id	sid	tid	token	lemma	pos
ejpam-4187	1	1	european	european	PROPN
ejpam-4187	1	2	journal	journal	PROPN
ejpam-4187	1	3	of	of	ADP
ejpam-4187	1	4	pure	pure	ADJ
ejpam-4187	1	5	and	and	CCONJ
ejpam-4187	1	6	applied	apply	VERB
ejpam-4187	1	7	mathematics	mathematic	NOUN
ejpam-4187	1	8	vol	vol	NOUN
ejpam-4187	1	9	.	.	PROPN
ejpam-4187	2	1	15	15	NUM
ejpam-4187	2	2	,	,	PUNCT
ejpam-4187	2	3	no	no	INTJ
ejpam-4187	2	4	.	.	NOUN
ejpam-4187	2	5	1	1	NUM
ejpam-4187	2	6	,	,	PUNCT
ejpam-4187	2	7	2022	2022	NUM
ejpam-4187	2	8	,	,	PUNCT
ejpam-4187	2	9	207	207	NUM
ejpam-4187	2	10	-	-	SYM
ejpam-4187	2	11	223	223	NUM
ejpam-4187	2	12	issn	issn	PROPN
ejpam-4187	2	13	1307	1307	NUM
ejpam-4187	2	14	-	-	SYM
ejpam-4187	2	15	5543	5543	NUM
ejpam-4187	2	16	–	–	PUNCT
ejpam-4187	2	17	ejpam.com	ejpam.com	X
ejpam-4187	2	18	published	publish	VERB
ejpam-4187	2	19	by	by	ADP
ejpam-4187	2	20	new	new	PROPN
ejpam-4187	2	21	york	york	PROPN
ejpam-4187	2	22	business	business	PROPN
ejpam-4187	2	23	global	global	ADJ
ejpam-4187	2	24	restrained	restrain	VERB
ejpam-4187	2	25	disjunctive	disjunctive	ADJ
ejpam-4187	2	26	domination	domination	NOUN
ejpam-4187	2	27	in	in	ADP
ejpam-4187	2	28	graphs	graph	NOUN
ejpam-4187	2	29	under	under	ADP
ejpam-4187	2	30	some	some	DET
ejpam-4187	2	31	binary	binary	ADJ
ejpam-4187	2	32	operations	operation	NOUN
ejpam-4187	2	33	rolando	rolando	PROPN
ejpam-4187	2	34	p.	p.	PROPN
ejpam-4187	2	35	malalay1,∗	malalay1,∗	PROPN
ejpam-4187	2	36	,	,	PUNCT
ejpam-4187	3	1	ferdinand	ferdinand	PROPN
ejpam-4187	3	2	p.	p.	PROPN
ejpam-4187	3	3	jamil2	jamil2	PROPN
ejpam-4187	4	1	1	1	NUM
ejpam-4187	4	2	college	college	NOUN
ejpam-4187	4	3	of	of	ADP
ejpam-4187	4	4	engineering	engineering	NOUN
ejpam-4187	4	5	and	and	CCONJ
ejpam-4187	4	6	technology	technology	NOUN
ejpam-4187	4	7	,	,	PUNCT
ejpam-4187	4	8	zamboanga	zamboanga	PROPN
ejpam-4187	4	9	peninsula	peninsula	PROPN
ejpam-4187	4	10	polytechnic	polytechnic	ADJ
ejpam-4187	4	11	state	state	NOUN
ejpam-4187	4	12	university	university	NOUN
ejpam-4187	4	13	,	,	PUNCT
ejpam-4187	4	14	7000	7000	NUM
ejpam-4187	4	15	zamboanga	zamboanga	PROPN
ejpam-4187	4	16	city	city	PROPN
ejpam-4187	4	17	,	,	PUNCT
ejpam-4187	4	18	philippines	philippines	PROPN
ejpam-4187	4	19	2	2	NUM
ejpam-4187	4	20	department	department	NOUN
ejpam-4187	4	21	of	of	ADP
ejpam-4187	4	22	mathematics	mathematic	NOUN
ejpam-4187	4	23	and	and	CCONJ
ejpam-4187	4	24	statistics	statistic	NOUN
ejpam-4187	4	25	,	,	PUNCT
ejpam-4187	4	26	college	college	NOUN
ejpam-4187	4	27	of	of	ADP
ejpam-4187	4	28	science	science	NOUN
ejpam-4187	4	29	and	and	CCONJ
ejpam-4187	4	30	mathematics	mathematic	NOUN
ejpam-4187	4	31	,	,	PUNCT
ejpam-4187	4	32	center	center	NOUN
ejpam-4187	4	33	of	of	ADP
ejpam-4187	4	34	graph	graph	NOUN
ejpam-4187	4	35	theory	theory	NOUN
ejpam-4187	4	36	,	,	PUNCT
ejpam-4187	4	37	algebra	algebra	NOUN
ejpam-4187	4	38	and	and	CCONJ
ejpam-4187	4	39	analysis	analysis	NOUN
ejpam-4187	4	40	,	,	PUNCT
ejpam-4187	4	41	premier	premier	PROPN
ejpam-4187	4	42	research	research	PROPN
ejpam-4187	4	43	institute	institute	PROPN
ejpam-4187	4	44	of	of	ADP
ejpam-4187	4	45	science	science	NOUN
ejpam-4187	4	46	and	and	CCONJ
ejpam-4187	4	47	mathematics	mathematic	NOUN
ejpam-4187	4	48	,	,	PUNCT
ejpam-4187	4	49	mindanao	mindanao	PROPN
ejpam-4187	4	50	state	state	PROPN
ejpam-4187	4	51	university	university	PROPN
ejpam-4187	4	52	-	-	PUNCT
ejpam-4187	4	53	iligan	iligan	PROPN
ejpam-4187	4	54	institute	institute	PROPN
ejpam-4187	4	55	of	of	ADP
ejpam-4187	4	56	technology	technology	PROPN
ejpam-4187	4	57	,	,	PUNCT
ejpam-4187	4	58	9200	9200	NUM
ejpam-4187	4	59	iligan	iligan	ADJ
ejpam-4187	4	60	city	city	NOUN
ejpam-4187	4	61	,	,	PUNCT
ejpam-4187	4	62	philippines	philippine	NOUN
ejpam-4187	4	63	abstract	abstract	ADJ
ejpam-4187	4	64	.	.	PUNCT
ejpam-4187	5	1	a	a	DET
ejpam-4187	5	2	set	set	NOUN
ejpam-4187	5	3	s	s	NOUN
ejpam-4187	5	4	⊆	⊆	NUM
ejpam-4187	5	5	v	v	NOUN
ejpam-4187	5	6	(	(	PUNCT
ejpam-4187	5	7	g	g	NOUN
ejpam-4187	5	8	)	)	PUNCT
ejpam-4187	5	9	is	be	AUX
ejpam-4187	5	10	a	a	DET
ejpam-4187	5	11	disjunctive	disjunctive	ADJ
ejpam-4187	5	12	dominating	dominating	NOUN
ejpam-4187	5	13	set	set	NOUN
ejpam-4187	5	14	of	of	ADP
ejpam-4187	5	15	a	a	DET
ejpam-4187	5	16	graph	graph	NOUN
ejpam-4187	5	17	g	g	NOUN
ejpam-4187	5	18	if	if	SCONJ
ejpam-4187	5	19	for	for	ADP
ejpam-4187	5	20	every	every	DET
ejpam-4187	5	21	v	v	NUM
ejpam-4187	5	22	∈	∈	NOUN
ejpam-4187	5	23	v	v	NOUN
ejpam-4187	5	24	(	(	PUNCT
ejpam-4187	5	25	g)\s	g)\s	NOUN
ejpam-4187	5	26	,	,	PUNCT
ejpam-4187	5	27	v	v	NOUN
ejpam-4187	5	28	is	be	AUX
ejpam-4187	5	29	a	a	DET
ejpam-4187	5	30	neighbor	neighbor	NOUN
ejpam-4187	5	31	of	of	ADP
ejpam-4187	5	32	a	a	DET
ejpam-4187	5	33	vertex	vertex	NOUN
ejpam-4187	5	34	in	in	ADP
ejpam-4187	5	35	s	s	PRON
ejpam-4187	5	36	or	or	CCONJ
ejpam-4187	5	37	s	s	NOUN
ejpam-4187	5	38	has	have	AUX
ejpam-4187	5	39	at	at	ADV
ejpam-4187	5	40	least	least	ADV
ejpam-4187	5	41	two	two	NUM
ejpam-4187	5	42	vertices	vertex	NOUN
ejpam-4187	5	43	each	each	PRON
ejpam-4187	5	44	at	at	ADP
ejpam-4187	5	45	distance	distance	NOUN
ejpam-4187	5	46	2	2	NUM
ejpam-4187	5	47	from	from	ADP
ejpam-4187	5	48	v.	v.	ADP
ejpam-4187	5	49	we	we	PRON
ejpam-4187	5	50	say	say	VERB
ejpam-4187	5	51	that	that	SCONJ
ejpam-4187	5	52	a	a	DET
ejpam-4187	5	53	disjunctive	disjunctive	ADJ
ejpam-4187	5	54	dominating	dominating	NOUN
ejpam-4187	5	55	set	set	NOUN
ejpam-4187	5	56	s	s	NOUN
ejpam-4187	5	57	of	of	ADP
ejpam-4187	5	58	g	g	PROPN
ejpam-4187	5	59	is	be	AUX
ejpam-4187	5	60	a	a	DET
ejpam-4187	5	61	restrained	restrained	ADJ
ejpam-4187	5	62	disjunctive	disjunctive	ADJ
ejpam-4187	5	63	dominating	dominating	NOUN
ejpam-4187	5	64	set	set	VERB
ejpam-4187	5	65	if	if	SCONJ
ejpam-4187	5	66	for	for	ADP
ejpam-4187	5	67	each	each	DET
ejpam-4187	5	68	v	v	NUM
ejpam-4187	5	69	∈	∈	NOUN
ejpam-4187	5	70	v	v	NOUN
ejpam-4187	5	71	(	(	PUNCT
ejpam-4187	5	72	g)\s	g)\s	NOUN
ejpam-4187	5	73	there	there	ADV
ejpam-4187	5	74	exists	exist	VERB
ejpam-4187	5	75	u	u	PROPN
ejpam-4187	5	76	∈	∈	PROPN
ejpam-4187	5	77	v	v	ADP
ejpam-4187	5	78	(	(	PUNCT
ejpam-4187	5	79	g	g	NOUN
ejpam-4187	5	80	)	)	PUNCT
ejpam-4187	5	81	\	\	PUNCT
ejpam-4187	6	1	s	s	VERB
ejpam-4187	6	2	such	such	ADJ
ejpam-4187	6	3	that	that	DET
ejpam-4187	6	4	uv	uv	PROPN
ejpam-4187	6	5	∈	∈	PROPN
ejpam-4187	6	6	e(g	e(g	PROPN
ejpam-4187	6	7	)	)	PUNCT
ejpam-4187	6	8	or	or	CCONJ
ejpam-4187	6	9	there	there	PRON
ejpam-4187	6	10	exist	exist	VERB
ejpam-4187	6	11	distinct	distinct	ADJ
ejpam-4187	6	12	vertices	vertex	NOUN
ejpam-4187	6	13	u	u	NOUN
ejpam-4187	6	14	,	,	PUNCT
ejpam-4187	6	15	w	w	PROPN
ejpam-4187	6	16	∈	∈	PROPN
ejpam-4187	6	17	v	v	ADP
ejpam-4187	6	18	(	(	PUNCT
ejpam-4187	6	19	g	g	NOUN
ejpam-4187	6	20	)	)	PUNCT
ejpam-4187	6	21	\	\	PUNCT
ejpam-4187	7	1	s	s	VERB
ejpam-4187	7	2	such	such	ADJ
ejpam-4187	7	3	that	that	DET
ejpam-4187	7	4	dg(u	dg(u	ADJ
ejpam-4187	7	5	,	,	PUNCT
ejpam-4187	7	6	v	v	NOUN
ejpam-4187	7	7	)	)	PUNCT
ejpam-4187	7	8	=	=	SYM
ejpam-4187	7	9	2	2	NUM
ejpam-4187	7	10	=	=	SYM
ejpam-4187	7	11	dg(w	dg(w	X
ejpam-4187	7	12	,	,	PUNCT
ejpam-4187	7	13	v	v	NOUN
ejpam-4187	7	14	)	)	PUNCT
ejpam-4187	7	15	.	.	PUNCT
ejpam-4187	8	1	the	the	DET
ejpam-4187	8	2	minimum	minimum	ADJ
ejpam-4187	8	3	cardinality	cardinality	NOUN
ejpam-4187	8	4	γd	γd	ADP
ejpam-4187	8	5	r	r	NOUN
ejpam-4187	8	6	(	(	PUNCT
ejpam-4187	8	7	g	g	NOUN
ejpam-4187	8	8	)	)	PUNCT
ejpam-4187	8	9	of	of	ADP
ejpam-4187	8	10	a	a	DET
ejpam-4187	8	11	restrained	restrained	ADJ
ejpam-4187	8	12	disjunctive	disjunctive	ADJ
ejpam-4187	8	13	dominating	dominating	NOUN
ejpam-4187	8	14	set	set	NOUN
ejpam-4187	8	15	of	of	ADP
ejpam-4187	8	16	g	g	PROPN
ejpam-4187	8	17	is	be	AUX
ejpam-4187	8	18	the	the	DET
ejpam-4187	8	19	restrained	restrain	VERB
ejpam-4187	8	20	disjunctive	disjunctive	ADJ
ejpam-4187	8	21	domination	domination	NOUN
ejpam-4187	8	22	number	number	NOUN
ejpam-4187	8	23	of	of	ADP
ejpam-4187	8	24	g.	g.	PROPN
ejpam-4187	8	25	in	in	ADP
ejpam-4187	8	26	this	this	DET
ejpam-4187	8	27	paper	paper	NOUN
ejpam-4187	8	28	,	,	PUNCT
ejpam-4187	8	29	we	we	PRON
ejpam-4187	8	30	characterize	characterize	VERB
ejpam-4187	8	31	the	the	DET
ejpam-4187	8	32	restrained	restrained	ADJ
ejpam-4187	8	33	disjunctive	disjunctive	ADJ
ejpam-4187	8	34	dominating	dominating	NOUN
ejpam-4187	8	35	sets	set	NOUN
ejpam-4187	8	36	in	in	ADP
ejpam-4187	8	37	some	some	DET
ejpam-4187	8	38	binary	binary	ADJ
ejpam-4187	8	39	operations	operation	NOUN
ejpam-4187	8	40	such	such	ADJ
ejpam-4187	8	41	as	as	ADP
ejpam-4187	8	42	the	the	DET
ejpam-4187	8	43	join	join	NOUN
ejpam-4187	8	44	,	,	PUNCT
ejpam-4187	8	45	corona	corona	NOUN
ejpam-4187	8	46	and	and	CCONJ
ejpam-4187	8	47	lexicographic	lexicographic	ADJ
ejpam-4187	8	48	product	product	NOUN
ejpam-4187	8	49	of	of	ADP
ejpam-4187	8	50	graphs	graph	NOUN
ejpam-4187	8	51	and	and	CCONJ
ejpam-4187	8	52	,	,	PUNCT
ejpam-4187	8	53	as	as	ADP
ejpam-4187	8	54	a	a	DET
ejpam-4187	8	55	result	result	NOUN
ejpam-4187	8	56	,	,	PUNCT
ejpam-4187	8	57	obtain	obtain	VERB
ejpam-4187	8	58	the	the	DET
ejpam-4187	8	59	values	value	NOUN
ejpam-4187	8	60	of	of	ADP
ejpam-4187	8	61	their	their	PRON
ejpam-4187	8	62	corresponding	corresponding	ADJ
ejpam-4187	8	63	restrained	restrain	VERB
ejpam-4187	8	64	disjunctive	disjunctive	ADJ
ejpam-4187	8	65	domination	domination	NOUN
ejpam-4187	8	66	numbers	number	NOUN
ejpam-4187	8	67	.	.	PUNCT
ejpam-4187	9	1	2020	2020	NUM
ejpam-4187	9	2	mathematics	mathematic	NOUN
ejpam-4187	9	3	subject	subject	NOUN
ejpam-4187	9	4	classifications	classification	NOUN
ejpam-4187	9	5	:	:	PUNCT
ejpam-4187	9	6	05c69	05c69	X
ejpam-4187	9	7	key	key	ADJ
ejpam-4187	9	8	words	word	NOUN
ejpam-4187	9	9	and	and	CCONJ
ejpam-4187	9	10	phrases	phrase	NOUN
ejpam-4187	9	11	:	:	PUNCT
ejpam-4187	9	12	disjunctive	disjunctive	ADJ
ejpam-4187	9	13	dominating	dominating	NOUN
ejpam-4187	9	14	set	set	NOUN
ejpam-4187	9	15	,	,	PUNCT
ejpam-4187	9	16	restrained	restrain	VERB
ejpam-4187	9	17	disjunctive	disjunctive	ADJ
ejpam-4187	9	18	dominating	dominating	NOUN
ejpam-4187	9	19	set	set	NOUN
ejpam-4187	9	20	,	,	PUNCT
ejpam-4187	9	21	restrained	restrain	VERB
ejpam-4187	9	22	disjunctive	disjunctive	ADJ
ejpam-4187	9	23	domination	domination	NOUN
ejpam-4187	9	24	number	number	NOUN
ejpam-4187	9	25	,	,	PUNCT
ejpam-4187	9	26	join	join	NOUN
ejpam-4187	9	27	,	,	PUNCT
ejpam-4187	9	28	corona	corona	NOUN
ejpam-4187	9	29	and	and	CCONJ
ejpam-4187	9	30	lexicographic	lexicographic	ADJ
ejpam-4187	9	31	product	product	NOUN
ejpam-4187	9	32	1	1	NUM
ejpam-4187	9	33	.	.	PUNCT
ejpam-4187	9	34	introduction	introduction	NOUN
ejpam-4187	9	35	the	the	DET
ejpam-4187	9	36	study	study	NOUN
ejpam-4187	9	37	of	of	ADP
ejpam-4187	9	38	restrained	restrained	ADJ
ejpam-4187	9	39	domination	domination	NOUN
ejpam-4187	9	40	in	in	ADP
ejpam-4187	9	41	graphs	graph	NOUN
ejpam-4187	9	42	was	be	AUX
ejpam-4187	9	43	first	first	ADV
ejpam-4187	9	44	initiated	initiate	VERB
ejpam-4187	9	45	by	by	ADP
ejpam-4187	9	46	domke	domke	PROPN
ejpam-4187	9	47	et	et	PROPN
ejpam-4187	9	48	al	al	PROPN
ejpam-4187	9	49	.	.	PUNCT
ejpam-4187	10	1	[	[	X
ejpam-4187	10	2	6	6	NUM
ejpam-4187	10	3	]	]	PUNCT
ejpam-4187	10	4	in	in	ADP
ejpam-4187	10	5	1997	1997	NUM
ejpam-4187	10	6	.	.	PUNCT
ejpam-4187	11	1	accordingly	accordingly	ADV
ejpam-4187	11	2	,	,	PUNCT
ejpam-4187	11	3	they	they	PRON
ejpam-4187	11	4	established	establish	VERB
ejpam-4187	11	5	the	the	DET
ejpam-4187	11	6	best	good	ADJ
ejpam-4187	11	7	possible	possible	ADJ
ejpam-4187	11	8	upper	upper	ADJ
ejpam-4187	11	9	and	and	CCONJ
ejpam-4187	11	10	lower	low	ADJ
ejpam-4187	11	11	bounds	bound	NOUN
ejpam-4187	11	12	for	for	ADP
ejpam-4187	11	13	the	the	DET
ejpam-4187	11	14	restrained	restrain	VERB
ejpam-4187	11	15	domination	domination	NOUN
ejpam-4187	11	16	number	number	NOUN
ejpam-4187	11	17	of	of	ADP
ejpam-4187	11	18	a	a	DET
ejpam-4187	11	19	connected	connected	ADJ
ejpam-4187	11	20	graph	graph	NOUN
ejpam-4187	11	21	g	g	PROPN
ejpam-4187	11	22	and	and	CCONJ
ejpam-4187	11	23	characterized	characterize	VERB
ejpam-4187	11	24	those	those	DET
ejpam-4187	11	25	graphs	graph	NOUN
ejpam-4187	11	26	achieving	achieve	VERB
ejpam-4187	11	27	these	these	DET
ejpam-4187	11	28	bounds	bound	NOUN
ejpam-4187	11	29	.	.	PUNCT
ejpam-4187	12	1	in	in	ADP
ejpam-4187	12	2	[	[	X
ejpam-4187	12	3	16	16	NUM
ejpam-4187	12	4	]	]	PUNCT
ejpam-4187	12	5	,	,	PUNCT
ejpam-4187	12	6	the	the	DET
ejpam-4187	12	7	restrained	restrain	VERB
ejpam-4187	12	8	dominating	dominating	NOUN
ejpam-4187	12	9	set	set	NOUN
ejpam-4187	12	10	of	of	ADP
ejpam-4187	12	11	trees	tree	NOUN
ejpam-4187	12	12	of	of	ADP
ejpam-4187	12	13	order	order	NOUN
ejpam-4187	12	14	n	n	PRON
ejpam-4187	12	15	were	be	AUX
ejpam-4187	12	16	characterized	characterize	VERB
ejpam-4187	12	17	,	,	PUNCT
ejpam-4187	12	18	and	and	CCONJ
ejpam-4187	12	19	the	the	DET
ejpam-4187	12	20	exact	exact	ADJ
ejpam-4187	12	21	values	value	NOUN
ejpam-4187	12	22	of	of	ADP
ejpam-4187	12	23	the	the	DET
ejpam-4187	12	24	restrained	restrain	VERB
ejpam-4187	12	25	domination	domination	NOUN
ejpam-4187	12	26	number	number	NOUN
ejpam-4187	12	27	were	be	AUX
ejpam-4187	12	28	determined	determine	VERB
ejpam-4187	12	29	.	.	PUNCT
ejpam-4187	13	1	some	some	DET
ejpam-4187	13	2	studies	study	NOUN
ejpam-4187	13	3	in	in	ADP
ejpam-4187	13	4	restrained	restrained	ADJ
ejpam-4187	13	5	domination	domination	NOUN
ejpam-4187	13	6	can	can	AUX
ejpam-4187	13	7	be	be	AUX
ejpam-4187	13	8	found	find	VERB
ejpam-4187	13	9	in	in	ADP
ejpam-4187	13	10	[	[	X
ejpam-4187	13	11	7	7	NUM
ejpam-4187	13	12	,	,	PUNCT
ejpam-4187	13	13	17	17	NUM
ejpam-4187	13	14	,	,	PUNCT
ejpam-4187	13	15	19	19	NUM
ejpam-4187	13	16	]	]	PUNCT
ejpam-4187	13	17	.	.	PUNCT
ejpam-4187	14	1	on	on	ADP
ejpam-4187	14	2	the	the	DET
ejpam-4187	14	3	other	other	ADJ
ejpam-4187	14	4	hand	hand	NOUN
ejpam-4187	14	5	,	,	PUNCT
ejpam-4187	14	6	disjunctive	disjunctive	ADJ
ejpam-4187	14	7	domination	domination	NOUN
ejpam-4187	14	8	in	in	ADP
ejpam-4187	14	9	graphs	graph	NOUN
ejpam-4187	14	10	,	,	PUNCT
ejpam-4187	14	11	specifically	specifically	ADV
ejpam-4187	14	12	b	b	NOUN
ejpam-4187	14	13	-	-	PUNCT
ejpam-4187	14	14	disjunctive	disjunctive	ADJ
ejpam-4187	14	15	,	,	PUNCT
ejpam-4187	14	16	first	first	ADV
ejpam-4187	14	17	introduced	introduce	VERB
ejpam-4187	14	18	by	by	ADP
ejpam-4187	14	19	goddard	goddard	PROPN
ejpam-4187	14	20	et	et	PROPN
ejpam-4187	14	21	al	al	PROPN
ejpam-4187	14	22	.	.	PUNCT
ejpam-4187	15	1	[	[	X
ejpam-4187	15	2	8	8	NUM
ejpam-4187	15	3	]	]	PUNCT
ejpam-4187	15	4	in	in	ADP
ejpam-4187	15	5	2014	2014	NUM
ejpam-4187	15	6	was	be	AUX
ejpam-4187	15	7	motivated	motivate	VERB
ejpam-4187	15	8	by	by	ADP
ejpam-4187	15	9	the	the	DET
ejpam-4187	15	10	concept	concept	NOUN
ejpam-4187	15	11	of	of	ADP
ejpam-4187	15	12	domination	domination	NOUN
ejpam-4187	15	13	∗corresponding	∗corresponde	VERB
ejpam-4187	15	14	author	author	NOUN
ejpam-4187	15	15	.	.	PUNCT
ejpam-4187	16	1	doi	doi	NOUN
ejpam-4187	16	2	:	:	PUNCT
ejpam-4187	17	1	https://doi.org/10.29020/nybg.ejpam.v15i1.4187	https://doi.org/10.29020/nybg.ejpam.v15i1.4187	ADJ
ejpam-4187	17	2	email	email	NOUN
ejpam-4187	17	3	addresses	address	VERB
ejpam-4187	17	4	:	:	PUNCT
ejpam-4187	17	5	orlandomalalay@gmail.com	orlandomalalay@gmail.com	X
ejpam-4187	17	6	(	(	PUNCT
ejpam-4187	17	7	r.	r.	PROPN
ejpam-4187	17	8	malalay	malalay	PROPN
ejpam-4187	17	9	)	)	PUNCT
ejpam-4187	17	10	,	,	PUNCT
ejpam-4187	17	11	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-4187	17	12	(	(	PUNCT
ejpam-4187	17	13	f.	f.	PROPN
ejpam-4187	17	14	jamil	jamil	PROPN
ejpam-4187	17	15	)	)	PUNCT
ejpam-4187	17	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4187	18	1	207	207	NUM
ejpam-4187	19	1	©	©	PROPN
ejpam-4187	19	2	2022	2022	NUM
ejpam-4187	19	3	ejpam	ejpam	VERB
ejpam-4187	19	4	all	all	DET
ejpam-4187	19	5	rights	right	NOUN
ejpam-4187	19	6	reserved	reserve	VERB
ejpam-4187	19	7	.	.	PUNCT
ejpam-4187	20	1	r.	r.	PROPN
ejpam-4187	20	2	malalay	malalay	PROPN
ejpam-4187	20	3	,	,	PUNCT
ejpam-4187	20	4	f.	f.	PROPN
ejpam-4187	20	5	jamil	jamil	PROPN
ejpam-4187	20	6	/	/	SYM
ejpam-4187	20	7	eur	eur	PROPN
ejpam-4187	20	8	.	.	PUNCT
ejpam-4187	21	1	j.	j.	PROPN
ejpam-4187	21	2	pure	pure	PROPN
ejpam-4187	21	3	appl	appl	PROPN
ejpam-4187	21	4	.	.	PROPN
ejpam-4187	21	5	math	math	PROPN
ejpam-4187	21	6	,	,	PUNCT
ejpam-4187	21	7	15	15	NUM
ejpam-4187	21	8	(	(	PUNCT
ejpam-4187	21	9	1	1	NUM
ejpam-4187	21	10	)	)	PUNCT
ejpam-4187	21	11	(	(	PUNCT
ejpam-4187	21	12	2022	2022	NUM
ejpam-4187	21	13	)	)	PUNCT
ejpam-4187	21	14	,	,	PUNCT
ejpam-4187	21	15	207	207	NUM
ejpam-4187	21	16	-	-	SYM
ejpam-4187	21	17	223	223	NUM
ejpam-4187	21	18	208	208	NUM
ejpam-4187	21	19	in	in	ADP
ejpam-4187	21	20	graphs	graph	NOUN
ejpam-4187	21	21	(	(	PUNCT
ejpam-4187	21	22	see	see	VERB
ejpam-4187	21	23	[	[	X
ejpam-4187	21	24	4	4	NUM
ejpam-4187	21	25	,	,	PUNCT
ejpam-4187	21	26	10	10	NUM
ejpam-4187	21	27	]	]	NUM
ejpam-4187	21	28	)	)	PUNCT
ejpam-4187	21	29	,	,	PUNCT
ejpam-4187	21	30	the	the	DET
ejpam-4187	21	31	distance	distance	NOUN
ejpam-4187	21	32	domination	domination	NOUN
ejpam-4187	21	33	(	(	PUNCT
ejpam-4187	21	34	see	see	VERB
ejpam-4187	21	35	[	[	X
ejpam-4187	21	36	5	5	NUM
ejpam-4187	21	37	]	]	PUNCT
ejpam-4187	21	38	)	)	PUNCT
ejpam-4187	21	39	and	and	CCONJ
ejpam-4187	21	40	the	the	DET
ejpam-4187	21	41	secondary	secondary	ADJ
ejpam-4187	21	42	domination	domination	NOUN
ejpam-4187	21	43	(	(	PUNCT
ejpam-4187	21	44	see	see	VERB
ejpam-4187	21	45	[	[	X
ejpam-4187	21	46	11	11	NUM
ejpam-4187	21	47	]	]	NUM
ejpam-4187	21	48	)	)	PUNCT
ejpam-4187	21	49	.	.	PUNCT
ejpam-4187	22	1	while	while	SCONJ
ejpam-4187	22	2	most	most	ADJ
ejpam-4187	22	3	of	of	ADP
ejpam-4187	22	4	the	the	DET
ejpam-4187	22	5	variations	variation	NOUN
ejpam-4187	22	6	on	on	ADP
ejpam-4187	22	7	dominating	dominating	NOUN
ejpam-4187	22	8	sets	set	NOUN
ejpam-4187	22	9	which	which	PRON
ejpam-4187	22	10	have	have	AUX
ejpam-4187	22	11	been	be	AUX
ejpam-4187	22	12	introduced	introduce	VERB
ejpam-4187	22	13	recently	recently	ADV
ejpam-4187	22	14	tend	tend	VERB
ejpam-4187	22	15	to	to	PART
ejpam-4187	22	16	increase	increase	VERB
ejpam-4187	22	17	the	the	DET
ejpam-4187	22	18	domination	domination	NOUN
ejpam-4187	22	19	number	number	NOUN
ejpam-4187	22	20	,	,	PUNCT
ejpam-4187	22	21	which	which	PRON
ejpam-4187	22	22	in	in	ADP
ejpam-4187	22	23	effect	effect	NOUN
ejpam-4187	22	24	raise	raise	VERB
ejpam-4187	22	25	implementation	implementation	NOUN
ejpam-4187	22	26	costs	cost	NOUN
ejpam-4187	22	27	,	,	PUNCT
ejpam-4187	22	28	disjunctive	disjunctive	ADJ
ejpam-4187	22	29	domination	domination	NOUN
ejpam-4187	22	30	is	be	AUX
ejpam-4187	22	31	a	a	DET
ejpam-4187	22	32	relaxation	relaxation	NOUN
ejpam-4187	22	33	of	of	ADP
ejpam-4187	22	34	the	the	DET
ejpam-4187	22	35	domination	domination	NOUN
ejpam-4187	22	36	number	number	NOUN
ejpam-4187	22	37	[	[	X
ejpam-4187	22	38	14	14	NUM
ejpam-4187	22	39	]	]	PUNCT
ejpam-4187	22	40	.	.	PUNCT
ejpam-4187	23	1	in	in	ADP
ejpam-4187	23	2	[	[	X
ejpam-4187	23	3	8	8	NUM
ejpam-4187	23	4	]	]	PUNCT
ejpam-4187	23	5	,	,	PUNCT
ejpam-4187	23	6	sharp	sharp	ADJ
ejpam-4187	23	7	bounds	bound	NOUN
ejpam-4187	23	8	for	for	ADP
ejpam-4187	23	9	the	the	DET
ejpam-4187	23	10	disjunctive	disjunctive	ADJ
ejpam-4187	23	11	domination	domination	NOUN
ejpam-4187	23	12	number	number	NOUN
ejpam-4187	23	13	were	be	AUX
ejpam-4187	23	14	established	establish	VERB
ejpam-4187	23	15	for	for	ADP
ejpam-4187	23	16	general	general	ADJ
ejpam-4187	23	17	graphs	graph	NOUN
ejpam-4187	23	18	,	,	PUNCT
ejpam-4187	23	19	and	and	CCONJ
ejpam-4187	23	20	exact	exact	ADJ
ejpam-4187	23	21	values	value	NOUN
ejpam-4187	23	22	were	be	AUX
ejpam-4187	23	23	determined	determine	VERB
ejpam-4187	23	24	for	for	ADP
ejpam-4187	23	25	specific	specific	ADJ
ejpam-4187	23	26	graphs	graph	NOUN
ejpam-4187	23	27	.	.	PUNCT
ejpam-4187	24	1	in	in	ADP
ejpam-4187	24	2	2016	2016	NUM
ejpam-4187	24	3	,	,	PUNCT
ejpam-4187	24	4	henning	henning	NOUN
ejpam-4187	24	5	and	and	CCONJ
ejpam-4187	24	6	naicker	naicker	PROPN
ejpam-4187	24	7	also	also	ADV
ejpam-4187	24	8	extended	extend	VERB
ejpam-4187	24	9	the	the	DET
ejpam-4187	24	10	concept	concept	NOUN
ejpam-4187	24	11	of	of	ADP
ejpam-4187	24	12	total	total	ADJ
ejpam-4187	24	13	domination	domination	NOUN
ejpam-4187	24	14	by	by	ADP
ejpam-4187	24	15	defining	define	VERB
ejpam-4187	24	16	the	the	DET
ejpam-4187	24	17	disjunctive	disjunctive	ADJ
ejpam-4187	24	18	total	total	ADJ
ejpam-4187	24	19	domination	domination	NOUN
ejpam-4187	24	20	.	.	PUNCT
ejpam-4187	25	1	accordingly	accordingly	ADV
ejpam-4187	25	2	,	,	PUNCT
ejpam-4187	25	3	it	it	PRON
ejpam-4187	25	4	allows	allow	VERB
ejpam-4187	25	5	for	for	ADP
ejpam-4187	25	6	greater	great	ADJ
ejpam-4187	25	7	flexibility	flexibility	NOUN
ejpam-4187	25	8	by	by	ADP
ejpam-4187	25	9	modeling	model	VERB
ejpam-4187	25	10	networks	network	NOUN
ejpam-4187	25	11	where	where	SCONJ
ejpam-4187	25	12	one	one	NUM
ejpam-4187	25	13	trades	trade	VERB
ejpam-4187	25	14	off	off	ADP
ejpam-4187	25	15	redundancy	redundancy	NOUN
ejpam-4187	25	16	and	and	CCONJ
ejpam-4187	25	17	backup	backup	ADJ
ejpam-4187	25	18	capability	capability	NOUN
ejpam-4187	25	19	with	with	ADP
ejpam-4187	25	20	resource	resource	NOUN
ejpam-4187	25	21	optimization	optimization	NOUN
ejpam-4187	25	22	[	[	X
ejpam-4187	25	23	14	14	NUM
ejpam-4187	25	24	]	]	PUNCT
ejpam-4187	25	25	.	.	PUNCT
ejpam-4187	26	1	the	the	DET
ejpam-4187	26	2	above	above	ADV
ejpam-4187	26	3	-	-	PUNCT
ejpam-4187	26	4	mentioned	mention	VERB
ejpam-4187	26	5	authors	author	NOUN
ejpam-4187	26	6	established	establish	VERB
ejpam-4187	26	7	in	in	ADP
ejpam-4187	26	8	[	[	X
ejpam-4187	26	9	14	14	NUM
ejpam-4187	26	10	]	]	X
ejpam-4187	26	11	tight	tight	ADJ
ejpam-4187	26	12	upper	upper	ADJ
ejpam-4187	26	13	bound	bind	VERB
ejpam-4187	26	14	on	on	ADP
ejpam-4187	26	15	the	the	DET
ejpam-4187	26	16	disjunctive	disjunctive	ADJ
ejpam-4187	26	17	total	total	ADJ
ejpam-4187	26	18	domination	domination	NOUN
ejpam-4187	26	19	number	number	NOUN
ejpam-4187	26	20	of	of	ADP
ejpam-4187	26	21	a	a	DET
ejpam-4187	26	22	graph	graph	NOUN
ejpam-4187	26	23	in	in	ADP
ejpam-4187	26	24	terms	term	NOUN
ejpam-4187	26	25	of	of	ADP
ejpam-4187	26	26	its	its	PRON
ejpam-4187	26	27	order	order	NOUN
ejpam-4187	26	28	and	and	CCONJ
ejpam-4187	26	29	characterized	characterize	VERB
ejpam-4187	26	30	the	the	DET
ejpam-4187	26	31	extremal	extremal	ADJ
ejpam-4187	26	32	graphs	graph	NOUN
ejpam-4187	26	33	,	,	PUNCT
ejpam-4187	26	34	and	and	CCONJ
ejpam-4187	26	35	then	then	ADV
ejpam-4187	26	36	proved	prove	VERB
ejpam-4187	26	37	that	that	SCONJ
ejpam-4187	26	38	this	this	PRON
ejpam-4187	26	39	bound	bind	VERB
ejpam-4187	26	40	can	can	AUX
ejpam-4187	26	41	be	be	AUX
ejpam-4187	26	42	significantly	significantly	ADV
ejpam-4187	26	43	improved	improve	VERB
ejpam-4187	26	44	if	if	SCONJ
ejpam-4187	26	45	claw	claw	NOUN
ejpam-4187	26	46	-	-	PUNCT
ejpam-4187	26	47	freeness	freeness	NOUN
ejpam-4187	26	48	of	of	ADP
ejpam-4187	26	49	a	a	DET
ejpam-4187	26	50	graph	graph	NOUN
ejpam-4187	26	51	is	be	AUX
ejpam-4187	26	52	imposed	impose	VERB
ejpam-4187	26	53	.	.	PUNCT
ejpam-4187	27	1	the	the	DET
ejpam-4187	27	2	same	same	ADJ
ejpam-4187	27	3	authors	author	NOUN
ejpam-4187	27	4	also	also	ADV
ejpam-4187	27	5	investigated	investigate	VERB
ejpam-4187	27	6	the	the	DET
ejpam-4187	27	7	variant	variant	NOUN
ejpam-4187	27	8	on	on	ADP
ejpam-4187	27	9	the	the	DET
ejpam-4187	27	10	class	class	NOUN
ejpam-4187	27	11	of	of	ADP
ejpam-4187	27	12	trees	tree	NOUN
ejpam-4187	27	13	in	in	ADP
ejpam-4187	27	14	[	[	X
ejpam-4187	27	15	12	12	NUM
ejpam-4187	27	16	,	,	PUNCT
ejpam-4187	27	17	13	13	NUM
ejpam-4187	27	18	]	]	PUNCT
ejpam-4187	27	19	.	.	PUNCT
ejpam-4187	28	1	motivated	motivate	VERB
ejpam-4187	28	2	by	by	ADP
ejpam-4187	28	3	the	the	DET
ejpam-4187	28	4	concepts	concept	NOUN
ejpam-4187	28	5	of	of	ADP
ejpam-4187	28	6	b	b	NOUN
ejpam-4187	28	7	-	-	PUNCT
ejpam-4187	28	8	disjunctive	disjunctive	ADJ
ejpam-4187	28	9	domination	domination	NOUN
ejpam-4187	28	10	and	and	CCONJ
ejpam-4187	28	11	disjunctive	disjunctive	ADJ
ejpam-4187	28	12	total	total	ADJ
ejpam-4187	28	13	domination	domination	NOUN
ejpam-4187	28	14	in	in	ADP
ejpam-4187	28	15	graphs	graph	NOUN
ejpam-4187	28	16	,	,	PUNCT
ejpam-4187	28	17	jamil	jamil	PROPN
ejpam-4187	28	18	and	and	CCONJ
ejpam-4187	28	19	malalay	malalay	VERB
ejpam-4187	28	20	[	[	X
ejpam-4187	28	21	15	15	NUM
ejpam-4187	28	22	]	]	PUNCT
ejpam-4187	28	23	in	in	ADP
ejpam-4187	28	24	2019	2019	NUM
ejpam-4187	28	25	extended	extend	VERB
ejpam-4187	28	26	the	the	DET
ejpam-4187	28	27	study	study	NOUN
ejpam-4187	28	28	of	of	ADP
ejpam-4187	28	29	disjunctive	disjunctive	ADJ
ejpam-4187	28	30	dominating	dominating	NOUN
ejpam-4187	28	31	,	,	PUNCT
ejpam-4187	28	32	particularly	particularly	ADV
ejpam-4187	28	33	2	2	NUM
ejpam-4187	28	34	-	-	PUNCT
ejpam-4187	28	35	disjunctive	disjunctive	ADJ
ejpam-4187	28	36	domination	domination	NOUN
ejpam-4187	28	37	,	,	PUNCT
ejpam-4187	28	38	and	and	CCONJ
ejpam-4187	28	39	the	the	DET
ejpam-4187	28	40	disjunctive	disjunctive	ADJ
ejpam-4187	28	41	total	total	ADJ
ejpam-4187	28	42	dominating	dominating	NOUN
ejpam-4187	28	43	sets	set	NOUN
ejpam-4187	28	44	under	under	ADP
ejpam-4187	28	45	some	some	DET
ejpam-4187	28	46	binary	binary	ADJ
ejpam-4187	28	47	operations	operation	NOUN
ejpam-4187	28	48	in	in	ADP
ejpam-4187	28	49	graphs	graph	NOUN
ejpam-4187	28	50	.	.	PUNCT
ejpam-4187	29	1	specifically	specifically	ADV
ejpam-4187	29	2	,	,	PUNCT
ejpam-4187	29	3	they	they	PRON
ejpam-4187	29	4	characterized	characterize	VERB
ejpam-4187	29	5	in	in	ADP
ejpam-4187	29	6	[	[	X
ejpam-4187	29	7	15	15	NUM
ejpam-4187	29	8	]	]	X
ejpam-4187	29	9	the	the	DET
ejpam-4187	29	10	disjunctive	disjunctive	ADJ
ejpam-4187	29	11	dominating	dominating	NOUN
ejpam-4187	29	12	sets	set	NOUN
ejpam-4187	29	13	and	and	CCONJ
ejpam-4187	29	14	the	the	DET
ejpam-4187	29	15	disjunctive	disjunctive	ADJ
ejpam-4187	29	16	total	total	ADJ
ejpam-4187	29	17	dominating	dominating	NOUN
ejpam-4187	29	18	sets	set	NOUN
ejpam-4187	29	19	in	in	ADP
ejpam-4187	29	20	the	the	DET
ejpam-4187	29	21	join	join	NOUN
ejpam-4187	29	22	,	,	PUNCT
ejpam-4187	29	23	corona	corona	NOUN
ejpam-4187	29	24	and	and	CCONJ
ejpam-4187	29	25	lexicographic	lexicographic	ADJ
ejpam-4187	29	26	product	product	NOUN
ejpam-4187	29	27	of	of	ADP
ejpam-4187	29	28	graphs	graph	NOUN
ejpam-4187	29	29	and	and	CCONJ
ejpam-4187	29	30	obtained	obtain	VERB
ejpam-4187	29	31	the	the	DET
ejpam-4187	29	32	values	value	NOUN
ejpam-4187	29	33	of	of	ADP
ejpam-4187	29	34	the	the	DET
ejpam-4187	29	35	respective	respective	ADJ
ejpam-4187	29	36	corresponding	corresponding	ADJ
ejpam-4187	29	37	disjunctive	disjunctive	ADJ
ejpam-4187	29	38	domination	domination	NOUN
ejpam-4187	29	39	numbers	number	NOUN
ejpam-4187	29	40	.	.	PUNCT
ejpam-4187	30	1	in	in	ADP
ejpam-4187	30	2	this	this	DET
ejpam-4187	30	3	paper	paper	NOUN
ejpam-4187	30	4	,	,	PUNCT
ejpam-4187	30	5	we	we	PRON
ejpam-4187	30	6	introduce	introduce	VERB
ejpam-4187	30	7	another	another	DET
ejpam-4187	30	8	variant	variant	NOUN
ejpam-4187	30	9	of	of	ADP
ejpam-4187	30	10	domination	domination	NOUN
ejpam-4187	30	11	,	,	PUNCT
ejpam-4187	30	12	namely	namely	ADV
ejpam-4187	30	13	restrained	restrained	ADJ
ejpam-4187	30	14	disjunctive	disjunctive	ADJ
ejpam-4187	30	15	domination	domination	NOUN
ejpam-4187	30	16	,	,	PUNCT
ejpam-4187	30	17	and	and	CCONJ
ejpam-4187	30	18	characterize	characterize	VERB
ejpam-4187	30	19	the	the	DET
ejpam-4187	30	20	restrained	restrained	ADJ
ejpam-4187	30	21	disjunctive	disjunctive	ADJ
ejpam-4187	30	22	dominating	dominating	NOUN
ejpam-4187	30	23	sets	set	NOUN
ejpam-4187	30	24	in	in	ADP
ejpam-4187	30	25	the	the	DET
ejpam-4187	30	26	join	join	NOUN
ejpam-4187	30	27	,	,	PUNCT
ejpam-4187	30	28	corona	corona	NOUN
ejpam-4187	30	29	and	and	CCONJ
ejpam-4187	30	30	lexicographic	lexicographic	ADJ
ejpam-4187	30	31	product	product	NOUN
ejpam-4187	30	32	of	of	ADP
ejpam-4187	30	33	graphs	graph	NOUN
ejpam-4187	30	34	.	.	PUNCT
ejpam-4187	31	1	in	in	ADP
ejpam-4187	31	2	here	here	ADV
ejpam-4187	31	3	,	,	PUNCT
ejpam-4187	31	4	by	by	ADP
ejpam-4187	31	5	a	a	DET
ejpam-4187	31	6	graph	graph	NOUN
ejpam-4187	31	7	we	we	PRON
ejpam-4187	31	8	mean	mean	VERB
ejpam-4187	31	9	a	a	DET
ejpam-4187	31	10	finite	finite	NOUN
ejpam-4187	31	11	,	,	PUNCT
ejpam-4187	31	12	simple	simple	ADJ
ejpam-4187	31	13	and	and	CCONJ
ejpam-4187	31	14	undirected	undirected	ADJ
ejpam-4187	31	15	connected	connected	ADJ
ejpam-4187	31	16	graph	graph	NOUN
ejpam-4187	31	17	g	g	PROPN
ejpam-4187	31	18	=	=	PUNCT
ejpam-4187	31	19	(	(	PUNCT
ejpam-4187	31	20	v	v	NOUN
ejpam-4187	31	21	(	(	PUNCT
ejpam-4187	31	22	g	g	NOUN
ejpam-4187	31	23	)	)	PUNCT
ejpam-4187	31	24	,	,	PUNCT
ejpam-4187	31	25	e(g	e(g	PROPN
ejpam-4187	31	26	)	)	PUNCT
ejpam-4187	31	27	)	)	PUNCT
ejpam-4187	31	28	.	.	PUNCT
ejpam-4187	32	1	all	all	DET
ejpam-4187	32	2	basic	basic	ADJ
ejpam-4187	32	3	terminologies	terminology	NOUN
ejpam-4187	32	4	used	use	VERB
ejpam-4187	32	5	here	here	ADV
ejpam-4187	32	6	are	be	AUX
ejpam-4187	32	7	adapted	adapt	VERB
ejpam-4187	32	8	from	from	ADP
ejpam-4187	32	9	[	[	X
ejpam-4187	32	10	2	2	NUM
ejpam-4187	32	11	]	]	PUNCT
ejpam-4187	32	12	.	.	PUNCT
ejpam-4187	33	1	the	the	DET
ejpam-4187	33	2	symbols	symbol	NOUN
ejpam-4187	33	3	v	v	ADP
ejpam-4187	33	4	(	(	PUNCT
ejpam-4187	33	5	g	g	NOUN
ejpam-4187	33	6	)	)	PUNCT
ejpam-4187	33	7	and	and	CCONJ
ejpam-4187	33	8	e(g	e(g	PROPN
ejpam-4187	33	9	)	)	PUNCT
ejpam-4187	33	10	are	be	AUX
ejpam-4187	33	11	the	the	DET
ejpam-4187	33	12	vertex	vertex	NOUN
ejpam-4187	33	13	-	-	PUNCT
ejpam-4187	33	14	set	set	VERB
ejpam-4187	33	15	and	and	CCONJ
ejpam-4187	33	16	edge	edge	NOUN
ejpam-4187	33	17	-	-	PUNCT
ejpam-4187	33	18	set	set	NOUN
ejpam-4187	33	19	,	,	PUNCT
ejpam-4187	33	20	respectively	respectively	ADV
ejpam-4187	33	21	,	,	PUNCT
ejpam-4187	33	22	of	of	ADP
ejpam-4187	33	23	g.	g.	NOUN
ejpam-4187	33	24	for	for	ADP
ejpam-4187	33	25	s	s	PROPN
ejpam-4187	33	26	⊆	⊆	NUM
ejpam-4187	33	27	v	v	NOUN
ejpam-4187	33	28	(	(	PUNCT
ejpam-4187	33	29	g	g	NOUN
ejpam-4187	33	30	)	)	PUNCT
ejpam-4187	33	31	,	,	PUNCT
ejpam-4187	33	32	|s|	|s|	PROPN
ejpam-4187	33	33	is	be	AUX
ejpam-4187	33	34	the	the	DET
ejpam-4187	33	35	cardinality	cardinality	NOUN
ejpam-4187	33	36	of	of	ADP
ejpam-4187	33	37	s.	s.	PROPN
ejpam-4187	33	38	in	in	ADP
ejpam-4187	33	39	particular	particular	ADJ
ejpam-4187	33	40	,	,	PUNCT
ejpam-4187	33	41	|v	|v	PROPN
ejpam-4187	33	42	(	(	PUNCT
ejpam-4187	33	43	g)|	g)|	PROPN
ejpam-4187	33	44	is	be	AUX
ejpam-4187	33	45	called	call	VERB
ejpam-4187	33	46	the	the	DET
ejpam-4187	33	47	order	order	NOUN
ejpam-4187	33	48	of	of	ADP
ejpam-4187	33	49	g.	g.	PROPN
ejpam-4187	33	50	the	the	DET
ejpam-4187	33	51	complement	complement	NOUN
ejpam-4187	33	52	of	of	ADP
ejpam-4187	33	53	g	g	PROPN
ejpam-4187	33	54	is	be	AUX
ejpam-4187	33	55	that	that	DET
ejpam-4187	33	56	graph	graph	NOUN
ejpam-4187	33	57	g	g	PROPN
ejpam-4187	33	58	,	,	PUNCT
ejpam-4187	33	59	where	where	SCONJ
ejpam-4187	33	60	v	v	X
ejpam-4187	33	61	(	(	PUNCT
ejpam-4187	33	62	g	g	NOUN
ejpam-4187	33	63	)	)	PUNCT
ejpam-4187	33	64	=	=	NOUN
ejpam-4187	34	1	v	v	X
ejpam-4187	34	2	(	(	PUNCT
ejpam-4187	34	3	g	g	NOUN
ejpam-4187	34	4	)	)	PUNCT
ejpam-4187	34	5	and	and	CCONJ
ejpam-4187	34	6	for	for	ADP
ejpam-4187	34	7	its	its	PRON
ejpam-4187	34	8	edges	edge	NOUN
ejpam-4187	34	9	,	,	PUNCT
ejpam-4187	34	10	xy	xy	PROPN
ejpam-4187	34	11	∈	∈	PROPN
ejpam-4187	34	12	e(g	e(g	PROPN
ejpam-4187	34	13	)	)	PUNCT
ejpam-4187	35	1	if	if	SCONJ
ejpam-4187	35	2	and	and	CCONJ
ejpam-4187	35	3	only	only	ADV
ejpam-4187	35	4	if	if	SCONJ
ejpam-4187	35	5	xy	xy	PROPN
ejpam-4187	35	6	/∈	/∈	PUNCT
ejpam-4187	35	7	e(g	e(g	PROPN
ejpam-4187	35	8	)	)	PUNCT
ejpam-4187	35	9	.	.	PUNCT
ejpam-4187	36	1	given	give	VERB
ejpam-4187	36	2	graphs	graph	NOUN
ejpam-4187	36	3	g	g	PROPN
ejpam-4187	36	4	and	and	CCONJ
ejpam-4187	36	5	h	h	NOUN
ejpam-4187	36	6	,	,	PUNCT
ejpam-4187	36	7	the	the	DET
ejpam-4187	36	8	join	join	NOUN
ejpam-4187	36	9	of	of	ADP
ejpam-4187	36	10	g	g	PROPN
ejpam-4187	36	11	and	and	CCONJ
ejpam-4187	36	12	h	h	NOUN
ejpam-4187	36	13	is	be	AUX
ejpam-4187	36	14	the	the	DET
ejpam-4187	36	15	graph	graph	NOUN
ejpam-4187	36	16	g	g	NOUN
ejpam-4187	36	17	+	+	CCONJ
ejpam-4187	36	18	h	h	NOUN
ejpam-4187	36	19	with	with	ADP
ejpam-4187	36	20	vertex	vertex	NOUN
ejpam-4187	36	21	set	set	VERB
ejpam-4187	36	22	v	v	NOUN
ejpam-4187	36	23	(	(	PUNCT
ejpam-4187	36	24	g	g	NOUN
ejpam-4187	36	25	)	)	PUNCT
ejpam-4187	36	26	∪	∪	NOUN
ejpam-4187	36	27	v	v	NOUN
ejpam-4187	36	28	(	(	PUNCT
ejpam-4187	36	29	h	h	NOUN
ejpam-4187	36	30	)	)	PUNCT
ejpam-4187	36	31	and	and	CCONJ
ejpam-4187	36	32	edge	edge	VERB
ejpam-4187	36	33	set	set	VERB
ejpam-4187	36	34	e(g	e(g	NOUN
ejpam-4187	36	35	)	)	PUNCT
ejpam-4187	36	36	∪	∪	ADP
ejpam-4187	36	37	e(h	e(h	PROPN
ejpam-4187	36	38	)	)	PUNCT
ejpam-4187	36	39	∪	∪	NOUN
ejpam-4187	36	40	{	{	PUNCT
ejpam-4187	36	41	uv	uv	NOUN
ejpam-4187	36	42	:	:	PUNCT
ejpam-4187	36	43	u	u	PROPN
ejpam-4187	36	44	∈	∈	PROPN
ejpam-4187	36	45	v	v	ADP
ejpam-4187	36	46	(	(	PUNCT
ejpam-4187	36	47	g	g	NOUN
ejpam-4187	36	48	)	)	PUNCT
ejpam-4187	36	49	,	,	PUNCT
ejpam-4187	36	50	v	v	X
ejpam-4187	36	51	∈	∈	PROPN
ejpam-4187	36	52	v	v	NOUN
ejpam-4187	36	53	(	(	PUNCT
ejpam-4187	36	54	h	h	NOUN
ejpam-4187	36	55	)	)	PUNCT
ejpam-4187	36	56	}	}	PUNCT
ejpam-4187	36	57	.	.	PUNCT
ejpam-4187	37	1	the	the	DET
ejpam-4187	37	2	corona	corona	NOUN
ejpam-4187	37	3	of	of	ADP
ejpam-4187	37	4	g	g	PROPN
ejpam-4187	37	5	and	and	CCONJ
ejpam-4187	37	6	h	h	NOUN
ejpam-4187	37	7	is	be	AUX
ejpam-4187	37	8	the	the	DET
ejpam-4187	37	9	graph	graph	NOUN
ejpam-4187	37	10	g	g	PROPN
ejpam-4187	37	11	◦	◦	NOUN
ejpam-4187	37	12	h	h	NOUN
ejpam-4187	37	13	obtained	obtain	VERB
ejpam-4187	37	14	by	by	ADP
ejpam-4187	37	15	taking	take	VERB
ejpam-4187	37	16	one	one	NUM
ejpam-4187	37	17	copy	copy	NOUN
ejpam-4187	37	18	of	of	ADP
ejpam-4187	37	19	g	g	PROPN
ejpam-4187	37	20	and	and	CCONJ
ejpam-4187	37	21	|v	|v	PROPN
ejpam-4187	37	22	(	(	PUNCT
ejpam-4187	37	23	g)|	g)|	NOUN
ejpam-4187	37	24	copies	copy	NOUN
ejpam-4187	37	25	of	of	ADP
ejpam-4187	37	26	h	h	NOUN
ejpam-4187	37	27	,	,	PUNCT
ejpam-4187	37	28	and	and	CCONJ
ejpam-4187	37	29	then	then	ADV
ejpam-4187	37	30	joining	join	VERB
ejpam-4187	37	31	the	the	DET
ejpam-4187	37	32	ith	ith	PROPN
ejpam-4187	37	33	vertex	vertex	NOUN
ejpam-4187	37	34	of	of	ADP
ejpam-4187	37	35	g	g	NOUN
ejpam-4187	37	36	to	to	ADP
ejpam-4187	37	37	every	every	DET
ejpam-4187	37	38	vertex	vertex	NOUN
ejpam-4187	37	39	in	in	ADP
ejpam-4187	37	40	the	the	DET
ejpam-4187	37	41	ith	ith	PROPN
ejpam-4187	37	42	copy	copy	NOUN
ejpam-4187	37	43	of	of	ADP
ejpam-4187	37	44	h.	h.	PROPN
ejpam-4187	37	45	in	in	ADP
ejpam-4187	37	46	particular	particular	ADJ
ejpam-4187	37	47	,	,	PUNCT
ejpam-4187	37	48	we	we	PRON
ejpam-4187	37	49	call	call	VERB
ejpam-4187	37	50	g	g	PROPN
ejpam-4187	37	51	◦	◦	NOUN
ejpam-4187	37	52	k1	k1	NOUN
ejpam-4187	37	53	the	the	DET
ejpam-4187	37	54	corona	corona	NOUN
ejpam-4187	37	55	of	of	ADP
ejpam-4187	37	56	g	g	PROPN
ejpam-4187	37	57	,	,	PUNCT
ejpam-4187	37	58	and	and	CCONJ
ejpam-4187	37	59	write	write	VERB
ejpam-4187	37	60	cor(g	cor(g	PROPN
ejpam-4187	37	61	)	)	PUNCT
ejpam-4187	37	62	=	=	SYM
ejpam-4187	37	63	g	g	PROPN
ejpam-4187	37	64	◦	◦	NOUN
ejpam-4187	37	65	k1	k1	NOUN
ejpam-4187	37	66	.	.	PUNCT
ejpam-4187	38	1	the	the	DET
ejpam-4187	38	2	lexicographic	lexicographic	ADJ
ejpam-4187	38	3	product	product	NOUN
ejpam-4187	38	4	of	of	ADP
ejpam-4187	38	5	g	g	PROPN
ejpam-4187	38	6	and	and	CCONJ
ejpam-4187	38	7	h	h	NOUN
ejpam-4187	38	8	is	be	AUX
ejpam-4187	38	9	the	the	DET
ejpam-4187	38	10	graph	graph	NOUN
ejpam-4187	38	11	g[h	g[h	PROPN
ejpam-4187	38	12	]	]	PUNCT
ejpam-4187	38	13	with	with	ADP
ejpam-4187	38	14	v	v	NOUN
ejpam-4187	38	15	(	(	PUNCT
ejpam-4187	38	16	g[h	g[h	PROPN
ejpam-4187	38	17	]	]	PUNCT
ejpam-4187	38	18	)	)	PUNCT
ejpam-4187	38	19	=	=	SYM
ejpam-4187	38	20	v	v	X
ejpam-4187	38	21	(	(	PUNCT
ejpam-4187	38	22	g	g	NOUN
ejpam-4187	38	23	)	)	PUNCT
ejpam-4187	38	24	×	×	NOUN
ejpam-4187	38	25	v	v	NOUN
ejpam-4187	38	26	(	(	PUNCT
ejpam-4187	38	27	h	h	NOUN
ejpam-4187	38	28	)	)	PUNCT
ejpam-4187	38	29	and	and	CCONJ
ejpam-4187	38	30	(	(	PUNCT
ejpam-4187	38	31	u	u	NOUN
ejpam-4187	38	32	,	,	PUNCT
ejpam-4187	38	33	v)(u′	v)(u′	NOUN
ejpam-4187	38	34	,	,	PUNCT
ejpam-4187	38	35	v′	v′	NOUN
ejpam-4187	38	36	)	)	PUNCT
ejpam-4187	38	37	∈	∈	NOUN
ejpam-4187	38	38	e(g[h	e(g[h	NOUN
ejpam-4187	38	39	]	]	PUNCT
ejpam-4187	38	40	)	)	PUNCT
ejpam-4187	38	41	if	if	SCONJ
ejpam-4187	38	42	and	and	CCONJ
ejpam-4187	38	43	only	only	ADV
ejpam-4187	38	44	if	if	SCONJ
ejpam-4187	38	45	either	either	CCONJ
ejpam-4187	38	46	uu′	uu′	PROPN
ejpam-4187	38	47	∈	∈	PROPN
ejpam-4187	38	48	e(g	e(g	PROPN
ejpam-4187	38	49	)	)	PUNCT
ejpam-4187	38	50	or	or	CCONJ
ejpam-4187	38	51	u	u	X
ejpam-4187	38	52	=	=	PUNCT
ejpam-4187	38	53	u′	u′	PROPN
ejpam-4187	38	54	and	and	CCONJ
ejpam-4187	38	55	vv′	vv′	NOUN
ejpam-4187	38	56	∈	∈	PROPN
ejpam-4187	38	57	e(h	e(h	PROPN
ejpam-4187	38	58	)	)	PUNCT
ejpam-4187	38	59	.	.	PUNCT
ejpam-4187	39	1	in	in	ADP
ejpam-4187	39	2	any	any	PRON
ejpam-4187	39	3	of	of	ADP
ejpam-4187	39	4	these	these	DET
ejpam-4187	39	5	graphs	graph	NOUN
ejpam-4187	39	6	,	,	PUNCT
ejpam-4187	39	7	g	g	PROPN
ejpam-4187	39	8	and	and	CCONJ
ejpam-4187	39	9	h	h	NOUN
ejpam-4187	39	10	are	be	AUX
ejpam-4187	39	11	referred	refer	VERB
ejpam-4187	39	12	to	to	ADP
ejpam-4187	39	13	as	as	ADP
ejpam-4187	39	14	their	their	PRON
ejpam-4187	39	15	basic	basic	ADJ
ejpam-4187	39	16	component	component	NOUN
ejpam-4187	39	17	graphs	graph	NOUN
ejpam-4187	39	18	.	.	PUNCT
ejpam-4187	40	1	vertices	vertice	VERB
ejpam-4187	40	2	u	u	NOUN
ejpam-4187	40	3	and	and	CCONJ
ejpam-4187	40	4	v	v	NOUN
ejpam-4187	40	5	of	of	ADP
ejpam-4187	40	6	a	a	DET
ejpam-4187	40	7	graph	graph	NOUN
ejpam-4187	40	8	g	g	NOUN
ejpam-4187	40	9	are	be	AUX
ejpam-4187	40	10	neighbors	neighbor	NOUN
ejpam-4187	40	11	if	if	SCONJ
ejpam-4187	40	12	uv	uv	PROPN
ejpam-4187	40	13	∈	∈	PROPN
ejpam-4187	40	14	e(g	e(g	PROPN
ejpam-4187	40	15	)	)	PUNCT
ejpam-4187	40	16	.	.	PUNCT
ejpam-4187	41	1	the	the	DET
ejpam-4187	41	2	open	open	ADJ
ejpam-4187	41	3	neighborhood	neighborhood	NOUN
ejpam-4187	41	4	of	of	ADP
ejpam-4187	41	5	v	v	NUM
ejpam-4187	41	6	∈	∈	NOUN
ejpam-4187	41	7	v	v	NOUN
ejpam-4187	41	8	(	(	PUNCT
ejpam-4187	41	9	g	g	NOUN
ejpam-4187	41	10	)	)	PUNCT
ejpam-4187	41	11	refers	refer	VERB
ejpam-4187	41	12	to	to	ADP
ejpam-4187	41	13	the	the	DET
ejpam-4187	41	14	set	set	NOUN
ejpam-4187	41	15	ng(v	ng(v	PUNCT
ejpam-4187	41	16	)	)	PUNCT
ejpam-4187	41	17	consisting	consist	VERB
ejpam-4187	41	18	of	of	ADP
ejpam-4187	41	19	all	all	DET
ejpam-4187	41	20	neighbors	neighbor	NOUN
ejpam-4187	41	21	of	of	ADP
ejpam-4187	41	22	v.	v.	ADP
ejpam-4187	41	23	the	the	DET
ejpam-4187	41	24	degree	degree	NOUN
ejpam-4187	41	25	of	of	ADP
ejpam-4187	41	26	v	v	NUM
ejpam-4187	41	27	∈	∈	NOUN
ejpam-4187	41	28	v	v	NOUN
ejpam-4187	41	29	(	(	PUNCT
ejpam-4187	41	30	g	g	NOUN
ejpam-4187	41	31	)	)	PUNCT
ejpam-4187	41	32	refers	refer	VERB
ejpam-4187	41	33	to	to	ADP
ejpam-4187	41	34	the	the	DET
ejpam-4187	41	35	cardinality	cardinality	NOUN
ejpam-4187	41	36	|ng(v)|	|ng(v)|	NOUN
ejpam-4187	41	37	of	of	ADP
ejpam-4187	41	38	the	the	DET
ejpam-4187	41	39	open	open	ADJ
ejpam-4187	41	40	neighborhood	neighborhood	NOUN
ejpam-4187	41	41	of	of	ADP
ejpam-4187	41	42	v	v	NOUN
ejpam-4187	41	43	,	,	PUNCT
ejpam-4187	41	44	δ(g	δ(g	PUNCT
ejpam-4187	41	45	)	)	PUNCT
ejpam-4187	41	46	is	be	AUX
ejpam-4187	41	47	the	the	DET
ejpam-4187	41	48	minimum	minimum	ADJ
ejpam-4187	41	49	degree	degree	NOUN
ejpam-4187	41	50	of	of	ADP
ejpam-4187	41	51	a	a	DET
ejpam-4187	41	52	vertex	vertex	NOUN
ejpam-4187	41	53	of	of	ADP
ejpam-4187	41	54	g	g	NOUN
ejpam-4187	41	55	,	,	PUNCT
ejpam-4187	41	56	and	and	CCONJ
ejpam-4187	41	57	∆(g	∆(g	NOUN
ejpam-4187	41	58	)	)	PUNCT
ejpam-4187	41	59	is	be	AUX
ejpam-4187	41	60	the	the	DET
ejpam-4187	41	61	maximum	maximum	ADJ
ejpam-4187	41	62	degree	degree	NOUN
ejpam-4187	41	63	of	of	ADP
ejpam-4187	41	64	g.	g.	PROPN
ejpam-4187	41	65	the	the	DET
ejpam-4187	41	66	closed	close	VERB
ejpam-4187	41	67	neighborhood	neighborhood	NOUN
ejpam-4187	41	68	of	of	ADP
ejpam-4187	41	69	v	v	NUM
ejpam-4187	41	70	∈	∈	NOUN
ejpam-4187	41	71	v	v	NOUN
ejpam-4187	41	72	(	(	PUNCT
ejpam-4187	41	73	g	g	NOUN
ejpam-4187	41	74	)	)	PUNCT
ejpam-4187	41	75	is	be	AUX
ejpam-4187	41	76	ng[v	ng[v	NOUN
ejpam-4187	41	77	]	]	X
ejpam-4187	41	78	=	=	SYM
ejpam-4187	41	79	ng(v	ng(v	X
ejpam-4187	41	80	)	)	PUNCT
ejpam-4187	41	81	∪	∪	ADP
ejpam-4187	41	82	{	{	PUNCT
ejpam-4187	41	83	v	v	NOUN
ejpam-4187	41	84	}	}	PUNCT
ejpam-4187	41	85	.	.	PUNCT
ejpam-4187	42	1	customarily	customarily	ADV
ejpam-4187	42	2	,	,	PUNCT
ejpam-4187	42	3	for	for	ADP
ejpam-4187	42	4	s	s	PROPN
ejpam-4187	42	5	⊆	⊆	NUM
ejpam-4187	42	6	v	v	NOUN
ejpam-4187	42	7	(	(	PUNCT
ejpam-4187	42	8	g	g	NOUN
ejpam-4187	42	9	)	)	PUNCT
ejpam-4187	42	10	,	,	PUNCT
ejpam-4187	42	11	ng(s	ng(s	NUM
ejpam-4187	42	12	)	)	PUNCT
ejpam-4187	43	1	=	=	SYM
ejpam-4187	43	2	⋃	⋃	ADP
ejpam-4187	43	3	v∈s	v∈s	NOUN
ejpam-4187	43	4	ng(v	ng(v	NUM
ejpam-4187	43	5	)	)	PUNCT
ejpam-4187	43	6	r.	r.	NOUN
ejpam-4187	43	7	malalay	malalay	PROPN
ejpam-4187	43	8	,	,	PUNCT
ejpam-4187	43	9	f.	f.	PROPN
ejpam-4187	43	10	jamil	jamil	PROPN
ejpam-4187	43	11	/	/	SYM
ejpam-4187	43	12	eur	eur	PROPN
ejpam-4187	43	13	.	.	PUNCT
ejpam-4187	44	1	j.	j.	PROPN
ejpam-4187	44	2	pure	pure	PROPN
ejpam-4187	44	3	appl	appl	PROPN
ejpam-4187	44	4	.	.	PROPN
ejpam-4187	44	5	math	math	PROPN
ejpam-4187	44	6	,	,	PUNCT
ejpam-4187	44	7	15	15	NUM
ejpam-4187	44	8	(	(	PUNCT
ejpam-4187	44	9	1	1	NUM
ejpam-4187	44	10	)	)	PUNCT
ejpam-4187	44	11	(	(	PUNCT
ejpam-4187	44	12	2022	2022	NUM
ejpam-4187	44	13	)	)	PUNCT
ejpam-4187	44	14	,	,	PUNCT
ejpam-4187	44	15	207	207	NUM
ejpam-4187	44	16	-	-	SYM
ejpam-4187	44	17	223	223	NUM
ejpam-4187	44	18	209	209	NUM
ejpam-4187	44	19	and	and	CCONJ
ejpam-4187	44	20	ng[s	ng[	NOUN
ejpam-4187	44	21	]	]	PUNCT
ejpam-4187	44	22	=	=	PUNCT
ejpam-4187	45	1	⋃	⋃	VERB
ejpam-4187	45	2	v∈s	v∈s	ADJ
ejpam-4187	45	3	ng[v	ng[v	NOUN
ejpam-4187	45	4	]	]	PUNCT
ejpam-4187	45	5	.	.	PUNCT
ejpam-4187	46	1	a	a	DET
ejpam-4187	46	2	subset	subset	NOUN
ejpam-4187	46	3	s	s	VERB
ejpam-4187	46	4	⊆	⊆	NUM
ejpam-4187	46	5	v	v	NOUN
ejpam-4187	46	6	(	(	PUNCT
ejpam-4187	46	7	g	g	NOUN
ejpam-4187	46	8	)	)	PUNCT
ejpam-4187	46	9	is	be	AUX
ejpam-4187	46	10	a	a	DET
ejpam-4187	46	11	dominating	dominating	NOUN
ejpam-4187	46	12	set	set	NOUN
ejpam-4187	46	13	of	of	ADP
ejpam-4187	46	14	g	g	PROPN
ejpam-4187	46	15	if	if	SCONJ
ejpam-4187	46	16	ng[s	ng[	NOUN
ejpam-4187	46	17	]	]	PUNCT
ejpam-4187	46	18	=	=	SYM
ejpam-4187	46	19	v	v	NOUN
ejpam-4187	46	20	(	(	PUNCT
ejpam-4187	46	21	g	g	NOUN
ejpam-4187	46	22	)	)	PUNCT
ejpam-4187	46	23	.	.	PUNCT
ejpam-4187	47	1	in	in	ADP
ejpam-4187	47	2	case	case	NOUN
ejpam-4187	47	3	,	,	PUNCT
ejpam-4187	47	4	s	s	VERB
ejpam-4187	47	5	is	be	AUX
ejpam-4187	47	6	a	a	DET
ejpam-4187	47	7	dominating	dominating	NOUN
ejpam-4187	47	8	set	set	NOUN
ejpam-4187	47	9	of	of	ADP
ejpam-4187	47	10	g	g	PROPN
ejpam-4187	47	11	and	and	CCONJ
ejpam-4187	47	12	every	every	DET
ejpam-4187	47	13	vertex	vertex	NOUN
ejpam-4187	47	14	in	in	ADP
ejpam-4187	47	15	v	v	NOUN
ejpam-4187	47	16	(	(	PUNCT
ejpam-4187	47	17	g	g	NOUN
ejpam-4187	47	18	)	)	PUNCT
ejpam-4187	47	19	\	\	PROPN
ejpam-4187	48	1	s	s	PART
ejpam-4187	48	2	is	be	AUX
ejpam-4187	48	3	adjacent	adjacent	ADJ
ejpam-4187	48	4	to	to	ADP
ejpam-4187	48	5	another	another	DET
ejpam-4187	48	6	vertex	vertex	NOUN
ejpam-4187	48	7	in	in	ADP
ejpam-4187	48	8	v	v	NOUN
ejpam-4187	48	9	(	(	PUNCT
ejpam-4187	48	10	g	g	NOUN
ejpam-4187	48	11	)	)	PUNCT
ejpam-4187	48	12	\	\	PROPN
ejpam-4187	49	1	s	s	X
ejpam-4187	49	2	,	,	PUNCT
ejpam-4187	49	3	then	then	ADV
ejpam-4187	49	4	s	s	VERB
ejpam-4187	49	5	is	be	AUX
ejpam-4187	49	6	a	a	DET
ejpam-4187	49	7	restrained	restrain	VERB
ejpam-4187	49	8	dominating	dominating	NOUN
ejpam-4187	49	9	set	set	NOUN
ejpam-4187	49	10	of	of	ADP
ejpam-4187	49	11	g.	g.	PROPN
ejpam-4187	49	12	the	the	DET
ejpam-4187	49	13	minimum	minimum	PROPN
ejpam-4187	49	14	cardinality	cardinality	PROPN
ejpam-4187	49	15	γ(g	γ(g	PROPN
ejpam-4187	49	16	)	)	PUNCT
ejpam-4187	49	17	of	of	ADP
ejpam-4187	49	18	a	a	DET
ejpam-4187	49	19	dominating	dominating	NOUN
ejpam-4187	49	20	set	set	NOUN
ejpam-4187	49	21	ofg	ofg	PROPN
ejpam-4187	49	22	is	be	AUX
ejpam-4187	49	23	the	the	DET
ejpam-4187	49	24	domination	domination	NOUN
ejpam-4187	49	25	number	number	NOUN
ejpam-4187	49	26	ofg	ofg	PROPN
ejpam-4187	49	27	,	,	PUNCT
ejpam-4187	49	28	and	and	CCONJ
ejpam-4187	49	29	the	the	DET
ejpam-4187	49	30	minimum	minimum	ADJ
ejpam-4187	49	31	cardinality	cardinality	PROPN
ejpam-4187	49	32	γr(g	γr(g	PROPN
ejpam-4187	49	33	)	)	PUNCT
ejpam-4187	49	34	of	of	ADP
ejpam-4187	49	35	a	a	DET
ejpam-4187	49	36	restrained	restrain	VERB
ejpam-4187	49	37	dominating	dominating	NOUN
ejpam-4187	49	38	set	set	NOUN
ejpam-4187	49	39	is	be	AUX
ejpam-4187	49	40	the	the	DET
ejpam-4187	49	41	restrained	restrained	ADJ
ejpam-4187	49	42	domination	domination	NOUN
ejpam-4187	49	43	number	number	NOUN
ejpam-4187	49	44	of	of	ADP
ejpam-4187	49	45	g.	g.	PROPN
ejpam-4187	49	46	a	a	DET
ejpam-4187	49	47	dominating	dominating	NOUN
ejpam-4187	49	48	set	set	NOUN
ejpam-4187	49	49	of	of	ADP
ejpam-4187	49	50	cardinality	cardinality	PROPN
ejpam-4187	49	51	γ(g	γ(g	PROPN
ejpam-4187	49	52	)	)	PUNCT
ejpam-4187	49	53	is	be	AUX
ejpam-4187	49	54	called	call	VERB
ejpam-4187	49	55	a	a	DET
ejpam-4187	49	56	γ	γ	NOUN
ejpam-4187	49	57	-	-	PUNCT
ejpam-4187	49	58	set	set	NOUN
ejpam-4187	49	59	of	of	ADP
ejpam-4187	49	60	g.	g.	PROPN
ejpam-4187	49	61	similarly	similarly	ADV
ejpam-4187	49	62	,	,	PUNCT
ejpam-4187	49	63	a	a	DET
ejpam-4187	49	64	γr	γr	PROPN
ejpam-4187	49	65	-	-	PUNCT
ejpam-4187	49	66	set	set	NOUN
ejpam-4187	49	67	is	be	AUX
ejpam-4187	49	68	a	a	DET
ejpam-4187	49	69	restrained	restrained	ADJ
ejpam-4187	49	70	dominating	dominating	NOUN
ejpam-4187	49	71	set	set	NOUN
ejpam-4187	49	72	of	of	ADP
ejpam-4187	49	73	cardinality	cardinality	PROPN
ejpam-4187	49	74	γr(g	γr(g	PROPN
ejpam-4187	49	75	)	)	PUNCT
ejpam-4187	49	76	.	.	PUNCT
ejpam-4187	50	1	the	the	DET
ejpam-4187	50	2	reader	reader	NOUN
ejpam-4187	50	3	is	be	AUX
ejpam-4187	50	4	referred	refer	VERB
ejpam-4187	50	5	to	to	ADP
ejpam-4187	50	6	[	[	X
ejpam-4187	50	7	1	1	NUM
ejpam-4187	50	8	,	,	PUNCT
ejpam-4187	50	9	4	4	NUM
ejpam-4187	50	10	,	,	PUNCT
ejpam-4187	50	11	6	6	NUM
ejpam-4187	50	12	,	,	PUNCT
ejpam-4187	50	13	10	10	NUM
ejpam-4187	50	14	,	,	PUNCT
ejpam-4187	50	15	18	18	NUM
ejpam-4187	50	16	]	]	PUNCT
ejpam-4187	50	17	for	for	ADP
ejpam-4187	50	18	the	the	DET
ejpam-4187	50	19	history	history	NOUN
ejpam-4187	50	20	,	,	PUNCT
ejpam-4187	50	21	fundamental	fundamental	ADJ
ejpam-4187	50	22	concepts	concept	NOUN
ejpam-4187	50	23	and	and	CCONJ
ejpam-4187	50	24	recent	recent	ADJ
ejpam-4187	50	25	developments	development	NOUN
ejpam-4187	50	26	of	of	ADP
ejpam-4187	50	27	domination	domination	NOUN
ejpam-4187	50	28	in	in	ADP
ejpam-4187	50	29	graphs	graph	NOUN
ejpam-4187	50	30	as	as	ADV
ejpam-4187	50	31	well	well	ADV
ejpam-4187	50	32	as	as	ADP
ejpam-4187	50	33	its	its	PRON
ejpam-4187	50	34	various	various	ADJ
ejpam-4187	50	35	applications	application	NOUN
ejpam-4187	50	36	.	.	PUNCT
ejpam-4187	51	1	a	a	DET
ejpam-4187	51	2	dominating	dominating	NOUN
ejpam-4187	51	3	set	set	NOUN
ejpam-4187	51	4	s	s	PROPN
ejpam-4187	51	5	⊆	⊆	NUM
ejpam-4187	51	6	v	v	NOUN
ejpam-4187	51	7	(	(	PUNCT
ejpam-4187	51	8	g	g	NOUN
ejpam-4187	51	9	)	)	PUNCT
ejpam-4187	51	10	is	be	AUX
ejpam-4187	51	11	a	a	DET
ejpam-4187	51	12	2	2	NUM
ejpam-4187	51	13	-	-	PUNCT
ejpam-4187	51	14	dominating	dominating	NOUN
ejpam-4187	51	15	set	set	NOUN
ejpam-4187	51	16	of	of	ADP
ejpam-4187	51	17	g	g	PROPN
ejpam-4187	51	18	if	if	SCONJ
ejpam-4187	51	19	for	for	ADP
ejpam-4187	51	20	each	each	PRON
ejpam-4187	51	21	v	v	NUM
ejpam-4187	51	22	∈	∈	PROPN
ejpam-4187	51	23	v	v	NOUN
ejpam-4187	51	24	(	(	PUNCT
ejpam-4187	51	25	g	g	NOUN
ejpam-4187	51	26	)	)	PUNCT
ejpam-4187	51	27	\	\	PROPN
ejpam-4187	52	1	s	s	X
ejpam-4187	52	2	,	,	PUNCT
ejpam-4187	52	3	|ng(v	|ng(v	ADJ
ejpam-4187	52	4	)	)	PUNCT
ejpam-4187	52	5	∩	∩	NOUN
ejpam-4187	52	6	s|	s|	VERB
ejpam-4187	52	7	≥	≥	NOUN
ejpam-4187	52	8	2	2	NUM
ejpam-4187	52	9	.	.	PUNCT
ejpam-4187	53	1	the	the	DET
ejpam-4187	53	2	minimum	minimum	ADJ
ejpam-4187	53	3	cardinality	cardinality	NOUN
ejpam-4187	53	4	of	of	ADP
ejpam-4187	53	5	a	a	DET
ejpam-4187	53	6	2	2	NUM
ejpam-4187	53	7	-	-	PUNCT
ejpam-4187	53	8	dominating	dominating	NOUN
ejpam-4187	53	9	set	set	NOUN
ejpam-4187	53	10	is	be	AUX
