id	sid	tid	token	lemma	pos
ejpam-5213	1	1	european	european	PROPN
ejpam-5213	1	2	journal	journal	PROPN
ejpam-5213	1	3	of	of	ADP
ejpam-5213	1	4	pure	pure	ADJ
ejpam-5213	1	5	and	and	CCONJ
ejpam-5213	1	6	applied	apply	VERB
ejpam-5213	1	7	mathematics	mathematic	NOUN
ejpam-5213	1	8	vol	vol	NOUN
ejpam-5213	1	9	.	.	PROPN
ejpam-5213	2	1	17	17	NUM
ejpam-5213	2	2	,	,	PUNCT
ejpam-5213	2	3	no	no	INTJ
ejpam-5213	2	4	.	.	NOUN
ejpam-5213	2	5	3	3	NUM
ejpam-5213	2	6	,	,	PUNCT
ejpam-5213	2	7	2024	2024	NUM
ejpam-5213	2	8	,	,	PUNCT
ejpam-5213	2	9	1585	1585	NUM
ejpam-5213	2	10	-	-	SYM
ejpam-5213	2	11	1601	1601	NUM
ejpam-5213	2	12	issn	issn	PROPN
ejpam-5213	2	13	1307	1307	NUM
ejpam-5213	2	14	-	-	SYM
ejpam-5213	2	15	5543	5543	NUM
ejpam-5213	2	16	–	–	PUNCT
ejpam-5213	2	17	ejpam.com	ejpam.com	X
ejpam-5213	2	18	published	publish	VERB
ejpam-5213	2	19	by	by	ADP
ejpam-5213	2	20	new	new	PROPN
ejpam-5213	2	21	york	york	PROPN
ejpam-5213	2	22	business	business	PROPN
ejpam-5213	2	23	global	global	ADJ
ejpam-5213	2	24	differentiating	differentiate	VERB
ejpam-5213	2	25	odd	odd	ADJ
ejpam-5213	2	26	dominating	dominating	NOUN
ejpam-5213	2	27	sets	set	NOUN
ejpam-5213	2	28	in	in	ADP
ejpam-5213	2	29	graphs	graph	NOUN
ejpam-5213	2	30	mary	mary	PROPN
ejpam-5213	2	31	ann	ann	PROPN
ejpam-5213	2	32	a.	a.	PROPN
ejpam-5213	2	33	carbero1∗	carbero1∗	PROPN
ejpam-5213	2	34	,	,	PUNCT
ejpam-5213	2	35	gina	gina	PROPN
ejpam-5213	2	36	a.	a.	PROPN
ejpam-5213	2	37	malacas1,2	malacas1,2	PROPN
ejpam-5213	2	38	,	,	PUNCT
ejpam-5213	2	39	sergio	sergio	PROPN
ejpam-5213	2	40	r.	r.	PROPN
ejpam-5213	2	41	canoy	canoy	PROPN
ejpam-5213	2	42	,	,	PUNCT
ejpam-5213	2	43	jr.1,2	jr.1,2	ADJ
ejpam-5213	2	44	1	1	NUM
ejpam-5213	2	45	department	department	NOUN
ejpam-5213	2	46	of	of	ADP
ejpam-5213	2	47	mathematics	mathematic	NOUN
ejpam-5213	2	48	and	and	CCONJ
ejpam-5213	2	49	statistics	statistic	NOUN
ejpam-5213	2	50	,	,	PUNCT
ejpam-5213	2	51	college	college	NOUN
ejpam-5213	2	52	of	of	ADP
ejpam-5213	2	53	science	science	NOUN
ejpam-5213	2	54	and	and	CCONJ
ejpam-5213	2	55	mathematics	mathematic	NOUN
ejpam-5213	2	56	,	,	PUNCT
ejpam-5213	2	57	msu	msu	PROPN
ejpam-5213	2	58	-	-	PUNCT
ejpam-5213	2	59	iligan	iligan	PROPN
ejpam-5213	2	60	institute	institute	PROPN
ejpam-5213	2	61	of	of	ADP
ejpam-5213	2	62	technology	technology	PROPN
ejpam-5213	2	63	,	,	PUNCT
ejpam-5213	2	64	9200	9200	NUM
ejpam-5213	2	65	iligan	iligan	ADJ
ejpam-5213	2	66	city	city	NOUN
ejpam-5213	2	67	,	,	PUNCT
ejpam-5213	2	68	philippines	philippine	NOUN
ejpam-5213	2	69	2	2	NUM
ejpam-5213	2	70	center	center	NOUN
ejpam-5213	2	71	for	for	ADP
ejpam-5213	2	72	mathematical	mathematical	ADJ
ejpam-5213	2	73	and	and	CCONJ
ejpam-5213	2	74	theoretical	theoretical	ADJ
ejpam-5213	2	75	physical	physical	ADJ
ejpam-5213	2	76	sciences	science	NOUN
ejpam-5213	2	77	,	,	PUNCT
ejpam-5213	2	78	premier	premier	PROPN
ejpam-5213	2	79	research	research	PROPN
ejpam-5213	2	80	institute	institute	PROPN
ejpam-5213	2	81	of	of	ADP
ejpam-5213	2	82	science	science	NOUN
ejpam-5213	2	83	and	and	CCONJ
ejpam-5213	2	84	mathematics	mathematic	NOUN
ejpam-5213	2	85	,	,	PUNCT
ejpam-5213	2	86	msu	msu	PROPN
ejpam-5213	2	87	-	-	PUNCT
ejpam-5213	2	88	iligan	iligan	PROPN
ejpam-5213	2	89	institute	institute	PROPN
ejpam-5213	2	90	of	of	ADP
ejpam-5213	2	91	technology	technology	PROPN
ejpam-5213	2	92	,	,	PUNCT
ejpam-5213	2	93	9200	9200	NUM
ejpam-5213	2	94	iligan	iligan	ADJ
ejpam-5213	2	95	city	city	NOUN
ejpam-5213	2	96	,	,	PUNCT
ejpam-5213	2	97	philippines	philippine	NOUN
ejpam-5213	2	98	abstract	abstract	ADJ
ejpam-5213	2	99	.	.	PUNCT
ejpam-5213	3	1	let	let	VERB
ejpam-5213	3	2	g	g	PROPN
ejpam-5213	3	3	=	=	SYM
ejpam-5213	3	4	(	(	PUNCT
ejpam-5213	3	5	v	v	NOUN
ejpam-5213	3	6	(	(	PUNCT
ejpam-5213	3	7	g	g	NOUN
ejpam-5213	3	8	)	)	PUNCT
ejpam-5213	3	9	,	,	PUNCT
ejpam-5213	3	10	e(g	e(g	PROPN
ejpam-5213	3	11	)	)	PUNCT
ejpam-5213	3	12	)	)	PUNCT
ejpam-5213	4	1	be	be	AUX
ejpam-5213	4	2	a	a	DET
ejpam-5213	4	3	simple	simple	ADJ
ejpam-5213	4	4	and	and	CCONJ
ejpam-5213	4	5	undirected	undirected	ADJ
ejpam-5213	4	6	graph	graph	NOUN
ejpam-5213	4	7	.	.	PUNCT
ejpam-5213	5	1	a	a	DET
ejpam-5213	5	2	dominating	dominating	NOUN
ejpam-5213	5	3	set	set	NOUN
ejpam-5213	5	4	s	s	PROPN
ejpam-5213	5	5	⊆	⊆	NUM
ejpam-5213	5	6	v	v	NOUN
ejpam-5213	5	7	(	(	PUNCT
ejpam-5213	5	8	g	g	NOUN
ejpam-5213	5	9	)	)	PUNCT
ejpam-5213	5	10	is	be	AUX
ejpam-5213	5	11	called	call	VERB
ejpam-5213	5	12	a	a	DET
ejpam-5213	5	13	differentiating	differentiate	VERB
ejpam-5213	5	14	odd	odd	ADJ
ejpam-5213	5	15	dominating	dominating	NOUN
ejpam-5213	5	16	set	set	VERB
ejpam-5213	5	17	if	if	SCONJ
ejpam-5213	5	18	for	for	ADP
ejpam-5213	5	19	every	every	DET
ejpam-5213	5	20	vertex	vertex	NOUN
ejpam-5213	5	21	v	v	ADP
ejpam-5213	5	22	∈	∈	NOUN
ejpam-5213	5	23	v	v	NOUN
ejpam-5213	5	24	(	(	PUNCT
ejpam-5213	5	25	g	g	NOUN
ejpam-5213	5	26	)	)	PUNCT
ejpam-5213	5	27	,	,	PUNCT
ejpam-5213	5	28	|n	|n	X
ejpam-5213	6	1	[	[	X
ejpam-5213	6	2	v	v	X
ejpam-5213	6	3	]	]	X
ejpam-5213	6	4	∩	∩	NOUN
ejpam-5213	6	5	s|	s|	NOUN
ejpam-5213	6	6	≡	≡	PROPN
ejpam-5213	6	7	1(mod	1(mod	NUM
ejpam-5213	6	8	2	2	NUM
ejpam-5213	6	9	)	)	PUNCT
ejpam-5213	6	10	and	and	CCONJ
ejpam-5213	6	11	ng[u	ng[u	PROPN
ejpam-5213	6	12	]	]	X
ejpam-5213	6	13	∩	∩	PROPN
ejpam-5213	6	14	s	s	PART
ejpam-5213	6	15	̸=	̸=	PROPN
ejpam-5213	6	16	ng[v	ng[v	X
ejpam-5213	6	17	]	]	X
ejpam-5213	6	18	∩	∩	PROPN
ejpam-5213	6	19	s	s	PART
ejpam-5213	6	20	for	for	ADP
ejpam-5213	6	21	every	every	DET
ejpam-5213	6	22	two	two	NUM
ejpam-5213	6	23	distinct	distinct	ADJ
ejpam-5213	6	24	vertices	vertex	NOUN
ejpam-5213	6	25	u	u	NOUN
ejpam-5213	6	26	and	and	CCONJ
ejpam-5213	6	27	v	v	NOUN
ejpam-5213	6	28	in	in	ADP
ejpam-5213	6	29	v	v	NOUN
ejpam-5213	6	30	(	(	PUNCT
ejpam-5213	6	31	g	g	NOUN
ejpam-5213	6	32	)	)	PUNCT
ejpam-5213	6	33	.	.	PUNCT
ejpam-5213	7	1	the	the	DET
ejpam-5213	7	2	minimum	minimum	ADJ
ejpam-5213	7	3	cardinality	cardinality	NOUN
ejpam-5213	7	4	of	of	ADP
ejpam-5213	7	5	a	a	DET
ejpam-5213	7	6	differentiating	differentiate	VERB
ejpam-5213	7	7	odd	odd	ADJ
ejpam-5213	7	8	dominating	dominating	NOUN
ejpam-5213	7	9	set	set	NOUN
ejpam-5213	7	10	of	of	ADP
ejpam-5213	7	11	g	g	NOUN
ejpam-5213	7	12	,	,	PUNCT
ejpam-5213	7	13	denoted	denote	VERB
ejpam-5213	7	14	by	by	ADP
ejpam-5213	7	15	γo	γo	PROPN
ejpam-5213	7	16	d(g	d(g	PROPN
ejpam-5213	7	17	)	)	PUNCT
ejpam-5213	7	18	,	,	PUNCT
ejpam-5213	7	19	is	be	AUX
ejpam-5213	7	20	called	call	VERB
ejpam-5213	7	21	the	the	DET
ejpam-5213	7	22	differentiating	differentiate	VERB
ejpam-5213	7	23	odd	odd	ADJ
ejpam-5213	7	24	domination	domination	NOUN
ejpam-5213	7	25	number	number	NOUN
ejpam-5213	7	26	.	.	PUNCT
ejpam-5213	8	1	in	in	ADP
ejpam-5213	8	2	this	this	DET
ejpam-5213	8	3	paper	paper	NOUN
ejpam-5213	8	4	,	,	PUNCT
ejpam-5213	8	5	we	we	PRON
ejpam-5213	8	6	discuss	discuss	VERB
ejpam-5213	8	7	differentiating	differentiate	VERB
ejpam-5213	8	8	odd	odd	ADJ
ejpam-5213	8	9	dominating	dominating	NOUN
ejpam-5213	8	10	sets	set	NOUN
ejpam-5213	8	11	and	and	CCONJ
ejpam-5213	8	12	give	give	VERB
ejpam-5213	8	13	bounds	bound	NOUN
ejpam-5213	8	14	or	or	CCONJ
ejpam-5213	8	15	exact	exact	ADJ
ejpam-5213	8	16	values	value	NOUN
ejpam-5213	8	17	of	of	ADP
ejpam-5213	8	18	the	the	DET
ejpam-5213	8	19	differentiating	differentiate	VERB
ejpam-5213	8	20	odd	odd	ADJ
ejpam-5213	8	21	domination	domination	NOUN
ejpam-5213	8	22	numbers	number	NOUN
ejpam-5213	8	23	of	of	ADP
ejpam-5213	8	24	some	some	DET
ejpam-5213	8	25	graphs	graph	NOUN
ejpam-5213	8	26	.	.	PUNCT
ejpam-5213	9	1	we	we	PRON
ejpam-5213	9	2	give	give	VERB
ejpam-5213	9	3	necessary	necessary	ADJ
ejpam-5213	9	4	and	and	CCONJ
ejpam-5213	9	5	sufficient	sufficient	ADJ
ejpam-5213	9	6	conditions	condition	NOUN
ejpam-5213	9	7	for	for	SCONJ
ejpam-5213	9	8	some	some	DET
ejpam-5213	9	9	graphs	graph	NOUN
ejpam-5213	9	10	to	to	PART
ejpam-5213	9	11	admit	admit	VERB
ejpam-5213	9	12	a	a	DET
ejpam-5213	9	13	differentiating	differentiate	VERB
ejpam-5213	9	14	odd	odd	ADJ
ejpam-5213	9	15	dominating	dominating	NOUN
ejpam-5213	9	16	set	set	NOUN
ejpam-5213	9	17	.	.	PUNCT
ejpam-5213	10	1	moreover	moreover	ADV
ejpam-5213	10	2	,	,	PUNCT
ejpam-5213	10	3	we	we	PRON
ejpam-5213	10	4	characterize	characterize	VERB
ejpam-5213	10	5	the	the	DET
ejpam-5213	10	6	differentiating	differentiate	VERB
ejpam-5213	10	7	odd	odd	ADJ
ejpam-5213	10	8	dominating	dominating	NOUN
ejpam-5213	10	9	sets	set	NOUN
ejpam-5213	10	10	in	in	ADP
ejpam-5213	10	11	graphs	graph	NOUN
ejpam-5213	10	12	resulting	result	VERB
ejpam-5213	10	13	from	from	ADP
ejpam-5213	10	14	join	join	NOUN
ejpam-5213	10	15	,	,	PUNCT
ejpam-5213	10	16	corona	corona	PROPN
ejpam-5213	10	17	,	,	PUNCT
ejpam-5213	10	18	and	and	CCONJ
ejpam-5213	10	19	lexicographic	lexicographic	ADJ
ejpam-5213	10	20	product	product	NOUN
ejpam-5213	10	21	of	of	ADP
ejpam-5213	10	22	some	some	DET
ejpam-5213	10	23	graphs	graph	NOUN
ejpam-5213	10	24	and	and	CCONJ
ejpam-5213	10	25	determine	determine	VERB
ejpam-5213	10	26	the	the	DET
ejpam-5213	10	27	differentiating	differentiate	VERB
ejpam-5213	10	28	odd	odd	ADJ
ejpam-5213	10	29	domination	domination	NOUN
ejpam-5213	10	30	numbers	number	NOUN
ejpam-5213	10	31	of	of	ADP
ejpam-5213	10	32	these	these	DET
ejpam-5213	10	33	graphs	graph	NOUN
ejpam-5213	10	34	.	.	PUNCT
ejpam-5213	11	1	2020	2020	NUM
ejpam-5213	11	2	mathematics	mathematic	NOUN
ejpam-5213	11	3	subject	subject	NOUN
ejpam-5213	11	4	classifications	classification	NOUN
ejpam-5213	11	5	:	:	PUNCT
ejpam-5213	11	6	05c69	05c69	X
ejpam-5213	11	7	key	key	ADJ
ejpam-5213	11	8	words	word	NOUN
ejpam-5213	11	9	and	and	CCONJ
ejpam-5213	11	10	phrases	phrase	NOUN
ejpam-5213	11	11	:	:	PUNCT
ejpam-5213	11	12	differentiating	differentiate	VERB
ejpam-5213	11	13	,	,	PUNCT
ejpam-5213	11	14	domination	domination	NOUN
ejpam-5213	11	15	,	,	PUNCT
ejpam-5213	11	16	odd	odd	ADJ
ejpam-5213	11	17	dominating	dominating	NOUN
ejpam-5213	11	18	,	,	PUNCT
ejpam-5213	11	19	differentiating	differentiate	VERB
ejpam-5213	11	20	-	-	PUNCT
ejpam-5213	11	21	dominating	dominating	NOUN
ejpam-5213	11	22	,	,	PUNCT
ejpam-5213	11	23	differentiating	differentiate	VERB
ejpam-5213	11	24	odd	odd	ADJ
ejpam-5213	11	25	dominating	dominating	NOUN
ejpam-5213	11	26	1	1	NUM
ejpam-5213	11	27	.	.	PUNCT
ejpam-5213	12	1	introduction	introduction	NOUN
ejpam-5213	12	2	domination	domination	NOUN
ejpam-5213	12	3	is	be	AUX
ejpam-5213	12	4	one	one	NUM
ejpam-5213	12	5	of	of	ADP
ejpam-5213	12	6	the	the	DET
ejpam-5213	12	7	most	most	ADV
ejpam-5213	12	8	explored	explore	VERB
ejpam-5213	12	9	areas	area	NOUN
ejpam-5213	12	10	in	in	ADP
ejpam-5213	12	11	graph	graph	NOUN
ejpam-5213	12	12	theory	theory	NOUN
ejpam-5213	12	13	.	.	PUNCT
ejpam-5213	13	1	indeed	indeed	ADV
ejpam-5213	13	2	,	,	PUNCT
ejpam-5213	13	3	numerous	numerous	ADJ
ejpam-5213	13	4	variations	variation	NOUN
ejpam-5213	13	5	of	of	ADP
ejpam-5213	13	6	domination	domination	NOUN
ejpam-5213	13	7	have	have	AUX
ejpam-5213	13	8	been	be	AUX
ejpam-5213	13	9	introduced	introduce	VERB
ejpam-5213	13	10	and	and	CCONJ
ejpam-5213	13	11	investigated	investigate	VERB
ejpam-5213	13	12	from	from	ADP
ejpam-5213	13	13	various	various	ADJ
ejpam-5213	13	14	perspectives	perspective	NOUN
ejpam-5213	13	15	and	and	CCONJ
ejpam-5213	13	16	approaches	approach	NOUN
ejpam-5213	13	17	(	(	PUNCT
ejpam-5213	13	18	see	see	VERB
ejpam-5213	13	19	[	[	X
ejpam-5213	13	20	1	1	NUM
ejpam-5213	13	21	]	]	PUNCT
ejpam-5213	13	22	,	,	PUNCT
ejpam-5213	13	23	[	[	X
ejpam-5213	13	24	2	2	NUM
ejpam-5213	13	25	]	]	PUNCT
ejpam-5213	13	26	,	,	PUNCT
ejpam-5213	13	27	[	[	X
ejpam-5213	13	28	5	5	NUM
ejpam-5213	13	29	]	]	PUNCT
ejpam-5213	13	30	,	,	PUNCT
ejpam-5213	13	31	[	[	X
ejpam-5213	13	32	7	7	NUM
ejpam-5213	13	33	]	]	PUNCT
ejpam-5213	13	34	,	,	PUNCT
ejpam-5213	13	35	[	[	X
ejpam-5213	13	36	10	10	NUM
ejpam-5213	13	37	]	]	PUNCT
ejpam-5213	13	38	,	,	PUNCT
ejpam-5213	13	39	[	[	X
ejpam-5213	13	40	13	13	NUM
ejpam-5213	13	41	]	]	PUNCT
ejpam-5213	13	42	,	,	PUNCT
ejpam-5213	13	43	[	[	X
ejpam-5213	13	44	14	14	NUM
ejpam-5213	13	45	]	]	PUNCT
ejpam-5213	13	46	,	,	PUNCT
ejpam-5213	13	47	and	and	CCONJ
ejpam-5213	13	48	[	[	X
ejpam-5213	13	49	18	18	NUM
ejpam-5213	13	50	]	]	NUM
ejpam-5213	13	51	)	)	PUNCT
ejpam-5213	13	52	.	.	PUNCT
ejpam-5213	14	1	one	one	NUM
ejpam-5213	14	2	prominent	prominent	ADJ
ejpam-5213	14	3	area	area	NOUN
ejpam-5213	14	4	of	of	ADP
ejpam-5213	14	5	research	research	NOUN
ejpam-5213	14	6	in	in	ADP
ejpam-5213	14	7	this	this	DET
ejpam-5213	14	8	domain	domain	NOUN
ejpam-5213	14	9	is	be	AUX
ejpam-5213	14	10	the	the	DET
ejpam-5213	14	11	investigation	investigation	NOUN
ejpam-5213	14	12	of	of	ADP
ejpam-5213	14	13	differentiating	differentiate	VERB
ejpam-5213	14	14	-	-	PUNCT
ejpam-5213	14	15	dominating	dominating	NOUN
ejpam-5213	14	16	sets	set	NOUN
ejpam-5213	14	17	in	in	ADP
ejpam-5213	14	18	graphs	graph	NOUN
ejpam-5213	14	19	,	,	PUNCT
ejpam-5213	14	20	which	which	PRON
ejpam-5213	14	21	are	be	AUX
ejpam-5213	14	22	alternatively	alternatively	ADV
ejpam-5213	14	23	referred	refer	VERB
ejpam-5213	14	24	to	to	ADP
ejpam-5213	14	25	as	as	ADP
ejpam-5213	14	26	identifying	identify	VERB
ejpam-5213	14	27	codes	code	NOUN
ejpam-5213	14	28	in	in	ADP
ejpam-5213	14	29	certain	certain	ADJ
ejpam-5213	14	30	contexts	context	NOUN
ejpam-5213	14	31	.	.	PUNCT
ejpam-5213	15	1	this	this	DET
ejpam-5213	15	2	research	research	NOUN
ejpam-5213	15	3	has	have	VERB
ejpam-5213	15	4	roots	root	NOUN
ejpam-5213	15	5	dating	date	VERB
ejpam-5213	15	6	back	back	ADV
ejpam-5213	15	7	to	to	ADP
ejpam-5213	15	8	1998	1998	NUM
ejpam-5213	15	9	when	when	SCONJ
ejpam-5213	15	10	karpovsky	karpovsky	PROPN
ejpam-5213	15	11	,	,	PUNCT
ejpam-5213	15	12	chakrabarty	chakrabarty	NOUN
ejpam-5213	15	13	,	,	PUNCT
ejpam-5213	15	14	and	and	CCONJ
ejpam-5213	15	15	levitin	levitin	NOUN
ejpam-5213	15	16	introduced	introduce	VERB
ejpam-5213	15	17	identifying	identify	VERB
ejpam-5213	15	18	codes	code	NOUN
ejpam-5213	15	19	(	(	PUNCT
ejpam-5213	15	20	see	see	VERB
ejpam-5213	15	21	[	[	X
ejpam-5213	15	22	4	4	NUM
ejpam-5213	15	23	]	]	PUNCT
ejpam-5213	15	24	)	)	PUNCT
ejpam-5213	15	25	and	and	CCONJ
ejpam-5213	15	26	have	have	AUX
ejpam-5213	15	27	been	be	AUX
ejpam-5213	15	28	investigated	investigate	VERB
ejpam-5213	15	29	further	far	ADV
ejpam-5213	15	30	by	by	ADP
ejpam-5213	15	31	frick	frick	PROPN
ejpam-5213	15	32	et	et	PROPN
ejpam-5213	15	33	al	al	PROPN
ejpam-5213	15	34	in	in	ADP
ejpam-5213	15	35	2008	2008	NUM
ejpam-5213	15	36	(	(	PUNCT
ejpam-5213	15	37	see	see	VERB
ejpam-5213	15	38	[	[	X
ejpam-5213	15	39	6	6	NUM
ejpam-5213	15	40	]	]	NUM
ejpam-5213	15	41	)	)	PUNCT
ejpam-5213	15	42	.	.	PUNCT
ejpam-5213	16	1	furthermore	furthermore	ADV
ejpam-5213	16	2	,	,	PUNCT
ejpam-5213	16	3	in	in	ADP
ejpam-5213	16	4	the	the	DET
ejpam-5213	16	5	study	study	NOUN
ejpam-5213	16	6	of	of	ADP
ejpam-5213	16	7	canoy	canoy	NOUN
ejpam-5213	16	8	and	and	CCONJ
ejpam-5213	16	9	malacas	malacas	NOUN
ejpam-5213	16	10	[	[	X
ejpam-5213	16	11	12	12	NUM
ejpam-5213	16	12	]	]	PUNCT
ejpam-5213	16	13	,	,	PUNCT
ejpam-5213	16	14	they	they	PRON
ejpam-5213	16	15	characterized	characterize	VERB
ejpam-5213	16	16	the	the	DET
ejpam-5213	16	17	differentiating	differentiate	VERB
ejpam-5213	16	18	-	-	PUNCT
ejpam-5213	16	19	dominating	dominating	NOUN
ejpam-5213	16	20	sets	set	NOUN
ejpam-5213	16	21	in	in	ADP
ejpam-5213	16	22	the	the	DET
ejpam-5213	16	23	join	join	NOUN
ejpam-5213	16	24	,	,	PUNCT
ejpam-5213	16	25	corona	corona	PROPN
ejpam-5213	16	26	,	,	PUNCT
ejpam-5213	16	27	and	and	CCONJ
ejpam-5213	16	28	lexicographic	lexicographic	ADJ
ejpam-5213	16	29	product	product	NOUN
ejpam-5213	16	30	of	of	ADP
ejpam-5213	16	31	∗corresponding	∗corresponde	VERB
ejpam-5213	16	32	author	author	NOUN
ejpam-5213	16	33	.	.	PUNCT
ejpam-5213	17	1	doi	doi	NOUN
ejpam-5213	17	2	:	:	PUNCT
ejpam-5213	17	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5213	https://doi.org/10.29020/nybg.ejpam.v17i3.5213	DET
ejpam-5213	17	4	email	email	NOUN
ejpam-5213	17	5	addresses	address	VERB
ejpam-5213	17	6	:	:	PUNCT
ejpam-5213	17	7	maryann.carbero@g.msuiit.edu.ph	maryann.carbero@g.msuiit.edu.ph	ADV
ejpam-5213	17	8	(	(	PUNCT
ejpam-5213	17	9	m.	m.	NOUN
ejpam-5213	17	10	carbero	carbero	PROPN
ejpam-5213	17	11	)	)	PUNCT
ejpam-5213	17	12	,	,	PUNCT
ejpam-5213	17	13	gina.malacas@g.msuiit.edu.ph	gina.malacas@g.msuiit.edu.ph	PROPN
ejpam-5213	17	14	(	(	PUNCT
ejpam-5213	17	15	g.	g.	PROPN
ejpam-5213	17	16	malacas	malacas	PROPN
ejpam-5213	17	17	)	)	PUNCT
ejpam-5213	17	18	,	,	PUNCT
ejpam-5213	17	19	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-5213	17	20	(	(	PUNCT
ejpam-5213	17	21	s.	s.	PROPN
ejpam-5213	17	22	canoy	canoy	PROPN
ejpam-5213	17	23	)	)	PUNCT
ejpam-5213	17	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5213	17	25	1585	1585	NUM
ejpam-5213	17	26	©	©	PROPN
ejpam-5213	17	27	2024	2024	NUM
ejpam-5213	17	28	ejpam	ejpam	NOUN
ejpam-5213	17	29	all	all	DET
ejpam-5213	17	30	rights	right	NOUN
ejpam-5213	17	31	reserved	reserve	VERB
ejpam-5213	17	32	.	.	PUNCT
ejpam-5213	18	1	m.	m.	NOUN
ejpam-5213	18	2	carbero	carbero	PROPN
ejpam-5213	18	3	,	,	PUNCT
ejpam-5213	18	4	g.	g.	PROPN
ejpam-5213	18	5	malacas	malacas	PROPN
ejpam-5213	18	6	,	,	PUNCT
ejpam-5213	18	7	s.	s.	PROPN
ejpam-5213	18	8	canoy	canoy	PROPN
ejpam-5213	18	9	,	,	PUNCT
ejpam-5213	18	10	jr	jr	PROPN
ejpam-5213	18	11	.	.	PROPN
ejpam-5213	18	12	/	/	SYM
ejpam-5213	18	13	eur	eur	PROPN
ejpam-5213	18	14	.	.	PUNCT
ejpam-5213	19	1	j.	j.	PROPN
ejpam-5213	19	2	pure	pure	PROPN
ejpam-5213	19	3	appl	appl	PROPN
ejpam-5213	19	4	.	.	PROPN
ejpam-5213	19	5	math	math	PROPN
ejpam-5213	19	6	,	,	PUNCT
ejpam-5213	19	7	17	17	NUM
ejpam-5213	19	8	(	(	PUNCT
ejpam-5213	19	9	3	3	NUM
ejpam-5213	19	10	)	)	PUNCT
ejpam-5213	19	11	(	(	PUNCT
ejpam-5213	19	12	2024	2024	NUM
ejpam-5213	19	13	)	)	PUNCT
ejpam-5213	19	14	,	,	PUNCT
ejpam-5213	19	15	1585	1585	NUM
ejpam-5213	19	16	-	-	SYM
ejpam-5213	19	17	1601	1601	NUM
ejpam-5213	19	18	1586	1586	NUM
ejpam-5213	19	19	graphs	graph	NOUN
ejpam-5213	19	20	and	and	CCONJ
ejpam-5213	19	21	determined	determine	VERB
ejpam-5213	19	22	the	the	DET
ejpam-5213	19	23	bounds	bound	NOUN
ejpam-5213	19	24	or	or	CCONJ
ejpam-5213	19	25	the	the	DET
ejpam-5213	19	26	exact	exact	ADJ
ejpam-5213	19	27	differentiating	differentiating	NOUN
ejpam-5213	19	28	-	-	PUNCT
ejpam-5213	19	29	domination	domination	NOUN
ejpam-5213	19	30	numbers	number	NOUN
ejpam-5213	19	31	of	of	ADP
ejpam-5213	19	32	the	the	DET
ejpam-5213	19	33	aforementioned	aforementioned	ADJ
ejpam-5213	19	34	graphs	graph	NOUN
ejpam-5213	19	35	.	.	PUNCT
ejpam-5213	20	1	other	other	ADJ
ejpam-5213	20	2	studies	study	NOUN
ejpam-5213	20	3	related	relate	VERB
ejpam-5213	20	4	to	to	ADP
ejpam-5213	20	5	the	the	DET
ejpam-5213	20	6	topic	topic	NOUN
ejpam-5213	20	7	can	can	AUX
ejpam-5213	20	8	be	be	AUX
ejpam-5213	20	9	found	find	VERB
ejpam-5213	20	10	in	in	ADP
ejpam-5213	20	11	[	[	X
ejpam-5213	20	12	8	8	NUM
ejpam-5213	20	13	]	]	PUNCT
ejpam-5213	20	14	,	,	PUNCT
ejpam-5213	20	15	[	[	X
ejpam-5213	20	16	9	9	NUM
ejpam-5213	20	17	]	]	PUNCT
ejpam-5213	20	18	,	,	PUNCT
ejpam-5213	20	19	[	[	X
ejpam-5213	20	20	11	11	NUM
ejpam-5213	20	21	]	]	PUNCT
ejpam-5213	20	22	,	,	PUNCT
ejpam-5213	20	23	[	[	X
ejpam-5213	20	24	15	15	NUM
ejpam-5213	20	25	]	]	PUNCT
ejpam-5213	20	26	,	,	PUNCT
ejpam-5213	20	27	[	[	X
ejpam-5213	20	28	16	16	NUM
ejpam-5213	20	29	]	]	PUNCT
ejpam-5213	20	30	,	,	PUNCT
ejpam-5213	20	31	and	and	CCONJ
ejpam-5213	20	32	[	[	X
ejpam-5213	20	33	17	17	NUM
ejpam-5213	20	34	]	]	PUNCT
ejpam-5213	20	35	.	.	PUNCT
ejpam-5213	21	1	in	in	ADP
ejpam-5213	21	2	1989	1989	NUM
ejpam-5213	21	3	,	,	PUNCT
ejpam-5213	21	4	sutner	sutner	NOUN
ejpam-5213	21	5	introduced	introduce	VERB
ejpam-5213	21	6	the	the	DET
ejpam-5213	21	7	concept	concept	NOUN
ejpam-5213	21	8	of	of	ADP
ejpam-5213	21	9	odd	odd	ADJ
ejpam-5213	21	10	dominating	dominating	NOUN
ejpam-5213	21	11	set	set	VERB
ejpam-5213	21	12	under	under	ADP
ejpam-5213	21	13	the	the	DET
ejpam-5213	21	14	name	name	NOUN
ejpam-5213	21	15	“	"	PUNCT
ejpam-5213	21	16	odd	odd	ADJ
ejpam-5213	21	17	-	-	PUNCT
ejpam-5213	21	18	parity	parity	NOUN
ejpam-5213	21	19	cover	cover	NOUN
ejpam-5213	21	20	”	"	PUNCT
ejpam-5213	21	21	(	(	PUNCT
ejpam-5213	21	22	see	see	VERB
ejpam-5213	21	23	[	[	X
ejpam-5213	21	24	19	19	NUM
ejpam-5213	21	25	]	]	NUM
ejpam-5213	21	26	)	)	PUNCT
ejpam-5213	21	27	.	.	PUNCT
ejpam-5213	22	1	specifically	specifically	ADV
ejpam-5213	22	2	,	,	PUNCT
ejpam-5213	22	3	he	he	PRON
ejpam-5213	22	4	showed	show	VERB
ejpam-5213	22	5	that	that	SCONJ
ejpam-5213	22	6	every	every	DET
ejpam-5213	22	7	graph	graph	NOUN
ejpam-5213	22	8	contains	contain	VERB
ejpam-5213	22	9	odd	odd	ADJ
ejpam-5213	22	10	dominating	dominating	NOUN
ejpam-5213	22	11	set	set	VERB
ejpam-5213	22	12	in	in	ADP
ejpam-5213	22	13	the	the	DET
ejpam-5213	22	14	context	context	NOUN
ejpam-5213	22	15	of	of	ADP
ejpam-5213	22	16	cellular	cellular	ADJ
ejpam-5213	22	17	automata	automata	NOUN
ejpam-5213	22	18	(	(	PUNCT
ejpam-5213	22	19	see	see	VERB
ejpam-5213	22	20	[	[	X
ejpam-5213	22	21	19	19	NUM
ejpam-5213	22	22	]	]	NUM
ejpam-5213	22	23	)	)	PUNCT
ejpam-5213	22	24	.	.	PUNCT
ejpam-5213	23	1	however	however	ADV
ejpam-5213	23	2	,	,	PUNCT
ejpam-5213	23	3	this	this	DET
ejpam-5213	23	4	parameter	parameter	NOUN
ejpam-5213	23	5	has	have	AUX
ejpam-5213	23	6	been	be	AUX
ejpam-5213	23	7	studied	study	VERB
ejpam-5213	23	8	very	very	ADV
ejpam-5213	23	9	little	little	ADJ
ejpam-5213	23	10	.	.	PUNCT
ejpam-5213	24	1	previous	previous	ADJ
ejpam-5213	24	2	studies	study	NOUN
ejpam-5213	24	3	on	on	ADP
ejpam-5213	24	4	parity	parity	NOUN
ejpam-5213	24	5	domination	domination	NOUN
ejpam-5213	24	6	mainly	mainly	ADV
ejpam-5213	24	7	focused	focus	VERB
ejpam-5213	24	8	on	on	ADP
ejpam-5213	24	9	algorithmic	algorithmic	ADJ
ejpam-5213	24	10	problems	problem	NOUN
ejpam-5213	24	11	and	and	CCONJ
ejpam-5213	24	12	even	even	ADV
ejpam-5213	24	13	dominating	dominate	VERB
ejpam-5213	24	14	sets	set	NOUN
ejpam-5213	24	15	[	[	X
ejpam-5213	24	16	3	3	NUM
ejpam-5213	24	17	]	]	PUNCT
ejpam-5213	24	18	.	.	PUNCT
ejpam-5213	25	1	in	in	ADP
ejpam-5213	25	2	this	this	DET
ejpam-5213	25	3	paper	paper	NOUN
ejpam-5213	25	4	,	,	PUNCT
ejpam-5213	25	5	we	we	PRON
ejpam-5213	25	6	introduce	introduce	VERB
ejpam-5213	25	7	the	the	DET
ejpam-5213	25	8	concept	concept	NOUN
ejpam-5213	25	9	of	of	ADP
ejpam-5213	25	10	differentiating	differentiate	VERB
ejpam-5213	25	11	odd	odd	ADJ
ejpam-5213	25	12	dominating	dominating	NOUN
ejpam-5213	25	13	sets	set	NOUN
ejpam-5213	25	14	in	in	ADP
ejpam-5213	25	15	graphs	graph	NOUN
ejpam-5213	25	16	.	.	PUNCT
ejpam-5213	26	1	note	note	VERB
ejpam-5213	26	2	that	that	SCONJ
ejpam-5213	26	3	the	the	DET
ejpam-5213	26	4	concept	concept	NOUN
ejpam-5213	26	5	of	of	ADP
ejpam-5213	26	6	differentiating	differentiate	VERB
ejpam-5213	26	7	-	-	PUNCT
ejpam-5213	26	8	dominating	dominating	NOUN
ejpam-5213	26	9	set	set	NOUN
ejpam-5213	26	10	may	may	AUX
ejpam-5213	26	11	be	be	AUX
ejpam-5213	26	12	used	use	VERB
ejpam-5213	26	13	to	to	PART
ejpam-5213	26	14	model	model	VERB
ejpam-5213	26	15	problems	problem	NOUN
ejpam-5213	26	16	which	which	PRON
ejpam-5213	26	17	involve	involve	VERB
ejpam-5213	26	18	protection	protection	NOUN
ejpam-5213	26	19	in	in	ADP
ejpam-5213	26	20	a	a	DET
ejpam-5213	26	21	given	give	VERB
ejpam-5213	26	22	network	network	NOUN
ejpam-5213	26	23	where	where	SCONJ
ejpam-5213	26	24	the	the	DET
ejpam-5213	26	25	goal	goal	NOUN
ejpam-5213	26	26	is	be	AUX
ejpam-5213	26	27	to	to	PART
ejpam-5213	26	28	specifically	specifically	ADV
ejpam-5213	26	29	determine	determine	VERB
ejpam-5213	26	30	the	the	DET
ejpam-5213	26	31	exact	exact	ADJ
ejpam-5213	26	32	location	location	NOUN
ejpam-5213	26	33	of	of	ADP
ejpam-5213	26	34	an	an	DET
ejpam-5213	26	35	intruder	intruder	NOUN
ejpam-5213	26	36	(	(	PUNCT
ejpam-5213	26	37	e.g.	e.g.	ADV
ejpam-5213	26	38	burglar	burglar	NOUN
ejpam-5213	26	39	or	or	CCONJ
ejpam-5213	26	40	fire	fire	NOUN
ejpam-5213	26	41	)	)	PUNCT
ejpam-5213	26	42	.	.	PUNCT
ejpam-5213	27	1	when	when	SCONJ
ejpam-5213	27	2	used	use	VERB
ejpam-5213	27	3	in	in	ADP
ejpam-5213	27	4	this	this	DET
ejpam-5213	27	5	case	case	NOUN
ejpam-5213	27	6	as	as	ADP
ejpam-5213	27	7	a	a	DET
ejpam-5213	27	8	protection	protection	NOUN
ejpam-5213	27	9	strategy	strategy	NOUN
ejpam-5213	27	10	,	,	PUNCT
ejpam-5213	27	11	an	an	DET
ejpam-5213	27	12	element	element	NOUN
ejpam-5213	27	13	of	of	ADP
ejpam-5213	27	14	a	a	DET
ejpam-5213	27	15	differentiating	differentiate	VERB
ejpam-5213	27	16	-	-	PUNCT
ejpam-5213	27	17	dominating	dominating	NOUN
ejpam-5213	27	18	set	set	NOUN
ejpam-5213	27	19	may	may	AUX
ejpam-5213	27	20	refer	refer	VERB
ejpam-5213	27	21	to	to	ADP
ejpam-5213	27	22	a	a	DET
ejpam-5213	27	23	monitoring	monitoring	NOUN
ejpam-5213	27	24	device	device	NOUN
ejpam-5213	27	25	or	or	CCONJ
ejpam-5213	27	26	location	location	NOUN
ejpam-5213	27	27	(	(	PUNCT
ejpam-5213	27	28	vertex	vertex	NOUN
ejpam-5213	27	29	)	)	PUNCT
ejpam-5213	27	30	where	where	SCONJ
ejpam-5213	27	31	a	a	DET
ejpam-5213	27	32	monitoring	monitoring	NOUN
ejpam-5213	27	33	device	device	NOUN
ejpam-5213	27	34	is	be	AUX
ejpam-5213	27	35	positioned	position	VERB
ejpam-5213	27	36	or	or	CCONJ
ejpam-5213	27	37	placed	place	VERB
ejpam-5213	27	38	.	.	PUNCT
ejpam-5213	28	1	when	when	SCONJ
ejpam-5213	28	2	,	,	PUNCT
ejpam-5213	28	3	in	in	ADP
ejpam-5213	28	4	addition	addition	NOUN
ejpam-5213	28	5	,	,	PUNCT
ejpam-5213	28	6	the	the	DET
ejpam-5213	28	7	number	number	NOUN
ejpam-5213	28	8	of	of	ADP
ejpam-5213	28	9	these	these	DET
ejpam-5213	28	10	locations	location	NOUN
ejpam-5213	28	11	or	or	CCONJ
ejpam-5213	28	12	monitors	monitor	NOUN
ejpam-5213	28	13	adjacent	adjacent	ADJ
ejpam-5213	28	14	to	to	ADP
ejpam-5213	28	15	a	a	DET
ejpam-5213	28	16	location	location	NOUN
ejpam-5213	28	17	(	(	PUNCT
ejpam-5213	28	18	with	with	ADP
ejpam-5213	28	19	or	or	CCONJ
ejpam-5213	28	20	with	with	ADP
ejpam-5213	28	21	no	no	DET
ejpam-5213	28	22	monitoring	monitoring	NOUN
ejpam-5213	28	23	device	device	NOUN
ejpam-5213	28	24	)	)	PUNCT
ejpam-5213	28	25	is	be	AUX
ejpam-5213	28	26	required	require	VERB
ejpam-5213	28	27	to	to	PART
ejpam-5213	28	28	be	be	AUX
ejpam-5213	28	29	odd	odd	ADJ
ejpam-5213	28	30	for	for	ADP
ejpam-5213	28	31	every	every	DET
ejpam-5213	28	32	location	location	NOUN
ejpam-5213	28	33	,	,	PUNCT
ejpam-5213	28	34	then	then	ADV
ejpam-5213	28	35	the	the	DET
ejpam-5213	28	36	concept	concept	NOUN
ejpam-5213	28	37	of	of	ADP
ejpam-5213	28	38	odd	odd	ADJ
ejpam-5213	28	39	dominating	dominating	NOUN
ejpam-5213	28	40	set	set	NOUN
ejpam-5213	28	41	is	be	AUX
ejpam-5213	28	42	also	also	ADV
ejpam-5213	28	43	imposed	impose	VERB
ejpam-5213	28	44	.	.	PUNCT
ejpam-5213	29	1	2	2	X
ejpam-5213	29	2	.	.	NOUN
ejpam-5213	29	3	terminologies	terminology	NOUN
ejpam-5213	29	4	and	and	CCONJ
ejpam-5213	29	5	notation	notation	NOUN
ejpam-5213	29	6	let	let	VERB
ejpam-5213	29	7	g	g	NOUN
ejpam-5213	29	8	=	=	SYM
ejpam-5213	29	9	(	(	PUNCT
ejpam-5213	29	10	v	v	NOUN
ejpam-5213	29	11	(	(	PUNCT
ejpam-5213	29	12	g	g	NOUN
ejpam-5213	29	13	)	)	PUNCT
ejpam-5213	29	14	,	,	PUNCT
ejpam-5213	29	15	e(g	e(g	PROPN
ejpam-5213	29	16	)	)	PUNCT
ejpam-5213	29	17	)	)	PUNCT
ejpam-5213	29	18	be	be	AUX
ejpam-5213	29	19	a	a	DET
ejpam-5213	29	20	simple	simple	ADJ
ejpam-5213	29	21	and	and	CCONJ
ejpam-5213	29	22	undirected	undirected	ADJ
ejpam-5213	29	23	graph	graph	NOUN
ejpam-5213	29	24	.	.	PUNCT
ejpam-5213	30	1	the	the	DET
ejpam-5213	30	2	open	open	ADJ
ejpam-5213	30	3	neighborhood	neighborhood	NOUN
ejpam-5213	30	4	of	of	ADP
ejpam-5213	30	5	a	a	DET
ejpam-5213	30	6	vertex	vertex	NOUN
ejpam-5213	30	7	v	v	NOUN
ejpam-5213	30	8	of	of	ADP
ejpam-5213	30	9	g	g	PROPN
ejpam-5213	30	10	is	be	AUX
ejpam-5213	30	11	the	the	DET
ejpam-5213	30	12	set	set	NOUN
ejpam-5213	30	13	ng(v	ng(v	PUNCT
ejpam-5213	30	14	)	)	PUNCT
ejpam-5213	30	15	=	=	SYM
ejpam-5213	31	1	{	{	PUNCT
ejpam-5213	31	2	u	u	NOUN
ejpam-5213	31	3	∈	∈	PROPN
ejpam-5213	31	4	v	v	NOUN
ejpam-5213	31	5	(	(	PUNCT
ejpam-5213	31	6	g	g	NOUN
ejpam-5213	31	7	)	)	PUNCT
ejpam-5213	31	8	:	:	PUNCT
ejpam-5213	31	9	uv	uv	PROPN
ejpam-5213	31	10	∈	∈	PROPN
ejpam-5213	31	11	e(g	e(g	PROPN
ejpam-5213	31	12	)	)	PUNCT
ejpam-5213	31	13	}	}	PUNCT
ejpam-5213	31	14	and	and	CCONJ
ejpam-5213	31	15	its	its	PRON
ejpam-5213	31	16	closed	closed	ADJ
ejpam-5213	31	17	neighborhood	neighborhood	NOUN
ejpam-5213	31	18	is	be	AUX
ejpam-5213	31	19	the	the	DET
ejpam-5213	31	20	set	set	NOUN
ejpam-5213	31	21	ng[v	ng[v	NOUN
ejpam-5213	31	22	]	]	X
ejpam-5213	31	23	=	=	SYM
ejpam-5213	31	24	ng(v	ng(v	X
ejpam-5213	31	25	)	)	PUNCT
ejpam-5213	31	26	∪	∪	ADP
ejpam-5213	31	27	{	{	PUNCT
ejpam-5213	31	28	v	v	NOUN
ejpam-5213	31	29	}	}	PUNCT
ejpam-5213	31	30	.	.	PUNCT
ejpam-5213	32	1	the	the	DET
ejpam-5213	32	2	open	open	ADJ
ejpam-5213	32	3	neighborhood	neighborhood	NOUN
ejpam-5213	32	4	of	of	ADP
ejpam-5213	32	5	a	a	DET
ejpam-5213	32	6	subset	subset	NOUN
ejpam-5213	32	7	s	s	NOUN
ejpam-5213	32	8	of	of	ADP
ejpam-5213	32	9	v	v	NOUN
ejpam-5213	32	10	(	(	PUNCT
ejpam-5213	32	11	g	g	NOUN
ejpam-5213	32	12	)	)	PUNCT
ejpam-5213	32	13	is	be	AUX
ejpam-5213	32	14	the	the	DET
ejpam-5213	32	15	set	set	NOUN
ejpam-5213	32	16	ng(s	ng(s	NOUN
ejpam-5213	32	17	)	)	PUNCT
ejpam-5213	32	18	=	=	SYM
ejpam-5213	32	19	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-5213	32	20	)	)	PUNCT
ejpam-5213	32	21	and	and	CCONJ
ejpam-5213	32	22	its	its	PRON
ejpam-5213	32	23	closed	closed	ADJ
ejpam-5213	32	24	neighborhood	neighborhood	NOUN
ejpam-5213	32	25	is	be	AUX
ejpam-5213	32	26	the	the	DET
ejpam-5213	32	27	set	set	VERB
ejpam-5213	32	28	ng[s	ng[	NOUN
ejpam-5213	32	29	]	]	PUNCT
ejpam-5213	32	30	=	=	SYM
ejpam-5213	32	31	ng(s	ng(s	X
ejpam-5213	32	32	)	)	PUNCT
ejpam-5213	32	33	∪	∪	ADP
ejpam-5213	32	34	s.	s.	PROPN
ejpam-5213	32	35	vertex	vertex	PROPN
ejpam-5213	32	36	v	v	PROPN
ejpam-5213	32	37	is	be	AUX
ejpam-5213	32	38	a	a	DET
ejpam-5213	32	39	leaf	leaf	NOUN
ejpam-5213	32	40	if	if	SCONJ
ejpam-5213	32	41	degg(v	degg(v	VERB
ejpam-5213	32	42	)	)	PUNCT
ejpam-5213	32	43	=	=	SYM
ejpam-5213	32	44	1	1	NUM
ejpam-5213	32	45	and	and	CCONJ
ejpam-5213	32	46	the	the	DET
ejpam-5213	32	47	vertex	vertex	NOUN
ejpam-5213	32	48	u	u	NOUN
ejpam-5213	32	49	∈	∈	PROPN
ejpam-5213	32	50	(	(	PUNCT
ejpam-5213	32	51	v	v	NOUN
ejpam-5213	32	52	(	(	PUNCT
ejpam-5213	32	53	g	g	NOUN
ejpam-5213	32	54	)	)	PUNCT
ejpam-5213	32	55	∩ng(v	∩ng(v	PROPN
ejpam-5213	32	56	)	)	PUNCT
ejpam-5213	32	57	)	)	PUNCT
ejpam-5213	33	1	is	be	AUX
ejpam-5213	33	2	called	call	VERB
ejpam-5213	33	3	a	a	DET
ejpam-5213	33	4	support	support	NOUN
ejpam-5213	33	5	vertex	vertex	NOUN
ejpam-5213	33	6	.	.	PUNCT
ejpam-5213	34	1	l(g	l(g	NOUN
ejpam-5213	34	2	)	)	PUNCT
ejpam-5213	34	3	and	and	CCONJ
ejpam-5213	34	4	s(g	s(g	PROPN
ejpam-5213	34	5	)	)	PUNCT
ejpam-5213	34	6	denote	denote	VERB
ejpam-5213	34	7	the	the	DET
ejpam-5213	34	8	sets	set	NOUN
ejpam-5213	34	9	consisting	consist	VERB
ejpam-5213	34	10	of	of	ADP
ejpam-5213	34	11	all	all	DET
ejpam-5213	34	12	leaves	leave	NOUN
ejpam-5213	34	13	and	and	CCONJ
ejpam-5213	34	14	support	support	NOUN
ejpam-5213	34	15	vertices	vertex	NOUN
ejpam-5213	34	16	in	in	ADP
ejpam-5213	34	17	g	g	NOUN
ejpam-5213	34	18	,	,	PUNCT
ejpam-5213	34	19	respectively	respectively	ADV
ejpam-5213	34	20	.	.	PUNCT
ejpam-5213	35	1	a	a	DET
ejpam-5213	35	2	graph	graph	NOUN
ejpam-5213	35	3	g	g	NOUN
ejpam-5213	35	4	of	of	ADP
ejpam-5213	35	5	order	order	NOUN
ejpam-5213	35	6	n	n	PRON
ejpam-5213	35	7	≥	≥	NOUN
ejpam-5213	35	8	3	3	NUM
ejpam-5213	35	9	is	be	AUX
ejpam-5213	35	10	point	point	NOUN
ejpam-5213	35	11	distinguishing	distinguish	VERB
ejpam-5213	35	12	if	if	SCONJ
ejpam-5213	35	13	for	for	ADP
ejpam-5213	35	14	any	any	DET
ejpam-5213	35	15	two	two	NUM
ejpam-5213	35	16	distinct	distinct	ADJ
ejpam-5213	35	17	vertices	vertex	NOUN
ejpam-5213	35	18	u	u	NOUN
ejpam-5213	35	19	and	and	CCONJ
ejpam-5213	35	20	v	v	NOUN
ejpam-5213	35	21	of	of	ADP
ejpam-5213	35	22	g	g	NOUN
ejpam-5213	35	23	,	,	PUNCT
ejpam-5213	35	24	ng[u	ng[u	PROPN
ejpam-5213	35	25	]	]	X
ejpam-5213	35	26	̸=	̸=	PROPN
ejpam-5213	35	27	ng[v	ng[v	PROPN
ejpam-5213	35	28	]	]	PUNCT
ejpam-5213	35	29	.	.	PUNCT
ejpam-5213	36	1	it	it	PRON
ejpam-5213	36	2	is	be	AUX
ejpam-5213	36	3	totally	totally	ADV
ejpam-5213	36	4	point	point	NOUN
ejpam-5213	36	5	determining	determine	VERB
ejpam-5213	36	6	if	if	SCONJ
ejpam-5213	36	7	for	for	ADP
ejpam-5213	36	8	any	any	DET
ejpam-5213	36	9	two	two	NUM
ejpam-5213	36	10	distinct	distinct	ADJ
ejpam-5213	36	11	vertices	vertex	NOUN
ejpam-5213	36	12	u	u	NOUN
ejpam-5213	36	13	and	and	CCONJ
ejpam-5213	36	14	v	v	NOUN
ejpam-5213	36	15	of	of	ADP
ejpam-5213	36	16	g	g	NOUN
ejpam-5213	36	17	,	,	PUNCT
ejpam-5213	36	18	ng(u	ng(u	NOUN
ejpam-5213	36	19	)	)	PUNCT
ejpam-5213	36	20	̸=	̸=	PROPN
ejpam-5213	36	21	ng(v	ng(v	PUNCT
ejpam-5213	36	22	)	)	PUNCT
ejpam-5213	36	23	and	and	CCONJ
ejpam-5213	36	24	ng[u	ng[u	PROPN
ejpam-5213	36	25	]	]	X
ejpam-5213	36	26	̸=	̸=	PROPN
ejpam-5213	36	27	ng[v	ng[v	PROPN
ejpam-5213	36	28	]	]	PUNCT
ejpam-5213	36	29	.	.	PUNCT
ejpam-5213	37	1	a	a	DET
ejpam-5213	37	2	set	set	NOUN
ejpam-5213	37	3	s	s	NOUN
ejpam-5213	37	4	⊆	⊆	NUM
ejpam-5213	37	5	v	v	NOUN
ejpam-5213	37	6	(	(	PUNCT
ejpam-5213	37	7	g	g	NOUN
ejpam-5213	37	8	)	)	PUNCT
ejpam-5213	37	9	is	be	AUX
ejpam-5213	37	10	a	a	DET
ejpam-5213	37	11	dominating	dominating	NOUN
ejpam-5213	37	12	set	set	NOUN
ejpam-5213	37	13	(	(	PUNCT
ejpam-5213	37	14	respectively	respectively	ADV
ejpam-5213	37	15	,	,	PUNCT
ejpam-5213	37	16	total	total	ADJ
ejpam-5213	37	17	dominating	dominating	NOUN
ejpam-5213	37	18	set	set	NOUN
ejpam-5213	37	19	)	)	PUNCT
ejpam-5213	37	20	in	in	ADP
ejpam-5213	37	21	g	g	PROPN
ejpam-5213	37	22	if	if	SCONJ
ejpam-5213	37	23	ng[s	ng[	NOUN
ejpam-5213	37	24	]	]	PUNCT
ejpam-5213	37	25	=	=	SYM
ejpam-5213	37	26	v	v	X
ejpam-5213	37	27	(	(	PUNCT
ejpam-5213	37	28	g	g	NOUN
ejpam-5213	37	29	)	)	PUNCT
ejpam-5213	37	30	(	(	PUNCT
ejpam-5213	37	31	respectively	respectively	ADV
ejpam-5213	37	32	,	,	PUNCT
ejpam-5213	37	33	ng(s	ng(s	NUM
ejpam-5213	37	34	)	)	PUNCT
ejpam-5213	38	1	=	=	SYM
ejpam-5213	38	2	v	v	X
ejpam-5213	38	3	(	(	PUNCT
ejpam-5213	38	4	g	g	NOUN
ejpam-5213	38	5	)	)	PUNCT
ejpam-5213	38	6	)	)	PUNCT
ejpam-5213	38	7	.	.	PUNCT
ejpam-5213	39	1	the	the	DET
ejpam-5213	39	2	smallest	small	ADJ
ejpam-5213	39	3	cardinality	cardinality	NOUN
ejpam-5213	39	4	of	of	ADP
ejpam-5213	39	5	a	a	DET
ejpam-5213	39	6	dominating	dominating	NOUN
ejpam-5213	39	7	set	set	NOUN
ejpam-5213	39	8	in	in	ADP
ejpam-5213	39	9	g	g	NOUN
ejpam-5213	39	10	,	,	PUNCT
ejpam-5213	39	11	denoted	denote	VERB
ejpam-5213	39	12	by	by	ADP
ejpam-5213	39	13	γ(g	γ(g	PROPN
ejpam-5213	39	14	)	)	PUNCT
ejpam-5213	39	15	,	,	PUNCT
ejpam-5213	39	16	is	be	AUX
ejpam-5213	39	17	called	call	VERB
ejpam-5213	39	18	the	the	DET
ejpam-5213	39	19	domination	domination	NOUN
ejpam-5213	39	20	number	number	NOUN
ejpam-5213	39	21	in	in	ADP
ejpam-5213	39	22	g.	g.	PROPN
ejpam-5213	39	23	a	a	DET
ejpam-5213	39	24	dominating	dominating	NOUN
ejpam-5213	39	25	set	set	NOUN
ejpam-5213	39	26	in	in	ADP
ejpam-5213	39	27	g	g	PROPN
ejpam-5213	39	28	with	with	ADP
ejpam-5213	39	29	cardinality	cardinality	PROPN
ejpam-5213	39	30	γ(g	γ(g	PROPN
ejpam-5213	39	31	)	)	PUNCT
ejpam-5213	39	32	is	be	AUX
ejpam-5213	39	33	called	call	VERB
ejpam-5213	39	34	a	a	DET
ejpam-5213	39	35	γ	γ	NOUN
ejpam-5213	39	36	-	-	PUNCT
ejpam-5213	39	37	set	set	NOUN
ejpam-5213	39	38	of	of	ADP
ejpam-5213	39	39	g.	g.	PROPN
ejpam-5213	39	40	a	a	DET
ejpam-5213	39	41	set	set	NOUN
ejpam-5213	39	42	of	of	ADP
ejpam-5213	39	43	vertices	vertex	NOUN
ejpam-5213	39	44	s	s	PART
ejpam-5213	39	45	is	be	AUX
ejpam-5213	39	46	called	call	VERB
ejpam-5213	39	47	an	an	DET
ejpam-5213	39	48	odd	odd	ADJ
ejpam-5213	39	49	dominating	dominating	NOUN
ejpam-5213	39	50	set	set	NOUN
ejpam-5213	39	51	(	(	PUNCT
ejpam-5213	39	52	respectively	respectively	ADV
ejpam-5213	39	53	,	,	PUNCT
ejpam-5213	39	54	even	even	ADV
ejpam-5213	39	55	dominating	dominate	VERB
ejpam-5213	39	56	set	set	NOUN
ejpam-5213	39	57	)	)	PUNCT
ejpam-5213	39	58	if	if	SCONJ
ejpam-5213	39	59	for	for	ADP
ejpam-5213	39	60	every	every	DET
ejpam-5213	39	61	vertex	vertex	NOUN
ejpam-5213	39	62	v	v	ADP
ejpam-5213	39	63	∈	∈	NOUN
ejpam-5213	39	64	v	v	NOUN
ejpam-5213	39	65	(	(	PUNCT
ejpam-5213	39	66	g	g	NOUN
ejpam-5213	39	67	)	)	PUNCT
ejpam-5213	39	68	,	,	PUNCT
ejpam-5213	39	69	|ng[v]∩s|	|ng[v]∩s|	X
ejpam-5213	39	70	≡	≡	PROPN
ejpam-5213	39	71	1(mod	1(mod	NUM
ejpam-5213	39	72	2	2	NUM
ejpam-5213	39	73	)	)	PUNCT
ejpam-5213	39	74	(	(	PUNCT
ejpam-5213	39	75	respectively	respectively	ADV
ejpam-5213	39	76	,	,	PUNCT
ejpam-5213	39	77	|ng[v]∩s|	|ng[v]∩s|	ADJ
ejpam-5213	39	78	≡	≡	PROPN
ejpam-5213	39	79	0(mod	0(mod	NOUN
ejpam-5213	39	80	2	2	NUM
ejpam-5213	39	81	)	)	PUNCT
ejpam-5213	39	82	)	)	PUNCT
ejpam-5213	39	83	.	.	PUNCT
ejpam-5213	40	1	the	the	DET
ejpam-5213	40	2	minimum	minimum	ADJ
ejpam-5213	40	3	cardinality	cardinality	NOUN
ejpam-5213	40	4	of	of	ADP
ejpam-5213	40	5	an	an	DET
ejpam-5213	40	6	odd	odd	ADJ
ejpam-5213	40	7	dominating	dominating	NOUN
ejpam-5213	40	8	set	set	NOUN
ejpam-5213	40	9	is	be	AUX
ejpam-5213	40	10	called	call	VERB
ejpam-5213	40	11	the	the	DET
ejpam-5213	40	12	odd	odd	ADJ
ejpam-5213	40	13	domination	domination	NOUN
ejpam-5213	40	14	number	number	NOUN
ejpam-5213	40	15	in	in	ADP
ejpam-5213	40	16	g	g	PROPN
ejpam-5213	40	17	(	(	PUNCT
ejpam-5213	40	18	respectively	respectively	ADV
ejpam-5213	40	19	,	,	PUNCT
ejpam-5213	40	20	even	even	ADV
ejpam-5213	40	21	domination	domination	NOUN
ejpam-5213	40	22	number	number	NOUN
ejpam-5213	40	23	)	)	PUNCT
ejpam-5213	40	24	,	,	PUNCT
ejpam-5213	40	25	denoted	denote	VERB
ejpam-5213	40	26	by	by	ADP
ejpam-5213	40	27	γodd(g	γodd(g	NOUN
ejpam-5213	40	28	)	)	PUNCT
ejpam-5213	40	29	(	(	PUNCT
ejpam-5213	40	30	respectively	respectively	ADV
ejpam-5213	40	31	,	,	PUNCT
ejpam-5213	40	32	γeven(g	γeven(g	NOUN
ejpam-5213	40	33	)	)	PUNCT
ejpam-5213	40	34	)	)	PUNCT
ejpam-5213	40	35	.	.	PUNCT
ejpam-5213	41	1	any	any	DET
ejpam-5213	41	2	odd	odd	ADJ
ejpam-5213	41	3	dominating	dominating	NOUN
ejpam-5213	41	4	set	set	VERB
ejpam-5213	41	5	with	with	ADP
ejpam-5213	41	6	cardinality	cardinality	NOUN
ejpam-5213	41	7	γodd(g	γodd(g	NOUN
ejpam-5213	41	8	)	)	PUNCT
ejpam-5213	41	9	is	be	AUX
ejpam-5213	41	10	called	call	VERB
ejpam-5213	41	11	a	a	DET
ejpam-5213	41	12	γodd	γodd	NOUN
ejpam-5213	41	13	-	-	PUNCT
ejpam-5213	41	14	set	set	NOUN
ejpam-5213	41	15	.	.	PUNCT
ejpam-5213	42	1	a	a	DET
ejpam-5213	42	2	set	set	NOUN
ejpam-5213	42	3	s	s	NOUN
ejpam-5213	42	4	⊆	⊆	NUM
ejpam-5213	42	5	v	v	NOUN
ejpam-5213	42	6	(	(	PUNCT
ejpam-5213	42	7	g	g	NOUN
ejpam-5213	42	8	)	)	PUNCT
ejpam-5213	42	9	is	be	AUX
ejpam-5213	42	10	a	a	DET
ejpam-5213	42	11	differentiating	differentiate	VERB
ejpam-5213	42	12	set	set	NOUN
ejpam-5213	42	13	in	in	ADP
ejpam-5213	42	14	a	a	DET
ejpam-5213	42	15	graph	graph	NOUN
ejpam-5213	42	16	g	g	NOUN
ejpam-5213	42	17	if	if	SCONJ
ejpam-5213	42	18	for	for	ADP
ejpam-5213	42	19	every	every	DET
ejpam-5213	42	20	two	two	NUM
ejpam-5213	42	21	distinct	distinct	ADJ
ejpam-5213	42	22	vertices	vertex	NOUN
ejpam-5213	42	23	u	u	NOUN
ejpam-5213	42	24	and	and	CCONJ
ejpam-5213	42	25	v	v	NOUN
ejpam-5213	42	26	in	in	ADP
ejpam-5213	42	27	g	g	PROPN
ejpam-5213	42	28	,	,	PUNCT
ejpam-5213	42	29	ng[u	ng[u	PROPN
ejpam-5213	42	30	]	]	PUNCT
ejpam-5213	42	31	∩	∩	PROPN
ejpam-5213	42	32	s	s	PART
ejpam-5213	42	33	̸=	̸=	PROPN
ejpam-5213	42	34	ng[v	ng[v	X
ejpam-5213	42	35	]	]	PUNCT
ejpam-5213	42	36	∩	∩	PROPN
ejpam-5213	42	37	s.	s.	PROPN
ejpam-5213	42	38	it	it	PRON
ejpam-5213	42	39	is	be	AUX
ejpam-5213	42	40	a	a	DET
ejpam-5213	42	41	strictly	strictly	ADV
ejpam-5213	42	42	differentiating	differentiate	VERB
ejpam-5213	42	43	set	set	NOUN
ejpam-5213	42	44	if	if	SCONJ
ejpam-5213	42	45	it	it	PRON
ejpam-5213	42	46	is	be	AUX
ejpam-5213	42	47	differentiating	differentiate	VERB
ejpam-5213	42	48	and	and	CCONJ
ejpam-5213	42	49	ng[u	ng[u	PROPN
ejpam-5213	42	50	]	]	X
ejpam-5213	42	51	∩	∩	X
ejpam-5213	42	52	s	s	PART
ejpam-5213	42	53	̸=	̸=	PROPN
ejpam-5213	42	54	s	s	PART
ejpam-5213	42	55	for	for	ADP
ejpam-5213	42	56	all	all	DET
ejpam-5213	42	57	u	u	NOUN
ejpam-5213	42	58	∈	∈	PROPN
ejpam-5213	42	59	v	v	NOUN
ejpam-5213	42	60	(	(	PUNCT
ejpam-5213	42	61	g	g	NOUN
ejpam-5213	42	62	)	)	PUNCT
ejpam-5213	42	63	.	.	PUNCT
ejpam-5213	43	1	a	a	DET
ejpam-5213	43	2	differentiating	differentiating	NOUN
ejpam-5213	43	3	(	(	PUNCT
ejpam-5213	43	4	respectively	respectively	ADV
ejpam-5213	43	5	,	,	PUNCT
ejpam-5213	43	6	strictly	strictly	ADV
ejpam-5213	43	7	differentiating	differentiate	VERB
ejpam-5213	43	8	)	)	PUNCT
ejpam-5213	43	9	subset	subset	NOUN
ejpam-5213	43	10	s	s	PROPN
ejpam-5213	43	11	of	of	ADP
ejpam-5213	43	12	v	v	NOUN
ejpam-5213	43	13	(	(	PUNCT
ejpam-5213	43	14	g	g	NOUN
ejpam-5213	43	15	)	)	PUNCT
ejpam-5213	43	16	which	which	PRON
ejpam-5213	43	17	is	be	AUX
ejpam-5213	43	18	also	also	ADV
ejpam-5213	43	19	dominating	dominate	VERB
ejpam-5213	43	20	is	be	AUX
ejpam-5213	43	21	called	call	VERB
ejpam-5213	43	22	a	a	DET
ejpam-5213	43	23	m.	m.	NOUN
ejpam-5213	43	24	carbero	carbero	NOUN
ejpam-5213	43	25	,	,	PUNCT
ejpam-5213	43	26	g.	g.	PROPN
ejpam-5213	43	27	malacas	malacas	PROPN
ejpam-5213	43	28	,	,	PUNCT
ejpam-5213	43	29	s.	s.	PROPN
ejpam-5213	43	30	canoy	canoy	PROPN
ejpam-5213	43	31	,	,	PUNCT
ejpam-5213	43	32	jr	jr	PROPN
ejpam-5213	43	33	.	.	PROPN
ejpam-5213	43	34	/	/	SYM
ejpam-5213	43	35	eur	eur	PROPN
ejpam-5213	43	36	.	.	PUNCT
ejpam-5213	44	1	j.	j.	PROPN
ejpam-5213	44	2	pure	pure	PROPN
ejpam-5213	44	3	appl	appl	PROPN
ejpam-5213	44	4	.	.	PROPN
ejpam-5213	44	5	math	math	PROPN
ejpam-5213	44	6	,	,	PUNCT
ejpam-5213	44	7	17	17	NUM
ejpam-5213	44	8	(	(	PUNCT
ejpam-5213	44	9	3	3	NUM
ejpam-5213	44	10	)	)	PUNCT
ejpam-5213	44	11	(	(	PUNCT
ejpam-5213	44	12	2024	2024	NUM
ejpam-5213	44	13	)	)	PUNCT
ejpam-5213	44	14	,	,	PUNCT
ejpam-5213	44	15	1585	1585	NUM
ejpam-5213	44	16	-	-	SYM
ejpam-5213	44	17	1601	1601	NUM
