpam-4354	286	5	(	(	PUNCT
ejpam-4354	286	6	y	y	NOUN
ejpam-4354	286	7	)	)	PUNCT
ejpam-4354	286	8	}	}	PUNCT
ejpam-4354	286	9	6=	6=	ADP
ejpam-4354	286	10	∅	∅	NOUN
ejpam-4354	286	11	by	by	ADP
ejpam-4354	286	12	property	property	NOUN
ejpam-4354	286	13	(	(	PUNCT
ejpam-4354	286	14	a	a	NOUN
ejpam-4354	286	15	)	)	PUNCT
ejpam-4354	286	16	of	of	ADP
ejpam-4354	286	17	vm(g	vm(g	NOUN
ejpam-4354	286	18	)	)	PUNCT
ejpam-4354	286	19	.	.	PUNCT
ejpam-4354	287	1	suppose	suppose	VERB
ejpam-4354	287	2	that	that	SCONJ
ejpam-4354	287	3	sw	sw	PROPN
ejpam-4354	287	4	6=	6=	PROPN
ejpam-4354	287	5	v	v	PROPN
ejpam-4354	287	6	(	(	PUNCT
ejpam-4354	287	7	hw	hw	NOUN
ejpam-4354	287	8	)	)	PUNCT
ejpam-4354	287	9	for	for	ADP
ejpam-4354	287	10	some	some	DET
ejpam-4354	287	11	w	w	PROPN
ejpam-4354	287	12	∈	∈	PROPN
ejpam-4354	287	13	qv	qv	INTJ
ejpam-4354	287	14	,	,	PUNCT
ejpam-4354	287	15	say	say	VERB
ejpam-4354	287	16	z	z	PROPN
ejpam-4354	287	17	∈	∈	PROPN
ejpam-4354	287	18	v	v	PROPN
ejpam-4354	287	19	(	(	PUNCT
ejpam-4354	287	20	hw)\sw	hw)\sw	NOUN
ejpam-4354	287	21	.	.	PUNCT
ejpam-4354	288	1	by	by	ADP
ejpam-4354	288	2	property	property	NOUN
ejpam-4354	288	3	(	(	PUNCT
ejpam-4354	288	4	b	b	NOUN
ejpam-4354	288	5	)	)	PUNCT
ejpam-4354	288	6	of	of	ADP
ejpam-4354	288	7	vm(g	vm(g	NOUN
ejpam-4354	288	8	)	)	PUNCT
ejpam-4354	288	9	,	,	PUNCT
ejpam-4354	288	10	it	it	PRON
ejpam-4354	288	11	follows	follow	VERB
ejpam-4354	288	12	that	that	SCONJ
ejpam-4354	288	13	|vm(g)∩nm	|vm(g)∩nm	PROPN
ejpam-4354	288	14	g	g	PROPN
ejpam-4354	288	15	(	(	PUNCT
ejpam-4354	288	16	w)|	w)|	VERB
ejpam-4354	288	17	=	=	SYM
ejpam-4354	288	18	{	{	PUNCT
ejpam-4354	288	19	v	v	NOUN
ejpam-4354	288	20	}	}	PUNCT
ejpam-4354	288	21	.	.	PUNCT
ejpam-4354	289	1	from	from	ADP
ejpam-4354	289	2	the	the	DET
ejpam-4354	289	3	assumption	assumption	NOUN
ejpam-4354	289	4	that	that	SCONJ
ejpam-4354	289	5	diamm(h	diamm(h	NOUN
ejpam-4354	289	6	)	)	PUNCT
ejpam-4354	289	7	<	<	X
ejpam-4354	289	8	radm(g)+2	radm(g)+2	PROPN
ejpam-4354	289	9	,	,	PUNCT
ejpam-4354	289	10	it	it	PRON
ejpam-4354	289	11	follows	follow	VERB
ejpam-4354	289	12	that	that	SCONJ
ejpam-4354	289	13	emhw(z	emhw(z	NOUN
ejpam-4354	289	14	)	)	PUNCT
ejpam-4354	289	15	<	<	X
ejpam-4354	289	16	emg	emg	PROPN
ejpam-4354	289	17	(	(	PUNCT
ejpam-4354	289	18	w)+2	w)+2	PROPN
ejpam-4354	289	19	.	.	PUNCT
ejpam-4354	290	1	hence	hence	ADV
ejpam-4354	290	2	,	,	PUNCT
ejpam-4354	290	3	emg	emg	NOUN
ejpam-4354	290	4	◦	◦	NOUN
ejpam-4354	290	5	h(z	h(z	NOUN
ejpam-4354	290	6	)	)	PUNCT
ejpam-4354	290	7	=	=	SYM
ejpam-4354	290	8	emg	emg	NOUN
ejpam-4354	290	9	(	(	PUNCT
ejpam-4354	290	10	w)+2	w)+2	X
ejpam-4354	290	11	=	=	SYM
ejpam-4354	290	12	dmg	dmg	X
ejpam-4354	290	13	(	(	PUNCT
ejpam-4354	290	14	w	w	PROPN
ejpam-4354	290	15	,	,	PUNCT
ejpam-4354	290	16	v)+2	v)+2	PROPN
ejpam-4354	290	17	.	.	PUNCT
ejpam-4354	291	1	since	since	SCONJ
ejpam-4354	291	2	s	s	PROPN
ejpam-4354	291	3	is	be	AUX
ejpam-4354	291	4	a	a	DET
ejpam-4354	291	5	monophonic	monophonic	ADJ
ejpam-4354	291	6	eccentric	eccentric	ADJ
ejpam-4354	291	7	dominating	dominating	NOUN
ejpam-4354	291	8	set	set	NOUN
ejpam-4354	291	9	of	of	ADP
ejpam-4354	291	10	g	g	PROPN
ejpam-4354	291	11	◦	◦	NOUN
ejpam-4354	291	12	h	h	NOUN
ejpam-4354	291	13	,	,	PUNCT
ejpam-4354	291	14	theorem	theorem	VERB
ejpam-4354	291	15	7(ii	7(ii	NUM
ejpam-4354	291	16	)	)	PUNCT
ejpam-4354	291	17	guarantees	guarantee	VERB
ejpam-4354	291	18	the	the	DET
ejpam-4354	291	19	existence	existence	NOUN
ejpam-4354	291	20	of	of	ADP
ejpam-4354	291	21	q	q	PROPN
ejpam-4354	291	22	∈	∈	PROPN
ejpam-4354	291	23	sv	sv	ADP
ejpam-4354	291	24	such	such	ADJ
ejpam-4354	291	25	that	that	DET
ejpam-4354	291	26	emg	emg	NOUN
ejpam-4354	291	27	◦	◦	NOUN
ejpam-4354	291	28	h(z	h(z	NOUN
ejpam-4354	291	29	)	)	PUNCT
ejpam-4354	291	30	=	=	SYM
ejpam-4354	291	31	dmg	dmg	VERB
ejpam-4354	291	32	◦	◦	NOUN
ejpam-4354	291	33	h(z	h(z	NOUN
ejpam-4354	291	34	,	,	PUNCT
ejpam-4354	291	35	q	q	NOUN
ejpam-4354	291	36	)	)	PUNCT
ejpam-4354	291	37	,	,	PUNCT
ejpam-4354	291	38	showing	show	VERB
ejpam-4354	291	39	that	that	PRON
ejpam-4354	291	40	sv	sv	PROPN
ejpam-4354	291	41	6=	6=	NOUN
ejpam-4354	291	42	∅.	∅.	VERB
ejpam-4354	291	43	for	for	ADP
ejpam-4354	291	44	the	the	DET
ejpam-4354	291	45	converse	converse	NOUN
ejpam-4354	291	46	,	,	PUNCT
ejpam-4354	291	47	suppose	suppose	VERB
ejpam-4354	291	48	that	that	SCONJ
ejpam-4354	291	49	the	the	DET
ejpam-4354	291	50	given	give	VERB
ejpam-4354	291	51	condition	condition	NOUN
ejpam-4354	291	52	holds	hold	VERB
ejpam-4354	291	53	.	.	PUNCT
ejpam-4354	292	1	let	let	VERB
ejpam-4354	292	2	z	z	NOUN
ejpam-4354	292	3	∈	∈	PROPN
ejpam-4354	292	4	v	v	NOUN
ejpam-4354	292	5	(	(	PUNCT
ejpam-4354	292	6	g	g	PROPN
ejpam-4354	292	7	◦	◦	NOUN
ejpam-4354	292	8	h	h	NOUN
ejpam-4354	292	9	)	)	PUNCT
ejpam-4354	292	10	\	\	PROPN
ejpam-4354	292	11	s	s	PART
ejpam-4354	292	12	and	and	CCONJ
ejpam-4354	292	13	let	let	VERB
ejpam-4354	292	14	w	w	PROPN
ejpam-4354	292	15	∈	∈	PROPN
ejpam-4354	292	16	v	v	ADP
ejpam-4354	292	17	(	(	PUNCT
ejpam-4354	292	18	g	g	NOUN
ejpam-4354	292	19	)	)	PUNCT
ejpam-4354	292	20	such	such	ADJ
ejpam-4354	292	21	that	that	SCONJ
ejpam-4354	292	22	z	z	PROPN
ejpam-4354	292	23	∈	∈	PROPN
ejpam-4354	292	24	v	v	NOUN
ejpam-4354	292	25	(	(	PUNCT
ejpam-4354	292	26	w	w	NOUN
ejpam-4354	292	27	+	+	NOUN
ejpam-4354	292	28	hw	hw	NOUN
ejpam-4354	292	29	)	)	PUNCT
ejpam-4354	292	30	.	.	PUNCT
ejpam-4354	293	1	let	let	VERB
ejpam-4354	293	2	v	v	X
ejpam-4354	293	3	∈	∈	PROPN
ejpam-4354	293	4	nm	nm	INTJ
ejpam-4354	293	5	g	g	NOUN
ejpam-4354	293	6	(	(	PUNCT
ejpam-4354	293	7	w	w	NOUN
ejpam-4354	293	8	)	)	PUNCT
ejpam-4354	293	9	∩	∩	NOUN
ejpam-4354	293	10	vm(g	vm(g	NUM
ejpam-4354	293	11	)	)	PUNCT
ejpam-4354	293	12	.	.	PUNCT
ejpam-4354	294	1	since	since	SCONJ
ejpam-4354	294	2	diamm(h	diamm(h	NOUN
ejpam-4354	294	3	)	)	PUNCT
ejpam-4354	294	4	<	<	X
ejpam-4354	294	5	radm(g	radm(g	NOUN
ejpam-4354	294	6	)	)	PUNCT
ejpam-4354	294	7	+	+	CCONJ
ejpam-4354	294	8	2	2	NUM
ejpam-4354	294	9	and	and	CCONJ
ejpam-4354	294	10	sv	sv	PROPN
ejpam-4354	294	11	6=	6=	NOUN
ejpam-4354	294	12	∅	∅	NOUN
ejpam-4354	294	13	by	by	ADP
ejpam-4354	294	14	assumption	assumption	NOUN
ejpam-4354	294	15	,	,	PUNCT
ejpam-4354	294	16	every	every	DET
ejpam-4354	294	17	element	element	NOUN
ejpam-4354	294	18	of	of	ADP
ejpam-4354	294	19	sv	sv	PROPN
ejpam-4354	294	20	is	be	AUX
ejpam-4354	294	21	a	a	DET
ejpam-4354	294	22	monophonic	monophonic	ADJ
ejpam-4354	294	23	eccentric	eccentric	ADJ
ejpam-4354	294	24	vertex	vertex	NOUN
ejpam-4354	294	25	of	of	ADP
ejpam-4354	294	26	z.	z.	PROPN
ejpam-4354	294	27	since	since	SCONJ
ejpam-4354	294	28	z	z	PROPN
ejpam-4354	294	29	was	be	AUX
ejpam-4354	294	30	arbitrarily	arbitrarily	ADV
ejpam-4354	294	31	chosen	choose	VERB
ejpam-4354	294	32	,	,	PUNCT
ejpam-4354	294	33	it	it	PRON
ejpam-4354	294	34	follows	follow	VERB
ejpam-4354	294	35	that	that	SCONJ
ejpam-4354	294	36	s	s	VERB
ejpam-4354	294	37	is	be	AUX
ejpam-4354	294	38	a	a	DET
ejpam-4354	294	39	monophonic	monophonic	ADJ
ejpam-4354	294	40	eccentric	eccentric	ADJ
ejpam-4354	294	41	dominating	dominating	NOUN
ejpam-4354	294	42	set	set	NOUN
ejpam-4354	294	43	of	of	ADP
ejpam-4354	294	44	g	g	PROPN
ejpam-4354	294	45	◦	◦	NOUN
ejpam-4354	294	46	h.	h.	PROPN
ejpam-4354	294	47	next	next	ADV
ejpam-4354	294	48	,	,	PUNCT
ejpam-4354	294	49	choose	choose	VERB
ejpam-4354	294	50	any	any	DET
ejpam-4354	294	51	point	point	NOUN
ejpam-4354	294	52	xv	xv	ADP
ejpam-4354	294	53	∈	∈	PROPN
ejpam-4354	294	54	v	v	PROPN
ejpam-4354	294	55	(	(	PUNCT
ejpam-4354	294	56	hv	hv	PROPN
ejpam-4354	294	57	)	)	PUNCT
ejpam-4354	294	58	for	for	ADP
ejpam-4354	294	59	each	each	DET
ejpam-4354	294	60	v	v	NOUN
ejpam-4354	294	61	∈	∈	PROPN
ejpam-4354	294	62	vm(g	vm(g	NOUN
ejpam-4354	294	63	)	)	PUNCT
ejpam-4354	294	64	and	and	CCONJ
ejpam-4354	294	65	let	let	VERB
ejpam-4354	294	66	s0	s0	PROPN
ejpam-4354	294	67	=	=	PUNCT
ejpam-4354	294	68	{	{	PUNCT
ejpam-4354	294	69	xv	xv	X
ejpam-4354	294	70	:	:	PUNCT
ejpam-4354	294	71	v	v	NUM
ejpam-4354	294	72	∈	∈	NOUN
ejpam-4354	294	73	vm(g	vm(g	NOUN
ejpam-4354	294	74	)	)	PUNCT
ejpam-4354	294	75	}	}	PUNCT
ejpam-4354	294	76	.	.	PUNCT
ejpam-4354	295	1	then	then	ADV
ejpam-4354	295	2	s0	s0	PROPN
ejpam-4354	295	3	is	be	AUX
ejpam-4354	295	4	a	a	DET
ejpam-4354	295	5	minimum	minimum	ADJ