ejpam-4187	53	11	the	the	DET
ejpam-4187	53	12	2	2	NUM
ejpam-4187	53	13	-	-	PUNCT
ejpam-4187	53	14	domination	domination	NOUN
ejpam-4187	53	15	number	number	NOUN
ejpam-4187	53	16	of	of	ADP
ejpam-4187	53	17	g	g	NOUN
ejpam-4187	53	18	,	,	PUNCT
ejpam-4187	53	19	denoted	denote	VERB
ejpam-4187	53	20	by	by	ADP
ejpam-4187	53	21	γ×2(g	γ×2(g	NOUN
ejpam-4187	53	22	)	)	PUNCT
ejpam-4187	53	23	.	.	PUNCT
ejpam-4187	54	1	any	any	DET
ejpam-4187	54	2	2	2	NUM
ejpam-4187	54	3	-	-	PUNCT
ejpam-4187	54	4	dominating	dominating	NOUN
ejpam-4187	54	5	set	set	NOUN
ejpam-4187	54	6	with	with	ADP
ejpam-4187	54	7	cardinality	cardinality	NOUN
ejpam-4187	54	8	γ×2(g	γ×2(g	PROPN
ejpam-4187	54	9	)	)	PUNCT
ejpam-4187	54	10	is	be	AUX
ejpam-4187	54	11	called	call	VERB
ejpam-4187	54	12	a	a	DET
ejpam-4187	54	13	γ×2	γ×2	NOUN
ejpam-4187	54	14	-	-	PUNCT
ejpam-4187	54	15	set	set	NOUN
ejpam-4187	54	16	of	of	ADP
ejpam-4187	54	17	g.	g.	PROPN
ejpam-4187	54	18	the	the	DET
ejpam-4187	54	19	2	2	NUM
ejpam-4187	54	20	-	-	PUNCT
ejpam-4187	54	21	domination	domination	NOUN
ejpam-4187	54	22	in	in	ADP
ejpam-4187	54	23	graphs	graph	NOUN
ejpam-4187	54	24	is	be	AUX
ejpam-4187	54	25	being	be	AUX
ejpam-4187	54	26	studied	study	VERB
ejpam-4187	54	27	in	in	ADP
ejpam-4187	54	28	[	[	X
ejpam-4187	54	29	3	3	NUM
ejpam-4187	54	30	,	,	PUNCT
ejpam-4187	54	31	7	7	NUM
ejpam-4187	54	32	,	,	PUNCT
ejpam-4187	54	33	9	9	NUM
ejpam-4187	54	34	]	]	PUNCT
ejpam-4187	54	35	.	.	PUNCT
ejpam-4187	55	1	for	for	ADP
ejpam-4187	55	2	a	a	DET
ejpam-4187	55	3	vertex	vertex	NOUN
ejpam-4187	55	4	v	v	NOUN
ejpam-4187	55	5	of	of	ADP
ejpam-4187	55	6	g	g	NOUN
ejpam-4187	55	7	,	,	PUNCT
ejpam-4187	55	8	ng(v	ng(v	X
ejpam-4187	55	9	,	,	PUNCT
ejpam-4187	55	10	2	2	X
ejpam-4187	55	11	)	)	PUNCT
ejpam-4187	55	12	=	=	PRON
ejpam-4187	55	13	{	{	PUNCT
ejpam-4187	55	14	u	u	NOUN
ejpam-4187	55	15	∈	∈	PROPN
ejpam-4187	55	16	v	v	NOUN
ejpam-4187	55	17	(	(	PUNCT
ejpam-4187	55	18	g	g	NOUN
ejpam-4187	55	19	)	)	PUNCT
ejpam-4187	55	20	\	\	NOUN
ejpam-4187	55	21	{	{	PUNCT
ejpam-4187	55	22	v	v	NOUN
ejpam-4187	55	23	}	}	PUNCT
ejpam-4187	55	24	:	:	PUNCT
ejpam-4187	55	25	dg(u	dg(u	X
ejpam-4187	55	26	,	,	PUNCT
ejpam-4187	55	27	v	v	NOUN
ejpam-4187	55	28	)	)	PUNCT
ejpam-4187	55	29	≤	≤	NOUN
ejpam-4187	55	30	2	2	NUM
ejpam-4187	55	31	}	}	PUNCT
ejpam-4187	55	32	.	.	PUNCT
ejpam-4187	56	1	for	for	ADP
ejpam-4187	56	2	s	s	PROPN
ejpam-4187	56	3	⊆	⊆	NUM
ejpam-4187	56	4	v	v	NOUN
ejpam-4187	56	5	(	(	PUNCT
ejpam-4187	56	6	g	g	NOUN
ejpam-4187	56	7	)	)	PUNCT
ejpam-4187	56	8	,	,	PUNCT
ejpam-4187	56	9	ng(s	ng(s	CCONJ
ejpam-4187	56	10	,	,	PUNCT
ejpam-4187	56	11	2	2	X
ejpam-4187	56	12	)	)	PUNCT
ejpam-4187	56	13	=	=	SYM
ejpam-4187	56	14	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-4187	56	15	,	,	PUNCT
ejpam-4187	56	16	2	2	NUM
ejpam-4187	56	17	)	)	PUNCT
ejpam-4187	56	18	.	.	PUNCT
ejpam-4187	57	1	a	a	DET
ejpam-4187	57	2	set	set	NOUN
ejpam-4187	57	3	s	s	NOUN
ejpam-4187	57	4	⊆	⊆	NUM
ejpam-4187	57	5	v	v	NOUN
ejpam-4187	57	6	(	(	PUNCT
ejpam-4187	57	7	g	g	NOUN
ejpam-4187	57	8	)	)	PUNCT
ejpam-4187	57	9	is	be	AUX
ejpam-4187	57	10	a	a	DET
ejpam-4187	57	11	distance	distance	NOUN
ejpam-4187	57	12	-	-	PUNCT
ejpam-4187	57	13	two	two	NUM
ejpam-4187	57	14	dominating	dominating	NOUN
ejpam-4187	57	15	set	set	NOUN
ejpam-4187	57	16	of	of	ADP
ejpam-4187	57	17	g	g	NOUN
ejpam-4187	57	18	provided	provide	VERB
ejpam-4187	57	19	v	v	NOUN
ejpam-4187	57	20	(	(	PUNCT
ejpam-4187	57	21	g)\s	g)\s	NOUN
ejpam-4187	57	22	⊆	⊆	NUM
ejpam-4187	57	23	ng(s	ng(s	NUM
ejpam-4187	57	24	,	,	PUNCT
ejpam-4187	57	25	2	2	NUM
ejpam-4187	57	26	)	)	PUNCT
ejpam-4187	57	27	,	,	PUNCT
ejpam-4187	57	28	i.e.	i.e.	X
ejpam-4187	57	29	,	,	PUNCT
ejpam-4187	57	30	if	if	SCONJ
ejpam-4187	57	31	for	for	ADP
ejpam-4187	57	32	every	every	DET
ejpam-4187	57	33	v	v	NUM
ejpam-4187	57	34	∈	∈	NOUN
ejpam-4187	57	35	v	v	NOUN
ejpam-4187	57	36	(	(	PUNCT
ejpam-4187	57	37	g)\s	g)\s	NOUN
ejpam-4187	57	38	there	there	ADV
ejpam-4187	57	39	exists	exist	VERB
ejpam-4187	57	40	u	u	PROPN
ejpam-4187	57	41	∈	∈	PROPN
ejpam-4187	57	42	s	s	VERB
ejpam-4187	57	43	such	such	ADJ
ejpam-4187	57	44	that	that	PRON
ejpam-4187	57	45	dg(u	dg(u	ADJ
ejpam-4187	57	46	,	,	PUNCT
ejpam-4187	57	47	v	v	NOUN
ejpam-4187	57	48	)	)	PUNCT
ejpam-4187	57	49	≤	≤	NOUN
ejpam-4187	57	50	2	2	NUM
ejpam-4187	57	51	.	.	PUNCT
ejpam-4187	58	1	the	the	DET
ejpam-4187	58	2	minimum	minimum	ADJ
ejpam-4187	58	3	cardinality	cardinality	NOUN
ejpam-4187	58	4	γ2(g	γ2(g	VERB
ejpam-4187	58	5	)	)	PUNCT
ejpam-4187	58	6	of	of	ADP
ejpam-4187	58	7	a	a	DET
ejpam-4187	58	8	distance	distance	NOUN
ejpam-4187	58	9	-	-	PUNCT
ejpam-4187	58	10	two	two	NUM
ejpam-4187	58	11	dominating	dominating	NOUN
ejpam-4187	58	12	set	set	NOUN
ejpam-4187	58	13	is	be	AUX
ejpam-4187	58	14	the	the	DET
ejpam-4187	58	15	distance	distance	NOUN
ejpam-4187	58	16	-	-	PUNCT
ejpam-4187	58	17	two	two	NUM
ejpam-4187	58	18	domination	domination	NOUN
ejpam-4187	58	19	number	number	NOUN
ejpam-4187	58	20	of	of	ADP
ejpam-4187	58	21	g.	g.	PROPN
ejpam-4187	58	22	a	a	DET
ejpam-4187	58	23	distance	distance	NOUN
ejpam-4187	58	24	-	-	PUNCT
ejpam-4187	58	25	two	two	NUM
ejpam-4187	58	26	dominating	dominating	NOUN
ejpam-4187	58	27	set	set	NOUN
ejpam-4187	58	28	of	of	ADP
ejpam-4187	58	29	cardinality	cardinality	NOUN
ejpam-4187	58	30	γ2(g	γ2(g	VERB
ejpam-4187	58	31	)	)	PUNCT
ejpam-4187	58	32	is	be	AUX
ejpam-4187	58	33	called	call	VERB
ejpam-4187	58	34	a	a	DET
ejpam-4187	58	35	γ2	γ2	NOUN
ejpam-4187	58	36	-	-	PUNCT
ejpam-4187	58	37	set	set	NOUN
ejpam-4187	58	38	.	.	PUNCT
ejpam-4187	59	1	some	some	DET
ejpam-4187	59	2	studies	study	NOUN
ejpam-4187	59	3	in	in	ADP
ejpam-4187	59	4	distance	distance	NOUN
ejpam-4187	59	5	-	-	PUNCT
ejpam-4187	59	6	two	two	NUM
ejpam-4187	59	7	domination	domination	NOUN
ejpam-4187	59	8	can	can	AUX
ejpam-4187	59	9	be	be	AUX
ejpam-4187	59	10	found	find	VERB
ejpam-4187	59	11	in	in	ADP
ejpam-4187	59	12	[	[	X
ejpam-4187	59	13	20	20	NUM
ejpam-4187	59	14	]	]	PUNCT
ejpam-4187	59	15	.	.	PUNCT
ejpam-4187	60	1	a	a	DET
ejpam-4187	60	2	set	set	NOUN
ejpam-4187	60	3	s	s	NOUN
ejpam-4187	60	4	⊆	⊆	NUM
ejpam-4187	60	5	v	v	NOUN
ejpam-4187	60	6	(	(	PUNCT
ejpam-4187	60	7	g	g	NOUN
ejpam-4187	60	8	)	)	PUNCT
ejpam-4187	60	9	is	be	AUX
ejpam-4187	60	10	a	a	DET
ejpam-4187	60	11	disjunctive	disjunctive	ADJ
ejpam-4187	60	12	dominating	dominating	NOUN
ejpam-4187	60	13	set	set	NOUN
ejpam-4187	60	14	of	of	ADP
ejpam-4187	60	15	g	g	PROPN
ejpam-4187	60	16	if	if	SCONJ
ejpam-4187	60	17	for	for	ADP
ejpam-4187	60	18	every	every	PRON
ejpam-4187	60	19	v	v	NUM
ejpam-4187	60	20	∈	∈	NOUN
ejpam-4187	60	21	v	v	NOUN
ejpam-4187	60	22	(	(	PUNCT
ejpam-4187	60	23	g	g	NOUN
ejpam-4187	60	24	)	)	PUNCT
ejpam-4187	60	25	\	\	PROPN
ejpam-4187	61	1	s	s	X
ejpam-4187	61	2	,	,	PUNCT
ejpam-4187	61	3	v	v	NOUN
ejpam-4187	61	4	is	be	AUX
ejpam-4187	61	5	a	a	DET
ejpam-4187	61	6	neighbor	neighbor	NOUN
ejpam-4187	61	7	of	of	ADP
ejpam-4187	61	8	a	a	DET
ejpam-4187	61	9	vertex	vertex	NOUN
ejpam-4187	61	10	in	in	ADP
ejpam-4187	61	11	s	s	PRON
ejpam-4187	61	12	or	or	CCONJ
ejpam-4187	61	13	s	s	NOUN
ejpam-4187	61	14	has	have	AUX
ejpam-4187	61	15	at	at	ADV
ejpam-4187	61	16	least	least	ADV
ejpam-4187	61	17	two	two	NUM
ejpam-4187	61	18	vertices	vertex	NOUN
ejpam-4187	61	19	each	each	PRON
ejpam-4187	61	20	at	at	ADP
ejpam-4187	61	21	distance	distance	NOUN
ejpam-4187	61	22	2	2	NUM
ejpam-4187	61	23	from	from	ADP
ejpam-4187	61	24	v.	v.	ADP
ejpam-4187	61	25	the	the	DET
ejpam-4187	61	26	minimum	minimum	ADJ
ejpam-4187	61	27	cardinality	cardinality	NOUN
ejpam-4187	61	28	of	of	ADP
ejpam-4187	61	29	a	a	DET
ejpam-4187	61	30	disjunctive	disjunctive	ADJ
ejpam-4187	61	31	dominating	dominating	NOUN
ejpam-4187	61	32	set	set	NOUN
ejpam-4187	61	33	is	be	AUX
ejpam-4187	61	34	the	the	DET
ejpam-4187	61	35	disjunctive	disjunctive	ADJ
ejpam-4187	61	36	domination	domination	NOUN
ejpam-4187	61	37	number	number	NOUN
ejpam-4187	61	38	of	of	ADP
ejpam-4187	61	39	g	g	NOUN
ejpam-4187	61	40	,	,	PUNCT
ejpam-4187	61	41	and	and	CCONJ
ejpam-4187	61	42	is	be	AUX
ejpam-4187	61	43	denoted	denote	VERB
ejpam-4187	61	44	by	by	ADP
ejpam-4187	61	45	γd(g	γd(g	NOUN
ejpam-4187	61	46	)	)	PUNCT
ejpam-4187	61	47	.	.	PUNCT
ejpam-4187	62	1	a	a	DET
ejpam-4187	62	2	disjunctive	disjunctive	ADJ
ejpam-4187	62	3	dominating	dominating	NOUN
ejpam-4187	62	4	set	set	NOUN
ejpam-4187	62	5	of	of	ADP
ejpam-4187	62	6	cardinality	cardinality	NOUN
ejpam-4187	62	7	γd(g	γd(g	NUM
ejpam-4187	62	8	)	)	PUNCT
ejpam-4187	62	9	is	be	AUX
ejpam-4187	62	10	called	call	VERB
ejpam-4187	62	11	a	a	DET
ejpam-4187	62	12	γd	γd	NOUN
ejpam-4187	62	13	-	-	PUNCT
ejpam-4187	62	14	set	set	ADJ
ejpam-4187	62	15	.	.	PUNCT
ejpam-4187	63	1	for	for	ADP
ejpam-4187	63	2	convenience	convenience	NOUN
ejpam-4187	63	3	,	,	PUNCT
ejpam-4187	63	4	the	the	DET
ejpam-4187	63	5	symbol	symbol	NOUN
ejpam-4187	63	6	nd	nd	PRON
ejpam-4187	63	7	g(s	g(s	PROPN
ejpam-4187	63	8	)	)	PUNCT
ejpam-4187	63	9	denotes	denote	VERB
ejpam-4187	63	10	the	the	DET
ejpam-4187	63	11	set	set	NOUN
ejpam-4187	63	12	of	of	ADP
ejpam-4187	63	13	all	all	PRON
ejpam-4187	63	14	x	x	SYM
ejpam-4187	63	15	∈	∈	PROPN
ejpam-4187	63	16	v	v	NOUN
ejpam-4187	63	17	(	(	PUNCT
ejpam-4187	63	18	g	g	NOUN
ejpam-4187	63	19	)	)	PUNCT
ejpam-4187	63	20	such	such	ADJ
ejpam-4187	63	21	that	that	SCONJ
ejpam-4187	63	22	xy	xy	PROPN
ejpam-4187	63	23	∈	∈	PROPN
ejpam-4187	63	24	e(g	e(g	PROPN
ejpam-4187	63	25	)	)	PUNCT
ejpam-4187	63	26	for	for	ADP
ejpam-4187	63	27	some	some	DET
ejpam-4187	63	28	y	y	PROPN
ejpam-4187	63	29	∈	∈	PROPN
ejpam-4187	63	30	s	s	PART
ejpam-4187	63	31	or	or	CCONJ
ejpam-4187	63	32	there	there	ADV
ejpam-4187	63	33	exist	exist	VERB
ejpam-4187	63	34	distinct	distinct	ADJ
ejpam-4187	63	35	u	u	NOUN
ejpam-4187	63	36	,	,	PUNCT
ejpam-4187	63	37	v	v	PROPN
ejpam-4187	63	38	∈	∈	NOUN
ejpam-4187	63	39	s	s	VERB
ejpam-4187	63	40	with	with	ADP
ejpam-4187	63	41	dg(x	dg(x	NUM
ejpam-4187	63	42	,	,	PUNCT
ejpam-4187	63	43	u	u	NOUN
ejpam-4187	63	44	)	)	PUNCT
ejpam-4187	63	45	=	=	SYM
ejpam-4187	63	46	2	2	NUM
ejpam-4187	63	47	=	=	SYM
ejpam-4187	63	48	dg(x	dg(x	NUM
ejpam-4187	63	49	,	,	PUNCT
ejpam-4187	63	50	v	v	NOUN
ejpam-4187	63	51	)	)	PUNCT
ejpam-4187	63	52	.	.	PUNCT
ejpam-4187	64	1	then	then	ADV
ejpam-4187	64	2	s	s	VERB
ejpam-4187	64	3	is	be	AUX
ejpam-4187	64	4	a	a	DET
ejpam-4187	64	5	disjunctive	disjunctive	ADJ
ejpam-4187	64	6	dominating	dominating	NOUN
ejpam-4187	64	7	set	set	NOUN
ejpam-4187	64	8	of	of	ADP
ejpam-4187	64	9	g	g	PROPN
ejpam-4187	64	10	if	if	SCONJ
ejpam-4187	64	11	and	and	CCONJ
ejpam-4187	64	12	only	only	ADV
ejpam-4187	64	13	if	if	SCONJ
ejpam-4187	64	14	v	v	INTJ
ejpam-4187	64	15	(	(	PUNCT
ejpam-4187	64	16	g	g	NOUN
ejpam-4187	64	17	)	)	PUNCT
ejpam-4187	64	18	\	\	PUNCT
ejpam-4187	65	1	s	s	PART
ejpam-4187	65	2	⊆	⊆	NUM
ejpam-4187	65	3	nd	nd	PRON
ejpam-4187	65	4	g(s	g(s	NOUN
ejpam-4187	65	5	)	)	PUNCT
ejpam-4187	65	6	.	.	PUNCT
ejpam-4187	66	1	since	since	SCONJ
ejpam-4187	66	2	ng(s	ng(s	NUM
ejpam-4187	66	3	)	)	PUNCT
ejpam-4187	66	4	⊆	⊆	NUM
ejpam-4187	66	5	nd	nd	PRON
ejpam-4187	66	6	g(s	g(s	PROPN
ejpam-4187	66	7	)	)	PUNCT
ejpam-4187	66	8	,	,	PUNCT
ejpam-4187	66	9	dominating	dominating	NOUN
ejpam-4187	66	10	sets	set	NOUN
ejpam-4187	66	11	are	be	AUX
ejpam-4187	66	12	disjunctive	disjunctive	ADJ
ejpam-4187	66	13	dominating	dominating	NOUN
ejpam-4187	66	14	sets	set	NOUN
ejpam-4187	66	15	.	.	PUNCT
ejpam-4187	67	1	in	in	ADP
ejpam-4187	67	2	particular	particular	ADJ
ejpam-4187	67	3	,	,	PUNCT
ejpam-4187	67	4	γd(g	γd(g	NUM
ejpam-4187	67	5	)	)	PUNCT
ejpam-4187	67	6	=	=	SYM
ejpam-4187	67	7	1	1	NUM
ejpam-4187	67	8	if	if	SCONJ
ejpam-4187	67	9	and	and	CCONJ
ejpam-4187	67	10	only	only	ADV
ejpam-4187	67	11	if	if	SCONJ
ejpam-4187	67	12	γ(g	γ(g	NOUN
ejpam-4187	67	13	)	)	PUNCT
ejpam-4187	67	14	=	=	PUNCT
ejpam-4187	68	1	1	1	X
ejpam-4187	68	2	.	.	PUNCT
ejpam-4187	68	3	a	a	DET
ejpam-4187	68	4	disjunctive	disjunctive	ADJ
ejpam-4187	68	5	dominating	dominating	NOUN
ejpam-4187	68	6	set	set	NOUN
ejpam-4187	68	7	s	s	NOUN
ejpam-4187	68	8	of	of	ADP
ejpam-4187	68	9	g	g	PROPN
ejpam-4187	68	10	is	be	AUX
ejpam-4187	68	11	a	a	DET
ejpam-4187	68	12	disjunctive	disjunctive	ADJ
ejpam-4187	68	13	total	total	ADJ
ejpam-4187	68	14	dominating	dominating	NOUN
ejpam-4187	68	15	set	set	NOUN
ejpam-4187	68	16	of	of	ADP
ejpam-4187	68	17	g	g	NOUN
ejpam-4187	68	18	provided	provide	VERB
ejpam-4187	68	19	v	v	ADP
ejpam-4187	68	20	(	(	PUNCT
ejpam-4187	68	21	g	g	NOUN
ejpam-4187	68	22	)	)	PUNCT
ejpam-4187	68	23	=	=	NOUN
ejpam-4187	68	24	nd	nd	PRON
ejpam-4187	68	25	g(s	g(s	PROPN
ejpam-4187	68	26	)	)	PUNCT
ejpam-4187	68	27	.	.	PUNCT
ejpam-4187	69	1	that	that	PRON
ejpam-4187	69	2	is	be	AUX
ejpam-4187	69	3	,	,	PUNCT
ejpam-4187	69	4	s	s	VERB
ejpam-4187	69	5	is	be	AUX
ejpam-4187	69	6	a	a	DET
ejpam-4187	69	7	disjunctive	disjunctive	ADJ
ejpam-4187	69	8	total	total	ADJ
ejpam-4187	69	9	dominating	dominating	NOUN
ejpam-4187	69	10	set	set	VERB
ejpam-4187	69	11	if	if	SCONJ
ejpam-4187	69	12	for	for	ADP
ejpam-4187	69	13	every	every	DET
ejpam-4187	69	14	v	v	NUM
ejpam-4187	69	15	∈	∈	PROPN
ejpam-4187	69	16	s	s	NOUN
ejpam-4187	69	17	,	,	PUNCT
ejpam-4187	69	18	v	v	NOUN
ejpam-4187	69	19	is	be	AUX
ejpam-4187	69	20	adjacent	adjacent	ADJ
ejpam-4187	69	21	to	to	ADP
ejpam-4187	69	22	a	a	DET
ejpam-4187	69	23	vertex	vertex	NOUN
ejpam-4187	69	24	of	of	ADP
ejpam-4187	69	25	s	s	PRON
ejpam-4187	69	26	or	or	CCONJ
ejpam-4187	69	27	s	s	NOUN
ejpam-4187	69	28	has	have	AUX
ejpam-4187	69	29	at	at	ADV
ejpam-4187	69	30	least	least	ADV
ejpam-4187	69	31	two	two	NUM
ejpam-4187	69	32	vertices	vertex	NOUN
ejpam-4187	69	33	each	each	PRON
ejpam-4187	69	34	at	at	ADP
ejpam-4187	69	35	distance	distance	NOUN
ejpam-4187	69	36	2	2	NUM
ejpam-4187	69	37	from	from	ADP
ejpam-4187	69	38	v.	v.	ADP
ejpam-4187	69	39	the	the	DET
ejpam-4187	69	40	minimum	minimum	ADJ
ejpam-4187	69	41	cardinality	cardinality	NOUN
ejpam-4187	69	42	of	of	ADP
ejpam-4187	69	43	a	a	DET
ejpam-4187	69	44	disjunctive	disjunctive	ADJ
ejpam-4187	69	45	total	total	ADJ
ejpam-4187	69	46	dominating	dominating	NOUN
ejpam-4187	69	47	set	set	NOUN
ejpam-4187	69	48	of	of	ADP
ejpam-4187	69	49	g	g	PROPN
ejpam-4187	69	50	is	be	AUX
ejpam-4187	69	51	the	the	DET
ejpam-4187	69	52	disjunctive	disjunctive	ADJ
ejpam-4187	69	53	total	total	ADJ
ejpam-4187	69	54	domination	domination	NOUN
ejpam-4187	69	55	number	number	NOUN
ejpam-4187	69	56	of	of	ADP
ejpam-4187	69	57	g	g	NOUN
ejpam-4187	69	58	,	,	PUNCT
ejpam-4187	69	59	and	and	CCONJ
ejpam-4187	69	60	is	be	AUX
ejpam-4187	69	61	denoted	denote	VERB
ejpam-4187	69	62	by	by	ADP
ejpam-4187	69	63	γdt	γdt	PROPN
ejpam-4187	69	64	(	(	PUNCT
ejpam-4187	69	65	g	g	NOUN
ejpam-4187	69	66	)	)	PUNCT
ejpam-4187	69	67	.	.	PUNCT
ejpam-4187	70	1	any	any	DET
ejpam-4187	70	2	disjunctive	disjunctive	ADJ
ejpam-4187	70	3	total	total	ADJ
ejpam-4187	70	4	dominating	dominating	NOUN
ejpam-4187	70	5	set	set	NOUN
ejpam-4187	70	6	of	of	ADP
ejpam-4187	70	7	cardinality	cardinality	PROPN
ejpam-4187	70	8	γdt	γdt	PROPN
ejpam-4187	70	9	(	(	PUNCT
ejpam-4187	70	10	g	g	NOUN
ejpam-4187	70	11	)	)	PUNCT
ejpam-4187	70	12	is	be	AUX
ejpam-4187	70	13	called	call	VERB
ejpam-4187	70	14	γdt	γdt	PROPN
ejpam-4187	70	15	-set	-set	ADJ
ejpam-4187	70	16	.	.	PUNCT
ejpam-4187	71	1	provided	provide	VERB
ejpam-4187	71	2	g	g	PROPN
ejpam-4187	71	3	has	have	VERB
ejpam-4187	71	4	no	no	DET
ejpam-4187	71	5	isolated	isolated	ADJ
ejpam-4187	71	6	vertices	vertex	NOUN
ejpam-4187	71	7	,	,	PUNCT
ejpam-4187	71	8	a	a	DET
ejpam-4187	71	9	disjunctive	disjunctive	ADJ
ejpam-4187	71	10	dominating	dominating	NOUN
ejpam-4187	71	11	set	set	NOUN
ejpam-4187	71	12	s	s	NOUN
ejpam-4187	71	13	of	of	ADP
ejpam-4187	71	14	g	g	PROPN
ejpam-4187	71	15	is	be	AUX
ejpam-4187	71	16	a	a	DET
ejpam-4187	71	17	restrained	restrained	ADJ
ejpam-4187	71	18	disjunctive	disjunctive	ADJ
ejpam-4187	71	19	dominating	dominating	NOUN
ejpam-4187	71	20	set	set	NOUN
ejpam-4187	71	21	of	of	ADP
ejpam-4187	71	22	g	g	PROPN
ejpam-4187	71	23	if	if	SCONJ
ejpam-4187	71	24	for	for	ADP
ejpam-4187	71	25	each	each	PRON
ejpam-4187	71	26	v	v	NUM
ejpam-4187	71	27	∈	∈	PROPN
ejpam-4187	71	28	v	v	NOUN
ejpam-4187	71	29	(	(	PUNCT
ejpam-4187	71	30	g	g	NOUN
ejpam-4187	71	31	)	)	PUNCT
ejpam-4187	71	32	\	\	PROPN
ejpam-4187	72	1	s	s	VERB
ejpam-4187	72	2	there	there	PRON
ejpam-4187	72	3	exists	exist	VERB
ejpam-4187	72	4	u	u	PROPN
ejpam-4187	72	5	∈	∈	PROPN
ejpam-4187	72	6	v	v	ADP
ejpam-4187	72	7	(	(	PUNCT
ejpam-4187	72	8	g	g	NOUN
ejpam-4187	72	9	)	)	PUNCT
ejpam-4187	72	10	\	\	PUNCT
ejpam-4187	73	1	s	s	VERB
ejpam-4187	73	2	such	such	ADJ
ejpam-4187	73	3	that	that	DET
ejpam-4187	73	4	uv	uv	PROPN
ejpam-4187	73	5	∈	∈	PROPN
ejpam-4187	73	6	e(g	e(g	PROPN
ejpam-4187	73	7	)	)	PUNCT
ejpam-4187	73	8	or	or	CCONJ
ejpam-4187	73	9	there	there	PRON
ejpam-4187	73	10	exist	exist	VERB
ejpam-4187	73	11	distinct	distinct	ADJ
ejpam-4187	73	12	vertices	vertex	NOUN
ejpam-4187	73	13	u	u	NOUN
ejpam-4187	73	14	,	,	PUNCT
ejpam-4187	73	15	w	w	PROPN
ejpam-4187	73	16	∈	∈	PROPN
ejpam-4187	73	17	v	v	ADP
ejpam-4187	73	18	(	(	PUNCT
ejpam-4187	73	19	g	g	NOUN
ejpam-4187	73	20	)	)	PUNCT
ejpam-4187	73	21	\	\	PUNCT
ejpam-4187	74	1	s	s	VERB
ejpam-4187	74	2	such	such	ADJ
ejpam-4187	74	3	that	that	DET
ejpam-4187	74	4	dg(u	dg(u	ADJ
ejpam-4187	74	5	,	,	PUNCT
ejpam-4187	74	6	v	v	NOUN
ejpam-4187	74	7	)	)	PUNCT
ejpam-4187	74	8	=	=	SYM
ejpam-4187	74	9	2	2	NUM
ejpam-4187	74	10	=	=	SYM
ejpam-4187	74	11	dg(w	dg(w	X
ejpam-4187	74	12	,	,	PUNCT
ejpam-4187	74	13	v	v	NOUN
ejpam-4187	74	14	)	)	PUNCT
ejpam-4187	74	15	.	.	PUNCT
ejpam-4187	75	1	the	the	DET
ejpam-4187	75	2	minimum	minimum	ADJ
ejpam-4187	75	3	cardinality	cardinality	NOUN
ejpam-4187	75	4	of	of	ADP
ejpam-4187	75	5	a	a	DET
ejpam-4187	75	6	restrained	restrained	ADJ
ejpam-4187	75	7	disjunctive	disjunctive	ADJ
ejpam-4187	75	8	dominating	dominating	NOUN
ejpam-4187	75	9	set	set	NOUN
ejpam-4187	75	10	of	of	ADP
ejpam-4187	75	11	g	g	PROPN
ejpam-4187	75	12	is	be	AUX
ejpam-4187	75	13	the	the	DET
ejpam-4187	75	14	restrained	restrain	VERB
ejpam-4187	75	15	disjunctive	disjunctive	ADJ
ejpam-4187	75	16	domination	domination	NOUN
ejpam-4187	75	17	number	number	NOUN
ejpam-4187	75	18	of	of	ADP
ejpam-4187	75	19	g	g	NOUN
ejpam-4187	75	20	,	,	PUNCT
ejpam-4187	75	21	and	and	CCONJ
ejpam-4187	75	22	is	be	AUX
ejpam-4187	75	23	denoted	denote	VERB
ejpam-4187	75	24	by	by	ADP
ejpam-4187	75	25	γdr	γdr	PROPN
ejpam-4187	75	26	(	(	PUNCT
ejpam-4187	75	27	g	g	NOUN
ejpam-4187	75	28	)	)	PUNCT
ejpam-4187	75	29	.	.	PUNCT
ejpam-4187	76	1	any	any	DET
ejpam-4187	76	2	restrained	restrained	ADJ
ejpam-4187	76	3	disjunctive	disjunctive	ADJ
ejpam-4187	76	4	dominating	dominating	NOUN
ejpam-4187	76	5	set	set	NOUN
ejpam-4187	76	6	of	of	ADP
ejpam-4187	76	7	cardinality	cardinality	PROPN
ejpam-4187	76	8	γdr	γdr	PROPN
ejpam-4187	77	1	(	(	PUNCT
ejpam-4187	77	2	g	g	NOUN
ejpam-4187	77	3	)	)	PUNCT
ejpam-4187	77	4	is	be	AUX
ejpam-4187	77	5	called	call	VERB
ejpam-4187	77	6	γdr	γdr	PROPN
ejpam-4187	77	7	-set	-set	PROPN
ejpam-4187	77	8	.	.	PUNCT
ejpam-4187	78	1	since	since	SCONJ
ejpam-4187	78	2	restrained	restrain	VERB
ejpam-4187	78	3	disjunctive	disjunctive	ADJ
ejpam-4187	78	4	dominating	dominating	NOUN
ejpam-4187	78	5	sets	set	NOUN
ejpam-4187	78	6	are	be	AUX
ejpam-4187	78	7	disjunctive	disjunctive	ADJ
ejpam-4187	78	8	dominating	dominating	NOUN
ejpam-4187	78	9	sets	set	NOUN
ejpam-4187	78	10	,	,	PUNCT
ejpam-4187	78	11	1	1	NUM
ejpam-4187	78	12	≤	≤	NUM
ejpam-4187	78	13	γd(g	γd(g	NUM
ejpam-4187	78	14	)	)	PUNCT
ejpam-4187	78	15	≤	≤	NUM
ejpam-4187	78	16	γdr	γdr	INTJ
ejpam-4187	79	1	(	(	PUNCT
ejpam-4187	79	2	g	g	NOUN
ejpam-4187	79	3	)	)	PUNCT
ejpam-4187	79	4	for	for	ADP
ejpam-4187	79	5	all	all	DET
ejpam-4187	79	6	graphs	graph	NOUN
ejpam-4187	79	7	g	g	NOUN
ejpam-4187	79	8	without	without	ADP
ejpam-4187	79	9	isolated	isolated	ADJ
ejpam-4187	79	10	vertices	vertex	NOUN
ejpam-4187	79	11	.	.	PUNCT
ejpam-4187	80	1	r.	r.	PROPN
ejpam-4187	80	2	malalay	malalay	PROPN
ejpam-4187	80	3	,	,	PUNCT
ejpam-4187	80	4	f.	f.	PROPN
ejpam-4187	80	5	jamil	jamil	PROPN
ejpam-4187	80	6	/	/	SYM
ejpam-4187	80	7	eur	eur	PROPN
ejpam-4187	80	8	.	.	PUNCT
ejpam-4187	81	1	j.	j.	PROPN
ejpam-4187	81	2	pure	pure	PROPN
ejpam-4187	81	3	appl	appl	PROPN
ejpam-4187	81	4	.	.	PROPN
ejpam-4187	81	5	math	math	PROPN
ejpam-4187	81	6	,	,	PUNCT
ejpam-4187	81	7	15	15	NUM
ejpam-4187	81	8	(	(	PUNCT
ejpam-4187	81	9	1	1	NUM
ejpam-4187	81	10	)	)	PUNCT
ejpam-4187	81	11	(	(	PUNCT
ejpam-4187	81	12	2022	2022	NUM
ejpam-4187	81	13	)	)	PUNCT
ejpam-4187	81	14	,	,	PUNCT
ejpam-4187	81	15	207	207	NUM
ejpam-4187	81	16	-	-	SYM
ejpam-4187	81	17	223	223	NUM
ejpam-4187	81	18	210	210	NUM
ejpam-4187	81	19	2	2	NUM
ejpam-4187	81	20	.	.	PUNCT
ejpam-4187	81	21	preliminaries	preliminary	NOUN
ejpam-4187	81	22	and	and	CCONJ
ejpam-4187	81	23	known	know	VERB
ejpam-4187	81	24	results	result	NOUN
ejpam-4187	81	25	the	the	DET
ejpam-4187	81	26	following	follow	VERB
ejpam-4187	81	27	are	be	AUX
ejpam-4187	81	28	some	some	DET
ejpam-4187	81	29	known	know	VERB
ejpam-4187	81	30	results	result	NOUN
ejpam-4187	81	31	for	for	ADP
ejpam-4187	81	32	paths	path	NOUN
ejpam-4187	81	33	and	and	CCONJ
ejpam-4187	81	34	cycles	cycle	NOUN
ejpam-4187	81	35	.	.	PUNCT
ejpam-4187	82	1	theorem	theorem	NOUN
ejpam-4187	82	2	1	1	NUM
ejpam-4187	82	3	.	.	PUNCT
ejpam-4187	83	1	(	(	PUNCT
ejpam-4187	83	2	i	i	NOUN
ejpam-4187	83	3	)	)	PUNCT
ejpam-4187	84	1	[	[	X
ejpam-4187	84	2	8	8	NUM
ejpam-4187	84	3	]	]	PUNCT
ejpam-4187	84	4	for	for	ADP
ejpam-4187	84	5	all	all	DET
ejpam-4187	84	6	n	n	CCONJ
ejpam-4187	84	7	,	,	PUNCT
ejpam-4187	84	8	γd(pn	γd(pn	NOUN
ejpam-4187	84	9	)	)	PUNCT
ejpam-4187	84	10	=	=	PUNCT
ejpam-4187	85	1	⌈n+1	⌈n+1	ADJ
ejpam-4187	85	2	4	4	NUM
ejpam-4187	85	3	⌉	⌉	NOUN
ejpam-4187	85	4	;	;	PUNCT
ejpam-4187	85	5	(	(	PUNCT
ejpam-4187	85	6	ii	ii	NOUN
ejpam-4187	85	7	)	)	PUNCT
ejpam-4187	86	1	[	[	X
ejpam-4187	86	2	8	8	NUM
ejpam-4187	86	3	]	]	PUNCT
ejpam-4187	86	4	for	for	ADP
ejpam-4187	86	5	cycle	cycle	NOUN
ejpam-4187	86	6	cn	cn	PROPN
ejpam-4187	86	7	,	,	PUNCT
ejpam-4187	86	8	n	n	PRON
ejpam-4187	86	9	≥	≥	NOUN
ejpam-4187	86	10	3	3	NUM
ejpam-4187	86	11	,	,	PUNCT
ejpam-4187	86	12	γd(cn	γd(cn	NOUN
ejpam-4187	86	13	)	)	PUNCT
ejpam-4187	86	14	=	=	SYM
ejpam-4187	86	15	2	2	NUM
ejpam-4187	86	16	for	for	ADP
ejpam-4187	86	17	n	n	NOUN
ejpam-4187	86	18	=	=	SYM
ejpam-4187	86	19	4	4	NUM
ejpam-4187	86	20	,	,	PUNCT
ejpam-4187	86	21	and	and	CCONJ
ejpam-4187	86	22	γd(cn	γd(cn	NOUN
ejpam-4187	86	23	)	)	PUNCT
ejpam-4187	86	24	=	=	PUNCT
ejpam-4187	86	25	⌈n4	⌈n4	VERB
ejpam-4187	86	26	⌉	⌉	X
ejpam-4187	86	27	for	for	ADP
ejpam-4187	86	28	n	n	PRON
ejpam-4187	86	29	̸=	̸=	PROPN
ejpam-4187	86	30	4	4	NUM
ejpam-4187	86	31	.	.	PUNCT
ejpam-4187	87	1	next	next	ADJ
ejpam-4187	87	2	are	be	AUX
ejpam-4187	87	3	our	our	PRON
ejpam-4187	87	4	preliminary	preliminary	ADJ
ejpam-4187	87	5	results	result	NOUN
ejpam-4187	87	6	which	which	PRON
ejpam-4187	87	7	have	have	VERB
ejpam-4187	87	8	exact	exact	ADJ
ejpam-4187	87	9	values	value	NOUN
ejpam-4187	87	10	or	or	CCONJ
ejpam-4187	87	11	bounds	bound	NOUN
ejpam-4187	87	12	of	of	ADP
ejpam-4187	87	13	some	some	DET
ejpam-4187	87	14	special	special	ADJ
ejpam-4187	87	15	graphs	graph	NOUN
ejpam-4187	87	16	in	in	ADP
ejpam-4187	87	17	terms	term	NOUN
ejpam-4187	87	18	of	of	ADP
ejpam-4187	87	19	the	the	DET
ejpam-4187	87	20	restrained	restrain	VERB
ejpam-4187	87	21	disjunctive	disjunctive	ADJ
ejpam-4187	87	22	domination	domination	NOUN
ejpam-4187	87	23	number	number	NOUN
ejpam-4187	87	24	.	.	PUNCT
ejpam-4187	88	1	let	let	VERB
ejpam-4187	88	2	g	g	PRON
ejpam-4187	88	3	be	be	AUX
ejpam-4187	88	4	a	a	DET
ejpam-4187	88	5	connected	connected	ADJ
ejpam-4187	88	6	graph	graph	NOUN
ejpam-4187	88	7	and	and	CCONJ
ejpam-4187	88	8	u	u	NOUN
ejpam-4187	88	9	,	,	PUNCT
ejpam-4187	88	10	v	v	PROPN
ejpam-4187	88	11	∈	∈	PROPN
ejpam-4187	88	12	v	v	NOUN
ejpam-4187	88	13	(	(	PUNCT
ejpam-4187	88	14	g	g	NOUN
ejpam-4187	88	15	)	)	PUNCT
ejpam-4187	88	16	such	such	ADJ
ejpam-4187	88	17	that	that	SCONJ
ejpam-4187	88	18	uv	uv	PROPN
ejpam-4187	88	19	∈	∈	PROPN
ejpam-4187	88	20	e(g	e(g	PROPN
ejpam-4187	88	21	)	)	PUNCT
ejpam-4187	88	22	.	.	PUNCT
ejpam-4187	89	1	if	if	SCONJ
ejpam-4187	89	2	u	u	NOUN
ejpam-4187	89	3	is	be	AUX
ejpam-4187	89	4	the	the	DET
ejpam-4187	89	5	end	end	NOUN
ejpam-4187	89	6	vertex	vertex	NOUN
ejpam-4187	89	7	of	of	ADP
ejpam-4187	89	8	graph	graph	NOUN
ejpam-4187	89	9	g	g	PROPN
ejpam-4187	89	10	and	and	CCONJ
ejpam-4187	89	11	degg(v	degg(v	PROPN
ejpam-4187	89	12	)	)	PUNCT
ejpam-4187	89	13	≤	≤	NOUN
ejpam-4187	89	14	2	2	NUM
ejpam-4187	89	15	,	,	PUNCT
ejpam-4187	89	16	then	then	ADV
ejpam-4187	89	17	u	u	PROPN
ejpam-4187	89	18	∈	∈	PROPN
ejpam-4187	89	19	s	s	X
ejpam-4187	89	20	for	for	ADP
ejpam-4187	89	21	all	all	DET
ejpam-4187	89	22	restrained	restrained	ADJ
ejpam-4187	89	23	disjunctive	disjunctive	ADJ
ejpam-4187	89	24	dominating	dominating	NOUN
ejpam-4187	89	25	sets	set	NOUN
ejpam-4187	89	26	s	s	PROPN
ejpam-4187	89	27	of	of	ADP
ejpam-4187	89	28	g.	g.	PROPN
ejpam-4187	89	29	proposition	proposition	NOUN
ejpam-4187	89	30	1	1	NUM
ejpam-4187	89	31	.	.	PUNCT
ejpam-4187	90	1	(	(	PUNCT
ejpam-4187	90	2	i	i	NOUN
ejpam-4187	90	3	)	)	PUNCT
ejpam-4187	90	4	for	for	ADP
ejpam-4187	90	5	path	path	NOUN
ejpam-4187	90	6	pn	pn	PROPN
ejpam-4187	90	7	,	,	PUNCT
ejpam-4187	90	8	n	n	PRON
ejpam-4187	90	9	≥	≥	NOUN
ejpam-4187	90	10	1	1	NUM
ejpam-4187	90	11	,	,	PUNCT
ejpam-4187	90	12	γdr	γdr	INTJ
ejpam-4187	90	13	(	(	PUNCT
ejpam-4187	90	14	pn	pn	NOUN
ejpam-4187	90	15	)	)	PUNCT
ejpam-4187	90	16	=	=	NOUN
ejpam-4187	90	17	{	{	PUNCT
ejpam-4187	90	18	3	3	NUM
ejpam-4187	90	19	,	,	PUNCT
ejpam-4187	90	20	if	if	SCONJ
ejpam-4187	90	21	n	n	NOUN
ejpam-4187	90	22	=	=	SYM
ejpam-4187	90	23	3	3	NUM
ejpam-4187	90	24	⌈n−1	⌈n−1	NOUN
ejpam-4187	90	25	4	4	NUM
ejpam-4187	90	26	⌉+	⌉+	SYM
ejpam-4187	90	27	1	1	NUM
ejpam-4187	90	28	,	,	PUNCT
ejpam-4187	90	29	if	if	SCONJ
ejpam-4187	90	30	n	n	PRON
ejpam-4187	90	31	̸=	̸=	PROPN
ejpam-4187	90	32	3	3	NUM
ejpam-4187	90	33	.	.	PUNCT
ejpam-4187	90	34	(	(	PUNCT
ejpam-4187	90	35	ii	ii	NOUN
ejpam-4187	90	36	)	)	PUNCT
ejpam-4187	90	37	for	for	ADP
ejpam-4187	90	38	cycle	cycle	NOUN
ejpam-4187	90	39	cn	cn	PROPN
ejpam-4187	90	40	,	,	PUNCT
ejpam-4187	90	41	n	n	PRON
ejpam-4187	90	42	≥	≥	NOUN
ejpam-4187	90	43	3	3	NUM
ejpam-4187	90	44	,	,	PUNCT
ejpam-4187	90	45	γdr	γdr	X
ejpam-4187	90	46	(	(	PUNCT
ejpam-4187	90	47	cn	cn	NOUN
ejpam-4187	90	48	)	)	PUNCT
ejpam-4187	90	49	=	=	SYM
ejpam-4187	91	1			NOUN
ejpam-4187	91	2	1	1	NUM
ejpam-4187	91	3	,	,	PUNCT
ejpam-4187	91	4	if	if	SCONJ
ejpam-4187	91	5	n	n	NOUN
ejpam-4187	91	6	=	=	SYM
ejpam-4187	91	7	3	3	NUM
ejpam-4187	91	8	2	2	NUM
ejpam-4187	91	9	,	,	PUNCT
ejpam-4187	91	10	if	if	SCONJ
ejpam-4187	91	11	n	n	NOUN
ejpam-4187	91	12	=	=	SYM
ejpam-4187	91	13	4	4	NUM
ejpam-4187	91	14	⌈n4	⌈n4	VERB
ejpam-4187	91	15	⌉	⌉	NOUN
ejpam-4187	91	16	,	,	PUNCT
ejpam-4187	91	17	if	if	SCONJ
ejpam-4187	91	18	n	n	PRON
ejpam-4187	91	19	≥	≥	NOUN
ejpam-4187	91	20	5	5	NUM
ejpam-4187	91	21	.	.	PUNCT
ejpam-4187	92	1	proof	proof	NOUN
ejpam-4187	92	2	.	.	PUNCT
ejpam-4187	93	1	to	to	PART
ejpam-4187	93	2	prove	prove	VERB
ejpam-4187	93	3	(	(	PUNCT
ejpam-4187	93	4	i	i	NOUN
ejpam-4187	93	5	)	)	PUNCT
ejpam-4187	93	6	,	,	PUNCT
ejpam-4187	93	7	let	let	VERB
ejpam-4187	93	8	pn	pn	VERB
ejpam-4187	93	9	=	=	PUNCT
ejpam-4187	94	1	[	[	X
ejpam-4187	94	2	x1	x1	PROPN
ejpam-4187	94	3	,	,	PUNCT
ejpam-4187	94	4	x2	x2	PROPN
ejpam-4187	94	5	,	,	PUNCT
ejpam-4187	94	6	.	.	PUNCT
ejpam-4187	94	7	.	.	PUNCT
ejpam-4187	95	1	.	.	PUNCT
ejpam-4187	96	1	,	,	PUNCT
ejpam-4187	96	2	xn	xn	PROPN
ejpam-4187	96	3	]	]	X
ejpam-4187	96	4	.	.	PUNCT
ejpam-4187	97	1	the	the	DET
ejpam-4187	97	2	case	case	NOUN
ejpam-4187	97	3	where	where	SCONJ
ejpam-4187	97	4	1	1	NUM
ejpam-4187	97	5	≤	≤	NOUN
ejpam-4187	97	6	n	n	PRON
ejpam-4187	97	7	≤	≤	NUM
ejpam-4187	97	8	4	4	NUM
ejpam-4187	97	9	is	be	AUX
ejpam-4187	97	10	obvious	obvious	ADJ
ejpam-4187	97	11	.	.	PUNCT
ejpam-4187	97	12	suppose	suppose	VERB
ejpam-4187	97	13	that	that	SCONJ
ejpam-4187	97	14	n	n	PROPN
ejpam-4187	97	15	≥	≥	NUM
ejpam-4187	97	16	5	5	NUM
ejpam-4187	97	17	.	.	PUNCT
ejpam-4187	98	1	let	let	VERB
ejpam-4187	98	2	k	k	PRON
ejpam-4187	98	3	be	be	AUX
ejpam-4187	98	4	the	the	DET
ejpam-4187	98	5	largest	large	ADJ
ejpam-4187	98	6	integer	integer	NOUN
ejpam-4187	98	7	for	for	ADP
ejpam-4187	98	8	which	which	PRON
ejpam-4187	98	9	4k	4k	NUM
ejpam-4187	98	10	+	+	CCONJ
ejpam-4187	98	11	1	1	NUM
ejpam-4187	98	12	≤	≤	NOUN
ejpam-4187	98	13	n.	n.	NOUN
ejpam-4187	98	14	if	if	SCONJ
ejpam-4187	98	15	n−	n−	PROPN
ejpam-4187	98	16	4k	4k	NOUN
ejpam-4187	98	17	−	−	NOUN
ejpam-4187	98	18	1	1	NUM
ejpam-4187	98	19	̸=	̸=	PROPN
ejpam-4187	98	20	2	2	NUM
ejpam-4187	98	21	,	,	PUNCT
ejpam-4187	98	22	take	take	VERB
ejpam-4187	98	23	s	s	PART
ejpam-4187	98	24	=	=	PUNCT
ejpam-4187	98	25	{	{	PUNCT
ejpam-4187	98	26	x1	x1	PROPN
ejpam-4187	98	27	,	,	PUNCT
ejpam-4187	98	28	x5	x5	PROPN
ejpam-4187	98	29	,	,	PUNCT
ejpam-4187	98	30	.	.	PUNCT
ejpam-4187	98	31	.	.	PUNCT
ejpam-4187	99	1	.	.	PUNCT
ejpam-4187	100	1	,	,	PUNCT
ejpam-4187	100	2	x4k+1	x4k+1	PROPN
ejpam-4187	100	3	,	,	PUNCT
ejpam-4187	100	4	xn	xn	NUM
ejpam-4187	100	5	}	}	PUNCT
ejpam-4187	100	6	.	.	PUNCT
ejpam-4187	101	1	otherwise	otherwise	ADV
ejpam-4187	101	2	,	,	PUNCT
ejpam-4187	101	3	take	take	VERB
ejpam-4187	101	4	s	s	PART
ejpam-4187	101	5	=	=	PUNCT
ejpam-4187	101	6	{	{	PUNCT
ejpam-4187	101	7	x1	x1	PROPN
ejpam-4187	101	8	,	,	PUNCT
ejpam-4187	101	9	x5	x5	PROPN
ejpam-4187	101	10	,	,	PUNCT
ejpam-4187	101	11	.	.	PUNCT
ejpam-4187	101	12	.	.	PUNCT
ejpam-4187	101	13	.	.	PUNCT
ejpam-4187	102	1	,	,	PUNCT
ejpam-4187	102	2	x4k	x4k	NOUN
ejpam-4187	102	3	,	,	PUNCT
ejpam-4187	102	4	xn	xn	NUM
ejpam-4187	102	5	}	}	PUNCT
ejpam-4187	102	6	.	.	PUNCT
ejpam-4187	103	1	then	then	ADV
ejpam-4187	103	2	s	s	VERB
ejpam-4187	103	3	is	be	AUX
ejpam-4187	103	4	a	a	DET
ejpam-4187	103	5	restrained	restrained	ADJ
ejpam-4187	103	6	disjunctive	disjunctive	ADJ
ejpam-4187	103	7	dominating	dominating	NOUN
ejpam-4187	103	8	set	set	NOUN
ejpam-4187	103	9	of	of	ADP
ejpam-4187	103	10	pn	pn	PROPN
ejpam-4187	103	11	.	.	PUNCT
ejpam-4187	103	12	thus	thus	ADV
ejpam-4187	103	13	,	,	PUNCT
ejpam-4187	103	14	γdr	γdr	INTJ
ejpam-4187	103	15	(	(	PUNCT
ejpam-4187	103	16	pn	pn	NOUN
ejpam-4187	103	17	)	)	PUNCT
ejpam-4187	103	18	≤	≤	NOUN
ejpam-4187	103	19	⌈n−1	⌈n−1	NOUN
ejpam-4187	103	20	4	4	NUM
ejpam-4187	103	21	⌉	⌉	NOUN
ejpam-4187	103	22	+	+	NOUN
ejpam-4187	103	23	1	1	X
ejpam-4187	103	24	.	.	PUNCT
ejpam-4187	103	25	now	now	ADV
ejpam-4187	103	26	,	,	PUNCT
ejpam-4187	103	27	suppose	suppose	VERB
ejpam-4187	103	28	that	that	SCONJ
ejpam-4187	103	29	s∗	s∗	PROPN
ejpam-4187	103	30	⊆	⊆	NUM
ejpam-4187	103	31	v	v	NOUN
ejpam-4187	103	32	(	(	PUNCT
ejpam-4187	103	33	g	g	NOUN
ejpam-4187	103	34	)	)	PUNCT
ejpam-4187	103	35	is	be	AUX
ejpam-4187	103	36	a	a	DET
ejpam-4187	103	37	restrained	restrained	ADJ
ejpam-4187	103	38	disjunctive	disjunctive	ADJ
ejpam-4187	103	39	dominating	dominating	NOUN
ejpam-4187	103	40	set	set	NOUN
ejpam-4187	103	41	of	of	ADP
ejpam-4187	103	42	g	g	NOUN
ejpam-4187	103	43	with	with	ADP
ejpam-4187	103	44	|s∗|	|s∗|	NUM
ejpam-4187	103	45	≤	≤	NUM
ejpam-4187	103	46	⌈n−1	⌈n−1	NOUN
ejpam-4187	103	47	4	4	NUM
ejpam-4187	103	48	⌉.	⌉.	ADV
ejpam-4187	103	49	in	in	ADP
ejpam-4187	103	50	view	view	NOUN
ejpam-4187	103	51	of	of	ADP
ejpam-4187	103	52	observation	observation	NOUN
ejpam-4187	103	53	2	2	NUM
ejpam-4187	103	54	,	,	PUNCT
ejpam-4187	103	55	x1	x1	PROPN
ejpam-4187	103	56	,	,	PUNCT
ejpam-4187	103	57	xn	xn	PROPN
ejpam-4187	103	58	∈	∈	PROPN
ejpam-4187	103	59	s∗.	s∗.	ADJ
ejpam-4187	103	60	in	in	ADP
ejpam-4187	103	61	particular	particular	ADJ
ejpam-4187	103	62	,	,	PUNCT
ejpam-4187	103	63	|s∗|	|s∗|	PUNCT
ejpam-4187	103	64	=	=	SYM
ejpam-4187	103	65	1	1	NUM
ejpam-4187	103	66	if	if	SCONJ
ejpam-4187	103	67	n	n	NOUN
ejpam-4187	103	68	=	=	SYM
ejpam-4187	103	69	5	5	NUM
ejpam-4187	103	70	,	,	PUNCT
ejpam-4187	103	71	which	which	PRON
ejpam-4187	103	72	is	be	AUX
ejpam-4187	103	73	impossible	impossible	ADJ
ejpam-4187	103	74	.	.	PUNCT
ejpam-4187	104	1	let	let	VERB
ejpam-4187	104	2	n	n	PRON
ejpam-4187	104	3	≥	≥	NUM
ejpam-4187	104	4	6	6	NUM
ejpam-4187	104	5	.	.	PUNCT
ejpam-4187	105	1	pick	pick	VERB
ejpam-4187	105	2	u	u	NOUN
ejpam-4187	105	3	,	,	PUNCT
ejpam-4187	105	4	v	v	PROPN
ejpam-4187	105	5	∈	∈	NOUN
ejpam-4187	105	6	s	s	VERB
ejpam-4187	105	7	such	such	ADJ
ejpam-4187	105	8	that	that	DET
ejpam-4187	105	9	dpn(u	dpn(u	PROPN
ejpam-4187	105	10	,	,	PUNCT
ejpam-4187	105	11	v	v	NOUN
ejpam-4187	105	12	)	)	PUNCT
ejpam-4187	105	13	is	be	AUX
ejpam-4187	105	14	maximum	maximum	ADJ
ejpam-4187	105	15	among	among	ADP
ejpam-4187	105	16	all	all	DET
ejpam-4187	105	17	pairs	pair	NOUN
ejpam-4187	105	18	(	(	PUNCT
ejpam-4187	105	19	x	x	NOUN
ejpam-4187	105	20	,	,	PUNCT
ejpam-4187	105	21	y	y	PROPN
ejpam-4187	105	22	)	)	PUNCT
ejpam-4187	105	23	∈	∈	PROPN
ejpam-4187	105	24	s	s	PART
ejpam-4187	105	25	×	×	NOUN
ejpam-4187	105	26	s	s	X
ejpam-4187	105	27	for	for	ADP
ejpam-4187	105	28	which	which	PRON
ejpam-4187	105	29	s	s	VERB
ejpam-4187	105	30	\	\	X
ejpam-4187	105	31	{	{	PUNCT
ejpam-4187	105	32	x	x	NOUN
ejpam-4187	105	33	,	,	PUNCT
ejpam-4187	105	34	y	y	PROPN
ejpam-4187	105	35	}	}	PUNCT
ejpam-4187	105	36	does	do	AUX
ejpam-4187	105	37	not	not	PART
ejpam-4187	105	38	contain	contain	VERB
ejpam-4187	105	39	a	a	DET
ejpam-4187	105	40	vertex	vertex	NOUN
ejpam-4187	105	41	lying	lie	VERB
ejpam-4187	105	42	in	in	ADP
ejpam-4187	105	43	the	the	DET
ejpam-4187	105	44	x	x	PROPN
ejpam-4187	105	45	-	-	PROPN
ejpam-4187	105	46	y	y	ADJ
ejpam-4187	105	47	path	path	NOUN
ejpam-4187	105	48	.	.	PUNCT
ejpam-4187	106	1	then	then	ADV
ejpam-4187	106	2	dpn(u	dpn(u	PROPN
ejpam-4187	106	3	,	,	PUNCT
ejpam-4187	106	4	v	v	NOUN
ejpam-4187	106	5	)	)	PUNCT
ejpam-4187	106	6	≥	≥	NOUN
ejpam-4187	106	7	5	5	NUM
ejpam-4187	106	8	.	.	PUNCT
ejpam-4187	106	9	thus	thus	ADV
ejpam-4187	106	10	,	,	PUNCT
ejpam-4187	106	11	there	there	PRON
ejpam-4187	106	12	exists	exist	VERB
ejpam-4187	106	13	w	w	PROPN
ejpam-4187	106	14	∈	∈	PROPN
ejpam-4187	106	15	v	v	NOUN
ejpam-4187	106	16	(	(	PUNCT
ejpam-4187	106	17	pn	pn	NOUN
ejpam-4187	106	18	)	)	PUNCT
ejpam-4187	106	19	\	\	PROPN
ejpam-4187	107	1	s	s	VERB
ejpam-4187	107	2	such	such	ADJ
ejpam-4187	107	3	that	that	PRON
ejpam-4187	107	4	w	w	PROPN
ejpam-4187	107	5	/∈	/∈	PROPN
ejpam-4187	107	6	nd	nd	INTJ
ejpam-4187	107	7	pn	pn	PROPN
ejpam-4187	107	8	(	(	PUNCT
ejpam-4187	107	9	s	s	PROPN
ejpam-4187	107	10	)	)	PUNCT
ejpam-4187	107	11	,	,	PUNCT
ejpam-4187	107	12	a	a	DET
ejpam-4187	107	13	contradiction	contradiction	NOUN
ejpam-4187	107	14	.	.	PUNCT
ejpam-4187	108	1	the	the	DET
ejpam-4187	108	2	case	case	NOUN
ejpam-4187	108	3	where	where	SCONJ
ejpam-4187	108	4	3	3	NUM
ejpam-4187	108	5	≤	≤	NOUN
ejpam-4187	108	6	n	n	PRON
ejpam-4187	108	7	≤	≤	NUM
ejpam-4187	108	8	4	4	NUM
ejpam-4187	108	9	is	be	AUX
ejpam-4187	108	10	obvious	obvious	ADJ
ejpam-4187	108	11	for	for	ADP
ejpam-4187	108	12	cn	cn	PROPN
ejpam-4187	108	13	.	.	PUNCT
ejpam-4187	109	1	let	let	VERB
ejpam-4187	109	2	n	n	PRON
ejpam-4187	109	3	≥	≥	NOUN
ejpam-4187	109	4	5	5	NUM
ejpam-4187	109	5	.	.	PUNCT
ejpam-4187	109	6	by	by	ADP
ejpam-4187	109	7	theorem	theorem	NOUN
ejpam-4187	109	8	1	1	NUM
ejpam-4187	109	9	,	,	PUNCT
ejpam-4187	109	10	⌈n4	⌈n4	VERB
ejpam-4187	109	11	⌉	⌉	ADP
ejpam-4187	109	12	=	=	SYM
ejpam-4187	109	13	γd(cn	γd(cn	NOUN
ejpam-4187	109	14	)	)	PUNCT
ejpam-4187	109	15	≤	≤	NUM
ejpam-4187	110	1	γdr	γdr	INTJ
ejpam-4187	110	2	(	(	PUNCT
ejpam-4187	110	3	cn	cn	PROPN
ejpam-4187	110	4	)	)	PUNCT
ejpam-4187	110	5	.	.	PUNCT
ejpam-4187	111	1	let	let	VERB
ejpam-4187	111	2	cn	cn	PROPN
ejpam-4187	111	3	=	=	PUNCT
ejpam-4187	112	1	[	[	X
ejpam-4187	112	2	x1	x1	PROPN
ejpam-4187	112	3	,	,	PUNCT
ejpam-4187	112	4	x2	x2	PROPN
ejpam-4187	112	5	,	,	PUNCT
ejpam-4187	112	6	.	.	PUNCT
ejpam-4187	112	7	.	.	PUNCT
ejpam-4187	113	1	.	.	PUNCT
ejpam-4187	114	1	,	,	PUNCT
ejpam-4187	114	2	xn	xn	PROPN
ejpam-4187	114	3	,	,	PUNCT
ejpam-4187	114	4	x1	x1	PROPN
ejpam-4187	114	5	]	]	PUNCT
ejpam-4187	114	6	.	.	PUNCT
ejpam-4187	115	1	define	define	VERB
ejpam-4187	115	2	s	s	NOUN
ejpam-4187	115	3	=	=	PUNCT
ejpam-4187	115	4	{	{	PUNCT
ejpam-4187	115	5	x1	x1	PROPN
ejpam-4187	115	6	,	,	PUNCT
ejpam-4187	115	7	x5	x5	PROPN
ejpam-4187	115	8	,	,	PUNCT
ejpam-4187	115	9	.	.	PUNCT
ejpam-4187	115	10	.	.	PUNCT
ejpam-4187	115	11	.	.	PUNCT
ejpam-4187	116	1	,	,	PUNCT
ejpam-4187	116	2	x4k+1	x4k+1	PROPN
ejpam-4187	116	3	}	}	PUNCT
ejpam-4187	116	4	,	,	PUNCT
ejpam-4187	116	5	where	where	SCONJ
ejpam-4187	116	6	k	k	PROPN
ejpam-4187	116	7	is	be	AUX
ejpam-4187	116	8	the	the	DET
ejpam-4187	116	9	largest	large	ADJ
ejpam-4187	116	10	integer	integer	NOUN
ejpam-4187	116	11	for	for	ADP
ejpam-4187	116	12	which	which	PRON
ejpam-4187	116	13	4k+	4k+	NUM
ejpam-4187	116	14	1	1	NUM
ejpam-4187	116	15	≤	≤	NOUN
ejpam-4187	116	16	n.	n.	NOUN
ejpam-4187	116	17	then	then	ADV
ejpam-4187	116	18	s	s	VERB
ejpam-4187	116	19	is	be	AUX
ejpam-4187	116	20	a	a	DET
ejpam-4187	116	21	restrained	restrained	ADJ
ejpam-4187	116	22	disjunctive	disjunctive	ADJ
ejpam-4187	116	23	dominating	dominating	NOUN
ejpam-4187	116	24	set	set	NOUN
ejpam-4187	116	25	of	of	ADP
ejpam-4187	116	26	cn	cn	PROPN
ejpam-4187	116	27	.	.	PUNCT
ejpam-4187	117	1	thus	thus	ADV
ejpam-4187	117	2	,	,	PUNCT
ejpam-4187	117	3	γ	γ	X
ejpam-4187	117	4	d	d	X
ejpam-4187	117	5	r	r	X
ejpam-4187	117	6	(	(	PUNCT
ejpam-4187	117	7	cn	cn	NOUN
ejpam-4187	117	8	)	)	PUNCT
ejpam-4187	117	9	≤	≤	NUM
ejpam-4187	117	10	|s|	|s|	PROPN
ejpam-4187	118	1	=	=	NOUN
ejpam-4187	118	2	⌈n4	⌈n4	VERB
ejpam-4187	118	3	⌉.	⌉.	ADV
ejpam-4187	118	4	theorem	theorem	ADJ
ejpam-4187	118	5	2	2	NUM
ejpam-4187	118	6	.	.	PUNCT
ejpam-4187	119	1	let	let	VERB
ejpam-4187	119	2	g	g	PRON
ejpam-4187	119	3	be	be	AUX
ejpam-4187	119	4	a	a	DET
ejpam-4187	119	5	connected	connected	ADJ
ejpam-4187	119	6	graph	graph	NOUN
ejpam-4187	119	7	of	of	ADP
ejpam-4187	119	8	order	order	NOUN
ejpam-4187	119	9	n	n	PRON
ejpam-4187	119	10	≥	≥	NOUN
ejpam-4187	119	11	2	2	NUM
ejpam-4187	119	12	.	.	PUNCT
ejpam-4187	120	1	then	then	ADV
ejpam-4187	120	2	(	(	PUNCT
ejpam-4187	120	3	i	i	NOUN
ejpam-4187	120	4	)	)	PUNCT
ejpam-4187	120	5	γdr	γdr	INTJ
ejpam-4187	120	6	(	(	PUNCT
ejpam-4187	120	7	g	g	NOUN
ejpam-4187	120	8	)	)	PUNCT
ejpam-4187	120	9	≤	≤	NUM
ejpam-4187	120	10	n−∆(g	n−∆(g	PROPN
ejpam-4187	120	11	)	)	PUNCT
ejpam-4187	120	12	provided	provide	VERB
ejpam-4187	120	13	∆(g	∆(g	PROPN
ejpam-4187	120	14	)	)	PUNCT
ejpam-4187	120	15	≥	≥	NOUN
ejpam-4187	120	16	3	3	NUM
ejpam-4187	120	17	.	.	PUNCT
ejpam-4187	120	18	(	(	PUNCT
ejpam-4187	120	19	ii	ii	NOUN
ejpam-4187	120	20	)	)	PUNCT
ejpam-4187	120	21	γdr	γdr	NOUN
ejpam-4187	121	1	(	(	PUNCT
ejpam-4187	121	2	g	g	NOUN
ejpam-4187	121	3	)	)	PUNCT
ejpam-4187	121	4	=	=	SYM
ejpam-4187	121	5	1	1	NUM
ejpam-4187	122	1	if	if	SCONJ
ejpam-4187	122	2	and	and	CCONJ
ejpam-4187	122	3	only	only	ADV
ejpam-4187	122	4	if	if	SCONJ
ejpam-4187	122	5	n	n	NUM
ejpam-4187	122	6	≥	≥	NOUN
ejpam-4187	122	7	3	3	NUM
ejpam-4187	122	8	,	,	PUNCT
ejpam-4187	122	9	g	g	PROPN
ejpam-4187	122	10	̸=	̸=	PROPN
ejpam-4187	122	11	p3	p3	PROPN
ejpam-4187	122	12	and	and	CCONJ
ejpam-4187	122	13	γ(g	γ(g	PROPN
ejpam-4187	122	14	)	)	PUNCT
ejpam-4187	122	15	=	=	SYM
ejpam-4187	122	16	1	1	X
ejpam-4187	122	17	.	.	PUNCT
ejpam-4187	122	18	r.	r.	PROPN
ejpam-4187	122	19	malalay	malalay	PROPN
ejpam-4187	122	20	,	,	PUNCT
ejpam-4187	122	21	f.	f.	PROPN
ejpam-4187	122	22	jamil	jamil	PROPN
ejpam-4187	122	23	/	/	SYM
ejpam-4187	122	24	eur	eur	PROPN
ejpam-4187	122	25	.	.	PUNCT
ejpam-4187	123	1	j.	j.	PROPN
ejpam-4187	123	2	pure	pure	PROPN
ejpam-4187	123	3	appl	appl	PROPN
ejpam-4187	123	4	.	.	PROPN
ejpam-4187	123	5	math	math	PROPN
ejpam-4187	123	6	,	,	PUNCT
ejpam-4187	123	7	15	15	NUM
ejpam-4187	123	8	(	(	PUNCT
ejpam-4187	123	9	1	1	NUM
ejpam-4187	123	10	)	)	PUNCT
ejpam-4187	123	11	(	(	PUNCT
ejpam-4187	123	12	2022	2022	NUM
ejpam-4187	123	13	)	)	PUNCT
ejpam-4187	123	14	,	,	PUNCT
ejpam-4187	123	15	207	207	NUM
ejpam-4187	123	16	-	-	SYM
ejpam-4187	123	17	223	223	NUM
ejpam-4187	123	18	211	211	NUM
ejpam-4187	123	19	proof	proof	NOUN
ejpam-4187	123	20	.	.	PUNCT
ejpam-4187	124	1	to	to	PART
ejpam-4187	124	2	prove	prove	VERB
ejpam-4187	124	3	(	(	PUNCT
ejpam-4187	124	4	i	i	NOUN
ejpam-4187	124	5	)	)	PUNCT
ejpam-4187	124	6	,	,	PUNCT
ejpam-4187	124	7	suppose	suppose	VERB
ejpam-4187	124	8	that	that	SCONJ
ejpam-4187	124	9	∆(g	∆(g	PROPN
ejpam-4187	124	10	)	)	PUNCT
ejpam-4187	124	11	≥	≥	NOUN
ejpam-4187	124	12	3	3	NUM
ejpam-4187	124	13	,	,	PUNCT
ejpam-4187	124	14	and	and	CCONJ
ejpam-4187	124	15	let	let	VERB
ejpam-4187	124	16	v	v	NUM
ejpam-4187	124	17	∈	∈	PROPN
ejpam-4187	124	18	v	v	NOUN
ejpam-4187	124	19	(	(	PUNCT
ejpam-4187	124	20	g	g	NOUN
ejpam-4187	124	21	)	)	PUNCT
ejpam-4187	124	22	for	for	ADP
ejpam-4187	124	23	which	which	PRON
ejpam-4187	124	24	degg(v	degg(v	PROPN
ejpam-4187	124	25	)	)	PUNCT
ejpam-4187	124	26	=	=	SYM
ejpam-4187	124	27	∆(g	∆(g	PROPN
ejpam-4187	124	28	)	)	PUNCT
ejpam-4187	124	29	.	.	PUNCT
ejpam-4187	125	1	put	put	VERB
ejpam-4187	125	2	s	s	PART
ejpam-4187	125	3	=	=	X
ejpam-4187	125	4	v	v	ADJ
ejpam-4187	125	5	(	(	PUNCT
ejpam-4187	125	6	g	g	NOUN
ejpam-4187	125	7	)	)	PUNCT
ejpam-4187	125	8	\	\	NOUN
ejpam-4187	125	9	ng(v	ng(v	PUNCT
ejpam-4187	125	10	)	)	PUNCT
ejpam-4187	125	11	.	.	PUNCT
ejpam-4187	126	1	then	then	ADV
ejpam-4187	126	2	s	s	VERB
ejpam-4187	126	3	is	be	AUX
ejpam-4187	126	4	a	a	DET
ejpam-4187	126	5	restrained	restrained	ADJ
ejpam-4187	126	6	disjunctive	disjunctive	ADJ
ejpam-4187	126	7	dominating	dominating	NOUN
ejpam-4187	126	8	set	set	NOUN
ejpam-4187	126	9	of	of	ADP
ejpam-4187	126	10	g	g	NOUN
ejpam-4187	126	11	,	,	PUNCT
ejpam-4187	126	12	and	and	CCONJ
ejpam-4187	126	13	the	the	DET
ejpam-4187	126	14	result	result	NOUN
ejpam-4187	126	15	follows	follow	VERB
ejpam-4187	126	16	.	.	PUNCT
ejpam-4187	127	1	to	to	PART
ejpam-4187	127	2	prove	prove	VERB
ejpam-4187	127	3	(	(	PUNCT
ejpam-4187	127	4	ii	ii	NOUN
ejpam-4187	127	5	)	)	PUNCT
ejpam-4187	127	6	,	,	PUNCT
ejpam-4187	127	7	suppose	suppose	VERB
ejpam-4187	128	1	that	that	SCONJ
ejpam-4187	128	2	γdr	γdr	INTJ
ejpam-4187	128	3	(	(	PUNCT
ejpam-4187	128	4	g	g	NOUN
ejpam-4187	128	5	)	)	PUNCT
ejpam-4187	128	6	=	=	SYM
ejpam-4187	128	7	1	1	X
ejpam-4187	128	8	.	.	PUNCT
ejpam-4187	128	9	in	in	ADP
ejpam-4187	128	10	view	view	NOUN
ejpam-4187	128	11	of	of	ADP
ejpam-4187	128	12	the	the	DET
ejpam-4187	128	13	remark	remark	NOUN
ejpam-4187	128	14	above	above	ADV
ejpam-4187	129	1	,	,	PUNCT
ejpam-4187	129	2	1	1	NUM
ejpam-4187	129	3	≤	≤	NUM
ejpam-4187	129	4	γd(g	γd(g	NUM
ejpam-4187	129	5	)	)	PUNCT
ejpam-4187	129	6	≤	≤	NUM
ejpam-4187	129	7	γdr	γdr	INTJ
ejpam-4187	129	8	(	(	PUNCT
ejpam-4187	129	9	g	g	NOUN
ejpam-4187	129	10	)	)	PUNCT
ejpam-4187	129	11	=	=	SYM
ejpam-4187	129	12	1	1	NUM
ejpam-4187	129	13	showing	show	VERB
ejpam-4187	129	14	that	that	PRON
ejpam-4187	129	15	γd(g	γd(g	PUNCT
ejpam-4187	129	16	)	)	PUNCT
ejpam-4187	129	17	=	=	SYM
ejpam-4187	130	1	1	1	X
ejpam-4187	130	2	.	.	PUNCT
ejpam-4187	130	3	by	by	ADP
ejpam-4187	130	4	the	the	DET
ejpam-4187	130	5	remark	remark	NOUN
ejpam-4187	130	6	above	above	ADP
ejpam-4187	130	7	,	,	PUNCT
ejpam-4187	130	8	γ(g	γ(g	PROPN
ejpam-4187	130	9	)	)	PUNCT
ejpam-4187	130	10	=	=	PUNCT
ejpam-4187	131	1	1	1	X
ejpam-4187	131	2	.	.	PUNCT
ejpam-4187	132	1	since	since	SCONJ
ejpam-4187	132	2	γdr	γdr	PROPN
ejpam-4187	132	3	(	(	PUNCT
ejpam-4187	132	4	p2	p2	PROPN
ejpam-4187	132	5	)	)	PUNCT
ejpam-4187	132	6	=	=	SYM
ejpam-4187	132	7	2	2	NUM
ejpam-4187	132	8	,	,	PUNCT
ejpam-4187	132	9	n	n	PRON
ejpam-4187	132	10	≥	≥	NOUN
ejpam-4187	132	11	3	3	NUM
ejpam-4187	132	12	.	.	PUNCT
ejpam-4187	133	1	in	in	ADP
ejpam-4187	133	2	the	the	DET
ejpam-4187	133	3	case	case	NOUN
ejpam-4187	133	4	where	where	SCONJ
ejpam-4187	133	5	n	n	PROPN
ejpam-4187	133	6	=	=	SYM
ejpam-4187	133	7	3	3	NUM
ejpam-4187	133	8	,	,	PUNCT
ejpam-4187	133	9	g	g	NOUN
ejpam-4187	133	10	=	=	SYM
ejpam-4187	133	11	k3	k3	PROPN
ejpam-4187	133	12	.	.	PUNCT
ejpam-4187	134	1	to	to	PART
ejpam-4187	134	2	prove	prove	VERB
ejpam-4187	134	3	the	the	DET
ejpam-4187	134	4	converse	converse	NOUN
ejpam-4187	134	5	,	,	PUNCT
ejpam-4187	134	6	it	it	PRON
ejpam-4187	134	7	is	be	AUX
ejpam-4187	134	8	enough	enough	ADJ
ejpam-4187	134	9	to	to	PART
ejpam-4187	134	10	consider	consider	VERB
ejpam-4187	134	11	only	only	ADV
ejpam-4187	134	12	the	the	DET
ejpam-4187	134	13	case	case	NOUN
ejpam-4187	134	14	where	where	SCONJ
ejpam-4187	134	15	n	n	NUM
ejpam-4187	134	16	≥	≥	NOUN
ejpam-4187	134	17	4	4	NUM
ejpam-4187	134	18	.	.	PUNCT
ejpam-4187	135	1	let	let	VERB
ejpam-4187	135	2	s	s	VERB
ejpam-4187	135	3	=	=	NOUN
ejpam-4187	135	4	{	{	PUNCT
ejpam-4187	135	5	v	v	NOUN
ejpam-4187	135	6	}	}	PUNCT
ejpam-4187	135	7	be	be	AUX
ejpam-4187	135	8	a	a	DET
ejpam-4187	135	9	dominating	dominating	NOUN
ejpam-4187	135	10	set	set	NOUN
ejpam-4187	135	11	of	of	ADP
ejpam-4187	135	12	g.	g.	PROPN
ejpam-4187	136	1	then	then	ADV
ejpam-4187	136	2	s	s	VERB
ejpam-4187	136	3	is	be	AUX
ejpam-4187	136	4	a	a	DET
ejpam-4187	136	5	disjunctive	disjunctive	ADJ
ejpam-4187	136	6	dominating	dominating	NOUN
ejpam-4187	136	7	set	set	NOUN
ejpam-4187	136	8	of	of	ADP
ejpam-4187	136	9	g.	g.	PROPN
ejpam-4187	136	10	let	let	VERB
ejpam-4187	136	11	u	u	PRON
ejpam-4187	136	12	∈	∈	PROPN
ejpam-4187	136	13	v	v	ADP
ejpam-4187	136	14	(	(	PUNCT
ejpam-4187	136	15	g	g	NOUN
ejpam-4187	136	16	)	)	PUNCT
ejpam-4187	136	17	\	\	PUNCT
ejpam-4187	137	1	s.	s.	PROPN
ejpam-4187	137	2	since	since	SCONJ
ejpam-4187	137	3	s	s	PROPN
ejpam-4187	137	4	is	be	AUX
ejpam-4187	137	5	a	a	DET
ejpam-4187	137	6	dominating	dominating	NOUN
ejpam-4187	137	7	set	set	NOUN
ejpam-4187	137	8	,	,	PUNCT
ejpam-4187	137	9	uv	uv	PROPN
ejpam-4187	137	10	∈	∈	PROPN
ejpam-4187	137	11	e(g	e(g	PROPN
ejpam-4187	137	12	)	)	PUNCT
ejpam-4187	137	13	.	.	PUNCT
ejpam-4187	138	1	since	since	SCONJ
ejpam-4187	138	2	n	n	PROPN
ejpam-4187	138	3	≥	≥	NOUN
ejpam-4187	138	4	4	4	NUM
ejpam-4187	138	5	,	,	PUNCT
ejpam-4187	138	6	we	we	PRON
ejpam-4187	138	7	can	can	AUX
ejpam-4187	138	8	pick	pick	VERB
ejpam-4187	138	9	distinct	distinct	ADJ
ejpam-4187	138	10	x	x	NOUN
ejpam-4187	138	11	,	,	PUNCT
ejpam-4187	138	12	y	y	PROPN
ejpam-4187	138	13	∈	∈	PROPN
ejpam-4187	138	14	v	v	ADP
ejpam-4187	138	15	(	(	PUNCT
ejpam-4187	138	16	g	g	NOUN
ejpam-4187	138	17	)	)	PUNCT
ejpam-4187	138	18	\	\	NOUN
ejpam-4187	138	19	{	{	PUNCT
ejpam-4187	138	20	u	u	NOUN
ejpam-4187	138	21	,	,	PUNCT
ejpam-4187	138	22	v	v	NOUN
ejpam-4187	138	23	}	}	PUNCT
ejpam-4187	138	24	.	.	PUNCT
ejpam-4187	139	1	then	then	ADV
ejpam-4187	139	2	vx	vx	PROPN
ejpam-4187	139	3	∈	∈	PROPN
ejpam-4187	139	4	e(g	e(g	PROPN
ejpam-4187	139	5	)	)	PUNCT
ejpam-4187	139	6	and	and	CCONJ
ejpam-4187	139	7	vy	vy	NOUN
ejpam-4187	139	8	∈	∈	PROPN
ejpam-4187	139	9	e(g	e(g	PROPN
ejpam-4187	139	10	)	)	PUNCT
ejpam-4187	139	11	.	.	PUNCT
ejpam-4187	140	1	if	if	SCONJ
ejpam-4187	140	2	ux	ux	PROPN
ejpam-4187	140	3	∈	∈	PROPN
ejpam-4187	140	4	e(g	e(g	PROPN
ejpam-4187	140	5	)	)	PUNCT
ejpam-4187	140	6	or	or	CCONJ
ejpam-4187	140	7	uv	uv	NOUN
ejpam-4187	140	8	∈	∈	PROPN
ejpam-4187	140	9	e(g	e(g	PROPN
ejpam-4187	140	10	)	)	PUNCT
ejpam-4187	140	11	,	,	PUNCT
ejpam-4187	140	12	then	then	ADV
ejpam-4187	140	13	we	we	PRON
ejpam-4187	140	14	are	be	AUX
ejpam-4187	140	15	done	do	VERB
ejpam-4187	140	16	.	.	PUNCT
ejpam-4187	141	1	suppose	suppose	VERB
ejpam-4187	141	2	that	that	SCONJ
ejpam-4187	141	3	ux	ux	PROPN
ejpam-4187	141	4	,	,	PUNCT
ejpam-4187	141	5	uy	uy	PROPN
ejpam-4187	141	6	/∈	/∈	PROPN
ejpam-4187	141	7	e(g	e(g	PROPN
ejpam-4187	141	8	)	)	PUNCT
ejpam-4187	141	9	.	.	PUNCT
ejpam-4187	142	1	then	then	ADV
ejpam-4187	142	2	[	[	X
ejpam-4187	142	3	u	u	NOUN
ejpam-4187	142	4	,	,	PUNCT
ejpam-4187	142	5	v	v	NOUN
ejpam-4187	142	6	,	,	PUNCT
ejpam-4187	142	7	x	x	X
ejpam-4187	142	8	]	]	X
ejpam-4187	142	9	is	be	AUX
ejpam-4187	142	10	a	a	DET
ejpam-4187	142	11	u	u	NOUN
ejpam-4187	142	12	-	-	NOUN
ejpam-4187	142	13	x	x	INTJ
ejpam-4187	142	14	geodesic	geodesic	NOUN
ejpam-4187	142	15	in	in	ADP
ejpam-4187	142	16	g.	g.	PROPN
ejpam-4187	142	17	thus	thus	ADV
ejpam-4187	142	18	,	,	PUNCT
ejpam-4187	142	19	dg(u	dg(u	X
ejpam-4187	142	20	,	,	PUNCT
ejpam-4187	142	21	x	x	X
ejpam-4187	142	22	)	)	PUNCT
ejpam-4187	142	23	=	=	SYM
ejpam-4187	142	24	2	2	X
ejpam-4187	142	25	.	.	X
ejpam-4187	142	26	similarly	similarly	ADV
ejpam-4187	142	27	,	,	PUNCT
ejpam-4187	142	28	dg(u	dg(u	X
ejpam-4187	142	29	,	,	PUNCT
ejpam-4187	142	30	y	y	NOUN
ejpam-4187	142	31	)	)	PUNCT
ejpam-4187	142	32	=	=	SYM
ejpam-4187	143	1	2	2	X
ejpam-4187	143	2	.	.	PUNCT
ejpam-4187	143	3	this	this	PRON
ejpam-4187	143	4	shows	show	VERB
