id	sid	tid	token	lemma	pos
ejpam-3985	1	1	european	european	PROPN
ejpam-3985	1	2	journal	journal	PROPN
ejpam-3985	1	3	of	of	ADP
ejpam-3985	1	4	pure	pure	ADJ
ejpam-3985	1	5	and	and	CCONJ
ejpam-3985	1	6	applied	apply	VERB
ejpam-3985	1	7	mathematics	mathematic	NOUN
ejpam-3985	1	8	vol	vol	NOUN
ejpam-3985	1	9	.	.	PUNCT
ejpam-3985	2	1	14	14	NUM
ejpam-3985	2	2	,	,	PUNCT
ejpam-3985	2	3	no	no	INTJ
ejpam-3985	2	4	.	.	NOUN
ejpam-3985	2	5	3	3	NUM
ejpam-3985	2	6	,	,	PUNCT
ejpam-3985	2	7	2021	2021	NUM
ejpam-3985	2	8	,	,	PUNCT
ejpam-3985	2	9	829	829	NUM
ejpam-3985	2	10	-	-	SYM
ejpam-3985	2	11	841	841	NUM
ejpam-3985	2	12	issn	issn	PROPN
ejpam-3985	2	13	1307	1307	NUM
ejpam-3985	2	14	-	-	SYM
ejpam-3985	2	15	5543	5543	NUM
ejpam-3985	2	16	–	–	PUNCT
ejpam-3985	2	17	ejpam.com	ejpam.com	X
ejpam-3985	2	18	published	publish	VERB
ejpam-3985	2	19	by	by	ADP
ejpam-3985	2	20	new	new	PROPN
ejpam-3985	2	21	york	york	PROPN
ejpam-3985	2	22	business	business	PROPN
ejpam-3985	2	23	global	global	ADJ
ejpam-3985	2	24	resolving	resolve	VERB
ejpam-3985	2	25	restrained	restrained	ADJ
ejpam-3985	2	26	domination	domination	NOUN
ejpam-3985	2	27	in	in	ADP
ejpam-3985	2	28	graphs	graphs	PROPN
ejpam-3985	2	29	gerald	gerald	PROPN
ejpam-3985	2	30	b.	b.	PROPN
ejpam-3985	2	31	monsanto1,∗	monsanto1,∗	PROPN
ejpam-3985	2	32	,	,	PUNCT
ejpam-3985	3	1	helen	helen	PROPN
ejpam-3985	3	2	m.	m.	PROPN
ejpam-3985	3	3	rara2	rara2	PROPN
ejpam-3985	4	1	1	1	NUM
ejpam-3985	4	2	college	college	NOUN
ejpam-3985	4	3	of	of	ADP
ejpam-3985	4	4	teacher	teacher	NOUN
ejpam-3985	4	5	education	education	NOUN
ejpam-3985	4	6	,	,	PUNCT
ejpam-3985	4	7	arts	art	NOUN
ejpam-3985	4	8	and	and	CCONJ
ejpam-3985	4	9	sciences	science	NOUN
ejpam-3985	4	10	,	,	PUNCT
ejpam-3985	4	11	visayas	visayas	PROPN
ejpam-3985	4	12	state	state	PROPN
ejpam-3985	4	13	university	university	PROPN
ejpam-3985	4	14	-	-	PUNCT
ejpam-3985	4	15	villaba	villaba	NOUN
ejpam-3985	4	16	,	,	PUNCT
ejpam-3985	4	17	6537	6537	NUM
ejpam-3985	4	18	villaba	villaba	NOUN
ejpam-3985	4	19	,	,	PUNCT
ejpam-3985	4	20	leyte	leyte	PROPN
ejpam-3985	4	21	,	,	PUNCT
ejpam-3985	4	22	philippines	philippines	PROPN
ejpam-3985	4	23	2	2	NUM
ejpam-3985	4	24	department	department	NOUN
ejpam-3985	4	25	of	of	ADP
ejpam-3985	4	26	mathematics	mathematic	NOUN
ejpam-3985	4	27	and	and	CCONJ
ejpam-3985	4	28	statistics	statistic	NOUN
ejpam-3985	4	29	,	,	PUNCT
ejpam-3985	4	30	college	college	NOUN
ejpam-3985	4	31	of	of	ADP
ejpam-3985	4	32	science	science	NOUN
ejpam-3985	4	33	and	and	CCONJ
ejpam-3985	4	34	mathematics	mathematic	NOUN
ejpam-3985	4	35	,	,	PUNCT
ejpam-3985	4	36	center	center	NOUN
ejpam-3985	4	37	of	of	ADP
ejpam-3985	4	38	graph	graph	NOUN
ejpam-3985	4	39	theory	theory	NOUN
ejpam-3985	4	40	,	,	PUNCT
ejpam-3985	4	41	algebra	algebra	NOUN
ejpam-3985	4	42	,	,	PUNCT
ejpam-3985	4	43	and	and	CCONJ
ejpam-3985	4	44	analysis	analysis	NOUN
ejpam-3985	4	45	-	-	PUNCT
ejpam-3985	4	46	premier	premier	NOUN
ejpam-3985	4	47	research	research	NOUN
ejpam-3985	4	48	institute	institute	PROPN
ejpam-3985	4	49	of	of	ADP
ejpam-3985	4	50	science	science	NOUN
ejpam-3985	4	51	and	and	CCONJ
ejpam-3985	4	52	mathematics	mathematic	NOUN
ejpam-3985	4	53	,	,	PUNCT
ejpam-3985	4	54	mindanao	mindanao	PROPN
ejpam-3985	4	55	state	state	PROPN
ejpam-3985	4	56	university	university	PROPN
ejpam-3985	4	57	-	-	PUNCT
ejpam-3985	4	58	iligan	iligan	PROPN
ejpam-3985	4	59	institute	institute	PROPN
ejpam-3985	4	60	of	of	ADP
ejpam-3985	4	61	technology	technology	PROPN
ejpam-3985	4	62	,	,	PUNCT
ejpam-3985	4	63	9200	9200	NUM
ejpam-3985	4	64	iligan	iligan	ADJ
ejpam-3985	4	65	city	city	NOUN
ejpam-3985	4	66	,	,	PUNCT
ejpam-3985	4	67	philippines	philippine	NOUN
ejpam-3985	4	68	abstract	abstract	ADJ
ejpam-3985	4	69	.	.	PUNCT
ejpam-3985	5	1	let	let	VERB
ejpam-3985	5	2	g	g	PRON
ejpam-3985	5	3	be	be	AUX
ejpam-3985	5	4	a	a	DET
ejpam-3985	5	5	connected	connected	ADJ
ejpam-3985	5	6	graph	graph	NOUN
ejpam-3985	5	7	.	.	PUNCT
ejpam-3985	6	1	brigham	brigham	PROPN
ejpam-3985	6	2	et	et	PROPN
ejpam-3985	6	3	al	al	PROPN
ejpam-3985	6	4	.	.	PUNCT
ejpam-3985	7	1	[	[	X
ejpam-3985	7	2	3	3	X
ejpam-3985	7	3	]	]	PUNCT
ejpam-3985	7	4	defined	define	VERB
ejpam-3985	7	5	a	a	DET
ejpam-3985	7	6	resolving	resolve	VERB
ejpam-3985	7	7	dominating	dominating	NOUN
ejpam-3985	7	8	set	set	VERB
ejpam-3985	7	9	as	as	ADP
ejpam-3985	7	10	a	a	DET
ejpam-3985	7	11	set	set	NOUN
ejpam-3985	7	12	s	s	NOUN
ejpam-3985	7	13	of	of	ADP
ejpam-3985	7	14	vertices	vertex	NOUN
ejpam-3985	7	15	of	of	ADP
ejpam-3985	7	16	a	a	DET
ejpam-3985	7	17	connected	connected	ADJ
ejpam-3985	7	18	graph	graph	NOUN
ejpam-3985	7	19	g	g	NOUN
ejpam-3985	7	20	that	that	PRON
ejpam-3985	7	21	is	be	AUX
ejpam-3985	7	22	both	both	PRON
ejpam-3985	7	23	resolving	resolve	VERB
ejpam-3985	7	24	and	and	CCONJ
ejpam-3985	7	25	dominating	dominating	NOUN
ejpam-3985	7	26	.	.	PUNCT
ejpam-3985	8	1	a	a	DET
ejpam-3985	8	2	set	set	NOUN
ejpam-3985	8	3	s	s	NOUN
ejpam-3985	8	4	⊆	⊆	NUM
ejpam-3985	8	5	v	v	NOUN
ejpam-3985	8	6	(	(	PUNCT
ejpam-3985	8	7	g	g	NOUN
ejpam-3985	8	8	)	)	PUNCT
ejpam-3985	8	9	is	be	AUX
ejpam-3985	8	10	a	a	DET
ejpam-3985	8	11	resolving	resolve	VERB
ejpam-3985	8	12	restrained	restrained	ADJ
ejpam-3985	8	13	dominating	dominating	NOUN
ejpam-3985	8	14	set	set	NOUN
ejpam-3985	8	15	of	of	ADP
ejpam-3985	8	16	g	g	PROPN
ejpam-3985	8	17	if	if	SCONJ
ejpam-3985	8	18	s	s	VERB
ejpam-3985	8	19	is	be	AUX
ejpam-3985	8	20	a	a	DET
ejpam-3985	8	21	resolving	resolve	VERB
ejpam-3985	8	22	dominating	dominating	NOUN
ejpam-3985	8	23	set	set	NOUN
ejpam-3985	8	24	of	of	ADP
ejpam-3985	8	25	g	g	PROPN
ejpam-3985	8	26	and	and	CCONJ
ejpam-3985	8	27	s	s	PART
ejpam-3985	8	28	=	=	SYM
ejpam-3985	8	29	v	v	X
ejpam-3985	8	30	(	(	PUNCT
ejpam-3985	8	31	g	g	NOUN
ejpam-3985	8	32	)	)	PUNCT
ejpam-3985	8	33	or	or	CCONJ
ejpam-3985	8	34	〈	〈	PROPN
ejpam-3985	8	35	v	v	X
ejpam-3985	8	36	(	(	PUNCT
ejpam-3985	8	37	g	g	NOUN
ejpam-3985	8	38	)	)	PUNCT
ejpam-3985	8	39	\	\	PUNCT
ejpam-3985	9	1	s	s	VERB
ejpam-3985	9	2	〉	〉	NOUN
ejpam-3985	9	3	has	have	VERB
ejpam-3985	9	4	no	no	DET
ejpam-3985	9	5	isolated	isolated	ADJ
ejpam-3985	9	6	vertex	vertex	NOUN
ejpam-3985	9	7	.	.	PUNCT
ejpam-3985	10	1	in	in	ADP
ejpam-3985	10	2	this	this	DET
ejpam-3985	10	3	paper	paper	NOUN
ejpam-3985	10	4	,	,	PUNCT
ejpam-3985	10	5	we	we	PRON
ejpam-3985	10	6	characterize	characterize	VERB
ejpam-3985	10	7	the	the	DET
ejpam-3985	10	8	resolving	resolve	VERB
ejpam-3985	10	9	restrained	restrained	ADJ
ejpam-3985	10	10	dominating	dominating	NOUN
ejpam-3985	10	11	sets	set	NOUN
ejpam-3985	10	12	in	in	ADP
ejpam-3985	10	13	the	the	DET
ejpam-3985	10	14	join	join	NOUN
ejpam-3985	10	15	,	,	PUNCT
ejpam-3985	10	16	corona	corona	NOUN
ejpam-3985	10	17	and	and	CCONJ
ejpam-3985	10	18	lexicographic	lexicographic	ADJ
ejpam-3985	10	19	product	product	NOUN
ejpam-3985	10	20	of	of	ADP
ejpam-3985	10	21	graphs	graph	NOUN
ejpam-3985	10	22	and	and	CCONJ
ejpam-3985	10	23	determine	determine	VERB
ejpam-3985	10	24	the	the	DET
ejpam-3985	10	25	resolving	resolve	VERB
ejpam-3985	10	26	restrained	restrained	ADJ
ejpam-3985	10	27	domination	domination	NOUN
ejpam-3985	10	28	number	number	NOUN
ejpam-3985	10	29	of	of	ADP
ejpam-3985	10	30	these	these	DET
ejpam-3985	10	31	graphs	graph	NOUN
ejpam-3985	10	32	.	.	PUNCT
ejpam-3985	11	1	2020	2020	NUM
ejpam-3985	11	2	mathematics	mathematic	NOUN
ejpam-3985	11	3	subject	subject	NOUN
ejpam-3985	11	4	classifications	classification	NOUN
ejpam-3985	11	5	:	:	PUNCT
ejpam-3985	11	6	05c69	05c69	X
ejpam-3985	11	7	key	key	ADJ
ejpam-3985	11	8	words	word	NOUN
ejpam-3985	11	9	and	and	CCONJ
ejpam-3985	11	10	phrases	phrase	NOUN
ejpam-3985	11	11	:	:	PUNCT
ejpam-3985	11	12	dominating	dominate	VERB
ejpam-3985	11	13	set	set	NOUN
ejpam-3985	11	14	,	,	PUNCT
ejpam-3985	11	15	resolving	resolve	VERB
ejpam-3985	11	16	set	set	NOUN
ejpam-3985	11	17	,	,	PUNCT
ejpam-3985	11	18	resolving	resolve	VERB
ejpam-3985	11	19	dominating	dominating	NOUN
ejpam-3985	11	20	set	set	NOUN
ejpam-3985	11	21	,	,	PUNCT
ejpam-3985	11	22	resolving	resolve	VERB
ejpam-3985	11	23	restrained	restrained	ADJ
ejpam-3985	11	24	dominating	dominating	NOUN
ejpam-3985	11	25	set	set	NOUN
ejpam-3985	11	26	,	,	PUNCT
ejpam-3985	11	27	join	join	NOUN
ejpam-3985	11	28	,	,	PUNCT
ejpam-3985	11	29	corona	corona	PROPN
ejpam-3985	11	30	,	,	PUNCT
ejpam-3985	11	31	lexicographic	lexicographic	ADJ
ejpam-3985	11	32	product	product	NOUN
ejpam-3985	11	33	1	1	NUM
ejpam-3985	11	34	.	.	PUNCT
ejpam-3985	12	1	introduction	introduction	NOUN
ejpam-3985	12	2	all	all	DET
ejpam-3985	12	3	graphs	graph	NOUN
ejpam-3985	12	4	considered	consider	VERB
ejpam-3985	12	5	in	in	ADP
ejpam-3985	12	6	this	this	DET
ejpam-3985	12	7	study	study	NOUN
ejpam-3985	12	8	are	be	AUX
ejpam-3985	12	9	finite	finite	ADJ
ejpam-3985	12	10	,	,	PUNCT
ejpam-3985	12	11	simple	simple	ADJ
ejpam-3985	12	12	,	,	PUNCT
ejpam-3985	12	13	and	and	CCONJ
ejpam-3985	12	14	undirected	undirected	ADJ
ejpam-3985	12	15	connected	connected	ADJ
ejpam-3985	12	16	graphs	graph	NOUN
ejpam-3985	12	17	,	,	PUNCT
ejpam-3985	12	18	that	that	ADV
ejpam-3985	12	19	is	is	ADV
ejpam-3985	12	20	,	,	PUNCT
ejpam-3985	12	21	without	without	ADP
ejpam-3985	12	22	loops	loop	NOUN
ejpam-3985	12	23	and	and	CCONJ
ejpam-3985	12	24	multiple	multiple	ADJ
ejpam-3985	12	25	edges	edge	NOUN
ejpam-3985	12	26	.	.	PUNCT
ejpam-3985	13	1	for	for	ADP
ejpam-3985	13	2	some	some	DET
ejpam-3985	13	3	basic	basic	ADJ
ejpam-3985	13	4	concepts	concept	NOUN
ejpam-3985	13	5	in	in	ADP
ejpam-3985	13	6	graph	graph	NOUN
ejpam-3985	13	7	theory	theory	NOUN
ejpam-3985	13	8	,	,	PUNCT
ejpam-3985	13	9	we	we	PRON
ejpam-3985	13	10	refer	refer	VERB
ejpam-3985	13	11	readers	reader	NOUN
ejpam-3985	13	12	to	to	ADP
ejpam-3985	13	13	[	[	X
ejpam-3985	13	14	7	7	NUM
ejpam-3985	13	15	]	]	PUNCT
ejpam-3985	13	16	.	.	PUNCT
ejpam-3985	14	1	let	let	VERB
ejpam-3985	14	2	g	g	NOUN
ejpam-3985	14	3	=	=	PUNCT
ejpam-3985	14	4	(	(	PUNCT
ejpam-3985	14	5	v	v	NOUN
ejpam-3985	14	6	(	(	PUNCT
ejpam-3985	14	7	g	g	NOUN
ejpam-3985	14	8	)	)	PUNCT
ejpam-3985	14	9	,	,	PUNCT
ejpam-3985	14	10	e(g	e(g	PROPN
ejpam-3985	14	11	)	)	PUNCT
ejpam-3985	14	12	)	)	PUNCT
ejpam-3985	15	1	be	be	AUX
ejpam-3985	15	2	a	a	DET
ejpam-3985	15	3	connected	connected	ADJ
ejpam-3985	15	4	graph	graph	NOUN
ejpam-3985	15	5	.	.	PUNCT
ejpam-3985	16	1	the	the	DET
ejpam-3985	16	2	open	open	ADJ
ejpam-3985	16	3	neighborhood	neighborhood	NOUN
ejpam-3985	16	4	of	of	ADP
ejpam-3985	16	5	v	v	NUM
ejpam-3985	16	6	∈	∈	NOUN
ejpam-3985	16	7	v	v	NOUN
ejpam-3985	16	8	(	(	PUNCT
ejpam-3985	16	9	g	g	NOUN
ejpam-3985	16	10	)	)	PUNCT
ejpam-3985	16	11	is	be	AUX
ejpam-3985	16	12	ng(v	ng(v	PUNCT
ejpam-3985	16	13	)	)	PUNCT
ejpam-3985	16	14	=	=	PRON
ejpam-3985	17	1	{	{	PUNCT
ejpam-3985	17	2	u	u	NOUN
ejpam-3985	17	3	∈	∈	PROPN
ejpam-3985	17	4	v	v	NOUN
ejpam-3985	17	5	(	(	PUNCT
ejpam-3985	17	6	g	g	NOUN
ejpam-3985	17	7	)	)	PUNCT
ejpam-3985	17	8	:	:	PUNCT
ejpam-3985	17	9	uv	uv	PROPN
ejpam-3985	17	10	∈	∈	PROPN
ejpam-3985	17	11	e(g	e(g	PROPN
ejpam-3985	17	12	)	)	PUNCT
ejpam-3985	17	13	}	}	PUNCT
ejpam-3985	17	14	.	.	PUNCT
ejpam-3985	18	1	any	any	DET
ejpam-3985	18	2	element	element	NOUN
ejpam-3985	18	3	u	u	NOUN
ejpam-3985	18	4	of	of	ADP
ejpam-3985	18	5	ng(v	ng(v	PUNCT
ejpam-3985	18	6	)	)	PUNCT
ejpam-3985	18	7	is	be	AUX
ejpam-3985	18	8	called	call	VERB
ejpam-3985	18	9	a	a	DET
ejpam-3985	18	10	neighbor	neighbor	NOUN
ejpam-3985	18	11	of	of	ADP
ejpam-3985	18	12	v.	v.	ADP
ejpam-3985	18	13	the	the	DET
ejpam-3985	18	14	closed	closed	ADJ
ejpam-3985	18	15	neighborhood	neighborhood	NOUN
ejpam-3985	18	16	v	v	ADP
ejpam-3985	18	17	∈	∈	NOUN
ejpam-3985	18	18	v	v	NOUN
ejpam-3985	18	19	(	(	PUNCT
ejpam-3985	18	20	g	g	NOUN
ejpam-3985	18	21	)	)	PUNCT
ejpam-3985	18	22	is	be	AUX
ejpam-3985	18	23	ng[v	ng[v	ADV
ejpam-3985	18	24	]	]	X
ejpam-3985	18	25	=	=	SYM
ejpam-3985	18	26	ng(v)∪{v	ng(v)∪{v	PROPN
ejpam-3985	18	27	}	}	PUNCT
ejpam-3985	18	28	.	.	PUNCT
ejpam-3985	19	1	thus	thus	ADV
ejpam-3985	19	2	,	,	PUNCT
ejpam-3985	19	3	the	the	DET
ejpam-3985	19	4	degree	degree	NOUN
ejpam-3985	19	5	of	of	ADP
ejpam-3985	19	6	v	v	NUM
ejpam-3985	19	7	∈	∈	NOUN
ejpam-3985	19	8	v	v	NOUN
ejpam-3985	19	9	(	(	PUNCT
ejpam-3985	19	10	g	g	NOUN
ejpam-3985	19	11	)	)	PUNCT
ejpam-3985	19	12	is	be	AUX
ejpam-3985	19	13	given	give	VERB
ejpam-3985	19	14	by	by	ADP
ejpam-3985	19	15	degg(v	degg(v	PROPN
ejpam-3985	19	16	)	)	PUNCT
ejpam-3985	19	17	=	=	SYM
ejpam-3985	19	18	|ng(v)|	|ng(v)|	NOUN
ejpam-3985	19	19	.	.	PUNCT
ejpam-3985	20	1	customarily	customarily	ADV
ejpam-3985	20	2	,	,	PUNCT
ejpam-3985	20	3	for	for	ADP
ejpam-3985	20	4	s	s	PROPN
ejpam-3985	20	5	⊆	⊆	NUM
ejpam-3985	20	6	v	v	NOUN
ejpam-3985	20	7	(	(	PUNCT
ejpam-3985	20	8	g	g	NOUN
ejpam-3985	20	9	)	)	PUNCT
ejpam-3985	20	10	,	,	PUNCT
ejpam-3985	20	11	ng(s	ng(s	NUM
ejpam-3985	20	12	)	)	PUNCT
ejpam-3985	21	1	=	=	SYM
ejpam-3985	22	1	⋃	⋃	ADP
ejpam-3985	22	2	v∈s	v∈s	NOUN
ejpam-3985	22	3	ng(v	ng(v	NOUN
ejpam-3985	22	4	)	)	PUNCT
ejpam-3985	22	5	and	and	CCONJ
ejpam-3985	22	6	ng[s	ng[	NOUN
ejpam-3985	22	7	]	]	PUNCT
ejpam-3985	22	8	=	=	PUNCT
ejpam-3985	22	9	⋃	⋃	VERB
ejpam-3985	22	10	v∈s	v∈s	ADJ
ejpam-3985	22	11	ng[v	ng[v	NOUN
ejpam-3985	22	12	]	]	PUNCT
ejpam-3985	22	13	.	.	PUNCT
ejpam-3985	23	1	a	a	DET
ejpam-3985	23	2	nonempty	nonempty	ADV
ejpam-3985	23	3	set	set	VERB
ejpam-3985	23	4	s	s	PROPN
ejpam-3985	23	5	⊆	⊆	NUM
ejpam-3985	23	6	v	v	NOUN
ejpam-3985	23	7	(	(	PUNCT
ejpam-3985	23	8	g	g	NOUN
ejpam-3985	23	9	)	)	PUNCT
ejpam-3985	23	10	is	be	AUX
ejpam-3985	23	11	a	a	DET
ejpam-3985	23	12	dominating	dominating	NOUN
ejpam-3985	23	13	set	set	VERB
ejpam-3985	23	14	in	in	ADP
ejpam-3985	23	15	graph	graph	NOUN
ejpam-3985	23	16	g	g	NOUN
ejpam-3985	23	17	if	if	SCONJ
ejpam-3985	23	18	ng[s	ng[	NOUN
ejpam-3985	23	19	]	]	PUNCT
ejpam-3985	23	20	=	=	SYM
ejpam-3985	23	21	v	v	NOUN
ejpam-3985	23	22	(	(	PUNCT
ejpam-3985	23	23	g	g	NOUN
ejpam-3985	23	24	)	)	PUNCT
ejpam-3985	23	25	.	.	PUNCT
ejpam-3985	24	1	otherwise	otherwise	ADV
ejpam-3985	24	2	,	,	PUNCT
ejpam-3985	24	3	we	we	PRON
ejpam-3985	24	4	say	say	VERB
ejpam-3985	24	5	s	s	PRON
ejpam-3985	24	6	is	be	AUX
ejpam-3985	24	7	a	a	DET
ejpam-3985	24	8	non	non	ADJ
ejpam-3985	24	9	-	-	ADJ
ejpam-3985	24	10	dominating	dominating	ADJ
ejpam-3985	24	11	set	set	NOUN
ejpam-3985	24	12	of	of	ADP
ejpam-3985	24	13	g.	g.	PROPN
ejpam-3985	24	14	the	the	DET
ejpam-3985	24	15	domination	domination	NOUN
ejpam-3985	24	16	number	number	NOUN
ejpam-3985	24	17	of	of	ADP
ejpam-3985	24	18	a	a	DET
ejpam-3985	24	19	graph	graph	NOUN
ejpam-3985	24	20	g	g	NOUN
ejpam-3985	24	21	,	,	PUNCT
ejpam-3985	24	22	denoted	denote	VERB
ejpam-3985	24	23	∗corresponding	∗corresponde	VERB
ejpam-3985	24	24	author	author	NOUN
ejpam-3985	24	25	.	.	PUNCT
ejpam-3985	25	1	doi	doi	NOUN
ejpam-3985	25	2	:	:	PUNCT
ejpam-3985	25	3	https://doi.org/10.29020/nybg.ejpam.v14i3.3985	https://doi.org/10.29020/nybg.ejpam.v14i3.3985	PRON
ejpam-3985	25	4	email	email	NOUN
ejpam-3985	25	5	addresses	address	VERB
ejpam-3985	25	6	:	:	PUNCT
ejpam-3985	25	7	gerald.monsanto@vsu.edu.ph	gerald.monsanto@vsu.edu.ph	PROPN
ejpam-3985	25	8	(	(	PUNCT
ejpam-3985	25	9	g.	g.	PROPN
ejpam-3985	25	10	monsanto	monsanto	PROPN
ejpam-3985	25	11	)	)	PUNCT
ejpam-3985	25	12	,	,	PUNCT
ejpam-3985	25	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-3985	25	14	(	(	PUNCT
ejpam-3985	25	15	h.	h.	PROPN
ejpam-3985	25	16	rara	rara	PROPN
ejpam-3985	25	17	)	)	PUNCT
ejpam-3985	25	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3985	26	1	829	829	NUM
ejpam-3985	26	2	©	©	PROPN
ejpam-3985	26	3	2021	2021	NUM
ejpam-3985	26	4	ejpam	ejpam	VERB
ejpam-3985	26	5	all	all	DET
ejpam-3985	26	6	rights	right	NOUN
ejpam-3985	26	7	reserved	reserve	VERB
ejpam-3985	26	8	.	.	PUNCT
ejpam-3985	27	1	g.	g.	PROPN
ejpam-3985	27	2	monsanto	monsanto	PROPN
ejpam-3985	27	3	,	,	PUNCT
ejpam-3985	27	4	h.	h.	PROPN
ejpam-3985	27	5	rara	rara	PROPN
ejpam-3985	27	6	/	/	SYM
ejpam-3985	27	7	eur	eur	PROPN
ejpam-3985	27	8	.	.	PUNCT
ejpam-3985	28	1	j.	j.	PROPN
ejpam-3985	28	2	pure	pure	PROPN
ejpam-3985	28	3	appl	appl	PROPN
ejpam-3985	28	4	.	.	PROPN
ejpam-3985	28	5	math	math	PROPN
ejpam-3985	28	6	,	,	PUNCT
ejpam-3985	28	7	14	14	NUM
ejpam-3985	28	8	(	(	PUNCT
ejpam-3985	28	9	3	3	NUM
ejpam-3985	28	10	)	)	PUNCT
ejpam-3985	28	11	(	(	PUNCT
ejpam-3985	28	12	2021	2021	NUM
ejpam-3985	28	13	)	)	PUNCT
ejpam-3985	28	14	,	,	PUNCT
ejpam-3985	28	15	829	829	NUM
ejpam-3985	28	16	-	-	SYM
ejpam-3985	28	17	841	841	NUM
ejpam-3985	28	18	830	830	NUM
ejpam-3985	28	19	by	by	ADP
ejpam-3985	28	20	γ(g	γ(g	PROPN
ejpam-3985	28	21	)	)	PUNCT
ejpam-3985	28	22	,	,	PUNCT
ejpam-3985	28	23	is	be	AUX
ejpam-3985	28	24	given	give	VERB
ejpam-3985	28	25	by	by	ADP
ejpam-3985	28	26	γ(g	γ(g	PROPN
ejpam-3985	28	27	)	)	PUNCT
ejpam-3985	29	1	=	=	NOUN
ejpam-3985	29	2	min{|s|	min{|s|	NOUN
ejpam-3985	29	3	:	:	PUNCT
ejpam-3985	29	4	s	s	VERB
ejpam-3985	29	5	is	be	AUX
ejpam-3985	29	6	a	a	DET
ejpam-3985	29	7	dominating	dominating	NOUN
ejpam-3985	29	8	set	set	NOUN
ejpam-3985	29	9	of	of	ADP
ejpam-3985	29	10	g	g	NOUN
ejpam-3985	29	11	}	}	PUNCT
ejpam-3985	29	12	.	.	PUNCT
ejpam-3985	30	1	if	if	SCONJ
ejpam-3985	30	2	s	s	NOUN
ejpam-3985	30	3	is	be	AUX
ejpam-3985	30	4	a	a	DET
ejpam-3985	30	5	dominating	dominating	NOUN
ejpam-3985	30	6	set	set	NOUN
ejpam-3985	30	7	of	of	ADP
ejpam-3985	30	8	g	g	PROPN
ejpam-3985	30	9	and	and	CCONJ
ejpam-3985	30	10	if	if	SCONJ
ejpam-3985	30	11	|s|	|s|	PROPN
ejpam-3985	30	12	=	=	SYM
ejpam-3985	30	13	γ(g	γ(g	PROPN
ejpam-3985	30	14	)	)	PUNCT
ejpam-3985	30	15	,	,	PUNCT
ejpam-3985	30	16	then	then	ADV
ejpam-3985	30	17	s	s	VERB
ejpam-3985	30	18	is	be	AUX
ejpam-3985	30	19	called	call	VERB
ejpam-3985	30	20	a	a	DET
ejpam-3985	30	21	minimum	minimum	ADJ
ejpam-3985	30	22	dominating	dominating	NOUN
ejpam-3985	30	23	set	set	NOUN
ejpam-3985	30	24	or	or	CCONJ
ejpam-3985	30	25	a	a	DET
ejpam-3985	30	26	γ	γ	NOUN
ejpam-3985	30	27	-	-	PUNCT
ejpam-3985	30	28	set	set	NOUN
ejpam-3985	30	29	of	of	ADP
ejpam-3985	30	30	g.	g.	PROPN
ejpam-3985	30	31	a	a	DET
ejpam-3985	30	32	vertex	vertex	NOUN
ejpam-3985	30	33	x	x	X
ejpam-3985	30	34	of	of	ADP
ejpam-3985	30	35	a	a	DET
ejpam-3985	30	36	connected	connected	ADJ
ejpam-3985	30	37	graph	graph	NOUN
ejpam-3985	30	38	g	g	NOUN
ejpam-3985	30	39	is	be	AUX
ejpam-3985	30	40	said	say	VERB
ejpam-3985	30	41	to	to	PART
ejpam-3985	30	42	resolve	resolve	VERB
ejpam-3985	30	43	two	two	NUM
ejpam-3985	30	44	vertices	vertex	NOUN
ejpam-3985	30	45	u	u	NOUN
ejpam-3985	30	46	and	and	CCONJ
ejpam-3985	30	47	v	v	NOUN
ejpam-3985	30	48	of	of	ADP
ejpam-3985	30	49	g	g	PROPN
ejpam-3985	30	50	if	if	SCONJ
ejpam-3985	30	51	dg(x	dg(x	NUM
ejpam-3985	30	52	,	,	PUNCT
ejpam-3985	30	53	u	u	NOUN
ejpam-3985	30	54	)	)	PUNCT
ejpam-3985	30	55	6=	6=	ADP
ejpam-3985	30	56	dg(x	dg(x	SYM
ejpam-3985	30	57	,	,	PUNCT
ejpam-3985	30	58	v	v	NOUN
ejpam-3985	30	59	)	)	PUNCT
ejpam-3985	30	60	.	.	PUNCT
ejpam-3985	31	1	for	for	ADP
ejpam-3985	31	2	an	an	DET
ejpam-3985	31	3	ordered	order	VERB
ejpam-3985	31	4	set	set	NOUN
ejpam-3985	31	5	w	w	NOUN
ejpam-3985	31	6	=	=	PUNCT
ejpam-3985	31	7	{	{	PUNCT
ejpam-3985	31	8	x1	x1	PROPN
ejpam-3985	31	9	,	,	PUNCT
ejpam-3985	31	10	.	.	PUNCT
ejpam-3985	31	11	.	.	PUNCT
ejpam-3985	31	12	.	.	PUNCT
ejpam-3985	32	1	,	,	PUNCT
ejpam-3985	32	2	xk	xk	ADJ
ejpam-3985	32	3	}	}	PUNCT
ejpam-3985	32	4	⊆	⊆	NUM
ejpam-3985	32	5	v	v	NOUN
ejpam-3985	32	6	(	(	PUNCT
ejpam-3985	32	7	g	g	NOUN
ejpam-3985	32	8	)	)	PUNCT
ejpam-3985	32	9	and	and	CCONJ
ejpam-3985	32	10	a	a	DET
ejpam-3985	32	11	vertex	vertex	NOUN
ejpam-3985	32	12	v	v	NOUN
ejpam-3985	32	13	in	in	ADP
ejpam-3985	32	14	g	g	PROPN
ejpam-3985	32	15	,	,	PUNCT
ejpam-3985	32	16	the	the	DET
ejpam-3985	32	17	k	k	NOUN
ejpam-3985	32	18	-	-	NOUN
ejpam-3985	32	19	vector	vector	NOUN
ejpam-3985	32	20	rg(v	rg(v	NOUN
ejpam-3985	32	21	/	/	SYM
ejpam-3985	32	22	w	w	NOUN
ejpam-3985	32	23	)	)	PUNCT
ejpam-3985	32	24	=	=	PRON
ejpam-3985	32	25	(	(	PUNCT
ejpam-3985	32	26	dg(v	dg(v	X
ejpam-3985	32	27	,	,	PUNCT
ejpam-3985	32	28	x1	x1	PROPN
ejpam-3985	32	29	)	)	PUNCT
ejpam-3985	32	30	,	,	PUNCT
ejpam-3985	32	31	dg(v	dg(v	X
ejpam-3985	32	32	,	,	PUNCT
ejpam-3985	32	33	x2	x2	PROPN
ejpam-3985	32	34	)	)	PUNCT
ejpam-3985	32	35	,	,	PUNCT
ejpam-3985	32	36	.	.	PUNCT
ejpam-3985	32	37	.	.	PUNCT
ejpam-3985	33	1	.	.	PUNCT
ejpam-3985	34	1	,	,	PUNCT
ejpam-3985	34	2	dg(v	dg(v	X
ejpam-3985	34	3	,	,	PUNCT
ejpam-3985	34	4	xk	xk	NOUN
ejpam-3985	34	5	)	)	PUNCT
ejpam-3985	34	6	)	)	PUNCT
ejpam-3985	34	7	is	be	AUX
ejpam-3985	34	8	called	call	VERB
ejpam-3985	34	9	the	the	DET
ejpam-3985	34	10	representation	representation	NOUN
ejpam-3985	34	11	of	of	ADP
ejpam-3985	34	12	v	v	NOUN
ejpam-3985	34	13	with	with	ADP
ejpam-3985	34	14	respect	respect	NOUN
ejpam-3985	34	15	to	to	ADP
ejpam-3985	34	16	w	w	PROPN
ejpam-3985	34	17	.	.	PUNCT
ejpam-3985	35	1	the	the	DET
ejpam-3985	35	2	set	set	NOUN
ejpam-3985	35	3	w	w	NOUN
ejpam-3985	35	4	is	be	AUX
ejpam-3985	35	5	a	a	DET
ejpam-3985	35	6	resolving	resolving	NOUN
ejpam-3985	35	7	set	set	VERB
ejpam-3985	35	8	for	for	ADP
ejpam-3985	35	9	g	g	PROPN
ejpam-3985	35	10	if	if	SCONJ
ejpam-3985	36	1	and	and	CCONJ
ejpam-3985	36	2	only	only	ADV
ejpam-3985	36	3	if	if	SCONJ
ejpam-3985	36	4	no	no	DET
ejpam-3985	36	5	two	two	NUM
ejpam-3985	36	6	vertices	vertex	NOUN
ejpam-3985	36	7	of	of	ADP
ejpam-3985	36	8	g	g	NOUN
ejpam-3985	36	9	have	have	VERB
ejpam-3985	36	10	the	the	DET
ejpam-3985	36	11	same	same	ADJ
ejpam-3985	36	12	representation	representation	NOUN
ejpam-3985	36	13	with	with	ADP
ejpam-3985	36	14	respect	respect	NOUN
ejpam-3985	36	15	to	to	ADP
ejpam-3985	36	16	w	w	PROPN
ejpam-3985	36	17	.	.	PUNCT
ejpam-3985	37	1	the	the	DET
ejpam-3985	37	2	metric	metric	ADJ
ejpam-3985	37	3	dimension	dimension	NOUN
ejpam-3985	37	4	of	of	ADP
ejpam-3985	37	5	g	g	NOUN
ejpam-3985	37	6	,	,	PUNCT
ejpam-3985	37	7	denoted	denote	VERB
ejpam-3985	37	8	by	by	ADP
ejpam-3985	37	9	dim(g	dim(g	PROPN
ejpam-3985	37	10	)	)	PUNCT
ejpam-3985	37	11	,	,	PUNCT
ejpam-3985	37	12	is	be	AUX
ejpam-3985	37	13	the	the	DET
ejpam-3985	37	14	minimum	minimum	ADJ
ejpam-3985	37	15	cardinality	cardinality	NOUN
ejpam-3985	37	16	over	over	ADP
ejpam-3985	37	17	all	all	DET
ejpam-3985	37	18	resolving	resolve	VERB
ejpam-3985	37	19	sets	set	NOUN
ejpam-3985	37	20	of	of	ADP
ejpam-3985	37	21	g.	g.	PROPN
ejpam-3985	37	22	a	a	DET
ejpam-3985	37	23	resolving	resolve	VERB
ejpam-3985	37	24	set	set	NOUN
ejpam-3985	37	25	of	of	ADP
ejpam-3985	37	26	cardinality	cardinality	PROPN
ejpam-3985	37	27	dim(g	dim(g	PROPN
ejpam-3985	37	28	)	)	PUNCT
ejpam-3985	37	29	is	be	AUX
ejpam-3985	37	30	called	call	VERB
ejpam-3985	37	31	a	a	DET
ejpam-3985	37	32	basis	basis	NOUN
ejpam-3985	37	33	.	.	PUNCT
ejpam-3985	38	1	brigham	brigham	PROPN
ejpam-3985	38	2	et	et	PROPN
ejpam-3985	38	3	al	al	PROPN
ejpam-3985	38	4	.	.	PUNCT
ejpam-3985	39	1	[	[	X
ejpam-3985	39	2	3	3	X
ejpam-3985	39	3	]	]	PUNCT
ejpam-3985	39	4	defined	define	VERB
ejpam-3985	39	5	a	a	DET
ejpam-3985	39	6	resolving	resolve	VERB
ejpam-3985	39	7	dominating	dominating	NOUN
ejpam-3985	39	8	set	set	VERB
ejpam-3985	39	9	as	as	ADP
ejpam-3985	39	10	a	a	DET
ejpam-3985	39	11	set	set	NOUN
ejpam-3985	39	12	s	s	NOUN
ejpam-3985	39	13	of	of	ADP
ejpam-3985	39	14	vertices	vertex	NOUN
ejpam-3985	39	15	of	of	ADP
ejpam-3985	39	16	a	a	DET
ejpam-3985	39	17	connected	connected	ADJ
ejpam-3985	39	18	graph	graph	NOUN
ejpam-3985	39	19	g	g	NOUN
ejpam-3985	39	20	that	that	PRON
ejpam-3985	39	21	is	be	AUX
ejpam-3985	39	22	both	both	PRON
ejpam-3985	39	23	resolving	resolve	VERB
ejpam-3985	39	24	and	and	CCONJ
ejpam-3985	39	25	dominating	dominating	NOUN
ejpam-3985	39	26	.	.	PUNCT
ejpam-3985	40	1	the	the	DET
ejpam-3985	40	2	cardinality	cardinality	NOUN
ejpam-3985	40	3	of	of	ADP
ejpam-3985	40	4	a	a	DET
ejpam-3985	40	5	minimum	minimum	ADJ
ejpam-3985	40	6	resolving	resolving	NOUN
ejpam-3985	40	7	dominating	dominating	NOUN
ejpam-3985	40	8	set	set	NOUN
ejpam-3985	40	9	is	be	AUX
ejpam-3985	40	10	called	call	VERB
ejpam-3985	40	11	the	the	DET
ejpam-3985	40	12	resolving	resolve	VERB
ejpam-3985	40	13	domination	domination	NOUN
ejpam-3985	40	14	number	number	NOUN
ejpam-3985	40	15	of	of	ADP
ejpam-3985	40	16	g	g	NOUN
ejpam-3985	40	17	and	and	CCONJ
ejpam-3985	40	18	is	be	AUX
ejpam-3985	40	19	denoted	denote	VERB
ejpam-3985	40	20	by	by	ADP
ejpam-3985	40	21	γr(g	γr(g	PROPN
ejpam-3985	40	22	)	)	PUNCT
ejpam-3985	40	23	.	.	PUNCT
ejpam-3985	41	1	a	a	DET
ejpam-3985	41	2	resolving	resolve	VERB
ejpam-3985	41	3	dominating	dominating	NOUN
ejpam-3985	41	4	set	set	NOUN
ejpam-3985	41	5	of	of	ADP
ejpam-3985	41	6	cardinality	cardinality	PROPN
ejpam-3985	41	7	γr(g	γr(g	PROPN
ejpam-3985	41	8	)	)	PUNCT
ejpam-3985	41	9	is	be	AUX
ejpam-3985	41	10	called	call	VERB
ejpam-3985	41	11	a	a	DET
ejpam-3985	41	12	γr	γr	PROPN
ejpam-3985	41	13	-	-	PUNCT
ejpam-3985	41	14	set	set	NOUN
ejpam-3985	41	15	of	of	ADP
ejpam-3985	41	16	g.	g.	PROPN
ejpam-3985	41	17	let	let	VERB
ejpam-3985	41	18	g	g	NOUN
ejpam-3985	41	19	be	be	AUX
ejpam-3985	41	20	a	a	DET
ejpam-3985	41	21	connected	connected	ADJ
ejpam-3985	41	22	graph	graph	NOUN
ejpam-3985	41	23	.	.	PUNCT
ejpam-3985	42	1	a	a	DET
ejpam-3985	42	2	set	set	NOUN
ejpam-3985	42	3	s	s	NOUN
ejpam-3985	42	4	⊆	⊆	NUM
ejpam-3985	42	5	v	v	NOUN
ejpam-3985	42	6	(	(	PUNCT
ejpam-3985	42	7	g	g	NOUN
ejpam-3985	42	8	)	)	PUNCT
ejpam-3985	42	9	is	be	AUX
ejpam-3985	42	10	a	a	DET
ejpam-3985	42	11	strictly	strictly	ADV
ejpam-3985	42	12	resolving	resolve	VERB
ejpam-3985	42	13	dominating	dominating	NOUN
ejpam-3985	42	14	set	set	NOUN
ejpam-3985	42	15	of	of	ADP
ejpam-3985	42	16	g	g	PROPN
ejpam-3985	42	17	if	if	SCONJ
ejpam-3985	42	18	it	it	PRON
ejpam-3985	42	19	is	be	AUX
ejpam-3985	42	20	a	a	DET
ejpam-3985	42	21	resolving	resolve	VERB
ejpam-3985	42	22	dominating	dominating	NOUN
ejpam-3985	42	23	set	set	NOUN
ejpam-3985	42	24	of	of	ADP
ejpam-3985	42	25	g	g	PROPN
ejpam-3985	42	26	and	and	CCONJ
ejpam-3985	42	27	ng(u	ng(u	NOUN
ejpam-3985	42	28	)	)	PUNCT
ejpam-3985	42	29	∩	∩	NOUN
ejpam-3985	42	30	s	s	PART
ejpam-3985	42	31	6=	6=	NUM
ejpam-3985	42	32	s	s	X
ejpam-3985	42	33	for	for	ADP
ejpam-3985	42	34	all	all	DET
ejpam-3985	42	35	u	u	NOUN
ejpam-3985	42	36	∈	∈	PROPN
ejpam-3985	42	37	v	v	NOUN
ejpam-3985	42	38	(	(	PUNCT
ejpam-3985	42	39	g	g	NOUN
ejpam-3985	42	40	)	)	PUNCT
ejpam-3985	42	41	\	\	PUNCT
ejpam-3985	43	1	s.	s.	PROPN
ejpam-3985	43	2	the	the	DET
ejpam-3985	43	3	strictly	strictly	ADV
ejpam-3985	43	4	resolving	resolve	VERB
ejpam-3985	43	5	dominating	dominating	NOUN
ejpam-3985	43	6	number	number	NOUN
ejpam-3985	43	7	of	of	ADP
ejpam-3985	43	8	g	g	NOUN
ejpam-3985	43	9	,	,	PUNCT
ejpam-3985	43	10	denoted	denote	VERB
ejpam-3985	43	11	by	by	ADP
ejpam-3985	43	12	γsr(g	γsr(g	PROPN
ejpam-3985	43	13	)	)	PUNCT
ejpam-3985	43	14	,	,	PUNCT
ejpam-3985	43	15	is	be	AUX
ejpam-3985	43	16	the	the	DET
ejpam-3985	43	17	smallest	small	ADJ
ejpam-3985	43	18	cardinality	cardinality	NOUN
ejpam-3985	43	19	of	of	ADP
ejpam-3985	43	20	a	a	DET
ejpam-3985	43	21	strictly	strictly	ADV
ejpam-3985	43	22	resolving	resolve	VERB
ejpam-3985	43	23	dominating	dominating	NOUN
ejpam-3985	43	24	set	set	NOUN
ejpam-3985	43	25	of	of	ADP
ejpam-3985	43	26	g.	g.	PROPN
ejpam-3985	43	27	a	a	DET
ejpam-3985	43	28	strictly	strictly	ADV
ejpam-3985	43	29	resolving	resolve	VERB
ejpam-3985	43	30	dominating	dominating	NOUN
ejpam-3985	43	31	set	set	NOUN
ejpam-3985	43	32	of	of	ADP
ejpam-3985	43	33	g	g	NOUN
ejpam-3985	43	34	of	of	ADP
ejpam-3985	43	35	cardinality	cardinality	PROPN
ejpam-3985	43	36	γsr(g	γsr(g	NOUN
ejpam-3985	43	37	)	)	PUNCT
ejpam-3985	43	38	is	be	AUX
ejpam-3985	43	39	referred	refer	VERB
ejpam-3985	43	40	to	to	ADP
ejpam-3985	43	41	as	as	SCONJ
ejpam-3985	43	42	γsr	γsr	PROPN
ejpam-3985	43	43	-	-	PUNCT
ejpam-3985	43	44	set	set	NOUN
ejpam-3985	43	45	of	of	ADP
ejpam-3985	43	46	g.	g.	PROPN
ejpam-3985	43	47	let	let	VERB
ejpam-3985	43	48	g	g	PROPN
ejpam-3985	43	49	=	=	SYM
ejpam-3985	43	50	(	(	PUNCT
ejpam-3985	43	51	v	v	NOUN
ejpam-3985	43	52	(	(	PUNCT
ejpam-3985	43	53	g	g	NOUN
ejpam-3985	43	54	)	)	PUNCT
ejpam-3985	43	55	,	,	PUNCT
ejpam-3985	43	56	e(g	e(g	PROPN
ejpam-3985	43	57	)	)	PUNCT
ejpam-3985	43	58	)	)	PUNCT
ejpam-3985	43	59	be	be	AUX
ejpam-3985	43	60	a	a	DET
ejpam-3985	43	61	graph	graph	NOUN
ejpam-3985	43	62	.	.	PUNCT
ejpam-3985	44	1	a	a	DET
ejpam-3985	44	2	set	set	NOUN
ejpam-3985	44	3	s	s	NOUN
ejpam-3985	44	4	⊆	⊆	NUM
ejpam-3985	44	5	v	v	NOUN
ejpam-3985	44	6	(	(	PUNCT
ejpam-3985	44	7	g	g	NOUN
ejpam-3985	44	8	)	)	PUNCT
ejpam-3985	44	9	is	be	AUX
ejpam-3985	44	10	a	a	DET
ejpam-3985	44	11	restrained	restrained	ADJ
ejpam-3985	44	12	dominating	dominating	NOUN
ejpam-3985	44	13	set	set	NOUN
ejpam-3985	44	14	of	of	ADP
ejpam-3985	44	15	g	g	PROPN
ejpam-3985	44	16	if	if	SCONJ
ejpam-3985	44	17	s	s	VERB
ejpam-3985	44	18	is	be	AUX
ejpam-3985	44	19	a	a	DET
ejpam-3985	44	20	dominating	dominating	NOUN
ejpam-3985	44	21	set	set	NOUN
ejpam-3985	44	22	of	of	ADP
ejpam-3985	44	23	g	g	PROPN
ejpam-3985	44	24	and	and	CCONJ
ejpam-3985	44	25	for	for	ADP
ejpam-3985	44	26	every	every	DET
ejpam-3985	44	27	v	v	NUM
ejpam-3985	44	28	∈	∈	NOUN
ejpam-3985	44	29	v	v	NOUN
ejpam-3985	44	30	(	(	PUNCT
ejpam-3985	44	31	g)\s	g)\s	NOUN
ejpam-3985	44	32	there	there	ADV
ejpam-3985	44	33	exists	exist	VERB
ejpam-3985	44	34	u	u	PROPN
ejpam-3985	44	35	∈	∈	PROPN
ejpam-3985	44	36	(	(	PUNCT
ejpam-3985	44	37	v	v	NOUN
ejpam-3985	44	38	(	(	PUNCT
ejpam-3985	44	39	g)\s)∩ng(v	g)\s)∩ng(v	NOUN
ejpam-3985	44	40	)	)	PUNCT
ejpam-3985	44	41	.	.	PUNCT
ejpam-3985	45	1	equivalently	equivalently	ADV
ejpam-3985	45	2	,	,	PUNCT
ejpam-3985	45	3	a	a	DET
ejpam-3985	45	4	dominating	dominating	NOUN
ejpam-3985	45	5	subset	subset	NOUN
ejpam-3985	45	6	s	s	PROPN
ejpam-3985	45	7	of	of	ADP
ejpam-3985	45	8	v	v	NOUN
ejpam-3985	45	9	(	(	PUNCT
ejpam-3985	45	10	g	g	NOUN
ejpam-3985	45	11	)	)	PUNCT
ejpam-3985	45	12	is	be	AUX
ejpam-3985	45	13	a	a	DET
ejpam-3985	45	14	restrained	restrained	ADJ
ejpam-3985	45	15	dominating	dominating	NOUN
ejpam-3985	45	16	set	set	NOUN
ejpam-3985	45	17	of	of	ADP
ejpam-3985	45	18	g	g	PROPN
ejpam-3985	45	19	if	if	SCONJ
ejpam-3985	45	20	s	s	VERB
ejpam-3985	45	21	=	=	SYM
ejpam-3985	45	22	v	v	X
ejpam-3985	45	23	(	(	PUNCT
ejpam-3985	45	24	g	g	NOUN
ejpam-3985	45	25	)	)	PUNCT
ejpam-3985	45	26	or	or	CCONJ
ejpam-3985	45	27	〈	〈	PROPN
ejpam-3985	45	28	v	v	X
ejpam-3985	45	29	(	(	PUNCT
ejpam-3985	45	30	g	g	NOUN
ejpam-3985	45	31	)	)	PUNCT
ejpam-3985	45	32	\	\	PUNCT
ejpam-3985	46	1	s	s	VERB
ejpam-3985	46	2	〉	〉	NOUN
ejpam-3985	46	3	has	have	VERB
ejpam-3985	46	4	no	no	DET
ejpam-3985	46	5	isolated	isolated	ADJ
ejpam-3985	46	6	vertex	vertex	NOUN
ejpam-3985	46	7	.	.	PUNCT
ejpam-3985	47	1	the	the	DET
ejpam-3985	47	2	restrained	restrained	ADJ
ejpam-3985	47	3	domination	domination	NOUN
ejpam-3985	47	4	number	number	NOUN
ejpam-3985	47	5	of	of	ADP
ejpam-3985	47	6	g	g	NOUN
ejpam-3985	47	7	,	,	PUNCT
ejpam-3985	47	8	denoted	denote	VERB
ejpam-3985	47	9	by	by	ADP
ejpam-3985	47	10	γr(g	γr(g	PROPN
ejpam-3985	47	11	)	)	PUNCT
ejpam-3985	47	12	is	be	AUX
ejpam-3985	47	13	the	the	DET
ejpam-3985	47	14	minimum	minimum	ADJ
ejpam-3985	47	15	cardinality	cardinality	NOUN
ejpam-3985	47	16	of	of	ADP
ejpam-3985	47	17	a	a	DET
ejpam-3985	47	18	restrained	restrained	ADJ
ejpam-3985	47	19	dominating	dominating	NOUN
ejpam-3985	47	20	set	set	NOUN
ejpam-3985	47	21	of	of	ADP
ejpam-3985	47	22	g.	g.	PROPN
ejpam-3985	47	23	any	any	DET
ejpam-3985	47	24	restrained	restrain	VERB
ejpam-3985	47	25	dominating	dominating	NOUN
ejpam-3985	47	26	set	set	NOUN
ejpam-3985	47	27	of	of	ADP
ejpam-3985	47	28	g	g	PROPN
ejpam-3985	47	29	of	of	ADP
ejpam-3985	47	30	cardinality	cardinality	PROPN
ejpam-3985	47	31	γr(g	γr(g	PROPN
ejpam-3985	47	32	)	)	PUNCT
ejpam-3985	47	33	is	be	AUX
ejpam-3985	47	34	referred	refer	VERB
ejpam-3985	47	35	to	to	ADP
ejpam-3985	47	36	as	as	SCONJ
ejpam-3985	47	37	a	a	DET
ejpam-3985	47	38	γr	γr	PROPN
ejpam-3985	47	39	-	-	PUNCT
ejpam-3985	47	40	set	set	NOUN
ejpam-3985	47	41	of	of	ADP
ejpam-3985	47	42	g.	g.	PROPN
ejpam-3985	47	43	let	let	VERB
ejpam-3985	47	44	g	g	NOUN
ejpam-3985	47	45	be	be	AUX
ejpam-3985	47	46	a	a	DET
ejpam-3985	47	47	connected	connected	ADJ
ejpam-3985	47	48	graph	graph	NOUN
ejpam-3985	47	49	.	.	PUNCT
ejpam-3985	48	1	a	a	DET
ejpam-3985	48	2	set	set	NOUN
ejpam-3985	48	3	s	s	NOUN
ejpam-3985	48	4	⊆	⊆	NUM
ejpam-3985	48	5	v	v	NOUN
ejpam-3985	48	6	(	(	PUNCT
ejpam-3985	48	7	g	g	NOUN
ejpam-3985	48	8	)	)	PUNCT
ejpam-3985	48	9	is	be	AUX
ejpam-3985	48	10	a	a	DET
ejpam-3985	48	11	resolving	resolve	VERB
ejpam-3985	48	12	restrained	restrained	ADJ
ejpam-3985	48	13	dominating	dominating	NOUN
ejpam-3985	48	14	set	set	NOUN
ejpam-3985	48	15	of	of	ADP
ejpam-3985	48	16	g	g	PROPN
ejpam-3985	48	17	if	if	SCONJ
ejpam-3985	48	18	s	s	VERB
ejpam-3985	48	19	is	be	AUX
ejpam-3985	48	20	a	a	DET
ejpam-3985	48	21	resolving	resolve	VERB
ejpam-3985	48	22	dominating	dominating	NOUN
ejpam-3985	48	23	set	set	NOUN
ejpam-3985	48	24	of	of	ADP
ejpam-3985	48	25	g	g	PROPN
ejpam-3985	48	26	and	and	CCONJ
ejpam-3985	48	27	s	s	PART
ejpam-3985	48	28	=	=	SYM
ejpam-3985	48	29	v	v	X
ejpam-3985	48	30	(	(	PUNCT
ejpam-3985	48	31	g	g	NOUN
ejpam-3985	48	32	)	)	PUNCT
ejpam-3985	48	33	or	or	CCONJ
ejpam-3985	48	34	〈	〈	PROPN
ejpam-3985	48	35	v	v	X
ejpam-3985	48	36	(	(	PUNCT
ejpam-3985	48	37	g	g	NOUN
ejpam-3985	48	38	)	)	PUNCT
ejpam-3985	48	39	\	\	PUNCT
ejpam-3985	49	1	s	s	VERB
ejpam-3985	49	2	〉	〉	NOUN
ejpam-3985	49	3	has	have	VERB
ejpam-3985	49	4	no	no	DET
ejpam-3985	49	5	isolated	isolated	ADJ
ejpam-3985	49	6	vertex	vertex	NOUN