ejpam-4354	295	6	monophonic	monophonic	ADJ
ejpam-4354	295	7	eccentric	eccentric	ADJ
ejpam-4354	295	8	dominating	dominating	NOUN
ejpam-4354	295	9	set	set	NOUN
ejpam-4354	295	10	of	of	ADP
ejpam-4354	295	11	g	g	PROPN
ejpam-4354	295	12	◦	◦	NOUN
ejpam-4354	295	13	h.	h.	PROPN
ejpam-4354	295	14	thus	thus	ADV
ejpam-4354	295	15	,	,	PUNCT
ejpam-4354	295	16	γme(g	γme(g	PROPN
ejpam-4354	295	17	◦	◦	NOUN
ejpam-4354	295	18	h	h	NOUN
ejpam-4354	295	19	)	)	PUNCT
ejpam-4354	296	1	=	=	SYM
ejpam-4354	296	2	|s0|	|s0|	NOUN
ejpam-4354	296	3	=	=	SYM
ejpam-4354	296	4	|vm(g)|	|vm(g)|	PROPN
ejpam-4354	296	5	.	.	PUNCT
ejpam-4354	297	1	theorem	theorem	VERB
ejpam-4354	297	2	10	10	NUM
ejpam-4354	297	3	.	.	PUNCT
ejpam-4354	298	1	let	let	VERB
ejpam-4354	298	2	g	g	NOUN
ejpam-4354	298	3	and	and	CCONJ
ejpam-4354	298	4	h	h	PROPN
ejpam-4354	298	5	be	be	VERB
ejpam-4354	298	6	non	non	ADJ
ejpam-4354	298	7	-	-	ADJ
ejpam-4354	298	8	trivial	trivial	ADJ
ejpam-4354	298	9	connected	connected	ADJ
ejpam-4354	298	10	graphs	graph	NOUN
ejpam-4354	299	1	such	such	ADJ
ejpam-4354	299	2	that	that	DET
ejpam-4354	299	3	radm(g	radm(g	NOUN
ejpam-4354	299	4	)	)	PUNCT
ejpam-4354	299	5	>	>	X
ejpam-4354	300	1	diamm(h	diamm(h	PROPN
ejpam-4354	300	2	)	)	PUNCT
ejpam-4354	300	3	.	.	PUNCT
ejpam-4354	301	1	then	then	ADV
ejpam-4354	301	2	c	c	X
ejpam-4354	301	3	=	=	PUNCT
ejpam-4354	301	4	⋃	⋃	PROPN
ejpam-4354	301	5	x∈s	x∈s	NOUN
ejpam-4354	302	1	[	[	X
ejpam-4354	302	2	{	{	PUNCT
ejpam-4354	302	3	x}×tx	x}×tx	X
ejpam-4354	302	4	]	]	X
ejpam-4354	302	5	,	,	PUNCT
ejpam-4354	302	6	where	where	SCONJ
ejpam-4354	302	7	s	s	VERB
ejpam-4354	302	8	⊆	⊆	NUM
ejpam-4354	302	9	v	v	NOUN
ejpam-4354	302	10	(	(	PUNCT
ejpam-4354	302	11	g	g	NOUN
ejpam-4354	302	12	)	)	PUNCT
ejpam-4354	302	13	and	and	CCONJ
ejpam-4354	302	14	tx	tx	VERB
ejpam-4354	302	15	⊆	⊆	NUM
ejpam-4354	302	16	v	v	NOUN
ejpam-4354	302	17	(	(	PUNCT
ejpam-4354	302	18	h	h	NOUN
ejpam-4354	302	19	)	)	PUNCT
ejpam-4354	302	20	for	for	ADP
ejpam-4354	302	21	each	each	DET
ejpam-4354	302	22	x	x	SYM
ejpam-4354	302	23	∈	∈	PROPN
ejpam-4354	302	24	s	s	NOUN
ejpam-4354	302	25	,	,	PUNCT
ejpam-4354	302	26	is	be	AUX
ejpam-4354	302	27	a	a	DET
ejpam-4354	302	28	monophonic	monophonic	ADJ
ejpam-4354	302	29	eccentric	eccentric	ADJ
ejpam-4354	302	30	dominating	dominating	NOUN
ejpam-4354	302	31	set	set	NOUN
ejpam-4354	302	32	of	of	ADP
ejpam-4354	302	33	g[h	g[h	PROPN
ejpam-4354	302	34	]	]	PUNCT
ejpam-4354	302	35	if	if	SCONJ
ejpam-4354	302	36	and	and	CCONJ
ejpam-4354	302	37	only	only	ADV
ejpam-4354	302	38	if	if	SCONJ
ejpam-4354	302	39	the	the	DET
ejpam-4354	302	40	following	follow	VERB
ejpam-4354	302	41	hold	hold	NOUN
ejpam-4354	302	42	:	:	PUNCT
ejpam-4354	302	43	(	(	PUNCT
ejpam-4354	302	44	i	i	NOUN
ejpam-4354	302	45	)	)	PUNCT
ejpam-4354	302	46	s	s	VERB
ejpam-4354	302	47	is	be	AUX
ejpam-4354	302	48	a	a	DET
ejpam-4354	302	49	monophonic	monophonic	ADJ
ejpam-4354	302	50	eccentric	eccentric	ADJ
ejpam-4354	302	51	dominating	dominating	NOUN
ejpam-4354	302	52	set	set	NOUN
ejpam-4354	302	53	of	of	ADP
ejpam-4354	302	54	g.	g.	PROPN
ejpam-4354	302	55	(	(	PUNCT
ejpam-4354	302	56	ii	ii	PROPN
ejpam-4354	302	57	)	)	PUNCT
ejpam-4354	302	58	for	for	ADP
ejpam-4354	302	59	each	each	DET
ejpam-4354	302	60	x	x	SYM
ejpam-4354	302	61	∈	∈	PROPN
ejpam-4354	302	62	s	s	VERB
ejpam-4354	302	63	such	such	ADJ
ejpam-4354	302	64	that	that	PRON
ejpam-4354	302	65	tx	tx	PROPN
ejpam-4354	302	66	6=	6=	PROPN
ejpam-4354	302	67	v	v	ADP
ejpam-4354	302	68	(	(	PUNCT
ejpam-4354	302	69	h	h	NOUN
ejpam-4354	302	70	)	)	PUNCT
ejpam-4354	302	71	,	,	PUNCT
ejpam-4354	302	72	s	s	VERB
ejpam-4354	302	73	∩nm	∩nm	ADJ
ejpam-4354	302	74	g	g	PROPN
ejpam-4354	302	75	(	(	PUNCT
ejpam-4354	302	76	x	x	X
ejpam-4354	302	77	)	)	PUNCT
ejpam-4354	302	78	6=	6=	ADP
ejpam-4354	302	79	∅.	∅.	PRON
ejpam-4354	302	80	proof	proof	NOUN
ejpam-4354	302	81	.	.	PUNCT
ejpam-4354	303	1	suppose	suppose	VERB
ejpam-4354	303	2	c	c	NOUN
ejpam-4354	303	3	is	be	AUX
ejpam-4354	303	4	a	a	DET
ejpam-4354	303	5	monophonic	monophonic	ADJ
ejpam-4354	303	6	eccentric	eccentric	ADJ
ejpam-4354	303	7	dominating	dominating	NOUN
ejpam-4354	303	8	set	set	NOUN
ejpam-4354	303	9	of	of	ADP
ejpam-4354	303	10	g[h	g[h	PROPN
ejpam-4354	303	11	]	]	PUNCT
ejpam-4354	303	12	and	and	CCONJ
ejpam-4354	303	13	let	let	VERB
ejpam-4354	303	14	v	v	NUM
ejpam-4354	303	15	∈	∈	PROPN
ejpam-4354	303	16	v	v	NOUN
ejpam-4354	303	17	(	(	PUNCT
ejpam-4354	303	18	g	g	NOUN
ejpam-4354	303	19	)	)	PUNCT
ejpam-4354	303	20	\	\	PUNCT
ejpam-4354	304	1	s.	s.	PROPN
ejpam-4354	304	2	pick	pick	VERB
ejpam-4354	304	3	any	any	PRON
ejpam-4354	304	4	a	a	DET
ejpam-4354	304	5	∈	∈	PROPN
ejpam-4354	304	6	v	v	NOUN
ejpam-4354	304	7	(	(	PUNCT
ejpam-4354	304	8	h	h	NOUN
ejpam-4354	304	9	)	)	PUNCT
ejpam-4354	304	10	.	.	PUNCT
ejpam-4354	305	1	then	then	ADV
ejpam-4354	305	2	(	(	PUNCT
ejpam-4354	305	3	v	v	NOUN
ejpam-4354	305	4	,	,	PUNCT
ejpam-4354	305	5	a	a	PRON
ejpam-4354	305	6	)	)	PUNCT
ejpam-4354	305	7	/∈	/∈	PUNCT
ejpam-4354	306	1	c	c	NOUN
ejpam-4354	307	1	and	and	CCONJ
ejpam-4354	307	2	so	so	ADV
ejpam-4354	307	3	by	by	ADP
ejpam-4354	307	4	assumption	assumption	NOUN
ejpam-4354	307	5	of	of	ADP
ejpam-4354	307	6	c	c	NOUN
ejpam-4354	307	7	,	,	PUNCT
ejpam-4354	307	8	there	there	PRON
ejpam-4354	307	9	exists	exist	VERB
ejpam-4354	307	10	(	(	PUNCT
ejpam-4354	307	11	w	w	PROPN
ejpam-4354	307	12	,	,	PUNCT
ejpam-4354	307	13	b	b	NOUN
ejpam-4354	307	14	)	)	PUNCT
ejpam-4354	307	15	∈	∈	PROPN
ejpam-4354	307	16	c	c	NOUN
ejpam-4354	307	17	such	such	ADJ
ejpam-4354	307	18	that	that	DET
ejpam-4354	307	19	emg[h]((v	emg[h]((v	PROPN
ejpam-4354	307	20	,	,	PUNCT
ejpam-4354	307	21	a	a	PRON
ejpam-4354	307	22	)	)	PUNCT
ejpam-4354	307	23	)	)	PUNCT
ejpam-4354	308	1	=	=	SYM
ejpam-4354	308	2	dmg[h]((v	dmg[h]((v	NOUN
ejpam-4354	308	3	,	,	PUNCT
ejpam-4354	308	4	a	a	PRON
ejpam-4354	308	5	)	)	PUNCT
ejpam-4354	308	6	,	,	PUNCT
ejpam-4354	308	7	(	(	PUNCT
ejpam-4354	308	8	w	w	PROPN
ejpam-4354	308	9	,	,	PUNCT
ejpam-4354	308	10	b	b	NOUN
ejpam-4354	308	11	)	)	PUNCT
ejpam-4354	308	12	)	)	PUNCT
ejpam-4354	308	13	.	.	PUNCT
ejpam-4354	309	1	it	it	PRON
ejpam-4354	309	2	follows	follow	VERB
ejpam-4354	309	3	that	that	PRON
ejpam-4354	309	4	v	v	ADP
ejpam-4354	309	5	6=	6=	ADP
ejpam-4354	309	6	w	w	NOUN
ejpam-4354	309	7	and	and	CCONJ
ejpam-4354	309	8	emg	emg	PROPN
ejpam-4354	309	9	(	(	PUNCT
ejpam-4354	309	10	v	v	NOUN
ejpam-4354	309	11	)	)	PUNCT
ejpam-4354	309	12	=	=	PUNCT
ejpam-4354	309	13	dmg	dmg	X
ejpam-4354	309	14	(	(	PUNCT
ejpam-4354	309	15	v	v	NOUN
ejpam-4354	309	16	,	,	PUNCT
ejpam-4354	309	17	w	w	NOUN
ejpam-4354	309	18	)	)	PUNCT
ejpam-4354	309	19	,	,	PUNCT
ejpam-4354	309	20	i.e.	i.e.	X
ejpam-4354	309	21	,	,	PUNCT
ejpam-4354	309	22	w	w	PROPN
ejpam-4354	309	23	∈	∈	PROPN
ejpam-4354	309	24	s	s	PART
ejpam-4354	309	25	∩nm	∩nm	ADJ
ejpam-4354	309	26	g	g	PROPN
ejpam-4354	309	27	(	(	PUNCT
ejpam-4354	309	28	v	v	NOUN
ejpam-4354	309	29	)	)	PUNCT
ejpam-4354	309	30	.	.	PUNCT
ejpam-4354	310	1	this	this	PRON
ejpam-4354	310	2	shows	show	VERB
ejpam-4354	310	3	that	that	SCONJ
ejpam-4354	310	4	s	s	VERB
ejpam-4354	310	5	is	be	AUX
ejpam-4354	310	6	a	a	DET
ejpam-4354	310	7	monophonic	monophonic	ADJ
ejpam-4354	310	8	eccentric	eccentric	ADJ
ejpam-4354	310	9	dominating	dominating	NOUN
ejpam-4354	310	10	set	set	NOUN
ejpam-4354	310	11	of	of	ADP
ejpam-4354	310	12	g.	g.	PROPN
ejpam-4354	310	13	next	next	ADV
ejpam-4354	310	14	,	,	PUNCT
ejpam-4354	310	15	let	let	VERB
ejpam-4354	310	16	x	x	PUNCT
ejpam-4354	310	17	∈	∈	NOUN
ejpam-4354	310	18	s	s	VERB
ejpam-4354	310	19	with	with	ADP
ejpam-4354	310	20	tx	tx	PROPN
ejpam-4354	310	21	6=	6=	PROPN
ejpam-4354	310	22	v	v	PROPN
ejpam-4354	310	23	(	(	PUNCT
ejpam-4354	310	24	h	h	NOUN
ejpam-4354	310	25	)	)	PUNCT
ejpam-4354	310	26	.	.	PUNCT
ejpam-4354	311	1	let	let	VERB
ejpam-4354	312	1	p	p	PRON
ejpam-4354	312	2	∈	∈	PROPN
ejpam-4354	312	3	v	v	ADP
ejpam-4354	312	4	(	(	PUNCT
ejpam-4354	312	5	h	h	NOUN
ejpam-4354	312	6	)	)	PUNCT
ejpam-4354	312	7	\	\	PROPN
ejpam-4354	312	8	tx	tx	PROPN
ejpam-4354	312	9	.	.	PUNCT
ejpam-4354	313	1	then	then	ADV
ejpam-4354	313	2	(	(	PUNCT
ejpam-4354	313	3	x	x	X
ejpam-4354	313	4	,	,	PUNCT
ejpam-4354	313	5	p	p	NOUN
ejpam-4354	313	6	)	)	PUNCT
ejpam-4354	313	7	∈	∈	PROPN
ejpam-4354	313	8	v	v	NOUN
ejpam-4354	313	9	(	(	PUNCT
ejpam-4354	313	10	g[h	g[h	PROPN