ejpam-4187	143	5	that	that	SCONJ
ejpam-4187	143	6	s	s	VERB
ejpam-4187	143	7	is	be	AUX
ejpam-4187	143	8	a	a	DET
ejpam-4187	143	9	restrained	restrained	ADJ
ejpam-4187	143	10	disjunctive	disjunctive	ADJ
ejpam-4187	143	11	dominating	dominating	NOUN
ejpam-4187	143	12	set	set	NOUN
ejpam-4187	143	13	of	of	ADP
ejpam-4187	143	14	g.	g.	PROPN
ejpam-4187	143	15	accordingly	accordingly	ADV
ejpam-4187	143	16	,	,	PUNCT
ejpam-4187	143	17	γdr	γdr	PROPN
ejpam-4187	143	18	(	(	PUNCT
ejpam-4187	143	19	g	g	NOUN
ejpam-4187	143	20	)	)	PUNCT
ejpam-4187	143	21	=	=	SYM
ejpam-4187	144	1	1	1	X
ejpam-4187	144	2	.	.	PUNCT
ejpam-4187	144	3	corollary	corollary	ADJ
ejpam-4187	144	4	1	1	NUM
ejpam-4187	144	5	.	.	PUNCT
ejpam-4187	145	1	for	for	ADP
ejpam-4187	145	2	a	a	DET
ejpam-4187	145	3	connected	connected	ADJ
ejpam-4187	145	4	graph	graph	NOUN
ejpam-4187	145	5	g	g	NOUN
ejpam-4187	145	6	of	of	ADP
ejpam-4187	145	7	order	order	NOUN
ejpam-4187	145	8	n	n	PRON
ejpam-4187	145	9	≥	≥	NOUN
ejpam-4187	145	10	3	3	NUM
ejpam-4187	145	11	,	,	PUNCT
ejpam-4187	145	12	γdr	γdr	INTJ
ejpam-4187	145	13	(	(	PUNCT
ejpam-4187	145	14	g	g	NOUN
ejpam-4187	145	15	)	)	PUNCT
ejpam-4187	145	16	=	=	SYM
ejpam-4187	145	17	1	1	NUM
ejpam-4187	145	18	if	if	SCONJ
ejpam-4187	145	19	and	and	CCONJ
ejpam-4187	145	20	only	only	ADV
ejpam-4187	145	21	if	if	SCONJ
ejpam-4187	145	22	g	g	NOUN
ejpam-4187	145	23	=	=	PUNCT
ejpam-4187	145	24	k3	k3	X
ejpam-4187	145	25	or	or	CCONJ
ejpam-4187	145	26	g	g	NOUN
ejpam-4187	145	27	=	=	PROPN
ejpam-4187	145	28	k1	k1	PROPN
ejpam-4187	146	1	+	+	NOUN
ejpam-4187	146	2	h	h	NOUN
ejpam-4187	146	3	for	for	ADP
ejpam-4187	146	4	some	some	DET
ejpam-4187	146	5	graph	graph	NOUN
ejpam-4187	146	6	h	h	NOUN
ejpam-4187	146	7	with	with	ADP
ejpam-4187	146	8	|v	|v	PROPN
ejpam-4187	146	9	(	(	PUNCT
ejpam-4187	146	10	h)|	h)|	PROPN
ejpam-4187	146	11	≥	≥	PROPN
ejpam-4187	146	12	3	3	NUM
ejpam-4187	146	13	.	.	X
ejpam-4187	146	14	note	note	VERB
ejpam-4187	146	15	that	that	SCONJ
ejpam-4187	146	16	since	since	SCONJ
ejpam-4187	146	17	γdr	γdr	PROPN
ejpam-4187	146	18	(	(	PUNCT
ejpam-4187	146	19	k1,n	k1,n	PROPN
ejpam-4187	146	20	)	)	PUNCT
ejpam-4187	146	21	=	=	SYM
ejpam-4187	146	22	1	1	NUM
ejpam-4187	146	23	for	for	ADP
ejpam-4187	146	24	all	all	DET
ejpam-4187	146	25	n	n	PRON
ejpam-4187	146	26	≥	≥	NOUN
ejpam-4187	146	27	3	3	NUM
ejpam-4187	146	28	,	,	PUNCT
ejpam-4187	146	29	the	the	DET
ejpam-4187	146	30	bound	bind	VERB
ejpam-4187	146	31	in	in	ADP
ejpam-4187	146	32	theorem	theorem	NOUN
ejpam-4187	146	33	2(i	2(i	NUM
ejpam-4187	146	34	)	)	PUNCT
ejpam-4187	146	35	is	be	AUX
ejpam-4187	146	36	sharp	sharp	ADJ
ejpam-4187	146	37	.	.	PUNCT
ejpam-4187	147	1	3	3	X
ejpam-4187	147	2	.	.	X
ejpam-4187	147	3	exploratory	exploratory	ADJ
ejpam-4187	147	4	examples	example	NOUN
ejpam-4187	147	5	for	for	ADP
ejpam-4187	147	6	any	any	DET
ejpam-4187	147	7	connected	connected	ADJ
ejpam-4187	147	8	graph	graph	NOUN
ejpam-4187	147	9	g	g	NOUN
ejpam-4187	147	10	,	,	PUNCT
ejpam-4187	147	11	γdr	γdr	PROPN
ejpam-4187	147	12	(	(	PUNCT
ejpam-4187	147	13	g	g	NOUN
ejpam-4187	147	14	)	)	PUNCT
ejpam-4187	147	15	≤	≤	NOUN
ejpam-4187	147	16	γr(g	γr(g	NUM
ejpam-4187	147	17	)	)	PUNCT
ejpam-4187	147	18	and	and	CCONJ
ejpam-4187	147	19	γd(g	γd(g	NUM
ejpam-4187	147	20	)	)	PUNCT
ejpam-4187	147	21	≤	≤	NUM
ejpam-4187	147	22	γdr	γdr	INTJ
ejpam-4187	147	23	(	(	PUNCT
ejpam-4187	147	24	g	g	NOUN
ejpam-4187	147	25	)	)	PUNCT
ejpam-4187	147	26	,	,	PUNCT
ejpam-4187	147	27	and	and	CCONJ
ejpam-4187	147	28	the	the	DET
ejpam-4187	147	29	following	follow	VERB
ejpam-4187	147	30	example	example	NOUN
ejpam-4187	147	31	shows	show	VERB
ejpam-4187	147	32	that	that	SCONJ
ejpam-4187	147	33	up	up	ADP
ejpam-4187	147	34	to	to	ADP
ejpam-4187	147	35	some	some	DET
ejpam-4187	147	36	extent	extent	NOUN
ejpam-4187	147	37	,	,	PUNCT
ejpam-4187	147	38	the	the	DET
ejpam-4187	147	39	values	value	NOUN
ejpam-4187	147	40	of	of	ADP
ejpam-4187	147	41	these	these	DET
ejpam-4187	147	42	parameters	parameter	NOUN
ejpam-4187	147	43	can	can	AUX
ejpam-4187	147	44	be	be	AUX
ejpam-4187	147	45	pre	pre	VERB
ejpam-4187	147	46	-	-	VERB
ejpam-4187	147	47	assigned	assign	VERB
ejpam-4187	147	48	.	.	PUNCT
ejpam-4187	148	1	example	example	NOUN
ejpam-4187	149	1	1	1	NUM
ejpam-4187	149	2	.	.	X
ejpam-4187	150	1	for	for	ADP
ejpam-4187	150	2	any	any	DET
ejpam-4187	150	3	positive	positive	ADJ
ejpam-4187	150	4	integers	integer	NOUN
ejpam-4187	150	5	a	a	DET
ejpam-4187	150	6	,	,	PUNCT
ejpam-4187	150	7	b	b	NOUN
ejpam-4187	150	8	with	with	ADP
ejpam-4187	150	9	2	2	NUM
ejpam-4187	150	10	≤	≤	NOUN
ejpam-4187	150	11	a	a	DET
ejpam-4187	150	12	≤	≤	NUM
ejpam-4187	150	13	b	b	NOUN
ejpam-4187	150	14	where	where	SCONJ
ejpam-4187	150	15	b	b	NOUN
ejpam-4187	150	16	≤	≤	X
ejpam-4187	150	17	3a	3a	NUM
ejpam-4187	150	18	−	−	NUM
ejpam-4187	150	19	1	1	NUM
ejpam-4187	150	20	,	,	PUNCT
ejpam-4187	150	21	there	there	PRON
ejpam-4187	150	22	exists	exist	VERB
ejpam-4187	150	23	a	a	DET
ejpam-4187	150	24	connected	connected	ADJ
ejpam-4187	150	25	graph	graph	NOUN
ejpam-4187	150	26	g	g	ADP
ejpam-4187	150	27	such	such	ADJ
ejpam-4187	150	28	that	that	DET
ejpam-4187	150	29	γdr	γdr	INTJ
ejpam-4187	150	30	(	(	PUNCT
ejpam-4187	150	31	g	g	NOUN
ejpam-4187	150	32	)	)	PUNCT
ejpam-4187	150	33	=	=	SYM
ejpam-4187	150	34	a	a	PRON
ejpam-4187	150	35	and	and	CCONJ
ejpam-4187	150	36	γr(g	γr(g	NUM
ejpam-4187	150	37	)	)	PUNCT
ejpam-4187	151	1	=	=	SYM
ejpam-4187	151	2	b.	b.	PROPN
ejpam-4187	151	3	to	to	PART
ejpam-4187	151	4	see	see	VERB
ejpam-4187	151	5	this	this	PRON
ejpam-4187	151	6	,	,	PUNCT
ejpam-4187	151	7	consider	consider	VERB
ejpam-4187	151	8	the	the	DET
ejpam-4187	151	9	following	follow	VERB
ejpam-4187	151	10	cases	case	NOUN
ejpam-4187	151	11	:	:	PUNCT
ejpam-4187	151	12	case	case	NOUN
ejpam-4187	151	13	1	1	NUM
ejpam-4187	151	14	.	.	PUNCT
ejpam-4187	152	1	a	a	DET
ejpam-4187	152	2	=	=	SYM
ejpam-4187	152	3	b	b	NOUN
ejpam-4187	152	4	in	in	ADP
ejpam-4187	152	5	this	this	DET
ejpam-4187	152	6	case	case	NOUN
ejpam-4187	152	7	,	,	PUNCT
ejpam-4187	152	8	we	we	PRON
ejpam-4187	152	9	take	take	VERB
ejpam-4187	152	10	g	g	NOUN
ejpam-4187	152	11	as	as	ADP
ejpam-4187	152	12	the	the	DET
ejpam-4187	152	13	graph	graph	NOUN
ejpam-4187	152	14	g1	g1	NOUN
ejpam-4187	152	15	obtained	obtain	VERB
ejpam-4187	152	16	by	by	ADP
ejpam-4187	152	17	connecting	connect	VERB
ejpam-4187	152	18	a	a	DET
ejpam-4187	152	19	copies	copy	NOUN
ejpam-4187	152	20	of	of	ADP
ejpam-4187	152	21	3	3	NUM
ejpam-4187	152	22	-	-	PUNCT
ejpam-4187	152	23	pan	pan	NOUN
ejpam-4187	152	24	graph	graph	NOUN
ejpam-4187	152	25	using	use	VERB
ejpam-4187	152	26	the	the	DET
ejpam-4187	152	27	path	path	NOUN
ejpam-4187	152	28	[	[	X
ejpam-4187	152	29	u1	u1	NOUN
ejpam-4187	152	30	,	,	PUNCT
ejpam-4187	152	31	u2	u2	NOUN
ejpam-4187	152	32	,	,	PUNCT
ejpam-4187	152	33	.	.	PUNCT
ejpam-4187	152	34	.	.	PUNCT
ejpam-4187	153	1	.	.	PUNCT
ejpam-4187	154	1	,	,	PUNCT
ejpam-4187	154	2	ua	ua	PROPN
ejpam-4187	154	3	]	]	X
ejpam-4187	154	4	,	,	PUNCT
ejpam-4187	154	5	where	where	SCONJ
ejpam-4187	154	6	ui	ui	PROPN
ejpam-4187	154	7	is	be	AUX
ejpam-4187	154	8	a	a	DET
ejpam-4187	154	9	pendant	pendant	NOUN
ejpam-4187	154	10	of	of	ADP
ejpam-4187	154	11	the	the	DET
ejpam-4187	154	12	ith	ith	PROPN
ejpam-4187	154	13	copy	copy	NOUN
ejpam-4187	154	14	of	of	ADP
ejpam-4187	154	15	3	3	NUM
ejpam-4187	154	16	-	-	PUNCT
ejpam-4187	154	17	pan	pan	NOUN
ejpam-4187	154	18	graph	graph	NOUN
ejpam-4187	154	19	for	for	ADP
ejpam-4187	154	20	each	each	DET
ejpam-4187	154	21	i	i	PRON
ejpam-4187	154	22	∈	∈	PROPN
ejpam-4187	154	23	{	{	PUNCT
ejpam-4187	154	24	1	1	NUM
ejpam-4187	154	25	,	,	PUNCT
ejpam-4187	154	26	2	2	NUM
ejpam-4187	154	27	,	,	PUNCT
ejpam-4187	154	28	.	.	PUNCT
ejpam-4187	154	29	.	.	PUNCT
ejpam-4187	155	1	.	.	PUNCT
ejpam-4187	156	1	,	,	PUNCT
ejpam-4187	156	2	a	a	PRON
ejpam-4187	156	3	}	}	PUNCT
ejpam-4187	156	4	as	as	SCONJ
ejpam-4187	156	5	shown	show	VERB
ejpam-4187	156	6	in	in	ADP
ejpam-4187	156	7	figure	figure	NOUN
ejpam-4187	156	8	1	1	NUM
ejpam-4187	156	9	.	.	PUNCT
ejpam-4187	157	1	denote	denote	VERB
ejpam-4187	157	2	by	by	ADP
ejpam-4187	157	3	p	p	PUNCT
ejpam-4187	157	4	u	u	NOUN
ejpam-4187	157	5	that	that	PRON
ejpam-4187	157	6	copy	copy	VERB
ejpam-4187	157	7	of	of	ADP
ejpam-4187	157	8	3	3	NUM
ejpam-4187	157	9	-	-	PUNCT
ejpam-4187	157	10	pan	pan	NOUN
ejpam-4187	157	11	graph	graph	NOUN
ejpam-4187	157	12	corresponding	correspond	VERB
ejpam-4187	157	13	to	to	ADP
ejpam-4187	157	14	vertex	vertex	NOUN
ejpam-4187	157	15	u.	u.	NOUN
ejpam-4187	157	16	figure	figure	NOUN
ejpam-4187	157	17	1	1	NUM
ejpam-4187	157	18	:	:	PUNCT
ejpam-4187	157	19	a	a	DET
ejpam-4187	157	20	graph	graph	NOUN
ejpam-4187	157	21	g	g	NOUN
ejpam-4187	157	22	with	with	ADP
ejpam-4187	157	23	2	2	NUM
ejpam-4187	157	24	≤	≤	NOUN
ejpam-4187	157	25	γd	γd	ADP
ejpam-4187	157	26	r	r	NOUN
ejpam-4187	157	27	(	(	PUNCT
ejpam-4187	157	28	g	g	NOUN
ejpam-4187	157	29	)	)	PUNCT
ejpam-4187	157	30	=	=	SYM
ejpam-4187	158	1	γr(g	γr(g	PROPN
ejpam-4187	158	2	)	)	PUNCT
ejpam-4187	158	3	since	since	SCONJ
ejpam-4187	158	4	the	the	DET
ejpam-4187	158	5	set	set	NOUN
ejpam-4187	158	6	s	s	PART
ejpam-4187	158	7	=	=	X
ejpam-4187	158	8	{	{	PUNCT
ejpam-4187	158	9	xi	xi	X
ejpam-4187	158	10	:	:	PUNCT
ejpam-4187	158	11	i	i	PROPN
ejpam-4187	158	12	∈	∈	PROPN
ejpam-4187	158	13	{	{	PUNCT
ejpam-4187	158	14	1	1	NUM
ejpam-4187	158	15	,	,	PUNCT
ejpam-4187	158	16	2	2	NUM
ejpam-4187	158	17	,	,	PUNCT
ejpam-4187	158	18	.	.	PUNCT
ejpam-4187	158	19	.	.	PUNCT
ejpam-4187	158	20	.	.	PUNCT
ejpam-4187	159	1	,	,	PUNCT
ejpam-4187	159	2	a	a	X
ejpam-4187	159	3	}	}	PUNCT
ejpam-4187	159	4	}	}	PUNCT
ejpam-4187	159	5	is	be	AUX
ejpam-4187	159	6	both	both	PRON
ejpam-4187	159	7	a	a	DET
ejpam-4187	159	8	restrained	restrained	ADJ
ejpam-4187	159	9	disjunctive	disjunctive	ADJ
ejpam-4187	159	10	dominating	dominating	NOUN
ejpam-4187	159	11	set	set	NOUN
ejpam-4187	159	12	and	and	CCONJ
ejpam-4187	159	13	a	a	DET
ejpam-4187	159	14	restrained	restrained	ADJ
ejpam-4187	159	15	dominating	dominating	NOUN
ejpam-4187	159	16	set	set	NOUN
ejpam-4187	159	17	of	of	ADP
ejpam-4187	159	18	g	g	NOUN
ejpam-4187	159	19	,	,	PUNCT
ejpam-4187	159	20	γdr	γdr	PROPN
ejpam-4187	159	21	(	(	PUNCT
ejpam-4187	159	22	g	g	NOUN
ejpam-4187	159	23	)	)	PUNCT
ejpam-4187	159	24	=	=	SYM
ejpam-4187	160	1	γr(g	γr(g	X
ejpam-4187	160	2	)	)	PUNCT
ejpam-4187	160	3	≤	≤	NUM
ejpam-4187	160	4	|s|	|s|	PROPN
ejpam-4187	160	5	=	=	NOUN
ejpam-4187	160	6	a.	a.	NOUN
ejpam-4187	160	7	let	let	VERB
ejpam-4187	160	8	d	d	PROPN
ejpam-4187	160	9	⊆	⊆	NUM
ejpam-4187	160	10	v	v	ADP
ejpam-4187	160	11	(	(	PUNCT
ejpam-4187	160	12	g	g	NOUN
ejpam-4187	160	13	)	)	PUNCT
ejpam-4187	160	14	r.	r.	NOUN
ejpam-4187	160	15	malalay	malalay	PROPN
ejpam-4187	160	16	,	,	PUNCT
ejpam-4187	160	17	f.	f.	PROPN
ejpam-4187	160	18	jamil	jamil	PROPN
ejpam-4187	160	19	/	/	SYM
ejpam-4187	160	20	eur	eur	PROPN
ejpam-4187	160	21	.	.	PUNCT
ejpam-4187	161	1	j.	j.	PROPN
ejpam-4187	161	2	pure	pure	PROPN
ejpam-4187	161	3	appl	appl	PROPN
ejpam-4187	161	4	.	.	PROPN
ejpam-4187	161	5	math	math	PROPN
ejpam-4187	161	6	,	,	PUNCT
ejpam-4187	161	7	15	15	NUM
ejpam-4187	161	8	(	(	PUNCT
ejpam-4187	161	9	1	1	NUM
ejpam-4187	161	10	)	)	PUNCT
ejpam-4187	161	11	(	(	PUNCT
ejpam-4187	161	12	2022	2022	NUM
ejpam-4187	161	13	)	)	PUNCT
ejpam-4187	161	14	,	,	PUNCT
ejpam-4187	161	15	207	207	NUM
ejpam-4187	161	16	-	-	SYM
ejpam-4187	161	17	223	223	NUM
ejpam-4187	161	18	212	212	NUM
ejpam-4187	161	19	such	such	ADJ
ejpam-4187	161	20	that	that	SCONJ
ejpam-4187	161	21	|d|	|d|	PROPN
ejpam-4187	161	22	<	<	X
ejpam-4187	161	23	a.	a.	NOUN
ejpam-4187	162	1	then	then	ADV
ejpam-4187	162	2	there	there	PRON
ejpam-4187	162	3	exists	exist	VERB
ejpam-4187	162	4	1	1	NUM
ejpam-4187	162	5	≤	≤	NUM
ejpam-4187	162	6	k	k	X
ejpam-4187	162	7	≤	≤	NOUN
ejpam-4187	162	8	a	a	DET
ejpam-4187	162	9	such	such	ADJ
ejpam-4187	162	10	that	that	SCONJ
ejpam-4187	162	11	d	d	PROPN
ejpam-4187	162	12	∩	∩	ADJ
ejpam-4187	162	13	v	v	NOUN
ejpam-4187	162	14	(	(	PUNCT
ejpam-4187	162	15	3	3	NUM
ejpam-4187	162	16	−	−	PROPN
ejpam-4187	162	17	p	p	PROPN
ejpam-4187	162	18	uk	uk	PROPN
ejpam-4187	162	19	)	)	PUNCT
ejpam-4187	162	20	=	=	PUNCT
ejpam-4187	162	21	∅.	∅.	NOUN
ejpam-4187	162	22	in	in	ADP
ejpam-4187	162	23	particular	particular	ADJ
ejpam-4187	162	24	,	,	PUNCT
ejpam-4187	162	25	v	v	INTJ
ejpam-4187	162	26	(	(	PUNCT
ejpam-4187	162	27	p	p	NOUN
ejpam-4187	162	28	uk)\{xk	uk)\{xk	PROPN
ejpam-4187	162	29	,	,	PUNCT
ejpam-4187	162	30	uk	uk	PROPN
ejpam-4187	162	31	}	}	PUNCT
ejpam-4187	162	32	is	be	AUX
ejpam-4187	162	33	not	not	PART
ejpam-4187	162	34	dominated	dominate	VERB
ejpam-4187	162	35	by	by	ADP
ejpam-4187	162	36	d	d	PROPN
ejpam-4187	162	37	in	in	ADP
ejpam-4187	162	38	the	the	DET
ejpam-4187	162	39	sense	sense	NOUN
ejpam-4187	162	40	of	of	ADP
ejpam-4187	162	41	disjunctive	disjunctive	ADJ
ejpam-4187	162	42	domination	domination	NOUN
ejpam-4187	162	43	and	and	CCONJ
ejpam-4187	162	44	the	the	DET
ejpam-4187	162	45	usual	usual	ADJ
ejpam-4187	162	46	domination	domination	NOUN
ejpam-4187	162	47	.	.	PUNCT
ejpam-4187	163	1	thus	thus	ADV
ejpam-4187	163	2	,	,	PUNCT
ejpam-4187	163	3	γdr	γdr	INTJ
ejpam-4187	163	4	(	(	PUNCT
ejpam-4187	163	5	g	g	NOUN
ejpam-4187	163	6	)	)	PUNCT
ejpam-4187	163	7	≥	≥	NOUN
ejpam-4187	163	8	a	a	PRON
ejpam-4187	163	9	and	and	CCONJ
ejpam-4187	163	10	γr(g	γr(g	NUM
ejpam-4187	163	11	)	)	PUNCT
ejpam-4187	163	12	≥	≥	PROPN
ejpam-4187	163	13	a.	a.	NOUN
ejpam-4187	163	14	consequently	consequently	ADV
ejpam-4187	163	15	,	,	PUNCT
ejpam-4187	163	16	γdr	γdr	PROPN
ejpam-4187	163	17	(	(	PUNCT
ejpam-4187	163	18	g	g	NOUN
ejpam-4187	163	19	)	)	PUNCT
ejpam-4187	163	20	=	=	SYM
ejpam-4187	163	21	a	a	PRON
ejpam-4187	163	22	and	and	CCONJ
ejpam-4187	163	23	γr(g	γr(g	NUM
ejpam-4187	163	24	)	)	PUNCT
ejpam-4187	164	1	=	=	PUNCT
ejpam-4187	164	2	a	a	DET
ejpam-4187	164	3	=	=	PROPN
ejpam-4187	164	4	b.	b.	NOUN
ejpam-4187	164	5	case	case	NOUN
ejpam-4187	164	6	2	2	NUM
ejpam-4187	164	7	:	:	PUNCT
ejpam-4187	164	8	a	a	DET
ejpam-4187	164	9	<	<	X
ejpam-4187	164	10	b	b	NOUN
ejpam-4187	164	11	here	here	ADV
ejpam-4187	164	12	,	,	PUNCT
ejpam-4187	164	13	we	we	PRON
ejpam-4187	164	14	write	write	VERB
ejpam-4187	164	15	b	b	PROPN
ejpam-4187	164	16	=	=	PRON
ejpam-4187	164	17	a+	a+	PUNCT
ejpam-4187	164	18	k	k	NOUN
ejpam-4187	164	19	,	,	PUNCT
ejpam-4187	164	20	where	where	SCONJ
ejpam-4187	164	21	k	k	PROPN
ejpam-4187	164	22	≥	≥	PROPN
ejpam-4187	164	23	1	1	NUM
ejpam-4187	164	24	.	.	PUNCT
ejpam-4187	165	1	obtain	obtain	VERB
ejpam-4187	165	2	the	the	DET
ejpam-4187	165	3	graph	graph	NOUN
ejpam-4187	165	4	g∗	g∗	NOUN
ejpam-4187	165	5	as	as	ADP
ejpam-4187	165	6	graph	graph	NOUN
ejpam-4187	165	7	g2	g2	PROPN
ejpam-4187	165	8	from	from	ADP
ejpam-4187	165	9	graph	graph	NOUN
ejpam-4187	165	10	g1	g1	NOUN
ejpam-4187	165	11	in	in	ADP
ejpam-4187	165	12	the	the	DET
ejpam-4187	165	13	first	first	ADJ
ejpam-4187	165	14	case	case	NOUN
ejpam-4187	165	15	by	by	ADP
ejpam-4187	165	16	adding	add	VERB
ejpam-4187	165	17	to	to	PART
ejpam-4187	165	18	g1	g1	VERB
ejpam-4187	165	19	the	the	DET
ejpam-4187	165	20	pendant	pendant	ADJ
ejpam-4187	165	21	edges	edge	NOUN
ejpam-4187	165	22	x1yi	x1yi	PUNCT
ejpam-4187	165	23	for	for	ADP
ejpam-4187	165	24	each	each	DET
ejpam-4187	165	25	i	i	PRON
ejpam-4187	165	26	∈	∈	PROPN
ejpam-4187	165	27	{	{	PUNCT
ejpam-4187	165	28	1	1	NUM
ejpam-4187	165	29	,	,	PUNCT
ejpam-4187	165	30	2	2	NUM
ejpam-4187	165	31	,	,	PUNCT
ejpam-4187	165	32	.	.	PUNCT
ejpam-4187	165	33	.	.	PUNCT
ejpam-4187	166	1	.	.	PUNCT
ejpam-4187	167	1	,	,	PUNCT
ejpam-4187	167	2	k	k	X
ejpam-4187	167	3	}	}	PUNCT
ejpam-4187	167	4	as	as	SCONJ
ejpam-4187	167	5	shown	show	VERB
ejpam-4187	167	6	in	in	ADP
ejpam-4187	167	7	figure	figure	NOUN
ejpam-4187	167	8	2	2	NUM
ejpam-4187	167	9	.	.	PUNCT
ejpam-4187	167	10	figure	figure	NOUN
ejpam-4187	167	11	2	2	NUM
ejpam-4187	167	12	:	:	PUNCT
ejpam-4187	167	13	a	a	DET
ejpam-4187	167	14	graph	graph	NOUN
ejpam-4187	167	15	g∗	g∗	VERB
ejpam-4187	167	16	with	with	ADP
ejpam-4187	167	17	2	2	NUM
ejpam-4187	167	18	≤	≤	NOUN
ejpam-4187	167	19	γd	γd	ADP
ejpam-4187	167	20	r	r	NOUN
ejpam-4187	167	21	(	(	PUNCT
ejpam-4187	167	22	g	g	NOUN
ejpam-4187	167	23	∗	∗	PROPN
ejpam-4187	167	24	)	)	PUNCT
ejpam-4187	168	1	<	<	X
ejpam-4187	168	2	γr(g	γr(g	PROPN
ejpam-4187	168	3	∗	∗	NOUN
ejpam-4187	168	4	)	)	PUNCT
ejpam-4187	168	5	since	since	SCONJ
ejpam-4187	168	6	s1	s1	NOUN
ejpam-4187	168	7	=	=	PUNCT
ejpam-4187	168	8	{	{	PUNCT
ejpam-4187	168	9	xi	xi	X
ejpam-4187	168	10	:	:	PUNCT
ejpam-4187	168	11	i	i	PROPN
ejpam-4187	168	12	∈	∈	PROPN
ejpam-4187	168	13	{	{	PUNCT
ejpam-4187	168	14	1	1	NUM
ejpam-4187	168	15	,	,	PUNCT
ejpam-4187	168	16	2	2	NUM
ejpam-4187	168	17	,	,	PUNCT
ejpam-4187	168	18	.	.	PUNCT
ejpam-4187	168	19	.	.	PUNCT
ejpam-4187	169	1	.	.	PUNCT
ejpam-4187	170	1	,	,	PUNCT
ejpam-4187	170	2	a	a	X
ejpam-4187	170	3	}	}	PUNCT
ejpam-4187	170	4	}	}	PUNCT
ejpam-4187	170	5	is	be	AUX
ejpam-4187	170	6	a	a	DET
ejpam-4187	170	7	γdr	γdr	NOUN
ejpam-4187	170	8	-set	-set	NOUN
ejpam-4187	170	9	of	of	ADP
ejpam-4187	170	10	g	g	PROPN
ejpam-4187	170	11	∗	∗	NOUN
ejpam-4187	170	12	,	,	PUNCT
ejpam-4187	170	13	γdr	γdr	PROPN
ejpam-4187	170	14	(	(	PUNCT
ejpam-4187	170	15	g	g	NOUN
ejpam-4187	170	16	∗	∗	NOUN
ejpam-4187	170	17	)	)	PUNCT
ejpam-4187	171	1	=	=	SYM
ejpam-4187	171	2	|s1|	|s1|	NOUN
ejpam-4187	171	3	=	=	SYM
ejpam-4187	171	4	a.	a.	NOUN
ejpam-4187	171	5	observe	observe	VERB
ejpam-4187	171	6	that	that	SCONJ
ejpam-4187	171	7	the	the	DET
ejpam-4187	171	8	set	set	ADJ
ejpam-4187	171	9	s2	s2	NOUN
ejpam-4187	171	10	=	=	SYM
ejpam-4187	171	11	s1	s1	PROPN
ejpam-4187	171	12	∪	∪	X
ejpam-4187	171	13	{	{	PUNCT
ejpam-4187	171	14	yj	yj	PROPN
ejpam-4187	171	15	:	:	PUNCT
ejpam-4187	171	16	j	j	PROPN
ejpam-4187	171	17	∈	∈	PROPN
ejpam-4187	171	18	{	{	PUNCT
ejpam-4187	171	19	1	1	NUM
ejpam-4187	171	20	,	,	PUNCT
ejpam-4187	171	21	2	2	NUM
ejpam-4187	171	22	,	,	PUNCT
ejpam-4187	171	23	.	.	PUNCT
ejpam-4187	171	24	.	.	PUNCT
ejpam-4187	171	25	.	.	PUNCT
ejpam-4187	172	1	,	,	PUNCT
ejpam-4187	172	2	k	k	X
ejpam-4187	172	3	}	}	PUNCT
ejpam-4187	172	4	}	}	PUNCT
ejpam-4187	172	5	is	be	AUX
ejpam-4187	172	6	a	a	DET
ejpam-4187	172	7	restrained	restrain	VERB
ejpam-4187	172	8	dominating	dominating	NOUN
ejpam-4187	172	9	set	set	NOUN
ejpam-4187	172	10	of	of	ADP
ejpam-4187	172	11	g∗	g∗	PROPN
ejpam-4187	172	12	showing	show	VERB
ejpam-4187	172	13	that	that	SCONJ
ejpam-4187	172	14	γr(g	γr(g	PROPN
ejpam-4187	172	15	∗	∗	NOUN
ejpam-4187	172	16	)	)	PUNCT
ejpam-4187	172	17	≤	≤	NUM
ejpam-4187	172	18	|s2|	|s2|	NOUN
ejpam-4187	172	19	=	=	SYM
ejpam-4187	172	20	a+	a+	PUNCT
ejpam-4187	172	21	k	k	PROPN
ejpam-4187	172	22	=	=	PROPN
ejpam-4187	172	23	b.	b.	PROPN
ejpam-4187	172	24	let	let	VERB
ejpam-4187	172	25	s	s	PRON
ejpam-4187	172	26	⊆	⊆	NUM
ejpam-4187	172	27	v	v	NOUN
ejpam-4187	172	28	(	(	PUNCT
ejpam-4187	172	29	g∗	g∗	PROPN
ejpam-4187	172	30	)	)	PUNCT
ejpam-4187	172	31	be	be	VERB
ejpam-4187	172	32	a	a	DET
ejpam-4187	172	33	γr	γr	PROPN
ejpam-4187	172	34	-	-	PUNCT
ejpam-4187	172	35	set	set	NOUN
ejpam-4187	172	36	of	of	ADP
ejpam-4187	172	37	g	g	PROPN
ejpam-4187	172	38	∗.	∗.	PROPN
ejpam-4187	172	39	then	then	ADV
ejpam-4187	172	40	s	s	AUX
ejpam-4187	172	41	contains	contain	VERB
ejpam-4187	172	42	s1	s1	NOUN
ejpam-4187	172	43	.	.	PUNCT
ejpam-4187	173	1	being	be	AUX
ejpam-4187	173	2	a	a	DET
ejpam-4187	173	3	restrained	restrained	ADJ
ejpam-4187	173	4	disjunctive	disjunctive	ADJ
ejpam-4187	173	5	dominating	dominating	NOUN
ejpam-4187	173	6	set	set	NOUN
ejpam-4187	173	7	of	of	ADP
ejpam-4187	173	8	g∗	g∗	PROPN
ejpam-4187	173	9	and	and	CCONJ
ejpam-4187	173	10	s	s	NOUN
ejpam-4187	173	11	contains	contain	VERB
ejpam-4187	173	12	s1	s1	NOUN
ejpam-4187	173	13	,	,	PUNCT
ejpam-4187	173	14	necessarily	necessarily	ADV
ejpam-4187	173	15	yj	yj	PROPN
ejpam-4187	173	16	∈	∈	PROPN
ejpam-4187	173	17	s	s	NOUN
ejpam-4187	173	18	,	,	PUNCT
ejpam-4187	173	19	for	for	ADP
ejpam-4187	173	20	each	each	DET
ejpam-4187	173	21	j	j	PROPN
ejpam-4187	173	22	∈	∈	PROPN
ejpam-4187	173	23	{	{	PUNCT
ejpam-4187	173	24	1	1	NUM
ejpam-4187	173	25	,	,	PUNCT
ejpam-4187	173	26	2	2	NUM
ejpam-4187	173	27	,	,	PUNCT
ejpam-4187	173	28	.	.	PUNCT
ejpam-4187	173	29	.	.	PUNCT
ejpam-4187	174	1	.	.	PUNCT
ejpam-4187	175	1	,	,	PUNCT
ejpam-4187	175	2	k	k	X
ejpam-4187	175	3	}	}	PUNCT
ejpam-4187	175	4	.	.	PUNCT
ejpam-4187	176	1	thus	thus	ADV
ejpam-4187	176	2	,	,	PUNCT
ejpam-4187	176	3	γr(g∗	γr(g∗	PROPN
ejpam-4187	176	4	)	)	PUNCT
ejpam-4187	176	5	≥	≥	NOUN
ejpam-4187	176	6	|s|	|s|	NOUN
ejpam-4187	176	7	=	=	SYM
ejpam-4187	176	8	a+	a+	PRON
ejpam-4187	176	9	k	k	PROPN
ejpam-4187	176	10	=	=	PROPN
ejpam-4187	176	11	b.	b.	PROPN
ejpam-4187	177	1	consequently	consequently	ADV
ejpam-4187	177	2	,	,	PUNCT
ejpam-4187	177	3	γr(g	γr(g	PROPN
ejpam-4187	177	4	∗	∗	NOUN
ejpam-4187	177	5	)	)	PUNCT
ejpam-4187	177	6	=	=	SYM
ejpam-4187	177	7	b.	b.	PROPN
ejpam-4187	177	8	example	example	NOUN
ejpam-4187	178	1	2	2	NUM
ejpam-4187	178	2	.	.	X
ejpam-4187	178	3	for	for	ADP
ejpam-4187	178	4	a	a	DET
ejpam-4187	178	5	pair	pair	NOUN
ejpam-4187	178	6	of	of	ADP
ejpam-4187	178	7	positive	positive	ADJ
ejpam-4187	178	8	integers	integer	NOUN
ejpam-4187	178	9	(	(	PUNCT
ejpam-4187	178	10	a	a	DET
ejpam-4187	178	11	,	,	PUNCT
ejpam-4187	178	12	b	b	NOUN
ejpam-4187	178	13	)	)	PUNCT
ejpam-4187	178	14	with	with	ADP
ejpam-4187	178	15	2	2	NUM
ejpam-4187	178	16	≤	≤	NOUN
ejpam-4187	178	17	a	a	DET
ejpam-4187	178	18	≤	≤	NUM
ejpam-4187	178	19	b	b	NOUN
ejpam-4187	178	20	where	where	SCONJ
ejpam-4187	178	21	either	either	CCONJ
ejpam-4187	178	22	b	b	PROPN
ejpam-4187	178	23	≤	≤	X
ejpam-4187	178	24	3a	3a	NUM
ejpam-4187	178	25	2	2	NUM
ejpam-4187	178	26	if	if	SCONJ
ejpam-4187	178	27	a	a	PRON
ejpam-4187	178	28	is	be	AUX
ejpam-4187	178	29	even	even	ADV
ejpam-4187	178	30	or	or	CCONJ
ejpam-4187	178	31	b	b	NOUN
ejpam-4187	178	32	≤	≤	ADJ
ejpam-4187	178	33	3a+1	3a+1	NOUN
ejpam-4187	178	34	2	2	NUM
ejpam-4187	178	35	when	when	SCONJ
ejpam-4187	178	36	a	a	PRON
ejpam-4187	178	37	is	be	AUX
ejpam-4187	178	38	odd	odd	ADJ
ejpam-4187	178	39	,	,	PUNCT
ejpam-4187	178	40	there	there	PRON
ejpam-4187	178	41	exists	exist	VERB
ejpam-4187	178	42	a	a	DET
ejpam-4187	178	43	connected	connected	ADJ
ejpam-4187	178	44	graph	graph	NOUN
ejpam-4187	178	45	g	g	ADP
ejpam-4187	178	46	such	such	ADJ
ejpam-4187	178	47	that	that	PRON
ejpam-4187	178	48	γd(g	γd(g	NUM
ejpam-4187	178	49	)	)	PUNCT
ejpam-4187	178	50	=	=	SYM
ejpam-4187	178	51	a	a	PROPN
ejpam-4187	178	52	and	and	CCONJ
ejpam-4187	178	53	γdr	γdr	ADJ
ejpam-4187	178	54	(	(	PUNCT
ejpam-4187	178	55	g	g	NOUN
ejpam-4187	178	56	)	)	PUNCT
ejpam-4187	178	57	=	=	SYM
ejpam-4187	178	58	b.	b.	PROPN
ejpam-4187	178	59	consider	consider	VERB
ejpam-4187	178	60	the	the	DET
ejpam-4187	178	61	following	follow	VERB
ejpam-4187	178	62	cases	case	NOUN
ejpam-4187	178	63	:	:	PUNCT
ejpam-4187	178	64	case	case	NOUN
ejpam-4187	178	65	1	1	NUM
ejpam-4187	178	66	.	.	PUNCT
ejpam-4187	179	1	a	a	PRON
ejpam-4187	179	2	=	=	SYM
ejpam-4187	179	3	b	b	AUX
ejpam-4187	179	4	take	take	VERB
ejpam-4187	179	5	g	g	NOUN
ejpam-4187	179	6	to	to	PART
ejpam-4187	179	7	be	be	AUX
ejpam-4187	179	8	the	the	DET
ejpam-4187	179	9	graph	graph	NOUN
ejpam-4187	179	10	g1	g1	NOUN
ejpam-4187	179	11	obtained	obtain	VERB
ejpam-4187	179	12	from	from	ADP
ejpam-4187	179	13	the	the	DET
ejpam-4187	179	14	path	path	NOUN
ejpam-4187	179	15	p2a−1	p2a−1	PROPN
ejpam-4187	180	1	=	=	PUNCT
ejpam-4187	181	1	[	[	X
ejpam-4187	181	2	u1	u1	NOUN
ejpam-4187	181	3	,	,	PUNCT
ejpam-4187	181	4	u2	u2	NOUN
ejpam-4187	181	5	,	,	PUNCT
ejpam-4187	181	6	.	.	PUNCT
ejpam-4187	181	7	.	.	PUNCT
ejpam-4187	181	8	.	.	PUNCT
ejpam-4187	182	1	,	,	PUNCT
ejpam-4187	182	2	u2a−1	u2a−1	PROPN
ejpam-4187	182	3	]	]	PUNCT
ejpam-4187	182	4	as	as	SCONJ
ejpam-4187	182	5	shown	show	VERB
ejpam-4187	182	6	in	in	ADP
ejpam-4187	182	7	figure	figure	NOUN
ejpam-4187	182	8	3	3	NUM
ejpam-4187	182	9	,	,	PUNCT
ejpam-4187	182	10	by	by	ADP
ejpam-4187	182	11	adding	add	VERB
ejpam-4187	182	12	to	to	PART
ejpam-4187	182	13	p2a−1	p2a−1	VERB
ejpam-4187	182	14	the	the	DET
ejpam-4187	182	15	pendant	pendant	ADJ
ejpam-4187	182	16	edges	edge	NOUN
ejpam-4187	182	17	xju2j−1	xju2j−1	NOUN
ejpam-4187	182	18	for	for	ADP
ejpam-4187	182	19	all	all	DET
ejpam-4187	182	20	j	j	NOUN
ejpam-4187	182	21	=	=	SYM
ejpam-4187	182	22	1	1	NUM
ejpam-4187	182	23	,	,	PUNCT
ejpam-4187	182	24	2	2	NUM
ejpam-4187	182	25	,	,	PUNCT
ejpam-4187	182	26	.	.	PUNCT
ejpam-4187	182	27	.	.	PUNCT
ejpam-4187	182	28	.	.	PUNCT
ejpam-4187	183	1	,	,	PUNCT
ejpam-4187	183	2	a.	a.	NOUN
ejpam-4187	183	3	the	the	DET
ejpam-4187	183	4	figure	figure	NOUN
ejpam-4187	183	5	3	3	NUM
ejpam-4187	183	6	:	:	PUNCT
ejpam-4187	183	7	a	a	DET
ejpam-4187	183	8	graph	graph	NOUN
ejpam-4187	183	9	g	g	NOUN
ejpam-4187	183	10	with	with	ADP
ejpam-4187	183	11	γd(g	γd(g	NUM
ejpam-4187	183	12	)	)	PUNCT
ejpam-4187	183	13	=	=	PUNCT
ejpam-4187	184	1	γd	γd	ADP
ejpam-4187	184	2	r	r	NOUN
ejpam-4187	184	3	(	(	PUNCT
ejpam-4187	184	4	g	g	NOUN
ejpam-4187	184	5	)	)	PUNCT
ejpam-4187	184	6	set	set	NOUN
ejpam-4187	184	7	{	{	PUNCT
ejpam-4187	184	8	xi	xi	X
ejpam-4187	184	9	:	:	PUNCT
ejpam-4187	184	10	i	i	NOUN
ejpam-4187	184	11	=	=	NOUN
ejpam-4187	184	12	1	1	NUM
ejpam-4187	184	13	,	,	PUNCT
ejpam-4187	184	14	2	2	NUM
ejpam-4187	184	15	,	,	PUNCT
ejpam-4187	184	16	.	.	PUNCT
ejpam-4187	184	17	.	.	PUNCT
ejpam-4187	185	1	.	.	PUNCT
ejpam-4187	186	1	,	,	PUNCT
ejpam-4187	186	2	a	a	PRON
ejpam-4187	186	3	}	}	PUNCT
ejpam-4187	186	4	is	be	AUX
ejpam-4187	186	5	both	both	CCONJ
ejpam-4187	186	6	a	a	DET
ejpam-4187	186	7	disjunctive	disjunctive	ADJ
ejpam-4187	186	8	dominating	dominating	NOUN
ejpam-4187	186	9	set	set	NOUN
ejpam-4187	186	10	and	and	CCONJ
ejpam-4187	186	11	a	a	DET
ejpam-4187	186	12	restrained	restrained	ADJ
ejpam-4187	186	13	disjunctive	disjunctive	ADJ
ejpam-4187	186	14	dominating	dominating	NOUN
ejpam-4187	186	15	of	of	ADP
ejpam-4187	186	16	g.	g.	PROPN
ejpam-4187	186	17	thus	thus	ADV
ejpam-4187	186	18	,	,	PUNCT
ejpam-4187	186	19	γd(g	γd(g	NUM
ejpam-4187	186	20	)	)	PUNCT
ejpam-4187	186	21	≤	≤	NOUN
ejpam-4187	186	22	a	a	DET
ejpam-4187	186	23	and	and	CCONJ
ejpam-4187	186	24	γdr	γdr	ADJ
ejpam-4187	186	25	(	(	PUNCT
ejpam-4187	186	26	g	g	NOUN
ejpam-4187	186	27	)	)	PUNCT
ejpam-4187	186	28	≤	≤	NOUN
ejpam-4187	186	29	a	a	DET
ejpam-4187	186	30	=	=	X
ejpam-4187	186	31	b.	b.	PROPN
ejpam-4187	186	32	let	let	VERB
ejpam-4187	186	33	s	s	PRON
ejpam-4187	186	34	⊆	⊆	NUM
ejpam-4187	186	35	v	v	NOUN
ejpam-4187	186	36	(	(	PUNCT
ejpam-4187	186	37	g	g	NOUN
ejpam-4187	186	38	)	)	PUNCT
ejpam-4187	186	39	be	be	AUX
ejpam-4187	186	40	a	a	DET
ejpam-4187	186	41	γd	γd	ADV
ejpam-4187	186	42	-	-	PUNCT
ejpam-4187	186	43	set	set	NOUN
ejpam-4187	186	44	of	of	ADP
ejpam-4187	186	45	g.	g.	PROPN
ejpam-4187	186	46	then	then	ADV
ejpam-4187	186	47	either	either	CCONJ
ejpam-4187	186	48	xj	xj	PROPN
ejpam-4187	186	49	∈	∈	PROPN
ejpam-4187	186	50	s	s	PART
ejpam-4187	186	51	or	or	CCONJ
ejpam-4187	186	52	u2j−1	u2j−1	PROPN
ejpam-4187	186	53	∈	∈	PROPN
ejpam-4187	186	54	s	s	NOUN
ejpam-4187	186	55	for	for	ADP
ejpam-4187	186	56	all	all	DET
ejpam-4187	186	57	j	j	NOUN
ejpam-4187	186	58	=	=	SYM
ejpam-4187	186	59	1	1	NUM
ejpam-4187	186	60	,	,	PUNCT
ejpam-4187	186	61	2	2	NUM
ejpam-4187	186	62	,	,	PUNCT
ejpam-4187	186	63	.	.	PUNCT
ejpam-4187	186	64	.	.	PUNCT
ejpam-4187	187	1	.	.	PUNCT
ejpam-4187	188	1	,	,	PUNCT
ejpam-4187	188	2	a.	a.	PROPN
ejpam-4187	188	3	also	also	ADV
ejpam-4187	188	4	,	,	PUNCT
ejpam-4187	188	5	being	be	AUX
ejpam-4187	188	6	a	a	DET
ejpam-4187	188	7	disjunctive	disjunctive	ADJ
ejpam-4187	188	8	dominating	dominating	NOUN
ejpam-4187	188	9	set	set	NOUN
ejpam-4187	188	10	of	of	ADP
ejpam-4187	188	11	g	g	NOUN
ejpam-4187	188	12	,	,	PUNCT
ejpam-4187	188	13	if	if	SCONJ
ejpam-4187	188	14	u2j−2	u2j−2	PROPN
ejpam-4187	188	15	∈	∈	PROPN
ejpam-4187	188	16	s	s	VERB
ejpam-4187	188	17	for	for	ADP
ejpam-4187	188	18	all	all	DET
ejpam-4187	188	19	j	j	NOUN
ejpam-4187	188	20	=	=	SYM
ejpam-4187	188	21	2	2	NUM
ejpam-4187	188	22	,	,	PUNCT
ejpam-4187	188	23	3	3	NUM
ejpam-4187	188	24	,	,	PUNCT
ejpam-4187	188	25	.	.	PUNCT
ejpam-4187	188	26	.	.	PUNCT
ejpam-4187	189	1	.	.	PUNCT
ejpam-4187	190	1	,	,	PUNCT
ejpam-4187	190	2	a	a	DET
ejpam-4187	190	3	,	,	PUNCT
ejpam-4187	190	4	then	then	ADV
ejpam-4187	190	5	necessarily	necessarily	ADV
ejpam-4187	190	6	u1u2a−1	u1u2a−1	NOUN
ejpam-4187	190	7	∈	∈	PROPN
ejpam-4187	190	8	s.	s.	PROPN
ejpam-4187	190	9	r.	r.	PROPN
ejpam-4187	190	10	malalay	malalay	PROPN
ejpam-4187	190	11	,	,	PUNCT
ejpam-4187	190	12	f.	f.	PROPN
ejpam-4187	190	13	jamil	jamil	PROPN
ejpam-4187	190	14	/	/	SYM
ejpam-4187	190	15	eur	eur	PROPN
ejpam-4187	190	16	.	.	PUNCT
ejpam-4187	191	1	j.	j.	PROPN
ejpam-4187	191	2	pure	pure	PROPN
ejpam-4187	191	3	appl	appl	PROPN
ejpam-4187	191	4	.	.	PROPN
ejpam-4187	191	5	math	math	PROPN
ejpam-4187	191	6	,	,	PUNCT
ejpam-4187	191	7	15	15	NUM
ejpam-4187	191	8	(	(	PUNCT
ejpam-4187	191	9	1	1	NUM
ejpam-4187	191	10	)	)	PUNCT
ejpam-4187	191	11	(	(	PUNCT
ejpam-4187	191	12	2022	2022	NUM
ejpam-4187	191	13	)	)	PUNCT
ejpam-4187	191	14	,	,	PUNCT
ejpam-4187	191	15	207	207	NUM
ejpam-4187	191	16	-	-	SYM
ejpam-4187	191	17	223	223	NUM
ejpam-4187	191	18	213	213	NUM
ejpam-4187	191	19	this	this	PRON
ejpam-4187	191	20	means	mean	VERB
ejpam-4187	191	21	that	that	SCONJ
ejpam-4187	191	22	γd(g	γd(g	NUM
ejpam-4187	191	23	)	)	PUNCT
ejpam-4187	191	24	≥	≥	PROPN
ejpam-4187	191	25	a.	a.	NOUN
ejpam-4187	191	26	thus	thus	ADV
ejpam-4187	191	27	,	,	PUNCT
ejpam-4187	191	28	γd(g	γd(g	NUM
ejpam-4187	191	29	)	)	PUNCT
ejpam-4187	191	30	=	=	PUNCT
ejpam-4187	192	1	a.	a.	NOUN
ejpam-4187	192	2	next	next	ADV
ejpam-4187	192	3	,	,	PUNCT
ejpam-4187	192	4	if	if	SCONJ
ejpam-4187	192	5	s	s	VERB
ejpam-4187	192	6	⊆	⊆	NUM
ejpam-4187	192	7	v	v	NOUN
ejpam-4187	192	8	(	(	PUNCT
ejpam-4187	192	9	g	g	NOUN
ejpam-4187	192	10	)	)	PUNCT
ejpam-4187	192	11	is	be	AUX
ejpam-4187	192	12	a	a	DET
ejpam-4187	192	13	γdr	γdr	NOUN
ejpam-4187	192	14	-set	-set	NOUN
ejpam-4187	192	15	of	of	ADP
ejpam-4187	192	16	g	g	PROPN
ejpam-4187	192	17	,	,	PUNCT
ejpam-4187	192	18	then	then	ADV
ejpam-4187	192	19	xi	xi	ADP
ejpam-4187	192	20	∈	∈	PROPN
ejpam-4187	192	21	s	s	PART
ejpam-4187	192	22	for	for	ADP
ejpam-4187	192	23	all	all	PRON
ejpam-4187	192	24	i	i	PRON
ejpam-4187	192	25	=	=	NOUN
ejpam-4187	192	26	1	1	NUM
ejpam-4187	192	27	,	,	PUNCT
ejpam-4187	192	28	2	2	NUM
ejpam-4187	192	29	,	,	PUNCT
ejpam-4187	192	30	.	.	PUNCT
ejpam-4187	192	31	.	.	PUNCT
ejpam-4187	193	1	.	.	PUNCT
ejpam-4187	194	1	,	,	PUNCT
ejpam-4187	194	2	a	a	PRON
ejpam-4187	194	3	or	or	CCONJ
ejpam-4187	194	4	x1xa	x1xa	SYM
ejpam-4187	194	5	∈	∈	PROPN
ejpam-4187	194	6	s	s	PART
ejpam-4187	194	7	and	and	CCONJ
ejpam-4187	194	8	u2j−1	u2j−1	PROPN
ejpam-4187	194	9	∈	∈	PROPN
ejpam-4187	194	10	s	s	NOUN
ejpam-4187	194	11	for	for	ADP
ejpam-4187	194	12	all	all	DET
ejpam-4187	194	13	j	j	NOUN
ejpam-4187	194	14	=	=	SYM
ejpam-4187	194	15	2	2	NUM
ejpam-4187	194	16	,	,	PUNCT
ejpam-4187	194	17	3	3	NUM
ejpam-4187	194	18	,	,	PUNCT
ejpam-4187	194	19	.	.	PUNCT
ejpam-4187	194	20	.	.	PUNCT
ejpam-4187	195	1	.	.	PUNCT
ejpam-4187	196	1	,	,	PUNCT
ejpam-4187	196	2	a	a	DET
ejpam-4187	196	3	−	−	NOUN
ejpam-4187	196	4	1	1	NUM
ejpam-4187	196	5	.	.	PUNCT
ejpam-4187	197	1	being	be	AUX
ejpam-4187	197	2	a	a	DET
ejpam-4187	197	3	restrained	restrained	ADJ
ejpam-4187	197	4	disjunctive	disjunctive	ADJ
ejpam-4187	197	5	dominating	dominating	NOUN
ejpam-4187	197	6	set	set	NOUN
ejpam-4187	197	7	of	of	ADP
ejpam-4187	197	8	g	g	NOUN
ejpam-4187	197	9	,	,	PUNCT
ejpam-4187	197	10	if	if	SCONJ
ejpam-4187	197	11	u2j−2	u2j−2	PROPN
ejpam-4187	197	12	∈	∈	PROPN
ejpam-4187	197	13	s	s	VERB
ejpam-4187	197	14	for	for	ADP
ejpam-4187	197	15	all	all	DET
ejpam-4187	197	16	j	j	NOUN
ejpam-4187	197	17	=	=	SYM
ejpam-4187	197	18	2	2	NUM
ejpam-4187	197	19	,	,	PUNCT
ejpam-4187	197	20	3	3	NUM
ejpam-4187	197	21	,	,	PUNCT
ejpam-4187	197	22	.	.	PUNCT
ejpam-4187	197	23	.	.	PUNCT
ejpam-4187	198	1	.	.	PUNCT
ejpam-4187	199	1	,	,	PUNCT
ejpam-4187	199	2	a	a	PRON
ejpam-4187	199	3	,	,	PUNCT
ejpam-4187	199	4	then	then	ADV
ejpam-4187	199	5	necessarily	necessarily	ADV
ejpam-4187	199	6	u1	u1	VERB
ejpam-4187	199	7	,	,	PUNCT
ejpam-4187	199	8	x1	x1	PROPN
ejpam-4187	199	9	,	,	PUNCT
ejpam-4187	199	10	u2a−1	u2a−1	PROPN
ejpam-4187	199	11	,	,	PUNCT
ejpam-4187	199	12	xa	xa	PROPN
ejpam-4187	199	13	∈	∈	PROPN
ejpam-4187	199	14	s.	s.	PROPN
ejpam-4187	199	15	similarly	similarly	ADV
ejpam-4187	199	16	,	,	PUNCT
ejpam-4187	199	17	if	if	SCONJ
ejpam-4187	199	18	u2j−1	u2j−1	PROPN
ejpam-4187	199	19	∈	∈	PROPN
ejpam-4187	199	20	s	s	PART
ejpam-4187	199	21	for	for	ADP
ejpam-4187	199	22	all	all	DET
ejpam-4187	199	23	j	j	NOUN
ejpam-4187	199	24	=	=	SYM
ejpam-4187	199	25	1	1	NUM
ejpam-4187	199	26	,	,	PUNCT
ejpam-4187	199	27	2	2	NUM
ejpam-4187	199	28	,	,	PUNCT
ejpam-4187	199	29	.	.	PUNCT
ejpam-4187	199	30	.	.	PUNCT
ejpam-4187	200	1	.	.	PUNCT
ejpam-4187	201	1	,	,	PUNCT
ejpam-4187	201	2	a	a	DET
ejpam-4187	201	3	,	,	PUNCT
ejpam-4187	201	4	then	then	ADV
ejpam-4187	201	5	necessarily	necessarily	ADV
ejpam-4187	201	6	x1	x1	NUM
ejpam-4187	201	7	,	,	PUNCT
ejpam-4187	201	8	xa	xa	PROPN
ejpam-4187	201	9	∈	∈	PROPN
ejpam-4187	201	10	s.	s.	PROPN
ejpam-4187	202	1	moreover	moreover	ADV
ejpam-4187	202	2	,	,	PUNCT
ejpam-4187	202	3	if	if	SCONJ
ejpam-4187	202	4	xju2j−1	xju2j−1	PROPN
ejpam-4187	202	5	∈	∈	PROPN
ejpam-4187	202	6	s	s	X
ejpam-4187	202	7	for	for	ADP
ejpam-4187	202	8	all	all	DET
ejpam-4187	202	9	j	j	NOUN
ejpam-4187	202	10	=	=	SYM
ejpam-4187	202	11	1	1	NUM
ejpam-4187	202	12	,	,	PUNCT
ejpam-4187	202	13	2	2	NUM
ejpam-4187	202	14	,	,	PUNCT
ejpam-4187	202	15	.	.	PUNCT
ejpam-4187	202	16	.	.	PUNCT
ejpam-4187	203	1	.	.	PUNCT
ejpam-4187	204	1	,	,	PUNCT
ejpam-4187	204	2	a	a	PRON
ejpam-4187	204	3	,	,	PUNCT
ejpam-4187	204	4	then	then	ADV
ejpam-4187	204	5	u2i−2	u2i−2	PROPN
ejpam-4187	204	6	∈	∈	NOUN
ejpam-4187	204	7	s	s	X
ejpam-4187	204	8	for	for	ADP
ejpam-4187	204	9	all	all	PRON
ejpam-4187	204	10	i	i	PRON
ejpam-4187	204	11	=	=	NOUN
ejpam-4187	204	12	2	2	NUM
ejpam-4187	204	13	,	,	PUNCT
ejpam-4187	204	14	3	3	NUM
ejpam-4187	204	15	,	,	PUNCT
ejpam-4187	204	16	.	.	PUNCT
ejpam-4187	204	17	.	.	PUNCT
ejpam-4187	205	1	.	.	PUNCT
ejpam-4187	206	1	,	,	PUNCT
ejpam-4187	206	2	a.	a.	NOUN
ejpam-4187	206	3	in	in	ADP
ejpam-4187	206	4	any	any	DET
ejpam-4187	206	5	case	case	NOUN
ejpam-4187	206	6	,	,	PUNCT
ejpam-4187	206	7	γdr	γdr	INTJ
ejpam-4187	206	8	(	(	PUNCT
ejpam-4187	206	9	g	g	NOUN
ejpam-4187	206	10	)	)	PUNCT
ejpam-4187	206	11	≥	≥	NOUN
ejpam-4187	206	12	a.	a.	NOUN
ejpam-4187	206	13	thus	thus	ADV
ejpam-4187	206	14	,	,	PUNCT
ejpam-4187	206	15	γdr	γdr	INTJ
ejpam-4187	206	16	(	(	PUNCT
ejpam-4187	206	17	g	g	NOUN
ejpam-4187	206	18	)	)	PUNCT
ejpam-4187	206	19	=	=	SYM
ejpam-4187	206	20	a	a	DET
ejpam-4187	206	21	=	=	PROPN
ejpam-4187	206	22	b.	b.	NOUN
ejpam-4187	206	23	case	case	NOUN
ejpam-4187	206	24	2	2	NUM
ejpam-4187	206	25	.	.	PUNCT
ejpam-4187	207	1	a	a	DET
ejpam-4187	207	2	<	<	X
ejpam-4187	207	3	b	b	NOUN
ejpam-4187	207	4	if	if	SCONJ
ejpam-4187	207	5	a	a	PRON
ejpam-4187	207	6	is	be	AUX
ejpam-4187	207	7	even	even	ADV
ejpam-4187	207	8	,	,	PUNCT
ejpam-4187	207	9	then	then	ADV
ejpam-4187	207	10	by	by	ADP
ejpam-4187	207	11	hypothesis	hypothesis	NOUN
ejpam-4187	207	12	,	,	PUNCT
ejpam-4187	207	13	b	b	PROPN
ejpam-4187	207	14	≤	≤	X
ejpam-4187	207	15	3a	3a	NUM
ejpam-4187	207	16	2	2	NUM
ejpam-4187	207	17	=	=	SYM
ejpam-4187	207	18	a	a	PRON
ejpam-4187	207	19	+	+	NOUN
ejpam-4187	207	20	a	a	DET
ejpam-4187	207	21	2	2	NUM
ejpam-4187	207	22	.	.	PUNCT
ejpam-4187	208	1	write	write	VERB
ejpam-4187	208	2	b	b	PROPN
ejpam-4187	208	3	=	=	PUNCT
ejpam-4187	208	4	a	a	PROPN
ejpam-4187	208	5	+	+	X
ejpam-4187	208	6	k	k	NOUN
ejpam-4187	208	7	,	,	PUNCT
ejpam-4187	208	8	where	where	SCONJ
ejpam-4187	208	9	1	1	NUM
ejpam-4187	208	10	≤	≤	NUM
ejpam-4187	208	11	k	k	NOUN
ejpam-4187	208	12	≤	≤	NUM
ejpam-4187	208	13	a	a	DET
ejpam-4187	208	14	2	2	NUM
ejpam-4187	208	15	.	.	PUNCT
ejpam-4187	209	1	take	take	VERB
ejpam-4187	209	2	g	g	NOUN
ejpam-4187	209	3	=	=	SYM
ejpam-4187	209	4	g2	g2	PROPN
ejpam-4187	209	5	obtained	obtain	VERB
ejpam-4187	209	6	from	from	ADP
ejpam-4187	209	7	g1	g1	NOUN
ejpam-4187	209	8	by	by	ADP
ejpam-4187	209	9	adding	add	VERB
ejpam-4187	209	10	pendant	pendant	ADJ
ejpam-4187	209	11	edges	edge	NOUN
ejpam-4187	209	12	xiyi	xiyi	ADJ
ejpam-4187	209	13	for	for	ADP
ejpam-4187	209	14	all	all	DET
ejpam-4187	209	15	i	i	PRON
ejpam-4187	209	16	=	=	NOUN
ejpam-4187	209	17	1	1	NUM
ejpam-4187	209	18	,	,	PUNCT
ejpam-4187	209	19	2	2	NUM
ejpam-4187	209	20	,	,	PUNCT
ejpam-4187	209	21	.	.	PUNCT
ejpam-4187	209	22	.	.	PUNCT
ejpam-4187	210	1	.	.	PUNCT
ejpam-4187	211	1	,	,	PUNCT
ejpam-4187	211	2	2k	2k	NOUN
ejpam-4187	211	3	−	−	NOUN
ejpam-4187	211	4	1	1	NUM
ejpam-4187	211	5	as	as	SCONJ
ejpam-4187	211	6	shown	show	VERB
ejpam-4187	211	7	in	in	ADP
ejpam-4187	211	8	figure	figure	NOUN
ejpam-4187	211	9	4	4	NUM
ejpam-4187	211	10	.	.	PUNCT
ejpam-4187	212	1	since	since	SCONJ
ejpam-4187	212	2	the	the	DET
ejpam-4187	212	3	set	set	NOUN
ejpam-4187	212	4	{	{	PUNCT
ejpam-4187	212	5	xi	xi	X
ejpam-4187	212	6	:	:	PUNCT
ejpam-4187	212	7	i	i	NOUN
ejpam-4187	212	8	=	=	NOUN
ejpam-4187	212	9	1	1	NUM
ejpam-4187	212	10	,	,	PUNCT
ejpam-4187	212	11	2	2	NUM
ejpam-4187	212	12	,	,	PUNCT
ejpam-4187	212	13	.	.	PUNCT
ejpam-4187	212	14	.	.	PUNCT
ejpam-4187	213	1	.	.	PUNCT
ejpam-4187	214	1	,	,	PUNCT
ejpam-4187	214	2	a	a	PRON
ejpam-4187	214	3	}	}	PUNCT
ejpam-4187	214	4	is	be	AUX
ejpam-4187	214	5	a	a	DET
ejpam-4187	214	6	γd	γd	ADV
ejpam-4187	214	7	-	-	PUNCT
ejpam-4187	214	8	set	set	NOUN
ejpam-4187	214	9	of	of	ADP
ejpam-4187	214	10	g	g	NOUN
ejpam-4187	214	11	,	,	PUNCT
ejpam-4187	214	12	γd(g	γd(g	NUM
ejpam-4187	214	13	)	)	PUNCT
ejpam-4187	214	14	=	=	SYM
ejpam-4187	214	15	a.	a.	NOUN
ejpam-4187	214	16	figure	figure	NOUN
ejpam-4187	214	17	4	4	NUM
ejpam-4187	214	18	:	:	PUNCT
ejpam-4187	214	19	a	a	DET
ejpam-4187	214	20	graph	graph	NOUN
ejpam-4187	214	21	g	g	NOUN
ejpam-4187	214	22	with	with	ADP
ejpam-4187	214	23	γd(g	γd(g	NUM
ejpam-4187	214	24	)	)	PUNCT
ejpam-4187	214	25	<	<	X
ejpam-4187	215	1	γd	γd	ADP
ejpam-4187	215	2	r	r	NOUN
ejpam-4187	215	3	(	(	PUNCT
ejpam-4187	215	4	g	g	NOUN
ejpam-4187	215	5	)	)	PUNCT
ejpam-4187	215	6	next	next	ADV
ejpam-4187	215	7	,	,	PUNCT
ejpam-4187	215	8	to	to	PART
ejpam-4187	215	9	determine	determine	VERB
ejpam-4187	215	10	the	the	DET
ejpam-4187	215	11	restrained	restrained	ADJ
ejpam-4187	215	12	disjunctive	disjunctive	ADJ
ejpam-4187	215	13	domination	domination	NOUN
ejpam-4187	215	14	number	number	NOUN
ejpam-4187	215	15	of	of	ADP
ejpam-4187	215	16	g	g	NOUN
ejpam-4187	215	17	,	,	PUNCT
ejpam-4187	215	18	first	first	ADV
ejpam-4187	215	19	consider	consider	VERB
ejpam-4187	215	20	the	the	DET
ejpam-4187	215	21	case	case	NOUN
ejpam-4187	215	22	where	where	SCONJ
ejpam-4187	215	23	4k	4k	PRON
ejpam-4187	215	24	−	−	PROPN
ejpam-4187	215	25	2	2	NUM
ejpam-4187	215	26	=	=	SYM
ejpam-4187	215	27	2a	2a	NUM
ejpam-4187	215	28	−	−	NUM
ejpam-4187	216	1	2	2	X
ejpam-4187	216	2	.	.	PUNCT
ejpam-4187	216	3	let	let	VERB
ejpam-4187	216	4	s	s	PRON
ejpam-4187	216	5	=	=	X
ejpam-4187	216	6	{	{	PUNCT
ejpam-4187	216	7	xi	xi	PROPN
ejpam-4187	216	8	,	,	PUNCT
ejpam-4187	216	9	yj	yj	PROPN
ejpam-4187	216	10	:	:	PUNCT
ejpam-4187	217	1	i	i	PROPN
ejpam-4187	217	2	=	=	SYM
ejpam-4187	217	3	2k	2k	NUM
ejpam-4187	217	4	,	,	PUNCT
ejpam-4187	217	5	2k	2k	NUM
ejpam-4187	217	6	+	+	CCONJ
ejpam-4187	217	7	1	1	NUM
ejpam-4187	217	8	,	,	PUNCT
ejpam-4187	217	9	.	.	PUNCT
ejpam-4187	217	10	.	.	PUNCT
ejpam-4187	218	1	.	.	PUNCT
ejpam-4187	219	1	,	,	PUNCT
ejpam-4187	219	2	a	a	PRON
ejpam-4187	219	3	;	;	PUNCT
ejpam-4187	219	4	j	j	PROPN
ejpam-4187	219	5	=	=	SYM
ejpam-4187	219	6	1	1	NUM
ejpam-4187	219	7	,	,	PUNCT
ejpam-4187	219	8	2	2	NUM
ejpam-4187	219	9	,	,	PUNCT
ejpam-4187	219	10	.	.	PUNCT
ejpam-4187	219	11	.	.	PUNCT
ejpam-4187	220	1	.	.	PUNCT
ejpam-4187	221	1	,	,	PUNCT
ejpam-4187	221	2	2k	2k	NOUN
ejpam-4187	221	3	−	−	NOUN
ejpam-4187	221	4	1	1	NUM
ejpam-4187	221	5	}	}	PUNCT
ejpam-4187	221	6	∪	∪	NOUN
ejpam-4187	221	7	{	{	PUNCT
ejpam-4187	221	8	u4k−4	u4k−4	PROPN
ejpam-4187	221	9	,	,	PUNCT
ejpam-4187	221	10	u2(2j−1	u2(2j−1	PROPN
ejpam-4187	221	11	)	)	PUNCT
ejpam-4187	221	12	:	:	PUNCT
ejpam-4187	222	1	j	j	X
ejpam-4187	222	2	=	=	SYM
ejpam-4187	222	3	1	1	NUM
ejpam-4187	222	4	,	,	PUNCT
ejpam-4187	222	5	2	2	NUM
ejpam-4187	222	6	,	,	PUNCT
ejpam-4187	222	7	.	.	PUNCT
ejpam-4187	222	8	.	.	PUNCT
ejpam-4187	223	1	.	.	PUNCT
ejpam-4187	224	1	,	,	PUNCT
ejpam-4187	225	1	k	k	PROPN
ejpam-4187	226	1	−	−	PROPN
ejpam-4187	227	1	1	1	NUM
ejpam-4187	227	2	}	}	PUNCT
ejpam-4187	227	3	.	.	PUNCT
ejpam-4187	228	1	then	then	ADV
ejpam-4187	228	2	s	s	VERB
ejpam-4187	228	3	is	be	AUX
ejpam-4187	228	4	a	a	DET
ejpam-4187	228	5	restrained	restrained	ADJ
ejpam-4187	228	6	disjunctive	disjunctive	ADJ
ejpam-4187	228	7	dominating	dominating	NOUN
ejpam-4187	228	8	set	set	NOUN
ejpam-4187	228	9	of	of	ADP
ejpam-4187	228	10	g.	g.	PROPN
ejpam-4187	228	11	hence	hence	ADV
ejpam-4187	228	12	,	,	PUNCT
ejpam-4187	228	13	γdr	γdr	INTJ
ejpam-4187	228	14	(	(	PUNCT
ejpam-4187	228	15	g	g	NOUN
ejpam-4187	228	16	)	)	PUNCT
ejpam-4187	228	17	≤	≤	NUM
ejpam-4187	228	18	|s|	|s|	PROPN
ejpam-4187	228	19	=	=	PUNCT
ejpam-4187	229	1	[	[	X
ejpam-4187	229	2	a	a	DET
ejpam-4187	229	3	−	−	PROPN
ejpam-4187	229	4	(	(	PUNCT
ejpam-4187	229	5	2k	2k	NOUN
ejpam-4187	229	6	−	−	NOUN
ejpam-4187	229	7	1	1	NUM
ejpam-4187	229	8	)	)	PUNCT
ejpam-4187	229	9	]	]	PUNCT
ejpam-4187	230	1	+	+	CCONJ
ejpam-4187	230	2	(	(	PUNCT
ejpam-4187	230	3	2k	2k	NOUN
ejpam-4187	230	4	−	−	NOUN
ejpam-4187	230	5	1	1	NUM
ejpam-4187	230	6	)	)	PUNCT
ejpam-4187	230	7	+	+	CCONJ
ejpam-4187	231	1	[	[	X
ejpam-4187	231	2	(	(	PUNCT
ejpam-4187	231	3	k	k	NOUN
ejpam-4187	231	4	−	−	PROPN
ejpam-4187	231	5	1	1	NUM
ejpam-4187	231	6	)	)	PUNCT
ejpam-4187	231	7	+	+	CCONJ
ejpam-4187	231	8	1	1	X
ejpam-4187	231	9	]	]	X
ejpam-4187	231	10	=	=	PUNCT
ejpam-4187	231	11	a	a	PRON
ejpam-4187	231	12	+	+	X
ejpam-4187	231	13	k	k	PROPN
ejpam-4187	231	14	=	=	SYM
ejpam-4187	231	15	b.	b.	PROPN
ejpam-4187	231	16	let	let	VERB
ejpam-4187	231	17	s	s	PRON
ejpam-4187	231	18	⊆	⊆	NUM
ejpam-4187	231	19	v	v	NOUN
ejpam-4187	231	20	(	(	PUNCT
ejpam-4187	231	21	g	g	NOUN
ejpam-4187	231	22	)	)	PUNCT
ejpam-4187	231	23	be	be	AUX
ejpam-4187	231	24	a	a	DET
ejpam-4187	231	25	γdr	γdr	NOUN
ejpam-4187	231	26	-set	-set	NOUN
ejpam-4187	231	27	of	of	ADP
ejpam-4187	231	28	g.	g.	PROPN
ejpam-4187	231	29	necessarily	necessarily	ADV
ejpam-4187	231	30	,	,	PUNCT
ejpam-4187	231	31	xa	xa	PROPN
ejpam-4187	231	32	,	,	PUNCT
ejpam-4187	231	33	yj	yj	PROPN
ejpam-4187	231	34	∈	∈	PROPN
ejpam-4187	231	35	s	s	PROPN
ejpam-4187	231	36	for	for	ADP
ejpam-4187	231	37	each	each	DET
ejpam-4187	231	38	j	j	PROPN
ejpam-4187	231	39	∈	∈	PROPN
ejpam-4187	231	40	{	{	PUNCT
ejpam-4187	231	41	1	1	NUM
ejpam-4187	231	42	,	,	PUNCT
ejpam-4187	231	43	2	2	NUM
ejpam-4187	231	44	,	,	PUNCT
ejpam-4187	231	45	.	.	PUNCT
ejpam-4187	231	46	.	.	PUNCT
ejpam-4187	232	1	.	.	PUNCT
ejpam-4187	233	1	,	,	PUNCT
ejpam-4187	233	2	2k	2k	NOUN
ejpam-4187	233	3	−	−	NOUN
ejpam-4187	233	4	1	1	NUM
ejpam-4187	233	5	}	}	PUNCT
ejpam-4187	233	6	.	.	PUNCT
ejpam-4187	234	1	observe	observe	VERB
ejpam-4187	234	2	that	that	SCONJ
ejpam-4187	234	3	,	,	PUNCT
ejpam-4187	234	4	if	if	SCONJ
ejpam-4187	234	5	xi	xi	PROPN
ejpam-4187	234	6	∈	∈	PROPN
ejpam-4187	234	7	s	s	X
ejpam-4187	234	8	for	for	ADP
ejpam-4187	234	9	each	each	DET
ejpam-4187	234	10	i	i	PRON
ejpam-4187	234	11	∈	∈	PROPN
ejpam-4187	234	12	{	{	PUNCT
ejpam-4187	234	13	1	1	NUM
ejpam-4187	234	14	,	,	PUNCT
ejpam-4187	234	15	2	2	NUM
ejpam-4187	234	16	,	,	PUNCT
ejpam-4187	234	17	.	.	PUNCT
ejpam-4187	234	18	.	.	PUNCT
ejpam-4187	235	1	.	.	PUNCT
ejpam-4187	236	1	,	,	PUNCT
ejpam-4187	236	2	a	a	DET
ejpam-4187	236	3	−	−	PROPN
ejpam-4187	236	4	1	1	NUM
ejpam-4187	236	5	}	}	PUNCT
ejpam-4187	236	6	or	or	CCONJ
ejpam-4187	236	7	u2a−1	u2a−1	ADJ
ejpam-4187	236	8	,	,	PUNCT
ejpam-4187	236	9	u2(2j−1	u2(2j−1	PROPN
ejpam-4187	236	10	)	)	PUNCT
ejpam-4187	236	11	∈	∈	PROPN
ejpam-4187	236	12	s	s	PART
ejpam-4187	236	13	for	for	ADP
ejpam-4187	236	14	each	each	DET
ejpam-4187	236	15	j	j	PROPN
ejpam-4187	236	16	∈	∈	PROPN
ejpam-4187	236	17	{	{	PUNCT
ejpam-4187	236	18	1	1	NUM
ejpam-4187	236	19	,	,	PUNCT
ejpam-4187	236	20	2	2	NUM
ejpam-4187	236	21	,	,	PUNCT
ejpam-4187	236	22	.	.	PUNCT
ejpam-4187	236	23	.	.	PUNCT
ejpam-4187	237	1	.	.	PUNCT
ejpam-4187	238	1	,	,	PUNCT
ejpam-4187	238	2	k	k	X
ejpam-4187	238	3	}	}	PUNCT
ejpam-4187	238	4	,	,	PUNCT
ejpam-4187	238	5	then	then	ADV
ejpam-4187	238	6	|s|	|s|	VERB
ejpam-4187	238	7	≥	≥	X
ejpam-4187	238	8	a+	a+	PUNCT
ejpam-4187	239	1	k	k	X
ejpam-4187	239	2	+	+	PROPN
ejpam-4187	239	3	1	1	NUM
ejpam-4187	239	4	which	which	PRON
ejpam-4187	239	5	is	be	AUX
ejpam-4187	239	6	a	a	DET
ejpam-4187	239	7	contradiction	contradiction	NOUN
ejpam-4187	239	8	.	.	PUNCT
ejpam-4187	240	1	this	this	PRON
ejpam-4187	240	2	implies	imply	VERB
ejpam-4187	240	3	that	that	SCONJ
ejpam-4187	240	4	the	the	DET
ejpam-4187	240	5	set	set	NOUN
ejpam-4187	240	6	{	{	PUNCT
ejpam-4187	240	7	xi	xi	PROPN
ejpam-4187	240	8	,	,	PUNCT
ejpam-4187	240	9	yj	yj	PROPN
ejpam-4187	240	10	:	:	PUNCT
ejpam-4187	240	11	i	i	PROPN
ejpam-4187	240	12	=	=	SYM
ejpam-4187	240	13	2k	2k	NUM
ejpam-4187	240	14	,	,	PUNCT
ejpam-4187	240	15	2k+1	2k+1	PROPN
ejpam-4187	240	16	,	,	PUNCT
ejpam-4187	240	17	.	.	PUNCT
ejpam-4187	240	18	.	.	PUNCT
ejpam-4187	240	19	.	.	PUNCT
ejpam-4187	241	1	,	,	PUNCT
ejpam-4187	241	2	a	a	PRON
ejpam-4187	241	3	;	;	PUNCT
ejpam-4187	241	4	j	j	PROPN
ejpam-4187	241	5	=	=	SYM
ejpam-4187	241	6	1	1	NUM
ejpam-4187	241	7	,	,	PUNCT
ejpam-4187	241	8	2	2	NUM
ejpam-4187	241	9	,	,	PUNCT
ejpam-4187	241	10	.	.	PUNCT
ejpam-4187	241	11	.	.	PUNCT
ejpam-4187	242	1	.	.	PUNCT
ejpam-4187	243	1	,	,	PUNCT
ejpam-4187	243	2	2k−1}∪{u4k−4	2k−1}∪{u4k−4	NUM
ejpam-4187	243	3	,	,	PUNCT
ejpam-4187	243	4	u2(2j−1	u2(2j−1	PROPN
ejpam-4187	243	5	)	)	PUNCT
ejpam-4187	243	6	:	:	PUNCT
ejpam-4187	244	1	j	j	X
ejpam-4187	244	2	=	=	SYM
ejpam-4187	244	3	1	1	NUM
ejpam-4187	244	4	,	,	PUNCT
ejpam-4187	244	5	2	2	NUM
ejpam-4187	244	6	,	,	PUNCT
ejpam-4187	244	7	.	.	PUNCT
ejpam-4187	244	8	.	.	PUNCT
ejpam-4187	245	1	.	.	PUNCT
ejpam-4187	246	1	,	,	PUNCT
ejpam-4187	246	2	k−1	k−1	PROPN
ejpam-4187	246	3	}	}	PUNCT
ejpam-4187	246	4	is	be	AUX
ejpam-4187	246	5	a	a	DET
ejpam-4187	246	6	γdr	γdr	NOUN
ejpam-4187	246	7	-set	-set	NOUN
ejpam-4187	246	8	of	of	ADP
ejpam-4187	246	9	g.	g.	PROPN
ejpam-4187	246	10	thus	thus	ADV
ejpam-4187	246	11	,	,	PUNCT
ejpam-4187	246	12	γdr	γdr	INTJ
ejpam-4187	246	13	(	(	PUNCT
ejpam-4187	246	14	g	g	NOUN
ejpam-4187	246	15	)	)	PUNCT
ejpam-4187	246	16	=	=	SYM
ejpam-4187	246	17	a+	a+	PUNCT
ejpam-4187	246	18	k	k	PROPN
ejpam-4187	246	19	=	=	PROPN
ejpam-4187	246	20	b.	b.	PROPN
ejpam-4187	246	21	suppose	suppose	VERB
ejpam-4187	246	22	that	that	SCONJ
ejpam-4187	246	23	4k−	4k−	PROPN
ejpam-4187	246	24	2	2	NUM
ejpam-4187	246	25	<	<	X
ejpam-4187	246	26	2a−	2a−	NUM
ejpam-4187	246	27	2	2	NUM
ejpam-4187	246	28	.	.	PUNCT
ejpam-4187	247	1	let	let	VERB
ejpam-4187	247	2	s	s	PRON
ejpam-4187	247	3	=	=	X
ejpam-4187	247	4	{	{	PUNCT
ejpam-4187	247	5	xi	xi	PROPN
ejpam-4187	247	6	,	,	PUNCT
ejpam-4187	247	7	yj	yj	PROPN
ejpam-4187	247	8	:	:	PUNCT
ejpam-4187	247	9	i	i	PROPN
ejpam-4187	247	10	=	=	SYM
ejpam-4187	247	11	2k	2k	NUM
ejpam-4187	247	12	,	,	PUNCT
ejpam-4187	247	13	2k	2k	NUM
ejpam-4187	247	14	+	+	CCONJ
ejpam-4187	247	15	1	1	NUM
ejpam-4187	247	16	,	,	PUNCT
ejpam-4187	247	17	.	.	PUNCT
ejpam-4187	247	18	.	.	PUNCT
ejpam-4187	248	1	.	.	PUNCT
ejpam-4187	249	1	,	,	PUNCT
ejpam-4187	249	2	a	a	PRON
ejpam-4187	249	3	;	;	PUNCT
ejpam-4187	249	4	j	j	PROPN
ejpam-4187	249	5	=	=	SYM
ejpam-4187	249	6	1	1	NUM
ejpam-4187	249	7	,	,	PUNCT
ejpam-4187	249	8	2	2	NUM
ejpam-4187	249	9	,	,	PUNCT
ejpam-4187	249	10	.	.	PUNCT
ejpam-4187	249	11	.	.	PUNCT
ejpam-4187	250	1	.	.	PUNCT
ejpam-4187	251	1	,	,	PUNCT
ejpam-4187	251	2	2k	2k	NOUN
ejpam-4187	251	3	−	−	NOUN
ejpam-4187	251	4	1	1	NUM
ejpam-4187	251	5	}	}	PUNCT
ejpam-4187	251	6	∪	∪	ADJ
ejpam-4187	251	7	{	{	PUNCT
ejpam-4187	251	8	u2(2j−1	u2(2j−1	PROPN
ejpam-4187	251	9	)	)	PUNCT
ejpam-4187	251	10	:	:	PUNCT
ejpam-4187	252	1	j	j	X
ejpam-4187	252	2	=	=	SYM
ejpam-4187	252	3	1	1	NUM
ejpam-4187	252	4	,	,	PUNCT
ejpam-4187	252	5	2	2	NUM
ejpam-4187	252	6	,	,	PUNCT
ejpam-4187	252	7	.	.	PUNCT
ejpam-4187	252	8	.	.	PUNCT
ejpam-4187	252	9	.	.	PUNCT
ejpam-4187	253	1	,	,	PUNCT
ejpam-4187	253	2	k	k	X
ejpam-4187	253	3	}	}	PUNCT
ejpam-4187	253	4	.	.	PUNCT
ejpam-4187	254	1	then	then	ADV
ejpam-4187	254	2	s	s	VERB
ejpam-4187	254	3	is	be	AUX
ejpam-4187	254	4	a	a	DET