ejpam-3985	49	7	.	.	PUNCT
ejpam-3985	50	1	the	the	DET
ejpam-3985	50	2	resolving	resolve	VERB
ejpam-3985	50	3	restrained	restrained	ADJ
ejpam-3985	50	4	domination	domination	NOUN
ejpam-3985	50	5	number	number	NOUN
ejpam-3985	50	6	of	of	ADP
ejpam-3985	50	7	g	g	NOUN
ejpam-3985	50	8	,	,	PUNCT
ejpam-3985	50	9	denoted	denote	VERB
ejpam-3985	50	10	by	by	ADP
ejpam-3985	50	11	γrr(g	γrr(g	PROPN
ejpam-3985	50	12	)	)	PUNCT
ejpam-3985	50	13	is	be	AUX
ejpam-3985	50	14	the	the	DET
ejpam-3985	50	15	smallest	small	ADJ
ejpam-3985	50	16	cardinality	cardinality	NOUN
ejpam-3985	50	17	of	of	ADP
ejpam-3985	50	18	a	a	DET
ejpam-3985	50	19	resolving	resolve	VERB
ejpam-3985	50	20	restrained	restrained	ADJ
ejpam-3985	50	21	dominating	dominating	NOUN
ejpam-3985	50	22	set	set	NOUN
ejpam-3985	50	23	of	of	ADP
ejpam-3985	50	24	g.	g.	PROPN
ejpam-3985	50	25	any	any	DET
ejpam-3985	50	26	resolving	resolve	VERB
ejpam-3985	50	27	restrained	restrained	ADJ
ejpam-3985	50	28	dominating	dominating	NOUN
ejpam-3985	50	29	set	set	NOUN
ejpam-3985	50	30	of	of	ADP
ejpam-3985	50	31	cardinality	cardinality	PROPN
ejpam-3985	50	32	γrr(g	γrr(g	PROPN
ejpam-3985	50	33	)	)	PUNCT
ejpam-3985	50	34	is	be	AUX
ejpam-3985	50	35	referred	refer	VERB
ejpam-3985	50	36	to	to	ADP
ejpam-3985	50	37	as	as	ADP
ejpam-3985	50	38	a	a	DET
ejpam-3985	50	39	γrr	γrr	NOUN
ejpam-3985	50	40	-	-	PUNCT
ejpam-3985	50	41	set	set	NOUN
ejpam-3985	50	42	of	of	ADP
ejpam-3985	50	43	g.	g.	PROPN
ejpam-3985	50	44	omega	omega	NOUN
ejpam-3985	50	45	and	and	CCONJ
ejpam-3985	50	46	canoy	canoy	ADJ
ejpam-3985	51	1	[	[	X
ejpam-3985	51	2	11	11	NUM
ejpam-3985	51	3	]	]	PUNCT
ejpam-3985	51	4	defined	define	VERB
ejpam-3985	51	5	a	a	DET
ejpam-3985	51	6	locating	locate	VERB
ejpam-3985	51	7	set	set	NOUN
ejpam-3985	51	8	of	of	ADP
ejpam-3985	51	9	g	g	PROPN
ejpam-3985	51	10	as	as	ADP
ejpam-3985	51	11	a	a	DET
ejpam-3985	51	12	set	set	NOUN
ejpam-3985	51	13	s	s	NOUN
ejpam-3985	51	14	⊆	⊆	NUM
ejpam-3985	51	15	v	v	NOUN
ejpam-3985	51	16	(	(	PUNCT
ejpam-3985	51	17	g	g	NOUN
ejpam-3985	51	18	)	)	PUNCT
ejpam-3985	51	19	if	if	SCONJ
ejpam-3985	51	20	for	for	ADP
ejpam-3985	51	21	every	every	DET
ejpam-3985	51	22	two	two	NUM
ejpam-3985	51	23	distinct	distinct	ADJ
ejpam-3985	51	24	vertices	vertex	NOUN
ejpam-3985	51	25	u	u	NOUN
ejpam-3985	51	26	and	and	CCONJ
ejpam-3985	51	27	v	v	NOUN
ejpam-3985	51	28	of	of	ADP
ejpam-3985	51	29	v	v	NOUN
ejpam-3985	51	30	(	(	PUNCT
ejpam-3985	51	31	g	g	NOUN
ejpam-3985	51	32	)	)	PUNCT
ejpam-3985	51	33	\	\	PROPN
ejpam-3985	52	1	s	s	PROPN
ejpam-3985	52	2	,	,	PUNCT
ejpam-3985	52	3	ng(u	ng(u	NOUN
ejpam-3985	52	4	)	)	PUNCT
ejpam-3985	52	5	∩	∩	X
ejpam-3985	52	6	s	s	PART
ejpam-3985	52	7	6=	6=	NUM
ejpam-3985	52	8	ng(v	ng(v	NUM
ejpam-3985	52	9	)	)	PUNCT
ejpam-3985	52	10	∩	∩	NOUN
ejpam-3985	52	11	s	s	PART
ejpam-3985	52	12	.	.	PUNCT
ejpam-3985	53	1	the	the	DET
ejpam-3985	53	2	locating	locate	VERB
ejpam-3985	53	3	number	number	NOUN
ejpam-3985	53	4	of	of	ADP
ejpam-3985	53	5	g	g	NOUN
ejpam-3985	53	6	,	,	PUNCT
ejpam-3985	53	7	denoted	denote	VERB
ejpam-3985	53	8	by	by	ADP
ejpam-3985	53	9	ln(g	ln(g	NOUN
ejpam-3985	53	10	)	)	PUNCT
ejpam-3985	53	11	,	,	PUNCT
ejpam-3985	53	12	is	be	AUX
ejpam-3985	53	13	the	the	DET
ejpam-3985	53	14	smallest	small	ADJ
ejpam-3985	53	15	cardinality	cardinality	NOUN
ejpam-3985	53	16	of	of	ADP
ejpam-3985	53	17	a	a	DET
ejpam-3985	53	18	locating	locating	NOUN
ejpam-3985	53	19	set	set	NOUN
ejpam-3985	53	20	of	of	ADP
ejpam-3985	53	21	g.	g.	PROPN
ejpam-3985	53	22	a	a	DET
ejpam-3985	53	23	locating	locate	VERB
ejpam-3985	53	24	set	set	NOUN
ejpam-3985	53	25	of	of	ADP
ejpam-3985	53	26	g	g	PROPN
ejpam-3985	53	27	of	of	ADP
ejpam-3985	53	28	cardinality	cardinality	PROPN
ejpam-3985	53	29	ln(g	ln(g	PUNCT
ejpam-3985	53	30	)	)	PUNCT
ejpam-3985	53	31	is	be	AUX
ejpam-3985	53	32	referred	refer	VERB
ejpam-3985	53	33	to	to	ADP
ejpam-3985	53	34	as	as	ADP
ejpam-3985	53	35	ln	ln	ADV
ejpam-3985	53	36	-	-	PUNCT
ejpam-3985	53	37	set	set	NOUN
ejpam-3985	53	38	of	of	ADP
ejpam-3985	53	39	g.	g.	PROPN
ejpam-3985	53	40	canoy	canoy	PROPN
ejpam-3985	53	41	and	and	CCONJ
ejpam-3985	53	42	malacas	malacas	NOUN
ejpam-3985	54	1	[	[	X
ejpam-3985	54	2	14	14	NUM
ejpam-3985	54	3	]	]	PUNCT
ejpam-3985	54	4	defined	define	VERB
ejpam-3985	54	5	a	a	DET
ejpam-3985	54	6	locating	locating	NOUN
ejpam-3985	54	7	(	(	PUNCT
ejpam-3985	54	8	resp	resp	NOUN
ejpam-3985	54	9	.	.	PUNCT
ejpam-3985	55	1	strictly	strictly	ADV
ejpam-3985	55	2	locating	locate	VERB
ejpam-3985	55	3	)	)	PUNCT
ejpam-3985	55	4	subset	subset	NOUN
ejpam-3985	55	5	s	s	PROPN
ejpam-3985	55	6	of	of	ADP
ejpam-3985	55	7	v	v	NOUN
ejpam-3985	55	8	(	(	PUNCT
ejpam-3985	55	9	g	g	NOUN
ejpam-3985	55	10	)	)	PUNCT
ejpam-3985	55	11	which	which	PRON
ejpam-3985	55	12	is	be	AUX
ejpam-3985	55	13	also	also	ADV
ejpam-3985	55	14	dominating	dominate	VERB
ejpam-3985	55	15	is	be	AUX
ejpam-3985	55	16	called	call	VERB
ejpam-3985	55	17	a	a	DET
ejpam-3985	55	18	locating	locate	VERB
ejpam-3985	55	19	-	-	PUNCT
ejpam-3985	55	20	dominating	dominate	VERB
ejpam-3985	55	21	(	(	PUNCT
ejpam-3985	55	22	resp	resp	NOUN
ejpam-3985	55	23	.	.	PUNCT
ejpam-3985	56	1	strictly	strictly	ADV
ejpam-3985	56	2	locating	locate	VERB
ejpam-3985	56	3	-	-	PUNCT
ejpam-3985	56	4	dominating	dominating	NOUN
ejpam-3985	56	5	)	)	PUNCT
ejpam-3985	56	6	set	set	VERB
ejpam-3985	56	7	in	in	ADP
ejpam-3985	56	8	a	a	DET
ejpam-3985	56	9	connected	connected	ADJ
ejpam-3985	56	10	graph	graph	NOUN
ejpam-3985	56	11	g.	g.	VERB
ejpam-3985	56	12	the	the	DET
ejpam-3985	56	13	minimum	minimum	ADJ
ejpam-3985	56	14	cardinality	cardinality	NOUN
ejpam-3985	56	15	of	of	ADP
ejpam-3985	56	16	a	a	DET
ejpam-3985	56	17	locating	locate	VERB
ejpam-3985	56	18	-	-	PUNCT
ejpam-3985	56	19	dominating	dominate	VERB
ejpam-3985	56	20	(	(	PUNCT
ejpam-3985	56	21	resp	resp	NOUN
ejpam-3985	56	22	.	.	PUNCT
ejpam-3985	57	1	strictly	strictly	ADV
ejpam-3985	57	2	locating	locate	VERB
ejpam-3985	57	3	-	-	PUNCT
ejpam-3985	57	4	dominating	dominating	NOUN
ejpam-3985	57	5	)	)	PUNCT
ejpam-3985	57	6	set	set	VERB
ejpam-3985	57	7	in	in	ADP
ejpam-3985	57	8	g	g	NOUN
ejpam-3985	57	9	,	,	PUNCT
ejpam-3985	57	10	denoted	denote	VERB
ejpam-3985	57	11	by	by	ADP
ejpam-3985	57	12	γl(g	γl(g	NUM
ejpam-3985	57	13	)	)	PUNCT
ejpam-3985	57	14	(	(	PUNCT
ejpam-3985	57	15	resp	resp	NOUN
ejpam-3985	57	16	.	.	PUNCT
ejpam-3985	58	1	γsl(g	γsl(g	X
ejpam-3985	58	2	)	)	PUNCT
ejpam-3985	58	3	)	)	PUNCT
ejpam-3985	59	1	,	,	PUNCT
ejpam-3985	59	2	is	be	AUX
ejpam-3985	59	3	called	call	VERB
ejpam-3985	59	4	the	the	DET
ejpam-3985	59	5	l	l	NOUN
ejpam-3985	59	6	-	-	NOUN
ejpam-3985	59	7	domination	domination	NOUN
ejpam-3985	59	8	(	(	PUNCT
ejpam-3985	59	9	resp	resp	NOUN
ejpam-3985	59	10	.	.	PUNCT
ejpam-3985	60	1	sl	sl	NOUN
ejpam-3985	60	2	-	-	PUNCT
ejpam-3985	60	3	domination	domination	NOUN
ejpam-3985	60	4	)	)	PUNCT
ejpam-3985	60	5	number	number	NOUN
ejpam-3985	60	6	of	of	ADP
ejpam-3985	60	7	g.	g.	PROPN
ejpam-3985	60	8	any	any	DET
ejpam-3985	60	9	l	l	NOUN
ejpam-3985	60	10	-	-	ADJ
ejpam-3985	60	11	dominating	dominate	VERB
ejpam-3985	60	12	(	(	PUNCT
ejpam-3985	60	13	resp	resp	NOUN
ejpam-3985	60	14	.	.	PUNCT
ejpam-3985	61	1	sldominating	sldominating	NOUN
ejpam-3985	61	2	)	)	PUNCT
ejpam-3985	61	3	set	set	NOUN
ejpam-3985	61	4	of	of	ADP
ejpam-3985	61	5	cardinality	cardinality	PROPN
ejpam-3985	61	6	γl(g	γl(g	NUM
ejpam-3985	61	7	)	)	PUNCT
ejpam-3985	61	8	(	(	PUNCT
ejpam-3985	61	9	resp	resp	NOUN
ejpam-3985	61	10	.	.	PUNCT
ejpam-3985	62	1	γsl(g	γsl(g	X
ejpam-3985	62	2	)	)	PUNCT
ejpam-3985	62	3	)	)	PUNCT
ejpam-3985	63	1	is	be	AUX
ejpam-3985	63	2	then	then	ADV
ejpam-3985	63	3	referred	refer	VERB
ejpam-3985	63	4	to	to	ADP
ejpam-3985	63	5	as	as	ADP
ejpam-3985	63	6	a	a	DET
ejpam-3985	63	7	γl	γl	NOUN
ejpam-3985	63	8	-	-	PUNCT
ejpam-3985	63	9	set	set	VERB
ejpam-3985	63	10	(	(	PUNCT
ejpam-3985	63	11	γsl	γsl	NOUN
ejpam-3985	63	12	-	-	PUNCT
ejpam-3985	63	13	set	set	NOUN
ejpam-3985	63	14	)	)	PUNCT
ejpam-3985	63	15	of	of	ADP
ejpam-3985	63	16	g.	g.	PROPN
ejpam-3985	63	17	let	let	VERB
ejpam-3985	63	18	g	g	NOUN
ejpam-3985	63	19	be	be	AUX
ejpam-3985	63	20	a	a	DET
ejpam-3985	63	21	connected	connected	ADJ
ejpam-3985	63	22	graph	graph	NOUN
ejpam-3985	63	23	.	.	PUNCT
ejpam-3985	64	1	a	a	DET
ejpam-3985	64	2	set	set	NOUN
ejpam-3985	64	3	s	s	NOUN
ejpam-3985	64	4	⊆	⊆	NUM
ejpam-3985	64	5	v	v	NOUN
ejpam-3985	64	6	(	(	PUNCT
ejpam-3985	64	7	g	g	NOUN
ejpam-3985	64	8	)	)	PUNCT
ejpam-3985	64	9	is	be	AUX
ejpam-3985	64	10	a	a	DET
ejpam-3985	64	11	strictly	strictly	ADV
ejpam-3985	64	12	locating	locate	VERB
ejpam-3985	64	13	set	set	NOUN
ejpam-3985	64	14	of	of	ADP
ejpam-3985	64	15	g	g	NOUN
ejpam-3985	64	16	if	if	SCONJ
ejpam-3985	64	17	it	it	PRON
ejpam-3985	64	18	is	be	AUX
ejpam-3985	64	19	a	a	DET
ejpam-3985	64	20	locating	locating	NOUN
ejpam-3985	64	21	set	set	NOUN
ejpam-3985	64	22	of	of	ADP
ejpam-3985	64	23	g	g	PROPN
ejpam-3985	64	24	and	and	CCONJ
ejpam-3985	64	25	ng(u)∩s	ng(u)∩s	PROPN
ejpam-3985	64	26	6=	6=	PROPN
ejpam-3985	64	27	s	s	X
ejpam-3985	64	28	for	for	ADP
ejpam-3985	64	29	all	all	DET
ejpam-3985	64	30	u	u	NOUN
ejpam-3985	64	31	∈	∈	PROPN
ejpam-3985	64	32	v	v	NOUN
ejpam-3985	64	33	(	(	PUNCT
ejpam-3985	64	34	g	g	NOUN
ejpam-3985	64	35	)	)	PUNCT
ejpam-3985	64	36	\s	\s	NOUN
ejpam-3985	64	37	.	.	PUNCT
ejpam-3985	65	1	the	the	DET
ejpam-3985	65	2	strictly	strictly	ADV
ejpam-3985	65	3	locating	locate	VERB
ejpam-3985	65	4	number	number	NOUN
ejpam-3985	65	5	of	of	ADP
ejpam-3985	65	6	g.	g.	PROPN
ejpam-3985	65	7	monsanto	monsanto	PROPN
ejpam-3985	65	8	,	,	PUNCT
ejpam-3985	65	9	h.	h.	PROPN
ejpam-3985	65	10	rara	rara	PROPN
ejpam-3985	65	11	/	/	SYM
ejpam-3985	65	12	eur	eur	PROPN
ejpam-3985	65	13	.	.	PUNCT
ejpam-3985	66	1	j.	j.	PROPN
ejpam-3985	66	2	pure	pure	PROPN
ejpam-3985	66	3	appl	appl	PROPN
ejpam-3985	66	4	.	.	PROPN
ejpam-3985	66	5	math	math	PROPN
ejpam-3985	66	6	,	,	PUNCT
ejpam-3985	66	7	14	14	NUM
ejpam-3985	66	8	(	(	PUNCT
ejpam-3985	66	9	3	3	NUM
ejpam-3985	66	10	)	)	PUNCT
ejpam-3985	66	11	(	(	PUNCT
ejpam-3985	66	12	2021	2021	NUM
ejpam-3985	66	13	)	)	PUNCT
ejpam-3985	66	14	,	,	PUNCT
ejpam-3985	66	15	829	829	NUM
ejpam-3985	66	16	-	-	SYM
ejpam-3985	66	17	841	841	NUM
ejpam-3985	66	18	831	831	NUM
ejpam-3985	66	19	g	g	NOUN
ejpam-3985	66	20	,	,	PUNCT
ejpam-3985	66	21	denoted	denote	VERB
ejpam-3985	66	22	by	by	ADP
ejpam-3985	66	23	sln(g	sln(g	PROPN
ejpam-3985	66	24	)	)	PUNCT
ejpam-3985	66	25	,	,	PUNCT
ejpam-3985	66	26	is	be	AUX
ejpam-3985	66	27	the	the	DET
ejpam-3985	66	28	smallest	small	ADJ
ejpam-3985	66	29	cardinality	cardinality	NOUN
ejpam-3985	66	30	of	of	ADP
ejpam-3985	66	31	a	a	DET
ejpam-3985	66	32	strictly	strictly	ADV
ejpam-3985	66	33	locating	locate	VERB
ejpam-3985	66	34	set	set	NOUN
ejpam-3985	66	35	of	of	ADP
ejpam-3985	66	36	g.	g.	PROPN
ejpam-3985	66	37	a	a	DET
ejpam-3985	66	38	strictly	strictly	ADV
ejpam-3985	66	39	locating	locate	VERB
ejpam-3985	66	40	set	set	NOUN
ejpam-3985	66	41	of	of	ADP
ejpam-3985	66	42	g	g	PROPN
ejpam-3985	66	43	of	of	ADP
ejpam-3985	66	44	cardinality	cardinality	PROPN
ejpam-3985	66	45	sln(g	sln(g	PROPN
ejpam-3985	66	46	)	)	PUNCT
ejpam-3985	66	47	is	be	AUX
ejpam-3985	66	48	referred	refer	VERB
ejpam-3985	66	49	to	to	ADP
ejpam-3985	66	50	as	as	SCONJ
ejpam-3985	66	51	a	a	DET
ejpam-3985	66	52	sln	sln	NOUN
ejpam-3985	66	53	-	-	PUNCT
ejpam-3985	66	54	set	set	NOUN
ejpam-3985	66	55	of	of	ADP
ejpam-3985	66	56	g.	g.	PROPN
ejpam-3985	66	57	let	let	VERB
ejpam-3985	66	58	g	g	NOUN
ejpam-3985	66	59	be	be	AUX
ejpam-3985	66	60	a	a	DET
ejpam-3985	66	61	connected	connected	ADJ
ejpam-3985	66	62	graph	graph	NOUN
ejpam-3985	66	63	.	.	PUNCT
ejpam-3985	67	1	a	a	DET
ejpam-3985	67	2	set	set	NOUN
ejpam-3985	67	3	s	s	NOUN
ejpam-3985	67	4	⊆	⊆	NUM
ejpam-3985	67	5	v	v	NOUN
ejpam-3985	67	6	(	(	PUNCT
ejpam-3985	67	7	g	g	NOUN
ejpam-3985	67	8	)	)	PUNCT
ejpam-3985	67	9	is	be	AUX
ejpam-3985	67	10	a	a	DET
ejpam-3985	67	11	restrained	restrained	ADJ
ejpam-3985	67	12	locating	locating	NOUN
ejpam-3985	67	13	set	set	NOUN
ejpam-3985	67	14	of	of	ADP
ejpam-3985	67	15	g	g	PROPN
ejpam-3985	67	16	if	if	SCONJ
ejpam-3985	67	17	s	s	VERB
ejpam-3985	67	18	is	be	AUX
ejpam-3985	67	19	a	a	DET
ejpam-3985	67	20	locating	locating	NOUN
ejpam-3985	67	21	set	set	NOUN
ejpam-3985	67	22	of	of	ADP
ejpam-3985	67	23	g	g	PROPN
ejpam-3985	67	24	and	and	CCONJ
ejpam-3985	67	25	s	s	PART
ejpam-3985	67	26	=	=	SYM
ejpam-3985	67	27	v	v	X
ejpam-3985	67	28	(	(	PUNCT
ejpam-3985	67	29	g	g	NOUN
ejpam-3985	67	30	)	)	PUNCT
ejpam-3985	67	31	or	or	CCONJ
ejpam-3985	67	32	〈	〈	PROPN
ejpam-3985	67	33	v	v	X
ejpam-3985	67	34	(	(	PUNCT
ejpam-3985	67	35	g	g	NOUN
ejpam-3985	67	36	)	)	PUNCT
ejpam-3985	67	37	\	\	PUNCT
ejpam-3985	68	1	s	s	VERB
ejpam-3985	68	2	〉	〉	NOUN
ejpam-3985	68	3	has	have	VERB
ejpam-3985	68	4	no	no	DET
ejpam-3985	68	5	isolated	isolated	ADJ
ejpam-3985	68	6	vertex	vertex	NOUN
ejpam-3985	68	7	.	.	PUNCT
ejpam-3985	69	1	the	the	DET
ejpam-3985	69	2	restrained	restrained	ADJ
ejpam-3985	69	3	locating	locating	NOUN
ejpam-3985	69	4	number	number	NOUN
ejpam-3985	69	5	of	of	ADP
ejpam-3985	69	6	g	g	NOUN
ejpam-3985	69	7	,	,	PUNCT
ejpam-3985	69	8	denoted	denote	VERB
ejpam-3985	69	9	rln(g	rln(g	NOUN
ejpam-3985	69	10	)	)	PUNCT
ejpam-3985	69	11	,	,	PUNCT
ejpam-3985	69	12	is	be	AUX
ejpam-3985	69	13	the	the	DET
ejpam-3985	69	14	smallest	small	ADJ
ejpam-3985	69	15	cardinality	cardinality	NOUN
ejpam-3985	69	16	of	of	ADP
ejpam-3985	69	17	a	a	DET
ejpam-3985	69	18	restrained	restrained	ADJ
ejpam-3985	69	19	locating	locating	NOUN
ejpam-3985	69	20	set	set	NOUN
ejpam-3985	69	21	of	of	ADP
ejpam-3985	69	22	g.	g.	PROPN
ejpam-3985	69	23	a	a	DET
ejpam-3985	69	24	restrained	restrained	ADJ
ejpam-3985	69	25	locating	locating	NOUN
ejpam-3985	69	26	set	set	NOUN
ejpam-3985	69	27	of	of	ADP
ejpam-3985	69	28	cardinality	cardinality	NOUN
ejpam-3985	69	29	rln(g	rln(g	NOUN
ejpam-3985	69	30	)	)	PUNCT
ejpam-3985	69	31	is	be	AUX
ejpam-3985	69	32	then	then	ADV
ejpam-3985	69	33	referred	refer	VERB
ejpam-3985	69	34	to	to	ADP
ejpam-3985	69	35	as	as	ADP
ejpam-3985	69	36	rln	rln	NOUN
ejpam-3985	69	37	-	-	PUNCT
ejpam-3985	69	38	set	set	NOUN
ejpam-3985	69	39	of	of	ADP
ejpam-3985	69	40	g.	g.	PROPN
ejpam-3985	69	41	a	a	DET
ejpam-3985	69	42	connected	connected	ADJ
ejpam-3985	69	43	graph	graph	NOUN
ejpam-3985	69	44	g	g	NOUN
ejpam-3985	69	45	of	of	ADP
ejpam-3985	69	46	order	order	NOUN
ejpam-3985	69	47	n	n	PRON
ejpam-3985	69	48	≥	≥	NOUN
ejpam-3985	69	49	3	3	NUM
ejpam-3985	69	50	is	be	AUX
ejpam-3985	69	51	point	point	NOUN
ejpam-3985	69	52	distinguishing	distinguish	VERB
ejpam-3985	69	53	if	if	SCONJ
ejpam-3985	69	54	for	for	ADP
ejpam-3985	69	55	any	any	DET
ejpam-3985	69	56	two	two	NUM
ejpam-3985	69	57	distinct	distinct	ADJ
ejpam-3985	69	58	vertices	vertex	NOUN
ejpam-3985	69	59	u	u	NOUN
ejpam-3985	69	60	and	and	CCONJ
ejpam-3985	69	61	v	v	NOUN
ejpam-3985	69	62	of	of	ADP
ejpam-3985	69	63	g	g	NOUN
ejpam-3985	69	64	,	,	PUNCT
ejpam-3985	69	65	ng[u	ng[u	PROPN
ejpam-3985	69	66	]	]	PUNCT
ejpam-3985	69	67	6=	6=	PUNCT
ejpam-3985	70	1	ng[v	ng[v	NOUN
ejpam-3985	70	2	]	]	PUNCT
ejpam-3985	70	3	.	.	PUNCT
ejpam-3985	71	1	it	it	PRON
ejpam-3985	71	2	is	be	AUX
ejpam-3985	71	3	totally	totally	ADV
ejpam-3985	71	4	point	point	NOUN
ejpam-3985	71	5	determining	determine	VERB
ejpam-3985	71	6	if	if	SCONJ
ejpam-3985	71	7	for	for	ADP
ejpam-3985	71	8	any	any	DET
ejpam-3985	71	9	two	two	NUM
ejpam-3985	71	10	distinct	distinct	ADJ
ejpam-3985	71	11	vertices	vertex	NOUN
ejpam-3985	71	12	u	u	NOUN
ejpam-3985	71	13	and	and	CCONJ
ejpam-3985	71	14	v	v	NOUN
ejpam-3985	71	15	of	of	ADP
ejpam-3985	71	16	g	g	NOUN
ejpam-3985	71	17	,	,	PUNCT
ejpam-3985	71	18	ng(u	ng(u	NOUN
ejpam-3985	71	19	)	)	PUNCT
ejpam-3985	71	20	6=	6=	NUM
ejpam-3985	71	21	ng(v	ng(v	NUM
ejpam-3985	71	22	)	)	PUNCT
ejpam-3985	71	23	and	and	CCONJ
ejpam-3985	71	24	ng[u	ng[u	PROPN
ejpam-3985	71	25	]	]	PUNCT
ejpam-3985	71	26	6=	6=	PUNCT
ejpam-3985	72	1	ng[v	ng[v	NOUN
ejpam-3985	72	2	]	]	PUNCT
ejpam-3985	72	3	.	.	PUNCT
ejpam-3985	73	1	in	in	ADP
ejpam-3985	73	2	recent	recent	ADJ
ejpam-3985	73	3	years	year	NOUN
ejpam-3985	73	4	,	,	PUNCT
ejpam-3985	73	5	the	the	DET
ejpam-3985	73	6	concept	concept	NOUN
ejpam-3985	73	7	of	of	ADP
ejpam-3985	73	8	domination	domination	NOUN
ejpam-3985	73	9	in	in	ADP
ejpam-3985	73	10	graphs	graph	NOUN
ejpam-3985	73	11	has	have	AUX
ejpam-3985	73	12	been	be	AUX
ejpam-3985	73	13	studied	study	VERB
ejpam-3985	73	14	extensively	extensively	ADV
ejpam-3985	73	15	and	and	CCONJ
ejpam-3985	73	16	several	several	ADJ
ejpam-3985	73	17	research	research	NOUN
ejpam-3985	73	18	papers	paper	NOUN
ejpam-3985	73	19	have	have	AUX
ejpam-3985	73	20	been	be	AUX
ejpam-3985	73	21	published	publish	VERB
ejpam-3985	73	22	on	on	ADP
ejpam-3985	73	23	this	this	DET
ejpam-3985	73	24	topic	topic	NOUN
ejpam-3985	73	25	.	.	PUNCT
ejpam-3985	74	1	the	the	DET
ejpam-3985	74	2	said	say	VERB
ejpam-3985	74	3	concept	concept	NOUN
ejpam-3985	74	4	was	be	AUX
ejpam-3985	74	5	not	not	PART
ejpam-3985	74	6	formally	formally	ADV
ejpam-3985	74	7	defined	define	VERB
ejpam-3985	74	8	mathematically	mathematically	ADV
ejpam-3985	74	9	until	until	ADP
ejpam-3985	74	10	the	the	DET
ejpam-3985	74	11	publications	publication	NOUN
ejpam-3985	74	12	of	of	ADP
ejpam-3985	74	13	the	the	DET
ejpam-3985	74	14	books	book	NOUN
ejpam-3985	74	15	by	by	ADP
ejpam-3985	74	16	claude	claude	PROPN
ejpam-3985	74	17	berge	berge	NOUN
ejpam-3985	75	1	[	[	X
ejpam-3985	75	2	2	2	X
ejpam-3985	75	3	]	]	PUNCT
ejpam-3985	75	4	in	in	ADP
ejpam-3985	75	5	1958	1958	NUM
ejpam-3985	75	6	and	and	CCONJ
ejpam-3985	75	7	oystein	oystein	ADJ
ejpam-3985	75	8	ore	ore	NOUN
ejpam-3985	75	9	in	in	ADP
ejpam-3985	75	10	1962	1962	NUM
ejpam-3985	75	11	.	.	PUNCT
ejpam-3985	76	1	in	in	ADP
ejpam-3985	76	2	1977	1977	NUM
ejpam-3985	76	3	,	,	PUNCT
ejpam-3985	76	4	a	a	DET
ejpam-3985	76	5	survey	survey	NOUN
ejpam-3985	76	6	paper	paper	NOUN
ejpam-3985	76	7	by	by	ADP
ejpam-3985	76	8	cockayne	cockayne	NOUN
ejpam-3985	76	9	and	and	CCONJ
ejpam-3985	76	10	hedetniemi	hedetniemi	X
ejpam-3985	76	11	[	[	X
ejpam-3985	76	12	4	4	NUM
ejpam-3985	76	13	]	]	PUNCT
ejpam-3985	76	14	began	begin	VERB
ejpam-3985	76	15	to	to	PART
ejpam-3985	76	16	study	study	VERB
ejpam-3985	76	17	the	the	DET
ejpam-3985	76	18	concept	concept	NOUN
ejpam-3985	76	19	of	of	ADP
ejpam-3985	76	20	domination	domination	NOUN
ejpam-3985	76	21	.	.	PUNCT
ejpam-3985	77	1	on	on	ADP
ejpam-3985	77	2	the	the	DET
ejpam-3985	77	3	other	other	ADJ
ejpam-3985	77	4	hand	hand	NOUN
ejpam-3985	77	5	,	,	PUNCT
ejpam-3985	77	6	the	the	DET
ejpam-3985	77	7	problem	problem	NOUN
ejpam-3985	77	8	of	of	ADP
ejpam-3985	77	9	uniquely	uniquely	ADV
ejpam-3985	77	10	recognizing	recognize	VERB
ejpam-3985	77	11	the	the	DET
ejpam-3985	77	12	possible	possible	ADJ
ejpam-3985	77	13	position	position	NOUN
ejpam-3985	77	14	of	of	ADP
ejpam-3985	77	15	an	an	DET
ejpam-3985	77	16	intruder	intruder	NOUN
ejpam-3985	77	17	such	such	ADJ
ejpam-3985	77	18	as	as	ADP
ejpam-3985	77	19	fault	fault	NOUN
ejpam-3985	77	20	in	in	ADP
ejpam-3985	77	21	a	a	DET
ejpam-3985	77	22	computer	computer	NOUN
ejpam-3985	77	23	network	network	NOUN
ejpam-3985	77	24	and	and	CCONJ
ejpam-3985	77	25	spoiled	spoiled	ADJ
ejpam-3985	77	26	device	device	NOUN
ejpam-3985	77	27	was	be	AUX
ejpam-3985	77	28	the	the	DET
ejpam-3985	77	29	principal	principal	ADJ
ejpam-3985	77	30	motivation	motivation	NOUN
ejpam-3985	77	31	in	in	ADP
ejpam-3985	77	32	introducing	introduce	VERB
ejpam-3985	77	33	the	the	DET
ejpam-3985	77	34	concept	concept	NOUN
ejpam-3985	77	35	of	of	ADP
ejpam-3985	77	36	metric	metric	ADJ
ejpam-3985	77	37	dimension	dimension	NOUN
ejpam-3985	77	38	in	in	ADP
ejpam-3985	77	39	graphs	graph	NOUN
ejpam-3985	77	40	.	.	PUNCT
ejpam-3985	78	1	slater	slater	NOUN
ejpam-3985	79	1	[	[	X
ejpam-3985	79	2	12	12	NUM
ejpam-3985	79	3	]	]	PUNCT
ejpam-3985	79	4	brought	bring	VERB
ejpam-3985	79	5	in	in	ADP
ejpam-3985	79	6	the	the	DET
ejpam-3985	79	7	notion	notion	NOUN
ejpam-3985	79	8	of	of	ADP
ejpam-3985	79	9	locating	locate	VERB
ejpam-3985	79	10	sets	set	NOUN
ejpam-3985	79	11	and	and	CCONJ
ejpam-3985	79	12	its	its	PRON
ejpam-3985	79	13	minimum	minimum	ADJ
ejpam-3985	79	14	cardinality	cardinality	NOUN
ejpam-3985	79	15	as	as	ADP
ejpam-3985	79	16	locating	locate	VERB
ejpam-3985	79	17	number	number	NOUN
ejpam-3985	79	18	.	.	PUNCT
ejpam-3985	80	1	the	the	DET
ejpam-3985	80	2	same	same	ADJ
ejpam-3985	80	3	concept	concept	NOUN
ejpam-3985	80	4	was	be	AUX
ejpam-3985	80	5	also	also	ADV
ejpam-3985	80	6	introduced	introduce	VERB
ejpam-3985	80	7	by	by	ADP
ejpam-3985	80	8	harary	harary	NOUN
ejpam-3985	80	9	and	and	CCONJ
ejpam-3985	80	10	melter	melter	NOUN
ejpam-3985	81	1	[	[	X
ejpam-3985	81	2	7	7	NUM
ejpam-3985	81	3	]	]	PUNCT
ejpam-3985	81	4	but	but	CCONJ
ejpam-3985	81	5	using	use	VERB
ejpam-3985	81	6	the	the	DET
ejpam-3985	81	7	terms	term	NOUN
ejpam-3985	81	8	resolving	resolve	VERB
ejpam-3985	81	9	sets	set	NOUN
ejpam-3985	81	10	and	and	CCONJ
ejpam-3985	81	11	metric	metric	ADJ
ejpam-3985	81	12	dimension	dimension	NOUN
ejpam-3985	81	13	to	to	PART
ejpam-3985	81	14	refer	refer	VERB
ejpam-3985	81	15	to	to	ADP
ejpam-3985	81	16	locating	locate	VERB
ejpam-3985	81	17	sets	set	NOUN
ejpam-3985	81	18	and	and	CCONJ
ejpam-3985	81	19	locating	locate	VERB
ejpam-3985	81	20	number	number	NOUN
ejpam-3985	81	21	,	,	PUNCT
ejpam-3985	81	22	respectively	respectively	ADV
ejpam-3985	81	23	.	.	PUNCT
ejpam-3985	82	1	however	however	ADV
ejpam-3985	82	2	,	,	PUNCT
ejpam-3985	82	3	in	in	ADP
ejpam-3985	82	4	recent	recent	ADJ
ejpam-3985	82	5	studies	study	NOUN
ejpam-3985	82	6	,	,	PUNCT
ejpam-3985	82	7	locating	locate	VERB
ejpam-3985	82	8	sets	set	NOUN
ejpam-3985	82	9	and	and	CCONJ
ejpam-3985	82	10	resolving	resolve	VERB
ejpam-3985	82	11	sets	set	NOUN
ejpam-3985	82	12	are	be	AUX
ejpam-3985	82	13	defined	define	VERB
ejpam-3985	82	14	differently	differently	ADV
ejpam-3985	82	15	.	.	PUNCT
ejpam-3985	83	1	in	in	ADP
ejpam-3985	83	2	2013	2013	NUM
ejpam-3985	83	3	,	,	PUNCT
ejpam-3985	83	4	canoy	canoy	NOUN
ejpam-3985	83	5	and	and	CCONJ
ejpam-3985	83	6	malacas	malacas	NOUN
ejpam-3985	84	1	[	[	X
ejpam-3985	84	2	13	13	NUM
ejpam-3985	84	3	]	]	PUNCT
ejpam-3985	84	4	,	,	PUNCT
ejpam-3985	84	5	defined	define	VERB
ejpam-3985	84	6	a	a	DET
ejpam-3985	84	7	locating	locating	NOUN
ejpam-3985	84	8	set	set	VERB
ejpam-3985	84	9	as	as	ADP
ejpam-3985	84	10	a	a	DET
ejpam-3985	84	11	subset	subset	NOUN
ejpam-3985	84	12	s	s	NOUN
ejpam-3985	84	13	of	of	ADP
ejpam-3985	84	14	v	v	NOUN
ejpam-3985	84	15	(	(	PUNCT
ejpam-3985	84	16	g	g	NOUN
ejpam-3985	84	17	)	)	PUNCT
ejpam-3985	84	18	in	in	ADP
ejpam-3985	84	19	a	a	DET
ejpam-3985	84	20	connected	connected	ADJ
ejpam-3985	84	21	graph	graph	NOUN
ejpam-3985	84	22	g	g	NOUN
ejpam-3985	84	23	satisfying	satisfy	VERB
ejpam-3985	84	24	the	the	DET
ejpam-3985	84	25	condition	condition	NOUN
ejpam-3985	84	26	that	that	SCONJ
ejpam-3985	84	27	ng(u	ng(u	NOUN
ejpam-3985	84	28	)	)	PUNCT
ejpam-3985	84	29	∩	∩	X
ejpam-3985	84	30	s	s	PART
ejpam-3985	84	31	6=	6=	NUM
ejpam-3985	84	32	ng(v	ng(v	NUM
ejpam-3985	84	33	)	)	PUNCT
ejpam-3985	84	34	∩	∩	NOUN
ejpam-3985	84	35	s	s	PART
ejpam-3985	84	36	for	for	ADP
ejpam-3985	84	37	all	all	DET
ejpam-3985	84	38	u	u	NOUN
ejpam-3985	84	39	,	,	PUNCT
ejpam-3985	84	40	v	v	NOUN
ejpam-3985	84	41	∈	∈	PROPN
ejpam-3985	84	42	v	v	NOUN
ejpam-3985	84	43	(	(	PUNCT
ejpam-3985	84	44	g	g	NOUN
ejpam-3985	84	45	)	)	PUNCT
ejpam-3985	84	46	\	\	PROPN
ejpam-3985	85	1	s	s	PART
ejpam-3985	85	2	with	with	ADP
ejpam-3985	85	3	u	u	PROPN
ejpam-3985	85	4	6=	6=	PROPN
ejpam-3985	85	5	v.	v.	ADP
ejpam-3985	85	6	meanwhile	meanwhile	ADV
ejpam-3985	85	7	,	,	PUNCT
ejpam-3985	85	8	in	in	ADP
ejpam-3985	85	9	the	the	DET
ejpam-3985	85	10	same	same	ADJ
ejpam-3985	85	11	year	year	NOUN
ejpam-3985	85	12	,	,	PUNCT
ejpam-3985	85	13	bailey	bailey	PROPN
ejpam-3985	85	14	et	et	PROPN
ejpam-3985	85	15	al	al	PROPN
ejpam-3985	85	16	.	.	PUNCT
ejpam-3985	86	1	[	[	X
ejpam-3985	86	2	1	1	X
ejpam-3985	86	3	]	]	PUNCT
ejpam-3985	86	4	defined	define	VERB
ejpam-3985	86	5	a	a	DET
ejpam-3985	86	6	resolving	resolving	NOUN
ejpam-3985	86	7	set	set	VERB
ejpam-3985	86	8	as	as	ADP
ejpam-3985	86	9	a	a	DET
ejpam-3985	86	10	set	set	NOUN
ejpam-3985	86	11	of	of	ADP
ejpam-3985	86	12	vertices	vertex	NOUN
ejpam-3985	86	13	s	s	PART
ejpam-3985	86	14	in	in	ADP
ejpam-3985	86	15	a	a	DET
ejpam-3985	86	16	graph	graph	NOUN
ejpam-3985	86	17	g	g	ADP
ejpam-3985	86	18	such	such	ADJ
ejpam-3985	86	19	that	that	PRON
ejpam-3985	86	20	for	for	ADP
ejpam-3985	86	21	any	any	DET
ejpam-3985	86	22	two	two	NUM
ejpam-3985	86	23	distinct	distinct	ADJ
ejpam-3985	86	24	vertices	vertex	NOUN
ejpam-3985	86	25	u	u	NOUN
ejpam-3985	86	26	,	,	PUNCT
ejpam-3985	86	27	v	v	NOUN
ejpam-3985	86	28	,	,	PUNCT
ejpam-3985	86	29	there	there	PRON
ejpam-3985	86	30	exists	exist	VERB
ejpam-3985	86	31	x	x	X
ejpam-3985	86	32	∈	∈	PROPN
ejpam-3985	86	33	s	s	VERB
ejpam-3985	86	34	such	such	ADJ
ejpam-3985	86	35	that	that	SCONJ
ejpam-3985	86	36	the	the	DET
ejpam-3985	86	37	distances	distance	NOUN
ejpam-3985	86	38	d(u	d(u	PROPN
ejpam-3985	86	39	,	,	PUNCT
ejpam-3985	86	40	x	x	X
ejpam-3985	86	41	)	)	PUNCT
ejpam-3985	86	42	6=	6=	ADP
ejpam-3985	87	1	d(v	d(v	PROPN
ejpam-3985	87	2	,	,	PUNCT
ejpam-3985	87	3	x	x	NOUN
ejpam-3985	87	4	)	)	PUNCT
ejpam-3985	87	5	.	.	PUNCT
ejpam-3985	88	1	in	in	ADP
ejpam-3985	88	2	1999	1999	NUM
ejpam-3985	88	3	,	,	PUNCT
ejpam-3985	88	4	domke	domke	PROPN
ejpam-3985	88	5	et	et	PROPN
ejpam-3985	88	6	al	al	PROPN
ejpam-3985	88	7	.	.	PUNCT
ejpam-3985	89	1	[	[	X
ejpam-3985	89	2	5	5	NUM
ejpam-3985	89	3	]	]	PUNCT
ejpam-3985	89	4	introduced	introduce	VERB
ejpam-3985	89	5	and	and	CCONJ
ejpam-3985	89	6	investigated	investigate	VERB
ejpam-3985	89	7	the	the	DET
ejpam-3985	89	8	concept	concept	NOUN
ejpam-3985	89	9	of	of	ADP
ejpam-3985	89	10	restrained	restrained	ADJ
ejpam-3985	89	11	domination	domination	NOUN
ejpam-3985	89	12	in	in	ADP
ejpam-3985	89	13	graphs	graph	NOUN
ejpam-3985	89	14	.	.	PUNCT
ejpam-3985	90	1	in	in	ADP
ejpam-3985	90	2	2008	2008	NUM
ejpam-3985	90	3	,	,	PUNCT
ejpam-3985	90	4	hattingh	hattingh	PROPN
ejpam-3985	90	5	et	et	PROPN
ejpam-3985	90	6	al	al	PROPN
ejpam-3985	90	7	.	.	PUNCT
ejpam-3985	91	1	[	[	X
ejpam-3985	91	2	8	8	NUM
ejpam-3985	91	3	]	]	PUNCT
ejpam-3985	91	4	investigated	investigate	VERB
ejpam-3985	91	5	the	the	DET
ejpam-3985	91	6	same	same	ADJ
ejpam-3985	91	7	concept	concept	NOUN
ejpam-3985	91	8	and	and	CCONJ
ejpam-3985	91	9	obtained	obtain	VERB
ejpam-3985	91	10	a	a	DET
ejpam-3985	91	11	nordhaus	nordhaus	NOUN
ejpam-3985	91	12	-	-	PUNCT
ejpam-3985	91	13	gaddum	gaddum	NOUN
ejpam-3985	91	14	results	result	NOUN
ejpam-3985	91	15	for	for	ADP
ejpam-3985	91	16	restrained	restrained	ADJ
ejpam-3985	91	17	domination	domination	NOUN
ejpam-3985	91	18	and	and	CCONJ
ejpam-3985	91	19	total	total	ADJ
ejpam-3985	91	20	restrained	restrained	ADJ
ejpam-3985	91	21	domination	domination	NOUN
ejpam-3985	91	22	in	in	ADP
ejpam-3985	91	23	graphs	graph	NOUN
ejpam-3985	91	24	.	.	PUNCT
ejpam-3985	92	1	moreover	moreover	ADV
ejpam-3985	92	2	,	,	PUNCT
ejpam-3985	92	3	in	in	ADP
ejpam-3985	92	4	2015	2015	NUM
ejpam-3985	92	5	,	,	PUNCT
ejpam-3985	92	6	omega	omega	NOUN
ejpam-3985	92	7	et	et	NOUN
ejpam-3985	92	8	al	al	PROPN
ejpam-3985	92	9	.	.	PUNCT
ejpam-3985	93	1	[	[	X
ejpam-3985	93	2	10	10	NUM
ejpam-3985	93	3	]	]	PUNCT
ejpam-3985	93	4	introduced	introduce	VERB
ejpam-3985	93	5	and	and	CCONJ
ejpam-3985	93	6	characterized	characterize	VERB
ejpam-3985	93	7	the	the	DET
ejpam-3985	93	8	restrained	restrained	ADJ
ejpam-3985	93	9	locating	locate	VERB
ejpam-3985	93	10	-	-	PUNCT
ejpam-3985	93	11	dominating	dominating	NOUN
ejpam-3985	93	12	sets	set	NOUN
ejpam-3985	93	13	of	of	ADP
ejpam-3985	93	14	some	some	DET
ejpam-3985	93	15	graphs	graph	NOUN
ejpam-3985	93	16	and	and	CCONJ
ejpam-3985	93	17	determined	determine	VERB
ejpam-3985	93	18	the	the	DET
ejpam-3985	93	19	restrained	restrained	ADJ
ejpam-3985	93	20	l	l	ADJ
ejpam-3985	93	21	-	-	PUNCT
ejpam-3985	93	22	domination	domination	NOUN
ejpam-3985	93	23	numbers	number	NOUN
ejpam-3985	93	24	of	of	ADP
ejpam-3985	93	25	these	these	DET
ejpam-3985	93	26	graphs	graph	NOUN
ejpam-3985	93	27	.	.	PUNCT
ejpam-3985	94	1	inspired	inspire	VERB
ejpam-3985	94	2	by	by	ADP
ejpam-3985	94	3	the	the	DET
ejpam-3985	94	4	above	above	ADJ
ejpam-3985	94	5	works	work	NOUN
ejpam-3985	94	6	,	,	PUNCT
ejpam-3985	94	7	this	this	DET
ejpam-3985	94	8	study	study	NOUN
ejpam-3985	94	9	aims	aim	VERB
ejpam-3985	94	10	to	to	PART
ejpam-3985	94	11	define	define	VERB
ejpam-3985	94	12	and	and	CCONJ
ejpam-3985	94	13	characterize	characterize	VERB
ejpam-3985	94	14	the	the	DET
ejpam-3985	94	15	resolving	resolve	VERB
ejpam-3985	94	16	restrained	restrained	ADJ
ejpam-3985	94	17	dominating	dominating	NOUN
ejpam-3985	94	18	sets	set	NOUN
ejpam-3985	94	19	and	and	CCONJ
ejpam-3985	94	20	determine	determine	VERB
ejpam-3985	94	21	the	the	DET
ejpam-3985	94	22	resolving	resolve	VERB
ejpam-3985	94	23	restrained	restrained	ADJ
ejpam-3985	94	24	domination	domination	NOUN
ejpam-3985	94	25	number	number	NOUN
ejpam-3985	94	26	in	in	ADP
ejpam-3985	94	27	the	the	DET
ejpam-3985	94	28	join	join	NOUN
ejpam-3985	94	29	,	,	PUNCT
ejpam-3985	94	30	corona	corona	NOUN
ejpam-3985	94	31	and	and	CCONJ
ejpam-3985	94	32	lexicographic	lexicographic	ADJ
ejpam-3985	94	33	product	product	NOUN
ejpam-3985	94	34	of	of	ADP
ejpam-3985	94	35	two	two	NUM
ejpam-3985	94	36	graphs	graph	NOUN
ejpam-3985	94	37	.	.	PUNCT
ejpam-3985	95	1	2	2	X
ejpam-3985	95	2	.	.	X
ejpam-3985	95	3	preliminary	preliminary	ADJ
ejpam-3985	95	4	results	result	NOUN
ejpam-3985	95	5	remark	remark	VERB
ejpam-3985	95	6	1	1	NUM
ejpam-3985	95	7	.	.	PUNCT
ejpam-3985	96	1	for	for	ADP
ejpam-3985	96	2	any	any	DET
ejpam-3985	96	3	connected	connected	ADJ
ejpam-3985	96	4	graph	graph	NOUN
ejpam-3985	96	5	g	g	NOUN
ejpam-3985	96	6	of	of	ADP
ejpam-3985	96	7	order	order	NOUN
ejpam-3985	96	8	n	n	PRON
ejpam-3985	96	9	≥	≥	NOUN
ejpam-3985	96	10	2	2	NUM
ejpam-3985	96	11	,	,	PUNCT
ejpam-3985	96	12	γrr(g	γrr(g	X
ejpam-3985	96	13	)	)	PUNCT
ejpam-3985	96	14	∈	∈	NOUN
ejpam-3985	96	15	{	{	PUNCT
ejpam-3985	96	16	2	2	NUM
ejpam-3985	96	17	,	,	PUNCT
ejpam-3985	96	18	3	3	NUM
ejpam-3985	96	19	,	,	PUNCT
ejpam-3985	96	20	4	4	NUM
ejpam-3985	96	21	,	,	PUNCT
ejpam-3985	96	22	.	.	PUNCT
ejpam-3985	96	23	.	.	PUNCT
ejpam-3985	96	24	.	.	PUNCT
ejpam-3985	97	1	,	,	PUNCT
ejpam-3985	97	2	n−	n−	NOUN
ejpam-3985	97	3	2	2	NUM
ejpam-3985	97	4	,	,	PUNCT
ejpam-3985	97	5	n	n	CCONJ
ejpam-3985	97	6	}	}	PUNCT
ejpam-3985	97	7	.	.	PUNCT
ejpam-3985	98	1	g.	g.	PROPN
ejpam-3985	98	2	monsanto	monsanto	PROPN
ejpam-3985	98	3	,	,	PUNCT
ejpam-3985	98	4	h.	h.	PROPN
ejpam-3985	98	5	rara	rara	PROPN
ejpam-3985	98	6	/	/	SYM
ejpam-3985	98	7	eur	eur	PROPN
ejpam-3985	98	8	.	.	PUNCT
ejpam-3985	99	1	j.	j.	PROPN
ejpam-3985	99	2	pure	pure	PROPN
ejpam-3985	99	3	appl	appl	PROPN
ejpam-3985	99	4	.	.	PROPN
ejpam-3985	99	5	math	math	PROPN
ejpam-3985	99	6	,	,	PUNCT
ejpam-3985	99	7	14	14	NUM
ejpam-3985	99	8	(	(	PUNCT
ejpam-3985	99	9	3	3	NUM
ejpam-3985	99	10	)	)	PUNCT
ejpam-3985	99	11	(	(	PUNCT
ejpam-3985	99	12	2021	2021	NUM
ejpam-3985	99	13	)	)	PUNCT
ejpam-3985	99	14	,	,	PUNCT
ejpam-3985	99	15	829	829	NUM
ejpam-3985	99	16	-	-	SYM
ejpam-3985	99	17	841	841	NUM
ejpam-3985	99	18	832	832	NUM
ejpam-3985	99	19	remark	remark	NOUN
ejpam-3985	99	20	2	2	NUM
ejpam-3985	99	21	.	.	PUNCT
ejpam-3985	100	1	every	every	DET
ejpam-3985	100	2	resolving	resolve	VERB
ejpam-3985	100	3	restrained	restrained	ADJ
ejpam-3985	100	4	dominating	dominating	NOUN
ejpam-3985	100	5	set	set	NOUN
ejpam-3985	100	6	of	of	ADP
ejpam-3985	100	7	a	a	DET
ejpam-3985	100	8	connected	connected	ADJ
ejpam-3985	100	9	graph	graph	NOUN
ejpam-3985	100	10	g	g	NOUN
ejpam-3985	100	11	of	of	ADP
ejpam-3985	100	12	order	order	NOUN
ejpam-3985	100	13	n	n	PRON
ejpam-3985	100	14	≥	≥	NOUN
ejpam-3985	100	15	2	2	NUM
ejpam-3985	100	16	is	be	AUX
ejpam-3985	100	17	a	a	DET
ejpam-3985	100	18	restrained	restrained	ADJ
ejpam-3985	100	19	dominating	dominating	NOUN
ejpam-3985	100	20	set	set	NOUN
ejpam-3985	100	21	of	of	ADP
ejpam-3985	100	22	g.	g.	PROPN
ejpam-3985	100	23	hence	hence	ADV
ejpam-3985	100	24	,	,	PUNCT
ejpam-3985	100	25	γr(g	γr(g	PROPN
ejpam-3985	100	26	)	)	PUNCT
ejpam-3985	100	27	≤	≤	NUM
ejpam-3985	101	1	γrr(g	γrr(g	NUM
ejpam-3985	101	2	)	)	PUNCT
ejpam-3985	101	3	.	.	PUNCT
ejpam-3985	102	1	theorem	theorem	NOUN
ejpam-3985	102	2	1	1	X
ejpam-3985	102	3	.	.	PUNCT
ejpam-3985	103	1	let	let	VERB
ejpam-3985	103	2	g	g	PRON
ejpam-3985	103	3	be	be	AUX
ejpam-3985	103	4	a	a	DET
ejpam-3985	103	5	connected	connected	ADJ
ejpam-3985	103	6	graph	graph	NOUN
ejpam-3985	103	7	of	of	ADP
ejpam-3985	103	8	order	order	NOUN
ejpam-3985	103	9	n	n	PRON
ejpam-3985	103	10	≥	≥	NOUN
ejpam-3985	103	11	2	2	NUM
ejpam-3985	103	12	.	.	PUNCT
ejpam-3985	104	1	then	then	ADV
ejpam-3985	104	2	γrr(g	γrr(g	NUM
ejpam-3985	104	3	)	)	PUNCT
ejpam-3985	105	1	=	=	SYM
ejpam-3985	105	2	n	n	NOUN
ejpam-3985	105	3	if	if	SCONJ
ejpam-3985	105	4	and	and	CCONJ
ejpam-3985	105	5	only	only	ADV
ejpam-3985	105	6	if	if	SCONJ
ejpam-3985	105	7	g	g	PROPN
ejpam-3985	105	8	∼=	∼=	PROPN
ejpam-3985	105	9	kn	kn	NOUN
ejpam-3985	105	10	or	or	CCONJ
ejpam-3985	105	11	g	g	NOUN
ejpam-3985	105	12	∼=	∼=	ADV
ejpam-3985	105	13	k1,n−1	k1,n−1	ADJ
ejpam-3985	105	14	.	.	PUNCT
ejpam-3985	106	1	proof	proof	NOUN
ejpam-3985	106	2	:	:	PUNCT
ejpam-3985	106	3	suppose	suppose	VERB
ejpam-3985	106	4	that	that	SCONJ
ejpam-3985	106	5	γrr(g	γrr(g	X