ejpam-4354	313	11	]	]	PUNCT
ejpam-4354	313	12	)	)	PUNCT
ejpam-4354	313	13	\	\	PROPN
ejpam-4354	314	1	c.	c.	PROPN
ejpam-4354	314	2	hence	hence	ADV
ejpam-4354	314	3	,	,	PUNCT
ejpam-4354	314	4	there	there	PRON
ejpam-4354	314	5	exists	exist	VERB
ejpam-4354	314	6	(	(	PUNCT
ejpam-4354	314	7	z	z	NOUN
ejpam-4354	314	8	,	,	PUNCT
ejpam-4354	314	9	q	q	X
ejpam-4354	314	10	)	)	PUNCT
ejpam-4354	314	11	∈	∈	PROPN
ejpam-4354	314	12	nm	nm	PRON
ejpam-4354	314	13	g[h]((x	g[h]((x	NOUN
ejpam-4354	314	14	,	,	PUNCT
ejpam-4354	314	15	p))∩c	p))∩c	NOUN
ejpam-4354	314	16	.	.	PUNCT
ejpam-4354	315	1	since	since	SCONJ
ejpam-4354	315	2	radm(g	radm(g	NOUN
ejpam-4354	315	3	)	)	PUNCT
ejpam-4354	315	4	>	>	X
ejpam-4354	315	5	diamm(h	diamm(h	PROPN
ejpam-4354	315	6	)	)	PUNCT
ejpam-4354	315	7	,	,	PUNCT
ejpam-4354	315	8	it	it	PRON
ejpam-4354	315	9	follows	follow	VERB
ejpam-4354	315	10	that	that	SCONJ
ejpam-4354	315	11	s.	s.	PROPN
ejpam-4354	315	12	canoy	canoy	PROPN
ejpam-4354	315	13	,	,	PUNCT
ejpam-4354	315	14	jr	jr	PROPN
ejpam-4354	315	15	.	.	PROPN
ejpam-4354	315	16	,	,	PUNCT
ejpam-4354	315	17	a.	a.	NOUN
ejpam-4354	315	18	gamorez	gamorez	PROPN
ejpam-4354	315	19	/	/	SYM
ejpam-4354	315	20	eur	eur	PROPN
ejpam-4354	315	21	.	.	PUNCT
ejpam-4354	316	1	j.	j.	PROPN
ejpam-4354	316	2	pure	pure	PROPN
ejpam-4354	316	3	appl	appl	PROPN
ejpam-4354	316	4	.	.	PROPN
ejpam-4354	316	5	math	math	PROPN
ejpam-4354	316	6	,	,	PUNCT
ejpam-4354	316	7	15	15	NUM
ejpam-4354	316	8	(	(	PUNCT
ejpam-4354	316	9	2	2	NUM
ejpam-4354	316	10	)	)	PUNCT
ejpam-4354	316	11	(	(	PUNCT
ejpam-4354	316	12	2022	2022	NUM
ejpam-4354	316	13	)	)	PUNCT
ejpam-4354	316	14	,	,	PUNCT
ejpam-4354	316	15	635	635	NUM
ejpam-4354	316	16	-	-	SYM
ejpam-4354	316	17	645	645	NUM
ejpam-4354	316	18	643	643	NUM
ejpam-4354	316	19	dmg	dmg	NOUN
ejpam-4354	316	20	(	(	PUNCT
ejpam-4354	316	21	x	x	NOUN
ejpam-4354	316	22	,	,	PUNCT
ejpam-4354	316	23	z	z	NOUN
ejpam-4354	316	24	)	)	PUNCT
ejpam-4354	316	25	>	>	X
ejpam-4354	317	1	dmh(p	dmh(p	PROPN
ejpam-4354	317	2	,	,	PUNCT
ejpam-4354	317	3	q	q	NOUN
ejpam-4354	317	4	)	)	PUNCT
ejpam-4354	317	5	.	.	PUNCT
ejpam-4354	318	1	hence	hence	ADV
ejpam-4354	318	2	,	,	PUNCT
ejpam-4354	318	3	dmg[h]((z	dmg[h]((z	PROPN
ejpam-4354	318	4	,	,	PUNCT
ejpam-4354	318	5	q	q	NOUN
ejpam-4354	318	6	)	)	PUNCT
ejpam-4354	318	7	,	,	PUNCT
ejpam-4354	318	8	(	(	PUNCT
ejpam-4354	318	9	x	x	X
ejpam-4354	318	10	,	,	PUNCT
ejpam-4354	318	11	p	p	NOUN
ejpam-4354	318	12	)	)	PUNCT
ejpam-4354	318	13	)	)	PUNCT
ejpam-4354	318	14	=	=	SYM
ejpam-4354	318	15	dmg	dmg	X
ejpam-4354	318	16	(	(	PUNCT
ejpam-4354	318	17	x	x	NOUN
ejpam-4354	318	18	,	,	PUNCT
ejpam-4354	318	19	z	z	NOUN
ejpam-4354	318	20	)	)	PUNCT
ejpam-4354	318	21	and	and	CCONJ
ejpam-4354	318	22	z	z	NOUN
ejpam-4354	318	23	∈	∈	PROPN
ejpam-4354	318	24	s	s	PART
ejpam-4354	318	25	∩	∩	NOUN
ejpam-4354	318	26	nm	nm	ADJ
ejpam-4354	318	27	g	g	NOUN
ejpam-4354	318	28	(	(	PUNCT
ejpam-4354	318	29	x	x	NOUN
ejpam-4354	318	30	)	)	PUNCT
ejpam-4354	318	31	,	,	PUNCT
ejpam-4354	318	32	showing	show	VERB
ejpam-4354	318	33	that	that	SCONJ
ejpam-4354	318	34	(	(	PUNCT
ejpam-4354	318	35	ii	ii	NOUN
ejpam-4354	318	36	)	)	PUNCT
ejpam-4354	318	37	holds	hold	VERB
ejpam-4354	318	38	.	.	PUNCT
ejpam-4354	319	1	for	for	ADP
ejpam-4354	319	2	the	the	DET
ejpam-4354	319	3	converse	converse	NOUN
ejpam-4354	319	4	,	,	PUNCT
ejpam-4354	319	5	suppose	suppose	VERB
ejpam-4354	319	6	that	that	SCONJ
ejpam-4354	319	7	(	(	PUNCT
ejpam-4354	319	8	i	i	NOUN
ejpam-4354	319	9	)	)	PUNCT
ejpam-4354	319	10	and	and	CCONJ
ejpam-4354	319	11	(	(	PUNCT
ejpam-4354	319	12	ii	ii	NOUN
ejpam-4354	319	13	)	)	PUNCT
ejpam-4354	319	14	hold	hold	VERB
ejpam-4354	319	15	.	.	PUNCT
ejpam-4354	320	1	let	let	VERB
ejpam-4354	320	2	(	(	PUNCT
ejpam-4354	320	3	v	v	NOUN
ejpam-4354	320	4	,	,	PUNCT
ejpam-4354	320	5	a	a	PRON
ejpam-4354	320	6	)	)	PUNCT
ejpam-4354	320	7	∈	∈	NOUN
ejpam-4354	320	8	v	v	NOUN
ejpam-4354	320	9	(	(	PUNCT
ejpam-4354	320	10	g[h	g[h	PROPN
ejpam-4354	320	11	]	]	PUNCT
ejpam-4354	320	12	)	)	PUNCT
ejpam-4354	320	13	\	\	PROPN
ejpam-4354	321	1	c.	c.	NOUN
ejpam-4354	321	2	if	if	SCONJ
ejpam-4354	321	3	v	v	NUM
ejpam-4354	321	4	/∈	/∈	PUNCT
ejpam-4354	322	1	s	s	X
ejpam-4354	322	2	,	,	PUNCT
ejpam-4354	322	3	then	then	ADV
ejpam-4354	322	4	there	there	PRON
ejpam-4354	322	5	exists	exist	VERB
ejpam-4354	322	6	w	w	PROPN
ejpam-4354	322	7	∈	∈	PROPN
ejpam-4354	322	8	nm	nm	INTJ
ejpam-4354	322	9	g	g	NOUN
ejpam-4354	322	10	(	(	PUNCT
ejpam-4354	322	11	v	v	NOUN
ejpam-4354	322	12	)	)	PUNCT
ejpam-4354	322	13	∩	∩	NOUN
ejpam-4354	322	14	s	s	PART
ejpam-4354	322	15	by	by	X
ejpam-4354	322	16	(	(	PUNCT
ejpam-4354	322	17	i	i	NOUN
ejpam-4354	322	18	)	)	PUNCT
ejpam-4354	322	19	.	.	PUNCT
ejpam-4354	323	1	let	let	VERB
ejpam-4354	323	2	d	d	X
ejpam-4354	323	3	∈	∈	PROPN
ejpam-4354	323	4	tw	tw	PROPN
ejpam-4354	323	5	.	.	PUNCT
ejpam-4354	324	1	then	then	ADV
ejpam-4354	324	2	(	(	PUNCT
ejpam-4354	324	3	w	w	PROPN
ejpam-4354	324	4	,	,	PUNCT
ejpam-4354	324	5	d	d	NOUN
ejpam-4354	324	6	)	)	PUNCT
ejpam-4354	324	7	∈	∈	PROPN
ejpam-4354	324	8	c.	c.	NOUN
ejpam-4354	324	9	now	now	ADV
ejpam-4354	324	10	,	,	PUNCT
ejpam-4354	324	11	because	because	SCONJ
ejpam-4354	324	12	radm(g	radm(g	NOUN
ejpam-4354	324	13	)	)	PUNCT
ejpam-4354	324	14	>	>	X
ejpam-4354	325	1	diamm(h	diamm(h	PROPN
ejpam-4354	325	2	)	)	PUNCT
ejpam-4354	325	3	,	,	PUNCT
ejpam-4354	325	4	it	it	PRON
ejpam-4354	325	5	follows	follow	VERB
ejpam-4354	325	6	that	that	SCONJ
ejpam-4354	325	7	emg[h]((v	emg[h]((v	PROPN
ejpam-4354	325	8	,	,	PUNCT
ejpam-4354	325	9	a	a	PRON
ejpam-4354	325	10	)	)	PUNCT
ejpam-4354	325	11	)	)	PUNCT
ejpam-4354	326	1	=	=	SYM
ejpam-4354	326	2	dmg[h]((v	dmg[h]((v	NOUN
ejpam-4354	326	3	,	,	PUNCT
ejpam-4354	326	4	a	a	PRON
ejpam-4354	326	5	)	)	PUNCT
ejpam-4354	326	6	,	,	PUNCT
ejpam-4354	326	7	(	(	PUNCT
ejpam-4354	326	8	w	w	NOUN
ejpam-4354	326	9	,	,	PUNCT
ejpam-4354	326	10	d	d	NOUN
ejpam-4354	326	11	)	)	PUNCT
ejpam-4354	326	12	)	)	PUNCT
ejpam-4354	327	1	=	=	SYM
ejpam-4354	327	2	dmg	dmg	X
ejpam-4354	327	3	(	(	PUNCT
ejpam-4354	327	4	w	w	PROPN
ejpam-4354	327	5	,	,	PUNCT
ejpam-4354	327	6	v	v	NOUN
ejpam-4354	327	7	)	)	PUNCT
ejpam-4354	327	8	=	=	SYM
ejpam-4354	327	9	emg	emg	NOUN
ejpam-4354	327	10	(	(	PUNCT
ejpam-4354	327	11	v	v	NOUN
ejpam-4354	327	12	)	)	PUNCT
ejpam-4354	327	13	.	.	PUNCT
ejpam-4354	328	1	suppose	suppose	VERB
ejpam-4354	328	2	v	v	ADP
ejpam-4354	328	3	∈	∈	PROPN
ejpam-4354	328	4	s.	s.	PROPN
ejpam-4354	328	5	then	then	ADV
ejpam-4354	328	6	a	a	DET
ejpam-4354	328	7	/∈	/∈	PUNCT
ejpam-4354	328	8	tv	tv	NOUN
ejpam-4354	328	9	,	,	PUNCT
ejpam-4354	328	10	i.e.	i.e.	X
ejpam-4354	328	11	,	,	PUNCT
ejpam-4354	328	12	tv	tv	NOUN
ejpam-4354	328	13	6=	6=	ADP
ejpam-4354	328	14	v	v	PROPN
ejpam-4354	328	15	(	(	PUNCT
ejpam-4354	328	16	h	h	NOUN
ejpam-4354	328	17	)	)	PUNCT
ejpam-4354	328	18	.	.	PUNCT
ejpam-4354	329	1	by	by	ADP
ejpam-4354	329	2	(	(	PUNCT
ejpam-4354	329	3	ii	ii	NOUN
ejpam-4354	329	4	)	)	PUNCT
ejpam-4354	329	5	,	,	PUNCT
ejpam-4354	329	6	it	it	PRON
ejpam-4354	329	7	follows	follow	VERB
ejpam-4354	329	8	that	that	SCONJ
ejpam-4354	329	9	there	there	PRON
ejpam-4354	329	10	exists	exist	VERB
ejpam-4354	329	11	z	z	PROPN
ejpam-4354	329	12	∈	∈	PROPN
ejpam-4354	329	13	s	s	VERB
ejpam-4354	329	14	∩nm	∩nm	ADJ
ejpam-4354	329	15	g	g	PROPN
ejpam-4354	329	16	(	(	PUNCT
ejpam-4354	329	17	v	v	NOUN
ejpam-4354	329	18	)	)	PUNCT
ejpam-4354	329	19	.	.	PUNCT
ejpam-4354	330	1	pick	pick	VERB
ejpam-4354	330	2	any	any	DET
ejpam-4354	330	3	b	b	PROPN
ejpam-4354	330	4	∈	∈	PROPN
ejpam-4354	330	5	tz	tz	NOUN
ejpam-4354	330	6	.	.	PUNCT
ejpam-4354	331	1	then	then	ADV
ejpam-4354	331	2	(	(	PUNCT
ejpam-4354	331	3	z	z	NOUN
ejpam-4354	331	4	,	,	PUNCT
ejpam-4354	331	5	b	b	NOUN
ejpam-4354	331	6	)	)	PUNCT
ejpam-4354	331	7	∈	∈	PROPN
ejpam-4354	331	8	c	c	PROPN
ejpam-4354	331	9	and	and	CCONJ
ejpam-4354	331	10	emg[h]((v	emg[h]((v	PROPN
ejpam-4354	331	11	,	,	PUNCT
ejpam-4354	331	12	a	a	PRON
ejpam-4354	331	13	)	)	PUNCT
ejpam-4354	331	14	)	)	PUNCT
ejpam-4354	332	1	=	=	SYM
ejpam-4354	332	2	dmg[h]((v	dmg[h]((v	NOUN
ejpam-4354	332	3	,	,	PUNCT
ejpam-4354	332	4	a	a	PRON
ejpam-4354	332	5	)	)	PUNCT
ejpam-4354	332	6	,	,	PUNCT
ejpam-4354	332	7	(	(	PUNCT
ejpam-4354	332	8	z	z	X
ejpam-4354	332	9	,	,	PUNCT
ejpam-4354	332	10	b	b	NOUN
ejpam-4354	332	11	)	)	PUNCT
ejpam-4354	332	12	)	)	PUNCT