ejpam-5213	44	18	1587	1587	NUM
ejpam-5213	44	19	differentiating	differentiating	NOUN
ejpam-5213	44	20	-	-	PUNCT
ejpam-5213	44	21	dominating	dominating	NOUN
ejpam-5213	44	22	(	(	PUNCT
ejpam-5213	44	23	respectively	respectively	ADV
ejpam-5213	44	24	,	,	PUNCT
ejpam-5213	44	25	strictly	strictly	ADV
ejpam-5213	44	26	differentiating	differentiate	VERB
ejpam-5213	44	27	-	-	PUNCT
ejpam-5213	44	28	dominating	dominating	NOUN
ejpam-5213	44	29	)	)	PUNCT
ejpam-5213	44	30	set	set	VERB
ejpam-5213	44	31	in	in	ADP
ejpam-5213	44	32	a	a	DET
ejpam-5213	44	33	graph	graph	NOUN
ejpam-5213	44	34	g.	g.	NOUN
ejpam-5213	44	35	the	the	DET
ejpam-5213	44	36	minimum	minimum	ADJ
ejpam-5213	44	37	cardinality	cardinality	NOUN
ejpam-5213	44	38	of	of	ADP
ejpam-5213	44	39	a	a	DET
ejpam-5213	44	40	differentiating	differentiate	VERB
ejpam-5213	44	41	-	-	PUNCT
ejpam-5213	44	42	dominating	dominating	NOUN
ejpam-5213	44	43	(	(	PUNCT
ejpam-5213	44	44	respectively	respectively	ADV
ejpam-5213	44	45	,	,	PUNCT
ejpam-5213	44	46	strictly	strictly	ADV
ejpam-5213	44	47	differentiating	differentiate	VERB
ejpam-5213	44	48	-	-	PUNCT
ejpam-5213	44	49	dominating	dominating	NOUN
ejpam-5213	44	50	)	)	PUNCT
ejpam-5213	44	51	set	set	VERB
ejpam-5213	44	52	in	in	ADP
ejpam-5213	44	53	g	g	NOUN
ejpam-5213	44	54	,	,	PUNCT
ejpam-5213	44	55	denoted	denote	VERB
ejpam-5213	44	56	by	by	ADP
ejpam-5213	44	57	γd(g	γd(g	NOUN
ejpam-5213	44	58	)	)	PUNCT
ejpam-5213	44	59	(	(	PUNCT
ejpam-5213	44	60	respectively	respectively	ADV
ejpam-5213	44	61	,	,	PUNCT
ejpam-5213	44	62	γsd(g	γsd(g	PROPN
ejpam-5213	44	63	)	)	PUNCT
ejpam-5213	44	64	)	)	PUNCT
ejpam-5213	45	1	,	,	PUNCT
ejpam-5213	45	2	is	be	AUX
ejpam-5213	45	3	called	call	VERB
ejpam-5213	45	4	the	the	DET
ejpam-5213	45	5	differentiating	differentiating	NOUN
ejpam-5213	45	6	-	-	PUNCT
ejpam-5213	45	7	domination	domination	NOUN
ejpam-5213	45	8	(	(	PUNCT
ejpam-5213	45	9	respectively	respectively	ADV
ejpam-5213	45	10	,	,	PUNCT
ejpam-5213	45	11	strictly	strictly	ADV
ejpam-5213	45	12	differentiating	differentiate	VERB
ejpam-5213	45	13	-	-	PUNCT
ejpam-5213	45	14	domination	domination	NOUN
ejpam-5213	45	15	)	)	PUNCT
ejpam-5213	45	16	number	number	NOUN
ejpam-5213	45	17	in	in	ADP
ejpam-5213	45	18	g.	g.	PROPN
ejpam-5213	45	19	any	any	DET
ejpam-5213	45	20	differentiating	differentiate	VERB
ejpam-5213	45	21	-	-	PUNCT
ejpam-5213	45	22	dominating	dominating	NOUN
ejpam-5213	45	23	(	(	PUNCT
ejpam-5213	45	24	respectively	respectively	ADV
ejpam-5213	45	25	,	,	PUNCT
ejpam-5213	45	26	strictly	strictly	ADV
ejpam-5213	45	27	differentiating	differentiate	VERB
ejpam-5213	45	28	-	-	PUNCT
ejpam-5213	45	29	dominating	dominating	NOUN
ejpam-5213	45	30	)	)	PUNCT
ejpam-5213	45	31	set	set	VERB
ejpam-5213	45	32	with	with	ADP
ejpam-5213	45	33	cardinality	cardinality	NOUN
ejpam-5213	45	34	γd(g	γd(g	NUM
ejpam-5213	45	35	)	)	PUNCT
ejpam-5213	45	36	(	(	PUNCT
ejpam-5213	45	37	respectively	respectively	ADV
ejpam-5213	45	38	,	,	PUNCT
ejpam-5213	45	39	γsd(g	γsd(g	PROPN
ejpam-5213	45	40	)	)	PUNCT
ejpam-5213	45	41	)	)	PUNCT
ejpam-5213	45	42	is	be	AUX
ejpam-5213	45	43	called	call	VERB
ejpam-5213	45	44	a	a	DET
ejpam-5213	45	45	γd	γd	ADV
ejpam-5213	45	46	-	-	PUNCT
ejpam-5213	45	47	set	set	VERB
ejpam-5213	45	48	(	(	PUNCT
ejpam-5213	45	49	respectively	respectively	ADV
ejpam-5213	45	50	,	,	PUNCT
ejpam-5213	45	51	γsdset	γsdset	ADJ
ejpam-5213	45	52	)	)	PUNCT
ejpam-5213	45	53	.	.	PUNCT
ejpam-5213	46	1	a	a	DET
ejpam-5213	46	2	set	set	NOUN
ejpam-5213	46	3	s	s	NOUN
ejpam-5213	46	4	⊆	⊆	NUM
ejpam-5213	46	5	v	v	NOUN
ejpam-5213	46	6	(	(	PUNCT
ejpam-5213	46	7	g	g	NOUN
ejpam-5213	46	8	)	)	PUNCT
ejpam-5213	46	9	is	be	AUX
ejpam-5213	46	10	a	a	DET
ejpam-5213	46	11	differentiating	differentiate	VERB
ejpam-5213	46	12	odd	odd	ADJ
ejpam-5213	46	13	dominating	dominating	NOUN
ejpam-5213	46	14	set	set	NOUN
ejpam-5213	46	15	(	(	PUNCT
ejpam-5213	46	16	respectively	respectively	ADV
ejpam-5213	46	17	,	,	PUNCT
ejpam-5213	46	18	differentiating	differentiate	VERB
ejpam-5213	46	19	even	even	ADV
ejpam-5213	46	20	dominating	dominate	VERB
ejpam-5213	46	21	set	set	NOUN
ejpam-5213	46	22	)	)	PUNCT
ejpam-5213	46	23	if	if	SCONJ
ejpam-5213	46	24	it	it	PRON
ejpam-5213	46	25	is	be	AUX
ejpam-5213	46	26	both	both	PRON
ejpam-5213	46	27	differentiating	differentiate	VERB
ejpam-5213	46	28	and	and	CCONJ
ejpam-5213	46	29	odd	odd	ADJ
ejpam-5213	46	30	dominating	dominating	NOUN
ejpam-5213	46	31	(	(	PUNCT
ejpam-5213	46	32	respectively	respectively	ADV
ejpam-5213	46	33	,	,	PUNCT
ejpam-5213	46	34	both	both	DET
ejpam-5213	46	35	differentiating	differentiate	VERB
ejpam-5213	46	36	and	and	CCONJ
ejpam-5213	46	37	even	even	ADV
ejpam-5213	46	38	dominating	dominate	VERB
ejpam-5213	46	39	)	)	PUNCT
ejpam-5213	46	40	.	.	PUNCT
ejpam-5213	47	1	a	a	DET
ejpam-5213	47	2	set	set	NOUN
ejpam-5213	47	3	s	s	NOUN
ejpam-5213	47	4	⊆	⊆	NUM
ejpam-5213	47	5	v	v	NOUN
ejpam-5213	47	6	(	(	PUNCT
ejpam-5213	47	7	g	g	NOUN
ejpam-5213	47	8	)	)	PUNCT
ejpam-5213	47	9	is	be	AUX
ejpam-5213	47	10	a	a	DET
ejpam-5213	47	11	strictly	strictly	ADV
ejpam-5213	47	12	differentiating	differentiate	VERB
ejpam-5213	47	13	odd	odd	ADJ
ejpam-5213	47	14	dominating	dominating	NOUN
ejpam-5213	47	15	set	set	NOUN
ejpam-5213	47	16	(	(	PUNCT
ejpam-5213	47	17	respectively	respectively	ADV
ejpam-5213	47	18	,	,	PUNCT
ejpam-5213	47	19	strictly	strictly	ADV
ejpam-5213	47	20	differentiating	differentiate	VERB
ejpam-5213	47	21	even	even	ADV
ejpam-5213	47	22	dominating	dominate	VERB
ejpam-5213	47	23	set	set	NOUN
ejpam-5213	47	24	)	)	PUNCT
ejpam-5213	47	25	if	if	SCONJ
ejpam-5213	47	26	it	it	PRON
ejpam-5213	47	27	is	be	AUX
ejpam-5213	47	28	both	both	PRON
ejpam-5213	47	29	strictly	strictly	ADV
ejpam-5213	47	30	differentiating	differentiate	VERB
ejpam-5213	47	31	and	and	CCONJ
ejpam-5213	47	32	odd	odd	ADJ
ejpam-5213	47	33	dominating	dominating	NOUN
ejpam-5213	47	34	(	(	PUNCT
ejpam-5213	47	35	respectively	respectively	ADV
ejpam-5213	47	36	,	,	PUNCT
ejpam-5213	47	37	both	both	PRON
ejpam-5213	47	38	strictly	strictly	ADV
ejpam-5213	47	39	differentiating	differentiate	VERB
ejpam-5213	47	40	and	and	CCONJ
ejpam-5213	47	41	even	even	ADV
ejpam-5213	47	42	dominating	dominate	VERB
ejpam-5213	47	43	)	)	PUNCT
ejpam-5213	47	44	.	.	PUNCT
ejpam-5213	48	1	the	the	DET
ejpam-5213	48	2	sets	set	NOUN
ejpam-5213	48	3	dod(g	dod(g	NOUN
ejpam-5213	48	4	)	)	PUNCT
ejpam-5213	48	5	and	and	CCONJ
ejpam-5213	48	6	ded(g	ded(g	NOUN
ejpam-5213	48	7	)	)	PUNCT
ejpam-5213	48	8	is	be	AUX
ejpam-5213	48	9	the	the	DET
ejpam-5213	48	10	set	set	NOUN
ejpam-5213	48	11	of	of	ADP
ejpam-5213	48	12	all	all	PRON
ejpam-5213	48	13	differentiating	differentiate	VERB
ejpam-5213	48	14	odd	odd	ADJ
ejpam-5213	48	15	dominating	dominating	NOUN
ejpam-5213	48	16	sets	set	NOUN
ejpam-5213	48	17	and	and	CCONJ
ejpam-5213	48	18	the	the	DET
ejpam-5213	48	19	set	set	NOUN
ejpam-5213	48	20	of	of	ADP
ejpam-5213	48	21	all	all	PRON
ejpam-5213	48	22	differentiating	differentiate	VERB
ejpam-5213	48	23	even	even	ADV
ejpam-5213	48	24	dominating	dominating	NOUN
ejpam-5213	48	25	sets	set	NOUN
ejpam-5213	48	26	,	,	PUNCT
ejpam-5213	48	27	respectively	respectively	ADV
ejpam-5213	48	28	,	,	PUNCT
ejpam-5213	48	29	in	in	ADP
ejpam-5213	48	30	g.	g.	PROPN
ejpam-5213	48	31	the	the	DET
ejpam-5213	48	32	sets	set	NOUN
ejpam-5213	48	33	sdod(g	sdod(g	PROPN
ejpam-5213	48	34	)	)	PUNCT
ejpam-5213	48	35	and	and	CCONJ
ejpam-5213	48	36	sded(g	sded(g	NOUN
ejpam-5213	48	37	)	)	PUNCT
ejpam-5213	48	38	is	be	AUX
ejpam-5213	48	39	the	the	DET
ejpam-5213	48	40	set	set	NOUN
ejpam-5213	48	41	of	of	ADP
ejpam-5213	48	42	all	all	PRON
ejpam-5213	48	43	strictly	strictly	ADV
ejpam-5213	48	44	differentiating	differentiate	VERB
ejpam-5213	48	45	odd	odd	ADJ
ejpam-5213	48	46	dominating	dominating	NOUN
ejpam-5213	48	47	sets	set	NOUN
ejpam-5213	48	48	and	and	CCONJ
ejpam-5213	48	49	the	the	DET
ejpam-5213	48	50	set	set	NOUN
ejpam-5213	48	51	of	of	ADP
ejpam-5213	48	52	all	all	PRON
ejpam-5213	48	53	strictly	strictly	ADV
ejpam-5213	48	54	differentiating	differentiate	VERB
ejpam-5213	48	55	even	even	ADV
ejpam-5213	48	56	dominating	dominating	NOUN
ejpam-5213	48	57	sets	set	NOUN
ejpam-5213	48	58	,	,	PUNCT
ejpam-5213	48	59	respectively	respectively	ADV
ejpam-5213	48	60	,	,	PUNCT
ejpam-5213	48	61	in	in	ADP
ejpam-5213	48	62	g.	g.	PROPN
ejpam-5213	48	63	the	the	DET
ejpam-5213	48	64	minimum	minimum	ADJ
ejpam-5213	48	65	cardinality	cardinality	NOUN
ejpam-5213	48	66	of	of	ADP
ejpam-5213	48	67	a	a	DET
ejpam-5213	48	68	differentiating	differentiate	VERB
ejpam-5213	48	69	odd	odd	ADJ
ejpam-5213	48	70	dominating	dominating	NOUN
ejpam-5213	48	71	(	(	PUNCT
ejpam-5213	48	72	respectively	respectively	ADV
ejpam-5213	48	73	,	,	PUNCT
ejpam-5213	48	74	differentiating	differentiate	VERB
ejpam-5213	48	75	even	even	ADV
ejpam-5213	48	76	dominating	dominating	NOUN
ejpam-5213	48	77	)	)	PUNCT
ejpam-5213	48	78	set	set	VERB
ejpam-5213	48	79	in	in	ADP
ejpam-5213	48	80	g	g	NOUN
ejpam-5213	48	81	,	,	PUNCT
ejpam-5213	48	82	denoted	denote	VERB
ejpam-5213	48	83	by	by	ADP
ejpam-5213	48	84	γod(g	γod(g	PROPN
ejpam-5213	48	85	)	)	PUNCT
ejpam-5213	48	86	(	(	PUNCT
ejpam-5213	48	87	respectively	respectively	ADV
ejpam-5213	48	88	,	,	PUNCT
ejpam-5213	48	89	γed(g	γed(g	PROPN
ejpam-5213	48	90	)	)	PUNCT
ejpam-5213	48	91	)	)	PUNCT
ejpam-5213	48	92	,	,	PUNCT
ejpam-5213	48	93	is	be	AUX
ejpam-5213	48	94	called	call	VERB
ejpam-5213	48	95	the	the	DET
ejpam-5213	48	96	differentiating	differentiate	VERB
ejpam-5213	48	97	odd	odd	ADJ
ejpam-5213	48	98	domination	domination	NOUN
ejpam-5213	48	99	number	number	NOUN
ejpam-5213	48	100	(	(	PUNCT
ejpam-5213	48	101	respectively	respectively	ADV
ejpam-5213	48	102	,	,	PUNCT
ejpam-5213	48	103	differentiating	differentiate	VERB
ejpam-5213	48	104	even	even	ADV
ejpam-5213	48	105	domination	domination	NOUN
ejpam-5213	48	106	number	number	NOUN
ejpam-5213	48	107	in	in	ADP
ejpam-5213	48	108	g.	g.	PROPN
ejpam-5213	48	109	the	the	DET
ejpam-5213	48	110	minimum	minimum	ADJ
ejpam-5213	48	111	cardinality	cardinality	NOUN
ejpam-5213	48	112	of	of	ADP
ejpam-5213	48	113	a	a	DET
ejpam-5213	48	114	strictly	strictly	ADV
ejpam-5213	48	115	differentiating	differentiate	VERB
ejpam-5213	48	116	odd	odd	ADJ
ejpam-5213	48	117	dominating	dominating	NOUN
ejpam-5213	48	118	(	(	PUNCT
ejpam-5213	48	119	respectively	respectively	ADV
ejpam-5213	48	120	,	,	PUNCT
ejpam-5213	48	121	strictly	strictly	ADV
ejpam-5213	48	122	differentiating	differentiate	VERB
ejpam-5213	48	123	even	even	ADV
ejpam-5213	48	124	dominating	dominating	NOUN
ejpam-5213	48	125	)	)	PUNCT
ejpam-5213	48	126	set	set	VERB
ejpam-5213	48	127	in	in	ADP
ejpam-5213	48	128	g	g	NOUN
ejpam-5213	48	129	,	,	PUNCT
ejpam-5213	48	130	denoted	denote	VERB
ejpam-5213	48	131	by	by	ADP
ejpam-5213	48	132	γosd(g	γosd(g	PROPN
ejpam-5213	48	133	)	)	PUNCT
ejpam-5213	48	134	(	(	PUNCT
ejpam-5213	48	135	respectively	respectively	ADV
ejpam-5213	48	136	,	,	PUNCT
ejpam-5213	48	137	γesd(g	γesd(g	NOUN
ejpam-5213	48	138	)	)	PUNCT
ejpam-5213	48	139	)	)	PUNCT
ejpam-5213	48	140	,	,	PUNCT
ejpam-5213	48	141	is	be	AUX
ejpam-5213	48	142	called	call	VERB
ejpam-5213	48	143	the	the	DET
ejpam-5213	48	144	strictly	strictly	ADV
ejpam-5213	48	145	differentiating	differentiate	VERB
ejpam-5213	48	146	odd	odd	ADJ
ejpam-5213	48	147	domination	domination	NOUN
ejpam-5213	48	148	number	number	NOUN
ejpam-5213	48	149	(	(	PUNCT
ejpam-5213	48	150	respectively	respectively	ADV
ejpam-5213	48	151	,	,	PUNCT
ejpam-5213	48	152	strictly	strictly	ADV
ejpam-5213	48	153	differentiating	differentiate	VERB
ejpam-5213	48	154	even	even	ADV
ejpam-5213	48	155	domination	domination	NOUN
ejpam-5213	48	156	number	number	NOUN
ejpam-5213	48	157	)	)	PUNCT
ejpam-5213	48	158	in	in	ADP
ejpam-5213	48	159	g.	g.	PROPN
ejpam-5213	48	160	any	any	DET
ejpam-5213	48	161	differentiating	differentiate	VERB
ejpam-5213	48	162	odd	odd	ADJ
ejpam-5213	48	163	dominating	dominating	NOUN
ejpam-5213	48	164	(	(	PUNCT
ejpam-5213	48	165	respectively	respectively	ADV
ejpam-5213	48	166	,	,	PUNCT
ejpam-5213	48	167	strictly	strictly	ADV
ejpam-5213	48	168	differentiating	differentiate	VERB
ejpam-5213	48	169	odd	odd	ADJ
ejpam-5213	48	170	dominating	dominating	NOUN
ejpam-5213	48	171	)	)	PUNCT
ejpam-5213	48	172	set	set	VERB
ejpam-5213	48	173	with	with	ADP
ejpam-5213	48	174	cardinality	cardinality	PROPN
ejpam-5213	48	175	γod(g	γod(g	PROPN
ejpam-5213	48	176	)	)	PUNCT
ejpam-5213	48	177	(	(	PUNCT
ejpam-5213	48	178	respectively	respectively	ADV
ejpam-5213	48	179	,	,	PUNCT
ejpam-5213	48	180	γosd(g	γosd(g	PROPN
ejpam-5213	48	181	)	)	PUNCT
ejpam-5213	48	182	)	)	PUNCT
ejpam-5213	48	183	is	be	AUX
ejpam-5213	48	184	called	call	VERB
ejpam-5213	48	185	a	a	DET
ejpam-5213	48	186	γod	γod	NOUN
ejpam-5213	48	187	-	-	PUNCT
ejpam-5213	48	188	set	set	ADJ
ejpam-5213	48	189	(	(	PUNCT
ejpam-5213	48	190	respectively	respectively	ADV
ejpam-5213	48	191	,	,	PUNCT
ejpam-5213	48	192	γosd	γosd	NOUN
ejpam-5213	48	193	-	-	PUNCT
ejpam-5213	48	194	set	set	NOUN
ejpam-5213	48	195	)	)	PUNCT
ejpam-5213	48	196	.	.	PUNCT
ejpam-5213	49	1	3	3	X
ejpam-5213	49	2	.	.	X
ejpam-5213	49	3	results	result	NOUN
ejpam-5213	49	4	remark	remark	VERB
ejpam-5213	49	5	1	1	NUM
ejpam-5213	49	6	.	.	PUNCT
ejpam-5213	50	1	every	every	DET
ejpam-5213	50	2	differentiating	differentiate	VERB
ejpam-5213	50	3	odd	odd	ADJ
ejpam-5213	50	4	dominating	dominating	NOUN
ejpam-5213	50	5	set	set	VERB
ejpam-5213	50	6	in	in	ADP
ejpam-5213	50	7	a	a	DET
ejpam-5213	50	8	connected	connected	ADJ
ejpam-5213	50	9	graph	graph	NOUN
ejpam-5213	50	10	g	g	PROPN
ejpam-5213	50	11	is	be	AUX
ejpam-5213	50	12	an	an	DET
ejpam-5213	50	13	odd	odd	ADJ
ejpam-5213	50	14	dominating	dominating	NOUN
ejpam-5213	50	15	set	set	NOUN
ejpam-5213	50	16	.	.	PUNCT
ejpam-5213	51	1	remark	remark	PROPN
ejpam-5213	51	2	2	2	NUM
ejpam-5213	51	3	.	.	PUNCT
ejpam-5213	52	1	every	every	DET
ejpam-5213	52	2	differentiating	differentiate	VERB
ejpam-5213	52	3	odd	odd	ADJ
ejpam-5213	52	4	dominating	dominating	NOUN
ejpam-5213	52	5	set	set	VERB
ejpam-5213	52	6	in	in	ADP
ejpam-5213	52	7	a	a	DET
ejpam-5213	52	8	connected	connected	ADJ
ejpam-5213	52	9	graph	graph	NOUN
ejpam-5213	52	10	g	g	PROPN
ejpam-5213	52	11	is	be	AUX
ejpam-5213	52	12	a	a	DET
ejpam-5213	52	13	differentiating	differentiate	VERB
ejpam-5213	52	14	-	-	PUNCT
ejpam-5213	52	15	dominating	dominating	NOUN
ejpam-5213	52	16	set	set	NOUN
ejpam-5213	52	17	.	.	PUNCT
ejpam-5213	53	1	theorem	theorem	NOUN
ejpam-5213	53	2	1	1	NUM
ejpam-5213	53	3	.	.	PUNCT
ejpam-5213	54	1	let	let	VERB
ejpam-5213	54	2	g	g	PRON
ejpam-5213	54	3	be	be	AUX
ejpam-5213	54	4	a	a	DET
ejpam-5213	54	5	graph	graph	NOUN
ejpam-5213	54	6	.	.	PUNCT
ejpam-5213	55	1	then	then	ADV
ejpam-5213	55	2	g	g	PROPN
ejpam-5213	55	3	admits	admit	VERB
ejpam-5213	55	4	a	a	DET
ejpam-5213	55	5	differentiating	differentiate	VERB
ejpam-5213	55	6	-	-	PUNCT
ejpam-5213	55	7	dominating	dominating	NOUN
ejpam-5213	55	8	set	set	NOUN
ejpam-5213	55	9	if	if	SCONJ
ejpam-5213	55	10	and	and	CCONJ
ejpam-5213	55	11	only	only	ADV
ejpam-5213	55	12	if	if	SCONJ
ejpam-5213	55	13	it	it	PRON
ejpam-5213	55	14	is	be	AUX
ejpam-5213	55	15	point	point	NOUN
ejpam-5213	55	16	distinguishing	distinguish	VERB
ejpam-5213	55	17	.	.	PUNCT
ejpam-5213	56	1	proof	proof	NOUN
ejpam-5213	56	2	.	.	PUNCT
ejpam-5213	57	1	suppose	suppose	VERB
ejpam-5213	57	2	g	g	PROPN
ejpam-5213	57	3	admits	admit	VERB
ejpam-5213	57	4	a	a	DET
ejpam-5213	57	5	differentiating	differentiate	VERB
ejpam-5213	57	6	set	set	NOUN
ejpam-5213	57	7	,	,	PUNCT
ejpam-5213	57	8	say	say	VERB
ejpam-5213	57	9	s.	s.	PROPN
ejpam-5213	57	10	suppose	suppose	VERB
ejpam-5213	57	11	g	g	PROPN
ejpam-5213	57	12	is	be	AUX
ejpam-5213	57	13	not	not	PART
ejpam-5213	57	14	point	point	NOUN
ejpam-5213	57	15	distinguishing	distinguish	VERB
ejpam-5213	57	16	.	.	PUNCT
ejpam-5213	58	1	then	then	ADV
ejpam-5213	58	2	there	there	PRON
ejpam-5213	58	3	exist	exist	VERB
ejpam-5213	58	4	distinct	distinct	ADJ
ejpam-5213	58	5	vertices	vertex	NOUN
ejpam-5213	58	6	a	a	PRON
ejpam-5213	58	7	,	,	PUNCT
ejpam-5213	58	8	b	b	PROPN
ejpam-5213	58	9	∈	∈	PROPN
ejpam-5213	58	10	v	v	NOUN
ejpam-5213	58	11	(	(	PUNCT
ejpam-5213	58	12	g	g	NOUN
ejpam-5213	58	13	)	)	PUNCT
ejpam-5213	58	14	such	such	ADJ
ejpam-5213	58	15	that	that	DET
ejpam-5213	58	16	ng[a	ng[a	NOUN
ejpam-5213	58	17	]	]	X
ejpam-5213	58	18	=	=	SYM
ejpam-5213	58	19	ng[b	ng[b	NOUN
ejpam-5213	58	20	]	]	PUNCT
ejpam-5213	58	21	.	.	PUNCT
ejpam-5213	59	1	this	this	PRON
ejpam-5213	59	2	implies	imply	VERB
ejpam-5213	59	3	that	that	SCONJ
ejpam-5213	59	4	ng[a]∩s	ng[a]∩s	PROPN
ejpam-5213	59	5	=	=	SYM
ejpam-5213	59	6	ng[b]∩s	ng[b]∩s	PROPN
ejpam-5213	59	7	,	,	PUNCT
ejpam-5213	59	8	a	a	DET
ejpam-5213	59	9	contradiction	contradiction	NOUN
ejpam-5213	59	10	.	.	PUNCT
ejpam-5213	60	1	thus	thus	ADV
ejpam-5213	60	2	,	,	PUNCT
ejpam-5213	60	3	g	g	PROPN
ejpam-5213	60	4	is	be	AUX
ejpam-5213	60	5	point	point	NOUN
ejpam-5213	60	6	distinguishing	distinguish	VERB
ejpam-5213	60	7	.	.	PUNCT
ejpam-5213	61	1	for	for	ADP
ejpam-5213	61	2	the	the	DET
ejpam-5213	61	3	converse	converse	NOUN
ejpam-5213	61	4	,	,	PUNCT
ejpam-5213	61	5	suppose	suppose	VERB
ejpam-5213	61	6	that	that	SCONJ
ejpam-5213	61	7	g	g	PROPN
ejpam-5213	61	8	is	be	AUX
ejpam-5213	61	9	point	point	NOUN
ejpam-5213	61	10	distinguishing	distinguish	VERB
ejpam-5213	61	11	.	.	PUNCT
ejpam-5213	62	1	then	then	ADV
ejpam-5213	62	2	s	s	VERB
ejpam-5213	62	3	=	=	SYM
ejpam-5213	62	4	v	v	PROPN
ejpam-5213	62	5	(	(	PUNCT
ejpam-5213	62	6	g	g	NOUN
ejpam-5213	62	7	)	)	PUNCT
ejpam-5213	62	8	is	be	AUX
ejpam-5213	62	9	a	a	DET
ejpam-5213	62	10	differentiating	differentiate	VERB
ejpam-5213	62	11	-	-	PUNCT
ejpam-5213	62	12	dominating	dominating	NOUN
ejpam-5213	62	13	set	set	NOUN
ejpam-5213	62	14	,	,	PUNCT
ejpam-5213	62	15	showing	show	VERB
ejpam-5213	62	16	that	that	SCONJ
ejpam-5213	62	17	g	g	PROPN
ejpam-5213	62	18	has	have	VERB
ejpam-5213	62	19	a	a	DET
ejpam-5213	62	20	differentiating	differentiate	VERB
ejpam-5213	62	21	-	-	PUNCT
ejpam-5213	62	22	dominating	dominating	NOUN
ejpam-5213	62	23	set	set	NOUN
ejpam-5213	62	24	.	.	PUNCT
ejpam-5213	63	1	lemma	lemma	PROPN
ejpam-5213	63	2	1	1	X
ejpam-5213	63	3	.	.	PUNCT
ejpam-5213	64	1	let	let	VERB
ejpam-5213	64	2	g	g	PRON
ejpam-5213	64	3	be	be	AUX
ejpam-5213	64	4	a	a	DET
ejpam-5213	64	5	connected	connected	ADJ
ejpam-5213	64	6	graph	graph	NOUN
ejpam-5213	64	7	of	of	ADP
ejpam-5213	64	8	order	order	NOUN
ejpam-5213	64	9	m	m	VERB
ejpam-5213	64	10	and	and	CCONJ
ejpam-5213	64	11	let	let	VERB
ejpam-5213	64	12	s	s	PRON
ejpam-5213	64	13	be	be	AUX
ejpam-5213	64	14	a	a	DET
ejpam-5213	64	15	differentiating	differentiate	VERB
ejpam-5213	64	16	odd	odd	ADJ
ejpam-5213	64	17	dominating	dominating	NOUN
ejpam-5213	64	18	set	set	VERB
ejpam-5213	64	19	in	in	ADP
ejpam-5213	64	20	g.	g.	PROPN
ejpam-5213	65	1	then	then	ADV
ejpam-5213	65	2	m	m	VERB
ejpam-5213	65	3	≤	≤	ADJ
ejpam-5213	65	4	2|s|−1	2|s|−1	NUM
ejpam-5213	65	5	.	.	PUNCT
ejpam-5213	66	1	in	in	ADP
ejpam-5213	66	2	particular	particular	ADJ
ejpam-5213	66	3	,	,	PUNCT
ejpam-5213	66	4	m	m	VERB
ejpam-5213	66	5	≤	≤	NOUN
ejpam-5213	66	6	2γ	2γ	NOUN
ejpam-5213	66	7	o	o	NOUN
ejpam-5213	66	8	d(g)−1	d(g)−1	NOUN
ejpam-5213	66	9	,	,	PUNCT
ejpam-5213	66	10	i.e.	i.e.	X
ejpam-5213	66	11	,	,	PUNCT
ejpam-5213	66	12	γod(g	γod(g	PROPN
ejpam-5213	66	13	)	)	PUNCT
ejpam-5213	66	14	≥	≥	NOUN
ejpam-5213	66	15	ln(m)+ln(2	ln(m)+ln(2	PROPN
ejpam-5213	66	16	)	)	PUNCT
ejpam-5213	66	17	ln(2	ln(2	NOUN
ejpam-5213	66	18	)	)	PUNCT
ejpam-5213	66	19	.	.	PUNCT
ejpam-5213	67	1	m.	m.	NOUN
ejpam-5213	67	2	carbero	carbero	PROPN
ejpam-5213	67	3	,	,	PUNCT
ejpam-5213	67	4	g.	g.	PROPN
ejpam-5213	67	5	malacas	malacas	PROPN
ejpam-5213	67	6	,	,	PUNCT
ejpam-5213	67	7	s.	s.	PROPN
ejpam-5213	67	8	canoy	canoy	PROPN
ejpam-5213	67	9	,	,	PUNCT
ejpam-5213	67	10	jr	jr	PROPN
ejpam-5213	67	11	.	.	PROPN
ejpam-5213	67	12	/	/	SYM
ejpam-5213	67	13	eur	eur	PROPN
ejpam-5213	67	14	.	.	PUNCT
ejpam-5213	68	1	j.	j.	PROPN
ejpam-5213	68	2	pure	pure	PROPN
ejpam-5213	68	3	appl	appl	PROPN
ejpam-5213	68	4	.	.	PROPN
ejpam-5213	68	5	math	math	PROPN
ejpam-5213	68	6	,	,	PUNCT
ejpam-5213	68	7	17	17	NUM
ejpam-5213	68	8	(	(	PUNCT
ejpam-5213	68	9	3	3	NUM
ejpam-5213	68	10	)	)	PUNCT
ejpam-5213	68	11	(	(	PUNCT
ejpam-5213	68	12	2024	2024	NUM
ejpam-5213	68	13	)	)	PUNCT
ejpam-5213	68	14	,	,	PUNCT
ejpam-5213	68	15	1585	1585	NUM
ejpam-5213	68	16	-	-	SYM
ejpam-5213	68	17	1601	1601	NUM
ejpam-5213	68	18	1588	1588	NUM
ejpam-5213	68	19	proof	proof	NOUN
ejpam-5213	68	20	.	.	PUNCT
ejpam-5213	69	1	let	let	VERB
ejpam-5213	69	2	s	s	PRON
ejpam-5213	69	3	be	be	AUX
ejpam-5213	69	4	a	a	DET
ejpam-5213	69	5	differentiating	differentiate	VERB
ejpam-5213	69	6	odd	odd	ADJ
ejpam-5213	69	7	dominating	dominating	NOUN
ejpam-5213	69	8	set	set	VERB
ejpam-5213	69	9	in	in	ADP
ejpam-5213	69	10	g	g	NOUN
ejpam-5213	69	11	and	and	CCONJ
ejpam-5213	69	12	let	let	VERB
ejpam-5213	69	13	k	k	PROPN
ejpam-5213	69	14	=	=	PUNCT
ejpam-5213	69	15	|s|	|s|	PROPN
ejpam-5213	69	16	.	.	PUNCT
ejpam-5213	70	1	let	let	VERB
ejpam-5213	70	2	d	d	NOUN
ejpam-5213	70	3	=	=	PRON
ejpam-5213	70	4	{	{	PUNCT
ejpam-5213	70	5	q	q	NOUN
ejpam-5213	70	6	⊆	⊆	NUM
ejpam-5213	70	7	s	s	NOUN
ejpam-5213	70	8	:	:	PUNCT
ejpam-5213	70	9	|q|	|q|	NUM
ejpam-5213	70	10	is	be	AUX
ejpam-5213	70	11	odd	odd	ADJ
ejpam-5213	70	12	}	}	PUNCT
ejpam-5213	70	13	.	.	PUNCT
ejpam-5213	71	1	then	then	ADV
ejpam-5213	71	2	|d|	|d|	PROPN
ejpam-5213	71	3	=	=	PUNCT
ejpam-5213	71	4	2k−1	2k−1	NUM
ejpam-5213	71	5	.	.	PUNCT
ejpam-5213	72	1	since	since	SCONJ
ejpam-5213	72	2	s	s	NOUN
ejpam-5213	72	3	is	be	AUX
ejpam-5213	72	4	differentiating	differentiate	VERB
ejpam-5213	72	5	odd	odd	ADJ
ejpam-5213	72	6	dominating	dominating	NOUN
ejpam-5213	72	7	,	,	PUNCT
ejpam-5213	72	8	m	m	VERB
ejpam-5213	72	9	≤	≤	NOUN
ejpam-5213	72	10	2k−1	2k−1	NUM
ejpam-5213	72	11	.	.	PUNCT
ejpam-5213	73	1	if	if	SCONJ
ejpam-5213	73	2	s	s	PROPN
ejpam-5213	73	3	is	be	AUX
ejpam-5213	73	4	a	a	DET
ejpam-5213	73	5	γod	γod	NOUN
ejpam-5213	73	6	-	-	PUNCT
ejpam-5213	73	7	set	set	NOUN
ejpam-5213	73	8	,	,	PUNCT
ejpam-5213	73	9	then	then	ADV
ejpam-5213	73	10	m	m	VERB
ejpam-5213	73	11	≤	≤	NOUN
ejpam-5213	73	12	2γ	2γ	NOUN
ejpam-5213	73	13	o	o	NOUN
ejpam-5213	73	14	d(g)−1	d(g)−1	NOUN
ejpam-5213	73	15	.	.	PUNCT
ejpam-5213	74	1	this	this	PRON
ejpam-5213	74	2	proves	prove	VERB
ejpam-5213	74	3	the	the	DET
ejpam-5213	74	4	assertion	assertion	NOUN
ejpam-5213	74	5	.	.	PUNCT
ejpam-5213	75	1	theorem	theorem	NOUN
ejpam-5213	75	2	2	2	NUM
ejpam-5213	75	3	.	.	PUNCT
ejpam-5213	76	1	let	let	VERB
ejpam-5213	76	2	g	g	PRON
ejpam-5213	76	3	be	be	AUX
ejpam-5213	76	4	a	a	DET
ejpam-5213	76	5	point	point	NOUN
ejpam-5213	76	6	distinguishing	distinguish	VERB
ejpam-5213	76	7	connected	connect	VERB
ejpam-5213	76	8	graph	graph	NOUN
ejpam-5213	76	9	.	.	PUNCT
ejpam-5213	77	1	(	(	PUNCT
ejpam-5213	77	2	i	i	NOUN
ejpam-5213	77	3	)	)	PUNCT
ejpam-5213	77	4	if	if	SCONJ
ejpam-5213	77	5	g	g	PROPN
ejpam-5213	77	6	has	have	VERB
ejpam-5213	77	7	a	a	DET
ejpam-5213	77	8	support	support	NOUN
ejpam-5213	77	9	vertex	vertex	NOUN
ejpam-5213	77	10	v	v	NOUN
ejpam-5213	77	11	with	with	ADP
ejpam-5213	77	12	|ng(v)|	|ng(v)|	NOUN
ejpam-5213	77	13	=	=	SYM
ejpam-5213	77	14	2	2	NUM
ejpam-5213	77	15	,	,	PUNCT
ejpam-5213	77	16	then	then	ADV
ejpam-5213	77	17	g	g	PROPN
ejpam-5213	77	18	does	do	AUX
ejpam-5213	77	19	not	not	PART
ejpam-5213	77	20	admit	admit	VERB
ejpam-5213	77	21	a	a	DET
ejpam-5213	77	22	differentiating	differentiate	VERB
ejpam-5213	77	23	odd	odd	ADJ
ejpam-5213	77	24	dominating	dominating	NOUN
ejpam-5213	77	25	set	set	NOUN
ejpam-5213	77	26	.	.	PUNCT
ejpam-5213	78	1	(	(	PUNCT
ejpam-5213	78	2	ii	ii	NOUN
ejpam-5213	78	3	)	)	PUNCT
ejpam-5213	78	4	if	if	SCONJ
ejpam-5213	78	5	s	s	NOUN
ejpam-5213	78	6	is	be	AUX
ejpam-5213	78	7	a	a	DET
ejpam-5213	78	8	differentiating	differentiate	VERB
ejpam-5213	78	9	odd	odd	ADJ
ejpam-5213	78	10	dominating	dominating	NOUN
ejpam-5213	78	11	set	set	VERB
ejpam-5213	78	12	in	in	ADP
ejpam-5213	78	13	g	g	PROPN
ejpam-5213	78	14	and	and	CCONJ
ejpam-5213	78	15	v	v	ADP
ejpam-5213	78	16	∈	∈	PROPN
ejpam-5213	78	17	v	v	NOUN
ejpam-5213	78	18	(	(	PUNCT
ejpam-5213	78	19	g	g	NOUN
ejpam-5213	78	20	)	)	PUNCT
ejpam-5213	78	21	with	with	ADP
ejpam-5213	78	22	|ng(v	|ng(v	NOUN
ejpam-5213	78	23	)	)	PUNCT
ejpam-5213	78	24	∩	∩	NOUN
ejpam-5213	78	25	l(g)|	l(g)|	X
ejpam-5213	78	26	≥	≥	NOUN
ejpam-5213	78	27	2	2	NUM
ejpam-5213	78	28	,	,	PUNCT
ejpam-5213	78	29	then	then	ADV
ejpam-5213	78	30	ng(v	ng(v	PUNCT
ejpam-5213	78	31	)	)	PUNCT
ejpam-5213	78	32	∩	∩	NOUN
ejpam-5213	78	33	l(g	l(g	NOUN
ejpam-5213	78	34	)	)	PUNCT
ejpam-5213	78	35	⊆	⊆	NUM
ejpam-5213	78	36	s	s	NOUN
ejpam-5213	78	37	and	and	CCONJ
ejpam-5213	78	38	v	v	NOUN
ejpam-5213	78	39	/∈	/∈	PUNCT
ejpam-5213	78	40	s.	s.	PROPN
ejpam-5213	78	41	proof	proof	PROPN
ejpam-5213	78	42	.	.	PUNCT
ejpam-5213	79	1	let	let	VERB
ejpam-5213	79	2	w	w	PROPN
ejpam-5213	79	3	∈	∈	PROPN
ejpam-5213	79	4	l(g)∩ng(v	l(g)∩ng(v	NOUN
ejpam-5213	79	5	)	)	PUNCT
ejpam-5213	79	6	and	and	CCONJ
ejpam-5213	79	7	let	let	VERB
ejpam-5213	79	8	z	z	NOUN
ejpam-5213	79	9	∈	∈	PROPN
ejpam-5213	79	10	ng(v)\{w	ng(v)\{w	NOUN
ejpam-5213	79	11	}	}	PUNCT
ejpam-5213	79	12	.	.	PUNCT
ejpam-5213	80	1	supposeg	supposeg	PROPN
ejpam-5213	80	2	has	have	VERB
ejpam-5213	80	3	a	a	DET
ejpam-5213	80	4	differentiating	differentiate	VERB
ejpam-5213	80	5	odd	odd	ADJ
ejpam-5213	80	6	dominating	dominating	NOUN
ejpam-5213	80	7	set	set	VERB
ejpam-5213	80	8	s.	s.	PROPN
ejpam-5213	80	9	if	if	SCONJ
ejpam-5213	80	10	w	w	PROPN
ejpam-5213	80	11	∈	∈	PROPN
ejpam-5213	80	12	s	s	NOUN
ejpam-5213	80	13	,	,	PUNCT
ejpam-5213	80	14	then	then	ADV
ejpam-5213	80	15	v	v	ADP
ejpam-5213	80	16	/∈	/∈	PUNCT
ejpam-5213	80	17	s	s	PART
ejpam-5213	81	1	because	because	SCONJ
ejpam-5213	81	2	s	s	NOUN
ejpam-5213	81	3	is	be	AUX
ejpam-5213	81	4	an	an	DET
ejpam-5213	81	5	odd	odd	ADJ
ejpam-5213	81	6	dominating	dominating	NOUN
ejpam-5213	81	7	set	set	NOUN
ejpam-5213	81	8	.	.	PUNCT
ejpam-5213	82	1	since	since	SCONJ
ejpam-5213	82	2	s	s	PROPN
ejpam-5213	82	3	is	be	AUX
ejpam-5213	82	4	a	a	DET
ejpam-5213	82	5	differentiating	differentiate	VERB
ejpam-5213	82	6	set	set	NOUN
ejpam-5213	82	7	,	,	PUNCT
ejpam-5213	82	8	ng[w	ng[w	PROPN
ejpam-5213	82	9	]	]	PUNCT
ejpam-5213	82	10	∩	∩	PROPN
ejpam-5213	82	11	s	s	PART
ejpam-5213	82	12	=	=	X
ejpam-5213	82	13	{	{	PUNCT
ejpam-5213	82	14	w	w	PROPN
ejpam-5213	82	15	}	}	PUNCT
ejpam-5213	82	16	̸=	̸=	PROPN
ejpam-5213	82	17	ng[v	ng[v	X
ejpam-5213	82	18	]	]	PUNCT
ejpam-5213	82	19	∩	∩	PROPN
ejpam-5213	82	20	s.	s.	PROPN
ejpam-5213	82	21	this	this	DET
ejpam-5213	82	22	forces	force	NOUN
ejpam-5213	82	23	z	z	PROPN
ejpam-5213	82	24	∈	∈	PROPN
ejpam-5213	82	25	s.	s.	PROPN
ejpam-5213	82	26	however	however	ADV
ejpam-5213	82	27	,	,	PUNCT
ejpam-5213	82	28	the	the	DET
ejpam-5213	82	29	assumption	assumption	NOUN
ejpam-5213	82	30	would	would	AUX
ejpam-5213	82	31	imply	imply	VERB
ejpam-5213	82	32	that	that	SCONJ
ejpam-5213	82	33	ng[v	ng[v	PROPN
ejpam-5213	82	34	]	]	PUNCT
ejpam-5213	82	35	∩	∩	X
ejpam-5213	82	36	s	s	PART
ejpam-5213	82	37	=	=	X
ejpam-5213	82	38	{	{	PUNCT
ejpam-5213	82	39	w	w	PROPN
ejpam-5213	82	40	,	,	PUNCT
ejpam-5213	82	41	z	z	NOUN
ejpam-5213	82	42	}	}	PUNCT
ejpam-5213	82	43	,	,	PUNCT
ejpam-5213	82	44	contradicting	contradict	VERB
ejpam-5213	82	45	the	the	DET
ejpam-5213	82	46	fact	fact	NOUN
ejpam-5213	82	47	that	that	SCONJ
ejpam-5213	82	48	s	s	VERB
ejpam-5213	82	49	is	be	AUX
ejpam-5213	82	50	an	an	DET
ejpam-5213	82	51	odd	odd	ADJ
ejpam-5213	82	52	dominating	dominating	NOUN
ejpam-5213	82	53	set	set	NOUN
ejpam-5213	82	54	.	.	PUNCT
ejpam-5213	83	1	thus	thus	ADV
ejpam-5213	83	2	,	,	PUNCT
ejpam-5213	83	3	w	w	PROPN
ejpam-5213	83	4	/∈	/∈	PROPN
ejpam-5213	83	5	s.	s.	PROPN
ejpam-5213	83	6	consequently	consequently	ADV
ejpam-5213	83	7	,	,	PUNCT
ejpam-5213	83	8	v	v	PROPN
ejpam-5213	83	9	∈	∈	PROPN
ejpam-5213	83	10	s.	s.	PROPN
ejpam-5213	83	11	since	since	SCONJ
ejpam-5213	83	12	s	s	PROPN
ejpam-5213	83	13	is	be	AUX
ejpam-5213	83	14	odd	odd	ADJ
ejpam-5213	83	15	dominating	dominating	NOUN
ejpam-5213	83	16	,	,	PUNCT
ejpam-5213	83	17	z	z	PROPN
ejpam-5213	83	18	/∈	/∈	PUNCT
ejpam-5213	84	1	s.	s.	PROPN
ejpam-5213	85	1	it	it	PRON
ejpam-5213	85	2	follows	follow	VERB
ejpam-5213	85	3	that	that	SCONJ
ejpam-5213	85	4	ng[w	ng[w	PROPN
ejpam-5213	85	5	]	]	PUNCT
ejpam-5213	85	6	∩	∩	PROPN
ejpam-5213	85	7	s	s	PART
ejpam-5213	85	8	=	=	VERB
ejpam-5213	85	9	{	{	PUNCT
ejpam-5213	85	10	v	v	NOUN
ejpam-5213	85	11	}	}	PUNCT
ejpam-5213	85	12	=	=	PUNCT
ejpam-5213	85	13	ng[v	ng[v	X
ejpam-5213	85	14	]	]	PUNCT
ejpam-5213	85	15	∩	∩	X
ejpam-5213	85	16	s	s	SYM
ejpam-5213	85	17	,	,	PUNCT
ejpam-5213	85	18	contrary	contrary	ADJ
ejpam-5213	85	19	to	to	ADP
ejpam-5213	85	20	the	the	DET
ejpam-5213	85	21	assumption	assumption	NOUN
ejpam-5213	85	22	that	that	SCONJ
ejpam-5213	85	23	s	s	VERB
ejpam-5213	85	24	is	be	AUX
ejpam-5213	85	25	a	a	DET
ejpam-5213	85	26	differentiating	differentiate	VERB
ejpam-5213	85	27	set	set	NOUN
ejpam-5213	85	28	.	.	PUNCT
ejpam-5213	86	1	therefore	therefore	ADV
ejpam-5213	86	2	,	,	PUNCT
ejpam-5213	86	3	g	g	PROPN
ejpam-5213	86	4	has	have	VERB
ejpam-5213	86	5	no	no	DET
ejpam-5213	86	6	differentiating	differentiate	VERB
ejpam-5213	86	7	odd	odd	ADJ
ejpam-5213	86	8	dominating	dominating	NOUN
ejpam-5213	86	9	set	set	NOUN
ejpam-5213	86	10	,	,	PUNCT
ejpam-5213	86	11	showing	show	VERB
ejpam-5213	86	12	that	that	SCONJ
ejpam-5213	86	13	(	(	PUNCT
ejpam-5213	86	14	i	i	NOUN
ejpam-5213	86	15	)	)	PUNCT
ejpam-5213	86	16	holds	hold	VERB
ejpam-5213	86	17	.	.	PUNCT
ejpam-5213	87	1	next	next	ADV
ejpam-5213	87	2	,	,	PUNCT
ejpam-5213	87	3	suppose	suppose	VERB
ejpam-5213	87	4	that	that	SCONJ
ejpam-5213	87	5	s	s	VERB
ejpam-5213	87	6	is	be	AUX
ejpam-5213	87	7	a	a	DET
ejpam-5213	87	8	differentiating	differentiate	VERB
ejpam-5213	87	9	odd	odd	ADJ
ejpam-5213	87	10	dominating	dominating	NOUN
ejpam-5213	87	11	set	set	NOUN
ejpam-5213	87	12	and	and	CCONJ
ejpam-5213	87	13	v	v	ADP
ejpam-5213	87	14	∈	∈	PROPN
ejpam-5213	87	15	v	v	NOUN
ejpam-5213	87	16	(	(	PUNCT
ejpam-5213	87	17	g	g	NOUN
ejpam-5213	87	18	)	)	PUNCT
ejpam-5213	87	19	with	with	ADP
ejpam-5213	87	20	|ng(v)∩l(g)|	|ng(v)∩l(g)|	NOUN
ejpam-5213	87	21	≥	≥	NOUN
ejpam-5213	87	22	2	2	NUM
ejpam-5213	87	23	.	.	PUNCT
ejpam-5213	87	24	suppose	suppose	VERB
ejpam-5213	87	25	v	v	ADP
ejpam-5213	87	26	∈	∈	PROPN
ejpam-5213	87	27	s.	s.	PROPN
ejpam-5213	87	28	since	since	SCONJ
ejpam-5213	87	29	s	s	PROPN
ejpam-5213	87	30	is	be	AUX
ejpam-5213	87	31	odd	odd	ADJ
ejpam-5213	87	32	dominating	dominating	NOUN
ejpam-5213	87	33	,	,	PUNCT
ejpam-5213	87	34	(	(	PUNCT
ejpam-5213	87	35	ng(v)∩l(g))∩s	ng(v)∩l(g))∩s	NOUN
ejpam-5213	87	36	=	=	PUNCT
ejpam-5213	87	37	∅.	∅.	AUX
ejpam-5213	87	38	let	let	VERB
ejpam-5213	87	39	x	x	PRON
ejpam-5213	87	40	,	,	PUNCT
ejpam-5213	87	41	y	y	PROPN
ejpam-5213	87	42	∈	∈	PROPN
ejpam-5213	87	43	ng(v	ng(v	PUNCT
ejpam-5213	87	44	)	)	PUNCT
ejpam-5213	87	45	∩	∩	NOUN
ejpam-5213	87	46	l(g	l(g	NOUN
ejpam-5213	87	47	)	)	PUNCT
ejpam-5213	87	48	where	where	SCONJ
ejpam-5213	87	49	x	x	X
ejpam-5213	87	50	̸=	̸=	PROPN
ejpam-5213	87	51	y.	y.	PROPN
ejpam-5213	87	52	then	then	ADV
ejpam-5213	87	53	ng[x	ng[x	PROPN
ejpam-5213	87	54	]	]	PUNCT
ejpam-5213	87	55	∩	∩	PROPN
ejpam-5213	87	56	s	s	PART
ejpam-5213	87	57	=	=	SYM
ejpam-5213	87	58	ng[y	ng[y	PROPN
ejpam-5213	87	59	]	]	PUNCT
ejpam-5213	87	60	∩	∩	X
ejpam-5213	87	61	s	s	PART
ejpam-5213	87	62	=	=	PUNCT
ejpam-5213	87	63	{	{	PUNCT
ejpam-5213	87	64	v	v	NOUN
ejpam-5213	87	65	}	}	PUNCT
ejpam-5213	87	66	,	,	PUNCT
ejpam-5213	87	67	contrary	contrary	ADV
ejpam-5213	87	68	to	to	ADP
ejpam-5213	87	69	the	the	DET
ejpam-5213	87	70	assumption	assumption	NOUN
ejpam-5213	87	71	that	that	SCONJ
ejpam-5213	87	72	s	s	VERB
ejpam-5213	87	73	is	be	AUX
ejpam-5213	87	74	a	a	DET
ejpam-5213	87	75	differentiating	differentiate	VERB
ejpam-5213	87	76	set	set	NOUN
ejpam-5213	87	77	.	.	PUNCT
ejpam-5213	88	1	therefore	therefore	ADV
ejpam-5213	88	2	,	,	PUNCT
ejpam-5213	88	3	v	v	INTJ
ejpam-5213	88	4	/∈	/∈	PUNCT
ejpam-5213	88	5	s.	s.	PROPN
ejpam-5213	88	6	since	since	SCONJ
ejpam-5213	88	7	s	s	PROPN
ejpam-5213	88	8	is	be	AUX
ejpam-5213	88	9	a	a	DET
ejpam-5213	88	10	dominating	dominating	NOUN
ejpam-5213	88	11	set	set	NOUN
ejpam-5213	88	12	,	,	PUNCT
ejpam-5213	88	13	ng(v	ng(v	PUNCT
ejpam-5213	88	14	)	)	PUNCT
ejpam-5213	88	15	∩	∩	NOUN
ejpam-5213	88	16	l(g	l(g	NOUN
ejpam-5213	88	17	)	)	PUNCT
ejpam-5213	88	18	⊆	⊆	NUM
ejpam-5213	88	19	s.	s.	PROPN
ejpam-5213	88	20	thus	thus	ADV
ejpam-5213	88	21	,	,	PUNCT
ejpam-5213	88	22	(	(	PUNCT
ejpam-5213	88	23	ii	ii	NOUN
ejpam-5213	88	24	)	)	PUNCT
ejpam-5213	88	25	holds	hold	VERB
ejpam-5213	88	26	.	.	PUNCT
ejpam-5213	89	1	the	the	DET
ejpam-5213	89	2	next	next	ADJ
ejpam-5213	89	3	results	result	NOUN
ejpam-5213	89	4	follow	follow	VERB
ejpam-5213	89	5	from	from	ADP
ejpam-5213	89	6	the	the	DET
ejpam-5213	89	7	preceding	precede	VERB
ejpam-5213	89	8	ones	one	NOUN
ejpam-5213	89	9	.	.	PUNCT
ejpam-5213	90	1	corollary	corollary	ADJ
ejpam-5213	90	2	1	1	NUM
ejpam-5213	90	3	.	.	PUNCT
ejpam-5213	91	1	for	for	ADP
ejpam-5213	91	2	n	n	PRON
ejpam-5213	91	3	≥	≥	NUM
ejpam-5213	91	4	2	2	NUM
ejpam-5213	91	5	,	,	PUNCT
ejpam-5213	91	6	kn	kn	PROPN
ejpam-5213	91	7	and	and	CCONJ
ejpam-5213	91	8	pn	pn	PROPN
ejpam-5213	91	9	do	do	AUX
ejpam-5213	91	10	not	not	PART
ejpam-5213	91	11	admit	admit	VERB
ejpam-5213	91	12	a	a	DET
ejpam-5213	91	13	differentiating	differentiate	VERB
ejpam-5213	91	14	odd	odd	ADJ
ejpam-5213	91	15	dominating	dominating	NOUN
ejpam-5213	91	16	set	set	NOUN
ejpam-5213	91	17	.	.	PUNCT
ejpam-5213	92	1	corollary	corollary	ADJ
ejpam-5213	92	2	2	2	NUM
ejpam-5213	92	3	.	.	PUNCT
ejpam-5213	93	1	let	let	VERB
ejpam-5213	93	2	sn	sn	PROPN
ejpam-5213	93	3	=	=	SYM
ejpam-5213	93	4	k1,n	k1,n	PROPN
ejpam-5213	93	5	be	be	VERB
ejpam-5213	93	6	a	a	DET
ejpam-5213	93	7	star	star	NOUN
ejpam-5213	93	8	of	of	ADP
ejpam-5213	93	9	order	order	NOUN
ejpam-5213	93	10	n	n	X
ejpam-5213	94	1	+	+	NOUN
ejpam-5213	94	2	1	1	NUM
ejpam-5213	94	3	where	where	SCONJ
ejpam-5213	94	4	n	n	PRON
ejpam-5213	94	5	≥	≥	NOUN
ejpam-5213	94	6	3	3	NUM
ejpam-5213	94	7	.	.	PUNCT
ejpam-5213	95	1	then	then	ADV
ejpam-5213	95	2	sn	sn	PROPN
ejpam-5213	95	3	admits	admit	VERB
ejpam-5213	95	4	a	a	DET
ejpam-5213	95	5	differentiating	differentiate	VERB
ejpam-5213	95	6	odd	odd	ADJ
ejpam-5213	95	7	dominating	dominating	NOUN
ejpam-5213	95	8	set	set	VERB
ejpam-5213	95	9	if	if	SCONJ
ejpam-5213	95	10	and	and	CCONJ
ejpam-5213	95	11	only	only	ADV
ejpam-5213	95	12	if	if	SCONJ
ejpam-5213	95	13	n	n	PRON
ejpam-5213	95	14	is	be	AUX
ejpam-5213	95	15	odd	odd	ADJ
ejpam-5213	95	16	.	.	PUNCT
ejpam-5213	96	1	moreover	moreover	ADV
ejpam-5213	96	2	,	,	PUNCT
ejpam-5213	96	3	if	if	SCONJ
ejpam-5213	96	4	n	n	PRON
ejpam-5213	96	5	is	be	AUX
ejpam-5213	96	6	odd	odd	ADJ
ejpam-5213	96	7	,	,	PUNCT
ejpam-5213	96	8	then	then	ADV
ejpam-5213	96	9	s	s	PART
ejpam-5213	96	10	=	=	SYM
ejpam-5213	96	11	v	v	PROPN
ejpam-5213	96	12	(	(	PUNCT
ejpam-5213	96	13	sn	sn	NOUN
ejpam-5213	96	14	)	)	PUNCT
ejpam-5213	96	15	\	\	PROPN
ejpam-5213	96	16	{	{	PUNCT
ejpam-5213	96	17	v0	v0	NOUN
ejpam-5213	96	18	}	}	PUNCT
ejpam-5213	96	19	where	where	SCONJ
ejpam-5213	96	20	degg(v0	degg(v0	ADJ
ejpam-5213	96	21	)	)	PUNCT
ejpam-5213	96	22	=	=	SYM
ejpam-5213	96	23	n	n	CCONJ
ejpam-5213	96	24	,	,	PUNCT
ejpam-5213	96	25	is	be	AUX
ejpam-5213	96	26	the	the	DET
ejpam-5213	96	27	only	only	ADJ
ejpam-5213	96	28	differentiating	differentiate	VERB
ejpam-5213	96	29	odd	odd	ADJ
ejpam-5213	96	30	dominating	dominating	NOUN
ejpam-5213	96	31	set	set	VERB
ejpam-5213	96	32	in	in	ADP
ejpam-5213	96	33	sn	sn	PROPN
ejpam-5213	96	34	.	.	PUNCT
ejpam-5213	97	1	in	in	ADP
ejpam-5213	97	2	particular	particular	ADJ
ejpam-5213	97	3	,	,	PUNCT
ejpam-5213	97	4	γod(sn	γod(sn	ADJ
ejpam-5213	97	5	)	)	PUNCT
ejpam-5213	97	6	=	=	SYM
ejpam-5213	97	7	n.	n.	NOUN
ejpam-5213	97	8	proof	proof	NOUN
ejpam-5213	97	9	.	.	PUNCT
ejpam-5213	98	1	let	let	VERB
ejpam-5213	98	2	v	v	X
ejpam-5213	98	3	(	(	PUNCT
ejpam-5213	98	4	sn	sn	PROPN
ejpam-5213	98	5	)	)	PUNCT
ejpam-5213	98	6	=	=	SYM
ejpam-5213	98	7	{	{	PUNCT
ejpam-5213	98	8	v0	v0	NOUN
ejpam-5213	98	9	,	,	PUNCT
ejpam-5213	98	10	v1	v1	NOUN
ejpam-5213	98	11	,	,	PUNCT
ejpam-5213	98	12	·	·	PUNCT
ejpam-5213	98	13	·	·	PUNCT
ejpam-5213	98	14	·	·	PUNCT
ejpam-5213	98	15	,	,	PUNCT
ejpam-5213	98	16	vn	vn	PROPN
ejpam-5213	98	17	}	}	PUNCT
ejpam-5213	98	18	,	,	PUNCT
ejpam-5213	98	19	where	where	SCONJ
ejpam-5213	98	20	degg(v0	degg(v0	ADJ
ejpam-5213	98	21	)	)	PUNCT
ejpam-5213	98	22	=	=	SYM
ejpam-5213	98	23	n.	n.	NOUN
ejpam-5213	98	24	suppose	suppose	VERB
ejpam-5213	98	25	sn	sn	PROPN
ejpam-5213	98	26	admits	admit	VERB
ejpam-5213	98	27	a	a	DET
ejpam-5213	98	28	differentiating	differentiate	VERB
ejpam-5213	98	29	odd	odd	ADJ
ejpam-5213	98	30	dominating	dominating	NOUN
ejpam-5213	98	31	set	set	NOUN
ejpam-5213	98	32	,	,	PUNCT
ejpam-5213	98	33	say	say	VERB
ejpam-5213	98	34	s.	s.	PROPN
ejpam-5213	98	35	by	by	ADP
ejpam-5213	98	36	theorem	theorem	ADJ
ejpam-5213	98	37	2(ii	2(ii	NUM
ejpam-5213	98	38	)	)	PUNCT
ejpam-5213	98	39	,	,	PUNCT
ejpam-5213	98	40	s	s	NOUN
ejpam-5213	98	41	=	=	SYM
ejpam-5213	98	42	v	v	PROPN
ejpam-5213	98	43	(	(	PUNCT
ejpam-5213	98	44	sn	sn	NOUN
ejpam-5213	98	45	)	)	PUNCT
ejpam-5213	98	46	\	\	PROPN
ejpam-5213	98	47	{	{	PUNCT
ejpam-5213	98	48	v0	v0	NOUN
ejpam-5213	98	49	}	}	PUNCT
ejpam-5213	98	50	.	.	PUNCT
ejpam-5213	99	1	since	since	SCONJ
ejpam-5213	99	2	s	s	PROPN
ejpam-5213	99	3	is	be	AUX
ejpam-5213	99	4	odd	odd	ADJ
ejpam-5213	99	5	dominating	dominating	NOUN
ejpam-5213	99	6	,	,	PUNCT
ejpam-5213	99	7	|nsn	|nsn	PUNCT
ejpam-5213	100	1	[	[	X
ejpam-5213	100	2	v	v	NOUN
ejpam-5213	100	3	]	]	X
ejpam-5213	100	4	∩	∩	NOUN
ejpam-5213	100	5	s|	s|	NOUN
ejpam-5213	100	6	=	=	SYM
ejpam-5213	100	7	|s|	|s|	NOUN
ejpam-5213	100	8	=	=	SYM
ejpam-5213	100	9	n	n	X
ejpam-5213	100	10	is	be	AUX
ejpam-5213	100	11	odd	odd	ADJ
ejpam-5213	100	12	.	.	PUNCT
ejpam-5213	101	1	for	for	ADP
ejpam-5213	101	2	the	the	DET
ejpam-5213	101	3	converse	converse	NOUN
ejpam-5213	101	4	,	,	PUNCT
ejpam-5213	101	5	suppose	suppose	VERB
ejpam-5213	101	6	that	that	SCONJ
ejpam-5213	101	7	n	n	PRON
ejpam-5213	101	8	is	be	AUX
ejpam-5213	101	9	odd	odd	ADJ
ejpam-5213	101	10	.	.	PUNCT
ejpam-5213	102	1	then	then	ADV
ejpam-5213	102	2	s	s	VERB
ejpam-5213	102	3	=	=	SYM
ejpam-5213	102	4	v	v	PROPN
ejpam-5213	102	5	(	(	PUNCT
ejpam-5213	102	6	sn	sn	NOUN
ejpam-5213	102	7	)	)	PUNCT
ejpam-5213	102	8	\	\	PROPN
ejpam-5213	102	9	{	{	PUNCT
ejpam-5213	102	10	v0	v0	NOUN
ejpam-5213	102	11	}	}	PUNCT
ejpam-5213	102	12	is	be	AUX
ejpam-5213	102	13	a	a	DET
ejpam-5213	102	14	differentiating	differentiate	VERB
ejpam-5213	102	15	odd	odd	ADJ
ejpam-5213	102	16	dominating	dominating	NOUN
ejpam-5213	102	17	set	set	VERB
ejpam-5213	102	18	in	in	ADP
ejpam-5213	102	19	sn	sn	PROPN
ejpam-5213	102	20	.	.	PUNCT
ejpam-5213	103	1	note	note	VERB
ejpam-5213	103	2	that	that	SCONJ
ejpam-5213	103	3	if	if	SCONJ
ejpam-5213	103	4	n	n	NOUN
ejpam-5213	103	5	is	be	AUX
ejpam-5213	103	6	odd	odd	ADJ
ejpam-5213	103	7	,	,	PUNCT
ejpam-5213	103	8	then	then	ADV
ejpam-5213	103	9	s	s	VERB
ejpam-5213	103	10	=	=	SYM
ejpam-5213	103	11	v	v	PROPN
ejpam-5213	103	12	(	(	PUNCT
ejpam-5213	103	13	sn)\{v0	sn)\{v0	PROPN
ejpam-5213	103	14	}	}	PUNCT
ejpam-5213	103	15	is	be	AUX
ejpam-5213	103	16	the	the	DET
ejpam-5213	103	17	only	only	ADJ
ejpam-5213	103	18	differentiating	differentiate	VERB
ejpam-5213	103	19	odd	odd	ADJ
ejpam-5213	103	20	dominating	dominating	NOUN
ejpam-5213	103	21	set	set	VERB
ejpam-5213	103	22	in	in	ADP
ejpam-5213	103	23	sn	sn	NOUN
ejpam-5213	103	24	by	by	ADP
ejpam-5213	103	25	theorem	theorem	ADJ
ejpam-5213	103	26	2(ii	2(ii	NUM
ejpam-5213	103	27	)	)	PUNCT
ejpam-5213	103	28	.	.	PUNCT
ejpam-5213	104	1	hence	hence	ADV
ejpam-5213	104	2	,	,	PUNCT
ejpam-5213	104	3	γod(sn	γod(sn	ADV
ejpam-5213	104	4	)	)	PUNCT
ejpam-5213	104	5	=	=	SYM
ejpam-5213	104	6	n.	n.	NOUN
ejpam-5213	104	7	corollary	corollary	NOUN
ejpam-5213	104	8	3	3	X
ejpam-5213	104	9	.	.	PUNCT
ejpam-5213	105	1	let	let	VERB
ejpam-5213	105	2	g	g	NOUN
ejpam-5213	105	3	be	be	AUX
ejpam-5213	105	4	any	any	DET
ejpam-5213	105	5	non	non	ADJ
ejpam-5213	105	6	-	-	ADJ
ejpam-5213	105	7	trivial	trivial	ADJ
ejpam-5213	105	8	connected	connected	ADJ
ejpam-5213	105	9	graph	graph	NOUN
ejpam-5213	105	10	of	of	ADP
ejpam-5213	105	11	order	order	NOUN
ejpam-5213	105	12	n	n	NOUN
ejpam-5213	105	13	and	and	CCONJ
ejpam-5213	105	14	let	let	VERB
ejpam-5213	105	15	m	m	PRON
ejpam-5213	105	16	be	be	AUX
ejpam-5213	105	17	a	a	DET
ejpam-5213	105	18	positive	positive	ADJ
ejpam-5213	105	19	odd	odd	ADJ
ejpam-5213	105	20	integer	integer	NOUN
ejpam-5213	105	21	with	with	ADP
ejpam-5213	105	22	m	m	PROPN
ejpam-5213	105	23	≥	≥	NOUN
ejpam-5213	105	24	3	3	NUM
ejpam-5213	105	25	.	.	PUNCT
ejpam-5213	106	1	then	then	ADV
ejpam-5213	106	2	there	there	PRON
ejpam-5213	106	3	exists	exist	VERB
ejpam-5213	106	4	a	a	DET
ejpam-5213	106	5	connected	connected	ADJ
ejpam-5213	106	6	graph	graph	NOUN
ejpam-5213	106	7	h	h	NOUN
ejpam-5213	106	8	obtained	obtain	VERB
ejpam-5213	106	9	from	from	ADP
ejpam-5213	106	10	g	g	PROPN
ejpam-5213	106	11	such	such	ADJ
ejpam-5213	106	12	that	that	DET
ejpam-5213	106	13	γod(h	γod(h	PROPN
ejpam-5213	106	14	)	)	PUNCT
ejpam-5213	106	15	=	=	SYM
ejpam-5213	106	16	mn	mn	PROPN
ejpam-5213	106	17	.	.	PUNCT
ejpam-5213	107	1	moreover	moreover	ADV
ejpam-5213	107	2	,	,	PUNCT
ejpam-5213	107	3	if	if	SCONJ
ejpam-5213	107	4	every	every	DET
ejpam-5213	107	5	vertex	vertex	NOUN
ejpam-5213	107	6	in	in	ADP
ejpam-5213	107	7	g	g	PROPN
ejpam-5213	107	8	has	have	AUX
ejpam-5213	107	9	even	even	ADV
ejpam-5213	107	10	degree	degree	NOUN
ejpam-5213	107	11	,	,	PUNCT
ejpam-5213	107	12	then	then	ADV
ejpam-5213	107	13	γodd(h	γodd(h	PROPN
ejpam-5213	107	14	)	)	PUNCT
ejpam-5213	108	1	=	=	VERB
ejpam-5213	108	2	n.	n.	NOUN