ejpam-4187	254	5	restrained	restrained	ADJ
ejpam-4187	254	6	disjunctive	disjunctive	ADJ
ejpam-4187	254	7	dominating	dominating	NOUN
ejpam-4187	254	8	set	set	VERB
ejpam-4187	254	9	ofg	ofg	PROPN
ejpam-4187	254	10	.	.	PUNCT
ejpam-4187	255	1	thus	thus	ADV
ejpam-4187	255	2	,	,	PUNCT
ejpam-4187	255	3	γdr	γdr	INTJ
ejpam-4187	255	4	(	(	PUNCT
ejpam-4187	255	5	g	g	NOUN
ejpam-4187	255	6	)	)	PUNCT
ejpam-4187	255	7	≤	≤	NUM
ejpam-4187	255	8	|s|	|s|	PROPN
ejpam-4187	255	9	=	=	SYM
ejpam-4187	256	1	[	[	X
ejpam-4187	256	2	a−(2k−1)]+(2k−1)+k	a−(2k−1)]+(2k−1)+k	ADJ
ejpam-4187	256	3	=	=	SYM
ejpam-4187	256	4	a+k	a+k	PROPN
ejpam-4187	256	5	=	=	SYM
ejpam-4187	256	6	b.	b.	PROPN
ejpam-4187	256	7	following	follow	VERB
ejpam-4187	256	8	similar	similar	ADJ
ejpam-4187	256	9	arguments	argument	NOUN
ejpam-4187	256	10	as	as	ADP
ejpam-4187	256	11	above	above	ADV
ejpam-4187	256	12	show	show	VERB
ejpam-4187	256	13	that	that	SCONJ
ejpam-4187	256	14	γdr	γdr	INTJ
ejpam-4187	256	15	(	(	PUNCT
ejpam-4187	256	16	g	g	NOUN
ejpam-4187	256	17	)	)	PUNCT
ejpam-4187	256	18	=	=	SYM
ejpam-4187	257	1	b.	b.	PROPN
ejpam-4187	258	1	now	now	ADV
ejpam-4187	258	2	,	,	PUNCT
ejpam-4187	258	3	suppose	suppose	VERB
ejpam-4187	258	4	that	that	SCONJ
ejpam-4187	258	5	a	a	PRON
ejpam-4187	258	6	is	be	AUX
ejpam-4187	258	7	odd	odd	ADJ
ejpam-4187	258	8	.	.	PUNCT
ejpam-4187	259	1	then	then	ADV
ejpam-4187	259	2	b	b	X
ejpam-4187	259	3	≤	≤	ADJ
ejpam-4187	259	4	3a+1	3a+1	NOUN
ejpam-4187	259	5	2	2	NUM
ejpam-4187	259	6	=	=	SYM
ejpam-4187	259	7	a	a	DET
ejpam-4187	259	8	+	+	NOUN
ejpam-4187	259	9	a+1	a+1	PROPN
ejpam-4187	259	10	2	2	NUM
ejpam-4187	259	11	.	.	PUNCT
ejpam-4187	260	1	let	let	VERB
ejpam-4187	260	2	b	b	X
ejpam-4187	260	3	=	=	PUNCT
ejpam-4187	260	4	a	a	PROPN
ejpam-4187	261	1	+	+	X
ejpam-4187	261	2	k	k	NOUN
ejpam-4187	261	3	,	,	PUNCT
ejpam-4187	261	4	where	where	SCONJ
ejpam-4187	261	5	1	1	NUM
ejpam-4187	261	6	≤	≤	NUM
ejpam-4187	261	7	k	k	X
ejpam-4187	261	8	≤	≤	NUM
ejpam-4187	261	9	a+1	a+1	DET
ejpam-4187	261	10	2	2	NUM
ejpam-4187	261	11	.	.	PUNCT
ejpam-4187	262	1	if	if	SCONJ
ejpam-4187	262	2	4k−2	4k−2	NUM
ejpam-4187	262	3	=	=	SYM
ejpam-4187	262	4	2a	2a	NUM
ejpam-4187	262	5	,	,	PUNCT
ejpam-4187	262	6	then	then	ADV
ejpam-4187	262	7	γdr	γdr	INTJ
ejpam-4187	262	8	(	(	PUNCT
ejpam-4187	262	9	g	g	NOUN
ejpam-4187	262	10	)	)	PUNCT
ejpam-4187	262	11	=	=	SYM
ejpam-4187	262	12	b	b	PROPN
ejpam-4187	262	13	as	as	SCONJ
ejpam-4187	262	14	determined	determine	VERB
ejpam-4187	262	15	by	by	ADP
ejpam-4187	262	16	the	the	DET
ejpam-4187	262	17	set	set	NOUN
ejpam-4187	262	18	{	{	PUNCT
ejpam-4187	262	19	xi	xi	PROPN
ejpam-4187	262	20	,	,	PUNCT
ejpam-4187	262	21	yj	yj	PROPN
ejpam-4187	262	22	:	:	PUNCT
ejpam-4187	262	23	i	i	PROPN
ejpam-4187	262	24	=	=	SYM
ejpam-4187	262	25	2k	2k	NUM
ejpam-4187	262	26	,	,	PUNCT
ejpam-4187	262	27	2k+	2k+	NUM
ejpam-4187	262	28	1	1	NUM
ejpam-4187	262	29	,	,	PUNCT
ejpam-4187	262	30	.	.	PUNCT
ejpam-4187	262	31	.	.	PUNCT
ejpam-4187	263	1	.	.	PUNCT
ejpam-4187	264	1	,	,	PUNCT
ejpam-4187	264	2	a	a	PRON
ejpam-4187	264	3	;	;	PUNCT
ejpam-4187	264	4	j	j	PROPN
ejpam-4187	264	5	=	=	SYM
ejpam-4187	264	6	1	1	NUM
ejpam-4187	264	7	,	,	PUNCT
ejpam-4187	264	8	2	2	NUM
ejpam-4187	264	9	,	,	PUNCT
ejpam-4187	264	10	.	.	PUNCT
ejpam-4187	264	11	.	.	PUNCT
ejpam-4187	265	1	.	.	PUNCT
ejpam-4187	266	1	,	,	PUNCT
ejpam-4187	266	2	2k	2k	NOUN
ejpam-4187	266	3	−	−	NOUN
ejpam-4187	266	4	1	1	NUM
ejpam-4187	266	5	}	}	PUNCT
ejpam-4187	266	6	∪	∪	NOUN
ejpam-4187	266	7	{	{	PUNCT
ejpam-4187	266	8	u4k−4	u4k−4	PROPN
ejpam-4187	266	9	,	,	PUNCT
ejpam-4187	266	10	u2(2j−1	u2(2j−1	PROPN
ejpam-4187	266	11	)	)	PUNCT
ejpam-4187	266	12	:	:	PUNCT
ejpam-4187	267	1	j	j	X
ejpam-4187	267	2	=	=	SYM
ejpam-4187	267	3	1	1	NUM
ejpam-4187	267	4	,	,	PUNCT
ejpam-4187	267	5	2	2	NUM
ejpam-4187	267	6	,	,	PUNCT
ejpam-4187	267	7	.	.	PUNCT
ejpam-4187	267	8	.	.	PUNCT
ejpam-4187	268	1	.	.	PUNCT
ejpam-4187	269	1	,	,	PUNCT
ejpam-4187	270	1	k	k	PROPN
ejpam-4187	270	2	−	−	PROPN
ejpam-4187	271	1	1	1	NUM
ejpam-4187	271	2	}	}	PUNCT
ejpam-4187	271	3	and	and	CCONJ
ejpam-4187	271	4	if	if	SCONJ
ejpam-4187	271	5	4k	4k	PRON
ejpam-4187	271	6	−	−	PROPN
ejpam-4187	271	7	2	2	NUM
ejpam-4187	271	8	<	<	X
ejpam-4187	271	9	2a	2a	NUM
ejpam-4187	271	10	,	,	PUNCT
ejpam-4187	271	11	then	then	ADV
ejpam-4187	271	12	s	s	VERB
ejpam-4187	271	13	=	=	PUNCT
ejpam-4187	271	14	{	{	PUNCT
ejpam-4187	271	15	xi	xi	PROPN
ejpam-4187	271	16	,	,	PUNCT
ejpam-4187	271	17	yj	yj	PROPN
ejpam-4187	271	18	:	:	PUNCT
ejpam-4187	272	1	i	i	PROPN
ejpam-4187	272	2	=	=	SYM
ejpam-4187	272	3	2k	2k	NUM
ejpam-4187	272	4	,	,	PUNCT
ejpam-4187	272	5	2k	2k	NUM
ejpam-4187	272	6	+	+	CCONJ
ejpam-4187	272	7	1	1	NUM
ejpam-4187	272	8	,	,	PUNCT
ejpam-4187	272	9	.	.	PUNCT
ejpam-4187	272	10	.	.	PUNCT
ejpam-4187	273	1	.	.	PUNCT
ejpam-4187	274	1	,	,	PUNCT
ejpam-4187	274	2	a	a	PRON
ejpam-4187	274	3	;	;	PUNCT
ejpam-4187	274	4	j	j	PROPN
ejpam-4187	274	5	=	=	SYM
ejpam-4187	274	6	1	1	NUM
ejpam-4187	274	7	,	,	PUNCT
ejpam-4187	274	8	2	2	NUM
ejpam-4187	274	9	,	,	PUNCT
ejpam-4187	274	10	.	.	PUNCT
ejpam-4187	274	11	.	.	PUNCT
ejpam-4187	275	1	.	.	PUNCT
ejpam-4187	276	1	,	,	PUNCT
ejpam-4187	276	2	2k	2k	NOUN
ejpam-4187	276	3	−	−	NOUN
ejpam-4187	276	4	1	1	NUM
ejpam-4187	276	5	}	}	PUNCT
ejpam-4187	276	6	∪	∪	ADJ
ejpam-4187	276	7	{	{	PUNCT
ejpam-4187	276	8	u2(2j−1	u2(2j−1	PROPN
ejpam-4187	276	9	)	)	PUNCT
ejpam-4187	276	10	:	:	PUNCT
ejpam-4187	277	1	j	j	X
ejpam-4187	277	2	=	=	SYM
ejpam-4187	277	3	1	1	NUM
ejpam-4187	277	4	,	,	PUNCT
ejpam-4187	277	5	2	2	NUM
ejpam-4187	277	6	,	,	PUNCT
ejpam-4187	277	7	.	.	PUNCT
ejpam-4187	277	8	.	.	PUNCT
ejpam-4187	277	9	.	.	PUNCT
ejpam-4187	278	1	,	,	PUNCT
ejpam-4187	278	2	k	k	X
ejpam-4187	278	3	}	}	PUNCT
ejpam-4187	278	4	is	be	AUX
ejpam-4187	278	5	a	a	DET
ejpam-4187	278	6	γdr	γdr	NOUN
ejpam-4187	278	7	-set	-set	NOUN
ejpam-4187	278	8	of	of	ADP
ejpam-4187	278	9	g.	g.	PROPN
ejpam-4187	278	10	thus	thus	ADV
ejpam-4187	278	11	,	,	PUNCT
ejpam-4187	278	12	γdr	γdr	INTJ
ejpam-4187	278	13	(	(	PUNCT
ejpam-4187	278	14	g	g	NOUN
ejpam-4187	278	15	)	)	PUNCT
ejpam-4187	278	16	=	=	SYM
ejpam-4187	278	17	b.	b.	PROPN
ejpam-4187	278	18	4	4	X
ejpam-4187	278	19	.	.	PUNCT
ejpam-4187	278	20	main	main	ADJ
ejpam-4187	278	21	results	result	NOUN
ejpam-4187	278	22	4.1	4.1	NUM
ejpam-4187	278	23	.	.	PUNCT
ejpam-4187	279	1	on	on	ADP
ejpam-4187	279	2	join	join	NOUN
ejpam-4187	279	3	of	of	ADP
ejpam-4187	279	4	graphs	graph	NOUN
ejpam-4187	279	5	theorem	theorem	VERB
ejpam-4187	279	6	3	3	NUM
ejpam-4187	279	7	.	.	PUNCT
ejpam-4187	280	1	[	[	X
ejpam-4187	280	2	15	15	NUM
ejpam-4187	280	3	]	]	PUNCT
ejpam-4187	280	4	let	let	VERB
ejpam-4187	280	5	g	g	NOUN
ejpam-4187	280	6	and	and	CCONJ
ejpam-4187	280	7	h	h	NOUN
ejpam-4187	280	8	be	be	VERB
ejpam-4187	280	9	any	any	DET
ejpam-4187	280	10	graphs	graph	NOUN
ejpam-4187	280	11	,	,	PUNCT
ejpam-4187	280	12	and	and	CCONJ
ejpam-4187	280	13	s	s	VERB
ejpam-4187	280	14	⊆	⊆	NUM
ejpam-4187	280	15	v	v	NOUN
ejpam-4187	280	16	(	(	PUNCT
ejpam-4187	280	17	g+h	g+h	PROPN
ejpam-4187	280	18	)	)	PUNCT
ejpam-4187	280	19	.	.	PUNCT
ejpam-4187	281	1	then	then	ADV
ejpam-4187	281	2	s	s	VERB
ejpam-4187	281	3	is	be	AUX
ejpam-4187	281	4	a	a	DET
ejpam-4187	281	5	disjunctive	disjunctive	ADJ
ejpam-4187	281	6	dominating	dominating	NOUN
ejpam-4187	281	7	set	set	NOUN
ejpam-4187	281	8	of	of	ADP
ejpam-4187	281	9	g+h	g+h	PROPN
ejpam-4187	281	10	if	if	SCONJ
ejpam-4187	281	11	and	and	CCONJ
ejpam-4187	281	12	only	only	ADV
ejpam-4187	281	13	if	if	SCONJ
ejpam-4187	281	14	one	one	NUM
ejpam-4187	281	15	of	of	ADP
ejpam-4187	281	16	the	the	DET
ejpam-4187	281	17	following	follow	VERB
ejpam-4187	281	18	holds	hold	NOUN
ejpam-4187	281	19	:	:	PUNCT
ejpam-4187	281	20	r.	r.	NOUN
ejpam-4187	281	21	malalay	malalay	PROPN
ejpam-4187	281	22	,	,	PUNCT
ejpam-4187	281	23	f.	f.	PROPN
ejpam-4187	281	24	jamil	jamil	PROPN
ejpam-4187	281	25	/	/	SYM
ejpam-4187	281	26	eur	eur	PROPN
ejpam-4187	281	27	.	.	PUNCT
ejpam-4187	282	1	j.	j.	PROPN
ejpam-4187	282	2	pure	pure	PROPN
ejpam-4187	282	3	appl	appl	PROPN
ejpam-4187	282	4	.	.	PROPN
ejpam-4187	282	5	math	math	PROPN
ejpam-4187	282	6	,	,	PUNCT
ejpam-4187	282	7	15	15	NUM
ejpam-4187	282	8	(	(	PUNCT
ejpam-4187	282	9	1	1	NUM
ejpam-4187	282	10	)	)	PUNCT
ejpam-4187	282	11	(	(	PUNCT
ejpam-4187	282	12	2022	2022	NUM
ejpam-4187	282	13	)	)	PUNCT
ejpam-4187	282	14	,	,	PUNCT
ejpam-4187	282	15	207	207	NUM
ejpam-4187	282	16	-	-	SYM
ejpam-4187	282	17	223	223	NUM
ejpam-4187	282	18	214	214	NUM
ejpam-4187	282	19	(	(	PUNCT
ejpam-4187	282	20	i	i	NOUN
ejpam-4187	282	21	)	)	PUNCT
ejpam-4187	282	22	s	s	VERB
ejpam-4187	282	23	⊆	⊆	NUM
ejpam-4187	282	24	v	v	NOUN
ejpam-4187	282	25	(	(	PUNCT
ejpam-4187	282	26	g	g	NOUN
ejpam-4187	282	27	)	)	PUNCT
ejpam-4187	282	28	for	for	ADP
ejpam-4187	282	29	which	which	PRON
ejpam-4187	282	30	either	either	CCONJ
ejpam-4187	282	31	|s|	|s|	PROPN
ejpam-4187	282	32	≥	≥	PROPN
ejpam-4187	282	33	2	2	NUM
ejpam-4187	282	34	or	or	CCONJ
ejpam-4187	282	35	s	s	NOUN
ejpam-4187	282	36	=	=	PUNCT
ejpam-4187	282	37	{	{	PUNCT
ejpam-4187	282	38	x	x	NOUN
ejpam-4187	282	39	}	}	PUNCT
ejpam-4187	282	40	where	where	SCONJ
ejpam-4187	282	41	ng[x	ng[x	PROPN
ejpam-4187	282	42	]	]	X
ejpam-4187	282	43	=	=	SYM
ejpam-4187	282	44	v	v	X
ejpam-4187	282	45	(	(	PUNCT
ejpam-4187	282	46	g	g	NOUN
ejpam-4187	282	47	)	)	PUNCT
ejpam-4187	282	48	.	.	PUNCT
ejpam-4187	283	1	(	(	PUNCT
ejpam-4187	283	2	ii	ii	NOUN
ejpam-4187	283	3	)	)	PUNCT
ejpam-4187	283	4	s	s	PART
ejpam-4187	283	5	⊆	⊆	NUM
ejpam-4187	283	6	v	v	NOUN
ejpam-4187	283	7	(	(	PUNCT
ejpam-4187	283	8	h	h	NOUN
ejpam-4187	283	9	)	)	PUNCT
ejpam-4187	283	10	for	for	ADP
ejpam-4187	283	11	which	which	PRON
ejpam-4187	283	12	either	either	CCONJ
ejpam-4187	283	13	|s|	|s|	PROPN
ejpam-4187	283	14	≥	≥	PROPN
ejpam-4187	283	15	2	2	NUM
ejpam-4187	283	16	or	or	CCONJ
ejpam-4187	283	17	s	s	NOUN
ejpam-4187	283	18	=	=	PUNCT
ejpam-4187	283	19	{	{	PUNCT
ejpam-4187	283	20	x	x	NOUN
ejpam-4187	283	21	}	}	PUNCT
ejpam-4187	283	22	where	where	SCONJ
ejpam-4187	283	23	nh	nh	PROPN
ejpam-4187	283	24	[	[	X
ejpam-4187	283	25	x	x	X
ejpam-4187	283	26	]	]	X
ejpam-4187	283	27	=	=	SYM
ejpam-4187	283	28	v	v	X
ejpam-4187	283	29	(	(	PUNCT
ejpam-4187	283	30	h	h	NOUN
ejpam-4187	283	31	)	)	PUNCT
ejpam-4187	283	32	.	.	PUNCT
ejpam-4187	284	1	(	(	PUNCT
ejpam-4187	284	2	iii	iii	X
ejpam-4187	284	3	)	)	PUNCT
ejpam-4187	284	4	s	s	PART
ejpam-4187	284	5	∩	∩	ADJ
ejpam-4187	284	6	v	v	ADJ
ejpam-4187	284	7	(	(	PUNCT
ejpam-4187	284	8	g	g	NOUN
ejpam-4187	284	9	)	)	PUNCT
ejpam-4187	284	10	̸=	̸=	PROPN
ejpam-4187	284	11	∅	∅	NOUN
ejpam-4187	284	12	and	and	CCONJ
ejpam-4187	284	13	s	s	VERB
ejpam-4187	284	14	∩	∩	ADJ
ejpam-4187	284	15	v	v	ADJ
ejpam-4187	284	16	(	(	PUNCT
ejpam-4187	284	17	h	h	NOUN
ejpam-4187	284	18	)	)	PUNCT
ejpam-4187	284	19	̸=	̸=	PROPN
ejpam-4187	284	20	∅.	∅.	VERB
ejpam-4187	284	21	for	for	ADP
ejpam-4187	284	22	any	any	DET
ejpam-4187	284	23	nontrivial	nontrivial	ADJ
ejpam-4187	284	24	graphs	graph	NOUN
ejpam-4187	284	25	g	g	NOUN
ejpam-4187	284	26	and	and	CCONJ
ejpam-4187	284	27	h	h	NOUN
ejpam-4187	284	28	,	,	PUNCT
ejpam-4187	284	29	if	if	SCONJ
ejpam-4187	284	30	s	s	VERB
ejpam-4187	284	31	⊆	⊆	NUM
ejpam-4187	284	32	v	v	NOUN
ejpam-4187	284	33	(	(	PUNCT
ejpam-4187	284	34	g+h	g+h	NOUN
ejpam-4187	284	35	)	)	PUNCT
ejpam-4187	284	36	intersects	intersect	NOUN
ejpam-4187	284	37	both	both	PRON
ejpam-4187	284	38	v	v	NOUN
ejpam-4187	284	39	(	(	PUNCT
ejpam-4187	284	40	g	g	NOUN
ejpam-4187	284	41	)	)	PUNCT
ejpam-4187	284	42	and	and	CCONJ
ejpam-4187	284	43	v	v	NOUN
ejpam-4187	284	44	(	(	PUNCT
ejpam-4187	284	45	h	h	NOUN
ejpam-4187	284	46	)	)	PUNCT
ejpam-4187	284	47	,	,	PUNCT
ejpam-4187	284	48	then	then	ADV
ejpam-4187	284	49	s	s	VERB
ejpam-4187	284	50	is	be	AUX
ejpam-4187	284	51	a	a	DET
ejpam-4187	284	52	(	(	PUNCT
ejpam-4187	284	53	restrained	restrained	ADJ
ejpam-4187	284	54	)	)	PUNCT
ejpam-4187	284	55	dominating	dominating	NOUN
ejpam-4187	284	56	set	set	NOUN
ejpam-4187	284	57	,	,	PUNCT
ejpam-4187	284	58	hence	hence	ADV
ejpam-4187	284	59	is	be	AUX
ejpam-4187	284	60	a	a	DET
ejpam-4187	284	61	(	(	PUNCT
ejpam-4187	284	62	restrained	restrained	ADJ
ejpam-4187	284	63	)	)	PUNCT
ejpam-4187	284	64	disjunctive	disjunctive	ADJ
ejpam-4187	284	65	dominating	dominating	NOUN
ejpam-4187	284	66	set	set	NOUN
ejpam-4187	284	67	of	of	ADP
ejpam-4187	284	68	g+h	g+h	PROPN
ejpam-4187	284	69	.	.	PUNCT
ejpam-4187	285	1	for	for	ADP
ejpam-4187	285	2	any	any	DET
ejpam-4187	285	3	graph	graph	NOUN
ejpam-4187	285	4	g	g	NOUN
ejpam-4187	285	5	,	,	PUNCT
ejpam-4187	285	6	γdr	γdr	PROPN
ejpam-4187	285	7	(	(	PUNCT
ejpam-4187	285	8	g+k1	g+k1	NOUN
ejpam-4187	285	9	)	)	PUNCT
ejpam-4187	285	10	=	=	PUNCT
ejpam-4187	285	11			NOUN
ejpam-4187	285	12	1	1	NUM
ejpam-4187	285	13	,	,	PUNCT
ejpam-4187	285	14	if	if	SCONJ
ejpam-4187	285	15	g	g	PROPN
ejpam-4187	285	16	=	=	SYM
ejpam-4187	285	17	k2	k2	PROPN
ejpam-4187	285	18	or	or	CCONJ
ejpam-4187	285	19	|v	|v	PROPN
ejpam-4187	285	20	(	(	PUNCT
ejpam-4187	285	21	g)|	g)|	X
ejpam-4187	285	22	≥	≥	NUM
ejpam-4187	285	23	3	3	NUM
ejpam-4187	285	24	2	2	NUM
ejpam-4187	285	25	,	,	PUNCT
ejpam-4187	285	26	if	if	SCONJ
ejpam-4187	285	27	g	g	NOUN
ejpam-4187	285	28	=	=	SYM
ejpam-4187	285	29	k1	k1	PROPN
ejpam-4187	285	30	3	3	NUM
ejpam-4187	285	31	,	,	PUNCT
ejpam-4187	285	32	if	if	SCONJ
ejpam-4187	285	33	g	g	PROPN
ejpam-4187	285	34	=	=	SYM
ejpam-4187	285	35	k2	k2	PROPN
ejpam-4187	285	36	.	.	PUNCT
ejpam-4187	286	1	theorem	theorem	VERB
ejpam-4187	286	2	4	4	NUM
ejpam-4187	286	3	.	.	PUNCT
ejpam-4187	287	1	let	let	VERB
ejpam-4187	287	2	g	g	NOUN
ejpam-4187	287	3	and	and	CCONJ
ejpam-4187	287	4	h	h	NOUN
ejpam-4187	287	5	be	be	AUX
ejpam-4187	287	6	nontrivial	nontrivial	ADJ
ejpam-4187	287	7	connected	connected	ADJ
ejpam-4187	287	8	graphs	graph	NOUN
ejpam-4187	287	9	.	.	PUNCT
ejpam-4187	288	1	then	then	ADV
ejpam-4187	288	2	s	s	VERB
ejpam-4187	288	3	⊆	⊆	NUM
ejpam-4187	288	4	v	v	NOUN
ejpam-4187	288	5	(	(	PUNCT
ejpam-4187	288	6	g	g	PROPN
ejpam-4187	288	7	+	+	NOUN
ejpam-4187	288	8	h	h	NOUN
ejpam-4187	288	9	)	)	PUNCT
ejpam-4187	288	10	is	be	AUX
ejpam-4187	288	11	a	a	DET
ejpam-4187	288	12	restrained	restrained	ADJ
ejpam-4187	288	13	disjunctive	disjunctive	ADJ
ejpam-4187	288	14	dominating	dominating	NOUN
ejpam-4187	288	15	set	set	NOUN
ejpam-4187	288	16	of	of	ADP
ejpam-4187	288	17	g+h	g+h	PROPN
ejpam-4187	289	1	if	if	SCONJ
ejpam-4187	289	2	and	and	CCONJ
ejpam-4187	289	3	only	only	ADV
ejpam-4187	289	4	if	if	SCONJ
ejpam-4187	289	5	one	one	NUM
ejpam-4187	289	6	of	of	ADP
ejpam-4187	289	7	the	the	DET
ejpam-4187	289	8	following	follow	VERB
ejpam-4187	289	9	holds	hold	NOUN
ejpam-4187	289	10	;	;	PUNCT
ejpam-4187	289	11	(	(	PUNCT
ejpam-4187	289	12	i	i	NOUN
ejpam-4187	289	13	)	)	PUNCT
ejpam-4187	289	14	s	s	VERB
ejpam-4187	289	15	⊆	⊆	NUM
ejpam-4187	289	16	v	v	NOUN
ejpam-4187	289	17	(	(	PUNCT
ejpam-4187	289	18	g	g	NOUN
ejpam-4187	289	19	)	)	PUNCT
ejpam-4187	289	20	and	and	CCONJ
ejpam-4187	289	21	either	either	CCONJ
ejpam-4187	289	22	|s|	|s|	PROPN
ejpam-4187	289	23	≥	≥	PROPN
ejpam-4187	289	24	2	2	NUM
ejpam-4187	289	25	or	or	CCONJ
ejpam-4187	289	26	s	s	NOUN
ejpam-4187	289	27	=	=	PUNCT
ejpam-4187	289	28	{	{	PUNCT
ejpam-4187	289	29	x	x	NOUN
ejpam-4187	289	30	}	}	PUNCT
ejpam-4187	289	31	where	where	SCONJ
ejpam-4187	289	32	ng[x	ng[x	PROPN
ejpam-4187	289	33	]	]	X
ejpam-4187	289	34	=	=	SYM
ejpam-4187	289	35	v	v	X
ejpam-4187	289	36	(	(	PUNCT
ejpam-4187	289	37	g	g	NOUN
ejpam-4187	289	38	)	)	PUNCT
ejpam-4187	289	39	;	;	PUNCT
ejpam-4187	289	40	(	(	PUNCT
ejpam-4187	289	41	ii	ii	NOUN
ejpam-4187	289	42	)	)	PUNCT
ejpam-4187	289	43	s	s	PART
ejpam-4187	289	44	⊆	⊆	NUM
ejpam-4187	289	45	v	v	NOUN
ejpam-4187	289	46	(	(	PUNCT
ejpam-4187	289	47	h	h	NOUN
ejpam-4187	289	48	)	)	PUNCT
ejpam-4187	289	49	and	and	CCONJ
ejpam-4187	289	50	either	either	CCONJ
ejpam-4187	289	51	|s|	|s|	PROPN
ejpam-4187	289	52	≥	≥	PROPN
ejpam-4187	289	53	2	2	NUM
ejpam-4187	289	54	or	or	CCONJ
ejpam-4187	289	55	s	s	NOUN
ejpam-4187	289	56	=	=	PUNCT
ejpam-4187	289	57	{	{	PUNCT
ejpam-4187	289	58	x	x	NOUN
ejpam-4187	289	59	}	}	PUNCT
ejpam-4187	289	60	where	where	SCONJ
ejpam-4187	289	61	nh	nh	PROPN
ejpam-4187	290	1	[	[	X
ejpam-4187	290	2	x	x	X
ejpam-4187	290	3	]	]	X
ejpam-4187	290	4	=	=	SYM
ejpam-4187	290	5	v	v	ADJ
ejpam-4187	290	6	(	(	PUNCT
ejpam-4187	290	7	h	h	NOUN
ejpam-4187	290	8	)	)	PUNCT
ejpam-4187	290	9	;	;	PUNCT
ejpam-4187	290	10	and	and	CCONJ
ejpam-4187	290	11	(	(	PUNCT
ejpam-4187	290	12	iii	iii	X
ejpam-4187	290	13	)	)	PUNCT
ejpam-4187	290	14	s	s	NOUN
ejpam-4187	290	15	intersects	intersect	NOUN
ejpam-4187	290	16	both	both	PRON
ejpam-4187	290	17	v	v	NOUN
ejpam-4187	290	18	(	(	PUNCT
ejpam-4187	290	19	g	g	NOUN
ejpam-4187	290	20	)	)	PUNCT
ejpam-4187	290	21	and	and	CCONJ
ejpam-4187	290	22	v	v	NOUN
ejpam-4187	290	23	(	(	PUNCT
ejpam-4187	290	24	h	h	NOUN
ejpam-4187	290	25	)	)	PUNCT
ejpam-4187	290	26	satisfying	satisfy	VERB
ejpam-4187	290	27	the	the	DET
ejpam-4187	290	28	following	following	NOUN
ejpam-4187	290	29	:	:	PUNCT
ejpam-4187	290	30	(	(	PUNCT
ejpam-4187	290	31	a	a	X
ejpam-4187	290	32	)	)	PUNCT
ejpam-4187	290	33	if	if	SCONJ
ejpam-4187	290	34	v	v	INTJ
ejpam-4187	290	35	(	(	PUNCT
ejpam-4187	290	36	g	g	NOUN
ejpam-4187	290	37	)	)	PUNCT
ejpam-4187	290	38	⊆	⊆	NUM
ejpam-4187	290	39	s	s	NOUN
ejpam-4187	290	40	,	,	PUNCT
ejpam-4187	290	41	then	then	ADV
ejpam-4187	290	42	v	v	X
ejpam-4187	290	43	(	(	PUNCT
ejpam-4187	290	44	h	h	NOUN
ejpam-4187	290	45	)	)	PUNCT
ejpam-4187	290	46	⊆	⊆	NUM
ejpam-4187	290	47	s	s	NOUN
ejpam-4187	290	48	or	or	CCONJ
ejpam-4187	290	49	⟨v	⟨v	NUM
ejpam-4187	290	50	(	(	PUNCT
ejpam-4187	290	51	h	h	NOUN
ejpam-4187	290	52	)	)	PUNCT
ejpam-4187	290	53	\	\	NOUN
ejpam-4187	290	54	s⟩	s⟩	NOUN
ejpam-4187	290	55	∼=	∼=	NOUN
ejpam-4187	290	56	k2	k2	NOUN
ejpam-4187	290	57	or	or	CCONJ
ejpam-4187	290	58	|v	|v	PROPN
ejpam-4187	290	59	(	(	PUNCT
ejpam-4187	290	60	h	h	NOUN
ejpam-4187	290	61	)	)	PUNCT
ejpam-4187	290	62	\	\	PROPN
ejpam-4187	290	63	s|	s|	VERB
ejpam-4187	290	64	≥	≥	NOUN
ejpam-4187	290	65	3	3	NUM
ejpam-4187	290	66	.	.	PUNCT
ejpam-4187	291	1	(	(	PUNCT
ejpam-4187	291	2	b	b	X
ejpam-4187	291	3	)	)	PUNCT
ejpam-4187	291	4	if	if	SCONJ
ejpam-4187	291	5	v	v	X
ejpam-4187	291	6	(	(	PUNCT
ejpam-4187	291	7	h	h	NOUN
ejpam-4187	291	8	)	)	PUNCT
ejpam-4187	291	9	⊆	⊆	NUM
ejpam-4187	291	10	s	s	NOUN
ejpam-4187	291	11	,	,	PUNCT
ejpam-4187	291	12	then	then	ADV
ejpam-4187	291	13	v	v	X
ejpam-4187	291	14	(	(	PUNCT
ejpam-4187	291	15	h	h	NOUN
ejpam-4187	291	16	)	)	PUNCT
ejpam-4187	291	17	⊆	⊆	NUM
ejpam-4187	291	18	s	s	NOUN
ejpam-4187	291	19	or	or	CCONJ
ejpam-4187	291	20	⟨v	⟨v	NUM
ejpam-4187	291	21	(	(	PUNCT
ejpam-4187	291	22	h	h	NOUN
ejpam-4187	291	23	)	)	PUNCT
ejpam-4187	291	24	\	\	NOUN
ejpam-4187	292	1	s⟩	s⟩	NOUN
ejpam-4187	292	2	∼=	∼=	NOUN
ejpam-4187	292	3	k2	k2	NOUN
ejpam-4187	292	4	or	or	CCONJ
ejpam-4187	292	5	|v	|v	PROPN
ejpam-4187	292	6	(	(	PUNCT
ejpam-4187	292	7	h	h	NOUN
ejpam-4187	292	8	)	)	PUNCT
ejpam-4187	292	9	\	\	PROPN
ejpam-4187	292	10	s|	s|	VERB
ejpam-4187	292	11	≥	≥	NOUN
ejpam-4187	292	12	3	3	NUM
ejpam-4187	292	13	.	.	PUNCT
ejpam-4187	293	1	proof	proof	NOUN
ejpam-4187	293	2	.	.	PUNCT
ejpam-4187	294	1	let	let	VERB
ejpam-4187	294	2	s	s	PRON
ejpam-4187	294	3	⊆	⊆	NUM
ejpam-4187	294	4	v	v	NOUN
ejpam-4187	294	5	(	(	PUNCT
ejpam-4187	294	6	g+h	g+h	NOUN
ejpam-4187	294	7	)	)	PUNCT
ejpam-4187	294	8	be	be	AUX
ejpam-4187	294	9	a	a	DET
ejpam-4187	294	10	restrained	restrained	ADJ
ejpam-4187	294	11	disjunctive	disjunctive	ADJ
ejpam-4187	294	12	dominating	dominating	NOUN
ejpam-4187	294	13	set	set	NOUN
ejpam-4187	294	14	of	of	ADP
ejpam-4187	294	15	g+h	g+h	PROPN
ejpam-4187	294	16	.	.	PUNCT
ejpam-4187	295	1	then	then	ADV
ejpam-4187	295	2	s	s	VERB
ejpam-4187	295	3	is	be	AUX
ejpam-4187	295	4	a	a	DET
ejpam-4187	295	5	disjunctive	disjunctive	ADJ
ejpam-4187	295	6	dominating	dominating	NOUN
ejpam-4187	295	7	set	set	NOUN
ejpam-4187	295	8	of	of	ADP
ejpam-4187	295	9	g	g	PROPN
ejpam-4187	295	10	+	+	CCONJ
ejpam-4187	295	11	h.	h.	PROPN
ejpam-4187	295	12	by	by	ADP
ejpam-4187	295	13	theorem	theorem	NOUN
ejpam-4187	295	14	3	3	NUM
ejpam-4187	295	15	,	,	PUNCT
ejpam-4187	295	16	if	if	SCONJ
ejpam-4187	295	17	s	s	VERB
ejpam-4187	295	18	⊆	⊆	NUM
ejpam-4187	295	19	v	v	NOUN
ejpam-4187	295	20	(	(	PUNCT
ejpam-4187	295	21	g	g	NOUN
ejpam-4187	295	22	)	)	PUNCT
ejpam-4187	295	23	,	,	PUNCT
ejpam-4187	295	24	then	then	ADV
ejpam-4187	295	25	either	either	CCONJ
ejpam-4187	295	26	|s|	|s|	PROPN
ejpam-4187	295	27	≥	≥	PROPN
ejpam-4187	295	28	2	2	NUM
ejpam-4187	295	29	or	or	CCONJ
ejpam-4187	295	30	s	s	NOUN
ejpam-4187	295	31	=	=	PUNCT
ejpam-4187	295	32	{	{	PUNCT
ejpam-4187	295	33	x	x	NOUN
ejpam-4187	295	34	}	}	PUNCT
ejpam-4187	295	35	where	where	SCONJ
ejpam-4187	295	36	ng[x	ng[x	PROPN
ejpam-4187	295	37	]	]	X
ejpam-4187	295	38	=	=	SYM
ejpam-4187	295	39	v	v	X
ejpam-4187	295	40	(	(	PUNCT
ejpam-4187	295	41	g	g	NOUN
ejpam-4187	295	42	)	)	PUNCT
ejpam-4187	295	43	.	.	PUNCT
ejpam-4187	296	1	similarly	similarly	ADV
ejpam-4187	296	2	,	,	PUNCT
ejpam-4187	296	3	if	if	SCONJ
ejpam-4187	296	4	s	s	VERB
ejpam-4187	296	5	⊆	⊆	NUM
ejpam-4187	296	6	v	v	NOUN
ejpam-4187	296	7	(	(	PUNCT
ejpam-4187	296	8	h	h	NOUN
ejpam-4187	296	9	)	)	PUNCT
ejpam-4187	296	10	,	,	PUNCT
ejpam-4187	296	11	then	then	ADV
ejpam-4187	296	12	either	either	CCONJ
ejpam-4187	296	13	|s|	|s|	PROPN
ejpam-4187	296	14	≥	≥	PROPN
ejpam-4187	296	15	2	2	NUM
ejpam-4187	296	16	or	or	CCONJ
ejpam-4187	296	17	s	s	NOUN
ejpam-4187	296	18	=	=	PUNCT
ejpam-4187	296	19	{	{	PUNCT
ejpam-4187	296	20	x	x	NOUN
ejpam-4187	296	21	}	}	PUNCT
ejpam-4187	296	22	where	where	SCONJ
ejpam-4187	296	23	nh	nh	PROPN
ejpam-4187	297	1	[	[	X
ejpam-4187	297	2	x	x	X
ejpam-4187	297	3	]	]	X
ejpam-4187	297	4	=	=	SYM
ejpam-4187	297	5	v	v	X
ejpam-4187	297	6	(	(	PUNCT
ejpam-4187	297	7	h	h	NOUN
ejpam-4187	297	8	)	)	PUNCT
ejpam-4187	297	9	.	.	PUNCT
ejpam-4187	298	1	now	now	ADV
ejpam-4187	298	2	suppose	suppose	VERB
ejpam-4187	298	3	that	that	SCONJ
ejpam-4187	298	4	s	s	VERB
ejpam-4187	298	5	intersects	intersect	NOUN
ejpam-4187	298	6	both	both	PRON
ejpam-4187	298	7	v	v	NOUN
ejpam-4187	298	8	(	(	PUNCT
ejpam-4187	298	9	g	g	NOUN
ejpam-4187	298	10	)	)	PUNCT
ejpam-4187	298	11	and	and	CCONJ
ejpam-4187	298	12	v	v	NOUN
ejpam-4187	298	13	(	(	PUNCT
ejpam-4187	298	14	h	h	NOUN
ejpam-4187	298	15	)	)	PUNCT
ejpam-4187	298	16	.	.	PUNCT
ejpam-4187	299	1	suppose	suppose	VERB
ejpam-4187	299	2	further	far	ADV
ejpam-4187	299	3	that	that	PRON
ejpam-4187	299	4	v	v	INTJ
ejpam-4187	299	5	(	(	PUNCT
ejpam-4187	299	6	g	g	NOUN
ejpam-4187	299	7	)	)	PUNCT
ejpam-4187	299	8	⊆	⊆	NUM
ejpam-4187	299	9	s.	s.	PROPN
ejpam-4187	299	10	let	let	VERB
ejpam-4187	299	11	v	v	ADP
ejpam-4187	299	12	∈	∈	PROPN
ejpam-4187	299	13	v	v	NOUN
ejpam-4187	299	14	(	(	PUNCT
ejpam-4187	299	15	h	h	NOUN
ejpam-4187	299	16	)	)	PUNCT
ejpam-4187	299	17	\	\	NOUN
ejpam-4187	300	1	s.	s.	PROPN
ejpam-4187	300	2	since	since	SCONJ
ejpam-4187	300	3	s	s	PROPN
ejpam-4187	300	4	is	be	AUX
ejpam-4187	300	5	a	a	DET
ejpam-4187	300	6	restrained	restrained	ADJ
ejpam-4187	300	7	disjunctive	disjunctive	ADJ
ejpam-4187	300	8	dominating	dominating	NOUN
ejpam-4187	300	9	set	set	NOUN
ejpam-4187	300	10	,	,	PUNCT
ejpam-4187	300	11	there	there	PRON
ejpam-4187	300	12	exists	exist	VERB
ejpam-4187	300	13	u	u	PROPN
ejpam-4187	300	14	∈	∈	PROPN
ejpam-4187	300	15	v	v	NOUN
ejpam-4187	300	16	(	(	PUNCT
ejpam-4187	300	17	h)\s	h)\s	NOUN
ejpam-4187	300	18	such	such	ADJ
ejpam-4187	300	19	that	that	SCONJ
ejpam-4187	300	20	uv	uv	PROPN
ejpam-4187	300	21	∈	∈	NOUN
ejpam-4187	300	22	e(g+h	e(g+h	NUM
ejpam-4187	300	23	)	)	PUNCT
ejpam-4187	300	24	or	or	CCONJ
ejpam-4187	300	25	there	there	PRON
ejpam-4187	300	26	exist	exist	VERB
ejpam-4187	300	27	distinct	distinct	ADJ
ejpam-4187	300	28	u	u	NOUN
ejpam-4187	300	29	,	,	PUNCT
ejpam-4187	300	30	w	w	PROPN
ejpam-4187	300	31	∈	∈	PROPN
ejpam-4187	300	32	v	v	ADP
ejpam-4187	300	33	(	(	PUNCT
ejpam-4187	300	34	h	h	NOUN
ejpam-4187	300	35	)	)	PUNCT
ejpam-4187	300	36	\	\	PUNCT
ejpam-4187	301	1	s	s	VERB
ejpam-4187	301	2	such	such	ADJ
ejpam-4187	301	3	that	that	SCONJ
ejpam-4187	301	4	dg+h(u	dg+h(u	PROPN
ejpam-4187	301	5	,	,	PUNCT
ejpam-4187	301	6	v	v	NOUN
ejpam-4187	301	7	)	)	PUNCT
ejpam-4187	301	8	=	=	SYM
ejpam-4187	301	9	2	2	NUM
ejpam-4187	301	10	=	=	SYM
ejpam-4187	301	11	dg+h(w	dg+h(w	PROPN
ejpam-4187	301	12	,	,	PUNCT
ejpam-4187	301	13	v	v	NOUN
ejpam-4187	301	14	)	)	PUNCT
ejpam-4187	301	15	.	.	PUNCT
ejpam-4187	302	1	if	if	SCONJ
ejpam-4187	302	2	the	the	DET
ejpam-4187	302	3	former	former	ADJ
ejpam-4187	302	4	holds	hold	VERB
ejpam-4187	302	5	,	,	PUNCT
ejpam-4187	302	6	then	then	ADV
ejpam-4187	302	7	v	v	X
ejpam-4187	302	8	(	(	PUNCT
ejpam-4187	302	9	h	h	NOUN
ejpam-4187	302	10	)	)	PUNCT
ejpam-4187	302	11	⊆	⊆	NUM
ejpam-4187	302	12	s	s	NOUN
ejpam-4187	302	13	or	or	CCONJ
ejpam-4187	302	14	⟨v	⟨v	NUM
ejpam-4187	302	15	(	(	PUNCT
ejpam-4187	302	16	h	h	NOUN
ejpam-4187	302	17	)	)	PUNCT
ejpam-4187	302	18	\	\	NOUN
ejpam-4187	302	19	s⟩	s⟩	NOUN
ejpam-4187	303	1	∼=	∼=	PROPN
ejpam-4187	303	2	k2	k2	NOUN
ejpam-4187	303	3	.	.	PUNCT
ejpam-4187	304	1	if	if	SCONJ
ejpam-4187	304	2	the	the	DET
ejpam-4187	304	3	latter	latter	ADJ
ejpam-4187	304	4	holds	hold	VERB
ejpam-4187	304	5	,	,	PUNCT
ejpam-4187	304	6	then	then	ADV
ejpam-4187	304	7	|v	|v	PROPN
ejpam-4187	304	8	(	(	PUNCT
ejpam-4187	304	9	h	h	NOUN
ejpam-4187	304	10	)	)	PUNCT
ejpam-4187	304	11	\	\	PROPN
ejpam-4187	304	12	s|	s|	VERB
ejpam-4187	304	13	≥	≥	NOUN
ejpam-4187	304	14	3	3	NUM
ejpam-4187	304	15	.	.	PUNCT
ejpam-4187	304	16	similarly	similarly	ADV
ejpam-4187	304	17	,	,	PUNCT
ejpam-4187	304	18	if	if	SCONJ
ejpam-4187	304	19	v	v	X
ejpam-4187	304	20	(	(	PUNCT
ejpam-4187	304	21	h	h	NOUN
ejpam-4187	304	22	)	)	PUNCT
ejpam-4187	304	23	⊆	⊆	NUM
ejpam-4187	304	24	s	s	NOUN
ejpam-4187	304	25	,	,	PUNCT
ejpam-4187	304	26	then	then	ADV
ejpam-4187	304	27	(	(	PUNCT
ejpam-4187	304	28	b	b	X
ejpam-4187	304	29	)	)	PUNCT
ejpam-4187	304	30	holds	hold	VERB
ejpam-4187	304	31	.	.	PUNCT
ejpam-4187	305	1	conversely	conversely	ADV
ejpam-4187	305	2	,	,	PUNCT
ejpam-4187	305	3	suppose	suppose	VERB
ejpam-4187	305	4	that	that	SCONJ
ejpam-4187	305	5	(	(	PUNCT
ejpam-4187	305	6	i	i	NOUN
ejpam-4187	305	7	)	)	PUNCT
ejpam-4187	305	8	holds	hold	VERB
ejpam-4187	305	9	for	for	ADP
ejpam-4187	305	10	s.	s.	PROPN
ejpam-4187	305	11	by	by	ADP
ejpam-4187	305	12	theorem	theorem	NOUN
ejpam-4187	305	13	3	3	NUM
ejpam-4187	305	14	,	,	PUNCT
ejpam-4187	305	15	s	s	VERB
ejpam-4187	305	16	is	be	AUX
ejpam-4187	305	17	a	a	DET
ejpam-4187	305	18	disjunctive	disjunctive	ADJ
ejpam-4187	305	19	dominating	dominating	NOUN
ejpam-4187	305	20	set	set	NOUN
ejpam-4187	305	21	of	of	ADP
ejpam-4187	305	22	g+h	g+h	PROPN
ejpam-4187	305	23	.	.	PUNCT
ejpam-4187	306	1	let	let	VERB
ejpam-4187	306	2	v	v	NUM
ejpam-4187	306	3	∈	∈	PROPN
ejpam-4187	306	4	v	v	NOUN
ejpam-4187	306	5	(	(	PUNCT
ejpam-4187	306	6	g+h	g+h	NOUN
ejpam-4187	306	7	)	)	PUNCT
ejpam-4187	306	8	\s	\s	NOUN
ejpam-4187	306	9	.	.	PUNCT
ejpam-4187	307	1	if	if	SCONJ
ejpam-4187	307	2	v	v	NUM
ejpam-4187	307	3	∈	∈	PROPN
ejpam-4187	307	4	v	v	NOUN
ejpam-4187	307	5	(	(	PUNCT
ejpam-4187	307	6	g	g	NOUN
ejpam-4187	307	7	)	)	PUNCT
ejpam-4187	307	8	,	,	PUNCT
ejpam-4187	307	9	then	then	ADV
ejpam-4187	307	10	uv	uv	NOUN
ejpam-4187	307	11	∈	∈	PROPN
ejpam-4187	307	12	e(g+h	e(g+h	NUM
ejpam-4187	307	13	)	)	PUNCT
ejpam-4187	307	14	for	for	ADP
ejpam-4187	307	15	any	any	DET
ejpam-4187	307	16	u	u	PROPN
ejpam-4187	307	17	∈	∈	PROPN
ejpam-4187	307	18	v	v	NOUN
ejpam-4187	307	19	(	(	PUNCT
ejpam-4187	307	20	h	h	NOUN
ejpam-4187	307	21	)	)	PUNCT
ejpam-4187	307	22	.	.	PUNCT
ejpam-4187	308	1	if	if	SCONJ
ejpam-4187	308	2	v	v	NUM
ejpam-4187	308	3	∈	∈	PROPN
ejpam-4187	308	4	v	v	NOUN
ejpam-4187	308	5	(	(	PUNCT
ejpam-4187	308	6	h	h	NOUN
ejpam-4187	308	7	)	)	PUNCT
ejpam-4187	308	8	,	,	PUNCT
ejpam-4187	308	9	then	then	ADV
ejpam-4187	308	10	pick	pick	VERB
ejpam-4187	308	11	any	any	DET
ejpam-4187	308	12	u	u	PROPN
ejpam-4187	308	13	∈	∈	PROPN
ejpam-4187	308	14	v	v	ADP
ejpam-4187	308	15	(	(	PUNCT
ejpam-4187	308	16	h	h	NOUN
ejpam-4187	308	17	)	)	PUNCT
ejpam-4187	308	18	for	for	ADP
ejpam-4187	308	19	which	which	PRON
ejpam-4187	308	20	uv	uv	NOUN
ejpam-4187	308	21	∈	∈	PROPN
ejpam-4187	308	22	e(h	e(h	PROPN
ejpam-4187	308	23	)	)	PUNCT
ejpam-4187	308	24	.	.	PUNCT
ejpam-4187	309	1	accordingly	accordingly	ADV
ejpam-4187	309	2	,	,	PUNCT
ejpam-4187	309	3	s	s	VERB
ejpam-4187	309	4	is	be	AUX
ejpam-4187	309	5	a	a	DET
ejpam-4187	309	6	restrained	restrained	ADJ
ejpam-4187	309	7	disjunctive	disjunctive	ADJ
ejpam-4187	309	8	dominating	dominating	NOUN
ejpam-4187	309	9	set	set	NOUN
ejpam-4187	309	10	of	of	ADP
ejpam-4187	309	11	g+h	g+h	PROPN
ejpam-4187	309	12	.	.	PUNCT
ejpam-4187	310	1	similarly	similarly	ADV
ejpam-4187	310	2	,	,	PUNCT
ejpam-4187	310	3	if	if	SCONJ
ejpam-4187	310	4	(	(	PUNCT
ejpam-4187	310	5	ii	ii	NOUN
ejpam-4187	310	6	)	)	PUNCT
ejpam-4187	310	7	holds	hold	VERB
ejpam-4187	310	8	for	for	ADP
ejpam-4187	310	9	s	s	PROPN
ejpam-4187	310	10	,	,	PUNCT
ejpam-4187	310	11	then	then	ADV
ejpam-4187	310	12	s	s	VERB
ejpam-4187	310	13	is	be	AUX
ejpam-4187	310	14	a	a	DET
ejpam-4187	310	15	restrained	restrained	ADJ
ejpam-4187	310	16	disjunctive	disjunctive	ADJ
ejpam-4187	310	17	dominating	dominating	NOUN
ejpam-4187	310	18	set	set	NOUN
ejpam-4187	310	19	of	of	ADP
ejpam-4187	310	20	g	g	PROPN
ejpam-4187	310	21	+	+	CCONJ
ejpam-4187	310	22	h.	h.	PROPN
ejpam-4187	310	23	suppose	suppose	VERB
ejpam-4187	310	24	that	that	SCONJ
ejpam-4187	310	25	(	(	PUNCT
ejpam-4187	310	26	iii	iii	NOUN
ejpam-4187	310	27	)	)	PUNCT
ejpam-4187	310	28	holds	hold	VERB
ejpam-4187	310	29	for	for	ADP
ejpam-4187	310	30	s.	s.	PROPN
ejpam-4187	310	31	by	by	ADP
ejpam-4187	310	32	theorem	theorem	NOUN
ejpam-4187	310	33	3	3	NUM
ejpam-4187	310	34	,	,	PUNCT
ejpam-4187	310	35	s	s	VERB
ejpam-4187	310	36	is	be	AUX
ejpam-4187	310	37	a	a	DET
ejpam-4187	310	38	disjunctive	disjunctive	ADJ
ejpam-4187	310	39	dominating	dominating	NOUN
ejpam-4187	310	40	set	set	NOUN
ejpam-4187	310	41	of	of	ADP
ejpam-4187	310	42	g	g	PROPN
ejpam-4187	310	43	+	+	CCONJ
ejpam-4187	310	44	h.	h.	NOUN
ejpam-4187	311	1	if	if	SCONJ
ejpam-4187	311	2	v	v	INTJ
ejpam-4187	311	3	(	(	PUNCT
ejpam-4187	311	4	g	g	NOUN
ejpam-4187	311	5	)	)	PUNCT
ejpam-4187	311	6	\	\	PUNCT
ejpam-4187	312	1	s	s	PART
ejpam-4187	312	2	̸=	̸=	PROPN
ejpam-4187	312	3	∅	∅	NOUN
ejpam-4187	312	4	and	and	CCONJ
ejpam-4187	312	5	v	v	NOUN
ejpam-4187	312	6	(	(	PUNCT
ejpam-4187	312	7	h	h	NOUN
ejpam-4187	312	8	)	)	PUNCT
ejpam-4187	312	9	\	\	PUNCT
ejpam-4187	313	1	s	s	PART
ejpam-4187	313	2	̸=	̸=	PROPN
ejpam-4187	313	3	∅	∅	NOUN
ejpam-4187	313	4	,	,	PUNCT
ejpam-4187	313	5	then	then	ADV
ejpam-4187	313	6	the	the	DET
ejpam-4187	313	7	conclusion	conclusion	NOUN
ejpam-4187	313	8	follows	follow	VERB
ejpam-4187	313	9	because	because	SCONJ
ejpam-4187	313	10	xy	xy	PROPN
ejpam-4187	313	11	∈	∈	PROPN
ejpam-4187	313	12	e(g	e(g	PROPN
ejpam-4187	314	1	+	+	CCONJ
ejpam-4187	314	2	h	h	NOUN
ejpam-4187	314	3	)	)	PUNCT
ejpam-4187	314	4	for	for	ADP
ejpam-4187	314	5	all	all	PRON
ejpam-4187	314	6	x	x	SYM
ejpam-4187	314	7	∈	∈	PROPN
ejpam-4187	314	8	v	v	NOUN
ejpam-4187	314	9	(	(	PUNCT
ejpam-4187	314	10	g	g	NOUN
ejpam-4187	314	11	)	)	PUNCT
ejpam-4187	314	12	and	and	CCONJ
ejpam-4187	314	13	for	for	ADP
ejpam-4187	314	14	all	all	PRON
ejpam-4187	314	15	y	y	PROPN
ejpam-4187	314	16	∈	∈	PROPN
ejpam-4187	314	17	v	v	ADP
ejpam-4187	314	18	(	(	PUNCT
ejpam-4187	314	19	h	h	NOUN
ejpam-4187	314	20	)	)	PUNCT
ejpam-4187	314	21	.	.	PUNCT
ejpam-4187	314	22	suppose	suppose	VERB
ejpam-4187	314	23	that	that	SCONJ
ejpam-4187	314	24	v	v	INTJ
ejpam-4187	314	25	(	(	PUNCT
ejpam-4187	314	26	g	g	NOUN
ejpam-4187	314	27	)	)	PUNCT
ejpam-4187	314	28	⊆	⊆	NUM
ejpam-4187	314	29	s	s	NOUN
ejpam-4187	314	30	,	,	PUNCT
ejpam-4187	314	31	and	and	CCONJ
ejpam-4187	314	32	let	let	VERB
ejpam-4187	314	33	v	v	NUM
ejpam-4187	314	34	∈	∈	PROPN
ejpam-4187	314	35	v	v	NOUN
ejpam-4187	314	36	(	(	PUNCT
ejpam-4187	314	37	g+h	g+h	NOUN
ejpam-4187	314	38	)	)	PUNCT
ejpam-4187	314	39	\s	\s	NOUN
ejpam-4187	314	40	.	.	PUNCT
ejpam-4187	315	1	since	since	SCONJ
ejpam-4187	315	2	v	v	NOUN
ejpam-4187	315	3	(	(	PUNCT
ejpam-4187	315	4	h	h	NOUN
ejpam-4187	315	5	)	)	PUNCT
ejpam-4187	315	6	⊆	⊆	NUM
ejpam-4187	315	7	s	s	NOUN
ejpam-4187	315	8	or	or	CCONJ
ejpam-4187	315	9	⟨v	⟨v	NUM
ejpam-4187	315	10	(	(	PUNCT
ejpam-4187	315	11	h	h	X
ejpam-4187	315	12	)	)	PUNCT
ejpam-4187	315	13	\s⟩	\s⟩	PROPN
ejpam-4187	315	14	∼=	∼=	PROPN
ejpam-4187	315	15	k2	k2	NOUN
ejpam-4187	315	16	,	,	PUNCT
ejpam-4187	315	17	v	v	NOUN
ejpam-4187	315	18	∈	∈	PROPN
ejpam-4187	315	19	v	v	NOUN
ejpam-4187	315	20	(	(	PUNCT
ejpam-4187	315	21	h	h	NOUN
ejpam-4187	315	22	)	)	PUNCT
ejpam-4187	315	23	\	\	PUNCT
ejpam-4187	315	24	s.	s.	PROPN
ejpam-4187	315	25	suppose	suppose	VERB
ejpam-4187	315	26	that	that	SCONJ
ejpam-4187	315	27	,	,	PUNCT
ejpam-4187	315	28	there	there	PRON
ejpam-4187	315	29	does	do	AUX
ejpam-4187	315	30	not	not	PART
ejpam-4187	315	31	exist	exist	VERB
ejpam-4187	315	32	u	u	PROPN
ejpam-4187	315	33	∈	∈	PROPN
ejpam-4187	315	34	v	v	ADP
ejpam-4187	315	35	(	(	PUNCT
ejpam-4187	315	36	h	h	NOUN
ejpam-4187	315	37	)	)	PUNCT
ejpam-4187	315	38	\	\	PROPN
ejpam-4187	315	39	s	s	PART
ejpam-4187	315	40	for	for	ADP
ejpam-4187	315	41	which	which	PRON
ejpam-4187	315	42	uv	uv	NOUN
ejpam-4187	315	43	∈	∈	PROPN
ejpam-4187	315	44	e(h	e(h	PROPN
ejpam-4187	315	45	)	)	PUNCT
ejpam-4187	315	46	,	,	PUNCT
ejpam-4187	315	47	r.	r.	PROPN
ejpam-4187	315	48	malalay	malalay	PROPN
ejpam-4187	315	49	,	,	PUNCT
ejpam-4187	315	50	f.	f.	PROPN
ejpam-4187	315	51	jamil	jamil	PROPN
ejpam-4187	315	52	/	/	SYM
ejpam-4187	315	53	eur	eur	PROPN
ejpam-4187	315	54	.	.	PUNCT
ejpam-4187	316	1	j.	j.	PROPN
ejpam-4187	316	2	pure	pure	PROPN
ejpam-4187	316	3	appl	appl	PROPN
ejpam-4187	316	4	.	.	PROPN
ejpam-4187	316	5	math	math	PROPN
ejpam-4187	316	6	,	,	PUNCT
ejpam-4187	316	7	15	15	NUM
ejpam-4187	316	8	(	(	PUNCT
ejpam-4187	316	9	1	1	NUM
ejpam-4187	316	10	)	)	PUNCT
ejpam-4187	316	11	(	(	PUNCT
ejpam-4187	316	12	2022	2022	NUM
ejpam-4187	316	13	)	)	PUNCT
ejpam-4187	316	14	,	,	PUNCT
ejpam-4187	316	15	207	207	NUM
ejpam-4187	316	16	-	-	SYM
ejpam-4187	316	17	223	223	NUM
ejpam-4187	316	18	215	215	NUM
ejpam-4187	316	19	then	then	ADV
ejpam-4187	316	20	|v	|v	PROPN
ejpam-4187	316	21	(	(	PUNCT
ejpam-4187	316	22	h	h	NOUN
ejpam-4187	316	23	)	)	PUNCT
ejpam-4187	316	24	\	\	PROPN
ejpam-4187	317	1	s|	s|	VERB
ejpam-4187	317	2	≥	≥	NOUN
ejpam-4187	317	3	3	3	NUM
ejpam-4187	317	4	.	.	PUNCT
ejpam-4187	318	1	in	in	ADP
ejpam-4187	318	2	particular	particular	ADJ
ejpam-4187	318	3	,	,	PUNCT
ejpam-4187	318	4	|v	|v	PROPN
ejpam-4187	318	5	(	(	PUNCT
ejpam-4187	318	6	h	h	NOUN
ejpam-4187	318	7	)	)	PUNCT
ejpam-4187	318	8	\	\	PUNCT
ejpam-4187	318	9	(	(	PUNCT
ejpam-4187	318	10	s	s	NOUN
ejpam-4187	318	11	∪	∪	X
ejpam-4187	318	12	{	{	PUNCT
ejpam-4187	318	13	v	v	NOUN
ejpam-4187	318	14	}	}	PUNCT
ejpam-4187	318	15	)	)	PUNCT
ejpam-4187	318	16	|	|	ADV
ejpam-4187	318	17	≥	≥	NOUN
ejpam-4187	318	18	2	2	NUM
ejpam-4187	318	19	,	,	PUNCT
ejpam-4187	318	20	say	say	VERB
ejpam-4187	318	21	u	u	NOUN
ejpam-4187	318	22	,	,	PUNCT
ejpam-4187	318	23	w	w	PROPN
ejpam-4187	318	24	∈	∈	PROPN
ejpam-4187	318	25	v	v	ADP
ejpam-4187	318	26	(	(	PUNCT
ejpam-4187	318	27	h	h	NOUN
ejpam-4187	318	28	)	)	PUNCT
ejpam-4187	318	29	\	\	PUNCT
ejpam-4187	319	1	(	(	PUNCT
ejpam-4187	319	2	s	s	NOUN
ejpam-4187	319	3	∪	∪	X
ejpam-4187	319	4	{	{	PUNCT
ejpam-4187	319	5	v	v	NOUN
ejpam-4187	319	6	}	}	PUNCT
ejpam-4187	319	7	)	)	PUNCT
ejpam-4187	319	8	,	,	PUNCT
ejpam-4187	319	9	with	with	ADP
ejpam-4187	319	10	u	u	NOUN
ejpam-4187	319	11	̸=	̸=	PROPN
ejpam-4187	319	12	w.	w.	PROPN
ejpam-4187	319	13	then	then	ADV
ejpam-4187	319	14	dg+k(u	dg+k(u	NUM
ejpam-4187	319	15	,	,	PUNCT
ejpam-4187	319	16	v	v	NOUN
ejpam-4187	319	17	)	)	PUNCT
ejpam-4187	319	18	=	=	SYM
ejpam-4187	319	19	2	2	NUM
ejpam-4187	319	20	=	=	SYM
ejpam-4187	319	21	dg+h(w	dg+h(w	PROPN
ejpam-4187	319	22	,	,	PUNCT
ejpam-4187	319	23	v	v	NOUN
ejpam-4187	319	24	)	)	PUNCT
ejpam-4187	319	25	.	.	PUNCT
ejpam-4187	320	1	similarly	similarly	ADV
ejpam-4187	320	2	,	,	PUNCT
ejpam-4187	320	3	if	if	SCONJ
ejpam-4187	320	4	v	v	X
ejpam-4187	320	5	(	(	PUNCT
ejpam-4187	320	6	h	h	NOUN
ejpam-4187	320	7	)	)	PUNCT
ejpam-4187	320	8	⊆	⊆	NUM
ejpam-4187	320	9	s	s	NOUN
ejpam-4187	320	10	,	,	PUNCT
ejpam-4187	320	11	then	then	ADV
ejpam-4187	320	12	for	for	ADP
ejpam-4187	320	13	each	each	DET
ejpam-4187	320	14	v	v	NUM
ejpam-4187	320	15	∈	∈	PROPN
ejpam-4187	320	16	v	v	NOUN
ejpam-4187	320	17	(	(	PUNCT
ejpam-4187	320	18	g	g	PROPN
ejpam-4187	320	19	+	+	NOUN
ejpam-4187	320	20	h	h	NOUN
ejpam-4187	320	21	)	)	PUNCT
ejpam-4187	320	22	\	\	PROPN
ejpam-4187	321	1	s	s	X
ejpam-4187	321	2	,	,	PUNCT
ejpam-4187	321	3	there	there	PRON
ejpam-4187	321	4	exists	exist	VERB
ejpam-4187	321	5	u	u	PROPN
ejpam-4187	321	6	∈	∈	PROPN
ejpam-4187	321	7	v	v	ADP
ejpam-4187	321	8	(	(	PUNCT
ejpam-4187	321	9	g	g	NOUN
ejpam-4187	321	10	)	)	PUNCT
ejpam-4187	321	11	\	\	PROPN
ejpam-4187	322	1	s	s	PART
ejpam-4187	322	2	for	for	ADP
ejpam-4187	322	3	which	which	PRON
ejpam-4187	322	4	uv	uv	NOUN
ejpam-4187	322	5	∈	∈	PROPN
ejpam-4187	322	6	e(g	e(g	NOUN
ejpam-4187	323	1	+	+	CCONJ
ejpam-4187	323	2	h	h	NOUN
ejpam-4187	323	3	)	)	PUNCT
ejpam-4187	323	4	or	or	CCONJ
ejpam-4187	323	5	there	there	PRON
ejpam-4187	323	6	exist	exist	VERB
ejpam-4187	323	7	distinct	distinct	ADJ
ejpam-4187	323	8	u	u	NOUN
ejpam-4187	323	9	,	,	PUNCT
ejpam-4187	323	10	w	w	PROPN
ejpam-4187	323	11	∈	∈	PROPN
ejpam-4187	323	12	v	v	ADP
ejpam-4187	323	13	(	(	PUNCT
ejpam-4187	323	14	g	g	NOUN
ejpam-4187	323	15	)	)	PUNCT
ejpam-4187	323	16	\	\	PUNCT
ejpam-4187	323	17	s	s	VERB
ejpam-4187	323	18	such	such	ADJ
ejpam-4187	323	19	that	that	SCONJ
ejpam-4187	323	20	dg+h(u	dg+h(u	PROPN
ejpam-4187	323	21	,	,	PUNCT
ejpam-4187	323	22	v	v	NOUN
ejpam-4187	323	23	)	)	PUNCT
ejpam-4187	323	24	=	=	SYM
ejpam-4187	323	25	2	2	NUM
ejpam-4187	323	26	=	=	SYM
ejpam-4187	323	27	dg+h(w	dg+h(w	PROPN
ejpam-4187	323	28	,	,	PUNCT
ejpam-4187	323	29	v	v	NOUN
ejpam-4187	323	30	)	)	PUNCT
ejpam-4187	323	31	.	.	PUNCT
ejpam-4187	324	1	accordingly	accordingly	ADV
ejpam-4187	324	2	,	,	PUNCT
ejpam-4187	324	3	s	s	VERB
ejpam-4187	324	4	is	be	AUX
ejpam-4187	324	5	a	a	DET
ejpam-4187	324	6	restrained	restrained	ADJ
ejpam-4187	324	7	disjunctive	disjunctive	ADJ
ejpam-4187	324	8	dominating	dominating	NOUN
ejpam-4187	324	9	set	set	NOUN
ejpam-4187	324	10	of	of	ADP
ejpam-4187	324	11	g+h	g+h	PROPN
ejpam-4187	324	12	.	.	PUNCT
ejpam-4187	325	1	corollary	corollary	ADJ
ejpam-4187	325	2	2	2	NUM
ejpam-4187	325	3	.	.	PUNCT
ejpam-4187	326	1	for	for	ADP
ejpam-4187	326	2	nontrivial	nontrivial	ADJ
ejpam-4187	326	3	connected	connect	VERB
ejpam-4187	326	4	graphs	graph	NOUN
ejpam-4187	326	5	g	g	NOUN
ejpam-4187	326	6	and	and	CCONJ
ejpam-4187	326	7	h	h	NOUN
ejpam-4187	326	8	,	,	PUNCT
ejpam-4187	326	9	γdr	γdr	PROPN
ejpam-4187	326	10	(	(	PUNCT
ejpam-4187	326	11	g+h	g+h	NOUN
ejpam-4187	326	12	)	)	PUNCT
ejpam-4187	327	1	=	=	PRON
ejpam-4187	327	2	{	{	PUNCT
ejpam-4187	327	3	1	1	NUM
ejpam-4187	327	4	,	,	PUNCT
ejpam-4187	327	5	if	if	SCONJ
ejpam-4187	327	6	γ(g	γ(g	PROPN
ejpam-4187	327	7	)	)	PUNCT
ejpam-4187	327	8	=	=	SYM
ejpam-4187	327	9	1	1	NUM
ejpam-4187	327	10	or	or	CCONJ
ejpam-4187	327	11	γ(h	γ(h	NOUN
ejpam-4187	327	12	)	)	PUNCT
ejpam-4187	327	13	=	=	SYM
ejpam-4187	327	14	1	1	NUM
ejpam-4187	327	15	2	2	NUM
ejpam-4187	327	16	,	,	PUNCT
ejpam-4187	327	17	otherwise	otherwise	ADV
ejpam-4187	327	18	.	.	PUNCT
ejpam-4187	328	1	proof	proof	NOUN
ejpam-4187	328	2	.	.	PUNCT
ejpam-4187	329	1	suppose	suppose	VERB
ejpam-4187	329	2	that	that	SCONJ
ejpam-4187	329	3	γ(g	γ(g	PROPN
ejpam-4187	329	4	)	)	PUNCT
ejpam-4187	329	5	=	=	SYM
ejpam-4187	329	6	1	1	NUM
ejpam-4187	329	7	,	,	PUNCT
ejpam-4187	329	8	and	and	CCONJ
ejpam-4187	329	9	let	let	VERB
ejpam-4187	329	10	s	s	PRON
ejpam-4187	329	11	=	=	NOUN
ejpam-4187	329	12	{	{	PUNCT
ejpam-4187	329	13	v	v	NOUN
ejpam-4187	329	14	}	}	PUNCT
ejpam-4187	329	15	be	be	AUX
ejpam-4187	329	16	a	a	DET
ejpam-4187	329	17	dominating	dominating	NOUN
ejpam-4187	329	18	set	set	NOUN
ejpam-4187	329	19	of	of	ADP
ejpam-4187	329	20	g.	g.	PROPN
ejpam-4187	329	21	then	then	ADV
ejpam-4187	329	22	s	s	VERB
ejpam-4187	329	23	is	be	AUX
ejpam-4187	329	24	a	a	DET
ejpam-4187	329	25	restrained	restrained	ADJ
ejpam-4187	329	26	disjunctive	disjunctive	ADJ
ejpam-4187	329	27	dominating	dominating	NOUN
ejpam-4187	329	28	set	set	NOUN
ejpam-4187	329	29	of	of	ADP
ejpam-4187	329	30	g+h	g+h	PROPN
ejpam-4187	329	31	by	by	ADP
ejpam-4187	329	32	theorem	theorem	NOUN
ejpam-4187	329	33	4	4	NUM
ejpam-4187	329	34	.	.	PUNCT
ejpam-4187	330	1	in	in	ADP
ejpam-4187	330	2	this	this	DET
ejpam-4187	330	3	case	case	NOUN
ejpam-4187	330	4	,	,	PUNCT
ejpam-4187	330	5	γdr	γdr	X
ejpam-4187	330	6	(	(	PUNCT
ejpam-4187	330	7	g+h	g+h	NOUN
ejpam-4187	330	8	)	)	PUNCT
ejpam-4187	330	9	=	=	SYM
ejpam-4187	331	1	1	1	X
ejpam-4187	331	2	.	.	X
ejpam-4187	331	3	similarly	similarly	ADV
ejpam-4187	331	4	,	,	PUNCT
ejpam-4187	331	5	if	if	SCONJ
ejpam-4187	331	6	γ(h	γ(h	NOUN
ejpam-4187	331	7	)	)	PUNCT
ejpam-4187	331	8	=	=	SYM
ejpam-4187	332	1	1	1	NUM
ejpam-4187	332	2	,	,	PUNCT
ejpam-4187	332	3	then	then	ADV
ejpam-4187	332	4	γdr	γdr	INTJ
ejpam-4187	333	1	(	(	PUNCT
ejpam-4187	333	2	g	g	NOUN
ejpam-4187	333	3	+	+	NOUN
ejpam-4187	333	4	h	h	NOUN
ejpam-4187	333	5	)	)	PUNCT
ejpam-4187	333	6	=	=	SYM
ejpam-4187	334	1	1	1	X
ejpam-4187	334	2	.	.	PUNCT
ejpam-4187	334	3	suppose	suppose	VERB
ejpam-4187	334	4	that	that	SCONJ
ejpam-4187	334	5	γ(g	γ(g	PROPN
ejpam-4187	334	6	)	)	PUNCT
ejpam-4187	334	7	≥	≥	NOUN
ejpam-4187	334	8	2	2	NUM
ejpam-4187	334	9	and	and	CCONJ
ejpam-4187	334	10	γ(h	γ(h	NOUN
ejpam-4187	334	11	)	)	PUNCT
ejpam-4187	334	12	≥	≥	NOUN
ejpam-4187	334	13	2	2	NUM
ejpam-4187	334	14	.	.	PUNCT
ejpam-4187	335	1	in	in	ADP
ejpam-4187	335	2	view	view	NOUN
ejpam-4187	335	3	of	of	ADP
ejpam-4187	335	4	theorem	theorem	ADJ
ejpam-4187	335	5	4	4	NUM
ejpam-4187	335	6	,	,	PUNCT
ejpam-4187	335	7	γdr	γdr	X
ejpam-4187	335	8	(	(	PUNCT
ejpam-4187	335	9	g+h	g+h	PROPN
ejpam-4187	335	10	)	)	PUNCT
ejpam-4187	335	11	≥	≥	NOUN
ejpam-4187	335	12	2	2	X
ejpam-4187	335	13	.	.	PUNCT
ejpam-4187	335	14	pick	pick	VERB
ejpam-4187	335	15	u	u	PRON
ejpam-4187	335	16	∈	∈	PROPN
ejpam-4187	335	17	v	v	ADP
ejpam-4187	335	18	(	(	PUNCT
ejpam-4187	335	19	g	g	NOUN
ejpam-4187	335	20	)	)	PUNCT
ejpam-4187	335	21	and	and	CCONJ
ejpam-4187	335	22	v	v	ADP
ejpam-4187	335	23	∈	∈	PROPN
ejpam-4187	335	24	v	v	NOUN
ejpam-4187	335	25	(	(	PUNCT
ejpam-4187	335	26	h	h	NOUN
ejpam-4187	335	27	)	)	PUNCT
ejpam-4187	335	28	.	.	PUNCT
ejpam-4187	336	1	by	by	ADP
ejpam-4187	336	2	theorem	theorem	NOUN
ejpam-4187	336	3	4	4	NUM
ejpam-4187	336	4	,	,	PUNCT
ejpam-4187	336	5	{	{	PUNCT
ejpam-4187	336	6	u	u	NOUN
ejpam-4187	336	7	,	,	PUNCT
ejpam-4187	336	8	v	v	NOUN
ejpam-4187	336	9	}	}	PUNCT
ejpam-4187	336	10	is	be	AUX
ejpam-4187	336	11	a	a	DET
ejpam-4187	336	12	restrained	restrained	ADJ
ejpam-4187	336	13	disjunctive	disjunctive	ADJ
ejpam-4187	336	14	dominating	dominating	NOUN
ejpam-4187	336	15	set	set	NOUN
ejpam-4187	336	16	of	of	ADP
ejpam-4187	336	17	g+h	g+h	PROPN
ejpam-4187	336	18	.	.	PUNCT
ejpam-4187	337	1	thus	thus	ADV
ejpam-4187	337	2	,	,	PUNCT
ejpam-4187	337	3	γdr	γdr	INTJ
ejpam-4187	337	4	(	(	PUNCT
ejpam-4187	337	5	g+h	g+h	NOUN
ejpam-4187	337	6	)	)	PUNCT
ejpam-4187	337	7	≤	≤	ADV
ejpam-4187	337	8	2	2	NUM
ejpam-4187	337	9	.	.	X
ejpam-4187	337	10	4.2	4.2	NUM
ejpam-4187	337	11	.	.	PUNCT
ejpam-4187	338	1	on	on	ADP
ejpam-4187	338	2	corona	corona	NOUN
ejpam-4187	338	3	of	of	ADP
ejpam-4187	338	4	graphs	graph	NOUN
ejpam-4187	338	5	it	it	PRON
ejpam-4187	338	6	is	be	AUX
ejpam-4187	338	7	worth	worth	ADJ
ejpam-4187	338	8	noting	note	VERB
ejpam-4187	338	9	that	that	SCONJ
ejpam-4187	338	10	g	g	PROPN
ejpam-4187	338	11	◦	◦	NOUN
ejpam-4187	338	12	h	h	NOUN
ejpam-4187	338	13	is	be	AUX
ejpam-4187	338	14	composed	compose	VERB
ejpam-4187	338	15	of	of	ADP
ejpam-4187	338	16	the	the	DET
ejpam-4187	338	17	subgraphs	subgraph	NOUN
ejpam-4187	338	18	hv	hv	PROPN
ejpam-4187	338	19	+	+	PROPN
ejpam-4187	338	20	⟨v⟩	⟨v⟩	PROPN
ejpam-4187	338	21	joined	join	VERB
ejpam-4187	338	22	together	together	ADV
ejpam-4187	338	23	by	by	ADP
ejpam-4187	338	24	the	the	DET
ejpam-4187	338	25	edges	edge	NOUN
ejpam-4187	338	26	of	of	ADP
ejpam-4187	338	27	g.	g.	PROPN
ejpam-4187	338	28	thus	thus	ADV
ejpam-4187	338	29	,	,	PUNCT
ejpam-4187	338	30	v	v	X
ejpam-4187	338	31	(	(	PUNCT
ejpam-4187	338	32	g	g	PROPN
ejpam-4187	338	33	◦	◦	NOUN
ejpam-4187	338	34	h	h	NOUN
ejpam-4187	338	35	)	)	PUNCT
ejpam-4187	339	1	=	=	NOUN
ejpam-4187	339	2	v	v	X
ejpam-4187	339	3	(	(	PUNCT
ejpam-4187	339	4	g	g	NOUN
ejpam-4187	339	5	)	)	PUNCT
ejpam-4187	339	6	∪	∪	NOUN
ejpam-4187	339	7	(	(	PUNCT
ejpam-4187	339	8	∪v∈v	∪v∈v	X
ejpam-4187	339	9	(	(	PUNCT
ejpam-4187	339	10	g)v	g)v	X
ejpam-4187	339	11	(	(	PUNCT
ejpam-4187	339	12	hv	hv	NOUN
ejpam-4187	339	13	)	)	PUNCT
ejpam-4187	339	14	)	)	PUNCT
ejpam-4187	340	1	=	=	PUNCT
ejpam-4187	341	1	∪v∈v	∪v∈v	X
ejpam-4187	341	2	(	(	PUNCT
ejpam-4187	341	3	g)v	g)v	X
ejpam-4187	341	4	(	(	PUNCT
ejpam-4187	341	5	hv	hv	PROPN
ejpam-4187	341	6	+	+	PROPN
ejpam-4187	341	7	v	v	NOUN
ejpam-4187	341	8	)	)	PUNCT
ejpam-4187	341	9	.	.	PUNCT
ejpam-4187	342	1	theorem	theorem	ADJ
ejpam-4187	342	2	5	5	NUM
ejpam-4187	342	3	.	.	PUNCT
ejpam-4187	343	1	[	[	X
ejpam-4187	343	2	15	15	NUM
ejpam-4187	343	3	]	]	PUNCT
ejpam-4187	343	4	let	let	VERB
ejpam-4187	343	5	g	g	PRON
ejpam-4187	343	6	be	be	AUX
ejpam-4187	343	7	a	a	DET
ejpam-4187	343	8	nontrivial	nontrivial	ADJ
ejpam-4187	343	9	connected	connect	VERB
ejpam-4187	343	10	graph	graph	NOUN
ejpam-4187	343	11	and	and	CCONJ
ejpam-4187	343	12	h	h	NOUN
ejpam-4187	343	13	be	be	AUX
ejpam-4187	343	14	any	any	DET
ejpam-4187	343	15	graph	graph	NOUN
ejpam-4187	343	16	,	,	PUNCT
ejpam-4187	343	17	and	and	CCONJ
ejpam-4187	343	18	let	let	VERB
ejpam-4187	343	19	s	s	PRON
ejpam-4187	343	20	⊆	⊆	NUM
ejpam-4187	343	21	v	v	NOUN
ejpam-4187	343	22	(	(	PUNCT
ejpam-4187	343	23	g	g	PROPN
ejpam-4187	343	24	◦	◦	NOUN
ejpam-4187	343	25	h	h	NOUN
ejpam-4187	343	26	)	)	PUNCT
ejpam-4187	343	27	.	.	PUNCT
ejpam-4187	344	1	then	then	ADV
ejpam-4187	344	2	s	s	VERB
ejpam-4187	344	3	is	be	AUX
ejpam-4187	344	4	a	a	DET
ejpam-4187	344	5	disjunctive	disjunctive	ADJ
ejpam-4187	344	6	dominating	dominating	NOUN
ejpam-4187	344	7	set	set	NOUN
ejpam-4187	344	8	of	of	ADP
ejpam-4187	344	9	g	g	PROPN
ejpam-4187	344	10	◦	◦	NOUN
ejpam-4187	344	11	h	h	NOUN
ejpam-4187	344	12	if	if	SCONJ
ejpam-4187	345	1	and	and	CCONJ
ejpam-4187	345	2	only	only	ADV
ejpam-4187	345	3	if	if	SCONJ
ejpam-4187	345	4	each	each	PRON
ejpam-4187	345	5	of	of	ADP
ejpam-4187	345	6	the	the	DET
ejpam-4187	345	7	following	following	NOUN
ejpam-4187	345	8	holds	hold	VERB
ejpam-4187	345	9	for	for	ADP
ejpam-4187	345	10	s	s	PRON
ejpam-4187	345	11	:	:	PUNCT
ejpam-4187	345	12	(	(	PUNCT
ejpam-4187	345	13	i	i	NOUN
ejpam-4187	345	14	)	)	PUNCT
ejpam-4187	345	15	|s	|s	PROPN
ejpam-4187	346	1	∩ng(v)|	∩ng(v)|	PROPN
ejpam-4187	346	2	≥	≥	NUM
ejpam-4187	346	3	2	2	NUM
ejpam-4187	346	4	for	for	ADP
ejpam-4187	346	5	all	all	PRON
ejpam-4187	346	6	v	v	ADP
ejpam-4187	346	7	∈	∈	NOUN
ejpam-4187	346	8	v	v	NOUN
ejpam-4187	346	9	(	(	PUNCT
ejpam-4187	346	10	g	g	NOUN
ejpam-4187	346	11	)	)	PUNCT
ejpam-4187	346	12	\	\	PUNCT
ejpam-4187	347	1	s	s	PART
ejpam-4187	347	2	with	with	ADP
ejpam-4187	347	3	s	s	PROPN
ejpam-4187	347	4	∩	∩	ADJ
ejpam-4187	347	5	v	v	X
ejpam-4187	347	6	(	(	PUNCT
ejpam-4187	347	7	hv	hv	NOUN
ejpam-4187	347	8	)	)	PUNCT
ejpam-4187	347	9	=	=	NOUN
ejpam-4187	347	10	∅	∅	NOUN
ejpam-4187	347	11	;	;	PUNCT
ejpam-4187	347	12	(	(	PUNCT
ejpam-4187	347	13	ii	ii	X
ejpam-4187	347	14	)	)	PUNCT
ejpam-4187	347	15	|s	|s	PROPN
ejpam-4187	347	16	∩	∩	PROPN
ejpam-4187	347	17	v	v	NOUN
ejpam-4187	347	18	(	(	PUNCT
ejpam-4187	347	19	hv)|	hv)|	X
ejpam-4187	347	20	≥	≥	NOUN
ejpam-4187	347	21	1	1	NUM
ejpam-4187	347	22	for	for	ADP
ejpam-4187	347	23	all	all	PRON
ejpam-4187	347	24	v	v	ADP
ejpam-4187	347	25	∈	∈	NUM
ejpam-4187	347	26	v	v	NOUN
ejpam-4187	347	27	(	(	PUNCT
ejpam-4187	347	28	g	g	NOUN
ejpam-4187	347	29	)	)	PUNCT
ejpam-4187	347	30	\	\	PROPN
ejpam-4187	348	1	s	s	PART
ejpam-4187	348	2	with	with	ADP
ejpam-4187	348	3	|s	|s	PROPN
ejpam-4187	349	1	∩ng(v)|	∩ng(v)|	PROPN
ejpam-4187	349	2	=	=	SYM
ejpam-4187	349	3	1	1	NUM
ejpam-4187	349	4	;	;	PUNCT
ejpam-4187	349	5	and	and	CCONJ
ejpam-4187	349	6	(	(	PUNCT
ejpam-4187	349	7	iii	iii	X
ejpam-4187	349	8	)	)	PUNCT
ejpam-4187	349	9	s	s	PART
ejpam-4187	349	10	∩	∩	ADJ
ejpam-4187	349	11	v	v	X
ejpam-4187	349	12	(	(	PUNCT
ejpam-4187	349	13	hv	hv	X