ejpam-4354	333	1	=	=	SYM
ejpam-4354	333	2	dmg	dmg	X
ejpam-4354	333	3	(	(	PUNCT
ejpam-4354	333	4	z	z	NOUN
ejpam-4354	333	5	,	,	PUNCT
ejpam-4354	333	6	v	v	NOUN
ejpam-4354	333	7	)	)	PUNCT
ejpam-4354	333	8	=	=	SYM
ejpam-4354	333	9	emg	emg	NOUN
ejpam-4354	333	10	(	(	PUNCT
ejpam-4354	333	11	v	v	NOUN
ejpam-4354	333	12	)	)	PUNCT
ejpam-4354	333	13	.	.	PUNCT
ejpam-4354	334	1	therefore	therefore	ADV
ejpam-4354	334	2	,	,	PUNCT
ejpam-4354	334	3	c	c	PROPN
ejpam-4354	334	4	is	be	AUX
ejpam-4354	334	5	a	a	DET
ejpam-4354	334	6	monophonic	monophonic	ADJ
ejpam-4354	334	7	eccentric	eccentric	ADJ
ejpam-4354	334	8	dominating	dominating	NOUN
ejpam-4354	334	9	set	set	NOUN
ejpam-4354	334	10	of	of	ADP
ejpam-4354	334	11	g[h	g[h	PROPN
ejpam-4354	334	12	]	]	PUNCT
ejpam-4354	334	13	.	.	PUNCT
ejpam-4354	335	1	corollary	corollary	ADJ
ejpam-4354	335	2	4	4	NUM
ejpam-4354	335	3	.	.	PUNCT
ejpam-4354	336	1	let	let	VERB
ejpam-4354	336	2	g	g	NOUN
ejpam-4354	336	3	and	and	CCONJ
ejpam-4354	336	4	h	h	PROPN
ejpam-4354	336	5	be	be	VERB
ejpam-4354	336	6	non	non	ADJ
ejpam-4354	336	7	-	-	ADJ
ejpam-4354	336	8	trivial	trivial	ADJ
ejpam-4354	336	9	connected	connected	ADJ
ejpam-4354	336	10	graphs	graph	NOUN
ejpam-4354	337	1	such	such	ADJ
ejpam-4354	337	2	that	that	DET
ejpam-4354	337	3	radm(g	radm(g	NOUN
ejpam-4354	337	4	)	)	PUNCT
ejpam-4354	337	5	>	>	X
ejpam-4354	338	1	diamm(h	diamm(h	PROPN
ejpam-4354	338	2	)	)	PUNCT
ejpam-4354	338	3	.	.	PUNCT
ejpam-4354	339	1	then	then	ADV
ejpam-4354	339	2	γme(g[h	γme(g[h	NUM
ejpam-4354	339	3	]	]	PUNCT
ejpam-4354	339	4	)	)	PUNCT
ejpam-4354	339	5	=	=	SYM
ejpam-4354	339	6	γtme(g	γtme(g	NOUN
ejpam-4354	339	7	)	)	PUNCT
ejpam-4354	339	8	.	.	PUNCT
ejpam-4354	340	1	proof	proof	NOUN
ejpam-4354	340	2	.	.	PUNCT
ejpam-4354	341	1	let	let	VERB
ejpam-4354	341	2	s	s	PRON
ejpam-4354	341	3	be	be	AUX
ejpam-4354	341	4	a	a	DET
ejpam-4354	341	5	γtme	γtme	NOUN
ejpam-4354	341	6	-	-	PUNCT
ejpam-4354	341	7	set	set	NOUN
ejpam-4354	341	8	of	of	ADP
ejpam-4354	341	9	g	g	NOUN
ejpam-4354	341	10	and	and	CCONJ
ejpam-4354	341	11	let	let	VERB
ejpam-4354	341	12	p	p	PRON
ejpam-4354	341	13	∈	∈	PROPN
ejpam-4354	341	14	v	v	ADP
ejpam-4354	341	15	(	(	PUNCT
ejpam-4354	341	16	h	h	NOUN
ejpam-4354	341	17	)	)	PUNCT
ejpam-4354	341	18	.	.	PUNCT
ejpam-4354	342	1	for	for	ADP
ejpam-4354	342	2	each	each	DET
ejpam-4354	342	3	x	x	SYM
ejpam-4354	342	4	∈	∈	PROPN
ejpam-4354	342	5	s	s	NOUN
ejpam-4354	342	6	,	,	PUNCT
ejpam-4354	342	7	let	let	VERB
ejpam-4354	342	8	tx	tx	VERB
ejpam-4354	342	9	=	=	PUNCT
ejpam-4354	342	10	{	{	PUNCT
ejpam-4354	342	11	p	p	X
ejpam-4354	342	12	}	}	PUNCT
ejpam-4354	342	13	.	.	PUNCT
ejpam-4354	343	1	then	then	ADV
ejpam-4354	343	2	c	c	X
ejpam-4354	343	3	=	=	PUNCT
ejpam-4354	343	4	⋃	⋃	PROPN
ejpam-4354	343	5	x∈s	x∈s	NOUN
ejpam-4354	344	1	[	[	X
ejpam-4354	344	2	{	{	PUNCT
ejpam-4354	344	3	x	x	NOUN
ejpam-4354	344	4	}	}	PUNCT
ejpam-4354	344	5	×	×	NOUN
ejpam-4354	344	6	tx	tx	NOUN
ejpam-4354	344	7	]	]	X
ejpam-4354	344	8	=	=	SYM
ejpam-4354	344	9	s	s	PART
ejpam-4354	344	10	×	×	NOUN
ejpam-4354	344	11	{	{	PUNCT
ejpam-4354	344	12	p	p	NOUN
ejpam-4354	344	13	}	}	PUNCT
ejpam-4354	344	14	is	be	AUX
ejpam-4354	344	15	a	a	DET
ejpam-4354	344	16	monophonic	monophonic	ADJ
ejpam-4354	344	17	eccentric	eccentric	ADJ
ejpam-4354	344	18	dominating	dominating	NOUN
ejpam-4354	344	19	set	set	NOUN
ejpam-4354	344	20	of	of	ADP
ejpam-4354	344	21	g[h	g[h	PROPN
ejpam-4354	344	22	]	]	PUNCT
ejpam-4354	344	23	by	by	ADP
ejpam-4354	344	24	theorem	theorem	NOUN
ejpam-4354	344	25	10	10	NUM
ejpam-4354	344	26	.	.	PUNCT
ejpam-4354	345	1	thus	thus	ADV
ejpam-4354	345	2	,	,	PUNCT
ejpam-4354	345	3	γme(g[h	γme(g[h	NUM
ejpam-4354	345	4	]	]	PUNCT
ejpam-4354	345	5	)	)	PUNCT
ejpam-4354	345	6	≤	≤	PROPN
ejpam-4354	345	7	|c|	|c|	PROPN
ejpam-4354	345	8	=	=	SYM
ejpam-4354	345	9	|s|	|s|	PROPN
ejpam-4354	345	10	=	=	SYM
ejpam-4354	345	11	γtme(g	γtme(g	PROPN
ejpam-4354	345	12	)	)	PUNCT
ejpam-4354	345	13	.	.	PUNCT
ejpam-4354	346	1	next	next	ADV
ejpam-4354	346	2	,	,	PUNCT
ejpam-4354	346	3	let	let	VERB
ejpam-4354	346	4	c0	c0	PROPN
ejpam-4354	346	5	=	=	PUNCT
ejpam-4354	347	1	⋃	⋃	PROPN
ejpam-4354	347	2	x∈s0	x∈s0	NOUN
ejpam-4354	348	1	[	[	X
ejpam-4354	348	2	{	{	PUNCT
ejpam-4354	348	3	x}×rx	x}×rx	X
ejpam-4354	348	4	]	]	X
ejpam-4354	348	5	be	be	VERB
ejpam-4354	348	6	a	a	DET
ejpam-4354	348	7	γme	γme	NOUN
ejpam-4354	348	8	-	-	PUNCT
ejpam-4354	348	9	set	set	NOUN
ejpam-4354	348	10	of	of	ADP
ejpam-4354	348	11	g[h	g[h	NOUN
ejpam-4354	348	12	]	]	PUNCT
ejpam-4354	348	13	.	.	PUNCT
ejpam-4354	349	1	then	then	ADV
ejpam-4354	349	2	s0	s0	PROPN
ejpam-4354	349	3	is	be	AUX
ejpam-4354	349	4	a	a	DET
ejpam-4354	349	5	monophonic	monophonic	ADJ
ejpam-4354	349	6	eccentric	eccentric	ADJ
ejpam-4354	349	7	dominating	dominating	NOUN
ejpam-4354	349	8	set	set	NOUN
ejpam-4354	349	9	of	of	ADP
ejpam-4354	349	10	g	g	NOUN
ejpam-4354	349	11	by	by	ADP
ejpam-4354	349	12	theorem	theorem	NOUN
ejpam-4354	349	13	10(i	10(i	NUM
ejpam-4354	349	14	)	)	PUNCT
ejpam-4354	349	15	.	.	PUNCT
ejpam-4354	350	1	if	if	SCONJ
ejpam-4354	350	2	s0	s0	PROPN
ejpam-4354	350	3	is	be	AUX
ejpam-4354	350	4	a	a	DET
ejpam-4354	350	5	total	total	ADJ
ejpam-4354	350	6	monophonic	monophonic	ADJ
ejpam-4354	350	7	eccentric	eccentric	ADJ
ejpam-4354	350	8	dominating	dominating	NOUN
ejpam-4354	350	9	set	set	NOUN
ejpam-4354	350	10	,	,	PUNCT
ejpam-4354	350	11	then	then	ADV
ejpam-4354	350	12	γme(g[h	γme(g[h	NUM
ejpam-4354	350	13	]	]	PUNCT
ejpam-4354	350	14	)	)	PUNCT
ejpam-4354	350	15	=	=	AUX
ejpam-4354	350	16	|c0|	|c0|	NOUN
ejpam-4354	350	17	≥	≥	PROPN
ejpam-4354	350	18	|s0|	|s0|	PROPN
ejpam-4354	350	19	≥	≥	PROPN
ejpam-4354	350	20	γtme(g	γtme(g	PROPN
ejpam-4354	350	21	)	)	PUNCT
ejpam-4354	350	22	.	.	PUNCT
ejpam-4354	351	1	suppose	suppose	VERB
ejpam-4354	351	2	s0	s0	NOUN
ejpam-4354	351	3	is	be	AUX
ejpam-4354	351	4	not	not	PART
ejpam-4354	351	5	a	a	DET
ejpam-4354	351	6	total	total	ADJ
ejpam-4354	351	7	monophonic	monophonic	ADJ
ejpam-4354	351	8	eccentric	eccentric	ADJ
ejpam-4354	351	9	dominating	dominating	NOUN
ejpam-4354	351	10	set	set	NOUN
ejpam-4354	351	11	.	.	PUNCT
ejpam-4354	352	1	then	then	ADV
ejpam-4354	352	2	there	there	PRON
ejpam-4354	352	3	exists	exist	VERB
ejpam-4354	352	4	y	y	PROPN
ejpam-4354	352	5	∈	∈	PROPN
ejpam-4354	352	6	s0	s0	NOUN
ejpam-4354	352	7	such	such	ADJ
ejpam-4354	352	8	that	that	SCONJ
ejpam-4354	352	9	nm	nm	VERB
ejpam-4354	352	10	g	g	NOUN
ejpam-4354	352	11	(	(	PUNCT
ejpam-4354	352	12	y	y	NOUN
ejpam-4354	352	13	)	)	PUNCT
ejpam-4354	352	14	∩	∩	ADJ
ejpam-4354	352	15	s0	s0	NOUN
ejpam-4354	352	16	=	=	PUNCT
ejpam-4354	352	17	∅.	∅.	NOUN
ejpam-4354	352	18	by	by	ADP
ejpam-4354	352	19	theorem	theorem	NOUN
ejpam-4354	352	20	10(ii	10(ii	NUM
ejpam-4354	352	21	)	)	PUNCT
ejpam-4354	352	22	,	,	PUNCT
ejpam-4354	352	23	ry	ry	NOUN
ejpam-4354	352	24	=	=	SYM
ejpam-4354	352	25	v	v	PROPN
ejpam-4354	352	26	(	(	PUNCT
ejpam-4354	352	27	h	h	NOUN
ejpam-4354	352	28	)	)	PUNCT
ejpam-4354	352	29	.	.	PUNCT
ejpam-4354	353	1	let	let	VERB
ejpam-4354	353	2	s1	s1	PROPN
ejpam-4354	353	3	=	=	PUNCT
ejpam-4354	353	4	{	{	PUNCT
ejpam-4354	353	5	v	v	NOUN
ejpam-4354	353	6	∈	∈	NOUN
ejpam-4354	353	7	s0	s0	NOUN
ejpam-4354	353	8	:	:	PUNCT
ejpam-4354	353	9	nm	nm	ADV
ejpam-4354	353	10	g	g	PROPN
ejpam-4354	353	11	(	(	PUNCT
ejpam-4354	353	12	v	v	NOUN
ejpam-4354	353	13	)	)	PUNCT
ejpam-4354	353	14	∩	∩	ADJ
ejpam-4354	353	15	s0	s0	NOUN
ejpam-4354	353	16	=	=	PUNCT
ejpam-4354	353	17	∅	∅	NOUN
ejpam-4354	353	18	}	}	PUNCT
ejpam-4354	353	19	.	.	PUNCT
ejpam-4354	354	1	again	again	ADV
ejpam-4354	354	2	,	,	PUNCT
ejpam-4354	354	3	rv	rv	PROPN
ejpam-4354	354	4	=	=	SYM
ejpam-4354	354	5	v	v	PROPN
ejpam-4354	354	6	(	(	PUNCT
ejpam-4354	354	7	h	h	NOUN
ejpam-4354	354	8	)	)	PUNCT
ejpam-4354	354	9	for	for	ADP
ejpam-4354	354	10	each	each	DET
ejpam-4354	354	11	v	v	X
ejpam-4354	354	12	∈	∈	NOUN
ejpam-4354	354	13	s1	s1	NOUN
ejpam-4354	354	14	by	by	ADP
ejpam-4354	354	15	theorem	theorem	NOUN
ejpam-4354	354	16	10(ii	10(ii	NUM
ejpam-4354	354	17	)	)	PUNCT
ejpam-4354	354	18	.	.	PUNCT
ejpam-4354	355	1	for	for	ADP
ejpam-4354	355	2	each	each	DET
ejpam-4354	355	3	v	v	NUM
ejpam-4354	355	4	∈	∈	PROPN
ejpam-4354	355	5	s1	s1	NOUN
ejpam-4354	355	6	,	,	PUNCT
ejpam-4354	355	7	choose	choose	VERB
ejpam-4354	355	8	a	a	DET
ejpam-4354	355	9	vertex	vertex	NOUN