ejpam-5213	108	3	in	in	ADP
ejpam-5213	108	4	particular	particular	ADJ
ejpam-5213	108	5	,	,	PUNCT
ejpam-5213	108	6	the	the	DET
ejpam-5213	108	7	difference	difference	NOUN
ejpam-5213	108	8	γod(g)−	γod(g)−	PROPN
ejpam-5213	108	9	γodd(g	γodd(g	NOUN
ejpam-5213	108	10	)	)	PUNCT
ejpam-5213	108	11	can	can	AUX
ejpam-5213	108	12	be	be	AUX
ejpam-5213	108	13	made	make	VERB
ejpam-5213	108	14	arbitrarily	arbitrarily	ADV
ejpam-5213	108	15	large	large	ADJ
ejpam-5213	108	16	.	.	PUNCT
ejpam-5213	109	1	m.	m.	NOUN
ejpam-5213	109	2	carbero	carbero	PROPN
ejpam-5213	109	3	,	,	PUNCT
ejpam-5213	109	4	g.	g.	PROPN
ejpam-5213	109	5	malacas	malacas	PROPN
ejpam-5213	109	6	,	,	PUNCT
ejpam-5213	109	7	s.	s.	PROPN
ejpam-5213	109	8	canoy	canoy	PROPN
ejpam-5213	109	9	,	,	PUNCT
ejpam-5213	109	10	jr	jr	PROPN
ejpam-5213	109	11	.	.	PROPN
ejpam-5213	109	12	/	/	SYM
ejpam-5213	109	13	eur	eur	PROPN
ejpam-5213	109	14	.	.	PUNCT
ejpam-5213	110	1	j.	j.	PROPN
ejpam-5213	110	2	pure	pure	PROPN
ejpam-5213	110	3	appl	appl	PROPN
ejpam-5213	110	4	.	.	PROPN
ejpam-5213	110	5	math	math	PROPN
ejpam-5213	110	6	,	,	PUNCT
ejpam-5213	110	7	17	17	NUM
ejpam-5213	110	8	(	(	PUNCT
ejpam-5213	110	9	3	3	NUM
ejpam-5213	110	10	)	)	PUNCT
ejpam-5213	110	11	(	(	PUNCT
ejpam-5213	110	12	2024	2024	NUM
ejpam-5213	110	13	)	)	PUNCT
ejpam-5213	110	14	,	,	PUNCT
ejpam-5213	110	15	1585	1585	NUM
ejpam-5213	110	16	-	-	SYM
ejpam-5213	110	17	1601	1601	NUM
ejpam-5213	110	18	1589	1589	NUM
ejpam-5213	110	19	proof	proof	NOUN
ejpam-5213	110	20	.	.	PUNCT
ejpam-5213	111	1	let	let	VERB
ejpam-5213	111	2	v	v	X
ejpam-5213	111	3	(	(	PUNCT
ejpam-5213	111	4	g	g	NOUN
ejpam-5213	111	5	)	)	PUNCT
ejpam-5213	111	6	=	=	SYM
ejpam-5213	111	7	{	{	PUNCT
ejpam-5213	111	8	v1	v1	PROPN
ejpam-5213	111	9	,	,	PUNCT
ejpam-5213	111	10	v2	v2	PROPN
ejpam-5213	111	11	,	,	PUNCT
ejpam-5213	111	12	·	·	PUNCT
ejpam-5213	111	13	·	·	PUNCT
ejpam-5213	111	14	·	·	PUNCT
ejpam-5213	111	15	,	,	PUNCT
ejpam-5213	111	16	vn	vn	INTJ
ejpam-5213	111	17	}	}	PUNCT
ejpam-5213	111	18	and	and	CCONJ
ejpam-5213	111	19	let	let	VERB
ejpam-5213	111	20	v	v	NOUN
ejpam-5213	111	21	(	(	PUNCT
ejpam-5213	111	22	km	km	NOUN
ejpam-5213	111	23	)	)	PUNCT
ejpam-5213	111	24	=	=	PRON
ejpam-5213	112	1	{	{	PUNCT
ejpam-5213	112	2	x1	x1	PROPN
ejpam-5213	112	3	,	,	PUNCT
ejpam-5213	112	4	x2	x2	PROPN
ejpam-5213	112	5	,	,	PUNCT
ejpam-5213	112	6	·	·	PUNCT
ejpam-5213	112	7	·	·	PUNCT
ejpam-5213	112	8	·	·	PUNCT
ejpam-5213	112	9	,	,	PUNCT
ejpam-5213	112	10	xm	xm	PROPN
ejpam-5213	112	11	}	}	PUNCT
ejpam-5213	112	12	.	.	PUNCT
ejpam-5213	113	1	let	let	VERB
ejpam-5213	113	2	h	h	NOUN
ejpam-5213	113	3	be	be	AUX
ejpam-5213	113	4	the	the	DET
ejpam-5213	113	5	graph	graph	NOUN
ejpam-5213	113	6	obtained	obtain	VERB
ejpam-5213	113	7	from	from	ADP
ejpam-5213	113	8	g	g	NOUN
ejpam-5213	113	9	by	by	ADP
ejpam-5213	113	10	adding	add	VERB
ejpam-5213	113	11	the	the	DET
ejpam-5213	113	12	edges	edge	NOUN
ejpam-5213	113	13	vixj	vixj	VERB
ejpam-5213	113	14	for	for	ADP
ejpam-5213	113	15	each	each	DET
ejpam-5213	113	16	i	i	PRON
ejpam-5213	113	17	∈	∈	PROPN
ejpam-5213	113	18	{	{	PUNCT
ejpam-5213	113	19	1	1	NUM
ejpam-5213	113	20	,	,	PUNCT
ejpam-5213	113	21	2	2	NUM
ejpam-5213	113	22	,	,	PUNCT
ejpam-5213	113	23	·	·	PUNCT
ejpam-5213	113	24	·	·	PUNCT
ejpam-5213	113	25	·	·	PUNCT
ejpam-5213	113	26	,	,	PUNCT
ejpam-5213	113	27	n	n	CCONJ
ejpam-5213	113	28	}	}	PUNCT
ejpam-5213	113	29	and	and	CCONJ
ejpam-5213	113	30	for	for	ADP
ejpam-5213	113	31	each	each	DET
ejpam-5213	113	32	j	j	PROPN
ejpam-5213	113	33	∈	∈	PROPN
ejpam-5213	113	34	{	{	PUNCT
ejpam-5213	113	35	1	1	NUM
ejpam-5213	113	36	,	,	PUNCT
ejpam-5213	113	37	2	2	NUM
ejpam-5213	113	38	,	,	PUNCT
ejpam-5213	113	39	·	·	PUNCT
ejpam-5213	113	40	·	·	PUNCT
ejpam-5213	113	41	·	·	PUNCT
ejpam-5213	113	42	,	,	PUNCT
ejpam-5213	113	43	m	m	NOUN
ejpam-5213	113	44	}	}	PUNCT
ejpam-5213	113	45	.	.	PUNCT
ejpam-5213	114	1	by	by	ADP
ejpam-5213	114	2	theorem	theorem	ADJ
ejpam-5213	114	3	2(ii	2(ii	NUM
ejpam-5213	114	4	)	)	PUNCT
ejpam-5213	114	5	,	,	PUNCT
ejpam-5213	114	6	s	s	NOUN
ejpam-5213	114	7	=	=	SYM
ejpam-5213	114	8	v	v	PROPN
ejpam-5213	114	9	(	(	PUNCT
ejpam-5213	114	10	h	h	NOUN
ejpam-5213	114	11	)	)	PUNCT
ejpam-5213	114	12	\	\	PROPN
ejpam-5213	114	13	v	v	X
ejpam-5213	114	14	(	(	PUNCT
ejpam-5213	114	15	g	g	NOUN
ejpam-5213	114	16	)	)	PUNCT
ejpam-5213	114	17	is	be	AUX
ejpam-5213	114	18	a	a	DET
ejpam-5213	114	19	γod	γod	NOUN
ejpam-5213	114	20	-	-	PUNCT
ejpam-5213	114	21	set	set	NOUN
ejpam-5213	114	22	in	in	ADP
ejpam-5213	114	23	h.	h.	PROPN
ejpam-5213	114	24	thus	thus	ADV
ejpam-5213	114	25	,	,	PUNCT
ejpam-5213	114	26	γod(h	γod(h	PROPN
ejpam-5213	114	27	)	)	PUNCT
ejpam-5213	115	1	=	=	SYM
ejpam-5213	115	2	mn	mn	PROPN
ejpam-5213	115	3	.	.	PROPN
ejpam-5213	115	4	cleary	cleary	PROPN
ejpam-5213	115	5	,	,	PUNCT
ejpam-5213	115	6	γodd(h	γodd(h	PROPN
ejpam-5213	115	7	)	)	PUNCT
ejpam-5213	116	1	=	=	VERB
ejpam-5213	116	2	n.	n.	PROPN
ejpam-5213	116	3	suppose	suppose	VERB
ejpam-5213	116	4	now	now	ADV
ejpam-5213	116	5	that	that	SCONJ
ejpam-5213	116	6	|ng(v)|	|ng(v)|	NOUN
ejpam-5213	116	7	is	be	AUX
ejpam-5213	116	8	even	even	ADV
ejpam-5213	116	9	for	for	ADP
ejpam-5213	116	10	every	every	DET
ejpam-5213	116	11	v	v	NUM
ejpam-5213	116	12	∈	∈	NOUN
ejpam-5213	116	13	v	v	NOUN
ejpam-5213	116	14	(	(	PUNCT
ejpam-5213	116	15	g	g	NOUN
ejpam-5213	116	16	)	)	PUNCT
ejpam-5213	116	17	.	.	PUNCT
ejpam-5213	117	1	since	since	SCONJ
ejpam-5213	117	2	v	v	NOUN
ejpam-5213	117	3	(	(	PUNCT
ejpam-5213	117	4	g	g	NOUN
ejpam-5213	117	5	)	)	PUNCT
ejpam-5213	117	6	is	be	AUX
ejpam-5213	117	7	a	a	DET
ejpam-5213	117	8	minimum	minimum	ADJ
ejpam-5213	117	9	dominating	dominating	NOUN
ejpam-5213	117	10	set	set	VERB
ejpam-5213	117	11	in	in	ADP
ejpam-5213	117	12	h	h	NOUN
ejpam-5213	117	13	and	and	CCONJ
ejpam-5213	117	14	|nh	|nh	NUM
ejpam-5213	117	15	[	[	X
ejpam-5213	117	16	x	x	X
ejpam-5213	117	17	]	]	X
ejpam-5213	117	18	∩	∩	ADJ
ejpam-5213	117	19	v	v	X
ejpam-5213	117	20	(	(	PUNCT
ejpam-5213	117	21	g)|	g)|	PROPN
ejpam-5213	117	22	is	be	AUX
ejpam-5213	117	23	odd	odd	ADJ
ejpam-5213	117	24	for	for	SCONJ
ejpam-5213	117	25	every	every	DET
ejpam-5213	117	26	x	x	SYM
ejpam-5213	117	27	∈	∈	PROPN
ejpam-5213	117	28	v	v	NOUN
ejpam-5213	117	29	(	(	PUNCT
ejpam-5213	117	30	h	h	NOUN
ejpam-5213	117	31	)	)	PUNCT
ejpam-5213	117	32	,	,	PUNCT
ejpam-5213	117	33	v	v	X
ejpam-5213	117	34	(	(	PUNCT
ejpam-5213	117	35	g	g	NOUN
ejpam-5213	117	36	)	)	PUNCT
ejpam-5213	117	37	is	be	AUX
ejpam-5213	117	38	a	a	DET
ejpam-5213	117	39	γodd	γodd	NOUN
ejpam-5213	117	40	-	-	PUNCT
ejpam-5213	117	41	set	set	NOUN
ejpam-5213	117	42	in	in	ADP
ejpam-5213	117	43	h.	h.	PROPN
ejpam-5213	117	44	thus	thus	ADV
ejpam-5213	117	45	,	,	PUNCT
ejpam-5213	117	46	γodd(h	γodd(h	PROPN
ejpam-5213	117	47	)	)	PUNCT
ejpam-5213	117	48	=	=	SYM
ejpam-5213	117	49	n.	n.	NOUN
ejpam-5213	117	50	suppose	suppose	VERB
ejpam-5213	117	51	γod(g	γod(g	NOUN
ejpam-5213	117	52	)	)	PUNCT
ejpam-5213	117	53	=	=	SYM
ejpam-5213	117	54	1	1	NUM
ejpam-5213	117	55	,	,	PUNCT
ejpam-5213	117	56	say	say	VERB
ejpam-5213	117	57	s	s	X
ejpam-5213	117	58	=	=	VERB
ejpam-5213	117	59	{	{	PUNCT
ejpam-5213	117	60	v	v	NOUN
ejpam-5213	117	61	}	}	PUNCT
ejpam-5213	117	62	is	be	AUX
ejpam-5213	117	63	a	a	DET
ejpam-5213	117	64	γod	γod	NOUN
ejpam-5213	117	65	-	-	PUNCT
ejpam-5213	117	66	set	set	VERB
ejpam-5213	117	67	in	in	ADP
ejpam-5213	117	68	g.	g.	PROPN
ejpam-5213	117	69	if	if	SCONJ
ejpam-5213	117	70	there	there	PRON
ejpam-5213	117	71	exists	exist	VERB
ejpam-5213	117	72	w	w	PROPN
ejpam-5213	117	73	∈	∈	PROPN
ejpam-5213	117	74	v	v	ADP
ejpam-5213	117	75	(	(	PUNCT
ejpam-5213	117	76	g	g	NOUN
ejpam-5213	117	77	)	)	PUNCT
ejpam-5213	117	78	\	\	NOUN
ejpam-5213	117	79	{	{	PUNCT
ejpam-5213	117	80	v	v	NOUN
ejpam-5213	117	81	}	}	PUNCT
ejpam-5213	117	82	,	,	PUNCT
ejpam-5213	117	83	then	then	ADV
ejpam-5213	117	84	ng[v	ng[v	NOUN
ejpam-5213	117	85	]	]	PUNCT
ejpam-5213	117	86	∩	∩	X
ejpam-5213	117	87	s	s	X
ejpam-5213	117	88	=	=	SYM
ejpam-5213	117	89	ng[w	ng[w	PROPN
ejpam-5213	117	90	]	]	PUNCT
ejpam-5213	117	91	∩	∩	X
ejpam-5213	117	92	s	s	PART
ejpam-5213	117	93	=	=	PUNCT
ejpam-5213	117	94	{	{	PUNCT
ejpam-5213	117	95	v	v	NOUN
ejpam-5213	117	96	}	}	PUNCT
ejpam-5213	117	97	,	,	PUNCT
ejpam-5213	117	98	contrary	contrary	ADV
ejpam-5213	117	99	to	to	ADP
ejpam-5213	117	100	the	the	DET
ejpam-5213	117	101	fact	fact	NOUN
ejpam-5213	117	102	that	that	SCONJ
ejpam-5213	117	103	s	s	VERB
ejpam-5213	117	104	is	be	AUX
ejpam-5213	117	105	a	a	DET
ejpam-5213	117	106	differentiating	differentiate	VERB
ejpam-5213	117	107	set	set	NOUN
ejpam-5213	117	108	.	.	PUNCT
ejpam-5213	118	1	thus	thus	ADV
ejpam-5213	118	2	,	,	PUNCT
ejpam-5213	118	3	g	g	PROPN
ejpam-5213	118	4	=	=	SYM
ejpam-5213	118	5	k1	k1	PROPN
ejpam-5213	118	6	.	.	PUNCT
ejpam-5213	119	1	we	we	PRON
ejpam-5213	119	2	state	state	VERB
ejpam-5213	119	3	this	this	PRON
ejpam-5213	119	4	formally	formally	ADV
ejpam-5213	119	5	.	.	PUNCT
ejpam-5213	120	1	remark	remark	PROPN
ejpam-5213	120	2	3	3	NUM
ejpam-5213	120	3	.	.	PUNCT
ejpam-5213	121	1	let	let	VERB
ejpam-5213	121	2	g	g	PRON
ejpam-5213	121	3	be	be	AUX
ejpam-5213	121	4	a	a	DET
ejpam-5213	121	5	graph	graph	NOUN
ejpam-5213	121	6	.	.	PUNCT
ejpam-5213	122	1	then	then	ADV
ejpam-5213	122	2	γod(g	γod(g	NUM
ejpam-5213	122	3	)	)	PUNCT
ejpam-5213	122	4	=	=	SYM
ejpam-5213	122	5	1	1	NUM
ejpam-5213	122	6	if	if	SCONJ
ejpam-5213	122	7	and	and	CCONJ
ejpam-5213	122	8	only	only	ADV
ejpam-5213	122	9	if	if	SCONJ
ejpam-5213	122	10	g	g	PROPN
ejpam-5213	122	11	=	=	SYM
ejpam-5213	122	12	k1	k1	PROPN
ejpam-5213	122	13	.	.	PUNCT
ejpam-5213	122	14	remark	remark	PROPN
ejpam-5213	122	15	4	4	NUM
ejpam-5213	122	16	.	.	PUNCT
ejpam-5213	123	1	there	there	PRON
ejpam-5213	123	2	exists	exist	VERB
ejpam-5213	123	3	no	no	DET
ejpam-5213	123	4	connected	connected	ADJ
ejpam-5213	123	5	graph	graph	NOUN
ejpam-5213	123	6	g	g	NOUN
ejpam-5213	123	7	with	with	ADP
ejpam-5213	123	8	γod(g	γod(g	PROPN
ejpam-5213	123	9	)	)	PUNCT
ejpam-5213	123	10	=	=	SYM
ejpam-5213	123	11	2	2	X
ejpam-5213	123	12	.	.	PUNCT
ejpam-5213	123	13	to	to	PART
ejpam-5213	123	14	see	see	VERB
ejpam-5213	123	15	this	this	PRON
ejpam-5213	123	16	,	,	PUNCT
ejpam-5213	123	17	suppose	suppose	VERB
ejpam-5213	123	18	that	that	SCONJ
ejpam-5213	123	19	such	such	DET
ejpam-5213	123	20	a	a	DET
ejpam-5213	123	21	connected	connected	ADJ
ejpam-5213	123	22	graphg	graphg	NOUN
ejpam-5213	123	23	exists	exist	VERB
ejpam-5213	123	24	.	.	PUNCT
ejpam-5213	124	1	then	then	ADV
ejpam-5213	124	2	|v	|v	PROPN
ejpam-5213	124	3	(	(	PUNCT
ejpam-5213	124	4	g)|	g)|	NOUN
ejpam-5213	124	5	=	=	SYM
ejpam-5213	124	6	2	2	NUM
ejpam-5213	124	7	according	accord	VERB
ejpam-5213	124	8	to	to	ADP
ejpam-5213	124	9	lemma	lemma	PROPN
ejpam-5213	124	10	1	1	NUM
ejpam-5213	124	11	.	.	PUNCT
ejpam-5213	125	1	hence	hence	ADV
ejpam-5213	125	2	,	,	PUNCT
ejpam-5213	125	3	g	g	PROPN
ejpam-5213	125	4	=	=	SYM
ejpam-5213	125	5	k2	k2	PROPN
ejpam-5213	125	6	.	.	PUNCT
ejpam-5213	126	1	this	this	PRON
ejpam-5213	126	2	,	,	PUNCT
ejpam-5213	126	3	however	however	ADV
ejpam-5213	126	4	,	,	PUNCT
ejpam-5213	126	5	is	be	AUX
ejpam-5213	126	6	not	not	PART
ejpam-5213	126	7	possible	possible	ADJ
ejpam-5213	126	8	by	by	ADP
ejpam-5213	126	9	corollary	corollary	ADJ
ejpam-5213	126	10	1	1	NUM
ejpam-5213	126	11	.	.	PUNCT
ejpam-5213	126	12	theorem	theorem	NOUN
ejpam-5213	126	13	3	3	X
ejpam-5213	126	14	.	.	PUNCT
ejpam-5213	127	1	let	let	VERB
ejpam-5213	127	2	g	g	PRON
ejpam-5213	127	3	be	be	AUX
ejpam-5213	127	4	a	a	DET
ejpam-5213	127	5	connected	connected	ADJ
ejpam-5213	127	6	graph	graph	NOUN
ejpam-5213	127	7	of	of	ADP
ejpam-5213	127	8	order	order	NOUN
ejpam-5213	127	9	n	n	PRON
ejpam-5213	127	10	≥	≥	NOUN
ejpam-5213	127	11	4	4	NUM
ejpam-5213	127	12	.	.	PUNCT
ejpam-5213	128	1	if	if	SCONJ
ejpam-5213	128	2	g	g	PROPN
ejpam-5213	128	3	admits	admit	VERB
ejpam-5213	128	4	a	a	DET
ejpam-5213	128	5	differentiating	differentiate	VERB
ejpam-5213	128	6	odd	odd	ADJ
ejpam-5213	128	7	dominating	dominating	NOUN
ejpam-5213	128	8	set	set	NOUN
ejpam-5213	128	9	,	,	PUNCT
ejpam-5213	128	10	then	then	ADV
ejpam-5213	128	11	max{γd(g	max{γd(g	PROPN
ejpam-5213	128	12	)	)	PUNCT
ejpam-5213	128	13	,	,	PUNCT
ejpam-5213	128	14	γodd(g	γodd(g	NOUN
ejpam-5213	128	15	)	)	PUNCT
ejpam-5213	128	16	,	,	PUNCT
ejpam-5213	128	17	3	3	X
ejpam-5213	128	18	}	}	PUNCT
ejpam-5213	128	19	≤	≤	NUM
ejpam-5213	128	20	γod(g	γod(g	PROPN
ejpam-5213	128	21	)	)	PUNCT
ejpam-5213	128	22	≤	≤	NOUN
ejpam-5213	129	1	n	n	CCONJ
ejpam-5213	129	2	−	−	PROPN
ejpam-5213	129	3	|s(g)|	|s(g)|	NOUN
ejpam-5213	129	4	.	.	PUNCT
ejpam-5213	130	1	moreover	moreover	ADV
ejpam-5213	130	2	,	,	PUNCT
ejpam-5213	130	3	γod(g	γod(g	PROPN
ejpam-5213	130	4	)	)	PUNCT
ejpam-5213	130	5	=	=	SYM
ejpam-5213	130	6	3	3	NUM
ejpam-5213	131	1	if	if	SCONJ
ejpam-5213	131	2	and	and	CCONJ
ejpam-5213	131	3	only	only	ADV
ejpam-5213	131	4	if	if	SCONJ
ejpam-5213	131	5	g	g	PROPN
ejpam-5213	131	6	=	=	PROPN
ejpam-5213	131	7	k1,3	k1,3	PROPN
ejpam-5213	131	8	.	.	PUNCT
ejpam-5213	131	9	proof	proof	NOUN
ejpam-5213	131	10	.	.	PUNCT
ejpam-5213	132	1	by	by	ADP
ejpam-5213	132	2	remarks	remark	NOUN
ejpam-5213	132	3	1	1	NUM
ejpam-5213	132	4	,	,	PUNCT
ejpam-5213	132	5	2	2	NUM
ejpam-5213	132	6	,	,	PUNCT
ejpam-5213	132	7	3	3	NUM
ejpam-5213	132	8	,	,	PUNCT
ejpam-5213	132	9	and	and	CCONJ
ejpam-5213	132	10	4	4	NUM
ejpam-5213	132	11	,	,	PUNCT
ejpam-5213	132	12	max{γd(g	max{γd(g	PROPN
ejpam-5213	132	13	)	)	PUNCT
ejpam-5213	132	14	,	,	PUNCT
ejpam-5213	132	15	γodd(g	γodd(g	NOUN
ejpam-5213	132	16	)	)	PUNCT
ejpam-5213	132	17	,	,	PUNCT
ejpam-5213	132	18	3	3	X
ejpam-5213	132	19	}	}	PUNCT
ejpam-5213	132	20	≤	≤	NUM
ejpam-5213	132	21	γod(g	γod(g	PROPN
ejpam-5213	132	22	)	)	PUNCT
ejpam-5213	132	23	.	.	PUNCT
ejpam-5213	133	1	next	next	ADV
ejpam-5213	133	2	,	,	PUNCT
ejpam-5213	133	3	let	let	VERB
ejpam-5213	133	4	s	s	PRON
ejpam-5213	133	5	be	be	AUX
ejpam-5213	133	6	a	a	DET
ejpam-5213	133	7	γod	γod	NOUN
ejpam-5213	133	8	-	-	PUNCT
ejpam-5213	133	9	set	set	VERB
ejpam-5213	133	10	in	in	ADP
ejpam-5213	133	11	g.	g.	PROPN
ejpam-5213	133	12	let	let	VERB
ejpam-5213	133	13	v	v	NUM
ejpam-5213	133	14	∈	∈	PROPN
ejpam-5213	133	15	s(g	s(g	PROPN
ejpam-5213	133	16	)	)	PUNCT
ejpam-5213	133	17	and	and	CCONJ
ejpam-5213	133	18	let	let	VERB
ejpam-5213	133	19	xv	xv	PRON
ejpam-5213	133	20	∈	∈	PROPN
ejpam-5213	133	21	l(g	l(g	PROPN
ejpam-5213	133	22	)	)	PUNCT
ejpam-5213	133	23	∩	∩	NOUN
ejpam-5213	133	24	ng(v	ng(v	X
ejpam-5213	133	25	)	)	PUNCT
ejpam-5213	133	26	be	be	AUX
ejpam-5213	133	27	fixed	fix	VERB
ejpam-5213	133	28	.	.	PUNCT
ejpam-5213	134	1	since	since	SCONJ
ejpam-5213	134	2	s	s	PROPN
ejpam-5213	134	3	is	be	AUX
ejpam-5213	134	4	an	an	DET
ejpam-5213	134	5	odd	odd	ADJ
ejpam-5213	134	6	dominating	dominating	NOUN
ejpam-5213	134	7	set	set	NOUN
ejpam-5213	134	8	,	,	PUNCT
ejpam-5213	134	9	v	v	ADP
ejpam-5213	134	10	∈	∈	NOUN
ejpam-5213	134	11	s	s	NOUN
ejpam-5213	134	12	or	or	CCONJ
ejpam-5213	134	13	xv	xv	PROPN
ejpam-5213	134	14	∈	∈	PROPN
ejpam-5213	134	15	s	s	PART
ejpam-5213	134	16	but	but	CCONJ
ejpam-5213	134	17	not	not	PART
ejpam-5213	134	18	both	both	PRON
ejpam-5213	134	19	.	.	PUNCT
ejpam-5213	135	1	let	let	VERB
ejpam-5213	135	2	dg	dg	VERB
ejpam-5213	135	3	=	=	VERB
ejpam-5213	135	4	{	{	PUNCT
ejpam-5213	135	5	w	w	PROPN
ejpam-5213	135	6	∈	∈	PROPN
ejpam-5213	135	7	v	v	ADP
ejpam-5213	135	8	(	(	PUNCT
ejpam-5213	135	9	g	g	NOUN
ejpam-5213	135	10	)	)	PUNCT
ejpam-5213	135	11	\	\	PUNCT
ejpam-5213	136	1	s	s	PART
ejpam-5213	136	2	:	:	PUNCT
ejpam-5213	136	3	w	w	PROPN
ejpam-5213	136	4	=	=	SYM
ejpam-5213	136	5	v	v	PROPN
ejpam-5213	136	6	∈	∈	PROPN
ejpam-5213	136	7	s(g	s(g	PROPN
ejpam-5213	136	8	)	)	PUNCT
ejpam-5213	136	9	or	or	CCONJ
ejpam-5213	136	10	w	w	PROPN
ejpam-5213	136	11	=	=	PUNCT
ejpam-5213	136	12	xv	xv	PROPN
ejpam-5213	136	13	}	}	PUNCT
ejpam-5213	136	14	.	.	PUNCT
ejpam-5213	137	1	then	then	ADV
ejpam-5213	137	2	|dg|	|dg|	PROPN
ejpam-5213	137	3	=	=	SYM
ejpam-5213	137	4	|s(g)|	|s(g)|	PROPN
ejpam-5213	137	5	and	and	CCONJ
ejpam-5213	137	6	s	s	VERB
ejpam-5213	137	7	⊆	⊆	NUM
ejpam-5213	137	8	v	v	NOUN
ejpam-5213	137	9	(	(	PUNCT
ejpam-5213	137	10	g	g	NOUN
ejpam-5213	137	11	)	)	PUNCT
ejpam-5213	137	12	\dg	\dg	PROPN
ejpam-5213	137	13	.	.	PUNCT
ejpam-5213	138	1	it	it	PRON
ejpam-5213	138	2	follows	follow	VERB
ejpam-5213	138	3	that	that	SCONJ
ejpam-5213	138	4	γ	γ	X
ejpam-5213	138	5	o	o	X
ejpam-5213	138	6	d(g	d(g	PROPN
ejpam-5213	138	7	)	)	PUNCT
ejpam-5213	138	8	=	=	SYM
ejpam-5213	138	9	|s|	|s|	PROPN
ejpam-5213	138	10	≤	≤	NUM
ejpam-5213	138	11	n−	n−	PROPN
ejpam-5213	138	12	|s(g)|	|s(g)|	NOUN
ejpam-5213	138	13	.	.	NOUN
ejpam-5213	139	1	for	for	ADP
ejpam-5213	139	2	the	the	DET
ejpam-5213	139	3	second	second	ADJ
ejpam-5213	139	4	part	part	NOUN
ejpam-5213	139	5	,	,	PUNCT
ejpam-5213	139	6	suppose	suppose	VERB
ejpam-5213	139	7	that	that	SCONJ
ejpam-5213	139	8	γod(g	γod(g	PROPN
ejpam-5213	139	9	)	)	PUNCT
ejpam-5213	139	10	=	=	SYM
ejpam-5213	139	11	3	3	X
ejpam-5213	139	12	.	.	X
ejpam-5213	139	13	from	from	ADP
ejpam-5213	139	14	lemma	lemma	PROPN
ejpam-5213	139	15	1	1	NUM
ejpam-5213	139	16	,	,	PUNCT
ejpam-5213	139	17	it	it	PRON
ejpam-5213	139	18	follows	follow	VERB
ejpam-5213	139	19	that	that	SCONJ
ejpam-5213	139	20	n	n	NOUN
ejpam-5213	139	21	=	=	SYM
ejpam-5213	139	22	4	4	X
ejpam-5213	139	23	.	.	PUNCT
ejpam-5213	140	1	it	it	PRON
ejpam-5213	140	2	can	can	AUX
ejpam-5213	140	3	easily	easily	ADV
ejpam-5213	140	4	be	be	AUX
ejpam-5213	140	5	verified	verify	VERB
ejpam-5213	140	6	that	that	SCONJ
ejpam-5213	140	7	among	among	ADP
ejpam-5213	140	8	the	the	DET
ejpam-5213	140	9	connected	connected	ADJ
ejpam-5213	140	10	graphs	graph	NOUN
ejpam-5213	140	11	of	of	ADP
ejpam-5213	140	12	order	order	NOUN
ejpam-5213	140	13	4	4	NUM
ejpam-5213	140	14	,	,	PUNCT
ejpam-5213	140	15	only	only	ADV
ejpam-5213	140	16	k1,3	k1,3	PRON
ejpam-5213	140	17	satisfies	satisfy	VERB
ejpam-5213	140	18	the	the	DET
ejpam-5213	140	19	given	give	VERB
ejpam-5213	140	20	property	property	NOUN
ejpam-5213	140	21	.	.	PUNCT
ejpam-5213	141	1	thus	thus	ADV
ejpam-5213	141	2	,	,	PUNCT
ejpam-5213	141	3	g	g	PROPN
ejpam-5213	141	4	=	=	PROPN
ejpam-5213	141	5	k1,3	k1,3	PROPN
ejpam-5213	141	6	.	.	PUNCT
ejpam-5213	142	1	the	the	DET
ejpam-5213	142	2	converse	converse	NOUN
ejpam-5213	142	3	is	be	AUX
ejpam-5213	142	4	easy	easy	ADJ
ejpam-5213	142	5	.	.	PUNCT
ejpam-5213	143	1	let	let	VERB
ejpam-5213	143	2	sp	sp	ADP
ejpam-5213	143	3	=	=	SYM
ejpam-5213	143	4	k1,p	k1,p	PROPN
ejpam-5213	143	5	and	and	CCONJ
ejpam-5213	143	6	sq	sq	PROPN
ejpam-5213	143	7	=	=	SYM
ejpam-5213	143	8	k1,q	k1,q	PROPN
ejpam-5213	143	9	be	be	VERB
ejpam-5213	143	10	stars	star	NOUN
ejpam-5213	143	11	with	with	ADP
ejpam-5213	143	12	central	central	ADJ
ejpam-5213	143	13	vertices	vertex	NOUN
ejpam-5213	143	14	(	(	PUNCT
ejpam-5213	143	15	support	support	NOUN
ejpam-5213	143	16	vertices	vertex	NOUN
ejpam-5213	143	17	)	)	PUNCT
ejpam-5213	143	18	v0	v0	NOUN
ejpam-5213	143	19	and	and	CCONJ
ejpam-5213	143	20	w0	w0	PROPN
ejpam-5213	143	21	,	,	PUNCT
ejpam-5213	143	22	respectively	respectively	ADV
ejpam-5213	143	23	.	.	PUNCT
ejpam-5213	144	1	then	then	ADV
ejpam-5213	144	2	the	the	DET
ejpam-5213	144	3	double	double	ADJ
ejpam-5213	144	4	star	star	NOUN
ejpam-5213	144	5	sp	sp	PROPN
ejpam-5213	144	6	,	,	PUNCT
ejpam-5213	144	7	q	q	X
ejpam-5213	144	8	is	be	AUX
ejpam-5213	144	9	the	the	DET
ejpam-5213	144	10	graph	graph	NOUN
ejpam-5213	144	11	obtained	obtain	VERB
ejpam-5213	144	12	from	from	ADP
ejpam-5213	144	13	sp	sp	ADP
ejpam-5213	144	14	and	and	CCONJ
ejpam-5213	144	15	sq	sq	INTJ
ejpam-5213	144	16	by	by	ADP
ejpam-5213	144	17	adding	add	VERB
ejpam-5213	144	18	the	the	DET
ejpam-5213	144	19	edge	edge	NOUN
ejpam-5213	144	20	v0w0	v0w0	PROPN
ejpam-5213	144	21	.	.	PROPN
ejpam-5213	144	22	corollary	corollary	ADJ
ejpam-5213	144	23	4	4	NUM
ejpam-5213	144	24	.	.	PUNCT
ejpam-5213	145	1	let	let	VERB
ejpam-5213	145	2	tn	tn	PRON
ejpam-5213	145	3	be	be	AUX
ejpam-5213	145	4	a	a	DET
ejpam-5213	145	5	tree	tree	NOUN
ejpam-5213	145	6	of	of	ADP
ejpam-5213	145	7	n	n	PRON
ejpam-5213	145	8	≥	≥	NOUN
ejpam-5213	145	9	4	4	NUM
ejpam-5213	145	10	.	.	PUNCT
ejpam-5213	146	1	if	if	SCONJ
ejpam-5213	146	2	tn	tn	PROPN
ejpam-5213	146	3	has	have	VERB
ejpam-5213	146	4	a	a	DET
ejpam-5213	146	5	differentiating	differentiate	VERB
ejpam-5213	146	6	odd	odd	ADJ
ejpam-5213	146	7	dominating	dominating	NOUN
ejpam-5213	146	8	set	set	NOUN
ejpam-5213	146	9	,	,	PUNCT
ejpam-5213	146	10	then	then	ADV
ejpam-5213	146	11	γod(tn	γod(tn	NOUN
ejpam-5213	146	12	)	)	PUNCT
ejpam-5213	146	13	≤	≤	NUM
ejpam-5213	146	14	n−	n−	NOUN
ejpam-5213	146	15	|s(tn)|	|s(tn)|	ADJ
ejpam-5213	146	16	with	with	ADP
ejpam-5213	146	17	equality	equality	NOUN
ejpam-5213	146	18	holding	hold	VERB
ejpam-5213	146	19	if	if	SCONJ
ejpam-5213	146	20	|ntn(v)∩l(tn)|	|ntn(v)∩l(tn)|	ADV
ejpam-5213	146	21	is	be	AUX
ejpam-5213	146	22	odd	odd	ADJ
ejpam-5213	146	23	and	and	CCONJ
ejpam-5213	146	24	at	at	ADV
ejpam-5213	146	25	least	least	ADJ
ejpam-5213	146	26	3	3	NUM
ejpam-5213	146	27	for	for	ADP
ejpam-5213	146	28	every	every	DET
ejpam-5213	146	29	v	v	NOUN
ejpam-5213	146	30	∈	∈	NOUN
ejpam-5213	146	31	s(tn	s(tn	NOUN
ejpam-5213	146	32	)	)	PUNCT
ejpam-5213	146	33	.	.	PUNCT
ejpam-5213	147	1	in	in	ADP
ejpam-5213	147	2	particular	particular	ADJ
ejpam-5213	147	3	,	,	PUNCT
ejpam-5213	147	4	if	if	SCONJ
ejpam-5213	147	5	tn	tn	NUM
ejpam-5213	147	6	=	=	SYM
ejpam-5213	147	7	sp	sp	NOUN
ejpam-5213	147	8	,	,	PUNCT
ejpam-5213	147	9	q	q	X
ejpam-5213	147	10	(	(	PUNCT
ejpam-5213	147	11	a	a	DET
ejpam-5213	147	12	double	double	ADJ
ejpam-5213	147	13	star	star	NOUN
ejpam-5213	147	14	)	)	PUNCT
ejpam-5213	147	15	,	,	PUNCT
ejpam-5213	147	16	where	where	SCONJ
ejpam-5213	147	17	p	p	PROPN
ejpam-5213	147	18	≥	≥	PUNCT
ejpam-5213	147	19	3	3	NUM
ejpam-5213	147	20	and	and	CCONJ
ejpam-5213	147	21	q	q	PROPN
ejpam-5213	147	22	≥	≥	NUM
ejpam-5213	147	23	3	3	NUM
ejpam-5213	147	24	and	and	CCONJ
ejpam-5213	147	25	are	be	AUX
ejpam-5213	147	26	odd	odd	ADJ
ejpam-5213	147	27	,	,	PUNCT
ejpam-5213	147	28	then	then	ADV
ejpam-5213	147	29	γod(tn	γod(tn	NOUN
ejpam-5213	147	30	)	)	PUNCT
ejpam-5213	148	1	=	=	SYM
ejpam-5213	148	2	n−	n−	NOUN
ejpam-5213	148	3	2	2	NUM
ejpam-5213	148	4	=	=	SYM
ejpam-5213	148	5	p+	p+	PROPN
ejpam-5213	148	6	q.	q.	PROPN
ejpam-5213	148	7	m.	m.	PROPN
ejpam-5213	148	8	carbero	carbero	PROPN
ejpam-5213	148	9	,	,	PUNCT
ejpam-5213	148	10	g.	g.	PROPN
ejpam-5213	148	11	malacas	malacas	PROPN
ejpam-5213	148	12	,	,	PUNCT
ejpam-5213	148	13	s.	s.	PROPN
ejpam-5213	148	14	canoy	canoy	PROPN
ejpam-5213	148	15	,	,	PUNCT
ejpam-5213	148	16	jr	jr	PROPN
ejpam-5213	148	17	.	.	PROPN
ejpam-5213	148	18	/	/	SYM
ejpam-5213	148	19	eur	eur	PROPN
ejpam-5213	148	20	.	.	PUNCT
ejpam-5213	149	1	j.	j.	PROPN
ejpam-5213	149	2	pure	pure	PROPN
ejpam-5213	149	3	appl	appl	PROPN
ejpam-5213	149	4	.	.	PROPN
ejpam-5213	149	5	math	math	PROPN
ejpam-5213	149	6	,	,	PUNCT
ejpam-5213	149	7	17	17	NUM
ejpam-5213	149	8	(	(	PUNCT
ejpam-5213	149	9	3	3	NUM
ejpam-5213	149	10	)	)	PUNCT
ejpam-5213	149	11	(	(	PUNCT
ejpam-5213	149	12	2024	2024	NUM
ejpam-5213	149	13	)	)	PUNCT
ejpam-5213	149	14	,	,	PUNCT
ejpam-5213	149	15	1585	1585	NUM
ejpam-5213	149	16	-	-	SYM
ejpam-5213	149	17	1601	1601	NUM
ejpam-5213	149	18	1590	1590	NUM
ejpam-5213	149	19	proof	proof	NOUN
ejpam-5213	149	20	.	.	PUNCT
ejpam-5213	150	1	suppose	suppose	VERB
ejpam-5213	150	2	s	s	PRON
ejpam-5213	150	3	is	be	AUX
ejpam-5213	150	4	a	a	DET
ejpam-5213	150	5	γod	γod	NOUN
ejpam-5213	150	6	-	-	PUNCT
ejpam-5213	150	7	set	set	VERB
ejpam-5213	150	8	in	in	ADP
ejpam-5213	150	9	tn	tn	PROPN
ejpam-5213	150	10	.	.	PUNCT
ejpam-5213	151	1	by	by	ADP
ejpam-5213	151	2	theorem	theorem	NOUN
ejpam-5213	151	3	3	3	NUM
ejpam-5213	151	4	,	,	PUNCT
ejpam-5213	151	5	γod(tn	γod(tn	NOUN
ejpam-5213	151	6	)	)	PUNCT
ejpam-5213	151	7	≤	≤	NOUN
ejpam-5213	151	8	n	n	CCONJ
ejpam-5213	151	9	−	−	PROPN
ejpam-5213	151	10	|s(tn)|	|s(tn)|	NOUN
ejpam-5213	151	11	.	.	PUNCT
ejpam-5213	152	1	next	next	ADV
ejpam-5213	152	2	,	,	PUNCT
ejpam-5213	152	3	suppose	suppose	VERB
ejpam-5213	152	4	that	that	SCONJ
ejpam-5213	152	5	|ntn(v	|ntn(v	PROPN
ejpam-5213	152	6	)	)	PUNCT
ejpam-5213	152	7	∩	∩	NOUN
ejpam-5213	152	8	l(tn)|	l(tn)|	PROPN
ejpam-5213	152	9	is	be	AUX
ejpam-5213	152	10	odd	odd	ADJ
ejpam-5213	152	11	and	and	CCONJ
ejpam-5213	152	12	at	at	ADV
ejpam-5213	152	13	least	least	ADJ
ejpam-5213	152	14	3	3	NUM
ejpam-5213	152	15	for	for	ADP
ejpam-5213	152	16	every	every	DET
ejpam-5213	152	17	v	v	NOUN
ejpam-5213	152	18	∈	∈	NOUN
ejpam-5213	152	19	s(tn	s(tn	NOUN
ejpam-5213	152	20	)	)	PUNCT
ejpam-5213	152	21	.	.	PUNCT
ejpam-5213	153	1	by	by	ADP
ejpam-5213	153	2	theorem	theorem	ADJ
ejpam-5213	153	3	2(ii	2(ii	NUM
ejpam-5213	153	4	)	)	PUNCT
ejpam-5213	153	5	,	,	PUNCT
ejpam-5213	153	6	it	it	PRON
ejpam-5213	153	7	follows	follow	VERB
ejpam-5213	153	8	that	that	SCONJ
ejpam-5213	153	9	ntn(v	ntn(v	PROPN
ejpam-5213	153	10	)	)	PUNCT
ejpam-5213	153	11	∩	∩	NOUN
ejpam-5213	153	12	l(tn	l(tn	NOUN
ejpam-5213	153	13	)	)	PUNCT
ejpam-5213	153	14	⊆	⊆	NUM
ejpam-5213	153	15	s	s	NOUN
ejpam-5213	153	16	and	and	CCONJ
ejpam-5213	153	17	v	v	NOUN
ejpam-5213	153	18	/∈	/∈	PUNCT
ejpam-5213	153	19	s	s	NOUN
ejpam-5213	153	20	for	for	ADP
ejpam-5213	153	21	every	every	DET
ejpam-5213	153	22	v	v	NOUN
ejpam-5213	153	23	∈	∈	NOUN
ejpam-5213	153	24	s(tn	s(tn	NOUN
ejpam-5213	153	25	)	)	PUNCT
ejpam-5213	153	26	.	.	PUNCT
ejpam-5213	154	1	therefore	therefore	ADV
ejpam-5213	154	2	,	,	PUNCT
ejpam-5213	154	3	s	s	PART
ejpam-5213	154	4	=	=	SYM
ejpam-5213	154	5	ntn(v)∩l(tn	ntn(v)∩l(tn	PROPN
ejpam-5213	154	6	)	)	PUNCT
ejpam-5213	154	7	and	and	CCONJ
ejpam-5213	154	8	γod(tn	γod(tn	NOUN
ejpam-5213	154	9	)	)	PUNCT
ejpam-5213	154	10	=	=	SYM
ejpam-5213	154	11	n−|s(tn)|	n−|s(tn)|	NUM
ejpam-5213	154	12	.	.	NOUN
ejpam-5213	155	1	from	from	ADP
ejpam-5213	155	2	this	this	PRON
ejpam-5213	155	3	,	,	PUNCT
ejpam-5213	155	4	it	it	PRON
ejpam-5213	155	5	follows	follow	VERB
ejpam-5213	155	6	that	that	SCONJ
ejpam-5213	155	7	γod(tn	γod(tn	NOUN
ejpam-5213	155	8	)	)	PUNCT
ejpam-5213	156	1	=	=	NOUN
ejpam-5213	156	2	p+q	p+q	NOUN
ejpam-5213	156	3	when	when	SCONJ
ejpam-5213	156	4	tn	tn	NOUN
ejpam-5213	156	5	=	=	SYM
ejpam-5213	156	6	sp	sp	PROPN
ejpam-5213	156	7	,	,	PUNCT
ejpam-5213	156	8	q.	q.	PROPN
ejpam-5213	156	9	theorem	theorem	VERB
ejpam-5213	156	10	4	4	NUM
ejpam-5213	156	11	.	.	NOUN
ejpam-5213	156	12	γod(cn	γod(cn	ADJ
ejpam-5213	156	13	)	)	PUNCT
ejpam-5213	156	14	=	=	SYM
ejpam-5213	156	15	n	n	PROPN
ejpam-5213	156	16	for	for	ADP
ejpam-5213	156	17	n	n	X
ejpam-5213	156	18	≥	≥	NOUN
ejpam-5213	156	19	4	4	NUM
ejpam-5213	156	20	.	.	PUNCT
ejpam-5213	157	1	proof	proof	NOUN
ejpam-5213	157	2	.	.	PUNCT
ejpam-5213	158	1	let	let	VERB
ejpam-5213	158	2	cn	cn	PROPN
ejpam-5213	158	3	=	=	PUNCT
ejpam-5213	159	1	[	[	X
ejpam-5213	159	2	v1	v1	NOUN
ejpam-5213	159	3	,	,	PUNCT
ejpam-5213	159	4	v2	v2	PROPN
ejpam-5213	159	5	,	,	PUNCT
ejpam-5213	159	6	...	...	PUNCT
ejpam-5213	159	7	,	,	PUNCT
ejpam-5213	159	8	vn	vn	INTJ
ejpam-5213	159	9	,	,	PUNCT
ejpam-5213	159	10	v1	v1	PROPN
ejpam-5213	159	11	]	]	PUNCT
ejpam-5213	159	12	and	and	CCONJ
ejpam-5213	159	13	let	let	VERB
ejpam-5213	159	14	s	s	PRON
ejpam-5213	159	15	be	be	AUX
ejpam-5213	159	16	a	a	DET
ejpam-5213	159	17	γod	γod	NOUN
ejpam-5213	159	18	-	-	PUNCT
ejpam-5213	159	19	set	set	VERB
ejpam-5213	159	20	in	in	ADP
ejpam-5213	159	21	cn	cn	PROPN
ejpam-5213	159	22	.	.	PUNCT
ejpam-5213	160	1	suppose	suppose	VERB
ejpam-5213	160	2	s	s	VERB
ejpam-5213	160	3	̸=	̸=	PROPN
ejpam-5213	160	4	v	v	NOUN
ejpam-5213	160	5	(	(	PUNCT
ejpam-5213	160	6	cn	cn	PROPN
ejpam-5213	160	7	)	)	PUNCT
ejpam-5213	160	8	.	.	PUNCT
ejpam-5213	161	1	then	then	ADV
ejpam-5213	161	2	there	there	PRON
ejpam-5213	161	3	exists	exist	VERB
ejpam-5213	161	4	v	v	ADP
ejpam-5213	161	5	∈	∈	PROPN
ejpam-5213	161	6	v	v	NOUN
ejpam-5213	161	7	(	(	PUNCT
ejpam-5213	161	8	cn	cn	PROPN
ejpam-5213	161	9	)	)	PUNCT
ejpam-5213	161	10	\	\	PROPN
ejpam-5213	161	11	s.	s.	PROPN
ejpam-5213	161	12	without	without	ADP
ejpam-5213	161	13	loss	loss	NOUN
ejpam-5213	161	14	of	of	ADP
ejpam-5213	161	15	generality	generality	NOUN
ejpam-5213	161	16	,	,	PUNCT
ejpam-5213	161	17	we	we	PRON
ejpam-5213	161	18	may	may	AUX
ejpam-5213	161	19	assume	assume	VERB
ejpam-5213	161	20	that	that	SCONJ
ejpam-5213	161	21	v	v	X
ejpam-5213	161	22	=	=	SYM
ejpam-5213	161	23	v1	v1	NOUN
ejpam-5213	161	24	.	.	PUNCT
ejpam-5213	162	1	since	since	SCONJ
ejpam-5213	162	2	s	s	PROPN
ejpam-5213	162	3	is	be	AUX
ejpam-5213	162	4	odd	odd	ADJ
ejpam-5213	162	5	dominating	dominating	NOUN
ejpam-5213	162	6	,	,	PUNCT
ejpam-5213	162	7	v2	v2	PROPN
ejpam-5213	162	8	∈	∈	PROPN
ejpam-5213	162	9	s	s	PART
ejpam-5213	162	10	or	or	CCONJ
ejpam-5213	162	11	vn	vn	ADP
ejpam-5213	162	12	∈	∈	PROPN
ejpam-5213	162	13	s	s	PART
ejpam-5213	162	14	but	but	CCONJ
ejpam-5213	162	15	not	not	PART
ejpam-5213	162	16	both	both	PRON
ejpam-5213	162	17	.	.	PUNCT
ejpam-5213	163	1	assume	assume	VERB
ejpam-5213	163	2	that	that	SCONJ
ejpam-5213	163	3	v2	v2	PROPN
ejpam-5213	163	4	∈	∈	PROPN
ejpam-5213	163	5	s.	s.	PROPN
ejpam-5213	163	6	then	then	ADV
ejpam-5213	163	7	vn	vn	PROPN
ejpam-5213	163	8	/∈	/∈	PUNCT
ejpam-5213	164	1	s.	s.	PROPN
ejpam-5213	164	2	since	since	SCONJ
ejpam-5213	164	3	|ncn	|ncn	PROPN
ejpam-5213	164	4	[	[	X
ejpam-5213	164	5	v2	v2	X
ejpam-5213	164	6	]	]	PUNCT
ejpam-5213	164	7	∩	∩	NOUN
ejpam-5213	164	8	s|	s|	NOUN
ejpam-5213	164	9	must	must	AUX
ejpam-5213	164	10	be	be	AUX
ejpam-5213	164	11	odd	odd	ADJ
ejpam-5213	164	12	,	,	PUNCT
ejpam-5213	164	13	v3	v3	PROPN
ejpam-5213	164	14	/∈	/∈	PUNCT
ejpam-5213	165	1	s.	s.	PROPN
ejpam-5213	165	2	this	this	PRON
ejpam-5213	165	3	implies	imply	VERB
ejpam-5213	165	4	that	that	SCONJ
ejpam-5213	165	5	ncn	ncn	NOUN
ejpam-5213	165	6	[	[	X
ejpam-5213	165	7	v1]∩s	v1]∩s	PROPN
ejpam-5213	165	8	=	=	ADJ
ejpam-5213	165	9	ncn	ncn	NOUN
ejpam-5213	166	1	[	[	X
ejpam-5213	166	2	v2]∩s	v2]∩s	NOUN
ejpam-5213	166	3	=	=	PUNCT
ejpam-5213	166	4	{	{	PUNCT
ejpam-5213	166	5	v2	v2	NOUN
ejpam-5213	166	6	}	}	PUNCT
ejpam-5213	166	7	,	,	PUNCT
ejpam-5213	166	8	contrary	contrary	ADV
ejpam-5213	166	9	to	to	ADP
ejpam-5213	166	10	the	the	DET
ejpam-5213	166	11	assumption	assumption	NOUN
ejpam-5213	166	12	that	that	SCONJ
ejpam-5213	166	13	s	s	VERB
ejpam-5213	166	14	is	be	AUX
ejpam-5213	166	15	a	a	DET
ejpam-5213	166	16	differentiating	differentiate	VERB
ejpam-5213	166	17	set	set	NOUN
ejpam-5213	166	18	.	.	PUNCT
ejpam-5213	167	1	therefore	therefore	ADV
ejpam-5213	167	2	,	,	PUNCT
ejpam-5213	167	3	s	s	NOUN
ejpam-5213	167	4	=	=	SYM
ejpam-5213	167	5	v	v	PROPN
ejpam-5213	167	6	(	(	PUNCT
ejpam-5213	167	7	cn	cn	PROPN
ejpam-5213	167	8	)	)	PUNCT
ejpam-5213	167	9	and	and	CCONJ
ejpam-5213	167	10	γod(cn	γod(cn	ADJ
ejpam-5213	167	11	)	)	PUNCT
ejpam-5213	167	12	=	=	SYM
ejpam-5213	167	13	n.	n.	NOUN
ejpam-5213	167	14	theorem	theorem	VERB
ejpam-5213	167	15	5	5	NUM
ejpam-5213	167	16	.	.	PUNCT
ejpam-5213	168	1	[	[	X
ejpam-5213	168	2	6	6	NUM
ejpam-5213	168	3	]	]	PUNCT
ejpam-5213	168	4	let	let	VERB
ejpam-5213	168	5	cn	cn	PROPN
ejpam-5213	168	6	be	be	AUX
ejpam-5213	168	7	the	the	DET
ejpam-5213	168	8	cycle	cycle	NOUN
ejpam-5213	168	9	on	on	ADP
ejpam-5213	168	10	n	n	DET
ejpam-5213	168	11	vertices	vertex	NOUN
ejpam-5213	168	12	.	.	PUNCT
ejpam-5213	169	1	for	for	ADP
ejpam-5213	169	2	n	n	PRON
ejpam-5213	169	3	≥	≥	NUM
ejpam-5213	169	4	3	3	NUM
ejpam-5213	169	5	,	,	PUNCT
ejpam-5213	169	6	γd(c2n	γd(c2n	NOUN
ejpam-5213	169	7	)	)	PUNCT
ejpam-5213	169	8	=	=	VERB
ejpam-5213	169	9	n.	n.	NOUN
ejpam-5213	169	10	corollary	corollary	NOUN
ejpam-5213	169	11	5	5	NUM
ejpam-5213	169	12	.	.	PUNCT
ejpam-5213	170	1	let	let	VERB
ejpam-5213	170	2	n	n	PRON
ejpam-5213	170	3	be	be	AUX
ejpam-5213	170	4	a	a	DET
ejpam-5213	170	5	positive	positive	ADJ
ejpam-5213	170	6	integer	integer	NOUN
ejpam-5213	170	7	such	such	ADJ
ejpam-5213	170	8	that	that	SCONJ
ejpam-5213	170	9	n	n	NUM
ejpam-5213	170	10	≥	≥	NOUN
ejpam-5213	170	11	3	3	NUM
ejpam-5213	170	12	.	.	PUNCT
ejpam-5213	171	1	then	then	ADV
ejpam-5213	171	2	there	there	PRON
ejpam-5213	171	3	exists	exist	VERB
ejpam-5213	171	4	a	a	DET
ejpam-5213	171	5	connected	connected	ADJ
ejpam-5213	171	6	graph	graph	NOUN
ejpam-5213	171	7	g	g	ADP
ejpam-5213	171	8	such	such	ADJ
ejpam-5213	171	9	that	that	DET
ejpam-5213	171	10	γod(g	γod(g	PROPN
ejpam-5213	171	11	)	)	PUNCT
ejpam-5213	171	12	−	−	NOUN
ejpam-5213	171	13	γd(g	γd(g	NUM
ejpam-5213	171	14	)	)	PUNCT
ejpam-5213	171	15	=	=	VERB
ejpam-5213	172	1	n.	n.	NOUN
ejpam-5213	172	2	in	in	ADP
ejpam-5213	172	3	other	other	ADJ
ejpam-5213	172	4	words	word	NOUN
ejpam-5213	172	5	,	,	PUNCT
ejpam-5213	172	6	the	the	DET
ejpam-5213	172	7	difference	difference	NOUN
ejpam-5213	172	8	γod	γod	ADP
ejpam-5213	172	9	−	−	NOUN
ejpam-5213	172	10	γd	γd	ADV
ejpam-5213	172	11	can	can	AUX
ejpam-5213	172	12	be	be	AUX
ejpam-5213	172	13	made	make	VERB
ejpam-5213	172	14	arbitrarily	arbitrarily	ADV
ejpam-5213	172	15	large	large	ADJ
ejpam-5213	172	16	.	.	PUNCT
ejpam-5213	173	1	proof	proof	NOUN
ejpam-5213	173	2	.	.	PUNCT
ejpam-5213	174	1	let	let	VERB
ejpam-5213	174	2	g	g	NOUN
ejpam-5213	174	3	=	=	NOUN
ejpam-5213	174	4	c2n	c2n	NOUN
ejpam-5213	174	5	.	.	PUNCT
ejpam-5213	175	1	by	by	ADP
ejpam-5213	175	2	theorem	theorem	NOUN
ejpam-5213	175	3	5	5	NUM
ejpam-5213	175	4	,	,	PUNCT
ejpam-5213	175	5	γd(c2n	γd(c2n	NOUN
ejpam-5213	175	6	)	)	PUNCT
ejpam-5213	175	7	=	=	SYM
ejpam-5213	175	8	n	n	NOUN
ejpam-5213	175	9	and	and	CCONJ
ejpam-5213	175	10	by	by	ADP
ejpam-5213	175	11	theorem	theorem	NOUN
ejpam-5213	175	12	4	4	NUM
ejpam-5213	175	13	,	,	PUNCT
ejpam-5213	175	14	γod(c2n	γod(c2n	NOUN
ejpam-5213	175	15	)	)	PUNCT
ejpam-5213	175	16	=	=	SYM
ejpam-5213	175	17	2n	2n	NUM
ejpam-5213	175	18	.	.	PUNCT
ejpam-5213	176	1	therefore	therefore	ADV
ejpam-5213	176	2	,	,	PUNCT
ejpam-5213	176	3	γod(g)−	γod(g)−	ADJ
ejpam-5213	176	4	γd(g	γd(g	NUM
ejpam-5213	176	5	)	)	PUNCT
ejpam-5213	176	6	=	=	SYM
ejpam-5213	176	7	n.	n.	NOUN
ejpam-5213	176	8	theorem	theorem	VERB
ejpam-5213	176	9	6	6	NUM
ejpam-5213	176	10	.	.	PUNCT
ejpam-5213	177	1	let	let	VERB
ejpam-5213	177	2	g	g	PROPN
ejpam-5213	177	3	=	=	SYM
ejpam-5213	177	4	kn1,n2,	kn1,n2,	PROPN
ejpam-5213	177	5	...	...	PUNCT
ejpam-5213	177	6	,nk	,nk	PUNCT
ejpam-5213	177	7	be	be	AUX
ejpam-5213	177	8	the	the	DET
ejpam-5213	177	9	complete	complete	ADJ
ejpam-5213	177	10	k	k	ADJ
ejpam-5213	177	11	-	-	ADJ
ejpam-5213	177	12	partite	partite	ADJ
ejpam-5213	177	13	graph	graph	NOUN
ejpam-5213	177	14	with	with	ADP
ejpam-5213	177	15	2	2	NUM
ejpam-5213	177	16	≤	≤	NUM
ejpam-5213	177	17	n1	n1	PROPN
ejpam-5213	177	18	≤	≤	NOUN
ejpam-5213	177	19	n2	n2	NOUN
ejpam-5213	177	20	≤	≤	NOUN
ejpam-5213	177	21	·	·	PUNCT
ejpam-5213	177	22	·	·	PUNCT
ejpam-5213	177	23	·	·	PUNCT
ejpam-5213	178	1	≤	≤	NUM
ejpam-5213	178	2	nk	nk	PROPN
ejpam-5213	178	3	,	,	PUNCT
ejpam-5213	178	4	where	where	SCONJ
ejpam-5213	178	5	k	k	PROPN
ejpam-5213	178	6	≥	≥	NUM
ejpam-5213	178	7	2	2	NUM
ejpam-5213	178	8	.	.	PUNCT
ejpam-5213	178	9	then	then	ADV
ejpam-5213	178	10	g	g	PROPN
ejpam-5213	178	11	admits	admit	VERB
ejpam-5213	178	12	a	a	DET
ejpam-5213	178	13	differentiating	differentiate	VERB
ejpam-5213	178	14	odd	odd	ADJ
ejpam-5213	178	15	dominating	dominating	NOUN
ejpam-5213	178	16	set	set	VERB
ejpam-5213	178	17	if	if	SCONJ
ejpam-5213	178	18	and	and	CCONJ
ejpam-5213	178	19	only	only	ADV
ejpam-5213	178	20	if	if	SCONJ
ejpam-5213	178	21	∑	∑	PROPN
ejpam-5213	178	22	j	j	PROPN
ejpam-5213	178	23	̸=t	̸=t	PROPN
ejpam-5213	178	24	nj	nj	PROPN
ejpam-5213	178	25	is	be	AUX
ejpam-5213	178	26	even	even	ADV
ejpam-5213	178	27	for	for	ADP
ejpam-5213	178	28	every	every	DET
ejpam-5213	178	29	t	t	NOUN
ejpam-5213	178	30	∈	∈	PROPN
ejpam-5213	178	31	{	{	PUNCT
ejpam-5213	178	32	1	1	NUM
ejpam-5213	178	33	,	,	PUNCT
ejpam-5213	178	34	2	2	NUM
ejpam-5213	178	35	,	,	PUNCT
ejpam-5213	178	36	.	.	PUNCT
ejpam-5213	178	37	.	.	PUNCT
ejpam-5213	179	1	.	.	PUNCT
ejpam-5213	180	1	,	,	PUNCT
ejpam-5213	180	2	k	k	X
ejpam-5213	180	3	}	}	PUNCT
ejpam-5213	180	4	.	.	PUNCT
ejpam-5213	181	1	moreover	moreover	ADV
ejpam-5213	181	2	,	,	PUNCT
ejpam-5213	181	3	in	in	ADP
ejpam-5213	181	4	this	this	DET
ejpam-5213	181	5	case	case	NOUN
ejpam-5213	181	6	,	,	PUNCT
ejpam-5213	181	7	γod(g	γod(g	PROPN
ejpam-5213	181	8	)	)	PUNCT
ejpam-5213	181	9	=	=	PUNCT
ejpam-5213	182	1	∑k	∑k	PROPN
ejpam-5213	182	2	j=1	j=1	PROPN
ejpam-5213	182	3	nj	nj	PROPN
ejpam-5213	182	4	.	.	PUNCT
ejpam-5213	183	1	proof	proof	NOUN
ejpam-5213	183	2	.	.	PUNCT
ejpam-5213	184	1	let	let	VERB
ejpam-5213	184	2	sn1	sn1	PROPN
ejpam-5213	184	3	,	,	PUNCT
ejpam-5213	184	4	sn2	sn2	PROPN
ejpam-5213	184	5	,	,	PUNCT
ejpam-5213	184	6	.	.	PUNCT
ejpam-5213	184	7	.	.	PUNCT
ejpam-5213	185	1	.	.	PUNCT
ejpam-5213	186	1	,	,	PUNCT
ejpam-5213	186	2	snk	snk	PROPN
ejpam-5213	186	3	be	be	AUX
ejpam-5213	186	4	the	the	DET
ejpam-5213	186	5	partite	partite	ADJ
ejpam-5213	186	6	sets	set	NOUN
ejpam-5213	186	7	in	in	ADP
ejpam-5213	186	8	g.	g.	PROPN
ejpam-5213	186	9	suppose	suppose	VERB
ejpam-5213	186	10	g	g	PROPN
ejpam-5213	186	11	admits	admit	VERB
ejpam-5213	186	12	a	a	DET
ejpam-5213	186	13	differentiating	differentiate	VERB
ejpam-5213	186	14	odd	odd	ADJ
ejpam-5213	186	15	dominating	dominating	NOUN
ejpam-5213	186	16	set	set	NOUN
ejpam-5213	186	17	s.	s.	PROPN
ejpam-5213	186	18	let	let	VERB
ejpam-5213	186	19	j	j	PROPN
ejpam-5213	186	20	∈	∈	PROPN
ejpam-5213	186	21	{	{	PUNCT
ejpam-5213	186	22	1	1	NUM
ejpam-5213	186	23	,	,	PUNCT
ejpam-5213	186	24	2	2	NUM
ejpam-5213	186	25	,	,	PUNCT
ejpam-5213	186	26	.	.	PUNCT
ejpam-5213	186	27	.	.	PUNCT
ejpam-5213	187	1	.	.	PUNCT
ejpam-5213	188	1	,	,	PUNCT
ejpam-5213	188	2	k	k	X
ejpam-5213	188	3	}	}	PUNCT
ejpam-5213	188	4	and	and	CCONJ
ejpam-5213	188	5	let	let	VERB
ejpam-5213	188	6	v	v	PRON
ejpam-5213	188	7	∈	∈	PROPN
ejpam-5213	188	8	snj	snj	NOUN
ejpam-5213	188	9	.	.	PUNCT
ejpam-5213	188	10	suppose	suppose	VERB
ejpam-5213	188	11	v	v	X
ejpam-5213	188	12	/∈	/∈	PUNCT
ejpam-5213	188	13	s.	s.	PROPN
ejpam-5213	188	14	note	note	VERB
ejpam-5213	188	15	that	that	SCONJ
ejpam-5213	188	16	since	since	SCONJ
ejpam-5213	188	17	s	s	PROPN
ejpam-5213	188	18	is	be	AUX
ejpam-5213	188	19	odd	odd	ADJ
ejpam-5213	188	20	dominating	dominating	NOUN
ejpam-5213	188	21	,	,	PUNCT
ejpam-5213	188	22	|ng[v	|ng[v	X
ejpam-5213	188	23	]	]	PUNCT
ejpam-5213	188	24	∩	∩	NOUN
ejpam-5213	188	25	s|	s|	NOUN
ejpam-5213	188	26	=	=	SYM
ejpam-5213	188	27	|ng(v	|ng(v	X
ejpam-5213	188	28	)	)	PUNCT
ejpam-5213	188	29	∩	∩	NOUN
ejpam-5213	188	30	s|	s|	NOUN
ejpam-5213	188	31	is	be	AUX
ejpam-5213	188	32	odd	odd	ADJ
ejpam-5213	188	33	.	.	PUNCT
ejpam-5213	189	1	pick	pick	VERB
ejpam-5213	189	2	any	any	DET
ejpam-5213	189	3	w	w	PROPN
ejpam-5213	189	4	∈	∈	PROPN
ejpam-5213	189	5	snj	snj	ADJ
ejpam-5213	189	6	\	\	PROPN
ejpam-5213	189	7	{	{	PUNCT
ejpam-5213	189	8	v	v	NOUN
ejpam-5213	189	9	}	}	PUNCT
ejpam-5213	189	10	.	.	PUNCT
ejpam-5213	190	1	since	since	SCONJ
ejpam-5213	190	2	s	s	NOUN
ejpam-5213	190	3	is	be	AUX
ejpam-5213	190	4	differentiating	differentiate	VERB
ejpam-5213	190	5	and	and	CCONJ
ejpam-5213	190	6	ng(w	ng(w	NOUN
ejpam-5213	190	7	)	)	PUNCT
ejpam-5213	190	8	∩	∩	NOUN
ejpam-5213	190	9	s	s	PART
ejpam-5213	190	10	=	=	PUNCT
ejpam-5213	190	11	ng(v	ng(v	X
ejpam-5213	190	12	)	)	PUNCT
ejpam-5213	190	13	∩	∩	NOUN
ejpam-5213	190	14	s	s	X
ejpam-5213	190	15	,	,	PUNCT
ejpam-5213	190	16	it	it	PRON
ejpam-5213	190	17	follows	follow	VERB
ejpam-5213	190	18	that	that	SCONJ
ejpam-5213	190	19	w	w	PROPN
ejpam-5213	190	20	∈	∈	PROPN
ejpam-5213	190	21	s	s	PART
ejpam-5213	190	22	and	and	CCONJ
ejpam-5213	190	23	ng[w	ng[w	PROPN
ejpam-5213	190	24	]	]	PUNCT
ejpam-5213	191	1	∩	∩	PROPN
ejpam-5213	191	2	s	s	PART
ejpam-5213	191	3	=	=	X
ejpam-5213	191	4	{	{	PUNCT
ejpam-5213	191	5	w	w	NOUN
ejpam-5213	191	6	}	}	PUNCT
ejpam-5213	191	7	∪	∪	X
ejpam-5213	191	8	(	(	PUNCT
ejpam-5213	191	9	ng(v	ng(v	NOUN
ejpam-5213	191	10	)	)	PUNCT
ejpam-5213	191	11	∩	∩	NOUN
ejpam-5213	191	12	s	s	PART
ejpam-5213	191	13	)	)	PUNCT
ejpam-5213	191	14	.	.	PUNCT
ejpam-5213	192	1	since	since	SCONJ
ejpam-5213	192	2	|ng(v	|ng(v	NOUN
ejpam-5213	192	3	)	)	PUNCT
ejpam-5213	192	4	∩	∩	NOUN
ejpam-5213	192	5	s|	s|	NOUN
ejpam-5213	192	6	is	be	AUX
ejpam-5213	192	7	odd	odd	ADJ
ejpam-5213	192	8	,	,	PUNCT
ejpam-5213	192	9	|ng[w	|ng[w	PROPN
ejpam-5213	192	10	]	]	PUNCT
ejpam-5213	192	11	∩	∩	NOUN
ejpam-5213	192	12	s|	s|	NOUN
ejpam-5213	192	13	is	be	AUX
ejpam-5213	192	14	even	even	ADV
ejpam-5213	192	15	,	,	PUNCT
ejpam-5213	192	16	contrary	contrary	ADV
ejpam-5213	192	17	to	to	ADP
ejpam-5213	192	18	the	the	DET
ejpam-5213	192	19	assumption	assumption	NOUN
ejpam-5213	192	20	that	that	SCONJ
ejpam-5213	192	21	s	s	VERB
ejpam-5213	192	22	is	be	AUX
ejpam-5213	192	23	an	an	DET
ejpam-5213	192	24	odd	odd	ADJ
ejpam-5213	192	25	dominating	dominating	NOUN
ejpam-5213	192	26	set	set	NOUN
ejpam-5213	192	27	.	.	PUNCT
ejpam-5213	193	1	therefore	therefore	ADV
ejpam-5213	193	2	,	,	PUNCT
ejpam-5213	193	3	snj	snj	VERB
ejpam-5213	193	4	⊆	⊆	NUM
ejpam-5213	193	5	s	s	NOUN
ejpam-5213	193	6	for	for	ADP
ejpam-5213	193	7	each	each	DET
ejpam-5213	193	8	j	j	PROPN
ejpam-5213	193	9	∈	∈	PROPN
ejpam-5213	193	10	{	{	PUNCT
ejpam-5213	193	11	1	1	NUM
ejpam-5213	193	12	,	,	PUNCT
ejpam-5213	193	13	2	2	NUM
ejpam-5213	193	14	,	,	PUNCT
ejpam-5213	193	15	.	.	PUNCT
ejpam-5213	193	16	.	.	PUNCT
ejpam-5213	193	17	.	.	PUNCT
ejpam-5213	194	1	,	,	PUNCT
ejpam-5213	194	2	k	k	X
ejpam-5213	194	3	}	}	PUNCT
ejpam-5213	194	4	,	,	PUNCT
ejpam-5213	194	5	i.e.	i.e.	X
ejpam-5213	194	6	,	,	PUNCT
ejpam-5213	194	7	s	s	NOUN
ejpam-5213	194	8	=	=	SYM
ejpam-5213	194	9	v	v	X
ejpam-5213	194	10	(	(	PUNCT
ejpam-5213	194	11	g	g	NOUN
ejpam-5213	194	12	)	)	PUNCT
ejpam-5213	194	13	.	.	PUNCT
ejpam-5213	195	1	now	now	ADV
ejpam-5213	195	2	,	,	PUNCT
ejpam-5213	195	3	let	let	VERB
ejpam-5213	195	4	t	t	PROPN
ejpam-5213	195	5	∈	∈	PROPN
ejpam-5213	195	6	{	{	PUNCT
ejpam-5213	195	7	1	1	NUM
ejpam-5213	195	8	,	,	PUNCT
ejpam-5213	195	9	2	2	NUM
ejpam-5213	195	10	,	,	PUNCT