ejpam-4187	349	14	)	)	PUNCT
ejpam-4187	349	15	is	be	AUX
ejpam-4187	349	16	a	a	DET
ejpam-4187	349	17	disjunctive	disjunctive	ADJ
ejpam-4187	349	18	dominating	dominating	NOUN
ejpam-4187	349	19	set	set	NOUN
ejpam-4187	349	20	of	of	ADP
ejpam-4187	349	21	hv	hv	PROPN
ejpam-4187	349	22	+	+	X
ejpam-4187	349	23	v	v	NOUN
ejpam-4187	349	24	for	for	ADP
ejpam-4187	349	25	all	all	PRON
ejpam-4187	349	26	v	v	ADP
ejpam-4187	349	27	∈	∈	NUM
ejpam-4187	349	28	v	v	NOUN
ejpam-4187	349	29	(	(	PUNCT
ejpam-4187	349	30	g	g	NOUN
ejpam-4187	349	31	)	)	PUNCT
ejpam-4187	349	32	\	\	PUNCT
ejpam-4187	350	1	s	s	PART
ejpam-4187	350	2	with	with	ADP
ejpam-4187	350	3	s	s	PROPN
ejpam-4187	350	4	∩ng(v	∩ng(v	PROPN
ejpam-4187	350	5	)	)	PUNCT
ejpam-4187	351	1	=	=	PUNCT
ejpam-4187	351	2	∅.	∅.	NOUN
ejpam-4187	351	3	in	in	ADP
ejpam-4187	351	4	particular	particular	ADJ
ejpam-4187	351	5	,	,	PUNCT
ejpam-4187	351	6	if	if	SCONJ
ejpam-4187	351	7	γ(h	γ(h	NOUN
ejpam-4187	351	8	)	)	PUNCT
ejpam-4187	351	9	>	>	X
ejpam-4187	352	1	1	1	NUM
ejpam-4187	352	2	,	,	PUNCT
ejpam-4187	352	3	then	then	ADV
ejpam-4187	352	4	|s	|s	PROPN
ejpam-4187	352	5	∩	∩	ADJ
ejpam-4187	352	6	v	v	X
ejpam-4187	352	7	(	(	PUNCT
ejpam-4187	352	8	hv)|	hv)|	X
ejpam-4187	352	9	≥	≥	NOUN
ejpam-4187	352	10	2	2	NUM
ejpam-4187	352	11	.	.	PUNCT
ejpam-4187	352	12	corollary	corollary	ADJ
ejpam-4187	352	13	3	3	NUM
ejpam-4187	352	14	.	.	PUNCT
ejpam-4187	353	1	[	[	X
ejpam-4187	353	2	15	15	NUM
ejpam-4187	353	3	]	]	PUNCT
ejpam-4187	353	4	let	let	VERB
ejpam-4187	353	5	g	g	PRON
ejpam-4187	353	6	be	be	AUX
ejpam-4187	353	7	a	a	DET
ejpam-4187	353	8	nontrivial	nontrivial	ADJ
ejpam-4187	353	9	connected	connect	VERB
ejpam-4187	353	10	graph	graph	NOUN
ejpam-4187	353	11	.	.	PUNCT
ejpam-4187	354	1	then	then	ADV
ejpam-4187	354	2	for	for	ADP
ejpam-4187	354	3	any	any	DET
ejpam-4187	354	4	graph	graph	NOUN
ejpam-4187	354	5	h	h	NOUN
ejpam-4187	354	6	,	,	PUNCT
ejpam-4187	354	7	γd(g	γd(g	PUNCT
ejpam-4187	354	8	◦	◦	NOUN
ejpam-4187	354	9	h	h	NOUN
ejpam-4187	354	10	)	)	PUNCT
ejpam-4187	354	11	=	=	SYM
ejpam-4187	354	12	γ×2(g	γ×2(g	PROPN
ejpam-4187	354	13	)	)	PUNCT
ejpam-4187	354	14	.	.	PUNCT
ejpam-4187	355	1	proposition	proposition	NOUN
ejpam-4187	355	2	2	2	NUM
ejpam-4187	355	3	.	.	PUNCT
ejpam-4187	356	1	let	let	VERB
ejpam-4187	356	2	g	g	PRON
ejpam-4187	356	3	be	be	AUX
ejpam-4187	356	4	a	a	DET
ejpam-4187	356	5	nontrivial	nontrivial	ADJ
ejpam-4187	356	6	connected	connect	VERB
ejpam-4187	356	7	graph	graph	NOUN
ejpam-4187	356	8	and	and	CCONJ
ejpam-4187	356	9	s	s	VERB
ejpam-4187	356	10	⊆	⊆	NUM
ejpam-4187	356	11	v	v	NOUN
ejpam-4187	356	12	(	(	PUNCT
ejpam-4187	356	13	g	g	PROPN
ejpam-4187	356	14	◦	◦	NOUN
ejpam-4187	356	15	k1	k1	NOUN
ejpam-4187	356	16	)	)	PUNCT
ejpam-4187	356	17	.	.	PUNCT
ejpam-4187	357	1	then	then	ADV
ejpam-4187	357	2	s	s	VERB
ejpam-4187	357	3	is	be	AUX
ejpam-4187	357	4	a	a	DET
ejpam-4187	357	5	restrained	restrained	ADJ
ejpam-4187	357	6	disjunctive	disjunctive	ADJ
ejpam-4187	357	7	dominating	dominating	NOUN
ejpam-4187	357	8	set	set	NOUN
ejpam-4187	357	9	of	of	ADP
ejpam-4187	357	10	g	g	PROPN
ejpam-4187	357	11	◦	◦	NOUN
ejpam-4187	357	12	k1	k1	NOUN
ejpam-4187	357	13	if	if	SCONJ
ejpam-4187	357	14	and	and	CCONJ
ejpam-4187	357	15	only	only	ADV
ejpam-4187	357	16	if	if	SCONJ
ejpam-4187	357	17	each	each	PRON
ejpam-4187	357	18	of	of	ADP
ejpam-4187	357	19	the	the	DET
ejpam-4187	357	20	following	follow	VERB
ejpam-4187	357	21	holds	hold	VERB
ejpam-4187	357	22	:	:	PUNCT
ejpam-4187	357	23	(	(	PUNCT
ejpam-4187	357	24	i	i	NOUN
ejpam-4187	357	25	)	)	PUNCT
ejpam-4187	357	26	uv	uv	PROPN
ejpam-4187	357	27	∈	∈	PROPN
ejpam-4187	357	28	s	s	NOUN
ejpam-4187	357	29	for	for	ADP
ejpam-4187	357	30	all	all	PRON
ejpam-4187	357	31	v	v	ADP
ejpam-4187	357	32	∈	∈	NOUN
ejpam-4187	357	33	end(g	end(g	PROPN
ejpam-4187	357	34	)	)	PUNCT
ejpam-4187	357	35	;	;	PUNCT
ejpam-4187	357	36	(	(	PUNCT
ejpam-4187	357	37	ii	ii	NOUN
ejpam-4187	357	38	)	)	PUNCT
ejpam-4187	357	39	for	for	ADP
ejpam-4187	357	40	each	each	DET
ejpam-4187	357	41	uv	uv	NOUN
ejpam-4187	357	42	/∈	/∈	PUNCT
ejpam-4187	358	1	s	s	PART
ejpam-4187	358	2	,	,	PUNCT
ejpam-4187	358	3	(	(	PUNCT
ejpam-4187	358	4	a	a	X
ejpam-4187	358	5	)	)	PUNCT
ejpam-4187	358	6	|ng(v	|ng(v	NOUN
ejpam-4187	358	7	)	)	PUNCT
ejpam-4187	358	8	∩	∩	NOUN
ejpam-4187	358	9	s|	s|	VERB
ejpam-4187	358	10	≥	≥	NOUN
ejpam-4187	358	11	2	2	NUM
ejpam-4187	358	12	whenever	whenever	SCONJ
ejpam-4187	358	13	v	v	NOUN
ejpam-4187	358	14	/∈	/∈	PUNCT
ejpam-4187	358	15	s	s	PART
ejpam-4187	358	16	;	;	PUNCT
ejpam-4187	358	17	r.	r.	NOUN
ejpam-4187	358	18	malalay	malalay	PROPN
ejpam-4187	358	19	,	,	PUNCT
ejpam-4187	358	20	f.	f.	PROPN
ejpam-4187	358	21	jamil	jamil	PROPN
ejpam-4187	358	22	/	/	SYM
ejpam-4187	358	23	eur	eur	PROPN
ejpam-4187	358	24	.	.	PUNCT
ejpam-4187	359	1	j.	j.	PROPN
ejpam-4187	359	2	pure	pure	PROPN
ejpam-4187	359	3	appl	appl	PROPN
ejpam-4187	359	4	.	.	PROPN
ejpam-4187	359	5	math	math	PROPN
ejpam-4187	359	6	,	,	PUNCT
ejpam-4187	359	7	15	15	NUM
ejpam-4187	359	8	(	(	PUNCT
ejpam-4187	359	9	1	1	NUM
ejpam-4187	359	10	)	)	PUNCT
ejpam-4187	359	11	(	(	PUNCT
ejpam-4187	359	12	2022	2022	NUM
ejpam-4187	359	13	)	)	PUNCT
ejpam-4187	359	14	,	,	PUNCT
ejpam-4187	359	15	207	207	NUM
ejpam-4187	359	16	-	-	SYM
ejpam-4187	359	17	223	223	NUM
ejpam-4187	359	18	216	216	NUM
ejpam-4187	359	19	(	(	PUNCT
ejpam-4187	359	20	b	b	NOUN
ejpam-4187	359	21	)	)	PUNCT
ejpam-4187	359	22	|ng(v	|ng(v	PROPN
ejpam-4187	359	23	)	)	PUNCT
ejpam-4187	359	24	\	\	PROPN
ejpam-4187	359	25	s|	s|	VERB
ejpam-4187	359	26	≥	≥	NOUN
ejpam-4187	359	27	2	2	NUM
ejpam-4187	359	28	whenever	whenever	SCONJ
ejpam-4187	359	29	v	v	X
ejpam-4187	359	30	∈	∈	PROPN
ejpam-4187	359	31	s.	s.	PROPN
ejpam-4187	359	32	(	(	PUNCT
ejpam-4187	359	33	iii	iii	NOUN
ejpam-4187	359	34	)	)	PUNCT
ejpam-4187	359	35	for	for	ADP
ejpam-4187	359	36	each	each	DET
ejpam-4187	359	37	v	v	NOUN
ejpam-4187	359	38	/∈	/∈	PUNCT
ejpam-4187	359	39	s	s	PART
ejpam-4187	359	40	with	with	ADP
ejpam-4187	359	41	ng(v	ng(v	NOUN
ejpam-4187	359	42	)	)	PUNCT
ejpam-4187	359	43	∪	∪	ADP
ejpam-4187	359	44	{	{	PUNCT
ejpam-4187	359	45	uv	uv	NOUN
ejpam-4187	359	46	}	}	PUNCT
ejpam-4187	359	47	⊆	⊆	NUM
ejpam-4187	359	48	s	s	NOUN
ejpam-4187	359	49	,	,	PUNCT
ejpam-4187	359	50	(	(	PUNCT
ejpam-4187	359	51	a	a	X
ejpam-4187	359	52	)	)	PUNCT
ejpam-4187	359	53	|ng(v	|ng(v	NOUN
ejpam-4187	359	54	,	,	PUNCT
ejpam-4187	359	55	2	2	NUM
ejpam-4187	359	56	)	)	PUNCT
ejpam-4187	359	57	\	\	PROPN
ejpam-4187	359	58	s|	s|	VERB
ejpam-4187	359	59	≥	≥	NOUN
ejpam-4187	359	60	2	2	NUM
ejpam-4187	359	61	whenever	whenever	SCONJ
ejpam-4187	359	62	uw	uw	PROPN
ejpam-4187	359	63	∈	∈	PROPN
ejpam-4187	359	64	s	s	X
ejpam-4187	359	65	for	for	ADP
ejpam-4187	359	66	all	all	DET
ejpam-4187	359	67	w	w	NOUN
ejpam-4187	359	68	∈	∈	NOUN
ejpam-4187	359	69	ng(v	ng(v	NOUN
ejpam-4187	359	70	)	)	PUNCT
ejpam-4187	359	71	;	;	PUNCT
ejpam-4187	359	72	and	and	CCONJ
ejpam-4187	359	73	(	(	PUNCT
ejpam-4187	359	74	b	b	X
ejpam-4187	359	75	)	)	PUNCT
ejpam-4187	359	76	|ng(v	|ng(v	NOUN
ejpam-4187	359	77	,	,	PUNCT
ejpam-4187	359	78	2	2	NUM
ejpam-4187	359	79	)	)	PUNCT
ejpam-4187	359	80	\	\	NOUN
ejpam-4187	360	1	s|	s|	VERB
ejpam-4187	360	2	≥	≥	NOUN
ejpam-4187	360	3	1	1	NUM
ejpam-4187	360	4	whenever	whenever	SCONJ
ejpam-4187	360	5	uw	uw	PROPN
ejpam-4187	360	6	/∈	/∈	PROPN
ejpam-4187	360	7	s	s	PART
ejpam-4187	360	8	for	for	ADP
ejpam-4187	360	9	exactly	exactly	ADV
ejpam-4187	360	10	one	one	NUM
ejpam-4187	360	11	w	w	NOUN
ejpam-4187	360	12	∈	∈	PROPN
ejpam-4187	360	13	ng(v	ng(v	NOUN
ejpam-4187	360	14	)	)	PUNCT
ejpam-4187	360	15	.	.	PUNCT
ejpam-4187	361	1	in	in	ADP
ejpam-4187	361	2	particular	particular	ADJ
ejpam-4187	361	3	,	,	PUNCT
ejpam-4187	361	4	v	v	ADP
ejpam-4187	361	5	∈	∈	NOUN
ejpam-4187	361	6	end(g	end(g	PROPN
ejpam-4187	361	7	)	)	PUNCT
ejpam-4187	362	1	if	if	SCONJ
ejpam-4187	362	2	and	and	CCONJ
ejpam-4187	362	3	only	only	ADV
ejpam-4187	362	4	if	if	SCONJ
ejpam-4187	362	5	|ng(v)|	|ng(v)|	PROPN
ejpam-4187	362	6	=	=	SYM
ejpam-4187	362	7	1	1	X
ejpam-4187	362	8	.	.	PUNCT
ejpam-4187	362	9	proof	proof	NOUN
ejpam-4187	362	10	.	.	PUNCT
ejpam-4187	363	1	let	let	VERB
ejpam-4187	363	2	s	s	PRON
ejpam-4187	363	3	⊆	⊆	NUM
ejpam-4187	363	4	v	v	NOUN
ejpam-4187	363	5	(	(	PUNCT
ejpam-4187	363	6	g	g	NOUN
ejpam-4187	363	7	◦	◦	NOUN
ejpam-4187	363	8	k1	k1	NOUN
ejpam-4187	363	9	)	)	PUNCT
ejpam-4187	363	10	be	be	VERB
ejpam-4187	363	11	a	a	DET
ejpam-4187	363	12	restrained	restrained	ADJ
ejpam-4187	363	13	disjunctive	disjunctive	ADJ
ejpam-4187	363	14	dominating	dominating	NOUN
ejpam-4187	363	15	set	set	NOUN
ejpam-4187	363	16	of	of	ADP
ejpam-4187	363	17	g	g	NOUN
ejpam-4187	363	18	◦	◦	NOUN
ejpam-4187	363	19	k1	k1	NOUN
ejpam-4187	363	20	.	.	PUNCT
ejpam-4187	364	1	let	let	VERB
ejpam-4187	364	2	v	v	X
ejpam-4187	364	3	∈	∈	PROPN
ejpam-4187	364	4	end(g	end(g	PROPN
ejpam-4187	364	5	)	)	PUNCT
ejpam-4187	364	6	.	.	PUNCT
ejpam-4187	365	1	suppose	suppose	VERB
ejpam-4187	365	2	that	that	SCONJ
ejpam-4187	365	3	uv	uv	NOUN
ejpam-4187	365	4	/∈	/∈	PUNCT
ejpam-4187	365	5	s.	s.	PROPN
ejpam-4187	366	1	if	if	SCONJ
ejpam-4187	366	2	v	v	NUM
ejpam-4187	366	3	∈	∈	PROPN
ejpam-4187	366	4	s	s	NOUN
ejpam-4187	366	5	,	,	PUNCT
ejpam-4187	366	6	then	then	ADV
ejpam-4187	366	7	since	since	SCONJ
ejpam-4187	366	8	s	s	NOUN
ejpam-4187	366	9	is	be	AUX
ejpam-4187	366	10	a	a	DET
ejpam-4187	366	11	restrained	restrained	ADJ
ejpam-4187	366	12	disjunctive	disjunctive	ADJ
ejpam-4187	366	13	dominating	dominating	NOUN
ejpam-4187	366	14	set	set	NOUN
ejpam-4187	366	15	,	,	PUNCT
ejpam-4187	366	16	there	there	PRON
ejpam-4187	366	17	exist	exist	VERB
ejpam-4187	366	18	distinct	distinct	ADJ
ejpam-4187	366	19	w	w	PROPN
ejpam-4187	366	20	,	,	PUNCT
ejpam-4187	366	21	z	z	PROPN
ejpam-4187	366	22	∈	∈	PROPN
ejpam-4187	366	23	ng(v	ng(v	PUNCT
ejpam-4187	366	24	)	)	PUNCT
ejpam-4187	366	25	\	\	PROPN
ejpam-4187	367	1	s	s	PART
ejpam-4187	367	2	for	for	ADP
ejpam-4187	367	3	which	which	PRON
ejpam-4187	367	4	dg	dg	VERB
ejpam-4187	367	5	◦	◦	NOUN
ejpam-4187	367	6	k1(u	k1(u	X
ejpam-4187	367	7	v	v	NOUN
ejpam-4187	367	8	,	,	PUNCT
ejpam-4187	367	9	w	w	NOUN
ejpam-4187	367	10	)	)	PUNCT
ejpam-4187	367	11	=	=	SYM
ejpam-4187	367	12	2	2	NUM
ejpam-4187	367	13	=	=	SYM
ejpam-4187	367	14	dg	dg	NOUN
ejpam-4187	367	15	◦	◦	NOUN
ejpam-4187	367	16	k1(u	k1(u	X
ejpam-4187	367	17	v	v	NOUN
ejpam-4187	367	18	,	,	PUNCT
ejpam-4187	367	19	z	z	NOUN
ejpam-4187	367	20	)	)	PUNCT
ejpam-4187	367	21	,	,	PUNCT
ejpam-4187	367	22	and	and	CCONJ
ejpam-4187	367	23	consequently	consequently	ADV
ejpam-4187	367	24	,	,	PUNCT
ejpam-4187	367	25	dg(w	dg(w	X
ejpam-4187	367	26	,	,	PUNCT
ejpam-4187	367	27	v	v	NOUN
ejpam-4187	367	28	)	)	PUNCT
ejpam-4187	367	29	=	=	SYM
ejpam-4187	367	30	1	1	NUM
ejpam-4187	367	31	=	=	SYM
ejpam-4187	367	32	dg(z	dg(z	NUM
ejpam-4187	367	33	,	,	PUNCT
ejpam-4187	367	34	v	v	NOUN
ejpam-4187	367	35	)	)	PUNCT
ejpam-4187	367	36	.	.	PUNCT
ejpam-4187	368	1	this	this	PRON
ejpam-4187	368	2	is	be	AUX
ejpam-4187	368	3	impossible	impossible	ADJ
ejpam-4187	368	4	since	since	SCONJ
ejpam-4187	368	5	v	v	NUM
ejpam-4187	368	6	∈	∈	PROPN
ejpam-4187	368	7	end(g	end(g	PROPN
ejpam-4187	368	8	)	)	PUNCT
ejpam-4187	368	9	.	.	PUNCT
ejpam-4187	369	1	if	if	SCONJ
ejpam-4187	369	2	v	v	NUM
ejpam-4187	369	3	/∈	/∈	SYM
ejpam-4187	369	4	s	s	X
ejpam-4187	369	5	,	,	PUNCT
ejpam-4187	369	6	then	then	ADV
ejpam-4187	369	7	since	since	SCONJ
ejpam-4187	369	8	s	s	NOUN
ejpam-4187	369	9	is	be	AUX
ejpam-4187	369	10	a	a	DET
ejpam-4187	369	11	disjunctive	disjunctive	ADJ
ejpam-4187	369	12	dominating	dominating	NOUN
ejpam-4187	369	13	set	set	NOUN
ejpam-4187	369	14	,	,	PUNCT
ejpam-4187	369	15	there	there	PRON
ejpam-4187	369	16	exist	exist	VERB
ejpam-4187	369	17	distinct	distinct	ADJ
ejpam-4187	369	18	w	w	PROPN
ejpam-4187	369	19	,	,	PUNCT
ejpam-4187	369	20	z	z	PROPN
ejpam-4187	369	21	∈	∈	PROPN
ejpam-4187	369	22	ng(v	ng(v	PUNCT
ejpam-4187	369	23	)	)	PUNCT
ejpam-4187	369	24	∩	∩	NOUN
ejpam-4187	369	25	s	s	PART
ejpam-4187	369	26	for	for	ADP
ejpam-4187	369	27	which	which	PRON
ejpam-4187	369	28	dg	dg	VERB
ejpam-4187	369	29	◦	◦	NOUN
ejpam-4187	369	30	k1(u	k1(u	X
ejpam-4187	369	31	v	v	NOUN
ejpam-4187	369	32	,	,	PUNCT
ejpam-4187	369	33	w	w	NOUN
ejpam-4187	369	34	)	)	PUNCT
ejpam-4187	369	35	=	=	SYM
ejpam-4187	369	36	2	2	NUM
ejpam-4187	369	37	=	=	SYM
ejpam-4187	369	38	dg	dg	NOUN
ejpam-4187	369	39	◦	◦	NOUN
ejpam-4187	369	40	k1(u	k1(u	X
ejpam-4187	369	41	v	v	NOUN
ejpam-4187	369	42	,	,	PUNCT
ejpam-4187	369	43	z	z	NOUN
ejpam-4187	369	44	)	)	PUNCT
ejpam-4187	369	45	,	,	PUNCT
ejpam-4187	369	46	which	which	PRON
ejpam-4187	369	47	for	for	ADP
ejpam-4187	369	48	the	the	DET
ejpam-4187	369	49	same	same	ADJ
ejpam-4187	369	50	reason	reason	NOUN
ejpam-4187	369	51	is	be	AUX
ejpam-4187	369	52	impossible	impossible	ADJ
ejpam-4187	369	53	.	.	PUNCT
ejpam-4187	370	1	thus	thus	ADV
ejpam-4187	370	2	,	,	PUNCT
ejpam-4187	370	3	uv	uv	PROPN
ejpam-4187	370	4	∈	∈	PROPN
ejpam-4187	370	5	s	s	PART
ejpam-4187	370	6	and	and	CCONJ
ejpam-4187	370	7	(	(	PUNCT
ejpam-4187	370	8	i	i	NOUN
ejpam-4187	370	9	)	)	PUNCT
ejpam-4187	370	10	holds	hold	VERB
ejpam-4187	370	11	.	.	PUNCT
ejpam-4187	371	1	let	let	VERB
ejpam-4187	371	2	uv	uv	NOUN
ejpam-4187	371	3	/∈	/∈	PUNCT
ejpam-4187	371	4	s.	s.	PROPN
ejpam-4187	372	1	by	by	ADP
ejpam-4187	372	2	(	(	PUNCT
ejpam-4187	372	3	i	i	NOUN
ejpam-4187	372	4	)	)	PUNCT
ejpam-4187	372	5	,	,	PUNCT
ejpam-4187	372	6	v	v	X
ejpam-4187	372	7	/∈	/∈	PUNCT
ejpam-4187	372	8	end(g	end(g	NUM
ejpam-4187	372	9	)	)	PUNCT
ejpam-4187	372	10	.	.	PUNCT
ejpam-4187	373	1	if	if	SCONJ
ejpam-4187	373	2	v	v	NUM
ejpam-4187	373	3	/∈	/∈	SYM
ejpam-4187	373	4	s	s	X
ejpam-4187	373	5	,	,	PUNCT
ejpam-4187	373	6	then	then	ADV
ejpam-4187	373	7	since	since	SCONJ
ejpam-4187	373	8	s	s	NOUN
ejpam-4187	373	9	is	be	AUX
ejpam-4187	373	10	a	a	DET
ejpam-4187	373	11	disjunctive	disjunctive	ADJ
ejpam-4187	373	12	dominating	dominating	NOUN
ejpam-4187	373	13	set	set	NOUN
ejpam-4187	373	14	,	,	PUNCT
ejpam-4187	373	15	there	there	PRON
ejpam-4187	373	16	exist	exist	VERB
ejpam-4187	373	17	distinct	distinct	ADJ
ejpam-4187	373	18	w	w	NOUN
ejpam-4187	373	19	,	,	PUNCT
ejpam-4187	373	20	z	z	PROPN
ejpam-4187	373	21	∈	∈	PROPN
ejpam-4187	374	1	ng(v)∩s	ng(v)∩s	PROPN
ejpam-4187	374	2	for	for	ADP
ejpam-4187	374	3	which	which	PRON
ejpam-4187	374	4	dg	dg	VERB
ejpam-4187	374	5	◦	◦	NOUN
ejpam-4187	374	6	k1(u	k1(u	X
ejpam-4187	374	7	v	v	NOUN
ejpam-4187	374	8	,	,	PUNCT
ejpam-4187	374	9	w	w	NOUN
ejpam-4187	374	10	)	)	PUNCT
ejpam-4187	374	11	=	=	SYM
ejpam-4187	374	12	2	2	NUM
ejpam-4187	374	13	=	=	SYM
ejpam-4187	374	14	dg	dg	NOUN
ejpam-4187	374	15	◦	◦	NOUN
ejpam-4187	374	16	k1(u	k1(u	X
ejpam-4187	374	17	v	v	NOUN
ejpam-4187	374	18	,	,	PUNCT
ejpam-4187	374	19	z	z	NOUN
ejpam-4187	374	20	)	)	PUNCT
ejpam-4187	374	21	.	.	PUNCT
ejpam-4187	375	1	thus	thus	ADV
ejpam-4187	375	2	,	,	PUNCT
ejpam-4187	375	3	|ng(v	|ng(v	NOUN
ejpam-4187	375	4	)	)	PUNCT
ejpam-4187	375	5	∩	∩	NOUN
ejpam-4187	375	6	s|	s|	VERB
ejpam-4187	375	7	≥	≥	NUM
ejpam-4187	375	8	2	2	NUM
ejpam-4187	375	9	and	and	CCONJ
ejpam-4187	375	10	property	property	NOUN
ejpam-4187	375	11	(	(	PUNCT
ejpam-4187	375	12	ii)(a	ii)(a	NOUN
ejpam-4187	375	13	)	)	PUNCT
ejpam-4187	375	14	holds	hold	VERB
ejpam-4187	375	15	for	for	ADP
ejpam-4187	375	16	s.	s.	PROPN
ejpam-4187	375	17	on	on	ADP
ejpam-4187	375	18	the	the	DET
ejpam-4187	375	19	other	other	ADJ
ejpam-4187	375	20	hand	hand	NOUN
ejpam-4187	375	21	,	,	PUNCT
ejpam-4187	375	22	if	if	SCONJ
ejpam-4187	375	23	v	v	NUM
ejpam-4187	375	24	∈	∈	PROPN
ejpam-4187	375	25	s	s	NOUN
ejpam-4187	375	26	,	,	PUNCT
ejpam-4187	375	27	then	then	ADV
ejpam-4187	375	28	since	since	SCONJ
ejpam-4187	375	29	s	s	NOUN
ejpam-4187	375	30	is	be	AUX
ejpam-4187	375	31	a	a	DET
ejpam-4187	375	32	restrained	restrained	ADJ
ejpam-4187	375	33	disjunctive	disjunctive	ADJ
ejpam-4187	375	34	dominating	dominating	NOUN
ejpam-4187	375	35	set	set	NOUN
ejpam-4187	375	36	,	,	PUNCT
ejpam-4187	375	37	there	there	PRON
ejpam-4187	375	38	exist	exist	VERB
ejpam-4187	375	39	distinct	distinct	ADJ
ejpam-4187	375	40	w	w	NOUN
ejpam-4187	375	41	,	,	PUNCT
ejpam-4187	375	42	z	z	PROPN
ejpam-4187	375	43	∈	∈	PROPN
ejpam-4187	375	44	v	v	ADP
ejpam-4187	375	45	(	(	PUNCT
ejpam-4187	375	46	g	g	NOUN
ejpam-4187	375	47	)	)	PUNCT
ejpam-4187	375	48	\	\	PROPN
ejpam-4187	376	1	s	s	PART
ejpam-4187	376	2	for	for	ADP
ejpam-4187	376	3	which	which	PRON
ejpam-4187	376	4	dg	dg	VERB
ejpam-4187	376	5	◦	◦	NOUN
ejpam-4187	376	6	k1(w	k1(w	PROPN
ejpam-4187	376	7	,	,	PUNCT
ejpam-4187	376	8	u	u	NOUN
ejpam-4187	376	9	v	v	NOUN
ejpam-4187	376	10	)	)	PUNCT
ejpam-4187	376	11	=	=	SYM
ejpam-4187	376	12	2	2	NUM
ejpam-4187	376	13	=	=	SYM
ejpam-4187	376	14	dg	dg	NOUN
ejpam-4187	376	15	◦	◦	NOUN
ejpam-4187	376	16	k1(z	k1(z	PROPN
ejpam-4187	376	17	,	,	PUNCT
ejpam-4187	376	18	u	u	NOUN
ejpam-4187	376	19	v	v	NOUN
ejpam-4187	376	20	)	)	PUNCT
ejpam-4187	376	21	.	.	PUNCT
ejpam-4187	377	1	this	this	PRON
ejpam-4187	377	2	proves	prove	VERB
ejpam-4187	377	3	that	that	SCONJ
ejpam-4187	377	4	property	property	NOUN
ejpam-4187	377	5	(	(	PUNCT
ejpam-4187	377	6	ii)(b	ii)(b	ADJ
ejpam-4187	377	7	)	)	PUNCT
ejpam-4187	377	8	holds	hold	VERB
ejpam-4187	377	9	for	for	ADP
ejpam-4187	377	10	s.	s.	PROPN
ejpam-4187	377	11	now	now	ADV
ejpam-4187	377	12	,	,	PUNCT
ejpam-4187	377	13	let	let	VERB
ejpam-4187	377	14	v	v	NUM
ejpam-4187	377	15	∈	∈	PROPN
ejpam-4187	377	16	v	v	NOUN
ejpam-4187	377	17	(	(	PUNCT
ejpam-4187	377	18	g	g	NOUN
ejpam-4187	377	19	)	)	PUNCT
ejpam-4187	377	20	\s	\s	NOUN
ejpam-4187	377	21	with	with	ADP
ejpam-4187	377	22	ng(v)∪{uv	ng(v)∪{uv	PROPN
ejpam-4187	377	23	}	}	PUNCT
ejpam-4187	377	24	⊆	⊆	NUM
ejpam-4187	377	25	s.	s.	PROPN
ejpam-4187	377	26	suppose	suppose	VERB
ejpam-4187	377	27	that	that	SCONJ
ejpam-4187	377	28	uw	uw	PROPN
ejpam-4187	377	29	∈	∈	PROPN
ejpam-4187	377	30	s	s	PART
ejpam-4187	377	31	for	for	ADP
ejpam-4187	377	32	all	all	DET
ejpam-4187	377	33	w	w	NOUN
ejpam-4187	377	34	∈	∈	NOUN
ejpam-4187	377	35	ng(v	ng(v	NOUN
ejpam-4187	377	36	)	)	PUNCT
ejpam-4187	377	37	.	.	PUNCT
ejpam-4187	378	1	since	since	SCONJ
ejpam-4187	378	2	s	s	PROPN
ejpam-4187	378	3	is	be	AUX
ejpam-4187	378	4	a	a	DET
ejpam-4187	378	5	restrained	restrained	ADJ
ejpam-4187	378	6	disjunctive	disjunctive	ADJ
ejpam-4187	378	7	dominating	dominating	NOUN
ejpam-4187	378	8	set	set	NOUN
ejpam-4187	378	9	,	,	PUNCT
ejpam-4187	378	10	there	there	PRON
ejpam-4187	378	11	exist	exist	VERB
ejpam-4187	378	12	distinct	distinct	ADJ
ejpam-4187	378	13	w	w	NOUN
ejpam-4187	378	14	,	,	PUNCT
ejpam-4187	378	15	z	z	PROPN
ejpam-4187	378	16	∈	∈	PROPN
ejpam-4187	378	17	s	s	X
ejpam-4187	378	18	for	for	ADP
ejpam-4187	378	19	which	which	PRON
ejpam-4187	378	20	dg	dg	ADP
ejpam-4187	378	21	◦	◦	NOUN
ejpam-4187	378	22	k1(v	k1(v	PROPN
ejpam-4187	378	23	,	,	PUNCT
ejpam-4187	378	24	w	w	PROPN
ejpam-4187	378	25	)	)	PUNCT
ejpam-4187	378	26	=	=	SYM
ejpam-4187	378	27	2	2	NUM
ejpam-4187	378	28	=	=	SYM
ejpam-4187	378	29	dg	dg	PROPN
ejpam-4187	378	30	◦	◦	NOUN
ejpam-4187	378	31	k1(v	k1(v	PROPN
ejpam-4187	378	32	,	,	PUNCT
ejpam-4187	378	33	z	z	PROPN
ejpam-4187	378	34	)	)	PUNCT
ejpam-4187	378	35	.	.	PUNCT
ejpam-4187	379	1	the	the	DET
ejpam-4187	379	2	hypothesis	hypothesis	NOUN
ejpam-4187	379	3	implies	imply	VERB
ejpam-4187	379	4	that	that	SCONJ
ejpam-4187	379	5	w	w	X
ejpam-4187	379	6	,	,	PUNCT
ejpam-4187	379	7	z	z	PROPN
ejpam-4187	379	8	∈	∈	PROPN
ejpam-4187	379	9	v	v	NOUN
ejpam-4187	379	10	(	(	PUNCT
ejpam-4187	379	11	g	g	NOUN
ejpam-4187	379	12	)	)	PUNCT
ejpam-4187	379	13	,	,	PUNCT
ejpam-4187	379	14	proving	prove	VERB
ejpam-4187	379	15	(	(	PUNCT
ejpam-4187	379	16	iii)(a	iii)(a	NOUN
ejpam-4187	379	17	)	)	PUNCT
ejpam-4187	379	18	.	.	PUNCT
ejpam-4187	380	1	similarly	similarly	ADV
ejpam-4187	380	2	,	,	PUNCT
ejpam-4187	380	3	(	(	PUNCT
ejpam-4187	380	4	iii)(b	iii)(b	ADJ
ejpam-4187	380	5	)	)	PUNCT
ejpam-4187	380	6	holds	hold	VERB
ejpam-4187	380	7	for	for	ADP
ejpam-4187	380	8	s.	s.	PROPN
ejpam-4187	380	9	conversely	conversely	ADV
ejpam-4187	380	10	,	,	PUNCT
ejpam-4187	380	11	suppose	suppose	VERB
ejpam-4187	380	12	that	that	SCONJ
ejpam-4187	380	13	all	all	DET
ejpam-4187	380	14	the	the	DET
ejpam-4187	380	15	properties	property	NOUN
ejpam-4187	380	16	hold	hold	VERB
ejpam-4187	380	17	for	for	ADP
ejpam-4187	380	18	s.	s.	PROPN
ejpam-4187	380	19	first	first	ADV
ejpam-4187	380	20	,	,	PUNCT
ejpam-4187	380	21	using	use	VERB
ejpam-4187	380	22	theorem	theorem	NOUN
ejpam-4187	380	23	5	5	NUM
ejpam-4187	380	24	we	we	PRON
ejpam-4187	380	25	prove	prove	VERB
ejpam-4187	380	26	that	that	SCONJ
ejpam-4187	380	27	s	s	VERB
ejpam-4187	380	28	is	be	AUX
ejpam-4187	380	29	a	a	DET
ejpam-4187	380	30	disjunctive	disjunctive	ADJ
ejpam-4187	380	31	dominating	dominating	NOUN
ejpam-4187	380	32	set	set	NOUN
ejpam-4187	380	33	of	of	ADP
ejpam-4187	380	34	g	g	PROPN
ejpam-4187	380	35	◦	◦	NOUN
ejpam-4187	380	36	k1	k1	NOUN
ejpam-4187	380	37	.	.	PUNCT
ejpam-4187	381	1	let	let	VERB
ejpam-4187	381	2	v	v	NUM
ejpam-4187	381	3	∈	∈	PROPN
ejpam-4187	381	4	v	v	NOUN
ejpam-4187	381	5	(	(	PUNCT
ejpam-4187	381	6	g	g	NOUN
ejpam-4187	381	7	)	)	PUNCT
ejpam-4187	381	8	\	\	PUNCT
ejpam-4187	382	1	s.	s.	PROPN
ejpam-4187	382	2	by	by	ADP
ejpam-4187	382	3	property	property	NOUN
ejpam-4187	382	4	(	(	PUNCT
ejpam-4187	382	5	ii)(a	ii)(a	PROPN
ejpam-4187	382	6	)	)	PUNCT
ejpam-4187	382	7	,	,	PUNCT
ejpam-4187	382	8	if	if	SCONJ
ejpam-4187	382	9	uv	uv	NOUN
ejpam-4187	382	10	/∈	/∈	PUNCT
ejpam-4187	382	11	s	s	X
ejpam-4187	382	12	,	,	PUNCT
ejpam-4187	382	13	then	then	ADV
ejpam-4187	382	14	|s	|s	PROPN
ejpam-4187	382	15	∩	∩	PROPN
ejpam-4187	382	16	ng(v)|	ng(v)|	NUM
ejpam-4187	382	17	≥	≥	X
ejpam-4187	382	18	2	2	NUM
ejpam-4187	382	19	.	.	PUNCT
ejpam-4187	382	20	by	by	ADP
ejpam-4187	382	21	the	the	DET
ejpam-4187	382	22	same	same	ADJ
ejpam-4187	382	23	property	property	NOUN
ejpam-4187	382	24	,	,	PUNCT
ejpam-4187	382	25	if	if	SCONJ
ejpam-4187	382	26	|s	|s	PROPN
ejpam-4187	382	27	∩	∩	NOUN
ejpam-4187	382	28	ng(v)|	ng(v)|	NOUN
ejpam-4187	382	29	=	=	SYM
ejpam-4187	382	30	1	1	NUM
ejpam-4187	382	31	,	,	PUNCT
ejpam-4187	382	32	then	then	ADV
ejpam-4187	382	33	uv	uv	PROPN
ejpam-4187	382	34	∈	∈	PROPN
ejpam-4187	382	35	s	s	VERB
ejpam-4187	382	36	so	so	SCONJ
ejpam-4187	382	37	that	that	SCONJ
ejpam-4187	382	38	|s	|s	PROPN
ejpam-4187	382	39	∩	∩	PROPN
ejpam-4187	382	40	v	v	PROPN
ejpam-4187	382	41	(	(	PUNCT
ejpam-4187	382	42	kv	kv	PROPN
ejpam-4187	382	43	1	1	NUM
ejpam-4187	382	44	)	)	PUNCT
ejpam-4187	382	45	|	|	ADV
ejpam-4187	382	46	=	=	SYM
ejpam-4187	382	47	1	1	X
ejpam-4187	382	48	.	.	PUNCT
ejpam-4187	382	49	now	now	ADV
ejpam-4187	382	50	suppose	suppose	VERB
ejpam-4187	382	51	that	that	SCONJ
ejpam-4187	382	52	s	s	VERB
ejpam-4187	382	53	∩	∩	NOUN
ejpam-4187	382	54	ng(v	ng(v	X
ejpam-4187	382	55	)	)	PUNCT
ejpam-4187	382	56	=	=	PUNCT
ejpam-4187	382	57	∅.	∅.	AUX
ejpam-4187	382	58	note	note	VERB
ejpam-4187	382	59	that	that	SCONJ
ejpam-4187	382	60	either	either	CCONJ
ejpam-4187	382	61	uv	uv	PROPN
ejpam-4187	382	62	∈	∈	PROPN
ejpam-4187	382	63	s	s	PART
ejpam-4187	382	64	or	or	CCONJ
ejpam-4187	382	65	uv	uv	NOUN
ejpam-4187	382	66	/∈	/∈	PUNCT
ejpam-4187	382	67	s.	s.	PROPN
ejpam-4187	383	1	if	if	SCONJ
ejpam-4187	383	2	uv	uv	NOUN
ejpam-4187	383	3	/∈	/∈	PUNCT
ejpam-4187	384	1	s	s	X
ejpam-4187	384	2	,	,	PUNCT
ejpam-4187	384	3	then	then	ADV
ejpam-4187	384	4	by	by	ADP
ejpam-4187	384	5	property	property	NOUN
ejpam-4187	384	6	(	(	PUNCT
ejpam-4187	384	7	ii)(a	ii)(a	PROPN
ejpam-4187	384	8	)	)	PUNCT
ejpam-4187	384	9	,	,	PUNCT
ejpam-4187	385	1	|s	|s	PROPN
ejpam-4187	385	2	∩	∩	PROPN
ejpam-4187	385	3	ng(v)|	ng(v)|	NUM
ejpam-4187	385	4	≥	≥	X
ejpam-4187	385	5	2	2	NUM
ejpam-4187	385	6	,	,	PUNCT
ejpam-4187	385	7	a	a	DET
ejpam-4187	385	8	contradiction	contradiction	NOUN
ejpam-4187	385	9	.	.	PUNCT
ejpam-4187	386	1	thus	thus	ADV
ejpam-4187	386	2	,	,	PUNCT
ejpam-4187	386	3	uv	uv	PROPN
ejpam-4187	386	4	∈	∈	PROPN
ejpam-4187	386	5	s	s	PART
ejpam-4187	386	6	and	and	CCONJ
ejpam-4187	386	7	s	s	X
ejpam-4187	386	8	∩	∩	ADJ
ejpam-4187	386	9	v	v	X
ejpam-4187	386	10	(	(	PUNCT
ejpam-4187	386	11	kv	kv	PROPN
ejpam-4187	386	12	1	1	NUM
ejpam-4187	386	13	)	)	PUNCT
ejpam-4187	386	14	=	=	PRON
ejpam-4187	386	15	{	{	PUNCT
ejpam-4187	386	16	uv	uv	NOUN
ejpam-4187	386	17	}	}	PUNCT
ejpam-4187	386	18	is	be	AUX
ejpam-4187	386	19	a	a	DET
ejpam-4187	386	20	disjunctive	disjunctive	ADJ
ejpam-4187	386	21	dominating	dominating	NOUN
ejpam-4187	386	22	set	set	NOUN
ejpam-4187	386	23	of	of	ADP
ejpam-4187	386	24	kv	kv	PROPN
ejpam-4187	386	25	1	1	NUM
ejpam-4187	386	26	+	+	CCONJ
ejpam-4187	386	27	v.	v.	CCONJ
ejpam-4187	386	28	therefore	therefore	ADV
ejpam-4187	386	29	,	,	PUNCT
ejpam-4187	386	30	s	s	VERB
ejpam-4187	386	31	is	be	AUX
ejpam-4187	386	32	a	a	DET
ejpam-4187	386	33	disjunctive	disjunctive	ADJ
ejpam-4187	386	34	dominating	dominating	NOUN
ejpam-4187	386	35	set	set	NOUN
ejpam-4187	386	36	of	of	ADP
ejpam-4187	386	37	g	g	PROPN
ejpam-4187	386	38	◦	◦	NOUN
ejpam-4187	386	39	k1	k1	NOUN
ejpam-4187	386	40	.	.	PUNCT
ejpam-4187	387	1	now	now	ADV
ejpam-4187	387	2	,	,	PUNCT
ejpam-4187	387	3	we	we	PRON
ejpam-4187	387	4	show	show	VERB
ejpam-4187	387	5	that	that	SCONJ
ejpam-4187	387	6	s	s	VERB
ejpam-4187	387	7	is	be	AUX
ejpam-4187	387	8	a	a	DET
ejpam-4187	387	9	restrained	restrained	ADJ
ejpam-4187	387	10	disjunctive	disjunctive	ADJ
ejpam-4187	387	11	dominating	dominating	NOUN
ejpam-4187	387	12	set	set	NOUN
ejpam-4187	387	13	.	.	PUNCT
ejpam-4187	388	1	let	let	VERB
ejpam-4187	388	2	x	x	SYM
ejpam-4187	388	3	∈	∈	PROPN
ejpam-4187	388	4	v	v	X
ejpam-4187	388	5	(	(	PUNCT
ejpam-4187	388	6	g	g	PROPN
ejpam-4187	388	7	◦	◦	NOUN
ejpam-4187	388	8	k1	k1	NOUN
ejpam-4187	388	9	)	)	PUNCT
ejpam-4187	388	10	\	\	PUNCT
ejpam-4187	389	1	s.	s.	PROPN
ejpam-4187	389	2	suppose	suppose	VERB
ejpam-4187	389	3	that	that	SCONJ
ejpam-4187	389	4	x	x	X
ejpam-4187	389	5	=	=	PUNCT
ejpam-4187	389	6	uv	uv	NOUN
ejpam-4187	389	7	for	for	ADP
ejpam-4187	389	8	some	some	DET
ejpam-4187	389	9	v	v	ADP
ejpam-4187	389	10	∈	∈	NOUN
ejpam-4187	389	11	v	v	NOUN
ejpam-4187	389	12	(	(	PUNCT
ejpam-4187	389	13	g	g	NOUN
ejpam-4187	389	14	)	)	PUNCT
ejpam-4187	389	15	.	.	PUNCT
ejpam-4187	390	1	if	if	SCONJ
ejpam-4187	390	2	v	v	NUM
ejpam-4187	390	3	/∈	/∈	SYM
ejpam-4187	391	1	s	s	X
ejpam-4187	391	2	,	,	PUNCT
ejpam-4187	391	3	then	then	ADV
ejpam-4187	391	4	we	we	PRON
ejpam-4187	391	5	are	be	AUX
ejpam-4187	391	6	done	do	VERB
ejpam-4187	391	7	.	.	PUNCT
ejpam-4187	392	1	if	if	SCONJ
ejpam-4187	392	2	v	v	NUM
ejpam-4187	392	3	∈	∈	PROPN
ejpam-4187	392	4	s	s	NOUN
ejpam-4187	392	5	,	,	PUNCT
ejpam-4187	392	6	then	then	ADV
ejpam-4187	392	7	we	we	PRON
ejpam-4187	392	8	pick	pick	VERB
ejpam-4187	392	9	distinct	distinct	ADJ
ejpam-4187	392	10	w	w	PROPN
ejpam-4187	392	11	,	,	PUNCT
ejpam-4187	392	12	z	z	PROPN
ejpam-4187	392	13	∈	∈	PROPN
ejpam-4187	392	14	ng(v	ng(v	PUNCT
ejpam-4187	392	15	)	)	PUNCT
ejpam-4187	392	16	\	\	PUNCT
ejpam-4187	393	1	s	s	X
ejpam-4187	393	2	,	,	PUNCT
ejpam-4187	393	3	as	as	SCONJ
ejpam-4187	393	4	guaranteed	guarantee	VERB
ejpam-4187	393	5	by	by	ADP
ejpam-4187	393	6	property	property	NOUN
ejpam-4187	393	7	(	(	PUNCT
ejpam-4187	393	8	ii)(b	ii)(b	PROPN
ejpam-4187	393	9	)	)	PUNCT
ejpam-4187	393	10	.	.	PUNCT
ejpam-4187	394	1	then	then	ADV
ejpam-4187	394	2	dg	dg	VERB
ejpam-4187	394	3	◦	◦	NOUN
ejpam-4187	394	4	k1(x	k1(x	PROPN
ejpam-4187	394	5	,	,	PUNCT
ejpam-4187	394	6	w	w	NOUN
ejpam-4187	394	7	)	)	PUNCT
ejpam-4187	394	8	=	=	SYM
ejpam-4187	394	9	2	2	NUM
ejpam-4187	394	10	=	=	SYM
ejpam-4187	394	11	dg	dg	PROPN
ejpam-4187	394	12	◦	◦	NOUN
ejpam-4187	394	13	k1(x	k1(x	PROPN
ejpam-4187	394	14	,	,	PUNCT
ejpam-4187	394	15	z	z	NOUN
ejpam-4187	394	16	)	)	PUNCT
ejpam-4187	394	17	.	.	PUNCT
ejpam-4187	395	1	suppose	suppose	VERB
ejpam-4187	395	2	that	that	SCONJ
ejpam-4187	395	3	x	x	SYM
ejpam-4187	395	4	∈	∈	NOUN
ejpam-4187	395	5	v	v	X
ejpam-4187	395	6	(	(	PUNCT
ejpam-4187	395	7	g	g	NOUN
ejpam-4187	395	8	)	)	PUNCT
ejpam-4187	395	9	.	.	PUNCT
ejpam-4187	396	1	if	if	SCONJ
ejpam-4187	396	2	ux	ux	PROPN
ejpam-4187	396	3	/∈	/∈	PUNCT
ejpam-4187	396	4	s	s	X
ejpam-4187	396	5	or	or	CCONJ
ejpam-4187	396	6	ng(x	ng(x	NUM
ejpam-4187	396	7	)	)	PUNCT
ejpam-4187	396	8	\	\	PUNCT
ejpam-4187	397	1	s	s	PART
ejpam-4187	397	2	̸=	̸=	PROPN
ejpam-4187	397	3	∅	∅	NOUN
ejpam-4187	397	4	,	,	PUNCT
ejpam-4187	397	5	then	then	ADV
ejpam-4187	397	6	we	we	PRON
ejpam-4187	397	7	are	be	AUX
ejpam-4187	397	8	done	do	VERB
ejpam-4187	397	9	.	.	PUNCT
ejpam-4187	398	1	suppose	suppose	VERB
ejpam-4187	398	2	that	that	SCONJ
ejpam-4187	398	3	ux	ux	PROPN
ejpam-4187	398	4	∈	∈	PROPN
ejpam-4187	398	5	s	s	X
ejpam-4187	398	6	and	and	CCONJ
ejpam-4187	398	7	ng(x	ng(x	NUM
ejpam-4187	398	8	)	)	PUNCT
ejpam-4187	398	9	⊆	⊆	NUM
ejpam-4187	398	10	s.	s.	PROPN
ejpam-4187	398	11	properties	property	NOUN
ejpam-4187	398	12	(	(	PUNCT
ejpam-4187	398	13	iii)(a	iii)(a	PROPN
ejpam-4187	398	14	)	)	PUNCT
ejpam-4187	398	15	and	and	CCONJ
ejpam-4187	398	16	(	(	PUNCT
ejpam-4187	398	17	iii)(b	iii)(b	NOUN
ejpam-4187	398	18	)	)	PUNCT
ejpam-4187	398	19	imply	imply	VERB
ejpam-4187	398	20	that	that	SCONJ
ejpam-4187	398	21	there	there	PRON
ejpam-4187	398	22	exists	exist	VERB
ejpam-4187	398	23	distinct	distinct	ADJ
ejpam-4187	398	24	w	w	PROPN
ejpam-4187	398	25	,	,	PUNCT
ejpam-4187	398	26	z	z	PROPN
ejpam-4187	398	27	∈	∈	PROPN
ejpam-4187	398	28	v	v	NOUN
ejpam-4187	398	29	(	(	PUNCT
ejpam-4187	398	30	g	g	PROPN
ejpam-4187	398	31	◦	◦	NOUN
ejpam-4187	398	32	k1	k1	NOUN
ejpam-4187	398	33	)	)	PUNCT
ejpam-4187	398	34	\	\	PROPN
ejpam-4187	399	1	s	s	PART
ejpam-4187	399	2	for	for	ADP
ejpam-4187	399	3	which	which	PRON
ejpam-4187	399	4	dg	dg	VERB
ejpam-4187	399	5	◦	◦	NOUN
ejpam-4187	399	6	k1(x	k1(x	NOUN
ejpam-4187	399	7	,	,	PUNCT
ejpam-4187	399	8	w	w	NOUN
ejpam-4187	399	9	)	)	PUNCT
ejpam-4187	399	10	=	=	SYM
ejpam-4187	399	11	2	2	NUM
ejpam-4187	399	12	=	=	SYM
ejpam-4187	399	13	dg	dg	PROPN
ejpam-4187	399	14	◦	◦	NOUN
ejpam-4187	399	15	k1(x	k1(x	PROPN
ejpam-4187	399	16	,	,	PUNCT
ejpam-4187	399	17	z	z	NOUN
ejpam-4187	399	18	)	)	PUNCT
ejpam-4187	399	19	.	.	PUNCT
ejpam-4187	400	1	corollary	corollary	ADJ
ejpam-4187	400	2	4	4	NUM
ejpam-4187	400	3	.	.	PUNCT
ejpam-4187	401	1	for	for	ADP
ejpam-4187	401	2	a	a	DET
ejpam-4187	401	3	nontrivial	nontrivial	ADJ
ejpam-4187	401	4	connected	connect	VERB
ejpam-4187	401	5	graph	graph	NOUN
ejpam-4187	401	6	g	g	NOUN
ejpam-4187	401	7	,	,	PUNCT
ejpam-4187	401	8	|end(g)|	|end(g)|	NOUN
ejpam-4187	401	9	≤	≤	X
ejpam-4187	401	10	γdr	γdr	INTJ
ejpam-4187	401	11	(	(	PUNCT
ejpam-4187	401	12	g	g	PROPN
ejpam-4187	401	13	◦	◦	NOUN
ejpam-4187	401	14	k1	k1	NOUN
ejpam-4187	401	15	)	)	PUNCT
ejpam-4187	401	16	≤	≤	PUNCT
ejpam-4187	401	17	|v	|v	X
ejpam-4187	401	18	(	(	PUNCT
ejpam-4187	401	19	g)|	g)|	NOUN
ejpam-4187	401	20	,	,	PUNCT
ejpam-4187	401	21	and	and	CCONJ
ejpam-4187	401	22	these	these	DET
ejpam-4187	401	23	bounds	bound	NOUN
ejpam-4187	401	24	are	be	AUX
ejpam-4187	401	25	sharp	sharp	ADJ
ejpam-4187	401	26	.	.	PUNCT
ejpam-4187	402	1	proof	proof	NOUN
ejpam-4187	402	2	.	.	PUNCT
ejpam-4187	403	1	the	the	DET
ejpam-4187	403	2	left	left	ADJ
ejpam-4187	403	3	-	-	PUNCT
ejpam-4187	403	4	hand	hand	NOUN
ejpam-4187	403	5	inequality	inequality	NOUN
ejpam-4187	403	6	follows	follow	VERB
ejpam-4187	403	7	immediately	immediately	ADV
ejpam-4187	403	8	from	from	ADP
ejpam-4187	403	9	property	property	NOUN
ejpam-4187	403	10	(	(	PUNCT
ejpam-4187	403	11	i	i	NOUN
ejpam-4187	403	12	)	)	PUNCT
ejpam-4187	403	13	of	of	ADP
ejpam-4187	403	14	proposition	proposition	NOUN
ejpam-4187	403	15	2	2	NUM
ejpam-4187	403	16	for	for	ADP
ejpam-4187	403	17	any	any	DET
ejpam-4187	403	18	restrained	restrained	ADJ
ejpam-4187	403	19	disjunctive	disjunctive	ADJ
ejpam-4187	403	20	dominating	dominating	NOUN
ejpam-4187	403	21	set	set	NOUN
ejpam-4187	403	22	.	.	PUNCT
ejpam-4187	404	1	let	let	VERB
ejpam-4187	404	2	s	s	PRON
ejpam-4187	404	3	=	=	PUNCT
ejpam-4187	404	4	{	{	PUNCT
ejpam-4187	404	5	uv	uv	NOUN
ejpam-4187	404	6	:	:	PUNCT
ejpam-4187	404	7	v	v	NUM
ejpam-4187	404	8	∈	∈	PROPN
ejpam-4187	404	9	v	v	NOUN
ejpam-4187	404	10	(	(	PUNCT
ejpam-4187	404	11	g	g	NOUN
ejpam-4187	404	12	)	)	PUNCT
ejpam-4187	404	13	}	}	PUNCT
ejpam-4187	404	14	.	.	PUNCT
ejpam-4187	405	1	then	then	ADV
ejpam-4187	405	2	s	s	VERB
ejpam-4187	405	3	is	be	AUX
ejpam-4187	405	4	r.	r.	PROPN
ejpam-4187	405	5	malalay	malalay	PROPN
ejpam-4187	405	6	,	,	PUNCT
ejpam-4187	405	7	f.	f.	PROPN
ejpam-4187	405	8	jamil	jamil	PROPN
ejpam-4187	405	9	/	/	SYM
ejpam-4187	405	10	eur	eur	PROPN
ejpam-4187	405	11	.	.	PUNCT
ejpam-4187	406	1	j.	j.	PROPN
ejpam-4187	406	2	pure	pure	PROPN
ejpam-4187	406	3	appl	appl	PROPN
ejpam-4187	406	4	.	.	PROPN
ejpam-4187	406	5	math	math	PROPN
ejpam-4187	406	6	,	,	PUNCT
ejpam-4187	406	7	15	15	NUM
ejpam-4187	406	8	(	(	PUNCT
ejpam-4187	406	9	1	1	NUM
ejpam-4187	406	10	)	)	PUNCT
ejpam-4187	406	11	(	(	PUNCT
ejpam-4187	406	12	2022	2022	NUM
ejpam-4187	406	13	)	)	PUNCT
ejpam-4187	406	14	,	,	PUNCT
ejpam-4187	406	15	207	207	NUM
ejpam-4187	406	16	-	-	SYM
ejpam-4187	406	17	223	223	NUM
ejpam-4187	406	18	217	217	NUM
ejpam-4187	406	19	a	a	DET
ejpam-4187	406	20	restrained	restrained	ADJ
ejpam-4187	406	21	disjunctive	disjunctive	ADJ
ejpam-4187	406	22	dominating	dominating	NOUN
ejpam-4187	406	23	set	set	NOUN
ejpam-4187	406	24	of	of	ADP
ejpam-4187	406	25	g	g	PROPN
ejpam-4187	406	26	◦	◦	NOUN
ejpam-4187	406	27	k1	k1	NOUN
ejpam-4187	406	28	by	by	ADP
ejpam-4187	406	29	proposition	proposition	NOUN
ejpam-4187	406	30	2	2	NUM
ejpam-4187	406	31	,	,	PUNCT
ejpam-4187	406	32	and	and	CCONJ
ejpam-4187	406	33	the	the	DET
ejpam-4187	406	34	right	right	ADJ
ejpam-4187	406	35	-	-	PUNCT
ejpam-4187	406	36	hand	hand	NOUN
ejpam-4187	406	37	inequality	inequality	NOUN
ejpam-4187	406	38	follows	follow	VERB
ejpam-4187	406	39	.	.	PUNCT
ejpam-4187	407	1	for	for	ADP
ejpam-4187	407	2	the	the	DET
ejpam-4187	407	3	sharpness	sharpness	NOUN
ejpam-4187	407	4	of	of	ADP
ejpam-4187	407	5	the	the	DET
ejpam-4187	407	6	bounds	bound	NOUN
ejpam-4187	407	7	,	,	PUNCT
ejpam-4187	407	8	verify	verify	VERB
ejpam-4187	407	9	that	that	SCONJ
ejpam-4187	407	10	γdr	γdr	PROPN
ejpam-4187	408	1	(	(	PUNCT
ejpam-4187	408	2	k1,n	k1,n	PROPN
ejpam-4187	408	3	◦	◦	NOUN
ejpam-4187	408	4	k1	k1	PROPN
ejpam-4187	408	5	)	)	PUNCT
ejpam-4187	408	6	=	=	SYM
ejpam-4187	409	1	n	n	NOUN
ejpam-4187	409	2	=	=	SYM
ejpam-4187	409	3	|end(k1,n)|	|end(k1,n)|	NOUN
ejpam-4187	409	4	for	for	ADP
ejpam-4187	409	5	any	any	DET
ejpam-4187	409	6	n	n	PRON
ejpam-4187	409	7	≥	≥	NOUN
ejpam-4187	409	8	2	2	NUM
ejpam-4187	409	9	and	and	CCONJ
ejpam-4187	409	10	γdr	γdr	PROPN
ejpam-4187	409	11	(	(	PUNCT
ejpam-4187	409	12	p3	p3	PROPN
ejpam-4187	409	13	◦	◦	NOUN
ejpam-4187	409	14	k1	k1	NOUN
ejpam-4187	409	15	)	)	PUNCT
ejpam-4187	409	16	=	=	SYM
ejpam-4187	409	17	3	3	NUM
ejpam-4187	409	18	=	=	SYM
ejpam-4187	409	19	|v	|v	X
ejpam-4187	409	20	(	(	PUNCT
ejpam-4187	409	21	p3)|	p3)|	NOUN
ejpam-4187	409	22	.	.	PUNCT
ejpam-4187	410	1	corollary	corollary	ADJ
ejpam-4187	410	2	5	5	NUM
ejpam-4187	410	3	.	.	PUNCT
ejpam-4187	411	1	(	(	PUNCT
ejpam-4187	411	2	i	i	NOUN
ejpam-4187	411	3	)	)	PUNCT
ejpam-4187	411	4	for	for	ADP
ejpam-4187	411	5	n	n	X
ejpam-4187	411	6	≥	≥	NUM
ejpam-4187	411	7	3	3	NUM
ejpam-4187	411	8	,	,	PUNCT
ejpam-4187	411	9	γdr	γdr	INTJ
ejpam-4187	411	10	(	(	PUNCT
ejpam-4187	411	11	pn	pn	PROPN
ejpam-4187	411	12	◦	◦	NOUN
ejpam-4187	411	13	k1	k1	PROPN
ejpam-4187	411	14	)	)	PUNCT
ejpam-4187	411	15	=	=	SYM
ejpam-4187	411	16	⌊n2	⌊n2	X
ejpam-4187	411	17	⌋+	⌋+	X
ejpam-4187	411	18	2	2	NUM
ejpam-4187	411	19	,	,	PUNCT
ejpam-4187	411	20	(	(	PUNCT
ejpam-4187	411	21	ii	ii	NOUN
ejpam-4187	411	22	)	)	PUNCT
ejpam-4187	411	23	for	for	ADP
ejpam-4187	411	24	n	n	X
ejpam-4187	411	25	≥	≥	NUM
ejpam-4187	411	26	3	3	NUM
ejpam-4187	411	27	,	,	PUNCT
ejpam-4187	411	28	γdr	γdr	PROPN
ejpam-4187	411	29	(	(	PUNCT
ejpam-4187	411	30	cn	cn	PROPN
ejpam-4187	411	31	◦	◦	NOUN
ejpam-4187	411	32	k1	k1	NOUN
ejpam-4187	411	33	)	)	PUNCT
ejpam-4187	412	1	=	=	PRON
ejpam-4187	412	2	{	{	PUNCT
ejpam-4187	412	3	⌊n2	⌊n2	X
ejpam-4187	412	4	⌋	⌋	ADJ
ejpam-4187	412	5	,	,	PUNCT
ejpam-4187	412	6	if	if	SCONJ
ejpam-4187	412	7	n	n	PRON
ejpam-4187	412	8	≡	≡	PROPN
ejpam-4187	412	9	0(mod	0(mod	NOUN
ejpam-4187	412	10	2	2	NUM
ejpam-4187	412	11	)	)	PUNCT
ejpam-4187	412	12	⌊n2	⌊n2	PUNCT
ejpam-4187	412	13	⌋+	⌋+	X
ejpam-4187	413	1	2	2	NUM
ejpam-4187	413	2	,	,	PUNCT
ejpam-4187	413	3	otherwise	otherwise	ADV
ejpam-4187	413	4	;	;	PUNCT
ejpam-4187	413	5	and	and	CCONJ
ejpam-4187	413	6	(	(	PUNCT
ejpam-4187	413	7	iii	iii	NOUN
ejpam-4187	413	8	)	)	PUNCT
ejpam-4187	413	9	for	for	ADP
ejpam-4187	413	10	m	m	PROPN
ejpam-4187	413	11	,	,	PUNCT
ejpam-4187	413	12	n	n	PRON
ejpam-4187	413	13	≥	≥	NOUN
ejpam-4187	413	14	2	2	NUM
ejpam-4187	413	15	,	,	PUNCT
ejpam-4187	413	16	γdr	γdr	PROPN
ejpam-4187	413	17	(	(	PUNCT
ejpam-4187	413	18	km	km	PROPN
ejpam-4187	413	19	,	,	PUNCT
ejpam-4187	413	20	n	n	PRON
ejpam-4187	413	21	◦	◦	NOUN
ejpam-4187	413	22	k1	k1	NOUN
ejpam-4187	413	23	)	)	PUNCT
ejpam-4187	413	24	=	=	SYM
ejpam-4187	413	25	min{m	min{m	PROPN
ejpam-4187	413	26	,	,	PUNCT
ejpam-4187	413	27	n	n	CCONJ
ejpam-4187	413	28	,	,	PUNCT
ejpam-4187	413	29	4	4	NUM
ejpam-4187	413	30	}	}	PUNCT
ejpam-4187	413	31	.	.	PUNCT
ejpam-4187	414	1	proof	proof	NOUN
ejpam-4187	414	2	.	.	PUNCT
ejpam-4187	415	1	let	let	VERB
ejpam-4187	415	2	pn	pn	VERB
ejpam-4187	415	3	=	=	PUNCT
ejpam-4187	416	1	[	[	X
ejpam-4187	416	2	x1	x1	PROPN
ejpam-4187	416	3	,	,	PUNCT
ejpam-4187	416	4	x2	x2	PROPN
ejpam-4187	416	5	,	,	PUNCT
ejpam-4187	416	6	.	.	PUNCT
ejpam-4187	416	7	.	.	PUNCT
ejpam-4187	417	1	.	.	PUNCT
ejpam-4187	418	1	,	,	PUNCT
ejpam-4187	418	2	xn	xn	X
ejpam-4187	418	3	]	]	PUNCT
ejpam-4187	418	4	and	and	CCONJ
ejpam-4187	418	5	k	k	X
ejpam-4187	418	6	=	=	PUNCT
ejpam-4187	418	7	⌊n2	⌊n2	X
ejpam-4187	418	8	⌋.	⌋.	X
ejpam-4187	418	9	since	since	SCONJ
ejpam-4187	418	10	by	by	ADP
ejpam-4187	418	11	proposition	proposition	NOUN
ejpam-4187	418	12	2	2	NUM
ejpam-4187	418	13	,	,	PUNCT
ejpam-4187	418	14	the	the	DET
ejpam-4187	418	15	set	set	NOUN
ejpam-4187	418	16	{	{	PUNCT
ejpam-4187	418	17	ux1	ux1	PROPN
ejpam-4187	418	18	,	,	PUNCT
ejpam-4187	418	19	x2	x2	PROPN
ejpam-4187	418	20	,	,	PUNCT
ejpam-4187	418	21	x4	x4	PROPN
ejpam-4187	418	22	,	,	PUNCT
ejpam-4187	418	23	.	.	PUNCT
ejpam-4187	418	24	.	.	PUNCT
ejpam-4187	418	25	.	.	PUNCT
ejpam-4187	419	1	,	,	PUNCT
ejpam-4187	419	2	x2k	x2k	NOUN
ejpam-4187	419	3	,	,	PUNCT
ejpam-4187	419	4	u	u	NOUN
ejpam-4187	419	5	xn	xn	PROPN
ejpam-4187	419	6	}	}	PUNCT
ejpam-4187	419	7	is	be	AUX
ejpam-4187	419	8	a	a	DET
ejpam-4187	419	9	restrained	restrain	VERB
ejpam-4187	419	10	dominating	dominating	NOUN
ejpam-4187	419	11	set	set	NOUN
ejpam-4187	419	12	,	,	PUNCT
ejpam-4187	419	13	γdr	γdr	PROPN
ejpam-4187	419	14	(	(	PUNCT
ejpam-4187	419	15	pn	pn	NOUN
ejpam-4187	419	16	)	)	PUNCT
ejpam-4187	419	17	≤	≤	NOUN
ejpam-4187	420	1	k	k	NOUN
ejpam-4187	421	1	+	+	CCONJ
ejpam-4187	421	2	2	2	X
ejpam-4187	421	3	.	.	PUNCT
ejpam-4187	421	4	suppose	suppose	VERB
ejpam-4187	421	5	that	that	SCONJ
ejpam-4187	421	6	s	s	VERB
ejpam-4187	421	7	⊆	⊆	NUM
ejpam-4187	421	8	v	v	NOUN
ejpam-4187	421	9	(	(	PUNCT
ejpam-4187	421	10	g	g	PROPN
ejpam-4187	421	11	◦	◦	NOUN
ejpam-4187	421	12	k1	k1	NOUN
ejpam-4187	421	13	)	)	PUNCT
ejpam-4187	421	14	is	be	AUX
ejpam-4187	421	15	a	a	DET
ejpam-4187	421	16	restrained	restrained	ADJ
ejpam-4187	421	17	disjunctive	disjunctive	ADJ
ejpam-4187	421	18	dominating	dominating	NOUN
ejpam-4187	421	19	set	set	NOUN
ejpam-4187	421	20	of	of	ADP
ejpam-4187	421	21	g	g	PROPN
ejpam-4187	421	22	◦	◦	NOUN
ejpam-4187	421	23	k1	k1	NOUN
ejpam-4187	421	24	with	with	ADP
ejpam-4187	421	25	|s|	|s|	NOUN
ejpam-4187	421	26	≤	≤	NUM
ejpam-4187	421	27	k	k	NOUN
ejpam-4187	422	1	+	+	PROPN
ejpam-4187	422	2	1	1	X
ejpam-4187	422	3	.	.	PUNCT
ejpam-4187	422	4	accordingly	accordingly	ADV
ejpam-4187	422	5	,	,	PUNCT
ejpam-4187	422	6	{	{	PUNCT
ejpam-4187	422	7	ux1	ux1	NOUN
ejpam-4187	422	8	,	,	PUNCT
ejpam-4187	422	9	uxn	uxn	NOUN
ejpam-4187	422	10	}	}	PUNCT
ejpam-4187	422	11	⊆	⊆	NUM
ejpam-4187	422	12	s.	s.	PROPN
ejpam-4187	422	13	apparently	apparently	ADV
ejpam-4187	422	14	,	,	PUNCT
ejpam-4187	422	15	there	there	PRON
ejpam-4187	422	16	exist	exist	VERB
ejpam-4187	422	17	w	w	PROPN
ejpam-4187	422	18	,	,	PUNCT
ejpam-4187	422	19	v	v	NOUN
ejpam-4187	422	20	∈	∈	PROPN
ejpam-4187	422	21	v	v	NOUN
ejpam-4187	422	22	(	(	PUNCT
ejpam-4187	422	23	pn	pn	NOUN
ejpam-4187	422	24	)	)	PUNCT
ejpam-4187	422	25	for	for	ADP
ejpam-4187	422	26	which	which	PRON
ejpam-4187	422	27	wv	wv	PROPN
ejpam-4187	422	28	∈	∈	PROPN
ejpam-4187	422	29	e(g	e(g	PROPN
ejpam-4187	422	30	)	)	PUNCT
ejpam-4187	422	31	and	and	CCONJ
ejpam-4187	422	32	all	all	DET
ejpam-4187	422	33	vertices	vertice	VERB
ejpam-4187	422	34	w	w	PROPN
ejpam-4187	422	35	,	,	PUNCT
ejpam-4187	422	36	v	v	NOUN
ejpam-4187	422	37	,	,	PUNCT
ejpam-4187	422	38	uv	uv	NOUN
ejpam-4187	422	39	,	,	PUNCT
ejpam-4187	422	40	uw	uw	PROPN
ejpam-4187	422	41	/∈	/∈	PUNCT
ejpam-4187	422	42	s.	s.	PROPN
ejpam-4187	422	43	in	in	ADP
ejpam-4187	422	44	particular	particular	ADJ
ejpam-4187	422	45	,	,	PUNCT
ejpam-4187	422	46	|ng(v	|ng(v	ADJ
ejpam-4187	422	47	)	)	PUNCT
ejpam-4187	422	48	∩	∩	NOUN
ejpam-4187	422	49	s|	s|	VERB
ejpam-4187	422	50	≥	≥	NOUN
ejpam-4187	422	51	2	2	NUM
ejpam-4187	422	52	by	by	ADP
ejpam-4187	422	53	proposition	proposition	NOUN
ejpam-4187	422	54	2	2	NUM
ejpam-4187	422	55	,	,	PUNCT
ejpam-4187	422	56	which	which	PRON
ejpam-4187	422	57	is	be	AUX
ejpam-4187	422	58	impossible	impossible	ADJ
ejpam-4187	422	59	since	since	SCONJ
ejpam-4187	422	60	w	w	PROPN
ejpam-4187	422	61	/∈	/∈	PROPN
ejpam-4187	422	62	s.	s.	PROPN
ejpam-4187	422	63	thus	thus	ADV
ejpam-4187	422	64	,	,	PUNCT
ejpam-4187	422	65	γdr	γdr	INTJ
ejpam-4187	422	66	(	(	PUNCT
ejpam-4187	422	67	pn	pn	NOUN
ejpam-4187	422	68	◦	◦	PROPN
ejpam-4187	422	69	k1	k1	PROPN
ejpam-4187	422	70	)	)	PUNCT
ejpam-4187	422	71	≥	≥	NOUN
ejpam-4187	422	72	k	k	X
ejpam-4187	423	1	+	+	CCONJ
ejpam-4187	423	2	2	2	X
ejpam-4187	423	3	.	.	PUNCT
ejpam-4187	423	4	this	this	PRON
ejpam-4187	423	5	proves	prove	VERB
ejpam-4187	423	6	property	property	NOUN
ejpam-4187	423	7	(	(	PUNCT
ejpam-4187	423	8	i	i	NOUN
ejpam-4187	423	9	)	)	PUNCT
ejpam-4187	423	10	.	.	PUNCT
ejpam-4187	424	1	to	to	PART
ejpam-4187	424	2	prove	prove	VERB
ejpam-4187	424	3	(	(	PUNCT
ejpam-4187	424	4	ii	ii	NOUN
ejpam-4187	424	5	)	)	PUNCT
ejpam-4187	424	6	,	,	PUNCT
ejpam-4187	424	7	let	let	VERB
ejpam-4187	424	8	cn	cn	PROPN
ejpam-4187	424	9	=	=	PUNCT
ejpam-4187	425	1	[	[	X
ejpam-4187	425	2	x1	x1	PROPN
ejpam-4187	425	3	,	,	PUNCT
ejpam-4187	425	4	x2	x2	PROPN
ejpam-4187	425	5	,	,	PUNCT
ejpam-4187	425	6	.	.	PUNCT
ejpam-4187	425	7	.	.	PUNCT
ejpam-4187	426	1	.	.	PUNCT
ejpam-4187	427	1	,	,	PUNCT
ejpam-4187	427	2	xn	xn	PROPN
ejpam-4187	427	3	]	]	PUNCT
ejpam-4187	427	4	.	.	PUNCT
ejpam-4187	428	1	let	let	VERB
ejpam-4187	428	2	k	k	PROPN
ejpam-4187	428	3	=	=	PUNCT
ejpam-4187	428	4	⌊n2	⌊n2	X
ejpam-4187	428	5	⌋.	⌋.	X
ejpam-4187	429	1	if	if	SCONJ
ejpam-4187	429	2	n	n	PROPN
ejpam-4187	429	3	=	=	SYM
ejpam-4187	429	4	2k	2k	NUM
ejpam-4187	429	5	,	,	PUNCT
ejpam-4187	429	6	then	then	ADV
ejpam-4187	429	7	the	the	DET
ejpam-4187	429	8	set	set	NOUN
ejpam-4187	429	9	{	{	PUNCT
ejpam-4187	429	10	x2	x2	PROPN
ejpam-4187	429	11	,	,	PUNCT
ejpam-4187	429	12	x4	x4	PROPN
ejpam-4187	429	13	,	,	PUNCT
ejpam-4187	429	14	.	.	PUNCT
ejpam-4187	429	15	.	.	PUNCT
ejpam-4187	429	16	.	.	PUNCT
ejpam-4187	430	1	,	,	PUNCT
ejpam-4187	430	2	x2k	x2k	NOUN
ejpam-4187	430	3	}	}	PUNCT
ejpam-4187	430	4	is	be	AUX
ejpam-4187	430	5	a	a	DET
ejpam-4187	430	6	restrained	restrained	ADJ
ejpam-4187	430	7	disjunctive	disjunctive	ADJ
ejpam-4187	430	8	dominating	dominating	NOUN
ejpam-4187	430	9	set	set	NOUN
ejpam-4187	430	10	of	of	ADP
ejpam-4187	430	11	cn	cn	PROPN
ejpam-4187	430	12	◦	◦	PROPN
ejpam-4187	430	13	k1	k1	NOUN
ejpam-4187	430	14	so	so	SCONJ
ejpam-4187	430	15	that	that	SCONJ
ejpam-4187	430	16	γdr	γdr	INTJ
ejpam-4187	430	17	(	(	PUNCT
ejpam-4187	430	18	cn	cn	PROPN
ejpam-4187	430	19	◦	◦	NOUN
ejpam-4187	430	20	k1	k1	NOUN
ejpam-4187	430	21	)	)	PUNCT
ejpam-4187	430	22	≤	≤	NOUN
ejpam-4187	430	23	k.	k.	ADV
ejpam-4187	431	1	on	on	ADP
ejpam-4187	431	2	the	the	DET
ejpam-4187	431	3	other	other	ADJ
ejpam-4187	431	4	hand	hand	NOUN
ejpam-4187	431	5	,	,	PUNCT
ejpam-4187	431	6	if	if	SCONJ
ejpam-4187	431	7	n	n	NOUN
ejpam-4187	431	8	=	=	SYM
ejpam-4187	431	9	2k+1	2k+1	NOUN
ejpam-4187	431	10	,	,	PUNCT
ejpam-4187	431	11	then	then	ADV
ejpam-4187	431	12	the	the	DET
ejpam-4187	431	13	set	set	NOUN
ejpam-4187	431	14	{	{	PUNCT
ejpam-4187	431	15	ux1	ux1	PROPN
ejpam-4187	431	16	,	,	PUNCT
ejpam-4187	431	17	x2	x2	PROPN
ejpam-4187	431	18	,	,	PUNCT
ejpam-4187	431	19	x4	x4	PROPN
ejpam-4187	431	20	,	,	PUNCT
ejpam-4187	431	21	.	.	PUNCT
ejpam-4187	431	22	.	.	PUNCT
ejpam-4187	431	23	.	.	PUNCT
ejpam-4187	432	1	,	,	PUNCT
ejpam-4187	432	2	x2k	x2k	NOUN
ejpam-4187	432	3	,	,	PUNCT
ejpam-4187	432	4	u	u	NOUN
ejpam-4187	432	5	xn	xn	PROPN
ejpam-4187	432	6	}	}	PUNCT
ejpam-4187	432	7	is	be	AUX
ejpam-4187	432	8	a	a	DET
ejpam-4187	432	9	restrained	restrained	ADJ
ejpam-4187	432	10	disjunctive	disjunctive	ADJ
ejpam-4187	432	11	dominating	dominating	NOUN
ejpam-4187	432	12	set	set	NOUN
ejpam-4187	432	13	of	of	ADP
ejpam-4187	432	14	cn	cn	PROPN
ejpam-4187	432	15	◦	◦	NOUN
ejpam-4187	432	16	k1	k1	PROPN
ejpam-4187	432	17	,	,	PUNCT
ejpam-4187	432	18	and	and	CCONJ
ejpam-4187	432	19	so	so	ADV
ejpam-4187	432	20	γdr	γdr	INTJ
ejpam-4187	432	21	(	(	PUNCT
ejpam-4187	432	22	cn	cn	PROPN
ejpam-4187	432	23	◦	◦	NOUN
ejpam-4187	432	24	k1	k1	NOUN
ejpam-4187	432	25	)	)	PUNCT
ejpam-4187	432	26	≤	≤	PUNCT
ejpam-4187	433	1	k	k	NOUN
ejpam-4187	434	1	+	+	PROPN
ejpam-4187	434	2	2	2	X
ejpam-4187	434	3	.	.	PUNCT
ejpam-4187	434	4	following	follow	VERB
ejpam-4187	434	5	similar	similar	ADJ
ejpam-4187	434	6	arguments	argument	NOUN
ejpam-4187	434	7	as	as	ADP
ejpam-4187	434	8	in	in	ADP
ejpam-4187	434	9	the	the	DET
ejpam-4187	434	10	proof	proof	NOUN
ejpam-4187	434	11	for	for	ADP
ejpam-4187	434	12	pn	pn	PROPN
ejpam-4187	434	13	,	,	PUNCT
ejpam-4187	434	14	the	the	DET
ejpam-4187	434	15	desired	desire	VERB
ejpam-4187	434	16	equality	equality	NOUN
ejpam-4187	434	17	is	be	AUX
ejpam-4187	434	18	attained	attain	VERB
ejpam-4187	434	19	.	.	PUNCT
ejpam-4187	435	1	let	let	VERB
ejpam-4187	435	2	u	u	PRON
ejpam-4187	435	3	and	and	CCONJ
ejpam-4187	435	4	v	v	NOUN
ejpam-4187	435	5	be	be	AUX
ejpam-4187	435	6	the	the	DET
ejpam-4187	435	7	partite	partite	ADJ
ejpam-4187	435	8	sets	set	NOUN
ejpam-4187	435	9	of	of	ADP
ejpam-4187	435	10	km	km	PROPN
ejpam-4187	435	11	,	,	PUNCT
ejpam-4187	435	12	n	n	CCONJ
ejpam-4187	435	13	with	with	ADP
ejpam-4187	435	14	|u	|u	ADJ
ejpam-4187	435	15	|	|	NOUN
ejpam-4187	435	16	=	=	NOUN
ejpam-4187	435	17	m	m	NOUN
ejpam-4187	435	18	and	and	CCONJ
ejpam-4187	435	19	|v	|v	VERB
ejpam-4187	435	20	|	|	ADV
ejpam-4187	435	21	=	=	PUNCT
ejpam-4187	435	22	n.	n.	NOUN
ejpam-4187	435	23	by	by	ADP
ejpam-4187	435	24	proposition	proposition	NOUN
ejpam-4187	435	25	2	2	NUM
ejpam-4187	435	26	,	,	PUNCT
ejpam-4187	435	27	u	u	NOUN
ejpam-4187	435	28	or	or	CCONJ
ejpam-4187	435	29	v	v	NOUN
ejpam-4187	435	30	are	be	AUX
ejpam-4187	435	31	restrained	restrain	VERB
ejpam-4187	435	32	disjunctive	disjunctive	ADJ
ejpam-4187	435	33	dominating	dominating	NOUN
ejpam-4187	435	34	sets	set	NOUN
ejpam-4187	435	35	of	of	ADP
ejpam-4187	435	36	km	km	PROPN
ejpam-4187	435	37	,	,	PUNCT
ejpam-4187	435	38	n	n	PRON
ejpam-4187	435	39	◦	◦	NOUN
ejpam-4187	435	40	k1	k1	NOUN
ejpam-4187	435	41	.	.	PUNCT
ejpam-4187	436	1	suppose	suppose	VERB
ejpam-4187	436	2	that	that	SCONJ
ejpam-4187	436	3	m	m	PROPN
ejpam-4187	436	4	≥	≥	NUM
ejpam-4187	436	5	4	4	NUM
ejpam-4187	436	6	and	and	CCONJ
ejpam-4187	436	7	n	n	PRON
ejpam-4187	436	8	≥	≥	NOUN
ejpam-4187	436	9	4	4	NUM
ejpam-4187	436	10	.	.	X
ejpam-4187	436	11	pick	pick	VERB
ejpam-4187	436	12	x	x	SYM
ejpam-4187	436	13	,	,	PUNCT
ejpam-4187	436	14	y	y	PROPN
ejpam-4187	436	15	∈	∈	PROPN
ejpam-4187	436	16	u	u	NOUN
ejpam-4187	436	17	and	and	CCONJ
ejpam-4187	436	18	a	a	DET
ejpam-4187	436	19	,	,	PUNCT
ejpam-4187	436	20	b	b	PROPN
ejpam-4187	436	21	∈	∈	PROPN
ejpam-4187	436	22	v	v	NOUN
ejpam-4187	436	23	.	.	PUNCT
ejpam-4187	437	1	by	by	ADP
ejpam-4187	437	2	proposition	proposition	NOUN
ejpam-4187	437	3	2	2	NUM
ejpam-4187	437	4	,	,	PUNCT
ejpam-4187	437	5	s	s	PART
ejpam-4187	437	6	=	=	PUNCT
ejpam-4187	437	7	{	{	PUNCT
ejpam-4187	437	8	x	x	PROPN
ejpam-4187	437	9	,	,	PUNCT
ejpam-4187	437	10	y	y	PROPN
ejpam-4187	437	11	,	,	PUNCT
ejpam-4187	437	12	a	a	DET
ejpam-4187	437	13	,	,	PUNCT
ejpam-4187	437	14	b	b	NOUN
ejpam-4187	437	15	}	}	PUNCT
ejpam-4187	437	16	is	be	AUX
ejpam-4187	437	17	a	a	DET