ejpam-4354	355	10	zv	zv	NOUN
ejpam-4354	355	11	∈	∈	PROPN
ejpam-4354	355	12	nm	nm	INTJ
ejpam-4354	355	13	g	g	NOUN
ejpam-4354	355	14	(	(	PUNCT
ejpam-4354	355	15	v	v	NOUN
ejpam-4354	355	16	)	)	PUNCT
ejpam-4354	355	17	and	and	CCONJ
ejpam-4354	355	18	set	set	VERB
ejpam-4354	355	19	s2	s2	NOUN
ejpam-4354	355	20	=	=	PUNCT
ejpam-4354	355	21	{	{	PUNCT
ejpam-4354	355	22	zv	zv	NOUN
ejpam-4354	355	23	:	:	PUNCT
ejpam-4354	355	24	v	v	NUM
ejpam-4354	355	25	∈	∈	PROPN
ejpam-4354	355	26	s1	s1	NOUN
ejpam-4354	355	27	}	}	PUNCT
ejpam-4354	355	28	.	.	PUNCT
ejpam-4354	356	1	then	then	ADV
ejpam-4354	356	2	s2	s2	VERB
ejpam-4354	356	3	∩	∩	ADJ
ejpam-4354	356	4	s0	s0	NOUN
ejpam-4354	356	5	=	=	PUNCT
ejpam-4354	356	6	∅	∅	NOUN
ejpam-4354	356	7	and	and	CCONJ
ejpam-4354	356	8	|s1|	|s1|	NOUN
ejpam-4354	356	9	≥	≥	NUM
ejpam-4354	356	10	|s2|	|s2|	NOUN
ejpam-4354	356	11	.	.	PUNCT
ejpam-4354	357	1	clearly	clearly	ADV
ejpam-4354	357	2	,	,	PUNCT
ejpam-4354	357	3	s∗	s∗	PROPN
ejpam-4354	357	4	=	=	SYM
ejpam-4354	357	5	s0	s0	PROPN
ejpam-4354	357	6	∪	∪	PROPN
ejpam-4354	357	7	s2	s2	PROPN
ejpam-4354	357	8	is	be	AUX
ejpam-4354	357	9	a	a	DET
ejpam-4354	357	10	total	total	ADJ
ejpam-4354	357	11	monophonic	monophonic	ADJ
ejpam-4354	357	12	eccentric	eccentric	ADJ
ejpam-4354	357	13	dominating	dominating	NOUN
ejpam-4354	357	14	set	set	NOUN
ejpam-4354	357	15	of	of	ADP
ejpam-4354	357	16	g	g	PROPN
ejpam-4354	357	17	and	and	CCONJ
ejpam-4354	357	18	we	we	PRON
ejpam-4354	357	19	have	have	VERB
ejpam-4354	357	20	s.	s.	PROPN
ejpam-4354	357	21	canoy	canoy	PROPN
ejpam-4354	357	22	,	,	PUNCT
ejpam-4354	357	23	jr	jr	PROPN
ejpam-4354	357	24	.	.	PROPN
ejpam-4354	357	25	,	,	PUNCT
ejpam-4354	357	26	a.	a.	NOUN
ejpam-4354	357	27	gamorez	gamorez	PROPN
ejpam-4354	357	28	/	/	SYM
ejpam-4354	357	29	eur	eur	PROPN
ejpam-4354	357	30	.	.	PUNCT
ejpam-4354	358	1	j.	j.	PROPN
ejpam-4354	358	2	pure	pure	PROPN
ejpam-4354	358	3	appl	appl	PROPN
ejpam-4354	358	4	.	.	PROPN
ejpam-4354	358	5	math	math	PROPN
ejpam-4354	358	6	,	,	PUNCT
ejpam-4354	358	7	15	15	NUM
ejpam-4354	358	8	(	(	PUNCT
ejpam-4354	358	9	2	2	NUM
ejpam-4354	358	10	)	)	PUNCT
ejpam-4354	358	11	(	(	PUNCT
ejpam-4354	358	12	2022	2022	NUM
ejpam-4354	358	13	)	)	PUNCT
ejpam-4354	358	14	,	,	PUNCT
ejpam-4354	358	15	635	635	NUM
ejpam-4354	358	16	-	-	SYM
ejpam-4354	358	17	645	645	NUM
ejpam-4354	358	18	644	644	NUM
ejpam-4354	358	19	γme(g[h	γme(g[h	NUM
ejpam-4354	358	20	]	]	PUNCT
ejpam-4354	358	21	)	)	PUNCT
ejpam-4354	359	1	=	=	SYM
ejpam-4354	359	2	|c0|	|c0|	NOUN
ejpam-4354	359	3	=	=	SYM
ejpam-4354	359	4	∑	∑	PUNCT
ejpam-4354	359	5	x∈s0	x∈s0	PROPN
ejpam-4354	359	6	|rx|	|rx|	NOUN
ejpam-4354	359	7	=	=	PUNCT
ejpam-4354	359	8	∑	∑	PROPN
ejpam-4354	359	9	x∈s0\s1	x∈s0\s1	VERB
ejpam-4354	359	10	|rx|+	|rx|+	ADV
ejpam-4354	359	11	∑	∑	PUNCT
ejpam-4354	359	12	x∈s1	x∈s1	PROPN
ejpam-4354	359	13	|rx|	|rx|	NOUN
ejpam-4354	359	14	=	=	PUNCT
ejpam-4354	359	15	∑	∑	PROPN
ejpam-4354	359	16	x∈s0\s1	x∈s0\s1	PROPN
ejpam-4354	359	17	|rx|+	|rx|+	ADV
ejpam-4354	359	18	|v	|v	X
ejpam-4354	359	19	(	(	PUNCT
ejpam-4354	359	20	h)||s1|	h)||s1|	X
ejpam-4354	359	21	≥	≥	NOUN
ejpam-4354	359	22	∑	∑	PROPN
ejpam-4354	359	23	x∈s0\s1	x∈s0\s1	PROPN
ejpam-4354	360	1	|rx|+	|rx|+	PRON
ejpam-4354	360	2	2|s1|	2|s1|	NUM
ejpam-4354	360	3	≥	≥	X
ejpam-4354	360	4	∑	∑	PROPN
ejpam-4354	360	5	x∈s0\s1	x∈s0\s1	PROPN
ejpam-4354	360	6	|rx|+	|rx|+	ADV
ejpam-4354	360	7	(	(	PUNCT
ejpam-4354	360	8	|s1|+	|s1|+	NOUN
ejpam-4354	360	9	|s2|	|s2|	NOUN
ejpam-4354	360	10	)	)	PUNCT
ejpam-4354	360	11	≥	≥	NOUN
ejpam-4354	360	12	|s0	|s0	NOUN
ejpam-4354	360	13	\	\	NOUN
ejpam-4354	360	14	s1|+	s1|+	PROPN
ejpam-4354	360	15	s1	s1	PROPN
ejpam-4354	360	16	+	+	CCONJ
ejpam-4354	360	17	s2	s2	NOUN
ejpam-4354	360	18	=	=	PUNCT
ejpam-4354	360	19	|s∗|	|s∗|	NUM
ejpam-4354	360	20	≥	≥	NOUN
ejpam-4354	360	21	γtme(g	γtme(g	NOUN
ejpam-4354	360	22	)	)	PUNCT
ejpam-4354	360	23	.	.	PUNCT
ejpam-4354	361	1	accordingly	accordingly	ADV
ejpam-4354	361	2	,	,	PUNCT
ejpam-4354	361	3	γme(g[h	γme(g[h	NUM
ejpam-4354	361	4	]	]	PUNCT
ejpam-4354	361	5	)	)	PUNCT
ejpam-4354	361	6	=	=	SYM
ejpam-4354	361	7	γtme(g	γtme(g	NOUN
ejpam-4354	361	8	)	)	PUNCT
ejpam-4354	361	9	.	.	PUNCT
ejpam-4354	362	1	theorem	theorem	NOUN
ejpam-4354	362	2	11	11	NUM
ejpam-4354	362	3	.	.	PUNCT
ejpam-4354	363	1	let	let	VERB
ejpam-4354	363	2	g	g	NOUN
ejpam-4354	363	3	and	and	CCONJ
ejpam-4354	363	4	h	h	PROPN
ejpam-4354	363	5	be	be	VERB
ejpam-4354	363	6	non	non	ADJ
ejpam-4354	363	7	-	-	ADJ
ejpam-4354	363	8	trivial	trivial	ADJ
ejpam-4354	363	9	connected	connected	ADJ
ejpam-4354	363	10	graphs	graph	NOUN
ejpam-4354	363	11	such	such	ADJ
ejpam-4354	363	12	that	that	DET
ejpam-4354	363	13	radm(h	radm(h	NOUN
ejpam-4354	363	14	)	)	PUNCT
ejpam-4354	363	15	>	>	X
ejpam-4354	364	1	diamm(g	diamm(g	PROPN
ejpam-4354	364	2	)	)	PUNCT
ejpam-4354	364	3	.	.	PUNCT
ejpam-4354	365	1	then	then	ADV
ejpam-4354	365	2	c	c	X
ejpam-4354	365	3	=	=	PUNCT
ejpam-4354	365	4	⋃	⋃	PROPN
ejpam-4354	365	5	x∈s	x∈s	NOUN
ejpam-4354	366	1	[	[	X
ejpam-4354	366	2	{	{	PUNCT
ejpam-4354	366	3	x	x	NOUN
ejpam-4354	366	4	}	}	PUNCT
ejpam-4354	366	5	×	×	PROPN
ejpam-4354	366	6	tx	tx	PROPN
ejpam-4354	366	7	]	]	X
ejpam-4354	366	8	,	,	PUNCT
ejpam-4354	366	9	where	where	SCONJ
ejpam-4354	366	10	s	s	VERB
ejpam-4354	366	11	⊆	⊆	NUM
ejpam-4354	366	12	v	v	NOUN
ejpam-4354	366	13	(	(	PUNCT
ejpam-4354	366	14	g	g	NOUN
ejpam-4354	366	15	)	)	PUNCT
ejpam-4354	366	16	and	and	CCONJ
ejpam-4354	366	17	tx	tx	VERB
ejpam-4354	366	18	⊆	⊆	NUM
ejpam-4354	366	19	v	v	NOUN
ejpam-4354	366	20	(	(	PUNCT
ejpam-4354	366	21	h	h	NOUN
ejpam-4354	366	22	)	)	PUNCT
ejpam-4354	366	23	for	for	ADP
ejpam-4354	366	24	each	each	DET
ejpam-4354	366	25	x	x	SYM
ejpam-4354	366	26	∈	∈	PROPN
ejpam-4354	366	27	s	s	NOUN
ejpam-4354	366	28	,	,	PUNCT
ejpam-4354	366	29	is	be	AUX
ejpam-4354	366	30	a	a	DET
ejpam-4354	366	31	monophonic	monophonic	ADJ
ejpam-4354	366	32	eccentric	eccentric	ADJ
ejpam-4354	366	33	dominating	dominating	NOUN
ejpam-4354	366	34	set	set	NOUN
ejpam-4354	366	35	of	of	ADP
ejpam-4354	366	36	g[h	g[h	PROPN
ejpam-4354	366	37	]	]	PUNCT
ejpam-4354	366	38	if	if	SCONJ
ejpam-4354	366	39	and	and	CCONJ
ejpam-4354	366	40	only	only	ADV
ejpam-4354	366	41	if	if	SCONJ
ejpam-4354	366	42	(	(	PUNCT
ejpam-4354	366	43	i	i	NOUN
ejpam-4354	366	44	)	)	PUNCT
ejpam-4354	366	45	s	s	PART
ejpam-4354	366	46	=	=	SYM
ejpam-4354	366	47	v	v	X
ejpam-4354	366	48	(	(	PUNCT
ejpam-4354	366	49	g	g	NOUN
ejpam-4354	366	50	)	)	PUNCT
ejpam-4354	366	51	and	and	CCONJ
ejpam-4354	366	52	(	(	PUNCT
ejpam-4354	366	53	ii	ii	NOUN
ejpam-4354	366	54	)	)	PUNCT
ejpam-4354	366	55	tx	tx	PROPN
ejpam-4354	366	56	is	be	AUX
ejpam-4354	366	57	a	a	DET
ejpam-4354	366	58	monophonic	monophonic	ADJ
ejpam-4354	366	59	eccentric	eccentric	ADJ
ejpam-4354	366	60	dominating	dominating	NOUN
ejpam-4354	366	61	set	set	NOUN
ejpam-4354	366	62	of	of	ADP
ejpam-4354	366	63	h	h	NOUN
ejpam-4354	366	64	for	for	ADP
ejpam-4354	366	65	each	each	DET
ejpam-4354	366	66	x	x	SYM
ejpam-4354	366	67	∈	∈	PROPN
ejpam-4354	366	68	v	v	NOUN
ejpam-4354	366	69	(	(	PUNCT
ejpam-4354	366	70	g	g	NOUN
ejpam-4354	366	71	)	)	PUNCT
ejpam-4354	366	72	.	.	PUNCT
ejpam-4354	367	1	proof	proof	NOUN
ejpam-4354	367	2	.	.	PUNCT
ejpam-4354	368	1	suppose	suppose	VERB
ejpam-4354	368	2	c	c	NOUN
ejpam-4354	368	3	is	be	AUX
ejpam-4354	368	4	a	a	DET
ejpam-4354	368	5	monophonic	monophonic	ADJ
ejpam-4354	368	6	eccentric	eccentric	ADJ
ejpam-4354	368	7	dominating	dominating	NOUN
ejpam-4354	368	8	set	set	NOUN
ejpam-4354	368	9	of	of	ADP
ejpam-4354	368	10	g[h	g[h	PROPN
ejpam-4354	368	11	]	]	PUNCT
ejpam-4354	368	12	.	.	PUNCT
ejpam-4354	369	1	suppose	suppose	VERB
ejpam-4354	369	2	s	s	PROPN
ejpam-4354	369	3	6=	6=	NUM
ejpam-4354	369	4	v	v	ADP
ejpam-4354	369	5	(	(	PUNCT
ejpam-4354	369	6	g	g	NOUN
ejpam-4354	369	7	)	)	PUNCT
ejpam-4354	369	8	,	,	PUNCT
ejpam-4354	369	9	say	say	VERB
ejpam-4354	369	10	x	x	X
ejpam-4354	369	11	∈	∈	NOUN
ejpam-4354	369	12	v	v	X
ejpam-4354	369	13	(	(	PUNCT
ejpam-4354	369	14	g)\s	g)\s	NOUN
ejpam-4354	369	15	.	.	PUNCT
ejpam-4354	370	1	pick	pick	VERB
ejpam-4354	370	2	any	any	PRON
ejpam-4354	370	3	a	a	DET
ejpam-4354	370	4	∈	∈	PROPN
ejpam-4354	370	5	v	v	NOUN
ejpam-4354	370	6	(	(	PUNCT
ejpam-4354	370	7	h	h	NOUN
ejpam-4354	370	8	)	)	PUNCT
ejpam-4354	370	9	.	.	PUNCT
ejpam-4354	371	1	then	then	ADV