ejpam-5213	195	11	.	.	PUNCT
ejpam-5213	195	12	.	.	PUNCT
ejpam-5213	196	1	.	.	PUNCT
ejpam-5213	197	1	,	,	PUNCT
ejpam-5213	197	2	k	k	X
ejpam-5213	197	3	}	}	PUNCT
ejpam-5213	197	4	and	and	CCONJ
ejpam-5213	197	5	let	let	VERB
ejpam-5213	197	6	a	a	DET
ejpam-5213	197	7	∈	∈	PROPN
ejpam-5213	197	8	snt	snt	NOUN
ejpam-5213	197	9	.	.	PUNCT
ejpam-5213	198	1	then	then	ADV
ejpam-5213	198	2	ng[a]∩s	ng[a]∩s	NUM
ejpam-5213	198	3	=	=	SYM
ejpam-5213	198	4	ng[a	ng[a	NOUN
ejpam-5213	198	5	]	]	X
ejpam-5213	198	6	=	=	SYM
ejpam-5213	198	7	{	{	PUNCT
ejpam-5213	198	8	a}∪	a}∪	NOUN
ejpam-5213	198	9	(	(	PUNCT
ejpam-5213	198	10	∪j	∪j	PROPN
ejpam-5213	198	11	̸=tsnj	̸=tsnj	PROPN
ejpam-5213	198	12	)	)	PUNCT
ejpam-5213	198	13	.	.	PUNCT
ejpam-5213	199	1	since	since	SCONJ
ejpam-5213	199	2	s	s	PROPN
ejpam-5213	199	3	is	be	AUX
ejpam-5213	199	4	odd	odd	ADJ
ejpam-5213	199	5	dominating	dominating	NOUN
ejpam-5213	199	6	,	,	PUNCT
ejpam-5213	199	7	|ng[a]|	|ng[a]|	NOUN
ejpam-5213	199	8	=	=	SYM
ejpam-5213	199	9	1	1	NUM
ejpam-5213	200	1	+	+	CCONJ
ejpam-5213	200	2	∑	∑	PROPN
ejpam-5213	200	3	j	j	PROPN
ejpam-5213	200	4	̸=t	̸=t	PROPN
ejpam-5213	200	5	|snj	|snj	PROPN
ejpam-5213	200	6	|	|	NOUN
ejpam-5213	200	7	=	=	SYM
ejpam-5213	200	8	1	1	NUM
ejpam-5213	200	9	+	+	CCONJ
ejpam-5213	200	10	∑	∑	PROPN
ejpam-5213	200	11	j	j	PROPN
ejpam-5213	200	12	̸=t	̸=t	PROPN
ejpam-5213	200	13	nj	nj	PROPN
ejpam-5213	200	14	is	be	AUX
ejpam-5213	200	15	odd	odd	ADJ
ejpam-5213	200	16	.	.	PUNCT
ejpam-5213	201	1	this	this	PRON
ejpam-5213	201	2	implies	imply	VERB
ejpam-5213	201	3	that	that	SCONJ
ejpam-5213	201	4	∑	∑	PROPN
ejpam-5213	201	5	j	j	PROPN
ejpam-5213	201	6	̸=t	̸=t	PROPN
ejpam-5213	201	7	nj	nj	PROPN
ejpam-5213	201	8	is	be	AUX
ejpam-5213	201	9	even	even	ADV
ejpam-5213	201	10	.	.	PUNCT
ejpam-5213	202	1	for	for	ADP
ejpam-5213	202	2	the	the	DET
ejpam-5213	202	3	converse	converse	NOUN
ejpam-5213	202	4	,	,	PUNCT
ejpam-5213	202	5	suppose	suppose	VERB
ejpam-5213	202	6	that	that	SCONJ
ejpam-5213	202	7	∑	∑	PROPN
ejpam-5213	202	8	j	j	PROPN
ejpam-5213	202	9	̸=t	̸=t	PROPN
ejpam-5213	202	10	nj	nj	PROPN
ejpam-5213	202	11	is	be	AUX
ejpam-5213	202	12	even	even	ADV
ejpam-5213	202	13	for	for	ADP
ejpam-5213	202	14	every	every	DET
ejpam-5213	202	15	t	t	NOUN
ejpam-5213	202	16	∈	∈	PROPN
ejpam-5213	202	17	{	{	PUNCT
ejpam-5213	202	18	1	1	NUM
ejpam-5213	202	19	,	,	PUNCT
ejpam-5213	202	20	2	2	NUM
ejpam-5213	202	21	,	,	PUNCT
ejpam-5213	202	22	.	.	PUNCT
ejpam-5213	202	23	.	.	PUNCT
ejpam-5213	203	1	.	.	PUNCT
ejpam-5213	204	1	,	,	PUNCT
ejpam-5213	204	2	k	k	X
ejpam-5213	204	3	}	}	PUNCT
ejpam-5213	204	4	.	.	PUNCT
ejpam-5213	205	1	let	let	VERB
ejpam-5213	205	2	d	d	NOUN
ejpam-5213	205	3	=	=	SYM
ejpam-5213	205	4	v	v	X
ejpam-5213	205	5	(	(	PUNCT
ejpam-5213	205	6	g	g	NOUN
ejpam-5213	205	7	)	)	PUNCT
ejpam-5213	205	8	and	and	CCONJ
ejpam-5213	205	9	let	let	VERB
ejpam-5213	205	10	x	x	PRON
ejpam-5213	205	11	,	,	PUNCT
ejpam-5213	205	12	y	y	PROPN
ejpam-5213	205	13	∈	∈	PROPN
ejpam-5213	205	14	v	v	ADP
ejpam-5213	205	15	(	(	PUNCT
ejpam-5213	205	16	g	g	NOUN
ejpam-5213	205	17	)	)	PUNCT
ejpam-5213	205	18	with	with	ADP
ejpam-5213	205	19	x	x	SYM
ejpam-5213	205	20	̸=	̸=	PROPN
ejpam-5213	205	21	y.	y.	NOUN
ejpam-5213	205	22	suppose	suppose	VERB
ejpam-5213	205	23	first	first	ADV
ejpam-5213	205	24	that	that	SCONJ
ejpam-5213	205	25	x	x	X
ejpam-5213	205	26	,	,	PUNCT
ejpam-5213	205	27	y	y	PROPN
ejpam-5213	205	28	∈	∈	PROPN
ejpam-5213	205	29	sr	sr	PROPN
ejpam-5213	205	30	for	for	ADP
ejpam-5213	205	31	some	some	DET
ejpam-5213	205	32	r	r	NOUN
ejpam-5213	205	33	∈	∈	PROPN
ejpam-5213	205	34	{	{	PUNCT
ejpam-5213	205	35	1	1	NUM
ejpam-5213	205	36	,	,	PUNCT
ejpam-5213	205	37	2	2	NUM
ejpam-5213	205	38	,	,	PUNCT
ejpam-5213	205	39	.	.	PUNCT
ejpam-5213	205	40	.	.	PUNCT
ejpam-5213	206	1	.	.	PUNCT
ejpam-5213	207	1	,	,	PUNCT
ejpam-5213	207	2	k	k	X
ejpam-5213	207	3	}	}	PUNCT
ejpam-5213	207	4	.	.	PUNCT
ejpam-5213	208	1	since	since	SCONJ
ejpam-5213	208	2	y	y	PROPN
ejpam-5213	208	3	/∈	/∈	PUNCT
ejpam-5213	208	4	ng[x	ng[x	PROPN
ejpam-5213	208	5	]	]	PUNCT
ejpam-5213	208	6	,	,	PUNCT
ejpam-5213	208	7	ng[x	ng[x	PROPN
ejpam-5213	208	8	]	]	PUNCT
ejpam-5213	208	9	∩	∩	PROPN
ejpam-5213	208	10	d	d	X
ejpam-5213	208	11	=	=	SYM
ejpam-5213	208	12	ng[x	ng[x	PROPN
ejpam-5213	208	13	]	]	PUNCT
ejpam-5213	208	14	̸=	̸=	PROPN
ejpam-5213	208	15	ng[y	ng[y	PROPN
ejpam-5213	208	16	]	]	X
ejpam-5213	208	17	=	=	SYM
ejpam-5213	208	18	ng[y	ng[y	PROPN
ejpam-5213	208	19	]	]	PUNCT
ejpam-5213	208	20	∩	∩	PROPN
ejpam-5213	208	21	d.	d.	PROPN
ejpam-5213	208	22	next	next	ADV
ejpam-5213	208	23	,	,	PUNCT
ejpam-5213	208	24	suppose	suppose	VERB
ejpam-5213	208	25	that	that	SCONJ
ejpam-5213	208	26	x	x	SYM
ejpam-5213	208	27	∈	∈	NOUN
ejpam-5213	208	28	sp	sp	ADP
ejpam-5213	208	29	and	and	CCONJ
ejpam-5213	208	30	y	y	PROPN
ejpam-5213	208	31	∈	∈	PROPN
ejpam-5213	208	32	sq	sq	INTJ
ejpam-5213	208	33	for	for	ADP
ejpam-5213	208	34	p	p	PROPN
ejpam-5213	208	35	̸=	̸=	PROPN
ejpam-5213	208	36	q	q	NOUN
ejpam-5213	208	37	,	,	PUNCT
ejpam-5213	208	38	where	where	SCONJ
ejpam-5213	208	39	p	p	X
ejpam-5213	208	40	,	,	PUNCT
ejpam-5213	208	41	q	q	NOUN
ejpam-5213	208	42	∈	∈	PROPN
ejpam-5213	208	43	{	{	PUNCT
ejpam-5213	208	44	1	1	NUM
ejpam-5213	208	45	,	,	PUNCT
ejpam-5213	208	46	2	2	NUM
ejpam-5213	208	47	,	,	PUNCT
ejpam-5213	208	48	.	.	PUNCT
ejpam-5213	208	49	.	.	PUNCT
ejpam-5213	208	50	.	.	PUNCT
ejpam-5213	209	1	,	,	PUNCT
ejpam-5213	209	2	k	k	X
ejpam-5213	209	3	}	}	PUNCT
ejpam-5213	209	4	.	.	PUNCT
ejpam-5213	210	1	since	since	SCONJ
ejpam-5213	210	2	v	v	X
ejpam-5213	210	3	(	(	PUNCT
ejpam-5213	210	4	sq	sq	ADJ
ejpam-5213	210	5	)	)	PUNCT
ejpam-5213	210	6	\	\	NOUN
ejpam-5213	210	7	{	{	PUNCT
ejpam-5213	210	8	y	y	NOUN
ejpam-5213	210	9	}	}	PUNCT
ejpam-5213	210	10	⊆	⊆	NUM
ejpam-5213	210	11	ng[x	ng[x	PROPN
ejpam-5213	210	12	]	]	PUNCT
ejpam-5213	210	13	\	\	PROPN
ejpam-5213	211	1	ng[y	ng[y	PROPN
ejpam-5213	211	2	]	]	PUNCT
ejpam-5213	211	3	,	,	PUNCT
ejpam-5213	211	4	ng[x	ng[x	PROPN
ejpam-5213	211	5	]	]	PUNCT
ejpam-5213	211	6	∩	∩	PROPN
ejpam-5213	211	7	d	d	X
ejpam-5213	211	8	=	=	SYM
ejpam-5213	211	9	ng[x	ng[x	PROPN
ejpam-5213	211	10	]	]	PUNCT
ejpam-5213	211	11	̸=	̸=	PROPN
ejpam-5213	211	12	ng[y	ng[y	PROPN
ejpam-5213	211	13	]	]	X
ejpam-5213	211	14	=	=	SYM
ejpam-5213	211	15	ng[y	ng[y	PROPN
ejpam-5213	211	16	]	]	PUNCT
ejpam-5213	211	17	∩	∩	PROPN
ejpam-5213	211	18	d.	d.	PROPN
ejpam-5213	211	19	hence	hence	ADV
ejpam-5213	211	20	,	,	PUNCT
ejpam-5213	211	21	d	d	PROPN
ejpam-5213	211	22	is	be	AUX
ejpam-5213	211	23	a	a	DET
ejpam-5213	211	24	differentiating	differentiate	VERB
ejpam-5213	211	25	set	set	NOUN
ejpam-5213	211	26	.	.	PUNCT
ejpam-5213	212	1	next	next	ADV
ejpam-5213	212	2	,	,	PUNCT
ejpam-5213	212	3	let	let	VERB
ejpam-5213	212	4	w	w	NOUN
ejpam-5213	212	5	∈	∈	PROPN
ejpam-5213	212	6	v	v	ADP
ejpam-5213	212	7	(	(	PUNCT
ejpam-5213	212	8	g	g	NOUN
ejpam-5213	212	9	)	)	PUNCT
ejpam-5213	212	10	and	and	CCONJ
ejpam-5213	212	11	let	let	VERB
ejpam-5213	212	12	w	w	PROPN
ejpam-5213	212	13	∈	∈	PROPN
ejpam-5213	212	14	st	st	PROPN
ejpam-5213	212	15	.	.	PROPN
ejpam-5213	212	16	then	then	ADV
ejpam-5213	212	17	,	,	PUNCT
ejpam-5213	212	18	by	by	ADP
ejpam-5213	212	19	assumption	assumption	NOUN
ejpam-5213	212	20	,	,	PUNCT
ejpam-5213	212	21	m.	m.	NOUN
ejpam-5213	212	22	carbero	carbero	NOUN
ejpam-5213	212	23	,	,	PUNCT
ejpam-5213	212	24	g.	g.	PROPN
ejpam-5213	212	25	malacas	malacas	PROPN
ejpam-5213	212	26	,	,	PUNCT
ejpam-5213	212	27	s.	s.	PROPN
ejpam-5213	212	28	canoy	canoy	PROPN
ejpam-5213	212	29	,	,	PUNCT
ejpam-5213	212	30	jr	jr	PROPN
ejpam-5213	212	31	.	.	PROPN
ejpam-5213	212	32	/	/	SYM
ejpam-5213	212	33	eur	eur	PROPN
ejpam-5213	212	34	.	.	PUNCT
ejpam-5213	213	1	j.	j.	PROPN
ejpam-5213	213	2	pure	pure	PROPN
ejpam-5213	213	3	appl	appl	PROPN
ejpam-5213	213	4	.	.	PROPN
ejpam-5213	213	5	math	math	PROPN
ejpam-5213	213	6	,	,	PUNCT
ejpam-5213	213	7	17	17	NUM
ejpam-5213	213	8	(	(	PUNCT
ejpam-5213	213	9	3	3	NUM
ejpam-5213	213	10	)	)	PUNCT
ejpam-5213	213	11	(	(	PUNCT
ejpam-5213	213	12	2024	2024	NUM
ejpam-5213	213	13	)	)	PUNCT
ejpam-5213	213	14	,	,	PUNCT
ejpam-5213	213	15	1585	1585	NUM
ejpam-5213	213	16	-	-	SYM
ejpam-5213	213	17	1601	1601	NUM
ejpam-5213	213	18	1591	1591	NUM
ejpam-5213	213	19	|ng[w	|ng[w	PROPN
ejpam-5213	213	20	]	]	PUNCT
ejpam-5213	213	21	∩d|	∩d|	PUNCT
ejpam-5213	214	1	=	=	PUNCT
ejpam-5213	214	2	|ng[w]|	|ng[w]|	NOUN
ejpam-5213	214	3	=	=	SYM
ejpam-5213	214	4	1	1	NUM
ejpam-5213	214	5	+	+	CCONJ
ejpam-5213	214	6	∑	∑	PROPN
ejpam-5213	214	7	j	j	PROPN
ejpam-5213	214	8	̸=t	̸=t	PROPN
ejpam-5213	214	9	nj	nj	PROPN
ejpam-5213	214	10	is	be	AUX
ejpam-5213	214	11	odd	odd	ADJ
ejpam-5213	214	12	.	.	PUNCT
ejpam-5213	215	1	therefore	therefore	ADV
ejpam-5213	215	2	,	,	PUNCT
ejpam-5213	215	3	d	d	PROPN
ejpam-5213	215	4	=	=	SYM
ejpam-5213	215	5	v	v	X
ejpam-5213	215	6	(	(	PUNCT
ejpam-5213	215	7	g	g	NOUN
ejpam-5213	215	8	)	)	PUNCT
ejpam-5213	215	9	is	be	AUX
ejpam-5213	215	10	a	a	DET
ejpam-5213	215	11	differentiating	differentiate	VERB
ejpam-5213	215	12	odd	odd	ADJ
ejpam-5213	215	13	dominating	dominating	NOUN
ejpam-5213	215	14	set	set	VERB
ejpam-5213	215	15	in	in	ADP
ejpam-5213	215	16	g.	g.	PROPN
ejpam-5213	215	17	whenever	whenever	SCONJ
ejpam-5213	215	18	the	the	DET
ejpam-5213	215	19	given	give	VERB
ejpam-5213	215	20	property	property	NOUN
ejpam-5213	215	21	is	be	AUX
ejpam-5213	215	22	satisfied	satisfied	ADJ
ejpam-5213	215	23	,	,	PUNCT
ejpam-5213	215	24	we	we	PRON
ejpam-5213	215	25	find	find	VERB
ejpam-5213	215	26	that	that	SCONJ
ejpam-5213	215	27	s	s	VERB
ejpam-5213	215	28	=	=	SYM
ejpam-5213	215	29	v	v	X
ejpam-5213	215	30	(	(	PUNCT
ejpam-5213	215	31	g	g	NOUN
ejpam-5213	215	32	)	)	PUNCT
ejpam-5213	215	33	is	be	AUX
ejpam-5213	215	34	the	the	DET
ejpam-5213	215	35	only	only	ADJ
ejpam-5213	215	36	differentiating	differentiate	VERB
ejpam-5213	215	37	odd	odd	ADJ
ejpam-5213	215	38	dominating	dominating	NOUN
ejpam-5213	215	39	set	set	VERB
ejpam-5213	215	40	in	in	ADP
ejpam-5213	215	41	g.	g.	PROPN
ejpam-5213	215	42	thus	thus	ADV
ejpam-5213	215	43	,	,	PUNCT
ejpam-5213	215	44	γod(g	γod(g	PROPN
ejpam-5213	215	45	)	)	PUNCT
ejpam-5213	216	1	=	=	SYM
ejpam-5213	216	2	|v	|v	PROPN
ejpam-5213	216	3	(	(	PUNCT
ejpam-5213	216	4	g)|	g)|	PROPN
ejpam-5213	216	5	=	=	SYM
ejpam-5213	216	6	∑k	∑k	PROPN
ejpam-5213	216	7	j=1	j=1	PROPN
ejpam-5213	216	8	nj	nj	PROPN
ejpam-5213	216	9	.	.	PUNCT
ejpam-5213	217	1	the	the	DET
ejpam-5213	217	2	next	next	ADJ
ejpam-5213	217	3	result	result	NOUN
ejpam-5213	217	4	is	be	AUX
ejpam-5213	217	5	immediate	immediate	ADJ
ejpam-5213	217	6	from	from	ADP
ejpam-5213	217	7	theorem	theorem	ADJ
ejpam-5213	217	8	6	6	NUM
ejpam-5213	217	9	.	.	PUNCT
ejpam-5213	217	10	corollary	corollary	ADJ
ejpam-5213	217	11	6	6	NUM
ejpam-5213	217	12	.	.	PUNCT
ejpam-5213	218	1	let	let	VERB
ejpam-5213	218	2	km	km	PROPN
ejpam-5213	218	3	,	,	PUNCT
ejpam-5213	218	4	n	n	PRON
ejpam-5213	218	5	be	be	VERB
ejpam-5213	218	6	a	a	DET
ejpam-5213	218	7	complete	complete	ADJ
ejpam-5213	218	8	bipartite	bipartite	NOUN
ejpam-5213	218	9	graph	graph	NOUN
ejpam-5213	218	10	such	such	ADJ
ejpam-5213	218	11	that	that	SCONJ
ejpam-5213	218	12	m	m	PROPN
ejpam-5213	218	13	≥	≥	NOUN
ejpam-5213	218	14	2	2	NUM
ejpam-5213	218	15	and	and	CCONJ
ejpam-5213	218	16	n	n	PRON
ejpam-5213	218	17	≥	≥	NOUN
ejpam-5213	218	18	2	2	NUM
ejpam-5213	218	19	.	.	PUNCT
ejpam-5213	219	1	then	then	ADV
ejpam-5213	219	2	km	km	PROPN
ejpam-5213	219	3	,	,	PUNCT
ejpam-5213	219	4	n	n	PRON
ejpam-5213	219	5	admits	admit	VERB
ejpam-5213	219	6	a	a	DET
ejpam-5213	219	7	differentiating	differentiate	VERB
ejpam-5213	219	8	odd	odd	ADJ
ejpam-5213	219	9	dominating	dominating	NOUN
ejpam-5213	219	10	set	set	VERB
ejpam-5213	219	11	if	if	SCONJ
ejpam-5213	219	12	and	and	CCONJ
ejpam-5213	219	13	only	only	ADV
ejpam-5213	219	14	if	if	SCONJ
ejpam-5213	219	15	m	m	VERB
ejpam-5213	219	16	and	and	CCONJ
ejpam-5213	219	17	n	n	PRON
ejpam-5213	219	18	are	be	AUX
ejpam-5213	219	19	both	both	PRON
ejpam-5213	219	20	even	even	ADV
ejpam-5213	219	21	.	.	PUNCT
ejpam-5213	220	1	moreover	moreover	ADV
ejpam-5213	220	2	,	,	PUNCT
ejpam-5213	220	3	γod(km	γod(km	PROPN
ejpam-5213	220	4	,	,	PUNCT
ejpam-5213	220	5	n	n	CCONJ
ejpam-5213	220	6	)	)	PUNCT
ejpam-5213	220	7	=	=	SYM
ejpam-5213	220	8	m+	m+	NUM
ejpam-5213	220	9	n.	n.	NOUN
ejpam-5213	220	10	theorem	theorem	VERB
ejpam-5213	220	11	7	7	NUM
ejpam-5213	220	12	.	.	PUNCT
ejpam-5213	221	1	let	let	VERB
ejpam-5213	221	2	g1	g1	PROPN
ejpam-5213	221	3	,	,	PUNCT
ejpam-5213	221	4	g2	g2	PROPN
ejpam-5213	221	5	,	,	PUNCT
ejpam-5213	221	6	·	·	PUNCT
ejpam-5213	221	7	·	·	PUNCT
ejpam-5213	221	8	·	·	PUNCT
ejpam-5213	221	9	,	,	PUNCT
ejpam-5213	221	10	gk	gk	PROPN
ejpam-5213	221	11	be	be	AUX
ejpam-5213	221	12	the	the	DET
ejpam-5213	221	13	components	component	NOUN
ejpam-5213	221	14	of	of	ADP
ejpam-5213	221	15	g.	g.	PROPN
ejpam-5213	221	16	then	then	ADV
ejpam-5213	221	17	g	g	PROPN
ejpam-5213	221	18	admits	admit	VERB
ejpam-5213	221	19	a	a	DET
ejpam-5213	221	20	differentiating	differentiate	VERB
ejpam-5213	221	21	odd	odd	ADJ
ejpam-5213	221	22	dominating	dominating	NOUN
ejpam-5213	221	23	set	set	VERB
ejpam-5213	221	24	if	if	SCONJ
ejpam-5213	221	25	and	and	CCONJ
ejpam-5213	221	26	only	only	ADV
ejpam-5213	221	27	if	if	SCONJ
ejpam-5213	221	28	gj	gj	NOUN
ejpam-5213	221	29	admits	admit	VERB
ejpam-5213	221	30	a	a	DET
ejpam-5213	221	31	differentiating	differentiate	VERB
ejpam-5213	221	32	odd	odd	ADJ
ejpam-5213	221	33	dominating	dominating	NOUN
ejpam-5213	221	34	set	set	NOUN
ejpam-5213	221	35	for	for	ADP
ejpam-5213	221	36	each	each	DET
ejpam-5213	221	37	j	j	PROPN
ejpam-5213	221	38	∈	∈	PROPN
ejpam-5213	221	39	{	{	PUNCT
ejpam-5213	221	40	1	1	NUM
ejpam-5213	221	41	,	,	PUNCT
ejpam-5213	221	42	2	2	NUM
ejpam-5213	221	43	,	,	PUNCT
ejpam-5213	221	44	.	.	PUNCT
ejpam-5213	221	45	.	.	PUNCT
ejpam-5213	222	1	.	.	PUNCT
ejpam-5213	223	1	,	,	PUNCT
ejpam-5213	223	2	k	k	X
ejpam-5213	223	3	}	}	PUNCT
ejpam-5213	223	4	.	.	PUNCT
ejpam-5213	224	1	in	in	ADP
ejpam-5213	224	2	this	this	DET
ejpam-5213	224	3	case	case	NOUN
ejpam-5213	224	4	,	,	PUNCT
ejpam-5213	224	5	γod(g	γod(g	PROPN
ejpam-5213	224	6	)	)	PUNCT
ejpam-5213	224	7	=	=	PUNCT
ejpam-5213	225	1	k∑	k∑	PROPN
ejpam-5213	225	2	j=1	j=1	NOUN
ejpam-5213	225	3	γod(gj	γod(gj	NUM
ejpam-5213	225	4	)	)	PUNCT
ejpam-5213	225	5	.	.	PUNCT
ejpam-5213	226	1	proof	proof	NOUN
ejpam-5213	226	2	.	.	PUNCT
ejpam-5213	227	1	suppose	suppose	VERB
ejpam-5213	227	2	g	g	PROPN
ejpam-5213	227	3	admits	admit	VERB
ejpam-5213	227	4	a	a	DET
ejpam-5213	227	5	differentiating	differentiate	VERB
ejpam-5213	227	6	odd	odd	ADJ
ejpam-5213	227	7	dominating	dominating	NOUN
ejpam-5213	227	8	set	set	NOUN
ejpam-5213	227	9	,	,	PUNCT
ejpam-5213	227	10	say	say	VERB
ejpam-5213	227	11	s.	s.	PROPN
ejpam-5213	227	12	let	let	VERB
ejpam-5213	227	13	sj	sj	INTJ
ejpam-5213	227	14	=	=	NOUN
ejpam-5213	227	15	s	s	PART
ejpam-5213	227	16	∩	∩	ADJ
ejpam-5213	227	17	v	v	NOUN
ejpam-5213	227	18	(	(	PUNCT
ejpam-5213	227	19	gj	gj	NOUN
ejpam-5213	227	20	)	)	PUNCT
ejpam-5213	227	21	for	for	ADP
ejpam-5213	227	22	each	each	DET
ejpam-5213	227	23	j	j	PROPN
ejpam-5213	227	24	∈	∈	PROPN
ejpam-5213	227	25	{	{	PUNCT
ejpam-5213	227	26	1	1	NUM
ejpam-5213	227	27	,	,	PUNCT
ejpam-5213	227	28	2	2	NUM
ejpam-5213	227	29	,	,	PUNCT
ejpam-5213	227	30	.	.	PUNCT
ejpam-5213	227	31	.	.	PUNCT
ejpam-5213	228	1	.	.	PUNCT
ejpam-5213	229	1	,	,	PUNCT
ejpam-5213	229	2	k	k	X
ejpam-5213	229	3	}	}	PUNCT
ejpam-5213	229	4	.	.	PUNCT
ejpam-5213	230	1	since	since	SCONJ
ejpam-5213	230	2	s	s	PROPN
ejpam-5213	230	3	is	be	AUX
ejpam-5213	230	4	dominating	dominate	VERB
ejpam-5213	230	5	,	,	PUNCT
ejpam-5213	230	6	sj	sj	PROPN
ejpam-5213	230	7	is	be	AUX
ejpam-5213	230	8	dominating	dominate	VERB
ejpam-5213	230	9	in	in	ADP
ejpam-5213	230	10	gj	gj	NOUN
ejpam-5213	230	11	for	for	ADP
ejpam-5213	230	12	each	each	DET
ejpam-5213	230	13	j	j	PROPN
ejpam-5213	230	14	∈	∈	PROPN
ejpam-5213	230	15	{	{	PUNCT
ejpam-5213	230	16	1	1	NUM
ejpam-5213	230	17	,	,	PUNCT
ejpam-5213	230	18	2	2	NUM
ejpam-5213	230	19	,	,	PUNCT
ejpam-5213	230	20	.	.	PUNCT
ejpam-5213	230	21	.	.	PUNCT
ejpam-5213	230	22	.	.	PUNCT
ejpam-5213	231	1	,	,	PUNCT
ejpam-5213	231	2	k	k	X
ejpam-5213	231	3	}	}	PUNCT
ejpam-5213	231	4	.	.	PUNCT
ejpam-5213	232	1	next	next	ADV
ejpam-5213	232	2	,	,	PUNCT
ejpam-5213	232	3	let	let	VERB
ejpam-5213	232	4	j	j	PROPN
ejpam-5213	232	5	∈	∈	PROPN
ejpam-5213	232	6	{	{	PUNCT
ejpam-5213	232	7	1	1	NUM
ejpam-5213	232	8	,	,	PUNCT
ejpam-5213	232	9	2	2	NUM
ejpam-5213	232	10	,	,	PUNCT
ejpam-5213	232	11	.	.	PUNCT
ejpam-5213	232	12	.	.	PUNCT
ejpam-5213	232	13	.	.	PUNCT
ejpam-5213	233	1	,	,	PUNCT
ejpam-5213	233	2	k	k	X
ejpam-5213	233	3	}	}	PUNCT
ejpam-5213	233	4	and	and	CCONJ
ejpam-5213	233	5	let	let	VERB
ejpam-5213	233	6	u	u	NOUN
ejpam-5213	233	7	,	,	PUNCT
ejpam-5213	233	8	v	v	NOUN
ejpam-5213	233	9	,	,	PUNCT
ejpam-5213	233	10	w	w	PROPN
ejpam-5213	233	11	∈	∈	PROPN
ejpam-5213	233	12	v	v	ADP
ejpam-5213	233	13	(	(	PUNCT
ejpam-5213	233	14	gj	gj	NOUN
ejpam-5213	233	15	)	)	PUNCT
ejpam-5213	233	16	,	,	PUNCT
ejpam-5213	234	1	where	where	SCONJ
ejpam-5213	234	2	u	u	NOUN
ejpam-5213	234	3	̸=	̸=	PROPN
ejpam-5213	234	4	v.	v.	ADV
ejpam-5213	234	5	since	since	SCONJ
ejpam-5213	234	6	s	s	PROPN
ejpam-5213	234	7	is	be	AUX
ejpam-5213	234	8	differentiating	differentiate	VERB
ejpam-5213	234	9	odd	odd	ADJ
ejpam-5213	234	10	dominating	dominating	NOUN
ejpam-5213	234	11	,	,	PUNCT
ejpam-5213	234	12	ngj	ngj	NOUN
ejpam-5213	235	1	[	[	X
ejpam-5213	235	2	u	u	X
ejpam-5213	235	3	]	]	X
ejpam-5213	235	4	∩	∩	ADJ
ejpam-5213	235	5	sj	sj	NOUN
ejpam-5213	235	6	=	=	SYM
ejpam-5213	235	7	ng[u	ng[u	PROPN
ejpam-5213	235	8	]	]	PUNCT
ejpam-5213	235	9	∩	∩	PROPN
ejpam-5213	235	10	s	s	PART
ejpam-5213	235	11	̸=	̸=	PROPN
ejpam-5213	235	12	ng[v	ng[v	X
ejpam-5213	235	13	]	]	PUNCT
ejpam-5213	235	14	∩	∩	PROPN
ejpam-5213	235	15	s	s	X
ejpam-5213	235	16	=	=	PUNCT
ejpam-5213	235	17	ngj	ngj	PROPN
ejpam-5213	235	18	[	[	X
ejpam-5213	235	19	v	v	X
ejpam-5213	235	20	]	]	X
ejpam-5213	235	21	∩	∩	ADJ
ejpam-5213	235	22	sj	sj	NOUN
ejpam-5213	235	23	and	and	CCONJ
ejpam-5213	235	24	|ngj	|ngj	NOUN
ejpam-5213	236	1	[	[	X
ejpam-5213	236	2	w]∩sj	w]∩sj	NOUN
ejpam-5213	236	3	|	|	ADV
ejpam-5213	236	4	is	be	AUX
ejpam-5213	236	5	odd	odd	ADJ
ejpam-5213	236	6	.	.	PUNCT
ejpam-5213	237	1	this	this	PRON
ejpam-5213	237	2	implies	imply	VERB
ejpam-5213	237	3	that	that	SCONJ
ejpam-5213	237	4	sj	sj	PROPN
ejpam-5213	237	5	is	be	AUX
ejpam-5213	237	6	a	a	DET
ejpam-5213	237	7	differentiating	differentiate	VERB
ejpam-5213	237	8	odd	odd	ADJ
ejpam-5213	237	9	dominating	dominating	NOUN
ejpam-5213	237	10	set	set	VERB
ejpam-5213	237	11	in	in	ADP
ejpam-5213	237	12	gj	gj	NOUN
ejpam-5213	237	13	.	.	PUNCT
ejpam-5213	238	1	for	for	ADP
ejpam-5213	238	2	the	the	DET
ejpam-5213	238	3	converse	converse	NOUN
ejpam-5213	238	4	,	,	PUNCT
ejpam-5213	238	5	suppose	suppose	VERB
ejpam-5213	238	6	that	that	SCONJ
ejpam-5213	238	7	each	each	DET
ejpam-5213	238	8	component	component	NOUN
ejpam-5213	238	9	gj	gj	NOUN
ejpam-5213	238	10	admits	admit	VERB
ejpam-5213	238	11	a	a	DET
ejpam-5213	238	12	differentiating	differentiate	VERB
ejpam-5213	238	13	odd	odd	ADJ
ejpam-5213	238	14	dominating	dominating	NOUN
ejpam-5213	238	15	set	set	NOUN
ejpam-5213	238	16	,	,	PUNCT
ejpam-5213	238	17	say	say	VERB
ejpam-5213	238	18	dj	dj	NOUN
ejpam-5213	238	19	.	.	PUNCT
ejpam-5213	239	1	then	then	ADV
ejpam-5213	239	2	,	,	PUNCT
ejpam-5213	239	3	clearly	clearly	ADV
ejpam-5213	239	4	,	,	PUNCT
ejpam-5213	239	5	s	s	VERB
ejpam-5213	239	6	′	′	NOUN
ejpam-5213	239	7	=	=	PUNCT
ejpam-5213	240	1	∪k	∪k	NUM
ejpam-5213	240	2	j=1dj	j=1dj	X
ejpam-5213	240	3	is	be	AUX
ejpam-5213	240	4	a	a	DET
ejpam-5213	240	5	differentiating	differentiate	VERB
ejpam-5213	240	6	odd	odd	ADJ
ejpam-5213	240	7	dominating	dominating	NOUN
ejpam-5213	240	8	set	set	VERB
ejpam-5213	240	9	in	in	ADP
ejpam-5213	240	10	g.	g.	PROPN
ejpam-5213	240	11	now	now	ADV
ejpam-5213	240	12	,	,	PUNCT
ejpam-5213	240	13	let	let	VERB
ejpam-5213	240	14	s0	s0	PROPN
ejpam-5213	240	15	be	be	AUX
ejpam-5213	240	16	a	a	DET
ejpam-5213	240	17	γod	γod	NOUN
ejpam-5213	240	18	-	-	PUNCT
ejpam-5213	240	19	set	set	VERB
ejpam-5213	240	20	in	in	ADP
ejpam-5213	240	21	g.	g.	PROPN
ejpam-5213	240	22	then	then	ADV
ejpam-5213	240	23	s′	s′	VERB
ejpam-5213	240	24	j	j	PROPN
ejpam-5213	240	25	=	=	SYM
ejpam-5213	240	26	s0	s0	PROPN
ejpam-5213	240	27	∩	∩	X
ejpam-5213	240	28	v	v	NOUN
ejpam-5213	240	29	(	(	PUNCT
ejpam-5213	240	30	gj	gj	NOUN
ejpam-5213	240	31	)	)	PUNCT
ejpam-5213	240	32	is	be	AUX
ejpam-5213	240	33	a	a	DET
ejpam-5213	240	34	differentiating	differentiate	VERB
ejpam-5213	240	35	odd	odd	ADJ
ejpam-5213	240	36	dominating	dominating	NOUN
ejpam-5213	240	37	set	set	VERB
ejpam-5213	240	38	in	in	ADP
ejpam-5213	240	39	gj	gj	NOUN
ejpam-5213	240	40	for	for	ADP
ejpam-5213	240	41	each	each	DET
ejpam-5213	240	42	j	j	PROPN
ejpam-5213	240	43	∈	∈	PROPN
ejpam-5213	240	44	{	{	PUNCT
ejpam-5213	240	45	1	1	NUM
ejpam-5213	240	46	,	,	PUNCT
ejpam-5213	240	47	2	2	NUM
ejpam-5213	240	48	,	,	PUNCT
ejpam-5213	240	49	.	.	PUNCT
ejpam-5213	240	50	.	.	PUNCT
ejpam-5213	241	1	.	.	PUNCT
ejpam-5213	242	1	,	,	PUNCT
ejpam-5213	242	2	k	k	X
ejpam-5213	242	3	}	}	PUNCT
ejpam-5213	242	4	and	and	CCONJ
ejpam-5213	242	5	s0	s0	PROPN
ejpam-5213	242	6	=	=	SYM
ejpam-5213	242	7	∪k	∪k	NUM
ejpam-5213	242	8	j=1s	j=1s	PROPN
ejpam-5213	242	9	′	′	PROPN
ejpam-5213	242	10	j	j	PROPN
ejpam-5213	242	11	.	.	PUNCT
ejpam-5213	243	1	hence	hence	ADV
ejpam-5213	243	2	,	,	PUNCT
ejpam-5213	243	3	γod(g	γod(g	PROPN
ejpam-5213	243	4	)	)	PUNCT
ejpam-5213	243	5	=	=	SYM
ejpam-5213	244	1	|s0|	|s0|	NOUN
ejpam-5213	244	2	=	=	SYM
ejpam-5213	244	3	k∑	k∑	PROPN
ejpam-5213	245	1	j=1	j=1	PROPN
ejpam-5213	245	2	|s′	|s′	NOUN
ejpam-5213	245	3	j	j	PROPN
ejpam-5213	245	4	|	|	ADV
ejpam-5213	245	5	≥	≥	NOUN
ejpam-5213	245	6	k∑	k∑	VERB
ejpam-5213	245	7	j=1	j=1	NOUN
ejpam-5213	245	8	γod(gj	γod(gj	NUM
ejpam-5213	245	9	)	)	PUNCT
ejpam-5213	245	10	.	.	PUNCT
ejpam-5213	246	1	on	on	ADP
ejpam-5213	246	2	the	the	DET
ejpam-5213	246	3	other	other	ADJ
ejpam-5213	246	4	hand	hand	NOUN
ejpam-5213	246	5	,	,	PUNCT
ejpam-5213	246	6	ifd′	ifd′	PROPN
ejpam-5213	246	7	j	j	PROPN
ejpam-5213	246	8	is	be	AUX
ejpam-5213	246	9	a	a	DET
ejpam-5213	246	10	γ	γ	X
ejpam-5213	246	11	o	o	X
ejpam-5213	246	12	d	d	VERB
ejpam-5213	246	13	-	-	PUNCT
ejpam-5213	246	14	set	set	VERB
ejpam-5213	246	15	ingj	ingj	NOUN
ejpam-5213	246	16	for	for	ADP
ejpam-5213	246	17	each	each	DET
ejpam-5213	246	18	j	j	PROPN
ejpam-5213	246	19	∈	∈	PROPN
ejpam-5213	246	20	{	{	PUNCT
ejpam-5213	246	21	1	1	NUM
ejpam-5213	246	22	,	,	PUNCT
ejpam-5213	246	23	2	2	NUM
ejpam-5213	246	24	,	,	PUNCT
ejpam-5213	246	25	.	.	PUNCT
ejpam-5213	246	26	.	.	PUNCT
ejpam-5213	247	1	.	.	PUNCT
ejpam-5213	248	1	,	,	PUNCT
ejpam-5213	248	2	k	k	X
ejpam-5213	248	3	}	}	PUNCT
ejpam-5213	248	4	,	,	PUNCT
ejpam-5213	248	5	then	then	ADV
ejpam-5213	248	6	s′	s′	X
ejpam-5213	248	7	0	0	NUM
ejpam-5213	248	8	=	=	SYM
ejpam-5213	248	9	∪k	∪k	NUM
ejpam-5213	248	10	j=1d	j=1d	NOUN
ejpam-5213	248	11	′	′	PROPN
ejpam-5213	248	12	j	j	PROPN
ejpam-5213	248	13	is	be	AUX
ejpam-5213	248	14	a	a	DET
ejpam-5213	248	15	differentiating	differentiate	VERB
ejpam-5213	248	16	odd	odd	ADJ
ejpam-5213	248	17	dominating	dominating	NOUN
ejpam-5213	248	18	set	set	VERB
ejpam-5213	248	19	in	in	ADP
ejpam-5213	248	20	g.	g.	PROPN
ejpam-5213	249	1	it	it	PRON
ejpam-5213	249	2	follows	follow	VERB
ejpam-5213	249	3	that	that	SCONJ
ejpam-5213	249	4	γod(g	γod(g	PROPN
ejpam-5213	249	5	)	)	PUNCT
ejpam-5213	249	6	≤	≤	NUM
ejpam-5213	249	7	|s′	|s′	NOUN
ejpam-5213	249	8	0|	0|	NUM
ejpam-5213	249	9	=	=	PUNCT
ejpam-5213	249	10	k∑	k∑	PROPN
ejpam-5213	250	1	j=1	j=1	PROPN
ejpam-5213	251	1	|d′	|d′	ADV
ejpam-5213	251	2	j	j	PROPN
ejpam-5213	251	3	|	|	NOUN
ejpam-5213	251	4	=	=	SYM
ejpam-5213	251	5	k∑	k∑	PROPN
ejpam-5213	251	6	j=1	j=1	NOUN
ejpam-5213	251	7	γod(gj	γod(gj	NUM
ejpam-5213	251	8	)	)	PUNCT
ejpam-5213	251	9	.	.	PUNCT
ejpam-5213	252	1	this	this	PRON
ejpam-5213	252	2	proves	prove	VERB
ejpam-5213	252	3	the	the	DET
ejpam-5213	252	4	desired	desire	VERB
ejpam-5213	252	5	equality	equality	NOUN
ejpam-5213	252	6	.	.	PUNCT
ejpam-5213	253	1	corollary	corollary	ADJ
ejpam-5213	253	2	7	7	NUM
ejpam-5213	253	3	.	.	PUNCT
ejpam-5213	254	1	let	let	VERB
ejpam-5213	254	2	g	g	PRON
ejpam-5213	254	3	be	be	AUX
ejpam-5213	254	4	a	a	DET
ejpam-5213	254	5	graph	graph	NOUN
ejpam-5213	254	6	.	.	PUNCT
ejpam-5213	255	1	then	then	ADV
ejpam-5213	255	2	each	each	PRON
ejpam-5213	255	3	of	of	ADP
ejpam-5213	255	4	the	the	DET
ejpam-5213	255	5	following	follow	VERB
ejpam-5213	255	6	holds	hold	NOUN
ejpam-5213	255	7	:	:	PUNCT
ejpam-5213	255	8	m.	m.	NOUN
ejpam-5213	255	9	carbero	carbero	PROPN
ejpam-5213	255	10	,	,	PUNCT
ejpam-5213	255	11	g.	g.	PROPN
ejpam-5213	255	12	malacas	malacas	PROPN
ejpam-5213	255	13	,	,	PUNCT
ejpam-5213	255	14	s.	s.	PROPN
ejpam-5213	255	15	canoy	canoy	PROPN
ejpam-5213	255	16	,	,	PUNCT
ejpam-5213	255	17	jr	jr	PROPN
ejpam-5213	255	18	.	.	PROPN
ejpam-5213	255	19	/	/	SYM
ejpam-5213	255	20	eur	eur	PROPN
ejpam-5213	255	21	.	.	PUNCT
ejpam-5213	256	1	j.	j.	PROPN
ejpam-5213	256	2	pure	pure	PROPN
ejpam-5213	256	3	appl	appl	PROPN
ejpam-5213	256	4	.	.	PROPN
ejpam-5213	256	5	math	math	PROPN
ejpam-5213	256	6	,	,	PUNCT
ejpam-5213	256	7	17	17	NUM
ejpam-5213	256	8	(	(	PUNCT
ejpam-5213	256	9	3	3	NUM
ejpam-5213	256	10	)	)	PUNCT
ejpam-5213	256	11	(	(	PUNCT
ejpam-5213	256	12	2024	2024	NUM
ejpam-5213	256	13	)	)	PUNCT
ejpam-5213	256	14	,	,	PUNCT
ejpam-5213	256	15	1585	1585	NUM
ejpam-5213	256	16	-	-	SYM
ejpam-5213	256	17	1601	1601	NUM
ejpam-5213	256	18	1592	1592	NUM
ejpam-5213	256	19	(	(	PUNCT
ejpam-5213	256	20	i	i	NOUN
ejpam-5213	256	21	)	)	PUNCT
ejpam-5213	256	22	if	if	SCONJ
ejpam-5213	256	23	g	g	PROPN
ejpam-5213	256	24	=	=	SYM
ejpam-5213	256	25	kn	kn	PROPN
ejpam-5213	256	26	,	,	PUNCT
ejpam-5213	256	27	then	then	ADV
ejpam-5213	256	28	γod(g	γod(g	NUM
ejpam-5213	256	29	)	)	PUNCT
ejpam-5213	256	30	=	=	SYM
ejpam-5213	256	31	n.	n.	NOUN
ejpam-5213	256	32	(	(	PUNCT
ejpam-5213	256	33	ii	ii	NOUN
ejpam-5213	256	34	)	)	PUNCT
ejpam-5213	256	35	γod(g	γod(g	PROPN
ejpam-5213	256	36	)	)	PUNCT
ejpam-5213	256	37	=	=	SYM
ejpam-5213	256	38	2	2	NUM
ejpam-5213	256	39	if	if	SCONJ
ejpam-5213	256	40	and	and	CCONJ
ejpam-5213	256	41	only	only	ADV
ejpam-5213	256	42	if	if	SCONJ
ejpam-5213	256	43	g	g	PROPN
ejpam-5213	256	44	=	=	SYM
ejpam-5213	256	45	k2	k2	PROPN
ejpam-5213	256	46	.	.	PUNCT
ejpam-5213	257	1	(	(	PUNCT
ejpam-5213	257	2	iii	iii	NOUN
ejpam-5213	257	3	)	)	PUNCT
ejpam-5213	257	4	γod(g	γod(g	PROPN
ejpam-5213	257	5	)	)	PUNCT
ejpam-5213	257	6	=	=	SYM
ejpam-5213	257	7	3	3	NUM
ejpam-5213	257	8	if	if	SCONJ
ejpam-5213	257	9	and	and	CCONJ
ejpam-5213	257	10	only	only	ADV
ejpam-5213	257	11	if	if	SCONJ
ejpam-5213	257	12	g	g	PROPN
ejpam-5213	257	13	∈	∈	PROPN
ejpam-5213	257	14	{	{	PUNCT
ejpam-5213	257	15	k3,k1,3	k3,k1,3	NOUN
ejpam-5213	257	16	}	}	PUNCT
ejpam-5213	257	17	.	.	PUNCT
ejpam-5213	258	1	the	the	DET
ejpam-5213	258	2	join	join	PROPN
ejpam-5213	258	3	g+h	g+h	PROPN
ejpam-5213	258	4	of	of	ADP
ejpam-5213	258	5	two	two	NUM
ejpam-5213	258	6	graphs	graph	NOUN
ejpam-5213	258	7	g	g	NOUN
ejpam-5213	258	8	and	and	CCONJ
ejpam-5213	258	9	h	h	NOUN
ejpam-5213	258	10	is	be	AUX
ejpam-5213	258	11	the	the	DET
ejpam-5213	258	12	graph	graph	NOUN
ejpam-5213	258	13	with	with	ADP
ejpam-5213	258	14	v	v	NOUN
ejpam-5213	258	15	(	(	PUNCT
ejpam-5213	258	16	g+h	g+h	NOUN
ejpam-5213	258	17	)	)	PUNCT
ejpam-5213	258	18	=	=	SYM
ejpam-5213	258	19	v	v	X
ejpam-5213	258	20	(	(	PUNCT
ejpam-5213	258	21	g)∪v	g)∪v	NOUN
ejpam-5213	258	22	(	(	PUNCT
ejpam-5213	258	23	h	h	NOUN
ejpam-5213	258	24	)	)	PUNCT
ejpam-5213	258	25	(	(	PUNCT
ejpam-5213	258	26	disjoint	disjoint	NOUN
ejpam-5213	258	27	union	union	NOUN
ejpam-5213	258	28	)	)	PUNCT
ejpam-5213	258	29	and	and	CCONJ
ejpam-5213	258	30	e(g+h	e(g+h	NUM
ejpam-5213	258	31	)	)	PUNCT
ejpam-5213	258	32	=	=	SYM
ejpam-5213	258	33	e(g	e(g	NOUN
ejpam-5213	258	34	)	)	PUNCT
ejpam-5213	258	35	∪	∪	ADP
ejpam-5213	258	36	e(h	e(h	PROPN
ejpam-5213	258	37	)	)	PUNCT
ejpam-5213	258	38	∪	∪	NOUN
ejpam-5213	258	39	{	{	PUNCT
ejpam-5213	258	40	uv	uv	NOUN
ejpam-5213	258	41	:	:	PUNCT
ejpam-5213	258	42	u	u	PROPN
ejpam-5213	258	43	∈	∈	PROPN
ejpam-5213	258	44	v	v	ADP
ejpam-5213	258	45	(	(	PUNCT
ejpam-5213	258	46	g	g	NOUN
ejpam-5213	258	47	)	)	PUNCT
ejpam-5213	258	48	and	and	CCONJ
ejpam-5213	258	49	v	v	ADP
ejpam-5213	258	50	∈	∈	PROPN
ejpam-5213	258	51	v	v	NOUN
ejpam-5213	258	52	(	(	PUNCT
ejpam-5213	258	53	h	h	NOUN
ejpam-5213	258	54	)	)	PUNCT
ejpam-5213	258	55	}	}	PUNCT
ejpam-5213	258	56	.	.	PUNCT
ejpam-5213	259	1	theorem	theorem	ADJ
ejpam-5213	259	2	8	8	NUM
ejpam-5213	259	3	.	.	PUNCT
ejpam-5213	260	1	let	let	VERB
ejpam-5213	260	2	g	g	PRON
ejpam-5213	260	3	be	be	AUX
ejpam-5213	260	4	a	a	DET
ejpam-5213	260	5	non	non	ADJ
ejpam-5213	260	6	-	-	ADJ
ejpam-5213	260	7	trivial	trivial	ADJ
ejpam-5213	260	8	point	point	NOUN
ejpam-5213	260	9	distinguishing	distinguish	VERB
ejpam-5213	260	10	graph	graph	NOUN
ejpam-5213	260	11	and	and	CCONJ
ejpam-5213	260	12	let	let	VERB
ejpam-5213	261	1	k1	k1	NOUN
ejpam-5213	261	2	=	=	SYM
ejpam-5213	261	3	⟨v⟩.	⟨v⟩.	PROPN
ejpam-5213	261	4	then	then	ADV
ejpam-5213	261	5	s	s	VERB
ejpam-5213	261	6	⊆	⊆	NUM
ejpam-5213	261	7	v	v	NOUN
ejpam-5213	261	8	(	(	PUNCT
ejpam-5213	261	9	k1	k1	NOUN
ejpam-5213	261	10	+	+	NOUN
ejpam-5213	261	11	g	g	NOUN
ejpam-5213	261	12	)	)	PUNCT
ejpam-5213	261	13	is	be	AUX
ejpam-5213	261	14	a	a	DET
ejpam-5213	261	15	differentiating	differentiate	VERB
ejpam-5213	261	16	odd	odd	ADJ
ejpam-5213	261	17	dominating	dominating	NOUN
ejpam-5213	261	18	set	set	VERB
ejpam-5213	261	19	in	in	ADP
ejpam-5213	261	20	k1	k1	NOUN
ejpam-5213	262	1	+	+	ADP
ejpam-5213	262	2	g	g	PROPN
ejpam-5213	262	3	if	if	SCONJ
ejpam-5213	262	4	and	and	CCONJ
ejpam-5213	262	5	only	only	ADV
ejpam-5213	262	6	if	if	SCONJ
ejpam-5213	262	7	one	one	NUM
ejpam-5213	262	8	of	of	ADP
ejpam-5213	262	9	the	the	DET
ejpam-5213	262	10	following	follow	VERB
ejpam-5213	262	11	holds	hold	VERB
ejpam-5213	262	12	:	:	PUNCT
ejpam-5213	262	13	(	(	PUNCT
ejpam-5213	262	14	i	i	NOUN
ejpam-5213	262	15	)	)	PUNCT
ejpam-5213	262	16	s	s	PART
ejpam-5213	263	1	=	=	PUNCT
ejpam-5213	263	2	{	{	PUNCT
ejpam-5213	263	3	v	v	NOUN
ejpam-5213	263	4	}	}	PUNCT
ejpam-5213	263	5	∪	∪	NOUN
ejpam-5213	263	6	sg	sg	ADP
ejpam-5213	263	7	where	where	SCONJ
ejpam-5213	263	8	sg	sg	PROPN
ejpam-5213	263	9	=	=	SYM
ejpam-5213	263	10	v	v	PROPN
ejpam-5213	263	11	(	(	PUNCT
ejpam-5213	263	12	g	g	NOUN
ejpam-5213	263	13	)	)	PUNCT
ejpam-5213	263	14	∩	∩	PROPN
ejpam-5213	263	15	s	s	PART
ejpam-5213	263	16	̸=	̸=	PROPN
ejpam-5213	263	17	∅	∅	NOUN
ejpam-5213	263	18	satisfies	satisfy	VERB
ejpam-5213	263	19	the	the	DET
ejpam-5213	263	20	following	following	NOUN
ejpam-5213	263	21	:	:	PUNCT
ejpam-5213	263	22	(	(	PUNCT
ejpam-5213	263	23	a	a	X
ejpam-5213	263	24	)	)	PUNCT
ejpam-5213	263	25	|sg|	|sg|	PROPN
ejpam-5213	263	26	is	be	AUX
ejpam-5213	263	27	even	even	ADV
ejpam-5213	263	28	and	and	CCONJ
ejpam-5213	263	29	sg	sg	PROPN
ejpam-5213	263	30	is	be	AUX
ejpam-5213	263	31	a	a	DET
ejpam-5213	263	32	strictly	strictly	ADV
ejpam-5213	263	33	differentiating	differentiate	VERB
ejpam-5213	263	34	set	set	NOUN
ejpam-5213	263	35	in	in	ADP
ejpam-5213	263	36	g	g	PROPN
ejpam-5213	263	37	(	(	PUNCT
ejpam-5213	263	38	b	b	NOUN
ejpam-5213	263	39	)	)	PUNCT
ejpam-5213	263	40	|ng[u	|ng[u	PROPN
ejpam-5213	263	41	]	]	PUNCT
ejpam-5213	263	42	∩	∩	NOUN
ejpam-5213	263	43	sg|	sg|	PROPN
ejpam-5213	263	44	is	be	AUX
ejpam-5213	263	45	even	even	ADV
ejpam-5213	263	46	for	for	ADP
ejpam-5213	263	47	all	all	PRON
ejpam-5213	263	48	u	u	NOUN
ejpam-5213	263	49	∈	∈	PROPN
ejpam-5213	263	50	v	v	NOUN
ejpam-5213	263	51	(	(	PUNCT
ejpam-5213	263	52	g	g	NOUN
ejpam-5213	263	53	)	)	PUNCT
ejpam-5213	263	54	(	(	PUNCT
ejpam-5213	263	55	ii	ii	NOUN
ejpam-5213	263	56	)	)	PUNCT
ejpam-5213	263	57	s	s	PART
ejpam-5213	263	58	⊆	⊆	NUM
ejpam-5213	263	59	v	v	NOUN
ejpam-5213	263	60	(	(	PUNCT
ejpam-5213	263	61	g	g	NOUN
ejpam-5213	263	62	)	)	PUNCT
ejpam-5213	263	63	,	,	PUNCT
ejpam-5213	263	64	|s|	|s|	PROPN
ejpam-5213	263	65	is	be	AUX
ejpam-5213	263	66	odd	odd	ADJ
ejpam-5213	263	67	,	,	PUNCT
ejpam-5213	263	68	and	and	CCONJ
ejpam-5213	263	69	s	s	VERB
ejpam-5213	263	70	is	be	AUX
ejpam-5213	263	71	a	a	DET
ejpam-5213	263	72	strictly	strictly	ADV
ejpam-5213	263	73	differentiating	differentiate	VERB
ejpam-5213	263	74	odd	odd	ADJ
ejpam-5213	263	75	dominating	dominating	NOUN
ejpam-5213	263	76	set	set	VERB
ejpam-5213	263	77	in	in	ADP
ejpam-5213	263	78	g.	g.	PROPN
ejpam-5213	263	79	proof	proof	PROPN
ejpam-5213	263	80	.	.	PUNCT
ejpam-5213	264	1	let	let	VERB
ejpam-5213	264	2	s	s	PRON
ejpam-5213	264	3	be	be	AUX
ejpam-5213	264	4	a	a	DET
ejpam-5213	264	5	differentiating	differentiate	VERB
ejpam-5213	264	6	odd	odd	ADJ
ejpam-5213	264	7	dominating	dominating	NOUN
ejpam-5213	264	8	set	set	VERB
ejpam-5213	264	9	in	in	ADP
ejpam-5213	264	10	k1	k1	PROPN
ejpam-5213	264	11	+	+	CCONJ
ejpam-5213	264	12	g.	g.	PROPN
ejpam-5213	264	13	let	let	VERB
ejpam-5213	264	14	v	v	NOUN
ejpam-5213	264	15	(	(	PUNCT
ejpam-5213	264	16	k1	k1	NOUN
ejpam-5213	264	17	)	)	PUNCT
ejpam-5213	264	18	=	=	SYM
ejpam-5213	264	19	{	{	PUNCT
ejpam-5213	264	20	v	v	NOUN
ejpam-5213	264	21	}	}	PUNCT
ejpam-5213	264	22	and	and	CCONJ
ejpam-5213	264	23	let	let	VERB
ejpam-5213	264	24	sg	sg	INTJ
ejpam-5213	264	25	=	=	NOUN
ejpam-5213	264	26	v	v	PROPN
ejpam-5213	264	27	(	(	PUNCT
ejpam-5213	264	28	g	g	NOUN
ejpam-5213	264	29	)	)	PUNCT
ejpam-5213	264	30	∩	∩	NOUN
ejpam-5213	264	31	s.	s.	PROPN
ejpam-5213	264	32	consider	consider	VERB
ejpam-5213	264	33	the	the	DET
ejpam-5213	264	34	following	follow	VERB
ejpam-5213	264	35	cases	case	NOUN
ejpam-5213	264	36	:	:	PUNCT
ejpam-5213	264	37	case	case	NOUN
ejpam-5213	264	38	1	1	NUM
ejpam-5213	264	39	:	:	SYM
ejpam-5213	264	40	v	v	NUM
ejpam-5213	264	41	∈	∈	NOUN
ejpam-5213	264	42	s.	s.	PROPN
ejpam-5213	264	43	then	then	ADV
ejpam-5213	264	44	s	s	AUX
ejpam-5213	264	45	=	=	SYM
ejpam-5213	264	46	{	{	PUNCT
ejpam-5213	264	47	v	v	NOUN
ejpam-5213	264	48	}	}	PUNCT
ejpam-5213	264	49	∪	∪	ADJ
ejpam-5213	264	50	sg	sg	PROPN
ejpam-5213	264	51	.	.	PUNCT
ejpam-5213	265	1	since	since	SCONJ
ejpam-5213	265	2	s	s	NOUN
ejpam-5213	265	3	is	be	AUX
ejpam-5213	265	4	differentiating	differentiate	VERB
ejpam-5213	265	5	in	in	ADP
ejpam-5213	265	6	k1	k1	NOUN
ejpam-5213	265	7	+	+	CCONJ
ejpam-5213	265	8	g	g	NOUN
ejpam-5213	265	9	,	,	PUNCT
ejpam-5213	265	10	sg	sg	ADP
ejpam-5213	265	11	̸=	̸=	PROPN
ejpam-5213	265	12	∅.	∅.	ADV
ejpam-5213	265	13	since	since	SCONJ
ejpam-5213	265	14	s	s	PROPN
ejpam-5213	265	15	is	be	AUX
ejpam-5213	265	16	odd	odd	ADJ
ejpam-5213	265	17	dominating	dominating	NOUN
ejpam-5213	265	18	in	in	ADP
ejpam-5213	265	19	k1+g	k1+g	NOUN
ejpam-5213	265	20	,	,	PUNCT
ejpam-5213	265	21	|nk1+g[v]∩s|	|nk1+g[v]∩s|	X
ejpam-5213	265	22	=	=	SYM
ejpam-5213	265	23	|{v}|+	|{v}|+	PROPN
ejpam-5213	265	24	|sg|	|sg|	PROPN
ejpam-5213	265	25	is	be	AUX
ejpam-5213	265	26	odd	odd	ADJ
ejpam-5213	265	27	.	.	PUNCT
ejpam-5213	266	1	it	it	PRON
ejpam-5213	266	2	follows	follow	VERB
ejpam-5213	266	3	that	that	SCONJ
ejpam-5213	266	4	|sg|	|sg|	NOUN
ejpam-5213	266	5	is	be	AUX
ejpam-5213	266	6	even	even	ADV
ejpam-5213	266	7	.	.	PUNCT
ejpam-5213	267	1	suppose	suppose	VERB
ejpam-5213	267	2	sg	sg	PROPN
ejpam-5213	267	3	is	be	AUX
ejpam-5213	267	4	not	not	PART
ejpam-5213	267	5	differentiating	differentiate	VERB
ejpam-5213	267	6	in	in	ADP
ejpam-5213	267	7	g.	g.	PROPN
ejpam-5213	267	8	then	then	ADV
ejpam-5213	267	9	there	there	PRON
ejpam-5213	267	10	exist	exist	VERB
ejpam-5213	267	11	x	x	NOUN
ejpam-5213	267	12	,	,	PUNCT
ejpam-5213	267	13	y	y	PROPN
ejpam-5213	267	14	∈	∈	PROPN
ejpam-5213	267	15	v	v	ADP
ejpam-5213	267	16	(	(	PUNCT
ejpam-5213	267	17	g	g	NOUN
ejpam-5213	267	18	)	)	PUNCT
ejpam-5213	267	19	and	and	CCONJ
ejpam-5213	267	20	x	x	SYM
ejpam-5213	267	21	̸=	̸=	PROPN
ejpam-5213	267	22	y	y	PRON
ejpam-5213	267	23	such	such	ADJ
ejpam-5213	267	24	that	that	DET
ejpam-5213	267	25	ng[x	ng[x	PROPN
ejpam-5213	267	26	]	]	PUNCT
ejpam-5213	267	27	∩	∩	PROPN
ejpam-5213	267	28	sg	sg	ADP
ejpam-5213	267	29	=	=	SYM
ejpam-5213	267	30	ng[y	ng[y	PROPN
ejpam-5213	267	31	]	]	PUNCT
ejpam-5213	267	32	∩	∩	PROPN
ejpam-5213	267	33	sg	sg	PROPN
ejpam-5213	267	34	.	.	PUNCT
ejpam-5213	268	1	it	it	PRON
ejpam-5213	268	2	follows	follow	VERB
ejpam-5213	268	3	that	that	SCONJ
ejpam-5213	268	4	nk1+g[x	nk1+g[x	PROPN
ejpam-5213	268	5	]	]	PUNCT
ejpam-5213	268	6	∩	∩	X
ejpam-5213	268	7	s	s	PART
ejpam-5213	268	8	=	=	VERB
ejpam-5213	268	9	{	{	PUNCT
ejpam-5213	268	10	v	v	NOUN
ejpam-5213	268	11	}	}	PUNCT
ejpam-5213	268	12	∪	∪	NOUN
ejpam-5213	268	13	(	(	PUNCT
ejpam-5213	268	14	ng[x	ng[x	PROPN
ejpam-5213	268	15	]	]	PUNCT
ejpam-5213	268	16	∩	∩	PROPN
ejpam-5213	268	17	sg	sg	ADP
ejpam-5213	268	18	)	)	PUNCT
ejpam-5213	268	19	=	=	SYM
ejpam-5213	268	20	nk1+g[y	nk1+g[y	X
ejpam-5213	268	21	]	]	X
ejpam-5213	268	22	∩	∩	X
ejpam-5213	268	23	s	s	SYM
ejpam-5213	268	24	,	,	PUNCT
ejpam-5213	268	25	a	a	DET
ejpam-5213	268	26	contradiction	contradiction	NOUN
ejpam-5213	268	27	to	to	ADP
ejpam-5213	268	28	the	the	DET
ejpam-5213	268	29	fact	fact	NOUN
ejpam-5213	268	30	that	that	SCONJ
ejpam-5213	268	31	s	s	VERB
ejpam-5213	268	32	is	be	AUX
ejpam-5213	268	33	differentiating	differentiate	VERB
ejpam-5213	268	34	in	in	ADP
ejpam-5213	268	35	k1	k1	PROPN
ejpam-5213	268	36	+	+	CCONJ
ejpam-5213	268	37	g.	g.	PROPN
ejpam-5213	268	38	therefore	therefore	ADV
ejpam-5213	268	39	,	,	PUNCT
ejpam-5213	268	40	sg	sg	PROPN
ejpam-5213	268	41	is	be	AUX
ejpam-5213	268	42	differentiating	differentiate	VERB
ejpam-5213	268	43	in	in	ADP
ejpam-5213	268	44	g.	g.	PROPN
ejpam-5213	268	45	furthermore	furthermore	ADV
ejpam-5213	268	46	,	,	PUNCT
ejpam-5213	268	47	suppose	suppose	VERB
ejpam-5213	268	48	sg	sg	PROPN
ejpam-5213	268	49	is	be	AUX
ejpam-5213	268	50	not	not	PART
ejpam-5213	268	51	strictly	strictly	ADV
ejpam-5213	268	52	differentiating	differentiate	VERB
ejpam-5213	268	53	in	in	ADP
ejpam-5213	268	54	g.	g.	PROPN
ejpam-5213	268	55	then	then	ADV
ejpam-5213	268	56	there	there	PRON
ejpam-5213	268	57	exists	exist	VERB
ejpam-5213	268	58	w	w	PROPN
ejpam-5213	268	59	∈	∈	PROPN
ejpam-5213	268	60	v	v	ADP
ejpam-5213	268	61	(	(	PUNCT
ejpam-5213	268	62	g	g	NOUN
ejpam-5213	268	63	)	)	PUNCT
ejpam-5213	268	64	such	such	ADJ
ejpam-5213	268	65	that	that	SCONJ
ejpam-5213	268	66	ng[w	ng[w	PROPN
ejpam-5213	268	67	]	]	PUNCT
ejpam-5213	268	68	∩	∩	PROPN
ejpam-5213	268	69	sg	sg	PROPN
ejpam-5213	268	70	=	=	SYM
ejpam-5213	268	71	sg	sg	PROPN
ejpam-5213	268	72	.	.	PUNCT
ejpam-5213	269	1	it	it	PRON
ejpam-5213	269	2	follows	follow	VERB
ejpam-5213	269	3	that	that	SCONJ
ejpam-5213	269	4	nk1+g[w	nk1+g[w	PROPN
ejpam-5213	269	5	]	]	PUNCT
ejpam-5213	269	6	∩	∩	PROPN
ejpam-5213	269	7	s	s	PART
ejpam-5213	269	8	=	=	VERB
ejpam-5213	269	9	{	{	PUNCT
ejpam-5213	269	10	v	v	NOUN
ejpam-5213	269	11	}	}	PUNCT
ejpam-5213	269	12	∪	∪	NOUN
ejpam-5213	269	13	sg	sg	ADV
ejpam-5213	269	14	=	=	SYM
ejpam-5213	269	15	nk1+g[v	nk1+g[v	PROPN
ejpam-5213	269	16	]	]	X
ejpam-5213	269	17	∩	∩	X
ejpam-5213	269	18	s	s	SYM
ejpam-5213	269	19	,	,	PUNCT
ejpam-5213	269	20	a	a	DET
ejpam-5213	269	21	contradiction	contradiction	NOUN
ejpam-5213	269	22	to	to	ADP
ejpam-5213	269	23	the	the	DET
ejpam-5213	269	24	fact	fact	NOUN
ejpam-5213	269	25	that	that	SCONJ
ejpam-5213	269	26	s	s	VERB
ejpam-5213	269	27	is	be	AUX
ejpam-5213	269	28	differentiating	differentiate	VERB
ejpam-5213	269	29	in	in	ADP
ejpam-5213	269	30	k1	k1	PROPN
ejpam-5213	269	31	+	+	CCONJ
ejpam-5213	269	32	g.	g.	PROPN
ejpam-5213	269	33	thus	thus	ADV
ejpam-5213	269	34	,	,	PUNCT
ejpam-5213	269	35	sg	sg	PROPN
ejpam-5213	269	36	is	be	AUX
ejpam-5213	269	37	strictly	strictly	ADV
ejpam-5213	269	38	differentiating	differentiate	VERB
ejpam-5213	269	39	in	in	ADP
ejpam-5213	269	40	g.	g.	PROPN
ejpam-5213	269	41	this	this	PRON
ejpam-5213	269	42	proves	prove	VERB
ejpam-5213	269	43	that	that	SCONJ
ejpam-5213	269	44	(	(	PUNCT
ejpam-5213	269	45	a	a	X
ejpam-5213	269	46	)	)	PUNCT
ejpam-5213	269	47	holds	hold	NOUN
ejpam-5213	269	48	.	.	PUNCT
ejpam-5213	270	1	now	now	ADV
ejpam-5213	270	2	,	,	PUNCT
ejpam-5213	270	3	let	let	VERB
ejpam-5213	270	4	u	u	PRON
ejpam-5213	270	5	∈	∈	PROPN
ejpam-5213	270	6	v	v	ADP
ejpam-5213	270	7	(	(	PUNCT
ejpam-5213	270	8	g	g	NOUN
ejpam-5213	270	9	)	)	PUNCT
ejpam-5213	270	10	.	.	PUNCT
ejpam-5213	271	1	since	since	SCONJ
ejpam-5213	271	2	s	s	PROPN
ejpam-5213	271	3	is	be	AUX
ejpam-5213	271	4	odd	odd	ADJ
ejpam-5213	271	5	dominating	dominating	NOUN
ejpam-5213	271	6	,	,	PUNCT
ejpam-5213	271	7	|nk1+g[u]∩s|	|nk1+g[u]∩s|	PRON
ejpam-5213	271	8	=	=	PUNCT
ejpam-5213	271	9	|{v}|+	|{v}|+	PROPN
ejpam-5213	271	10	|ng[u]∩sg|	|ng[u]∩sg|	PROPN
ejpam-5213	271	11	is	be	AUX
ejpam-5213	271	12	odd	odd	ADJ
ejpam-5213	271	13	.	.	PUNCT
ejpam-5213	272	1	thus	thus	ADV
ejpam-5213	272	2	,	,	PUNCT
ejpam-5213	272	3	|ng[u	|ng[u	PROPN
ejpam-5213	272	4	]	]	PUNCT
ejpam-5213	272	5	∩	∩	NOUN
ejpam-5213	272	6	sg|	sg|	PROPN
ejpam-5213	272	7	is	be	AUX
ejpam-5213	272	8	even	even	ADV
ejpam-5213	272	9	.	.	PUNCT
ejpam-5213	273	1	this	this	PRON
ejpam-5213	273	2	shows	show	VERB
ejpam-5213	273	3	that	that	SCONJ
ejpam-5213	273	4	(	(	PUNCT
ejpam-5213	273	5	b	b	X
ejpam-5213	273	6	)	)	PUNCT
ejpam-5213	273	7	holds	hold	NOUN
ejpam-5213	273	8	.	.	PUNCT
ejpam-5213	274	1	hence	hence	ADV
ejpam-5213	274	2	,	,	PUNCT
ejpam-5213	274	3	(	(	PUNCT
ejpam-5213	274	4	i	i	NOUN
ejpam-5213	274	5	)	)	PUNCT
ejpam-5213	274	6	holds	hold	VERB
ejpam-5213	274	7	.	.	PUNCT
ejpam-5213	275	1	case	case	NOUN
ejpam-5213	275	2	2	2	NUM
ejpam-5213	275	3	:	:	PUNCT
ejpam-5213	275	4	v	v	NUM
ejpam-5213	275	5	̸∈	̸∈	PROPN
ejpam-5213	275	6	s.	s.	PROPN
ejpam-5213	275	7	then	then	ADV
ejpam-5213	275	8	s	s	VERB
ejpam-5213	275	9	⊆	⊆	NUM
ejpam-5213	275	10	v	v	NOUN
ejpam-5213	275	11	(	(	PUNCT
ejpam-5213	275	12	g	g	NOUN