ejpam-4187	437	18	restrained	restrained	ADJ
ejpam-4187	437	19	disjunctive	disjunctive	ADJ
ejpam-4187	437	20	dominating	dominating	NOUN
ejpam-4187	437	21	set	set	NOUN
ejpam-4187	437	22	of	of	ADP
ejpam-4187	437	23	km	km	PROPN
ejpam-4187	437	24	,	,	PUNCT
ejpam-4187	437	25	n	n	PRON
ejpam-4187	437	26	◦	◦	NOUN
ejpam-4187	437	27	k1	k1	NOUN
ejpam-4187	437	28	.	.	PUNCT
ejpam-4187	438	1	thus	thus	ADV
ejpam-4187	438	2	,	,	PUNCT
ejpam-4187	438	3	γdr	γdr	INTJ
ejpam-4187	438	4	(	(	PUNCT
ejpam-4187	438	5	km	km	PROPN
ejpam-4187	438	6	,	,	PUNCT
ejpam-4187	438	7	n	n	PRON
ejpam-4187	438	8	◦	◦	NOUN
ejpam-4187	438	9	k1	k1	NOUN
ejpam-4187	438	10	)	)	PUNCT
ejpam-4187	438	11	≤	≤	NUM
ejpam-4187	438	12	min	min	NOUN
ejpam-4187	438	13	{	{	PUNCT
ejpam-4187	438	14	m	m	PROPN
ejpam-4187	438	15	,	,	PUNCT
ejpam-4187	438	16	n	n	CCONJ
ejpam-4187	438	17	,	,	PUNCT
ejpam-4187	438	18	4	4	NUM
ejpam-4187	438	19	}	}	PUNCT
ejpam-4187	438	20	.	.	PUNCT
ejpam-4187	439	1	now	now	ADV
ejpam-4187	439	2	,	,	PUNCT
ejpam-4187	439	3	let	let	VERB
ejpam-4187	439	4	s	s	PRON
ejpam-4187	439	5	⊆	⊆	NUM
ejpam-4187	439	6	v	v	NOUN
ejpam-4187	439	7	(	(	PUNCT
ejpam-4187	439	8	km	km	PROPN
ejpam-4187	439	9	,	,	PUNCT
ejpam-4187	439	10	n	n	PRON
ejpam-4187	439	11	◦	◦	NOUN
ejpam-4187	439	12	k1	k1	NOUN
ejpam-4187	439	13	)	)	PUNCT
ejpam-4187	439	14	be	be	VERB
ejpam-4187	439	15	a	a	DET
ejpam-4187	439	16	restrained	restrained	ADJ
ejpam-4187	439	17	disjunctive	disjunctive	ADJ
ejpam-4187	439	18	dominating	dominating	NOUN
ejpam-4187	439	19	set	set	NOUN
ejpam-4187	439	20	of	of	ADP
ejpam-4187	439	21	km	km	PROPN
ejpam-4187	439	22	,	,	PUNCT
ejpam-4187	439	23	n	n	PRON
ejpam-4187	439	24	◦	◦	NOUN
ejpam-4187	439	25	k1	k1	NOUN
ejpam-4187	439	26	.	.	PUNCT
ejpam-4187	439	27	suppose	suppose	VERB
ejpam-4187	439	28	that	that	SCONJ
ejpam-4187	439	29	|s|	|s|	VERB
ejpam-4187	439	30	≤	≤	ADV
ejpam-4187	439	31	3	3	NUM
ejpam-4187	439	32	.	.	PUNCT
ejpam-4187	440	1	then	then	ADV
ejpam-4187	440	2	there	there	PRON
ejpam-4187	440	3	exists	exist	VERB
ejpam-4187	440	4	v	v	ADP
ejpam-4187	440	5	∈	∈	PROPN
ejpam-4187	440	6	v	v	NOUN
ejpam-4187	440	7	(	(	PUNCT
ejpam-4187	440	8	km	km	PROPN
ejpam-4187	440	9	,	,	PUNCT
ejpam-4187	440	10	n	n	PRON
ejpam-4187	440	11	◦	◦	NOUN
ejpam-4187	440	12	k1	k1	NOUN
ejpam-4187	440	13	)	)	PUNCT
ejpam-4187	440	14	for	for	ADP
ejpam-4187	440	15	which	which	PRON
ejpam-4187	440	16	uv	uv	NOUN
ejpam-4187	440	17	∈	∈	PROPN
ejpam-4187	440	18	s.	s.	PROPN
ejpam-4187	440	19	in	in	ADP
ejpam-4187	440	20	view	view	NOUN
ejpam-4187	440	21	of	of	ADP
ejpam-4187	440	22	proposition	proposition	NOUN
ejpam-4187	440	23	2	2	NUM
ejpam-4187	440	24	,	,	PUNCT
ejpam-4187	440	25	this	this	PRON
ejpam-4187	440	26	is	be	AUX
ejpam-4187	440	27	only	only	ADV
ejpam-4187	440	28	possible	possible	ADJ
ejpam-4187	440	29	if	if	SCONJ
ejpam-4187	440	30	s	s	VERB
ejpam-4187	440	31	=	=	NOUN
ejpam-4187	440	32	u	u	NOUN
ejpam-4187	440	33	or	or	CCONJ
ejpam-4187	440	34	s	s	NOUN
ejpam-4187	440	35	=	=	X
ejpam-4187	440	36	v	v	NOUN
ejpam-4187	440	37	.	.	PUNCT
ejpam-4187	441	1	thus	thus	ADV
ejpam-4187	441	2	,	,	PUNCT
ejpam-4187	441	3	γdr	γdr	INTJ
ejpam-4187	441	4	(	(	PUNCT
ejpam-4187	441	5	km	km	PROPN
ejpam-4187	441	6	,	,	PUNCT
ejpam-4187	441	7	n	n	PRON
ejpam-4187	441	8	◦	◦	NOUN
ejpam-4187	441	9	k1	k1	NOUN
ejpam-4187	441	10	)	)	PUNCT
ejpam-4187	441	11	≥	≥	PROPN
ejpam-4187	441	12	min	min	PROPN
ejpam-4187	441	13	{	{	PUNCT
ejpam-4187	441	14	m	m	PROPN
ejpam-4187	441	15	,	,	PUNCT
ejpam-4187	441	16	n	n	CCONJ
ejpam-4187	441	17	,	,	PUNCT
ejpam-4187	441	18	4	4	NUM
ejpam-4187	441	19	}	}	PUNCT
ejpam-4187	441	20	.	.	PUNCT
ejpam-4187	442	1	theorem	theorem	NOUN
ejpam-4187	442	2	6	6	NUM
ejpam-4187	442	3	.	.	PUNCT
ejpam-4187	443	1	let	let	VERB
ejpam-4187	443	2	g	g	NOUN
ejpam-4187	443	3	and	and	CCONJ
ejpam-4187	443	4	h	h	NOUN
ejpam-4187	443	5	be	be	AUX
ejpam-4187	443	6	nontrivial	nontrivial	ADJ
ejpam-4187	443	7	connected	connected	ADJ
ejpam-4187	443	8	graphs	graph	NOUN
ejpam-4187	443	9	,	,	PUNCT
ejpam-4187	443	10	and	and	CCONJ
ejpam-4187	443	11	let	let	VERB
ejpam-4187	443	12	s	s	PRON
ejpam-4187	443	13	⊆	⊆	NUM
ejpam-4187	443	14	v	v	NOUN
ejpam-4187	443	15	(	(	PUNCT
ejpam-4187	443	16	g	g	PROPN
ejpam-4187	443	17	◦	◦	NOUN
ejpam-4187	443	18	h	h	NOUN
ejpam-4187	443	19	)	)	PUNCT
ejpam-4187	443	20	.	.	PUNCT
ejpam-4187	444	1	then	then	ADV
ejpam-4187	444	2	s	s	VERB
ejpam-4187	444	3	is	be	AUX
ejpam-4187	444	4	a	a	DET
ejpam-4187	444	5	restrained	restrained	ADJ
ejpam-4187	444	6	disjunctive	disjunctive	ADJ
ejpam-4187	444	7	dominating	dominating	NOUN
ejpam-4187	444	8	set	set	NOUN
ejpam-4187	444	9	of	of	ADP
ejpam-4187	444	10	g	g	PROPN
ejpam-4187	444	11	◦	◦	NOUN
ejpam-4187	444	12	h	h	NOUN
ejpam-4187	444	13	if	if	SCONJ
ejpam-4187	445	1	and	and	CCONJ
ejpam-4187	445	2	only	only	ADV
ejpam-4187	445	3	if	if	SCONJ
ejpam-4187	445	4	s	s	ADP
ejpam-4187	445	5	satisfies	satisfy	VERB
ejpam-4187	445	6	all	all	DET
ejpam-4187	445	7	the	the	DET
ejpam-4187	445	8	properties	property	NOUN
ejpam-4187	445	9	in	in	ADP
ejpam-4187	445	10	theorem	theorem	NOUN
ejpam-4187	445	11	5	5	NUM
ejpam-4187	445	12	as	as	ADV
ejpam-4187	445	13	well	well	ADV
ejpam-4187	445	14	as	as	ADP
ejpam-4187	445	15	each	each	PRON
ejpam-4187	445	16	of	of	ADP
ejpam-4187	445	17	the	the	DET
ejpam-4187	445	18	following	follow	VERB
ejpam-4187	445	19	properties	property	NOUN
ejpam-4187	445	20	:	:	PUNCT
ejpam-4187	445	21	(	(	PUNCT
ejpam-4187	445	22	i	i	NOUN
ejpam-4187	445	23	)	)	PUNCT
ejpam-4187	445	24	for	for	ADP
ejpam-4187	445	25	each	each	DET
ejpam-4187	445	26	v	v	NUM
ejpam-4187	445	27	∈	∈	PROPN
ejpam-4187	445	28	s	s	PART
ejpam-4187	445	29	∩	∩	ADJ
ejpam-4187	445	30	v	v	X
ejpam-4187	445	31	(	(	PUNCT
ejpam-4187	445	32	g	g	NOUN
ejpam-4187	445	33	)	)	PUNCT
ejpam-4187	445	34	,	,	PUNCT
ejpam-4187	445	35	at	at	ADP
ejpam-4187	445	36	least	least	ADJ
ejpam-4187	445	37	one	one	NUM
ejpam-4187	445	38	of	of	ADP
ejpam-4187	445	39	the	the	DET
ejpam-4187	445	40	following	follow	VERB
ejpam-4187	445	41	holds	hold	NOUN
ejpam-4187	445	42	:	:	PUNCT
ejpam-4187	445	43	r.	r.	NOUN
ejpam-4187	445	44	malalay	malalay	PROPN
ejpam-4187	445	45	,	,	PUNCT
ejpam-4187	445	46	f.	f.	PROPN
ejpam-4187	445	47	jamil	jamil	PROPN
ejpam-4187	445	48	/	/	SYM
ejpam-4187	445	49	eur	eur	PROPN
ejpam-4187	445	50	.	.	PUNCT
ejpam-4187	446	1	j.	j.	PROPN
ejpam-4187	446	2	pure	pure	PROPN
ejpam-4187	446	3	appl	appl	PROPN
ejpam-4187	446	4	.	.	PROPN
ejpam-4187	446	5	math	math	PROPN
ejpam-4187	446	6	,	,	PUNCT
ejpam-4187	446	7	15	15	NUM
ejpam-4187	446	8	(	(	PUNCT
ejpam-4187	446	9	1	1	NUM
ejpam-4187	446	10	)	)	PUNCT
ejpam-4187	446	11	(	(	PUNCT
ejpam-4187	446	12	2022	2022	NUM
ejpam-4187	446	13	)	)	PUNCT
ejpam-4187	446	14	,	,	PUNCT
ejpam-4187	446	15	207	207	NUM
ejpam-4187	446	16	-	-	SYM
ejpam-4187	446	17	223	223	NUM
ejpam-4187	446	18	218	218	NUM
ejpam-4187	446	19	(	(	PUNCT
ejpam-4187	446	20	a	a	NOUN
ejpam-4187	446	21	)	)	PUNCT
ejpam-4187	446	22	s	s	NOUN
ejpam-4187	446	23	∩	∩	ADJ
ejpam-4187	446	24	v	v	X
ejpam-4187	446	25	(	(	PUNCT
ejpam-4187	446	26	hv	hv	PROPN
ejpam-4187	446	27	+	+	PROPN
ejpam-4187	446	28	v	v	NOUN
ejpam-4187	446	29	)	)	PUNCT
ejpam-4187	446	30	is	be	AUX
ejpam-4187	446	31	a	a	DET
ejpam-4187	446	32	restrained	restrained	ADJ
ejpam-4187	446	33	disjunctive	disjunctive	ADJ
ejpam-4187	446	34	dominating	dominating	NOUN
ejpam-4187	446	35	set	set	NOUN
ejpam-4187	446	36	of	of	ADP
ejpam-4187	446	37	hv	hv	PROPN
ejpam-4187	446	38	+	+	CCONJ
ejpam-4187	446	39	v	v	ADP
ejpam-4187	446	40	whenever	whenever	SCONJ
ejpam-4187	446	41	ng(v	ng(v	NOUN
ejpam-4187	446	42	)	)	PUNCT
ejpam-4187	446	43	⊆	⊆	NUM
ejpam-4187	446	44	s	s	NOUN
ejpam-4187	446	45	;	;	PUNCT
ejpam-4187	446	46	or	or	CCONJ
ejpam-4187	446	47	(	(	PUNCT
ejpam-4187	446	48	b	b	NOUN
ejpam-4187	446	49	)	)	PUNCT
ejpam-4187	446	50	|v	|v	PROPN
ejpam-4187	446	51	(	(	PUNCT
ejpam-4187	446	52	hv	hv	PROPN
ejpam-4187	446	53	)	)	PUNCT
ejpam-4187	446	54	\	\	PROPN
ejpam-4187	447	1	s|	s|	VERB
ejpam-4187	447	2	≥	≥	NOUN
ejpam-4187	447	3	2	2	NUM
ejpam-4187	447	4	whenever	whenever	SCONJ
ejpam-4187	447	5	|ng(v	|ng(v	NOUN
ejpam-4187	447	6	)	)	PUNCT
ejpam-4187	447	7	\	\	NOUN
ejpam-4187	447	8	s|	s|	NOUN
ejpam-4187	447	9	=	=	SYM
ejpam-4187	447	10	1	1	NUM
ejpam-4187	447	11	and	and	CCONJ
ejpam-4187	447	12	v	v	NOUN
ejpam-4187	447	13	(	(	PUNCT
ejpam-4187	447	14	hv	hv	PROPN
ejpam-4187	447	15	)	)	PUNCT
ejpam-4187	447	16	\	\	PROPN
ejpam-4187	448	1	s	s	PART
ejpam-4187	448	2	̸=	̸=	PROPN
ejpam-4187	448	3	∅.	∅.	X
ejpam-4187	448	4	(	(	PUNCT
ejpam-4187	448	5	ii	ii	NOUN
ejpam-4187	448	6	)	)	PUNCT
ejpam-4187	448	7	for	for	ADP
ejpam-4187	448	8	each	each	PRON
ejpam-4187	448	9	v	v	NUM
ejpam-4187	448	10	∈	∈	PROPN
ejpam-4187	448	11	v	v	NOUN
ejpam-4187	448	12	(	(	PUNCT
ejpam-4187	448	13	g	g	NOUN
ejpam-4187	448	14	)	)	PUNCT
ejpam-4187	448	15	\s	\s	NOUN
ejpam-4187	448	16	for	for	ADP
ejpam-4187	448	17	which	which	PRON
ejpam-4187	448	18	s	s	VERB
ejpam-4187	448	19	∩v	∩v	PROPN
ejpam-4187	448	20	(	(	PUNCT
ejpam-4187	448	21	hv	hv	NOUN
ejpam-4187	448	22	)	)	PUNCT
ejpam-4187	448	23	̸=	̸=	PROPN
ejpam-4187	448	24	∅	∅	NOUN
ejpam-4187	448	25	,	,	PUNCT
ejpam-4187	448	26	at	at	ADV
ejpam-4187	448	27	least	least	ADJ
ejpam-4187	448	28	one	one	NUM
ejpam-4187	448	29	of	of	ADP
ejpam-4187	448	30	the	the	DET
ejpam-4187	448	31	following	following	NOUN
ejpam-4187	448	32	holds	hold	VERB
ejpam-4187	448	33	:	:	PUNCT
ejpam-4187	448	34	(	(	PUNCT
ejpam-4187	448	35	a	a	X
ejpam-4187	448	36	)	)	PUNCT
ejpam-4187	448	37	v	v	NOUN
ejpam-4187	448	38	(	(	PUNCT
ejpam-4187	448	39	hv	hv	PROPN
ejpam-4187	448	40	)	)	PUNCT
ejpam-4187	448	41	\	\	PROPN
ejpam-4187	449	1	s	s	PART
ejpam-4187	449	2	̸=	̸=	PROPN
ejpam-4187	449	3	∅	∅	NOUN
ejpam-4187	449	4	;	;	PUNCT
ejpam-4187	449	5	(	(	PUNCT
ejpam-4187	449	6	b	b	NOUN
ejpam-4187	449	7	)	)	PUNCT
ejpam-4187	449	8	ng(v	ng(v	PUNCT
ejpam-4187	449	9	)	)	PUNCT
ejpam-4187	449	10	\	\	PUNCT
ejpam-4187	450	1	s	s	PART
ejpam-4187	450	2	̸=	̸=	PROPN
ejpam-4187	450	3	∅	∅	NOUN
ejpam-4187	450	4	;	;	PUNCT
ejpam-4187	450	5	or	or	CCONJ
ejpam-4187	450	6	(	(	PUNCT
ejpam-4187	450	7	c	c	NOUN
ejpam-4187	450	8	)	)	PUNCT
ejpam-4187	450	9	|ng(v	|ng(v	NOUN
ejpam-4187	450	10	,	,	PUNCT
ejpam-4187	450	11	2	2	X
ejpam-4187	450	12	)	)	PUNCT
ejpam-4187	450	13	∩	∩	NOUN
ejpam-4187	451	1	[	[	X
ejpam-4187	451	2	v	v	X
ejpam-4187	451	3	(	(	PUNCT
ejpam-4187	451	4	g	g	NOUN
ejpam-4187	451	5	)	)	PUNCT
ejpam-4187	451	6	\	\	PROPN
ejpam-4187	451	7	s]|	s]|	PROPN
ejpam-4187	451	8	≥	≥	NUM
ejpam-4187	451	9	2	2	NUM
ejpam-4187	451	10	.	.	PUNCT
ejpam-4187	451	11	proof	proof	NOUN
ejpam-4187	451	12	.	.	PUNCT
ejpam-4187	451	13	suppose	suppose	VERB
ejpam-4187	451	14	that	that	SCONJ
ejpam-4187	451	15	s	s	VERB
ejpam-4187	451	16	is	be	AUX
ejpam-4187	451	17	a	a	DET
ejpam-4187	451	18	restrained	restrained	ADJ
ejpam-4187	451	19	disjunctive	disjunctive	ADJ
ejpam-4187	451	20	dominating	dominating	NOUN
ejpam-4187	451	21	set	set	NOUN
ejpam-4187	451	22	of	of	ADP
ejpam-4187	451	23	g	g	PROPN
ejpam-4187	451	24	◦	◦	PROPN
ejpam-4187	451	25	h.	h.	NOUN
ejpam-4187	451	26	since	since	SCONJ
ejpam-4187	451	27	s	s	PROPN
ejpam-4187	451	28	is	be	AUX
ejpam-4187	451	29	a	a	DET
ejpam-4187	451	30	disjunctive	disjunctive	ADJ
ejpam-4187	451	31	dominating	dominating	NOUN
ejpam-4187	451	32	set	set	NOUN
ejpam-4187	451	33	,	,	PUNCT
ejpam-4187	451	34	all	all	DET
ejpam-4187	451	35	properties	property	NOUN
ejpam-4187	451	36	in	in	ADP
ejpam-4187	451	37	theorem	theorem	ADJ
ejpam-4187	451	38	5	5	NUM
ejpam-4187	451	39	hold	hold	NOUN
ejpam-4187	451	40	for	for	SCONJ
ejpam-4187	451	41	s.	s.	PROPN
ejpam-4187	451	42	to	to	PART
ejpam-4187	451	43	prove	prove	VERB
ejpam-4187	451	44	(	(	PUNCT
ejpam-4187	451	45	i	i	NOUN
ejpam-4187	451	46	)	)	PUNCT
ejpam-4187	451	47	,	,	PUNCT
ejpam-4187	451	48	let	let	VERB
ejpam-4187	451	49	v	v	NUM
ejpam-4187	451	50	∈	∈	NOUN
ejpam-4187	451	51	s	s	PART
ejpam-4187	451	52	∩	∩	ADJ
ejpam-4187	451	53	v	v	X
ejpam-4187	451	54	(	(	PUNCT
ejpam-4187	451	55	g	g	NOUN
ejpam-4187	451	56	)	)	PUNCT
ejpam-4187	451	57	.	.	PUNCT
ejpam-4187	452	1	suppose	suppose	VERB
ejpam-4187	452	2	that	that	SCONJ
ejpam-4187	452	3	ng(v	ng(v	NOUN
ejpam-4187	452	4	)	)	PUNCT
ejpam-4187	452	5	⊆	⊆	NUM
ejpam-4187	452	6	s.	s.	PROPN
ejpam-4187	452	7	since	since	SCONJ
ejpam-4187	452	8	v	v	PROPN
ejpam-4187	452	9	(	(	PUNCT
ejpam-4187	452	10	hv	hv	PROPN
ejpam-4187	452	11	)	)	PUNCT
ejpam-4187	452	12	⊆	⊆	NUM
ejpam-4187	452	13	nhv+v(v	nhv+v(v	PROPN
ejpam-4187	452	14	)	)	PUNCT
ejpam-4187	452	15	,	,	PUNCT
ejpam-4187	452	16	sv	sv	PUNCT
ejpam-4187	453	1	=	=	SYM
ejpam-4187	453	2	s	s	PROPN
ejpam-4187	453	3	∩	∩	ADJ
ejpam-4187	453	4	v	v	X
ejpam-4187	453	5	(	(	PUNCT
ejpam-4187	453	6	hv	hv	PROPN
ejpam-4187	453	7	+	+	PROPN
ejpam-4187	453	8	v	v	NOUN
ejpam-4187	453	9	)	)	PUNCT
ejpam-4187	453	10	is	be	AUX
ejpam-4187	453	11	a	a	DET
ejpam-4187	453	12	disjunctive	disjunctive	ADJ
ejpam-4187	453	13	dominating	dominating	NOUN
ejpam-4187	453	14	set	set	NOUN
ejpam-4187	453	15	of	of	ADP
ejpam-4187	453	16	hv	hv	PROPN
ejpam-4187	453	17	+	+	X
ejpam-4187	453	18	v.	v.	CCONJ
ejpam-4187	453	19	let	let	VERB
ejpam-4187	453	20	u	u	PRON
ejpam-4187	453	21	∈	∈	PROPN
ejpam-4187	453	22	v	v	X
ejpam-4187	453	23	(	(	PUNCT
ejpam-4187	453	24	hv	hv	PROPN
ejpam-4187	453	25	+	+	PROPN
ejpam-4187	453	26	v	v	NOUN
ejpam-4187	453	27	)	)	PUNCT
ejpam-4187	453	28	\	\	NOUN
ejpam-4187	454	1	sv	sv	PROPN
ejpam-4187	454	2	.	.	PUNCT
ejpam-4187	455	1	then	then	ADV
ejpam-4187	455	2	u	u	PROPN
ejpam-4187	455	3	∈	∈	PROPN
ejpam-4187	455	4	v	v	ADP
ejpam-4187	455	5	(	(	PUNCT
ejpam-4187	455	6	hv	hv	PROPN
ejpam-4187	455	7	)	)	PUNCT
ejpam-4187	455	8	\	\	PROPN
ejpam-4187	455	9	s.	s.	PROPN
ejpam-4187	455	10	since	since	SCONJ
ejpam-4187	455	11	s	s	PROPN
ejpam-4187	455	12	is	be	AUX
ejpam-4187	455	13	a	a	DET
ejpam-4187	455	14	restrained	restrained	ADJ
ejpam-4187	455	15	disjunctive	disjunctive	ADJ
ejpam-4187	455	16	dominating	dominating	NOUN
ejpam-4187	455	17	set	set	NOUN
ejpam-4187	455	18	,	,	PUNCT
ejpam-4187	455	19	there	there	PRON
ejpam-4187	455	20	exists	exist	VERB
ejpam-4187	455	21	w	w	PROPN
ejpam-4187	455	22	∈	∈	PROPN
ejpam-4187	455	23	v	v	NOUN
ejpam-4187	455	24	(	(	PUNCT
ejpam-4187	455	25	g	g	NOUN
ejpam-4187	455	26	◦	◦	NOUN
ejpam-4187	455	27	h)\s	h)\s	NOUN
ejpam-4187	455	28	such	such	ADJ
ejpam-4187	455	29	that	that	SCONJ
ejpam-4187	455	30	uw	uw	PROPN
ejpam-4187	455	31	∈	∈	PROPN
ejpam-4187	455	32	e(g	e(g	PROPN
ejpam-4187	455	33	◦	◦	PROPN
ejpam-4187	455	34	h	h	NOUN
ejpam-4187	455	35	)	)	PUNCT
ejpam-4187	455	36	or	or	CCONJ
ejpam-4187	455	37	there	there	PRON
ejpam-4187	455	38	exist	exist	VERB
ejpam-4187	455	39	distinct	distinct	ADJ
ejpam-4187	455	40	w	w	NOUN
ejpam-4187	455	41	,	,	PUNCT
ejpam-4187	455	42	z	z	PROPN
ejpam-4187	455	43	∈	∈	PROPN
ejpam-4187	455	44	v	v	NOUN
ejpam-4187	455	45	(	(	PUNCT
ejpam-4187	455	46	g	g	PROPN
ejpam-4187	455	47	◦	◦	NOUN
ejpam-4187	455	48	h	h	NOUN
ejpam-4187	455	49	)	)	PUNCT
ejpam-4187	455	50	\	\	PROPN
ejpam-4187	456	1	s	s	PART
ejpam-4187	456	2	for	for	ADP
ejpam-4187	456	3	which	which	PRON
ejpam-4187	456	4	dg	dg	VERB
ejpam-4187	456	5	◦	◦	PROPN
ejpam-4187	456	6	h(u	h(u	PROPN
ejpam-4187	456	7	,	,	PUNCT
ejpam-4187	456	8	w	w	NOUN
ejpam-4187	456	9	)	)	PUNCT
ejpam-4187	456	10	=	=	SYM
ejpam-4187	456	11	2	2	NUM
ejpam-4187	456	12	=	=	SYM
ejpam-4187	456	13	dg	dg	NOUN
ejpam-4187	456	14	◦	◦	NOUN
ejpam-4187	456	15	h(u	h(u	PROPN
ejpam-4187	456	16	,	,	PUNCT
ejpam-4187	456	17	z	z	NOUN
ejpam-4187	456	18	)	)	PUNCT
ejpam-4187	456	19	.	.	PUNCT
ejpam-4187	457	1	in	in	ADP
ejpam-4187	457	2	case	case	NOUN
ejpam-4187	457	3	the	the	DET
ejpam-4187	457	4	former	former	ADJ
ejpam-4187	457	5	holds	hold	VERB
ejpam-4187	457	6	,	,	PUNCT
ejpam-4187	457	7	w	w	PROPN
ejpam-4187	457	8	∈	∈	PROPN
ejpam-4187	457	9	v	v	ADP
ejpam-4187	457	10	(	(	PUNCT
ejpam-4187	457	11	hv	hv	PROPN
ejpam-4187	457	12	)	)	PUNCT
ejpam-4187	457	13	\	\	PROPN
ejpam-4187	457	14	sv	sv	PROPN
ejpam-4187	457	15	and	and	CCONJ
ejpam-4187	457	16	uw	uw	PROPN
ejpam-4187	457	17	∈	∈	PROPN
ejpam-4187	457	18	e(hv	e(hv	PROPN
ejpam-4187	457	19	+	+	CCONJ
ejpam-4187	457	20	v	v	NOUN
ejpam-4187	457	21	)	)	PUNCT
ejpam-4187	457	22	.	.	PUNCT
ejpam-4187	458	1	if	if	SCONJ
ejpam-4187	458	2	the	the	DET
ejpam-4187	458	3	latter	latter	ADJ
ejpam-4187	458	4	holds	hold	VERB
ejpam-4187	458	5	,	,	PUNCT
ejpam-4187	458	6	then	then	ADV
ejpam-4187	458	7	w	w	PROPN
ejpam-4187	458	8	and	and	CCONJ
ejpam-4187	458	9	z	z	NOUN
ejpam-4187	458	10	are	be	AUX
ejpam-4187	458	11	distinct	distinct	ADJ
ejpam-4187	458	12	vertices	vertex	NOUN
ejpam-4187	458	13	in	in	ADP
ejpam-4187	458	14	v	v	NOUN
ejpam-4187	458	15	(	(	PUNCT
ejpam-4187	458	16	hv)\sv	hv)\sv	ADJ
ejpam-4187	458	17	with	with	ADP
ejpam-4187	458	18	dhv+v(u	dhv+v(u	PROPN
ejpam-4187	458	19	,	,	PUNCT
ejpam-4187	458	20	w	w	NOUN
ejpam-4187	458	21	)	)	PUNCT
ejpam-4187	458	22	=	=	SYM
ejpam-4187	458	23	2	2	NUM
ejpam-4187	458	24	=	=	SYM
ejpam-4187	458	25	dhv+v(u	dhv+v(u	PROPN
ejpam-4187	458	26	,	,	PUNCT
ejpam-4187	458	27	z	z	NOUN
ejpam-4187	458	28	)	)	PUNCT
ejpam-4187	458	29	.	.	PUNCT
ejpam-4187	459	1	thus	thus	ADV
ejpam-4187	459	2	,	,	PUNCT
ejpam-4187	459	3	sv	sv	PROPN
ejpam-4187	459	4	is	be	AUX
ejpam-4187	459	5	a	a	DET
ejpam-4187	459	6	restrained	restrained	ADJ
ejpam-4187	459	7	disjunctive	disjunctive	ADJ
ejpam-4187	459	8	dominating	dominating	NOUN
ejpam-4187	459	9	set	set	NOUN
ejpam-4187	459	10	of	of	ADP
ejpam-4187	459	11	hv	hv	PROPN
ejpam-4187	459	12	+	+	X
ejpam-4187	459	13	v.	v.	ADP
ejpam-4187	459	14	this	this	PRON
ejpam-4187	459	15	proves	prove	VERB
ejpam-4187	459	16	(	(	PUNCT
ejpam-4187	459	17	i)(a	i)(a	NOUN
ejpam-4187	459	18	)	)	PUNCT
ejpam-4187	459	19	.	.	PUNCT
ejpam-4187	460	1	now	now	ADV
ejpam-4187	460	2	,	,	PUNCT
ejpam-4187	460	3	suppose	suppose	VERB
ejpam-4187	460	4	that	that	SCONJ
ejpam-4187	460	5	v	v	PROPN
ejpam-4187	460	6	(	(	PUNCT
ejpam-4187	460	7	hv	hv	PROPN
ejpam-4187	460	8	)	)	PUNCT
ejpam-4187	460	9	\	\	PROPN
ejpam-4187	460	10	s	s	PART
ejpam-4187	460	11	̸=	̸=	PROPN
ejpam-4187	460	12	∅	∅	NOUN
ejpam-4187	460	13	and	and	CCONJ
ejpam-4187	460	14	|ng(v	|ng(v	NUM
ejpam-4187	460	15	)	)	PUNCT
ejpam-4187	460	16	\	\	NOUN
ejpam-4187	460	17	s|	s|	NOUN
ejpam-4187	460	18	=	=	SYM
ejpam-4187	461	1	1	1	X
ejpam-4187	461	2	.	.	PUNCT
ejpam-4187	461	3	let	let	VERB
ejpam-4187	461	4	u	u	PRON
ejpam-4187	461	5	∈	∈	PROPN
ejpam-4187	461	6	v	v	X
ejpam-4187	461	7	(	(	PUNCT
ejpam-4187	461	8	hv	hv	PROPN
ejpam-4187	461	9	)	)	PUNCT
ejpam-4187	461	10	\	\	PROPN
ejpam-4187	462	1	s	s	PROPN
ejpam-4187	462	2	,	,	PUNCT
ejpam-4187	462	3	and	and	CCONJ
ejpam-4187	462	4	suppose	suppose	VERB
ejpam-4187	462	5	that	that	SCONJ
ejpam-4187	462	6	|v	|v	PROPN
ejpam-4187	462	7	(	(	PUNCT
ejpam-4187	462	8	hv	hv	PROPN
ejpam-4187	462	9	)	)	PUNCT
ejpam-4187	462	10	\	\	NOUN
ejpam-4187	462	11	s|	s|	NOUN
ejpam-4187	462	12	=	=	SYM
ejpam-4187	463	1	1	1	X
ejpam-4187	463	2	.	.	PUNCT
ejpam-4187	464	1	since	since	SCONJ
ejpam-4187	464	2	s	s	PROPN
ejpam-4187	464	3	is	be	AUX
ejpam-4187	464	4	a	a	DET
ejpam-4187	464	5	restrained	restrained	ADJ
ejpam-4187	464	6	disjunctive	disjunctive	ADJ
ejpam-4187	464	7	dominating	dominating	NOUN
ejpam-4187	464	8	set	set	NOUN
ejpam-4187	464	9	and	and	CCONJ
ejpam-4187	464	10	w	w	ADP
ejpam-4187	464	11	∈	∈	NOUN
ejpam-4187	464	12	s	s	NOUN
ejpam-4187	464	13	for	for	ADP
ejpam-4187	464	14	all	all	DET
ejpam-4187	464	15	w	w	PROPN
ejpam-4187	464	16	∈	∈	PROPN
ejpam-4187	464	17	v	v	NOUN
ejpam-4187	464	18	(	(	PUNCT
ejpam-4187	464	19	g	g	PROPN
ejpam-4187	464	20	◦	◦	NOUN
ejpam-4187	464	21	h	h	NOUN
ejpam-4187	464	22	)	)	PUNCT
ejpam-4187	464	23	for	for	ADP
ejpam-4187	464	24	which	which	PRON
ejpam-4187	464	25	uw	uw	PROPN
ejpam-4187	464	26	∈	∈	PROPN
ejpam-4187	464	27	e(g	e(g	PROPN
ejpam-4187	464	28	◦	◦	PROPN
ejpam-4187	464	29	h	h	NOUN
ejpam-4187	464	30	)	)	PUNCT
ejpam-4187	464	31	,	,	PUNCT
ejpam-4187	464	32	there	there	PRON
ejpam-4187	464	33	exist	exist	VERB
ejpam-4187	464	34	distinct	distinct	ADJ
ejpam-4187	464	35	x	x	NOUN
ejpam-4187	464	36	,	,	PUNCT
ejpam-4187	464	37	y	y	PROPN
ejpam-4187	464	38	∈	∈	PROPN
ejpam-4187	464	39	v	v	NOUN
ejpam-4187	464	40	(	(	PUNCT
ejpam-4187	464	41	g	g	PROPN
ejpam-4187	464	42	◦	◦	NOUN
ejpam-4187	464	43	h	h	NOUN
ejpam-4187	464	44	)	)	PUNCT
ejpam-4187	464	45	\	\	PROPN
ejpam-4187	465	1	s	s	AUX
ejpam-4187	465	2	such	such	ADJ
ejpam-4187	465	3	that	that	SCONJ
ejpam-4187	465	4	dg	dg	PROPN
ejpam-4187	465	5	◦	◦	PROPN
ejpam-4187	465	6	h(u	h(u	PROPN
ejpam-4187	465	7	,	,	PUNCT
ejpam-4187	465	8	x	x	NOUN
ejpam-4187	465	9	)	)	PUNCT
ejpam-4187	465	10	=	=	SYM
ejpam-4187	465	11	2	2	NUM
ejpam-4187	465	12	=	=	SYM
ejpam-4187	465	13	dg	dg	NOUN
ejpam-4187	465	14	◦	◦	NOUN
ejpam-4187	465	15	h(u	h(u	PROPN
ejpam-4187	465	16	,	,	PUNCT
ejpam-4187	465	17	y	y	PROPN
ejpam-4187	465	18	)	)	PUNCT
ejpam-4187	465	19	.	.	PUNCT
ejpam-4187	466	1	necessarily	necessarily	ADV
ejpam-4187	466	2	,	,	PUNCT
ejpam-4187	466	3	x	x	PRON
ejpam-4187	466	4	,	,	PUNCT
ejpam-4187	466	5	y	y	PROPN
ejpam-4187	466	6	∈	∈	PROPN
ejpam-4187	466	7	ng(v	ng(v	NOUN
ejpam-4187	466	8	)	)	PUNCT
ejpam-4187	466	9	,	,	PUNCT
ejpam-4187	466	10	a	a	DET
ejpam-4187	466	11	contradiction	contradiction	NOUN
ejpam-4187	466	12	.	.	PUNCT
ejpam-4187	467	1	thus	thus	ADV
ejpam-4187	467	2	|v	|v	PROPN
ejpam-4187	467	3	(	(	PUNCT
ejpam-4187	467	4	hv	hv	PROPN
ejpam-4187	467	5	)	)	PUNCT
ejpam-4187	467	6	\	\	PROPN
ejpam-4187	467	7	s|	s|	VERB
ejpam-4187	467	8	≥	≥	NOUN
ejpam-4187	467	9	2	2	NUM
ejpam-4187	467	10	,	,	PUNCT
ejpam-4187	467	11	proving	prove	VERB
ejpam-4187	467	12	(	(	PUNCT
ejpam-4187	467	13	i)(b	i)(b	NUM
ejpam-4187	467	14	)	)	PUNCT
ejpam-4187	467	15	.	.	PUNCT
ejpam-4187	468	1	to	to	PART
ejpam-4187	468	2	prove	prove	VERB
ejpam-4187	468	3	(	(	PUNCT
ejpam-4187	468	4	ii	ii	NOUN
ejpam-4187	468	5	)	)	PUNCT
ejpam-4187	468	6	,	,	PUNCT
ejpam-4187	468	7	let	let	VERB
ejpam-4187	468	8	v	v	NUM
ejpam-4187	468	9	∈	∈	PROPN
ejpam-4187	468	10	v	v	NOUN
ejpam-4187	468	11	(	(	PUNCT
ejpam-4187	468	12	g	g	NOUN
ejpam-4187	468	13	)	)	PUNCT
ejpam-4187	468	14	\	\	PROPN
ejpam-4187	469	1	s	s	PART
ejpam-4187	469	2	for	for	ADP
ejpam-4187	469	3	which	which	PRON
ejpam-4187	469	4	s	s	VERB
ejpam-4187	469	5	∩	∩	ADJ
ejpam-4187	469	6	v	v	X
ejpam-4187	469	7	(	(	PUNCT
ejpam-4187	469	8	hv	hv	NOUN
ejpam-4187	469	9	)	)	PUNCT
ejpam-4187	469	10	̸=	̸=	PROPN
ejpam-4187	469	11	∅.	∅.	ADV
ejpam-4187	469	12	since	since	SCONJ
ejpam-4187	469	13	s	s	PROPN
ejpam-4187	469	14	is	be	AUX
ejpam-4187	469	15	a	a	DET
ejpam-4187	469	16	restrained	restrained	ADJ
ejpam-4187	469	17	disjunctive	disjunctive	ADJ
ejpam-4187	469	18	dominating	dominating	NOUN
ejpam-4187	469	19	set	set	NOUN
ejpam-4187	469	20	and	and	CCONJ
ejpam-4187	469	21	v	v	ADP
ejpam-4187	469	22	∈	∈	PROPN
ejpam-4187	469	23	v	v	NOUN
ejpam-4187	469	24	(	(	PUNCT
ejpam-4187	469	25	g	g	PROPN
ejpam-4187	469	26	◦	◦	NOUN
ejpam-4187	469	27	h	h	NOUN
ejpam-4187	469	28	)	)	PUNCT
ejpam-4187	469	29	\	\	PROPN
ejpam-4187	470	1	s	s	X
ejpam-4187	470	2	,	,	PUNCT
ejpam-4187	470	3	there	there	PRON
ejpam-4187	470	4	exists	exist	VERB
ejpam-4187	470	5	u	u	PROPN
ejpam-4187	470	6	∈	∈	PROPN
ejpam-4187	470	7	v	v	NOUN
ejpam-4187	470	8	(	(	PUNCT
ejpam-4187	470	9	g	g	PROPN
ejpam-4187	470	10	◦	◦	NOUN
ejpam-4187	470	11	h	h	NOUN
ejpam-4187	470	12	)	)	PUNCT
ejpam-4187	470	13	\	\	PROPN
ejpam-4187	471	1	s	s	VERB
ejpam-4187	471	2	such	such	ADJ
ejpam-4187	471	3	that	that	DET
ejpam-4187	471	4	uv	uv	PROPN
ejpam-4187	471	5	∈	∈	PROPN
ejpam-4187	471	6	e(g	e(g	PROPN
ejpam-4187	471	7	◦	◦	PROPN
ejpam-4187	471	8	h	h	NOUN
ejpam-4187	471	9	)	)	PUNCT
ejpam-4187	471	10	or	or	CCONJ
ejpam-4187	471	11	there	there	PRON
ejpam-4187	471	12	exist	exist	VERB
ejpam-4187	471	13	distinct	distinct	ADJ
ejpam-4187	471	14	x	x	NOUN
ejpam-4187	471	15	,	,	PUNCT
ejpam-4187	472	1	y	y	PROPN
ejpam-4187	472	2	∈	∈	PROPN
ejpam-4187	472	3	v	v	NOUN
ejpam-4187	472	4	(	(	PUNCT
ejpam-4187	472	5	g	g	PROPN
ejpam-4187	472	6	◦	◦	NOUN
ejpam-4187	472	7	h	h	NOUN
ejpam-4187	472	8	)	)	PUNCT
ejpam-4187	472	9	\	\	PROPN
ejpam-4187	473	1	s	s	PART
ejpam-4187	473	2	for	for	ADP
ejpam-4187	473	3	which	which	PRON
ejpam-4187	473	4	dg	dg	VERB
ejpam-4187	473	5	◦	◦	NOUN
ejpam-4187	473	6	h(v	h(v	PROPN
ejpam-4187	473	7	,	,	PUNCT
ejpam-4187	473	8	x	x	NOUN
ejpam-4187	473	9	)	)	PUNCT
ejpam-4187	473	10	=	=	SYM
ejpam-4187	473	11	2	2	NUM
ejpam-4187	473	12	=	=	SYM
ejpam-4187	473	13	dg	dg	NOUN
ejpam-4187	473	14	◦	◦	NOUN
ejpam-4187	473	15	h(v	h(v	PROPN
ejpam-4187	473	16	,	,	PUNCT
ejpam-4187	473	17	y	y	NOUN
ejpam-4187	473	18	)	)	PUNCT
ejpam-4187	473	19	.	.	PUNCT
ejpam-4187	474	1	note	note	VERB
ejpam-4187	474	2	that	that	SCONJ
ejpam-4187	474	3	for	for	ADP
ejpam-4187	474	4	such	such	ADJ
ejpam-4187	474	5	u	u	NOUN
ejpam-4187	474	6	,	,	PUNCT
ejpam-4187	474	7	either	either	CCONJ
ejpam-4187	474	8	u	u	PROPN
ejpam-4187	474	9	∈	∈	PROPN
ejpam-4187	474	10	v	v	ADP
ejpam-4187	474	11	(	(	PUNCT
ejpam-4187	474	12	hv	hv	NOUN
ejpam-4187	474	13	)	)	PUNCT
ejpam-4187	474	14	or	or	CCONJ
ejpam-4187	474	15	u	u	PROPN
ejpam-4187	474	16	∈	∈	PROPN
ejpam-4187	474	17	ng(v	ng(v	PRON
ejpam-4187	474	18	)	)	PUNCT
ejpam-4187	474	19	.	.	PUNCT
ejpam-4187	475	1	that	that	PRON
ejpam-4187	475	2	is	be	AUX
ejpam-4187	475	3	,	,	PUNCT
ejpam-4187	475	4	(	(	PUNCT
ejpam-4187	475	5	a	a	X
ejpam-4187	475	6	)	)	PUNCT
ejpam-4187	475	7	or	or	CCONJ
ejpam-4187	475	8	(	(	PUNCT
ejpam-4187	475	9	b	b	NOUN
ejpam-4187	475	10	)	)	PUNCT
ejpam-4187	475	11	holds	hold	VERB
ejpam-4187	475	12	.	.	PUNCT
ejpam-4187	476	1	on	on	ADP
ejpam-4187	476	2	the	the	DET
ejpam-4187	476	3	other	other	ADJ
ejpam-4187	476	4	hand	hand	NOUN
ejpam-4187	476	5	,	,	PUNCT
ejpam-4187	476	6	if	if	SCONJ
ejpam-4187	476	7	(	(	PUNCT
ejpam-4187	476	8	a	a	NOUN
ejpam-4187	476	9	)	)	PUNCT
ejpam-4187	476	10	and	and	CCONJ
ejpam-4187	476	11	(	(	PUNCT
ejpam-4187	476	12	b	b	X
ejpam-4187	476	13	)	)	PUNCT
ejpam-4187	476	14	do	do	AUX
ejpam-4187	476	15	not	not	PART
ejpam-4187	476	16	hold	hold	VERB
ejpam-4187	476	17	,	,	PUNCT
ejpam-4187	476	18	x	x	PRON
ejpam-4187	476	19	,	,	PUNCT
ejpam-4187	476	20	y	y	PROPN
ejpam-4187	476	21	∈	∈	PROPN
ejpam-4187	476	22	v	v	ADP
ejpam-4187	476	23	(	(	PUNCT
ejpam-4187	476	24	g	g	NOUN
ejpam-4187	476	25	)	)	PUNCT
ejpam-4187	476	26	and	and	CCONJ
ejpam-4187	476	27	dg(x	dg(x	NUM
ejpam-4187	476	28	,	,	PUNCT
ejpam-4187	476	29	v	v	NOUN
ejpam-4187	476	30	)	)	PUNCT
ejpam-4187	476	31	=	=	SYM
ejpam-4187	476	32	2	2	NUM
ejpam-4187	476	33	=	=	SYM
ejpam-4187	476	34	dg(y	dg(y	ADJ
ejpam-4187	476	35	,	,	PUNCT
ejpam-4187	476	36	v	v	NOUN
ejpam-4187	476	37	)	)	PUNCT
ejpam-4187	476	38	showing	show	VERB
ejpam-4187	476	39	that	that	SCONJ
ejpam-4187	476	40	|ng(v	|ng(v	ADP
ejpam-4187	476	41	,	,	PUNCT
ejpam-4187	476	42	2	2	X
ejpam-4187	476	43	)	)	PUNCT
ejpam-4187	476	44	∩	∩	NOUN
ejpam-4187	476	45	[	[	X
ejpam-4187	476	46	v	v	X
ejpam-4187	476	47	(	(	PUNCT
ejpam-4187	476	48	g	g	NOUN
ejpam-4187	476	49	)	)	PUNCT
ejpam-4187	476	50	\	\	PROPN
ejpam-4187	476	51	s]|	s]|	PROPN
ejpam-4187	476	52	≥	≥	NUM
ejpam-4187	476	53	2	2	NUM
ejpam-4187	476	54	.	.	PUNCT
ejpam-4187	477	1	conversely	conversely	ADV
ejpam-4187	477	2	,	,	PUNCT
ejpam-4187	477	3	note	note	VERB
ejpam-4187	477	4	first	first	ADV
ejpam-4187	477	5	that	that	SCONJ
ejpam-4187	477	6	because	because	SCONJ
ejpam-4187	477	7	s	s	PART
ejpam-4187	477	8	satisfies	satisfy	VERB
ejpam-4187	477	9	the	the	DET
ejpam-4187	477	10	properties	property	NOUN
ejpam-4187	477	11	in	in	ADP
ejpam-4187	477	12	theorem	theorem	NOUN
ejpam-4187	477	13	5	5	NUM
ejpam-4187	477	14	,	,	PUNCT
ejpam-4187	477	15	s	s	VERB
ejpam-4187	477	16	is	be	AUX
ejpam-4187	477	17	a	a	DET
ejpam-4187	477	18	disjunctive	disjunctive	ADJ
ejpam-4187	477	19	dominating	dominating	NOUN
ejpam-4187	477	20	set	set	NOUN
ejpam-4187	477	21	of	of	ADP
ejpam-4187	477	22	g	g	PROPN
ejpam-4187	477	23	◦	◦	PROPN
ejpam-4187	477	24	h.	h.	PROPN
ejpam-4187	477	25	let	let	VERB
ejpam-4187	477	26	u	u	PRON
ejpam-4187	477	27	∈	∈	PROPN
ejpam-4187	477	28	v	v	NOUN
ejpam-4187	477	29	(	(	PUNCT
ejpam-4187	477	30	g	g	PROPN
ejpam-4187	477	31	◦	◦	NOUN
ejpam-4187	477	32	h	h	NOUN
ejpam-4187	477	33	)	)	PUNCT
ejpam-4187	477	34	\	\	PROPN
ejpam-4187	478	1	s	s	PROPN
ejpam-4187	478	2	,	,	PUNCT
ejpam-4187	478	3	and	and	CCONJ
ejpam-4187	478	4	let	let	VERB
ejpam-4187	478	5	v	v	NUM
ejpam-4187	478	6	∈	∈	PROPN
ejpam-4187	478	7	v	v	NOUN
ejpam-4187	478	8	(	(	PUNCT
ejpam-4187	478	9	g	g	NOUN
ejpam-4187	478	10	)	)	PUNCT
ejpam-4187	478	11	such	such	ADJ
ejpam-4187	478	12	that	that	SCONJ
ejpam-4187	478	13	u	u	PROPN
ejpam-4187	478	14	∈	∈	PROPN
ejpam-4187	478	15	v	v	NOUN
ejpam-4187	478	16	(	(	PUNCT
ejpam-4187	478	17	hv	hv	PROPN
ejpam-4187	478	18	+	+	PROPN
ejpam-4187	478	19	v	v	NOUN
ejpam-4187	478	20	)	)	PUNCT
ejpam-4187	478	21	.	.	PUNCT
ejpam-4187	479	1	suppose	suppose	VERB
ejpam-4187	479	2	that	that	SCONJ
ejpam-4187	479	3	u	u	PROPN
ejpam-4187	479	4	=	=	NOUN
ejpam-4187	480	1	v.	v.	CCONJ
ejpam-4187	480	2	then	then	ADV
ejpam-4187	480	3	u	u	X
ejpam-4187	480	4	=	=	PROPN
ejpam-4187	480	5	v	v	ADP
ejpam-4187	480	6	∈	∈	PROPN
ejpam-4187	480	7	v	v	NOUN
ejpam-4187	480	8	(	(	PUNCT
ejpam-4187	480	9	g	g	NOUN
ejpam-4187	480	10	)	)	PUNCT
ejpam-4187	480	11	\	\	PUNCT
ejpam-4187	481	1	s.	s.	PROPN
ejpam-4187	481	2	if	if	SCONJ
ejpam-4187	481	3	s	s	VERB
ejpam-4187	481	4	∩	∩	ADJ
ejpam-4187	481	5	v	v	X
ejpam-4187	481	6	(	(	PUNCT
ejpam-4187	481	7	hv	hv	NOUN
ejpam-4187	481	8	)	)	PUNCT
ejpam-4187	481	9	=	=	NOUN
ejpam-4187	481	10	∅	∅	NOUN
ejpam-4187	481	11	,	,	PUNCT
ejpam-4187	481	12	then	then	ADV
ejpam-4187	481	13	ux	ux	PROPN
ejpam-4187	481	14	∈	∈	PROPN
ejpam-4187	481	15	e(g	e(g	PROPN
ejpam-4187	481	16	◦	◦	PROPN
ejpam-4187	481	17	h	h	NOUN
ejpam-4187	481	18	)	)	PUNCT
ejpam-4187	481	19	for	for	ADP
ejpam-4187	481	20	any	any	DET
ejpam-4187	481	21	x	x	SYM
ejpam-4187	481	22	∈	∈	PROPN
ejpam-4187	481	23	v	v	ADP
ejpam-4187	481	24	(	(	PUNCT
ejpam-4187	481	25	hv	hv	PROPN
ejpam-4187	481	26	)	)	PUNCT
ejpam-4187	481	27	.	.	PUNCT
ejpam-4187	482	1	suppose	suppose	VERB
ejpam-4187	482	2	that	that	SCONJ
ejpam-4187	482	3	s	s	VERB
ejpam-4187	482	4	∩	∩	ADJ
ejpam-4187	482	5	v	v	X
ejpam-4187	482	6	(	(	PUNCT
ejpam-4187	482	7	hv	hv	NOUN
ejpam-4187	482	8	)	)	PUNCT
ejpam-4187	482	9	̸=	̸=	PROPN
ejpam-4187	482	10	∅.	∅.	AUX
ejpam-4187	482	11	pick	pick	VERB
ejpam-4187	482	12	x	x	PUNCT
ejpam-4187	482	13	∈	∈	PROPN
ejpam-4187	482	14	v	v	ADP
ejpam-4187	482	15	(	(	PUNCT
ejpam-4187	482	16	hv	hv	PROPN
ejpam-4187	482	17	)	)	PUNCT
ejpam-4187	482	18	\	\	PROPN
ejpam-4187	482	19	s	s	PART
ejpam-4187	482	20	or	or	CCONJ
ejpam-4187	482	21	x	x	SYM
ejpam-4187	482	22	∈	∈	NOUN
ejpam-4187	482	23	ng(v	ng(v	PRON
ejpam-4187	482	24	)	)	PUNCT
ejpam-4187	482	25	\	\	PUNCT
ejpam-4187	483	1	s	s	PART
ejpam-4187	483	2	in	in	ADP
ejpam-4187	483	3	case	case	NOUN
ejpam-4187	483	4	(	(	PUNCT
ejpam-4187	483	5	ii)(a	ii)(a	PROPN
ejpam-4187	483	6	)	)	PUNCT
ejpam-4187	483	7	or	or	CCONJ
ejpam-4187	483	8	(	(	PUNCT
ejpam-4187	483	9	ii)(b	ii)(b	ADJ
ejpam-4187	483	10	)	)	PUNCT
ejpam-4187	483	11	holds	hold	NOUN
ejpam-4187	483	12	,	,	PUNCT
ejpam-4187	483	13	respectively	respectively	ADV
ejpam-4187	483	14	.	.	PUNCT
ejpam-4187	484	1	then	then	ADV
ejpam-4187	484	2	ux	ux	PROPN
ejpam-4187	484	3	∈	∈	PROPN
ejpam-4187	484	4	e(g	e(g	PROPN
ejpam-4187	484	5	◦	◦	PROPN
ejpam-4187	484	6	h	h	NOUN
ejpam-4187	484	7	)	)	PUNCT
ejpam-4187	484	8	.	.	PUNCT
ejpam-4187	485	1	if	if	SCONJ
ejpam-4187	485	2	(	(	PUNCT
ejpam-4187	485	3	ii)(c	ii)(c	PROPN
ejpam-4187	485	4	)	)	PUNCT
ejpam-4187	485	5	holds	hold	VERB
ejpam-4187	485	6	,	,	PUNCT
ejpam-4187	485	7	then	then	ADV
ejpam-4187	485	8	pick	pick	VERB
ejpam-4187	485	9	distinct	distinct	ADJ
ejpam-4187	485	10	x	x	NOUN
ejpam-4187	485	11	,	,	PUNCT
ejpam-4187	485	12	y	y	PROPN
ejpam-4187	485	13	∈	∈	PROPN
ejpam-4187	485	14	v	v	ADP
ejpam-4187	485	15	(	(	PUNCT
ejpam-4187	485	16	g	g	NOUN
ejpam-4187	485	17	)	)	PUNCT
ejpam-4187	485	18	for	for	ADP
ejpam-4187	485	19	which	which	PRON
ejpam-4187	485	20	dg(u	dg(u	NOUN
ejpam-4187	485	21	,	,	PUNCT
ejpam-4187	485	22	x	x	X
ejpam-4187	485	23	)	)	PUNCT
ejpam-4187	485	24	=	=	SYM
ejpam-4187	485	25	2	2	NUM
ejpam-4187	485	26	=	=	SYM
ejpam-4187	485	27	dg(u	dg(u	X
ejpam-4187	485	28	,	,	PUNCT
ejpam-4187	485	29	y	y	NOUN
ejpam-4187	485	30	)	)	PUNCT
ejpam-4187	485	31	.	.	PUNCT
ejpam-4187	486	1	then	then	ADV
ejpam-4187	486	2	dg	dg	VERB
ejpam-4187	486	3	◦	◦	NOUN
ejpam-4187	486	4	h(u	h(u	PROPN
ejpam-4187	486	5	,	,	PUNCT
ejpam-4187	486	6	x	x	NOUN
ejpam-4187	486	7	)	)	PUNCT
ejpam-4187	486	8	=	=	SYM
ejpam-4187	486	9	2	2	NUM
ejpam-4187	486	10	=	=	SYM
ejpam-4187	486	11	dg	dg	NOUN
ejpam-4187	486	12	◦	◦	NOUN
ejpam-4187	486	13	h(u	h(u	PROPN
ejpam-4187	486	14	,	,	PUNCT
ejpam-4187	486	15	y	y	PROPN
ejpam-4187	486	16	)	)	PUNCT
ejpam-4187	486	17	.	.	PUNCT
ejpam-4187	487	1	suppose	suppose	VERB
ejpam-4187	487	2	that	that	SCONJ
ejpam-4187	487	3	u	u	PROPN
ejpam-4187	487	4	∈	∈	PROPN
ejpam-4187	487	5	v	v	ADP
ejpam-4187	487	6	(	(	PUNCT
ejpam-4187	487	7	hv	hv	PROPN
ejpam-4187	487	8	)	)	PUNCT
ejpam-4187	487	9	.	.	PUNCT
ejpam-4187	488	1	if	if	SCONJ
ejpam-4187	488	2	v	v	NUM
ejpam-4187	488	3	/∈	/∈	SYM
ejpam-4187	488	4	s	s	X
ejpam-4187	488	5	,	,	PUNCT
ejpam-4187	488	6	then	then	ADV
ejpam-4187	488	7	v	v	NOUN
ejpam-4187	488	8	is	be	AUX
ejpam-4187	488	9	the	the	DET
ejpam-4187	488	10	required	require	VERB
ejpam-4187	488	11	vertex	vertex	NOUN
ejpam-4187	488	12	for	for	ADP
ejpam-4187	488	13	which	which	PRON
ejpam-4187	488	14	uv	uv	NOUN
ejpam-4187	488	15	∈	∈	PROPN
ejpam-4187	488	16	e(g	e(g	PROPN
ejpam-4187	488	17	◦	◦	NOUN
ejpam-4187	488	18	h	h	NOUN
ejpam-4187	488	19	)	)	PUNCT
ejpam-4187	488	20	.	.	PUNCT
ejpam-4187	489	1	suppose	suppose	VERB
ejpam-4187	489	2	that	that	SCONJ
ejpam-4187	489	3	v	v	PROPN
ejpam-4187	489	4	∈	∈	PROPN
ejpam-4187	489	5	s.	s.	PROPN
ejpam-4187	489	6	suppose	suppose	VERB
ejpam-4187	489	7	further	far	ADV
ejpam-4187	489	8	that	that	SCONJ
ejpam-4187	489	9	ng(v	ng(v	PUNCT
ejpam-4187	489	10	)	)	PUNCT
ejpam-4187	489	11	⊆	⊆	NUM
ejpam-4187	489	12	s.	s.	PROPN
ejpam-4187	489	13	by	by	ADP
ejpam-4187	489	14	(	(	PUNCT
ejpam-4187	489	15	i)(a	i)(a	NOUN
ejpam-4187	489	16	)	)	PUNCT
ejpam-4187	489	17	,	,	PUNCT
ejpam-4187	489	18	there	there	PRON
ejpam-4187	489	19	exists	exist	VERB
ejpam-4187	489	20	w	w	PROPN
ejpam-4187	489	21	∈	∈	PROPN
ejpam-4187	489	22	v	v	ADP
ejpam-4187	489	23	(	(	PUNCT
ejpam-4187	489	24	hv	hv	PROPN
ejpam-4187	489	25	)	)	PUNCT
ejpam-4187	489	26	\	\	PROPN
ejpam-4187	490	1	s	s	VERB
ejpam-4187	490	2	such	such	ADJ
ejpam-4187	490	3	that	that	SCONJ
ejpam-4187	490	4	uw	uw	PROPN
ejpam-4187	490	5	∈	∈	PROPN
ejpam-4187	490	6	e(hv	e(hv	PROPN
ejpam-4187	490	7	+	+	CCONJ
ejpam-4187	490	8	v	v	NOUN
ejpam-4187	490	9	)	)	PUNCT
ejpam-4187	490	10	or	or	CCONJ
ejpam-4187	490	11	there	there	PRON
ejpam-4187	490	12	exist	exist	VERB
ejpam-4187	490	13	distinct	distinct	ADJ
ejpam-4187	490	14	w	w	NOUN
ejpam-4187	490	15	,	,	PUNCT
ejpam-4187	490	16	z	z	PROPN
ejpam-4187	490	17	∈	∈	PROPN
ejpam-4187	490	18	v	v	ADP
ejpam-4187	490	19	(	(	PUNCT
ejpam-4187	490	20	hv	hv	PROPN
ejpam-4187	490	21	)	)	PUNCT
ejpam-4187	490	22	\	\	PROPN
ejpam-4187	491	1	s	s	PART
ejpam-4187	491	2	for	for	ADP
ejpam-4187	491	3	which	which	PRON
ejpam-4187	491	4	dhv+v(u	dhv+v(u	PROPN
ejpam-4187	491	5	,	,	PUNCT
ejpam-4187	491	6	w	w	NOUN
ejpam-4187	491	7	)	)	PUNCT
ejpam-4187	491	8	=	=	SYM
ejpam-4187	491	9	2	2	NUM
ejpam-4187	491	10	=	=	SYM
ejpam-4187	491	11	dhv+v(u	dhv+v(u	PROPN
ejpam-4187	491	12	,	,	PUNCT
ejpam-4187	491	13	z	z	NOUN
ejpam-4187	491	14	)	)	PUNCT
ejpam-4187	491	15	.	.	PUNCT
ejpam-4187	492	1	this	this	PRON
ejpam-4187	492	2	implies	imply	VERB
ejpam-4187	492	3	that	that	SCONJ
ejpam-4187	492	4	there	there	PRON
ejpam-4187	492	5	exists	exist	VERB
ejpam-4187	492	6	w	w	PROPN
ejpam-4187	492	7	∈	∈	PROPN
ejpam-4187	492	8	v	v	NOUN
ejpam-4187	492	9	(	(	PUNCT
ejpam-4187	492	10	g	g	PROPN
ejpam-4187	492	11	◦	◦	NOUN
ejpam-4187	492	12	h	h	NOUN
ejpam-4187	492	13	)	)	PUNCT
ejpam-4187	492	14	\s	\s	VERB
ejpam-4187	492	15	such	such	ADJ
ejpam-4187	492	16	that	that	SCONJ
ejpam-4187	492	17	uw	uw	PROPN
ejpam-4187	492	18	∈	∈	PROPN
ejpam-4187	492	19	e(g	e(g	PROPN
ejpam-4187	492	20	◦	◦	PROPN
ejpam-4187	492	21	h	h	NOUN
ejpam-4187	492	22	)	)	PUNCT
ejpam-4187	492	23	or	or	CCONJ
ejpam-4187	492	24	there	there	PRON
ejpam-4187	492	25	exist	exist	VERB
ejpam-4187	492	26	distinct	distinct	ADJ
ejpam-4187	492	27	w	w	NOUN
ejpam-4187	492	28	,	,	PUNCT
ejpam-4187	492	29	z	z	PROPN
ejpam-4187	492	30	∈	∈	PROPN
ejpam-4187	492	31	v	v	NOUN
ejpam-4187	492	32	(	(	PUNCT
ejpam-4187	492	33	g	g	PROPN
ejpam-4187	492	34	◦	◦	NOUN
ejpam-4187	492	35	h	h	NOUN
ejpam-4187	492	36	)	)	PUNCT
ejpam-4187	492	37	\s	\s	NOUN
ejpam-4187	492	38	for	for	ADP
ejpam-4187	492	39	which	which	PRON
ejpam-4187	492	40	dg	dg	VERB
ejpam-4187	492	41	◦	◦	PROPN
ejpam-4187	492	42	h(u	h(u	PROPN
ejpam-4187	492	43	,	,	PUNCT
ejpam-4187	492	44	w	w	NOUN
ejpam-4187	492	45	)	)	PUNCT
ejpam-4187	492	46	=	=	SYM
ejpam-4187	492	47	2	2	NUM
ejpam-4187	492	48	=	=	SYM
ejpam-4187	492	49	dg	dg	NOUN
ejpam-4187	492	50	◦	◦	NOUN
ejpam-4187	492	51	h(u	h(u	PROPN
ejpam-4187	492	52	,	,	PUNCT
ejpam-4187	492	53	z	z	NOUN
ejpam-4187	492	54	)	)	PUNCT
ejpam-4187	492	55	.	.	PUNCT
ejpam-4187	493	1	finally	finally	ADV
ejpam-4187	493	2	,	,	PUNCT
ejpam-4187	493	3	suppose	suppose	VERB
ejpam-4187	493	4	that	that	SCONJ
ejpam-4187	493	5	ng(v)\s	ng(v)\s	ADV
ejpam-4187	493	6	̸=	̸=	PROPN
ejpam-4187	493	7	∅.	∅.	ADV
ejpam-4187	493	8	if	if	SCONJ
ejpam-4187	493	9	|ng(v)\s|	|ng(v)\s|	PROPN
ejpam-4187	493	10	≥	≥	PROPN
ejpam-4187	493	11	r.	r.	PROPN
ejpam-4187	493	12	malalay	malalay	PROPN
ejpam-4187	493	13	,	,	PUNCT
ejpam-4187	493	14	f.	f.	PROPN
ejpam-4187	493	15	jamil	jamil	PROPN
ejpam-4187	493	16	/	/	SYM
ejpam-4187	493	17	eur	eur	PROPN
ejpam-4187	493	18	.	.	PUNCT
ejpam-4187	494	1	j.	j.	PROPN
ejpam-4187	494	2	pure	pure	PROPN
ejpam-4187	494	3	appl	appl	PROPN
ejpam-4187	494	4	.	.	PROPN
ejpam-4187	494	5	math	math	PROPN
ejpam-4187	494	6	,	,	PUNCT
ejpam-4187	494	7	15	15	NUM
ejpam-4187	494	8	(	(	PUNCT
ejpam-4187	494	9	1	1	NUM
ejpam-4187	494	10	)	)	PUNCT
ejpam-4187	494	11	(	(	PUNCT
ejpam-4187	494	12	2022	2022	NUM
ejpam-4187	494	13	)	)	PUNCT
ejpam-4187	494	14	,	,	PUNCT
ejpam-4187	494	15	207	207	NUM
ejpam-4187	494	16	-	-	SYM
ejpam-4187	494	17	223	223	NUM
ejpam-4187	494	18	219	219	NUM
ejpam-4187	494	19	2	2	NUM
ejpam-4187	494	20	,	,	PUNCT
ejpam-4187	494	21	then	then	ADV
ejpam-4187	494	22	there	there	PRON
ejpam-4187	494	23	exist	exist	VERB
ejpam-4187	494	24	distinct	distinct	ADJ
ejpam-4187	494	25	x	x	NOUN
ejpam-4187	494	26	,	,	PUNCT
ejpam-4187	494	27	y	y	PROPN
ejpam-4187	494	28	∈	∈	PROPN
ejpam-4187	494	29	ng(v	ng(v	PUNCT
ejpam-4187	494	30	)	)	PUNCT
ejpam-4187	494	31	\	\	PUNCT
ejpam-4187	494	32	s	s	VERB
ejpam-4187	494	33	such	such	ADJ
ejpam-4187	494	34	that	that	SCONJ
ejpam-4187	494	35	dg	dg	PROPN
ejpam-4187	494	36	◦	◦	PROPN
ejpam-4187	494	37	h(u	h(u	PROPN
ejpam-4187	494	38	,	,	PUNCT
ejpam-4187	494	39	x	x	NOUN
ejpam-4187	494	40	)	)	PUNCT
ejpam-4187	494	41	=	=	SYM
ejpam-4187	494	42	2	2	NUM
ejpam-4187	494	43	=	=	SYM
ejpam-4187	494	44	dg	dg	NOUN
ejpam-4187	494	45	◦	◦	NOUN
ejpam-4187	494	46	h(u	h(u	PROPN
ejpam-4187	494	47	,	,	PUNCT
ejpam-4187	494	48	y	y	PROPN
ejpam-4187	494	49	)	)	PUNCT
ejpam-4187	494	50	.	.	PUNCT
ejpam-4187	495	1	suppose	suppose	VERB
ejpam-4187	495	2	that	that	SCONJ
ejpam-4187	495	3	|ng(v	|ng(v	ADP
ejpam-4187	495	4	)	)	PUNCT
ejpam-4187	495	5	\	\	NOUN
ejpam-4187	495	6	s|	s|	NOUN
ejpam-4187	495	7	=	=	SYM
ejpam-4187	495	8	1	1	NUM
ejpam-4187	495	9	,	,	PUNCT
ejpam-4187	495	10	say	say	VERB
ejpam-4187	495	11	x	x	SYM
ejpam-4187	495	12	∈	∈	NOUN
ejpam-4187	495	13	ng(v	ng(v	PRON
ejpam-4187	495	14	)	)	PUNCT
ejpam-4187	495	15	\	\	PUNCT
ejpam-4187	496	1	s.	s.	PROPN
ejpam-4187	496	2	we	we	PRON
ejpam-4187	496	3	may	may	AUX
ejpam-4187	496	4	also	also	ADV
ejpam-4187	496	5	pick	pick	VERB
ejpam-4187	496	6	y	y	PROPN
ejpam-4187	496	7	∈	∈	PROPN
ejpam-4187	496	8	v	v	PROPN
ejpam-4187	496	9	(	(	PUNCT
ejpam-4187	496	10	hv	hv	PROPN
ejpam-4187	496	11	)	)	PUNCT
ejpam-4187	496	12	\	\	PROPN
ejpam-4187	497	1	s	s	PART
ejpam-4187	497	2	with	with	ADP
ejpam-4187	497	3	u	u	NOUN
ejpam-4187	497	4	̸=	̸=	PROPN
ejpam-4187	497	5	y	y	PROPN
ejpam-4187	497	6	by	by	ADP
ejpam-4187	497	7	(	(	PUNCT
ejpam-4187	497	8	i)(b	i)(b	NUM
ejpam-4187	497	9	)	)	PUNCT
ejpam-4187	497	10	.	.	PUNCT
ejpam-4187	498	1	then	then	ADV
ejpam-4187	498	2	uy	uy	PROPN
ejpam-4187	498	3	∈	∈	PROPN
ejpam-4187	498	4	e(g	e(g	PROPN
ejpam-4187	498	5	◦	◦	PROPN
ejpam-4187	498	6	h	h	NOUN
ejpam-4187	498	7	)	)	PUNCT
ejpam-4187	498	8	or	or	CCONJ
ejpam-4187	498	9	dg	dg	NOUN
ejpam-4187	498	10	◦	◦	PROPN
ejpam-4187	498	11	h(u	h(u	PROPN
ejpam-4187	498	12	,	,	PUNCT
ejpam-4187	498	13	y	y	NOUN
ejpam-4187	498	14	)	)	PUNCT
ejpam-4187	498	15	=	=	SYM
ejpam-4187	498	16	2	2	NUM
ejpam-4187	498	17	=	=	SYM
ejpam-4187	498	18	dg	dg	NOUN
ejpam-4187	498	19	◦	◦	NOUN
ejpam-4187	498	20	h(u	h(u	PROPN
ejpam-4187	498	21	,	,	PUNCT
ejpam-4187	498	22	x	x	NOUN
ejpam-4187	498	23	)	)	PUNCT
ejpam-4187	498	24	.	.	PUNCT
ejpam-4187	499	1	accordingly	accordingly	ADV
ejpam-4187	499	2	,	,	PUNCT
ejpam-4187	499	3	s	s	VERB
ejpam-4187	499	4	is	be	AUX
ejpam-4187	499	5	a	a	DET
ejpam-4187	499	6	restrained	restrained	ADJ
ejpam-4187	499	7	disjunctive	disjunctive	ADJ
ejpam-4187	499	8	dominating	dominating	NOUN
ejpam-4187	499	9	set	set	NOUN
ejpam-4187	499	10	of	of	ADP
ejpam-4187	499	11	g	g	PROPN
ejpam-4187	499	12	◦	◦	NOUN
ejpam-4187	499	13	h.	h.	PROPN
ejpam-4187	499	14	corollary	corollary	ADJ
ejpam-4187	499	15	6	6	NUM
ejpam-4187	499	16	.	.	PUNCT
ejpam-4187	500	1	for	for	ADP
ejpam-4187	500	2	nontrivial	nontrivial	ADJ
ejpam-4187	500	3	connected	connect	VERB
ejpam-4187	500	4	graphs	graph	NOUN
ejpam-4187	500	5	g	g	NOUN
ejpam-4187	500	6	and	and	CCONJ
ejpam-4187	500	7	h	h	NOUN
ejpam-4187	500	8	,	,	PUNCT
ejpam-4187	500	9	γdr	γdr	PROPN
ejpam-4187	500	10	(	(	PUNCT
ejpam-4187	500	11	g	g	PROPN
ejpam-4187	500	12	◦	◦	NOUN
ejpam-4187	500	13	h	h	NOUN
ejpam-4187	500	14	)	)	PUNCT
ejpam-4187	500	15	=	=	SYM
ejpam-4187	500	16	γ×2(g	γ×2(g	PROPN
ejpam-4187	500	17	)	)	PUNCT
ejpam-4187	500	18	.	.	PUNCT
ejpam-4187	501	1	proof	proof	NOUN
ejpam-4187	501	2	.	.	PUNCT
ejpam-4187	502	1	let	let	VERB
ejpam-4187	502	2	s	s	PRON
ejpam-4187	502	3	⊆	⊆	NUM
ejpam-4187	502	4	v	v	NOUN
ejpam-4187	502	5	(	(	PUNCT
ejpam-4187	502	6	g	g	NOUN
ejpam-4187	502	7	)	)	PUNCT
ejpam-4187	502	8	be	be	AUX
ejpam-4187	502	9	a	a	DET
ejpam-4187	502	10	2	2	NUM
ejpam-4187	502	11	-	-	PUNCT
ejpam-4187	502	12	dominating	dominating	NOUN
ejpam-4187	502	13	set	set	NOUN
ejpam-4187	502	14	of	of	ADP
ejpam-4187	502	15	g.	g.	PROPN
ejpam-4187	502	16	by	by	ADP
ejpam-4187	502	17	corollary	corollary	ADJ
ejpam-4187	502	18	3	3	NUM
ejpam-4187	502	19	,	,	PUNCT
ejpam-4187	502	20	s	s	VERB
ejpam-4187	502	21	is	be	AUX
ejpam-4187	502	22	a	a	DET
ejpam-4187	502	23	disjunctive	disjunctive	ADJ
ejpam-4187	502	24	dominating	dominating	NOUN
ejpam-4187	502	25	set	set	NOUN
ejpam-4187	502	26	of	of	ADP
ejpam-4187	502	27	g	g	PROPN
ejpam-4187	502	28	◦	◦	NOUN
ejpam-4187	502	29	h.	h.	NOUN
ejpam-4187	502	30	moreover	moreover	ADV
ejpam-4187	502	31	,	,	PUNCT
ejpam-4187	502	32	since	since	SCONJ
ejpam-4187	502	33	all	all	DET
ejpam-4187	502	34	the	the	DET
ejpam-4187	502	35	properties	property	NOUN
ejpam-4187	502	36	in	in	ADP
ejpam-4187	502	37	theorem	theorem	ADJ
ejpam-4187	502	38	6	6	NUM
ejpam-4187	502	39	hold	hold	NOUN
ejpam-4187	502	40	for	for	ADP
ejpam-4187	502	41	s	s	NOUN
ejpam-4187	502	42	,	,	PUNCT
ejpam-4187	502	43	s	s	VERB
ejpam-4187	502	44	is	be	AUX
ejpam-4187	502	45	a	a	DET
ejpam-4187	502	46	restrained	restrained	ADJ
ejpam-4187	502	47	disjunctive	disjunctive	ADJ
ejpam-4187	502	48	dominating	dominating	NOUN
ejpam-4187	502	49	set	set	NOUN
ejpam-4187	502	50	of	of	ADP
ejpam-4187	502	51	g	g	PROPN
ejpam-4187	502	52	◦	◦	PROPN
ejpam-4187	502	53	h.	h.	PROPN
ejpam-4187	502	54	thus	thus	ADV
ejpam-4187	502	55	,	,	PUNCT
ejpam-4187	502	56	γdr	γdr	INTJ
ejpam-4187	502	57	(	(	PUNCT
ejpam-4187	502	58	g	g	PROPN
ejpam-4187	502	59	◦	◦	NOUN
ejpam-4187	502	60	h	h	NOUN
ejpam-4187	502	61	)	)	PUNCT
ejpam-4187	502	62	≤	≤	NUM
ejpam-4187	502	63	|s|	|s|	PROPN
ejpam-4187	502	64	.	.	PUNCT
ejpam-4187	503	1	since	since	SCONJ
ejpam-4187	503	2	s	s	NOUN
ejpam-4187	503	3	is	be	AUX
ejpam-4187	503	4	arbitrary	arbitrary	ADJ
ejpam-4187	503	5	,	,	PUNCT
ejpam-4187	503	6	γdr	γdr	INTJ
ejpam-4187	504	1	(	(	PUNCT
ejpam-4187	504	2	g	g	PROPN
ejpam-4187	504	3	◦	◦	NOUN
ejpam-4187	504	4	h	h	NOUN
ejpam-4187	504	5	)	)	PUNCT
ejpam-4187	504	6	≤	≤	NOUN
ejpam-4187	504	7	γ×2(g	γ×2(g	PROPN
ejpam-4187	504	8	)	)	PUNCT
ejpam-4187	504	9	.	.	PUNCT
ejpam-4187	505	1	further	far	ADV
ejpam-4187	505	2	,	,	PUNCT
ejpam-4187	505	3	using	use	VERB
ejpam-4187	505	4	corollary	corollary	NOUN
ejpam-4187	505	5	3	3	NUM
ejpam-4187	505	6	again	again	ADV
ejpam-4187	505	7	,	,	PUNCT
ejpam-4187	505	8	γ×2(g	γ×2(g	PROPN
ejpam-4187	505	9	)	)	PUNCT
ejpam-4187	505	10	≤	≤	NOUN
ejpam-4187	505	11	γdr	γdr	INTJ
ejpam-4187	506	1	(	(	PUNCT
ejpam-4187	506	2	g	g	PROPN
ejpam-4187	506	3	◦	◦	NOUN
ejpam-4187	506	4	h	h	NOUN
ejpam-4187	506	5	)	)	PUNCT
ejpam-4187	506	6	≤	≤	NOUN
ejpam-4187	506	7	γ×2(g	γ×2(g	PROPN
ejpam-4187	506	8	)	)	PUNCT
ejpam-4187	506	9	.	.	PUNCT
ejpam-4187	507	1	this	this	PRON
ejpam-4187	507	2	proves	prove	VERB
ejpam-4187	507	3	the	the	DET
ejpam-4187	507	4	equality	equality	NOUN
ejpam-4187	507	5	.	.	PUNCT
ejpam-4187	508	1	4.3	4.3	NUM
ejpam-4187	508	2	.	.	PUNCT
ejpam-4187	509	1	on	on	ADP
ejpam-4187	509	2	lexicographic	lexicographic	ADJ
ejpam-4187	509	3	product	product	NOUN
ejpam-4187	509	4	of	of	ADP
ejpam-4187	509	5	graphs	graph	NOUN
ejpam-4187	509	6	[	[	X
ejpam-4187	509	7	15	15	NUM
ejpam-4187	509	8	]	]	PUNCT
ejpam-4187	509	9	for	for	ADP
ejpam-4187	509	10	any	any	DET
ejpam-4187	509	11	graphs	graph	NOUN
ejpam-4187	509	12	g	g	NOUN
ejpam-4187	509	13	and	and	CCONJ
ejpam-4187	509	14	h	h	NOUN
ejpam-4187	509	15	and	and	CCONJ
ejpam-4187	509	16	for	for	ADP
ejpam-4187	509	17	any	any	DET
ejpam-4187	509	18	c	c	NOUN
ejpam-4187	509	19	⊆	⊆	NUM
ejpam-4187	509	20	v	v	NOUN
ejpam-4187	509	21	(	(	PUNCT
ejpam-4187	509	22	g[h	g[h	PROPN
ejpam-4187	509	23	]	]	PUNCT
ejpam-4187	509	24	)	)	PUNCT
ejpam-4187	509	25	,	,	PUNCT
ejpam-4187	509	26	there	there	PRON
ejpam-4187	509	27	exists	exist	VERB
ejpam-4187	509	28	s	s	PROPN
ejpam-4187	509	29	⊆	⊆	NUM
ejpam-4187	509	30	v	v	NOUN
ejpam-4187	509	31	(	(	PUNCT
ejpam-4187	509	32	g	g	NOUN
ejpam-4187	509	33	)	)	PUNCT
ejpam-4187	509	34	for	for	ADP
ejpam-4187	509	35	which	which	PRON
ejpam-4187	509	36	c	c	NOUN
ejpam-4187	509	37	=	=	SYM
ejpam-4187	509	38	∪x∈s	∪x∈s	PROPN
ejpam-4187	509	39	(	(	PUNCT
ejpam-4187	509	40	{	{	PUNCT
ejpam-4187	509	41	x	x	NOUN
ejpam-4187	509	42	}	}	PUNCT
ejpam-4187	509	43	×	×	PROPN
ejpam-4187	509	44	tx	tx	PROPN
ejpam-4187	509	45	)	)	PUNCT
ejpam-4187	509	46	,	,	PUNCT
ejpam-4187	509	47	where	where	SCONJ
ejpam-4187	509	48	tx	tx	PROPN
ejpam-4187	509	49	⊆	⊆	NUM
ejpam-4187	509	50	v	v	NOUN
ejpam-4187	509	51	(	(	PUNCT
ejpam-4187	509	52	h	h	NOUN
ejpam-4187	509	53	)	)	PUNCT
ejpam-4187	509	54	for	for	ADP
ejpam-4187	509	55	each	each	PRON
ejpam-4187	509	56	x	x	PROPN
ejpam-4187	509	57	∈	∈	PROPN
ejpam-4187	509	58	s.	s.	PROPN
ejpam-4187	509	59	theorem	theorem	VERB
ejpam-4187	509	60	7	7	NUM
ejpam-4187	509	61	.	.	PUNCT
ejpam-4187	510	1	[	[	X
ejpam-4187	510	2	15	15	NUM
ejpam-4187	510	3	]	]	PUNCT
ejpam-4187	510	4	let	let	VERB
ejpam-4187	510	5	g	g	NOUN
ejpam-4187	510	6	and	and	CCONJ
ejpam-4187	510	7	h	h	NOUN
ejpam-4187	510	8	be	be	AUX
ejpam-4187	510	9	nontrivial	nontrivial	ADJ
ejpam-4187	510	10	connected	connected	ADJ
ejpam-4187	510	11	graphs	graph	NOUN
ejpam-4187	510	12	,	,	PUNCT
ejpam-4187	510	13	and	and	CCONJ
ejpam-4187	510	14	let	let	VERB
ejpam-4187	510	15	c	c	NOUN
ejpam-4187	510	16	=	=	SYM
ejpam-4187	510	17	∪x∈s	∪x∈s	PROPN
ejpam-4187	510	18	(	(	PUNCT
ejpam-4187	510	19	{	{	PUNCT
ejpam-4187	510	20	x	x	NOUN
ejpam-4187	510	21	}	}	PUNCT
ejpam-4187	510	22	×	×	PROPN
ejpam-4187	510	23	tx	tx	PROPN
ejpam-4187	510	24	)	)	PUNCT
ejpam-4187	510	25	.	.	PUNCT
ejpam-4187	511	1	then	then	ADV
ejpam-4187	511	2	c	c	PROPN
ejpam-4187	511	3	is	be	AUX
ejpam-4187	511	4	a	a	DET
ejpam-4187	511	5	disjunctive	disjunctive	ADJ
ejpam-4187	511	6	dominating	dominating	NOUN
ejpam-4187	511	7	set	set	NOUN
ejpam-4187	511	8	of	of	ADP
ejpam-4187	511	9	g[h	g[h	PROPN
ejpam-4187	511	10	]	]	PUNCT
ejpam-4187	511	11	if	if	SCONJ
ejpam-4187	511	12	and	and	CCONJ
ejpam-4187	511	13	only	only	ADV
ejpam-4187	511	14	if	if	SCONJ
ejpam-4187	511	15	one	one	NUM
ejpam-4187	511	16	of	of	ADP
ejpam-4187	511	17	the	the	DET
ejpam-4187	511	18	following	follow	VERB
ejpam-4187	511	19	holds	hold	VERB
ejpam-4187	511	20	:	:	PUNCT
ejpam-4187	511	21	(	(	PUNCT
ejpam-4187	511	22	i	i	NOUN
ejpam-4187	511	23	)	)	PUNCT