ejpam-3985	106	6	)	)	PUNCT
ejpam-3985	106	7	=	=	VERB
ejpam-3985	107	1	n.	n.	NOUN
ejpam-3985	107	2	if	if	SCONJ
ejpam-3985	107	3	n	n	NOUN
ejpam-3985	107	4	=	=	SYM
ejpam-3985	107	5	2	2	NUM
ejpam-3985	107	6	,	,	PUNCT
ejpam-3985	107	7	then	then	ADV
ejpam-3985	107	8	g	g	PROPN
ejpam-3985	107	9	=	=	SYM
ejpam-3985	107	10	k2	k2	PROPN
ejpam-3985	107	11	.	.	PUNCT
ejpam-3985	108	1	if	if	SCONJ
ejpam-3985	108	2	n	n	NUM
ejpam-3985	108	3	=	=	SYM
ejpam-3985	108	4	3	3	NUM
ejpam-3985	108	5	,	,	PUNCT
ejpam-3985	108	6	then	then	ADV
ejpam-3985	108	7	g	g	PROPN
ejpam-3985	108	8	∼=	∼=	PROPN
ejpam-3985	108	9	k3	k3	ADJ
ejpam-3985	108	10	or	or	CCONJ
ejpam-3985	108	11	g	g	NOUN
ejpam-3985	108	12	∼=	∼=	PROPN
ejpam-3985	108	13	k1,2	k1,2	PROPN
ejpam-3985	108	14	.	.	PUNCT
ejpam-3985	108	15	suppose	suppose	VERB
ejpam-3985	108	16	that	that	SCONJ
ejpam-3985	108	17	n	n	PROPN
ejpam-3985	108	18	≥	≥	X
ejpam-3985	108	19	4	4	NUM
ejpam-3985	108	20	and	and	CCONJ
ejpam-3985	108	21	suppose	suppose	VERB
ejpam-3985	108	22	further	far	ADV
ejpam-3985	108	23	that	that	SCONJ
ejpam-3985	108	24	g	g	PROPN
ejpam-3985	108	25	�	�	PROPN
ejpam-3985	108	26	kn	kn	PROPN
ejpam-3985	108	27	.	.	PUNCT
ejpam-3985	109	1	let	let	VERB
ejpam-3985	109	2	x	x	SYM
ejpam-3985	109	3	∈	∈	PROPN
ejpam-3985	109	4	v	v	X
ejpam-3985	109	5	(	(	PUNCT
ejpam-3985	109	6	g	g	NOUN
ejpam-3985	109	7	)	)	PUNCT
ejpam-3985	109	8	with	with	ADP
ejpam-3985	109	9	degg(x	degg(x	NOUN
ejpam-3985	109	10	)	)	PUNCT
ejpam-3985	109	11	=	=	SYM
ejpam-3985	109	12	∆(g	∆(g	NOUN
ejpam-3985	109	13	)	)	PUNCT
ejpam-3985	109	14	.	.	PUNCT
ejpam-3985	110	1	suppose	suppose	VERB
ejpam-3985	110	2	there	there	PRON
ejpam-3985	110	3	exists	exist	VERB
ejpam-3985	110	4	y	y	PROPN
ejpam-3985	110	5	∈	∈	PROPN
ejpam-3985	110	6	v	v	ADP
ejpam-3985	110	7	(	(	PUNCT
ejpam-3985	110	8	g	g	NOUN
ejpam-3985	110	9	)	)	PUNCT
ejpam-3985	110	10	\	\	NOUN
ejpam-3985	110	11	{	{	PUNCT
ejpam-3985	110	12	x	x	X
ejpam-3985	110	13	}	}	PUNCT
ejpam-3985	110	14	such	such	ADJ
ejpam-3985	110	15	that	that	PRON
ejpam-3985	110	16	xy	xy	PROPN
ejpam-3985	110	17	/∈	/∈	PUNCT
ejpam-3985	110	18	e(g	e(g	PROPN
ejpam-3985	110	19	)	)	PUNCT
ejpam-3985	110	20	.	.	PUNCT
ejpam-3985	111	1	since	since	SCONJ
ejpam-3985	111	2	g	g	PROPN
ejpam-3985	111	3	is	be	AUX
ejpam-3985	111	4	connected	connect	VERB
ejpam-3985	111	5	,	,	PUNCT
ejpam-3985	111	6	y	y	PROPN
ejpam-3985	111	7	can	can	AUX
ejpam-3985	111	8	be	be	AUX
ejpam-3985	111	9	chosen	choose	VERB
ejpam-3985	111	10	so	so	SCONJ
ejpam-3985	111	11	that	that	SCONJ
ejpam-3985	111	12	dg(x	dg(x	NOUN
ejpam-3985	111	13	,	,	PUNCT
ejpam-3985	111	14	y	y	NOUN
ejpam-3985	111	15	)	)	PUNCT
ejpam-3985	111	16	=	=	SYM
ejpam-3985	112	1	2	2	X
ejpam-3985	112	2	.	.	X
ejpam-3985	112	3	let	let	VERB
ejpam-3985	112	4	z	z	NOUN
ejpam-3985	112	5	∈	∈	PROPN
ejpam-3985	112	6	ng(x)∩ng(y	ng(x)∩ng(y	PROPN
ejpam-3985	112	7	)	)	PUNCT
ejpam-3985	112	8	.	.	PUNCT
ejpam-3985	113	1	if	if	SCONJ
ejpam-3985	113	2	yp	yp	PROPN
ejpam-3985	113	3	∈	∈	PROPN
ejpam-3985	113	4	e(g	e(g	PROPN
ejpam-3985	113	5	)	)	PUNCT
ejpam-3985	113	6	for	for	ADP
ejpam-3985	113	7	all	all	DET
ejpam-3985	113	8	p	p	NOUN
ejpam-3985	113	9	∈	∈	PROPN
ejpam-3985	113	10	ng(x	ng(x	NUM
ejpam-3985	113	11	)	)	PUNCT
ejpam-3985	113	12	,	,	PUNCT
ejpam-3985	113	13	then	then	ADV
ejpam-3985	113	14	choose	choose	VERB
ejpam-3985	113	15	w	w	PROPN
ejpam-3985	113	16	=	=	SYM
ejpam-3985	113	17	v	v	PROPN
ejpam-3985	113	18	(	(	PUNCT
ejpam-3985	113	19	g	g	NOUN
ejpam-3985	113	20	)	)	PUNCT
ejpam-3985	113	21	\	\	NOUN
ejpam-3985	113	22	{	{	PUNCT
ejpam-3985	113	23	y	y	PROPN
ejpam-3985	113	24	,	,	PUNCT
ejpam-3985	113	25	z	z	NOUN
ejpam-3985	113	26	}	}	PUNCT
ejpam-3985	113	27	.	.	PUNCT
ejpam-3985	114	1	since	since	SCONJ
ejpam-3985	114	2	degg(x	degg(x	NUM
ejpam-3985	114	3	)	)	PUNCT
ejpam-3985	114	4	≥	≥	NOUN
ejpam-3985	114	5	degg(z	degg(z	PROPN
ejpam-3985	114	6	)	)	PUNCT
ejpam-3985	114	7	≥	≥	NOUN
ejpam-3985	114	8	2	2	NUM
ejpam-3985	114	9	,	,	PUNCT
ejpam-3985	114	10	there	there	PRON
ejpam-3985	114	11	exists	exist	VERB
ejpam-3985	114	12	u	u	PROPN
ejpam-3985	114	13	∈	∈	PROPN
ejpam-3985	114	14	ng(x	ng(x	NUM
ejpam-3985	114	15	)	)	PUNCT
ejpam-3985	114	16	\	\	NOUN
ejpam-3985	115	1	{	{	PUNCT
ejpam-3985	115	2	z	z	NOUN
ejpam-3985	115	3	}	}	PUNCT
ejpam-3985	115	4	.	.	PUNCT
ejpam-3985	116	1	let	let	VERB
ejpam-3985	116	2	w	w	NOUN
ejpam-3985	116	3	=	=	SYM
ejpam-3985	116	4	v	v	X
ejpam-3985	116	5	(	(	PUNCT
ejpam-3985	116	6	g	g	NOUN
ejpam-3985	116	7	)	)	PUNCT
ejpam-3985	116	8	\	\	NOUN
ejpam-3985	116	9	{	{	PUNCT
ejpam-3985	116	10	x	x	X
ejpam-3985	116	11	,	,	PUNCT
ejpam-3985	116	12	z	z	NOUN
ejpam-3985	116	13	}	}	PUNCT
ejpam-3985	116	14	.	.	PUNCT
ejpam-3985	117	1	since	since	SCONJ
ejpam-3985	117	2	xz	xz	PROPN
ejpam-3985	117	3	,	,	PUNCT
ejpam-3985	117	4	xu	xu	PROPN
ejpam-3985	117	5	,	,	PUNCT
ejpam-3985	117	6	zy	zy	PROPN
ejpam-3985	117	7	∈	∈	PROPN
ejpam-3985	117	8	e(g	e(g	PROPN
ejpam-3985	117	9	)	)	PUNCT
ejpam-3985	117	10	,	,	PUNCT
ejpam-3985	117	11	w	w	PROPN
ejpam-3985	117	12	is	be	AUX
ejpam-3985	117	13	a	a	DET
ejpam-3985	117	14	restrained	restrained	ADJ
ejpam-3985	117	15	dominating	dominating	NOUN
ejpam-3985	117	16	set	set	NOUN
ejpam-3985	117	17	of	of	ADP
ejpam-3985	117	18	g.	g.	PROPN
ejpam-3985	117	19	moreover	moreover	ADV
ejpam-3985	117	20	,	,	PUNCT
ejpam-3985	117	21	because	because	SCONJ
ejpam-3985	117	22	y	y	PROPN
ejpam-3985	117	23	∈	∈	PROPN
ejpam-3985	117	24	ng(z)\ng(x	ng(z)\ng(x	NOUN
ejpam-3985	117	25	)	)	PUNCT
ejpam-3985	117	26	,	,	PUNCT
ejpam-3985	117	27	rg(x	rg(x	X
ejpam-3985	117	28	/	/	SYM
ejpam-3985	117	29	w	w	NOUN
ejpam-3985	117	30	)	)	PUNCT
ejpam-3985	117	31	6=	6=	ADP
ejpam-3985	117	32	rg(z	rg(z	PROPN
ejpam-3985	117	33	/	/	SYM
ejpam-3985	117	34	w	w	PROPN
ejpam-3985	117	35	)	)	PUNCT
ejpam-3985	117	36	.	.	PUNCT
ejpam-3985	118	1	thus	thus	ADV
ejpam-3985	118	2	,	,	PUNCT
ejpam-3985	118	3	w	w	PROPN
ejpam-3985	118	4	is	be	AUX
ejpam-3985	118	5	a	a	DET
ejpam-3985	118	6	resolving	resolving	NOUN
ejpam-3985	118	7	set	set	NOUN
ejpam-3985	118	8	of	of	ADP
ejpam-3985	118	9	g	g	PROPN
ejpam-3985	118	10	and	and	CCONJ
ejpam-3985	118	11	we	we	PRON
ejpam-3985	118	12	have	have	VERB
ejpam-3985	118	13	γrr(g	γrr(g	NUM
ejpam-3985	118	14	)	)	PUNCT
ejpam-3985	118	15	≤	≤	NOUN
ejpam-3985	118	16	|w	|w	NOUN
ejpam-3985	119	1	|	|	NOUN
ejpam-3985	119	2	=	=	SYM
ejpam-3985	119	3	n−	n−	NOUN
ejpam-3985	119	4	2	2	NUM
ejpam-3985	119	5	,	,	PUNCT
ejpam-3985	119	6	a	a	DET
ejpam-3985	119	7	contradiction	contradiction	NOUN
ejpam-3985	119	8	.	.	PUNCT
ejpam-3985	120	1	therefore	therefore	ADV
ejpam-3985	120	2	,	,	PUNCT
ejpam-3985	120	3	xy	xy	PROPN
ejpam-3985	120	4	∈	∈	PROPN
ejpam-3985	120	5	e(g	e(g	PROPN
ejpam-3985	120	6	)	)	PUNCT
ejpam-3985	120	7	for	for	ADP
ejpam-3985	120	8	all	all	DET
ejpam-3985	120	9	y	y	PROPN
ejpam-3985	120	10	∈	∈	PROPN
ejpam-3985	120	11	v	v	ADP
ejpam-3985	120	12	(	(	PUNCT
ejpam-3985	120	13	g	g	NOUN
ejpam-3985	120	14	)	)	PUNCT
ejpam-3985	120	15	\	\	NOUN
ejpam-3985	120	16	{	{	PUNCT
ejpam-3985	120	17	x	x	NOUN
ejpam-3985	120	18	}	}	PUNCT
ejpam-3985	120	19	.	.	PUNCT
ejpam-3985	121	1	it	it	PRON
ejpam-3985	121	2	remains	remain	VERB
ejpam-3985	121	3	to	to	PART
ejpam-3985	121	4	show	show	VERB
ejpam-3985	121	5	that	that	PRON
ejpam-3985	121	6	uv	uv	NOUN
ejpam-3985	121	7	/∈	/∈	PUNCT
ejpam-3985	121	8	e(g	e(g	PROPN
ejpam-3985	121	9	)	)	PUNCT
ejpam-3985	121	10	for	for	ADP
ejpam-3985	121	11	every	every	DET
ejpam-3985	121	12	distinct	distinct	ADJ
ejpam-3985	121	13	vertices	vertex	NOUN
ejpam-3985	121	14	u	u	NOUN
ejpam-3985	121	15	,	,	PUNCT
ejpam-3985	121	16	v	v	NOUN
ejpam-3985	121	17	∈	∈	PROPN
ejpam-3985	121	18	v	v	NOUN
ejpam-3985	121	19	(	(	PUNCT
ejpam-3985	121	20	g	g	NOUN
ejpam-3985	121	21	)	)	PUNCT
ejpam-3985	121	22	\	\	NOUN
ejpam-3985	121	23	{	{	PUNCT
ejpam-3985	121	24	x	x	NOUN
ejpam-3985	121	25	}	}	PUNCT
ejpam-3985	121	26	.	.	PUNCT
ejpam-3985	122	1	to	to	ADP
ejpam-3985	122	2	this	this	DET
ejpam-3985	122	3	end	end	NOUN
ejpam-3985	122	4	,	,	PUNCT
ejpam-3985	122	5	suppose	suppose	VERB
ejpam-3985	122	6	there	there	PRON
ejpam-3985	122	7	exist	exist	VERB
ejpam-3985	122	8	distinct	distinct	ADJ
ejpam-3985	122	9	vertices	vertex	NOUN
ejpam-3985	122	10	u	u	NOUN
ejpam-3985	122	11	and	and	CCONJ
ejpam-3985	122	12	v	v	NOUN
ejpam-3985	122	13	in	in	ADP
ejpam-3985	122	14	v	v	NUM
ejpam-3985	122	15	(	(	PUNCT
ejpam-3985	122	16	g	g	NOUN
ejpam-3985	122	17	)	)	PUNCT
ejpam-3985	122	18	\	\	NOUN
ejpam-3985	122	19	{	{	PUNCT
ejpam-3985	122	20	x	x	X
ejpam-3985	122	21	}	}	PUNCT
ejpam-3985	122	22	such	such	ADJ
ejpam-3985	122	23	that	that	SCONJ
ejpam-3985	122	24	uv	uv	PROPN
ejpam-3985	122	25	∈	∈	PROPN
ejpam-3985	122	26	e(g	e(g	PROPN
ejpam-3985	122	27	)	)	PUNCT
ejpam-3985	122	28	.	.	PUNCT
ejpam-3985	123	1	since	since	SCONJ
ejpam-3985	123	2	g	g	PROPN
ejpam-3985	123	3	6=	6=	PROPN
ejpam-3985	123	4	kn	kn	PROPN
ejpam-3985	123	5	,	,	PUNCT
ejpam-3985	123	6	there	there	PRON
ejpam-3985	123	7	exist	exist	VERB
ejpam-3985	123	8	a	a	DET
ejpam-3985	123	9	,	,	PUNCT
ejpam-3985	123	10	b	b	PROPN
ejpam-3985	123	11	∈	∈	PROPN
ejpam-3985	123	12	v	v	NOUN
ejpam-3985	123	13	(	(	PUNCT
ejpam-3985	123	14	g	g	NOUN
ejpam-3985	123	15	)	)	PUNCT
ejpam-3985	123	16	such	such	ADJ
ejpam-3985	123	17	that	that	SCONJ
ejpam-3985	123	18	ab	ab	PROPN
ejpam-3985	123	19	/∈	/∈	PUNCT
ejpam-3985	123	20	e(g	e(g	PROPN
ejpam-3985	123	21	)	)	PUNCT
ejpam-3985	123	22	.	.	PUNCT
ejpam-3985	124	1	if	if	SCONJ
ejpam-3985	124	2	av	av	PROPN
ejpam-3985	124	3	∈	∈	PROPN
ejpam-3985	124	4	e(g	e(g	PROPN
ejpam-3985	124	5	)	)	PUNCT
ejpam-3985	124	6	or	or	CCONJ
ejpam-3985	124	7	bv	bv	PROPN
ejpam-3985	124	8	∈	∈	PROPN
ejpam-3985	124	9	e(g	e(g	PROPN
ejpam-3985	124	10	)	)	PUNCT
ejpam-3985	124	11	,	,	PUNCT
ejpam-3985	124	12	say	say	VERB
ejpam-3985	124	13	av	av	PROPN
ejpam-3985	124	14	∈	∈	PROPN
ejpam-3985	124	15	e(g	e(g	PROPN
ejpam-3985	124	16	)	)	PUNCT
ejpam-3985	124	17	,	,	PUNCT
ejpam-3985	124	18	then	then	ADV
ejpam-3985	124	19	consider	consider	VERB
ejpam-3985	124	20	w	w	NOUN
ejpam-3985	124	21	=	=	SYM
ejpam-3985	124	22	v	v	ADJ
ejpam-3985	124	23	(	(	PUNCT
ejpam-3985	124	24	g	g	NOUN
ejpam-3985	124	25	)	)	PUNCT
ejpam-3985	124	26	\	\	NOUN
ejpam-3985	124	27	{	{	PUNCT
ejpam-3985	124	28	x	x	NOUN
ejpam-3985	124	29	,	,	PUNCT
ejpam-3985	124	30	a	a	PRON
ejpam-3985	124	31	}	}	PUNCT
ejpam-3985	124	32	.	.	PUNCT
ejpam-3985	125	1	note	note	VERB
ejpam-3985	125	2	that	that	SCONJ
ejpam-3985	125	3	xv	xv	PROPN
ejpam-3985	125	4	,	,	PUNCT
ejpam-3985	125	5	av	av	PROPN
ejpam-3985	125	6	∈	∈	PROPN
ejpam-3985	125	7	e(g	e(g	PROPN
ejpam-3985	125	8	)	)	PUNCT
ejpam-3985	125	9	.	.	PUNCT
ejpam-3985	126	1	thus	thus	ADV
ejpam-3985	126	2	,	,	PUNCT
ejpam-3985	126	3	w	w	PROPN
ejpam-3985	126	4	is	be	AUX
ejpam-3985	126	5	a	a	DET
ejpam-3985	126	6	dominating	dominating	NOUN
ejpam-3985	126	7	set	set	NOUN
ejpam-3985	126	8	of	of	ADP
ejpam-3985	126	9	g.	g.	PROPN
ejpam-3985	126	10	since	since	SCONJ
ejpam-3985	126	11	b	b	PROPN
ejpam-3985	126	12	∈	∈	PROPN
ejpam-3985	126	13	ng(x	ng(x	NUM
ejpam-3985	126	14	)	)	PUNCT
ejpam-3985	126	15	\	\	NOUN
ejpam-3985	126	16	ng(a	ng(a	NOUN
ejpam-3985	126	17	)	)	PUNCT
ejpam-3985	126	18	,	,	PUNCT
ejpam-3985	126	19	rg(a	rg(a	PROPN
ejpam-3985	126	20	/	/	SYM
ejpam-3985	126	21	w	w	PROPN
ejpam-3985	126	22	)	)	PUNCT
ejpam-3985	126	23	6=	6=	X
ejpam-3985	126	24	rg(x	rg(x	ADP
ejpam-3985	126	25	/	/	SYM
ejpam-3985	126	26	w	w	NOUN
ejpam-3985	126	27	)	)	PUNCT
ejpam-3985	126	28	.	.	PUNCT
ejpam-3985	127	1	thus	thus	ADV
ejpam-3985	127	2	,	,	PUNCT
ejpam-3985	127	3	w	w	PROPN
ejpam-3985	127	4	is	be	AUX
ejpam-3985	127	5	a	a	DET
ejpam-3985	127	6	resolving	resolve	VERB
ejpam-3985	127	7	dominating	dominating	NOUN
ejpam-3985	127	8	set	set	NOUN
ejpam-3985	127	9	of	of	ADP
ejpam-3985	127	10	g.	g.	PROPN
ejpam-3985	127	11	since	since	SCONJ
ejpam-3985	127	12	v	v	PROPN
ejpam-3985	127	13	(	(	PUNCT
ejpam-3985	127	14	g	g	NOUN
ejpam-3985	127	15	)	)	PUNCT
ejpam-3985	127	16	\	\	PROPN
ejpam-3985	128	1	w	w	NOUN
ejpam-3985	128	2	=	=	SYM
ejpam-3985	128	3	{	{	PUNCT
ejpam-3985	128	4	x	x	NOUN
ejpam-3985	128	5	,	,	PUNCT
ejpam-3985	128	6	a	a	PRON
ejpam-3985	128	7	}	}	PUNCT
ejpam-3985	128	8	and	and	CCONJ
ejpam-3985	128	9	xa	xa	PROPN
ejpam-3985	128	10	∈	∈	PROPN
ejpam-3985	128	11	e(g	e(g	PROPN
ejpam-3985	128	12	)	)	PUNCT
ejpam-3985	128	13	,	,	PUNCT
ejpam-3985	128	14	it	it	PRON
ejpam-3985	128	15	follows	follow	VERB
ejpam-3985	128	16	that	that	SCONJ
ejpam-3985	128	17	w	w	NOUN
ejpam-3985	128	18	is	be	AUX
ejpam-3985	128	19	a	a	DET
ejpam-3985	128	20	resolving	resolve	VERB
ejpam-3985	128	21	restrained	restrained	ADJ
ejpam-3985	128	22	dominating	dominating	NOUN
ejpam-3985	128	23	set	set	NOUN
ejpam-3985	128	24	of	of	ADP
ejpam-3985	128	25	g.	g.	PROPN
ejpam-3985	128	26	if	if	SCONJ
ejpam-3985	128	27	av	av	PROPN
ejpam-3985	128	28	,	,	PUNCT
ejpam-3985	128	29	bv	bv	PROPN
ejpam-3985	128	30	/∈	/∈	PROPN
ejpam-3985	128	31	e(g	e(g	PROPN
ejpam-3985	128	32	)	)	PUNCT
ejpam-3985	128	33	,	,	PUNCT
ejpam-3985	128	34	then	then	ADV
ejpam-3985	128	35	take	take	VERB
ejpam-3985	128	36	w	w	NOUN
ejpam-3985	128	37	=	=	SYM
ejpam-3985	128	38	v	v	ADJ
ejpam-3985	128	39	(	(	PUNCT
ejpam-3985	128	40	g	g	NOUN
ejpam-3985	128	41	)	)	PUNCT
ejpam-3985	128	42	\	\	NOUN
ejpam-3985	128	43	{	{	PUNCT
ejpam-3985	128	44	x	x	NOUN
ejpam-3985	128	45	,	,	PUNCT
ejpam-3985	128	46	v	v	NOUN
ejpam-3985	128	47	}	}	PUNCT
ejpam-3985	128	48	.	.	PUNCT
ejpam-3985	129	1	again	again	ADV
ejpam-3985	129	2	,	,	PUNCT
ejpam-3985	129	3	w	w	PROPN
ejpam-3985	129	4	is	be	AUX
ejpam-3985	129	5	a	a	DET
ejpam-3985	129	6	resolving	resolve	VERB
ejpam-3985	129	7	restrained	restrained	ADJ
ejpam-3985	129	8	dominating	dominating	NOUN
ejpam-3985	129	9	set	set	NOUN
ejpam-3985	129	10	of	of	ADP
ejpam-3985	129	11	g.	g.	PROPN
ejpam-3985	129	12	in	in	ADP
ejpam-3985	129	13	either	either	DET
ejpam-3985	129	14	case	case	NOUN
ejpam-3985	129	15	,	,	PUNCT
ejpam-3985	129	16	γr(g	γr(g	NUM
ejpam-3985	129	17	)	)	PUNCT
ejpam-3985	129	18	≤	≤	NUM
ejpam-3985	130	1	|w	|w	NOUN
ejpam-3985	130	2	|	|	NOUN
ejpam-3985	130	3	=	=	SYM
ejpam-3985	130	4	n−	n−	NOUN
ejpam-3985	130	5	2	2	NUM
ejpam-3985	130	6	,	,	PUNCT
ejpam-3985	130	7	a	a	DET
ejpam-3985	130	8	contradiction	contradiction	NOUN
ejpam-3985	130	9	to	to	ADP
ejpam-3985	130	10	the	the	DET
ejpam-3985	130	11	asssumption	asssumption	NOUN
ejpam-3985	130	12	.	.	PUNCT
ejpam-3985	131	1	therefore	therefore	ADV
ejpam-3985	131	2	,	,	PUNCT
ejpam-3985	131	3	uv	uv	PROPN
ejpam-3985	131	4	/∈	/∈	PUNCT
ejpam-3985	131	5	e(g	e(g	PROPN
ejpam-3985	131	6	)	)	PUNCT
ejpam-3985	132	1	for	for	ADP
ejpam-3985	132	2	every	every	DET
ejpam-3985	132	3	two	two	NUM
ejpam-3985	132	4	distinct	distinct	ADJ
ejpam-3985	132	5	vertices	vertex	NOUN
ejpam-3985	132	6	u	u	NOUN
ejpam-3985	132	7	,	,	PUNCT
ejpam-3985	132	8	v	v	NOUN
ejpam-3985	132	9	∈	∈	PROPN
ejpam-3985	132	10	v	v	NOUN
ejpam-3985	132	11	(	(	PUNCT
ejpam-3985	132	12	g	g	NOUN
ejpam-3985	132	13	)	)	PUNCT
ejpam-3985	132	14	\	\	NOUN
ejpam-3985	132	15	{	{	PUNCT
ejpam-3985	132	16	x	x	NOUN
ejpam-3985	132	17	}	}	PUNCT
ejpam-3985	132	18	.	.	PUNCT
ejpam-3985	133	1	thus	thus	ADV
ejpam-3985	133	2	,	,	PUNCT
ejpam-3985	133	3	g	g	PROPN
ejpam-3985	133	4	∼=	∼=	PROPN
ejpam-3985	133	5	k1,n−1	k1,n−1	ADJ
ejpam-3985	133	6	.	.	PUNCT
ejpam-3985	134	1	the	the	DET
ejpam-3985	134	2	converse	converse	NOUN
ejpam-3985	134	3	is	be	AUX
ejpam-3985	134	4	easy	easy	ADJ
ejpam-3985	134	5	.	.	PUNCT
ejpam-3985	135	1	theorem	theorem	NOUN
ejpam-3985	135	2	2	2	NUM
ejpam-3985	135	3	.	.	PUNCT
ejpam-3985	136	1	let	let	VERB
ejpam-3985	136	2	g	g	PRON
ejpam-3985	136	3	be	be	AUX
ejpam-3985	136	4	a	a	DET
ejpam-3985	136	5	connected	connected	ADJ
ejpam-3985	136	6	graph	graph	NOUN
ejpam-3985	136	7	of	of	ADP
ejpam-3985	136	8	order	order	NOUN
ejpam-3985	136	9	n	n	NOUN
ejpam-3985	136	10	=	=	SYM
ejpam-3985	136	11	4	4	X
ejpam-3985	136	12	.	.	PUNCT
ejpam-3985	136	13	then	then	ADV
ejpam-3985	136	14	γrr	γrr	NOUN
ejpam-3985	136	15	=	=	SYM
ejpam-3985	136	16	2	2	NUM
ejpam-3985	137	1	if	if	SCONJ
ejpam-3985	137	2	and	and	CCONJ
ejpam-3985	137	3	only	only	ADV
ejpam-3985	137	4	if	if	SCONJ
ejpam-3985	137	5	g	g	PROPN
ejpam-3985	137	6	/∈	/∈	PUNCT
ejpam-3985	137	7	{	{	PUNCT
ejpam-3985	137	8	k4,k1,3	k4,k1,3	PROPN
ejpam-3985	137	9	}	}	PUNCT
ejpam-3985	137	10	.	.	PUNCT
ejpam-3985	138	1	proof	proof	NOUN
ejpam-3985	138	2	:	:	PUNCT
ejpam-3985	138	3	suppose	suppose	VERB
ejpam-3985	138	4	that	that	SCONJ
ejpam-3985	138	5	γrr(g	γrr(g	X
ejpam-3985	138	6	)	)	PUNCT
ejpam-3985	138	7	=	=	SYM
ejpam-3985	138	8	2	2	X
ejpam-3985	138	9	.	.	PUNCT
ejpam-3985	138	10	then	then	ADV
ejpam-3985	138	11	by	by	ADP
ejpam-3985	138	12	theorem	theorem	NOUN
ejpam-3985	138	13	1	1	NUM
ejpam-3985	138	14	,	,	PUNCT
ejpam-3985	138	15	g	g	NOUN
ejpam-3985	138	16	/∈	/∈	PUNCT
ejpam-3985	138	17	{	{	PUNCT
ejpam-3985	138	18	k4,k1,3	k4,k1,3	PROPN
ejpam-3985	138	19	}	}	PUNCT
ejpam-3985	138	20	.	.	PUNCT
ejpam-3985	139	1	for	for	ADP
ejpam-3985	139	2	the	the	DET
ejpam-3985	139	3	converse	converse	NOUN
ejpam-3985	139	4	,	,	PUNCT
ejpam-3985	139	5	suppose	suppose	VERB
ejpam-3985	139	6	that	that	SCONJ
ejpam-3985	139	7	g	g	PROPN
ejpam-3985	139	8	/∈	/∈	PUNCT
ejpam-3985	139	9	{	{	PUNCT
ejpam-3985	139	10	k4,k1,3	k4,k1,3	PROPN
ejpam-3985	139	11	}	}	PUNCT
ejpam-3985	139	12	.	.	PUNCT
ejpam-3985	140	1	since	since	SCONJ
ejpam-3985	140	2	n	n	NOUN
ejpam-3985	140	3	=	=	SYM
ejpam-3985	140	4	4	4	NUM
ejpam-3985	140	5	,	,	PUNCT
ejpam-3985	140	6	γr(g	γr(g	NUM
ejpam-3985	140	7	)	)	PUNCT
ejpam-3985	140	8	≥	≥	NOUN
ejpam-3985	140	9	2	2	X
ejpam-3985	140	10	.	.	PUNCT
ejpam-3985	140	11	choose	choose	VERB
ejpam-3985	140	12	x	x	X
ejpam-3985	140	13	,	,	PUNCT
ejpam-3985	140	14	y	y	PROPN
ejpam-3985	140	15	∈	∈	PROPN
ejpam-3985	140	16	v	v	ADP
ejpam-3985	140	17	(	(	PUNCT
ejpam-3985	140	18	g	g	NOUN
ejpam-3985	140	19	)	)	PUNCT
ejpam-3985	140	20	such	such	ADJ
ejpam-3985	140	21	that	that	DET
ejpam-3985	140	22	dg(x	dg(x	PROPN
ejpam-3985	140	23	,	,	PUNCT
ejpam-3985	140	24	y	y	NOUN
ejpam-3985	140	25	)	)	PUNCT
ejpam-3985	140	26	=	=	SYM
ejpam-3985	141	1	2	2	X
ejpam-3985	141	2	.	.	X
ejpam-3985	141	3	let	let	VERB
ejpam-3985	141	4	z	z	NOUN
ejpam-3985	141	5	∈	∈	PROPN
ejpam-3985	141	6	ng(x	ng(x	NUM
ejpam-3985	141	7	)	)	PUNCT
ejpam-3985	141	8	∩	∩	NOUN
ejpam-3985	141	9	ng(y	ng(y	NOUN
ejpam-3985	141	10	)	)	PUNCT
ejpam-3985	141	11	and	and	CCONJ
ejpam-3985	141	12	p	p	PROPN
ejpam-3985	141	13	∈	∈	PROPN
ejpam-3985	141	14	v	v	ADP
ejpam-3985	141	15	(	(	PUNCT
ejpam-3985	141	16	g	g	NOUN
ejpam-3985	141	17	)	)	PUNCT
ejpam-3985	141	18	\	\	NOUN
ejpam-3985	142	1	{	{	PUNCT
ejpam-3985	142	2	x	x	NOUN
ejpam-3985	142	3	,	,	PUNCT
ejpam-3985	142	4	y	y	PROPN
ejpam-3985	142	5	,	,	PUNCT
ejpam-3985	142	6	z	z	NOUN
ejpam-3985	142	7	}	}	PUNCT
ejpam-3985	142	8	.	.	PUNCT
ejpam-3985	143	1	consider	consider	VERB
ejpam-3985	143	2	the	the	DET
ejpam-3985	143	3	following	follow	VERB
ejpam-3985	143	4	cases	case	NOUN
ejpam-3985	143	5	:	:	PUNCT
ejpam-3985	143	6	case	case	NOUN
ejpam-3985	143	7	1	1	NUM
ejpam-3985	143	8	.	.	PUNCT
ejpam-3985	143	9	suppose	suppose	VERB
ejpam-3985	143	10	that	that	SCONJ
ejpam-3985	143	11	p	p	PROPN
ejpam-3985	143	12	∈	∈	PROPN
ejpam-3985	143	13	ng(x	ng(x	NUM
ejpam-3985	143	14	)	)	PUNCT
ejpam-3985	143	15	∩ng(y	∩ng(y	PROPN
ejpam-3985	143	16	)	)	PUNCT
ejpam-3985	143	17	.	.	PUNCT
ejpam-3985	144	1	let	let	VERB
ejpam-3985	144	2	w	w	VERB
ejpam-3985	144	3	=	=	PRON
ejpam-3985	144	4	{	{	PUNCT
ejpam-3985	144	5	x	x	NOUN
ejpam-3985	144	6	,	,	PUNCT
ejpam-3985	144	7	z	z	NOUN
ejpam-3985	144	8	}	}	PUNCT
ejpam-3985	144	9	.	.	PUNCT
ejpam-3985	145	1	then	then	ADV
ejpam-3985	145	2	w	w	PROPN
ejpam-3985	145	3	is	be	AUX
ejpam-3985	145	4	a	a	DET
ejpam-3985	145	5	resolving	resolve	VERB
ejpam-3985	145	6	restrained	restrained	ADJ
ejpam-3985	145	7	dominating	dominating	NOUN
ejpam-3985	145	8	set	set	NOUN
ejpam-3985	145	9	of	of	ADP
ejpam-3985	145	10	g.	g.	PROPN
ejpam-3985	145	11	case	case	NOUN
ejpam-3985	145	12	2	2	X
ejpam-3985	145	13	.	.	PUNCT
ejpam-3985	145	14	suppose	suppose	VERB
ejpam-3985	145	15	that	that	SCONJ
ejpam-3985	145	16	p	p	PROPN
ejpam-3985	145	17	∈	∈	PROPN
ejpam-3985	145	18	ng(x	ng(x	NUM
ejpam-3985	145	19	)	)	PUNCT
ejpam-3985	145	20	\ng(y	\ng(y	NOUN
ejpam-3985	145	21	)	)	PUNCT
ejpam-3985	145	22	.	.	PUNCT
ejpam-3985	146	1	then	then	ADV
ejpam-3985	146	2	w	w	X
ejpam-3985	146	3	=	=	SYM
ejpam-3985	146	4	{	{	PUNCT
ejpam-3985	146	5	y	y	PROPN
ejpam-3985	146	6	,	,	PUNCT
ejpam-3985	146	7	p	p	NOUN
ejpam-3985	146	8	}	}	PUNCT
ejpam-3985	146	9	,	,	PUNCT
ejpam-3985	146	10	thus	thus	ADV
ejpam-3985	146	11	w	w	NOUN
ejpam-3985	146	12	is	be	AUX
ejpam-3985	146	13	a	a	DET
ejpam-3985	146	14	resolving	resolve	VERB
ejpam-3985	146	15	restrained	restrained	ADJ
ejpam-3985	146	16	dominating	dominating	NOUN
ejpam-3985	146	17	set	set	NOUN
ejpam-3985	146	18	of	of	ADP
ejpam-3985	146	19	g.	g.	PROPN
ejpam-3985	146	20	case	case	PROPN
ejpam-3985	146	21	3	3	X
ejpam-3985	146	22	.	.	PUNCT
ejpam-3985	146	23	suppose	suppose	VERB
ejpam-3985	146	24	that	that	SCONJ
ejpam-3985	146	25	p	p	PROPN
ejpam-3985	146	26	∈	∈	PROPN
ejpam-3985	146	27	ng(y	ng(y	NOUN
ejpam-3985	146	28	)	)	PUNCT
ejpam-3985	146	29	\ng(x	\ng(x	NUM
ejpam-3985	146	30	)	)	PUNCT
ejpam-3985	146	31	.	.	PUNCT
ejpam-3985	147	1	then	then	ADV
ejpam-3985	147	2	w	w	X
ejpam-3985	147	3	=	=	SYM
ejpam-3985	147	4	{	{	PUNCT
ejpam-3985	147	5	x	x	NOUN
ejpam-3985	147	6	,	,	PUNCT
ejpam-3985	147	7	p	p	NOUN
ejpam-3985	147	8	}	}	PUNCT
ejpam-3985	147	9	,	,	PUNCT
ejpam-3985	147	10	hence	hence	ADV
ejpam-3985	147	11	w	w	PROPN
ejpam-3985	147	12	is	be	AUX
ejpam-3985	147	13	a	a	DET
ejpam-3985	147	14	resolving	resolve	VERB
ejpam-3985	147	15	restrained	restrained	ADJ
ejpam-3985	147	16	dominating	dominating	NOUN
ejpam-3985	147	17	set	set	NOUN
ejpam-3985	147	18	of	of	ADP
ejpam-3985	147	19	g.	g.	PROPN
ejpam-3985	147	20	therefore	therefore	ADV
ejpam-3985	147	21	,	,	PUNCT
ejpam-3985	147	22	in	in	ADP
ejpam-3985	147	23	all	all	DET
ejpam-3985	147	24	cases	case	NOUN
ejpam-3985	147	25	,	,	PUNCT
ejpam-3985	147	26	γrr(g	γrr(g	X
ejpam-3985	147	27	)	)	PUNCT
ejpam-3985	147	28	=	=	SYM
ejpam-3985	148	1	2	2	X
ejpam-3985	148	2	.	.	X
ejpam-3985	148	3	theorem	theorem	NOUN
ejpam-3985	148	4	3	3	X
ejpam-3985	148	5	.	.	PUNCT
ejpam-3985	149	1	let	let	VERB
ejpam-3985	149	2	g	g	PRON
ejpam-3985	149	3	be	be	AUX
ejpam-3985	149	4	a	a	DET
ejpam-3985	149	5	connected	connected	ADJ
ejpam-3985	149	6	graph	graph	NOUN
ejpam-3985	149	7	of	of	ADP
ejpam-3985	149	8	order	order	NOUN
ejpam-3985	149	9	n	n	NOUN
ejpam-3985	149	10	=	=	SYM
ejpam-3985	149	11	5	5	NUM
ejpam-3985	149	12	.	.	PUNCT
ejpam-3985	149	13	then	then	ADV
ejpam-3985	149	14	γrr(g	γrr(g	NUM
ejpam-3985	149	15	)	)	PUNCT
ejpam-3985	150	1	=	=	SYM
ejpam-3985	150	2	2	2	NUM
ejpam-3985	150	3	if	if	SCONJ
ejpam-3985	150	4	and	and	CCONJ
ejpam-3985	150	5	only	only	ADV
ejpam-3985	150	6	if	if	SCONJ
ejpam-3985	150	7	there	there	PRON
ejpam-3985	150	8	exist	exist	VERB
ejpam-3985	150	9	distinct	distinct	ADJ
ejpam-3985	150	10	vertices	vertex	NOUN
ejpam-3985	150	11	x	x	PUNCT
ejpam-3985	150	12	and	and	CCONJ
ejpam-3985	150	13	y	y	PROPN
ejpam-3985	150	14	that	that	PRON
ejpam-3985	150	15	dominate	dominate	VERB
ejpam-3985	150	16	g	g	PRON
ejpam-3985	150	17	such	such	ADJ
ejpam-3985	150	18	that	that	DET
ejpam-3985	150	19	|ng(x	|ng(x	ADJ
ejpam-3985	150	20	)	)	PUNCT
ejpam-3985	150	21	∩	∩	NOUN
ejpam-3985	150	22	ng(y)|	ng(y)|	NOUN
ejpam-3985	150	23	=	=	SYM
ejpam-3985	150	24	1	1	NUM
ejpam-3985	150	25	,	,	PUNCT
ejpam-3985	150	26	|ng(x	|ng(x	NUM
ejpam-3985	150	27	)	)	PUNCT
ejpam-3985	150	28	\	\	NOUN
ejpam-3985	150	29	{	{	PUNCT
ejpam-3985	150	30	y	y	NOUN
ejpam-3985	150	31	}	}	PUNCT
ejpam-3985	151	1	|	|	NOUN
ejpam-3985	151	2	=	=	SYM
ejpam-3985	151	3	|ng(y	|ng(y	NUM
ejpam-3985	151	4	)	)	PUNCT
ejpam-3985	151	5	\	\	NOUN
ejpam-3985	151	6	{	{	PUNCT
ejpam-3985	151	7	x	x	NOUN
ejpam-3985	151	8	}	}	PUNCT
ejpam-3985	151	9	|	|	ADV
ejpam-3985	151	10	=	=	SYM
ejpam-3985	151	11	2	2	NUM
ejpam-3985	151	12	and	and	CCONJ
ejpam-3985	151	13	〈	〈	PROPN
ejpam-3985	151	14	v	v	X
ejpam-3985	151	15	(	(	PUNCT
ejpam-3985	151	16	g	g	NOUN
ejpam-3985	151	17	)	)	PUNCT
ejpam-3985	151	18	\	\	NOUN
ejpam-3985	151	19	{	{	PUNCT
ejpam-3985	151	20	x	x	NOUN
ejpam-3985	151	21	,	,	PUNCT
ejpam-3985	151	22	y	y	PROPN
ejpam-3985	151	23	}	}	PUNCT
ejpam-3985	151	24	〉	〉	PROPN
ejpam-3985	151	25	has	have	VERB
ejpam-3985	151	26	no	no	DET
ejpam-3985	151	27	isolated	isolated	ADJ
ejpam-3985	151	28	vertex	vertex	NOUN
ejpam-3985	151	29	.	.	PUNCT
ejpam-3985	152	1	g.	g.	PROPN
ejpam-3985	152	2	monsanto	monsanto	PROPN
ejpam-3985	152	3	,	,	PUNCT
ejpam-3985	152	4	h.	h.	PROPN
ejpam-3985	152	5	rara	rara	PROPN
ejpam-3985	152	6	/	/	SYM
ejpam-3985	152	7	eur	eur	PROPN
ejpam-3985	152	8	.	.	PUNCT
ejpam-3985	153	1	j.	j.	PROPN
ejpam-3985	153	2	pure	pure	PROPN
ejpam-3985	153	3	appl	appl	PROPN
ejpam-3985	153	4	.	.	PROPN
ejpam-3985	153	5	math	math	PROPN
ejpam-3985	153	6	,	,	PUNCT
ejpam-3985	153	7	14	14	NUM
ejpam-3985	153	8	(	(	PUNCT
ejpam-3985	153	9	3	3	NUM
ejpam-3985	153	10	)	)	PUNCT
ejpam-3985	153	11	(	(	PUNCT
ejpam-3985	153	12	2021	2021	NUM
ejpam-3985	153	13	)	)	PUNCT
ejpam-3985	153	14	,	,	PUNCT
ejpam-3985	153	15	829	829	NUM
ejpam-3985	153	16	-	-	SYM
ejpam-3985	153	17	841	841	NUM
ejpam-3985	153	18	833	833	NUM
ejpam-3985	153	19	proof	proof	NOUN
ejpam-3985	153	20	:	:	PUNCT
ejpam-3985	153	21	suppose	suppose	VERB
ejpam-3985	153	22	that	that	SCONJ
ejpam-3985	153	23	γrr(g	γrr(g	X
ejpam-3985	153	24	)	)	PUNCT
ejpam-3985	153	25	=	=	SYM
ejpam-3985	153	26	2	2	X
ejpam-3985	153	27	.	.	PUNCT
ejpam-3985	153	28	then	then	ADV
ejpam-3985	153	29	there	there	PRON
ejpam-3985	153	30	exist	exist	VERB
ejpam-3985	153	31	distinct	distinct	ADJ
ejpam-3985	153	32	vertices	vertex	NOUN
ejpam-3985	153	33	x	x	PUNCT
ejpam-3985	153	34	and	and	CCONJ
ejpam-3985	153	35	y	y	PROPN
ejpam-3985	153	36	such	such	ADJ
ejpam-3985	153	37	that	that	PRON
ejpam-3985	153	38	w	w	NOUN
ejpam-3985	153	39	=	=	PRON
ejpam-3985	153	40	{	{	PUNCT
ejpam-3985	153	41	x	x	PROPN
ejpam-3985	153	42	,	,	PUNCT
ejpam-3985	153	43	y	y	PRON
ejpam-3985	153	44	}	}	PUNCT
ejpam-3985	153	45	is	be	AUX
ejpam-3985	153	46	a	a	DET
ejpam-3985	153	47	minimum	minimum	ADJ
ejpam-3985	153	48	restrained	restrained	ADJ
ejpam-3985	153	49	resolving	resolve	VERB
ejpam-3985	153	50	dominating	dominating	NOUN
ejpam-3985	153	51	set	set	NOUN
ejpam-3985	153	52	of	of	ADP
ejpam-3985	153	53	g.	g.	PROPN
ejpam-3985	153	54	hence	hence	ADV
ejpam-3985	153	55	,	,	PUNCT
ejpam-3985	153	56	|ng(x	|ng(x	NUM
ejpam-3985	153	57	)	)	PUNCT
ejpam-3985	153	58	∩	∩	NOUN
ejpam-3985	153	59	ng(y)|	ng(y)|	CCONJ
ejpam-3985	153	60	≤	≤	ADV
ejpam-3985	153	61	1	1	NUM
ejpam-3985	153	62	.	.	PUNCT
ejpam-3985	153	63	suppose	suppose	VERB
ejpam-3985	153	64	|ng(x	|ng(x	PUNCT
ejpam-3985	153	65	)	)	PUNCT
ejpam-3985	153	66	∩ng(y)|	∩ng(y)|	PROPN
ejpam-3985	153	67	=	=	PUNCT
ejpam-3985	154	1	0	0	X
ejpam-3985	154	2	.	.	PUNCT
ejpam-3985	155	1	then	then	ADV
ejpam-3985	155	2	one	one	NUM
ejpam-3985	155	3	of	of	ADP
ejpam-3985	155	4	x	x	PUNCT
ejpam-3985	155	5	and	and	CCONJ
ejpam-3985	155	6	y	y	PROPN
ejpam-3985	155	7	,	,	PUNCT
ejpam-3985	155	8	say	say	VERB
ejpam-3985	155	9	x	x	X
ejpam-3985	155	10	,	,	PUNCT
ejpam-3985	155	11	has	have	VERB
ejpam-3985	155	12	at	at	ADV
ejpam-3985	155	13	least	least	ADV
ejpam-3985	155	14	two	two	NUM
ejpam-3985	155	15	neighbors	neighbor	NOUN
ejpam-3985	155	16	,	,	PUNCT
ejpam-3985	155	17	u1	u1	NOUN
ejpam-3985	155	18	,	,	PUNCT
ejpam-3985	155	19	u2	u2	PROPN
ejpam-3985	155	20	∈	∈	PROPN
ejpam-3985	155	21	(	(	PUNCT
ejpam-3985	155	22	v	v	NOUN
ejpam-3985	155	23	(	(	PUNCT
ejpam-3985	155	24	g	g	NOUN
ejpam-3985	155	25	)	)	PUNCT
ejpam-3985	155	26	\w	\w	ADJ
ejpam-3985	155	27	)	)	PUNCT
ejpam-3985	155	28	\	\	NOUN
ejpam-3985	155	29	ng(y	ng(y	NOUN
ejpam-3985	155	30	)	)	PUNCT
ejpam-3985	155	31	.	.	PUNCT
ejpam-3985	156	1	thus	thus	ADV
ejpam-3985	156	2	,	,	PUNCT
ejpam-3985	156	3	rg(u1	rg(u1	NOUN
ejpam-3985	156	4	/	/	SYM
ejpam-3985	156	5	w	w	NOUN
ejpam-3985	156	6	)	)	PUNCT
ejpam-3985	157	1	=	=	SYM
ejpam-3985	157	2	rg(u2	rg(u2	NOUN
ejpam-3985	157	3	/	/	SYM
ejpam-3985	157	4	w	w	PROPN
ejpam-3985	157	5	)	)	PUNCT
ejpam-3985	157	6	,	,	PUNCT
ejpam-3985	157	7	a	a	DET
ejpam-3985	157	8	contradiction	contradiction	NOUN
ejpam-3985	157	9	to	to	ADP
ejpam-3985	157	10	the	the	DET
ejpam-3985	157	11	assumption	assumption	NOUN
ejpam-3985	157	12	.	.	PUNCT
ejpam-3985	158	1	hence	hence	ADV
ejpam-3985	158	2	,	,	PUNCT
ejpam-3985	158	3	|ng(x	|ng(x	NUM
ejpam-3985	158	4	)	)	PUNCT
ejpam-3985	158	5	∩	∩	NOUN
ejpam-3985	158	6	ng(y)|	ng(y)|	X
ejpam-3985	158	7	=	=	PROPN
ejpam-3985	158	8	1	1	X
ejpam-3985	158	9	.	.	PUNCT
ejpam-3985	159	1	next	next	ADV
ejpam-3985	159	2	,	,	PUNCT
ejpam-3985	159	3	let	let	VERB
ejpam-3985	159	4	z	z	NOUN
ejpam-3985	159	5	∈	∈	PROPN
ejpam-3985	159	6	ng(x	ng(x	NUM
ejpam-3985	159	7	)	)	PUNCT
ejpam-3985	159	8	∩	∩	NOUN
ejpam-3985	159	9	ng(y	ng(y	NOUN
ejpam-3985	159	10	)	)	PUNCT
ejpam-3985	159	11	and	and	CCONJ
ejpam-3985	159	12	let	let	VERB
ejpam-3985	159	13	b	b	X
ejpam-3985	159	14	,	,	PUNCT
ejpam-3985	159	15	c	c	PROPN
ejpam-3985	159	16	∈	∈	PROPN
ejpam-3985	159	17	v	v	ADP
ejpam-3985	159	18	(	(	PUNCT
ejpam-3985	159	19	g	g	NOUN
ejpam-3985	159	20	)	)	PUNCT
ejpam-3985	159	21	\	\	NOUN
ejpam-3985	160	1	{	{	PUNCT
ejpam-3985	160	2	x	x	NOUN
ejpam-3985	160	3	,	,	PUNCT
ejpam-3985	160	4	y	y	PROPN
ejpam-3985	160	5	,	,	PUNCT
ejpam-3985	160	6	z	z	NOUN
ejpam-3985	160	7	}	}	PUNCT
ejpam-3985	160	8	.	.	PUNCT
ejpam-3985	161	1	then	then	ADV
ejpam-3985	161	2	b	b	X
ejpam-3985	161	3	,	,	PUNCT
ejpam-3985	161	4	c	c	NOUN
ejpam-3985	161	5	/∈	/∈	PUNCT
ejpam-3985	161	6	ng(x	ng(x	NUM
ejpam-3985	161	7	)	)	PUNCT
ejpam-3985	161	8	∩ng(y	∩ng(y	PROPN
ejpam-3985	161	9	)	)	PUNCT
ejpam-3985	161	10	.	.	PUNCT
ejpam-3985	162	1	since	since	SCONJ
ejpam-3985	162	2	w	w	PROPN
ejpam-3985	162	3	is	be	AUX
ejpam-3985	162	4	dominating	dominate	VERB
ejpam-3985	162	5	,	,	PUNCT
ejpam-3985	162	6	b	b	PROPN
ejpam-3985	162	7	∈	∈	PROPN
ejpam-3985	162	8	ng(x	ng(x	NUM
ejpam-3985	162	9	)	)	PUNCT
ejpam-3985	162	10	or	or	CCONJ
ejpam-3985	162	11	b	b	X
ejpam-3985	162	12	∈	∈	PROPN
ejpam-3985	162	13	ng(y	ng(y	NOUN
ejpam-3985	162	14	)	)	PUNCT
ejpam-3985	162	15	.	.	PUNCT
ejpam-3985	163	1	suppose	suppose	VERB
ejpam-3985	163	2	b	b	X
ejpam-3985	163	3	∈	∈	PROPN
ejpam-3985	163	4	ng(x	ng(x	NUM
ejpam-3985	163	5	)	)	PUNCT
ejpam-3985	163	6	.	.	PUNCT
ejpam-3985	164	1	then	then	ADV
ejpam-3985	164	2	w	w	PROPN
ejpam-3985	164	3	is	be	AUX
ejpam-3985	164	4	a	a	DET
ejpam-3985	164	5	resolving	resolve	VERB
ejpam-3985	164	6	dominating	dominating	NOUN
ejpam-3985	164	7	set	set	NOUN
ejpam-3985	164	8	of	of	ADP
ejpam-3985	164	9	g	g	PROPN
ejpam-3985	164	10	implies	imply	VERB
ejpam-3985	164	11	that	that	SCONJ
ejpam-3985	164	12	c	c	PROPN
ejpam-3985	164	13	∈	∈	PROPN
ejpam-3985	164	14	ng(y	ng(y	NOUN
ejpam-3985	164	15	)	)	PUNCT
ejpam-3985	164	16	\	\	NOUN
ejpam-3985	164	17	ng(x	ng(x	NUM
ejpam-3985	164	18	)	)	PUNCT
ejpam-3985	164	19	.	.	PUNCT
ejpam-3985	165	1	hence	hence	ADV
ejpam-3985	165	2	,	,	PUNCT
ejpam-3985	165	3	|ng(x	|ng(x	NOUN
ejpam-3985	165	4	)	)	PUNCT
ejpam-3985	165	5	\	\	NOUN
ejpam-3985	166	1	{	{	PUNCT
ejpam-3985	166	2	y	y	NOUN
ejpam-3985	166	3	}	}	PUNCT
ejpam-3985	166	4	|	|	NOUN
ejpam-3985	166	5	=	=	SYM
ejpam-3985	166	6	|ng(y	|ng(y	NUM
ejpam-3985	166	7	)	)	PUNCT
ejpam-3985	166	8	\	\	NOUN
ejpam-3985	166	9	{	{	PUNCT
ejpam-3985	166	10	x	x	NOUN
ejpam-3985	166	11	}	}	PUNCT
ejpam-3985	166	12	|	|	ADV
ejpam-3985	166	13	=	=	NOUN
ejpam-3985	166	14	2	2	X
ejpam-3985	166	15	.	.	PUNCT
ejpam-3985	166	16	since	since	SCONJ
ejpam-3985	166	17	w	w	PROPN
ejpam-3985	166	18	is	be	AUX
ejpam-3985	166	19	a	a	DET
ejpam-3985	166	20	restrained	restrained	ADJ
ejpam-3985	166	21	resolving	resolve	VERB
ejpam-3985	166	22	dominating	dominating	NOUN
ejpam-3985	166	23	set	set	NOUN
ejpam-3985	166	24	,	,	PUNCT
ejpam-3985	166	25	〈	〈	PROPN
ejpam-3985	166	26	v	v	X
ejpam-3985	166	27	(	(	PUNCT
ejpam-3985	166	28	g	g	NOUN
ejpam-3985	166	29	)	)	PUNCT
ejpam-3985	166	30	\w	\w	ADJ
ejpam-3985	166	31	〉	〉	NOUN
ejpam-3985	166	32	has	have	VERB
ejpam-3985	166	33	no	no	DET
ejpam-3985	166	34	isolated	isolated	ADJ
ejpam-3985	166	35	vertex	vertex	NOUN
ejpam-3985	166	36	.	.	PUNCT
ejpam-3985	167	1	for	for	ADP
ejpam-3985	167	2	the	the	DET
ejpam-3985	167	3	converse	converse	NOUN
ejpam-3985	167	4	,	,	PUNCT
ejpam-3985	167	5	suppose	suppose	VERB
ejpam-3985	167	6	there	there	PRON
ejpam-3985	167	7	exist	exist	VERB
ejpam-3985	167	8	distinct	distinct	ADJ
ejpam-3985	167	9	vertices	vertex	NOUN
ejpam-3985	167	10	x	x	X
ejpam-3985	167	11	,	,	PUNCT
ejpam-3985	167	12	y	y	PROPN
ejpam-3985	167	13	∈	∈	PROPN
ejpam-3985	167	14	v	v	ADP
ejpam-3985	167	15	(	(	PUNCT
ejpam-3985	167	16	g	g	NOUN
ejpam-3985	167	17	)	)	PUNCT
ejpam-3985	167	18	satisfying	satisfy	VERB
ejpam-3985	167	19	the	the	DET
ejpam-3985	167	20	given	give	VERB
ejpam-3985	167	21	properties	property	NOUN
ejpam-3985	167	22	.	.	PUNCT
ejpam-3985	168	1	let	let	VERB
ejpam-3985	168	2	w	w	VERB
ejpam-3985	168	3	=	=	PRON
ejpam-3985	168	4	{	{	PUNCT
ejpam-3985	168	5	x	x	PROPN
ejpam-3985	168	6	,	,	PUNCT
ejpam-3985	168	7	y	y	PROPN
ejpam-3985	168	8	}	}	PUNCT
ejpam-3985	168	9	.	.	PUNCT
ejpam-3985	169	1	then	then	ADV
ejpam-3985	169	2	w	w	PROPN
ejpam-3985	169	3	is	be	AUX
ejpam-3985	169	4	a	a	DET
ejpam-3985	169	5	resolving	resolve	VERB
ejpam-3985	169	6	restrained	restrained	ADJ
ejpam-3985	169	7	dominating	dominating	NOUN
ejpam-3985	169	8	set	set	NOUN
ejpam-3985	169	9	of	of	ADP
ejpam-3985	169	10	g.	g.	PROPN
ejpam-3985	169	11	hence	hence	ADV