ejpam-5213	275	13	)	)	PUNCT
ejpam-5213	275	14	.	.	PUNCT
ejpam-5213	276	1	since	since	SCONJ
ejpam-5213	276	2	s	s	PROPN
ejpam-5213	276	3	is	be	AUX
ejpam-5213	276	4	odd	odd	ADJ
ejpam-5213	276	5	dominating	dominating	NOUN
ejpam-5213	276	6	,	,	PUNCT
ejpam-5213	276	7	|nk1+g[v	|nk1+g[v	NOUN
ejpam-5213	276	8	]	]	PUNCT
ejpam-5213	277	1	∩	∩	NOUN
ejpam-5213	277	2	s|	s|	NOUN
ejpam-5213	277	3	=	=	SYM
ejpam-5213	277	4	|s|	|s|	PROPN
ejpam-5213	277	5	is	be	AUX
ejpam-5213	277	6	odd	odd	ADJ
ejpam-5213	277	7	.	.	PUNCT
ejpam-5213	278	1	since	since	SCONJ
ejpam-5213	278	2	s	s	PROPN
ejpam-5213	278	3	is	be	AUX
ejpam-5213	278	4	odd	odd	ADJ
ejpam-5213	278	5	dominating	dominating	NOUN
ejpam-5213	278	6	and	and	CCONJ
ejpam-5213	278	7	v	v	NOUN
ejpam-5213	278	8	/∈	/∈	PUNCT
ejpam-5213	279	1	s	s	X
ejpam-5213	279	2	,	,	PUNCT
ejpam-5213	279	3	it	it	PRON
ejpam-5213	279	4	follows	follow	VERB
ejpam-5213	279	5	that	that	SCONJ
ejpam-5213	279	6	s	s	VERB
ejpam-5213	279	7	is	be	AUX
ejpam-5213	279	8	odd	odd	ADJ
ejpam-5213	279	9	dominating	dominate	VERB
ejpam-5213	279	10	in	in	ADP
ejpam-5213	279	11	g.	g.	PROPN
ejpam-5213	279	12	moreover	moreover	ADV
ejpam-5213	279	13	,	,	PUNCT
ejpam-5213	279	14	as	as	SCONJ
ejpam-5213	279	15	in	in	ADP
ejpam-5213	279	16	case	case	NOUN
ejpam-5213	279	17	1	1	NUM
ejpam-5213	279	18	,	,	PUNCT
ejpam-5213	279	19	s	s	VERB
ejpam-5213	279	20	is	be	AUX
ejpam-5213	279	21	strictly	strictly	ADV
ejpam-5213	279	22	differentiating	differentiate	VERB
ejpam-5213	279	23	in	in	ADP
ejpam-5213	279	24	g.	g.	PROPN
ejpam-5213	279	25	therefore	therefore	ADV
ejpam-5213	279	26	,	,	PUNCT
ejpam-5213	279	27	(	(	PUNCT
ejpam-5213	279	28	ii	ii	NOUN
ejpam-5213	279	29	)	)	PUNCT
ejpam-5213	279	30	holds	hold	VERB
ejpam-5213	279	31	.	.	PUNCT
ejpam-5213	280	1	m.	m.	NOUN
ejpam-5213	280	2	carbero	carbero	PROPN
ejpam-5213	280	3	,	,	PUNCT
ejpam-5213	280	4	g.	g.	PROPN
ejpam-5213	280	5	malacas	malacas	PROPN
ejpam-5213	280	6	,	,	PUNCT
ejpam-5213	280	7	s.	s.	PROPN
ejpam-5213	280	8	canoy	canoy	PROPN
ejpam-5213	280	9	,	,	PUNCT
ejpam-5213	280	10	jr	jr	PROPN
ejpam-5213	280	11	.	.	PROPN
ejpam-5213	280	12	/	/	SYM
ejpam-5213	280	13	eur	eur	PROPN
ejpam-5213	280	14	.	.	PUNCT
ejpam-5213	281	1	j.	j.	PROPN
ejpam-5213	281	2	pure	pure	PROPN
ejpam-5213	281	3	appl	appl	PROPN
ejpam-5213	281	4	.	.	PROPN
ejpam-5213	281	5	math	math	PROPN
ejpam-5213	281	6	,	,	PUNCT
ejpam-5213	281	7	17	17	NUM
ejpam-5213	281	8	(	(	PUNCT
ejpam-5213	281	9	3	3	NUM
ejpam-5213	281	10	)	)	PUNCT
ejpam-5213	281	11	(	(	PUNCT
ejpam-5213	281	12	2024	2024	NUM
ejpam-5213	281	13	)	)	PUNCT
ejpam-5213	281	14	,	,	PUNCT
ejpam-5213	281	15	1585	1585	NUM
ejpam-5213	281	16	-	-	SYM
ejpam-5213	281	17	1601	1601	NUM
ejpam-5213	281	18	1593	1593	NUM
ejpam-5213	281	19	conversely	conversely	ADV
ejpam-5213	281	20	,	,	PUNCT
ejpam-5213	281	21	suppose	suppose	VERB
ejpam-5213	281	22	(	(	PUNCT
ejpam-5213	281	23	i	i	NOUN
ejpam-5213	281	24	)	)	PUNCT
ejpam-5213	281	25	holds	hold	VERB
ejpam-5213	281	26	.	.	PUNCT
ejpam-5213	282	1	let	let	VERB
ejpam-5213	282	2	x	x	PRON
ejpam-5213	282	3	,	,	PUNCT
ejpam-5213	282	4	y	y	PROPN
ejpam-5213	282	5	be	be	VERB
ejpam-5213	282	6	distinct	distinct	ADJ
ejpam-5213	282	7	vertices	vertex	NOUN
ejpam-5213	282	8	in	in	ADP
ejpam-5213	282	9	v	v	NOUN
ejpam-5213	282	10	(	(	PUNCT
ejpam-5213	282	11	k1	k1	NOUN
ejpam-5213	282	12	+	+	CCONJ
ejpam-5213	282	13	g	g	NOUN
ejpam-5213	282	14	)	)	PUNCT
ejpam-5213	282	15	.	.	PUNCT
ejpam-5213	283	1	if	if	SCONJ
ejpam-5213	283	2	x	x	X
ejpam-5213	283	3	,	,	PUNCT
ejpam-5213	283	4	y	y	PROPN
ejpam-5213	283	5	∈	∈	PROPN
ejpam-5213	283	6	v	v	NOUN
ejpam-5213	283	7	(	(	PUNCT
ejpam-5213	283	8	g	g	NOUN
ejpam-5213	283	9	)	)	PUNCT
ejpam-5213	283	10	,	,	PUNCT
ejpam-5213	283	11	then	then	ADV
ejpam-5213	283	12	ng[x	ng[x	PROPN
ejpam-5213	283	13	]	]	PUNCT
ejpam-5213	283	14	∩	∩	PROPN
ejpam-5213	283	15	sg	sg	ADP
ejpam-5213	283	16	̸=	̸=	PROPN
ejpam-5213	283	17	n	n	PROPN
ejpam-5213	283	18	[	[	X
ejpam-5213	283	19	y	y	X
ejpam-5213	283	20	]	]	X
ejpam-5213	283	21	∩	∩	X
ejpam-5213	283	22	sg	sg	X
ejpam-5213	283	23	by	by	ADP
ejpam-5213	283	24	(	(	PUNCT
ejpam-5213	283	25	a	a	NOUN
ejpam-5213	283	26	)	)	PUNCT
ejpam-5213	283	27	.	.	PUNCT
ejpam-5213	284	1	it	it	PRON
ejpam-5213	284	2	follows	follow	VERB
ejpam-5213	284	3	that	that	SCONJ
ejpam-5213	284	4	nk1+g[x	nk1+g[x	PROPN
ejpam-5213	284	5	]	]	PUNCT
ejpam-5213	284	6	∩	∩	X
ejpam-5213	284	7	s	s	PART
ejpam-5213	284	8	=	=	VERB
ejpam-5213	284	9	{	{	PUNCT
ejpam-5213	284	10	v	v	NOUN
ejpam-5213	284	11	}	}	PUNCT
ejpam-5213	284	12	∪	∪	NOUN
ejpam-5213	284	13	[	[	X
ejpam-5213	284	14	ng[x	ng[x	NOUN
ejpam-5213	284	15	]	]	PUNCT
ejpam-5213	284	16	∩	∩	PROPN
ejpam-5213	284	17	sg	sg	ADP
ejpam-5213	284	18	]	]	X
ejpam-5213	284	19	̸=	̸=	PROPN
ejpam-5213	284	20	{	{	PUNCT
ejpam-5213	284	21	v	v	NOUN
ejpam-5213	284	22	}	}	PUNCT
ejpam-5213	284	23	∪	∪	NOUN
ejpam-5213	284	24	[	[	PUNCT
ejpam-5213	284	25	ng[y	ng[y	NOUN
ejpam-5213	284	26	]	]	PUNCT
ejpam-5213	284	27	∩	∩	NOUN
ejpam-5213	284	28	sg	sg	ADP
ejpam-5213	284	29	]	]	X
ejpam-5213	284	30	=	=	SYM
ejpam-5213	284	31	nk1+g[y	nk1+g[y	X
ejpam-5213	284	32	]	]	PUNCT
ejpam-5213	284	33	∩	∩	PROPN
ejpam-5213	284	34	s.	s.	PROPN
ejpam-5213	284	35	suppose	suppose	VERB
ejpam-5213	284	36	x	x	X
ejpam-5213	285	1	=	=	PUNCT
ejpam-5213	285	2	v.	v.	ADP
ejpam-5213	285	3	then	then	ADV
ejpam-5213	285	4	ng[y	ng[y	PROPN
ejpam-5213	285	5	]	]	PUNCT
ejpam-5213	285	6	∩	∩	NOUN
ejpam-5213	285	7	sg	sg	ADP
ejpam-5213	285	8	̸=	̸=	PROPN
ejpam-5213	285	9	sg	sg	X
ejpam-5213	285	10	because	because	SCONJ
ejpam-5213	285	11	sg	sg	PROPN
ejpam-5213	285	12	is	be	AUX
ejpam-5213	285	13	strictly	strictly	ADV
ejpam-5213	285	14	differentiating	differentiate	VERB
ejpam-5213	285	15	.	.	PUNCT
ejpam-5213	286	1	since	since	SCONJ
ejpam-5213	286	2	nk1+g[x	nk1+g[x	PROPN
ejpam-5213	286	3	]	]	PUNCT
ejpam-5213	286	4	∩	∩	X
ejpam-5213	286	5	s	s	PART
ejpam-5213	286	6	=	=	PUNCT
ejpam-5213	286	7	sg	sg	X
ejpam-5213	286	8	∪	∪	ADJ
ejpam-5213	286	9	{	{	PUNCT
ejpam-5213	286	10	v	v	NOUN
ejpam-5213	286	11	}	}	PUNCT
ejpam-5213	286	12	,	,	PUNCT
ejpam-5213	286	13	then	then	ADV
ejpam-5213	286	14	nk1+g[x	nk1+g[x	PROPN
ejpam-5213	286	15	]	]	PUNCT
ejpam-5213	286	16	∩	∩	PROPN
ejpam-5213	286	17	s	s	PART
ejpam-5213	286	18	̸=	̸=	PROPN
ejpam-5213	286	19	nk1+g[y	nk1+g[y	NUM
ejpam-5213	286	20	]	]	PUNCT
ejpam-5213	286	21	∩	∩	PROPN
ejpam-5213	286	22	s.	s.	PROPN
ejpam-5213	286	23	since	since	SCONJ
ejpam-5213	286	24	|sg|	|sg|	PROPN
ejpam-5213	286	25	is	be	AUX
ejpam-5213	286	26	even	even	ADV
ejpam-5213	286	27	and	and	CCONJ
ejpam-5213	286	28	(	(	PUNCT
ejpam-5213	286	29	b	b	NOUN
ejpam-5213	286	30	)	)	PUNCT
ejpam-5213	286	31	holds	hold	VERB
ejpam-5213	286	32	,	,	PUNCT
ejpam-5213	286	33	it	it	PRON
ejpam-5213	286	34	follows	follow	VERB
ejpam-5213	286	35	that	that	SCONJ
ejpam-5213	286	36	|nk1+g[z	|nk1+g[z	PROPN
ejpam-5213	286	37	]	]	PUNCT
ejpam-5213	286	38	∩	∩	NOUN
ejpam-5213	286	39	s|	s|	NOUN
ejpam-5213	286	40	is	be	AUX
ejpam-5213	286	41	odd	odd	ADJ
ejpam-5213	286	42	for	for	ADP
ejpam-5213	286	43	all	all	DET
ejpam-5213	286	44	z	z	NOUN
ejpam-5213	286	45	∈	∈	PROPN
ejpam-5213	286	46	v	v	NOUN
ejpam-5213	286	47	(	(	PUNCT
ejpam-5213	286	48	k1	k1	NOUN
ejpam-5213	286	49	+	+	PROPN
ejpam-5213	286	50	g	g	NOUN
ejpam-5213	286	51	)	)	PUNCT
ejpam-5213	286	52	.	.	PUNCT
ejpam-5213	287	1	therefore	therefore	ADV
ejpam-5213	287	2	,	,	PUNCT
ejpam-5213	287	3	s	s	VERB
ejpam-5213	287	4	is	be	AUX
ejpam-5213	287	5	a	a	DET
ejpam-5213	287	6	differentiating	differentiate	VERB
ejpam-5213	287	7	odd	odd	ADJ
ejpam-5213	287	8	dominating	dominating	NOUN
ejpam-5213	287	9	set	set	VERB
ejpam-5213	287	10	in	in	ADP
ejpam-5213	287	11	k1	k1	PROPN
ejpam-5213	287	12	+	+	PROPN
ejpam-5213	287	13	g.	g.	PROPN
ejpam-5213	287	14	next	next	ADV
ejpam-5213	287	15	,	,	PUNCT
ejpam-5213	287	16	suppose	suppose	VERB
ejpam-5213	287	17	(	(	PUNCT
ejpam-5213	287	18	ii	ii	NOUN
ejpam-5213	287	19	)	)	PUNCT
ejpam-5213	287	20	holds	hold	VERB
ejpam-5213	287	21	.	.	PUNCT
ejpam-5213	288	1	since	since	SCONJ
ejpam-5213	288	2	s	s	NOUN
ejpam-5213	288	3	is	be	AUX
ejpam-5213	288	4	strictly	strictly	ADV
ejpam-5213	288	5	differentiating	differentiate	VERB
ejpam-5213	288	6	-	-	PUNCT
ejpam-5213	288	7	dominating	dominating	NOUN
ejpam-5213	288	8	set	set	NOUN
ejpam-5213	288	9	in	in	ADP
ejpam-5213	288	10	g	g	NOUN
ejpam-5213	288	11	,	,	PUNCT
ejpam-5213	288	12	s	s	PART
ejpam-5213	288	13	is	be	AUX
ejpam-5213	288	14	differentiating	differentiate	VERB
ejpam-5213	288	15	-	-	PUNCT
ejpam-5213	288	16	dominating	dominating	NOUN
ejpam-5213	288	17	in	in	ADP
ejpam-5213	288	18	k1	k1	PROPN
ejpam-5213	288	19	+	+	CCONJ
ejpam-5213	288	20	g.	g.	PROPN
ejpam-5213	288	21	let	let	VERB
ejpam-5213	288	22	w	w	NOUN
ejpam-5213	288	23	∈	∈	PROPN
ejpam-5213	288	24	v	v	NOUN
ejpam-5213	288	25	(	(	PUNCT
ejpam-5213	288	26	k1	k1	NOUN
ejpam-5213	288	27	+	+	CCONJ
ejpam-5213	288	28	g	g	NOUN
ejpam-5213	288	29	)	)	PUNCT
ejpam-5213	288	30	.	.	PUNCT
ejpam-5213	289	1	if	if	SCONJ
ejpam-5213	289	2	w	w	PROPN
ejpam-5213	289	3	=	=	SYM
ejpam-5213	289	4	v	v	NOUN
ejpam-5213	289	5	,	,	PUNCT
ejpam-5213	289	6	then	then	ADV
ejpam-5213	289	7	|nk1+g[w	|nk1+g[w	PROPN
ejpam-5213	289	8	]	]	PUNCT
ejpam-5213	289	9	∩	∩	NOUN
ejpam-5213	289	10	s|	s|	NOUN
ejpam-5213	289	11	=	=	SYM
ejpam-5213	289	12	|s|	|s|	NOUN
ejpam-5213	289	13	is	be	AUX
ejpam-5213	289	14	odd	odd	ADJ
ejpam-5213	289	15	,	,	PUNCT
ejpam-5213	289	16	by	by	ADP
ejpam-5213	289	17	assumption	assumption	NOUN
ejpam-5213	289	18	.	.	PUNCT
ejpam-5213	290	1	if	if	SCONJ
ejpam-5213	290	2	w	w	PROPN
ejpam-5213	290	3	∈	∈	PROPN
ejpam-5213	290	4	v	v	ADP
ejpam-5213	290	5	(	(	PUNCT
ejpam-5213	290	6	g	g	NOUN
ejpam-5213	290	7	)	)	PUNCT
ejpam-5213	290	8	,	,	PUNCT
ejpam-5213	290	9	then	then	ADV
ejpam-5213	290	10	|nk1+g[w]∩s|	|nk1+g[w]∩s|	PROPN
ejpam-5213	290	11	=	=	SYM
ejpam-5213	290	12	|ng[w]∩s|	|ng[w]∩s|	PROPN
ejpam-5213	290	13	is	be	AUX
ejpam-5213	290	14	odd	odd	ADJ
ejpam-5213	290	15	because	because	SCONJ
ejpam-5213	290	16	s	s	PROPN
ejpam-5213	290	17	is	be	AUX
ejpam-5213	290	18	odd	odd	ADJ
ejpam-5213	290	19	dominating	dominating	NOUN
ejpam-5213	290	20	in	in	ADP
ejpam-5213	290	21	g.	g.	PROPN
ejpam-5213	290	22	therefore	therefore	ADV
ejpam-5213	290	23	,	,	PUNCT
ejpam-5213	290	24	s	s	VERB
ejpam-5213	290	25	is	be	AUX
ejpam-5213	290	26	a	a	DET
ejpam-5213	290	27	differentiating	differentiate	VERB
ejpam-5213	290	28	odd	odd	ADJ
ejpam-5213	290	29	dominating	dominating	NOUN
ejpam-5213	290	30	set	set	VERB
ejpam-5213	290	31	in	in	ADP
ejpam-5213	290	32	k1	k1	PROPN
ejpam-5213	290	33	+	+	CCONJ
ejpam-5213	290	34	g.	g.	NOUN
ejpam-5213	290	35	the	the	DET
ejpam-5213	290	36	graphs	graph	NOUN
ejpam-5213	290	37	g	g	NOUN
ejpam-5213	290	38	and	and	CCONJ
ejpam-5213	290	39	k1	k1	NOUN
ejpam-5213	290	40	+	+	CCONJ
ejpam-5213	290	41	g	g	NOUN
ejpam-5213	290	42	in	in	ADP
ejpam-5213	290	43	figure	figure	NOUN
ejpam-5213	290	44	1	1	NUM
ejpam-5213	290	45	illustrate	illustrate	VERB
ejpam-5213	290	46	the	the	DET
ejpam-5213	290	47	graphs	graph	NOUN
ejpam-5213	290	48	described	describe	VERB
ejpam-5213	290	49	in	in	ADP
ejpam-5213	290	50	thereom	thereom	PROPN
ejpam-5213	290	51	8(i	8(i	NUM
ejpam-5213	290	52	)	)	PUNCT
ejpam-5213	290	53	.	.	PUNCT
ejpam-5213	291	1	z	z	PUNCT
ejpam-5213	292	1	d	d	NOUN
ejpam-5213	292	2	h	h	NOUN
ejpam-5213	293	1	c	c	NOUN
ejpam-5213	293	2	g	g	NOUN
ejpam-5213	293	3	x	x	PROPN
ejpam-5213	294	1	w	w	PROPN
ejpam-5213	294	2	u	u	PROPN
ejpam-5213	294	3	b	b	PROPN
ejpam-5213	294	4	f	f	PROPN
ejpam-5213	294	5	y	y	PROPN
ejpam-5213	294	6	a	a	X
ejpam-5213	294	7	e	e	X
ejpam-5213	294	8	g	g	NOUN
ejpam-5213	294	9	:	:	PUNCT
ejpam-5213	294	10	z	z	NOUN
ejpam-5213	295	1	d	d	NOUN
ejpam-5213	295	2	h	h	NOUN
ejpam-5213	296	1	c	c	NOUN
ejpam-5213	296	2	g	g	NOUN
ejpam-5213	296	3	x	x	PROPN
ejpam-5213	297	1	w	w	PROPN
ejpam-5213	297	2	u	u	PROPN
ejpam-5213	297	3	b	b	PROPN
ejpam-5213	297	4	f	f	PROPN
ejpam-5213	297	5	y	y	PROPN
ejpam-5213	297	6	a	a	DET
ejpam-5213	297	7	e	e	X
ejpam-5213	297	8	v	v	ADP
ejpam-5213	297	9	k1	k1	NOUN
ejpam-5213	297	10	+	+	ADP
ejpam-5213	297	11	g	g	NOUN
ejpam-5213	297	12	:	:	PUNCT
ejpam-5213	297	13	figure	figure	NOUN
ejpam-5213	297	14	1	1	NUM
ejpam-5213	297	15	:	:	PUNCT
ejpam-5213	297	16	graphs	graphs	VERB
ejpam-5213	297	17	g	g	NOUN
ejpam-5213	297	18	and	and	CCONJ
ejpam-5213	297	19	k1	k1	NOUN
ejpam-5213	298	1	+	+	ADV
ejpam-5213	298	2	g	g	NOUN
ejpam-5213	298	3	illustrating	illustrate	VERB
ejpam-5213	298	4	theorem	theorem	ADJ
ejpam-5213	298	5	8	8	NUM
ejpam-5213	298	6	(	(	PUNCT
ejpam-5213	298	7	i	i	NOUN
ejpam-5213	298	8	)	)	PUNCT
ejpam-5213	298	9	in	in	ADP
ejpam-5213	298	10	the	the	DET
ejpam-5213	298	11	next	next	ADJ
ejpam-5213	298	12	results	result	NOUN
ejpam-5213	298	13	,	,	PUNCT
ejpam-5213	298	14	we	we	PRON
ejpam-5213	298	15	use	use	VERB
ejpam-5213	298	16	the	the	DET
ejpam-5213	298	17	following	follow	VERB
ejpam-5213	298	18	parameters	parameter	NOUN
ejpam-5213	298	19	for	for	ADP
ejpam-5213	298	20	any	any	DET
ejpam-5213	298	21	graph	graph	NOUN
ejpam-5213	298	22	g′	g′	NOUN
ejpam-5213	298	23	admitting	admit	VERB
ejpam-5213	298	24	the	the	DET
ejpam-5213	298	25	given	give	VERB
ejpam-5213	298	26	set	set	NOUN
ejpam-5213	298	27	:	:	PUNCT
ejpam-5213	298	28	γeod	γeod	NOUN
ejpam-5213	298	29	(	(	PUNCT
ejpam-5213	298	30	g′	g′	NOUN
ejpam-5213	298	31	)	)	PUNCT
ejpam-5213	299	1	=	=	NOUN
ejpam-5213	299	2	min{|s|	min{|s|	NOUN
ejpam-5213	299	3	:	:	PUNCT
ejpam-5213	299	4	|s|	|s|	PROPN
ejpam-5213	299	5	is	be	AUX
ejpam-5213	299	6	even	even	ADV
ejpam-5213	299	7	and	and	CCONJ
ejpam-5213	299	8	s	s	VERB
ejpam-5213	299	9	∈	∈	PROPN
ejpam-5213	299	10	dod(g′	dod(g′	NOUN
ejpam-5213	299	11	)	)	PUNCT
ejpam-5213	299	12	}	}	PUNCT
ejpam-5213	299	13	γeosd(g	γeosd(g	ADP
ejpam-5213	299	14	′	′	NUM
ejpam-5213	299	15	)	)	PUNCT
ejpam-5213	300	1	=	=	NOUN
ejpam-5213	300	2	min{|s|	min{|s|	NOUN
ejpam-5213	300	3	:	:	PUNCT
ejpam-5213	300	4	|s|	|s|	PROPN
ejpam-5213	300	5	is	be	AUX
ejpam-5213	300	6	even	even	ADV
ejpam-5213	300	7	and	and	CCONJ
ejpam-5213	300	8	s	s	PROPN
ejpam-5213	300	9	∈	∈	PROPN
ejpam-5213	300	10	sdod(g′	sdod(g′	NUM
ejpam-5213	300	11	)	)	PUNCT
ejpam-5213	300	12	}	}	PUNCT
ejpam-5213	300	13	γoosd(g	γoosd(g	ADP
ejpam-5213	300	14	′	′	NUM
ejpam-5213	300	15	)	)	PUNCT
ejpam-5213	301	1	=	=	NOUN
ejpam-5213	301	2	min{|s|	min{|s|	NOUN
ejpam-5213	301	3	:	:	PUNCT
ejpam-5213	301	4	|s|	|s|	PROPN
ejpam-5213	301	5	is	be	AUX
ejpam-5213	301	6	odd	odd	ADJ
ejpam-5213	301	7	and	and	CCONJ
ejpam-5213	301	8	s	s	PROPN
ejpam-5213	301	9	∈	∈	PROPN
ejpam-5213	301	10	sdod(g′	sdod(g′	NUM
ejpam-5213	301	11	)	)	PUNCT
ejpam-5213	301	12	}	}	PUNCT
ejpam-5213	302	1	γeesd(g	γeesd(g	NUM
ejpam-5213	302	2	′	′	NOUN
ejpam-5213	302	3	)	)	PUNCT
ejpam-5213	303	1	=	=	NOUN
ejpam-5213	303	2	min{|s|	min{|s|	NOUN
ejpam-5213	303	3	:	:	PUNCT
ejpam-5213	303	4	|s|	|s|	PROPN
ejpam-5213	303	5	is	be	AUX
ejpam-5213	303	6	even	even	ADV
ejpam-5213	303	7	and	and	CCONJ
ejpam-5213	303	8	s	s	VERB
ejpam-5213	303	9	∈	∈	PROPN
ejpam-5213	303	10	sded(g′	sded(g′	NUM
ejpam-5213	303	11	)	)	PUNCT
ejpam-5213	303	12	}	}	PUNCT
ejpam-5213	303	13	corollary	corollary	ADJ
ejpam-5213	303	14	8	8	NUM
ejpam-5213	303	15	.	.	PUNCT
ejpam-5213	304	1	let	let	VERB
ejpam-5213	304	2	g	g	PRON
ejpam-5213	304	3	be	be	AUX
ejpam-5213	304	4	a	a	DET
ejpam-5213	304	5	point	point	NOUN
ejpam-5213	304	6	distinguishing	distinguish	VERB
ejpam-5213	304	7	graph	graph	NOUN
ejpam-5213	304	8	.	.	PUNCT
ejpam-5213	305	1	m.	m.	NOUN
ejpam-5213	305	2	carbero	carbero	PROPN
ejpam-5213	305	3	,	,	PUNCT
ejpam-5213	305	4	g.	g.	PROPN
ejpam-5213	305	5	malacas	malacas	PROPN
ejpam-5213	305	6	,	,	PUNCT
ejpam-5213	305	7	s.	s.	PROPN
ejpam-5213	305	8	canoy	canoy	PROPN
ejpam-5213	305	9	,	,	PUNCT
ejpam-5213	305	10	jr	jr	PROPN
ejpam-5213	305	11	.	.	PROPN
ejpam-5213	305	12	/	/	SYM
ejpam-5213	305	13	eur	eur	PROPN
ejpam-5213	305	14	.	.	PUNCT
ejpam-5213	306	1	j.	j.	PROPN
ejpam-5213	306	2	pure	pure	PROPN
ejpam-5213	306	3	appl	appl	PROPN
ejpam-5213	306	4	.	.	PROPN
ejpam-5213	306	5	math	math	PROPN
ejpam-5213	306	6	,	,	PUNCT
ejpam-5213	306	7	17	17	NUM
ejpam-5213	306	8	(	(	PUNCT
ejpam-5213	306	9	3	3	NUM
ejpam-5213	306	10	)	)	PUNCT
ejpam-5213	306	11	(	(	PUNCT
ejpam-5213	306	12	2024	2024	NUM
ejpam-5213	306	13	)	)	PUNCT
ejpam-5213	306	14	,	,	PUNCT
ejpam-5213	306	15	1585	1585	NUM
ejpam-5213	306	16	-	-	SYM
ejpam-5213	306	17	1601	1601	NUM
ejpam-5213	306	18	1594	1594	NUM
ejpam-5213	306	19	(	(	PUNCT
ejpam-5213	306	20	i	i	NOUN
ejpam-5213	306	21	)	)	PUNCT
ejpam-5213	306	22	if	if	SCONJ
ejpam-5213	306	23	g	g	PROPN
ejpam-5213	306	24	admits	admit	VERB
ejpam-5213	306	25	a	a	DET
ejpam-5213	306	26	strictly	strictly	ADV
ejpam-5213	306	27	differentiating	differentiate	VERB
ejpam-5213	306	28	odd	odd	ADJ
ejpam-5213	306	29	dominating	dominating	NOUN
ejpam-5213	306	30	set	set	VERB
ejpam-5213	306	31	with	with	ADP
ejpam-5213	306	32	odd	odd	ADJ
ejpam-5213	306	33	cardinality	cardinality	NOUN
ejpam-5213	306	34	,	,	PUNCT
ejpam-5213	306	35	then	then	ADV
ejpam-5213	306	36	γod(k1+g	γod(k1+g	PROPN
ejpam-5213	306	37	)	)	PUNCT
ejpam-5213	306	38	≤	≤	NOUN
ejpam-5213	307	1	γoosd(g	γoosd(g	NOUN
ejpam-5213	307	2	)	)	PUNCT
ejpam-5213	307	3	and	and	CCONJ
ejpam-5213	307	4	equality	equality	NOUN
ejpam-5213	307	5	holds	hold	VERB
ejpam-5213	307	6	if	if	SCONJ
ejpam-5213	307	7	g	g	PROPN
ejpam-5213	307	8	does	do	AUX
ejpam-5213	307	9	not	not	PART
ejpam-5213	307	10	admit	admit	VERB
ejpam-5213	307	11	a	a	DET
ejpam-5213	307	12	differentiating	differentiate	VERB
ejpam-5213	307	13	even	even	ADV
ejpam-5213	307	14	dominating	dominate	VERB
ejpam-5213	307	15	set	set	NOUN
ejpam-5213	307	16	.	.	PUNCT
ejpam-5213	308	1	(	(	PUNCT
ejpam-5213	308	2	ii	ii	NOUN
ejpam-5213	308	3	)	)	PUNCT
ejpam-5213	308	4	if	if	SCONJ
ejpam-5213	308	5	g	g	PROPN
ejpam-5213	308	6	admits	admit	VERB
ejpam-5213	308	7	a	a	DET
ejpam-5213	308	8	strictly	strictly	ADV
ejpam-5213	308	9	differentiating	differentiate	VERB
ejpam-5213	308	10	even	even	ADV
ejpam-5213	308	11	dominating	dominate	VERB
ejpam-5213	308	12	set	set	VERB
ejpam-5213	308	13	with	with	ADP
ejpam-5213	308	14	even	even	ADV
ejpam-5213	308	15	cardinality	cardinality	NOUN
ejpam-5213	308	16	,	,	PUNCT
ejpam-5213	308	17	then	then	ADV
ejpam-5213	308	18	γod(k1	γod(k1	PUNCT
ejpam-5213	309	1	+	+	NOUN
ejpam-5213	309	2	g	g	NOUN
ejpam-5213	309	3	)	)	PUNCT
ejpam-5213	309	4	≤	≤	NOUN
ejpam-5213	309	5	γeesd(g	γeesd(g	PROPN
ejpam-5213	309	6	)	)	PUNCT
ejpam-5213	309	7	+	+	CCONJ
ejpam-5213	309	8	1	1	NUM
ejpam-5213	309	9	and	and	CCONJ
ejpam-5213	309	10	equality	equality	NOUN
ejpam-5213	309	11	holds	hold	VERB
ejpam-5213	309	12	if	if	SCONJ
ejpam-5213	309	13	g	g	PROPN
ejpam-5213	309	14	does	do	AUX
ejpam-5213	309	15	not	not	PART
ejpam-5213	309	16	admit	admit	VERB
ejpam-5213	309	17	a	a	DET
ejpam-5213	309	18	differentiating	differentiate	VERB
ejpam-5213	309	19	odd	odd	ADJ
ejpam-5213	309	20	dominating	dominating	NOUN
ejpam-5213	309	21	set	set	VERB
ejpam-5213	309	22	with	with	ADP
ejpam-5213	309	23	odd	odd	ADJ
ejpam-5213	309	24	cardinality	cardinality	NOUN
ejpam-5213	309	25	.	.	PUNCT
ejpam-5213	310	1	corollary	corollary	ADJ
ejpam-5213	310	2	9	9	NUM
ejpam-5213	310	3	.	.	PUNCT
ejpam-5213	311	1	all	all	DET
ejpam-5213	311	2	fans	fan	NOUN
ejpam-5213	311	3	fn	fn	NOUN
ejpam-5213	311	4	=	=	SYM
ejpam-5213	311	5	k1+pn	k1+pn	PROPN
ejpam-5213	311	6	of	of	ADP
ejpam-5213	311	7	order	order	NOUN
ejpam-5213	311	8	n+1	n+1	PRON
ejpam-5213	311	9	have	have	VERB
ejpam-5213	311	10	no	no	DET
ejpam-5213	311	11	differentiating	differentiate	VERB
ejpam-5213	311	12	odd	odd	ADJ
ejpam-5213	311	13	dominating	dominating	NOUN
ejpam-5213	311	14	set	set	NOUN
ejpam-5213	311	15	for	for	ADP
ejpam-5213	311	16	all	all	DET
ejpam-5213	311	17	n.	n.	NOUN
ejpam-5213	311	18	proof	proof	NOUN
ejpam-5213	311	19	.	.	PUNCT
ejpam-5213	312	1	clearly	clearly	ADV
ejpam-5213	312	2	,	,	PUNCT
ejpam-5213	312	3	f1	f1	NOUN
ejpam-5213	312	4	and	and	CCONJ
ejpam-5213	312	5	f2	f2	PROPN
ejpam-5213	312	6	do	do	AUX
ejpam-5213	312	7	not	not	PART
ejpam-5213	312	8	admit	admit	VERB
ejpam-5213	312	9	a	a	DET
ejpam-5213	312	10	differentiating	differentiate	VERB
ejpam-5213	312	11	odd	odd	ADJ
ejpam-5213	312	12	dominating	dominating	NOUN
ejpam-5213	312	13	set	set	NOUN
ejpam-5213	312	14	.	.	PUNCT
ejpam-5213	313	1	suppose	suppose	VERB
ejpam-5213	313	2	now	now	ADV
ejpam-5213	313	3	that	that	SCONJ
ejpam-5213	313	4	n	n	NUM
ejpam-5213	313	5	≥	≥	NOUN
ejpam-5213	313	6	3	3	NUM
ejpam-5213	313	7	.	.	PUNCT
ejpam-5213	314	1	let	let	VERB
ejpam-5213	314	2	k1	k1	NOUN
ejpam-5213	314	3	=	=	PROPN
ejpam-5213	314	4	⟨v⟩	⟨v⟩	PROPN
ejpam-5213	314	5	and	and	CCONJ
ejpam-5213	314	6	g	g	NOUN
ejpam-5213	314	7	=	=	PROPN
ejpam-5213	314	8	pn	pn	PROPN
ejpam-5213	314	9	=	=	PUNCT
ejpam-5213	315	1	[	[	X
ejpam-5213	315	2	v1	v1	NOUN
ejpam-5213	315	3	,	,	PUNCT
ejpam-5213	315	4	v2	v2	NOUN
ejpam-5213	315	5	,	,	PUNCT
ejpam-5213	315	6	.	.	PUNCT
ejpam-5213	315	7	.	.	PUNCT
ejpam-5213	315	8	.	.	PUNCT
ejpam-5213	316	1	,	,	PUNCT
ejpam-5213	316	2	vn	vn	X
ejpam-5213	316	3	]	]	PUNCT
ejpam-5213	316	4	.	.	PUNCT
ejpam-5213	317	1	suppose	suppose	VERB
ejpam-5213	317	2	fn	fn	NOUN
ejpam-5213	317	3	has	have	VERB
ejpam-5213	317	4	a	a	DET
ejpam-5213	317	5	differentiating	differentiate	VERB
ejpam-5213	317	6	odd	odd	ADJ
ejpam-5213	317	7	dominating	dominating	NOUN
ejpam-5213	317	8	set	set	NOUN
ejpam-5213	317	9	,	,	PUNCT
ejpam-5213	317	10	say	say	VERB
ejpam-5213	317	11	s.	s.	PROPN
ejpam-5213	317	12	suppose	suppose	VERB
ejpam-5213	317	13	s	s	AUX
ejpam-5213	317	14	=	=	SYM
ejpam-5213	317	15	{	{	PUNCT
ejpam-5213	317	16	v	v	NOUN
ejpam-5213	317	17	}	}	PUNCT
ejpam-5213	317	18	∪	∪	ADJ
ejpam-5213	317	19	sg	sg	PROPN
ejpam-5213	317	20	,	,	PUNCT
ejpam-5213	317	21	where	where	SCONJ
ejpam-5213	317	22	sg	sg	ADP
ejpam-5213	317	23	satisfies	satisfie	NOUN
ejpam-5213	317	24	(	(	PUNCT
ejpam-5213	317	25	a	a	X
ejpam-5213	317	26	)	)	PUNCT
ejpam-5213	317	27	and	and	CCONJ
ejpam-5213	317	28	(	(	PUNCT
ejpam-5213	317	29	b	b	NOUN
ejpam-5213	317	30	)	)	PUNCT
ejpam-5213	317	31	in	in	ADP
ejpam-5213	317	32	theorem	theorem	NOUN
ejpam-5213	317	33	8	8	NUM
ejpam-5213	317	34	.	.	PUNCT
ejpam-5213	318	1	if	if	SCONJ
ejpam-5213	318	2	v1	v1	VERB
ejpam-5213	318	3	∈	∈	PROPN
ejpam-5213	318	4	sg	sg	NOUN
ejpam-5213	318	5	,	,	PUNCT
ejpam-5213	318	6	then	then	ADV
ejpam-5213	318	7	v2	v2	PROPN
ejpam-5213	318	8	∈	∈	PROPN
ejpam-5213	318	9	sg	sg	NOUN
ejpam-5213	318	10	by	by	ADP
ejpam-5213	318	11	property	property	NOUN
ejpam-5213	318	12	(	(	PUNCT
ejpam-5213	318	13	b	b	NOUN
ejpam-5213	318	14	)	)	PUNCT
ejpam-5213	318	15	.	.	PUNCT
ejpam-5213	319	1	hence	hence	ADV
ejpam-5213	319	2	,	,	PUNCT
ejpam-5213	319	3	by	by	ADP
ejpam-5213	319	4	the	the	DET
ejpam-5213	319	5	same	same	ADJ
ejpam-5213	319	6	property	property	NOUN
ejpam-5213	319	7	(	(	PUNCT
ejpam-5213	319	8	b	b	NOUN
ejpam-5213	319	9	)	)	PUNCT
ejpam-5213	319	10	,	,	PUNCT
ejpam-5213	319	11	v3	v3	PROPN
ejpam-5213	319	12	/∈	/∈	PUNCT
ejpam-5213	319	13	sg	sg	PROPN
ejpam-5213	319	14	.	.	PUNCT
ejpam-5213	320	1	this	this	PRON
ejpam-5213	320	2	implies	imply	VERB
ejpam-5213	320	3	that	that	SCONJ
ejpam-5213	320	4	ng[v1]∩sg	ng[v1]∩sg	NOUN
ejpam-5213	320	5	=	=	SYM
ejpam-5213	320	6	ng[v2]∩sg	ng[v2]∩sg	NOUN
ejpam-5213	320	7	=	=	SYM
ejpam-5213	320	8	{	{	PUNCT
ejpam-5213	320	9	v1	v1	NOUN
ejpam-5213	320	10	,	,	PUNCT
ejpam-5213	320	11	v2	v2	PROPN
ejpam-5213	320	12	}	}	PUNCT
ejpam-5213	320	13	,	,	PUNCT
ejpam-5213	320	14	contradicting	contradict	VERB
ejpam-5213	320	15	property	property	NOUN
ejpam-5213	320	16	(	(	PUNCT
ejpam-5213	320	17	a	a	NOUN
ejpam-5213	320	18	)	)	PUNCT
ejpam-5213	320	19	.	.	PUNCT
ejpam-5213	321	1	this	this	DET
ejpam-5213	321	2	forces	force	NOUN
ejpam-5213	321	3	v1	v1	VERB
ejpam-5213	321	4	/∈	/∈	PUNCT
ejpam-5213	322	1	sg	sg	PROPN
ejpam-5213	322	2	.	.	PUNCT
ejpam-5213	323	1	by	by	ADP
ejpam-5213	323	2	property	property	NOUN
ejpam-5213	323	3	(	(	PUNCT
ejpam-5213	323	4	b	b	NOUN
ejpam-5213	323	5	)	)	PUNCT
ejpam-5213	323	6	,	,	PUNCT
ejpam-5213	323	7	v2	v2	PROPN
ejpam-5213	323	8	,	,	PUNCT
ejpam-5213	323	9	v3	v3	PROPN
ejpam-5213	323	10	/∈	/∈	PUNCT
ejpam-5213	323	11	sg	sg	PROPN
ejpam-5213	323	12	.	.	PUNCT
ejpam-5213	324	1	thus	thus	ADV
ejpam-5213	324	2	,	,	PUNCT
ejpam-5213	324	3	ng[v1	ng[v1	PROPN
ejpam-5213	324	4	]	]	X
ejpam-5213	324	5	∩	∩	ADJ
ejpam-5213	324	6	sg	sg	ADP
ejpam-5213	324	7	=	=	SYM
ejpam-5213	324	8	ng[v2	ng[v2	PROPN
ejpam-5213	324	9	]	]	X
ejpam-5213	324	10	∩	∩	NOUN
ejpam-5213	324	11	sg	sg	ADP
ejpam-5213	324	12	=	=	SYM
ejpam-5213	324	13	∅	∅	NOUN
ejpam-5213	324	14	,	,	PUNCT
ejpam-5213	324	15	contradicting	contradict	VERB
ejpam-5213	324	16	(	(	PUNCT
ejpam-5213	324	17	a	a	NOUN
ejpam-5213	324	18	)	)	PUNCT
ejpam-5213	324	19	.	.	PUNCT
ejpam-5213	325	1	therefore	therefore	ADV
ejpam-5213	325	2	,	,	PUNCT
ejpam-5213	325	3	s	s	VERB
ejpam-5213	325	4	⊆	⊆	NUM
ejpam-5213	325	5	v	v	NOUN
ejpam-5213	325	6	(	(	PUNCT
ejpam-5213	325	7	pn	pn	NOUN
ejpam-5213	325	8	)	)	PUNCT
ejpam-5213	325	9	and	and	CCONJ
ejpam-5213	325	10	satisfies	satisfie	NOUN
ejpam-5213	325	11	(	(	PUNCT
ejpam-5213	325	12	ii	ii	NOUN
ejpam-5213	325	13	)	)	PUNCT
ejpam-5213	325	14	in	in	ADP
ejpam-5213	325	15	theorem	theorem	NOUN
ejpam-5213	325	16	8	8	NUM
ejpam-5213	325	17	.	.	PUNCT
ejpam-5213	326	1	if	if	SCONJ
ejpam-5213	326	2	v1	v1	VERB
ejpam-5213	326	3	∈	∈	PROPN
ejpam-5213	326	4	s	s	NOUN
ejpam-5213	326	5	,	,	PUNCT
ejpam-5213	326	6	then	then	ADV
ejpam-5213	326	7	v2	v2	PROPN
ejpam-5213	326	8	,	,	PUNCT
ejpam-5213	326	9	v3	v3	PROPN
ejpam-5213	326	10	/∈	/∈	PUNCT
ejpam-5213	326	11	s	s	PART
ejpam-5213	327	1	because	because	SCONJ
ejpam-5213	327	2	s	s	NOUN
ejpam-5213	327	3	is	be	AUX
ejpam-5213	327	4	odd	odd	ADJ
ejpam-5213	327	5	dominating	dominating	NOUN
ejpam-5213	327	6	in	in	ADP
ejpam-5213	327	7	g.	g.	PROPN
ejpam-5213	327	8	this	this	PRON
ejpam-5213	327	9	would	would	AUX
ejpam-5213	327	10	imply	imply	VERB
ejpam-5213	327	11	that	that	SCONJ
ejpam-5213	327	12	sg	sg	PROPN
ejpam-5213	327	13	is	be	AUX
ejpam-5213	327	14	not	not	PART
ejpam-5213	327	15	differentiating	differentiate	VERB
ejpam-5213	327	16	in	in	ADP
ejpam-5213	327	17	g	g	NOUN
ejpam-5213	327	18	,	,	PUNCT
ejpam-5213	327	19	contradicting	contradict	VERB
ejpam-5213	327	20	(	(	PUNCT
ejpam-5213	327	21	ii	ii	NOUN
ejpam-5213	327	22	)	)	PUNCT
ejpam-5213	327	23	.	.	PUNCT
ejpam-5213	328	1	hence	hence	ADV
ejpam-5213	328	2	,	,	PUNCT
ejpam-5213	328	3	v1	v1	PROPN
ejpam-5213	328	4	/∈	/∈	PUNCT
ejpam-5213	329	1	s.	s.	PROPN
ejpam-5213	329	2	since	since	SCONJ
ejpam-5213	329	3	s	s	PROPN
ejpam-5213	329	4	is	be	AUX
ejpam-5213	329	5	odd	odd	ADJ
ejpam-5213	329	6	dominating	dominate	VERB
ejpam-5213	329	7	in	in	ADP
ejpam-5213	329	8	g	g	NOUN
ejpam-5213	329	9	,	,	PUNCT
ejpam-5213	329	10	v2	v2	PROPN
ejpam-5213	329	11	∈	∈	PROPN
ejpam-5213	329	12	s	s	NOUN
ejpam-5213	329	13	and	and	CCONJ
ejpam-5213	329	14	v3	v3	PROPN
ejpam-5213	329	15	/∈	/∈	PUNCT
ejpam-5213	330	1	s.	s.	PROPN
ejpam-5213	330	2	this	this	PRON
ejpam-5213	330	3	implies	imply	VERB
ejpam-5213	330	4	that	that	SCONJ
ejpam-5213	330	5	ng[v1	ng[v1	PROPN
ejpam-5213	330	6	]	]	PUNCT
ejpam-5213	330	7	∩	∩	PROPN
ejpam-5213	330	8	s	s	PART
ejpam-5213	330	9	=	=	SYM
ejpam-5213	330	10	ng[v2	ng[v2	PROPN
ejpam-5213	330	11	]	]	X
ejpam-5213	330	12	∩	∩	X
ejpam-5213	330	13	s	s	PART
ejpam-5213	330	14	=	=	PUNCT
ejpam-5213	330	15	{	{	PUNCT
ejpam-5213	330	16	v2	v2	PROPN
ejpam-5213	330	17	}	}	PUNCT
ejpam-5213	330	18	,	,	PUNCT
ejpam-5213	330	19	contrary	contrary	ADV
ejpam-5213	330	20	to	to	ADP
ejpam-5213	330	21	the	the	DET
ejpam-5213	330	22	assumption	assumption	NOUN
ejpam-5213	330	23	that	that	SCONJ
ejpam-5213	330	24	s	s	VERB
ejpam-5213	330	25	is	be	AUX
ejpam-5213	330	26	differentiating	differentiate	VERB
ejpam-5213	330	27	in	in	ADP
ejpam-5213	330	28	g.	g.	PROPN
ejpam-5213	330	29	therefore	therefore	ADV
ejpam-5213	330	30	,	,	PUNCT
ejpam-5213	330	31	such	such	ADJ
ejpam-5213	330	32	s	s	VERB
ejpam-5213	330	33	does	do	AUX
ejpam-5213	330	34	not	not	PART
ejpam-5213	330	35	exist	exist	VERB
ejpam-5213	330	36	,	,	PUNCT
ejpam-5213	330	37	i.e.	i.e.	X
ejpam-5213	330	38	,	,	PUNCT
ejpam-5213	330	39	fn	fn	NOUN
ejpam-5213	330	40	does	do	AUX
ejpam-5213	330	41	not	not	PART
ejpam-5213	330	42	admit	admit	VERB
ejpam-5213	330	43	a	a	DET
ejpam-5213	330	44	differentiating	differentiate	VERB
ejpam-5213	330	45	odd	odd	ADJ
ejpam-5213	330	46	dominating	dominating	NOUN
ejpam-5213	330	47	set	set	NOUN
ejpam-5213	330	48	.	.	PUNCT
ejpam-5213	331	1	corollary	corollary	ADJ
ejpam-5213	331	2	10	10	NUM
ejpam-5213	331	3	.	.	PUNCT
ejpam-5213	332	1	the	the	DET
ejpam-5213	332	2	wheel	wheel	NOUN
ejpam-5213	332	3	wn	wn	PROPN
ejpam-5213	332	4	=	=	PROPN
ejpam-5213	332	5	k1	k1	PROPN
ejpam-5213	333	1	+	+	PROPN
ejpam-5213	333	2	cn	cn	PROPN
ejpam-5213	333	3	admits	admit	VERB
ejpam-5213	333	4	a	a	DET
ejpam-5213	333	5	differentiating	differentiate	VERB
ejpam-5213	333	6	odd	odd	ADJ
ejpam-5213	333	7	dominating	dominating	NOUN
ejpam-5213	333	8	set	set	VERB
ejpam-5213	333	9	if	if	SCONJ
ejpam-5213	333	10	and	and	CCONJ
ejpam-5213	333	11	only	only	ADV
ejpam-5213	333	12	if	if	SCONJ
ejpam-5213	333	13	n	n	PRON
ejpam-5213	333	14	is	be	AUX
ejpam-5213	333	15	odd	odd	ADJ
ejpam-5213	333	16	and	and	CCONJ
ejpam-5213	333	17	n	n	DET
ejpam-5213	333	18	̸=	̸=	PROPN
ejpam-5213	333	19	3	3	NUM
ejpam-5213	333	20	.	.	PUNCT
ejpam-5213	334	1	moreover	moreover	ADV
ejpam-5213	334	2	,	,	PUNCT
ejpam-5213	334	3	if	if	SCONJ
ejpam-5213	334	4	n	n	PRON
ejpam-5213	334	5	is	be	AUX
ejpam-5213	334	6	odd	odd	ADJ
ejpam-5213	334	7	and	and	CCONJ
ejpam-5213	334	8	n	n	PRON
ejpam-5213	334	9	≥	≥	NOUN
ejpam-5213	334	10	5	5	NUM
ejpam-5213	334	11	,	,	PUNCT
ejpam-5213	334	12	then	then	ADV
ejpam-5213	334	13	γod(wn	γod(wn	NOUN
ejpam-5213	334	14	)	)	PUNCT
ejpam-5213	334	15	=	=	SYM
ejpam-5213	334	16	n.	n.	NOUN
ejpam-5213	334	17	proof	proof	NOUN
ejpam-5213	334	18	.	.	PUNCT
ejpam-5213	335	1	suppose	suppose	VERB
ejpam-5213	335	2	wn	wn	PROPN
ejpam-5213	335	3	admits	admit	VERB
ejpam-5213	335	4	a	a	DET
ejpam-5213	335	5	differentiating	differentiate	VERB
ejpam-5213	335	6	odd	odd	ADJ
ejpam-5213	335	7	dominating	dominating	NOUN
ejpam-5213	335	8	set	set	NOUN
ejpam-5213	335	9	,	,	PUNCT
ejpam-5213	335	10	say	say	VERB
ejpam-5213	335	11	s.	s.	PROPN
ejpam-5213	335	12	since	since	SCONJ
ejpam-5213	335	13	w3	w3	PROPN
ejpam-5213	335	14	=	=	PROPN
ejpam-5213	335	15	k4	k4	PROPN
ejpam-5213	335	16	is	be	AUX
ejpam-5213	335	17	not	not	PART
ejpam-5213	335	18	point	point	NOUN
ejpam-5213	335	19	distinguishing	distinguishing	NOUN
ejpam-5213	335	20	,	,	PUNCT
ejpam-5213	335	21	n	n	CCONJ
ejpam-5213	335	22	̸=	̸=	PROPN
ejpam-5213	335	23	3	3	NUM
ejpam-5213	335	24	.	.	PUNCT
ejpam-5213	336	1	letk1	letk1	PROPN
ejpam-5213	336	2	=	=	PUNCT
ejpam-5213	337	1	⟨v⟩	⟨v⟩	PROPN
ejpam-5213	337	2	andg	andg	NOUN
ejpam-5213	337	3	=	=	PUNCT
ejpam-5213	337	4	cn	cn	PROPN
ejpam-5213	337	5	=	=	PUNCT
ejpam-5213	338	1	[	[	X
ejpam-5213	338	2	v1	v1	NOUN
ejpam-5213	338	3	,	,	PUNCT
ejpam-5213	338	4	v2	v2	NOUN
ejpam-5213	338	5	,	,	PUNCT
ejpam-5213	338	6	.	.	PUNCT
ejpam-5213	338	7	.	.	PUNCT
ejpam-5213	338	8	.	.	PUNCT
ejpam-5213	339	1	,	,	PUNCT
ejpam-5213	339	2	vn	vn	X
ejpam-5213	339	3	,	,	PUNCT
ejpam-5213	339	4	v1	v1	PROPN
ejpam-5213	339	5	]	]	PUNCT
ejpam-5213	339	6	.	.	PUNCT
ejpam-5213	340	1	suppose	suppose	VERB
ejpam-5213	340	2	s	s	VERB
ejpam-5213	340	3	=	=	SYM
ejpam-5213	340	4	{	{	PUNCT
ejpam-5213	340	5	v	v	NOUN
ejpam-5213	340	6	}	}	PUNCT
ejpam-5213	340	7	∪	∪	ADJ
ejpam-5213	340	8	sg	sg	PROPN
ejpam-5213	340	9	,	,	PUNCT
ejpam-5213	340	10	where	where	SCONJ
ejpam-5213	340	11	sg	sg	ADP
ejpam-5213	340	12	satisfies	satisfie	NOUN
ejpam-5213	340	13	(	(	PUNCT
ejpam-5213	340	14	a	a	X
ejpam-5213	340	15	)	)	PUNCT
ejpam-5213	340	16	and	and	CCONJ
ejpam-5213	340	17	(	(	PUNCT
ejpam-5213	340	18	b	b	NOUN
ejpam-5213	340	19	)	)	PUNCT
ejpam-5213	340	20	in	in	ADP
ejpam-5213	340	21	theorem	theorem	ADJ
ejpam-5213	340	22	8(i	8(i	NUM
ejpam-5213	340	23	)	)	PUNCT
ejpam-5213	340	24	.	.	PUNCT
ejpam-5213	341	1	if	if	SCONJ
ejpam-5213	341	2	v1	v1	PROPN
ejpam-5213	341	3	∈	∈	PROPN
ejpam-5213	341	4	sg	sg	NOUN
ejpam-5213	341	5	,	,	PUNCT
ejpam-5213	341	6	then	then	ADV
ejpam-5213	341	7	v2	v2	PROPN
ejpam-5213	341	8	∈	∈	PROPN
ejpam-5213	341	9	sg	sg	ADV
ejpam-5213	341	10	or	or	CCONJ
ejpam-5213	341	11	vn	vn	ADP
ejpam-5213	341	12	∈	∈	PROPN
ejpam-5213	341	13	sg	sg	PROPN
ejpam-5213	341	14	but	but	CCONJ
ejpam-5213	341	15	not	not	PART
ejpam-5213	341	16	both	both	PRON
ejpam-5213	341	17	by	by	ADP
ejpam-5213	341	18	(	(	PUNCT
ejpam-5213	341	19	b	b	NOUN
ejpam-5213	341	20	)	)	PUNCT
ejpam-5213	341	21	.	.	PUNCT
ejpam-5213	342	1	we	we	PRON
ejpam-5213	342	2	may	may	AUX
ejpam-5213	342	3	assume	assume	VERB
ejpam-5213	342	4	that	that	SCONJ
ejpam-5213	342	5	v2	v2	PROPN
ejpam-5213	342	6	∈	∈	PROPN
ejpam-5213	342	7	sg	sg	PROPN
ejpam-5213	342	8	.	.	PUNCT
ejpam-5213	343	1	then	then	ADV
ejpam-5213	343	2	vn	vn	PROPN
ejpam-5213	343	3	/∈	/∈	PUNCT
ejpam-5213	344	1	sg	sg	PROPN
ejpam-5213	344	2	.	.	PUNCT
ejpam-5213	344	3	again	again	ADV
ejpam-5213	344	4	,	,	PUNCT
ejpam-5213	344	5	by	by	ADP
ejpam-5213	344	6	property	property	NOUN
ejpam-5213	344	7	(	(	PUNCT
ejpam-5213	344	8	b	b	NOUN
ejpam-5213	344	9	)	)	PUNCT
ejpam-5213	344	10	,	,	PUNCT
ejpam-5213	344	11	v3	v3	PROPN
ejpam-5213	344	12	/∈	/∈	PUNCT
ejpam-5213	344	13	sg	sg	PROPN
ejpam-5213	344	14	.	.	PUNCT
ejpam-5213	345	1	it	it	PRON
ejpam-5213	345	2	follows	follow	VERB
ejpam-5213	345	3	that	that	SCONJ
ejpam-5213	345	4	ng[v1	ng[v1	PROPN
ejpam-5213	345	5	]	]	PUNCT
ejpam-5213	345	6	∩	∩	ADJ
ejpam-5213	345	7	sg	sg	ADP
ejpam-5213	345	8	=	=	SYM
ejpam-5213	345	9	ng[v2	ng[v2	PROPN
ejpam-5213	345	10	]	]	X
ejpam-5213	345	11	∩	∩	NOUN
ejpam-5213	345	12	sg	sg	ADP
ejpam-5213	345	13	=	=	SYM
ejpam-5213	345	14	{	{	PUNCT
ejpam-5213	345	15	v1	v1	PROPN
ejpam-5213	345	16	,	,	PUNCT
ejpam-5213	345	17	v2	v2	PROPN
ejpam-5213	345	18	}	}	PUNCT
ejpam-5213	345	19	,	,	PUNCT
ejpam-5213	345	20	contradicting	contradict	VERB
ejpam-5213	345	21	property	property	NOUN
ejpam-5213	345	22	(	(	PUNCT
ejpam-5213	345	23	a	a	NOUN
ejpam-5213	345	24	)	)	PUNCT
ejpam-5213	345	25	.	.	PUNCT
ejpam-5213	346	1	consequently	consequently	ADV
ejpam-5213	346	2	,	,	PUNCT
ejpam-5213	346	3	v1	v1	PROPN
ejpam-5213	346	4	/∈	/∈	PUNCT
ejpam-5213	347	1	sg	sg	PROPN
ejpam-5213	347	2	.	.	PUNCT
ejpam-5213	348	1	by	by	ADP
ejpam-5213	348	2	property	property	NOUN
ejpam-5213	348	3	(	(	PUNCT
ejpam-5213	348	4	b	b	NOUN
ejpam-5213	348	5	)	)	PUNCT
ejpam-5213	348	6	,	,	PUNCT
ejpam-5213	348	7	v2	v2	PROPN
ejpam-5213	348	8	,	,	PUNCT
ejpam-5213	348	9	v3	v3	PROPN
ejpam-5213	348	10	,	,	PUNCT
ejpam-5213	348	11	vn	vn	PROPN
ejpam-5213	348	12	∈	∈	PROPN
ejpam-5213	348	13	sg	sg	PROPN
ejpam-5213	348	14	and	and	CCONJ
ejpam-5213	348	15	v4	v4	PROPN
ejpam-5213	348	16	/∈	/∈	PUNCT
ejpam-5213	349	1	sg	sg	INTJ
ejpam-5213	349	2	(	(	PUNCT
ejpam-5213	349	3	hence	hence	ADV
ejpam-5213	349	4	,	,	PUNCT
ejpam-5213	349	5	n	n	CCONJ
ejpam-5213	349	6	̸=	̸=	PROPN
ejpam-5213	349	7	4	4	NUM
ejpam-5213	349	8	)	)	PUNCT
ejpam-5213	349	9	.	.	PUNCT
ejpam-5213	350	1	this	this	PRON
ejpam-5213	350	2	implies	imply	VERB
ejpam-5213	350	3	that	that	SCONJ
ejpam-5213	350	4	ng[v2	ng[v2	PROPN
ejpam-5213	350	5	]	]	X
ejpam-5213	350	6	∩	∩	ADJ
ejpam-5213	350	7	sg	sg	ADP
ejpam-5213	350	8	=	=	SYM
ejpam-5213	350	9	ng[v3	ng[v3	PROPN
ejpam-5213	350	10	]	]	PUNCT
ejpam-5213	350	11	∩	∩	NOUN
ejpam-5213	350	12	sg	sg	ADP
ejpam-5213	350	13	=	=	SYM
ejpam-5213	350	14	{	{	PUNCT
ejpam-5213	350	15	v2	v2	PROPN
ejpam-5213	350	16	,	,	PUNCT
ejpam-5213	350	17	v3	v3	PROPN
ejpam-5213	350	18	}	}	PUNCT
ejpam-5213	350	19	,	,	PUNCT
ejpam-5213	350	20	contradicting	contradict	VERB
ejpam-5213	350	21	property	property	NOUN
ejpam-5213	350	22	(	(	PUNCT
ejpam-5213	350	23	a	a	NOUN
ejpam-5213	350	24	)	)	PUNCT
ejpam-5213	350	25	.	.	PUNCT
ejpam-5213	351	1	therefore	therefore	ADV
ejpam-5213	351	2	,	,	PUNCT
ejpam-5213	351	3	v	v	PROPN
ejpam-5213	351	4	/∈	/∈	PUNCT
ejpam-5213	351	5	s.	s.	PROPN
ejpam-5213	352	1	thus	thus	ADV
ejpam-5213	352	2	,	,	PUNCT
ejpam-5213	352	3	s	s	VERB
ejpam-5213	352	4	⊆	⊆	NUM
ejpam-5213	352	5	v	v	NOUN
ejpam-5213	352	6	(	(	PUNCT
ejpam-5213	352	7	g	g	NOUN
ejpam-5213	352	8	)	)	PUNCT
ejpam-5213	352	9	and	and	CCONJ
ejpam-5213	352	10	satisfies	satisfie	NOUN
ejpam-5213	352	11	(	(	PUNCT
ejpam-5213	352	12	ii	ii	NOUN
ejpam-5213	352	13	)	)	PUNCT
ejpam-5213	352	14	of	of	ADP
ejpam-5213	352	15	theorem	theorem	NOUN
ejpam-5213	352	16	8	8	NUM
ejpam-5213	352	17	.	.	PUNCT
ejpam-5213	353	1	suppose	suppose	VERB
ejpam-5213	353	2	s	s	VERB
ejpam-5213	353	3	̸=	̸=	PROPN
ejpam-5213	353	4	v	v	NOUN
ejpam-5213	353	5	(	(	PUNCT
ejpam-5213	353	6	g	g	NOUN
ejpam-5213	353	7	)	)	PUNCT
ejpam-5213	353	8	.	.	PUNCT
ejpam-5213	354	1	we	we	PRON
ejpam-5213	354	2	may	may	AUX
ejpam-5213	354	3	assume	assume	VERB
ejpam-5213	354	4	that	that	SCONJ
ejpam-5213	354	5	v1	v1	NOUN
ejpam-5213	354	6	∈	∈	PROPN
ejpam-5213	354	7	v	v	NOUN
ejpam-5213	354	8	(	(	PUNCT
ejpam-5213	354	9	g	g	NOUN
ejpam-5213	354	10	)	)	PUNCT
ejpam-5213	354	11	\	\	PUNCT
ejpam-5213	354	12	s.	s.	PROPN
ejpam-5213	354	13	since	since	SCONJ
ejpam-5213	354	14	s	s	PROPN
ejpam-5213	354	15	is	be	AUX
ejpam-5213	354	16	odd	odd	ADJ
ejpam-5213	354	17	dominating	dominating	NOUN
ejpam-5213	354	18	,	,	PUNCT
ejpam-5213	354	19	v2	v2	PROPN
ejpam-5213	354	20	∈	∈	PROPN
ejpam-5213	354	21	s	s	PART
ejpam-5213	354	22	or	or	CCONJ
ejpam-5213	354	23	vn	vn	ADP
ejpam-5213	354	24	∈	∈	PROPN
ejpam-5213	354	25	s	s	PART
ejpam-5213	354	26	but	but	CCONJ
ejpam-5213	354	27	not	not	PART
ejpam-5213	354	28	both	both	PRON
ejpam-5213	354	29	.	.	PUNCT
ejpam-5213	355	1	assume	assume	VERB
ejpam-5213	355	2	that	that	SCONJ
ejpam-5213	355	3	v2	v2	PROPN
ejpam-5213	355	4	∈	∈	PROPN
ejpam-5213	355	5	s.	s.	PROPN
ejpam-5213	355	6	then	then	ADV
ejpam-5213	355	7	vn	vn	PROPN
ejpam-5213	355	8	/∈	/∈	PUNCT
ejpam-5213	355	9	s.	s.	PROPN
ejpam-5213	355	10	again	again	ADV
ejpam-5213	355	11	,	,	PUNCT
ejpam-5213	355	12	since	since	SCONJ
ejpam-5213	355	13	s	s	NOUN
ejpam-5213	355	14	is	be	AUX
ejpam-5213	355	15	odd	odd	ADJ
ejpam-5213	355	16	dominating	dominating	NOUN
ejpam-5213	355	17	,	,	PUNCT
ejpam-5213	355	18	v3	v3	PROPN
ejpam-5213	355	19	/∈	/∈	PUNCT
ejpam-5213	356	1	s.	s.	PROPN
ejpam-5213	356	2	therefore	therefore	ADV
ejpam-5213	356	3	,	,	PUNCT
ejpam-5213	356	4	ng[v1]∩s	ng[v1]∩s	NOUN
ejpam-5213	356	5	=	=	PUNCT
ejpam-5213	356	6	ng[v2]∩s	ng[v2]∩s	ADJ
ejpam-5213	356	7	=	=	X
ejpam-5213	356	8	{	{	PUNCT
ejpam-5213	356	9	v2	v2	PROPN
ejpam-5213	356	10	}	}	PUNCT
ejpam-5213	356	11	,	,	PUNCT
ejpam-5213	356	12	contrary	contrary	ADV
ejpam-5213	356	13	to	to	ADP
ejpam-5213	356	14	the	the	DET
ejpam-5213	356	15	fact	fact	NOUN
ejpam-5213	356	16	that	that	SCONJ
ejpam-5213	356	17	s	s	VERB
ejpam-5213	356	18	is	be	AUX
ejpam-5213	356	19	differentiating	differentiate	VERB
ejpam-5213	356	20	in	in	ADP
ejpam-5213	356	21	g.	g.	PROPN
ejpam-5213	356	22	thus	thus	ADV
ejpam-5213	356	23	,	,	PUNCT
ejpam-5213	356	24	s	s	VERB
ejpam-5213	356	25	=	=	SYM
ejpam-5213	356	26	v	v	X
ejpam-5213	356	27	(	(	PUNCT
ejpam-5213	356	28	g	g	NOUN
ejpam-5213	356	29	)	)	PUNCT
ejpam-5213	356	30	.	.	PUNCT
ejpam-5213	357	1	since	since	SCONJ
ejpam-5213	357	2	s	s	PROPN
ejpam-5213	357	3	is	be	AUX
ejpam-5213	357	4	odd	odd	ADJ
ejpam-5213	357	5	dominating	dominating	NOUN
ejpam-5213	357	6	and	and	CCONJ
ejpam-5213	357	7	v	v	NOUN
ejpam-5213	357	8	/∈	/∈	PUNCT
ejpam-5213	357	9	s	s	X
ejpam-5213	357	10	,	,	PUNCT
ejpam-5213	357	11	|nwn	|nwn	PUNCT
ejpam-5213	357	12	[	[	X
ejpam-5213	357	13	v	v	X
ejpam-5213	357	14	]	]	X
ejpam-5213	357	15	∩	∩	NOUN
ejpam-5213	357	16	s|	s|	NOUN
ejpam-5213	357	17	=	=	SYM
ejpam-5213	357	18	|v	|v	X
ejpam-5213	357	19	(	(	PUNCT
ejpam-5213	357	20	cn)|	cn)|	X
ejpam-5213	357	21	=	=	SYM
ejpam-5213	357	22	n	n	X
ejpam-5213	357	23	is	be	AUX
ejpam-5213	357	24	odd	odd	ADJ
ejpam-5213	357	25	.	.	PUNCT
ejpam-5213	358	1	for	for	ADP
ejpam-5213	358	2	the	the	DET
ejpam-5213	358	3	converse	converse	NOUN
ejpam-5213	358	4	suppose	suppose	VERB
ejpam-5213	358	5	that	that	SCONJ
ejpam-5213	358	6	n	n	PROPN
ejpam-5213	358	7	≥	≥	NUM
ejpam-5213	358	8	5	5	NUM
ejpam-5213	358	9	and	and	CCONJ
ejpam-5213	358	10	is	be	AUX
ejpam-5213	358	11	odd	odd	ADJ
ejpam-5213	358	12	.	.	PUNCT
ejpam-5213	359	1	by	by	ADP
ejpam-5213	359	2	theorem	theorem	NOUN
ejpam-5213	359	3	8	8	NUM
ejpam-5213	359	4	,	,	PUNCT
ejpam-5213	359	5	s0	s0	PROPN
ejpam-5213	359	6	=	=	SYM
ejpam-5213	359	7	v	v	PROPN
ejpam-5213	359	8	(	(	PUNCT
ejpam-5213	359	9	cn	cn	PROPN
ejpam-5213	359	10	)	)	PUNCT
ejpam-5213	359	11	is	be	AUX
ejpam-5213	359	12	a	a	DET
ejpam-5213	359	13	differentiating	differentiate	VERB
ejpam-5213	359	14	odd	odd	ADJ
ejpam-5213	359	15	dominating	dominating	NOUN
ejpam-5213	359	16	set	set	VERB
ejpam-5213	359	17	in	in	ADP
ejpam-5213	359	18	wn	wn	PROPN
ejpam-5213	359	19	.	.	PUNCT
ejpam-5213	360	1	as	as	SCONJ
ejpam-5213	360	2	seen	see	VERB
ejpam-5213	360	3	earlier	early	ADV
ejpam-5213	360	4	,	,	PUNCT
ejpam-5213	360	5	if	if	SCONJ
ejpam-5213	360	6	n	n	PRON
ejpam-5213	360	7	is	be	AUX
ejpam-5213	360	8	odd	odd	ADJ
ejpam-5213	360	9	and	and	CCONJ
ejpam-5213	360	10	n	n	PRON
ejpam-5213	360	11	≥	≥	NOUN
ejpam-5213	360	12	5	5	NUM
ejpam-5213	360	13	,	,	PUNCT
ejpam-5213	360	14	then	then	ADV
ejpam-5213	360	15	v	v	INTJ
ejpam-5213	360	16	(	(	PUNCT
ejpam-5213	360	17	cn	cn	PROPN
ejpam-5213	360	18	)	)	PUNCT
ejpam-5213	360	19	is	be	AUX
ejpam-5213	360	20	the	the	DET
ejpam-5213	360	21	only	only	ADJ
ejpam-5213	360	22	differentiating	differentiate	VERB
ejpam-5213	360	23	odd	odd	ADJ
ejpam-5213	360	24	dominating	dominating	NOUN
ejpam-5213	360	25	set	set	VERB
ejpam-5213	360	26	in	in	ADP
ejpam-5213	360	27	wn	wn	PROPN
ejpam-5213	360	28	.	.	PUNCT
ejpam-5213	361	1	accordingly	accordingly	ADV
ejpam-5213	361	2	,	,	PUNCT
ejpam-5213	361	3	γ	γ	X
ejpam-5213	361	4	o	o	NOUN
ejpam-5213	361	5	d(wn	d(wn	PROPN
ejpam-5213	361	6	)	)	PUNCT
ejpam-5213	361	7	=	=	SYM
ejpam-5213	361	8	n.	n.	NOUN
ejpam-5213	361	9	m.	m.	NOUN
ejpam-5213	361	10	carbero	carbero	PROPN
ejpam-5213	361	11	,	,	PUNCT