ejpam-4354	371	2	(	(	PUNCT
ejpam-4354	371	3	v	v	NOUN
ejpam-4354	371	4	,	,	PUNCT
ejpam-4354	371	5	a	a	PRON
ejpam-4354	371	6	)	)	PUNCT
ejpam-4354	371	7	/∈	/∈	PUNCT
ejpam-4354	372	1	c.	c.	NOUN
ejpam-4354	372	2	as	as	SCONJ
ejpam-4354	372	3	c	c	PROPN
ejpam-4354	372	4	is	be	AUX
ejpam-4354	372	5	a	a	DET
ejpam-4354	372	6	monophonic	monophonic	ADJ
ejpam-4354	372	7	eccentric	eccentric	ADJ
ejpam-4354	372	8	dominating	dominating	NOUN
ejpam-4354	372	9	set	set	NOUN
ejpam-4354	372	10	of	of	ADP
ejpam-4354	372	11	g[h	g[h	PROPN
ejpam-4354	372	12	]	]	PUNCT
ejpam-4354	372	13	,	,	PUNCT
ejpam-4354	372	14	there	there	PRON
ejpam-4354	372	15	exists	exist	VERB
ejpam-4354	372	16	(	(	PUNCT
ejpam-4354	372	17	w	w	PROPN
ejpam-4354	372	18	,	,	PUNCT
ejpam-4354	372	19	b	b	NOUN
ejpam-4354	372	20	)	)	PUNCT
ejpam-4354	372	21	∈	∈	PROPN
ejpam-4354	372	22	c	c	NOUN
ejpam-4354	372	23	such	such	ADJ
ejpam-4354	372	24	that	that	DET
ejpam-4354	372	25	emg[h]((v	emg[h]((v	PROPN
ejpam-4354	372	26	,	,	PUNCT
ejpam-4354	372	27	a	a	PRON
ejpam-4354	372	28	)	)	PUNCT
ejpam-4354	372	29	)	)	PUNCT
ejpam-4354	373	1	=	=	SYM
ejpam-4354	373	2	dmg[h]((v	dmg[h]((v	NOUN
ejpam-4354	373	3	,	,	PUNCT
ejpam-4354	373	4	a	a	PRON
ejpam-4354	373	5	)	)	PUNCT
ejpam-4354	373	6	,	,	PUNCT
ejpam-4354	373	7	(	(	PUNCT
ejpam-4354	373	8	w	w	PROPN
ejpam-4354	373	9	,	,	PUNCT
ejpam-4354	373	10	b	b	NOUN
ejpam-4354	373	11	)	)	PUNCT
ejpam-4354	373	12	)	)	PUNCT
ejpam-4354	373	13	.	.	PUNCT
ejpam-4354	374	1	however	however	ADV
ejpam-4354	374	2	,	,	PUNCT
ejpam-4354	374	3	the	the	DET
ejpam-4354	374	4	assumption	assumption	NOUN
ejpam-4354	374	5	that	that	SCONJ
ejpam-4354	374	6	radm(h	radm(h	VERB
ejpam-4354	374	7	)	)	PUNCT
ejpam-4354	374	8	>	>	X
ejpam-4354	375	1	diamm(g	diamm(g	PROPN
ejpam-4354	375	2	)	)	PUNCT
ejpam-4354	375	3	implies	imply	VERB
ejpam-4354	375	4	that	that	SCONJ
ejpam-4354	375	5	emg[h]((v	emg[h]((v	PROPN
ejpam-4354	375	6	,	,	PUNCT
ejpam-4354	375	7	a	a	PRON
ejpam-4354	375	8	)	)	PUNCT
ejpam-4354	375	9	)	)	PUNCT
ejpam-4354	376	1	=	=	PUNCT
ejpam-4354	376	2	emh(a	emh(a	PROPN
ejpam-4354	376	3	)	)	PUNCT
ejpam-4354	376	4	=	=	SYM
ejpam-4354	376	5	dmh(a	dmh(a	PROPN
ejpam-4354	376	6	,	,	PUNCT
ejpam-4354	376	7	b	b	NOUN
ejpam-4354	376	8	)	)	PUNCT
ejpam-4354	376	9	>	>	X
ejpam-4354	376	10	emg	emg	PROPN
ejpam-4354	376	11	(	(	PUNCT
ejpam-4354	376	12	v	v	NOUN
ejpam-4354	376	13	)	)	PUNCT
ejpam-4354	376	14	.	.	PUNCT
ejpam-4354	377	1	this	this	PRON
ejpam-4354	377	2	is	be	AUX
ejpam-4354	377	3	impossible	impossible	ADJ
ejpam-4354	377	4	because	because	SCONJ
ejpam-4354	377	5	w	w	PROPN
ejpam-4354	377	6	6=	6=	PROPN
ejpam-4354	377	7	x.	x.	NOUN
ejpam-4354	377	8	thus	thus	ADV
ejpam-4354	377	9	,	,	PUNCT
ejpam-4354	377	10	s	s	NOUN
ejpam-4354	377	11	=	=	SYM
ejpam-4354	377	12	v	v	X
ejpam-4354	377	13	(	(	PUNCT
ejpam-4354	377	14	g	g	NOUN
ejpam-4354	377	15	)	)	PUNCT
ejpam-4354	377	16	,	,	PUNCT
ejpam-4354	377	17	showing	show	VERB
ejpam-4354	377	18	that	that	SCONJ
ejpam-4354	377	19	(	(	PUNCT
ejpam-4354	377	20	i	i	NOUN
ejpam-4354	377	21	)	)	PUNCT
ejpam-4354	377	22	holds	hold	VERB
ejpam-4354	377	23	.	.	PUNCT
ejpam-4354	378	1	let	let	VERB
ejpam-4354	378	2	x	x	SYM
ejpam-4354	378	3	∈	∈	PROPN
ejpam-4354	378	4	v	v	X
ejpam-4354	378	5	(	(	PUNCT
ejpam-4354	378	6	g	g	NOUN
ejpam-4354	378	7	)	)	PUNCT
ejpam-4354	378	8	.	.	PUNCT
ejpam-4354	379	1	if	if	SCONJ
ejpam-4354	379	2	tx	tx	PROPN
ejpam-4354	379	3	=	=	SYM
ejpam-4354	379	4	v	v	PROPN
ejpam-4354	379	5	(	(	PUNCT
ejpam-4354	379	6	g	g	NOUN
ejpam-4354	379	7	)	)	PUNCT
ejpam-4354	379	8	,	,	PUNCT
ejpam-4354	379	9	then	then	ADV
ejpam-4354	379	10	it	it	PRON
ejpam-4354	379	11	is	be	AUX
ejpam-4354	379	12	a	a	DET
ejpam-4354	379	13	monophonic	monophonic	ADJ
ejpam-4354	379	14	eccentric	eccentric	ADJ
ejpam-4354	379	15	dominating	dominating	NOUN
ejpam-4354	379	16	set	set	NOUN
ejpam-4354	379	17	of	of	ADP
ejpam-4354	379	18	h.	h.	PROPN
ejpam-4354	379	19	suppose	suppose	VERB
ejpam-4354	379	20	tx	tx	PROPN
ejpam-4354	379	21	6=	6=	PROPN
ejpam-4354	379	22	v	v	ADP
ejpam-4354	379	23	(	(	PUNCT
ejpam-4354	379	24	h	h	NOUN
ejpam-4354	379	25	)	)	PUNCT
ejpam-4354	379	26	and	and	CCONJ
ejpam-4354	379	27	let	let	VERB
ejpam-4354	380	1	q	q	PROPN
ejpam-4354	380	2	∈	∈	PROPN
ejpam-4354	380	3	v	v	ADP
ejpam-4354	380	4	(	(	PUNCT
ejpam-4354	380	5	h	h	NOUN
ejpam-4354	380	6	)	)	PUNCT
ejpam-4354	380	7	\	\	PROPN
ejpam-4354	380	8	tx	tx	PROPN
ejpam-4354	380	9	.	.	PUNCT
ejpam-4354	381	1	since	since	SCONJ
ejpam-4354	381	2	(	(	PUNCT
ejpam-4354	381	3	x	x	X
ejpam-4354	381	4	,	,	PUNCT
ejpam-4354	381	5	q	q	NOUN
ejpam-4354	381	6	)	)	PUNCT
ejpam-4354	381	7	∈	∈	NOUN
ejpam-4354	381	8	v	v	NOUN
ejpam-4354	381	9	(	(	PUNCT
ejpam-4354	381	10	g[h	g[h	PROPN
ejpam-4354	381	11	]	]	PUNCT
ejpam-4354	381	12	)	)	PUNCT
ejpam-4354	381	13	\	\	PROPN
ejpam-4354	381	14	c	c	PROPN
ejpam-4354	381	15	and	and	CCONJ
ejpam-4354	381	16	emg[h]((x	emg[h]((x	PROPN
ejpam-4354	381	17	,	,	PUNCT
ejpam-4354	381	18	q	q	NOUN
ejpam-4354	381	19	)	)	PUNCT
ejpam-4354	381	20	)	)	PUNCT
ejpam-4354	381	21	=	=	SYM
ejpam-4354	381	22	emh(q	emh(q	NOUN
ejpam-4354	381	23	)	)	PUNCT
ejpam-4354	381	24	,	,	PUNCT
ejpam-4354	381	25	it	it	PRON
ejpam-4354	381	26	follows	follow	VERB
ejpam-4354	381	27	that	that	SCONJ
ejpam-4354	381	28	there	there	PRON
ejpam-4354	381	29	exists	exist	VERB
ejpam-4354	381	30	p	p	PROPN
ejpam-4354	381	31	∈	∈	PROPN
ejpam-4354	381	32	tx	tx	PROPN
ejpam-4354	381	33	∩	∩	ADJ
ejpam-4354	381	34	nm	nm	ADJ
ejpam-4354	381	35	h	h	NOUN
ejpam-4354	381	36	(	(	PUNCT
ejpam-4354	381	37	q	q	NOUN
ejpam-4354	381	38	)	)	PUNCT
ejpam-4354	381	39	.	.	PUNCT
ejpam-4354	382	1	hence	hence	ADV
ejpam-4354	382	2	,	,	PUNCT
ejpam-4354	382	3	tx	tx	PROPN
ejpam-4354	382	4	is	be	AUX
ejpam-4354	382	5	a	a	DET
ejpam-4354	382	6	monophonic	monophonic	ADJ
ejpam-4354	382	7	eccentric	eccentric	ADJ
ejpam-4354	382	8	dominating	dominating	NOUN
ejpam-4354	382	9	set	set	NOUN
ejpam-4354	382	10	of	of	ADP
ejpam-4354	382	11	h.	h.	PROPN
ejpam-4354	382	12	this	this	PRON
ejpam-4354	382	13	shows	show	VERB
ejpam-4354	382	14	that	that	SCONJ
ejpam-4354	382	15	(	(	PUNCT
ejpam-4354	382	16	ii	ii	NOUN
ejpam-4354	382	17	)	)	PUNCT
ejpam-4354	382	18	holds	hold	VERB
ejpam-4354	382	19	.	.	PUNCT
ejpam-4354	383	1	for	for	ADP
ejpam-4354	383	2	the	the	DET
ejpam-4354	383	3	converse	converse	NOUN
ejpam-4354	383	4	,	,	PUNCT
ejpam-4354	383	5	suppose	suppose	VERB
ejpam-4354	383	6	that	that	SCONJ
ejpam-4354	383	7	(	(	PUNCT
ejpam-4354	383	8	i	i	NOUN
ejpam-4354	383	9	)	)	PUNCT
ejpam-4354	383	10	and	and	CCONJ
ejpam-4354	383	11	(	(	PUNCT
ejpam-4354	383	12	ii	ii	NOUN
ejpam-4354	383	13	)	)	PUNCT
ejpam-4354	383	14	hold	hold	VERB
ejpam-4354	383	15	.	.	PUNCT
ejpam-4354	384	1	let	let	VERB
ejpam-4354	384	2	(	(	PUNCT
ejpam-4354	384	3	z	z	NOUN
ejpam-4354	384	4	,	,	PUNCT
ejpam-4354	384	5	a	a	PRON
ejpam-4354	384	6	)	)	PUNCT
ejpam-4354	384	7	∈	∈	NOUN
ejpam-4354	384	8	v	v	NOUN
ejpam-4354	384	9	(	(	PUNCT
ejpam-4354	384	10	g[h	g[h	PROPN
ejpam-4354	384	11	]	]	PUNCT
ejpam-4354	384	12	)	)	PUNCT
ejpam-4354	384	13	\	\	PROPN
ejpam-4354	385	1	c.	c.	NOUN
ejpam-4354	385	2	since	since	SCONJ
ejpam-4354	385	3	s	s	PROPN
ejpam-4354	385	4	=	=	SYM
ejpam-4354	385	5	v	v	PROPN
ejpam-4354	385	6	(	(	PUNCT
ejpam-4354	385	7	g	g	NOUN
ejpam-4354	385	8	)	)	PUNCT
ejpam-4354	385	9	,	,	PUNCT
ejpam-4354	385	10	it	it	PRON
ejpam-4354	385	11	follows	follow	VERB
ejpam-4354	385	12	that	that	SCONJ
ejpam-4354	385	13	a	a	DET
ejpam-4354	385	14	/∈	/∈	INTJ
ejpam-4354	385	15	tx	tx	PROPN
ejpam-4354	385	16	.	.	PUNCT
ejpam-4354	386	1	as	as	SCONJ
ejpam-4354	386	2	tx	tx	PROPN
ejpam-4354	386	3	is	be	AUX
ejpam-4354	386	4	a	a	DET
ejpam-4354	386	5	monophonic	monophonic	ADJ
ejpam-4354	386	6	eccentric	eccentric	ADJ
ejpam-4354	386	7	dominating	dominating	NOUN
ejpam-4354	386	8	set	set	NOUN
ejpam-4354	386	9	of	of	ADP
ejpam-4354	386	10	h	h	NOUN
ejpam-4354	386	11	according	accord	VERB
ejpam-4354	386	12	to	to	ADP
ejpam-4354	386	13	(	(	PUNCT
ejpam-4354	386	14	ii	ii	NOUN
ejpam-4354	386	15	)	)	PUNCT
ejpam-4354	386	16	,	,	PUNCT
ejpam-4354	386	17	there	there	PRON
ejpam-4354	386	18	exists	exist	VERB
ejpam-4354	386	19	b	b	PROPN
ejpam-4354	386	20	∈	∈	PROPN
ejpam-4354	386	21	tx	tx	ADP
ejpam-4354	386	22	such	such	ADJ
ejpam-4354	386	23	that	that	DET
ejpam-4354	386	24	emh(a	emh(a	NOUN
ejpam-4354	386	25	)	)	PUNCT
ejpam-4354	386	26	=	=	SYM