ejpam-3985	169	12	,	,	PUNCT
ejpam-3985	169	13	γrr(g	γrr(g	PROPN
ejpam-3985	169	14	)	)	PUNCT
ejpam-3985	169	15	=	=	SYM
ejpam-3985	170	1	2	2	NUM
ejpam-3985	170	2	.	.	NOUN
ejpam-3985	170	3	3	3	X
ejpam-3985	170	4	.	.	X
ejpam-3985	170	5	resolving	resolve	VERB
ejpam-3985	170	6	restrained	restrained	ADJ
ejpam-3985	170	7	domination	domination	NOUN
ejpam-3985	170	8	in	in	ADP
ejpam-3985	170	9	the	the	DET
ejpam-3985	170	10	join	join	NOUN
ejpam-3985	170	11	of	of	ADP
ejpam-3985	170	12	graphs	graph	NOUN
ejpam-3985	170	13	theorem	theorem	VERB
ejpam-3985	170	14	4	4	NUM
ejpam-3985	170	15	.	.	PUNCT
ejpam-3985	171	1	[	[	X
ejpam-3985	171	2	6	6	NUM
ejpam-3985	171	3	]	]	PUNCT
ejpam-3985	171	4	let	let	VERB
ejpam-3985	171	5	g	g	PROPN
ejpam-3985	171	6	and	and	CCONJ
ejpam-3985	171	7	h	h	NOUN
ejpam-3985	171	8	be	be	AUX
ejpam-3985	171	9	connected	connect	VERB
ejpam-3985	171	10	graphs	graph	NOUN
ejpam-3985	171	11	.	.	PUNCT
ejpam-3985	172	1	then	then	ADV
ejpam-3985	172	2	c	c	PROPN
ejpam-3985	172	3	⊆	⊆	NUM
ejpam-3985	172	4	v	v	NOUN
ejpam-3985	172	5	(	(	PUNCT
ejpam-3985	172	6	g+h	g+h	PROPN
ejpam-3985	172	7	)	)	PUNCT
ejpam-3985	172	8	is	be	AUX
ejpam-3985	172	9	a	a	DET
ejpam-3985	172	10	dominating	dominating	NOUN
ejpam-3985	172	11	set	set	VERB
ejpam-3985	172	12	in	in	ADP
ejpam-3985	172	13	g+h	g+h	PROPN
ejpam-3985	172	14	if	if	SCONJ
ejpam-3985	172	15	and	and	CCONJ
ejpam-3985	172	16	only	only	ADV
ejpam-3985	172	17	if	if	SCONJ
ejpam-3985	172	18	at	at	ADV
ejpam-3985	172	19	least	least	ADJ
ejpam-3985	172	20	one	one	NUM
ejpam-3985	172	21	of	of	ADP
ejpam-3985	172	22	the	the	DET
ejpam-3985	172	23	following	follow	VERB
ejpam-3985	172	24	is	be	AUX
ejpam-3985	172	25	true	true	ADJ
ejpam-3985	172	26	:	:	PUNCT
ejpam-3985	172	27	(	(	PUNCT
ejpam-3985	172	28	i	i	NOUN
ejpam-3985	172	29	)	)	PUNCT
ejpam-3985	172	30	c	c	PROPN
ejpam-3985	172	31	∩	∩	PROPN
ejpam-3985	172	32	v	v	X
ejpam-3985	172	33	(	(	PUNCT
ejpam-3985	172	34	g	g	NOUN
ejpam-3985	172	35	)	)	PUNCT
ejpam-3985	172	36	is	be	AUX
ejpam-3985	172	37	a	a	DET
ejpam-3985	172	38	dominating	dominating	NOUN
ejpam-3985	172	39	set	set	VERB
ejpam-3985	172	40	in	in	ADP
ejpam-3985	172	41	g.	g.	PROPN
ejpam-3985	172	42	(	(	PUNCT
ejpam-3985	172	43	ii	ii	PROPN
ejpam-3985	172	44	)	)	PUNCT
ejpam-3985	172	45	c	c	NOUN
ejpam-3985	172	46	∩	∩	PROPN
ejpam-3985	172	47	v	v	X
ejpam-3985	172	48	(	(	PUNCT
ejpam-3985	172	49	h	h	NOUN
ejpam-3985	172	50	)	)	PUNCT
ejpam-3985	172	51	is	be	AUX
ejpam-3985	172	52	a	a	DET
ejpam-3985	172	53	dominating	dominating	NOUN
ejpam-3985	172	54	set	set	NOUN
ejpam-3985	172	55	in	in	ADP
ejpam-3985	172	56	h.	h.	PROPN
ejpam-3985	172	57	(	(	PUNCT
ejpam-3985	172	58	iii	iii	NOUN
ejpam-3985	172	59	)	)	PUNCT
ejpam-3985	172	60	c	c	NOUN
ejpam-3985	172	61	∩	∩	X
ejpam-3985	172	62	v	v	X
ejpam-3985	172	63	(	(	PUNCT
ejpam-3985	172	64	g	g	NOUN
ejpam-3985	172	65	)	)	PUNCT
ejpam-3985	172	66	6=	6=	ADP
ejpam-3985	172	67	∅	∅	NOUN
ejpam-3985	172	68	and	and	CCONJ
ejpam-3985	172	69	c	c	NOUN
ejpam-3985	172	70	∩	∩	ADJ
ejpam-3985	172	71	v	v	X
ejpam-3985	172	72	(	(	PUNCT
ejpam-3985	172	73	h	h	NOUN
ejpam-3985	172	74	)	)	PUNCT
ejpam-3985	172	75	6=	6=	ADP
ejpam-3985	172	76	∅.	∅.	NOUN
ejpam-3985	172	77	theorem	theorem	VERB
ejpam-3985	172	78	5	5	NUM
ejpam-3985	172	79	.	.	PUNCT
ejpam-3985	173	1	[	[	X
ejpam-3985	173	2	14	14	NUM
ejpam-3985	173	3	]	]	PUNCT
ejpam-3985	173	4	let	let	VERB
ejpam-3985	173	5	g	g	NOUN
ejpam-3985	173	6	and	and	CCONJ
ejpam-3985	173	7	h	h	PROPN
ejpam-3985	173	8	be	be	VERB
ejpam-3985	173	9	non	non	ADJ
ejpam-3985	173	10	-	-	ADJ
ejpam-3985	173	11	trivial	trivial	ADJ
ejpam-3985	173	12	connected	connected	ADJ
ejpam-3985	173	13	graphs	graph	NOUN
ejpam-3985	173	14	.	.	PUNCT
ejpam-3985	174	1	a	a	DET
ejpam-3985	174	2	set	set	NOUN
ejpam-3985	174	3	w	w	PROPN
ejpam-3985	174	4	⊆	⊆	NUM
ejpam-3985	174	5	v	v	NOUN
ejpam-3985	174	6	(	(	PUNCT
ejpam-3985	174	7	g+h	g+h	NOUN
ejpam-3985	174	8	)	)	PUNCT
ejpam-3985	174	9	is	be	AUX
ejpam-3985	174	10	a	a	DET
ejpam-3985	174	11	locating	locate	VERB
ejpam-3985	174	12	-	-	PUNCT
ejpam-3985	174	13	dominating	dominate	VERB
ejpam-3985	174	14	set	set	NOUN
ejpam-3985	174	15	of	of	ADP
ejpam-3985	174	16	g+h	g+h	PROPN
ejpam-3985	174	17	if	if	SCONJ
ejpam-3985	174	18	and	and	CCONJ
ejpam-3985	174	19	only	only	ADV
ejpam-3985	174	20	if	if	SCONJ
ejpam-3985	174	21	w	w	PROPN
ejpam-3985	174	22	=	=	VERB
ejpam-3985	174	23	wg	wg	PROPN
ejpam-3985	174	24	∪wh	∪wh	NOUN
ejpam-3985	174	25	where	where	SCONJ
ejpam-3985	174	26	wg	wg	PROPN
ejpam-3985	174	27	⊆	⊆	NUM
ejpam-3985	174	28	v	v	NOUN
ejpam-3985	174	29	(	(	PUNCT
ejpam-3985	174	30	g	g	NOUN
ejpam-3985	174	31	)	)	PUNCT
ejpam-3985	174	32	and	and	CCONJ
ejpam-3985	174	33	wh	wh	VERB
ejpam-3985	174	34	⊆	⊆	NUM
ejpam-3985	174	35	v	v	NOUN
ejpam-3985	174	36	(	(	PUNCT
ejpam-3985	174	37	h	h	NOUN
ejpam-3985	174	38	)	)	PUNCT
ejpam-3985	174	39	are	be	AUX
ejpam-3985	174	40	locating	locate	VERB
ejpam-3985	174	41	-	-	PUNCT
ejpam-3985	174	42	dominating	dominating	NOUN
ejpam-3985	174	43	sets	set	NOUN
ejpam-3985	174	44	of	of	ADP
ejpam-3985	174	45	g	g	PROPN
ejpam-3985	174	46	and	and	CCONJ
ejpam-3985	174	47	h	h	NOUN
ejpam-3985	174	48	,	,	PUNCT
ejpam-3985	174	49	respectively	respectively	ADV
ejpam-3985	174	50	,	,	PUNCT
ejpam-3985	174	51	where	where	SCONJ
ejpam-3985	174	52	wg	wg	NOUN
ejpam-3985	174	53	or	or	CCONJ
ejpam-3985	174	54	wh	wh	PROPN
ejpam-3985	174	55	is	be	AUX
ejpam-3985	174	56	a	a	DET
ejpam-3985	174	57	strictly	strictly	ADV
ejpam-3985	174	58	locating	locate	VERB
ejpam-3985	174	59	set	set	NOUN
ejpam-3985	174	60	.	.	PUNCT
ejpam-3985	175	1	theorem	theorem	VERB
ejpam-3985	175	2	6	6	NUM
ejpam-3985	175	3	.	.	PUNCT
ejpam-3985	176	1	[	[	X
ejpam-3985	176	2	9	9	NUM
ejpam-3985	176	3	]	]	PUNCT
ejpam-3985	176	4	let	let	VERB
ejpam-3985	176	5	g	g	NOUN
ejpam-3985	176	6	and	and	CCONJ
ejpam-3985	176	7	h	h	PROPN
ejpam-3985	176	8	be	be	VERB
ejpam-3985	176	9	non	non	ADJ
ejpam-3985	176	10	-	-	ADJ
ejpam-3985	176	11	trivial	trivial	ADJ
ejpam-3985	176	12	connected	connected	ADJ
ejpam-3985	176	13	graphs	graph	NOUN
ejpam-3985	176	14	.	.	PUNCT
ejpam-3985	177	1	a	a	DET
ejpam-3985	177	2	set	set	NOUN
ejpam-3985	177	3	w	w	PROPN
ejpam-3985	177	4	⊆	⊆	NUM
ejpam-3985	177	5	v	v	NOUN
ejpam-3985	177	6	(	(	PUNCT
ejpam-3985	177	7	g+h	g+h	NOUN
ejpam-3985	177	8	)	)	PUNCT
ejpam-3985	177	9	is	be	AUX
ejpam-3985	177	10	a	a	DET
ejpam-3985	177	11	resolving	resolving	NOUN
ejpam-3985	177	12	set	set	NOUN
ejpam-3985	177	13	of	of	ADP
ejpam-3985	177	14	g+h	g+h	PROPN
ejpam-3985	177	15	if	if	SCONJ
ejpam-3985	177	16	and	and	CCONJ
ejpam-3985	177	17	only	only	ADV
ejpam-3985	177	18	if	if	SCONJ
ejpam-3985	177	19	w	w	PROPN
ejpam-3985	177	20	=	=	VERB
ejpam-3985	177	21	wg	wg	PROPN
ejpam-3985	177	22	∪wh	∪wh	NOUN
ejpam-3985	177	23	where	where	SCONJ
ejpam-3985	177	24	wg	wg	PROPN
ejpam-3985	177	25	⊆	⊆	NUM
ejpam-3985	177	26	v	v	NOUN
ejpam-3985	177	27	(	(	PUNCT
ejpam-3985	177	28	g	g	NOUN
ejpam-3985	177	29	)	)	PUNCT
ejpam-3985	177	30	and	and	CCONJ
ejpam-3985	177	31	wh	wh	VERB
ejpam-3985	177	32	⊆	⊆	NUM
ejpam-3985	177	33	v	v	NOUN
ejpam-3985	177	34	(	(	PUNCT
ejpam-3985	177	35	h	h	NOUN
ejpam-3985	177	36	)	)	PUNCT
ejpam-3985	177	37	are	be	AUX
ejpam-3985	177	38	locating	locate	VERB
ejpam-3985	177	39	sets	set	NOUN
ejpam-3985	177	40	of	of	ADP
ejpam-3985	177	41	g	g	PROPN
ejpam-3985	177	42	and	and	CCONJ
ejpam-3985	177	43	h	h	NOUN
ejpam-3985	177	44	,	,	PUNCT
ejpam-3985	177	45	respectively	respectively	ADV
ejpam-3985	177	46	,	,	PUNCT
ejpam-3985	177	47	where	where	SCONJ
ejpam-3985	177	48	wg	wg	NOUN
ejpam-3985	177	49	or	or	CCONJ
ejpam-3985	177	50	wh	wh	PROPN
ejpam-3985	177	51	is	be	AUX
ejpam-3985	177	52	a	a	DET
ejpam-3985	177	53	strictly	strictly	ADV
ejpam-3985	177	54	locating	locate	VERB
ejpam-3985	177	55	set	set	NOUN
ejpam-3985	177	56	.	.	PUNCT
ejpam-3985	178	1	theorem	theorem	VERB
ejpam-3985	178	2	7	7	NUM
ejpam-3985	178	3	.	.	PUNCT
ejpam-3985	179	1	let	let	VERB
ejpam-3985	179	2	g	g	NOUN
ejpam-3985	179	3	and	and	CCONJ
ejpam-3985	179	4	h	h	PROPN
ejpam-3985	179	5	be	be	VERB
ejpam-3985	179	6	non	non	ADJ
ejpam-3985	179	7	-	-	ADJ
ejpam-3985	179	8	trivial	trivial	ADJ
ejpam-3985	179	9	connected	connected	ADJ
ejpam-3985	179	10	graphs	graph	NOUN
ejpam-3985	179	11	.	.	PUNCT
ejpam-3985	180	1	a	a	DET
ejpam-3985	180	2	set	set	NOUN
ejpam-3985	180	3	w	w	PROPN
ejpam-3985	180	4	⊆	⊆	NUM
ejpam-3985	180	5	v	v	NOUN
ejpam-3985	180	6	(	(	PUNCT
ejpam-3985	180	7	g	g	PROPN
ejpam-3985	180	8	+	+	NOUN
ejpam-3985	180	9	h	h	NOUN
ejpam-3985	180	10	)	)	PUNCT
ejpam-3985	180	11	is	be	AUX
ejpam-3985	180	12	a	a	DET
ejpam-3985	180	13	resolving	resolve	VERB
ejpam-3985	180	14	dominating	dominating	NOUN
ejpam-3985	180	15	set	set	NOUN
ejpam-3985	180	16	of	of	ADP
ejpam-3985	180	17	g+h	g+h	PROPN
ejpam-3985	181	1	if	if	SCONJ
ejpam-3985	181	2	and	and	CCONJ
ejpam-3985	181	3	only	only	ADV
ejpam-3985	181	4	if	if	SCONJ
ejpam-3985	181	5	w	w	NOUN
ejpam-3985	181	6	is	be	AUX
ejpam-3985	181	7	a	a	DET
ejpam-3985	181	8	locating	locate	VERB
ejpam-3985	181	9	-	-	PUNCT
ejpam-3985	181	10	dominating	dominate	VERB
ejpam-3985	181	11	set	set	NOUN
ejpam-3985	181	12	of	of	ADP
ejpam-3985	181	13	g+h	g+h	PROPN
ejpam-3985	181	14	.	.	PUNCT
ejpam-3985	182	1	proof	proof	NOUN
ejpam-3985	182	2	:	:	PUNCT
ejpam-3985	182	3	suppose	suppose	VERB
ejpam-3985	182	4	that	that	SCONJ
ejpam-3985	182	5	w	w	NOUN
ejpam-3985	182	6	is	be	AUX
ejpam-3985	182	7	a	a	DET
ejpam-3985	182	8	resolving	resolve	VERB
ejpam-3985	182	9	dominating	dominating	NOUN
ejpam-3985	182	10	set	set	NOUN
ejpam-3985	182	11	of	of	ADP
ejpam-3985	182	12	g+h	g+h	PROPN
ejpam-3985	182	13	.	.	PUNCT
ejpam-3985	183	1	then	then	ADV
ejpam-3985	183	2	w	w	PROPN
ejpam-3985	183	3	is	be	AUX
ejpam-3985	183	4	a	a	DET
ejpam-3985	183	5	resolving	resolving	NOUN
ejpam-3985	183	6	set	set	NOUN
ejpam-3985	183	7	of	of	ADP
ejpam-3985	183	8	g	g	PROPN
ejpam-3985	183	9	+	+	CCONJ
ejpam-3985	183	10	h.	h.	PROPN
ejpam-3985	183	11	by	by	ADP
ejpam-3985	183	12	theorem	theorem	NOUN
ejpam-3985	183	13	6	6	NUM
ejpam-3985	183	14	,	,	PUNCT
ejpam-3985	183	15	w	w	NOUN
ejpam-3985	183	16	=	=	PUNCT
ejpam-3985	183	17	wg	wg	PROPN
ejpam-3985	183	18	∪wh	∪wh	NOUN
ejpam-3985	183	19	where	where	SCONJ
ejpam-3985	183	20	wg	wg	PROPN
ejpam-3985	183	21	⊆	⊆	NUM
ejpam-3985	183	22	v	v	NOUN
ejpam-3985	183	23	(	(	PUNCT
ejpam-3985	183	24	g	g	NOUN
ejpam-3985	183	25	)	)	PUNCT
ejpam-3985	183	26	and	and	CCONJ
ejpam-3985	183	27	wh	wh	VERB
ejpam-3985	183	28	⊆	⊆	NUM
ejpam-3985	183	29	v	v	NOUN
ejpam-3985	183	30	(	(	PUNCT
ejpam-3985	183	31	h	h	NOUN
ejpam-3985	183	32	)	)	PUNCT
ejpam-3985	183	33	are	be	AUX
ejpam-3985	183	34	locating	locate	VERB
ejpam-3985	183	35	sets	set	NOUN
ejpam-3985	183	36	of	of	ADP
ejpam-3985	183	37	g	g	PROPN
ejpam-3985	183	38	and	and	CCONJ
ejpam-3985	183	39	h	h	NOUN
ejpam-3985	183	40	,	,	PUNCT
ejpam-3985	183	41	respectively	respectively	ADV
ejpam-3985	183	42	,	,	PUNCT
ejpam-3985	183	43	where	where	SCONJ
ejpam-3985	183	44	wg	wg	NOUN
ejpam-3985	183	45	or	or	CCONJ
ejpam-3985	183	46	wh	wh	PROPN
ejpam-3985	183	47	is	be	AUX
ejpam-3985	183	48	a	a	DET
ejpam-3985	183	49	strictly	strictly	ADV
ejpam-3985	183	50	locating	locate	VERB
ejpam-3985	183	51	set	set	NOUN
ejpam-3985	183	52	.	.	PUNCT
ejpam-3985	184	1	since	since	SCONJ
ejpam-3985	184	2	w	w	PROPN
ejpam-3985	184	3	is	be	AUX
ejpam-3985	184	4	a	a	DET
ejpam-3985	184	5	dominating	dominating	NOUN
ejpam-3985	184	6	set	set	NOUN
ejpam-3985	184	7	of	of	ADP
ejpam-3985	184	8	g	g	PROPN
ejpam-3985	184	9	+	+	CCONJ
ejpam-3985	184	10	h	h	NOUN
ejpam-3985	184	11	,	,	PUNCT
ejpam-3985	184	12	wg	wg	VERB
ejpam-3985	184	13	and	and	CCONJ
ejpam-3985	184	14	wh	wh	PROPN
ejpam-3985	184	15	are	be	AUX
ejpam-3985	184	16	also	also	ADV
ejpam-3985	184	17	dominatings	dominating	NOUN
ejpam-3985	184	18	sets	set	NOUN
ejpam-3985	184	19	of	of	ADP
ejpam-3985	184	20	g	g	PROPN
ejpam-3985	184	21	and	and	CCONJ
ejpam-3985	184	22	h	h	NOUN
ejpam-3985	184	23	,	,	PUNCT
ejpam-3985	184	24	respectively	respectively	ADV
ejpam-3985	184	25	.	.	PUNCT
ejpam-3985	185	1	by	by	ADP
ejpam-3985	185	2	theorem	theorem	NOUN
ejpam-3985	185	3	5	5	NUM
ejpam-3985	185	4	,	,	PUNCT
ejpam-3985	185	5	w	w	PROPN
ejpam-3985	185	6	is	be	AUX
ejpam-3985	185	7	a	a	DET
ejpam-3985	185	8	locating	locate	VERB
ejpam-3985	185	9	-	-	PUNCT
ejpam-3985	185	10	dominating	dominate	VERB
ejpam-3985	185	11	set	set	NOUN
ejpam-3985	185	12	of	of	ADP
ejpam-3985	185	13	g+h	g+h	PROPN
ejpam-3985	185	14	.	.	PUNCT
ejpam-3985	186	1	the	the	DET
ejpam-3985	186	2	converse	converse	NOUN
ejpam-3985	186	3	immediately	immediately	ADV
ejpam-3985	186	4	follows	follow	VERB
ejpam-3985	186	5	from	from	ADP
ejpam-3985	186	6	theorem	theorem	ADJ
ejpam-3985	186	7	5	5	NUM
ejpam-3985	186	8	and	and	CCONJ
ejpam-3985	186	9	theorem	theorem	ADJ
ejpam-3985	186	10	4(iii	4(iii	NUM
ejpam-3985	186	11	)	)	PUNCT
ejpam-3985	186	12	.	.	PUNCT
ejpam-3985	187	1	the	the	DET
ejpam-3985	187	2	next	next	ADJ
ejpam-3985	187	3	result	result	NOUN
ejpam-3985	187	4	follows	follow	VERB
ejpam-3985	187	5	immediately	immediately	ADV
ejpam-3985	187	6	from	from	ADP
ejpam-3985	187	7	theorem	theorem	ADJ
ejpam-3985	187	8	5	5	NUM
ejpam-3985	187	9	.	.	PUNCT
ejpam-3985	187	10	theorem	theorem	NOUN
ejpam-3985	187	11	8	8	NUM
ejpam-3985	187	12	.	.	PUNCT
ejpam-3985	188	1	let	let	VERB
ejpam-3985	188	2	g	g	NOUN
ejpam-3985	188	3	and	and	CCONJ
ejpam-3985	188	4	h	h	PROPN
ejpam-3985	188	5	be	be	VERB
ejpam-3985	188	6	non	non	ADJ
ejpam-3985	188	7	-	-	ADJ
ejpam-3985	188	8	trivial	trivial	ADJ
ejpam-3985	188	9	connected	connected	ADJ
ejpam-3985	188	10	graphs	graph	NOUN
ejpam-3985	188	11	.	.	PUNCT
ejpam-3985	189	1	a	a	DET
ejpam-3985	189	2	set	set	NOUN
ejpam-3985	189	3	w	w	PROPN
ejpam-3985	189	4	⊆	⊆	NUM
ejpam-3985	189	5	v	v	NOUN
ejpam-3985	189	6	(	(	PUNCT
ejpam-3985	189	7	g	g	PROPN
ejpam-3985	189	8	+	+	NOUN
ejpam-3985	189	9	h	h	NOUN
ejpam-3985	189	10	)	)	PUNCT
ejpam-3985	189	11	is	be	AUX
ejpam-3985	189	12	a	a	DET
ejpam-3985	189	13	resolving	resolve	VERB
ejpam-3985	189	14	dominating	dominating	NOUN
ejpam-3985	189	15	set	set	NOUN
ejpam-3985	189	16	of	of	ADP
ejpam-3985	189	17	g+h	g+h	PROPN
ejpam-3985	190	1	if	if	SCONJ
ejpam-3985	190	2	and	and	CCONJ
ejpam-3985	190	3	only	only	ADV
ejpam-3985	190	4	if	if	SCONJ
ejpam-3985	190	5	w	w	PROPN
ejpam-3985	190	6	=	=	VERB
ejpam-3985	190	7	wg	wg	PROPN
ejpam-3985	190	8	∪wh	∪wh	NOUN
ejpam-3985	190	9	where	where	SCONJ
ejpam-3985	190	10	wg	wg	PROPN
ejpam-3985	190	11	=	=	SYM
ejpam-3985	190	12	v	v	NOUN
ejpam-3985	190	13	(	(	PUNCT
ejpam-3985	190	14	g	g	NOUN
ejpam-3985	190	15	)	)	PUNCT
ejpam-3985	190	16	∩w	∩w	NOUN
ejpam-3985	190	17	and	and	CCONJ
ejpam-3985	190	18	wh	wh	VERB
ejpam-3985	190	19	=	=	SYM
ejpam-3985	190	20	v	v	PROPN
ejpam-3985	190	21	(	(	PUNCT
ejpam-3985	190	22	h	h	NOUN
ejpam-3985	190	23	)	)	PUNCT
ejpam-3985	190	24	∩w	∩w	NOUN
ejpam-3985	190	25	are	be	AUX
ejpam-3985	190	26	locating	locate	VERB
ejpam-3985	190	27	sets	set	NOUN
ejpam-3985	190	28	of	of	ADP
ejpam-3985	190	29	g	g	PROPN
ejpam-3985	190	30	and	and	CCONJ
ejpam-3985	190	31	h	h	NOUN
ejpam-3985	190	32	,	,	PUNCT
ejpam-3985	190	33	respectively	respectively	ADV
ejpam-3985	190	34	,	,	PUNCT
ejpam-3985	190	35	where	where	SCONJ
ejpam-3985	190	36	wg	wg	NOUN
ejpam-3985	190	37	or	or	CCONJ
ejpam-3985	190	38	wh	wh	PROPN
ejpam-3985	190	39	is	be	AUX
ejpam-3985	190	40	a	a	DET
ejpam-3985	190	41	strictly	strictly	ADV
ejpam-3985	190	42	locating	locate	VERB
ejpam-3985	190	43	set	set	NOUN
ejpam-3985	190	44	.	.	PUNCT
ejpam-3985	191	1	g.	g.	PROPN
ejpam-3985	191	2	monsanto	monsanto	PROPN
ejpam-3985	191	3	,	,	PUNCT
ejpam-3985	191	4	h.	h.	PROPN
ejpam-3985	191	5	rara	rara	PROPN
ejpam-3985	191	6	/	/	SYM
ejpam-3985	191	7	eur	eur	PROPN
ejpam-3985	191	8	.	.	PUNCT
ejpam-3985	192	1	j.	j.	PROPN
ejpam-3985	192	2	pure	pure	PROPN
ejpam-3985	192	3	appl	appl	PROPN
ejpam-3985	192	4	.	.	PROPN
ejpam-3985	192	5	math	math	PROPN
ejpam-3985	192	6	,	,	PUNCT
ejpam-3985	192	7	14	14	NUM
ejpam-3985	192	8	(	(	PUNCT
ejpam-3985	192	9	3	3	NUM
ejpam-3985	192	10	)	)	PUNCT
ejpam-3985	192	11	(	(	PUNCT
ejpam-3985	192	12	2021	2021	NUM
ejpam-3985	192	13	)	)	PUNCT
ejpam-3985	192	14	,	,	PUNCT
ejpam-3985	192	15	829	829	NUM
ejpam-3985	192	16	-	-	SYM
ejpam-3985	192	17	841	841	NUM
ejpam-3985	192	18	834	834	NUM
ejpam-3985	192	19	theorem	theorem	NOUN
ejpam-3985	192	20	9	9	NUM
ejpam-3985	192	21	.	.	PUNCT
ejpam-3985	193	1	let	let	VERB
ejpam-3985	193	2	g	g	NOUN
ejpam-3985	193	3	and	and	CCONJ
ejpam-3985	193	4	h	h	NOUN
ejpam-3985	193	5	be	be	AUX
ejpam-3985	193	6	nontrivial	nontrivial	ADJ
ejpam-3985	193	7	connected	connected	ADJ
ejpam-3985	193	8	graphs	graph	NOUN
ejpam-3985	193	9	.	.	PUNCT
ejpam-3985	194	1	a	a	DET
ejpam-3985	194	2	set	set	NOUN
ejpam-3985	194	3	w	w	PROPN
ejpam-3985	194	4	⊆	⊆	NUM
ejpam-3985	194	5	v	v	NOUN
ejpam-3985	194	6	(	(	PUNCT
ejpam-3985	194	7	g	g	PROPN
ejpam-3985	194	8	+	+	NOUN
ejpam-3985	194	9	h	h	NOUN
ejpam-3985	194	10	)	)	PUNCT
ejpam-3985	194	11	is	be	AUX
ejpam-3985	194	12	a	a	DET
ejpam-3985	194	13	resolving	resolve	VERB
ejpam-3985	194	14	restrained	restrained	ADJ
ejpam-3985	194	15	dominating	dominating	NOUN
ejpam-3985	194	16	set	set	NOUN
ejpam-3985	194	17	of	of	ADP
ejpam-3985	194	18	g	g	PROPN
ejpam-3985	195	1	+	+	CCONJ
ejpam-3985	195	2	h	h	NOUN
ejpam-3985	195	3	if	if	SCONJ
ejpam-3985	195	4	and	and	CCONJ
ejpam-3985	195	5	only	only	ADV
ejpam-3985	195	6	if	if	SCONJ
ejpam-3985	195	7	w	w	PROPN
ejpam-3985	195	8	=	=	VERB
ejpam-3985	195	9	wg	wg	PROPN
ejpam-3985	195	10	∪wh	∪wh	NOUN
ejpam-3985	195	11	and	and	CCONJ
ejpam-3985	195	12	satisfies	satisfy	VERB
ejpam-3985	195	13	the	the	DET
ejpam-3985	195	14	following	follow	VERB
ejpam-3985	195	15	conditions	condition	NOUN
ejpam-3985	195	16	:	:	PUNCT
ejpam-3985	195	17	(	(	PUNCT
ejpam-3985	195	18	i	i	NOUN
ejpam-3985	195	19	)	)	PUNCT
ejpam-3985	195	20	wg	wg	VERB
ejpam-3985	195	21	and	and	CCONJ
ejpam-3985	195	22	wh	wh	PROPN
ejpam-3985	195	23	are	be	AUX
ejpam-3985	195	24	locating	locate	VERB
ejpam-3985	195	25	sets	set	NOUN
ejpam-3985	195	26	of	of	ADP
ejpam-3985	195	27	g	g	PROPN
ejpam-3985	195	28	and	and	CCONJ
ejpam-3985	195	29	h	h	NOUN
ejpam-3985	195	30	,	,	PUNCT
ejpam-3985	195	31	respectively	respectively	ADV
ejpam-3985	195	32	;	;	PUNCT
ejpam-3985	195	33	(	(	PUNCT
ejpam-3985	195	34	ii	ii	NOUN
ejpam-3985	195	35	)	)	PUNCT
ejpam-3985	195	36	wg	wg	PROPN
ejpam-3985	195	37	(	(	PUNCT
ejpam-3985	195	38	wh	wh	NOUN
ejpam-3985	195	39	)	)	PUNCT
ejpam-3985	195	40	is	be	AUX
ejpam-3985	195	41	a	a	DET
ejpam-3985	195	42	restrained	restrained	ADJ
ejpam-3985	195	43	locating	locating	NOUN
ejpam-3985	195	44	set	set	NOUN
ejpam-3985	195	45	of	of	ADP
ejpam-3985	195	46	g	g	PROPN
ejpam-3985	195	47	(	(	PUNCT
ejpam-3985	195	48	resp	resp	NOUN
ejpam-3985	195	49	.	.	PUNCT
ejpam-3985	196	1	h	h	X
ejpam-3985	196	2	)	)	PUNCT
ejpam-3985	196	3	whenever	whenever	SCONJ
ejpam-3985	196	4	wg	wg	PROPN
ejpam-3985	196	5	=	=	SYM
ejpam-3985	196	6	v	v	X
ejpam-3985	196	7	(	(	PUNCT
ejpam-3985	196	8	g	g	NOUN
ejpam-3985	196	9	)	)	PUNCT
ejpam-3985	196	10	(	(	PUNCT
ejpam-3985	196	11	resp	resp	NOUN
ejpam-3985	196	12	.	.	PUNCT
ejpam-3985	197	1	wh	wh	VERB
ejpam-3985	197	2	=	=	SYM
ejpam-3985	197	3	v	v	PROPN
ejpam-3985	197	4	(	(	PUNCT
ejpam-3985	197	5	h	h	NOUN
ejpam-3985	197	6	)	)	PUNCT
ejpam-3985	197	7	)	)	PUNCT
ejpam-3985	197	8	;	;	PUNCT
ejpam-3985	197	9	and	and	CCONJ
ejpam-3985	197	10	(	(	PUNCT
ejpam-3985	197	11	iii	iii	X
ejpam-3985	197	12	)	)	PUNCT
ejpam-3985	197	13	wg	wg	NOUN
ejpam-3985	197	14	or	or	CCONJ
ejpam-3985	197	15	wh	wh	PROPN
ejpam-3985	197	16	is	be	AUX
ejpam-3985	197	17	a	a	DET
ejpam-3985	197	18	strictly	strictly	ADV
ejpam-3985	197	19	locating	locate	VERB
ejpam-3985	197	20	set	set	NOUN
ejpam-3985	197	21	.	.	PUNCT
ejpam-3985	198	1	proof	proof	NOUN
ejpam-3985	198	2	:	:	PUNCT
ejpam-3985	198	3	let	let	VERB
ejpam-3985	198	4	w	w	ADP
ejpam-3985	198	5	⊆	⊆	NUM
ejpam-3985	198	6	v	v	NOUN
ejpam-3985	198	7	(	(	PUNCT
ejpam-3985	198	8	g+h	g+h	NOUN
ejpam-3985	198	9	)	)	PUNCT
ejpam-3985	198	10	be	be	AUX
ejpam-3985	198	11	a	a	DET
ejpam-3985	198	12	resolving	resolve	VERB
ejpam-3985	198	13	restrained	restrained	ADJ
ejpam-3985	198	14	dominating	dominating	NOUN
ejpam-3985	198	15	set	set	NOUN
ejpam-3985	198	16	of	of	ADP
ejpam-3985	198	17	g+h	g+h	PROPN
ejpam-3985	198	18	.	.	PUNCT
ejpam-3985	199	1	then	then	ADV
ejpam-3985	199	2	by	by	ADP
ejpam-3985	199	3	theorem	theorem	NOUN
ejpam-3985	199	4	8	8	NUM
ejpam-3985	199	5	,	,	PUNCT
ejpam-3985	199	6	wg	wg	NOUN
ejpam-3985	199	7	=	=	SYM
ejpam-3985	199	8	v	v	NOUN
ejpam-3985	199	9	(	(	PUNCT
ejpam-3985	199	10	g	g	NOUN
ejpam-3985	199	11	)	)	PUNCT
ejpam-3985	199	12	∩w	∩w	NOUN
ejpam-3985	199	13	and	and	CCONJ
ejpam-3985	199	14	wh	wh	VERB
ejpam-3985	199	15	=	=	SYM
ejpam-3985	199	16	v	v	PROPN
ejpam-3985	199	17	(	(	PUNCT
ejpam-3985	199	18	h	h	NOUN
ejpam-3985	199	19	)	)	PUNCT
ejpam-3985	199	20	∩w	∩w	NOUN
ejpam-3985	199	21	are	be	AUX
ejpam-3985	199	22	locating	locate	VERB
ejpam-3985	199	23	sets	set	NOUN
ejpam-3985	199	24	of	of	ADP
ejpam-3985	199	25	g	g	PROPN
ejpam-3985	199	26	and	and	CCONJ
ejpam-3985	199	27	h	h	NOUN
ejpam-3985	199	28	,	,	PUNCT
ejpam-3985	199	29	respectively	respectively	ADV
ejpam-3985	199	30	,	,	PUNCT
ejpam-3985	199	31	where	where	SCONJ
ejpam-3985	199	32	wg	wg	NOUN
ejpam-3985	199	33	or	or	CCONJ
ejpam-3985	199	34	wh	wh	PROPN
ejpam-3985	199	35	is	be	AUX
ejpam-3985	199	36	a	a	DET
ejpam-3985	199	37	strictly	strictly	ADV
ejpam-3985	199	38	locating	locate	VERB
ejpam-3985	199	39	set	set	NOUN
ejpam-3985	199	40	.	.	PUNCT
ejpam-3985	200	1	hence	hence	ADV
ejpam-3985	200	2	,	,	PUNCT
ejpam-3985	200	3	(	(	PUNCT
ejpam-3985	200	4	i	i	NOUN
ejpam-3985	200	5	)	)	PUNCT
ejpam-3985	200	6	and	and	CCONJ
ejpam-3985	200	7	(	(	PUNCT
ejpam-3985	200	8	iii	iii	NOUN
ejpam-3985	200	9	)	)	PUNCT
ejpam-3985	200	10	hold	hold	NOUN
ejpam-3985	200	11	.	.	PUNCT
ejpam-3985	201	1	suppose	suppose	VERB
ejpam-3985	201	2	wg	wg	VERB
ejpam-3985	201	3	=	=	SYM
ejpam-3985	201	4	v	v	PROPN
ejpam-3985	201	5	(	(	PUNCT
ejpam-3985	201	6	g	g	NOUN
ejpam-3985	201	7	)	)	PUNCT
ejpam-3985	201	8	or	or	CCONJ
ejpam-3985	201	9	wh	wh	VERB
ejpam-3985	201	10	=	=	SYM
ejpam-3985	201	11	v	v	PROPN
ejpam-3985	201	12	(	(	PUNCT
ejpam-3985	201	13	h	h	NOUN
ejpam-3985	201	14	)	)	PUNCT
ejpam-3985	201	15	.	.	PUNCT
ejpam-3985	202	1	since	since	SCONJ
ejpam-3985	202	2	w	w	PROPN
ejpam-3985	202	3	=	=	SYM
ejpam-3985	202	4	v	v	NOUN
ejpam-3985	202	5	(	(	PUNCT
ejpam-3985	202	6	g	g	PROPN
ejpam-3985	202	7	+	+	NOUN
ejpam-3985	202	8	h	h	NOUN
ejpam-3985	202	9	)	)	PUNCT
ejpam-3985	202	10	or	or	CCONJ
ejpam-3985	202	11	v	v	NOUN
ejpam-3985	202	12	(	(	PUNCT
ejpam-3985	202	13	g	g	NOUN
ejpam-3985	202	14	+	+	NOUN
ejpam-3985	202	15	h	h	NOUN
ejpam-3985	202	16	)	)	PUNCT
ejpam-3985	202	17	\w	\w	ADJ
ejpam-3985	202	18	has	have	VERB
ejpam-3985	202	19	no	no	DET
ejpam-3985	202	20	isolated	isolated	ADJ
ejpam-3985	202	21	vertex	vertex	NOUN
ejpam-3985	202	22	,	,	PUNCT
ejpam-3985	202	23	wh	wh	NOUN
ejpam-3985	202	24	=	=	SYM
ejpam-3985	202	25	v	v	PROPN
ejpam-3985	202	26	(	(	PUNCT
ejpam-3985	202	27	h	h	NOUN
ejpam-3985	202	28	)	)	PUNCT
ejpam-3985	202	29	or	or	CCONJ
ejpam-3985	202	30	v	v	NOUN
ejpam-3985	202	31	(	(	PUNCT
ejpam-3985	202	32	h	h	NOUN
ejpam-3985	202	33	)	)	PUNCT
ejpam-3985	202	34	\wh	\wh	PROPN
ejpam-3985	202	35	has	have	VERB
ejpam-3985	202	36	no	no	DET
ejpam-3985	202	37	isolated	isolated	ADJ
ejpam-3985	202	38	vertex	vertex	NOUN
ejpam-3985	202	39	.	.	PUNCT
ejpam-3985	203	1	hence	hence	ADV
ejpam-3985	203	2	,	,	PUNCT
ejpam-3985	203	3	wh	wh	PROPN
ejpam-3985	203	4	is	be	AUX
ejpam-3985	203	5	a	a	DET
ejpam-3985	203	6	restrained	restrained	ADJ
ejpam-3985	203	7	locating	locating	NOUN
ejpam-3985	203	8	set	set	NOUN
ejpam-3985	203	9	of	of	ADP
ejpam-3985	203	10	h.	h.	NOUN
ejpam-3985	203	11	similarly	similarly	ADV
ejpam-3985	203	12	,	,	PUNCT
ejpam-3985	203	13	wg	wg	PROPN
ejpam-3985	203	14	is	be	AUX
ejpam-3985	203	15	a	a	DET
ejpam-3985	203	16	restrained	restrained	ADJ
ejpam-3985	203	17	locating	locating	NOUN
ejpam-3985	203	18	set	set	NOUN
ejpam-3985	203	19	of	of	ADP
ejpam-3985	203	20	g	g	NOUN
ejpam-3985	203	21	if	if	SCONJ
ejpam-3985	203	22	wh	wh	VERB
ejpam-3985	203	23	=	=	SYM
ejpam-3985	203	24	v	v	PROPN
ejpam-3985	203	25	(	(	PUNCT
ejpam-3985	203	26	h	h	NOUN
ejpam-3985	203	27	)	)	PUNCT
ejpam-3985	203	28	.	.	PUNCT
ejpam-3985	204	1	thus	thus	ADV
ejpam-3985	204	2	,	,	PUNCT
ejpam-3985	204	3	(	(	PUNCT
ejpam-3985	204	4	ii	ii	NOUN
ejpam-3985	204	5	)	)	PUNCT
ejpam-3985	204	6	holds	hold	VERB
ejpam-3985	204	7	.	.	PUNCT
ejpam-3985	205	1	for	for	ADP
ejpam-3985	205	2	the	the	DET
ejpam-3985	205	3	converse	converse	NOUN
ejpam-3985	205	4	,	,	PUNCT
ejpam-3985	205	5	suppose	suppose	VERB
ejpam-3985	205	6	that	that	SCONJ
ejpam-3985	205	7	w	w	PROPN
ejpam-3985	205	8	=	=	PUNCT
ejpam-3985	205	9	wg	wg	PROPN
ejpam-3985	205	10	∪wh	∪wh	NOUN
ejpam-3985	205	11	and	and	CCONJ
ejpam-3985	205	12	satisfies	satisfie	NOUN
ejpam-3985	205	13	(	(	PUNCT
ejpam-3985	205	14	i	i	NOUN
ejpam-3985	205	15	)	)	PUNCT
ejpam-3985	205	16	,	,	PUNCT
ejpam-3985	205	17	(	(	PUNCT
ejpam-3985	205	18	ii	ii	NOUN
ejpam-3985	205	19	)	)	PUNCT
ejpam-3985	205	20	,	,	PUNCT
ejpam-3985	205	21	and	and	CCONJ
ejpam-3985	205	22	(	(	PUNCT
ejpam-3985	205	23	iii	iii	NOUN
ejpam-3985	205	24	)	)	PUNCT
ejpam-3985	205	25	,	,	PUNCT
ejpam-3985	205	26	where	where	SCONJ
ejpam-3985	205	27	wg	wg	NOUN
ejpam-3985	205	28	and	and	CCONJ
ejpam-3985	205	29	wh	wh	PROPN
ejpam-3985	205	30	are	be	AUX
ejpam-3985	205	31	locating	locate	VERB
ejpam-3985	205	32	sets	set	NOUN
ejpam-3985	205	33	of	of	ADP
ejpam-3985	205	34	g	g	PROPN
ejpam-3985	205	35	and	and	CCONJ
ejpam-3985	205	36	h	h	NOUN
ejpam-3985	205	37	,	,	PUNCT
ejpam-3985	205	38	respectively	respectively	ADV
ejpam-3985	205	39	,	,	PUNCT
ejpam-3985	205	40	and	and	CCONJ
ejpam-3985	205	41	wg	wg	PROPN
ejpam-3985	205	42	or	or	CCONJ
ejpam-3985	205	43	wh	wh	PROPN
ejpam-3985	205	44	is	be	AUX
ejpam-3985	205	45	a	a	DET
ejpam-3985	205	46	strictly	strictly	ADV
ejpam-3985	205	47	locating	locate	VERB
ejpam-3985	205	48	set	set	NOUN
ejpam-3985	205	49	.	.	PUNCT
ejpam-3985	206	1	then	then	ADV
ejpam-3985	206	2	by	by	ADP
ejpam-3985	206	3	theorem	theorem	NOUN
ejpam-3985	206	4	8	8	NUM
ejpam-3985	206	5	,	,	PUNCT
ejpam-3985	206	6	w	w	NOUN
ejpam-3985	206	7	is	be	AUX
ejpam-3985	206	8	a	a	DET
ejpam-3985	206	9	resolving	resolve	VERB
ejpam-3985	206	10	dominating	dominating	NOUN
ejpam-3985	206	11	set	set	NOUN
ejpam-3985	206	12	of	of	ADP
ejpam-3985	206	13	g+h	g+h	PROPN
ejpam-3985	206	14	.	.	PUNCT
ejpam-3985	207	1	by	by	ADP
ejpam-3985	207	2	(	(	PUNCT
ejpam-3985	207	3	ii	ii	NOUN
ejpam-3985	207	4	)	)	PUNCT
ejpam-3985	207	5	and	and	CCONJ
ejpam-3985	207	6	the	the	DET
ejpam-3985	207	7	fact	fact	NOUN
ejpam-3985	207	8	that	that	SCONJ
ejpam-3985	207	9	wg	wg	PROPN
ejpam-3985	207	10	and	and	CCONJ
ejpam-3985	207	11	wh	wh	PROPN
ejpam-3985	207	12	are	be	AUX
ejpam-3985	207	13	non	non	ADJ
ejpam-3985	207	14	-	-	ADJ
ejpam-3985	207	15	empty	empty	ADJ
ejpam-3985	207	16	,	,	PUNCT
ejpam-3985	207	17	w	w	NOUN
ejpam-3985	207	18	is	be	AUX
ejpam-3985	207	19	a	a	DET
ejpam-3985	207	20	restrained	restrained	ADJ
ejpam-3985	207	21	dominating	dominating	NOUN
ejpam-3985	207	22	set	set	NOUN
ejpam-3985	207	23	of	of	ADP
ejpam-3985	207	24	g+h	g+h	PROPN
ejpam-3985	207	25	.	.	PUNCT
ejpam-3985	208	1	lemma	lemma	PROPN
ejpam-3985	208	2	1	1	X
ejpam-3985	208	3	.	.	PUNCT
ejpam-3985	209	1	let	let	VERB
ejpam-3985	209	2	g	g	NOUN
ejpam-3985	209	3	and	and	CCONJ
ejpam-3985	209	4	h	h	PROPN
ejpam-3985	209	5	be	be	VERB
ejpam-3985	209	6	non	non	ADJ
ejpam-3985	209	7	-	-	ADJ
ejpam-3985	209	8	trivial	trivial	ADJ
ejpam-3985	209	9	connected	connected	ADJ
ejpam-3985	209	10	graphs	graph	NOUN
ejpam-3985	209	11	such	such	ADJ
ejpam-3985	209	12	that	that	DET
ejpam-3985	209	13	sln(g	sln(g	NOUN
ejpam-3985	209	14	)	)	PUNCT
ejpam-3985	210	1	=	=	SYM
ejpam-3985	210	2	|v	|v	PROPN
ejpam-3985	210	3	(	(	PUNCT
ejpam-3985	210	4	g)|	g)|	NOUN
ejpam-3985	210	5	=	=	PUNCT
ejpam-3985	210	6	m	m	PROPN
ejpam-3985	210	7	and	and	CCONJ
ejpam-3985	210	8	sln(h	sln(h	PROPN
ejpam-3985	210	9	)	)	PUNCT
ejpam-3985	210	10	6=	6=	NUM
ejpam-3985	210	11	|v	|v	PROPN
ejpam-3985	210	12	(	(	PUNCT
ejpam-3985	210	13	h)|	h)|	PROPN
ejpam-3985	210	14	.	.	PUNCT
ejpam-3985	211	1	then	then	ADV
ejpam-3985	211	2	m+	m+	NUM
ejpam-3985	211	3	rln(h	rln(h	PROPN
ejpam-3985	211	4	)	)	PUNCT
ejpam-3985	211	5	≥	≥	NOUN
ejpam-3985	211	6	sln(h	sln(h	VERB
ejpam-3985	211	7	)	)	PUNCT
ejpam-3985	212	1	+	+	NUM
ejpam-3985	213	1	ln(g	ln(g	NUM
ejpam-3985	213	2	)	)	PUNCT
ejpam-3985	213	3	.	.	PUNCT
ejpam-3985	214	1	proof	proof	NOUN
ejpam-3985	214	2	:	:	PUNCT
ejpam-3985	214	3	if	if	SCONJ
ejpam-3985	214	4	ln(h	ln(h	VERB
ejpam-3985	214	5	)	)	PUNCT
ejpam-3985	214	6	=	=	PUNCT
ejpam-3985	215	1	sln(h	sln(h	VERB
ejpam-3985	215	2	)	)	PUNCT
ejpam-3985	215	3	,	,	PUNCT
ejpam-3985	215	4	then	then	ADV
ejpam-3985	215	5	m	m	VERB
ejpam-3985	215	6	+	+	NUM
ejpam-3985	215	7	rln(h	rln(h	PROPN
ejpam-3985	215	8	)	)	PUNCT
ejpam-3985	215	9	≥	≥	NOUN
ejpam-3985	215	10	ln(g	ln(g	PUNCT
ejpam-3985	215	11	)	)	PUNCT
ejpam-3985	216	1	+	+	CCONJ
ejpam-3985	216	2	sln(h	sln(h	ADJ
ejpam-3985	216	3	)	)	PUNCT
ejpam-3985	216	4	.	.	PUNCT
ejpam-3985	217	1	suppose	suppose	VERB
ejpam-3985	217	2	ln(h	ln(h	PUNCT
ejpam-3985	217	3	)	)	PUNCT
ejpam-3985	217	4	<	<	X
ejpam-3985	217	5	sln(h	sln(h	PROPN
ejpam-3985	217	6	)	)	PUNCT
ejpam-3985	217	7	.	.	PUNCT
ejpam-3985	218	1	then	then	ADV
ejpam-3985	218	2	ln(h	ln(h	VERB
ejpam-3985	218	3	)	)	PUNCT
ejpam-3985	219	1	=	=	VERB
ejpam-3985	219	2	sln(h)−	sln(h)−	ADJ
ejpam-3985	219	3	1	1	NUM
ejpam-3985	219	4	≤	≤	NUM
ejpam-3985	219	5	rln(h	rln(h	PROPN
ejpam-3985	219	6	)	)	PUNCT
ejpam-3985	219	7	.	.	PUNCT
ejpam-3985	220	1	hence	hence	ADV
ejpam-3985	220	2	,	,	PUNCT
ejpam-3985	220	3	m+	m+	NOUN
ejpam-3985	220	4	rln(h	rln(h	PROPN
ejpam-3985	220	5	)	)	PUNCT
ejpam-3985	220	6	≥	≥	NOUN
ejpam-3985	220	7	m+	m+	NUM
ejpam-3985	220	8	sln(h)−	sln(h)−	VERB
ejpam-3985	220	9	1	1	NUM
ejpam-3985	220	10	=	=	SYM
ejpam-3985	220	11	sln(h	sln(h	VERB
ejpam-3985	220	12	)	)	PUNCT
ejpam-3985	221	1	+	+	CCONJ
ejpam-3985	221	2	(	(	PUNCT
ejpam-3985	221	3	m−	m−	PROPN
ejpam-3985	221	4	1	1	NUM
ejpam-3985	221	5	)	)	PUNCT
ejpam-3985	221	6	=	=	PUNCT
ejpam-3985	221	7	sln(h	sln(h	ADJ
ejpam-3985	221	8	)	)	PUNCT
ejpam-3985	221	9	+	+	NUM
ejpam-3985	221	10	ln(g	ln(g	NUM
ejpam-3985	221	11	)	)	PUNCT
ejpam-3985	221	12	.	.	PUNCT
ejpam-3985	222	1	theorem	theorem	ADJ
ejpam-3985	222	2	10	10	NUM
ejpam-3985	222	3	.	.	PUNCT
ejpam-3985	223	1	[	[	X
ejpam-3985	223	2	11	11	NUM
ejpam-3985	223	3	]	]	PUNCT
ejpam-3985	223	4	let	let	VERB
ejpam-3985	223	5	g	g	PRON
ejpam-3985	223	6	be	be	AUX
ejpam-3985	223	7	a	a	DET
ejpam-3985	223	8	connected	connected	ADJ
ejpam-3985	223	9	graph	graph	NOUN
ejpam-3985	223	10	of	of	ADP
ejpam-3985	223	11	order	order	NOUN
ejpam-3985	223	12	n	n	PRON
ejpam-3985	223	13	≥	≥	NOUN
ejpam-3985	223	14	2	2	NUM
ejpam-3985	223	15	.	.	PUNCT
ejpam-3985	224	1	if	if	SCONJ
ejpam-3985	224	2	ln(g	ln(g	NUM
ejpam-3985	224	3	)	)	PUNCT
ejpam-3985	225	1	<	<	X
ejpam-3985	225	2	sln(g	sln(g	PROPN
ejpam-3985	225	3	)	)	PUNCT
ejpam-3985	225	4	,	,	PUNCT
ejpam-3985	225	5	then	then	ADV
ejpam-3985	225	6	1	1	NUM
ejpam-3985	225	7	+	+	NUM
ejpam-3985	225	8	ln(g	ln(g	X
ejpam-3985	225	9	)	)	PUNCT
ejpam-3985	225	10	=	=	PUNCT
ejpam-3985	225	11	sln(g	sln(g	PROPN
ejpam-3985	225	12	)	)	PUNCT
ejpam-3985	225	13	.	.	PUNCT
ejpam-3985	226	1	corollary	corollary	ADJ
ejpam-3985	226	2	1	1	NUM
ejpam-3985	226	3	.	.	PUNCT
ejpam-3985	227	1	let	let	VERB
ejpam-3985	227	2	g	g	NOUN
ejpam-3985	227	3	and	and	CCONJ
ejpam-3985	227	4	h	h	PROPN
ejpam-3985	227	5	be	be	VERB
ejpam-3985	227	6	non	non	ADJ
ejpam-3985	227	7	-	-	ADJ
ejpam-3985	227	8	trivial	trivial	ADJ
ejpam-3985	227	9	connected	connected	ADJ
ejpam-3985	227	10	graphs	graph	NOUN
ejpam-3985	227	11	of	of	ADP
ejpam-3985	227	12	order	order	NOUN
ejpam-3985	227	13	m	m	VERB
ejpam-3985	227	14	and	and	CCONJ
ejpam-3985	227	15	n	n	CCONJ
ejpam-3985	227	16	,	,	PUNCT
ejpam-3985	227	17	respectively	respectively	ADV
ejpam-3985	227	18	.	.	PUNCT
ejpam-3985	228	1	then	then	ADV
ejpam-3985	228	2	γrr(g+h	γrr(g+h	NOUN
ejpam-3985	228	3	)	)	PUNCT
ejpam-3985	228	4	=	=	PUNCT
ejpam-3985	229	1			NUM
ejpam-3985	229	2	m+	m+	NUM
ejpam-3985	230	1	n	n	INTJ
ejpam-3985	230	2	,	,	PUNCT
ejpam-3985	230	3	if	if	SCONJ
ejpam-3985	230	4	sln(g	sln(g	PROPN
ejpam-3985	230	5	)	)	PUNCT
ejpam-3985	231	1	=	=	SYM
ejpam-3985	231	2	m	m	PROPN
ejpam-3985	231	3	and	and	CCONJ
ejpam-3985	231	4	sln(h	sln(h	ADJ
ejpam-3985	231	5	)	)	PUNCT
ejpam-3985	231	6	=	=	SYM
ejpam-3985	231	7	n	n	PRON
ejpam-3985	231	8	sln(h	sln(h	PROPN
ejpam-3985	231	9	)	)	PUNCT
ejpam-3985	231	10	+	+	NUM
ejpam-3985	231	11	ln(g	ln(g	X
ejpam-3985	231	12	)	)	PUNCT
ejpam-3985	231	13	,	,	PUNCT
ejpam-3985	231	14	if	if	SCONJ
ejpam-3985	231	15	sln(g	sln(g	X
ejpam-3985	231	16	)	)	PUNCT
ejpam-3985	231	17	=	=	SYM
ejpam-3985	231	18	m	m	PROPN
ejpam-3985	231	19	and	and	CCONJ
ejpam-3985	231	20	sln(h	sln(h	PROPN
ejpam-3985	231	21	)	)	PUNCT
ejpam-3985	231	22	6=	6=	NUM
ejpam-3985	231	23	n	n	DET
ejpam-3985	231	24	sln(g	sln(g	PROPN
ejpam-3985	231	25	)	)	PUNCT
ejpam-3985	232	1	+	+	CCONJ
ejpam-3985	232	2	ln(h	ln(h	NUM
ejpam-3985	232	3	)	)	PUNCT
ejpam-3985	233	1	,	,	PUNCT
ejpam-3985	233	2	if	if	SCONJ
ejpam-3985	233	3	sln(g	sln(g	PROPN
ejpam-3985	233	4	)	)	PUNCT
ejpam-3985	233	5	6=	6=	ADP
ejpam-3985	233	6	m	m	PROPN
ejpam-3985	233	7	and	and	CCONJ
ejpam-3985	233	8	sln(h	sln(h	ADJ
ejpam-3985	233	9	)	)	PUNCT
ejpam-3985	233	10	=	=	SYM
ejpam-3985	233	11	n	n	PRON