ejpam-5213	361	12	g.	g.	PROPN
ejpam-5213	361	13	malacas	malacas	PROPN
ejpam-5213	361	14	,	,	PUNCT
ejpam-5213	361	15	s.	s.	PROPN
ejpam-5213	361	16	canoy	canoy	PROPN
ejpam-5213	361	17	,	,	PUNCT
ejpam-5213	361	18	jr	jr	PROPN
ejpam-5213	361	19	.	.	PROPN
ejpam-5213	361	20	/	/	SYM
ejpam-5213	361	21	eur	eur	PROPN
ejpam-5213	361	22	.	.	PUNCT
ejpam-5213	362	1	j.	j.	PROPN
ejpam-5213	362	2	pure	pure	PROPN
ejpam-5213	362	3	appl	appl	PROPN
ejpam-5213	362	4	.	.	PROPN
ejpam-5213	362	5	math	math	PROPN
ejpam-5213	362	6	,	,	PUNCT
ejpam-5213	362	7	17	17	NUM
ejpam-5213	362	8	(	(	PUNCT
ejpam-5213	362	9	3	3	NUM
ejpam-5213	362	10	)	)	PUNCT
ejpam-5213	362	11	(	(	PUNCT
ejpam-5213	362	12	2024	2024	NUM
ejpam-5213	362	13	)	)	PUNCT
ejpam-5213	362	14	,	,	PUNCT
ejpam-5213	362	15	1585	1585	NUM
ejpam-5213	362	16	-	-	SYM
ejpam-5213	362	17	1601	1601	NUM
ejpam-5213	362	18	1595	1595	NUM
ejpam-5213	362	19	the	the	DET
ejpam-5213	362	20	next	next	ADJ
ejpam-5213	362	21	result	result	NOUN
ejpam-5213	362	22	is	be	AUX
ejpam-5213	362	23	due	due	ADJ
ejpam-5213	362	24	to	to	ADP
ejpam-5213	362	25	canoy	canoy	NOUN
ejpam-5213	362	26	and	and	CCONJ
ejpam-5213	362	27	malacas	malacas	NOUN
ejpam-5213	363	1	[	[	X
ejpam-5213	363	2	12	12	NUM
ejpam-5213	363	3	]	]	PUNCT
ejpam-5213	363	4	.	.	PUNCT
ejpam-5213	364	1	theorem	theorem	VERB
ejpam-5213	364	2	9	9	NUM
ejpam-5213	364	3	.	.	PUNCT
ejpam-5213	365	1	[	[	X
ejpam-5213	365	2	12	12	NUM
ejpam-5213	365	3	]	]	PUNCT
ejpam-5213	365	4	let	let	VERB
ejpam-5213	365	5	g	g	NOUN
ejpam-5213	365	6	and	and	CCONJ
ejpam-5213	365	7	h	h	PROPN
ejpam-5213	365	8	be	be	VERB
ejpam-5213	365	9	non	non	ADJ
ejpam-5213	365	10	-	-	ADJ
ejpam-5213	365	11	trivial	trivial	ADJ
ejpam-5213	365	12	graphs	graph	NOUN
ejpam-5213	365	13	of	of	ADP
ejpam-5213	365	14	orders	order	NOUN
ejpam-5213	365	15	m	m	VERB
ejpam-5213	365	16	≥	≥	NOUN
ejpam-5213	365	17	2	2	NUM
ejpam-5213	365	18	and	and	CCONJ
ejpam-5213	365	19	n	n	PRON
ejpam-5213	365	20	≥	≥	NOUN
ejpam-5213	365	21	2	2	NUM
ejpam-5213	365	22	,	,	PUNCT
ejpam-5213	365	23	respectively	respectively	ADV
ejpam-5213	365	24	.	.	PUNCT
ejpam-5213	366	1	then	then	ADV
ejpam-5213	366	2	s	s	VERB
ejpam-5213	366	3	⊆	⊆	NUM
ejpam-5213	366	4	v	v	NOUN
ejpam-5213	366	5	(	(	PUNCT
ejpam-5213	366	6	g	g	PROPN
ejpam-5213	366	7	+	+	NOUN
ejpam-5213	366	8	h	h	NOUN
ejpam-5213	366	9	)	)	PUNCT
ejpam-5213	366	10	is	be	AUX
ejpam-5213	366	11	a	a	DET
ejpam-5213	366	12	differentiating	differentiate	VERB
ejpam-5213	366	13	-	-	PUNCT
ejpam-5213	366	14	dominating	dominating	NOUN
ejpam-5213	366	15	set	set	NOUN
ejpam-5213	366	16	in	in	ADP
ejpam-5213	366	17	g	g	PROPN
ejpam-5213	367	1	+	+	NOUN
ejpam-5213	367	2	h	h	NOUN
ejpam-5213	367	3	if	if	SCONJ
ejpam-5213	367	4	and	and	CCONJ
ejpam-5213	367	5	only	only	ADV
ejpam-5213	367	6	if	if	SCONJ
ejpam-5213	367	7	sg	sg	PROPN
ejpam-5213	367	8	=	=	SYM
ejpam-5213	367	9	v	v	PROPN
ejpam-5213	367	10	(	(	PUNCT
ejpam-5213	367	11	g	g	NOUN
ejpam-5213	367	12	)	)	PUNCT
ejpam-5213	367	13	∩	∩	NOUN
ejpam-5213	367	14	s	s	NOUN
ejpam-5213	367	15	and	and	CCONJ
ejpam-5213	367	16	sh	sh	PROPN
ejpam-5213	367	17	=	=	SYM
ejpam-5213	367	18	v	v	PROPN
ejpam-5213	367	19	(	(	PUNCT
ejpam-5213	367	20	h	h	NOUN
ejpam-5213	367	21	)	)	PUNCT
ejpam-5213	367	22	∩	∩	NOUN
ejpam-5213	367	23	s	s	PART
ejpam-5213	367	24	are	be	AUX
ejpam-5213	367	25	differentiating	differentiate	VERB
ejpam-5213	367	26	sets	set	NOUN
ejpam-5213	367	27	in	in	ADP
ejpam-5213	367	28	g	g	PROPN
ejpam-5213	367	29	and	and	CCONJ
ejpam-5213	367	30	h	h	NOUN
ejpam-5213	367	31	,	,	PUNCT
ejpam-5213	367	32	respectively	respectively	ADV
ejpam-5213	367	33	,	,	PUNCT
ejpam-5213	367	34	and	and	CCONJ
ejpam-5213	367	35	either	either	CCONJ
ejpam-5213	367	36	sg	sg	PROPN
ejpam-5213	367	37	or	or	CCONJ
ejpam-5213	367	38	sh	sh	PROPN
ejpam-5213	367	39	is	be	AUX
ejpam-5213	367	40	strictly	strictly	ADV
ejpam-5213	367	41	differentiating	differentiate	VERB
ejpam-5213	367	42	.	.	PUNCT
ejpam-5213	368	1	theorem	theorem	ADJ
ejpam-5213	368	2	10	10	NUM
ejpam-5213	368	3	.	.	PUNCT
ejpam-5213	369	1	let	let	VERB
ejpam-5213	369	2	g	g	NOUN
ejpam-5213	369	3	and	and	CCONJ
ejpam-5213	369	4	h	h	NOUN
ejpam-5213	369	5	be	be	AUX
ejpam-5213	369	6	non	non	ADJ
ejpam-5213	369	7	-	-	ADJ
ejpam-5213	369	8	complete	complete	ADJ
ejpam-5213	369	9	graphs	graph	NOUN
ejpam-5213	369	10	of	of	ADP
ejpam-5213	369	11	order	order	NOUN
ejpam-5213	369	12	m	m	VERB
ejpam-5213	369	13	≥	≥	NOUN
ejpam-5213	369	14	4	4	NUM
ejpam-5213	369	15	and	and	CCONJ
ejpam-5213	369	16	n	n	PRON
ejpam-5213	369	17	≥	≥	NOUN
ejpam-5213	369	18	4	4	NUM
ejpam-5213	369	19	,	,	PUNCT
ejpam-5213	369	20	respectively	respectively	ADV
ejpam-5213	369	21	.	.	PUNCT
ejpam-5213	370	1	then	then	ADV
ejpam-5213	370	2	s	s	VERB
ejpam-5213	370	3	⊆	⊆	NUM
ejpam-5213	370	4	v	v	NOUN
ejpam-5213	370	5	(	(	PUNCT
ejpam-5213	370	6	g	g	PROPN
ejpam-5213	370	7	+	+	NOUN
ejpam-5213	370	8	h	h	NOUN
ejpam-5213	370	9	)	)	PUNCT
ejpam-5213	370	10	is	be	AUX
ejpam-5213	370	11	a	a	DET
ejpam-5213	370	12	differentiating	differentiate	VERB
ejpam-5213	370	13	odd	odd	ADJ
ejpam-5213	370	14	dominating	dominating	NOUN
ejpam-5213	370	15	set	set	VERB
ejpam-5213	370	16	in	in	ADP
ejpam-5213	370	17	g	g	PROPN
ejpam-5213	371	1	+	+	NOUN
ejpam-5213	371	2	h	h	NOUN
ejpam-5213	371	3	if	if	SCONJ
ejpam-5213	371	4	and	and	CCONJ
ejpam-5213	371	5	only	only	ADV
ejpam-5213	371	6	if	if	SCONJ
ejpam-5213	371	7	s	s	VERB
ejpam-5213	371	8	=	=	PUNCT
ejpam-5213	371	9	sg	sg	X
ejpam-5213	371	10	∪	∪	ADJ
ejpam-5213	371	11	sh	sh	PROPN
ejpam-5213	371	12	,	,	PUNCT
ejpam-5213	371	13	where	where	SCONJ
ejpam-5213	371	14	sg	sg	PROPN
ejpam-5213	371	15	and	and	CCONJ
ejpam-5213	371	16	sh	sh	PROPN
ejpam-5213	371	17	are	be	AUX
ejpam-5213	371	18	differentiating	differentiate	VERB
ejpam-5213	371	19	sets	set	NOUN
ejpam-5213	371	20	in	in	ADP
ejpam-5213	371	21	g	g	PROPN
ejpam-5213	371	22	and	and	CCONJ
ejpam-5213	371	23	h	h	NOUN
ejpam-5213	371	24	,	,	PUNCT
ejpam-5213	371	25	respectively	respectively	ADV
ejpam-5213	371	26	,	,	PUNCT
ejpam-5213	371	27	either	either	CCONJ
ejpam-5213	371	28	sg	sg	PROPN
ejpam-5213	371	29	or	or	CCONJ
ejpam-5213	371	30	sh	sh	PROPN
ejpam-5213	371	31	is	be	AUX
ejpam-5213	371	32	strictly	strictly	ADV
ejpam-5213	371	33	differentiating	differentiate	VERB
ejpam-5213	371	34	,	,	PUNCT
ejpam-5213	371	35	and	and	CCONJ
ejpam-5213	371	36	one	one	NUM
ejpam-5213	371	37	of	of	ADP
ejpam-5213	371	38	the	the	DET
ejpam-5213	371	39	following	following	ADJ
ejpam-5213	371	40	statements	statement	NOUN
ejpam-5213	371	41	holds	hold	VERB
ejpam-5213	371	42	:	:	PUNCT
ejpam-5213	371	43	(	(	PUNCT
ejpam-5213	371	44	i	i	NOUN
ejpam-5213	371	45	)	)	PUNCT
ejpam-5213	371	46	|sg|	|sg|	PROPN
ejpam-5213	371	47	and	and	CCONJ
ejpam-5213	371	48	|sh	|sh	PROPN
ejpam-5213	371	49	|	|	ADV
ejpam-5213	371	50	are	be	AUX
ejpam-5213	371	51	even	even	ADV
ejpam-5213	371	52	,	,	PUNCT
ejpam-5213	371	53	and	and	CCONJ
ejpam-5213	371	54	sg	sg	PROPN
ejpam-5213	371	55	and	and	CCONJ
ejpam-5213	371	56	sh	sh	PROPN
ejpam-5213	371	57	are	be	AUX
ejpam-5213	371	58	both	both	PRON
ejpam-5213	371	59	odd	odd	ADJ
ejpam-5213	371	60	dominating	dominating	NOUN
ejpam-5213	371	61	sets	set	NOUN
ejpam-5213	371	62	in	in	ADP
ejpam-5213	371	63	g	g	PROPN
ejpam-5213	371	64	and	and	CCONJ
ejpam-5213	371	65	h	h	NOUN
ejpam-5213	371	66	,	,	PUNCT
ejpam-5213	371	67	respectively	respectively	ADV
ejpam-5213	371	68	.	.	PUNCT
ejpam-5213	372	1	(	(	PUNCT
ejpam-5213	372	2	ii	ii	NOUN
ejpam-5213	372	3	)	)	PUNCT
ejpam-5213	372	4	|sg|	|sg|	PROPN
ejpam-5213	372	5	and	and	CCONJ
ejpam-5213	372	6	|sh	|sh	PROPN
ejpam-5213	372	7	|	|	ADV
ejpam-5213	372	8	are	be	AUX
ejpam-5213	372	9	odd	odd	ADJ
ejpam-5213	372	10	,	,	PUNCT
ejpam-5213	372	11	and	and	CCONJ
ejpam-5213	372	12	sg	sg	PROPN
ejpam-5213	372	13	and	and	CCONJ
ejpam-5213	372	14	sh	sh	PROPN
ejpam-5213	372	15	are	be	AUX
ejpam-5213	372	16	both	both	PRON
ejpam-5213	372	17	even	even	ADV
ejpam-5213	372	18	dominating	dominate	VERB
ejpam-5213	372	19	sets	set	NOUN
ejpam-5213	372	20	in	in	ADP
ejpam-5213	372	21	g	g	PROPN
ejpam-5213	372	22	and	and	CCONJ
ejpam-5213	372	23	h	h	NOUN
ejpam-5213	372	24	,	,	PUNCT
ejpam-5213	372	25	respectively	respectively	ADV
ejpam-5213	372	26	.	.	PUNCT
ejpam-5213	373	1	(	(	PUNCT
ejpam-5213	373	2	iii	iii	X
ejpam-5213	373	3	)	)	PUNCT
ejpam-5213	373	4	|sg|	|sg|	NOUN
ejpam-5213	373	5	is	be	AUX
ejpam-5213	373	6	odd	odd	ADJ
ejpam-5213	373	7	,	,	PUNCT
ejpam-5213	373	8	|sh	|sh	ADJ
ejpam-5213	373	9	|	|	ADV
ejpam-5213	373	10	is	be	AUX
ejpam-5213	373	11	even	even	ADV
ejpam-5213	373	12	,	,	PUNCT
ejpam-5213	373	13	sg	sg	PROPN
ejpam-5213	373	14	is	be	AUX
ejpam-5213	373	15	odd	odd	ADJ
ejpam-5213	373	16	dominating	dominate	VERB
ejpam-5213	373	17	in	in	ADP
ejpam-5213	373	18	g	g	PROPN
ejpam-5213	373	19	,	,	PUNCT
ejpam-5213	373	20	sh	sh	PROPN
ejpam-5213	373	21	is	be	AUX
ejpam-5213	373	22	even	even	ADV
ejpam-5213	373	23	dominating	dominate	VERB
ejpam-5213	373	24	set	set	VERB
ejpam-5213	373	25	in	in	ADP
ejpam-5213	373	26	h.	h.	PROPN
ejpam-5213	373	27	(	(	PUNCT
ejpam-5213	373	28	iv	iv	X
ejpam-5213	373	29	)	)	PUNCT
ejpam-5213	373	30	|sg|	|sg|	NOUN
ejpam-5213	373	31	is	be	AUX
ejpam-5213	373	32	even	even	ADV
ejpam-5213	373	33	,	,	PUNCT
ejpam-5213	373	34	|sh	|sh	ADJ
ejpam-5213	373	35	|	|	ADV
ejpam-5213	373	36	is	be	AUX
ejpam-5213	373	37	odd	odd	ADJ
ejpam-5213	373	38	,	,	PUNCT
ejpam-5213	373	39	sg	sg	PROPN
ejpam-5213	373	40	is	be	AUX
ejpam-5213	373	41	even	even	ADV
ejpam-5213	373	42	dominating	dominate	VERB
ejpam-5213	373	43	in	in	ADP
ejpam-5213	373	44	g	g	NOUN
ejpam-5213	373	45	,	,	PUNCT
ejpam-5213	373	46	and	and	CCONJ
ejpam-5213	373	47	sh	sh	PROPN
ejpam-5213	373	48	is	be	AUX
ejpam-5213	373	49	odd	odd	ADJ
ejpam-5213	373	50	dominating	dominating	NOUN
ejpam-5213	373	51	sets	set	NOUN
ejpam-5213	373	52	in	in	ADP
ejpam-5213	373	53	h.	h.	NOUN
ejpam-5213	373	54	proof	proof	NOUN
ejpam-5213	373	55	.	.	PUNCT
ejpam-5213	374	1	let	let	VERB
ejpam-5213	374	2	s	s	PRON
ejpam-5213	374	3	⊆	⊆	NUM
ejpam-5213	374	4	v	v	NOUN
ejpam-5213	374	5	(	(	PUNCT
ejpam-5213	374	6	g	g	PROPN
ejpam-5213	374	7	+	+	NOUN
ejpam-5213	374	8	h	h	NOUN
ejpam-5213	374	9	)	)	PUNCT
ejpam-5213	374	10	be	be	VERB
ejpam-5213	374	11	a	a	DET
ejpam-5213	374	12	differentiating	differentiate	VERB
ejpam-5213	374	13	odd	odd	ADJ
ejpam-5213	374	14	dominating	dominating	NOUN
ejpam-5213	374	15	set	set	VERB
ejpam-5213	374	16	in	in	ADP
ejpam-5213	374	17	g	g	PROPN
ejpam-5213	375	1	+	+	CCONJ
ejpam-5213	375	2	h.	h.	PROPN
ejpam-5213	375	3	let	let	VERB
ejpam-5213	375	4	sg	sg	PROPN
ejpam-5213	375	5	=	=	SYM
ejpam-5213	375	6	v	v	PROPN
ejpam-5213	375	7	(	(	PUNCT
ejpam-5213	375	8	g	g	NOUN
ejpam-5213	375	9	)	)	PUNCT
ejpam-5213	375	10	∩	∩	NOUN
ejpam-5213	375	11	s	s	NOUN
ejpam-5213	375	12	and	and	CCONJ
ejpam-5213	375	13	sh	sh	PROPN
ejpam-5213	375	14	=	=	SYM
ejpam-5213	375	15	v	v	PROPN
ejpam-5213	375	16	(	(	PUNCT
ejpam-5213	375	17	h	h	NOUN
ejpam-5213	375	18	)	)	PUNCT
ejpam-5213	375	19	∩	∩	NOUN
ejpam-5213	375	20	s.	s.	PROPN
ejpam-5213	375	21	by	by	ADP
ejpam-5213	375	22	theorem	theorem	NOUN
ejpam-5213	375	23	9	9	NUM
ejpam-5213	375	24	,	,	PUNCT
ejpam-5213	375	25	sg	sg	PROPN
ejpam-5213	375	26	and	and	CCONJ
ejpam-5213	375	27	sh	sh	PROPN
ejpam-5213	375	28	are	be	AUX
ejpam-5213	375	29	differentiatingdominating	differentiatingdominate	VERB
ejpam-5213	375	30	sets	set	NOUN
ejpam-5213	375	31	in	in	ADP
ejpam-5213	375	32	g	g	PROPN
ejpam-5213	375	33	and	and	CCONJ
ejpam-5213	375	34	h	h	NOUN
ejpam-5213	375	35	,	,	PUNCT
ejpam-5213	375	36	respectively	respectively	ADV
ejpam-5213	375	37	,	,	PUNCT
ejpam-5213	375	38	and	and	CCONJ
ejpam-5213	375	39	either	either	CCONJ
ejpam-5213	375	40	sg	sg	PROPN
ejpam-5213	375	41	or	or	CCONJ
ejpam-5213	375	42	sh	sh	PROPN
ejpam-5213	375	43	is	be	AUX
ejpam-5213	375	44	stricly	stricly	ADV
ejpam-5213	375	45	differentiating	differentiate	VERB
ejpam-5213	375	46	.	.	PUNCT
ejpam-5213	376	1	now	now	ADV
ejpam-5213	376	2	,	,	PUNCT
ejpam-5213	376	3	since	since	SCONJ
ejpam-5213	376	4	s	s	PROPN
ejpam-5213	376	5	is	be	AUX
ejpam-5213	376	6	odd	odd	ADJ
ejpam-5213	376	7	dominating	dominate	VERB
ejpam-5213	376	8	in	in	ADP
ejpam-5213	376	9	g	g	PROPN
ejpam-5213	376	10	+	+	CCONJ
ejpam-5213	376	11	h	h	NOUN
ejpam-5213	376	12	,	,	PUNCT
ejpam-5213	376	13	|ng+h	|ng+h	PUNCT
ejpam-5213	377	1	[	[	X
ejpam-5213	377	2	x	x	X
ejpam-5213	377	3	]	]	X
ejpam-5213	377	4	∩	∩	ADJ
ejpam-5213	377	5	s|	s|	NOUN
ejpam-5213	377	6	=	=	SYM
ejpam-5213	377	7	|ng[x	|ng[x	NOUN
ejpam-5213	377	8	]	]	PUNCT
ejpam-5213	377	9	∩	∩	NOUN
ejpam-5213	377	10	sg|	sg|	VERB
ejpam-5213	377	11	+	+	CCONJ
ejpam-5213	377	12	|sh	|sh	NUM
ejpam-5213	377	13	|	|	ADV
ejpam-5213	377	14	and	and	CCONJ
ejpam-5213	377	15	|ng+h	|ng+h	X
ejpam-5213	378	1	[	[	X
ejpam-5213	378	2	y]∩s|	y]∩s|	NOUN
ejpam-5213	378	3	=	=	SYM
ejpam-5213	378	4	|nh	|nh	NUM
ejpam-5213	378	5	[	[	PUNCT
ejpam-5213	378	6	y]∩sh	y]∩sh	ADJ
ejpam-5213	378	7	|+	|+	NOUN
ejpam-5213	378	8	|sg|	|sg|	NOUN
ejpam-5213	378	9	are	be	AUX
ejpam-5213	378	10	odd	odd	ADJ
ejpam-5213	378	11	for	for	ADP
ejpam-5213	378	12	every	every	DET
ejpam-5213	378	13	x	x	SYM
ejpam-5213	378	14	∈	∈	PROPN
ejpam-5213	378	15	v	v	ADP
ejpam-5213	378	16	(	(	PUNCT
ejpam-5213	378	17	g	g	NOUN
ejpam-5213	378	18	)	)	PUNCT
ejpam-5213	378	19	and	and	CCONJ
ejpam-5213	378	20	for	for	ADP
ejpam-5213	378	21	every	every	DET
ejpam-5213	378	22	y	y	PROPN
ejpam-5213	378	23	∈	∈	PROPN
ejpam-5213	378	24	v	v	ADP
ejpam-5213	378	25	(	(	PUNCT
ejpam-5213	378	26	h	h	NOUN
ejpam-5213	378	27	)	)	PUNCT
ejpam-5213	378	28	.	.	PUNCT
ejpam-5213	379	1	hence	hence	ADV
ejpam-5213	379	2	,	,	PUNCT
ejpam-5213	379	3	if	if	SCONJ
ejpam-5213	379	4	|sg|	|sg|	PROPN
ejpam-5213	379	5	is	be	AUX
ejpam-5213	379	6	even	even	ADV
ejpam-5213	379	7	(	(	PUNCT
ejpam-5213	379	8	or	or	CCONJ
ejpam-5213	379	9	|sh	|sh	VERB
ejpam-5213	379	10	|	|	ADV
ejpam-5213	379	11	is	be	AUX
ejpam-5213	379	12	even	even	ADV
ejpam-5213	379	13	)	)	PUNCT
ejpam-5213	379	14	,	,	PUNCT
ejpam-5213	379	15	then	then	ADV
ejpam-5213	379	16	|nh	|nh	NUM
ejpam-5213	379	17	[	[	X
ejpam-5213	379	18	y	y	X
ejpam-5213	379	19	]	]	X
ejpam-5213	379	20	∩	∩	NOUN
ejpam-5213	379	21	sh	sh	PROPN
ejpam-5213	379	22	|	|	ADV
ejpam-5213	379	23	is	be	AUX
ejpam-5213	379	24	odd	odd	ADJ
ejpam-5213	379	25	(	(	PUNCT
ejpam-5213	379	26	resp	resp	NOUN
ejpam-5213	379	27	.	.	PUNCT
ejpam-5213	380	1	|ng[x	|ng[x	NUM
ejpam-5213	380	2	]	]	PUNCT
ejpam-5213	380	3	∩	∩	PROPN
ejpam-5213	380	4	sg|	sg|	PROPN
ejpam-5213	380	5	is	be	AUX
ejpam-5213	380	6	odd	odd	ADJ
ejpam-5213	380	7	)	)	PUNCT
ejpam-5213	380	8	.	.	PUNCT
ejpam-5213	381	1	this	this	PRON
ejpam-5213	381	2	implies	imply	VERB
ejpam-5213	381	3	that	that	SCONJ
ejpam-5213	381	4	sh	sh	PROPN
ejpam-5213	381	5	is	be	AUX
ejpam-5213	381	6	odd	odd	ADJ
ejpam-5213	381	7	dominating	dominating	NOUN
ejpam-5213	381	8	(	(	PUNCT
ejpam-5213	381	9	resp	resp	NOUN
ejpam-5213	381	10	.	.	PUNCT
ejpam-5213	382	1	sg	sg	PROPN
ejpam-5213	382	2	is	be	AUX
ejpam-5213	382	3	odd	odd	ADJ
ejpam-5213	382	4	dominating	dominating	NOUN
ejpam-5213	382	5	)	)	PUNCT
ejpam-5213	382	6	.	.	PUNCT
ejpam-5213	383	1	if	if	SCONJ
ejpam-5213	383	2	|sg|	|sg|	PROPN
ejpam-5213	383	3	is	be	AUX
ejpam-5213	383	4	odd	odd	ADJ
ejpam-5213	383	5	(	(	PUNCT
ejpam-5213	383	6	or	or	CCONJ
ejpam-5213	383	7	|sh	|sh	VERB
ejpam-5213	383	8	|	|	ADV
ejpam-5213	383	9	is	be	AUX
ejpam-5213	383	10	odd	odd	ADJ
ejpam-5213	383	11	)	)	PUNCT
ejpam-5213	383	12	,	,	PUNCT
ejpam-5213	383	13	then	then	ADV
ejpam-5213	383	14	|nh	|nh	NUM
ejpam-5213	383	15	[	[	X
ejpam-5213	383	16	y	y	X
ejpam-5213	383	17	]	]	X
ejpam-5213	383	18	∩	∩	NOUN
ejpam-5213	383	19	sh	sh	PROPN
ejpam-5213	383	20	|	|	ADV
ejpam-5213	383	21	is	be	AUX
ejpam-5213	383	22	even	even	ADV
ejpam-5213	383	23	(	(	PUNCT
ejpam-5213	383	24	resp	resp	NOUN
ejpam-5213	383	25	.	.	PUNCT
ejpam-5213	384	1	|ng[x	|ng[x	NUM
ejpam-5213	384	2	]	]	PUNCT
ejpam-5213	384	3	∩	∩	PROPN
ejpam-5213	384	4	sg|	sg|	PROPN
ejpam-5213	384	5	is	be	AUX
ejpam-5213	384	6	even	even	ADV
ejpam-5213	384	7	)	)	PUNCT
ejpam-5213	384	8	.	.	PUNCT
ejpam-5213	385	1	hence	hence	ADV
ejpam-5213	385	2	,	,	PUNCT
ejpam-5213	385	3	sh	sh	PROPN
ejpam-5213	385	4	is	be	AUX
ejpam-5213	385	5	even	even	ADV
ejpam-5213	385	6	dominating	dominate	VERB
ejpam-5213	385	7	(	(	PUNCT
ejpam-5213	385	8	resp	resp	NOUN
ejpam-5213	385	9	.	.	PUNCT
ejpam-5213	386	1	sg	sg	PROPN
ejpam-5213	386	2	is	be	AUX
ejpam-5213	386	3	even	even	ADV
ejpam-5213	386	4	dominating	dominate	VERB
ejpam-5213	386	5	)	)	PUNCT
ejpam-5213	386	6	.	.	PUNCT
ejpam-5213	387	1	therefore	therefore	ADV
ejpam-5213	387	2	,	,	PUNCT
ejpam-5213	387	3	(	(	PUNCT
ejpam-5213	387	4	i	i	NOUN
ejpam-5213	387	5	)	)	PUNCT
ejpam-5213	387	6	,	,	PUNCT
ejpam-5213	387	7	or	or	CCONJ
ejpam-5213	387	8	(	(	PUNCT
ejpam-5213	387	9	ii	ii	NOUN
ejpam-5213	387	10	)	)	PUNCT
ejpam-5213	387	11	,	,	PUNCT
ejpam-5213	387	12	or	or	CCONJ
ejpam-5213	387	13	(	(	PUNCT
ejpam-5213	387	14	iii	iii	NOUN
ejpam-5213	387	15	)	)	PUNCT
ejpam-5213	387	16	,	,	PUNCT
ejpam-5213	387	17	or	or	CCONJ
ejpam-5213	387	18	(	(	PUNCT
ejpam-5213	387	19	iv	iv	X
ejpam-5213	387	20	)	)	PUNCT
ejpam-5213	387	21	holds	hold	NOUN
ejpam-5213	387	22	.	.	PUNCT
ejpam-5213	388	1	for	for	ADP
ejpam-5213	388	2	the	the	DET
ejpam-5213	388	3	converse	converse	NOUN
ejpam-5213	388	4	,	,	PUNCT
ejpam-5213	388	5	suppose	suppose	VERB
ejpam-5213	388	6	that	that	SCONJ
ejpam-5213	388	7	s	s	VERB
ejpam-5213	388	8	=	=	PUNCT
ejpam-5213	388	9	sg	sg	X
ejpam-5213	388	10	∪	∪	ADJ
ejpam-5213	388	11	sh	sh	PROPN
ejpam-5213	388	12	,	,	PUNCT
ejpam-5213	388	13	where	where	SCONJ
ejpam-5213	388	14	sg	sg	PROPN
ejpam-5213	388	15	and	and	CCONJ
ejpam-5213	388	16	sh	sh	PROPN
ejpam-5213	388	17	are	be	AUX
ejpam-5213	388	18	differentiatingdominating	differentiatingdominate	VERB
ejpam-5213	388	19	sets	set	NOUN
ejpam-5213	388	20	in	in	ADP
ejpam-5213	388	21	g	g	PROPN
ejpam-5213	388	22	and	and	CCONJ
ejpam-5213	388	23	h	h	NOUN
ejpam-5213	388	24	,	,	PUNCT
ejpam-5213	388	25	respectively	respectively	ADV
ejpam-5213	388	26	,	,	PUNCT
ejpam-5213	388	27	and	and	CCONJ
ejpam-5213	388	28	either	either	CCONJ
ejpam-5213	388	29	sg	sg	PROPN
ejpam-5213	388	30	or	or	CCONJ
ejpam-5213	388	31	sh	sh	PROPN
ejpam-5213	388	32	is	be	AUX
ejpam-5213	388	33	strictly	strictly	ADV
ejpam-5213	388	34	differentiating	differentiate	VERB
ejpam-5213	388	35	.	.	PUNCT
ejpam-5213	389	1	then	then	ADV
ejpam-5213	389	2	s	s	VERB
ejpam-5213	389	3	is	be	AUX
ejpam-5213	389	4	a	a	DET
ejpam-5213	389	5	differentiating	differentiate	VERB
ejpam-5213	389	6	set	set	NOUN
ejpam-5213	389	7	in	in	ADP
ejpam-5213	389	8	g+h	g+h	PROPN
ejpam-5213	389	9	.	.	PUNCT
ejpam-5213	390	1	now	now	ADV
ejpam-5213	390	2	let	let	VERB
ejpam-5213	390	3	p	p	PRON
ejpam-5213	390	4	∈	∈	PROPN
ejpam-5213	390	5	v	v	NOUN
ejpam-5213	390	6	(	(	PUNCT
ejpam-5213	390	7	g+h	g+h	PROPN
ejpam-5213	390	8	)	)	PUNCT
ejpam-5213	390	9	.	.	PUNCT
ejpam-5213	391	1	then	then	ADV
ejpam-5213	391	2	|ng+h	|ng+h	X
ejpam-5213	392	1	[	[	X
ejpam-5213	392	2	p]∩s|	p]∩s|	NOUN
ejpam-5213	392	3	=	=	SYM
ejpam-5213	392	4	|ng[p]∩sg|+	|ng[p]∩sg|+	NOUN
ejpam-5213	392	5	|sh	|sh	ADP
ejpam-5213	392	6	|	|	ADV
ejpam-5213	392	7	if	if	SCONJ
ejpam-5213	392	8	p	p	PROPN
ejpam-5213	392	9	∈	∈	PROPN
ejpam-5213	392	10	v	v	ADP
ejpam-5213	392	11	(	(	PUNCT
ejpam-5213	392	12	g	g	NOUN
ejpam-5213	392	13	)	)	PUNCT
ejpam-5213	392	14	and	and	CCONJ
ejpam-5213	392	15	|ng+h	|ng+h	X
ejpam-5213	393	1	[	[	X
ejpam-5213	393	2	p]∩s|	p]∩s|	NOUN
ejpam-5213	393	3	=	=	SYM
ejpam-5213	393	4	|nh	|nh	X
ejpam-5213	393	5	[	[	PUNCT
ejpam-5213	393	6	p]∩sh	p]∩sh	ADJ
ejpam-5213	393	7	|+	|+	NOUN
ejpam-5213	393	8	|sg|	|sg|	NOUN
ejpam-5213	393	9	if	if	SCONJ
ejpam-5213	393	10	p	p	PROPN
ejpam-5213	393	11	∈	∈	PROPN
ejpam-5213	393	12	v	v	ADP
ejpam-5213	393	13	(	(	PUNCT
ejpam-5213	393	14	h	h	NOUN
ejpam-5213	393	15	)	)	PUNCT
ejpam-5213	393	16	.	.	PUNCT
ejpam-5213	394	1	hence	hence	ADV
ejpam-5213	394	2	,	,	PUNCT
ejpam-5213	394	3	if	if	SCONJ
ejpam-5213	394	4	one	one	NUM
ejpam-5213	394	5	of	of	ADP
ejpam-5213	394	6	(	(	PUNCT
ejpam-5213	394	7	i	i	NOUN
ejpam-5213	394	8	)	)	PUNCT
ejpam-5213	394	9	,	,	PUNCT
ejpam-5213	394	10	(	(	PUNCT
ejpam-5213	394	11	ii	ii	NOUN
ejpam-5213	394	12	)	)	PUNCT
ejpam-5213	394	13	,	,	PUNCT
ejpam-5213	394	14	(	(	PUNCT
ejpam-5213	394	15	iii	iii	NOUN
ejpam-5213	394	16	)	)	PUNCT
ejpam-5213	394	17	,	,	PUNCT
ejpam-5213	394	18	and	and	CCONJ
ejpam-5213	394	19	(	(	PUNCT
ejpam-5213	394	20	iv	iv	X
ejpam-5213	394	21	)	)	PUNCT
ejpam-5213	394	22	holds	hold	NOUN
ejpam-5213	394	23	,	,	PUNCT
ejpam-5213	394	24	then	then	ADV
ejpam-5213	394	25	s	s	VERB
ejpam-5213	394	26	is	be	AUX
ejpam-5213	394	27	an	an	DET
ejpam-5213	394	28	odd	odd	ADJ
ejpam-5213	394	29	dominating	dominating	NOUN
ejpam-5213	394	30	set	set	VERB
ejpam-5213	394	31	in	in	ADP
ejpam-5213	394	32	g+h	g+h	PROPN
ejpam-5213	394	33	.	.	PUNCT
ejpam-5213	395	1	corollary	corollary	ADJ
ejpam-5213	395	2	11	11	NUM
ejpam-5213	395	3	.	.	PUNCT
ejpam-5213	396	1	let	let	VERB
ejpam-5213	396	2	g	g	NOUN
ejpam-5213	396	3	and	and	CCONJ
ejpam-5213	396	4	h	h	PROPN
ejpam-5213	396	5	be	be	VERB
ejpam-5213	396	6	a	a	DET
ejpam-5213	396	7	non	non	ADJ
ejpam-5213	396	8	-	-	ADJ
ejpam-5213	396	9	complete	complete	ADJ
ejpam-5213	396	10	graphs	graph	NOUN
ejpam-5213	396	11	of	of	ADP
ejpam-5213	396	12	order	order	NOUN
ejpam-5213	396	13	m	m	VERB
ejpam-5213	396	14	≥	≥	NOUN
ejpam-5213	396	15	4	4	NUM
ejpam-5213	396	16	and	and	CCONJ
ejpam-5213	396	17	n	n	PRON
ejpam-5213	396	18	≥	≥	NOUN
ejpam-5213	396	19	4	4	NUM
ejpam-5213	396	20	,	,	PUNCT
ejpam-5213	396	21	respectively	respectively	ADV
ejpam-5213	396	22	,	,	PUNCT
ejpam-5213	396	23	such	such	ADJ
ejpam-5213	396	24	that	that	SCONJ
ejpam-5213	396	25	g	g	PROPN
ejpam-5213	396	26	+	+	PROPN
ejpam-5213	396	27	h	h	NOUN
ejpam-5213	396	28	admits	admits	AUX
ejpam-5213	396	29	differentiating	differentiate	VERB
ejpam-5213	396	30	odd	odd	ADJ
ejpam-5213	396	31	dominating	dominating	NOUN
ejpam-5213	396	32	set	set	NOUN
ejpam-5213	396	33	.	.	PUNCT
ejpam-5213	397	1	if	if	SCONJ
ejpam-5213	397	2	both	both	PRON
ejpam-5213	397	3	g	g	PROPN
ejpam-5213	397	4	and	and	CCONJ
ejpam-5213	397	5	h	h	NOUN
ejpam-5213	397	6	do	do	AUX
ejpam-5213	397	7	not	not	PART
ejpam-5213	397	8	have	have	VERB
ejpam-5213	397	9	an	an	DET
ejpam-5213	397	10	even	even	ADV
ejpam-5213	397	11	dominating	dominating	NOUN
ejpam-5213	397	12	set	set	NOUN
ejpam-5213	397	13	and	and	CCONJ
ejpam-5213	397	14	both	both	DET
ejpam-5213	397	15	g	g	PROPN
ejpam-5213	397	16	and	and	CCONJ
ejpam-5213	397	17	h	h	PROPN
ejpam-5213	397	18	admit	admit	VERB
ejpam-5213	397	19	a	a	DET
ejpam-5213	397	20	strictly	strictly	ADV
ejpam-5213	397	21	differentiating	differentiate	VERB
ejpam-5213	397	22	set	set	NOUN
ejpam-5213	397	23	then	then	ADV
ejpam-5213	397	24	γod(g+h	γod(g+h	PUNCT
ejpam-5213	397	25	)	)	PUNCT
ejpam-5213	398	1	=	=	VERB
ejpam-5213	398	2	min{γeod	min{γeod	ADJ
ejpam-5213	398	3	(	(	PUNCT
ejpam-5213	398	4	g	g	NOUN
ejpam-5213	398	5	)	)	PUNCT
ejpam-5213	398	6	+	+	CCONJ
ejpam-5213	398	7	γeosd(h	γeosd(h	NOUN
ejpam-5213	398	8	)	)	PUNCT
ejpam-5213	398	9	,	,	PUNCT
ejpam-5213	398	10	γeod	γeod	NOUN
ejpam-5213	398	11	(	(	PUNCT
ejpam-5213	398	12	h	h	NOUN
ejpam-5213	398	13	)	)	PUNCT
ejpam-5213	398	14	+	+	CCONJ
ejpam-5213	398	15	γeosd(g	γeosd(g	ADP
ejpam-5213	398	16	)	)	PUNCT
ejpam-5213	398	17	}	}	PUNCT
ejpam-5213	398	18	,	,	PUNCT
ejpam-5213	398	19	m.	m.	NOUN
ejpam-5213	398	20	carbero	carbero	PROPN
ejpam-5213	398	21	,	,	PUNCT
ejpam-5213	398	22	g.	g.	PROPN
ejpam-5213	398	23	malacas	malacas	PROPN
ejpam-5213	398	24	,	,	PUNCT
ejpam-5213	398	25	s.	s.	PROPN
ejpam-5213	398	26	canoy	canoy	PROPN
ejpam-5213	398	27	,	,	PUNCT
ejpam-5213	398	28	jr	jr	PROPN
ejpam-5213	398	29	.	.	PROPN
ejpam-5213	398	30	/	/	SYM
ejpam-5213	398	31	eur	eur	PROPN
ejpam-5213	398	32	.	.	PUNCT
ejpam-5213	399	1	j.	j.	PROPN
ejpam-5213	399	2	pure	pure	PROPN
ejpam-5213	399	3	appl	appl	PROPN
ejpam-5213	399	4	.	.	PROPN
ejpam-5213	399	5	math	math	PROPN
ejpam-5213	399	6	,	,	PUNCT
ejpam-5213	399	7	17	17	NUM
ejpam-5213	399	8	(	(	PUNCT
ejpam-5213	399	9	3	3	NUM
ejpam-5213	399	10	)	)	PUNCT
ejpam-5213	399	11	(	(	PUNCT
ejpam-5213	399	12	2024	2024	NUM
ejpam-5213	399	13	)	)	PUNCT
ejpam-5213	399	14	,	,	PUNCT
ejpam-5213	399	15	1585	1585	NUM
ejpam-5213	399	16	-	-	SYM
ejpam-5213	399	17	1601	1601	NUM
ejpam-5213	399	18	1596	1596	NUM
ejpam-5213	399	19	where	where	SCONJ
ejpam-5213	399	20	we	we	PRON
ejpam-5213	399	21	set	set	VERB
ejpam-5213	399	22	γeosd(g	γeosd(g	ADP
ejpam-5213	399	23	′	′	NOUN
ejpam-5213	399	24	)	)	PUNCT
ejpam-5213	399	25	=	=	PUNCT
ejpam-5213	400	1	+	+	PUNCT
ejpam-5213	400	2	∞	∞	NUM
ejpam-5213	400	3	whenever	whenever	SCONJ
ejpam-5213	400	4	sdod(g′	sdod(g′	X
ejpam-5213	400	5	)	)	PUNCT
ejpam-5213	400	6	=	=	SYM
ejpam-5213	400	7	∅	∅	NOUN
ejpam-5213	400	8	,	,	PUNCT
ejpam-5213	400	9	where	where	SCONJ
ejpam-5213	400	10	g′	g′	NOUN
ejpam-5213	400	11	∈	∈	PROPN
ejpam-5213	400	12	{	{	PUNCT
ejpam-5213	400	13	g	g	PROPN
ejpam-5213	400	14	,	,	PUNCT
ejpam-5213	400	15	h	h	NOUN
ejpam-5213	400	16	}	}	PUNCT
ejpam-5213	400	17	.	.	PUNCT
ejpam-5213	400	18	example	example	NOUN
ejpam-5213	401	1	1	1	NUM
ejpam-5213	401	2	.	.	PUNCT
ejpam-5213	402	1	let	let	VERB
ejpam-5213	402	2	g	g	PROPN
ejpam-5213	402	3	=	=	VERB
ejpam-5213	402	4	sp	sp	PROPN
ejpam-5213	402	5	,	,	PUNCT
ejpam-5213	402	6	q	q	NOUN
ejpam-5213	402	7	and	and	CCONJ
ejpam-5213	402	8	h	h	PROPN
ejpam-5213	402	9	=	=	SYM
ejpam-5213	402	10	sr	sr	PROPN
ejpam-5213	402	11	,	,	PUNCT
ejpam-5213	402	12	t	t	PROPN
ejpam-5213	402	13	(	(	PUNCT
ejpam-5213	402	14	double	double	ADJ
ejpam-5213	402	15	stars	star	NOUN
ejpam-5213	402	16	)	)	PUNCT
ejpam-5213	402	17	,	,	PUNCT
ejpam-5213	402	18	where	where	SCONJ
ejpam-5213	402	19	p	p	X
ejpam-5213	402	20	,	,	PUNCT
ejpam-5213	402	21	q	q	ADJ
ejpam-5213	402	22	,	,	PUNCT
ejpam-5213	402	23	r	r	NOUN
ejpam-5213	402	24	,	,	PUNCT
ejpam-5213	402	25	and	and	CCONJ
ejpam-5213	402	26	t	t	PROPN
ejpam-5213	402	27	are	be	AUX
ejpam-5213	402	28	odd	odd	ADJ
ejpam-5213	402	29	numbers	number	NOUN
ejpam-5213	402	30	greater	great	ADJ
ejpam-5213	402	31	than	than	ADP
ejpam-5213	402	32	2	2	NUM
ejpam-5213	402	33	.	.	PUNCT
ejpam-5213	402	34	by	by	ADP
ejpam-5213	402	35	corollary	corollary	ADJ
ejpam-5213	402	36	4	4	NUM
ejpam-5213	402	37	,	,	PUNCT
ejpam-5213	402	38	γod(g	γod(g	PROPN
ejpam-5213	402	39	)	)	PUNCT
ejpam-5213	402	40	=	=	SYM
ejpam-5213	403	1	γeod	γeod	NOUN
ejpam-5213	403	2	(	(	PUNCT
ejpam-5213	403	3	g	g	NOUN
ejpam-5213	403	4	)	)	PUNCT
ejpam-5213	403	5	=	=	PUNCT
ejpam-5213	403	6	γeosd(g	γeosd(g	ADP
ejpam-5213	403	7	)	)	PUNCT
ejpam-5213	403	8	=	=	SYM
ejpam-5213	404	1	p	p	NOUN
ejpam-5213	404	2	+	+	NOUN
ejpam-5213	404	3	q	q	NOUN
ejpam-5213	404	4	and	and	CCONJ
ejpam-5213	404	5	γod(h	γod(h	NOUN
ejpam-5213	404	6	)	)	PUNCT
ejpam-5213	405	1	=	=	SYM
ejpam-5213	405	2	γeod	γeod	NOUN
ejpam-5213	405	3	(	(	PUNCT
ejpam-5213	405	4	h	h	NOUN
ejpam-5213	405	5	)	)	PUNCT
ejpam-5213	405	6	=	=	SYM
ejpam-5213	405	7	γeosd(h	γeosd(h	NOUN
ejpam-5213	405	8	)	)	PUNCT
ejpam-5213	405	9	=	=	SYM
ejpam-5213	405	10	r	r	NOUN
ejpam-5213	406	1	+	+	NOUN
ejpam-5213	406	2	t.	t.	NOUN
ejpam-5213	406	3	by	by	ADP
ejpam-5213	406	4	corollary	corollary	ADJ
ejpam-5213	406	5	11	11	NUM
ejpam-5213	406	6	,	,	PUNCT
ejpam-5213	406	7	γod(g+h	γod(g+h	ADJ
ejpam-5213	406	8	)	)	PUNCT
ejpam-5213	407	1	=	=	PRON
ejpam-5213	407	2	p+	p+	VERB
ejpam-5213	407	3	q	q	NOUN
ejpam-5213	408	1	+	+	CCONJ
ejpam-5213	408	2	r	r	NOUN
ejpam-5213	408	3	+	+	X
ejpam-5213	408	4	t.	t.	NOUN
ejpam-5213	408	5	the	the	DET
ejpam-5213	408	6	corona	corona	NOUN
ejpam-5213	408	7	g	g	PROPN
ejpam-5213	408	8	◦	◦	NOUN
ejpam-5213	408	9	h	h	NOUN
ejpam-5213	408	10	of	of	ADP
ejpam-5213	408	11	two	two	NUM
ejpam-5213	408	12	graphs	graph	NOUN
ejpam-5213	408	13	g	g	NOUN
ejpam-5213	408	14	and	and	CCONJ
ejpam-5213	408	15	h	h	NOUN
ejpam-5213	408	16	is	be	AUX
ejpam-5213	408	17	the	the	DET
ejpam-5213	408	18	graph	graph	NOUN
ejpam-5213	408	19	obtained	obtain	VERB
ejpam-5213	408	20	by	by	ADP
ejpam-5213	408	21	taking	take	VERB
ejpam-5213	408	22	one	one	NUM
ejpam-5213	408	23	copy	copy	NOUN
ejpam-5213	408	24	of	of	ADP
ejpam-5213	408	25	g	g	NOUN
ejpam-5213	408	26	of	of	ADP
ejpam-5213	408	27	order	order	NOUN
ejpam-5213	408	28	n	n	NOUN
ejpam-5213	408	29	and	and	CCONJ
ejpam-5213	408	30	n	n	PRON
ejpam-5213	408	31	copies	copy	NOUN
ejpam-5213	408	32	of	of	ADP
ejpam-5213	408	33	h	h	NOUN
ejpam-5213	408	34	,	,	PUNCT
ejpam-5213	408	35	and	and	CCONJ
ejpam-5213	408	36	then	then	ADV
ejpam-5213	408	37	joining	join	VERB
ejpam-5213	408	38	the	the	DET
ejpam-5213	408	39	ith	ith	PROPN
ejpam-5213	408	40	vertex	vertex	NOUN
ejpam-5213	408	41	of	of	ADP
ejpam-5213	408	42	g	g	NOUN
ejpam-5213	408	43	to	to	ADP
ejpam-5213	408	44	every	every	DET
ejpam-5213	408	45	vertex	vertex	NOUN
ejpam-5213	408	46	in	in	ADP
ejpam-5213	408	47	the	the	DET
ejpam-5213	408	48	ith	ith	PROPN
ejpam-5213	408	49	copy	copy	NOUN
ejpam-5213	408	50	of	of	ADP
ejpam-5213	408	51	h.	h.	PROPN
ejpam-5213	408	52	for	for	ADP
ejpam-5213	408	53	every	every	DET
ejpam-5213	408	54	v	v	NUM
ejpam-5213	408	55	∈	∈	PROPN
ejpam-5213	408	56	v	v	NOUN
ejpam-5213	408	57	(	(	PUNCT
ejpam-5213	408	58	g	g	NOUN
ejpam-5213	408	59	)	)	PUNCT
ejpam-5213	408	60	,	,	PUNCT
ejpam-5213	408	61	we	we	PRON
ejpam-5213	408	62	denote	denote	VERB
ejpam-5213	408	63	by	by	ADP
ejpam-5213	408	64	hv	hv	PROPN
ejpam-5213	409	1	the	the	DET
ejpam-5213	409	2	copy	copy	NOUN
ejpam-5213	409	3	of	of	ADP
ejpam-5213	409	4	h	h	NOUN
ejpam-5213	409	5	whose	whose	DET
ejpam-5213	409	6	vertices	vertex	NOUN
ejpam-5213	409	7	are	be	AUX
ejpam-5213	409	8	attached	attach	VERB
ejpam-5213	409	9	one	one	NUM
ejpam-5213	409	10	by	by	ADP
ejpam-5213	409	11	one	one	NUM
ejpam-5213	409	12	to	to	ADP
ejpam-5213	409	13	the	the	DET
ejpam-5213	409	14	vertex	vertex	NOUN
ejpam-5213	409	15	v.	v.	ADP
ejpam-5213	409	16	subsequently	subsequently	ADV
ejpam-5213	409	17	,	,	PUNCT
ejpam-5213	409	18	we	we	PRON
ejpam-5213	409	19	denote	denote	VERB
ejpam-5213	409	20	by	by	ADP
ejpam-5213	409	21	v+hv	v+hv	PROPN
ejpam-5213	409	22	the	the	DET
ejpam-5213	409	23	subgraph	subgraph	NOUN
ejpam-5213	409	24	of	of	ADP
ejpam-5213	409	25	the	the	DET
ejpam-5213	409	26	corona	corona	NOUN
ejpam-5213	409	27	g	g	PROPN
ejpam-5213	409	28	◦	◦	NOUN
ejpam-5213	409	29	h	h	NOUN
ejpam-5213	409	30	corresponding	correspond	VERB
ejpam-5213	409	31	to	to	ADP
ejpam-5213	409	32	the	the	DET
ejpam-5213	409	33	join	join	PROPN
ejpam-5213	409	34	⟨v⟩+hv	⟨v⟩+hv	PROPN
ejpam-5213	409	35	,	,	PUNCT
ejpam-5213	409	36	where	where	SCONJ
ejpam-5213	409	37	v	v	X
ejpam-5213	409	38	∈	∈	PROPN
ejpam-5213	409	39	v	v	NOUN
ejpam-5213	409	40	(	(	PUNCT
ejpam-5213	409	41	g	g	NOUN
ejpam-5213	409	42	)	)	PUNCT
ejpam-5213	409	43	.	.	PUNCT
ejpam-5213	410	1	theorem	theorem	VERB
ejpam-5213	410	2	11	11	NUM
ejpam-5213	410	3	.	.	PUNCT
ejpam-5213	411	1	[	[	X
ejpam-5213	411	2	12	12	NUM
ejpam-5213	411	3	]	]	PUNCT
ejpam-5213	411	4	let	let	VERB
ejpam-5213	411	5	g	g	PROPN
ejpam-5213	411	6	(	(	PUNCT
ejpam-5213	411	7	not	not	PART
ejpam-5213	411	8	necessarily	necessarily	ADV
ejpam-5213	411	9	point	point	VERB
ejpam-5213	411	10	distinguishing	distinguishing	NOUN
ejpam-5213	411	11	)	)	PUNCT
ejpam-5213	411	12	and	and	CCONJ
ejpam-5213	411	13	let	let	VERB
ejpam-5213	411	14	h	h	NOUN
ejpam-5213	411	15	be	be	AUX
ejpam-5213	411	16	non	non	ADJ
ejpam-5213	411	17	-	-	ADJ
ejpam-5213	411	18	trivial	trivial	ADJ
ejpam-5213	411	19	connected	connected	ADJ
ejpam-5213	411	20	graphs	graph	NOUN
ejpam-5213	411	21	.	.	PUNCT
ejpam-5213	412	1	then	then	ADV
ejpam-5213	412	2	c	c	PROPN
ejpam-5213	412	3	⊆	⊆	NUM
ejpam-5213	412	4	v	v	NOUN
ejpam-5213	412	5	(	(	PUNCT
ejpam-5213	412	6	g	g	PROPN
ejpam-5213	412	7	◦	◦	NOUN
ejpam-5213	412	8	h	h	NOUN
ejpam-5213	412	9	)	)	PUNCT
ejpam-5213	412	10	is	be	AUX
ejpam-5213	412	11	a	a	DET
ejpam-5213	412	12	differentiating	differentiate	VERB
ejpam-5213	412	13	-	-	PUNCT
ejpam-5213	412	14	dominating	dominating	NOUN
ejpam-5213	412	15	set	set	NOUN
ejpam-5213	412	16	in	in	ADP
ejpam-5213	412	17	g	g	PROPN
ejpam-5213	412	18	◦	◦	NOUN
ejpam-5213	412	19	h	h	NOUN
ejpam-5213	413	1	if	if	SCONJ
ejpam-5213	414	1	and	and	CCONJ
ejpam-5213	414	2	only	only	ADV
ejpam-5213	414	3	if	if	SCONJ
ejpam-5213	414	4	for	for	ADP
ejpam-5213	414	5	every	every	PRON
ejpam-5213	414	6	v	v	NUM
ejpam-5213	414	7	∈	∈	NOUN
ejpam-5213	414	8	v	v	NOUN
ejpam-5213	414	9	(	(	PUNCT
ejpam-5213	414	10	g	g	NOUN
ejpam-5213	414	11	)	)	PUNCT
ejpam-5213	414	12	,	,	PUNCT
ejpam-5213	414	13	one	one	NUM
ejpam-5213	414	14	of	of	ADP
ejpam-5213	414	15	the	the	DET
ejpam-5213	414	16	following	follow	VERB
ejpam-5213	414	17	is	be	AUX
ejpam-5213	414	18	true	true	ADJ
ejpam-5213	414	19	:	:	PUNCT
ejpam-5213	414	20	(	(	PUNCT
ejpam-5213	414	21	i	i	NOUN
ejpam-5213	414	22	)	)	PUNCT
ejpam-5213	414	23	v	v	ADP
ejpam-5213	414	24	∈	∈	PROPN
ejpam-5213	414	25	c	c	NOUN
ejpam-5213	414	26	,	,	PUNCT
ejpam-5213	414	27	ng(v	ng(v	PUNCT
ejpam-5213	414	28	)	)	PUNCT
ejpam-5213	414	29	∩	∩	NOUN
ejpam-5213	414	30	c	c	PROPN
ejpam-5213	414	31	̸=	̸=	PROPN
ejpam-5213	414	32	∅	∅	NOUN
ejpam-5213	414	33	,	,	PUNCT
ejpam-5213	414	34	and	and	CCONJ
ejpam-5213	414	35	c	c	PROPN
ejpam-5213	414	36	∩	∩	ADJ
ejpam-5213	414	37	v	v	X
ejpam-5213	414	38	(	(	PUNCT
ejpam-5213	414	39	hv	hv	X
ejpam-5213	414	40	)	)	PUNCT
ejpam-5213	414	41	is	be	AUX
ejpam-5213	414	42	a	a	DET
ejpam-5213	414	43	differentiating	differentiate	VERB
ejpam-5213	414	44	set	set	NOUN
ejpam-5213	414	45	in	in	ADP
ejpam-5213	414	46	hv	hv	PROPN
ejpam-5213	414	47	;	;	PUNCT
ejpam-5213	414	48	(	(	PUNCT
ejpam-5213	414	49	ii	ii	NOUN
ejpam-5213	414	50	)	)	PUNCT
ejpam-5213	414	51	v	v	ADP
ejpam-5213	414	52	∈	∈	PROPN
ejpam-5213	414	53	c	c	NOUN
ejpam-5213	414	54	,	,	PUNCT
ejpam-5213	414	55	ng(v	ng(v	PUNCT
ejpam-5213	414	56	)	)	PUNCT
ejpam-5213	414	57	∩	∩	NOUN
ejpam-5213	414	58	c	c	NOUN
ejpam-5213	414	59	=	=	SYM
ejpam-5213	414	60	∅	∅	NOUN
ejpam-5213	414	61	,	,	PUNCT
ejpam-5213	414	62	and	and	CCONJ
ejpam-5213	414	63	c	c	PROPN
ejpam-5213	414	64	∩	∩	ADJ
ejpam-5213	414	65	v	v	X
ejpam-5213	414	66	(	(	PUNCT
ejpam-5213	414	67	hv	hv	X
ejpam-5213	414	68	)	)	PUNCT
ejpam-5213	414	69	is	be	AUX
ejpam-5213	414	70	a	a	DET
ejpam-5213	414	71	strictly	strictly	ADV
ejpam-5213	414	72	differentiating	differentiate	VERB
ejpam-5213	414	73	set	set	NOUN
ejpam-5213	414	74	in	in	ADP
ejpam-5213	414	75	hv	hv	PROPN
ejpam-5213	414	76	;	;	PUNCT
ejpam-5213	414	77	(	(	PUNCT
ejpam-5213	414	78	iii	iii	X
ejpam-5213	414	79	)	)	PUNCT
ejpam-5213	414	80	v	v	NOUN
ejpam-5213	414	81	/∈	/∈	PUNCT
ejpam-5213	415	1	c	c	X
ejpam-5213	415	2	,	,	PUNCT
ejpam-5213	415	3	ng(v	ng(v	PUNCT
ejpam-5213	415	4	)	)	PUNCT
ejpam-5213	415	5	∩	∩	NOUN
ejpam-5213	415	6	c	c	PROPN
ejpam-5213	415	7	̸=	̸=	PROPN
ejpam-5213	415	8	∅	∅	NOUN
ejpam-5213	415	9	,	,	PUNCT
ejpam-5213	415	10	and	and	CCONJ
ejpam-5213	415	11	c1	c1	PROPN
ejpam-5213	415	12	=	=	PROPN
ejpam-5213	415	13	v	v	PROPN
ejpam-5213	415	14	(	(	PUNCT
ejpam-5213	415	15	hv	hv	NOUN
ejpam-5213	415	16	)	)	PUNCT
ejpam-5213	415	17	∩	∩	NOUN
ejpam-5213	415	18	c	c	PROPN
ejpam-5213	415	19	is	be	AUX
ejpam-5213	415	20	a	a	DET
ejpam-5213	415	21	differentiating	differentiate	VERB
ejpam-5213	415	22	-	-	PUNCT
ejpam-5213	415	23	dominating	dominating	NOUN
ejpam-5213	415	24	set	set	NOUN
ejpam-5213	415	25	in	in	ADP
ejpam-5213	415	26	hv	hv	PROPN
ejpam-5213	415	27	;	;	PUNCT
ejpam-5213	415	28	or	or	CCONJ
ejpam-5213	415	29	(	(	PUNCT
ejpam-5213	415	30	iv	iv	X
ejpam-5213	415	31	)	)	PUNCT
ejpam-5213	415	32	v	v	NOUN
ejpam-5213	415	33	/∈	/∈	PUNCT
ejpam-5213	416	1	c	c	X
ejpam-5213	416	2	,	,	PUNCT
ejpam-5213	416	3	ng(v)∩c	ng(v)∩c	NOUN
ejpam-5213	416	4	=	=	NOUN
ejpam-5213	416	5	∅	∅	NOUN
ejpam-5213	416	6	,	,	PUNCT
ejpam-5213	416	7	and	and	CCONJ
ejpam-5213	416	8	c1	c1	PROPN
ejpam-5213	416	9	=	=	PROPN
ejpam-5213	416	10	v	v	PROPN
ejpam-5213	416	11	(	(	PUNCT
ejpam-5213	416	12	hv)∩c	hv)∩c	ADJ
ejpam-5213	416	13	is	be	AUX
ejpam-5213	416	14	a	a	DET
ejpam-5213	416	15	strictly	strictly	ADV
ejpam-5213	416	16	differentiating	differentiate	VERB
ejpam-5213	416	17	-	-	PUNCT
ejpam-5213	416	18	dominating	dominating	NOUN
ejpam-5213	416	19	set	set	NOUN
ejpam-5213	416	20	in	in	ADP
ejpam-5213	416	21	hv	hv	PROPN
ejpam-5213	416	22	.	.	PUNCT
ejpam-5213	417	1	theorem	theorem	PROPN
ejpam-5213	417	2	12	12	NUM
ejpam-5213	417	3	.	.	PUNCT
ejpam-5213	418	1	let	let	VERB
ejpam-5213	418	2	g	g	PRON
ejpam-5213	418	3	be	be	AUX
ejpam-5213	418	4	a	a	DET
ejpam-5213	418	5	non	non	ADJ
ejpam-5213	418	6	-	-	ADJ
ejpam-5213	418	7	trivial	trivial	ADJ
ejpam-5213	418	8	connected	connected	ADJ
ejpam-5213	418	9	graph	graph	NOUN
ejpam-5213	418	10	and	and	CCONJ
ejpam-5213	418	11	let	let	VERB
ejpam-5213	418	12	h	h	NOUN
ejpam-5213	418	13	be	be	AUX
ejpam-5213	418	14	any	any	DET
ejpam-5213	418	15	non	non	ADJ
ejpam-5213	418	16	-	-	ADJ
ejpam-5213	418	17	trivial	trivial	ADJ
ejpam-5213	418	18	graph	graph	NOUN
ejpam-5213	418	19	such	such	ADJ
ejpam-5213	418	20	that	that	SCONJ
ejpam-5213	418	21	g	g	PROPN
ejpam-5213	418	22	◦	◦	NOUN
ejpam-5213	418	23	h	h	NOUN
ejpam-5213	418	24	admits	admit	VERB
ejpam-5213	418	25	a	a	DET
ejpam-5213	418	26	differentiating	differentiate	VERB
ejpam-5213	418	27	odd	odd	ADJ
ejpam-5213	418	28	dominating	dominating	NOUN
ejpam-5213	418	29	set	set	NOUN
ejpam-5213	418	30	.	.	PUNCT
ejpam-5213	419	1	then	then	ADV
ejpam-5213	419	2	s	s	VERB
ejpam-5213	419	3	⊆	⊆	NUM
ejpam-5213	419	4	v	v	NOUN
ejpam-5213	419	5	(	(	PUNCT
ejpam-5213	419	6	g	g	PROPN
ejpam-5213	419	7	◦	◦	NOUN
ejpam-5213	419	8	h	h	NOUN
ejpam-5213	419	9	)	)	PUNCT
ejpam-5213	419	10	is	be	AUX
ejpam-5213	419	11	a	a	DET
ejpam-5213	419	12	differentiating	differentiate	VERB
ejpam-5213	419	13	odd	odd	ADJ
ejpam-5213	419	14	dominating	dominating	NOUN
ejpam-5213	419	15	set	set	VERB
ejpam-5213	419	16	in	in	ADP
ejpam-5213	419	17	g	g	PROPN
ejpam-5213	419	18	◦	◦	NOUN
ejpam-5213	419	19	h	h	NOUN
ejpam-5213	419	20	if	if	SCONJ
ejpam-5213	420	1	and	and	CCONJ
ejpam-5213	420	2	only	only	ADV
ejpam-5213	420	3	if	if	SCONJ
ejpam-5213	420	4	s	s	VERB
ejpam-5213	420	5	=	=	PUNCT
ejpam-5213	420	6	sg	sg	X
ejpam-5213	420	7	∪	∪	ADP
ejpam-5213	420	8	[	[	X
ejpam-5213	420	9	∪v∈v	∪v∈v	X
ejpam-5213	420	10	(	(	PUNCT
ejpam-5213	420	11	g)sv	g)sv	PROPN
ejpam-5213	420	12	]	]	X
ejpam-5213	420	13	,	,	PUNCT
ejpam-5213	420	14	where	where	SCONJ
ejpam-5213	420	15	sg	sg	ADP
ejpam-5213	420	16	⊆	⊆	NUM
ejpam-5213	420	17	v	v	NOUN
ejpam-5213	420	18	(	(	PUNCT
ejpam-5213	420	19	g	g	NOUN
ejpam-5213	420	20	)	)	PUNCT
ejpam-5213	420	21	and	and	CCONJ
ejpam-5213	420	22	sv	sv	X
ejpam-5213	420	23	⊆	⊆	NUM
ejpam-5213	420	24	v	v	X
ejpam-5213	420	25	(	(	PUNCT
ejpam-5213	420	26	hv	hv	PROPN
ejpam-5213	420	27	)	)	PUNCT
ejpam-5213	420	28	for	for	ADP
ejpam-5213	420	29	each	each	DET
ejpam-5213	420	30	v	v	NUM
ejpam-5213	420	31	∈	∈	PROPN
ejpam-5213	420	32	v	v	NOUN
ejpam-5213	420	33	(	(	PUNCT
ejpam-5213	420	34	g	g	NOUN
ejpam-5213	420	35	)	)	PUNCT
ejpam-5213	420	36	,	,	PUNCT
ejpam-5213	420	37	and	and	CCONJ
ejpam-5213	420	38	satisfies	satisfy	VERB
ejpam-5213	420	39	the	the	DET
ejpam-5213	420	40	following	follow	VERB
ejpam-5213	420	41	conditions	condition	NOUN
ejpam-5213	420	42	:	:	PUNCT
ejpam-5213	420	43	(	(	PUNCT
ejpam-5213	420	44	i	i	NOUN
ejpam-5213	420	45	)	)	PUNCT
ejpam-5213	420	46	for	for	ADP
ejpam-5213	420	47	each	each	DET
ejpam-5213	420	48	v	v	NUM
ejpam-5213	420	49	∈	∈	PROPN
ejpam-5213	420	50	sg	sg	NOUN
ejpam-5213	420	51	with	with	ADP
ejpam-5213	420	52	|ng(v	|ng(v	NOUN
ejpam-5213	420	53	)	)	PUNCT
ejpam-5213	420	54	∩	∩	NOUN
ejpam-5213	420	55	sg|	sg|	VERB
ejpam-5213	420	56	̸=	̸=	PROPN
ejpam-5213	420	57	0	0	NUM
ejpam-5213	420	58	,	,	PUNCT
ejpam-5213	420	59	sv	sv	PROPN
ejpam-5213	420	60	is	be	AUX
ejpam-5213	420	61	differentiating	differentiate	VERB
ejpam-5213	420	62	even	even	ADV
ejpam-5213	420	63	dominating	dominate	VERB
ejpam-5213	420	64	in	in	ADP
ejpam-5213	420	65	hv	hv	PROPN
ejpam-5213	420	66	,	,	PUNCT
ejpam-5213	420	67	and	and	CCONJ
ejpam-5213	420	68	either	either	CCONJ
ejpam-5213	420	69	(	(	PUNCT
ejpam-5213	420	70	a	a	X
ejpam-5213	420	71	)	)	PUNCT
ejpam-5213	420	72	|ng(v	|ng(v	NOUN
ejpam-5213	420	73	)	)	PUNCT
ejpam-5213	420	74	∩	∩	NOUN
ejpam-5213	420	75	sg|	sg|	NOUN
ejpam-5213	420	76	and	and	CCONJ
ejpam-5213	420	77	|sv|	|sv|	PROPN
ejpam-5213	420	78	are	be	AUX
ejpam-5213	420	79	odd	odd	ADJ
ejpam-5213	420	80	or	or	CCONJ
ejpam-5213	420	81	(	(	PUNCT
ejpam-5213	420	82	b	b	NOUN
ejpam-5213	420	83	)	)	PUNCT
ejpam-5213	420	84	|ng(v	|ng(v	NOUN
ejpam-5213	420	85	)	)	PUNCT
ejpam-5213	420	86	∩	∩	NOUN
ejpam-5213	420	87	sg|	sg|	NOUN
ejpam-5213	420	88	and	and	CCONJ
ejpam-5213	420	89	|sv|	|sv|	PROPN
ejpam-5213	420	90	are	be	AUX
ejpam-5213	420	91	even	even	ADV
ejpam-5213	420	92	.	.	PUNCT
ejpam-5213	421	1	(	(	PUNCT
ejpam-5213	421	2	ii	ii	NOUN
ejpam-5213	421	3	)	)	PUNCT
ejpam-5213	421	4	for	for	ADP
ejpam-5213	421	5	each	each	DET
ejpam-5213	421	6	w	w	PROPN
ejpam-5213	421	7	∈	∈	PROPN
ejpam-5213	421	8	v	v	NOUN
ejpam-5213	421	9	(	(	PUNCT
ejpam-5213	421	10	g)\sg	g)\sg	PROPN
ejpam-5213	421	11	with	with	ADP
ejpam-5213	421	12	|ng(w)∩sg|	|ng(w)∩sg|	NOUN
ejpam-5213	421	13	=	=	NOUN
ejpam-5213	421	14	̸	̸	NUM
ejpam-5213	421	15	0	0	NUM
ejpam-5213	421	16	,	,	PUNCT
ejpam-5213	421	17	sw	sw	PROPN
ejpam-5213	421	18	is	be	AUX
ejpam-5213	421	19	differentiating	differentiate	VERB
ejpam-5213	421	20	odd	odd	ADJ
ejpam-5213	421	21	dominating	dominating	NOUN
ejpam-5213	421	22	in	in	ADP
ejpam-5213	421	23	hw	hw	NOUN
ejpam-5213	421	24	,	,	PUNCT
ejpam-5213	421	25	and	and	CCONJ
ejpam-5213	421	26	either	either	CCONJ
ejpam-5213	421	27	(	(	PUNCT
ejpam-5213	421	28	c	c	X
ejpam-5213	421	29	)	)	PUNCT
ejpam-5213	421	30	|ng(w	|ng(w	NOUN
ejpam-5213	421	31	)	)	PUNCT
ejpam-5213	421	32	∩	∩	NOUN
ejpam-5213	421	33	sg|	sg|	PROPN
ejpam-5213	421	34	is	be	AUX
ejpam-5213	421	35	even	even	ADV
ejpam-5213	421	36	and	and	CCONJ
ejpam-5213	421	37	|sw|	|sw|	PROPN
ejpam-5213	421	38	is	be	AUX
ejpam-5213	421	39	odd	odd	ADJ
ejpam-5213	421	40	or	or	CCONJ
ejpam-5213	421	41	(	(	PUNCT
ejpam-5213	421	42	d	d	NOUN
ejpam-5213	421	43	)	)	PUNCT