ejpam-4187	511	24	s	s	VERB
ejpam-4187	511	25	is	be	AUX
ejpam-4187	511	26	a	a	DET
ejpam-4187	511	27	disjunctive	disjunctive	ADJ
ejpam-4187	511	28	total	total	ADJ
ejpam-4187	511	29	dominating	dominating	NOUN
ejpam-4187	511	30	set	set	VERB
ejpam-4187	511	31	in	in	ADP
ejpam-4187	511	32	g	g	PROPN
ejpam-4187	511	33	;	;	PUNCT
ejpam-4187	511	34	or	or	CCONJ
ejpam-4187	511	35	(	(	PUNCT
ejpam-4187	511	36	ii	ii	NOUN
ejpam-4187	511	37	)	)	PUNCT
ejpam-4187	512	1	s	s	VERB
ejpam-4187	512	2	is	be	AUX
ejpam-4187	512	3	a	a	DET
ejpam-4187	512	4	distance	distance	NOUN
ejpam-4187	512	5	-	-	PUNCT
ejpam-4187	512	6	two	two	NUM
ejpam-4187	512	7	dominating	dominating	NOUN
ejpam-4187	512	8	set	set	NOUN
ejpam-4187	512	9	of	of	ADP
ejpam-4187	512	10	g	g	PROPN
ejpam-4187	512	11	satisfying	satisfy	VERB
ejpam-4187	512	12	the	the	DET
ejpam-4187	512	13	following	following	NOUN
ejpam-4187	512	14	:	:	PUNCT
ejpam-4187	512	15	(	(	PUNCT
ejpam-4187	512	16	a	a	X
ejpam-4187	512	17	)	)	PUNCT
ejpam-4187	512	18	for	for	ADP
ejpam-4187	512	19	each	each	DET
ejpam-4187	512	20	x	x	SYM
ejpam-4187	512	21	∈	∈	PROPN
ejpam-4187	512	22	v	v	ADP
ejpam-4187	512	23	(	(	PUNCT
ejpam-4187	512	24	g	g	NOUN
ejpam-4187	512	25	)	)	PUNCT
ejpam-4187	512	26	\nd	\nd	PROPN
ejpam-4187	512	27	g[s	g[	NOUN
ejpam-4187	512	28	]	]	PUNCT
ejpam-4187	512	29	,	,	PUNCT
ejpam-4187	512	30	where	where	SCONJ
ejpam-4187	512	31	nd	nd	NOUN
ejpam-4187	512	32	g[s	g[s	X
ejpam-4187	512	33	]	]	X
ejpam-4187	512	34	=	=	SYM
ejpam-4187	512	35	s	s	PROPN
ejpam-4187	512	36	∪nd	∪nd	NOUN
ejpam-4187	512	37	g(s	g(s	PROPN
ejpam-4187	512	38	)	)	PUNCT
ejpam-4187	512	39	,	,	PUNCT
ejpam-4187	512	40	there	there	PRON
ejpam-4187	512	41	exists	exist	VERB
ejpam-4187	512	42	u	u	PROPN
ejpam-4187	512	43	∈	∈	PROPN
ejpam-4187	512	44	s	s	X
ejpam-4187	512	45	for	for	ADP
ejpam-4187	512	46	which	which	PRON
ejpam-4187	512	47	dg(u	dg(u	NOUN
ejpam-4187	512	48	,	,	PUNCT
ejpam-4187	512	49	x	x	X
ejpam-4187	512	50	)	)	PUNCT
ejpam-4187	512	51	=	=	SYM
ejpam-4187	512	52	2	2	NUM
ejpam-4187	512	53	and	and	CCONJ
ejpam-4187	512	54	|tu|	|tu|	NOUN
ejpam-4187	512	55	≥	≥	NOUN
ejpam-4187	512	56	2	2	NUM
ejpam-4187	512	57	.	.	PUNCT
ejpam-4187	512	58	(	(	PUNCT
ejpam-4187	512	59	b	b	NOUN
ejpam-4187	512	60	)	)	PUNCT
ejpam-4187	512	61	for	for	ADP
ejpam-4187	512	62	each	each	DET
ejpam-4187	512	63	x	x	SYM
ejpam-4187	512	64	∈	∈	PROPN
ejpam-4187	512	65	s	s	PART
ejpam-4187	512	66	\	\	NOUN
ejpam-4187	512	67	ng(s	ng(s	NUM
ejpam-4187	512	68	,	,	PUNCT
ejpam-4187	512	69	2	2	NUM
ejpam-4187	512	70	)	)	PUNCT
ejpam-4187	512	71	,	,	PUNCT
ejpam-4187	512	72	either	either	CCONJ
ejpam-4187	512	73	tx	tx	PROPN
ejpam-4187	512	74	=	=	SYM
ejpam-4187	512	75	{	{	PUNCT
ejpam-4187	512	76	y	y	NOUN
ejpam-4187	512	77	}	}	PUNCT
ejpam-4187	512	78	and	and	CCONJ
ejpam-4187	512	79	is	be	AUX
ejpam-4187	512	80	a	a	DET
ejpam-4187	512	81	dominating	dominating	NOUN
ejpam-4187	512	82	set	set	NOUN
ejpam-4187	512	83	of	of	ADP
ejpam-4187	512	84	h	h	NOUN
ejpam-4187	512	85	or	or	CCONJ
ejpam-4187	512	86	|tx|	|tx|	PROPN
ejpam-4187	512	87	≥	≥	NUM
ejpam-4187	512	88	2	2	NUM
ejpam-4187	512	89	.	.	PUNCT
ejpam-4187	512	90	theorem	theorem	NOUN
ejpam-4187	512	91	8	8	NUM
ejpam-4187	512	92	.	.	PUNCT
ejpam-4187	513	1	let	let	VERB
ejpam-4187	513	2	g	g	NOUN
ejpam-4187	513	3	and	and	CCONJ
ejpam-4187	513	4	h	h	NOUN
ejpam-4187	513	5	be	be	AUX
ejpam-4187	513	6	nontrivial	nontrivial	ADJ
ejpam-4187	513	7	connected	connected	ADJ
ejpam-4187	513	8	graphs	graph	NOUN
ejpam-4187	513	9	,	,	PUNCT
ejpam-4187	513	10	and	and	CCONJ
ejpam-4187	513	11	let	let	VERB
ejpam-4187	513	12	c	c	NOUN
ejpam-4187	513	13	=	=	SYM
ejpam-4187	513	14	∪x∈s	∪x∈s	PROPN
ejpam-4187	513	15	(	(	PUNCT
ejpam-4187	513	16	{	{	PUNCT
ejpam-4187	513	17	x	x	NOUN
ejpam-4187	513	18	}	}	PUNCT
ejpam-4187	513	19	×	×	PROPN
ejpam-4187	513	20	tx	tx	PROPN
ejpam-4187	513	21	)	)	PUNCT
ejpam-4187	513	22	be	be	AUX
ejpam-4187	513	23	a	a	DET
ejpam-4187	513	24	disjunctive	disjunctive	ADJ
ejpam-4187	513	25	dominating	dominating	NOUN
ejpam-4187	513	26	set	set	NOUN
ejpam-4187	513	27	of	of	ADP
ejpam-4187	513	28	g[h	g[h	PROPN
ejpam-4187	513	29	]	]	PUNCT
ejpam-4187	513	30	.	.	PUNCT
ejpam-4187	514	1	then	then	ADV
ejpam-4187	514	2	c	c	PROPN
ejpam-4187	514	3	is	be	AUX
ejpam-4187	514	4	a	a	DET
ejpam-4187	514	5	restrained	restrained	ADJ
ejpam-4187	514	6	disjunctive	disjunctive	ADJ
ejpam-4187	514	7	dominating	dominating	NOUN
ejpam-4187	514	8	set	set	NOUN
ejpam-4187	514	9	of	of	ADP
ejpam-4187	514	10	g[h	g[h	PROPN
ejpam-4187	514	11	]	]	PUNCT
ejpam-4187	514	12	if	if	SCONJ
ejpam-4187	514	13	and	and	CCONJ
ejpam-4187	514	14	only	only	ADV
ejpam-4187	514	15	if	if	SCONJ
ejpam-4187	514	16	(	(	PUNCT
ejpam-4187	514	17	i	i	NOUN
ejpam-4187	514	18	)	)	PUNCT
ejpam-4187	514	19	or	or	CCONJ
ejpam-4187	514	20	(	(	PUNCT
ejpam-4187	514	21	ii	ii	NOUN
ejpam-4187	514	22	)	)	PUNCT
ejpam-4187	514	23	of	of	ADP
ejpam-4187	514	24	theorem	theorem	ADJ
ejpam-4187	514	25	7	7	NUM
ejpam-4187	514	26	holds	hold	NOUN
ejpam-4187	514	27	and	and	CCONJ
ejpam-4187	514	28	each	each	PRON
ejpam-4187	514	29	of	of	ADP
ejpam-4187	514	30	the	the	DET
ejpam-4187	514	31	following	following	NOUN
ejpam-4187	514	32	holds	hold	VERB
ejpam-4187	514	33	for	for	ADP
ejpam-4187	514	34	s	s	NOUN
ejpam-4187	514	35	:	:	PUNCT
ejpam-4187	514	36	for	for	ADP
ejpam-4187	514	37	each	each	DET
ejpam-4187	514	38	x	x	SYM
ejpam-4187	514	39	∈	∈	PROPN
ejpam-4187	514	40	s	s	PART
ejpam-4187	514	41	\	\	PUNCT
ejpam-4187	514	42	(	(	PUNCT
ejpam-4187	514	43	ng(v	ng(v	X
ejpam-4187	514	44	(	(	PUNCT
ejpam-4187	514	45	g	g	NOUN
ejpam-4187	514	46	)	)	PUNCT
ejpam-4187	514	47	\	\	PUNCT
ejpam-4187	515	1	(	(	PUNCT
ejpam-4187	515	2	s	s	NOUN
ejpam-4187	515	3	,	,	PUNCT
ejpam-4187	515	4	2	2	NUM
ejpam-4187	515	5	)	)	PUNCT
ejpam-4187	515	6	)	)	PUNCT
ejpam-4187	515	7	for	for	ADP
ejpam-4187	515	8	which	which	PRON
ejpam-4187	515	9	tx	tx	ADP
ejpam-4187	515	10	̸=	̸=	PROPN
ejpam-4187	515	11	v	v	PROPN
ejpam-4187	515	12	(	(	PUNCT
ejpam-4187	515	13	h	h	NOUN
ejpam-4187	515	14	)	)	PUNCT
ejpam-4187	515	15	,	,	PUNCT
ejpam-4187	515	16	(	(	PUNCT
ejpam-4187	515	17	a	a	X
ejpam-4187	515	18	)	)	PUNCT
ejpam-4187	515	19	if	if	SCONJ
ejpam-4187	515	20	tu	tu	PROPN
ejpam-4187	515	21	=	=	SYM
ejpam-4187	515	22	v	v	PROPN
ejpam-4187	515	23	(	(	PUNCT
ejpam-4187	515	24	h	h	NOUN
ejpam-4187	515	25	)	)	PUNCT
ejpam-4187	515	26	for	for	ADP
ejpam-4187	515	27	all	all	PRON
ejpam-4187	515	28	u	u	PROPN
ejpam-4187	515	29	∈	∈	PROPN
ejpam-4187	515	30	ng(x	ng(x	NUM
ejpam-4187	515	31	,	,	PUNCT
ejpam-4187	515	32	2	2	NUM
ejpam-4187	515	33	)	)	PUNCT
ejpam-4187	515	34	,	,	PUNCT
ejpam-4187	515	35	then	then	ADV
ejpam-4187	515	36	either	either	CCONJ
ejpam-4187	515	37	|v	|v	PROPN
ejpam-4187	515	38	(	(	PUNCT
ejpam-4187	515	39	h)\tx|	h)\tx|	X
ejpam-4187	515	40	≥	≥	NOUN
ejpam-4187	515	41	3	3	NUM
ejpam-4187	515	42	or	or	CCONJ
ejpam-4187	515	43	⟨v	⟨v	NUM
ejpam-4187	515	44	(	(	PUNCT
ejpam-4187	515	45	h)\tx⟩	h)\tx⟩	VERB
ejpam-4187	515	46	=	=	SYM
ejpam-4187	515	47	k2	k2	NOUN
ejpam-4187	515	48	.	.	PUNCT
ejpam-4187	516	1	(	(	PUNCT
ejpam-4187	516	2	b	b	X
ejpam-4187	516	3	)	)	PUNCT
ejpam-4187	516	4	if	if	SCONJ
ejpam-4187	516	5	⟨v	⟨v	NUM
ejpam-4187	516	6	(	(	PUNCT
ejpam-4187	516	7	h	h	NOUN
ejpam-4187	516	8	)	)	PUNCT
ejpam-4187	516	9	\	\	NOUN
ejpam-4187	516	10	tx⟩	tx⟩	PROPN
ejpam-4187	516	11	=	=	SYM
ejpam-4187	516	12	k2	k2	PROPN
ejpam-4187	516	13	,	,	PUNCT
ejpam-4187	516	14	then	then	ADV
ejpam-4187	516	15	there	there	PRON
ejpam-4187	516	16	exists	exist	VERB
ejpam-4187	516	17	u	u	PROPN
ejpam-4187	516	18	∈	∈	PROPN
ejpam-4187	516	19	ng(x	ng(x	NUM
ejpam-4187	516	20	,	,	PUNCT
ejpam-4187	516	21	2	2	NUM
ejpam-4187	516	22	)	)	PUNCT
ejpam-4187	516	23	for	for	ADP
ejpam-4187	516	24	which	which	PRON
ejpam-4187	516	25	tu	tu	PROPN
ejpam-4187	516	26	̸=	̸=	PROPN
ejpam-4187	516	27	v	v	PROPN
ejpam-4187	516	28	(	(	PUNCT
ejpam-4187	516	29	h	h	NOUN
ejpam-4187	516	30	)	)	PUNCT
ejpam-4187	516	31	.	.	PUNCT
ejpam-4187	517	1	(	(	PUNCT
ejpam-4187	517	2	c	c	X
ejpam-4187	517	3	)	)	PUNCT
ejpam-4187	517	4	if	if	SCONJ
ejpam-4187	517	5	|v	|v	PROPN
ejpam-4187	517	6	(	(	PUNCT
ejpam-4187	517	7	h)\tx|	h)\tx|	X
ejpam-4187	517	8	=	=	SYM
ejpam-4187	517	9	1	1	NUM
ejpam-4187	517	10	,	,	PUNCT
ejpam-4187	517	11	then	then	ADV
ejpam-4187	517	12	one	one	NUM
ejpam-4187	517	13	of	of	ADP
ejpam-4187	517	14	the	the	DET
ejpam-4187	517	15	following	follow	VERB
ejpam-4187	517	16	holds	hold	VERB
ejpam-4187	517	17	:	:	PUNCT
ejpam-4187	517	18	there	there	PRON
ejpam-4187	517	19	exists	exist	VERB
ejpam-4187	517	20	u	u	PROPN
ejpam-4187	517	21	∈	∈	PROPN
ejpam-4187	517	22	ng(x	ng(x	NUM
ejpam-4187	517	23	)	)	PUNCT
ejpam-4187	517	24	for	for	ADP
ejpam-4187	517	25	which	which	PRON
ejpam-4187	517	26	tu	tu	PROPN
ejpam-4187	517	27	̸=	̸=	PROPN
ejpam-4187	517	28	v	v	PROPN
ejpam-4187	517	29	(	(	PUNCT
ejpam-4187	517	30	h	h	NOUN
ejpam-4187	517	31	)	)	PUNCT
ejpam-4187	517	32	;	;	PUNCT
ejpam-4187	517	33	there	there	PRON
ejpam-4187	517	34	exists	exist	VERB
ejpam-4187	517	35	u	u	PROPN
ejpam-4187	517	36	∈	∈	PROPN
ejpam-4187	517	37	ng(x	ng(x	NUM
ejpam-4187	517	38	,	,	PUNCT
ejpam-4187	517	39	2	2	NUM
ejpam-4187	517	40	)	)	PUNCT
ejpam-4187	517	41	for	for	ADP
ejpam-4187	517	42	which	which	PRON
ejpam-4187	517	43	|v	|v	PROPN
ejpam-4187	517	44	(	(	PUNCT
ejpam-4187	517	45	h	h	NOUN
ejpam-4187	517	46	)	)	PUNCT
ejpam-4187	517	47	\	\	PUNCT
ejpam-4187	518	1	tu|	tu|	ADP
ejpam-4187	518	2	≥	≥	NOUN
ejpam-4187	518	3	2	2	NUM
ejpam-4187	518	4	;	;	PUNCT
ejpam-4187	518	5	there	there	PRON
ejpam-4187	518	6	exist	exist	VERB
ejpam-4187	518	7	distinct	distinct	ADJ
ejpam-4187	518	8	u	u	NOUN
ejpam-4187	518	9	,	,	PUNCT
ejpam-4187	518	10	z	z	PROPN
ejpam-4187	518	11	∈	∈	PROPN
ejpam-4187	518	12	ng(x	ng(x	NUM
ejpam-4187	518	13	,	,	PUNCT
ejpam-4187	518	14	2	2	NUM
ejpam-4187	518	15	)	)	PUNCT
ejpam-4187	518	16	for	for	ADP
ejpam-4187	518	17	which	which	PRON
ejpam-4187	518	18	tu	tu	PROPN
ejpam-4187	518	19	̸=	̸=	PROPN
ejpam-4187	518	20	v	v	ADP
ejpam-4187	518	21	(	(	PUNCT
ejpam-4187	518	22	h	h	NOUN
ejpam-4187	518	23	)	)	PUNCT
ejpam-4187	518	24	and	and	CCONJ
ejpam-4187	518	25	tz	tz	PROPN
ejpam-4187	518	26	̸=	̸=	PROPN
ejpam-4187	518	27	v	v	NOUN
ejpam-4187	518	28	(	(	PUNCT
ejpam-4187	518	29	h	h	NOUN
ejpam-4187	518	30	)	)	PUNCT
ejpam-4187	518	31	.	.	PUNCT
ejpam-4187	519	1	r.	r.	PROPN
ejpam-4187	519	2	malalay	malalay	PROPN
ejpam-4187	519	3	,	,	PUNCT
ejpam-4187	519	4	f.	f.	PROPN
ejpam-4187	519	5	jamil	jamil	PROPN
ejpam-4187	519	6	/	/	SYM
ejpam-4187	519	7	eur	eur	PROPN
ejpam-4187	519	8	.	.	PUNCT
ejpam-4187	520	1	j.	j.	PROPN
ejpam-4187	520	2	pure	pure	PROPN
ejpam-4187	520	3	appl	appl	PROPN
ejpam-4187	520	4	.	.	PROPN
ejpam-4187	520	5	math	math	PROPN
ejpam-4187	520	6	,	,	PUNCT
ejpam-4187	520	7	15	15	NUM
ejpam-4187	520	8	(	(	PUNCT
ejpam-4187	520	9	1	1	NUM
ejpam-4187	520	10	)	)	PUNCT
ejpam-4187	520	11	(	(	PUNCT
ejpam-4187	520	12	2022	2022	NUM
ejpam-4187	520	13	)	)	PUNCT
ejpam-4187	520	14	,	,	PUNCT
ejpam-4187	520	15	207	207	NUM
ejpam-4187	520	16	-	-	SYM
ejpam-4187	520	17	223	223	NUM
ejpam-4187	520	18	220	220	NUM
ejpam-4187	520	19	proof	proof	NOUN
ejpam-4187	520	20	.	.	PUNCT
ejpam-4187	520	21	suppose	suppose	VERB
ejpam-4187	520	22	that	that	SCONJ
ejpam-4187	520	23	c	c	PROPN
ejpam-4187	520	24	is	be	AUX
ejpam-4187	520	25	a	a	DET
ejpam-4187	520	26	restrained	restrained	ADJ
ejpam-4187	520	27	disjunctive	disjunctive	ADJ
ejpam-4187	520	28	dominating	dominating	NOUN
ejpam-4187	520	29	set	set	NOUN
ejpam-4187	520	30	of	of	ADP
ejpam-4187	520	31	g[h	g[h	NOUN
ejpam-4187	520	32	]	]	PUNCT
ejpam-4187	520	33	.	.	PUNCT
ejpam-4187	521	1	since	since	SCONJ
ejpam-4187	521	2	c	c	PROPN
ejpam-4187	521	3	is	be	AUX
ejpam-4187	521	4	a	a	DET
ejpam-4187	521	5	disjunctive	disjunctive	ADJ
ejpam-4187	521	6	dominating	dominating	NOUN
ejpam-4187	521	7	set	set	NOUN
ejpam-4187	521	8	of	of	ADP
ejpam-4187	521	9	g[h	g[h	PROPN
ejpam-4187	521	10	]	]	PUNCT
ejpam-4187	521	11	,	,	PUNCT
ejpam-4187	521	12	(	(	PUNCT
ejpam-4187	521	13	i	i	NOUN
ejpam-4187	521	14	)	)	PUNCT
ejpam-4187	521	15	or	or	CCONJ
ejpam-4187	521	16	(	(	PUNCT
ejpam-4187	521	17	ii	ii	NOUN
ejpam-4187	521	18	)	)	PUNCT
ejpam-4187	521	19	of	of	ADP
ejpam-4187	521	20	theorem	theorem	ADJ
ejpam-4187	521	21	7	7	NUM
ejpam-4187	521	22	holds	hold	NOUN
ejpam-4187	521	23	.	.	PUNCT
ejpam-4187	522	1	now	now	ADV
ejpam-4187	522	2	,	,	PUNCT
ejpam-4187	522	3	let	let	VERB
ejpam-4187	522	4	x	x	PUNCT
ejpam-4187	522	5	∈	∈	PROPN
ejpam-4187	522	6	s	s	PART
ejpam-4187	522	7	\	\	PUNCT
ejpam-4187	522	8	(	(	PUNCT
ejpam-4187	522	9	ng(v	ng(v	X
ejpam-4187	522	10	(	(	PUNCT
ejpam-4187	522	11	g	g	NOUN
ejpam-4187	522	12	)	)	PUNCT
ejpam-4187	522	13	\	\	PUNCT
ejpam-4187	523	1	(	(	PUNCT
ejpam-4187	523	2	s	s	NOUN
ejpam-4187	523	3	,	,	PUNCT
ejpam-4187	523	4	2	2	NUM
ejpam-4187	523	5	)	)	PUNCT
ejpam-4187	523	6	)	)	PUNCT
ejpam-4187	523	7	)	)	PUNCT
ejpam-4187	524	1	for	for	ADP
ejpam-4187	524	2	which	which	PRON
ejpam-4187	524	3	tx	tx	ADP
ejpam-4187	524	4	̸=	̸=	PROPN
ejpam-4187	524	5	v	v	PROPN
ejpam-4187	524	6	(	(	PUNCT
ejpam-4187	524	7	h	h	NOUN
ejpam-4187	524	8	)	)	PUNCT
ejpam-4187	524	9	.	.	PUNCT
ejpam-4187	525	1	then	then	ADV
ejpam-4187	525	2	u	u	PROPN
ejpam-4187	525	3	∈	∈	PROPN
ejpam-4187	525	4	s	s	X
ejpam-4187	525	5	for	for	ADP
ejpam-4187	525	6	all	all	PRON
ejpam-4187	525	7	u	u	PROPN
ejpam-4187	525	8	∈	∈	PROPN
ejpam-4187	525	9	ng(x	ng(x	NUM
ejpam-4187	525	10	,	,	PUNCT
ejpam-4187	525	11	2	2	NUM
ejpam-4187	525	12	)	)	PUNCT
ejpam-4187	525	13	.	.	PUNCT
ejpam-4187	526	1	first	first	ADV
ejpam-4187	526	2	,	,	PUNCT
ejpam-4187	526	3	suppose	suppose	VERB
ejpam-4187	526	4	that	that	SCONJ
ejpam-4187	526	5	tu	tu	PROPN
ejpam-4187	526	6	=	=	SYM
ejpam-4187	526	7	v	v	PROPN
ejpam-4187	526	8	(	(	PUNCT
ejpam-4187	526	9	h	h	NOUN
ejpam-4187	526	10	)	)	PUNCT
ejpam-4187	526	11	for	for	ADP
ejpam-4187	526	12	all	all	PRON
ejpam-4187	526	13	u	u	PROPN
ejpam-4187	526	14	∈	∈	PROPN
ejpam-4187	526	15	ng(x	ng(x	NUM
ejpam-4187	526	16	,	,	PUNCT
ejpam-4187	526	17	2	2	NUM
ejpam-4187	526	18	)	)	PUNCT
ejpam-4187	526	19	.	.	PUNCT
ejpam-4187	527	1	pick	pick	VERB
ejpam-4187	527	2	y	y	PROPN
ejpam-4187	527	3	∈	∈	PROPN
ejpam-4187	527	4	v	v	ADP
ejpam-4187	527	5	(	(	PUNCT
ejpam-4187	527	6	h	h	NOUN
ejpam-4187	527	7	)	)	PUNCT
ejpam-4187	527	8	\	\	PROPN
ejpam-4187	528	1	tx	tx	PROPN
ejpam-4187	528	2	.	.	PUNCT
ejpam-4187	529	1	then	then	ADV
ejpam-4187	529	2	(	(	PUNCT
ejpam-4187	529	3	x	x	X
ejpam-4187	529	4	,	,	PUNCT
ejpam-4187	529	5	y	y	PROPN
ejpam-4187	529	6	)	)	PUNCT
ejpam-4187	529	7	/∈	/∈	PUNCT
ejpam-4187	530	1	c	c	AUX
ejpam-4187	531	1	so	so	SCONJ
ejpam-4187	531	2	that	that	SCONJ
ejpam-4187	531	3	there	there	PRON
ejpam-4187	531	4	exists	exist	VERB
ejpam-4187	531	5	(	(	PUNCT
ejpam-4187	531	6	u	u	NOUN
ejpam-4187	531	7	,	,	PUNCT
ejpam-4187	531	8	v	v	NOUN
ejpam-4187	531	9	)	)	PUNCT
ejpam-4187	531	10	∈	∈	NOUN
ejpam-4187	531	11	v	v	NOUN
ejpam-4187	531	12	(	(	PUNCT
ejpam-4187	531	13	g[h])\c	g[h])\c	VERB
ejpam-4187	531	14	such	such	ADJ
ejpam-4187	531	15	that	that	SCONJ
ejpam-4187	531	16	(	(	PUNCT
ejpam-4187	531	17	x	x	X
ejpam-4187	531	18	,	,	PUNCT
ejpam-4187	531	19	y)(u	y)(u	ADJ
ejpam-4187	531	20	,	,	PUNCT
ejpam-4187	531	21	v	v	NOUN
ejpam-4187	531	22	)	)	PUNCT
ejpam-4187	531	23	∈	∈	NOUN
ejpam-4187	531	24	e(g[h	e(g[h	NOUN
ejpam-4187	531	25	]	]	PUNCT
ejpam-4187	531	26	)	)	PUNCT
ejpam-4187	531	27	or	or	CCONJ
ejpam-4187	531	28	there	there	PRON
ejpam-4187	531	29	exist	exist	VERB
ejpam-4187	531	30	distinct	distinct	ADJ
ejpam-4187	531	31	vertices	vertex	NOUN
ejpam-4187	531	32	(	(	PUNCT
ejpam-4187	531	33	u	u	NOUN
ejpam-4187	531	34	,	,	PUNCT
ejpam-4187	531	35	v	v	NOUN
ejpam-4187	531	36	)	)	PUNCT
ejpam-4187	531	37	,	,	PUNCT
ejpam-4187	531	38	(	(	PUNCT
ejpam-4187	531	39	z	z	X
ejpam-4187	531	40	,	,	PUNCT
ejpam-4187	531	41	w	w	NOUN
ejpam-4187	531	42	)	)	PUNCT
ejpam-4187	531	43	∈	∈	NOUN
ejpam-4187	531	44	v	v	NOUN
ejpam-4187	531	45	(	(	PUNCT
ejpam-4187	531	46	g[h	g[h	PROPN
ejpam-4187	531	47	]	]	PUNCT
ejpam-4187	531	48	)	)	PUNCT
ejpam-4187	531	49	\	\	PROPN
ejpam-4187	532	1	c	c	PROPN
ejpam-4187	532	2	for	for	ADP
ejpam-4187	532	3	which	which	PRON
ejpam-4187	532	4	dg[h]((x	dg[h]((x	PROPN
ejpam-4187	532	5	,	,	PUNCT
ejpam-4187	532	6	y	y	PROPN
ejpam-4187	532	7	)	)	PUNCT
ejpam-4187	532	8	,	,	PUNCT
ejpam-4187	532	9	(	(	PUNCT
ejpam-4187	532	10	u	u	NOUN
ejpam-4187	532	11	,	,	PUNCT
ejpam-4187	532	12	v	v	NOUN
ejpam-4187	532	13	)	)	PUNCT
ejpam-4187	532	14	)	)	PUNCT
ejpam-4187	532	15	=	=	SYM
ejpam-4187	533	1	2	2	NUM
ejpam-4187	533	2	=	=	SYM
ejpam-4187	533	3	dg[h]((x	dg[h]((x	NOUN
ejpam-4187	533	4	,	,	PUNCT
ejpam-4187	533	5	y	y	PROPN
ejpam-4187	533	6	)	)	PUNCT
ejpam-4187	533	7	,	,	PUNCT
ejpam-4187	533	8	(	(	PUNCT
ejpam-4187	533	9	z	z	NOUN
ejpam-4187	533	10	,	,	PUNCT
ejpam-4187	533	11	w	w	NOUN
ejpam-4187	533	12	)	)	PUNCT
ejpam-4187	533	13	)	)	PUNCT
ejpam-4187	533	14	.	.	PUNCT
ejpam-4187	534	1	since	since	SCONJ
ejpam-4187	534	2	x	x	PROPN
ejpam-4187	534	3	/∈	/∈	PRON
ejpam-4187	534	4	ng(v	ng(v	PUNCT
ejpam-4187	534	5	(	(	PUNCT
ejpam-4187	534	6	g	g	NOUN
ejpam-4187	534	7	)	)	PUNCT
ejpam-4187	534	8	\	\	PUNCT
ejpam-4187	534	9	(	(	PUNCT
ejpam-4187	534	10	s	s	NOUN
ejpam-4187	534	11	,	,	PUNCT
ejpam-4187	534	12	2	2	NUM
ejpam-4187	534	13	)	)	PUNCT
ejpam-4187	534	14	)	)	PUNCT
ejpam-4187	534	15	,	,	PUNCT
ejpam-4187	534	16	the	the	DET
ejpam-4187	534	17	preceding	precede	VERB
ejpam-4187	534	18	statement	statement	NOUN
ejpam-4187	534	19	implies	imply	VERB
ejpam-4187	534	20	that	that	SCONJ
ejpam-4187	534	21	x	x	X
ejpam-4187	534	22	=	=	SYM
ejpam-4187	534	23	u	u	NOUN
ejpam-4187	534	24	,	,	PUNCT
ejpam-4187	534	25	in	in	ADP
ejpam-4187	534	26	which	which	DET
ejpam-4187	534	27	case	case	NOUN
ejpam-4187	534	28	v	v	ADP
ejpam-4187	534	29	∈	∈	PROPN
ejpam-4187	534	30	v	v	NOUN
ejpam-4187	534	31	(	(	PUNCT
ejpam-4187	534	32	h	h	NOUN
ejpam-4187	534	33	)	)	PUNCT
ejpam-4187	534	34	\	\	PROPN
ejpam-4187	534	35	tx	tx	PROPN
ejpam-4187	534	36	and	and	CCONJ
ejpam-4187	534	37	yw	yw	PROPN
ejpam-4187	534	38	∈	∈	PROPN
ejpam-4187	534	39	e(h	e(h	PROPN
ejpam-4187	534	40	)	)	PUNCT
ejpam-4187	534	41	,	,	PUNCT
ejpam-4187	534	42	or	or	CCONJ
ejpam-4187	534	43	u	u	X
ejpam-4187	534	44	=	=	NOUN
ejpam-4187	534	45	x	x	SYM
ejpam-4187	534	46	=	=	SYM
ejpam-4187	534	47	z	z	PROPN
ejpam-4187	534	48	and	and	CCONJ
ejpam-4187	534	49	y	y	PROPN
ejpam-4187	534	50	,	,	PUNCT
ejpam-4187	534	51	v	v	NOUN
ejpam-4187	534	52	and	and	CCONJ
ejpam-4187	534	53	w	w	NOUN
ejpam-4187	534	54	are	be	AUX
ejpam-4187	534	55	distinct	distinct	ADJ
ejpam-4187	534	56	vertices	vertex	NOUN
ejpam-4187	534	57	in	in	ADP
ejpam-4187	534	58	v	v	ADP
ejpam-4187	534	59	(	(	PUNCT
ejpam-4187	534	60	h	h	NOUN
ejpam-4187	534	61	)	)	PUNCT
ejpam-4187	534	62	\	\	PROPN
ejpam-4187	535	1	tx	tx	PROPN
ejpam-4187	535	2	.	.	PUNCT
ejpam-4187	536	1	this	this	PRON
ejpam-4187	536	2	establishes	establish	VERB
ejpam-4187	536	3	(	(	PUNCT
ejpam-4187	536	4	a	a	NOUN
ejpam-4187	536	5	)	)	PUNCT
ejpam-4187	536	6	.	.	PUNCT
ejpam-4187	537	1	next	next	ADV
ejpam-4187	537	2	,	,	PUNCT
ejpam-4187	537	3	suppose	suppose	VERB
ejpam-4187	537	4	that	that	SCONJ
ejpam-4187	537	5	⟨v	⟨v	NOUN
ejpam-4187	537	6	(	(	PUNCT
ejpam-4187	537	7	h	h	NOUN
ejpam-4187	537	8	)	)	PUNCT
ejpam-4187	537	9	\	\	NOUN
ejpam-4187	537	10	tx⟩	tx⟩	PROPN
ejpam-4187	537	11	=	=	SYM
ejpam-4187	537	12	k2	k2	PROPN
ejpam-4187	537	13	.	.	PUNCT
ejpam-4187	538	1	let	let	VERB
ejpam-4187	538	2	y	y	NOUN
ejpam-4187	538	3	,	,	PUNCT
ejpam-4187	538	4	w	w	PROPN
ejpam-4187	538	5	∈	∈	PROPN
ejpam-4187	538	6	⟨v	⟨v	PUNCT
ejpam-4187	538	7	(	(	PUNCT
ejpam-4187	538	8	h	h	NOUN
ejpam-4187	538	9	)	)	PUNCT
ejpam-4187	538	10	\	\	PUNCT
ejpam-4187	539	1	tx⟩.	tx⟩.	NOUN
ejpam-4187	539	2	suppose	suppose	VERB
ejpam-4187	539	3	that	that	SCONJ
ejpam-4187	539	4	(	(	PUNCT
ejpam-4187	539	5	u	u	NOUN
ejpam-4187	539	6	,	,	PUNCT
ejpam-4187	539	7	v	v	NOUN
ejpam-4187	539	8	)	)	PUNCT
ejpam-4187	539	9	∈	∈	NOUN
ejpam-4187	539	10	v	v	NOUN
ejpam-4187	539	11	(	(	PUNCT
ejpam-4187	539	12	g[h	g[h	PROPN
ejpam-4187	539	13	]	]	PUNCT
ejpam-4187	539	14	)	)	PUNCT
ejpam-4187	539	15	\	\	PUNCT
ejpam-4187	540	1	c	c	NOUN
ejpam-4187	540	2	such	such	ADJ
ejpam-4187	540	3	that	that	PRON
ejpam-4187	540	4	(	(	PUNCT
ejpam-4187	540	5	x	x	X
ejpam-4187	540	6	,	,	PUNCT
ejpam-4187	540	7	y)(u	y)(u	ADJ
ejpam-4187	540	8	,	,	PUNCT
ejpam-4187	540	9	v	v	NOUN
ejpam-4187	540	10	)	)	PUNCT
ejpam-4187	540	11	∈	∈	NOUN
ejpam-4187	540	12	e(g[h	e(g[h	NOUN
ejpam-4187	540	13	]	]	PUNCT
ejpam-4187	540	14	)	)	PUNCT
ejpam-4187	540	15	.	.	PUNCT
ejpam-4187	541	1	since	since	SCONJ
ejpam-4187	541	2	y	y	PROPN
ejpam-4187	541	3	,	,	PUNCT
ejpam-4187	541	4	w	w	PROPN
ejpam-4187	541	5	∈	∈	PROPN
ejpam-4187	541	6	⟨v	⟨v	PUNCT
ejpam-4187	541	7	(	(	PUNCT
ejpam-4187	541	8	h	h	NOUN
ejpam-4187	541	9	)	)	PUNCT
ejpam-4187	541	10	\	\	PROPN
ejpam-4187	541	11	tx⟩	tx⟩	PROPN
ejpam-4187	541	12	,	,	PUNCT
ejpam-4187	541	13	it	it	PRON
ejpam-4187	541	14	is	be	AUX
ejpam-4187	541	15	necessary	necessary	ADJ
ejpam-4187	541	16	that	that	SCONJ
ejpam-4187	541	17	u	u	PRON
ejpam-4187	541	18	̸=	̸=	PROPN
ejpam-4187	541	19	x.	x.	NOUN
ejpam-4187	541	20	hence	hence	ADV
ejpam-4187	541	21	u	u	NOUN
ejpam-4187	541	22	∈	∈	PROPN
ejpam-4187	541	23	ng(x	ng(x	NUM
ejpam-4187	541	24	)	)	PUNCT
ejpam-4187	541	25	and	and	CCONJ
ejpam-4187	541	26	v	v	ADP
ejpam-4187	541	27	∈	∈	PROPN
ejpam-4187	541	28	v	v	NOUN
ejpam-4187	541	29	(	(	PUNCT
ejpam-4187	541	30	h	h	NOUN
ejpam-4187	541	31	)	)	PUNCT
ejpam-4187	541	32	\	\	PROPN
ejpam-4187	541	33	tu	tu	PROPN
ejpam-4187	541	34	.	.	PUNCT
ejpam-4187	542	1	consequently	consequently	ADV
ejpam-4187	542	2	,	,	PUNCT
ejpam-4187	542	3	tu	tu	PROPN
ejpam-4187	542	4	̸=	̸=	PROPN
ejpam-4187	542	5	v	v	PROPN
ejpam-4187	542	6	(	(	PUNCT
ejpam-4187	542	7	h	h	NOUN
ejpam-4187	542	8	)	)	PUNCT
ejpam-4187	542	9	.	.	PUNCT
ejpam-4187	543	1	suppose	suppose	VERB
ejpam-4187	543	2	that	that	SCONJ
ejpam-4187	543	3	(	(	PUNCT
ejpam-4187	543	4	u	u	NOUN
ejpam-4187	543	5	,	,	PUNCT
ejpam-4187	543	6	v	v	NOUN
ejpam-4187	543	7	)	)	PUNCT
ejpam-4187	543	8	,	,	PUNCT
ejpam-4187	543	9	(	(	PUNCT
ejpam-4187	543	10	z	z	X
ejpam-4187	543	11	,	,	PUNCT
ejpam-4187	543	12	w	w	NOUN
ejpam-4187	543	13	)	)	PUNCT
ejpam-4187	543	14	∈	∈	NOUN
ejpam-4187	543	15	v	v	NOUN
ejpam-4187	543	16	(	(	PUNCT
ejpam-4187	543	17	g[h	g[h	PROPN
ejpam-4187	543	18	]	]	PUNCT
ejpam-4187	543	19	)	)	PUNCT
ejpam-4187	543	20	\	\	PROPN
ejpam-4187	544	1	c	c	NOUN
ejpam-4187	544	2	are	be	AUX
ejpam-4187	544	3	distinct	distinct	ADJ
ejpam-4187	544	4	for	for	ADP
ejpam-4187	544	5	which	which	PRON
ejpam-4187	544	6	dg[h]((x	dg[h]((x	PROPN
ejpam-4187	544	7	,	,	PUNCT
ejpam-4187	544	8	y	y	PROPN
ejpam-4187	544	9	)	)	PUNCT
ejpam-4187	544	10	,	,	PUNCT
ejpam-4187	544	11	(	(	PUNCT
ejpam-4187	544	12	u	u	NOUN
ejpam-4187	544	13	,	,	PUNCT
ejpam-4187	544	14	v	v	NOUN
ejpam-4187	544	15	)	)	PUNCT
ejpam-4187	544	16	)	)	PUNCT
ejpam-4187	545	1	=	=	SYM
ejpam-4187	545	2	2	2	NUM
ejpam-4187	545	3	=	=	SYM
ejpam-4187	545	4	dg[h]((x	dg[h]((x	NOUN
ejpam-4187	545	5	,	,	PUNCT
ejpam-4187	545	6	y	y	PROPN
ejpam-4187	545	7	)	)	PUNCT
ejpam-4187	545	8	,	,	PUNCT
ejpam-4187	545	9	(	(	PUNCT
ejpam-4187	545	10	z	z	NOUN
ejpam-4187	545	11	,	,	PUNCT
ejpam-4187	545	12	w	w	NOUN
ejpam-4187	545	13	)	)	PUNCT
ejpam-4187	545	14	)	)	PUNCT
ejpam-4187	545	15	.	.	PUNCT
ejpam-4187	546	1	the	the	DET
ejpam-4187	546	2	assumption	assumption	NOUN
ejpam-4187	546	3	implies	imply	VERB
ejpam-4187	546	4	that	that	SCONJ
ejpam-4187	546	5	u	u	PROPN
ejpam-4187	546	6	∈	∈	PROPN
ejpam-4187	546	7	ng(x	ng(x	NUM
ejpam-4187	546	8	,	,	PUNCT
ejpam-4187	546	9	2	2	NUM
ejpam-4187	546	10	)	)	PUNCT
ejpam-4187	546	11	or	or	CCONJ
ejpam-4187	546	12	z	z	NOUN
ejpam-4187	546	13	∈	∈	PROPN
ejpam-4187	546	14	ng(x	ng(x	NUM
ejpam-4187	546	15	,	,	PUNCT
ejpam-4187	546	16	2	2	NUM
ejpam-4187	546	17	)	)	PUNCT
ejpam-4187	546	18	.	.	PUNCT
ejpam-4187	547	1	if	if	SCONJ
ejpam-4187	547	2	u	u	PROPN
ejpam-4187	547	3	∈	∈	PROPN
ejpam-4187	547	4	ng(x	ng(x	NUM
ejpam-4187	547	5	,	,	PUNCT
ejpam-4187	547	6	2	2	NUM
ejpam-4187	547	7	)	)	PUNCT
ejpam-4187	547	8	,	,	PUNCT
ejpam-4187	547	9	then	then	ADV
ejpam-4187	547	10	tu	tu	PROPN
ejpam-4187	547	11	̸=	̸=	PROPN
ejpam-4187	547	12	v	v	PROPN
ejpam-4187	547	13	(	(	PUNCT
ejpam-4187	547	14	h	h	NOUN
ejpam-4187	547	15	)	)	PUNCT
ejpam-4187	547	16	,	,	PUNCT
ejpam-4187	547	17	and	and	CCONJ
ejpam-4187	547	18	if	if	SCONJ
ejpam-4187	547	19	z	z	PROPN
ejpam-4187	547	20	∈	∈	PROPN
ejpam-4187	547	21	ng(x	ng(x	NUM
ejpam-4187	547	22	,	,	PUNCT
ejpam-4187	547	23	2	2	NUM
ejpam-4187	547	24	)	)	PUNCT
ejpam-4187	547	25	,	,	PUNCT
ejpam-4187	547	26	then	then	ADV
ejpam-4187	547	27	tz	tz	PROPN
ejpam-4187	547	28	̸=	̸=	PROPN
ejpam-4187	547	29	v	v	NOUN
ejpam-4187	547	30	(	(	PUNCT
ejpam-4187	547	31	h	h	NOUN
ejpam-4187	547	32	)	)	PUNCT
ejpam-4187	547	33	.	.	PUNCT
ejpam-4187	548	1	hence	hence	ADV
ejpam-4187	548	2	,	,	PUNCT
ejpam-4187	548	3	(	(	PUNCT
ejpam-4187	548	4	b	b	X
ejpam-4187	548	5	)	)	PUNCT
ejpam-4187	548	6	holds	hold	VERB
ejpam-4187	548	7	.	.	PUNCT
ejpam-4187	549	1	lastly	lastly	ADV
ejpam-4187	549	2	,	,	PUNCT
ejpam-4187	549	3	suppose	suppose	VERB
ejpam-4187	549	4	that	that	SCONJ
ejpam-4187	549	5	|v	|v	PROPN
ejpam-4187	549	6	(	(	PUNCT
ejpam-4187	549	7	h	h	NOUN
ejpam-4187	549	8	)	)	PUNCT
ejpam-4187	549	9	\	\	PUNCT
ejpam-4187	549	10	tx|	tx|	PROPN
ejpam-4187	549	11	=	=	SYM
ejpam-4187	549	12	1	1	NUM
ejpam-4187	549	13	,	,	PUNCT
ejpam-4187	549	14	say	say	VERB
ejpam-4187	549	15	v	v	INTJ
ejpam-4187	549	16	(	(	PUNCT
ejpam-4187	549	17	h	h	NOUN
ejpam-4187	549	18	\	\	PROPN
ejpam-4187	549	19	tx	tx	PROPN
ejpam-4187	549	20	=	=	PUNCT
ejpam-4187	549	21	{	{	PUNCT
ejpam-4187	549	22	y	y	NOUN
ejpam-4187	549	23	}	}	PUNCT
ejpam-4187	549	24	.	.	PUNCT
ejpam-4187	550	1	if	if	SCONJ
ejpam-4187	550	2	(	(	PUNCT
ejpam-4187	550	3	u	u	NOUN
ejpam-4187	550	4	,	,	PUNCT
ejpam-4187	550	5	v	v	NOUN
ejpam-4187	550	6	)	)	PUNCT
ejpam-4187	550	7	∈	∈	NOUN
ejpam-4187	550	8	v	v	NOUN
ejpam-4187	550	9	(	(	PUNCT
ejpam-4187	550	10	g[h	g[h	PROPN
ejpam-4187	550	11	]	]	PUNCT
ejpam-4187	550	12	)	)	PUNCT
ejpam-4187	550	13	\	\	PUNCT
ejpam-4187	550	14	c	c	NOUN
ejpam-4187	550	15	such	such	ADJ
ejpam-4187	550	16	that	that	PRON
ejpam-4187	550	17	(	(	PUNCT
ejpam-4187	550	18	u	u	NOUN
ejpam-4187	550	19	,	,	PUNCT
ejpam-4187	550	20	v)(x	v)(x	NOUN
ejpam-4187	550	21	,	,	PUNCT
ejpam-4187	550	22	y	y	NOUN
ejpam-4187	550	23	)	)	PUNCT
ejpam-4187	550	24	∈	∈	NOUN
ejpam-4187	550	25	e(g[h	e(g[h	NOUN
ejpam-4187	550	26	]	]	PUNCT
ejpam-4187	550	27	)	)	PUNCT
ejpam-4187	550	28	,	,	PUNCT
ejpam-4187	550	29	then	then	ADV
ejpam-4187	550	30	since	since	SCONJ
ejpam-4187	550	31	tx	tx	PROPN
ejpam-4187	550	32	=	=	PUNCT
ejpam-4187	550	33	{	{	PUNCT
ejpam-4187	550	34	y	y	NOUN
ejpam-4187	550	35	}	}	PUNCT
ejpam-4187	550	36	,	,	PUNCT
ejpam-4187	550	37	u	u	PROPN
ejpam-4187	550	38	∈	∈	PROPN
ejpam-4187	550	39	ng(x	ng(x	NUM
ejpam-4187	550	40	)	)	PUNCT
ejpam-4187	550	41	and	and	CCONJ
ejpam-4187	550	42	tu	tu	PROPN
ejpam-4187	550	43	̸=	̸=	PROPN
ejpam-4187	550	44	v	v	PROPN
ejpam-4187	550	45	(	(	PUNCT
ejpam-4187	550	46	h	h	NOUN
ejpam-4187	550	47	)	)	PUNCT
ejpam-4187	550	48	.	.	PUNCT
ejpam-4187	551	1	on	on	ADP
ejpam-4187	551	2	the	the	DET
ejpam-4187	551	3	other	other	ADJ
ejpam-4187	551	4	hand	hand	NOUN
ejpam-4187	551	5	,	,	PUNCT
ejpam-4187	551	6	if	if	SCONJ
ejpam-4187	551	7	(	(	PUNCT
ejpam-4187	551	8	u	u	NOUN
ejpam-4187	551	9	,	,	PUNCT
ejpam-4187	551	10	v	v	NOUN
ejpam-4187	551	11	)	)	PUNCT
ejpam-4187	551	12	,	,	PUNCT
ejpam-4187	551	13	(	(	PUNCT
ejpam-4187	551	14	z	z	X
ejpam-4187	551	15	,	,	PUNCT
ejpam-4187	551	16	w	w	NOUN
ejpam-4187	551	17	)	)	PUNCT
ejpam-4187	551	18	∈	∈	NOUN
ejpam-4187	551	19	v	v	NOUN
ejpam-4187	551	20	(	(	PUNCT
ejpam-4187	551	21	g[h	g[h	PROPN
ejpam-4187	551	22	]	]	PUNCT
ejpam-4187	551	23	)	)	PUNCT
ejpam-4187	551	24	\c	\c	NOUN
ejpam-4187	551	25	are	be	AUX
ejpam-4187	551	26	distinct	distinct	ADJ
ejpam-4187	551	27	for	for	ADP
ejpam-4187	551	28	which	which	PRON
ejpam-4187	551	29	dg[h]((x	dg[h]((x	PROPN
ejpam-4187	551	30	,	,	PUNCT
ejpam-4187	551	31	y	y	PROPN
ejpam-4187	551	32	)	)	PUNCT
ejpam-4187	551	33	,	,	PUNCT
ejpam-4187	551	34	(	(	PUNCT
ejpam-4187	551	35	u	u	NOUN
ejpam-4187	551	36	,	,	PUNCT
ejpam-4187	551	37	v	v	NOUN
ejpam-4187	551	38	)	)	PUNCT
ejpam-4187	551	39	)	)	PUNCT
ejpam-4187	552	1	=	=	SYM
ejpam-4187	552	2	2	2	NUM
ejpam-4187	552	3	=	=	SYM
ejpam-4187	552	4	dg[h]((x	dg[h]((x	NOUN
ejpam-4187	552	5	,	,	PUNCT
ejpam-4187	552	6	y	y	PROPN
ejpam-4187	552	7	)	)	PUNCT
ejpam-4187	552	8	,	,	PUNCT
ejpam-4187	552	9	(	(	PUNCT
ejpam-4187	552	10	z	z	NOUN
ejpam-4187	552	11	,	,	PUNCT
ejpam-4187	552	12	w	w	NOUN
ejpam-4187	552	13	)	)	PUNCT
ejpam-4187	552	14	)	)	PUNCT
ejpam-4187	552	15	,	,	PUNCT
ejpam-4187	552	16	then	then	ADV
ejpam-4187	552	17	dg(x	dg(x	NUM
ejpam-4187	552	18	,	,	PUNCT
ejpam-4187	552	19	u	u	NOUN
ejpam-4187	552	20	)	)	PUNCT
ejpam-4187	552	21	=	=	SYM
ejpam-4187	552	22	2	2	NUM
ejpam-4187	552	23	=	=	SYM
ejpam-4187	552	24	dg(x	dg(x	NUM
ejpam-4187	552	25	,	,	PUNCT
ejpam-4187	552	26	z	z	NOUN
ejpam-4187	552	27	)	)	PUNCT
ejpam-4187	552	28	.	.	PUNCT
ejpam-4187	553	1	if	if	SCONJ
ejpam-4187	553	2	u	u	PROPN
ejpam-4187	553	3	=	=	PROPN
ejpam-4187	553	4	z	z	PROPN
ejpam-4187	553	5	,	,	PUNCT
ejpam-4187	553	6	then	then	ADV
ejpam-4187	553	7	|v	|v	PROPN
ejpam-4187	553	8	(	(	PUNCT
ejpam-4187	553	9	h	h	NOUN
ejpam-4187	553	10	)	)	PUNCT
ejpam-4187	553	11	\	\	PUNCT
ejpam-4187	554	1	tu|	tu|	ADP
ejpam-4187	554	2	≥	≥	NOUN
ejpam-4187	554	3	2	2	NUM
ejpam-4187	554	4	.	.	PUNCT
ejpam-4187	555	1	otherwise	otherwise	ADV
ejpam-4187	555	2	,	,	PUNCT
ejpam-4187	555	3	tu	tu	PROPN
ejpam-4187	555	4	̸=	̸=	PROPN
ejpam-4187	555	5	v	v	PROPN
ejpam-4187	555	6	(	(	PUNCT
ejpam-4187	555	7	h	h	NOUN
ejpam-4187	555	8	)	)	PUNCT
ejpam-4187	555	9	and	and	CCONJ
ejpam-4187	555	10	tz	tz	PROPN
ejpam-4187	555	11	̸=	̸=	PROPN
ejpam-4187	555	12	v	v	NOUN
ejpam-4187	555	13	(	(	PUNCT
ejpam-4187	555	14	h	h	NOUN
ejpam-4187	555	15	)	)	PUNCT
ejpam-4187	555	16	.	.	PUNCT
ejpam-4187	556	1	conversely	conversely	ADV
ejpam-4187	556	2	,	,	PUNCT
ejpam-4187	556	3	suppose	suppose	VERB
ejpam-4187	556	4	that	that	SCONJ
ejpam-4187	556	5	conditions	condition	NOUN
ejpam-4187	556	6	(	(	PUNCT
ejpam-4187	556	7	i	i	NOUN
ejpam-4187	556	8	)	)	PUNCT
ejpam-4187	556	9	or	or	CCONJ
ejpam-4187	556	10	(	(	PUNCT
ejpam-4187	556	11	ii	ii	NOUN
ejpam-4187	556	12	)	)	PUNCT
ejpam-4187	556	13	of	of	ADP
ejpam-4187	556	14	theorem	theorem	ADJ
ejpam-4187	556	15	7	7	NUM
ejpam-4187	556	16	holds	hold	NOUN
ejpam-4187	556	17	.	.	PUNCT
ejpam-4187	557	1	then	then	ADV
ejpam-4187	557	2	c	c	PROPN
ejpam-4187	557	3	is	be	AUX
ejpam-4187	557	4	a	a	DET
ejpam-4187	557	5	disjunctive	disjunctive	ADJ
ejpam-4187	557	6	dominating	dominating	NOUN
ejpam-4187	557	7	set	set	NOUN
ejpam-4187	557	8	of	of	ADP
ejpam-4187	557	9	g[h	g[h	PROPN
ejpam-4187	557	10	]	]	PUNCT
ejpam-4187	557	11	.	.	PUNCT
ejpam-4187	558	1	suppose	suppose	VERB
ejpam-4187	558	2	further	far	ADV
ejpam-4187	558	3	that	that	SCONJ
ejpam-4187	558	4	all	all	DET
ejpam-4187	558	5	properties	property	NOUN
ejpam-4187	558	6	in	in	ADP
ejpam-4187	558	7	theorem	theorem	ADJ
ejpam-4187	558	8	8	8	NUM
ejpam-4187	558	9	hold	hold	NOUN
ejpam-4187	558	10	for	for	ADP
ejpam-4187	558	11	s.	s.	PROPN
ejpam-4187	558	12	let	let	AUX
ejpam-4187	558	13	(	(	PUNCT
ejpam-4187	558	14	x	x	NOUN
ejpam-4187	558	15	,	,	PUNCT
ejpam-4187	558	16	y	y	NOUN
ejpam-4187	558	17	)	)	PUNCT
ejpam-4187	558	18	∈	∈	PROPN
ejpam-4187	558	19	v	v	NOUN
ejpam-4187	558	20	(	(	PUNCT
ejpam-4187	558	21	g[h	g[h	PROPN
ejpam-4187	558	22	]	]	PUNCT
ejpam-4187	558	23	)	)	PUNCT
ejpam-4187	558	24	\	\	PROPN
ejpam-4187	559	1	c.	c.	NOUN
ejpam-4187	559	2	case	case	NOUN
ejpam-4187	559	3	1	1	NUM
ejpam-4187	559	4	:	:	PUNCT
ejpam-4187	559	5	if	if	SCONJ
ejpam-4187	559	6	x	x	PROPN
ejpam-4187	559	7	/∈	/∈	PROPN
ejpam-4187	560	1	s	s	PART
ejpam-4187	560	2	,	,	PUNCT
ejpam-4187	560	3	then	then	ADV
ejpam-4187	560	4	pick	pick	VERB
ejpam-4187	560	5	z	z	PROPN
ejpam-4187	560	6	∈	∈	PROPN
ejpam-4187	560	7	v	v	ADP
ejpam-4187	560	8	(	(	PUNCT
ejpam-4187	560	9	h	h	NOUN
ejpam-4187	560	10	)	)	PUNCT
ejpam-4187	560	11	\	\	NOUN
ejpam-4187	560	12	{	{	PUNCT
ejpam-4187	560	13	y	y	NOUN
ejpam-4187	560	14	}	}	PUNCT
ejpam-4187	560	15	for	for	ADP
ejpam-4187	560	16	which	which	PRON
ejpam-4187	560	17	zy	zy	PROPN
ejpam-4187	560	18	∈	∈	PROPN
ejpam-4187	560	19	e(h	e(h	PROPN
ejpam-4187	560	20	)	)	PUNCT
ejpam-4187	560	21	.	.	PUNCT
ejpam-4187	561	1	in	in	ADP
ejpam-4187	561	2	this	this	DET
ejpam-4187	561	3	case	case	NOUN
ejpam-4187	561	4	,	,	PUNCT
ejpam-4187	561	5	(	(	PUNCT
ejpam-4187	561	6	x	x	X
ejpam-4187	561	7	,	,	PUNCT
ejpam-4187	561	8	z	z	NOUN
ejpam-4187	561	9	)	)	PUNCT
ejpam-4187	561	10	∈	∈	NOUN
ejpam-4187	561	11	v	v	NOUN
ejpam-4187	561	12	(	(	PUNCT
ejpam-4187	561	13	g[h	g[h	PROPN
ejpam-4187	561	14	]	]	PUNCT
ejpam-4187	561	15	)	)	PUNCT
ejpam-4187	561	16	\	\	PROPN
ejpam-4187	562	1	c	c	PROPN
ejpam-4187	562	2	and	and	CCONJ
ejpam-4187	562	3	(	(	PUNCT
ejpam-4187	562	4	x	x	NOUN
ejpam-4187	562	5	,	,	PUNCT
ejpam-4187	562	6	y)(x	y)(x	PROPN
ejpam-4187	562	7	,	,	PUNCT
ejpam-4187	562	8	z	z	NOUN
ejpam-4187	562	9	)	)	PUNCT
ejpam-4187	562	10	∈	∈	NOUN
ejpam-4187	562	11	e(g[h	e(g[h	NOUN
ejpam-4187	562	12	]	]	PUNCT
ejpam-4187	562	13	)	)	PUNCT
ejpam-4187	562	14	.	.	PUNCT
ejpam-4187	563	1	case	case	NOUN
ejpam-4187	563	2	2	2	NUM
ejpam-4187	563	3	:	:	PUNCT
ejpam-4187	563	4	suppose	suppose	VERB
ejpam-4187	563	5	that	that	SCONJ
ejpam-4187	563	6	x	x	PROPN
ejpam-4187	563	7	∈	∈	PROPN
ejpam-4187	563	8	s.	s.	PROPN
ejpam-4187	563	9	then	then	ADV
ejpam-4187	563	10	y	y	PROPN
ejpam-4187	563	11	/∈	/∈	PUNCT
ejpam-4187	564	1	tx	tx	PROPN
ejpam-4187	564	2	.	.	PUNCT
ejpam-4187	565	1	first	first	ADV
ejpam-4187	565	2	,	,	PUNCT
ejpam-4187	565	3	consider	consider	VERB
ejpam-4187	565	4	having	have	VERB
ejpam-4187	565	5	x	x	PROPN
ejpam-4187	565	6	∈	∈	PROPN
ejpam-4187	565	7	nd	nd	PRON
ejpam-4187	565	8	g(v	g(v	PROPN
ejpam-4187	565	9	(	(	PUNCT
ejpam-4187	565	10	g	g	NOUN
ejpam-4187	565	11	)	)	PUNCT
ejpam-4187	565	12	\	\	PROPN
ejpam-4187	566	1	s	s	X
ejpam-4187	566	2	)	)	PUNCT
ejpam-4187	566	3	.	.	PUNCT
ejpam-4187	567	1	suppose	suppose	VERB
ejpam-4187	567	2	u	u	PRON
ejpam-4187	567	3	∈	∈	PROPN
ejpam-4187	567	4	v	v	ADP
ejpam-4187	567	5	(	(	PUNCT
ejpam-4187	567	6	g	g	NOUN
ejpam-4187	567	7	)	)	PUNCT
ejpam-4187	567	8	\	\	PUNCT
ejpam-4187	567	9	s	s	VERB
ejpam-4187	567	10	such	such	ADJ
ejpam-4187	567	11	that	that	SCONJ
ejpam-4187	567	12	ux	ux	PROPN
ejpam-4187	567	13	∈	∈	PROPN
ejpam-4187	567	14	e(g	e(g	PROPN
ejpam-4187	567	15	)	)	PUNCT
ejpam-4187	567	16	.	.	PUNCT
ejpam-4187	568	1	pick	pick	VERB
ejpam-4187	568	2	v	v	NUM
ejpam-4187	568	3	∈	∈	PROPN
ejpam-4187	568	4	v	v	NOUN
ejpam-4187	568	5	(	(	PUNCT
ejpam-4187	568	6	h	h	NOUN
ejpam-4187	568	7	)	)	PUNCT
ejpam-4187	568	8	.	.	PUNCT
ejpam-4187	569	1	then	then	ADV
ejpam-4187	569	2	(	(	PUNCT
ejpam-4187	569	3	u	u	NOUN
ejpam-4187	569	4	,	,	PUNCT
ejpam-4187	569	5	v	v	NOUN
ejpam-4187	569	6	)	)	PUNCT
ejpam-4187	569	7	/∈	/∈	PUNCT
ejpam-4187	570	1	c	c	NOUN
ejpam-4187	570	2	and	and	CCONJ
ejpam-4187	570	3	(	(	PUNCT
ejpam-4187	570	4	x	x	X
ejpam-4187	570	5	,	,	PUNCT
ejpam-4187	570	6	y)(u	y)(u	ADJ
ejpam-4187	570	7	,	,	PUNCT
ejpam-4187	570	8	v	v	NOUN
ejpam-4187	570	9	)	)	PUNCT
ejpam-4187	570	10	∈	∈	NOUN
ejpam-4187	570	11	e(g[h	e(g[h	NOUN
ejpam-4187	570	12	]	]	PUNCT
ejpam-4187	570	13	)	)	PUNCT
ejpam-4187	570	14	.	.	PUNCT
ejpam-4187	571	1	suppose	suppose	VERB
ejpam-4187	571	2	,	,	PUNCT
ejpam-4187	571	3	on	on	ADP
ejpam-4187	571	4	the	the	DET
ejpam-4187	571	5	other	other	ADJ
ejpam-4187	571	6	hand	hand	NOUN
ejpam-4187	571	7	,	,	PUNCT
ejpam-4187	571	8	that	that	DET
ejpam-4187	571	9	u	u	NOUN
ejpam-4187	571	10	,	,	PUNCT
ejpam-4187	571	11	z	z	PROPN
ejpam-4187	571	12	∈	∈	PROPN
ejpam-4187	571	13	v	v	ADP
ejpam-4187	571	14	(	(	PUNCT
ejpam-4187	571	15	g	g	NOUN
ejpam-4187	571	16	)	)	PUNCT
ejpam-4187	571	17	\	\	PROPN
ejpam-4187	571	18	s	s	PART
ejpam-4187	571	19	for	for	ADP
ejpam-4187	571	20	which	which	PRON
ejpam-4187	571	21	dg(x	dg(x	NUM
ejpam-4187	571	22	,	,	PUNCT
ejpam-4187	571	23	u	u	NOUN
ejpam-4187	571	24	)	)	PUNCT
ejpam-4187	571	25	=	=	SYM
ejpam-4187	571	26	2	2	NUM
ejpam-4187	571	27	=	=	SYM
ejpam-4187	571	28	dg(x	dg(x	NUM
ejpam-4187	571	29	,	,	PUNCT
ejpam-4187	571	30	z	z	NOUN
ejpam-4187	571	31	)	)	PUNCT
ejpam-4187	571	32	.	.	PUNCT
ejpam-4187	572	1	pick	pick	VERB
ejpam-4187	572	2	v	v	NOUN
ejpam-4187	572	3	,	,	PUNCT
ejpam-4187	572	4	w	w	PROPN
ejpam-4187	572	5	∈	∈	PROPN
ejpam-4187	572	6	v	v	ADP
ejpam-4187	572	7	(	(	PUNCT
ejpam-4187	572	8	h	h	NOUN
ejpam-4187	572	9	)	)	PUNCT
ejpam-4187	572	10	.	.	PUNCT
ejpam-4187	573	1	then	then	ADV
ejpam-4187	573	2	(	(	PUNCT
ejpam-4187	573	3	u	u	NOUN
ejpam-4187	573	4	,	,	PUNCT
ejpam-4187	573	5	v	v	NOUN
ejpam-4187	573	6	)	)	PUNCT
ejpam-4187	573	7	,	,	PUNCT
ejpam-4187	573	8	(	(	PUNCT
ejpam-4187	573	9	z	z	X
ejpam-4187	573	10	,	,	PUNCT
ejpam-4187	573	11	w	w	PROPN
ejpam-4187	573	12	)	)	PUNCT
ejpam-4187	573	13	/∈	/∈	PUNCT
ejpam-4187	574	1	c	c	NOUN
ejpam-4187	574	2	and	and	CCONJ
ejpam-4187	574	3	dg[h]((x	dg[h]((x	PROPN
ejpam-4187	574	4	,	,	PUNCT
ejpam-4187	574	5	y	y	PROPN
ejpam-4187	574	6	)	)	PUNCT
ejpam-4187	574	7	,	,	PUNCT
ejpam-4187	574	8	(	(	PUNCT
ejpam-4187	574	9	u	u	NOUN
ejpam-4187	574	10	,	,	PUNCT
ejpam-4187	574	11	v	v	NOUN
ejpam-4187	574	12	)	)	PUNCT
ejpam-4187	574	13	)	)	PUNCT
ejpam-4187	575	1	=	=	SYM
ejpam-4187	575	2	2	2	NUM
ejpam-4187	575	3	=	=	SYM
ejpam-4187	575	4	dg[h]((x	dg[h]((x	NOUN
ejpam-4187	575	5	,	,	PUNCT
ejpam-4187	575	6	y	y	PROPN
ejpam-4187	575	7	)	)	PUNCT
ejpam-4187	575	8	,	,	PUNCT
ejpam-4187	575	9	(	(	PUNCT
ejpam-4187	575	10	z	z	NOUN
ejpam-4187	575	11	,	,	PUNCT
ejpam-4187	575	12	w	w	NOUN
ejpam-4187	575	13	)	)	PUNCT
ejpam-4187	575	14	)	)	PUNCT
ejpam-4187	575	15	.	.	PUNCT
ejpam-4187	576	1	next	next	ADV
ejpam-4187	576	2	,	,	PUNCT
ejpam-4187	576	3	suppose	suppose	VERB
ejpam-4187	576	4	that	that	SCONJ
ejpam-4187	576	5	x	x	X
ejpam-4187	576	6	/∈	/∈	PROPN
ejpam-4187	577	1	nd	nd	INTJ
ejpam-4187	577	2	g(v	g(v	PROPN
ejpam-4187	577	3	(	(	PUNCT
ejpam-4187	577	4	g	g	NOUN
ejpam-4187	577	5	)	)	PUNCT
ejpam-4187	577	6	\	\	PROPN
ejpam-4187	578	1	s	s	X
ejpam-4187	578	2	)	)	PUNCT
ejpam-4187	578	3	.	.	PUNCT
ejpam-4187	579	1	suppose	suppose	VERB
ejpam-4187	579	2	further	far	ADV
ejpam-4187	579	3	that	that	SCONJ
ejpam-4187	579	4	x	x	SYM
ejpam-4187	579	5	∈	∈	NOUN
ejpam-4187	579	6	ng(v	ng(v	X
ejpam-4187	579	7	(	(	PUNCT
ejpam-4187	579	8	g	g	NOUN
ejpam-4187	579	9	)	)	PUNCT
ejpam-4187	579	10	\	\	PUNCT
ejpam-4187	580	1	(	(	PUNCT
ejpam-4187	580	2	s	s	NOUN
ejpam-4187	580	3	,	,	PUNCT
ejpam-4187	580	4	2	2	NUM
ejpam-4187	580	5	)	)	PUNCT
ejpam-4187	580	6	)	)	PUNCT
ejpam-4187	580	7	.	.	PUNCT
ejpam-4187	581	1	pick	pick	VERB
ejpam-4187	581	2	u	u	PRON
ejpam-4187	581	3	∈	∈	PROPN
ejpam-4187	581	4	v	v	ADP
ejpam-4187	581	5	(	(	PUNCT
ejpam-4187	581	6	g	g	NOUN
ejpam-4187	581	7	)	)	PUNCT
ejpam-4187	581	8	\	\	PUNCT
ejpam-4187	582	1	s	s	VERB
ejpam-4187	582	2	such	such	ADJ
ejpam-4187	582	3	that	that	SCONJ
ejpam-4187	582	4	1	1	NUM
ejpam-4187	582	5	≤	≤	NOUN
ejpam-4187	582	6	dg(x	dg(x	NUM
ejpam-4187	582	7	,	,	PUNCT
ejpam-4187	582	8	u	u	NOUN
ejpam-4187	582	9	)	)	PUNCT
ejpam-4187	582	10	≤	≤	NOUN
ejpam-4187	582	11	2	2	NUM
ejpam-4187	582	12	.	.	PUNCT
ejpam-4187	583	1	if	if	SCONJ
ejpam-4187	583	2	ux	ux	PROPN
ejpam-4187	583	3	∈	∈	PROPN
ejpam-4187	583	4	e(g	e(g	PROPN
ejpam-4187	583	5	)	)	PUNCT
ejpam-4187	583	6	,	,	PUNCT
ejpam-4187	583	7	then	then	ADV
ejpam-4187	583	8	(	(	PUNCT
ejpam-4187	583	9	u	u	NOUN
ejpam-4187	583	10	,	,	PUNCT
ejpam-4187	583	11	v	v	NOUN
ejpam-4187	583	12	)	)	PUNCT
ejpam-4187	583	13	/∈	/∈	PUNCT
ejpam-4187	584	1	c	c	NOUN
ejpam-4187	584	2	and	and	CCONJ
ejpam-4187	584	3	(	(	PUNCT
ejpam-4187	584	4	u	u	NOUN
ejpam-4187	584	5	,	,	PUNCT
ejpam-4187	584	6	v)(x	v)(x	NOUN
ejpam-4187	584	7	,	,	PUNCT
ejpam-4187	584	8	y	y	NOUN
ejpam-4187	584	9	)	)	PUNCT
ejpam-4187	584	10	∈	∈	NOUN
ejpam-4187	584	11	e(g[h	e(g[h	NOUN
ejpam-4187	584	12	]	]	PUNCT
ejpam-4187	584	13	)	)	PUNCT
ejpam-4187	584	14	for	for	ADP
ejpam-4187	584	15	any	any	DET
ejpam-4187	584	16	v	v	NUM
ejpam-4187	584	17	∈	∈	PROPN
ejpam-4187	584	18	v	v	NOUN
ejpam-4187	584	19	(	(	PUNCT
ejpam-4187	584	20	h	h	NOUN
ejpam-4187	584	21	)	)	PUNCT
ejpam-4187	584	22	.	.	PUNCT
ejpam-4187	585	1	otherwise	otherwise	ADV
ejpam-4187	585	2	,	,	PUNCT
ejpam-4187	585	3	pick	pick	VERB
ejpam-4187	585	4	distinct	distinct	ADJ
ejpam-4187	585	5	v	v	NOUN
ejpam-4187	585	6	,	,	PUNCT
ejpam-4187	585	7	w	w	PROPN
ejpam-4187	585	8	∈	∈	PROPN
ejpam-4187	585	9	v	v	ADP
ejpam-4187	585	10	(	(	PUNCT
ejpam-4187	585	11	h	h	NOUN
ejpam-4187	585	12	)	)	PUNCT
ejpam-4187	585	13	.	.	PUNCT
ejpam-4187	586	1	then	then	ADV
ejpam-4187	586	2	(	(	PUNCT
ejpam-4187	586	3	u	u	NOUN
ejpam-4187	586	4	,	,	PUNCT
ejpam-4187	586	5	v	v	NOUN
ejpam-4187	586	6	)	)	PUNCT
ejpam-4187	586	7	and	and	CCONJ
ejpam-4187	586	8	(	(	PUNCT
ejpam-4187	586	9	u	u	NOUN
ejpam-4187	586	10	,	,	PUNCT
ejpam-4187	586	11	w	w	NOUN
ejpam-4187	586	12	)	)	PUNCT
ejpam-4187	586	13	are	be	AUX
ejpam-4187	586	14	distinct	distinct	ADJ
ejpam-4187	586	15	vertices	vertex	NOUN
ejpam-4187	586	16	in	in	ADP
ejpam-4187	586	17	v	v	NOUN
ejpam-4187	586	18	(	(	PUNCT
ejpam-4187	586	19	g[h	g[h	PROPN
ejpam-4187	586	20	]	]	PUNCT
ejpam-4187	586	21	)	)	PUNCT
ejpam-4187	586	22	\	\	PROPN
ejpam-4187	587	1	c	c	NOUN
ejpam-4187	587	2	with	with	ADP
ejpam-4187	587	3	dg[h]((x	dg[h]((x	PROPN
ejpam-4187	587	4	,	,	PUNCT
ejpam-4187	587	5	y	y	PROPN
ejpam-4187	587	6	)	)	PUNCT
ejpam-4187	587	7	,	,	PUNCT
ejpam-4187	587	8	(	(	PUNCT
ejpam-4187	587	9	u	u	NOUN
ejpam-4187	587	10	,	,	PUNCT
ejpam-4187	587	11	v	v	NOUN
ejpam-4187	587	12	)	)	PUNCT
ejpam-4187	587	13	)	)	PUNCT
ejpam-4187	587	14	=	=	SYM
ejpam-4187	587	15	2	2	NUM
ejpam-4187	587	16	=	=	SYM
ejpam-4187	587	17	dg[h]((x	dg[h]((x	NOUN
ejpam-4187	587	18	,	,	PUNCT
ejpam-4187	587	19	y	y	PROPN
ejpam-4187	587	20	)	)	PUNCT
ejpam-4187	587	21	,	,	PUNCT
ejpam-4187	587	22	(	(	PUNCT
ejpam-4187	587	23	u	u	NOUN
ejpam-4187	587	24	,	,	PUNCT
ejpam-4187	587	25	w	w	NOUN
ejpam-4187	587	26	)	)	PUNCT
ejpam-4187	587	27	)	)	PUNCT
ejpam-4187	587	28	.	.	PUNCT
ejpam-4187	588	1	finally	finally	ADV
ejpam-4187	588	2	,	,	PUNCT
ejpam-4187	588	3	suppose	suppose	VERB
ejpam-4187	588	4	that	that	SCONJ
ejpam-4187	588	5	x	x	PUNCT
ejpam-4187	588	6	/∈	/∈	PRON
ejpam-4187	588	7	ng(v	ng(v	PUNCT
ejpam-4187	588	8	(	(	PUNCT
ejpam-4187	588	9	g	g	NOUN
ejpam-4187	588	10	)	)	PUNCT
ejpam-4187	588	11	\	\	PUNCT
ejpam-4187	589	1	(	(	PUNCT
ejpam-4187	589	2	s	s	NOUN
ejpam-4187	589	3	,	,	PUNCT
ejpam-4187	589	4	2	2	NUM
ejpam-4187	589	5	)	)	PUNCT
ejpam-4187	589	6	)	)	PUNCT
ejpam-4187	589	7	.	.	PUNCT
ejpam-4187	590	1	we	we	PRON
ejpam-4187	590	2	consider	consider	VERB
ejpam-4187	590	3	the	the	DET
ejpam-4187	590	4	following	follow	VERB
ejpam-4187	590	5	subcases	subcase	NOUN
ejpam-4187	590	6	:	:	PUNCT
ejpam-4187	590	7	subcase	subcase	NOUN
ejpam-4187	590	8	2.1	2.1	NUM
ejpam-4187	590	9	:	:	PUNCT
ejpam-4187	590	10	suppose	suppose	VERB
ejpam-4187	590	11	that	that	SCONJ
ejpam-4187	590	12	tu	tu	PROPN
ejpam-4187	590	13	=	=	SYM
ejpam-4187	590	14	v	v	PROPN
ejpam-4187	590	15	(	(	PUNCT
ejpam-4187	590	16	h	h	NOUN
ejpam-4187	590	17	)	)	PUNCT
ejpam-4187	590	18	for	for	ADP
ejpam-4187	590	19	all	all	PRON
ejpam-4187	590	20	u	u	PROPN
ejpam-4187	590	21	∈	∈	PROPN
ejpam-4187	590	22	ng(x	ng(x	NUM
ejpam-4187	590	23	,	,	PUNCT
ejpam-4187	590	24	2	2	NUM
ejpam-4187	590	25	)	)	PUNCT
ejpam-4187	590	26	.	.	PUNCT
ejpam-4187	591	1	by	by	ADP
ejpam-4187	591	2	condition	condition	NOUN
ejpam-4187	591	3	(	(	PUNCT
ejpam-4187	591	4	a	a	X
ejpam-4187	591	5	)	)	PUNCT
ejpam-4187	591	6	,	,	PUNCT
ejpam-4187	591	7	either	either	CCONJ
ejpam-4187	591	8	|v	|v	PROPN
ejpam-4187	591	9	(	(	PUNCT
ejpam-4187	591	10	h	h	NOUN
ejpam-4187	591	11	)	)	PUNCT
ejpam-4187	591	12	\	\	PUNCT
ejpam-4187	591	13	tx|	tx|	PROPN
ejpam-4187	591	14	≥	≥	NUM
ejpam-4187	591	15	3	3	NUM
ejpam-4187	591	16	or	or	CCONJ
ejpam-4187	591	17	⟨v	⟨v	NUM
ejpam-4187	591	18	(	(	PUNCT
ejpam-4187	591	19	h	h	NOUN
ejpam-4187	591	20	)	)	PUNCT
ejpam-4187	591	21	\	\	NOUN
ejpam-4187	591	22	tx⟩	tx⟩	PROPN
ejpam-4187	591	23	=	=	SYM
ejpam-4187	591	24	k2	k2	PROPN
ejpam-4187	591	25	.	.	PUNCT
ejpam-4187	592	1	let	let	VERB
ejpam-4187	592	2	y	y	NOUN
ejpam-4187	593	1	,	,	PUNCT
ejpam-4187	593	2	w	w	PROPN
ejpam-4187	593	3	∈	∈	PROPN
ejpam-4187	593	4	v	v	ADP
ejpam-4187	593	5	(	(	PUNCT
ejpam-4187	593	6	h	h	NOUN
ejpam-4187	593	7	)	)	PUNCT
ejpam-4187	593	8	\	\	PROPN
ejpam-4187	593	9	tx	tx	PROPN
ejpam-4187	593	10	.	.	PUNCT
ejpam-4187	594	1	if	if	SCONJ
ejpam-4187	594	2	|v	|v	PROPN
ejpam-4187	594	3	(	(	PUNCT
ejpam-4187	594	4	h	h	NOUN
ejpam-4187	594	5	)	)	PUNCT
ejpam-4187	594	6	\	\	PUNCT
ejpam-4187	594	7	tx|	tx|	PROPN
ejpam-4187	594	8	≥	≥	NUM
ejpam-4187	594	9	3	3	NUM
ejpam-4187	594	10	and	and	CCONJ
ejpam-4187	594	11	v	v	NOUN
ejpam-4187	594	12	,	,	PUNCT
ejpam-4187	594	13	w	w	PROPN
ejpam-4187	594	14	∈	∈	PROPN
ejpam-4187	594	15	(	(	PUNCT
ejpam-4187	594	16	v	v	NOUN
ejpam-4187	594	17	(	(	PUNCT
ejpam-4187	594	18	h	h	NOUN
ejpam-4187	594	19	)	)	PUNCT
ejpam-4187	594	20	\	\	PROPN
ejpam-4187	595	1	tx	tx	PROPN
ejpam-4187	595	2	)	)	PUNCT
ejpam-4187	595	3	\	\	NOUN
ejpam-4187	595	4	{	{	PUNCT
ejpam-4187	595	5	y	y	NOUN
ejpam-4187	595	6	}	}	PUNCT
ejpam-4187	595	7	are	be	AUX
ejpam-4187	595	8	distinct	distinct	ADJ
ejpam-4187	595	9	,	,	PUNCT
ejpam-4187	595	10	then	then	ADV
ejpam-4187	595	11	(	(	PUNCT
ejpam-4187	595	12	x	x	NOUN
ejpam-4187	595	13	,	,	PUNCT
ejpam-4187	595	14	v	v	NOUN
ejpam-4187	595	15	)	)	PUNCT
ejpam-4187	595	16	and	and	CCONJ
ejpam-4187	595	17	(	(	PUNCT
ejpam-4187	595	18	x	x	NOUN
ejpam-4187	595	19	,	,	PUNCT
ejpam-4187	595	20	w	w	NOUN
ejpam-4187	595	21	)	)	PUNCT
ejpam-4187	595	22	are	be	AUX
ejpam-4187	595	23	distinct	distinct	ADJ
ejpam-4187	595	24	vertices	vertex	NOUN
ejpam-4187	595	25	in	in	ADP
ejpam-4187	595	26	v	v	NOUN
ejpam-4187	595	27	(	(	PUNCT
ejpam-4187	595	28	g[h])\c	g[h])\c	VERB
ejpam-4187	595	29	with	with	ADP
ejpam-4187	595	30	dg[h]((x	dg[h]((x	NOUN
ejpam-4187	595	31	,	,	PUNCT
ejpam-4187	595	32	y	y	PROPN
ejpam-4187	595	33	)	)	PUNCT
ejpam-4187	595	34	,	,	PUNCT
ejpam-4187	595	35	(	(	PUNCT
ejpam-4187	595	36	x	x	NOUN
ejpam-4187	595	37	,	,	PUNCT
ejpam-4187	595	38	v	v	NOUN
ejpam-4187	595	39	)	)	PUNCT
ejpam-4187	595	40	)	)	PUNCT
ejpam-4187	596	1	≤	≤	NUM
ejpam-4187	596	2	2	2	NUM
ejpam-4187	596	3	and	and	CCONJ
ejpam-4187	596	4	dg[h]((x	dg[h]((x	NOUN
ejpam-4187	596	5	,	,	PUNCT
ejpam-4187	596	6	y	y	PROPN
ejpam-4187	596	7	)	)	PUNCT
ejpam-4187	596	8	,	,	PUNCT
ejpam-4187	596	9	(	(	PUNCT
ejpam-4187	596	10	x	x	NOUN
ejpam-4187	596	11	,	,	PUNCT
ejpam-4187	596	12	w	w	NOUN
ejpam-4187	596	13	)	)	PUNCT
ejpam-4187	596	14	)	)	PUNCT
ejpam-4187	596	15	≤	≤	NUM
ejpam-4187	596	16	2	2	NUM
ejpam-4187	596	17	.	.	PUNCT
ejpam-4187	597	1	on	on	ADP
ejpam-4187	597	2	the	the	DET
ejpam-4187	597	3	other	other	ADJ
ejpam-4187	597	4	hand	hand	NOUN
ejpam-4187	597	5	,	,	PUNCT
ejpam-4187	597	6	if	if	SCONJ
ejpam-4187	597	7	y	y	PROPN
ejpam-4187	597	8	,	,	PUNCT
ejpam-4187	597	9	w	w	PROPN
ejpam-4187	597	10	∈	∈	PROPN
ejpam-4187	597	11	⟨v	⟨v	PUNCT
ejpam-4187	597	12	(	(	PUNCT
ejpam-4187	597	13	h	h	NOUN
ejpam-4187	597	14	)	)	PUNCT
ejpam-4187	597	15	\	\	NOUN
ejpam-4187	597	16	tx⟩	tx⟩	PROPN
ejpam-4187	597	17	=	=	SYM
ejpam-4187	597	18	k2	k2	PROPN
ejpam-4187	597	19	,	,	PUNCT
ejpam-4187	597	20	then	then	ADV
ejpam-4187	597	21	(	(	PUNCT
ejpam-4187	597	22	x	x	NOUN
ejpam-4187	597	23	,	,	PUNCT
ejpam-4187	597	24	w	w	NOUN
ejpam-4187	597	25	)	)	PUNCT
ejpam-4187	597	26	∈	∈	NOUN
ejpam-4187	597	27	v	v	NOUN
ejpam-4187	597	28	(	(	PUNCT
ejpam-4187	597	29	g[h	g[h	PROPN
ejpam-4187	597	30	]	]	PUNCT
ejpam-4187	597	31	)	)	PUNCT
ejpam-4187	597	32	\	\	PROPN
ejpam-4187	598	1	c	c	NOUN
ejpam-4187	598	2	with	with	ADP
ejpam-4187	598	3	(	(	PUNCT
ejpam-4187	598	4	x	x	NOUN
ejpam-4187	598	5	,	,	PUNCT
ejpam-4187	598	6	y)(x	y)(x	PROPN
ejpam-4187	598	7	,	,	PUNCT
ejpam-4187	598	8	w	w	NOUN
ejpam-4187	598	9	)	)	PUNCT
ejpam-4187	598	10	∈	∈	NOUN
ejpam-4187	598	11	e(g[h	e(g[h	NOUN
ejpam-4187	598	12	]	]	PUNCT
ejpam-4187	598	13	)	)	PUNCT
ejpam-4187	598	14	.	.	PUNCT
ejpam-4187	599	1	subcase	subcase	PROPN
ejpam-4187	599	2	2.2	2.2	NUM
ejpam-4187	599	3	:	:	PUNCT
ejpam-4187	599	4	suppose	suppose	VERB
ejpam-4187	599	5	that	that	SCONJ
ejpam-4187	599	6	tu	tu	PROPN
ejpam-4187	599	7	̸=	̸=	PROPN
ejpam-4187	599	8	v	v	PROPN
ejpam-4187	599	9	(	(	PUNCT
ejpam-4187	599	10	h	h	NOUN
ejpam-4187	599	11	)	)	PUNCT
ejpam-4187	599	12	for	for	ADP
ejpam-4187	599	13	some	some	DET
ejpam-4187	599	14	u	u	NOUN
ejpam-4187	599	15	∈	∈	PROPN
ejpam-4187	599	16	ng(x	ng(x	NUM
ejpam-4187	599	17	,	,	PUNCT
ejpam-4187	599	18	2	2	NUM
ejpam-4187	599	19	)	)	PUNCT