ejpam-3985	233	12	min	min	NOUN
ejpam-3985	233	13	{	{	PUNCT
ejpam-3985	233	14	sln(h	sln(h	PROPN
ejpam-3985	233	15	)	)	PUNCT
ejpam-3985	233	16	+	+	NUM
ejpam-3985	233	17	ln(g	ln(g	NUM
ejpam-3985	233	18	)	)	PUNCT
ejpam-3985	233	19	,	,	PUNCT
ejpam-3985	233	20	sln(g	sln(g	PROPN
ejpam-3985	233	21	)	)	PUNCT
ejpam-3985	233	22	+	+	NUM
ejpam-3985	233	23	ln(h	ln(h	NUM
ejpam-3985	233	24	)	)	PUNCT
ejpam-3985	233	25	}	}	PUNCT
ejpam-3985	233	26	,	,	PUNCT
ejpam-3985	233	27	if	if	SCONJ
ejpam-3985	233	28	sln(g	sln(g	PROPN
ejpam-3985	233	29	)	)	PUNCT
ejpam-3985	233	30	6=	6=	ADP
ejpam-3985	233	31	m	m	PROPN
ejpam-3985	233	32	and	and	CCONJ
ejpam-3985	233	33	sln(h	sln(h	PROPN
ejpam-3985	233	34	)	)	PUNCT
ejpam-3985	233	35	6=	6=	ADP
ejpam-3985	233	36	n.	n.	PROPN
ejpam-3985	233	37	g.	g.	PROPN
ejpam-3985	233	38	monsanto	monsanto	PROPN
ejpam-3985	233	39	,	,	PUNCT
ejpam-3985	233	40	h.	h.	PROPN
ejpam-3985	233	41	rara	rara	PROPN
ejpam-3985	233	42	/	/	SYM
ejpam-3985	233	43	eur	eur	PROPN
ejpam-3985	233	44	.	.	PUNCT
ejpam-3985	234	1	j.	j.	PROPN
ejpam-3985	234	2	pure	pure	PROPN
ejpam-3985	234	3	appl	appl	PROPN
ejpam-3985	234	4	.	.	PROPN
ejpam-3985	234	5	math	math	PROPN
ejpam-3985	234	6	,	,	PUNCT
ejpam-3985	234	7	14	14	NUM
ejpam-3985	234	8	(	(	PUNCT
ejpam-3985	234	9	3	3	NUM
ejpam-3985	234	10	)	)	PUNCT
ejpam-3985	234	11	(	(	PUNCT
ejpam-3985	234	12	2021	2021	NUM
ejpam-3985	234	13	)	)	PUNCT
ejpam-3985	234	14	,	,	PUNCT
ejpam-3985	234	15	829	829	NUM
ejpam-3985	234	16	-	-	SYM
ejpam-3985	234	17	841	841	NUM
ejpam-3985	234	18	835	835	NUM
ejpam-3985	234	19	proof	proof	NOUN
ejpam-3985	234	20	:	:	PUNCT
ejpam-3985	234	21	consider	consider	VERB
ejpam-3985	234	22	the	the	DET
ejpam-3985	234	23	following	follow	VERB
ejpam-3985	234	24	cases	case	NOUN
ejpam-3985	234	25	:	:	PUNCT
ejpam-3985	234	26	case	case	NOUN
ejpam-3985	234	27	1	1	NUM
ejpam-3985	234	28	.	.	PUNCT
ejpam-3985	234	29	suppose	suppose	VERB
ejpam-3985	235	1	sln(g	sln(g	NOUN
ejpam-3985	235	2	)	)	PUNCT
ejpam-3985	235	3	=	=	SYM
ejpam-3985	235	4	m	m	PROPN
ejpam-3985	235	5	and	and	CCONJ
ejpam-3985	235	6	sln(h	sln(h	ADJ
ejpam-3985	235	7	)	)	PUNCT
ejpam-3985	235	8	=	=	VERB
ejpam-3985	235	9	n.	n.	NOUN
ejpam-3985	235	10	then	then	ADV
ejpam-3985	235	11	v	v	INTJ
ejpam-3985	235	12	(	(	PUNCT
ejpam-3985	235	13	g	g	NOUN
ejpam-3985	235	14	)	)	PUNCT
ejpam-3985	235	15	and	and	CCONJ
ejpam-3985	235	16	v	v	NOUN
ejpam-3985	235	17	(	(	PUNCT
ejpam-3985	235	18	h	h	NOUN
ejpam-3985	235	19	)	)	PUNCT
ejpam-3985	235	20	are	be	AUX
ejpam-3985	235	21	the	the	DET
ejpam-3985	235	22	only	only	ADJ
ejpam-3985	235	23	strictly	strictly	ADV
ejpam-3985	235	24	locating	locate	VERB
ejpam-3985	235	25	sets	set	NOUN
ejpam-3985	235	26	of	of	ADP
ejpam-3985	235	27	g	g	PROPN
ejpam-3985	235	28	and	and	CCONJ
ejpam-3985	235	29	h	h	NOUN
ejpam-3985	235	30	,	,	PUNCT
ejpam-3985	235	31	respectively	respectively	ADV
ejpam-3985	235	32	.	.	PUNCT
ejpam-3985	236	1	since	since	SCONJ
ejpam-3985	236	2	ln(g	ln(g	NUM
ejpam-3985	236	3	)	)	PUNCT
ejpam-3985	236	4	≤	≤	NUM
ejpam-3985	236	5	m	m	VERB
ejpam-3985	236	6	−	−	PROPN
ejpam-3985	236	7	1	1	NUM
ejpam-3985	236	8	,	,	PUNCT
ejpam-3985	236	9	with	with	ADP
ejpam-3985	236	10	1	1	NUM
ejpam-3985	236	11	+	+	CCONJ
ejpam-3985	236	12	ln(g	ln(g	PUNCT
ejpam-3985	236	13	)	)	PUNCT
ejpam-3985	236	14	=	=	PUNCT
ejpam-3985	236	15	sln(g	sln(g	PROPN
ejpam-3985	236	16	)	)	PUNCT
ejpam-3985	236	17	by	by	ADP
ejpam-3985	236	18	theorem	theorem	NOUN
ejpam-3985	236	19	10	10	NUM
ejpam-3985	236	20	.	.	PUNCT
ejpam-3985	236	21	thus	thus	ADV
ejpam-3985	236	22	,	,	PUNCT
ejpam-3985	236	23	ln(g	ln(g	PUNCT
ejpam-3985	236	24	)	)	PUNCT
ejpam-3985	237	1	=	=	PUNCT
ejpam-3985	238	1	m	m	VERB
ejpam-3985	238	2	−	−	NOUN
ejpam-3985	238	3	1	1	NUM
ejpam-3985	238	4	.	.	PUNCT
ejpam-3985	239	1	since	since	SCONJ
ejpam-3985	239	2	ln(g	ln(g	NUM
ejpam-3985	239	3	)	)	PUNCT
ejpam-3985	239	4	≤	≤	NOUN
ejpam-3985	239	5	rln(g	rln(g	NUM
ejpam-3985	239	6	)	)	PUNCT
ejpam-3985	239	7	and	and	CCONJ
ejpam-3985	239	8	rln(g	rln(g	NOUN
ejpam-3985	239	9	)	)	PUNCT
ejpam-3985	239	10	can	can	AUX
ejpam-3985	239	11	not	not	PART
ejpam-3985	239	12	be	be	AUX
ejpam-3985	239	13	equal	equal	ADJ
ejpam-3985	239	14	to	to	ADP
ejpam-3985	239	15	m	m	PROPN
ejpam-3985	239	16	−	−	PROPN
ejpam-3985	239	17	1	1	NUM
ejpam-3985	239	18	,	,	PUNCT
ejpam-3985	239	19	it	it	PRON
ejpam-3985	239	20	follows	follow	VERB
ejpam-3985	239	21	that	that	SCONJ
ejpam-3985	239	22	rln(g	rln(g	X
ejpam-3985	239	23	)	)	PUNCT
ejpam-3985	239	24	=	=	SYM
ejpam-3985	239	25	m.	m.	NOUN
ejpam-3985	239	26	similarly	similarly	ADV
ejpam-3985	239	27	,	,	PUNCT
ejpam-3985	239	28	rln(h	rln(h	PROPN
ejpam-3985	239	29	)	)	PUNCT
ejpam-3985	239	30	=	=	VERB
ejpam-3985	239	31	n.	n.	PROPN
ejpam-3985	239	32	thus	thus	ADV
ejpam-3985	239	33	,	,	PUNCT
ejpam-3985	239	34	v	v	INTJ
ejpam-3985	239	35	(	(	PUNCT
ejpam-3985	239	36	g	g	NOUN
ejpam-3985	239	37	)	)	PUNCT
ejpam-3985	239	38	and	and	CCONJ
ejpam-3985	239	39	v	v	NOUN
ejpam-3985	239	40	(	(	PUNCT
ejpam-3985	239	41	h	h	NOUN
ejpam-3985	239	42	)	)	PUNCT
ejpam-3985	239	43	are	be	AUX
ejpam-3985	239	44	the	the	DET
ejpam-3985	239	45	only	only	ADJ
ejpam-3985	239	46	restrained	restrained	ADJ
ejpam-3985	239	47	locating	locating	NOUN
ejpam-3985	239	48	sets	set	NOUN
ejpam-3985	239	49	of	of	ADP
ejpam-3985	239	50	g	g	PROPN
ejpam-3985	239	51	and	and	CCONJ
ejpam-3985	239	52	h	h	NOUN
ejpam-3985	239	53	,	,	PUNCT
ejpam-3985	239	54	respectively	respectively	ADV
ejpam-3985	239	55	.	.	PUNCT
ejpam-3985	240	1	hence	hence	ADV
ejpam-3985	240	2	,	,	PUNCT
ejpam-3985	240	3	by	by	ADP
ejpam-3985	240	4	theorem	theorem	NOUN
ejpam-3985	240	5	10	10	NUM
ejpam-3985	240	6	,	,	PUNCT
ejpam-3985	240	7	if	if	SCONJ
ejpam-3985	240	8	w	w	NOUN
ejpam-3985	240	9	is	be	AUX
ejpam-3985	240	10	a	a	DET
ejpam-3985	240	11	minimum	minimum	ADJ
ejpam-3985	240	12	restrained	restrained	ADJ
ejpam-3985	240	13	resolving	resolve	VERB
ejpam-3985	240	14	dominating	dominating	NOUN
ejpam-3985	240	15	set	set	NOUN
ejpam-3985	240	16	of	of	ADP
ejpam-3985	240	17	g+h	g+h	PROPN
ejpam-3985	240	18	,	,	PUNCT
ejpam-3985	240	19	then	then	ADV
ejpam-3985	240	20	w	w	PROPN
ejpam-3985	240	21	=	=	SYM
ejpam-3985	240	22	v	v	PROPN
ejpam-3985	240	23	(	(	PUNCT
ejpam-3985	240	24	g	g	NOUN
ejpam-3985	240	25	)	)	PUNCT
ejpam-3985	240	26	∪	∪	NOUN
ejpam-3985	240	27	v	v	NOUN
ejpam-3985	240	28	(	(	PUNCT
ejpam-3985	240	29	h	h	NOUN
ejpam-3985	240	30	)	)	PUNCT
ejpam-3985	240	31	.	.	PUNCT
ejpam-3985	241	1	therefore	therefore	ADV
ejpam-3985	241	2	,	,	PUNCT
ejpam-3985	241	3	γrr(g+h	γrr(g+h	NOUN
ejpam-3985	241	4	)	)	PUNCT
ejpam-3985	241	5	=	=	SYM
ejpam-3985	242	1	m+	m+	NUM
ejpam-3985	242	2	n.	n.	NOUN
ejpam-3985	242	3	case	case	NOUN
ejpam-3985	242	4	2	2	X
ejpam-3985	242	5	.	.	PUNCT
ejpam-3985	242	6	suppose	suppose	VERB
ejpam-3985	242	7	sln(g	sln(g	NOUN
ejpam-3985	242	8	)	)	PUNCT
ejpam-3985	242	9	=	=	SYM
ejpam-3985	242	10	m	m	PROPN
ejpam-3985	242	11	and	and	CCONJ
ejpam-3985	242	12	sln(h	sln(h	PROPN
ejpam-3985	242	13	)	)	PUNCT
ejpam-3985	242	14	6=	6=	PROPN
ejpam-3985	242	15	n.	n.	PROPN
ejpam-3985	242	16	suppose	suppose	VERB
ejpam-3985	242	17	first	first	ADV
ejpam-3985	242	18	that	that	SCONJ
ejpam-3985	242	19	sln(g	sln(g	NOUN
ejpam-3985	242	20	)	)	PUNCT
ejpam-3985	243	1	=	=	SYM
ejpam-3985	243	2	m	m	PROPN
ejpam-3985	243	3	and	and	CCONJ
ejpam-3985	243	4	sln(h	sln(h	PROPN
ejpam-3985	243	5	)	)	PUNCT
ejpam-3985	243	6	6=	6=	PUNCT
ejpam-3985	244	1	n.	n.	PROPN
ejpam-3985	244	2	let	let	VERB
ejpam-3985	244	3	wg	wg	VERB
ejpam-3985	244	4	and	and	CCONJ
ejpam-3985	244	5	wh	wh	VERB
ejpam-3985	244	6	be	be	AUX
ejpam-3985	244	7	minimum	minimum	ADJ
ejpam-3985	244	8	locating	locating	NOUN
ejpam-3985	244	9	set	set	VERB
ejpam-3985	244	10	and	and	CCONJ
ejpam-3985	244	11	minimum	minimum	NOUN
ejpam-3985	244	12	strictly	strictly	ADV
ejpam-3985	244	13	locating	locate	VERB
ejpam-3985	244	14	set	set	NOUN
ejpam-3985	244	15	of	of	ADP
ejpam-3985	244	16	g	g	PROPN
ejpam-3985	244	17	and	and	CCONJ
ejpam-3985	244	18	h	h	NOUN
ejpam-3985	244	19	,	,	PUNCT
ejpam-3985	244	20	respectively	respectively	ADV
ejpam-3985	244	21	.	.	PUNCT
ejpam-3985	245	1	then	then	ADV
ejpam-3985	245	2	by	by	ADP
ejpam-3985	245	3	theorem	theorem	NOUN
ejpam-3985	245	4	9	9	NUM
ejpam-3985	245	5	,	,	PUNCT
ejpam-3985	245	6	w	w	NOUN
ejpam-3985	245	7	=	=	PUNCT
ejpam-3985	245	8	wg	wg	PROPN
ejpam-3985	245	9	∪wh	∪wh	NOUN
ejpam-3985	245	10	is	be	AUX
ejpam-3985	245	11	a	a	DET
ejpam-3985	245	12	restrained	restrained	ADJ
ejpam-3985	245	13	resolving	resolving	NOUN
ejpam-3985	245	14	dominating	dominating	NOUN
ejpam-3985	245	15	set	set	NOUN
ejpam-3985	245	16	of	of	ADP
ejpam-3985	245	17	g	g	PROPN
ejpam-3985	245	18	+	+	PROPN
ejpam-3985	245	19	h.	h.	PROPN
ejpam-3985	245	20	thus	thus	ADV
ejpam-3985	245	21	,	,	PUNCT
ejpam-3985	245	22	γrr(g	γrr(g	PROPN
ejpam-3985	245	23	+	+	NUM
ejpam-3985	245	24	h	h	NOUN
ejpam-3985	245	25	)	)	PUNCT
ejpam-3985	245	26	≤	≤	NOUN
ejpam-3985	245	27	|w	|w	NOUN
ejpam-3985	246	1	|	|	NOUN
ejpam-3985	246	2	=	=	PUNCT
ejpam-3985	246	3	sln(h	sln(h	PROPN
ejpam-3985	246	4	)	)	PUNCT
ejpam-3985	246	5	+	+	NUM
ejpam-3985	246	6	ln(g	ln(g	NUM
ejpam-3985	246	7	)	)	PUNCT
ejpam-3985	246	8	.	.	PUNCT
ejpam-3985	247	1	case	case	NOUN
ejpam-3985	247	2	3	3	X
ejpam-3985	247	3	.	.	PUNCT
ejpam-3985	247	4	suppose	suppose	VERB
ejpam-3985	247	5	sln(g	sln(g	NOUN
ejpam-3985	247	6	)	)	PUNCT
ejpam-3985	247	7	6=	6=	ADP
ejpam-3985	247	8	m	m	PROPN
ejpam-3985	247	9	and	and	CCONJ
ejpam-3985	247	10	sln(h	sln(h	ADJ
ejpam-3985	247	11	)	)	PUNCT
ejpam-3985	247	12	=	=	VERB
ejpam-3985	247	13	n.	n.	PROPN
ejpam-3985	247	14	now	now	ADV
ejpam-3985	247	15	,	,	PUNCT
ejpam-3985	247	16	suppose	suppose	VERB
ejpam-3985	247	17	that	that	SCONJ
ejpam-3985	247	18	w	w	PROPN
ejpam-3985	247	19	′	′	NUM
ejpam-3985	247	20	is	be	AUX
ejpam-3985	247	21	a	a	DET
ejpam-3985	247	22	minimum	minimum	ADJ
ejpam-3985	247	23	resolving	resolving	NOUN
ejpam-3985	247	24	restrained	restrained	ADJ
ejpam-3985	247	25	dominating	dominating	NOUN
ejpam-3985	247	26	set	set	NOUN
ejpam-3985	247	27	of	of	ADP
ejpam-3985	247	28	g	g	PROPN
ejpam-3985	247	29	+	+	CCONJ
ejpam-3985	247	30	h.	h.	PROPN
ejpam-3985	247	31	then	then	ADV
ejpam-3985	247	32	by	by	ADP
ejpam-3985	247	33	theorem	theorem	NOUN
ejpam-3985	247	34	9	9	NUM
ejpam-3985	247	35	,	,	PUNCT
ejpam-3985	247	36	w	w	NOUN
ejpam-3985	247	37	′	′	NOUN
ejpam-3985	248	1	=	=	PUNCT
ejpam-3985	248	2	w	w	NOUN
ejpam-3985	248	3	′g	′g	PROPN
ejpam-3985	248	4	∪	∪	X
ejpam-3985	248	5	w	w	PROPN
ejpam-3985	248	6	′h	′h	PROPN
ejpam-3985	248	7	,	,	PUNCT
ejpam-3985	248	8	where	where	SCONJ
ejpam-3985	248	9	w	w	ADP
ejpam-3985	248	10	′g	′g	PROPN
ejpam-3985	248	11	6=	6=	SYM
ejpam-3985	248	12	v	v	NOUN
ejpam-3985	248	13	(	(	PUNCT
ejpam-3985	248	14	g	g	NOUN
ejpam-3985	248	15	)	)	PUNCT
ejpam-3985	248	16	is	be	AUX
ejpam-3985	248	17	a	a	DET
ejpam-3985	248	18	locating	locating	NOUN
ejpam-3985	248	19	set	set	NOUN
ejpam-3985	248	20	of	of	ADP
ejpam-3985	248	21	g	g	PROPN
ejpam-3985	248	22	and	and	CCONJ
ejpam-3985	248	23	w	w	PROPN
ejpam-3985	248	24	′h	′h	PROPN
ejpam-3985	248	25	6=	6=	ADP
ejpam-3985	248	26	v	v	PROPN
ejpam-3985	248	27	(	(	PUNCT
ejpam-3985	248	28	h	h	NOUN
ejpam-3985	248	29	)	)	PUNCT
ejpam-3985	248	30	is	be	AUX
ejpam-3985	248	31	a	a	DET
ejpam-3985	248	32	strictly	strictly	ADV
ejpam-3985	248	33	locating	locate	VERB
ejpam-3985	248	34	set	set	NOUN
ejpam-3985	248	35	of	of	ADP
ejpam-3985	248	36	h.	h.	PROPN
ejpam-3985	248	37	hence	hence	PROPN
ejpam-3985	248	38	,	,	PUNCT
ejpam-3985	248	39	γrr(g+h	γrr(g+h	NOUN
ejpam-3985	248	40	)	)	PUNCT
ejpam-3985	249	1	=	=	SYM
ejpam-3985	250	1	|w	|w	ADJ
ejpam-3985	250	2	′|	′|	NUM
ejpam-3985	250	3	≥	≥	NOUN
ejpam-3985	250	4	ln(g	ln(g	PUNCT
ejpam-3985	250	5	)	)	PUNCT
ejpam-3985	250	6	+	+	CCONJ
ejpam-3985	250	7	sln(h	sln(h	ADJ
ejpam-3985	250	8	)	)	PUNCT
ejpam-3985	250	9	.	.	PUNCT
ejpam-3985	251	1	therefore	therefore	ADV
ejpam-3985	251	2	,	,	PUNCT
ejpam-3985	251	3	γrr(g+h	γrr(g+h	NOUN
ejpam-3985	251	4	)	)	PUNCT
ejpam-3985	251	5	=	=	SYM
ejpam-3985	251	6	ln(g	ln(g	X
ejpam-3985	251	7	)	)	PUNCT
ejpam-3985	252	1	+	+	CCONJ
ejpam-3985	252	2	sln(h	sln(h	ADJ
ejpam-3985	252	3	)	)	PUNCT
ejpam-3985	252	4	.	.	PUNCT
ejpam-3985	253	1	similarly	similarly	ADV
ejpam-3985	253	2	,	,	PUNCT
ejpam-3985	253	3	if	if	SCONJ
ejpam-3985	253	4	sln(g	sln(g	PROPN
ejpam-3985	253	5	)	)	PUNCT
ejpam-3985	254	1	6=	6=	ADP
ejpam-3985	254	2	m	m	PROPN
ejpam-3985	254	3	and	and	CCONJ
ejpam-3985	254	4	sln(h	sln(h	ADJ
ejpam-3985	254	5	)	)	PUNCT
ejpam-3985	254	6	=	=	SYM
ejpam-3985	254	7	n	n	CCONJ
ejpam-3985	254	8	,	,	PUNCT
ejpam-3985	254	9	then	then	ADV
ejpam-3985	254	10	γrr(g+h	γrr(g+h	NOUN
ejpam-3985	254	11	)	)	PUNCT
ejpam-3985	254	12	=	=	PUNCT
ejpam-3985	254	13	sln(g	sln(g	PROPN
ejpam-3985	254	14	)	)	PUNCT
ejpam-3985	254	15	+	+	NUM
ejpam-3985	254	16	ln(h	ln(h	NUM
ejpam-3985	254	17	)	)	PUNCT
ejpam-3985	254	18	.	.	PUNCT
ejpam-3985	255	1	case	case	NOUN
ejpam-3985	255	2	4	4	X
ejpam-3985	255	3	.	.	PUNCT
ejpam-3985	255	4	suppose	suppose	VERB
ejpam-3985	255	5	sln(g	sln(g	NOUN
ejpam-3985	255	6	)	)	PUNCT
ejpam-3985	255	7	6=	6=	ADP
ejpam-3985	255	8	m	m	PROPN
ejpam-3985	255	9	and	and	CCONJ
ejpam-3985	255	10	sln(h	sln(h	PROPN
ejpam-3985	255	11	)	)	PUNCT
ejpam-3985	255	12	6=	6=	PUNCT
ejpam-3985	255	13	n.	n.	PROPN
ejpam-3985	255	14	let	let	VERB
ejpam-3985	255	15	w	w	NOUN
ejpam-3985	255	16	be	be	AUX
ejpam-3985	255	17	a	a	DET
ejpam-3985	255	18	minimum	minimum	ADJ
ejpam-3985	255	19	resolving	resolving	NOUN
ejpam-3985	255	20	restrained	restrained	ADJ
ejpam-3985	255	21	dominating	dominating	NOUN
ejpam-3985	255	22	set	set	NOUN
ejpam-3985	255	23	of	of	ADP
ejpam-3985	255	24	g	g	PROPN
ejpam-3985	255	25	+	+	CCONJ
ejpam-3985	255	26	h.	h.	PROPN
ejpam-3985	255	27	let	let	VERB
ejpam-3985	255	28	wg	wg	VERB
ejpam-3985	255	29	=	=	SYM
ejpam-3985	255	30	v	v	NOUN
ejpam-3985	255	31	(	(	PUNCT
ejpam-3985	255	32	g	g	NOUN
ejpam-3985	255	33	)	)	PUNCT
ejpam-3985	255	34	∩w	∩w	NOUN
ejpam-3985	255	35	and	and	CCONJ
ejpam-3985	255	36	wh	wh	VERB
ejpam-3985	255	37	=	=	SYM
ejpam-3985	255	38	v	v	PROPN
ejpam-3985	255	39	(	(	PUNCT
ejpam-3985	255	40	h	h	NOUN
ejpam-3985	255	41	)	)	PUNCT
ejpam-3985	255	42	∩w	∩w	NOUN
ejpam-3985	255	43	.	.	PUNCT
ejpam-3985	256	1	then	then	ADV
ejpam-3985	256	2	by	by	ADP
ejpam-3985	256	3	theorem	theorem	NOUN
ejpam-3985	256	4	9	9	NUM
ejpam-3985	256	5	,	,	PUNCT
ejpam-3985	256	6	wg	wg	VERB
ejpam-3985	256	7	and	and	CCONJ
ejpam-3985	256	8	wh	wh	PROPN
ejpam-3985	256	9	are	be	AUX
ejpam-3985	256	10	locating	locate	VERB
ejpam-3985	256	11	sets	set	NOUN
ejpam-3985	256	12	of	of	ADP
ejpam-3985	256	13	g	g	PROPN
ejpam-3985	256	14	and	and	CCONJ
ejpam-3985	256	15	h	h	NOUN
ejpam-3985	256	16	,	,	PUNCT
ejpam-3985	256	17	respectively	respectively	ADV
ejpam-3985	256	18	,	,	PUNCT
ejpam-3985	256	19	where	where	SCONJ
ejpam-3985	256	20	wg	wg	NOUN
ejpam-3985	256	21	or	or	CCONJ
ejpam-3985	256	22	wh	wh	PROPN
ejpam-3985	256	23	is	be	AUX
ejpam-3985	256	24	a	a	DET
ejpam-3985	256	25	strictly	strictly	ADV
ejpam-3985	256	26	locating	locate	VERB
ejpam-3985	256	27	set	set	NOUN
ejpam-3985	256	28	.	.	PUNCT
ejpam-3985	257	1	if	if	SCONJ
ejpam-3985	257	2	wg	wg	PROPN
ejpam-3985	257	3	=	=	SYM
ejpam-3985	257	4	v	v	NOUN
ejpam-3985	257	5	(	(	PUNCT
ejpam-3985	257	6	g	g	NOUN
ejpam-3985	257	7	)	)	PUNCT
ejpam-3985	257	8	,	,	PUNCT
ejpam-3985	257	9	then	then	ADV
ejpam-3985	257	10	by	by	ADP
ejpam-3985	257	11	theorem	theorem	NOUN
ejpam-3985	257	12	10(i	10(i	NUM
ejpam-3985	257	13	)	)	PUNCT
ejpam-3985	257	14	,	,	PUNCT
ejpam-3985	257	15	wh	wh	PROPN
ejpam-3985	257	16	is	be	AUX
ejpam-3985	257	17	a	a	DET
ejpam-3985	257	18	restrained	restrained	ADJ
ejpam-3985	257	19	locating	locating	NOUN
ejpam-3985	257	20	set	set	NOUN
ejpam-3985	257	21	of	of	ADP
ejpam-3985	257	22	h.	h.	PROPN
ejpam-3985	257	23	thus	thus	ADV
ejpam-3985	257	24	,	,	PUNCT
ejpam-3985	257	25	γrr(g+h	γrr(g+h	NOUN
ejpam-3985	257	26	)	)	PUNCT
ejpam-3985	257	27	=	=	SYM
ejpam-3985	257	28	m+	m+	NUM
ejpam-3985	257	29	rln(h	rln(h	PROPN
ejpam-3985	257	30	)	)	PUNCT
ejpam-3985	257	31	≥	≥	NOUN
ejpam-3985	257	32	sln(g	sln(g	X
ejpam-3985	257	33	)	)	PUNCT
ejpam-3985	257	34	+	+	CCONJ
ejpam-3985	257	35	ln(h	ln(h	NUM
ejpam-3985	257	36	)	)	PUNCT
ejpam-3985	257	37	by	by	ADP
ejpam-3985	257	38	lemma	lemma	PROPN
ejpam-3985	257	39	1	1	NUM
ejpam-3985	257	40	.	.	PUNCT
ejpam-3985	257	41	similarly	similarly	ADV
ejpam-3985	257	42	,	,	PUNCT
ejpam-3985	257	43	by	by	ADP
ejpam-3985	257	44	theorem	theorem	NOUN
ejpam-3985	257	45	9(i	9(i	NUM
ejpam-3985	257	46	)	)	PUNCT
ejpam-3985	257	47	,	,	PUNCT
ejpam-3985	257	48	if	if	SCONJ
ejpam-3985	257	49	wh	wh	NOUN
ejpam-3985	257	50	=	=	SYM
ejpam-3985	257	51	v	v	PROPN
ejpam-3985	257	52	(	(	PUNCT
ejpam-3985	257	53	h	h	NOUN
ejpam-3985	257	54	)	)	PUNCT
ejpam-3985	257	55	,	,	PUNCT
ejpam-3985	257	56	then	then	ADV
ejpam-3985	257	57	γrr(g+h	γrr(g+h	NOUN
ejpam-3985	257	58	)	)	PUNCT
ejpam-3985	257	59	=	=	SYM
ejpam-3985	258	1	n+rln(g	n+rln(g	X
ejpam-3985	258	2	)	)	PUNCT
ejpam-3985	258	3	≥	≥	NOUN
ejpam-3985	258	4	sln(h	sln(h	VERB
ejpam-3985	258	5	)	)	PUNCT
ejpam-3985	258	6	+	+	NUM
ejpam-3985	258	7	ln(g	ln(g	X
ejpam-3985	258	8	)	)	PUNCT
ejpam-3985	258	9	by	by	ADP
ejpam-3985	258	10	lemma	lemma	PROPN
ejpam-3985	258	11	1	1	NUM
ejpam-3985	258	12	.	.	PUNCT
ejpam-3985	258	13	suppose	suppose	VERB
ejpam-3985	258	14	that	that	SCONJ
ejpam-3985	258	15	wg	wg	PROPN
ejpam-3985	258	16	6=	6=	ADP
ejpam-3985	258	17	v	v	ADP
ejpam-3985	258	18	(	(	PUNCT
ejpam-3985	258	19	g	g	NOUN
ejpam-3985	258	20	)	)	PUNCT
ejpam-3985	258	21	and	and	CCONJ
ejpam-3985	258	22	wh	wh	VERB
ejpam-3985	258	23	6=	6=	ADP
ejpam-3985	258	24	v	v	ADP
ejpam-3985	258	25	(	(	PUNCT
ejpam-3985	258	26	h	h	NOUN
ejpam-3985	258	27	)	)	PUNCT
ejpam-3985	258	28	.	.	PUNCT
ejpam-3985	259	1	assume	assume	VERB
ejpam-3985	259	2	first	first	ADV
ejpam-3985	259	3	that	that	SCONJ
ejpam-3985	259	4	wg	wg	PROPN
ejpam-3985	259	5	is	be	AUX
ejpam-3985	259	6	a	a	DET
ejpam-3985	259	7	strictly	strictly	ADV
ejpam-3985	259	8	locating	locate	VERB
ejpam-3985	259	9	set	set	NOUN
ejpam-3985	259	10	of	of	ADP
ejpam-3985	259	11	g.	g.	PROPN
ejpam-3985	259	12	then	then	ADV
ejpam-3985	259	13	sln(g	sln(g	PROPN
ejpam-3985	259	14	)	)	PUNCT
ejpam-3985	260	1	+	+	CCONJ
ejpam-3985	260	2	ln(h	ln(h	X
ejpam-3985	260	3	)	)	PUNCT
ejpam-3985	260	4	≤	≤	NOUN
ejpam-3985	260	5	|wg|+	|wg|+	ADV
ejpam-3985	260	6	|wh	|wh	ADP
ejpam-3985	260	7	|	|	ADV
ejpam-3985	260	8	=	=	SYM
ejpam-3985	260	9	|w	|w	NOUN
ejpam-3985	261	1	|	|	NOUN
ejpam-3985	261	2	=	=	SYM
ejpam-3985	261	3	γrr(g+h	γrr(g+h	NOUN
ejpam-3985	261	4	)	)	PUNCT
ejpam-3985	261	5	.	.	PUNCT
ejpam-3985	262	1	if	if	SCONJ
ejpam-3985	262	2	wh	wh	PROPN
ejpam-3985	262	3	is	be	AUX
ejpam-3985	262	4	a	a	DET
ejpam-3985	262	5	strictly	strictly	ADV
ejpam-3985	262	6	locating	locate	VERB
ejpam-3985	262	7	set	set	NOUN
ejpam-3985	262	8	of	of	ADP
ejpam-3985	262	9	h	h	NOUN
ejpam-3985	262	10	,	,	PUNCT
ejpam-3985	262	11	then	then	ADV
ejpam-3985	262	12	sln(h	sln(h	VERB
ejpam-3985	262	13	)	)	PUNCT
ejpam-3985	262	14	+	+	NUM
ejpam-3985	262	15	ln(g	ln(g	X
ejpam-3985	262	16	)	)	PUNCT
ejpam-3985	262	17	≤	≤	NUM
ejpam-3985	262	18	|wh	|wh	ADP
ejpam-3985	262	19	|+	|+	NOUN
ejpam-3985	262	20	|wg|	|wg|	NOUN
ejpam-3985	262	21	=	=	NOUN
ejpam-3985	262	22	|w	|w	NOUN
ejpam-3985	262	23	|	|	NOUN
ejpam-3985	262	24	=	=	SYM
ejpam-3985	262	25	γrr(g+h	γrr(g+h	NOUN
ejpam-3985	262	26	)	)	PUNCT
ejpam-3985	262	27	.	.	PUNCT
ejpam-3985	263	1	thus	thus	ADV
ejpam-3985	263	2	,	,	PUNCT
ejpam-3985	263	3	γrr(g+h	γrr(g+h	PROPN
ejpam-3985	263	4	)	)	PUNCT
ejpam-3985	263	5	≥	≥	PROPN
ejpam-3985	263	6	min	min	PROPN
ejpam-3985	263	7	{	{	PUNCT
ejpam-3985	263	8	sln(g	sln(g	NOUN
ejpam-3985	263	9	)	)	PUNCT
ejpam-3985	263	10	+	+	NUM
ejpam-3985	263	11	ln(h	ln(h	NUM
ejpam-3985	263	12	)	)	PUNCT
ejpam-3985	263	13	,	,	PUNCT
ejpam-3985	263	14	sln(h	sln(h	PROPN
ejpam-3985	263	15	)	)	PUNCT
ejpam-3985	263	16	+	+	NUM
ejpam-3985	263	17	ln(g	ln(g	X
ejpam-3985	263	18	)	)	PUNCT
ejpam-3985	263	19	}	}	PUNCT
ejpam-3985	263	20	.	.	PUNCT
ejpam-3985	264	1	let	let	AUX
ejpam-3985	264	2	wg	wg	VERB
ejpam-3985	264	3	and	and	CCONJ
ejpam-3985	264	4	w	w	PROPN
ejpam-3985	264	5	′h	′h	PROPN
ejpam-3985	264	6	be	be	VERB
ejpam-3985	264	7	minimum	minimum	ADJ
ejpam-3985	264	8	strictly	strictly	ADV
ejpam-3985	264	9	locating	locate	VERB
ejpam-3985	264	10	sets	set	NOUN
ejpam-3985	264	11	of	of	ADP
ejpam-3985	264	12	g	g	PROPN
ejpam-3985	264	13	and	and	CCONJ
ejpam-3985	264	14	h	h	NOUN
ejpam-3985	264	15	,	,	PUNCT
ejpam-3985	264	16	respectively	respectively	ADV
ejpam-3985	264	17	,	,	PUNCT
ejpam-3985	264	18	and	and	CCONJ
ejpam-3985	264	19	let	let	VERB
ejpam-3985	264	20	wh	wh	VERB
ejpam-3985	264	21	and	and	CCONJ
ejpam-3985	264	22	w	w	ADP
ejpam-3985	264	23	′g	′g	PROPN
ejpam-3985	264	24	be	be	VERB
ejpam-3985	264	25	minimum	minimum	ADJ
ejpam-3985	264	26	locating	locating	NOUN
ejpam-3985	264	27	sets	set	NOUN
ejpam-3985	264	28	of	of	ADP
ejpam-3985	264	29	h	h	NOUN
ejpam-3985	264	30	and	and	CCONJ
ejpam-3985	264	31	g	g	NOUN
ejpam-3985	264	32	,	,	PUNCT
ejpam-3985	264	33	respectively	respectively	ADV
ejpam-3985	264	34	.	.	PUNCT
ejpam-3985	265	1	then	then	ADV
ejpam-3985	265	2	w	w	PROPN
ejpam-3985	265	3	=	=	PUNCT
ejpam-3985	265	4	wg	wg	PROPN
ejpam-3985	265	5	∪wh	∪wh	NOUN
ejpam-3985	265	6	and	and	CCONJ
ejpam-3985	265	7	w	w	NOUN
ejpam-3985	265	8	′	′	NOUN
ejpam-3985	265	9	=	=	PUNCT
ejpam-3985	266	1	w	w	NOUN
ejpam-3985	266	2	′g	′g	PROPN
ejpam-3985	266	3	∪w	∪w	PROPN
ejpam-3985	266	4	′h	′h	PROPN
ejpam-3985	266	5	are	be	AUX
ejpam-3985	266	6	resolving	resolve	VERB
ejpam-3985	266	7	restrained	restrained	ADJ
ejpam-3985	266	8	dominating	dominating	NOUN
ejpam-3985	266	9	sets	set	NOUN
ejpam-3985	266	10	of	of	ADP
ejpam-3985	266	11	g	g	PROPN
ejpam-3985	266	12	+	+	CCONJ
ejpam-3985	266	13	h	h	NOUN
ejpam-3985	266	14	by	by	ADP
ejpam-3985	266	15	theorem	theorem	NOUN
ejpam-3985	266	16	8	8	NUM
ejpam-3985	266	17	.	.	PUNCT
ejpam-3985	267	1	thus	thus	ADV
ejpam-3985	267	2	,	,	PUNCT
ejpam-3985	267	3	γrr(g+h	γrr(g+h	NOUN
ejpam-3985	267	4	)	)	PUNCT
ejpam-3985	267	5	≤	≤	NOUN
ejpam-3985	267	6	|w	|w	NOUN
ejpam-3985	267	7	|	|	NOUN
ejpam-3985	267	8	=	=	PUNCT
ejpam-3985	267	9	|wg|+	|wg|+	NOUN
ejpam-3985	267	10	|wh	|wh	X
ejpam-3985	267	11	|	|	NOUN
ejpam-3985	267	12	=	=	SYM
ejpam-3985	267	13	sln(g	sln(g	PROPN
ejpam-3985	267	14	)	)	PUNCT
ejpam-3985	267	15	+	+	CCONJ
ejpam-3985	267	16	ln(h	ln(h	NUM
ejpam-3985	267	17	)	)	PUNCT
ejpam-3985	267	18	and	and	CCONJ
ejpam-3985	267	19	γrr(g+h	γrr(g+h	NOUN
ejpam-3985	267	20	)	)	PUNCT
ejpam-3985	267	21	≤	≤	NOUN
ejpam-3985	268	1	|w	|w	ADJ
ejpam-3985	268	2	′|	′|	NUM
ejpam-3985	268	3	=	=	SYM
ejpam-3985	268	4	ln(g	ln(g	X
ejpam-3985	268	5	)	)	PUNCT
ejpam-3985	269	1	+	+	CCONJ
ejpam-3985	269	2	sln(h	sln(h	ADJ
ejpam-3985	269	3	)	)	PUNCT
ejpam-3985	269	4	.	.	PUNCT
ejpam-3985	270	1	therefore	therefore	ADV
ejpam-3985	270	2	,	,	PUNCT
ejpam-3985	270	3	γrr(g+h	γrr(g+h	NOUN
ejpam-3985	270	4	)	)	PUNCT
ejpam-3985	270	5	=	=	SYM
ejpam-3985	270	6	min	min	PROPN
ejpam-3985	270	7	{	{	PUNCT
ejpam-3985	270	8	sln(g	sln(g	NOUN
ejpam-3985	270	9	)	)	PUNCT
ejpam-3985	270	10	+	+	NUM
ejpam-3985	270	11	ln(h	ln(h	NUM
ejpam-3985	270	12	)	)	PUNCT
ejpam-3985	270	13	,	,	PUNCT
ejpam-3985	270	14	sln(h	sln(h	PROPN
ejpam-3985	270	15	)	)	PUNCT
ejpam-3985	270	16	+	+	NUM
ejpam-3985	270	17	ln(g	ln(g	X
ejpam-3985	270	18	)	)	PUNCT
ejpam-3985	270	19	}	}	PUNCT
ejpam-3985	270	20	.	.	PUNCT
ejpam-3985	271	1	g.	g.	PROPN
ejpam-3985	271	2	monsanto	monsanto	PROPN
ejpam-3985	271	3	,	,	PUNCT
ejpam-3985	271	4	h.	h.	PROPN
ejpam-3985	271	5	rara	rara	PROPN
ejpam-3985	271	6	/	/	SYM
ejpam-3985	271	7	eur	eur	PROPN
ejpam-3985	271	8	.	.	PUNCT
ejpam-3985	272	1	j.	j.	PROPN
ejpam-3985	272	2	pure	pure	PROPN
ejpam-3985	272	3	appl	appl	PROPN
ejpam-3985	272	4	.	.	PROPN
ejpam-3985	272	5	math	math	PROPN
ejpam-3985	272	6	,	,	PUNCT
ejpam-3985	272	7	14	14	NUM
ejpam-3985	272	8	(	(	PUNCT
ejpam-3985	272	9	3	3	NUM
ejpam-3985	272	10	)	)	PUNCT
ejpam-3985	272	11	(	(	PUNCT
ejpam-3985	272	12	2021	2021	NUM
ejpam-3985	272	13	)	)	PUNCT
ejpam-3985	272	14	,	,	PUNCT
ejpam-3985	272	15	829	829	NUM
ejpam-3985	272	16	-	-	SYM
ejpam-3985	272	17	841	841	NUM
ejpam-3985	272	18	836	836	NUM
ejpam-3985	272	19	lemma	lemma	PROPN
ejpam-3985	272	20	2	2	NUM
ejpam-3985	272	21	.	.	PUNCT
ejpam-3985	273	1	let	let	VERB
ejpam-3985	273	2	h	h	PRON
ejpam-3985	273	3	be	be	AUX
ejpam-3985	273	4	a	a	DET
ejpam-3985	273	5	non	non	ADJ
ejpam-3985	273	6	-	-	ADJ
ejpam-3985	273	7	trivial	trivial	ADJ
ejpam-3985	273	8	connected	connected	ADJ
ejpam-3985	273	9	graph	graph	NOUN
ejpam-3985	273	10	of	of	ADP
ejpam-3985	273	11	order	order	NOUN
ejpam-3985	273	12	m	m	VERB
ejpam-3985	273	13	and	and	CCONJ
ejpam-3985	273	14	let	let	VERB
ejpam-3985	273	15	kn	kn	PROPN
ejpam-3985	273	16	be	be	AUX
ejpam-3985	273	17	a	a	DET
ejpam-3985	273	18	complete	complete	ADJ
ejpam-3985	273	19	graph	graph	NOUN
ejpam-3985	273	20	of	of	ADP
ejpam-3985	273	21	order	order	NOUN
ejpam-3985	273	22	n	n	PRON
ejpam-3985	273	23	≥	≥	NOUN
ejpam-3985	273	24	3	3	NUM
ejpam-3985	273	25	.	.	PUNCT
ejpam-3985	274	1	then	then	ADV
ejpam-3985	274	2	n−	n−	NOUN
ejpam-3985	274	3	1	1	NUM
ejpam-3985	274	4	+	+	CCONJ
ejpam-3985	274	5	sln(h	sln(h	ADJ
ejpam-3985	274	6	)	)	PUNCT
ejpam-3985	274	7	≤	≤	NOUN
ejpam-3985	274	8	n+	n+	PUNCT
ejpam-3985	274	9	rln(h	rln(h	NOUN
ejpam-3985	274	10	)	)	PUNCT
ejpam-3985	274	11	.	.	PUNCT
ejpam-3985	275	1	proof	proof	NOUN
ejpam-3985	275	2	:	:	PUNCT
ejpam-3985	275	3	suppose	suppose	VERB
ejpam-3985	275	4	ln(h	ln(h	PUNCT
ejpam-3985	275	5	)	)	PUNCT
ejpam-3985	275	6	<	<	X
ejpam-3985	275	7	sln(h	sln(h	PROPN
ejpam-3985	275	8	)	)	PUNCT
ejpam-3985	275	9	.	.	PUNCT
ejpam-3985	276	1	then	then	ADV
ejpam-3985	276	2	ln(h	ln(h	VERB
ejpam-3985	276	3	)	)	PUNCT
ejpam-3985	276	4	=	=	SYM
ejpam-3985	276	5	sln(h)−1	sln(h)−1	NOUN
ejpam-3985	276	6	.	.	PUNCT
ejpam-3985	277	1	if	if	SCONJ
ejpam-3985	277	2	ln(h	ln(h	VERB
ejpam-3985	277	3	)	)	PUNCT
ejpam-3985	277	4	=	=	SYM
ejpam-3985	277	5	rln(h	rln(h	PROPN
ejpam-3985	277	6	)	)	PUNCT
ejpam-3985	277	7	.	.	PUNCT
ejpam-3985	278	1	then	then	ADV
ejpam-3985	278	2	rln(h	rln(h	PROPN
ejpam-3985	278	3	)	)	PUNCT
ejpam-3985	278	4	=	=	PUNCT
ejpam-3985	279	1	sln(h	sln(h	ADJ
ejpam-3985	279	2	)	)	PUNCT
ejpam-3985	279	3	−	−	PROPN
ejpam-3985	280	1	1	1	NUM
ejpam-3985	280	2	.	.	PUNCT
ejpam-3985	281	1	hence	hence	ADV
ejpam-3985	281	2	,	,	PUNCT
ejpam-3985	281	3	sln(h	sln(h	PROPN
ejpam-3985	281	4	)	)	PUNCT
ejpam-3985	281	5	+	+	CCONJ
ejpam-3985	282	1	n	n	CCONJ
ejpam-3985	282	2	−	−	PROPN
ejpam-3985	282	3	1	1	NUM
ejpam-3985	282	4	=	=	SYM
ejpam-3985	282	5	n	n	PROPN
ejpam-3985	282	6	+	+	NUM
ejpam-3985	282	7	rln(h	rln(h	NOUN
ejpam-3985	282	8	)	)	PUNCT
ejpam-3985	282	9	.	.	PUNCT
ejpam-3985	283	1	if	if	SCONJ
ejpam-3985	283	2	ln(h	ln(h	VERB
ejpam-3985	283	3	)	)	PUNCT
ejpam-3985	284	1	=	=	PUNCT
ejpam-3985	284	2	sln(h	sln(h	VERB
ejpam-3985	284	3	)	)	PUNCT
ejpam-3985	284	4	,	,	PUNCT
ejpam-3985	284	5	then	then	ADV
ejpam-3985	284	6	sln(h	sln(h	PROPN
ejpam-3985	284	7	)	)	PUNCT
ejpam-3985	284	8	≤	≤	NUM
ejpam-3985	284	9	rln(h	rln(h	PROPN
ejpam-3985	284	10	)	)	PUNCT
ejpam-3985	284	11	.	.	PUNCT
ejpam-3985	285	1	hence	hence	ADV
ejpam-3985	285	2	,	,	PUNCT
ejpam-3985	285	3	sln(h)−	sln(h)−	VERB
ejpam-3985	285	4	1	1	NUM
ejpam-3985	285	5	<	<	X
ejpam-3985	285	6	rln(h	rln(h	PROPN
ejpam-3985	285	7	)	)	PUNCT
ejpam-3985	285	8	,	,	PUNCT
ejpam-3985	285	9	that	that	ADV
ejpam-3985	285	10	is	is	ADV
ejpam-3985	285	11	,	,	PUNCT
ejpam-3985	285	12	n−	n−	PROPN
ejpam-3985	285	13	1	1	NUM
ejpam-3985	285	14	+	+	CCONJ
ejpam-3985	285	15	sln(h	sln(h	ADJ
ejpam-3985	285	16	)	)	PUNCT
ejpam-3985	285	17	<	<	X
ejpam-3985	285	18	n+	n+	PUNCT
ejpam-3985	285	19	rln(h	rln(h	NOUN
ejpam-3985	285	20	)	)	PUNCT
ejpam-3985	285	21	.	.	PUNCT
ejpam-3985	286	1	the	the	DET
ejpam-3985	286	2	next	next	ADJ
ejpam-3985	286	3	result	result	NOUN
ejpam-3985	286	4	follows	follow	VERB
ejpam-3985	286	5	immediately	immediately	ADV
ejpam-3985	286	6	from	from	ADP
ejpam-3985	286	7	corollary	corollary	ADJ
ejpam-3985	286	8	1	1	NUM
ejpam-3985	286	9	.	.	PUNCT
ejpam-3985	286	10	corollary	corollary	ADJ
ejpam-3985	286	11	2	2	NUM
ejpam-3985	286	12	.	.	PUNCT
ejpam-3985	287	1	let	let	VERB
ejpam-3985	287	2	h	h	PRON
ejpam-3985	287	3	be	be	AUX
ejpam-3985	287	4	a	a	DET
ejpam-3985	287	5	non	non	ADJ
ejpam-3985	287	6	-	-	ADJ
ejpam-3985	287	7	trivial	trivial	ADJ
ejpam-3985	287	8	connected	connected	ADJ
ejpam-3985	287	9	graph	graph	NOUN
ejpam-3985	287	10	of	of	ADP
ejpam-3985	287	11	order	order	NOUN
ejpam-3985	287	12	m	m	VERB
ejpam-3985	287	13	and	and	CCONJ
ejpam-3985	287	14	let	let	VERB
ejpam-3985	287	15	kn	kn	PROPN
ejpam-3985	287	16	be	be	AUX
ejpam-3985	287	17	a	a	DET
ejpam-3985	287	18	complete	complete	ADJ
ejpam-3985	287	19	graph	graph	NOUN
ejpam-3985	287	20	of	of	ADP
ejpam-3985	287	21	order	order	NOUN
ejpam-3985	287	22	n	n	PRON
ejpam-3985	287	23	≥	≥	NOUN
ejpam-3985	287	24	3	3	NUM
ejpam-3985	287	25	.	.	PUNCT
ejpam-3985	288	1	then	then	ADV
ejpam-3985	288	2	γrr(h	γrr(h	PROPN
ejpam-3985	288	3	+	+	PROPN
ejpam-3985	288	4	kn	kn	PROPN
ejpam-3985	288	5	)	)	PUNCT
ejpam-3985	288	6	=	=	PRON
ejpam-3985	288	7	{	{	PUNCT
ejpam-3985	288	8	sln(h	sln(h	PROPN
ejpam-3985	288	9	)	)	PUNCT
ejpam-3985	289	1	+	+	NUM
ejpam-3985	289	2	n−	n−	NOUN
ejpam-3985	289	3	1	1	NUM
ejpam-3985	289	4	,	,	PUNCT
ejpam-3985	289	5	if	if	SCONJ
ejpam-3985	289	6	sln(h	sln(h	VERB
ejpam-3985	289	7	)	)	PUNCT
ejpam-3985	289	8	6=	6=	ADP
ejpam-3985	289	9	m	m	PROPN
ejpam-3985	290	1	m+	m+	NUM
ejpam-3985	290	2	n	n	PROPN
ejpam-3985	290	3	,	,	PUNCT
ejpam-3985	290	4	otherwise	otherwise	ADV
ejpam-3985	290	5	.	.	PUNCT
ejpam-3985	291	1	theorem	theorem	VERB
ejpam-3985	291	2	11	11	NUM
ejpam-3985	291	3	.	.	PUNCT
ejpam-3985	292	1	[	[	X
ejpam-3985	292	2	14	14	NUM
ejpam-3985	292	3	]	]	PUNCT
ejpam-3985	292	4	let	let	VERB
ejpam-3985	292	5	h	h	PRON
ejpam-3985	292	6	be	be	AUX
ejpam-3985	292	7	a	a	DET
ejpam-3985	292	8	non	non	ADJ
ejpam-3985	292	9	-	-	ADJ
ejpam-3985	292	10	trivial	trivial	ADJ
ejpam-3985	292	11	connected	connected	ADJ
ejpam-3985	292	12	graph	graph	NOUN
ejpam-3985	292	13	and	and	CCONJ
ejpam-3985	292	14	let	let	VERB
ejpam-3985	292	15	k1	k1	NOUN
ejpam-3985	292	16	=	=	PUNCT
ejpam-3985	292	17	〈	〈	PROPN
ejpam-3985	292	18	v	v	NOUN
ejpam-3985	292	19	〉	〉	PROPN
ejpam-3985	292	20	.	.	PUNCT
ejpam-3985	293	1	then	then	ADV
ejpam-3985	293	2	w	w	PROPN
ejpam-3985	293	3	⊆	⊆	NUM
ejpam-3985	293	4	v	v	NOUN
ejpam-3985	293	5	(	(	PUNCT
ejpam-3985	293	6	h	h	NOUN
ejpam-3985	293	7	)	)	PUNCT
ejpam-3985	293	8	is	be	AUX
ejpam-3985	293	9	a	a	DET
ejpam-3985	293	10	locating	locate	VERB
ejpam-3985	293	11	-	-	PUNCT
ejpam-3985	293	12	dominating	dominate	VERB
ejpam-3985	293	13	set	set	NOUN
ejpam-3985	293	14	of	of	ADP
ejpam-3985	293	15	h	h	NOUN
ejpam-3985	293	16	+	+	NOUN
ejpam-3985	293	17	k1	k1	NOUN
ejpam-3985	293	18	if	if	SCONJ
ejpam-3985	293	19	and	and	CCONJ
ejpam-3985	293	20	only	only	ADV
ejpam-3985	293	21	if	if	SCONJ
ejpam-3985	293	22	either	either	PRON
ejpam-3985	293	23	v	v	NOUN
ejpam-3985	293	24	/∈	/∈	PROPN
ejpam-3985	294	1	w	w	NOUN
ejpam-3985	294	2	and	and	CCONJ
ejpam-3985	294	3	w	w	PROPN
ejpam-3985	294	4	is	be	AUX
ejpam-3985	294	5	a	a	DET
ejpam-3985	294	6	strictly	strictly	ADV
ejpam-3985	294	7	locating	locate	VERB
ejpam-3985	294	8	-	-	PUNCT
ejpam-3985	294	9	dominating	dominate	VERB
ejpam-3985	294	10	set	set	NOUN
ejpam-3985	294	11	of	of	ADP
ejpam-3985	294	12	h	h	NOUN
ejpam-3985	294	13	or	or	CCONJ
ejpam-3985	294	14	w	w	NOUN
ejpam-3985	294	15	=	=	PRON
ejpam-3985	294	16	{	{	PUNCT
ejpam-3985	294	17	v}∪w1	v}∪w1	NOUN
ejpam-3985	294	18	,	,	PUNCT
ejpam-3985	294	19	where	where	SCONJ
ejpam-3985	294	20	w1	w1	NOUN
ejpam-3985	294	21	is	be	AUX
ejpam-3985	294	22	a	a	DET
ejpam-3985	294	23	locating	locate	VERB
ejpam-3985	294	24	set	set	NOUN
ejpam-3985	294	25	of	of	ADP
ejpam-3985	294	26	h.	h.	PROPN
ejpam-3985	294	27	the	the	DET
ejpam-3985	294	28	next	next	ADJ
ejpam-3985	294	29	result	result	NOUN
ejpam-3985	294	30	follows	follow	VERB
ejpam-3985	294	31	immediately	immediately	ADV
ejpam-3985	294	32	from	from	ADP
ejpam-3985	294	33	theorem	theorem	ADJ
ejpam-3985	294	34	11	11	NUM
ejpam-3985	294	35	.	.	PUNCT
ejpam-3985	295	1	theorem	theorem	NOUN
ejpam-3985	295	2	12	12	NUM
ejpam-3985	295	3	.	.	PUNCT
ejpam-3985	296	1	let	let	VERB
ejpam-3985	296	2	h	h	PRON
ejpam-3985	296	3	be	be	AUX
ejpam-3985	296	4	a	a	DET
ejpam-3985	296	5	non	non	ADJ
ejpam-3985	296	6	-	-	ADJ
ejpam-3985	296	7	trivial	trivial	ADJ
ejpam-3985	296	8	connected	connected	ADJ
ejpam-3985	296	9	graph	graph	NOUN
ejpam-3985	296	10	and	and	CCONJ
ejpam-3985	296	11	let	let	VERB
ejpam-3985	296	12	k1	k1	NOUN
ejpam-3985	296	13	=	=	PUNCT
ejpam-3985	296	14	〈	〈	PROPN
ejpam-3985	296	15	v	v	NOUN
ejpam-3985	296	16	〉	〉	PROPN
ejpam-3985	296	17	.	.	PUNCT
ejpam-3985	297	1	then	then	ADV
ejpam-3985	297	2	w	w	PROPN
ejpam-3985	297	3	⊆	⊆	NUM
ejpam-3985	297	4	v	v	NOUN
ejpam-3985	297	5	(	(	PUNCT
ejpam-3985	297	6	h	h	NOUN
ejpam-3985	297	7	)	)	PUNCT
ejpam-3985	297	8	is	be	AUX
ejpam-3985	297	9	a	a	DET
ejpam-3985	297	10	resolving	resolve	VERB
ejpam-3985	297	11	dominating	dominating	NOUN
ejpam-3985	297	12	set	set	NOUN
ejpam-3985	297	13	of	of	ADP
ejpam-3985	297	14	h	h	NOUN
ejpam-3985	297	15	+	+	CCONJ
ejpam-3985	297	16	k1	k1	NOUN
ejpam-3985	298	1	if	if	SCONJ
ejpam-3985	299	1	and	and	CCONJ
ejpam-3985	299	2	only	only	ADV
ejpam-3985	299	3	if	if	SCONJ
ejpam-3985	299	4	either	either	PRON
ejpam-3985	299	5	v	v	NOUN
ejpam-3985	299	6	/∈	/∈	PROPN
ejpam-3985	300	1	w	w	NOUN
ejpam-3985	300	2	and	and	CCONJ