ejpam-4354	386	27	dmh(a	dmh(a	PROPN
ejpam-4354	386	28	,	,	PUNCT
ejpam-4354	386	29	b	b	NOUN
ejpam-4354	386	30	)	)	PUNCT
ejpam-4354	386	31	.	.	PUNCT
ejpam-4354	387	1	with	with	ADP
ejpam-4354	387	2	the	the	DET
ejpam-4354	387	3	assumption	assumption	NOUN
ejpam-4354	387	4	that	that	SCONJ
ejpam-4354	387	5	radm(h	radm(h	VERB
ejpam-4354	387	6	)	)	PUNCT
ejpam-4354	387	7	>	>	X
ejpam-4354	388	1	diamm(g	diamm(g	PROPN
ejpam-4354	388	2	)	)	PUNCT
ejpam-4354	388	3	,	,	PUNCT
ejpam-4354	388	4	it	it	PRON
ejpam-4354	388	5	follows	follow	VERB
ejpam-4354	388	6	that	that	SCONJ
ejpam-4354	388	7	emg[h]((z	emg[h]((z	PROPN
ejpam-4354	388	8	,	,	PUNCT
ejpam-4354	388	9	a	a	PRON
ejpam-4354	388	10	)	)	PUNCT
ejpam-4354	388	11	)	)	PUNCT
ejpam-4354	389	1	=	=	PUNCT
ejpam-4354	389	2	emh(a	emh(a	PROPN
ejpam-4354	389	3	)	)	PUNCT
ejpam-4354	389	4	=	=	SYM
ejpam-4354	389	5	dmh(a	dmh(a	PROPN
ejpam-4354	389	6	,	,	PUNCT
ejpam-4354	389	7	b	b	NOUN
ejpam-4354	389	8	)	)	PUNCT
ejpam-4354	389	9	=	=	SYM
ejpam-4354	389	10	dmg[h]((z	dmg[h]((z	PROPN
ejpam-4354	389	11	,	,	PUNCT
ejpam-4354	389	12	a	a	NOUN
ejpam-4354	389	13	)	)	PUNCT
ejpam-4354	389	14	,	,	PUNCT
ejpam-4354	389	15	(	(	PUNCT
ejpam-4354	389	16	z	z	X
ejpam-4354	389	17	,	,	PUNCT
ejpam-4354	389	18	b	b	NOUN
ejpam-4354	389	19	)	)	PUNCT
ejpam-4354	389	20	)	)	PUNCT
ejpam-4354	389	21	,	,	PUNCT
ejpam-4354	389	22	where	where	SCONJ
ejpam-4354	389	23	(	(	PUNCT
ejpam-4354	389	24	z	z	NOUN
ejpam-4354	389	25	,	,	PUNCT
ejpam-4354	389	26	b	b	NOUN
ejpam-4354	389	27	)	)	PUNCT
ejpam-4354	389	28	∈	∈	PROPN
ejpam-4354	389	29	c.	c.	NOUN
ejpam-4354	389	30	therefore	therefore	ADV
ejpam-4354	389	31	,	,	PUNCT
ejpam-4354	389	32	c	c	PROPN
ejpam-4354	389	33	is	be	AUX
ejpam-4354	389	34	monophonic	monophonic	ADJ
ejpam-4354	389	35	eccentric	eccentric	ADJ
ejpam-4354	389	36	dominating	dominating	NOUN
ejpam-4354	389	37	set	set	NOUN
ejpam-4354	389	38	of	of	ADP
ejpam-4354	389	39	g[h	g[h	PROPN
ejpam-4354	389	40	]	]	PUNCT
ejpam-4354	389	41	.	.	PUNCT
ejpam-4354	390	1	references	reference	NOUN
ejpam-4354	390	2	645	645	NUM
ejpam-4354	390	3	the	the	DET
ejpam-4354	390	4	next	next	ADJ
ejpam-4354	390	5	result	result	NOUN
ejpam-4354	390	6	is	be	AUX
ejpam-4354	390	7	an	an	DET
ejpam-4354	390	8	immediate	immediate	ADJ
ejpam-4354	390	9	consequence	consequence	NOUN
ejpam-4354	390	10	of	of	ADP
ejpam-4354	390	11	theorem	theorem	NOUN
ejpam-4354	390	12	11	11	NUM
ejpam-4354	390	13	.	.	PUNCT
ejpam-4354	391	1	corollary	corollary	ADJ
ejpam-4354	391	2	5	5	NUM
ejpam-4354	391	3	.	.	PUNCT
ejpam-4354	392	1	let	let	VERB
ejpam-4354	392	2	g	g	NOUN
ejpam-4354	392	3	and	and	CCONJ
ejpam-4354	392	4	h	h	PROPN
ejpam-4354	392	5	be	be	VERB
ejpam-4354	392	6	non	non	ADJ
ejpam-4354	392	7	-	-	ADJ
ejpam-4354	392	8	trivial	trivial	ADJ
ejpam-4354	392	9	connected	connected	ADJ
ejpam-4354	392	10	graphs	graph	NOUN
ejpam-4354	392	11	such	such	ADJ
ejpam-4354	392	12	that	that	DET
ejpam-4354	392	13	radm(h	radm(h	NOUN
ejpam-4354	392	14	)	)	PUNCT
ejpam-4354	392	15	>	>	X
ejpam-4354	393	1	diamm(g	diamm(g	PROPN
ejpam-4354	393	2	)	)	PUNCT
ejpam-4354	393	3	.	.	PUNCT
ejpam-4354	394	1	then	then	ADV
ejpam-4354	394	2	γme(g[h	γme(g[h	NUM
ejpam-4354	394	3	]	]	PUNCT
ejpam-4354	394	4	)	)	PUNCT
ejpam-4354	395	1	=	=	SYM
ejpam-4354	395	2	|v	|v	X
ejpam-4354	395	3	(	(	PUNCT
ejpam-4354	395	4	g)|γme(h	g)|γme(h	NOUN
ejpam-4354	395	5	)	)	PUNCT
ejpam-4354	395	6	.	.	PUNCT
ejpam-4354	396	1	conclusion	conclusion	NOUN
ejpam-4354	396	2	:	:	PUNCT
ejpam-4354	396	3	monophonic	monophonic	ADJ
ejpam-4354	396	4	paths	path	NOUN
ejpam-4354	396	5	and	and	CCONJ
ejpam-4354	396	6	monophonic	monophonic	ADJ
ejpam-4354	396	7	distance	distance	NOUN
ejpam-4354	396	8	-	-	PUNCT
ejpam-4354	396	9	related	relate	VERB
ejpam-4354	396	10	concepts	concept	NOUN
ejpam-4354	396	11	had	have	AUX
ejpam-4354	396	12	been	be	AUX
ejpam-4354	396	13	used	use	VERB
ejpam-4354	396	14	to	to	PART
ejpam-4354	396	15	define	define	VERB
ejpam-4354	396	16	monophonic	monophonic	ADJ
ejpam-4354	396	17	eccentric	eccentric	ADJ
ejpam-4354	396	18	dominating	dominating	NOUN
ejpam-4354	396	19	set	set	VERB
ejpam-4354	396	20	and	and	CCONJ
ejpam-4354	396	21	monophonic	monophonic	ADJ
ejpam-4354	396	22	eccentric	eccentric	ADJ
ejpam-4354	396	23	domination	domination	NOUN
ejpam-4354	396	24	number	number	NOUN
ejpam-4354	396	25	of	of	ADP
ejpam-4354	396	26	a	a	DET
ejpam-4354	396	27	graph	graph	NOUN
ejpam-4354	396	28	.	.	PUNCT
ejpam-4354	397	1	it	it	PRON
ejpam-4354	397	2	was	be	AUX
ejpam-4354	397	3	shown	show	VERB
ejpam-4354	397	4	that	that	SCONJ
ejpam-4354	397	5	the	the	DET
ejpam-4354	397	6	absolute	absolute	ADJ
ejpam-4354	397	7	difference	difference	NOUN
ejpam-4354	397	8	of	of	ADP
ejpam-4354	397	9	the	the	DET
ejpam-4354	397	10	domination	domination	NOUN
ejpam-4354	397	11	number	number	NOUN
ejpam-4354	397	12	and	and	CCONJ
ejpam-4354	397	13	the	the	DET
ejpam-4354	397	14	monophonic	monophonic	ADJ
ejpam-4354	397	15	eccentric	eccentric	ADJ
ejpam-4354	397	16	domination	domination	NOUN
ejpam-4354	397	17	number	number	NOUN
ejpam-4354	397	18	can	can	AUX
ejpam-4354	397	19	be	be	AUX
ejpam-4354	397	20	made	make	VERB
ejpam-4354	397	21	arbitrarily	arbitrarily	ADV
ejpam-4354	397	22	large	large	ADJ
ejpam-4354	397	23	.	.	PUNCT
ejpam-4354	398	1	monophonic	monophonic	ADJ
ejpam-4354	398	2	eccentric	eccentric	ADJ
ejpam-4354	398	3	dominating	dominating	NOUN
ejpam-4354	398	4	sets	set	NOUN
ejpam-4354	398	5	in	in	ADP
ejpam-4354	398	6	the	the	DET
ejpam-4354	398	7	join	join	NOUN
ejpam-4354	398	8	,	,	PUNCT
ejpam-4354	398	9	corona	corona	PROPN
ejpam-4354	398	10	,	,	PUNCT
ejpam-4354	398	11	and	and	CCONJ
ejpam-4354	398	12	lexicographic	lexicographic	ADJ
ejpam-4354	398	13	product	product	NOUN
ejpam-4354	398	14	of	of	ADP
ejpam-4354	398	15	two	two	NUM
ejpam-4354	398	16	graphs	graph	NOUN
ejpam-4354	398	17	were	be	AUX
ejpam-4354	398	18	characterized	characterize	VERB
ejpam-4354	398	19	and	and	CCONJ
ejpam-4354	398	20	,	,	PUNCT
ejpam-4354	398	21	under	under	ADP
ejpam-4354	398	22	some	some	DET
ejpam-4354	398	23	conditions	condition	NOUN
ejpam-4354	398	24	,	,	PUNCT
ejpam-4354	398	25	their	their	PRON
ejpam-4354	398	26	monophonic	monophonic	ADJ
ejpam-4354	398	27	eccentric	eccentric	ADJ
ejpam-4354	398	28	domination	domination	NOUN
ejpam-4354	398	29	numbers	number	NOUN
ejpam-4354	398	30	were	be	AUX
ejpam-4354	398	31	subsequently	subsequently	ADV
ejpam-4354	398	32	determined	determine	VERB
ejpam-4354	398	33	.	.	PUNCT
ejpam-4354	399	1	several	several	ADJ
ejpam-4354	399	2	aspects	aspect	NOUN
ejpam-4354	399	3	of	of	ADP
ejpam-4354	399	4	the	the	DET
ejpam-4354	399	5	concept	concept	NOUN
ejpam-4354	399	6	(	(	PUNCT
ejpam-4354	399	7	e.g.	e.g.	ADV
ejpam-4354	399	8	its	its	PRON
ejpam-4354	399	9	complexity	complexity	NOUN
ejpam-4354	399	10	)	)	PUNCT
ejpam-4354	399	11	and	and	CCONJ
ejpam-4354	399	12	the	the	DET
ejpam-4354	399	13	corresponding	corresponding	ADJ
ejpam-4354	399	14	parameter	parameter	NOUN
ejpam-4354	399	15	remains	remain	VERB
ejpam-4354	399	16	to	to	PART
ejpam-4354	399	17	be	be	AUX
ejpam-4354	399	18	investigated	investigate	VERB
ejpam-4354	399	19	.	.	PUNCT
ejpam-4354	400	1	moreover	moreover	ADV
ejpam-4354	400	2	,	,	PUNCT
ejpam-4354	400	3	other	other	ADJ
ejpam-4354	400	4	variants	variant	NOUN
ejpam-4354	400	5	of	of	ADP
ejpam-4354	400	6	the	the	DET
ejpam-4354	400	7	concept	concept	NOUN
ejpam-4354	400	8	may	may	AUX
ejpam-4354	400	9	as	as	ADV
ejpam-4354	400	10	well	well	ADV
ejpam-4354	400	11	be	be	AUX
ejpam-4354	400	12	introduced	introduce	VERB
ejpam-4354	400	13	and	and	CCONJ
ejpam-4354	400	14	studied	study	VERB
ejpam-4354	400	15	.	.	PUNCT
ejpam-4354	401	1	acknowledgements	acknowledgement	NOUN
ejpam-4354	401	2	the	the	DET
ejpam-4354	401	3	authors	author	NOUN
ejpam-4354	401	4	would	would	AUX
ejpam-4354	401	5	like	like	VERB
ejpam-4354	401	6	to	to	PART
ejpam-4354	401	7	thank	thank	VERB
ejpam-4354	401	8	the	the	DET
ejpam-4354	401	9	referees	referee	NOUN
ejpam-4354	401	10	for	for	ADP
ejpam-4354	401	11	reviewing	review	VERB
ejpam-4354	401	12	the	the	DET
ejpam-4354	401	13	paper	paper	NOUN
ejpam-4354	401	14	and	and	CCONJ
ejpam-4354	401	15	for	for	ADP
ejpam-4354	401	16	the	the	DET
ejpam-4354	401	17	comments	comment	NOUN
ejpam-4354	401	18	and	and	CCONJ
ejpam-4354	401	19	suggestions	suggestion	NOUN
ejpam-4354	401	20	they	they	PRON