ejpam-4187	599	20	.	.	PUNCT
ejpam-4187	600	1	if	if	SCONJ
ejpam-4187	600	2	|v	|v	PROPN
ejpam-4187	600	3	(	(	PUNCT
ejpam-4187	600	4	h	h	NOUN
ejpam-4187	600	5	)	)	PUNCT
ejpam-4187	600	6	\	\	PUNCT
ejpam-4187	600	7	tx|	tx|	PROPN
ejpam-4187	600	8	≥	≥	NUM
ejpam-4187	600	9	3	3	NUM
ejpam-4187	600	10	,	,	PUNCT
ejpam-4187	600	11	then	then	ADV
ejpam-4187	600	12	,	,	PUNCT
ejpam-4187	600	13	r.	r.	PROPN
ejpam-4187	600	14	malalay	malalay	PROPN
ejpam-4187	600	15	,	,	PUNCT
ejpam-4187	600	16	f.	f.	PROPN
ejpam-4187	600	17	jamil	jamil	PROPN
ejpam-4187	600	18	/	/	SYM
ejpam-4187	600	19	eur	eur	PROPN
ejpam-4187	600	20	.	.	PUNCT
ejpam-4187	601	1	j.	j.	PROPN
ejpam-4187	601	2	pure	pure	PROPN
ejpam-4187	601	3	appl	appl	PROPN
ejpam-4187	601	4	.	.	PROPN
ejpam-4187	601	5	math	math	PROPN
ejpam-4187	601	6	,	,	PUNCT
ejpam-4187	601	7	15	15	NUM
ejpam-4187	601	8	(	(	PUNCT
ejpam-4187	601	9	1	1	NUM
ejpam-4187	601	10	)	)	PUNCT
ejpam-4187	601	11	(	(	PUNCT
ejpam-4187	601	12	2022	2022	NUM
ejpam-4187	601	13	)	)	PUNCT
ejpam-4187	601	14	,	,	PUNCT
ejpam-4187	601	15	207	207	NUM
ejpam-4187	601	16	-	-	SYM
ejpam-4187	601	17	223	223	NUM
ejpam-4187	601	18	221	221	NUM
ejpam-4187	601	19	as	as	SCONJ
ejpam-4187	601	20	done	do	VERB
ejpam-4187	601	21	in	in	ADP
ejpam-4187	601	22	subcase	subcase	NOUN
ejpam-4187	601	23	2.1	2.1	NUM
ejpam-4187	601	24	,	,	PUNCT
ejpam-4187	601	25	there	there	PRON
ejpam-4187	601	26	exists	exist	VERB
ejpam-4187	601	27	(	(	PUNCT
ejpam-4187	601	28	x	x	X
ejpam-4187	601	29	,	,	PUNCT
ejpam-4187	601	30	v	v	NOUN
ejpam-4187	601	31	)	)	PUNCT
ejpam-4187	601	32	∈	∈	NOUN
ejpam-4187	601	33	v	v	NOUN
ejpam-4187	601	34	(	(	PUNCT
ejpam-4187	601	35	g[h	g[h	PROPN
ejpam-4187	601	36	]	]	PUNCT
ejpam-4187	601	37	)	)	PUNCT
ejpam-4187	602	1	\c	\c	ADP
ejpam-4187	602	2	such	such	ADJ
ejpam-4187	602	3	that	that	PRON
ejpam-4187	602	4	(	(	PUNCT
ejpam-4187	602	5	x	x	NOUN
ejpam-4187	602	6	,	,	PUNCT
ejpam-4187	602	7	y)(x	y)(x	PROPN
ejpam-4187	602	8	,	,	PUNCT
ejpam-4187	602	9	v	v	NOUN
ejpam-4187	602	10	)	)	PUNCT
ejpam-4187	602	11	∈	∈	NOUN
ejpam-4187	602	12	e(g[h	e(g[h	NOUN
ejpam-4187	602	13	]	]	PUNCT
ejpam-4187	602	14	)	)	PUNCT
ejpam-4187	602	15	or	or	CCONJ
ejpam-4187	602	16	there	there	PRON
ejpam-4187	602	17	exist	exist	VERB
ejpam-4187	602	18	distinct	distinct	ADJ
ejpam-4187	602	19	(	(	PUNCT
ejpam-4187	602	20	x	x	NOUN
ejpam-4187	602	21	,	,	PUNCT
ejpam-4187	602	22	v	v	NOUN
ejpam-4187	602	23	)	)	PUNCT
ejpam-4187	602	24	,	,	PUNCT
ejpam-4187	602	25	(	(	PUNCT
ejpam-4187	602	26	x	x	NOUN
ejpam-4187	602	27	,	,	PUNCT
ejpam-4187	602	28	w	w	NOUN
ejpam-4187	602	29	)	)	PUNCT
ejpam-4187	602	30	∈	∈	NOUN
ejpam-4187	602	31	v	v	NOUN
ejpam-4187	602	32	(	(	PUNCT
ejpam-4187	602	33	g[h	g[h	PROPN
ejpam-4187	602	34	]	]	PUNCT
ejpam-4187	602	35	)	)	PUNCT
ejpam-4187	602	36	\	\	PROPN
ejpam-4187	603	1	c	c	PROPN
ejpam-4187	603	2	for	for	ADP
ejpam-4187	603	3	which	which	PRON
ejpam-4187	603	4	dg[h]((x	dg[h]((x	PROPN
ejpam-4187	603	5	,	,	PUNCT
ejpam-4187	603	6	y	y	PROPN
ejpam-4187	603	7	)	)	PUNCT
ejpam-4187	603	8	,	,	PUNCT
ejpam-4187	603	9	(	(	PUNCT
ejpam-4187	603	10	x	x	NOUN
ejpam-4187	603	11	,	,	PUNCT
ejpam-4187	603	12	v	v	NOUN
ejpam-4187	603	13	)	)	PUNCT
ejpam-4187	603	14	)	)	PUNCT
ejpam-4187	604	1	=	=	SYM
ejpam-4187	604	2	2	2	NUM
ejpam-4187	604	3	=	=	SYM
ejpam-4187	604	4	dg[h]((x	dg[h]((x	NOUN
ejpam-4187	604	5	,	,	PUNCT
ejpam-4187	604	6	y	y	PROPN
ejpam-4187	604	7	)	)	PUNCT
ejpam-4187	604	8	,	,	PUNCT
ejpam-4187	604	9	(	(	PUNCT
ejpam-4187	604	10	x	x	NOUN
ejpam-4187	604	11	,	,	PUNCT
ejpam-4187	604	12	w	w	NOUN
ejpam-4187	604	13	)	)	PUNCT
ejpam-4187	604	14	)	)	PUNCT
ejpam-4187	604	15	.	.	PUNCT
ejpam-4187	605	1	suppose	suppose	VERB
ejpam-4187	605	2	that	that	SCONJ
ejpam-4187	605	3	yw	yw	PROPN
ejpam-4187	605	4	∈	∈	PROPN
ejpam-4187	605	5	⟨v	⟨v	PUNCT
ejpam-4187	605	6	(	(	PUNCT
ejpam-4187	605	7	h	h	NOUN
ejpam-4187	605	8	)	)	PUNCT
ejpam-4187	605	9	\	\	NOUN
ejpam-4187	605	10	tx⟩	tx⟩	PROPN
ejpam-4187	605	11	=	=	SYM
ejpam-4187	605	12	k2	k2	PROPN
ejpam-4187	605	13	.	.	PUNCT
ejpam-4187	606	1	then	then	ADV
ejpam-4187	606	2	(	(	PUNCT
ejpam-4187	606	3	x	x	NOUN
ejpam-4187	606	4	,	,	PUNCT
ejpam-4187	606	5	w	w	NOUN
ejpam-4187	606	6	)	)	PUNCT
ejpam-4187	606	7	∈	∈	NOUN
ejpam-4187	606	8	v	v	NOUN
ejpam-4187	606	9	(	(	PUNCT
ejpam-4187	606	10	g[h	g[h	PROPN
ejpam-4187	606	11	]	]	PUNCT
ejpam-4187	606	12	)	)	PUNCT
ejpam-4187	606	13	\	\	PROPN
ejpam-4187	607	1	c	c	NOUN
ejpam-4187	607	2	with	with	ADP
ejpam-4187	607	3	(	(	PUNCT
ejpam-4187	607	4	x	x	NOUN
ejpam-4187	607	5	,	,	PUNCT
ejpam-4187	607	6	y)(x	y)(x	PROPN
ejpam-4187	607	7	,	,	PUNCT
ejpam-4187	607	8	w	w	NOUN
ejpam-4187	607	9	)	)	PUNCT
ejpam-4187	607	10	∈	∈	NOUN
ejpam-4187	607	11	e(g[h	e(g[h	NOUN
ejpam-4187	607	12	]	]	PUNCT
ejpam-4187	607	13	)	)	PUNCT
ejpam-4187	607	14	.	.	PUNCT
ejpam-4187	608	1	if	if	SCONJ
ejpam-4187	608	2	yw	yw	PROPN
ejpam-4187	608	3	∈	∈	PROPN
ejpam-4187	608	4	⟨v	⟨v	PUNCT
ejpam-4187	608	5	(	(	PUNCT
ejpam-4187	608	6	h)\tx⟩	h)\tx⟩	X
ejpam-4187	608	7	=	=	SYM
ejpam-4187	608	8	k2	k2	NOUN
ejpam-4187	608	9	,	,	PUNCT
ejpam-4187	608	10	then	then	ADV
ejpam-4187	608	11	there	there	PRON
ejpam-4187	608	12	exists	exist	VERB
ejpam-4187	608	13	u	u	PROPN
ejpam-4187	608	14	∈	∈	PROPN
ejpam-4187	608	15	ng(x	ng(x	NUM
ejpam-4187	608	16	,	,	PUNCT
ejpam-4187	608	17	2	2	NUM
ejpam-4187	608	18	)	)	PUNCT
ejpam-4187	608	19	for	for	ADP
ejpam-4187	608	20	which	which	PRON
ejpam-4187	608	21	tu	tu	PROPN
ejpam-4187	608	22	̸=	̸=	PROPN
ejpam-4187	608	23	v	v	PROPN
ejpam-4187	608	24	(	(	PUNCT
ejpam-4187	608	25	h	h	NOUN
ejpam-4187	608	26	)	)	PUNCT
ejpam-4187	608	27	,	,	PUNCT
ejpam-4187	608	28	by	by	ADP
ejpam-4187	608	29	condition	condition	NOUN
ejpam-4187	608	30	(	(	PUNCT
ejpam-4187	608	31	b	b	NOUN
ejpam-4187	608	32	)	)	PUNCT
ejpam-4187	608	33	.	.	PUNCT
ejpam-4187	609	1	here	here	ADV
ejpam-4187	609	2	,	,	PUNCT
ejpam-4187	609	3	dg[h]((x	dg[h]((x	PROPN
ejpam-4187	609	4	,	,	PUNCT
ejpam-4187	609	5	y	y	PROPN
ejpam-4187	609	6	)	)	PUNCT
ejpam-4187	609	7	,	,	PUNCT
ejpam-4187	609	8	(	(	PUNCT
ejpam-4187	609	9	x	x	NOUN
ejpam-4187	609	10	,	,	PUNCT
ejpam-4187	609	11	w	w	NOUN
ejpam-4187	609	12	)	)	PUNCT
ejpam-4187	609	13	=	=	SYM
ejpam-4187	609	14	2	2	X
ejpam-4187	609	15	.	.	X
ejpam-4187	609	16	pick	pick	VERB
ejpam-4187	609	17	v	v	NUM
ejpam-4187	609	18	∈	∈	PROPN
ejpam-4187	609	19	v	v	NOUN
ejpam-4187	609	20	(	(	PUNCT
ejpam-4187	609	21	h	h	NOUN
ejpam-4187	609	22	)	)	PUNCT
ejpam-4187	609	23	\	\	PROPN
ejpam-4187	609	24	tu	tu	PROPN
ejpam-4187	609	25	.	.	PUNCT
ejpam-4187	610	1	then	then	ADV
ejpam-4187	610	2	(	(	PUNCT
ejpam-4187	610	3	u	u	NOUN
ejpam-4187	610	4	,	,	PUNCT
ejpam-4187	610	5	v	v	NOUN
ejpam-4187	610	6	)	)	PUNCT
ejpam-4187	610	7	/∈	/∈	PUNCT
ejpam-4187	611	1	c	c	NOUN
ejpam-4187	611	2	and	and	CCONJ
ejpam-4187	611	3	dg[h]((x	dg[h]((x	PROPN
ejpam-4187	611	4	,	,	PUNCT
ejpam-4187	611	5	y	y	PROPN
ejpam-4187	611	6	)	)	PUNCT
ejpam-4187	611	7	,	,	PUNCT
ejpam-4187	611	8	(	(	PUNCT
ejpam-4187	611	9	u	u	NOUN
ejpam-4187	611	10	,	,	PUNCT
ejpam-4187	611	11	v	v	NOUN
ejpam-4187	611	12	)	)	PUNCT
ejpam-4187	611	13	≤	≤	NOUN
ejpam-4187	611	14	2	2	NUM
ejpam-4187	611	15	.	.	PUNCT
ejpam-4187	612	1	finally	finally	ADV
ejpam-4187	612	2	,	,	PUNCT
ejpam-4187	612	3	suppose	suppose	VERB
ejpam-4187	612	4	that	that	SCONJ
ejpam-4187	612	5	|v	|v	PROPN
ejpam-4187	612	6	(	(	PUNCT
ejpam-4187	612	7	h	h	NOUN
ejpam-4187	612	8	)	)	PUNCT
ejpam-4187	612	9	\	\	PUNCT
ejpam-4187	612	10	tx|	tx|	PROPN
ejpam-4187	612	11	=	=	PUNCT
ejpam-4187	612	12	1	1	X
ejpam-4187	612	13	.	.	PUNCT
ejpam-4187	612	14	by	by	ADP
ejpam-4187	612	15	condition	condition	NOUN
ejpam-4187	612	16	(	(	PUNCT
ejpam-4187	612	17	c	c	NOUN
ejpam-4187	612	18	)	)	PUNCT
ejpam-4187	612	19	,	,	PUNCT
ejpam-4187	612	20	one	one	NUM
ejpam-4187	612	21	of	of	ADP
ejpam-4187	612	22	the	the	DET
ejpam-4187	612	23	following	follow	VERB
ejpam-4187	612	24	holds	hold	VERB
ejpam-4187	612	25	:	:	PUNCT
ejpam-4187	612	26	there	there	PRON
ejpam-4187	612	27	exists	exist	VERB
ejpam-4187	612	28	u	u	PROPN
ejpam-4187	612	29	∈	∈	PROPN
ejpam-4187	612	30	ng(x	ng(x	NUM
ejpam-4187	612	31	)	)	PUNCT
ejpam-4187	612	32	for	for	ADP
ejpam-4187	612	33	which	which	PRON
ejpam-4187	612	34	tu	tu	PROPN
ejpam-4187	612	35	̸=	̸=	PROPN
ejpam-4187	612	36	v	v	PROPN
ejpam-4187	612	37	(	(	PUNCT
ejpam-4187	612	38	h	h	NOUN
ejpam-4187	612	39	)	)	PUNCT
ejpam-4187	612	40	;	;	PUNCT
ejpam-4187	612	41	there	there	PRON
ejpam-4187	612	42	exists	exist	VERB
ejpam-4187	612	43	u	u	PROPN
ejpam-4187	612	44	∈	∈	PROPN
ejpam-4187	612	45	ng(x	ng(x	NUM
ejpam-4187	612	46	,	,	PUNCT
ejpam-4187	612	47	2	2	NUM
ejpam-4187	612	48	)	)	PUNCT
ejpam-4187	612	49	for	for	ADP
ejpam-4187	612	50	which	which	PRON
ejpam-4187	612	51	|v	|v	PROPN
ejpam-4187	612	52	(	(	PUNCT
ejpam-4187	612	53	h)\tx|	h)\tx|	X
ejpam-4187	612	54	≥	≥	NUM
ejpam-4187	612	55	2	2	NUM
ejpam-4187	612	56	;	;	PUNCT
ejpam-4187	612	57	there	there	PRON
ejpam-4187	612	58	exist	exist	VERB
ejpam-4187	612	59	distinct	distinct	ADJ
ejpam-4187	612	60	u	u	NOUN
ejpam-4187	612	61	,	,	PUNCT
ejpam-4187	612	62	z	z	PROPN
ejpam-4187	612	63	∈	∈	PROPN
ejpam-4187	612	64	ng(x	ng(x	NUM
ejpam-4187	612	65	,	,	PUNCT
ejpam-4187	612	66	2	2	NUM
ejpam-4187	612	67	)	)	PUNCT
ejpam-4187	612	68	for	for	ADP
ejpam-4187	612	69	which	which	PRON
ejpam-4187	612	70	tu	tu	PROPN
ejpam-4187	612	71	̸=	̸=	PROPN
ejpam-4187	612	72	v	v	ADP
ejpam-4187	612	73	(	(	PUNCT
ejpam-4187	612	74	h	h	NOUN
ejpam-4187	612	75	)	)	PUNCT
ejpam-4187	612	76	and	and	CCONJ
ejpam-4187	612	77	tz	tz	PROPN
ejpam-4187	612	78	̸=	̸=	PROPN
ejpam-4187	612	79	v	v	NOUN
ejpam-4187	612	80	(	(	PUNCT
ejpam-4187	612	81	h	h	NOUN
ejpam-4187	612	82	)	)	PUNCT
ejpam-4187	612	83	.	.	PUNCT
ejpam-4187	613	1	if	if	SCONJ
ejpam-4187	613	2	u	u	PROPN
ejpam-4187	613	3	∈	∈	PROPN
ejpam-4187	613	4	ng(x	ng(x	NUM
ejpam-4187	613	5	)	)	PUNCT
ejpam-4187	613	6	and	and	CCONJ
ejpam-4187	613	7	v	v	ADP
ejpam-4187	613	8	∈	∈	PROPN
ejpam-4187	613	9	v	v	NOUN
ejpam-4187	613	10	(	(	PUNCT
ejpam-4187	613	11	h	h	NOUN
ejpam-4187	613	12	)	)	PUNCT
ejpam-4187	613	13	\	\	PROPN
ejpam-4187	613	14	tu	tu	PROPN
ejpam-4187	613	15	,	,	PUNCT
ejpam-4187	613	16	then	then	ADV
ejpam-4187	613	17	(	(	PUNCT
ejpam-4187	613	18	u	u	NOUN
ejpam-4187	613	19	,	,	PUNCT
ejpam-4187	613	20	v	v	NOUN
ejpam-4187	613	21	)	)	PUNCT
ejpam-4187	613	22	/∈	/∈	PUNCT
ejpam-4187	614	1	c	c	NOUN
ejpam-4187	614	2	and	and	CCONJ
ejpam-4187	614	3	(	(	PUNCT
ejpam-4187	614	4	x	x	X
ejpam-4187	614	5	,	,	PUNCT
ejpam-4187	614	6	y)(u	y)(u	ADJ
ejpam-4187	614	7	,	,	PUNCT
ejpam-4187	614	8	v	v	NOUN
ejpam-4187	614	9	)	)	PUNCT
ejpam-4187	614	10	∈	∈	NOUN
ejpam-4187	614	11	e(g[h	e(g[h	NOUN
ejpam-4187	614	12	]	]	PUNCT
ejpam-4187	614	13	)	)	PUNCT
ejpam-4187	614	14	.	.	PUNCT
ejpam-4187	615	1	if	if	SCONJ
ejpam-4187	615	2	u	u	PROPN
ejpam-4187	615	3	∈	∈	PROPN
ejpam-4187	615	4	ng(x	ng(x	NUM
ejpam-4187	615	5	,	,	PUNCT
ejpam-4187	615	6	2	2	NUM
ejpam-4187	615	7	)	)	PUNCT
ejpam-4187	615	8	for	for	ADP
ejpam-4187	615	9	which	which	PRON
ejpam-4187	615	10	|v	|v	PROPN
ejpam-4187	615	11	(	(	PUNCT
ejpam-4187	615	12	h	h	NOUN
ejpam-4187	615	13	)	)	PUNCT
ejpam-4187	615	14	\	\	PUNCT
ejpam-4187	616	1	tu|	tu|	ADP
ejpam-4187	616	2	≥	≥	NUM
ejpam-4187	616	3	2	2	NUM
ejpam-4187	616	4	and	and	CCONJ
ejpam-4187	616	5	v	v	NOUN
ejpam-4187	616	6	,	,	PUNCT
ejpam-4187	616	7	w	w	PROPN
ejpam-4187	616	8	∈	∈	PROPN
ejpam-4187	616	9	v	v	ADP
ejpam-4187	616	10	(	(	PUNCT
ejpam-4187	616	11	h	h	NOUN
ejpam-4187	616	12	)	)	PUNCT
ejpam-4187	616	13	\	\	PROPN
ejpam-4187	616	14	tu	tu	PROPN
ejpam-4187	616	15	are	be	AUX
ejpam-4187	616	16	distinct	distinct	ADJ
ejpam-4187	616	17	,	,	PUNCT
ejpam-4187	616	18	then	then	ADV
ejpam-4187	616	19	(	(	PUNCT
ejpam-4187	616	20	u	u	NOUN
ejpam-4187	616	21	,	,	PUNCT
ejpam-4187	616	22	v	v	NOUN
ejpam-4187	616	23	)	)	PUNCT
ejpam-4187	616	24	and	and	CCONJ
ejpam-4187	616	25	(	(	PUNCT
ejpam-4187	616	26	u	u	NOUN
ejpam-4187	616	27	,	,	PUNCT
ejpam-4187	616	28	w	w	NOUN
ejpam-4187	616	29	)	)	PUNCT
ejpam-4187	616	30	are	be	AUX
ejpam-4187	616	31	distinct	distinct	ADJ
ejpam-4187	616	32	in	in	ADP
ejpam-4187	616	33	v	v	NOUN
ejpam-4187	616	34	(	(	PUNCT
ejpam-4187	616	35	g[h])\c	g[h])\c	NOUN
ejpam-4187	616	36	and	and	CCONJ
ejpam-4187	616	37	dg[h]((x	dg[h]((x	NOUN
ejpam-4187	616	38	,	,	PUNCT
ejpam-4187	616	39	y	y	PROPN
ejpam-4187	616	40	)	)	PUNCT
ejpam-4187	616	41	,	,	PUNCT
ejpam-4187	616	42	(	(	PUNCT
ejpam-4187	616	43	u	u	NOUN
ejpam-4187	616	44	,	,	PUNCT
ejpam-4187	616	45	v	v	NOUN
ejpam-4187	616	46	)	)	PUNCT
ejpam-4187	616	47	)	)	PUNCT
ejpam-4187	616	48	≤	≤	NUM
ejpam-4187	616	49	2	2	NUM
ejpam-4187	616	50	and	and	CCONJ
ejpam-4187	616	51	dg[h]((x	dg[h]((x	NOUN
ejpam-4187	616	52	,	,	PUNCT
ejpam-4187	616	53	y	y	PROPN
ejpam-4187	616	54	)	)	PUNCT
ejpam-4187	616	55	,	,	PUNCT
ejpam-4187	616	56	(	(	PUNCT
ejpam-4187	616	57	u	u	NOUN
ejpam-4187	616	58	,	,	PUNCT
ejpam-4187	616	59	w	w	NOUN
ejpam-4187	616	60	)	)	PUNCT
ejpam-4187	616	61	)	)	PUNCT
ejpam-4187	617	1	≤	≤	NUM
ejpam-4187	617	2	2	2	NUM
ejpam-4187	617	3	.	.	PUNCT
ejpam-4187	618	1	if	if	SCONJ
ejpam-4187	618	2	u	u	PROPN
ejpam-4187	618	3	,	,	PUNCT
ejpam-4187	618	4	z	z	PROPN
ejpam-4187	618	5	∈	∈	PROPN
ejpam-4187	618	6	ng(x	ng(x	NUM
ejpam-4187	618	7	,	,	PUNCT
ejpam-4187	618	8	2	2	NUM
ejpam-4187	618	9	)	)	PUNCT
ejpam-4187	618	10	are	be	AUX
ejpam-4187	618	11	distinct	distinct	ADJ
ejpam-4187	618	12	for	for	ADP
ejpam-4187	618	13	which	which	PRON
ejpam-4187	618	14	tu	tu	PROPN
ejpam-4187	618	15	̸=	̸=	PROPN
ejpam-4187	618	16	v	v	ADP
ejpam-4187	618	17	(	(	PUNCT
ejpam-4187	618	18	h	h	NOUN
ejpam-4187	618	19	)	)	PUNCT
ejpam-4187	618	20	and	and	CCONJ
ejpam-4187	618	21	tz	tz	PROPN
ejpam-4187	618	22	̸=	̸=	PROPN
ejpam-4187	618	23	v	v	PROPN
ejpam-4187	618	24	(	(	PUNCT
ejpam-4187	618	25	h	h	NOUN
ejpam-4187	618	26	)	)	PUNCT
ejpam-4187	618	27	,	,	PUNCT
ejpam-4187	618	28	then	then	ADV
ejpam-4187	618	29	(	(	PUNCT
ejpam-4187	618	30	u	u	NOUN
ejpam-4187	618	31	,	,	PUNCT
ejpam-4187	618	32	v	v	NOUN
ejpam-4187	618	33	)	)	PUNCT
ejpam-4187	618	34	and	and	CCONJ
ejpam-4187	618	35	(	(	PUNCT
ejpam-4187	618	36	z	z	NOUN
ejpam-4187	618	37	,	,	PUNCT
ejpam-4187	618	38	w	w	NOUN
ejpam-4187	618	39	)	)	PUNCT
ejpam-4187	618	40	are	be	AUX
ejpam-4187	618	41	distinct	distinct	ADJ
ejpam-4187	618	42	vertices	vertex	NOUN
ejpam-4187	618	43	in	in	ADP
ejpam-4187	618	44	v	v	NOUN
ejpam-4187	618	45	(	(	PUNCT
ejpam-4187	618	46	g[h])\c	g[h])\c	VERB
ejpam-4187	618	47	for	for	ADP
ejpam-4187	618	48	all	all	PRON
ejpam-4187	618	49	v	v	ADP
ejpam-4187	618	50	∈	∈	NOUN
ejpam-4187	618	51	v	v	NOUN
ejpam-4187	618	52	(	(	PUNCT
ejpam-4187	618	53	h)\tu	h)\tu	PROPN
ejpam-4187	618	54	and	and	CCONJ
ejpam-4187	618	55	w	w	PROPN
ejpam-4187	618	56	∈	∈	PROPN
ejpam-4187	618	57	v	v	ADP
ejpam-4187	618	58	(	(	PUNCT
ejpam-4187	618	59	h	h	NOUN
ejpam-4187	618	60	)	)	PUNCT
ejpam-4187	618	61	\	\	NOUN
ejpam-4187	618	62	tz	tz	NOUN
ejpam-4187	618	63	with	with	ADP
ejpam-4187	618	64	dg[h]((x	dg[h]((x	PROPN
ejpam-4187	618	65	,	,	PUNCT
ejpam-4187	618	66	y	y	PROPN
ejpam-4187	618	67	)	)	PUNCT
ejpam-4187	618	68	,	,	PUNCT
ejpam-4187	618	69	(	(	PUNCT
ejpam-4187	618	70	u	u	NOUN
ejpam-4187	618	71	,	,	PUNCT
ejpam-4187	618	72	v	v	NOUN
ejpam-4187	618	73	)	)	PUNCT
ejpam-4187	618	74	)	)	PUNCT
ejpam-4187	619	1	=	=	SYM
ejpam-4187	619	2	2	2	NUM
ejpam-4187	619	3	=	=	SYM
ejpam-4187	619	4	dg[h]((x	dg[h]((x	NOUN
ejpam-4187	619	5	,	,	PUNCT
ejpam-4187	619	6	y	y	PROPN
ejpam-4187	619	7	)	)	PUNCT
ejpam-4187	619	8	,	,	PUNCT
ejpam-4187	619	9	(	(	PUNCT
ejpam-4187	619	10	z	z	NOUN
ejpam-4187	619	11	,	,	PUNCT
ejpam-4187	619	12	w	w	NOUN
ejpam-4187	619	13	)	)	PUNCT
ejpam-4187	619	14	)	)	PUNCT
ejpam-4187	619	15	.	.	PUNCT
ejpam-4187	620	1	accordingly	accordingly	ADV
ejpam-4187	620	2	,	,	PUNCT
ejpam-4187	620	3	c	c	PROPN
ejpam-4187	620	4	is	be	AUX
ejpam-4187	620	5	a	a	DET
ejpam-4187	620	6	restrained	restrained	ADJ
ejpam-4187	620	7	disjunctive	disjunctive	ADJ
ejpam-4187	620	8	dominating	dominating	NOUN
ejpam-4187	620	9	set	set	NOUN
ejpam-4187	620	10	of	of	ADP
ejpam-4187	620	11	g[h	g[h	PROPN
ejpam-4187	620	12	]	]	PUNCT
ejpam-4187	620	13	.	.	PUNCT
ejpam-4187	621	1	corollary	corollary	ADJ
ejpam-4187	621	2	7	7	NUM
ejpam-4187	621	3	.	.	PUNCT
ejpam-4187	622	1	let	let	VERB
ejpam-4187	622	2	g	g	NOUN
ejpam-4187	622	3	and	and	CCONJ
ejpam-4187	622	4	h	h	NOUN
ejpam-4187	622	5	be	be	AUX
ejpam-4187	622	6	nontrivial	nontrivial	ADJ
ejpam-4187	622	7	connected	connected	ADJ
ejpam-4187	622	8	graphs	graph	NOUN
ejpam-4187	622	9	.	.	PUNCT
ejpam-4187	623	1	then	then	ADV
ejpam-4187	623	2	γdr	γdr	INTJ
ejpam-4187	623	3	(	(	PUNCT
ejpam-4187	623	4	g[h	g[h	NOUN
ejpam-4187	623	5	]	]	PUNCT
ejpam-4187	623	6	)	)	PUNCT
ejpam-4187	623	7	≤	≤	NUM
ejpam-4187	623	8	min	min	NOUN
ejpam-4187	623	9	{	{	PUNCT
ejpam-4187	623	10	γdt	γdt	NOUN
ejpam-4187	623	11	(	(	PUNCT
ejpam-4187	623	12	g	g	NOUN
ejpam-4187	623	13	)	)	PUNCT
ejpam-4187	623	14	,	,	PUNCT
ejpam-4187	623	15	2γ2(g	2γ2(g	NUM
ejpam-4187	623	16	)	)	PUNCT
ejpam-4187	623	17	}	}	PUNCT
ejpam-4187	623	18	.	.	PUNCT
ejpam-4187	624	1	proof	proof	NOUN
ejpam-4187	624	2	.	.	PUNCT
ejpam-4187	625	1	let	let	VERB
ejpam-4187	625	2	s	s	PRON
ejpam-4187	625	3	⊆	⊆	NUM
ejpam-4187	625	4	v	v	NOUN
ejpam-4187	625	5	(	(	PUNCT
ejpam-4187	625	6	g	g	NOUN
ejpam-4187	625	7	)	)	PUNCT
ejpam-4187	625	8	be	be	AUX
ejpam-4187	625	9	a	a	DET
ejpam-4187	625	10	disjunctive	disjunctive	ADJ
ejpam-4187	625	11	total	total	ADJ
ejpam-4187	625	12	dominating	dominating	NOUN
ejpam-4187	625	13	set	set	NOUN
ejpam-4187	625	14	of	of	ADP
ejpam-4187	625	15	g	g	NOUN
ejpam-4187	625	16	,	,	PUNCT
ejpam-4187	625	17	and	and	CCONJ
ejpam-4187	625	18	let	let	VERB
ejpam-4187	625	19	u	u	PRON
ejpam-4187	625	20	∈	∈	PROPN
ejpam-4187	625	21	v	v	ADP
ejpam-4187	625	22	(	(	PUNCT
ejpam-4187	625	23	h	h	NOUN
ejpam-4187	625	24	)	)	PUNCT
ejpam-4187	625	25	.	.	PUNCT
ejpam-4187	626	1	then	then	ADV
ejpam-4187	626	2	s	s	VERB
ejpam-4187	626	3	×	×	PROPN
ejpam-4187	626	4	{	{	PUNCT
ejpam-4187	626	5	u	u	NOUN
ejpam-4187	626	6	}	}	PUNCT
ejpam-4187	626	7	=	=	SYM
ejpam-4187	626	8	∪x∈s	∪x∈s	PROPN
ejpam-4187	626	9	(	(	PUNCT
ejpam-4187	626	10	{	{	PUNCT
ejpam-4187	626	11	x	x	NOUN
ejpam-4187	626	12	}	}	PUNCT
ejpam-4187	626	13	×	×	PROPN
ejpam-4187	626	14	{	{	PUNCT
ejpam-4187	626	15	u	u	NOUN
ejpam-4187	626	16	}	}	PUNCT
ejpam-4187	626	17	)	)	PUNCT
ejpam-4187	626	18	is	be	AUX
ejpam-4187	626	19	a	a	DET
ejpam-4187	626	20	disjunctive	disjunctive	ADJ
ejpam-4187	626	21	dominating	dominating	NOUN
ejpam-4187	626	22	set	set	NOUN
ejpam-4187	626	23	of	of	ADP
ejpam-4187	626	24	g[h	g[h	PROPN
ejpam-4187	626	25	]	]	PUNCT
ejpam-4187	626	26	by	by	ADP
ejpam-4187	626	27	theorem	theorem	NOUN
ejpam-4187	626	28	7	7	NUM
ejpam-4187	626	29	.	.	PUNCT
ejpam-4187	627	1	since	since	SCONJ
ejpam-4187	627	2	s	s	PART
ejpam-4187	627	3	satisfies	satisfie	NOUN
ejpam-4187	627	4	condition	condition	NOUN
ejpam-4187	627	5	(	(	PUNCT
ejpam-4187	627	6	ii	ii	NOUN
ejpam-4187	627	7	)	)	PUNCT
ejpam-4187	627	8	of	of	ADP
ejpam-4187	627	9	theorem	theorem	ADJ
ejpam-4187	627	10	8	8	NUM
ejpam-4187	627	11	,	,	PUNCT
ejpam-4187	627	12	s	s	VERB
ejpam-4187	627	13	is	be	AUX
ejpam-4187	627	14	a	a	DET
ejpam-4187	627	15	restrained	restrained	ADJ
ejpam-4187	627	16	disjunctive	disjunctive	ADJ
ejpam-4187	627	17	dominating	dominating	NOUN
ejpam-4187	627	18	set	set	NOUN
ejpam-4187	627	19	of	of	ADP
ejpam-4187	627	20	g[h	g[h	PROPN
ejpam-4187	627	21	]	]	PUNCT
ejpam-4187	627	22	.	.	PUNCT
ejpam-4187	628	1	consequently	consequently	ADV
ejpam-4187	628	2	,	,	PUNCT
ejpam-4187	628	3	γdr	γdr	PROPN
ejpam-4187	628	4	(	(	PUNCT
ejpam-4187	628	5	g[h	g[h	NOUN
ejpam-4187	628	6	]	]	PUNCT
ejpam-4187	628	7	)	)	PUNCT
ejpam-4187	628	8	≤	≤	NUM
ejpam-4187	628	9	|s|	|s|	PROPN
ejpam-4187	628	10	.	.	PUNCT
ejpam-4187	629	1	since	since	SCONJ
ejpam-4187	629	2	s	s	NOUN
ejpam-4187	629	3	is	be	AUX
ejpam-4187	629	4	arbitrary	arbitrary	ADJ
ejpam-4187	629	5	,	,	PUNCT
ejpam-4187	629	6	γdr	γdr	INTJ
ejpam-4187	629	7	(	(	PUNCT
ejpam-4187	629	8	g[h	g[h	NOUN
ejpam-4187	629	9	]	]	PUNCT
ejpam-4187	629	10	)	)	PUNCT
ejpam-4187	630	1	≤	≤	NUM
ejpam-4187	630	2	γdt	γdt	NOUN
ejpam-4187	630	3	(	(	PUNCT
ejpam-4187	630	4	g	g	NOUN
ejpam-4187	630	5	)	)	PUNCT
ejpam-4187	630	6	.	.	PUNCT
ejpam-4187	631	1	similar	similar	ADJ
ejpam-4187	631	2	arguments	argument	NOUN
ejpam-4187	631	3	as	as	ADP
ejpam-4187	631	4	above	above	ADV
ejpam-4187	631	5	,	,	PUNCT
ejpam-4187	631	6	if	if	SCONJ
ejpam-4187	631	7	s	s	VERB
ejpam-4187	631	8	⊆	⊆	NUM
ejpam-4187	631	9	v	v	NOUN
ejpam-4187	631	10	(	(	PUNCT
ejpam-4187	631	11	g	g	NOUN
ejpam-4187	631	12	)	)	PUNCT
ejpam-4187	631	13	is	be	AUX
ejpam-4187	631	14	a	a	DET
ejpam-4187	631	15	distance	distance	NOUN
ejpam-4187	631	16	-	-	PUNCT
ejpam-4187	631	17	two	two	NUM
ejpam-4187	631	18	dominating	dominating	NOUN
ejpam-4187	631	19	set	set	NOUN
ejpam-4187	631	20	of	of	ADP
ejpam-4187	631	21	g	g	NOUN
ejpam-4187	631	22	satisfying	satisfy	VERB
ejpam-4187	631	23	condition	condition	NOUN
ejpam-4187	631	24	(	(	PUNCT
ejpam-4187	631	25	ii	ii	NOUN
ejpam-4187	631	26	)	)	PUNCT
ejpam-4187	631	27	of	of	ADP
ejpam-4187	631	28	theorem	theorem	NOUN
ejpam-4187	631	29	7	7	NUM
ejpam-4187	631	30	,	,	PUNCT
ejpam-4187	631	31	then	then	ADV
ejpam-4187	631	32	2s	2s	PROPN
ejpam-4187	631	33	is	be	AUX
ejpam-4187	631	34	a	a	DET
ejpam-4187	631	35	restrained	restrained	ADJ
ejpam-4187	631	36	disjunctive	disjunctive	ADJ
ejpam-4187	631	37	dominating	dominating	NOUN
ejpam-4187	631	38	set	set	NOUN
ejpam-4187	631	39	of	of	ADP
ejpam-4187	631	40	g[h	g[h	PROPN
ejpam-4187	631	41	]	]	PUNCT
ejpam-4187	631	42	.	.	PUNCT
ejpam-4187	632	1	thus	thus	ADV
ejpam-4187	632	2	,	,	PUNCT
ejpam-4187	632	3	γdr	γdr	INTJ
ejpam-4187	632	4	(	(	PUNCT
ejpam-4187	632	5	g[h	g[h	NOUN
ejpam-4187	632	6	]	]	PUNCT
ejpam-4187	632	7	)	)	PUNCT
ejpam-4187	632	8	≤	≤	NOUN
ejpam-4187	632	9	2γ2(g	2γ2(g	NUM
ejpam-4187	632	10	)	)	PUNCT
ejpam-4187	632	11	.	.	PUNCT
ejpam-4187	633	1	therefore	therefore	ADV
ejpam-4187	633	2	,	,	PUNCT
ejpam-4187	633	3	γdr	γdr	INTJ
ejpam-4187	633	4	(	(	PUNCT
ejpam-4187	633	5	g[h	g[h	NOUN
ejpam-4187	633	6	]	]	PUNCT
ejpam-4187	633	7	)	)	PUNCT
ejpam-4187	633	8	≤	≤	NUM
ejpam-4187	633	9	min	min	NOUN
ejpam-4187	633	10	{	{	PUNCT
ejpam-4187	633	11	γdt	γdt	NOUN
ejpam-4187	633	12	(	(	PUNCT
ejpam-4187	633	13	g	g	NOUN
ejpam-4187	633	14	)	)	PUNCT
ejpam-4187	633	15	,	,	PUNCT
ejpam-4187	633	16	2γ2(g	2γ2(g	NUM
ejpam-4187	633	17	)	)	PUNCT
ejpam-4187	633	18	}	}	PUNCT
ejpam-4187	633	19	.	.	PUNCT
ejpam-4187	634	1	since	since	SCONJ
ejpam-4187	634	2	γdr	γdr	PROPN
ejpam-4187	634	3	(	(	PUNCT
ejpam-4187	634	4	c7[p8	c7[p8	X
ejpam-4187	634	5	]	]	X
ejpam-4187	634	6	)	)	PUNCT
ejpam-4187	634	7	=	=	SYM
ejpam-4187	634	8	γdt	γdt	NOUN
ejpam-4187	634	9	(	(	PUNCT
ejpam-4187	634	10	c7	c7	PROPN
ejpam-4187	634	11	)	)	PUNCT
ejpam-4187	634	12	=	=	SYM
ejpam-4187	634	13	2γ2(c7	2γ2(c7	NUM
ejpam-4187	634	14	)	)	PUNCT
ejpam-4187	634	15	=	=	SYM
ejpam-4187	634	16	4	4	NUM
ejpam-4187	634	17	,	,	PUNCT
ejpam-4187	634	18	the	the	DET
ejpam-4187	634	19	inequality	inequality	NOUN
ejpam-4187	634	20	in	in	ADP
ejpam-4187	634	21	corollary	corollary	ADJ
ejpam-4187	634	22	7	7	NUM
ejpam-4187	634	23	is	be	AUX
ejpam-4187	634	24	sharp	sharp	ADJ
ejpam-4187	634	25	.	.	PUNCT
ejpam-4187	635	1	5	5	X
ejpam-4187	635	2	.	.	X
ejpam-4187	635	3	conclusion	conclusion	NOUN
ejpam-4187	635	4	let	let	VERB
ejpam-4187	635	5	g	g	NOUN
ejpam-4187	635	6	andh	andh	NOUN
ejpam-4187	635	7	be	be	AUX
ejpam-4187	635	8	nontrivial	nontrivial	ADJ
ejpam-4187	635	9	connected	connected	ADJ
ejpam-4187	635	10	graphs	graph	NOUN
ejpam-4187	635	11	.	.	PUNCT
ejpam-4187	636	1	it	it	PRON
ejpam-4187	636	2	is	be	AUX
ejpam-4187	636	3	shown	show	VERB
ejpam-4187	636	4	that	that	SCONJ
ejpam-4187	636	5	the	the	DET
ejpam-4187	636	6	restrained	restrain	VERB
ejpam-4187	636	7	disjunctive	disjunctive	ADJ
ejpam-4187	636	8	domination	domination	NOUN
ejpam-4187	636	9	number	number	NOUN
ejpam-4187	636	10	in	in	ADP
ejpam-4187	636	11	the	the	DET
ejpam-4187	636	12	join	join	NOUN
ejpam-4187	636	13	of	of	ADP
ejpam-4187	636	14	two	two	NUM
ejpam-4187	636	15	graphs	graph	NOUN
ejpam-4187	636	16	(	(	PUNCT
ejpam-4187	636	17	g+h	g+h	NOUN
ejpam-4187	636	18	)	)	PUNCT
ejpam-4187	636	19	is	be	AUX
ejpam-4187	636	20	the	the	DET
ejpam-4187	636	21	min{γ(g	min{γ(g	PROPN
ejpam-4187	636	22	)	)	PUNCT
ejpam-4187	636	23	,	,	PUNCT
ejpam-4187	636	24	γ(h	γ(h	NOUN
ejpam-4187	636	25	)	)	PUNCT
ejpam-4187	636	26	,	,	PUNCT
ejpam-4187	636	27	2	2	X
ejpam-4187	636	28	}	}	PUNCT
ejpam-4187	636	29	and	and	CCONJ
ejpam-4187	636	30	the	the	DET
ejpam-4187	636	31	restrained	restrain	VERB
ejpam-4187	636	32	disjunctive	disjunctive	ADJ
ejpam-4187	636	33	domination	domination	NOUN
ejpam-4187	636	34	number	number	NOUN
ejpam-4187	636	35	in	in	ADP
ejpam-4187	636	36	the	the	DET
ejpam-4187	636	37	corona	corona	NOUN
ejpam-4187	636	38	of	of	ADP
ejpam-4187	636	39	two	two	NUM
ejpam-4187	636	40	graphs	graph	NOUN
ejpam-4187	636	41	(	(	PUNCT
ejpam-4187	636	42	g	g	PROPN
ejpam-4187	636	43	◦	◦	NOUN
ejpam-4187	636	44	h	h	NOUN
ejpam-4187	636	45	)	)	PUNCT
ejpam-4187	636	46	is	be	AUX
ejpam-4187	636	47	the	the	DET
ejpam-4187	636	48	(	(	PUNCT
ejpam-4187	636	49	γ×2(g	γ×2(g	PROPN
ejpam-4187	636	50	)	)	PUNCT
ejpam-4187	636	51	)	)	PUNCT
ejpam-4187	636	52	.	.	PUNCT
ejpam-4187	637	1	under	under	ADP
ejpam-4187	637	2	the	the	DET
ejpam-4187	637	3	same	same	ADJ
ejpam-4187	637	4	condition	condition	NOUN
ejpam-4187	637	5	,	,	PUNCT
ejpam-4187	637	6	the	the	DET
ejpam-4187	637	7	minimum	minimum	NOUN
ejpam-4187	637	8	of	of	ADP
ejpam-4187	637	9	the	the	DET
ejpam-4187	637	10	sets	set	NOUN
ejpam-4187	637	11	between	between	ADP
ejpam-4187	637	12	disjuntive	disjuntive	ADJ
ejpam-4187	637	13	total	total	ADJ
ejpam-4187	637	14	domination	domination	NOUN
ejpam-4187	637	15	number	number	NOUN
ejpam-4187	637	16	of	of	ADP
ejpam-4187	637	17	graph	graph	NOUN
ejpam-4187	637	18	g	g	PROPN
ejpam-4187	637	19	and	and	CCONJ
ejpam-4187	637	20	twice	twice	ADV
ejpam-4187	637	21	of	of	ADP
ejpam-4187	637	22	distance-2	distance-2	NUM
ejpam-4187	637	23	domination	domination	NOUN
ejpam-4187	637	24	number	number	NOUN
ejpam-4187	637	25	of	of	ADP
ejpam-4187	637	26	graph	graph	NOUN
ejpam-4187	637	27	g	g	NOUN
ejpam-4187	637	28	,	,	PUNCT
ejpam-4187	637	29	denoted	denote	VERB
ejpam-4187	637	30	by	by	ADP
ejpam-4187	637	31	min{γdt	min{γdt	NOUN
ejpam-4187	637	32	(	(	PUNCT
ejpam-4187	637	33	g	g	NOUN
ejpam-4187	637	34	)	)	PUNCT
ejpam-4187	637	35	,	,	PUNCT
ejpam-4187	637	36	2γ2(g	2γ2(g	NUM
ejpam-4187	637	37	)	)	PUNCT
ejpam-4187	637	38	}	}	PUNCT
ejpam-4187	637	39	proves	prove	VERB
ejpam-4187	637	40	to	to	PART
ejpam-4187	637	41	be	be	AUX
ejpam-4187	637	42	a	a	DET
ejpam-4187	637	43	sharp	sharp	ADJ
ejpam-4187	637	44	bound	bind	VERB
ejpam-4187	637	45	for	for	ADP
ejpam-4187	637	46	the	the	DET
ejpam-4187	637	47	restrained	restrain	VERB
ejpam-4187	637	48	disjunctive	disjunctive	ADJ
ejpam-4187	637	49	domination	domination	NOUN
ejpam-4187	637	50	number	number	NOUN
ejpam-4187	637	51	of	of	ADP
ejpam-4187	637	52	the	the	DET
ejpam-4187	637	53	lexicographic	lexicographic	ADJ
ejpam-4187	637	54	product	product	NOUN
ejpam-4187	637	55	of	of	ADP
ejpam-4187	637	56	graphs	graph	NOUN
ejpam-4187	637	57	g	g	PROPN
ejpam-4187	637	58	and	and	CCONJ
ejpam-4187	637	59	h.	h.	PROPN
ejpam-4187	637	60	references	reference	NOUN
ejpam-4187	637	61	222	222	NUM
ejpam-4187	637	62	acknowledgements	acknowledgement	NOUN
ejpam-4187	637	63	this	this	DET
ejpam-4187	637	64	research	research	NOUN
ejpam-4187	637	65	was	be	AUX
ejpam-4187	637	66	undertaken	undertake	VERB
ejpam-4187	637	67	at	at	ADP
ejpam-4187	637	68	the	the	DET
ejpam-4187	637	69	technische	technische	PROPN
ejpam-4187	637	70	universitat	universitat	PROPN
ejpam-4187	637	71	kaiserslautern	kaiserslautern	PROPN
ejpam-4187	637	72	,	,	PUNCT
ejpam-4187	637	73	germany	germany	PROPN
ejpam-4187	637	74	,	,	PUNCT
ejpam-4187	637	75	under	under	ADP
ejpam-4187	637	76	the	the	DET
ejpam-4187	637	77	faculty	faculty	NOUN
ejpam-4187	637	78	and	and	CCONJ
ejpam-4187	637	79	student	student	NOUN
ejpam-4187	637	80	exchange	exchange	NOUN
ejpam-4187	637	81	program	program	NOUN
ejpam-4187	637	82	of	of	ADP
ejpam-4187	637	83	the	the	DET
ejpam-4187	637	84	project	project	NOUN
ejpam-4187	637	85	”	"	PUNCT
ejpam-4187	637	86	graph	graph	NOUN
ejpam-4187	637	87	theory	theory	NOUN
ejpam-4187	637	88	and	and	CCONJ
ejpam-4187	637	89	optimization	optimization	NOUN
ejpam-4187	637	90	(	(	PUNCT
ejpam-4187	637	91	gratho	gratho	NOUN
ejpam-4187	637	92	)	)	PUNCT
ejpam-4187	637	93	with	with	ADP
ejpam-4187	637	94	applications	application	NOUN
ejpam-4187	637	95	in	in	ADP
ejpam-4187	637	96	industry	industry	NOUN
ejpam-4187	637	97	and	and	CCONJ
ejpam-4187	637	98	society	society	NOUN
ejpam-4187	637	99	”	"	PUNCT
ejpam-4187	637	100	and	and	CCONJ
ejpam-4187	637	101	funded	fund	VERB
ejpam-4187	637	102	by	by	ADP
ejpam-4187	637	103	the	the	DET
ejpam-4187	637	104	zamboanga	zamboanga	PROPN
ejpam-4187	637	105	peninsula	peninsula	PROPN
ejpam-4187	637	106	polytechnic	polytechnic	PROPN
ejpam-4187	637	107	state	state	PROPN
ejpam-4187	637	108	university	university	PROPN
ejpam-4187	637	109	,	,	PUNCT
ejpam-4187	637	110	philippines	philippine	NOUN
ejpam-4187	637	111	.	.	PUNCT
ejpam-4187	638	1	also	also	ADV
ejpam-4187	638	2	,	,	PUNCT
ejpam-4187	638	3	the	the	DET
ejpam-4187	638	4	authors	author	NOUN
ejpam-4187	638	5	would	would	AUX
ejpam-4187	638	6	like	like	VERB
ejpam-4187	638	7	to	to	PART
ejpam-4187	638	8	recognize	recognize	VERB
ejpam-4187	638	9	the	the	DET
ejpam-4187	638	10	efforts	effort	NOUN
ejpam-4187	638	11	of	of	ADP
ejpam-4187	638	12	the	the	DET
ejpam-4187	638	13	anonymous	anonymous	ADJ
ejpam-4187	638	14	reviewers	reviewer	NOUN
ejpam-4187	638	15	whose	whose	DET
ejpam-4187	638	16	suggestions	suggestion	NOUN
ejpam-4187	638	17	and	and	CCONJ
ejpam-4187	638	18	recommendations	recommendation	NOUN
ejpam-4187	638	19	contributed	contribute	VERB
ejpam-4187	638	20	to	to	ADP
ejpam-4187	638	21	the	the	DET
ejpam-4187	638	22	big	big	ADJ
ejpam-4187	638	23	improvement	improvement	NOUN
ejpam-4187	638	24	of	of	ADP
ejpam-4187	638	25	the	the	DET
ejpam-4187	638	26	paper	paper	NOUN
ejpam-4187	638	27	.	.	PUNCT
ejpam-4187	639	1	references	reference	NOUN
ejpam-4187	639	2	[	[	X
ejpam-4187	639	3	1	1	NUM
ejpam-4187	639	4	]	]	PUNCT
ejpam-4187	639	5	c.	c.	PROPN
ejpam-4187	639	6	berge	berge	PROPN
ejpam-4187	639	7	.	.	PUNCT
ejpam-4187	640	1	theorie	theorie	PROPN
ejpam-4187	640	2	des	des	PROPN
ejpam-4187	640	3	graphes	graphes	PROPN
ejpam-4187	640	4	et	et	PROPN
ejpam-4187	640	5	ses	ses	PROPN
ejpam-4187	640	6	applications	application	NOUN
ejpam-4187	640	7	.	.	PUNCT
ejpam-4187	641	1	dunod	dunod	PROPN
ejpam-4187	641	2	,	,	PUNCT
ejpam-4187	641	3	paris	paris	PROPN
ejpam-4187	641	4	,	,	PUNCT
ejpam-4187	641	5	1958	1958	NUM
ejpam-4187	641	6	.	.	PUNCT
ejpam-4187	642	1	[	[	X
ejpam-4187	642	2	2	2	NUM
ejpam-4187	642	3	]	]	X
ejpam-4187	642	4	f.	f.	PROPN
ejpam-4187	642	5	buckley	buckley	PROPN
ejpam-4187	642	6	and	and	CCONJ
ejpam-4187	642	7	f.	f.	PROPN
ejpam-4187	642	8	haray	haray	PROPN
ejpam-4187	642	9	.	.	PUNCT
ejpam-4187	643	1	distance	distance	NOUN
ejpam-4187	643	2	in	in	ADP
ejpam-4187	643	3	graphs	graph	NOUN
ejpam-4187	643	4	.	.	PUNCT
ejpam-4187	644	1	addison	addison	PROPN
ejpam-4187	644	2	-	-	PUNCT
ejpam-4187	644	3	wesley	wesley	PROPN
ejpam-4187	644	4	publishing	publishing	PROPN
ejpam-4187	644	5	company	company	NOUN
ejpam-4187	644	6	,	,	PUNCT
ejpam-4187	644	7	redwood	redwood	NOUN
ejpam-4187	644	8	city	city	NOUN
ejpam-4187	644	9	,	,	PUNCT
ejpam-4187	644	10	1990	1990	NUM
ejpam-4187	644	11	.	.	PUNCT
ejpam-4187	645	1	[	[	X
ejpam-4187	645	2	3	3	X
ejpam-4187	645	3	]	]	X
ejpam-4187	645	4	m.	m.	NOUN
ejpam-4187	645	5	chellali	chellali	PROPN
ejpam-4187	645	6	.	.	PUNCT
ejpam-4187	646	1	bounds	bound	VERB
ejpam-4187	646	2	on	on	ADP
ejpam-4187	646	3	the	the	DET
ejpam-4187	646	4	2	2	NUM
ejpam-4187	646	5	-	-	PUNCT
ejpam-4187	646	6	domination	domination	NOUN
ejpam-4187	646	7	number	number	NOUN
ejpam-4187	646	8	in	in	ADP
ejpam-4187	646	9	cactus	cactus	NOUN
ejpam-4187	646	10	graphs	graph	NOUN
ejpam-4187	646	11	.	.	PUNCT
ejpam-4187	647	1	opuscula	opuscula	PROPN
ejpam-4187	647	2	mathematica	mathematica	PROPN
ejpam-4187	647	3	,	,	PUNCT
ejpam-4187	647	4	26:5–12	26:5–12	NUM
ejpam-4187	647	5	,	,	PUNCT
ejpam-4187	647	6	2006	2006	NUM
ejpam-4187	647	7	.	.	PUNCT
ejpam-4187	648	1	[	[	X
ejpam-4187	648	2	4	4	X
ejpam-4187	648	3	]	]	X
ejpam-4187	648	4	e.	e.	PROPN
ejpam-4187	648	5	cockayne	cockayne	PROPN
ejpam-4187	648	6	and	and	CCONJ
ejpam-4187	648	7	s.	s.	PROPN
ejpam-4187	648	8	hedetniemi	hedetniemi	PROPN
ejpam-4187	648	9	.	.	PUNCT
ejpam-4187	649	1	towards	towards	ADP
ejpam-4187	649	2	a	a	DET
ejpam-4187	649	3	theory	theory	NOUN
ejpam-4187	649	4	of	of	ADP
ejpam-4187	649	5	domination	domination	NOUN
ejpam-4187	649	6	in	in	ADP
ejpam-4187	649	7	graphs	graph	NOUN
ejpam-4187	649	8	.	.	PUNCT
ejpam-4187	650	1	networks	network	NOUN
ejpam-4187	650	2	,	,	PUNCT
ejpam-4187	650	3	7(3):247–261	7(3):247–261	NUM
ejpam-4187	650	4	,	,	PUNCT
ejpam-4187	650	5	1977	1977	NUM
ejpam-4187	650	6	.	.	PUNCT
ejpam-4187	651	1	[	[	X
ejpam-4187	651	2	5	5	NUM
ejpam-4187	651	3	]	]	X
ejpam-4187	651	4	dankelmann	dankelmann	PROPN
ejpam-4187	651	5	,	,	PUNCT
ejpam-4187	651	6	d.	d.	PROPN
ejpam-4187	651	7	day	day	PROPN
ejpam-4187	651	8	,	,	PUNCT
ejpam-4187	651	9	d.	d.	PROPN
ejpam-4187	651	10	erwin	erwin	PROPN
ejpam-4187	651	11	,	,	PUNCT
ejpam-4187	651	12	s.	s.	PROPN
ejpam-4187	651	13	mukwembi	mukwembi	PROPN
ejpam-4187	651	14	,	,	PUNCT
ejpam-4187	651	15	and	and	CCONJ
ejpam-4187	651	16	h.	h.	PROPN
ejpam-4187	651	17	swart	swart	PROPN
ejpam-4187	651	18	.	.	PUNCT
ejpam-4187	651	19	domination	domination	NOUN
ejpam-4187	651	20	with	with	ADP
ejpam-4187	651	21	exponential	exponential	ADJ
ejpam-4187	651	22	decay	decay	NOUN
ejpam-4187	651	23	.	.	PUNCT
ejpam-4187	652	1	discrete	discrete	ADJ
ejpam-4187	652	2	mathematics	mathematic	NOUN
ejpam-4187	652	3	,	,	PUNCT
ejpam-4187	652	4	309:5877	309:5877	NUM
ejpam-4187	652	5	–	–	PUNCT
ejpam-4187	652	6	5883	5883	NUM
ejpam-4187	652	7	,	,	PUNCT
ejpam-4187	652	8	2009	2009	NUM
ejpam-4187	652	9	.	.	PUNCT
ejpam-4187	653	1	[	[	X
ejpam-4187	653	2	6	6	NUM
ejpam-4187	653	3	]	]	X
ejpam-4187	653	4	g.s	g.s	PROPN
ejpam-4187	653	5	.	.	PROPN
ejpam-4187	653	6	domke	domke	PROPN
ejpam-4187	653	7	,	,	PUNCT
ejpam-4187	653	8	j.h	j.h	PROPN
ejpam-4187	653	9	.	.	PROPN
ejpam-4187	653	10	hatting	hatting	PROPN
ejpam-4187	653	11	,	,	PUNCT
ejpam-4187	653	12	s.t	s.t	PROPN
ejpam-4187	653	13	.	.	PROPN
ejpam-4187	653	14	hedetniemi	hedetniemi	PROPN
ejpam-4187	653	15	,	,	PUNCT
ejpam-4187	653	16	r.c	r.c	PROPN
ejpam-4187	653	17	.	.	PROPN
ejpam-4187	653	18	laskar	laskar	PROPN
ejpam-4187	653	19	,	,	PUNCT
ejpam-4187	653	20	and	and	CCONJ
ejpam-4187	653	21	l.r	l.r	PROPN
ejpam-4187	653	22	.	.	PROPN
ejpam-4187	653	23	markus	markus	PROPN
ejpam-4187	653	24	.	.	PUNCT
ejpam-4187	654	1	restrained	restrained	ADJ
ejpam-4187	654	2	domination	domination	NOUN
ejpam-4187	654	3	in	in	ADP
ejpam-4187	654	4	graphs	graph	NOUN
ejpam-4187	654	5	.	.	PUNCT
ejpam-4187	655	1	discrete	discrete	ADJ
ejpam-4187	655	2	mathematics	mathematic	NOUN
ejpam-4187	655	3	,	,	PUNCT
ejpam-4187	655	4	203:61–69	203:61–69	NUM
ejpam-4187	655	5	,	,	PUNCT
ejpam-4187	655	6	1999	1999	NUM
ejpam-4187	655	7	.	.	PUNCT
ejpam-4187	656	1	[	[	X
ejpam-4187	656	2	7	7	X
ejpam-4187	656	3	]	]	X
ejpam-4187	656	4	b.d	b.d	PROPN
ejpam-4187	656	5	.	.	PROPN
ejpam-4187	656	6	domolan	domolan	PROPN
ejpam-4187	656	7	and	and	CCONJ
ejpam-4187	656	8	s.r	s.r	PROPN
ejpam-4187	656	9	.	.	PROPN
ejpam-4187	656	10	canoy	canoy	PROPN
ejpam-4187	656	11	jr	jr	PROPN
ejpam-4187	656	12	.	.	PROPN
ejpam-4187	656	13	2	2	NUM
ejpam-4187	656	14	-	-	PUNCT
ejpam-4187	656	15	domination	domination	NOUN
ejpam-4187	656	16	and	and	CCONJ
ejpam-4187	656	17	restrained	restrain	VERB
ejpam-4187	656	18	2	2	NUM
ejpam-4187	656	19	-	-	PUNCT
ejpam-4187	656	20	domination	domination	NOUN
ejpam-4187	656	21	in	in	ADP
ejpam-4187	656	22	graphs	graph	NOUN
ejpam-4187	656	23	.	.	PUNCT
ejpam-4187	657	1	applied	apply	VERB
ejpam-4187	657	2	mathematical	mathematical	ADJ
ejpam-4187	657	3	sciences	science	NOUN
ejpam-4187	657	4	,	,	PUNCT
ejpam-4187	657	5	9:5651–5659	9:5651–5659	NUM
ejpam-4187	657	6	,	,	PUNCT
ejpam-4187	657	7	2015	2015	NUM
ejpam-4187	657	8	.	.	PUNCT
ejpam-4187	658	1	[	[	X
ejpam-4187	658	2	8	8	NUM
ejpam-4187	658	3	]	]	X
ejpam-4187	658	4	w.	w.	PROPN
ejpam-4187	658	5	goddard	goddard	PROPN
ejpam-4187	658	6	,	,	PUNCT
ejpam-4187	658	7	m.a	m.a	PROPN
ejpam-4187	658	8	.	.	PROPN
ejpam-4187	658	9	henning	henning	PROPN
ejpam-4187	658	10	,	,	PUNCT
ejpam-4187	658	11	and	and	CCONJ
ejpam-4187	658	12	c.a	c.a	PROPN
ejpam-4187	658	13	.	.	PROPN
ejpam-4187	658	14	mcpillan	mcpillan	PROPN
ejpam-4187	658	15	.	.	PUNCT
ejpam-4187	659	1	the	the	DET
ejpam-4187	659	2	disjunctive	disjunctive	ADJ
ejpam-4187	659	3	domination	domination	NOUN
ejpam-4187	659	4	number	number	NOUN
ejpam-4187	659	5	of	of	ADP
ejpam-4187	659	6	a	a	DET
ejpam-4187	659	7	graph	graph	NOUN
ejpam-4187	659	8	.	.	PUNCT
ejpam-4187	660	1	quaestiones	quaestione	NOUN
ejpam-4187	660	2	mathematicae	mathematicae	PROPN
ejpam-4187	660	3	,	,	PUNCT
ejpam-4187	660	4	37:547–561	37:547–561	PROPN
ejpam-4187	660	5	,	,	PUNCT
ejpam-4187	660	6	2014	2014	NUM
ejpam-4187	660	7	.	.	PUNCT
ejpam-4187	661	1	[	[	X
ejpam-4187	661	2	9	9	NUM
ejpam-4187	661	3	]	]	PUNCT
ejpam-4187	661	4	a.	a.	NOUN
ejpam-4187	661	5	hansberg	hansberg	PROPN
ejpam-4187	661	6	and	and	CCONJ
ejpam-4187	661	7	l.	l.	PROPN
ejpam-4187	661	8	volkmann	volkmann	PROPN
ejpam-4187	661	9	.	.	PUNCT
ejpam-4187	662	1	note	note	VERB
ejpam-4187	662	2	on	on	ADP
ejpam-4187	662	3	graphs	graph	NOUN
ejpam-4187	662	4	with	with	ADP
ejpam-4187	662	5	equal	equal	ADJ
ejpam-4187	662	6	domination	domination	NOUN
ejpam-4187	662	7	and	and	CCONJ
ejpam-4187	662	8	2domination	2domination	NUM
ejpam-4187	662	9	numbers	number	NOUN
ejpam-4187	662	10	.	.	PUNCT
ejpam-4187	663	1	discrete	discrete	ADJ
ejpam-4187	663	2	mathematics	mathematic	NOUN
ejpam-4187	663	3	,	,	PUNCT
ejpam-4187	663	4	308:2277–2281	308:2277–2281	NUM
ejpam-4187	663	5	,	,	PUNCT
ejpam-4187	663	6	2008	2008	NUM
ejpam-4187	663	7	.	.	PUNCT
ejpam-4187	664	1	[	[	X
ejpam-4187	664	2	10	10	NUM
ejpam-4187	664	3	]	]	X
ejpam-4187	664	4	t.w	t.w	PROPN
ejpam-4187	664	5	.	.	PROPN
ejpam-4187	664	6	haynes	haynes	PROPN
ejpam-4187	664	7	,	,	PUNCT
ejpam-4187	664	8	s.t	s.t	PROPN
ejpam-4187	664	9	.	.	PROPN
ejpam-4187	664	10	hedetniemi	hedetniemi	PROPN
ejpam-4187	664	11	,	,	PUNCT
ejpam-4187	664	12	and	and	CCONJ
ejpam-4187	664	13	p.j	p.j	PROPN
ejpam-4187	664	14	.	.	PROPN
ejpam-4187	664	15	slater	slater	PROPN
ejpam-4187	664	16	.	.	PUNCT
ejpam-4187	665	1	fundamentals	fundamental	NOUN
ejpam-4187	665	2	of	of	ADP
ejpam-4187	665	3	domination	domination	NOUN
ejpam-4187	665	4	in	in	ADP
ejpam-4187	665	5	graphs	graph	NOUN
ejpam-4187	665	6	.	.	PUNCT
ejpam-4187	666	1	marcel	marcel	PROPN
ejpam-4187	666	2	dekker	dekker	PROPN
ejpam-4187	666	3	,	,	PUNCT
ejpam-4187	666	4	inc	inc	PROPN
ejpam-4187	666	5	.	.	PROPN
ejpam-4187	666	6	,	,	PUNCT
ejpam-4187	666	7	new	new	PROPN
ejpam-4187	666	8	york	york	PROPN
ejpam-4187	666	9	,	,	PUNCT
ejpam-4187	666	10	1998	1998	NUM
ejpam-4187	666	11	.	.	PUNCT
ejpam-4187	667	1	[	[	X
ejpam-4187	667	2	11	11	NUM
ejpam-4187	667	3	]	]	X
ejpam-4187	667	4	s.m	s.m	PROPN
ejpam-4187	667	5	.	.	PROPN
ejpam-4187	667	6	hedetniemi	hedetniemi	PROPN
ejpam-4187	667	7	,	,	PUNCT
ejpam-4187	667	8	s.t	s.t	PROPN
ejpam-4187	667	9	.	.	PROPN
ejpam-4187	667	10	hedetniemi	hedetniemi	PROPN
ejpam-4187	667	11	,	,	PUNCT
ejpam-4187	668	1	j.	j.	PROPN
ejpam-4187	668	2	knisely	knisely	ADV
ejpam-4187	668	3	,	,	PUNCT
ejpam-4187	668	4	and	and	CCONJ
ejpam-4187	668	5	d.f	d.f	PROPN
ejpam-4187	668	6	.	.	PROPN
ejpam-4187	668	7	rall	rall	PROPN
ejpam-4187	668	8	.	.	PUNCT
ejpam-4187	668	9	secondary	secondary	ADJ
ejpam-4187	668	10	domination	domination	NOUN
ejpam-4187	668	11	in	in	ADP
ejpam-4187	668	12	graphs	graph	NOUN
ejpam-4187	668	13	.	.	PUNCT
ejpam-4187	669	1	akce	akce	PROPN
ejpam-4187	669	2	int	int	PROPN
ejpam-4187	669	3	.	.	PUNCT
ejpam-4187	670	1	j.	j.	PROPN
ejpam-4187	670	2	graphs	graphs	PROPN
ejpam-4187	670	3	comb	comb	PROPN
ejpam-4187	670	4	.	.	PUNCT
ejpam-4187	670	5	,	,	PUNCT
ejpam-4187	670	6	5:103	5:103	NUM
ejpam-4187	670	7	–	–	PUNCT
ejpam-4187	670	8	115	115	NUM
ejpam-4187	670	9	,	,	PUNCT
ejpam-4187	670	10	2008	2008	NUM
ejpam-4187	670	11	.	.	PUNCT
ejpam-4187	671	1	[	[	X
ejpam-4187	671	2	12	12	NUM
ejpam-4187	671	3	]	]	X
ejpam-4187	671	4	m.a	m.a	PROPN
ejpam-4187	671	5	.	.	PROPN
ejpam-4187	671	6	henning	henning	PROPN
ejpam-4187	671	7	and	and	CCONJ
ejpam-4187	671	8	v.	v.	ADP
ejpam-4187	671	9	naicker	naicker	NOUN
ejpam-4187	671	10	.	.	PUNCT
ejpam-4187	672	1	graphs	graph	NOUN
ejpam-4187	672	2	with	with	ADP
ejpam-4187	672	3	large	large	ADJ
ejpam-4187	672	4	disjunctive	disjunctive	ADJ
ejpam-4187	672	5	total	total	ADJ
ejpam-4187	672	6	domination	domination	NOUN
ejpam-4187	672	7	number	number	NOUN
ejpam-4187	672	8	.	.	PUNCT
ejpam-4187	673	1	discrete	discrete	ADJ
ejpam-4187	673	2	mathematics	mathematic	NOUN
ejpam-4187	673	3	,	,	PUNCT
ejpam-4187	673	4	17:255–282	17:255–282	NUM
ejpam-4187	673	5	,	,	PUNCT
ejpam-4187	673	6	2015	2015	NUM
ejpam-4187	673	7	.	.	PUNCT
ejpam-4187	674	1	[	[	X
ejpam-4187	674	2	13	13	NUM
ejpam-4187	674	3	]	]	X
ejpam-4187	674	4	m.a	m.a	PROPN
ejpam-4187	674	5	.	.	PROPN
ejpam-4187	674	6	henning	henning	PROPN
ejpam-4187	674	7	and	and	CCONJ
ejpam-4187	674	8	v.	v.	ADP
ejpam-4187	674	9	naicker	naicker	PROPN
ejpam-4187	674	10	.	.	PUNCT
ejpam-4187	675	1	bounds	bound	NOUN
ejpam-4187	675	2	on	on	ADP
ejpam-4187	675	3	the	the	DET
ejpam-4187	675	4	disjunctive	disjunctive	ADJ
ejpam-4187	675	5	total	total	ADJ
ejpam-4187	675	6	domination	domination	NOUN
ejpam-4187	675	7	number	number	NOUN
ejpam-4187	675	8	of	of	ADP
ejpam-4187	675	9	a	a	DET
ejpam-4187	675	10	tree	tree	NOUN
ejpam-4187	675	11	.	.	PUNCT
ejpam-4187	676	1	discussiones	discussione	NOUN
ejpam-4187	676	2	mathematicae	mathematicae	PROPN
ejpam-4187	676	3	,	,	PUNCT
ejpam-4187	676	4	36:153	36:153	NUM
ejpam-4187	676	5	–	–	PUNCT
ejpam-4187	676	6	171	171	NUM
ejpam-4187	676	7	,	,	PUNCT
ejpam-4187	676	8	2016	2016	NUM
ejpam-4187	676	9	.	.	PUNCT
ejpam-4187	677	1	references	reference	NOUN
ejpam-4187	677	2	223	223	NUM
ejpam-4187	678	1	[	[	X
ejpam-4187	678	2	14	14	NUM
ejpam-4187	678	3	]	]	X
ejpam-4187	678	4	m.a	m.a	PROPN
ejpam-4187	678	5	.	.	PROPN
ejpam-4187	678	6	henning	henning	PROPN
ejpam-4187	678	7	and	and	CCONJ
ejpam-4187	678	8	v.	v.	ADP
ejpam-4187	678	9	naicker	naicker	PROPN
ejpam-4187	678	10	.	.	PUNCT
ejpam-4187	679	1	disjunctive	disjunctive	ADJ
ejpam-4187	679	2	total	total	ADJ
ejpam-4187	679	3	domination	domination	NOUN
ejpam-4187	679	4	in	in	ADP
ejpam-4187	679	5	graphs	graph	NOUN
ejpam-4187	679	6	.	.	PUNCT
ejpam-4187	680	1	comb	comb	NOUN
ejpam-4187	680	2	.	.	PUNCT
ejpam-4187	681	1	opti	opti	PROPN
ejpam-4187	681	2	.	.	PROPN
ejpam-4187	681	3	,	,	PUNCT
ejpam-4187	681	4	31:1090–1110	31:1090–1110	PROPN
ejpam-4187	681	5	,	,	PUNCT
ejpam-4187	681	6	2016	2016	NUM
ejpam-4187	681	7	.	.	PUNCT
ejpam-4187	682	1	[	[	X
ejpam-4187	682	2	15	15	NUM
ejpam-4187	682	3	]	]	X
ejpam-4187	682	4	f.	f.	PROPN
ejpam-4187	682	5	jamil	jamil	PROPN
ejpam-4187	682	6	and	and	CCONJ
ejpam-4187	682	7	r.	r.	PROPN
ejpam-4187	682	8	malalay	malalay	PROPN
ejpam-4187	682	9	.	.	PUNCT
ejpam-4187	683	1	on	on	ADP
ejpam-4187	683	2	disjuntive	disjuntive	ADJ
ejpam-4187	683	3	domination	domination	NOUN
ejpam-4187	683	4	in	in	ADP
ejpam-4187	683	5	graphs	graph	NOUN
ejpam-4187	683	6	.	.	PUNCT
ejpam-4187	684	1	quaestiones	quaestione	NOUN
ejpam-4187	684	2	mathematicae	mathematicae	PROPN
ejpam-4187	684	3	,	,	PUNCT
ejpam-4187	684	4	43:149	43:149	NUM
ejpam-4187	684	5	–	–	PUNCT
ejpam-4187	684	6	168	168	NUM
ejpam-4187	684	7	,	,	PUNCT
ejpam-4187	684	8	2019	2019	NUM
ejpam-4187	684	9	.	.	PUNCT
ejpam-4187	685	1	[	[	X
ejpam-4187	685	2	16	16	NUM
ejpam-4187	685	3	]	]	X
ejpam-4187	685	4	g.	g.	PROPN
ejpam-4187	685	5	kokilambal	kokilambal	PROPN
ejpam-4187	685	6	and	and	CCONJ
ejpam-4187	685	7	k	k	PROPN
ejpam-4187	685	8	kayathri	kayathri	PROPN
ejpam-4187	685	9	.	.	PUNCT
ejpam-4187	686	1	restrained	restrained	ADJ
ejpam-4187	686	2	domination	domination	NOUN
ejpam-4187	686	3	in	in	ADP
ejpam-4187	686	4	trees	tree	NOUN
ejpam-4187	686	5	.	.	PUNCT
ejpam-4187	687	1	international	international	ADJ
ejpam-4187	687	2	journal	journal	NOUN
ejpam-4187	687	3	of	of	ADP
ejpam-4187	687	4	applied	apply	VERB
ejpam-4187	687	5	engineering	engineering	NOUN
ejpam-4187	687	6	research	research	NOUN
ejpam-4187	687	7	,	,	PUNCT
ejpam-4187	687	8	14:0973–4562	14:0973–4562	NUM
ejpam-4187	687	9	,	,	PUNCT
ejpam-4187	687	10	2020	2020	NUM
ejpam-4187	687	11	.	.	PUNCT
ejpam-4187	688	1	[	[	X
ejpam-4187	688	2	17	17	NUM
ejpam-4187	688	3	]	]	X
ejpam-4187	688	4	g.b	g.b	PROPN
ejpam-4187	688	5	.	.	PUNCT
ejpam-4187	688	6	monsanto	monsanto	PROPN
ejpam-4187	688	7	and	and	CCONJ
ejpam-4187	688	8	h.m	h.m	PROPN
ejpam-4187	688	9	.	.	PROPN
ejpam-4187	688	10	rara	rara	PROPN
ejpam-4187	688	11	.	.	PUNCT
ejpam-4187	689	1	resolving	resolve	VERB
ejpam-4187	689	2	restrained	restrained	ADJ
ejpam-4187	689	3	domination	domination	NOUN
ejpam-4187	689	4	in	in	ADP
ejpam-4187	689	5	graphs	graph	NOUN
ejpam-4187	689	6	.	.	PUNCT
ejpam-4187	690	1	european	european	ADJ
ejpam-4187	690	2	journal	journal	PROPN
ejpam-4187	690	3	of	of	ADP
ejpam-4187	690	4	pure	pure	ADJ
ejpam-4187	690	5	and	and	CCONJ
ejpam-4187	690	6	applied	applied	ADJ
ejpam-4187	690	7	mathematics	mathematic	NOUN
ejpam-4187	690	8	,	,	PUNCT
ejpam-4187	690	9	14:829–841	14:829–841	NUM
ejpam-4187	690	10	,	,	PUNCT
ejpam-4187	690	11	2021	2021	NUM
ejpam-4187	690	12	.	.	PUNCT
ejpam-4187	691	1	[	[	X
ejpam-4187	691	2	18	18	NUM
ejpam-4187	691	3	]	]	X
ejpam-4187	691	4	o.	o.	PROPN
ejpam-4187	691	5	ore	ore	PROPN
ejpam-4187	691	6	.	.	PUNCT
ejpam-4187	692	1	theory	theory	NOUN
ejpam-4187	692	2	of	of	ADP
ejpam-4187	692	3	graphs	graph	NOUN
ejpam-4187	692	4	.	.	PUNCT
ejpam-4187	693	1	amer	amer	PROPN
ejpam-4187	693	2	.	.	PUNCT
ejpam-4187	693	3	math	math	PROPN
ejpam-4187	693	4	.	.	PUNCT
ejpam-4187	694	1	soc	soc	PROPN
ejpam-4187	694	2	.	.	PUNCT
ejpam-4187	695	1	colloq	colloq	PROPN
ejpam-4187	695	2	.	.	PUNCT
ejpam-4187	696	1	publ	publ	PROPN
ejpam-4187	696	2	.	.	PUNCT
ejpam-4187	696	3	,	,	PUNCT
ejpam-4187	696	4	chicago	chicago	PROPN
ejpam-4187	696	5	,	,	PUNCT
ejpam-4187	696	6	1962	1962	NUM
ejpam-4187	696	7	.	.	PUNCT
ejpam-4187	697	1	[	[	X
ejpam-4187	697	2	19	19	NUM
ejpam-4187	697	3	]	]	X
ejpam-4187	697	4	m.n	m.n	PROPN
ejpam-4187	697	5	.	.	PROPN
ejpam-4187	697	6	paspasan	paspasan	NOUN
ejpam-4187	697	7	and	and	CCONJ
ejpam-4187	697	8	s.r	s.r	PROPN
ejpam-4187	697	9	.	.	PROPN
ejpam-4187	697	10	canoy	canoy	PROPN
ejpam-4187	697	11	jr	jr	PROPN
ejpam-4187	697	12	.	.	PROPN
ejpam-4187	697	13	restrained	restrained	ADJ
ejpam-4187	697	14	total	total	ADJ
ejpam-4187	697	15	edge	edge	NOUN
ejpam-4187	697	16	domination	domination	NOUN
ejpam-4187	697	17	in	in	ADP
ejpam-4187	697	18	graphs	graph	NOUN
ejpam-4187	697	19	.	.	PUNCT
ejpam-4187	698	1	applied	apply	VERB
ejpam-4187	698	2	mathematical	mathematical	ADJ
ejpam-4187	698	3	sciences	science	NOUN
ejpam-4187	698	4	,	,	PUNCT
ejpam-4187	698	5	9:7139–7148	9:7139–7148	NUM
ejpam-4187	698	6	,	,	PUNCT
ejpam-4187	698	7	2015	2015	NUM
ejpam-4187	698	8	.	.	PUNCT
ejpam-4187	699	1	[	[	X
ejpam-4187	699	2	20	20	NUM
ejpam-4187	699	3	]	]	X
ejpam-4187	699	4	n.	n.	NOUN
ejpam-4187	699	5	sridharan	sridharan	ADJ
ejpam-4187	699	6	,	,	PUNCT
ejpam-4187	699	7	v.s.a	v.s.a	ADJ
ejpam-4187	699	8	.	.	PUNCT
ejpam-4187	699	9	subramanian	subramanian	PROPN
ejpam-4187	699	10	,	,	PUNCT
ejpam-4187	699	11	and	and	CCONJ
ejpam-4187	699	12	m.d	m.d	PROPN
ejpam-4187	699	13	.	.	PROPN
ejpam-4187	699	14	elias	elias	PROPN
ejpam-4187	699	15	.	.	PROPN
ejpam-4187	699	16	bounds	bound	NOUN
ejpam-4187	699	17	on	on	ADP
ejpam-4187	699	18	the	the	DET
ejpam-4187	699	19	distance	distance	NOUN
ejpam-4187	699	20	twodomination	twodomination	NOUN
ejpam-4187	699	21	number	number	NOUN
ejpam-4187	699	22	of	of	ADP
ejpam-4187	699	23	a	a	DET
ejpam-4187	699	24	graph	graph	NOUN
ejpam-4187	699	25	.	.	PUNCT
ejpam-4187	700	1	graphs	graph	NOUN
ejpam-4187	700	2	and	and	CCONJ
ejpam-4187	700	3	combinatorics	combinatoric	NOUN
ejpam-4187	700	4	(	(	PUNCT
ejpam-4187	700	5	springer	springer	NOUN
ejpam-4187	700	6	-	-	PUNCT
ejpam-4187	700	7	verlag	verlag	PROPN
ejpam-4187	700	8	)	)	PUNCT
ejpam-4187	700	9	,	,	PUNCT
ejpam-4187	700	10	18:667	18:667	NUM
ejpam-4187	700	11	–	–	PUNCT
ejpam-4187	700	12	675	675	NUM
ejpam-4187	700	13	,	,	PUNCT
ejpam-4187	700	14	2002	2002	NUM
ejpam-4187	700	15	.	.	PUNCT