ejpam-3985	300	3	w	w	PROPN
ejpam-3985	300	4	is	be	AUX
ejpam-3985	300	5	a	a	DET
ejpam-3985	300	6	strictly	strictly	ADV
ejpam-3985	300	7	resolving	resolve	VERB
ejpam-3985	300	8	dominating	dominating	NOUN
ejpam-3985	300	9	set	set	NOUN
ejpam-3985	300	10	of	of	ADP
ejpam-3985	300	11	h	h	NOUN
ejpam-3985	300	12	or	or	CCONJ
ejpam-3985	300	13	w	w	NOUN
ejpam-3985	300	14	=	=	PUNCT
ejpam-3985	300	15	{	{	PUNCT
ejpam-3985	300	16	v	v	NOUN
ejpam-3985	300	17	}	}	PUNCT
ejpam-3985	300	18	∪wh	∪wh	NOUN
ejpam-3985	300	19	,	,	PUNCT
ejpam-3985	300	20	where	where	SCONJ
ejpam-3985	300	21	wh	wh	NOUN
ejpam-3985	300	22	is	be	AUX
ejpam-3985	300	23	a	a	DET
ejpam-3985	300	24	locating	locate	VERB
ejpam-3985	300	25	set	set	NOUN
ejpam-3985	300	26	of	of	ADP
ejpam-3985	300	27	h.	h.	PROPN
ejpam-3985	300	28	theorem	theorem	PROPN
ejpam-3985	300	29	13	13	NUM
ejpam-3985	300	30	.	.	PUNCT
ejpam-3985	301	1	let	let	VERB
ejpam-3985	301	2	h	h	PRON
ejpam-3985	301	3	be	be	AUX
ejpam-3985	301	4	a	a	DET
ejpam-3985	301	5	non	non	ADJ
ejpam-3985	301	6	-	-	ADJ
ejpam-3985	301	7	trivial	trivial	ADJ
ejpam-3985	301	8	connected	connected	ADJ
ejpam-3985	301	9	graph	graph	NOUN
ejpam-3985	301	10	and	and	CCONJ
ejpam-3985	301	11	let	let	VERB
ejpam-3985	301	12	k1	k1	NOUN
ejpam-3985	301	13	=	=	PUNCT
ejpam-3985	301	14	〈	〈	PROPN
ejpam-3985	301	15	v	v	NOUN
ejpam-3985	301	16	〉	〉	PROPN
ejpam-3985	301	17	.	.	PUNCT
ejpam-3985	302	1	then	then	ADV
ejpam-3985	302	2	w	w	PROPN
ejpam-3985	302	3	⊆	⊆	NUM
ejpam-3985	302	4	v	v	NOUN
ejpam-3985	302	5	(	(	PUNCT
ejpam-3985	302	6	h	h	NOUN
ejpam-3985	302	7	+	+	NOUN
ejpam-3985	302	8	k1	k1	NOUN
ejpam-3985	302	9	)	)	PUNCT
ejpam-3985	302	10	is	be	AUX
ejpam-3985	302	11	a	a	DET
ejpam-3985	302	12	resolving	resolve	VERB
ejpam-3985	302	13	restrained	restrained	ADJ
ejpam-3985	302	14	dominating	dominating	NOUN
ejpam-3985	302	15	set	set	NOUN
ejpam-3985	302	16	of	of	ADP
ejpam-3985	302	17	h	h	NOUN
ejpam-3985	302	18	+	+	NOUN
ejpam-3985	302	19	k1	k1	NOUN
ejpam-3985	302	20	if	if	SCONJ
ejpam-3985	302	21	and	and	CCONJ
ejpam-3985	302	22	only	only	ADV
ejpam-3985	302	23	if	if	SCONJ
ejpam-3985	302	24	either	either	CCONJ
ejpam-3985	302	25	v	v	NOUN
ejpam-3985	302	26	/∈w	/∈w	PUNCT
ejpam-3985	302	27	and	and	CCONJ
ejpam-3985	302	28	w	w	PROPN
ejpam-3985	302	29	is	be	AUX
ejpam-3985	302	30	a	a	DET
ejpam-3985	302	31	strictly	strictly	ADV
ejpam-3985	302	32	resolving	resolve	VERB
ejpam-3985	302	33	dominating	dominating	NOUN
ejpam-3985	302	34	set	set	NOUN
ejpam-3985	302	35	of	of	ADP
ejpam-3985	302	36	h	h	NOUN
ejpam-3985	302	37	with	with	ADP
ejpam-3985	302	38	v	v	PROPN
ejpam-3985	302	39	(	(	PUNCT
ejpam-3985	302	40	h	h	NOUN
ejpam-3985	302	41	)	)	PUNCT
ejpam-3985	302	42	6=	6=	ADP
ejpam-3985	303	1	w	w	NOUN
ejpam-3985	303	2	or	or	CCONJ
ejpam-3985	303	3	w	w	NOUN
ejpam-3985	303	4	=	=	PUNCT
ejpam-3985	303	5	{	{	PUNCT
ejpam-3985	303	6	v	v	NOUN
ejpam-3985	303	7	}	}	PUNCT
ejpam-3985	303	8	∪wh	∪wh	NOUN
ejpam-3985	303	9	,	,	PUNCT
ejpam-3985	303	10	where	where	SCONJ
ejpam-3985	303	11	wh	wh	NOUN
ejpam-3985	303	12	is	be	AUX
ejpam-3985	303	13	a	a	DET
ejpam-3985	303	14	restrained	restrained	ADJ
ejpam-3985	303	15	locating	locating	NOUN
ejpam-3985	303	16	set	set	NOUN
ejpam-3985	303	17	of	of	ADP
ejpam-3985	303	18	h.	h.	NOUN
ejpam-3985	303	19	proof	proof	PROPN
ejpam-3985	303	20	:	:	PUNCT
ejpam-3985	303	21	suppose	suppose	VERB
ejpam-3985	303	22	that	that	SCONJ
ejpam-3985	303	23	w	w	NOUN
ejpam-3985	303	24	is	be	AUX
ejpam-3985	303	25	a	a	DET
ejpam-3985	303	26	resolving	resolve	VERB
ejpam-3985	303	27	restrained	restrained	ADJ
ejpam-3985	303	28	dominating	dominating	NOUN
ejpam-3985	303	29	set	set	NOUN
ejpam-3985	303	30	of	of	ADP
ejpam-3985	303	31	h	h	NOUN
ejpam-3985	303	32	+	+	CCONJ
ejpam-3985	303	33	k1	k1	NOUN
ejpam-3985	303	34	and	and	CCONJ
ejpam-3985	303	35	let	let	VERB
ejpam-3985	303	36	wh	wh	VERB
ejpam-3985	303	37	=	=	SYM
ejpam-3985	303	38	v	v	PROPN
ejpam-3985	303	39	(	(	PUNCT
ejpam-3985	303	40	h	h	NOUN
ejpam-3985	303	41	)	)	PUNCT
ejpam-3985	303	42	∩	∩	PROPN
ejpam-3985	303	43	w	w	X
ejpam-3985	303	44	.	.	PUNCT
ejpam-3985	304	1	then	then	ADV
ejpam-3985	304	2	by	by	ADP
ejpam-3985	304	3	theorem	theorem	NOUN
ejpam-3985	304	4	12	12	NUM
ejpam-3985	304	5	,	,	PUNCT
ejpam-3985	304	6	w	w	NOUN
ejpam-3985	304	7	=	=	PUNCT
ejpam-3985	304	8	wh	wh	X
ejpam-3985	304	9	∪	∪	NOUN
ejpam-3985	304	10	{	{	PUNCT
ejpam-3985	304	11	v	v	NOUN
ejpam-3985	304	12	}	}	PUNCT
ejpam-3985	304	13	,	,	PUNCT
ejpam-3985	304	14	where	where	SCONJ
ejpam-3985	304	15	wh	wh	NOUN
ejpam-3985	304	16	is	be	AUX
ejpam-3985	304	17	a	a	DET
ejpam-3985	304	18	locating	locate	VERB
ejpam-3985	304	19	set	set	NOUN
ejpam-3985	304	20	of	of	ADP
ejpam-3985	304	21	h	h	NOUN
ejpam-3985	304	22	or	or	CCONJ
ejpam-3985	304	23	v	v	ADP
ejpam-3985	304	24	/∈	/∈	PUNCT
ejpam-3985	305	1	w	w	NOUN
ejpam-3985	305	2	and	and	CCONJ
ejpam-3985	305	3	w	w	PROPN
ejpam-3985	305	4	is	be	AUX
ejpam-3985	305	5	a	a	DET
ejpam-3985	305	6	strictly	strictly	ADV
ejpam-3985	305	7	resolving	resolve	VERB
ejpam-3985	305	8	dominating	dominating	NOUN
ejpam-3985	305	9	set	set	NOUN
ejpam-3985	305	10	of	of	ADP
ejpam-3985	305	11	h.	h.	PROPN
ejpam-3985	305	12	suppose	suppose	VERB
ejpam-3985	305	13	that	that	SCONJ
ejpam-3985	305	14	v	v	X
ejpam-3985	305	15	/∈	/∈	PUNCT
ejpam-3985	306	1	w	w	INTJ
ejpam-3985	306	2	.	.	PUNCT
ejpam-3985	307	1	since	since	SCONJ
ejpam-3985	307	2	〈	〈	PROPN
ejpam-3985	307	3	v	v	PROPN
ejpam-3985	307	4	(	(	PUNCT
ejpam-3985	307	5	h	h	NOUN
ejpam-3985	307	6	+	+	NOUN
ejpam-3985	307	7	k1	k1	NOUN
ejpam-3985	307	8	)	)	PUNCT
ejpam-3985	307	9	\w	\w	VERB
ejpam-3985	307	10	〉	〉	NOUN
ejpam-3985	307	11	=	=	SYM
ejpam-3985	307	12	〈	〈	PROPN
ejpam-3985	307	13	{	{	PUNCT
ejpam-3985	307	14	v	v	NOUN
ejpam-3985	307	15	}	}	PUNCT
ejpam-3985	307	16	∪	∪	NOUN
ejpam-3985	307	17	(	(	PUNCT
ejpam-3985	307	18	v	v	NOUN
ejpam-3985	307	19	(	(	PUNCT
ejpam-3985	307	20	h	h	NOUN
ejpam-3985	307	21	)	)	PUNCT
ejpam-3985	307	22	\w	\w	ADJ
ejpam-3985	307	23	)	)	PUNCT
ejpam-3985	307	24	〉	〉	PROPN
ejpam-3985	307	25	has	have	VERB
ejpam-3985	307	26	no	no	DET
ejpam-3985	307	27	isolated	isolated	ADJ
ejpam-3985	307	28	vertex	vertex	NOUN
ejpam-3985	307	29	,	,	PUNCT
ejpam-3985	307	30	it	it	PRON
ejpam-3985	307	31	follows	follow	VERB
ejpam-3985	307	32	that	that	PRON
ejpam-3985	307	33	w	w	PROPN
ejpam-3985	307	34	6=	6=	ADP
ejpam-3985	307	35	v	v	ADP
ejpam-3985	307	36	(	(	PUNCT
ejpam-3985	307	37	h	h	NOUN
ejpam-3985	307	38	)	)	PUNCT
ejpam-3985	307	39	.	.	PUNCT
ejpam-3985	308	1	next	next	ADV
ejpam-3985	308	2	,	,	PUNCT
ejpam-3985	308	3	suppose	suppose	VERB
ejpam-3985	308	4	that	that	SCONJ
ejpam-3985	308	5	w	w	PROPN
ejpam-3985	308	6	=	=	PUNCT
ejpam-3985	308	7	wh	wh	X
ejpam-3985	308	8	∪	∪	NOUN
ejpam-3985	308	9	{	{	PUNCT
ejpam-3985	308	10	v	v	NOUN
ejpam-3985	308	11	}	}	PUNCT
ejpam-3985	308	12	.	.	PUNCT
ejpam-3985	309	1	again	again	ADV
ejpam-3985	309	2	,	,	PUNCT
ejpam-3985	309	3	since	since	SCONJ
ejpam-3985	309	4	〈	〈	PROPN
ejpam-3985	309	5	v	v	X
ejpam-3985	309	6	(	(	PUNCT
ejpam-3985	309	7	h	h	NOUN
ejpam-3985	309	8	+	+	NOUN
ejpam-3985	309	9	k1	k1	NOUN
ejpam-3985	309	10	)	)	PUNCT
ejpam-3985	309	11	\w	\w	VERB
ejpam-3985	309	12	〉	〉	NOUN
ejpam-3985	309	13	=	=	SYM
ejpam-3985	309	14	〈	〈	PROPN
ejpam-3985	309	15	v	v	ADP
ejpam-3985	309	16	(	(	PUNCT
ejpam-3985	309	17	h	h	NOUN
ejpam-3985	309	18	)	)	PUNCT
ejpam-3985	309	19	\wh	\wh	PROPN
ejpam-3985	309	20	〉	〉	PROPN
ejpam-3985	309	21	,	,	PUNCT
ejpam-3985	309	22	and	and	CCONJ
ejpam-3985	309	23	w	w	NOUN
ejpam-3985	309	24	is	be	AUX
ejpam-3985	309	25	a	a	DET
ejpam-3985	309	26	restrained	restrained	ADJ
ejpam-3985	309	27	locating	locating	NOUN
ejpam-3985	309	28	set	set	NOUN
ejpam-3985	309	29	,	,	PUNCT
ejpam-3985	309	30	it	it	PRON
ejpam-3985	309	31	follows	follow	VERB
ejpam-3985	309	32	that	that	PRON
ejpam-3985	309	33	wh	wh	VERB
ejpam-3985	309	34	=	=	SYM
ejpam-3985	309	35	v	v	PROPN
ejpam-3985	309	36	(	(	PUNCT
ejpam-3985	309	37	h	h	NOUN
ejpam-3985	309	38	)	)	PUNCT
ejpam-3985	309	39	or	or	CCONJ
ejpam-3985	309	40	〈	〈	PROPN
ejpam-3985	309	41	v	v	ADJ
ejpam-3985	309	42	(	(	PUNCT
ejpam-3985	309	43	h	h	NOUN
ejpam-3985	309	44	)	)	PUNCT
ejpam-3985	309	45	\wh	\wh	PROPN
ejpam-3985	309	46	〉	〉	PROPN
ejpam-3985	309	47	has	have	VERB
ejpam-3985	309	48	no	no	DET
ejpam-3985	309	49	isolated	isolated	ADJ
ejpam-3985	309	50	vertex	vertex	NOUN
ejpam-3985	309	51	.	.	PUNCT
ejpam-3985	310	1	hence	hence	ADV
ejpam-3985	310	2	,	,	PUNCT
ejpam-3985	310	3	wh	wh	PROPN
ejpam-3985	310	4	is	be	AUX
ejpam-3985	310	5	a	a	DET
ejpam-3985	310	6	restrained	restrained	ADJ
ejpam-3985	310	7	locating	locating	NOUN
ejpam-3985	310	8	set	set	NOUN
ejpam-3985	310	9	of	of	ADP
ejpam-3985	310	10	h.	h.	NOUN
ejpam-3985	310	11	conversely	conversely	ADV
ejpam-3985	310	12	,	,	PUNCT
ejpam-3985	310	13	assume	assume	VERB
ejpam-3985	310	14	first	first	ADV
ejpam-3985	310	15	that	that	PRON
ejpam-3985	310	16	v	v	ADP
ejpam-3985	310	17	/∈	/∈	PUNCT
ejpam-3985	311	1	w	w	NOUN
ejpam-3985	311	2	and	and	CCONJ
ejpam-3985	311	3	w	w	PROPN
ejpam-3985	311	4	is	be	AUX
ejpam-3985	311	5	a	a	DET
ejpam-3985	311	6	strictly	strictly	ADV
ejpam-3985	311	7	resolving	resolve	VERB
ejpam-3985	311	8	dominating	dominating	NOUN
ejpam-3985	311	9	set	set	NOUN
ejpam-3985	311	10	of	of	ADP
ejpam-3985	311	11	h	h	PROPN
ejpam-3985	311	12	with	with	ADP
ejpam-3985	311	13	w	w	PROPN
ejpam-3985	311	14	6=	6=	PROPN
ejpam-3985	311	15	v	v	ADP
ejpam-3985	311	16	(	(	PUNCT
ejpam-3985	311	17	h	h	NOUN
ejpam-3985	311	18	)	)	PUNCT
ejpam-3985	311	19	.	.	PUNCT
ejpam-3985	312	1	by	by	ADP
ejpam-3985	312	2	theorem	theorem	NOUN
ejpam-3985	312	3	12	12	NUM
ejpam-3985	312	4	,	,	PUNCT
ejpam-3985	312	5	w	w	NOUN
ejpam-3985	312	6	is	be	AUX
ejpam-3985	312	7	a	a	DET
ejpam-3985	312	8	resolving	resolve	VERB
ejpam-3985	312	9	dominating	dominating	NOUN
ejpam-3985	312	10	set	set	NOUN
ejpam-3985	312	11	of	of	ADP
ejpam-3985	312	12	h	h	NOUN
ejpam-3985	312	13	+	+	X
ejpam-3985	312	14	k1	k1	NOUN
ejpam-3985	312	15	.	.	PUNCT
ejpam-3985	313	1	since	since	SCONJ
ejpam-3985	313	2	〈	〈	PROPN
ejpam-3985	313	3	v	v	PROPN
ejpam-3985	313	4	(	(	PUNCT
ejpam-3985	313	5	h	h	NOUN
ejpam-3985	313	6	+	+	NOUN
ejpam-3985	313	7	k1	k1	NOUN
ejpam-3985	313	8	)	)	PUNCT
ejpam-3985	313	9	\w	\w	ADJ
ejpam-3985	313	10	〉	〉	NOUN
ejpam-3985	313	11	has	have	VERB
ejpam-3985	313	12	no	no	DET
ejpam-3985	313	13	isolated	isolated	ADJ
ejpam-3985	313	14	vertex	vertex	NOUN
ejpam-3985	313	15	.	.	PUNCT
ejpam-3985	314	1	thus	thus	ADV
ejpam-3985	314	2	,	,	PUNCT
ejpam-3985	314	3	w	w	PROPN
ejpam-3985	314	4	is	be	AUX
ejpam-3985	314	5	a	a	DET
ejpam-3985	314	6	restrained	restrained	ADJ
ejpam-3985	314	7	dominating	dominating	NOUN
ejpam-3985	314	8	set	set	NOUN
ejpam-3985	314	9	of	of	ADP
ejpam-3985	314	10	h	h	NOUN
ejpam-3985	314	11	+	+	X
ejpam-3985	314	12	k1	k1	NOUN
ejpam-3985	314	13	.	.	PUNCT
ejpam-3985	315	1	finally	finally	ADV
ejpam-3985	315	2	,	,	PUNCT
ejpam-3985	315	3	suppose	suppose	VERB
ejpam-3985	315	4	that	that	SCONJ
ejpam-3985	315	5	w	w	PROPN
ejpam-3985	315	6	=	=	PUNCT
ejpam-3985	315	7	wh	wh	X
ejpam-3985	315	8	∪	∪	NOUN
ejpam-3985	315	9	{	{	PUNCT
ejpam-3985	315	10	v	v	NOUN
ejpam-3985	315	11	}	}	PUNCT
ejpam-3985	315	12	,	,	PUNCT
ejpam-3985	315	13	where	where	SCONJ
ejpam-3985	315	14	wh	wh	NOUN
ejpam-3985	315	15	is	be	AUX
ejpam-3985	315	16	a	a	DET
ejpam-3985	315	17	restrained	restrained	ADJ
ejpam-3985	315	18	locating	locating	NOUN
ejpam-3985	315	19	set	set	NOUN
ejpam-3985	315	20	of	of	ADP
ejpam-3985	315	21	h.	h.	PROPN
ejpam-3985	315	22	by	by	ADP
ejpam-3985	315	23	theorem	theorem	NOUN
ejpam-3985	315	24	12	12	NUM
ejpam-3985	315	25	,	,	PUNCT
ejpam-3985	315	26	w	w	NOUN
ejpam-3985	315	27	is	be	AUX
ejpam-3985	315	28	a	a	DET
ejpam-3985	315	29	resolving	resolve	VERB
ejpam-3985	315	30	dominating	dominating	NOUN
ejpam-3985	315	31	set	set	NOUN
ejpam-3985	315	32	of	of	ADP
ejpam-3985	315	33	h	h	NOUN
ejpam-3985	315	34	+	+	NOUN
ejpam-3985	315	35	k1	k1	NOUN
ejpam-3985	315	36	.	.	PUNCT
ejpam-3985	316	1	consequently	consequently	ADV
ejpam-3985	316	2	,	,	PUNCT
ejpam-3985	316	3	w	w	PROPN
ejpam-3985	316	4	is	be	AUX
ejpam-3985	316	5	a	a	DET
ejpam-3985	316	6	restrained	restrained	ADJ
ejpam-3985	316	7	dominating	dominating	NOUN
ejpam-3985	316	8	set	set	NOUN
ejpam-3985	316	9	of	of	ADP
ejpam-3985	316	10	h	h	NOUN
ejpam-3985	316	11	+	+	X
ejpam-3985	316	12	k1	k1	NOUN
ejpam-3985	316	13	.	.	PUNCT
ejpam-3985	317	1	therefore	therefore	ADV
ejpam-3985	317	2	,	,	PUNCT
ejpam-3985	317	3	w	w	PROPN
ejpam-3985	317	4	is	be	AUX
ejpam-3985	317	5	a	a	DET
ejpam-3985	317	6	resolving	resolve	VERB
ejpam-3985	317	7	restrained	restrained	ADJ
ejpam-3985	317	8	dominating	dominating	NOUN
ejpam-3985	317	9	set	set	NOUN
ejpam-3985	317	10	of	of	ADP
ejpam-3985	317	11	h	h	NOUN
ejpam-3985	317	12	+	+	NOUN
ejpam-3985	317	13	k1	k1	NOUN
ejpam-3985	317	14	.	.	PUNCT
ejpam-3985	318	1	g.	g.	PROPN
ejpam-3985	318	2	monsanto	monsanto	PROPN
ejpam-3985	318	3	,	,	PUNCT
ejpam-3985	318	4	h.	h.	PROPN
ejpam-3985	318	5	rara	rara	PROPN
ejpam-3985	318	6	/	/	SYM
ejpam-3985	318	7	eur	eur	PROPN
ejpam-3985	318	8	.	.	PUNCT
ejpam-3985	319	1	j.	j.	PROPN
ejpam-3985	319	2	pure	pure	PROPN
ejpam-3985	319	3	appl	appl	PROPN
ejpam-3985	319	4	.	.	PROPN
ejpam-3985	319	5	math	math	PROPN
ejpam-3985	319	6	,	,	PUNCT
ejpam-3985	319	7	14	14	NUM
ejpam-3985	319	8	(	(	PUNCT
ejpam-3985	319	9	3	3	NUM
ejpam-3985	319	10	)	)	PUNCT
ejpam-3985	319	11	(	(	PUNCT
ejpam-3985	319	12	2021	2021	NUM
ejpam-3985	319	13	)	)	PUNCT
ejpam-3985	319	14	,	,	PUNCT
ejpam-3985	319	15	829	829	NUM
ejpam-3985	319	16	-	-	SYM
ejpam-3985	319	17	841	841	NUM
ejpam-3985	319	18	837	837	NUM
ejpam-3985	319	19	corollary	corollary	ADJ
ejpam-3985	319	20	3	3	NUM
ejpam-3985	319	21	.	.	PUNCT
ejpam-3985	320	1	let	let	VERB
ejpam-3985	320	2	g	g	PRON
ejpam-3985	320	3	be	be	AUX
ejpam-3985	320	4	a	a	DET
ejpam-3985	320	5	non	non	ADJ
ejpam-3985	320	6	-	-	ADJ
ejpam-3985	320	7	trivial	trivial	ADJ
ejpam-3985	320	8	connected	connected	ADJ
ejpam-3985	320	9	graph	graph	NOUN
ejpam-3985	320	10	of	of	ADP
ejpam-3985	320	11	order	order	NOUN
ejpam-3985	320	12	m.	m.	NOUN
ejpam-3985	320	13	then	then	ADV
ejpam-3985	320	14	γrr(g+k1	γrr(g+k1	PRON
ejpam-3985	320	15	)	)	PUNCT
ejpam-3985	321	1	=	=	PUNCT
ejpam-3985	322	1			VERB
ejpam-3985	322	2	m	m	ADJ
ejpam-3985	322	3	,	,	PUNCT
ejpam-3985	322	4	if	if	SCONJ
ejpam-3985	322	5	γsr(g	γsr(g	NOUN
ejpam-3985	322	6	)	)	PUNCT
ejpam-3985	322	7	=	=	SYM
ejpam-3985	322	8	m	m	PROPN
ejpam-3985	322	9	and	and	CCONJ
ejpam-3985	322	10	rln(g	rln(g	NUM
ejpam-3985	322	11	)	)	PUNCT
ejpam-3985	322	12	=	=	SYM
ejpam-3985	322	13	m	m	NOUN
ejpam-3985	322	14	;	;	PUNCT
ejpam-3985	322	15	rln(g	rln(g	X
ejpam-3985	322	16	)	)	PUNCT
ejpam-3985	323	1	+	+	NUM
ejpam-3985	323	2	1	1	NUM
ejpam-3985	323	3	,	,	PUNCT
ejpam-3985	323	4	if	if	SCONJ
ejpam-3985	323	5	γsr(g	γsr(g	NOUN
ejpam-3985	323	6	)	)	PUNCT
ejpam-3985	323	7	=	=	SYM
ejpam-3985	323	8	m	m	PROPN
ejpam-3985	323	9	and	and	CCONJ
ejpam-3985	323	10	rln(g	rln(g	NOUN
ejpam-3985	323	11	)	)	PUNCT
ejpam-3985	323	12	6=	6=	NUM
ejpam-3985	323	13	m	m	PROPN
ejpam-3985	323	14	;	;	PUNCT
ejpam-3985	323	15	min	min	NOUN
ejpam-3985	323	16	{	{	PUNCT
ejpam-3985	323	17	γsr(g	γsr(g	NOUN
ejpam-3985	323	18	)	)	PUNCT
ejpam-3985	323	19	,	,	PUNCT
ejpam-3985	323	20	rln(g	rln(g	X
ejpam-3985	323	21	)	)	PUNCT
ejpam-3985	323	22	+	+	CCONJ
ejpam-3985	323	23	1	1	NUM
ejpam-3985	323	24	}	}	PUNCT
ejpam-3985	323	25	,	,	PUNCT
ejpam-3985	323	26	if	if	SCONJ
ejpam-3985	323	27	γsr(g	γsr(g	NOUN
ejpam-3985	323	28	)	)	PUNCT
ejpam-3985	323	29	6=	6=	ADP
ejpam-3985	323	30	m	m	PROPN
ejpam-3985	323	31	and	and	CCONJ
ejpam-3985	323	32	rln(g	rln(g	NUM
ejpam-3985	323	33	)	)	PUNCT
ejpam-3985	323	34	6=	6=	NUM
ejpam-3985	323	35	m.	m.	NOUN
ejpam-3985	323	36	4	4	NUM
ejpam-3985	323	37	.	.	X
ejpam-3985	323	38	resolving	resolve	VERB
ejpam-3985	323	39	restrained	restrained	ADJ
ejpam-3985	323	40	domination	domination	NOUN
ejpam-3985	323	41	in	in	ADP
ejpam-3985	323	42	the	the	DET
ejpam-3985	323	43	corona	corona	NOUN
ejpam-3985	323	44	of	of	ADP
ejpam-3985	323	45	graphs	graph	NOUN
ejpam-3985	323	46	theorem	theorem	VERB
ejpam-3985	323	47	14	14	NUM
ejpam-3985	323	48	.	.	PUNCT
ejpam-3985	324	1	[	[	X
ejpam-3985	324	2	9	9	NUM
ejpam-3985	324	3	]	]	PUNCT
ejpam-3985	324	4	let	let	VERB
ejpam-3985	324	5	g	g	NOUN
ejpam-3985	324	6	and	and	CCONJ
ejpam-3985	324	7	h	h	PROPN
ejpam-3985	324	8	be	be	VERB
ejpam-3985	324	9	non	non	ADJ
ejpam-3985	324	10	-	-	ADJ
ejpam-3985	324	11	trivial	trivial	ADJ
ejpam-3985	324	12	connected	connected	ADJ
ejpam-3985	324	13	graphs	graph	NOUN
ejpam-3985	324	14	.	.	PUNCT
ejpam-3985	325	1	then	then	ADV
ejpam-3985	325	2	w	w	PROPN
ejpam-3985	325	3	⊆	⊆	NUM
ejpam-3985	325	4	v	v	NOUN
ejpam-3985	325	5	(	(	PUNCT
ejpam-3985	325	6	g	g	PROPN
ejpam-3985	325	7	◦	◦	NOUN
ejpam-3985	325	8	h	h	NOUN
ejpam-3985	325	9	)	)	PUNCT
ejpam-3985	325	10	is	be	AUX
ejpam-3985	325	11	a	a	DET
ejpam-3985	325	12	resolving	resolving	NOUN
ejpam-3985	325	13	set	set	NOUN
ejpam-3985	325	14	of	of	ADP
ejpam-3985	325	15	g	g	PROPN
ejpam-3985	325	16	◦	◦	NOUN
ejpam-3985	325	17	h	h	NOUN
ejpam-3985	325	18	if	if	SCONJ
ejpam-3985	326	1	and	and	CCONJ
ejpam-3985	326	2	only	only	ADV
ejpam-3985	326	3	if	if	SCONJ
ejpam-3985	326	4	w	w	NUM
ejpam-3985	326	5	∩v	∩v	NOUN
ejpam-3985	326	6	(	(	PUNCT
ejpam-3985	326	7	hv	hv	PROPN
ejpam-3985	326	8	)	)	PUNCT
ejpam-3985	326	9	6=	6=	ADP
ejpam-3985	326	10	∅	∅	NOUN
ejpam-3985	326	11	for	for	ADP
ejpam-3985	326	12	every	every	DET
ejpam-3985	326	13	v	v	NUM
ejpam-3985	326	14	∈	∈	PROPN
ejpam-3985	326	15	v	v	NOUN
ejpam-3985	326	16	(	(	PUNCT
ejpam-3985	326	17	g	g	NOUN
ejpam-3985	326	18	)	)	PUNCT
ejpam-3985	326	19	and	and	CCONJ
ejpam-3985	326	20	w	w	NOUN
ejpam-3985	326	21	=	=	SYM
ejpam-3985	326	22	a∪b	a∪b	NOUN
ejpam-3985	326	23	,	,	PUNCT
ejpam-3985	326	24	where	where	SCONJ
ejpam-3985	326	25	a	a	DET
ejpam-3985	326	26	⊆	⊆	NUM
ejpam-3985	326	27	v	v	NOUN
ejpam-3985	326	28	(	(	PUNCT
ejpam-3985	326	29	g	g	NOUN
ejpam-3985	326	30	)	)	PUNCT
ejpam-3985	326	31	and	and	CCONJ
ejpam-3985	326	32	b	b	X
ejpam-3985	326	33	=	=	SYM
ejpam-3985	326	34	∪{bv	∪{bv	NOUN
ejpam-3985	326	35	:	:	PUNCT
ejpam-3985	326	36	v	v	NUM
ejpam-3985	326	37	∈	∈	PROPN
ejpam-3985	326	38	a	a	PRON
ejpam-3985	326	39	and	and	CCONJ
ejpam-3985	326	40	bv	bv	PROPN
ejpam-3985	326	41	is	be	AUX
ejpam-3985	326	42	a	a	DET
ejpam-3985	326	43	locating	locate	VERB
ejpam-3985	326	44	set	set	NOUN
ejpam-3985	326	45	of	of	ADP
ejpam-3985	326	46	hv	hv	PROPN
ejpam-3985	326	47	}	}	PUNCT
ejpam-3985	326	48	.	.	PUNCT
ejpam-3985	327	1	theorem	theorem	NOUN
ejpam-3985	327	2	15	15	NUM
ejpam-3985	327	3	.	.	PUNCT
ejpam-3985	328	1	let	let	VERB
ejpam-3985	328	2	g	g	NOUN
ejpam-3985	328	3	and	and	CCONJ
ejpam-3985	328	4	h	h	PROPN
ejpam-3985	328	5	be	be	VERB
ejpam-3985	328	6	non	non	ADJ
ejpam-3985	328	7	-	-	ADJ
ejpam-3985	328	8	trivial	trivial	ADJ
ejpam-3985	328	9	connected	connected	ADJ
ejpam-3985	328	10	graphs	graph	NOUN
ejpam-3985	328	11	.	.	PUNCT
ejpam-3985	329	1	then	then	ADV
ejpam-3985	329	2	w	w	PROPN
ejpam-3985	329	3	⊆	⊆	NUM
ejpam-3985	329	4	v	v	NOUN
ejpam-3985	329	5	(	(	PUNCT
ejpam-3985	329	6	g	g	PROPN
ejpam-3985	329	7	◦	◦	NOUN
ejpam-3985	329	8	h	h	NOUN
ejpam-3985	329	9	)	)	PUNCT
ejpam-3985	329	10	is	be	AUX
ejpam-3985	329	11	a	a	DET
ejpam-3985	329	12	resolving	resolve	VERB
ejpam-3985	329	13	dominating	dominating	NOUN
ejpam-3985	329	14	set	set	NOUN
ejpam-3985	329	15	of	of	ADP
ejpam-3985	329	16	g	g	PROPN
ejpam-3985	329	17	◦	◦	NOUN
ejpam-3985	329	18	h	h	NOUN
ejpam-3985	329	19	if	if	SCONJ
ejpam-3985	330	1	and	and	CCONJ
ejpam-3985	330	2	only	only	ADV
ejpam-3985	330	3	if	if	SCONJ
ejpam-3985	330	4	w	w	PROPN
ejpam-3985	330	5	∩	∩	ADJ
ejpam-3985	330	6	v	v	X
ejpam-3985	330	7	(	(	PUNCT
ejpam-3985	330	8	hv	hv	PROPN
ejpam-3985	330	9	)	)	PUNCT
ejpam-3985	330	10	6=	6=	NOUN
ejpam-3985	330	11	∅	∅	NOUN
ejpam-3985	330	12	for	for	ADP
ejpam-3985	330	13	every	every	DET
ejpam-3985	330	14	v	v	NUM
ejpam-3985	330	15	∈	∈	PROPN
ejpam-3985	330	16	v	v	NOUN
ejpam-3985	330	17	(	(	PUNCT
ejpam-3985	330	18	g	g	NOUN
ejpam-3985	330	19	)	)	PUNCT
ejpam-3985	330	20	and	and	CCONJ
ejpam-3985	330	21	w	w	X
ejpam-3985	330	22	=	=	PUNCT
ejpam-3985	330	23	a	a	PRON
ejpam-3985	330	24	∪b	∪b	X
ejpam-3985	330	25	∪d	∪d	NUM
ejpam-3985	330	26	,	,	PUNCT
ejpam-3985	330	27	where	where	SCONJ
ejpam-3985	330	28	a	a	DET
ejpam-3985	330	29	⊆	⊆	NUM
ejpam-3985	330	30	v	v	NOUN
ejpam-3985	330	31	(	(	PUNCT
ejpam-3985	330	32	g	g	NOUN
ejpam-3985	330	33	)	)	PUNCT
ejpam-3985	330	34	,	,	PUNCT
ejpam-3985	330	35	b	b	X
ejpam-3985	330	36	=	=	SYM
ejpam-3985	330	37	∪{bv	∪{bv	NOUN
ejpam-3985	330	38	:	:	PUNCT
ejpam-3985	330	39	v	v	NUM
ejpam-3985	330	40	∈	∈	PROPN
ejpam-3985	330	41	a	a	PRON
ejpam-3985	330	42	and	and	CCONJ
ejpam-3985	330	43	bv	bv	PROPN
ejpam-3985	330	44	is	be	AUX
ejpam-3985	330	45	a	a	DET
ejpam-3985	330	46	locating	locate	VERB
ejpam-3985	330	47	set	set	NOUN
ejpam-3985	330	48	of	of	ADP
ejpam-3985	330	49	hv	hv	PROPN
ejpam-3985	330	50	}	}	PUNCT
ejpam-3985	330	51	and	and	CCONJ
ejpam-3985	330	52	d	d	NOUN
ejpam-3985	330	53	=	=	PUNCT
ejpam-3985	330	54	∪{du	∪{du	PROPN
ejpam-3985	330	55	:	:	PUNCT
ejpam-3985	330	56	u	u	NOUN
ejpam-3985	330	57	/∈	/∈	VERB
ejpam-3985	330	58	a	a	PRON
ejpam-3985	330	59	and	and	CCONJ
ejpam-3985	330	60	du	du	PROPN
ejpam-3985	330	61	is	be	AUX
ejpam-3985	330	62	a	a	DET
ejpam-3985	330	63	locating	locate	VERB
ejpam-3985	330	64	-	-	PUNCT
ejpam-3985	330	65	dominating	dominate	VERB
ejpam-3985	330	66	set	set	NOUN
ejpam-3985	330	67	of	of	ADP
ejpam-3985	330	68	hu	hu	PROPN
ejpam-3985	330	69	}	}	PUNCT
ejpam-3985	330	70	.	.	PUNCT
ejpam-3985	331	1	proof	proof	NOUN
ejpam-3985	331	2	:	:	PUNCT
ejpam-3985	331	3	let	let	VERB
ejpam-3985	331	4	w	w	PART
ejpam-3985	331	5	be	be	AUX
ejpam-3985	331	6	a	a	DET
ejpam-3985	331	7	resolving	resolve	VERB
ejpam-3985	331	8	dominating	dominating	NOUN
ejpam-3985	331	9	set	set	NOUN
ejpam-3985	331	10	of	of	ADP
ejpam-3985	331	11	g	g	PROPN
ejpam-3985	331	12	◦	◦	PROPN
ejpam-3985	331	13	h.	h.	NOUN
ejpam-3985	331	14	then	then	ADV
ejpam-3985	331	15	by	by	ADP
ejpam-3985	331	16	theorem	theorem	NOUN
ejpam-3985	331	17	14	14	NUM
ejpam-3985	331	18	,	,	PUNCT
ejpam-3985	331	19	w	w	PROPN
ejpam-3985	331	20	∩	∩	ADJ
ejpam-3985	331	21	v	v	X
ejpam-3985	331	22	(	(	PUNCT
ejpam-3985	331	23	hv	hv	PROPN
ejpam-3985	331	24	)	)	PUNCT
ejpam-3985	331	25	6=	6=	NOUN
ejpam-3985	331	26	∅	∅	NOUN
ejpam-3985	331	27	for	for	ADP
ejpam-3985	331	28	any	any	DET
ejpam-3985	331	29	v	v	NUM
ejpam-3985	331	30	∈	∈	NOUN
ejpam-3985	331	31	v	v	NOUN
ejpam-3985	331	32	(	(	PUNCT
ejpam-3985	331	33	g	g	NOUN
ejpam-3985	331	34	)	)	PUNCT
ejpam-3985	331	35	.	.	PUNCT
ejpam-3985	332	1	since	since	SCONJ
ejpam-3985	332	2	w	w	PROPN
ejpam-3985	332	3	is	be	AUX
ejpam-3985	332	4	a	a	DET
ejpam-3985	332	5	resolving	resolving	NOUN
ejpam-3985	332	6	set	set	NOUN
ejpam-3985	332	7	,	,	PUNCT
ejpam-3985	332	8	g	g	PROPN
ejpam-3985	332	9	=	=	PUNCT
ejpam-3985	332	10	a	a	PRON
ejpam-3985	332	11	∪	∪	ADJ
ejpam-3985	332	12	b∗	b∗	ADJ
ejpam-3985	332	13	,	,	PUNCT
ejpam-3985	332	14	where	where	SCONJ
ejpam-3985	332	15	a	a	DET
ejpam-3985	332	16	⊆	⊆	NUM
ejpam-3985	332	17	v	v	NOUN
ejpam-3985	332	18	(	(	PUNCT
ejpam-3985	332	19	g	g	NOUN
ejpam-3985	332	20	)	)	PUNCT
ejpam-3985	332	21	and	and	CCONJ
ejpam-3985	332	22	b∗	b∗	ADJ
ejpam-3985	332	23	=	=	SYM
ejpam-3985	332	24	∪{bv	∪{bv	NOUN
ejpam-3985	332	25	:	:	PUNCT
ejpam-3985	332	26	v	v	NUM
ejpam-3985	332	27	∈	∈	PROPN
ejpam-3985	332	28	v	v	NOUN
ejpam-3985	332	29	(	(	PUNCT
ejpam-3985	332	30	g	g	NOUN
ejpam-3985	332	31	)	)	PUNCT
ejpam-3985	332	32	and	and	CCONJ
ejpam-3985	332	33	bv	bv	PROPN
ejpam-3985	332	34	is	be	AUX
ejpam-3985	332	35	a	a	DET
ejpam-3985	332	36	locating	locate	VERB
ejpam-3985	332	37	set	set	NOUN
ejpam-3985	332	38	of	of	ADP
ejpam-3985	332	39	hv	hv	PROPN
ejpam-3985	332	40	}	}	PUNCT
ejpam-3985	332	41	by	by	ADP
ejpam-3985	332	42	theorem	theorem	NOUN
ejpam-3985	332	43	14	14	NUM
ejpam-3985	332	44	.	.	PUNCT
ejpam-3985	333	1	let	let	VERB
ejpam-3985	333	2	b	b	NOUN
ejpam-3985	333	3	=	=	SYM
ejpam-3985	333	4	∪{bv	∪{bv	NOUN
ejpam-3985	333	5	:	:	PUNCT
ejpam-3985	333	6	v	v	NUM
ejpam-3985	333	7	∈	∈	PROPN
ejpam-3985	333	8	a	a	PRON
ejpam-3985	333	9	}	}	PUNCT
ejpam-3985	333	10	and	and	CCONJ
ejpam-3985	333	11	d	d	NOUN
ejpam-3985	333	12	=	=	PUNCT
ejpam-3985	333	13	∪{bu	∪{bu	NOUN
ejpam-3985	333	14	:	:	PUNCT
ejpam-3985	334	1	u	u	NOUN
ejpam-3985	334	2	∈	∈	PROPN
ejpam-3985	334	3	v	v	ADP
ejpam-3985	334	4	(	(	PUNCT
ejpam-3985	334	5	g	g	NOUN
ejpam-3985	334	6	)	)	PUNCT
ejpam-3985	334	7	\	\	PUNCT
ejpam-3985	335	1	a	a	PRON
ejpam-3985	335	2	}	}	PUNCT
ejpam-3985	335	3	.	.	PUNCT
ejpam-3985	336	1	since	since	SCONJ
ejpam-3985	336	2	w	w	PROPN
ejpam-3985	336	3	is	be	AUX
ejpam-3985	336	4	a	a	DET
ejpam-3985	336	5	dominating	dominating	NOUN
ejpam-3985	336	6	set	set	NOUN
ejpam-3985	336	7	,	,	PUNCT
ejpam-3985	336	8	it	it	PRON
ejpam-3985	336	9	follows	follow	VERB
ejpam-3985	336	10	that	that	SCONJ
ejpam-3985	336	11	bu	bu	PROPN
ejpam-3985	336	12	is	be	AUX
ejpam-3985	336	13	a	a	DET
ejpam-3985	336	14	dominating	dominating	NOUN
ejpam-3985	336	15	set	set	NOUN
ejpam-3985	336	16	for	for	ADP
ejpam-3985	336	17	each	each	DET
ejpam-3985	336	18	u	u	PROPN
ejpam-3985	336	19	∈	∈	PROPN
ejpam-3985	336	20	v	v	ADP
ejpam-3985	336	21	(	(	PUNCT
ejpam-3985	336	22	g	g	NOUN
ejpam-3985	336	23	)	)	PUNCT
ejpam-3985	336	24	\a	\a	ADJ
ejpam-3985	336	25	.	.	PUNCT
ejpam-3985	337	1	for	for	ADP
ejpam-3985	337	2	the	the	DET
ejpam-3985	337	3	converse	converse	NOUN
ejpam-3985	337	4	,	,	PUNCT
ejpam-3985	337	5	suppose	suppose	VERB
ejpam-3985	337	6	w	w	ADP
ejpam-3985	337	7	=	=	PUNCT
ejpam-3985	337	8	a	a	DET
ejpam-3985	337	9	∪	∪	X
ejpam-3985	337	10	b	b	NOUN
ejpam-3985	337	11	∪d	∪d	NOUN
ejpam-3985	337	12	,	,	PUNCT
ejpam-3985	337	13	where	where	SCONJ
ejpam-3985	337	14	a	a	DET
ejpam-3985	337	15	,	,	PUNCT
ejpam-3985	337	16	b	b	NOUN
ejpam-3985	337	17	and	and	CCONJ
ejpam-3985	337	18	d	d	NOUN
ejpam-3985	337	19	are	be	AUX
ejpam-3985	337	20	the	the	DET
ejpam-3985	337	21	sets	set	NOUN
ejpam-3985	337	22	possesing	possese	VERB
ejpam-3985	337	23	the	the	DET
ejpam-3985	337	24	properties	property	NOUN
ejpam-3985	337	25	described	describe	VERB
ejpam-3985	337	26	.	.	PUNCT
ejpam-3985	338	1	then	then	ADV
ejpam-3985	338	2	by	by	ADP
ejpam-3985	338	3	theorem	theorem	NOUN
ejpam-3985	338	4	14	14	NUM
ejpam-3985	338	5	,	,	PUNCT
ejpam-3985	338	6	w	w	NOUN
ejpam-3985	338	7	is	be	AUX
ejpam-3985	338	8	a	a	DET
ejpam-3985	338	9	resolving	resolving	NOUN
ejpam-3985	338	10	set	set	NOUN
ejpam-3985	338	11	of	of	ADP
ejpam-3985	338	12	g	g	PROPN
ejpam-3985	338	13	◦	◦	PROPN
ejpam-3985	338	14	h.	h.	PROPN
ejpam-3985	338	15	since	since	SCONJ
ejpam-3985	338	16	du	du	PROPN
ejpam-3985	338	17	is	be	AUX
ejpam-3985	338	18	a	a	DET
ejpam-3985	338	19	dominating	dominating	NOUN
ejpam-3985	338	20	set	set	NOUN
ejpam-3985	338	21	of	of	ADP
ejpam-3985	338	22	hu	hu	PROPN
ejpam-3985	338	23	for	for	SCONJ
ejpam-3985	338	24	each	each	DET
ejpam-3985	338	25	u	u	NOUN
ejpam-3985	338	26	/∈w	/∈w	PUNCT
ejpam-3985	338	27	,	,	PUNCT
ejpam-3985	338	28	w	w	NOUN
ejpam-3985	338	29	is	be	AUX
ejpam-3985	338	30	a	a	DET
ejpam-3985	338	31	resolving	resolve	VERB
ejpam-3985	338	32	dominating	dominating	NOUN
ejpam-3985	338	33	set	set	NOUN
ejpam-3985	338	34	of	of	ADP
ejpam-3985	338	35	g	g	PROPN
ejpam-3985	338	36	◦	◦	PROPN
ejpam-3985	338	37	h.	h.	PROPN
ejpam-3985	338	38	theorem	theorem	VERB
ejpam-3985	338	39	16	16	NUM
ejpam-3985	338	40	.	.	PUNCT
ejpam-3985	339	1	let	let	VERB
ejpam-3985	339	2	g	g	NOUN
ejpam-3985	339	3	and	and	CCONJ
ejpam-3985	339	4	h	h	PROPN
ejpam-3985	339	5	be	be	VERB
ejpam-3985	339	6	non	non	ADJ
ejpam-3985	339	7	-	-	ADJ
ejpam-3985	339	8	trivial	trivial	ADJ
ejpam-3985	339	9	connected	connected	ADJ
ejpam-3985	339	10	graphs	graph	NOUN
ejpam-3985	339	11	.	.	PUNCT
ejpam-3985	340	1	then	then	ADV
ejpam-3985	340	2	w	w	PROPN
ejpam-3985	340	3	⊆	⊆	NUM
ejpam-3985	340	4	v	v	NOUN
ejpam-3985	340	5	(	(	PUNCT
ejpam-3985	340	6	g	g	PROPN
ejpam-3985	340	7	◦	◦	NOUN
ejpam-3985	340	8	h	h	NOUN
ejpam-3985	340	9	)	)	PUNCT
ejpam-3985	340	10	is	be	AUX
ejpam-3985	340	11	a	a	DET
ejpam-3985	340	12	resolving	resolve	VERB
ejpam-3985	340	13	restrained	restrained	ADJ
ejpam-3985	340	14	dominating	dominating	NOUN
ejpam-3985	340	15	set	set	NOUN
ejpam-3985	340	16	of	of	ADP
ejpam-3985	340	17	g	g	PROPN
ejpam-3985	340	18	◦	◦	NOUN
ejpam-3985	340	19	h	h	NOUN
ejpam-3985	341	1	if	if	SCONJ
ejpam-3985	342	1	and	and	CCONJ
ejpam-3985	342	2	only	only	ADV
ejpam-3985	342	3	if	if	SCONJ
ejpam-3985	342	4	w	w	PROPN
ejpam-3985	342	5	∩	∩	ADJ
ejpam-3985	342	6	v	v	X
ejpam-3985	342	7	(	(	PUNCT
ejpam-3985	342	8	hv	hv	PROPN
ejpam-3985	342	9	)	)	PUNCT
ejpam-3985	342	10	6=	6=	NOUN
ejpam-3985	342	11	∅	∅	NOUN
ejpam-3985	342	12	for	for	ADP
ejpam-3985	342	13	every	every	DET
ejpam-3985	342	14	v	v	NUM
ejpam-3985	342	15	∈	∈	PROPN
ejpam-3985	342	16	v	v	NOUN
ejpam-3985	342	17	(	(	PUNCT
ejpam-3985	342	18	g	g	NOUN
ejpam-3985	342	19	)	)	PUNCT
ejpam-3985	342	20	and	and	CCONJ
ejpam-3985	342	21	w	w	X
ejpam-3985	342	22	=	=	PUNCT
ejpam-3985	342	23	a	a	PRON
ejpam-3985	342	24	∪b	∪b	X
ejpam-3985	342	25	∪d	∪d	NUM
ejpam-3985	342	26	,	,	PUNCT
ejpam-3985	342	27	where	where	SCONJ
ejpam-3985	342	28	a	a	DET
ejpam-3985	342	29	⊆	⊆	NUM
ejpam-3985	342	30	v	v	NOUN
ejpam-3985	342	31	(	(	PUNCT
ejpam-3985	342	32	g	g	NOUN
ejpam-3985	342	33	)	)	PUNCT
ejpam-3985	342	34	,	,	PUNCT
ejpam-3985	342	35	b	b	X
ejpam-3985	342	36	=	=	SYM
ejpam-3985	342	37	∪{bv	∪{bv	NOUN
ejpam-3985	342	38	:	:	PUNCT
ejpam-3985	342	39	v	v	NUM
ejpam-3985	342	40	∈	∈	PROPN
ejpam-3985	342	41	a	a	PRON
ejpam-3985	342	42	and	and	CCONJ
ejpam-3985	342	43	bv	bv	PROPN
ejpam-3985	342	44	is	be	AUX
ejpam-3985	342	45	a	a	DET
ejpam-3985	342	46	restrained	restrained	ADJ
ejpam-3985	342	47	locating	locating	NOUN
ejpam-3985	342	48	set	set	NOUN
ejpam-3985	342	49	of	of	ADP
ejpam-3985	342	50	hv	hv	PROPN
ejpam-3985	342	51	}	}	PUNCT
ejpam-3985	342	52	and	and	CCONJ
ejpam-3985	342	53	d	d	NOUN
ejpam-3985	342	54	=	=	PUNCT
ejpam-3985	342	55	∪{du	∪{du	PROPN
ejpam-3985	342	56	:	:	PUNCT
ejpam-3985	342	57	u	u	NOUN
ejpam-3985	342	58	/∈	/∈	VERB
ejpam-3985	342	59	a	a	PRON
ejpam-3985	342	60	and	and	CCONJ
ejpam-3985	342	61	du	du	PROPN
ejpam-3985	342	62	is	be	AUX
ejpam-3985	342	63	a	a	DET
ejpam-3985	342	64	locating	locate	VERB
ejpam-3985	342	65	-	-	PUNCT
ejpam-3985	342	66	dominating	dominate	VERB
ejpam-3985	342	67	set	set	NOUN
ejpam-3985	342	68	of	of	ADP
ejpam-3985	342	69	hu	hu	PROPN
ejpam-3985	342	70	}	}	PUNCT
ejpam-3985	342	71	where	where	SCONJ
ejpam-3985	342	72	u	u	PROPN
ejpam-3985	342	73	∈	∈	PROPN
ejpam-3985	342	74	ng(v	ng(v	X
ejpam-3985	342	75	(	(	PUNCT
ejpam-3985	342	76	g	g	NOUN
ejpam-3985	342	77	)	)	PUNCT
ejpam-3985	342	78	\a	\a	NUM
ejpam-3985	342	79	)	)	PUNCT
ejpam-3985	342	80	if	if	SCONJ
ejpam-3985	342	81	du	du	PROPN
ejpam-3985	342	82	=	=	SYM
ejpam-3985	342	83	v	v	PROPN
ejpam-3985	342	84	(	(	PUNCT
ejpam-3985	342	85	hu	hu	PROPN
ejpam-3985	342	86	)	)	PUNCT
ejpam-3985	342	87	}	}	PUNCT
ejpam-3985	342	88	.	.	PUNCT
ejpam-3985	343	1	proof	proof	NOUN
ejpam-3985	343	2	:	:	PUNCT
ejpam-3985	343	3	suppose	suppose	VERB
ejpam-3985	343	4	w	w	NOUN
ejpam-3985	343	5	is	be	AUX
ejpam-3985	343	6	a	a	DET
ejpam-3985	343	7	resolving	resolving	NOUN
ejpam-3985	343	8	restrained	restrain	VERB
ejpam-3985	343	9	set	set	NOUN
ejpam-3985	343	10	of	of	ADP
ejpam-3985	343	11	g	g	PROPN
ejpam-3985	343	12	◦	◦	NOUN
ejpam-3985	343	13	h.	h.	NOUN
ejpam-3985	343	14	by	by	ADP
ejpam-3985	343	15	theorem	theorem	NOUN
ejpam-3985	343	16	15	15	NUM
ejpam-3985	343	17	,	,	PUNCT
ejpam-3985	343	18	w	w	NOUN
ejpam-3985	343	19	∩v	∩v	NOUN
ejpam-3985	343	20	(	(	PUNCT
ejpam-3985	343	21	hv	hv	PROPN
ejpam-3985	343	22	)	)	PUNCT
ejpam-3985	343	23	6=	6=	NOUN
ejpam-3985	343	24	∅	∅	NOUN
ejpam-3985	343	25	for	for	ADP
ejpam-3985	343	26	all	all	PRON
ejpam-3985	343	27	v	v	ADP
ejpam-3985	343	28	∈	∈	NUM
ejpam-3985	343	29	v	v	NOUN
ejpam-3985	343	30	(	(	PUNCT
ejpam-3985	343	31	g	g	NOUN
ejpam-3985	343	32	)	)	PUNCT
ejpam-3985	343	33	and	and	CCONJ
ejpam-3985	343	34	w	w	NOUN
ejpam-3985	343	35	=	=	SYM
ejpam-3985	343	36	a∪b	a∪b	NOUN
ejpam-3985	343	37	∪d	∪d	PUNCT
ejpam-3985	343	38	where	where	SCONJ
ejpam-3985	343	39	a	a	DET
ejpam-3985	343	40	,	,	PUNCT
ejpam-3985	343	41	b	b	NOUN
ejpam-3985	343	42	and	and	CCONJ
ejpam-3985	343	43	d	d	NOUN
ejpam-3985	343	44	are	be	AUX
ejpam-3985	343	45	sets	set	NOUN
ejpam-3985	343	46	described	describe	VERB
ejpam-3985	343	47	in	in	ADP
ejpam-3985	343	48	theorem	theorem	NOUN
ejpam-3985	343	49	15	15	NUM
ejpam-3985	343	50	.	.	PUNCT
ejpam-3985	344	1	since	since	SCONJ
ejpam-3985	344	2	w	w	PROPN
ejpam-3985	344	3	is	be	AUX
ejpam-3985	344	4	a	a	DET
ejpam-3985	344	5	restrained	restrained	ADJ
ejpam-3985	344	6	dominating	dominating	NOUN
ejpam-3985	344	7	set	set	NOUN
ejpam-3985	344	8	of	of	ADP
ejpam-3985	344	9	g	g	PROPN
ejpam-3985	344	10	◦	◦	NOUN
ejpam-3985	344	11	h	h	NOUN
ejpam-3985	344	12	,	,	PUNCT
ejpam-3985	344	13	bv	bv	PROPN
ejpam-3985	344	14	is	be	AUX
ejpam-3985	344	15	a	a	DET
ejpam-3985	344	16	restrained	restrained	ADJ
ejpam-3985	344	17	dominating	dominating	NOUN
ejpam-3985	344	18	set	set	NOUN
ejpam-3985	344	19	of	of	ADP
ejpam-3985	344	20	hv	hv	PROPN
ejpam-3985	344	21	for	for	ADP
ejpam-3985	344	22	each	each	DET
ejpam-3985	344	23	v	v	ADP
ejpam-3985	344	24	∈	∈	PROPN
ejpam-3985	344	25	a	a	PRON
ejpam-3985	344	26	,	,	PUNCT
ejpam-3985	344	27	and	and	CCONJ
ejpam-3985	344	28	u	u	PROPN
ejpam-3985	344	29	∈	∈	PROPN
ejpam-3985	344	30	ng(v	ng(v	X
ejpam-3985	344	31	(	(	PUNCT