ejpam-4354	401	21	provided	provide	VERB
ejpam-4354	401	22	.	.	PUNCT
ejpam-4354	402	1	also	also	ADV
ejpam-4354	402	2	,	,	PUNCT
ejpam-4354	402	3	the	the	DET
ejpam-4354	402	4	authors	author	NOUN
ejpam-4354	402	5	would	would	AUX
ejpam-4354	402	6	like	like	VERB
ejpam-4354	402	7	to	to	PART
ejpam-4354	402	8	extend	extend	VERB
ejpam-4354	402	9	their	their	PRON
ejpam-4354	402	10	gratefulness	gratefulness	NOUN
ejpam-4354	402	11	to	to	ADP
ejpam-4354	402	12	the	the	DET
ejpam-4354	402	13	msu	msu	PROPN
ejpam-4354	402	14	-	-	PUNCT
ejpam-4354	402	15	iligan	iligan	PROPN
ejpam-4354	402	16	institute	institute	PROPN
ejpam-4354	402	17	of	of	ADP
ejpam-4354	402	18	technology	technology	PROPN
ejpam-4354	402	19	,	,	PUNCT
ejpam-4354	402	20	philippines	philippine	NOUN
ejpam-4354	402	21	and	and	CCONJ
ejpam-4354	402	22	western	western	ADJ
ejpam-4354	402	23	mindanao	mindanao	PROPN
ejpam-4354	402	24	state	state	PROPN
ejpam-4354	402	25	university	university	PROPN
ejpam-4354	402	26	,	,	PUNCT
ejpam-4354	402	27	philippines	philippine	NOUN
ejpam-4354	402	28	for	for	ADP
ejpam-4354	402	29	the	the	DET
ejpam-4354	402	30	steadfast	steadfast	ADJ
ejpam-4354	402	31	support	support	NOUN
ejpam-4354	402	32	these	these	DET
ejpam-4354	402	33	institutions	institution	NOUN
ejpam-4354	402	34	have	have	AUX
ejpam-4354	402	35	afforded	afford	VERB
ejpam-4354	402	36	them	they	PRON
ejpam-4354	402	37	.	.	PUNCT
ejpam-4354	403	1	references	reference	NOUN
ejpam-4354	403	2	[	[	X
ejpam-4354	403	3	1	1	NUM
ejpam-4354	403	4	]	]	PUNCT
ejpam-4354	403	5	a.	a.	NOUN
ejpam-4354	403	6	gamorez	gamorez	NOUN
ejpam-4354	403	7	and	and	CCONJ
ejpam-4354	403	8	s.	s.	PROPN
ejpam-4354	403	9	canoy	canoy	PROPN
ejpam-4354	403	10	jr	jr	PROPN
ejpam-4354	403	11	.	.	PROPN
ejpam-4354	404	1	on	on	ADP
ejpam-4354	404	2	a	a	DET
ejpam-4354	404	3	topological	topological	ADJ
ejpam-4354	404	4	space	space	NOUN
ejpam-4354	404	5	generated	generate	VERB
ejpam-4354	404	6	by	by	ADP
ejpam-4354	404	7	monophonic	monophonic	ADJ
ejpam-4354	404	8	eccentric	eccentric	ADJ
ejpam-4354	404	9	neighborhoods	neighborhood	NOUN
ejpam-4354	404	10	of	of	ADP
ejpam-4354	404	11	a	a	DET
ejpam-4354	404	12	graph	graph	NOUN
ejpam-4354	404	13	.	.	PUNCT
ejpam-4354	404	14	eur	eur	PROPN
ejpam-4354	404	15	.	.	PUNCT
ejpam-4354	405	1	j.	j.	PROPN
ejpam-4354	405	2	pure	pure	PROPN
ejpam-4354	405	3	appl	appl	PROPN
ejpam-4354	405	4	.	.	PUNCT
ejpam-4354	405	5	math	math	PROPN
ejpam-4354	405	6	.	.	PUNCT
ejpam-4354	405	7	,	,	PUNCT
ejpam-4354	405	8	14(3):695–705	14(3):695–705	NUM
ejpam-4354	405	9	,	,	PUNCT
ejpam-4354	405	10	2021	2021	NUM
ejpam-4354	405	11	.	.	PUNCT
ejpam-4354	406	1	[	[	X
ejpam-4354	406	2	2	2	NUM
ejpam-4354	406	3	]	]	PUNCT
ejpam-4354	406	4	a.	a.	NOUN
ejpam-4354	406	5	gamorez	gamorez	NOUN
ejpam-4354	406	6	and	and	CCONJ
ejpam-4354	406	7	s.	s.	PROPN
ejpam-4354	406	8	canoy	canoy	PROPN
ejpam-4354	406	9	jr	jr	PROPN
ejpam-4354	406	10	.	.	PROPN
ejpam-4354	406	11	subbasic	subbasic	ADJ
ejpam-4354	406	12	open	open	ADJ
ejpam-4354	406	13	sets	set	NOUN
ejpam-4354	406	14	in	in	ADP
ejpam-4354	406	15	graphs	graph	NOUN
ejpam-4354	406	16	generated	generate	VERB
ejpam-4354	406	17	by	by	ADP
ejpam-4354	406	18	monophonic	monophonic	ADJ
ejpam-4354	406	19	eccentric	eccentric	ADJ
ejpam-4354	406	20	neighborhoods	neighborhood	NOUN
ejpam-4354	406	21	.	.	PUNCT
ejpam-4354	407	1	journal	journal	NOUN
ejpam-4354	407	2	of	of	ADP
ejpam-4354	407	3	discrete	discrete	ADJ
ejpam-4354	407	4	mathematical	mathematical	ADJ
ejpam-4354	407	5	sciences	science	NOUN
ejpam-4354	407	6	and	and	CCONJ
ejpam-4354	407	7	cryptography	cryptography	NOUN
ejpam-4354	407	8	,	,	PUNCT
ejpam-4354	407	9	24(7):1989–2000	24(7):1989–2000	NUM
ejpam-4354	407	10	,	,	PUNCT
ejpam-4354	407	11	2021	2021	NUM
ejpam-4354	407	12	.	.	PUNCT
ejpam-4354	408	1	[	[	X
ejpam-4354	408	2	3	3	NUM
ejpam-4354	408	3	]	]	PUNCT
ejpam-4354	408	4	a.	a.	NOUN
ejpam-4354	408	5	santhakumaran	santhakumaran	NOUN
ejpam-4354	408	6	and	and	CCONJ
ejpam-4354	408	7	p.	p.	PROPN
ejpam-4354	408	8	titus	titus	PROPN
ejpam-4354	408	9	.	.	PROPN
ejpam-4354	409	1	monophonic	monophonic	ADJ
ejpam-4354	409	2	distance	distance	NOUN
ejpam-4354	409	3	in	in	ADP
ejpam-4354	409	4	graphs	graph	NOUN
ejpam-4354	409	5	.	.	PUNCT
ejpam-4354	410	1	discrete	discrete	ADJ
ejpam-4354	410	2	mathematics	mathematic	NOUN
ejpam-4354	410	3	,	,	PUNCT
ejpam-4354	410	4	algorithms	algorithm	NOUN
ejpam-4354	410	5	and	and	CCONJ
ejpam-4354	410	6	applications	application	NOUN
ejpam-4354	410	7	,	,	PUNCT
ejpam-4354	410	8	3(2):159–169	3(2):159–169	NUM
ejpam-4354	410	9	,	,	PUNCT
ejpam-4354	410	10	2011	2011	NUM
ejpam-4354	410	11	.	.	PUNCT
ejpam-4354	411	1	[	[	X
ejpam-4354	411	2	4	4	NUM
ejpam-4354	411	3	]	]	X
ejpam-4354	411	4	a.p	a.p	PROPN
ejpam-4354	411	5	.	.	PROPN
ejpam-4354	411	6	santhakumaran	santhakumaran	PROPN
ejpam-4354	411	7	and	and	CCONJ
ejpam-4354	411	8	p.	p.	PROPN
ejpam-4354	411	9	titus	titus	PROPN
ejpam-4354	411	10	.	.	PUNCT
ejpam-4354	412	1	a	a	DET
ejpam-4354	412	2	note	note	NOUN
ejpam-4354	412	3	on	on	ADP
ejpam-4354	412	4	monophonic	monophonic	ADJ
ejpam-4354	412	5	distance	distance	NOUN
ejpam-4354	412	6	in	in	ADP
ejpam-4354	412	7	graphs	graph	NOUN
ejpam-4354	412	8	.	.	PUNCT
ejpam-4354	413	1	4	4	NUM
ejpam-4354	413	2	,	,	PUNCT
ejpam-4354	413	3	doi	doi	NOUN
ejpam-4354	413	4	:	:	PUNCT
ejpam-4354	413	5	10.1142	10.1142	NUM
ejpam-4354	413	6	/	/	SYM
ejpam-4354	413	7	s1793830912500188	s1793830912500188	NOUN
ejpam-4354	413	8	,	,	PUNCT
ejpam-4354	413	9	2012	2012	NUM
ejpam-4354	413	10	.	.	PUNCT
ejpam-4354	414	1	[	[	X
ejpam-4354	414	2	5	5	X
ejpam-4354	414	3	]	]	PUNCT
ejpam-4354	414	4	p.	p.	NOUN
ejpam-4354	414	5	titus	titus	PROPN
ejpam-4354	414	6	and	and	CCONJ
ejpam-4354	414	7	j.	j.	PROPN
ejpam-4354	414	8	fancy	fancy	PROPN
ejpam-4354	414	9	.	.	PUNCT
ejpam-4354	415	1	total	total	ADJ
ejpam-4354	415	2	monophonic	monophonic	ADJ
ejpam-4354	415	3	eccentric	eccentric	ADJ
ejpam-4354	415	4	domination	domination	NOUN
ejpam-4354	415	5	in	in	ADP
ejpam-4354	415	6	graphs	graph	NOUN
ejpam-4354	415	7	.	.	PUNCT
ejpam-4354	416	1	communicated	communicate	VERB
ejpam-4354	416	2	,	,	PUNCT
ejpam-4354	416	3	pages	page	NOUN
ejpam-4354	416	4	913–927	913–927	NUM
ejpam-4354	416	5	.	.	PUNCT
ejpam-4354	417	1	[	[	X
ejpam-4354	417	2	6	6	NUM
ejpam-4354	417	3	]	]	PUNCT
ejpam-4354	417	4	p.	p.	PROPN
ejpam-4354	417	5	titus	titus	PROPN
ejpam-4354	417	6	,	,	PUNCT
ejpam-4354	417	7	j.	j.	PROPN
ejpam-4354	417	8	fancy	fancy	PROPN
ejpam-4354	417	9	,	,	PUNCT
ejpam-4354	417	10	and	and	CCONJ
ejpam-4354	417	11	a.	a.	NOUN
ejpam-4354	417	12	santhakumaran	santhakumaran	PROPN
ejpam-4354	417	13	.	.	PUNCT
ejpam-4354	418	1	monophonic	monophonic	ADJ
ejpam-4354	418	2	eccentric	eccentric	ADJ
ejpam-4354	418	3	domination	domination	NOUN
ejpam-4354	418	4	in	in	ADP
ejpam-4354	418	5	graphs	graph	NOUN
ejpam-4354	418	6	.	.	PUNCT
ejpam-4354	419	1	communicated	communicate	VERB
ejpam-4354	419	2	.	.	PUNCT
ejpam-4354	420	1	[	[	X
ejpam-4354	420	2	7	7	X
ejpam-4354	420	3	]	]	X
ejpam-4354	420	4	p.	p.	PROPN
ejpam-4354	420	5	titus	titus	PROPN
ejpam-4354	420	6	,	,	PUNCT
ejpam-4354	420	7	j.	j.	PROPN
ejpam-4354	420	8	fancy	fancy	PROPN
ejpam-4354	420	9	,	,	PUNCT
ejpam-4354	420	10	and	and	CCONJ
ejpam-4354	420	11	a.	a.	NOUN
ejpam-4354	420	12	santhakumaran	santhakumaran	PROPN
ejpam-4354	420	13	.	.	PUNCT
ejpam-4354	421	1	monophonic	monophonic	ADJ
ejpam-4354	421	2	eccentric	eccentric	ADJ
ejpam-4354	421	3	domination	domination	NOUN
ejpam-4354	421	4	number	number	NOUN
ejpam-4354	421	5	of	of	ADP
ejpam-4354	421	6	corona	corona	NOUN
ejpam-4354	421	7	product	product	NOUN
ejpam-4354	421	8	of	of	ADP
ejpam-4354	421	9	complete	complete	ADJ
ejpam-4354	421	10	and	and	CCONJ
ejpam-4354	421	11	complete	complete	ADJ
ejpam-4354	421	12	bipartite	bipartite	NOUN
ejpam-4354	421	13	graphs	graph	NOUN
ejpam-4354	421	14	with	with	ADP
ejpam-4354	421	15	some	some	DET
ejpam-4354	421	16	standard	standard	ADJ
ejpam-4354	421	17	graphs	graph	NOUN
ejpam-4354	421	18	.	.	PUNCT
ejpam-4354	422	1	caribbean	caribbean	ADJ
ejpam-4354	422	2	journal	journal	PROPN
ejpam-4354	422	3	of	of	ADP
ejpam-4354	422	4	science	science	NOUN
ejpam-4354	422	5	,	,	PUNCT
ejpam-4354	422	6	53(2):723–737	53(2):723–737	PROPN
ejpam-4354	422	7	,	,	PUNCT
ejpam-4354	422	8	2019	2019	NUM
ejpam-4354	422	9	.	.	PUNCT