ejpam-5213	421	44	|ng(w	|ng(w	NOUN
ejpam-5213	421	45	)	)	PUNCT
ejpam-5213	421	46	∩	∩	NOUN
ejpam-5213	421	47	sg|	sg|	PROPN
ejpam-5213	421	48	is	be	AUX
ejpam-5213	421	49	odd	odd	ADJ
ejpam-5213	421	50	and	and	CCONJ
ejpam-5213	421	51	|sw|	|sw|	PROPN
ejpam-5213	421	52	is	be	AUX
ejpam-5213	421	53	even	even	ADV
ejpam-5213	421	54	.	.	PUNCT
ejpam-5213	422	1	(	(	PUNCT
ejpam-5213	422	2	iii	iii	X
ejpam-5213	422	3	)	)	PUNCT
ejpam-5213	422	4	for	for	ADP
ejpam-5213	422	5	each	each	PRON
ejpam-5213	422	6	v	v	NUM
ejpam-5213	422	7	∈	∈	PROPN
ejpam-5213	422	8	v	v	NOUN
ejpam-5213	422	9	(	(	PUNCT
ejpam-5213	422	10	g	g	NOUN
ejpam-5213	422	11	)	)	PUNCT
ejpam-5213	422	12	with	with	ADP
ejpam-5213	422	13	|ng(v	|ng(v	NOUN
ejpam-5213	422	14	)	)	PUNCT
ejpam-5213	422	15	∩	∩	NOUN
ejpam-5213	422	16	sg|	sg|	NOUN
ejpam-5213	422	17	=	=	SYM
ejpam-5213	422	18	0	0	NUM
ejpam-5213	422	19	,	,	PUNCT
ejpam-5213	422	20	it	it	PRON
ejpam-5213	422	21	holds	hold	VERB
ejpam-5213	422	22	that	that	SCONJ
ejpam-5213	422	23	(	(	PUNCT
ejpam-5213	422	24	e	e	NOUN
ejpam-5213	422	25	)	)	PUNCT
ejpam-5213	422	26	sv	sv	PROPN
ejpam-5213	422	27	is	be	AUX
ejpam-5213	422	28	a	a	DET
ejpam-5213	422	29	strictly	strictly	ADV
ejpam-5213	422	30	differentiating	differentiate	VERB
ejpam-5213	422	31	even	even	ADV
ejpam-5213	422	32	dominating	dominate	VERB
ejpam-5213	422	33	set	set	VERB
ejpam-5213	422	34	in	in	ADP
ejpam-5213	422	35	hv	hv	PROPN
ejpam-5213	422	36	and	and	CCONJ
ejpam-5213	422	37	|sv|	|sv|	PROPN
ejpam-5213	422	38	is	be	AUX
ejpam-5213	422	39	even	even	ADV
ejpam-5213	422	40	if	if	SCONJ
ejpam-5213	422	41	v	v	NUM
ejpam-5213	422	42	∈	∈	PROPN
ejpam-5213	422	43	sg	sg	NOUN
ejpam-5213	422	44	and	and	CCONJ
ejpam-5213	422	45	m.	m.	NOUN
ejpam-5213	422	46	carbero	carbero	PROPN
ejpam-5213	422	47	,	,	PUNCT
ejpam-5213	422	48	g.	g.	PROPN
ejpam-5213	422	49	malacas	malacas	PROPN
ejpam-5213	422	50	,	,	PUNCT
ejpam-5213	422	51	s.	s.	PROPN
ejpam-5213	422	52	canoy	canoy	PROPN
ejpam-5213	422	53	,	,	PUNCT
ejpam-5213	422	54	jr	jr	PROPN
ejpam-5213	422	55	.	.	PROPN
ejpam-5213	422	56	/	/	SYM
ejpam-5213	422	57	eur	eur	PROPN
ejpam-5213	422	58	.	.	PUNCT
ejpam-5213	423	1	j.	j.	PROPN
ejpam-5213	423	2	pure	pure	PROPN
ejpam-5213	423	3	appl	appl	PROPN
ejpam-5213	423	4	.	.	PROPN
ejpam-5213	423	5	math	math	PROPN
ejpam-5213	423	6	,	,	PUNCT
ejpam-5213	423	7	17	17	NUM
ejpam-5213	423	8	(	(	PUNCT
ejpam-5213	423	9	3	3	NUM
ejpam-5213	423	10	)	)	PUNCT
ejpam-5213	423	11	(	(	PUNCT
ejpam-5213	423	12	2024	2024	NUM
ejpam-5213	423	13	)	)	PUNCT
ejpam-5213	423	14	,	,	PUNCT
ejpam-5213	423	15	1585	1585	NUM
ejpam-5213	423	16	-	-	SYM
ejpam-5213	423	17	1601	1601	NUM
ejpam-5213	423	18	1597	1597	NUM
ejpam-5213	423	19	(	(	PUNCT
ejpam-5213	423	20	f	f	X
ejpam-5213	423	21	)	)	PUNCT
ejpam-5213	423	22	sv	sv	PROPN
ejpam-5213	423	23	is	be	AUX
ejpam-5213	423	24	strictly	strictly	ADV
ejpam-5213	423	25	differentiating	differentiate	VERB
ejpam-5213	423	26	odd	odd	ADJ
ejpam-5213	423	27	dominating	dominating	NOUN
ejpam-5213	423	28	and	and	CCONJ
ejpam-5213	423	29	|sv|	|sv|	PROPN
ejpam-5213	423	30	is	be	AUX
ejpam-5213	423	31	odd	odd	ADJ
ejpam-5213	423	32	if	if	SCONJ
ejpam-5213	423	33	v	v	ADP
ejpam-5213	423	34	∈	∈	PROPN
ejpam-5213	423	35	v	v	NOUN
ejpam-5213	423	36	(	(	PUNCT
ejpam-5213	423	37	g	g	NOUN
ejpam-5213	423	38	)	)	PUNCT
ejpam-5213	423	39	\sg	\sg	PROPN
ejpam-5213	423	40	.	.	PUNCT
ejpam-5213	424	1	proof	proof	NOUN
ejpam-5213	424	2	.	.	PUNCT
ejpam-5213	425	1	suppose	suppose	VERB
ejpam-5213	425	2	s	s	PRON
ejpam-5213	425	3	is	be	AUX
ejpam-5213	425	4	a	a	DET
ejpam-5213	425	5	differentiating	differentiate	VERB
ejpam-5213	425	6	odd	odd	ADJ
ejpam-5213	425	7	dominating	dominating	NOUN
ejpam-5213	425	8	set	set	VERB
ejpam-5213	425	9	in	in	ADP
ejpam-5213	425	10	g	g	PROPN
ejpam-5213	425	11	◦	◦	PROPN
ejpam-5213	425	12	h.	h.	PROPN
ejpam-5213	425	13	let	let	VERB
ejpam-5213	425	14	sg	sg	VERB
ejpam-5213	425	15	=	=	VERB
ejpam-5213	425	16	s	s	PART
ejpam-5213	425	17	∩v	∩v	NOUN
ejpam-5213	425	18	(	(	PUNCT
ejpam-5213	425	19	g	g	NOUN
ejpam-5213	425	20	)	)	PUNCT
ejpam-5213	425	21	and	and	CCONJ
ejpam-5213	425	22	let	let	VERB
ejpam-5213	425	23	sv	sv	VERB
ejpam-5213	425	24	=	=	VERB
ejpam-5213	425	25	s	s	PART
ejpam-5213	425	26	∩v	∩v	NOUN
ejpam-5213	425	27	(	(	PUNCT
ejpam-5213	425	28	hv	hv	X
ejpam-5213	425	29	)	)	PUNCT
ejpam-5213	425	30	for	for	ADP
ejpam-5213	425	31	each	each	DET
ejpam-5213	425	32	v	v	NUM
ejpam-5213	425	33	∈	∈	PROPN
ejpam-5213	425	34	v	v	NOUN
ejpam-5213	425	35	(	(	PUNCT
ejpam-5213	425	36	g	g	NOUN
ejpam-5213	425	37	)	)	PUNCT
ejpam-5213	425	38	.	.	PUNCT
ejpam-5213	426	1	then	then	ADV
ejpam-5213	426	2	s	s	VERB
ejpam-5213	426	3	=	=	SYM
ejpam-5213	426	4	sg∪	sg∪	PUNCT
ejpam-5213	427	1	[	[	X
ejpam-5213	427	2	∪v∈v	∪v∈v	X
ejpam-5213	427	3	(	(	PUNCT
ejpam-5213	427	4	g)sv	g)sv	PROPN
ejpam-5213	427	5	]	]	PUNCT
ejpam-5213	427	6	.	.	PUNCT
ejpam-5213	428	1	let	let	VERB
ejpam-5213	428	2	v	v	X
ejpam-5213	428	3	∈	∈	NOUN
ejpam-5213	428	4	sg	sg	ADP
ejpam-5213	428	5	such	such	ADJ
ejpam-5213	428	6	that	that	DET
ejpam-5213	428	7	|ng(v	|ng(v	NOUN
ejpam-5213	428	8	)	)	PUNCT
ejpam-5213	428	9	∩	∩	NOUN
ejpam-5213	428	10	sg|	sg|	NOUN
ejpam-5213	428	11	=	=	NOUN
ejpam-5213	428	12	̸	̸	NUM
ejpam-5213	428	13	0	0	NUM
ejpam-5213	428	14	.	.	PUNCT
ejpam-5213	429	1	by	by	ADP
ejpam-5213	429	2	theorem	theorem	NOUN
ejpam-5213	429	3	11	11	NUM
ejpam-5213	429	4	,	,	PUNCT
ejpam-5213	429	5	sv	sv	PROPN
ejpam-5213	429	6	is	be	AUX
ejpam-5213	429	7	a	a	DET
ejpam-5213	429	8	differentiating	differentiate	VERB
ejpam-5213	429	9	set	set	NOUN
ejpam-5213	429	10	in	in	ADP
ejpam-5213	429	11	hv	hv	PROPN
ejpam-5213	429	12	.	.	PROPN
ejpam-5213	430	1	suppose	suppose	VERB
ejpam-5213	430	2	first	first	ADV
ejpam-5213	430	3	that	that	SCONJ
ejpam-5213	430	4	|ng(v	|ng(v	VERB
ejpam-5213	430	5	)	)	PUNCT
ejpam-5213	430	6	∩	∩	NOUN
ejpam-5213	430	7	sg|	sg|	PROPN
ejpam-5213	430	8	is	be	AUX
ejpam-5213	430	9	odd	odd	ADJ
ejpam-5213	430	10	.	.	PUNCT
ejpam-5213	431	1	since	since	SCONJ
ejpam-5213	431	2	s	s	PROPN
ejpam-5213	431	3	is	be	AUX
ejpam-5213	431	4	odd	odd	ADJ
ejpam-5213	431	5	dominating	dominate	VERB
ejpam-5213	431	6	in	in	ADP
ejpam-5213	431	7	g	g	PROPN
ejpam-5213	431	8	◦	◦	NOUN
ejpam-5213	431	9	h	h	NOUN
ejpam-5213	431	10	,	,	PUNCT
ejpam-5213	431	11	|ng	|ng	NOUN
ejpam-5213	431	12	◦	◦	NOUN
ejpam-5213	431	13	h	h	NOUN
ejpam-5213	432	1	[	[	X
ejpam-5213	432	2	p	p	X
ejpam-5213	432	3	]	]	X
ejpam-5213	432	4	∩	∩	ADJ
ejpam-5213	432	5	s|	s|	NOUN
ejpam-5213	432	6	=	=	PUNCT
ejpam-5213	432	7	|nhv	|nhv	NOUN
ejpam-5213	432	8	[	[	X
ejpam-5213	432	9	p	p	X
ejpam-5213	432	10	]	]	X
ejpam-5213	432	11	∩	∩	NOUN
ejpam-5213	432	12	sv|	sv|	NOUN
ejpam-5213	432	13	+	+	CCONJ
ejpam-5213	432	14	|{v}|	|{v}|	PUNCT
ejpam-5213	432	15	is	be	AUX
ejpam-5213	432	16	odd	odd	ADJ
ejpam-5213	432	17	for	for	ADP
ejpam-5213	432	18	every	every	DET
ejpam-5213	432	19	p	p	PROPN
ejpam-5213	432	20	∈	∈	PROPN
ejpam-5213	432	21	v	v	ADP
ejpam-5213	432	22	(	(	PUNCT
ejpam-5213	432	23	hv	hv	PROPN
ejpam-5213	432	24	)	)	PUNCT
ejpam-5213	432	25	.	.	PUNCT
ejpam-5213	433	1	this	this	PRON
ejpam-5213	433	2	implies	imply	VERB
ejpam-5213	433	3	that	that	SCONJ
ejpam-5213	433	4	|nhv	|nhv	NOUN
ejpam-5213	433	5	[	[	X
ejpam-5213	433	6	p	p	X
ejpam-5213	433	7	]	]	X
ejpam-5213	433	8	∩	∩	NOUN
ejpam-5213	433	9	sv|	sv|	NOUN
ejpam-5213	433	10	is	be	AUX
ejpam-5213	433	11	even	even	ADV
ejpam-5213	433	12	for	for	ADP
ejpam-5213	433	13	every	every	DET
ejpam-5213	433	14	p	p	PROPN
ejpam-5213	433	15	∈	∈	PROPN
ejpam-5213	433	16	v	v	ADP
ejpam-5213	433	17	(	(	PUNCT
ejpam-5213	433	18	hv	hv	PROPN
ejpam-5213	433	19	)	)	PUNCT
ejpam-5213	433	20	.	.	PUNCT
ejpam-5213	434	1	thus	thus	ADV
ejpam-5213	434	2	,	,	PUNCT
ejpam-5213	434	3	sv	sv	INTJ
ejpam-5213	434	4	is	be	AUX
ejpam-5213	434	5	even	even	ADV
ejpam-5213	434	6	dominating	dominate	VERB
ejpam-5213	434	7	in	in	ADP
ejpam-5213	434	8	hv	hv	PROPN
ejpam-5213	434	9	.	.	PUNCT
ejpam-5213	435	1	moreover	moreover	ADV
ejpam-5213	435	2	,	,	PUNCT
ejpam-5213	435	3	because	because	SCONJ
ejpam-5213	435	4	|ng	|ng	VERB
ejpam-5213	435	5	◦	◦	NOUN
ejpam-5213	435	6	h	h	NOUN
ejpam-5213	436	1	[	[	X
ejpam-5213	436	2	v]∩s|	v]∩s|	ADV
ejpam-5213	436	3	=	=	SYM
ejpam-5213	436	4	|ng(v)∩sg|+	|ng(v)∩sg|+	NOUN
ejpam-5213	436	5	(	(	PUNCT
ejpam-5213	436	6	|{v}|+	|{v}|+	PROPN
ejpam-5213	436	7	|sv|	|sv|	PROPN
ejpam-5213	436	8	)	)	PUNCT
ejpam-5213	436	9	is	be	AUX
ejpam-5213	436	10	also	also	ADV
ejpam-5213	436	11	odd	odd	ADJ
ejpam-5213	436	12	,	,	PUNCT
ejpam-5213	436	13	|sv|	|sv|	PROPN
ejpam-5213	436	14	is	be	AUX
ejpam-5213	436	15	odd	odd	ADJ
ejpam-5213	436	16	.	.	PUNCT
ejpam-5213	437	1	this	this	PRON
ejpam-5213	437	2	shows	show	VERB
ejpam-5213	437	3	that	that	SCONJ
ejpam-5213	437	4	(	(	PUNCT
ejpam-5213	437	5	i)(a	i)(a	NOUN
ejpam-5213	437	6	)	)	PUNCT
ejpam-5213	437	7	holds	hold	VERB
ejpam-5213	437	8	.	.	PUNCT
ejpam-5213	438	1	similarly	similarly	ADV
ejpam-5213	438	2	,	,	PUNCT
ejpam-5213	438	3	(	(	PUNCT
ejpam-5213	438	4	i)(b	i)(b	NUM
ejpam-5213	438	5	)	)	PUNCT
ejpam-5213	438	6	also	also	ADV
ejpam-5213	438	7	holds	hold	VERB
ejpam-5213	438	8	.	.	PUNCT
ejpam-5213	439	1	therefore	therefore	ADV
ejpam-5213	439	2	,	,	PUNCT
ejpam-5213	439	3	(	(	PUNCT
ejpam-5213	439	4	i	i	NOUN
ejpam-5213	439	5	)	)	PUNCT
ejpam-5213	439	6	holds	hold	VERB
ejpam-5213	439	7	.	.	PUNCT
ejpam-5213	440	1	next	next	ADV
ejpam-5213	440	2	,	,	PUNCT
ejpam-5213	440	3	let	let	VERB
ejpam-5213	440	4	w	w	NOUN
ejpam-5213	440	5	∈	∈	PROPN
ejpam-5213	440	6	v	v	ADP
ejpam-5213	440	7	(	(	PUNCT
ejpam-5213	440	8	g	g	NOUN
ejpam-5213	440	9	)	)	PUNCT
ejpam-5213	440	10	\	\	NOUN
ejpam-5213	441	1	sg	sg	ADP
ejpam-5213	441	2	with	with	ADP
ejpam-5213	441	3	|ng(w	|ng(w	PRON
ejpam-5213	441	4	)	)	PUNCT
ejpam-5213	441	5	∩	∩	NOUN
ejpam-5213	441	6	sg|	sg|	NOUN
ejpam-5213	441	7	=	=	NOUN
ejpam-5213	441	8	̸	̸	NUM
ejpam-5213	441	9	0	0	NUM
ejpam-5213	441	10	.	.	PUNCT
ejpam-5213	441	11	again	again	ADV
ejpam-5213	441	12	,	,	PUNCT
ejpam-5213	441	13	by	by	ADP
ejpam-5213	441	14	theorem	theorem	NOUN
ejpam-5213	441	15	11	11	NUM
ejpam-5213	441	16	,	,	PUNCT
ejpam-5213	441	17	sw	sw	PROPN
ejpam-5213	441	18	is	be	AUX
ejpam-5213	441	19	a	a	DET
ejpam-5213	441	20	differentiating	differentiate	VERB
ejpam-5213	441	21	set	set	NOUN
ejpam-5213	441	22	in	in	ADP
ejpam-5213	441	23	hw	hw	PRON
ejpam-5213	441	24	.	.	PUNCT
ejpam-5213	442	1	suppose	suppose	VERB
ejpam-5213	442	2	|ng(w	|ng(w	NOUN
ejpam-5213	442	3	)	)	PUNCT
ejpam-5213	442	4	∩	∩	NOUN
ejpam-5213	442	5	sg|	sg|	PROPN
ejpam-5213	442	6	is	be	AUX
ejpam-5213	442	7	even	even	ADV
ejpam-5213	442	8	.	.	PUNCT
ejpam-5213	443	1	since	since	SCONJ
ejpam-5213	443	2	s	s	PROPN
ejpam-5213	443	3	is	be	AUX
ejpam-5213	443	4	odd	odd	ADJ
ejpam-5213	443	5	dominating	dominate	VERB
ejpam-5213	443	6	in	in	ADP
ejpam-5213	443	7	g	g	PROPN
ejpam-5213	443	8	◦	◦	NOUN
ejpam-5213	443	9	h	h	NOUN
ejpam-5213	443	10	,	,	PUNCT
ejpam-5213	443	11	|ng	|ng	NOUN
ejpam-5213	443	12	◦	◦	NOUN
ejpam-5213	443	13	h	h	NOUN
ejpam-5213	444	1	[	[	X
ejpam-5213	444	2	q	q	X
ejpam-5213	444	3	]	]	X
ejpam-5213	444	4	∩	∩	NOUN
ejpam-5213	444	5	s|	s|	NOUN
ejpam-5213	444	6	=	=	PUNCT
ejpam-5213	444	7	|nhw	|nhw	PROPN
ejpam-5213	444	8	[	[	X
ejpam-5213	444	9	q	q	X
ejpam-5213	444	10	]	]	X
ejpam-5213	444	11	∩	∩	ADJ
ejpam-5213	444	12	sw|	sw|	NOUN
ejpam-5213	444	13	is	be	AUX
ejpam-5213	444	14	odd	odd	ADJ
ejpam-5213	444	15	for	for	ADP
ejpam-5213	444	16	every	every	DET
ejpam-5213	444	17	q	q	PROPN
ejpam-5213	444	18	∈	∈	PROPN
ejpam-5213	444	19	v	v	NOUN
ejpam-5213	444	20	(	(	PUNCT
ejpam-5213	444	21	hw	hw	NOUN
ejpam-5213	444	22	)	)	PUNCT
ejpam-5213	444	23	.	.	PUNCT
ejpam-5213	445	1	it	it	PRON
ejpam-5213	445	2	follows	follow	VERB
ejpam-5213	445	3	that	that	SCONJ
ejpam-5213	445	4	sw	sw	PROPN
ejpam-5213	445	5	is	be	AUX
ejpam-5213	445	6	differentiating	differentiate	VERB
ejpam-5213	445	7	odd	odd	ADJ
ejpam-5213	445	8	dominating	dominating	NOUN
ejpam-5213	445	9	in	in	ADP
ejpam-5213	445	10	hv	hv	PROPN
ejpam-5213	445	11	.	.	PUNCT
ejpam-5213	446	1	since	since	SCONJ
ejpam-5213	446	2	|ng	|ng	NUM
ejpam-5213	446	3	◦	◦	NOUN
ejpam-5213	446	4	h	h	NOUN
ejpam-5213	446	5	[	[	X
ejpam-5213	446	6	w]∩s|	w]∩s|	NOUN
ejpam-5213	446	7	=	=	PRON
ejpam-5213	446	8	|ng(w)∩sg|+	|ng(w)∩sg|+	PROPN
ejpam-5213	446	9	|sw|	|sw|	PROPN
ejpam-5213	446	10	is	be	AUX
ejpam-5213	446	11	odd	odd	ADJ
ejpam-5213	446	12	and	and	CCONJ
ejpam-5213	446	13	|ng(w)∩sg|	|ng(w)∩sg|	PROPN
ejpam-5213	446	14	is	be	AUX
ejpam-5213	446	15	even	even	ADV
ejpam-5213	446	16	,	,	PUNCT
ejpam-5213	446	17	|sw|	|sw|	PROPN
ejpam-5213	446	18	is	be	AUX
ejpam-5213	446	19	odd	odd	ADJ
ejpam-5213	446	20	.	.	PUNCT
ejpam-5213	447	1	this	this	PRON
ejpam-5213	447	2	shows	show	VERB
ejpam-5213	447	3	that	that	SCONJ
ejpam-5213	447	4	(	(	PUNCT
ejpam-5213	447	5	ii)(c	ii)(c	PROPN
ejpam-5213	447	6	)	)	PUNCT
ejpam-5213	447	7	holds	hold	VERB
ejpam-5213	447	8	.	.	PUNCT
ejpam-5213	448	1	similar	similar	ADJ
ejpam-5213	448	2	arguments	argument	NOUN
ejpam-5213	448	3	will	will	AUX
ejpam-5213	448	4	show	show	VERB
ejpam-5213	448	5	that	that	SCONJ
ejpam-5213	448	6	(	(	PUNCT
ejpam-5213	448	7	ii)(d	ii)(d	PROPN
ejpam-5213	448	8	)	)	PUNCT
ejpam-5213	448	9	holds	hold	VERB
ejpam-5213	448	10	.	.	PUNCT
ejpam-5213	449	1	thus	thus	ADV
ejpam-5213	449	2	,	,	PUNCT
ejpam-5213	449	3	(	(	PUNCT
ejpam-5213	449	4	ii	ii	NOUN
ejpam-5213	449	5	)	)	PUNCT
ejpam-5213	449	6	holds	hold	VERB
ejpam-5213	449	7	.	.	PUNCT
ejpam-5213	450	1	finally	finally	ADV
ejpam-5213	450	2	,	,	PUNCT
ejpam-5213	450	3	let	let	VERB
ejpam-5213	450	4	v	v	NUM
ejpam-5213	450	5	∈	∈	PROPN
ejpam-5213	450	6	v	v	NOUN
ejpam-5213	450	7	(	(	PUNCT
ejpam-5213	450	8	g	g	NOUN
ejpam-5213	450	9	)	)	PUNCT
ejpam-5213	450	10	such	such	ADJ
ejpam-5213	450	11	that	that	SCONJ
ejpam-5213	450	12	|ng(v	|ng(v	NOUN
ejpam-5213	450	13	)	)	PUNCT
ejpam-5213	450	14	∩	∩	NOUN
ejpam-5213	450	15	sg|	sg|	NOUN
ejpam-5213	450	16	=	=	SYM
ejpam-5213	450	17	0	0	X
ejpam-5213	450	18	.	.	PUNCT
ejpam-5213	450	19	suppose	suppose	VERB
ejpam-5213	450	20	first	first	ADV
ejpam-5213	450	21	that	that	SCONJ
ejpam-5213	450	22	v	v	X
ejpam-5213	450	23	∈	∈	PROPN
ejpam-5213	450	24	sg	sg	NOUN
ejpam-5213	450	25	.	.	PUNCT
ejpam-5213	451	1	then	then	ADV
ejpam-5213	451	2	,	,	PUNCT
ejpam-5213	451	3	by	by	ADP
ejpam-5213	451	4	theorem	theorem	NOUN
ejpam-5213	451	5	8(i	8(i	NUM
ejpam-5213	451	6	)	)	PUNCT
ejpam-5213	451	7	,	,	PUNCT
ejpam-5213	451	8	|sv|	|sv|	PROPN
ejpam-5213	451	9	is	be	AUX
ejpam-5213	451	10	even	even	ADV
ejpam-5213	451	11	and	and	CCONJ
ejpam-5213	451	12	sv	sv	PROPN
ejpam-5213	451	13	is	be	AUX
ejpam-5213	451	14	a	a	DET
ejpam-5213	451	15	strictly	strictly	ADV
ejpam-5213	451	16	differentiating	differentiate	VERB
ejpam-5213	451	17	even	even	ADV
ejpam-5213	451	18	dominating	dominate	VERB
ejpam-5213	451	19	set	set	VERB
ejpam-5213	451	20	in	in	ADP
ejpam-5213	451	21	hv	hv	PROPN
ejpam-5213	451	22	.	.	PUNCT
ejpam-5213	452	1	if	if	SCONJ
ejpam-5213	452	2	v	v	NUM
ejpam-5213	452	3	∈	∈	PROPN
ejpam-5213	452	4	v	v	NOUN
ejpam-5213	452	5	(	(	PUNCT
ejpam-5213	452	6	g	g	NOUN
ejpam-5213	452	7	)	)	PUNCT
ejpam-5213	452	8	\	\	PROPN
ejpam-5213	452	9	sg	sg	PROPN
ejpam-5213	452	10	,	,	PUNCT
ejpam-5213	452	11	then	then	ADV
ejpam-5213	452	12	sv	sv	PROPN
ejpam-5213	452	13	is	be	AUX
ejpam-5213	452	14	odd	odd	ADJ
ejpam-5213	452	15	and	and	CCONJ
ejpam-5213	452	16	sv	sv	PROPN
ejpam-5213	452	17	is	be	AUX
ejpam-5213	452	18	strictly	strictly	ADV
ejpam-5213	452	19	differentiating	differentiate	VERB
ejpam-5213	452	20	odd	odd	ADJ
ejpam-5213	452	21	dominating	dominating	NOUN
ejpam-5213	452	22	in	in	ADP
ejpam-5213	452	23	hv	hv	PROPN
ejpam-5213	452	24	by	by	ADP
ejpam-5213	452	25	theorem	theorem	PROPN
ejpam-5213	452	26	8(ii	8(ii	NUM
ejpam-5213	452	27	)	)	PUNCT
ejpam-5213	452	28	.	.	PUNCT
ejpam-5213	453	1	thus	thus	ADV
ejpam-5213	453	2	,	,	PUNCT
ejpam-5213	453	3	(	(	PUNCT
ejpam-5213	453	4	iii	iii	NOUN
ejpam-5213	453	5	)	)	PUNCT
ejpam-5213	453	6	holds	hold	VERB
ejpam-5213	453	7	.	.	PUNCT
ejpam-5213	454	1	for	for	ADP
ejpam-5213	454	2	the	the	DET
ejpam-5213	454	3	converse	converse	NOUN
ejpam-5213	454	4	,	,	PUNCT
ejpam-5213	454	5	suppose	suppose	VERB
ejpam-5213	454	6	that	that	SCONJ
ejpam-5213	454	7	s	s	VERB
ejpam-5213	454	8	satisfies	satisfie	NOUN
ejpam-5213	454	9	(	(	PUNCT
ejpam-5213	454	10	i	i	NOUN
ejpam-5213	454	11	)	)	PUNCT
ejpam-5213	454	12	,	,	PUNCT
ejpam-5213	454	13	(	(	PUNCT
ejpam-5213	454	14	ii	ii	NOUN
ejpam-5213	454	15	)	)	PUNCT
ejpam-5213	454	16	,	,	PUNCT
ejpam-5213	454	17	and	and	CCONJ
ejpam-5213	454	18	(	(	PUNCT
ejpam-5213	454	19	iii	iii	NOUN
ejpam-5213	454	20	)	)	PUNCT
ejpam-5213	454	21	.	.	PUNCT
ejpam-5213	455	1	by	by	ADP
ejpam-5213	455	2	theorem	theorem	NOUN
ejpam-5213	455	3	11	11	NUM
ejpam-5213	455	4	,	,	PUNCT
ejpam-5213	455	5	s	s	VERB
ejpam-5213	455	6	is	be	AUX
ejpam-5213	455	7	a	a	DET
ejpam-5213	455	8	differentiating	differentiate	VERB
ejpam-5213	455	9	-	-	PUNCT
ejpam-5213	455	10	dominating	dominating	NOUN
ejpam-5213	455	11	set	set	NOUN
ejpam-5213	455	12	in	in	ADP
ejpam-5213	455	13	g	g	PROPN
ejpam-5213	455	14	◦	◦	PROPN
ejpam-5213	455	15	h.	h.	PROPN
ejpam-5213	455	16	let	let	VERB
ejpam-5213	455	17	x	x	SYM
ejpam-5213	455	18	∈	∈	PROPN
ejpam-5213	455	19	v	v	X
ejpam-5213	455	20	(	(	PUNCT
ejpam-5213	455	21	g	g	PROPN
ejpam-5213	455	22	◦	◦	NOUN
ejpam-5213	455	23	h	h	NOUN
ejpam-5213	455	24	)	)	PUNCT
ejpam-5213	455	25	\	\	PROPN
ejpam-5213	455	26	s	s	PART
ejpam-5213	455	27	and	and	CCONJ
ejpam-5213	455	28	v	v	ADP
ejpam-5213	455	29	∈	∈	NOUN
ejpam-5213	455	30	v	v	NOUN
ejpam-5213	455	31	(	(	PUNCT
ejpam-5213	455	32	g	g	NOUN
ejpam-5213	455	33	)	)	PUNCT
ejpam-5213	455	34	be	be	AUX
ejpam-5213	455	35	such	such	ADJ
ejpam-5213	455	36	that	that	SCONJ
ejpam-5213	455	37	x	x	SYM
ejpam-5213	455	38	∈	∈	NOUN
ejpam-5213	455	39	v	v	NOUN
ejpam-5213	455	40	(	(	PUNCT
ejpam-5213	455	41	v	v	PROPN
ejpam-5213	455	42	+	+	PROPN
ejpam-5213	455	43	hv	hv	NOUN
ejpam-5213	455	44	)	)	PUNCT
ejpam-5213	455	45	.	.	PUNCT
ejpam-5213	456	1	suppose	suppose	VERB
ejpam-5213	456	2	|ng(x	|ng(x	NOUN
ejpam-5213	456	3	)	)	PUNCT
ejpam-5213	456	4	∩	∩	NOUN
ejpam-5213	456	5	sg|	sg|	NOUN
ejpam-5213	456	6	=	=	NOUN
ejpam-5213	456	7	̸	̸	NUM
ejpam-5213	456	8	0	0	NOUN
ejpam-5213	456	9	.	.	PUNCT
ejpam-5213	457	1	if	if	SCONJ
ejpam-5213	457	2	v	v	NUM
ejpam-5213	457	3	∈	∈	PROPN
ejpam-5213	457	4	sg	sg	PROPN
ejpam-5213	457	5	,	,	PUNCT
ejpam-5213	457	6	then	then	ADV
ejpam-5213	457	7	|ng	|ng	NOUN
ejpam-5213	457	8	◦	◦	NOUN
ejpam-5213	457	9	h	h	NOUN
ejpam-5213	457	10	[	[	X
ejpam-5213	457	11	x	x	X
ejpam-5213	457	12	]	]	X
ejpam-5213	457	13	∩	∩	NOUN
ejpam-5213	457	14	s|	s|	NOUN
ejpam-5213	457	15	=	=	SYM
ejpam-5213	457	16	|ng(x	|ng(x	NUM
ejpam-5213	457	17	)	)	PUNCT
ejpam-5213	457	18	∩	∩	NOUN
ejpam-5213	457	19	sg|+	sg|+	PROPN
ejpam-5213	457	20	(	(	PUNCT
ejpam-5213	457	21	|sv|+	|sv|+	NOUN
ejpam-5213	457	22	1	1	NUM
ejpam-5213	457	23	)	)	PUNCT
ejpam-5213	457	24	if	if	SCONJ
ejpam-5213	457	25	x	x	X
ejpam-5213	457	26	=	=	SYM
ejpam-5213	457	27	v	v	NOUN
ejpam-5213	457	28	;	;	PUNCT
ejpam-5213	457	29	otherwise	otherwise	ADV
ejpam-5213	457	30	,	,	PUNCT
ejpam-5213	457	31	|ng	|ng	NOUN
ejpam-5213	457	32	◦	◦	NOUN
ejpam-5213	457	33	h	h	NOUN
ejpam-5213	457	34	[	[	X
ejpam-5213	457	35	x	x	X
ejpam-5213	457	36	]	]	X
ejpam-5213	457	37	∩	∩	ADJ
ejpam-5213	457	38	s|	s|	NOUN
ejpam-5213	457	39	=	=	PUNCT
ejpam-5213	457	40	|nhv	|nhv	NOUN
ejpam-5213	457	41	[	[	X
ejpam-5213	457	42	x	x	X
ejpam-5213	457	43	]	]	X
ejpam-5213	457	44	∩	∩	ADJ
ejpam-5213	457	45	sv|	sv|	NOUN
ejpam-5213	457	46	+	+	CCONJ
ejpam-5213	457	47	1	1	X
ejpam-5213	457	48	.	.	PUNCT
ejpam-5213	457	49	by	by	ADP
ejpam-5213	457	50	(	(	PUNCT
ejpam-5213	457	51	a	a	X
ejpam-5213	457	52	)	)	PUNCT
ejpam-5213	457	53	and	and	CCONJ
ejpam-5213	457	54	(	(	PUNCT
ejpam-5213	457	55	b	b	NOUN
ejpam-5213	457	56	)	)	PUNCT
ejpam-5213	457	57	,	,	PUNCT
ejpam-5213	457	58	|ng	|ng	VERB
ejpam-5213	457	59	◦	◦	NOUN
ejpam-5213	457	60	h	h	NOUN
ejpam-5213	457	61	[	[	X
ejpam-5213	457	62	x	x	X
ejpam-5213	457	63	]	]	X
ejpam-5213	457	64	∩	∩	NOUN
ejpam-5213	457	65	s|	s|	NOUN
ejpam-5213	457	66	is	be	AUX
ejpam-5213	457	67	odd	odd	ADJ
ejpam-5213	457	68	.	.	PUNCT
ejpam-5213	458	1	suppose	suppose	VERB
ejpam-5213	458	2	v	v	ADP
ejpam-5213	458	3	∈	∈	PROPN
ejpam-5213	458	4	v	v	NOUN
ejpam-5213	458	5	(	(	PUNCT
ejpam-5213	458	6	g	g	NOUN
ejpam-5213	458	7	)	)	PUNCT
ejpam-5213	458	8	\	\	PROPN
ejpam-5213	458	9	sg	sg	PROPN
ejpam-5213	458	10	.	.	PUNCT
ejpam-5213	459	1	then	then	ADV
ejpam-5213	459	2	|ng	|ng	VERB
ejpam-5213	459	3	◦	◦	NOUN
ejpam-5213	459	4	h	h	NOUN
ejpam-5213	459	5	[	[	X
ejpam-5213	459	6	x	x	X
ejpam-5213	459	7	]	]	X
ejpam-5213	459	8	∩	∩	NOUN
ejpam-5213	459	9	s|	s|	NOUN
ejpam-5213	459	10	=	=	PUNCT
ejpam-5213	459	11	|sv|	|sv|	VERB
ejpam-5213	459	12	if	if	SCONJ
ejpam-5213	459	13	x	x	PROPN
ejpam-5213	459	14	=	=	SYM
ejpam-5213	459	15	v	v	NOUN
ejpam-5213	459	16	;	;	PUNCT
ejpam-5213	459	17	otherwise	otherwise	ADV
ejpam-5213	459	18	,	,	PUNCT
ejpam-5213	459	19	|ng	|ng	NOUN
ejpam-5213	459	20	◦	◦	NOUN
ejpam-5213	459	21	h	h	NOUN
ejpam-5213	459	22	[	[	X
ejpam-5213	459	23	x	x	X
ejpam-5213	459	24	]	]	X
ejpam-5213	459	25	∩	∩	ADJ
ejpam-5213	459	26	s|	s|	NOUN
ejpam-5213	459	27	=	=	PUNCT
ejpam-5213	459	28	|nhv	|nhv	NOUN
ejpam-5213	459	29	[	[	X
ejpam-5213	459	30	x	x	X
ejpam-5213	459	31	]	]	X
ejpam-5213	459	32	∩	∩	ADJ
ejpam-5213	459	33	sv|	sv|	PROPN
ejpam-5213	459	34	.	.	PUNCT
ejpam-5213	460	1	by	by	ADP
ejpam-5213	460	2	(	(	PUNCT
ejpam-5213	460	3	c	c	NOUN
ejpam-5213	460	4	)	)	PUNCT
ejpam-5213	460	5	and	and	CCONJ
ejpam-5213	460	6	(	(	PUNCT
ejpam-5213	460	7	d	d	NOUN
ejpam-5213	460	8	)	)	PUNCT
ejpam-5213	460	9	,	,	PUNCT
ejpam-5213	460	10	|ng	|ng	VERB
ejpam-5213	460	11	◦	◦	NOUN
ejpam-5213	460	12	h	h	NOUN
ejpam-5213	461	1	[	[	X
ejpam-5213	461	2	x	x	X
ejpam-5213	461	3	]	]	X
ejpam-5213	461	4	∩	∩	NOUN
ejpam-5213	461	5	s|	s|	NOUN
ejpam-5213	461	6	is	be	AUX
ejpam-5213	461	7	odd	odd	ADJ
ejpam-5213	461	8	.	.	PUNCT
ejpam-5213	462	1	lastly	lastly	ADV
ejpam-5213	462	2	,	,	PUNCT
ejpam-5213	462	3	suppose	suppose	VERB
ejpam-5213	462	4	that	that	SCONJ
ejpam-5213	462	5	|ng(x	|ng(x	PUNCT
ejpam-5213	462	6	)	)	PUNCT
ejpam-5213	462	7	∩	∩	NOUN
ejpam-5213	462	8	sg|	sg|	NOUN
ejpam-5213	462	9	=	=	SYM
ejpam-5213	462	10	0	0	X
ejpam-5213	462	11	.	.	PUNCT
ejpam-5213	463	1	then	then	ADV
ejpam-5213	463	2	parts	part	NOUN
ejpam-5213	463	3	of	of	ADP
ejpam-5213	463	4	(	(	PUNCT
ejpam-5213	463	5	e	e	NOUN
ejpam-5213	463	6	)	)	PUNCT
ejpam-5213	463	7	and	and	CCONJ
ejpam-5213	463	8	(	(	PUNCT
ejpam-5213	463	9	f	f	X
ejpam-5213	463	10	)	)	PUNCT
ejpam-5213	463	11	would	would	AUX
ejpam-5213	463	12	imply	imply	VERB
ejpam-5213	463	13	that	that	PRON
ejpam-5213	463	14	|ng	|ng	VERB
ejpam-5213	463	15	◦	◦	NOUN
ejpam-5213	463	16	h	h	NOUN
ejpam-5213	463	17	[	[	X
ejpam-5213	463	18	x	x	X
ejpam-5213	463	19	]	]	X
ejpam-5213	463	20	∩	∩	NOUN
ejpam-5213	463	21	s|	s|	NOUN
ejpam-5213	463	22	is	be	AUX
ejpam-5213	463	23	odd	odd	ADJ
ejpam-5213	463	24	.	.	PUNCT
ejpam-5213	464	1	therefore	therefore	ADV
ejpam-5213	464	2	,	,	PUNCT
ejpam-5213	464	3	s	s	VERB
ejpam-5213	464	4	is	be	AUX
ejpam-5213	464	5	a	a	DET
ejpam-5213	464	6	differentiating	differentiate	VERB
ejpam-5213	464	7	odd	odd	ADJ
ejpam-5213	464	8	dominating	dominating	NOUN
ejpam-5213	464	9	set	set	VERB
ejpam-5213	464	10	in	in	ADP
ejpam-5213	464	11	g	g	PROPN
ejpam-5213	464	12	◦	◦	NOUN
ejpam-5213	464	13	h.	h.	NOUN
ejpam-5213	464	14	corollary	corollary	ADJ
ejpam-5213	464	15	12	12	NUM
ejpam-5213	464	16	.	.	PUNCT
ejpam-5213	465	1	let	let	VERB
ejpam-5213	465	2	g	g	PRON
ejpam-5213	465	3	be	be	AUX
ejpam-5213	465	4	a	a	DET
ejpam-5213	465	5	non	non	ADJ
ejpam-5213	465	6	-	-	ADJ
ejpam-5213	465	7	trivial	trivial	ADJ
ejpam-5213	465	8	connected	connected	ADJ
ejpam-5213	465	9	graph	graph	NOUN
ejpam-5213	465	10	of	of	ADP
ejpam-5213	465	11	order	order	NOUN
ejpam-5213	465	12	n	n	NOUN
ejpam-5213	466	1	and	and	CCONJ
ejpam-5213	466	2	let	let	VERB
ejpam-5213	466	3	h	h	NOUN
ejpam-5213	466	4	be	be	AUX
ejpam-5213	466	5	a	a	DET
ejpam-5213	466	6	graph	graph	NOUN
ejpam-5213	466	7	that	that	PRON
ejpam-5213	466	8	admits	admit	VERB
ejpam-5213	466	9	a	a	DET
ejpam-5213	466	10	strictly	strictly	ADV
ejpam-5213	466	11	differentiating	differentiate	VERB
ejpam-5213	466	12	odd	odd	ADJ
ejpam-5213	466	13	dominating	dominating	NOUN
ejpam-5213	466	14	set	set	VERB
ejpam-5213	466	15	with	with	ADP
ejpam-5213	466	16	odd	odd	ADJ
ejpam-5213	466	17	cardinality	cardinality	NOUN
ejpam-5213	466	18	.	.	PUNCT
ejpam-5213	467	1	then	then	ADV
ejpam-5213	467	2	γod(g	γod(g	NUM
ejpam-5213	467	3	◦	◦	NOUN
ejpam-5213	467	4	h	h	NOUN
ejpam-5213	467	5	)	)	PUNCT
ejpam-5213	467	6	≤	≤	NOUN
ejpam-5213	467	7	|v	|v	X
ejpam-5213	467	8	(	(	PUNCT
ejpam-5213	467	9	g)|γoosd(h	g)|γoosd(h	PROPN
ejpam-5213	467	10	)	)	PUNCT
ejpam-5213	467	11	and	and	CCONJ
ejpam-5213	467	12	equality	equality	NOUN
ejpam-5213	467	13	holds	hold	VERB
ejpam-5213	467	14	if	if	SCONJ
ejpam-5213	467	15	h	h	NOUN
ejpam-5213	467	16	=	=	SYM
ejpam-5213	467	17	kp	kp	NOUN
ejpam-5213	467	18	,	,	PUNCT
ejpam-5213	467	19	where	where	SCONJ
ejpam-5213	467	20	p	p	NOUN
ejpam-5213	467	21	is	be	AUX
ejpam-5213	467	22	odd	odd	ADJ
ejpam-5213	467	23	and	and	CCONJ
ejpam-5213	467	24	at	at	ADV
ejpam-5213	467	25	least	least	ADJ
ejpam-5213	467	26	3	3	NUM
ejpam-5213	467	27	.	.	PUNCT
ejpam-5213	467	28	proof	proof	NOUN
ejpam-5213	467	29	.	.	PUNCT
ejpam-5213	468	1	let	let	VERB
ejpam-5213	468	2	sv	sv	PROPN
ejpam-5213	468	3	⊆	⊆	NUM
ejpam-5213	468	4	v	v	X
ejpam-5213	468	5	(	(	PUNCT
ejpam-5213	468	6	hv	hv	NOUN
ejpam-5213	468	7	)	)	PUNCT
ejpam-5213	468	8	be	be	VERB
ejpam-5213	468	9	a	a	DET
ejpam-5213	468	10	strictly	strictly	ADV
ejpam-5213	468	11	differentiating	differentiate	VERB
ejpam-5213	468	12	odd	odd	ADJ
ejpam-5213	468	13	dominating	dominating	NOUN
ejpam-5213	468	14	set	set	VERB
ejpam-5213	468	15	with	with	ADP
ejpam-5213	468	16	odd	odd	ADJ
ejpam-5213	468	17	cardinality	cardinality	NOUN
ejpam-5213	468	18	such	such	ADJ
ejpam-5213	468	19	that	that	SCONJ
ejpam-5213	468	20	|sv|	|sv|	PROPN
ejpam-5213	468	21	=	=	PUNCT
ejpam-5213	468	22	γoosd(h	γoosd(h	NUM
ejpam-5213	468	23	v	v	NOUN
ejpam-5213	468	24	)	)	PUNCT
ejpam-5213	468	25	for	for	ADP
ejpam-5213	468	26	each	each	DET
ejpam-5213	468	27	v	v	NUM
ejpam-5213	468	28	∈	∈	PROPN
ejpam-5213	468	29	v	v	NOUN
ejpam-5213	468	30	(	(	PUNCT
ejpam-5213	468	31	g	g	NOUN
ejpam-5213	468	32	)	)	PUNCT
ejpam-5213	468	33	.	.	PUNCT
ejpam-5213	469	1	set	set	VERB
ejpam-5213	469	2	s	s	PART
ejpam-5213	469	3	=	=	X
ejpam-5213	469	4	∪v∈v	∪v∈v	X
ejpam-5213	469	5	(	(	PUNCT
ejpam-5213	469	6	g)sv	g)sv	PROPN
ejpam-5213	469	7	.	.	PROPN
ejpam-5213	469	8	by	by	ADP
ejpam-5213	469	9	theorem	theorem	NOUN
ejpam-5213	469	10	12	12	NUM
ejpam-5213	469	11	,	,	PUNCT
ejpam-5213	469	12	s	s	PART
ejpam-5213	469	13	is	be	AUX
ejpam-5213	469	14	a	a	DET
ejpam-5213	469	15	differentiating	differentiate	VERB
ejpam-5213	469	16	odd	odd	ADJ
ejpam-5213	469	17	dominating	dominating	NOUN
ejpam-5213	469	18	set	set	VERB
ejpam-5213	469	19	in	in	ADP
ejpam-5213	469	20	g	g	PROPN
ejpam-5213	469	21	◦	◦	PROPN
ejpam-5213	469	22	h.	h.	PROPN
ejpam-5213	470	1	thus	thus	ADV
ejpam-5213	470	2	,	,	PUNCT
ejpam-5213	470	3	γod(g	γod(g	PROPN
ejpam-5213	470	4	◦	◦	NOUN
ejpam-5213	470	5	h	h	NOUN
ejpam-5213	470	6	)	)	PUNCT
ejpam-5213	470	7	≤	≤	NUM
ejpam-5213	470	8	|s|	|s|	PROPN
ejpam-5213	470	9	=	=	SYM
ejpam-5213	470	10	nγoosd(h	nγoosd(h	PROPN
ejpam-5213	470	11	)	)	PUNCT
ejpam-5213	470	12	.	.	PUNCT
ejpam-5213	471	1	if	if	SCONJ
ejpam-5213	471	2	h	h	PRON
ejpam-5213	471	3	=	=	SYM
ejpam-5213	471	4	kp	kp	PROPN
ejpam-5213	471	5	,	,	PUNCT
ejpam-5213	471	6	then	then	ADV
ejpam-5213	471	7	γosd(h	γosd(h	PROPN
ejpam-5213	471	8	)	)	PUNCT
ejpam-5213	471	9	=	=	VERB
ejpam-5213	472	1	p.	p.	NOUN
ejpam-5213	472	2	desired	desire	VERB
ejpam-5213	472	3	equality	equality	NOUN
ejpam-5213	472	4	follows	follow	VERB
ejpam-5213	472	5	now	now	ADV
ejpam-5213	472	6	from	from	ADP
ejpam-5213	472	7	theorem	theorem	ADJ
ejpam-5213	472	8	2(ii	2(ii	NUM
ejpam-5213	472	9	)	)	PUNCT
ejpam-5213	472	10	.	.	PUNCT
ejpam-5213	473	1	corollary	corollary	ADJ
ejpam-5213	473	2	13	13	NUM
ejpam-5213	473	3	.	.	PUNCT
ejpam-5213	474	1	let	let	VERB
ejpam-5213	474	2	g	g	PRON
ejpam-5213	474	3	be	be	AUX
ejpam-5213	474	4	a	a	DET
ejpam-5213	474	5	non	non	ADJ
ejpam-5213	474	6	-	-	ADJ
ejpam-5213	474	7	trivial	trivial	ADJ
ejpam-5213	474	8	connected	connected	ADJ
ejpam-5213	474	9	graph	graph	NOUN
ejpam-5213	474	10	of	of	ADP
ejpam-5213	474	11	order	order	NOUN
ejpam-5213	474	12	n	n	NOUN
ejpam-5213	475	1	and	and	CCONJ
ejpam-5213	475	2	let	let	VERB
ejpam-5213	475	3	h	h	NOUN
ejpam-5213	475	4	be	be	AUX
ejpam-5213	475	5	a	a	DET
ejpam-5213	475	6	graph	graph	NOUN
ejpam-5213	475	7	that	that	PRON
ejpam-5213	475	8	admits	admit	VERB
ejpam-5213	475	9	a	a	DET
ejpam-5213	475	10	differentiating	differentiate	VERB
ejpam-5213	475	11	even	even	ADV
ejpam-5213	475	12	dominating	dominate	VERB
ejpam-5213	475	13	set	set	VERB
ejpam-5213	475	14	with	with	ADP
ejpam-5213	475	15	even	even	ADV
ejpam-5213	475	16	cardinality	cardinality	NOUN
ejpam-5213	475	17	.	.	PUNCT
ejpam-5213	476	1	if	if	SCONJ
ejpam-5213	476	2	g	g	PROPN
ejpam-5213	476	3	is	be	AUX
ejpam-5213	476	4	r	r	NOUN
ejpam-5213	476	5	-	-	ADJ
ejpam-5213	476	6	regular	regular	ADJ
ejpam-5213	476	7	,	,	PUNCT
ejpam-5213	476	8	where	where	SCONJ
ejpam-5213	476	9	r	r	NOUN
ejpam-5213	476	10	is	be	AUX
ejpam-5213	476	11	a	a	DET
ejpam-5213	476	12	positive	positive	ADJ
ejpam-5213	476	13	even	even	ADV
ejpam-5213	476	14	integer	integer	NOUN
ejpam-5213	476	15	,	,	PUNCT
ejpam-5213	476	16	then	then	ADV
ejpam-5213	476	17	γod(g	γod(g	PROPN
ejpam-5213	476	18	◦	◦	NOUN
ejpam-5213	476	19	h	h	NOUN
ejpam-5213	476	20	)	)	PUNCT
ejpam-5213	476	21	≤	≤	NOUN
ejpam-5213	476	22	n+	n+	PUNCT
ejpam-5213	476	23	nγeed	nγeed	NOUN
ejpam-5213	476	24	(	(	PUNCT
ejpam-5213	476	25	h	h	NOUN
ejpam-5213	476	26	)	)	PUNCT
ejpam-5213	476	27	.	.	PUNCT
ejpam-5213	477	1	m.	m.	NOUN
ejpam-5213	477	2	carbero	carbero	PROPN
ejpam-5213	477	3	,	,	PUNCT
ejpam-5213	477	4	g.	g.	PROPN
ejpam-5213	477	5	malacas	malacas	PROPN
ejpam-5213	477	6	,	,	PUNCT
ejpam-5213	477	7	s.	s.	PROPN
ejpam-5213	477	8	canoy	canoy	PROPN
ejpam-5213	477	9	,	,	PUNCT
ejpam-5213	477	10	jr	jr	PROPN
ejpam-5213	477	11	.	.	PROPN
ejpam-5213	477	12	/	/	SYM
ejpam-5213	477	13	eur	eur	PROPN
ejpam-5213	477	14	.	.	PUNCT
ejpam-5213	478	1	j.	j.	PROPN
ejpam-5213	478	2	pure	pure	PROPN
ejpam-5213	478	3	appl	appl	PROPN
ejpam-5213	478	4	.	.	PROPN
ejpam-5213	478	5	math	math	PROPN
ejpam-5213	478	6	,	,	PUNCT
ejpam-5213	478	7	17	17	NUM
ejpam-5213	478	8	(	(	PUNCT
ejpam-5213	478	9	3	3	NUM
ejpam-5213	478	10	)	)	PUNCT
ejpam-5213	478	11	(	(	PUNCT
ejpam-5213	478	12	2024	2024	NUM
ejpam-5213	478	13	)	)	PUNCT
ejpam-5213	478	14	,	,	PUNCT
ejpam-5213	478	15	1585	1585	NUM
ejpam-5213	478	16	-	-	SYM
ejpam-5213	478	17	1601	1601	NUM
ejpam-5213	478	18	1598	1598	NUM
ejpam-5213	478	19	the	the	DET
ejpam-5213	478	20	lexicographic	lexicographic	ADJ
ejpam-5213	478	21	product	product	NOUN
ejpam-5213	478	22	g[h	g[h	PROPN
ejpam-5213	478	23	]	]	PUNCT
ejpam-5213	478	24	also	also	ADV
ejpam-5213	478	25	has	have	VERB
ejpam-5213	478	26	v	v	NUM
ejpam-5213	478	27	(	(	PUNCT
ejpam-5213	478	28	g[h	g[h	NOUN
ejpam-5213	478	29	]	]	PUNCT
ejpam-5213	478	30	)	)	PUNCT
ejpam-5213	479	1	=	=	SYM
ejpam-5213	479	2	v	v	X
ejpam-5213	479	3	(	(	PUNCT
ejpam-5213	479	4	g	g	NOUN
ejpam-5213	479	5	)	)	PUNCT
ejpam-5213	479	6	×	×	NOUN
ejpam-5213	479	7	v	v	NOUN
ejpam-5213	479	8	(	(	PUNCT
ejpam-5213	479	9	h	h	NOUN
ejpam-5213	479	10	)	)	PUNCT
ejpam-5213	479	11	as	as	ADP
ejpam-5213	479	12	its	its	PRON
ejpam-5213	479	13	vertex	vertex	NOUN
ejpam-5213	479	14	set	set	NOUN
ejpam-5213	479	15	,	,	PUNCT
ejpam-5213	479	16	and	and	CCONJ
ejpam-5213	479	17	u	u	NOUN
ejpam-5213	479	18	=	=	PUNCT
ejpam-5213	479	19	(	(	PUNCT
ejpam-5213	479	20	u1	u1	PROPN
ejpam-5213	479	21	,	,	PUNCT
ejpam-5213	479	22	u2	u2	PROPN
ejpam-5213	479	23	)	)	PUNCT
ejpam-5213	479	24	is	be	AUX
ejpam-5213	479	25	adjacent	adjacent	ADJ
ejpam-5213	479	26	with	with	ADP
ejpam-5213	479	27	v	v	NOUN
ejpam-5213	479	28	=	=	SYM
ejpam-5213	479	29	(	(	PUNCT
ejpam-5213	479	30	v1	v1	NOUN
ejpam-5213	479	31	,	,	PUNCT
ejpam-5213	479	32	v2	v2	PROPN
ejpam-5213	479	33	)	)	PUNCT
ejpam-5213	479	34	whenever	whenever	SCONJ
ejpam-5213	479	35	u1v1	u1v1	PROPN
ejpam-5213	479	36	∈	∈	PROPN
ejpam-5213	479	37	e(g	e(g	NOUN
ejpam-5213	479	38	)	)	PUNCT
ejpam-5213	479	39	or	or	CCONJ
ejpam-5213	479	40	u1	u1	NOUN
ejpam-5213	479	41	=	=	SYM
ejpam-5213	479	42	v1	v1	NOUN
ejpam-5213	479	43	and	and	CCONJ
ejpam-5213	479	44	u2v2	u2v2	ADJ
ejpam-5213	479	45	∈	∈	PROPN
ejpam-5213	479	46	e(h	e(h	PROPN
ejpam-5213	479	47	)	)	PUNCT
ejpam-5213	479	48	.	.	PUNCT
ejpam-5213	480	1	observe	observe	VERB
ejpam-5213	480	2	that	that	SCONJ
ejpam-5213	480	3	any	any	DET
ejpam-5213	480	4	subset	subset	NOUN
ejpam-5213	480	5	c	c	NOUN
ejpam-5213	480	6	of	of	ADP
ejpam-5213	480	7	v	v	PROPN
ejpam-5213	480	8	(	(	PUNCT
ejpam-5213	480	9	g	g	NOUN
ejpam-5213	480	10	)	)	PUNCT
ejpam-5213	480	11	×	×	NOUN
ejpam-5213	480	12	v	v	NOUN
ejpam-5213	480	13	(	(	PUNCT
ejpam-5213	480	14	h	h	NOUN
ejpam-5213	480	15	)	)	PUNCT
ejpam-5213	480	16	(	(	PUNCT
ejpam-5213	480	17	infact	infact	PROPN
ejpam-5213	480	18	,	,	PUNCT
ejpam-5213	480	19	any	any	DET
ejpam-5213	480	20	set	set	NOUN
ejpam-5213	480	21	of	of	ADP
ejpam-5213	480	22	ordered	order	VERB
ejpam-5213	480	23	-	-	PUNCT
ejpam-5213	480	24	pairs	pair	NOUN
ejpam-5213	480	25	)	)	PUNCT
ejpam-5213	480	26	can	can	AUX
ejpam-5213	480	27	be	be	AUX
ejpam-5213	480	28	written	write	VERB
ejpam-5213	480	29	as	as	ADP
ejpam-5213	480	30	c	c	PROPN
ejpam-5213	480	31	=	=	SYM
ejpam-5213	480	32	∪v∈a({v	∪v∈a({v	PROPN
ejpam-5213	480	33	}	}	PUNCT
ejpam-5213	480	34	×	×	PROPN
ejpam-5213	480	35	bv	bv	PROPN
ejpam-5213	480	36	)	)	PUNCT
ejpam-5213	480	37	,	,	PUNCT
ejpam-5213	480	38	where	where	SCONJ
ejpam-5213	480	39	s	s	VERB
ejpam-5213	480	40	⊆	⊆	NUM
ejpam-5213	480	41	v	v	NOUN
ejpam-5213	480	42	(	(	PUNCT
ejpam-5213	480	43	g	g	NOUN
ejpam-5213	480	44	)	)	PUNCT
ejpam-5213	480	45	and	and	CCONJ
ejpam-5213	480	46	bv	bv	PROPN
ejpam-5213	480	47	⊆	⊆	NUM
ejpam-5213	480	48	v	v	PROPN
ejpam-5213	480	49	(	(	PUNCT
ejpam-5213	480	50	h	h	NOUN
ejpam-5213	480	51	)	)	PUNCT
ejpam-5213	480	52	for	for	ADP
ejpam-5213	480	53	each	each	DET
ejpam-5213	480	54	v	v	NOUN
ejpam-5213	480	55	∈	∈	PROPN
ejpam-5213	480	56	s.	s.	PROPN
ejpam-5213	480	57	henceforth	henceforth	ADV
ejpam-5213	480	58	,	,	PUNCT
ejpam-5213	480	59	we	we	PRON
ejpam-5213	480	60	shall	shall	AUX
ejpam-5213	480	61	use	use	VERB
ejpam-5213	480	62	this	this	DET
ejpam-5213	480	63	form	form	NOUN
ejpam-5213	480	64	to	to	PART
ejpam-5213	480	65	denote	denote	VERB
ejpam-5213	480	66	any	any	DET
ejpam-5213	480	67	subset	subset	NOUN
ejpam-5213	480	68	c	c	NOUN
ejpam-5213	480	69	of	of	ADP
ejpam-5213	480	70	v	v	PROPN
ejpam-5213	480	71	(	(	PUNCT
ejpam-5213	480	72	g)v	g)v	X
ejpam-5213	480	73	(	(	PUNCT
ejpam-5213	480	74	h	h	NOUN
ejpam-5213	480	75	)	)	PUNCT
ejpam-5213	480	76	.	.	PUNCT
ejpam-5213	481	1	theorem	theorem	VERB
ejpam-5213	481	2	13	13	NUM
ejpam-5213	481	3	.	.	PUNCT
ejpam-5213	482	1	[	[	X
ejpam-5213	482	2	12	12	NUM
ejpam-5213	482	3	]	]	PUNCT
ejpam-5213	482	4	let	let	VERB
ejpam-5213	482	5	g	g	PROPN
ejpam-5213	482	6	(	(	PUNCT
ejpam-5213	482	7	not	not	PART
ejpam-5213	482	8	necessarily	necessarily	ADV
ejpam-5213	482	9	point	point	VERB
ejpam-5213	482	10	distinguishing	distinguishing	NOUN
ejpam-5213	482	11	)	)	PUNCT
ejpam-5213	482	12	and	and	CCONJ
ejpam-5213	482	13	h	h	NOUN
ejpam-5213	482	14	be	be	VERB
ejpam-5213	482	15	non	non	ADJ
ejpam-5213	482	16	-	-	ADJ
ejpam-5213	482	17	trivial	trivial	ADJ
ejpam-5213	482	18	connected	connected	ADJ
ejpam-5213	482	19	graphs	graph	NOUN
ejpam-5213	482	20	.	.	PUNCT
ejpam-5213	483	1	then	then	ADV
ejpam-5213	483	2	c	c	X
ejpam-5213	483	3	=	=	SYM
ejpam-5213	483	4	∪x∈s({x}×tx	∪x∈s({x}×tx	PROPN
ejpam-5213	483	5	)	)	PUNCT
ejpam-5213	483	6	,	,	PUNCT
ejpam-5213	483	7	where	where	SCONJ
ejpam-5213	483	8	s	s	VERB
ejpam-5213	483	9	⊆	⊆	NUM
ejpam-5213	483	10	v	v	NOUN
ejpam-5213	483	11	(	(	PUNCT
ejpam-5213	483	12	g	g	NOUN
ejpam-5213	483	13	)	)	PUNCT
ejpam-5213	483	14	and	and	CCONJ
ejpam-5213	483	15	tx	tx	VERB
ejpam-5213	483	16	⊆	⊆	NUM
ejpam-5213	483	17	v	v	NOUN
ejpam-5213	483	18	(	(	PUNCT
ejpam-5213	483	19	h	h	NOUN
ejpam-5213	483	20	)	)	PUNCT
ejpam-5213	483	21	for	for	ADP
ejpam-5213	483	22	each	each	DET
ejpam-5213	483	23	x	x	SYM
ejpam-5213	483	24	∈	∈	PROPN
ejpam-5213	483	25	s	s	NOUN
ejpam-5213	483	26	,	,	PUNCT
ejpam-5213	483	27	is	be	AUX
ejpam-5213	483	28	a	a	DET
ejpam-5213	483	29	differentiating	differentiate	VERB
ejpam-5213	483	30	-	-	PUNCT
ejpam-5213	483	31	dominating	dominating	NOUN
ejpam-5213	483	32	set	set	NOUN
ejpam-5213	483	33	in	in	ADP
ejpam-5213	483	34	g[h	g[h	PROPN
ejpam-5213	483	35	]	]	PUNCT
ejpam-5213	483	36	if	if	SCONJ
ejpam-5213	483	37	and	and	CCONJ
ejpam-5213	483	38	only	only	ADV
ejpam-5213	483	39	if	if	SCONJ
ejpam-5213	483	40	(	(	PUNCT
ejpam-5213	483	41	i	i	NOUN
ejpam-5213	483	42	)	)	PUNCT
ejpam-5213	483	43	s	s	PART
ejpam-5213	483	44	=	=	SYM
ejpam-5213	483	45	v	v	NOUN
ejpam-5213	483	46	(	(	PUNCT
ejpam-5213	483	47	g	g	NOUN
ejpam-5213	483	48	)	)	PUNCT
ejpam-5213	483	49	;	;	PUNCT
ejpam-5213	483	50	(	(	PUNCT
ejpam-5213	483	51	ii	ii	NOUN
ejpam-5213	483	52	)	)	PUNCT
ejpam-5213	483	53	tx	tx	PROPN
ejpam-5213	483	54	is	be	AUX
ejpam-5213	483	55	a	a	DET
ejpam-5213	483	56	differentiating	differentiate	VERB
ejpam-5213	483	57	set	set	NOUN
ejpam-5213	483	58	in	in	ADP
ejpam-5213	483	59	h	h	NOUN
ejpam-5213	483	60	for	for	ADP
ejpam-5213	483	61	every	every	DET
ejpam-5213	483	62	x	x	SYM
ejpam-5213	483	63	∈	∈	PROPN
ejpam-5213	483	64	v	v	NOUN
ejpam-5213	483	65	(	(	PUNCT
ejpam-5213	483	66	g	g	NOUN
ejpam-5213	483	67	)	)	PUNCT
ejpam-5213	483	68	;	;	PUNCT
ejpam-5213	483	69	(	(	PUNCT
ejpam-5213	483	70	iii	iii	X
ejpam-5213	483	71	)	)	PUNCT
ejpam-5213	483	72	tx	tx	NOUN
ejpam-5213	484	1	or	or	CCONJ
ejpam-5213	484	2	ty	ty	INTJ
ejpam-5213	484	3	is	be	AUX
ejpam-5213	484	4	strictly	strictly	ADV
ejpam-5213	484	5	differentiating	differentiate	VERB
ejpam-5213	484	6	in	in	ADP
ejpam-5213	484	7	h	h	NOUN
ejpam-5213	484	8	whenever	whenever	SCONJ
ejpam-5213	484	9	x	x	PRON
ejpam-5213	484	10	and	and	CCONJ
ejpam-5213	484	11	y	y	PROPN
ejpam-5213	484	12	are	be	AUX
ejpam-5213	484	13	adjacent	adjacent	ADJ
ejpam-5213	484	14	vertices	vertex	NOUN
ejpam-5213	484	15	of	of	ADP
ejpam-5213	484	16	g	g	NOUN
ejpam-5213	484	17	with	with	ADP
ejpam-5213	484	18	ng[x	ng[x	PROPN
ejpam-5213	484	19	]	]	X
ejpam-5213	484	20	=	=	PUNCT
ejpam-5213	484	21	ng[y	ng[y	PROPN
ejpam-5213	484	22	]	]	X
ejpam-5213	484	23	;	;	PUNCT
ejpam-5213	484	24	and	and	CCONJ
ejpam-5213	484	25	(	(	PUNCT
ejpam-5213	484	26	iv	iv	X
ejpam-5213	484	27	)	)	PUNCT
ejpam-5213	484	28	tx	tx	NOUN
ejpam-5213	484	29	or	or	CCONJ
ejpam-5213	484	30	ty	ty	INTJ
ejpam-5213	484	31	is	be	AUX
ejpam-5213	484	32	(	(	PUNCT
ejpam-5213	484	33	differentiating	differentiate	VERB
ejpam-5213	484	34	)	)	PUNCT
ejpam-5213	484	35	dominating	dominating	NOUN
ejpam-5213	484	36	in	in	ADP
ejpam-5213	484	37	h	h	NOUN
ejpam-5213	484	38	whenever	whenever	SCONJ
ejpam-5213	484	39	x	x	PRON
ejpam-5213	484	40	and	and	CCONJ
ejpam-5213	484	41	y	y	PROPN
ejpam-5213	484	42	are	be	AUX
ejpam-5213	484	43	distinct	distinct	ADJ
ejpam-5213	484	44	non	non	ADJ
ejpam-5213	484	45	-	-	ADJ
ejpam-5213	484	46	adjacent	adjacent	ADJ
ejpam-5213	484	47	vertices	vertex	NOUN
ejpam-5213	484	48	of	of	ADP
ejpam-5213	484	49	g	g	NOUN
ejpam-5213	484	50	with	with	ADP
ejpam-5213	484	51	ng(x	ng(x	NUM
ejpam-5213	484	52	)	)	PUNCT
ejpam-5213	484	53	=	=	PUNCT
ejpam-5213	484	54	ng(y	ng(y	NOUN
ejpam-5213	484	55	)	)	PUNCT
ejpam-5213	484	56	.	.	PUNCT
ejpam-5213	485	1	theorem	theorem	NOUN
ejpam-5213	485	2	14	14	NUM
ejpam-5213	485	3	.	.	PUNCT
ejpam-5213	486	1	let	let	VERB
ejpam-5213	486	2	g	g	PRON
ejpam-5213	486	3	be	be	AUX
ejpam-5213	486	4	a	a	DET
ejpam-5213	486	5	non	non	ADJ
ejpam-5213	486	6	-	-	ADJ
ejpam-5213	486	7	trivial	trivial	ADJ
ejpam-5213	486	8	connected	connected	ADJ
ejpam-5213	486	9	graph	graph	NOUN
ejpam-5213	486	10	and	and	CCONJ
ejpam-5213	486	11	let	let	VERB
ejpam-5213	486	12	h	h	PRON
ejpam-5213	486	13	be	be	AUX
ejpam-5213	486	14	a	a	DET
ejpam-5213	486	15	non	non	ADJ
ejpam-5213	486	16	-	-	ADJ
ejpam-5213	486	17	trivial	trivial	ADJ
ejpam-5213	486	18	point	point	NOUN
ejpam-5213	486	19	distinguishing	distinguish	VERB
ejpam-5213	486	20	connected	connected	ADJ
ejpam-5213	486	21	graph	graph	NOUN
ejpam-5213	486	22	.	.	PUNCT
ejpam-5213	487	1	then	then	ADV
ejpam-5213	487	2	s	s	VERB
ejpam-5213	487	3	=	=	SYM
ejpam-5213	487	4	∪v∈a({v	∪v∈a({v	PROPN
ejpam-5213	487	5	}	}	PUNCT
ejpam-5213	487	6	×	×	PROPN
ejpam-5213	487	7	bv	bv	PROPN
ejpam-5213	487	8	)	)	PUNCT
ejpam-5213	487	9	,	,	PUNCT
ejpam-5213	487	10	where	where	SCONJ
ejpam-5213	487	11	a	a	DET
ejpam-5213	487	12	⊆	⊆	NUM
ejpam-5213	487	13	v	v	NOUN
ejpam-5213	487	14	(	(	PUNCT
ejpam-5213	487	15	g	g	NOUN
ejpam-5213	487	16	)	)	PUNCT
ejpam-5213	487	17	and	and	CCONJ
ejpam-5213	487	18	bv	bv	PROPN
ejpam-5213	487	19	⊆	⊆	NUM
ejpam-5213	487	20	v	v	PROPN
ejpam-5213	487	21	(	(	PUNCT
ejpam-5213	487	22	h	h	NOUN
ejpam-5213	487	23	)	)	PUNCT
ejpam-5213	487	24	for	for	ADP
ejpam-5213	487	25	each	each	DET
ejpam-5213	487	26	v	v	ADP
ejpam-5213	487	27	∈	∈	PRON
ejpam-5213	487	28	a	a	PRON
ejpam-5213	487	29	,	,	PUNCT
ejpam-5213	487	30	is	be	AUX
ejpam-5213	487	31	a	a	DET
ejpam-5213	487	32	differentiating	differentiate	VERB
ejpam-5213	487	33	odd	odd	ADJ
ejpam-5213	487	34	dominating	dominating	NOUN
ejpam-5213	487	35	set	set	VERB
ejpam-5213	487	36	in	in	ADP
ejpam-5213	487	37	g[h	g[h	PROPN
ejpam-5213	487	38	]	]	PUNCT
ejpam-5213	488	1	if	if	SCONJ
ejpam-5213	488	2	and	and	CCONJ
ejpam-5213	488	3	only	only	ADV
ejpam-5213	488	4	if	if	SCONJ
ejpam-5213	488	5	(	(	PUNCT
ejpam-5213	488	6	i	i	NOUN
ejpam-5213	488	7	)	)	PUNCT
ejpam-5213	488	8	a	a	PRON
ejpam-5213	488	9	=	=	SYM
ejpam-5213	488	10	v	v	NOUN