ejpam-3985	344	32	g	g	NOUN
ejpam-3985	344	33	)	)	PUNCT
ejpam-3985	344	34	\	\	PROPN
ejpam-3985	345	1	a	a	PRON
ejpam-3985	345	2	)	)	PUNCT
ejpam-3985	345	3	for	for	ADP
ejpam-3985	345	4	each	each	DET
ejpam-3985	345	5	u	u	PROPN
ejpam-3985	345	6	∈	∈	PROPN
ejpam-3985	345	7	v	v	ADP
ejpam-3985	345	8	(	(	PUNCT
ejpam-3985	345	9	g	g	NOUN
ejpam-3985	345	10	)	)	PUNCT
ejpam-3985	345	11	\	\	PROPN
ejpam-3985	346	1	a	a	PRON
ejpam-3985	346	2	with	with	ADP
ejpam-3985	346	3	du	du	PROPN
ejpam-3985	346	4	=	=	SYM
ejpam-3985	346	5	v	v	PROPN
ejpam-3985	346	6	(	(	PUNCT
ejpam-3985	346	7	hu	hu	PROPN
ejpam-3985	346	8	)	)	PUNCT
ejpam-3985	346	9	.	.	PUNCT
ejpam-3985	347	1	therefore	therefore	ADV
ejpam-3985	347	2	,	,	PUNCT
ejpam-3985	347	3	b	b	X
ejpam-3985	347	4	=	=	SYM
ejpam-3985	347	5	∪{bv	∪{bv	NOUN
ejpam-3985	347	6	:	:	PUNCT
ejpam-3985	347	7	v	v	NUM
ejpam-3985	347	8	∈	∈	PROPN
ejpam-3985	347	9	a	a	PRON
ejpam-3985	347	10	and	and	CCONJ
ejpam-3985	347	11	bv	bv	PROPN
ejpam-3985	347	12	is	be	AUX
ejpam-3985	347	13	a	a	DET
ejpam-3985	347	14	restrained	restrained	ADJ
ejpam-3985	347	15	locating	locating	NOUN
ejpam-3985	347	16	set	set	NOUN
ejpam-3985	347	17	of	of	ADP
ejpam-3985	347	18	hv	hv	PROPN
ejpam-3985	347	19	}	}	PUNCT
ejpam-3985	347	20	and	and	CCONJ
ejpam-3985	347	21	g.	g.	PROPN
ejpam-3985	347	22	monsanto	monsanto	PROPN
ejpam-3985	347	23	,	,	PUNCT
ejpam-3985	347	24	h.	h.	PROPN
ejpam-3985	347	25	rara	rara	PROPN
ejpam-3985	347	26	/	/	SYM
ejpam-3985	347	27	eur	eur	PROPN
ejpam-3985	347	28	.	.	PUNCT
ejpam-3985	348	1	j.	j.	PROPN
ejpam-3985	348	2	pure	pure	PROPN
ejpam-3985	348	3	appl	appl	PROPN
ejpam-3985	348	4	.	.	PROPN
ejpam-3985	348	5	math	math	PROPN
ejpam-3985	348	6	,	,	PUNCT
ejpam-3985	348	7	14	14	NUM
ejpam-3985	348	8	(	(	PUNCT
ejpam-3985	348	9	3	3	NUM
ejpam-3985	348	10	)	)	PUNCT
ejpam-3985	348	11	(	(	PUNCT
ejpam-3985	348	12	2021	2021	NUM
ejpam-3985	348	13	)	)	PUNCT
ejpam-3985	348	14	,	,	PUNCT
ejpam-3985	348	15	829	829	NUM
ejpam-3985	348	16	-	-	SYM
ejpam-3985	348	17	841	841	NUM
ejpam-3985	348	18	838	838	NUM
ejpam-3985	348	19	d	d	NOUN
ejpam-3985	348	20	=	=	PUNCT
ejpam-3985	348	21	∪{du	∪{du	PROPN
ejpam-3985	348	22	:	:	PUNCT
ejpam-3985	348	23	u	u	NOUN
ejpam-3985	348	24	/∈	/∈	VERB
ejpam-3985	348	25	a	a	PRON
ejpam-3985	348	26	and	and	CCONJ
ejpam-3985	348	27	du	du	PROPN
ejpam-3985	348	28	is	be	AUX
ejpam-3985	348	29	a	a	DET
ejpam-3985	348	30	locating	locate	VERB
ejpam-3985	348	31	dominating	dominating	NOUN
ejpam-3985	348	32	set	set	NOUN
ejpam-3985	348	33	of	of	ADP
ejpam-3985	348	34	hu	hu	PROPN
ejpam-3985	348	35	}	}	PUNCT
ejpam-3985	348	36	where	where	SCONJ
ejpam-3985	348	37	u	u	PROPN
ejpam-3985	348	38	∈	∈	PROPN
ejpam-3985	348	39	ng	ng	PROPN
ejpam-3985	348	40	(	(	PUNCT
ejpam-3985	348	41	v	v	NOUN
ejpam-3985	348	42	(	(	PUNCT
ejpam-3985	348	43	g	g	NOUN
ejpam-3985	348	44	)	)	PUNCT
ejpam-3985	348	45	\a	\a	PUNCT
ejpam-3985	348	46	)	)	PUNCT
ejpam-3985	349	1	if	if	SCONJ
ejpam-3985	349	2	du	du	PROPN
ejpam-3985	349	3	=	=	SYM
ejpam-3985	349	4	v	v	PROPN
ejpam-3985	349	5	(	(	PUNCT
ejpam-3985	349	6	hu	hu	PROPN
ejpam-3985	349	7	)	)	PUNCT
ejpam-3985	349	8	}	}	PUNCT
ejpam-3985	349	9	.	.	PUNCT
ejpam-3985	350	1	for	for	ADP
ejpam-3985	350	2	the	the	DET
ejpam-3985	350	3	converse	converse	NOUN
ejpam-3985	350	4	,	,	PUNCT
ejpam-3985	350	5	suppose	suppose	VERB
ejpam-3985	350	6	that	that	SCONJ
ejpam-3985	350	7	w	w	PROPN
ejpam-3985	350	8	∩v	∩v	PROPN
ejpam-3985	350	9	(	(	PUNCT
ejpam-3985	350	10	hv	hv	PROPN
ejpam-3985	350	11	)	)	PUNCT
ejpam-3985	350	12	6=	6=	ADP
ejpam-3985	350	13	∅	∅	NOUN
ejpam-3985	350	14	for	for	ADP
ejpam-3985	350	15	every	every	DET
ejpam-3985	350	16	v	v	NUM
ejpam-3985	350	17	∈	∈	PROPN
ejpam-3985	350	18	v	v	NOUN
ejpam-3985	350	19	(	(	PUNCT
ejpam-3985	350	20	g	g	NOUN
ejpam-3985	350	21	)	)	PUNCT
ejpam-3985	350	22	and	and	CCONJ
ejpam-3985	350	23	w	w	NOUN
ejpam-3985	350	24	=	=	PUNCT
ejpam-3985	350	25	a∪b∪d	a∪b∪d	NOUN
ejpam-3985	350	26	where	where	SCONJ
ejpam-3985	350	27	a	a	DET
ejpam-3985	350	28	,	,	PUNCT
ejpam-3985	350	29	b	b	NOUN
ejpam-3985	350	30	and	and	CCONJ
ejpam-3985	350	31	d	d	NOUN
ejpam-3985	350	32	are	be	AUX
ejpam-3985	350	33	as	as	ADP
ejpam-3985	350	34	described	describe	VERB
ejpam-3985	350	35	above	above	ADV
ejpam-3985	350	36	.	.	PUNCT
ejpam-3985	351	1	by	by	ADP
ejpam-3985	351	2	theorem	theorem	NOUN
ejpam-3985	351	3	15	15	NUM
ejpam-3985	351	4	,	,	PUNCT
ejpam-3985	351	5	w	w	NOUN
ejpam-3985	351	6	is	be	AUX
ejpam-3985	351	7	a	a	DET
ejpam-3985	351	8	resolving	resolve	VERB
ejpam-3985	351	9	dominating	dominating	NOUN
ejpam-3985	351	10	set	set	NOUN
ejpam-3985	351	11	of	of	ADP
ejpam-3985	351	12	g	g	PROPN
ejpam-3985	351	13	◦	◦	NOUN
ejpam-3985	351	14	h.	h.	NOUN
ejpam-3985	351	15	further	far	ADV
ejpam-3985	351	16	,	,	PUNCT
ejpam-3985	351	17	because	because	SCONJ
ejpam-3985	351	18	of	of	ADP
ejpam-3985	351	19	the	the	DET
ejpam-3985	351	20	additional	additional	ADJ
ejpam-3985	351	21	properties	property	NOUN
ejpam-3985	351	22	of	of	ADP
ejpam-3985	351	23	the	the	DET
ejpam-3985	351	24	sets	set	NOUN
ejpam-3985	351	25	in	in	ADP
ejpam-3985	351	26	b	b	PROPN
ejpam-3985	351	27	and	and	CCONJ
ejpam-3985	351	28	d	d	NOUN
ejpam-3985	351	29	,	,	PUNCT
ejpam-3985	351	30	w	w	PROPN
ejpam-3985	351	31	is	be	AUX
ejpam-3985	351	32	a	a	DET
ejpam-3985	351	33	restrained	restrained	ADJ
ejpam-3985	351	34	dominating	dominating	NOUN
ejpam-3985	351	35	set	set	NOUN
ejpam-3985	351	36	of	of	ADP
ejpam-3985	351	37	g	g	PROPN
ejpam-3985	351	38	◦	◦	PROPN
ejpam-3985	351	39	h.	h.	PROPN
ejpam-3985	351	40	remark	remark	NOUN
ejpam-3985	351	41	3	3	NUM
ejpam-3985	351	42	.	.	PUNCT
ejpam-3985	352	1	[	[	X
ejpam-3985	352	2	11	11	NUM
ejpam-3985	352	3	]	]	PUNCT
ejpam-3985	352	4	for	for	ADP
ejpam-3985	352	5	any	any	DET
ejpam-3985	352	6	connected	connected	ADJ
ejpam-3985	352	7	graph	graph	NOUN
ejpam-3985	352	8	g	g	NOUN
ejpam-3985	352	9	,	,	PUNCT
ejpam-3985	352	10	ln(g	ln(g	NUM
ejpam-3985	352	11	)	)	PUNCT
ejpam-3985	352	12	≤	≤	NUM
ejpam-3985	352	13	γl(g	γl(g	NUM
ejpam-3985	352	14	)	)	PUNCT
ejpam-3985	352	15	≤	≤	NUM
ejpam-3985	352	16	γsl(g	γsl(g	NOUN
ejpam-3985	352	17	)	)	PUNCT
ejpam-3985	352	18	.	.	PUNCT
ejpam-3985	353	1	theorem	theorem	VERB
ejpam-3985	353	2	17	17	NUM
ejpam-3985	353	3	.	.	PUNCT
ejpam-3985	354	1	[	[	X
ejpam-3985	354	2	11	11	NUM
ejpam-3985	354	3	]	]	PUNCT
ejpam-3985	354	4	let	let	VERB
ejpam-3985	354	5	g	g	PRON
ejpam-3985	354	6	be	be	AUX
ejpam-3985	354	7	a	a	DET
ejpam-3985	354	8	connected	connected	ADJ
ejpam-3985	354	9	graph	graph	NOUN
ejpam-3985	354	10	of	of	ADP
ejpam-3985	354	11	order	order	NOUN
ejpam-3985	354	12	n	n	PRON
ejpam-3985	354	13	≥	≥	NUM
ejpam-3985	354	14	2	2	NUM
ejpam-3985	354	15	(	(	PUNCT
ejpam-3985	354	16	i	i	NOUN
ejpam-3985	354	17	)	)	PUNCT
ejpam-3985	354	18	if	if	SCONJ
ejpam-3985	354	19	ln(g	ln(g	NUM
ejpam-3985	354	20	)	)	PUNCT
ejpam-3985	354	21	<	<	X
ejpam-3985	354	22	sln(g	sln(g	PROPN
ejpam-3985	354	23	)	)	PUNCT
ejpam-3985	354	24	,	,	PUNCT
ejpam-3985	354	25	then	then	ADV
ejpam-3985	354	26	1	1	NUM
ejpam-3985	354	27	+	+	NUM
ejpam-3985	354	28	ln(g	ln(g	X
ejpam-3985	354	29	)	)	PUNCT
ejpam-3985	354	30	=	=	PUNCT
ejpam-3985	354	31	sln(g	sln(g	PROPN
ejpam-3985	354	32	)	)	PUNCT
ejpam-3985	354	33	.	.	PUNCT
ejpam-3985	355	1	(	(	PUNCT
ejpam-3985	355	2	ii	ii	NOUN
ejpam-3985	355	3	)	)	PUNCT
ejpam-3985	355	4	if	if	SCONJ
ejpam-3985	355	5	ln(g	ln(g	NUM
ejpam-3985	355	6	)	)	PUNCT
ejpam-3985	355	7	<	<	X
ejpam-3985	355	8	γl(g	γl(g	NUM
ejpam-3985	355	9	)	)	PUNCT
ejpam-3985	355	10	,	,	PUNCT
ejpam-3985	355	11	then	then	ADV
ejpam-3985	355	12	1	1	NUM
ejpam-3985	355	13	+	+	NUM
ejpam-3985	355	14	ln(g	ln(g	X
ejpam-3985	355	15	)	)	PUNCT
ejpam-3985	355	16	=	=	SYM
ejpam-3985	356	1	γl(g	γl(g	NUM
ejpam-3985	356	2	)	)	PUNCT
ejpam-3985	356	3	.	.	PUNCT
ejpam-3985	357	1	(	(	PUNCT
ejpam-3985	357	2	iii	iii	X
ejpam-3985	357	3	)	)	PUNCT
ejpam-3985	357	4	if	if	SCONJ
ejpam-3985	357	5	sln(g	sln(g	PROPN
ejpam-3985	357	6	)	)	PUNCT
ejpam-3985	357	7	<	<	X
ejpam-3985	357	8	γsl(g	γsl(g	X
ejpam-3985	357	9	)	)	PUNCT
ejpam-3985	357	10	,	,	PUNCT
ejpam-3985	357	11	then	then	ADV
ejpam-3985	357	12	1	1	NUM
ejpam-3985	357	13	+	+	CCONJ
ejpam-3985	357	14	sln(g	sln(g	NOUN
ejpam-3985	357	15	)	)	PUNCT
ejpam-3985	357	16	=	=	SYM
ejpam-3985	357	17	γsl(g	γsl(g	PROPN
ejpam-3985	357	18	)	)	PUNCT
ejpam-3985	357	19	.	.	PUNCT
ejpam-3985	358	1	corollary	corollary	ADJ
ejpam-3985	358	2	4	4	NUM
ejpam-3985	358	3	.	.	PUNCT
ejpam-3985	359	1	let	let	VERB
ejpam-3985	359	2	g	g	NOUN
ejpam-3985	359	3	and	and	CCONJ
ejpam-3985	359	4	h	h	PROPN
ejpam-3985	359	5	be	be	VERB
ejpam-3985	359	6	non	non	ADJ
ejpam-3985	359	7	-	-	ADJ
ejpam-3985	359	8	trivial	trivial	ADJ
ejpam-3985	359	9	connected	connected	ADJ
ejpam-3985	359	10	graphs	graph	NOUN
ejpam-3985	359	11	with	with	ADP
ejpam-3985	359	12	|v	|v	PROPN
ejpam-3985	359	13	(	(	PUNCT
ejpam-3985	359	14	g)|	g)|	NOUN
ejpam-3985	359	15	=	=	NOUN
ejpam-3985	359	16	n.	n.	NOUN
ejpam-3985	360	1	then	then	ADV
ejpam-3985	360	2	γrr(g	γrr(g	PROPN
ejpam-3985	360	3	◦	◦	NOUN
ejpam-3985	360	4	h	h	NOUN
ejpam-3985	360	5	)	)	PUNCT
ejpam-3985	360	6	=	=	SYM
ejpam-3985	361	1	n	n	X
ejpam-3985	361	2	·	·	PUNCT
ejpam-3985	361	3	γl(h	γl(h	NUM
ejpam-3985	361	4	)	)	PUNCT
ejpam-3985	361	5	.	.	PUNCT
ejpam-3985	362	1	proof	proof	NOUN
ejpam-3985	362	2	:	:	PUNCT
ejpam-3985	362	3	let	let	VERB
ejpam-3985	362	4	w	w	PART
ejpam-3985	362	5	be	be	AUX
ejpam-3985	362	6	a	a	DET
ejpam-3985	362	7	minimum	minimum	ADJ
ejpam-3985	362	8	resolving	resolving	NOUN
ejpam-3985	362	9	restrained	restrained	ADJ
ejpam-3985	362	10	dominating	dominating	NOUN
ejpam-3985	362	11	of	of	ADP
ejpam-3985	362	12	g	g	PROPN
ejpam-3985	362	13	◦	◦	PROPN
ejpam-3985	362	14	h.	h.	PROPN
ejpam-3985	363	1	then	then	ADV
ejpam-3985	363	2	w	w	PROPN
ejpam-3985	363	3	=	=	SYM
ejpam-3985	363	4	a∪b	a∪b	NOUN
ejpam-3985	363	5	∪d	∪d	NUM
ejpam-3985	363	6	are	be	AUX
ejpam-3985	363	7	the	the	DET
ejpam-3985	363	8	sets	set	NOUN
ejpam-3985	363	9	described	describe	VERB
ejpam-3985	363	10	in	in	ADP
ejpam-3985	363	11	theorem	theorem	ADJ
ejpam-3985	363	12	16	16	NUM
ejpam-3985	363	13	.	.	PUNCT
ejpam-3985	364	1	by	by	ADP
ejpam-3985	364	2	remark	remark	NOUN
ejpam-3985	364	3	3	3	NUM
ejpam-3985	364	4	and	and	CCONJ
ejpam-3985	364	5	theorem	theorem	VERB
ejpam-3985	364	6	17	17	NUM
ejpam-3985	364	7	,	,	PUNCT
ejpam-3985	364	8	it	it	PRON
ejpam-3985	364	9	follows	follow	VERB
ejpam-3985	364	10	that	that	SCONJ
ejpam-3985	364	11	γrr(g	γrr(g	PROPN
ejpam-3985	364	12	◦	◦	NOUN
ejpam-3985	364	13	h	h	NOUN
ejpam-3985	364	14	)	)	PUNCT
ejpam-3985	364	15	=	=	SYM
ejpam-3985	365	1	|w	|w	NOUN
ejpam-3985	365	2	|	|	NOUN
ejpam-3985	365	3	=	=	PUNCT
ejpam-3985	366	1	|a|+	|a|+	NOUN
ejpam-3985	366	2	|b|+	|b|+	NOUN
ejpam-3985	366	3	|d|	|d|	PROPN
ejpam-3985	366	4	≥	≥	AUX
ejpam-3985	366	5	|a|+	|a|+	VERB
ejpam-3985	366	6	|a|	|a|	PROPN
ejpam-3985	366	7	·	·	SYM
ejpam-3985	366	8	rln(h	rln(h	PROPN
ejpam-3985	366	9	)	)	PUNCT
ejpam-3985	366	10	+	+	CCONJ
ejpam-3985	366	11	(	(	PUNCT
ejpam-3985	366	12	n−	n−	NOUN
ejpam-3985	366	13	|a|	|a|	NOUN
ejpam-3985	366	14	)	)	PUNCT
ejpam-3985	366	15	·	·	PUNCT
ejpam-3985	366	16	γl(h	γl(h	X
ejpam-3985	366	17	)	)	PUNCT
ejpam-3985	366	18	≥	≥	NOUN
ejpam-3985	366	19	|a|+	|a|+	VERB
ejpam-3985	366	20	|a|	|a|	PROPN
ejpam-3985	366	21	·	·	PUNCT
ejpam-3985	366	22	ln(h	ln(h	NUM
ejpam-3985	366	23	)	)	PUNCT
ejpam-3985	367	1	+	+	CCONJ
ejpam-3985	367	2	(	(	PUNCT
ejpam-3985	367	3	n−	n−	NOUN
ejpam-3985	367	4	|a|	|a|	NOUN
ejpam-3985	367	5	)	)	PUNCT
ejpam-3985	367	6	·	·	PUNCT
ejpam-3985	367	7	γl(h	γl(h	X
ejpam-3985	367	8	)	)	PUNCT
ejpam-3985	367	9	=	=	SYM
ejpam-3985	367	10	|a|	|a|	PROPN
ejpam-3985	367	11	(	(	PUNCT
ejpam-3985	367	12	1	1	NUM
ejpam-3985	367	13	+	+	CCONJ
ejpam-3985	367	14	ln(h	ln(h	NUM
ejpam-3985	367	15	)	)	PUNCT
ejpam-3985	367	16	)	)	PUNCT
ejpam-3985	368	1	+	+	CCONJ
ejpam-3985	368	2	(	(	PUNCT
ejpam-3985	368	3	n−	n−	NOUN
ejpam-3985	368	4	|a|	|a|	NOUN
ejpam-3985	368	5	)	)	PUNCT
ejpam-3985	368	6	·	·	PUNCT
ejpam-3985	368	7	γl(h	γl(h	X
ejpam-3985	368	8	)	)	PUNCT
ejpam-3985	368	9	≥	≥	PROPN
ejpam-3985	368	10	|a|	|a|	NUM
ejpam-3985	368	11	·	·	PUNCT
ejpam-3985	368	12	γl(h	γl(h	PUNCT
ejpam-3985	368	13	)	)	PUNCT
ejpam-3985	369	1	+	+	CCONJ
ejpam-3985	369	2	(	(	PUNCT
ejpam-3985	369	3	n−	n−	NOUN
ejpam-3985	369	4	|a|	|a|	NOUN
ejpam-3985	369	5	)	)	PUNCT
ejpam-3985	369	6	·	·	PUNCT
ejpam-3985	369	7	γl(h	γl(h	X
ejpam-3985	369	8	)	)	PUNCT
ejpam-3985	369	9	=	=	SYM
ejpam-3985	369	10	n	n	X
ejpam-3985	369	11	·	·	PUNCT
ejpam-3985	369	12	γl(h	γl(h	NUM
ejpam-3985	369	13	)	)	PUNCT
ejpam-3985	369	14	.	.	PUNCT
ejpam-3985	370	1	now	now	ADV
ejpam-3985	370	2	,	,	PUNCT
ejpam-3985	370	3	let	let	VERB
ejpam-3985	370	4	f	f	PRON
ejpam-3985	370	5	be	be	AUX
ejpam-3985	370	6	a	a	DET
ejpam-3985	370	7	minimum	minimum	ADJ
ejpam-3985	370	8	locating	locating	NOUN
ejpam-3985	370	9	-	-	PUNCT
ejpam-3985	370	10	dominating	dominate	VERB
ejpam-3985	370	11	set	set	NOUN
ejpam-3985	370	12	of	of	ADP
ejpam-3985	370	13	h.	h.	PROPN
ejpam-3985	370	14	for	for	ADP
ejpam-3985	370	15	each	each	DET
ejpam-3985	370	16	v	v	NUM
ejpam-3985	370	17	∈	∈	PROPN
ejpam-3985	370	18	v	v	NOUN
ejpam-3985	370	19	(	(	PUNCT
ejpam-3985	370	20	g	g	NOUN
ejpam-3985	370	21	)	)	PUNCT
ejpam-3985	370	22	,	,	PUNCT
ejpam-3985	370	23	pick	pick	VERB
ejpam-3985	370	24	fv	fv	PROPN
ejpam-3985	370	25	⊆	⊆	NUM
ejpam-3985	370	26	v	v	PROPN
ejpam-3985	370	27	(	(	PUNCT
ejpam-3985	370	28	hv	hv	NOUN
ejpam-3985	370	29	)	)	PUNCT
ejpam-3985	370	30	with	with	ADP
ejpam-3985	370	31	〈	〈	PROPN
ejpam-3985	370	32	fv	fv	ADP
ejpam-3985	370	33	〉	〉	NOUN
ejpam-3985	370	34	∼=	∼=	PROPN
ejpam-3985	370	35	〈	〈	PROPN
ejpam-3985	370	36	f	f	PROPN
ejpam-3985	370	37	〉	〉	PROPN
ejpam-3985	370	38	.	.	PUNCT
ejpam-3985	371	1	then	then	ADV
ejpam-3985	371	2	w	w	PROPN
ejpam-3985	371	3	=	=	PUNCT
ejpam-3985	371	4	⋃	⋃	NOUN
ejpam-3985	371	5	v∈v	v∈v	NOUN
ejpam-3985	371	6	(	(	PUNCT
ejpam-3985	371	7	g	g	NOUN
ejpam-3985	371	8	)	)	PUNCT
ejpam-3985	371	9	fv	fv	PROPN
ejpam-3985	371	10	is	be	AUX
ejpam-3985	371	11	a	a	DET
ejpam-3985	371	12	resolving	resolve	VERB
ejpam-3985	371	13	restrained	restrained	ADJ
ejpam-3985	371	14	dominating	dominating	NOUN
ejpam-3985	371	15	set	set	NOUN
ejpam-3985	371	16	of	of	ADP
ejpam-3985	371	17	g	g	PROPN
ejpam-3985	371	18	◦	◦	NOUN
ejpam-3985	371	19	h	h	NOUN
ejpam-3985	371	20	by	by	ADP
ejpam-3985	371	21	theorem	theorem	NOUN
ejpam-3985	371	22	16	16	NUM
ejpam-3985	371	23	.	.	PUNCT
ejpam-3985	372	1	hence	hence	ADV
ejpam-3985	372	2	,	,	PUNCT
ejpam-3985	372	3	γrr(g	γrr(g	PROPN
ejpam-3985	372	4	◦	◦	NOUN
ejpam-3985	372	5	h	h	NOUN
ejpam-3985	372	6	)	)	PUNCT
ejpam-3985	372	7	≤	≤	NOUN
ejpam-3985	372	8	|w	|w	NOUN
ejpam-3985	372	9	|	|	NOUN
ejpam-3985	372	10	=	=	SYM
ejpam-3985	372	11	n	n	NOUN
ejpam-3985	372	12	·	·	PUNCT
ejpam-3985	372	13	γl(h	γl(h	NUM
ejpam-3985	372	14	)	)	PUNCT
ejpam-3985	372	15	.	.	PUNCT
ejpam-3985	373	1	therefore	therefore	ADV
ejpam-3985	373	2	,	,	PUNCT
ejpam-3985	373	3	γrr(g	γrr(g	X
ejpam-3985	373	4	◦	◦	NOUN
ejpam-3985	373	5	h	h	NOUN
ejpam-3985	373	6	)	)	PUNCT
ejpam-3985	373	7	=	=	SYM
ejpam-3985	373	8	n	n	X
ejpam-3985	373	9	·	·	PUNCT
ejpam-3985	373	10	γl(h	γl(h	NUM
ejpam-3985	373	11	)	)	PUNCT
ejpam-3985	373	12	.	.	PUNCT
ejpam-3985	374	1	5	5	X
ejpam-3985	374	2	.	.	X
ejpam-3985	374	3	resolving	resolve	VERB
ejpam-3985	374	4	restrained	restrained	ADJ
ejpam-3985	374	5	domination	domination	NOUN
ejpam-3985	374	6	in	in	ADP
ejpam-3985	374	7	the	the	DET
ejpam-3985	374	8	lexicographic	lexicographic	ADJ
ejpam-3985	374	9	product	product	NOUN
ejpam-3985	374	10	of	of	ADP
ejpam-3985	374	11	graphs	graph	NOUN
ejpam-3985	374	12	theorem	theorem	VERB
ejpam-3985	374	13	18	18	NUM
ejpam-3985	374	14	.	.	PUNCT
ejpam-3985	375	1	[	[	X
ejpam-3985	375	2	9	9	NUM
ejpam-3985	375	3	]	]	PUNCT
ejpam-3985	375	4	let	let	VERB
ejpam-3985	375	5	g	g	NOUN
ejpam-3985	375	6	and	and	CCONJ
ejpam-3985	375	7	h	h	PROPN
ejpam-3985	375	8	be	be	VERB
ejpam-3985	375	9	non	non	ADJ
ejpam-3985	375	10	-	-	ADJ
ejpam-3985	375	11	trivial	trivial	ADJ
ejpam-3985	375	12	connected	connected	ADJ
ejpam-3985	375	13	graphs	graph	NOUN
ejpam-3985	375	14	with	with	ADP
ejpam-3985	375	15	∆(h	∆(h	NOUN
ejpam-3985	375	16	)	)	PUNCT
ejpam-3985	375	17	≤	≤	NOUN
ejpam-3985	375	18	|v	|v	X
ejpam-3985	375	19	(	(	PUNCT
ejpam-3985	375	20	h)|	h)|	NOUN
ejpam-3985	375	21	−	−	PROPN
ejpam-3985	375	22	2	2	NUM
ejpam-3985	375	23	.	.	PUNCT
ejpam-3985	376	1	then	then	ADV
ejpam-3985	376	2	w	w	PROPN
ejpam-3985	376	3	=	=	PUNCT
ejpam-3985	376	4	⋃	⋃	PROPN
ejpam-3985	376	5	x∈s	x∈s	NOUN
ejpam-3985	376	6	[	[	PUNCT
ejpam-3985	376	7	{	{	PUNCT
ejpam-3985	376	8	x}×tx	x}×tx	X
ejpam-3985	376	9	]	]	PUNCT
ejpam-3985	376	10	,	,	PUNCT
ejpam-3985	376	11	where	where	SCONJ
ejpam-3985	376	12	s	s	VERB
ejpam-3985	376	13	⊆	⊆	NUM
ejpam-3985	376	14	v	v	NOUN
ejpam-3985	376	15	(	(	PUNCT
ejpam-3985	376	16	g	g	NOUN
ejpam-3985	376	17	)	)	PUNCT
ejpam-3985	376	18	and	and	CCONJ
ejpam-3985	376	19	tx	tx	VERB
ejpam-3985	376	20	⊆	⊆	NUM
ejpam-3985	376	21	v	v	NOUN
ejpam-3985	376	22	(	(	PUNCT
ejpam-3985	376	23	h	h	NOUN
ejpam-3985	376	24	)	)	PUNCT
ejpam-3985	376	25	for	for	ADP
ejpam-3985	376	26	each	each	DET
ejpam-3985	376	27	x	x	SYM
ejpam-3985	376	28	∈	∈	PROPN
ejpam-3985	376	29	s	s	NOUN
ejpam-3985	376	30	,	,	PUNCT
ejpam-3985	376	31	is	be	AUX
ejpam-3985	376	32	a	a	DET
ejpam-3985	376	33	resolving	resolving	NOUN
ejpam-3985	376	34	set	set	NOUN
ejpam-3985	376	35	of	of	ADP
ejpam-3985	376	36	g[h	g[h	NOUN
ejpam-3985	376	37	]	]	PUNCT
ejpam-3985	376	38	if	if	SCONJ
ejpam-3985	377	1	and	and	CCONJ
ejpam-3985	377	2	only	only	ADV
ejpam-3985	377	3	if	if	SCONJ
ejpam-3985	377	4	w	w	NOUN
ejpam-3985	377	5	is	be	AUX
ejpam-3985	377	6	a	a	DET
ejpam-3985	377	7	locating	locating	NOUN
ejpam-3985	377	8	set	set	NOUN
ejpam-3985	377	9	of	of	ADP
ejpam-3985	377	10	g[h	g[h	NOUN
ejpam-3985	377	11	]	]	PUNCT
ejpam-3985	377	12	.	.	PUNCT
ejpam-3985	378	1	g.	g.	PROPN
ejpam-3985	378	2	monsanto	monsanto	PROPN
ejpam-3985	378	3	,	,	PUNCT
ejpam-3985	378	4	h.	h.	PROPN
ejpam-3985	378	5	rara	rara	PROPN
ejpam-3985	378	6	/	/	SYM
ejpam-3985	378	7	eur	eur	PROPN
ejpam-3985	378	8	.	.	PUNCT
ejpam-3985	379	1	j.	j.	PROPN
ejpam-3985	379	2	pure	pure	PROPN
ejpam-3985	379	3	appl	appl	PROPN
ejpam-3985	379	4	.	.	PROPN
ejpam-3985	379	5	math	math	PROPN
ejpam-3985	379	6	,	,	PUNCT
ejpam-3985	379	7	14	14	NUM
ejpam-3985	379	8	(	(	PUNCT
ejpam-3985	379	9	3	3	NUM
ejpam-3985	379	10	)	)	PUNCT
ejpam-3985	379	11	(	(	PUNCT
ejpam-3985	379	12	2021	2021	NUM
ejpam-3985	379	13	)	)	PUNCT
ejpam-3985	379	14	,	,	PUNCT
ejpam-3985	379	15	829	829	NUM
ejpam-3985	379	16	-	-	SYM
ejpam-3985	379	17	841	841	NUM
ejpam-3985	379	18	839	839	NUM
ejpam-3985	379	19	theorem	theorem	NOUN
ejpam-3985	379	20	19	19	NUM
ejpam-3985	379	21	.	.	PUNCT
ejpam-3985	380	1	[	[	X
ejpam-3985	380	2	6	6	NUM
ejpam-3985	380	3	]	]	PUNCT
ejpam-3985	380	4	let	let	VERB
ejpam-3985	380	5	g	g	NOUN
ejpam-3985	380	6	and	and	CCONJ
ejpam-3985	380	7	h	h	PROPN
ejpam-3985	380	8	be	be	VERB
ejpam-3985	380	9	non	non	ADJ
ejpam-3985	380	10	-	-	ADJ
ejpam-3985	380	11	trivial	trivial	ADJ
ejpam-3985	380	12	connected	connected	ADJ
ejpam-3985	380	13	graphs	graph	NOUN
ejpam-3985	380	14	.	.	PUNCT
ejpam-3985	381	1	then	then	ADV
ejpam-3985	381	2	c	c	PROPN
ejpam-3985	381	3	⊆	⊆	NUM
ejpam-3985	381	4	v	v	NOUN
ejpam-3985	381	5	(	(	PUNCT
ejpam-3985	381	6	g[h	g[h	PROPN
ejpam-3985	381	7	]	]	PUNCT
ejpam-3985	381	8	)	)	PUNCT
ejpam-3985	381	9	is	be	AUX
ejpam-3985	381	10	a	a	DET
ejpam-3985	381	11	dominating	dominating	NOUN
ejpam-3985	381	12	set	set	VERB
ejpam-3985	381	13	in	in	ADP
ejpam-3985	381	14	g[h	g[h	PROPN
ejpam-3985	381	15	]	]	PUNCT
ejpam-3985	381	16	if	if	SCONJ
ejpam-3985	382	1	and	and	CCONJ
ejpam-3985	382	2	only	only	ADV
ejpam-3985	382	3	if	if	SCONJ
ejpam-3985	382	4	c	c	NOUN
ejpam-3985	382	5	=	=	SYM
ejpam-3985	382	6	⋃	⋃	PROPN
ejpam-3985	382	7	x∈s	x∈s	NOUN
ejpam-3985	382	8	[	[	PUNCT
ejpam-3985	382	9	{	{	PUNCT
ejpam-3985	382	10	x	x	NOUN
ejpam-3985	382	11	}	}	PUNCT
ejpam-3985	382	12	×	×	NOUN
ejpam-3985	382	13	tx	tx	NOUN
ejpam-3985	382	14	]	]	PUNCT
ejpam-3985	382	15	and	and	CCONJ
ejpam-3985	382	16	either	either	CCONJ
ejpam-3985	382	17	(	(	PUNCT
ejpam-3985	382	18	i	i	NOUN
ejpam-3985	382	19	)	)	PUNCT
ejpam-3985	382	20	s	s	VERB
ejpam-3985	382	21	is	be	AUX
ejpam-3985	382	22	a	a	DET
ejpam-3985	382	23	total	total	ADJ
ejpam-3985	382	24	dominating	dominating	NOUN
ejpam-3985	382	25	set	set	NOUN
ejpam-3985	382	26	in	in	ADP
ejpam-3985	382	27	g	g	PROPN
ejpam-3985	382	28	or	or	CCONJ
ejpam-3985	382	29	(	(	PUNCT
ejpam-3985	382	30	ii	ii	NOUN
ejpam-3985	382	31	)	)	PUNCT
ejpam-3985	382	32	s	s	VERB
ejpam-3985	382	33	is	be	AUX
ejpam-3985	382	34	a	a	DET
ejpam-3985	382	35	dominating	dominating	NOUN
ejpam-3985	382	36	set	set	NOUN
ejpam-3985	382	37	in	in	ADP
ejpam-3985	382	38	g	g	PROPN
ejpam-3985	382	39	and	and	CCONJ
ejpam-3985	382	40	tx	tx	PROPN
ejpam-3985	382	41	is	be	AUX
ejpam-3985	382	42	a	a	DET
ejpam-3985	382	43	dominating	dominating	NOUN
ejpam-3985	382	44	set	set	VERB
ejpam-3985	382	45	in	in	ADP
ejpam-3985	382	46	h	h	NOUN
ejpam-3985	382	47	for	for	ADP
ejpam-3985	382	48	every	every	DET
ejpam-3985	382	49	x	x	SYM
ejpam-3985	382	50	∈	∈	PROPN
ejpam-3985	382	51	s	s	PART
ejpam-3985	382	52	\ng(s	\ng(s	NOUN
ejpam-3985	382	53	)	)	PUNCT
ejpam-3985	382	54	.	.	PUNCT
ejpam-3985	383	1	theorem	theorem	NOUN
ejpam-3985	383	2	20	20	NUM
ejpam-3985	383	3	.	.	PUNCT
ejpam-3985	384	1	[	[	X
ejpam-3985	384	2	14	14	NUM
ejpam-3985	384	3	]	]	PUNCT
ejpam-3985	384	4	let	let	VERB
ejpam-3985	384	5	g	g	NOUN
ejpam-3985	384	6	and	and	CCONJ
ejpam-3985	384	7	h	h	PROPN
ejpam-3985	384	8	be	be	VERB
ejpam-3985	384	9	non	non	ADJ
ejpam-3985	384	10	-	-	ADJ
ejpam-3985	384	11	trivial	trivial	ADJ
ejpam-3985	384	12	connected	connected	ADJ
ejpam-3985	384	13	graphs	graph	NOUN
ejpam-3985	384	14	with	with	ADP
ejpam-3985	384	15	∆(h	∆(h	NOUN
ejpam-3985	384	16	)	)	PUNCT
ejpam-3985	384	17	≤	≤	NOUN
ejpam-3985	384	18	|v	|v	X
ejpam-3985	384	19	(	(	PUNCT
ejpam-3985	384	20	h)|−2	h)|−2	PROPN
ejpam-3985	384	21	.	.	PUNCT
ejpam-3985	385	1	then	then	ADV
ejpam-3985	385	2	w	w	PROPN
ejpam-3985	385	3	=	=	PUNCT
ejpam-3985	385	4	⋃	⋃	PROPN
ejpam-3985	385	5	x∈s	x∈s	NOUN
ejpam-3985	385	6	[	[	PUNCT
ejpam-3985	385	7	{	{	PUNCT
ejpam-3985	385	8	x	x	NOUN
ejpam-3985	385	9	}	}	PUNCT
ejpam-3985	385	10	×	×	NOUN
ejpam-3985	385	11	tx	tx	PROPN
ejpam-3985	385	12	]	]	PUNCT
ejpam-3985	385	13	,	,	PUNCT
ejpam-3985	385	14	where	where	SCONJ
ejpam-3985	385	15	s	s	VERB
ejpam-3985	385	16	⊆	⊆	NUM
ejpam-3985	385	17	v	v	NOUN
ejpam-3985	385	18	(	(	PUNCT
ejpam-3985	385	19	g	g	NOUN
ejpam-3985	385	20	)	)	PUNCT
ejpam-3985	385	21	and	and	CCONJ
ejpam-3985	385	22	tx	tx	VERB
ejpam-3985	385	23	⊆	⊆	NUM
ejpam-3985	385	24	v	v	NOUN
ejpam-3985	385	25	(	(	PUNCT
ejpam-3985	385	26	h	h	NOUN
ejpam-3985	385	27	)	)	PUNCT
ejpam-3985	385	28	for	for	ADP
ejpam-3985	385	29	each	each	DET
ejpam-3985	385	30	x	x	SYM
ejpam-3985	385	31	∈	∈	PROPN
ejpam-3985	385	32	s	s	NOUN
ejpam-3985	385	33	,	,	PUNCT
ejpam-3985	385	34	is	be	AUX
ejpam-3985	385	35	a	a	DET
ejpam-3985	385	36	locating	locate	VERB
ejpam-3985	385	37	-	-	PUNCT
ejpam-3985	385	38	dominating	dominate	VERB
ejpam-3985	385	39	set	set	NOUN
ejpam-3985	385	40	of	of	ADP
ejpam-3985	385	41	g[h	g[h	NOUN
ejpam-3985	385	42	]	]	PUNCT
ejpam-3985	386	1	if	if	SCONJ
ejpam-3985	386	2	and	and	CCONJ
ejpam-3985	386	3	only	only	ADV
ejpam-3985	386	4	if	if	SCONJ
ejpam-3985	386	5	(	(	PUNCT
ejpam-3985	386	6	i	i	NOUN
ejpam-3985	386	7	)	)	PUNCT
ejpam-3985	386	8	s	s	PART
ejpam-3985	386	9	=	=	SYM
ejpam-3985	386	10	v	v	NOUN
ejpam-3985	386	11	(	(	PUNCT
ejpam-3985	386	12	g	g	NOUN
ejpam-3985	386	13	)	)	PUNCT
ejpam-3985	386	14	;	;	PUNCT
ejpam-3985	386	15	(	(	PUNCT
ejpam-3985	386	16	ii	ii	NOUN
ejpam-3985	386	17	)	)	PUNCT
ejpam-3985	386	18	tx	tx	PROPN
ejpam-3985	386	19	is	be	AUX
ejpam-3985	386	20	a	a	DET
ejpam-3985	386	21	locating	locating	NOUN
ejpam-3985	386	22	set	set	NOUN
ejpam-3985	386	23	of	of	ADP
ejpam-3985	386	24	h	h	NOUN
ejpam-3985	386	25	for	for	ADP
ejpam-3985	386	26	every	every	DET
ejpam-3985	386	27	x	x	SYM
ejpam-3985	386	28	∈	∈	PROPN
ejpam-3985	386	29	v	v	NOUN
ejpam-3985	386	30	(	(	PUNCT
ejpam-3985	386	31	g	g	NOUN
ejpam-3985	386	32	)	)	PUNCT
ejpam-3985	386	33	;	;	PUNCT
ejpam-3985	386	34	(	(	PUNCT
ejpam-3985	386	35	iii	iii	X
ejpam-3985	386	36	)	)	PUNCT
ejpam-3985	386	37	tx	tx	NOUN
ejpam-3985	387	1	or	or	CCONJ
ejpam-3985	387	2	ty	ty	INTJ
ejpam-3985	387	3	is	be	AUX
ejpam-3985	387	4	strictly	strictly	ADV
ejpam-3985	387	5	locating	locate	VERB
ejpam-3985	387	6	set	set	NOUN
ejpam-3985	387	7	of	of	ADP
ejpam-3985	387	8	h	h	NOUN
ejpam-3985	387	9	whenever	whenever	SCONJ
ejpam-3985	387	10	x	x	PRON
ejpam-3985	387	11	and	and	CCONJ
ejpam-3985	387	12	y	y	PROPN
ejpam-3985	387	13	are	be	AUX
ejpam-3985	387	14	adjacent	adjacent	ADJ
ejpam-3985	387	15	vertices	vertex	NOUN
ejpam-3985	387	16	of	of	ADP
ejpam-3985	387	17	g	g	NOUN
ejpam-3985	387	18	with	with	ADP
ejpam-3985	387	19	ng[x	ng[x	PROPN
ejpam-3985	387	20	]	]	X
ejpam-3985	387	21	=	=	PUNCT
ejpam-3985	387	22	ng[y	ng[y	PROPN
ejpam-3985	387	23	]	]	X
ejpam-3985	387	24	;	;	PUNCT
ejpam-3985	387	25	and	and	CCONJ
ejpam-3985	387	26	(	(	PUNCT
ejpam-3985	387	27	iv	iv	X
ejpam-3985	387	28	)	)	PUNCT
ejpam-3985	387	29	tx	tx	NOUN
ejpam-3985	387	30	or	or	CCONJ
ejpam-3985	387	31	ty	ty	INTJ
ejpam-3985	387	32	is	be	AUX
ejpam-3985	387	33	(	(	PUNCT
ejpam-3985	387	34	locating	locate	VERB
ejpam-3985	387	35	)	)	PUNCT
ejpam-3985	387	36	dominating	dominating	NOUN
ejpam-3985	387	37	set	set	NOUN
ejpam-3985	387	38	of	of	ADP
ejpam-3985	387	39	h	h	NOUN
ejpam-3985	387	40	whenever	whenever	SCONJ
ejpam-3985	387	41	x	x	PRON
ejpam-3985	387	42	and	and	CCONJ
ejpam-3985	387	43	y	y	PROPN
ejpam-3985	387	44	are	be	AUX
ejpam-3985	387	45	nonadjacent	nonadjacent	ADJ
ejpam-3985	387	46	vertices	vertex	NOUN
ejpam-3985	387	47	of	of	ADP
ejpam-3985	387	48	g	g	NOUN
ejpam-3985	387	49	with	with	ADP
ejpam-3985	387	50	ng(x	ng(x	NUM
ejpam-3985	387	51	)	)	PUNCT
ejpam-3985	387	52	=	=	PUNCT
ejpam-3985	387	53	ng(y	ng(y	NOUN
ejpam-3985	387	54	)	)	PUNCT
ejpam-3985	387	55	.	.	PUNCT
ejpam-3985	388	1	theorem	theorem	NOUN
ejpam-3985	388	2	21	21	NUM
ejpam-3985	388	3	.	.	PUNCT
ejpam-3985	389	1	let	let	VERB
ejpam-3985	389	2	g	g	NOUN
ejpam-3985	389	3	and	and	CCONJ
ejpam-3985	389	4	h	h	PROPN
ejpam-3985	389	5	be	be	VERB
ejpam-3985	389	6	non	non	ADJ
ejpam-3985	389	7	-	-	ADJ
ejpam-3985	389	8	trivial	trivial	ADJ
ejpam-3985	389	9	connected	connected	ADJ
ejpam-3985	389	10	graphs	graph	NOUN
ejpam-3985	389	11	with	with	ADP
ejpam-3985	389	12	∆(h	∆(h	NOUN
ejpam-3985	389	13	)	)	PUNCT
ejpam-3985	389	14	≤	≤	NOUN
ejpam-3985	389	15	|v	|v	X
ejpam-3985	389	16	(	(	PUNCT
ejpam-3985	389	17	h)|	h)|	NOUN
ejpam-3985	389	18	−	−	PROPN
ejpam-3985	389	19	2	2	NUM
ejpam-3985	389	20	.	.	PUNCT
ejpam-3985	390	1	then	then	ADV
ejpam-3985	390	2	w	w	PROPN
ejpam-3985	390	3	=	=	PUNCT
ejpam-3985	390	4	⋃	⋃	PROPN
ejpam-3985	390	5	x∈s	x∈s	NOUN
ejpam-3985	390	6	[	[	PUNCT
ejpam-3985	390	7	{	{	PUNCT
ejpam-3985	390	8	x}×tx	x}×tx	X
ejpam-3985	390	9	]	]	PUNCT
ejpam-3985	390	10	,	,	PUNCT
ejpam-3985	390	11	where	where	SCONJ
ejpam-3985	390	12	s	s	VERB
ejpam-3985	390	13	⊆	⊆	NUM
ejpam-3985	390	14	v	v	NOUN
ejpam-3985	390	15	(	(	PUNCT
ejpam-3985	390	16	g	g	NOUN
ejpam-3985	390	17	)	)	PUNCT
ejpam-3985	390	18	and	and	CCONJ
ejpam-3985	390	19	tx	tx	VERB
ejpam-3985	390	20	⊆	⊆	NUM
ejpam-3985	390	21	v	v	NOUN
ejpam-3985	390	22	(	(	PUNCT
ejpam-3985	390	23	h	h	NOUN
ejpam-3985	390	24	)	)	PUNCT
ejpam-3985	390	25	for	for	ADP
ejpam-3985	390	26	each	each	DET
ejpam-3985	390	27	x	x	SYM
ejpam-3985	390	28	∈	∈	PROPN
ejpam-3985	390	29	s	s	NOUN
ejpam-3985	390	30	,	,	PUNCT
ejpam-3985	390	31	is	be	AUX
ejpam-3985	390	32	a	a	DET
ejpam-3985	390	33	resolving	resolve	VERB
ejpam-3985	390	34	dominating	dominating	NOUN
ejpam-3985	390	35	set	set	NOUN
ejpam-3985	390	36	of	of	ADP
ejpam-3985	390	37	g[h	g[h	PROPN
ejpam-3985	390	38	]	]	PUNCT
ejpam-3985	390	39	if	if	SCONJ
ejpam-3985	391	1	and	and	CCONJ
ejpam-3985	391	2	only	only	ADV
ejpam-3985	391	3	if	if	SCONJ
ejpam-3985	391	4	w	w	NOUN
ejpam-3985	391	5	is	be	AUX
ejpam-3985	391	6	a	a	DET
ejpam-3985	391	7	locating	locate	VERB
ejpam-3985	391	8	-	-	PUNCT
ejpam-3985	391	9	dominating	dominate	VERB
ejpam-3985	391	10	set	set	NOUN
ejpam-3985	391	11	of	of	ADP
ejpam-3985	391	12	g[h	g[h	PROPN
ejpam-3985	391	13	]	]	PUNCT
ejpam-3985	391	14	.	.	PUNCT
ejpam-3985	392	1	proof	proof	NOUN
ejpam-3985	392	2	:	:	PUNCT
ejpam-3985	392	3	suppose	suppose	VERB
ejpam-3985	392	4	w	w	NOUN
ejpam-3985	392	5	is	be	AUX
ejpam-3985	392	6	a	a	DET
ejpam-3985	392	7	resolving	resolve	VERB
ejpam-3985	392	8	dominating	dominating	NOUN
ejpam-3985	392	9	set	set	NOUN
ejpam-3985	392	10	of	of	ADP
ejpam-3985	392	11	g[h	g[h	PROPN
ejpam-3985	392	12	]	]	PUNCT
ejpam-3985	392	13	.	.	PUNCT
ejpam-3985	393	1	then	then	ADV
ejpam-3985	393	2	by	by	ADP
ejpam-3985	393	3	theorem	theorem	NOUN
ejpam-3985	393	4	20	20	NUM
ejpam-3985	393	5	,	,	PUNCT
ejpam-3985	393	6	w	w	NOUN
ejpam-3985	393	7	is	be	AUX
ejpam-3985	393	8	a	a	DET
ejpam-3985	393	9	locating	locate	VERB
ejpam-3985	393	10	-	-	PUNCT
ejpam-3985	393	11	dominating	dominate	VERB
ejpam-3985	393	12	set	set	NOUN
ejpam-3985	393	13	of	of	ADP
ejpam-3985	393	14	g[h	g[h	NOUN
ejpam-3985	393	15	]	]	PUNCT
ejpam-3985	393	16	.	.	PUNCT
ejpam-3985	394	1	the	the	DET
ejpam-3985	394	2	converse	converse	NOUN
ejpam-3985	394	3	follows	follow	VERB
ejpam-3985	394	4	from	from	ADP
ejpam-3985	394	5	theorem	theorem	ADJ
ejpam-3985	394	6	20	20	NUM
ejpam-3985	394	7	and	and	CCONJ
ejpam-3985	394	8	theorem	theorem	VERB
ejpam-3985	394	9	19	19	NUM
ejpam-3985	394	10	.	.	PUNCT
ejpam-3985	395	1	the	the	DET
ejpam-3985	395	2	next	next	ADJ
ejpam-3985	395	3	result	result	NOUN
ejpam-3985	395	4	follows	follow	VERB
ejpam-3985	395	5	immediately	immediately	ADV
ejpam-3985	395	6	from	from	ADP
ejpam-3985	395	7	theorem	theorem	ADJ
ejpam-3985	395	8	20	20	NUM
ejpam-3985	395	9	and	and	CCONJ
ejpam-3985	395	10	theorem	theorem	VERB
ejpam-3985	395	11	21	21	NUM
ejpam-3985	395	12	.	.	PUNCT
ejpam-3985	396	1	theorem	theorem	NOUN
ejpam-3985	396	2	22	22	NUM
ejpam-3985	396	3	.	.	PUNCT
ejpam-3985	397	1	let	let	VERB
ejpam-3985	397	2	g	g	NOUN
ejpam-3985	397	3	and	and	CCONJ
ejpam-3985	397	4	h	h	PROPN
ejpam-3985	397	5	be	be	VERB
ejpam-3985	397	6	non	non	ADJ
ejpam-3985	397	7	-	-	ADJ
ejpam-3985	397	8	trivial	trivial	ADJ
ejpam-3985	397	9	connected	connected	ADJ
ejpam-3985	397	10	graphs	graph	NOUN
ejpam-3985	397	11	with	with	ADP
ejpam-3985	397	12	∆(h	∆(h	NOUN
ejpam-3985	397	13	)	)	PUNCT
ejpam-3985	397	14	≤	≤	NOUN
ejpam-3985	397	15	|v	|v	X
ejpam-3985	397	16	(	(	PUNCT
ejpam-3985	397	17	h)|	h)|	NOUN
ejpam-3985	397	18	−	−	PROPN
ejpam-3985	397	19	2	2	NUM
ejpam-3985	397	20	.	.	PUNCT
ejpam-3985	398	1	then	then	ADV
ejpam-3985	398	2	w	w	PROPN
ejpam-3985	398	3	=	=	PUNCT
ejpam-3985	398	4	⋃	⋃	PROPN
ejpam-3985	398	5	x∈s	x∈s	NOUN
ejpam-3985	398	6	[	[	PUNCT
ejpam-3985	398	7	{	{	PUNCT
ejpam-3985	398	8	x}×tx	x}×tx	X
ejpam-3985	398	9	]	]	PUNCT
ejpam-3985	398	10	,	,	PUNCT
ejpam-3985	398	11	where	where	SCONJ
ejpam-3985	398	12	s	s	VERB
ejpam-3985	398	13	⊆	⊆	NUM
ejpam-3985	398	14	v	v	NOUN
ejpam-3985	398	15	(	(	PUNCT
ejpam-3985	398	16	g	g	NOUN
ejpam-3985	398	17	)	)	PUNCT
ejpam-3985	398	18	and	and	CCONJ
ejpam-3985	398	19	tx	tx	VERB
ejpam-3985	398	20	⊆	⊆	NUM
ejpam-3985	398	21	v	v	NOUN
ejpam-3985	398	22	(	(	PUNCT
ejpam-3985	398	23	h	h	NOUN
ejpam-3985	398	24	)	)	PUNCT
ejpam-3985	398	25	for	for	ADP
ejpam-3985	398	26	each	each	DET
ejpam-3985	398	27	x	x	SYM
ejpam-3985	398	28	∈	∈	PROPN
ejpam-3985	398	29	s	s	NOUN
ejpam-3985	398	30	,	,	PUNCT
ejpam-3985	398	31	is	be	AUX
ejpam-3985	398	32	a	a	DET
ejpam-3985	398	33	resolving	resolve	VERB
ejpam-3985	398	34	dominating	dominating	NOUN
ejpam-3985	398	35	set	set	NOUN
ejpam-3985	398	36	of	of	ADP
ejpam-3985	398	37	g[h	g[h	PROPN
ejpam-3985	398	38	]	]	PUNCT
ejpam-3985	398	39	if	if	SCONJ
ejpam-3985	398	40	and	and	CCONJ
ejpam-3985	398	41	only	only	ADV
ejpam-3985	398	42	if	if	SCONJ
ejpam-3985	398	43	(	(	PUNCT
ejpam-3985	398	44	i	i	NOUN
ejpam-3985	398	45	)	)	PUNCT
ejpam-3985	398	46	s	s	PART
ejpam-3985	398	47	=	=	SYM
ejpam-3985	398	48	v	v	NOUN
ejpam-3985	398	49	(	(	PUNCT
ejpam-3985	398	50	g	g	NOUN
ejpam-3985	398	51	)	)	PUNCT
ejpam-3985	398	52	;	;	PUNCT
ejpam-3985	398	53	(	(	PUNCT
ejpam-3985	398	54	ii	ii	NOUN
ejpam-3985	398	55	)	)	PUNCT
ejpam-3985	398	56	tx	tx	PROPN
ejpam-3985	398	57	is	be	AUX
ejpam-3985	398	58	a	a	DET
ejpam-3985	398	59	locating	locating	NOUN
ejpam-3985	398	60	set	set	NOUN
ejpam-3985	398	61	of	of	ADP
ejpam-3985	398	62	h	h	NOUN
ejpam-3985	398	63	for	for	ADP
ejpam-3985	398	64	every	every	DET
ejpam-3985	398	65	x	x	SYM
ejpam-3985	398	66	∈	∈	PROPN
ejpam-3985	398	67	v	v	NOUN
ejpam-3985	398	68	(	(	PUNCT
ejpam-3985	398	69	g	g	NOUN
ejpam-3985	398	70	)	)	PUNCT
ejpam-3985	398	71	;	;	PUNCT
ejpam-3985	398	72	(	(	PUNCT
ejpam-3985	398	73	iii	iii	X
ejpam-3985	398	74	)	)	PUNCT
ejpam-3985	398	75	tx	tx	NOUN
ejpam-3985	399	1	or	or	CCONJ
ejpam-3985	399	2	ty	ty	INTJ
ejpam-3985	399	3	is	be	AUX
ejpam-3985	399	4	strictly	strictly	ADV
ejpam-3985	399	5	locating	locate	VERB
ejpam-3985	399	6	set	set	NOUN
ejpam-3985	399	7	of	of	ADP
ejpam-3985	399	8	h	h	NOUN
ejpam-3985	399	9	whenever	whenever	SCONJ
ejpam-3985	399	10	x	x	PRON
ejpam-3985	399	11	and	and	CCONJ
ejpam-3985	399	12	y	y	PROPN
ejpam-3985	399	13	are	be	AUX
ejpam-3985	399	14	adjacent	adjacent	ADJ
ejpam-3985	399	15	vertices	vertex	NOUN
ejpam-3985	399	16	of	of	ADP
ejpam-3985	399	17	g	g	NOUN
ejpam-3985	399	18	with	with	ADP
ejpam-3985	399	19	ng[x	ng[x	PROPN
ejpam-3985	399	20	]	]	X
ejpam-3985	399	21	=	=	PUNCT
ejpam-3985	399	22	ng[y	ng[y	PROPN
ejpam-3985	399	23	]	]	X
ejpam-3985	399	24	;	;	PUNCT
ejpam-3985	399	25	and	and	CCONJ
ejpam-3985	399	26	(	(	PUNCT
ejpam-3985	399	27	iv	iv	X
ejpam-3985	399	28	)	)	PUNCT
ejpam-3985	399	29	tx	tx	NOUN
ejpam-3985	399	30	or	or	CCONJ
ejpam-3985	399	31	ty	ty	INTJ
ejpam-3985	399	32	is	be	AUX
ejpam-3985	399	33	locating	locate	VERB
ejpam-3985	399	34	-	-	PUNCT
ejpam-3985	399	35	dominating	dominate	VERB
ejpam-3985	399	36	set	set	NOUN
ejpam-3985	399	37	of	of	ADP
ejpam-3985	399	38	h	h	NOUN
ejpam-3985	399	39	whenever	whenever	SCONJ
ejpam-3985	399	40	x	x	PRON
ejpam-3985	399	41	and	and	CCONJ
ejpam-3985	399	42	y	y	PROPN
ejpam-3985	399	43	are	be	AUX
ejpam-3985	399	44	nonadjacent	nonadjacent	ADJ
ejpam-3985	399	45	vertices	vertex	NOUN
ejpam-3985	399	46	of	of	ADP
ejpam-3985	399	47	g	g	NOUN
ejpam-3985	399	48	with	with	ADP
ejpam-3985	399	49	ng(x	ng(x	NUM
ejpam-3985	399	50	)	)	PUNCT
ejpam-3985	399	51	=	=	PUNCT
ejpam-3985	399	52	ng(y	ng(y	NOUN
ejpam-3985	399	53	)	)	PUNCT
ejpam-3985	399	54	.	.	PUNCT
ejpam-3985	400	1	theorem	theorem	VERB
ejpam-3985	400	2	23	23	NUM
ejpam-3985	400	3	.	.	PUNCT
ejpam-3985	401	1	let	let	VERB
ejpam-3985	401	2	g	g	NOUN
ejpam-3985	401	3	and	and	CCONJ
ejpam-3985	401	4	h	h	PROPN
ejpam-3985	401	5	be	be	VERB
ejpam-3985	401	6	non	non	ADJ
ejpam-3985	401	7	-	-	ADJ
ejpam-3985	401	8	trivial	trivial	ADJ
ejpam-3985	401	9	connected	connected	ADJ
ejpam-3985	401	10	graphs	graph	NOUN
ejpam-3985	401	11	with	with	ADP
ejpam-3985	401	12	∆(h	∆(h	NOUN
ejpam-3985	401	13	)	)	PUNCT
ejpam-3985	401	14	≤	≤	NOUN
ejpam-3985	401	15	|v	|v	X
ejpam-3985	401	16	(	(	PUNCT
ejpam-3985	401	17	h)|	h)|	NOUN
ejpam-3985	401	18	−	−	PROPN
ejpam-3985	401	19	2	2	NUM
ejpam-3985	401	20	.	.	PUNCT
ejpam-3985	402	1	then	then	ADV
ejpam-3985	402	2	w	w	PROPN
ejpam-3985	402	3	=	=	PUNCT
ejpam-3985	402	4	⋃	⋃	PROPN
ejpam-3985	402	5	x∈s	x∈s	NOUN
ejpam-3985	402	6	[	[	PUNCT
ejpam-3985	402	7	{	{	PUNCT
ejpam-3985	402	8	x}×tx	x}×tx	X
ejpam-3985	402	9	]	]	PUNCT
ejpam-3985	402	10	,	,	PUNCT
ejpam-3985	402	11	where	where	SCONJ
ejpam-3985	402	12	s	s	VERB
ejpam-3985	402	13	⊆	⊆	NUM
ejpam-3985	402	14	v	v	NOUN
ejpam-3985	402	15	(	(	PUNCT
ejpam-3985	402	16	g	g	NOUN
ejpam-3985	402	17	)	)	PUNCT
ejpam-3985	402	18	and	and	CCONJ
ejpam-3985	402	19	tx	tx	VERB
ejpam-3985	402	20	⊆	⊆	NUM
ejpam-3985	402	21	v	v	NOUN
ejpam-3985	402	22	(	(	PUNCT
ejpam-3985	402	23	h	h	NOUN
ejpam-3985	402	24	)	)	PUNCT
ejpam-3985	402	25	for	for	ADP
ejpam-3985	402	26	each	each	DET
ejpam-3985	402	27	x	x	SYM
ejpam-3985	402	28	∈	∈	PROPN
ejpam-3985	402	29	s	s	NOUN
ejpam-3985	402	30	,	,	PUNCT
ejpam-3985	402	31	is	be	AUX
ejpam-3985	402	32	a	a	DET
ejpam-3985	402	33	resolving	resolve	VERB
ejpam-3985	402	34	restrained	restrained	ADJ
ejpam-3985	402	35	dominating	dominating	NOUN
ejpam-3985	402	36	set	set	NOUN
ejpam-3985	402	37	of	of	ADP
ejpam-3985	402	38	g[h	g[h	PROPN
ejpam-3985	402	39	]	]	PUNCT
ejpam-3985	402	40	if	if	SCONJ
ejpam-3985	403	1	and	and	CCONJ
ejpam-3985	403	2	only	only	ADV
ejpam-3985	403	3	if	if	SCONJ
ejpam-3985	403	4	it	it	PRON
ejpam-3985	403	5	is	be	AUX
ejpam-3985	403	6	a	a	DET
ejpam-3985	403	7	resolving	resolve	VERB
ejpam-3985	403	8	dominating	dominating	NOUN
ejpam-3985	403	9	set	set	NOUN
ejpam-3985	403	10	.	.	PUNCT
ejpam-3985	404	1	references	reference	NOUN
ejpam-3985	404	2	840	840	NUM
ejpam-3985	404	3	proof	proof	NOUN
ejpam-3985	404	4	:	:	PUNCT
ejpam-3985	404	5	let	let	VERB
ejpam-3985	404	6	w	w	NOUN
ejpam-3985	404	7	=	=	PUNCT
ejpam-3985	404	8	⋃	⋃	PROPN
ejpam-3985	404	9	x∈s	x∈s	NOUN
ejpam-3985	404	10	[	[	PUNCT
ejpam-3985	404	11	{	{	PUNCT
ejpam-3985	404	12	x	x	NOUN
ejpam-3985	404	13	}	}	PUNCT
ejpam-3985	404	14	×	×	NOUN
ejpam-3985	404	15	tx	tx	NOUN
ejpam-3985	404	16	]	]	PUNCT
ejpam-3985	404	17	where	where	SCONJ
ejpam-3985	404	18	s	s	VERB
ejpam-3985	404	19	⊆	⊆	NUM
ejpam-3985	404	20	v	v	NOUN
ejpam-3985	404	21	(	(	PUNCT
ejpam-3985	404	22	g	g	NOUN
ejpam-3985	404	23	)	)	PUNCT
ejpam-3985	404	24	and	and	CCONJ
ejpam-3985	404	25	tx	tx	VERB
ejpam-3985	404	26	⊆	⊆	NUM
ejpam-3985	404	27	v	v	NOUN
ejpam-3985	404	28	(	(	PUNCT
ejpam-3985	404	29	h	h	NOUN
ejpam-3985	404	30	)	)	PUNCT
ejpam-3985	404	31	for	for	ADP
ejpam-3985	404	32	each	each	DET
ejpam-3985	404	33	x	x	SYM
ejpam-3985	404	34	∈	∈	PROPN
ejpam-3985	404	35	s	s	AUX
ejpam-3985	404	36	be	be	AUX
ejpam-3985	404	37	a	a	DET
ejpam-3985	404	38	resolving	resolve	VERB
ejpam-3985	404	39	restrained	restrained	ADJ
ejpam-3985	404	40	dominating	dominating	NOUN
ejpam-3985	404	41	set	set	NOUN
ejpam-3985	404	42	of	of	ADP
ejpam-3985	404	43	g[h	g[h	PROPN
ejpam-3985	404	44	]	]	PUNCT
ejpam-3985	404	45	.	.	PUNCT
ejpam-3985	405	1	then	then	ADV
ejpam-3985	405	2	by	by	ADP
ejpam-3985	405	3	theorem	theorem	NOUN
ejpam-3985	405	4	22	22	NUM
ejpam-3985	405	5	,	,	PUNCT
ejpam-3985	405	6	(	(	PUNCT
ejpam-3985	405	7	i	i	NOUN
ejpam-3985	405	8	)	)	PUNCT
ejpam-3985	405	9	,	,	PUNCT
ejpam-3985	405	10	(	(	PUNCT
ejpam-3985	405	11	iii	iii	NOUN
ejpam-3985	405	12	)	)	PUNCT
ejpam-3985	405	13	and	and	CCONJ
ejpam-3985	405	14	(	(	PUNCT
ejpam-3985	405	15	iv	iv	X
ejpam-3985	405	16	)	)	PUNCT
ejpam-3985	405	17	hold	hold	NOUN
ejpam-3985	405	18	and	and	CCONJ
ejpam-3985	405	19	tx	tx	PROPN
ejpam-3985	405	20	is	be	AUX
ejpam-3985	405	21	a	a	DET
ejpam-3985	405	22	locating	locating	NOUN
ejpam-3985	405	23	set	set	NOUN
ejpam-3985	405	24	of	of	ADP
ejpam-3985	405	25	h	h	NOUN
ejpam-3985	405	26	for	for	ADP
ejpam-3985	405	27	every	every	DET
ejpam-3985	405	28	x	x	SYM
ejpam-3985	405	29	∈	∈	PROPN
ejpam-3985	405	30	v	v	NOUN
ejpam-3985	405	31	(	(	PUNCT
ejpam-3985	405	32	g	g	NOUN
ejpam-3985	405	33	)	)	PUNCT
ejpam-3985	405	34	.	.	PUNCT
ejpam-3985	406	1	now	now	ADV
ejpam-3985	406	2	,	,	PUNCT
ejpam-3985	406	3	let	let	VERB
ejpam-3985	406	4	s′	s′	ADJ
ejpam-3985	406	5	=	=	PUNCT
ejpam-3985	406	6	{	{	PUNCT
ejpam-3985	406	7	y	y	PROPN
ejpam-3985	406	8	∈	∈	PROPN
ejpam-3985	406	9	v	v	NOUN
ejpam-3985	406	10	(	(	PUNCT
ejpam-3985	406	11	g	g	NOUN
ejpam-3985	406	12	)	)	PUNCT
ejpam-3985	406	13	:	:	PUNCT
ejpam-3985	407	1	ty	ty	INTJ
ejpam-3985	407	2	6=	6=	NUM
ejpam-3985	407	3	v	v	ADP
ejpam-3985	407	4	(	(	PUNCT
ejpam-3985	407	5	h	h	NOUN
ejpam-3985	407	6	)	)	PUNCT
ejpam-3985	407	7	}	}	PUNCT
ejpam-3985	407	8	and	and	CCONJ
ejpam-3985	407	9	let	let	VERB
ejpam-3985	407	10	x	x	X
ejpam-3985	407	11	∈	∈	PROPN
ejpam-3985	407	12	s′\ng(s′	s′\ng(s′	PROPN
ejpam-3985	407	13	)	)	PUNCT
ejpam-3985	407	14	.	.	PUNCT
ejpam-3985	408	1	suppose	suppose	VERB
ejpam-3985	408	2	that	that	SCONJ
ejpam-3985	408	3	tx	tx	PROPN
ejpam-3985	408	4	is	be	AUX
ejpam-3985	408	5	not	not	PART
ejpam-3985	408	6	a	a	DET
ejpam-3985	408	7	restrained	restrained	ADJ
ejpam-3985	408	8	locating	locating	NOUN
ejpam-3985	408	9	set	set	NOUN
ejpam-3985	408	10	.	.	PUNCT
ejpam-3985	409	1	then	then	ADV
ejpam-3985	409	2	〈	〈	PROPN
ejpam-3985	409	3	v	v	PROPN
ejpam-3985	409	4	(	(	PUNCT
ejpam-3985	409	5	h	h	NOUN
ejpam-3985	409	6	)	)	PUNCT
ejpam-3985	409	7	\	\	PUNCT
ejpam-3985	410	1	tx	tx	AUX
ejpam-3985	410	2	〉	〉	PROPN
ejpam-3985	410	3	has	have	VERB
ejpam-3985	410	4	an	an	DET
ejpam-3985	410	5	isolated	isolated	ADJ
ejpam-3985	410	6	vertex	vertex	NOUN
ejpam-3985	410	7	,	,	PUNCT
ejpam-3985	410	8	say	say	VERB
ejpam-3985	410	9	u.	u.	NOUN
ejpam-3985	410	10	then	then	ADV
ejpam-3985	410	11	(	(	PUNCT
ejpam-3985	410	12	x	x	X
ejpam-3985	410	13	,	,	PUNCT
ejpam-3985	410	14	u	u	NOUN
ejpam-3985	410	15	)	)	PUNCT
ejpam-3985	410	16	is	be	AUX
ejpam-3985	410	17	an	an	DET
ejpam-3985	410	18	isolated	isolated	ADJ
ejpam-3985	410	19	vertex	vertex	NOUN
ejpam-3985	410	20	in	in	ADP
ejpam-3985	410	21	v	v	NOUN
ejpam-3985	410	22	(	(	PUNCT
ejpam-3985	410	23	g[h	g[h	PROPN
ejpam-3985	410	24	]	]	PUNCT
ejpam-3985	410	25	)	)	PUNCT
ejpam-3985	410	26	\w	\w	ADJ
ejpam-3985	410	27	,	,	PUNCT
ejpam-3985	410	28	contrary	contrary	ADV
ejpam-3985	410	29	to	to	ADP
ejpam-3985	410	30	the	the	DET
ejpam-3985	410	31	assumption	assumption	NOUN
ejpam-3985	410	32	that	that	SCONJ
ejpam-3985	410	33	w	w	NOUN
ejpam-3985	410	34	is	be	AUX
ejpam-3985	410	35	a	a	DET
ejpam-3985	410	36	resolving	resolve	VERB
ejpam-3985	410	37	restrained	restrained	ADJ
ejpam-3985	410	38	dominating	dominating	NOUN
ejpam-3985	410	39	set	set	NOUN
ejpam-3985	410	40	of	of	ADP
ejpam-3985	410	41	g[h	g[h	NOUN
ejpam-3985	410	42	]	]	PUNCT
ejpam-3985	410	43	.	.	PUNCT
ejpam-3985	411	1	hence	hence	ADV
ejpam-3985	411	2	,	,	PUNCT
ejpam-3985	411	3	tx	tx	PROPN
ejpam-3985	411	4	is	be	AUX
ejpam-3985	411	5	a	a	DET
ejpam-3985	411	6	restrained	restrained	ADJ
ejpam-3985	411	7	locating	locating	NOUN
ejpam-3985	411	8	set	set	NOUN
ejpam-3985	411	9	of	of	ADP
ejpam-3985	411	10	h	h	NOUN
ejpam-3985	411	11	for	for	ADP
ejpam-3985	411	12	all	all	DET
ejpam-3985	411	13	x	x	PROPN
ejpam-3985	411	14	∈	∈	PROPN
ejpam-3985	411	15	s′\ng(s′	s′\ng(s′	NOUN
ejpam-3985	411	16	)	)	PUNCT
ejpam-3985	411	17	.	.	PUNCT
ejpam-3985	412	1	therefore	therefore	ADV
ejpam-3985	412	2	,	,	PUNCT
ejpam-3985	412	3	w	w	PROPN
ejpam-3985	412	4	is	be	AUX
ejpam-3985	412	5	a	a	DET
ejpam-3985	412	6	resolving	resolve	VERB
ejpam-3985	412	7	dominating	dominating	NOUN
ejpam-3985	412	8	set	set	NOUN
ejpam-3985	412	9	of	of	ADP
ejpam-3985	412	10	g[h	g[h	NOUN
ejpam-3985	412	11	]	]	PUNCT
ejpam-3985	412	12	.	.	PUNCT
ejpam-3985	413	1	for	for	ADP
ejpam-3985	413	2	the	the	DET
ejpam-3985	413	3	converse	converse	NOUN
ejpam-3985	413	4	,	,	PUNCT
ejpam-3985	413	5	suppose	suppose	VERB
ejpam-3985	413	6	that	that	SCONJ
ejpam-3985	413	7	w	w	PROPN
ejpam-3985	413	8	=	=	PUNCT
ejpam-3985	413	9	⋃	⋃	PROPN
ejpam-3985	413	10	x∈s	x∈s	NOUN
ejpam-3985	413	11	[	[	PUNCT
ejpam-3985	413	12	{	{	PUNCT
ejpam-3985	413	13	x	x	NOUN
ejpam-3985	413	14	}	}	PUNCT
ejpam-3985	413	15	×	×	NOUN
ejpam-3985	413	16	tx	tx	PROPN
ejpam-3985	413	17	]	]	PUNCT
ejpam-3985	413	18	is	be	AUX
ejpam-3985	413	19	a	a	DET
ejpam-3985	413	20	resolving	resolve	VERB
ejpam-3985	413	21	dominating	dominating	NOUN
ejpam-3985	413	22	set	set	NOUN
ejpam-3985	413	23	of	of	ADP
ejpam-3985	413	24	g[h	g[h	PROPN
ejpam-3985	413	25	]	]	PUNCT
ejpam-3985	413	26	.	.	PUNCT
ejpam-3985	413	27	suppose	suppose	VERB
ejpam-3985	413	28	that	that	SCONJ
ejpam-3985	413	29	v	v	X
ejpam-3985	413	30	(	(	PUNCT
ejpam-3985	413	31	g[h	g[h	PROPN
ejpam-3985	413	32	]	]	PUNCT
ejpam-3985	413	33	)	)	PUNCT
ejpam-3985	414	1	=	=	PUNCT
ejpam-3985	414	2	w	w	X
ejpam-3985	414	3	.	.	PUNCT
ejpam-3985	415	1	then	then	ADV
ejpam-3985	415	2	w	w	PROPN
ejpam-3985	415	3	is	be	AUX
ejpam-3985	415	4	a	a	DET
ejpam-3985	415	5	resolving	resolve	VERB
ejpam-3985	415	6	restrained	restrained	ADJ
ejpam-3985	415	7	dominating	dominating	NOUN
ejpam-3985	415	8	set	set	NOUN
ejpam-3985	415	9	of	of	ADP
ejpam-3985	415	10	g[h	g[h	PROPN
ejpam-3985	415	11	]	]	PUNCT
ejpam-3985	415	12	.	.	PUNCT
ejpam-3985	416	1	suppose	suppose	VERB
ejpam-3985	416	2	that	that	SCONJ
ejpam-3985	416	3	v	v	X
ejpam-3985	416	4	(	(	PUNCT
ejpam-3985	416	5	g[h	g[h	PROPN
ejpam-3985	416	6	]	]	PUNCT
ejpam-3985	416	7	)	)	PUNCT
ejpam-3985	417	1	6=	6=	X
ejpam-3985	418	1	w	w	X
ejpam-3985	418	2	.	.	PUNCT
ejpam-3985	419	1	let	let	VERB
ejpam-3985	419	2	(	(	PUNCT
ejpam-3985	419	3	y	y	NOUN
ejpam-3985	419	4	,	,	PUNCT
ejpam-3985	419	5	u	u	NOUN
ejpam-3985	419	6	)	)	PUNCT
ejpam-3985	419	7	∈	∈	NOUN
ejpam-3985	419	8	v	v	NOUN
ejpam-3985	419	9	(	(	PUNCT
ejpam-3985	419	10	g[h	g[h	PROPN
ejpam-3985	419	11	]	]	PUNCT
ejpam-3985	419	12	)	)	PUNCT
ejpam-3985	419	13	\w	\w	ADJ
ejpam-3985	419	14	.	.	PUNCT
ejpam-3985	420	1	then	then	ADV
ejpam-3985	420	2	u	u	X
ejpam-3985	420	3	/∈	/∈	PROPN
ejpam-3985	421	1	ty	ty	INTJ
ejpam-3985	421	2	.	.	PUNCT
ejpam-3985	422	1	hence	hence	ADV
ejpam-3985	422	2	,	,	PUNCT
ejpam-3985	422	3	y	y	PROPN
ejpam-3985	422	4	∈	∈	PROPN
ejpam-3985	422	5	s′.	s′.	PROPN
ejpam-3985	423	1	if	if	SCONJ
ejpam-3985	423	2	y	y	PROPN
ejpam-3985	423	3	∈	∈	PROPN
ejpam-3985	423	4	ng(s′	ng(s′	PROPN
ejpam-3985	423	5	)	)	PUNCT
ejpam-3985	423	6	,	,	PUNCT
ejpam-3985	423	7	then	then	ADV
ejpam-3985	423	8	there	there	PRON
ejpam-3985	423	9	exists	exist	VERB
ejpam-3985	423	10	z	z	PROPN
ejpam-3985	423	11	∈	∈	PROPN
ejpam-3985	423	12	s′	s′	VERB
ejpam-3985	424	1	∩ng(y	∩ng(y	PROPN
ejpam-3985	424	2	)	)	PUNCT
ejpam-3985	424	3	.	.	PUNCT
ejpam-3985	425	1	pick	pick	VERB
ejpam-3985	425	2	any	any	DET
ejpam-3985	425	3	v	v	NOUN
ejpam-3985	425	4	∈	∈	PROPN
ejpam-3985	425	5	v	v	NOUN
ejpam-3985	425	6	(	(	PUNCT
ejpam-3985	425	7	h	h	NOUN
ejpam-3985	425	8	)	)	PUNCT
ejpam-3985	425	9	\	\	PROPN
ejpam-3985	425	10	tz	tz	PROPN
ejpam-3985	425	11	.	.	PUNCT
ejpam-3985	426	1	then	then	ADV
ejpam-3985	426	2	(	(	PUNCT
ejpam-3985	426	3	y	y	NOUN
ejpam-3985	426	4	,	,	PUNCT
ejpam-3985	426	5	u)(z	u)(z	NOUN
ejpam-3985	426	6	,	,	PUNCT
ejpam-3985	426	7	v	v	NOUN
ejpam-3985	426	8	)	)	PUNCT
ejpam-3985	426	9	∈	∈	PROPN
ejpam-3985	426	10	e	e	X
ejpam-3985	426	11	(	(	PUNCT
ejpam-3985	426	12	g[h	g[h	PROPN
ejpam-3985	426	13	]	]	PUNCT
ejpam-3985	426	14	)	)	PUNCT
ejpam-3985	426	15	.	.	PUNCT
ejpam-3985	427	1	if	if	SCONJ
ejpam-3985	427	2	y	y	PROPN
ejpam-3985	427	3	/∈	/∈	PUNCT
ejpam-3985	427	4	ng(s′	ng(s′	PROPN
ejpam-3985	427	5	)	)	PUNCT
ejpam-3985	427	6	,	,	PUNCT
ejpam-3985	427	7	then	then	ADV
ejpam-3985	427	8	by	by	ADP
ejpam-3985	427	9	(	(	PUNCT
ejpam-3985	427	10	ii	ii	NOUN
ejpam-3985	427	11	)	)	PUNCT
ejpam-3985	427	12	,	,	PUNCT
ejpam-3985	427	13	there	there	PRON
ejpam-3985	427	14	exists	exist	VERB
ejpam-3985	427	15	p	p	PROPN
ejpam-3985	427	16	∈	∈	PROPN
ejpam-3985	427	17	(	(	PUNCT
ejpam-3985	427	18	v	v	NOUN
ejpam-3985	427	19	(	(	PUNCT
ejpam-3985	427	20	h	h	NOUN
ejpam-3985	427	21	)	)	PUNCT
ejpam-3985	427	22	\ty	\ty	PROPN
ejpam-3985	427	23	)	)	PUNCT
ejpam-3985	427	24	∩ng(u	∩ng(u	PROPN
ejpam-3985	427	25	)	)	PUNCT
ejpam-3985	427	26	.	.	PUNCT
ejpam-3985	428	1	thus	thus	ADV
ejpam-3985	428	2	,	,	PUNCT
ejpam-3985	428	3	(	(	PUNCT
ejpam-3985	428	4	y	y	PROPN
ejpam-3985	428	5	,	,	PUNCT
ejpam-3985	428	6	u)(y	u)(y	PROPN
ejpam-3985	428	7	,	,	PUNCT
ejpam-3985	428	8	p	p	NOUN
ejpam-3985	428	9	)	)	PUNCT
ejpam-3985	428	10	∈	∈	PROPN
ejpam-3985	428	11	e	e	X
ejpam-3985	428	12	(	(	PUNCT
ejpam-3985	428	13	g[h	g[h	PROPN
ejpam-3985	428	14	]	]	PUNCT
ejpam-3985	428	15	)	)	PUNCT
ejpam-3985	428	16	.	.	PUNCT
ejpam-3985	429	1	hence	hence	ADV
ejpam-3985	429	2	〈	〈	PROPN
ejpam-3985	429	3	v	v	NOUN
ejpam-3985	429	4	(	(	PUNCT
ejpam-3985	429	5	g[h	g[h	PROPN
ejpam-3985	429	6	]	]	PUNCT
ejpam-3985	429	7	)	)	PUNCT
ejpam-3985	429	8	\w	\w	ADJ
ejpam-3985	429	9	〉	〉	NOUN
ejpam-3985	429	10	has	have	VERB
ejpam-3985	429	11	no	no	DET
ejpam-3985	429	12	isolated	isolated	ADJ
ejpam-3985	429	13	vertex	vertex	NOUN
ejpam-3985	429	14	.	.	PUNCT
ejpam-3985	430	1	therefore	therefore	ADV
ejpam-3985	430	2	,	,	PUNCT
ejpam-3985	430	3	w	w	PROPN
ejpam-3985	430	4	is	be	AUX
ejpam-3985	430	5	a	a	DET
ejpam-3985	430	6	resolving	resolve	VERB
ejpam-3985	430	7	restrained	restrained	ADJ
ejpam-3985	430	8	dominating	dominating	NOUN
ejpam-3985	430	9	set	set	NOUN
ejpam-3985	430	10	of	of	ADP
ejpam-3985	430	11	g[h	g[h	PROPN
ejpam-3985	430	12	]	]	PUNCT
ejpam-3985	430	13	.	.	PUNCT
ejpam-3985	431	1	corollary	corollary	ADJ
ejpam-3985	431	2	5	5	NUM
ejpam-3985	431	3	.	.	PUNCT
ejpam-3985	432	1	let	let	VERB
ejpam-3985	432	2	g	g	PRON
ejpam-3985	432	3	be	be	AUX
ejpam-3985	432	4	a	a	DET
ejpam-3985	432	5	connected	connected	ADJ
ejpam-3985	432	6	totally	totally	ADV
ejpam-3985	432	7	point	point	NOUN
ejpam-3985	432	8	determining	determine	VERB
ejpam-3985	432	9	graph	graph	NOUN
ejpam-3985	432	10	of	of	ADP
ejpam-3985	432	11	order	order	NOUN
ejpam-3985	432	12	n	n	PRON
ejpam-3985	432	13	≥	≥	NOUN
ejpam-3985	432	14	3	3	NUM
ejpam-3985	432	15	and	and	CCONJ
ejpam-3985	432	16	let	let	VERB
ejpam-3985	432	17	h	h	NOUN
ejpam-3985	432	18	be	be	AUX
ejpam-3985	432	19	any	any	DET
ejpam-3985	432	20	non	non	ADJ
ejpam-3985	432	21	-	-	ADJ
ejpam-3985	432	22	trivial	trivial	ADJ
ejpam-3985	432	23	connected	connected	ADJ
ejpam-3985	432	24	graph	graph	NOUN
ejpam-3985	432	25	.	.	PUNCT
ejpam-3985	433	1	then	then	ADV
ejpam-3985	433	2	γrr	γrr	NOUN
ejpam-3985	433	3	(	(	PUNCT
ejpam-3985	433	4	g[h	g[h	PROPN
ejpam-3985	433	5	]	]	PUNCT
ejpam-3985	433	6	)	)	PUNCT
ejpam-3985	433	7	≤	≤	NUM
ejpam-3985	433	8	|v	|v	X
ejpam-3985	433	9	(	(	PUNCT
ejpam-3985	433	10	g)|	g)|	NOUN
ejpam-3985	433	11	·	·	PUNCT
ejpam-3985	433	12	ln(h	ln(h	NUM
ejpam-3985	433	13	)	)	PUNCT
ejpam-3985	433	14	.	.	PUNCT
ejpam-3985	434	1	proof	proof	NOUN
ejpam-3985	434	2	:	:	PUNCT
ejpam-3985	434	3	let	let	VERB
ejpam-3985	434	4	d	d	PRON
ejpam-3985	434	5	be	be	AUX
ejpam-3985	434	6	a	a	DET
ejpam-3985	434	7	minimum	minimum	ADJ
ejpam-3985	434	8	locating	locating	NOUN
ejpam-3985	434	9	set	set	NOUN
ejpam-3985	434	10	of	of	ADP
ejpam-3985	434	11	h	h	NOUN
ejpam-3985	434	12	and	and	CCONJ
ejpam-3985	434	13	let	let	VERB
ejpam-3985	434	14	tx	tx	VERB
ejpam-3985	434	15	=	=	PUNCT
ejpam-3985	435	1	d	d	PROPN
ejpam-3985	435	2	for	for	ADP
ejpam-3985	435	3	each	each	DET
ejpam-3985	435	4	x	x	SYM
ejpam-3985	435	5	∈	∈	PROPN
ejpam-3985	435	6	v	v	NOUN
ejpam-3985	435	7	(	(	PUNCT
ejpam-3985	435	8	g	g	NOUN
ejpam-3985	435	9	)	)	PUNCT
ejpam-3985	435	10	.	.	PUNCT
ejpam-3985	436	1	then	then	ADV
ejpam-3985	436	2	tx	tx	VERB
ejpam-3985	436	3	6=	6=	PROPN
ejpam-3985	436	4	v	v	ADP
ejpam-3985	436	5	(	(	PUNCT
ejpam-3985	436	6	h	h	NOUN
ejpam-3985	436	7	)	)	PUNCT
ejpam-3985	436	8	for	for	ADP
ejpam-3985	436	9	all	all	PRON
ejpam-3985	436	10	x	x	SYM
ejpam-3985	436	11	∈	∈	PROPN
ejpam-3985	436	12	v	v	NOUN
ejpam-3985	436	13	(	(	PUNCT
ejpam-3985	436	14	g	g	NOUN
ejpam-3985	436	15	)	)	PUNCT
ejpam-3985	436	16	,	,	PUNCT
ejpam-3985	436	17	that	that	ADV
ejpam-3985	436	18	is	is	ADV
ejpam-3985	436	19	,	,	PUNCT
ejpam-3985	436	20	s′	s′	ADJ
ejpam-3985	436	21	=	=	SYM
ejpam-3985	436	22	v	v	NOUN
ejpam-3985	436	23	(	(	PUNCT
ejpam-3985	436	24	g	g	NOUN
ejpam-3985	436	25	)	)	PUNCT
ejpam-3985	436	26	.	.	PUNCT
ejpam-3985	437	1	by	by	ADP
ejpam-3985	437	2	theorem	theorem	ADJ
ejpam-3985	437	3	23	23	NUM
ejpam-3985	437	4	and	and	CCONJ
ejpam-3985	437	5	hypothesis	hypothesis	NOUN
ejpam-3985	437	6	,	,	PUNCT
ejpam-3985	437	7	w	w	PROPN
ejpam-3985	437	8	=	=	NOUN
ejpam-3985	437	9	⋃	⋃	PROPN
ejpam-3985	437	10	x∈v	x∈v	PROPN
ejpam-3985	437	11	(	(	PUNCT
ejpam-3985	437	12	g	g	NOUN
ejpam-3985	437	13	)	)	PUNCT
ejpam-3985	437	14	[	[	PUNCT
ejpam-3985	437	15	{	{	PUNCT
ejpam-3985	437	16	x	x	NOUN
ejpam-3985	437	17	}	}	PUNCT
ejpam-3985	437	18	×	×	NOUN
ejpam-3985	437	19	tx	tx	PROPN
ejpam-3985	437	20	]	]	PUNCT
ejpam-3985	437	21	is	be	AUX
ejpam-3985	437	22	a	a	DET
ejpam-3985	437	23	resolving	resolve	VERB
ejpam-3985	437	24	restrained	restrained	ADJ
ejpam-3985	437	25	dominating	dominating	NOUN
ejpam-3985	437	26	set	set	NOUN
ejpam-3985	437	27	of	of	ADP
ejpam-3985	437	28	g[h	g[h	PROPN
ejpam-3985	437	29	]	]	PUNCT
ejpam-3985	437	30	.	.	PUNCT
ejpam-3985	438	1	thus	thus	ADV
ejpam-3985	438	2	,	,	PUNCT
ejpam-3985	438	3	γrr	γrr	NOUN
ejpam-3985	438	4	(	(	PUNCT
ejpam-3985	438	5	g[h	g[h	NOUN
ejpam-3985	438	6	]	]	PUNCT
ejpam-3985	438	7	)	)	PUNCT
ejpam-3985	438	8	≤	≤	NUM
ejpam-3985	438	9	|w	|w	NOUN
ejpam-3985	438	10	|	|	NOUN
ejpam-3985	438	11	=	=	SYM
ejpam-3985	438	12	|v	|v	PROPN
ejpam-3985	438	13	(	(	PUNCT
ejpam-3985	438	14	g)|	g)|	NOUN
ejpam-3985	438	15	·	·	PUNCT
ejpam-3985	438	16	ln(h	ln(h	NUM
ejpam-3985	438	17	)	)	PUNCT
ejpam-3985	438	18	.	.	PUNCT
ejpam-3985	439	1	acknowledgements	acknowledgement	NOUN
ejpam-3985	439	2	this	this	DET
ejpam-3985	439	3	research	research	NOUN
ejpam-3985	439	4	is	be	AUX
ejpam-3985	439	5	funded	fund	VERB
ejpam-3985	439	6	by	by	ADP
ejpam-3985	439	7	the	the	DET
ejpam-3985	439	8	commission	commission	NOUN
ejpam-3985	439	9	on	on	ADP
ejpam-3985	439	10	higher	high	ADJ
ejpam-3985	439	11	education	education	NOUN
ejpam-3985	439	12	(	(	PUNCT
ejpam-3985	439	13	ched	che	VERB
ejpam-3985	439	14	)	)	PUNCT
ejpam-3985	439	15	and	and	CCONJ
ejpam-3985	439	16	mindanao	mindanao	PROPN
ejpam-3985	439	17	state	state	PROPN
ejpam-3985	439	18	university	university	PROPN
ejpam-3985	439	19	-	-	PUNCT
ejpam-3985	439	20	iligan	iligan	PROPN
ejpam-3985	439	21	institute	institute	PROPN
ejpam-3985	439	22	of	of	ADP
ejpam-3985	439	23	technology	technology	PROPN
ejpam-3985	439	24	,	,	PUNCT
ejpam-3985	439	25	philippines	philippine	NOUN
ejpam-3985	439	26	.	.	PUNCT
ejpam-3985	440	1	references	reference	NOUN
ejpam-3985	440	2	[	[	X
ejpam-3985	440	3	1	1	NUM
ejpam-3985	440	4	]	]	X
ejpam-3985	440	5	r.f	r.f	PROPN
ejpam-3985	440	6	.	.	PROPN
ejpam-3985	440	7	bailey	bailey	PROPN
ejpam-3985	440	8	,	,	PUNCT
ejpam-3985	440	9	j.cáceres	j.cáceres	PROPN
ejpam-3985	440	10	,	,	PUNCT
ejpam-3985	440	11	a.	a.	PROPN
ejpam-3985	440	12	gonzález	gonzález	PROPN
ejpam-3985	440	13	d.	d.	PROPN
ejpam-3985	440	14	garijo	garijo	PROPN
ejpam-3985	440	15	,	,	PUNCT
ejpam-3985	440	16	a.	a.	NOUN
ejpam-3985	440	17	márquez	márquez	PROPN
ejpam-3985	440	18	.	.	PROPN
ejpam-3985	440	19	k.	k.	PROPN
ejpam-3985	440	20	meagher	meagher	PROPN
ejpam-3985	440	21	,	,	PUNCT
ejpam-3985	440	22	and	and	CCONJ
ejpam-3985	440	23	m.l	m.l	PROPN
ejpam-3985	440	24	.	.	PROPN
ejpam-3985	440	25	puertas	puertas	PROPN
ejpam-3985	440	26	.	.	PUNCT
ejpam-3985	441	1	resolving	resolve	VERB
ejpam-3985	441	2	sets	set	NOUN
ejpam-3985	441	3	for	for	ADP
ejpam-3985	441	4	johnson	johnson	PROPN
ejpam-3985	441	5	and	and	CCONJ
ejpam-3985	441	6	kneser	kneser	NOUN
ejpam-3985	441	7	graphs	graph	NOUN
ejpam-3985	441	8	.	.	PUNCT
ejpam-3985	442	1	european	european	ADJ
ejpam-3985	442	2	journal	journal	PROPN
ejpam-3985	442	3	of	of	ADP
ejpam-3985	442	4	combinatorics	combinatoric	NOUN
ejpam-3985	442	5	,	,	PUNCT
ejpam-3985	442	6	34:736–751	34:736–751	NUM
ejpam-3985	442	7	,	,	PUNCT
ejpam-3985	442	8	2013	2013	NUM
ejpam-3985	442	9	.	.	PUNCT
ejpam-3985	443	1	[	[	X
ejpam-3985	443	2	2	2	NUM
ejpam-3985	443	3	]	]	PUNCT
ejpam-3985	443	4	c.	c.	PROPN
ejpam-3985	443	5	berge	berge	PROPN
ejpam-3985	443	6	.	.	PUNCT
ejpam-3985	444	1	theorie	theorie	PROPN
ejpam-3985	444	2	des	des	PROPN
ejpam-3985	444	3	graphes	graphes	PROPN
ejpam-3985	444	4	et	et	PROPN
ejpam-3985	444	5	ses	ses	PROPN
ejpam-3985	444	6	applications	application	NOUN
ejpam-3985	444	7	.	.	PUNCT
ejpam-3985	445	1	dunod	dunod	PROPN
ejpam-3985	445	2	,	,	PUNCT
ejpam-3985	445	3	paris	paris	PROPN
ejpam-3985	445	4	,	,	PUNCT
ejpam-3985	445	5	1958	1958	NUM
ejpam-3985	445	6	.	.	PUNCT
ejpam-3985	446	1	[	[	X
ejpam-3985	446	2	3	3	NUM
ejpam-3985	446	3	]	]	X
ejpam-3985	446	4	r.c	r.c	PROPN
ejpam-3985	446	5	.	.	PROPN
ejpam-3985	446	6	brigham	brigham	PROPN
ejpam-3985	446	7	,	,	PUNCT
ejpam-3985	446	8	g.	g.	PROPN
ejpam-3985	446	9	chartrand	chartrand	PROPN
ejpam-3985	446	10	,	,	PUNCT
ejpam-3985	446	11	r.d	r.d	PROPN
ejpam-3985	446	12	.	.	PROPN
ejpam-3985	446	13	dutton	dutton	PROPN
ejpam-3985	446	14	,	,	PUNCT
ejpam-3985	446	15	and	and	CCONJ
ejpam-3985	446	16	p.	p.	PROPN
ejpam-3985	446	17	zhang	zhang	PROPN
ejpam-3985	446	18	.	.	PUNCT
ejpam-3985	447	1	resolving	resolve	VERB
ejpam-3985	447	2	domination	domination	NOUN
ejpam-3985	447	3	in	in	ADP
ejpam-3985	447	4	graphs	graph	NOUN
ejpam-3985	447	5	.	.	PUNCT
ejpam-3985	448	1	mathematica	mathematica	PROPN
ejpam-3985	448	2	bohemica	bohemica	PROPN
ejpam-3985	448	3	,	,	PUNCT
ejpam-3985	448	4	1:25–36	1:25–36	NUM
ejpam-3985	448	5	,	,	PUNCT
ejpam-3985	448	6	2003	2003	NUM
ejpam-3985	448	7	.	.	PUNCT
ejpam-3985	449	1	[	[	X
ejpam-3985	449	2	4	4	X
ejpam-3985	449	3	]	]	X
ejpam-3985	449	4	e.	e.	PROPN
ejpam-3985	449	5	cockayne	cockayne	PROPN
ejpam-3985	449	6	and	and	CCONJ
ejpam-3985	449	7	s.	s.	PROPN
ejpam-3985	449	8	hedetniemi	hedetniemi	PROPN
ejpam-3985	449	9	.	.	PUNCT
ejpam-3985	450	1	towards	towards	ADP
ejpam-3985	450	2	a	a	DET
ejpam-3985	450	3	theory	theory	NOUN
ejpam-3985	450	4	of	of	ADP
ejpam-3985	450	5	domination	domination	NOUN
ejpam-3985	450	6	in	in	ADP
ejpam-3985	450	7	graphs	graph	NOUN
ejpam-3985	450	8	.	.	PUNCT
ejpam-3985	451	1	networks	network	NOUN
ejpam-3985	451	2	,	,	PUNCT
ejpam-3985	451	3	7(3):247–261	7(3):247–261	NUM
ejpam-3985	451	4	,	,	PUNCT
ejpam-3985	451	5	1977	1977	NUM
ejpam-3985	451	6	.	.	PUNCT
ejpam-3985	452	1	references	reference	NOUN
ejpam-3985	452	2	841	841	NUM
ejpam-3985	452	3	[	[	SYM
ejpam-3985	452	4	5	5	NUM
ejpam-3985	452	5	]	]	X
ejpam-3985	452	6	g.s	g.s	PROPN
ejpam-3985	452	7	.	.	PROPN
ejpam-3985	452	8	domke	domke	PROPN
ejpam-3985	452	9	,	,	PUNCT
ejpam-3985	452	10	j.s	j.s	PROPN
ejpam-3985	452	11	.	.	PROPN
ejpam-3985	452	12	hattingh	hattingh	PROPN
ejpam-3985	452	13	,	,	PUNCT
ejpam-3985	452	14	s.t	s.t	PROPN
ejpam-3985	452	15	.	.	PROPN
ejpam-3985	452	16	hedetniemi	hedetniemi	PROPN
ejpam-3985	452	17	,	,	PUNCT
ejpam-3985	452	18	r.c	r.c	PROPN
ejpam-3985	452	19	.	.	PROPN
ejpam-3985	452	20	laskar	laskar	PROPN
ejpam-3985	452	21	,	,	PUNCT
ejpam-3985	452	22	and	and	CCONJ
ejpam-3985	452	23	l.r	l.r	PROPN
ejpam-3985	452	24	.	.	PROPN
ejpam-3985	452	25	markus	markus	PROPN
ejpam-3985	452	26	.	.	PUNCT
ejpam-3985	453	1	restrained	restrained	ADJ
ejpam-3985	453	2	domination	domination	NOUN
ejpam-3985	453	3	in	in	ADP
ejpam-3985	453	4	graphs	graph	NOUN
ejpam-3985	453	5	.	.	PUNCT
ejpam-3985	454	1	discrete	discrete	ADJ
ejpam-3985	454	2	mathematics	mathematic	NOUN
ejpam-3985	454	3	,	,	PUNCT
ejpam-3985	454	4	203:61–69	203:61–69	NUM
ejpam-3985	454	5	,	,	PUNCT
ejpam-3985	454	6	1999	1999	NUM
ejpam-3985	454	7	.	.	PUNCT
ejpam-3985	455	1	[	[	X
ejpam-3985	455	2	6	6	NUM
ejpam-3985	455	3	]	]	X
ejpam-3985	455	4	c.	c.	NOUN
ejpam-3985	455	5	go	go	VERB
ejpam-3985	455	6	and	and	CCONJ
ejpam-3985	455	7	jr	jr	PROPN
ejpam-3985	455	8	.	.	PUNCT
ejpam-3985	456	1	s.r	s.r	PROPN
ejpam-3985	456	2	.	.	PROPN
ejpam-3985	456	3	canoy	canoy	PROPN
ejpam-3985	456	4	.	.	PUNCT
ejpam-3985	457	1	some	some	DET
ejpam-3985	457	2	types	type	NOUN
ejpam-3985	457	3	of	of	ADP
ejpam-3985	457	4	dominating	dominating	NOUN
ejpam-3985	457	5	sets	set	NOUN
ejpam-3985	457	6	and	and	CCONJ
ejpam-3985	457	7	domination	domination	NOUN
ejpam-3985	457	8	numbers	number	NOUN
ejpam-3985	457	9	in	in	ADP
ejpam-3985	457	10	graphs	graph	NOUN
ejpam-3985	457	11	.	.	PUNCT
ejpam-3985	458	1	[	[	X
ejpam-3985	458	2	7	7	X
ejpam-3985	458	3	]	]	X
ejpam-3985	458	4	f.	f.	PROPN
ejpam-3985	458	5	harary	harary	PROPN
ejpam-3985	458	6	.	.	PUNCT
ejpam-3985	459	1	graph	graph	NOUN
ejpam-3985	459	2	theory	theory	NOUN
ejpam-3985	459	3	.	.	PUNCT
ejpam-3985	460	1	addison	addison	PROPN
ejpam-3985	460	2	-	-	PUNCT
ejpam-3985	460	3	wesley	wesley	PROPN
ejpam-3985	460	4	publishing	publishing	PROPN
ejpam-3985	460	5	company	company	NOUN
ejpam-3985	460	6	,	,	PUNCT
ejpam-3985	460	7	usa	usa	PROPN
ejpam-3985	460	8	,	,	PUNCT
ejpam-3985	460	9	1969	1969	NUM
ejpam-3985	460	10	.	.	PUNCT
ejpam-3985	461	1	[	[	X
ejpam-3985	461	2	8	8	NUM
ejpam-3985	461	3	]	]	X
ejpam-3985	461	4	j.h	j.h	PROPN
ejpam-3985	461	5	.	.	PROPN
ejpam-3985	461	6	hattingh	hattingh	PROPN
ejpam-3985	461	7	,	,	PUNCT
ejpam-3985	461	8	e.	e.	PROPN
ejpam-3985	461	9	jonck	jonck	PROPN
ejpam-3985	461	10	,	,	PUNCT
ejpam-3985	461	11	e.j	e.j	PROPN
ejpam-3985	461	12	.	.	PROPN
ejpam-3985	461	13	joubert	joubert	PROPN
ejpam-3985	461	14	,	,	PUNCT
ejpam-3985	461	15	and	and	CCONJ
ejpam-3985	461	16	a.r	a.r	PROPN
ejpam-3985	461	17	.	.	PROPN
ejpam-3985	461	18	plummer	plummer	PROPN
ejpam-3985	461	19	.	.	PUNCT
ejpam-3985	462	1	nordhaus	nordhaus	PROPN
ejpam-3985	462	2	-	-	PUNCT
ejpam-3985	462	3	gaddum	gaddum	PROPN
ejpam-3985	462	4	results	result	VERB
ejpam-3985	462	5	forn	forn	PROPN
ejpam-3985	462	6	restrained	restrained	ADJ
ejpam-3985	462	7	domination	domination	NOUN
ejpam-3985	462	8	and	and	CCONJ
ejpam-3985	462	9	total	total	ADJ
ejpam-3985	462	10	restrained	restrained	ADJ
ejpam-3985	462	11	domination	domination	NOUN
ejpam-3985	462	12	in	in	ADP
ejpam-3985	462	13	graphs	graph	NOUN
ejpam-3985	462	14	.	.	PUNCT
ejpam-3985	463	1	discrete	discrete	ADJ
ejpam-3985	463	2	mathematics	mathematic	NOUN
ejpam-3985	463	3	,	,	PUNCT
ejpam-3985	463	4	308:1080–1087	308:1080–1087	NUM
ejpam-3985	463	5	,	,	PUNCT
ejpam-3985	463	6	2008	2008	NUM
ejpam-3985	463	7	.	.	PUNCT
ejpam-3985	464	1	[	[	X
ejpam-3985	464	2	9	9	NUM
ejpam-3985	464	3	]	]	X
ejpam-3985	464	4	g.b	g.b	PROPN
ejpam-3985	464	5	.	.	PUNCT
ejpam-3985	464	6	monsanto	monsanto	PROPN
ejpam-3985	464	7	and	and	CCONJ
ejpam-3985	464	8	h.m	h.m	PROPN
ejpam-3985	464	9	.	.	PROPN
ejpam-3985	464	10	rara	rara	PROPN
ejpam-3985	464	11	.	.	PUNCT
ejpam-3985	465	1	resolving	resolve	VERB
ejpam-3985	465	2	sets	set	NOUN
ejpam-3985	465	3	in	in	ADP
ejpam-3985	465	4	graphs	graph	NOUN
ejpam-3985	465	5	.	.	PUNCT
ejpam-3985	466	1	italian	italian	ADJ
ejpam-3985	466	2	journal	journal	NOUN
ejpam-3985	466	3	of	of	ADP
ejpam-3985	466	4	pure	pure	ADJ
ejpam-3985	466	5	and	and	CCONJ
ejpam-3985	466	6	applied	applied	ADJ
ejpam-3985	466	7	mathematics	mathematic	NOUN
ejpam-3985	466	8	,	,	PUNCT
ejpam-3985	466	9	accepted	accept	VERB
ejpam-3985	466	10	for	for	ADP
ejpam-3985	466	11	publication	publication	NOUN
ejpam-3985	466	12	.	.	PUNCT
ejpam-3985	467	1	[	[	X
ejpam-3985	467	2	10	10	NUM
ejpam-3985	467	3	]	]	X
ejpam-3985	467	4	s.a	s.a	PROPN
ejpam-3985	467	5	.	.	PROPN
ejpam-3985	467	6	omega	omega	NOUN
ejpam-3985	467	7	and	and	CCONJ
ejpam-3985	467	8	s.r	s.r	PROPN
ejpam-3985	467	9	.	.	PROPN
ejpam-3985	467	10	canoy	canoy	PROPN
ejpam-3985	467	11	jr	jr	PROPN
ejpam-3985	467	12	.	.	PROPN
ejpam-3985	467	13	restrained	restrained	ADJ
ejpam-3985	467	14	locating	locate	VERB
ejpam-3985	467	15	-	-	PUNCT
ejpam-3985	467	16	domination	domination	NOUN
ejpam-3985	467	17	in	in	ADP
ejpam-3985	467	18	graphs	graph	NOUN
ejpam-3985	467	19	.	.	PUNCT
ejpam-3985	468	1	international	international	ADJ
ejpam-3985	468	2	journal	journal	PROPN
ejpam-3985	468	3	of	of	ADP
ejpam-3985	468	4	mathematical	mathematical	ADJ
ejpam-3985	468	5	analysis	analysis	NOUN
ejpam-3985	468	6	,	,	PUNCT
ejpam-3985	468	7	9(3):1129–1140	9(3):1129–1140	NUM
ejpam-3985	468	8	,	,	PUNCT
ejpam-3985	468	9	2015	2015	NUM
ejpam-3985	468	10	.	.	PUNCT
ejpam-3985	469	1	[	[	X
ejpam-3985	469	2	11	11	NUM
ejpam-3985	469	3	]	]	X
ejpam-3985	469	4	s.a	s.a	PROPN
ejpam-3985	469	5	.	.	PROPN
ejpam-3985	469	6	omega	omega	PROPN
ejpam-3985	469	7	and	and	CCONJ
ejpam-3985	469	8	jr	jr	PROPN
ejpam-3985	469	9	.	.	PUNCT
ejpam-3985	469	10	s.r	s.r	PROPN
ejpam-3985	469	11	.	.	PROPN
ejpam-3985	469	12	canoy	canoy	PROPN
ejpam-3985	469	13	.	.	PUNCT
ejpam-3985	470	1	locating	locate	VERB
ejpam-3985	470	2	sets	set	NOUN
ejpam-3985	470	3	in	in	ADP
ejpam-3985	470	4	a	a	DET
ejpam-3985	470	5	graph	graph	NOUN
ejpam-3985	470	6	.	.	PUNCT
ejpam-3985	471	1	applied	apply	VERB
ejpam-3985	471	2	mathematical	mathematical	ADJ
ejpam-3985	471	3	sciences	science	NOUN
ejpam-3985	471	4	,	,	PUNCT
ejpam-3985	471	5	9(60):2957–2964	9(60):2957–2964	NUM
ejpam-3985	471	6	,	,	PUNCT
ejpam-3985	471	7	2015	2015	NUM
ejpam-3985	471	8	.	.	PUNCT
ejpam-3985	472	1	[	[	X
ejpam-3985	472	2	12	12	NUM
ejpam-3985	472	3	]	]	X
ejpam-3985	472	4	p.	p.	NOUN
ejpam-3985	472	5	slater	slater	PROPN
ejpam-3985	472	6	.	.	PUNCT
ejpam-3985	473	1	dominating	dominating	NOUN
ejpam-3985	473	2	and	and	CCONJ
ejpam-3985	473	3	reference	reference	NOUN
ejpam-3985	473	4	sets	set	NOUN
ejpam-3985	473	5	in	in	ADP
ejpam-3985	473	6	a	a	DET
ejpam-3985	473	7	graph	graph	NOUN
ejpam-3985	473	8	.	.	PUNCT
ejpam-3985	474	1	journal	journal	NOUN
ejpam-3985	474	2	of	of	ADP
ejpam-3985	474	3	mathematics	mathematic	NOUN
ejpam-3985	474	4	and	and	CCONJ
ejpam-3985	474	5	physical	physical	ADJ
ejpam-3985	474	6	science	science	NOUN
ejpam-3985	474	7	,	,	PUNCT
ejpam-3985	474	8	22(4):445–455	22(4):445–455	PROPN
ejpam-3985	474	9	,	,	PUNCT
ejpam-3985	474	10	1988	1988	NUM
ejpam-3985	474	11	.	.	PUNCT
ejpam-3985	475	1	[	[	X
ejpam-3985	475	2	13	13	NUM
ejpam-3985	475	3	]	]	SYM
ejpam-3985	475	4	jr	jr	PROPN
ejpam-3985	475	5	.	.	PUNCT
ejpam-3985	475	6	s.r	s.r	PROPN
ejpam-3985	475	7	.	.	PROPN
ejpam-3985	475	8	canoy	canoy	PROPN
ejpam-3985	475	9	and	and	CCONJ
ejpam-3985	475	10	g.a	g.a	PROPN
ejpam-3985	475	11	.	.	PROPN
ejpam-3985	475	12	malacas	malacas	PROPN
ejpam-3985	475	13	.	.	PUNCT
ejpam-3985	476	1	determining	determine	VERB
ejpam-3985	476	2	the	the	DET
ejpam-3985	476	3	intruder	intruder	NOUN
ejpam-3985	476	4	’s	’s	PART
ejpam-3985	476	5	location	location	NOUN
ejpam-3985	476	6	in	in	ADP
ejpam-3985	476	7	a	a	DET
ejpam-3985	476	8	given	give	VERB
ejpam-3985	476	9	network	network	NOUN
ejpam-3985	476	10	.	.	PUNCT
ejpam-3985	477	1	nrcp	nrcp	PROPN
ejpam-3985	477	2	research	research	PROPN
ejpam-3985	477	3	journal	journal	PROPN
ejpam-3985	477	4	,	,	PUNCT
ejpam-3985	477	5	13(1	13(1	NUM
ejpam-3985	477	6	)	)	PUNCT
ejpam-3985	477	7	,	,	PUNCT
ejpam-3985	477	8	2013	2013	NUM
ejpam-3985	477	9	.	.	PUNCT
ejpam-3985	478	1	[	[	X
ejpam-3985	478	2	14	14	NUM
ejpam-3985	478	3	]	]	X
ejpam-3985	478	4	jr	jr	PROPN
ejpam-3985	478	5	.	.	PUNCT
ejpam-3985	478	6	s.r	s.r	PROPN
ejpam-3985	478	7	.	.	PROPN
ejpam-3985	478	8	canoy	canoy	PROPN
ejpam-3985	478	9	and	and	CCONJ
ejpam-3985	478	10	g.a	g.a	PROPN
ejpam-3985	478	11	.	.	PROPN
ejpam-3985	478	12	malacas	malacas	PROPN
ejpam-3985	478	13	.	.	PUNCT
ejpam-3985	479	1	locating	locate	VERB
ejpam-3985	479	2	-	-	PUNCT
ejpam-3985	479	3	dominating	dominating	NOUN
ejpam-3985	479	4	sets	set	NOUN
ejpam-3985	479	5	in	in	ADP
ejpam-3985	479	6	a	a	DET
ejpam-3985	479	7	graph	graph	NOUN
ejpam-3985	479	8	.	.	PUNCT
ejpam-3985	480	1	applied	apply	VERB
ejpam-3985	480	2	mathematical	mathematical	ADJ
ejpam-3985	480	3	sciences	science	NOUN
ejpam-3985	480	4	,	,	PUNCT
ejpam-3985	480	5	8(88):4381–4388	8(88):4381–4388	NUM
ejpam-3985	480	6	,	,	PUNCT
ejpam-3985	480	7	2014	2014	NUM
ejpam-3985	480	8	.	.	PUNCT