ejpam-5213	488	11	(	(	PUNCT
ejpam-5213	488	12	g	g	NOUN
ejpam-5213	488	13	)	)	PUNCT
ejpam-5213	488	14	;	;	PUNCT
ejpam-5213	488	15	(	(	PUNCT
ejpam-5213	488	16	ii	ii	NOUN
ejpam-5213	488	17	)	)	PUNCT
ejpam-5213	488	18	bv	bv	PROPN
ejpam-5213	488	19	is	be	AUX
ejpam-5213	488	20	a	a	DET
ejpam-5213	488	21	differentiating	differentiate	VERB
ejpam-5213	488	22	set	set	NOUN
ejpam-5213	488	23	in	in	ADP
ejpam-5213	488	24	h	h	NOUN
ejpam-5213	488	25	for	for	ADP
ejpam-5213	488	26	every	every	DET
ejpam-5213	488	27	v	v	NUM
ejpam-5213	488	28	∈	∈	PROPN
ejpam-5213	488	29	v	v	NOUN
ejpam-5213	488	30	(	(	PUNCT
ejpam-5213	488	31	g	g	NOUN
ejpam-5213	488	32	)	)	PUNCT
ejpam-5213	488	33	;	;	PUNCT
ejpam-5213	488	34	(	(	PUNCT
ejpam-5213	488	35	iii	iii	X
ejpam-5213	488	36	)	)	PUNCT
ejpam-5213	488	37	bv	bv	PROPN
ejpam-5213	488	38	or	or	CCONJ
ejpam-5213	488	39	bu	bu	PROPN
ejpam-5213	488	40	is	be	AUX
ejpam-5213	488	41	strictly	strictly	ADV
ejpam-5213	488	42	differentiating	differentiate	VERB
ejpam-5213	488	43	in	in	ADP
ejpam-5213	488	44	h	h	NOUN
ejpam-5213	488	45	whenever	whenever	SCONJ
ejpam-5213	488	46	u	u	NOUN
ejpam-5213	488	47	and	and	CCONJ
ejpam-5213	488	48	v	v	NOUN
ejpam-5213	488	49	are	be	AUX
ejpam-5213	488	50	adjacent	adjacent	ADJ
ejpam-5213	488	51	vertices	vertex	NOUN
ejpam-5213	488	52	of	of	ADP
ejpam-5213	488	53	g	g	NOUN
ejpam-5213	488	54	with	with	ADP
ejpam-5213	488	55	ng[u	ng[u	PROPN
ejpam-5213	488	56	]	]	X
ejpam-5213	488	57	=	=	PUNCT
ejpam-5213	489	1	ng[v	ng[v	NOUN
ejpam-5213	489	2	]	]	PUNCT
ejpam-5213	489	3	;	;	PUNCT
ejpam-5213	489	4	(	(	PUNCT
ejpam-5213	489	5	iv	iv	X
ejpam-5213	489	6	)	)	PUNCT
ejpam-5213	489	7	bv	bv	PROPN
ejpam-5213	489	8	or	or	CCONJ
ejpam-5213	489	9	bu	bu	PROPN
ejpam-5213	489	10	is	be	AUX
ejpam-5213	489	11	differentiating	differentiate	VERB
ejpam-5213	489	12	-	-	PUNCT
ejpam-5213	489	13	dominating	dominating	NOUN
ejpam-5213	489	14	in	in	ADP
ejpam-5213	489	15	h	h	NOUN
ejpam-5213	489	16	whenever	whenever	SCONJ
ejpam-5213	489	17	u	u	NOUN
ejpam-5213	489	18	and	and	CCONJ
ejpam-5213	489	19	v	v	NOUN
ejpam-5213	489	20	are	be	AUX
ejpam-5213	489	21	distinct	distinct	ADJ
ejpam-5213	489	22	non	non	ADJ
ejpam-5213	489	23	-	-	ADJ
ejpam-5213	489	24	adjacent	adjacent	ADJ
ejpam-5213	489	25	vertices	vertex	NOUN
ejpam-5213	489	26	of	of	ADP
ejpam-5213	489	27	g	g	NOUN
ejpam-5213	489	28	with	with	ADP
ejpam-5213	489	29	ng(u	ng(u	NOUN
ejpam-5213	489	30	)	)	PUNCT
ejpam-5213	489	31	=	=	PUNCT
ejpam-5213	489	32	ng(v	ng(v	X
ejpam-5213	489	33	)	)	PUNCT
ejpam-5213	489	34	;	;	PUNCT
ejpam-5213	489	35	and	and	CCONJ
ejpam-5213	489	36	(	(	PUNCT
ejpam-5213	489	37	v	v	NOUN
ejpam-5213	489	38	)	)	PUNCT
ejpam-5213	489	39	for	for	ADP
ejpam-5213	489	40	every	every	DET
ejpam-5213	489	41	v	v	NUM
ejpam-5213	489	42	∈	∈	PROPN
ejpam-5213	489	43	v	v	NOUN
ejpam-5213	489	44	(	(	PUNCT
ejpam-5213	489	45	g	g	NOUN
ejpam-5213	489	46	)	)	PUNCT
ejpam-5213	489	47	and	and	CCONJ
ejpam-5213	489	48	for	for	ADP
ejpam-5213	489	49	every	every	PRON
ejpam-5213	489	50	p	p	PROPN
ejpam-5213	489	51	∈	∈	PROPN
ejpam-5213	489	52	v	v	ADP
ejpam-5213	489	53	(	(	PUNCT
ejpam-5213	489	54	h	h	NOUN
ejpam-5213	489	55	)	)	PUNCT
ejpam-5213	489	56	,	,	PUNCT
ejpam-5213	489	57	|nh	|nh	NUM
ejpam-5213	489	58	[	[	PUNCT
ejpam-5213	489	59	p]∩bv|+	p]∩bv|+	PROPN
ejpam-5213	489	60	∑	∑	PART
ejpam-5213	489	61	w∈ng(u	w∈ng(u	PROPN
ejpam-5213	489	62	)	)	PUNCT
ejpam-5213	489	63	|bw|	|bw|	PROPN
ejpam-5213	489	64	is	be	AUX
ejpam-5213	489	65	odd	odd	ADJ
ejpam-5213	489	66	.	.	PUNCT
ejpam-5213	490	1	proof	proof	NOUN
ejpam-5213	490	2	.	.	PUNCT
ejpam-5213	491	1	suppose	suppose	VERB
ejpam-5213	491	2	s	s	PRON
ejpam-5213	491	3	is	be	AUX
ejpam-5213	491	4	a	a	DET
ejpam-5213	491	5	differentiating	differentiate	VERB
ejpam-5213	491	6	odd	odd	ADJ
ejpam-5213	491	7	dominating	dominating	NOUN
ejpam-5213	491	8	set	set	VERB
ejpam-5213	491	9	in	in	ADP
ejpam-5213	491	10	g[h	g[h	PROPN
ejpam-5213	491	11	]	]	PUNCT
ejpam-5213	491	12	.	.	PUNCT
ejpam-5213	492	1	then	then	ADV
ejpam-5213	492	2	(	(	PUNCT
ejpam-5213	492	3	i	i	NOUN
ejpam-5213	492	4	)	)	PUNCT
ejpam-5213	492	5	,	,	PUNCT
ejpam-5213	492	6	(	(	PUNCT
ejpam-5213	492	7	ii	ii	NOUN
ejpam-5213	492	8	)	)	PUNCT
ejpam-5213	492	9	,	,	PUNCT
ejpam-5213	492	10	(	(	PUNCT
ejpam-5213	492	11	iii	iii	NOUN
ejpam-5213	492	12	)	)	PUNCT
ejpam-5213	492	13	and	and	CCONJ
ejpam-5213	492	14	(	(	PUNCT
ejpam-5213	492	15	iv	iv	X
ejpam-5213	492	16	)	)	PUNCT
ejpam-5213	492	17	hold	hold	NOUN
ejpam-5213	492	18	by	by	ADP
ejpam-5213	492	19	theorem	theorem	NOUN
ejpam-5213	492	20	13	13	NUM
ejpam-5213	492	21	.	.	PUNCT
ejpam-5213	493	1	let	let	VERB
ejpam-5213	493	2	v	v	NUM
ejpam-5213	493	3	∈	∈	PROPN
ejpam-5213	493	4	v	v	NOUN
ejpam-5213	493	5	(	(	PUNCT
ejpam-5213	493	6	g	g	NOUN
ejpam-5213	493	7	)	)	PUNCT
ejpam-5213	493	8	and	and	CCONJ
ejpam-5213	493	9	p	p	PROPN
ejpam-5213	493	10	∈	∈	PROPN
ejpam-5213	493	11	v	v	ADP
ejpam-5213	493	12	(	(	PUNCT
ejpam-5213	493	13	h	h	NOUN
ejpam-5213	493	14	)	)	PUNCT
ejpam-5213	493	15	.	.	PUNCT
ejpam-5213	494	1	then	then	ADV
ejpam-5213	494	2	ng[h][(v	ng[h][(v	PROPN
ejpam-5213	494	3	,	,	PUNCT
ejpam-5213	494	4	p	p	NOUN
ejpam-5213	494	5	)	)	PUNCT
ejpam-5213	494	6	]	]	PUNCT
ejpam-5213	495	1	=	=	PUNCT
ejpam-5213	495	2	[	[	X
ejpam-5213	495	3	{	{	PUNCT
ejpam-5213	495	4	v	v	NOUN
ejpam-5213	495	5	}	}	PUNCT
ejpam-5213	495	6	×	×	NOUN
ejpam-5213	495	7	(	(	PUNCT
ejpam-5213	495	8	nh	nh	X
ejpam-5213	495	9	[	[	X
ejpam-5213	495	10	p	p	X
ejpam-5213	495	11	]	]	X
ejpam-5213	495	12	∩bv	∩bv	NOUN
ejpam-5213	495	13	)	)	PUNCT
ejpam-5213	495	14	]	]	PUNCT
ejpam-5213	495	15	∪	∪	ADP
ejpam-5213	495	16	[	[	X
ejpam-5213	495	17	∪w∈ng(v)({w	∪w∈ng(v)({w	ADJ
ejpam-5213	495	18	}	}	PUNCT
ejpam-5213	495	19	×bw	×bw	PROPN
ejpam-5213	495	20	)	)	PUNCT
ejpam-5213	495	21	]	]	PUNCT
ejpam-5213	495	22	.	.	PUNCT
ejpam-5213	496	1	since	since	SCONJ
ejpam-5213	496	2	s	s	PROPN
ejpam-5213	496	3	is	be	AUX
ejpam-5213	496	4	odd	odd	ADJ
ejpam-5213	496	5	dominating	dominate	VERB
ejpam-5213	496	6	in	in	ADP
ejpam-5213	496	7	g[h	g[h	PROPN
ejpam-5213	496	8	]	]	PUNCT
ejpam-5213	496	9	,	,	PUNCT
ejpam-5213	496	10	|ng[h][(v	|ng[h][(v	ADJ
ejpam-5213	496	11	,	,	PUNCT
ejpam-5213	496	12	p	p	NOUN
ejpam-5213	496	13	)	)	PUNCT
ejpam-5213	496	14	]	]	PUNCT
ejpam-5213	496	15	∩	∩	NOUN
ejpam-5213	496	16	s|	s|	NOUN
ejpam-5213	496	17	=	=	PUNCT
ejpam-5213	496	18	|nh	|nh	NUM
ejpam-5213	496	19	[	[	X
ejpam-5213	496	20	p	p	X
ejpam-5213	496	21	]	]	X
ejpam-5213	496	22	∩bv|+	∩bv|+	ADJ
ejpam-5213	496	23	∑	∑	PUNCT
ejpam-5213	496	24	w∈ng(v	w∈ng(v	PROPN
ejpam-5213	496	25	)	)	PUNCT
ejpam-5213	496	26	|bw|	|bw|	PROPN
ejpam-5213	496	27	is	be	AUX
ejpam-5213	496	28	odd	odd	ADJ
ejpam-5213	496	29	,	,	PUNCT
ejpam-5213	496	30	showing	show	VERB
ejpam-5213	496	31	that	that	SCONJ
ejpam-5213	496	32	(	(	PUNCT
ejpam-5213	496	33	v	v	NOUN
ejpam-5213	496	34	)	)	PUNCT
ejpam-5213	496	35	holds	hold	NOUN
ejpam-5213	496	36	.	.	PUNCT
ejpam-5213	497	1	for	for	ADP
ejpam-5213	497	2	the	the	DET
ejpam-5213	497	3	converse	converse	NOUN
ejpam-5213	497	4	,	,	PUNCT
ejpam-5213	497	5	suppose	suppose	VERB
ejpam-5213	497	6	that	that	SCONJ
ejpam-5213	497	7	s	s	VERB
ejpam-5213	497	8	satifies	satifie	NOUN
ejpam-5213	497	9	the	the	DET
ejpam-5213	497	10	five	five	NUM
ejpam-5213	497	11	conditions	condition	NOUN
ejpam-5213	497	12	.	.	PUNCT
ejpam-5213	498	1	since	since	SCONJ
ejpam-5213	498	2	(	(	PUNCT
ejpam-5213	498	3	i	i	NOUN
ejpam-5213	498	4	)	)	PUNCT
ejpam-5213	498	5	,	,	PUNCT
ejpam-5213	498	6	(	(	PUNCT
ejpam-5213	498	7	ii	ii	NOUN
ejpam-5213	498	8	)	)	PUNCT
ejpam-5213	498	9	,	,	PUNCT
ejpam-5213	498	10	(	(	PUNCT
ejpam-5213	498	11	iii	iii	NOUN
ejpam-5213	498	12	)	)	PUNCT
ejpam-5213	498	13	,	,	PUNCT
ejpam-5213	498	14	and	and	CCONJ
ejpam-5213	498	15	(	(	PUNCT
ejpam-5213	498	16	iv	iv	X
ejpam-5213	498	17	)	)	PUNCT
ejpam-5213	498	18	hold	hold	NOUN
ejpam-5213	498	19	,	,	PUNCT
ejpam-5213	498	20	s	s	VERB
ejpam-5213	498	21	is	be	AUX
ejpam-5213	498	22	a	a	DET
ejpam-5213	498	23	differentiating	differentiate	VERB
ejpam-5213	498	24	-	-	PUNCT
ejpam-5213	498	25	dominating	dominating	NOUN
ejpam-5213	498	26	set	set	NOUN
ejpam-5213	498	27	in	in	ADP
ejpam-5213	498	28	g[h	g[h	PROPN
ejpam-5213	498	29	]	]	PUNCT
ejpam-5213	498	30	by	by	ADP
ejpam-5213	498	31	theorem	theorem	NOUN
ejpam-5213	498	32	13	13	NUM
ejpam-5213	498	33	.	.	PUNCT
ejpam-5213	499	1	by	by	ADP
ejpam-5213	499	2	(	(	PUNCT
ejpam-5213	499	3	v	v	NOUN
ejpam-5213	499	4	)	)	PUNCT
ejpam-5213	499	5	,	,	PUNCT
ejpam-5213	499	6	it	it	PRON
ejpam-5213	499	7	follows	follow	VERB
ejpam-5213	499	8	that	that	SCONJ
ejpam-5213	499	9	s	s	VERB
ejpam-5213	499	10	is	be	AUX
ejpam-5213	499	11	odd	odd	ADJ
ejpam-5213	499	12	dominating	dominating	NOUN
ejpam-5213	499	13	.	.	PUNCT
ejpam-5213	500	1	references	reference	NOUN
ejpam-5213	500	2	1599	1599	NUM
ejpam-5213	500	3	corollary	corollary	ADJ
ejpam-5213	500	4	14	14	NUM
ejpam-5213	500	5	.	.	PUNCT
ejpam-5213	501	1	let	let	VERB
ejpam-5213	501	2	g	g	NOUN
ejpam-5213	501	3	be	be	AUX
ejpam-5213	501	4	non	non	ADJ
ejpam-5213	501	5	-	-	ADJ
ejpam-5213	501	6	trivial	trivial	ADJ
ejpam-5213	501	7	totally	totally	ADV
ejpam-5213	501	8	point	point	NOUN
ejpam-5213	501	9	determining	determine	VERB
ejpam-5213	501	10	graph	graph	NOUN
ejpam-5213	501	11	and	and	CCONJ
ejpam-5213	501	12	let	let	VERB
ejpam-5213	501	13	h	h	PRON
ejpam-5213	501	14	be	be	AUX
ejpam-5213	501	15	a	a	DET
ejpam-5213	501	16	point	point	NOUN
ejpam-5213	501	17	distinguishing	distinguish	VERB
ejpam-5213	501	18	connected	connected	ADJ
ejpam-5213	501	19	graph	graph	NOUN
ejpam-5213	501	20	.	.	PUNCT
ejpam-5213	502	1	if	if	SCONJ
ejpam-5213	502	2	h	h	PROPN
ejpam-5213	502	3	admits	admit	VERB
ejpam-5213	502	4	a	a	DET
ejpam-5213	502	5	differentiating	differentiate	VERB
ejpam-5213	502	6	odd	odd	ADJ
ejpam-5213	502	7	dominating	dominating	NOUN
ejpam-5213	502	8	set	set	VERB
ejpam-5213	502	9	with	with	ADP
ejpam-5213	502	10	even	even	ADV
ejpam-5213	502	11	cardinality	cardinality	NOUN
ejpam-5213	502	12	,	,	PUNCT
ejpam-5213	502	13	then	then	ADV
ejpam-5213	502	14	γod(g[h	γod(g[h	NUM
ejpam-5213	502	15	]	]	PUNCT
ejpam-5213	502	16	)	)	PUNCT
ejpam-5213	502	17	≤	≤	NUM
ejpam-5213	502	18	|v	|v	X
ejpam-5213	502	19	(	(	PUNCT
ejpam-5213	502	20	g)|γeod	g)|γeod	NOUN
ejpam-5213	502	21	(	(	PUNCT
ejpam-5213	502	22	h	h	NOUN
ejpam-5213	502	23	)	)	PUNCT
ejpam-5213	502	24	.	.	PUNCT
ejpam-5213	503	1	proof	proof	NOUN
ejpam-5213	503	2	.	.	PUNCT
ejpam-5213	504	1	for	for	ADP
ejpam-5213	504	2	each	each	DET
ejpam-5213	504	3	v	v	NUM
ejpam-5213	504	4	∈	∈	PROPN
ejpam-5213	504	5	v	v	NOUN
ejpam-5213	504	6	(	(	PUNCT
ejpam-5213	504	7	g	g	NOUN
ejpam-5213	504	8	)	)	PUNCT
ejpam-5213	504	9	,	,	PUNCT
ejpam-5213	504	10	let	let	VERB
ejpam-5213	504	11	bv	bv	PRON
ejpam-5213	504	12	be	be	AUX
ejpam-5213	504	13	a	a	DET
ejpam-5213	504	14	differentiating	differentiate	VERB
ejpam-5213	504	15	odd	odd	ADJ
ejpam-5213	504	16	dominating	dominating	NOUN
ejpam-5213	504	17	set	set	VERB
ejpam-5213	504	18	with	with	ADP
ejpam-5213	504	19	even	even	ADV
ejpam-5213	504	20	cardinality	cardinality	NOUN
ejpam-5213	505	1	such	such	ADJ
ejpam-5213	505	2	that	that	PRON
ejpam-5213	505	3	|bv|	|bv|	NOUN
ejpam-5213	506	1	=	=	SYM
ejpam-5213	507	1	γeod	γeod	NOUN
ejpam-5213	508	1	(	(	PUNCT
ejpam-5213	509	1	h	h	NOUN
ejpam-5213	509	2	)	)	PUNCT
ejpam-5213	509	3	.	.	PUNCT
ejpam-5213	510	1	then	then	ADV
ejpam-5213	510	2	s	s	VERB
ejpam-5213	510	3	=	=	SYM
ejpam-5213	510	4	∪v∈v	∪v∈v	X
ejpam-5213	510	5	(	(	PUNCT
ejpam-5213	510	6	g)({v	g)({v	PROPN
ejpam-5213	510	7	}	}	PUNCT
ejpam-5213	510	8	×	×	PROPN
ejpam-5213	510	9	bv	bv	PROPN
ejpam-5213	510	10	)	)	PUNCT
ejpam-5213	510	11	satisfies	satisfy	VERB
ejpam-5213	510	12	the	the	DET
ejpam-5213	510	13	first	first	ADJ
ejpam-5213	510	14	four	four	NUM
ejpam-5213	510	15	properties	property	NOUN
ejpam-5213	510	16	in	in	ADP
ejpam-5213	510	17	theorem	theorem	NOUN
ejpam-5213	510	18	14	14	NUM
ejpam-5213	510	19	.	.	PUNCT
ejpam-5213	511	1	now	now	ADV
ejpam-5213	511	2	let	let	VERB
ejpam-5213	511	3	v	v	ADP
ejpam-5213	511	4	∈	∈	PROPN
ejpam-5213	511	5	v	v	NOUN
ejpam-5213	511	6	(	(	PUNCT
ejpam-5213	511	7	g	g	NOUN
ejpam-5213	511	8	)	)	PUNCT
ejpam-5213	511	9	and	and	CCONJ
ejpam-5213	511	10	p	p	PROPN
ejpam-5213	511	11	∈	∈	PROPN
ejpam-5213	511	12	v	v	ADP
ejpam-5213	511	13	(	(	PUNCT
ejpam-5213	511	14	h	h	NOUN
ejpam-5213	511	15	)	)	PUNCT
ejpam-5213	511	16	.	.	PUNCT
ejpam-5213	512	1	since	since	SCONJ
ejpam-5213	512	2	bv	bv	PROPN
ejpam-5213	512	3	is	be	AUX
ejpam-5213	512	4	differentiating	differentiate	VERB
ejpam-5213	512	5	odd	odd	ADJ
ejpam-5213	512	6	dominating	dominating	NOUN
ejpam-5213	512	7	in	in	ADP
ejpam-5213	512	8	h	h	NOUN
ejpam-5213	512	9	,	,	PUNCT
ejpam-5213	512	10	|nh	|nh	NUM
ejpam-5213	512	11	[	[	X
ejpam-5213	512	12	p	p	X
ejpam-5213	512	13	]	]	X
ejpam-5213	512	14	∩	∩	NOUN
ejpam-5213	512	15	bv|	bv|	NOUN
ejpam-5213	512	16	is	be	AUX
ejpam-5213	512	17	odd	odd	ADJ
ejpam-5213	512	18	.	.	PUNCT
ejpam-5213	513	1	moreover	moreover	ADV
ejpam-5213	513	2	,	,	PUNCT
ejpam-5213	513	3	since	since	SCONJ
ejpam-5213	513	4	|bw|	|bw|	PROPN
ejpam-5213	513	5	is	be	AUX
ejpam-5213	513	6	even	even	ADV
ejpam-5213	513	7	for	for	ADP
ejpam-5213	513	8	every	every	DET
ejpam-5213	513	9	w	w	PROPN
ejpam-5213	513	10	∈	∈	PROPN
ejpam-5213	513	11	v	v	ADP
ejpam-5213	513	12	(	(	PUNCT
ejpam-5213	513	13	g	g	NOUN
ejpam-5213	513	14	)	)	PUNCT
ejpam-5213	513	15	,	,	PUNCT
ejpam-5213	513	16	it	it	PRON
ejpam-5213	513	17	follows	follow	VERB
ejpam-5213	513	18	that	that	SCONJ
ejpam-5213	513	19	∑	∑	PUNCT
ejpam-5213	513	20	w∈ng(v	w∈ng(v	PROPN
ejpam-5213	513	21	)	)	PUNCT
ejpam-5213	513	22	|bw|	|bw|	PROPN
ejpam-5213	513	23	is	be	AUX
ejpam-5213	513	24	even	even	ADV
ejpam-5213	513	25	.	.	PUNCT
ejpam-5213	514	1	therefore	therefore	ADV
ejpam-5213	514	2	,	,	PUNCT
ejpam-5213	514	3	|nh	|nh	NUM
ejpam-5213	514	4	[	[	X
ejpam-5213	514	5	p	p	X
ejpam-5213	514	6	]	]	X
ejpam-5213	514	7	∩	∩	ADJ
ejpam-5213	514	8	bv|	bv|	PROPN
ejpam-5213	514	9	+	+	CCONJ
ejpam-5213	514	10	∑	∑	PUNCT
ejpam-5213	514	11	w∈ng(v	w∈ng(v	PROPN
ejpam-5213	514	12	)	)	PUNCT
ejpam-5213	514	13	|bw|	|bw|	PROPN
ejpam-5213	514	14	is	be	AUX
ejpam-5213	514	15	odd	odd	ADJ
ejpam-5213	514	16	,	,	PUNCT
ejpam-5213	514	17	showing	show	VERB
ejpam-5213	514	18	that	that	PRON
ejpam-5213	514	19	property	property	NOUN
ejpam-5213	514	20	(	(	PUNCT
ejpam-5213	514	21	v	v	NOUN
ejpam-5213	514	22	)	)	PUNCT
ejpam-5213	514	23	in	in	ADP
ejpam-5213	514	24	theorem	theorem	NOUN
ejpam-5213	514	25	14	14	NUM
ejpam-5213	514	26	is	be	AUX
ejpam-5213	514	27	also	also	ADV
ejpam-5213	514	28	satisfied	satisfied	ADJ
ejpam-5213	514	29	.	.	PUNCT
ejpam-5213	515	1	accordingly	accordingly	ADV
ejpam-5213	515	2	,	,	PUNCT
ejpam-5213	515	3	s	s	VERB
ejpam-5213	515	4	is	be	AUX
ejpam-5213	515	5	a	a	DET
ejpam-5213	515	6	differentiating	differentiate	VERB
ejpam-5213	515	7	odd	odd	ADJ
ejpam-5213	515	8	dominating	dominating	NOUN
ejpam-5213	515	9	set	set	VERB
ejpam-5213	515	10	in	in	ADP
ejpam-5213	515	11	g[h	g[h	PROPN
ejpam-5213	515	12	]	]	PUNCT
ejpam-5213	515	13	and	and	CCONJ
ejpam-5213	515	14	γod(g[h	γod(g[h	NUM
ejpam-5213	515	15	]	]	PUNCT
ejpam-5213	515	16	)	)	PUNCT
ejpam-5213	515	17	≤	≤	NUM
ejpam-5213	515	18	|s|	|s|	PROPN
ejpam-5213	515	19	=	=	SYM
ejpam-5213	515	20	|v	|v	X
ejpam-5213	515	21	(	(	PUNCT
ejpam-5213	515	22	g)|γeod	g)|γeod	NOUN
ejpam-5213	515	23	(	(	PUNCT
ejpam-5213	515	24	h	h	NOUN
ejpam-5213	515	25	)	)	PUNCT
ejpam-5213	515	26	.	.	PUNCT
ejpam-5213	516	1	conclusion	conclusion	NOUN
ejpam-5213	516	2	the	the	DET
ejpam-5213	516	3	concept	concept	NOUN
ejpam-5213	516	4	of	of	ADP
ejpam-5213	516	5	differentiating	differentiate	VERB
ejpam-5213	516	6	odd	odd	ADJ
ejpam-5213	516	7	dominating	dominating	NOUN
ejpam-5213	516	8	set	set	NOUN
ejpam-5213	516	9	has	have	AUX
ejpam-5213	516	10	been	be	AUX
ejpam-5213	516	11	introduced	introduce	VERB
ejpam-5213	516	12	and	and	CCONJ
ejpam-5213	516	13	initially	initially	ADV
ejpam-5213	516	14	investigated	investigate	VERB
ejpam-5213	516	15	in	in	ADP
ejpam-5213	516	16	this	this	DET
ejpam-5213	516	17	study	study	NOUN
ejpam-5213	516	18	.	.	PUNCT
ejpam-5213	517	1	the	the	DET
ejpam-5213	517	2	differentiating	differentiate	VERB
ejpam-5213	517	3	odd	odd	ADJ
ejpam-5213	517	4	domination	domination	NOUN
ejpam-5213	517	5	number	number	NOUN
ejpam-5213	517	6	of	of	ADP
ejpam-5213	517	7	a	a	DET
ejpam-5213	517	8	graph	graph	NOUN
ejpam-5213	517	9	on	on	ADP
ejpam-5213	517	10	at	at	ADV
ejpam-5213	517	11	least	least	ADJ
ejpam-5213	517	12	four	four	NUM
ejpam-5213	517	13	vertices	vertex	NOUN
ejpam-5213	517	14	is	be	AUX
ejpam-5213	517	15	at	at	ADP
ejpam-5213	517	16	least	least	ADJ
ejpam-5213	517	17	equal	equal	ADJ
ejpam-5213	517	18	to	to	ADP
ejpam-5213	517	19	the	the	DET
ejpam-5213	517	20	maximum	maximum	NOUN
ejpam-5213	517	21	of	of	ADP
ejpam-5213	517	22	the	the	DET
ejpam-5213	517	23	odd	odd	ADJ
ejpam-5213	517	24	domination	domination	NOUN
ejpam-5213	517	25	number	number	NOUN
ejpam-5213	517	26	,	,	PUNCT
ejpam-5213	517	27	the	the	DET
ejpam-5213	517	28	differentiating	differentiate	VERB
ejpam-5213	517	29	-	-	PUNCT
ejpam-5213	517	30	domination	domination	NOUN
ejpam-5213	517	31	number	number	NOUN
ejpam-5213	517	32	of	of	ADP
ejpam-5213	517	33	the	the	DET
ejpam-5213	517	34	graph	graph	NOUN
ejpam-5213	517	35	and	and	CCONJ
ejpam-5213	517	36	,	,	PUNCT
ejpam-5213	517	37	3	3	NUM
ejpam-5213	517	38	,	,	PUNCT
ejpam-5213	517	39	and	and	CCONJ
ejpam-5213	517	40	at	at	ADP
ejpam-5213	517	41	most	most	ADV
ejpam-5213	517	42	equal	equal	ADJ
ejpam-5213	517	43	to	to	ADP
ejpam-5213	517	44	the	the	DET
ejpam-5213	517	45	difference	difference	NOUN
ejpam-5213	517	46	of	of	ADP
ejpam-5213	517	47	the	the	DET
ejpam-5213	517	48	order	order	NOUN
ejpam-5213	517	49	of	of	ADP
ejpam-5213	517	50	the	the	DET
ejpam-5213	517	51	graph	graph	NOUN
ejpam-5213	517	52	and	and	CCONJ
ejpam-5213	517	53	the	the	DET
ejpam-5213	517	54	number	number	NOUN
ejpam-5213	517	55	of	of	ADP
ejpam-5213	517	56	its	its	PRON
ejpam-5213	517	57	support	support	NOUN
ejpam-5213	517	58	vertices	vertex	NOUN
ejpam-5213	517	59	.	.	PUNCT
ejpam-5213	518	1	as	as	SCONJ
ejpam-5213	518	2	shown	show	VERB
ejpam-5213	518	3	in	in	ADP
ejpam-5213	518	4	this	this	DET
ejpam-5213	518	5	study	study	NOUN
ejpam-5213	518	6	,	,	PUNCT
ejpam-5213	518	7	some	some	DET
ejpam-5213	518	8	graphs	graph	NOUN
ejpam-5213	518	9	do	do	AUX
ejpam-5213	518	10	not	not	PART
ejpam-5213	518	11	admit	admit	VERB
ejpam-5213	518	12	this	this	DET
ejpam-5213	518	13	kind	kind	NOUN
ejpam-5213	518	14	of	of	ADP
ejpam-5213	518	15	dominating	dominating	NOUN
ejpam-5213	518	16	set	set	NOUN
ejpam-5213	518	17	.	.	PUNCT
ejpam-5213	519	1	the	the	DET
ejpam-5213	519	2	newly	newly	ADV
ejpam-5213	519	3	defined	define	VERB
ejpam-5213	519	4	concept	concept	NOUN
ejpam-5213	519	5	and	and	CCONJ
ejpam-5213	519	6	parameter	parameter	NOUN
ejpam-5213	519	7	have	have	AUX
ejpam-5213	519	8	been	be	AUX
ejpam-5213	519	9	investigated	investigate	VERB
ejpam-5213	519	10	for	for	ADP
ejpam-5213	519	11	the	the	DET
ejpam-5213	519	12	join	join	NOUN
ejpam-5213	519	13	,	,	PUNCT
ejpam-5213	519	14	corona	corona	PROPN
ejpam-5213	519	15	,	,	PUNCT
ejpam-5213	519	16	and	and	CCONJ
ejpam-5213	519	17	lexicographic	lexicographic	ADJ
ejpam-5213	519	18	products	product	NOUN
ejpam-5213	519	19	of	of	ADP
ejpam-5213	519	20	some	some	DET
ejpam-5213	519	21	classes	class	NOUN
ejpam-5213	519	22	of	of	ADP
ejpam-5213	519	23	graphs	graph	NOUN
ejpam-5213	519	24	.	.	PUNCT
ejpam-5213	520	1	it	it	PRON
ejpam-5213	520	2	may	may	AUX
ejpam-5213	520	3	be	be	AUX
ejpam-5213	520	4	interesting	interesting	ADJ
ejpam-5213	520	5	and	and	CCONJ
ejpam-5213	520	6	worthwhile	worthwhile	ADJ
ejpam-5213	520	7	to	to	PART
ejpam-5213	520	8	find	find	VERB
ejpam-5213	520	9	necessary	necessary	ADJ
ejpam-5213	520	10	and	and	CCONJ
ejpam-5213	520	11	sufficient	sufficient	ADJ
ejpam-5213	520	12	conditions	condition	NOUN
ejpam-5213	520	13	for	for	ADP
ejpam-5213	520	14	a	a	DET
ejpam-5213	520	15	graph	graph	NOUN
ejpam-5213	520	16	to	to	PART
ejpam-5213	520	17	admit	admit	VERB
ejpam-5213	520	18	a	a	DET
ejpam-5213	520	19	differentiating	differentiate	VERB
ejpam-5213	520	20	odd	odd	ADJ
ejpam-5213	520	21	dominating	dominating	NOUN
ejpam-5213	520	22	set	set	NOUN
ejpam-5213	520	23	,	,	PUNCT
ejpam-5213	520	24	study	study	VERB
ejpam-5213	520	25	the	the	DET
ejpam-5213	520	26	complexity	complexity	NOUN
ejpam-5213	520	27	of	of	ADP
ejpam-5213	520	28	the	the	DET
ejpam-5213	520	29	decision	decision	NOUN
ejpam-5213	520	30	problem	problem	NOUN
ejpam-5213	520	31	involving	involve	VERB
ejpam-5213	520	32	the	the	DET
ejpam-5213	520	33	parameter	parameter	NOUN
ejpam-5213	520	34	,	,	PUNCT
ejpam-5213	520	35	and	and	CCONJ
ejpam-5213	520	36	investigate	investigate	VERB
ejpam-5213	520	37	the	the	DET
ejpam-5213	520	38	parameter	parameter	NOUN
ejpam-5213	520	39	for	for	ADP
ejpam-5213	520	40	some	some	DET
ejpam-5213	520	41	other	other	ADJ
ejpam-5213	520	42	families	family	NOUN
ejpam-5213	520	43	of	of	ADP
ejpam-5213	520	44	graphs	graph	NOUN
ejpam-5213	520	45	.	.	PUNCT
ejpam-5213	521	1	acknowledgements	acknowledgement	NOUN
ejpam-5213	521	2	the	the	DET
ejpam-5213	521	3	authors	author	NOUN
ejpam-5213	521	4	would	would	AUX
ejpam-5213	521	5	like	like	VERB
ejpam-5213	521	6	to	to	PART
ejpam-5213	521	7	express	express	VERB
ejpam-5213	521	8	their	their	PRON
ejpam-5213	521	9	gratitude	gratitude	NOUN
ejpam-5213	521	10	to	to	ADP
ejpam-5213	521	11	the	the	DET
ejpam-5213	521	12	referees	referee	NOUN
ejpam-5213	521	13	for	for	ADP
ejpam-5213	521	14	their	their	PRON
ejpam-5213	521	15	insightful	insightful	ADJ
ejpam-5213	521	16	comments	comment	NOUN
ejpam-5213	521	17	and	and	CCONJ
ejpam-5213	521	18	suggestions	suggestion	NOUN
ejpam-5213	521	19	.	.	PUNCT
ejpam-5213	522	1	special	special	ADJ
ejpam-5213	522	2	thanks	thank	NOUN
ejpam-5213	522	3	must	must	AUX
ejpam-5213	522	4	go	go	VERB
ejpam-5213	522	5	to	to	ADP
ejpam-5213	522	6	the	the	DET
ejpam-5213	522	7	department	department	NOUN
ejpam-5213	522	8	of	of	ADP
ejpam-5213	522	9	science	science	NOUN
ejpam-5213	522	10	and	and	CCONJ
ejpam-5213	522	11	technology	technology	NOUN
ejpam-5213	522	12	accelerated	accelerate	VERB
ejpam-5213	522	13	science	science	NOUN
ejpam-5213	522	14	and	and	CCONJ
ejpam-5213	522	15	technology	technology	NOUN
ejpam-5213	522	16	human	human	ADJ
ejpam-5213	522	17	resource	resource	NOUN
ejpam-5213	522	18	development	development	NOUN
ejpam-5213	522	19	program	program	NOUN
ejpam-5213	522	20	(	(	PUNCT
ejpam-5213	522	21	dost	dost	NOUN
ejpam-5213	522	22	-	-	PUNCT
ejpam-5213	522	23	asthrdp)-philippines	asthrdp)-philippines	PROPN
ejpam-5213	522	24	and	and	CCONJ
ejpam-5213	522	25	msu	msu	PROPN
ejpam-5213	522	26	-	-	PUNCT
ejpam-5213	522	27	iligan	iligan	PROPN
ejpam-5213	522	28	institute	institute	PROPN
ejpam-5213	522	29	of	of	ADP
ejpam-5213	522	30	technology	technology	NOUN
ejpam-5213	522	31	for	for	ADP
ejpam-5213	522	32	providing	provide	VERB
ejpam-5213	522	33	funding	funding	NOUN
ejpam-5213	522	34	for	for	ADP
ejpam-5213	522	35	this	this	DET
ejpam-5213	522	36	research	research	NOUN
ejpam-5213	522	37	.	.	PUNCT
ejpam-5213	523	1	references	reference	NOUN
ejpam-5213	523	2	[	[	X
ejpam-5213	523	3	1	1	NUM
ejpam-5213	523	4	]	]	PUNCT
ejpam-5213	523	5	b.	b.	NOUN
ejpam-5213	523	6	brešar	brešar	PROPN
ejpam-5213	523	7	and	and	CCONJ
ejpam-5213	523	8	s.	s.	PROPN
ejpam-5213	523	9	brezovnik	brezovnik	PROPN
ejpam-5213	523	10	.	.	PUNCT
ejpam-5213	524	1	grundy	grundy	PROPN
ejpam-5213	524	2	domination	domination	NOUN
ejpam-5213	524	3	and	and	CCONJ
ejpam-5213	524	4	zero	zero	NUM
ejpam-5213	524	5	forcing	force	VERB
ejpam-5213	524	6	in	in	ADP
ejpam-5213	524	7	regular	regular	ADJ
ejpam-5213	524	8	graphs	graph	NOUN
ejpam-5213	524	9	.	.	PUNCT
ejpam-5213	525	1	bulletin	bulletin	NOUN
ejpam-5213	525	2	of	of	ADP
ejpam-5213	525	3	the	the	DET
ejpam-5213	525	4	malaysian	malaysian	PROPN
ejpam-5213	525	5	mathematical	mathematical	PROPN
ejpam-5213	525	6	sciences	sciences	PROPN
ejpam-5213	525	7	society	society	NOUN
ejpam-5213	525	8	,	,	PUNCT
ejpam-5213	525	9	44(6):3637–3661	44(6):3637–3661	NUM
ejpam-5213	525	10	,	,	PUNCT
ejpam-5213	525	11	2021	2021	NUM
ejpam-5213	525	12	.	.	PUNCT
ejpam-5213	526	1	[	[	X
ejpam-5213	526	2	2	2	NUM
ejpam-5213	526	3	]	]	X
ejpam-5213	526	4	s.r	s.r	PROPN
ejpam-5213	526	5	.	.	PROPN
ejpam-5213	526	6	canoy	canoy	PROPN
ejpam-5213	526	7	.	.	PUNCT
ejpam-5213	527	1	a	a	DET
ejpam-5213	527	2	short	short	ADJ
ejpam-5213	527	3	note	note	NOUN
ejpam-5213	527	4	on	on	ADP
ejpam-5213	527	5	convexity	convexity	NOUN
ejpam-5213	527	6	and	and	CCONJ
ejpam-5213	527	7	convex	convex	NOUN
ejpam-5213	527	8	domination	domination	NOUN
ejpam-5213	527	9	in	in	ADP
ejpam-5213	527	10	g[km	g[km	PROPN
ejpam-5213	527	11	]	]	PUNCT
ejpam-5213	527	12	.	.	PUNCT
ejpam-5213	528	1	applied	apply	VERB
ejpam-5213	528	2	mathematical	mathematical	ADJ
ejpam-5213	528	3	sciences	science	NOUN
ejpam-5213	528	4	,	,	PUNCT
ejpam-5213	528	5	8(115):5737–5741	8(115):5737–5741	NUM
ejpam-5213	528	6	,	,	PUNCT
ejpam-5213	528	7	2014	2014	NUM
ejpam-5213	528	8	.	.	PUNCT
ejpam-5213	529	1	references	reference	NOUN
ejpam-5213	529	2	1600	1600	NUM
ejpam-5213	529	3	[	[	X
ejpam-5213	529	4	3	3	NUM
ejpam-5213	529	5	]	]	X
ejpam-5213	529	6	y.	y.	PROPN
ejpam-5213	529	7	caro	caro	PROPN
ejpam-5213	529	8	and	and	CCONJ
ejpam-5213	529	9	w.	w.	PROPN
ejpam-5213	529	10	klostermeyer	klostermeyer	PROPN
ejpam-5213	529	11	.	.	PUNCT
ejpam-5213	530	1	the	the	DET
ejpam-5213	530	2	odd	odd	ADJ
ejpam-5213	530	3	-	-	PUNCT
ejpam-5213	530	4	domiantion	domiantion	NOUN
ejpam-5213	530	5	number	number	NOUN
ejpam-5213	530	6	of	of	ADP
ejpam-5213	530	7	a	a	DET
ejpam-5213	530	8	graph	graph	NOUN
ejpam-5213	530	9	.	.	PUNCT
ejpam-5213	530	10	journal	journal	NOUN
ejpam-5213	530	11	of	of	ADP
ejpam-5213	530	12	combinatorial	combinatorial	ADJ
ejpam-5213	530	13	mathematics	mathematic	NOUN
ejpam-5213	530	14	and	and	CCONJ
ejpam-5213	530	15	combinatorial	combinatorial	ADJ
ejpam-5213	530	16	computing	computing	NOUN
ejpam-5213	530	17	,	,	PUNCT
ejpam-5213	530	18	44:65–83	44:65–83	NUM
ejpam-5213	530	19	,	,	PUNCT
ejpam-5213	530	20	2003	2003	NUM
ejpam-5213	530	21	.	.	PUNCT
ejpam-5213	531	1	[	[	X
ejpam-5213	531	2	4	4	X
ejpam-5213	531	3	]	]	PUNCT
ejpam-5213	531	4	k.	k.	PROPN
ejpam-5213	531	5	chakrabarty	chakrabarty	PROPN
ejpam-5213	531	6	,	,	PUNCT
ejpam-5213	531	7	m.	m.	NOUN
ejpam-5213	531	8	g.	g.	PROPN
ejpam-5213	531	9	karpovsky	karpovsky	PROPN
ejpam-5213	531	10	,	,	PUNCT
ejpam-5213	531	11	and	and	CCONJ
ejpam-5213	531	12	l.	l.	PROPN
ejpam-5213	531	13	b.	b.	PROPN
ejpam-5213	531	14	levitin	levitin	PROPN
ejpam-5213	531	15	.	.	PUNCT
ejpam-5213	532	1	on	on	ADP
ejpam-5213	532	2	a	a	DET
ejpam-5213	532	3	new	new	ADJ
ejpam-5213	532	4	class	class	NOUN
ejpam-5213	532	5	of	of	ADP
ejpam-5213	532	6	codes	code	NOUN
ejpam-5213	532	7	for	for	ADP
ejpam-5213	532	8	identifying	identify	VERB
ejpam-5213	532	9	vertices	vertex	NOUN
ejpam-5213	532	10	in	in	ADP
ejpam-5213	532	11	graphs	graph	NOUN
ejpam-5213	532	12	.	.	PUNCT
ejpam-5213	533	1	ieee	ieee	PROPN
ejpam-5213	533	2	trans	trans	PROPN
ejpam-5213	533	3	.	.	PUNCT
ejpam-5213	534	1	inform	inform	NOUN
ejpam-5213	534	2	.	.	PUNCT
ejpam-5213	535	1	theory	theory	NOUN
ejpam-5213	535	2	,	,	PUNCT
ejpam-5213	535	3	44(2):599–611	44(2):599–611	PROPN
ejpam-5213	535	4	,	,	PUNCT
ejpam-5213	535	5	1998	1998	NUM
ejpam-5213	535	6	.	.	PUNCT
ejpam-5213	536	1	[	[	X
ejpam-5213	536	2	5	5	NUM
ejpam-5213	536	3	]	]	SYM
ejpam-5213	536	4	e.j	e.j	PROPN
ejpam-5213	536	5	.	.	PROPN
ejpam-5213	536	6	cockayne	cockayne	PROPN
ejpam-5213	536	7	,	,	PUNCT
ejpam-5213	536	8	r.m	r.m	PROPN
ejpam-5213	536	9	.	.	PROPN
ejpam-5213	536	10	dawes	dawes	PROPN
ejpam-5213	536	11	,	,	PUNCT
ejpam-5213	536	12	and	and	CCONJ
ejpam-5213	536	13	s.t	s.t	PROPN
ejpam-5213	536	14	.	.	PROPN
ejpam-5213	536	15	hedetniemi	hedetniemi	PROPN
ejpam-5213	536	16	.	.	PUNCT
ejpam-5213	537	1	total	total	ADJ
ejpam-5213	537	2	domination	domination	NOUN
ejpam-5213	537	3	in	in	ADP
ejpam-5213	537	4	graphs	graph	NOUN
ejpam-5213	537	5	.	.	PUNCT
ejpam-5213	538	1	networks	network	NOUN
ejpam-5213	538	2	,	,	PUNCT
ejpam-5213	538	3	10(3):211–219	10(3):211–219	NUM
ejpam-5213	538	4	,	,	PUNCT
ejpam-5213	538	5	1980	1980	NUM
ejpam-5213	538	6	.	.	PUNCT
ejpam-5213	539	1	[	[	X
ejpam-5213	539	2	6	6	NUM
ejpam-5213	539	3	]	]	PUNCT
ejpam-5213	539	4	m.	m.	NOUN
ejpam-5213	539	5	frick	frick	PROPN
ejpam-5213	539	6	,	,	PUNCT
ejpam-5213	539	7	c.	c.	PROPN
ejpam-5213	539	8	m.	m.	PROPN
ejpam-5213	539	9	mynhardt	mynhardt	PROPN
ejpam-5213	539	10	,	,	PUNCT
ejpam-5213	539	11	and	and	CCONJ
ejpam-5213	539	12	r.	r.	PROPN
ejpam-5213	539	13	d	d	PROPN
ejpam-5213	539	14	skaggs	skaggs	PROPN
ejpam-5213	539	15	.	.	PUNCT
ejpam-5213	540	1	critical	critical	ADJ
ejpam-5213	540	2	graphs	graph	NOUN
ejpam-5213	540	3	with	with	ADP
ejpam-5213	540	4	respect	respect	NOUN
ejpam-5213	540	5	to	to	ADP
ejpam-5213	540	6	vertex	vertex	NOUN
ejpam-5213	540	7	identification	identification	NOUN
ejpam-5213	540	8	.	.	PUNCT
ejpam-5213	541	1	utilitas	utilitas	PROPN
ejpam-5213	541	2	mathematica	mathematica	PROPN
ejpam-5213	541	3	,	,	PUNCT
ejpam-5213	541	4	76:213–227	76:213–227	PROPN
ejpam-5213	541	5	,	,	PUNCT
ejpam-5213	541	6	2008	2008	NUM
ejpam-5213	541	7	.	.	PUNCT
ejpam-5213	542	1	[	[	X
ejpam-5213	542	2	7	7	X
ejpam-5213	542	3	]	]	X
ejpam-5213	542	4	t.w	t.w	PROPN
ejpam-5213	542	5	.	.	PROPN
ejpam-5213	542	6	haynes	haynes	PROPN
ejpam-5213	542	7	,	,	PUNCT
ejpam-5213	542	8	s.	s.	PROPN
ejpam-5213	542	9	hedetniemi	hedetniemi	PROPN
ejpam-5213	542	10	,	,	PUNCT
ejpam-5213	542	11	and	and	CCONJ
ejpam-5213	542	12	p.	p.	PROPN
ejpam-5213	542	13	slater	slater	PROPN
ejpam-5213	542	14	.	.	PUNCT
ejpam-5213	543	1	fundamentals	fundamental	NOUN
ejpam-5213	543	2	of	of	ADP
ejpam-5213	543	3	domination	domination	NOUN
ejpam-5213	543	4	in	in	ADP
ejpam-5213	543	5	graphs	graph	NOUN
ejpam-5213	543	6	.	.	PUNCT
ejpam-5213	544	1	crc	crc	PROPN
ejpam-5213	544	2	press	press	PROPN
ejpam-5213	544	3	,	,	PUNCT
ejpam-5213	544	4	2013	2013	NUM
ejpam-5213	544	5	.	.	PUNCT
ejpam-5213	545	1	[	[	X
ejpam-5213	545	2	8	8	NUM
ejpam-5213	545	3	]	]	X
ejpam-5213	545	4	w.	w.	PROPN
ejpam-5213	545	5	haynes	haynes	PROPN
ejpam-5213	545	6	,	,	PUNCT
ejpam-5213	545	7	m.	m.	NOUN
ejpam-5213	545	8	henning	henning	PROPN
ejpam-5213	545	9	,	,	PUNCT
ejpam-5213	545	10	and	and	CCONJ
ejpam-5213	545	11	j.	j.	PROPN
ejpam-5213	545	12	howard	howard	PROPN
ejpam-5213	545	13	.	.	PUNCT
ejpam-5213	546	1	locating	locate	VERB
ejpam-5213	546	2	and	and	CCONJ
ejpam-5213	546	3	total	total	ADJ
ejpam-5213	546	4	dominating	dominating	NOUN
ejpam-5213	546	5	sets	set	NOUN
ejpam-5213	546	6	in	in	ADP
ejpam-5213	546	7	trees	tree	NOUN
ejpam-5213	546	8	.	.	PUNCT
ejpam-5213	547	1	discrete	discrete	ADJ
ejpam-5213	547	2	applied	apply	VERB
ejpam-5213	547	3	mathematics	mathematic	NOUN
ejpam-5213	547	4	,	,	PUNCT
ejpam-5213	547	5	154:1293–1300	154:1293–1300	NUM
ejpam-5213	547	6	,	,	PUNCT
ejpam-5213	547	7	2006	2006	NUM
ejpam-5213	547	8	.	.	PUNCT
ejpam-5213	548	1	[	[	X
ejpam-5213	548	2	9	9	NUM
ejpam-5213	548	3	]	]	X
ejpam-5213	548	4	m.	m.	NOUN
ejpam-5213	548	5	henning	henning	PROPN
ejpam-5213	548	6	and	and	CCONJ
ejpam-5213	548	7	n.	n.	PROPN
ejpam-5213	548	8	rad	rad	PROPN
ejpam-5213	548	9	.	.	PROPN
ejpam-5213	548	10	locatingtotal	locatingtotal	ADJ
ejpam-5213	548	11	domination	domination	NOUN
ejpam-5213	548	12	in	in	ADP
ejpam-5213	548	13	graphs	graph	NOUN
ejpam-5213	548	14	.	.	PUNCT
ejpam-5213	549	1	discrete	discrete	ADJ
ejpam-5213	549	2	applied	apply	VERB
ejpam-5213	549	3	mathematics	mathematic	NOUN
ejpam-5213	549	4	,	,	PUNCT
ejpam-5213	549	5	160:1986–1993	160:1986–1993	NUM
ejpam-5213	549	6	,	,	PUNCT
ejpam-5213	549	7	2012	2012	NUM
ejpam-5213	549	8	.	.	PUNCT
ejpam-5213	550	1	[	[	X
ejpam-5213	550	2	10	10	NUM
ejpam-5213	550	3	]	]	X
ejpam-5213	550	4	r.	r.	PROPN
ejpam-5213	550	5	hinampas	hinampas	PROPN
ejpam-5213	550	6	jr	jr	PROPN
ejpam-5213	550	7	.	.	PROPN
ejpam-5213	550	8	and	and	CCONJ
ejpam-5213	550	9	s.	s.	PROPN
ejpam-5213	550	10	canoy	canoy	PROPN
ejpam-5213	550	11	jr	jr	PROPN
ejpam-5213	550	12	.	.	PROPN
ejpam-5213	550	13	1	1	NUM
ejpam-5213	550	14	-	-	PUNCT
ejpam-5213	550	15	movable	movable	ADJ
ejpam-5213	550	16	domination	domination	NOUN
ejpam-5213	550	17	in	in	ADP
ejpam-5213	550	18	graphs	graph	NOUN
ejpam-5213	550	19	.	.	PUNCT
ejpam-5213	550	20	applied	apply	VERB
ejpam-5213	550	21	mathematical	mathematical	ADJ
ejpam-5213	550	22	sciences	sciences	PROPN
ejpam-5213	550	23	,	,	PUNCT
ejpam-5213	550	24	8(172):8565–8571	8(172):8565–8571	NUM
ejpam-5213	550	25	,	,	PUNCT
ejpam-5213	550	26	2014	2014	NUM
ejpam-5213	550	27	.	.	PUNCT
ejpam-5213	551	1	[	[	X
ejpam-5213	551	2	11	11	NUM
ejpam-5213	551	3	]	]	X
ejpam-5213	551	4	s.	s.	PROPN
ejpam-5213	551	5	canoy	canoy	PROPN
ejpam-5213	551	6	jr	jr	PROPN
ejpam-5213	551	7	and	and	CCONJ
ejpam-5213	551	8	g.	g.	PROPN
ejpam-5213	551	9	malacas	malacas	PROPN
ejpam-5213	551	10	.	.	PUNCT
ejpam-5213	552	1	determining	determine	VERB
ejpam-5213	552	2	the	the	DET
ejpam-5213	552	3	intruder	intruder	NOUN
ejpam-5213	552	4	’s	’s	PART
ejpam-5213	552	5	location	location	NOUN
ejpam-5213	552	6	in	in	ADP
ejpam-5213	552	7	a	a	DET
ejpam-5213	552	8	given	give	VERB
ejpam-5213	552	9	network	network	NOUN
ejpam-5213	552	10	:	:	PUNCT
ejpam-5213	552	11	locating	locate	VERB
ejpam-5213	552	12	-	-	PUNCT
ejpam-5213	552	13	dominating	dominating	NOUN
ejpam-5213	552	14	sets	set	NOUN
ejpam-5213	552	15	in	in	ADP
ejpam-5213	552	16	a	a	DET
ejpam-5213	552	17	graph	graph	NOUN
ejpam-5213	552	18	.	.	PUNCT
ejpam-5213	553	1	nrcp	nrcp	PROPN
ejpam-5213	553	2	research	research	PROPN
ejpam-5213	553	3	journal	journal	PROPN
ejpam-5213	553	4	,	,	PUNCT
ejpam-5213	553	5	13(1):1–8	13(1):1–8	NUM
ejpam-5213	553	6	,	,	PUNCT
ejpam-5213	553	7	2013	2013	NUM
ejpam-5213	553	8	.	.	PUNCT
ejpam-5213	554	1	[	[	X
ejpam-5213	554	2	12	12	NUM
ejpam-5213	554	3	]	]	X
ejpam-5213	554	4	s.	s.	PROPN
ejpam-5213	554	5	canoy	canoy	PROPN
ejpam-5213	554	6	jr	jr	PROPN
ejpam-5213	554	7	and	and	CCONJ
ejpam-5213	554	8	g.	g.	PROPN
ejpam-5213	554	9	malacas	malacas	PROPN
ejpam-5213	554	10	.	.	PUNCT
ejpam-5213	555	1	differentiating	differentiate	VERB
ejpam-5213	555	2	-	-	PUNCT
ejpam-5213	555	3	dominating	dominating	NOUN
ejpam-5213	555	4	sets	set	NOUN
ejpam-5213	555	5	in	in	ADP
ejpam-5213	555	6	graphs	graph	NOUN
ejpam-5213	555	7	under	under	ADP
ejpam-5213	555	8	binary	binary	ADJ
ejpam-5213	555	9	operations	operation	NOUN
ejpam-5213	555	10	.	.	PUNCT
ejpam-5213	556	1	tamkang	tamkang	PROPN
ejpam-5213	556	2	journal	journal	PROPN
ejpam-5213	556	3	of	of	ADP
ejpam-5213	556	4	mathematics	mathematic	NOUN
ejpam-5213	556	5	,	,	PUNCT
ejpam-5213	556	6	46(1):51–60	46(1):51–60	NOUN
ejpam-5213	556	7	,	,	PUNCT
ejpam-5213	556	8	2015	2015	NUM
ejpam-5213	556	9	.	.	PUNCT
ejpam-5213	557	1	[	[	X
ejpam-5213	557	2	13	13	NUM
ejpam-5213	557	3	]	]	X
ejpam-5213	557	4	m.a	m.a	PROPN
ejpam-5213	557	5	.	.	PROPN
ejpam-5213	557	6	labendia	labendia	PROPN
ejpam-5213	557	7	and	and	CCONJ
ejpam-5213	557	8	s.r	s.r	PROPN
ejpam-5213	557	9	.	.	PROPN
ejpam-5213	557	10	canoy	canoy	PROPN
ejpam-5213	557	11	.	.	PUNCT
ejpam-5213	558	1	convex	convex	PROPN
ejpam-5213	558	2	dominatioin	dominatioin	NOUN
ejpam-5213	558	3	in	in	ADP
ejpam-5213	558	4	the	the	DET
ejpam-5213	558	5	composition	composition	NOUN
ejpam-5213	558	6	and	and	CCONJ
ejpam-5213	558	7	cartesian	cartesian	ADJ
ejpam-5213	558	8	product	product	NOUN
ejpam-5213	558	9	of	of	ADP
ejpam-5213	558	10	graphs	graph	NOUN
ejpam-5213	558	11	.	.	PUNCT
ejpam-5213	559	1	czechoslovak	czechoslovak	ADJ
ejpam-5213	559	2	mathematical	mathematical	PROPN
ejpam-5213	559	3	journal	journal	PROPN
ejpam-5213	559	4	,	,	PUNCT
ejpam-5213	559	5	62:1003–1009	62:1003–1009	NUM
ejpam-5213	559	6	,	,	PUNCT
ejpam-5213	559	7	2012	2012	NUM
ejpam-5213	559	8	.	.	PUNCT
ejpam-5213	560	1	[	[	X
ejpam-5213	560	2	14	14	NUM
ejpam-5213	560	3	]	]	PUNCT
ejpam-5213	560	4	m.	m.	NOUN
ejpam-5213	560	5	lemanska	lemanska	PROPN
ejpam-5213	560	6	.	.	PUNCT
ejpam-5213	561	1	weakly	weakly	ADJ
ejpam-5213	561	2	convex	convex	NOUN
ejpam-5213	561	3	and	and	CCONJ
ejpam-5213	561	4	convex	convex	ADJ
ejpam-5213	561	5	domination	domination	NOUN
ejpam-5213	561	6	numbers	number	NOUN
ejpam-5213	561	7	.	.	PUNCT
ejpam-5213	562	1	opuscula	opuscula	PROPN
ejpam-5213	562	2	mathematica	mathematica	PROPN
ejpam-5213	562	3	,	,	PUNCT
ejpam-5213	562	4	24(2):181–188	24(2):181–188	PROPN
ejpam-5213	562	5	,	,	PUNCT
ejpam-5213	562	6	2004	2004	NUM
ejpam-5213	562	7	.	.	PUNCT
ejpam-5213	563	1	[	[	X
ejpam-5213	563	2	15	15	NUM
ejpam-5213	563	3	]	]	X
ejpam-5213	563	4	b.	b.	NOUN
ejpam-5213	563	5	omamalin	omamalin	PROPN
ejpam-5213	563	6	,	,	PUNCT
ejpam-5213	563	7	s.	s.	PROPN
ejpam-5213	563	8	canoy	canoy	PROPN
ejpam-5213	563	9	jr	jr	PROPN
ejpam-5213	563	10	,	,	PUNCT
ejpam-5213	563	11	and	and	CCONJ
ejpam-5213	563	12	h.	h.	PROPN
ejpam-5213	563	13	rara	rara	PROPN
ejpam-5213	563	14	.	.	PUNCT
ejpam-5213	564	1	differentiating	differentiate	VERB
ejpam-5213	564	2	total	total	ADJ
ejpam-5213	564	3	domination	domination	NOUN
ejpam-5213	564	4	in	in	ADP
ejpam-5213	564	5	graphs	graph	NOUN
ejpam-5213	564	6	:	:	PUNCT
ejpam-5213	564	7	revisited	revisit	VERB
ejpam-5213	564	8	.	.	PUNCT
ejpam-5213	565	1	international	international	ADJ
ejpam-5213	565	2	journal	journal	PROPN
ejpam-5213	565	3	of	of	ADP
ejpam-5213	565	4	mathematical	mathematical	ADJ
ejpam-5213	565	5	analysis	analysis	NOUN
ejpam-5213	565	6	,	,	PUNCT
ejpam-5213	565	7	8(56):2789–2798	8(56):2789–2798	NUM
ejpam-5213	565	8	,	,	PUNCT
ejpam-5213	565	9	2014	2014	NUM
ejpam-5213	565	10	.	.	PUNCT
ejpam-5213	566	1	[	[	X
ejpam-5213	566	2	16	16	NUM
ejpam-5213	566	3	]	]	PUNCT
ejpam-5213	566	4	b.	b.	PROPN
ejpam-5213	566	5	omamalin	omamalin	PROPN
ejpam-5213	566	6	,	,	PUNCT
ejpam-5213	566	7	s.	s.	PROPN
ejpam-5213	566	8	canoy	canoy	PROPN
ejpam-5213	566	9	jr	jr	PROPN
ejpam-5213	566	10	,	,	PUNCT
ejpam-5213	566	11	and	and	CCONJ
ejpam-5213	566	12	m.	m.	NOUN
ejpam-5213	566	13	rara	rara	PROPN
ejpam-5213	566	14	.	.	PUNCT
ejpam-5213	567	1	differentiating	differentiate	VERB
ejpam-5213	567	2	total	total	ADJ
ejpam-5213	567	3	dominating	dominating	NOUN
ejpam-5213	567	4	sets	set	NOUN
ejpam-5213	567	5	in	in	ADP
ejpam-5213	567	6	the	the	DET
ejpam-5213	567	7	join	join	NOUN
ejpam-5213	567	8	,	,	PUNCT
ejpam-5213	567	9	corona	corona	NOUN
ejpam-5213	567	10	and	and	CCONJ
ejpam-5213	567	11	composition	composition	NOUN
ejpam-5213	567	12	of	of	ADP
ejpam-5213	567	13	graphs	graph	NOUN
ejpam-5213	567	14	.	.	PUNCT
ejpam-5213	568	1	international	international	ADJ
ejpam-5213	568	2	journal	journal	PROPN
ejpam-5213	568	3	of	of	ADP
ejpam-5213	568	4	mathematical	mathematical	ADJ
ejpam-5213	568	5	analysis	analysis	NOUN
ejpam-5213	568	6	,	,	PUNCT
ejpam-5213	568	7	8:1275–1284	8:1275–1284	NUM
ejpam-5213	568	8	,	,	PUNCT
ejpam-5213	568	9	2014	2014	NUM
ejpam-5213	568	10	.	.	PUNCT
ejpam-5213	569	1	[	[	X
ejpam-5213	569	2	17	17	NUM
ejpam-5213	569	3	]	]	PUNCT
ejpam-5213	569	4	b.	b.	PROPN
ejpam-5213	569	5	omamalin	omamalin	PROPN
ejpam-5213	569	6	,	,	PUNCT
ejpam-5213	569	7	h.	h.	PROPN
ejpam-5213	569	8	rara	rara	PROPN
ejpam-5213	569	9	,	,	PUNCT
ejpam-5213	569	10	and	and	CCONJ
ejpam-5213	569	11	s.	s.	PROPN
ejpam-5213	569	12	canoy	canoy	PROPN
ejpam-5213	569	13	jr	jr	PROPN
ejpam-5213	569	14	.	.	AUX
ejpam-5213	569	15	locating	locate	VERB
ejpam-5213	569	16	total	total	ADJ
ejpam-5213	569	17	dominating	dominating	NOUN
ejpam-5213	569	18	sets	set	NOUN
ejpam-5213	569	19	in	in	ADP
ejpam-5213	569	20	the	the	DET
ejpam-5213	569	21	join	join	NOUN
ejpam-5213	569	22	,	,	PUNCT
ejpam-5213	569	23	corona	corona	NOUN
ejpam-5213	569	24	and	and	CCONJ
ejpam-5213	569	25	composition	composition	NOUN
ejpam-5213	569	26	of	of	ADP
ejpam-5213	569	27	graphs	graph	NOUN
ejpam-5213	569	28	.	.	PUNCT
ejpam-5213	570	1	applied	apply	VERB
ejpam-5213	570	2	mathematical	mathematical	ADJ
ejpam-5213	570	3	sciences	science	NOUN
ejpam-5213	570	4	,	,	PUNCT
ejpam-5213	570	5	8(48):2363–2374	8(48):2363–2374	NUM
ejpam-5213	570	6	,	,	PUNCT
ejpam-5213	570	7	2014	2014	NUM
ejpam-5213	570	8	.	.	PUNCT
ejpam-5213	571	1	[	[	X
ejpam-5213	571	2	18	18	NUM
ejpam-5213	571	3	]	]	X
ejpam-5213	571	4	g.	g.	NOUN
ejpam-5213	571	5	salasalan	salasalan	NOUN
ejpam-5213	571	6	and	and	CCONJ
ejpam-5213	571	7	s.	s.	PROPN
ejpam-5213	571	8	canoy	canoy	PROPN
ejpam-5213	571	9	jr	jr	PROPN
ejpam-5213	571	10	.	.	PROPN
ejpam-5213	571	11	global	global	PROPN
ejpam-5213	571	12	hop	hop	PROPN
ejpam-5213	571	13	domination	domination	PROPN
ejpam-5213	571	14	numbers	number	NOUN
ejpam-5213	571	15	of	of	ADP
ejpam-5213	571	16	graphs	graph	NOUN
ejpam-5213	571	17	.	.	PUNCT
ejpam-5213	572	1	european	european	ADJ
ejpam-5213	572	2	journal	journal	PROPN
ejpam-5213	572	3	of	of	ADP
ejpam-5213	572	4	pure	pure	ADJ
ejpam-5213	572	5	and	and	CCONJ
ejpam-5213	572	6	applied	applied	ADJ
ejpam-5213	572	7	mathematics	mathematic	NOUN
ejpam-5213	572	8	,	,	PUNCT
ejpam-5213	572	9	14(1):112–125	14(1):112–125	NUM
ejpam-5213	572	10	,	,	PUNCT
ejpam-5213	572	11	2021	2021	NUM
ejpam-5213	572	12	.	.	PUNCT
ejpam-5213	573	1	references	reference	NOUN
ejpam-5213	573	2	1601	1601	NUM
ejpam-5213	573	3	[	[	X
ejpam-5213	573	4	19	19	NUM
ejpam-5213	573	5	]	]	PUNCT
ejpam-5213	573	6	k.	k.	PROPN
ejpam-5213	573	7	sutner	sutner	PROPN
ejpam-5213	573	8	.	.	PUNCT
ejpam-5213	574	1	linear	linear	ADJ
ejpam-5213	574	2	cellular	cellular	ADJ
ejpam-5213	574	3	automata	automata	NOUN
ejpam-5213	574	4	and	and	CCONJ
ejpam-5213	574	5	the	the	DET
ejpam-5213	574	6	garden	garden	NOUN
ejpam-5213	574	7	-	-	PUNCT
ejpam-5213	574	8	of	of	ADP
ejpam-5213	574	9	-	-	PUNCT
ejpam-5213	574	10	eden	eden	NOUN
ejpam-5213	574	11	.	.	PUNCT
ejpam-5213	575	1	the	the	DET
ejpam-5213	575	2	mathematical	mathematical	ADJ
ejpam-5213	575	3	intelligence	intelligence	NOUN
ejpam-5213	575	4	,	,	PUNCT
ejpam-5213	575	5	11(2):49–53	11(2):49–53	NUM
ejpam-5213	575	6	,	,	PUNCT
ejpam-5213	575	7	1989	1989	NUM
ejpam-5213	575	8	.	.	PUNCT